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Segmentation/72d5919b-3823-475f-9939-cac5c29b48a5_content_list.json @@ -0,0 +1,1538 @@ +[ + { + "type": "text", + "text": "Preparing the Future for Continual Semantic Segmentation", + "text_level": 1, + "bbox": [ + 184, + 130, + 785, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zihan Lin1 Zilei Wang*1 Yixin Zhang1,2", + "bbox": [ + 305, + 179, + 663, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 University of Science and Technology of China", + "bbox": [ + 292, + 198, + 678, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Institute of Artificial Intelligence, Hefei Comprehensive National Science Center", + "bbox": [ + 158, + 215, + 808, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "myustc@mail.ustc.edu.cn, {zlwang, zhyx12}@ustc.edu.cn", + "bbox": [ + 250, + 236, + 718, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this study, we focus on Continual Semantic Segmentation (CSS) and present a novel approach to tackle the issue of existing methods struggling to learn new classes. The primary challenge of CSS is to learn new knowledge while retaining old knowledge, which is commonly known as the rigidity-plasticity dilemma. Existing approaches strive to address this by carefully balancing the learning of new and old classes during training on new data. Differently, this work aims to avoid this dilemma fundamentally rather than handling the difficulties involved in it. Specifically, we reveal that this dilemma mainly arises from the greater fluctuation of knowledge for new classes because they have never been learned before the current step. Additionally, the data available in incremental steps are usually inadequate, which can impede the model's ability to learn discriminative features for both new and old classes. To address these challenges, we introduce a novel concept of pre-learning for future knowledge. Our approach entails optimizing the feature space and output space for unlabeled data, which thus enables the model to acquire knowledge for future classes. With this approach, updating the model for new classes becomes as smooth as for old classes, effectively avoiding the rigidity-plasticity dilemma. We conducted extensive experiments and the results demonstrate a significant improvement in the learning of new classes compared to previous state-of-the-art methods.", + "bbox": [ + 75, + 316, + 472, + 710 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 739, + 209, + 753 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep neural networks have demonstrated their superiority in many computer vision tasks [26, 31, 14]. Conventionally, they are trained in an offline manner with all data collected beforehand. When novel classes need to be handled, the networks need to be re-trained using either updated training set with both new and previous data, or directly finetuned on new data. The former has higher costs and is even impracticable sometimes like, when privacy raises concerns. The latter is prone to forget previ", + "bbox": [ + 75, + 763, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/301e91d65d39335f139ddfa2115135c85334d75e9536194ad13a2b6c5bd7c493.jpg", + "image_caption": [ + "Figure 1. On VOC2012 benchmark, our method boosts the performance of new classes by a significant margin, while also achieving promising performance for old classes, compared to recent state-of-the-art methods." + ], + "image_footnote": [], + "bbox": [ + 519, + 292, + 870, + 462 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ously learned knowledge, which is called catastrophic forgetting (CF) [25]. To better fit neural networks into real-world scenarios, we want them to have the ability to learn new concepts while preserving the old knowledge (or even improve it using new knowledge). This is known as the continual learning (CL) problem and receives increasing attention recently. It has been explored first in the field of image classification [28, 42, 17, 11, 57, 44, 43], and some methods are proposed recently targeting semantic segmentation [5, 10, 6, 54, 51, 37]. Generally, it is often achieved by applying forgetting-preventing constraints between current and previous networks to prevent CF, which raises the rigidity (i.e., the ability to preserve old states) but harms the plasticity (i.e., the ability to learn new knowledge). It is known as the rigidity-plasticity (R-P) dilemma. A key aspect in designing constraints is to balance between rigidity and plasticity, which is what most works focus on.", + "bbox": [ + 496, + 549, + 893, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite that several new constraints have been proposed for CSS to better tackle the dilemma, existing works still struggle to learn new classes. Taking the VOC2012 benchmark as an example, most methods can only achieve a performance around $70\\%$ of that of the upperbound for 15-5 setup and around $50\\%$ for 19-1 setup, which is even worse", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11910", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "for harder setups. To get a clear picture of why this happens, we first analyze the intermediate features of the network and find it suffers serious underfitting for new classes, which indicates a large amount of knowledge is not learned. We then examine the CSS training pipeline and find two main obstacles causing this phenomenon. (1) R-P Dilemma: the network has no knowledge w.r.t. new classes until they are introduced. This generally requires a rather large update to incorporate the new knowledge, which will be significantly hindered by the forgetting-preventing constraints punishing the network from drifting away from its previous states. (2) Inadequate data for training: the amount of data available in incremental steps is usually limited, and this problem becomes more severe when a single class is added, resulting in a tiny training set with only a few negative samples. This can significantly limit the network to properly discriminate between old and new classes. This problem has never been explicitly considered before.", + "bbox": [ + 76, + 90, + 472, + 362 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unlike existing works trying to tackle the R-P dilemma directly, we are the first to argue that this obstacle can be elegantly avoided by exploring future knowledge in an unsupervised way. Assume that the network has obtained partial knowledge of future classes in advance, then the network needs fewer updates to learn the upcoming knowledge, which consequently lowers the impacts of the R-P dilemma. The more future knowledge it learns in advance, the fewer the impacts will be caused. Considering an extreme situation where all the future knowledge is learned beforehand, the network does not need any update, and thus the influence of constraints could be totally avoided. On top of this, it makes us the first attempt to explicitly tackle the second obstacle by utilizing the abundant data in previous steps to optimize discriminability between old and new classes. Based on these understandings, we design a novel framework where unsupervised contrastive learning is performed on intermediate features to optimize future classes with both visual similarity and feature affinity as supervisions. One step further, an auxiliary classifier is trained using pseudo labels of future classes generated via clustering, which is used to initialize the actual classifier for future steps. Our method surpasses existing works by a huge margin as shown in Figure 1 and the effectiveness is further demonstrated with extensive experiments. Our contributions are summarized as follows.", + "bbox": [ + 76, + 363, + 472, + 755 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose to pre-learn future knowledge for CSS with the aim of improving the performance especially for new classes, which can simultaneously tackle the R-P dilemma and the obstacle of inadequate data.", + "- We design a novel framework that can pre-learn future knowledge in an unsupervised way, where both the feature space and output space are handled.", + "- We have validated the effectiveness of our proposed" + ], + "bbox": [ + 76, + 762, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "approach through extensive experiments. The results demonstrate significant improvement on standard CSS benchmarks.", + "bbox": [ + 511, + 90, + 890, + 137 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 152, + 640, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Continual Learning (CL). Continual learning has been studied for years in image classification. Existing techniques can be roughly divided into regularization methods, rehearsal methods, and architectural methods. Regularization methods apply consistency constraints between current network and previous network to avoid drifts from previous states. They can be applied on network weights [53, 25, 1], the intermediate features [9, 11, 45, 13, 22] or the output logits [28, 42, 17, 48]. Parameter regularization is rarely seen recently due to the lack of plasticity, while the other two are mostly based on knowledge distillation (KD) [16]. To better solve the forgetting problem, rehearsal methods replay previous data in the incremental steps, including image replay [42, 41, 3], generative replay [49, 39], feature replay [20, 57], and memory management [30, 29]. Architectural methods use a dynamic network to handle incoming knowledge, like sub-network [32, 33], complementary network [47, 40] or expandable network [27, 50, 52].", + "bbox": [ + 496, + 178, + 890, + 450 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Continual Semantic Segmentation (CSS). Some works extended the aforementioned techniques to semantic segmentation tasks. For the KD-based methods, MiB [5] formalized and targeted background shift problem with output space distillation. PLOP [10], SDR [36], and RCIL [54] use feature space distillation to further mitigate forgetting. For the rehearsal-based methods, SSUL [6] and RECALL [34] utilize memory or external data to overcome forgetting and work well in multiple-step learning. For the architectural methods, RCIL [54] proposes a structural reparameterization design to better learn new knowledge.", + "bbox": [ + 496, + 450, + 890, + 618 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unsupervised Semantic Segmentation. These works focus on learning to cluster semantically related pixels without human labeling. Existing works can be roughly divided into three types. PiCIE [8] iteratively performs clustering and uses it to refine network features. This relies on the architectural prior and is prone to degenerate solutions. IIC [21] maximizes the mutual information between two augmentations of the same image which enforces spatial stability on them. But this solution has trouble dealing with complex scenes. The last type uses visual similarity. These works [19, 55, 46, 23] use handcrafted priors, like boundary, superpixels, or saliency detectors to first group pixels by visual similarity. This is then used to learn pixel-level representations using contrastive learning.", + "bbox": [ + 496, + 618, + 890, + 829 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 844, + 638, + 859 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we first explain the definition of CSS (Sec. 3.1), and present the underfitting phenomenon of new", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11911", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7c464a504f500bccef080c7376cf9f4d8e5a117b9e37411e79d55f94d75c2aa6.jpg", + "image_caption": [ + "Figure 2. Feature fitness analysis of different methods using L1 norm (Left), activation strength (Mid), and cosine similarity (Right) on VOC2012 15-5 setup. It is demonstrated that existing works suffer underfitting on both intra-class level (left and mid) and inter-class level (right) for new classes. Our method effectively addresses this problem." + ], + "image_footnote": [], + "bbox": [ + 91, + 102, + 344, + 214 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/196888f1c316e672db90607467f10607b1ec82a221c00885053b765c22d1160e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 359, + 102, + 609, + 215 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4f84dd7ca2e2af2a43674bb3157b812ed37d730691a0015ce1dc4f2aa1c259c0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 625, + 102, + 872, + 215 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "classes (Sec. 3.2). After that, we analyze how the performance is impacted in CSS (Sec. 3.3). Finally, we discuss the solutions to boost new class performance (Sec. 3.4).", + "bbox": [ + 75, + 284, + 470, + 330 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. CSS Definition", + "text_level": 1, + "bbox": [ + 76, + 340, + 227, + 357 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In CSS, the training procedure is composed of a series of $T$ learning steps. At each step $t$ where $t \\in \\{1, \\dots, T\\}$ , a set of new categories $\\mathcal{C}_t$ are introduced with a training set $D_t = \\{(x_n, y_n)\\}$ where $x_n$ is an image and $y_n$ is the corresponding label. Only $\\mathcal{C}_t$ is labeled in $y_n$ and all the other classes are labeled as background. It is assumed that the categories learned at each step are disjoint, i.e., $\\mathcal{C}_i \\cap \\mathcal{C}_j = \\emptyset$ . The network is trained sequentially on each step, where it learns the knowledge w.r.t. $\\mathcal{C}_t$ and expands its output space to $\\mathcal{C}_{1:t} = \\mathcal{C}_{1:t-1} \\cup \\mathcal{C}_t$ . After all learning steps, the network is expected to perform well on all classes.", + "bbox": [ + 75, + 364, + 470, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Analysis of Feature Fitness", + "text_level": 1, + "bbox": [ + 76, + 542, + 320, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To get a clear view of why new classes perform poorly in existing methods, we analyze the intermediate features of two works: MiB [5] based on conventional logits distillation, and a more recent work, RCIL [54], based on feature distillation and structural re-parameterization aiming to better tackle the R-P dilemma. To simplify the situation, we opt for the two-step 15-5 setup on VOC2012 to conduct the analysis. The results are reported in Figure 2 (Detailed information about incremental setups and validation set can be found in Section 5.). The results of joint training (i.e., performance upperbound) and initial state (i.e., backbone is initialized with ImageNet pre-trained weights while the other parts are randomly initialized) are also provided for reference. Ideally, the results are expected to be close to that of the upperbound in order to achieve good performance.", + "bbox": [ + 75, + 566, + 468, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Intra-class Fitness. We first evaluate how well the network fits to each individual class. In neural networks, each channel in the feature vectors could represent a certain pattern [4] which composes the learned classes [58]. When the network fits a class well, the output feature vector should have specific channels being activated while the others deactivated, resulting in sparsity in the feature vector. The", + "bbox": [ + 75, + 795, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "activation strength further shows how strong the network's response is to each pattern. Both of them can serve as clues indicating how well the network fits a class. We use the average L1 norm of L2-normalized feature vectors to measure the sparsity, and the average top activation values to measure the response strength. As can be seen in Figure 2 (left and mid), the new classes of both MiB and RCIL have high L1 norm and low activation strength, indicating a serious underfitting problem.", + "bbox": [ + 496, + 284, + 893, + 419 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inter-class Fitness. We further evaluate how well the network learns to distinguish different classes, which is measured by the cosine similarity between the feature vectors of different classes. The better the network can distinguish each class, the lower the cosine similarities will be. We compute the mean cosine distance of a class to any other classes, which is then averaged based on class group to get the final results, as shown in Figure 2 (right). It can be seen that the network has good discriminative power on old classes, but the new classes again present poor results. It indicates the network cannot distinguish a new class between other classes well.", + "bbox": [ + 496, + 421, + 892, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Discussion. From the above analyses, it is evident that new classes suffer serious underfitting on both intra-class and inter-class aspects. This exactly explains why most methods show low performance on new classes, even in simple setups with only a single incremental step.", + "bbox": [ + 496, + 604, + 893, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Understanding Training Pipeline", + "text_level": 1, + "bbox": [ + 500, + 693, + 790, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this part, we dive deeper to investigate why the underfitting problem happens for new classes in the conventional training pipeline. We use Figure 3 to give a clear view of how the two obstacles impact the performance in a conventional pipeline (green background). Without loss of generality, a two-step situation is adopted as an example.", + "bbox": [ + 496, + 718, + 893, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Starting from step 1 where $\\mathcal{C}_1$ is labeled in the given data $D_{1}$ while others are marked as background, the network acquires most knowledge of $\\mathcal{C}_1$ (i.e., distinguish between classes in $\\mathcal{C}_1$ ) after finishing this step. Considering that it only accesses partial data at this step compared to joint training, the knowledge of $\\mathcal{C}_1$ remains to be updated", + "bbox": [ + 496, + 810, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11912", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a284cd579c0221d99adab4bb6e6c37940eaaaffa4cfdeabfc8de1a28bfe70af4.jpg", + "image_caption": [ + "Figure 3. Illustration of the difference between knowledge learning in a conventional training pipeline (green background) and our solution (blue background). We jointly optimize new classes together with old classes in an unsupervised way before new classes are introduced." + ], + "image_footnote": [], + "bbox": [ + 86, + 89, + 460, + 265 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "in the next step. However, even though the future classes $\\mathcal{C}_2$ do exist in $D_{1}$ , they do not receive explicit supervision, thus the network obtains almost no knowledge of $\\mathcal{C}_2$ after finishing step 1.", + "bbox": [ + 75, + 363, + 468, + 425 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Moving to step 2, a constraint is usually applied to avoid forgetting previous knowledge by punishing the network from drifting away from its previous states. In this step, the network needs to update its knowledge of $\\mathcal{C}_1$ on $D_2$ . Given that $\\mathcal{C}_1$ is already properly optimized at step 1, the network only needs a small adjustment to complete its knowledge of $\\mathcal{C}_1$ and receives little punishment from the constraint. However, the network is also intended to learn the knowledge w.r.t. $\\mathcal{C}_2$ (i.e., distinguish the classes in $\\mathcal{C}_2$ and distinguish between $\\mathcal{C}_2$ and $\\mathcal{C}_1$ ) from the start, which requires a rather large update. Based on the fact that the constraints make more punishment for greater changes, this update will be suppressed more severely compared to that of $\\mathcal{C}_1$ , making more knowledge w.r.t. $\\mathcal{C}_2$ cannot be learned. This is why the R-P dilemma often leads to low performance for new classes. To make matters worse, the scale of the training set is usually limited in incremental steps, especially for the situation when a single class is added with only a few samples of $\\mathcal{C}_1$ . Such limited data could impede the network from successfully distinguishing between $\\mathcal{C}_1$ and $\\mathcal{C}_2$ , which is the inadequate data obstacle. Both of these factors result in the inability to properly learn knowledge w.r.t. $\\mathcal{C}_2$ and contribute to the aforementioned underfitting phenomenon.", + "bbox": [ + 75, + 425, + 468, + 773 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Discussions for Solutions", + "text_level": 1, + "bbox": [ + 76, + 785, + 303, + 800 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Pre-learning future knowledge. Based on the analysis, if we modify the training pipeline by adding explicit supervision to $\\mathcal{C}_2$ before it is introduced (blue background in Figure 3). The knowledge w.r.t. $\\mathcal{C}_2$ could be learned in advance. By doing so, we first avoid the R-P dilemma by reducing the great update to learning the knowledge w.r.t. $\\mathcal{C}_2$ at the next", + "bbox": [ + 75, + 809, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "step. Meanwhile, we can use the abundant samples of $\\mathcal{C}_1$ at step 1 to make the network better learn how to distinguish between $\\mathcal{C}_2$ and $\\mathcal{C}_1$ , mitigating the influence of inadequate data of $\\mathcal{C}_1$ at next step. Consequently, both obstacles are tackled in a uniform and elegant way. The main challenge falls to how we can learn knowledge w.r.t. $\\mathcal{C}_2$ as accurately as possible in an unsupervised way in order to reduce the extent of updates required in the future.", + "bbox": [ + 496, + 90, + 890, + 210 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Memory. Memory is a widely used technique in CL and has been adapted to CSS recently [6, 34]. Based on our analysis above, here we clearly explain the effect of memory in CSS. Memory is applied only in incremental steps. With the help of it, new classes are possible to be optimized with partial previous data, which can also alleviate the impact of inadequate data. Meanwhile, memory helps to ease the forgetting problem, which makes it possible to relax the constraints without forgetting. As a result, new knowledge can be more easily learned. We would like to point out that memory can be used to solve the two obstacles at a different aspect. It could further boost the performance in conjunction with our solution.", + "bbox": [ + 496, + 210, + 892, + 407 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 500, + 420, + 589, + 435 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we introduce a novel framework based on pre-learning future knowledge as depicted in Figure 4. It takes into account future knowledge in an unsupervised way, both in the feature space (green background) and the output space (blue background).", + "bbox": [ + 496, + 446, + 890, + 522 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Learning Future Knowledge in Feature Space", + "text_level": 1, + "bbox": [ + 498, + 530, + 885, + 546 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Contrastive learning. Contrastive learning is a widely used technique in unsupervised learning [7, 15]. In our work, we resort to it to optimize future classes in feature space. In semantic segmentation, directly using feature vectors at pixel level to perform pixel-pixel contrastive is redundant and results in high computational cost. Therefore, we follow [24, 46, 18] to perform contrast in a pixel-segment manner. Formally, supposing an image $I$ is partitioned into segments $S$ by a given prior. Let $\\pmb{f}_i$ be the unit-length feature vector of pixel $i$ , we define the (normalized) prototype $\\pmb{p}$ of a segment $s \\in S$ by the average of feature vectors within this segment.", + "bbox": [ + 496, + 553, + 890, + 734 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {p} _ {s} = \\frac {1}{| s |} \\sum_ {i \\in s} \\boldsymbol {f} _ {i}, \\| \\boldsymbol {p} _ {s} \\| = 1 \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 744, + 890, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We adopt the InfoNCE [38] loss and formalize our loss as", + "bbox": [ + 500, + 785, + 880, + 800 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} \\left(\\boldsymbol {f} _ {i}, S\\right) = - \\log \\frac {\\exp \\left(\\boldsymbol {f} _ {i} \\cdot \\boldsymbol {p} _ {s _ {+}} / \\tau\\right)}{\\exp \\left(\\boldsymbol {f} _ {i} \\cdot \\boldsymbol {p} _ {s _ {+}} / \\tau\\right) + \\sum_ {s _ {-}} \\exp \\left(\\boldsymbol {f} _ {i} \\cdot \\boldsymbol {p} _ {s _ {-}} / \\tau\\right)} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 503, + 821, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tau$ is a temperature hyper-parameter. Ideally, it pulls $f_{i}$ close to the positive segment $s_{+}$ and pushes it away from", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11913", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/578b344b9dfb493d19462b36cf82484cdfcd0bea0835ebb175e0fdbc86fb417a.jpg", + "image_caption": [ + "Figure 4. Overall framework. Given an image at step $t$ , a projection head maps the features from feature extractor $F_{t}$ into an embedding space where $\\mathcal{L}_{c}$ is used to optimize future classes (green block). Next, the features from $F_{t}$ are also used to train an auxiliary classifier $G_{aux}$ to initialize the classifier for future classes (blue block). Last, the pseudo label technique together with a knowledge distillation loss are adopted to mitigate forgetting (yellow block)." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 459, + 297 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "all the negative segments $s_{-}$ . For a given pixel, the segment it belongs to serves as $s_{+}$ , whereas other segments, including those from other images, serve as $s_{-}$ .", + "bbox": [ + 75, + 441, + 468, + 488 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Contrast by Visual Similarity. In pixel-segment contrastive learning, the partition scheme determines how the network is optimized. We first resort to visual boundaries as a prior to partition the images into visual coherent segments $S_{v}$ by OWT-UCM [2], which is a decent choice in unsupervised segmentation [19, 55, 23]. By utilizing visual similarity as supervision, we can bootstrap the representation learning and ground the features to respect low-level visual cues. But using this supervision alone makes the network hard to capture semantic-level information of future classes, and still needs further updates to properly learn them. This contradicts our goal to make the necessary updates as few as possible in the future.", + "bbox": [ + 75, + 489, + 468, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Contrast by Feature Affinity. We also need a partition method that can match actual future classes accurately to serve as another supervision. Due to the bootstrap effect of the previous contrast, we can resort to clustering methods to explore feature affinity as semantic-level supervision without relying on architectural prior like [8]. However, applying clustering directly cannot generate satisfying results. In practice, we find that by hierarchically combining an over-clustering result, we could obtain much more accurate results. More in detail, starting from an over-clustering generated using intermediate features, we merge the two most similar segments each time till all segments are merged as one. The similarity between segments is measured by the cosine similarity between their prototypes. This procedure", + "bbox": [ + 75, + 688, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3b3e192f3dd6e2b2518246bf9e82b12904482820528cf8133922f17ae7952bc6.jpg", + "image_caption": [ + "Figure 5. Segments obtained using visual similarity and feature affinity respectively. Top: Segments generated by OWT-UCM [2] using boundaries. Bottom: Segments that are likely to match the actual classes are selected from a hierarchical combination of fine-grained clustering results." + ], + "image_footnote": [], + "bbox": [ + 501, + 90, + 885, + 224 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "generates consistent segments across all granularities. But different classes naturally have different levels of granularities, directly selecting segments from a single granularity is often suboptimal. We further propose a confidence score to evaluate how likely a segment matches a class accurately to select segments across granularities. The design of the confidence score is based on the following observations. In the combination procedure where the most similar segments are merged each time, the longer a segment can remain not merged, the more different it is to all other segments, and is more likely to match a class. What's more, given that this procedure starts from an over-clustering, the segments in later steps have a higher chance to match a class and should be assigned higher weights. A possible choice is to use the cosine distance between the segments to be merged at each step as a weight factor, which monotonously increases by step. Formally, assuming segments $a$ and $b$ are merged into a new segment $c$ at step $n$ in this procedure, set $S_{n}$ indicates all segments that are merged from start till now (include $a$ and $b$ ). The confidence score $u$ for a segment $s$ at step $n$ is defined recursively as follows.", + "bbox": [ + 496, + 320, + 893, + 638 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nu _ {s} ^ {n} = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} s = c, \\\\ u _ {s} ^ {n - 1} & \\text {e l i f} s \\in S _ {n}, \\\\ u _ {s} ^ {n - 1} + \\left(1 - \\boldsymbol {p} _ {a} \\cdot \\boldsymbol {p} _ {b}\\right) & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 654, + 890, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After finishing this procedure, we use the final score of each segment to select those with scores above the threshold to serve as high-confidence segments $S_{f}$ and participate in contrastive learning. If two selected segments are partially overlapped, we only reserve the one with a higher score. This procedure is performed for each training sample before each epoch to select high-confidence segments as the network updates itself, except for the first epoch since the feature cannot be clustered at that moment.", + "bbox": [ + 496, + 719, + 893, + 853 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Overall Contrastive Loss. In our contrastive learning, the pixels of $\\mathcal{C}_t$ with ground truth annotations and $\\mathcal{C}_{1:t-1}$ with pseudo labels are excluded. Meanwhile, they can naturally", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11914", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "serve as high-confidence negative segments in contrastive learning. Since the batch size is limited in segmentation while the number of negative samples is crucial in contrastive learning [7, 15], we use a memory bank to cache the features of recent four batches to increase the number of negative samples. Given the segments $S_{v}$ generate by visual similarity and segments $S_{f}$ generated by feature affinity, our contrastive loss is formalized as", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal{L}_{c} = \\frac{1}{|S_{v}|}\\sum_{\\substack{i\\in S_{v}\\\\ i\\notin \\mathcal{C}_{1:t}}}\\mathcal{L}(\\boldsymbol{f}_{i},S_{v}) + \\frac{1}{|S_{f}|}\\sum_{\\substack{i\\in S_{f}\\\\ i\\notin \\mathcal{C}_{1:t}}}\\mathcal{L}(\\boldsymbol{f}_{i},S_{f}) \\tag{4}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 228, + 468, + 276 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $|S|$ means the pixel number in all segments within $S$ .", + "bbox": [ + 76, + 281, + 467, + 297 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Learning Future Knowledge in Output Space", + "text_level": 1, + "bbox": [ + 76, + 303, + 460, + 320 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Previous work [5] has claimed that a proper initialization of classifier weight at step $t > 1$ could also benefit the performance and is widely adopted by other works [10, 54]. This motivates us to further introduce future knowledge to the output space. Existing practice eases the misalignment between features and classifier weights by using the weight of the background to initialize that of the new classes. But in the update process, the weights of new classes should be updated to separate them from the background. Making the classifier weights to be identical to that of the background has the risk of increasing the necessary update, which has a negative effect based on previous analysis.", + "bbox": [ + 75, + 325, + 468, + 507 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To address this issue, we want the classifier to be initialized as close to the final optimal value as possible. When optimizing feature space, we manage to obtain high-confidence segments of future classes, and the intermediate features are also optimized accordingly. We could naturally utilize them to train an auxiliary classifier that can classify future classes in advance and use its weights as initialization. More in detail, we first perform clustering on the prototypes of segments to assign an auxiliary semantic label to each segment, which is then used to optimize the auxiliary classifier using cross-entropy loss. Note that the network receives no gradient from this classifier. In the next step when initialization is needed, we compute the prototype of each new class and select the auxiliary classifier weight which is closest to the prototype to initialize the actual classifier weight of it. On the one hand, we can make the classifier converge more easily and avoid the R-P dilemma. On the other hand, it solves the inadequate data obstacle in output space by utilizing the data of current step to serve as the negative samples of future classes, which can further boost the discriminability of the classifier compared to training it directly on the future steps.", + "bbox": [ + 75, + 508, + 470, + 840 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Overall Framework", + "text_level": 1, + "bbox": [ + 76, + 847, + 266, + 861 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our proposed framework is depicted in Figure 4. $\\mathcal{L}_{ce}$ and $\\mathcal{L}_{aux}$ are both cross-entropy loss to learn new classes and to", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "train the auxiliary classifier, respectively. To complete our framework, we still need a KD loss to overcome forgetting. Since our focus is not on this part, we adopt the CKD loss in MiB [5] as $\\mathcal{L}_{kd}$ to assist our training, with the addition of a temperature parameter as in original KD loss [16] to enhance its ability in knowledge preserving. This makes the overall loss function of our framework as follows.", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {c e} + \\alpha \\mathcal {L} _ {k d} + \\beta \\mathcal {L} _ {c} + \\mathcal {L} _ {\\text {a u x}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 208, + 890, + 224 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\alpha$ and $\\beta$ are hyper-parameters.", + "bbox": [ + 500, + 234, + 746, + 250 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 263, + 633, + 280 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Implement Details", + "text_level": 1, + "bbox": [ + 500, + 287, + 678, + 304 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. Following previous works, we evaluate our method on VOC2012 [12] and ADE20K [56], which are the standard CSS benchmarks. We report the performance on the official validation set of each dataset. We also exclude $20\\%$ of the training set as a validation set to tune hyperparameters and perform all analyses.", + "bbox": [ + 496, + 311, + 890, + 402 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Protocols. There are two settings in CSS benchmarks: disjoint and overlapped. The disjoint setting limits the given images to contain pixels only belong to $\\mathcal{C}_{1:t}$ , while the latter does not have this restriction, which means the pixels can also belong to the future classes, i.e., $\\mathcal{C}_{t+1:T}$ . Note that the overlapped setting is considered to be more realistic and more challenging by all existing works [5, 10, 6, 37], and the disjoint setting is even ignored in some works [6, 37]. In design, our work is fully based on the overlapped setting. Evaluation. The CSS benchmark setups are denoted as $N_{o} - N_{n}$ where $N_{o}$ and $N_{n}$ are the number of classes to be learned at the initial step and each incremental step, respectively. For example, the 15-1 setup of VOC2012 gives 15 classes at the initial step and adds one class per incremental step, resulting in a total of 6 steps. On VOC2012, we conduct experiments on four setups: 19-1 (2 steps), 15-5 (2 steps), 15-1 (6 steps), and 10-1 (11 steps). On ADE20K, we use three setups: 100-50 (2 tasks), 50-50 (3 tasks), and 100-10 (6 tasks). The network is evaluated after finishing all learning steps using mean Intersection over Union (mIoU) as metric. The performance of initial classes $\\mathcal{C}_{1}$ , incremental classes $\\mathcal{C}_{2:T}$ , and all classes $\\mathcal{C}_{1:T}$ are denoted as old, new, and all, respectively.", + "bbox": [ + 496, + 402, + 892, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training. Following previous works [5, 10], we adopt DeepLab-V3 with an output stride of 16. ResNet-101 serves as the backbone, which is pre-trained on ImageNet. We use the SGD optimizer with momentum set to 0.9. The learning rate is set to 1e-2 for the initial learning step and 1e-3 for the following learning step. The learning rate is adjusted by the polynomial decay schedule with power set to 0.9. The network is trained on VOC2012 for 30 epochs, and 60 epochs on ADE20K, both with a batch size of 16. The image is cropped to $512 \\times 512$ for both training and validation, with", + "bbox": [ + 496, + 750, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11915", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/38b65846c664a259995b1d4175be99b52341fc5acbf7b347db38c31a8af6a499.jpg", + "table_caption": [ + "Table 1. Results of different methods on VOC2012. The best is in bold while the second best is in underline. Results are averaged over 3 runs with standard deviation provided." + ], + "table_footnote": [], + "table_body": "
Method19-1 (2 tasks)15-5 (2 tasks)15-1 (6 tasks)10-1 (11 tasks)
oldnewalloldnewalloldnewalloldnewall
ILT [35]67.112.364.466.340.659.94.97.85.7---
MiB [5]70.222.167.875.549.469.035.113.529.712.213.012.6
PLOP [10]75.337.373.575.751.770.065.121.154.644.015.522.9
SDR [36]69.132.667.475.452.669.944.721.839.2---
SSUL [6]77.729.675.477.850.171.277.336.567.671.345.959.2
RCIL [54]---78.852.072.470.623.759.455.415.134.3
ALIFE [37]76.649.375.377.152.571.364.434.957.4---
Ours77.7 ±0.2259.8 ±1.3876.8 ±0.3579.1 ±0.2167.7 ±0.4676.4 ±0.2975.2 ±0.7552.2 ±1.3369.7 ±1.0968.1 ±0.9654.5 ±1.5761.6 ±1.13
RECALL [34]68.155.368.667.754.365.667.850.964.865.053.760.7
SSUL-M [6]77.849.776.478.455.873.078.349.071.374.053.264.1
ALIFE-M [37]76.752.275.577.655.272.366.038.859.5---
Ours-M77.9 ±0.1967.7 ±0.7477.4 ±0.3279.3 ±0.2270.2 ±0.2977.1 ±0.2477.1 ±0.6560.4 ±0.7373.1 ±0.6869.5 ±0.6063.2 ±1.2566.5 ±0.78
Joint77.677.777.679.571.577.679.571.577.678.576.677.6
", + "bbox": [ + 127, + 114, + 841, + 329 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2b878ddc6981c3a914540097085f7266c34ce9cbd1eb7f2d42df5bd25ce58653.jpg", + "table_caption": [ + "Table 2. Results of different methods on ADE20K. The best is in bold while the second best is in underline. Results are averaged over 3 runs with standard deviation provided." + ], + "table_footnote": [], + "table_body": "
Method100-50 (2 tasks)50-50 (3 tasks)100-10 (6 tasks).
oldnewalloldnewalloldnewall
ILT [35]18.214.417.03.512.89.70.11.30.5
MiB [5]40.517.132.745.521.029.338.211.129.2
PLOP [10]41.814.832.948.820.930.440.413.631.5
SSUL [6]41.218.033.548.320.129.540.218.733.1
RCIL [54]42.318.834.548.325.032.939.317.632.1
ALIFE [37]42.123.035.848.925.633.541.022.734.9
Ours43.1 ±0.1726.0 ±0.3637.4 ±0.2549.1 ±0.2428.3 ±0.4335.2 ±0.3341.4 ±0.2825.5 ±0.4536.1 ±0.35
SSUL-M [6]42.717.534.349.120.129.742.817.634.4
ALIFE-M [37]42.223.536.049.026.133.841.123.035.1
Ours-M43.1 ±0.1526.2 ±0.2937.5 ±0.2149.2 ±0.1228.5 ±0.2735.4 ±0.1841.6 ±0.2125.8 ±0.2636.3 ±0.22
Joint43.529.438.850.332.738.843.529.438.8
", + "bbox": [ + 202, + 371, + 764, + 563 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8066eebb0a9e448826a25a517bbc4d23e5e8c44466d09326524826b0c4261577.jpg", + "image_caption": [ + "Figure 6. mIoU comparison between CSS methods over steps on VOC 15-1 setups. The performance of initial classes and each new class added per step are plotted separately from left to right. Our method shows great ability in learning new classes." + ], + "image_footnote": [], + "bbox": [ + 91, + 580, + 212, + 667 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1456f2f508fda48f3552742c5238f4220be55d929a74f03258c36cdbf422fa04.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 223, + 580, + 346, + 667 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dac3a1bc85afb87d35a21c63297a342ca4d3799976f2363f7fe10305dd3f7269.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 357, + 580, + 478, + 667 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d9b160afa6126415c6d98b25328ea13e8e956f48c714c7043319d87f48c4b57a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 580, + 609, + 667 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f72d05b7f88f7d937ef29b727e0e21a3d6c265214cd0beee4f49af21cc17dcb3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 622, + 580, + 743, + 667 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8c7e91b67ba41d4d2802679391173cca990126900e950f96ecc2612a4a149e96.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 754, + 580, + 875, + 667 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "a random scaling and a random left-right flip additionally applied to training.", + "bbox": [ + 75, + 724, + 467, + 755 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Results", + "text_level": 1, + "bbox": [ + 76, + 768, + 169, + 784 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We provide the results on VOC2012 and ADE20K in Table 1 and Table 2, respectively. Some works [6, 34] exploit memory or external data to assist training. We also report the results obtained using memory (denoted by -M) following the implementation of [6] to fairly compare with these methods. The result of joint training is also provided as the upperbound for reference.", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For all setups on VOC2012, our method surpasses all existing methods by a large margin on new classes. This demonstrates the strong ability of our method to learn new classes. Note that our method also shows promising results on old classes even with a simple approach to preserve old knowledge. This is due to that a higher performance on new classes indicates that there also might be less confusion between old and new classes, which also benefits the mIoU of old classes. On the more challenging setups with multiple steps (15-1, 10-1), the new classes cannot be properly learned in the first place for most methods. To", + "bbox": [ + 496, + 724, + 890, + 891 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11916", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "make matters worse, these poorly optimized new classes will suffer forgetting in the following steps which further reduces their performance. Even in these challenging circumstances, our method still shows great performance in learning new classes, as shown in Figure 6. We can also see that even though SSUL shows higher performance on old classes on long-term setups, it relies on completely freezing the feature extractor to prevent forgetting, which does help a lot for old classes on these steps, but also harms its flexibility greatly. We believe that if equipped with a modern knowledge-preserving constraint, our method could offer another boost in performance.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "On the more challenging ADE20K benchmarks, we obtain similar results as that of VOC2012. Our method shows some improvement on old classes and is significantly better on new classes. On top of the results of VOC2012 benchmark, this further demonstrates that our approach works well on more complex datasets, and has the ability to handle both scenes and objects centric datasets.", + "bbox": [ + 75, + 276, + 468, + 381 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "When memory is applied on both benchmarks, our method receives further improvements and holds the leading position. This also indicates that our proposed training method has a non-overlapping effect with the memory technique. They can be used as two complementary techniques as pointed out in Section 3.4", + "bbox": [ + 75, + 386, + 468, + 476 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 497, + 228, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We investigate the effects of the proposed components in our framework using both 15-1 and 15-5 setups on VOC2012. Starting from a baseline composed of $L_{ce}$ , $L_{kd}$ and pseudo label, we add the components one by one and show the ablation results in Table 3. As can be seen, the performance increase steadily as each proposed component is gradually added. Only applying contrast by visual similarity does not receive much improvement since it cannot instruct the network to capture semantic-level information. After applying contrast by feature affinity, the performance receives the highest gain, indicating the necessity to add semantic-level supervision and make the network learn more accurate knowledge. On top of that, the performance receives another boost from our classifier initialization technique which introduces future knowledge to output space.", + "bbox": [ + 75, + 525, + 470, + 752 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/07afd2a5f13f14635242afd93d61c36a9d2ecd7cbdc8724f34625d556a36271a.jpg", + "table_caption": [ + "Table 3. Ablation study on VOC2012 15-1 and 15-5 setup." + ], + "table_footnote": [], + "table_body": "
Method15-1 (6 tasks)15-5 (2 tasks)
oldnewalloldnewall
baseline65.318.854.276.951.370.8
+ visual similarity contrast67.126.357.477.254.571.8
+ feature affinity contrast74.545.167.578.765.475.5
+ classifier initialization75.252.269.779.167.776.4
", + "bbox": [ + 78, + 786, + 470, + 873 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/40581768f3806ea880e27c8aa7a621e968f63154814aa1b47d483e2c1282af1f.jpg", + "image_caption": [ + "Figure 7. Visualization of clustering results of direct clustering and our practice. The high-confidence segments selected by our criterion are also presented on the right." + ], + "image_footnote": [], + "bbox": [ + 506, + 88, + 888, + 258 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8218f054600d24222cc7444f31ca5dd8a5fb4bc3003c0c7e2acc0718c776b4d1.jpg", + "image_caption": [ + "Figure 8. Performance comparison between different classifier initialization over training epochs on VOC2012 19-1 setup." + ], + "image_footnote": [], + "bbox": [ + 550, + 319, + 839, + 470 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Further Discussion", + "text_level": 1, + "bbox": [ + 500, + 527, + 681, + 542 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Feature Quality Analysis. To further demonstrate the effect of our method to solve the underfitting problem pointed out in Section 3.2, we conduct the same analysis on our method and incorporate the findings into Figure 2 (denoted by Ours). As can be seen, pre-learning future classes can significantly improve both intra-class and inter-class fitness.", + "bbox": [ + 496, + 551, + 890, + 643 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Segment Generation. We provide a qualitative comparison between direct clustering and our proposed hierarchical combination at different granularities to validate our design in Section 4.1. The results are generated from the same intermediate features and are plotted in Figure 7. As can be seen, our practice consistently generates better results across different granularities. We also present the high-confidence segments selected by our criterion for each image, which match the actual classes with high precision.", + "bbox": [ + 496, + 643, + 890, + 779 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Classifier Initialization. We give a comparison of performance over training epochs for different classifier initialization methods in Figure 8. As can be seen, the initialization technique proposed by MiB [5] converges much slower due to larger update paces. Random initialization converges fast but the performance stops increasing shortly afterward. Among all of them, our method stands out with its fast convergence speed and superior performance.", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11917", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Limitation and Conclusion", + "text_level": 1, + "bbox": [ + 76, + 90, + 326, + 104 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Our method has two limitations. Firstly, it relies on the natural attribute of CSS that unlabeled future classes exist in current training data. So it may not perform well when there are only a few unlabeled future classes in the current training data. However, in such cases, we can still leverage external unlabeled data, such as web-crawled data as used in RECALL [34]. Secondly, we point out that even though our proposed framework achieves great performance, it as a practicable solution might not be able to unleash the full potential of the training method, which requires further exploration in future works.", + "bbox": [ + 75, + 116, + 468, + 282 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this work, we present an in-depth analysis of the reason why existing methods suffer low performance on new classes. Building on this analysis, we introduce a novel training pipeline for CSS that optimizes potential future classes in the current training step. This offers a new perspective for enhancing new class performance in contrast to existing works that focus on addressing the R-P dilemma. We propose a framework based on this pipeline and it shows a significant improvement for new classes, while also benefiting the performance of old classes. We believe that this work can provide valuable insights for the research community on CSS.", + "bbox": [ + 75, + 282, + 472, + 464 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "7. Acknowledgements", + "text_level": 1, + "bbox": [ + 76, + 481, + 264, + 500 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work is supported by the National Natural Science Foundation of China under Grant 62176246 and Grant 61836008. This work is also supported by Anhui Province Key Research and Development Plan (202304a05020045), Anhui Provincial Natural Science Foundation 2208085UD17 and the Fundamental Research Funds for the Central Universities (WK3490000006).", + "bbox": [ + 75, + 507, + 468, + 613 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 76, + 630, + 174, + 645 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware synapses: Learning what (not) to forget. In ECCV, 2018.", + "[2] Pablo Arbelaez, Michael Maire, Charless Fowlkes, and Jitendra Malik. Contour detection and hierarchical image segmentation. IEEE transactions on pattern analysis and machine intelligence, 33(5):898-916, 2010.", + "[3] Jihwan Bang, Heesu Kim, YoungJoon Yoo, Jung-Woo Ha, and Jonghyun Choi. 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In Proceedings of the 28th ACM International Conference on Multimedia, pages 156-164, 2020." + ], + "bbox": [ + 78, + 90, + 468, + 204 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "11920", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Preparing the Future for Continual Semantic Segmentation/72d5919b-3823-475f-9939-cac5c29b48a5_model.json b/2023/Preparing the Future for Continual Semantic Segmentation/72d5919b-3823-475f-9939-cac5c29b48a5_model.json new file mode 100644 index 0000000000000000000000000000000000000000..cb66a88536073f786f593b2c74fc3fe4afb37505 --- /dev/null +++ b/2023/Preparing the Future for Continual Semantic Segmentation/72d5919b-3823-475f-9939-cac5c29b48a5_model.json @@ -0,0 +1,2202 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.185, + 0.131, + 0.787, + 0.154 + ], + "angle": 0, + "content": "Preparing the Future for Continual Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.306, + 0.18, + 0.664, + 0.199 + ], + "angle": 0, + "content": "Zihan Lin1 Zilei Wang*1 Yixin Zhang1,2" + }, + { + "type": "text", + "bbox": [ + 0.293, + 0.199, + 0.679, + 0.217 + ], + "angle": 0, + "content": "1 University of Science and Technology of China" + }, + { + "type": "text", + "bbox": [ + 0.16, + 0.217, + 0.81, + 0.235 + ], + "angle": 0, + "content": "\\(^{2}\\) Institute of Artificial Intelligence, Hefei Comprehensive National Science Center" + }, + { + "type": "text", + "bbox": [ + 0.25, + 0.237, + 0.72, + 0.252 + ], + "angle": 0, + "content": "myustc@mail.ustc.edu.cn, {zlwang, zhyx12}@ustc.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.473, + 0.712 + ], + "angle": 0, + "content": "In this study, we focus on Continual Semantic Segmentation (CSS) and present a novel approach to tackle the issue of existing methods struggling to learn new classes. The primary challenge of CSS is to learn new knowledge while retaining old knowledge, which is commonly known as the rigidity-plasticity dilemma. Existing approaches strive to address this by carefully balancing the learning of new and old classes during training on new data. Differently, this work aims to avoid this dilemma fundamentally rather than handling the difficulties involved in it. Specifically, we reveal that this dilemma mainly arises from the greater fluctuation of knowledge for new classes because they have never been learned before the current step. Additionally, the data available in incremental steps are usually inadequate, which can impede the model's ability to learn discriminative features for both new and old classes. To address these challenges, we introduce a novel concept of pre-learning for future knowledge. Our approach entails optimizing the feature space and output space for unlabeled data, which thus enables the model to acquire knowledge for future classes. With this approach, updating the model for new classes becomes as smooth as for old classes, effectively avoiding the rigidity-plasticity dilemma. We conducted extensive experiments and the results demonstrate a significant improvement in the learning of new classes compared to previous state-of-the-art methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.74, + 0.21, + 0.755 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Deep neural networks have demonstrated their superiority in many computer vision tasks [26, 31, 14]. Conventionally, they are trained in an offline manner with all data collected beforehand. When novel classes need to be handled, the networks need to be re-trained using either updated training set with both new and previous data, or directly finetuned on new data. The former has higher costs and is even impracticable sometimes like, when privacy raises concerns. The latter is prone to forget previ" + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.293, + 0.871, + 0.463 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.466, + 0.895, + 0.521 + ], + "angle": 0, + "content": "Figure 1. On VOC2012 benchmark, our method boosts the performance of new classes by a significant margin, while also achieving promising performance for old classes, compared to recent state-of-the-art methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.895, + 0.807 + ], + "angle": 0, + "content": "ously learned knowledge, which is called catastrophic forgetting (CF) [25]. To better fit neural networks into real-world scenarios, we want them to have the ability to learn new concepts while preserving the old knowledge (or even improve it using new knowledge). This is known as the continual learning (CL) problem and receives increasing attention recently. It has been explored first in the field of image classification [28, 42, 17, 11, 57, 44, 43], and some methods are proposed recently targeting semantic segmentation [5, 10, 6, 54, 51, 37]. Generally, it is often achieved by applying forgetting-preventing constraints between current and previous networks to prevent CF, which raises the rigidity (i.e., the ability to preserve old states) but harms the plasticity (i.e., the ability to learn new knowledge). It is known as the rigidity-plasticity (R-P) dilemma. A key aspect in designing constraints is to balance between rigidity and plasticity, which is what most works focus on." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Despite that several new constraints have been proposed for CSS to better tackle the dilemma, existing works still struggle to learn new classes. Taking the VOC2012 benchmark as an example, most methods can only achieve a performance around \\(70\\%\\) of that of the upperbound for 15-5 setup and around \\(50\\%\\) for 19-1 setup, which is even worse" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "11910" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.363 + ], + "angle": 0, + "content": "for harder setups. To get a clear picture of why this happens, we first analyze the intermediate features of the network and find it suffers serious underfitting for new classes, which indicates a large amount of knowledge is not learned. We then examine the CSS training pipeline and find two main obstacles causing this phenomenon. (1) R-P Dilemma: the network has no knowledge w.r.t. new classes until they are introduced. This generally requires a rather large update to incorporate the new knowledge, which will be significantly hindered by the forgetting-preventing constraints punishing the network from drifting away from its previous states. (2) Inadequate data for training: the amount of data available in incremental steps is usually limited, and this problem becomes more severe when a single class is added, resulting in a tiny training set with only a few negative samples. This can significantly limit the network to properly discriminate between old and new classes. This problem has never been explicitly considered before." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.364, + 0.473, + 0.756 + ], + "angle": 0, + "content": "Unlike existing works trying to tackle the R-P dilemma directly, we are the first to argue that this obstacle can be elegantly avoided by exploring future knowledge in an unsupervised way. Assume that the network has obtained partial knowledge of future classes in advance, then the network needs fewer updates to learn the upcoming knowledge, which consequently lowers the impacts of the R-P dilemma. The more future knowledge it learns in advance, the fewer the impacts will be caused. Considering an extreme situation where all the future knowledge is learned beforehand, the network does not need any update, and thus the influence of constraints could be totally avoided. On top of this, it makes us the first attempt to explicitly tackle the second obstacle by utilizing the abundant data in previous steps to optimize discriminability between old and new classes. Based on these understandings, we design a novel framework where unsupervised contrastive learning is performed on intermediate features to optimize future classes with both visual similarity and feature affinity as supervisions. One step further, an auxiliary classifier is trained using pseudo labels of future classes generated via clustering, which is used to initialize the actual classifier for future steps. Our method surpasses existing works by a huge margin as shown in Figure 1 and the effectiveness is further demonstrated with extensive experiments. Our contributions are summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.763, + 0.47, + 0.825 + ], + "angle": 0, + "content": "- We propose to pre-learn future knowledge for CSS with the aim of improving the performance especially for new classes, which can simultaneously tackle the R-P dilemma and the obstacle of inadequate data." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.832, + 0.47, + 0.878 + ], + "angle": 0, + "content": "- We design a novel framework that can pre-learn future knowledge in an unsupervised way, where both the feature space and output space are handled." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "- We have validated the effectiveness of our proposed" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.763, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "approach through extensive experiments. The results demonstrate significant improvement on standard CSS benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.153, + 0.642, + 0.169 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.179, + 0.892, + 0.451 + ], + "angle": 0, + "content": "Continual Learning (CL). Continual learning has been studied for years in image classification. Existing techniques can be roughly divided into regularization methods, rehearsal methods, and architectural methods. Regularization methods apply consistency constraints between current network and previous network to avoid drifts from previous states. They can be applied on network weights [53, 25, 1], the intermediate features [9, 11, 45, 13, 22] or the output logits [28, 42, 17, 48]. Parameter regularization is rarely seen recently due to the lack of plasticity, while the other two are mostly based on knowledge distillation (KD) [16]. To better solve the forgetting problem, rehearsal methods replay previous data in the incremental steps, including image replay [42, 41, 3], generative replay [49, 39], feature replay [20, 57], and memory management [30, 29]. Architectural methods use a dynamic network to handle incoming knowledge, like sub-network [32, 33], complementary network [47, 40] or expandable network [27, 50, 52]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.452, + 0.892, + 0.619 + ], + "angle": 0, + "content": "Continual Semantic Segmentation (CSS). Some works extended the aforementioned techniques to semantic segmentation tasks. For the KD-based methods, MiB [5] formalized and targeted background shift problem with output space distillation. PLOP [10], SDR [36], and RCIL [54] use feature space distillation to further mitigate forgetting. For the rehearsal-based methods, SSUL [6] and RECALL [34] utilize memory or external data to overcome forgetting and work well in multiple-step learning. For the architectural methods, RCIL [54] proposes a structural reparameterization design to better learn new knowledge." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.619, + 0.892, + 0.83 + ], + "angle": 0, + "content": "Unsupervised Semantic Segmentation. These works focus on learning to cluster semantically related pixels without human labeling. Existing works can be roughly divided into three types. PiCIE [8] iteratively performs clustering and uses it to refine network features. This relies on the architectural prior and is prone to degenerate solutions. IIC [21] maximizes the mutual information between two augmentations of the same image which enforces spatial stability on them. But this solution has trouble dealing with complex scenes. The last type uses visual similarity. These works [19, 55, 46, 23] use handcrafted priors, like boundary, superpixels, or saliency detectors to first group pixels by visual similarity. This is then used to learn pixel-level representations using contrastive learning." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.845, + 0.64, + 0.861 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In this section, we first explain the definition of CSS (Sec. 3.1), and present the underfitting phenomenon of new" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11911" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.103, + 0.346, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.361, + 0.103, + 0.61, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.626, + 0.103, + 0.874, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.218, + 0.895, + 0.262 + ], + "angle": 0, + "content": "Figure 2. Feature fitness analysis of different methods using L1 norm (Left), activation strength (Mid), and cosine similarity (Right) on VOC2012 15-5 setup. It is demonstrated that existing works suffer underfitting on both intra-class level (left and mid) and inter-class level (right) for new classes. Our method effectively addresses this problem." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.285, + 0.471, + 0.332 + ], + "angle": 0, + "content": "classes (Sec. 3.2). After that, we analyze how the performance is impacted in CSS (Sec. 3.3). Finally, we discuss the solutions to boost new class performance (Sec. 3.4)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.342, + 0.228, + 0.358 + ], + "angle": 0, + "content": "3.1. CSS Definition" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.471, + 0.534 + ], + "angle": 0, + "content": "In CSS, the training procedure is composed of a series of \\( T \\) learning steps. At each step \\( t \\) where \\( t \\in \\{1, \\dots, T\\} \\), a set of new categories \\( \\mathcal{C}_t \\) are introduced with a training set \\( D_t = \\{(x_n, y_n)\\} \\) where \\( x_n \\) is an image and \\( y_n \\) is the corresponding label. Only \\( \\mathcal{C}_t \\) is labeled in \\( y_n \\) and all the other classes are labeled as background. It is assumed that the categories learned at each step are disjoint, i.e., \\( \\mathcal{C}_i \\cap \\mathcal{C}_j = \\emptyset \\). The network is trained sequentially on each step, where it learns the knowledge w.r.t. \\( \\mathcal{C}_t \\) and expands its output space to \\( \\mathcal{C}_{1:t} = \\mathcal{C}_{1:t-1} \\cup \\mathcal{C}_t \\). After all learning steps, the network is expected to perform well on all classes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.544, + 0.321, + 0.56 + ], + "angle": 0, + "content": "3.2. Analysis of Feature Fitness" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.47, + 0.795 + ], + "angle": 0, + "content": "To get a clear view of why new classes perform poorly in existing methods, we analyze the intermediate features of two works: MiB [5] based on conventional logits distillation, and a more recent work, RCIL [54], based on feature distillation and structural re-parameterization aiming to better tackle the R-P dilemma. To simplify the situation, we opt for the two-step 15-5 setup on VOC2012 to conduct the analysis. The results are reported in Figure 2 (Detailed information about incremental setups and validation set can be found in Section 5.). The results of joint training (i.e., performance upperbound) and initial state (i.e., backbone is initialized with ImageNet pre-trained weights while the other parts are randomly initialized) are also provided for reference. Ideally, the results are expected to be close to that of the upperbound in order to achieve good performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Intra-class Fitness. We first evaluate how well the network fits to each individual class. In neural networks, each channel in the feature vectors could represent a certain pattern [4] which composes the learned classes [58]. When the network fits a class well, the output feature vector should have specific channels being activated while the others deactivated, resulting in sparsity in the feature vector. The" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.285, + 0.895, + 0.42 + ], + "angle": 0, + "content": "activation strength further shows how strong the network's response is to each pattern. Both of them can serve as clues indicating how well the network fits a class. We use the average L1 norm of L2-normalized feature vectors to measure the sparsity, and the average top activation values to measure the response strength. As can be seen in Figure 2 (left and mid), the new classes of both MiB and RCIL have high L1 norm and low activation strength, indicating a serious underfitting problem." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.422, + 0.893, + 0.603 + ], + "angle": 0, + "content": "Inter-class Fitness. We further evaluate how well the network learns to distinguish different classes, which is measured by the cosine similarity between the feature vectors of different classes. The better the network can distinguish each class, the lower the cosine similarities will be. We compute the mean cosine distance of a class to any other classes, which is then averaged based on class group to get the final results, as shown in Figure 2 (right). It can be seen that the network has good discriminative power on old classes, but the new classes again present poor results. It indicates the network cannot distinguish a new class between other classes well." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.605, + 0.894, + 0.682 + ], + "angle": 0, + "content": "Discussion. From the above analyses, it is evident that new classes suffer serious underfitting on both intra-class and inter-class aspects. This exactly explains why most methods show low performance on new classes, even in simple setups with only a single incremental step." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.694, + 0.791, + 0.71 + ], + "angle": 0, + "content": "3.3. Understanding Training Pipeline" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.894, + 0.809 + ], + "angle": 0, + "content": "In this part, we dive deeper to investigate why the underfitting problem happens for new classes in the conventional training pipeline. We use Figure 3 to give a clear view of how the two obstacles impact the performance in a conventional pipeline (green background). Without loss of generality, a two-step situation is adopted as an example." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Starting from step 1 where \\(\\mathcal{C}_1\\) is labeled in the given data \\(D_{1}\\) while others are marked as background, the network acquires most knowledge of \\(\\mathcal{C}_1\\) (i.e., distinguish between classes in \\(\\mathcal{C}_1\\)) after finishing this step. Considering that it only accesses partial data at this step compared to joint training, the knowledge of \\(\\mathcal{C}_1\\) remains to be updated" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "11912" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.09, + 0.462, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.27, + 0.47, + 0.339 + ], + "angle": 0, + "content": "Figure 3. Illustration of the difference between knowledge learning in a conventional training pipeline (green background) and our solution (blue background). We jointly optimize new classes together with old classes in an unsupervised way before new classes are introduced." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.469, + 0.426 + ], + "angle": 0, + "content": "in the next step. However, even though the future classes \\(\\mathcal{C}_2\\) do exist in \\(D_{1}\\), they do not receive explicit supervision, thus the network obtains almost no knowledge of \\(\\mathcal{C}_2\\) after finishing step 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.426, + 0.47, + 0.775 + ], + "angle": 0, + "content": "Moving to step 2, a constraint is usually applied to avoid forgetting previous knowledge by punishing the network from drifting away from its previous states. In this step, the network needs to update its knowledge of \\( \\mathcal{C}_1 \\) on \\( D_2 \\). Given that \\( \\mathcal{C}_1 \\) is already properly optimized at step 1, the network only needs a small adjustment to complete its knowledge of \\( \\mathcal{C}_1 \\) and receives little punishment from the constraint. However, the network is also intended to learn the knowledge w.r.t. \\( \\mathcal{C}_2 \\) (i.e., distinguish the classes in \\( \\mathcal{C}_2 \\) and distinguish between \\( \\mathcal{C}_2 \\) and \\( \\mathcal{C}_1 \\)) from the start, which requires a rather large update. Based on the fact that the constraints make more punishment for greater changes, this update will be suppressed more severely compared to that of \\( \\mathcal{C}_1 \\), making more knowledge w.r.t. \\( \\mathcal{C}_2 \\) cannot be learned. This is why the R-P dilemma often leads to low performance for new classes. To make matters worse, the scale of the training set is usually limited in incremental steps, especially for the situation when a single class is added with only a few samples of \\( \\mathcal{C}_1 \\). Such limited data could impede the network from successfully distinguishing between \\( \\mathcal{C}_1 \\) and \\( \\mathcal{C}_2 \\), which is the inadequate data obstacle. Both of these factors result in the inability to properly learn knowledge w.r.t. \\( \\mathcal{C}_2 \\) and contribute to the aforementioned underfitting phenomenon." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.786, + 0.305, + 0.801 + ], + "angle": 0, + "content": "3.4. Discussions for Solutions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Pre-learning future knowledge. Based on the analysis, if we modify the training pipeline by adding explicit supervision to \\(\\mathcal{C}_2\\) before it is introduced (blue background in Figure 3). The knowledge w.r.t. \\(\\mathcal{C}_2\\) could be learned in advance. By doing so, we first avoid the R-P dilemma by reducing the great update to learning the knowledge w.r.t. \\(\\mathcal{C}_2\\) at the next" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.212 + ], + "angle": 0, + "content": "step. Meanwhile, we can use the abundant samples of \\(\\mathcal{C}_1\\) at step 1 to make the network better learn how to distinguish between \\(\\mathcal{C}_2\\) and \\(\\mathcal{C}_1\\), mitigating the influence of inadequate data of \\(\\mathcal{C}_1\\) at next step. Consequently, both obstacles are tackled in a uniform and elegant way. The main challenge falls to how we can learn knowledge w.r.t. \\(\\mathcal{C}_2\\) as accurately as possible in an unsupervised way in order to reduce the extent of updates required in the future." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.212, + 0.893, + 0.408 + ], + "angle": 0, + "content": "Memory. Memory is a widely used technique in CL and has been adapted to CSS recently [6, 34]. Based on our analysis above, here we clearly explain the effect of memory in CSS. Memory is applied only in incremental steps. With the help of it, new classes are possible to be optimized with partial previous data, which can also alleviate the impact of inadequate data. Meanwhile, memory helps to ease the forgetting problem, which makes it possible to relax the constraints without forgetting. As a result, new knowledge can be more easily learned. We would like to point out that memory can be used to solve the two obstacles at a different aspect. It could further boost the performance in conjunction with our solution." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.421, + 0.591, + 0.436 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.447, + 0.892, + 0.523 + ], + "angle": 0, + "content": "In this section, we introduce a novel framework based on pre-learning future knowledge as depicted in Figure 4. It takes into account future knowledge in an unsupervised way, both in the feature space (green background) and the output space (blue background)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.531, + 0.886, + 0.547 + ], + "angle": 0, + "content": "4.1. Learning Future Knowledge in Feature Space" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.735 + ], + "angle": 0, + "content": "Contrastive learning. Contrastive learning is a widely used technique in unsupervised learning [7, 15]. In our work, we resort to it to optimize future classes in feature space. In semantic segmentation, directly using feature vectors at pixel level to perform pixel-pixel contrastive is redundant and results in high computational cost. Therefore, we follow [24, 46, 18] to perform contrast in a pixel-segment manner. Formally, supposing an image \\(I\\) is partitioned into segments \\(S\\) by a given prior. Let \\(\\pmb{f}_i\\) be the unit-length feature vector of pixel \\(i\\), we define the (normalized) prototype \\(\\pmb{p}\\) of a segment \\(s \\in S\\) by the average of feature vectors within this segment." + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.745, + 0.891, + 0.78 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {p} _ {s} = \\frac {1}{| s |} \\sum_ {i \\in s} \\boldsymbol {f} _ {i}, \\| \\boldsymbol {p} _ {s} \\| = 1 \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.786, + 0.882, + 0.801 + ], + "angle": 0, + "content": "We adopt the InfoNCE [38] loss and formalize our loss as" + }, + { + "type": "equation", + "bbox": [ + 0.504, + 0.822, + 0.891, + 0.87 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} \\left(\\boldsymbol {f} _ {i}, S\\right) = - \\log \\frac {\\exp \\left(\\boldsymbol {f} _ {i} \\cdot \\boldsymbol {p} _ {s _ {+}} / \\tau\\right)}{\\exp \\left(\\boldsymbol {f} _ {i} \\cdot \\boldsymbol {p} _ {s _ {+}} / \\tau\\right) + \\sum_ {s _ {-}} \\exp \\left(\\boldsymbol {f} _ {i} \\cdot \\boldsymbol {p} _ {s _ {-}} / \\tau\\right)} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\(\\tau\\) is a temperature hyper-parameter. Ideally, it pulls \\(f_{i}\\) close to the positive segment \\(s_{+}\\) and pushes it away from" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11913" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.46, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.302, + 0.473, + 0.414 + ], + "angle": 0, + "content": "Figure 4. Overall framework. Given an image at step \\( t \\), a projection head maps the features from feature extractor \\( F_{t} \\) into an embedding space where \\( \\mathcal{L}_{c} \\) is used to optimize future classes (green block). Next, the features from \\( F_{t} \\) are also used to train an auxiliary classifier \\( G_{aux} \\) to initialize the classifier for future classes (blue block). Last, the pseudo label technique together with a knowledge distillation loss are adopted to mitigate forgetting (yellow block)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.443, + 0.47, + 0.489 + ], + "angle": 0, + "content": "all the negative segments \\( s_{-} \\). For a given pixel, the segment it belongs to serves as \\( s_{+} \\), whereas other segments, including those from other images, serve as \\( s_{-} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.47, + 0.687 + ], + "angle": 0, + "content": "Contrast by Visual Similarity. In pixel-segment contrastive learning, the partition scheme determines how the network is optimized. We first resort to visual boundaries as a prior to partition the images into visual coherent segments \\( S_{v} \\) by OWT-UCM [2], which is a decent choice in unsupervised segmentation [19, 55, 23]. By utilizing visual similarity as supervision, we can bootstrap the representation learning and ground the features to respect low-level visual cues. But using this supervision alone makes the network hard to capture semantic-level information of future classes, and still needs further updates to properly learn them. This contradicts our goal to make the necessary updates as few as possible in the future." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Contrast by Feature Affinity. We also need a partition method that can match actual future classes accurately to serve as another supervision. Due to the bootstrap effect of the previous contrast, we can resort to clustering methods to explore feature affinity as semantic-level supervision without relying on architectural prior like [8]. However, applying clustering directly cannot generate satisfying results. In practice, we find that by hierarchically combining an over-clustering result, we could obtain much more accurate results. More in detail, starting from an over-clustering generated using intermediate features, we merge the two most similar segments each time till all segments are merged as one. The similarity between segments is measured by the cosine similarity between their prototypes. This procedure" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.092, + 0.887, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.228, + 0.895, + 0.299 + ], + "angle": 0, + "content": "Figure 5. Segments obtained using visual similarity and feature affinity respectively. Top: Segments generated by OWT-UCM [2] using boundaries. Bottom: Segments that are likely to match the actual classes are selected from a hierarchical combination of fine-grained clustering results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.321, + 0.895, + 0.64 + ], + "angle": 0, + "content": "generates consistent segments across all granularities. But different classes naturally have different levels of granularities, directly selecting segments from a single granularity is often suboptimal. We further propose a confidence score to evaluate how likely a segment matches a class accurately to select segments across granularities. The design of the confidence score is based on the following observations. In the combination procedure where the most similar segments are merged each time, the longer a segment can remain not merged, the more different it is to all other segments, and is more likely to match a class. What's more, given that this procedure starts from an over-clustering, the segments in later steps have a higher chance to match a class and should be assigned higher weights. A possible choice is to use the cosine distance between the segments to be merged at each step as a weight factor, which monotonously increases by step. Formally, assuming segments \\(a\\) and \\(b\\) are merged into a new segment \\(c\\) at step \\(n\\) in this procedure, set \\(S_{n}\\) indicates all segments that are merged from start till now (include \\(a\\) and \\(b\\)). The confidence score \\(u\\) for a segment \\(s\\) at step \\(n\\) is defined recursively as follows." + }, + { + "type": "equation", + "bbox": [ + 0.548, + 0.655, + 0.892, + 0.711 + ], + "angle": 0, + "content": "\\[\nu _ {s} ^ {n} = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} s = c, \\\\ u _ {s} ^ {n - 1} & \\text {e l i f} s \\in S _ {n}, \\\\ u _ {s} ^ {n - 1} + \\left(1 - \\boldsymbol {p} _ {a} \\cdot \\boldsymbol {p} _ {b}\\right) & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.854 + ], + "angle": 0, + "content": "After finishing this procedure, we use the final score of each segment to select those with scores above the threshold to serve as high-confidence segments \\( S_{f} \\) and participate in contrastive learning. If two selected segments are partially overlapped, we only reserve the one with a higher score. This procedure is performed for each training sample before each epoch to select high-confidence segments as the network updates itself, except for the first epoch since the feature cannot be clustered at that moment." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Overall Contrastive Loss. In our contrastive learning, the pixels of \\( \\mathcal{C}_t \\) with ground truth annotations and \\( \\mathcal{C}_{1:t-1} \\) with pseudo labels are excluded. Meanwhile, they can naturally" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11914" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "serve as high-confidence negative segments in contrastive learning. Since the batch size is limited in segmentation while the number of negative samples is crucial in contrastive learning [7, 15], we use a memory bank to cache the features of recent four batches to increase the number of negative samples. Given the segments \\( S_{v} \\) generate by visual similarity and segments \\( S_{f} \\) generated by feature affinity, our contrastive loss is formalized as" + }, + { + "type": "equation", + "bbox": [ + 0.096, + 0.229, + 0.47, + 0.277 + ], + "angle": 0, + "content": "\\[\n\\mathcal{L}_{c} = \\frac{1}{|S_{v}|}\\sum_{\\substack{i\\in S_{v}\\\\ i\\notin \\mathcal{C}_{1:t}}}\\mathcal{L}(\\boldsymbol{f}_{i},S_{v}) + \\frac{1}{|S_{f}|}\\sum_{\\substack{i\\in S_{f}\\\\ i\\notin \\mathcal{C}_{1:t}}}\\mathcal{L}(\\boldsymbol{f}_{i},S_{f}) \\tag{4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.282, + 0.468, + 0.298 + ], + "angle": 0, + "content": "where \\(|S|\\) means the pixel number in all segments within \\(S\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.304, + 0.462, + 0.321 + ], + "angle": 0, + "content": "4.2. Learning Future Knowledge in Output Space" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.327, + 0.47, + 0.508 + ], + "angle": 0, + "content": "Previous work [5] has claimed that a proper initialization of classifier weight at step \\( t > 1 \\) could also benefit the performance and is widely adopted by other works [10, 54]. This motivates us to further introduce future knowledge to the output space. Existing practice eases the misalignment between features and classifier weights by using the weight of the background to initialize that of the new classes. But in the update process, the weights of new classes should be updated to separate them from the background. Making the classifier weights to be identical to that of the background has the risk of increasing the necessary update, which has a negative effect based on previous analysis." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.471, + 0.841 + ], + "angle": 0, + "content": "To address this issue, we want the classifier to be initialized as close to the final optimal value as possible. When optimizing feature space, we manage to obtain high-confidence segments of future classes, and the intermediate features are also optimized accordingly. We could naturally utilize them to train an auxiliary classifier that can classify future classes in advance and use its weights as initialization. More in detail, we first perform clustering on the prototypes of segments to assign an auxiliary semantic label to each segment, which is then used to optimize the auxiliary classifier using cross-entropy loss. Note that the network receives no gradient from this classifier. In the next step when initialization is needed, we compute the prototype of each new class and select the auxiliary classifier weight which is closest to the prototype to initialize the actual classifier weight of it. On the one hand, we can make the classifier converge more easily and avoid the R-P dilemma. On the other hand, it solves the inadequate data obstacle in output space by utilizing the data of current step to serve as the negative samples of future classes, which can further boost the discriminability of the classifier compared to training it directly on the future steps." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.267, + 0.862 + ], + "angle": 0, + "content": "4.3. Overall Framework" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Our proposed framework is depicted in Figure 4. \\(\\mathcal{L}_{ce}\\) and \\(\\mathcal{L}_{aux}\\) are both cross-entropy loss to learn new classes and to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "train the auxiliary classifier, respectively. To complete our framework, we still need a KD loss to overcome forgetting. Since our focus is not on this part, we adopt the CKD loss in MiB [5] as \\(\\mathcal{L}_{kd}\\) to assist our training, with the addition of a temperature parameter as in original KD loss [16] to enhance its ability in knowledge preserving. This makes the overall loss function of our framework as follows." + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.209, + 0.892, + 0.226 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {c e} + \\alpha \\mathcal {L} _ {k d} + \\beta \\mathcal {L} _ {c} + \\mathcal {L} _ {\\text {a u x}}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.236, + 0.747, + 0.251 + ], + "angle": 0, + "content": "where \\(\\alpha\\) and \\(\\beta\\) are hyper-parameters." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.265, + 0.634, + 0.281 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.289, + 0.679, + 0.305 + ], + "angle": 0, + "content": "5.1. Implement Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.312, + 0.892, + 0.403 + ], + "angle": 0, + "content": "Datasets. Following previous works, we evaluate our method on VOC2012 [12] and ADE20K [56], which are the standard CSS benchmarks. We report the performance on the official validation set of each dataset. We also exclude \\(20\\%\\) of the training set as a validation set to tune hyperparameters and perform all analyses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.403, + 0.893, + 0.75 + ], + "angle": 0, + "content": "Protocols. There are two settings in CSS benchmarks: disjoint and overlapped. The disjoint setting limits the given images to contain pixels only belong to \\(\\mathcal{C}_{1:t}\\), while the latter does not have this restriction, which means the pixels can also belong to the future classes, i.e., \\(\\mathcal{C}_{t+1:T}\\). Note that the overlapped setting is considered to be more realistic and more challenging by all existing works [5, 10, 6, 37], and the disjoint setting is even ignored in some works [6, 37]. In design, our work is fully based on the overlapped setting. Evaluation. The CSS benchmark setups are denoted as \\(N_{o} - N_{n}\\) where \\(N_{o}\\) and \\(N_{n}\\) are the number of classes to be learned at the initial step and each incremental step, respectively. For example, the 15-1 setup of VOC2012 gives 15 classes at the initial step and adds one class per incremental step, resulting in a total of 6 steps. On VOC2012, we conduct experiments on four setups: 19-1 (2 steps), 15-5 (2 steps), 15-1 (6 steps), and 10-1 (11 steps). On ADE20K, we use three setups: 100-50 (2 tasks), 50-50 (3 tasks), and 100-10 (6 tasks). The network is evaluated after finishing all learning steps using mean Intersection over Union (mIoU) as metric. The performance of initial classes \\(\\mathcal{C}_{1}\\), incremental classes \\(\\mathcal{C}_{2:T}\\), and all classes \\(\\mathcal{C}_{1:T}\\) are denoted as old, new, and all, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Training. Following previous works [5, 10], we adopt DeepLab-V3 with an output stride of 16. ResNet-101 serves as the backbone, which is pre-trained on ImageNet. We use the SGD optimizer with momentum set to 0.9. The learning rate is set to 1e-2 for the initial learning step and 1e-3 for the following learning step. The learning rate is adjusted by the polynomial decay schedule with power set to 0.9. The network is trained on VOC2012 for 30 epochs, and 60 epochs on ADE20K, both with a batch size of 16. The image is cropped to \\(512 \\times 512\\) for both training and validation, with" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11915" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.892, + 0.114 + ], + "angle": 0, + "content": "Table 1. Results of different methods on VOC2012. The best is in bold while the second best is in underline. Results are averaged over 3 runs with standard deviation provided." + }, + { + "type": "table", + "bbox": [ + 0.128, + 0.115, + 0.842, + 0.33 + ], + "angle": 0, + "content": "
Method19-1 (2 tasks)15-5 (2 tasks)15-1 (6 tasks)10-1 (11 tasks)
oldnewalloldnewalloldnewalloldnewall
ILT [35]67.112.364.466.340.659.94.97.85.7---
MiB [5]70.222.167.875.549.469.035.113.529.712.213.012.6
PLOP [10]75.337.373.575.751.770.065.121.154.644.015.522.9
SDR [36]69.132.667.475.452.669.944.721.839.2---
SSUL [6]77.729.675.477.850.171.277.336.567.671.345.959.2
RCIL [54]---78.852.072.470.623.759.455.415.134.3
ALIFE [37]76.649.375.377.152.571.364.434.957.4---
Ours77.7 ±0.2259.8 ±1.3876.8 ±0.3579.1 ±0.2167.7 ±0.4676.4 ±0.2975.2 ±0.7552.2 ±1.3369.7 ±1.0968.1 ±0.9654.5 ±1.5761.6 ±1.13
RECALL [34]68.155.368.667.754.365.667.850.964.865.053.760.7
SSUL-M [6]77.849.776.478.455.873.078.349.071.374.053.264.1
ALIFE-M [37]76.752.275.577.655.272.366.038.859.5---
Ours-M77.9 ±0.1967.7 ±0.7477.4 ±0.3279.3 ±0.2270.2 ±0.2977.1 ±0.2477.1 ±0.6560.4 ±0.7373.1 ±0.6869.5 ±0.6063.2 ±1.2566.5 ±0.78
Joint77.677.777.679.571.577.679.571.577.678.576.677.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.345, + 0.892, + 0.371 + ], + "angle": 0, + "content": "Table 2. Results of different methods on ADE20K. The best is in bold while the second best is in underline. Results are averaged over 3 runs with standard deviation provided." + }, + { + "type": "table", + "bbox": [ + 0.204, + 0.372, + 0.766, + 0.564 + ], + "angle": 0, + "content": "
Method100-50 (2 tasks)50-50 (3 tasks)100-10 (6 tasks).
oldnewalloldnewalloldnewall
ILT [35]18.214.417.03.512.89.70.11.30.5
MiB [5]40.517.132.745.521.029.338.211.129.2
PLOP [10]41.814.832.948.820.930.440.413.631.5
SSUL [6]41.218.033.548.320.129.540.218.733.1
RCIL [54]42.318.834.548.325.032.939.317.632.1
ALIFE [37]42.123.035.848.925.633.541.022.734.9
Ours43.1 ±0.1726.0 ±0.3637.4 ±0.2549.1 ±0.2428.3 ±0.4335.2 ±0.3341.4 ±0.2825.5 ±0.4536.1 ±0.35
SSUL-M [6]42.717.534.349.120.129.742.817.634.4
ALIFE-M [37]42.223.536.049.026.133.841.123.035.1
Ours-M43.1 ±0.1526.2 ±0.2937.5 ±0.2149.2 ±0.1228.5 ±0.2735.4 ±0.1841.6 ±0.2125.8 ±0.2636.3 ±0.22
Joint43.529.438.850.332.738.843.529.438.8
" + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.582, + 0.214, + 0.669 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.224, + 0.582, + 0.347, + 0.669 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.358, + 0.582, + 0.479, + 0.669 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.581, + 0.611, + 0.669 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.582, + 0.744, + 0.668 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.756, + 0.582, + 0.876, + 0.669 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.673, + 0.89, + 0.701 + ], + "angle": 0, + "content": "Figure 6. mIoU comparison between CSS methods over steps on VOC 15-1 setups. The performance of initial classes and each new class added per step are plotted separately from left to right. Our method shows great ability in learning new classes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.726, + 0.468, + 0.756 + ], + "angle": 0, + "content": "a random scaling and a random left-right flip additionally applied to training." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.77, + 0.17, + 0.785 + ], + "angle": 0, + "content": "5.2. Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We provide the results on VOC2012 and ADE20K in Table 1 and Table 2, respectively. Some works [6, 34] exploit memory or external data to assist training. We also report the results obtained using memory (denoted by -M) following the implementation of [6] to fairly compare with these methods. The result of joint training is also provided as the upperbound for reference." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.726, + 0.892, + 0.892 + ], + "angle": 0, + "content": "For all setups on VOC2012, our method surpasses all existing methods by a large margin on new classes. This demonstrates the strong ability of our method to learn new classes. Note that our method also shows promising results on old classes even with a simple approach to preserve old knowledge. This is due to that a higher performance on new classes indicates that there also might be less confusion between old and new classes, which also benefits the mIoU of old classes. On the more challenging setups with multiple steps (15-1, 10-1), the new classes cannot be properly learned in the first place for most methods. To" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11916" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "make matters worse, these poorly optimized new classes will suffer forgetting in the following steps which further reduces their performance. Even in these challenging circumstances, our method still shows great performance in learning new classes, as shown in Figure 6. We can also see that even though SSUL shows higher performance on old classes on long-term setups, it relies on completely freezing the feature extractor to prevent forgetting, which does help a lot for old classes on these steps, but also harms its flexibility greatly. We believe that if equipped with a modern knowledge-preserving constraint, our method could offer another boost in performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.277, + 0.47, + 0.382 + ], + "angle": 0, + "content": "On the more challenging ADE20K benchmarks, we obtain similar results as that of VOC2012. Our method shows some improvement on old classes and is significantly better on new classes. On top of the results of VOC2012 benchmark, this further demonstrates that our approach works well on more complex datasets, and has the ability to handle both scenes and objects centric datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.387, + 0.47, + 0.477 + ], + "angle": 0, + "content": "When memory is applied on both benchmarks, our method receives further improvements and holds the leading position. This also indicates that our proposed training method has a non-overlapping effect with the memory technique. They can be used as two complementary techniques as pointed out in Section 3.4" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.498, + 0.23, + 0.515 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.526, + 0.471, + 0.753 + ], + "angle": 0, + "content": "We investigate the effects of the proposed components in our framework using both 15-1 and 15-5 setups on VOC2012. Starting from a baseline composed of \\( L_{ce} \\), \\( L_{kd} \\) and pseudo label, we add the components one by one and show the ablation results in Table 3. As can be seen, the performance increase steadily as each proposed component is gradually added. Only applying contrast by visual similarity does not receive much improvement since it cannot instruct the network to capture semantic-level information. After applying contrast by feature affinity, the performance receives the highest gain, indicating the necessity to add semantic-level supervision and make the network learn more accurate knowledge. On top of that, the performance receives another boost from our classifier initialization technique which introduces future knowledge to output space." + }, + { + "type": "table_caption", + "bbox": [ + 0.099, + 0.772, + 0.446, + 0.786 + ], + "angle": 0, + "content": "Table 3. Ablation study on VOC2012 15-1 and 15-5 setup." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.787, + 0.472, + 0.874 + ], + "angle": 0, + "content": "
Method15-1 (6 tasks)15-5 (2 tasks)
oldnewalloldnewall
baseline65.318.854.276.951.370.8
+ visual similarity contrast67.126.357.477.254.571.8
+ feature affinity contrast74.545.167.578.765.475.5
+ classifier initialization75.252.269.779.167.776.4
" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.089, + 0.889, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.262, + 0.892, + 0.304 + ], + "angle": 0, + "content": "Figure 7. Visualization of clustering results of direct clustering and our practice. The high-confidence segments selected by our criterion are also presented on the right." + }, + { + "type": "image", + "bbox": [ + 0.552, + 0.32, + 0.84, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.476, + 0.891, + 0.505 + ], + "angle": 0, + "content": "Figure 8. Performance comparison between different classifier initialization over training epochs on VOC2012 19-1 setup." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.529, + 0.683, + 0.544 + ], + "angle": 0, + "content": "5.4. Further Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.644 + ], + "angle": 0, + "content": "Feature Quality Analysis. To further demonstrate the effect of our method to solve the underfitting problem pointed out in Section 3.2, we conduct the same analysis on our method and incorporate the findings into Figure 2 (denoted by Ours). As can be seen, pre-learning future classes can significantly improve both intra-class and inter-class fitness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.78 + ], + "angle": 0, + "content": "Segment Generation. We provide a qualitative comparison between direct clustering and our proposed hierarchical combination at different granularities to validate our design in Section 4.1. The results are generated from the same intermediate features and are plotted in Figure 7. As can be seen, our practice consistently generates better results across different granularities. We also present the high-confidence segments selected by our criterion for each image, which match the actual classes with high precision." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Classifier Initialization. We give a comparison of performance over training epochs for different classifier initialization methods in Figure 8. As can be seen, the initialization technique proposed by MiB [5] converges much slower due to larger update paces. Random initialization converges fast but the performance stops increasing shortly afterward. Among all of them, our method stands out with its fast convergence speed and superior performance." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11917" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.327, + 0.106 + ], + "angle": 0, + "content": "6. Limitation and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.117, + 0.47, + 0.283 + ], + "angle": 0, + "content": "Our method has two limitations. Firstly, it relies on the natural attribute of CSS that unlabeled future classes exist in current training data. So it may not perform well when there are only a few unlabeled future classes in the current training data. However, in such cases, we can still leverage external unlabeled data, such as web-crawled data as used in RECALL [34]. Secondly, we point out that even though our proposed framework achieves great performance, it as a practicable solution might not be able to unleash the full potential of the training method, which requires further exploration in future works." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.284, + 0.473, + 0.465 + ], + "angle": 0, + "content": "In this work, we present an in-depth analysis of the reason why existing methods suffer low performance on new classes. Building on this analysis, we introduce a novel training pipeline for CSS that optimizes potential future classes in the current training step. This offers a new perspective for enhancing new class performance in contrast to existing works that focus on addressing the R-P dilemma. We propose a framework based on this pipeline and it shows a significant improvement for new classes, while also benefiting the performance of old classes. We believe that this work can provide valuable insights for the research community on CSS." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.482, + 0.266, + 0.5 + ], + "angle": 0, + "content": "7. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.614 + ], + "angle": 0, + "content": "This work is supported by the National Natural Science Foundation of China under Grant 62176246 and Grant 61836008. This work is also supported by Anhui Province Key Research and Development Plan (202304a05020045), Anhui Provincial Natural Science Foundation 2208085UD17 and the Fundamental Research Funds for the Central Universities (WK3490000006)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.631, + 0.175, + 0.646 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.085, + 0.656, + 0.47, + 0.699 + ], + "angle": 0, + "content": "[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware synapses: Learning what (not) to forget. In ECCV, 2018." + }, + { + "type": "ref_text", + "bbox": [ + 0.085, + 0.699, + 0.472, + 0.757 + ], + "angle": 0, + "content": "[2] Pablo Arbelaez, Michael Maire, Charless Fowlkes, and Jitendra Malik. Contour detection and hierarchical image segmentation. 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In Proceedings of the 28th ACM International Conference on Multimedia, pages 156-164, 2020." + }, + { + "type": "list", + "bbox": [ + 0.079, + 0.092, + 0.47, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11920" + } + ] +] \ No newline at end of file diff --git a/2023/Preparing the Future for Continual Semantic Segmentation/72d5919b-3823-475f-9939-cac5c29b48a5_origin.pdf b/2023/Preparing the Future for Continual Semantic Segmentation/72d5919b-3823-475f-9939-cac5c29b48a5_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..871591cb6c5b3346b335c3f0529b61d5eb2006ad --- /dev/null +++ b/2023/Preparing the Future for Continual Semantic Segmentation/72d5919b-3823-475f-9939-cac5c29b48a5_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d26cf624ccd36fff4dff89997a02f719a75552b6ffc11286af1b3258c5617d41 +size 3408325 diff --git a/2023/Preparing the Future for Continual Semantic Segmentation/full.md b/2023/Preparing the Future for Continual Semantic Segmentation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..4e65a473dad98363c91aae2062dbb6cfd6de77c2 --- /dev/null +++ b/2023/Preparing the Future for Continual Semantic Segmentation/full.md @@ -0,0 +1,303 @@ +# Preparing the Future for Continual Semantic Segmentation + +Zihan Lin1 Zilei Wang*1 Yixin Zhang1,2 + +1 University of Science and Technology of China + +$^{2}$ Institute of Artificial Intelligence, Hefei Comprehensive National Science Center + +myustc@mail.ustc.edu.cn, {zlwang, zhyx12}@ustc.edu.cn + +# Abstract + +In this study, we focus on Continual Semantic Segmentation (CSS) and present a novel approach to tackle the issue of existing methods struggling to learn new classes. The primary challenge of CSS is to learn new knowledge while retaining old knowledge, which is commonly known as the rigidity-plasticity dilemma. Existing approaches strive to address this by carefully balancing the learning of new and old classes during training on new data. Differently, this work aims to avoid this dilemma fundamentally rather than handling the difficulties involved in it. Specifically, we reveal that this dilemma mainly arises from the greater fluctuation of knowledge for new classes because they have never been learned before the current step. Additionally, the data available in incremental steps are usually inadequate, which can impede the model's ability to learn discriminative features for both new and old classes. To address these challenges, we introduce a novel concept of pre-learning for future knowledge. Our approach entails optimizing the feature space and output space for unlabeled data, which thus enables the model to acquire knowledge for future classes. With this approach, updating the model for new classes becomes as smooth as for old classes, effectively avoiding the rigidity-plasticity dilemma. We conducted extensive experiments and the results demonstrate a significant improvement in the learning of new classes compared to previous state-of-the-art methods. + +# 1. Introduction + +Deep neural networks have demonstrated their superiority in many computer vision tasks [26, 31, 14]. Conventionally, they are trained in an offline manner with all data collected beforehand. When novel classes need to be handled, the networks need to be re-trained using either updated training set with both new and previous data, or directly finetuned on new data. The former has higher costs and is even impracticable sometimes like, when privacy raises concerns. The latter is prone to forget previ + +![](images/301e91d65d39335f139ddfa2115135c85334d75e9536194ad13a2b6c5bd7c493.jpg) +Figure 1. On VOC2012 benchmark, our method boosts the performance of new classes by a significant margin, while also achieving promising performance for old classes, compared to recent state-of-the-art methods. + +ously learned knowledge, which is called catastrophic forgetting (CF) [25]. To better fit neural networks into real-world scenarios, we want them to have the ability to learn new concepts while preserving the old knowledge (or even improve it using new knowledge). This is known as the continual learning (CL) problem and receives increasing attention recently. It has been explored first in the field of image classification [28, 42, 17, 11, 57, 44, 43], and some methods are proposed recently targeting semantic segmentation [5, 10, 6, 54, 51, 37]. Generally, it is often achieved by applying forgetting-preventing constraints between current and previous networks to prevent CF, which raises the rigidity (i.e., the ability to preserve old states) but harms the plasticity (i.e., the ability to learn new knowledge). It is known as the rigidity-plasticity (R-P) dilemma. A key aspect in designing constraints is to balance between rigidity and plasticity, which is what most works focus on. + +Despite that several new constraints have been proposed for CSS to better tackle the dilemma, existing works still struggle to learn new classes. Taking the VOC2012 benchmark as an example, most methods can only achieve a performance around $70\%$ of that of the upperbound for 15-5 setup and around $50\%$ for 19-1 setup, which is even worse + +for harder setups. To get a clear picture of why this happens, we first analyze the intermediate features of the network and find it suffers serious underfitting for new classes, which indicates a large amount of knowledge is not learned. We then examine the CSS training pipeline and find two main obstacles causing this phenomenon. (1) R-P Dilemma: the network has no knowledge w.r.t. new classes until they are introduced. This generally requires a rather large update to incorporate the new knowledge, which will be significantly hindered by the forgetting-preventing constraints punishing the network from drifting away from its previous states. (2) Inadequate data for training: the amount of data available in incremental steps is usually limited, and this problem becomes more severe when a single class is added, resulting in a tiny training set with only a few negative samples. This can significantly limit the network to properly discriminate between old and new classes. This problem has never been explicitly considered before. + +Unlike existing works trying to tackle the R-P dilemma directly, we are the first to argue that this obstacle can be elegantly avoided by exploring future knowledge in an unsupervised way. Assume that the network has obtained partial knowledge of future classes in advance, then the network needs fewer updates to learn the upcoming knowledge, which consequently lowers the impacts of the R-P dilemma. The more future knowledge it learns in advance, the fewer the impacts will be caused. Considering an extreme situation where all the future knowledge is learned beforehand, the network does not need any update, and thus the influence of constraints could be totally avoided. On top of this, it makes us the first attempt to explicitly tackle the second obstacle by utilizing the abundant data in previous steps to optimize discriminability between old and new classes. Based on these understandings, we design a novel framework where unsupervised contrastive learning is performed on intermediate features to optimize future classes with both visual similarity and feature affinity as supervisions. One step further, an auxiliary classifier is trained using pseudo labels of future classes generated via clustering, which is used to initialize the actual classifier for future steps. Our method surpasses existing works by a huge margin as shown in Figure 1 and the effectiveness is further demonstrated with extensive experiments. Our contributions are summarized as follows. + +- We propose to pre-learn future knowledge for CSS with the aim of improving the performance especially for new classes, which can simultaneously tackle the R-P dilemma and the obstacle of inadequate data. +- We design a novel framework that can pre-learn future knowledge in an unsupervised way, where both the feature space and output space are handled. +- We have validated the effectiveness of our proposed + +approach through extensive experiments. The results demonstrate significant improvement on standard CSS benchmarks. + +# 2. Related Work + +Continual Learning (CL). Continual learning has been studied for years in image classification. Existing techniques can be roughly divided into regularization methods, rehearsal methods, and architectural methods. Regularization methods apply consistency constraints between current network and previous network to avoid drifts from previous states. They can be applied on network weights [53, 25, 1], the intermediate features [9, 11, 45, 13, 22] or the output logits [28, 42, 17, 48]. Parameter regularization is rarely seen recently due to the lack of plasticity, while the other two are mostly based on knowledge distillation (KD) [16]. To better solve the forgetting problem, rehearsal methods replay previous data in the incremental steps, including image replay [42, 41, 3], generative replay [49, 39], feature replay [20, 57], and memory management [30, 29]. Architectural methods use a dynamic network to handle incoming knowledge, like sub-network [32, 33], complementary network [47, 40] or expandable network [27, 50, 52]. + +Continual Semantic Segmentation (CSS). Some works extended the aforementioned techniques to semantic segmentation tasks. For the KD-based methods, MiB [5] formalized and targeted background shift problem with output space distillation. PLOP [10], SDR [36], and RCIL [54] use feature space distillation to further mitigate forgetting. For the rehearsal-based methods, SSUL [6] and RECALL [34] utilize memory or external data to overcome forgetting and work well in multiple-step learning. For the architectural methods, RCIL [54] proposes a structural reparameterization design to better learn new knowledge. + +Unsupervised Semantic Segmentation. These works focus on learning to cluster semantically related pixels without human labeling. Existing works can be roughly divided into three types. PiCIE [8] iteratively performs clustering and uses it to refine network features. This relies on the architectural prior and is prone to degenerate solutions. IIC [21] maximizes the mutual information between two augmentations of the same image which enforces spatial stability on them. But this solution has trouble dealing with complex scenes. The last type uses visual similarity. These works [19, 55, 46, 23] use handcrafted priors, like boundary, superpixels, or saliency detectors to first group pixels by visual similarity. This is then used to learn pixel-level representations using contrastive learning. + +# 3. Preliminaries + +In this section, we first explain the definition of CSS (Sec. 3.1), and present the underfitting phenomenon of new + +![](images/7c464a504f500bccef080c7376cf9f4d8e5a117b9e37411e79d55f94d75c2aa6.jpg) +Figure 2. Feature fitness analysis of different methods using L1 norm (Left), activation strength (Mid), and cosine similarity (Right) on VOC2012 15-5 setup. It is demonstrated that existing works suffer underfitting on both intra-class level (left and mid) and inter-class level (right) for new classes. Our method effectively addresses this problem. + +![](images/196888f1c316e672db90607467f10607b1ec82a221c00885053b765c22d1160e.jpg) + +![](images/4f84dd7ca2e2af2a43674bb3157b812ed37d730691a0015ce1dc4f2aa1c259c0.jpg) + +classes (Sec. 3.2). After that, we analyze how the performance is impacted in CSS (Sec. 3.3). Finally, we discuss the solutions to boost new class performance (Sec. 3.4). + +# 3.1. CSS Definition + +In CSS, the training procedure is composed of a series of $T$ learning steps. At each step $t$ where $t \in \{1, \dots, T\}$ , a set of new categories $\mathcal{C}_t$ are introduced with a training set $D_t = \{(x_n, y_n)\}$ where $x_n$ is an image and $y_n$ is the corresponding label. Only $\mathcal{C}_t$ is labeled in $y_n$ and all the other classes are labeled as background. It is assumed that the categories learned at each step are disjoint, i.e., $\mathcal{C}_i \cap \mathcal{C}_j = \emptyset$ . The network is trained sequentially on each step, where it learns the knowledge w.r.t. $\mathcal{C}_t$ and expands its output space to $\mathcal{C}_{1:t} = \mathcal{C}_{1:t-1} \cup \mathcal{C}_t$ . After all learning steps, the network is expected to perform well on all classes. + +# 3.2. Analysis of Feature Fitness + +To get a clear view of why new classes perform poorly in existing methods, we analyze the intermediate features of two works: MiB [5] based on conventional logits distillation, and a more recent work, RCIL [54], based on feature distillation and structural re-parameterization aiming to better tackle the R-P dilemma. To simplify the situation, we opt for the two-step 15-5 setup on VOC2012 to conduct the analysis. The results are reported in Figure 2 (Detailed information about incremental setups and validation set can be found in Section 5.). The results of joint training (i.e., performance upperbound) and initial state (i.e., backbone is initialized with ImageNet pre-trained weights while the other parts are randomly initialized) are also provided for reference. Ideally, the results are expected to be close to that of the upperbound in order to achieve good performance. + +Intra-class Fitness. We first evaluate how well the network fits to each individual class. In neural networks, each channel in the feature vectors could represent a certain pattern [4] which composes the learned classes [58]. When the network fits a class well, the output feature vector should have specific channels being activated while the others deactivated, resulting in sparsity in the feature vector. The + +activation strength further shows how strong the network's response is to each pattern. Both of them can serve as clues indicating how well the network fits a class. We use the average L1 norm of L2-normalized feature vectors to measure the sparsity, and the average top activation values to measure the response strength. As can be seen in Figure 2 (left and mid), the new classes of both MiB and RCIL have high L1 norm and low activation strength, indicating a serious underfitting problem. + +Inter-class Fitness. We further evaluate how well the network learns to distinguish different classes, which is measured by the cosine similarity between the feature vectors of different classes. The better the network can distinguish each class, the lower the cosine similarities will be. We compute the mean cosine distance of a class to any other classes, which is then averaged based on class group to get the final results, as shown in Figure 2 (right). It can be seen that the network has good discriminative power on old classes, but the new classes again present poor results. It indicates the network cannot distinguish a new class between other classes well. + +Discussion. From the above analyses, it is evident that new classes suffer serious underfitting on both intra-class and inter-class aspects. This exactly explains why most methods show low performance on new classes, even in simple setups with only a single incremental step. + +# 3.3. Understanding Training Pipeline + +In this part, we dive deeper to investigate why the underfitting problem happens for new classes in the conventional training pipeline. We use Figure 3 to give a clear view of how the two obstacles impact the performance in a conventional pipeline (green background). Without loss of generality, a two-step situation is adopted as an example. + +Starting from step 1 where $\mathcal{C}_1$ is labeled in the given data $D_{1}$ while others are marked as background, the network acquires most knowledge of $\mathcal{C}_1$ (i.e., distinguish between classes in $\mathcal{C}_1$ ) after finishing this step. Considering that it only accesses partial data at this step compared to joint training, the knowledge of $\mathcal{C}_1$ remains to be updated + +![](images/a284cd579c0221d99adab4bb6e6c37940eaaaffa4cfdeabfc8de1a28bfe70af4.jpg) +Figure 3. Illustration of the difference between knowledge learning in a conventional training pipeline (green background) and our solution (blue background). We jointly optimize new classes together with old classes in an unsupervised way before new classes are introduced. + +in the next step. However, even though the future classes $\mathcal{C}_2$ do exist in $D_{1}$ , they do not receive explicit supervision, thus the network obtains almost no knowledge of $\mathcal{C}_2$ after finishing step 1. + +Moving to step 2, a constraint is usually applied to avoid forgetting previous knowledge by punishing the network from drifting away from its previous states. In this step, the network needs to update its knowledge of $\mathcal{C}_1$ on $D_2$ . Given that $\mathcal{C}_1$ is already properly optimized at step 1, the network only needs a small adjustment to complete its knowledge of $\mathcal{C}_1$ and receives little punishment from the constraint. However, the network is also intended to learn the knowledge w.r.t. $\mathcal{C}_2$ (i.e., distinguish the classes in $\mathcal{C}_2$ and distinguish between $\mathcal{C}_2$ and $\mathcal{C}_1$ ) from the start, which requires a rather large update. Based on the fact that the constraints make more punishment for greater changes, this update will be suppressed more severely compared to that of $\mathcal{C}_1$ , making more knowledge w.r.t. $\mathcal{C}_2$ cannot be learned. This is why the R-P dilemma often leads to low performance for new classes. To make matters worse, the scale of the training set is usually limited in incremental steps, especially for the situation when a single class is added with only a few samples of $\mathcal{C}_1$ . Such limited data could impede the network from successfully distinguishing between $\mathcal{C}_1$ and $\mathcal{C}_2$ , which is the inadequate data obstacle. Both of these factors result in the inability to properly learn knowledge w.r.t. $\mathcal{C}_2$ and contribute to the aforementioned underfitting phenomenon. + +# 3.4. Discussions for Solutions + +Pre-learning future knowledge. Based on the analysis, if we modify the training pipeline by adding explicit supervision to $\mathcal{C}_2$ before it is introduced (blue background in Figure 3). The knowledge w.r.t. $\mathcal{C}_2$ could be learned in advance. By doing so, we first avoid the R-P dilemma by reducing the great update to learning the knowledge w.r.t. $\mathcal{C}_2$ at the next + +step. Meanwhile, we can use the abundant samples of $\mathcal{C}_1$ at step 1 to make the network better learn how to distinguish between $\mathcal{C}_2$ and $\mathcal{C}_1$ , mitigating the influence of inadequate data of $\mathcal{C}_1$ at next step. Consequently, both obstacles are tackled in a uniform and elegant way. The main challenge falls to how we can learn knowledge w.r.t. $\mathcal{C}_2$ as accurately as possible in an unsupervised way in order to reduce the extent of updates required in the future. + +Memory. Memory is a widely used technique in CL and has been adapted to CSS recently [6, 34]. Based on our analysis above, here we clearly explain the effect of memory in CSS. Memory is applied only in incremental steps. With the help of it, new classes are possible to be optimized with partial previous data, which can also alleviate the impact of inadequate data. Meanwhile, memory helps to ease the forgetting problem, which makes it possible to relax the constraints without forgetting. As a result, new knowledge can be more easily learned. We would like to point out that memory can be used to solve the two obstacles at a different aspect. It could further boost the performance in conjunction with our solution. + +# 4. Method + +In this section, we introduce a novel framework based on pre-learning future knowledge as depicted in Figure 4. It takes into account future knowledge in an unsupervised way, both in the feature space (green background) and the output space (blue background). + +# 4.1. Learning Future Knowledge in Feature Space + +Contrastive learning. Contrastive learning is a widely used technique in unsupervised learning [7, 15]. In our work, we resort to it to optimize future classes in feature space. In semantic segmentation, directly using feature vectors at pixel level to perform pixel-pixel contrastive is redundant and results in high computational cost. Therefore, we follow [24, 46, 18] to perform contrast in a pixel-segment manner. Formally, supposing an image $I$ is partitioned into segments $S$ by a given prior. Let $\pmb{f}_i$ be the unit-length feature vector of pixel $i$ , we define the (normalized) prototype $\pmb{p}$ of a segment $s \in S$ by the average of feature vectors within this segment. + +$$ +\boldsymbol {p} _ {s} = \frac {1}{| s |} \sum_ {i \in s} \boldsymbol {f} _ {i}, \| \boldsymbol {p} _ {s} \| = 1 \tag {1} +$$ + +We adopt the InfoNCE [38] loss and formalize our loss as + +$$ +\mathcal {L} \left(\boldsymbol {f} _ {i}, S\right) = - \log \frac {\exp \left(\boldsymbol {f} _ {i} \cdot \boldsymbol {p} _ {s _ {+}} / \tau\right)}{\exp \left(\boldsymbol {f} _ {i} \cdot \boldsymbol {p} _ {s _ {+}} / \tau\right) + \sum_ {s _ {-}} \exp \left(\boldsymbol {f} _ {i} \cdot \boldsymbol {p} _ {s _ {-}} / \tau\right)} \tag {2} +$$ + +where $\tau$ is a temperature hyper-parameter. Ideally, it pulls $f_{i}$ close to the positive segment $s_{+}$ and pushes it away from + +![](images/578b344b9dfb493d19462b36cf82484cdfcd0bea0835ebb175e0fdbc86fb417a.jpg) +Figure 4. Overall framework. Given an image at step $t$ , a projection head maps the features from feature extractor $F_{t}$ into an embedding space where $\mathcal{L}_{c}$ is used to optimize future classes (green block). Next, the features from $F_{t}$ are also used to train an auxiliary classifier $G_{aux}$ to initialize the classifier for future classes (blue block). Last, the pseudo label technique together with a knowledge distillation loss are adopted to mitigate forgetting (yellow block). + +all the negative segments $s_{-}$ . For a given pixel, the segment it belongs to serves as $s_{+}$ , whereas other segments, including those from other images, serve as $s_{-}$ . + +Contrast by Visual Similarity. In pixel-segment contrastive learning, the partition scheme determines how the network is optimized. We first resort to visual boundaries as a prior to partition the images into visual coherent segments $S_{v}$ by OWT-UCM [2], which is a decent choice in unsupervised segmentation [19, 55, 23]. By utilizing visual similarity as supervision, we can bootstrap the representation learning and ground the features to respect low-level visual cues. But using this supervision alone makes the network hard to capture semantic-level information of future classes, and still needs further updates to properly learn them. This contradicts our goal to make the necessary updates as few as possible in the future. + +Contrast by Feature Affinity. We also need a partition method that can match actual future classes accurately to serve as another supervision. Due to the bootstrap effect of the previous contrast, we can resort to clustering methods to explore feature affinity as semantic-level supervision without relying on architectural prior like [8]. However, applying clustering directly cannot generate satisfying results. In practice, we find that by hierarchically combining an over-clustering result, we could obtain much more accurate results. More in detail, starting from an over-clustering generated using intermediate features, we merge the two most similar segments each time till all segments are merged as one. The similarity between segments is measured by the cosine similarity between their prototypes. This procedure + +![](images/3b3e192f3dd6e2b2518246bf9e82b12904482820528cf8133922f17ae7952bc6.jpg) +Figure 5. Segments obtained using visual similarity and feature affinity respectively. Top: Segments generated by OWT-UCM [2] using boundaries. Bottom: Segments that are likely to match the actual classes are selected from a hierarchical combination of fine-grained clustering results. + +generates consistent segments across all granularities. But different classes naturally have different levels of granularities, directly selecting segments from a single granularity is often suboptimal. We further propose a confidence score to evaluate how likely a segment matches a class accurately to select segments across granularities. The design of the confidence score is based on the following observations. In the combination procedure where the most similar segments are merged each time, the longer a segment can remain not merged, the more different it is to all other segments, and is more likely to match a class. What's more, given that this procedure starts from an over-clustering, the segments in later steps have a higher chance to match a class and should be assigned higher weights. A possible choice is to use the cosine distance between the segments to be merged at each step as a weight factor, which monotonously increases by step. Formally, assuming segments $a$ and $b$ are merged into a new segment $c$ at step $n$ in this procedure, set $S_{n}$ indicates all segments that are merged from start till now (include $a$ and $b$ ). The confidence score $u$ for a segment $s$ at step $n$ is defined recursively as follows. + +$$ +u _ {s} ^ {n} = \left\{ \begin{array}{l l} 0 & \text {i f} s = c, \\ u _ {s} ^ {n - 1} & \text {e l i f} s \in S _ {n}, \\ u _ {s} ^ {n - 1} + \left(1 - \boldsymbol {p} _ {a} \cdot \boldsymbol {p} _ {b}\right) & \text {o t h e r w i s e .} \end{array} \right. \tag {3} +$$ + +After finishing this procedure, we use the final score of each segment to select those with scores above the threshold to serve as high-confidence segments $S_{f}$ and participate in contrastive learning. If two selected segments are partially overlapped, we only reserve the one with a higher score. This procedure is performed for each training sample before each epoch to select high-confidence segments as the network updates itself, except for the first epoch since the feature cannot be clustered at that moment. + +Overall Contrastive Loss. In our contrastive learning, the pixels of $\mathcal{C}_t$ with ground truth annotations and $\mathcal{C}_{1:t-1}$ with pseudo labels are excluded. Meanwhile, they can naturally + +serve as high-confidence negative segments in contrastive learning. Since the batch size is limited in segmentation while the number of negative samples is crucial in contrastive learning [7, 15], we use a memory bank to cache the features of recent four batches to increase the number of negative samples. Given the segments $S_{v}$ generate by visual similarity and segments $S_{f}$ generated by feature affinity, our contrastive loss is formalized as + +$$ +\mathcal{L}_{c} = \frac{1}{|S_{v}|}\sum_{\substack{i\in S_{v}\\ i\notin \mathcal{C}_{1:t}}}\mathcal{L}(\boldsymbol{f}_{i},S_{v}) + \frac{1}{|S_{f}|}\sum_{\substack{i\in S_{f}\\ i\notin \mathcal{C}_{1:t}}}\mathcal{L}(\boldsymbol{f}_{i},S_{f}) \tag{4} +$$ + +where $|S|$ means the pixel number in all segments within $S$ . + +# 4.2. Learning Future Knowledge in Output Space + +Previous work [5] has claimed that a proper initialization of classifier weight at step $t > 1$ could also benefit the performance and is widely adopted by other works [10, 54]. This motivates us to further introduce future knowledge to the output space. Existing practice eases the misalignment between features and classifier weights by using the weight of the background to initialize that of the new classes. But in the update process, the weights of new classes should be updated to separate them from the background. Making the classifier weights to be identical to that of the background has the risk of increasing the necessary update, which has a negative effect based on previous analysis. + +To address this issue, we want the classifier to be initialized as close to the final optimal value as possible. When optimizing feature space, we manage to obtain high-confidence segments of future classes, and the intermediate features are also optimized accordingly. We could naturally utilize them to train an auxiliary classifier that can classify future classes in advance and use its weights as initialization. More in detail, we first perform clustering on the prototypes of segments to assign an auxiliary semantic label to each segment, which is then used to optimize the auxiliary classifier using cross-entropy loss. Note that the network receives no gradient from this classifier. In the next step when initialization is needed, we compute the prototype of each new class and select the auxiliary classifier weight which is closest to the prototype to initialize the actual classifier weight of it. On the one hand, we can make the classifier converge more easily and avoid the R-P dilemma. On the other hand, it solves the inadequate data obstacle in output space by utilizing the data of current step to serve as the negative samples of future classes, which can further boost the discriminability of the classifier compared to training it directly on the future steps. + +# 4.3. Overall Framework + +Our proposed framework is depicted in Figure 4. $\mathcal{L}_{ce}$ and $\mathcal{L}_{aux}$ are both cross-entropy loss to learn new classes and to + +train the auxiliary classifier, respectively. To complete our framework, we still need a KD loss to overcome forgetting. Since our focus is not on this part, we adopt the CKD loss in MiB [5] as $\mathcal{L}_{kd}$ to assist our training, with the addition of a temperature parameter as in original KD loss [16] to enhance its ability in knowledge preserving. This makes the overall loss function of our framework as follows. + +$$ +\mathcal {L} = \mathcal {L} _ {c e} + \alpha \mathcal {L} _ {k d} + \beta \mathcal {L} _ {c} + \mathcal {L} _ {\text {a u x}}, \tag {5} +$$ + +where $\alpha$ and $\beta$ are hyper-parameters. + +# 5. Experiments + +# 5.1. Implement Details + +Datasets. Following previous works, we evaluate our method on VOC2012 [12] and ADE20K [56], which are the standard CSS benchmarks. We report the performance on the official validation set of each dataset. We also exclude $20\%$ of the training set as a validation set to tune hyperparameters and perform all analyses. + +Protocols. There are two settings in CSS benchmarks: disjoint and overlapped. The disjoint setting limits the given images to contain pixels only belong to $\mathcal{C}_{1:t}$ , while the latter does not have this restriction, which means the pixels can also belong to the future classes, i.e., $\mathcal{C}_{t+1:T}$ . Note that the overlapped setting is considered to be more realistic and more challenging by all existing works [5, 10, 6, 37], and the disjoint setting is even ignored in some works [6, 37]. In design, our work is fully based on the overlapped setting. Evaluation. The CSS benchmark setups are denoted as $N_{o} - N_{n}$ where $N_{o}$ and $N_{n}$ are the number of classes to be learned at the initial step and each incremental step, respectively. For example, the 15-1 setup of VOC2012 gives 15 classes at the initial step and adds one class per incremental step, resulting in a total of 6 steps. On VOC2012, we conduct experiments on four setups: 19-1 (2 steps), 15-5 (2 steps), 15-1 (6 steps), and 10-1 (11 steps). On ADE20K, we use three setups: 100-50 (2 tasks), 50-50 (3 tasks), and 100-10 (6 tasks). The network is evaluated after finishing all learning steps using mean Intersection over Union (mIoU) as metric. The performance of initial classes $\mathcal{C}_{1}$ , incremental classes $\mathcal{C}_{2:T}$ , and all classes $\mathcal{C}_{1:T}$ are denoted as old, new, and all, respectively. + +Training. Following previous works [5, 10], we adopt DeepLab-V3 with an output stride of 16. ResNet-101 serves as the backbone, which is pre-trained on ImageNet. We use the SGD optimizer with momentum set to 0.9. The learning rate is set to 1e-2 for the initial learning step and 1e-3 for the following learning step. The learning rate is adjusted by the polynomial decay schedule with power set to 0.9. The network is trained on VOC2012 for 30 epochs, and 60 epochs on ADE20K, both with a batch size of 16. The image is cropped to $512 \times 512$ for both training and validation, with + +Table 1. Results of different methods on VOC2012. The best is in bold while the second best is in underline. Results are averaged over 3 runs with standard deviation provided. + +
Method19-1 (2 tasks)15-5 (2 tasks)15-1 (6 tasks)10-1 (11 tasks)
oldnewalloldnewalloldnewalloldnewall
ILT [35]67.112.364.466.340.659.94.97.85.7---
MiB [5]70.222.167.875.549.469.035.113.529.712.213.012.6
PLOP [10]75.337.373.575.751.770.065.121.154.644.015.522.9
SDR [36]69.132.667.475.452.669.944.721.839.2---
SSUL [6]77.729.675.477.850.171.277.336.567.671.345.959.2
RCIL [54]---78.852.072.470.623.759.455.415.134.3
ALIFE [37]76.649.375.377.152.571.364.434.957.4---
Ours77.7 ±0.2259.8 ±1.3876.8 ±0.3579.1 ±0.2167.7 ±0.4676.4 ±0.2975.2 ±0.7552.2 ±1.3369.7 ±1.0968.1 ±0.9654.5 ±1.5761.6 ±1.13
RECALL [34]68.155.368.667.754.365.667.850.964.865.053.760.7
SSUL-M [6]77.849.776.478.455.873.078.349.071.374.053.264.1
ALIFE-M [37]76.752.275.577.655.272.366.038.859.5---
Ours-M77.9 ±0.1967.7 ±0.7477.4 ±0.3279.3 ±0.2270.2 ±0.2977.1 ±0.2477.1 ±0.6560.4 ±0.7373.1 ±0.6869.5 ±0.6063.2 ±1.2566.5 ±0.78
Joint77.677.777.679.571.577.679.571.577.678.576.677.6
+ +Table 2. Results of different methods on ADE20K. The best is in bold while the second best is in underline. Results are averaged over 3 runs with standard deviation provided. + +
Method100-50 (2 tasks)50-50 (3 tasks)100-10 (6 tasks).
oldnewalloldnewalloldnewall
ILT [35]18.214.417.03.512.89.70.11.30.5
MiB [5]40.517.132.745.521.029.338.211.129.2
PLOP [10]41.814.832.948.820.930.440.413.631.5
SSUL [6]41.218.033.548.320.129.540.218.733.1
RCIL [54]42.318.834.548.325.032.939.317.632.1
ALIFE [37]42.123.035.848.925.633.541.022.734.9
Ours43.1 ±0.1726.0 ±0.3637.4 ±0.2549.1 ±0.2428.3 ±0.4335.2 ±0.3341.4 ±0.2825.5 ±0.4536.1 ±0.35
SSUL-M [6]42.717.534.349.120.129.742.817.634.4
ALIFE-M [37]42.223.536.049.026.133.841.123.035.1
Ours-M43.1 ±0.1526.2 ±0.2937.5 ±0.2149.2 ±0.1228.5 ±0.2735.4 ±0.1841.6 ±0.2125.8 ±0.2636.3 ±0.22
Joint43.529.438.850.332.738.843.529.438.8
+ +![](images/8066eebb0a9e448826a25a517bbc4d23e5e8c44466d09326524826b0c4261577.jpg) +Figure 6. mIoU comparison between CSS methods over steps on VOC 15-1 setups. The performance of initial classes and each new class added per step are plotted separately from left to right. Our method shows great ability in learning new classes. + +![](images/1456f2f508fda48f3552742c5238f4220be55d929a74f03258c36cdbf422fa04.jpg) + +![](images/dac3a1bc85afb87d35a21c63297a342ca4d3799976f2363f7fe10305dd3f7269.jpg) + +![](images/d9b160afa6126415c6d98b25328ea13e8e956f48c714c7043319d87f48c4b57a.jpg) + +![](images/f72d05b7f88f7d937ef29b727e0e21a3d6c265214cd0beee4f49af21cc17dcb3.jpg) + +![](images/8c7e91b67ba41d4d2802679391173cca990126900e950f96ecc2612a4a149e96.jpg) + +a random scaling and a random left-right flip additionally applied to training. + +# 5.2. Results + +We provide the results on VOC2012 and ADE20K in Table 1 and Table 2, respectively. Some works [6, 34] exploit memory or external data to assist training. We also report the results obtained using memory (denoted by -M) following the implementation of [6] to fairly compare with these methods. The result of joint training is also provided as the upperbound for reference. + +For all setups on VOC2012, our method surpasses all existing methods by a large margin on new classes. This demonstrates the strong ability of our method to learn new classes. Note that our method also shows promising results on old classes even with a simple approach to preserve old knowledge. This is due to that a higher performance on new classes indicates that there also might be less confusion between old and new classes, which also benefits the mIoU of old classes. On the more challenging setups with multiple steps (15-1, 10-1), the new classes cannot be properly learned in the first place for most methods. To + +make matters worse, these poorly optimized new classes will suffer forgetting in the following steps which further reduces their performance. Even in these challenging circumstances, our method still shows great performance in learning new classes, as shown in Figure 6. We can also see that even though SSUL shows higher performance on old classes on long-term setups, it relies on completely freezing the feature extractor to prevent forgetting, which does help a lot for old classes on these steps, but also harms its flexibility greatly. We believe that if equipped with a modern knowledge-preserving constraint, our method could offer another boost in performance. + +On the more challenging ADE20K benchmarks, we obtain similar results as that of VOC2012. Our method shows some improvement on old classes and is significantly better on new classes. On top of the results of VOC2012 benchmark, this further demonstrates that our approach works well on more complex datasets, and has the ability to handle both scenes and objects centric datasets. + +When memory is applied on both benchmarks, our method receives further improvements and holds the leading position. This also indicates that our proposed training method has a non-overlapping effect with the memory technique. They can be used as two complementary techniques as pointed out in Section 3.4 + +# 5.3. Ablation Study + +We investigate the effects of the proposed components in our framework using both 15-1 and 15-5 setups on VOC2012. Starting from a baseline composed of $L_{ce}$ , $L_{kd}$ and pseudo label, we add the components one by one and show the ablation results in Table 3. As can be seen, the performance increase steadily as each proposed component is gradually added. Only applying contrast by visual similarity does not receive much improvement since it cannot instruct the network to capture semantic-level information. After applying contrast by feature affinity, the performance receives the highest gain, indicating the necessity to add semantic-level supervision and make the network learn more accurate knowledge. On top of that, the performance receives another boost from our classifier initialization technique which introduces future knowledge to output space. + +Table 3. Ablation study on VOC2012 15-1 and 15-5 setup. + +
Method15-1 (6 tasks)15-5 (2 tasks)
oldnewalloldnewall
baseline65.318.854.276.951.370.8
+ visual similarity contrast67.126.357.477.254.571.8
+ feature affinity contrast74.545.167.578.765.475.5
+ classifier initialization75.252.269.779.167.776.4
+ +![](images/40581768f3806ea880e27c8aa7a621e968f63154814aa1b47d483e2c1282af1f.jpg) +Figure 7. Visualization of clustering results of direct clustering and our practice. The high-confidence segments selected by our criterion are also presented on the right. + +![](images/8218f054600d24222cc7444f31ca5dd8a5fb4bc3003c0c7e2acc0718c776b4d1.jpg) +Figure 8. Performance comparison between different classifier initialization over training epochs on VOC2012 19-1 setup. + +# 5.4. Further Discussion + +Feature Quality Analysis. To further demonstrate the effect of our method to solve the underfitting problem pointed out in Section 3.2, we conduct the same analysis on our method and incorporate the findings into Figure 2 (denoted by Ours). As can be seen, pre-learning future classes can significantly improve both intra-class and inter-class fitness. + +Segment Generation. We provide a qualitative comparison between direct clustering and our proposed hierarchical combination at different granularities to validate our design in Section 4.1. The results are generated from the same intermediate features and are plotted in Figure 7. As can be seen, our practice consistently generates better results across different granularities. We also present the high-confidence segments selected by our criterion for each image, which match the actual classes with high precision. + +Classifier Initialization. We give a comparison of performance over training epochs for different classifier initialization methods in Figure 8. As can be seen, the initialization technique proposed by MiB [5] converges much slower due to larger update paces. Random initialization converges fast but the performance stops increasing shortly afterward. Among all of them, our method stands out with its fast convergence speed and superior performance. + +# 6. Limitation and Conclusion + +Our method has two limitations. Firstly, it relies on the natural attribute of CSS that unlabeled future classes exist in current training data. So it may not perform well when there are only a few unlabeled future classes in the current training data. However, in such cases, we can still leverage external unlabeled data, such as web-crawled data as used in RECALL [34]. Secondly, we point out that even though our proposed framework achieves great performance, it as a practicable solution might not be able to unleash the full potential of the training method, which requires further exploration in future works. + +In this work, we present an in-depth analysis of the reason why existing methods suffer low performance on new classes. Building on this analysis, we introduce a novel training pipeline for CSS that optimizes potential future classes in the current training step. 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In Proceedings of the 28th ACM International Conference on Multimedia, pages 156-164, 2020. \ No newline at end of file diff --git a/2023/Preparing the Future for Continual Semantic Segmentation/images.zip b/2023/Preparing the Future for Continual Semantic Segmentation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..46856b6a17d3b1c91afa1892d11227633170563f --- /dev/null +++ b/2023/Preparing the Future for Continual Semantic Segmentation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d24bb8eddcad4bb943db4d6bcac98256a77d9b8c2ac9445736f6173240254d46 +size 432379 diff --git a/2023/Preparing the Future for Continual Semantic Segmentation/layout.json b/2023/Preparing the Future for Continual Semantic Segmentation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..7f0cbfd3afb8d0e798291ea2d3dcc194f110a14f --- /dev/null +++ b/2023/Preparing the Future for Continual Semantic Segmentation/layout.json @@ -0,0 +1,8721 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 113, + 103, + 481, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 103, + 481, + 121 + ], + "spans": [ + { + "bbox": [ + 113, + 103, + 481, + 121 + ], + "type": "text", + "content": "Preparing the Future for Continual Semantic Segmentation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 187, + 142, + 406, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 187, + 142, + 406, + 157 + ], + "spans": [ + { + "bbox": [ + 187, + 142, + 406, + 157 + ], + "type": "text", + "content": "Zihan Lin1 Zilei Wang*1 Yixin Zhang1,2" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 179, + 157, + 415, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 179, + 157, + 415, + 171 + ], + "spans": [ + { + "bbox": [ + 179, + 157, + 415, + 171 + ], + "type": "text", + "content": "1 University of Science and Technology of China" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 97, + 171, + 495, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 171, + 495, + 186 + ], + "spans": [ + { + "bbox": [ + 97, + 171, + 495, + 186 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 97, + 171, + 495, + 186 + ], + "type": "text", + "content": " Institute of Artificial Intelligence, Hefei Comprehensive National Science Center" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 153, + 187, + 440, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 153, + 187, + 440, + 199 + ], + "spans": [ + { + "bbox": [ + 153, + 187, + 440, + 199 + ], + "type": "text", + "content": "myustc@mail.ustc.edu.cn, {zlwang, zhyx12}@ustc.edu.cn" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 251, + 289, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 289, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 289, + 563 + ], + "type": "text", + "content": "In this study, we focus on Continual Semantic Segmentation (CSS) and present a novel approach to tackle the issue of existing methods struggling to learn new classes. The primary challenge of CSS is to learn new knowledge while retaining old knowledge, which is commonly known as the rigidity-plasticity dilemma. Existing approaches strive to address this by carefully balancing the learning of new and old classes during training on new data. Differently, this work aims to avoid this dilemma fundamentally rather than handling the difficulties involved in it. Specifically, we reveal that this dilemma mainly arises from the greater fluctuation of knowledge for new classes because they have never been learned before the current step. Additionally, the data available in incremental steps are usually inadequate, which can impede the model's ability to learn discriminative features for both new and old classes. To address these challenges, we introduce a novel concept of pre-learning for future knowledge. Our approach entails optimizing the feature space and output space for unlabeled data, which thus enables the model to acquire knowledge for future classes. With this approach, updating the model for new classes becomes as smooth as for old classes, effectively avoiding the rigidity-plasticity dilemma. We conducted extensive experiments and the results demonstrate a significant improvement in the learning of new classes compared to previous state-of-the-art methods." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 586, + 128, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 128, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 128, + 597 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": "Deep neural networks have demonstrated their superiority in many computer vision tasks [26, 31, 14]. Conventionally, they are trained in an offline manner with all data collected beforehand. When novel classes need to be handled, the networks need to be re-trained using either updated training set with both new and previous data, or directly finetuned on new data. The former has higher costs and is even impracticable sometimes like, when privacy raises concerns. The latter is prone to forget previ" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 318, + 232, + 533, + 366 + ], + "blocks": [ + { + "bbox": [ + 318, + 232, + 533, + 366 + ], + "lines": [ + { + "bbox": [ + 318, + 232, + 533, + 366 + ], + "spans": [ + { + "bbox": [ + 318, + 232, + 533, + 366 + ], + "type": "image", + "image_path": "301e91d65d39335f139ddfa2115135c85334d75e9536194ad13a2b6c5bd7c493.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 369, + 547, + 412 + ], + "lines": [ + { + "bbox": [ + 305, + 369, + 547, + 412 + ], + "spans": [ + { + "bbox": [ + 305, + 369, + 547, + 412 + ], + "type": "text", + "content": "Figure 1. On VOC2012 benchmark, our method boosts the performance of new classes by a significant margin, while also achieving promising performance for old classes, compared to recent state-of-the-art methods." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 435, + 547, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 547, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 547, + 639 + ], + "type": "text", + "content": "ously learned knowledge, which is called catastrophic forgetting (CF) [25]. To better fit neural networks into real-world scenarios, we want them to have the ability to learn new concepts while preserving the old knowledge (or even improve it using new knowledge). This is known as the continual learning (CL) problem and receives increasing attention recently. It has been explored first in the field of image classification [28, 42, 17, 11, 57, 44, 43], and some methods are proposed recently targeting semantic segmentation [5, 10, 6, 54, 51, 37]. Generally, it is often achieved by applying forgetting-preventing constraints between current and previous networks to prevent CF, which raises the rigidity (i.e., the ability to preserve old states) but harms the plasticity (i.e., the ability to learn new knowledge). It is known as the rigidity-plasticity (R-P) dilemma. A key aspect in designing constraints is to balance between rigidity and plasticity, which is what most works focus on." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "Despite that several new constraints have been proposed for CSS to better tackle the dilemma, existing works still struggle to learn new classes. Taking the VOC2012 benchmark as an example, most methods can only achieve a performance around " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "70\\%" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " of that of the upperbound for 15-5 setup and around " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " for 19-1 setup, which is even worse" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "11910" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 287 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 287 + ], + "type": "text", + "content": "for harder setups. To get a clear picture of why this happens, we first analyze the intermediate features of the network and find it suffers serious underfitting for new classes, which indicates a large amount of knowledge is not learned. We then examine the CSS training pipeline and find two main obstacles causing this phenomenon. (1) R-P Dilemma: the network has no knowledge w.r.t. new classes until they are introduced. This generally requires a rather large update to incorporate the new knowledge, which will be significantly hindered by the forgetting-preventing constraints punishing the network from drifting away from its previous states. (2) Inadequate data for training: the amount of data available in incremental steps is usually limited, and this problem becomes more severe when a single class is added, resulting in a tiny training set with only a few negative samples. This can significantly limit the network to properly discriminate between old and new classes. This problem has never been explicitly considered before." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 288, + 289, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 288, + 289, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 288, + 289, + 598 + ], + "type": "text", + "content": "Unlike existing works trying to tackle the R-P dilemma directly, we are the first to argue that this obstacle can be elegantly avoided by exploring future knowledge in an unsupervised way. Assume that the network has obtained partial knowledge of future classes in advance, then the network needs fewer updates to learn the upcoming knowledge, which consequently lowers the impacts of the R-P dilemma. The more future knowledge it learns in advance, the fewer the impacts will be caused. Considering an extreme situation where all the future knowledge is learned beforehand, the network does not need any update, and thus the influence of constraints could be totally avoided. On top of this, it makes us the first attempt to explicitly tackle the second obstacle by utilizing the abundant data in previous steps to optimize discriminability between old and new classes. Based on these understandings, we design a novel framework where unsupervised contrastive learning is performed on intermediate features to optimize future classes with both visual similarity and feature affinity as supervisions. One step further, an auxiliary classifier is trained using pseudo labels of future classes generated via clustering, which is used to initialize the actual classifier for future steps. Our method surpasses existing works by a huge margin as shown in Figure 1 and the effectiveness is further demonstrated with extensive experiments. Our contributions are summarized as follows." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 604, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 604, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 604, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 604, + 287, + 653 + ], + "type": "text", + "content": "- We propose to pre-learn future knowledge for CSS with the aim of improving the performance especially for new classes, which can simultaneously tackle the R-P dilemma and the obstacle of inadequate data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 658, + 287, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 287, + 695 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 287, + 695 + ], + "type": "text", + "content": "- We design a novel framework that can pre-learn future knowledge in an unsupervised way, where both the feature space and output space are handled." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "content": "- We have validated the effectiveness of our proposed" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 545, + 109 + ], + "type": "text", + "content": "approach through extensive experiments. The results demonstrate significant improvement on standard CSS benchmarks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 121, + 392, + 133 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 121, + 392, + 133 + ], + "spans": [ + { + "bbox": [ + 306, + 121, + 392, + 133 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 141, + 545, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 141, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 304, + 141, + 545, + 357 + ], + "type": "text", + "content": "Continual Learning (CL). Continual learning has been studied for years in image classification. Existing techniques can be roughly divided into regularization methods, rehearsal methods, and architectural methods. Regularization methods apply consistency constraints between current network and previous network to avoid drifts from previous states. They can be applied on network weights [53, 25, 1], the intermediate features [9, 11, 45, 13, 22] or the output logits [28, 42, 17, 48]. Parameter regularization is rarely seen recently due to the lack of plasticity, while the other two are mostly based on knowledge distillation (KD) [16]. To better solve the forgetting problem, rehearsal methods replay previous data in the incremental steps, including image replay [42, 41, 3], generative replay [49, 39], feature replay [20, 57], and memory management [30, 29]. Architectural methods use a dynamic network to handle incoming knowledge, like sub-network [32, 33], complementary network [47, 40] or expandable network [27, 50, 52]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 357, + 545, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 357, + 545, + 490 + ], + "spans": [ + { + "bbox": [ + 304, + 357, + 545, + 490 + ], + "type": "text", + "content": "Continual Semantic Segmentation (CSS). Some works extended the aforementioned techniques to semantic segmentation tasks. For the KD-based methods, MiB [5] formalized and targeted background shift problem with output space distillation. PLOP [10], SDR [36], and RCIL [54] use feature space distillation to further mitigate forgetting. For the rehearsal-based methods, SSUL [6] and RECALL [34] utilize memory or external data to overcome forgetting and work well in multiple-step learning. For the architectural methods, RCIL [54] proposes a structural reparameterization design to better learn new knowledge." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 490, + 545, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 490, + 545, + 657 + ], + "spans": [ + { + "bbox": [ + 304, + 490, + 545, + 657 + ], + "type": "text", + "content": "Unsupervised Semantic Segmentation. These works focus on learning to cluster semantically related pixels without human labeling. Existing works can be roughly divided into three types. PiCIE [8] iteratively performs clustering and uses it to refine network features. This relies on the architectural prior and is prone to degenerate solutions. IIC [21] maximizes the mutual information between two augmentations of the same image which enforces spatial stability on them. But this solution has trouble dealing with complex scenes. The last type uses visual similarity. These works [19, 55, 46, 23] use handcrafted priors, like boundary, superpixels, or saliency detectors to first group pixels by visual similarity. This is then used to learn pixel-level representations using contrastive learning." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 669, + 391, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 391, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 391, + 681 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "In this section, we first explain the definition of CSS (Sec. 3.1), and present the underfitting phenomenon of new" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "11911" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 81, + 211, + 170 + ], + "blocks": [ + { + "bbox": [ + 56, + 81, + 211, + 170 + ], + "lines": [ + { + "bbox": [ + 56, + 81, + 211, + 170 + ], + "spans": [ + { + "bbox": [ + 56, + 81, + 211, + 170 + ], + "type": "image", + "image_path": "7c464a504f500bccef080c7376cf9f4d8e5a117b9e37411e79d55f94d75c2aa6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 172, + 547, + 207 + ], + "lines": [ + { + "bbox": [ + 46, + 172, + 547, + 207 + ], + "spans": [ + { + "bbox": [ + 46, + 172, + 547, + 207 + ], + "type": "text", + "content": "Figure 2. Feature fitness analysis of different methods using L1 norm (Left), activation strength (Mid), and cosine similarity (Right) on VOC2012 15-5 setup. It is demonstrated that existing works suffer underfitting on both intra-class level (left and mid) and inter-class level (right) for new classes. Our method effectively addresses this problem." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 220, + 81, + 373, + 171 + ], + "blocks": [ + { + "bbox": [ + 220, + 81, + 373, + 171 + ], + "lines": [ + { + "bbox": [ + 220, + 81, + 373, + 171 + ], + "spans": [ + { + "bbox": [ + 220, + 81, + 373, + 171 + ], + "type": "image", + "image_path": "196888f1c316e672db90607467f10607b1ec82a221c00885053b765c22d1160e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 383, + 81, + 534, + 171 + ], + "blocks": [ + { + "bbox": [ + 383, + 81, + 534, + 171 + ], + "lines": [ + { + "bbox": [ + 383, + 81, + 534, + 171 + ], + "spans": [ + { + "bbox": [ + 383, + 81, + 534, + 171 + ], + "type": "image", + "image_path": "4f84dd7ca2e2af2a43674bb3157b812ed37d730691a0015ce1dc4f2aa1c259c0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 225, + 288, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 225, + 288, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 225, + 288, + 262 + ], + "type": "text", + "content": "classes (Sec. 3.2). After that, we analyze how the performance is impacted in CSS (Sec. 3.3). Finally, we discuss the solutions to boost new class performance (Sec. 3.4)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 270, + 139, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 270, + 139, + 283 + ], + "spans": [ + { + "bbox": [ + 47, + 270, + 139, + 283 + ], + "type": "text", + "content": "3.1. CSS Definition" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "text", + "content": "In CSS, the training procedure is composed of a series of " + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "text", + "content": " learning steps. At each step " + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "inline_equation", + "content": "t \\in \\{1, \\dots, T\\}" + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "text", + "content": ", a set of new categories " + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_t" + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "text", + "content": " are introduced with a training set " + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "inline_equation", + "content": "D_t = \\{(x_n, y_n)\\}" + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "inline_equation", + "content": "x_n" + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "text", + "content": " is an image and " + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "inline_equation", + "content": "y_n" + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "text", + "content": " is the corresponding label. Only " + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_t" + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "text", + "content": " is labeled in " + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "inline_equation", + "content": "y_n" + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "text", + "content": " and all the other classes are labeled as background. It is assumed that the categories learned at each step are disjoint, i.e., " + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_i \\cap \\mathcal{C}_j = \\emptyset" + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "text", + "content": ". The network is trained sequentially on each step, where it learns the knowledge w.r.t. " + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_t" + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "text", + "content": " and expands its output space to " + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{1:t} = \\mathcal{C}_{1:t-1} \\cup \\mathcal{C}_t" + }, + { + "bbox": [ + 46, + 289, + 288, + 422 + ], + "type": "text", + "content": ". After all learning steps, the network is expected to perform well on all classes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 430, + 196, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 196, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 196, + 443 + ], + "type": "text", + "content": "3.2. Analysis of Feature Fitness" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 449, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 629 + ], + "type": "text", + "content": "To get a clear view of why new classes perform poorly in existing methods, we analyze the intermediate features of two works: MiB [5] based on conventional logits distillation, and a more recent work, RCIL [54], based on feature distillation and structural re-parameterization aiming to better tackle the R-P dilemma. To simplify the situation, we opt for the two-step 15-5 setup on VOC2012 to conduct the analysis. The results are reported in Figure 2 (Detailed information about incremental setups and validation set can be found in Section 5.). The results of joint training (i.e., performance upperbound) and initial state (i.e., backbone is initialized with ImageNet pre-trained weights while the other parts are randomly initialized) are also provided for reference. Ideally, the results are expected to be close to that of the upperbound in order to achieve good performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": "Intra-class Fitness. We first evaluate how well the network fits to each individual class. In neural networks, each channel in the feature vectors could represent a certain pattern [4] which composes the learned classes [58]. When the network fits a class well, the output feature vector should have specific channels being activated while the others deactivated, resulting in sparsity in the feature vector. The" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 225, + 547, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 225, + 547, + 332 + ], + "spans": [ + { + "bbox": [ + 304, + 225, + 547, + 332 + ], + "type": "text", + "content": "activation strength further shows how strong the network's response is to each pattern. Both of them can serve as clues indicating how well the network fits a class. We use the average L1 norm of L2-normalized feature vectors to measure the sparsity, and the average top activation values to measure the response strength. As can be seen in Figure 2 (left and mid), the new classes of both MiB and RCIL have high L1 norm and low activation strength, indicating a serious underfitting problem." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 334, + 546, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 334, + 546, + 477 + ], + "spans": [ + { + "bbox": [ + 304, + 334, + 546, + 477 + ], + "type": "text", + "content": "Inter-class Fitness. We further evaluate how well the network learns to distinguish different classes, which is measured by the cosine similarity between the feature vectors of different classes. The better the network can distinguish each class, the lower the cosine similarities will be. We compute the mean cosine distance of a class to any other classes, which is then averaged based on class group to get the final results, as shown in Figure 2 (right). It can be seen that the network has good discriminative power on old classes, but the new classes again present poor results. It indicates the network cannot distinguish a new class between other classes well." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 479, + 547, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 547, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 547, + 540 + ], + "type": "text", + "content": "Discussion. From the above analyses, it is evident that new classes suffer serious underfitting on both intra-class and inter-class aspects. This exactly explains why most methods show low performance on new classes, even in simple setups with only a single incremental step." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 549, + 484, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 549, + 484, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 549, + 484, + 562 + ], + "type": "text", + "content": "3.3. Understanding Training Pipeline" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 569, + 547, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 547, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 547, + 640 + ], + "type": "text", + "content": "In this part, we dive deeper to investigate why the underfitting problem happens for new classes in the conventional training pipeline. We use Figure 3 to give a clear view of how the two obstacles impact the performance in a conventional pipeline (green background). Without loss of generality, a two-step situation is adopted as an example." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": "Starting from step 1 where " + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_1" + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": " is labeled in the given data " + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "inline_equation", + "content": "D_{1}" + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": " while others are marked as background, the network acquires most knowledge of " + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_1" + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": " (i.e., distinguish between classes in " + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_1" + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": ") after finishing this step. Considering that it only accesses partial data at this step compared to joint training, the knowledge of " + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_1" + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": " remains to be updated" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11912" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 71, + 282, + 210 + ], + "blocks": [ + { + "bbox": [ + 53, + 71, + 282, + 210 + ], + "lines": [ + { + "bbox": [ + 53, + 71, + 282, + 210 + ], + "spans": [ + { + "bbox": [ + 53, + 71, + 282, + 210 + ], + "type": "image", + "image_path": "a284cd579c0221d99adab4bb6e6c37940eaaaffa4cfdeabfc8de1a28bfe70af4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 213, + 287, + 268 + ], + "lines": [ + { + "bbox": [ + 46, + 213, + 287, + 268 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 287, + 268 + ], + "type": "text", + "content": "Figure 3. Illustration of the difference between knowledge learning in a conventional training pipeline (green background) and our solution (blue background). We jointly optimize new classes together with old classes in an unsupervised way before new classes are introduced." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "text", + "content": "in the next step. However, even though the future classes " + }, + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_2" + }, + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "text", + "content": " do exist in " + }, + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "inline_equation", + "content": "D_{1}" + }, + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "text", + "content": ", they do not receive explicit supervision, thus the network obtains almost no knowledge of " + }, + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_2" + }, + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "text", + "content": " after finishing step 1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "text", + "content": "Moving to step 2, a constraint is usually applied to avoid forgetting previous knowledge by punishing the network from drifting away from its previous states. In this step, the network needs to update its knowledge of " + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_1" + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "inline_equation", + "content": "D_2" + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "text", + "content": ". Given that " + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_1" + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "text", + "content": " is already properly optimized at step 1, the network only needs a small adjustment to complete its knowledge of " + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_1" + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "text", + "content": " and receives little punishment from the constraint. However, the network is also intended to learn the knowledge w.r.t. " + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_2" + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "text", + "content": " (i.e., distinguish the classes in " + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_2" + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "text", + "content": " and distinguish between " + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_2" + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_1" + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "text", + "content": ") from the start, which requires a rather large update. Based on the fact that the constraints make more punishment for greater changes, this update will be suppressed more severely compared to that of " + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_1" + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "text", + "content": ", making more knowledge w.r.t. " + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_2" + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "text", + "content": " cannot be learned. This is why the R-P dilemma often leads to low performance for new classes. To make matters worse, the scale of the training set is usually limited in incremental steps, especially for the situation when a single class is added with only a few samples of " + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_1" + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "text", + "content": ". Such limited data could impede the network from successfully distinguishing between " + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_1" + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_2" + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "text", + "content": ", which is the inadequate data obstacle. Both of these factors result in the inability to properly learn knowledge w.r.t. " + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_2" + }, + { + "bbox": [ + 46, + 337, + 287, + 613 + ], + "type": "text", + "content": " and contribute to the aforementioned underfitting phenomenon." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 622, + 186, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 622, + 186, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 622, + 186, + 634 + ], + "type": "text", + "content": "3.4. Discussions for Solutions" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": "Pre-learning future knowledge. Based on the analysis, if we modify the training pipeline by adding explicit supervision to " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_2" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": " before it is introduced (blue background in Figure 3). The knowledge w.r.t. " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_2" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": " could be learned in advance. By doing so, we first avoid the R-P dilemma by reducing the great update to learning the knowledge w.r.t. " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_2" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": " at the next" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": "step. Meanwhile, we can use the abundant samples of " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_1" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": " at step 1 to make the network better learn how to distinguish between " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_2" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_1" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": ", mitigating the influence of inadequate data of " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_1" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": " at next step. Consequently, both obstacles are tackled in a uniform and elegant way. The main challenge falls to how we can learn knowledge w.r.t. " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_2" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": " as accurately as possible in an unsupervised way in order to reduce the extent of updates required in the future." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 167, + 546, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 167, + 546, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 167, + 546, + 323 + ], + "type": "text", + "content": "Memory. Memory is a widely used technique in CL and has been adapted to CSS recently [6, 34]. Based on our analysis above, here we clearly explain the effect of memory in CSS. Memory is applied only in incremental steps. With the help of it, new classes are possible to be optimized with partial previous data, which can also alleviate the impact of inadequate data. Meanwhile, memory helps to ease the forgetting problem, which makes it possible to relax the constraints without forgetting. As a result, new knowledge can be more easily learned. We would like to point out that memory can be used to solve the two obstacles at a different aspect. It could further boost the performance in conjunction with our solution." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 333, + 361, + 345 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 333, + 361, + 345 + ], + "spans": [ + { + "bbox": [ + 306, + 333, + 361, + 345 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 354, + 545, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 414 + ], + "type": "text", + "content": "In this section, we introduce a novel framework based on pre-learning future knowledge as depicted in Figure 4. It takes into account future knowledge in an unsupervised way, both in the feature space (green background) and the output space (blue background)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 420, + 542, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 420, + 542, + 433 + ], + "spans": [ + { + "bbox": [ + 305, + 420, + 542, + 433 + ], + "type": "text", + "content": "4.1. Learning Future Knowledge in Feature Space" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "text", + "content": "Contrastive learning. Contrastive learning is a widely used technique in unsupervised learning [7, 15]. In our work, we resort to it to optimize future classes in feature space. In semantic segmentation, directly using feature vectors at pixel level to perform pixel-pixel contrastive is redundant and results in high computational cost. Therefore, we follow [24, 46, 18] to perform contrast in a pixel-segment manner. Formally, supposing an image " + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "text", + "content": " is partitioned into segments " + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "text", + "content": " by a given prior. Let " + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\pmb{f}_i" + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "text", + "content": " be the unit-length feature vector of pixel " + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "text", + "content": ", we define the (normalized) prototype " + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\pmb{p}" + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "text", + "content": " of a segment " + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "inline_equation", + "content": "s \\in S" + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "text", + "content": " by the average of feature vectors within this segment." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 367, + 590, + 545, + 617 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 590, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 367, + 590, + 545, + 617 + ], + "type": "interline_equation", + "content": "\\boldsymbol {p} _ {s} = \\frac {1}{| s |} \\sum_ {i \\in s} \\boldsymbol {f} _ {i}, \\| \\boldsymbol {p} _ {s} \\| = 1 \\tag {1}", + "image_path": "1d83198b480dbe14570505fe9252dd446ff263d33745084f7847b396e7803f17.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 622, + 539, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 622, + 539, + 634 + ], + "spans": [ + { + "bbox": [ + 306, + 622, + 539, + 634 + ], + "type": "text", + "content": "We adopt the InfoNCE [38] loss and formalize our loss as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 308, + 651, + 545, + 689 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 651, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 308, + 651, + 545, + 689 + ], + "type": "interline_equation", + "content": "\\mathcal {L} \\left(\\boldsymbol {f} _ {i}, S\\right) = - \\log \\frac {\\exp \\left(\\boldsymbol {f} _ {i} \\cdot \\boldsymbol {p} _ {s _ {+}} / \\tau\\right)}{\\exp \\left(\\boldsymbol {f} _ {i} \\cdot \\boldsymbol {p} _ {s _ {+}} / \\tau\\right) + \\sum_ {s _ {-}} \\exp \\left(\\boldsymbol {f} _ {i} \\cdot \\boldsymbol {p} _ {s _ {-}} / \\tau\\right)} \\tag {2}", + "image_path": "15e8e2221ceedfdb5dbc184bda3b3fbfbb5aaeab0b1410bc51dcd5af0cb7606c.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " is a temperature hyper-parameter. Ideally, it pulls " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " close to the positive segment " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "s_{+}" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " and pushes it away from" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11913" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 281, + 236 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 281, + 236 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 281, + 236 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 281, + 236 + ], + "type": "image", + "image_path": "578b344b9dfb493d19462b36cf82484cdfcd0bea0835ebb175e0fdbc86fb417a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 239, + 289, + 327 + ], + "lines": [ + { + "bbox": [ + 46, + 239, + 289, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 289, + 327 + ], + "type": "text", + "content": "Figure 4. Overall framework. Given an image at step " + }, + { + "bbox": [ + 46, + 239, + 289, + 327 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 239, + 289, + 327 + ], + "type": "text", + "content": ", a projection head maps the features from feature extractor " + }, + { + "bbox": [ + 46, + 239, + 289, + 327 + ], + "type": "inline_equation", + "content": "F_{t}" + }, + { + "bbox": [ + 46, + 239, + 289, + 327 + ], + "type": "text", + "content": " into an embedding space where " + }, + { + "bbox": [ + 46, + 239, + 289, + 327 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{c}" + }, + { + "bbox": [ + 46, + 239, + 289, + 327 + ], + "type": "text", + "content": " is used to optimize future classes (green block). Next, the features from " + }, + { + "bbox": [ + 46, + 239, + 289, + 327 + ], + "type": "inline_equation", + "content": "F_{t}" + }, + { + "bbox": [ + 46, + 239, + 289, + 327 + ], + "type": "text", + "content": " are also used to train an auxiliary classifier " + }, + { + "bbox": [ + 46, + 239, + 289, + 327 + ], + "type": "inline_equation", + "content": "G_{aux}" + }, + { + "bbox": [ + 46, + 239, + 289, + 327 + ], + "type": "text", + "content": " to initialize the classifier for future classes (blue block). Last, the pseudo label technique together with a knowledge distillation loss are adopted to mitigate forgetting (yellow block)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 350, + 287, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 387 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 387 + ], + "type": "text", + "content": "all the negative segments " + }, + { + "bbox": [ + 46, + 350, + 287, + 387 + ], + "type": "inline_equation", + "content": "s_{-}" + }, + { + "bbox": [ + 46, + 350, + 287, + 387 + ], + "type": "text", + "content": ". For a given pixel, the segment it belongs to serves as " + }, + { + "bbox": [ + 46, + 350, + 287, + 387 + ], + "type": "inline_equation", + "content": "s_{+}" + }, + { + "bbox": [ + 46, + 350, + 287, + 387 + ], + "type": "text", + "content": ", whereas other segments, including those from other images, serve as " + }, + { + "bbox": [ + 46, + 350, + 287, + 387 + ], + "type": "inline_equation", + "content": "s_{-}" + }, + { + "bbox": [ + 46, + 350, + 287, + 387 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 388, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 544 + ], + "type": "text", + "content": "Contrast by Visual Similarity. In pixel-segment contrastive learning, the partition scheme determines how the network is optimized. We first resort to visual boundaries as a prior to partition the images into visual coherent segments " + }, + { + "bbox": [ + 46, + 388, + 287, + 544 + ], + "type": "inline_equation", + "content": "S_{v}" + }, + { + "bbox": [ + 46, + 388, + 287, + 544 + ], + "type": "text", + "content": " by OWT-UCM [2], which is a decent choice in unsupervised segmentation [19, 55, 23]. By utilizing visual similarity as supervision, we can bootstrap the representation learning and ground the features to respect low-level visual cues. But using this supervision alone makes the network hard to capture semantic-level information of future classes, and still needs further updates to properly learn them. This contradicts our goal to make the necessary updates as few as possible in the future." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": "Contrast by Feature Affinity. We also need a partition method that can match actual future classes accurately to serve as another supervision. Due to the bootstrap effect of the previous contrast, we can resort to clustering methods to explore feature affinity as semantic-level supervision without relying on architectural prior like [8]. However, applying clustering directly cannot generate satisfying results. In practice, we find that by hierarchically combining an over-clustering result, we could obtain much more accurate results. More in detail, starting from an over-clustering generated using intermediate features, we merge the two most similar segments each time till all segments are merged as one. The similarity between segments is measured by the cosine similarity between their prototypes. This procedure" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 307, + 72, + 542, + 178 + ], + "blocks": [ + { + "bbox": [ + 307, + 72, + 542, + 178 + ], + "lines": [ + { + "bbox": [ + 307, + 72, + 542, + 178 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 542, + 178 + ], + "type": "image", + "image_path": "3b3e192f3dd6e2b2518246bf9e82b12904482820528cf8133922f17ae7952bc6.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 180, + 547, + 236 + ], + "lines": [ + { + "bbox": [ + 304, + 180, + 547, + 236 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 547, + 236 + ], + "type": "text", + "content": "Figure 5. Segments obtained using visual similarity and feature affinity respectively. Top: Segments generated by OWT-UCM [2] using boundaries. Bottom: Segments that are likely to match the actual classes are selected from a hierarchical combination of fine-grained clustering results." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "text", + "content": "generates consistent segments across all granularities. But different classes naturally have different levels of granularities, directly selecting segments from a single granularity is often suboptimal. We further propose a confidence score to evaluate how likely a segment matches a class accurately to select segments across granularities. The design of the confidence score is based on the following observations. In the combination procedure where the most similar segments are merged each time, the longer a segment can remain not merged, the more different it is to all other segments, and is more likely to match a class. What's more, given that this procedure starts from an over-clustering, the segments in later steps have a higher chance to match a class and should be assigned higher weights. A possible choice is to use the cosine distance between the segments to be merged at each step as a weight factor, which monotonously increases by step. Formally, assuming segments " + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "text", + "content": " are merged into a new segment " + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "text", + "content": " at step " + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "text", + "content": " in this procedure, set " + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "inline_equation", + "content": "S_{n}" + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "text", + "content": " indicates all segments that are merged from start till now (include " + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "text", + "content": "). The confidence score " + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "text", + "content": " for a segment " + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "text", + "content": " at step " + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 254, + 547, + 506 + ], + "type": "text", + "content": " is defined recursively as follows." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 335, + 518, + 545, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 518, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 335, + 518, + 545, + 563 + ], + "type": "interline_equation", + "content": "u _ {s} ^ {n} = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} s = c, \\\\ u _ {s} ^ {n - 1} & \\text {e l i f} s \\in S _ {n}, \\\\ u _ {s} ^ {n - 1} + \\left(1 - \\boldsymbol {p} _ {a} \\cdot \\boldsymbol {p} _ {b}\\right) & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {3}", + "image_path": "132c05023f92425ada9e79fe861341cfd2a50fc5e6e9f7baa922c9a4be92548b.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 570, + 547, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 676 + ], + "type": "text", + "content": "After finishing this procedure, we use the final score of each segment to select those with scores above the threshold to serve as high-confidence segments " + }, + { + "bbox": [ + 304, + 570, + 547, + 676 + ], + "type": "inline_equation", + "content": "S_{f}" + }, + { + "bbox": [ + 304, + 570, + 547, + 676 + ], + "type": "text", + "content": " and participate in contrastive learning. If two selected segments are partially overlapped, we only reserve the one with a higher score. This procedure is performed for each training sample before each epoch to select high-confidence segments as the network updates itself, except for the first epoch since the feature cannot be clustered at that moment." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "Overall Contrastive Loss. In our contrastive learning, the pixels of " + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_t" + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": " with ground truth annotations and " + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{1:t-1}" + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": " with pseudo labels are excluded. Meanwhile, they can naturally" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11914" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "serve as high-confidence negative segments in contrastive learning. Since the batch size is limited in segmentation while the number of negative samples is crucial in contrastive learning [7, 15], we use a memory bank to cache the features of recent four batches to increase the number of negative samples. Given the segments " + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "S_{v}" + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": " generate by visual similarity and segments " + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "S_{f}" + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": " generated by feature affinity, our contrastive loss is formalized as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 58, + 181, + 287, + 219 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 181, + 287, + 219 + ], + "spans": [ + { + "bbox": [ + 58, + 181, + 287, + 219 + ], + "type": "interline_equation", + "content": "\\mathcal{L}_{c} = \\frac{1}{|S_{v}|}\\sum_{\\substack{i\\in S_{v}\\\\ i\\notin \\mathcal{C}_{1:t}}}\\mathcal{L}(\\boldsymbol{f}_{i},S_{v}) + \\frac{1}{|S_{f}|}\\sum_{\\substack{i\\in S_{f}\\\\ i\\notin \\mathcal{C}_{1:t}}}\\mathcal{L}(\\boldsymbol{f}_{i},S_{f}) \\tag{4}", + "image_path": "f0953861b5b26f6f8303ef448429d05d1b39c1919162771582f1e70f26194a74.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 223, + 286, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 223, + 286, + 236 + ], + "spans": [ + { + "bbox": [ + 47, + 223, + 286, + 236 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 223, + 286, + 236 + ], + "type": "inline_equation", + "content": "|S|" + }, + { + "bbox": [ + 47, + 223, + 286, + 236 + ], + "type": "text", + "content": " means the pixel number in all segments within " + }, + { + "bbox": [ + 47, + 223, + 286, + 236 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 223, + 286, + 236 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 240, + 282, + 254 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 240, + 282, + 254 + ], + "spans": [ + { + "bbox": [ + 47, + 240, + 282, + 254 + ], + "type": "text", + "content": "4.2. Learning Future Knowledge in Output Space" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 258, + 287, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 287, + 402 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 287, + 402 + ], + "type": "text", + "content": "Previous work [5] has claimed that a proper initialization of classifier weight at step " + }, + { + "bbox": [ + 46, + 258, + 287, + 402 + ], + "type": "inline_equation", + "content": "t > 1" + }, + { + "bbox": [ + 46, + 258, + 287, + 402 + ], + "type": "text", + "content": " could also benefit the performance and is widely adopted by other works [10, 54]. This motivates us to further introduce future knowledge to the output space. Existing practice eases the misalignment between features and classifier weights by using the weight of the background to initialize that of the new classes. But in the update process, the weights of new classes should be updated to separate them from the background. Making the classifier weights to be identical to that of the background has the risk of increasing the necessary update, which has a negative effect based on previous analysis." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 403, + 288, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 288, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 288, + 666 + ], + "type": "text", + "content": "To address this issue, we want the classifier to be initialized as close to the final optimal value as possible. When optimizing feature space, we manage to obtain high-confidence segments of future classes, and the intermediate features are also optimized accordingly. We could naturally utilize them to train an auxiliary classifier that can classify future classes in advance and use its weights as initialization. More in detail, we first perform clustering on the prototypes of segments to assign an auxiliary semantic label to each segment, which is then used to optimize the auxiliary classifier using cross-entropy loss. Note that the network receives no gradient from this classifier. In the next step when initialization is needed, we compute the prototype of each new class and select the auxiliary classifier weight which is closest to the prototype to initialize the actual classifier weight of it. On the one hand, we can make the classifier converge more easily and avoid the R-P dilemma. On the other hand, it solves the inadequate data obstacle in output space by utilizing the data of current step to serve as the negative samples of future classes, which can further boost the discriminability of the classifier compared to training it directly on the future steps." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 671, + 163, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 163, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 163, + 682 + ], + "type": "text", + "content": "4.3. Overall Framework" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "Our proposed framework is depicted in Figure 4. " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ce}" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{aux}" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": " are both cross-entropy loss to learn new classes and to" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "train the auxiliary classifier, respectively. To complete our framework, we still need a KD loss to overcome forgetting. Since our focus is not on this part, we adopt the CKD loss in MiB [5] as " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{kd}" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " to assist our training, with the addition of a temperature parameter as in original KD loss [16] to enhance its ability in knowledge preserving. This makes the overall loss function of our framework as follows." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 357, + 165, + 545, + 178 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 165, + 545, + 178 + ], + "spans": [ + { + "bbox": [ + 357, + 165, + 545, + 178 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {c e} + \\alpha \\mathcal {L} _ {k d} + \\beta \\mathcal {L} _ {c} + \\mathcal {L} _ {\\text {a u x}}, \\tag {5}", + "image_path": "8f133ac367d9a4ac6233cff0a2fa9a01e52817b48abfaa73a430de10493b8899.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 186, + 457, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 186, + 457, + 198 + ], + "spans": [ + { + "bbox": [ + 306, + 186, + 457, + 198 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 186, + 457, + 198 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 306, + 186, + 457, + 198 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 186, + 457, + 198 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 306, + 186, + 457, + 198 + ], + "type": "text", + "content": " are hyper-parameters." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 209, + 388, + 222 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 209, + 388, + 222 + ], + "spans": [ + { + "bbox": [ + 306, + 209, + 388, + 222 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 228, + 415, + 241 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 228, + 415, + 241 + ], + "spans": [ + { + "bbox": [ + 306, + 228, + 415, + 241 + ], + "type": "text", + "content": "5.1. Implement Details" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "type": "text", + "content": "Datasets. Following previous works, we evaluate our method on VOC2012 [12] and ADE20K [56], which are the standard CSS benchmarks. We report the performance on the official validation set of each dataset. We also exclude " + }, + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "type": "text", + "content": " of the training set as a validation set to tune hyperparameters and perform all analyses." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "type": "text", + "content": "Protocols. There are two settings in CSS benchmarks: disjoint and overlapped. The disjoint setting limits the given images to contain pixels only belong to " + }, + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{1:t}" + }, + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "type": "text", + "content": ", while the latter does not have this restriction, which means the pixels can also belong to the future classes, i.e., " + }, + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{t+1:T}" + }, + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "type": "text", + "content": ". Note that the overlapped setting is considered to be more realistic and more challenging by all existing works [5, 10, 6, 37], and the disjoint setting is even ignored in some works [6, 37]. In design, our work is fully based on the overlapped setting. Evaluation. The CSS benchmark setups are denoted as " + }, + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "type": "inline_equation", + "content": "N_{o} - N_{n}" + }, + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "type": "inline_equation", + "content": "N_{o}" + }, + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "type": "inline_equation", + "content": "N_{n}" + }, + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "type": "text", + "content": " are the number of classes to be learned at the initial step and each incremental step, respectively. For example, the 15-1 setup of VOC2012 gives 15 classes at the initial step and adds one class per incremental step, resulting in a total of 6 steps. On VOC2012, we conduct experiments on four setups: 19-1 (2 steps), 15-5 (2 steps), 15-1 (6 steps), and 10-1 (11 steps). On ADE20K, we use three setups: 100-50 (2 tasks), 50-50 (3 tasks), and 100-10 (6 tasks). The network is evaluated after finishing all learning steps using mean Intersection over Union (mIoU) as metric. The performance of initial classes " + }, + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{1}" + }, + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "type": "text", + "content": ", incremental classes " + }, + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{2:T}" + }, + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "type": "text", + "content": ", and all classes " + }, + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{1:T}" + }, + { + "bbox": [ + 304, + 319, + 546, + 594 + ], + "type": "text", + "content": " are denoted as old, new, and all, respectively." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": "Training. Following previous works [5, 10], we adopt DeepLab-V3 with an output stride of 16. ResNet-101 serves as the backbone, which is pre-trained on ImageNet. We use the SGD optimizer with momentum set to 0.9. The learning rate is set to 1e-2 for the initial learning step and 1e-3 for the following learning step. The learning rate is adjusted by the polynomial decay schedule with power set to 0.9. The network is trained on VOC2012 for 30 epochs, and 60 epochs on ADE20K, both with a batch size of 16. The image is cropped to " + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": " for both training and validation, with" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11915" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 78, + 91, + 515, + 261 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 545, + 90 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 545, + 90 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 545, + 90 + ], + "type": "text", + "content": "Table 1. Results of different methods on VOC2012. The best is in bold while the second best is in underline. Results are averaged over 3 runs with standard deviation provided." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 78, + 91, + 515, + 261 + ], + "lines": [ + { + "bbox": [ + 78, + 91, + 515, + 261 + ], + "spans": [ + { + "bbox": [ + 78, + 91, + 515, + 261 + ], + "type": "table", + "html": "
Method19-1 (2 tasks)15-5 (2 tasks)15-1 (6 tasks)10-1 (11 tasks)
oldnewalloldnewalloldnewalloldnewall
ILT [35]67.112.364.466.340.659.94.97.85.7---
MiB [5]70.222.167.875.549.469.035.113.529.712.213.012.6
PLOP [10]75.337.373.575.751.770.065.121.154.644.015.522.9
SDR [36]69.132.667.475.452.669.944.721.839.2---
SSUL [6]77.729.675.477.850.171.277.336.567.671.345.959.2
RCIL [54]---78.852.072.470.623.759.455.415.134.3
ALIFE [37]76.649.375.377.152.571.364.434.957.4---
Ours77.7 ±0.2259.8 ±1.3876.8 ±0.3579.1 ±0.2167.7 ±0.4676.4 ±0.2975.2 ±0.7552.2 ±1.3369.7 ±1.0968.1 ±0.9654.5 ±1.5761.6 ±1.13
RECALL [34]68.155.368.667.754.365.667.850.964.865.053.760.7
SSUL-M [6]77.849.776.478.455.873.078.349.071.374.053.264.1
ALIFE-M [37]76.752.275.577.655.272.366.038.859.5---
Ours-M77.9 ±0.1967.7 ±0.7477.4 ±0.3279.3 ±0.2270.2 ±0.2977.1 ±0.2477.1 ±0.6560.4 ±0.7373.1 ±0.6869.5 ±0.6063.2 ±1.2566.5 ±0.78
Joint77.677.777.679.571.577.679.571.577.678.576.677.6
", + "image_path": "38b65846c664a259995b1d4175be99b52341fc5acbf7b347db38c31a8af6a499.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 124, + 294, + 468, + 446 + ], + "blocks": [ + { + "bbox": [ + 47, + 273, + 545, + 293 + ], + "lines": [ + { + "bbox": [ + 47, + 273, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 47, + 273, + 545, + 293 + ], + "type": "text", + "content": "Table 2. Results of different methods on ADE20K. The best is in bold while the second best is in underline. Results are averaged over 3 runs with standard deviation provided." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 124, + 294, + 468, + 446 + ], + "lines": [ + { + "bbox": [ + 124, + 294, + 468, + 446 + ], + "spans": [ + { + "bbox": [ + 124, + 294, + 468, + 446 + ], + "type": "table", + "html": "
Method100-50 (2 tasks)50-50 (3 tasks)100-10 (6 tasks).
oldnewalloldnewalloldnewall
ILT [35]18.214.417.03.512.89.70.11.30.5
MiB [5]40.517.132.745.521.029.338.211.129.2
PLOP [10]41.814.832.948.820.930.440.413.631.5
SSUL [6]41.218.033.548.320.129.540.218.733.1
RCIL [54]42.318.834.548.325.032.939.317.632.1
ALIFE [37]42.123.035.848.925.633.541.022.734.9
Ours43.1 ±0.1726.0 ±0.3637.4 ±0.2549.1 ±0.2428.3 ±0.4335.2 ±0.3341.4 ±0.2825.5 ±0.4536.1 ±0.35
SSUL-M [6]42.717.534.349.120.129.742.817.634.4
ALIFE-M [37]42.223.536.049.026.133.841.123.035.1
Ours-M43.1 ±0.1526.2 ±0.2937.5 ±0.2149.2 ±0.1228.5 ±0.2735.4 ±0.1841.6 ±0.2125.8 ±0.2636.3 ±0.22
Joint43.529.438.850.332.738.843.529.438.8
", + "image_path": "2b878ddc6981c3a914540097085f7266c34ce9cbd1eb7f2d42df5bd25ce58653.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 56, + 460, + 130, + 529 + ], + "blocks": [ + { + "bbox": [ + 56, + 460, + 130, + 529 + ], + "lines": [ + { + "bbox": [ + 56, + 460, + 130, + 529 + ], + "spans": [ + { + "bbox": [ + 56, + 460, + 130, + 529 + ], + "type": "image", + "image_path": "8066eebb0a9e448826a25a517bbc4d23e5e8c44466d09326524826b0c4261577.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 533, + 544, + 555 + ], + "lines": [ + { + "bbox": [ + 46, + 533, + 544, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 544, + 555 + ], + "type": "text", + "content": "Figure 6. mIoU comparison between CSS methods over steps on VOC 15-1 setups. The performance of initial classes and each new class added per step are plotted separately from left to right. Our method shows great ability in learning new classes." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 137, + 460, + 212, + 529 + ], + "blocks": [ + { + "bbox": [ + 137, + 460, + 212, + 529 + ], + "lines": [ + { + "bbox": [ + 137, + 460, + 212, + 529 + ], + "spans": [ + { + "bbox": [ + 137, + 460, + 212, + 529 + ], + "type": "image", + "image_path": "1456f2f508fda48f3552742c5238f4220be55d929a74f03258c36cdbf422fa04.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 219, + 460, + 293, + 529 + ], + "blocks": [ + { + "bbox": [ + 219, + 460, + 293, + 529 + ], + "lines": [ + { + "bbox": [ + 219, + 460, + 293, + 529 + ], + "spans": [ + { + "bbox": [ + 219, + 460, + 293, + 529 + ], + "type": "image", + "image_path": "dac3a1bc85afb87d35a21c63297a342ca4d3799976f2363f7fe10305dd3f7269.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 299, + 460, + 373, + 529 + ], + "blocks": [ + { + "bbox": [ + 299, + 460, + 373, + 529 + ], + "lines": [ + { + "bbox": [ + 299, + 460, + 373, + 529 + ], + "spans": [ + { + "bbox": [ + 299, + 460, + 373, + 529 + ], + "type": "image", + "image_path": "d9b160afa6126415c6d98b25328ea13e8e956f48c714c7043319d87f48c4b57a.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 381, + 460, + 455, + 529 + ], + "blocks": [ + { + "bbox": [ + 381, + 460, + 455, + 529 + ], + "lines": [ + { + "bbox": [ + 381, + 460, + 455, + 529 + ], + "spans": [ + { + "bbox": [ + 381, + 460, + 455, + 529 + ], + "type": "image", + "image_path": "f72d05b7f88f7d937ef29b727e0e21a3d6c265214cd0beee4f49af21cc17dcb3.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 462, + 460, + 536, + 529 + ], + "blocks": [ + { + "bbox": [ + 462, + 460, + 536, + 529 + ], + "lines": [ + { + "bbox": [ + 462, + 460, + 536, + 529 + ], + "spans": [ + { + "bbox": [ + 462, + 460, + 536, + 529 + ], + "type": "image", + "image_path": "8c7e91b67ba41d4d2802679391173cca990126900e950f96ecc2612a4a149e96.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 574, + 286, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 286, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 286, + 598 + ], + "type": "text", + "content": "a random scaling and a random left-right flip additionally applied to training." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 609, + 104, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 104, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 104, + 621 + ], + "type": "text", + "content": "5.2. Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "We provide the results on VOC2012 and ADE20K in Table 1 and Table 2, respectively. Some works [6, 34] exploit memory or external data to assist training. We also report the results obtained using memory (denoted by -M) following the implementation of [6] to fairly compare with these methods. The result of joint training is also provided as the upperbound for reference." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 574, + 545, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 574, + 545, + 706 + ], + "spans": [ + { + "bbox": [ + 304, + 574, + 545, + 706 + ], + "type": "text", + "content": "For all setups on VOC2012, our method surpasses all existing methods by a large margin on new classes. This demonstrates the strong ability of our method to learn new classes. Note that our method also shows promising results on old classes even with a simple approach to preserve old knowledge. This is due to that a higher performance on new classes indicates that there also might be less confusion between old and new classes, which also benefits the mIoU of old classes. On the more challenging setups with multiple steps (15-1, 10-1), the new classes cannot be properly learned in the first place for most methods. To" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "11916" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "make matters worse, these poorly optimized new classes will suffer forgetting in the following steps which further reduces their performance. Even in these challenging circumstances, our method still shows great performance in learning new classes, as shown in Figure 6. We can also see that even though SSUL shows higher performance on old classes on long-term setups, it relies on completely freezing the feature extractor to prevent forgetting, which does help a lot for old classes on these steps, but also harms its flexibility greatly. We believe that if equipped with a modern knowledge-preserving constraint, our method could offer another boost in performance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 219, + 287, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 219, + 287, + 302 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 287, + 302 + ], + "type": "text", + "content": "On the more challenging ADE20K benchmarks, we obtain similar results as that of VOC2012. Our method shows some improvement on old classes and is significantly better on new classes. On top of the results of VOC2012 benchmark, this further demonstrates that our approach works well on more complex datasets, and has the ability to handle both scenes and objects centric datasets." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 306, + 287, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 306, + 287, + 377 + ], + "spans": [ + { + "bbox": [ + 46, + 306, + 287, + 377 + ], + "type": "text", + "content": "When memory is applied on both benchmarks, our method receives further improvements and holds the leading position. This also indicates that our proposed training method has a non-overlapping effect with the memory technique. They can be used as two complementary techniques as pointed out in Section 3.4" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 394, + 140, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 394, + 140, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 394, + 140, + 407 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 416, + 288, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 416, + 288, + 596 + ], + "spans": [ + { + "bbox": [ + 46, + 416, + 288, + 596 + ], + "type": "text", + "content": "We investigate the effects of the proposed components in our framework using both 15-1 and 15-5 setups on VOC2012. Starting from a baseline composed of " + }, + { + "bbox": [ + 46, + 416, + 288, + 596 + ], + "type": "inline_equation", + "content": "L_{ce}" + }, + { + "bbox": [ + 46, + 416, + 288, + 596 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 416, + 288, + 596 + ], + "type": "inline_equation", + "content": "L_{kd}" + }, + { + "bbox": [ + 46, + 416, + 288, + 596 + ], + "type": "text", + "content": " and pseudo label, we add the components one by one and show the ablation results in Table 3. As can be seen, the performance increase steadily as each proposed component is gradually added. Only applying contrast by visual similarity does not receive much improvement since it cannot instruct the network to capture semantic-level information. After applying contrast by feature affinity, the performance receives the highest gain, indicating the necessity to add semantic-level supervision and make the network learn more accurate knowledge. On top of that, the performance receives another boost from our classifier initialization technique which introduces future knowledge to output space." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 48, + 623, + 288, + 692 + ], + "blocks": [ + { + "bbox": [ + 60, + 611, + 272, + 622 + ], + "lines": [ + { + "bbox": [ + 60, + 611, + 272, + 622 + ], + "spans": [ + { + "bbox": [ + 60, + 611, + 272, + 622 + ], + "type": "text", + "content": "Table 3. Ablation study on VOC2012 15-1 and 15-5 setup." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 623, + 288, + 692 + ], + "lines": [ + { + "bbox": [ + 48, + 623, + 288, + 692 + ], + "spans": [ + { + "bbox": [ + 48, + 623, + 288, + 692 + ], + "type": "table", + "html": "
Method15-1 (6 tasks)15-5 (2 tasks)
oldnewalloldnewall
baseline65.318.854.276.951.370.8
+ visual similarity contrast67.126.357.477.254.571.8
+ feature affinity contrast74.545.167.578.765.475.5
+ classifier initialization75.252.269.779.167.776.4
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The high-confidence segments selected by our criterion are also presented on the right." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 337, + 253, + 514, + 373 + ], + "blocks": [ + { + "bbox": [ + 337, + 253, + 514, + 373 + ], + "lines": [ + { + "bbox": [ + 337, + 253, + 514, + 373 + ], + "spans": [ + { + "bbox": [ + 337, + 253, + 514, + 373 + ], + "type": "image", + "image_path": "8218f054600d24222cc7444f31ca5dd8a5fb4bc3003c0c7e2acc0718c776b4d1.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 376, + 545, + 399 + ], + "lines": [ + { + "bbox": [ + 306, + 376, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 306, + 376, + 545, + 399 + ], + "type": "text", + "content": "Figure 8. Performance comparison between different classifier initialization over training epochs on VOC2012 19-1 setup." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 418, + 417, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 418, + 417, + 430 + ], + "spans": [ + { + "bbox": [ + 306, + 418, + 417, + 430 + ], + "type": "text", + "content": "5.4. Further Discussion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 437, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 510 + ], + "type": "text", + "content": "Feature Quality Analysis. To further demonstrate the effect of our method to solve the underfitting problem pointed out in Section 3.2, we conduct the same analysis on our method and incorporate the findings into Figure 2 (denoted by Ours). As can be seen, pre-learning future classes can significantly improve both intra-class and inter-class fitness." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 510, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 617 + ], + "type": "text", + "content": "Segment Generation. We provide a qualitative comparison between direct clustering and our proposed hierarchical combination at different granularities to validate our design in Section 4.1. The results are generated from the same intermediate features and are plotted in Figure 7. As can be seen, our practice consistently generates better results across different granularities. We also present the high-confidence segments selected by our criterion for each image, which match the actual classes with high precision." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Classifier Initialization. We give a comparison of performance over training epochs for different classifier initialization methods in Figure 8. As can be seen, the initialization technique proposed by MiB [5] converges much slower due to larger update paces. Random initialization converges fast but the performance stops increasing shortly afterward. Among all of them, our method stands out with its fast convergence speed and superior performance." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11917" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 200, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 200, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 200, + 83 + ], + "type": "text", + "content": "6. Limitation and Conclusion" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 92, + 287, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 92, + 287, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 92, + 287, + 224 + ], + "type": "text", + "content": "Our method has two limitations. Firstly, it relies on the natural attribute of CSS that unlabeled future classes exist in current training data. So it may not perform well when there are only a few unlabeled future classes in the current training data. However, in such cases, we can still leverage external unlabeled data, such as web-crawled data as used in RECALL [34]. Secondly, we point out that even though our proposed framework achieves great performance, it as a practicable solution might not be able to unleash the full potential of the training method, which requires further exploration in future works." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 224, + 289, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 289, + 368 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 289, + 368 + ], + "type": "text", + "content": "In this work, we present an in-depth analysis of the reason why existing methods suffer low performance on new classes. Building on this analysis, we introduce a novel training pipeline for CSS that optimizes potential future classes in the current training step. This offers a new perspective for enhancing new class performance in contrast to existing works that focus on addressing the R-P dilemma. We propose a framework based on this pipeline and it shows a significant improvement for new classes, while also benefiting the performance of old classes. We believe that this work can provide valuable insights for the research community on CSS." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 381, + 162, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 381, + 162, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 381, + 162, + 396 + ], + "type": "text", + "content": "7. Acknowledgements" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 402, + 287, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 486 + ], + "type": "text", + "content": "This work is supported by the National Natural Science Foundation of China under Grant 62176246 and Grant 61836008. This work is also supported by Anhui Province Key Research and Development Plan (202304a05020045), Anhui Provincial Natural Science Foundation 2208085UD17 and the Fundamental Research Funds for the Central Universities (WK3490000006)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 499, + 107, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 499, + 107, + 511 + ], + "spans": [ + { + "bbox": [ + 47, + 499, + 107, + 511 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 519, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 52, + 519, + 287, + 553 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 519, + 287, + 553 + ], + "spans": [ + { + "bbox": [ + 52, + 519, + 287, + 553 + ], + "type": "text", + "content": "[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. 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In Proceedings of the 28th ACM International Conference on Multimedia, pages 156-164, 2020." + } + ] + } + ], + "index": 1 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "11920" + } + ] + } + ], + "index": 3 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Preserve Your Own Correlation_ A Noise Prior for Video Diffusion Models/12c6fb66-a455-4547-8b5a-4a378b5ee51f_content_list.json b/2023/Preserve Your Own Correlation_ A Noise Prior for Video Diffusion Models/12c6fb66-a455-4547-8b5a-4a378b5ee51f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..6379a0cdcae6029fa4d41333d705e41b496b383a --- /dev/null +++ b/2023/Preserve Your Own Correlation_ A Noise Prior for Video Diffusion Models/12c6fb66-a455-4547-8b5a-4a378b5ee51f_content_list.json @@ -0,0 +1,1835 @@ +[ + { + "type": "text", + "text": "Preserve Your Own Correlation: A Noise Prior for Video Diffusion Models", + "text_level": 1, + "bbox": [ + 109, + 130, + 861, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Songwei Ge*", + "bbox": [ + 137, + 181, + 243, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "University of Maryland", + "bbox": [ + 116, + 200, + 258, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Seungjun Nah \nNVIDIA", + "bbox": [ + 297, + 181, + 413, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Guilin Liu NVIDIA", + "bbox": [ + 454, + 181, + 539, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tyler Poon", + "bbox": [ + 602, + 181, + 691, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "University of Chicago", + "bbox": [ + 580, + 200, + 712, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Andrew Tao NVIDIA", + "bbox": [ + 753, + 181, + 852, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Bryan Catanzaro", + "bbox": [ + 94, + 242, + 228, + 258 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "NVIDIA", + "bbox": [ + 133, + 262, + 189, + 275 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "David Jacobs", + "bbox": [ + 282, + 242, + 388, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "University of Maryland", + "bbox": [ + 264, + 262, + 406, + 276 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jia-Bin Huang", + "bbox": [ + 454, + 242, + 571, + 258 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "University of Maryland", + "bbox": [ + 444, + 262, + 584, + 276 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ming-Yu Liu", + "bbox": [ + 620, + 242, + 725, + 258 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "NVIDIA", + "bbox": [ + 645, + 262, + 700, + 275 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yogesh Balaji", + "bbox": [ + 764, + 242, + 875, + 258 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "NVIDIA", + "bbox": [ + 792, + 262, + 846, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A very happy fuzzy panda dressed as a chef eating pizza in the New York street food truck.", + "bbox": [ + 76, + 512, + 341, + 555 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The supernova explosion of a white dwarf in the universe, photo realistic.", + "bbox": [ + 348, + 520, + 609, + 549 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A high-quality 3D render of hyperrealist, super strong, multicolor stripped, and fluffy bear with wings, highly detailed.", + "bbox": [ + 617, + 513, + 883, + 556 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Figure 1: Given a text description, our approach can faithfully generate videos that are consistent with the input text while being photorealistic and temporally consistent. Best viewed with Acrobat Reader. Click the images to play the video clips.", + "bbox": [ + 75, + 566, + 892, + 598 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 616, + 313, + 632 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite tremendous progress in generating high-quality images using diffusion models, synthesizing a sequence of animated frames that are both photorealistic and temporally coherent is still in its infancy. While off-the-shelf billion-scale datasets for image generation are available, collecting similar video data of the same scale is still challenging. Also, training a video diffusion model is computationally much more expensive than its image counterpart. In this work, we explore finetuning a pretrained image diffusion model with video data as a practical solution for the video synthesis task. We find that naively extending the image noise prior to video noise prior in video diffusion leads to sub-optimal performance. Our carefully designed video noise prior leads to substantially better performance. Extensive experimental validation shows that our", + "bbox": [ + 73, + 648, + 473, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "model, Preserve Your Own COrelation (PYoCo), attains SOTA zero-shot text-to-video results on the UCF-101 and MSR-VTT benchmarks. It also achieves SOTA video generation quality on the small-scale UCF-101 benchmark with a $10 \\times$ smaller model using significantly less computation than the prior art. The project page is available at https://research.nvidia.com/labs/dir/pyoco/.", + "bbox": [ + 500, + 617, + 893, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 753, + 630, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Large-scale diffusion-based text-to-image models [38, 42, 2] have demonstrated impressive capabilities in turning complex text descriptions into photorealistic images. They can generate images with novel concepts unseen during training. Sophisticated image editing and processing tasks can easily be accomplished through guidance control and embedding techniques. Due to the immense success in several applications [30, 67, 5], these models are established as pow-", + "bbox": [ + 496, + 779, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work done during an internship at NVIDIA.", + "bbox": [ + 94, + 886, + 336, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22930", + "bbox": [ + 478, + 924, + 519, + 936 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3ea06ec868739f34b3665eb70207e13f0537015064d7770050b4c180314a5265.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 78, + 87, + 524, + 273 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e6d7c286fd69acb9c2a133e2940d19045711e89bb8826830f27c7352a116b27c.jpg", + "image_caption": [ + "(b)", + "Figure 2: Visualizing the noise map correlations. (a) visualizes the t-SNE plot of the noise maps corresponding to input frames randomly sampled from videos. These noise maps are obtained by running a diffusion ODE [49, 48] on the input frames using a trained text-to-image model, but in the opposite direction of image synthesis ( $\\sigma : 0 \\to \\sigma_{\\max}$ ). The green dots in the background denote the reference noise maps sampled from an i.i.d. Gaussian distribution. The red dots and yellow dots are noise maps corresponding to input frames coming from different videos. We found they are spread out and share no correlation. On the other hand, the noise maps corresponding to the frames coming from the same video (shown in blue dots) are clustered together. (b) Using an i.i.d. noise model (orange dots) for finetuning text-to-image models for video synthesis is not ideal since temporal correlations between frames are not modeled. To remedy this, we propose a progressive noise model in which the correlation between different noise maps is injected along the temporal axis. Our progressive noise model (blue dots) aptly models the correlations present in the video noise maps." + ], + "image_footnote": [], + "bbox": [ + 588, + 93, + 879, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "erful image synthesis tools for content generation. As image synthesis is largely democratized with the success of these text-to-image models, it is natural to ask whether we can repeat the same success in video synthesis with large-scale diffusion-based text-to-video models.", + "bbox": [ + 75, + 483, + 470, + 558 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multiple attempts have been made to build large-scale video diffusion models. Ho et al. [17] proposed a UNet-based architecture for the video synthesis task that is trained using joint image-video denoising losses.Imagen video [14] extends the cascaded text-to-image generation architecture ofImagen [42] for video generation. In both works, the authors directly train a video generation model from scratch. While these approaches achieve great success and produce high-quality videos, they are inherently expensive to train, requiring hundreds of high-end GPUs or TPU's and several weeks of training. After all, video generators not only need to learn to form individual images but should also learn to synthesize coherent temporal dynamics, which makes the video generation task much more challenging. While the formation of individual frames is a shared component in an image and video synthesis, these works disregard the existence of powerful pretrained text-to-image diffusion models and train their video generators from scratch.", + "bbox": [ + 75, + 563, + 470, + 835 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We explore a different avenue for building large-scale text-to-video diffusion models by starting with a pretrained text-to-image diffusion model. Our motivation is that most of the components learned for the image synthesis task can", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "effectively be reused for video generation, leading to knowledge transfer and efficient training. A similar idea is adopted by several recent works [46, 69, 4]. Without exception, when finetuning, they naively extend the image diffusion noise prior (i.i.d. noise) used in the text-to-image model to a video diffusion noise prior by adding an extra dimension to the 2D noise map. We argue that this approach is not ideal as it does not utilize the natural correlations in videos that are already learned by the image models. This is illustrated in Figure 2, where we visualize the t-SNE plot of noise maps corresponding to different input frames as obtained from a pretrained text-to-image diffusion model. The noise maps corresponding to different frames coming from the same video (blue dots in Figure 2a are clustered together, exhibiting a high degree of correlation. The use of i.i.d. noise prior does not model this correlation, which would impede the finetuning process. Our careful analysis of the video diffusion noise prior leads us to a noise prior that is better tailored for finetuning an image synthesis model to the video generation task. As illustrated in Figure 2b, our proposed noise prior (shown in blue dots) aptly captures the correlations in noise maps corresponding to video frames.", + "bbox": [ + 496, + 483, + 893, + 816 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We then proceed to build a large-scale diffusion-based text-to-video model. We leverage several design choices from the prior works, including the use of temporal attention [17], joint image-video finetuning [17], a cascaded generation architecture [14], and an ensemble of expert denois-", + "bbox": [ + 496, + 824, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22931", + "bbox": [ + 478, + 924, + 517, + 936 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ers [2]. Together with these techniques and the proposed video noise prior, our model establishes a new state-of-the-art for video generation outperforming competing methods on several benchmark datasets. Figure 1 shows our model can achieve high-quality zero-shot video synthesis capability with SOTA photorealism and temporal consistency.", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In short, our work makes the following key contributions.", + "bbox": [ + 96, + 181, + 468, + 196 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We propose a video diffusion noise tailored for finetuning text-to-image diffusion models for text-to-video.", + "2. We conduct extensive experimental validation and verify the effectiveness of the proposed noise prior.", + "3. We build a large-scale text-to-video diffusion model by finetuning a pretrained eDiff-I model with our noise prior and achieve state-of-the-art results on several benchmarks." + ], + "bbox": [ + 70, + 205, + 468, + 319 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 330, + 218, + 345 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion-based text-to-image models: Diffusion models have significantly advanced the progress of text-based photorealistic, compositional image generation [38, 42]. Given the nature of the iterative denoising process that requires massive numbers of score function evaluations, earlier diffusion models focused on generating low-resolution images, e.g., $64 \\times 64$ [15, 48]. To generate high-resolution images, two common approaches have been used. The first approach applies cascaded super-resolution models in the RGB space [32, 16, 42, 38], while the second approach leverages a decoder to exploit latent space [40, 11]. Based on these models, advanced image and video editing have been achieved through finetuning the model [41, 67, 5, 23, 61, 29] or controlling the inference process [30, 13, 34, 10, 35, 7, 31, 3]. Here, we study the problem of using large-scale diffusion models for text-to-video generation.", + "bbox": [ + 75, + 357, + 468, + 598 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Video generation models: Generating realistic and novel videos have long been an attractive and essential research direction [58, 39, 65]. Previously studies have resorted to different types of generative models such as GANs [58, 43, 54, 52, 45], Autoregressive models [51, 63, 25, 9, 18], and implicit neural representations [47, 66]. Recently, driven by the tremendous success of applying the diffusion model to image synthesis, multiple works have proposed to explore diffusion models for conditional and unconditional video synthesis [57, 12, 69, 61, 4, 22, 19, 57, 64, 33, 28, 1, 59]. For example, Singer et al. extend the unCLIP framework [38] to text-to-video generation, which allows training without video captions [46]. Ho et al. [17] extend the Imagen framework [42] by repeatedly up-scaling low-resolution small-fps videos in both spatial and temporal directions with multiple models [14]. Our work also falls into this line of work which uses a diffusion model. We focus on augmenting an image diffusion model for video and study the design choice of the diffusion noise priors for such an image-to-video finetuning task.", + "bbox": [ + 75, + 598, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Leverage knowledge from images for text-to-video generation: Like text-to-image models, text-to-video models require massive amounts of data to learn caption-relatedness, frame photorealism, and temporal dynamics. But in contrast to the abundant image data resource, video data are more limited in style, volume, and quality. To resolve such scarcity issue of text-video data, previous works have resorted to different strategies to leverage knowledge from image data for text-to-video generation, including joint training on the text-image data from scratch [17, 14, 56, 60], first training a text-to-image model and then finetuning partially [18, 4, 61, 29] or entirely [46, 8] on the video dataset, and using CLIP image features as the conditional information [46, 69]. In this paper, we propose a new video diffusion noise prior that is tailored for finetuning a pretrained diffusion-based image generation model for the video generation task. We reuse several design choices in the prior work by finetuning jointly on text-image and text-video datasets. As a result, we can build a text-to-video generation system that achieves state-of-the-art zero-shot performances.", + "bbox": [ + 496, + 90, + 893, + 393 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 409, + 637, + 425 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models generate data by iteratively denoising samples drawn from a noise distribution. In the case of text-to-video models, text embeddings obtained from a pre-trained text encoder are used as additional inputs in the denoising process. Formally, let $D(\\mathbf{x}, \\mathbf{e}, \\sigma)$ denote a denoising network that operates on the noisy input video $\\mathbf{x} \\in \\mathbb{R}^{b \\times n_s \\times 3 \\times h \\times w}$ where $\\mathbf{e}$ is the text embedding, and $\\sigma$ is the noise level. Here $n_s$ is the sequence length of the input video, $b$ is the batch size, and $h \\times w$ is the spatial resolution. The model $D$ is trained to denoise the input $\\mathbf{x}$ .", + "bbox": [ + 496, + 435, + 893, + 585 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Training We follow the EDM formulation of Karras et al. [21] to optimize the denoiser $D$ using the following objective", + "bbox": [ + 500, + 609, + 893, + 640 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbb {E} _ {p _ {\\text {d a t a}} (\\mathbf {x} _ {\\text {c l e a n}}, \\mathbf {e}), p (\\epsilon), p (\\sigma)} \\left[ \\lambda (\\sigma) \\| D \\left(\\mathbf {x} _ {\\text {n o i s e}}; \\mathbf {e}, \\sigma\\right) - \\mathbf {x} _ {\\text {c l e a n}} \\| _ {2} ^ {2} \\right] \\tag {1} \\\\ w h e r e \\quad \\mathbf {x} _ {\\text {n o i s e}} = \\mathbf {x} _ {\\text {c l e a n}} + \\sigma \\epsilon \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 652, + 890, + 704 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, $\\mathbf{x}_{\\mathrm{noise}}$ is the noisy sample obtained by corrupting the clean video $\\mathbf{x}$ with noise $\\sigma \\epsilon$ , where $p(\\epsilon) = \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ and $\\sigma$ is a scalar for the noise level drawn from $p(\\sigma)$ . The loss weight, $\\lambda (\\sigma)$ , is a function of $\\sigma$ given by $\\lambda (\\sigma) = (\\sigma^2 +\\sigma_{\\mathrm{data}}^2) / (\\sigma \\cdot \\sigma_{\\mathrm{data}})^2$ . Eq. (1) is a simple denoising objective in which the denoiser $D$ is trained to estimate the clean video $\\mathbf{x}_{\\mathrm{clean}}$ from the noisy input $\\mathbf{x}_{\\mathrm{noise}}$ . Following EDM, we use a log-normal distribution for $\\sigma$ i.e., $\\ln (p(\\sigma)) = \\mathcal{N}(P_{\\mathrm{mean}},P_{\\mathrm{std}}^2)$ with $P_{\\mathrm{mean}} = -1.2$ and $P_{\\mathrm{std}} = 1.2$ .", + "bbox": [ + 496, + 718, + 893, + 853 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To train the denoising model, EDM uses preconditioning terms in its objective function to properly scale the inputs and output of the denoiser model $D$ . More specifically, the", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22932", + "bbox": [ + 478, + 924, + 517, + 936 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "denoising model $D$ is written as", + "bbox": [ + 76, + 90, + 292, + 104 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nD (\\mathbf {x}; \\mathbf {e}, \\sigma) := \\left(\\frac {\\sigma_ {\\mathrm {d a t a}}}{\\sigma^ {*}}\\right) ^ {2} \\mathbf {x} + \\frac {\\sigma \\cdot \\sigma_ {\\mathrm {d a t a}}}{\\sigma^ {*}} F _ {\\theta} \\left(\\frac {\\mathbf {x}}{\\sigma^ {*}}; \\mathbf {e}, \\frac {\\ln (\\sigma)}{4}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 116, + 450, + 148 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, $F_{\\theta}$ is a neural network with parameters $\\theta$ and $\\sigma^{*} = \\sqrt{\\sigma^{2} + \\sigma_{\\mathrm{data}}^{2}}$ . We use $\\sigma_{\\mathrm{data}} = 0.5$ .", + "bbox": [ + 76, + 156, + 468, + 188 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Sampling Once the denoising model is trained, sampling can be performed by solving the following ODE [21]", + "bbox": [ + 76, + 205, + 468, + 234 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {d \\mathbf {x}}{d \\sigma} = - \\sigma \\nabla_ {\\mathbf {x}} \\log p (\\mathbf {x} | \\mathbf {e}, \\sigma) = \\frac {\\mathbf {x} - D (\\mathbf {x} ; \\mathbf {e} , \\sigma)}{\\sigma} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 244, + 468, + 276 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "for $\\sigma$ flowing backwards from $\\sigma = \\sigma_{\\mathrm{max}}$ to $\\sigma = 0$ . The initial value for $\\mathbf{x}$ is obtained by sampling from the prior distribution $\\mathbf{x} \\sim \\mathcal{N}(\\mathbf{0}, \\sigma_{\\mathrm{max}}^2 \\mathbf{I})$ . Over the recent years, several samplers have been proposed for sampling from the trained diffusion models [68, 48, 26, 27, 15]. In this paper, we use DEIS [68] and its stochastic variant [21] for synthesizing samples from our model.", + "bbox": [ + 76, + 285, + 470, + 390 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 76, + 402, + 168, + 419 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training text-to-video models is much more challenging than training text-to-image diffusion models due to practical difficulties in collecting billion-scale video datasets and securing enough computational resources. Additionally, generating videos is much more challenging since individual frames need to be both photorealistic and temporally coherent. Prior works leverage large-scale image datasets to mitigate these difficulties by either joint training on the image datasets [60, 17, 14] or finetuning a text-to-image model on the video datasets [18, 46]. Here, we are interested in finetuning text-to-image diffusion models jointly on image and video datasets. We postulate that naively extending the image noise prior to video diffusion is not ideal. We carefully explore the design space of noise priors and propose one that is well suited for our video finetuning task, which leads to significant performance gains.", + "bbox": [ + 75, + 429, + 472, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Correlated noise model An image diffusion model is trained to denoise independent noise from a perturbed image. The noise vector $\\epsilon$ in the denoising objective (1) is sampled from an i.i.d. Gaussian distribution $\\epsilon \\sim \\mathcal{N}(0, \\mathbf{I})$ . However, after training the image diffusion model and applying it to reverse real frames from a video into the noise space in a per-frame manner, we find that the noise maps corresponding to different frames are highly correlated. This is illustrated in Figure 2, where the t-SNE plot of noise maps corresponding to different video frames are plotted. When the input frames come from the same video (shown in blue dots in Figure 2a, noise maps are clustered. The use of i.i.d. sampling (shown in orange dots in Figure 2b does not capture these correlations. This is also depicted quantitatively", + "bbox": [ + 75, + 688, + 472, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1: Cosine similarity of the reversed noise. The noise maps corresponding to the frames sampled from the same videos have a higher similarity than those sampled from different videos.", + "bbox": [ + 496, + 88, + 893, + 148 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/4383742137095222d6e0d6fa310f41451b12d67c8f340416c502a161b125485a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Cosine Similarity
(a) Same video noise0.206±0.156
(b) Different video noise0.001±0.009
", + "bbox": [ + 529, + 154, + 862, + 215 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "in Table 1 where we compute the average pairwise cosine similarity between noise corresponding to (a) same video and (b) different video. (a) is much higher than (b). As a result, the video diffusion model trained with i.i.d. noise is coerced to forget such correlation among the noise between different frames, making it difficult to preserve knowledge from the image diffusion model. Motivated by this observation, we propose to modify the noise process to preserve the correlation between different frames. To this end, we investigate two noisng strategies - mixed and progressive noising.", + "bbox": [ + 496, + 237, + 893, + 402 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Mixed noise model: Let $\\epsilon^1, \\epsilon^2, \\ldots, \\epsilon^{n_s}$ denote the noise corresponding to individual video frames i.e., $\\epsilon^i$ corresponds to the $i^{th}$ element of the noise tensor $\\epsilon$ . In the mixed noise model, we generate two noise vectors $\\epsilon_{\\mathrm{shared}}$ and $\\epsilon_{\\mathrm{ind}}$ . $\\epsilon_{\\mathrm{shared}}$ is a common noise vector shared among all video frames, while $\\epsilon_{\\mathrm{ind}}$ is the individual noise per frame. The linear combination of both these vectors is used as the final noise.", + "bbox": [ + 496, + 402, + 893, + 508 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\epsilon_ {\\text {s h a r e d}} \\sim \\mathcal {N} \\left(\\mathbf {0}, \\frac {\\alpha^ {2}}{1 + \\alpha^ {2}} \\mathbf {I}\\right), \\epsilon_ {\\text {i n d}} ^ {i} \\sim \\mathcal {N} \\left(\\mathbf {0}, \\frac {1}{1 + \\alpha^ {2}} \\mathbf {I}\\right) \\tag {3} \\\\ \\epsilon^ {i} = \\epsilon_ {\\mathrm {s h a r e d}} + \\epsilon_ {\\mathrm {i n d}} ^ {i} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 512, + 893, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Progressive noise model: In the progressive noise model, the noise for each frame is generated in an autoregressive fashion in which the noise at frame $i$ is generated by perturbing the noise at frame $i - 1$ . Let $\\epsilon_{\\mathrm{ind}}^i$ denote the independent noise generated for frame $i$ . Then, progressive noising can be formulated as", + "bbox": [ + 496, + 571, + 893, + 662 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\epsilon^ {0} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}) \\quad \\epsilon_ {\\mathrm {i n d}} ^ {i} \\sim \\mathcal {N} (\\mathbf {0}, \\frac {1}{1 + \\alpha^ {2}} \\mathbf {I}) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 667, + 893, + 699 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\epsilon^ {i} = \\frac {\\alpha}{\\sqrt {1 + \\alpha^ {2}}} \\epsilon^ {i - 1} + \\epsilon_ {\\mathrm {i n d}} ^ {i}\n$$\n", + "text_format": "latex", + "bbox": [ + 629, + 700, + 803, + 729 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In both these models, $\\alpha$ controls how much noise is shared among different video frames. The higher the value of $\\alpha$ , the more correlation exists among the noise maps corresponding to different frames. As $\\alpha \\rightarrow \\infty$ , all frames would have the same noise which results in generating a frozen video. On the other hand, $\\alpha = 0$ corresponds to i.i.d. noise.", + "bbox": [ + 496, + 734, + 893, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Figure 2b, the use of progressive noise sampling (blue dots) better models the correlations between different noise maps by obtaining similar clustering patterns to the noise maps of real video frames embedded by a pretrained text-to-image model in Figure 2a (blue dots).", + "bbox": [ + 496, + 825, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "footer", + "text": "22933", + "bbox": [ + 478, + 924, + 519, + 936 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8d6b3d4c8df87f34a0ce9703c0a7f610b6687418e672edb194d3268825477a99.jpg", + "image_caption": [ + "Figure 3: Model architecture. Our pipeline consists of a cascade of four networks — a base model and three upsampling models. All four models take inputs as the text embeddings obtained from the T5 encoder and the CLIP text encoder. The base model produces 16 video frames of spatial resolution $64 \\times 64$ with a frameskip of 5. The first upsampling model performs a temporal interpolation, resulting in videos of size $76 \\times 64 \\times 64$ while the subsequent two super-resolution models perform spatial super-resolution to produce videos of sizes $76 \\times 256 \\times 256$ and $76 \\times 1024 \\times 1024$ ." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 893, + 296 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Model architecture As visualized in Figure 3, our model consists of a cascade of four networks — a base network and three upsampling stacks. The base network generates an output video of dimension $16 \\times 64 \\times 64$ with a frameskip of 5. It generates the frames $\\{1,6,11,\\ldots,76\\}$ . The first upsampling network performs a temporal interpolation to produce a video of size $76 \\times 64 \\times 64$ . The second and the third super-resolution network performs spatial upsampling to produce the outputs of sizes $76 \\times 256 \\times 256$ and $76 \\times 1024 \\times 1024$ . We utilize eDiff-I [2], a state-of-the-art text-to-image diffusion model, to initialize our base and spatial super-resolution models. Similar to prior works [17, 46], we adapt the image-based U-Net model for the video synthesis task by making the following changes: (1) Transforming 2D convolutions to 3D by adding a dimension 1 to temporal axis and (2) Adding temporal attention layers. Please refer to the supplementary material for more details.", + "bbox": [ + 75, + 409, + 472, + 666 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similar to Ho et al. [17], we jointly finetune the model on video and image datasets by concatenating videos and images in the temporal axis and applying our temporal modules only on the video part. Similarly to eDiff-I, our model uses both T5 text embeddings [37] and CLIP text embeddings [36]. We drop each of the embeddings independently at random during training, as in eDiff-I.", + "bbox": [ + 75, + 666, + 470, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 784, + 209, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we evaluate our proposed strategy of training diffusion models for video synthesis on two sets of experiments. We first comprehensively analyze our proposed noise model on the small-scale UCF-101 dataset. We then scale up our experiments to the challenging large-scale text-to-video synthesis task.", + "bbox": [ + 75, + 810, + 472, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Experimental Setups", + "text_level": 1, + "bbox": [ + 500, + 409, + 696, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct ablation experiments in a small-scale unconditional video generation setting and pick the best configuration for our large-scale text-to-video generation run.", + "bbox": [ + 498, + 431, + 895, + 478 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets We train our model on the UCF-101 dataset [50] for the small-scale experiments, where we follow the protocol defined in Ho et al. [17] to generate videos of size $16 \\times 64 \\times 64$ . UCF-101 dataset contains 13,320 videos. We randomly sample frames from these videos to train our image synthesis model. For our large-scale experiments, we use a combination of public and proprietary datasets for text-to-image and text-to-video finetuning. Most of the videos are of 2K resolution with 16:9 aspect ratio. All data was filtered using a preset CLIP and aesthetic scores* to ensure high quality. Our final image dataset contains around 1.2 billion text-image pairs and 22.5 million text-video pairs.", + "bbox": [ + 496, + 497, + 893, + 679 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training details In the unconditional generation experiment on the UCF-101 dataset, to do an ablation study on the model size, we design 3 models where each model has 69M, 112M, and 253M parameters, respectively. As a comparison, the baseline Video Diffusion Model (VDM) [17] contains 1.2B parameters. In the large-scale text-to-video experiment, our base and temporal interpolation models contain 1.08B parameters. Our super-resolution model adapted from the efficient U-Net [42] architecture with temporal convolution layers [14, 46] contains 313M parameters. Please refer to the supplementary material for more training details.", + "bbox": [ + 496, + 699, + 893, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "\\*https://github.com/christophschuhmann/ improved-aesthetic-predictor", + "bbox": [ + 500, + 875, + 823, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22934", + "bbox": [ + 478, + 924, + 517, + 936 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/be0d32f6c5261750250a55f4cff915a053e9259ad86489ddce09cc007e0763ed.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 89, + 277, + 241 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4b5f2ccad8a2a714b4777005a783956b00b8fe07cd922ddc9476fa3b96ba75c6.jpg", + "image_caption": [ + "An epic tornado attacking above a glowing city at night, the tornado is made of smoke, highly detailed." + ], + "image_footnote": [], + "bbox": [ + 277, + 89, + 473, + 241 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0b71e5432321661882bb8e9d07f88930204323a4e84990b34323694870a32f4e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 473, + 89, + 671, + 241 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7497cd615041a3013314d3ae02fc31c19b21ba4245c7efeae2c13dcc7ecf9e74.jpg", + "image_caption": [ + "A golden retriever puppy holding a green sign that says \"NVIDIA ROCKS\". Background is a classroom." + ], + "image_footnote": [], + "bbox": [ + 671, + 89, + 870, + 241 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/31f24d40b980ff0fc7922ccd7cfcbfe5b0d5a54f03b55e39df6481d82290aaca.jpg", + "image_caption": [ + "A cute corgi wearing a red robe holding a sign that says \"Merry Christmas\". There is a Christmas tree in the background." + ], + "image_footnote": [], + "bbox": [ + 80, + 308, + 276, + 460 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/181156bf69a3ac777b674dfabb451cac0bf126ed68722d49f6b63b74c54d733f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 308, + 473, + 460 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8f9a5a97c5cd51d09128de896bf9ded108cfd243c94a7f05c4a9a840b15e6ebf.jpg", + "image_caption": [ + "Small boat sailing in the ocean, giant Cthulhu monster coming out a dense mist in the background, giant waves attacking." + ], + "image_footnote": [], + "bbox": [ + 473, + 308, + 671, + 460 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a8e97061fcc21c77cd0c887851bf593e0b2b7dfd929be30c5adb3933145bc9a8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 671, + 308, + 870, + 460 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8962c3cab1893100cc256b523b53fa2604524a275958c2bb078790ce3e85c544.jpg", + "image_caption": [ + "A cute funny robot dancing, centered, award winning watercolor pen illustration.", + "A skull burning while being held up by a skeletal hand.", + "Figure 4: Sample generations. Please check our project website to view the videos." + ], + "image_footnote": [], + "bbox": [ + 80, + 512, + 277, + 662 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e7fd793e68cfa900bbc13500147bbcb8cac48b979f63a288ea6c2e2090c78b53.jpg", + "image_caption": [ + "A cartoon white wolf is giving puppy-dog eyes, detailed fur, very cute kid's film character.", + "A huge dinosaur skeleton walking in a golden wheat field on a bright sunny day." + ], + "image_footnote": [], + "bbox": [ + 277, + 511, + 473, + 662 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8f943694a9daad4968571f69c1d1f69ba8a562ee9e68557a56bed7b52081d8ff.jpg", + "image_caption": [ + "A lightning striking atop of eiffel tower, dark clouds in the sky, slow motion.", + "A cute rabbit is eating grass, wildlife photography." + ], + "image_footnote": [], + "bbox": [ + 473, + 511, + 671, + 662 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/de933d40c5692d4eb338a50bcf8966472a661d2ba6bdafedbe195396e20a70fa.jpg", + "image_caption": [ + "An anime girl looks at the beautiful nature through the window of a moving train, well rendered.", + "Tomato sauce pouring over fries." + ], + "image_footnote": [], + "bbox": [ + 671, + 511, + 870, + 662 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation For the small-scale experiments on UCF-101 dataset, we follow the protocol defined in the prior approaches [52, 47, 17] and report the Inception Score (IS) [44] calculated by a trained C3D model [53] and Fréchet Video Distance (FVD) [55] by a trained I3D model [6]. For the large-scale text-to-video experiments, we perform the zero-shot evaluation of the video generation quality on the UCF-101 and MSR-VTT datasets following Make-A-Video [46]. We carefully discuss the evaluation process below.", + "bbox": [ + 75, + 761, + 473, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "UCF-101 experiment We use IS and FVD for evaluation in our small-scale experiments. UCF-101 is a categorical video dataset designed for action recognition. When sampling from the text-to-video model, we devise a set of prompts for each class name to be used as the conditional input. This is necessary as some class names (such as jump rope) are not descriptive. We list all the prompts we use in the supplementary material. We sample 20 videos for each prompt to compute the IS metric. For FVD, we follow the", + "bbox": [ + 496, + 761, + 893, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22935", + "bbox": [ + 478, + 924, + 519, + 936 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/de325ac2e516572d7c1e70adc0f690a8cdaed82b24974216a2bf2eb5007c177f.jpg", + "table_caption": [ + "Table 2: Zero-shot text to video generation on UCF-101. Our approach gives significant performance gains compared to the prior baselines both in inception score and FVD metrics." + ], + "table_footnote": [], + "table_body": "
MethodIS (↑)FVD (↓)
CogVideo [18] (Chinese)23.55751.34
CogVideo [18] (English)25.27701.59
Make-A-Video [46]33.00367.23
MagicVideo [69]-655.00
Video LDM [4]33.45550.61
VideoFactory [59]-410.00
PYoCo47.76355.19
", + "bbox": [ + 120, + 138, + 426, + 276 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/98ef80e11a92ad26e3ddf3b139388c1b0c92e278f338771783a4c35a635f056f.jpg", + "table_caption": [ + "Table 3: Text conditional zero-shot generation on MSRVTT. Our approach with the base config achieves the best results, and using an ensemble further improves the FIDs." + ], + "table_footnote": [], + "table_body": "
MethodCLIP-FID (↓)FID (↓)
NUWA [60] (Chinese)47.68-
CogVideo [18] (Chinese)24.78-
CogVideo [18] (English)23.59-
Make-A-Video [46]13.17-
MagicVideo [69]-36.50
Latent-Shift [1]15.23-
PYoCo (Config-A)10.2125.39
PYoCo (Config-B)9.9524.28
PYoCo (Config-C)9.9124.54
PYoCo (Config-D)9.7322.14
", + "bbox": [ + 98, + 347, + 450, + 530 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "prior work [25, 52] and sample 2, 048 videos for evaluation.", + "bbox": [ + 75, + 556, + 470, + 571 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "MSR-VTT experiment MSR-VTT [62] test set contains 2,990 videos as well as 59,794 captions. All the videos have the same resolution of $320 \\times 240$ . We generate a $76 \\times 256 \\times 256$ video for each 59,794 caption and save the videos in an mp4 format with a high bit rate. To compare with Make-A-Video, we compute FID using a ViT-B/32 model [24]. We also report a more common FID metric computed by an Inception-V3 model. We also examine the idea of ensemble denoiser [2] by finetuning the level-1 experts of each model. We denote Config-A as the configuration of using only baseline models and Config-B to Config-D as incrementally changing super-resolution model, temporal interpolation model, and base model with the corresponding ensemble models.", + "bbox": [ + 75, + 593, + 470, + 803 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Main Results", + "text_level": 1, + "bbox": [ + 76, + 816, + 215, + 830 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Large-scale text-to-video synthesis We quantitatively compare our method against Make-A-Video [46], NUWA [60], CogVideo [18], and several concurrent works [4, 69, 4, 59, 1]. Table 2 shows that our method", + "bbox": [ + 75, + 839, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f62d1eeed007f3585f1e09ece8f1a1362f075440aaf56762c2188274607b354d.jpg", + "table_caption": [ + "Table 4: Unconditional UCF-101 generation results. Our approach achieves the state-of-the-art inception score and FVD, while having considerably smaller parameter count compared to other diffusion-based approaches such as VDM (1B parameters)." + ], + "table_footnote": [], + "table_body": "
MethodIS (↑)FVD (↓)
TGAN [43]15.83±.18-
LDVD-GAN [20]22.91±.19-
VideoGPT [63]24.69±.30-
MoCoGAN-HD [52]32.36838
DIGAN [66]29.71±.53655±22
CCVS [25]24.47±.13386±15
StyleGAN-V [47]23.94±.73-
VDM [17]57.00±.62-
TATS [9]57.63±.73430 ±18
PYoCo (112M)57.93±.24332 ±13
PYoCo (253M)60.01±.51310 ±13
", + "bbox": [ + 526, + 169, + 864, + 367 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "outperforms all the baselines on the UCF-101 dataset and improves the zero-shot Inception Score from 33.45 to 47.76. In Table 3, we show that our baseline model achieves a new state-of-the-art CLIP-FID score [24] of 10.21, while using ensemble models further improves both CLIP-FID and FID scores. In Figure 4, we qualitatively visualize the synthesis capability of our approach. Our model achieves high-quality zero-shot video synthesis capability with good photorealism and temporal coherency. We also provide a qualitative comparison with Make-A-Video [46] andImagen Video [14] in Figure 5. We observe that our model is able to produce videos with better details than both approaches, as shown in the animal videos. We also produce better-stylized videos thanImagen Video.", + "bbox": [ + 496, + 383, + 893, + 595 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Small-scale unconditional video synthesis We report IS and FVD scores on UCF-101 dataset in Table 4 and compare our model with multiple unconditional video generation baselines. Note that using class labels as conditional information could lead to sizeable improvement in IS and FVD scores [9], which we do not consider as the comparison. Our method attains state-of-the-art unconditional video generation quality. Compared with previous diffusion-based unconditional generation model [17], our model is $\\sim 10\\times$ smaller and has $\\sim 14\\times$ less training time (75 GPU-days vs. 925 GPU-days).", + "bbox": [ + 496, + 628, + 893, + 796 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 813, + 653, + 830 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We quantitatively compare several training strategies for video diffusion models. Then, we perform ablation on the correlation ratio in the Equations 3 and 4, a key hyperparameter in our approach.", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22936", + "bbox": [ + 478, + 924, + 519, + 936 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f6a0d29dd22ed069c738d632fc980df02d7577656b6e6bd19cd3796a56121db7.jpg", + "image_caption": [ + "Make-A-Video [46]" + ], + "image_footnote": [], + "bbox": [ + 80, + 104, + 251, + 237 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5df5207698abb05a05e378f80ce72886b6456c216ebda1f9d3b371c0e5609342.jpg", + "image_caption": [ + "PYoCo" + ], + "image_footnote": [], + "bbox": [ + 251, + 104, + 421, + 237 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/83d81abbfb238a9855453e259f275ebda3921ee15a564c7b3fb9f7db156e2345.jpg", + "image_caption": [ + "Imagen Video [14]" + ], + "image_footnote": [], + "bbox": [ + 426, + 104, + 709, + 237 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9ff683812bea89fc21a52045226a7b707e14228bab302290c9f1d4b390656de3.jpg", + "image_caption": [ + "PYoCo" + ], + "image_footnote": [], + "bbox": [ + 709, + 104, + 880, + 237 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/948ed773c9da2f0cccb1b0ded2fb2dbac6a3addc8835810020572224731d24f0.jpg", + "image_caption": [ + "A confused grizzly bear in calculus class." + ], + "image_footnote": [], + "bbox": [ + 80, + 257, + 250, + 388 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/250a4b80c2e0ad72e8ae4221f419e71914963a8b29b642054accdce2d7f86fd6.jpg", + "image_caption": [ + "Sailboat sailing on a sunny day in a mountainlake." + ], + "image_footnote": [], + "bbox": [ + 250, + 257, + 421, + 388 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2856d764a26c0dceff776c469c325eecabc2d37157d43553670cc7bc4a9a8161.jpg", + "image_caption": [ + "A sheep to the right of a wineglass.", + "A cat eating food out of a bowl, in style of Van Gogh." + ], + "image_footnote": [], + "bbox": [ + 426, + 257, + 709, + 388 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/05aba182271478008d147821594306e7c1e14e854c9c1fa92d32d525b402c841.jpg", + "image_caption": [ + "Figure 5: Qualitative comparison with baseline approaches. The two panels on the left show the comparison of our approach with Make-A-Video [46], while those on the right show the comparison withImagen Video [14]. PYoCo achieves better photorealism compared to the two approaches." + ], + "image_footnote": [], + "bbox": [ + 709, + 257, + 880, + 388 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b7e8a40bf3b433a6bb279667cea21e9ce3bc29e8fdbe343d7f1c35b135b3875f.jpg", + "table_caption": [ + "Table 5: Quantitative results of different training strategies on UCF-101 dataset." + ], + "table_footnote": [], + "table_body": "
IS(↑)FVD (↓)FID (↓)
Image Diffusion (ID)--30.05
Training from scratch28.25903.37124.75
Finetuning from ID41.25566.6756.43
+ Mixed Noise52.71337.4031.57
+ Progressive Noise53.52339.6731.88
", + "bbox": [ + 86, + 526, + 457, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Training strategies We compare training from scratch, a simple finetuning baseline, finetuning with mixed noising, and progressive noising using IS, FVD, and averaged frame FID metrics on the UCF-101 dataset in Table 5. We first find that finetuning from an image diffusion model is much more effective than training from scratch. For finetuning from the image model, the correlated noise model produces better video generation quality than the independent noise model. In addition, we notice that the correlated noise better preserves the image quality learned by the pretrained image model and produces a lower frame FID. This is particularly desired in large-scale text-to-video training to fulfill the goal of inheriting the knowledge from the image model missing in the video datasets. Specifically, most videos contain realistic scenes captured by cameras and have infrequent media types like paintings, illustrations, sketches, etc. Moreover, the", + "bbox": [ + 75, + 659, + 472, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "video data is much smaller in volume, and the scenes are less diverse than image datasets. As shown in Figure 4, our model can preserve properties learned from image datasets that are not presented in our video dataset, such as the artistic styles, and generate faithful motion on them.", + "bbox": [ + 496, + 493, + 892, + 569 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Correlation ratio The hyperparameter $\\alpha$ in the Equations 3 and 4 controls the correlation between the noise of different frames. A larger $\\alpha$ injects more correlation into the noise. The correlation disappears when $\\alpha \\rightarrow 0$ , and the mixed and progressive noise models reproduce the vanilla noise model. To find optimal $\\alpha$ , we train our UCF-small model (69M parameters) using $\\alpha \\in \\{0, 0.1, 0.2, 0.5, 1, 1, 2, 5, 10, \\infty\\}$ and report FVD in Figure 7. For each $\\alpha$ value, we repeat the experiment 3 times and report the mean. Note that $\\alpha = 0$ indicates finetuning with the independent frame noise, and $\\alpha = \\infty$ indicates using identical noise maps for all the frames, which produces frozen videos during the inference time. Finetuning an image diffusion model almost consistently outperforms the training-from-scratch baseline with different $\\alpha$ s. Using $\\alpha = 1$ for mixed noisng and $\\alpha = 2$ for progressive noisng produces similar best results. We also show qualitative results for models trained with $\\alpha = 0, 1, 10$ in Figure 6. When $\\alpha$ is too small, we notice a degradation in visual quality in the generated video frames and a reduced video diversity. For example, we notice many repeated samples and black borders in almost every video generated with", + "bbox": [ + 496, + 583, + 893, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22937", + "bbox": [ + 478, + 924, + 517, + 936 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/84043d9b5f0034b76c6835e2d4e087432971d2d22535d277eb4e1c20e2e5608a.jpg", + "image_caption": [ + "$\\alpha = 0$" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 344, + 292 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/999c099386c0fd284da43b5fb62b6ec5de5670e01424725f8869ea74c5d45ab6.jpg", + "image_caption": [ + "$\\alpha = 1$" + ], + "image_footnote": [], + "bbox": [ + 344, + 88, + 609, + 292 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/26e5b0e3adcaeb96a05393aada9def68b3f50bb8173fd43ac1a8b5ee7ec07265.jpg", + "image_caption": [ + "$\\alpha = 10$" + ], + "image_footnote": [], + "bbox": [ + 609, + 89, + 874, + 292 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/2e6035bc99550b824a6ea57ef45e3d24c183214050feafa286f4413540cd2415.jpg", + "image_caption": [ + "Figure 6: Visual ablation on $\\alpha$ . Small $\\alpha = 0$ reduces video quality and diversity and large $\\alpha = 10$ yields motion artifacts." + ], + "image_footnote": [], + "bbox": [ + 86, + 358, + 465, + 506 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "$\\alpha = 0$ . On the other hand, when $\\alpha$ is too large, the model has difficulty generating proper motions.", + "bbox": [ + 75, + 623, + 468, + 655 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Model size We pick the best $\\alpha$ for the mixed and progressive noise models and compare them with the model trained from scratch on models with different numbers of parameters, 69M, 112M, and 253M. Figure 8 shows that our mixed and progressive models outperform the baseline consistently by a large margin in terms of FVD. Overall, mixed and progressive noising provide similar performance. In our large large-scale experiments, we choose progressive noising with $\\alpha = 2$ due to its autoregressive nature.", + "bbox": [ + 75, + 676, + 470, + 813 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 829, + 194, + 844 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We proposed a new efficient way of training text-to-video generation models. By observing that the noise maps generating the frames of a video are clustered together, we study", + "bbox": [ + 75, + 854, + 470, + 901 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/0230cc56489705efdce7ccceeafb558d19fccf3188e8d60146c865c67f51f050.jpg", + "image_caption": [ + "Figure 7: Quantitative ablation on hyperparameter $\\alpha$ . Finetuning with temporally correlated prior improves over training from scratch. Using a too-large or too-small $\\alpha$ leads to inferior results. $\\alpha = 1$ , $\\alpha = 2$ each works the best for mixed and progressive noising, respectively.", + "Figure 8: Ablation on model size. Larger models consistently improve the performance of both finetuning and training from scratch. Finetuning from image model consistently outperforms training from scratch." + ], + "image_footnote": [], + "bbox": [ + 509, + 358, + 887, + 506 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "mixed and progressive noise priors well-suited for sequential video frame generation. We apply our progressive noise prior to finetuning a state-of-the-art diffusion-based text-to-image model to achieve a state-of-the-art large-scale text-to-video model. The high quality of the generated videos and the state-of-the-art Inception and FID scores demonstrate the strength of our approach.", + "bbox": [ + 496, + 611, + 890, + 717 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgment. We would like to thank Amanda Moran, John Dickinson, Sivakumar Arayandi Thottakara, David Page, Ranjitha Prasanna, Venkata Karri, and others in NGC and PBSS team for the computing infrastructure support. We also give thanks to Qinsheng Zhang, Zekun Hao, Tsung-Yi Lin, Ajay Jain, and Chen-Hsuan Lin for useful discussions and feedback. Thanks also go to Yin Xi and Thomas Hayes for clarifying the evaluation protocol of Make-A-Video and to Ming Ding for the details of CogVideo. We thank the ICCV PCs, ACs, and reviewers for their service and valuable feedback. This work is partly supported by NSF grants No. IIS-1910132 and IIS-2213335.", + "bbox": [ + 496, + 719, + 893, + 898 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "22938", + "bbox": [ + 478, + 924, + 517, + 936 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jie An, Songyang Zhang, Harry Yang, Sonal Gupta, Jia-Bin Huang, Jiebo Luo, and Xi Yin. 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Videofactory: Swap attention in spatiotemporal diffusions for text-to-video generation. arXiv preprint arXiv:2305.10874, 2023. 3, 7", + "[60] Chenfei Wu, Jian Liang, Lei Ji, Fan Yang, Yuejian Fang, Daxin Jiang, and Nan Duan. Nüwa: Visual synthesis pretraining for neural visual world creation. In ECCV, pages 720-736. Springer, 2022. 3, 4, 7" + ], + "bbox": [ + 501, + 92, + 893, + 900 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "22940", + "bbox": [ + 478, + 924, + 519, + 936 + ], + "page_idx": 10 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[61] Jay Zhangjie Wu, Yixiao Ge, Xintao Wang, Weixian Lei, Yuchao Gu, Wynne Hsu, Ying Shan, Xiaohu Qie, and Mike Zheng Shou. Tune-a-video: One-shot tuning of image diffusion models for text-to-video generation. arXiv preprint arXiv:2212.11565, 2022.3", + "[62] Jun Xu, Tao Mei, Ting Yao, and Yong Rui. Msr-vtt: A large video description dataset for bridging video and language. In CVPR, 2016. 7", + "[63] Wilson Yan, Yunzhi Zhang, Pieter Abbeel, and Aravind Srinivas. Videogpt: Video generation using vq-vae and transformers. arXiv preprint arXiv:2104.10157, 2021. 3, 7", + "[64] Ruihan Yang, Prakhar Srivastava, and Stephan Mandt. Diffusion probabilistic modeling for video generation. arXiv preprint arXiv:2203.09481, 2022. 3", + "[65] Lijun Yu, Yong Cheng, Kihyuk Sohn, José Lezama, Han Zhang, Huiwen Chang, Alexander G Hauptmann, Ming-Hsuan Yang, Yuan Hao, Irfan Essa, et al. Magvit: Masked generative video transformer. arXiv preprint arXiv:2212.05199, 2022.3", + "[66] Sihyun Yu, Jihoon Tack, Sangwoo Mo, Hyunsu Kim, Junho Kim, Jung-Woo Ha, and Jinwoo Shin. Generating videos with dynamics-aware implicit generative adversarial networks. In ICLR, 2021. 3, 7", + "[67] Lvmin Zhang and Maneesh Agrawala. Adding conditional control to text-to-image diffusion models. arXiv preprint arXiv:2302.05543, 2023. 1, 3", + "[68] Qinsheng Zhang and Yongxin Chen. Fast sampling of diffusion models with exponential integrator. In ICLR, 2023. 4", + "[69] Daquan Zhou, Weimin Wang, Hanshu Yan, Weiwei Lv, Yizhe Zhu, and Jiashi Feng. Magicvideo: Efficient video generation with latent diffusion models. arXiv preprint arXiv:2211.11018, 2022. 2, 3, 7" + ], + "bbox": [ + 78, + 90, + 470, + 558 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "22941", + "bbox": [ + 478, + 924, + 517, + 936 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Preserve Your Own Correlation_ A Noise Prior for Video Diffusion Models/12c6fb66-a455-4547-8b5a-4a378b5ee51f_model.json b/2023/Preserve Your Own Correlation_ A Noise Prior for Video Diffusion Models/12c6fb66-a455-4547-8b5a-4a378b5ee51f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ec69df132fa4aa401354c2a35740e57742abda7a --- /dev/null +++ b/2023/Preserve Your Own Correlation_ A Noise Prior for Video Diffusion Models/12c6fb66-a455-4547-8b5a-4a378b5ee51f_model.json @@ -0,0 +1,2820 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.11, + 0.131, + 0.862, + 0.152 + ], + "angle": 0, + "content": "Preserve Your Own Correlation: A Noise Prior for Video Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.138, + 0.182, + 0.245, + 0.199 + ], + "angle": 0, + "content": "Songwei Ge*" + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.202, + 0.259, + 0.216 + ], + "angle": 0, + "content": "University of Maryland" + }, + { + "type": "text", + "bbox": [ + 0.299, + 0.182, + 0.414, + 0.216 + ], + "angle": 0, + "content": "Seungjun Nah \nNVIDIA" + }, + { + "type": "text", + "bbox": [ + 0.455, + 0.182, + 0.54, + 0.216 + ], + "angle": 0, + "content": "Guilin Liu NVIDIA" + }, + { + "type": "text", + "bbox": [ + 0.603, + 0.182, + 0.692, + 0.199 + ], + "angle": 0, + "content": "Tyler Poon" + }, + { + "type": "text", + "bbox": [ + 0.581, + 0.202, + 0.713, + 0.216 + ], + "angle": 0, + "content": "University of Chicago" + }, + { + "type": "text", + "bbox": [ + 0.754, + 0.182, + 0.854, + 0.216 + ], + "angle": 0, + "content": "Andrew Tao NVIDIA" + }, + { + "type": "text", + "bbox": [ + 0.095, + 0.243, + 0.23, + 0.259 + ], + "angle": 0, + "content": "Bryan Catanzaro" + }, + { + "type": "text", + "bbox": [ + 0.134, + 0.263, + 0.19, + 0.276 + ], + "angle": 0, + "content": "NVIDIA" + }, + { + "type": "text", + "bbox": [ + 0.283, + 0.243, + 0.39, + 0.258 + ], + "angle": 0, + "content": "David Jacobs" + }, + { + "type": "text", + "bbox": [ + 0.266, + 0.263, + 0.407, + 0.277 + ], + "angle": 0, + "content": "University of Maryland" + }, + { + "type": "text", + "bbox": [ + 0.455, + 0.243, + 0.573, + 0.26 + ], + "angle": 0, + "content": "Jia-Bin Huang" + }, + { + "type": "text", + "bbox": [ + 0.445, + 0.263, + 0.585, + 0.277 + ], + "angle": 0, + "content": "University of Maryland" + }, + { + "type": "text", + "bbox": [ + 0.622, + 0.243, + 0.727, + 0.26 + ], + "angle": 0, + "content": "Ming-Yu Liu" + }, + { + "type": "text", + "bbox": [ + 0.647, + 0.263, + 0.702, + 0.276 + ], + "angle": 0, + "content": "NVIDIA" + }, + { + "type": "text", + "bbox": [ + 0.765, + 0.243, + 0.876, + 0.26 + ], + "angle": 0, + "content": "Yogesh Balaji" + }, + { + "type": "text", + "bbox": [ + 0.793, + 0.263, + 0.848, + 0.275 + ], + "angle": 0, + "content": "NVIDIA" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.513, + 0.342, + 0.556 + ], + "angle": 0, + "content": "A very happy fuzzy panda dressed as a chef eating pizza in the New York street food truck." + }, + { + "type": "text", + "bbox": [ + 0.349, + 0.521, + 0.611, + 0.55 + ], + "angle": 0, + "content": "The supernova explosion of a white dwarf in the universe, photo realistic." + }, + { + "type": "text", + "bbox": [ + 0.619, + 0.514, + 0.884, + 0.557 + ], + "angle": 0, + "content": "A high-quality 3D render of hyperrealist, super strong, multicolor stripped, and fluffy bear with wings, highly detailed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.893, + 0.599 + ], + "angle": 0, + "content": "Figure 1: Given a text description, our approach can faithfully generate videos that are consistent with the input text while being photorealistic and temporally consistent. Best viewed with Acrobat Reader. Click the images to play the video clips." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.617, + 0.314, + 0.633 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.649, + 0.474, + 0.876 + ], + "angle": 0, + "content": "Despite tremendous progress in generating high-quality images using diffusion models, synthesizing a sequence of animated frames that are both photorealistic and temporally coherent is still in its infancy. While off-the-shelf billion-scale datasets for image generation are available, collecting similar video data of the same scale is still challenging. Also, training a video diffusion model is computationally much more expensive than its image counterpart. In this work, we explore finetuning a pretrained image diffusion model with video data as a practical solution for the video synthesis task. We find that naively extending the image noise prior to video noise prior in video diffusion leads to sub-optimal performance. Our carefully designed video noise prior leads to substantially better performance. Extensive experimental validation shows that our" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.618, + 0.895, + 0.725 + ], + "angle": 0, + "content": "model, Preserve Your Own COrelation (PYoCo), attains SOTA zero-shot text-to-video results on the UCF-101 and MSR-VTT benchmarks. It also achieves SOTA video generation quality on the small-scale UCF-101 benchmark with a \\(10 \\times\\) smaller model using significantly less computation than the prior art. The project page is available at https://research.nvidia.com/labs/dir/pyoco/." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.755, + 0.631, + 0.77 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Large-scale diffusion-based text-to-image models [38, 42, 2] have demonstrated impressive capabilities in turning complex text descriptions into photorealistic images. They can generate images with novel concepts unseen during training. Sophisticated image editing and processing tasks can easily be accomplished through guidance control and embedding techniques. Due to the immense success in several applications [30, 67, 5], these models are established as pow-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.337, + 0.9 + ], + "angle": 0, + "content": "*Work done during an internship at NVIDIA." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.925, + 0.521, + 0.937 + ], + "angle": 0, + "content": "22930" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.079, + 0.088, + 0.526, + 0.274 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.289, + 0.281, + 0.308, + 0.294 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.589, + 0.094, + 0.88, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.724, + 0.281, + 0.744, + 0.293 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.306, + 0.895, + 0.457 + ], + "angle": 0, + "content": "Figure 2: Visualizing the noise map correlations. (a) visualizes the t-SNE plot of the noise maps corresponding to input frames randomly sampled from videos. These noise maps are obtained by running a diffusion ODE [49, 48] on the input frames using a trained text-to-image model, but in the opposite direction of image synthesis (\\(\\sigma : 0 \\to \\sigma_{\\max}\\)). The green dots in the background denote the reference noise maps sampled from an i.i.d. Gaussian distribution. The red dots and yellow dots are noise maps corresponding to input frames coming from different videos. We found they are spread out and share no correlation. On the other hand, the noise maps corresponding to the frames coming from the same video (shown in blue dots) are clustered together. (b) Using an i.i.d. noise model (orange dots) for finetuning text-to-image models for video synthesis is not ideal since temporal correlations between frames are not modeled. To remedy this, we propose a progressive noise model in which the correlation between different noise maps is injected along the temporal axis. Our progressive noise model (blue dots) aptly models the correlations present in the video noise maps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.484, + 0.471, + 0.559 + ], + "angle": 0, + "content": "erful image synthesis tools for content generation. As image synthesis is largely democratized with the success of these text-to-image models, it is natural to ask whether we can repeat the same success in video synthesis with large-scale diffusion-based text-to-video models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.564, + 0.471, + 0.837 + ], + "angle": 0, + "content": "Multiple attempts have been made to build large-scale video diffusion models. Ho et al. [17] proposed a UNet-based architecture for the video synthesis task that is trained using joint image-video denoising losses.Imagen video [14] extends the cascaded text-to-image generation architecture ofImagen [42] for video generation. In both works, the authors directly train a video generation model from scratch. While these approaches achieve great success and produce high-quality videos, they are inherently expensive to train, requiring hundreds of high-end GPUs or TPU's and several weeks of training. After all, video generators not only need to learn to form individual images but should also learn to synthesize coherent temporal dynamics, which makes the video generation task much more challenging. While the formation of individual frames is a shared component in an image and video synthesis, these works disregard the existence of powerful pretrained text-to-image diffusion models and train their video generators from scratch." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "We explore a different avenue for building large-scale text-to-video diffusion models by starting with a pretrained text-to-image diffusion model. Our motivation is that most of the components learned for the image synthesis task can" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.484, + 0.895, + 0.817 + ], + "angle": 0, + "content": "effectively be reused for video generation, leading to knowledge transfer and efficient training. A similar idea is adopted by several recent works [46, 69, 4]. Without exception, when finetuning, they naively extend the image diffusion noise prior (i.i.d. noise) used in the text-to-image model to a video diffusion noise prior by adding an extra dimension to the 2D noise map. We argue that this approach is not ideal as it does not utilize the natural correlations in videos that are already learned by the image models. This is illustrated in Figure 2, where we visualize the t-SNE plot of noise maps corresponding to different input frames as obtained from a pretrained text-to-image diffusion model. The noise maps corresponding to different frames coming from the same video (blue dots in Figure 2a are clustered together, exhibiting a high degree of correlation. The use of i.i.d. noise prior does not model this correlation, which would impede the finetuning process. Our careful analysis of the video diffusion noise prior leads us to a noise prior that is better tailored for finetuning an image synthesis model to the video generation task. As illustrated in Figure 2b, our proposed noise prior (shown in blue dots) aptly captures the correlations in noise maps corresponding to video frames." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.897, + 0.903 + ], + "angle": 0, + "content": "We then proceed to build a large-scale diffusion-based text-to-video model. We leverage several design choices from the prior works, including the use of temporal attention [17], joint image-video finetuning [17], a cascaded generation architecture [14], and an ensemble of expert denois-" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.518, + 0.937 + ], + "angle": 0, + "content": "22931" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.182 + ], + "angle": 0, + "content": "ers [2]. Together with these techniques and the proposed video noise prior, our model establishes a new state-of-the-art for video generation outperforming competing methods on several benchmark datasets. Figure 1 shows our model can achieve high-quality zero-shot video synthesis capability with SOTA photorealism and temporal consistency." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.183, + 0.47, + 0.197 + ], + "angle": 0, + "content": "In short, our work makes the following key contributions." + }, + { + "type": "text", + "bbox": [ + 0.071, + 0.207, + 0.469, + 0.236 + ], + "angle": 0, + "content": "1. We propose a video diffusion noise tailored for finetuning text-to-image diffusion models for text-to-video." + }, + { + "type": "text", + "bbox": [ + 0.071, + 0.242, + 0.469, + 0.272 + ], + "angle": 0, + "content": "2. We conduct extensive experimental validation and verify the effectiveness of the proposed noise prior." + }, + { + "type": "text", + "bbox": [ + 0.071, + 0.276, + 0.469, + 0.32 + ], + "angle": 0, + "content": "3. We build a large-scale text-to-video diffusion model by finetuning a pretrained eDiff-I model with our noise prior and achieve state-of-the-art results on several benchmarks." + }, + { + "type": "list", + "bbox": [ + 0.071, + 0.207, + 0.469, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.332, + 0.219, + 0.347 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.358, + 0.47, + 0.599 + ], + "angle": 0, + "content": "Diffusion-based text-to-image models: Diffusion models have significantly advanced the progress of text-based photorealistic, compositional image generation [38, 42]. Given the nature of the iterative denoising process that requires massive numbers of score function evaluations, earlier diffusion models focused on generating low-resolution images, e.g., \\(64 \\times 64\\) [15, 48]. To generate high-resolution images, two common approaches have been used. The first approach applies cascaded super-resolution models in the RGB space [32, 16, 42, 38], while the second approach leverages a decoder to exploit latent space [40, 11]. Based on these models, advanced image and video editing have been achieved through finetuning the model [41, 67, 5, 23, 61, 29] or controlling the inference process [30, 13, 34, 10, 35, 7, 31, 3]. Here, we study the problem of using large-scale diffusion models for text-to-video generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Video generation models: Generating realistic and novel videos have long been an attractive and essential research direction [58, 39, 65]. Previously studies have resorted to different types of generative models such as GANs [58, 43, 54, 52, 45], Autoregressive models [51, 63, 25, 9, 18], and implicit neural representations [47, 66]. Recently, driven by the tremendous success of applying the diffusion model to image synthesis, multiple works have proposed to explore diffusion models for conditional and unconditional video synthesis [57, 12, 69, 61, 4, 22, 19, 57, 64, 33, 28, 1, 59]. For example, Singer et al. extend the unCLIP framework [38] to text-to-video generation, which allows training without video captions [46]. Ho et al. [17] extend the Imagen framework [42] by repeatedly up-scaling low-resolution small-fps videos in both spatial and temporal directions with multiple models [14]. Our work also falls into this line of work which uses a diffusion model. We focus on augmenting an image diffusion model for video and study the design choice of the diffusion noise priors for such an image-to-video finetuning task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.394 + ], + "angle": 0, + "content": "Leverage knowledge from images for text-to-video generation: Like text-to-image models, text-to-video models require massive amounts of data to learn caption-relatedness, frame photorealism, and temporal dynamics. But in contrast to the abundant image data resource, video data are more limited in style, volume, and quality. To resolve such scarcity issue of text-video data, previous works have resorted to different strategies to leverage knowledge from image data for text-to-video generation, including joint training on the text-image data from scratch [17, 14, 56, 60], first training a text-to-image model and then finetuning partially [18, 4, 61, 29] or entirely [46, 8] on the video dataset, and using CLIP image features as the conditional information [46, 69]. In this paper, we propose a new video diffusion noise prior that is tailored for finetuning a pretrained diffusion-based image generation model for the video generation task. We reuse several design choices in the prior work by finetuning jointly on text-image and text-video datasets. As a result, we can build a text-to-video generation system that achieves state-of-the-art zero-shot performances." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.41, + 0.638, + 0.426 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.436, + 0.894, + 0.587 + ], + "angle": 0, + "content": "Diffusion models generate data by iteratively denoising samples drawn from a noise distribution. In the case of text-to-video models, text embeddings obtained from a pre-trained text encoder are used as additional inputs in the denoising process. Formally, let \\( D(\\mathbf{x}, \\mathbf{e}, \\sigma) \\) denote a denoising network that operates on the noisy input video \\( \\mathbf{x} \\in \\mathbb{R}^{b \\times n_s \\times 3 \\times h \\times w} \\) where \\( \\mathbf{e} \\) is the text embedding, and \\( \\sigma \\) is the noise level. Here \\( n_s \\) is the sequence length of the input video, \\( b \\) is the batch size, and \\( h \\times w \\) is the spatial resolution. The model \\( D \\) is trained to denoise the input \\( \\mathbf{x} \\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.61, + 0.894, + 0.641 + ], + "angle": 0, + "content": "Training We follow the EDM formulation of Karras et al. [21] to optimize the denoiser \\( D \\) using the following objective" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.653, + 0.892, + 0.705 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbb {E} _ {p _ {\\text {d a t a}} (\\mathbf {x} _ {\\text {c l e a n}}, \\mathbf {e}), p (\\epsilon), p (\\sigma)} \\left[ \\lambda (\\sigma) \\| D \\left(\\mathbf {x} _ {\\text {n o i s e}}; \\mathbf {e}, \\sigma\\right) - \\mathbf {x} _ {\\text {c l e a n}} \\| _ {2} ^ {2} \\right] \\tag {1} \\\\ w h e r e \\quad \\mathbf {x} _ {\\text {n o i s e}} = \\mathbf {x} _ {\\text {c l e a n}} + \\sigma \\epsilon \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.894, + 0.854 + ], + "angle": 0, + "content": "Here, \\(\\mathbf{x}_{\\mathrm{noise}}\\) is the noisy sample obtained by corrupting the clean video \\(\\mathbf{x}\\) with noise \\(\\sigma \\epsilon\\), where \\(p(\\epsilon) = \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) and \\(\\sigma\\) is a scalar for the noise level drawn from \\(p(\\sigma)\\). The loss weight, \\(\\lambda (\\sigma)\\), is a function of \\(\\sigma\\) given by \\(\\lambda (\\sigma) = (\\sigma^2 +\\sigma_{\\mathrm{data}}^2) / (\\sigma \\cdot \\sigma_{\\mathrm{data}})^2\\). Eq. (1) is a simple denoising objective in which the denoiser \\(D\\) is trained to estimate the clean video \\(\\mathbf{x}_{\\mathrm{clean}}\\) from the noisy input \\(\\mathbf{x}_{\\mathrm{noise}}\\). Following EDM, we use a log-normal distribution for \\(\\sigma\\) i.e., \\(\\ln (p(\\sigma)) = \\mathcal{N}(P_{\\mathrm{mean}},P_{\\mathrm{std}}^2)\\) with \\(P_{\\mathrm{mean}} = -1.2\\) and \\(P_{\\mathrm{std}} = 1.2\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To train the denoising model, EDM uses preconditioning terms in its objective function to properly scale the inputs and output of the denoiser model \\( D \\). More specifically, the" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "22932" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.294, + 0.106 + ], + "angle": 0, + "content": "denoising model \\(D\\) is written as" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.117, + 0.452, + 0.149 + ], + "angle": 0, + "content": "\\[\nD (\\mathbf {x}; \\mathbf {e}, \\sigma) := \\left(\\frac {\\sigma_ {\\mathrm {d a t a}}}{\\sigma^ {*}}\\right) ^ {2} \\mathbf {x} + \\frac {\\sigma \\cdot \\sigma_ {\\mathrm {d a t a}}}{\\sigma^ {*}} F _ {\\theta} \\left(\\frac {\\mathbf {x}}{\\sigma^ {*}}; \\mathbf {e}, \\frac {\\ln (\\sigma)}{4}\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.157, + 0.47, + 0.189 + ], + "angle": 0, + "content": "Here, \\( F_{\\theta} \\) is a neural network with parameters \\( \\theta \\) and \\( \\sigma^{*} = \\sqrt{\\sigma^{2} + \\sigma_{\\mathrm{data}}^{2}} \\). We use \\( \\sigma_{\\mathrm{data}} = 0.5 \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.206, + 0.47, + 0.236 + ], + "angle": 0, + "content": "Sampling Once the denoising model is trained, sampling can be performed by solving the following ODE [21]" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.245, + 0.47, + 0.277 + ], + "angle": 0, + "content": "\\[\n\\frac {d \\mathbf {x}}{d \\sigma} = - \\sigma \\nabla_ {\\mathbf {x}} \\log p (\\mathbf {x} | \\mathbf {e}, \\sigma) = \\frac {\\mathbf {x} - D (\\mathbf {x} ; \\mathbf {e} , \\sigma)}{\\sigma} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.286, + 0.471, + 0.391 + ], + "angle": 0, + "content": "for \\(\\sigma\\) flowing backwards from \\(\\sigma = \\sigma_{\\mathrm{max}}\\) to \\(\\sigma = 0\\). The initial value for \\(\\mathbf{x}\\) is obtained by sampling from the prior distribution \\(\\mathbf{x} \\sim \\mathcal{N}(\\mathbf{0}, \\sigma_{\\mathrm{max}}^2 \\mathbf{I})\\). Over the recent years, several samplers have been proposed for sampling from the trained diffusion models [68, 48, 26, 27, 15]. In this paper, we use DEIS [68] and its stochastic variant [21] for synthesizing samples from our model." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.404, + 0.169, + 0.42 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.473, + 0.673 + ], + "angle": 0, + "content": "Training text-to-video models is much more challenging than training text-to-image diffusion models due to practical difficulties in collecting billion-scale video datasets and securing enough computational resources. Additionally, generating videos is much more challenging since individual frames need to be both photorealistic and temporally coherent. Prior works leverage large-scale image datasets to mitigate these difficulties by either joint training on the image datasets [60, 17, 14] or finetuning a text-to-image model on the video datasets [18, 46]. Here, we are interested in finetuning text-to-image diffusion models jointly on image and video datasets. We postulate that naively extending the image noise prior to video diffusion is not ideal. We carefully explore the design space of noise priors and propose one that is well suited for our video finetuning task, which leads to significant performance gains." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Correlated noise model An image diffusion model is trained to denoise independent noise from a perturbed image. The noise vector \\(\\epsilon\\) in the denoising objective (1) is sampled from an i.i.d. Gaussian distribution \\(\\epsilon \\sim \\mathcal{N}(0, \\mathbf{I})\\). However, after training the image diffusion model and applying it to reverse real frames from a video into the noise space in a per-frame manner, we find that the noise maps corresponding to different frames are highly correlated. This is illustrated in Figure 2, where the t-SNE plot of noise maps corresponding to different video frames are plotted. When the input frames come from the same video (shown in blue dots in Figure 2a, noise maps are clustered. The use of i.i.d. sampling (shown in orange dots in Figure 2b does not capture these correlations. This is also depicted quantitatively" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.089, + 0.894, + 0.15 + ], + "angle": 0, + "content": "Table 1: Cosine similarity of the reversed noise. The noise maps corresponding to the frames sampled from the same videos have a higher similarity than those sampled from different videos." + }, + { + "type": "table", + "bbox": [ + 0.53, + 0.155, + 0.864, + 0.217 + ], + "angle": 0, + "content": "
Cosine Similarity
(a) Same video noise0.206±0.156
(b) Different video noise0.001±0.009
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.238, + 0.895, + 0.403 + ], + "angle": 0, + "content": "in Table 1 where we compute the average pairwise cosine similarity between noise corresponding to (a) same video and (b) different video. (a) is much higher than (b). As a result, the video diffusion model trained with i.i.d. noise is coerced to forget such correlation among the noise between different frames, making it difficult to preserve knowledge from the image diffusion model. Motivated by this observation, we propose to modify the noise process to preserve the correlation between different frames. To this end, we investigate two noisng strategies - mixed and progressive noising." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.404, + 0.895, + 0.509 + ], + "angle": 0, + "content": "Mixed noise model: Let \\(\\epsilon^1, \\epsilon^2, \\ldots, \\epsilon^{n_s}\\) denote the noise corresponding to individual video frames i.e., \\(\\epsilon^i\\) corresponds to the \\(i^{th}\\) element of the noise tensor \\(\\epsilon\\). In the mixed noise model, we generate two noise vectors \\(\\epsilon_{\\mathrm{shared}}\\) and \\(\\epsilon_{\\mathrm{ind}}\\). \\(\\epsilon_{\\mathrm{shared}}\\) is a common noise vector shared among all video frames, while \\(\\epsilon_{\\mathrm{ind}}\\) is the individual noise per frame. The linear combination of both these vectors is used as the final noise." + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.513, + 0.894, + 0.567 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\epsilon_ {\\text {s h a r e d}} \\sim \\mathcal {N} \\left(\\mathbf {0}, \\frac {\\alpha^ {2}}{1 + \\alpha^ {2}} \\mathbf {I}\\right), \\epsilon_ {\\text {i n d}} ^ {i} \\sim \\mathcal {N} \\left(\\mathbf {0}, \\frac {1}{1 + \\alpha^ {2}} \\mathbf {I}\\right) \\tag {3} \\\\ \\epsilon^ {i} = \\epsilon_ {\\mathrm {s h a r e d}} + \\epsilon_ {\\mathrm {i n d}} ^ {i} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.573, + 0.894, + 0.664 + ], + "angle": 0, + "content": "Progressive noise model: In the progressive noise model, the noise for each frame is generated in an autoregressive fashion in which the noise at frame \\( i \\) is generated by perturbing the noise at frame \\( i - 1 \\). Let \\( \\epsilon_{\\mathrm{ind}}^i \\) denote the independent noise generated for frame \\( i \\). Then, progressive noising can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.569, + 0.669, + 0.894, + 0.7 + ], + "angle": 0, + "content": "\\[\n\\epsilon^ {0} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}) \\quad \\epsilon_ {\\mathrm {i n d}} ^ {i} \\sim \\mathcal {N} (\\mathbf {0}, \\frac {1}{1 + \\alpha^ {2}} \\mathbf {I}) \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.63, + 0.701, + 0.804, + 0.731 + ], + "angle": 0, + "content": "\\[\n\\epsilon^ {i} = \\frac {\\alpha}{\\sqrt {1 + \\alpha^ {2}}} \\epsilon^ {i - 1} + \\epsilon_ {\\mathrm {i n d}} ^ {i}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.894, + 0.825 + ], + "angle": 0, + "content": "In both these models, \\(\\alpha\\) controls how much noise is shared among different video frames. The higher the value of \\(\\alpha\\), the more correlation exists among the noise maps corresponding to different frames. As \\(\\alpha \\rightarrow \\infty\\), all frames would have the same noise which results in generating a frozen video. On the other hand, \\(\\alpha = 0\\) corresponds to i.i.d. noise." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.901 + ], + "angle": 0, + "content": "As shown in Figure 2b, the use of progressive noise sampling (blue dots) better models the correlations between different noise maps by obtaining similar clustering patterns to the noise maps of real video frames embedded by a pretrained text-to-image model in Figure 2a (blue dots)." + }, + { + "type": "footer", + "bbox": [ + 0.479, + 0.925, + 0.521, + 0.937 + ], + "angle": 0, + "content": "22933" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.895, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.314, + 0.896, + 0.391 + ], + "angle": 0, + "content": "Figure 3: Model architecture. Our pipeline consists of a cascade of four networks — a base model and three upsampling models. All four models take inputs as the text embeddings obtained from the T5 encoder and the CLIP text encoder. The base model produces 16 video frames of spatial resolution \\(64 \\times 64\\) with a frameskip of 5. The first upsampling model performs a temporal interpolation, resulting in videos of size \\(76 \\times 64 \\times 64\\) while the subsequent two super-resolution models perform spatial super-resolution to produce videos of sizes \\(76 \\times 256 \\times 256\\) and \\(76 \\times 1024 \\times 1024\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.473, + 0.667 + ], + "angle": 0, + "content": "Model architecture As visualized in Figure 3, our model consists of a cascade of four networks — a base network and three upsampling stacks. The base network generates an output video of dimension \\(16 \\times 64 \\times 64\\) with a frameskip of 5. It generates the frames \\(\\{1,6,11,\\ldots,76\\}\\). The first upsampling network performs a temporal interpolation to produce a video of size \\(76 \\times 64 \\times 64\\). The second and the third super-resolution network performs spatial upsampling to produce the outputs of sizes \\(76 \\times 256 \\times 256\\) and \\(76 \\times 1024 \\times 1024\\). We utilize eDiff-I [2], a state-of-the-art text-to-image diffusion model, to initialize our base and spatial super-resolution models. Similar to prior works [17, 46], we adapt the image-based U-Net model for the video synthesis task by making the following changes: (1) Transforming 2D convolutions to 3D by adding a dimension 1 to temporal axis and (2) Adding temporal attention layers. Please refer to the supplementary material for more details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.667, + 0.472, + 0.773 + ], + "angle": 0, + "content": "Similar to Ho et al. [17], we jointly finetune the model on video and image datasets by concatenating videos and images in the temporal axis and applying our temporal modules only on the video part. Similarly to eDiff-I, our model uses both T5 text embeddings [37] and CLIP text embeddings [36]. We drop each of the embeddings independently at random during training, as in eDiff-I." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.785, + 0.21, + 0.803 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.473, + 0.902 + ], + "angle": 0, + "content": "In this section, we evaluate our proposed strategy of training diffusion models for video synthesis on two sets of experiments. We first comprehensively analyze our proposed noise model on the small-scale UCF-101 dataset. We then scale up our experiments to the challenging large-scale text-to-video synthesis task." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.41, + 0.697, + 0.426 + ], + "angle": 0, + "content": "5.1. Experimental Setups" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.433, + 0.896, + 0.479 + ], + "angle": 0, + "content": "We conduct ablation experiments in a small-scale unconditional video generation setting and pick the best configuration for our large-scale text-to-video generation run." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.498, + 0.895, + 0.68 + ], + "angle": 0, + "content": "Datasets We train our model on the UCF-101 dataset [50] for the small-scale experiments, where we follow the protocol defined in Ho et al. [17] to generate videos of size \\( 16 \\times 64 \\times 64 \\). UCF-101 dataset contains 13,320 videos. We randomly sample frames from these videos to train our image synthesis model. For our large-scale experiments, we use a combination of public and proprietary datasets for text-to-image and text-to-video finetuning. Most of the videos are of 2K resolution with 16:9 aspect ratio. All data was filtered using a preset CLIP and aesthetic scores* to ensure high quality. Our final image dataset contains around 1.2 billion text-image pairs and 22.5 million text-video pairs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.895, + 0.867 + ], + "angle": 0, + "content": "Training details In the unconditional generation experiment on the UCF-101 dataset, to do an ablation study on the model size, we design 3 models where each model has 69M, 112M, and 253M parameters, respectively. As a comparison, the baseline Video Diffusion Model (VDM) [17] contains 1.2B parameters. In the large-scale text-to-video experiment, our base and temporal interpolation models contain 1.08B parameters. Our super-resolution model adapted from the efficient U-Net [42] architecture with temporal convolution layers [14, 46] contains 313M parameters. Please refer to the supplementary material for more training details." + }, + { + "type": "page_footnote", + "bbox": [ + 0.501, + 0.876, + 0.825, + 0.901 + ], + "angle": 0, + "content": "\\*https://github.com/christophschuhmann/ improved-aesthetic-predictor" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "22934" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.278, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.248, + 0.274, + 0.307 + ], + "angle": 0, + "content": "A cute corgi wearing a red robe holding a sign that says \"Merry Christmas\". There is a Christmas tree in the background." + }, + { + "type": "image", + "bbox": [ + 0.279, + 0.09, + 0.475, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.279, + 0.248, + 0.474, + 0.306 + ], + "angle": 0, + "content": "An epic tornado attacking above a glowing city at night, the tornado is made of smoke, highly detailed." + }, + { + "type": "image", + "bbox": [ + 0.475, + 0.09, + 0.673, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.479, + 0.248, + 0.675, + 0.307 + ], + "angle": 0, + "content": "Small boat sailing in the ocean, giant Cthulhu monster coming out a dense mist in the background, giant waves attacking." + }, + { + "type": "image", + "bbox": [ + 0.673, + 0.09, + 0.871, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.68, + 0.248, + 0.876, + 0.306 + ], + "angle": 0, + "content": "A golden retriever puppy holding a green sign that says \"NVIDIA ROCKS\". Background is a classroom." + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.309, + 0.277, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.467, + 0.273, + 0.51 + ], + "angle": 0, + "content": "A cute funny robot dancing, centered, award winning watercolor pen illustration." + }, + { + "type": "image", + "bbox": [ + 0.279, + 0.309, + 0.475, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.28, + 0.467, + 0.475, + 0.51 + ], + "angle": 0, + "content": "A cartoon white wolf is giving puppy-dog eyes, detailed fur, very cute kid's film character." + }, + { + "type": "image", + "bbox": [ + 0.475, + 0.309, + 0.673, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.479, + 0.467, + 0.676, + 0.509 + ], + "angle": 0, + "content": "A lightning striking atop of eiffel tower, dark clouds in the sky, slow motion." + }, + { + "type": "image", + "bbox": [ + 0.673, + 0.309, + 0.871, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.68, + 0.467, + 0.876, + 0.51 + ], + "angle": 0, + "content": "An anime girl looks at the beautiful nature through the window of a moving train, well rendered." + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.513, + 0.278, + 0.664 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.678, + 0.273, + 0.707 + ], + "angle": 0, + "content": "A skull burning while being held up by a skeletal hand." + }, + { + "type": "image", + "bbox": [ + 0.279, + 0.512, + 0.475, + 0.664 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.28, + 0.671, + 0.475, + 0.714 + ], + "angle": 0, + "content": "A huge dinosaur skeleton walking in a golden wheat field on a bright sunny day." + }, + { + "type": "image", + "bbox": [ + 0.475, + 0.512, + 0.673, + 0.664 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.48, + 0.678, + 0.675, + 0.707 + ], + "angle": 0, + "content": "A cute rabbit is eating grass, wildlife photography." + }, + { + "type": "image", + "bbox": [ + 0.673, + 0.512, + 0.871, + 0.664 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.682, + 0.686, + 0.873, + 0.699 + ], + "angle": 0, + "content": "Tomato sauce pouring over fries." + }, + { + "type": "image_caption", + "bbox": [ + 0.212, + 0.727, + 0.757, + 0.743 + ], + "angle": 0, + "content": "Figure 4: Sample generations. Please check our project website to view the videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.762, + 0.474, + 0.899 + ], + "angle": 0, + "content": "Evaluation For the small-scale experiments on UCF-101 dataset, we follow the protocol defined in the prior approaches [52, 47, 17] and report the Inception Score (IS) [44] calculated by a trained C3D model [53] and Fréchet Video Distance (FVD) [55] by a trained I3D model [6]. For the large-scale text-to-video experiments, we perform the zero-shot evaluation of the video generation quality on the UCF-101 and MSR-VTT datasets following Make-A-Video [46]. We carefully discuss the evaluation process below." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.762, + 0.895, + 0.899 + ], + "angle": 0, + "content": "UCF-101 experiment We use IS and FVD for evaluation in our small-scale experiments. UCF-101 is a categorical video dataset designed for action recognition. When sampling from the text-to-video model, we devise a set of prompts for each class name to be used as the conditional input. This is necessary as some class names (such as jump rope) are not descriptive. We list all the prompts we use in the supplementary material. We sample 20 videos for each prompt to compute the IS metric. For FVD, we follow the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.925, + 0.52, + 0.937 + ], + "angle": 0, + "content": "22935" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.472, + 0.135 + ], + "angle": 0, + "content": "Table 2: Zero-shot text to video generation on UCF-101. Our approach gives significant performance gains compared to the prior baselines both in inception score and FVD metrics." + }, + { + "type": "table", + "bbox": [ + 0.121, + 0.14, + 0.428, + 0.277 + ], + "angle": 0, + "content": "
MethodIS (↑)FVD (↓)
CogVideo [18] (Chinese)23.55751.34
CogVideo [18] (English)25.27701.59
Make-A-Video [46]33.00367.23
MagicVideo [69]-655.00
Video LDM [4]33.45550.61
VideoFactory [59]-410.00
PYoCo47.76355.19
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.291, + 0.472, + 0.337 + ], + "angle": 0, + "content": "Table 3: Text conditional zero-shot generation on MSRVTT. Our approach with the base config achieves the best results, and using an ensemble further improves the FIDs." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.348, + 0.451, + 0.531 + ], + "angle": 0, + "content": "
MethodCLIP-FID (↓)FID (↓)
NUWA [60] (Chinese)47.68-
CogVideo [18] (Chinese)24.78-
CogVideo [18] (English)23.59-
Make-A-Video [46]13.17-
MagicVideo [69]-36.50
Latent-Shift [1]15.23-
PYoCo (Config-A)10.2125.39
PYoCo (Config-B)9.9524.28
PYoCo (Config-C)9.9124.54
PYoCo (Config-D)9.7322.14
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.558, + 0.471, + 0.573 + ], + "angle": 0, + "content": "prior work [25, 52] and sample 2, 048 videos for evaluation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.594, + 0.472, + 0.804 + ], + "angle": 0, + "content": "MSR-VTT experiment MSR-VTT [62] test set contains 2,990 videos as well as 59,794 captions. All the videos have the same resolution of \\(320 \\times 240\\). We generate a \\(76 \\times 256 \\times 256\\) video for each 59,794 caption and save the videos in an mp4 format with a high bit rate. To compare with Make-A-Video, we compute FID using a ViT-B/32 model [24]. We also report a more common FID metric computed by an Inception-V3 model. We also examine the idea of ensemble denoiser [2] by finetuning the level-1 experts of each model. We denote Config-A as the configuration of using only baseline models and Config-B to Config-D as incrementally changing super-resolution model, temporal interpolation model, and base model with the corresponding ensemble models." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.216, + 0.831 + ], + "angle": 0, + "content": "5.2. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.472, + 0.901 + ], + "angle": 0, + "content": "Large-scale text-to-video synthesis We quantitatively compare our method against Make-A-Video [46], NUWA [60], CogVideo [18], and several concurrent works [4, 69, 4, 59, 1]. Table 2 shows that our method" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.089, + 0.894, + 0.166 + ], + "angle": 0, + "content": "Table 4: Unconditional UCF-101 generation results. Our approach achieves the state-of-the-art inception score and FVD, while having considerably smaller parameter count compared to other diffusion-based approaches such as VDM (1B parameters)." + }, + { + "type": "table", + "bbox": [ + 0.527, + 0.17, + 0.865, + 0.368 + ], + "angle": 0, + "content": "
MethodIS (↑)FVD (↓)
TGAN [43]15.83±.18-
LDVD-GAN [20]22.91±.19-
VideoGPT [63]24.69±.30-
MoCoGAN-HD [52]32.36838
DIGAN [66]29.71±.53655±22
CCVS [25]24.47±.13386±15
StyleGAN-V [47]23.94±.73-
VDM [17]57.00±.62-
TATS [9]57.63±.73430 ±18
PYoCo (112M)57.93±.24332 ±13
PYoCo (253M)60.01±.51310 ±13
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.895, + 0.596 + ], + "angle": 0, + "content": "outperforms all the baselines on the UCF-101 dataset and improves the zero-shot Inception Score from 33.45 to 47.76. In Table 3, we show that our baseline model achieves a new state-of-the-art CLIP-FID score [24] of 10.21, while using ensemble models further improves both CLIP-FID and FID scores. In Figure 4, we qualitatively visualize the synthesis capability of our approach. Our model achieves high-quality zero-shot video synthesis capability with good photorealism and temporal coherency. We also provide a qualitative comparison with Make-A-Video [46] andImagen Video [14] in Figure 5. We observe that our model is able to produce videos with better details than both approaches, as shown in the animal videos. We also produce better-stylized videos thanImagen Video." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.895, + 0.797 + ], + "angle": 0, + "content": "Small-scale unconditional video synthesis We report IS and FVD scores on UCF-101 dataset in Table 4 and compare our model with multiple unconditional video generation baselines. Note that using class labels as conditional information could lead to sizeable improvement in IS and FVD scores [9], which we do not consider as the comparison. Our method attains state-of-the-art unconditional video generation quality. Compared with previous diffusion-based unconditional generation model [17], our model is \\(\\sim 10\\times\\) smaller and has \\(\\sim 14\\times\\) less training time (75 GPU-days vs. 925 GPU-days)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.814, + 0.654, + 0.831 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We quantitatively compare several training strategies for video diffusion models. Then, we perform ablation on the correlation ratio in the Equations 3 and 4, a key hyperparameter in our approach." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.52, + 0.937 + ], + "angle": 0, + "content": "22936" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.104, + 0.09, + 0.237, + 0.104 + ], + "angle": 0, + "content": "Make-A-Video [46]" + }, + { + "type": "image_caption", + "bbox": [ + 0.308, + 0.09, + 0.357, + 0.103 + ], + "angle": 0, + "content": "PYoCo" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.106, + 0.252, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.252, + 0.106, + 0.422, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.53, + 0.09, + 0.655, + 0.105 + ], + "angle": 0, + "content": "Imagen Video [14]" + }, + { + "type": "image", + "bbox": [ + 0.427, + 0.106, + 0.71, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.775, + 0.09, + 0.825, + 0.103 + ], + "angle": 0, + "content": "PYoCo" + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.106, + 0.882, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.138, + 0.243, + 0.383, + 0.256 + ], + "angle": 0, + "content": "A confused grizzly bear in calculus class." + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.258, + 0.25, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.251, + 0.258, + 0.422, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.554, + 0.243, + 0.763, + 0.257 + ], + "angle": 0, + "content": "A sheep to the right of a wineglass." + }, + { + "type": "image", + "bbox": [ + 0.427, + 0.258, + 0.71, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.258, + 0.881, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.115, + 0.395, + 0.416, + 0.409 + ], + "angle": 0, + "content": "Sailboat sailing on a sunny day in a mountainlake." + }, + { + "type": "image_caption", + "bbox": [ + 0.514, + 0.395, + 0.818, + 0.41 + ], + "angle": 0, + "content": "A cat eating food out of a bowl, in style of Van Gogh." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.422, + 0.895, + 0.468 + ], + "angle": 0, + "content": "Figure 5: Qualitative comparison with baseline approaches. The two panels on the left show the comparison of our approach with Make-A-Video [46], while those on the right show the comparison withImagen Video [14]. PYoCo achieves better photorealism compared to the two approaches." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.492, + 0.47, + 0.521 + ], + "angle": 0, + "content": "Table 5: Quantitative results of different training strategies on UCF-101 dataset." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.527, + 0.458, + 0.635 + ], + "angle": 0, + "content": "
IS(↑)FVD (↓)FID (↓)
Image Diffusion (ID)--30.05
Training from scratch28.25903.37124.75
Finetuning from ID41.25566.6756.43
+ Mixed Noise52.71337.4031.57
+ Progressive Noise53.52339.6731.88
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.473, + 0.901 + ], + "angle": 0, + "content": "Training strategies We compare training from scratch, a simple finetuning baseline, finetuning with mixed noising, and progressive noising using IS, FVD, and averaged frame FID metrics on the UCF-101 dataset in Table 5. We first find that finetuning from an image diffusion model is much more effective than training from scratch. For finetuning from the image model, the correlated noise model produces better video generation quality than the independent noise model. In addition, we notice that the correlated noise better preserves the image quality learned by the pretrained image model and produces a lower frame FID. This is particularly desired in large-scale text-to-video training to fulfill the goal of inheriting the knowledge from the image model missing in the video datasets. Specifically, most videos contain realistic scenes captured by cameras and have infrequent media types like paintings, illustrations, sketches, etc. Moreover, the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.494, + 0.893, + 0.57 + ], + "angle": 0, + "content": "video data is much smaller in volume, and the scenes are less diverse than image datasets. As shown in Figure 4, our model can preserve properties learned from image datasets that are not presented in our video dataset, such as the artistic styles, and generate faithful motion on them." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Correlation ratio The hyperparameter \\(\\alpha\\) in the Equations 3 and 4 controls the correlation between the noise of different frames. A larger \\(\\alpha\\) injects more correlation into the noise. The correlation disappears when \\(\\alpha \\rightarrow 0\\), and the mixed and progressive noise models reproduce the vanilla noise model. To find optimal \\(\\alpha\\), we train our UCF-small model (69M parameters) using \\(\\alpha \\in \\{0, 0.1, 0.2, 0.5, 1, 1, 2, 5, 10, \\infty\\}\\) and report FVD in Figure 7. For each \\(\\alpha\\) value, we repeat the experiment 3 times and report the mean. Note that \\(\\alpha = 0\\) indicates finetuning with the independent frame noise, and \\(\\alpha = \\infty\\) indicates using identical noise maps for all the frames, which produces frozen videos during the inference time. Finetuning an image diffusion model almost consistently outperforms the training-from-scratch baseline with different \\(\\alpha\\)s. Using \\(\\alpha = 1\\) for mixed noisng and \\(\\alpha = 2\\) for progressive noisng produces similar best results. We also show qualitative results for models trained with \\(\\alpha = 0, 1, 10\\) in Figure 6. When \\(\\alpha\\) is too small, we notice a degradation in visual quality in the generated video frames and a reduced video diversity. For example, we notice many repeated samples and black borders in almost every video generated with" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "22937" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.346, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.202, + 0.296, + 0.244, + 0.307 + ], + "angle": 0, + "content": "\\(\\alpha = 0\\)" + }, + { + "type": "image", + "bbox": [ + 0.346, + 0.089, + 0.61, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.459, + 0.296, + 0.501, + 0.307 + ], + "angle": 0, + "content": "\\(\\alpha = 1\\)" + }, + { + "type": "image", + "bbox": [ + 0.61, + 0.09, + 0.875, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.717, + 0.296, + 0.767, + 0.307 + ], + "angle": 0, + "content": "\\(\\alpha = 10\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.082, + 0.319, + 0.885, + 0.335 + ], + "angle": 0, + "content": "Figure 6: Visual ablation on \\(\\alpha\\). Small \\(\\alpha = 0\\) reduces video quality and diversity and large \\(\\alpha = 10\\) yields motion artifacts." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.359, + 0.466, + 0.507 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.519, + 0.471, + 0.596 + ], + "angle": 0, + "content": "Figure 7: Quantitative ablation on hyperparameter \\(\\alpha\\). Finetuning with temporally correlated prior improves over training from scratch. Using a too-large or too-small \\(\\alpha\\) leads to inferior results. \\(\\alpha = 1\\), \\(\\alpha = 2\\) each works the best for mixed and progressive noising, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.47, + 0.656 + ], + "angle": 0, + "content": "\\(\\alpha = 0\\). On the other hand, when \\(\\alpha\\) is too large, the model has difficulty generating proper motions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.677, + 0.472, + 0.814 + ], + "angle": 0, + "content": "Model size We pick the best \\(\\alpha\\) for the mixed and progressive noise models and compare them with the model trained from scratch on models with different numbers of parameters, 69M, 112M, and 253M. Figure 8 shows that our mixed and progressive models outperform the baseline consistently by a large margin in terms of FVD. Overall, mixed and progressive noising provide similar performance. In our large large-scale experiments, we choose progressive noising with \\(\\alpha = 2\\) due to its autoregressive nature." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.83, + 0.196, + 0.845 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We proposed a new efficient way of training text-to-video generation models. By observing that the noise maps generating the frames of a video are clustered together, we study" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.359, + 0.888, + 0.507 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.521, + 0.895, + 0.582 + ], + "angle": 0, + "content": "Figure 8: Ablation on model size. Larger models consistently improve the performance of both finetuning and training from scratch. Finetuning from image model consistently outperforms training from scratch." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.892, + 0.718 + ], + "angle": 0, + "content": "mixed and progressive noise priors well-suited for sequential video frame generation. We apply our progressive noise prior to finetuning a state-of-the-art diffusion-based text-to-image model to achieve a state-of-the-art large-scale text-to-video model. The high quality of the generated videos and the state-of-the-art Inception and FID scores demonstrate the strength of our approach." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.9 + ], + "angle": 0, + "content": "Acknowledgment. We would like to thank Amanda Moran, John Dickinson, Sivakumar Arayandi Thottakara, David Page, Ranjitha Prasanna, Venkata Karri, and others in NGC and PBSS team for the computing infrastructure support. We also give thanks to Qinsheng Zhang, Zekun Hao, Tsung-Yi Lin, Ajay Jain, and Chen-Hsuan Lin for useful discussions and feedback. Thanks also go to Yin Xi and Thomas Hayes for clarifying the evaluation protocol of Make-A-Video and to Ming Ding for the details of CogVideo. We thank the ICCV PCs, ACs, and reviewers for their service and valuable feedback. This work is partly supported by NSF grants No. IIS-1910132 and IIS-2213335." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "22938" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.472, + 0.171 + ], + "angle": 0, + "content": "[1] Jie An, Songyang Zhang, Harry Yang, Sonal Gupta, Jia-Bin Huang, Jiebo Luo, and Xi Yin. 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Best viewed with Acrobat Reader. Click the images to play the video clips. + +# Abstract + +Despite tremendous progress in generating high-quality images using diffusion models, synthesizing a sequence of animated frames that are both photorealistic and temporally coherent is still in its infancy. While off-the-shelf billion-scale datasets for image generation are available, collecting similar video data of the same scale is still challenging. Also, training a video diffusion model is computationally much more expensive than its image counterpart. In this work, we explore finetuning a pretrained image diffusion model with video data as a practical solution for the video synthesis task. We find that naively extending the image noise prior to video noise prior in video diffusion leads to sub-optimal performance. Our carefully designed video noise prior leads to substantially better performance. Extensive experimental validation shows that our + +model, Preserve Your Own COrelation (PYoCo), attains SOTA zero-shot text-to-video results on the UCF-101 and MSR-VTT benchmarks. It also achieves SOTA video generation quality on the small-scale UCF-101 benchmark with a $10 \times$ smaller model using significantly less computation than the prior art. The project page is available at https://research.nvidia.com/labs/dir/pyoco/. + +# 1. Introduction + +Large-scale diffusion-based text-to-image models [38, 42, 2] have demonstrated impressive capabilities in turning complex text descriptions into photorealistic images. They can generate images with novel concepts unseen during training. Sophisticated image editing and processing tasks can easily be accomplished through guidance control and embedding techniques. Due to the immense success in several applications [30, 67, 5], these models are established as pow- + +![](images/3ea06ec868739f34b3665eb70207e13f0537015064d7770050b4c180314a5265.jpg) +(a) + +![](images/e6d7c286fd69acb9c2a133e2940d19045711e89bb8826830f27c7352a116b27c.jpg) +(b) +Figure 2: Visualizing the noise map correlations. (a) visualizes the t-SNE plot of the noise maps corresponding to input frames randomly sampled from videos. These noise maps are obtained by running a diffusion ODE [49, 48] on the input frames using a trained text-to-image model, but in the opposite direction of image synthesis ( $\sigma : 0 \to \sigma_{\max}$ ). The green dots in the background denote the reference noise maps sampled from an i.i.d. Gaussian distribution. The red dots and yellow dots are noise maps corresponding to input frames coming from different videos. We found they are spread out and share no correlation. On the other hand, the noise maps corresponding to the frames coming from the same video (shown in blue dots) are clustered together. (b) Using an i.i.d. noise model (orange dots) for finetuning text-to-image models for video synthesis is not ideal since temporal correlations between frames are not modeled. To remedy this, we propose a progressive noise model in which the correlation between different noise maps is injected along the temporal axis. Our progressive noise model (blue dots) aptly models the correlations present in the video noise maps. + +erful image synthesis tools for content generation. As image synthesis is largely democratized with the success of these text-to-image models, it is natural to ask whether we can repeat the same success in video synthesis with large-scale diffusion-based text-to-video models. + +Multiple attempts have been made to build large-scale video diffusion models. Ho et al. [17] proposed a UNet-based architecture for the video synthesis task that is trained using joint image-video denoising losses.Imagen video [14] extends the cascaded text-to-image generation architecture ofImagen [42] for video generation. In both works, the authors directly train a video generation model from scratch. While these approaches achieve great success and produce high-quality videos, they are inherently expensive to train, requiring hundreds of high-end GPUs or TPU's and several weeks of training. After all, video generators not only need to learn to form individual images but should also learn to synthesize coherent temporal dynamics, which makes the video generation task much more challenging. While the formation of individual frames is a shared component in an image and video synthesis, these works disregard the existence of powerful pretrained text-to-image diffusion models and train their video generators from scratch. + +We explore a different avenue for building large-scale text-to-video diffusion models by starting with a pretrained text-to-image diffusion model. Our motivation is that most of the components learned for the image synthesis task can + +effectively be reused for video generation, leading to knowledge transfer and efficient training. A similar idea is adopted by several recent works [46, 69, 4]. Without exception, when finetuning, they naively extend the image diffusion noise prior (i.i.d. noise) used in the text-to-image model to a video diffusion noise prior by adding an extra dimension to the 2D noise map. We argue that this approach is not ideal as it does not utilize the natural correlations in videos that are already learned by the image models. This is illustrated in Figure 2, where we visualize the t-SNE plot of noise maps corresponding to different input frames as obtained from a pretrained text-to-image diffusion model. The noise maps corresponding to different frames coming from the same video (blue dots in Figure 2a are clustered together, exhibiting a high degree of correlation. The use of i.i.d. noise prior does not model this correlation, which would impede the finetuning process. Our careful analysis of the video diffusion noise prior leads us to a noise prior that is better tailored for finetuning an image synthesis model to the video generation task. As illustrated in Figure 2b, our proposed noise prior (shown in blue dots) aptly captures the correlations in noise maps corresponding to video frames. + +We then proceed to build a large-scale diffusion-based text-to-video model. We leverage several design choices from the prior works, including the use of temporal attention [17], joint image-video finetuning [17], a cascaded generation architecture [14], and an ensemble of expert denois- + +ers [2]. Together with these techniques and the proposed video noise prior, our model establishes a new state-of-the-art for video generation outperforming competing methods on several benchmark datasets. Figure 1 shows our model can achieve high-quality zero-shot video synthesis capability with SOTA photorealism and temporal consistency. + +In short, our work makes the following key contributions. + +1. We propose a video diffusion noise tailored for finetuning text-to-image diffusion models for text-to-video. +2. We conduct extensive experimental validation and verify the effectiveness of the proposed noise prior. +3. We build a large-scale text-to-video diffusion model by finetuning a pretrained eDiff-I model with our noise prior and achieve state-of-the-art results on several benchmarks. + +# 2. Related Work + +Diffusion-based text-to-image models: Diffusion models have significantly advanced the progress of text-based photorealistic, compositional image generation [38, 42]. Given the nature of the iterative denoising process that requires massive numbers of score function evaluations, earlier diffusion models focused on generating low-resolution images, e.g., $64 \times 64$ [15, 48]. To generate high-resolution images, two common approaches have been used. The first approach applies cascaded super-resolution models in the RGB space [32, 16, 42, 38], while the second approach leverages a decoder to exploit latent space [40, 11]. Based on these models, advanced image and video editing have been achieved through finetuning the model [41, 67, 5, 23, 61, 29] or controlling the inference process [30, 13, 34, 10, 35, 7, 31, 3]. Here, we study the problem of using large-scale diffusion models for text-to-video generation. + +Video generation models: Generating realistic and novel videos have long been an attractive and essential research direction [58, 39, 65]. Previously studies have resorted to different types of generative models such as GANs [58, 43, 54, 52, 45], Autoregressive models [51, 63, 25, 9, 18], and implicit neural representations [47, 66]. Recently, driven by the tremendous success of applying the diffusion model to image synthesis, multiple works have proposed to explore diffusion models for conditional and unconditional video synthesis [57, 12, 69, 61, 4, 22, 19, 57, 64, 33, 28, 1, 59]. For example, Singer et al. extend the unCLIP framework [38] to text-to-video generation, which allows training without video captions [46]. Ho et al. [17] extend the Imagen framework [42] by repeatedly up-scaling low-resolution small-fps videos in both spatial and temporal directions with multiple models [14]. Our work also falls into this line of work which uses a diffusion model. We focus on augmenting an image diffusion model for video and study the design choice of the diffusion noise priors for such an image-to-video finetuning task. + +Leverage knowledge from images for text-to-video generation: Like text-to-image models, text-to-video models require massive amounts of data to learn caption-relatedness, frame photorealism, and temporal dynamics. But in contrast to the abundant image data resource, video data are more limited in style, volume, and quality. To resolve such scarcity issue of text-video data, previous works have resorted to different strategies to leverage knowledge from image data for text-to-video generation, including joint training on the text-image data from scratch [17, 14, 56, 60], first training a text-to-image model and then finetuning partially [18, 4, 61, 29] or entirely [46, 8] on the video dataset, and using CLIP image features as the conditional information [46, 69]. In this paper, we propose a new video diffusion noise prior that is tailored for finetuning a pretrained diffusion-based image generation model for the video generation task. We reuse several design choices in the prior work by finetuning jointly on text-image and text-video datasets. As a result, we can build a text-to-video generation system that achieves state-of-the-art zero-shot performances. + +# 3. Preliminaries + +Diffusion models generate data by iteratively denoising samples drawn from a noise distribution. In the case of text-to-video models, text embeddings obtained from a pre-trained text encoder are used as additional inputs in the denoising process. Formally, let $D(\mathbf{x}, \mathbf{e}, \sigma)$ denote a denoising network that operates on the noisy input video $\mathbf{x} \in \mathbb{R}^{b \times n_s \times 3 \times h \times w}$ where $\mathbf{e}$ is the text embedding, and $\sigma$ is the noise level. Here $n_s$ is the sequence length of the input video, $b$ is the batch size, and $h \times w$ is the spatial resolution. The model $D$ is trained to denoise the input $\mathbf{x}$ . + +Training We follow the EDM formulation of Karras et al. [21] to optimize the denoiser $D$ using the following objective + +$$ +\begin{array}{l} \mathbb {E} _ {p _ {\text {d a t a}} (\mathbf {x} _ {\text {c l e a n}}, \mathbf {e}), p (\epsilon), p (\sigma)} \left[ \lambda (\sigma) \| D \left(\mathbf {x} _ {\text {n o i s e}}; \mathbf {e}, \sigma\right) - \mathbf {x} _ {\text {c l e a n}} \| _ {2} ^ {2} \right] \tag {1} \\ w h e r e \quad \mathbf {x} _ {\text {n o i s e}} = \mathbf {x} _ {\text {c l e a n}} + \sigma \epsilon \\ \end{array} +$$ + +Here, $\mathbf{x}_{\mathrm{noise}}$ is the noisy sample obtained by corrupting the clean video $\mathbf{x}$ with noise $\sigma \epsilon$ , where $p(\epsilon) = \mathcal{N}(\mathbf{0},\mathbf{I})$ and $\sigma$ is a scalar for the noise level drawn from $p(\sigma)$ . The loss weight, $\lambda (\sigma)$ , is a function of $\sigma$ given by $\lambda (\sigma) = (\sigma^2 +\sigma_{\mathrm{data}}^2) / (\sigma \cdot \sigma_{\mathrm{data}})^2$ . Eq. (1) is a simple denoising objective in which the denoiser $D$ is trained to estimate the clean video $\mathbf{x}_{\mathrm{clean}}$ from the noisy input $\mathbf{x}_{\mathrm{noise}}$ . Following EDM, we use a log-normal distribution for $\sigma$ i.e., $\ln (p(\sigma)) = \mathcal{N}(P_{\mathrm{mean}},P_{\mathrm{std}}^2)$ with $P_{\mathrm{mean}} = -1.2$ and $P_{\mathrm{std}} = 1.2$ . + +To train the denoising model, EDM uses preconditioning terms in its objective function to properly scale the inputs and output of the denoiser model $D$ . More specifically, the + +denoising model $D$ is written as + +$$ +D (\mathbf {x}; \mathbf {e}, \sigma) := \left(\frac {\sigma_ {\mathrm {d a t a}}}{\sigma^ {*}}\right) ^ {2} \mathbf {x} + \frac {\sigma \cdot \sigma_ {\mathrm {d a t a}}}{\sigma^ {*}} F _ {\theta} \left(\frac {\mathbf {x}}{\sigma^ {*}}; \mathbf {e}, \frac {\ln (\sigma)}{4}\right) +$$ + +Here, $F_{\theta}$ is a neural network with parameters $\theta$ and $\sigma^{*} = \sqrt{\sigma^{2} + \sigma_{\mathrm{data}}^{2}}$ . We use $\sigma_{\mathrm{data}} = 0.5$ . + +Sampling Once the denoising model is trained, sampling can be performed by solving the following ODE [21] + +$$ +\frac {d \mathbf {x}}{d \sigma} = - \sigma \nabla_ {\mathbf {x}} \log p (\mathbf {x} | \mathbf {e}, \sigma) = \frac {\mathbf {x} - D (\mathbf {x} ; \mathbf {e} , \sigma)}{\sigma} \tag {2} +$$ + +for $\sigma$ flowing backwards from $\sigma = \sigma_{\mathrm{max}}$ to $\sigma = 0$ . The initial value for $\mathbf{x}$ is obtained by sampling from the prior distribution $\mathbf{x} \sim \mathcal{N}(\mathbf{0}, \sigma_{\mathrm{max}}^2 \mathbf{I})$ . Over the recent years, several samplers have been proposed for sampling from the trained diffusion models [68, 48, 26, 27, 15]. In this paper, we use DEIS [68] and its stochastic variant [21] for synthesizing samples from our model. + +# 4. Method + +Training text-to-video models is much more challenging than training text-to-image diffusion models due to practical difficulties in collecting billion-scale video datasets and securing enough computational resources. Additionally, generating videos is much more challenging since individual frames need to be both photorealistic and temporally coherent. Prior works leverage large-scale image datasets to mitigate these difficulties by either joint training on the image datasets [60, 17, 14] or finetuning a text-to-image model on the video datasets [18, 46]. Here, we are interested in finetuning text-to-image diffusion models jointly on image and video datasets. We postulate that naively extending the image noise prior to video diffusion is not ideal. We carefully explore the design space of noise priors and propose one that is well suited for our video finetuning task, which leads to significant performance gains. + +Correlated noise model An image diffusion model is trained to denoise independent noise from a perturbed image. The noise vector $\epsilon$ in the denoising objective (1) is sampled from an i.i.d. Gaussian distribution $\epsilon \sim \mathcal{N}(0, \mathbf{I})$ . However, after training the image diffusion model and applying it to reverse real frames from a video into the noise space in a per-frame manner, we find that the noise maps corresponding to different frames are highly correlated. This is illustrated in Figure 2, where the t-SNE plot of noise maps corresponding to different video frames are plotted. When the input frames come from the same video (shown in blue dots in Figure 2a, noise maps are clustered. The use of i.i.d. sampling (shown in orange dots in Figure 2b does not capture these correlations. This is also depicted quantitatively + +Table 1: Cosine similarity of the reversed noise. The noise maps corresponding to the frames sampled from the same videos have a higher similarity than those sampled from different videos. + +
Cosine Similarity
(a) Same video noise0.206±0.156
(b) Different video noise0.001±0.009
+ +in Table 1 where we compute the average pairwise cosine similarity between noise corresponding to (a) same video and (b) different video. (a) is much higher than (b). As a result, the video diffusion model trained with i.i.d. noise is coerced to forget such correlation among the noise between different frames, making it difficult to preserve knowledge from the image diffusion model. Motivated by this observation, we propose to modify the noise process to preserve the correlation between different frames. To this end, we investigate two noisng strategies - mixed and progressive noising. + +Mixed noise model: Let $\epsilon^1, \epsilon^2, \ldots, \epsilon^{n_s}$ denote the noise corresponding to individual video frames i.e., $\epsilon^i$ corresponds to the $i^{th}$ element of the noise tensor $\epsilon$ . In the mixed noise model, we generate two noise vectors $\epsilon_{\mathrm{shared}}$ and $\epsilon_{\mathrm{ind}}$ . $\epsilon_{\mathrm{shared}}$ is a common noise vector shared among all video frames, while $\epsilon_{\mathrm{ind}}$ is the individual noise per frame. The linear combination of both these vectors is used as the final noise. + +$$ +\begin{array}{l} \epsilon_ {\text {s h a r e d}} \sim \mathcal {N} \left(\mathbf {0}, \frac {\alpha^ {2}}{1 + \alpha^ {2}} \mathbf {I}\right), \epsilon_ {\text {i n d}} ^ {i} \sim \mathcal {N} \left(\mathbf {0}, \frac {1}{1 + \alpha^ {2}} \mathbf {I}\right) \tag {3} \\ \epsilon^ {i} = \epsilon_ {\mathrm {s h a r e d}} + \epsilon_ {\mathrm {i n d}} ^ {i} \\ \end{array} +$$ + +Progressive noise model: In the progressive noise model, the noise for each frame is generated in an autoregressive fashion in which the noise at frame $i$ is generated by perturbing the noise at frame $i - 1$ . Let $\epsilon_{\mathrm{ind}}^i$ denote the independent noise generated for frame $i$ . Then, progressive noising can be formulated as + +$$ +\epsilon^ {0} \sim \mathcal {N} (\mathbf {0}, \mathbf {I}) \quad \epsilon_ {\mathrm {i n d}} ^ {i} \sim \mathcal {N} (\mathbf {0}, \frac {1}{1 + \alpha^ {2}} \mathbf {I}) \tag {4} +$$ + +$$ +\epsilon^ {i} = \frac {\alpha}{\sqrt {1 + \alpha^ {2}}} \epsilon^ {i - 1} + \epsilon_ {\mathrm {i n d}} ^ {i} +$$ + +In both these models, $\alpha$ controls how much noise is shared among different video frames. The higher the value of $\alpha$ , the more correlation exists among the noise maps corresponding to different frames. As $\alpha \rightarrow \infty$ , all frames would have the same noise which results in generating a frozen video. On the other hand, $\alpha = 0$ corresponds to i.i.d. noise. + +As shown in Figure 2b, the use of progressive noise sampling (blue dots) better models the correlations between different noise maps by obtaining similar clustering patterns to the noise maps of real video frames embedded by a pretrained text-to-image model in Figure 2a (blue dots). + +![](images/8d6b3d4c8df87f34a0ce9703c0a7f610b6687418e672edb194d3268825477a99.jpg) +Figure 3: Model architecture. Our pipeline consists of a cascade of four networks — a base model and three upsampling models. All four models take inputs as the text embeddings obtained from the T5 encoder and the CLIP text encoder. The base model produces 16 video frames of spatial resolution $64 \times 64$ with a frameskip of 5. The first upsampling model performs a temporal interpolation, resulting in videos of size $76 \times 64 \times 64$ while the subsequent two super-resolution models perform spatial super-resolution to produce videos of sizes $76 \times 256 \times 256$ and $76 \times 1024 \times 1024$ . + +Model architecture As visualized in Figure 3, our model consists of a cascade of four networks — a base network and three upsampling stacks. The base network generates an output video of dimension $16 \times 64 \times 64$ with a frameskip of 5. It generates the frames $\{1,6,11,\ldots,76\}$ . The first upsampling network performs a temporal interpolation to produce a video of size $76 \times 64 \times 64$ . The second and the third super-resolution network performs spatial upsampling to produce the outputs of sizes $76 \times 256 \times 256$ and $76 \times 1024 \times 1024$ . We utilize eDiff-I [2], a state-of-the-art text-to-image diffusion model, to initialize our base and spatial super-resolution models. Similar to prior works [17, 46], we adapt the image-based U-Net model for the video synthesis task by making the following changes: (1) Transforming 2D convolutions to 3D by adding a dimension 1 to temporal axis and (2) Adding temporal attention layers. Please refer to the supplementary material for more details. + +Similar to Ho et al. [17], we jointly finetune the model on video and image datasets by concatenating videos and images in the temporal axis and applying our temporal modules only on the video part. Similarly to eDiff-I, our model uses both T5 text embeddings [37] and CLIP text embeddings [36]. We drop each of the embeddings independently at random during training, as in eDiff-I. + +# 5. Experiments + +In this section, we evaluate our proposed strategy of training diffusion models for video synthesis on two sets of experiments. We first comprehensively analyze our proposed noise model on the small-scale UCF-101 dataset. We then scale up our experiments to the challenging large-scale text-to-video synthesis task. + +# 5.1. Experimental Setups + +We conduct ablation experiments in a small-scale unconditional video generation setting and pick the best configuration for our large-scale text-to-video generation run. + +Datasets We train our model on the UCF-101 dataset [50] for the small-scale experiments, where we follow the protocol defined in Ho et al. [17] to generate videos of size $16 \times 64 \times 64$ . UCF-101 dataset contains 13,320 videos. We randomly sample frames from these videos to train our image synthesis model. For our large-scale experiments, we use a combination of public and proprietary datasets for text-to-image and text-to-video finetuning. Most of the videos are of 2K resolution with 16:9 aspect ratio. All data was filtered using a preset CLIP and aesthetic scores* to ensure high quality. Our final image dataset contains around 1.2 billion text-image pairs and 22.5 million text-video pairs. + +Training details In the unconditional generation experiment on the UCF-101 dataset, to do an ablation study on the model size, we design 3 models where each model has 69M, 112M, and 253M parameters, respectively. As a comparison, the baseline Video Diffusion Model (VDM) [17] contains 1.2B parameters. In the large-scale text-to-video experiment, our base and temporal interpolation models contain 1.08B parameters. Our super-resolution model adapted from the efficient U-Net [42] architecture with temporal convolution layers [14, 46] contains 313M parameters. Please refer to the supplementary material for more training details. + +![](images/be0d32f6c5261750250a55f4cff915a053e9259ad86489ddce09cc007e0763ed.jpg) + +![](images/4b5f2ccad8a2a714b4777005a783956b00b8fe07cd922ddc9476fa3b96ba75c6.jpg) +An epic tornado attacking above a glowing city at night, the tornado is made of smoke, highly detailed. + +![](images/0b71e5432321661882bb8e9d07f88930204323a4e84990b34323694870a32f4e.jpg) + +![](images/7497cd615041a3013314d3ae02fc31c19b21ba4245c7efeae2c13dcc7ecf9e74.jpg) +A golden retriever puppy holding a green sign that says "NVIDIA ROCKS". Background is a classroom. + +![](images/31f24d40b980ff0fc7922ccd7cfcbfe5b0d5a54f03b55e39df6481d82290aaca.jpg) +A cute corgi wearing a red robe holding a sign that says "Merry Christmas". There is a Christmas tree in the background. + +![](images/181156bf69a3ac777b674dfabb451cac0bf126ed68722d49f6b63b74c54d733f.jpg) + +![](images/8f9a5a97c5cd51d09128de896bf9ded108cfd243c94a7f05c4a9a840b15e6ebf.jpg) +Small boat sailing in the ocean, giant Cthulhu monster coming out a dense mist in the background, giant waves attacking. + +![](images/a8e97061fcc21c77cd0c887851bf593e0b2b7dfd929be30c5adb3933145bc9a8.jpg) + +![](images/8962c3cab1893100cc256b523b53fa2604524a275958c2bb078790ce3e85c544.jpg) +A cute funny robot dancing, centered, award winning watercolor pen illustration. +A skull burning while being held up by a skeletal hand. +Figure 4: Sample generations. Please check our project website to view the videos. + +![](images/e7fd793e68cfa900bbc13500147bbcb8cac48b979f63a288ea6c2e2090c78b53.jpg) +A cartoon white wolf is giving puppy-dog eyes, detailed fur, very cute kid's film character. +A huge dinosaur skeleton walking in a golden wheat field on a bright sunny day. + +![](images/8f943694a9daad4968571f69c1d1f69ba8a562ee9e68557a56bed7b52081d8ff.jpg) +A lightning striking atop of eiffel tower, dark clouds in the sky, slow motion. +A cute rabbit is eating grass, wildlife photography. + +![](images/de933d40c5692d4eb338a50bcf8966472a661d2ba6bdafedbe195396e20a70fa.jpg) +An anime girl looks at the beautiful nature through the window of a moving train, well rendered. +Tomato sauce pouring over fries. + +Evaluation For the small-scale experiments on UCF-101 dataset, we follow the protocol defined in the prior approaches [52, 47, 17] and report the Inception Score (IS) [44] calculated by a trained C3D model [53] and Fréchet Video Distance (FVD) [55] by a trained I3D model [6]. For the large-scale text-to-video experiments, we perform the zero-shot evaluation of the video generation quality on the UCF-101 and MSR-VTT datasets following Make-A-Video [46]. We carefully discuss the evaluation process below. + +UCF-101 experiment We use IS and FVD for evaluation in our small-scale experiments. UCF-101 is a categorical video dataset designed for action recognition. When sampling from the text-to-video model, we devise a set of prompts for each class name to be used as the conditional input. This is necessary as some class names (such as jump rope) are not descriptive. We list all the prompts we use in the supplementary material. We sample 20 videos for each prompt to compute the IS metric. For FVD, we follow the + +Table 2: Zero-shot text to video generation on UCF-101. Our approach gives significant performance gains compared to the prior baselines both in inception score and FVD metrics. + +
MethodIS (↑)FVD (↓)
CogVideo [18] (Chinese)23.55751.34
CogVideo [18] (English)25.27701.59
Make-A-Video [46]33.00367.23
MagicVideo [69]-655.00
Video LDM [4]33.45550.61
VideoFactory [59]-410.00
PYoCo47.76355.19
+ +Table 3: Text conditional zero-shot generation on MSRVTT. Our approach with the base config achieves the best results, and using an ensemble further improves the FIDs. + +
MethodCLIP-FID (↓)FID (↓)
NUWA [60] (Chinese)47.68-
CogVideo [18] (Chinese)24.78-
CogVideo [18] (English)23.59-
Make-A-Video [46]13.17-
MagicVideo [69]-36.50
Latent-Shift [1]15.23-
PYoCo (Config-A)10.2125.39
PYoCo (Config-B)9.9524.28
PYoCo (Config-C)9.9124.54
PYoCo (Config-D)9.7322.14
+ +prior work [25, 52] and sample 2, 048 videos for evaluation. + +MSR-VTT experiment MSR-VTT [62] test set contains 2,990 videos as well as 59,794 captions. All the videos have the same resolution of $320 \times 240$ . We generate a $76 \times 256 \times 256$ video for each 59,794 caption and save the videos in an mp4 format with a high bit rate. To compare with Make-A-Video, we compute FID using a ViT-B/32 model [24]. We also report a more common FID metric computed by an Inception-V3 model. We also examine the idea of ensemble denoiser [2] by finetuning the level-1 experts of each model. We denote Config-A as the configuration of using only baseline models and Config-B to Config-D as incrementally changing super-resolution model, temporal interpolation model, and base model with the corresponding ensemble models. + +# 5.2. Main Results + +Large-scale text-to-video synthesis We quantitatively compare our method against Make-A-Video [46], NUWA [60], CogVideo [18], and several concurrent works [4, 69, 4, 59, 1]. Table 2 shows that our method + +Table 4: Unconditional UCF-101 generation results. Our approach achieves the state-of-the-art inception score and FVD, while having considerably smaller parameter count compared to other diffusion-based approaches such as VDM (1B parameters). + +
MethodIS (↑)FVD (↓)
TGAN [43]15.83±.18-
LDVD-GAN [20]22.91±.19-
VideoGPT [63]24.69±.30-
MoCoGAN-HD [52]32.36838
DIGAN [66]29.71±.53655±22
CCVS [25]24.47±.13386±15
StyleGAN-V [47]23.94±.73-
VDM [17]57.00±.62-
TATS [9]57.63±.73430 ±18
PYoCo (112M)57.93±.24332 ±13
PYoCo (253M)60.01±.51310 ±13
+ +outperforms all the baselines on the UCF-101 dataset and improves the zero-shot Inception Score from 33.45 to 47.76. In Table 3, we show that our baseline model achieves a new state-of-the-art CLIP-FID score [24] of 10.21, while using ensemble models further improves both CLIP-FID and FID scores. In Figure 4, we qualitatively visualize the synthesis capability of our approach. Our model achieves high-quality zero-shot video synthesis capability with good photorealism and temporal coherency. We also provide a qualitative comparison with Make-A-Video [46] andImagen Video [14] in Figure 5. We observe that our model is able to produce videos with better details than both approaches, as shown in the animal videos. We also produce better-stylized videos thanImagen Video. + +Small-scale unconditional video synthesis We report IS and FVD scores on UCF-101 dataset in Table 4 and compare our model with multiple unconditional video generation baselines. Note that using class labels as conditional information could lead to sizeable improvement in IS and FVD scores [9], which we do not consider as the comparison. Our method attains state-of-the-art unconditional video generation quality. Compared with previous diffusion-based unconditional generation model [17], our model is $\sim 10\times$ smaller and has $\sim 14\times$ less training time (75 GPU-days vs. 925 GPU-days). + +# 5.3. Ablation Study + +We quantitatively compare several training strategies for video diffusion models. Then, we perform ablation on the correlation ratio in the Equations 3 and 4, a key hyperparameter in our approach. + +![](images/f6a0d29dd22ed069c738d632fc980df02d7577656b6e6bd19cd3796a56121db7.jpg) +Make-A-Video [46] + +![](images/5df5207698abb05a05e378f80ce72886b6456c216ebda1f9d3b371c0e5609342.jpg) +PYoCo + +![](images/83d81abbfb238a9855453e259f275ebda3921ee15a564c7b3fb9f7db156e2345.jpg) +Imagen Video [14] + +![](images/9ff683812bea89fc21a52045226a7b707e14228bab302290c9f1d4b390656de3.jpg) +PYoCo + +![](images/948ed773c9da2f0cccb1b0ded2fb2dbac6a3addc8835810020572224731d24f0.jpg) +A confused grizzly bear in calculus class. + +![](images/250a4b80c2e0ad72e8ae4221f419e71914963a8b29b642054accdce2d7f86fd6.jpg) +Sailboat sailing on a sunny day in a mountainlake. + +![](images/2856d764a26c0dceff776c469c325eecabc2d37157d43553670cc7bc4a9a8161.jpg) +A sheep to the right of a wineglass. +A cat eating food out of a bowl, in style of Van Gogh. + +![](images/05aba182271478008d147821594306e7c1e14e854c9c1fa92d32d525b402c841.jpg) +Figure 5: Qualitative comparison with baseline approaches. The two panels on the left show the comparison of our approach with Make-A-Video [46], while those on the right show the comparison withImagen Video [14]. PYoCo achieves better photorealism compared to the two approaches. + +Table 5: Quantitative results of different training strategies on UCF-101 dataset. + +
IS(↑)FVD (↓)FID (↓)
Image Diffusion (ID)--30.05
Training from scratch28.25903.37124.75
Finetuning from ID41.25566.6756.43
+ Mixed Noise52.71337.4031.57
+ Progressive Noise53.52339.6731.88
+ +Training strategies We compare training from scratch, a simple finetuning baseline, finetuning with mixed noising, and progressive noising using IS, FVD, and averaged frame FID metrics on the UCF-101 dataset in Table 5. We first find that finetuning from an image diffusion model is much more effective than training from scratch. For finetuning from the image model, the correlated noise model produces better video generation quality than the independent noise model. In addition, we notice that the correlated noise better preserves the image quality learned by the pretrained image model and produces a lower frame FID. This is particularly desired in large-scale text-to-video training to fulfill the goal of inheriting the knowledge from the image model missing in the video datasets. Specifically, most videos contain realistic scenes captured by cameras and have infrequent media types like paintings, illustrations, sketches, etc. Moreover, the + +video data is much smaller in volume, and the scenes are less diverse than image datasets. As shown in Figure 4, our model can preserve properties learned from image datasets that are not presented in our video dataset, such as the artistic styles, and generate faithful motion on them. + +Correlation ratio The hyperparameter $\alpha$ in the Equations 3 and 4 controls the correlation between the noise of different frames. A larger $\alpha$ injects more correlation into the noise. The correlation disappears when $\alpha \rightarrow 0$ , and the mixed and progressive noise models reproduce the vanilla noise model. To find optimal $\alpha$ , we train our UCF-small model (69M parameters) using $\alpha \in \{0, 0.1, 0.2, 0.5, 1, 1, 2, 5, 10, \infty\}$ and report FVD in Figure 7. For each $\alpha$ value, we repeat the experiment 3 times and report the mean. Note that $\alpha = 0$ indicates finetuning with the independent frame noise, and $\alpha = \infty$ indicates using identical noise maps for all the frames, which produces frozen videos during the inference time. Finetuning an image diffusion model almost consistently outperforms the training-from-scratch baseline with different $\alpha$ s. Using $\alpha = 1$ for mixed noisng and $\alpha = 2$ for progressive noisng produces similar best results. We also show qualitative results for models trained with $\alpha = 0, 1, 10$ in Figure 6. When $\alpha$ is too small, we notice a degradation in visual quality in the generated video frames and a reduced video diversity. For example, we notice many repeated samples and black borders in almost every video generated with + +![](images/84043d9b5f0034b76c6835e2d4e087432971d2d22535d277eb4e1c20e2e5608a.jpg) +$\alpha = 0$ + +![](images/999c099386c0fd284da43b5fb62b6ec5de5670e01424725f8869ea74c5d45ab6.jpg) +$\alpha = 1$ + +![](images/26e5b0e3adcaeb96a05393aada9def68b3f50bb8173fd43ac1a8b5ee7ec07265.jpg) +$\alpha = 10$ + +![](images/2e6035bc99550b824a6ea57ef45e3d24c183214050feafa286f4413540cd2415.jpg) +Figure 6: Visual ablation on $\alpha$ . Small $\alpha = 0$ reduces video quality and diversity and large $\alpha = 10$ yields motion artifacts. + +$\alpha = 0$ . On the other hand, when $\alpha$ is too large, the model has difficulty generating proper motions. + +Model size We pick the best $\alpha$ for the mixed and progressive noise models and compare them with the model trained from scratch on models with different numbers of parameters, 69M, 112M, and 253M. Figure 8 shows that our mixed and progressive models outperform the baseline consistently by a large margin in terms of FVD. Overall, mixed and progressive noising provide similar performance. In our large large-scale experiments, we choose progressive noising with $\alpha = 2$ due to its autoregressive nature. + +# 6. Conclusion + +We proposed a new efficient way of training text-to-video generation models. By observing that the noise maps generating the frames of a video are clustered together, we study + +![](images/0230cc56489705efdce7ccceeafb558d19fccf3188e8d60146c865c67f51f050.jpg) +Figure 7: Quantitative ablation on hyperparameter $\alpha$ . Finetuning with temporally correlated prior improves over training from scratch. Using a too-large or too-small $\alpha$ leads to inferior results. $\alpha = 1$ , $\alpha = 2$ each works the best for mixed and progressive noising, respectively. +Figure 8: Ablation on model size. Larger models consistently improve the performance of both finetuning and training from scratch. Finetuning from image model consistently outperforms training from scratch. + +mixed and progressive noise priors well-suited for sequential video frame generation. We apply our progressive noise prior to finetuning a state-of-the-art diffusion-based text-to-image model to achieve a state-of-the-art large-scale text-to-video model. The high quality of the generated videos and the state-of-the-art Inception and FID scores demonstrate the strength of our approach. + +Acknowledgment. We would like to thank Amanda Moran, John Dickinson, Sivakumar Arayandi Thottakara, David Page, Ranjitha Prasanna, Venkata Karri, and others in NGC and PBSS team for the computing infrastructure support. We also give thanks to Qinsheng Zhang, Zekun Hao, Tsung-Yi Lin, Ajay Jain, and Chen-Hsuan Lin for useful discussions and feedback. Thanks also go to Yin Xi and Thomas Hayes for clarifying the evaluation protocol of Make-A-Video and to Ming Ding for the details of CogVideo. We thank the ICCV PCs, ACs, and reviewers for their service and valuable feedback. This work is partly supported by NSF grants No. IIS-1910132 and IIS-2213335. + +# References + +[1] Jie An, Songyang Zhang, Harry Yang, Sonal Gupta, Jia-Bin Huang, Jiebo Luo, and Xi Yin. Latent-shift: Latent diffusion with temporal shift for efficient text-to-video generation. arXiv preprint arXiv:2304.08477, 2023. 3, 7 +[2] Yogesh Balaji, Seungjun Nah, Xun Huang, Arash Vahdat, Jiaming Song, Qinsheng Zhang, Karsten Kreis, Miika Aittala, Timo Aila, Samuli Laine, Bryan Catanzaro, et al. eDiff-I: Text-to-image diffusion models with an ensemble of expert denoisers. arXiv preprint arXiv:2211.01324, 2022. 1, 3, 5, 7 +[3] Omer Bar-Tal, Dolev Ofri-Amar, Rafail Fridman, Yoni Kasten, and Tali Dekel. Text2live: Text-driven layered image and video editing. 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+ ], + "type": "text", + "content": "The supernova explosion of a white dwarf in the universe, photo realistic." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 378, + 407, + 541, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 407, + 541, + 441 + ], + "spans": [ + { + "bbox": [ + 378, + 407, + 541, + 441 + ], + "type": "text", + "content": "A high-quality 3D render of hyperrealist, super strong, multicolor stripped, and fluffy bear with wings, highly detailed." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 449, + 546, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 546, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 546, + 474 + ], + "type": "text", + "content": "Figure 1: Given a text description, our approach can faithfully generate videos that are consistent with the input text while being photorealistic and temporally consistent. Best viewed with Acrobat Reader. Click the images to play the video clips." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 143, + 488, + 192, + 501 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 488, + 192, + 501 + ], + "spans": [ + { + "bbox": [ + 143, + 488, + 192, + 501 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 45, + 514, + 290, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 514, + 290, + 693 + ], + "spans": [ + { + "bbox": [ + 45, + 514, + 290, + 693 + ], + "type": "text", + "content": "Despite tremendous progress in generating high-quality images using diffusion models, synthesizing a sequence of animated frames that are both photorealistic and temporally coherent is still in its infancy. While off-the-shelf billion-scale datasets for image generation are available, collecting similar video data of the same scale is still challenging. Also, training a video diffusion model is computationally much more expensive than its image counterpart. In this work, we explore finetuning a pretrained image diffusion model with video data as a practical solution for the video synthesis task. We find that naively extending the image noise prior to video noise prior in video diffusion leads to sub-optimal performance. Our carefully designed video noise prior leads to substantially better performance. Extensive experimental validation shows that our" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 489, + 547, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 489, + 547, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 489, + 547, + 574 + ], + "type": "text", + "content": "model, Preserve Your Own COrelation (PYoCo), attains SOTA zero-shot text-to-video results on the UCF-101 and MSR-VTT benchmarks. It also achieves SOTA video generation quality on the small-scale UCF-101 benchmark with a " + }, + { + "bbox": [ + 306, + 489, + 547, + 574 + ], + "type": "inline_equation", + "content": "10 \\times" + }, + { + "bbox": [ + 306, + 489, + 547, + 574 + ], + "type": "text", + "content": " smaller model using significantly less computation than the prior art. The project page is available at https://research.nvidia.com/labs/dir/pyoco/." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 597, + 386, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 386, + 609 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 386, + 609 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 617, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 548, + 715 + ], + "type": "text", + "content": "Large-scale diffusion-based text-to-image models [38, 42, 2] have demonstrated impressive capabilities in turning complex text descriptions into photorealistic images. They can generate images with novel concepts unseen during training. Sophisticated image editing and processing tasks can easily be accomplished through guidance control and embedding techniques. Due to the immense success in several applications [30, 67, 5], these models are established as pow-" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 206, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 206, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 206, + 712 + ], + "type": "text", + "content": "*Work done during an internship at NVIDIA." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "text", + "content": "22930" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 69, + 321, + 217 + ], + "blocks": [ + { + "bbox": [ + 48, + 69, + 321, + 217 + ], + "lines": [ + { + "bbox": [ + 48, + 69, + 321, + 217 + ], + "spans": [ + { + "bbox": [ + 48, + 69, + 321, + 217 + ], + "type": "image", + "image_path": "3ea06ec868739f34b3665eb70207e13f0537015064d7770050b4c180314a5265.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 176, + 222, + 188, + 232 + ], + "lines": [ + { + "bbox": [ + 176, + 222, + 188, + 232 + ], + "spans": [ + { + "bbox": [ + 176, + 222, + 188, + 232 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 360, + 74, + 538, + 215 + ], + "blocks": [ + { + "bbox": [ + 360, + 74, + 538, + 215 + ], + "lines": [ + { + "bbox": [ + 360, + 74, + 538, + 215 + ], + "spans": [ + { + "bbox": [ + 360, + 74, + 538, + 215 + ], + "type": "image", + "image_path": "e6d7c286fd69acb9c2a133e2940d19045711e89bb8826830f27c7352a116b27c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 443, + 222, + 455, + 232 + ], + "lines": [ + { + "bbox": [ + 443, + 222, + 455, + 232 + ], + "spans": [ + { + "bbox": [ + 443, + 222, + 455, + 232 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 242, + 547, + 361 + ], + "lines": [ + { + "bbox": [ + 46, + 242, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 242, + 547, + 361 + ], + "type": "text", + "content": "Figure 2: Visualizing the noise map correlations. (a) visualizes the t-SNE plot of the noise maps corresponding to input frames randomly sampled from videos. These noise maps are obtained by running a diffusion ODE [49, 48] on the input frames using a trained text-to-image model, but in the opposite direction of image synthesis (" + }, + { + "bbox": [ + 46, + 242, + 547, + 361 + ], + "type": "inline_equation", + "content": "\\sigma : 0 \\to \\sigma_{\\max}" + }, + { + "bbox": [ + 46, + 242, + 547, + 361 + ], + "type": "text", + "content": "). The green dots in the background denote the reference noise maps sampled from an i.i.d. Gaussian distribution. The red dots and yellow dots are noise maps corresponding to input frames coming from different videos. We found they are spread out and share no correlation. On the other hand, the noise maps corresponding to the frames coming from the same video (shown in blue dots) are clustered together. (b) Using an i.i.d. noise model (orange dots) for finetuning text-to-image models for video synthesis is not ideal since temporal correlations between frames are not modeled. To remedy this, we propose a progressive noise model in which the correlation between different noise maps is injected along the temporal axis. Our progressive noise model (blue dots) aptly models the correlations present in the video noise maps." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 383, + 288, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 383, + 288, + 442 + ], + "spans": [ + { + "bbox": [ + 46, + 383, + 288, + 442 + ], + "type": "text", + "content": "erful image synthesis tools for content generation. As image synthesis is largely democratized with the success of these text-to-image models, it is natural to ask whether we can repeat the same success in video synthesis with large-scale diffusion-based text-to-video models." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 446, + 288, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 446, + 288, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 446, + 288, + 662 + ], + "type": "text", + "content": "Multiple attempts have been made to build large-scale video diffusion models. Ho et al. [17] proposed a UNet-based architecture for the video synthesis task that is trained using joint image-video denoising losses.Imagen video [14] extends the cascaded text-to-image generation architecture ofImagen [42] for video generation. In both works, the authors directly train a video generation model from scratch. While these approaches achieve great success and produce high-quality videos, they are inherently expensive to train, requiring hundreds of high-end GPUs or TPU's and several weeks of training. After all, video generators not only need to learn to form individual images but should also learn to synthesize coherent temporal dynamics, which makes the video generation task much more challenging. While the formation of individual frames is a shared component in an image and video synthesis, these works disregard the existence of powerful pretrained text-to-image diffusion models and train their video generators from scratch." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "We explore a different avenue for building large-scale text-to-video diffusion models by starting with a pretrained text-to-image diffusion model. Our motivation is that most of the components learned for the image synthesis task can" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 383, + 547, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 383, + 547, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 383, + 547, + 647 + ], + "type": "text", + "content": "effectively be reused for video generation, leading to knowledge transfer and efficient training. A similar idea is adopted by several recent works [46, 69, 4]. Without exception, when finetuning, they naively extend the image diffusion noise prior (i.i.d. noise) used in the text-to-image model to a video diffusion noise prior by adding an extra dimension to the 2D noise map. We argue that this approach is not ideal as it does not utilize the natural correlations in videos that are already learned by the image models. This is illustrated in Figure 2, where we visualize the t-SNE plot of noise maps corresponding to different input frames as obtained from a pretrained text-to-image diffusion model. The noise maps corresponding to different frames coming from the same video (blue dots in Figure 2a are clustered together, exhibiting a high degree of correlation. The use of i.i.d. noise prior does not model this correlation, which would impede the finetuning process. Our careful analysis of the video diffusion noise prior leads us to a noise prior that is better tailored for finetuning an image synthesis model to the video generation task. As illustrated in Figure 2b, our proposed noise prior (shown in blue dots) aptly captures the correlations in noise maps corresponding to video frames." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 653, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 548, + 715 + ], + "type": "text", + "content": "We then proceed to build a large-scale diffusion-based text-to-video model. We leverage several design choices from the prior works, including the use of temporal attention [17], joint image-video finetuning [17], a cascaded generation architecture [14], and an ensemble of expert denois-" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "22931" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "ers [2]. Together with these techniques and the proposed video noise prior, our model establishes a new state-of-the-art for video generation outperforming competing methods on several benchmark datasets. Figure 1 shows our model can achieve high-quality zero-shot video synthesis capability with SOTA photorealism and temporal consistency." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 144, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 144, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 59, + 144, + 287, + 156 + ], + "type": "text", + "content": "In short, our work makes the following key contributions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 43, + 163, + 287, + 253 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 43, + 163, + 287, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 43, + 163, + 287, + 186 + ], + "spans": [ + { + "bbox": [ + 43, + 163, + 287, + 186 + ], + "type": "text", + "content": "1. We propose a video diffusion noise tailored for finetuning text-to-image diffusion models for text-to-video." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 43, + 191, + 287, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 43, + 191, + 287, + 215 + ], + "spans": [ + { + "bbox": [ + 43, + 191, + 287, + 215 + ], + "type": "text", + "content": "2. We conduct extensive experimental validation and verify the effectiveness of the proposed noise prior." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 43, + 218, + 287, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 43, + 218, + 287, + 253 + ], + "spans": [ + { + "bbox": [ + 43, + 218, + 287, + 253 + ], + "type": "text", + "content": "3. We build a large-scale text-to-video diffusion model by finetuning a pretrained eDiff-I model with our noise prior and achieve state-of-the-art results on several benchmarks." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 262, + 134, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 262, + 134, + 274 + ], + "spans": [ + { + "bbox": [ + 47, + 262, + 134, + 274 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 283, + 287, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 283, + 287, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 283, + 287, + 474 + ], + "type": "text", + "content": "Diffusion-based text-to-image models: Diffusion models have significantly advanced the progress of text-based photorealistic, compositional image generation [38, 42]. Given the nature of the iterative denoising process that requires massive numbers of score function evaluations, earlier diffusion models focused on generating low-resolution images, e.g., " + }, + { + "bbox": [ + 46, + 283, + 287, + 474 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 46, + 283, + 287, + 474 + ], + "type": "text", + "content": " [15, 48]. To generate high-resolution images, two common approaches have been used. The first approach applies cascaded super-resolution models in the RGB space [32, 16, 42, 38], while the second approach leverages a decoder to exploit latent space [40, 11]. Based on these models, advanced image and video editing have been achieved through finetuning the model [41, 67, 5, 23, 61, 29] or controlling the inference process [30, 13, 34, 10, 35, 7, 31, 3]. Here, we study the problem of using large-scale diffusion models for text-to-video generation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 288, + 714 + ], + "type": "text", + "content": "Video generation models: Generating realistic and novel videos have long been an attractive and essential research direction [58, 39, 65]. Previously studies have resorted to different types of generative models such as GANs [58, 43, 54, 52, 45], Autoregressive models [51, 63, 25, 9, 18], and implicit neural representations [47, 66]. Recently, driven by the tremendous success of applying the diffusion model to image synthesis, multiple works have proposed to explore diffusion models for conditional and unconditional video synthesis [57, 12, 69, 61, 4, 22, 19, 57, 64, 33, 28, 1, 59]. For example, Singer et al. extend the unCLIP framework [38] to text-to-video generation, which allows training without video captions [46]. Ho et al. [17] extend the Imagen framework [42] by repeatedly up-scaling low-resolution small-fps videos in both spatial and temporal directions with multiple models [14]. Our work also falls into this line of work which uses a diffusion model. We focus on augmenting an image diffusion model for video and study the design choice of the diffusion noise priors for such an image-to-video finetuning task." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 547, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 312 + ], + "type": "text", + "content": "Leverage knowledge from images for text-to-video generation: Like text-to-image models, text-to-video models require massive amounts of data to learn caption-relatedness, frame photorealism, and temporal dynamics. But in contrast to the abundant image data resource, video data are more limited in style, volume, and quality. To resolve such scarcity issue of text-video data, previous works have resorted to different strategies to leverage knowledge from image data for text-to-video generation, including joint training on the text-image data from scratch [17, 14, 56, 60], first training a text-to-image model and then finetuning partially [18, 4, 61, 29] or entirely [46, 8] on the video dataset, and using CLIP image features as the conditional information [46, 69]. In this paper, we propose a new video diffusion noise prior that is tailored for finetuning a pretrained diffusion-based image generation model for the video generation task. We reuse several design choices in the prior work by finetuning jointly on text-image and text-video datasets. As a result, we can build a text-to-video generation system that achieves state-of-the-art zero-shot performances." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 324, + 390, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 324, + 390, + 337 + ], + "spans": [ + { + "bbox": [ + 306, + 324, + 390, + 337 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "spans": [ + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "text", + "content": "Diffusion models generate data by iteratively denoising samples drawn from a noise distribution. In the case of text-to-video models, text embeddings obtained from a pre-trained text encoder are used as additional inputs in the denoising process. Formally, let " + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "inline_equation", + "content": "D(\\mathbf{x}, \\mathbf{e}, \\sigma)" + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "text", + "content": " denote a denoising network that operates on the noisy input video " + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^{b \\times n_s \\times 3 \\times h \\times w}" + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "inline_equation", + "content": "\\mathbf{e}" + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "text", + "content": " is the text embedding, and " + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "text", + "content": " is the noise level. Here " + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "inline_equation", + "content": "n_s" + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "text", + "content": " is the sequence length of the input video, " + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "text", + "content": " is the batch size, and " + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "inline_equation", + "content": "h \\times w" + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "text", + "content": " is the spatial resolution. The model " + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "text", + "content": " is trained to denoise the input " + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 345, + 547, + 464 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 483, + 547, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 483, + 547, + 507 + ], + "spans": [ + { + "bbox": [ + 306, + 483, + 547, + 507 + ], + "type": "text", + "content": "Training We follow the EDM formulation of Karras et al. [21] to optimize the denoiser " + }, + { + "bbox": [ + 306, + 483, + 547, + 507 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 306, + 483, + 547, + 507 + ], + "type": "text", + "content": " using the following objective" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 517, + 545, + 558 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 517, + 545, + 558 + ], + "spans": [ + { + "bbox": [ + 315, + 517, + 545, + 558 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbb {E} _ {p _ {\\text {d a t a}} (\\mathbf {x} _ {\\text {c l e a n}}, \\mathbf {e}), p (\\epsilon), p (\\sigma)} \\left[ \\lambda (\\sigma) \\| D \\left(\\mathbf {x} _ {\\text {n o i s e}}; \\mathbf {e}, \\sigma\\right) - \\mathbf {x} _ {\\text {c l e a n}} \\| _ {2} ^ {2} \\right] \\tag {1} \\\\ w h e r e \\quad \\mathbf {x} _ {\\text {n o i s e}} = \\mathbf {x} _ {\\text {c l e a n}} + \\sigma \\epsilon \\\\ \\end{array}", + "image_path": "26d73508980f20890390f365c70ba3ea636609a31cccb9fd6680fe0fd3910cad.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{noise}}" + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": " is the noisy sample obtained by corrupting the clean video " + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": " with noise " + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\sigma \\epsilon" + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "inline_equation", + "content": "p(\\epsilon) = \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": " is a scalar for the noise level drawn from " + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "inline_equation", + "content": "p(\\sigma)" + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": ". The loss weight, " + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\lambda (\\sigma)" + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": ", is a function of " + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": " given by " + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\lambda (\\sigma) = (\\sigma^2 +\\sigma_{\\mathrm{data}}^2) / (\\sigma \\cdot \\sigma_{\\mathrm{data}})^2" + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": ". Eq. (1) is a simple denoising objective in which the denoiser " + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": " is trained to estimate the clean video " + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{clean}}" + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": " from the noisy input " + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathrm{noise}}" + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": ". Following EDM, we use a log-normal distribution for " + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": " i.e., " + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\ln (p(\\sigma)) = \\mathcal{N}(P_{\\mathrm{mean}},P_{\\mathrm{std}}^2)" + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{mean}} = -1.2" + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{std}} = 1.2" + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "To train the denoising model, EDM uses preconditioning terms in its objective function to properly scale the inputs and output of the denoiser model " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": ". More specifically, the" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "22932" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 179, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 179, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 179, + 83 + ], + "type": "text", + "content": "denoising model " + }, + { + "bbox": [ + 47, + 72, + 179, + 83 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 72, + 179, + 83 + ], + "type": "text", + "content": " is written as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 58, + 92, + 276, + 118 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 92, + 276, + 118 + ], + "spans": [ + { + "bbox": [ + 58, + 92, + 276, + 118 + ], + "type": "interline_equation", + "content": "D (\\mathbf {x}; \\mathbf {e}, \\sigma) := \\left(\\frac {\\sigma_ {\\mathrm {d a t a}}}{\\sigma^ {*}}\\right) ^ {2} \\mathbf {x} + \\frac {\\sigma \\cdot \\sigma_ {\\mathrm {d a t a}}}{\\sigma^ {*}} F _ {\\theta} \\left(\\frac {\\mathbf {x}}{\\sigma^ {*}}; \\mathbf {e}, \\frac {\\ln (\\sigma)}{4}\\right)", + "image_path": "ee33060d3d02bc6cfc91d09991e5f25c6b53f309e1b5109142c12eef254acffa.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 124, + 287, + 149 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 124, + 287, + 149 + ], + "spans": [ + { + "bbox": [ + 47, + 124, + 287, + 149 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 47, + 124, + 287, + 149 + ], + "type": "inline_equation", + "content": "F_{\\theta}" + }, + { + "bbox": [ + 47, + 124, + 287, + 149 + ], + "type": "text", + "content": " is a neural network with parameters " + }, + { + "bbox": [ + 47, + 124, + 287, + 149 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 124, + 287, + 149 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 124, + 287, + 149 + ], + "type": "inline_equation", + "content": "\\sigma^{*} = \\sqrt{\\sigma^{2} + \\sigma_{\\mathrm{data}}^{2}}" + }, + { + "bbox": [ + 47, + 124, + 287, + 149 + ], + "type": "text", + "content": ". We use " + }, + { + "bbox": [ + 47, + 124, + 287, + 149 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{data}} = 0.5" + }, + { + "bbox": [ + 47, + 124, + 287, + 149 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 163, + 287, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 163, + 287, + 186 + ], + "spans": [ + { + "bbox": [ + 47, + 163, + 287, + 186 + ], + "type": "text", + "content": "Sampling Once the denoising model is trained, sampling can be performed by solving the following ODE [21]" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 73, + 194, + 287, + 219 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 194, + 287, + 219 + ], + "spans": [ + { + "bbox": [ + 73, + 194, + 287, + 219 + ], + "type": "interline_equation", + "content": "\\frac {d \\mathbf {x}}{d \\sigma} = - \\sigma \\nabla_ {\\mathbf {x}} \\log p (\\mathbf {x} | \\mathbf {e}, \\sigma) = \\frac {\\mathbf {x} - D (\\mathbf {x} ; \\mathbf {e} , \\sigma)}{\\sigma} \\tag {2}", + "image_path": "18632e7a98f8dac3881f7bc871fea5f3b01be2f798d67e10b3df414a6f11203a.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 226, + 288, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 226, + 288, + 309 + ], + "spans": [ + { + "bbox": [ + 47, + 226, + 288, + 309 + ], + "type": "text", + "content": "for " + }, + { + "bbox": [ + 47, + 226, + 288, + 309 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 226, + 288, + 309 + ], + "type": "text", + "content": " flowing backwards from " + }, + { + "bbox": [ + 47, + 226, + 288, + 309 + ], + "type": "inline_equation", + "content": "\\sigma = \\sigma_{\\mathrm{max}}" + }, + { + "bbox": [ + 47, + 226, + 288, + 309 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 226, + 288, + 309 + ], + "type": "inline_equation", + "content": "\\sigma = 0" + }, + { + "bbox": [ + 47, + 226, + 288, + 309 + ], + "type": "text", + "content": ". The initial value for " + }, + { + "bbox": [ + 47, + 226, + 288, + 309 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 47, + 226, + 288, + 309 + ], + "type": "text", + "content": " is obtained by sampling from the prior distribution " + }, + { + "bbox": [ + 47, + 226, + 288, + 309 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\sim \\mathcal{N}(\\mathbf{0}, \\sigma_{\\mathrm{max}}^2 \\mathbf{I})" + }, + { + "bbox": [ + 47, + 226, + 288, + 309 + ], + "type": "text", + "content": ". Over the recent years, several samplers have been proposed for sampling from the trained diffusion models [68, 48, 26, 27, 15]. In this paper, we use DEIS [68] and its stochastic variant [21] for synthesizing samples from our model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 319, + 103, + 332 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 319, + 103, + 332 + ], + "spans": [ + { + "bbox": [ + 47, + 319, + 103, + 332 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 340, + 289, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 289, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 289, + 533 + ], + "type": "text", + "content": "Training text-to-video models is much more challenging than training text-to-image diffusion models due to practical difficulties in collecting billion-scale video datasets and securing enough computational resources. Additionally, generating videos is much more challenging since individual frames need to be both photorealistic and temporally coherent. Prior works leverage large-scale image datasets to mitigate these difficulties by either joint training on the image datasets [60, 17, 14] or finetuning a text-to-image model on the video datasets [18, 46]. Here, we are interested in finetuning text-to-image diffusion models jointly on image and video datasets. We postulate that naively extending the image noise prior to video diffusion is not ideal. We carefully explore the design space of noise priors and propose one that is well suited for our video finetuning task, which leads to significant performance gains." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 545, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 289, + 714 + ], + "type": "text", + "content": "Correlated noise model An image diffusion model is trained to denoise independent noise from a perturbed image. The noise vector " + }, + { + "bbox": [ + 46, + 545, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 545, + 289, + 714 + ], + "type": "text", + "content": " in the denoising objective (1) is sampled from an i.i.d. Gaussian distribution " + }, + { + "bbox": [ + 46, + 545, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0, \\mathbf{I})" + }, + { + "bbox": [ + 46, + 545, + 289, + 714 + ], + "type": "text", + "content": ". However, after training the image diffusion model and applying it to reverse real frames from a video into the noise space in a per-frame manner, we find that the noise maps corresponding to different frames are highly correlated. This is illustrated in Figure 2, where the t-SNE plot of noise maps corresponding to different video frames are plotted. When the input frames come from the same video (shown in blue dots in Figure 2a, noise maps are clustered. The use of i.i.d. sampling (shown in orange dots in Figure 2b does not capture these correlations. This is also depicted quantitatively" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 70, + 547, + 118 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 70, + 547, + 118 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 547, + 118 + ], + "type": "text", + "content": "Table 1: Cosine similarity of the reversed noise. The noise maps corresponding to the frames sampled from the same videos have a higher similarity than those sampled from different videos." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 324, + 122, + 528, + 171 + ], + "blocks": [ + { + "bbox": [ + 324, + 122, + 528, + 171 + ], + "lines": [ + { + "bbox": [ + 324, + 122, + 528, + 171 + ], + "spans": [ + { + "bbox": [ + 324, + 122, + 528, + 171 + ], + "type": "table", + "html": "
Cosine Similarity
(a) Same video noise0.206±0.156
(b) Different video noise0.001±0.009
", + "image_path": "4383742137095222d6e0d6fa310f41451b12d67c8f340416c502a161b125485a.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 188, + 547, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 188, + 547, + 319 + ], + "spans": [ + { + "bbox": [ + 304, + 188, + 547, + 319 + ], + "type": "text", + "content": "in Table 1 where we compute the average pairwise cosine similarity between noise corresponding to (a) same video and (b) different video. (a) is much higher than (b). As a result, the video diffusion model trained with i.i.d. noise is coerced to forget such correlation among the noise between different frames, making it difficult to preserve knowledge from the image diffusion model. Motivated by this observation, we propose to modify the noise process to preserve the correlation between different frames. To this end, we investigate two noisng strategies - mixed and progressive noising." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "content": "Mixed noise model: Let " + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "inline_equation", + "content": "\\epsilon^1, \\epsilon^2, \\ldots, \\epsilon^{n_s}" + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "content": " denote the noise corresponding to individual video frames i.e., " + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "inline_equation", + "content": "\\epsilon^i" + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "content": " corresponds to the " + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "content": " element of the noise tensor " + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "content": ". In the mixed noise model, we generate two noise vectors " + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mathrm{shared}}" + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mathrm{ind}}" + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mathrm{shared}}" + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "content": " is a common noise vector shared among all video frames, while " + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mathrm{ind}}" + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "content": " is the individual noise per frame. The linear combination of both these vectors is used as the final noise." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 406, + 547, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 406, + 547, + 449 + ], + "spans": [ + { + "bbox": [ + 313, + 406, + 547, + 449 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\epsilon_ {\\text {s h a r e d}} \\sim \\mathcal {N} \\left(\\mathbf {0}, \\frac {\\alpha^ {2}}{1 + \\alpha^ {2}} \\mathbf {I}\\right), \\epsilon_ {\\text {i n d}} ^ {i} \\sim \\mathcal {N} \\left(\\mathbf {0}, \\frac {1}{1 + \\alpha^ {2}} \\mathbf {I}\\right) \\tag {3} \\\\ \\epsilon^ {i} = \\epsilon_ {\\mathrm {s h a r e d}} + \\epsilon_ {\\mathrm {i n d}} ^ {i} \\\\ \\end{array}", + "image_path": "dca847bc8f7704f295db237e4db10772ef10e8b0b7ae619e72832ee7b86de264.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 453, + 547, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 547, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 547, + 525 + ], + "type": "text", + "content": "Progressive noise model: In the progressive noise model, the noise for each frame is generated in an autoregressive fashion in which the noise at frame " + }, + { + "bbox": [ + 304, + 453, + 547, + 525 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 453, + 547, + 525 + ], + "type": "text", + "content": " is generated by perturbing the noise at frame " + }, + { + "bbox": [ + 304, + 453, + 547, + 525 + ], + "type": "inline_equation", + "content": "i - 1" + }, + { + "bbox": [ + 304, + 453, + 547, + 525 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 304, + 453, + 547, + 525 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mathrm{ind}}^i" + }, + { + "bbox": [ + 304, + 453, + 547, + 525 + ], + "type": "text", + "content": " denote the independent noise generated for frame " + }, + { + "bbox": [ + 304, + 453, + 547, + 525 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 453, + 547, + 525 + ], + "type": "text", + "content": ". Then, progressive noising can be formulated as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 348, + 529, + 547, + 554 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 529, + 547, + 554 + ], + "spans": [ + { + "bbox": [ + 348, + 529, + 547, + 554 + ], + "type": "interline_equation", + "content": "\\epsilon^ {0} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}) \\quad \\epsilon_ {\\mathrm {i n d}} ^ {i} \\sim \\mathcal {N} (\\mathbf {0}, \\frac {1}{1 + \\alpha^ {2}} \\mathbf {I}) \\tag {4}", + "image_path": "44ef6a678f219a548d5db8ae77704fa44843eff670ca329c41f0ff1a1e72a69c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 385, + 555, + 492, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 385, + 555, + 492, + 578 + ], + "spans": [ + { + "bbox": [ + 385, + 555, + 492, + 578 + ], + "type": "interline_equation", + "content": "\\epsilon^ {i} = \\frac {\\alpha}{\\sqrt {1 + \\alpha^ {2}}} \\epsilon^ {i - 1} + \\epsilon_ {\\mathrm {i n d}} ^ {i}", + "image_path": "12a0fc2a80a8530f4cf6cef049ec24f1074871c41d0cba403471a46ea0e608ce.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 582, + 547, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 653 + ], + "type": "text", + "content": "In both these models, " + }, + { + "bbox": [ + 304, + 582, + 547, + 653 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 582, + 547, + 653 + ], + "type": "text", + "content": " controls how much noise is shared among different video frames. The higher the value of " + }, + { + "bbox": [ + 304, + 582, + 547, + 653 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 582, + 547, + 653 + ], + "type": "text", + "content": ", the more correlation exists among the noise maps corresponding to different frames. As " + }, + { + "bbox": [ + 304, + 582, + 547, + 653 + ], + "type": "inline_equation", + "content": "\\alpha \\rightarrow \\infty" + }, + { + "bbox": [ + 304, + 582, + 547, + 653 + ], + "type": "text", + "content": ", all frames would have the same noise which results in generating a frozen video. On the other hand, " + }, + { + "bbox": [ + 304, + 582, + 547, + 653 + ], + "type": "inline_equation", + "content": "\\alpha = 0" + }, + { + "bbox": [ + 304, + 582, + 547, + 653 + ], + "type": "text", + "content": " corresponds to i.i.d. noise." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": "As shown in Figure 2b, the use of progressive noise sampling (blue dots) better models the correlations between different noise maps by obtaining similar clustering patterns to the noise maps of real video frames embedded by a pretrained text-to-image model in Figure 2a (blue dots)." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "text", + "content": "22933" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 547, + 235 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 547, + 235 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 547, + 235 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 547, + 235 + ], + "type": "image", + "image_path": "8d6b3d4c8df87f34a0ce9703c0a7f610b6687418e672edb194d3268825477a99.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 248, + 548, + 309 + ], + "lines": [ + { + "bbox": [ + 46, + 248, + 548, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 248, + 548, + 309 + ], + "type": "text", + "content": "Figure 3: Model architecture. Our pipeline consists of a cascade of four networks — a base model and three upsampling models. All four models take inputs as the text embeddings obtained from the T5 encoder and the CLIP text encoder. The base model produces 16 video frames of spatial resolution " + }, + { + "bbox": [ + 46, + 248, + 548, + 309 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 46, + 248, + 548, + 309 + ], + "type": "text", + "content": " with a frameskip of 5. The first upsampling model performs a temporal interpolation, resulting in videos of size " + }, + { + "bbox": [ + 46, + 248, + 548, + 309 + ], + "type": "inline_equation", + "content": "76 \\times 64 \\times 64" + }, + { + "bbox": [ + 46, + 248, + 548, + 309 + ], + "type": "text", + "content": " while the subsequent two super-resolution models perform spatial super-resolution to produce videos of sizes " + }, + { + "bbox": [ + 46, + 248, + 548, + 309 + ], + "type": "inline_equation", + "content": "76 \\times 256 \\times 256" + }, + { + "bbox": [ + 46, + 248, + 548, + 309 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 248, + 548, + 309 + ], + "type": "inline_equation", + "content": "76 \\times 1024 \\times 1024" + }, + { + "bbox": [ + 46, + 248, + 548, + 309 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 324, + 289, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 289, + 528 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 289, + 528 + ], + "type": "text", + "content": "Model architecture As visualized in Figure 3, our model consists of a cascade of four networks — a base network and three upsampling stacks. The base network generates an output video of dimension " + }, + { + "bbox": [ + 46, + 324, + 289, + 528 + ], + "type": "inline_equation", + "content": "16 \\times 64 \\times 64" + }, + { + "bbox": [ + 46, + 324, + 289, + 528 + ], + "type": "text", + "content": " with a frameskip of 5. It generates the frames " + }, + { + "bbox": [ + 46, + 324, + 289, + 528 + ], + "type": "inline_equation", + "content": "\\{1,6,11,\\ldots,76\\}" + }, + { + "bbox": [ + 46, + 324, + 289, + 528 + ], + "type": "text", + "content": ". The first upsampling network performs a temporal interpolation to produce a video of size " + }, + { + "bbox": [ + 46, + 324, + 289, + 528 + ], + "type": "inline_equation", + "content": "76 \\times 64 \\times 64" + }, + { + "bbox": [ + 46, + 324, + 289, + 528 + ], + "type": "text", + "content": ". The second and the third super-resolution network performs spatial upsampling to produce the outputs of sizes " + }, + { + "bbox": [ + 46, + 324, + 289, + 528 + ], + "type": "inline_equation", + "content": "76 \\times 256 \\times 256" + }, + { + "bbox": [ + 46, + 324, + 289, + 528 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 324, + 289, + 528 + ], + "type": "inline_equation", + "content": "76 \\times 1024 \\times 1024" + }, + { + "bbox": [ + 46, + 324, + 289, + 528 + ], + "type": "text", + "content": ". We utilize eDiff-I [2], a state-of-the-art text-to-image diffusion model, to initialize our base and spatial super-resolution models. Similar to prior works [17, 46], we adapt the image-based U-Net model for the video synthesis task by making the following changes: (1) Transforming 2D convolutions to 3D by adding a dimension 1 to temporal axis and (2) Adding temporal attention layers. Please refer to the supplementary material for more details." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 528, + 288, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 528, + 288, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 528, + 288, + 612 + ], + "type": "text", + "content": "Similar to Ho et al. [17], we jointly finetune the model on video and image datasets by concatenating videos and images in the temporal axis and applying our temporal modules only on the video part. Similarly to eDiff-I, our model uses both T5 text embeddings [37] and CLIP text embeddings [36]. We drop each of the embeddings independently at random during training, as in eDiff-I." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 621, + 128, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 128, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 128, + 635 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 642, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 289, + 714 + ], + "type": "text", + "content": "In this section, we evaluate our proposed strategy of training diffusion models for video synthesis on two sets of experiments. We first comprehensively analyze our proposed noise model on the small-scale UCF-101 dataset. We then scale up our experiments to the challenging large-scale text-to-video synthesis task." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 324, + 426, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 324, + 426, + 337 + ], + "spans": [ + { + "bbox": [ + 306, + 324, + 426, + 337 + ], + "type": "text", + "content": "5.1. Experimental Setups" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 342, + 548, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 342, + 548, + 379 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 548, + 379 + ], + "type": "text", + "content": "We conduct ablation experiments in a small-scale unconditional video generation setting and pick the best configuration for our large-scale text-to-video generation run." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 394, + 547, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 394, + 547, + 538 + ], + "spans": [ + { + "bbox": [ + 304, + 394, + 547, + 538 + ], + "type": "text", + "content": "Datasets We train our model on the UCF-101 dataset [50] for the small-scale experiments, where we follow the protocol defined in Ho et al. [17] to generate videos of size " + }, + { + "bbox": [ + 304, + 394, + 547, + 538 + ], + "type": "inline_equation", + "content": "16 \\times 64 \\times 64" + }, + { + "bbox": [ + 304, + 394, + 547, + 538 + ], + "type": "text", + "content": ". UCF-101 dataset contains 13,320 videos. We randomly sample frames from these videos to train our image synthesis model. For our large-scale experiments, we use a combination of public and proprietary datasets for text-to-image and text-to-video finetuning. Most of the videos are of 2K resolution with 16:9 aspect ratio. All data was filtered using a preset CLIP and aesthetic scores* to ensure high quality. Our final image dataset contains around 1.2 billion text-image pairs and 22.5 million text-video pairs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 554, + 547, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 554, + 547, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 547, + 686 + ], + "type": "text", + "content": "Training details In the unconditional generation experiment on the UCF-101 dataset, to do an ablation study on the model size, we design 3 models where each model has 69M, 112M, and 253M parameters, respectively. As a comparison, the baseline Video Diffusion Model (VDM) [17] contains 1.2B parameters. In the large-scale text-to-video experiment, our base and temporal interpolation models contain 1.08B parameters. Our super-resolution model adapted from the efficient U-Net [42] architecture with temporal convolution layers [14, 46] contains 313M parameters. Please refer to the supplementary material for more training details." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 504, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 504, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 504, + 713 + ], + "type": "text", + "content": "\\*https://github.com/christophschuhmann/ improved-aesthetic-predictor" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "22934" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 170, + 191 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 170, + 191 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 170, + 191 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 170, + 191 + ], + "type": "image", + "image_path": "be0d32f6c5261750250a55f4cff915a053e9259ad86489ddce09cc007e0763ed.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 170, + 71, + 290, + 191 + ], + "blocks": [ + { + "bbox": [ + 170, + 71, + 290, + 191 + ], + "lines": [ + { + "bbox": [ + 170, + 71, + 290, + 191 + ], + "spans": [ + { + "bbox": [ + 170, + 71, + 290, + 191 + ], + "type": "image", + "image_path": "4b5f2ccad8a2a714b4777005a783956b00b8fe07cd922ddc9476fa3b96ba75c6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 170, + 196, + 290, + 242 + ], + "lines": [ + { + "bbox": [ + 170, + 196, + 290, + 242 + ], + "spans": [ + { + "bbox": [ + 170, + 196, + 290, + 242 + ], + "type": "text", + "content": "An epic tornado attacking above a glowing city at night, the tornado is made of smoke, highly detailed." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 290, + 71, + 411, + 191 + ], + "blocks": [ + { + "bbox": [ + 290, + 71, + 411, + 191 + ], + "lines": [ + { + "bbox": [ + 290, + 71, + 411, + 191 + ], + "spans": [ + { + "bbox": [ + 290, + 71, + 411, + 191 + ], + "type": "image", + "image_path": "0b71e5432321661882bb8e9d07f88930204323a4e84990b34323694870a32f4e.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 411, + 71, + 533, + 191 + ], + "blocks": [ + { + "bbox": [ + 411, + 71, + 533, + 191 + ], + "lines": [ + { + "bbox": [ + 411, + 71, + 533, + 191 + ], + "spans": [ + { + "bbox": [ + 411, + 71, + 533, + 191 + ], + "type": "image", + "image_path": "7497cd615041a3013314d3ae02fc31c19b21ba4245c7efeae2c13dcc7ecf9e74.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 416, + 196, + 536, + 242 + ], + "lines": [ + { + "bbox": [ + 416, + 196, + 536, + 242 + ], + "spans": [ + { + "bbox": [ + 416, + 196, + 536, + 242 + ], + "type": "text", + "content": "A golden retriever puppy holding a green sign that says \"NVIDIA ROCKS\". 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For the large-scale text-to-video experiments, we perform the zero-shot evaluation of the video generation quality on the UCF-101 and MSR-VTT datasets following Make-A-Video [46]. We carefully discuss the evaluation process below." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 603, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 603, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 603, + 547, + 712 + ], + "type": "text", + "content": "UCF-101 experiment We use IS and FVD for evaluation in our small-scale experiments. UCF-101 is a categorical video dataset designed for action recognition. When sampling from the text-to-video model, we devise a set of prompts for each class name to be used as the conditional input. This is necessary as some class names (such as jump rope) are not descriptive. We list all the prompts we use in the supplementary material. We sample 20 videos for each prompt to compute the IS metric. For FVD, we follow the" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "text", + "content": "22935" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 74, + 110, + 261, + 219 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 288, + 106 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 288, + 106 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 288, + 106 + ], + "type": "text", + "content": "Table 2: Zero-shot text to video generation on UCF-101. Our approach gives significant performance gains compared to the prior baselines both in inception score and FVD metrics." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 74, + 110, + 261, + 219 + ], + "lines": [ + { + "bbox": [ + 74, + 110, + 261, + 219 + ], + "spans": [ + { + "bbox": [ + 74, + 110, + 261, + 219 + ], + "type": "table", + "html": "
MethodIS (↑)FVD (↓)
CogVideo [18] (Chinese)23.55751.34
CogVideo [18] (English)25.27701.59
Make-A-Video [46]33.00367.23
MagicVideo [69]-655.00
Video LDM [4]33.45550.61
VideoFactory [59]-410.00
PYoCo47.76355.19
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MethodCLIP-FID (↓)FID (↓)
NUWA [60] (Chinese)47.68-
CogVideo [18] (Chinese)24.78-
CogVideo [18] (English)23.59-
Make-A-Video [46]13.17-
MagicVideo [69]-36.50
Latent-Shift [1]15.23-
PYoCo (Config-A)10.2125.39
PYoCo (Config-B)9.9524.28
PYoCo (Config-C)9.9124.54
PYoCo (Config-D)9.7322.14
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MethodIS (↑)FVD (↓)
TGAN [43]15.83±.18-
LDVD-GAN [20]22.91±.19-
VideoGPT [63]24.69±.30-
MoCoGAN-HD [52]32.36838
DIGAN [66]29.71±.53655±22
CCVS [25]24.47±.13386±15
StyleGAN-V [47]23.94±.73-
VDM [17]57.00±.62-
TATS [9]57.63±.73430 ±18
PYoCo (112M)57.93±.24332 ±13
PYoCo (253M)60.01±.51310 ±13
", + "image_path": "f62d1eeed007f3585f1e09ece8f1a1362f075440aaf56762c2188274607b354d.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "type": "text", + "content": "outperforms all the baselines on the UCF-101 dataset and improves the zero-shot Inception Score from 33.45 to 47.76. In Table 3, we show that our baseline model achieves a new state-of-the-art CLIP-FID score [24] of 10.21, while using ensemble models further improves both CLIP-FID and FID scores. In Figure 4, we qualitatively visualize the synthesis capability of our approach. Our model achieves high-quality zero-shot video synthesis capability with good photorealism and temporal coherency. We also provide a qualitative comparison with Make-A-Video [46] andImagen Video [14] in Figure 5. We observe that our model is able to produce videos with better details than both approaches, as shown in the animal videos. We also produce better-stylized videos thanImagen Video." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 498, + 547, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 631 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 631 + ], + "type": "text", + "content": "Small-scale unconditional video synthesis We report IS and FVD scores on UCF-101 dataset in Table 4 and compare our model with multiple unconditional video generation baselines. Note that using class labels as conditional information could lead to sizeable improvement in IS and FVD scores [9], which we do not consider as the comparison. Our method attains state-of-the-art unconditional video generation quality. Compared with previous diffusion-based unconditional generation model [17], our model is " + }, + { + "bbox": [ + 304, + 498, + 547, + 631 + ], + "type": "inline_equation", + "content": "\\sim 10\\times" + }, + { + "bbox": [ + 304, + 498, + 547, + 631 + ], + "type": "text", + "content": " smaller and has " + }, + { + "bbox": [ + 304, + 498, + 547, + 631 + ], + "type": "inline_equation", + "content": "\\sim 14\\times" + }, + { + "bbox": [ + 304, + 498, + 547, + 631 + ], + "type": "text", + "content": " less training time (75 GPU-days vs. 925 GPU-days)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 644, + 400, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 644, + 400, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 644, + 400, + 658 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "We quantitatively compare several training strategies for video diffusion models. 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bowl, in style of Van Gogh." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 434, + 204, + 539, + 308 + ], + "blocks": [ + { + "bbox": [ + 434, + 204, + 539, + 308 + ], + "lines": [ + { + "bbox": [ + 434, + 204, + 539, + 308 + ], + "spans": [ + { + "bbox": [ + 434, + 204, + 539, + 308 + ], + "type": "image", + "image_path": "05aba182271478008d147821594306e7c1e14e854c9c1fa92d32d525b402c841.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 334, + 547, + 370 + ], + "lines": [ + { + "bbox": [ + 46, + 334, + 547, + 370 + ], + "spans": [ + { + "bbox": [ + 46, + 334, + 547, + 370 + ], + "type": "text", + "content": "Figure 5: Qualitative comparison with baseline approaches. The two panels on the left show the comparison of our approach with Make-A-Video [46], while those on the right show the comparison withImagen Video [14]. PYoCo achieves better photorealism compared to the two approaches." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 53, + 417, + 280, + 502 + ], + "blocks": [ + { + "bbox": [ + 46, + 389, + 287, + 412 + ], + "lines": [ + { + "bbox": [ + 46, + 389, + 287, + 412 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 287, + 412 + ], + "type": "text", + "content": "Table 5: Quantitative results of different training strategies on UCF-101 dataset." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 417, + 280, + 502 + ], + "lines": [ + { + "bbox": [ + 53, + 417, + 280, + 502 + ], + "spans": [ + { + "bbox": [ + 53, + 417, + 280, + 502 + ], + "type": "table", + "html": "
IS(↑)FVD (↓)FID (↓)
Image Diffusion (ID)--30.05
Training from scratch28.25903.37124.75
Finetuning from ID41.25566.6756.43
+ Mixed Noise52.71337.4031.57
+ Progressive Noise53.52339.6731.88
", + "image_path": "b7e8a40bf3b433a6bb279667cea21e9ce3bc29e8fdbe343d7f1c35b135b3875f.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_body" + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 522, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 289, + 713 + ], + "type": "text", + "content": "Training strategies We compare training from scratch, a simple finetuning baseline, finetuning with mixed noising, and progressive noising using IS, FVD, and averaged frame FID metrics on the UCF-101 dataset in Table 5. We first find that finetuning from an image diffusion model is much more effective than training from scratch. For finetuning from the image model, the correlated noise model produces better video generation quality than the independent noise model. In addition, we notice that the correlated noise better preserves the image quality learned by the pretrained image model and produces a lower frame FID. This is particularly desired in large-scale text-to-video training to fulfill the goal of inheriting the knowledge from the image model missing in the video datasets. Specifically, most videos contain realistic scenes captured by cameras and have infrequent media types like paintings, illustrations, sketches, etc. Moreover, the" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 391, + 546, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 391, + 546, + 451 + ], + "spans": [ + { + "bbox": [ + 304, + 391, + 546, + 451 + ], + "type": "text", + "content": "video data is much smaller in volume, and the scenes are less diverse than image datasets. As shown in Figure 4, our model can preserve properties learned from image datasets that are not presented in our video dataset, such as the artistic styles, and generate faithful motion on them." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "text", + "content": "Correlation ratio The hyperparameter " + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "text", + "content": " in the Equations 3 and 4 controls the correlation between the noise of different frames. A larger " + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "text", + "content": " injects more correlation into the noise. The correlation disappears when " + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\alpha \\rightarrow 0" + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "text", + "content": ", and the mixed and progressive noise models reproduce the vanilla noise model. To find optimal " + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "text", + "content": ", we train our UCF-small model (69M parameters) using " + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\alpha \\in \\{0, 0.1, 0.2, 0.5, 1, 1, 2, 5, 10, \\infty\\}" + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "text", + "content": " and report FVD in Figure 7. For each " + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "text", + "content": " value, we repeat the experiment 3 times and report the mean. Note that " + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\alpha = 0" + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "text", + "content": " indicates finetuning with the independent frame noise, and " + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\alpha = \\infty" + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "text", + "content": " indicates using identical noise maps for all the frames, which produces frozen videos during the inference time. Finetuning an image diffusion model almost consistently outperforms the training-from-scratch baseline with different " + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "text", + "content": "s. Using " + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\alpha = 1" + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "text", + "content": " for mixed noisng and " + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\alpha = 2" + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "text", + "content": " for progressive noisng produces similar best results. We also show qualitative results for models trained with " + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\alpha = 0, 1, 10" + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "text", + "content": " in Figure 6. When " + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "text", + "content": " is too small, we notice a degradation in visual quality in the generated video frames and a reduced video diversity. For example, we notice many repeated samples and black borders in almost every video generated with" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "22937" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 211, + 232 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 211, + 232 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 211, + 232 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 211, + 232 + ], + "type": "image", + "image_path": "84043d9b5f0034b76c6835e2d4e087432971d2d22535d277eb4e1c20e2e5608a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 123, + 234, + 149, + 243 + ], + "lines": [ + { + "bbox": [ + 123, + 234, + 149, + 243 + ], + "spans": [ + { + "bbox": [ + 123, + 234, + 149, + 243 + ], + "type": "inline_equation", + "content": "\\alpha = 0" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 211, + 70, + 373, + 232 + ], + "blocks": [ + { + "bbox": [ + 211, + 70, + 373, + 232 + ], + "lines": [ + { + "bbox": [ + 211, + 70, + 373, + 232 + ], + "spans": [ + { + "bbox": [ + 211, + 70, + 373, + 232 + ], + "type": "image", + "image_path": "999c099386c0fd284da43b5fb62b6ec5de5670e01424725f8869ea74c5d45ab6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 280, + 234, + 306, + 243 + ], + "lines": [ + { + "bbox": [ + 280, + 234, + 306, + 243 + ], + "spans": [ + { + "bbox": [ + 280, + 234, + 306, + 243 + ], + "type": "inline_equation", + "content": "\\alpha = 1" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 373, + 71, + 535, + 232 + ], + "blocks": [ + { + "bbox": [ + 373, + 71, + 535, + 232 + ], + "lines": [ + { + "bbox": [ + 373, + 71, + 535, + 232 + ], + "spans": [ + { + "bbox": [ + 373, + 71, + 535, + 232 + ], + "type": "image", + "image_path": "26e5b0e3adcaeb96a05393aada9def68b3f50bb8173fd43ac1a8b5ee7ec07265.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 438, + 234, + 469, + 243 + ], + "lines": [ + { + "bbox": [ + 438, + 234, + 469, + 243 + ], + "spans": [ + { + "bbox": [ + 438, + 234, + 469, + 243 + ], + "type": "inline_equation", + "content": "\\alpha = 10" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 53, + 284, + 285, + 401 + ], + "blocks": [ + { + "bbox": [ + 50, + 252, + 541, + 265 + ], + "lines": [ + { + "bbox": [ + 50, + 252, + 541, + 265 + ], + "spans": [ + { + "bbox": [ + 50, + 252, + 541, + 265 + ], + "type": "text", + "content": "Figure 6: Visual ablation on " + }, + { + "bbox": [ + 50, + 252, + 541, + 265 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 50, + 252, + 541, + 265 + ], + "type": "text", + "content": ". Small " + }, + { + "bbox": [ + 50, + 252, + 541, + 265 + ], + "type": "inline_equation", + "content": "\\alpha = 0" + }, + { + "bbox": [ + 50, + 252, + 541, + 265 + ], + "type": "text", + "content": " reduces video quality and diversity and large " + }, + { + "bbox": [ + 50, + 252, + 541, + 265 + ], + "type": "inline_equation", + "content": "\\alpha = 10" + }, + { + "bbox": [ + 50, + 252, + 541, + 265 + ], + "type": "text", + "content": " yields motion artifacts." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 53, + 284, + 285, + 401 + ], + "lines": [ + { + "bbox": [ + 53, + 284, + 285, + 401 + ], + "spans": [ + { + "bbox": [ + 53, + 284, + 285, + 401 + ], + "type": "image", + "image_path": "2e6035bc99550b824a6ea57ef45e3d24c183214050feafa286f4413540cd2415.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 494, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 287, + 519 + ], + "type": "inline_equation", + "content": "\\alpha = 0" + }, + { + "bbox": [ + 46, + 494, + 287, + 519 + ], + "type": "text", + "content": ". On the other hand, when " + }, + { + "bbox": [ + 46, + 494, + 287, + 519 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 494, + 287, + 519 + ], + "type": "text", + "content": " is too large, the model has difficulty generating proper motions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 536, + 288, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 288, + 644 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 288, + 644 + ], + "type": "text", + "content": "Model size We pick the best " + }, + { + "bbox": [ + 46, + 536, + 288, + 644 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 536, + 288, + 644 + ], + "type": "text", + "content": " for the mixed and progressive noise models and compare them with the model trained from scratch on models with different numbers of parameters, 69M, 112M, and 253M. Figure 8 shows that our mixed and progressive models outperform the baseline consistently by a large margin in terms of FVD. Overall, mixed and progressive noising provide similar performance. In our large large-scale experiments, we choose progressive noising with " + }, + { + "bbox": [ + 46, + 536, + 288, + 644 + ], + "type": "inline_equation", + "content": "\\alpha = 2" + }, + { + "bbox": [ + 46, + 536, + 288, + 644 + ], + "type": "text", + "content": " due to its autoregressive nature." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 657, + 119, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 119, + 669 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 119, + 669 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "content": "We proposed a new efficient way of training text-to-video generation models. By observing that the noise maps generating the frames of a video are clustered together, we study" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 312, + 284, + 543, + 401 + ], + "blocks": [ + { + "bbox": [ + 46, + 411, + 288, + 472 + ], + "lines": [ + { + "bbox": [ + 46, + 411, + 288, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 288, + 472 + ], + "type": "text", + "content": "Figure 7: Quantitative ablation on hyperparameter " + }, + { + "bbox": [ + 46, + 411, + 288, + 472 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 411, + 288, + 472 + ], + "type": "text", + "content": ". Finetuning with temporally correlated prior improves over training from scratch. Using a too-large or too-small " + }, + { + "bbox": [ + 46, + 411, + 288, + 472 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 411, + 288, + 472 + ], + "type": "text", + "content": " leads to inferior results. " + }, + { + "bbox": [ + 46, + 411, + 288, + 472 + ], + "type": "inline_equation", + "content": "\\alpha = 1" + }, + { + "bbox": [ + 46, + 411, + 288, + 472 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 411, + 288, + 472 + ], + "type": "inline_equation", + "content": "\\alpha = 2" + }, + { + "bbox": [ + 46, + 411, + 288, + 472 + ], + "type": "text", + "content": " each works the best for mixed and progressive noising, respectively." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 312, + 284, + 543, + 401 + ], + "lines": [ + { + "bbox": [ + 312, + 284, + 543, + 401 + ], + "spans": [ + { + "bbox": [ + 312, + 284, + 543, + 401 + ], + "type": "image", + "image_path": "0230cc56489705efdce7ccceeafb558d19fccf3188e8d60146c865c67f51f050.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 412, + 547, + 460 + ], + "lines": [ + { + "bbox": [ + 304, + 412, + 547, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 547, + 460 + ], + "type": "text", + "content": "Figure 8: Ablation on model size. Larger models consistently improve the performance of both finetuning and training from scratch. Finetuning from image model consistently outperforms training from scratch." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 484, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 545, + 568 + ], + "type": "text", + "content": "mixed and progressive noise priors well-suited for sequential video frame generation. We apply our progressive noise prior to finetuning a state-of-the-art diffusion-based text-to-image model to achieve a state-of-the-art large-scale text-to-video model. The high quality of the generated videos and the state-of-the-art Inception and FID scores demonstrate the strength of our approach." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 570, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 712 + ], + "type": "text", + "content": "Acknowledgment. We would like to thank Amanda Moran, John Dickinson, Sivakumar Arayandi Thottakara, David Page, Ranjitha Prasanna, Venkata Karri, and others in NGC and PBSS team for the computing infrastructure support. We also give thanks to Qinsheng Zhang, Zekun Hao, Tsung-Yi Lin, Ajay Jain, and Chen-Hsuan Lin for useful discussions and feedback. Thanks also go to Yin Xi and Thomas Hayes for clarifying the evaluation protocol of Make-A-Video and to Ming Ding for the details of CogVideo. We thank the ICCV PCs, ACs, and reviewers for their service and valuable feedback. This work is partly supported by NSF grants No. IIS-1910132 and IIS-2213335." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "22938" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 288, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 288, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 288, + 135 + ], + "type": "text", + "content": "[1] Jie An, Songyang Zhang, Harry Yang, Sonal Gupta, Jia-Bin Huang, Jiebo Luo, and Xi Yin. 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Magicvideo: Efficient video generation with latent diffusion models. arXiv preprint arXiv:2211.11018, 2022. 2, 3, 7" + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "22941" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Preserving Modality Structure Improves Multi-Modal Learning/9786f414-b2fe-4822-86c7-2868d21a76fe_content_list.json b/2023/Preserving Modality Structure Improves Multi-Modal Learning/9786f414-b2fe-4822-86c7-2868d21a76fe_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9eda4ee5c5ca7e8abcd181850e4f536443958f77 --- /dev/null +++ b/2023/Preserving Modality Structure Improves Multi-Modal Learning/9786f414-b2fe-4822-86c7-2868d21a76fe_content_list.json @@ -0,0 +1,1886 @@ +[ + { + "type": "text", + "text": "Preserving Modality Structure Improves Multi-Modal Learning", + "text_level": 1, + "bbox": [ + 163, + 130, + 808, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sirnam Swetha1, Mamshad Nayeem Rizve1, Nina Shvetsova2,3, Hilde Kuehne2,3,4, Mubarak Shah1", + "bbox": [ + 96, + 191, + 870, + 212 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ CRCV, University of Central Florida, $^{2}$ Goethe University Frankfurt Germany, $^{3}$ University of Bonn Germany, $^{4}$ MIT-IBM Watson AI Lab", + "bbox": [ + 168, + 222, + 800, + 258 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 304, + 313, + 320 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Self-supervised learning on large-scale multi-modal datasets allows learning semantically meaningful embeddings in a joint multi-modal representation space without relying on human annotations. These joint embeddings enable zero-shot cross-modal tasks like retrieval and classification. However, these methods often struggle to generalize well on out-of-domain data as they ignore the semantic structure present in modality-specific embeddings. In this context, we propose a novel Semantic-Structure-Preserving Consistency approach to improve generalizability by preserving the modality-specific relationships in the joint embedding space. To capture modality-specific semantic relationships between samples, we propose to learn multiple anchors and represent the multifaceted relationship between samples with respect to their relationship with these anchors. To assign multiple anchors to each sample, we propose a novel Multi-Assignment Sinkhorn-Knopp algorithm. Our experimentation demonstrates that our proposed approach learns semantically meaningful anchors in a self-supervised manner. Furthermore, our evaluation on MSR-VTT and YouCook2 datasets demonstrates that our proposed multi-anchor assignment based solution achieves state-of-the-art performance and generalizes to both in-and out-of-domain datasets. Code: https://github.com/Swetha5/Multi_Sinkhorn_Knopp", + "bbox": [ + 76, + 338, + 472, + 717 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 752, + 209, + 767 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Humans often rely on multiple sensory inputs to have a better understanding of everyday events. Most commonly, we utilize vision, audio, and language to perceive an event as they provide complementary information for robust reasoning. The closest approximation of this setup is video data as it provides both visual and audio information along with a text description as a caption. Recently, researchers have started to explore learning meaningful representations", + "bbox": [ + 75, + 780, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "by leveraging multiple modalities to train efficient models at scale [5, 11, 42]. Such systems focus on representation learning that either improves features for each modality separately [5] or learns a joint multi-modal embedding [11, 42] space that enables various zero-shot tasks like retrieval or classification. However, given the inherent differences across the modalities, it is challenging to learn effective joint embeddings. Furthermore, the real-world data presents additional challenges like misalignment between modalities, leading to weak supervision.", + "bbox": [ + 496, + 305, + 893, + 457 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Current pre-training approaches in this area usually employ a contrastive objective [33] to learn the joint embeddings that pulls the cross-modal embeddings of a sample from the same temporal instance closer and pushes embeddings of other samples farther. Despite promising performances, these methods struggle with generalizability. This is particularly evident in previous approaches trained on HT100M [11, 42], which do well on the closely related downstream dataset YouCook2 but struggle to improve on the MSR-VTT dataset, which exhibits a relatively larger domain shift with respect to HT100M [42]. This is due to the contrastive objective's emphasis on strict alignment between modalities in the joint embedding space while ignoring the inherent weak alignment between different modalities [45], as well as the underlying semantic structure across samples [43, 50]. Recent works have tackled these issues, either by using joint multi-modal clustering [11] to preserve the semantic structure in the joint embedding space or by incorporating a reconstruction objective [11, 25] to retain modality-specific features in the joint embedding space, allowing for weak multi-modal alignment. However, the usual reconstruction objective trivially tries to retain most modality-specific features in the joint space, thus preventing the learning of optimal features for cross-modal tasks. And the multi-modal clustering approaches perform hard-clustering making it less flexible. Therefore, the limitations of the contrastive objective cannot be adequately addressed even after combining these independent objectives.", + "bbox": [ + 496, + 460, + 895, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address this, we propose a semantic-structure", + "bbox": [ + 519, + 885, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 805, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21993", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "preserving consistency loss (SSPC) to only retain information that is beneficial for both cross-modal embedding learning and retaining modality-specific semantic structure. In particular, for SSPC loss we consider each sample (e.g., a video clip) to be composed of multiple concepts: scene or objects involved in the downstream task. Therefore, the relationship between samples is multifaceted, representing both shared and unique concepts across samples. To capture this multifaceted relationship in a flexible manner, we propose to learn anchors (latent codes) and model the relationship between samples with respect to their relationships with these anchors. Therefore, these anchors act as a proxy to represent the modality-specific relationships between samples (semantic structure) which can be preserved using the proposed SSPC loss. Since we have no supervision to learn these anchors, we formulate this anchor learning problem as a many-to-many assignment problem, as modeling this multifaceted relationship simultaneously involves assigning multiple anchors to one sample and multiple samples to one anchor. Although there is a vast literature on solving the many-to-one assignment problem [9, 5, 38, 48], there is no efficient way to solve this many-to-many assignment problem.", + "bbox": [ + 76, + 90, + 472, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we propose a novel Multi-Assignment Sinkhorn-Knopp (Multi-SK) algorithm that iteratively optimizes the many-to-many anchor assignments for both the modality-specific embeddings (in input space) and modality-agnostic multi-modal embeddings (in joint embedding space). To allow for weak alignment between modalities, we select the dominant anchors for each sample to represent the relationship between different samples. Our proposed SSPC loss enforces consistency between the dominant anchor assignments at the input and joint embedding spaces to preserve the modality-specific semantic structure. To demonstrate the effectiveness of our proposed solution, we train our model on HT100M dataset and test on 6 zero-shot tasks on multiple downstream datasets and observe that our approach leads to state-of-the-art results in all settings.", + "bbox": [ + 76, + 439, + 472, + 665 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, we make the following contributions: (i) We propose a flexible modality-specific semantic-structure-preserving approach to improve the generalizability of cross-modal features. (ii) We introduce Multi-Assignment Sinkhorn-Knopp, a novel algorithm to enable multiple assignments for flexible sample relationship modeling. (iii) Our proposed method outperforms the current state-of-the-art for multi-modal self-supervised representation learning on both in- and out-of domain datasets.", + "bbox": [ + 76, + 665, + 472, + 800 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 814, + 218, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Multi-Modal Learning", + "text_level": 1, + "bbox": [ + 76, + 835, + 287, + 852 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With the availability of large-scale multi-modal datasets [31, 41, 7], multi-modal learning research has received a lot of attention. It comprises of vision-language", + "bbox": [ + 76, + 854, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "learning [35, 51], vision-audio learning [2, 4, 6, 12, 46], video-audio-language learning [39, 11, 42], zero-shot learning [21, 28], cross-modal generation [37, 53, 27] and multi-modal multi-task learning [22]. Miech et al. [31] proposed a large-scale multi-modal dataset consisting of video, audio and text by collecting instructional videos from YouTube without requiring any human annotations. Note that the text is generated from audio using Automatic Speech Recognition (ASR) and has noisy alignment between the text and video. They also proposed a multimodal system to demonstrate the potential for learning video-text embedding via contrastive loss. To handle the noise in the dataset, Amrani et al. [3] proposed a noise estimation for multi-modal data via multi-modal density estimation. A noise-contrastive estimation approach in a multi-instance learning framework was proposed by Miech et al. [29]. XDC [2] performs clustering on audio-video for learning better features for each modality separately. These works utilize only two modalities for multi-modal learning, while others have explored utilizing audio, video, and text together for multi-modal learning. Multi-Modal versatile networks [1] was proposed to learn different embedding spaces for each combination of modalities. AVLNet [39] proposed to learn a shared embedding that maps all modalities to a single joint embedding space. Following this, MCN [11] proposed to perform joint clustering and reconstruction to learn joint embedding space. Note that, [11] performs multi-modal K-means clustering to learn hard semantic clusters. Unlike strict assignment in [11], we propose flexible learning with multiple assignments and separately for each modality. More recently, EAO [42] utilizes transformers and combinatorial fusion of modalities to learn the joint embedding with contrastive loss.", + "bbox": [ + 496, + 90, + 893, + 590 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Most of these works, utilize contrastive or clustering loss over fused multi-modal representation to learn the joint embedding space. By doing so, these models do not retain the modality-specific semantic structuring between samples encoded by the pre-trained modality specific backbones, hurting the generalization ability of the model. Additionally, recent works have reported that large-scale contrastive multimodal models (e.g., CLIP [36]) are somewhat robust to distributional shifts mainly due to diverse large-scale training data and prompt-engineering [15]. Therefore, our work focuses on making the pre-training objective robust to distributional shifts. In this context, we propose a novel approach to preserve the modality-specific semantic relationships in the joint embedding space by modeling the relationship between samples w.r.t learnable anchors. To enable flexible relationship modeling between samples, we learn multiple anchor assignments per sample, where anchors shared across samples model the commonality between them, and the distinct anchors between samples highlight the uniqueness of the samples.", + "bbox": [ + 496, + 598, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21994", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/36b1353f0d482ab61ec574a70a19b3d49c9e6d43f912d0b1a2da048bb98354b6.jpg", + "image_caption": [ + "Figure 1: Overview of the proposed model. Given weakly aligned text, video, and audio, we first extract features using frozen modality-specific backbones. These features are then passed through a token projection layer to obtain input features $(\\mathbf{v},\\mathbf{t},\\mathbf{a})$ specific to each modality. Next, the modality-specific transformer models project the input features into a joint multi-modal representation space $(\\hat{\\mathbf{v}},\\hat{\\mathbf{t}},\\hat{\\mathbf{a}})$ . The similarity between the input features $(\\mathbf{v},\\mathbf{t},\\mathbf{a})$ and input space anchors $(\\mathbf{Z}_{\\mathbf{v}},\\mathbf{Z}_{\\mathbf{t}},\\mathbf{Z}_{\\mathbf{a}})$ (projected features $(\\hat{\\mathbf{v}},\\hat{\\mathbf{t}},\\hat{\\mathbf{a}})$ and projected space anchors $(\\hat{\\mathbf{Z}}_{\\mathbf{v}},\\hat{\\mathbf{Z}}_{\\mathbf{t}},\\hat{\\mathbf{Z}}_{\\mathbf{a}}))$ is computed, and our Multi-SK algorithm $(M(.))$ is used to optimize multiple anchor assignments per sample, as shown in the Input Space Assignments (Projected Space Assignments). We do this for each modality and enforce the respective consistency losses, but in this figure we only show modality-specific consistency loss for text anchors and cross-modal consistency between text and video modalities for brevity. LN, MHSA represents LayerNorm and Multi-Head Self-Attention." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 895, + 410 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Sinkhorn-Knopp", + "text_level": 1, + "bbox": [ + 76, + 551, + 246, + 569 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, Sinkhorn-Knopp algorithm [44] has drawn huge attention because of its effectiveness in solving optimal-transport problems [23, 8]. Specifically, [13] proposed an entropic relaxation of the optimal transport problem which can be efficiently solved using Sinkhorn's matrix scaling algorithm. Many following works have since successfully utilized the Sinkhorn-Knopp algorithm to solve different label assignment problems framed as an optimal transport problems. For instance, SeLa [48] cast the unsupervised clustering problem as a pseudo-label assignment problem and used the Sinkhorn-Knopp algorithm to solve it. SeLaVi [5] extended this idea to self-supervised representation learning for multi-modal data where the cluster assignments between different modalities are swapped to encourage modality invariant representation learning. Similarly, SwAV [9] used the Sinkhorn-Knopp algorithm for self-supervised representation learning and proposed to swap the pseudo-labels for differently augmented versions of a sample and use soft assignments instead of hard pseudolabels. In contrast to these works, SuperGlue [40] used the Sinkhorn-Knopp algorithm to solve the correspondence", + "bbox": [ + 75, + 583, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "problem between two sets of local features. Moreover, Sinkhorn-Knopp has been used in detection problems [17], where it was used to match the anchors with ground truths. Recently, UNO [16], and TRSSL [38] have successfully used the Sinkhorn-Knopp algorithm in solving novel class discovery and open-world semi-supervised learning problems, respectively. One key limitation of the traditional Sinkhorn-Knopp algorithm is that it cannot be directly utilized to compute multiple assignments necessary to perform multi-anchor based learning i.e. many-to-many assignments.", + "bbox": [ + 496, + 553, + 890, + 718 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Some prior works [18, 26] have attempted to solve many-to-many assignments in indirect ways. While authors of [18] use an intermediate graph to match groups of vertices from source to target graph, which can only perform group-to-group assignments and is inadequate for our problem that requires true many-to-many matching. [26] modifies the Sinkhorn-Knopp row and column constraints to obtain many-to-many assignment to model dense correspondences, however, we have found this approach to be inferior in solving the multiple anchor assignment problem. The modified Sinkhorn-Knopp constraints approach yields suboptimal results, as discussed in Sec. 4.4. To address these", + "bbox": [ + 496, + 719, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21995", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "limitations, we propose a novel algorithm Multi-SK, which outperforms the modified Sinkhorn-Knopp constraints approach to get true many-to-many assignments.", + "bbox": [ + 75, + 90, + 468, + 137 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 145, + 168, + 160 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a set of multi-modal inputs $\\{\\mathbf{t}^{(i)},\\mathbf{v}^{(i)},\\mathbf{a}^{(i)}\\}_{i = 1}^{N}$ from N video clips, we learn modality-specific projection functions $f_{t},f_{v},f_{a}$ , that transform t,v,a into a d-dimensional joint embedding space, $\\mathbb{R}^d$ to obtain $\\hat{\\mathbf{t}},\\hat{\\mathbf{v}},\\hat{\\mathbf{a}}$ respectively. Our goal is to optimize the parameters of $f_{t},f_{v},f_{a}$ in such a way that they maintain the semantic structure amongst samples from a particular modality in the joint embedding space, as discussed in Sec 3.1, and simultaneously brings the semantically related cross-modal inputs closer. In the following, first, we formulate our approach to modeling the relationship between samples using anchors in Sec 3.1, then in Sec 3.2, we discuss our novel Multi-SK algorithm to learn these anchors for representing sample relationships, and finally, we present the overall training objective to train the model in Sec 3.3.", + "bbox": [ + 75, + 169, + 472, + 398 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Modeling Sample Relationships with Anchors", + "text_level": 1, + "bbox": [ + 76, + 406, + 465, + 422 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our work aims to preserve the relationship between samples i.e. $\\mathbf{x}^{(i)},\\mathbf{x}^{(j)}$ from a particular modality, to better generalize on the unseen data. To this end, we propose to model the relationship between samples using anchors, where the similarity of each sample w.r.t. anchors encodes the semantic structure of the feature space. Unlike clustering approaches, which involve hard-assignment to a specific cluster, our approach offers flexibility i.e., there can be shared and unique anchors across samples that define the relationship between them. To be particular, for each sample, we learn $K$ anchors, and the similarity of assignments over these anchors represents the relationship (which we want to preserve) between samples from a particular modality.", + "bbox": [ + 75, + 431, + 468, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As the pre-trained features extracted from modality-specific backbones encode the semantic structure between samples within that particular modality, preserving such modality-specific relationships in the joint embedding space would boost the generalizability of the model. To achieve this, we define two sets of $K$ learnable anchors $\\mathbf{z} = \\{\\mathbf{z}^{(i)}\\}_{i=1}^{K}$ , and $\\hat{\\mathbf{z}} = \\{\\hat{\\mathbf{z}}^{(i)}\\}_{i=1}^{K}$ to model the sample relationships before and after projecting them to the joint embedding space respectively. We repeat this for all the modalities, $t, v, a$ . We propose to preserve the modality-specific semantic structure at the joint embedding space by enforcing consistency in anchor assignments before and after performing feature projections (Eq. 3).", + "bbox": [ + 75, + 628, + 468, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We still have one remaining challenge, i.e. how to learn/discover these anchors in an unsupervised manner. To this end, we cast the anchor discovery as a label assignment task with a uniform prior, i.e. each anchor will have an equal number of sample assignments. Additionally, to", + "bbox": [ + 75, + 825, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "encourage flexible modeling, we enforce multiple anchor assignments per sample. However, it is difficult to estimate the exact number of anchors for each sample without additional prior information, thus we select the top $K'$ anchors for each sample to effectively model the sample relationships. Even though this optimization task may seem like a difficult combinatorial problem, we model this combinatorial optimization task as an optimal transport problem. Following recent works [5, 9], one might assume the Sinkhorn-Knopp algorithm is a natural choice to solve this problem, however, the vanilla Sinkhorn-Knopp algorithm cannot handle multiple assignments per sample i.e. many-to-many assignment. To address this limitation, we propose Multi-Assignment Sinkhorn-Knopp algorithm, presented in the following.", + "bbox": [ + 496, + 90, + 893, + 318 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Multi-Assignment Sinkhorn-Knopp", + "text_level": 1, + "bbox": [ + 498, + 329, + 808, + 345 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a sample matrix $\\mathbf{B}$ s.t. $\\mathbf{B} \\in \\mathbb{R}^{N \\times d}$ , representing $N$ samples and an anchor matrix $\\mathbf{Z}$ s.t. $\\mathbf{Z} \\in \\mathbb{R}^{K \\times d}$ , of $K$ anchor vectors, we obtain the similarity matrix $\\mathbf{S}$ s.t. $\\mathbf{S} = \\mathbf{B}\\mathbf{Z}^{\\intercal}$ and $\\mathbf{S} \\in \\mathbb{R}^{N \\times K}$ , where, $\\mathbf{S}_{ij}$ is the probability of assigning $j$ th anchor to the $i$ th sample vector. The goal is to find an anchor assignment matrix, $\\mathbf{Q}$ , such that it satisfies the following constraints: (i) a sample should be assigned to exactly $K'$ anchors, to learn top $K'$ anchor assignments per sample. (ii) anchor assignments must be equally partitioned i.e each anchor must be selected exactly $N \\times K' / K$ times, for uniform anchor assignment.", + "bbox": [ + 496, + 352, + 893, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To obtain such multiple anchor assignments per sample, we propose to create a substitute 3D assignment matrix $\\mathbf{Q}'$ s.t. $\\mathbf{Q}' \\in \\mathbb{R}^{K \\times N \\times K}$ . We also generate a 3D similarity matrix $\\mathbf{S}'$ from the 2D similarity matrix $\\mathbf{S}$ by introducing $K$ channels (depth dimension) to get $K \\times N \\times K$ matrix such that each channel is a scaled matrix of $S$ with a predefined ranking between the channels enabling top $K'$ anchor selection. Since we are only interested in selecting the top $K'$ anchors, we set the first $K'$ channels of $\\mathbf{S}'$ to be the same as $\\mathbf{S}$ . The remaining $K - K'$ channels are set to $\\mu \\mathbf{S}$ . Here, $\\mu$ is a damping factor s.t. $0 < \\mu < 1$ , to help select the top $K'$ anchors for each sample. We discuss alternate designs for $\\mathbf{S}'$ generation in the Supplementary Sec. 2.", + "bbox": [ + 496, + 520, + 893, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The optimization objective of Multi-Assignment Sinkhorn-Knopp is to find an assignment matrix $\\mathbf{Q}'$ such that it satisfies our multi-anchor assignment constraints while maximizing similarity with the initial assignment/similarity matrix, $\\mathbf{S}'$ . This optimization problem is defined as:", + "bbox": [ + 496, + 717, + 893, + 805 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {Q} ^ {*}: \\max _ {\\mathbf {Q} ^ {\\prime}} < \\mathbf {Q} ^ {\\prime}, \\mathbf {S} ^ {\\prime} > + \\epsilon H (\\mathbf {Q} ^ {\\prime}) \\\\ H \\left(\\mathbf {Q} ^ {*}\\right) = - \\sum \\mathbf {Q} _ {i j k} ^ {\\prime} \\log \\mathbf {Q} _ {i j k} ^ {\\prime} \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 803, + 890, + 852 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbf{Q}^*$ needs to satisfy the following constraints to be a valid solution for our multi-anchor assignment problem.", + "bbox": [ + 496, + 851, + 890, + 881 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "- $\\mathbf{Q}^*$ Row Constraint: Within a channel, the sum of all el", + "bbox": [ + 500, + 885, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21996", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ements in a particular row must be equal to one. This is because we only want one anchor assignment for a sample in a particular channel. $\\forall i,k\\sum_{j}\\mathbf{Q}^{*}_{ijk} = 1$", + "bbox": [ + 89, + 90, + 468, + 138 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- $\\mathbf{Q}^*$ Column Constraint: In a channel, the sum of all elements in a column should be equal to $N / K$ . This constraint enforces equal partitioning of anchor assignments. $\\forall j, k \\sum_{i} \\mathbf{Q}^{*}_{ijk} = N / K$ .", + "- $\\mathbf{Q}^*$ Depth constraint: Depth-wise sum should be equal to one for every sample and anchor combination. This constraint prevents selecting the same anchor across different channels. $\\forall i, j \\sum_{k} \\mathbf{Q}^{*}_{ijk} = 1$ ." + ], + "bbox": [ + 76, + 142, + 468, + 271 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The traditional Sinkhorn-Knopp method uses an iterative matrix scaling algorithm that scales the rows and columns alternatively (with desired constraints) till the desired assignment matrix is obtained. We employ a similar scheme and extend the iterative scaling to the depth dimension for estimating $\\mathbf{Q}^*$ . We iteratively scale the rows, columns, and channels (depth dimension) till convergence. The final 2D assignment matrix $\\mathbf{Q}$ is computed by performing a depth-wise sum on the top $K^{\\prime}$ channels. We provide Pytorch-style pseudo-code for our Multi-Assignment Sinkhorn-Knop algorithm in the Supplementary Sec 3.", + "bbox": [ + 75, + 272, + 470, + 438 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Training Objective", + "text_level": 1, + "bbox": [ + 76, + 445, + 259, + 462 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Semantic Structure Preserving Consistency Loss. To preserve the semantic structure of each modality, $t, v, a$ , we apply consistency loss to enforce similar anchor assignments between input and joint embedding space. As the cross-modal contrastive loss in the joint embedding space tries to bring different modalities together, features in the joint embedding space from a particular modality should preserve the common anchors that exist in corresponding features from the other modalities. Therefore, we also apply cross-modal anchor consistency across all modalities as shown in Eq. 3. Since we are dealing with 3 input modalities, this cross-modal consistency results in 9 consistency constraints.", + "bbox": [ + 75, + 468, + 468, + 664 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Let's denote $\\mathcal{L}(\\mathbf{t},\\hat{\\mathbf{v}},\\mathbf{z}_t,\\hat{\\mathbf{z}}_t)$ as the consistency loss between text anchor assignment in the input space and the textual anchor assignment of the corresponding video features at the joint embedding space as shown below in Eq. 2:", + "bbox": [ + 75, + 665, + 468, + 726 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} (\\mathbf {t}, \\hat {\\mathbf {v}}, \\mathbf {z} _ {t}, \\hat {\\mathbf {z}} _ {t}) = \\alpha_ {\\mathbf {t}, \\hat {\\mathbf {v}}} g \\left(\\operatorname {s i m} \\left(\\mathbf {t}, \\mathbf {z} _ {t}\\right), M \\left(\\operatorname {s i m} \\left(\\hat {\\mathbf {v}}, \\hat {\\mathbf {z}} _ {t}\\right)\\right)\\right) (2) \\\\ + \\beta_ {\\mathbf {t}, \\hat {\\mathbf {v}}} g (\\operatorname {s i m} (\\hat {\\mathbf {v}}, \\hat {\\mathbf {z}} _ {t})), M (\\operatorname {s i m} (\\mathbf {t}, \\mathbf {z} _ {t}))), (2) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 731, + 468, + 766 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $\\mathbf{z}_t, \\hat{\\mathbf{z}}_t$ respectively represent input and output learnable anchor vectors for the text modality. $g(.)$ , and $M(.)$ respectively represent binary cross-entropy-with-logits loss and Multi-Assignment Sinkhorn-Knopp (discussed in Sec. 3.2), $\\alpha$ and $\\beta$ represents loss coefficients, and $\\mathrm{sim}(\\mathbf{a},\\mathbf{b}) = \\exp (\\mathbf{a.b} / \\tau \\| \\mathbf{a}\\| \\| \\mathbf{b}\\|)$ , $\\tau$ is the temperature hyperparameter of the similarity metric.", + "bbox": [ + 75, + 766, + 468, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Overall semantic structure preserving consistency loss for all the modalities is defined as:", + "bbox": [ + 75, + 869, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s s p c} = \\sum_ {m \\in \\{t, v, a \\}} \\sum_ {n \\in \\{t, v, a \\}} \\mathcal {L} (\\mathbf {m}, \\hat {\\mathbf {n}}, \\mathbf {z} _ {m}, \\hat {\\mathbf {z}} _ {m}). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 102, + 890, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Contrastive Loss. Following [11, 42], we also use contrastive loss to bring cross-modal embeddings of the same sample closer while pushing away embeddings from other sample. For this, we use 3 pairwise single-modality constrastive losses, $\\mathcal{L}_{nce\\_ tv}$ , $\\mathcal{L}_{nce\\_ ta}$ , $\\mathcal{L}_{nce\\_ va}$ between $(t,v)$ , $(t,a)$ , $(v,a)$ respectively. Specifically, we use Noise Contrastive Estimation [33] with temperature $\\kappa$ as shown in Eq. 4.", + "bbox": [ + 496, + 135, + 893, + 256 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {n c e - x y} = - \\log \\frac {\\exp \\left(\\mathbf {x} ^ {\\intercal} \\mathbf {y} / \\kappa\\right)}{\\sum_ {i = 1} ^ {N} \\exp \\left(\\mathbf {x} ^ {(i) \\intercal} \\mathbf {y} ^ {(i)} / \\kappa\\right)} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 268, + 890, + 306 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall contrastive loss for all modalities is defined as $\\mathcal{L}_{nce} = \\lambda_{tv}\\mathcal{L}_{nce\\_tv} + \\lambda_{ta}\\mathcal{L}_{nce\\_ta} + \\lambda_{va}\\mathcal{L}_{nce\\_va}$", + "bbox": [ + 498, + 311, + 890, + 343 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Overall Loss", + "text_level": 1, + "bbox": [ + 500, + 357, + 611, + 372 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall training objective is a combination of SSPC loss (Eq. 3) and contrastive loss (4): $\\mathcal{L}_f = \\lambda_{sspc}\\mathcal{L}_{sspc} + \\lambda_{nce}\\mathcal{L}_{nce}$ , where, $\\lambda_{sspc}$ and $\\lambda_{nce}$ are loss coefficients. By combining both losses, the model learns a more generic joint embedding space which preserves the modality-specific semantic structure by enforcing the anchor assignment similarity before and after feature projection and also brings representations of different modalities together by utilizing contrastive loss.", + "bbox": [ + 496, + 382, + 890, + 518 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 534, + 633, + 550 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 559, + 689, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Backbones. For comparability, we follow the same setup of previous works [31, 39, 11, 42]. As visual backbone, we use a combination of 2D features from ResNet-152 [20] pretrained onImagenet [14], and 3D features from ResNeXt101 [19] pretrained on Kinetics [10]. The text backbone is GoogleNews pretrained Word2vec model [32]. These backbones are fixed and not finetuned during training. Following [11, 42], we use a trainable CNN with residual layers as an audio backbone. We provide additional details in the Supplementary Sec. 5.", + "bbox": [ + 496, + 582, + 890, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Data Sampling. We use a batch of 216 videos and randomly sample ten 8-second clips per video. If the sampled clip contains narration (95% clips), we use ASR time stamps to select clip borders. To disentangle high text-audio correlation in HT100M, we shift the audio clip randomly by 4 seconds with respect to the video and text boundaries.", + "bbox": [ + 496, + 734, + 890, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Projections. Following [42, 11, 39], we use a gated linear projection [30] to project features into common token space, as well as to project resulting tokens into shared embedding space. We set the dimension of the common token space to 4096 and of the shared embedding space to 6144.", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21997", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/ed572caec3374f9dd60945e2e137049d9279ef7f7644f808f777eba12bd1a223.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodRetrievalTrainVisualTrainable BBMSR-VTTYouCook2
DatasetBBtvaR@5↑R@10↑MedR↓MeanR↓R@5↑R@10↑MedR↓MeanR↓
ActBERT [54]t → vHT100MRes3D+Faster R-CNN23.433.136-26.738.019-
SupportSet [34]t → vHT100MR152 + R(2+1)D-34✓23.031.131-----
HT100M [31]t → vHT100MR152 + RX10121.229.638-17.324.846-
AVLNet [39]t → vHT100MR152 + RX101✓24.734.2--21.129.6--
EAO [42]t → vHT100MR152 + RX101✓24.635.32590.427.938.919119.6
Ourst → vHT100MR152 + RX101✓26.435.12392.229.440.718111.8
AVLNet [39]v → tHT100MR152 + RX101✓27.235.72586.522.832.930142.2
EAO [42]v → tHT100MR152 + RX101✓27.636.6258531.870.51591.9
Oursv → tHT100MR152 + RX101✓27.237.12384.532721585.2
AVLNet [39]t → v + aHT100MR152 + RX101✓19.227.447-36.144.316-
MCN [11]t → v + aHT100MR152 + RX101✓25.233.8--35.545.2--
EAO [42]t → v + aHT100MR152 + RX101✓23.333.22994.838.549.21182.7
Ourst → v + aHT100MR152 + RX101✓25.134.52691.839.450.11083.3
AVLNet [39]v + a → tHT100MR152 + RX101✓1926.344128.148.858.4667.1
EAO [42]v + a → tHT100MR152 + RX101✓21.831.428.598.94960.9643.8
Oursv + a → tHT100MR152 + RX101✓24322795.948.861.3643.5
", + "bbox": [ + 78, + 88, + 895, + 315 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1: Zero-shot Retrieval results on MSR-VTT/YouCook2. For fair comparison, we compare with models trained on text, video and audio. Retrieval column represents the evaluation task. BB=Backbone. Bold, underline represent highest and second-highest scores.", + "bbox": [ + 75, + 320, + 893, + 349 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use a single transformer block with hidden size of 4096 with 64 heads and an MLP size of 4096. We set the number of anchors $K$ as 64 and $K'$ as 32 with damping factor $\\mu$ as 0.25. We train all models for 15 epochs using an Adam optimizer [24] with a learning rate of 5e-5, exponential decay of 0.9 and the temperature of cosine similarity $(\\tau)$ as 0.1. We maintain a memory-bank of size 5500 while performing Multi-SK. Following [1, 42], we set higher weight for loss terms that involve text-video in Eq. 3, i.e., for all text-video terms the weight is set to 1.0 and the rest of the weights are set to 0.1.", + "bbox": [ + 75, + 364, + 472, + 531 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Datasets, Tasks, Metrics", + "text_level": 1, + "bbox": [ + 76, + 542, + 299, + 559 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Pretraining Dataset. We train our model on the HT100M dataset [31], which contains over 1 million instructional videos with automatically generated text narrations. The text narrations can be assumed to be noisy and to not always describe the video scene.", + "bbox": [ + 75, + 566, + 468, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Zero-shot Retrieval. We use MSR-VTT [47] and YouCook2 [52] datasets to evaluate the zero-shot retrieval capability of our model. We report performance on 4 retrieval tasks: (i) Text-to-Video retrieval, (ii) Video-to-Text retrieval, (iii) Text-to-Video-Audio retrieval, (iv) Video-Audio-to-Text retrieval. The YouCook2 dataset contains cooking videos from YouTube with human-annotated clips ( $\\sim$ 2 - 200 secs). For evaluation we use at maximum first 48 seconds of clip, since most clips are shorter than that. The MSR-VTT dataset contains human-annotated clips ( $\\sim$ 10 - 30 secs) on various topics and provides captions with natural language sentences. Following [31, 39, 11, 42], to evaluate our model on MSR-VTT, we use the 1k set of test clips [49], and for YouCook2, we use 3,350 validation clips [31]. To perform $(t\\rightarrow v + a)$ retrieval, we compute similarities by dot product between a text query $t$ and all videos in the dataset using a averaged $v + a$ representa", + "bbox": [ + 75, + 643, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tion for each video. We report standard recall metrics $\\mathbf{R}@\\mathbf{5}$ , $\\mathbf{R}@\\mathbf{10}$ , median rank (MedR) and the mean rank(MeanR). Further, we also evaluate our model using CLIP backbone and report results in Sec. 1 of the Supplementary.", + "bbox": [ + 496, + 364, + 890, + 425 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Zero-Shot Full-Video Retrieval. Following [11], we evaluate Zero-Shot Full Video Retrieval from a set of captions on YouCook2 dataset. We report recall metrics following Caption averaging method [11] that finds maximal prediction over all the clips of video for each caption and averaging over set of captions in query leading to a single prediction for full video.", + "bbox": [ + 496, + 426, + 890, + 530 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Text-to-video Retrieval after Fine-tuning. We additionally evaluate the retrieval performance of the models fine-tuned on downstream tasks. We use 6783 clips from MSR-VTT (which contain audio) and 9586 clips from YouCook2 train datasets to fine-tune the model as proposed by [39].", + "bbox": [ + 496, + 532, + 890, + 608 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We also evaluate our model for Zero-shot Classification and report additional results in Sec. 1 of the Supplementary.", + "bbox": [ + 496, + 608, + 890, + 640 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison with State-of-the-art", + "text_level": 1, + "bbox": [ + 498, + 650, + 794, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Zero-shot Retrieval Tasks. In Tab. 1, we report the performance of the learned multi-modal representations on four zero-shot retrieval tasks, (i) Text-to-Video, (ii) Video-to-Text, (iii) Text-to-Video-Audio, (iv) Video-Audio-to-Text., on MSR-VTT and YouCook2 datasets. For a fair comparison, we only compare with models trained on all three modalities i.e. text, video and audio. In summary, our proposed method outperforms the current state-of-the-art methods by a noticeable margin on both the datasets. The results on the MSR-VTT dataset are particularly interesting since it demonstrates the generalizability of our model. In particular, HT100M consists of instructional videos and the textual descriptions are generated from audio using ASR. The text narration has noisy alignment with video and typically describes the steps in the video. YouCook2 shares", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21998", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9771281867bec15a8ba481b4691adaa823ae740ed92b82472ea88a3ea6b3067b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodRetrievalTrainVisualTrainable BBMSR-VTTYouCook2
DatasetBBtvaR@5↑R@10↑MedR↓MeanR↓R@5↑R@10↑MedR↓MeanR↓
AVLNet [39]t → vHT100MR152 + RX101✓42.256.2735.123.732.728122.6
EAO [42]t → vHT100MR152 + RX101✓47.759.3635.633.945.81370.7
Ourst → vHT100MR152 + RX101✓48.760.6533.135.648.11264.9
", + "bbox": [ + 78, + 88, + 893, + 165 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e0dcb005520344e71c5cd8360820be3a47f7dd7e4e2773a2fa5d75082e01241d.jpg", + "table_caption": [ + "Table 2: Text-to-video retrieval results on MSR-VTT/YouCook2 in the fine-tune setting. For fair comparison, we compare with models trained on all 3 modalities i.e. text, video and audio. Bold, underline represent best and second-best scores." + ], + "table_footnote": [], + "table_body": "
MethodAggregationR@1↑R@5↑R@10↑
Random-0.231.152.32
HT100M [31]Caption Avg.43.168.679.1
MIL-NCE [29]Caption Avg.46.674.383.7
MCN [11]Caption Avg.53.475.081.4
EAO [42]Caption Avg.62.980.586.7
OursCaption Avg.65.183.287.6
", + "bbox": [ + 78, + 214, + 468, + 327 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "domain similarity with HT100M as its videos are instructional format, and the text descriptions correspond to specific steps in the recipe. In contrast, MSR-VTT is not restricted to instructional videos and the text is typically a single sentence caption describing the whole video. As a result, there is a distributional shift between HT100M and MSR-VTT. Therefore, zero-shot retrieval on MSR-VTT has to overcome distributional shift, which is a crucial requirement for practical deployment. Our proposed method shows relatively higher improvement on this task validating the effectiveness of anchor-based learning.", + "bbox": [ + 75, + 378, + 468, + 545 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In case of text-to-video-audio retrieval, our method improves the Median and Mean rank of the baseline [42] by $3\\%$ on MSR-VTT along with gains on recall metrics $R@5$ and $R@10$ . For video-audio-to-text retrieval, our methods perform very well on MSR-VTT with $3\\%$ improvement on MeanR, $2.2\\%$ improvement on $R@5$ . We also observe similar improvements on the YouCook2 dataset. Similarly, our proposed method outperforms the current state-of-the-art on most of the metrics for text-video-retrieval video-text-retrieval. Additionally, to compare our approach with text-video only model, we train our model on video and text to compare the performance with state-of-the-art in Sec 1 of the Supplementary.", + "bbox": [ + 75, + 547, + 470, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Zero-shot Full Video Retrieval. In Tab. 3, we report results for text-to-full-video retrieval task. Our approach outperforms prior works by $2.2\\%$ , $2.7\\%$ on R@1 and R@5 respectively.", + "bbox": [ + 75, + 746, + 468, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Retrieval after Fine-tuning. We also evaluate the retrieval performance of our model after fine-tuning on the downstream datasets as shown in Tab. 2. For a fair comparison, we only report the baselines that use the same training split. We outperform state-of-the-art consistently on all the metrics and on both MSR-VTT & YouCook2 datasets", + "bbox": [ + 75, + 810, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "as shown in Tab. 2.", + "bbox": [ + 500, + 217, + 629, + 231 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 239, + 663, + 253 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "First we analyze the impact of the proposed components and report results in Tab. 4, followed by the effect of number of anchors $(K)$ & $(K^{\\prime})$ in Tab. 5.", + "bbox": [ + 498, + 263, + 893, + 309 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/bf6e4abd95019bf4aba296720631dbbb6302db5fe0ddfe7c23dcb464d71a72a9.jpg", + "table_caption": [ + "Table 3: Zero-Shot Text-to-Full Video retrieval on YouCook2. Averaging across captions is used to obtain video-level predictions." + ], + "table_footnote": [], + "table_body": "
MethodMSR-VTTYouCook2
R@5↑R@10↑R@5↑R@10↑
Recon. + CL23.132.437.848.7
w/o CM SSPCL22.731.836.948.3
w/o SSPCL23.833.337.948.8
Modified SK23.431.337.948.3
Ours25.134.539.450.1
", + "bbox": [ + 514, + 319, + 875, + 438 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4: Ablation studies showing the impact of various components for zero-shot retrieval task. Recon.=Reconstruction Loss, CM SSPCL=Cross-Modal SSPC Loss, SK=Sinkhorn-Knopp, CL=Contrastive Loss.", + "bbox": [ + 498, + 444, + 892, + 503 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of Proposed Components. We report the results for this ablation in Tab. 4. In first row, we report results using reconstruction loss and contrastive loss, we notice that using reconstruction loss reduces the performance by $2\\%$ on all metrics indicating the effectiveness of the proposed SSPC loss. In the second row, we report results without our proposed cross-modal SSPC loss ('w/o CM SSPC'). We employ this loss to bring the cross-modal representations closer in the joint embedding space to obtain better performance in zero-shot cross-modal tasks. We notice that removing the cross-modal SSPC loss drastically decreases the zero-shot retrieval performance on both MSR-VTT and YouCook2 datasets, $2.4\\%$ and $2.5\\%$ drop in R@5 performance respectively. This empirically validates the effectiveness of the cross-modal SSPC loss in obtaining better cross-modal representations.", + "bbox": [ + 496, + 537, + 890, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In the third row, we analyze the effect of the proposed SSPC loss ('w/o SSPCL'). We apply the SSPC loss to retain modality-specific semantic structure from the pretrained models in the joint embedding space. To investigate its impact, we remove the anchor consistency between the modality-specific and joint embedding spaces. Instead, we enforce the anchor assignments before Multi-SK to be consistent with the Multi-SK optimized anchor as", + "bbox": [ + 496, + 779, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21999", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b2cc957fe4de615732ae3dfbc2a05de5dbf12c811084fd877125e2262a3ada0f.jpg", + "image_caption": [ + "(a) UMeazzCYlps (Holidays and Traditions)" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 197, + 141 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8263a7ab1f21a9d5ba54fa0df65dff181159df1cd90f2150283e72300b5f1d53.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 202, + 88, + 321, + 141 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/61fe488eb9ef28b0a46f636b11a59fdb546ec4494b06ce9f624e88b67cc4cfe5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 326, + 88, + 446, + 141 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2deac40873fcf07f5e27e410e2c90f9c34d5c2d674c8dbd2d806a878162499c0.jpg", + "image_caption": [ + "(b) fdUgKk-G5Tw (Food and Entertaining)" + ], + "image_footnote": [], + "bbox": [ + 522, + 88, + 643, + 141 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/96296052ffce8bfcf13cced27a5f7ebc8c2ffa957ebf7b27539e93f161741a84.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 647, + 88, + 766, + 141 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6a69f6250264733e7faaad8f4cccfab0da2a185e5af60020327526c5625df11b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 772, + 88, + 890, + 141 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f9c1f037b7e0082a484beb440766b9e3808933f28d379e5e1d01b1bd205ba1be.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 172, + 883, + 202 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/57f91f9de5423015637a8942a535d6095aeb60cc0d73e585210e8e50ea094708.jpg", + "image_caption": [ + "(d) A0hURqF7h-c (Personal Care and Style)" + ], + "image_footnote": [], + "bbox": [ + 78, + 226, + 197, + 280 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/24c730676e7520321e775bf58e7956c85dc832f12e26efc1912c06d46d44371c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 202, + 226, + 321, + 279 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b4b48feb9d8852948609348aa4acd1ffb68a3512ae000e6de3bd7ed5e96af616.jpg", + "image_caption": [ + "(c) Video Anchor Assignments" + ], + "image_footnote": [], + "bbox": [ + 326, + 226, + 446, + 279 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5eb9eb018f1a5cdd6437b2ab14e1e16f6076521c5f5a8a8b1778559db2862949.jpg", + "image_caption": [ + "Figure 2: Anchor assignments illustrated in this figure demonstrate the visual similarity between video samples from two related categories i.e. (a) Holidays and Tradition and (b) Food and Entertaining; and two different categories i.e. (d) Personal Care ans Style and (e) Finance and Business within the HowTo100M dataset. The visual similarity is also reflected in video anchor assignments (c) as most assigned anchors are similar with minor differences in assignments, thereby showcasing the flexibility and effectiveness of our approach. (d), (e) samples look very different and therefore the anchor assignments are also very different as shown in (f). Green cell $\\rightarrow$ Anchor assigned, Yellow $\\rightarrow$ Anchor not assigned. Difference in anchor assignments indicated in red." + ], + "image_footnote": [], + "bbox": [ + 522, + 226, + 642, + 279 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/51d8ddbe79ea5b9f265920a633c0e65b28d235cdf409ee39c8ee4e284455718d.jpg", + "image_caption": [ + "(e) _Y51yX3KJoE (Finance and Business)" + ], + "image_footnote": [], + "bbox": [ + 645, + 226, + 766, + 279 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/90effec5408bbe895c6bb2857e4cf0a5e5319eef736e15b533f5ccddcbf34d57.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 772, + 226, + 890, + 279 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6199cb8143c1a217676b9c629e752f1e33284306eea87dafd469e07455f56cd4.jpg", + "image_caption": [ + "(f) Video anchors Assignments" + ], + "image_footnote": [], + "bbox": [ + 84, + 310, + 883, + 339 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3809ccd243e6e9c7791b0aa9a5648baa913ca6551d8f7aec7e1c65d43add8e20.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
KK'MSR-VTTYouCook2
R@5↑R@10↑R@5↑R@10↑
16823.13237.147.5
321623.232.136.147.6
641623.331.836.747.2
644823.732.136.747.7
64(Ours)3225.134.539.450.1
", + "bbox": [ + 89, + 489, + 457, + 616 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5: Effect of different # of anchors on zero-shot retrieval. $K \\rightarrow$ # of anchors and $K' \\rightarrow$ # of selected anchors, respectively.", + "bbox": [ + 76, + 627, + 462, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "signments from the same embedding space. We also apply the cross-modal SSPC loss to only isolate the impact of the proposed SSPC loss across feature projections. We observe that removing the anchor consistency between the modality-specific and joint embedding spaces reduces the zero-shot retrieval performance by a significant margin ( $\\sim 1.5\\%$ drop in R@5 performance), indicating the importance of SSPC loss in maintaining modality-specific semantic structure in the joint embedding space for better performance.", + "bbox": [ + 75, + 686, + 467, + 823 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, in the fourth row of Tab. 4, we analyse the effectiveness of the proposed Multi-Assignment Sinkhorn-Knoppalgorithm. To this end, we modify the vanilla Sinkhorn-Knopp [13] to obtain multiple anchor assignments per sample (refer to Sec. 5 of the Supplementary", + "bbox": [ + 75, + 824, + 467, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "for details). We notice that the modified Sinkhorn-Knopp does not perform well with a drop in performance ( $\\sim 1.6\\%$ drop in R@5) on both MSR-VTT and YouCook2 datasets on all the metrics indicating the significance of our proposed MULTI-SK algorithm.", + "bbox": [ + 496, + 493, + 890, + 568 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of Number of Anchors. To analyze the effect of the number of anchors, we conduct experiments with different number of anchors, $K$ , and different number of selected anchors, $K'$ . We report the results in Tab. 5. We conduct experiments on both MSR-VTT and YouCook2 datasets. From the top half of Tab. 5, we observe that the performance of our proposed method improves with the increasing number of anchors. This is to be expected since a higher number of anchors have a higher representation learning capacity. We also observe that the method performs reasonably well even with a very small number of anchors showing the general effectiveness of our proposed solution. We notice that the performance of the proposed method improves as we select more anchors as shown in bottom half of Tab. 5. However, selecting a very large number of anchors (48 out of 64 for this experiment) adds more constraints leading to poor performance.", + "bbox": [ + 496, + 575, + 892, + 833 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Qualitative Analysis", + "text_level": 1, + "bbox": [ + 500, + 845, + 691, + 862 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Here, first we present a fine-grained visual analysis of the learned anchors, followed by qualitative retrieval results.", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22000", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "\"Animated comic scene of guy cutting up food for dinner\"", + "bbox": [ + 76, + 104, + 236, + 143 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "\"a woman holding a ribbon\"", + "bbox": [ + 76, + 175, + 233, + 200 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "\"mix ingredients refrigerate\"", + "bbox": [ + 76, + 219, + 233, + 244 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "\"add mutton pan\"", + "bbox": [ + 102, + 276, + 210, + 291 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/f7e7e48075b15f9cebdea991dca2cd685f88583ac000e5ef483866cdd5b9ec21.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 251, + 87, + 354, + 146 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/6fef8ff10153ebdf7ac5c77cc855c27afb983fdf4313f22ded1e74fa85fa38ab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 251, + 146, + 354, + 205 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/512d1d94ddde5cf43663e4a2e81964b05b5a7cdddeecacf992d07d761e849b06.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 251, + 205, + 354, + 247 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/ab8c55517bc30b4c7669d599c469af248a5b5e51ff5f07ba41c1f57877828df4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 251, + 247, + 354, + 292 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/d0e9f4499376fb190e25ebf377003bdc013496e0898fcf285a4aee1788216100.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 88, + 455, + 146 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/2606ee2d6bb550f4e50b4634782c64cb43f4270c6676bdfc28678fc1ae9cab97.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 146, + 455, + 204 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/338f294da97650e8d905b2ca23441cd769228c343f180bf1a2f58a7b7a4e2240.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 204, + 455, + 247 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/29b37b8697b4b205debcf43945958609e3896f11874ae2e6902d41eb45c53fd2.jpg", + "image_caption": [ + "Ours", + "Figure 3: Examples of Zero-Shot Text-to-Video Retrieval on MSR-VTT and YouCook2 datasets. Each row consists of Textual Query (left), and top-3 retrieved videos for our method (center) and the state-of-the-art method EAO [42](right). Match indicates correct video for the query." + ], + "image_footnote": [], + "bbox": [ + 354, + 247, + 455, + 292 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/0cb0d4848fc921cc9b6e19727e77b9028c0e698a01a9a16bd45e24f76aeee2b9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 457, + 88, + 558, + 204 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/ed979fe8cc4337ba93053f95e71750f1bc7a26534d33199d5f8127cca553dc1b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 457, + 204, + 558, + 292 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/a658fa31a34597a89d52f8422fe597aad42e5d996fd7433d7224243c46167342.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 580, + 88, + 681, + 205 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/599738612238d178becabd032ef3bf12f1be5ee833e3f691923c2f63c7c539b4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 580, + 205, + 681, + 247 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/e1af4cc6a71efce0bb02d25715f16f879b7a83012168aedf932c43e3be5d1b70.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 580, + 247, + 681, + 292 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/87c0cfcde940184f1dd6aeb55faae211d18f326ea0d359136eb4099f0ebfeeea.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 683, + 88, + 784, + 204 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/c867ea629bf90de482f897293f68428df213fce06ca51f8f1c8aeb0a598b9dc4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 683, + 204, + 784, + 247 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/951cc2b16efba37ab8c6d6d9d3dc1b77bea082db667bd05ce5e81007f9f65907.jpg", + "image_caption": [ + "EAO [42]" + ], + "image_footnote": [], + "bbox": [ + 683, + 247, + 784, + 292 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/87ae398794fc54d31a8d14024f3f4bfe97471dba08d74bf625b58a5b64e3c8c9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 785, + 88, + 885, + 204 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/314daf3ecc2444e258048b4629fd33d4ecdd430322a99058b0db9be5655dede1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 785, + 204, + 885, + 247 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/5adc6043e40230bd6ac85dbe81b708b0840445aa16714abd37e90bff2a8abdf3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 785, + 247, + 885, + 292 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We show fine-grained analysis of the learned anchors in Fig. 2. For the purpose of this analysis, we visualize the anchor assignments as binary assignments. However, during training we use soft anchor assignments. In Fig. 2(c), we compare the anchor assignments for samples from similar categories. It can be seen that the videos are visually similar even though they belong to different categories and the anchor assignments for these two examples are able to capture the sample similarity. In Fig. 2(f), we compare the anchor assignments for videos from different categories and it can be seen that the anchor assignments are very different as expected. This further validates our claim that our proposed method can assign semantically meaningful anchors without any explicit supervision. Further, we show qualitative retrieval comparison with EAO [42] in Fig. 3. We present more qualitative analysis in Supplementary Sec. 4.", + "bbox": [ + 75, + 396, + 472, + 640 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 660, + 194, + 676 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We proposed a novel approach that preserves the modality-specific semantic relationship between samples in the joint multi-modal embedding space. To this end, we propose a flexible sample relationship modeling approach by assigning multiple anchors to each sample, which captures both shared and unique aspects of samples. To obtain these assignments, we develop a novel Multi-Assignment Sinkhorn-Knopp (Multi-SK) algorithm, and also utilize the proposed anchor consistency loss to learn these anchors. Our qualitative results demonstrate that our learnt anchors correspond to meaningful semantic concepts. Our extensive experimentation demonstrates that the proposed approach improves generalizability by outperforming state-of-the-art methods on both in- and out-of-domain datasets. We also", + "bbox": [ + 75, + 689, + 470, + 900 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "show that our method achieves state-of-the-art performance on multiple zero-shot tasks, and also outperforms when fine-tuned on downstream datasets.", + "bbox": [ + 498, + 396, + 892, + 441 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 457, + 666, + 474 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Research was sponsored by the Army Research Office and was accomplished under Grant Number W911NF-19-1-0356. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. Nina Shvetsova is supported by German Federal Ministry of Education and Research (BMBF) project STCL - 01IS22067.", + "bbox": [ + 498, + 482, + 892, + 650 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 664, + 596, + 679 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jean-Baptiste Alayrac, Adria Recasens, Rosalia Schneider, Relja Arandjelovic, Jason Ramapuram, Jeffrey De Fauw, Lucas Smaira, Sander Dieleman, and Andrew Zisserman. Self-supervised multimodal versatile networks. Advances in Neural Information Processing Systems, 33:25-37, 2020. 2, 6", + "[2] Humam Alwassel, Dhruv Mahajan, Bruno Korbar, Lorenzo Torresani, Bernard Ghanem, and Du Tran. Self-supervised learning by cross-modal audio-video clustering. Advances in Neural Information Processing Systems, 33:9758-9770, 2020. 2", + "[3] Elad Amrani, Rami Ben-Ari, Daniel Rotman, and Alex Bronstein. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2020. 6" + ], + "bbox": [ + 501, + 92, + 893, + 852 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "22003", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Preserving Modality Structure Improves Multi-Modal Learning/9786f414-b2fe-4822-86c7-2868d21a76fe_model.json b/2023/Preserving Modality Structure Improves Multi-Modal Learning/9786f414-b2fe-4822-86c7-2868d21a76fe_model.json new file mode 100644 index 0000000000000000000000000000000000000000..863aee9a24ca533cfce6c55b02f6558bc7552a9f --- /dev/null +++ b/2023/Preserving Modality Structure Improves Multi-Modal Learning/9786f414-b2fe-4822-86c7-2868d21a76fe_model.json @@ -0,0 +1,2477 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.807, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.165, + 0.131, + 0.809, + 0.154 + ], + "angle": 0, + "content": "Preserving Modality Structure Improves Multi-Modal Learning" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.193, + 0.872, + 0.213 + ], + "angle": 0, + "content": "Sirnam Swetha1, Mamshad Nayeem Rizve1, Nina Shvetsova2,3, Hilde Kuehne2,3,4, Mubarak Shah1" + }, + { + "type": "text", + "bbox": [ + 0.169, + 0.223, + 0.802, + 0.26 + ], + "angle": 0, + "content": "\\(^{1}\\)CRCV, University of Central Florida, \\(^{2}\\)Goethe University Frankfurt Germany, \\(^{3}\\)University of Bonn Germany, \\(^{4}\\)MIT-IBM Watson AI Lab" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.314, + 0.321 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.339, + 0.473, + 0.718 + ], + "angle": 0, + "content": "Self-supervised learning on large-scale multi-modal datasets allows learning semantically meaningful embeddings in a joint multi-modal representation space without relying on human annotations. These joint embeddings enable zero-shot cross-modal tasks like retrieval and classification. However, these methods often struggle to generalize well on out-of-domain data as they ignore the semantic structure present in modality-specific embeddings. In this context, we propose a novel Semantic-Structure-Preserving Consistency approach to improve generalizability by preserving the modality-specific relationships in the joint embedding space. To capture modality-specific semantic relationships between samples, we propose to learn multiple anchors and represent the multifaceted relationship between samples with respect to their relationship with these anchors. To assign multiple anchors to each sample, we propose a novel Multi-Assignment Sinkhorn-Knopp algorithm. Our experimentation demonstrates that our proposed approach learns semantically meaningful anchors in a self-supervised manner. Furthermore, our evaluation on MSR-VTT and YouCook2 datasets demonstrates that our proposed multi-anchor assignment based solution achieves state-of-the-art performance and generalizes to both in-and out-of-domain datasets. Code: https://github.com/Swetha5/Multi_Sinkhorn_Knopp" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.753, + 0.21, + 0.768 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Humans often rely on multiple sensory inputs to have a better understanding of everyday events. Most commonly, we utilize vision, audio, and language to perceive an event as they provide complementary information for robust reasoning. The closest approximation of this setup is video data as it provides both visual and audio information along with a text description as a caption. Recently, researchers have started to explore learning meaningful representations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.306, + 0.895, + 0.458 + ], + "angle": 0, + "content": "by leveraging multiple modalities to train efficient models at scale [5, 11, 42]. Such systems focus on representation learning that either improves features for each modality separately [5] or learns a joint multi-modal embedding [11, 42] space that enables various zero-shot tasks like retrieval or classification. However, given the inherent differences across the modalities, it is challenging to learn effective joint embeddings. Furthermore, the real-world data presents additional challenges like misalignment between modalities, leading to weak supervision." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.896, + 0.884 + ], + "angle": 0, + "content": "Current pre-training approaches in this area usually employ a contrastive objective [33] to learn the joint embeddings that pulls the cross-modal embeddings of a sample from the same temporal instance closer and pushes embeddings of other samples farther. Despite promising performances, these methods struggle with generalizability. This is particularly evident in previous approaches trained on HT100M [11, 42], which do well on the closely related downstream dataset YouCook2 but struggle to improve on the MSR-VTT dataset, which exhibits a relatively larger domain shift with respect to HT100M [42]. This is due to the contrastive objective's emphasis on strict alignment between modalities in the joint embedding space while ignoring the inherent weak alignment between different modalities [45], as well as the underlying semantic structure across samples [43, 50]. Recent works have tackled these issues, either by using joint multi-modal clustering [11] to preserve the semantic structure in the joint embedding space or by incorporating a reconstruction objective [11, 25] to retain modality-specific features in the joint embedding space, allowing for weak multi-modal alignment. However, the usual reconstruction objective trivially tries to retain most modality-specific features in the joint space, thus preventing the learning of optimal features for cross-modal tasks. And the multi-modal clustering approaches perform hard-clustering making it less flexible. Therefore, the limitations of the contrastive objective cannot be adequately addressed even after combining these independent objectives." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "To address this, we propose a semantic-structure" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21993" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.438 + ], + "angle": 0, + "content": "preserving consistency loss (SSPC) to only retain information that is beneficial for both cross-modal embedding learning and retaining modality-specific semantic structure. In particular, for SSPC loss we consider each sample (e.g., a video clip) to be composed of multiple concepts: scene or objects involved in the downstream task. Therefore, the relationship between samples is multifaceted, representing both shared and unique concepts across samples. To capture this multifaceted relationship in a flexible manner, we propose to learn anchors (latent codes) and model the relationship between samples with respect to their relationships with these anchors. Therefore, these anchors act as a proxy to represent the modality-specific relationships between samples (semantic structure) which can be preserved using the proposed SSPC loss. Since we have no supervision to learn these anchors, we formulate this anchor learning problem as a many-to-many assignment problem, as modeling this multifaceted relationship simultaneously involves assigning multiple anchors to one sample and multiple samples to one anchor. Although there is a vast literature on solving the many-to-one assignment problem [9, 5, 38, 48], there is no efficient way to solve this many-to-many assignment problem." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.44, + 0.473, + 0.666 + ], + "angle": 0, + "content": "To this end, we propose a novel Multi-Assignment Sinkhorn-Knopp (Multi-SK) algorithm that iteratively optimizes the many-to-many anchor assignments for both the modality-specific embeddings (in input space) and modality-agnostic multi-modal embeddings (in joint embedding space). To allow for weak alignment between modalities, we select the dominant anchors for each sample to represent the relationship between different samples. Our proposed SSPC loss enforces consistency between the dominant anchor assignments at the input and joint embedding spaces to preserve the modality-specific semantic structure. To demonstrate the effectiveness of our proposed solution, we train our model on HT100M dataset and test on 6 zero-shot tasks on multiple downstream datasets and observe that our approach leads to state-of-the-art results in all settings." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.666, + 0.473, + 0.801 + ], + "angle": 0, + "content": "In summary, we make the following contributions: (i) We propose a flexible modality-specific semantic-structure-preserving approach to improve the generalizability of cross-modal features. (ii) We introduce Multi-Assignment Sinkhorn-Knopp, a novel algorithm to enable multiple assignments for flexible sample relationship modeling. (iii) Our proposed method outperforms the current state-of-the-art for multi-modal self-supervised representation learning on both in- and out-of domain datasets." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.815, + 0.22, + 0.831 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.836, + 0.288, + 0.853 + ], + "angle": 0, + "content": "2.1. Multi-Modal Learning" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.472, + 0.903 + ], + "angle": 0, + "content": "With the availability of large-scale multi-modal datasets [31, 41, 7], multi-modal learning research has received a lot of attention. It comprises of vision-language" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.591 + ], + "angle": 0, + "content": "learning [35, 51], vision-audio learning [2, 4, 6, 12, 46], video-audio-language learning [39, 11, 42], zero-shot learning [21, 28], cross-modal generation [37, 53, 27] and multi-modal multi-task learning [22]. Miech et al. [31] proposed a large-scale multi-modal dataset consisting of video, audio and text by collecting instructional videos from YouTube without requiring any human annotations. Note that the text is generated from audio using Automatic Speech Recognition (ASR) and has noisy alignment between the text and video. They also proposed a multimodal system to demonstrate the potential for learning video-text embedding via contrastive loss. To handle the noise in the dataset, Amrani et al. [3] proposed a noise estimation for multi-modal data via multi-modal density estimation. A noise-contrastive estimation approach in a multi-instance learning framework was proposed by Miech et al. [29]. XDC [2] performs clustering on audio-video for learning better features for each modality separately. These works utilize only two modalities for multi-modal learning, while others have explored utilizing audio, video, and text together for multi-modal learning. Multi-Modal versatile networks [1] was proposed to learn different embedding spaces for each combination of modalities. AVLNet [39] proposed to learn a shared embedding that maps all modalities to a single joint embedding space. Following this, MCN [11] proposed to perform joint clustering and reconstruction to learn joint embedding space. Note that, [11] performs multi-modal K-means clustering to learn hard semantic clusters. Unlike strict assignment in [11], we propose flexible learning with multiple assignments and separately for each modality. More recently, EAO [42] utilizes transformers and combinatorial fusion of modalities to learn the joint embedding with contrastive loss." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Most of these works, utilize contrastive or clustering loss over fused multi-modal representation to learn the joint embedding space. By doing so, these models do not retain the modality-specific semantic structuring between samples encoded by the pre-trained modality specific backbones, hurting the generalization ability of the model. Additionally, recent works have reported that large-scale contrastive multimodal models (e.g., CLIP [36]) are somewhat robust to distributional shifts mainly due to diverse large-scale training data and prompt-engineering [15]. Therefore, our work focuses on making the pre-training objective robust to distributional shifts. In this context, we propose a novel approach to preserve the modality-specific semantic relationships in the joint embedding space by modeling the relationship between samples w.r.t learnable anchors. To enable flexible relationship modeling between samples, we learn multiple anchor assignments per sample, where anchors shared across samples model the commonality between them, and the distinct anchors between samples highlight the uniqueness of the samples." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21994" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.896, + 0.411 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.429, + 0.897, + 0.542 + ], + "angle": 0, + "content": "Figure 1: Overview of the proposed model. Given weakly aligned text, video, and audio, we first extract features using frozen modality-specific backbones. These features are then passed through a token projection layer to obtain input features \\((\\mathbf{v},\\mathbf{t},\\mathbf{a})\\) specific to each modality. Next, the modality-specific transformer models project the input features into a joint multi-modal representation space \\((\\hat{\\mathbf{v}},\\hat{\\mathbf{t}},\\hat{\\mathbf{a}})\\). The similarity between the input features \\((\\mathbf{v},\\mathbf{t},\\mathbf{a})\\) and input space anchors \\((\\mathbf{Z}_{\\mathbf{v}},\\mathbf{Z}_{\\mathbf{t}},\\mathbf{Z}_{\\mathbf{a}})\\) (projected features \\((\\hat{\\mathbf{v}},\\hat{\\mathbf{t}},\\hat{\\mathbf{a}})\\) and projected space anchors \\((\\hat{\\mathbf{Z}}_{\\mathbf{v}},\\hat{\\mathbf{Z}}_{\\mathbf{t}},\\hat{\\mathbf{Z}}_{\\mathbf{a}}))\\) is computed, and our Multi-SK algorithm \\((M(.))\\) is used to optimize multiple anchor assignments per sample, as shown in the Input Space Assignments (Projected Space Assignments). We do this for each modality and enforce the respective consistency losses, but in this figure we only show modality-specific consistency loss for text anchors and cross-modal consistency between text and video modalities for brevity. LN, MHSA represents LayerNorm and Multi-Head Self-Attention." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.553, + 0.248, + 0.57 + ], + "angle": 0, + "content": "2.2. Sinkhorn-Knopp" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Recently, Sinkhorn-Knopp algorithm [44] has drawn huge attention because of its effectiveness in solving optimal-transport problems [23, 8]. Specifically, [13] proposed an entropic relaxation of the optimal transport problem which can be efficiently solved using Sinkhorn's matrix scaling algorithm. Many following works have since successfully utilized the Sinkhorn-Knopp algorithm to solve different label assignment problems framed as an optimal transport problems. For instance, SeLa [48] cast the unsupervised clustering problem as a pseudo-label assignment problem and used the Sinkhorn-Knopp algorithm to solve it. SeLaVi [5] extended this idea to self-supervised representation learning for multi-modal data where the cluster assignments between different modalities are swapped to encourage modality invariant representation learning. Similarly, SwAV [9] used the Sinkhorn-Knopp algorithm for self-supervised representation learning and proposed to swap the pseudo-labels for differently augmented versions of a sample and use soft assignments instead of hard pseudolabels. In contrast to these works, SuperGlue [40] used the Sinkhorn-Knopp algorithm to solve the correspondence" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.719 + ], + "angle": 0, + "content": "problem between two sets of local features. Moreover, Sinkhorn-Knopp has been used in detection problems [17], where it was used to match the anchors with ground truths. Recently, UNO [16], and TRSSL [38] have successfully used the Sinkhorn-Knopp algorithm in solving novel class discovery and open-world semi-supervised learning problems, respectively. One key limitation of the traditional Sinkhorn-Knopp algorithm is that it cannot be directly utilized to compute multiple assignments necessary to perform multi-anchor based learning i.e. many-to-many assignments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Some prior works [18, 26] have attempted to solve many-to-many assignments in indirect ways. While authors of [18] use an intermediate graph to match groups of vertices from source to target graph, which can only perform group-to-group assignments and is inadequate for our problem that requires true many-to-many matching. [26] modifies the Sinkhorn-Knopp row and column constraints to obtain many-to-many assignment to model dense correspondences, however, we have found this approach to be inferior in solving the multiple anchor assignment problem. The modified Sinkhorn-Knopp constraints approach yields suboptimal results, as discussed in Sec. 4.4. To address these" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21995" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.138 + ], + "angle": 0, + "content": "limitations, we propose a novel algorithm Multi-SK, which outperforms the modified Sinkhorn-Knopp constraints approach to get true many-to-many assignments." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.146, + 0.169, + 0.161 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.17, + 0.473, + 0.399 + ], + "angle": 0, + "content": "Given a set of multi-modal inputs \\(\\{\\mathbf{t}^{(i)},\\mathbf{v}^{(i)},\\mathbf{a}^{(i)}\\}_{i = 1}^{N}\\) from N video clips, we learn modality-specific projection functions \\(f_{t},f_{v},f_{a}\\), that transform t,v,a into a d-dimensional joint embedding space, \\(\\mathbb{R}^d\\) to obtain \\(\\hat{\\mathbf{t}},\\hat{\\mathbf{v}},\\hat{\\mathbf{a}}\\) respectively. Our goal is to optimize the parameters of \\(f_{t},f_{v},f_{a}\\) in such a way that they maintain the semantic structure amongst samples from a particular modality in the joint embedding space, as discussed in Sec 3.1, and simultaneously brings the semantically related cross-modal inputs closer. In the following, first, we formulate our approach to modeling the relationship between samples using anchors in Sec 3.1, then in Sec 3.2, we discuss our novel Multi-SK algorithm to learn these anchors for representing sample relationships, and finally, we present the overall training objective to train the model in Sec 3.3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.407, + 0.466, + 0.423 + ], + "angle": 0, + "content": "3.1. Modeling Sample Relationships with Anchors" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.432, + 0.47, + 0.627 + ], + "angle": 0, + "content": "Our work aims to preserve the relationship between samples i.e. \\(\\mathbf{x}^{(i)},\\mathbf{x}^{(j)}\\) from a particular modality, to better generalize on the unseen data. To this end, we propose to model the relationship between samples using anchors, where the similarity of each sample w.r.t. anchors encodes the semantic structure of the feature space. Unlike clustering approaches, which involve hard-assignment to a specific cluster, our approach offers flexibility i.e., there can be shared and unique anchors across samples that define the relationship between them. To be particular, for each sample, we learn \\(K\\) anchors, and the similarity of assignments over these anchors represents the relationship (which we want to preserve) between samples from a particular modality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.47, + 0.825 + ], + "angle": 0, + "content": "As the pre-trained features extracted from modality-specific backbones encode the semantic structure between samples within that particular modality, preserving such modality-specific relationships in the joint embedding space would boost the generalizability of the model. To achieve this, we define two sets of \\( K \\) learnable anchors \\( \\mathbf{z} = \\{\\mathbf{z}^{(i)}\\}_{i=1}^{K} \\), and \\( \\hat{\\mathbf{z}} = \\{\\hat{\\mathbf{z}}^{(i)}\\}_{i=1}^{K} \\) to model the sample relationships before and after projecting them to the joint embedding space respectively. We repeat this for all the modalities, \\( t, v, a \\). We propose to preserve the modality-specific semantic structure at the joint embedding space by enforcing consistency in anchor assignments before and after performing feature projections (Eq. 3)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.902 + ], + "angle": 0, + "content": "We still have one remaining challenge, i.e. how to learn/discover these anchors in an unsupervised manner. To this end, we cast the anchor discovery as a label assignment task with a uniform prior, i.e. each anchor will have an equal number of sample assignments. Additionally, to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.319 + ], + "angle": 0, + "content": "encourage flexible modeling, we enforce multiple anchor assignments per sample. However, it is difficult to estimate the exact number of anchors for each sample without additional prior information, thus we select the top \\( K' \\) anchors for each sample to effectively model the sample relationships. Even though this optimization task may seem like a difficult combinatorial problem, we model this combinatorial optimization task as an optimal transport problem. Following recent works [5, 9], one might assume the Sinkhorn-Knopp algorithm is a natural choice to solve this problem, however, the vanilla Sinkhorn-Knopp algorithm cannot handle multiple assignments per sample i.e. many-to-many assignment. To address this limitation, we propose Multi-Assignment Sinkhorn-Knopp algorithm, presented in the following." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.33, + 0.81, + 0.347 + ], + "angle": 0, + "content": "3.2. Multi-Assignment Sinkhorn-Knopp" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.353, + 0.895, + 0.52 + ], + "angle": 0, + "content": "Given a sample matrix \\(\\mathbf{B}\\) s.t. \\(\\mathbf{B} \\in \\mathbb{R}^{N \\times d}\\), representing \\(N\\) samples and an anchor matrix \\(\\mathbf{Z}\\) s.t. \\(\\mathbf{Z} \\in \\mathbb{R}^{K \\times d}\\), of \\(K\\) anchor vectors, we obtain the similarity matrix \\(\\mathbf{S}\\) s.t. \\(\\mathbf{S} = \\mathbf{B}\\mathbf{Z}^{\\intercal}\\) and \\(\\mathbf{S} \\in \\mathbb{R}^{N \\times K}\\), where, \\(\\mathbf{S}_{ij}\\) is the probability of assigning \\(j\\)th anchor to the \\(i\\)th sample vector. The goal is to find an anchor assignment matrix, \\(\\mathbf{Q}\\), such that it satisfies the following constraints: (i) a sample should be assigned to exactly \\(K'\\) anchors, to learn top \\(K'\\) anchor assignments per sample. (ii) anchor assignments must be equally partitioned i.e each anchor must be selected exactly \\(N \\times K' / K\\) times, for uniform anchor assignment." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.895, + 0.717 + ], + "angle": 0, + "content": "To obtain such multiple anchor assignments per sample, we propose to create a substitute 3D assignment matrix \\(\\mathbf{Q}'\\) s.t. \\(\\mathbf{Q}' \\in \\mathbb{R}^{K \\times N \\times K}\\). We also generate a 3D similarity matrix \\(\\mathbf{S}'\\) from the 2D similarity matrix \\(\\mathbf{S}\\) by introducing \\(K\\) channels (depth dimension) to get \\(K \\times N \\times K\\) matrix such that each channel is a scaled matrix of \\(S\\) with a predefined ranking between the channels enabling top \\(K'\\) anchor selection. Since we are only interested in selecting the top \\(K'\\) anchors, we set the first \\(K'\\) channels of \\(\\mathbf{S}'\\) to be the same as \\(\\mathbf{S}\\). The remaining \\(K - K'\\) channels are set to \\(\\mu \\mathbf{S}\\). Here, \\(\\mu\\) is a damping factor s.t. \\(0 < \\mu < 1\\), to help select the top \\(K'\\) anchors for each sample. We discuss alternate designs for \\(\\mathbf{S}'\\) generation in the Supplementary Sec. 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.718, + 0.894, + 0.806 + ], + "angle": 0, + "content": "The optimization objective of Multi-Assignment Sinkhorn-Knopp is to find an assignment matrix \\(\\mathbf{Q}'\\) such that it satisfies our multi-anchor assignment constraints while maximizing similarity with the initial assignment/similarity matrix, \\(\\mathbf{S}'\\). This optimization problem is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.804, + 0.891, + 0.853 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {Q} ^ {*}: \\max _ {\\mathbf {Q} ^ {\\prime}} < \\mathbf {Q} ^ {\\prime}, \\mathbf {S} ^ {\\prime} > + \\epsilon H (\\mathbf {Q} ^ {\\prime}) \\\\ H \\left(\\mathbf {Q} ^ {*}\\right) = - \\sum \\mathbf {Q} _ {i j k} ^ {\\prime} \\log \\mathbf {Q} _ {i j k} ^ {\\prime} \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.852, + 0.892, + 0.882 + ], + "angle": 0, + "content": "\\(\\mathbf{Q}^*\\) needs to satisfy the following constraints to be a valid solution for our multi-anchor assignment problem." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "- \\(\\mathbf{Q}^*\\) Row Constraint: Within a channel, the sum of all el" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21996" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.09, + 0.092, + 0.47, + 0.14 + ], + "angle": 0, + "content": "ements in a particular row must be equal to one. This is because we only want one anchor assignment for a sample in a particular channel. \\(\\forall i,k\\sum_{j}\\mathbf{Q}^{*}_{ijk} = 1\\)" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.143, + 0.47, + 0.206 + ], + "angle": 0, + "content": "- \\(\\mathbf{Q}^*\\) Column Constraint: In a channel, the sum of all elements in a column should be equal to \\(N / K\\). This constraint enforces equal partitioning of anchor assignments. \\(\\forall j, k \\sum_{i} \\mathbf{Q}^{*}_{ijk} = N / K\\)." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.209, + 0.47, + 0.272 + ], + "angle": 0, + "content": "- \\(\\mathbf{Q}^*\\) Depth constraint: Depth-wise sum should be equal to one for every sample and anchor combination. This constraint prevents selecting the same anchor across different channels. \\(\\forall i, j \\sum_{k} \\mathbf{Q}^{*}_{ijk} = 1\\)." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.143, + 0.47, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.471, + 0.439 + ], + "angle": 0, + "content": "The traditional Sinkhorn-Knopp method uses an iterative matrix scaling algorithm that scales the rows and columns alternatively (with desired constraints) till the desired assignment matrix is obtained. We employ a similar scheme and extend the iterative scaling to the depth dimension for estimating \\(\\mathbf{Q}^*\\). We iteratively scale the rows, columns, and channels (depth dimension) till convergence. The final 2D assignment matrix \\(\\mathbf{Q}\\) is computed by performing a depth-wise sum on the top \\(K^{\\prime}\\) channels. We provide Pytorch-style pseudo-code for our Multi-Assignment Sinkhorn-Knop algorithm in the Supplementary Sec 3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.446, + 0.26, + 0.463 + ], + "angle": 0, + "content": "3.3. Training Objective" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.469, + 0.47, + 0.665 + ], + "angle": 0, + "content": "Semantic Structure Preserving Consistency Loss. To preserve the semantic structure of each modality, \\( t, v, a \\), we apply consistency loss to enforce similar anchor assignments between input and joint embedding space. As the cross-modal contrastive loss in the joint embedding space tries to bring different modalities together, features in the joint embedding space from a particular modality should preserve the common anchors that exist in corresponding features from the other modalities. Therefore, we also apply cross-modal anchor consistency across all modalities as shown in Eq. 3. Since we are dealing with 3 input modalities, this cross-modal consistency results in 9 consistency constraints." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.666, + 0.47, + 0.727 + ], + "angle": 0, + "content": "Let's denote \\(\\mathcal{L}(\\mathbf{t},\\hat{\\mathbf{v}},\\mathbf{z}_t,\\hat{\\mathbf{z}}_t)\\) as the consistency loss between text anchor assignment in the input space and the textual anchor assignment of the corresponding video features at the joint embedding space as shown below in Eq. 2:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.732, + 0.47, + 0.767 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} (\\mathbf {t}, \\hat {\\mathbf {v}}, \\mathbf {z} _ {t}, \\hat {\\mathbf {z}} _ {t}) = \\alpha_ {\\mathbf {t}, \\hat {\\mathbf {v}}} g \\left(\\operatorname {s i m} \\left(\\mathbf {t}, \\mathbf {z} _ {t}\\right), M \\left(\\operatorname {s i m} \\left(\\hat {\\mathbf {v}}, \\hat {\\mathbf {z}} _ {t}\\right)\\right)\\right) (2) \\\\ + \\beta_ {\\mathbf {t}, \\hat {\\mathbf {v}}} g (\\operatorname {s i m} (\\hat {\\mathbf {v}}, \\hat {\\mathbf {z}} _ {t})), M (\\operatorname {s i m} (\\mathbf {t}, \\mathbf {z} _ {t}))), (2) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.767, + 0.469, + 0.871 + ], + "angle": 0, + "content": "Here, \\(\\mathbf{z}_t, \\hat{\\mathbf{z}}_t\\) respectively represent input and output learnable anchor vectors for the text modality. \\(g(.)\\), and \\(M(.)\\) respectively represent binary cross-entropy-with-logits loss and Multi-Assignment Sinkhorn-Knopp (discussed in Sec. 3.2), \\(\\alpha\\) and \\(\\beta\\) represents loss coefficients, and \\(\\mathrm{sim}(\\mathbf{a},\\mathbf{b}) = \\exp (\\mathbf{a.b} / \\tau \\| \\mathbf{a}\\| \\| \\mathbf{b}\\|)\\), \\(\\tau\\) is the temperature hyperparameter of the similarity metric." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Overall semantic structure preserving consistency loss for all the modalities is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.103, + 0.892, + 0.137 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s s p c} = \\sum_ {m \\in \\{t, v, a \\}} \\sum_ {n \\in \\{t, v, a \\}} \\mathcal {L} (\\mathbf {m}, \\hat {\\mathbf {n}}, \\mathbf {z} _ {m}, \\hat {\\mathbf {z}} _ {m}). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.136, + 0.894, + 0.257 + ], + "angle": 0, + "content": "Contrastive Loss. Following [11, 42], we also use contrastive loss to bring cross-modal embeddings of the same sample closer while pushing away embeddings from other sample. For this, we use 3 pairwise single-modality constrastive losses, \\(\\mathcal{L}_{nce\\_ tv}\\), \\(\\mathcal{L}_{nce\\_ ta}\\), \\(\\mathcal{L}_{nce\\_ va}\\) between \\((t,v)\\), \\((t,a)\\), \\((v,a)\\) respectively. Specifically, we use Noise Contrastive Estimation [33] with temperature \\(\\kappa\\) as shown in Eq. 4." + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.269, + 0.892, + 0.307 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {n c e - x y} = - \\log \\frac {\\exp \\left(\\mathbf {x} ^ {\\intercal} \\mathbf {y} / \\kappa\\right)}{\\sum_ {i = 1} ^ {N} \\exp \\left(\\mathbf {x} ^ {(i) \\intercal} \\mathbf {y} ^ {(i)} / \\kappa\\right)} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.313, + 0.892, + 0.344 + ], + "angle": 0, + "content": "The overall contrastive loss for all modalities is defined as \\(\\mathcal{L}_{nce} = \\lambda_{tv}\\mathcal{L}_{nce\\_tv} + \\lambda_{ta}\\mathcal{L}_{nce\\_ta} + \\lambda_{va}\\mathcal{L}_{nce\\_va}\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.358, + 0.612, + 0.373 + ], + "angle": 0, + "content": "Overall Loss" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.383, + 0.892, + 0.52 + ], + "angle": 0, + "content": "The overall training objective is a combination of SSPC loss (Eq. 3) and contrastive loss (4): \\(\\mathcal{L}_f = \\lambda_{sspc}\\mathcal{L}_{sspc} + \\lambda_{nce}\\mathcal{L}_{nce}\\), where, \\(\\lambda_{sspc}\\) and \\(\\lambda_{nce}\\) are loss coefficients. By combining both losses, the model learns a more generic joint embedding space which preserves the modality-specific semantic structure by enforcing the anchor assignment similarity before and after feature projection and also brings representations of different modalities together by utilizing contrastive loss." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.535, + 0.634, + 0.551 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.56, + 0.691, + 0.575 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.734 + ], + "angle": 0, + "content": "Backbones. For comparability, we follow the same setup of previous works [31, 39, 11, 42]. As visual backbone, we use a combination of 2D features from ResNet-152 [20] pretrained onImagenet [14], and 3D features from ResNeXt101 [19] pretrained on Kinetics [10]. The text backbone is GoogleNews pretrained Word2vec model [32]. These backbones are fixed and not finetuned during training. Following [11, 42], we use a trainable CNN with residual layers as an audio backbone. We provide additional details in the Supplementary Sec. 5." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.825 + ], + "angle": 0, + "content": "Data Sampling. We use a batch of 216 videos and randomly sample ten 8-second clips per video. If the sampled clip contains narration (95% clips), we use ASR time stamps to select clip borders. To disentangle high text-audio correlation in HT100M, we shift the audio clip randomly by 4 seconds with respect to the video and text boundaries." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Projections. Following [42, 11, 39], we use a gated linear projection [30] to project features into common token space, as well as to project resulting tokens into shared embedding space. We set the dimension of the common token space to 4096 and of the shared embedding space to 6144." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21997" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.896, + 0.316 + ], + "angle": 0, + "content": "
MethodRetrievalTrainVisualTrainable BBMSR-VTTYouCook2
DatasetBBtvaR@5↑R@10↑MedR↓MeanR↓R@5↑R@10↑MedR↓MeanR↓
ActBERT [54]t → vHT100MRes3D+Faster R-CNN23.433.136-26.738.019-
SupportSet [34]t → vHT100MR152 + R(2+1)D-34✓23.031.131-----
HT100M [31]t → vHT100MR152 + RX10121.229.638-17.324.846-
AVLNet [39]t → vHT100MR152 + RX101✓24.734.2--21.129.6--
EAO [42]t → vHT100MR152 + RX101✓24.635.32590.427.938.919119.6
Ourst → vHT100MR152 + RX101✓26.435.12392.229.440.718111.8
AVLNet [39]v → tHT100MR152 + RX101✓27.235.72586.522.832.930142.2
EAO [42]v → tHT100MR152 + RX101✓27.636.6258531.870.51591.9
Oursv → tHT100MR152 + RX101✓27.237.12384.532721585.2
AVLNet [39]t → v + aHT100MR152 + RX101✓19.227.447-36.144.316-
MCN [11]t → v + aHT100MR152 + RX101✓25.233.8--35.545.2--
EAO [42]t → v + aHT100MR152 + RX101✓23.333.22994.838.549.21182.7
Ourst → v + aHT100MR152 + RX101✓25.134.52691.839.450.11083.3
AVLNet [39]v + a → tHT100MR152 + RX101✓1926.344128.148.858.4667.1
EAO [42]v + a → tHT100MR152 + RX101✓21.831.428.598.94960.9643.8
Oursv + a → tHT100MR152 + RX101✓24322795.948.861.3643.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.321, + 0.895, + 0.351 + ], + "angle": 0, + "content": "Table 1: Zero-shot Retrieval results on MSR-VTT/YouCook2. For fair comparison, we compare with models trained on text, video and audio. Retrieval column represents the evaluation task. BB=Backbone. Bold, underline represent highest and second-highest scores." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.473, + 0.532 + ], + "angle": 0, + "content": "We use a single transformer block with hidden size of 4096 with 64 heads and an MLP size of 4096. We set the number of anchors \\( K \\) as 64 and \\( K' \\) as 32 with damping factor \\( \\mu \\) as 0.25. We train all models for 15 epochs using an Adam optimizer [24] with a learning rate of 5e-5, exponential decay of 0.9 and the temperature of cosine similarity \\( (\\tau) \\) as 0.1. We maintain a memory-bank of size 5500 while performing Multi-SK. Following [1, 42], we set higher weight for loss terms that involve text-video in Eq. 3, i.e., for all text-video terms the weight is set to 1.0 and the rest of the weights are set to 0.1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.544, + 0.3, + 0.56 + ], + "angle": 0, + "content": "4.2. Datasets, Tasks, Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.47, + 0.644 + ], + "angle": 0, + "content": "Pretraining Dataset. We train our model on the HT100M dataset [31], which contains over 1 million instructional videos with automatically generated text narrations. The text narrations can be assumed to be noisy and to not always describe the video scene." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Zero-shot Retrieval. We use MSR-VTT [47] and YouCook2 [52] datasets to evaluate the zero-shot retrieval capability of our model. We report performance on 4 retrieval tasks: (i) Text-to-Video retrieval, (ii) Video-to-Text retrieval, (iii) Text-to-Video-Audio retrieval, (iv) Video-Audio-to-Text retrieval. The YouCook2 dataset contains cooking videos from YouTube with human-annotated clips (\\(\\sim\\) 2 - 200 secs). For evaluation we use at maximum first 48 seconds of clip, since most clips are shorter than that. The MSR-VTT dataset contains human-annotated clips (\\(\\sim\\) 10 - 30 secs) on various topics and provides captions with natural language sentences. Following [31, 39, 11, 42], to evaluate our model on MSR-VTT, we use the 1k set of test clips [49], and for YouCook2, we use 3,350 validation clips [31]. To perform \\((t\\rightarrow v + a)\\) retrieval, we compute similarities by dot product between a text query \\(t\\) and all videos in the dataset using a averaged \\(v + a\\) representa" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.892, + 0.426 + ], + "angle": 0, + "content": "tion for each video. We report standard recall metrics \\( \\mathbf{R}@\\mathbf{5} \\), \\( \\mathbf{R}@\\mathbf{10} \\), median rank (MedR) and the mean rank(MeanR). Further, we also evaluate our model using CLIP backbone and report results in Sec. 1 of the Supplementary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.427, + 0.892, + 0.531 + ], + "angle": 0, + "content": "Zero-Shot Full-Video Retrieval. Following [11], we evaluate Zero-Shot Full Video Retrieval from a set of captions on YouCook2 dataset. We report recall metrics following Caption averaging method [11] that finds maximal prediction over all the clips of video for each caption and averaging over set of captions in query leading to a single prediction for full video." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.533, + 0.892, + 0.609 + ], + "angle": 0, + "content": "Text-to-video Retrieval after Fine-tuning. We additionally evaluate the retrieval performance of the models fine-tuned on downstream tasks. We use 6783 clips from MSR-VTT (which contain audio) and 9586 clips from YouCook2 train datasets to fine-tune the model as proposed by [39]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.892, + 0.641 + ], + "angle": 0, + "content": "We also evaluate our model for Zero-shot Classification and report additional results in Sec. 1 of the Supplementary." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.651, + 0.795, + 0.667 + ], + "angle": 0, + "content": "4.3. Comparison with State-of-the-art" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Zero-shot Retrieval Tasks. In Tab. 1, we report the performance of the learned multi-modal representations on four zero-shot retrieval tasks, (i) Text-to-Video, (ii) Video-to-Text, (iii) Text-to-Video-Audio, (iv) Video-Audio-to-Text., on MSR-VTT and YouCook2 datasets. For a fair comparison, we only compare with models trained on all three modalities i.e. text, video and audio. In summary, our proposed method outperforms the current state-of-the-art methods by a noticeable margin on both the datasets. The results on the MSR-VTT dataset are particularly interesting since it demonstrates the generalizability of our model. In particular, HT100M consists of instructional videos and the textual descriptions are generated from audio using ASR. The text narration has noisy alignment with video and typically describes the steps in the video. YouCook2 shares" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21998" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.894, + 0.166 + ], + "angle": 0, + "content": "
MethodRetrievalTrainVisualTrainable BBMSR-VTTYouCook2
DatasetBBtvaR@5↑R@10↑MedR↓MeanR↓R@5↑R@10↑MedR↓MeanR↓
AVLNet [39]t → vHT100MR152 + RX101✓42.256.2735.123.732.728122.6
EAO [42]t → vHT100MR152 + RX101✓47.759.3635.633.945.81370.7
Ourst → vHT100MR152 + RX101✓48.760.6533.135.648.11264.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.172, + 0.893, + 0.203 + ], + "angle": 0, + "content": "Table 2: Text-to-video retrieval results on MSR-VTT/YouCook2 in the fine-tune setting. For fair comparison, we compare with models trained on all 3 modalities i.e. text, video and audio. Bold, underline represent best and second-best scores." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.215, + 0.47, + 0.328 + ], + "angle": 0, + "content": "
MethodAggregationR@1↑R@5↑R@10↑
Random-0.231.152.32
HT100M [31]Caption Avg.43.168.679.1
MIL-NCE [29]Caption Avg.46.674.383.7
MCN [11]Caption Avg.53.475.081.4
EAO [42]Caption Avg.62.980.586.7
OursCaption Avg.65.183.287.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.335, + 0.47, + 0.365 + ], + "angle": 0, + "content": "Table 3: Zero-Shot Text-to-Full Video retrieval on YouCook2. Averaging across captions is used to obtain video-level predictions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.38, + 0.47, + 0.546 + ], + "angle": 0, + "content": "domain similarity with HT100M as its videos are instructional format, and the text descriptions correspond to specific steps in the recipe. In contrast, MSR-VTT is not restricted to instructional videos and the text is typically a single sentence caption describing the whole video. As a result, there is a distributional shift between HT100M and MSR-VTT. Therefore, zero-shot retrieval on MSR-VTT has to overcome distributional shift, which is a crucial requirement for practical deployment. Our proposed method shows relatively higher improvement on this task validating the effectiveness of anchor-based learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.549, + 0.471, + 0.746 + ], + "angle": 0, + "content": "In case of text-to-video-audio retrieval, our method improves the Median and Mean rank of the baseline [42] by \\(3\\%\\) on MSR-VTT along with gains on recall metrics \\(R@5\\) and \\(R@10\\). For video-audio-to-text retrieval, our methods perform very well on MSR-VTT with \\(3\\%\\) improvement on MeanR, \\(2.2\\%\\) improvement on \\(R@5\\). We also observe similar improvements on the YouCook2 dataset. Similarly, our proposed method outperforms the current state-of-the-art on most of the metrics for text-video-retrieval video-text-retrieval. Additionally, to compare our approach with text-video only model, we train our model on video and text to compare the performance with state-of-the-art in Sec 1 of the Supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.747, + 0.47, + 0.809 + ], + "angle": 0, + "content": "Zero-shot Full Video Retrieval. In Tab. 3, we report results for text-to-full-video retrieval task. Our approach outperforms prior works by \\(2.2\\%\\), \\(2.7\\%\\) on R@1 and R@5 respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Retrieval after Fine-tuning. We also evaluate the retrieval performance of our model after fine-tuning on the downstream datasets as shown in Tab. 2. For a fair comparison, we only report the baselines that use the same training split. We outperform state-of-the-art consistently on all the metrics and on both MSR-VTT & YouCook2 datasets" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.218, + 0.63, + 0.232 + ], + "angle": 0, + "content": "as shown in Tab. 2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.24, + 0.665, + 0.255 + ], + "angle": 0, + "content": "4.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.264, + 0.894, + 0.31 + ], + "angle": 0, + "content": "First we analyze the impact of the proposed components and report results in Tab. 4, followed by the effect of number of anchors \\((K)\\) & \\((K^{\\prime})\\) in Tab. 5." + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.32, + 0.876, + 0.439 + ], + "angle": 0, + "content": "
MethodMSR-VTTYouCook2
R@5↑R@10↑R@5↑R@10↑
Recon. + CL23.132.437.848.7
w/o CM SSPCL22.731.836.948.3
w/o SSPCL23.833.337.948.8
Modified SK23.431.337.948.3
Ours25.134.539.450.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.445, + 0.893, + 0.504 + ], + "angle": 0, + "content": "Table 4: Ablation studies showing the impact of various components for zero-shot retrieval task. Recon.=Reconstruction Loss, CM SSPCL=Cross-Modal SSPC Loss, SK=Sinkhorn-Knopp, CL=Contrastive Loss." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.892, + 0.779 + ], + "angle": 0, + "content": "Effect of Proposed Components. We report the results for this ablation in Tab. 4. In first row, we report results using reconstruction loss and contrastive loss, we notice that using reconstruction loss reduces the performance by \\(2\\%\\) on all metrics indicating the effectiveness of the proposed SSPC loss. In the second row, we report results without our proposed cross-modal SSPC loss ('w/o CM SSPC'). We employ this loss to bring the cross-modal representations closer in the joint embedding space to obtain better performance in zero-shot cross-modal tasks. We notice that removing the cross-modal SSPC loss drastically decreases the zero-shot retrieval performance on both MSR-VTT and YouCook2 datasets, \\(2.4\\%\\) and \\(2.5\\%\\) drop in R@5 performance respectively. This empirically validates the effectiveness of the cross-modal SSPC loss in obtaining better cross-modal representations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.893, + 0.901 + ], + "angle": 0, + "content": "In the third row, we analyze the effect of the proposed SSPC loss ('w/o SSPCL'). We apply the SSPC loss to retain modality-specific semantic structure from the pretrained models in the joint embedding space. To investigate its impact, we remove the anchor consistency between the modality-specific and joint embedding spaces. Instead, we enforce the anchor assignments before Multi-SK to be consistent with the Multi-SK optimized anchor as" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21999" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.198, + 0.142 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.126, + 0.148, + 0.4, + 0.162 + ], + "angle": 0, + "content": "(a) UMeazzCYlps (Holidays and Traditions)" + }, + { + "type": "image", + "bbox": [ + 0.204, + 0.089, + 0.323, + 0.142 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.328, + 0.089, + 0.447, + 0.142 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.524, + 0.089, + 0.644, + 0.142 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.648, + 0.089, + 0.767, + 0.142 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.773, + 0.089, + 0.892, + 0.142 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.575, + 0.148, + 0.84, + 0.162 + ], + "angle": 0, + "content": "(b) fdUgKk-G5Tw (Food and Entertaining)" + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.174, + 0.885, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.393, + 0.213, + 0.578, + 0.226 + ], + "angle": 0, + "content": "(c) Video Anchor Assignments" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.227, + 0.199, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.126, + 0.286, + 0.4, + 0.3 + ], + "angle": 0, + "content": "(d) A0hURqF7h-c (Personal Care and Style)" + }, + { + "type": "image", + "bbox": [ + 0.204, + 0.227, + 0.323, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.328, + 0.227, + 0.447, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.524, + 0.227, + 0.643, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.647, + 0.227, + 0.767, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.773, + 0.227, + 0.892, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.579, + 0.286, + 0.836, + 0.3 + ], + "angle": 0, + "content": "(e) _Y51yX3KJoE (Finance and Business)" + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.311, + 0.885, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.392, + 0.35, + 0.578, + 0.364 + ], + "angle": 0, + "content": "(f) Video anchors Assignments" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.377, + 0.892, + 0.468 + ], + "angle": 0, + "content": "Figure 2: Anchor assignments illustrated in this figure demonstrate the visual similarity between video samples from two related categories i.e. (a) Holidays and Tradition and (b) Food and Entertaining; and two different categories i.e. (d) Personal Care ans Style and (e) Finance and Business within the HowTo100M dataset. The visual similarity is also reflected in video anchor assignments (c) as most assigned anchors are similar with minor differences in assignments, thereby showcasing the flexibility and effectiveness of our approach. (d), (e) samples look very different and therefore the anchor assignments are also very different as shown in (f). Green cell \\(\\rightarrow\\) Anchor assigned, Yellow \\(\\rightarrow\\) Anchor not assigned. Difference in anchor assignments indicated in red." + }, + { + "type": "table", + "bbox": [ + 0.091, + 0.491, + 0.458, + 0.617 + ], + "angle": 0, + "content": "
KK'MSR-VTTYouCook2
R@5↑R@10↑R@5↑R@10↑
16823.13237.147.5
321623.232.136.147.6
641623.331.836.747.2
644823.732.136.747.7
64(Ours)3225.134.539.450.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.628, + 0.464, + 0.658 + ], + "angle": 0, + "content": "Table 5: Effect of different # of anchors on zero-shot retrieval. \\(K \\rightarrow\\) # of anchors and \\(K' \\rightarrow\\) # of selected anchors, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.468, + 0.824 + ], + "angle": 0, + "content": "signments from the same embedding space. We also apply the cross-modal SSPC loss to only isolate the impact of the proposed SSPC loss across feature projections. We observe that removing the anchor consistency between the modality-specific and joint embedding spaces reduces the zero-shot retrieval performance by a significant margin (\\(\\sim 1.5\\%\\) drop in R@5 performance), indicating the importance of SSPC loss in maintaining modality-specific semantic structure in the joint embedding space for better performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.902 + ], + "angle": 0, + "content": "Finally, in the fourth row of Tab. 4, we analyse the effectiveness of the proposed Multi-Assignment Sinkhorn-Knoppalgorithm. To this end, we modify the vanilla Sinkhorn-Knopp [13] to obtain multiple anchor assignments per sample (refer to Sec. 5 of the Supplementary" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.494, + 0.892, + 0.569 + ], + "angle": 0, + "content": "for details). We notice that the modified Sinkhorn-Knopp does not perform well with a drop in performance (\\(\\sim 1.6\\%\\) drop in R@5) on both MSR-VTT and YouCook2 datasets on all the metrics indicating the significance of our proposed MULTI-SK algorithm." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.893, + 0.834 + ], + "angle": 0, + "content": "Effect of Number of Anchors. To analyze the effect of the number of anchors, we conduct experiments with different number of anchors, \\( K \\), and different number of selected anchors, \\( K' \\). We report the results in Tab. 5. We conduct experiments on both MSR-VTT and YouCook2 datasets. From the top half of Tab. 5, we observe that the performance of our proposed method improves with the increasing number of anchors. This is to be expected since a higher number of anchors have a higher representation learning capacity. We also observe that the method performs reasonably well even with a very small number of anchors showing the general effectiveness of our proposed solution. We notice that the performance of the proposed method improves as we select more anchors as shown in bottom half of Tab. 5. However, selecting a very large number of anchors (48 out of 64 for this experiment) adds more constraints leading to poor performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.846, + 0.692, + 0.863 + ], + "angle": 0, + "content": "4.5. Qualitative Analysis" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.891, + 0.901 + ], + "angle": 0, + "content": "Here, first we present a fine-grained visual analysis of the learned anchors, followed by qualitative retrieval results." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22000" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.105, + 0.237, + 0.145 + ], + "angle": 0, + "content": "\"Animated comic scene of guy cutting up food for dinner\"" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.176, + 0.235, + 0.202 + ], + "angle": 0, + "content": "\"a woman holding a ribbon\"" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.22, + 0.235, + 0.246 + ], + "angle": 0, + "content": "\"mix ingredients refrigerate\"" + }, + { + "type": "text", + "bbox": [ + 0.104, + 0.277, + 0.212, + 0.292 + ], + "angle": 0, + "content": "\"add mutton pan\"" + }, + { + "type": "image", + "bbox": [ + 0.253, + 0.088, + 0.355, + 0.147 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.253, + 0.147, + 0.355, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.253, + 0.206, + 0.355, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.253, + 0.248, + 0.355, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.356, + 0.089, + 0.456, + 0.147 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.356, + 0.147, + 0.456, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.356, + 0.205, + 0.456, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.356, + 0.248, + 0.456, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.393, + 0.3, + 0.424, + 0.311 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.458, + 0.089, + 0.56, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.458, + 0.205, + 0.56, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.581, + 0.089, + 0.682, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.581, + 0.206, + 0.682, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.581, + 0.248, + 0.682, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.684, + 0.089, + 0.785, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.684, + 0.205, + 0.785, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.684, + 0.248, + 0.785, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.089, + 0.887, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.205, + 0.887, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.248, + 0.887, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.706, + 0.299, + 0.766, + 0.312 + ], + "angle": 0, + "content": "EAO [42]" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.325, + 0.894, + 0.37 + ], + "angle": 0, + "content": "Figure 3: Examples of Zero-Shot Text-to-Video Retrieval on MSR-VTT and YouCook2 datasets. Each row consists of Textual Query (left), and top-3 retrieved videos for our method (center) and the state-of-the-art method EAO [42](right). Match indicates correct video for the query." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.397, + 0.473, + 0.641 + ], + "angle": 0, + "content": "We show fine-grained analysis of the learned anchors in Fig. 2. For the purpose of this analysis, we visualize the anchor assignments as binary assignments. However, during training we use soft anchor assignments. In Fig. 2(c), we compare the anchor assignments for samples from similar categories. It can be seen that the videos are visually similar even though they belong to different categories and the anchor assignments for these two examples are able to capture the sample similarity. In Fig. 2(f), we compare the anchor assignments for videos from different categories and it can be seen that the anchor assignments are very different as expected. This further validates our claim that our proposed method can assign semantically meaningful anchors without any explicit supervision. Further, we show qualitative retrieval comparison with EAO [42] in Fig. 3. We present more qualitative analysis in Supplementary Sec. 4." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.661, + 0.196, + 0.677 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.472, + 0.901 + ], + "angle": 0, + "content": "We proposed a novel approach that preserves the modality-specific semantic relationship between samples in the joint multi-modal embedding space. To this end, we propose a flexible sample relationship modeling approach by assigning multiple anchors to each sample, which captures both shared and unique aspects of samples. To obtain these assignments, we develop a novel Multi-Assignment Sinkhorn-Knopp (Multi-SK) algorithm, and also utilize the proposed anchor consistency loss to learn these anchors. Our qualitative results demonstrate that our learnt anchors correspond to meaningful semantic concepts. Our extensive experimentation demonstrates that the proposed approach improves generalizability by outperforming state-of-the-art methods on both in- and out-of-domain datasets. We also" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.397, + 0.893, + 0.443 + ], + "angle": 0, + "content": "show that our method achieves state-of-the-art performance on multiple zero-shot tasks, and also outperforms when fine-tuned on downstream datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.458, + 0.667, + 0.475 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.483, + 0.893, + 0.651 + ], + "angle": 0, + "content": "Research was sponsored by the Army Research Office and was accomplished under Grant Number W911NF-19-1-0356. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. Nina Shvetsova is supported by German Federal Ministry of Education and Research (BMBF) project STCL - 01IS22067." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.665, + 0.597, + 0.68 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.689, + 0.892, + 0.759 + ], + "angle": 0, + "content": "[1] Jean-Baptiste Alayrac, Adria Recasens, Rosalia Schneider, Relja Arandjelovic, Jason Ramapuram, Jeffrey De Fauw, Lucas Smaira, Sander Dieleman, and Andrew Zisserman. Self-supervised multimodal versatile networks. Advances in Neural Information Processing Systems, 33:25-37, 2020. 2, 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.509, + 0.761, + 0.894, + 0.829 + ], + "angle": 0, + "content": "[2] Humam Alwassel, Dhruv Mahajan, Bruno Korbar, Lorenzo Torresani, Bernard Ghanem, and Du Tran. Self-supervised learning by cross-modal audio-video clustering. 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These joint embeddings enable zero-shot cross-modal tasks like retrieval and classification. However, these methods often struggle to generalize well on out-of-domain data as they ignore the semantic structure present in modality-specific embeddings. In this context, we propose a novel Semantic-Structure-Preserving Consistency approach to improve generalizability by preserving the modality-specific relationships in the joint embedding space. To capture modality-specific semantic relationships between samples, we propose to learn multiple anchors and represent the multifaceted relationship between samples with respect to their relationship with these anchors. To assign multiple anchors to each sample, we propose a novel Multi-Assignment Sinkhorn-Knopp algorithm. Our experimentation demonstrates that our proposed approach learns semantically meaningful anchors in a self-supervised manner. Furthermore, our evaluation on MSR-VTT and YouCook2 datasets demonstrates that our proposed multi-anchor assignment based solution achieves state-of-the-art performance and generalizes to both in-and out-of-domain datasets. Code: https://github.com/Swetha5/Multi_Sinkhorn_Knopp + +# 1. Introduction + +Humans often rely on multiple sensory inputs to have a better understanding of everyday events. Most commonly, we utilize vision, audio, and language to perceive an event as they provide complementary information for robust reasoning. The closest approximation of this setup is video data as it provides both visual and audio information along with a text description as a caption. Recently, researchers have started to explore learning meaningful representations + +by leveraging multiple modalities to train efficient models at scale [5, 11, 42]. Such systems focus on representation learning that either improves features for each modality separately [5] or learns a joint multi-modal embedding [11, 42] space that enables various zero-shot tasks like retrieval or classification. However, given the inherent differences across the modalities, it is challenging to learn effective joint embeddings. Furthermore, the real-world data presents additional challenges like misalignment between modalities, leading to weak supervision. + +Current pre-training approaches in this area usually employ a contrastive objective [33] to learn the joint embeddings that pulls the cross-modal embeddings of a sample from the same temporal instance closer and pushes embeddings of other samples farther. Despite promising performances, these methods struggle with generalizability. This is particularly evident in previous approaches trained on HT100M [11, 42], which do well on the closely related downstream dataset YouCook2 but struggle to improve on the MSR-VTT dataset, which exhibits a relatively larger domain shift with respect to HT100M [42]. This is due to the contrastive objective's emphasis on strict alignment between modalities in the joint embedding space while ignoring the inherent weak alignment between different modalities [45], as well as the underlying semantic structure across samples [43, 50]. Recent works have tackled these issues, either by using joint multi-modal clustering [11] to preserve the semantic structure in the joint embedding space or by incorporating a reconstruction objective [11, 25] to retain modality-specific features in the joint embedding space, allowing for weak multi-modal alignment. However, the usual reconstruction objective trivially tries to retain most modality-specific features in the joint space, thus preventing the learning of optimal features for cross-modal tasks. And the multi-modal clustering approaches perform hard-clustering making it less flexible. Therefore, the limitations of the contrastive objective cannot be adequately addressed even after combining these independent objectives. + +To address this, we propose a semantic-structure + +preserving consistency loss (SSPC) to only retain information that is beneficial for both cross-modal embedding learning and retaining modality-specific semantic structure. In particular, for SSPC loss we consider each sample (e.g., a video clip) to be composed of multiple concepts: scene or objects involved in the downstream task. Therefore, the relationship between samples is multifaceted, representing both shared and unique concepts across samples. To capture this multifaceted relationship in a flexible manner, we propose to learn anchors (latent codes) and model the relationship between samples with respect to their relationships with these anchors. Therefore, these anchors act as a proxy to represent the modality-specific relationships between samples (semantic structure) which can be preserved using the proposed SSPC loss. Since we have no supervision to learn these anchors, we formulate this anchor learning problem as a many-to-many assignment problem, as modeling this multifaceted relationship simultaneously involves assigning multiple anchors to one sample and multiple samples to one anchor. Although there is a vast literature on solving the many-to-one assignment problem [9, 5, 38, 48], there is no efficient way to solve this many-to-many assignment problem. + +To this end, we propose a novel Multi-Assignment Sinkhorn-Knopp (Multi-SK) algorithm that iteratively optimizes the many-to-many anchor assignments for both the modality-specific embeddings (in input space) and modality-agnostic multi-modal embeddings (in joint embedding space). To allow for weak alignment between modalities, we select the dominant anchors for each sample to represent the relationship between different samples. Our proposed SSPC loss enforces consistency between the dominant anchor assignments at the input and joint embedding spaces to preserve the modality-specific semantic structure. To demonstrate the effectiveness of our proposed solution, we train our model on HT100M dataset and test on 6 zero-shot tasks on multiple downstream datasets and observe that our approach leads to state-of-the-art results in all settings. + +In summary, we make the following contributions: (i) We propose a flexible modality-specific semantic-structure-preserving approach to improve the generalizability of cross-modal features. (ii) We introduce Multi-Assignment Sinkhorn-Knopp, a novel algorithm to enable multiple assignments for flexible sample relationship modeling. (iii) Our proposed method outperforms the current state-of-the-art for multi-modal self-supervised representation learning on both in- and out-of domain datasets. + +# 2. Related Work + +# 2.1. Multi-Modal Learning + +With the availability of large-scale multi-modal datasets [31, 41, 7], multi-modal learning research has received a lot of attention. It comprises of vision-language + +learning [35, 51], vision-audio learning [2, 4, 6, 12, 46], video-audio-language learning [39, 11, 42], zero-shot learning [21, 28], cross-modal generation [37, 53, 27] and multi-modal multi-task learning [22]. Miech et al. [31] proposed a large-scale multi-modal dataset consisting of video, audio and text by collecting instructional videos from YouTube without requiring any human annotations. Note that the text is generated from audio using Automatic Speech Recognition (ASR) and has noisy alignment between the text and video. They also proposed a multimodal system to demonstrate the potential for learning video-text embedding via contrastive loss. To handle the noise in the dataset, Amrani et al. [3] proposed a noise estimation for multi-modal data via multi-modal density estimation. A noise-contrastive estimation approach in a multi-instance learning framework was proposed by Miech et al. [29]. XDC [2] performs clustering on audio-video for learning better features for each modality separately. These works utilize only two modalities for multi-modal learning, while others have explored utilizing audio, video, and text together for multi-modal learning. Multi-Modal versatile networks [1] was proposed to learn different embedding spaces for each combination of modalities. AVLNet [39] proposed to learn a shared embedding that maps all modalities to a single joint embedding space. Following this, MCN [11] proposed to perform joint clustering and reconstruction to learn joint embedding space. Note that, [11] performs multi-modal K-means clustering to learn hard semantic clusters. Unlike strict assignment in [11], we propose flexible learning with multiple assignments and separately for each modality. More recently, EAO [42] utilizes transformers and combinatorial fusion of modalities to learn the joint embedding with contrastive loss. + +Most of these works, utilize contrastive or clustering loss over fused multi-modal representation to learn the joint embedding space. By doing so, these models do not retain the modality-specific semantic structuring between samples encoded by the pre-trained modality specific backbones, hurting the generalization ability of the model. Additionally, recent works have reported that large-scale contrastive multimodal models (e.g., CLIP [36]) are somewhat robust to distributional shifts mainly due to diverse large-scale training data and prompt-engineering [15]. Therefore, our work focuses on making the pre-training objective robust to distributional shifts. In this context, we propose a novel approach to preserve the modality-specific semantic relationships in the joint embedding space by modeling the relationship between samples w.r.t learnable anchors. To enable flexible relationship modeling between samples, we learn multiple anchor assignments per sample, where anchors shared across samples model the commonality between them, and the distinct anchors between samples highlight the uniqueness of the samples. + +![](images/36b1353f0d482ab61ec574a70a19b3d49c9e6d43f912d0b1a2da048bb98354b6.jpg) +Figure 1: Overview of the proposed model. Given weakly aligned text, video, and audio, we first extract features using frozen modality-specific backbones. These features are then passed through a token projection layer to obtain input features $(\mathbf{v},\mathbf{t},\mathbf{a})$ specific to each modality. Next, the modality-specific transformer models project the input features into a joint multi-modal representation space $(\hat{\mathbf{v}},\hat{\mathbf{t}},\hat{\mathbf{a}})$ . The similarity between the input features $(\mathbf{v},\mathbf{t},\mathbf{a})$ and input space anchors $(\mathbf{Z}_{\mathbf{v}},\mathbf{Z}_{\mathbf{t}},\mathbf{Z}_{\mathbf{a}})$ (projected features $(\hat{\mathbf{v}},\hat{\mathbf{t}},\hat{\mathbf{a}})$ and projected space anchors $(\hat{\mathbf{Z}}_{\mathbf{v}},\hat{\mathbf{Z}}_{\mathbf{t}},\hat{\mathbf{Z}}_{\mathbf{a}}))$ is computed, and our Multi-SK algorithm $(M(.))$ is used to optimize multiple anchor assignments per sample, as shown in the Input Space Assignments (Projected Space Assignments). We do this for each modality and enforce the respective consistency losses, but in this figure we only show modality-specific consistency loss for text anchors and cross-modal consistency between text and video modalities for brevity. LN, MHSA represents LayerNorm and Multi-Head Self-Attention. + +# 2.2. Sinkhorn-Knopp + +Recently, Sinkhorn-Knopp algorithm [44] has drawn huge attention because of its effectiveness in solving optimal-transport problems [23, 8]. Specifically, [13] proposed an entropic relaxation of the optimal transport problem which can be efficiently solved using Sinkhorn's matrix scaling algorithm. Many following works have since successfully utilized the Sinkhorn-Knopp algorithm to solve different label assignment problems framed as an optimal transport problems. For instance, SeLa [48] cast the unsupervised clustering problem as a pseudo-label assignment problem and used the Sinkhorn-Knopp algorithm to solve it. SeLaVi [5] extended this idea to self-supervised representation learning for multi-modal data where the cluster assignments between different modalities are swapped to encourage modality invariant representation learning. Similarly, SwAV [9] used the Sinkhorn-Knopp algorithm for self-supervised representation learning and proposed to swap the pseudo-labels for differently augmented versions of a sample and use soft assignments instead of hard pseudolabels. In contrast to these works, SuperGlue [40] used the Sinkhorn-Knopp algorithm to solve the correspondence + +problem between two sets of local features. Moreover, Sinkhorn-Knopp has been used in detection problems [17], where it was used to match the anchors with ground truths. Recently, UNO [16], and TRSSL [38] have successfully used the Sinkhorn-Knopp algorithm in solving novel class discovery and open-world semi-supervised learning problems, respectively. One key limitation of the traditional Sinkhorn-Knopp algorithm is that it cannot be directly utilized to compute multiple assignments necessary to perform multi-anchor based learning i.e. many-to-many assignments. + +Some prior works [18, 26] have attempted to solve many-to-many assignments in indirect ways. While authors of [18] use an intermediate graph to match groups of vertices from source to target graph, which can only perform group-to-group assignments and is inadequate for our problem that requires true many-to-many matching. [26] modifies the Sinkhorn-Knopp row and column constraints to obtain many-to-many assignment to model dense correspondences, however, we have found this approach to be inferior in solving the multiple anchor assignment problem. The modified Sinkhorn-Knopp constraints approach yields suboptimal results, as discussed in Sec. 4.4. To address these + +limitations, we propose a novel algorithm Multi-SK, which outperforms the modified Sinkhorn-Knopp constraints approach to get true many-to-many assignments. + +# 3. Method + +Given a set of multi-modal inputs $\{\mathbf{t}^{(i)},\mathbf{v}^{(i)},\mathbf{a}^{(i)}\}_{i = 1}^{N}$ from N video clips, we learn modality-specific projection functions $f_{t},f_{v},f_{a}$ , that transform t,v,a into a d-dimensional joint embedding space, $\mathbb{R}^d$ to obtain $\hat{\mathbf{t}},\hat{\mathbf{v}},\hat{\mathbf{a}}$ respectively. Our goal is to optimize the parameters of $f_{t},f_{v},f_{a}$ in such a way that they maintain the semantic structure amongst samples from a particular modality in the joint embedding space, as discussed in Sec 3.1, and simultaneously brings the semantically related cross-modal inputs closer. In the following, first, we formulate our approach to modeling the relationship between samples using anchors in Sec 3.1, then in Sec 3.2, we discuss our novel Multi-SK algorithm to learn these anchors for representing sample relationships, and finally, we present the overall training objective to train the model in Sec 3.3. + +# 3.1. Modeling Sample Relationships with Anchors + +Our work aims to preserve the relationship between samples i.e. $\mathbf{x}^{(i)},\mathbf{x}^{(j)}$ from a particular modality, to better generalize on the unseen data. To this end, we propose to model the relationship between samples using anchors, where the similarity of each sample w.r.t. anchors encodes the semantic structure of the feature space. Unlike clustering approaches, which involve hard-assignment to a specific cluster, our approach offers flexibility i.e., there can be shared and unique anchors across samples that define the relationship between them. To be particular, for each sample, we learn $K$ anchors, and the similarity of assignments over these anchors represents the relationship (which we want to preserve) between samples from a particular modality. + +As the pre-trained features extracted from modality-specific backbones encode the semantic structure between samples within that particular modality, preserving such modality-specific relationships in the joint embedding space would boost the generalizability of the model. To achieve this, we define two sets of $K$ learnable anchors $\mathbf{z} = \{\mathbf{z}^{(i)}\}_{i=1}^{K}$ , and $\hat{\mathbf{z}} = \{\hat{\mathbf{z}}^{(i)}\}_{i=1}^{K}$ to model the sample relationships before and after projecting them to the joint embedding space respectively. We repeat this for all the modalities, $t, v, a$ . We propose to preserve the modality-specific semantic structure at the joint embedding space by enforcing consistency in anchor assignments before and after performing feature projections (Eq. 3). + +We still have one remaining challenge, i.e. how to learn/discover these anchors in an unsupervised manner. To this end, we cast the anchor discovery as a label assignment task with a uniform prior, i.e. each anchor will have an equal number of sample assignments. Additionally, to + +encourage flexible modeling, we enforce multiple anchor assignments per sample. However, it is difficult to estimate the exact number of anchors for each sample without additional prior information, thus we select the top $K'$ anchors for each sample to effectively model the sample relationships. Even though this optimization task may seem like a difficult combinatorial problem, we model this combinatorial optimization task as an optimal transport problem. Following recent works [5, 9], one might assume the Sinkhorn-Knopp algorithm is a natural choice to solve this problem, however, the vanilla Sinkhorn-Knopp algorithm cannot handle multiple assignments per sample i.e. many-to-many assignment. To address this limitation, we propose Multi-Assignment Sinkhorn-Knopp algorithm, presented in the following. + +# 3.2. Multi-Assignment Sinkhorn-Knopp + +Given a sample matrix $\mathbf{B}$ s.t. $\mathbf{B} \in \mathbb{R}^{N \times d}$ , representing $N$ samples and an anchor matrix $\mathbf{Z}$ s.t. $\mathbf{Z} \in \mathbb{R}^{K \times d}$ , of $K$ anchor vectors, we obtain the similarity matrix $\mathbf{S}$ s.t. $\mathbf{S} = \mathbf{B}\mathbf{Z}^{\intercal}$ and $\mathbf{S} \in \mathbb{R}^{N \times K}$ , where, $\mathbf{S}_{ij}$ is the probability of assigning $j$ th anchor to the $i$ th sample vector. The goal is to find an anchor assignment matrix, $\mathbf{Q}$ , such that it satisfies the following constraints: (i) a sample should be assigned to exactly $K'$ anchors, to learn top $K'$ anchor assignments per sample. (ii) anchor assignments must be equally partitioned i.e each anchor must be selected exactly $N \times K' / K$ times, for uniform anchor assignment. + +To obtain such multiple anchor assignments per sample, we propose to create a substitute 3D assignment matrix $\mathbf{Q}'$ s.t. $\mathbf{Q}' \in \mathbb{R}^{K \times N \times K}$ . We also generate a 3D similarity matrix $\mathbf{S}'$ from the 2D similarity matrix $\mathbf{S}$ by introducing $K$ channels (depth dimension) to get $K \times N \times K$ matrix such that each channel is a scaled matrix of $S$ with a predefined ranking between the channels enabling top $K'$ anchor selection. Since we are only interested in selecting the top $K'$ anchors, we set the first $K'$ channels of $\mathbf{S}'$ to be the same as $\mathbf{S}$ . The remaining $K - K'$ channels are set to $\mu \mathbf{S}$ . Here, $\mu$ is a damping factor s.t. $0 < \mu < 1$ , to help select the top $K'$ anchors for each sample. We discuss alternate designs for $\mathbf{S}'$ generation in the Supplementary Sec. 2. + +The optimization objective of Multi-Assignment Sinkhorn-Knopp is to find an assignment matrix $\mathbf{Q}'$ such that it satisfies our multi-anchor assignment constraints while maximizing similarity with the initial assignment/similarity matrix, $\mathbf{S}'$ . This optimization problem is defined as: + +$$ +\begin{array}{l} \mathbf {Q} ^ {*}: \max _ {\mathbf {Q} ^ {\prime}} < \mathbf {Q} ^ {\prime}, \mathbf {S} ^ {\prime} > + \epsilon H (\mathbf {Q} ^ {\prime}) \\ H \left(\mathbf {Q} ^ {*}\right) = - \sum \mathbf {Q} _ {i j k} ^ {\prime} \log \mathbf {Q} _ {i j k} ^ {\prime} \tag {1} \\ \end{array} +$$ + +$\mathbf{Q}^*$ needs to satisfy the following constraints to be a valid solution for our multi-anchor assignment problem. + +- $\mathbf{Q}^*$ Row Constraint: Within a channel, the sum of all el + +ements in a particular row must be equal to one. This is because we only want one anchor assignment for a sample in a particular channel. $\forall i,k\sum_{j}\mathbf{Q}^{*}_{ijk} = 1$ + +- $\mathbf{Q}^*$ Column Constraint: In a channel, the sum of all elements in a column should be equal to $N / K$ . This constraint enforces equal partitioning of anchor assignments. $\forall j, k \sum_{i} \mathbf{Q}^{*}_{ijk} = N / K$ . +- $\mathbf{Q}^*$ Depth constraint: Depth-wise sum should be equal to one for every sample and anchor combination. This constraint prevents selecting the same anchor across different channels. $\forall i, j \sum_{k} \mathbf{Q}^{*}_{ijk} = 1$ . + +The traditional Sinkhorn-Knopp method uses an iterative matrix scaling algorithm that scales the rows and columns alternatively (with desired constraints) till the desired assignment matrix is obtained. We employ a similar scheme and extend the iterative scaling to the depth dimension for estimating $\mathbf{Q}^*$ . We iteratively scale the rows, columns, and channels (depth dimension) till convergence. The final 2D assignment matrix $\mathbf{Q}$ is computed by performing a depth-wise sum on the top $K^{\prime}$ channels. We provide Pytorch-style pseudo-code for our Multi-Assignment Sinkhorn-Knop algorithm in the Supplementary Sec 3. + +# 3.3. Training Objective + +Semantic Structure Preserving Consistency Loss. To preserve the semantic structure of each modality, $t, v, a$ , we apply consistency loss to enforce similar anchor assignments between input and joint embedding space. As the cross-modal contrastive loss in the joint embedding space tries to bring different modalities together, features in the joint embedding space from a particular modality should preserve the common anchors that exist in corresponding features from the other modalities. Therefore, we also apply cross-modal anchor consistency across all modalities as shown in Eq. 3. Since we are dealing with 3 input modalities, this cross-modal consistency results in 9 consistency constraints. + +Let's denote $\mathcal{L}(\mathbf{t},\hat{\mathbf{v}},\mathbf{z}_t,\hat{\mathbf{z}}_t)$ as the consistency loss between text anchor assignment in the input space and the textual anchor assignment of the corresponding video features at the joint embedding space as shown below in Eq. 2: + +$$ +\begin{array}{l} \mathcal {L} (\mathbf {t}, \hat {\mathbf {v}}, \mathbf {z} _ {t}, \hat {\mathbf {z}} _ {t}) = \alpha_ {\mathbf {t}, \hat {\mathbf {v}}} g \left(\operatorname {s i m} \left(\mathbf {t}, \mathbf {z} _ {t}\right), M \left(\operatorname {s i m} \left(\hat {\mathbf {v}}, \hat {\mathbf {z}} _ {t}\right)\right)\right) (2) \\ + \beta_ {\mathbf {t}, \hat {\mathbf {v}}} g (\operatorname {s i m} (\hat {\mathbf {v}}, \hat {\mathbf {z}} _ {t})), M (\operatorname {s i m} (\mathbf {t}, \mathbf {z} _ {t}))), (2) \\ \end{array} +$$ + +Here, $\mathbf{z}_t, \hat{\mathbf{z}}_t$ respectively represent input and output learnable anchor vectors for the text modality. $g(.)$ , and $M(.)$ respectively represent binary cross-entropy-with-logits loss and Multi-Assignment Sinkhorn-Knopp (discussed in Sec. 3.2), $\alpha$ and $\beta$ represents loss coefficients, and $\mathrm{sim}(\mathbf{a},\mathbf{b}) = \exp (\mathbf{a.b} / \tau \| \mathbf{a}\| \| \mathbf{b}\|)$ , $\tau$ is the temperature hyperparameter of the similarity metric. + +Overall semantic structure preserving consistency loss for all the modalities is defined as: + +$$ +\mathcal {L} _ {s s p c} = \sum_ {m \in \{t, v, a \}} \sum_ {n \in \{t, v, a \}} \mathcal {L} (\mathbf {m}, \hat {\mathbf {n}}, \mathbf {z} _ {m}, \hat {\mathbf {z}} _ {m}). \tag {3} +$$ + +Contrastive Loss. Following [11, 42], we also use contrastive loss to bring cross-modal embeddings of the same sample closer while pushing away embeddings from other sample. For this, we use 3 pairwise single-modality constrastive losses, $\mathcal{L}_{nce\_ tv}$ , $\mathcal{L}_{nce\_ ta}$ , $\mathcal{L}_{nce\_ va}$ between $(t,v)$ , $(t,a)$ , $(v,a)$ respectively. Specifically, we use Noise Contrastive Estimation [33] with temperature $\kappa$ as shown in Eq. 4. + +$$ +\mathcal {L} _ {n c e - x y} = - \log \frac {\exp \left(\mathbf {x} ^ {\intercal} \mathbf {y} / \kappa\right)}{\sum_ {i = 1} ^ {N} \exp \left(\mathbf {x} ^ {(i) \intercal} \mathbf {y} ^ {(i)} / \kappa\right)} \tag {4} +$$ + +The overall contrastive loss for all modalities is defined as $\mathcal{L}_{nce} = \lambda_{tv}\mathcal{L}_{nce\_tv} + \lambda_{ta}\mathcal{L}_{nce\_ta} + \lambda_{va}\mathcal{L}_{nce\_va}$ + +# Overall Loss + +The overall training objective is a combination of SSPC loss (Eq. 3) and contrastive loss (4): $\mathcal{L}_f = \lambda_{sspc}\mathcal{L}_{sspc} + \lambda_{nce}\mathcal{L}_{nce}$ , where, $\lambda_{sspc}$ and $\lambda_{nce}$ are loss coefficients. By combining both losses, the model learns a more generic joint embedding space which preserves the modality-specific semantic structure by enforcing the anchor assignment similarity before and after feature projection and also brings representations of different modalities together by utilizing contrastive loss. + +# 4. Experiments + +# 4.1. Experimental Setup + +Backbones. For comparability, we follow the same setup of previous works [31, 39, 11, 42]. As visual backbone, we use a combination of 2D features from ResNet-152 [20] pretrained onImagenet [14], and 3D features from ResNeXt101 [19] pretrained on Kinetics [10]. The text backbone is GoogleNews pretrained Word2vec model [32]. These backbones are fixed and not finetuned during training. Following [11, 42], we use a trainable CNN with residual layers as an audio backbone. We provide additional details in the Supplementary Sec. 5. + +Data Sampling. We use a batch of 216 videos and randomly sample ten 8-second clips per video. If the sampled clip contains narration (95% clips), we use ASR time stamps to select clip borders. To disentangle high text-audio correlation in HT100M, we shift the audio clip randomly by 4 seconds with respect to the video and text boundaries. + +Projections. Following [42, 11, 39], we use a gated linear projection [30] to project features into common token space, as well as to project resulting tokens into shared embedding space. We set the dimension of the common token space to 4096 and of the shared embedding space to 6144. + +
MethodRetrievalTrainVisualTrainable BBMSR-VTTYouCook2
DatasetBBtvaR@5↑R@10↑MedR↓MeanR↓R@5↑R@10↑MedR↓MeanR↓
ActBERT [54]t → vHT100MRes3D+Faster R-CNN23.433.136-26.738.019-
SupportSet [34]t → vHT100MR152 + R(2+1)D-34✓23.031.131-----
HT100M [31]t → vHT100MR152 + RX10121.229.638-17.324.846-
AVLNet [39]t → vHT100MR152 + RX101✓24.734.2--21.129.6--
EAO [42]t → vHT100MR152 + RX101✓24.635.32590.427.938.919119.6
Ourst → vHT100MR152 + RX101✓26.435.12392.229.440.718111.8
AVLNet [39]v → tHT100MR152 + RX101✓27.235.72586.522.832.930142.2
EAO [42]v → tHT100MR152 + RX101✓27.636.6258531.870.51591.9
Oursv → tHT100MR152 + RX101✓27.237.12384.532721585.2
AVLNet [39]t → v + aHT100MR152 + RX101✓19.227.447-36.144.316-
MCN [11]t → v + aHT100MR152 + RX101✓25.233.8--35.545.2--
EAO [42]t → v + aHT100MR152 + RX101✓23.333.22994.838.549.21182.7
Ourst → v + aHT100MR152 + RX101✓25.134.52691.839.450.11083.3
AVLNet [39]v + a → tHT100MR152 + RX101✓1926.344128.148.858.4667.1
EAO [42]v + a → tHT100MR152 + RX101✓21.831.428.598.94960.9643.8
Oursv + a → tHT100MR152 + RX101✓24322795.948.861.3643.5
+ +Table 1: Zero-shot Retrieval results on MSR-VTT/YouCook2. For fair comparison, we compare with models trained on text, video and audio. Retrieval column represents the evaluation task. BB=Backbone. Bold, underline represent highest and second-highest scores. + +We use a single transformer block with hidden size of 4096 with 64 heads and an MLP size of 4096. We set the number of anchors $K$ as 64 and $K'$ as 32 with damping factor $\mu$ as 0.25. We train all models for 15 epochs using an Adam optimizer [24] with a learning rate of 5e-5, exponential decay of 0.9 and the temperature of cosine similarity $(\tau)$ as 0.1. We maintain a memory-bank of size 5500 while performing Multi-SK. Following [1, 42], we set higher weight for loss terms that involve text-video in Eq. 3, i.e., for all text-video terms the weight is set to 1.0 and the rest of the weights are set to 0.1. + +# 4.2. Datasets, Tasks, Metrics + +Pretraining Dataset. We train our model on the HT100M dataset [31], which contains over 1 million instructional videos with automatically generated text narrations. The text narrations can be assumed to be noisy and to not always describe the video scene. + +Zero-shot Retrieval. We use MSR-VTT [47] and YouCook2 [52] datasets to evaluate the zero-shot retrieval capability of our model. We report performance on 4 retrieval tasks: (i) Text-to-Video retrieval, (ii) Video-to-Text retrieval, (iii) Text-to-Video-Audio retrieval, (iv) Video-Audio-to-Text retrieval. The YouCook2 dataset contains cooking videos from YouTube with human-annotated clips ( $\sim$ 2 - 200 secs). For evaluation we use at maximum first 48 seconds of clip, since most clips are shorter than that. The MSR-VTT dataset contains human-annotated clips ( $\sim$ 10 - 30 secs) on various topics and provides captions with natural language sentences. Following [31, 39, 11, 42], to evaluate our model on MSR-VTT, we use the 1k set of test clips [49], and for YouCook2, we use 3,350 validation clips [31]. To perform $(t\rightarrow v + a)$ retrieval, we compute similarities by dot product between a text query $t$ and all videos in the dataset using a averaged $v + a$ representa + +tion for each video. We report standard recall metrics $\mathbf{R}@\mathbf{5}$ , $\mathbf{R}@\mathbf{10}$ , median rank (MedR) and the mean rank(MeanR). Further, we also evaluate our model using CLIP backbone and report results in Sec. 1 of the Supplementary. + +Zero-Shot Full-Video Retrieval. Following [11], we evaluate Zero-Shot Full Video Retrieval from a set of captions on YouCook2 dataset. We report recall metrics following Caption averaging method [11] that finds maximal prediction over all the clips of video for each caption and averaging over set of captions in query leading to a single prediction for full video. + +Text-to-video Retrieval after Fine-tuning. We additionally evaluate the retrieval performance of the models fine-tuned on downstream tasks. We use 6783 clips from MSR-VTT (which contain audio) and 9586 clips from YouCook2 train datasets to fine-tune the model as proposed by [39]. + +We also evaluate our model for Zero-shot Classification and report additional results in Sec. 1 of the Supplementary. + +# 4.3. Comparison with State-of-the-art + +Zero-shot Retrieval Tasks. In Tab. 1, we report the performance of the learned multi-modal representations on four zero-shot retrieval tasks, (i) Text-to-Video, (ii) Video-to-Text, (iii) Text-to-Video-Audio, (iv) Video-Audio-to-Text., on MSR-VTT and YouCook2 datasets. For a fair comparison, we only compare with models trained on all three modalities i.e. text, video and audio. In summary, our proposed method outperforms the current state-of-the-art methods by a noticeable margin on both the datasets. The results on the MSR-VTT dataset are particularly interesting since it demonstrates the generalizability of our model. In particular, HT100M consists of instructional videos and the textual descriptions are generated from audio using ASR. The text narration has noisy alignment with video and typically describes the steps in the video. YouCook2 shares + +
MethodRetrievalTrainVisualTrainable BBMSR-VTTYouCook2
DatasetBBtvaR@5↑R@10↑MedR↓MeanR↓R@5↑R@10↑MedR↓MeanR↓
AVLNet [39]t → vHT100MR152 + RX101✓42.256.2735.123.732.728122.6
EAO [42]t → vHT100MR152 + RX101✓47.759.3635.633.945.81370.7
Ourst → vHT100MR152 + RX101✓48.760.6533.135.648.11264.9
+ +Table 2: Text-to-video retrieval results on MSR-VTT/YouCook2 in the fine-tune setting. For fair comparison, we compare with models trained on all 3 modalities i.e. text, video and audio. Bold, underline represent best and second-best scores. + +
MethodAggregationR@1↑R@5↑R@10↑
Random-0.231.152.32
HT100M [31]Caption Avg.43.168.679.1
MIL-NCE [29]Caption Avg.46.674.383.7
MCN [11]Caption Avg.53.475.081.4
EAO [42]Caption Avg.62.980.586.7
OursCaption Avg.65.183.287.6
+ +domain similarity with HT100M as its videos are instructional format, and the text descriptions correspond to specific steps in the recipe. In contrast, MSR-VTT is not restricted to instructional videos and the text is typically a single sentence caption describing the whole video. As a result, there is a distributional shift between HT100M and MSR-VTT. Therefore, zero-shot retrieval on MSR-VTT has to overcome distributional shift, which is a crucial requirement for practical deployment. Our proposed method shows relatively higher improvement on this task validating the effectiveness of anchor-based learning. + +In case of text-to-video-audio retrieval, our method improves the Median and Mean rank of the baseline [42] by $3\%$ on MSR-VTT along with gains on recall metrics $R@5$ and $R@10$ . For video-audio-to-text retrieval, our methods perform very well on MSR-VTT with $3\%$ improvement on MeanR, $2.2\%$ improvement on $R@5$ . We also observe similar improvements on the YouCook2 dataset. Similarly, our proposed method outperforms the current state-of-the-art on most of the metrics for text-video-retrieval video-text-retrieval. Additionally, to compare our approach with text-video only model, we train our model on video and text to compare the performance with state-of-the-art in Sec 1 of the Supplementary. + +Zero-shot Full Video Retrieval. In Tab. 3, we report results for text-to-full-video retrieval task. Our approach outperforms prior works by $2.2\%$ , $2.7\%$ on R@1 and R@5 respectively. + +Retrieval after Fine-tuning. We also evaluate the retrieval performance of our model after fine-tuning on the downstream datasets as shown in Tab. 2. For a fair comparison, we only report the baselines that use the same training split. We outperform state-of-the-art consistently on all the metrics and on both MSR-VTT & YouCook2 datasets + +as shown in Tab. 2. + +# 4.4. Ablation Studies + +First we analyze the impact of the proposed components and report results in Tab. 4, followed by the effect of number of anchors $(K)$ & $(K^{\prime})$ in Tab. 5. + +Table 3: Zero-Shot Text-to-Full Video retrieval on YouCook2. Averaging across captions is used to obtain video-level predictions. + +
MethodMSR-VTTYouCook2
R@5↑R@10↑R@5↑R@10↑
Recon. + CL23.132.437.848.7
w/o CM SSPCL22.731.836.948.3
w/o SSPCL23.833.337.948.8
Modified SK23.431.337.948.3
Ours25.134.539.450.1
+ +Table 4: Ablation studies showing the impact of various components for zero-shot retrieval task. Recon.=Reconstruction Loss, CM SSPCL=Cross-Modal SSPC Loss, SK=Sinkhorn-Knopp, CL=Contrastive Loss. + +Effect of Proposed Components. We report the results for this ablation in Tab. 4. In first row, we report results using reconstruction loss and contrastive loss, we notice that using reconstruction loss reduces the performance by $2\%$ on all metrics indicating the effectiveness of the proposed SSPC loss. In the second row, we report results without our proposed cross-modal SSPC loss ('w/o CM SSPC'). We employ this loss to bring the cross-modal representations closer in the joint embedding space to obtain better performance in zero-shot cross-modal tasks. We notice that removing the cross-modal SSPC loss drastically decreases the zero-shot retrieval performance on both MSR-VTT and YouCook2 datasets, $2.4\%$ and $2.5\%$ drop in R@5 performance respectively. This empirically validates the effectiveness of the cross-modal SSPC loss in obtaining better cross-modal representations. + +In the third row, we analyze the effect of the proposed SSPC loss ('w/o SSPCL'). We apply the SSPC loss to retain modality-specific semantic structure from the pretrained models in the joint embedding space. To investigate its impact, we remove the anchor consistency between the modality-specific and joint embedding spaces. Instead, we enforce the anchor assignments before Multi-SK to be consistent with the Multi-SK optimized anchor as + +![](images/b2cc957fe4de615732ae3dfbc2a05de5dbf12c811084fd877125e2262a3ada0f.jpg) +(a) UMeazzCYlps (Holidays and Traditions) + +![](images/8263a7ab1f21a9d5ba54fa0df65dff181159df1cd90f2150283e72300b5f1d53.jpg) + +![](images/61fe488eb9ef28b0a46f636b11a59fdb546ec4494b06ce9f624e88b67cc4cfe5.jpg) + +![](images/2deac40873fcf07f5e27e410e2c90f9c34d5c2d674c8dbd2d806a878162499c0.jpg) +(b) fdUgKk-G5Tw (Food and Entertaining) + +![](images/96296052ffce8bfcf13cced27a5f7ebc8c2ffa957ebf7b27539e93f161741a84.jpg) + +![](images/6a69f6250264733e7faaad8f4cccfab0da2a185e5af60020327526c5625df11b.jpg) + +![](images/f9c1f037b7e0082a484beb440766b9e3808933f28d379e5e1d01b1bd205ba1be.jpg) + +![](images/57f91f9de5423015637a8942a535d6095aeb60cc0d73e585210e8e50ea094708.jpg) +(d) A0hURqF7h-c (Personal Care and Style) + +![](images/24c730676e7520321e775bf58e7956c85dc832f12e26efc1912c06d46d44371c.jpg) + +![](images/b4b48feb9d8852948609348aa4acd1ffb68a3512ae000e6de3bd7ed5e96af616.jpg) +(c) Video Anchor Assignments + +![](images/5eb9eb018f1a5cdd6437b2ab14e1e16f6076521c5f5a8a8b1778559db2862949.jpg) +Figure 2: Anchor assignments illustrated in this figure demonstrate the visual similarity between video samples from two related categories i.e. (a) Holidays and Tradition and (b) Food and Entertaining; and two different categories i.e. (d) Personal Care ans Style and (e) Finance and Business within the HowTo100M dataset. The visual similarity is also reflected in video anchor assignments (c) as most assigned anchors are similar with minor differences in assignments, thereby showcasing the flexibility and effectiveness of our approach. (d), (e) samples look very different and therefore the anchor assignments are also very different as shown in (f). Green cell $\rightarrow$ Anchor assigned, Yellow $\rightarrow$ Anchor not assigned. Difference in anchor assignments indicated in red. + +![](images/51d8ddbe79ea5b9f265920a633c0e65b28d235cdf409ee39c8ee4e284455718d.jpg) +(e) _Y51yX3KJoE (Finance and Business) + +![](images/90effec5408bbe895c6bb2857e4cf0a5e5319eef736e15b533f5ccddcbf34d57.jpg) + +![](images/6199cb8143c1a217676b9c629e752f1e33284306eea87dafd469e07455f56cd4.jpg) +(f) Video anchors Assignments + +
KK'MSR-VTTYouCook2
R@5↑R@10↑R@5↑R@10↑
16823.13237.147.5
321623.232.136.147.6
641623.331.836.747.2
644823.732.136.747.7
64(Ours)3225.134.539.450.1
+ +Table 5: Effect of different # of anchors on zero-shot retrieval. $K \rightarrow$ # of anchors and $K' \rightarrow$ # of selected anchors, respectively. + +signments from the same embedding space. We also apply the cross-modal SSPC loss to only isolate the impact of the proposed SSPC loss across feature projections. We observe that removing the anchor consistency between the modality-specific and joint embedding spaces reduces the zero-shot retrieval performance by a significant margin ( $\sim 1.5\%$ drop in R@5 performance), indicating the importance of SSPC loss in maintaining modality-specific semantic structure in the joint embedding space for better performance. + +Finally, in the fourth row of Tab. 4, we analyse the effectiveness of the proposed Multi-Assignment Sinkhorn-Knoppalgorithm. To this end, we modify the vanilla Sinkhorn-Knopp [13] to obtain multiple anchor assignments per sample (refer to Sec. 5 of the Supplementary + +for details). We notice that the modified Sinkhorn-Knopp does not perform well with a drop in performance ( $\sim 1.6\%$ drop in R@5) on both MSR-VTT and YouCook2 datasets on all the metrics indicating the significance of our proposed MULTI-SK algorithm. + +Effect of Number of Anchors. To analyze the effect of the number of anchors, we conduct experiments with different number of anchors, $K$ , and different number of selected anchors, $K'$ . We report the results in Tab. 5. We conduct experiments on both MSR-VTT and YouCook2 datasets. From the top half of Tab. 5, we observe that the performance of our proposed method improves with the increasing number of anchors. This is to be expected since a higher number of anchors have a higher representation learning capacity. We also observe that the method performs reasonably well even with a very small number of anchors showing the general effectiveness of our proposed solution. We notice that the performance of the proposed method improves as we select more anchors as shown in bottom half of Tab. 5. However, selecting a very large number of anchors (48 out of 64 for this experiment) adds more constraints leading to poor performance. + +# 4.5. Qualitative Analysis + +Here, first we present a fine-grained visual analysis of the learned anchors, followed by qualitative retrieval results. + +"Animated comic scene of guy cutting up food for dinner" + +"a woman holding a ribbon" + +"mix ingredients refrigerate" + +"add mutton pan" + +![](images/f7e7e48075b15f9cebdea991dca2cd685f88583ac000e5ef483866cdd5b9ec21.jpg) + +![](images/6fef8ff10153ebdf7ac5c77cc855c27afb983fdf4313f22ded1e74fa85fa38ab.jpg) + +![](images/512d1d94ddde5cf43663e4a2e81964b05b5a7cdddeecacf992d07d761e849b06.jpg) + +![](images/ab8c55517bc30b4c7669d599c469af248a5b5e51ff5f07ba41c1f57877828df4.jpg) + +![](images/d0e9f4499376fb190e25ebf377003bdc013496e0898fcf285a4aee1788216100.jpg) + +![](images/2606ee2d6bb550f4e50b4634782c64cb43f4270c6676bdfc28678fc1ae9cab97.jpg) + +![](images/338f294da97650e8d905b2ca23441cd769228c343f180bf1a2f58a7b7a4e2240.jpg) + +![](images/29b37b8697b4b205debcf43945958609e3896f11874ae2e6902d41eb45c53fd2.jpg) +Ours +Figure 3: Examples of Zero-Shot Text-to-Video Retrieval on MSR-VTT and YouCook2 datasets. Each row consists of Textual Query (left), and top-3 retrieved videos for our method (center) and the state-of-the-art method EAO [42](right). Match indicates correct video for the query. + +![](images/0cb0d4848fc921cc9b6e19727e77b9028c0e698a01a9a16bd45e24f76aeee2b9.jpg) + +![](images/ed979fe8cc4337ba93053f95e71750f1bc7a26534d33199d5f8127cca553dc1b.jpg) + +![](images/a658fa31a34597a89d52f8422fe597aad42e5d996fd7433d7224243c46167342.jpg) + +![](images/599738612238d178becabd032ef3bf12f1be5ee833e3f691923c2f63c7c539b4.jpg) + +![](images/e1af4cc6a71efce0bb02d25715f16f879b7a83012168aedf932c43e3be5d1b70.jpg) + +![](images/87c0cfcde940184f1dd6aeb55faae211d18f326ea0d359136eb4099f0ebfeeea.jpg) + +![](images/c867ea629bf90de482f897293f68428df213fce06ca51f8f1c8aeb0a598b9dc4.jpg) + +![](images/951cc2b16efba37ab8c6d6d9d3dc1b77bea082db667bd05ce5e81007f9f65907.jpg) +EAO [42] + +![](images/87ae398794fc54d31a8d14024f3f4bfe97471dba08d74bf625b58a5b64e3c8c9.jpg) + +![](images/314daf3ecc2444e258048b4629fd33d4ecdd430322a99058b0db9be5655dede1.jpg) + +![](images/5adc6043e40230bd6ac85dbe81b708b0840445aa16714abd37e90bff2a8abdf3.jpg) + +We show fine-grained analysis of the learned anchors in Fig. 2. For the purpose of this analysis, we visualize the anchor assignments as binary assignments. However, during training we use soft anchor assignments. In Fig. 2(c), we compare the anchor assignments for samples from similar categories. It can be seen that the videos are visually similar even though they belong to different categories and the anchor assignments for these two examples are able to capture the sample similarity. In Fig. 2(f), we compare the anchor assignments for videos from different categories and it can be seen that the anchor assignments are very different as expected. This further validates our claim that our proposed method can assign semantically meaningful anchors without any explicit supervision. Further, we show qualitative retrieval comparison with EAO [42] in Fig. 3. We present more qualitative analysis in Supplementary Sec. 4. + +# 5. Conclusion + +We proposed a novel approach that preserves the modality-specific semantic relationship between samples in the joint multi-modal embedding space. To this end, we propose a flexible sample relationship modeling approach by assigning multiple anchors to each sample, which captures both shared and unique aspects of samples. To obtain these assignments, we develop a novel Multi-Assignment Sinkhorn-Knopp (Multi-SK) algorithm, and also utilize the proposed anchor consistency loss to learn these anchors. Our qualitative results demonstrate that our learnt anchors correspond to meaningful semantic concepts. Our extensive experimentation demonstrates that the proposed approach improves generalizability by outperforming state-of-the-art methods on both in- and out-of-domain datasets. We also + +show that our method achieves state-of-the-art performance on multiple zero-shot tasks, and also outperforms when fine-tuned on downstream datasets. + +# Acknowledgements + +Research was sponsored by the Army Research Office and was accomplished under Grant Number W911NF-19-1-0356. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. Nina Shvetsova is supported by German Federal Ministry of Education and Research (BMBF) project STCL - 01IS22067. + +# References + +[1] Jean-Baptiste Alayrac, Adria Recasens, Rosalia Schneider, Relja Arandjelovic, Jason Ramapuram, Jeffrey De Fauw, Lucas Smaira, Sander Dieleman, and Andrew Zisserman. 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These joint embeddings enable zero-shot cross-modal tasks like retrieval and classification. However, these methods often struggle to generalize well on out-of-domain data as they ignore the semantic structure present in modality-specific embeddings. In this context, we propose a novel Semantic-Structure-Preserving Consistency approach to improve generalizability by preserving the modality-specific relationships in the joint embedding space. To capture modality-specific semantic relationships between samples, we propose to learn multiple anchors and represent the multifaceted relationship between samples with respect to their relationship with these anchors. To assign multiple anchors to each sample, we propose a novel Multi-Assignment Sinkhorn-Knopp algorithm. Our experimentation demonstrates that our proposed approach learns semantically meaningful anchors in a self-supervised manner. Furthermore, our evaluation on MSR-VTT and YouCook2 datasets demonstrates that our proposed multi-anchor assignment based solution achieves state-of-the-art performance and generalizes to both in-and out-of-domain datasets. Code: https://github.com/Swetha5/Multi_Sinkhorn_Knopp" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 596, + 128, + 608 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 596, + 128, + 608 + ], + "spans": [ + { + "bbox": [ + 47, + 596, + 128, + 608 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": "Humans often rely on multiple sensory inputs to have a better understanding of everyday events. Most commonly, we utilize vision, audio, and language to perceive an event as they provide complementary information for robust reasoning. The closest approximation of this setup is video data as it provides both visual and audio information along with a text description as a caption. Recently, researchers have started to explore learning meaningful representations" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 242, + 547, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 242, + 547, + 362 + ], + "spans": [ + { + "bbox": [ + 304, + 242, + 547, + 362 + ], + "type": "text", + "content": "by leveraging multiple modalities to train efficient models at scale [5, 11, 42]. Such systems focus on representation learning that either improves features for each modality separately [5] or learns a joint multi-modal embedding [11, 42] space that enables various zero-shot tasks like retrieval or classification. However, given the inherent differences across the modalities, it is challenging to learn effective joint embeddings. Furthermore, the real-world data presents additional challenges like misalignment between modalities, leading to weak supervision." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 365, + 548, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 548, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 548, + 700 + ], + "type": "text", + "content": "Current pre-training approaches in this area usually employ a contrastive objective [33] to learn the joint embeddings that pulls the cross-modal embeddings of a sample from the same temporal instance closer and pushes embeddings of other samples farther. Despite promising performances, these methods struggle with generalizability. This is particularly evident in previous approaches trained on HT100M [11, 42], which do well on the closely related downstream dataset YouCook2 but struggle to improve on the MSR-VTT dataset, which exhibits a relatively larger domain shift with respect to HT100M [42]. This is due to the contrastive objective's emphasis on strict alignment between modalities in the joint embedding space while ignoring the inherent weak alignment between different modalities [45], as well as the underlying semantic structure across samples [43, 50]. Recent works have tackled these issues, either by using joint multi-modal clustering [11] to preserve the semantic structure in the joint embedding space or by incorporating a reconstruction objective [11, 25] to retain modality-specific features in the joint embedding space, allowing for weak multi-modal alignment. However, the usual reconstruction objective trivially tries to retain most modality-specific features in the joint space, thus preventing the learning of optimal features for cross-modal tasks. And the multi-modal clustering approaches perform hard-clustering making it less flexible. Therefore, the limitations of the contrastive objective cannot be adequately addressed even after combining these independent objectives." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "content": "To address this, we propose a semantic-structure" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21993" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "text", + "content": "preserving consistency loss (SSPC) to only retain information that is beneficial for both cross-modal embedding learning and retaining modality-specific semantic structure. In particular, for SSPC loss we consider each sample (e.g., a video clip) to be composed of multiple concepts: scene or objects involved in the downstream task. Therefore, the relationship between samples is multifaceted, representing both shared and unique concepts across samples. To capture this multifaceted relationship in a flexible manner, we propose to learn anchors (latent codes) and model the relationship between samples with respect to their relationships with these anchors. Therefore, these anchors act as a proxy to represent the modality-specific relationships between samples (semantic structure) which can be preserved using the proposed SSPC loss. Since we have no supervision to learn these anchors, we formulate this anchor learning problem as a many-to-many assignment problem, as modeling this multifaceted relationship simultaneously involves assigning multiple anchors to one sample and multiple samples to one anchor. Although there is a vast literature on solving the many-to-one assignment problem [9, 5, 38, 48], there is no efficient way to solve this many-to-many assignment problem." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 348, + 289, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 348, + 289, + 527 + ], + "spans": [ + { + "bbox": [ + 47, + 348, + 289, + 527 + ], + "type": "text", + "content": "To this end, we propose a novel Multi-Assignment Sinkhorn-Knopp (Multi-SK) algorithm that iteratively optimizes the many-to-many anchor assignments for both the modality-specific embeddings (in input space) and modality-agnostic multi-modal embeddings (in joint embedding space). To allow for weak alignment between modalities, we select the dominant anchors for each sample to represent the relationship between different samples. Our proposed SSPC loss enforces consistency between the dominant anchor assignments at the input and joint embedding spaces to preserve the modality-specific semantic structure. To demonstrate the effectiveness of our proposed solution, we train our model on HT100M dataset and test on 6 zero-shot tasks on multiple downstream datasets and observe that our approach leads to state-of-the-art results in all settings." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 527, + 289, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 289, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 289, + 634 + ], + "type": "text", + "content": "In summary, we make the following contributions: (i) We propose a flexible modality-specific semantic-structure-preserving approach to improve the generalizability of cross-modal features. (ii) We introduce Multi-Assignment Sinkhorn-Knopp, a novel algorithm to enable multiple assignments for flexible sample relationship modeling. (iii) Our proposed method outperforms the current state-of-the-art for multi-modal self-supervised representation learning on both in- and out-of domain datasets." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 645, + 134, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 134, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 134, + 658 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 662, + 176, + 675 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 662, + 176, + 675 + ], + "spans": [ + { + "bbox": [ + 47, + 662, + 176, + 675 + ], + "type": "text", + "content": "2.1. Multi-Modal Learning" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": "With the availability of large-scale multi-modal datasets [31, 41, 7], multi-modal learning research has received a lot of attention. It comprises of vision-language" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 468 + ], + "type": "text", + "content": "learning [35, 51], vision-audio learning [2, 4, 6, 12, 46], video-audio-language learning [39, 11, 42], zero-shot learning [21, 28], cross-modal generation [37, 53, 27] and multi-modal multi-task learning [22]. Miech et al. [31] proposed a large-scale multi-modal dataset consisting of video, audio and text by collecting instructional videos from YouTube without requiring any human annotations. Note that the text is generated from audio using Automatic Speech Recognition (ASR) and has noisy alignment between the text and video. They also proposed a multimodal system to demonstrate the potential for learning video-text embedding via contrastive loss. To handle the noise in the dataset, Amrani et al. [3] proposed a noise estimation for multi-modal data via multi-modal density estimation. A noise-contrastive estimation approach in a multi-instance learning framework was proposed by Miech et al. [29]. XDC [2] performs clustering on audio-video for learning better features for each modality separately. These works utilize only two modalities for multi-modal learning, while others have explored utilizing audio, video, and text together for multi-modal learning. Multi-Modal versatile networks [1] was proposed to learn different embedding spaces for each combination of modalities. AVLNet [39] proposed to learn a shared embedding that maps all modalities to a single joint embedding space. Following this, MCN [11] proposed to perform joint clustering and reconstruction to learn joint embedding space. Note that, [11] performs multi-modal K-means clustering to learn hard semantic clusters. Unlike strict assignment in [11], we propose flexible learning with multiple assignments and separately for each modality. More recently, EAO [42] utilizes transformers and combinatorial fusion of modalities to learn the joint embedding with contrastive loss." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 474, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 548, + 715 + ], + "type": "text", + "content": "Most of these works, utilize contrastive or clustering loss over fused multi-modal representation to learn the joint embedding space. By doing so, these models do not retain the modality-specific semantic structuring between samples encoded by the pre-trained modality specific backbones, hurting the generalization ability of the model. Additionally, recent works have reported that large-scale contrastive multimodal models (e.g., CLIP [36]) are somewhat robust to distributional shifts mainly due to diverse large-scale training data and prompt-engineering [15]. Therefore, our work focuses on making the pre-training objective robust to distributional shifts. In this context, we propose a novel approach to preserve the modality-specific semantic relationships in the joint embedding space by modeling the relationship between samples w.r.t learnable anchors. To enable flexible relationship modeling between samples, we learn multiple anchor assignments per sample, where anchors shared across samples model the commonality between them, and the distinct anchors between samples highlight the uniqueness of the samples." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "21994" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 548, + 325 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 548, + 325 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 548, + 325 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 548, + 325 + ], + "type": "image", + "image_path": "36b1353f0d482ab61ec574a70a19b3d49c9e6d43f912d0b1a2da048bb98354b6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 339, + 548, + 429 + ], + "lines": [ + { + "bbox": [ + 46, + 339, + 548, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 339, + 548, + 429 + ], + "type": "text", + "content": "Figure 1: Overview of the proposed model. Given weakly aligned text, video, and audio, we first extract features using frozen modality-specific backbones. These features are then passed through a token projection layer to obtain input features " + }, + { + "bbox": [ + 46, + 339, + 548, + 429 + ], + "type": "inline_equation", + "content": "(\\mathbf{v},\\mathbf{t},\\mathbf{a})" + }, + { + "bbox": [ + 46, + 339, + 548, + 429 + ], + "type": "text", + "content": " specific to each modality. Next, the modality-specific transformer models project the input features into a joint multi-modal representation space " + }, + { + "bbox": [ + 46, + 339, + 548, + 429 + ], + "type": "inline_equation", + "content": "(\\hat{\\mathbf{v}},\\hat{\\mathbf{t}},\\hat{\\mathbf{a}})" + }, + { + "bbox": [ + 46, + 339, + 548, + 429 + ], + "type": "text", + "content": ". The similarity between the input features " + }, + { + "bbox": [ + 46, + 339, + 548, + 429 + ], + "type": "inline_equation", + "content": "(\\mathbf{v},\\mathbf{t},\\mathbf{a})" + }, + { + "bbox": [ + 46, + 339, + 548, + 429 + ], + "type": "text", + "content": " and input space anchors " + }, + { + "bbox": [ + 46, + 339, + 548, + 429 + ], + "type": "inline_equation", + "content": "(\\mathbf{Z}_{\\mathbf{v}},\\mathbf{Z}_{\\mathbf{t}},\\mathbf{Z}_{\\mathbf{a}})" + }, + { + "bbox": [ + 46, + 339, + 548, + 429 + ], + "type": "text", + "content": " (projected features " + }, + { + "bbox": [ + 46, + 339, + 548, + 429 + ], + "type": "inline_equation", + "content": "(\\hat{\\mathbf{v}},\\hat{\\mathbf{t}},\\hat{\\mathbf{a}})" + }, + { + "bbox": [ + 46, + 339, + 548, + 429 + ], + "type": "text", + "content": " and projected space anchors " + }, + { + "bbox": [ + 46, + 339, + 548, + 429 + ], + "type": "inline_equation", + "content": "(\\hat{\\mathbf{Z}}_{\\mathbf{v}},\\hat{\\mathbf{Z}}_{\\mathbf{t}},\\hat{\\mathbf{Z}}_{\\mathbf{a}}))" + }, + { + "bbox": [ + 46, + 339, + 548, + 429 + ], + "type": "text", + "content": " is computed, and our Multi-SK algorithm " + }, + { + "bbox": [ + 46, + 339, + 548, + 429 + ], + "type": "inline_equation", + "content": "(M(.))" + }, + { + "bbox": [ + 46, + 339, + 548, + 429 + ], + "type": "text", + "content": " is used to optimize multiple anchor assignments per sample, as shown in the Input Space Assignments (Projected Space Assignments). We do this for each modality and enforce the respective consistency losses, but in this figure we only show modality-specific consistency loss for text anchors and cross-modal consistency between text and video modalities for brevity. LN, MHSA represents LayerNorm and Multi-Head Self-Attention." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 437, + 151, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 437, + 151, + 451 + ], + "spans": [ + { + "bbox": [ + 47, + 437, + 151, + 451 + ], + "type": "text", + "content": "2.2. Sinkhorn-Knopp" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 462, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 289, + 715 + ], + "type": "text", + "content": "Recently, Sinkhorn-Knopp algorithm [44] has drawn huge attention because of its effectiveness in solving optimal-transport problems [23, 8]. Specifically, [13] proposed an entropic relaxation of the optimal transport problem which can be efficiently solved using Sinkhorn's matrix scaling algorithm. Many following works have since successfully utilized the Sinkhorn-Knopp algorithm to solve different label assignment problems framed as an optimal transport problems. For instance, SeLa [48] cast the unsupervised clustering problem as a pseudo-label assignment problem and used the Sinkhorn-Knopp algorithm to solve it. SeLaVi [5] extended this idea to self-supervised representation learning for multi-modal data where the cluster assignments between different modalities are swapped to encourage modality invariant representation learning. Similarly, SwAV [9] used the Sinkhorn-Knopp algorithm for self-supervised representation learning and proposed to swap the pseudo-labels for differently augmented versions of a sample and use soft assignments instead of hard pseudolabels. In contrast to these works, SuperGlue [40] used the Sinkhorn-Knopp algorithm to solve the correspondence" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 438, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 569 + ], + "type": "text", + "content": "problem between two sets of local features. Moreover, Sinkhorn-Knopp has been used in detection problems [17], where it was used to match the anchors with ground truths. Recently, UNO [16], and TRSSL [38] have successfully used the Sinkhorn-Knopp algorithm in solving novel class discovery and open-world semi-supervised learning problems, respectively. One key limitation of the traditional Sinkhorn-Knopp algorithm is that it cannot be directly utilized to compute multiple assignments necessary to perform multi-anchor based learning i.e. many-to-many assignments." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "content": "Some prior works [18, 26] have attempted to solve many-to-many assignments in indirect ways. While authors of [18] use an intermediate graph to match groups of vertices from source to target graph, which can only perform group-to-group assignments and is inadequate for our problem that requires true many-to-many matching. [26] modifies the Sinkhorn-Knopp row and column constraints to obtain many-to-many assignment to model dense correspondences, however, we have found this approach to be inferior in solving the multiple anchor assignment problem. The modified Sinkhorn-Knopp constraints approach yields suboptimal results, as discussed in Sec. 4.4. To address these" + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21995" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": "limitations, we propose a novel algorithm Multi-SK, which outperforms the modified Sinkhorn-Knopp constraints approach to get true many-to-many assignments." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 115, + 103, + 127 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 115, + 103, + 127 + ], + "spans": [ + { + "bbox": [ + 47, + 115, + 103, + 127 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 134, + 289, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 134, + 289, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 134, + 289, + 316 + ], + "type": "text", + "content": "Given a set of multi-modal inputs " + }, + { + "bbox": [ + 46, + 134, + 289, + 316 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{t}^{(i)},\\mathbf{v}^{(i)},\\mathbf{a}^{(i)}\\}_{i = 1}^{N}" + }, + { + "bbox": [ + 46, + 134, + 289, + 316 + ], + "type": "text", + "content": " from N video clips, we learn modality-specific projection functions " + }, + { + "bbox": [ + 46, + 134, + 289, + 316 + ], + "type": "inline_equation", + "content": "f_{t},f_{v},f_{a}" + }, + { + "bbox": [ + 46, + 134, + 289, + 316 + ], + "type": "text", + "content": ", that transform t,v,a into a d-dimensional joint embedding space, " + }, + { + "bbox": [ + 46, + 134, + 289, + 316 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^d" + }, + { + "bbox": [ + 46, + 134, + 289, + 316 + ], + "type": "text", + "content": " to obtain " + }, + { + "bbox": [ + 46, + 134, + 289, + 316 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{t}},\\hat{\\mathbf{v}},\\hat{\\mathbf{a}}" + }, + { + "bbox": [ + 46, + 134, + 289, + 316 + ], + "type": "text", + "content": " respectively. Our goal is to optimize the parameters of " + }, + { + "bbox": [ + 46, + 134, + 289, + 316 + ], + "type": "inline_equation", + "content": "f_{t},f_{v},f_{a}" + }, + { + "bbox": [ + 46, + 134, + 289, + 316 + ], + "type": "text", + "content": " in such a way that they maintain the semantic structure amongst samples from a particular modality in the joint embedding space, as discussed in Sec 3.1, and simultaneously brings the semantically related cross-modal inputs closer. In the following, first, we formulate our approach to modeling the relationship between samples using anchors in Sec 3.1, then in Sec 3.2, we discuss our novel Multi-SK algorithm to learn these anchors for representing sample relationships, and finally, we present the overall training objective to train the model in Sec 3.3." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 322, + 285, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 322, + 285, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 322, + 285, + 335 + ], + "type": "text", + "content": "3.1. Modeling Sample Relationships with Anchors" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 342, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 496 + ], + "type": "text", + "content": "Our work aims to preserve the relationship between samples i.e. " + }, + { + "bbox": [ + 46, + 342, + 287, + 496 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{(i)},\\mathbf{x}^{(j)}" + }, + { + "bbox": [ + 46, + 342, + 287, + 496 + ], + "type": "text", + "content": " from a particular modality, to better generalize on the unseen data. To this end, we propose to model the relationship between samples using anchors, where the similarity of each sample w.r.t. anchors encodes the semantic structure of the feature space. Unlike clustering approaches, which involve hard-assignment to a specific cluster, our approach offers flexibility i.e., there can be shared and unique anchors across samples that define the relationship between them. To be particular, for each sample, we learn " + }, + { + "bbox": [ + 46, + 342, + 287, + 496 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 342, + 287, + 496 + ], + "type": "text", + "content": " anchors, and the similarity of assignments over these anchors represents the relationship (which we want to preserve) between samples from a particular modality." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 498, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 653 + ], + "type": "text", + "content": "As the pre-trained features extracted from modality-specific backbones encode the semantic structure between samples within that particular modality, preserving such modality-specific relationships in the joint embedding space would boost the generalizability of the model. To achieve this, we define two sets of " + }, + { + "bbox": [ + 46, + 498, + 287, + 653 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 498, + 287, + 653 + ], + "type": "text", + "content": " learnable anchors " + }, + { + "bbox": [ + 46, + 498, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = \\{\\mathbf{z}^{(i)}\\}_{i=1}^{K}" + }, + { + "bbox": [ + 46, + 498, + 287, + 653 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 498, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}} = \\{\\hat{\\mathbf{z}}^{(i)}\\}_{i=1}^{K}" + }, + { + "bbox": [ + 46, + 498, + 287, + 653 + ], + "type": "text", + "content": " to model the sample relationships before and after projecting them to the joint embedding space respectively. We repeat this for all the modalities, " + }, + { + "bbox": [ + 46, + 498, + 287, + 653 + ], + "type": "inline_equation", + "content": "t, v, a" + }, + { + "bbox": [ + 46, + 498, + 287, + 653 + ], + "type": "text", + "content": ". We propose to preserve the modality-specific semantic structure at the joint embedding space by enforcing consistency in anchor assignments before and after performing feature projections (Eq. 3)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": "We still have one remaining challenge, i.e. how to learn/discover these anchors in an unsupervised manner. To this end, we cast the anchor discovery as a label assignment task with a uniform prior, i.e. each anchor will have an equal number of sample assignments. Additionally, to" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 252 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 252 + ], + "type": "text", + "content": "encourage flexible modeling, we enforce multiple anchor assignments per sample. However, it is difficult to estimate the exact number of anchors for each sample without additional prior information, thus we select the top " + }, + { + "bbox": [ + 304, + 72, + 547, + 252 + ], + "type": "inline_equation", + "content": "K'" + }, + { + "bbox": [ + 304, + 72, + 547, + 252 + ], + "type": "text", + "content": " anchors for each sample to effectively model the sample relationships. Even though this optimization task may seem like a difficult combinatorial problem, we model this combinatorial optimization task as an optimal transport problem. Following recent works [5, 9], one might assume the Sinkhorn-Knopp algorithm is a natural choice to solve this problem, however, the vanilla Sinkhorn-Knopp algorithm cannot handle multiple assignments per sample i.e. many-to-many assignment. To address this limitation, we propose Multi-Assignment Sinkhorn-Knopp algorithm, presented in the following." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 261, + 495, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 261, + 495, + 274 + ], + "spans": [ + { + "bbox": [ + 305, + 261, + 495, + 274 + ], + "type": "text", + "content": "3.2. Multi-Assignment Sinkhorn-Knopp" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "text", + "content": "Given a sample matrix " + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{B}" + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "text", + "content": " s.t. " + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{B} \\in \\mathbb{R}^{N \\times d}" + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "text", + "content": ", representing " + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "text", + "content": " samples and an anchor matrix " + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}" + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "text", + "content": " s.t. " + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{Z} \\in \\mathbb{R}^{K \\times d}" + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "text", + "content": ", of " + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "text", + "content": " anchor vectors, we obtain the similarity matrix " + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "text", + "content": " s.t. " + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{S} = \\mathbf{B}\\mathbf{Z}^{\\intercal}" + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{S} \\in \\mathbb{R}^{N \\times K}" + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "text", + "content": ", where, " + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{ij}" + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "text", + "content": " is the probability of assigning " + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "text", + "content": "th anchor to the " + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "text", + "content": "th sample vector. The goal is to find an anchor assignment matrix, " + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "text", + "content": ", such that it satisfies the following constraints: (i) a sample should be assigned to exactly " + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "inline_equation", + "content": "K'" + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "text", + "content": " anchors, to learn top " + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "inline_equation", + "content": "K'" + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "text", + "content": " anchor assignments per sample. (ii) anchor assignments must be equally partitioned i.e each anchor must be selected exactly " + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "inline_equation", + "content": "N \\times K' / K" + }, + { + "bbox": [ + 304, + 279, + 547, + 411 + ], + "type": "text", + "content": " times, for uniform anchor assignment." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": "To obtain such multiple anchor assignments per sample, we propose to create a substitute 3D assignment matrix " + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}'" + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": " s.t. " + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}' \\in \\mathbb{R}^{K \\times N \\times K}" + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": ". We also generate a 3D similarity matrix " + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{S}'" + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": " from the 2D similarity matrix " + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": " by introducing " + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": " channels (depth dimension) to get " + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "inline_equation", + "content": "K \\times N \\times K" + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": " matrix such that each channel is a scaled matrix of " + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": " with a predefined ranking between the channels enabling top " + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "inline_equation", + "content": "K'" + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": " anchor selection. Since we are only interested in selecting the top " + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "inline_equation", + "content": "K'" + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": " anchors, we set the first " + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "inline_equation", + "content": "K'" + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": " channels of " + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{S}'" + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": " to be the same as " + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": ". The remaining " + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "inline_equation", + "content": "K - K'" + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": " channels are set to " + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "inline_equation", + "content": "\\mu \\mathbf{S}" + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": " is a damping factor s.t. " + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "inline_equation", + "content": "0 < \\mu < 1" + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": ", to help select the top " + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "inline_equation", + "content": "K'" + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": " anchors for each sample. We discuss alternate designs for " + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{S}'" + }, + { + "bbox": [ + 304, + 412, + 547, + 567 + ], + "type": "text", + "content": " generation in the Supplementary Sec. 2." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 568, + 547, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 568, + 547, + 638 + ], + "spans": [ + { + "bbox": [ + 304, + 568, + 547, + 638 + ], + "type": "text", + "content": "The optimization objective of Multi-Assignment Sinkhorn-Knopp is to find an assignment matrix " + }, + { + "bbox": [ + 304, + 568, + 547, + 638 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}'" + }, + { + "bbox": [ + 304, + 568, + 547, + 638 + ], + "type": "text", + "content": " such that it satisfies our multi-anchor assignment constraints while maximizing similarity with the initial assignment/similarity matrix, " + }, + { + "bbox": [ + 304, + 568, + 547, + 638 + ], + "type": "inline_equation", + "content": "\\mathbf{S}'" + }, + { + "bbox": [ + 304, + 568, + 547, + 638 + ], + "type": "text", + "content": ". This optimization problem is defined as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 353, + 636, + 545, + 675 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 636, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 353, + 636, + 545, + 675 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {Q} ^ {*}: \\max _ {\\mathbf {Q} ^ {\\prime}} < \\mathbf {Q} ^ {\\prime}, \\mathbf {S} ^ {\\prime} > + \\epsilon H (\\mathbf {Q} ^ {\\prime}) \\\\ H \\left(\\mathbf {Q} ^ {*}\\right) = - \\sum \\mathbf {Q} _ {i j k} ^ {\\prime} \\log \\mathbf {Q} _ {i j k} ^ {\\prime} \\tag {1} \\\\ \\end{array}", + "image_path": "322393ce6862611f7b16a06d1acba39e3d8620d48ae49465be04f697f7fe36a4.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 674, + 545, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 674, + 545, + 698 + ], + "spans": [ + { + "bbox": [ + 304, + 674, + 545, + 698 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}^*" + }, + { + "bbox": [ + 304, + 674, + 545, + 698 + ], + "type": "text", + "content": " needs to satisfy the following constraints to be a valid solution for our multi-anchor assignment problem." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}^*" + }, + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "content": " Row Constraint: Within a channel, the sum of all el" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "21996" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 287, + 110 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 287, + 110 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 287, + 110 + ], + "type": "text", + "content": "ements in a particular row must be equal to one. This is because we only want one anchor assignment for a sample in a particular channel. " + }, + { + "bbox": [ + 55, + 72, + 287, + 110 + ], + "type": "inline_equation", + "content": "\\forall i,k\\sum_{j}\\mathbf{Q}^{*}_{ijk} = 1" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 113, + 287, + 215 + ], + "type": "list", + "angle": 0, + "index": 3, + "blocks": [ + { + "bbox": [ + 47, + 113, + 287, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 113, + 287, + 163 + ], + "spans": [ + { + "bbox": [ + 47, + 113, + 287, + 163 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 47, + 113, + 287, + 163 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}^*" + }, + { + "bbox": [ + 47, + 113, + 287, + 163 + ], + "type": "text", + "content": " Column Constraint: In a channel, the sum of all elements in a column should be equal to " + }, + { + "bbox": [ + 47, + 113, + 287, + 163 + ], + "type": "inline_equation", + "content": "N / K" + }, + { + "bbox": [ + 47, + 113, + 287, + 163 + ], + "type": "text", + "content": ". This constraint enforces equal partitioning of anchor assignments. " + }, + { + "bbox": [ + 47, + 113, + 287, + 163 + ], + "type": "inline_equation", + "content": "\\forall j, k \\sum_{i} \\mathbf{Q}^{*}_{ijk} = N / K" + }, + { + "bbox": [ + 47, + 113, + 287, + 163 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 165, + 287, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 165, + 287, + 215 + ], + "spans": [ + { + "bbox": [ + 47, + 165, + 287, + 215 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 47, + 165, + 287, + 215 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}^*" + }, + { + "bbox": [ + 47, + 165, + 287, + 215 + ], + "type": "text", + "content": " Depth constraint: Depth-wise sum should be equal to one for every sample and anchor combination. This constraint prevents selecting the same anchor across different channels. " + }, + { + "bbox": [ + 47, + 165, + 287, + 215 + ], + "type": "inline_equation", + "content": "\\forall i, j \\sum_{k} \\mathbf{Q}^{*}_{ijk} = 1" + }, + { + "bbox": [ + 47, + 165, + 287, + 215 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 216, + 288, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 288, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 288, + 347 + ], + "type": "text", + "content": "The traditional Sinkhorn-Knopp method uses an iterative matrix scaling algorithm that scales the rows and columns alternatively (with desired constraints) till the desired assignment matrix is obtained. We employ a similar scheme and extend the iterative scaling to the depth dimension for estimating " + }, + { + "bbox": [ + 46, + 216, + 288, + 347 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}^*" + }, + { + "bbox": [ + 46, + 216, + 288, + 347 + ], + "type": "text", + "content": ". We iteratively scale the rows, columns, and channels (depth dimension) till convergence. The final 2D assignment matrix " + }, + { + "bbox": [ + 46, + 216, + 288, + 347 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 46, + 216, + 288, + 347 + ], + "type": "text", + "content": " is computed by performing a depth-wise sum on the top " + }, + { + "bbox": [ + 46, + 216, + 288, + 347 + ], + "type": "inline_equation", + "content": "K^{\\prime}" + }, + { + "bbox": [ + 46, + 216, + 288, + 347 + ], + "type": "text", + "content": " channels. We provide Pytorch-style pseudo-code for our Multi-Assignment Sinkhorn-Knop algorithm in the Supplementary Sec 3." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 353, + 159, + 366 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 353, + 159, + 366 + ], + "spans": [ + { + "bbox": [ + 47, + 353, + 159, + 366 + ], + "type": "text", + "content": "3.3. Training Objective" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 371, + 287, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 371, + 287, + 526 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 287, + 526 + ], + "type": "text", + "content": "Semantic Structure Preserving Consistency Loss. To preserve the semantic structure of each modality, " + }, + { + "bbox": [ + 46, + 371, + 287, + 526 + ], + "type": "inline_equation", + "content": "t, v, a" + }, + { + "bbox": [ + 46, + 371, + 287, + 526 + ], + "type": "text", + "content": ", we apply consistency loss to enforce similar anchor assignments between input and joint embedding space. As the cross-modal contrastive loss in the joint embedding space tries to bring different modalities together, features in the joint embedding space from a particular modality should preserve the common anchors that exist in corresponding features from the other modalities. Therefore, we also apply cross-modal anchor consistency across all modalities as shown in Eq. 3. Since we are dealing with 3 input modalities, this cross-modal consistency results in 9 consistency constraints." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 527, + 287, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 527, + 287, + 575 + ], + "spans": [ + { + "bbox": [ + 46, + 527, + 287, + 575 + ], + "type": "text", + "content": "Let's denote " + }, + { + "bbox": [ + 46, + 527, + 287, + 575 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\mathbf{t},\\hat{\\mathbf{v}},\\mathbf{z}_t,\\hat{\\mathbf{z}}_t)" + }, + { + "bbox": [ + 46, + 527, + 287, + 575 + ], + "type": "text", + "content": " as the consistency loss between text anchor assignment in the input space and the textual anchor assignment of the corresponding video features at the joint embedding space as shown below in Eq. 2:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 579, + 287, + 607 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 579, + 287, + 607 + ], + "spans": [ + { + "bbox": [ + 59, + 579, + 287, + 607 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} (\\mathbf {t}, \\hat {\\mathbf {v}}, \\mathbf {z} _ {t}, \\hat {\\mathbf {z}} _ {t}) = \\alpha_ {\\mathbf {t}, \\hat {\\mathbf {v}}} g \\left(\\operatorname {s i m} \\left(\\mathbf {t}, \\mathbf {z} _ {t}\\right), M \\left(\\operatorname {s i m} \\left(\\hat {\\mathbf {v}}, \\hat {\\mathbf {z}} _ {t}\\right)\\right)\\right) (2) \\\\ + \\beta_ {\\mathbf {t}, \\hat {\\mathbf {v}}} g (\\operatorname {s i m} (\\hat {\\mathbf {v}}, \\hat {\\mathbf {z}} _ {t})), M (\\operatorname {s i m} (\\mathbf {t}, \\mathbf {z} _ {t}))), (2) \\\\ \\end{array}", + "image_path": "2c79d93aba6eb965e59ded8a39cdeb3d577673ff49b1d51f397b69ad4357ffe3.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 607, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 607, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 607, + 287, + 689 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 46, + 607, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t, \\hat{\\mathbf{z}}_t" + }, + { + "bbox": [ + 46, + 607, + 287, + 689 + ], + "type": "text", + "content": " respectively represent input and output learnable anchor vectors for the text modality. " + }, + { + "bbox": [ + 46, + 607, + 287, + 689 + ], + "type": "inline_equation", + "content": "g(.)" + }, + { + "bbox": [ + 46, + 607, + 287, + 689 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 607, + 287, + 689 + ], + "type": "inline_equation", + "content": "M(.)" + }, + { + "bbox": [ + 46, + 607, + 287, + 689 + ], + "type": "text", + "content": " respectively represent binary cross-entropy-with-logits loss and Multi-Assignment Sinkhorn-Knopp (discussed in Sec. 3.2), " + }, + { + "bbox": [ + 46, + 607, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 607, + 287, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 607, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 607, + 287, + 689 + ], + "type": "text", + "content": " represents loss coefficients, and " + }, + { + "bbox": [ + 46, + 607, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathrm{sim}(\\mathbf{a},\\mathbf{b}) = \\exp (\\mathbf{a.b} / \\tau \\| \\mathbf{a}\\| \\| \\mathbf{b}\\|)" + }, + { + "bbox": [ + 46, + 607, + 287, + 689 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 607, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 607, + 287, + 689 + ], + "type": "text", + "content": " is the temperature hyperparameter of the similarity metric." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 689, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 712 + ], + "type": "text", + "content": "Overall semantic structure preserving consistency loss for all the modalities is defined as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 332, + 81, + 545, + 108 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 81, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 332, + 81, + 545, + 108 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s s p c} = \\sum_ {m \\in \\{t, v, a \\}} \\sum_ {n \\in \\{t, v, a \\}} \\mathcal {L} (\\mathbf {m}, \\hat {\\mathbf {n}}, \\mathbf {z} _ {m}, \\hat {\\mathbf {z}} _ {m}). \\tag {3}", + "image_path": "ffef848884f0ae9a31f9edf6c4ee0f35c99ea077cb2b0f2529041cc69438ecce.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 107, + 547, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 107, + 547, + 203 + ], + "spans": [ + { + "bbox": [ + 304, + 107, + 547, + 203 + ], + "type": "text", + "content": "Contrastive Loss. Following [11, 42], we also use contrastive loss to bring cross-modal embeddings of the same sample closer while pushing away embeddings from other sample. For this, we use 3 pairwise single-modality constrastive losses, " + }, + { + "bbox": [ + 304, + 107, + 547, + 203 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{nce\\_ tv}" + }, + { + "bbox": [ + 304, + 107, + 547, + 203 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 107, + 547, + 203 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{nce\\_ ta}" + }, + { + "bbox": [ + 304, + 107, + 547, + 203 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 107, + 547, + 203 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{nce\\_ va}" + }, + { + "bbox": [ + 304, + 107, + 547, + 203 + ], + "type": "text", + "content": " between " + }, + { + "bbox": [ + 304, + 107, + 547, + 203 + ], + "type": "inline_equation", + "content": "(t,v)" + }, + { + "bbox": [ + 304, + 107, + 547, + 203 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 107, + 547, + 203 + ], + "type": "inline_equation", + "content": "(t,a)" + }, + { + "bbox": [ + 304, + 107, + 547, + 203 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 107, + 547, + 203 + ], + "type": "inline_equation", + "content": "(v,a)" + }, + { + "bbox": [ + 304, + 107, + 547, + 203 + ], + "type": "text", + "content": " respectively. Specifically, we use Noise Contrastive Estimation [33] with temperature " + }, + { + "bbox": [ + 304, + 107, + 547, + 203 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 304, + 107, + 547, + 203 + ], + "type": "text", + "content": " as shown in Eq. 4." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 341, + 213, + 545, + 243 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 213, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 341, + 213, + 545, + 243 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {n c e - x y} = - \\log \\frac {\\exp \\left(\\mathbf {x} ^ {\\intercal} \\mathbf {y} / \\kappa\\right)}{\\sum_ {i = 1} ^ {N} \\exp \\left(\\mathbf {x} ^ {(i) \\intercal} \\mathbf {y} ^ {(i)} / \\kappa\\right)} \\tag {4}", + "image_path": "d7a6e6588c0459402cfe28e213b7a1e8a3f31b2cdc340d7b37ec2811f1ec3153.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 247, + 545, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 247, + 545, + 272 + ], + "spans": [ + { + "bbox": [ + 305, + 247, + 545, + 272 + ], + "type": "text", + "content": "The overall contrastive loss for all modalities is defined as " + }, + { + "bbox": [ + 305, + 247, + 545, + 272 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{nce} = \\lambda_{tv}\\mathcal{L}_{nce\\_tv} + \\lambda_{ta}\\mathcal{L}_{nce\\_ta} + \\lambda_{va}\\mathcal{L}_{nce\\_va}" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 283, + 374, + 295 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 283, + 374, + 295 + ], + "spans": [ + { + "bbox": [ + 306, + 283, + 374, + 295 + ], + "type": "text", + "content": "Overall Loss" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 303, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 303, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 303, + 545, + 411 + ], + "type": "text", + "content": "The overall training objective is a combination of SSPC loss (Eq. 3) and contrastive loss (4): " + }, + { + "bbox": [ + 304, + 303, + 545, + 411 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_f = \\lambda_{sspc}\\mathcal{L}_{sspc} + \\lambda_{nce}\\mathcal{L}_{nce}" + }, + { + "bbox": [ + 304, + 303, + 545, + 411 + ], + "type": "text", + "content": ", where, " + }, + { + "bbox": [ + 304, + 303, + 545, + 411 + ], + "type": "inline_equation", + "content": "\\lambda_{sspc}" + }, + { + "bbox": [ + 304, + 303, + 545, + 411 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 303, + 545, + 411 + ], + "type": "inline_equation", + "content": "\\lambda_{nce}" + }, + { + "bbox": [ + 304, + 303, + 545, + 411 + ], + "type": "text", + "content": " are loss coefficients. By combining both losses, the model learns a more generic joint embedding space which preserves the modality-specific semantic structure by enforcing the anchor assignment similarity before and after feature projection and also brings representations of different modalities together by utilizing contrastive loss." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 423, + 388, + 436 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 423, + 388, + 436 + ], + "spans": [ + { + "bbox": [ + 306, + 423, + 388, + 436 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 443, + 422, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 443, + 422, + 455 + ], + "spans": [ + { + "bbox": [ + 306, + 443, + 422, + 455 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "text", + "content": "Backbones. For comparability, we follow the same setup of previous works [31, 39, 11, 42]. As visual backbone, we use a combination of 2D features from ResNet-152 [20] pretrained onImagenet [14], and 3D features from ResNeXt101 [19] pretrained on Kinetics [10]. The text backbone is GoogleNews pretrained Word2vec model [32]. These backbones are fixed and not finetuned during training. Following [11, 42], we use a trainable CNN with residual layers as an audio backbone. We provide additional details in the Supplementary Sec. 5." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 582, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 653 + ], + "type": "text", + "content": "Data Sampling. We use a batch of 216 videos and randomly sample ten 8-second clips per video. If the sampled clip contains narration (95% clips), we use ASR time stamps to select clip borders. To disentangle high text-audio correlation in HT100M, we shift the audio clip randomly by 4 seconds with respect to the video and text boundaries." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Projections. Following [42, 11, 39], we use a gated linear projection [30] to project features into common token space, as well as to project resulting tokens into shared embedding space. We set the dimension of the common token space to 4096 and of the shared embedding space to 6144." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21997" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 548, + 250 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 548, + 250 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 548, + 250 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 548, + 250 + ], + "type": "table", + "html": "
MethodRetrievalTrainVisualTrainable BBMSR-VTTYouCook2
DatasetBBtvaR@5↑R@10↑MedR↓MeanR↓R@5↑R@10↑MedR↓MeanR↓
ActBERT [54]t → vHT100MRes3D+Faster R-CNN23.433.136-26.738.019-
SupportSet [34]t → vHT100MR152 + R(2+1)D-34✓23.031.131-----
HT100M [31]t → vHT100MR152 + RX10121.229.638-17.324.846-
AVLNet [39]t → vHT100MR152 + RX101✓24.734.2--21.129.6--
EAO [42]t → vHT100MR152 + RX101✓24.635.32590.427.938.919119.6
Ourst → vHT100MR152 + RX101✓26.435.12392.229.440.718111.8
AVLNet [39]v → tHT100MR152 + RX101✓27.235.72586.522.832.930142.2
EAO [42]v → tHT100MR152 + RX101✓27.636.6258531.870.51591.9
Oursv → tHT100MR152 + RX101✓27.237.12384.532721585.2
AVLNet [39]t → v + aHT100MR152 + RX101✓19.227.447-36.144.316-
MCN [11]t → v + aHT100MR152 + RX101✓25.233.8--35.545.2--
EAO [42]t → v + aHT100MR152 + RX101✓23.333.22994.838.549.21182.7
Ourst → v + aHT100MR152 + RX101✓25.134.52691.839.450.11083.3
AVLNet [39]v + a → tHT100MR152 + RX101✓1926.344128.148.858.4667.1
EAO [42]v + a → tHT100MR152 + RX101✓21.831.428.598.94960.9643.8
Oursv + a → tHT100MR152 + RX101✓24322795.948.861.3643.5
", + "image_path": "ed572caec3374f9dd60945e2e137049d9279ef7f7644f808f777eba12bd1a223.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 254, + 547, + 277 + ], + "lines": [ + { + "bbox": [ + 46, + 254, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 254, + 547, + 277 + ], + "type": "text", + "content": "Table 1: Zero-shot Retrieval results on MSR-VTT/YouCook2. For fair comparison, we compare with models trained on text, video and audio. Retrieval column represents the evaluation task. BB=Backbone. Bold, underline represent highest and second-highest scores." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 289, + 289, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 289, + 421 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 289, + 421 + ], + "type": "text", + "content": "We use a single transformer block with hidden size of 4096 with 64 heads and an MLP size of 4096. We set the number of anchors " + }, + { + "bbox": [ + 46, + 289, + 289, + 421 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 289, + 289, + 421 + ], + "type": "text", + "content": " as 64 and " + }, + { + "bbox": [ + 46, + 289, + 289, + 421 + ], + "type": "inline_equation", + "content": "K'" + }, + { + "bbox": [ + 46, + 289, + 289, + 421 + ], + "type": "text", + "content": " as 32 with damping factor " + }, + { + "bbox": [ + 46, + 289, + 289, + 421 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 289, + 289, + 421 + ], + "type": "text", + "content": " as 0.25. We train all models for 15 epochs using an Adam optimizer [24] with a learning rate of 5e-5, exponential decay of 0.9 and the temperature of cosine similarity " + }, + { + "bbox": [ + 46, + 289, + 289, + 421 + ], + "type": "inline_equation", + "content": "(\\tau)" + }, + { + "bbox": [ + 46, + 289, + 289, + 421 + ], + "type": "text", + "content": " as 0.1. We maintain a memory-bank of size 5500 while performing Multi-SK. Following [1, 42], we set higher weight for loss terms that involve text-video in Eq. 3, i.e., for all text-video terms the weight is set to 1.0 and the rest of the weights are set to 0.1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 430, + 183, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 183, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 183, + 443 + ], + "type": "text", + "content": "4.2. Datasets, Tasks, Metrics" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 449, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 510 + ], + "type": "text", + "content": "Pretraining Dataset. We train our model on the HT100M dataset [31], which contains over 1 million instructional videos with automatically generated text narrations. The text narrations can be assumed to be noisy and to not always describe the video scene." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": "Zero-shot Retrieval. We use MSR-VTT [47] and YouCook2 [52] datasets to evaluate the zero-shot retrieval capability of our model. We report performance on 4 retrieval tasks: (i) Text-to-Video retrieval, (ii) Video-to-Text retrieval, (iii) Text-to-Video-Audio retrieval, (iv) Video-Audio-to-Text retrieval. The YouCook2 dataset contains cooking videos from YouTube with human-annotated clips (" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\sim" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " 2 - 200 secs). For evaluation we use at maximum first 48 seconds of clip, since most clips are shorter than that. The MSR-VTT dataset contains human-annotated clips (" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\sim" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " 10 - 30 secs) on various topics and provides captions with natural language sentences. Following [31, 39, 11, 42], to evaluate our model on MSR-VTT, we use the 1k set of test clips [49], and for YouCook2, we use 3,350 validation clips [31]. To perform " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "(t\\rightarrow v + a)" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " retrieval, we compute similarities by dot product between a text query " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " and all videos in the dataset using a averaged " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "v + a" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " representa" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 289, + 545, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 337 + ], + "type": "text", + "content": "tion for each video. We report standard recall metrics " + }, + { + "bbox": [ + 304, + 289, + 545, + 337 + ], + "type": "inline_equation", + "content": "\\mathbf{R}@\\mathbf{5}" + }, + { + "bbox": [ + 304, + 289, + 545, + 337 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 289, + 545, + 337 + ], + "type": "inline_equation", + "content": "\\mathbf{R}@\\mathbf{10}" + }, + { + "bbox": [ + 304, + 289, + 545, + 337 + ], + "type": "text", + "content": ", median rank (MedR) and the mean rank(MeanR). Further, we also evaluate our model using CLIP backbone and report results in Sec. 1 of the Supplementary." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 338, + 545, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 545, + 420 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 545, + 420 + ], + "type": "text", + "content": "Zero-Shot Full-Video Retrieval. Following [11], we evaluate Zero-Shot Full Video Retrieval from a set of captions on YouCook2 dataset. We report recall metrics following Caption averaging method [11] that finds maximal prediction over all the clips of video for each caption and averaging over set of captions in query leading to a single prediction for full video." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 422, + 545, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 545, + 482 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 545, + 482 + ], + "type": "text", + "content": "Text-to-video Retrieval after Fine-tuning. We additionally evaluate the retrieval performance of the models fine-tuned on downstream tasks. We use 6783 clips from MSR-VTT (which contain audio) and 9586 clips from YouCook2 train datasets to fine-tune the model as proposed by [39]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 482, + 545, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 545, + 507 + ], + "type": "text", + "content": "We also evaluate our model for Zero-shot Classification and report additional results in Sec. 1 of the Supplementary." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 515, + 486, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 515, + 486, + 528 + ], + "spans": [ + { + "bbox": [ + 305, + 515, + 486, + 528 + ], + "type": "text", + "content": "4.3. Comparison with State-of-the-art" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "Zero-shot Retrieval Tasks. In Tab. 1, we report the performance of the learned multi-modal representations on four zero-shot retrieval tasks, (i) Text-to-Video, (ii) Video-to-Text, (iii) Text-to-Video-Audio, (iv) Video-Audio-to-Text., on MSR-VTT and YouCook2 datasets. For a fair comparison, we only compare with models trained on all three modalities i.e. text, video and audio. In summary, our proposed method outperforms the current state-of-the-art methods by a noticeable margin on both the datasets. The results on the MSR-VTT dataset are particularly interesting since it demonstrates the generalizability of our model. In particular, HT100M consists of instructional videos and the textual descriptions are generated from audio using ASR. The text narration has noisy alignment with video and typically describes the steps in the video. YouCook2 shares" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21998" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 547, + 131 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 547, + 131 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 547, + 131 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 547, + 131 + ], + "type": "table", + "html": "
MethodRetrievalTrainVisualTrainable BBMSR-VTTYouCook2
DatasetBBtvaR@5↑R@10↑MedR↓MeanR↓R@5↑R@10↑MedR↓MeanR↓
AVLNet [39]t → vHT100MR152 + RX101✓42.256.2735.123.732.728122.6
EAO [42]t → vHT100MR152 + RX101✓47.759.3635.633.945.81370.7
Ourst → vHT100MR152 + RX101✓48.760.6533.135.648.11264.9
", + "image_path": "9771281867bec15a8ba481b4691adaa823ae740ed92b82472ea88a3ea6b3067b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 170, + 287, + 259 + ], + "blocks": [ + { + "bbox": [ + 46, + 136, + 546, + 160 + ], + "lines": [ + { + "bbox": [ + 46, + 136, + 546, + 160 + ], + "spans": [ + { + "bbox": [ + 46, + 136, + 546, + 160 + ], + "type": "text", + "content": "Table 2: Text-to-video retrieval results on MSR-VTT/YouCook2 in the fine-tune setting. For fair comparison, we compare with models trained on all 3 modalities i.e. text, video and audio. Bold, underline represent best and second-best scores." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 170, + 287, + 259 + ], + "lines": [ + { + "bbox": [ + 48, + 170, + 287, + 259 + ], + "spans": [ + { + "bbox": [ + 48, + 170, + 287, + 259 + ], + "type": "table", + "html": "
MethodAggregationR@1↑R@5↑R@10↑
Random-0.231.152.32
HT100M [31]Caption Avg.43.168.679.1
MIL-NCE [29]Caption Avg.46.674.383.7
MCN [11]Caption Avg.53.475.081.4
EAO [42]Caption Avg.62.980.586.7
OursCaption Avg.65.183.287.6
", + "image_path": "e0dcb005520344e71c5cd8360820be3a47f7dd7e4e2773a2fa5d75082e01241d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 300, + 287, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 432 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 432 + ], + "type": "text", + "content": "domain similarity with HT100M as its videos are instructional format, and the text descriptions correspond to specific steps in the recipe. In contrast, MSR-VTT is not restricted to instructional videos and the text is typically a single sentence caption describing the whole video. As a result, there is a distributional shift between HT100M and MSR-VTT. Therefore, zero-shot retrieval on MSR-VTT has to overcome distributional shift, which is a crucial requirement for practical deployment. Our proposed method shows relatively higher improvement on this task validating the effectiveness of anchor-based learning." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 434, + 288, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 288, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 288, + 590 + ], + "type": "text", + "content": "In case of text-to-video-audio retrieval, our method improves the Median and Mean rank of the baseline [42] by " + }, + { + "bbox": [ + 46, + 434, + 288, + 590 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 46, + 434, + 288, + 590 + ], + "type": "text", + "content": " on MSR-VTT along with gains on recall metrics " + }, + { + "bbox": [ + 46, + 434, + 288, + 590 + ], + "type": "inline_equation", + "content": "R@5" + }, + { + "bbox": [ + 46, + 434, + 288, + 590 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 434, + 288, + 590 + ], + "type": "inline_equation", + "content": "R@10" + }, + { + "bbox": [ + 46, + 434, + 288, + 590 + ], + "type": "text", + "content": ". For video-audio-to-text retrieval, our methods perform very well on MSR-VTT with " + }, + { + "bbox": [ + 46, + 434, + 288, + 590 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 46, + 434, + 288, + 590 + ], + "type": "text", + "content": " improvement on MeanR, " + }, + { + "bbox": [ + 46, + 434, + 288, + 590 + ], + "type": "inline_equation", + "content": "2.2\\%" + }, + { + "bbox": [ + 46, + 434, + 288, + 590 + ], + "type": "text", + "content": " improvement on " + }, + { + "bbox": [ + 46, + 434, + 288, + 590 + ], + "type": "inline_equation", + "content": "R@5" + }, + { + "bbox": [ + 46, + 434, + 288, + 590 + ], + "type": "text", + "content": ". We also observe similar improvements on the YouCook2 dataset. Similarly, our proposed method outperforms the current state-of-the-art on most of the metrics for text-video-retrieval video-text-retrieval. Additionally, to compare our approach with text-video only model, we train our model on video and text to compare the performance with state-of-the-art in Sec 1 of the Supplementary." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 591, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 591, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 591, + 287, + 640 + ], + "type": "text", + "content": "Zero-shot Full Video Retrieval. In Tab. 3, we report results for text-to-full-video retrieval task. Our approach outperforms prior works by " + }, + { + "bbox": [ + 46, + 591, + 287, + 640 + ], + "type": "inline_equation", + "content": "2.2\\%" + }, + { + "bbox": [ + 46, + 591, + 287, + 640 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 591, + 287, + 640 + ], + "type": "inline_equation", + "content": "2.7\\%" + }, + { + "bbox": [ + 46, + 591, + 287, + 640 + ], + "type": "text", + "content": " on R@1 and R@5 respectively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "type": "text", + "content": "Retrieval after Fine-tuning. We also evaluate the retrieval performance of our model after fine-tuning on the downstream datasets as shown in Tab. 2. For a fair comparison, we only report the baselines that use the same training split. We outperform state-of-the-art consistently on all the metrics and on both MSR-VTT & YouCook2 datasets" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 172, + 385, + 183 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 172, + 385, + 183 + ], + "spans": [ + { + "bbox": [ + 306, + 172, + 385, + 183 + ], + "type": "text", + "content": "as shown in Tab. 2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 190, + 406, + 201 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 190, + 406, + 201 + ], + "spans": [ + { + "bbox": [ + 306, + 190, + 406, + 201 + ], + "type": "text", + "content": "4.4. Ablation Studies" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 209, + 547, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 209, + 547, + 245 + ], + "spans": [ + { + "bbox": [ + 305, + 209, + 547, + 245 + ], + "type": "text", + "content": "First we analyze the impact of the proposed components and report results in Tab. 4, followed by the effect of number of anchors " + }, + { + "bbox": [ + 305, + 209, + 547, + 245 + ], + "type": "inline_equation", + "content": "(K)" + }, + { + "bbox": [ + 305, + 209, + 547, + 245 + ], + "type": "text", + "content": " & " + }, + { + "bbox": [ + 305, + 209, + 547, + 245 + ], + "type": "inline_equation", + "content": "(K^{\\prime})" + }, + { + "bbox": [ + 305, + 209, + 547, + 245 + ], + "type": "text", + "content": " in Tab. 5." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 315, + 253, + 536, + 347 + ], + "blocks": [ + { + "bbox": [ + 46, + 265, + 287, + 289 + ], + "lines": [ + { + "bbox": [ + 46, + 265, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 265, + 287, + 289 + ], + "type": "text", + "content": "Table 3: Zero-Shot Text-to-Full Video retrieval on YouCook2. Averaging across captions is used to obtain video-level predictions." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 253, + 536, + 347 + ], + "lines": [ + { + "bbox": [ + 315, + 253, + 536, + 347 + ], + "spans": [ + { + "bbox": [ + 315, + 253, + 536, + 347 + ], + "type": "table", + "html": "
MethodMSR-VTTYouCook2
R@5↑R@10↑R@5↑R@10↑
Recon. + CL23.132.437.848.7
w/o CM SSPCL22.731.836.948.3
w/o SSPCL23.833.337.948.8
Modified SK23.431.337.948.3
Ours25.134.539.450.1
", + "image_path": "bf6e4abd95019bf4aba296720631dbbb6302db5fe0ddfe7c23dcb464d71a72a9.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 352, + 546, + 399 + ], + "lines": [ + { + "bbox": [ + 305, + 352, + 546, + 399 + ], + "spans": [ + { + "bbox": [ + 305, + 352, + 546, + 399 + ], + "type": "text", + "content": "Table 4: Ablation studies showing the impact of various components for zero-shot retrieval task. Recon.=Reconstruction Loss, CM SSPCL=Cross-Modal SSPC Loss, SK=Sinkhorn-Knopp, CL=Contrastive Loss." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 426, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 616 + ], + "type": "text", + "content": "Effect of Proposed Components. We report the results for this ablation in Tab. 4. In first row, we report results using reconstruction loss and contrastive loss, we notice that using reconstruction loss reduces the performance by " + }, + { + "bbox": [ + 304, + 426, + 545, + 616 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 304, + 426, + 545, + 616 + ], + "type": "text", + "content": " on all metrics indicating the effectiveness of the proposed SSPC loss. In the second row, we report results without our proposed cross-modal SSPC loss ('w/o CM SSPC'). We employ this loss to bring the cross-modal representations closer in the joint embedding space to obtain better performance in zero-shot cross-modal tasks. We notice that removing the cross-modal SSPC loss drastically decreases the zero-shot retrieval performance on both MSR-VTT and YouCook2 datasets, " + }, + { + "bbox": [ + 304, + 426, + 545, + 616 + ], + "type": "inline_equation", + "content": "2.4\\%" + }, + { + "bbox": [ + 304, + 426, + 545, + 616 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 426, + 545, + 616 + ], + "type": "inline_equation", + "content": "2.5\\%" + }, + { + "bbox": [ + 304, + 426, + 545, + 616 + ], + "type": "text", + "content": " drop in R@5 performance respectively. This empirically validates the effectiveness of the cross-modal SSPC loss in obtaining better cross-modal representations." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "content": "In the third row, we analyze the effect of the proposed SSPC loss ('w/o SSPCL'). We apply the SSPC loss to retain modality-specific semantic structure from the pretrained models in the joint embedding space. To investigate its impact, we remove the anchor consistency between the modality-specific and joint embedding spaces. Instead, we enforce the anchor assignments before Multi-SK to be consistent with the Multi-SK optimized anchor as" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21999" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 121, + 112 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 121, + 112 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 121, + 112 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 121, + 112 + ], + "type": "image", + "image_path": "b2cc957fe4de615732ae3dfbc2a05de5dbf12c811084fd877125e2262a3ada0f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 77, + 117, + 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demonstrate the visual similarity between video samples from two related categories i.e. (a) Holidays and Tradition and (b) Food and Entertaining; and two different categories i.e. (d) Personal Care ans Style and (e) Finance and Business within the HowTo100M dataset. The visual similarity is also reflected in video anchor assignments (c) as most assigned anchors are similar with minor differences in assignments, thereby showcasing the flexibility and effectiveness of our approach. (d), (e) samples look very different and therefore the anchor assignments are also very different as shown in (f). Green cell " + }, + { + "bbox": [ + 46, + 298, + 545, + 370 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 298, + 545, + 370 + ], + "type": "text", + "content": " Anchor assigned, Yellow " + }, + { + "bbox": [ + 46, + 298, + 545, + 370 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 298, + 545, + 370 + ], + "type": "text", + "content": " Anchor not assigned. Difference in anchor assignments indicated in red." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 395, + 179, + 469, + 221 + ], + "blocks": [ + { + "bbox": [ + 395, + 179, + 469, + 221 + ], + "lines": [ + { + "bbox": [ + 395, + 179, + 469, + 221 + ], + "spans": [ + { + "bbox": [ + 395, + 179, + 469, + 221 + ], + "type": "image", + "image_path": "51d8ddbe79ea5b9f265920a633c0e65b28d235cdf409ee39c8ee4e284455718d.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 354, + 226, + 511, + 237 + ], + "lines": [ + { + "bbox": [ + 354, + 226, + 511, + 237 + ], + "spans": [ + { + "bbox": [ + 354, + 226, + 511, + 237 + ], + "type": "text", + "content": "(e) _Y51yX3KJoE (Finance and Business)" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 473, + 179, + 545, + 221 + ], + "blocks": [ + { + "bbox": [ + 473, + 179, + 545, + 221 + ], + "lines": [ + { + "bbox": [ + 473, + 179, + 545, + 221 + ], + "spans": [ + { + "bbox": [ + 473, + 179, + 545, + 221 + ], + "type": "image", + "image_path": "90effec5408bbe895c6bb2857e4cf0a5e5319eef736e15b533f5ccddcbf34d57.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 52, + 246, + 541, + 269 + ], + "blocks": [ + { + "bbox": [ + 52, + 246, + 541, + 269 + ], + "lines": [ + { + "bbox": [ + 52, + 246, + 541, + 269 + ], + "spans": [ + { + "bbox": [ + 52, + 246, + 541, + 269 + ], + "type": "image", + "image_path": "6199cb8143c1a217676b9c629e752f1e33284306eea87dafd469e07455f56cd4.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 239, + 277, + 353, + 288 + ], + "lines": [ + { + "bbox": [ + 239, + 277, + 353, + 288 + ], + "spans": [ + { + "bbox": [ + 239, + 277, + 353, + 288 + ], + "type": "text", + "content": "(f) Video anchors Assignments" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "table", + "bbox": [ + 55, + 388, + 280, + 488 + ], + "blocks": [ + { + "bbox": [ + 55, + 388, + 280, + 488 + ], + "lines": [ + { + "bbox": [ + 55, + 388, + 280, + 488 + ], + "spans": [ + { + "bbox": [ + 55, + 388, + 280, + 488 + ], + "type": "table", + "html": "
KK'MSR-VTTYouCook2
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", + "image_path": "3809ccd243e6e9c7791b0aa9a5648baa913ca6551d8f7aec7e1c65d43add8e20.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "table_body" + } + ], + "index": 21 + }, + { + "bbox": [ + 47, + 497, + 283, + 521 + ], + "lines": [ + { + "bbox": [ + 47, + 497, + 283, + 521 + ], + "spans": [ + { + "bbox": [ + 47, + 497, + 283, + 521 + ], + "type": "text", + "content": "Table 5: Effect of different # of anchors on zero-shot retrieval. " + }, + { + "bbox": [ + 47, + 497, + 283, + 521 + ], + "type": "inline_equation", + "content": "K \\rightarrow" + }, + { + "bbox": [ + 47, + 497, + 283, + 521 + ], + "type": "text", + "content": " # of anchors and " + }, + { + "bbox": [ + 47, + 497, + 283, + 521 + ], + "type": "inline_equation", + "content": "K' \\rightarrow" + }, + { + "bbox": [ + 47, + 497, + 283, + 521 + ], + "type": "text", + "content": " # of selected anchors, respectively." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 544, + 286, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 286, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 286, + 652 + ], + "type": "text", + "content": "signments from the same embedding space. We also apply the cross-modal SSPC loss to only isolate the impact of the proposed SSPC loss across feature projections. We observe that removing the anchor consistency between the modality-specific and joint embedding spaces reduces the zero-shot retrieval performance by a significant margin (" + }, + { + "bbox": [ + 46, + 544, + 286, + 652 + ], + "type": "inline_equation", + "content": "\\sim 1.5\\%" + }, + { + "bbox": [ + 46, + 544, + 286, + 652 + ], + "type": "text", + "content": " drop in R@5 performance), indicating the importance of SSPC loss in maintaining modality-specific semantic structure in the joint embedding space for better performance." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 653, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 714 + ], + "type": "text", + "content": "Finally, in the fourth row of Tab. 4, we analyse the effectiveness of the proposed Multi-Assignment Sinkhorn-Knoppalgorithm. To this end, we modify the vanilla Sinkhorn-Knopp [13] to obtain multiple anchor assignments per sample (refer to Sec. 5 of the Supplementary" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 391, + 545, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 391, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 304, + 391, + 545, + 450 + ], + "type": "text", + "content": "for details). We notice that the modified Sinkhorn-Knopp does not perform well with a drop in performance (" + }, + { + "bbox": [ + 304, + 391, + 545, + 450 + ], + "type": "inline_equation", + "content": "\\sim 1.6\\%" + }, + { + "bbox": [ + 304, + 391, + 545, + 450 + ], + "type": "text", + "content": " drop in R@5) on both MSR-VTT and YouCook2 datasets on all the metrics indicating the significance of our proposed MULTI-SK algorithm." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 456, + 546, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 546, + 660 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 546, + 660 + ], + "type": "text", + "content": "Effect of Number of Anchors. To analyze the effect of the number of anchors, we conduct experiments with different number of anchors, " + }, + { + "bbox": [ + 304, + 456, + 546, + 660 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 456, + 546, + 660 + ], + "type": "text", + "content": ", and different number of selected anchors, " + }, + { + "bbox": [ + 304, + 456, + 546, + 660 + ], + "type": "inline_equation", + "content": "K'" + }, + { + "bbox": [ + 304, + 456, + 546, + 660 + ], + "type": "text", + "content": ". We report the results in Tab. 5. We conduct experiments on both MSR-VTT and YouCook2 datasets. From the top half of Tab. 5, we observe that the performance of our proposed method improves with the increasing number of anchors. This is to be expected since a higher number of anchors have a higher representation learning capacity. We also observe that the method performs reasonably well even with a very small number of anchors showing the general effectiveness of our proposed solution. We notice that the performance of the proposed method improves as we select more anchors as shown in bottom half of Tab. 5. However, selecting a very large number of anchors (48 out of 64 for this experiment) adds more constraints leading to poor performance." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 670, + 423, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 423, + 683 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 423, + 683 + ], + "type": "text", + "content": "4.5. Qualitative Analysis" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Here, first we present a fine-grained visual analysis of the learned anchors, followed by qualitative retrieval results." + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22000" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 83, + 145, + 114 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 83, + 145, + 114 + ], + "spans": [ + { + 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481, + 196, + 542, + 232 + ], + "blocks": [ + { + "bbox": [ + 481, + 196, + 542, + 232 + ], + "lines": [ + { + "bbox": [ + 481, + 196, + 542, + 232 + ], + "spans": [ + { + "bbox": [ + 481, + 196, + 542, + 232 + ], + "type": "image", + "image_path": "5adc6043e40230bd6ac85dbe81b708b0840445aa16714abd37e90bff2a8abdf3.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 314, + 289, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 314, + 289, + 507 + ], + "spans": [ + { + "bbox": [ + 46, + 314, + 289, + 507 + ], + "type": "text", + "content": "We show fine-grained analysis of the learned anchors in Fig. 2. For the purpose of this analysis, we visualize the anchor assignments as binary assignments. However, during training we use soft anchor assignments. In Fig. 2(c), we compare the anchor assignments for samples from similar categories. It can be seen that the videos are visually similar even though they belong to different categories and the anchor assignments for these two examples are able to capture the sample similarity. In Fig. 2(f), we compare the anchor assignments for videos from different categories and it can be seen that the anchor assignments are very different as expected. This further validates our claim that our proposed method can assign semantically meaningful anchors without any explicit supervision. Further, we show qualitative retrieval comparison with EAO [42] in Fig. 3. We present more qualitative analysis in Supplementary Sec. 4." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 47, + 523, + 119, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 523, + 119, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 523, + 119, + 536 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "type": "text", + "content": "We proposed a novel approach that preserves the modality-specific semantic relationship between samples in the joint multi-modal embedding space. To this end, we propose a flexible sample relationship modeling approach by assigning multiple anchors to each sample, which captures both shared and unique aspects of samples. To obtain these assignments, we develop a novel Multi-Assignment Sinkhorn-Knopp (Multi-SK) algorithm, and also utilize the proposed anchor consistency loss to learn these anchors. Our qualitative results demonstrate that our learnt anchors correspond to meaningful semantic concepts. Our extensive experimentation demonstrates that the proposed approach improves generalizability by outperforming state-of-the-art methods on both in- and out-of-domain datasets. We also" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 305, + 314, + 546, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 314, + 546, + 350 + ], + "spans": [ + { + "bbox": [ + 305, + 314, + 546, + 350 + ], + "type": "text", + "content": "show that our method achieves state-of-the-art performance on multiple zero-shot tasks, and also outperforms when fine-tuned on downstream datasets." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 362, + 408, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 362, + 408, + 376 + ], + "spans": [ + { + "bbox": [ + 306, + 362, + 408, + 376 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 305, + 382, + 546, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 382, + 546, + 515 + ], + "spans": [ + { + "bbox": [ + 305, + 382, + 546, + 515 + ], + "type": "text", + "content": "Research was sponsored by the Army Research Office and was accomplished under Grant Number W911NF-19-1-0356. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. Nina Shvetsova is supported by German Federal Ministry of Education and Research (BMBF) project STCL - 01IS22067." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 306, + 526, + 365, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 526, + 365, + 538 + ], + "spans": [ + { + "bbox": [ + 306, + 526, + 365, + 538 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 310, + 545, + 547, + 712 + ], + "type": "list", + "angle": 0, + "index": 36, + "blocks": [ + { + "bbox": [ + 310, + 545, + 545, + 601 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 545, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 310, + 545, + 545, + 601 + ], + "type": "text", + "content": "[1] Jean-Baptiste Alayrac, Adria Recasens, Rosalia Schneider, Relja Arandjelovic, Jason Ramapuram, Jeffrey De Fauw, Lucas Smaira, Sander Dieleman, and Andrew Zisserman. Self-supervised multimodal versatile networks. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2020. 6" + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "22003" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Preserving Tumor Volumes for Unsupervised Medical Image Registration/dbd41759-9a48-41b9-9206-f4ea354bc2a2_content_list.json b/2023/Preserving Tumor Volumes for Unsupervised Medical Image Registration/dbd41759-9a48-41b9-9206-f4ea354bc2a2_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..264513d893c588454128e2a911ead20e864a719d --- /dev/null +++ b/2023/Preserving Tumor Volumes for Unsupervised Medical Image Registration/dbd41759-9a48-41b9-9206-f4ea354bc2a2_content_list.json @@ -0,0 +1,1714 @@ +[ + { + "type": "text", + "text": "Preserving Tumor Volumes for Unsupervised Medical Image Registration", + "text_level": 1, + "bbox": [ + 114, + 130, + 854, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Qihua Dong $^{1}$ , Hao Du $^{1}$ , Ying Song $^{2}$ , Yan Xu $^{3*}$ , Jing Liao $^{1*}$", + "bbox": [ + 248, + 179, + 718, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Department of Computer Science, City University of Hong Kong", + "bbox": [ + 223, + 198, + 745, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ National Cancer Center/National Clinical Research Center for Cancer/Cancer Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College $^{3}$ School of Biological Science and Medical Engineering, Beihang University", + "bbox": [ + 138, + 215, + 831, + 270 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "dongqh078@gmail.com, haodu8-c@my.cityu.edu.hk, jingliao@cityu.edu.hk;", + "bbox": [ + 179, + 272, + 787, + 287 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "songying1770@hotmail.com", + "bbox": [ + 377, + 290, + 591, + 303 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "xuyan04@gmail.com", + "bbox": [ + 406, + 308, + 560, + 321 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 356, + 312, + 372 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Medical image registration is a critical task that estimates the spatial correspondence between pairs of images. However, current traditional and deep-learning-based methods rely on similarity measures to generate a deforming field, which often results in disproportionate volume changes in dissimilar regions, especially in tumor regions. These changes can significantly alter the tumor size and underlying anatomy, which limits the practical use of image registration in clinical diagnosis. To address this issue, we have formulated image registration with tumors as a constraint problem that preserves tumor volumes while maximizing image similarity in other normal regions. Our proposed strategy involves a two-stage process. In the first stage, we use similarity-based registration to identify potential tumor regions by their volume change, generating a soft tumor mask accordingly. In the second stage, we propose a volume-preserving registration with a novel adaptive volume-preserving loss that penalizes the change in size adaptively based on the masks calculated from the previous stage. Our approach balances image similarity and volume preservation in different regions, i.e., normal and tumor regions, by using soft tumor masks to adjust the imposition of volume-preserving loss on each one. This ensures that the tumor volume is preserved during the registration process. We have evaluated our strategy on various datasets and network architectures, demonstrating that our method successfully preserves the tumor volume while achieving comparable registration results with state-of-the-art methods. Our codes is available at: https://dddraxxx.github.io/Volume-Preserving-Registration/.", + "bbox": [ + 75, + 393, + 473, + 845 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 356, + 630, + 372 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3c773565a73bf98b9747bd76d71e915cf6c3c99ab9b4b4ae399abdb539649b8e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 526, + 391, + 686, + 513 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/657ff349d7c2a03bbddd4c7a8472927f39480b62c2a453cd8914b61720acb5f5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 707, + 391, + 866, + 513 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5501f7c771a1a7977cd66eb7f46958891ea67ce1d7b7ca64e1a6c7819722c45a.jpg", + "image_caption": [ + "Fixed Image", + "Moving Image", + "Figure 1. Red boxes represent the location of tumors in the moving image before warped. In image registration with tumors, similarity-based registration typically leads to significant alterations in tumor size while our volume-preserving registration is capable of preserving tumor anatomy." + ], + "image_footnote": [], + "bbox": [ + 526, + 530, + 684, + 651 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cf51c67221ba2f991df800d0691c3d451ed0df7e8b666712eb207107aaa1d580.jpg", + "image_caption": [ + "Similarity-Based Registration", + "Volume-Preserving Registration" + ], + "image_footnote": [], + "bbox": [ + 707, + 529, + 866, + 651 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deformable image registration is a fundamental task that estimates non-linear spatial correspondences between two images. It is useful for medical image studies that involve 3D images of organs or tissues, such as MR brain scans and CT liver scans. Recently, a wide range of deep-learning-based methods are proposed in the field, with better performance and obvious speed-ups in inference time compared to the traditional registration methods [5, 38, 32, 14, 15].", + "bbox": [ + 496, + 750, + 892, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Currently, most of the learning-based methods [5, 38] train a registration model to achieve high similarity in either", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding authors", + "bbox": [ + 94, + 886, + 223, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21208", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "image intensity [38, 5] or anatomy label maps [14]. While this is useful in various medical applications, such as atlas-based segmentation and image fusion [8], problem emerges, however, when studying images with tumors [4, 12, 24]. Tracking tumor growth is a core task in cancer treatment, which can be used to evaluate the outcomes of radiotherapy and chemotherapy, and plan optimal postoperative treatment [12]. The process requires registration to align the anatomy of images from different periods of the patient, while preserving tumor properties e.g., the size. Traditional models using regular registration have struggled to accomplish this task [12]. We have observed that this remains an issue for current learning-based methods, and a viable solution has yet to be proposed.", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As shown in Figure 1, the volume of tumors significantly reduces when using popular unsupervised registration networks to align tumor images with atlas images. The issue is widespread since mainstream registration networks focus on optimizing the similarity between image pairs while ignoring tumor regions. Tumor regions often lack corresponding parts, and even for images of the same patient, the size and location of tumors may vary greatly. This can happen because tumors can change shape, size, location, or disappear over time. Therefore, in deformable settings, the size of tumors will change disproportionately to maximize the image similarity. This problem may be more severe when the registration network has better warping ability, leading to better performance in evaluations from previous works, as confirmed by our experiments in Section 4. The disproportionate change of tumor volume in deformable registration is lethal for clinical evaluation of tumor growth and greatly hinders the application of registration in clinics.", + "bbox": [ + 75, + 304, + 472, + 578 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we re-formulate the deformable registration problem as a constraint problem that preserves the properties of tumors in the original images, i.e., the shape and the size of the tumor, while maximizing image similarity in non-tumor regions. For instance, in tumor image registration with atlas, besides the alignment of anatomical structures, the tumor should have similar morphing behaviours as its surrounding organs, i.e., the size of it should change proportionally to the size of the organ. However, this poses two major challenges for our strategy. Firstly, due to the limited availability of annotated data, most existing registration methods resort to unsupervised learning. Therefore, a key question is how to identify tumor regions in the unsupervised setting. Second, after the tumor regions have been identified, the challenge still remains of preserving tumor volumes while simultaneously maximizing similarity in other regions. Finding a way to balance these two competing objectives is crucial for achieving effective tumor image registration.", + "bbox": [ + 75, + 580, + 472, + 867 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To tackle the challenges, we propose a novel two-stage strategy that operates in an unsupervised manner. In the first", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "stage, we leverage a similarity-based registration network to identify regions that undergo excessive volume change during registration. Such regions are indicative of the presence of tumors, as tumors tend to exhibit larger changes in volume due to a lack of correspondence between image pairs. The outcome of the first stage is a soft tumor mask that distinguishes normal and possible tumor regions. In the second stage, we introduce an adaptive volume-preserving loss to train a volume-preserving registration network. Based on the soft tumor mask obtained from the first stage, this loss is designed to adaptively penalize volume changes in different regions of the image. Possible tumor regions are assigned larger loss weights, and similarity loss weights are adjusted accordingly in the opposite direction. The application of the adaptive volume-preserving loss effectively balances similarity and volume preservation in different parts of the image.", + "bbox": [ + 496, + 90, + 893, + 348 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "It should be noted that the soft masks from stage one do not need to be highly accurate to achieve desirable results, as our stage two is robust, which is demonstrated by our ablation experiments in section 4. In addition to evaluating the robustness of our proposed strategy on various datasets and frameworks, including CNN and transformer, as well as different types of imaging data such as brain and abdominal, MRI and CT images, we have also introduced the Square Tumor Size Ratio (STSR) metric to measure the preservation of tumor volumes. The results demonstrate that our methods achieve comparable warping performance metrics such as Dice coefficient and average landmark distances while effectively preserving tumor properties as measured by the STSR.", + "bbox": [ + 496, + 349, + 893, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To conclude, our contribution includes: (1) We have reformulated image registration with tumors as a constraint problem that preserves tumor volumes while maximizes image similarity in other normal regions. (2) We have designed a two-stage process that the first stage performs regular registration to estimate tumor regions, and the second stage performs volume-preserving registration on tumor regions based on the adaptive volume-preserving loss. (3) We have proposed the STSR metric to measure the preservation of tumor volumes in registration, and have evaluated the effectiveness of our strategy on different network architectures and various datasets.", + "bbox": [ + 496, + 561, + 893, + 742 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 758, + 640, + 776 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Learning-Based Deformable Image Registration", + "text_level": 1, + "bbox": [ + 500, + 785, + 890, + 815 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Compared to conventional registration methods, deep networks have achieved remarkable registration accuracy and speed using various network structures, i.e., CNN and Transformer, in applications like atlas-image registration [29, 7, 16, 6, 32, 38, 5, 14, 15, 8]. They generally", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21209", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "adopts unsupervised learning, utilizing image similarity on either image intensities [29, 7, 6, 38] or synthesized label maps [14, 15] as well as smoothness regularization to supervise the registration network [7, 6, 14, 15, 38]. Advancements are often made through the introduction of novel regularization such as cycle consistency [16] and geometry preservation [1], or through innovative network structures like multi-scale architectures [28, 23]. However, existing methods do not adequately consider cases where tumors exist. Tumors often have no corresponding part between image pairs, and therefore, optimizing for similarity can excessively change their volumes, which limits the application of registration networks in critical clinical applications like cancer treatment. To the best of our knowledge, we are the first to study this problem with learning-based methods and propose a metric to measure volume preservation specifically for tumors.", + "bbox": [ + 75, + 90, + 472, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Deformable Image Registration with Tumors", + "text_level": 1, + "bbox": [ + 76, + 358, + 459, + 376 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Conventional registration models often resolve registering images with tumor by (1) excluding the similarity measure on tumors [11, 18], which requires either massive manual segmentation [11] or initial seed to explicitly model tumor-growth [12, 18]. (2) jointly segmenting and registering images [9], which is time-consuming since it need to iteratively detect dissimilarity in image intensities and perform resection and retraction. (3) reconstructing quasi-normal images from pathological ones [13, 19], which is also slow since the reconstruction need to be iteratively improved.", + "bbox": [ + 75, + 382, + 472, + 547 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, learning-based methods for registration with tumors [24, 21, 33] are proposed for the release of BraTS-Reg dataset [4]. They aim to improve the spatial correspondence for non-tumor regions, thus either directly annotates landmarks to supervise registration [21] or introducing invertibility of the registration to mask non-inverted regions and ensure high correspondence in others [24, 33]. However, these methods assume the absence of tumors in one image of the registered pair, which may not be applicable in practical applications where we need to compare two tumor images from one patient to track the tumor growth. In this scenario, invertibility in tumors is still possible and thus, it is essential to consider the preservation of tumor properties during registration.", + "bbox": [ + 75, + 549, + 472, + 760 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Unsupervised Tumor Segmentation", + "text_level": 1, + "bbox": [ + 76, + 771, + 385, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To ensure the preservation of tumor volumes during registration, it is crucial to first identify the locations of tumors. Current deep learning methods have made remarkable progress in unsupervised tumor segmentation, as demonstrated by recent studies [34, 35, 20]. These methods typically use GAN models or simulate tumors on healthy images to generate synthetic data, which is then used to", + "bbox": [ + 75, + 795, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "train the segmentation network. Although the well-trained network can achieve high segmentation accuracy, it often requires complex training strategies and additional models or testing steps to achieve the desired performance, as noted in recent research [35, 20]. However, in our approach, we do not rely on sophisticated segmentation methods to accurately segment tumors. Instead, our experiments, as presented in Section 4, demonstrate that our tumor mask estimation is sufficient for our strategy to learn a volume-preserving registration for tumors.", + "bbox": [ + 496, + 90, + 893, + 243 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.4. Volume-Preserving Deformable Image Registration", + "text_level": 1, + "bbox": [ + 498, + 250, + 893, + 280 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Volume-preserving registration has been studied extensively to improve the accuracy of anatomical registration. In pulmonary CT image registration, for example, tissue intensity changes between inspiration and expiration phases can be utilized as prior knowledge, and adding a volume-preserving constraint has been shown to be effective [31, 37]. In other cases, such as when soft tissues are incompressible or when images come from different modalities, a volume-preserving constraint can also serve as a helpful regularization [25, 30]. Our work, instead, focuses on using volume-preservation to maintain the properties of tumors during image registration. The proposed strategy imposes this constraint adaptively on different parts of the images in order to preserve tumor volumes and ensure anatomical accuracy, while previous works have either preserved volumes for the entire images [25, 30] or can use simple methods to determine the regions to be preserved [31, 37].", + "bbox": [ + 496, + 287, + 893, + 546 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 498, + 556, + 635, + 574 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 580, + 640, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Problem Setting. Given a moving image $I_{m}$ and fixed image $I_{f}$ defined over $d$ -dimensional (d=3 in this paper) space $\\Omega$ , deformable image registration aims to find a dense deformation filed $\\phi : \\Omega \\to \\Omega$ . This field warps $I_{m}$ , meaning it projects every pixel position $x$ in warped image $I_{w}$ to $I_{m}$ to achieve alignment with $I_{f}$ . In this paper, the task is to construct a registration network $F_{\\theta}$ that takes input $I_{m}, I_{f}$ to predict the deformation field $\\phi$ .", + "bbox": [ + 496, + 604, + 893, + 726 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\phi = F _ {\\theta} \\left(I _ {m}, I _ {f}\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 647, + 733, + 890, + 750 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nI _ {w} (x) = I _ {m} (\\phi (x) + x) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 616, + 752, + 890, + 768 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nI _ {w} \\sim I _ {f} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 638, + 771, + 890, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Evaluation Criteria. In general, a successful deformable image registration involves accurately aligning the anatomical structures while also ensuring a smooth deformation field. This is often achieved through the use of similarity-based objectives and regularization methods that promote smoothness. However, in the context of image registration with tumors, simply aligning the anatomy is not", + "bbox": [ + 496, + 795, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21210", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5cb5a1782ab687053e0200bb173bbb0a88140e957c50a252f9b6032916461fd0.jpg", + "image_caption": [ + "Figure 2. Main Framework. Our strategy consists of two stages. In the first stage, a soft mask indicating tumor regions is estimated by analyzing the Jacobian matrix of the deformation field obtained by a registration network pre-trained on similarity loss. In the second stage, the soft mask is used to guide the calculation of both volume-preserving and similarity losses for training the volume-preserving registration network. This deformation field estimated by the stage two ensures that both the image similarity and the preservation of tumor sizes." + ], + "image_footnote": [], + "bbox": [ + 122, + 95, + 831, + 397 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "sufficient. Preserving the volume of the tumors is crucial for accurately tracking tumor growth, as previously discussed. To be specific, given the moving image $I_{m}$ with the tumor $T_{m}$ and its surrounding organ $O_{m}$ and the warped moving image $I_{w}$ with $T_{w}$ and $O_{w}$ , the morphing of tumor $T_{m}$ should be similar to that of $O_{m}$ . Thus in respect of the volume preservation, the change of tumor size $|T_{m}|$ should be proportionate to the change of the containing organ $|O_{m}|$ , i.e.:", + "bbox": [ + 75, + 489, + 470, + 625 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nT S R \\left(I _ {m}\\right) = \\frac {\\left| T _ {m} \\right|}{\\left| O _ {m} \\right|} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 633, + 468, + 666 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nT S R \\left(I _ {m}\\right) \\approx T S R \\left(I _ {w}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 667, + 468, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We therefore define the tumor size ratio (TSR) as $\\frac{|T|}{|O|}$ , which should be preserved after registration, and the re-formulated registration objective is now maximizing image similarity while preserving the volumes of tumors, i.e., the TSR.", + "bbox": [ + 76, + 698, + 468, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Overall Strategy", + "text_level": 1, + "bbox": [ + 76, + 771, + 240, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The proposed strategy consists of two stages, as shown in Figure 2. The first stage estimates potential tumor regions and generates a soft mask for them. This is done by analyzing volume changes, specifically the Jacobian matrix, in the deformation field obtained by an existing similarity-based registration network. As tumor regions tend to undergo excessive volume change during registration, they can", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "be identified through this analysis. In the second stage, we perform volume-preserving registration for tumors using an adaptive volume-preserving loss. This loss is designed to guide the volume-preserving process effectively and is associated with the tumor masks estimated in the first stage. Through the assignment of distinct weights to diverse regions, including both normal and tumor regions, it is possible to preserve tumor volumes while also ensuring a high degree of similarity in other regions.", + "bbox": [ + 496, + 489, + 890, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Importantly, our strategy can be applied to nearly any learning-based registration network without introducing any additional modules.", + "bbox": [ + 496, + 626, + 890, + 671 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Stage 1: Unsupervised Tumor Mask Estimation", + "text_level": 1, + "bbox": [ + 500, + 693, + 883, + 709 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following previous works [5, 6, 38], we first train a similarity-based registration network $F_{\\theta_1}$ with parameters $\\theta_1$ and fix its parameters. As shown in Figure 1, tumors in medical images can be detected by analyzing the change in volume through similarity-based registration. Our goal is to utilize this characteristic to facilitate the unsupervised estimation of the tumor mask for volume preservation during registration.", + "bbox": [ + 496, + 718, + 890, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To determine the volume change at voxel $x$ , we calculate the determinant of the Jacobian matrix of the deformation field $(J_{\\theta})$ with model parameter $\\theta$ . Our objective is to ensure that the volume change in each point of the tumor region is", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21211", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "similar to the volume change of the organ, which is an indicator of the organ's size change (as shown in Equation 6). To measure the distance between the two, we calculate the number of times one ratio exceeds another, denoted as $D_{\\theta}$ , using Equations 8 and 7 where $D_{\\theta}'(x)$ represents the relative volume change of voxel $x$ with respect to organ areas.", + "bbox": [ + 76, + 90, + 472, + 183 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\left| T _ {w} \\right|}{\\left| O _ {w} \\right|} / \\frac {\\left| T _ {m} \\right|}{\\left| O _ {m} \\right|} \\approx 1 \\Rightarrow \\frac {\\left| T _ {w} \\right|}{\\left| T _ {m} \\right|} / \\frac {\\left| O _ {w} \\right|}{\\left| O _ {m} \\right|} \\approx 1, \\text {f r o m E q .} 5, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 200, + 468, + 234 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nD _ {\\theta} ^ {\\prime} (x) = \\left| J _ {\\theta (x)} \\right| / \\frac {\\left| O _ {w} \\right|}{\\left| O _ {m} \\right|}, x \\in \\Omega , \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 234, + 468, + 268 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nD _ {\\theta} (x) = \\max \\left(D _ {\\theta} ^ {\\prime} (x), 1 / D _ {\\theta} ^ {\\prime} (x)\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 270, + 468, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In practice, we estimate the organ masks $O_{m}$ and $O_{w}$ by warping a reference image with the ground truth (GT) organ segmentation. We randomly select the reference image from the training dataset, and the choice of reference image does not significantly impact the results because registration for organs achieves high accuracy, as evidenced by the dice value in table 1. By warping the reference image, we obtain the organ segmentation for the moving image $O_{m}$ . We then calculate the organ segmentation for the warped image $O_{w}$ .", + "bbox": [ + 76, + 295, + 468, + 430 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To obtain a soft tumor mask $STM$ from the distance $D_{\\theta_1}$ defined in 8, we use a transformation function $Tr$ . This function can be formulated as the following equation:", + "bbox": [ + 76, + 431, + 468, + 476 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS T M (x) = T r \\left(D _ {\\theta_ {1}} (x)\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 484, + 468, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $D_{\\theta_1}(x)$ represents the distance value at pixel $x$ , and $Tr$ transforms values from the range of $[0,\\infty]$ to the range of $[0,1]$ . A value of 1 indicates the presence of a tumor, while a value of 0 indicates a normal region. In practical implementation, we use $Tr(x) = \\text{Sign}(5 \\cdot (x - 1.5))$ since the sigmoid function is widely adopted for converting values to the range of $[0,1]$ and to our experience, the size of tumor regions averagely changes around 1.5 times. However, the choice of transformation functions is not exclusive, as demonstrated in our experiments in Section 4. We also set the regions outside the organ mask to 0.", + "bbox": [ + 76, + 508, + 468, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We observed that some normal regions, particularly those close to the organ boundary, may also exhibit some volume changes after registration. As a result, these regions may be incorrectly included in the tumor mask, as shown in Figure 3 (a). To address this issue, we implemented a preregistration step to first align the edges and exclude volume changes caused by edge alignment. Specifically, in the preregistration step, we applied a bilateral filter to the moving image, which preserves the edges while smoothing the interior regions. We then used the registration network to register the filtered moving image with the fixed image in order to align their edges. After this, an unfiltered warped image was obtained by spatially transforming the unfiltered moving image with the deformation field. The second registration process was then performed on the unfiltered warped", + "bbox": [ + 76, + 674, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ae5b9c79bfc3f87b3cbe338bdb6f8cec305e153515e9eefa29531f91634fa745.jpg", + "image_caption": [ + "(a)Tumor Mask" + ], + "image_footnote": [], + "bbox": [ + 526, + 88, + 686, + 210 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ee6ad0dfa4d53dd393bd7326b429ac9e80ca121224703f18d3a870c56fd5e7a6.jpg", + "image_caption": [ + "(b)Tumor Mask after pre-registration", + "Figure 3. Visualization of the soft tumor mask. (a) is the estimated soft tumor mask without pre-registration and (b) is the one with pre-registration. The gray colors with intensity variations denote the soft mask, while the green and red colors represent the ground truth segmentation for the liver and tumors, respectively." + ], + "image_footnote": [], + "bbox": [ + 705, + 88, + 867, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "image, which focused on the registration of interior regions and was able to accurately estimate a tumor mask, as shown in Figure 3 (b). Therefore, this pre-registration approach effectively selects the tumor regions while filtering out the non-tumor regions.", + "bbox": [ + 498, + 324, + 890, + 400 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.2 Stage 2: Volume-Preserving Registration for Tumors", + "text_level": 1, + "bbox": [ + 500, + 424, + 890, + 453 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After obtaining the soft tumor mask $STM$ , we can adaptively select tumor regions to maintain the size ratio. Here, we define the volume-preserving loss directly as the distance $D_{\\theta_2}$ , as shown in Equation 8. By minimizing the distance, we can achieve smaller volume changes, indicating better preservation of tumor volume. The volume-preserving loss is multiplied by the soft tumor mask. This ensures that the volume-preserving constraints are adaptively applied to the tumor regions and not to the normal regions, which can be formulated as:", + "bbox": [ + 498, + 465, + 890, + 616 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {V P}} = \\frac {1}{\\left| I _ {m} \\right|} \\sum_ {x \\in \\Omega} D _ {\\theta_ {2}} (x) \\cdot S T M (x), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 628, + 890, + 665 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, in the second stage, the registration network takes the soft tumor mask as input, which serves as an indicator for the regions that need to be preserved in terms of volume. We follow the similarity and registration loss formulation in [38], but we use a weighted similarity loss to adapt to the volume-preserving loss, where $Cov$ is the covariance between two images $I_1, I_2$ , $\\hat{I}$ is the mean of $I$ , and $Cov'$ is the adapted version utilizing $STM$ weight:", + "bbox": [ + 498, + 678, + 890, + 799 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {C o v} ^ {\\prime} \\left[ I _ {1}, I _ {2} \\right] = \\frac {\\sum \\left(I _ {1} - \\hat {I _ {1}}\\right) \\left(I _ {2} - \\hat {I _ {2}}\\right) (1 - S T M)}{\\sum (1 - S T M)}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 825, + 890, + 861 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {w} - \\mathrm {s i m}} (x) = \\frac {\\operatorname {C o v} ^ {\\prime} \\left[ I _ {w} , I _ {f} \\right]}{\\sqrt {\\operatorname {C o v} \\left[ I _ {w} , I _ {w} \\right] \\operatorname {C o v} \\left[ I _ {f} , I _ {f} \\right]}}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 531, + 862, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21212", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Therefore, the training loss of the second stage is:", + "bbox": [ + 76, + 90, + 406, + 106 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL = L _ {\\mathrm {w} \\text {- s i m}} + \\alpha_ {1} \\cdot L _ {\\mathrm {V P}} + \\alpha_ {2} \\cdot L _ {\\mathrm {r e g}}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 119, + 468, + 135 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where we use the smoothness regularization from Voxel-Morph [5] as $L_{reg}$ , and $\\alpha_{1}$ and $\\alpha_{2}$ as hyperparameters to control the relative importance of the volume-preserving loss and the regularization loss.", + "bbox": [ + 76, + 147, + 468, + 208 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 222, + 209, + 239 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 76, + 247, + 282, + 263 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation. Following the implementation of Recursive Cascaded Network (RCN) [38], we employed PyTorch and utilized the same similarity loss and regularization losses (for affine and deformable, respectively) for baseline methods. The weight of the volume-preserving losses is set to 0.1 while the weights of similarity loss is 1 and regularization loss is 0.1. Models were trained on one NVIDIA GeForce RTX 3090 GPU with a batch size of 4. During the training stage, we used the Adam optimizer [36] and ran for a total of 5 epochs, with 20000 iterations in each epoch. The learning rate was set to $10^{-4}$ .", + "bbox": [ + 75, + 271, + 468, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. We re-implemented our strategy on four SOTA learning-based models that have distinct network architectures: 1) recursive cascaded network with VTN base network (VTN) [38], which stacks CNN networks to achieve higher registration accuracy; 2) VoxelMorph [5], which is a widely used CNN network that utilize stationary vector field to register images; 3) TransMorph [6], which is a well-performed hybrid Transformer-ConvNet network; 4) LapIRN [23], which is a Laplacian Pyramid network designed to operate in a coarse-to-fine manner. We fit these learning-based networks into our strategy with minor efforts and achieve good performance. Additionally, we compare our proposed method with two state-of-the-art traditional methods for deformable image registration, SyN [2] (integrated in ANTs [3] with the affine stage) and B-spline [26] (integrated in Elastix [17] with the affine stage) following [38].", + "bbox": [ + 75, + 467, + 468, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. The evaluation of the proposed strategy is composed of five metrics: Dice score, landmark distance to measure the anatomical alignment, and Square Tumor Size Ratio metric to measure the volume preservation of tumors. More specifically, the Dice score is calculated using the following formula:", + "bbox": [ + 75, + 724, + 468, + 815 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nD i c e \\left(I _ {1}, I _ {2}\\right) = \\frac {2 \\left| I _ {1} \\cap I _ {2} \\right|}{\\left| I _ {1} \\right| + \\left| I _ {2} \\right|}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 825, + 468, + 859 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Additionally, we also use landmark annotations to measure the anatomical alignment between the warped image and", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the fixed image. We calculate the average distance between the fixed image's landmarks and the warped landmarks of the moving image, as also introduced in RCN [38]. To quantify the diffeomorphism and smoothness of the deformation fields, we followed the methodology of previous works such as [7, 6, 39]. Here, two metrics were employed: the average percentage of voxels with non-positive Jacobian determinant $(|J_{\\theta}| < 0(\\%))$ in the deformation fields, and the standard deviation of the Jacobian determinant $(Std.|J_{\\theta}|)$ .", + "bbox": [ + 496, + 90, + 890, + 242 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To measure the volume preservation of tumors, we propose Square Tumor Size Ratio metric (STSR), which is calculated from the change of tumor size ratio (TSR) defined in Equation 4:", + "bbox": [ + 496, + 243, + 890, + 303 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nS T S R = \\max \\left(\\left(\\frac {T S R \\left(I _ {m}\\right)}{T S R \\left(I _ {w}\\right)}\\right), \\left(\\frac {T S R \\left(I _ {w}\\right)}{T S R \\left(I _ {m}\\right)}\\right)\\right) ^ {2}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 316, + 890, + 349 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here, $I_{m}, I_{w}$ refers to the moving image and the warped moving image. The square term is used o account for larger changes in tumor volumes, which can have a more significant impact on the accuracy of tumor growth estimation in clinical applications. By utilizing the STSR metric, we are able to accurately evaluate the performance of our proposed strategy.", + "bbox": [ + 496, + 362, + 890, + 467 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Preprocessing. In our study, we follow standard preprocessing steps as outlined in VTN [39] and VoxelMorph [5]. The raw scans are resampled into $128 \\times 128 \\times 128$ voxels after cropping any unnecessary areas around the target object.", + "bbox": [ + 496, + 469, + 890, + 544 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Datasets", + "text_level": 1, + "bbox": [ + 500, + 558, + 601, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training. To train our model, we utilized two publicly available datasets: (1) LiTS17 [10]: The LiTS dataset comprises 201 CT scans that were acquired using various CT scanners and devices. The resolution of the images in this dataset ranges from $0.56\\mathrm{mm}$ to $1.0\\mathrm{mm}$ in the axial direction and from $0.45\\mathrm{mm}$ to $6.0\\mathrm{mm}$ in the $z$ direction. The number of slices in the $z$ direction ranges from 42 to 1026. (2) BraTS20 [22]: It consists of 369 MRI scans of brain tumors, each with ground truth segmentation of four different tumor components. For training our neural network, we utilized the T1ce modality and treated all four components as tumors, while considering the entire brain as the surrounding organ.", + "bbox": [ + 496, + 582, + 890, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Testing. For testing, we utilized a set of 10 cases of CT liver scans with metastatic tumors, and 10 MRI brain scans with metastatic tumors. The modality of MRI brain scans is T1ce. Each case included both pre- and post-treatment images of the same patients, resulting in a total of 20 scans for each set. Following [27], the segmentation of the scans, which contains the organ (liver or brain) and the tumor inside, were carefully annotated by three experts in the field.", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21213", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2e42f463d4be0f91f0d1d06d5ddaca8fecaa2047459b42efd043552603df60a6.jpg", + "image_caption": [ + "Fixed" + ], + "image_footnote": [], + "bbox": [ + 99, + 166, + 169, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b1a7e7fddb152d1de4077cb4ad0753ac84c031c0007beba59b782801589a1a04.jpg", + "image_caption": [ + "Moving" + ], + "image_footnote": [], + "bbox": [ + 176, + 166, + 246, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/51ab0beed0cf28f8fbcd4e4d1010e4d440278149705dab1eb4955ca24c0c5c1d.jpg", + "image_caption": [ + "Fixed GT" + ], + "image_footnote": [], + "bbox": [ + 99, + 232, + 169, + 286 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a86685584960360e104e78114dcfe893f15d653fcdadd8bd6eb4597615b23e44.jpg", + "image_caption": [ + "Moving GT" + ], + "image_footnote": [], + "bbox": [ + 176, + 232, + 246, + 286 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/64e7e18e954134102460c267fd341a992df289e493aad2bed3fcc0c13f3c5175.jpg", + "image_caption": [ + "eannnnnne nnnnne eannnnnne", + "VTN", + "Regular", + "Figure 4. Qualitative comparison of different volume-preserving (VP) methods trained on the Liver Tumor Segmentation (LiTS) dataset. The left side of the figure shows two sets of images: Fixed and Ground Truth (GT), and Moving and GT. The first row of the figure displays the warped moving image, while the second row illustrates the organ outlines in green and red for the moving and fixed images, respectively. The yellow overlay highlights the tumors. Our proposed volume-preserving (VP) method ensures the preservation of tumor volume while aligning the images, as demonstrated by reduced number of visible changes in tumor size. In the third row, the Jacobian matrix of the deformation field is visualized. The green and red lines represent the organ and tumor outlines, respectively. The white areas indicate a large Jacobian, which corresponds to a more significant change in volume. The method without volume-preserving loss demonstrates a larger white area in the tumor, indicating a greater volume change of tumor volume. The last row of the figure displays the deformation field. Due to space limitations, qualitative results for BraTS20 dataset are provided in the supplemental material." + ], + "image_footnote": [], + "bbox": [ + 303, + 99, + 372, + 325 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/26233b76521c2fd6aea02034266fb08e635933235c2f5a87bc53c8351c632a23.jpg", + "image_caption": [ + "VTN", + "Ours" + ], + "image_footnote": [], + "bbox": [ + 374, + 99, + 442, + 325 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f8e1a32aa61351d4c5d1c93e39ef98466c1ee3c707d4c8a1e3c41a95c57adb31.jpg", + "image_caption": [ + "VXM", + "Regular" + ], + "image_footnote": [], + "bbox": [ + 446, + 99, + 514, + 325 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/258b2ba85af0dd80532b0a7eeba60664abc8102b7adde7e0677b65dc3c3b4db7.jpg", + "image_caption": [ + "VXM", + "Ours" + ], + "image_footnote": [], + "bbox": [ + 516, + 99, + 584, + 325 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/75787e95360e42407cf70ede43f41ee18f9ebe0b5a60e2dbcd184dd36a6858ad.jpg", + "image_caption": [ + "Trans.", + "Regular" + ], + "image_footnote": [], + "bbox": [ + 584, + 99, + 653, + 325 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/13bbbab58f2c237f5207e5501ee9c2bdf3621ed2347b5de9ace53472bf452c20.jpg", + "image_caption": [ + "Trans.", + "Ours" + ], + "image_footnote": [], + "bbox": [ + 655, + 99, + 723, + 325 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/57311016b929b767ece3f36a86addd2f31f6c392c98128a9fc3a9ec2345870f9.jpg", + "image_caption": [ + "LapIRN", + "Regular" + ], + "image_footnote": [], + "bbox": [ + 727, + 99, + 795, + 325 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/45b405b4edf9e1156fa4cb0bd953473ee8d7311edda6a4f32fc201939e30ea29.jpg", + "image_caption": [ + "LapIRN", + "Ours" + ], + "image_footnote": [], + "bbox": [ + 800, + 99, + 870, + 325 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b07572ddd504240b53b2bcfaf87deccec765aafe2247e6352494f7cd6c1d3954.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Quantitative comparison with state-of-the-art registration methods. Our strategy was applied to two datasets, namely LiTS17 and BraTS20, and three network architectures In addition, five metrics were employed for the evaluation process. The results of the comparison indicate that our proposed strategy can be well generalized to other state-of-the-art methods to preserve tumor volumes while achieving comparable or better performance on other metrics." + ], + "table_body": "
NetworkMethodsLiTs17BraTS20
Dice ↑Lm. Dist ↓|Jθ| < 0(%) ↓Std. |Jθ| ↓STSR ↓Dice ↑Lm. Dist ↓|Jθ| < 0(%) ↓Std. |Jθ| ↓STSR ↓
SyN-0.85012.360.1920.2211.5640.95604.010.2760.2261.512
B-Spline-0.85314.220.0030.2881.3300.96014.510.0010.1711.622
VTNRegular0.91210.463.5452.0482.3300.97842.980.3960.7252.263
Ours0.90810.772.9561.1241.2600.97383.100.5960.2851.416
VXMRegular0.86012.624.1911.6991.7380.97013.560.0240.4481.929
Ours0.85712.431.6810.6911.2410.97413.600.0300.2261.463
TransMorphRegular0.85913.356.3771.9061.7850.97104.010.1640.4681.868
Ours0.85613.194.0840.8271.3020.97583.980.0190.1941.319
LapIRNRegular0.893310.235.3011.7882.3600.97503.403.0200.3011.889
Ours0.889310.554.1200.9881.6450.97433.360.0400.1051.224
", + "bbox": [ + 78, + 500, + 890, + 655 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Landmarks were also annotated by three experts in the field to evaluate the registration accuracy of our strategy.", + "bbox": [ + 75, + 736, + 468, + 767 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Main Results", + "text_level": 1, + "bbox": [ + 76, + 782, + 215, + 797 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative Comparison. In Table 1, we present a comprehensive comparison of our proposed strategy with two traditional methods and three learning-based methods with different network architectures (CNN, cascaded CNN and hybrid transformer-CNN). We compare the methods using a similarity-based manner (regular) following the settings", + "bbox": [ + 75, + 809, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "in [38], as well as our volume-preserving manners. Our results demonstrate that our proposed strategy outperforms all other methods in terms of the STSR metrics, while achieving comparable results in Dice and Landmark Dist, and often better results in folding detection $(|J_{\\theta}| < 0)$ and smoothness quality $(Std. |J_{\\theta}|)$ . Furthermore, we observe that registration networks that achieve better performance in terms of previous metrics such as Dice tend to have worse performance in preserving tumor volumes (STSR). This observation highlights the need to balance these two objectives", + "bbox": [ + 496, + 736, + 893, + 888 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21214", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5219a19dba0415b543f916c89125ddb38cd37e3049ede55a640d9c82564896d2.jpg", + "table_caption": [], + "table_footnote": [ + "Table 2. Effectiveness of adaptive volume-preserving loss in unsupervised registration frameworks on LiTs17 dataset. Three networks, namely VTN in [38], VXM in [5], and TransMorph in [6], were applied. The methods used in the study were regular unsupervised (first row), weighted similarity loss only based on the ground truth (GT) mask (second row), volume-preserving loss based on GT(third row), volume-preserving loss on the whole organ based on estimation (fourth row), and on the tumor based on estimation (ours)." + ], + "table_body": "
#NetworkUnsupervisedAdaptiveRegionLiTs17
Dice ↑Lm. Dist ↓|Jθ| < 0(%) ↓Std. |Jθ| ↓STSR ↓
1VTN✓--0.91210.463.5452.0482.330
2×--0.91410.223.2411.1651.648
3××Tumor0.91110.742.8831.0171.205
4✓×Organ0.90411.073.1941.0151.640
5✓✓Organ0.90810.772.9561.1241.260
6VXM✓--0.86012.624.1911.6991.738
7×--0.86312.221.6030.6911.417
8××Tumor0.85912.381.5670.6981.291
9✓×Organ0.85612.781.6350.6751.407
10✓✓Organ0.85712.431.6810.6911.241
11TransMorph✓--0.85913.356.3371.9061.785
12×--0.86313.104.9231.5401.540
13××Tumor0.85813.214.4010.8771.227
14✓×Organ0.84913.024.6510.8451.454
15✓✓Organ0.85613.194.0840.8271.302
", + "bbox": [ + 102, + 88, + 867, + 325 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "in order to achieve competitive results.", + "bbox": [ + 78, + 393, + 331, + 407 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative Comparison. Figure 5 presents a qualitative comparison of our proposed strategy with different state-of-the-art methods. Comparing the \"VTN/VXM/Trans./LapIRN regular\" column and the \"VTN/VXM/Trans./LapIRN ours\" column, it is evident that our method outperforms other methods in terms of volume preservation in the warped image $(1_{\\mathrm{st}}$ row) and the corresponding deformation field $(4_{\\mathrm{th}}$ row). Furthermore, in terms of visualization of the registration accuracy and the overlay of the tumor $(2_{\\mathrm{nd}}$ row), our proposed method achieves better volume preservation with comparable accuracy compared to other methods. Lastly, the Jacobian determinant of the deformation field $(3_{\\mathrm{rd}}$ row) reveals that regular methods tend to have a larger Jacobian in tumor regions, indicating greater volume change, compared to our method. This highlights the effectiveness of our volume-preserving approach in preserving tumor volumes while aligning the images.", + "bbox": [ + 78, + 409, + 467, + 679 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation study", + "text_level": 1, + "bbox": [ + 78, + 694, + 223, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Volume-Preserving Losses. In Table 2, we present the results of our evaluation of the effectiveness of various versions of volume-preserving losses. For each sub-table, the first row (#1, #6, and #11) represents using only the similarity loss, while the second row (#2, #7, and #12) utilizes the ground truth as a weighted similarity loss. The third row (#3, #8, and #13) uses the ground truth binary mask as a tumor mask, while the fourth row (#4, #9, and #14) uses the mask of the entire organ as a tumor mask. The fifth row (#5, #10, and #15) represents our proposed strategy.", + "bbox": [ + 78, + 718, + 467, + 868 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "By comparing the first and second rows of each sub-table with the fifth row, we observe that our proposed volume-", + "bbox": [ + 78, + 869, + 467, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "preserving loss can effectively preserve details and achieve superior performance across various metrics. The improvement from the third and fourth rows to the fifth row indicates the importance of adaptiveness in preserving the volume of the organ and tumor, respectively. It should be noted that we do not require pixel-wise ground truth for tumor volume preservation.", + "bbox": [ + 501, + 393, + 890, + 497 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Robustness to Tumor Mask Estimation. In Figure 5, we showcase the robustness of our proposed strategy in the presence of noisy ground truth segmentation masks. To evaluate this, we randomly select points within organs to ensure that tumors have a certain Dice score with respect to the ground truth segmentation of tumors. As depicted in the figure, despite the variations in the noisy ground truth segmentation masks, our strategy's performance remains consistent. Specifically, when the tumor mask has a Dice score above a certain threshold, such as 0.15, the estimated tumor mask consistently achieves a Dice score of approximately 0.17. In contrast, using the whole organ as mask in volume-preserving loss causes degradation in performance as it only has a dice score of roughly 0.05. This highlights the necessity and efficiency of our tumor mask estimation in stage one.", + "bbox": [ + 503, + 500, + 890, + 738 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 503, + 755, + 624, + 768 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In summary, this work addressed the problem of preserving tumor volumes while maximizing similarity during learning-based registration, which is crucial for tracking tumor growth. We proposed a two-stage unsupervised strategy that effectively preserves the size ratio of tumors, without requiring extra networks. Our approach involves generating a soft tumor mask in the first stage using a similarity-based registration network and incorporating", + "bbox": [ + 503, + 780, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21215", + "bbox": [ + 478, + 946, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3fa7600e12f5561e2b1165278e52e24243ef91cdb3f409a4ecb8e16d3efe6156.jpg", + "image_caption": [ + "Figure 5. Robustness of our tumor mask estimation. We evaluated the robustness of our tumor mask estimation by running our strategy using RCN on the LiTS datasets with different noisy ground truth (GT) masks as tumor masks, each with specific Dice scores with tumors. We plotted the results on a graph with the Dice score on the x-axis and the STSR in the test set on the y-axis (where smaller values are better)." + ], + "image_footnote": [], + "bbox": [ + 122, + 93, + 423, + 243 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "an adaptive volume-preserving loss and a weighted similarity loss in the second stage to improve registration performance. To evaluate our strategy's performance, we introduced a new metric, the Square Tumor Size Ratio (STSR), which measures the preservation of tumor volume. Our proposed strategy was evaluated on various networks and demonstrated superior performance in tumor volume preservation, while achieving comparable results in other metrics. This highlights the effectiveness of our approach in tracking tumor growth and its ability to generalize well to different registration networks. Additionally, we noted that the volume preservation approach could be extended to other lesions besides tumors.", + "bbox": [ + 75, + 375, + 468, + 569 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgement: This work was supported by the HKSAR Innovation and Technology Commission (ITC) under ITF Project MHP/109/19, the National Natural Science Foundation in China under Grant 62022010, the Beijing Natural Science Foundation Haidian District Joint Fund in China under Grant L222032 and the Fundamental Research Funds for the Central Universities of China from the State Key Laboratory of Software Development Environment in Beihang University in China.", + "bbox": [ + 75, + 585, + 468, + 723 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "21216", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Moab Arar, Yiftach Ginger, Dov Danon, Amit H Bermano, and Daniel Cohen-Or. 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IEEE journal of biomedical and health informatics, 24(5):1394-1404, 2019. 6" + ], + "bbox": [ + 501, + 92, + 890, + 371 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "21218", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Preserving Tumor Volumes for Unsupervised Medical Image Registration/dbd41759-9a48-41b9-9206-f4ea354bc2a2_model.json b/2023/Preserving Tumor Volumes for Unsupervised Medical Image Registration/dbd41759-9a48-41b9-9206-f4ea354bc2a2_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c1508b324032ad35ebb27a706624353b9a7fdbbe --- /dev/null +++ b/2023/Preserving Tumor Volumes for Unsupervised Medical Image Registration/dbd41759-9a48-41b9-9206-f4ea354bc2a2_model.json @@ -0,0 +1,2367 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.131, + 0.856, + 0.154 + ], + "angle": 0, + "content": "Preserving Tumor Volumes for Unsupervised Medical Image Registration" + }, + { + "type": "text", + "bbox": [ + 0.249, + 0.18, + 0.719, + 0.199 + ], + "angle": 0, + "content": "Qihua Dong\\(^{1}\\), Hao Du\\(^{1}\\), Ying Song\\(^{2}\\), Yan Xu\\(^{3*}\\), Jing Liao\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.225, + 0.199, + 0.746, + 0.218 + ], + "angle": 0, + "content": "\\(^{1}\\)Department of Computer Science, City University of Hong Kong" + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.217, + 0.832, + 0.271 + ], + "angle": 0, + "content": "\\(^{2}\\)National Cancer Center/National Clinical Research Center for Cancer/Cancer Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College \\(^{3}\\)School of Biological Science and Medical Engineering, Beihang University" + }, + { + "type": "text", + "bbox": [ + 0.18, + 0.273, + 0.788, + 0.288 + ], + "angle": 0, + "content": "dongqh078@gmail.com, haodu8-c@my.cityu.edu.hk, jingliao@cityu.edu.hk;" + }, + { + "type": "text", + "bbox": [ + 0.378, + 0.291, + 0.593, + 0.304 + ], + "angle": 0, + "content": "songying1770@hotmail.com" + }, + { + "type": "text", + "bbox": [ + 0.408, + 0.309, + 0.562, + 0.322 + ], + "angle": 0, + "content": "xuyan04@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.357, + 0.313, + 0.373 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.394, + 0.474, + 0.846 + ], + "angle": 0, + "content": "Medical image registration is a critical task that estimates the spatial correspondence between pairs of images. However, current traditional and deep-learning-based methods rely on similarity measures to generate a deforming field, which often results in disproportionate volume changes in dissimilar regions, especially in tumor regions. These changes can significantly alter the tumor size and underlying anatomy, which limits the practical use of image registration in clinical diagnosis. To address this issue, we have formulated image registration with tumors as a constraint problem that preserves tumor volumes while maximizing image similarity in other normal regions. Our proposed strategy involves a two-stage process. In the first stage, we use similarity-based registration to identify potential tumor regions by their volume change, generating a soft tumor mask accordingly. In the second stage, we propose a volume-preserving registration with a novel adaptive volume-preserving loss that penalizes the change in size adaptively based on the masks calculated from the previous stage. Our approach balances image similarity and volume preservation in different regions, i.e., normal and tumor regions, by using soft tumor masks to adjust the imposition of volume-preserving loss on each one. This ensures that the tumor volume is preserved during the registration process. We have evaluated our strategy on various datasets and network architectures, demonstrating that our method successfully preserves the tumor volume while achieving comparable registration results with state-of-the-art methods. Our codes is available at: https://dddraxxx.github.io/Volume-Preserving-Registration/." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.357, + 0.632, + 0.373 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.392, + 0.687, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.576, + 0.52, + 0.636, + 0.53 + ], + "angle": 0, + "content": "Fixed Image" + }, + { + "type": "image", + "bbox": [ + 0.709, + 0.392, + 0.867, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.72, + 0.52, + 0.856, + 0.53 + ], + "angle": 0, + "content": "Similarity-Based Registration" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.531, + 0.686, + 0.652 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.571, + 0.657, + 0.641, + 0.669 + ], + "angle": 0, + "content": "Moving Image" + }, + { + "type": "image", + "bbox": [ + 0.709, + 0.53, + 0.867, + 0.652 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.714, + 0.657, + 0.862, + 0.668 + ], + "angle": 0, + "content": "Volume-Preserving Registration" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.682, + 0.892, + 0.751 + ], + "angle": 0, + "content": "Figure 1. Red boxes represent the location of tumors in the moving image before warped. In image registration with tumors, similarity-based registration typically leads to significant alterations in tumor size while our volume-preserving registration is capable of preserving tumor anatomy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.751, + 0.893, + 0.871 + ], + "angle": 0, + "content": "Deformable image registration is a fundamental task that estimates non-linear spatial correspondences between two images. It is useful for medical image studies that involve 3D images of organs or tissues, such as MR brain scans and CT liver scans. Recently, a wide range of deep-learning-based methods are proposed in the field, with better performance and obvious speed-ups in inference time compared to the traditional registration methods [5, 38, 32, 14, 15]." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Currently, most of the learning-based methods [5, 38] train a registration model to achieve high similarity in either" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.225, + 0.9 + ], + "angle": 0, + "content": "*Corresponding authors" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21208" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.304 + ], + "angle": 0, + "content": "image intensity [38, 5] or anatomy label maps [14]. While this is useful in various medical applications, such as atlas-based segmentation and image fusion [8], problem emerges, however, when studying images with tumors [4, 12, 24]. Tracking tumor growth is a core task in cancer treatment, which can be used to evaluate the outcomes of radiotherapy and chemotherapy, and plan optimal postoperative treatment [12]. The process requires registration to align the anatomy of images from different periods of the patient, while preserving tumor properties e.g., the size. Traditional models using regular registration have struggled to accomplish this task [12]. We have observed that this remains an issue for current learning-based methods, and a viable solution has yet to be proposed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.305, + 0.473, + 0.579 + ], + "angle": 0, + "content": "As shown in Figure 1, the volume of tumors significantly reduces when using popular unsupervised registration networks to align tumor images with atlas images. The issue is widespread since mainstream registration networks focus on optimizing the similarity between image pairs while ignoring tumor regions. Tumor regions often lack corresponding parts, and even for images of the same patient, the size and location of tumors may vary greatly. This can happen because tumors can change shape, size, location, or disappear over time. Therefore, in deformable settings, the size of tumors will change disproportionately to maximize the image similarity. This problem may be more severe when the registration network has better warping ability, leading to better performance in evaluations from previous works, as confirmed by our experiments in Section 4. The disproportionate change of tumor volume in deformable registration is lethal for clinical evaluation of tumor growth and greatly hinders the application of registration in clinics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.473, + 0.868 + ], + "angle": 0, + "content": "In this paper, we re-formulate the deformable registration problem as a constraint problem that preserves the properties of tumors in the original images, i.e., the shape and the size of the tumor, while maximizing image similarity in non-tumor regions. For instance, in tumor image registration with atlas, besides the alignment of anatomical structures, the tumor should have similar morphing behaviours as its surrounding organs, i.e., the size of it should change proportionally to the size of the organ. However, this poses two major challenges for our strategy. Firstly, due to the limited availability of annotated data, most existing registration methods resort to unsupervised learning. Therefore, a key question is how to identify tumor regions in the unsupervised setting. Second, after the tumor regions have been identified, the challenge still remains of preserving tumor volumes while simultaneously maximizing similarity in other regions. Finding a way to balance these two competing objectives is crucial for achieving effective tumor image registration." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.472, + 0.903 + ], + "angle": 0, + "content": "To tackle the challenges, we propose a novel two-stage strategy that operates in an unsupervised manner. In the first" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.349 + ], + "angle": 0, + "content": "stage, we leverage a similarity-based registration network to identify regions that undergo excessive volume change during registration. Such regions are indicative of the presence of tumors, as tumors tend to exhibit larger changes in volume due to a lack of correspondence between image pairs. The outcome of the first stage is a soft tumor mask that distinguishes normal and possible tumor regions. In the second stage, we introduce an adaptive volume-preserving loss to train a volume-preserving registration network. Based on the soft tumor mask obtained from the first stage, this loss is designed to adaptively penalize volume changes in different regions of the image. Possible tumor regions are assigned larger loss weights, and similarity loss weights are adjusted accordingly in the opposite direction. The application of the adaptive volume-preserving loss effectively balances similarity and volume preservation in different parts of the image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.35, + 0.895, + 0.56 + ], + "angle": 0, + "content": "It should be noted that the soft masks from stage one do not need to be highly accurate to achieve desirable results, as our stage two is robust, which is demonstrated by our ablation experiments in section 4. In addition to evaluating the robustness of our proposed strategy on various datasets and frameworks, including CNN and transformer, as well as different types of imaging data such as brain and abdominal, MRI and CT images, we have also introduced the Square Tumor Size Ratio (STSR) metric to measure the preservation of tumor volumes. The results demonstrate that our methods achieve comparable warping performance metrics such as Dice coefficient and average landmark distances while effectively preserving tumor properties as measured by the STSR." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.562, + 0.895, + 0.743 + ], + "angle": 0, + "content": "To conclude, our contribution includes: (1) We have reformulated image registration with tumors as a constraint problem that preserves tumor volumes while maximizes image similarity in other normal regions. (2) We have designed a two-stage process that the first stage performs regular registration to estimate tumor regions, and the second stage performs volume-preserving registration on tumor regions based on the adaptive volume-preserving loss. (3) We have proposed the STSR metric to measure the preservation of tumor volumes in registration, and have evaluated the effectiveness of our strategy on different network architectures and various datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.76, + 0.642, + 0.777 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.786, + 0.892, + 0.816 + ], + "angle": 0, + "content": "2.1. Learning-Based Deformable Image Registration" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Compared to conventional registration methods, deep networks have achieved remarkable registration accuracy and speed using various network structures, i.e., CNN and Transformer, in applications like atlas-image registration [29, 7, 16, 6, 32, 38, 5, 14, 15, 8]. They generally" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21209" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.35 + ], + "angle": 0, + "content": "adopts unsupervised learning, utilizing image similarity on either image intensities [29, 7, 6, 38] or synthesized label maps [14, 15] as well as smoothness regularization to supervise the registration network [7, 6, 14, 15, 38]. Advancements are often made through the introduction of novel regularization such as cycle consistency [16] and geometry preservation [1], or through innovative network structures like multi-scale architectures [28, 23]. However, existing methods do not adequately consider cases where tumors exist. Tumors often have no corresponding part between image pairs, and therefore, optimizing for similarity can excessively change their volumes, which limits the application of registration networks in critical clinical applications like cancer treatment. To the best of our knowledge, we are the first to study this problem with learning-based methods and propose a metric to measure volume preservation specifically for tumors." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.359, + 0.46, + 0.377 + ], + "angle": 0, + "content": "2.2. Deformable Image Registration with Tumors" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.383, + 0.473, + 0.548 + ], + "angle": 0, + "content": "Conventional registration models often resolve registering images with tumor by (1) excluding the similarity measure on tumors [11, 18], which requires either massive manual segmentation [11] or initial seed to explicitly model tumor-growth [12, 18]. (2) jointly segmenting and registering images [9], which is time-consuming since it need to iteratively detect dissimilarity in image intensities and perform resection and retraction. (3) reconstructing quasi-normal images from pathological ones [13, 19], which is also slow since the reconstruction need to be iteratively improved." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.473, + 0.761 + ], + "angle": 0, + "content": "Recently, learning-based methods for registration with tumors [24, 21, 33] are proposed for the release of BraTS-Reg dataset [4]. They aim to improve the spatial correspondence for non-tumor regions, thus either directly annotates landmarks to supervise registration [21] or introducing invertibility of the registration to mask non-inverted regions and ensure high correspondence in others [24, 33]. However, these methods assume the absence of tumors in one image of the registered pair, which may not be applicable in practical applications where we need to compare two tumor images from one patient to track the tumor growth. In this scenario, invertibility in tumors is still possible and thus, it is essential to consider the preservation of tumor properties during registration." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.772, + 0.387, + 0.789 + ], + "angle": 0, + "content": "2.3. Unsupervised Tumor Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.473, + 0.903 + ], + "angle": 0, + "content": "To ensure the preservation of tumor volumes during registration, it is crucial to first identify the locations of tumors. Current deep learning methods have made remarkable progress in unsupervised tumor segmentation, as demonstrated by recent studies [34, 35, 20]. These methods typically use GAN models or simulate tumors on healthy images to generate synthetic data, which is then used to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.244 + ], + "angle": 0, + "content": "train the segmentation network. Although the well-trained network can achieve high segmentation accuracy, it often requires complex training strategies and additional models or testing steps to achieve the desired performance, as noted in recent research [35, 20]. However, in our approach, we do not rely on sophisticated segmentation methods to accurately segment tumors. Instead, our experiments, as presented in Section 4, demonstrate that our tumor mask estimation is sufficient for our strategy to learn a volume-preserving registration for tumors." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.25, + 0.895, + 0.281 + ], + "angle": 0, + "content": "2.4. Volume-Preserving Deformable Image Registration" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.895, + 0.547 + ], + "angle": 0, + "content": "Volume-preserving registration has been studied extensively to improve the accuracy of anatomical registration. In pulmonary CT image registration, for example, tissue intensity changes between inspiration and expiration phases can be utilized as prior knowledge, and adding a volume-preserving constraint has been shown to be effective [31, 37]. In other cases, such as when soft tissues are incompressible or when images come from different modalities, a volume-preserving constraint can also serve as a helpful regularization [25, 30]. Our work, instead, focuses on using volume-preservation to maintain the properties of tumors during image registration. The proposed strategy imposes this constraint adaptively on different parts of the images in order to preserve tumor volumes and ensure anatomical accuracy, while previous works have either preserved volumes for the entire images [25, 30] or can use simple methods to determine the regions to be preserved [31, 37]." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.558, + 0.637, + 0.575 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.582, + 0.642, + 0.597 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.605, + 0.895, + 0.727 + ], + "angle": 0, + "content": "Problem Setting. Given a moving image \\( I_{m} \\) and fixed image \\( I_{f} \\) defined over \\( d \\)-dimensional (d=3 in this paper) space \\( \\Omega \\), deformable image registration aims to find a dense deformation filed \\( \\phi : \\Omega \\to \\Omega \\). This field warps \\( I_{m} \\), meaning it projects every pixel position \\( x \\) in warped image \\( I_{w} \\) to \\( I_{m} \\) to achieve alignment with \\( I_{f} \\). In this paper, the task is to construct a registration network \\( F_{\\theta} \\) that takes input \\( I_{m}, I_{f} \\) to predict the deformation field \\( \\phi \\)." + }, + { + "type": "equation", + "bbox": [ + 0.648, + 0.734, + 0.891, + 0.751 + ], + "angle": 0, + "content": "\\[\n\\phi = F _ {\\theta} \\left(I _ {m}, I _ {f}\\right) \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.617, + 0.753, + 0.891, + 0.769 + ], + "angle": 0, + "content": "\\[\nI _ {w} (x) = I _ {m} (\\phi (x) + x) \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.64, + 0.772, + 0.891, + 0.789 + ], + "angle": 0, + "content": "\\[\nI _ {w} \\sim I _ {f} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Evaluation Criteria. In general, a successful deformable image registration involves accurately aligning the anatomical structures while also ensuring a smooth deformation field. This is often achieved through the use of similarity-based objectives and regularization methods that promote smoothness. However, in the context of image registration with tumors, simply aligning the anatomy is not" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21210" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.096, + 0.833, + 0.398 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.405, + 0.895, + 0.475 + ], + "angle": 0, + "content": "Figure 2. Main Framework. Our strategy consists of two stages. In the first stage, a soft mask indicating tumor regions is estimated by analyzing the Jacobian matrix of the deformation field obtained by a registration network pre-trained on similarity loss. In the second stage, the soft mask is used to guide the calculation of both volume-preserving and similarity losses for training the volume-preserving registration network. This deformation field estimated by the stage two ensures that both the image similarity and the preservation of tumor sizes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.472, + 0.625 + ], + "angle": 0, + "content": "sufficient. Preserving the volume of the tumors is crucial for accurately tracking tumor growth, as previously discussed. To be specific, given the moving image \\( I_{m} \\) with the tumor \\( T_{m} \\) and its surrounding organ \\( O_{m} \\) and the warped moving image \\( I_{w} \\) with \\( T_{w} \\) and \\( O_{w} \\), the morphing of tumor \\( T_{m} \\) should be similar to that of \\( O_{m} \\). Thus in respect of the volume preservation, the change of tumor size \\( |T_{m}| \\) should be proportionate to the change of the containing organ \\( |O_{m}| \\), i.e.:" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.634, + 0.47, + 0.667 + ], + "angle": 0, + "content": "\\[\nT S R \\left(I _ {m}\\right) = \\frac {\\left| T _ {m} \\right|}{\\left| O _ {m} \\right|} \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.669, + 0.469, + 0.687 + ], + "angle": 0, + "content": "\\[\nT S R \\left(I _ {m}\\right) \\approx T S R \\left(I _ {w}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.699, + 0.47, + 0.764 + ], + "angle": 0, + "content": "We therefore define the tumor size ratio (TSR) as \\( \\frac{|T|}{|O|} \\), which should be preserved after registration, and the re-formulated registration objective is now maximizing image similarity while preserving the volumes of tumors, i.e., the TSR." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.772, + 0.241, + 0.789 + ], + "angle": 0, + "content": "3.2. Overall Strategy" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "The proposed strategy consists of two stages, as shown in Figure 2. The first stage estimates potential tumor regions and generates a soft mask for them. This is done by analyzing volume changes, specifically the Jacobian matrix, in the deformation field obtained by an existing similarity-based registration network. As tumor regions tend to undergo excessive volume change during registration, they can" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.892, + 0.626 + ], + "angle": 0, + "content": "be identified through this analysis. In the second stage, we perform volume-preserving registration for tumors using an adaptive volume-preserving loss. This loss is designed to guide the volume-preserving process effectively and is associated with the tumor masks estimated in the first stage. Through the assignment of distinct weights to diverse regions, including both normal and tumor regions, it is possible to preserve tumor volumes while also ensuring a high degree of similarity in other regions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.892, + 0.672 + ], + "angle": 0, + "content": "Importantly, our strategy can be applied to nearly any learning-based registration network without introducing any additional modules." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.694, + 0.885, + 0.71 + ], + "angle": 0, + "content": "3.2.1 Stage 1: Unsupervised Tumor Mask Estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.892, + 0.839 + ], + "angle": 0, + "content": "Following previous works [5, 6, 38], we first train a similarity-based registration network \\( F_{\\theta_1} \\) with parameters \\( \\theta_1 \\) and fix its parameters. As shown in Figure 1, tumors in medical images can be detected by analyzing the change in volume through similarity-based registration. Our goal is to utilize this characteristic to facilitate the unsupervised estimation of the tumor mask for volume preservation during registration." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "To determine the volume change at voxel \\( x \\), we calculate the determinant of the Jacobian matrix of the deformation field \\( (J_{\\theta}) \\) with model parameter \\( \\theta \\). Our objective is to ensure that the volume change in each point of the tumor region is" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21211" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.184 + ], + "angle": 0, + "content": "similar to the volume change of the organ, which is an indicator of the organ's size change (as shown in Equation 6). To measure the distance between the two, we calculate the number of times one ratio exceeds another, denoted as \\( D_{\\theta} \\), using Equations 8 and 7 where \\( D_{\\theta}'(x) \\) represents the relative volume change of voxel \\( x \\) with respect to organ areas." + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.201, + 0.47, + 0.235 + ], + "angle": 0, + "content": "\\[\n\\frac {\\left| T _ {w} \\right|}{\\left| O _ {w} \\right|} / \\frac {\\left| T _ {m} \\right|}{\\left| O _ {m} \\right|} \\approx 1 \\Rightarrow \\frac {\\left| T _ {w} \\right|}{\\left| T _ {m} \\right|} / \\frac {\\left| O _ {w} \\right|}{\\left| O _ {m} \\right|} \\approx 1, \\text {f r o m E q .} 5, \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.236, + 0.469, + 0.269 + ], + "angle": 0, + "content": "\\[\nD _ {\\theta} ^ {\\prime} (x) = \\left| J _ {\\theta (x)} \\right| / \\frac {\\left| O _ {w} \\right|}{\\left| O _ {m} \\right|}, x \\in \\Omega , \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.271, + 0.469, + 0.288 + ], + "angle": 0, + "content": "\\[\nD _ {\\theta} (x) = \\max \\left(D _ {\\theta} ^ {\\prime} (x), 1 / D _ {\\theta} ^ {\\prime} (x)\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.296, + 0.469, + 0.431 + ], + "angle": 0, + "content": "In practice, we estimate the organ masks \\( O_{m} \\) and \\( O_{w} \\) by warping a reference image with the ground truth (GT) organ segmentation. We randomly select the reference image from the training dataset, and the choice of reference image does not significantly impact the results because registration for organs achieves high accuracy, as evidenced by the dice value in table 1. By warping the reference image, we obtain the organ segmentation for the moving image \\( O_{m} \\). We then calculate the organ segmentation for the warped image \\( O_{w} \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.432, + 0.469, + 0.477 + ], + "angle": 0, + "content": "To obtain a soft tumor mask \\( STM \\) from the distance \\( D_{\\theta_1} \\) defined in 8, we use a transformation function \\( Tr \\). This function can be formulated as the following equation:" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.485, + 0.469, + 0.501 + ], + "angle": 0, + "content": "\\[\nS T M (x) = T r \\left(D _ {\\theta_ {1}} (x)\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.509, + 0.47, + 0.674 + ], + "angle": 0, + "content": "Here, \\( D_{\\theta_1}(x) \\) represents the distance value at pixel \\( x \\), and \\( Tr \\) transforms values from the range of \\( [0,\\infty] \\) to the range of \\( [0,1] \\). A value of 1 indicates the presence of a tumor, while a value of 0 indicates a normal region. In practical implementation, we use \\( Tr(x) = \\text{Sign}(5 \\cdot (x - 1.5)) \\) since the sigmoid function is widely adopted for converting values to the range of \\( [0,1] \\) and to our experience, the size of tumor regions averagely changes around 1.5 times. However, the choice of transformation functions is not exclusive, as demonstrated in our experiments in Section 4. We also set the regions outside the organ mask to 0." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.675, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We observed that some normal regions, particularly those close to the organ boundary, may also exhibit some volume changes after registration. As a result, these regions may be incorrectly included in the tumor mask, as shown in Figure 3 (a). To address this issue, we implemented a preregistration step to first align the edges and exclude volume changes caused by edge alignment. Specifically, in the preregistration step, we applied a bilateral filter to the moving image, which preserves the edges while smoothing the interior regions. We then used the registration network to register the filtered moving image with the fixed image in order to align their edges. After this, an unfiltered warped image was obtained by spatially transforming the unfiltered moving image with the deformation field. The second registration process was then performed on the unfiltered warped" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.089, + 0.687, + 0.211 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.562, + 0.217, + 0.636, + 0.227 + ], + "angle": 0, + "content": "(a)Tumor Mask" + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.089, + 0.868, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.714, + 0.217, + 0.885, + 0.228 + ], + "angle": 0, + "content": "(b)Tumor Mask after pre-registration" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.241, + 0.892, + 0.311 + ], + "angle": 0, + "content": "Figure 3. Visualization of the soft tumor mask. (a) is the estimated soft tumor mask without pre-registration and (b) is the one with pre-registration. The gray colors with intensity variations denote the soft mask, while the green and red colors represent the ground truth segmentation for the liver and tumors, respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.325, + 0.892, + 0.401 + ], + "angle": 0, + "content": "image, which focused on the registration of interior regions and was able to accurately estimate a tumor mask, as shown in Figure 3 (b). Therefore, this pre-registration approach effectively selects the tumor regions while filtering out the non-tumor regions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.425, + 0.892, + 0.454 + ], + "angle": 0, + "content": "3.2.2 Stage 2: Volume-Preserving Registration for Tumors" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.466, + 0.892, + 0.617 + ], + "angle": 0, + "content": "After obtaining the soft tumor mask \\( STM \\), we can adaptively select tumor regions to maintain the size ratio. Here, we define the volume-preserving loss directly as the distance \\( D_{\\theta_2} \\), as shown in Equation 8. By minimizing the distance, we can achieve smaller volume changes, indicating better preservation of tumor volume. The volume-preserving loss is multiplied by the soft tumor mask. This ensures that the volume-preserving constraints are adaptively applied to the tumor regions and not to the normal regions, which can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.629, + 0.892, + 0.666 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {V P}} = \\frac {1}{\\left| I _ {m} \\right|} \\sum_ {x \\in \\Omega} D _ {\\theta_ {2}} (x) \\cdot S T M (x), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.679, + 0.892, + 0.8 + ], + "angle": 0, + "content": "Here, in the second stage, the registration network takes the soft tumor mask as input, which serves as an indicator for the regions that need to be preserved in terms of volume. We follow the similarity and registration loss formulation in [38], but we use a weighted similarity loss to adapt to the volume-preserving loss, where \\( Cov \\) is the covariance between two images \\( I_1, I_2 \\), \\( \\hat{I} \\) is the mean of \\( I \\), and \\( Cov' \\) is the adapted version utilizing \\( STM \\) weight:" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.827, + 0.892, + 0.862 + ], + "angle": 0, + "content": "\\[\n\\operatorname {C o v} ^ {\\prime} \\left[ I _ {1}, I _ {2} \\right] = \\frac {\\sum \\left(I _ {1} - \\hat {I _ {1}}\\right) \\left(I _ {2} - \\hat {I _ {2}}\\right) (1 - S T M)}{\\sum (1 - S T M)}, \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.532, + 0.863, + 0.892, + 0.899 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {w} - \\mathrm {s i m}} (x) = \\frac {\\operatorname {C o v} ^ {\\prime} \\left[ I _ {w} , I _ {f} \\right]}{\\sqrt {\\operatorname {C o v} \\left[ I _ {w} , I _ {w} \\right] \\operatorname {C o v} \\left[ I _ {f} , I _ {f} \\right]}}, \\tag {12}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21212" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.408, + 0.107 + ], + "angle": 0, + "content": "Therefore, the training loss of the second stage is:" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.12, + 0.469, + 0.136 + ], + "angle": 0, + "content": "\\[\nL = L _ {\\mathrm {w} \\text {- s i m}} + \\alpha_ {1} \\cdot L _ {\\mathrm {V P}} + \\alpha_ {2} \\cdot L _ {\\mathrm {r e g}}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.148, + 0.469, + 0.209 + ], + "angle": 0, + "content": "where we use the smoothness regularization from Voxel-Morph [5] as \\( L_{reg} \\), and \\( \\alpha_{1} \\) and \\( \\alpha_{2} \\) as hyperparameters to control the relative importance of the volume-preserving loss and the regularization loss." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.223, + 0.21, + 0.24 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.248, + 0.284, + 0.265 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.272, + 0.47, + 0.438 + ], + "angle": 0, + "content": "Implementation. Following the implementation of Recursive Cascaded Network (RCN) [38], we employed PyTorch and utilized the same similarity loss and regularization losses (for affine and deformable, respectively) for baseline methods. The weight of the volume-preserving losses is set to 0.1 while the weights of similarity loss is 1 and regularization loss is 0.1. Models were trained on one NVIDIA GeForce RTX 3090 GPU with a batch size of 4. During the training stage, we used the Adam optimizer [36] and ran for a total of 5 epochs, with 20000 iterations in each epoch. The learning rate was set to \\(10^{-4}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.468, + 0.469, + 0.725 + ], + "angle": 0, + "content": "Baselines. We re-implemented our strategy on four SOTA learning-based models that have distinct network architectures: 1) recursive cascaded network with VTN base network (VTN) [38], which stacks CNN networks to achieve higher registration accuracy; 2) VoxelMorph [5], which is a widely used CNN network that utilize stationary vector field to register images; 3) TransMorph [6], which is a well-performed hybrid Transformer-ConvNet network; 4) LapIRN [23], which is a Laplacian Pyramid network designed to operate in a coarse-to-fine manner. We fit these learning-based networks into our strategy with minor efforts and achieve good performance. Additionally, we compare our proposed method with two state-of-the-art traditional methods for deformable image registration, SyN [2] (integrated in ANTs [3] with the affine stage) and B-spline [26] (integrated in Elastix [17] with the affine stage) following [38]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.726, + 0.469, + 0.816 + ], + "angle": 0, + "content": "Evaluation Metrics. The evaluation of the proposed strategy is composed of five metrics: Dice score, landmark distance to measure the anatomical alignment, and Square Tumor Size Ratio metric to measure the volume preservation of tumors. More specifically, the Dice score is calculated using the following formula:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.827, + 0.469, + 0.86 + ], + "angle": 0, + "content": "\\[\nD i c e \\left(I _ {1}, I _ {2}\\right) = \\frac {2 \\left| I _ {1} \\cap I _ {2} \\right|}{\\left| I _ {1} \\right| + \\left| I _ {2} \\right|}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Additionally, we also use landmark annotations to measure the anatomical alignment between the warped image and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.243 + ], + "angle": 0, + "content": "the fixed image. We calculate the average distance between the fixed image's landmarks and the warped landmarks of the moving image, as also introduced in RCN [38]. To quantify the diffeomorphism and smoothness of the deformation fields, we followed the methodology of previous works such as [7, 6, 39]. Here, two metrics were employed: the average percentage of voxels with non-positive Jacobian determinant \\((|J_{\\theta}| < 0(\\%))\\) in the deformation fields, and the standard deviation of the Jacobian determinant \\((Std.|J_{\\theta}|)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.244, + 0.892, + 0.304 + ], + "angle": 0, + "content": "To measure the volume preservation of tumors, we propose Square Tumor Size Ratio metric (STSR), which is calculated from the change of tumor size ratio (TSR) defined in Equation 4:" + }, + { + "type": "equation", + "bbox": [ + 0.53, + 0.317, + 0.892, + 0.351 + ], + "angle": 0, + "content": "\\[\nS T S R = \\max \\left(\\left(\\frac {T S R \\left(I _ {m}\\right)}{T S R \\left(I _ {w}\\right)}\\right), \\left(\\frac {T S R \\left(I _ {w}\\right)}{T S R \\left(I _ {m}\\right)}\\right)\\right) ^ {2}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.363, + 0.892, + 0.468 + ], + "angle": 0, + "content": "Here, \\( I_{m}, I_{w} \\) refers to the moving image and the warped moving image. The square term is used o account for larger changes in tumor volumes, which can have a more significant impact on the accuracy of tumor growth estimation in clinical applications. By utilizing the STSR metric, we are able to accurately evaluate the performance of our proposed strategy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.47, + 0.892, + 0.545 + ], + "angle": 0, + "content": "Preprocessing. In our study, we follow standard preprocessing steps as outlined in VTN [39] and VoxelMorph [5]. The raw scans are resampled into \\(128 \\times 128 \\times 128\\) voxels after cropping any unnecessary areas around the target object." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.559, + 0.602, + 0.573 + ], + "angle": 0, + "content": "4.2. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.779 + ], + "angle": 0, + "content": "Training. To train our model, we utilized two publicly available datasets: (1) LiTS17 [10]: The LiTS dataset comprises 201 CT scans that were acquired using various CT scanners and devices. The resolution of the images in this dataset ranges from \\(0.56\\mathrm{mm}\\) to \\(1.0\\mathrm{mm}\\) in the axial direction and from \\(0.45\\mathrm{mm}\\) to \\(6.0\\mathrm{mm}\\) in the \\(z\\) direction. The number of slices in the \\(z\\) direction ranges from 42 to 1026. (2) BraTS20 [22]: It consists of 369 MRI scans of brain tumors, each with ground truth segmentation of four different tumor components. For training our neural network, we utilized the T1ce modality and treated all four components as tumors, while considering the entire brain as the surrounding organ." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Testing. For testing, we utilized a set of 10 cases of CT liver scans with metastatic tumors, and 10 MRI brain scans with metastatic tumors. The modality of MRI brain scans is T1ce. Each case included both pre- and post-treatment images of the same patients, resulting in a total of 20 scans for each set. Following [27], the segmentation of the scans, which contains the organ (liver or brain) and the tumor inside, were carefully annotated by three experts in the field." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21213" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.167, + 0.17, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.124, + 0.222, + 0.146, + 0.229 + ], + "angle": 0, + "content": "Fixed" + }, + { + "type": "image", + "bbox": [ + 0.178, + 0.167, + 0.248, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.197, + 0.223, + 0.228, + 0.23 + ], + "angle": 0, + "content": "Moving" + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.233, + 0.17, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.288, + 0.154, + 0.296 + ], + "angle": 0, + "content": "Fixed GT" + }, + { + "type": "image", + "bbox": [ + 0.178, + 0.233, + 0.248, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.19, + 0.288, + 0.235, + 0.296 + ], + "angle": 0, + "content": "Moving GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.115, + 0.294, + 0.321 + ], + "angle": 0, + "content": "eannnnnne nnnnne eannnnnne" + }, + { + "type": "image", + "bbox": [ + 0.304, + 0.1, + 0.373, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.325, + 0.329, + 0.355, + 0.337 + ], + "angle": 0, + "content": "VTN" + }, + { + "type": "image_caption", + "bbox": [ + 0.323, + 0.338, + 0.355, + 0.345 + ], + "angle": 0, + "content": "Regular" + }, + { + "type": "image", + "bbox": [ + 0.375, + 0.1, + 0.444, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.399, + 0.329, + 0.421, + 0.337 + ], + "angle": 0, + "content": "VTN" + }, + { + "type": "image_caption", + "bbox": [ + 0.399, + 0.338, + 0.42, + 0.345 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.447, + 0.1, + 0.515, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.465, + 0.329, + 0.491, + 0.337 + ], + "angle": 0, + "content": "VXM" + }, + { + "type": "image_caption", + "bbox": [ + 0.465, + 0.338, + 0.496, + 0.345 + ], + "angle": 0, + "content": "Regular" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.1, + 0.585, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.329, + 0.562, + 0.337 + ], + "angle": 0, + "content": "VXM" + }, + { + "type": "image_caption", + "bbox": [ + 0.54, + 0.338, + 0.561, + 0.345 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.585, + 0.1, + 0.655, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.607, + 0.329, + 0.636, + 0.337 + ], + "angle": 0, + "content": "Trans." + }, + { + "type": "image_caption", + "bbox": [ + 0.605, + 0.338, + 0.637, + 0.345 + ], + "angle": 0, + "content": "Regular" + }, + { + "type": "image", + "bbox": [ + 0.656, + 0.1, + 0.725, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.676, + 0.329, + 0.702, + 0.337 + ], + "angle": 0, + "content": "Trans." + }, + { + "type": "image_caption", + "bbox": [ + 0.677, + 0.338, + 0.7, + 0.345 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.728, + 0.1, + 0.797, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.75, + 0.329, + 0.782, + 0.337 + ], + "angle": 0, + "content": "LapIRN" + }, + { + "type": "image_caption", + "bbox": [ + 0.75, + 0.338, + 0.782, + 0.345 + ], + "angle": 0, + "content": "Regular" + }, + { + "type": "image", + "bbox": [ + 0.802, + 0.1, + 0.871, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.816, + 0.329, + 0.849, + 0.337 + ], + "angle": 0, + "content": "LapIRN" + }, + { + "type": "image_caption", + "bbox": [ + 0.821, + 0.338, + 0.844, + 0.344 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.363, + 0.892, + 0.488 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison of different volume-preserving (VP) methods trained on the Liver Tumor Segmentation (LiTS) dataset. The left side of the figure shows two sets of images: Fixed and Ground Truth (GT), and Moving and GT. The first row of the figure displays the warped moving image, while the second row illustrates the organ outlines in green and red for the moving and fixed images, respectively. The yellow overlay highlights the tumors. Our proposed volume-preserving (VP) method ensures the preservation of tumor volume while aligning the images, as demonstrated by reduced number of visible changes in tumor size. In the third row, the Jacobian matrix of the deformation field is visualized. The green and red lines represent the organ and tumor outlines, respectively. The white areas indicate a large Jacobian, which corresponds to a more significant change in volume. The method without volume-preserving loss demonstrates a larger white area in the tumor, indicating a greater volume change of tumor volume. The last row of the figure displays the deformation field. Due to space limitations, qualitative results for BraTS20 dataset are provided in the supplemental material." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.5, + 0.891, + 0.656 + ], + "angle": 0, + "content": "
NetworkMethodsLiTs17BraTS20
Dice ↑Lm. Dist ↓|Jθ| < 0(%) ↓Std. |Jθ| ↓STSR ↓Dice ↑Lm. Dist ↓|Jθ| < 0(%) ↓Std. |Jθ| ↓STSR ↓
SyN-0.85012.360.1920.2211.5640.95604.010.2760.2261.512
B-Spline-0.85314.220.0030.2881.3300.96014.510.0010.1711.622
VTNRegular0.91210.463.5452.0482.3300.97842.980.3960.7252.263
Ours0.90810.772.9561.1241.2600.97383.100.5960.2851.416
VXMRegular0.86012.624.1911.6991.7380.97013.560.0240.4481.929
Ours0.85712.431.6810.6911.2410.97413.600.0300.2261.463
TransMorphRegular0.85913.356.3771.9061.7850.97104.010.1640.4681.868
Ours0.85613.194.0840.8271.3020.97583.980.0190.1941.319
LapIRNRegular0.893310.235.3011.7882.3600.97503.403.0200.3011.889
Ours0.889310.554.1200.9881.6450.97433.360.0400.1051.224
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.657, + 0.892, + 0.711 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison with state-of-the-art registration methods. Our strategy was applied to two datasets, namely LiTS17 and BraTS20, and three network architectures In addition, five metrics were employed for the evaluation process. The results of the comparison indicate that our proposed strategy can be well generalized to other state-of-the-art methods to preserve tumor volumes while achieving comparable or better performance on other metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.737, + 0.47, + 0.768 + ], + "angle": 0, + "content": "Landmarks were also annotated by three experts in the field to evaluate the registration accuracy of our strategy." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.784, + 0.216, + 0.799 + ], + "angle": 0, + "content": "4.3. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Quantitative Comparison. In Table 1, we present a comprehensive comparison of our proposed strategy with two traditional methods and three learning-based methods with different network architectures (CNN, cascaded CNN and hybrid transformer-CNN). We compare the methods using a similarity-based manner (regular) following the settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.737, + 0.895, + 0.89 + ], + "angle": 0, + "content": "in [38], as well as our volume-preserving manners. Our results demonstrate that our proposed strategy outperforms all other methods in terms of the STSR metrics, while achieving comparable results in Dice and Landmark Dist, and often better results in folding detection \\((|J_{\\theta}| < 0)\\) and smoothness quality \\((Std. |J_{\\theta}|)\\). Furthermore, we observe that registration networks that achieve better performance in terms of previous metrics such as Dice tend to have worse performance in preserving tumor volumes (STSR). This observation highlights the need to balance these two objectives" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21214" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.104, + 0.089, + 0.868, + 0.326 + ], + "angle": 0, + "content": "
#NetworkUnsupervisedAdaptiveRegionLiTs17
Dice ↑Lm. Dist ↓|Jθ| < 0(%) ↓Std. |Jθ| ↓STSR ↓
1VTN✓--0.91210.463.5452.0482.330
2×--0.91410.223.2411.1651.648
3××Tumor0.91110.742.8831.0171.205
4✓×Organ0.90411.073.1941.0151.640
5✓✓Organ0.90810.772.9561.1241.260
6VXM✓--0.86012.624.1911.6991.738
7×--0.86312.221.6030.6911.417
8××Tumor0.85912.381.5670.6981.291
9✓×Organ0.85612.781.6350.6751.407
10✓✓Organ0.85712.431.6810.6911.241
11TransMorph✓--0.85913.356.3371.9061.785
12×--0.86313.104.9231.5401.540
13××Tumor0.85813.214.4010.8771.227
14✓×Organ0.84913.024.6510.8451.454
15✓✓Organ0.85613.194.0840.8271.302
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.08, + 0.328, + 0.892, + 0.382 + ], + "angle": 0, + "content": "Table 2. Effectiveness of adaptive volume-preserving loss in unsupervised registration frameworks on LiTs17 dataset. Three networks, namely VTN in [38], VXM in [5], and TransMorph in [6], were applied. The methods used in the study were regular unsupervised (first row), weighted similarity loss only based on the ground truth (GT) mask (second row), volume-preserving loss based on GT(third row), volume-preserving loss on the whole organ based on estimation (fourth row), and on the tumor based on estimation (ours)." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.395, + 0.333, + 0.408 + ], + "angle": 0, + "content": "in order to achieve competitive results." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.41, + 0.468, + 0.68 + ], + "angle": 0, + "content": "Qualitative Comparison. Figure 5 presents a qualitative comparison of our proposed strategy with different state-of-the-art methods. Comparing the \"VTN/VXM/Trans./LapIRN regular\" column and the \"VTN/VXM/Trans./LapIRN ours\" column, it is evident that our method outperforms other methods in terms of volume preservation in the warped image \\((1_{\\mathrm{st}}\\) row) and the corresponding deformation field \\((4_{\\mathrm{th}}\\) row). Furthermore, in terms of visualization of the registration accuracy and the overlay of the tumor \\((2_{\\mathrm{nd}}\\) row), our proposed method achieves better volume preservation with comparable accuracy compared to other methods. Lastly, the Jacobian determinant of the deformation field \\((3_{\\mathrm{rd}}\\) row) reveals that regular methods tend to have a larger Jacobian in tumor regions, indicating greater volume change, compared to our method. This highlights the effectiveness of our volume-preserving approach in preserving tumor volumes while aligning the images." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.695, + 0.225, + 0.71 + ], + "angle": 0, + "content": "4.4. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.719, + 0.468, + 0.869 + ], + "angle": 0, + "content": "Volume-Preserving Losses. In Table 2, we present the results of our evaluation of the effectiveness of various versions of volume-preserving losses. For each sub-table, the first row (#1, #6, and #11) represents using only the similarity loss, while the second row (#2, #7, and #12) utilizes the ground truth as a weighted similarity loss. The third row (#3, #8, and #13) uses the ground truth binary mask as a tumor mask, while the fourth row (#4, #9, and #14) uses the mask of the entire organ as a tumor mask. The fifth row (#5, #10, and #15) represents our proposed strategy." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.871, + 0.468, + 0.9 + ], + "angle": 0, + "content": "By comparing the first and second rows of each sub-table with the fifth row, we observe that our proposed volume-" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.394, + 0.891, + 0.498 + ], + "angle": 0, + "content": "preserving loss can effectively preserve details and achieve superior performance across various metrics. The improvement from the third and fourth rows to the fifth row indicates the importance of adaptiveness in preserving the volume of the organ and tumor, respectively. It should be noted that we do not require pixel-wise ground truth for tumor volume preservation." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.5, + 0.891, + 0.739 + ], + "angle": 0, + "content": "Robustness to Tumor Mask Estimation. In Figure 5, we showcase the robustness of our proposed strategy in the presence of noisy ground truth segmentation masks. To evaluate this, we randomly select points within organs to ensure that tumors have a certain Dice score with respect to the ground truth segmentation of tumors. As depicted in the figure, despite the variations in the noisy ground truth segmentation masks, our strategy's performance remains consistent. Specifically, when the tumor mask has a Dice score above a certain threshold, such as 0.15, the estimated tumor mask consistently achieves a Dice score of approximately 0.17. In contrast, using the whole organ as mask in volume-preserving loss causes degradation in performance as it only has a dice score of roughly 0.05. This highlights the necessity and efficiency of our tumor mask estimation in stage one." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.756, + 0.625, + 0.77 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.781, + 0.891, + 0.9 + ], + "angle": 0, + "content": "In summary, this work addressed the problem of preserving tumor volumes while maximizing similarity during learning-based registration, which is crucial for tracking tumor growth. We proposed a two-stage unsupervised strategy that effectively preserves the size ratio of tumors, without requiring extra networks. Our approach involves generating a soft tumor mask in the first stage using a similarity-based registration network and incorporating" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.947, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21215" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.124, + 0.094, + 0.424, + 0.244 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.258, + 0.472, + 0.356 + ], + "angle": 0, + "content": "Figure 5. Robustness of our tumor mask estimation. We evaluated the robustness of our tumor mask estimation by running our strategy using RCN on the LiTS datasets with different noisy ground truth (GT) masks as tumor masks, each with specific Dice scores with tumors. We plotted the results on a graph with the Dice score on the x-axis and the STSR in the test set on the y-axis (where smaller values are better)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.375, + 0.47, + 0.57 + ], + "angle": 0, + "content": "an adaptive volume-preserving loss and a weighted similarity loss in the second stage to improve registration performance. To evaluate our strategy's performance, we introduced a new metric, the Square Tumor Size Ratio (STSR), which measures the preservation of tumor volume. Our proposed strategy was evaluated on various networks and demonstrated superior performance in tumor volume preservation, while achieving comparable results in other metrics. This highlights the effectiveness of our approach in tracking tumor growth and its ability to generalize well to different registration networks. Additionally, we noted that the volume preservation approach could be extended to other lesions besides tumors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.587, + 0.47, + 0.724 + ], + "angle": 0, + "content": "Acknowledgement: This work was supported by the HKSAR Innovation and Technology Commission (ITC) under ITF Project MHP/109/19, the National Natural Science Foundation in China under Grant 62022010, the Beijing Natural Science Foundation Haidian District Joint Fund in China under Grant L222032 and the Fundamental Research Funds for the Central Universities of China from the State Key Laboratory of Software Development Environment in Beihang University in China." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21216" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.198 + ], + "angle": 0, + "content": "[1] Moab Arar, Yiftach Ginger, Dov Danon, Amit H Bermano, and Daniel Cohen-Or. 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IEEE journal of biomedical and health informatics, 24(5):1394-1404, 2019. 6" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21218" + } + ] +] \ No newline at end of file diff --git a/2023/Preserving Tumor Volumes for Unsupervised Medical Image Registration/dbd41759-9a48-41b9-9206-f4ea354bc2a2_origin.pdf b/2023/Preserving Tumor Volumes for Unsupervised Medical Image Registration/dbd41759-9a48-41b9-9206-f4ea354bc2a2_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d72a00b449fc41c708a9be8eb9a06f6428ad12b3 --- /dev/null +++ b/2023/Preserving Tumor Volumes for Unsupervised Medical Image Registration/dbd41759-9a48-41b9-9206-f4ea354bc2a2_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ab59fc64231b15ecf9f05da79caf857b48309dfd1d77cda550a77fb0fe627558 +size 1086763 diff --git a/2023/Preserving Tumor Volumes for Unsupervised Medical Image Registration/full.md b/2023/Preserving Tumor Volumes for Unsupervised Medical Image Registration/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f95a328095473a5d81a55f509fe1b21be4d98efa --- /dev/null +++ b/2023/Preserving Tumor Volumes for Unsupervised Medical Image Registration/full.md @@ -0,0 +1,351 @@ +# Preserving Tumor Volumes for Unsupervised Medical Image Registration + +Qihua Dong $^{1}$ , Hao Du $^{1}$ , Ying Song $^{2}$ , Yan Xu $^{3*}$ , Jing Liao $^{1*}$ + +$^{1}$ Department of Computer Science, City University of Hong Kong + +$^{2}$ National Cancer Center/National Clinical Research Center for Cancer/Cancer Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College $^{3}$ School of Biological Science and Medical Engineering, Beihang University + +dongqh078@gmail.com, haodu8-c@my.cityu.edu.hk, jingliao@cityu.edu.hk; + +songying1770@hotmail.com + +xuyan04@gmail.com + +# Abstract + +Medical image registration is a critical task that estimates the spatial correspondence between pairs of images. However, current traditional and deep-learning-based methods rely on similarity measures to generate a deforming field, which often results in disproportionate volume changes in dissimilar regions, especially in tumor regions. These changes can significantly alter the tumor size and underlying anatomy, which limits the practical use of image registration in clinical diagnosis. To address this issue, we have formulated image registration with tumors as a constraint problem that preserves tumor volumes while maximizing image similarity in other normal regions. Our proposed strategy involves a two-stage process. In the first stage, we use similarity-based registration to identify potential tumor regions by their volume change, generating a soft tumor mask accordingly. In the second stage, we propose a volume-preserving registration with a novel adaptive volume-preserving loss that penalizes the change in size adaptively based on the masks calculated from the previous stage. Our approach balances image similarity and volume preservation in different regions, i.e., normal and tumor regions, by using soft tumor masks to adjust the imposition of volume-preserving loss on each one. This ensures that the tumor volume is preserved during the registration process. We have evaluated our strategy on various datasets and network architectures, demonstrating that our method successfully preserves the tumor volume while achieving comparable registration results with state-of-the-art methods. Our codes is available at: https://dddraxxx.github.io/Volume-Preserving-Registration/. + +# 1. Introduction + +![](images/3c773565a73bf98b9747bd76d71e915cf6c3c99ab9b4b4ae399abdb539649b8e.jpg) + +![](images/657ff349d7c2a03bbddd4c7a8472927f39480b62c2a453cd8914b61720acb5f5.jpg) + +![](images/5501f7c771a1a7977cd66eb7f46958891ea67ce1d7b7ca64e1a6c7819722c45a.jpg) +Fixed Image +Moving Image +Figure 1. Red boxes represent the location of tumors in the moving image before warped. In image registration with tumors, similarity-based registration typically leads to significant alterations in tumor size while our volume-preserving registration is capable of preserving tumor anatomy. + +![](images/cf51c67221ba2f991df800d0691c3d451ed0df7e8b666712eb207107aaa1d580.jpg) +Similarity-Based Registration +Volume-Preserving Registration + +Deformable image registration is a fundamental task that estimates non-linear spatial correspondences between two images. It is useful for medical image studies that involve 3D images of organs or tissues, such as MR brain scans and CT liver scans. Recently, a wide range of deep-learning-based methods are proposed in the field, with better performance and obvious speed-ups in inference time compared to the traditional registration methods [5, 38, 32, 14, 15]. + +Currently, most of the learning-based methods [5, 38] train a registration model to achieve high similarity in either + +image intensity [38, 5] or anatomy label maps [14]. While this is useful in various medical applications, such as atlas-based segmentation and image fusion [8], problem emerges, however, when studying images with tumors [4, 12, 24]. Tracking tumor growth is a core task in cancer treatment, which can be used to evaluate the outcomes of radiotherapy and chemotherapy, and plan optimal postoperative treatment [12]. The process requires registration to align the anatomy of images from different periods of the patient, while preserving tumor properties e.g., the size. Traditional models using regular registration have struggled to accomplish this task [12]. We have observed that this remains an issue for current learning-based methods, and a viable solution has yet to be proposed. + +As shown in Figure 1, the volume of tumors significantly reduces when using popular unsupervised registration networks to align tumor images with atlas images. The issue is widespread since mainstream registration networks focus on optimizing the similarity between image pairs while ignoring tumor regions. Tumor regions often lack corresponding parts, and even for images of the same patient, the size and location of tumors may vary greatly. This can happen because tumors can change shape, size, location, or disappear over time. Therefore, in deformable settings, the size of tumors will change disproportionately to maximize the image similarity. This problem may be more severe when the registration network has better warping ability, leading to better performance in evaluations from previous works, as confirmed by our experiments in Section 4. The disproportionate change of tumor volume in deformable registration is lethal for clinical evaluation of tumor growth and greatly hinders the application of registration in clinics. + +In this paper, we re-formulate the deformable registration problem as a constraint problem that preserves the properties of tumors in the original images, i.e., the shape and the size of the tumor, while maximizing image similarity in non-tumor regions. For instance, in tumor image registration with atlas, besides the alignment of anatomical structures, the tumor should have similar morphing behaviours as its surrounding organs, i.e., the size of it should change proportionally to the size of the organ. However, this poses two major challenges for our strategy. Firstly, due to the limited availability of annotated data, most existing registration methods resort to unsupervised learning. Therefore, a key question is how to identify tumor regions in the unsupervised setting. Second, after the tumor regions have been identified, the challenge still remains of preserving tumor volumes while simultaneously maximizing similarity in other regions. Finding a way to balance these two competing objectives is crucial for achieving effective tumor image registration. + +To tackle the challenges, we propose a novel two-stage strategy that operates in an unsupervised manner. In the first + +stage, we leverage a similarity-based registration network to identify regions that undergo excessive volume change during registration. Such regions are indicative of the presence of tumors, as tumors tend to exhibit larger changes in volume due to a lack of correspondence between image pairs. The outcome of the first stage is a soft tumor mask that distinguishes normal and possible tumor regions. In the second stage, we introduce an adaptive volume-preserving loss to train a volume-preserving registration network. Based on the soft tumor mask obtained from the first stage, this loss is designed to adaptively penalize volume changes in different regions of the image. Possible tumor regions are assigned larger loss weights, and similarity loss weights are adjusted accordingly in the opposite direction. The application of the adaptive volume-preserving loss effectively balances similarity and volume preservation in different parts of the image. + +It should be noted that the soft masks from stage one do not need to be highly accurate to achieve desirable results, as our stage two is robust, which is demonstrated by our ablation experiments in section 4. In addition to evaluating the robustness of our proposed strategy on various datasets and frameworks, including CNN and transformer, as well as different types of imaging data such as brain and abdominal, MRI and CT images, we have also introduced the Square Tumor Size Ratio (STSR) metric to measure the preservation of tumor volumes. The results demonstrate that our methods achieve comparable warping performance metrics such as Dice coefficient and average landmark distances while effectively preserving tumor properties as measured by the STSR. + +To conclude, our contribution includes: (1) We have reformulated image registration with tumors as a constraint problem that preserves tumor volumes while maximizes image similarity in other normal regions. (2) We have designed a two-stage process that the first stage performs regular registration to estimate tumor regions, and the second stage performs volume-preserving registration on tumor regions based on the adaptive volume-preserving loss. (3) We have proposed the STSR metric to measure the preservation of tumor volumes in registration, and have evaluated the effectiveness of our strategy on different network architectures and various datasets. + +# 2. Related Work + +# 2.1. Learning-Based Deformable Image Registration + +Compared to conventional registration methods, deep networks have achieved remarkable registration accuracy and speed using various network structures, i.e., CNN and Transformer, in applications like atlas-image registration [29, 7, 16, 6, 32, 38, 5, 14, 15, 8]. They generally + +adopts unsupervised learning, utilizing image similarity on either image intensities [29, 7, 6, 38] or synthesized label maps [14, 15] as well as smoothness regularization to supervise the registration network [7, 6, 14, 15, 38]. Advancements are often made through the introduction of novel regularization such as cycle consistency [16] and geometry preservation [1], or through innovative network structures like multi-scale architectures [28, 23]. However, existing methods do not adequately consider cases where tumors exist. Tumors often have no corresponding part between image pairs, and therefore, optimizing for similarity can excessively change their volumes, which limits the application of registration networks in critical clinical applications like cancer treatment. To the best of our knowledge, we are the first to study this problem with learning-based methods and propose a metric to measure volume preservation specifically for tumors. + +# 2.2. Deformable Image Registration with Tumors + +Conventional registration models often resolve registering images with tumor by (1) excluding the similarity measure on tumors [11, 18], which requires either massive manual segmentation [11] or initial seed to explicitly model tumor-growth [12, 18]. (2) jointly segmenting and registering images [9], which is time-consuming since it need to iteratively detect dissimilarity in image intensities and perform resection and retraction. (3) reconstructing quasi-normal images from pathological ones [13, 19], which is also slow since the reconstruction need to be iteratively improved. + +Recently, learning-based methods for registration with tumors [24, 21, 33] are proposed for the release of BraTS-Reg dataset [4]. They aim to improve the spatial correspondence for non-tumor regions, thus either directly annotates landmarks to supervise registration [21] or introducing invertibility of the registration to mask non-inverted regions and ensure high correspondence in others [24, 33]. However, these methods assume the absence of tumors in one image of the registered pair, which may not be applicable in practical applications where we need to compare two tumor images from one patient to track the tumor growth. In this scenario, invertibility in tumors is still possible and thus, it is essential to consider the preservation of tumor properties during registration. + +# 2.3. Unsupervised Tumor Segmentation + +To ensure the preservation of tumor volumes during registration, it is crucial to first identify the locations of tumors. Current deep learning methods have made remarkable progress in unsupervised tumor segmentation, as demonstrated by recent studies [34, 35, 20]. These methods typically use GAN models or simulate tumors on healthy images to generate synthetic data, which is then used to + +train the segmentation network. Although the well-trained network can achieve high segmentation accuracy, it often requires complex training strategies and additional models or testing steps to achieve the desired performance, as noted in recent research [35, 20]. However, in our approach, we do not rely on sophisticated segmentation methods to accurately segment tumors. Instead, our experiments, as presented in Section 4, demonstrate that our tumor mask estimation is sufficient for our strategy to learn a volume-preserving registration for tumors. + +# 2.4. Volume-Preserving Deformable Image Registration + +Volume-preserving registration has been studied extensively to improve the accuracy of anatomical registration. In pulmonary CT image registration, for example, tissue intensity changes between inspiration and expiration phases can be utilized as prior knowledge, and adding a volume-preserving constraint has been shown to be effective [31, 37]. In other cases, such as when soft tissues are incompressible or when images come from different modalities, a volume-preserving constraint can also serve as a helpful regularization [25, 30]. Our work, instead, focuses on using volume-preservation to maintain the properties of tumors during image registration. The proposed strategy imposes this constraint adaptively on different parts of the images in order to preserve tumor volumes and ensure anatomical accuracy, while previous works have either preserved volumes for the entire images [25, 30] or can use simple methods to determine the regions to be preserved [31, 37]. + +# 3. Methodology + +# 3.1. Preliminaries + +Problem Setting. Given a moving image $I_{m}$ and fixed image $I_{f}$ defined over $d$ -dimensional (d=3 in this paper) space $\Omega$ , deformable image registration aims to find a dense deformation filed $\phi : \Omega \to \Omega$ . This field warps $I_{m}$ , meaning it projects every pixel position $x$ in warped image $I_{w}$ to $I_{m}$ to achieve alignment with $I_{f}$ . In this paper, the task is to construct a registration network $F_{\theta}$ that takes input $I_{m}, I_{f}$ to predict the deformation field $\phi$ . + +$$ +\phi = F _ {\theta} \left(I _ {m}, I _ {f}\right) \tag {1} +$$ + +$$ +I _ {w} (x) = I _ {m} (\phi (x) + x) \tag {2} +$$ + +$$ +I _ {w} \sim I _ {f} \tag {3} +$$ + +Evaluation Criteria. In general, a successful deformable image registration involves accurately aligning the anatomical structures while also ensuring a smooth deformation field. This is often achieved through the use of similarity-based objectives and regularization methods that promote smoothness. However, in the context of image registration with tumors, simply aligning the anatomy is not + +![](images/5cb5a1782ab687053e0200bb173bbb0a88140e957c50a252f9b6032916461fd0.jpg) +Figure 2. Main Framework. Our strategy consists of two stages. In the first stage, a soft mask indicating tumor regions is estimated by analyzing the Jacobian matrix of the deformation field obtained by a registration network pre-trained on similarity loss. In the second stage, the soft mask is used to guide the calculation of both volume-preserving and similarity losses for training the volume-preserving registration network. This deformation field estimated by the stage two ensures that both the image similarity and the preservation of tumor sizes. + +sufficient. Preserving the volume of the tumors is crucial for accurately tracking tumor growth, as previously discussed. To be specific, given the moving image $I_{m}$ with the tumor $T_{m}$ and its surrounding organ $O_{m}$ and the warped moving image $I_{w}$ with $T_{w}$ and $O_{w}$ , the morphing of tumor $T_{m}$ should be similar to that of $O_{m}$ . Thus in respect of the volume preservation, the change of tumor size $|T_{m}|$ should be proportionate to the change of the containing organ $|O_{m}|$ , i.e.: + +$$ +T S R \left(I _ {m}\right) = \frac {\left| T _ {m} \right|}{\left| O _ {m} \right|} \tag {4} +$$ + +$$ +T S R \left(I _ {m}\right) \approx T S R \left(I _ {w}\right) \tag {5} +$$ + +We therefore define the tumor size ratio (TSR) as $\frac{|T|}{|O|}$ , which should be preserved after registration, and the re-formulated registration objective is now maximizing image similarity while preserving the volumes of tumors, i.e., the TSR. + +# 3.2. Overall Strategy + +The proposed strategy consists of two stages, as shown in Figure 2. The first stage estimates potential tumor regions and generates a soft mask for them. This is done by analyzing volume changes, specifically the Jacobian matrix, in the deformation field obtained by an existing similarity-based registration network. As tumor regions tend to undergo excessive volume change during registration, they can + +be identified through this analysis. In the second stage, we perform volume-preserving registration for tumors using an adaptive volume-preserving loss. This loss is designed to guide the volume-preserving process effectively and is associated with the tumor masks estimated in the first stage. Through the assignment of distinct weights to diverse regions, including both normal and tumor regions, it is possible to preserve tumor volumes while also ensuring a high degree of similarity in other regions. + +Importantly, our strategy can be applied to nearly any learning-based registration network without introducing any additional modules. + +# 3.2.1 Stage 1: Unsupervised Tumor Mask Estimation + +Following previous works [5, 6, 38], we first train a similarity-based registration network $F_{\theta_1}$ with parameters $\theta_1$ and fix its parameters. As shown in Figure 1, tumors in medical images can be detected by analyzing the change in volume through similarity-based registration. Our goal is to utilize this characteristic to facilitate the unsupervised estimation of the tumor mask for volume preservation during registration. + +To determine the volume change at voxel $x$ , we calculate the determinant of the Jacobian matrix of the deformation field $(J_{\theta})$ with model parameter $\theta$ . Our objective is to ensure that the volume change in each point of the tumor region is + +similar to the volume change of the organ, which is an indicator of the organ's size change (as shown in Equation 6). To measure the distance between the two, we calculate the number of times one ratio exceeds another, denoted as $D_{\theta}$ , using Equations 8 and 7 where $D_{\theta}'(x)$ represents the relative volume change of voxel $x$ with respect to organ areas. + +$$ +\frac {\left| T _ {w} \right|}{\left| O _ {w} \right|} / \frac {\left| T _ {m} \right|}{\left| O _ {m} \right|} \approx 1 \Rightarrow \frac {\left| T _ {w} \right|}{\left| T _ {m} \right|} / \frac {\left| O _ {w} \right|}{\left| O _ {m} \right|} \approx 1, \text {f r o m E q .} 5, \tag {6} +$$ + +$$ +D _ {\theta} ^ {\prime} (x) = \left| J _ {\theta (x)} \right| / \frac {\left| O _ {w} \right|}{\left| O _ {m} \right|}, x \in \Omega , \tag {7} +$$ + +$$ +D _ {\theta} (x) = \max \left(D _ {\theta} ^ {\prime} (x), 1 / D _ {\theta} ^ {\prime} (x)\right), \tag {8} +$$ + +In practice, we estimate the organ masks $O_{m}$ and $O_{w}$ by warping a reference image with the ground truth (GT) organ segmentation. We randomly select the reference image from the training dataset, and the choice of reference image does not significantly impact the results because registration for organs achieves high accuracy, as evidenced by the dice value in table 1. By warping the reference image, we obtain the organ segmentation for the moving image $O_{m}$ . We then calculate the organ segmentation for the warped image $O_{w}$ . + +To obtain a soft tumor mask $STM$ from the distance $D_{\theta_1}$ defined in 8, we use a transformation function $Tr$ . This function can be formulated as the following equation: + +$$ +S T M (x) = T r \left(D _ {\theta_ {1}} (x)\right), \tag {9} +$$ + +Here, $D_{\theta_1}(x)$ represents the distance value at pixel $x$ , and $Tr$ transforms values from the range of $[0,\infty]$ to the range of $[0,1]$ . A value of 1 indicates the presence of a tumor, while a value of 0 indicates a normal region. In practical implementation, we use $Tr(x) = \text{Sign}(5 \cdot (x - 1.5))$ since the sigmoid function is widely adopted for converting values to the range of $[0,1]$ and to our experience, the size of tumor regions averagely changes around 1.5 times. However, the choice of transformation functions is not exclusive, as demonstrated in our experiments in Section 4. We also set the regions outside the organ mask to 0. + +We observed that some normal regions, particularly those close to the organ boundary, may also exhibit some volume changes after registration. As a result, these regions may be incorrectly included in the tumor mask, as shown in Figure 3 (a). To address this issue, we implemented a preregistration step to first align the edges and exclude volume changes caused by edge alignment. Specifically, in the preregistration step, we applied a bilateral filter to the moving image, which preserves the edges while smoothing the interior regions. We then used the registration network to register the filtered moving image with the fixed image in order to align their edges. After this, an unfiltered warped image was obtained by spatially transforming the unfiltered moving image with the deformation field. The second registration process was then performed on the unfiltered warped + +![](images/ae5b9c79bfc3f87b3cbe338bdb6f8cec305e153515e9eefa29531f91634fa745.jpg) +(a)Tumor Mask + +![](images/ee6ad0dfa4d53dd393bd7326b429ac9e80ca121224703f18d3a870c56fd5e7a6.jpg) +(b)Tumor Mask after pre-registration +Figure 3. Visualization of the soft tumor mask. (a) is the estimated soft tumor mask without pre-registration and (b) is the one with pre-registration. The gray colors with intensity variations denote the soft mask, while the green and red colors represent the ground truth segmentation for the liver and tumors, respectively. + +image, which focused on the registration of interior regions and was able to accurately estimate a tumor mask, as shown in Figure 3 (b). Therefore, this pre-registration approach effectively selects the tumor regions while filtering out the non-tumor regions. + +# 3.2.2 Stage 2: Volume-Preserving Registration for Tumors + +After obtaining the soft tumor mask $STM$ , we can adaptively select tumor regions to maintain the size ratio. Here, we define the volume-preserving loss directly as the distance $D_{\theta_2}$ , as shown in Equation 8. By minimizing the distance, we can achieve smaller volume changes, indicating better preservation of tumor volume. The volume-preserving loss is multiplied by the soft tumor mask. This ensures that the volume-preserving constraints are adaptively applied to the tumor regions and not to the normal regions, which can be formulated as: + +$$ +L _ {\mathrm {V P}} = \frac {1}{\left| I _ {m} \right|} \sum_ {x \in \Omega} D _ {\theta_ {2}} (x) \cdot S T M (x), \tag {10} +$$ + +Here, in the second stage, the registration network takes the soft tumor mask as input, which serves as an indicator for the regions that need to be preserved in terms of volume. We follow the similarity and registration loss formulation in [38], but we use a weighted similarity loss to adapt to the volume-preserving loss, where $Cov$ is the covariance between two images $I_1, I_2$ , $\hat{I}$ is the mean of $I$ , and $Cov'$ is the adapted version utilizing $STM$ weight: + +$$ +\operatorname {C o v} ^ {\prime} \left[ I _ {1}, I _ {2} \right] = \frac {\sum \left(I _ {1} - \hat {I _ {1}}\right) \left(I _ {2} - \hat {I _ {2}}\right) (1 - S T M)}{\sum (1 - S T M)}, \tag {11} +$$ + +$$ +L _ {\mathrm {w} - \mathrm {s i m}} (x) = \frac {\operatorname {C o v} ^ {\prime} \left[ I _ {w} , I _ {f} \right]}{\sqrt {\operatorname {C o v} \left[ I _ {w} , I _ {w} \right] \operatorname {C o v} \left[ I _ {f} , I _ {f} \right]}}, \tag {12} +$$ + +Therefore, the training loss of the second stage is: + +$$ +L = L _ {\mathrm {w} \text {- s i m}} + \alpha_ {1} \cdot L _ {\mathrm {V P}} + \alpha_ {2} \cdot L _ {\mathrm {r e g}}, \tag {13} +$$ + +where we use the smoothness regularization from Voxel-Morph [5] as $L_{reg}$ , and $\alpha_{1}$ and $\alpha_{2}$ as hyperparameters to control the relative importance of the volume-preserving loss and the regularization loss. + +# 4. Experiments + +# 4.1. Experimental Settings + +Implementation. Following the implementation of Recursive Cascaded Network (RCN) [38], we employed PyTorch and utilized the same similarity loss and regularization losses (for affine and deformable, respectively) for baseline methods. The weight of the volume-preserving losses is set to 0.1 while the weights of similarity loss is 1 and regularization loss is 0.1. Models were trained on one NVIDIA GeForce RTX 3090 GPU with a batch size of 4. During the training stage, we used the Adam optimizer [36] and ran for a total of 5 epochs, with 20000 iterations in each epoch. The learning rate was set to $10^{-4}$ . + +Baselines. We re-implemented our strategy on four SOTA learning-based models that have distinct network architectures: 1) recursive cascaded network with VTN base network (VTN) [38], which stacks CNN networks to achieve higher registration accuracy; 2) VoxelMorph [5], which is a widely used CNN network that utilize stationary vector field to register images; 3) TransMorph [6], which is a well-performed hybrid Transformer-ConvNet network; 4) LapIRN [23], which is a Laplacian Pyramid network designed to operate in a coarse-to-fine manner. We fit these learning-based networks into our strategy with minor efforts and achieve good performance. Additionally, we compare our proposed method with two state-of-the-art traditional methods for deformable image registration, SyN [2] (integrated in ANTs [3] with the affine stage) and B-spline [26] (integrated in Elastix [17] with the affine stage) following [38]. + +Evaluation Metrics. The evaluation of the proposed strategy is composed of five metrics: Dice score, landmark distance to measure the anatomical alignment, and Square Tumor Size Ratio metric to measure the volume preservation of tumors. More specifically, the Dice score is calculated using the following formula: + +$$ +D i c e \left(I _ {1}, I _ {2}\right) = \frac {2 \left| I _ {1} \cap I _ {2} \right|}{\left| I _ {1} \right| + \left| I _ {2} \right|}, \tag {14} +$$ + +Additionally, we also use landmark annotations to measure the anatomical alignment between the warped image and + +the fixed image. We calculate the average distance between the fixed image's landmarks and the warped landmarks of the moving image, as also introduced in RCN [38]. To quantify the diffeomorphism and smoothness of the deformation fields, we followed the methodology of previous works such as [7, 6, 39]. Here, two metrics were employed: the average percentage of voxels with non-positive Jacobian determinant $(|J_{\theta}| < 0(\%))$ in the deformation fields, and the standard deviation of the Jacobian determinant $(Std.|J_{\theta}|)$ . + +To measure the volume preservation of tumors, we propose Square Tumor Size Ratio metric (STSR), which is calculated from the change of tumor size ratio (TSR) defined in Equation 4: + +$$ +S T S R = \max \left(\left(\frac {T S R \left(I _ {m}\right)}{T S R \left(I _ {w}\right)}\right), \left(\frac {T S R \left(I _ {w}\right)}{T S R \left(I _ {m}\right)}\right)\right) ^ {2}, \tag {15} +$$ + +Here, $I_{m}, I_{w}$ refers to the moving image and the warped moving image. The square term is used o account for larger changes in tumor volumes, which can have a more significant impact on the accuracy of tumor growth estimation in clinical applications. By utilizing the STSR metric, we are able to accurately evaluate the performance of our proposed strategy. + +Preprocessing. In our study, we follow standard preprocessing steps as outlined in VTN [39] and VoxelMorph [5]. The raw scans are resampled into $128 \times 128 \times 128$ voxels after cropping any unnecessary areas around the target object. + +# 4.2. Datasets + +Training. To train our model, we utilized two publicly available datasets: (1) LiTS17 [10]: The LiTS dataset comprises 201 CT scans that were acquired using various CT scanners and devices. The resolution of the images in this dataset ranges from $0.56\mathrm{mm}$ to $1.0\mathrm{mm}$ in the axial direction and from $0.45\mathrm{mm}$ to $6.0\mathrm{mm}$ in the $z$ direction. The number of slices in the $z$ direction ranges from 42 to 1026. (2) BraTS20 [22]: It consists of 369 MRI scans of brain tumors, each with ground truth segmentation of four different tumor components. For training our neural network, we utilized the T1ce modality and treated all four components as tumors, while considering the entire brain as the surrounding organ. + +Testing. For testing, we utilized a set of 10 cases of CT liver scans with metastatic tumors, and 10 MRI brain scans with metastatic tumors. The modality of MRI brain scans is T1ce. Each case included both pre- and post-treatment images of the same patients, resulting in a total of 20 scans for each set. Following [27], the segmentation of the scans, which contains the organ (liver or brain) and the tumor inside, were carefully annotated by three experts in the field. + +![](images/2e42f463d4be0f91f0d1d06d5ddaca8fecaa2047459b42efd043552603df60a6.jpg) +Fixed + +![](images/b1a7e7fddb152d1de4077cb4ad0753ac84c031c0007beba59b782801589a1a04.jpg) +Moving + +![](images/51ab0beed0cf28f8fbcd4e4d1010e4d440278149705dab1eb4955ca24c0c5c1d.jpg) +Fixed GT + +![](images/a86685584960360e104e78114dcfe893f15d653fcdadd8bd6eb4597615b23e44.jpg) +Moving GT + +![](images/64e7e18e954134102460c267fd341a992df289e493aad2bed3fcc0c13f3c5175.jpg) +eannnnnne nnnnne eannnnnne +VTN +Regular +Figure 4. Qualitative comparison of different volume-preserving (VP) methods trained on the Liver Tumor Segmentation (LiTS) dataset. The left side of the figure shows two sets of images: Fixed and Ground Truth (GT), and Moving and GT. The first row of the figure displays the warped moving image, while the second row illustrates the organ outlines in green and red for the moving and fixed images, respectively. The yellow overlay highlights the tumors. Our proposed volume-preserving (VP) method ensures the preservation of tumor volume while aligning the images, as demonstrated by reduced number of visible changes in tumor size. In the third row, the Jacobian matrix of the deformation field is visualized. The green and red lines represent the organ and tumor outlines, respectively. The white areas indicate a large Jacobian, which corresponds to a more significant change in volume. The method without volume-preserving loss demonstrates a larger white area in the tumor, indicating a greater volume change of tumor volume. The last row of the figure displays the deformation field. Due to space limitations, qualitative results for BraTS20 dataset are provided in the supplemental material. + +![](images/26233b76521c2fd6aea02034266fb08e635933235c2f5a87bc53c8351c632a23.jpg) +VTN +Ours + +![](images/f8e1a32aa61351d4c5d1c93e39ef98466c1ee3c707d4c8a1e3c41a95c57adb31.jpg) +VXM +Regular + +![](images/258b2ba85af0dd80532b0a7eeba60664abc8102b7adde7e0677b65dc3c3b4db7.jpg) +VXM +Ours + +![](images/75787e95360e42407cf70ede43f41ee18f9ebe0b5a60e2dbcd184dd36a6858ad.jpg) +Trans. +Regular + +![](images/13bbbab58f2c237f5207e5501ee9c2bdf3621ed2347b5de9ace53472bf452c20.jpg) +Trans. +Ours + +![](images/57311016b929b767ece3f36a86addd2f31f6c392c98128a9fc3a9ec2345870f9.jpg) +LapIRN +Regular + +![](images/45b405b4edf9e1156fa4cb0bd953473ee8d7311edda6a4f32fc201939e30ea29.jpg) +LapIRN +Ours + +
NetworkMethodsLiTs17BraTS20
Dice ↑Lm. Dist ↓|Jθ| < 0(%) ↓Std. |Jθ| ↓STSR ↓Dice ↑Lm. Dist ↓|Jθ| < 0(%) ↓Std. |Jθ| ↓STSR ↓
SyN-0.85012.360.1920.2211.5640.95604.010.2760.2261.512
B-Spline-0.85314.220.0030.2881.3300.96014.510.0010.1711.622
VTNRegular0.91210.463.5452.0482.3300.97842.980.3960.7252.263
Ours0.90810.772.9561.1241.2600.97383.100.5960.2851.416
VXMRegular0.86012.624.1911.6991.7380.97013.560.0240.4481.929
Ours0.85712.431.6810.6911.2410.97413.600.0300.2261.463
TransMorphRegular0.85913.356.3771.9061.7850.97104.010.1640.4681.868
Ours0.85613.194.0840.8271.3020.97583.980.0190.1941.319
LapIRNRegular0.893310.235.3011.7882.3600.97503.403.0200.3011.889
Ours0.889310.554.1200.9881.6450.97433.360.0400.1051.224
+ +Table 1. Quantitative comparison with state-of-the-art registration methods. Our strategy was applied to two datasets, namely LiTS17 and BraTS20, and three network architectures In addition, five metrics were employed for the evaluation process. The results of the comparison indicate that our proposed strategy can be well generalized to other state-of-the-art methods to preserve tumor volumes while achieving comparable or better performance on other metrics. + +Landmarks were also annotated by three experts in the field to evaluate the registration accuracy of our strategy. + +# 4.3. Main Results + +Quantitative Comparison. In Table 1, we present a comprehensive comparison of our proposed strategy with two traditional methods and three learning-based methods with different network architectures (CNN, cascaded CNN and hybrid transformer-CNN). We compare the methods using a similarity-based manner (regular) following the settings + +in [38], as well as our volume-preserving manners. Our results demonstrate that our proposed strategy outperforms all other methods in terms of the STSR metrics, while achieving comparable results in Dice and Landmark Dist, and often better results in folding detection $(|J_{\theta}| < 0)$ and smoothness quality $(Std. |J_{\theta}|)$ . Furthermore, we observe that registration networks that achieve better performance in terms of previous metrics such as Dice tend to have worse performance in preserving tumor volumes (STSR). This observation highlights the need to balance these two objectives + +
#NetworkUnsupervisedAdaptiveRegionLiTs17
Dice ↑Lm. Dist ↓|Jθ| < 0(%) ↓Std. |Jθ| ↓STSR ↓
1VTN✓--0.91210.463.5452.0482.330
2×--0.91410.223.2411.1651.648
3××Tumor0.91110.742.8831.0171.205
4✓×Organ0.90411.073.1941.0151.640
5✓✓Organ0.90810.772.9561.1241.260
6VXM✓--0.86012.624.1911.6991.738
7×--0.86312.221.6030.6911.417
8××Tumor0.85912.381.5670.6981.291
9✓×Organ0.85612.781.6350.6751.407
10✓✓Organ0.85712.431.6810.6911.241
11TransMorph✓--0.85913.356.3371.9061.785
12×--0.86313.104.9231.5401.540
13××Tumor0.85813.214.4010.8771.227
14✓×Organ0.84913.024.6510.8451.454
15✓✓Organ0.85613.194.0840.8271.302
+ +Table 2. Effectiveness of adaptive volume-preserving loss in unsupervised registration frameworks on LiTs17 dataset. Three networks, namely VTN in [38], VXM in [5], and TransMorph in [6], were applied. The methods used in the study were regular unsupervised (first row), weighted similarity loss only based on the ground truth (GT) mask (second row), volume-preserving loss based on GT(third row), volume-preserving loss on the whole organ based on estimation (fourth row), and on the tumor based on estimation (ours). + +in order to achieve competitive results. + +Qualitative Comparison. Figure 5 presents a qualitative comparison of our proposed strategy with different state-of-the-art methods. Comparing the "VTN/VXM/Trans./LapIRN regular" column and the "VTN/VXM/Trans./LapIRN ours" column, it is evident that our method outperforms other methods in terms of volume preservation in the warped image $(1_{\mathrm{st}}$ row) and the corresponding deformation field $(4_{\mathrm{th}}$ row). Furthermore, in terms of visualization of the registration accuracy and the overlay of the tumor $(2_{\mathrm{nd}}$ row), our proposed method achieves better volume preservation with comparable accuracy compared to other methods. Lastly, the Jacobian determinant of the deformation field $(3_{\mathrm{rd}}$ row) reveals that regular methods tend to have a larger Jacobian in tumor regions, indicating greater volume change, compared to our method. This highlights the effectiveness of our volume-preserving approach in preserving tumor volumes while aligning the images. + +# 4.4. Ablation study + +Volume-Preserving Losses. In Table 2, we present the results of our evaluation of the effectiveness of various versions of volume-preserving losses. For each sub-table, the first row (#1, #6, and #11) represents using only the similarity loss, while the second row (#2, #7, and #12) utilizes the ground truth as a weighted similarity loss. The third row (#3, #8, and #13) uses the ground truth binary mask as a tumor mask, while the fourth row (#4, #9, and #14) uses the mask of the entire organ as a tumor mask. The fifth row (#5, #10, and #15) represents our proposed strategy. + +By comparing the first and second rows of each sub-table with the fifth row, we observe that our proposed volume- + +preserving loss can effectively preserve details and achieve superior performance across various metrics. The improvement from the third and fourth rows to the fifth row indicates the importance of adaptiveness in preserving the volume of the organ and tumor, respectively. It should be noted that we do not require pixel-wise ground truth for tumor volume preservation. + +Robustness to Tumor Mask Estimation. In Figure 5, we showcase the robustness of our proposed strategy in the presence of noisy ground truth segmentation masks. To evaluate this, we randomly select points within organs to ensure that tumors have a certain Dice score with respect to the ground truth segmentation of tumors. As depicted in the figure, despite the variations in the noisy ground truth segmentation masks, our strategy's performance remains consistent. Specifically, when the tumor mask has a Dice score above a certain threshold, such as 0.15, the estimated tumor mask consistently achieves a Dice score of approximately 0.17. In contrast, using the whole organ as mask in volume-preserving loss causes degradation in performance as it only has a dice score of roughly 0.05. This highlights the necessity and efficiency of our tumor mask estimation in stage one. + +# 5. Conclusions + +In summary, this work addressed the problem of preserving tumor volumes while maximizing similarity during learning-based registration, which is crucial for tracking tumor growth. We proposed a two-stage unsupervised strategy that effectively preserves the size ratio of tumors, without requiring extra networks. Our approach involves generating a soft tumor mask in the first stage using a similarity-based registration network and incorporating + +![](images/3fa7600e12f5561e2b1165278e52e24243ef91cdb3f409a4ecb8e16d3efe6156.jpg) +Figure 5. Robustness of our tumor mask estimation. We evaluated the robustness of our tumor mask estimation by running our strategy using RCN on the LiTS datasets with different noisy ground truth (GT) masks as tumor masks, each with specific Dice scores with tumors. We plotted the results on a graph with the Dice score on the x-axis and the STSR in the test set on the y-axis (where smaller values are better). + +an adaptive volume-preserving loss and a weighted similarity loss in the second stage to improve registration performance. To evaluate our strategy's performance, we introduced a new metric, the Square Tumor Size Ratio (STSR), which measures the preservation of tumor volume. Our proposed strategy was evaluated on various networks and demonstrated superior performance in tumor volume preservation, while achieving comparable results in other metrics. This highlights the effectiveness of our approach in tracking tumor growth and its ability to generalize well to different registration networks. Additionally, we noted that the volume preservation approach could be extended to other lesions besides tumors. + +Acknowledgement: This work was supported by the HKSAR Innovation and Technology Commission (ITC) under ITF Project MHP/109/19, the National Natural Science Foundation in China under Grant 62022010, the Beijing Natural Science Foundation Haidian District Joint Fund in China under Grant L222032 and the Fundamental Research Funds for the Central Universities of China from the State Key Laboratory of Software Development Environment in Beihang University in China. + +# References + +[1] Moab Arar, Yiftach Ginger, Dov Danon, Amit H Bermano, and Daniel Cohen-Or. Unsupervised multi-modal image registration via geometry preserving image-to-image translation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 13410–13419, 2020. 3 +[2] Brian B Avants, Charles L Epstein, Murray Grossman, and James C Gee. 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"content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 312, + 290, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 290, + 670 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 290, + 670 + ], + "type": "text", + "content": "Medical image registration is a critical task that estimates the spatial correspondence between pairs of images. However, current traditional and deep-learning-based methods rely on similarity measures to generate a deforming field, which often results in disproportionate volume changes in dissimilar regions, especially in tumor regions. These changes can significantly alter the tumor size and underlying anatomy, which limits the practical use of image registration in clinical diagnosis. To address this issue, we have formulated image registration with tumors as a constraint problem that preserves tumor volumes while maximizing image similarity in other normal regions. Our proposed strategy involves a two-stage process. In the first stage, we use similarity-based registration to identify potential tumor regions by their volume change, generating a soft tumor mask accordingly. In the second stage, we propose a volume-preserving registration with a novel adaptive volume-preserving loss that penalizes the change in size adaptively based on the masks calculated from the previous stage. 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Red boxes represent the location of tumors in the moving image before warped. In image registration with tumors, similarity-based registration typically leads to significant alterations in tumor size while our volume-preserving registration is capable of preserving tumor anatomy." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 433, + 419, + 530, + 516 + ], + "blocks": [ + { + "bbox": [ + 440, + 411, + 523, + 419 + ], + "lines": [ + { + "bbox": [ + 440, + 411, + 523, + 419 + ], + "spans": [ + { + "bbox": [ + 440, + 411, + 523, + 419 + ], + "type": "text", + "content": "Similarity-Based Registration" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 433, + 419, + 530, + 516 + ], + "lines": [ + { + "bbox": [ + 433, + 419, + 530, + 516 + ], + "spans": [ + { + "bbox": [ + 433, + 419, + 530, + 516 + ], + "type": "image", + "image_path": "cf51c67221ba2f991df800d0691c3d451ed0df7e8b666712eb207107aaa1d580.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 436, + 520, + 527, + 529 + ], + "lines": [ + { + "bbox": [ + 436, + 520, + 527, + 529 + ], + "spans": [ + { + "bbox": [ + 436, + 520, + 527, + 529 + ], + "type": "text", + "content": "Volume-Preserving Registration" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 594, + 546, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 689 + ], + "type": "text", + "content": "Deformable image registration is a fundamental task that estimates non-linear spatial correspondences between two images. It is useful for medical image studies that involve 3D images of organs or tissues, such as MR brain scans and CT liver scans. Recently, a wide range of deep-learning-based methods are proposed in the field, with better performance and obvious speed-ups in inference time compared to the traditional registration methods [5, 38, 32, 14, 15]." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Currently, most of the learning-based methods [5, 38] train a registration model to achieve high similarity in either" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "text", + "content": "*Corresponding authors" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21208" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "image intensity [38, 5] or anatomy label maps [14]. While this is useful in various medical applications, such as atlas-based segmentation and image fusion [8], problem emerges, however, when studying images with tumors [4, 12, 24]. Tracking tumor growth is a core task in cancer treatment, which can be used to evaluate the outcomes of radiotherapy and chemotherapy, and plan optimal postoperative treatment [12]. The process requires registration to align the anatomy of images from different periods of the patient, while preserving tumor properties e.g., the size. Traditional models using regular registration have struggled to accomplish this task [12]. We have observed that this remains an issue for current learning-based methods, and a viable solution has yet to be proposed." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 241, + 289, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 241, + 289, + 458 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 289, + 458 + ], + "type": "text", + "content": "As shown in Figure 1, the volume of tumors significantly reduces when using popular unsupervised registration networks to align tumor images with atlas images. The issue is widespread since mainstream registration networks focus on optimizing the similarity between image pairs while ignoring tumor regions. Tumor regions often lack corresponding parts, and even for images of the same patient, the size and location of tumors may vary greatly. This can happen because tumors can change shape, size, location, or disappear over time. Therefore, in deformable settings, the size of tumors will change disproportionately to maximize the image similarity. This problem may be more severe when the registration network has better warping ability, leading to better performance in evaluations from previous works, as confirmed by our experiments in Section 4. The disproportionate change of tumor volume in deformable registration is lethal for clinical evaluation of tumor growth and greatly hinders the application of registration in clinics." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 460, + 289, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 289, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 289, + 687 + ], + "type": "text", + "content": "In this paper, we re-formulate the deformable registration problem as a constraint problem that preserves the properties of tumors in the original images, i.e., the shape and the size of the tumor, while maximizing image similarity in non-tumor regions. For instance, in tumor image registration with atlas, besides the alignment of anatomical structures, the tumor should have similar morphing behaviours as its surrounding organs, i.e., the size of it should change proportionally to the size of the organ. However, this poses two major challenges for our strategy. Firstly, due to the limited availability of annotated data, most existing registration methods resort to unsupervised learning. Therefore, a key question is how to identify tumor regions in the unsupervised setting. Second, after the tumor regions have been identified, the challenge still remains of preserving tumor volumes while simultaneously maximizing similarity in other regions. Finding a way to balance these two competing objectives is crucial for achieving effective tumor image registration." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "To tackle the challenges, we propose a novel two-stage strategy that operates in an unsupervised manner. In the first" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 276 + ], + "type": "text", + "content": "stage, we leverage a similarity-based registration network to identify regions that undergo excessive volume change during registration. Such regions are indicative of the presence of tumors, as tumors tend to exhibit larger changes in volume due to a lack of correspondence between image pairs. The outcome of the first stage is a soft tumor mask that distinguishes normal and possible tumor regions. In the second stage, we introduce an adaptive volume-preserving loss to train a volume-preserving registration network. Based on the soft tumor mask obtained from the first stage, this loss is designed to adaptively penalize volume changes in different regions of the image. Possible tumor regions are assigned larger loss weights, and similarity loss weights are adjusted accordingly in the opposite direction. The application of the adaptive volume-preserving loss effectively balances similarity and volume preservation in different parts of the image." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 277, + 547, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 547, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 547, + 443 + ], + "type": "text", + "content": "It should be noted that the soft masks from stage one do not need to be highly accurate to achieve desirable results, as our stage two is robust, which is demonstrated by our ablation experiments in section 4. In addition to evaluating the robustness of our proposed strategy on various datasets and frameworks, including CNN and transformer, as well as different types of imaging data such as brain and abdominal, MRI and CT images, we have also introduced the Square Tumor Size Ratio (STSR) metric to measure the preservation of tumor volumes. The results demonstrate that our methods achieve comparable warping performance metrics such as Dice coefficient and average landmark distances while effectively preserving tumor properties as measured by the STSR." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 445, + 547, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 547, + 588 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 547, + 588 + ], + "type": "text", + "content": "To conclude, our contribution includes: (1) We have reformulated image registration with tumors as a constraint problem that preserves tumor volumes while maximizes image similarity in other normal regions. (2) We have designed a two-stage process that the first stage performs regular registration to estimate tumor regions, and the second stage performs volume-preserving registration on tumor regions based on the adaptive volume-preserving loss. (3) We have proposed the STSR metric to measure the preservation of tumor volumes in registration, and have evaluated the effectiveness of our strategy on different network architectures and various datasets." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 601, + 392, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 601, + 392, + 615 + ], + "spans": [ + { + "bbox": [ + 306, + 601, + 392, + 615 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 622, + 545, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 622, + 545, + 646 + ], + "spans": [ + { + "bbox": [ + 306, + 622, + 545, + 646 + ], + "type": "text", + "content": "2.1. Learning-Based Deformable Image Registration" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "Compared to conventional registration methods, deep networks have achieved remarkable registration accuracy and speed using various network structures, i.e., CNN and Transformer, in applications like atlas-image registration [29, 7, 16, 6, 32, 38, 5, 14, 15, 8]. They generally" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21209" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "type": "text", + "content": "adopts unsupervised learning, utilizing image similarity on either image intensities [29, 7, 6, 38] or synthesized label maps [14, 15] as well as smoothness regularization to supervise the registration network [7, 6, 14, 15, 38]. Advancements are often made through the introduction of novel regularization such as cycle consistency [16] and geometry preservation [1], or through innovative network structures like multi-scale architectures [28, 23]. However, existing methods do not adequately consider cases where tumors exist. Tumors often have no corresponding part between image pairs, and therefore, optimizing for similarity can excessively change their volumes, which limits the application of registration networks in critical clinical applications like cancer treatment. To the best of our knowledge, we are the first to study this problem with learning-based methods and propose a metric to measure volume preservation specifically for tumors." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 284, + 281, + 298 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 284, + 281, + 298 + ], + "spans": [ + { + "bbox": [ + 47, + 284, + 281, + 298 + ], + "type": "text", + "content": "2.2. Deformable Image Registration with Tumors" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 303, + 289, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 303, + 289, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 289, + 434 + ], + "type": "text", + "content": "Conventional registration models often resolve registering images with tumor by (1) excluding the similarity measure on tumors [11, 18], which requires either massive manual segmentation [11] or initial seed to explicitly model tumor-growth [12, 18]. (2) jointly segmenting and registering images [9], which is time-consuming since it need to iteratively detect dissimilarity in image intensities and perform resection and retraction. (3) reconstructing quasi-normal images from pathological ones [13, 19], which is also slow since the reconstruction need to be iteratively improved." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 435, + 289, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 289, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 289, + 602 + ], + "type": "text", + "content": "Recently, learning-based methods for registration with tumors [24, 21, 33] are proposed for the release of BraTS-Reg dataset [4]. They aim to improve the spatial correspondence for non-tumor regions, thus either directly annotates landmarks to supervise registration [21] or introducing invertibility of the registration to mask non-inverted regions and ensure high correspondence in others [24, 33]. However, these methods assume the absence of tumors in one image of the registered pair, which may not be applicable in practical applications where we need to compare two tumor images from one patient to track the tumor growth. In this scenario, invertibility in tumors is still possible and thus, it is essential to consider the preservation of tumor properties during registration." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 611, + 236, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 236, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 236, + 624 + ], + "type": "text", + "content": "2.3. Unsupervised Tumor Segmentation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 630, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 289, + 715 + ], + "type": "text", + "content": "To ensure the preservation of tumor volumes during registration, it is crucial to first identify the locations of tumors. Current deep learning methods have made remarkable progress in unsupervised tumor segmentation, as demonstrated by recent studies [34, 35, 20]. These methods typically use GAN models or simulate tumors on healthy images to generate synthetic data, which is then used to" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "content": "train the segmentation network. Although the well-trained network can achieve high segmentation accuracy, it often requires complex training strategies and additional models or testing steps to achieve the desired performance, as noted in recent research [35, 20]. However, in our approach, we do not rely on sophisticated segmentation methods to accurately segment tumors. Instead, our experiments, as presented in Section 4, demonstrate that our tumor mask estimation is sufficient for our strategy to learn a volume-preserving registration for tumors." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 198, + 547, + 222 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 198, + 547, + 222 + ], + "spans": [ + { + "bbox": [ + 305, + 198, + 547, + 222 + ], + "type": "text", + "content": "2.4. Volume-Preserving Deformable Image Registration" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 228, + 547, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 547, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 547, + 433 + ], + "type": "text", + "content": "Volume-preserving registration has been studied extensively to improve the accuracy of anatomical registration. In pulmonary CT image registration, for example, tissue intensity changes between inspiration and expiration phases can be utilized as prior knowledge, and adding a volume-preserving constraint has been shown to be effective [31, 37]. In other cases, such as when soft tissues are incompressible or when images come from different modalities, a volume-preserving constraint can also serve as a helpful regularization [25, 30]. Our work, instead, focuses on using volume-preservation to maintain the properties of tumors during image registration. The proposed strategy imposes this constraint adaptively on different parts of the images in order to preserve tumor volumes and ensure anatomical accuracy, while previous works have either preserved volumes for the entire images [25, 30] or can use simple methods to determine the regions to be preserved [31, 37]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 441, + 389, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 441, + 389, + 455 + ], + "spans": [ + { + "bbox": [ + 305, + 441, + 389, + 455 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 460, + 392, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 460, + 392, + 472 + ], + "spans": [ + { + "bbox": [ + 306, + 460, + 392, + 472 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "text", + "content": "Problem Setting. Given a moving image " + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "inline_equation", + "content": "I_{m}" + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "text", + "content": " and fixed image " + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "inline_equation", + "content": "I_{f}" + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "text", + "content": " defined over " + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "text", + "content": "-dimensional (d=3 in this paper) space " + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "text", + "content": ", deformable image registration aims to find a dense deformation filed " + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "inline_equation", + "content": "\\phi : \\Omega \\to \\Omega" + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "text", + "content": ". This field warps " + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "inline_equation", + "content": "I_{m}" + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "text", + "content": ", meaning it projects every pixel position " + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "text", + "content": " in warped image " + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "inline_equation", + "content": "I_{w}" + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "inline_equation", + "content": "I_{m}" + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "text", + "content": " to achieve alignment with " + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "inline_equation", + "content": "I_{f}" + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "text", + "content": ". In this paper, the task is to construct a registration network " + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "inline_equation", + "content": "F_{\\theta}" + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "text", + "content": " that takes input " + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "inline_equation", + "content": "I_{m}, I_{f}" + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "text", + "content": " to predict the deformation field " + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 479, + 547, + 575 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 396, + 581, + 545, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 396, + 581, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 396, + 581, + 545, + 594 + ], + "type": "interline_equation", + "content": "\\phi = F _ {\\theta} \\left(I _ {m}, I _ {f}\\right) \\tag {1}", + "image_path": "c37825c01cdf7a2ae7c6d5d2ca109a85bf88ffad97b99fe50cc05f9e2f4a1bdf.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 377, + 596, + 545, + 609 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 377, + 596, + 545, + 609 + ], + "spans": [ + { + "bbox": [ + 377, + 596, + 545, + 609 + ], + "type": "interline_equation", + "content": "I _ {w} (x) = I _ {m} (\\phi (x) + x) \\tag {2}", + "image_path": "fb0108d4a4bb56e3d6994175bd8fcf446fc47a4f963175de900f49065d35569e.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 391, + 611, + 545, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 391, + 611, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 391, + 611, + 545, + 624 + ], + "type": "interline_equation", + "content": "I _ {w} \\sim I _ {f} \\tag {3}", + "image_path": "55531d3c43715511bce09c14c9730a0f2b4754da1c1340337545a61aa77b7d7c.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": "Evaluation Criteria. In general, a successful deformable image registration involves accurately aligning the anatomical structures while also ensuring a smooth deformation field. This is often achieved through the use of similarity-based objectives and regularization methods that promote smoothness. However, in the context of image registration with tumors, simply aligning the anatomy is not" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21210" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 76, + 509, + 315 + ], + "blocks": [ + { + "bbox": [ + 75, + 76, + 509, + 315 + ], + "lines": [ + { + "bbox": [ + 75, + 76, + 509, + 315 + ], + "spans": [ + { + "bbox": [ + 75, + 76, + 509, + 315 + ], + "type": "image", + "image_path": "5cb5a1782ab687053e0200bb173bbb0a88140e957c50a252f9b6032916461fd0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 320, + 547, + 376 + ], + "lines": [ + { + "bbox": [ + 46, + 320, + 547, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 320, + 547, + 376 + ], + "type": "text", + "content": "Figure 2. Main Framework. Our strategy consists of two stages. In the first stage, a soft mask indicating tumor regions is estimated by analyzing the Jacobian matrix of the deformation field obtained by a registration network pre-trained on similarity loss. In the second stage, the soft mask is used to guide the calculation of both volume-preserving and similarity losses for training the volume-preserving registration network. This deformation field estimated by the stage two ensures that both the image similarity and the preservation of tumor sizes." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "text", + "content": "sufficient. Preserving the volume of the tumors is crucial for accurately tracking tumor growth, as previously discussed. To be specific, given the moving image " + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "inline_equation", + "content": "I_{m}" + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "text", + "content": " with the tumor " + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "inline_equation", + "content": "T_{m}" + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "text", + "content": " and its surrounding organ " + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "inline_equation", + "content": "O_{m}" + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "text", + "content": " and the warped moving image " + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "inline_equation", + "content": "I_{w}" + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "inline_equation", + "content": "T_{w}" + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "inline_equation", + "content": "O_{w}" + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "text", + "content": ", the morphing of tumor " + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "inline_equation", + "content": "T_{m}" + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "text", + "content": " should be similar to that of " + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "inline_equation", + "content": "O_{m}" + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "text", + "content": ". Thus in respect of the volume preservation, the change of tumor size " + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "inline_equation", + "content": "|T_{m}|" + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "text", + "content": " should be proportionate to the change of the containing organ " + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "inline_equation", + "content": "|O_{m}|" + }, + { + "bbox": [ + 46, + 388, + 288, + 495 + ], + "type": "text", + "content": ", i.e.:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 117, + 502, + 287, + 528 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 502, + 287, + 528 + ], + "spans": [ + { + "bbox": [ + 117, + 502, + 287, + 528 + ], + "type": "interline_equation", + "content": "T S R \\left(I _ {m}\\right) = \\frac {\\left| T _ {m} \\right|}{\\left| O _ {m} \\right|} \\tag {4}", + "image_path": "5958472b32eaecbf90e385929bf3be2bfe3f8122a2e1099aef97589dd1b3e539.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 118, + 529, + 287, + 544 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 529, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 118, + 529, + 287, + 544 + ], + "type": "interline_equation", + "content": "T S R \\left(I _ {m}\\right) \\approx T S R \\left(I _ {w}\\right) \\tag {5}", + "image_path": "3b1846e3f565216e314bdc5c1f2c82159969edb190f8bc791244c7ed431fce0a.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 553, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 553, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 47, + 553, + 287, + 605 + ], + "type": "text", + "content": "We therefore define the tumor size ratio (TSR) as " + }, + { + "bbox": [ + 47, + 553, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\frac{|T|}{|O|}" + }, + { + "bbox": [ + 47, + 553, + 287, + 605 + ], + "type": "text", + "content": ", which should be preserved after registration, and the re-formulated registration objective is now maximizing image similarity while preserving the volumes of tumors, i.e., the TSR." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 611, + 147, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 147, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 147, + 624 + ], + "type": "text", + "content": "3.2. Overall Strategy" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "The proposed strategy consists of two stages, as shown in Figure 2. The first stage estimates potential tumor regions and generates a soft mask for them. This is done by analyzing volume changes, specifically the Jacobian matrix, in the deformation field obtained by an existing similarity-based registration network. As tumor regions tend to undergo excessive volume change during registration, they can" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 388, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 495 + ], + "type": "text", + "content": "be identified through this analysis. In the second stage, we perform volume-preserving registration for tumors using an adaptive volume-preserving loss. This loss is designed to guide the volume-preserving process effectively and is associated with the tumor masks estimated in the first stage. Through the assignment of distinct weights to diverse regions, including both normal and tumor regions, it is possible to preserve tumor volumes while also ensuring a high degree of similarity in other regions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 545, + 532 + ], + "type": "text", + "content": "Importantly, our strategy can be applied to nearly any learning-based registration network without introducing any additional modules." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 549, + 541, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 549, + 541, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 549, + 541, + 562 + ], + "type": "text", + "content": "3.2.1 Stage 1: Unsupervised Tumor Mask Estimation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 569, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 545, + 664 + ], + "type": "text", + "content": "Following previous works [5, 6, 38], we first train a similarity-based registration network " + }, + { + "bbox": [ + 304, + 569, + 545, + 664 + ], + "type": "inline_equation", + "content": "F_{\\theta_1}" + }, + { + "bbox": [ + 304, + 569, + 545, + 664 + ], + "type": "text", + "content": " with parameters " + }, + { + "bbox": [ + 304, + 569, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\theta_1" + }, + { + "bbox": [ + 304, + 569, + 545, + 664 + ], + "type": "text", + "content": " and fix its parameters. As shown in Figure 1, tumors in medical images can be detected by analyzing the change in volume through similarity-based registration. Our goal is to utilize this characteristic to facilitate the unsupervised estimation of the tumor mask for volume preservation during registration." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "To determine the volume change at voxel " + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": ", we calculate the determinant of the Jacobian matrix of the deformation field " + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "inline_equation", + "content": "(J_{\\theta})" + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": " with model parameter " + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": ". Our objective is to ensure that the volume change in each point of the tumor region is" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21211" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "text", + "content": "similar to the volume change of the organ, which is an indicator of the organ's size change (as shown in Equation 6). To measure the distance between the two, we calculate the number of times one ratio exceeds another, denoted as " + }, + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "D_{\\theta}" + }, + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "text", + "content": ", using Equations 8 and 7 where " + }, + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "D_{\\theta}'(x)" + }, + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "text", + "content": " represents the relative volume change of voxel " + }, + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "text", + "content": " with respect to organ areas." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 159, + 287, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 159, + 287, + 186 + ], + "spans": [ + { + "bbox": [ + 59, + 159, + 287, + 186 + ], + "type": "interline_equation", + "content": "\\frac {\\left| T _ {w} \\right|}{\\left| O _ {w} \\right|} / \\frac {\\left| T _ {m} \\right|}{\\left| O _ {m} \\right|} \\approx 1 \\Rightarrow \\frac {\\left| T _ {w} \\right|}{\\left| T _ {m} \\right|} / \\frac {\\left| O _ {w} \\right|}{\\left| O _ {m} \\right|} \\approx 1, \\text {f r o m E q .} 5, \\tag {6}", + "image_path": "a42d399e3090eda559528816b8a39744010ed09445906a568e7f97a637f60709.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 102, + 186, + 287, + 213 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 186, + 287, + 213 + ], + "spans": [ + { + "bbox": [ + 102, + 186, + 287, + 213 + ], + "type": "interline_equation", + "content": "D _ {\\theta} ^ {\\prime} (x) = \\left| J _ {\\theta (x)} \\right| / \\frac {\\left| O _ {w} \\right|}{\\left| O _ {m} \\right|}, x \\in \\Omega , \\tag {7}", + "image_path": "bb5496df1adebf58f93b2e574ed756c00a173587f4e7236f7163d5eebcde1af7.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 102, + 214, + 287, + 228 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 214, + 287, + 228 + ], + "spans": [ + { + "bbox": [ + 102, + 214, + 287, + 228 + ], + "type": "interline_equation", + "content": "D _ {\\theta} (x) = \\max \\left(D _ {\\theta} ^ {\\prime} (x), 1 / D _ {\\theta} ^ {\\prime} (x)\\right), \\tag {8}", + "image_path": "d0aa55910ca095dcf146005349191bd4f03f0bb7dbe37e8f9407c72cb879a548.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 234, + 287, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 234, + 287, + 341 + ], + "spans": [ + { + "bbox": [ + 47, + 234, + 287, + 341 + ], + "type": "text", + "content": "In practice, we estimate the organ masks " + }, + { + "bbox": [ + 47, + 234, + 287, + 341 + ], + "type": "inline_equation", + "content": "O_{m}" + }, + { + "bbox": [ + 47, + 234, + 287, + 341 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 234, + 287, + 341 + ], + "type": "inline_equation", + "content": "O_{w}" + }, + { + "bbox": [ + 47, + 234, + 287, + 341 + ], + "type": "text", + "content": " by warping a reference image with the ground truth (GT) organ segmentation. We randomly select the reference image from the training dataset, and the choice of reference image does not significantly impact the results because registration for organs achieves high accuracy, as evidenced by the dice value in table 1. By warping the reference image, we obtain the organ segmentation for the moving image " + }, + { + "bbox": [ + 47, + 234, + 287, + 341 + ], + "type": "inline_equation", + "content": "O_{m}" + }, + { + "bbox": [ + 47, + 234, + 287, + 341 + ], + "type": "text", + "content": ". We then calculate the organ segmentation for the warped image " + }, + { + "bbox": [ + 47, + 234, + 287, + 341 + ], + "type": "inline_equation", + "content": "O_{w}" + }, + { + "bbox": [ + 47, + 234, + 287, + 341 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 342, + 287, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 342, + 287, + 377 + ], + "spans": [ + { + "bbox": [ + 47, + 342, + 287, + 377 + ], + "type": "text", + "content": "To obtain a soft tumor mask " + }, + { + "bbox": [ + 47, + 342, + 287, + 377 + ], + "type": "inline_equation", + "content": "STM" + }, + { + "bbox": [ + 47, + 342, + 287, + 377 + ], + "type": "text", + "content": " from the distance " + }, + { + "bbox": [ + 47, + 342, + 287, + 377 + ], + "type": "inline_equation", + "content": "D_{\\theta_1}" + }, + { + "bbox": [ + 47, + 342, + 287, + 377 + ], + "type": "text", + "content": " defined in 8, we use a transformation function " + }, + { + "bbox": [ + 47, + 342, + 287, + 377 + ], + "type": "inline_equation", + "content": "Tr" + }, + { + "bbox": [ + 47, + 342, + 287, + 377 + ], + "type": "text", + "content": ". This function can be formulated as the following equation:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 113, + 384, + 287, + 396 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 384, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 113, + 384, + 287, + 396 + ], + "type": "interline_equation", + "content": "S T M (x) = T r \\left(D _ {\\theta_ {1}} (x)\\right), \\tag {9}", + "image_path": "16b65e58c0bf98da22710b44cbee435fcffed8e7d82713696bb5b5b153f5cc55.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 403, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 403, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 47, + 403, + 287, + 533 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 47, + 403, + 287, + 533 + ], + "type": "inline_equation", + "content": "D_{\\theta_1}(x)" + }, + { + "bbox": [ + 47, + 403, + 287, + 533 + ], + "type": "text", + "content": " represents the distance value at pixel " + }, + { + "bbox": [ + 47, + 403, + 287, + 533 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 403, + 287, + 533 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 403, + 287, + 533 + ], + "type": "inline_equation", + "content": "Tr" + }, + { + "bbox": [ + 47, + 403, + 287, + 533 + ], + "type": "text", + "content": " transforms values from the range of " + }, + { + "bbox": [ + 47, + 403, + 287, + 533 + ], + "type": "inline_equation", + "content": "[0,\\infty]" + }, + { + "bbox": [ + 47, + 403, + 287, + 533 + ], + "type": "text", + "content": " to the range of " + }, + { + "bbox": [ + 47, + 403, + 287, + 533 + ], + "type": "inline_equation", + "content": "[0,1]" + }, + { + "bbox": [ + 47, + 403, + 287, + 533 + ], + "type": "text", + "content": ". A value of 1 indicates the presence of a tumor, while a value of 0 indicates a normal region. In practical implementation, we use " + }, + { + "bbox": [ + 47, + 403, + 287, + 533 + ], + "type": "inline_equation", + "content": "Tr(x) = \\text{Sign}(5 \\cdot (x - 1.5))" + }, + { + "bbox": [ + 47, + 403, + 287, + 533 + ], + "type": "text", + "content": " since the sigmoid function is widely adopted for converting values to the range of " + }, + { + "bbox": [ + 47, + 403, + 287, + 533 + ], + "type": "inline_equation", + "content": "[0,1]" + }, + { + "bbox": [ + 47, + 403, + 287, + 533 + ], + "type": "text", + "content": " and to our experience, the size of tumor regions averagely changes around 1.5 times. However, the choice of transformation functions is not exclusive, as demonstrated in our experiments in Section 4. We also set the regions outside the organ mask to 0." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 534, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 534, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 534, + 288, + 714 + ], + "type": "text", + "content": "We observed that some normal regions, particularly those close to the organ boundary, may also exhibit some volume changes after registration. As a result, these regions may be incorrectly included in the tumor mask, as shown in Figure 3 (a). To address this issue, we implemented a preregistration step to first align the edges and exclude volume changes caused by edge alignment. Specifically, in the preregistration step, we applied a bilateral filter to the moving image, which preserves the edges while smoothing the interior regions. We then used the registration network to register the filtered moving image with the fixed image in order to align their edges. After this, an unfiltered warped image was obtained by spatially transforming the unfiltered moving image with the deformation field. The second registration process was then performed on the unfiltered warped" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 322, + 70, + 420, + 167 + ], + "blocks": [ + { + "bbox": [ + 322, + 70, + 420, + 167 + ], + "lines": [ + { + "bbox": [ + 322, + 70, + 420, + 167 + ], + "spans": [ + { + "bbox": [ + 322, + 70, + 420, + 167 + ], + "type": "image", + "image_path": "ae5b9c79bfc3f87b3cbe338bdb6f8cec305e153515e9eefa29531f91634fa745.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 343, + 171, + 389, + 179 + ], + "lines": [ + { + "bbox": [ + 343, + 171, + 389, + 179 + ], + "spans": [ + { + "bbox": [ + 343, + 171, + 389, + 179 + ], + "type": "text", + "content": "(a)Tumor Mask" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 432, + 70, + 531, + 167 + ], + "blocks": [ + { + "bbox": [ + 432, + 70, + 531, + 167 + ], + "lines": [ + { + "bbox": [ + 432, + 70, + 531, + 167 + ], + "spans": [ + { + "bbox": [ + 432, + 70, + 531, + 167 + ], + "type": "image", + "image_path": "ee6ad0dfa4d53dd393bd7326b429ac9e80ca121224703f18d3a870c56fd5e7a6.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 436, + 171, + 541, + 180 + ], + "lines": [ + { + "bbox": [ + 436, + 171, + 541, + 180 + ], + "spans": [ + { + "bbox": [ + 436, + 171, + 541, + 180 + ], + "type": "text", + "content": "(b)Tumor Mask after pre-registration" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 190, + 545, + 246 + ], + "lines": [ + { + "bbox": [ + 305, + 190, + 545, + 246 + ], + "spans": [ + { + "bbox": [ + 305, + 190, + 545, + 246 + ], + "type": "text", + "content": "Figure 3. Visualization of the soft tumor mask. (a) is the estimated soft tumor mask without pre-registration and (b) is the one with pre-registration. The gray colors with intensity variations denote the soft mask, while the green and red colors represent the ground truth segmentation for the liver and tumors, respectively." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 257, + 545, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 257, + 545, + 317 + ], + "spans": [ + { + "bbox": [ + 305, + 257, + 545, + 317 + ], + "type": "text", + "content": "image, which focused on the registration of interior regions and was able to accurately estimate a tumor mask, as shown in Figure 3 (b). Therefore, this pre-registration approach effectively selects the tumor regions while filtering out the non-tumor regions." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 336, + 545, + 359 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 336, + 545, + 359 + ], + "spans": [ + { + "bbox": [ + 306, + 336, + 545, + 359 + ], + "type": "text", + "content": "3.2.2 Stage 2: Volume-Preserving Registration for Tumors" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 369, + 545, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 369, + 545, + 488 + ], + "spans": [ + { + "bbox": [ + 305, + 369, + 545, + 488 + ], + "type": "text", + "content": "After obtaining the soft tumor mask " + }, + { + "bbox": [ + 305, + 369, + 545, + 488 + ], + "type": "inline_equation", + "content": "STM" + }, + { + "bbox": [ + 305, + 369, + 545, + 488 + ], + "type": "text", + "content": ", we can adaptively select tumor regions to maintain the size ratio. Here, we define the volume-preserving loss directly as the distance " + }, + { + "bbox": [ + 305, + 369, + 545, + 488 + ], + "type": "inline_equation", + "content": "D_{\\theta_2}" + }, + { + "bbox": [ + 305, + 369, + 545, + 488 + ], + "type": "text", + "content": ", as shown in Equation 8. By minimizing the distance, we can achieve smaller volume changes, indicating better preservation of tumor volume. The volume-preserving loss is multiplied by the soft tumor mask. This ensures that the volume-preserving constraints are adaptively applied to the tumor regions and not to the normal regions, which can be formulated as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 351, + 498, + 545, + 527 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 498, + 545, + 527 + ], + "spans": [ + { + "bbox": [ + 351, + 498, + 545, + 527 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {V P}} = \\frac {1}{\\left| I _ {m} \\right|} \\sum_ {x \\in \\Omega} D _ {\\theta_ {2}} (x) \\cdot S T M (x), \\tag {10}", + "image_path": "bdec906f79a0b55af2b83b363453422e86b6550898396e7099e9bd4e370ac160.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 537, + 545, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 537, + 545, + 633 + ], + "spans": [ + { + "bbox": [ + 305, + 537, + 545, + 633 + ], + "type": "text", + "content": "Here, in the second stage, the registration network takes the soft tumor mask as input, which serves as an indicator for the regions that need to be preserved in terms of volume. We follow the similarity and registration loss formulation in [38], but we use a weighted similarity loss to adapt to the volume-preserving loss, where " + }, + { + "bbox": [ + 305, + 537, + 545, + 633 + ], + "type": "inline_equation", + "content": "Cov" + }, + { + "bbox": [ + 305, + 537, + 545, + 633 + ], + "type": "text", + "content": " is the covariance between two images " + }, + { + "bbox": [ + 305, + 537, + 545, + 633 + ], + "type": "inline_equation", + "content": "I_1, I_2" + }, + { + "bbox": [ + 305, + 537, + 545, + 633 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 537, + 545, + 633 + ], + "type": "inline_equation", + "content": "\\hat{I}" + }, + { + "bbox": [ + 305, + 537, + 545, + 633 + ], + "type": "text", + "content": " is the mean of " + }, + { + "bbox": [ + 305, + 537, + 545, + 633 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 305, + 537, + 545, + 633 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 537, + 545, + 633 + ], + "type": "inline_equation", + "content": "Cov'" + }, + { + "bbox": [ + 305, + 537, + 545, + 633 + ], + "type": "text", + "content": " is the adapted version utilizing " + }, + { + "bbox": [ + 305, + 537, + 545, + 633 + ], + "type": "inline_equation", + "content": "STM" + }, + { + "bbox": [ + 305, + 537, + 545, + 633 + ], + "type": "text", + "content": " weight:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 314, + 654, + 545, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 654, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 314, + 654, + 545, + 682 + ], + "type": "interline_equation", + "content": "\\operatorname {C o v} ^ {\\prime} \\left[ I _ {1}, I _ {2} \\right] = \\frac {\\sum \\left(I _ {1} - \\hat {I _ {1}}\\right) \\left(I _ {2} - \\hat {I _ {2}}\\right) (1 - S T M)}{\\sum (1 - S T M)}, \\tag {11}", + "image_path": "45b073ef9ab8f6d45b0ec1e7b58ad890bc84fe0dfa3c4a85c4a0a4be918b2d54.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 325, + 683, + 545, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 683, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 325, + 683, + 545, + 712 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {w} - \\mathrm {s i m}} (x) = \\frac {\\operatorname {C o v} ^ {\\prime} \\left[ I _ {w} , I _ {f} \\right]}{\\sqrt {\\operatorname {C o v} \\left[ I _ {w} , I _ {w} \\right] \\operatorname {C o v} \\left[ I _ {f} , I _ {f} \\right]}}, \\tag {12}", + "image_path": "24f06a2fc64e5decdc1f0cc39ad925c8bec242ecc23889684b51ce07204e1a18.jpg" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21212" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 249, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 249, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 249, + 84 + ], + "type": "text", + "content": "Therefore, the training loss of the second stage is:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 95, + 95, + 287, + 107 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 95, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 95, + 95, + 287, + 107 + ], + "type": "interline_equation", + "content": "L = L _ {\\mathrm {w} \\text {- s i m}} + \\alpha_ {1} \\cdot L _ {\\mathrm {V P}} + \\alpha_ {2} \\cdot L _ {\\mathrm {r e g}}, \\tag {13}", + "image_path": "665b6849f10f3a52407f096ec1f95ad483668d49d5552cbb511cde6ba7fb9190.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 117, + 287, + 165 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 117, + 287, + 165 + ], + "spans": [ + { + "bbox": [ + 47, + 117, + 287, + 165 + ], + "type": "text", + "content": "where we use the smoothness regularization from Voxel-Morph [5] as " + }, + { + "bbox": [ + 47, + 117, + 287, + 165 + ], + "type": "inline_equation", + "content": "L_{reg}" + }, + { + "bbox": [ + 47, + 117, + 287, + 165 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 117, + 287, + 165 + ], + "type": "inline_equation", + "content": "\\alpha_{1}" + }, + { + "bbox": [ + 47, + 117, + 287, + 165 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 117, + 287, + 165 + ], + "type": "inline_equation", + "content": "\\alpha_{2}" + }, + { + "bbox": [ + 47, + 117, + 287, + 165 + ], + "type": "text", + "content": " as hyperparameters to control the relative importance of the volume-preserving loss and the regularization loss." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 176, + 128, + 190 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 176, + 128, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 176, + 128, + 190 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 196, + 173, + 209 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 196, + 173, + 209 + ], + "spans": [ + { + "bbox": [ + 47, + 196, + 173, + 209 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 215, + 287, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 215, + 287, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 287, + 346 + ], + "type": "text", + "content": "Implementation. Following the implementation of Recursive Cascaded Network (RCN) [38], we employed PyTorch and utilized the same similarity loss and regularization losses (for affine and deformable, respectively) for baseline methods. The weight of the volume-preserving losses is set to 0.1 while the weights of similarity loss is 1 and regularization loss is 0.1. Models were trained on one NVIDIA GeForce RTX 3090 GPU with a batch size of 4. During the training stage, we used the Adam optimizer [36] and ran for a total of 5 epochs, with 20000 iterations in each epoch. The learning rate was set to " + }, + { + "bbox": [ + 46, + 215, + 287, + 346 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 46, + 215, + 287, + 346 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 370, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 370, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 370, + 287, + 574 + ], + "type": "text", + "content": "Baselines. We re-implemented our strategy on four SOTA learning-based models that have distinct network architectures: 1) recursive cascaded network with VTN base network (VTN) [38], which stacks CNN networks to achieve higher registration accuracy; 2) VoxelMorph [5], which is a widely used CNN network that utilize stationary vector field to register images; 3) TransMorph [6], which is a well-performed hybrid Transformer-ConvNet network; 4) LapIRN [23], which is a Laplacian Pyramid network designed to operate in a coarse-to-fine manner. We fit these learning-based networks into our strategy with minor efforts and achieve good performance. Additionally, we compare our proposed method with two state-of-the-art traditional methods for deformable image registration, SyN [2] (integrated in ANTs [3] with the affine stage) and B-spline [26] (integrated in Elastix [17] with the affine stage) following [38]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 574, + 287, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 287, + 646 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 287, + 646 + ], + "type": "text", + "content": "Evaluation Metrics. The evaluation of the proposed strategy is composed of five metrics: Dice score, landmark distance to measure the anatomical alignment, and Square Tumor Size Ratio metric to measure the volume preservation of tumors. More specifically, the Dice score is calculated using the following formula:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 110, + 654, + 287, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 654, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 110, + 654, + 287, + 681 + ], + "type": "interline_equation", + "content": "D i c e \\left(I _ {1}, I _ {2}\\right) = \\frac {2 \\left| I _ {1} \\cap I _ {2} \\right|}{\\left| I _ {1} \\right| + \\left| I _ {2} \\right|}, \\tag {14}", + "image_path": "c2ccf2feb5c30d28ef366771ef5588a9bcc825ebaf202e71d89df37dc4e4338c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Additionally, we also use landmark annotations to measure the anatomical alignment between the warped image and" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": "the fixed image. We calculate the average distance between the fixed image's landmarks and the warped landmarks of the moving image, as also introduced in RCN [38]. To quantify the diffeomorphism and smoothness of the deformation fields, we followed the methodology of previous works such as [7, 6, 39]. Here, two metrics were employed: the average percentage of voxels with non-positive Jacobian determinant " + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "(|J_{\\theta}| < 0(\\%))" + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": " in the deformation fields, and the standard deviation of the Jacobian determinant " + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "(Std.|J_{\\theta}|)" + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 193, + 545, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 193, + 545, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 193, + 545, + 240 + ], + "type": "text", + "content": "To measure the volume preservation of tumors, we propose Square Tumor Size Ratio metric (STSR), which is calculated from the change of tumor size ratio (TSR) defined in Equation 4:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 324, + 251, + 545, + 277 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 251, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 324, + 251, + 545, + 277 + ], + "type": "interline_equation", + "content": "S T S R = \\max \\left(\\left(\\frac {T S R \\left(I _ {m}\\right)}{T S R \\left(I _ {w}\\right)}\\right), \\left(\\frac {T S R \\left(I _ {w}\\right)}{T S R \\left(I _ {m}\\right)}\\right)\\right) ^ {2}, \\tag {15}", + "image_path": "6b82375580216496a8c154705d528a7f6209ab96b34347ca30e898039528d86d.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 287, + 545, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 287, + 545, + 370 + ], + "spans": [ + { + "bbox": [ + 304, + 287, + 545, + 370 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 304, + 287, + 545, + 370 + ], + "type": "inline_equation", + "content": "I_{m}, I_{w}" + }, + { + "bbox": [ + 304, + 287, + 545, + 370 + ], + "type": "text", + "content": " refers to the moving image and the warped moving image. The square term is used o account for larger changes in tumor volumes, which can have a more significant impact on the accuracy of tumor growth estimation in clinical applications. By utilizing the STSR metric, we are able to accurately evaluate the performance of our proposed strategy." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 372, + 545, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 372, + 545, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 372, + 545, + 431 + ], + "type": "text", + "content": "Preprocessing. In our study, we follow standard preprocessing steps as outlined in VTN [39] and VoxelMorph [5]. The raw scans are resampled into " + }, + { + "bbox": [ + 304, + 372, + 545, + 431 + ], + "type": "inline_equation", + "content": "128 \\times 128 \\times 128" + }, + { + "bbox": [ + 304, + 372, + 545, + 431 + ], + "type": "text", + "content": " voxels after cropping any unnecessary areas around the target object." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 442, + 368, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 442, + 368, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 442, + 368, + 453 + ], + "type": "text", + "content": "4.2. Datasets" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 461, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 616 + ], + "type": "text", + "content": "Training. To train our model, we utilized two publicly available datasets: (1) LiTS17 [10]: The LiTS dataset comprises 201 CT scans that were acquired using various CT scanners and devices. The resolution of the images in this dataset ranges from " + }, + { + "bbox": [ + 304, + 461, + 545, + 616 + ], + "type": "inline_equation", + "content": "0.56\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 461, + 545, + 616 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 461, + 545, + 616 + ], + "type": "inline_equation", + "content": "1.0\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 461, + 545, + 616 + ], + "type": "text", + "content": " in the axial direction and from " + }, + { + "bbox": [ + 304, + 461, + 545, + 616 + ], + "type": "inline_equation", + "content": "0.45\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 461, + 545, + 616 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 461, + 545, + 616 + ], + "type": "inline_equation", + "content": "6.0\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 461, + 545, + 616 + ], + "type": "text", + "content": " in the " + }, + { + "bbox": [ + 304, + 461, + 545, + 616 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 461, + 545, + 616 + ], + "type": "text", + "content": " direction. The number of slices in the " + }, + { + "bbox": [ + 304, + 461, + 545, + 616 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 461, + 545, + 616 + ], + "type": "text", + "content": " direction ranges from 42 to 1026. (2) BraTS20 [22]: It consists of 369 MRI scans of brain tumors, each with ground truth segmentation of four different tumor components. For training our neural network, we utilized the T1ce modality and treated all four components as tumors, while considering the entire brain as the surrounding organ." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Testing. For testing, we utilized a set of 10 cases of CT liver scans with metastatic tumors, and 10 MRI brain scans with metastatic tumors. The modality of MRI brain scans is T1ce. Each case included both pre- and post-treatment images of the same patients, resulting in a total of 20 scans for each set. 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Qualitative comparison of different volume-preserving (VP) methods trained on the Liver Tumor Segmentation (LiTS) dataset. The left side of the figure shows two sets of images: Fixed and Ground Truth (GT), and Moving and GT. The first row of the figure displays the warped moving image, while the second row illustrates the organ outlines in green and red for the moving and fixed images, respectively. The yellow overlay highlights the tumors. Our proposed volume-preserving (VP) method ensures the preservation of tumor volume while aligning the images, as demonstrated by reduced number of visible changes in tumor size. In the third row, the Jacobian matrix of the deformation field is visualized. The green and red lines represent the organ and tumor outlines, respectively. The white areas indicate a large Jacobian, which corresponds to a more significant change in volume. The method without volume-preserving loss demonstrates a larger white area in the tumor, indicating a greater volume change of tumor volume. The last row of the figure displays the deformation field. 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} + ], + "index": 31, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 502, + 267, + 516, + 272 + ], + "lines": [ + { + "bbox": [ + 502, + 267, + 516, + 272 + ], + "spans": [ + { + "bbox": [ + 502, + 267, + 516, + 272 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_caption" + } + ], + "index": 30 + }, + { + "type": "table", + "bbox": [ + 48, + 396, + 545, + 519 + ], + "blocks": [ + { + "bbox": [ + 48, + 396, + 545, + 519 + ], + "lines": [ + { + "bbox": [ + 48, + 396, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 48, + 396, + 545, + 519 + ], + "type": "table", + "html": "
NetworkMethodsLiTs17BraTS20
Dice ↑Lm. Dist ↓|Jθ| < 0(%) ↓Std. |Jθ| ↓STSR ↓Dice ↑Lm. Dist ↓|Jθ| < 0(%) ↓Std. |Jθ| ↓STSR ↓
SyN-0.85012.360.1920.2211.5640.95604.010.2760.2261.512
B-Spline-0.85314.220.0030.2881.3300.96014.510.0010.1711.622
VTNRegular0.91210.463.5452.0482.3300.97842.980.3960.7252.263
Ours0.90810.772.9561.1241.2600.97383.100.5960.2851.416
VXMRegular0.86012.624.1911.6991.7380.97013.560.0240.4481.929
Ours0.85712.431.6810.6911.2410.97413.600.0300.2261.463
TransMorphRegular0.85913.356.3771.9061.7850.97104.010.1640.4681.868
Ours0.85613.194.0840.8271.3020.97583.980.0190.1941.319
LapIRNRegular0.893310.235.3011.7882.3600.97503.403.0200.3011.889
Ours0.889310.554.1200.9881.6450.97433.360.0400.1051.224
", + "image_path": "b07572ddd504240b53b2bcfaf87deccec765aafe2247e6352494f7cd6c1d3954.jpg" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 520, + 545, + 563 + ], + "lines": [ + { + "bbox": [ + 46, + 520, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 545, + 563 + ], + "type": "text", + "content": "Table 1. Quantitative comparison with state-of-the-art registration methods. Our strategy was applied to two datasets, namely LiTS17 and BraTS20, and three network architectures In addition, five metrics were employed for the evaluation process. The results of the comparison indicate that our proposed strategy can be well generalized to other state-of-the-art methods to preserve tumor volumes while achieving comparable or better performance on other metrics." + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 34 + }, + { + "bbox": [ + 46, + 583, + 287, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 583, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 46, + 583, + 287, + 608 + ], + "type": "text", + "content": "Landmarks were also annotated by three experts in the field to evaluate the registration accuracy of our strategy." + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 47, + 620, + 132, + 632 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 620, + 132, + 632 + ], + "spans": [ + { + "bbox": [ + 47, + 620, + 132, + 632 + ], + "type": "text", + "content": "4.3. Main Results" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "type": "text", + "content": "Quantitative Comparison. In Table 1, we present a comprehensive comparison of our proposed strategy with two traditional methods and three learning-based methods with different network architectures (CNN, cascaded CNN and hybrid transformer-CNN). We compare the methods using a similarity-based manner (regular) following the settings" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 304, + 583, + 547, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 583, + 547, + 704 + ], + "spans": [ + { + "bbox": [ + 304, + 583, + 547, + 704 + ], + "type": "text", + "content": "in [38], as well as our volume-preserving manners. Our results demonstrate that our proposed strategy outperforms all other methods in terms of the STSR metrics, while achieving comparable results in Dice and Landmark Dist, and often better results in folding detection " + }, + { + "bbox": [ + 304, + 583, + 547, + 704 + ], + "type": "inline_equation", + "content": "(|J_{\\theta}| < 0)" + }, + { + "bbox": [ + 304, + 583, + 547, + 704 + ], + "type": "text", + "content": " and smoothness quality " + }, + { + "bbox": [ + 304, + 583, + 547, + 704 + ], + "type": "inline_equation", + "content": "(Std. |J_{\\theta}|)" + }, + { + "bbox": [ + 304, + 583, + 547, + 704 + ], + "type": "text", + "content": ". Furthermore, we observe that registration networks that achieve better performance in terms of previous metrics such as Dice tend to have worse performance in preserving tumor volumes (STSR). This observation highlights the need to balance these two objectives" + } + ] + } + ], + "index": 39 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21214" + } + ] + } + ], + "index": 40 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 63, + 70, + 531, + 258 + ], + "blocks": [ + { + "bbox": [ + 63, + 70, + 531, + 258 + ], + "lines": [ + { + "bbox": [ + 63, + 70, + 531, + 258 + ], + "spans": [ + { + "bbox": [ + 63, + 70, + 531, + 258 + ], + "type": "table", + "html": "
#NetworkUnsupervisedAdaptiveRegionLiTs17
Dice ↑Lm. Dist ↓|Jθ| < 0(%) ↓Std. |Jθ| ↓STSR ↓
1VTN✓--0.91210.463.5452.0482.330
2×--0.91410.223.2411.1651.648
3××Tumor0.91110.742.8831.0171.205
4✓×Organ0.90411.073.1941.0151.640
5✓✓Organ0.90810.772.9561.1241.260
6VXM✓--0.86012.624.1911.6991.738
7×--0.86312.221.6030.6911.417
8××Tumor0.85912.381.5670.6981.291
9✓×Organ0.85612.781.6350.6751.407
10✓✓Organ0.85712.431.6810.6911.241
11TransMorph✓--0.85913.356.3371.9061.785
12×--0.86313.104.9231.5401.540
13××Tumor0.85813.214.4010.8771.227
14✓×Organ0.84913.024.6510.8451.454
15✓✓Organ0.85613.194.0840.8271.302
", + "image_path": "5219a19dba0415b543f916c89125ddb38cd37e3049ede55a640d9c82564896d2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 48, + 259, + 545, + 302 + ], + "lines": [ + { + "bbox": [ + 48, + 259, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 48, + 259, + 545, + 302 + ], + "type": "text", + "content": "Table 2. Effectiveness of adaptive volume-preserving loss in unsupervised registration frameworks on LiTs17 dataset. Three networks, namely VTN in [38], VXM in [5], and TransMorph in [6], were applied. The methods used in the study were regular unsupervised (first row), weighted similarity loss only based on the ground truth (GT) mask (second row), volume-preserving loss based on GT(third row), volume-preserving loss on the whole organ based on estimation (fourth row), and on the tumor based on estimation (ours)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 312, + 203, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 312, + 203, + 323 + ], + "spans": [ + { + "bbox": [ + 48, + 312, + 203, + 323 + ], + "type": "text", + "content": "in order to achieve competitive results." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 324, + 286, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 324, + 286, + 538 + ], + "spans": [ + { + "bbox": [ + 48, + 324, + 286, + 538 + ], + "type": "text", + "content": "Qualitative Comparison. Figure 5 presents a qualitative comparison of our proposed strategy with different state-of-the-art methods. Comparing the \"VTN/VXM/Trans./LapIRN regular\" column and the \"VTN/VXM/Trans./LapIRN ours\" column, it is evident that our method outperforms other methods in terms of volume preservation in the warped image " + }, + { + "bbox": [ + 48, + 324, + 286, + 538 + ], + "type": "inline_equation", + "content": "(1_{\\mathrm{st}}" + }, + { + "bbox": [ + 48, + 324, + 286, + 538 + ], + "type": "text", + "content": " row) and the corresponding deformation field " + }, + { + "bbox": [ + 48, + 324, + 286, + 538 + ], + "type": "inline_equation", + "content": "(4_{\\mathrm{th}}" + }, + { + "bbox": [ + 48, + 324, + 286, + 538 + ], + "type": "text", + "content": " row). Furthermore, in terms of visualization of the registration accuracy and the overlay of the tumor " + }, + { + "bbox": [ + 48, + 324, + 286, + 538 + ], + "type": "inline_equation", + "content": "(2_{\\mathrm{nd}}" + }, + { + "bbox": [ + 48, + 324, + 286, + 538 + ], + "type": "text", + "content": " row), our proposed method achieves better volume preservation with comparable accuracy compared to other methods. Lastly, the Jacobian determinant of the deformation field " + }, + { + "bbox": [ + 48, + 324, + 286, + 538 + ], + "type": "inline_equation", + "content": "(3_{\\mathrm{rd}}" + }, + { + "bbox": [ + 48, + 324, + 286, + 538 + ], + "type": "text", + "content": " row) reveals that regular methods tend to have a larger Jacobian in tumor regions, indicating greater volume change, compared to our method. This highlights the effectiveness of our volume-preserving approach in preserving tumor volumes while aligning the images." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 550, + 137, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 550, + 137, + 562 + ], + "spans": [ + { + "bbox": [ + 48, + 550, + 137, + 562 + ], + "type": "text", + "content": "4.4. Ablation study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 48, + 569, + 286, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 569, + 286, + 688 + ], + "spans": [ + { + "bbox": [ + 48, + 569, + 286, + 688 + ], + "type": "text", + "content": "Volume-Preserving Losses. In Table 2, we present the results of our evaluation of the effectiveness of various versions of volume-preserving losses. For each sub-table, the first row (#1, #6, and #11) represents using only the similarity loss, while the second row (#2, #7, and #12) utilizes the ground truth as a weighted similarity loss. The third row (#3, #8, and #13) uses the ground truth binary mask as a tumor mask, while the fourth row (#4, #9, and #14) uses the mask of the entire organ as a tumor mask. The fifth row (#5, #10, and #15) represents our proposed strategy." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 48, + 689, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 689, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 689, + 286, + 712 + ], + "type": "text", + "content": "By comparing the first and second rows of each sub-table with the fifth row, we observe that our proposed volume-" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 307, + 312, + 545, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 312, + 545, + 394 + ], + "spans": [ + { + "bbox": [ + 307, + 312, + 545, + 394 + ], + "type": "text", + "content": "preserving loss can effectively preserve details and achieve superior performance across various metrics. The improvement from the third and fourth rows to the fifth row indicates the importance of adaptiveness in preserving the volume of the organ and tumor, respectively. It should be noted that we do not require pixel-wise ground truth for tumor volume preservation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 396, + 545, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 396, + 545, + 585 + ], + "spans": [ + { + "bbox": [ + 308, + 396, + 545, + 585 + ], + "type": "text", + "content": "Robustness to Tumor Mask Estimation. In Figure 5, we showcase the robustness of our proposed strategy in the presence of noisy ground truth segmentation masks. To evaluate this, we randomly select points within organs to ensure that tumors have a certain Dice score with respect to the ground truth segmentation of tumors. As depicted in the figure, despite the variations in the noisy ground truth segmentation masks, our strategy's performance remains consistent. Specifically, when the tumor mask has a Dice score above a certain threshold, such as 0.15, the estimated tumor mask consistently achieves a Dice score of approximately 0.17. In contrast, using the whole organ as mask in volume-preserving loss causes degradation in performance as it only has a dice score of roughly 0.05. This highlights the necessity and efficiency of our tumor mask estimation in stage one." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 308, + 598, + 382, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 598, + 382, + 609 + ], + "spans": [ + { + "bbox": [ + 308, + 598, + 382, + 609 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 618, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 618, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 618, + 545, + 712 + ], + "type": "text", + "content": "In summary, this work addressed the problem of preserving tumor volumes while maximizing similarity during learning-based registration, which is crucial for tracking tumor growth. We proposed a two-stage unsupervised strategy that effectively preserves the size ratio of tumors, without requiring extra networks. Our approach involves generating a soft tumor mask in the first stage using a similarity-based registration network and incorporating" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 750, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 750, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 750, + 317, + 757 + ], + "type": "text", + "content": "21215" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 74, + 259, + 193 + ], + "blocks": [ + { + "bbox": [ + 75, + 74, + 259, + 193 + ], + "lines": [ + { + "bbox": [ + 75, + 74, + 259, + 193 + ], + "spans": [ + { + "bbox": [ + 75, + 74, + 259, + 193 + ], + "type": "image", + "image_path": "3fa7600e12f5561e2b1165278e52e24243ef91cdb3f409a4ecb8e16d3efe6156.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 204, + 288, + 281 + ], + "lines": [ + { + "bbox": [ + 46, + 204, + 288, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 288, + 281 + ], + "type": "text", + "content": "Figure 5. Robustness of our tumor mask estimation. We evaluated the robustness of our tumor mask estimation by running our strategy using RCN on the LiTS datasets with different noisy ground truth (GT) masks as tumor masks, each with specific Dice scores with tumors. We plotted the results on a graph with the Dice score on the x-axis and the STSR in the test set on the y-axis (where smaller values are better)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 297, + 287, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 287, + 451 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 287, + 451 + ], + "type": "text", + "content": "an adaptive volume-preserving loss and a weighted similarity loss in the second stage to improve registration performance. To evaluate our strategy's performance, we introduced a new metric, the Square Tumor Size Ratio (STSR), which measures the preservation of tumor volume. Our proposed strategy was evaluated on various networks and demonstrated superior performance in tumor volume preservation, while achieving comparable results in other metrics. This highlights the effectiveness of our approach in tracking tumor growth and its ability to generalize well to different registration networks. Additionally, we noted that the volume preservation approach could be extended to other lesions besides tumors." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 464, + 287, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 573 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 573 + ], + "type": "text", + "content": "Acknowledgement: This work was supported by the HKSAR Innovation and Technology Commission (ITC) under ITF Project MHP/109/19, the National Natural Science Foundation in China under Grant 62022010, the Beijing Natural Science Foundation Haidian District Joint Fund in China under Grant L222032 and the Fundamental Research Funds for the Central Universities of China from the State Key Laboratory of Software Development Environment in Beihang University in China." + } + ] + } + ], + "index": 3 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21216" + } + ] + } + ], + "index": 4 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "text", + "content": "[1] Moab Arar, Yiftach Ginger, Dov Danon, Amit H Bermano, and Daniel Cohen-Or. 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IEEE journal of biomedical and health informatics, 24(5):1394-1404, 2019. 6" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "21218" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Pretrained Language Models as Visual Planners for Human Assistance/057af23b-bb0a-449d-acad-c434ed40a938_content_list.json b/2023/Pretrained Language Models as Visual Planners for Human Assistance/057af23b-bb0a-449d-acad-c434ed40a938_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..8727886a1eacebd893429a211a45ce1d7f33d64b --- /dev/null +++ b/2023/Pretrained Language Models as Visual Planners for Human Assistance/057af23b-bb0a-449d-acad-c434ed40a938_content_list.json @@ -0,0 +1,1788 @@ +[ + { + "type": "text", + "text": "Pretrained Language Models as Visual Planners for Human Assistance", + "text_level": 1, + "bbox": [ + 127, + 130, + 841, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dhruvesh Patel $^{1,2}$ Hamid Eghbalzadeh $^{1}$ Nitin Kamra $^{1}$ Michael Louis Iuzzolino $^{1}$ Unnat Jain $^{1*}$ Ruta Desai $^{1*†}$ $^{1}$ Meta $^{2}$ UMass Amherst https://github.com/facebookresearch/vlamp", + "bbox": [ + 251, + 179, + 725, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In our pursuit of advancing multi-modal AI assistants capable of guiding users to achieve complex multi-step goals, we propose the task of 'Visual Planning for Assistance (VPA)'. Given a succinct natural language goal, e.g., \"make a shelf\", and a video of the user's progress so far, the aim of VPA is to devise a plan, i.e. a sequence of actions such as \"sand shelf\", \"paint shelf\", etc. to realize the specified goal. This requires assessing the user's progress from the (untrimmed) video, and relating it to the requirements of natural language goal, i.e. which actions to select and in what order? Consequently, this requires handling long video history and arbitrarily complex action dependencies. To address these challenges, we decompose VPA into video action segmentation and forecasting. Importantly, we experiment by formulating the forecasting step as a multimodal sequence modeling problem, allowing us to leverage the strength of pre-trained LMs (as the sequence model). This novel approach, which we call Visual Language Model based Planner (VLaMP), outperforms baselines across a suite of metrics that gauge the quality of the generated plans. Furthermore, through comprehensive ablations, we also isolate the value of each component - language pretraining, visual observations, and goal information. We have open-sourced all the data, model checkpoints, and training code.", + "bbox": [ + 75, + 318, + 473, + 696 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 727, + 209, + 742 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Imagine assembling a new piece of furniture or following a new recipe for a dinner party. To achieve such a goal, you might follow a manual or a video tutorial, going back and forth as you perform the steps. Instead of fumbling through a manual, imagine an assistive agent capable of being invoked through natural language, having the ability to understand human actions, and providing actionable multi-step guidance for achieving your desired goal. Such multi-", + "bbox": [ + 75, + 753, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1ec0e91231c15a34a02907bea4c7c18d3395949578a3dd3ca32d00ace36a79d4.jpg", + "image_caption": [ + "Figure 1: Visual Planning for Assistance overview (top) and general methodology (bottom). Given a user-specified, natural language goal (\"build a shelf\") and corresponding visual history of the user's progress till now, VPA involves predicting a sequence of actions, to assist the user towards the goal (\"cut\", \"sand\", \"paint\"). Our approach is based on multi-modal sequence modeling where we reuse pre-trained video segmentation and language models." + ], + "image_footnote": [], + "bbox": [ + 506, + 284, + 893, + 460 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "modal assistive agents should be able to reason human activities from visual observations, contextualize them to the goal at hand, and plan future actions for providing guidance.", + "bbox": [ + 496, + 625, + 892, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To quantify the progress and aid the development of such multi-modal neural models, we need a intuitive task, as illustrated in the example in Fig. 1 (top). We call this Visual Planning for Assistance (VPA) that we detail next. Given a user-specified goal in natural language (\"build shelf\") and corresponding video observations of the user's progress towards this goal, the task objective should be to generate the ordered sequence of next actions towards achieving the goal (\"cut $\\rightarrow$ sand $\\rightarrow$ paint\"). We base VPA off instructional YouTube videos of such procedural activities from large, open-sourced datasets - CrossTask [89] and COIN [73]. This is a natural choice as procedural human activities (cooking, assembly, repair, etc.) are a perfect source of multi-step and complex sequence of actions, where humans routinely seek guidance. Realistic nature", + "bbox": [ + 496, + 674, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*equal mentoring † corresponding author", + "bbox": [ + 94, + 886, + 321, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15302", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "of VPA makes it particularly challenging. Operating on untrimmed videos requires dealing with potentially many irrelevant background frames, chunking actions in the videos will also be imperative. Another challenge is the validity of the plan of actions i.e. they must respect the constraints of the activity – the shelf shouldn't be painted before sanding.", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The natural next question is - what's a good way to tackle VPA? Marrying research from video forecasting & anticipation with embodied AI [19, 17], we cast VPA as goal-conditioned task planning. We approach VPA by utilizing video action segmentation and transformer-based neural sequence modeling - the former allows us to deal with long video history and the latter can handle arbitrary sequential constraints [86, 39]. The formulation (particularly, transformer-based neural sequence modeling) allows us to tap into the prowess of pre-trained language models (PTLMs). These PTLMs contain useful priors about action-action similarity, action-goal association, and action ordering [7, 30, 58], that our formulation can piggy-back off. Particularly, our model - Visual Language Model Planner (VLaMP) - conditions the generated plan onto the visual history by using a transformer-based mapper network that projects embeddings corresponding to visual history into the input space of the LM. Using VPA as the testbed, we show that VLaMP outperforms a range of standardized baselines. We undertake head-on ablations to quantify effect of each component of VLaMP - language pre-training of the LM, the visual history, and goal description. We believe the modularity of our approach can allow researchers to swap components with their own, to make rapid progress towards VPA.", + "bbox": [ + 75, + 181, + 470, + 556 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our main contributions are: (1) a new task VPA on human interaction videos capturing unique aspects of real-world vision-powered assistive agents; (2) a general-purpose methodology for VPA, which allows leveraging pre-trained multi-modal encoders and sequence models; (3) an instantiation of this methodology (we call VLaMP), where we reuse sequence priors from PTLM and investigate its efficacy across two, well-studied datasets of procedural human activities.", + "bbox": [ + 75, + 559, + 468, + 694 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 709, + 218, + 724 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Forecasting in Videos. VPA entails future action sequence prediction for a video and is closely related to anticipation in video understanding, including future localization [22, 40, 78], future frame prediction [77, 46, 53], next active object estimation [21, 5, 25, 67, 4, 24, 44], as well as short- and long-term action anticipation [66, 15, 20, 23, 25, 65, 64, 57, 45, 1, 52, 50, 11, 79]. While short-term forecasting approaches, such as [66], are limited to predicting the single next action occurring only a few seconds into the future, our work focuses on predicting sequences of actions over longer time horizons (on the order of minutes)", + "bbox": [ + 75, + 734, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/6ff69421a6caa4068fed88e96c207d6103895396482c1ec76bf5287d0290ae74.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Action PredictionGoal ModalityVisual Reasoning
Action anticipation [14]SingleNoneVideo-based
Action forecasting [25]Multiple, orderedNoneVideo-based
Procedural planning [9]Multiple, orderedVisionImage-based
VPA (ours)Multiple, orderedNatural LanguageVideo-based
", + "bbox": [ + 500, + 88, + 893, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Table 1: VPA vs. prior tasks related to forecasting of real-world human activities. We predict an ordered sequence of actions given video history with a focus on natural language goal-conditioning for human-assistive applications.", + "bbox": [ + 496, + 178, + 893, + 252 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "into the future. The long-term action (LTA) forecasting benchmarking was recently established on a small subset of Ego4D [25], and although VPA is similarly devised to predict a temporally ordered sequence of actions conditioned on video-based visual observations, our approach differs in that the LTA task does no goal-conditioning. Our task incorporates goal-conditioning on long term sequence prediction as we argue this will drive the development of critical system aspects, such as virtual assistants that afford human interaction via the natural language goals. Additionally, in contrast to LTA, we focus on a wide range of goal-oriented activities available within the CrossTask and COIN datasets. Tab. 1 highlights the differences between VPA and other forecasting tasks.", + "bbox": [ + 496, + 280, + 892, + 491 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Procedural Planning Approaches. VPA is similar to the task of procedure planning [9], wherein given a starting and terminating visual observation, the aim is to predict the actions that would transform the state from starting to terminating. However, we argue that due to the unavailability of the terminating visual state, the procedure planning task is not useful in a real-world assistance setting. While several recent works introduce novel models for procedure planning, these models cannot be deployed for VPA either because they rely heavily on the availability of visual goal [70, 87, 6], or assume access to true action history [49]. Transformers for Decision Making. VLaMP autoregressively predicts future states and/or observations and actions and is similar in spirit to sequence models for decision making such as GATO [61], Decision Transformer [12], and Trajectory Transformer [35]. VLaMP extends such models to work with egocentric observations that humans observe in the day-to-day activities.", + "bbox": [ + 496, + 492, + 892, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Planning in Embodied AI using LMs. Past research has leveraged PTLMs for task planning in real world for embodied agents [30, 68, 41, 7, 42, 31, 18, 16, 36]. Many of these works focus on converting a high-level task or instruction into sequence of low-level steps and then ground them in the environment using either affordance functions [7], visual feedback [31], or multimodal prompts [36, 18]. Owing to their focus on robotic agents, these works focus on predominately pick-place tasks. Instead VPA is focused on", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15303", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "complex tasks, in which humans might require assistance in the form of recommended future actions. Consequently, VLaMP requires grounding and reasoning of much more complex states and actions, which it accomplishes by finetuning a pretrained LM on multimodal sequences of (visual) observations and (text-based) actions.", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multi-modal LMs. Recent works have successfully used the transformer architecture for modeling multi-modal sequences that have visual tokens. For instance, [47, 59, 2, 48, 29, 18] train large transformer based multi-modal sequence prediction models. While [3, 74, 56] focus on adapting pre-trained LMs to work with visual tokens by aligning the representation spaces of the two modalities. VLaMP's approach of modeling sequence of visual and textual representations using PTLMs is similar in spirit to these, i.e. VLaMP also uses a mapper network to align video representations to LM's token space and jointly learns the mapper with LM finetuning for VPA. However, in contrast to previous works, VLaMP predicts the visual tokens autoregressively at inference time to enable forecasting of the state for planning. Consequently, VLaMP's token prediction loss is multi-modal, unlike most multi-modal LMs that only use token prediction loss for text tokens.", + "bbox": [ + 75, + 181, + 472, + 441 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Visual Planning for Assistance", + "text_level": 1, + "bbox": [ + 76, + 455, + 356, + 472 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, we introduce the task of Visual Planning for Assistance (VPA), towards enabling multi-step guidance to humans in their real-world activities. We instantiate VPA for procedural activities, where humans routinely seek assistance. In this section, we include the definition of VPA, and describe the evaluation protocol.", + "bbox": [ + 75, + 482, + 468, + 574 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Task Definition", + "text_level": 1, + "bbox": [ + 76, + 585, + 230, + 601 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The following two intuitive inputs are given to any model performing VPA.", + "bbox": [ + 75, + 609, + 468, + 640 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Goal Prompt $(G)$ . The natural language description (in short phrase) of the user's goal, emulating a typical user's request for assistance for a day-to-day task. Examples include, \"build a shelf\" and \"change a tire\".", + "bbox": [ + 75, + 641, + 468, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Visual History $(V_{t})$ . An untrimmed video that provides context about the user's progress towards a goal from the start till time, say $t$ . We assume that $V_{t}$ contains $k$ actions or steps $\\{a_1,\\ldots ,a_k\\}$ pertaining to the goal. However, VPA doesn't have access to $\\{a_1,\\dots ,a_k\\}$ or $k$ and must work with $V_{t}$ .", + "bbox": [ + 75, + 702, + 468, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given these two inputs, $V_{t}$ and $G$ , the objective of VPA is to generate a plan $\\mathcal{T}$ . The plan is a sequence of actions that should be executed (in the next steps) to assist the user in achieving the goal $G$ . Concretely, the prediction is denoted by $\\mathcal{T} = (a_{k + 1},\\dots ,a_{k + l})$ , where $a_{i}$ are represented in natural language but come from a closed set $\\mathcal{A}$ . Here, $l\\leq K$ denotes the number of future actions that should be predicted,", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "out of the $K$ number of remaining actions required to accomplish the goal. For our shelf-building example, the correct $\\mathcal{T} =$ (sand shelf, paint shelf, attach shelf), capturing the remaining 3 future actions (here, $l = N = 3$ ).", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In day-to-day activities, we request assistance for goals in natural language. However, prior works procedural planning [9, 6] assume access to visual goal state. This is not a realistic assumption for an AI agent assisting humans. Hence, we purposefully relax this assumption, making our formulation of the task significantly more practical. Moreover, an agent with access to the visual modality, should be able to improve its plan by filtering out relevant information from the raw video stream of the progress. These are the two central assumptions around which we formulate the task of VPA.", + "bbox": [ + 496, + 152, + 892, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Evaluation", + "text_level": 1, + "bbox": [ + 500, + 327, + 620, + 342 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Open-Sourced Video Data. We leverage existing datasets CrossTask [89] and COIN [73], originally developed to enable video action understanding for VPA, based on the following three requirements:", + "bbox": [ + 496, + 351, + 890, + 411 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Rich diversity of activities from multiple domains: The data from different domains such as cooking, assembly etc., enables testing of VPA models in a more generalized manner.", + "- Goal-oriented activities consisting of long sequences of actions: Since the objective is to generate $l$ future actions, activities in these datasets that require diverse sequences of actions e.g., \"making a pancake\", instead of \"running\" are more suitable for VPA.", + "- Action annotations from a fixed closed set of actions: Action labels described using verb-noun from a finite set [14], which are temporally aligned with the videos. This makes evaluating the accuracy of $\\mathcal{T}$ prediction straightforward. Specifically, free-form, narration-style descriptions of actions that are available in recent video datasets aid in efficient multi-modal representation learning for video understanding [25, 54]. However, evaluating the quality of action sequences towards goal achievement, where each action is described in free-form natural language, is non-trivial. We leave the instantiation of VPA with free-form natural language actions as future work.", + "Table 2 summarizes the features from CrossTask and COIN, aligned with the above requirements." + ], + "bbox": [ + 500, + 412, + 893, + 760 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Metrics. The planning performance of a VPA model is measured by comparing the generated plan $\\hat{\\mathcal{T}} = (\\hat{a}_{k + 1},\\dots ,\\hat{a}_{k + l})$ to the ground truth plan $\\mathcal{T}$ for $l$ actions in the future, given $V_{t}$ and $G$ . Here $\\hat{a}_{k + i}$ denotes the prediction for the $k + i$ -th step given history till $k$ -th step. Consistent with community practices [9, 6], we use the following metrics, listed in decreasing order of strictness: success rate (SR), mean accuracy (mAcc), mean intersection over union", + "bbox": [ + 496, + 779, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15304", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/45e3b53acb6fb4edb98c509784f25925f5ff1e3dc0c5f2c3918e1906d5e6c238.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Dataset# train videos# test videos# test samplesactions per video# goals# domains
CrossTask [89]175675241237.6 ± 4.3183
COIN [73]9428104720113.9 ± 2.418012
", + "bbox": [ + 76, + 88, + 470, + 146 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 2: VPA datasets. We evaluate VPA on two existing video datasets containing multiple goal-oriented procedural activities from varied domains. Such activities contain sequences of multiple actions making them ideal for VPA.", + "bbox": [ + 75, + 154, + 468, + 215 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(mIOU). Success rate requires an exact match between all actions and their sequence between $\\hat{\\mathcal{T}}$ and $\\mathcal{T}$ . Mean accuracy is the accuracy of the actions at each step. Unlike success rate, mean accuracy does not require a $100\\%$ match to ground truth. Instead it considers matching at each individual step. Lastly, mean intersection over union captures the cases where the model predicts the steps correctly, but fails to identify the correct order. Concretely,", + "bbox": [ + 75, + 242, + 470, + 364 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {m I O U} _ {l} = \\frac {\\left| \\hat {a} _ {\\{k + 1 : k + l \\}} \\bigcap a _ {\\{k + 1 : k + l \\}} \\right|}{\\left| \\hat {a} _ {\\{k + 1 : k + l \\}} \\bigcup a _ {\\{k + 1 : k + l \\}} \\right|}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 387, + 468, + 426 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {m A c c} _ {l} = \\frac {1}{l} \\sum_ {i = 1} ^ {l} \\mathbb {1} [ \\hat {a} _ {k + i,} = a _ {k + i} ], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 428, + 468, + 468 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {S R} _ {l} = \\prod_ {i = 1} ^ {l} \\mathbb {1} [ \\hat {a} _ {k + i} = a _ {k + i} ], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 472, + 468, + 513 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbb{1}[\\cdot ]$ is the identity function, which is 1 when the condition in its input is true, and 0, and $\\hat{a}_{\\{k + 1:k + l\\}}$ denotes the set of $l$ future actions in $\\tilde{\\mathcal{T}}$ , i.e., a sequence but disregarding the order. To complement the above metrics, we also measure the accuracy of predicting the next action i.e. nAcc, as defined in (4), where 'n' stands for next. Note that all metrics are averaged over the test set details of which are included in Sec. 5.", + "bbox": [ + 75, + 523, + 468, + 647 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {n A c c} = \\mathbb {1} [ \\hat {a} _ {k + 1} = a _ {k + 1} ] \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 660, + 468, + 678 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Visual LM Planner", + "text_level": 1, + "bbox": [ + 76, + 691, + 263, + 707 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "VPA can be viewed as a sequential decision making problem, where the model (say, $\\pi$ ) predicting the sequence of next actions is a policy conditioned on the visual history $V_{t}$ , serving as (partially-observed) state, and goal prompt $G$ . Inspired by the offline learning formulation closest to 'learning from offline demonstrations' [27, 76, 37, 81], in VLaMP, we formulate VPA as a goal-conditioned, multimodal sequence prediction problem. This formulation allows us to leverage high-capacity sequence models like", + "bbox": [ + 75, + 715, + 468, + 853 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Transformers [75], which have been successfully applied to sequential decision making [35, 12]. Furthermore, inspired by the recent success of pre-trained transformer language models (PTLMs) on such tasks, [62, 30, 12], we propose to leverage PTLMs as the sequence model in our formulation. In the remainder of this section we describe our approach for VPA, called Visual Language Model based Planner (VLaMP), consisting of a segmentation module and PTLM based sequence prediction module.", + "bbox": [ + 496, + 90, + 890, + 227 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Planning with Segmentation and Forecasting", + "text_level": 1, + "bbox": [ + 498, + 239, + 879, + 256 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We define $\\pi$ as a goal-conditioned, multi-modal sequence prediction problem:", + "bbox": [ + 498, + 263, + 890, + 294 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\pi = P \\left(a _ {k + 1}, a _ {k + 2}, \\dots \\mid V _ {t}, G\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 308, + 890, + 325 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\pi$ models the probability of goal-relevant and valid future actions sequences conditioned on $V_{t}$ and $G$ .", + "bbox": [ + 496, + 338, + 890, + 367 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Modeling the multi-modal sequence in Eq. 5 is computationally expensive and difficult to scale because of the high-dimensional state space of raw untrimmed video $V_{t}$ . Also, there is limited data to learn the distribution over valid action sequences for goals in real-world applications. Tackling these challenges, we argue that the latent space of factors influencing the future plan can indeed be expressed in lesser dimensions. Particularly, to ensure scalability for handling raw videos and sample efficiency in learning valid action sequence distributions, we decompose our policy $\\pi$ into two modules. The first module is video segmentation, which converts the untrimmed video history $V_{t}$ into a sequence of video segments i.e. a segment history $S_{k} = (s_{1},\\dots ,s_{k})$ , where each segment corresponds to an action $a_{i}$ that occurred in the video. The second module enables forecasting i.e. it transforms the output of the segmentation module and generates the plan (see Fig. 1 (bottom)). While a probabilistic formulation of this decomposition can be expressed as:", + "bbox": [ + 496, + 369, + 892, + 655 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\pi = \\sum_ {S _ {k}} \\underbrace {P \\left(a _ {k + 1} , a _ {k + 2} , \\cdots \\mid S _ {k} , G\\right)} _ {\\text {F o r e c a s t i n g}} \\underbrace {P \\left(S _ {k} \\mid V _ {t}\\right)} _ {\\text {S e g m e n t a t i o n}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 669, + 890, + 705 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the segment history $S_{k}$ is a latent variable, the summation over all possible segment histories is intractable. We, however, use Eq. 6 as the guiding expression to formulate the input and output of both modules. Next, we include the technical details of both of these modules.", + "bbox": [ + 496, + 719, + 890, + 794 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Segmentation Module", + "text_level": 1, + "bbox": [ + 500, + 806, + 705, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This module splits the untrimmed video history $V_{t}$ into segment history $S_{k}$ of multiple segments, each segment", + "bbox": [ + 498, + 830, + 890, + 862 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "1Future works may explore alternate policy optimizations based on reward shaping, inverse RL, or by employing additional online interactions through photorealistic simulation [38, 63, 71, 69, 82, 33, 34, 10, 80].", + "bbox": [ + 75, + 862, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "$^{2}$ A typical untrimmed video of 100p video of 5 minutes at 8fps will have $2^{7}$ raw pixel values.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15305", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/087d67a1de51d94c1b34f3dfb37dc87fc6774ac21ebb63bfdfaf6e3967206c84.jpg", + "image_caption": [ + "Figure 2: VLaMP - Segmentation Module. The untrimmed visual history $V_{t}$ is converted into segments, each consisting of observation $o_{i}$ and the action $a_{i}$ . The observation $o_{i}$ is the collection of video frames of $\\delta$ seconds around the start time stamp $t_{i}$ of the corresponding action $a_{i}$ . Two such segments are shown here." + ], + "image_footnote": [], + "bbox": [ + 86, + 92, + 460, + 233 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "corresponding to an action. The segmentation is done using a video-action segmentation model in three steps: preprocessing, classification, and consolidation. In the preprocessing step, the raw video frames from $V_{t}$ are bundled into fixed-length window clips $c_{i}$ , each of length 1 second, to obtain $V_{t} = (c_{1},\\dots ,c_{t})$ . In the classification step, a video-action segmentation model is used to output the most probable action for each clip $c_{i}$ , which can be denoted as $\\tilde{A}_t = (\\tilde{a}_1,\\tilde{a}_2,\\ldots ,\\tilde{a}_t)$ . Finally, in the consolidation steps, we convert $\\tilde{A}_t$ into a form that can be used by the forecasting module; this form consists of two sequences: action history $A_{k}$ and observation history $O_{k}$ . To this end, same actions in consecutive seconds in $\\tilde{A}_t$ are consolidated to form the action history $A_{k} = (a_{1},\\dots ,a_{k})$ . As illustrated in Fig. 2, assuming $t_i$ denotes the starting timestamp for $a_{i}$ , we also extract video frames from $t_i - \\delta /2$ to $t_i + \\delta /2$ to obtain an observation window $o_i$ corresponding to $a_{i}$ , and consequently the full observation history $O_{k} = (o_{1},\\dots,o_{k})$ . The resultant segment history is termed $S_{k} = ((o_{1},a_{1}),\\dots ,(o_{k},a_{k}))$ , summarized in Fig. 2.", + "bbox": [ + 75, + 366, + 472, + 670 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Forecasting Module", + "text_level": 1, + "bbox": [ + 76, + 678, + 266, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The usefulness of $\\pi$ 's decomposition expressed in Eq. (6) becomes apparent now. Modeling the segmentation module's output as segment history $S_{k}$ , where each segment consisting of action and observations, allows writing the output of the forecasting module in an autoregressive manner:", + "bbox": [ + 75, + 702, + 468, + 790 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} P \\left(a _ {k + 1}, a _ {k + 2}, \\dots \\mid o _ {1}, a _ {1}, \\dots , o _ {k}, a _ {k}, G\\right) \\\\ = \\prod_ {i > 0} \\sum_ {o _ {k + i}} P \\left(o _ {k + i}, a _ {k + i} \\mid o _ {1}, a _ {1}, \\dots , o _ {k}, a _ {k}, G\\right). \\tag {7} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 805, + 468, + 859 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Illustrated in Fig. 3, this autoregressive expression allows the possibility of using any sequence-to-sequence neural", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "network as the forecasting module in combination with pretrained text and video encoders for representing action and observation history $A_{k}$ and $O_{k}$ . This general-purpose framework allows the use of any neural sequence model – LSTM [28], GRU [13], Transformers [75], etc. We choose to instantiate the forecasting module for $\\pi$ using a pretrained transformer-based LM. Next we present the details of the encoders for the two modalities and the LM based sequence model.", + "bbox": [ + 496, + 90, + 890, + 224 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Action encoder $(f_{\\mathrm{act}})$ Each action $a_i$ in $A_k$ is encoded by $f_{\\mathrm{act}}$ and the output is denoted by $\\alpha_i$ . Concretely, token embeddings are expressed as:", + "bbox": [ + 498, + 227, + 890, + 272 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\left(\\alpha_ {1}, \\dots , \\alpha_ {k}\\right) = \\left(f _ {\\text {a c t}} \\left(a _ {1}\\right), \\dots , f _ {\\text {a c t}} \\left(a _ {k}\\right)\\right), \\text {w h e r e} \\\\ \\alpha_ {i} = \\left(\\alpha_ {i} ^ {1}, \\dots , \\alpha_ {i} ^ {r _ {i}}\\right) \\in \\mathbb {R} ^ {r _ {i} \\times d} \\tag {8} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 281, + 890, + 319 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As we illustrate in Fig. 3 (left), each action $a_i$ is tokenized into $r_i$ tokens using appropriate tokenizer for the LM, the tokens are indexed using the vocabulary of the LM, and are represented using an embedding lookup from the token embeddings of the LM to produce $\\alpha_i$ . Here, $r_i$ is the number of tokens and $d$ is the dimensionality of token embeddings.", + "bbox": [ + 496, + 327, + 890, + 417 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Observation encoder $(f_{\\mathrm{obs}})$ . Visual cues play an integral role in knowing what actions lie ahead, towards achieving the goal prompt $G$ . To this end, the visual observations $O_k$ are encoded and play a critical role in the planner. Recall, the visual observation history $O_k$ comprises of $o_i$ corresponding to action $a_i$ , each of $\\delta$ frames. As illustrated in Fig. 3 (middle), we transform each $o_i$ employing the widely-adopted S3D backbone [84] $f_{\\mathrm{S3D^*}}$ (* denotes backbone is frozen). We must project visual encodings to a shared latent space of action (language) embeddings described before $(\\alpha_i)$ . To this end, we map S3D features via a trainable transformer mapper $f_{\\mathrm{map}}$ . Concretely,", + "bbox": [ + 496, + 417, + 890, + 599 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\left(\\beta_ {1}, \\dots , \\beta_ {k}\\right) = \\left(f _ {\\mathrm {o b s}} \\left(o _ {1}\\right), \\dots , f _ {\\mathrm {o b s}} \\left(o _ {k}\\right)\\right), \\text {w h e r e} \\\\ \\beta_ {i} = \\left(\\beta_ {i} ^ {1}, \\dots , \\beta_ {i} ^ {\\delta}\\right) \\in \\mathbb {R} ^ {\\delta \\times d} \\text {a n d} f _ {\\mathrm {o b s}} = f _ {\\mathrm {S 3 D} ^ {*}} \\circ f _ {\\mathrm {m a p}} \\tag {9} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 608, + 890, + 647 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Overall, as we show in Fig. 3 (right), the resultant encoded sequence of representation for $S_{k}$ is thus", + "bbox": [ + 498, + 654, + 890, + 685 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\text {e n c}} (S _ {k}) = \\left(\\beta_ {1}, \\alpha_ {1}, \\dots , \\beta_ {k}, \\alpha_ {k}\\right) = H _ {k},\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 694, + 826, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sequence model $(f_{\\mathrm{seq}})$ . Given the above encoding for the segment history $S_{k}$ , the role of the sequence model is to predict a representation of the next token, that would in return enable VLaMP plan generation capabilities for VPA. Importantly, in the process of generating sequence of future actions autoregressively, we would also need to generate the representations of 'future observations'. Therefore, as we shown in Fig. 3, our sequence model, which consists of the transformer layers of a PTLM, also produces representations for vision (in addition to the necessary action tokens). Before proceeding further, we pause and introduce additional notation for the sequence model, which", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15306", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7b9f0c8b9772067c8dede95c30a238593029dd56f40d5f96be0718231733c1c2.jpg", + "image_caption": [ + "Figure 3: VLaMP - Forecasting Module. As shown in left and middle, actions and observations obtained from the segmentation module are encoded using appropriate modality encoders. The observation encoder leverages pretrained video encoder for observations, while also learning a mapper that aligns the representations from observations with actions. As shown on the right, VLaMP uses a joint sequence model on top of interleaved action (blue) and observation (gray) representations to forecast autoregressively the next representation." + ], + "image_footnote": [], + "bbox": [ + 158, + 88, + 480, + 229 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0ada3fca083539da731052742542fd4ea73f4bbc817e7d19b6f807cdaddccf2d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 88, + 846, + 229 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d581d41982481ea46b81e5bcf8d3975617081858294f2818bc57ff561951c912.jpg", + "image_caption": [ + "Figure 4: Tokenized Sequence with Masks. The encoded sequence of representations for $k = 2$ segments, denoted alternatively using modality agnostic notation of $H_{2}$ and mask $M$ for next token prediction training." + ], + "image_footnote": [], + "bbox": [ + 127, + 344, + 429, + 425 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "will make the subsequent explanation for training and inference easier to follow. As shown in Figure 4, we alternatively denote the sequence of representations $(\\beta_{1},\\alpha_{1},\\ldots ,\\beta_{k},\\alpha_{k})$ by $H_{k} = (h_{1},\\dots,h_{n})$ , with $n = k\\delta +\\sum_{i = 1}^{k}r_{i}$ . A binary mask $M = (m_{1},\\dots,m_{n})$ , where $m_{i}$ is 1 if the corresponding representation is for an action and 0 otherwise, can help obtain necessary action or visual observations. With this notation, given first $j$ representations denoted as $h_{1:j}$ , one step of the sequence model produces the representation for $j + 1$ , i.e., $f_{\\mathrm{seq}}(h_{1:j}) = \\hat{h}_{j + 1}$ .", + "bbox": [ + 75, + 527, + 468, + 683 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Training", + "text_level": 1, + "bbox": [ + 76, + 690, + 181, + 705 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The joint training of the segmentation and forecasting modules following Eq. (6) is intractable. But, by exploiting the availability of unpaired training data, we approximate Eq. (6) by feeding in the output of the segmentation module to the forecasting module and training them separately, each on their respective labeled data. The video-action segmentation model is trained utilizing the VideoCLIP setup [85], where in the segmentation model performs classification to predict the action for each second of the video. The forecasting model is trained by adopting the", + "bbox": [ + 75, + 713, + 468, + 864 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "next representation prediction objective. Unlike vanilla LM pretraining, however, we also need to train for predicting visual representations in addition to text (action). Therefore, we use two different losses $L_{\\mathrm{act}}$ and $L_{\\mathrm{obs}}$ for text and visual representations respectively. Specifically, $L_{\\mathrm{act}}$ is the conventional cross-entropy loss over the LM's vocabulary $V_{\\mathrm{LM}}$ for the action representations while $L_{\\mathrm{obs}}$ is the mean-squared error between the predicted and the ground truth observation representations. The total loss is the sum of both the loss terms as shown in Eq. (11).", + "bbox": [ + 500, + 348, + 890, + 501 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL = - \\sum_ {j = 1} ^ {n} m _ {j} L _ {\\mathrm {a c t}} (\\hat {h} _ {j}) + (1 - m _ {j}) L _ {\\mathrm {o b s}} (\\hat {h} _ {j}), \\text {w h e r e}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 518, + 864, + 560 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {a c t}} = h _ {j} \\cdot \\hat {h} _ {j} - \\log \\sum_ {p = 1} ^ {| V _ {\\mathrm {L M}} |} \\exp \\left(h _ {p} \\cdot \\hat {h} _ {j}\\right); \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 563, + 890, + 608 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {o b s}} = \\frac {\\| h _ {j} - \\hat {h} _ {j} \\| _ {2} ^ {2}}{d} \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 565, + 611, + 890, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In order to have a stable training, we use ground truth action history to construct $S_{k}$ (and subsequently $H_{k}$ ) instead of the output of the segmentation module. Appendix B provides further details on loss and optimizers for training.", + "bbox": [ + 500, + 648, + 890, + 709 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Inference. We next detail the inference procedure for VLaMP. Recall that we use $1:n$ to denote a sequence of $n$ representations (i.e, $h_{1:n} = (h_1,\\ldots ,h_n)$ ). Additionally, we denote the concatenation operator over two representation sequences by \" $\\diamond$ \". With this notation at hand, we define the score of an action $a\\in \\mathcal{A}$ for following history $h_{1:n}$ as", + "bbox": [ + 500, + 710, + 890, + 801 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\phi \\left(h _ {1: n} \\diamond f _ {\\mathrm {a c t}} (a)\\right) = \\sum_ {j = 1} ^ {r _ {a}} a ^ {j} \\cdot f _ {\\mathrm {s e q}} \\left(h _ {1: n} \\diamond a ^ {1: j}\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 531, + 820, + 890, + 861 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\cdot$ is the vector dot product, and $f_{\\mathrm{act}}(a) = \\alpha^{1:r_a} = (\\alpha^1,\\ldots ,\\alpha^{r_a})$ is the sequence of encoded representations", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "3Despite tuning attempts, we found joint optimization to be intractable and inefficient on resources.", + "bbox": [ + 76, + 875, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15307", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "for action $a$ . In other words, this score is the sum of unnormalized log-probability under the sequence model using the standard softmax distribution. We use this scoring function with to perform beam search (detailed inference algorithm: Algo. 1 in App. B).", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 183, + 209, + 200 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We instantiate VLaMP's segmentation module utilizing VideoCLIP [85] that has been fine-tuned on COIN and CrossTask. Similarly, we instantiate VLaMP's sequence model $f_{\\mathrm{seq}}$ (in the forecasting module) by GPT2 [60]. We utilize the open-sourced model weights of GPT2 (from HuggingFace [83]). For inference, we use Algo. 1 presented in Appendix B, with beam size $B = 10$ for CrossTask and a $B = 3$ for COIN.", + "bbox": [ + 75, + 209, + 470, + 329 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Data and Baselines", + "text_level": 1, + "bbox": [ + 76, + 342, + 261, + 357 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Data. For a video $V$ with goal $G$ , both CrossTask [89] and COIN [73] provide annotations of the form $\\{a_k, (t_k, t'_k)\\}_{k=1}^K$ , where $a_k$ are the actions in the video, and $t_k$ (resp. $t'_k$ ) are the start (resp. end) timestamps for $a_k$ . Given an annotated video consisting of $K$ steps, we generate $K - l$ examples, each with input $x_k = (G, V_{t_k})$ and output $y_k = (a_{k+1}, \\ldots, a_{k+l})$ , for $k = 1, \\ldots, K - l$ (leaving at least $l$ steps to predict in each example). Therefore from $M$ videos, we generated $N = \\sum_{m=1}^{M} (K_m - l)$ examples, where $K_m$ is the number of steps in the $m$ -th video, forming a dataset $\\mathcal{D} = \\{x^{(j)}, y^{(j)}\\}_{j=1}^N$ suitable for VPA (total number of samples in shown in Table 2).", + "bbox": [ + 75, + 366, + 468, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baselines. As a first step towards benchmarking, we utilize two heuristic baselines - a random baseline and most probable action baseline. Additionally, we also adopt a variety of strong goal-conditioned models. The procedure planning task is most relevant task from the literature to VPA, therefore, we adapt (details in App. A.1) the widely used DDN model introduced by Chang et al. [9], which is an established model in many procedural planning benchmarks in prior works [6, 87, 70]. Building bridges to the research community working on Ego4D's Long Term action Anticipation benchmark (LTA) [25], we also evaluate their best performing baseline. Finally, we include a prompt-based GPT-3 planner. Zooming out, these baselines span several paradigms: prompt-based, and random baselines are learning-free, the most-probable and random baselines are non-neural, while DDN and LTA baselines are learned and", + "bbox": [ + 75, + 549, + 468, + 791 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "neural. Succinct descriptions of baselines are included next (details are deferred to Appendix A):", + "bbox": [ + 500, + 90, + 890, + 119 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Random: Predicts the plan by picking all $l$ actions uniformly randomly from the set of all actions $\\mathcal{A}$ .", + "- Random $w/$ goal: A stronger baseline; for each goal $G$ , we allow privilege access to a set of applicable actions to that goal $\\mathcal{A}_G \\subseteq \\mathcal{A}$ , and predicts the plan by randomly picking actions from the restricted set.", + "- Most probable action: Given the previous action $a_j$ , picks the most probable next action $a_j$ according conditional probability $Pr(a_i | a_j)$ obtained using frequency count from the training.", + "- Most probable action $w/$ goal: Akin to random $w/$ goal baseline, we also evaluate a goal-conditioned most probable action baseline, that uses a goal-specific set of actions $\\mathcal{A}_G \\subset \\mathcal{A}$ during sampling. Since the most probable baselines, provide a probability distribution over the actions, we also employ beam search (for fairness, with the same beam size same as VLaMP), and pick the highest scoring plan.", + "- Dual Dynamics Network (DDN) [9]: Accounting for the difference in task definition, i.e. lack of visual goal, a direct application of DDN inference algorithm was not possible. So we keep DDN's network structure but use Algo.1 for inference on VPA.", + "- Ego4D Long Term Action Anticipation (LTA) [25]: The best performing baseline for LTA uses a SlowFast visual encoder followed by a transformer aggregator. We adapt this baseline using the S3D encoder for a fair apples-to-apples comparison with VLaMP.", + "- Prompt-based GPT-3 Planner: Huang et al. [30] utilize a LLM as zero-shot planners, we also experiment with prompting a frozen pretrained large language model i.e. GPT-3 for VPA (additional details in App. A.2)." + ], + "bbox": [ + 500, + 122, + 890, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Quantitative Results", + "text_level": 1, + "bbox": [ + 500, + 632, + 692, + 648 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In the following, we include quantitative findings of benchmarking methods on two video data sources (Tab. 3) and head-on ablations (Tab. 4).", + "bbox": [ + 498, + 657, + 890, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Improved performance across video datasets. As we show in Tab. 3, VLaMP significantly outperforms the baselines for both CrossTask and COIN. DDN that is customized for procedural tasks performs significantly better than heuristic baselines leading to a mAcc boost from $12.7 \\rightarrow 24.1\\%$ (row 2 and 5, $l = 4$ , Tab. 3). With our novel decomposition and pretraining objective, VLaMP outperforms DDN with a further bump up from $24.1 \\rightarrow 31.7\\%$ (row 5 and 7).", + "bbox": [ + 498, + 703, + 890, + 837 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Steady gains in short & long horizon predictions. As length of prediction $l$ increases ( $l = 1$ to $l = 4$ ), the performance naturally decreases, across all baselines and tasks. With this in mind and zooming in on COIN re", + "bbox": [ + 498, + 839, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "4Despite the presence of prepositions, majority of actions in COIN and CrossTask can be described using a verb-noun pair. While similar verbs exist, they are never paired with the same nouns. Therefore, there are no repeated actions. Example: while verb 'lift' w/ noun 'barbell' and verb 'pickup' w/ 'button' exists in the action library, the complements ('lift button' & 'pick up barbell') do not. 5Since we evaluate for three and four next steps on our datasets, we use the maximum required length and set $l = 4$", + "bbox": [ + 75, + 801, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15308", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f68017a0e5cc3d90ab22822918d0f508a7b23091b7fc7f6612b9ca098442e61c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methodl = 1l = 3l = 4
{n/m}AccSRmAccmIOUSRmAccmIOU
CrossTask Video Dataset [89]
Random0.90.00.91.50.00.91.9
Random w/ goal13.20.313.423.60.012.727.8
Most probable10.41.76.19.91.35.513.9
Most probable w/ goal12.42.48.915.51.57.920.5
DDN [9]33.46.825.835.23.624.137.0
LTA [25]26.92.424.035.21.221.736.8
VLaMP (ours)50.610.335.344.04.431.743.4
COIN Video Dataset [73]
Random0.10.00.10.20.00.10.2
Random w/ goal24.51.721.442.70.320.147.7
Most probable0.71.64.36.81.68.215.3
Most probable w/ goal23.910.918.024.99.116.332.2
DDN [9]29.310.122.332.27.021.037.3
GPT-3 prompt-based [30]19.31.711.119.50.010.521.0
VLaMP (ours)45.218.339.256.69.035.254.2
", + "bbox": [ + 76, + 88, + 470, + 323 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "sults, we observe large gains of VLaMP over DDN (next best method). Particularly, a relative improvement of $54\\%$ $(29.3 \\rightarrow 45.2)$ in mAcc for $l = 1$ (row 7 and 8, Tab. 3) and $68\\%$ $(21.0 \\rightarrow 35.2)$ for $l = 4$ is demonstrated by VLaMP over DDN.", + "bbox": [ + 75, + 458, + 468, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Goal-conditioning is crucial. A key difference between the task formulations of LTA and VPA is goal conditioning (see Sec. 2). Comparing rows for LTA model and VLaMP-there is almost $2\\mathrm{x}$ gap $(27\\%$ vs. $51\\%$ $l = 1$ Tab.3). This underscores the importance of goal-conditioning. To second this inference, in Tab. 4 (rows 1 and 2), we precisely ablate the effect of providing the goal as a textual description for the basic (last-observation-only) model. The only difference is goal prompt $G$ , which increases mAcc performance from $44.5\\rightarrow 53.1\\%$ for $l = 1$ and $28.3\\to 34.7\\%$ for $l = 3$", + "bbox": [ + 75, + 535, + 470, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Goal-conditioned random and most probable baseline come close to DDN on easy metrics. For fair comparisons, we include heuristic baselines. We observe the performance of random $w/$ goal and most probable $w/$ goal comes close to DDN, when evaluated using lenient metrics like mAcc and mIOU (see COIN results in Tab. 3). Note, that these two baselines enjoy the privileged access to (a much smaller) 'relevant actions set' for a given goal. On an average, the relevant or feasible action set is smaller for COIN than CrossTask videos. This apriori access to feasible actions makes random $w/$ goal and most probable $w/$ goal competitive (albeit, slightly unfair) baselines.", + "bbox": [ + 75, + 686, + 470, + 868 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Prompt-based LLM planner is not competitive. We evaluate the prompt-based GPT-3 planner on COIN and find", + "bbox": [ + 75, + 869, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9107097bec053a1958d0e6c97593d08a526dab6b13d847a1ac086611e0272555.jpg", + "table_caption": [ + "Table 3: Performance on different datasets and horizons. The mean of various metrics (Sec. 3.1) obtained using 5 runs with different random seeds (std. errors are provide in Appendix E). Note that the action and observation history are the output of the separately finetuned video-action segmentation model and hence are noisy compared to the ground truth history." + ], + "table_footnote": [], + "table_body": "
GAkOkl = 3l = 1
SRmAccmIOUnAcc
1XXok6.8 ± 0.328.3 ± 1.934.8 ± 2.044.5 ± 3.8
2✓Xok8.9 ± 0.234.7 ± 0.741.6 ± 0.853.1 ± 2.0
3✓✓X14.9 ± 0.337.8 ± 0.450.8 ± 0.648.0 ± 0.2
4✓✓Ok15.2 ± 0.343.5 ± 0.851.4 ± 0.964.8 ± 0.9
R✓✓Ok10.7 ± 0.236.5 ± 0.741.7 ± 0.661.4 ± 1.8
", + "bbox": [ + 498, + 88, + 893, + 210 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4: Role of different inputs and LM pre-training in VLaMP. $G$ , $A_{k}$ , $O_{k}$ denote the three inputs to VLaMP: goal, action history and observation history, respectively. Shorthand of $o_{k}$ means only the most recent observation of the full history ( $O_{k}$ ) is used. Mean $\\pm$ std. error over 5 random seeds on CrossTask are reported. The row R corresponds to the forecasting module of VLaMP trained with random initialization (same model architecture) as opposed to initialization using the weights of a pre-trained LM.", + "bbox": [ + 496, + 220, + 893, + 357 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "that the prompt based model performs significantly worse than VLaMP. This highlights that VPA is not easy to solve using just a PTLM and prompting.", + "bbox": [ + 496, + 383, + 890, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Ablations and Error Analysis", + "text_level": 1, + "bbox": [ + 498, + 439, + 764, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We undertake head-on ablations to quantify effect of each component of VLaMP - action history, the visual history, and language pre-training of the LM. To remove confounding factors, in Tab. 4 we use the ground truth output for the segmentation module. Following this, we include detailed error analysis.", + "bbox": [ + 496, + 462, + 890, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Action and observation history improve complementary planning metrics. As seen in all the rows with action history Tab. 4 (i.e. $A_{k}$ ), the provision of action history increases difficult metrics such as SR. In comparing rows 2 and 3, we see that SR increases relatively by $67\\%$ ( $8.9 \\rightarrow 14.9$ ), simply by using action history even without access to any past observation. However, the lack of observation history affects nAcc, which drops relatively by $10\\%$ ( $53.1 \\rightarrow 48.0$ ) when observation history is swapped by action history between rows 2 and 3. This implies that observation history is important to predict the person's state in the task and what they might do next.", + "bbox": [ + 496, + 553, + 890, + 734 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Priors from the pre-trained LM improve performance. In Tab. 4 row $\\mathbf{R}$ , we report the performance of VLaMP when its forecasting module is trained with random weight initialization, i.e., the transformer of the same architecture trained from scratch instead of LM pre-training. We find the performance in row $\\mathbf{R}$ is thus much lower than that of VLaMP with pre-trained LM shown in row 4. This underscores the crucial importance of LM pre-training.", + "bbox": [ + 496, + 734, + 890, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Segmentation errors are detrimental. While the accuracy of video-action segmentation module (particularly, VideoCLIP model) is quite good - $80.2\\%$ for CrossTask $(68.7\\%)$", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15309", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "for COIN), we believe this should be a major focus for future research. Why? The effect of this segmentation error in VLaMP's performance is quantified by comparing VLaMP row in Tab. 3 (CrossTask) with corresponding performance assuming perfect segmentation (Tab. 4, row 4). A relative $50\\%$ gap in success and big gaps in all other metrics.", + "bbox": [ + 75, + 90, + 470, + 183 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/1a3965aa5361235b0aeb78132271c2c58450cde177458ff8458ef9f46b8fe7fb.jpg", + "image_caption": [ + "Figure 5: Effect of segmentation errors. Performance of VLaMP on CrossTask with classification errors $(\\%)$ in the video-action segmentation. As the errors increase, the performance gap between the full model and the one without access to observations increases." + ], + "image_footnote": [], + "bbox": [ + 109, + 202, + 429, + 421 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Visual observation history mitigates effect of video-action segmentation errors. Errors by segmentation module lead to mis-classification of actions, in turn leading to erroneous action history. To precisely study the effect of erroneous action history on VLaMP's performance, we perform controlled experiments wherein we add noise in the ground truth segmentation. This helps us tune desired segmentation error, irrespective of VideoCLIP's accuracy (in segmentation module). We achieve this by replacing a calculated $\\%$ of ground-truth actions by random actions. Decreasing performance, with increasing segmentation classification error, is expected and observed in Fig. 5. Further, we compare two models variations, VLaMP $(G, A_k, O_k)$ i.e. the full model (uses both action and observation history) and VLaMP $(A, A_k)$ that does not have visual observation history. As we increase segmentation classification error, the gap in the performance of these model variations increases. We infer that visual observations add robustness in VPA against video-action segmentation errors.", + "bbox": [ + 75, + 521, + 468, + 808 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Errors do not drop as more history is provided. In Fig. 6, we show mAcc w.r.t. the number of steps $k$ in the history i.e. length of $(O_k, A_k)$ . As more information is available (due to more steps in the history), one may expect the accuracy to improve. However, this isn't the trend for many tasks. For e.g., note the accuracy drops for the task \"add oil to your", + "bbox": [ + 75, + 810, + 468, + 901 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/983469d45deed55ff647f7b9a6fea5e7bdadcd974307ea4747d1428276bdfc34.jpg", + "image_caption": [ + "Figure 6: Accuracy in the tail of long activities is challenging. Longer history $(O_{k},A_{k})$ do not necessary lead to better accuracy. Further longer histories occur with increasing rarity, leading to learning challenges. (Plot shows mAcc for $l = 3$ CrossTask vs. the #steps in history $k$ )" + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 893, + 250 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "car” w.r.t $k$ . Digging deeper, we find two reasons for this pattern. First, we find that tasks with long history like “add oil to your car” tend to have repetitive steps towards the end of their action trajectories, making it difficult to predict the precise number and the pattern of such repetitions in VPA. Second is simply a data issue – long trajectories are also exponentially less frequent in the dataset. This forms the tail of the data distribution of action sequences in the dataset (see App. E for statistics). Consequently, prediction in this tail of activities, is a pertinent challenge for future research.", + "bbox": [ + 496, + 363, + 890, + 515 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 530, + 617, + 545 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Visual Planning for Assistance is a new and intuitive formulation to support planning from natural visual observations for assisting humans in day-to-day activities. We benchmark VPA using standardized suite of prior baselines and a new multi-modal sequence modeling formation of VLaMP. The novel decomposition of a VLaMP policy into video action segmentation and forecasting leads to several efficiency and modeling benefits, that benefit the community, even beyond VPA. Particularly, this allows to leverage pre-trained LM that leads to significant performance gains. Alternative decompositions, self-supervised pre-training objectives for PTLMs, modeling multiple actors, and tapping into other modalities (audio, camera metadata, etc.) [26, 55, 43, 72, 32, 88] are interesting ways forward for the community, on the exciting task of VPA.", + "bbox": [ + 496, + 555, + 890, + 782 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements: The authors are indebted to Brian Chen for his efforts to open-source the code and LTA experiments, and to Gideon Stocek for supporting with the cluster management. We thank Vasu Sharma, Tushar Nagarajan, and Homanga Bharadhwaj for their writing feedback. We thank Weichao Mao for early discussions and Asli Celikyilmaz for her constant guidance.", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "15310", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Yazan Abu Farha, Alexander Richard, and Juergen Gall. When will you do what?-anticipating temporal occurrences of activities. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 5343-5352, 2018. 2", + "[2] Armen Aghajanyan, Bernie Huang, Candace Ross, Vladimir Karpukhin, Hu Xu, Naman Goyal, Dmytro Okhonko, Mandar Joshi, Gargi Ghosh, Mike Lewis, et al. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3537-3545, 2019. 1, 3, 4, 7, 8" + ], + "bbox": [ + 78, + 90, + 468, + 766 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "15314", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 12 + } +] \ No newline at end of file diff --git a/2023/Pretrained Language Models as Visual Planners for Human Assistance/057af23b-bb0a-449d-acad-c434ed40a938_model.json b/2023/Pretrained Language Models as Visual Planners for Human Assistance/057af23b-bb0a-449d-acad-c434ed40a938_model.json new file mode 100644 index 0000000000000000000000000000000000000000..96904c1bba46aa219c0494941567a1091c6cc8c1 --- /dev/null +++ b/2023/Pretrained Language Models as Visual Planners for Human Assistance/057af23b-bb0a-449d-acad-c434ed40a938_model.json @@ -0,0 +1,2811 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.128, + 0.131, + 0.843, + 0.154 + ], + "angle": 0, + "content": "Pretrained Language Models as Visual Planners for Human Assistance" + }, + { + "type": "text", + "bbox": [ + 0.253, + 0.18, + 0.726, + 0.253 + ], + "angle": 0, + "content": "Dhruvesh Patel\\(^{1,2}\\) Hamid Eghbalzadeh\\(^{1}\\) Nitin Kamra\\(^{1}\\) Michael Louis Iuzzolino\\(^{1}\\) Unnat Jain\\(^{1*}\\) Ruta Desai\\(^{1*†}\\) \\(^{1}\\)Meta \\(^{2}\\)UMass Amherst https://github.com/facebookresearch/vlamp" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.474, + 0.697 + ], + "angle": 0, + "content": "In our pursuit of advancing multi-modal AI assistants capable of guiding users to achieve complex multi-step goals, we propose the task of 'Visual Planning for Assistance (VPA)'. Given a succinct natural language goal, e.g., \"make a shelf\", and a video of the user's progress so far, the aim of VPA is to devise a plan, i.e. a sequence of actions such as \"sand shelf\", \"paint shelf\", etc. to realize the specified goal. This requires assessing the user's progress from the (untrimmed) video, and relating it to the requirements of natural language goal, i.e. which actions to select and in what order? Consequently, this requires handling long video history and arbitrarily complex action dependencies. To address these challenges, we decompose VPA into video action segmentation and forecasting. Importantly, we experiment by formulating the forecasting step as a multimodal sequence modeling problem, allowing us to leverage the strength of pre-trained LMs (as the sequence model). This novel approach, which we call Visual Language Model based Planner (VLaMP), outperforms baselines across a suite of metrics that gauge the quality of the generated plans. Furthermore, through comprehensive ablations, we also isolate the value of each component - language pretraining, visual observations, and goal information. We have open-sourced all the data, model checkpoints, and training code." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.728, + 0.21, + 0.743 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.754, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Imagine assembling a new piece of furniture or following a new recipe for a dinner party. To achieve such a goal, you might follow a manual or a video tutorial, going back and forth as you perform the steps. Instead of fumbling through a manual, imagine an assistive agent capable of being invoked through natural language, having the ability to understand human actions, and providing actionable multi-step guidance for achieving your desired goal. Such multi-" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.285, + 0.895, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.473, + 0.893, + 0.596 + ], + "angle": 0, + "content": "Figure 1: Visual Planning for Assistance overview (top) and general methodology (bottom). Given a user-specified, natural language goal (\"build a shelf\") and corresponding visual history of the user's progress till now, VPA involves predicting a sequence of actions, to assist the user towards the goal (\"cut\", \"sand\", \"paint\"). Our approach is based on multi-modal sequence modeling where we reuse pre-trained video segmentation and language models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.893, + 0.673 + ], + "angle": 0, + "content": "modal assistive agents should be able to reason human activities from visual observations, contextualize them to the goal at hand, and plan future actions for providing guidance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.902 + ], + "angle": 0, + "content": "To quantify the progress and aid the development of such multi-modal neural models, we need a intuitive task, as illustrated in the example in Fig. 1 (top). We call this Visual Planning for Assistance (VPA) that we detail next. Given a user-specified goal in natural language (\"build shelf\") and corresponding video observations of the user's progress towards this goal, the task objective should be to generate the ordered sequence of next actions towards achieving the goal (\"cut \\(\\rightarrow\\) sand \\(\\rightarrow\\) paint\"). We base VPA off instructional YouTube videos of such procedural activities from large, open-sourced datasets - CrossTask [89] and COIN [73]. This is a natural choice as procedural human activities (cooking, assembly, repair, etc.) are a perfect source of multi-step and complex sequence of actions, where humans routinely seek guidance. Realistic nature" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.322, + 0.901 + ], + "angle": 0, + "content": "*equal mentoring † corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15302" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.182 + ], + "angle": 0, + "content": "of VPA makes it particularly challenging. Operating on untrimmed videos requires dealing with potentially many irrelevant background frames, chunking actions in the videos will also be imperative. Another challenge is the validity of the plan of actions i.e. they must respect the constraints of the activity – the shelf shouldn't be painted before sanding." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.471, + 0.558 + ], + "angle": 0, + "content": "The natural next question is - what's a good way to tackle VPA? Marrying research from video forecasting & anticipation with embodied AI [19, 17], we cast VPA as goal-conditioned task planning. We approach VPA by utilizing video action segmentation and transformer-based neural sequence modeling - the former allows us to deal with long video history and the latter can handle arbitrary sequential constraints [86, 39]. The formulation (particularly, transformer-based neural sequence modeling) allows us to tap into the prowess of pre-trained language models (PTLMs). These PTLMs contain useful priors about action-action similarity, action-goal association, and action ordering [7, 30, 58], that our formulation can piggy-back off. Particularly, our model - Visual Language Model Planner (VLaMP) - conditions the generated plan onto the visual history by using a transformer-based mapper network that projects embeddings corresponding to visual history into the input space of the LM. Using VPA as the testbed, we show that VLaMP outperforms a range of standardized baselines. We undertake head-on ablations to quantify effect of each component of VLaMP - language pre-training of the LM, the visual history, and goal description. We believe the modularity of our approach can allow researchers to swap components with their own, to make rapid progress towards VPA." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.56, + 0.47, + 0.695 + ], + "angle": 0, + "content": "In summary, our main contributions are: (1) a new task VPA on human interaction videos capturing unique aspects of real-world vision-powered assistive agents; (2) a general-purpose methodology for VPA, which allows leveraging pre-trained multi-modal encoders and sequence models; (3) an instantiation of this methodology (we call VLaMP), where we reuse sequence priors from PTLM and investigate its efficacy across two, well-studied datasets of procedural human activities." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.71, + 0.219, + 0.725 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Forecasting in Videos. VPA entails future action sequence prediction for a video and is closely related to anticipation in video understanding, including future localization [22, 40, 78], future frame prediction [77, 46, 53], next active object estimation [21, 5, 25, 67, 4, 24, 44], as well as short- and long-term action anticipation [66, 15, 20, 23, 25, 65, 64, 57, 45, 1, 52, 50, 11, 79]. While short-term forecasting approaches, such as [66], are limited to predicting the single next action occurring only a few seconds into the future, our work focuses on predicting sequences of actions over longer time horizons (on the order of minutes)" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.089, + 0.894, + 0.169 + ], + "angle": 0, + "content": "
Action PredictionGoal ModalityVisual Reasoning
Action anticipation [14]SingleNoneVideo-based
Action forecasting [25]Multiple, orderedNoneVideo-based
Procedural planning [9]Multiple, orderedVisionImage-based
VPA (ours)Multiple, orderedNatural LanguageVideo-based
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.179, + 0.894, + 0.253 + ], + "angle": 0, + "content": "Table 1: VPA vs. prior tasks related to forecasting of real-world human activities. We predict an ordered sequence of actions given video history with a focus on natural language goal-conditioning for human-assistive applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.281, + 0.893, + 0.492 + ], + "angle": 0, + "content": "into the future. The long-term action (LTA) forecasting benchmarking was recently established on a small subset of Ego4D [25], and although VPA is similarly devised to predict a temporally ordered sequence of actions conditioned on video-based visual observations, our approach differs in that the LTA task does no goal-conditioning. Our task incorporates goal-conditioning on long term sequence prediction as we argue this will drive the development of critical system aspects, such as virtual assistants that afford human interaction via the natural language goals. Additionally, in contrast to LTA, we focus on a wide range of goal-oriented activities available within the CrossTask and COIN datasets. Tab. 1 highlights the differences between VPA and other forecasting tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.893, + 0.765 + ], + "angle": 0, + "content": "Procedural Planning Approaches. VPA is similar to the task of procedure planning [9], wherein given a starting and terminating visual observation, the aim is to predict the actions that would transform the state from starting to terminating. However, we argue that due to the unavailability of the terminating visual state, the procedure planning task is not useful in a real-world assistance setting. While several recent works introduce novel models for procedure planning, these models cannot be deployed for VPA either because they rely heavily on the availability of visual goal [70, 87, 6], or assume access to true action history [49]. Transformers for Decision Making. VLaMP autoregressively predicts future states and/or observations and actions and is similar in spirit to sequence models for decision making such as GATO [61], Decision Transformer [12], and Trajectory Transformer [35]. VLaMP extends such models to work with egocentric observations that humans observe in the day-to-day activities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Planning in Embodied AI using LMs. Past research has leveraged PTLMs for task planning in real world for embodied agents [30, 68, 41, 7, 42, 31, 18, 16, 36]. Many of these works focus on converting a high-level task or instruction into sequence of low-level steps and then ground them in the environment using either affordance functions [7], visual feedback [31], or multimodal prompts [36, 18]. Owing to their focus on robotic agents, these works focus on predominately pick-place tasks. Instead VPA is focused on" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15303" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.182 + ], + "angle": 0, + "content": "complex tasks, in which humans might require assistance in the form of recommended future actions. Consequently, VLaMP requires grounding and reasoning of much more complex states and actions, which it accomplishes by finetuning a pretrained LM on multimodal sequences of (visual) observations and (text-based) actions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.473, + 0.442 + ], + "angle": 0, + "content": "Multi-modal LMs. Recent works have successfully used the transformer architecture for modeling multi-modal sequences that have visual tokens. For instance, [47, 59, 2, 48, 29, 18] train large transformer based multi-modal sequence prediction models. While [3, 74, 56] focus on adapting pre-trained LMs to work with visual tokens by aligning the representation spaces of the two modalities. VLaMP's approach of modeling sequence of visual and textual representations using PTLMs is similar in spirit to these, i.e. VLaMP also uses a mapper network to align video representations to LM's token space and jointly learns the mapper with LM finetuning for VPA. However, in contrast to previous works, VLaMP predicts the visual tokens autoregressively at inference time to enable forecasting of the state for planning. Consequently, VLaMP's token prediction loss is multi-modal, unlike most multi-modal LMs that only use token prediction loss for text tokens." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.457, + 0.357, + 0.473 + ], + "angle": 0, + "content": "3. Visual Planning for Assistance" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.483, + 0.47, + 0.575 + ], + "angle": 0, + "content": "Here, we introduce the task of Visual Planning for Assistance (VPA), towards enabling multi-step guidance to humans in their real-world activities. We instantiate VPA for procedural activities, where humans routinely seek assistance. In this section, we include the definition of VPA, and describe the evaluation protocol." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.587, + 0.232, + 0.602 + ], + "angle": 0, + "content": "3.1. Task Definition" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.611, + 0.469, + 0.641 + ], + "angle": 0, + "content": "The following two intuitive inputs are given to any model performing VPA." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.469, + 0.702 + ], + "angle": 0, + "content": "Goal Prompt \\((G)\\). The natural language description (in short phrase) of the user's goal, emulating a typical user's request for assistance for a day-to-day task. Examples include, \"build a shelf\" and \"change a tire\"." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.469, + 0.793 + ], + "angle": 0, + "content": "Visual History \\((V_{t})\\). An untrimmed video that provides context about the user's progress towards a goal from the start till time, say \\(t\\). We assume that \\(V_{t}\\) contains \\(k\\) actions or steps \\(\\{a_1,\\ldots ,a_k\\}\\) pertaining to the goal. However, VPA doesn't have access to \\(\\{a_1,\\dots ,a_k\\}\\) or \\(k\\) and must work with \\(V_{t}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.903 + ], + "angle": 0, + "content": "Given these two inputs, \\( V_{t} \\) and \\( G \\), the objective of VPA is to generate a plan \\( \\mathcal{T} \\). The plan is a sequence of actions that should be executed (in the next steps) to assist the user in achieving the goal \\( G \\). Concretely, the prediction is denoted by \\( \\mathcal{T} = (a_{k + 1},\\dots ,a_{k + l}) \\), where \\( a_{i} \\) are represented in natural language but come from a closed set \\( \\mathcal{A} \\). Here, \\( l\\leq K \\) denotes the number of future actions that should be predicted," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "out of the \\(K\\) number of remaining actions required to accomplish the goal. For our shelf-building example, the correct \\(\\mathcal{T} =\\) (sand shelf, paint shelf, attach shelf), capturing the remaining 3 future actions (here, \\(l = N = 3\\))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.153, + 0.893, + 0.318 + ], + "angle": 0, + "content": "In day-to-day activities, we request assistance for goals in natural language. However, prior works procedural planning [9, 6] assume access to visual goal state. This is not a realistic assumption for an AI agent assisting humans. Hence, we purposefully relax this assumption, making our formulation of the task significantly more practical. Moreover, an agent with access to the visual modality, should be able to improve its plan by filtering out relevant information from the raw video stream of the progress. These are the two central assumptions around which we formulate the task of VPA." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.328, + 0.621, + 0.343 + ], + "angle": 0, + "content": "3.2. Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.352, + 0.892, + 0.412 + ], + "angle": 0, + "content": "Open-Sourced Video Data. We leverage existing datasets CrossTask [89] and COIN [73], originally developed to enable video action understanding for VPA, based on the following three requirements:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.413, + 0.892, + 0.472 + ], + "angle": 0, + "content": "- Rich diversity of activities from multiple domains: The data from different domains such as cooking, assembly etc., enables testing of VPA models in a more generalized manner." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.474, + 0.894, + 0.547 + ], + "angle": 0, + "content": "- Goal-oriented activities consisting of long sequences of actions: Since the objective is to generate \\( l \\) future actions, activities in these datasets that require diverse sequences of actions e.g., \"making a pancake\", instead of \"running\" are more suitable for VPA." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.549, + 0.892, + 0.73 + ], + "angle": 0, + "content": "- Action annotations from a fixed closed set of actions: Action labels described using verb-noun from a finite set [14], which are temporally aligned with the videos. This makes evaluating the accuracy of \\(\\mathcal{T}\\) prediction straightforward. Specifically, free-form, narration-style descriptions of actions that are available in recent video datasets aid in efficient multi-modal representation learning for video understanding [25, 54]. However, evaluating the quality of action sequences towards goal achievement, where each action is described in free-form natural language, is non-trivial. We leave the instantiation of VPA with free-form natural language actions as future work." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.731, + 0.892, + 0.761 + ], + "angle": 0, + "content": "Table 2 summarizes the features from CrossTask and COIN, aligned with the above requirements." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.413, + 0.894, + 0.761 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Metrics. The planning performance of a VPA model is measured by comparing the generated plan \\(\\hat{\\mathcal{T}} = (\\hat{a}_{k + 1},\\dots ,\\hat{a}_{k + l})\\) to the ground truth plan \\(\\mathcal{T}\\) for \\(l\\) actions in the future, given \\(V_{t}\\) and \\(G\\). Here \\(\\hat{a}_{k + i}\\) denotes the prediction for the \\(k + i\\)-th step given history till \\(k\\)-th step. Consistent with community practices [9, 6], we use the following metrics, listed in decreasing order of strictness: success rate (SR), mean accuracy (mAcc), mean intersection over union" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15304" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.089, + 0.472, + 0.147 + ], + "angle": 0, + "content": "
Dataset# train videos# test videos# test samplesactions per video# goals# domains
CrossTask [89]175675241237.6 ± 4.3183
COIN [73]9428104720113.9 ± 2.418012
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.155, + 0.47, + 0.217 + ], + "angle": 0, + "content": "Table 2: VPA datasets. We evaluate VPA on two existing video datasets containing multiple goal-oriented procedural activities from varied domains. Such activities contain sequences of multiple actions making them ideal for VPA." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.471, + 0.366 + ], + "angle": 0, + "content": "(mIOU). Success rate requires an exact match between all actions and their sequence between \\(\\hat{\\mathcal{T}}\\) and \\(\\mathcal{T}\\). Mean accuracy is the accuracy of the actions at each step. Unlike success rate, mean accuracy does not require a \\(100\\%\\) match to ground truth. Instead it considers matching at each individual step. Lastly, mean intersection over union captures the cases where the model predicts the steps correctly, but fails to identify the correct order. Concretely," + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.388, + 0.47, + 0.427 + ], + "angle": 0, + "content": "\\[\n\\mathrm {m I O U} _ {l} = \\frac {\\left| \\hat {a} _ {\\{k + 1 : k + l \\}} \\bigcap a _ {\\{k + 1 : k + l \\}} \\right|}{\\left| \\hat {a} _ {\\{k + 1 : k + l \\}} \\bigcup a _ {\\{k + 1 : k + l \\}} \\right|}, \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.429, + 0.469, + 0.469 + ], + "angle": 0, + "content": "\\[\n\\mathrm {m A c c} _ {l} = \\frac {1}{l} \\sum_ {i = 1} ^ {l} \\mathbb {1} [ \\hat {a} _ {k + i,} = a _ {k + i} ], \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.473, + 0.469, + 0.514 + ], + "angle": 0, + "content": "\\[\n\\mathrm {S R} _ {l} = \\prod_ {i = 1} ^ {l} \\mathbb {1} [ \\hat {a} _ {k + i} = a _ {k + i} ], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.525, + 0.47, + 0.648 + ], + "angle": 0, + "content": "where \\(\\mathbb{1}[\\cdot ]\\) is the identity function, which is 1 when the condition in its input is true, and 0, and \\(\\hat{a}_{\\{k + 1:k + l\\}}\\) denotes the set of \\(l\\) future actions in \\(\\tilde{\\mathcal{T}}\\), i.e., a sequence but disregarding the order. To complement the above metrics, we also measure the accuracy of predicting the next action i.e. nAcc, as defined in (4), where 'n' stands for next. Note that all metrics are averaged over the test set details of which are included in Sec. 5." + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.661, + 0.469, + 0.679 + ], + "angle": 0, + "content": "\\[\n\\mathrm {n A c c} = \\mathbb {1} [ \\hat {a} _ {k + 1} = a _ {k + 1} ] \\tag {4}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.692, + 0.264, + 0.708 + ], + "angle": 0, + "content": "4. Visual LM Planner" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.717, + 0.47, + 0.854 + ], + "angle": 0, + "content": "VPA can be viewed as a sequential decision making problem, where the model (say, \\(\\pi\\)) predicting the sequence of next actions is a policy conditioned on the visual history \\(V_{t}\\), serving as (partially-observed) state, and goal prompt \\(G\\). Inspired by the offline learning formulation closest to 'learning from offline demonstrations' [27, 76, 37, 81], in VLaMP, we formulate VPA as a goal-conditioned, multimodal sequence prediction problem. This formulation allows us to leverage high-capacity sequence models like" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.863, + 0.469, + 0.901 + ], + "angle": 0, + "content": "1Future works may explore alternate policy optimizations based on reward shaping, inverse RL, or by employing additional online interactions through photorealistic simulation [38, 63, 71, 69, 82, 33, 34, 10, 80]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.228 + ], + "angle": 0, + "content": "Transformers [75], which have been successfully applied to sequential decision making [35, 12]. Furthermore, inspired by the recent success of pre-trained transformer language models (PTLMs) on such tasks, [62, 30, 12], we propose to leverage PTLMs as the sequence model in our formulation. In the remainder of this section we describe our approach for VPA, called Visual Language Model based Planner (VLaMP), consisting of a segmentation module and PTLM based sequence prediction module." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.24, + 0.88, + 0.257 + ], + "angle": 0, + "content": "4.1. Planning with Segmentation and Forecasting" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.264, + 0.892, + 0.295 + ], + "angle": 0, + "content": "We define \\(\\pi\\) as a goal-conditioned, multi-modal sequence prediction problem:" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.309, + 0.892, + 0.326 + ], + "angle": 0, + "content": "\\[\n\\pi = P \\left(a _ {k + 1}, a _ {k + 2}, \\dots \\mid V _ {t}, G\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.892, + 0.368 + ], + "angle": 0, + "content": "where \\(\\pi\\) models the probability of goal-relevant and valid future actions sequences conditioned on \\(V_{t}\\) and \\(G\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.37, + 0.893, + 0.656 + ], + "angle": 0, + "content": "Modeling the multi-modal sequence in Eq. 5 is computationally expensive and difficult to scale because of the high-dimensional state space of raw untrimmed video \\( V_{t} \\). Also, there is limited data to learn the distribution over valid action sequences for goals in real-world applications. Tackling these challenges, we argue that the latent space of factors influencing the future plan can indeed be expressed in lesser dimensions. Particularly, to ensure scalability for handling raw videos and sample efficiency in learning valid action sequence distributions, we decompose our policy \\( \\pi \\) into two modules. The first module is video segmentation, which converts the untrimmed video history \\( V_{t} \\) into a sequence of video segments i.e. a segment history \\( S_{k} = (s_{1},\\dots ,s_{k}) \\), where each segment corresponds to an action \\( a_{i} \\) that occurred in the video. The second module enables forecasting i.e. it transforms the output of the segmentation module and generates the plan (see Fig. 1 (bottom)). While a probabilistic formulation of this decomposition can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.67, + 0.892, + 0.707 + ], + "angle": 0, + "content": "\\[\n\\pi = \\sum_ {S _ {k}} \\underbrace {P \\left(a _ {k + 1} , a _ {k + 2} , \\cdots \\mid S _ {k} , G\\right)} _ {\\text {F o r e c a s t i n g}} \\underbrace {P \\left(S _ {k} \\mid V _ {t}\\right)} _ {\\text {S e g m e n t a t i o n}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.795 + ], + "angle": 0, + "content": "where the segment history \\( S_{k} \\) is a latent variable, the summation over all possible segment histories is intractable. We, however, use Eq. 6 as the guiding expression to formulate the input and output of both modules. Next, we include the technical details of both of these modules." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.808, + 0.706, + 0.824 + ], + "angle": 0, + "content": "4.2. Segmentation Module" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.832, + 0.892, + 0.863 + ], + "angle": 0, + "content": "This module splits the untrimmed video history \\( V_{t} \\) into segment history \\( S_{k} \\) of multiple segments, each segment" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\(^{2}\\)A typical untrimmed video of 100p video of 5 minutes at 8fps will have \\(2^{7}\\) raw pixel values." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15305" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.093, + 0.462, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.248, + 0.47, + 0.339 + ], + "angle": 0, + "content": "Figure 2: VLaMP - Segmentation Module. The untrimmed visual history \\( V_{t} \\) is converted into segments, each consisting of observation \\( o_{i} \\) and the action \\( a_{i} \\). The observation \\( o_{i} \\) is the collection of video frames of \\( \\delta \\) seconds around the start time stamp \\( t_{i} \\) of the corresponding action \\( a_{i} \\). Two such segments are shown here." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.367, + 0.473, + 0.671 + ], + "angle": 0, + "content": "corresponding to an action. The segmentation is done using a video-action segmentation model in three steps: preprocessing, classification, and consolidation. In the preprocessing step, the raw video frames from \\( V_{t} \\) are bundled into fixed-length window clips \\( c_{i} \\), each of length 1 second, to obtain \\( V_{t} = (c_{1},\\dots ,c_{t}) \\). In the classification step, a video-action segmentation model is used to output the most probable action for each clip \\( c_{i} \\), which can be denoted as \\( \\tilde{A}_t = (\\tilde{a}_1,\\tilde{a}_2,\\ldots ,\\tilde{a}_t) \\). Finally, in the consolidation steps, we convert \\( \\tilde{A}_t \\) into a form that can be used by the forecasting module; this form consists of two sequences: action history \\( A_{k} \\) and observation history \\( O_{k} \\). To this end, same actions in consecutive seconds in \\( \\tilde{A}_t \\) are consolidated to form the action history \\( A_{k} = (a_{1},\\dots ,a_{k}) \\). As illustrated in Fig. 2, assuming \\( t_i \\) denotes the starting timestamp for \\( a_{i} \\), we also extract video frames from \\( t_i - \\delta /2 \\) to \\( t_i + \\delta /2 \\) to obtain an observation window \\( o_i \\) corresponding to \\( a_{i} \\), and consequently the full observation history \\( O_{k} = (o_{1},\\dots,o_{k}) \\). The resultant segment history is termed \\( S_{k} = ((o_{1},a_{1}),\\dots ,(o_{k},a_{k})) \\), summarized in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.679, + 0.267, + 0.695 + ], + "angle": 0, + "content": "4.3. Forecasting Module" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.47, + 0.791 + ], + "angle": 0, + "content": "The usefulness of \\(\\pi\\)'s decomposition expressed in Eq. (6) becomes apparent now. Modeling the segmentation module's output as segment history \\(S_{k}\\), where each segment consisting of action and observations, allows writing the output of the forecasting module in an autoregressive manner:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.806, + 0.47, + 0.86 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} P \\left(a _ {k + 1}, a _ {k + 2}, \\dots \\mid o _ {1}, a _ {1}, \\dots , o _ {k}, a _ {k}, G\\right) \\\\ = \\prod_ {i > 0} \\sum_ {o _ {k + i}} P \\left(o _ {k + i}, a _ {k + i} \\mid o _ {1}, a _ {1}, \\dots , o _ {k}, a _ {k}, G\\right). \\tag {7} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Illustrated in Fig. 3, this autoregressive expression allows the possibility of using any sequence-to-sequence neural" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.226 + ], + "angle": 0, + "content": "network as the forecasting module in combination with pretrained text and video encoders for representing action and observation history \\( A_{k} \\) and \\( O_{k} \\). This general-purpose framework allows the use of any neural sequence model – LSTM [28], GRU [13], Transformers [75], etc. We choose to instantiate the forecasting module for \\( \\pi \\) using a pretrained transformer-based LM. Next we present the details of the encoders for the two modalities and the LM based sequence model." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.228, + 0.892, + 0.273 + ], + "angle": 0, + "content": "Action encoder \\((f_{\\mathrm{act}})\\) Each action \\(a_i\\) in \\(A_k\\) is encoded by \\(f_{\\mathrm{act}}\\) and the output is denoted by \\(\\alpha_i\\). Concretely, token embeddings are expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.282, + 0.891, + 0.32 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\left(\\alpha_ {1}, \\dots , \\alpha_ {k}\\right) = \\left(f _ {\\text {a c t}} \\left(a _ {1}\\right), \\dots , f _ {\\text {a c t}} \\left(a _ {k}\\right)\\right), \\text {w h e r e} \\\\ \\alpha_ {i} = \\left(\\alpha_ {i} ^ {1}, \\dots , \\alpha_ {i} ^ {r _ {i}}\\right) \\in \\mathbb {R} ^ {r _ {i} \\times d} \\tag {8} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.328, + 0.892, + 0.418 + ], + "angle": 0, + "content": "As we illustrate in Fig. 3 (left), each action \\( a_i \\) is tokenized into \\( r_i \\) tokens using appropriate tokenizer for the LM, the tokens are indexed using the vocabulary of the LM, and are represented using an embedding lookup from the token embeddings of the LM to produce \\( \\alpha_i \\). Here, \\( r_i \\) is the number of tokens and \\( d \\) is the dimensionality of token embeddings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.419, + 0.892, + 0.601 + ], + "angle": 0, + "content": "Observation encoder \\((f_{\\mathrm{obs}})\\). Visual cues play an integral role in knowing what actions lie ahead, towards achieving the goal prompt \\(G\\). To this end, the visual observations \\(O_k\\) are encoded and play a critical role in the planner. Recall, the visual observation history \\(O_k\\) comprises of \\(o_i\\) corresponding to action \\(a_i\\), each of \\(\\delta\\) frames. As illustrated in Fig. 3 (middle), we transform each \\(o_i\\) employing the widely-adopted S3D backbone [84] \\(f_{\\mathrm{S3D^*}}\\) (* denotes backbone is frozen). We must project visual encodings to a shared latent space of action (language) embeddings described before \\((\\alpha_i)\\). To this end, we map S3D features via a trainable transformer mapper \\(f_{\\mathrm{map}}\\). Concretely," + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.609, + 0.892, + 0.648 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\left(\\beta_ {1}, \\dots , \\beta_ {k}\\right) = \\left(f _ {\\mathrm {o b s}} \\left(o _ {1}\\right), \\dots , f _ {\\mathrm {o b s}} \\left(o _ {k}\\right)\\right), \\text {w h e r e} \\\\ \\beta_ {i} = \\left(\\beta_ {i} ^ {1}, \\dots , \\beta_ {i} ^ {\\delta}\\right) \\in \\mathbb {R} ^ {\\delta \\times d} \\text {a n d} f _ {\\mathrm {o b s}} = f _ {\\mathrm {S 3 D} ^ {*}} \\circ f _ {\\mathrm {m a p}} \\tag {9} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.655, + 0.892, + 0.686 + ], + "angle": 0, + "content": "Overall, as we show in Fig. 3 (right), the resultant encoded sequence of representation for \\( S_{k} \\) is thus" + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.695, + 0.828, + 0.712 + ], + "angle": 0, + "content": "\\[\nf _ {\\text {e n c}} (S _ {k}) = \\left(\\beta_ {1}, \\alpha_ {1}, \\dots , \\beta_ {k}, \\alpha_ {k}\\right) = H _ {k},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Sequence model \\((f_{\\mathrm{seq}})\\). Given the above encoding for the segment history \\(S_{k}\\), the role of the sequence model is to predict a representation of the next token, that would in return enable VLaMP plan generation capabilities for VPA. Importantly, in the process of generating sequence of future actions autoregressively, we would also need to generate the representations of 'future observations'. Therefore, as we shown in Fig. 3, our sequence model, which consists of the transformer layers of a PTLM, also produces representations for vision (in addition to the necessary action tokens). Before proceeding further, we pause and introduce additional notation for the sequence model, which" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15306" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.16, + 0.089, + 0.481, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.089, + 0.847, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.247, + 0.895, + 0.325 + ], + "angle": 0, + "content": "Figure 3: VLaMP - Forecasting Module. As shown in left and middle, actions and observations obtained from the segmentation module are encoded using appropriate modality encoders. The observation encoder leverages pretrained video encoder for observations, while also learning a mapper that aligns the representations from observations with actions. As shown on the right, VLaMP uses a joint sequence model on top of interleaved action (blue) and observation (gray) representations to forecast autoregressively the next representation." + }, + { + "type": "image", + "bbox": [ + 0.129, + 0.345, + 0.431, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.44, + 0.471, + 0.502 + ], + "angle": 0, + "content": "Figure 4: Tokenized Sequence with Masks. The encoded sequence of representations for \\( k = 2 \\) segments, denoted alternatively using modality agnostic notation of \\( H_{2} \\) and mask \\( M \\) for next token prediction training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.528, + 0.47, + 0.684 + ], + "angle": 0, + "content": "will make the subsequent explanation for training and inference easier to follow. As shown in Figure 4, we alternatively denote the sequence of representations \\((\\beta_{1},\\alpha_{1},\\ldots ,\\beta_{k},\\alpha_{k})\\) by \\(H_{k} = (h_{1},\\dots,h_{n})\\), with \\(n = k\\delta +\\sum_{i = 1}^{k}r_{i}\\). A binary mask \\(M = (m_{1},\\dots,m_{n})\\), where \\(m_{i}\\) is 1 if the corresponding representation is for an action and 0 otherwise, can help obtain necessary action or visual observations. With this notation, given first \\(j\\) representations denoted as \\(h_{1:j}\\), one step of the sequence model produces the representation for \\(j + 1\\), i.e., \\(f_{\\mathrm{seq}}(h_{1:j}) = \\hat{h}_{j + 1}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.691, + 0.182, + 0.707 + ], + "angle": 0, + "content": "4.4. Training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.714, + 0.469, + 0.866 + ], + "angle": 0, + "content": "The joint training of the segmentation and forecasting modules following Eq. (6) is intractable. But, by exploiting the availability of unpaired training data, we approximate Eq. (6) by feeding in the output of the segmentation module to the forecasting module and training them separately, each on their respective labeled data. The video-action segmentation model is trained utilizing the VideoCLIP setup [85], where in the segmentation model performs classification to predict the action for each second of the video. The forecasting model is trained by adopting the" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.349, + 0.892, + 0.502 + ], + "angle": 0, + "content": "next representation prediction objective. Unlike vanilla LM pretraining, however, we also need to train for predicting visual representations in addition to text (action). Therefore, we use two different losses \\( L_{\\mathrm{act}} \\) and \\( L_{\\mathrm{obs}} \\) for text and visual representations respectively. Specifically, \\( L_{\\mathrm{act}} \\) is the conventional cross-entropy loss over the LM's vocabulary \\( V_{\\mathrm{LM}} \\) for the action representations while \\( L_{\\mathrm{obs}} \\) is the mean-squared error between the predicted and the ground truth observation representations. The total loss is the sum of both the loss terms as shown in Eq. (11)." + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.52, + 0.866, + 0.561 + ], + "angle": 0, + "content": "\\[\nL = - \\sum_ {j = 1} ^ {n} m _ {j} L _ {\\mathrm {a c t}} (\\hat {h} _ {j}) + (1 - m _ {j}) L _ {\\mathrm {o b s}} (\\hat {h} _ {j}), \\text {w h e r e}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.564, + 0.892, + 0.609 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {a c t}} = h _ {j} \\cdot \\hat {h} _ {j} - \\log \\sum_ {p = 1} ^ {| V _ {\\mathrm {L M}} |} \\exp \\left(h _ {p} \\cdot \\hat {h} _ {j}\\right); \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.566, + 0.612, + 0.892, + 0.645 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {o b s}} = \\frac {\\| h _ {j} - \\hat {h} _ {j} \\| _ {2} ^ {2}}{d} \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.65, + 0.892, + 0.71 + ], + "angle": 0, + "content": "In order to have a stable training, we use ground truth action history to construct \\( S_{k} \\) (and subsequently \\( H_{k} \\)) instead of the output of the segmentation module. Appendix B provides further details on loss and optimizers for training." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.711, + 0.892, + 0.802 + ], + "angle": 0, + "content": "Inference. We next detail the inference procedure for VLaMP. Recall that we use \\(1:n\\) to denote a sequence of \\(n\\) representations (i.e, \\(h_{1:n} = (h_1,\\ldots ,h_n)\\)). Additionally, we denote the concatenation operator over two representation sequences by \"\\(\\diamond\\)\". With this notation at hand, we define the score of an action \\(a\\in \\mathcal{A}\\) for following history \\(h_{1:n}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.532, + 0.821, + 0.892, + 0.862 + ], + "angle": 0, + "content": "\\[\n\\phi \\left(h _ {1: n} \\diamond f _ {\\mathrm {a c t}} (a)\\right) = \\sum_ {j = 1} ^ {r _ {a}} a ^ {j} \\cdot f _ {\\mathrm {s e q}} \\left(h _ {1: n} \\diamond a ^ {1: j}\\right), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.87, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\(\\cdot\\) is the vector dot product, and \\(f_{\\mathrm{act}}(a) = \\alpha^{1:r_a} = (\\alpha^1,\\ldots ,\\alpha^{r_a})\\) is the sequence of encoded representations" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.47, + 0.9 + ], + "angle": 0, + "content": "3Despite tuning attempts, we found joint optimization to be intractable and inefficient on resources." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15307" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "for action \\( a \\). In other words, this score is the sum of unnormalized log-probability under the sequence model using the standard softmax distribution. We use this scoring function with to perform beam search (detailed inference algorithm: Algo. 1 in App. B)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.184, + 0.21, + 0.202 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.21, + 0.471, + 0.33 + ], + "angle": 0, + "content": "We instantiate VLaMP's segmentation module utilizing VideoCLIP [85] that has been fine-tuned on COIN and CrossTask. Similarly, we instantiate VLaMP's sequence model \\( f_{\\mathrm{seq}} \\) (in the forecasting module) by GPT2 [60]. We utilize the open-sourced model weights of GPT2 (from HuggingFace [83]). For inference, we use Algo. 1 presented in Appendix B, with beam size \\( B = 10 \\) for CrossTask and a \\( B = 3 \\) for COIN." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.343, + 0.262, + 0.358 + ], + "angle": 0, + "content": "5.1. Data and Baselines" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.367, + 0.47, + 0.548 + ], + "angle": 0, + "content": "Data. For a video \\(V\\) with goal \\(G\\), both CrossTask [89] and COIN [73] provide annotations of the form \\(\\{a_k, (t_k, t'_k)\\}_{k=1}^K\\), where \\(a_k\\) are the actions in the video, and \\(t_k\\) (resp. \\(t'_k\\)) are the start (resp. end) timestamps for \\(a_k\\). Given an annotated video consisting of \\(K\\) steps, we generate \\(K - l\\) examples, each with input \\(x_k = (G, V_{t_k})\\) and output \\(y_k = (a_{k+1}, \\ldots, a_{k+l})\\), for \\(k = 1, \\ldots, K - l\\) (leaving at least \\(l\\) steps to predict in each example). Therefore from \\(M\\) videos, we generated \\(N = \\sum_{m=1}^{M} (K_m - l)\\) examples, where \\(K_m\\) is the number of steps in the \\(m\\)-th video, forming a dataset \\(\\mathcal{D} = \\{x^{(j)}, y^{(j)}\\}_{j=1}^N\\) suitable for VPA (total number of samples in shown in Table 2)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.47, + 0.792 + ], + "angle": 0, + "content": "Baselines. As a first step towards benchmarking, we utilize two heuristic baselines - a random baseline and most probable action baseline. Additionally, we also adopt a variety of strong goal-conditioned models. The procedure planning task is most relevant task from the literature to VPA, therefore, we adapt (details in App. A.1) the widely used DDN model introduced by Chang et al. [9], which is an established model in many procedural planning benchmarks in prior works [6, 87, 70]. Building bridges to the research community working on Ego4D's Long Term action Anticipation benchmark (LTA) [25], we also evaluate their best performing baseline. Finally, we include a prompt-based GPT-3 planner. Zooming out, these baselines span several paradigms: prompt-based, and random baselines are learning-free, the most-probable and random baselines are non-neural, while DDN and LTA baselines are learned and" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "neural. Succinct descriptions of baselines are included next (details are deferred to Appendix A):" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.123, + 0.892, + 0.152 + ], + "angle": 0, + "content": "- Random: Predicts the plan by picking all \\( l \\) actions uniformly randomly from the set of all actions \\( \\mathcal{A} \\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.153, + 0.892, + 0.213 + ], + "angle": 0, + "content": "- Random \\( w/ \\) goal: A stronger baseline; for each goal \\( G \\), we allow privilege access to a set of applicable actions to that goal \\( \\mathcal{A}_G \\subseteq \\mathcal{A} \\), and predicts the plan by randomly picking actions from the restricted set." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.214, + 0.892, + 0.273 + ], + "angle": 0, + "content": "- Most probable action: Given the previous action \\( a_j \\), picks the most probable next action \\( a_j \\) according conditional probability \\( Pr(a_i | a_j) \\) obtained using frequency count from the training." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.274, + 0.892, + 0.394 + ], + "angle": 0, + "content": "- Most probable action \\( w/ \\) goal: Akin to random \\( w/ \\) goal baseline, we also evaluate a goal-conditioned most probable action baseline, that uses a goal-specific set of actions \\( \\mathcal{A}_G \\subset \\mathcal{A} \\) during sampling. Since the most probable baselines, provide a probability distribution over the actions, we also employ beam search (for fairness, with the same beam size same as VLaMP), and pick the highest scoring plan." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.395, + 0.892, + 0.468 + ], + "angle": 0, + "content": "- Dual Dynamics Network (DDN) [9]: Accounting for the difference in task definition, i.e. lack of visual goal, a direct application of DDN inference algorithm was not possible. So we keep DDN's network structure but use Algo.1 for inference on VPA." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.47, + 0.892, + 0.545 + ], + "angle": 0, + "content": "- Ego4D Long Term Action Anticipation (LTA) [25]: The best performing baseline for LTA uses a SlowFast visual encoder followed by a transformer aggregator. We adapt this baseline using the S3D encoder for a fair apples-to-apples comparison with VLaMP." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.546, + 0.892, + 0.606 + ], + "angle": 0, + "content": "- Prompt-based GPT-3 Planner: Huang et al. [30] utilize a LLM as zero-shot planners, we also experiment with prompting a frozen pretrained large language model i.e. GPT-3 for VPA (additional details in App. A.2)." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.123, + 0.892, + 0.606 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.633, + 0.694, + 0.649 + ], + "angle": 0, + "content": "5.2. Quantitative Results" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.658, + 0.892, + 0.702 + ], + "angle": 0, + "content": "In the following, we include quantitative findings of benchmarking methods on two video data sources (Tab. 3) and head-on ablations (Tab. 4)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.704, + 0.892, + 0.838 + ], + "angle": 0, + "content": "Improved performance across video datasets. As we show in Tab. 3, VLaMP significantly outperforms the baselines for both CrossTask and COIN. DDN that is customized for procedural tasks performs significantly better than heuristic baselines leading to a mAcc boost from \\(12.7 \\rightarrow 24.1\\%\\) (row 2 and 5, \\(l = 4\\), Tab. 3). With our novel decomposition and pretraining objective, VLaMP outperforms DDN with a further bump up from \\(24.1 \\rightarrow 31.7\\%\\) (row 5 and 7)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Steady gains in short & long horizon predictions. As length of prediction \\( l \\) increases (\\( l = 1 \\) to \\( l = 4 \\)), the performance naturally decreases, across all baselines and tasks. With this in mind and zooming in on COIN re" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.803, + 0.47, + 0.901 + ], + "angle": 0, + "content": "4Despite the presence of prepositions, majority of actions in COIN and CrossTask can be described using a verb-noun pair. While similar verbs exist, they are never paired with the same nouns. Therefore, there are no repeated actions. Example: while verb 'lift' w/ noun 'barbell' and verb 'pickup' w/ 'button' exists in the action library, the complements ('lift button' & 'pick up barbell') do not. 5Since we evaluate for three and four next steps on our datasets, we use the maximum required length and set \\(l = 4\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15308" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.089, + 0.472, + 0.324 + ], + "angle": 0, + "content": "
Methodl = 1l = 3l = 4
{n/m}AccSRmAccmIOUSRmAccmIOU
CrossTask Video Dataset [89]
Random0.90.00.91.50.00.91.9
Random w/ goal13.20.313.423.60.012.727.8
Most probable10.41.76.19.91.35.513.9
Most probable w/ goal12.42.48.915.51.57.920.5
DDN [9]33.46.825.835.23.624.137.0
LTA [25]26.92.424.035.21.221.736.8
VLaMP (ours)50.610.335.344.04.431.743.4
COIN Video Dataset [73]
Random0.10.00.10.20.00.10.2
Random w/ goal24.51.721.442.70.320.147.7
Most probable0.71.64.36.81.68.215.3
Most probable w/ goal23.910.918.024.99.116.332.2
DDN [9]29.310.122.332.27.021.037.3
GPT-3 prompt-based [30]19.31.711.119.50.010.521.0
VLaMP (ours)45.218.339.256.69.035.254.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.334, + 0.47, + 0.44 + ], + "angle": 0, + "content": "Table 3: Performance on different datasets and horizons. The mean of various metrics (Sec. 3.1) obtained using 5 runs with different random seeds (std. errors are provide in Appendix E). Note that the action and observation history are the output of the separately finetuned video-action segmentation model and hence are noisy compared to the ground truth history." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.47, + 0.534 + ], + "angle": 0, + "content": "sults, we observe large gains of VLaMP over DDN (next best method). Particularly, a relative improvement of \\(54\\%\\) \\((29.3 \\rightarrow 45.2)\\) in mAcc for \\(l = 1\\) (row 7 and 8, Tab. 3) and \\(68\\%\\) \\((21.0 \\rightarrow 35.2)\\) for \\(l = 4\\) is demonstrated by VLaMP over DDN." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.472, + 0.687 + ], + "angle": 0, + "content": "Goal-conditioning is crucial. A key difference between the task formulations of LTA and VPA is goal conditioning (see Sec. 2). Comparing rows for LTA model and VLaMP-there is almost \\(2\\mathrm{x}\\) gap \\((27\\%\\) vs. \\(51\\%\\) \\(l = 1\\) Tab.3). This underscores the importance of goal-conditioning. To second this inference, in Tab. 4 (rows 1 and 2), we precisely ablate the effect of providing the goal as a textual description for the basic (last-observation-only) model. The only difference is goal prompt \\(G\\) , which increases mAcc performance from \\(44.5\\rightarrow 53.1\\%\\) for \\(l = 1\\) and \\(28.3\\to 34.7\\%\\) for \\(l = 3\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.472, + 0.869 + ], + "angle": 0, + "content": "Goal-conditioned random and most probable baseline come close to DDN on easy metrics. For fair comparisons, we include heuristic baselines. We observe the performance of random \\( w/ \\) goal and most probable \\( w/ \\) goal comes close to DDN, when evaluated using lenient metrics like mAcc and mIOU (see COIN results in Tab. 3). Note, that these two baselines enjoy the privileged access to (a much smaller) 'relevant actions set' for a given goal. On an average, the relevant or feasible action set is smaller for COIN than CrossTask videos. This apriori access to feasible actions makes random \\( w/ \\) goal and most probable \\( w/ \\) goal competitive (albeit, slightly unfair) baselines." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Prompt-based LLM planner is not competitive. We evaluate the prompt-based GPT-3 planner on COIN and find" + }, + { + "type": "table", + "bbox": [ + 0.499, + 0.089, + 0.895, + 0.212 + ], + "angle": 0, + "content": "
GAkOkl = 3l = 1
SRmAccmIOUnAcc
1XXok6.8 ± 0.328.3 ± 1.934.8 ± 2.044.5 ± 3.8
2✓Xok8.9 ± 0.234.7 ± 0.741.6 ± 0.853.1 ± 2.0
3✓✓X14.9 ± 0.337.8 ± 0.450.8 ± 0.648.0 ± 0.2
4✓✓Ok15.2 ± 0.343.5 ± 0.851.4 ± 0.964.8 ± 0.9
R✓✓Ok10.7 ± 0.236.5 ± 0.741.7 ± 0.661.4 ± 1.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.222, + 0.895, + 0.358 + ], + "angle": 0, + "content": "Table 4: Role of different inputs and LM pre-training in VLaMP. \\(G\\), \\(A_{k}\\), \\(O_{k}\\) denote the three inputs to VLaMP: goal, action history and observation history, respectively. Shorthand of \\(o_{k}\\) means only the most recent observation of the full history (\\(O_{k}\\)) is used. Mean \\(\\pm\\) std. error over 5 random seeds on CrossTask are reported. The row R corresponds to the forecasting module of VLaMP trained with random initialization (same model architecture) as opposed to initialization using the weights of a pre-trained LM." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.892, + 0.432 + ], + "angle": 0, + "content": "that the prompt based model performs significantly worse than VLaMP. This highlights that VPA is not easy to solve using just a PTLM and prompting." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.44, + 0.766, + 0.456 + ], + "angle": 0, + "content": "5.3. Ablations and Error Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.892, + 0.553 + ], + "angle": 0, + "content": "We undertake head-on ablations to quantify effect of each component of VLaMP - action history, the visual history, and language pre-training of the LM. To remove confounding factors, in Tab. 4 we use the ground truth output for the segmentation module. Following this, we include detailed error analysis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.735 + ], + "angle": 0, + "content": "Action and observation history improve complementary planning metrics. As seen in all the rows with action history Tab. 4 (i.e. \\( A_{k} \\)), the provision of action history increases difficult metrics such as SR. In comparing rows 2 and 3, we see that SR increases relatively by \\( 67\\% \\) (\\( 8.9 \\rightarrow 14.9 \\)), simply by using action history even without access to any past observation. However, the lack of observation history affects nAcc, which drops relatively by \\( 10\\% \\) (\\( 53.1 \\rightarrow 48.0 \\)) when observation history is swapped by action history between rows 2 and 3. This implies that observation history is important to predict the person's state in the task and what they might do next." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.856 + ], + "angle": 0, + "content": "Priors from the pre-trained LM improve performance. In Tab. 4 row \\(\\mathbf{R}\\), we report the performance of VLaMP when its forecasting module is trained with random weight initialization, i.e., the transformer of the same architecture trained from scratch instead of LM pre-training. We find the performance in row \\(\\mathbf{R}\\) is thus much lower than that of VLaMP with pre-trained LM shown in row 4. This underscores the crucial importance of LM pre-training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Segmentation errors are detrimental. While the accuracy of video-action segmentation module (particularly, VideoCLIP model) is quite good - \\(80.2\\%\\) for CrossTask \\((68.7\\%)\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15309" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.471, + 0.184 + ], + "angle": 0, + "content": "for COIN), we believe this should be a major focus for future research. Why? The effect of this segmentation error in VLaMP's performance is quantified by comparing VLaMP row in Tab. 3 (CrossTask) with corresponding performance assuming perfect segmentation (Tab. 4, row 4). A relative \\(50\\%\\) gap in success and big gaps in all other metrics." + }, + { + "type": "image", + "bbox": [ + 0.111, + 0.203, + 0.43, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.426, + 0.471, + 0.502 + ], + "angle": 0, + "content": "Figure 5: Effect of segmentation errors. Performance of VLaMP on CrossTask with classification errors \\((\\%)\\) in the video-action segmentation. As the errors increase, the performance gap between the full model and the one without access to observations increases." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.47, + 0.809 + ], + "angle": 0, + "content": "Visual observation history mitigates effect of video-action segmentation errors. Errors by segmentation module lead to mis-classification of actions, in turn leading to erroneous action history. To precisely study the effect of erroneous action history on VLaMP's performance, we perform controlled experiments wherein we add noise in the ground truth segmentation. This helps us tune desired segmentation error, irrespective of VideoCLIP's accuracy (in segmentation module). We achieve this by replacing a calculated \\(\\%\\) of ground-truth actions by random actions. Decreasing performance, with increasing segmentation classification error, is expected and observed in Fig. 5. Further, we compare two models variations, VLaMP\\((G, A_k, O_k)\\) i.e. the full model (uses both action and observation history) and VLaMP\\((A, A_k)\\) that does not have visual observation history. As we increase segmentation classification error, the gap in the performance of these model variations increases. We infer that visual observations add robustness in VPA against video-action segmentation errors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Errors do not drop as more history is provided. In Fig. 6, we show mAcc w.r.t. the number of steps \\( k \\) in the history i.e. length of \\( (O_k, A_k) \\). As more information is available (due to more steps in the history), one may expect the accuracy to improve. However, this isn't the trend for many tasks. For e.g., note the accuracy drops for the task \"add oil to your" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.089, + 0.895, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.261, + 0.895, + 0.339 + ], + "angle": 0, + "content": "Figure 6: Accuracy in the tail of long activities is challenging. Longer history \\((O_{k},A_{k})\\) do not necessary lead to better accuracy. Further longer histories occur with increasing rarity, leading to learning challenges. (Plot shows mAcc for \\(l = 3\\) CrossTask vs. the #steps in history \\(k\\))" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.364, + 0.892, + 0.516 + ], + "angle": 0, + "content": "car” w.r.t \\( k \\). Digging deeper, we find two reasons for this pattern. First, we find that tasks with long history like “add oil to your car” tend to have repetitive steps towards the end of their action trajectories, making it difficult to predict the precise number and the pattern of such repetitions in VPA. Second is simply a data issue – long trajectories are also exponentially less frequent in the dataset. This forms the tail of the data distribution of action sequences in the dataset (see App. E for statistics). Consequently, prediction in this tail of activities, is a pertinent challenge for future research." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.531, + 0.619, + 0.546 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.556, + 0.892, + 0.783 + ], + "angle": 0, + "content": "Visual Planning for Assistance is a new and intuitive formulation to support planning from natural visual observations for assisting humans in day-to-day activities. We benchmark VPA using standardized suite of prior baselines and a new multi-modal sequence modeling formation of VLaMP. The novel decomposition of a VLaMP policy into video action segmentation and forecasting leads to several efficiency and modeling benefits, that benefit the community, even beyond VPA. Particularly, this allows to leverage pre-trained LM that leads to significant performance gains. Alternative decompositions, self-supervised pre-training objectives for PTLMs, modeling multiple actors, and tapping into other modalities (audio, camera metadata, etc.) [26, 55, 43, 72, 32, 88] are interesting ways forward for the community, on the exciting task of VPA." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements: The authors are indebted to Brian Chen for his efforts to open-source the code and LTA experiments, and to Gideon Stocek for supporting with the cluster management. We thank Vasu Sharma, Tushar Nagarajan, and Homanga Bharadhwaj for their writing feedback. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3537-3545, 2019. 1, 3, 4, 7, 8" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.469, + 0.767 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "15314" + } + ] +] \ No newline at end of file diff --git a/2023/Pretrained Language Models as Visual Planners for Human Assistance/057af23b-bb0a-449d-acad-c434ed40a938_origin.pdf b/2023/Pretrained Language Models as Visual Planners for Human Assistance/057af23b-bb0a-449d-acad-c434ed40a938_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..37a459dcb16e7cad4d977e7269bfe39c23ef1b7e --- /dev/null +++ b/2023/Pretrained Language Models as Visual Planners for Human Assistance/057af23b-bb0a-449d-acad-c434ed40a938_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:21dafe893b03856348540e4cf0c60fe77cba31daf64cd743695cff282d7f8da5 +size 1222911 diff --git a/2023/Pretrained Language Models as Visual Planners for Human Assistance/full.md b/2023/Pretrained Language Models as Visual Planners for Human Assistance/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f0880b4662177b527e869fdc0982efaf00809a64 --- /dev/null +++ b/2023/Pretrained Language Models as Visual Planners for Human Assistance/full.md @@ -0,0 +1,377 @@ +# Pretrained Language Models as Visual Planners for Human Assistance + +Dhruvesh Patel $^{1,2}$ Hamid Eghbalzadeh $^{1}$ Nitin Kamra $^{1}$ Michael Louis Iuzzolino $^{1}$ Unnat Jain $^{1*}$ Ruta Desai $^{1*†}$ $^{1}$ Meta $^{2}$ UMass Amherst https://github.com/facebookresearch/vlamp + +# Abstract + +In our pursuit of advancing multi-modal AI assistants capable of guiding users to achieve complex multi-step goals, we propose the task of 'Visual Planning for Assistance (VPA)'. Given a succinct natural language goal, e.g., "make a shelf", and a video of the user's progress so far, the aim of VPA is to devise a plan, i.e. a sequence of actions such as "sand shelf", "paint shelf", etc. to realize the specified goal. This requires assessing the user's progress from the (untrimmed) video, and relating it to the requirements of natural language goal, i.e. which actions to select and in what order? Consequently, this requires handling long video history and arbitrarily complex action dependencies. To address these challenges, we decompose VPA into video action segmentation and forecasting. Importantly, we experiment by formulating the forecasting step as a multimodal sequence modeling problem, allowing us to leverage the strength of pre-trained LMs (as the sequence model). This novel approach, which we call Visual Language Model based Planner (VLaMP), outperforms baselines across a suite of metrics that gauge the quality of the generated plans. Furthermore, through comprehensive ablations, we also isolate the value of each component - language pretraining, visual observations, and goal information. We have open-sourced all the data, model checkpoints, and training code. + +# 1. Introduction + +Imagine assembling a new piece of furniture or following a new recipe for a dinner party. To achieve such a goal, you might follow a manual or a video tutorial, going back and forth as you perform the steps. Instead of fumbling through a manual, imagine an assistive agent capable of being invoked through natural language, having the ability to understand human actions, and providing actionable multi-step guidance for achieving your desired goal. Such multi- + +![](images/1ec0e91231c15a34a02907bea4c7c18d3395949578a3dd3ca32d00ace36a79d4.jpg) +Figure 1: Visual Planning for Assistance overview (top) and general methodology (bottom). Given a user-specified, natural language goal ("build a shelf") and corresponding visual history of the user's progress till now, VPA involves predicting a sequence of actions, to assist the user towards the goal ("cut", "sand", "paint"). Our approach is based on multi-modal sequence modeling where we reuse pre-trained video segmentation and language models. + +modal assistive agents should be able to reason human activities from visual observations, contextualize them to the goal at hand, and plan future actions for providing guidance. + +To quantify the progress and aid the development of such multi-modal neural models, we need a intuitive task, as illustrated in the example in Fig. 1 (top). We call this Visual Planning for Assistance (VPA) that we detail next. Given a user-specified goal in natural language ("build shelf") and corresponding video observations of the user's progress towards this goal, the task objective should be to generate the ordered sequence of next actions towards achieving the goal ("cut $\rightarrow$ sand $\rightarrow$ paint"). We base VPA off instructional YouTube videos of such procedural activities from large, open-sourced datasets - CrossTask [89] and COIN [73]. This is a natural choice as procedural human activities (cooking, assembly, repair, etc.) are a perfect source of multi-step and complex sequence of actions, where humans routinely seek guidance. Realistic nature + +of VPA makes it particularly challenging. Operating on untrimmed videos requires dealing with potentially many irrelevant background frames, chunking actions in the videos will also be imperative. Another challenge is the validity of the plan of actions i.e. they must respect the constraints of the activity – the shelf shouldn't be painted before sanding. + +The natural next question is - what's a good way to tackle VPA? Marrying research from video forecasting & anticipation with embodied AI [19, 17], we cast VPA as goal-conditioned task planning. We approach VPA by utilizing video action segmentation and transformer-based neural sequence modeling - the former allows us to deal with long video history and the latter can handle arbitrary sequential constraints [86, 39]. The formulation (particularly, transformer-based neural sequence modeling) allows us to tap into the prowess of pre-trained language models (PTLMs). These PTLMs contain useful priors about action-action similarity, action-goal association, and action ordering [7, 30, 58], that our formulation can piggy-back off. Particularly, our model - Visual Language Model Planner (VLaMP) - conditions the generated plan onto the visual history by using a transformer-based mapper network that projects embeddings corresponding to visual history into the input space of the LM. Using VPA as the testbed, we show that VLaMP outperforms a range of standardized baselines. We undertake head-on ablations to quantify effect of each component of VLaMP - language pre-training of the LM, the visual history, and goal description. We believe the modularity of our approach can allow researchers to swap components with their own, to make rapid progress towards VPA. + +In summary, our main contributions are: (1) a new task VPA on human interaction videos capturing unique aspects of real-world vision-powered assistive agents; (2) a general-purpose methodology for VPA, which allows leveraging pre-trained multi-modal encoders and sequence models; (3) an instantiation of this methodology (we call VLaMP), where we reuse sequence priors from PTLM and investigate its efficacy across two, well-studied datasets of procedural human activities. + +# 2. Related Work + +Forecasting in Videos. VPA entails future action sequence prediction for a video and is closely related to anticipation in video understanding, including future localization [22, 40, 78], future frame prediction [77, 46, 53], next active object estimation [21, 5, 25, 67, 4, 24, 44], as well as short- and long-term action anticipation [66, 15, 20, 23, 25, 65, 64, 57, 45, 1, 52, 50, 11, 79]. While short-term forecasting approaches, such as [66], are limited to predicting the single next action occurring only a few seconds into the future, our work focuses on predicting sequences of actions over longer time horizons (on the order of minutes) + +
Action PredictionGoal ModalityVisual Reasoning
Action anticipation [14]SingleNoneVideo-based
Action forecasting [25]Multiple, orderedNoneVideo-based
Procedural planning [9]Multiple, orderedVisionImage-based
VPA (ours)Multiple, orderedNatural LanguageVideo-based
+ +Table 1: VPA vs. prior tasks related to forecasting of real-world human activities. We predict an ordered sequence of actions given video history with a focus on natural language goal-conditioning for human-assistive applications. + +into the future. The long-term action (LTA) forecasting benchmarking was recently established on a small subset of Ego4D [25], and although VPA is similarly devised to predict a temporally ordered sequence of actions conditioned on video-based visual observations, our approach differs in that the LTA task does no goal-conditioning. Our task incorporates goal-conditioning on long term sequence prediction as we argue this will drive the development of critical system aspects, such as virtual assistants that afford human interaction via the natural language goals. Additionally, in contrast to LTA, we focus on a wide range of goal-oriented activities available within the CrossTask and COIN datasets. Tab. 1 highlights the differences between VPA and other forecasting tasks. + +Procedural Planning Approaches. VPA is similar to the task of procedure planning [9], wherein given a starting and terminating visual observation, the aim is to predict the actions that would transform the state from starting to terminating. However, we argue that due to the unavailability of the terminating visual state, the procedure planning task is not useful in a real-world assistance setting. While several recent works introduce novel models for procedure planning, these models cannot be deployed for VPA either because they rely heavily on the availability of visual goal [70, 87, 6], or assume access to true action history [49]. Transformers for Decision Making. VLaMP autoregressively predicts future states and/or observations and actions and is similar in spirit to sequence models for decision making such as GATO [61], Decision Transformer [12], and Trajectory Transformer [35]. VLaMP extends such models to work with egocentric observations that humans observe in the day-to-day activities. + +Planning in Embodied AI using LMs. Past research has leveraged PTLMs for task planning in real world for embodied agents [30, 68, 41, 7, 42, 31, 18, 16, 36]. Many of these works focus on converting a high-level task or instruction into sequence of low-level steps and then ground them in the environment using either affordance functions [7], visual feedback [31], or multimodal prompts [36, 18]. Owing to their focus on robotic agents, these works focus on predominately pick-place tasks. Instead VPA is focused on + +complex tasks, in which humans might require assistance in the form of recommended future actions. Consequently, VLaMP requires grounding and reasoning of much more complex states and actions, which it accomplishes by finetuning a pretrained LM on multimodal sequences of (visual) observations and (text-based) actions. + +Multi-modal LMs. Recent works have successfully used the transformer architecture for modeling multi-modal sequences that have visual tokens. For instance, [47, 59, 2, 48, 29, 18] train large transformer based multi-modal sequence prediction models. While [3, 74, 56] focus on adapting pre-trained LMs to work with visual tokens by aligning the representation spaces of the two modalities. VLaMP's approach of modeling sequence of visual and textual representations using PTLMs is similar in spirit to these, i.e. VLaMP also uses a mapper network to align video representations to LM's token space and jointly learns the mapper with LM finetuning for VPA. However, in contrast to previous works, VLaMP predicts the visual tokens autoregressively at inference time to enable forecasting of the state for planning. Consequently, VLaMP's token prediction loss is multi-modal, unlike most multi-modal LMs that only use token prediction loss for text tokens. + +# 3. Visual Planning for Assistance + +Here, we introduce the task of Visual Planning for Assistance (VPA), towards enabling multi-step guidance to humans in their real-world activities. We instantiate VPA for procedural activities, where humans routinely seek assistance. In this section, we include the definition of VPA, and describe the evaluation protocol. + +# 3.1. Task Definition + +The following two intuitive inputs are given to any model performing VPA. + +Goal Prompt $(G)$ . The natural language description (in short phrase) of the user's goal, emulating a typical user's request for assistance for a day-to-day task. Examples include, "build a shelf" and "change a tire". + +Visual History $(V_{t})$ . An untrimmed video that provides context about the user's progress towards a goal from the start till time, say $t$ . We assume that $V_{t}$ contains $k$ actions or steps $\{a_1,\ldots ,a_k\}$ pertaining to the goal. However, VPA doesn't have access to $\{a_1,\dots ,a_k\}$ or $k$ and must work with $V_{t}$ . + +Given these two inputs, $V_{t}$ and $G$ , the objective of VPA is to generate a plan $\mathcal{T}$ . The plan is a sequence of actions that should be executed (in the next steps) to assist the user in achieving the goal $G$ . Concretely, the prediction is denoted by $\mathcal{T} = (a_{k + 1},\dots ,a_{k + l})$ , where $a_{i}$ are represented in natural language but come from a closed set $\mathcal{A}$ . Here, $l\leq K$ denotes the number of future actions that should be predicted, + +out of the $K$ number of remaining actions required to accomplish the goal. For our shelf-building example, the correct $\mathcal{T} =$ (sand shelf, paint shelf, attach shelf), capturing the remaining 3 future actions (here, $l = N = 3$ ). + +In day-to-day activities, we request assistance for goals in natural language. However, prior works procedural planning [9, 6] assume access to visual goal state. This is not a realistic assumption for an AI agent assisting humans. Hence, we purposefully relax this assumption, making our formulation of the task significantly more practical. Moreover, an agent with access to the visual modality, should be able to improve its plan by filtering out relevant information from the raw video stream of the progress. These are the two central assumptions around which we formulate the task of VPA. + +# 3.2. Evaluation + +Open-Sourced Video Data. We leverage existing datasets CrossTask [89] and COIN [73], originally developed to enable video action understanding for VPA, based on the following three requirements: + +- Rich diversity of activities from multiple domains: The data from different domains such as cooking, assembly etc., enables testing of VPA models in a more generalized manner. +- Goal-oriented activities consisting of long sequences of actions: Since the objective is to generate $l$ future actions, activities in these datasets that require diverse sequences of actions e.g., "making a pancake", instead of "running" are more suitable for VPA. +- Action annotations from a fixed closed set of actions: Action labels described using verb-noun from a finite set [14], which are temporally aligned with the videos. This makes evaluating the accuracy of $\mathcal{T}$ prediction straightforward. Specifically, free-form, narration-style descriptions of actions that are available in recent video datasets aid in efficient multi-modal representation learning for video understanding [25, 54]. However, evaluating the quality of action sequences towards goal achievement, where each action is described in free-form natural language, is non-trivial. We leave the instantiation of VPA with free-form natural language actions as future work. +Table 2 summarizes the features from CrossTask and COIN, aligned with the above requirements. + +Metrics. The planning performance of a VPA model is measured by comparing the generated plan $\hat{\mathcal{T}} = (\hat{a}_{k + 1},\dots ,\hat{a}_{k + l})$ to the ground truth plan $\mathcal{T}$ for $l$ actions in the future, given $V_{t}$ and $G$ . Here $\hat{a}_{k + i}$ denotes the prediction for the $k + i$ -th step given history till $k$ -th step. Consistent with community practices [9, 6], we use the following metrics, listed in decreasing order of strictness: success rate (SR), mean accuracy (mAcc), mean intersection over union + +
Dataset# train videos# test videos# test samplesactions per video# goals# domains
CrossTask [89]175675241237.6 ± 4.3183
COIN [73]9428104720113.9 ± 2.418012
+ +Table 2: VPA datasets. We evaluate VPA on two existing video datasets containing multiple goal-oriented procedural activities from varied domains. Such activities contain sequences of multiple actions making them ideal for VPA. + +(mIOU). Success rate requires an exact match between all actions and their sequence between $\hat{\mathcal{T}}$ and $\mathcal{T}$ . Mean accuracy is the accuracy of the actions at each step. Unlike success rate, mean accuracy does not require a $100\%$ match to ground truth. Instead it considers matching at each individual step. Lastly, mean intersection over union captures the cases where the model predicts the steps correctly, but fails to identify the correct order. Concretely, + +$$ +\mathrm {m I O U} _ {l} = \frac {\left| \hat {a} _ {\{k + 1 : k + l \}} \bigcap a _ {\{k + 1 : k + l \}} \right|}{\left| \hat {a} _ {\{k + 1 : k + l \}} \bigcup a _ {\{k + 1 : k + l \}} \right|}, \tag {1} +$$ + +$$ +\mathrm {m A c c} _ {l} = \frac {1}{l} \sum_ {i = 1} ^ {l} \mathbb {1} [ \hat {a} _ {k + i,} = a _ {k + i} ], \tag {2} +$$ + +$$ +\mathrm {S R} _ {l} = \prod_ {i = 1} ^ {l} \mathbb {1} [ \hat {a} _ {k + i} = a _ {k + i} ], \tag {3} +$$ + +where $\mathbb{1}[\cdot ]$ is the identity function, which is 1 when the condition in its input is true, and 0, and $\hat{a}_{\{k + 1:k + l\}}$ denotes the set of $l$ future actions in $\tilde{\mathcal{T}}$ , i.e., a sequence but disregarding the order. To complement the above metrics, we also measure the accuracy of predicting the next action i.e. nAcc, as defined in (4), where 'n' stands for next. Note that all metrics are averaged over the test set details of which are included in Sec. 5. + +$$ +\mathrm {n A c c} = \mathbb {1} [ \hat {a} _ {k + 1} = a _ {k + 1} ] \tag {4} +$$ + +# 4. Visual LM Planner + +VPA can be viewed as a sequential decision making problem, where the model (say, $\pi$ ) predicting the sequence of next actions is a policy conditioned on the visual history $V_{t}$ , serving as (partially-observed) state, and goal prompt $G$ . Inspired by the offline learning formulation closest to 'learning from offline demonstrations' [27, 76, 37, 81], in VLaMP, we formulate VPA as a goal-conditioned, multimodal sequence prediction problem. This formulation allows us to leverage high-capacity sequence models like + +Transformers [75], which have been successfully applied to sequential decision making [35, 12]. Furthermore, inspired by the recent success of pre-trained transformer language models (PTLMs) on such tasks, [62, 30, 12], we propose to leverage PTLMs as the sequence model in our formulation. In the remainder of this section we describe our approach for VPA, called Visual Language Model based Planner (VLaMP), consisting of a segmentation module and PTLM based sequence prediction module. + +# 4.1. Planning with Segmentation and Forecasting + +We define $\pi$ as a goal-conditioned, multi-modal sequence prediction problem: + +$$ +\pi = P \left(a _ {k + 1}, a _ {k + 2}, \dots \mid V _ {t}, G\right). \tag {5} +$$ + +where $\pi$ models the probability of goal-relevant and valid future actions sequences conditioned on $V_{t}$ and $G$ . + +Modeling the multi-modal sequence in Eq. 5 is computationally expensive and difficult to scale because of the high-dimensional state space of raw untrimmed video $V_{t}$ . Also, there is limited data to learn the distribution over valid action sequences for goals in real-world applications. Tackling these challenges, we argue that the latent space of factors influencing the future plan can indeed be expressed in lesser dimensions. Particularly, to ensure scalability for handling raw videos and sample efficiency in learning valid action sequence distributions, we decompose our policy $\pi$ into two modules. The first module is video segmentation, which converts the untrimmed video history $V_{t}$ into a sequence of video segments i.e. a segment history $S_{k} = (s_{1},\dots ,s_{k})$ , where each segment corresponds to an action $a_{i}$ that occurred in the video. The second module enables forecasting i.e. it transforms the output of the segmentation module and generates the plan (see Fig. 1 (bottom)). While a probabilistic formulation of this decomposition can be expressed as: + +$$ +\pi = \sum_ {S _ {k}} \underbrace {P \left(a _ {k + 1} , a _ {k + 2} , \cdots \mid S _ {k} , G\right)} _ {\text {F o r e c a s t i n g}} \underbrace {P \left(S _ {k} \mid V _ {t}\right)} _ {\text {S e g m e n t a t i o n}}, \tag {6} +$$ + +where the segment history $S_{k}$ is a latent variable, the summation over all possible segment histories is intractable. We, however, use Eq. 6 as the guiding expression to formulate the input and output of both modules. Next, we include the technical details of both of these modules. + +# 4.2. Segmentation Module + +This module splits the untrimmed video history $V_{t}$ into segment history $S_{k}$ of multiple segments, each segment + +![](images/087d67a1de51d94c1b34f3dfb37dc87fc6774ac21ebb63bfdfaf6e3967206c84.jpg) +Figure 2: VLaMP - Segmentation Module. The untrimmed visual history $V_{t}$ is converted into segments, each consisting of observation $o_{i}$ and the action $a_{i}$ . The observation $o_{i}$ is the collection of video frames of $\delta$ seconds around the start time stamp $t_{i}$ of the corresponding action $a_{i}$ . Two such segments are shown here. + +corresponding to an action. The segmentation is done using a video-action segmentation model in three steps: preprocessing, classification, and consolidation. In the preprocessing step, the raw video frames from $V_{t}$ are bundled into fixed-length window clips $c_{i}$ , each of length 1 second, to obtain $V_{t} = (c_{1},\dots ,c_{t})$ . In the classification step, a video-action segmentation model is used to output the most probable action for each clip $c_{i}$ , which can be denoted as $\tilde{A}_t = (\tilde{a}_1,\tilde{a}_2,\ldots ,\tilde{a}_t)$ . Finally, in the consolidation steps, we convert $\tilde{A}_t$ into a form that can be used by the forecasting module; this form consists of two sequences: action history $A_{k}$ and observation history $O_{k}$ . To this end, same actions in consecutive seconds in $\tilde{A}_t$ are consolidated to form the action history $A_{k} = (a_{1},\dots ,a_{k})$ . As illustrated in Fig. 2, assuming $t_i$ denotes the starting timestamp for $a_{i}$ , we also extract video frames from $t_i - \delta /2$ to $t_i + \delta /2$ to obtain an observation window $o_i$ corresponding to $a_{i}$ , and consequently the full observation history $O_{k} = (o_{1},\dots,o_{k})$ . The resultant segment history is termed $S_{k} = ((o_{1},a_{1}),\dots ,(o_{k},a_{k}))$ , summarized in Fig. 2. + +# 4.3. Forecasting Module + +The usefulness of $\pi$ 's decomposition expressed in Eq. (6) becomes apparent now. Modeling the segmentation module's output as segment history $S_{k}$ , where each segment consisting of action and observations, allows writing the output of the forecasting module in an autoregressive manner: + +$$ +\begin{array}{l} P \left(a _ {k + 1}, a _ {k + 2}, \dots \mid o _ {1}, a _ {1}, \dots , o _ {k}, a _ {k}, G\right) \\ = \prod_ {i > 0} \sum_ {o _ {k + i}} P \left(o _ {k + i}, a _ {k + i} \mid o _ {1}, a _ {1}, \dots , o _ {k}, a _ {k}, G\right). \tag {7} \\ \end{array} +$$ + +Illustrated in Fig. 3, this autoregressive expression allows the possibility of using any sequence-to-sequence neural + +network as the forecasting module in combination with pretrained text and video encoders for representing action and observation history $A_{k}$ and $O_{k}$ . This general-purpose framework allows the use of any neural sequence model – LSTM [28], GRU [13], Transformers [75], etc. We choose to instantiate the forecasting module for $\pi$ using a pretrained transformer-based LM. Next we present the details of the encoders for the two modalities and the LM based sequence model. + +Action encoder $(f_{\mathrm{act}})$ Each action $a_i$ in $A_k$ is encoded by $f_{\mathrm{act}}$ and the output is denoted by $\alpha_i$ . Concretely, token embeddings are expressed as: + +$$ +\begin{array}{l} \left(\alpha_ {1}, \dots , \alpha_ {k}\right) = \left(f _ {\text {a c t}} \left(a _ {1}\right), \dots , f _ {\text {a c t}} \left(a _ {k}\right)\right), \text {w h e r e} \\ \alpha_ {i} = \left(\alpha_ {i} ^ {1}, \dots , \alpha_ {i} ^ {r _ {i}}\right) \in \mathbb {R} ^ {r _ {i} \times d} \tag {8} \\ \end{array} +$$ + +As we illustrate in Fig. 3 (left), each action $a_i$ is tokenized into $r_i$ tokens using appropriate tokenizer for the LM, the tokens are indexed using the vocabulary of the LM, and are represented using an embedding lookup from the token embeddings of the LM to produce $\alpha_i$ . Here, $r_i$ is the number of tokens and $d$ is the dimensionality of token embeddings. + +Observation encoder $(f_{\mathrm{obs}})$ . Visual cues play an integral role in knowing what actions lie ahead, towards achieving the goal prompt $G$ . To this end, the visual observations $O_k$ are encoded and play a critical role in the planner. Recall, the visual observation history $O_k$ comprises of $o_i$ corresponding to action $a_i$ , each of $\delta$ frames. As illustrated in Fig. 3 (middle), we transform each $o_i$ employing the widely-adopted S3D backbone [84] $f_{\mathrm{S3D^*}}$ (* denotes backbone is frozen). We must project visual encodings to a shared latent space of action (language) embeddings described before $(\alpha_i)$ . To this end, we map S3D features via a trainable transformer mapper $f_{\mathrm{map}}$ . Concretely, + +$$ +\begin{array}{l} \left(\beta_ {1}, \dots , \beta_ {k}\right) = \left(f _ {\mathrm {o b s}} \left(o _ {1}\right), \dots , f _ {\mathrm {o b s}} \left(o _ {k}\right)\right), \text {w h e r e} \\ \beta_ {i} = \left(\beta_ {i} ^ {1}, \dots , \beta_ {i} ^ {\delta}\right) \in \mathbb {R} ^ {\delta \times d} \text {a n d} f _ {\mathrm {o b s}} = f _ {\mathrm {S 3 D} ^ {*}} \circ f _ {\mathrm {m a p}} \tag {9} \\ \end{array} +$$ + +Overall, as we show in Fig. 3 (right), the resultant encoded sequence of representation for $S_{k}$ is thus + +$$ +f _ {\text {e n c}} (S _ {k}) = \left(\beta_ {1}, \alpha_ {1}, \dots , \beta_ {k}, \alpha_ {k}\right) = H _ {k}, +$$ + +Sequence model $(f_{\mathrm{seq}})$ . Given the above encoding for the segment history $S_{k}$ , the role of the sequence model is to predict a representation of the next token, that would in return enable VLaMP plan generation capabilities for VPA. Importantly, in the process of generating sequence of future actions autoregressively, we would also need to generate the representations of 'future observations'. Therefore, as we shown in Fig. 3, our sequence model, which consists of the transformer layers of a PTLM, also produces representations for vision (in addition to the necessary action tokens). Before proceeding further, we pause and introduce additional notation for the sequence model, which + +![](images/7b9f0c8b9772067c8dede95c30a238593029dd56f40d5f96be0718231733c1c2.jpg) +Figure 3: VLaMP - Forecasting Module. As shown in left and middle, actions and observations obtained from the segmentation module are encoded using appropriate modality encoders. The observation encoder leverages pretrained video encoder for observations, while also learning a mapper that aligns the representations from observations with actions. As shown on the right, VLaMP uses a joint sequence model on top of interleaved action (blue) and observation (gray) representations to forecast autoregressively the next representation. + +![](images/0ada3fca083539da731052742542fd4ea73f4bbc817e7d19b6f807cdaddccf2d.jpg) + +![](images/d581d41982481ea46b81e5bcf8d3975617081858294f2818bc57ff561951c912.jpg) +Figure 4: Tokenized Sequence with Masks. The encoded sequence of representations for $k = 2$ segments, denoted alternatively using modality agnostic notation of $H_{2}$ and mask $M$ for next token prediction training. + +will make the subsequent explanation for training and inference easier to follow. As shown in Figure 4, we alternatively denote the sequence of representations $(\beta_{1},\alpha_{1},\ldots ,\beta_{k},\alpha_{k})$ by $H_{k} = (h_{1},\dots,h_{n})$ , with $n = k\delta +\sum_{i = 1}^{k}r_{i}$ . A binary mask $M = (m_{1},\dots,m_{n})$ , where $m_{i}$ is 1 if the corresponding representation is for an action and 0 otherwise, can help obtain necessary action or visual observations. With this notation, given first $j$ representations denoted as $h_{1:j}$ , one step of the sequence model produces the representation for $j + 1$ , i.e., $f_{\mathrm{seq}}(h_{1:j}) = \hat{h}_{j + 1}$ . + +# 4.4. Training + +The joint training of the segmentation and forecasting modules following Eq. (6) is intractable. But, by exploiting the availability of unpaired training data, we approximate Eq. (6) by feeding in the output of the segmentation module to the forecasting module and training them separately, each on their respective labeled data. The video-action segmentation model is trained utilizing the VideoCLIP setup [85], where in the segmentation model performs classification to predict the action for each second of the video. The forecasting model is trained by adopting the + +next representation prediction objective. Unlike vanilla LM pretraining, however, we also need to train for predicting visual representations in addition to text (action). Therefore, we use two different losses $L_{\mathrm{act}}$ and $L_{\mathrm{obs}}$ for text and visual representations respectively. Specifically, $L_{\mathrm{act}}$ is the conventional cross-entropy loss over the LM's vocabulary $V_{\mathrm{LM}}$ for the action representations while $L_{\mathrm{obs}}$ is the mean-squared error between the predicted and the ground truth observation representations. The total loss is the sum of both the loss terms as shown in Eq. (11). + +$$ +L = - \sum_ {j = 1} ^ {n} m _ {j} L _ {\mathrm {a c t}} (\hat {h} _ {j}) + (1 - m _ {j}) L _ {\mathrm {o b s}} (\hat {h} _ {j}), \text {w h e r e} +$$ + +$$ +L _ {\mathrm {a c t}} = h _ {j} \cdot \hat {h} _ {j} - \log \sum_ {p = 1} ^ {| V _ {\mathrm {L M}} |} \exp \left(h _ {p} \cdot \hat {h} _ {j}\right); \tag {10} +$$ + +$$ +L _ {\mathrm {o b s}} = \frac {\| h _ {j} - \hat {h} _ {j} \| _ {2} ^ {2}}{d} \tag {11} +$$ + +In order to have a stable training, we use ground truth action history to construct $S_{k}$ (and subsequently $H_{k}$ ) instead of the output of the segmentation module. Appendix B provides further details on loss and optimizers for training. + +Inference. We next detail the inference procedure for VLaMP. Recall that we use $1:n$ to denote a sequence of $n$ representations (i.e, $h_{1:n} = (h_1,\ldots ,h_n)$ ). Additionally, we denote the concatenation operator over two representation sequences by " $\diamond$ ". With this notation at hand, we define the score of an action $a\in \mathcal{A}$ for following history $h_{1:n}$ as + +$$ +\phi \left(h _ {1: n} \diamond f _ {\mathrm {a c t}} (a)\right) = \sum_ {j = 1} ^ {r _ {a}} a ^ {j} \cdot f _ {\mathrm {s e q}} \left(h _ {1: n} \diamond a ^ {1: j}\right), \tag {12} +$$ + +where $\cdot$ is the vector dot product, and $f_{\mathrm{act}}(a) = \alpha^{1:r_a} = (\alpha^1,\ldots ,\alpha^{r_a})$ is the sequence of encoded representations + +for action $a$ . In other words, this score is the sum of unnormalized log-probability under the sequence model using the standard softmax distribution. We use this scoring function with to perform beam search (detailed inference algorithm: Algo. 1 in App. B). + +# 5. Experiments + +We instantiate VLaMP's segmentation module utilizing VideoCLIP [85] that has been fine-tuned on COIN and CrossTask. Similarly, we instantiate VLaMP's sequence model $f_{\mathrm{seq}}$ (in the forecasting module) by GPT2 [60]. We utilize the open-sourced model weights of GPT2 (from HuggingFace [83]). For inference, we use Algo. 1 presented in Appendix B, with beam size $B = 10$ for CrossTask and a $B = 3$ for COIN. + +# 5.1. Data and Baselines + +Data. For a video $V$ with goal $G$ , both CrossTask [89] and COIN [73] provide annotations of the form $\{a_k, (t_k, t'_k)\}_{k=1}^K$ , where $a_k$ are the actions in the video, and $t_k$ (resp. $t'_k$ ) are the start (resp. end) timestamps for $a_k$ . Given an annotated video consisting of $K$ steps, we generate $K - l$ examples, each with input $x_k = (G, V_{t_k})$ and output $y_k = (a_{k+1}, \ldots, a_{k+l})$ , for $k = 1, \ldots, K - l$ (leaving at least $l$ steps to predict in each example). Therefore from $M$ videos, we generated $N = \sum_{m=1}^{M} (K_m - l)$ examples, where $K_m$ is the number of steps in the $m$ -th video, forming a dataset $\mathcal{D} = \{x^{(j)}, y^{(j)}\}_{j=1}^N$ suitable for VPA (total number of samples in shown in Table 2). + +Baselines. As a first step towards benchmarking, we utilize two heuristic baselines - a random baseline and most probable action baseline. Additionally, we also adopt a variety of strong goal-conditioned models. The procedure planning task is most relevant task from the literature to VPA, therefore, we adapt (details in App. A.1) the widely used DDN model introduced by Chang et al. [9], which is an established model in many procedural planning benchmarks in prior works [6, 87, 70]. Building bridges to the research community working on Ego4D's Long Term action Anticipation benchmark (LTA) [25], we also evaluate their best performing baseline. Finally, we include a prompt-based GPT-3 planner. Zooming out, these baselines span several paradigms: prompt-based, and random baselines are learning-free, the most-probable and random baselines are non-neural, while DDN and LTA baselines are learned and + +neural. Succinct descriptions of baselines are included next (details are deferred to Appendix A): + +- Random: Predicts the plan by picking all $l$ actions uniformly randomly from the set of all actions $\mathcal{A}$ . +- Random $w/$ goal: A stronger baseline; for each goal $G$ , we allow privilege access to a set of applicable actions to that goal $\mathcal{A}_G \subseteq \mathcal{A}$ , and predicts the plan by randomly picking actions from the restricted set. +- Most probable action: Given the previous action $a_j$ , picks the most probable next action $a_j$ according conditional probability $Pr(a_i | a_j)$ obtained using frequency count from the training. +- Most probable action $w/$ goal: Akin to random $w/$ goal baseline, we also evaluate a goal-conditioned most probable action baseline, that uses a goal-specific set of actions $\mathcal{A}_G \subset \mathcal{A}$ during sampling. Since the most probable baselines, provide a probability distribution over the actions, we also employ beam search (for fairness, with the same beam size same as VLaMP), and pick the highest scoring plan. +- Dual Dynamics Network (DDN) [9]: Accounting for the difference in task definition, i.e. lack of visual goal, a direct application of DDN inference algorithm was not possible. So we keep DDN's network structure but use Algo.1 for inference on VPA. +- Ego4D Long Term Action Anticipation (LTA) [25]: The best performing baseline for LTA uses a SlowFast visual encoder followed by a transformer aggregator. We adapt this baseline using the S3D encoder for a fair apples-to-apples comparison with VLaMP. +- Prompt-based GPT-3 Planner: Huang et al. [30] utilize a LLM as zero-shot planners, we also experiment with prompting a frozen pretrained large language model i.e. GPT-3 for VPA (additional details in App. A.2). + +# 5.2. Quantitative Results + +In the following, we include quantitative findings of benchmarking methods on two video data sources (Tab. 3) and head-on ablations (Tab. 4). + +Improved performance across video datasets. As we show in Tab. 3, VLaMP significantly outperforms the baselines for both CrossTask and COIN. DDN that is customized for procedural tasks performs significantly better than heuristic baselines leading to a mAcc boost from $12.7 \rightarrow 24.1\%$ (row 2 and 5, $l = 4$ , Tab. 3). With our novel decomposition and pretraining objective, VLaMP outperforms DDN with a further bump up from $24.1 \rightarrow 31.7\%$ (row 5 and 7). + +Steady gains in short & long horizon predictions. As length of prediction $l$ increases ( $l = 1$ to $l = 4$ ), the performance naturally decreases, across all baselines and tasks. With this in mind and zooming in on COIN re + +
Methodl = 1l = 3l = 4
{n/m}AccSRmAccmIOUSRmAccmIOU
CrossTask Video Dataset [89]
Random0.90.00.91.50.00.91.9
Random w/ goal13.20.313.423.60.012.727.8
Most probable10.41.76.19.91.35.513.9
Most probable w/ goal12.42.48.915.51.57.920.5
DDN [9]33.46.825.835.23.624.137.0
LTA [25]26.92.424.035.21.221.736.8
VLaMP (ours)50.610.335.344.04.431.743.4
COIN Video Dataset [73]
Random0.10.00.10.20.00.10.2
Random w/ goal24.51.721.442.70.320.147.7
Most probable0.71.64.36.81.68.215.3
Most probable w/ goal23.910.918.024.99.116.332.2
DDN [9]29.310.122.332.27.021.037.3
GPT-3 prompt-based [30]19.31.711.119.50.010.521.0
VLaMP (ours)45.218.339.256.69.035.254.2
+ +sults, we observe large gains of VLaMP over DDN (next best method). Particularly, a relative improvement of $54\%$ $(29.3 \rightarrow 45.2)$ in mAcc for $l = 1$ (row 7 and 8, Tab. 3) and $68\%$ $(21.0 \rightarrow 35.2)$ for $l = 4$ is demonstrated by VLaMP over DDN. + +Goal-conditioning is crucial. A key difference between the task formulations of LTA and VPA is goal conditioning (see Sec. 2). Comparing rows for LTA model and VLaMP-there is almost $2\mathrm{x}$ gap $(27\%$ vs. $51\%$ $l = 1$ Tab.3). This underscores the importance of goal-conditioning. To second this inference, in Tab. 4 (rows 1 and 2), we precisely ablate the effect of providing the goal as a textual description for the basic (last-observation-only) model. The only difference is goal prompt $G$ , which increases mAcc performance from $44.5\rightarrow 53.1\%$ for $l = 1$ and $28.3\to 34.7\%$ for $l = 3$ + +Goal-conditioned random and most probable baseline come close to DDN on easy metrics. For fair comparisons, we include heuristic baselines. We observe the performance of random $w/$ goal and most probable $w/$ goal comes close to DDN, when evaluated using lenient metrics like mAcc and mIOU (see COIN results in Tab. 3). Note, that these two baselines enjoy the privileged access to (a much smaller) 'relevant actions set' for a given goal. On an average, the relevant or feasible action set is smaller for COIN than CrossTask videos. This apriori access to feasible actions makes random $w/$ goal and most probable $w/$ goal competitive (albeit, slightly unfair) baselines. + +Prompt-based LLM planner is not competitive. We evaluate the prompt-based GPT-3 planner on COIN and find + +Table 3: Performance on different datasets and horizons. The mean of various metrics (Sec. 3.1) obtained using 5 runs with different random seeds (std. errors are provide in Appendix E). Note that the action and observation history are the output of the separately finetuned video-action segmentation model and hence are noisy compared to the ground truth history. + +
GAkOkl = 3l = 1
SRmAccmIOUnAcc
1XXok6.8 ± 0.328.3 ± 1.934.8 ± 2.044.5 ± 3.8
2✓Xok8.9 ± 0.234.7 ± 0.741.6 ± 0.853.1 ± 2.0
3✓✓X14.9 ± 0.337.8 ± 0.450.8 ± 0.648.0 ± 0.2
4✓✓Ok15.2 ± 0.343.5 ± 0.851.4 ± 0.964.8 ± 0.9
R✓✓Ok10.7 ± 0.236.5 ± 0.741.7 ± 0.661.4 ± 1.8
+ +Table 4: Role of different inputs and LM pre-training in VLaMP. $G$ , $A_{k}$ , $O_{k}$ denote the three inputs to VLaMP: goal, action history and observation history, respectively. Shorthand of $o_{k}$ means only the most recent observation of the full history ( $O_{k}$ ) is used. Mean $\pm$ std. error over 5 random seeds on CrossTask are reported. The row R corresponds to the forecasting module of VLaMP trained with random initialization (same model architecture) as opposed to initialization using the weights of a pre-trained LM. + +that the prompt based model performs significantly worse than VLaMP. This highlights that VPA is not easy to solve using just a PTLM and prompting. + +# 5.3. Ablations and Error Analysis + +We undertake head-on ablations to quantify effect of each component of VLaMP - action history, the visual history, and language pre-training of the LM. To remove confounding factors, in Tab. 4 we use the ground truth output for the segmentation module. Following this, we include detailed error analysis. + +Action and observation history improve complementary planning metrics. As seen in all the rows with action history Tab. 4 (i.e. $A_{k}$ ), the provision of action history increases difficult metrics such as SR. In comparing rows 2 and 3, we see that SR increases relatively by $67\%$ ( $8.9 \rightarrow 14.9$ ), simply by using action history even without access to any past observation. However, the lack of observation history affects nAcc, which drops relatively by $10\%$ ( $53.1 \rightarrow 48.0$ ) when observation history is swapped by action history between rows 2 and 3. This implies that observation history is important to predict the person's state in the task and what they might do next. + +Priors from the pre-trained LM improve performance. In Tab. 4 row $\mathbf{R}$ , we report the performance of VLaMP when its forecasting module is trained with random weight initialization, i.e., the transformer of the same architecture trained from scratch instead of LM pre-training. We find the performance in row $\mathbf{R}$ is thus much lower than that of VLaMP with pre-trained LM shown in row 4. This underscores the crucial importance of LM pre-training. + +Segmentation errors are detrimental. While the accuracy of video-action segmentation module (particularly, VideoCLIP model) is quite good - $80.2\%$ for CrossTask $(68.7\%)$ + +for COIN), we believe this should be a major focus for future research. Why? The effect of this segmentation error in VLaMP's performance is quantified by comparing VLaMP row in Tab. 3 (CrossTask) with corresponding performance assuming perfect segmentation (Tab. 4, row 4). A relative $50\%$ gap in success and big gaps in all other metrics. + +![](images/1a3965aa5361235b0aeb78132271c2c58450cde177458ff8458ef9f46b8fe7fb.jpg) +Figure 5: Effect of segmentation errors. Performance of VLaMP on CrossTask with classification errors $(\%)$ in the video-action segmentation. As the errors increase, the performance gap between the full model and the one without access to observations increases. + +Visual observation history mitigates effect of video-action segmentation errors. Errors by segmentation module lead to mis-classification of actions, in turn leading to erroneous action history. To precisely study the effect of erroneous action history on VLaMP's performance, we perform controlled experiments wherein we add noise in the ground truth segmentation. This helps us tune desired segmentation error, irrespective of VideoCLIP's accuracy (in segmentation module). We achieve this by replacing a calculated $\%$ of ground-truth actions by random actions. Decreasing performance, with increasing segmentation classification error, is expected and observed in Fig. 5. Further, we compare two models variations, VLaMP $(G, A_k, O_k)$ i.e. the full model (uses both action and observation history) and VLaMP $(A, A_k)$ that does not have visual observation history. As we increase segmentation classification error, the gap in the performance of these model variations increases. We infer that visual observations add robustness in VPA against video-action segmentation errors. + +Errors do not drop as more history is provided. In Fig. 6, we show mAcc w.r.t. the number of steps $k$ in the history i.e. length of $(O_k, A_k)$ . As more information is available (due to more steps in the history), one may expect the accuracy to improve. However, this isn't the trend for many tasks. For e.g., note the accuracy drops for the task "add oil to your + +![](images/983469d45deed55ff647f7b9a6fea5e7bdadcd974307ea4747d1428276bdfc34.jpg) +Figure 6: Accuracy in the tail of long activities is challenging. Longer history $(O_{k},A_{k})$ do not necessary lead to better accuracy. Further longer histories occur with increasing rarity, leading to learning challenges. (Plot shows mAcc for $l = 3$ CrossTask vs. the #steps in history $k$ ) + +car” w.r.t $k$ . Digging deeper, we find two reasons for this pattern. First, we find that tasks with long history like “add oil to your car” tend to have repetitive steps towards the end of their action trajectories, making it difficult to predict the precise number and the pattern of such repetitions in VPA. Second is simply a data issue – long trajectories are also exponentially less frequent in the dataset. This forms the tail of the data distribution of action sequences in the dataset (see App. E for statistics). Consequently, prediction in this tail of activities, is a pertinent challenge for future research. + +# 6. Conclusion + +Visual Planning for Assistance is a new and intuitive formulation to support planning from natural visual observations for assisting humans in day-to-day activities. We benchmark VPA using standardized suite of prior baselines and a new multi-modal sequence modeling formation of VLaMP. The novel decomposition of a VLaMP policy into video action segmentation and forecasting leads to several efficiency and modeling benefits, that benefit the community, even beyond VPA. Particularly, this allows to leverage pre-trained LM that leads to significant performance gains. Alternative decompositions, self-supervised pre-training objectives for PTLMs, modeling multiple actors, and tapping into other modalities (audio, camera metadata, etc.) [26, 55, 43, 72, 32, 88] are interesting ways forward for the community, on the exciting task of VPA. + +Acknowledgements: The authors are indebted to Brian Chen for his efforts to open-source the code and LTA experiments, and to Gideon Stocek for supporting with the cluster management. We thank Vasu Sharma, Tushar Nagarajan, and Homanga Bharadhwaj for their writing feedback. We thank Weichao Mao for early discussions and Asli Celikyilmaz for her constant guidance. + +# References + +[1] Yazan Abu Farha, Alexander Richard, and Juergen Gall. When will you do what?-anticipating temporal occurrences of activities. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3537-3545, 2019. 1, 3, 4, 7, 8 \ No newline at end of file diff --git a/2023/Pretrained Language Models as Visual Planners for Human Assistance/images.zip b/2023/Pretrained Language Models as Visual Planners for Human Assistance/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..12ffef1afa464b2d2662f134f8d5852d24c0e3ee --- /dev/null +++ b/2023/Pretrained Language Models as Visual Planners for Human Assistance/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1ba0f3d03f4688f27606bab3d469fdc6da02578366f1b32f1ba3624fd6998475 +size 395643 diff --git a/2023/Pretrained Language Models as Visual Planners for Human Assistance/layout.json b/2023/Pretrained Language Models as Visual Planners for Human Assistance/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..6e3f76e542f82319f48cea35c9aeee4d13f24f39 --- /dev/null +++ b/2023/Pretrained Language Models as Visual Planners for Human Assistance/layout.json @@ -0,0 +1,12997 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 78, + 103, + 515, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 103, + 515, + 121 + ], + "spans": [ + { + "bbox": [ + 78, + 103, + 515, + 121 + ], + "type": "text", + "content": "Pretrained Language Models as Visual Planners for Human Assistance" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 154, + 142, + 444, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 154, + 142, + 444, + 200 + ], + "spans": [ + { + "bbox": [ + 154, + 142, + 444, + 200 + ], + "type": "text", + "content": "Dhruvesh Patel" + }, + { + "bbox": [ + 154, + 142, + 444, + 200 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 154, + 142, + 444, + 200 + ], + "type": "text", + "content": " Hamid Eghbalzadeh" + }, + { + "bbox": [ + 154, + 142, + 444, + 200 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 154, + 142, + 444, + 200 + ], + "type": "text", + "content": " Nitin Kamra" + }, + { + "bbox": [ + 154, + 142, + 444, + 200 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 154, + 142, + 444, + 200 + ], + "type": "text", + "content": " Michael Louis Iuzzolino" + }, + { + "bbox": [ + 154, + 142, + 444, + 200 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 154, + 142, + 444, + 200 + ], + "type": "text", + "content": " Unnat Jain" + }, + { + "bbox": [ + 154, + 142, + 444, + 200 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 154, + 142, + 444, + 200 + ], + "type": "text", + "content": " Ruta Desai" + }, + { + "bbox": [ + 154, + 142, + 444, + 200 + ], + "type": "inline_equation", + "content": "^{1*†}" + }, + { + "bbox": [ + 154, + 142, + 444, + 200 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 154, + 142, + 444, + 200 + ], + "type": "text", + "content": "Meta " + }, + { + "bbox": [ + 154, + 142, + 444, + 200 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 154, + 142, + 444, + 200 + ], + "type": "text", + "content": "UMass Amherst https://github.com/facebookresearch/vlamp" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 252, + 290, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 290, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 290, + 552 + ], + "type": "text", + "content": "In our pursuit of advancing multi-modal AI assistants capable of guiding users to achieve complex multi-step goals, we propose the task of 'Visual Planning for Assistance (VPA)'. Given a succinct natural language goal, e.g., \"make a shelf\", and a video of the user's progress so far, the aim of VPA is to devise a plan, i.e. a sequence of actions such as \"sand shelf\", \"paint shelf\", etc. to realize the specified goal. This requires assessing the user's progress from the (untrimmed) video, and relating it to the requirements of natural language goal, i.e. which actions to select and in what order? Consequently, this requires handling long video history and arbitrarily complex action dependencies. To address these challenges, we decompose VPA into video action segmentation and forecasting. Importantly, we experiment by formulating the forecasting step as a multimodal sequence modeling problem, allowing us to leverage the strength of pre-trained LMs (as the sequence model). This novel approach, which we call Visual Language Model based Planner (VLaMP), outperforms baselines across a suite of metrics that gauge the quality of the generated plans. Furthermore, through comprehensive ablations, we also isolate the value of each component - language pretraining, visual observations, and goal information. We have open-sourced all the data, model checkpoints, and training code." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 576, + 128, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 576, + 128, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 576, + 128, + 588 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 597, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 287, + 693 + ], + "type": "text", + "content": "Imagine assembling a new piece of furniture or following a new recipe for a dinner party. To achieve such a goal, you might follow a manual or a video tutorial, going back and forth as you perform the steps. Instead of fumbling through a manual, imagine an assistive agent capable of being invoked through natural language, having the ability to understand human actions, and providing actionable multi-step guidance for achieving your desired goal. Such multi-" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 225, + 547, + 365 + ], + "blocks": [ + { + "bbox": [ + 310, + 225, + 547, + 365 + ], + "lines": [ + { + "bbox": [ + 310, + 225, + 547, + 365 + ], + "spans": [ + { + "bbox": [ + 310, + 225, + 547, + 365 + ], + "type": "image", + "image_path": "1ec0e91231c15a34a02907bea4c7c18d3395949578a3dd3ca32d00ace36a79d4.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 374, + 546, + 472 + ], + "lines": [ + { + "bbox": [ + 305, + 374, + 546, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 374, + 546, + 472 + ], + "type": "text", + "content": "Figure 1: Visual Planning for Assistance overview (top) and general methodology (bottom). Given a user-specified, natural language goal (\"build a shelf\") and corresponding visual history of the user's progress till now, VPA involves predicting a sequence of actions, to assist the user towards the goal (\"cut\", \"sand\", \"paint\"). Our approach is based on multi-modal sequence modeling where we reuse pre-trained video segmentation and language models." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 495, + 546, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 546, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 546, + 533 + ], + "type": "text", + "content": "modal assistive agents should be able to reason human activities from visual observations, contextualize them to the goal at hand, and plan future actions for providing guidance." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": "To quantify the progress and aid the development of such multi-modal neural models, we need a intuitive task, as illustrated in the example in Fig. 1 (top). We call this Visual Planning for Assistance (VPA) that we detail next. Given a user-specified goal in natural language (\"build shelf\") and corresponding video observations of the user's progress towards this goal, the task objective should be to generate the ordered sequence of next actions towards achieving the goal (\"cut " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " sand " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " paint\"). We base VPA off instructional YouTube videos of such procedural activities from large, open-sourced datasets - CrossTask [89] and COIN [73]. This is a natural choice as procedural human activities (cooking, assembly, repair, etc.) are a perfect source of multi-step and complex sequence of actions, where humans routinely seek guidance. Realistic nature" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 197, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 197, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 197, + 713 + ], + "type": "text", + "content": "*equal mentoring † corresponding author" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15302" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "of VPA makes it particularly challenging. Operating on untrimmed videos requires dealing with potentially many irrelevant background frames, chunking actions in the videos will also be imperative. Another challenge is the validity of the plan of actions i.e. they must respect the constraints of the activity – the shelf shouldn't be painted before sanding." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 288, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 288, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 288, + 441 + ], + "type": "text", + "content": "The natural next question is - what's a good way to tackle VPA? Marrying research from video forecasting & anticipation with embodied AI [19, 17], we cast VPA as goal-conditioned task planning. We approach VPA by utilizing video action segmentation and transformer-based neural sequence modeling - the former allows us to deal with long video history and the latter can handle arbitrary sequential constraints [86, 39]. The formulation (particularly, transformer-based neural sequence modeling) allows us to tap into the prowess of pre-trained language models (PTLMs). These PTLMs contain useful priors about action-action similarity, action-goal association, and action ordering [7, 30, 58], that our formulation can piggy-back off. Particularly, our model - Visual Language Model Planner (VLaMP) - conditions the generated plan onto the visual history by using a transformer-based mapper network that projects embeddings corresponding to visual history into the input space of the LM. Using VPA as the testbed, we show that VLaMP outperforms a range of standardized baselines. We undertake head-on ablations to quantify effect of each component of VLaMP - language pre-training of the LM, the visual history, and goal description. We believe the modularity of our approach can allow researchers to swap components with their own, to make rapid progress towards VPA." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 443, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 443, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 443, + 287, + 550 + ], + "type": "text", + "content": "In summary, our main contributions are: (1) a new task VPA on human interaction videos capturing unique aspects of real-world vision-powered assistive agents; (2) a general-purpose methodology for VPA, which allows leveraging pre-trained multi-modal encoders and sequence models; (3) an instantiation of this methodology (we call VLaMP), where we reuse sequence priors from PTLM and investigate its efficacy across two, well-studied datasets of procedural human activities." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 562, + 134, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 134, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 134, + 574 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": "Forecasting in Videos. VPA entails future action sequence prediction for a video and is closely related to anticipation in video understanding, including future localization [22, 40, 78], future frame prediction [77, 46, 53], next active object estimation [21, 5, 25, 67, 4, 24, 44], as well as short- and long-term action anticipation [66, 15, 20, 23, 25, 65, 64, 57, 45, 1, 52, 50, 11, 79]. While short-term forecasting approaches, such as [66], are limited to predicting the single next action occurring only a few seconds into the future, our work focuses on predicting sequences of actions over longer time horizons (on the order of minutes)" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 306, + 70, + 547, + 133 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 547, + 133 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 547, + 133 + ], + "type": "table", + "html": "
Action PredictionGoal ModalityVisual Reasoning
Action anticipation [14]SingleNoneVideo-based
Action forecasting [25]Multiple, orderedNoneVideo-based
Procedural planning [9]Multiple, orderedVisionImage-based
VPA (ours)Multiple, orderedNatural LanguageVideo-based
", + "image_path": "6ff69421a6caa4068fed88e96c207d6103895396482c1ec76bf5287d0290ae74.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 141, + 547, + 200 + ], + "lines": [ + { + "bbox": [ + 304, + 141, + 547, + 200 + ], + "spans": [ + { + "bbox": [ + 304, + 141, + 547, + 200 + ], + "type": "text", + "content": "Table 1: VPA vs. prior tasks related to forecasting of real-world human activities. We predict an ordered sequence of actions given video history with a focus on natural language goal-conditioning for human-assistive applications." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 222, + 546, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 222, + 546, + 389 + ], + "spans": [ + { + "bbox": [ + 304, + 222, + 546, + 389 + ], + "type": "text", + "content": "into the future. The long-term action (LTA) forecasting benchmarking was recently established on a small subset of Ego4D [25], and although VPA is similarly devised to predict a temporally ordered sequence of actions conditioned on video-based visual observations, our approach differs in that the LTA task does no goal-conditioning. Our task incorporates goal-conditioning on long term sequence prediction as we argue this will drive the development of critical system aspects, such as virtual assistants that afford human interaction via the natural language goals. Additionally, in contrast to LTA, we focus on a wide range of goal-oriented activities available within the CrossTask and COIN datasets. Tab. 1 highlights the differences between VPA and other forecasting tasks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 390, + 546, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 546, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 546, + 605 + ], + "type": "text", + "content": "Procedural Planning Approaches. VPA is similar to the task of procedure planning [9], wherein given a starting and terminating visual observation, the aim is to predict the actions that would transform the state from starting to terminating. However, we argue that due to the unavailability of the terminating visual state, the procedure planning task is not useful in a real-world assistance setting. While several recent works introduce novel models for procedure planning, these models cannot be deployed for VPA either because they rely heavily on the availability of visual goal [70, 87, 6], or assume access to true action history [49]. Transformers for Decision Making. VLaMP autoregressively predicts future states and/or observations and actions and is similar in spirit to sequence models for decision making such as GATO [61], Decision Transformer [12], and Trajectory Transformer [35]. VLaMP extends such models to work with egocentric observations that humans observe in the day-to-day activities." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "Planning in Embodied AI using LMs. Past research has leveraged PTLMs for task planning in real world for embodied agents [30, 68, 41, 7, 42, 31, 18, 16, 36]. Many of these works focus on converting a high-level task or instruction into sequence of low-level steps and then ground them in the environment using either affordance functions [7], visual feedback [31], or multimodal prompts [36, 18]. Owing to their focus on robotic agents, these works focus on predominately pick-place tasks. Instead VPA is focused on" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15303" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "complex tasks, in which humans might require assistance in the form of recommended future actions. Consequently, VLaMP requires grounding and reasoning of much more complex states and actions, which it accomplishes by finetuning a pretrained LM on multimodal sequences of (visual) observations and (text-based) actions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 289, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 289, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 289, + 350 + ], + "type": "text", + "content": "Multi-modal LMs. Recent works have successfully used the transformer architecture for modeling multi-modal sequences that have visual tokens. For instance, [47, 59, 2, 48, 29, 18] train large transformer based multi-modal sequence prediction models. While [3, 74, 56] focus on adapting pre-trained LMs to work with visual tokens by aligning the representation spaces of the two modalities. VLaMP's approach of modeling sequence of visual and textual representations using PTLMs is similar in spirit to these, i.e. VLaMP also uses a mapper network to align video representations to LM's token space and jointly learns the mapper with LM finetuning for VPA. However, in contrast to previous works, VLaMP predicts the visual tokens autoregressively at inference time to enable forecasting of the state for planning. Consequently, VLaMP's token prediction loss is multi-modal, unlike most multi-modal LMs that only use token prediction loss for text tokens." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 361, + 218, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 361, + 218, + 374 + ], + "spans": [ + { + "bbox": [ + 47, + 361, + 218, + 374 + ], + "type": "text", + "content": "3. Visual Planning for Assistance" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 382, + 287, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 382, + 287, + 455 + ], + "spans": [ + { + "bbox": [ + 46, + 382, + 287, + 455 + ], + "type": "text", + "content": "Here, we introduce the task of Visual Planning for Assistance (VPA), towards enabling multi-step guidance to humans in their real-world activities. We instantiate VPA for procedural activities, where humans routinely seek assistance. In this section, we include the definition of VPA, and describe the evaluation protocol." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 464, + 141, + 476 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 141, + 476 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 141, + 476 + ], + "type": "text", + "content": "3.1. Task Definition" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 483, + 287, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 287, + 507 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 287, + 507 + ], + "type": "text", + "content": "The following two intuitive inputs are given to any model performing VPA." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 508, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 287, + 555 + ], + "type": "text", + "content": "Goal Prompt " + }, + { + "bbox": [ + 46, + 508, + 287, + 555 + ], + "type": "inline_equation", + "content": "(G)" + }, + { + "bbox": [ + 46, + 508, + 287, + 555 + ], + "type": "text", + "content": ". The natural language description (in short phrase) of the user's goal, emulating a typical user's request for assistance for a day-to-day task. Examples include, \"build a shelf\" and \"change a tire\"." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "content": "Visual History " + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "inline_equation", + "content": "(V_{t})" + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "content": ". An untrimmed video that provides context about the user's progress towards a goal from the start till time, say " + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "content": ". We assume that " + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "inline_equation", + "content": "V_{t}" + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "content": " contains " + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "content": " actions or steps " + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\{a_1,\\ldots ,a_k\\}" + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "content": " pertaining to the goal. However, VPA doesn't have access to " + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\{a_1,\\dots ,a_k\\}" + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "content": " and must work with " + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "inline_equation", + "content": "V_{t}" + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "Given these two inputs, " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "V_{t}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": ", the objective of VPA is to generate a plan " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": ". The plan is a sequence of actions that should be executed (in the next steps) to assist the user in achieving the goal " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": ". Concretely, the prediction is denoted by " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{T} = (a_{k + 1},\\dots ,a_{k + l})" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "a_{i}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " are represented in natural language but come from a closed set " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "l\\leq K" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " denotes the number of future actions that should be predicted," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "out of the " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " number of remaining actions required to accomplish the goal. For our shelf-building example, the correct " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{T} =" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " (sand shelf, paint shelf, attach shelf), capturing the remaining 3 future actions (here, " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "l = N = 3" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 121, + 546, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 121, + 546, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 121, + 546, + 251 + ], + "type": "text", + "content": "In day-to-day activities, we request assistance for goals in natural language. However, prior works procedural planning [9, 6] assume access to visual goal state. This is not a realistic assumption for an AI agent assisting humans. Hence, we purposefully relax this assumption, making our formulation of the task significantly more practical. Moreover, an agent with access to the visual modality, should be able to improve its plan by filtering out relevant information from the raw video stream of the progress. These are the two central assumptions around which we formulate the task of VPA." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 259, + 380, + 271 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 259, + 380, + 271 + ], + "spans": [ + { + "bbox": [ + 306, + 259, + 380, + 271 + ], + "type": "text", + "content": "3.2. Evaluation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 278, + 545, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 278, + 545, + 326 + ], + "spans": [ + { + "bbox": [ + 304, + 278, + 545, + 326 + ], + "type": "text", + "content": "Open-Sourced Video Data. We leverage existing datasets CrossTask [89] and COIN [73], originally developed to enable video action understanding for VPA, based on the following three requirements:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 327, + 547, + 602 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 306, + 327, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 327, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 306, + 327, + 545, + 373 + ], + "type": "text", + "content": "- Rich diversity of activities from multiple domains: The data from different domains such as cooking, assembly etc., enables testing of VPA models in a more generalized manner." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 375, + 547, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 375, + 547, + 433 + ], + "spans": [ + { + "bbox": [ + 306, + 375, + 547, + 433 + ], + "type": "text", + "content": "- Goal-oriented activities consisting of long sequences of actions: Since the objective is to generate " + }, + { + "bbox": [ + 306, + 375, + 547, + 433 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 306, + 375, + 547, + 433 + ], + "type": "text", + "content": " future actions, activities in these datasets that require diverse sequences of actions e.g., \"making a pancake\", instead of \"running\" are more suitable for VPA." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 434, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 434, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 306, + 434, + 545, + 578 + ], + "type": "text", + "content": "- Action annotations from a fixed closed set of actions: Action labels described using verb-noun from a finite set [14], which are temporally aligned with the videos. This makes evaluating the accuracy of " + }, + { + "bbox": [ + 306, + 434, + 545, + 578 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 306, + 434, + 545, + 578 + ], + "type": "text", + "content": " prediction straightforward. Specifically, free-form, narration-style descriptions of actions that are available in recent video datasets aid in efficient multi-modal representation learning for video understanding [25, 54]. However, evaluating the quality of action sequences towards goal achievement, where each action is described in free-form natural language, is non-trivial. We leave the instantiation of VPA with free-form natural language actions as future work." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 578, + 545, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 578, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 306, + 578, + 545, + 602 + ], + "type": "text", + "content": "Table 2 summarizes the features from CrossTask and COIN, aligned with the above requirements." + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "content": "Metrics. The planning performance of a VPA model is measured by comparing the generated plan " + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{T}} = (\\hat{a}_{k + 1},\\dots ,\\hat{a}_{k + l})" + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "content": " to the ground truth plan " + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "content": " actions in the future, given " + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "inline_equation", + "content": "V_{t}" + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "content": ". Here " + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\hat{a}_{k + i}" + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "content": " denotes the prediction for the " + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "inline_equation", + "content": "k + i" + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "content": "-th step given history till " + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "content": "-th step. Consistent with community practices [9, 6], we use the following metrics, listed in decreasing order of strictness: success rate (SR), mean accuracy (mAcc), mean intersection over union" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15304" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 70, + 288, + 116 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 116 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 116 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 116 + ], + "type": "table", + "html": "
Dataset# train videos# test videos# test samplesactions per video# goals# domains
CrossTask [89]175675241237.6 ± 4.3183
COIN [73]9428104720113.9 ± 2.418012
", + "image_path": "45e3b53acb6fb4edb98c509784f25925f5ff1e3dc0c5f2c3918e1906d5e6c238.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 122, + 287, + 171 + ], + "lines": [ + { + "bbox": [ + 46, + 122, + 287, + 171 + ], + "spans": [ + { + "bbox": [ + 46, + 122, + 287, + 171 + ], + "type": "text", + "content": "Table 2: VPA datasets. We evaluate VPA on two existing video datasets containing multiple goal-oriented procedural activities from varied domains. Such activities contain sequences of multiple actions making them ideal for VPA." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 192, + 288, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 288, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 288, + 289 + ], + "type": "text", + "content": "(mIOU). Success rate requires an exact match between all actions and their sequence between " + }, + { + "bbox": [ + 46, + 192, + 288, + 289 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{T}}" + }, + { + "bbox": [ + 46, + 192, + 288, + 289 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 192, + 288, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 192, + 288, + 289 + ], + "type": "text", + "content": ". Mean accuracy is the accuracy of the actions at each step. Unlike success rate, mean accuracy does not require a " + }, + { + "bbox": [ + 46, + 192, + 288, + 289 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 192, + 288, + 289 + ], + "type": "text", + "content": " match to ground truth. Instead it considers matching at each individual step. Lastly, mean intersection over union captures the cases where the model predicts the steps correctly, but fails to identify the correct order. Concretely," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 87, + 307, + 287, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 307, + 287, + 338 + ], + "spans": [ + { + "bbox": [ + 87, + 307, + 287, + 338 + ], + "type": "interline_equation", + "content": "\\mathrm {m I O U} _ {l} = \\frac {\\left| \\hat {a} _ {\\{k + 1 : k + l \\}} \\bigcap a _ {\\{k + 1 : k + l \\}} \\right|}{\\left| \\hat {a} _ {\\{k + 1 : k + l \\}} \\bigcup a _ {\\{k + 1 : k + l \\}} \\right|}, \\tag {1}", + "image_path": "0f3a997e6497c836717dcdc0c1f924767798c32cb9c2233a68bc79e5f316e195.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 91, + 339, + 287, + 371 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 339, + 287, + 371 + ], + "spans": [ + { + "bbox": [ + 91, + 339, + 287, + 371 + ], + "type": "interline_equation", + "content": "\\mathrm {m A c c} _ {l} = \\frac {1}{l} \\sum_ {i = 1} ^ {l} \\mathbb {1} [ \\hat {a} _ {k + i,} = a _ {k + i} ], \\tag {2}", + "image_path": "9b8c95ce9655dca732c88553e5a2b61af9c182c3929e80b6bd9afce0da56cbd1.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 102, + 374, + 287, + 407 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 374, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 102, + 374, + 287, + 407 + ], + "type": "interline_equation", + "content": "\\mathrm {S R} _ {l} = \\prod_ {i = 1} ^ {l} \\mathbb {1} [ \\hat {a} _ {k + i} = a _ {k + i} ], \\tag {3}", + "image_path": "c043801ea62f66afb6c7d05ef9ede8aaae16451416ed6ae43000de29c53e0b8f.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 415, + 287, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 513 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 415, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\mathbb{1}[\\cdot ]" + }, + { + "bbox": [ + 46, + 415, + 287, + 513 + ], + "type": "text", + "content": " is the identity function, which is 1 when the condition in its input is true, and 0, and " + }, + { + "bbox": [ + 46, + 415, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\hat{a}_{\\{k + 1:k + l\\}}" + }, + { + "bbox": [ + 46, + 415, + 287, + 513 + ], + "type": "text", + "content": " denotes the set of " + }, + { + "bbox": [ + 46, + 415, + 287, + 513 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 415, + 287, + 513 + ], + "type": "text", + "content": " future actions in " + }, + { + "bbox": [ + 46, + 415, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{T}}" + }, + { + "bbox": [ + 46, + 415, + 287, + 513 + ], + "type": "text", + "content": ", i.e., a sequence but disregarding the order. To complement the above metrics, we also measure the accuracy of predicting the next action i.e. nAcc, as defined in (4), where 'n' stands for next. Note that all metrics are averaged over the test set details of which are included in Sec. 5." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 115, + 523, + 287, + 537 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 523, + 287, + 537 + ], + "spans": [ + { + "bbox": [ + 115, + 523, + 287, + 537 + ], + "type": "interline_equation", + "content": "\\mathrm {n A c c} = \\mathbb {1} [ \\hat {a} _ {k + 1} = a _ {k + 1} ] \\tag {4}", + "image_path": "fd30bfcadf32e3787f81420bc47f8d3734b16c9b956777c52b2e8911e78f7512.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 548, + 161, + 560 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 161, + 560 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 161, + 560 + ], + "type": "text", + "content": "4. Visual LM Planner" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 567, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 676 + ], + "type": "text", + "content": "VPA can be viewed as a sequential decision making problem, where the model (say, " + }, + { + "bbox": [ + 46, + 567, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 567, + 287, + 676 + ], + "type": "text", + "content": ") predicting the sequence of next actions is a policy conditioned on the visual history " + }, + { + "bbox": [ + 46, + 567, + 287, + 676 + ], + "type": "inline_equation", + "content": "V_{t}" + }, + { + "bbox": [ + 46, + 567, + 287, + 676 + ], + "type": "text", + "content": ", serving as (partially-observed) state, and goal prompt " + }, + { + "bbox": [ + 46, + 567, + 287, + 676 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 567, + 287, + 676 + ], + "type": "text", + "content": ". Inspired by the offline learning formulation closest to 'learning from offline demonstrations' [27, 76, 37, 81], in VLaMP, we formulate VPA as a goal-conditioned, multimodal sequence prediction problem. This formulation allows us to leverage high-capacity sequence models like" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": "Transformers [75], which have been successfully applied to sequential decision making [35, 12]. Furthermore, inspired by the recent success of pre-trained transformer language models (PTLMs) on such tasks, [62, 30, 12], we propose to leverage PTLMs as the sequence model in our formulation. In the remainder of this section we describe our approach for VPA, called Visual Language Model based Planner (VLaMP), consisting of a segmentation module and PTLM based sequence prediction module." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 190, + 538, + 203 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 190, + 538, + 203 + ], + "spans": [ + { + "bbox": [ + 305, + 190, + 538, + 203 + ], + "type": "text", + "content": "4.1. Planning with Segmentation and Forecasting" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 209, + 545, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 209, + 545, + 233 + ], + "spans": [ + { + "bbox": [ + 305, + 209, + 545, + 233 + ], + "type": "text", + "content": "We define " + }, + { + "bbox": [ + 305, + 209, + 545, + 233 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 305, + 209, + 545, + 233 + ], + "type": "text", + "content": " as a goal-conditioned, multi-modal sequence prediction problem:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 359, + 244, + 545, + 258 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 244, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 359, + 244, + 545, + 258 + ], + "type": "interline_equation", + "content": "\\pi = P \\left(a _ {k + 1}, a _ {k + 2}, \\dots \\mid V _ {t}, G\\right). \\tag {5}", + "image_path": "6f59c491f8ce8b506f68b3a4bd52e9d6a6dbbb632d564cd7c71cea237b03ab74.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 268, + 545, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 268, + 545, + 291 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 545, + 291 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 268, + 545, + 291 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 268, + 545, + 291 + ], + "type": "text", + "content": " models the probability of goal-relevant and valid future actions sequences conditioned on " + }, + { + "bbox": [ + 304, + 268, + 545, + 291 + ], + "type": "inline_equation", + "content": "V_{t}" + }, + { + "bbox": [ + 304, + 268, + 545, + 291 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 268, + 545, + 291 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 268, + 545, + 291 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 293, + 546, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 546, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 546, + 519 + ], + "type": "text", + "content": "Modeling the multi-modal sequence in Eq. 5 is computationally expensive and difficult to scale because of the high-dimensional state space of raw untrimmed video " + }, + { + "bbox": [ + 304, + 293, + 546, + 519 + ], + "type": "inline_equation", + "content": "V_{t}" + }, + { + "bbox": [ + 304, + 293, + 546, + 519 + ], + "type": "text", + "content": ". Also, there is limited data to learn the distribution over valid action sequences for goals in real-world applications. Tackling these challenges, we argue that the latent space of factors influencing the future plan can indeed be expressed in lesser dimensions. Particularly, to ensure scalability for handling raw videos and sample efficiency in learning valid action sequence distributions, we decompose our policy " + }, + { + "bbox": [ + 304, + 293, + 546, + 519 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 293, + 546, + 519 + ], + "type": "text", + "content": " into two modules. The first module is video segmentation, which converts the untrimmed video history " + }, + { + "bbox": [ + 304, + 293, + 546, + 519 + ], + "type": "inline_equation", + "content": "V_{t}" + }, + { + "bbox": [ + 304, + 293, + 546, + 519 + ], + "type": "text", + "content": " into a sequence of video segments i.e. a segment history " + }, + { + "bbox": [ + 304, + 293, + 546, + 519 + ], + "type": "inline_equation", + "content": "S_{k} = (s_{1},\\dots ,s_{k})" + }, + { + "bbox": [ + 304, + 293, + 546, + 519 + ], + "type": "text", + "content": ", where each segment corresponds to an action " + }, + { + "bbox": [ + 304, + 293, + 546, + 519 + ], + "type": "inline_equation", + "content": "a_{i}" + }, + { + "bbox": [ + 304, + 293, + 546, + 519 + ], + "type": "text", + "content": " that occurred in the video. The second module enables forecasting i.e. it transforms the output of the segmentation module and generates the plan (see Fig. 1 (bottom)). While a probabilistic formulation of this decomposition can be expressed as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 321, + 530, + 545, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 530, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 321, + 530, + 545, + 559 + ], + "type": "interline_equation", + "content": "\\pi = \\sum_ {S _ {k}} \\underbrace {P \\left(a _ {k + 1} , a _ {k + 2} , \\cdots \\mid S _ {k} , G\\right)} _ {\\text {F o r e c a s t i n g}} \\underbrace {P \\left(S _ {k} \\mid V _ {t}\\right)} _ {\\text {S e g m e n t a t i o n}}, \\tag {6}", + "image_path": "334f8ed8fabfcfcb8b2ea36188144aad4cf5f2569c44bbbdf5f666816277898c.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 570, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 629 + ], + "type": "text", + "content": "where the segment history " + }, + { + "bbox": [ + 304, + 570, + 545, + 629 + ], + "type": "inline_equation", + "content": "S_{k}" + }, + { + "bbox": [ + 304, + 570, + 545, + 629 + ], + "type": "text", + "content": " is a latent variable, the summation over all possible segment histories is intractable. We, however, use Eq. 6 as the guiding expression to formulate the input and output of both modules. Next, we include the technical details of both of these modules." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 639, + 432, + 652 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 639, + 432, + 652 + ], + "spans": [ + { + "bbox": [ + 306, + 639, + 432, + 652 + ], + "type": "text", + "content": "4.2. Segmentation Module" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 658, + 545, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 658, + 545, + 683 + ], + "spans": [ + { + "bbox": [ + 305, + 658, + 545, + 683 + ], + "type": "text", + "content": "This module splits the untrimmed video history " + }, + { + "bbox": [ + 305, + 658, + 545, + 683 + ], + "type": "inline_equation", + "content": "V_{t}" + }, + { + "bbox": [ + 305, + 658, + 545, + 683 + ], + "type": "text", + "content": " into segment history " + }, + { + "bbox": [ + 305, + 658, + 545, + 683 + ], + "type": "inline_equation", + "content": "S_{k}" + }, + { + "bbox": [ + 305, + 658, + 545, + 683 + ], + "type": "text", + "content": " of multiple segments, each segment" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "text", + "content": "1Future works may explore alternate policy optimizations based on reward shaping, inverse RL, or by employing additional online interactions through photorealistic simulation [38, 63, 71, 69, 82, 33, 34, 10, 80]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "A typical untrimmed video of 100p video of 5 minutes at 8fps will have " + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "2^{7}" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": " raw pixel values." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15305" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 73, + 282, + 185 + ], + "blocks": [ + { + "bbox": [ + 53, + 73, + 282, + 185 + ], + "lines": [ + { + "bbox": [ + 53, + 73, + 282, + 185 + ], + "spans": [ + { + "bbox": [ + 53, + 73, + 282, + 185 + ], + "type": "image", + "image_path": "087d67a1de51d94c1b34f3dfb37dc87fc6774ac21ebb63bfdfaf6e3967206c84.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 196, + 287, + 268 + ], + "lines": [ + { + "bbox": [ + 46, + 196, + 287, + 268 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 287, + 268 + ], + "type": "text", + "content": "Figure 2: VLaMP - Segmentation Module. The untrimmed visual history " + }, + { + "bbox": [ + 46, + 196, + 287, + 268 + ], + "type": "inline_equation", + "content": "V_{t}" + }, + { + "bbox": [ + 46, + 196, + 287, + 268 + ], + "type": "text", + "content": " is converted into segments, each consisting of observation " + }, + { + "bbox": [ + 46, + 196, + 287, + 268 + ], + "type": "inline_equation", + "content": "o_{i}" + }, + { + "bbox": [ + 46, + 196, + 287, + 268 + ], + "type": "text", + "content": " and the action " + }, + { + "bbox": [ + 46, + 196, + 287, + 268 + ], + "type": "inline_equation", + "content": "a_{i}" + }, + { + "bbox": [ + 46, + 196, + 287, + 268 + ], + "type": "text", + "content": ". The observation " + }, + { + "bbox": [ + 46, + 196, + 287, + 268 + ], + "type": "inline_equation", + "content": "o_{i}" + }, + { + "bbox": [ + 46, + 196, + 287, + 268 + ], + "type": "text", + "content": " is the collection of video frames of " + }, + { + "bbox": [ + 46, + 196, + 287, + 268 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 196, + 287, + 268 + ], + "type": "text", + "content": " seconds around the start time stamp " + }, + { + "bbox": [ + 46, + 196, + 287, + 268 + ], + "type": "inline_equation", + "content": "t_{i}" + }, + { + "bbox": [ + 46, + 196, + 287, + 268 + ], + "type": "text", + "content": " of the corresponding action " + }, + { + "bbox": [ + 46, + 196, + 287, + 268 + ], + "type": "inline_equation", + "content": "a_{i}" + }, + { + "bbox": [ + 46, + 196, + 287, + 268 + ], + "type": "text", + "content": ". Two such segments are shown here." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": "corresponding to an action. The segmentation is done using a video-action segmentation model in three steps: preprocessing, classification, and consolidation. In the preprocessing step, the raw video frames from " + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "inline_equation", + "content": "V_{t}" + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": " are bundled into fixed-length window clips " + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": ", each of length 1 second, to obtain " + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "inline_equation", + "content": "V_{t} = (c_{1},\\dots ,c_{t})" + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": ". In the classification step, a video-action segmentation model is used to output the most probable action for each clip " + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": ", which can be denoted as " + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "inline_equation", + "content": "\\tilde{A}_t = (\\tilde{a}_1,\\tilde{a}_2,\\ldots ,\\tilde{a}_t)" + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": ". Finally, in the consolidation steps, we convert " + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "inline_equation", + "content": "\\tilde{A}_t" + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": " into a form that can be used by the forecasting module; this form consists of two sequences: action history " + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "inline_equation", + "content": "A_{k}" + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": " and observation history " + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "inline_equation", + "content": "O_{k}" + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": ". To this end, same actions in consecutive seconds in " + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "inline_equation", + "content": "\\tilde{A}_t" + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": " are consolidated to form the action history " + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "inline_equation", + "content": "A_{k} = (a_{1},\\dots ,a_{k})" + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": ". As illustrated in Fig. 2, assuming " + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": " denotes the starting timestamp for " + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "inline_equation", + "content": "a_{i}" + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": ", we also extract video frames from " + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "inline_equation", + "content": "t_i - \\delta /2" + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "inline_equation", + "content": "t_i + \\delta /2" + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": " to obtain an observation window " + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "inline_equation", + "content": "o_i" + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": " corresponding to " + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "inline_equation", + "content": "a_{i}" + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": ", and consequently the full observation history " + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "inline_equation", + "content": "O_{k} = (o_{1},\\dots,o_{k})" + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": ". The resultant segment history is termed " + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "inline_equation", + "content": "S_{k} = ((o_{1},a_{1}),\\dots ,(o_{k},a_{k}))" + }, + { + "bbox": [ + 46, + 290, + 289, + 531 + ], + "type": "text", + "content": ", summarized in Fig. 2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 537, + 163, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 537, + 163, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 537, + 163, + 550 + ], + "type": "text", + "content": "4.3. Forecasting Module" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 556, + 287, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 287, + 626 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 287, + 626 + ], + "type": "text", + "content": "The usefulness of " + }, + { + "bbox": [ + 46, + 556, + 287, + 626 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 556, + 287, + 626 + ], + "type": "text", + "content": "'s decomposition expressed in Eq. (6) becomes apparent now. Modeling the segmentation module's output as segment history " + }, + { + "bbox": [ + 46, + 556, + 287, + 626 + ], + "type": "inline_equation", + "content": "S_{k}" + }, + { + "bbox": [ + 46, + 556, + 287, + 626 + ], + "type": "text", + "content": ", where each segment consisting of action and observations, allows writing the output of the forecasting module in an autoregressive manner:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 61, + 638, + 287, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 638, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 61, + 638, + 287, + 681 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} P \\left(a _ {k + 1}, a _ {k + 2}, \\dots \\mid o _ {1}, a _ {1}, \\dots , o _ {k}, a _ {k}, G\\right) \\\\ = \\prod_ {i > 0} \\sum_ {o _ {k + i}} P \\left(o _ {k + i}, a _ {k + i} \\mid o _ {1}, a _ {1}, \\dots , o _ {k}, a _ {k}, G\\right). \\tag {7} \\\\ \\end{array}", + "image_path": "51a7b24e729f67c07a97d4028123a8fd3fab962aa5274b516afb7cadbf2222b7.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Illustrated in Fig. 3, this autoregressive expression allows the possibility of using any sequence-to-sequence neural" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 178 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 178 + ], + "type": "text", + "content": "network as the forecasting module in combination with pretrained text and video encoders for representing action and observation history " + }, + { + "bbox": [ + 304, + 72, + 545, + 178 + ], + "type": "inline_equation", + "content": "A_{k}" + }, + { + "bbox": [ + 304, + 72, + 545, + 178 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 178 + ], + "type": "inline_equation", + "content": "O_{k}" + }, + { + "bbox": [ + 304, + 72, + 545, + 178 + ], + "type": "text", + "content": ". This general-purpose framework allows the use of any neural sequence model – LSTM [28], GRU [13], Transformers [75], etc. We choose to instantiate the forecasting module for " + }, + { + "bbox": [ + 304, + 72, + 545, + 178 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 72, + 545, + 178 + ], + "type": "text", + "content": " using a pretrained transformer-based LM. Next we present the details of the encoders for the two modalities and the LM based sequence model." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 180, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 180, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 305, + 180, + 545, + 216 + ], + "type": "text", + "content": "Action encoder " + }, + { + "bbox": [ + 305, + 180, + 545, + 216 + ], + "type": "inline_equation", + "content": "(f_{\\mathrm{act}})" + }, + { + "bbox": [ + 305, + 180, + 545, + 216 + ], + "type": "text", + "content": " Each action " + }, + { + "bbox": [ + 305, + 180, + 545, + 216 + ], + "type": "inline_equation", + "content": "a_i" + }, + { + "bbox": [ + 305, + 180, + 545, + 216 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 305, + 180, + 545, + 216 + ], + "type": "inline_equation", + "content": "A_k" + }, + { + "bbox": [ + 305, + 180, + 545, + 216 + ], + "type": "text", + "content": " is encoded by " + }, + { + "bbox": [ + 305, + 180, + 545, + 216 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{act}}" + }, + { + "bbox": [ + 305, + 180, + 545, + 216 + ], + "type": "text", + "content": " and the output is denoted by " + }, + { + "bbox": [ + 305, + 180, + 545, + 216 + ], + "type": "inline_equation", + "content": "\\alpha_i" + }, + { + "bbox": [ + 305, + 180, + 545, + 216 + ], + "type": "text", + "content": ". Concretely, token embeddings are expressed as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 330, + 223, + 545, + 253 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 223, + 545, + 253 + ], + "spans": [ + { + "bbox": [ + 330, + 223, + 545, + 253 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\left(\\alpha_ {1}, \\dots , \\alpha_ {k}\\right) = \\left(f _ {\\text {a c t}} \\left(a _ {1}\\right), \\dots , f _ {\\text {a c t}} \\left(a _ {k}\\right)\\right), \\text {w h e r e} \\\\ \\alpha_ {i} = \\left(\\alpha_ {i} ^ {1}, \\dots , \\alpha_ {i} ^ {r _ {i}}\\right) \\in \\mathbb {R} ^ {r _ {i} \\times d} \\tag {8} \\\\ \\end{array}", + "image_path": "aa34d15977052d2b1d60302af60fe5aaa1abbdf111a71a0028234c8626cda6bb.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 259, + 545, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 259, + 545, + 331 + ], + "spans": [ + { + "bbox": [ + 304, + 259, + 545, + 331 + ], + "type": "text", + "content": "As we illustrate in Fig. 3 (left), each action " + }, + { + "bbox": [ + 304, + 259, + 545, + 331 + ], + "type": "inline_equation", + "content": "a_i" + }, + { + "bbox": [ + 304, + 259, + 545, + 331 + ], + "type": "text", + "content": " is tokenized into " + }, + { + "bbox": [ + 304, + 259, + 545, + 331 + ], + "type": "inline_equation", + "content": "r_i" + }, + { + "bbox": [ + 304, + 259, + 545, + 331 + ], + "type": "text", + "content": " tokens using appropriate tokenizer for the LM, the tokens are indexed using the vocabulary of the LM, and are represented using an embedding lookup from the token embeddings of the LM to produce " + }, + { + "bbox": [ + 304, + 259, + 545, + 331 + ], + "type": "inline_equation", + "content": "\\alpha_i" + }, + { + "bbox": [ + 304, + 259, + 545, + 331 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 304, + 259, + 545, + 331 + ], + "type": "inline_equation", + "content": "r_i" + }, + { + "bbox": [ + 304, + 259, + 545, + 331 + ], + "type": "text", + "content": " is the number of tokens and " + }, + { + "bbox": [ + 304, + 259, + 545, + 331 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 259, + 545, + 331 + ], + "type": "text", + "content": " is the dimensionality of token embeddings." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "content": "Observation encoder " + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "inline_equation", + "content": "(f_{\\mathrm{obs}})" + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "content": ". Visual cues play an integral role in knowing what actions lie ahead, towards achieving the goal prompt " + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "content": ". To this end, the visual observations " + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "inline_equation", + "content": "O_k" + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "content": " are encoded and play a critical role in the planner. Recall, the visual observation history " + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "inline_equation", + "content": "O_k" + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "content": " comprises of " + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "inline_equation", + "content": "o_i" + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "content": " corresponding to action " + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "inline_equation", + "content": "a_i" + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "content": ", each of " + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "content": " frames. As illustrated in Fig. 3 (middle), we transform each " + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "inline_equation", + "content": "o_i" + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "content": " employing the widely-adopted S3D backbone [84] " + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{S3D^*}}" + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "content": " (* denotes backbone is frozen). We must project visual encodings to a shared latent space of action (language) embeddings described before " + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "inline_equation", + "content": "(\\alpha_i)" + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "content": ". To this end, we map S3D features via a trainable transformer mapper " + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{map}}" + }, + { + "bbox": [ + 304, + 331, + 545, + 475 + ], + "type": "text", + "content": ". Concretely," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 316, + 482, + 545, + 513 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 482, + 545, + 513 + ], + "spans": [ + { + "bbox": [ + 316, + 482, + 545, + 513 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\left(\\beta_ {1}, \\dots , \\beta_ {k}\\right) = \\left(f _ {\\mathrm {o b s}} \\left(o _ {1}\\right), \\dots , f _ {\\mathrm {o b s}} \\left(o _ {k}\\right)\\right), \\text {w h e r e} \\\\ \\beta_ {i} = \\left(\\beta_ {i} ^ {1}, \\dots , \\beta_ {i} ^ {\\delta}\\right) \\in \\mathbb {R} ^ {\\delta \\times d} \\text {a n d} f _ {\\mathrm {o b s}} = f _ {\\mathrm {S 3 D} ^ {*}} \\circ f _ {\\mathrm {m a p}} \\tag {9} \\\\ \\end{array}", + "image_path": "cc04da78697b039796f0b36ecedde165b5d15d2671ae3c31ed861e7f3a281a74.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 518, + 545, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 518, + 545, + 543 + ], + "spans": [ + { + "bbox": [ + 305, + 518, + 545, + 543 + ], + "type": "text", + "content": "Overall, as we show in Fig. 3 (right), the resultant encoded sequence of representation for " + }, + { + "bbox": [ + 305, + 518, + 545, + 543 + ], + "type": "inline_equation", + "content": "S_{k}" + }, + { + "bbox": [ + 305, + 518, + 545, + 543 + ], + "type": "text", + "content": " is thus" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 345, + 550, + 506, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 550, + 506, + 563 + ], + "spans": [ + { + "bbox": [ + 345, + 550, + 506, + 563 + ], + "type": "interline_equation", + "content": "f _ {\\text {e n c}} (S _ {k}) = \\left(\\beta_ {1}, \\alpha_ {1}, \\dots , \\beta_ {k}, \\alpha_ {k}\\right) = H _ {k},", + "image_path": "1af58d84332de351901377feacf3d670137829105a7b01539172b8f175a145ac.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Sequence model " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "(f_{\\mathrm{seq}})" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": ". Given the above encoding for the segment history " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "S_{k}" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": ", the role of the sequence model is to predict a representation of the next token, that would in return enable VLaMP plan generation capabilities for VPA. Importantly, in the process of generating sequence of future actions autoregressively, we would also need to generate the representations of 'future observations'. Therefore, as we shown in Fig. 3, our sequence model, which consists of the transformer layers of a PTLM, also produces representations for vision (in addition to the necessary action tokens). Before proceeding further, we pause and introduce additional notation for the sequence model, which" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15306" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 97, + 70, + 294, + 182 + ], + "blocks": [ + { + "bbox": [ + 97, + 70, + 294, + 182 + ], + "lines": [ + { + "bbox": [ + 97, + 70, + 294, + 182 + ], + "spans": [ + { + "bbox": [ + 97, + 70, + 294, + 182 + ], + "type": "image", + "image_path": "7b9f0c8b9772067c8dede95c30a238593029dd56f40d5f96be0718231733c1c2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 195, + 547, + 257 + ], + "lines": [ + { + "bbox": [ + 45, + 195, + 547, + 257 + ], + "spans": [ + { + "bbox": [ + 45, + 195, + 547, + 257 + ], + "type": "text", + "content": "Figure 3: VLaMP - Forecasting Module. As shown in left and middle, actions and observations obtained from the segmentation module are encoded using appropriate modality encoders. The observation encoder leverages pretrained video encoder for observations, while also learning a mapper that aligns the representations from observations with actions. As shown on the right, VLaMP uses a joint sequence model on top of interleaved action (blue) and observation (gray) representations to forecast autoregressively the next representation." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 301, + 70, + 518, + 182 + ], + "blocks": [ + { + "bbox": [ + 301, + 70, + 518, + 182 + ], + "lines": [ + { + "bbox": [ + 301, + 70, + 518, + 182 + ], + "spans": [ + { + "bbox": [ + 301, + 70, + 518, + 182 + ], + "type": "image", + "image_path": "0ada3fca083539da731052742542fd4ea73f4bbc817e7d19b6f807cdaddccf2d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 78, + 273, + 263, + 337 + ], + "blocks": [ + { + "bbox": [ + 78, + 273, + 263, + 337 + ], + "lines": [ + { + "bbox": [ + 78, + 273, + 263, + 337 + ], + "spans": [ + { + "bbox": [ + 78, + 273, + 263, + 337 + ], + "type": "image", + "image_path": "d581d41982481ea46b81e5bcf8d3975617081858294f2818bc57ff561951c912.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 348, + 288, + 397 + ], + "lines": [ + { + "bbox": [ + 46, + 348, + 288, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 288, + 397 + ], + "type": "text", + "content": "Figure 4: Tokenized Sequence with Masks. The encoded sequence of representations for " + }, + { + "bbox": [ + 46, + 348, + 288, + 397 + ], + "type": "inline_equation", + "content": "k = 2" + }, + { + "bbox": [ + 46, + 348, + 288, + 397 + ], + "type": "text", + "content": " segments, denoted alternatively using modality agnostic notation of " + }, + { + "bbox": [ + 46, + 348, + 288, + 397 + ], + "type": "inline_equation", + "content": "H_{2}" + }, + { + "bbox": [ + 46, + 348, + 288, + 397 + ], + "type": "text", + "content": " and mask " + }, + { + "bbox": [ + 46, + 348, + 288, + 397 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 348, + 288, + 397 + ], + "type": "text", + "content": " for next token prediction training." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "text", + "content": "will make the subsequent explanation for training and inference easier to follow. As shown in Figure 4, we alternatively denote the sequence of representations " + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "inline_equation", + "content": "(\\beta_{1},\\alpha_{1},\\ldots ,\\beta_{k},\\alpha_{k})" + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "inline_equation", + "content": "H_{k} = (h_{1},\\dots,h_{n})" + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "inline_equation", + "content": "n = k\\delta +\\sum_{i = 1}^{k}r_{i}" + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "text", + "content": ". A binary mask " + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "inline_equation", + "content": "M = (m_{1},\\dots,m_{n})" + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "inline_equation", + "content": "m_{i}" + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "text", + "content": " is 1 if the corresponding representation is for an action and 0 otherwise, can help obtain necessary action or visual observations. With this notation, given first " + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "text", + "content": " representations denoted as " + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "inline_equation", + "content": "h_{1:j}" + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "text", + "content": ", one step of the sequence model produces the representation for " + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "inline_equation", + "content": "j + 1" + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{seq}}(h_{1:j}) = \\hat{h}_{j + 1}" + }, + { + "bbox": [ + 46, + 418, + 287, + 541 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 547, + 111, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 547, + 111, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 547, + 111, + 559 + ], + "type": "text", + "content": "4.4. Training" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 565, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 565, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 565, + 287, + 685 + ], + "type": "text", + "content": "The joint training of the segmentation and forecasting modules following Eq. (6) is intractable. But, by exploiting the availability of unpaired training data, we approximate Eq. (6) by feeding in the output of the segmentation module to the forecasting module and training them separately, each on their respective labeled data. The video-action segmentation model is trained utilizing the VideoCLIP setup [85], where in the segmentation model performs classification to predict the action for each second of the video. The forecasting model is trained by adopting the" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 276, + 545, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 276, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 306, + 276, + 545, + 397 + ], + "type": "text", + "content": "next representation prediction objective. Unlike vanilla LM pretraining, however, we also need to train for predicting visual representations in addition to text (action). Therefore, we use two different losses " + }, + { + "bbox": [ + 306, + 276, + 545, + 397 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{act}}" + }, + { + "bbox": [ + 306, + 276, + 545, + 397 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 276, + 545, + 397 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{obs}}" + }, + { + "bbox": [ + 306, + 276, + 545, + 397 + ], + "type": "text", + "content": " for text and visual representations respectively. Specifically, " + }, + { + "bbox": [ + 306, + 276, + 545, + 397 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{act}}" + }, + { + "bbox": [ + 306, + 276, + 545, + 397 + ], + "type": "text", + "content": " is the conventional cross-entropy loss over the LM's vocabulary " + }, + { + "bbox": [ + 306, + 276, + 545, + 397 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{LM}}" + }, + { + "bbox": [ + 306, + 276, + 545, + 397 + ], + "type": "text", + "content": " for the action representations while " + }, + { + "bbox": [ + 306, + 276, + 545, + 397 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{obs}}" + }, + { + "bbox": [ + 306, + 276, + 545, + 397 + ], + "type": "text", + "content": " is the mean-squared error between the predicted and the ground truth observation representations. The total loss is the sum of both the loss terms as shown in Eq. (11)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 318, + 411, + 529, + 444 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 411, + 529, + 444 + ], + "spans": [ + { + "bbox": [ + 318, + 411, + 529, + 444 + ], + "type": "interline_equation", + "content": "L = - \\sum_ {j = 1} ^ {n} m _ {j} L _ {\\mathrm {a c t}} (\\hat {h} _ {j}) + (1 - m _ {j}) L _ {\\mathrm {o b s}} (\\hat {h} _ {j}), \\text {w h e r e}", + "image_path": "7fcaabc05cb8e41ee1a8a8e7ed66557c1e736d5e4ff5e72adf07d8ce2c41ab1b.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 347, + 446, + 545, + 482 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 446, + 545, + 482 + ], + "spans": [ + { + "bbox": [ + 347, + 446, + 545, + 482 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {a c t}} = h _ {j} \\cdot \\hat {h} _ {j} - \\log \\sum_ {p = 1} ^ {| V _ {\\mathrm {L M}} |} \\exp \\left(h _ {p} \\cdot \\hat {h} _ {j}\\right); \\tag {10}", + "image_path": "e878e68e0b9444dcfcb1afdc37b1a4382f4ce29e3f2ee5379bbde38d725872e2.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 346, + 484, + 545, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 484, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 346, + 484, + 545, + 510 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {o b s}} = \\frac {\\| h _ {j} - \\hat {h} _ {j} \\| _ {2} ^ {2}}{d} \\tag {11}", + "image_path": "cc1fc44ce464ff13e40816afe1d21914976fba8b76609069077abc4a6e53cf00.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 514, + 545, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 545, + 562 + ], + "type": "text", + "content": "In order to have a stable training, we use ground truth action history to construct " + }, + { + "bbox": [ + 306, + 514, + 545, + 562 + ], + "type": "inline_equation", + "content": "S_{k}" + }, + { + "bbox": [ + 306, + 514, + 545, + 562 + ], + "type": "text", + "content": " (and subsequently " + }, + { + "bbox": [ + 306, + 514, + 545, + 562 + ], + "type": "inline_equation", + "content": "H_{k}" + }, + { + "bbox": [ + 306, + 514, + 545, + 562 + ], + "type": "text", + "content": ") instead of the output of the segmentation module. Appendix B provides further details on loss and optimizers for training." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 563, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 545, + 635 + ], + "type": "text", + "content": "Inference. We next detail the inference procedure for VLaMP. Recall that we use " + }, + { + "bbox": [ + 306, + 563, + 545, + 635 + ], + "type": "inline_equation", + "content": "1:n" + }, + { + "bbox": [ + 306, + 563, + 545, + 635 + ], + "type": "text", + "content": " to denote a sequence of " + }, + { + "bbox": [ + 306, + 563, + 545, + 635 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 306, + 563, + 545, + 635 + ], + "type": "text", + "content": " representations (i.e, " + }, + { + "bbox": [ + 306, + 563, + 545, + 635 + ], + "type": "inline_equation", + "content": "h_{1:n} = (h_1,\\ldots ,h_n)" + }, + { + "bbox": [ + 306, + 563, + 545, + 635 + ], + "type": "text", + "content": "). Additionally, we denote the concatenation operator over two representation sequences by \"" + }, + { + "bbox": [ + 306, + 563, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\diamond" + }, + { + "bbox": [ + 306, + 563, + 545, + 635 + ], + "type": "text", + "content": "\". With this notation at hand, we define the score of an action " + }, + { + "bbox": [ + 306, + 563, + 545, + 635 + ], + "type": "inline_equation", + "content": "a\\in \\mathcal{A}" + }, + { + "bbox": [ + 306, + 563, + 545, + 635 + ], + "type": "text", + "content": " for following history " + }, + { + "bbox": [ + 306, + 563, + 545, + 635 + ], + "type": "inline_equation", + "content": "h_{1:n}" + }, + { + "bbox": [ + 306, + 563, + 545, + 635 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 325, + 650, + 545, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 650, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 325, + 650, + 545, + 682 + ], + "type": "interline_equation", + "content": "\\phi \\left(h _ {1: n} \\diamond f _ {\\mathrm {a c t}} (a)\\right) = \\sum_ {j = 1} ^ {r _ {a}} a ^ {j} \\cdot f _ {\\mathrm {s e q}} \\left(h _ {1: n} \\diamond a ^ {1: j}\\right), \\tag {12}", + "image_path": "95940264226463ab895e657631ebabe3192d881d9bc4059a9e76ec4ef50fd13f.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\cdot" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " is the vector dot product, and " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{act}}(a) = \\alpha^{1:r_a} = (\\alpha^1,\\ldots ,\\alpha^{r_a})" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " is the sequence of encoded representations" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "text", + "content": "3Despite tuning attempts, we found joint optimization to be intractable and inefficient on resources." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15307" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "for action " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": ". In other words, this score is the sum of unnormalized log-probability under the sequence model using the standard softmax distribution. We use this scoring function with to perform beam search (detailed inference algorithm: Algo. 1 in App. B)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 145, + 128, + 159 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 145, + 128, + 159 + ], + "spans": [ + { + "bbox": [ + 47, + 145, + 128, + 159 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 166, + 288, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 166, + 288, + 261 + ], + "spans": [ + { + "bbox": [ + 46, + 166, + 288, + 261 + ], + "type": "text", + "content": "We instantiate VLaMP's segmentation module utilizing VideoCLIP [85] that has been fine-tuned on COIN and CrossTask. Similarly, we instantiate VLaMP's sequence model " + }, + { + "bbox": [ + 46, + 166, + 288, + 261 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{seq}}" + }, + { + "bbox": [ + 46, + 166, + 288, + 261 + ], + "type": "text", + "content": " (in the forecasting module) by GPT2 [60]. We utilize the open-sourced model weights of GPT2 (from HuggingFace [83]). For inference, we use Algo. 1 presented in Appendix B, with beam size " + }, + { + "bbox": [ + 46, + 166, + 288, + 261 + ], + "type": "inline_equation", + "content": "B = 10" + }, + { + "bbox": [ + 46, + 166, + 288, + 261 + ], + "type": "text", + "content": " for CrossTask and a " + }, + { + "bbox": [ + 46, + 166, + 288, + 261 + ], + "type": "inline_equation", + "content": "B = 3" + }, + { + "bbox": [ + 46, + 166, + 288, + 261 + ], + "type": "text", + "content": " for COIN." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 271, + 160, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 271, + 160, + 283 + ], + "spans": [ + { + "bbox": [ + 47, + 271, + 160, + 283 + ], + "type": "text", + "content": "5.1. Data and Baselines" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": "Data. For a video " + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": " with goal " + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": ", both CrossTask [89] and COIN [73] provide annotations of the form " + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\{a_k, (t_k, t'_k)\\}_{k=1}^K" + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "inline_equation", + "content": "a_k" + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": " are the actions in the video, and " + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "inline_equation", + "content": "t_k" + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": " (resp. " + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "inline_equation", + "content": "t'_k" + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": ") are the start (resp. end) timestamps for " + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "inline_equation", + "content": "a_k" + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": ". Given an annotated video consisting of " + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": " steps, we generate " + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "inline_equation", + "content": "K - l" + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": " examples, each with input " + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "inline_equation", + "content": "x_k = (G, V_{t_k})" + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": " and output " + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "inline_equation", + "content": "y_k = (a_{k+1}, \\ldots, a_{k+l})" + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": ", for " + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "inline_equation", + "content": "k = 1, \\ldots, K - l" + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": " (leaving at least " + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": " steps to predict in each example). Therefore from " + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": " videos, we generated " + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "inline_equation", + "content": "N = \\sum_{m=1}^{M} (K_m - l)" + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": " examples, where " + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "inline_equation", + "content": "K_m" + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": " is the number of steps in the " + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": "-th video, forming a dataset " + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{x^{(j)}, y^{(j)}\\}_{j=1}^N" + }, + { + "bbox": [ + 46, + 290, + 287, + 434 + ], + "type": "text", + "content": " suitable for VPA (total number of samples in shown in Table 2)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 435, + 287, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 287, + 627 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 287, + 627 + ], + "type": "text", + "content": "Baselines. As a first step towards benchmarking, we utilize two heuristic baselines - a random baseline and most probable action baseline. Additionally, we also adopt a variety of strong goal-conditioned models. The procedure planning task is most relevant task from the literature to VPA, therefore, we adapt (details in App. A.1) the widely used DDN model introduced by Chang et al. [9], which is an established model in many procedural planning benchmarks in prior works [6, 87, 70]. Building bridges to the research community working on Ego4D's Long Term action Anticipation benchmark (LTA) [25], we also evaluate their best performing baseline. Finally, we include a prompt-based GPT-3 planner. Zooming out, these baselines span several paradigms: prompt-based, and random baselines are learning-free, the most-probable and random baselines are non-neural, while DDN and LTA baselines are learned and" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 95 + ], + "type": "text", + "content": "neural. Succinct descriptions of baselines are included next (details are deferred to Appendix A):" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 97, + 545, + 479 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 306, + 97, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 97, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 306, + 97, + 545, + 120 + ], + "type": "text", + "content": "- Random: Predicts the plan by picking all " + }, + { + "bbox": [ + 306, + 97, + 545, + 120 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 306, + 97, + 545, + 120 + ], + "type": "text", + "content": " actions uniformly randomly from the set of all actions " + }, + { + "bbox": [ + 306, + 97, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 306, + 97, + 545, + 120 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 121, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 121, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 306, + 121, + 545, + 168 + ], + "type": "text", + "content": "- Random " + }, + { + "bbox": [ + 306, + 121, + 545, + 168 + ], + "type": "inline_equation", + "content": "w/" + }, + { + "bbox": [ + 306, + 121, + 545, + 168 + ], + "type": "text", + "content": " goal: A stronger baseline; for each goal " + }, + { + "bbox": [ + 306, + 121, + 545, + 168 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 306, + 121, + 545, + 168 + ], + "type": "text", + "content": ", we allow privilege access to a set of applicable actions to that goal " + }, + { + "bbox": [ + 306, + 121, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_G \\subseteq \\mathcal{A}" + }, + { + "bbox": [ + 306, + 121, + 545, + 168 + ], + "type": "text", + "content": ", and predicts the plan by randomly picking actions from the restricted set." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 169, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 169, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 306, + 169, + 545, + 216 + ], + "type": "text", + "content": "- Most probable action: Given the previous action " + }, + { + "bbox": [ + 306, + 169, + 545, + 216 + ], + "type": "inline_equation", + "content": "a_j" + }, + { + "bbox": [ + 306, + 169, + 545, + 216 + ], + "type": "text", + "content": ", picks the most probable next action " + }, + { + "bbox": [ + 306, + 169, + 545, + 216 + ], + "type": "inline_equation", + "content": "a_j" + }, + { + "bbox": [ + 306, + 169, + 545, + 216 + ], + "type": "text", + "content": " according conditional probability " + }, + { + "bbox": [ + 306, + 169, + 545, + 216 + ], + "type": "inline_equation", + "content": "Pr(a_i | a_j)" + }, + { + "bbox": [ + 306, + 169, + 545, + 216 + ], + "type": "text", + "content": " obtained using frequency count from the training." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 217, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 217, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 217, + 545, + 312 + ], + "type": "text", + "content": "- Most probable action " + }, + { + "bbox": [ + 306, + 217, + 545, + 312 + ], + "type": "inline_equation", + "content": "w/" + }, + { + "bbox": [ + 306, + 217, + 545, + 312 + ], + "type": "text", + "content": " goal: Akin to random " + }, + { + "bbox": [ + 306, + 217, + 545, + 312 + ], + "type": "inline_equation", + "content": "w/" + }, + { + "bbox": [ + 306, + 217, + 545, + 312 + ], + "type": "text", + "content": " goal baseline, we also evaluate a goal-conditioned most probable action baseline, that uses a goal-specific set of actions " + }, + { + "bbox": [ + 306, + 217, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_G \\subset \\mathcal{A}" + }, + { + "bbox": [ + 306, + 217, + 545, + 312 + ], + "type": "text", + "content": " during sampling. Since the most probable baselines, provide a probability distribution over the actions, we also employ beam search (for fairness, with the same beam size same as VLaMP), and pick the highest scoring plan." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 312, + 545, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 312, + 545, + 370 + ], + "spans": [ + { + "bbox": [ + 306, + 312, + 545, + 370 + ], + "type": "text", + "content": "- Dual Dynamics Network (DDN) [9]: Accounting for the difference in task definition, i.e. lack of visual goal, a direct application of DDN inference algorithm was not possible. So we keep DDN's network structure but use Algo.1 for inference on VPA." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 372, + 545, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 372, + 545, + 431 + ], + "spans": [ + { + "bbox": [ + 306, + 372, + 545, + 431 + ], + "type": "text", + "content": "- Ego4D Long Term Action Anticipation (LTA) [25]: The best performing baseline for LTA uses a SlowFast visual encoder followed by a transformer aggregator. We adapt this baseline using the S3D encoder for a fair apples-to-apples comparison with VLaMP." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 432, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 432, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 432, + 545, + 479 + ], + "type": "text", + "content": "- Prompt-based GPT-3 Planner: Huang et al. [30] utilize a LLM as zero-shot planners, we also experiment with prompting a frozen pretrained large language model i.e. GPT-3 for VPA (additional details in App. A.2)." + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 501, + 424, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 501, + 424, + 514 + ], + "spans": [ + { + "bbox": [ + 306, + 501, + 424, + 514 + ], + "type": "text", + "content": "5.2. Quantitative Results" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 521, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 521, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 305, + 521, + 545, + 555 + ], + "type": "text", + "content": "In the following, we include quantitative findings of benchmarking methods on two video data sources (Tab. 3) and head-on ablations (Tab. 4)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 557, + 545, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 557, + 545, + 663 + ], + "spans": [ + { + "bbox": [ + 305, + 557, + 545, + 663 + ], + "type": "text", + "content": "Improved performance across video datasets. As we show in Tab. 3, VLaMP significantly outperforms the baselines for both CrossTask and COIN. DDN that is customized for procedural tasks performs significantly better than heuristic baselines leading to a mAcc boost from " + }, + { + "bbox": [ + 305, + 557, + 545, + 663 + ], + "type": "inline_equation", + "content": "12.7 \\rightarrow 24.1\\%" + }, + { + "bbox": [ + 305, + 557, + 545, + 663 + ], + "type": "text", + "content": " (row 2 and 5, " + }, + { + "bbox": [ + 305, + 557, + 545, + 663 + ], + "type": "inline_equation", + "content": "l = 4" + }, + { + "bbox": [ + 305, + 557, + 545, + 663 + ], + "type": "text", + "content": ", Tab. 3). With our novel decomposition and pretraining objective, VLaMP outperforms DDN with a further bump up from " + }, + { + "bbox": [ + 305, + 557, + 545, + 663 + ], + "type": "inline_equation", + "content": "24.1 \\rightarrow 31.7\\%" + }, + { + "bbox": [ + 305, + 557, + 545, + 663 + ], + "type": "text", + "content": " (row 5 and 7)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "type": "text", + "content": "Steady gains in short & long horizon predictions. As length of prediction " + }, + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "type": "text", + "content": " increases (" + }, + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "type": "inline_equation", + "content": "l = 1" + }, + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "type": "inline_equation", + "content": "l = 4" + }, + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "type": "text", + "content": "), the performance naturally decreases, across all baselines and tasks. With this in mind and zooming in on COIN re" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 635, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 635, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 635, + 287, + 713 + ], + "type": "text", + "content": "4Despite the presence of prepositions, majority of actions in COIN and CrossTask can be described using a verb-noun pair. While similar verbs exist, they are never paired with the same nouns. Therefore, there are no repeated actions. Example: while verb 'lift' w/ noun 'barbell' and verb 'pickup' w/ 'button' exists in the action library, the complements ('lift button' & 'pick up barbell') do not. 5Since we evaluate for three and four next steps on our datasets, we use the maximum required length and set " + }, + { + "bbox": [ + 46, + 635, + 287, + 713 + ], + "type": "inline_equation", + "content": "l = 4" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15308" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 70, + 288, + 256 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 256 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 256 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 256 + ], + "type": "table", + "html": "
Methodl = 1l = 3l = 4
{n/m}AccSRmAccmIOUSRmAccmIOU
CrossTask Video Dataset [89]
Random0.90.00.91.50.00.91.9
Random w/ goal13.20.313.423.60.012.727.8
Most probable10.41.76.19.91.35.513.9
Most probable w/ goal12.42.48.915.51.57.920.5
DDN [9]33.46.825.835.23.624.137.0
LTA [25]26.92.424.035.21.221.736.8
VLaMP (ours)50.610.335.344.04.431.743.4
COIN Video Dataset [73]
Random0.10.00.10.20.00.10.2
Random w/ goal24.51.721.442.70.320.147.7
Most probable0.71.64.36.81.68.215.3
Most probable w/ goal23.910.918.024.99.116.332.2
DDN [9]29.310.122.332.27.021.037.3
GPT-3 prompt-based [30]19.31.711.119.50.010.521.0
VLaMP (ours)45.218.339.256.69.035.254.2
", + "image_path": "f68017a0e5cc3d90ab22822918d0f508a7b23091b7fc7f6612b9ca098442e61c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 363, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 287, + 422 + ], + "type": "text", + "content": "sults, we observe large gains of VLaMP over DDN (next best method). Particularly, a relative improvement of " + }, + { + "bbox": [ + 46, + 363, + 287, + 422 + ], + "type": "inline_equation", + "content": "54\\%" + }, + { + "bbox": [ + 46, + 363, + 287, + 422 + ], + "type": "inline_equation", + "content": "(29.3 \\rightarrow 45.2)" + }, + { + "bbox": [ + 46, + 363, + 287, + 422 + ], + "type": "text", + "content": " in mAcc for " + }, + { + "bbox": [ + 46, + 363, + 287, + 422 + ], + "type": "inline_equation", + "content": "l = 1" + }, + { + "bbox": [ + 46, + 363, + 287, + 422 + ], + "type": "text", + "content": " (row 7 and 8, Tab. 3) and " + }, + { + "bbox": [ + 46, + 363, + 287, + 422 + ], + "type": "inline_equation", + "content": "68\\%" + }, + { + "bbox": [ + 46, + 363, + 287, + 422 + ], + "type": "inline_equation", + "content": "(21.0 \\rightarrow 35.2)" + }, + { + "bbox": [ + 46, + 363, + 287, + 422 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 363, + 287, + 422 + ], + "type": "inline_equation", + "content": "l = 4" + }, + { + "bbox": [ + 46, + 363, + 287, + 422 + ], + "type": "text", + "content": " is demonstrated by VLaMP over DDN." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "type": "text", + "content": "Goal-conditioning is crucial. A key difference between the task formulations of LTA and VPA is goal conditioning (see Sec. 2). Comparing rows for LTA model and VLaMP-there is almost " + }, + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "type": "inline_equation", + "content": "2\\mathrm{x}" + }, + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "type": "text", + "content": " gap " + }, + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "type": "inline_equation", + "content": "(27\\%" + }, + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "type": "text", + "content": " vs. " + }, + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "type": "inline_equation", + "content": "51\\%" + }, + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "type": "inline_equation", + "content": "l = 1" + }, + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "type": "text", + "content": " Tab.3). This underscores the importance of goal-conditioning. To second this inference, in Tab. 4 (rows 1 and 2), we precisely ablate the effect of providing the goal as a textual description for the basic (last-observation-only) model. The only difference is goal prompt " + }, + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "type": "text", + "content": " , which increases mAcc performance from " + }, + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "type": "inline_equation", + "content": "44.5\\rightarrow 53.1\\%" + }, + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "type": "inline_equation", + "content": "l = 1" + }, + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "type": "inline_equation", + "content": "28.3\\to 34.7\\%" + }, + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 424, + 288, + 544 + ], + "type": "inline_equation", + "content": "l = 3" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 544, + 288, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 288, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 288, + 688 + ], + "type": "text", + "content": "Goal-conditioned random and most probable baseline come close to DDN on easy metrics. For fair comparisons, we include heuristic baselines. We observe the performance of random " + }, + { + "bbox": [ + 46, + 544, + 288, + 688 + ], + "type": "inline_equation", + "content": "w/" + }, + { + "bbox": [ + 46, + 544, + 288, + 688 + ], + "type": "text", + "content": " goal and most probable " + }, + { + "bbox": [ + 46, + 544, + 288, + 688 + ], + "type": "inline_equation", + "content": "w/" + }, + { + "bbox": [ + 46, + 544, + 288, + 688 + ], + "type": "text", + "content": " goal comes close to DDN, when evaluated using lenient metrics like mAcc and mIOU (see COIN results in Tab. 3). Note, that these two baselines enjoy the privileged access to (a much smaller) 'relevant actions set' for a given goal. On an average, the relevant or feasible action set is smaller for COIN than CrossTask videos. This apriori access to feasible actions makes random " + }, + { + "bbox": [ + 46, + 544, + 288, + 688 + ], + "type": "inline_equation", + "content": "w/" + }, + { + "bbox": [ + 46, + 544, + 288, + 688 + ], + "type": "text", + "content": " goal and most probable " + }, + { + "bbox": [ + 46, + 544, + 288, + 688 + ], + "type": "inline_equation", + "content": "w/" + }, + { + "bbox": [ + 46, + 544, + 288, + 688 + ], + "type": "text", + "content": " goal competitive (albeit, slightly unfair) baselines." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "content": "Prompt-based LLM planner is not competitive. We evaluate the prompt-based GPT-3 planner on COIN and find" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 305, + 70, + 547, + 167 + ], + "blocks": [ + { + "bbox": [ + 46, + 264, + 287, + 348 + ], + "lines": [ + { + "bbox": [ + 46, + 264, + 287, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 287, + 348 + ], + "type": "text", + "content": "Table 3: Performance on different datasets and horizons. The mean of various metrics (Sec. 3.1) obtained using 5 runs with different random seeds (std. errors are provide in Appendix E). Note that the action and observation history are the output of the separately finetuned video-action segmentation model and hence are noisy compared to the ground truth history." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 305, + 70, + 547, + 167 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 547, + 167 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 547, + 167 + ], + "type": "table", + "html": "
GAkOkl = 3l = 1
SRmAccmIOUnAcc
1XXok6.8 ± 0.328.3 ± 1.934.8 ± 2.044.5 ± 3.8
2✓Xok8.9 ± 0.234.7 ± 0.741.6 ± 0.853.1 ± 2.0
3✓✓X14.9 ± 0.337.8 ± 0.450.8 ± 0.648.0 ± 0.2
4✓✓Ok15.2 ± 0.343.5 ± 0.851.4 ± 0.964.8 ± 0.9
R✓✓Ok10.7 ± 0.236.5 ± 0.741.7 ± 0.661.4 ± 1.8
", + "image_path": "9107097bec053a1958d0e6c97593d08a526dab6b13d847a1ac086611e0272555.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 175, + 547, + 283 + ], + "lines": [ + { + "bbox": [ + 304, + 175, + 547, + 283 + ], + "spans": [ + { + "bbox": [ + 304, + 175, + 547, + 283 + ], + "type": "text", + "content": "Table 4: Role of different inputs and LM pre-training in VLaMP. " + }, + { + "bbox": [ + 304, + 175, + 547, + 283 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 175, + 547, + 283 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 175, + 547, + 283 + ], + "type": "inline_equation", + "content": "A_{k}" + }, + { + "bbox": [ + 304, + 175, + 547, + 283 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 175, + 547, + 283 + ], + "type": "inline_equation", + "content": "O_{k}" + }, + { + "bbox": [ + 304, + 175, + 547, + 283 + ], + "type": "text", + "content": " denote the three inputs to VLaMP: goal, action history and observation history, respectively. Shorthand of " + }, + { + "bbox": [ + 304, + 175, + 547, + 283 + ], + "type": "inline_equation", + "content": "o_{k}" + }, + { + "bbox": [ + 304, + 175, + 547, + 283 + ], + "type": "text", + "content": " means only the most recent observation of the full history (" + }, + { + "bbox": [ + 304, + 175, + 547, + 283 + ], + "type": "inline_equation", + "content": "O_{k}" + }, + { + "bbox": [ + 304, + 175, + 547, + 283 + ], + "type": "text", + "content": ") is used. Mean " + }, + { + "bbox": [ + 304, + 175, + 547, + 283 + ], + "type": "inline_equation", + "content": "\\pm" + }, + { + "bbox": [ + 304, + 175, + 547, + 283 + ], + "type": "text", + "content": " std. error over 5 random seeds on CrossTask are reported. The row R corresponds to the forecasting module of VLaMP trained with random initialization (same model architecture) as opposed to initialization using the weights of a pre-trained LM." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 304, + 545, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 545, + 342 + ], + "type": "text", + "content": "that the prompt based model performs significantly worse than VLaMP. This highlights that VPA is not easy to solve using just a PTLM and prompting." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 348, + 468, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 348, + 468, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 348, + 468, + 361 + ], + "type": "text", + "content": "5.3. Ablations and Error Analysis" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "content": "We undertake head-on ablations to quantify effect of each component of VLaMP - action history, the visual history, and language pre-training of the LM. To remove confounding factors, in Tab. 4 we use the ground truth output for the segmentation module. Following this, we include detailed error analysis." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "text", + "content": "Action and observation history improve complementary planning metrics. As seen in all the rows with action history Tab. 4 (i.e. " + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "inline_equation", + "content": "A_{k}" + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "text", + "content": "), the provision of action history increases difficult metrics such as SR. In comparing rows 2 and 3, we see that SR increases relatively by " + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "inline_equation", + "content": "67\\%" + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "inline_equation", + "content": "8.9 \\rightarrow 14.9" + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "text", + "content": "), simply by using action history even without access to any past observation. However, the lack of observation history affects nAcc, which drops relatively by " + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "inline_equation", + "content": "53.1 \\rightarrow 48.0" + }, + { + "bbox": [ + 304, + 438, + 545, + 582 + ], + "type": "text", + "content": ") when observation history is swapped by action history between rows 2 and 3. This implies that observation history is important to predict the person's state in the task and what they might do next." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "type": "text", + "content": "Priors from the pre-trained LM improve performance. In Tab. 4 row " + }, + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "type": "text", + "content": ", we report the performance of VLaMP when its forecasting module is trained with random weight initialization, i.e., the transformer of the same architecture trained from scratch instead of LM pre-training. We find the performance in row " + }, + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "type": "text", + "content": " is thus much lower than that of VLaMP with pre-trained LM shown in row 4. This underscores the crucial importance of LM pre-training." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Segmentation errors are detrimental. While the accuracy of video-action segmentation module (particularly, VideoCLIP model) is quite good - " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "80.2\\%" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " for CrossTask " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "(68.7\\%)" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15309" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 145 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 145 + ], + "type": "text", + "content": "for COIN), we believe this should be a major focus for future research. Why? The effect of this segmentation error in VLaMP's performance is quantified by comparing VLaMP row in Tab. 3 (CrossTask) with corresponding performance assuming perfect segmentation (Tab. 4, row 4). A relative " + }, + { + "bbox": [ + 46, + 72, + 288, + 145 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 72, + 288, + 145 + ], + "type": "text", + "content": " gap in success and big gaps in all other metrics." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 67, + 160, + 263, + 334 + ], + "blocks": [ + { + "bbox": [ + 67, + 160, + 263, + 334 + ], + "lines": [ + { + "bbox": [ + 67, + 160, + 263, + 334 + ], + "spans": [ + { + "bbox": [ + 67, + 160, + 263, + 334 + ], + "type": "image", + "image_path": "1a3965aa5361235b0aeb78132271c2c58450cde177458ff8458ef9f46b8fe7fb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 337, + 288, + 397 + ], + "lines": [ + { + "bbox": [ + 46, + 337, + 288, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 337, + 288, + 397 + ], + "type": "text", + "content": "Figure 5: Effect of segmentation errors. Performance of VLaMP on CrossTask with classification errors " + }, + { + "bbox": [ + 46, + 337, + 288, + 397 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 337, + 288, + 397 + ], + "type": "text", + "content": " in the video-action segmentation. As the errors increase, the performance gap between the full model and the one without access to observations increases." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 413, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 640 + ], + "type": "text", + "content": "Visual observation history mitigates effect of video-action segmentation errors. Errors by segmentation module lead to mis-classification of actions, in turn leading to erroneous action history. To precisely study the effect of erroneous action history on VLaMP's performance, we perform controlled experiments wherein we add noise in the ground truth segmentation. This helps us tune desired segmentation error, irrespective of VideoCLIP's accuracy (in segmentation module). We achieve this by replacing a calculated " + }, + { + "bbox": [ + 46, + 413, + 287, + 640 + ], + "type": "inline_equation", + "content": "\\%" + }, + { + "bbox": [ + 46, + 413, + 287, + 640 + ], + "type": "text", + "content": " of ground-truth actions by random actions. Decreasing performance, with increasing segmentation classification error, is expected and observed in Fig. 5. Further, we compare two models variations, VLaMP" + }, + { + "bbox": [ + 46, + 413, + 287, + 640 + ], + "type": "inline_equation", + "content": "(G, A_k, O_k)" + }, + { + "bbox": [ + 46, + 413, + 287, + 640 + ], + "type": "text", + "content": " i.e. the full model (uses both action and observation history) and VLaMP" + }, + { + "bbox": [ + 46, + 413, + 287, + 640 + ], + "type": "inline_equation", + "content": "(A, A_k)" + }, + { + "bbox": [ + 46, + 413, + 287, + 640 + ], + "type": "text", + "content": " that does not have visual observation history. As we increase segmentation classification error, the gap in the performance of these model variations increases. We infer that visual observations add robustness in VPA against video-action segmentation errors." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": "Errors do not drop as more history is provided. In Fig. 6, we show mAcc w.r.t. the number of steps " + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": " in the history i.e. length of " + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "inline_equation", + "content": "(O_k, A_k)" + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": ". As more information is available (due to more steps in the history), one may expect the accuracy to improve. However, this isn't the trend for many tasks. For e.g., note the accuracy drops for the task \"add oil to your" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 547, + 198 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 547, + 198 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 547, + 198 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 547, + 198 + ], + "type": "image", + "image_path": "983469d45deed55ff647f7b9a6fea5e7bdadcd974307ea4747d1428276bdfc34.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 206, + 547, + 268 + ], + "lines": [ + { + "bbox": [ + 304, + 206, + 547, + 268 + ], + "spans": [ + { + "bbox": [ + 304, + 206, + 547, + 268 + ], + "type": "text", + "content": "Figure 6: Accuracy in the tail of long activities is challenging. Longer history " + }, + { + "bbox": [ + 304, + 206, + 547, + 268 + ], + "type": "inline_equation", + "content": "(O_{k},A_{k})" + }, + { + "bbox": [ + 304, + 206, + 547, + 268 + ], + "type": "text", + "content": " do not necessary lead to better accuracy. Further longer histories occur with increasing rarity, leading to learning challenges. (Plot shows mAcc for " + }, + { + "bbox": [ + 304, + 206, + 547, + 268 + ], + "type": "inline_equation", + "content": "l = 3" + }, + { + "bbox": [ + 304, + 206, + 547, + 268 + ], + "type": "text", + "content": " CrossTask vs. the #steps in history " + }, + { + "bbox": [ + 304, + 206, + 547, + 268 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 206, + 547, + 268 + ], + "type": "text", + "content": ")" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 288, + 545, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 288, + 545, + 408 + ], + "spans": [ + { + "bbox": [ + 304, + 288, + 545, + 408 + ], + "type": "text", + "content": "car” w.r.t " + }, + { + "bbox": [ + 304, + 288, + 545, + 408 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 288, + 545, + 408 + ], + "type": "text", + "content": ". Digging deeper, we find two reasons for this pattern. First, we find that tasks with long history like “add oil to your car” tend to have repetitive steps towards the end of their action trajectories, making it difficult to predict the precise number and the pattern of such repetitions in VPA. Second is simply a data issue – long trajectories are also exponentially less frequent in the dataset. This forms the tail of the data distribution of action sequences in the dataset (see App. E for statistics). Consequently, prediction in this tail of activities, is a pertinent challenge for future research." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 420, + 378, + 432 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 420, + 378, + 432 + ], + "spans": [ + { + "bbox": [ + 306, + 420, + 378, + 432 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 440, + 545, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 440, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 304, + 440, + 545, + 620 + ], + "type": "text", + "content": "Visual Planning for Assistance is a new and intuitive formulation to support planning from natural visual observations for assisting humans in day-to-day activities. We benchmark VPA using standardized suite of prior baselines and a new multi-modal sequence modeling formation of VLaMP. The novel decomposition of a VLaMP policy into video action segmentation and forecasting leads to several efficiency and modeling benefits, that benefit the community, even beyond VPA. Particularly, this allows to leverage pre-trained LM that leads to significant performance gains. Alternative decompositions, self-supervised pre-training objectives for PTLMs, modeling multiple actors, and tapping into other modalities (audio, camera metadata, etc.) [26, 55, 43, 72, 32, 88] are interesting ways forward for the community, on the exciting task of VPA." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements: The authors are indebted to Brian Chen for his efforts to open-source the code and LTA experiments, and to Gideon Stocek for supporting with the cluster management. We thank Vasu Sharma, Tushar Nagarajan, and Homanga Bharadhwaj for their writing feedback. We thank Weichao Mao for early discussions and Asli Celikyilmaz for her constant guidance." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15310" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 144 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 144 + ], + "type": "text", + "content": "[1] Yazan Abu Farha, Alexander Richard, and Juergen Gall. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3537-3545, 2019. 1, 3, 4, 7, 8" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "15314" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 12 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Preventing Zero-Shot Transfer Degradation in Continual Learning of Vision-Language Models/438697ca-0d24-4663-a1e4-f11b5f684ada_content_list.json b/2023/Preventing Zero-Shot Transfer Degradation in Continual Learning of Vision-Language Models/438697ca-0d24-4663-a1e4-f11b5f684ada_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..fbbc7cf0919f290c0f35671dc5de861615d69298 --- /dev/null +++ b/2023/Preventing Zero-Shot Transfer Degradation in Continual Learning of Vision-Language Models/438697ca-0d24-4663-a1e4-f11b5f684ada_content_list.json @@ -0,0 +1,1763 @@ +[ + { + "type": "text", + "text": "Preventing Zero-Shot Transfer Degradation in Continual Learning of Vision-Language Models", + "text_level": 1, + "bbox": [ + 135, + 130, + 836, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zangwei Zheng $^{1}$ Mingyuan Ma $^{2}$ Kai Wang $^{1}$ Ziheng Qin $^{1}$ Xiangyu Yue $^{3}$ Yang You $^{1}$ $^{1}$ National University of Singapore $^{2}$ UC Berkeley $^{3}$ The Chinese University of Hong Kong", + "bbox": [ + 114, + 202, + 846, + 244 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ {zangwei, kai.wang, zihengq, youy} $@$ comp.nus.edu.sg $^{2}$ mamingyuan2001@berkeley.edu $^{3}$ xyyue@ie.cuhk.edu.hk", + "bbox": [ + 102, + 250, + 866, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 301, + 313, + 316 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Continual learning (CL) can help pre-trained vision-language models efficiently adapt to new or under-trained data distributions without re-training. Nevertheless, during the continual training of the Contrastive Language-Image Pre-training (CLIP) model, we observe that the model's zero-shot transfer ability significantly degrades due to catastrophic forgetting. Existing CL methods can mitigate forgetting by replaying previous data. However, since the CLIP dataset is private, replay methods cannot access the pre-training dataset. In addition, replaying data of previously learned downstream tasks can enhance their performance but comes at the cost of sacrificing zero-shot performance. To address this challenge, we propose a novel method ZSCL to prevent zero-shot transfer degradation in the continual learning of vision-language models in both feature and parameter space. In the feature space, a reference dataset is introduced for distillation between the current and initial models. The reference dataset should have semantic diversity but no need to be labeled, seen in pre-training, or matched image-text pairs. In parameter space, we prevent a large parameter shift by averaging weights during the training. We propose a more challenging Multi-domain Task Incremental Learning (MTIL) benchmark to evaluate different methods, where tasks are from various domains instead of class-separated in a single dataset. Our method outperforms other methods in the traditional class-incremental learning setting and the MTIL by $9.7\\%$ average score. Our code locates at https://github.com/Thunderbee/ZSCL.", + "bbox": [ + 75, + 333, + 473, + 771 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 800, + 209, + 815 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most deep learning models can access all the data during training [27, 16, 12]. If we want to expand a model's knowledge, such as learning a newly found animal species [41], we can re-train the model by adding new classes to the training dataset. However, re-training a large model is", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c75e1ac3f0a441aaf322335722a181e73f7abc48d7a8e895bf06511d5e2d2e42.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 301, + 874, + 362 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/92b6c94e2754d253747798a82044fa5a64cabb9b7c6aac94cce33f61f2e5f62c.jpg", + "image_caption": [ + "(a) Comparison between traditional CL and CL with a pre-trained vision-language model" + ], + "image_footnote": [], + "bbox": [ + 517, + 364, + 874, + 473 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c10d291ca81dad6cd99c3f2ff141da5b1ae32d191427ee18e0d17d2af6230b2d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 493, + 687, + 616 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8ba2320b7369d63df75ed8058fd16d5665eb588e431df7dda0453ed1636163e1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 707, + 493, + 875, + 616 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ed563a5c3d2b32f87328dfb825d0c8cc14c019a03e0d56a799d5d00ddf5c9f04.jpg", + "image_caption": [ + "(b) Performance of different methods on preventing forgetting phenomenon" + ], + "image_footnote": [], + "bbox": [ + 517, + 617, + 686, + 719 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/10428b9b041ff7ba9f51c846f7aa5a3ff0160dd0426e8cfc094ca94774103d1d.jpg", + "image_caption": [ + "Figure 1. a) Conventional CL learns distinct task-specific heads, while CL with vision-language models can predict both learned tasks and out-of-distribution tasks. b) Accuracy (\\%) changes during CL of four datasets on 11 datasets. Our method is superior to others in preventing the forgetting of both zero-shot transfer ability and new knowledge." + ], + "image_footnote": [], + "bbox": [ + 709, + 617, + 875, + 719 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "costly. In contrast, continual learning (CL) [33, 47] incrementally learns task one after another. It can reduce", + "bbox": [ + 496, + 869, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 47 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19125", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "this cost by only learning the new data, thereby presenting itself as an efficient alternative to conventional learning methods [43, 34, 5]. Nonetheless, a model tends to forget previous information catastrophically when learning new tasks [47, 33, 59]. The \"catastrophic forgetting\" phenomenon is a great challenge for CL.", + "bbox": [ + 75, + 90, + 470, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, vision-language models have shown powerful zero-shot transfer ability [44, 23, 32]. They can give zero-shot predictions without any training examples of a task. However, the performance on some tasks is poor due to insufficient relevant image-text pairs in the pre-training datasets. For example, it is difficult for CLIP [44] to distinguish among digital numbers, with an accuracy on MNIST [8] below $60\\%$ much lower than a naively trained CNN [29]. If we want to widen the knowledge in the vision-language model by re-training, the computational cost is too large (e.g., CLIP is pretrained on 400 million image-text pairs). Fine-tuning downstream tasks achieves high performance, but one model for a task takes much memory, and the model is not reusable. Prompt learning [64, 63] keeps the backbone parameters unchanged. However, it is only effective with limited training data due to a limited prompt length [64, 24]. In contrast, continual learning makes learning new knowledge a lifelong process for the vision-language model. The continually learned model can handle any image-text input and can be further used for downstream tasks [11, 53].", + "bbox": [ + 75, + 185, + 473, + 501 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We find that existing CL methods hardly prevent the forgetting phenomenon for zero-shot transfer ability in continual learning of a pre-trained vision-language model. As shown in Fig. 1 (a), the CL with a pre-trained vision-language model differs from the traditional one. Besides forgetting previously learned task knowledge, the CLIP-based CL suffers from forgetting pre-training knowledge, namely a degradation of zero-shot transfer ability. For the replay-based CL methods [47, 50, 36, 21, 28, 42], the dataset during pre-training may be private and inaccessible during fine-tuning. For distillation-based CL methods [33, 10, 13, 11], they do not lay enough emphasis on the pre-trained model. On the one hand, a large model state change hinders tasks thereafter from using high-quality feature representations. On the other hand, it significantly degrades zero-shot performance on unseen datasets.", + "bbox": [ + 75, + 505, + 470, + 747 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our method ZSCL protects the Zero-Shot transfer ability during Continual Learning. We view the knowledge stored in the pre-training model from two perspectives: a well-learned feature space and a good value in the parameter space. In feature space, we re-design previous distillation loss [18, 47] with different loss styles, teacher models, and data sources. We find the original CLIP model, as opposed to the newly acquired model, is the best option for the teacher model. Instead of using data collected from previous tasks [47] or current task [18], we find a reference", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "dataset with diverse semantics (e.g., images sampled from ImageNet) is a good option for distillation loss. The reference images need not be labeled or matched with the text. Preserving the relative similarity between reference images and texts makes the feature space deviate little from the original. In the parameter space, WiSE-FT [58] proposes interpolating the initial and fine-tuned model for better performance. Inspired by this, we ensemble the weights throughout continuous training to prevent a significant shift from the initial CLIP, which can be seen as interpolating models of different zero-shot transfer and downstream task performance tradeoffs. The weight ensemble method is more stable and not sensitive to hyper-parameters.", + "bbox": [ + 496, + 90, + 890, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To better evaluate our method, we propose a new benchmark Multi-domain Task Incremental Learning (MTIL). Previous CL tasks are crafted by separating classes in one dataset [14, 60, 65], where the images and classes are within a single domain. In contrast, MTIL consists of data from different sources requiring different expert knowledge. It comprises 11 tasks ranging from animal species to aircraft series recognition. As displayed in Fig. 1 (b), when sequentially training CLIP on 11 datasets, the drop in the performance of task $i$ after training task $i$ is the traditional forgetting phenomenon. The degradation in the accuracy compared to the original zero-shot one before training task $i$ represents the forgetting in zero-shot transfer ability. Our method better protects the zero-shot transfer ability and preserves the learned knowledge. We outperform previous methods in both conventional class-incremental learning and MTIL settings. In Fig. 1 (b),", + "bbox": [ + 496, + 287, + 892, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, our contributions are as follows:", + "bbox": [ + 517, + 544, + 834, + 558 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We investigate continual training with the vision-language model and demonstrate the importance of preserving zero-shot transfer ability. A more challenging benchmark MTIL is proposed to evaluate CL methods where the tasks come from distinct domains.", + "- We propose a novel method ZSCL to mitigate the catastrophic forgetting problem in continual learning of the vision-language model by distillation in the feature space and weight ensemble in the parameter space.", + "- The proposed ZSCL outperforms all state-of-the-art methods across multiple benchmark datasets. On 10 steps CL of CIFAR100 and TinyImageNet, our method outperforms the best of previous ones by $7.7\\%$ and $6.0\\%$ for the Last accuracy. On MTCL, ZSCL outperforms others by $10.9\\%$ on Transfer and $9.7\\%$ on Avg. scores." + ], + "bbox": [ + 517, + 569, + 890, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 844, + 640, + 859 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Vision-Language Models. Inspired by the success of language foundation models such as GPT-3 [3] and T5 [45], a", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19126", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "series of work pre-train vision-language models on large-scale image-text datasets [31, 44, 23]. Among them, Contrastive Language-Vision Pre-training [44] achieves remarkable performance on various downstream tasks. It concentrates on aligning images and texts to acquire a joint embedding space. The CLIP model contains an image encoder [16, 12] and a text encoder [9]. During pre-training, contrastive learning is performed in which a paired image-text is a positive pair while image and text from different image-text pairs form a negative pair. For inference, the closest text embedding for the image is chosen as the prediction. Vision-language models can give zero-shot predictions on unseen tasks with a robust zero-shot transfer ability on various downstream tasks.", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Continual Learning Methods. Most existing continual learning methods can be categorized into four groups: parameter expansion, memory replay, distillation loss, and parameter regularization. Parameter expansion methods such as DyTox [14] and DEN [61] introduce new parameters for new tasks. As we want to achieve a more powerful CLIP model at the end of CL, we do not change the architecture of the CLIP model. Memory replay methods [50, 36, 42, 28, 40] including iCaRL [47] and SER [21] keep a memory for exemplars from previously learned tasks. However, pre-training datasets are too large for choosing exemplars or may not be available at downstream training, and downstream data are not good exemplars for preserving the pretraining knowledge. Distillation loss such as LwF [33], LwM [10], LwF-VR [11], and PodNet [13] aligns current output space with previous ones, whereas distillation based on current tasks are not strong enough to maintain foundational knowledge. For the CLIP model, we find that general images, even if never seen by the model, plus sentences with enough semantics, can be a good \"replay\" for the distillation loss. The parameter regularization loss restricts the flexibility of model parameters by training loss [25, 62, 1] or weight averaging [30, 58]. Although this type of strategy performs badly compared to other ways in previous research [55, 2], we found it helpful for CLIP continual learning. The limited parameter space prevents the model from diverging significantly from its original state.", + "bbox": [ + 75, + 321, + 472, + 731 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Vision-Language Models for Downstream Tasks. Many works propose different training strategies of vision-language models for better performance on downstream tasks, such as CoOp [64], CLIP-Adapter [15] and WiSE-FT [58]. However, very few attempts at continual learning exist. While [52, 56] focus on CL in the pretrain of VL and [39] trains VL from scratch using a small dataset, our problem setting differs as we address CL in downstream tasks with a pretrained VL. Currently, most VL models are trained directly on an accessible large", + "bbox": [ + 75, + 750, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "dataset, yet integrating knowledge continuously into a pretrained VL is a practical necessity. None of these studies address the zero-shot transfer degradation phenomenon, instead focusing on the traditional forgetting of learned knowledge. Recently, Thengane et al. [53] shows CLIP zero-shot prediction achieves state-of-the-art performance in CL settings even without any training. LwF-VR [11] is a modified LwF method for the CLIP model where random-generated sentences are used for distillation loss. However, it only considers the feature space, and the distillation with random sentences cannot protect the vision backbone. Differently, we re-examine what should be used for distillation in the feature space and combine the parameter space weight ensemble to provide better performance for the vision-language model continual learning.", + "bbox": [ + 496, + 90, + 893, + 320 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 500, + 329, + 609, + 345 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 353, + 640, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Continual Learning. Given $n$ tasks $[\\mathcal{T}^1, \\mathcal{T}^2, \\dots, \\mathcal{T}^n]$ , continual training is conducted in sequence on each task $\\mathcal{T}^i = (\\mathcal{D}^i, C^i)$ , $i = 1, \\dots, n$ . Here, $\\mathcal{D}^i$ represents the task dataset $\\{(x_j^i, y_j^i)\\}_{j=1}^{N_i}$ , where $x_j^i$ is an image, $y_j^i$ is a one-hot vector indicating the ground truth, and $N_i$ is the number of images in the dataset. Class names $C^i = \\{c_j^i\\}_{j=1}^{m_i}$ maps the label of an image to an object name, where $m_i$ is the number of classes for task $\\mathcal{T}^i$ . The objective of continual learning is to achieve good performance on all tasks.", + "bbox": [ + 496, + 376, + 893, + 513 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Two continual learning settings are focused on in this study [55]. In task-incremental learning, at inference, the image $\\pmb{x}$ to be predicted is given with its task identity $t$ , so the model only needs to distinguish between different classes in $C^t$ . In class-incremental learning, the task identity $t$ is not given. Thus we need to predict with the combined class set $C = \\bigcup_{i=1}^{n} C^i$ .", + "bbox": [ + 496, + 513, + 893, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "CLIP model. The CLIP model contains an image encoder $f_{i}$ and a text encoder $f_{t}$ . The inference process of the CLIP model for image classification is as follows. First, for task $\\mathcal{T}^i$ , each class $c$ is transformed into a sentence by a template like \"a photo of $\\{c\\}$ \". Then $f_{t}$ encodes the classes into text embeddings $\\{\\pmb{t}_{j}^{i}\\}_{j = 1}^{m_{i}}$ . An image encoder encodes input image $\\pmb{x}_k$ . The similarity score between the image embedding and text embeddings are calculated as $s_{k,j}^{i} = \\langle f_{i}(\\pmb{x}_{k}),\\pmb{t}_{j}^{i}\\rangle$ where $\\langle \\cdot ,\\cdot \\rangle$ denotes the cosine similarity. The class with the largest similarity score is the prediction for the image.", + "bbox": [ + 496, + 636, + 893, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To fine-tune the CLIP model for downstream tasks, cross-entropy loss CE is applied to the similarity score with a temperature scaling:", + "bbox": [ + 496, + 787, + 893, + 833 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {C E}} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathrm {C E} (\\tau \\cdot \\boldsymbol {s} _ {i}, \\boldsymbol {y} _ {i}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 838, + 890, + 880 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\tau$ is a parameter learned during the pre-training.", + "bbox": [ + 500, + 885, + 861, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19127", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4329bff0d636ac16c1e23263b5d689cb7dbc7b4b289e45b30094e3f0c1b8cdce.jpg", + "image_caption": [ + "Figure 2. Illustration of ZSCL in feature space. Fig. 3(a) shows the pipeline of distillation. The original and the current model encode the reference images and texts, respectively. The probability distribution of images and texts with respect to each other is distilled. Fig. 3(b) displays how distillation loss preserves the feature space. Compared with the reference dataset, the features of fine-tuning tasks lie in a small subspace. The distillation loss preserves the structure of the feature space by maintaining relative distances." + ], + "image_footnote": [], + "bbox": [ + 81, + 93, + 478, + 253 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f03a900cd5ed94daddb29f1585000c813ccaa2207a4462c7b9f5c88529204ab8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 496, + 93, + 893, + 257 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Distillation in Feature Space", + "text_level": 1, + "bbox": [ + 76, + 351, + 331, + 368 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Well-learned feature space for aligned images and texts enables vision-language models' strong zero-shot transfer ability. It also facilitates the learning of downstream tasks. Compared with the pre-training dataset, downstream datasets lie in a small scope in the feature space (shown in Fig. 2(b)). Direct fine-tuning of downstream tasks greatly distorts the feature distribution of out-of-distribution data, which leads to a significant drop in zero-shot prediction performance.", + "bbox": [ + 75, + 375, + 468, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While the cross-entropy improves the performance by altering fine-tuned feature subspace, we need a new regularization to preserve the potential out-of-distribution feature space. The relative similarity between one image and different texts is:", + "bbox": [ + 75, + 510, + 468, + 585 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {p} = \\operatorname {S o f t m a x} \\left(\\boldsymbol {s} _ {1}, \\dots , \\boldsymbol {s} _ {m}\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 599, + 468, + 616 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We hope the above similarity distribution is stable during fine-tuning for all potential images and texts. Given a teacher model $\\overline{f}$ , distillation loss can be applied to penalize changes from the original distribution:", + "bbox": [ + 75, + 626, + 468, + 686 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {d i s t . i m g}} = \\operatorname {C E} (\\boldsymbol {p}, \\bar {\\boldsymbol {p}}) = - \\sum_ {j = 1} ^ {m} \\boldsymbol {p} _ {j} \\cdot \\log \\bar {\\boldsymbol {p}} _ {j}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 698, + 468, + 738 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\overline{\\pmb{p}}$ is the distribution given by the teacher model.", + "bbox": [ + 76, + 750, + 437, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although the distillation form has been widely used in previous methods [18, 33, 47], they are applied to continual learning from scratch. We investigate different components of the distillation loss for enhancing pre-trained vision-language models.", + "bbox": [ + 75, + 763, + 468, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Three components are discussed in this paper in detail: the data source, the teacher model, and the loss design. Sec. 5.1 shows the performance for the different choices. First, for the data source, LwF [33] uses data from the cur", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "rent task, while iCarl [47] carefully selects data from previous tasks. However, data from downstream tasks span a small subspace and are not good enough to preserve the whole feature space. An ideal choice is the pre-training dataset. However, the CLIP pre-training dataset is private, and the size is too large to load. To solve this challenge, we introduce the reference dataset. A reference dataset is a publicly available image dataset with enough semantics. Enough semantics can be seen as random sampling in the whole feature space. The texts can be related class names, unrelated sentences, or even random tokens. This is because text semantics are easier to sample, and we need not ground truth to calculate the distance between one image to sufficient text samples spread among feature space.", + "bbox": [ + 496, + 352, + 890, + 564 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the teacher model, [33, 47] use the model after learning task i-1 and before learning task i as the teacher model. During the continual training of the vision-language model, the feature space deviates gradually from the initial model. Using fine-tuned models as teacher models enlarges this change. In contrast, we find using the pre-trained model as a teacher model not only preserves the zero-shot transfer ability but also takes advantage of well-learned feature space for better downstream performance.", + "bbox": [ + 496, + 575, + 890, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, previous distillation loss is applied on traditional backbones, where a classification head gives the probability for different labels. For the vision-language model, the probability is calculated based on the relative distance between images and texts. Thus, in addition to Eq. (3), we impose regularization $\\mathcal{L}_{\\mathrm{dist\\_txt}}$ on the distances from a text to a batch of images. The whole framework is shown in Fig. 2 (a) with the following training loss:", + "bbox": [ + 496, + 724, + 890, + 847 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {c e}} + \\lambda \\cdot \\left(\\mathcal {L} _ {\\mathrm {l w f . i m g}} + \\mathcal {L} _ {\\mathrm {l w f . t x t}}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 885, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19128", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/eb3d24a46c63689d28133592e77841b07804ba7d89e7f0c1fa29b32d5c02b588.jpg", + "image_caption": [ + "Figure 3. Models during training contain different tradeoffs between zero-shot and new task performance. Points for FT are sampled every 100 iterations, and the ones for WiSE-FT means different $\\alpha$ choices. WE ensembles models during training and achieve better performance." + ], + "image_footnote": [], + "bbox": [ + 114, + 87, + 433, + 263 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Weight Ensemble in Parameter Space", + "text_level": 1, + "bbox": [ + 76, + 366, + 403, + 383 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Machine learning models integrate learned knowledge in their parameters. To mitigate the forgetting problem, a series of works [25, 62, 1] impose regularization losses on the changes of parameters. Weight consolidation (WC) [25] imposes the following loss:", + "bbox": [ + 75, + 390, + 470, + 465 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {W C}} = \\sum_ {i} \\left(\\theta_ {i} - \\bar {\\theta} _ {i}\\right) ^ {2}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 474, + 468, + 506 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\theta$ is the parameters of the current model, and $\\overline{\\theta}$ is the reference ones. Although this regularization prevents forgetting, it hinders learning new tasks in a challenging CL setting.", + "bbox": [ + 75, + 516, + 468, + 577 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Apart from regularization losses, another method in parameter space is to ensemble different model weights. Model soup [57] averages weights of multiple fine-tuned models to improve the model's robustness but introduces additional training costs. WiSE-FT [58] propose a weighted average between fine-tuned model and the original model to improve the out-of-distribution prediction robustness:", + "bbox": [ + 75, + 578, + 468, + 683 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf (x; (1 - \\alpha) \\cdot \\theta_ {0} + \\alpha \\cdot \\theta_ {1}), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 693, + 468, + 709 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\theta_0$ is the original model and $\\theta_{1}$ is the fine-tuned one. However, this method is hyper-parameter-sensitive where different $\\alpha$ gives different tradeoffs between zero-shot transfer ability and downstream task performance (blue line in Fig. 3.", + "bbox": [ + 75, + 719, + 468, + 795 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspired by this, we extend the weighted average to the CL setting. The motivation for the weighted average is to prevent fine-tuning from losing too much knowledge in the original model. As training goes by (green line in Fig. 3), the model performs better on new tasks while losing accuracy on previous ones. The models among training compose a sequence of different learning-forgetting tradeoffs.", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c1c8038706070e6074aff8433598727beaf8d68f06790075ab76e09402bafbd0.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 506, + 108, + 578, + 179 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7612a0001597f0d99113646e1932e6b9a2dfdfa5b9fc31e1b66a56d4a369c262.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 593, + 108, + 666, + 179 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/816e3786999b886a7661b676ba1153e0a0d8b60c6ea218d1e5871216e42d0f37.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 508, + 188, + 576, + 261 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/952c17a62f4e4c386253f86e5ba5a7e8676eb7209cde979b79afbd3ab84319b1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 594, + 188, + 666, + 260 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/81e23c68abd350a661469da9d431633c4fcb113cc4ec578215ac9647b344ca15.jpg", + "image_caption": [ + "(b)", + "Figure 4. Fig.(a): examples of tasks from different domains in MTIL benchmark. Fig.(b): illustration of calculating metrics Transfer, Avg. and Last during continual learning." + ], + "image_footnote": [], + "bbox": [ + 684, + 104, + 890, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Instead of interpolating only between the initial and the final model, our method weight ensemble (WE) averages the weights in the sequence during the training time:", + "bbox": [ + 498, + 364, + 892, + 411 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\theta} _ {t} = \\left\\{ \\begin{array}{l l} \\theta_ {0} & t = 0 \\\\ \\frac {1}{t + 1} \\theta_ {t} + \\frac {t}{t + 1} \\cdot \\hat {\\theta} _ {t - 1} & \\text {e v e r y I i t e r a t i o n s} \\end{array} . \\right. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 419, + 890, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where model weight sampling happens every $I$ iteration. The method is related to Stochastic Weight Averaging (SWA) [22], but we do not use a modified learning rate schedule here because instead of getting better generalization ability, WE aim to give an improved learning-forgetting tradeoff. As shown in Fig. 3, WE achieves better performance on downstream tasks than WiSE-FT. In addition, while WiSE-FT is sensitive to different values of $\\alpha$ , our method is much more robust under different hyperparameter $(I)$ choices.", + "bbox": [ + 498, + 469, + 890, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Multi-domain Task Incremental Learning", + "text_level": 1, + "bbox": [ + 498, + 633, + 874, + 650 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Conventional Continual Learning Benchmark. A benchmark consisting of several tasks is needed to evaluate different methods for continual learning. Most previous benchmarks are built by separating classes in a single dataset, such as MNIST [55], CIFAR100 [14], TinyImageNet [60], and ImageNet [60, 65]. We also evaluate our method with traditional benchmarks. In CIFAR100 [26], classes are separated into groups to build tasks. Suppose the dataset has $m$ classes, a $k$ -step setting means we learn $m / k$ classes in each new task. The CIFAR100 contains 100 classes, and the setting of 10, 20, and 50 steps are visited. For TinyImageNet with $m = 200$ , the first step learns 100 classes, and the rest is learned with 5, 10, and 20 steps. As for ImageNet-100, we have two settings: ImageNet-100-B0, which includes the same amount of classes for each step, and ImageNet-100-B50, which has", + "bbox": [ + 496, + 657, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19129", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/bd47b8cc97b89c696691abf6145c7fa7b7975a21209b7a49d0a2c12b27dbebbe.jpg", + "table_caption": [ + "Table 1. Ablation experiments. Default settings are marked in gray, which uses image and text distillation loss with the initial CLIP model on 100k ImageNet images and texts generated from ImageNet classes with a simple template.", + "(a) Continual learning loss." + ], + "table_footnote": [], + "table_body": "
lossTransferAvg.Last
CE only44.655.977.3
Feat. Dist.47.658.777.1
Image-only56.568.982.1
Text-only56.769.082.6
Both56.869.283.0
", + "bbox": [ + 86, + 146, + 336, + 224 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/aa1d0b2e84d0d8395d5958f4119eb749f0b5b6e3f4a5e35a6c7cbb93ff77a63a.jpg", + "table_caption": [ + "(d) Teacher model." + ], + "table_footnote": [], + "table_body": "
sourceTransferAvg.Last
Initial56.869.283.0
n-153.966.680.7
WiSE(0.5)56.468.982.9
WiSE(0.8)56.267.881.3
", + "bbox": [ + 86, + 241, + 341, + 308 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e7a53235fc55eabdceac0aed247a87eb840a49f999bd06615b82055e6889be59.jpg", + "table_caption": [ + "(b) Data sources for replay." + ], + "table_footnote": [], + "table_body": "
sourceTransferAvg.Last
current56.766.580.2
ImageNet56.869.283.0
CC57.268.580.9
CIFAR10055.265.980.7
Flowers54.766.080.8
", + "bbox": [ + 367, + 147, + 620, + 224 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1bdffdf8de7307efbe544e64fd3f83a288a35b2bfb186dc9758440726f83378b.jpg", + "table_caption": [ + "(e) # images for replay." + ], + "table_footnote": [], + "table_body": "
#imageTransferAvg.Last
1M58.770.183.2
100k56.869.283.0
10k57.868.781.2
1k56.367.680.8
", + "bbox": [ + 367, + 241, + 620, + 306 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/89a67456fdb955935a5376d6ef17aa5c518dd36a1e1af1bfedd4d3b100627246.jpg", + "table_caption": [ + "(c) Text sources for replay." + ], + "table_footnote": [], + "table_body": "
sourceTransferAvg.Last
current51.864.982.0
prev. all54.070.283.7
1k classes (IN)56.869.283.0
13k Sent. (CC)58.970.584.0
1k Rand. Sent.58.770.283.8
", + "bbox": [ + 645, + 147, + 898, + 224 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1fbef6a5fee68628c0b246ae13a2e24e77befe915ade7a66d22af3cc956111c2.jpg", + "table_caption": [ + "(f) # image classes for replay." + ], + "table_footnote": [], + "table_body": "
#classTransferAvg.Last
100056.867.683.0
10056.767.382.3
1053.866.481.0
153.165.580.5
", + "bbox": [ + 645, + 241, + 898, + 306 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c391686ce697cfd0b0b4f8435ebbc81c674df95a2fd0850f219f8c907a0ccd04.jpg", + "table_caption": [ + "Table 2. Ablation study of different components for ZSCL." + ], + "table_footnote": [], + "table_body": "
MethodTransferΔAvg.ΔLastΔ
CLIP ViT-B/16@224px
Zero-shot69.40.065.30.065.30.0
Continual Learning44.6-24.855.9-9.477.3+12.0
+ Distillation58.9-10.570.5+5.283.8+18.5
+ WiSE-FT (best α)61.7-7.771.6+6.383.3+18.0
+ WE (ZSCL*)62.2-7.272.6+7.384.5+19.2
+ WC67.6-1.874.5+9.283.2+17.9
+ WiSE-FT67.7-1.774.2+8.981.9+16.6
+ WE (ZSCL)68.1-1.375.4+10.183.6+18.3
", + "bbox": [ + 78, + 357, + 473, + 483 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "50 classes for the first step, and the remaining 50 classes are observed progressively over the next 10 stages. For ImageNet [7], we investigate a 10-step setting, which learns 100 new classes per task.", + "bbox": [ + 75, + 508, + 470, + 570 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "MTIL Benchmark. Different classes from one dataset share the common image source and a similar style [48, 17]. Thus, we propose Multi-domain Task Incremental Learning (MTIL), a cross-domain version of task incremental learning. Different tasks are collected from different domains, requiring different domain knowledge for humans to achieve high accuracy. Our MTIL benchmark consists of 11 tasks (detailed in supplementary materials), as some of the tasks illustrated in Fig. 4 (a). The MTIL benchmark is very challenging with a total number of 1,201 classes. Two orders are used for the evaluation; the first one is alphabet order (Order-I): Aircraft, Caltech101, CIFAR100, DTD, EuroSAT, Flowers, Food, MNIST, OxfordPet, StanfordCars, SUN397. And the second one is a random order (Order-II): StanfordCars, Food, MNIST, OxfordPet, Flowers, SUN397, Aircraft, Caltech101, DTD, EuroSAT, CIFAR100. Experiments are done in Order I by default.", + "bbox": [ + 75, + 590, + 470, + 849 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. The metrics of MTIL are illustrated in Fig. 4(b), where rows represent training steps and a", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "column shows performance for one dataset. For conventional continual learning, only scores under the diagonal are meaningful, since they cannot give zero-shot predictions on unseen tasks. In contrast, the zeros-hot transfer ability enables a vision-language model to provide predictions for all datasets. The average accuracy on all datasets among all timestamps is the \"Avg\" metric. The \"Last\" metric is the average performance of all tasks after CL. The \"Transfer\" metric is the average task performance in the upper-right triangle of the matrix. Every task's performance is first averaged to equal the weight of each dataset. It measures to what extent the zero-shot transfer ability is preserved. Before learning task $i$ , tasks not earlier than $i$ are not finetuned. Thus, their performance is an indicator of zero-shot transfer ability.", + "bbox": [ + 496, + 333, + 893, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 575, + 633, + 593 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation. We use CLIP [44] model with image encoder ViT-B/16 [12]. We conduct training with AdamW [37] optimizer and use a label smoothing [38] technique for a better baseline result. For multi-domain task continual learning, we train 1K iterations for each task, while for class-incremental learning, we follow the same evaluation setting in [14]. More implementation details can be found in the supplementary material.", + "bbox": [ + 496, + 601, + 893, + 723 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Main Properties", + "text_level": 1, + "bbox": [ + 500, + 734, + 661, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We ablate our method in feature-space in Tab. 1, and different choices for parameter-space regularization in Tab. 2. Several interesting characteristics are noted.", + "bbox": [ + 496, + 757, + 890, + 804 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Continual learning loss. In Tab. 1a, several types of loss for feature space are tested. The Feature Distance penalizing absolute distances achieves a low accuracy. Distillation loss on probability distribution regularizes relative distance in the feature space. With image-only or text-only distilla", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19130", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/486e0281799167fdc39ad25fe08f6ed1648465a543e6415e44a1f33130cf66aa.jpg", + "image_caption": [ + "Figure 5. t-SNE on five models' outputs together of Aircraft datasets after MTCL training: only our model maintains a similar feature distribution to the original CLIP ones with minor shift, while the rest significantly distort the feature space." + ], + "image_footnote": [], + "bbox": [ + 86, + 90, + 243, + 205 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7784c328f4cdf2b9bb2ed7f173c38e0d41ae1044f2237fb671b5c4c8254a9dc8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 248, + 90, + 405, + 205 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/09b430fabc5fe55f1527a5618eccc3aa9a80fbc30f1e07b877ca20d9e3d1d5a5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 408, + 90, + 566, + 205 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/eb90c5de160688afb191eadaa39b87a75136e54a5cc737262f85f987cb769e3e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 571, + 90, + 728, + 205 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e8277e097f9a1ced82aa1b0687e58001beb7132aad61f8a706e47c69a5d84737.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 732, + 90, + 885, + 205 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/93a36b72b943f7cd603380a954c6668578e979820d207fe6599536d19724b99c.jpg", + "table_caption": [ + "Table 3. Comparison of different methods on MTIL in Order I." + ], + "table_footnote": [], + "table_body": "
MethodTransferΔAvg.ΔLastΔ
CLIP ViT-B/16@224px
Zero-shot69.40.065.30.065.30.0
Continual Learning44.6-24.855.9-9.477.3+12.0
LwF [33]56.9-12.564.7-0.674.6+9.0
iCaRL [47]50.4-19.065.7+0.480.1+14.8
LwF-VR [11]57.2-12.265.1-0.276.6+11.3
WiSE-FT [58]52.3-17.160.7-4.677.7+12.4
ZSCL* (Ours)62.2-7.272.6+7.384.5+19.2
ZSCL (Ours)68.1-1.375.4+10.183.6+18.3
", + "bbox": [ + 78, + 292, + 470, + 426 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tion, the Transfer, Avg., and Last accuracy all improve. A further boost in performance occurs with both of the distillation losses.", + "bbox": [ + 75, + 450, + 468, + 496 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Data source for replay. Tabs. 1b, 1c, 1e and 1f seek the standard for a good reference dataset. As shown in Tab. 1b, distillation on images of current tasks achieves a good Transfer score. However, it hinders the learning on new tasks and results in a low Avg. and Last score. Images in a specific domain (e.g., Flowers) are also not good choices. General images in ImageNet and Conceptual Caption (CC) datasets are examples of good reference datasets. These images are easily available by a web crawler [54]. Text with more semantics can improve performance (shown in Tab. 1c). When using sentences from the Conceptual Caption dataset [49], or even sentences randomly generated from the CLIP vocabulary, there is no ground truth target among the texts for the image from the ImageNet dataset. However, they all achieve an improvement due to more semantics. The reference image dataset does not need to be labeled, matched with the text, or seen by the CLIP model.", + "bbox": [ + 75, + 521, + 468, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Enough semantics in the reference image dataset boosts the distillation performance. In Tabs. 1e and 1f, a smaller number of images and classes all lead to a degradation in the performance. Fewer classes of images in the reference dataset have a worse impact on the performance compared with the image numbers. To keep a reasonable memory buffer, we randomly sample $100\\mathrm{k}$ images from ImageNet for MTIL and use texts from CC dataset. For class-", + "bbox": [ + 75, + 779, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a3c81c468e3153ab25efe2bc7736f185000675360c5f0818bbee81b4145c0144.jpg", + "table_caption": [ + "Table 4. Comparison of different methods on MTIL in Order II." + ], + "table_footnote": [], + "table_body": "
MethodTransferΔAvg.ΔLastΔ
CLIP ViT-B/16@224px
Zero-shot65.40.065.30.065.30.0
Continual Learning46.6-18.856.2-9.167.4+2.1
LwF [33]53.2-12.262.2-5.271.9+6.6
iCaRL [47]50.9-14.556.9-8.471.6+6.3
LwF-VR [11]53.1-12.360.6-7.468.3+0.9
WiSE-FT [58]51.0-14.461.5-5.972.2+6.9
ZSCL*59.8-5.671.8+6.583.3+18.0
ZSCL64.2-1.274.5+9.283.4+18.1
", + "bbox": [ + 500, + 292, + 893, + 426 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "incremental learning, conceptual caption dataset's validation set (28k images) is used to avoid information leakage.", + "bbox": [ + 498, + 452, + 890, + 483 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Teacher model. Tab. 1d shows the performance of distillation loss with different teacher models. Unlike conventional continual learning, the teacher model should not be the one trained on the previous task; otherwise, the deviation from the initial CLIP in the previous task may be amplified. In contrast, with the initial CLIP as the teacher model, not only is the zero-shot performance improved but the Mean and Last scores are also boosted, indicating that preserving high-quality feature space facilitates continual learning.", + "bbox": [ + 496, + 502, + 892, + 654 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Parameter-space regularization. In Tab. 2, we experiment with three different parameter-space regularizations. We experiment with two variants of WiSE-FT [58]: the weighted average between the current model with the initial CLIP or the one at the previous task. The result shows the latter one is a better choice because keeping weight averaging with initial CLIP loses the newly learned knowledge. We experiment with different $\\alpha$ choices for WiSE, and the best result is reported. While distillation loss improves the whole performance, the parameter-space regularization further protects the zero-shot transfer ability with a higher Transfer. Among the three parameter-space regularizations, only WE achieve a better Last score. WC greatly improves the Transfer scores with a lower Last score. A combination of the weight consolidation loss with weight", + "bbox": [ + 496, + 674, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19131", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9c645337f982c4049b97a0b2cbd146fe3651998e8ffb2db64402112ddaccf5f9.jpg", + "table_caption": [ + "Table 5. Transfer, Avg., and Last scores (%) of different continue training methods on MTIL benchmark." + ], + "table_footnote": [], + "table_body": "
MethodAircraftCaltech101CIFAR100DTDEuroSATFlowersFoodMNISTOxfordPetCarsSUN397
CLIP ViT-B/16@224px
Zero-shot24.388.468.244.654.971.088.559.489.064.765.2
Fine-tune62.095.189.679.598.997.592.799.694.789.681.8
Transfer
Continual-FT67.146.032.135.635.057.744.160.820.546.6
LwF [33]74.556.939.151.152.672.860.675.130.355.9
iCaRL [47]56.644.632.739.346.668.046.077.431.960.5
LwF-VR [11]77.161.040.545.354.474.647.976.736.358.6
WiSE-FT [58]73.555.635.641.547.068.353.969.326.851.9
Dist. only80.162.240.239.958.180.853.474.638.161.9
ZSCL*78.364.042.945.263.584.256.178.944.164.3
ZSCL86.067.445.450.469.187.661.886.860.166.8
Avg.
Continual-FT25.581.559.153.264.751.863.264.369.731.849.7
LwF [33]36.386.972.059.073.760.073.674.880.037.358.1
iCaRL [47]35.589.272.260.668.870.078.262.381.841.262.5
LwF-VR [11]29.687.774.459.572.463.677.066.781.243.760.7
WiSE-FT [58]26.786.564.357.165.758.771.170.575.836.954.6
Dist. only48.190.679.863.275.672.584.770.279.846.963.7
ZSCL*50.790.979.863.876.677.387.071.983.052.065.9
ZSCL45.192.080.164.379.581.689.675.288.964.768.0
Last
Continual-FT31.089.365.867.388.971.185.699.692.977.381.1
LwF [33]26.387.571.966.679.966.983.899.692.166.180.4
iCaRL [47]35.893.077.070.283.388.590.486.793.281.281.9
LwF-VR [11]20.589.872.367.685.573.885.799.693.173.380.9
WiSE-FT [58]27.290.868.068.986.974.087.699.692.677.881.3
Dist. only43.391.981.372.495.190.590.499.792.585.181.8
ZSCL*46.092.381.272.493.092.190.899.693.386.681.7
ZSCL40.692.281.370.594.890.591.998.793.985.380.2
", + "bbox": [ + 107, + 114, + 864, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ensemble achieves a better tradeoff between Transfer and Last value. While $\\mathrm{ZSCL}^*$ , a variant without the WC loss, obtains the highest Last score, the ZSCL with WC loss outperforms it with $2.8\\%$ Avg. and $5.9\\%$ Transfer scores.", + "bbox": [ + 75, + 585, + 470, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2. Multi-domain Task Incremental Learning", + "text_level": 1, + "bbox": [ + 76, + 662, + 434, + 680 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tab. 3 displays the performance of different methods on the MTIL benchmark, and Tab. 5 presents the detailed Transfer, Avg, and Last metrics on each dataset. Zero-shot denotes the zero-shot prediction performance of the initial CLIP model, and Fine-tune means the direct fine-tuning accuracy on each dataset, which can be seen as an upperbound where no forgetting phenomenon happens. Continual learning uses cross-entropy loss to learn each dataset sequentially, where there is a significant forgetting issue on both zero-shot predictions (Transfer drops by $24.8\\%$ ) and newly learned knowledge (Last drops by $9.4\\%$ ). Previous methods improve the Last performance slightly and cannot maintain a high zero-shot prediction performance. Without WC, $\\mathrm{ZSCL}^*$ achieves the best Last scores, outperforming", + "bbox": [ + 75, + 688, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the previous best one by $4.4\\%$ . Our method ZSCL improves $9.1\\%$ on Transfer accuracy, with only $1.3\\%$ drops compared with the initial CLIP model, and achieves a $10.1\\%$ gain in the Avg. accuracy.", + "bbox": [ + 498, + 585, + 890, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure Fig. 5 provides a visualization of the feature space on Aircraft of the original CLIP and four methods trained at the end of MTCL (t-SNE conducted only once on all features collected). This shows our method is capable of maintaining the pretrained feature distribution with a small averaged feature distance and thus preserving zero-shot performance.", + "bbox": [ + 496, + 652, + 893, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The result of the MTIL method in Order-II is presented in Tab. 4. Our method surpasses previous methods in another order setting of the MTIL benchmark. A similar conclusion holds from the results of MTIL Order-II compared with MTIL Order-I. Our method ZSCL outperforms others by $9.2\\%$ on the Avg. score and $18.1\\%$ on the Last score with only a $1.2\\%$ performance loss on the Transfer score. This shows our approach can work for different orders of the multi-domain task incremental learning. In addition,", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19132", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d650b00a134f12b88b67cba437bcb07263b2d4a1ef65ad84a9d666ca2cd3cbb3.jpg", + "table_caption": [ + "Table 6. Comparison of state-of-the-art CL methods on CIFAR100 benchmark in class-incremental setting." + ], + "table_footnote": [], + "table_body": "
Methods10 steps20 steps50 steps
AvgLastAvgLastAvgLast
UCIR [19]58.6643.3958.1740.6356.8637.09
BiC [59]68.8053.5466.4847.0262.0941.04
RPSNet [46]68.6057.05----
PODNet [13]58.0341.0553.9735.0251.1932.99
DER [60]74.6464.3573.9862.5572.0559.76
DyTox+ [14]74.1062.3471.6257.4368.9051.09
CLIP [44]74.4765.9275.2065.7475.6765.94
FT65.4653.2359.6943.1339.2318.89
LwF [33]65.8648.0460.6440.5647.6932.90
iCaRL [47]79.3570.9773.3264.5571.2859.07
LwF-VR [11]78.8170.7574.5463.5471.0259.45
ZSCL (Ours)82.1573.6580.3969.5879.9267.36
Impr+7.68+7.73+5.19+3.84+3.95+1.42
", + "bbox": [ + 76, + 128, + 470, + 343 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "compared with Order-I, previous methods achieve a much lower Last score (e.g., for Continual-Learning, Order-I has $77.3\\%$ , while Order-II has $65.3\\%$ ). With ZSCL, the Last score is similar ( $83.6\\%$ compared with $83.4\\%$ ). This shows our method is more robust towards different training orders.", + "bbox": [ + 75, + 378, + 468, + 455 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5.3. Class Incremental Learning", + "text_level": 1, + "bbox": [ + 76, + 462, + 328, + 479 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We evaluate our methods on conventional class incremental learning. Tabs. 6 and 7 display results on CIFAR100 and TinyImageNet, respectively. We re-implement some previous methods with a CLIP backbone (after CLIP in the table), while others using a special network design cannot be easily adapted. Although zero-shot CLIP prediction achieves a good result on these benchmarks, continual learning with direct fine-tuning or LwF [33] degrades the performance greatly, especially under the setting of a large step number. This demonstrates a severe catastrophic forgetting phenomenon in fine-tuning the CLIP model. Our method consistently improves the performance of the CLIP model on both Avg. and Last scores with a large gap towards previous ones.", + "bbox": [ + 75, + 484, + 470, + 696 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Limitation and Future Work", + "text_level": 1, + "bbox": [ + 76, + 709, + 341, + 724 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Our proposed method has a limitation that a reference dataset is needed. A promising direction of the work is to preserve the zero-shot transfer ability without the need for an outside dataset. For example, we may generate a synthetic image dataset as the reference dataset. Methods like [51] can synthesize datasets from a network.", + "bbox": [ + 75, + 734, + 468, + 824 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The deep learning community tends to build large models with a huge dataset [3, 6], including vision-language models [44, 20]. As re-training cost upsurges, continual learning is an efficient approach for updating these models with custom usage.", + "bbox": [ + 75, + 825, + 468, + 902 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/6479759bcc82c523d84cd2ef77a9de148b862d90a7cef21e31d139d08fbb221e.jpg", + "table_caption": [ + "Table 7. Comparison of different methods on TinyImageNet splits in class-incremental settings with 100 base classes." + ], + "table_footnote": [], + "table_body": "
Methods5 steps10 steps20 steps
AvgLastAvgLastAvgLast
EWC [25]19.016.0015.823.7912.354.73
EEIL [4]47.1735.1245.0334.6440.4129.72
UCIR [19]50.3039.4248.5837.2942.8430.85
MUC [35]32.2319.2026.6715.3321.8910.32
PASS [65]49.5441.6447.1939.2742.0132.93
DyTox [14]55.5847.2352.2642.7946.1836.21
CLIP [44]69.6265.3069.5565.5969.4965.30
FT61.5446.6657.0541.5454.6244.55
LwF [33]60.9748.7757.6044.0054.7942.26
iCaRL [47]77.0270.3973.4865.9769.6564.68
LwF-VR [11]77.5670.8974.1267.0569.9463.89
ZSCL (Ours)80.2773.5778.6171.6277.1868.30
Impr+10.65+8.27+9.06+6.03+7.69+3.00
", + "bbox": [ + 500, + 128, + 893, + 343 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In some cases, we want to correct wrong information in the pre-training dataset or update old information with the latest one. How to conduct this task with a reference dataset is left as future work.", + "bbox": [ + 498, + 383, + 890, + 443 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Lately, a noticeable trend involves the creation of multimodality models utilizing large language models, showcasing encouraging outcomes in tasks such as Visual Question Answering (VQA). Expanding our approach to encompass the next token prediction task remains an avenue for future exploration and research.", + "bbox": [ + 498, + 445, + 890, + 536 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 555, + 619, + 571 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we investigate continual learning with the vision-language model. We propose a better continual learning algorithm to protect the zero-shot transfer ability in the vision-language model learned in the pre-training stage. Our algorithm mitigates the catastrophic forgetting in both feature space and parameter space. In feature space, distilling the initial model on a reference dataset significantly boosts the model's performance. In parameter space, weight ensemble among different training stages alleviates the forgetting issue. We propose a more challenging Multidomain Task Incremental Learning (MTIL) benchmark to evaluate the continual learning methods better. On both conventional and new benchmarks, our method achieves state-of-the-art performance.", + "bbox": [ + 496, + 582, + 890, + 792 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 813, + 666, + 830 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Yang You's research group is being sponsored by the NUS startup grant (Presidential Young Professorship), Singapore MOE Tier-1 grant, ByteDance grant, ARCTIC grant, SMI grant, and Alibaba grant.", + "bbox": [ + 498, + 839, + 890, + 902 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "19133", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5871-5880, 2021. 2, 5, 9" + ], + "bbox": [ + 78, + 90, + 470, + 837 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "19136", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Preventing Zero-Shot Transfer Degradation in Continual Learning of Vision-Language Models/438697ca-0d24-4663-a1e4-f11b5f684ada_model.json b/2023/Preventing Zero-Shot Transfer Degradation in Continual Learning of Vision-Language Models/438697ca-0d24-4663-a1e4-f11b5f684ada_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0632ebf13dcfec6f758cddd9676a86c9fe78c6f2 --- /dev/null +++ b/2023/Preventing Zero-Shot Transfer Degradation in Continual Learning of Vision-Language Models/438697ca-0d24-4663-a1e4-f11b5f684ada_model.json @@ -0,0 +1,2567 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.048 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.136, + 0.131, + 0.838, + 0.177 + ], + "angle": 0, + "content": "Preventing Zero-Shot Transfer Degradation in Continual Learning of Vision-Language Models" + }, + { + "type": "text", + "bbox": [ + 0.115, + 0.203, + 0.848, + 0.245 + ], + "angle": 0, + "content": "Zangwei Zheng\\(^{1}\\) Mingyuan Ma\\(^{2}\\) Kai Wang\\(^{1}\\) Ziheng Qin\\(^{1}\\) Xiangyu Yue\\(^{3}\\) Yang You\\(^{1}\\) \n\\(^{1}\\)National University of Singapore \\(^{2}\\)UC Berkeley \\(^{3}\\)The Chinese University of Hong Kong" + }, + { + "type": "text", + "bbox": [ + 0.104, + 0.251, + 0.867, + 0.269 + ], + "angle": 0, + "content": "\\(^{1}\\) {zangwei, kai.wang, zihengq, youy} \\(@\\) comp.nus.edu.sg \\(^{2}\\)mamingyuan2001@berkeley.edu \\(^{3}\\)xyyue@ie.cuhk.edu.hk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.303, + 0.314, + 0.318 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.474, + 0.772 + ], + "angle": 0, + "content": "Continual learning (CL) can help pre-trained vision-language models efficiently adapt to new or under-trained data distributions without re-training. Nevertheless, during the continual training of the Contrastive Language-Image Pre-training (CLIP) model, we observe that the model's zero-shot transfer ability significantly degrades due to catastrophic forgetting. Existing CL methods can mitigate forgetting by replaying previous data. However, since the CLIP dataset is private, replay methods cannot access the pre-training dataset. In addition, replaying data of previously learned downstream tasks can enhance their performance but comes at the cost of sacrificing zero-shot performance. To address this challenge, we propose a novel method ZSCL to prevent zero-shot transfer degradation in the continual learning of vision-language models in both feature and parameter space. In the feature space, a reference dataset is introduced for distillation between the current and initial models. The reference dataset should have semantic diversity but no need to be labeled, seen in pre-training, or matched image-text pairs. In parameter space, we prevent a large parameter shift by averaging weights during the training. We propose a more challenging Multi-domain Task Incremental Learning (MTIL) benchmark to evaluate different methods, where tasks are from various domains instead of class-separated in a single dataset. Our method outperforms other methods in the traditional class-incremental learning setting and the MTIL by \\(9.7\\%\\) average score. Our code locates at https://github.com/Thunderbee/ZSCL." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.801, + 0.21, + 0.816 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Most deep learning models can access all the data during training [27, 16, 12]. If we want to expand a model's knowledge, such as learning a newly found animal species [41], we can re-train the model by adding new classes to the training dataset. However, re-training a large model is" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.302, + 0.875, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.365, + 0.875, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.505, + 0.476, + 0.89, + 0.488 + ], + "angle": 0, + "content": "(a) Comparison between traditional CL and CL with a pre-trained vision-language model" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.494, + 0.688, + 0.617 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.709, + 0.494, + 0.877, + 0.617 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.618, + 0.687, + 0.72 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.618, + 0.877, + 0.72 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.529, + 0.723, + 0.864, + 0.734 + ], + "angle": 0, + "content": "(b) Performance of different methods on preventing forgetting phenomenon" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.746, + 0.894, + 0.83 + ], + "angle": 0, + "content": "Figure 1. a) Conventional CL learns distinct task-specific heads, while CL with vision-language models can predict both learned tasks and out-of-distribution tasks. b) Accuracy (\\%) changes during CL of four datasets on 11 datasets. Our method is superior to others in preventing the forgetting of both zero-shot transfer ability and new knowledge." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.893, + 0.901 + ], + "angle": 0, + "content": "costly. In contrast, continual learning (CL) [33, 47] incrementally learns task one after another. It can reduce" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19125" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.182 + ], + "angle": 0, + "content": "this cost by only learning the new data, thereby presenting itself as an efficient alternative to conventional learning methods [43, 34, 5]. Nonetheless, a model tends to forget previous information catastrophically when learning new tasks [47, 33, 59]. The \"catastrophic forgetting\" phenomenon is a great challenge for CL." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.186, + 0.474, + 0.502 + ], + "angle": 0, + "content": "Recently, vision-language models have shown powerful zero-shot transfer ability [44, 23, 32]. They can give zero-shot predictions without any training examples of a task. However, the performance on some tasks is poor due to insufficient relevant image-text pairs in the pre-training datasets. For example, it is difficult for CLIP [44] to distinguish among digital numbers, with an accuracy on MNIST [8] below \\(60\\%\\) much lower than a naively trained CNN [29]. If we want to widen the knowledge in the vision-language model by re-training, the computational cost is too large (e.g., CLIP is pretrained on 400 million image-text pairs). Fine-tuning downstream tasks achieves high performance, but one model for a task takes much memory, and the model is not reusable. Prompt learning [64, 63] keeps the backbone parameters unchanged. However, it is only effective with limited training data due to a limited prompt length [64, 24]. In contrast, continual learning makes learning new knowledge a lifelong process for the vision-language model. The continually learned model can handle any image-text input and can be further used for downstream tasks [11, 53]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.471, + 0.748 + ], + "angle": 0, + "content": "We find that existing CL methods hardly prevent the forgetting phenomenon for zero-shot transfer ability in continual learning of a pre-trained vision-language model. As shown in Fig. 1 (a), the CL with a pre-trained vision-language model differs from the traditional one. Besides forgetting previously learned task knowledge, the CLIP-based CL suffers from forgetting pre-training knowledge, namely a degradation of zero-shot transfer ability. For the replay-based CL methods [47, 50, 36, 21, 28, 42], the dataset during pre-training may be private and inaccessible during fine-tuning. For distillation-based CL methods [33, 10, 13, 11], they do not lay enough emphasis on the pre-trained model. On the one hand, a large model state change hinders tasks thereafter from using high-quality feature representations. On the other hand, it significantly degrades zero-shot performance on unseen datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Our method ZSCL protects the Zero-Shot transfer ability during Continual Learning. We view the knowledge stored in the pre-training model from two perspectives: a well-learned feature space and a good value in the parameter space. In feature space, we re-design previous distillation loss [18, 47] with different loss styles, teacher models, and data sources. We find the original CLIP model, as opposed to the newly acquired model, is the best option for the teacher model. Instead of using data collected from previous tasks [47] or current task [18], we find a reference" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.288 + ], + "angle": 0, + "content": "dataset with diverse semantics (e.g., images sampled from ImageNet) is a good option for distillation loss. The reference images need not be labeled or matched with the text. Preserving the relative similarity between reference images and texts makes the feature space deviate little from the original. In the parameter space, WiSE-FT [58] proposes interpolating the initial and fine-tuned model for better performance. Inspired by this, we ensemble the weights throughout continuous training to prevent a significant shift from the initial CLIP, which can be seen as interpolating models of different zero-shot transfer and downstream task performance tradeoffs. The weight ensemble method is more stable and not sensitive to hyper-parameters." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.893, + 0.544 + ], + "angle": 0, + "content": "To better evaluate our method, we propose a new benchmark Multi-domain Task Incremental Learning (MTIL). Previous CL tasks are crafted by separating classes in one dataset [14, 60, 65], where the images and classes are within a single domain. In contrast, MTIL consists of data from different sources requiring different expert knowledge. It comprises 11 tasks ranging from animal species to aircraft series recognition. As displayed in Fig. 1 (b), when sequentially training CLIP on 11 datasets, the drop in the performance of task \\( i \\) after training task \\( i \\) is the traditional forgetting phenomenon. The degradation in the accuracy compared to the original zero-shot one before training task \\( i \\) represents the forgetting in zero-shot transfer ability. Our method better protects the zero-shot transfer ability and preserves the learned knowledge. We outperform previous methods in both conventional class-incremental learning and MTIL settings. In Fig. 1 (b)," + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.545, + 0.836, + 0.559 + ], + "angle": 0, + "content": "To summarize, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.57, + 0.892, + 0.645 + ], + "angle": 0, + "content": "- We investigate continual training with the vision-language model and demonstrate the importance of preserving zero-shot transfer ability. A more challenging benchmark MTIL is proposed to evaluate CL methods where the tasks come from distinct domains." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.656, + 0.892, + 0.716 + ], + "angle": 0, + "content": "- We propose a novel method ZSCL to mitigate the catastrophic forgetting problem in continual learning of the vision-language model by distillation in the feature space and weight ensemble in the parameter space." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.726, + 0.892, + 0.831 + ], + "angle": 0, + "content": "- The proposed ZSCL outperforms all state-of-the-art methods across multiple benchmark datasets. On 10 steps CL of CIFAR100 and TinyImageNet, our method outperforms the best of previous ones by \\(7.7\\%\\) and \\(6.0\\%\\) for the Last accuracy. On MTCL, ZSCL outperforms others by \\(10.9\\%\\) on Transfer and \\(9.7\\%\\) on Avg. scores." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.57, + 0.892, + 0.831 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.845, + 0.642, + 0.861 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Vision-Language Models. Inspired by the success of language foundation models such as GPT-3 [3] and T5 [45], a" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19126" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.304 + ], + "angle": 0, + "content": "series of work pre-train vision-language models on large-scale image-text datasets [31, 44, 23]. Among them, Contrastive Language-Vision Pre-training [44] achieves remarkable performance on various downstream tasks. It concentrates on aligning images and texts to acquire a joint embedding space. The CLIP model contains an image encoder [16, 12] and a text encoder [9]. During pre-training, contrastive learning is performed in which a paired image-text is a positive pair while image and text from different image-text pairs form a negative pair. For inference, the closest text embedding for the image is chosen as the prediction. Vision-language models can give zero-shot predictions on unseen tasks with a robust zero-shot transfer ability on various downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.323, + 0.473, + 0.732 + ], + "angle": 0, + "content": "Continual Learning Methods. Most existing continual learning methods can be categorized into four groups: parameter expansion, memory replay, distillation loss, and parameter regularization. Parameter expansion methods such as DyTox [14] and DEN [61] introduce new parameters for new tasks. As we want to achieve a more powerful CLIP model at the end of CL, we do not change the architecture of the CLIP model. Memory replay methods [50, 36, 42, 28, 40] including iCaRL [47] and SER [21] keep a memory for exemplars from previously learned tasks. However, pre-training datasets are too large for choosing exemplars or may not be available at downstream training, and downstream data are not good exemplars for preserving the pretraining knowledge. Distillation loss such as LwF [33], LwM [10], LwF-VR [11], and PodNet [13] aligns current output space with previous ones, whereas distillation based on current tasks are not strong enough to maintain foundational knowledge. For the CLIP model, we find that general images, even if never seen by the model, plus sentences with enough semantics, can be a good \"replay\" for the distillation loss. The parameter regularization loss restricts the flexibility of model parameters by training loss [25, 62, 1] or weight averaging [30, 58]. Although this type of strategy performs badly compared to other ways in previous research [55, 2], we found it helpful for CLIP continual learning. The limited parameter space prevents the model from diverging significantly from its original state." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Vision-Language Models for Downstream Tasks. Many works propose different training strategies of vision-language models for better performance on downstream tasks, such as CoOp [64], CLIP-Adapter [15] and WiSE-FT [58]. However, very few attempts at continual learning exist. While [52, 56] focus on CL in the pretrain of VL and [39] trains VL from scratch using a small dataset, our problem setting differs as we address CL in downstream tasks with a pretrained VL. Currently, most VL models are trained directly on an accessible large" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.321 + ], + "angle": 0, + "content": "dataset, yet integrating knowledge continuously into a pretrained VL is a practical necessity. None of these studies address the zero-shot transfer degradation phenomenon, instead focusing on the traditional forgetting of learned knowledge. Recently, Thengane et al. [53] shows CLIP zero-shot prediction achieves state-of-the-art performance in CL settings even without any training. LwF-VR [11] is a modified LwF method for the CLIP model where random-generated sentences are used for distillation loss. However, it only considers the feature space, and the distillation with random sentences cannot protect the vision backbone. Differently, we re-examine what should be used for distillation in the feature space and combine the parameter space weight ensemble to provide better performance for the vision-language model continual learning." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.33, + 0.611, + 0.347 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.354, + 0.642, + 0.37 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.377, + 0.895, + 0.514 + ], + "angle": 0, + "content": "Continual Learning. Given \\( n \\) tasks \\( [\\mathcal{T}^1, \\mathcal{T}^2, \\dots, \\mathcal{T}^n] \\), continual training is conducted in sequence on each task \\( \\mathcal{T}^i = (\\mathcal{D}^i, C^i) \\), \\( i = 1, \\dots, n \\). Here, \\( \\mathcal{D}^i \\) represents the task dataset \\( \\{(x_j^i, y_j^i)\\}_{j=1}^{N_i} \\), where \\( x_j^i \\) is an image, \\( y_j^i \\) is a one-hot vector indicating the ground truth, and \\( N_i \\) is the number of images in the dataset. Class names \\( C^i = \\{c_j^i\\}_{j=1}^{m_i} \\) maps the label of an image to an object name, where \\( m_i \\) is the number of classes for task \\( \\mathcal{T}^i \\). The objective of continual learning is to achieve good performance on all tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.514, + 0.895, + 0.621 + ], + "angle": 0, + "content": "Two continual learning settings are focused on in this study [55]. In task-incremental learning, at inference, the image \\( \\pmb{x} \\) to be predicted is given with its task identity \\( t \\), so the model only needs to distinguish between different classes in \\( C^t \\). In class-incremental learning, the task identity \\( t \\) is not given. Thus we need to predict with the combined class set \\( C = \\bigcup_{i=1}^{n} C^i \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.637, + 0.895, + 0.788 + ], + "angle": 0, + "content": "CLIP model. The CLIP model contains an image encoder \\( f_{i} \\) and a text encoder \\( f_{t} \\). The inference process of the CLIP model for image classification is as follows. First, for task \\( \\mathcal{T}^i \\), each class \\( c \\) is transformed into a sentence by a template like \"a photo of \\( \\{c\\} \\)\". Then \\( f_{t} \\) encodes the classes into text embeddings \\( \\{\\pmb{t}_{j}^{i}\\}_{j = 1}^{m_{i}} \\). An image encoder encodes input image \\( \\pmb{x}_k \\). The similarity score between the image embedding and text embeddings are calculated as \\( s_{k,j}^{i} = \\langle f_{i}(\\pmb{x}_{k}),\\pmb{t}_{j}^{i}\\rangle \\) where \\( \\langle \\cdot ,\\cdot \\rangle \\) denotes the cosine similarity. The class with the largest similarity score is the prediction for the image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.788, + 0.895, + 0.834 + ], + "angle": 0, + "content": "To fine-tune the CLIP model for downstream tasks, cross-entropy loss CE is applied to the similarity score with a temperature scaling:" + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.839, + 0.892, + 0.881 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {C E}} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathrm {C E} (\\tau \\cdot \\boldsymbol {s} _ {i}, \\boldsymbol {y} _ {i}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.862, + 0.902 + ], + "angle": 0, + "content": "where \\(\\tau\\) is a parameter learned during the pre-training." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19127" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.083, + 0.094, + 0.48, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.498, + 0.094, + 0.895, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.27, + 0.895, + 0.327 + ], + "angle": 0, + "content": "Figure 2. Illustration of ZSCL in feature space. Fig. 3(a) shows the pipeline of distillation. The original and the current model encode the reference images and texts, respectively. The probability distribution of images and texts with respect to each other is distilled. Fig. 3(b) displays how distillation loss preserves the feature space. Compared with the reference dataset, the features of fine-tuning tasks lie in a small subspace. The distillation loss preserves the structure of the feature space by maintaining relative distances." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.352, + 0.332, + 0.369 + ], + "angle": 0, + "content": "3.2. Distillation in Feature Space" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.375, + 0.47, + 0.51 + ], + "angle": 0, + "content": "Well-learned feature space for aligned images and texts enables vision-language models' strong zero-shot transfer ability. It also facilitates the learning of downstream tasks. Compared with the pre-training dataset, downstream datasets lie in a small scope in the feature space (shown in Fig. 2(b)). Direct fine-tuning of downstream tasks greatly distorts the feature distribution of out-of-distribution data, which leads to a significant drop in zero-shot prediction performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.511, + 0.47, + 0.587 + ], + "angle": 0, + "content": "While the cross-entropy improves the performance by altering fine-tuned feature subspace, we need a new regularization to preserve the potential out-of-distribution feature space. The relative similarity between one image and different texts is:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.6, + 0.47, + 0.617 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {p} = \\operatorname {S o f t m a x} \\left(\\boldsymbol {s} _ {1}, \\dots , \\boldsymbol {s} _ {m}\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.47, + 0.687 + ], + "angle": 0, + "content": "We hope the above similarity distribution is stable during fine-tuning for all potential images and texts. Given a teacher model \\(\\overline{f}\\), distillation loss can be applied to penalize changes from the original distribution:" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.699, + 0.47, + 0.739 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {d i s t . i m g}} = \\operatorname {C E} (\\boldsymbol {p}, \\bar {\\boldsymbol {p}}) = - \\sum_ {j = 1} ^ {m} \\boldsymbol {p} _ {j} \\cdot \\log \\bar {\\boldsymbol {p}} _ {j}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.75, + 0.439, + 0.765 + ], + "angle": 0, + "content": "where \\(\\overline{\\pmb{p}}\\) is the distribution given by the teacher model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.84 + ], + "angle": 0, + "content": "Although the distillation form has been widely used in previous methods [18, 33, 47], they are applied to continual learning from scratch. We investigate different components of the distillation loss for enhancing pre-trained vision-language models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Three components are discussed in this paper in detail: the data source, the teacher model, and the loss design. Sec. 5.1 shows the performance for the different choices. First, for the data source, LwF [33] uses data from the cur" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.353, + 0.892, + 0.565 + ], + "angle": 0, + "content": "rent task, while iCarl [47] carefully selects data from previous tasks. However, data from downstream tasks span a small subspace and are not good enough to preserve the whole feature space. An ideal choice is the pre-training dataset. However, the CLIP pre-training dataset is private, and the size is too large to load. To solve this challenge, we introduce the reference dataset. A reference dataset is a publicly available image dataset with enough semantics. Enough semantics can be seen as random sampling in the whole feature space. The texts can be related class names, unrelated sentences, or even random tokens. This is because text semantics are easier to sample, and we need not ground truth to calculate the distance between one image to sufficient text samples spread among feature space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.713 + ], + "angle": 0, + "content": "For the teacher model, [33, 47] use the model after learning task i-1 and before learning task i as the teacher model. During the continual training of the vision-language model, the feature space deviates gradually from the initial model. Using fine-tuned models as teacher models enlarges this change. In contrast, we find using the pre-trained model as a teacher model not only preserves the zero-shot transfer ability but also takes advantage of well-learned feature space for better downstream performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.726, + 0.892, + 0.848 + ], + "angle": 0, + "content": "Finally, previous distillation loss is applied on traditional backbones, where a classification head gives the probability for different labels. For the vision-language model, the probability is calculated based on the relative distance between images and texts. Thus, in addition to Eq. (3), we impose regularization \\(\\mathcal{L}_{\\mathrm{dist\\_txt}}\\) on the distances from a text to a batch of images. The whole framework is shown in Fig. 2 (a) with the following training loss:" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {c e}} + \\lambda \\cdot \\left(\\mathcal {L} _ {\\mathrm {l w f . i m g}} + \\mathcal {L} _ {\\mathrm {l w f . t x t}}\\right). \\tag {4}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19128" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.116, + 0.088, + 0.434, + 0.264 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.273, + 0.473, + 0.345 + ], + "angle": 0, + "content": "Figure 3. Models during training contain different tradeoffs between zero-shot and new task performance. Points for FT are sampled every 100 iterations, and the ones for WiSE-FT means different \\(\\alpha\\) choices. WE ensembles models during training and achieve better performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.367, + 0.405, + 0.385 + ], + "angle": 0, + "content": "3.3. Weight Ensemble in Parameter Space" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.391, + 0.471, + 0.466 + ], + "angle": 0, + "content": "Machine learning models integrate learned knowledge in their parameters. To mitigate the forgetting problem, a series of works [25, 62, 1] impose regularization losses on the changes of parameters. Weight consolidation (WC) [25] imposes the following loss:" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.475, + 0.47, + 0.507 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {W C}} = \\sum_ {i} \\left(\\theta_ {i} - \\bar {\\theta} _ {i}\\right) ^ {2}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.47, + 0.578 + ], + "angle": 0, + "content": "where \\(\\theta\\) is the parameters of the current model, and \\(\\overline{\\theta}\\) is the reference ones. Although this regularization prevents forgetting, it hinders learning new tasks in a challenging CL setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.579, + 0.47, + 0.684 + ], + "angle": 0, + "content": "Apart from regularization losses, another method in parameter space is to ensemble different model weights. Model soup [57] averages weights of multiple fine-tuned models to improve the model's robustness but introduces additional training costs. WiSE-FT [58] propose a weighted average between fine-tuned model and the original model to improve the out-of-distribution prediction robustness:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.694, + 0.47, + 0.71 + ], + "angle": 0, + "content": "\\[\nf (x; (1 - \\alpha) \\cdot \\theta_ {0} + \\alpha \\cdot \\theta_ {1}), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.796 + ], + "angle": 0, + "content": "where \\(\\theta_0\\) is the original model and \\(\\theta_{1}\\) is the fine-tuned one. However, this method is hyper-parameter-sensitive where different \\(\\alpha\\) gives different tradeoffs between zero-shot transfer ability and downstream task performance (blue line in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Inspired by this, we extend the weighted average to the CL setting. The motivation for the weighted average is to prevent fine-tuning from losing too much knowledge in the original model. As training goes by (green line in Fig. 3), the model performs better on new tasks while losing accuracy on previous ones. The models among training compose a sequence of different learning-forgetting tradeoffs." + }, + { + "type": "image_caption", + "bbox": [ + 0.511, + 0.093, + 0.525, + 0.103 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.109, + 0.58, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.594, + 0.109, + 0.667, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.189, + 0.577, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.596, + 0.189, + 0.668, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.685, + 0.093, + 0.7, + 0.103 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.686, + 0.105, + 0.892, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.299, + 0.894, + 0.342 + ], + "angle": 0, + "content": "Figure 4. Fig.(a): examples of tasks from different domains in MTIL benchmark. Fig.(b): illustration of calculating metrics Transfer, Avg. and Last during continual learning." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.366, + 0.893, + 0.412 + ], + "angle": 0, + "content": "Instead of interpolating only between the initial and the final model, our method weight ensemble (WE) averages the weights in the sequence during the training time:" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.42, + 0.892, + 0.462 + ], + "angle": 0, + "content": "\\[\n\\hat {\\theta} _ {t} = \\left\\{ \\begin{array}{l l} \\theta_ {0} & t = 0 \\\\ \\frac {1}{t + 1} \\theta_ {t} + \\frac {t}{t + 1} \\cdot \\hat {\\theta} _ {t - 1} & \\text {e v e r y I i t e r a t i o n s} \\end{array} . \\right. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.47, + 0.892, + 0.621 + ], + "angle": 0, + "content": "where model weight sampling happens every \\(I\\) iteration. The method is related to Stochastic Weight Averaging (SWA) [22], but we do not use a modified learning rate schedule here because instead of getting better generalization ability, WE aim to give an improved learning-forgetting tradeoff. As shown in Fig. 3, WE achieves better performance on downstream tasks than WiSE-FT. In addition, while WiSE-FT is sensitive to different values of \\(\\alpha\\), our method is much more robust under different hyperparameter \\((I)\\) choices." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.634, + 0.875, + 0.651 + ], + "angle": 0, + "content": "4. Multi-domain Task Incremental Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Conventional Continual Learning Benchmark. A benchmark consisting of several tasks is needed to evaluate different methods for continual learning. Most previous benchmarks are built by separating classes in a single dataset, such as MNIST [55], CIFAR100 [14], TinyImageNet [60], and ImageNet [60, 65]. We also evaluate our method with traditional benchmarks. In CIFAR100 [26], classes are separated into groups to build tasks. Suppose the dataset has \\( m \\) classes, a \\( k \\)-step setting means we learn \\( m / k \\) classes in each new task. The CIFAR100 contains 100 classes, and the setting of 10, 20, and 50 steps are visited. For TinyImageNet with \\( m = 200 \\), the first step learns 100 classes, and the rest is learned with 5, 10, and 20 steps. As for ImageNet-100, we have two settings: ImageNet-100-B0, which includes the same amount of classes for each step, and ImageNet-100-B50, which has" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19129" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.121 + ], + "angle": 0, + "content": "Table 1. Ablation experiments. Default settings are marked in gray, which uses image and text distillation loss with the initial CLIP model on 100k ImageNet images and texts generated from ImageNet classes with a simple template." + }, + { + "type": "table_caption", + "bbox": [ + 0.127, + 0.131, + 0.28, + 0.144 + ], + "angle": 0, + "content": "(a) Continual learning loss." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.147, + 0.337, + 0.226 + ], + "angle": 0, + "content": "
lossTransferAvg.Last
CE only44.655.977.3
Feat. Dist.47.658.777.1
Image-only56.568.982.1
Text-only56.769.082.6
Both56.869.283.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.151, + 0.227, + 0.257, + 0.238 + ], + "angle": 0, + "content": "(d) Teacher model." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.242, + 0.342, + 0.309 + ], + "angle": 0, + "content": "
sourceTransferAvg.Last
Initial56.869.283.0
n-153.966.680.7
WiSE(0.5)56.468.982.9
WiSE(0.8)56.267.881.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.406, + 0.131, + 0.56, + 0.144 + ], + "angle": 0, + "content": "(b) Data sources for replay." + }, + { + "type": "table", + "bbox": [ + 0.368, + 0.148, + 0.621, + 0.225 + ], + "angle": 0, + "content": "
sourceTransferAvg.Last
current56.766.580.2
ImageNet56.869.283.0
CC57.268.580.9
CIFAR10055.265.980.7
Flowers54.766.080.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.418, + 0.226, + 0.548, + 0.239 + ], + "angle": 0, + "content": "(e) # images for replay." + }, + { + "type": "table", + "bbox": [ + 0.368, + 0.242, + 0.621, + 0.308 + ], + "angle": 0, + "content": "
#imageTransferAvg.Last
1M58.770.183.2
100k56.869.283.0
10k57.868.781.2
1k56.367.680.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.687, + 0.131, + 0.838, + 0.144 + ], + "angle": 0, + "content": "(c) Text sources for replay." + }, + { + "type": "table", + "bbox": [ + 0.647, + 0.148, + 0.9, + 0.225 + ], + "angle": 0, + "content": "
sourceTransferAvg.Last
current51.864.982.0
prev. all54.070.283.7
1k classes (IN)56.869.283.0
13k Sent. (CC)58.970.584.0
1k Rand. Sent.58.770.283.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.68, + 0.226, + 0.845, + 0.239 + ], + "angle": 0, + "content": "(f) # image classes for replay." + }, + { + "type": "table", + "bbox": [ + 0.647, + 0.242, + 0.9, + 0.308 + ], + "angle": 0, + "content": "
#classTransferAvg.Last
100056.867.683.0
10056.767.382.3
1053.866.481.0
153.165.580.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.098, + 0.332, + 0.449, + 0.347 + ], + "angle": 0, + "content": "Table 2. Ablation study of different components for ZSCL." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.358, + 0.475, + 0.484 + ], + "angle": 0, + "content": "
MethodTransferΔAvg.ΔLastΔ
CLIP ViT-B/16@224px
Zero-shot69.40.065.30.065.30.0
Continual Learning44.6-24.855.9-9.477.3+12.0
+ Distillation58.9-10.570.5+5.283.8+18.5
+ WiSE-FT (best α)61.7-7.771.6+6.383.3+18.0
+ WE (ZSCL*)62.2-7.272.6+7.384.5+19.2
+ WC67.6-1.874.5+9.283.2+17.9
+ WiSE-FT67.7-1.774.2+8.981.9+16.6
+ WE (ZSCL)68.1-1.375.4+10.183.6+18.3
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.51, + 0.471, + 0.571 + ], + "angle": 0, + "content": "50 classes for the first step, and the remaining 50 classes are observed progressively over the next 10 stages. For ImageNet [7], we investigate a 10-step setting, which learns 100 new classes per task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.592, + 0.471, + 0.851 + ], + "angle": 0, + "content": "MTIL Benchmark. Different classes from one dataset share the common image source and a similar style [48, 17]. Thus, we propose Multi-domain Task Incremental Learning (MTIL), a cross-domain version of task incremental learning. Different tasks are collected from different domains, requiring different domain knowledge for humans to achieve high accuracy. Our MTIL benchmark consists of 11 tasks (detailed in supplementary materials), as some of the tasks illustrated in Fig. 4 (a). The MTIL benchmark is very challenging with a total number of 1,201 classes. Two orders are used for the evaluation; the first one is alphabet order (Order-I): Aircraft, Caltech101, CIFAR100, DTD, EuroSAT, Flowers, Food, MNIST, OxfordPet, StanfordCars, SUN397. And the second one is a random order (Order-II): StanfordCars, Food, MNIST, OxfordPet, Flowers, SUN397, Aircraft, Caltech101, DTD, EuroSAT, CIFAR100. Experiments are done in Order I by default." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Evaluation Metrics. The metrics of MTIL are illustrated in Fig. 4(b), where rows represent training steps and a" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.334, + 0.895, + 0.562 + ], + "angle": 0, + "content": "column shows performance for one dataset. For conventional continual learning, only scores under the diagonal are meaningful, since they cannot give zero-shot predictions on unseen tasks. In contrast, the zeros-hot transfer ability enables a vision-language model to provide predictions for all datasets. The average accuracy on all datasets among all timestamps is the \"Avg\" metric. The \"Last\" metric is the average performance of all tasks after CL. The \"Transfer\" metric is the average task performance in the upper-right triangle of the matrix. Every task's performance is first averaged to equal the weight of each dataset. It measures to what extent the zero-shot transfer ability is preserved. Before learning task \\( i \\), tasks not earlier than \\( i \\) are not finetuned. Thus, their performance is an indicator of zero-shot transfer ability." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.576, + 0.634, + 0.594 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.602, + 0.894, + 0.724 + ], + "angle": 0, + "content": "Implementation. We use CLIP [44] model with image encoder ViT-B/16 [12]. We conduct training with AdamW [37] optimizer and use a label smoothing [38] technique for a better baseline result. For multi-domain task continual learning, we train 1K iterations for each task, while for class-incremental learning, we follow the same evaluation setting in [14]. More implementation details can be found in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.735, + 0.663, + 0.751 + ], + "angle": 0, + "content": "5.1. Main Properties" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.758, + 0.892, + 0.805 + ], + "angle": 0, + "content": "We ablate our method in feature-space in Tab. 1, and different choices for parameter-space regularization in Tab. 2. Several interesting characteristics are noted." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Continual learning loss. In Tab. 1a, several types of loss for feature space are tested. The Feature Distance penalizing absolute distances achieves a low accuracy. Distillation loss on probability distribution regularizes relative distance in the feature space. With image-only or text-only distilla" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19130" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.092, + 0.245, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.249, + 0.092, + 0.406, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.41, + 0.092, + 0.568, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.572, + 0.092, + 0.729, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.733, + 0.092, + 0.887, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.216, + 0.893, + 0.245 + ], + "angle": 0, + "content": "Figure 5. t-SNE on five models' outputs together of Aircraft datasets after MTCL training: only our model maintains a similar feature distribution to the original CLIP ones with minor shift, while the rest significantly distort the feature space." + }, + { + "type": "table_caption", + "bbox": [ + 0.086, + 0.269, + 0.461, + 0.284 + ], + "angle": 0, + "content": "Table 3. Comparison of different methods on MTIL in Order I." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.294, + 0.472, + 0.427 + ], + "angle": 0, + "content": "
MethodTransferΔAvg.ΔLastΔ
CLIP ViT-B/16@224px
Zero-shot69.40.065.30.065.30.0
Continual Learning44.6-24.855.9-9.477.3+12.0
LwF [33]56.9-12.564.7-0.674.6+9.0
iCaRL [47]50.4-19.065.7+0.480.1+14.8
LwF-VR [11]57.2-12.265.1-0.276.6+11.3
WiSE-FT [58]52.3-17.160.7-4.677.7+12.4
ZSCL* (Ours)62.2-7.272.6+7.384.5+19.2
ZSCL (Ours)68.1-1.375.4+10.183.6+18.3
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.452, + 0.47, + 0.497 + ], + "angle": 0, + "content": "tion, the Transfer, Avg., and Last accuracy all improve. A further boost in performance occurs with both of the distillation losses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.47, + 0.779 + ], + "angle": 0, + "content": "Data source for replay. Tabs. 1b, 1c, 1e and 1f seek the standard for a good reference dataset. As shown in Tab. 1b, distillation on images of current tasks achieves a good Transfer score. However, it hinders the learning on new tasks and results in a low Avg. and Last score. Images in a specific domain (e.g., Flowers) are also not good choices. General images in ImageNet and Conceptual Caption (CC) datasets are examples of good reference datasets. These images are easily available by a web crawler [54]. Text with more semantics can improve performance (shown in Tab. 1c). When using sentences from the Conceptual Caption dataset [49], or even sentences randomly generated from the CLIP vocabulary, there is no ground truth target among the texts for the image from the ImageNet dataset. However, they all achieve an improvement due to more semantics. The reference image dataset does not need to be labeled, matched with the text, or seen by the CLIP model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Enough semantics in the reference image dataset boosts the distillation performance. In Tabs. 1e and 1f, a smaller number of images and classes all lead to a degradation in the performance. Fewer classes of images in the reference dataset have a worse impact on the performance compared with the image numbers. To keep a reasonable memory buffer, we randomly sample \\(100\\mathrm{k}\\) images from ImageNet for MTIL and use texts from CC dataset. For class-" + }, + { + "type": "table_caption", + "bbox": [ + 0.506, + 0.269, + 0.885, + 0.284 + ], + "angle": 0, + "content": "Table 4. Comparison of different methods on MTIL in Order II." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.294, + 0.895, + 0.427 + ], + "angle": 0, + "content": "
MethodTransferΔAvg.ΔLastΔ
CLIP ViT-B/16@224px
Zero-shot65.40.065.30.065.30.0
Continual Learning46.6-18.856.2-9.167.4+2.1
LwF [33]53.2-12.262.2-5.271.9+6.6
iCaRL [47]50.9-14.556.9-8.471.6+6.3
LwF-VR [11]53.1-12.360.6-7.468.3+0.9
WiSE-FT [58]51.0-14.461.5-5.972.2+6.9
ZSCL*59.8-5.671.8+6.583.3+18.0
ZSCL64.2-1.274.5+9.283.4+18.1
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.453, + 0.892, + 0.484 + ], + "angle": 0, + "content": "incremental learning, conceptual caption dataset's validation set (28k images) is used to avoid information leakage." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.503, + 0.893, + 0.655 + ], + "angle": 0, + "content": "Teacher model. Tab. 1d shows the performance of distillation loss with different teacher models. Unlike conventional continual learning, the teacher model should not be the one trained on the previous task; otherwise, the deviation from the initial CLIP in the previous task may be amplified. In contrast, with the initial CLIP as the teacher model, not only is the zero-shot performance improved but the Mean and Last scores are also boosted, indicating that preserving high-quality feature space facilitates continual learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Parameter-space regularization. In Tab. 2, we experiment with three different parameter-space regularizations. We experiment with two variants of WiSE-FT [58]: the weighted average between the current model with the initial CLIP or the one at the previous task. The result shows the latter one is a better choice because keeping weight averaging with initial CLIP loses the newly learned knowledge. We experiment with different \\(\\alpha\\) choices for WiSE, and the best result is reported. While distillation loss improves the whole performance, the parameter-space regularization further protects the zero-shot transfer ability with a higher Transfer. Among the three parameter-space regularizations, only WE achieve a better Last score. WC greatly improves the Transfer scores with a lower Last score. A combination of the weight consolidation loss with weight" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19131" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.175, + 0.089, + 0.794, + 0.104 + ], + "angle": 0, + "content": "Table 5. Transfer, Avg., and Last scores (%) of different continue training methods on MTIL benchmark." + }, + { + "type": "table", + "bbox": [ + 0.108, + 0.115, + 0.865, + 0.562 + ], + "angle": 0, + "content": "
MethodAircraftCaltech101CIFAR100DTDEuroSATFlowersFoodMNISTOxfordPetCarsSUN397
CLIP ViT-B/16@224px
Zero-shot24.388.468.244.654.971.088.559.489.064.765.2
Fine-tune62.095.189.679.598.997.592.799.694.789.681.8
Transfer
Continual-FT67.146.032.135.635.057.744.160.820.546.6
LwF [33]74.556.939.151.152.672.860.675.130.355.9
iCaRL [47]56.644.632.739.346.668.046.077.431.960.5
LwF-VR [11]77.161.040.545.354.474.647.976.736.358.6
WiSE-FT [58]73.555.635.641.547.068.353.969.326.851.9
Dist. only80.162.240.239.958.180.853.474.638.161.9
ZSCL*78.364.042.945.263.584.256.178.944.164.3
ZSCL86.067.445.450.469.187.661.886.860.166.8
Avg.
Continual-FT25.581.559.153.264.751.863.264.369.731.849.7
LwF [33]36.386.972.059.073.760.073.674.880.037.358.1
iCaRL [47]35.589.272.260.668.870.078.262.381.841.262.5
LwF-VR [11]29.687.774.459.572.463.677.066.781.243.760.7
WiSE-FT [58]26.786.564.357.165.758.771.170.575.836.954.6
Dist. only48.190.679.863.275.672.584.770.279.846.963.7
ZSCL*50.790.979.863.876.677.387.071.983.052.065.9
ZSCL45.192.080.164.379.581.689.675.288.964.768.0
Last
Continual-FT31.089.365.867.388.971.185.699.692.977.381.1
LwF [33]26.387.571.966.679.966.983.899.692.166.180.4
iCaRL [47]35.893.077.070.283.388.590.486.793.281.281.9
LwF-VR [11]20.589.872.367.685.573.885.799.693.173.380.9
WiSE-FT [58]27.290.868.068.986.974.087.699.692.677.881.3
Dist. only43.391.981.372.495.190.590.499.792.585.181.8
ZSCL*46.092.381.272.493.092.190.899.693.386.681.7
ZSCL40.692.281.370.594.890.591.998.793.985.380.2
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.587, + 0.471, + 0.649 + ], + "angle": 0, + "content": "ensemble achieves a better tradeoff between Transfer and Last value. While \\(\\mathrm{ZSCL}^*\\), a variant without the WC loss, obtains the highest Last score, the ZSCL with WC loss outperforms it with \\(2.8\\%\\) Avg. and \\(5.9\\%\\) Transfer scores." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.664, + 0.436, + 0.681 + ], + "angle": 0, + "content": "5.2. Multi-domain Task Incremental Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Tab. 3 displays the performance of different methods on the MTIL benchmark, and Tab. 5 presents the detailed Transfer, Avg, and Last metrics on each dataset. Zero-shot denotes the zero-shot prediction performance of the initial CLIP model, and Fine-tune means the direct fine-tuning accuracy on each dataset, which can be seen as an upperbound where no forgetting phenomenon happens. Continual learning uses cross-entropy loss to learn each dataset sequentially, where there is a significant forgetting issue on both zero-shot predictions (Transfer drops by \\(24.8\\%\\)) and newly learned knowledge (Last drops by \\(9.4\\%\\)). Previous methods improve the Last performance slightly and cannot maintain a high zero-shot prediction performance. Without WC, \\(\\mathrm{ZSCL}^*\\) achieves the best Last scores, outperforming" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.587, + 0.892, + 0.649 + ], + "angle": 0, + "content": "the previous best one by \\(4.4\\%\\). Our method ZSCL improves \\(9.1\\%\\) on Transfer accuracy, with only \\(1.3\\%\\) drops compared with the initial CLIP model, and achieves a \\(10.1\\%\\) gain in the Avg. accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.653, + 0.894, + 0.759 + ], + "angle": 0, + "content": "Figure Fig. 5 provides a visualization of the feature space on Aircraft of the original CLIP and four methods trained at the end of MTCL (t-SNE conducted only once on all features collected). This shows our method is capable of maintaining the pretrained feature distribution with a small averaged feature distance and thus preserving zero-shot performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "The result of the MTIL method in Order-II is presented in Tab. 4. Our method surpasses previous methods in another order setting of the MTIL benchmark. A similar conclusion holds from the results of MTIL Order-II compared with MTIL Order-I. Our method ZSCL outperforms others by \\(9.2\\%\\) on the Avg. score and \\(18.1\\%\\) on the Last score with only a \\(1.2\\%\\) performance loss on the Transfer score. This shows our approach can work for different orders of the multi-domain task incremental learning. In addition," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19132" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.089, + 0.47, + 0.118 + ], + "angle": 0, + "content": "Table 6. Comparison of state-of-the-art CL methods on CIFAR100 benchmark in class-incremental setting." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.13, + 0.472, + 0.344 + ], + "angle": 0, + "content": "
Methods10 steps20 steps50 steps
AvgLastAvgLastAvgLast
UCIR [19]58.6643.3958.1740.6356.8637.09
BiC [59]68.8053.5466.4847.0262.0941.04
RPSNet [46]68.6057.05----
PODNet [13]58.0341.0553.9735.0251.1932.99
DER [60]74.6464.3573.9862.5572.0559.76
DyTox+ [14]74.1062.3471.6257.4368.9051.09
CLIP [44]74.4765.9275.2065.7475.6765.94
FT65.4653.2359.6943.1339.2318.89
LwF [33]65.8648.0460.6440.5647.6932.90
iCaRL [47]79.3570.9773.3264.5571.2859.07
LwF-VR [11]78.8170.7574.5463.5471.0259.45
ZSCL (Ours)82.1573.6580.3969.5879.9267.36
Impr+7.68+7.73+5.19+3.84+3.95+1.42
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.47, + 0.456 + ], + "angle": 0, + "content": "compared with Order-I, previous methods achieve a much lower Last score (e.g., for Continual-Learning, Order-I has \\(77.3\\%\\), while Order-II has \\(65.3\\%\\)). With ZSCL, the Last score is similar (\\(83.6\\%\\) compared with \\(83.4\\%\\)). This shows our method is more robust towards different training orders." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.463, + 0.33, + 0.48 + ], + "angle": 0, + "content": "5.3. Class Incremental Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.471, + 0.698 + ], + "angle": 0, + "content": "We evaluate our methods on conventional class incremental learning. Tabs. 6 and 7 display results on CIFAR100 and TinyImageNet, respectively. We re-implement some previous methods with a CLIP backbone (after CLIP in the table), while others using a special network design cannot be easily adapted. Although zero-shot CLIP prediction achieves a good result on these benchmarks, continual learning with direct fine-tuning or LwF [33] degrades the performance greatly, especially under the setting of a large step number. This demonstrates a severe catastrophic forgetting phenomenon in fine-tuning the CLIP model. Our method consistently improves the performance of the CLIP model on both Avg. and Last scores with a large gap towards previous ones." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.71, + 0.342, + 0.726 + ], + "angle": 0, + "content": "6. Limitation and Future Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.825 + ], + "angle": 0, + "content": "Our proposed method has a limitation that a reference dataset is needed. A promising direction of the work is to preserve the zero-shot transfer ability without the need for an outside dataset. For example, we may generate a synthetic image dataset as the reference dataset. Methods like [51] can synthesize datasets from a network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.903 + ], + "angle": 0, + "content": "The deep learning community tends to build large models with a huge dataset [3, 6], including vision-language models [44, 20]. As re-training cost upsurges, continual learning is an efficient approach for updating these models with custom usage." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 7. Comparison of different methods on TinyImageNet splits in class-incremental settings with 100 base classes." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.13, + 0.894, + 0.344 + ], + "angle": 0, + "content": "
Methods5 steps10 steps20 steps
AvgLastAvgLastAvgLast
EWC [25]19.016.0015.823.7912.354.73
EEIL [4]47.1735.1245.0334.6440.4129.72
UCIR [19]50.3039.4248.5837.2942.8430.85
MUC [35]32.2319.2026.6715.3321.8910.32
PASS [65]49.5441.6447.1939.2742.0132.93
DyTox [14]55.5847.2352.2642.7946.1836.21
CLIP [44]69.6265.3069.5565.5969.4965.30
FT61.5446.6657.0541.5454.6244.55
LwF [33]60.9748.7757.6044.0054.7942.26
iCaRL [47]77.0270.3973.4865.9769.6564.68
LwF-VR [11]77.5670.8974.1267.0569.9463.89
ZSCL (Ours)80.2773.5778.6171.6277.1868.30
Impr+10.65+8.27+9.06+6.03+7.69+3.00
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.384, + 0.892, + 0.444 + ], + "angle": 0, + "content": "In some cases, we want to correct wrong information in the pre-training dataset or update old information with the latest one. How to conduct this task with a reference dataset is left as future work." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.446, + 0.892, + 0.537 + ], + "angle": 0, + "content": "Lately, a noticeable trend involves the creation of multimodality models utilizing large language models, showcasing encouraging outcomes in tasks such as Visual Question Answering (VQA). Expanding our approach to encompass the next token prediction task remains an avenue for future exploration and research." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.556, + 0.62, + 0.572 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.794 + ], + "angle": 0, + "content": "In this paper, we investigate continual learning with the vision-language model. We propose a better continual learning algorithm to protect the zero-shot transfer ability in the vision-language model learned in the pre-training stage. Our algorithm mitigates the catastrophic forgetting in both feature space and parameter space. In feature space, distilling the initial model on a reference dataset significantly boosts the model's performance. In parameter space, weight ensemble among different training stages alleviates the forgetting issue. We propose a more challenging Multidomain Task Incremental Learning (MTIL) benchmark to evaluate the continual learning methods better. On both conventional and new benchmarks, our method achieves state-of-the-art performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.814, + 0.668, + 0.831 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Yang You's research group is being sponsored by the NUS startup grant (Presidential Young Professorship), Singapore MOE Tier-1 grant, ByteDance grant, ARCTIC grant, SMI grant, and Alibaba grant." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19133" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. 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Nevertheless, during the continual training of the Contrastive Language-Image Pre-training (CLIP) model, we observe that the model's zero-shot transfer ability significantly degrades due to catastrophic forgetting. Existing CL methods can mitigate forgetting by replaying previous data. However, since the CLIP dataset is private, replay methods cannot access the pre-training dataset. In addition, replaying data of previously learned downstream tasks can enhance their performance but comes at the cost of sacrificing zero-shot performance. To address this challenge, we propose a novel method ZSCL to prevent zero-shot transfer degradation in the continual learning of vision-language models in both feature and parameter space. In the feature space, a reference dataset is introduced for distillation between the current and initial models. The reference dataset should have semantic diversity but no need to be labeled, seen in pre-training, or matched image-text pairs. In parameter space, we prevent a large parameter shift by averaging weights during the training. We propose a more challenging Multi-domain Task Incremental Learning (MTIL) benchmark to evaluate different methods, where tasks are from various domains instead of class-separated in a single dataset. Our method outperforms other methods in the traditional class-incremental learning setting and the MTIL by $9.7\%$ average score. Our code locates at https://github.com/Thunderbee/ZSCL. + +# 1. Introduction + +Most deep learning models can access all the data during training [27, 16, 12]. If we want to expand a model's knowledge, such as learning a newly found animal species [41], we can re-train the model by adding new classes to the training dataset. However, re-training a large model is + +![](images/c75e1ac3f0a441aaf322335722a181e73f7abc48d7a8e895bf06511d5e2d2e42.jpg) + +![](images/92b6c94e2754d253747798a82044fa5a64cabb9b7c6aac94cce33f61f2e5f62c.jpg) +(a) Comparison between traditional CL and CL with a pre-trained vision-language model + +![](images/c10d291ca81dad6cd99c3f2ff141da5b1ae32d191427ee18e0d17d2af6230b2d.jpg) + +![](images/8ba2320b7369d63df75ed8058fd16d5665eb588e431df7dda0453ed1636163e1.jpg) + +![](images/ed563a5c3d2b32f87328dfb825d0c8cc14c019a03e0d56a799d5d00ddf5c9f04.jpg) +(b) Performance of different methods on preventing forgetting phenomenon + +![](images/10428b9b041ff7ba9f51c846f7aa5a3ff0160dd0426e8cfc094ca94774103d1d.jpg) +Figure 1. a) Conventional CL learns distinct task-specific heads, while CL with vision-language models can predict both learned tasks and out-of-distribution tasks. b) Accuracy (\%) changes during CL of four datasets on 11 datasets. Our method is superior to others in preventing the forgetting of both zero-shot transfer ability and new knowledge. + +costly. In contrast, continual learning (CL) [33, 47] incrementally learns task one after another. It can reduce + +this cost by only learning the new data, thereby presenting itself as an efficient alternative to conventional learning methods [43, 34, 5]. Nonetheless, a model tends to forget previous information catastrophically when learning new tasks [47, 33, 59]. The "catastrophic forgetting" phenomenon is a great challenge for CL. + +Recently, vision-language models have shown powerful zero-shot transfer ability [44, 23, 32]. They can give zero-shot predictions without any training examples of a task. However, the performance on some tasks is poor due to insufficient relevant image-text pairs in the pre-training datasets. For example, it is difficult for CLIP [44] to distinguish among digital numbers, with an accuracy on MNIST [8] below $60\%$ much lower than a naively trained CNN [29]. If we want to widen the knowledge in the vision-language model by re-training, the computational cost is too large (e.g., CLIP is pretrained on 400 million image-text pairs). Fine-tuning downstream tasks achieves high performance, but one model for a task takes much memory, and the model is not reusable. Prompt learning [64, 63] keeps the backbone parameters unchanged. However, it is only effective with limited training data due to a limited prompt length [64, 24]. In contrast, continual learning makes learning new knowledge a lifelong process for the vision-language model. The continually learned model can handle any image-text input and can be further used for downstream tasks [11, 53]. + +We find that existing CL methods hardly prevent the forgetting phenomenon for zero-shot transfer ability in continual learning of a pre-trained vision-language model. As shown in Fig. 1 (a), the CL with a pre-trained vision-language model differs from the traditional one. Besides forgetting previously learned task knowledge, the CLIP-based CL suffers from forgetting pre-training knowledge, namely a degradation of zero-shot transfer ability. For the replay-based CL methods [47, 50, 36, 21, 28, 42], the dataset during pre-training may be private and inaccessible during fine-tuning. For distillation-based CL methods [33, 10, 13, 11], they do not lay enough emphasis on the pre-trained model. On the one hand, a large model state change hinders tasks thereafter from using high-quality feature representations. On the other hand, it significantly degrades zero-shot performance on unseen datasets. + +Our method ZSCL protects the Zero-Shot transfer ability during Continual Learning. We view the knowledge stored in the pre-training model from two perspectives: a well-learned feature space and a good value in the parameter space. In feature space, we re-design previous distillation loss [18, 47] with different loss styles, teacher models, and data sources. We find the original CLIP model, as opposed to the newly acquired model, is the best option for the teacher model. Instead of using data collected from previous tasks [47] or current task [18], we find a reference + +dataset with diverse semantics (e.g., images sampled from ImageNet) is a good option for distillation loss. The reference images need not be labeled or matched with the text. Preserving the relative similarity between reference images and texts makes the feature space deviate little from the original. In the parameter space, WiSE-FT [58] proposes interpolating the initial and fine-tuned model for better performance. Inspired by this, we ensemble the weights throughout continuous training to prevent a significant shift from the initial CLIP, which can be seen as interpolating models of different zero-shot transfer and downstream task performance tradeoffs. The weight ensemble method is more stable and not sensitive to hyper-parameters. + +To better evaluate our method, we propose a new benchmark Multi-domain Task Incremental Learning (MTIL). Previous CL tasks are crafted by separating classes in one dataset [14, 60, 65], where the images and classes are within a single domain. In contrast, MTIL consists of data from different sources requiring different expert knowledge. It comprises 11 tasks ranging from animal species to aircraft series recognition. As displayed in Fig. 1 (b), when sequentially training CLIP on 11 datasets, the drop in the performance of task $i$ after training task $i$ is the traditional forgetting phenomenon. The degradation in the accuracy compared to the original zero-shot one before training task $i$ represents the forgetting in zero-shot transfer ability. Our method better protects the zero-shot transfer ability and preserves the learned knowledge. We outperform previous methods in both conventional class-incremental learning and MTIL settings. In Fig. 1 (b), + +To summarize, our contributions are as follows: + +- We investigate continual training with the vision-language model and demonstrate the importance of preserving zero-shot transfer ability. A more challenging benchmark MTIL is proposed to evaluate CL methods where the tasks come from distinct domains. +- We propose a novel method ZSCL to mitigate the catastrophic forgetting problem in continual learning of the vision-language model by distillation in the feature space and weight ensemble in the parameter space. +- The proposed ZSCL outperforms all state-of-the-art methods across multiple benchmark datasets. On 10 steps CL of CIFAR100 and TinyImageNet, our method outperforms the best of previous ones by $7.7\%$ and $6.0\%$ for the Last accuracy. On MTCL, ZSCL outperforms others by $10.9\%$ on Transfer and $9.7\%$ on Avg. scores. + +# 2. Related Work + +Vision-Language Models. Inspired by the success of language foundation models such as GPT-3 [3] and T5 [45], a + +series of work pre-train vision-language models on large-scale image-text datasets [31, 44, 23]. Among them, Contrastive Language-Vision Pre-training [44] achieves remarkable performance on various downstream tasks. It concentrates on aligning images and texts to acquire a joint embedding space. The CLIP model contains an image encoder [16, 12] and a text encoder [9]. During pre-training, contrastive learning is performed in which a paired image-text is a positive pair while image and text from different image-text pairs form a negative pair. For inference, the closest text embedding for the image is chosen as the prediction. Vision-language models can give zero-shot predictions on unseen tasks with a robust zero-shot transfer ability on various downstream tasks. + +Continual Learning Methods. Most existing continual learning methods can be categorized into four groups: parameter expansion, memory replay, distillation loss, and parameter regularization. Parameter expansion methods such as DyTox [14] and DEN [61] introduce new parameters for new tasks. As we want to achieve a more powerful CLIP model at the end of CL, we do not change the architecture of the CLIP model. Memory replay methods [50, 36, 42, 28, 40] including iCaRL [47] and SER [21] keep a memory for exemplars from previously learned tasks. However, pre-training datasets are too large for choosing exemplars or may not be available at downstream training, and downstream data are not good exemplars for preserving the pretraining knowledge. Distillation loss such as LwF [33], LwM [10], LwF-VR [11], and PodNet [13] aligns current output space with previous ones, whereas distillation based on current tasks are not strong enough to maintain foundational knowledge. For the CLIP model, we find that general images, even if never seen by the model, plus sentences with enough semantics, can be a good "replay" for the distillation loss. The parameter regularization loss restricts the flexibility of model parameters by training loss [25, 62, 1] or weight averaging [30, 58]. Although this type of strategy performs badly compared to other ways in previous research [55, 2], we found it helpful for CLIP continual learning. The limited parameter space prevents the model from diverging significantly from its original state. + +Vision-Language Models for Downstream Tasks. Many works propose different training strategies of vision-language models for better performance on downstream tasks, such as CoOp [64], CLIP-Adapter [15] and WiSE-FT [58]. However, very few attempts at continual learning exist. While [52, 56] focus on CL in the pretrain of VL and [39] trains VL from scratch using a small dataset, our problem setting differs as we address CL in downstream tasks with a pretrained VL. Currently, most VL models are trained directly on an accessible large + +dataset, yet integrating knowledge continuously into a pretrained VL is a practical necessity. None of these studies address the zero-shot transfer degradation phenomenon, instead focusing on the traditional forgetting of learned knowledge. Recently, Thengane et al. [53] shows CLIP zero-shot prediction achieves state-of-the-art performance in CL settings even without any training. LwF-VR [11] is a modified LwF method for the CLIP model where random-generated sentences are used for distillation loss. However, it only considers the feature space, and the distillation with random sentences cannot protect the vision backbone. Differently, we re-examine what should be used for distillation in the feature space and combine the parameter space weight ensemble to provide better performance for the vision-language model continual learning. + +# 3. Approach + +# 3.1. Preliminaries + +Continual Learning. Given $n$ tasks $[\mathcal{T}^1, \mathcal{T}^2, \dots, \mathcal{T}^n]$ , continual training is conducted in sequence on each task $\mathcal{T}^i = (\mathcal{D}^i, C^i)$ , $i = 1, \dots, n$ . Here, $\mathcal{D}^i$ represents the task dataset $\{(x_j^i, y_j^i)\}_{j=1}^{N_i}$ , where $x_j^i$ is an image, $y_j^i$ is a one-hot vector indicating the ground truth, and $N_i$ is the number of images in the dataset. Class names $C^i = \{c_j^i\}_{j=1}^{m_i}$ maps the label of an image to an object name, where $m_i$ is the number of classes for task $\mathcal{T}^i$ . The objective of continual learning is to achieve good performance on all tasks. + +Two continual learning settings are focused on in this study [55]. In task-incremental learning, at inference, the image $\pmb{x}$ to be predicted is given with its task identity $t$ , so the model only needs to distinguish between different classes in $C^t$ . In class-incremental learning, the task identity $t$ is not given. Thus we need to predict with the combined class set $C = \bigcup_{i=1}^{n} C^i$ . + +CLIP model. The CLIP model contains an image encoder $f_{i}$ and a text encoder $f_{t}$ . The inference process of the CLIP model for image classification is as follows. First, for task $\mathcal{T}^i$ , each class $c$ is transformed into a sentence by a template like "a photo of $\{c\}$ ". Then $f_{t}$ encodes the classes into text embeddings $\{\pmb{t}_{j}^{i}\}_{j = 1}^{m_{i}}$ . An image encoder encodes input image $\pmb{x}_k$ . The similarity score between the image embedding and text embeddings are calculated as $s_{k,j}^{i} = \langle f_{i}(\pmb{x}_{k}),\pmb{t}_{j}^{i}\rangle$ where $\langle \cdot ,\cdot \rangle$ denotes the cosine similarity. The class with the largest similarity score is the prediction for the image. + +To fine-tune the CLIP model for downstream tasks, cross-entropy loss CE is applied to the similarity score with a temperature scaling: + +$$ +\mathcal {L} _ {\mathrm {C E}} = \frac {1}{N} \sum_ {i = 1} ^ {N} \mathrm {C E} (\tau \cdot \boldsymbol {s} _ {i}, \boldsymbol {y} _ {i}), \tag {1} +$$ + +where $\tau$ is a parameter learned during the pre-training. + +![](images/4329bff0d636ac16c1e23263b5d689cb7dbc7b4b289e45b30094e3f0c1b8cdce.jpg) +Figure 2. Illustration of ZSCL in feature space. Fig. 3(a) shows the pipeline of distillation. The original and the current model encode the reference images and texts, respectively. The probability distribution of images and texts with respect to each other is distilled. Fig. 3(b) displays how distillation loss preserves the feature space. Compared with the reference dataset, the features of fine-tuning tasks lie in a small subspace. The distillation loss preserves the structure of the feature space by maintaining relative distances. + +![](images/f03a900cd5ed94daddb29f1585000c813ccaa2207a4462c7b9f5c88529204ab8.jpg) + +# 3.2. Distillation in Feature Space + +Well-learned feature space for aligned images and texts enables vision-language models' strong zero-shot transfer ability. It also facilitates the learning of downstream tasks. Compared with the pre-training dataset, downstream datasets lie in a small scope in the feature space (shown in Fig. 2(b)). Direct fine-tuning of downstream tasks greatly distorts the feature distribution of out-of-distribution data, which leads to a significant drop in zero-shot prediction performance. + +While the cross-entropy improves the performance by altering fine-tuned feature subspace, we need a new regularization to preserve the potential out-of-distribution feature space. The relative similarity between one image and different texts is: + +$$ +\boldsymbol {p} = \operatorname {S o f t m a x} \left(\boldsymbol {s} _ {1}, \dots , \boldsymbol {s} _ {m}\right). \tag {2} +$$ + +We hope the above similarity distribution is stable during fine-tuning for all potential images and texts. Given a teacher model $\overline{f}$ , distillation loss can be applied to penalize changes from the original distribution: + +$$ +\mathcal {L} _ {\text {d i s t . i m g}} = \operatorname {C E} (\boldsymbol {p}, \bar {\boldsymbol {p}}) = - \sum_ {j = 1} ^ {m} \boldsymbol {p} _ {j} \cdot \log \bar {\boldsymbol {p}} _ {j}, \tag {3} +$$ + +where $\overline{\pmb{p}}$ is the distribution given by the teacher model. + +Although the distillation form has been widely used in previous methods [18, 33, 47], they are applied to continual learning from scratch. We investigate different components of the distillation loss for enhancing pre-trained vision-language models. + +Three components are discussed in this paper in detail: the data source, the teacher model, and the loss design. Sec. 5.1 shows the performance for the different choices. First, for the data source, LwF [33] uses data from the cur + +rent task, while iCarl [47] carefully selects data from previous tasks. However, data from downstream tasks span a small subspace and are not good enough to preserve the whole feature space. An ideal choice is the pre-training dataset. However, the CLIP pre-training dataset is private, and the size is too large to load. To solve this challenge, we introduce the reference dataset. A reference dataset is a publicly available image dataset with enough semantics. Enough semantics can be seen as random sampling in the whole feature space. The texts can be related class names, unrelated sentences, or even random tokens. This is because text semantics are easier to sample, and we need not ground truth to calculate the distance between one image to sufficient text samples spread among feature space. + +For the teacher model, [33, 47] use the model after learning task i-1 and before learning task i as the teacher model. During the continual training of the vision-language model, the feature space deviates gradually from the initial model. Using fine-tuned models as teacher models enlarges this change. In contrast, we find using the pre-trained model as a teacher model not only preserves the zero-shot transfer ability but also takes advantage of well-learned feature space for better downstream performance. + +Finally, previous distillation loss is applied on traditional backbones, where a classification head gives the probability for different labels. For the vision-language model, the probability is calculated based on the relative distance between images and texts. Thus, in addition to Eq. (3), we impose regularization $\mathcal{L}_{\mathrm{dist\_txt}}$ on the distances from a text to a batch of images. The whole framework is shown in Fig. 2 (a) with the following training loss: + +$$ +\mathcal {L} = \mathcal {L} _ {\mathrm {c e}} + \lambda \cdot \left(\mathcal {L} _ {\mathrm {l w f . i m g}} + \mathcal {L} _ {\mathrm {l w f . t x t}}\right). \tag {4} +$$ + +![](images/eb3d24a46c63689d28133592e77841b07804ba7d89e7f0c1fa29b32d5c02b588.jpg) +Figure 3. Models during training contain different tradeoffs between zero-shot and new task performance. Points for FT are sampled every 100 iterations, and the ones for WiSE-FT means different $\alpha$ choices. WE ensembles models during training and achieve better performance. + +# 3.3. Weight Ensemble in Parameter Space + +Machine learning models integrate learned knowledge in their parameters. To mitigate the forgetting problem, a series of works [25, 62, 1] impose regularization losses on the changes of parameters. Weight consolidation (WC) [25] imposes the following loss: + +$$ +\mathcal {L} _ {\mathrm {W C}} = \sum_ {i} \left(\theta_ {i} - \bar {\theta} _ {i}\right) ^ {2}. \tag {5} +$$ + +where $\theta$ is the parameters of the current model, and $\overline{\theta}$ is the reference ones. Although this regularization prevents forgetting, it hinders learning new tasks in a challenging CL setting. + +Apart from regularization losses, another method in parameter space is to ensemble different model weights. Model soup [57] averages weights of multiple fine-tuned models to improve the model's robustness but introduces additional training costs. WiSE-FT [58] propose a weighted average between fine-tuned model and the original model to improve the out-of-distribution prediction robustness: + +$$ +f (x; (1 - \alpha) \cdot \theta_ {0} + \alpha \cdot \theta_ {1}), \tag {6} +$$ + +where $\theta_0$ is the original model and $\theta_{1}$ is the fine-tuned one. However, this method is hyper-parameter-sensitive where different $\alpha$ gives different tradeoffs between zero-shot transfer ability and downstream task performance (blue line in Fig. 3. + +Inspired by this, we extend the weighted average to the CL setting. The motivation for the weighted average is to prevent fine-tuning from losing too much knowledge in the original model. As training goes by (green line in Fig. 3), the model performs better on new tasks while losing accuracy on previous ones. The models among training compose a sequence of different learning-forgetting tradeoffs. + +![](images/c1c8038706070e6074aff8433598727beaf8d68f06790075ab76e09402bafbd0.jpg) +(a) + +![](images/7612a0001597f0d99113646e1932e6b9a2dfdfa5b9fc31e1b66a56d4a369c262.jpg) + +![](images/816e3786999b886a7661b676ba1153e0a0d8b60c6ea218d1e5871216e42d0f37.jpg) + +![](images/952c17a62f4e4c386253f86e5ba5a7e8676eb7209cde979b79afbd3ab84319b1.jpg) + +![](images/81e23c68abd350a661469da9d431633c4fcb113cc4ec578215ac9647b344ca15.jpg) +(b) +Figure 4. Fig.(a): examples of tasks from different domains in MTIL benchmark. Fig.(b): illustration of calculating metrics Transfer, Avg. and Last during continual learning. + +Instead of interpolating only between the initial and the final model, our method weight ensemble (WE) averages the weights in the sequence during the training time: + +$$ +\hat {\theta} _ {t} = \left\{ \begin{array}{l l} \theta_ {0} & t = 0 \\ \frac {1}{t + 1} \theta_ {t} + \frac {t}{t + 1} \cdot \hat {\theta} _ {t - 1} & \text {e v e r y I i t e r a t i o n s} \end{array} . \right. \tag {7} +$$ + +where model weight sampling happens every $I$ iteration. The method is related to Stochastic Weight Averaging (SWA) [22], but we do not use a modified learning rate schedule here because instead of getting better generalization ability, WE aim to give an improved learning-forgetting tradeoff. As shown in Fig. 3, WE achieves better performance on downstream tasks than WiSE-FT. In addition, while WiSE-FT is sensitive to different values of $\alpha$ , our method is much more robust under different hyperparameter $(I)$ choices. + +# 4. Multi-domain Task Incremental Learning + +Conventional Continual Learning Benchmark. A benchmark consisting of several tasks is needed to evaluate different methods for continual learning. Most previous benchmarks are built by separating classes in a single dataset, such as MNIST [55], CIFAR100 [14], TinyImageNet [60], and ImageNet [60, 65]. We also evaluate our method with traditional benchmarks. In CIFAR100 [26], classes are separated into groups to build tasks. Suppose the dataset has $m$ classes, a $k$ -step setting means we learn $m / k$ classes in each new task. The CIFAR100 contains 100 classes, and the setting of 10, 20, and 50 steps are visited. For TinyImageNet with $m = 200$ , the first step learns 100 classes, and the rest is learned with 5, 10, and 20 steps. As for ImageNet-100, we have two settings: ImageNet-100-B0, which includes the same amount of classes for each step, and ImageNet-100-B50, which has + +Table 1. Ablation experiments. Default settings are marked in gray, which uses image and text distillation loss with the initial CLIP model on 100k ImageNet images and texts generated from ImageNet classes with a simple template. +(a) Continual learning loss. + +
lossTransferAvg.Last
CE only44.655.977.3
Feat. Dist.47.658.777.1
Image-only56.568.982.1
Text-only56.769.082.6
Both56.869.283.0
+ +(d) Teacher model. + +
sourceTransferAvg.Last
Initial56.869.283.0
n-153.966.680.7
WiSE(0.5)56.468.982.9
WiSE(0.8)56.267.881.3
+ +(b) Data sources for replay. + +
sourceTransferAvg.Last
current56.766.580.2
ImageNet56.869.283.0
CC57.268.580.9
CIFAR10055.265.980.7
Flowers54.766.080.8
+ +(e) # images for replay. + +
#imageTransferAvg.Last
1M58.770.183.2
100k56.869.283.0
10k57.868.781.2
1k56.367.680.8
+ +(c) Text sources for replay. + +
sourceTransferAvg.Last
current51.864.982.0
prev. all54.070.283.7
1k classes (IN)56.869.283.0
13k Sent. (CC)58.970.584.0
1k Rand. Sent.58.770.283.8
+ +(f) # image classes for replay. + +
#classTransferAvg.Last
100056.867.683.0
10056.767.382.3
1053.866.481.0
153.165.580.5
+ +Table 2. Ablation study of different components for ZSCL. + +
MethodTransferΔAvg.ΔLastΔ
CLIP ViT-B/16@224px
Zero-shot69.40.065.30.065.30.0
Continual Learning44.6-24.855.9-9.477.3+12.0
+ Distillation58.9-10.570.5+5.283.8+18.5
+ WiSE-FT (best α)61.7-7.771.6+6.383.3+18.0
+ WE (ZSCL*)62.2-7.272.6+7.384.5+19.2
+ WC67.6-1.874.5+9.283.2+17.9
+ WiSE-FT67.7-1.774.2+8.981.9+16.6
+ WE (ZSCL)68.1-1.375.4+10.183.6+18.3
+ +50 classes for the first step, and the remaining 50 classes are observed progressively over the next 10 stages. For ImageNet [7], we investigate a 10-step setting, which learns 100 new classes per task. + +MTIL Benchmark. Different classes from one dataset share the common image source and a similar style [48, 17]. Thus, we propose Multi-domain Task Incremental Learning (MTIL), a cross-domain version of task incremental learning. Different tasks are collected from different domains, requiring different domain knowledge for humans to achieve high accuracy. Our MTIL benchmark consists of 11 tasks (detailed in supplementary materials), as some of the tasks illustrated in Fig. 4 (a). The MTIL benchmark is very challenging with a total number of 1,201 classes. Two orders are used for the evaluation; the first one is alphabet order (Order-I): Aircraft, Caltech101, CIFAR100, DTD, EuroSAT, Flowers, Food, MNIST, OxfordPet, StanfordCars, SUN397. And the second one is a random order (Order-II): StanfordCars, Food, MNIST, OxfordPet, Flowers, SUN397, Aircraft, Caltech101, DTD, EuroSAT, CIFAR100. Experiments are done in Order I by default. + +Evaluation Metrics. The metrics of MTIL are illustrated in Fig. 4(b), where rows represent training steps and a + +column shows performance for one dataset. For conventional continual learning, only scores under the diagonal are meaningful, since they cannot give zero-shot predictions on unseen tasks. In contrast, the zeros-hot transfer ability enables a vision-language model to provide predictions for all datasets. The average accuracy on all datasets among all timestamps is the "Avg" metric. The "Last" metric is the average performance of all tasks after CL. The "Transfer" metric is the average task performance in the upper-right triangle of the matrix. Every task's performance is first averaged to equal the weight of each dataset. It measures to what extent the zero-shot transfer ability is preserved. Before learning task $i$ , tasks not earlier than $i$ are not finetuned. Thus, their performance is an indicator of zero-shot transfer ability. + +# 5. Experiments + +Implementation. We use CLIP [44] model with image encoder ViT-B/16 [12]. We conduct training with AdamW [37] optimizer and use a label smoothing [38] technique for a better baseline result. For multi-domain task continual learning, we train 1K iterations for each task, while for class-incremental learning, we follow the same evaluation setting in [14]. More implementation details can be found in the supplementary material. + +# 5.1. Main Properties + +We ablate our method in feature-space in Tab. 1, and different choices for parameter-space regularization in Tab. 2. Several interesting characteristics are noted. + +Continual learning loss. In Tab. 1a, several types of loss for feature space are tested. The Feature Distance penalizing absolute distances achieves a low accuracy. Distillation loss on probability distribution regularizes relative distance in the feature space. With image-only or text-only distilla + +![](images/486e0281799167fdc39ad25fe08f6ed1648465a543e6415e44a1f33130cf66aa.jpg) +Figure 5. t-SNE on five models' outputs together of Aircraft datasets after MTCL training: only our model maintains a similar feature distribution to the original CLIP ones with minor shift, while the rest significantly distort the feature space. + +![](images/7784c328f4cdf2b9bb2ed7f173c38e0d41ae1044f2237fb671b5c4c8254a9dc8.jpg) + +![](images/09b430fabc5fe55f1527a5618eccc3aa9a80fbc30f1e07b877ca20d9e3d1d5a5.jpg) + +![](images/eb90c5de160688afb191eadaa39b87a75136e54a5cc737262f85f987cb769e3e.jpg) + +![](images/e8277e097f9a1ced82aa1b0687e58001beb7132aad61f8a706e47c69a5d84737.jpg) + +Table 3. Comparison of different methods on MTIL in Order I. + +
MethodTransferΔAvg.ΔLastΔ
CLIP ViT-B/16@224px
Zero-shot69.40.065.30.065.30.0
Continual Learning44.6-24.855.9-9.477.3+12.0
LwF [33]56.9-12.564.7-0.674.6+9.0
iCaRL [47]50.4-19.065.7+0.480.1+14.8
LwF-VR [11]57.2-12.265.1-0.276.6+11.3
WiSE-FT [58]52.3-17.160.7-4.677.7+12.4
ZSCL* (Ours)62.2-7.272.6+7.384.5+19.2
ZSCL (Ours)68.1-1.375.4+10.183.6+18.3
+ +tion, the Transfer, Avg., and Last accuracy all improve. A further boost in performance occurs with both of the distillation losses. + +Data source for replay. Tabs. 1b, 1c, 1e and 1f seek the standard for a good reference dataset. As shown in Tab. 1b, distillation on images of current tasks achieves a good Transfer score. However, it hinders the learning on new tasks and results in a low Avg. and Last score. Images in a specific domain (e.g., Flowers) are also not good choices. General images in ImageNet and Conceptual Caption (CC) datasets are examples of good reference datasets. These images are easily available by a web crawler [54]. Text with more semantics can improve performance (shown in Tab. 1c). When using sentences from the Conceptual Caption dataset [49], or even sentences randomly generated from the CLIP vocabulary, there is no ground truth target among the texts for the image from the ImageNet dataset. However, they all achieve an improvement due to more semantics. The reference image dataset does not need to be labeled, matched with the text, or seen by the CLIP model. + +Enough semantics in the reference image dataset boosts the distillation performance. In Tabs. 1e and 1f, a smaller number of images and classes all lead to a degradation in the performance. Fewer classes of images in the reference dataset have a worse impact on the performance compared with the image numbers. To keep a reasonable memory buffer, we randomly sample $100\mathrm{k}$ images from ImageNet for MTIL and use texts from CC dataset. For class- + +Table 4. Comparison of different methods on MTIL in Order II. + +
MethodTransferΔAvg.ΔLastΔ
CLIP ViT-B/16@224px
Zero-shot65.40.065.30.065.30.0
Continual Learning46.6-18.856.2-9.167.4+2.1
LwF [33]53.2-12.262.2-5.271.9+6.6
iCaRL [47]50.9-14.556.9-8.471.6+6.3
LwF-VR [11]53.1-12.360.6-7.468.3+0.9
WiSE-FT [58]51.0-14.461.5-5.972.2+6.9
ZSCL*59.8-5.671.8+6.583.3+18.0
ZSCL64.2-1.274.5+9.283.4+18.1
+ +incremental learning, conceptual caption dataset's validation set (28k images) is used to avoid information leakage. + +Teacher model. Tab. 1d shows the performance of distillation loss with different teacher models. Unlike conventional continual learning, the teacher model should not be the one trained on the previous task; otherwise, the deviation from the initial CLIP in the previous task may be amplified. In contrast, with the initial CLIP as the teacher model, not only is the zero-shot performance improved but the Mean and Last scores are also boosted, indicating that preserving high-quality feature space facilitates continual learning. + +Parameter-space regularization. In Tab. 2, we experiment with three different parameter-space regularizations. We experiment with two variants of WiSE-FT [58]: the weighted average between the current model with the initial CLIP or the one at the previous task. The result shows the latter one is a better choice because keeping weight averaging with initial CLIP loses the newly learned knowledge. We experiment with different $\alpha$ choices for WiSE, and the best result is reported. While distillation loss improves the whole performance, the parameter-space regularization further protects the zero-shot transfer ability with a higher Transfer. Among the three parameter-space regularizations, only WE achieve a better Last score. WC greatly improves the Transfer scores with a lower Last score. A combination of the weight consolidation loss with weight + +Table 5. Transfer, Avg., and Last scores (%) of different continue training methods on MTIL benchmark. + +
MethodAircraftCaltech101CIFAR100DTDEuroSATFlowersFoodMNISTOxfordPetCarsSUN397
CLIP ViT-B/16@224px
Zero-shot24.388.468.244.654.971.088.559.489.064.765.2
Fine-tune62.095.189.679.598.997.592.799.694.789.681.8
Transfer
Continual-FT67.146.032.135.635.057.744.160.820.546.6
LwF [33]74.556.939.151.152.672.860.675.130.355.9
iCaRL [47]56.644.632.739.346.668.046.077.431.960.5
LwF-VR [11]77.161.040.545.354.474.647.976.736.358.6
WiSE-FT [58]73.555.635.641.547.068.353.969.326.851.9
Dist. only80.162.240.239.958.180.853.474.638.161.9
ZSCL*78.364.042.945.263.584.256.178.944.164.3
ZSCL86.067.445.450.469.187.661.886.860.166.8
Avg.
Continual-FT25.581.559.153.264.751.863.264.369.731.849.7
LwF [33]36.386.972.059.073.760.073.674.880.037.358.1
iCaRL [47]35.589.272.260.668.870.078.262.381.841.262.5
LwF-VR [11]29.687.774.459.572.463.677.066.781.243.760.7
WiSE-FT [58]26.786.564.357.165.758.771.170.575.836.954.6
Dist. only48.190.679.863.275.672.584.770.279.846.963.7
ZSCL*50.790.979.863.876.677.387.071.983.052.065.9
ZSCL45.192.080.164.379.581.689.675.288.964.768.0
Last
Continual-FT31.089.365.867.388.971.185.699.692.977.381.1
LwF [33]26.387.571.966.679.966.983.899.692.166.180.4
iCaRL [47]35.893.077.070.283.388.590.486.793.281.281.9
LwF-VR [11]20.589.872.367.685.573.885.799.693.173.380.9
WiSE-FT [58]27.290.868.068.986.974.087.699.692.677.881.3
Dist. only43.391.981.372.495.190.590.499.792.585.181.8
ZSCL*46.092.381.272.493.092.190.899.693.386.681.7
ZSCL40.692.281.370.594.890.591.998.793.985.380.2
+ +ensemble achieves a better tradeoff between Transfer and Last value. While $\mathrm{ZSCL}^*$ , a variant without the WC loss, obtains the highest Last score, the ZSCL with WC loss outperforms it with $2.8\%$ Avg. and $5.9\%$ Transfer scores. + +# 5.2. Multi-domain Task Incremental Learning + +Tab. 3 displays the performance of different methods on the MTIL benchmark, and Tab. 5 presents the detailed Transfer, Avg, and Last metrics on each dataset. Zero-shot denotes the zero-shot prediction performance of the initial CLIP model, and Fine-tune means the direct fine-tuning accuracy on each dataset, which can be seen as an upperbound where no forgetting phenomenon happens. Continual learning uses cross-entropy loss to learn each dataset sequentially, where there is a significant forgetting issue on both zero-shot predictions (Transfer drops by $24.8\%$ ) and newly learned knowledge (Last drops by $9.4\%$ ). Previous methods improve the Last performance slightly and cannot maintain a high zero-shot prediction performance. Without WC, $\mathrm{ZSCL}^*$ achieves the best Last scores, outperforming + +the previous best one by $4.4\%$ . Our method ZSCL improves $9.1\%$ on Transfer accuracy, with only $1.3\%$ drops compared with the initial CLIP model, and achieves a $10.1\%$ gain in the Avg. accuracy. + +Figure Fig. 5 provides a visualization of the feature space on Aircraft of the original CLIP and four methods trained at the end of MTCL (t-SNE conducted only once on all features collected). This shows our method is capable of maintaining the pretrained feature distribution with a small averaged feature distance and thus preserving zero-shot performance. + +The result of the MTIL method in Order-II is presented in Tab. 4. Our method surpasses previous methods in another order setting of the MTIL benchmark. A similar conclusion holds from the results of MTIL Order-II compared with MTIL Order-I. Our method ZSCL outperforms others by $9.2\%$ on the Avg. score and $18.1\%$ on the Last score with only a $1.2\%$ performance loss on the Transfer score. This shows our approach can work for different orders of the multi-domain task incremental learning. In addition, + +Table 6. Comparison of state-of-the-art CL methods on CIFAR100 benchmark in class-incremental setting. + +
Methods10 steps20 steps50 steps
AvgLastAvgLastAvgLast
UCIR [19]58.6643.3958.1740.6356.8637.09
BiC [59]68.8053.5466.4847.0262.0941.04
RPSNet [46]68.6057.05----
PODNet [13]58.0341.0553.9735.0251.1932.99
DER [60]74.6464.3573.9862.5572.0559.76
DyTox+ [14]74.1062.3471.6257.4368.9051.09
CLIP [44]74.4765.9275.2065.7475.6765.94
FT65.4653.2359.6943.1339.2318.89
LwF [33]65.8648.0460.6440.5647.6932.90
iCaRL [47]79.3570.9773.3264.5571.2859.07
LwF-VR [11]78.8170.7574.5463.5471.0259.45
ZSCL (Ours)82.1573.6580.3969.5879.9267.36
Impr+7.68+7.73+5.19+3.84+3.95+1.42
+ +compared with Order-I, previous methods achieve a much lower Last score (e.g., for Continual-Learning, Order-I has $77.3\%$ , while Order-II has $65.3\%$ ). With ZSCL, the Last score is similar ( $83.6\%$ compared with $83.4\%$ ). This shows our method is more robust towards different training orders. + +# 5.3. Class Incremental Learning + +We evaluate our methods on conventional class incremental learning. Tabs. 6 and 7 display results on CIFAR100 and TinyImageNet, respectively. We re-implement some previous methods with a CLIP backbone (after CLIP in the table), while others using a special network design cannot be easily adapted. Although zero-shot CLIP prediction achieves a good result on these benchmarks, continual learning with direct fine-tuning or LwF [33] degrades the performance greatly, especially under the setting of a large step number. This demonstrates a severe catastrophic forgetting phenomenon in fine-tuning the CLIP model. Our method consistently improves the performance of the CLIP model on both Avg. and Last scores with a large gap towards previous ones. + +# 6. Limitation and Future Work + +Our proposed method has a limitation that a reference dataset is needed. A promising direction of the work is to preserve the zero-shot transfer ability without the need for an outside dataset. For example, we may generate a synthetic image dataset as the reference dataset. Methods like [51] can synthesize datasets from a network. + +The deep learning community tends to build large models with a huge dataset [3, 6], including vision-language models [44, 20]. As re-training cost upsurges, continual learning is an efficient approach for updating these models with custom usage. + +Table 7. Comparison of different methods on TinyImageNet splits in class-incremental settings with 100 base classes. + +
Methods5 steps10 steps20 steps
AvgLastAvgLastAvgLast
EWC [25]19.016.0015.823.7912.354.73
EEIL [4]47.1735.1245.0334.6440.4129.72
UCIR [19]50.3039.4248.5837.2942.8430.85
MUC [35]32.2319.2026.6715.3321.8910.32
PASS [65]49.5441.6447.1939.2742.0132.93
DyTox [14]55.5847.2352.2642.7946.1836.21
CLIP [44]69.6265.3069.5565.5969.4965.30
FT61.5446.6657.0541.5454.6244.55
LwF [33]60.9748.7757.6044.0054.7942.26
iCaRL [47]77.0270.3973.4865.9769.6564.68
LwF-VR [11]77.5670.8974.1267.0569.9463.89
ZSCL (Ours)80.2773.5778.6171.6277.1868.30
Impr+10.65+8.27+9.06+6.03+7.69+3.00
+ +In some cases, we want to correct wrong information in the pre-training dataset or update old information with the latest one. How to conduct this task with a reference dataset is left as future work. + +Lately, a noticeable trend involves the creation of multimodality models utilizing large language models, showcasing encouraging outcomes in tasks such as Visual Question Answering (VQA). Expanding our approach to encompass the next token prediction task remains an avenue for future exploration and research. + +# 7. Conclusion + +In this paper, we investigate continual learning with the vision-language model. We propose a better continual learning algorithm to protect the zero-shot transfer ability in the vision-language model learned in the pre-training stage. Our algorithm mitigates the catastrophic forgetting in both feature space and parameter space. In feature space, distilling the initial model on a reference dataset significantly boosts the model's performance. In parameter space, weight ensemble among different training stages alleviates the forgetting issue. We propose a more challenging Multidomain Task Incremental Learning (MTIL) benchmark to evaluate the continual learning methods better. On both conventional and new benchmarks, our method achieves state-of-the-art performance. + +# Acknowledgements + +Yang You's research group is being sponsored by the NUS startup grant (Presidential Young Professorship), Singapore MOE Tier-1 grant, ByteDance grant, ARCTIC grant, SMI grant, and Alibaba grant. + +# References + +[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware synapses: Learning what (not) to forget. In Proceedings of the European Conference on Computer Vision (ECCV), pages 139-154, 2018. 3, 5 +[2] Eden Belouadah, Adrian Popescu, and Ioannis Kanellos. A comprehensive study of class incremental learning algorithms for visual tasks. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5871-5880, 2021. 2, 5, 9 \ No newline at end of file diff --git a/2023/Preventing Zero-Shot Transfer Degradation in Continual Learning of Vision-Language Models/images.zip b/2023/Preventing Zero-Shot Transfer Degradation in Continual Learning of Vision-Language Models/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..2049128de62cc7c350e6a94a59efb1451ea62056 --- /dev/null +++ b/2023/Preventing Zero-Shot Transfer Degradation in Continual Learning of Vision-Language Models/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:465b863ef1b8357943637e91cb430f7f659bc85d9012ef20687d532a19b3becd +size 764821 diff --git a/2023/Preventing Zero-Shot Transfer Degradation in Continual Learning of Vision-Language Models/layout.json b/2023/Preventing Zero-Shot Transfer Degradation in Continual Learning of Vision-Language Models/layout.json new file mode 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+ 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 290, + 611 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 290, + 611 + ], + "type": "text", + "content": "Continual learning (CL) can help pre-trained vision-language models efficiently adapt to new or under-trained data distributions without re-training. Nevertheless, during the continual training of the Contrastive Language-Image Pre-training (CLIP) model, we observe that the model's zero-shot transfer ability significantly degrades due to catastrophic forgetting. Existing CL methods can mitigate forgetting by replaying previous data. However, since the CLIP dataset is private, replay methods cannot access the pre-training dataset. In addition, replaying data of previously learned downstream tasks can enhance their performance but comes at the cost of sacrificing zero-shot performance. To address this challenge, we propose a novel method ZSCL to prevent zero-shot transfer degradation in the continual learning of vision-language models in both feature and parameter space. In the feature space, a reference dataset is introduced for distillation between the current and initial models. The reference dataset should have semantic diversity but no need to be labeled, seen in pre-training, or matched image-text pairs. In parameter space, we prevent a large parameter shift by averaging weights during the training. We propose a more challenging Multi-domain Task Incremental Learning (MTIL) benchmark to evaluate different methods, where tasks are from various domains instead of class-separated in a single dataset. Our method outperforms other methods in the traditional class-incremental learning setting and the MTIL by " + }, + { + "bbox": [ + 46, + 264, + 290, + 611 + ], + "type": "inline_equation", + "content": "9.7\\%" + }, + { + "bbox": [ + 46, + 264, + 290, + 611 + ], + "type": "text", + "content": " average score. Our code locates at https://github.com/Thunderbee/ZSCL." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 634, + 128, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 128, + 646 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 128, + 646 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Most deep learning models can access all the data during training [27, 16, 12]. If we want to expand a model's knowledge, such as learning a newly found animal species [41], we can re-train the model by adding new classes to the training dataset. 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Our method is superior to others in preventing the forgetting of both zero-shot transfer ability and new knowledge." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 689, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 546, + 713 + ], + "type": "text", + "content": "costly. In contrast, continual learning (CL) [33, 47] incrementally learns task one after another. It can reduce" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 38 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 38 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 38 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19125" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "content": "this cost by only learning the new data, thereby presenting itself as an efficient alternative to conventional learning methods [43, 34, 5]. Nonetheless, a model tends to forget previous information catastrophically when learning new tasks [47, 33, 59]. The \"catastrophic forgetting\" phenomenon is a great challenge for CL." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 147, + 290, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 147, + 290, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 147, + 290, + 397 + ], + "type": "text", + "content": "Recently, vision-language models have shown powerful zero-shot transfer ability [44, 23, 32]. They can give zero-shot predictions without any training examples of a task. However, the performance on some tasks is poor due to insufficient relevant image-text pairs in the pre-training datasets. For example, it is difficult for CLIP [44] to distinguish among digital numbers, with an accuracy on MNIST [8] below " + }, + { + "bbox": [ + 46, + 147, + 290, + 397 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 46, + 147, + 290, + 397 + ], + "type": "text", + "content": " much lower than a naively trained CNN [29]. If we want to widen the knowledge in the vision-language model by re-training, the computational cost is too large (e.g., CLIP is pretrained on 400 million image-text pairs). Fine-tuning downstream tasks achieves high performance, but one model for a task takes much memory, and the model is not reusable. Prompt learning [64, 63] keeps the backbone parameters unchanged. However, it is only effective with limited training data due to a limited prompt length [64, 24]. In contrast, continual learning makes learning new knowledge a lifelong process for the vision-language model. The continually learned model can handle any image-text input and can be further used for downstream tasks [11, 53]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 400, + 288, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 288, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 288, + 592 + ], + "type": "text", + "content": "We find that existing CL methods hardly prevent the forgetting phenomenon for zero-shot transfer ability in continual learning of a pre-trained vision-language model. As shown in Fig. 1 (a), the CL with a pre-trained vision-language model differs from the traditional one. Besides forgetting previously learned task knowledge, the CLIP-based CL suffers from forgetting pre-training knowledge, namely a degradation of zero-shot transfer ability. For the replay-based CL methods [47, 50, 36, 21, 28, 42], the dataset during pre-training may be private and inaccessible during fine-tuning. For distillation-based CL methods [33, 10, 13, 11], they do not lay enough emphasis on the pre-trained model. On the one hand, a large model state change hinders tasks thereafter from using high-quality feature representations. On the other hand, it significantly degrades zero-shot performance on unseen datasets." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "Our method ZSCL protects the Zero-Shot transfer ability during Continual Learning. We view the knowledge stored in the pre-training model from two perspectives: a well-learned feature space and a good value in the parameter space. In feature space, we re-design previous distillation loss [18, 47] with different loss styles, teacher models, and data sources. We find the original CLIP model, as opposed to the newly acquired model, is the best option for the teacher model. Instead of using data collected from previous tasks [47] or current task [18], we find a reference" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "dataset with diverse semantics (e.g., images sampled from ImageNet) is a good option for distillation loss. The reference images need not be labeled or matched with the text. Preserving the relative similarity between reference images and texts makes the feature space deviate little from the original. In the parameter space, WiSE-FT [58] proposes interpolating the initial and fine-tuned model for better performance. Inspired by this, we ensemble the weights throughout continuous training to prevent a significant shift from the initial CLIP, which can be seen as interpolating models of different zero-shot transfer and downstream task performance tradeoffs. The weight ensemble method is more stable and not sensitive to hyper-parameters." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 228, + 546, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 546, + 430 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 546, + 430 + ], + "type": "text", + "content": "To better evaluate our method, we propose a new benchmark Multi-domain Task Incremental Learning (MTIL). Previous CL tasks are crafted by separating classes in one dataset [14, 60, 65], where the images and classes are within a single domain. In contrast, MTIL consists of data from different sources requiring different expert knowledge. It comprises 11 tasks ranging from animal species to aircraft series recognition. As displayed in Fig. 1 (b), when sequentially training CLIP on 11 datasets, the drop in the performance of task " + }, + { + "bbox": [ + 304, + 228, + 546, + 430 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 228, + 546, + 430 + ], + "type": "text", + "content": " after training task " + }, + { + "bbox": [ + 304, + 228, + 546, + 430 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 228, + 546, + 430 + ], + "type": "text", + "content": " is the traditional forgetting phenomenon. The degradation in the accuracy compared to the original zero-shot one before training task " + }, + { + "bbox": [ + 304, + 228, + 546, + 430 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 228, + 546, + 430 + ], + "type": "text", + "content": " represents the forgetting in zero-shot transfer ability. Our method better protects the zero-shot transfer ability and preserves the learned knowledge. We outperform previous methods in both conventional class-incremental learning and MTIL settings. In Fig. 1 (b)," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 431, + 511, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 431, + 511, + 442 + ], + "spans": [ + { + "bbox": [ + 317, + 431, + 511, + 442 + ], + "type": "text", + "content": "To summarize, our contributions are as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 451, + 545, + 658 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 317, + 451, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 451, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 317, + 451, + 545, + 510 + ], + "type": "text", + "content": "- We investigate continual training with the vision-language model and demonstrate the importance of preserving zero-shot transfer ability. A more challenging benchmark MTIL is proposed to evaluate CL methods where the tasks come from distinct domains." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 519, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 519, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 317, + 519, + 545, + 567 + ], + "type": "text", + "content": "- We propose a novel method ZSCL to mitigate the catastrophic forgetting problem in continual learning of the vision-language model by distillation in the feature space and weight ensemble in the parameter space." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 574, + 545, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 574, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 317, + 574, + 545, + 658 + ], + "type": "text", + "content": "- The proposed ZSCL outperforms all state-of-the-art methods across multiple benchmark datasets. On 10 steps CL of CIFAR100 and TinyImageNet, our method outperforms the best of previous ones by " + }, + { + "bbox": [ + 317, + 574, + 545, + 658 + ], + "type": "inline_equation", + "content": "7.7\\%" + }, + { + "bbox": [ + 317, + 574, + 545, + 658 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 317, + 574, + 545, + 658 + ], + "type": "inline_equation", + "content": "6.0\\%" + }, + { + "bbox": [ + 317, + 574, + 545, + 658 + ], + "type": "text", + "content": " for the Last accuracy. On MTCL, ZSCL outperforms others by " + }, + { + "bbox": [ + 317, + 574, + 545, + 658 + ], + "type": "inline_equation", + "content": "10.9\\%" + }, + { + "bbox": [ + 317, + 574, + 545, + 658 + ], + "type": "text", + "content": " on Transfer and " + }, + { + "bbox": [ + 317, + 574, + 545, + 658 + ], + "type": "inline_equation", + "content": "9.7\\%" + }, + { + "bbox": [ + 317, + 574, + 545, + 658 + ], + "type": "text", + "content": " on Avg. scores." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 669, + 392, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 392, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 392, + 681 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "Vision-Language Models. Inspired by the success of language foundation models such as GPT-3 [3] and T5 [45], a" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19126" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "series of work pre-train vision-language models on large-scale image-text datasets [31, 44, 23]. Among them, Contrastive Language-Vision Pre-training [44] achieves remarkable performance on various downstream tasks. It concentrates on aligning images and texts to acquire a joint embedding space. The CLIP model contains an image encoder [16, 12] and a text encoder [9]. During pre-training, contrastive learning is performed in which a paired image-text is a positive pair while image and text from different image-text pairs form a negative pair. For inference, the closest text embedding for the image is chosen as the prediction. Vision-language models can give zero-shot predictions on unseen tasks with a robust zero-shot transfer ability on various downstream tasks." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 255, + 289, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 255, + 289, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 289, + 579 + ], + "type": "text", + "content": "Continual Learning Methods. Most existing continual learning methods can be categorized into four groups: parameter expansion, memory replay, distillation loss, and parameter regularization. Parameter expansion methods such as DyTox [14] and DEN [61] introduce new parameters for new tasks. As we want to achieve a more powerful CLIP model at the end of CL, we do not change the architecture of the CLIP model. Memory replay methods [50, 36, 42, 28, 40] including iCaRL [47] and SER [21] keep a memory for exemplars from previously learned tasks. However, pre-training datasets are too large for choosing exemplars or may not be available at downstream training, and downstream data are not good exemplars for preserving the pretraining knowledge. Distillation loss such as LwF [33], LwM [10], LwF-VR [11], and PodNet [13] aligns current output space with previous ones, whereas distillation based on current tasks are not strong enough to maintain foundational knowledge. For the CLIP model, we find that general images, even if never seen by the model, plus sentences with enough semantics, can be a good \"replay\" for the distillation loss. The parameter regularization loss restricts the flexibility of model parameters by training loss [25, 62, 1] or weight averaging [30, 58]. Although this type of strategy performs badly compared to other ways in previous research [55, 2], we found it helpful for CLIP continual learning. The limited parameter space prevents the model from diverging significantly from its original state." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": "Vision-Language Models for Downstream Tasks. Many works propose different training strategies of vision-language models for better performance on downstream tasks, such as CoOp [64], CLIP-Adapter [15] and WiSE-FT [58]. However, very few attempts at continual learning exist. While [52, 56] focus on CL in the pretrain of VL and [39] trains VL from scratch using a small dataset, our problem setting differs as we address CL in downstream tasks with a pretrained VL. Currently, most VL models are trained directly on an accessible large" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 254 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 254 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 254 + ], + "type": "text", + "content": "dataset, yet integrating knowledge continuously into a pretrained VL is a practical necessity. None of these studies address the zero-shot transfer degradation phenomenon, instead focusing on the traditional forgetting of learned knowledge. Recently, Thengane et al. [53] shows CLIP zero-shot prediction achieves state-of-the-art performance in CL settings even without any training. LwF-VR [11] is a modified LwF method for the CLIP model where random-generated sentences are used for distillation loss. However, it only considers the feature space, and the distillation with random sentences cannot protect the vision backbone. Differently, we re-examine what should be used for distillation in the feature space and combine the parameter space weight ensemble to provide better performance for the vision-language model continual learning." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 261, + 373, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 261, + 373, + 274 + ], + "spans": [ + { + "bbox": [ + 306, + 261, + 373, + 274 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 280, + 392, + 293 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 280, + 392, + 293 + ], + "spans": [ + { + "bbox": [ + 306, + 280, + 392, + 293 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "text", + "content": "Continual Learning. Given " + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "text", + "content": " tasks " + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "inline_equation", + "content": "[\\mathcal{T}^1, \\mathcal{T}^2, \\dots, \\mathcal{T}^n]" + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "text", + "content": ", continual training is conducted in sequence on each task " + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^i = (\\mathcal{D}^i, C^i)" + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "inline_equation", + "content": "i = 1, \\dots, n" + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^i" + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "text", + "content": " represents the task dataset " + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "inline_equation", + "content": "\\{(x_j^i, y_j^i)\\}_{j=1}^{N_i}" + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "inline_equation", + "content": "x_j^i" + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "text", + "content": " is an image, " + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "inline_equation", + "content": "y_j^i" + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "text", + "content": " is a one-hot vector indicating the ground truth, and " + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "inline_equation", + "content": "N_i" + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "text", + "content": " is the number of images in the dataset. Class names " + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "inline_equation", + "content": "C^i = \\{c_j^i\\}_{j=1}^{m_i}" + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "text", + "content": " maps the label of an image to an object name, where " + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "inline_equation", + "content": "m_i" + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "text", + "content": " is the number of classes for task " + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^i" + }, + { + "bbox": [ + 304, + 298, + 547, + 407 + ], + "type": "text", + "content": ". The objective of continual learning is to achieve good performance on all tasks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 407, + 547, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 547, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 547, + 491 + ], + "type": "text", + "content": "Two continual learning settings are focused on in this study [55]. In task-incremental learning, at inference, the image " + }, + { + "bbox": [ + 304, + 407, + 547, + 491 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 304, + 407, + 547, + 491 + ], + "type": "text", + "content": " to be predicted is given with its task identity " + }, + { + "bbox": [ + 304, + 407, + 547, + 491 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 407, + 547, + 491 + ], + "type": "text", + "content": ", so the model only needs to distinguish between different classes in " + }, + { + "bbox": [ + 304, + 407, + 547, + 491 + ], + "type": "inline_equation", + "content": "C^t" + }, + { + "bbox": [ + 304, + 407, + 547, + 491 + ], + "type": "text", + "content": ". In class-incremental learning, the task identity " + }, + { + "bbox": [ + 304, + 407, + 547, + 491 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 407, + 547, + 491 + ], + "type": "text", + "content": " is not given. Thus we need to predict with the combined class set " + }, + { + "bbox": [ + 304, + 407, + 547, + 491 + ], + "type": "inline_equation", + "content": "C = \\bigcup_{i=1}^{n} C^i" + }, + { + "bbox": [ + 304, + 407, + 547, + 491 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "text", + "content": "CLIP model. The CLIP model contains an image encoder " + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "text", + "content": " and a text encoder " + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "text", + "content": ". The inference process of the CLIP model for image classification is as follows. First, for task " + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^i" + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "text", + "content": ", each class " + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "text", + "content": " is transformed into a sentence by a template like \"a photo of " + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "inline_equation", + "content": "\\{c\\}" + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "text", + "content": "\". Then " + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "text", + "content": " encodes the classes into text embeddings " + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "inline_equation", + "content": "\\{\\pmb{t}_{j}^{i}\\}_{j = 1}^{m_{i}}" + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "text", + "content": ". An image encoder encodes input image " + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "inline_equation", + "content": "\\pmb{x}_k" + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "text", + "content": ". The similarity score between the image embedding and text embeddings are calculated as " + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "inline_equation", + "content": "s_{k,j}^{i} = \\langle f_{i}(\\pmb{x}_{k}),\\pmb{t}_{j}^{i}\\rangle" + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "inline_equation", + "content": "\\langle \\cdot ,\\cdot \\rangle" + }, + { + "bbox": [ + 304, + 504, + 547, + 624 + ], + "type": "text", + "content": " denotes the cosine similarity. The class with the largest similarity score is the prediction for the image." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 624, + 547, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 624, + 547, + 660 + ], + "spans": [ + { + "bbox": [ + 304, + 624, + 547, + 660 + ], + "type": "text", + "content": "To fine-tune the CLIP model for downstream tasks, cross-entropy loss CE is applied to the similarity score with a temperature scaling:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 365, + 664, + 545, + 697 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 664, + 545, + 697 + ], + "spans": [ + { + "bbox": [ + 365, + 664, + 545, + 697 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {C E}} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathrm {C E} (\\tau \\cdot \\boldsymbol {s} _ {i}, \\boldsymbol {y} _ {i}), \\tag {1}", + "image_path": "5a8b1f8056eaf7ae3f2a81468e5ed80e89ac7c55458beddbe53879074df524b7.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 701, + 527, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 527, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 527, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 701, + 527, + 714 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 306, + 701, + 527, + 714 + ], + "type": "text", + "content": " is a parameter learned during the pre-training." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19127" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 74, + 293, + 201 + ], + "blocks": [ + { + "bbox": [ + 50, + 74, + 293, + 201 + ], + "lines": [ + { + "bbox": [ + 50, + 74, + 293, + 201 + ], + "spans": [ + { + "bbox": [ + 50, + 74, + 293, + 201 + ], + "type": "image", + "image_path": "4329bff0d636ac16c1e23263b5d689cb7dbc7b4b289e45b30094e3f0c1b8cdce.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 213, + 547, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 213, + 547, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 547, + 258 + ], + "type": "text", + "content": "Figure 2. Illustration of ZSCL in feature space. Fig. 3(a) shows the pipeline of distillation. The original and the current model encode the reference images and texts, respectively. The probability distribution of images and texts with respect to each other is distilled. Fig. 3(b) displays how distillation loss preserves the feature space. Compared with the reference dataset, the features of fine-tuning tasks lie in a small subspace. The distillation loss preserves the structure of the feature space by maintaining relative distances." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 304, + 74, + 547, + 204 + ], + "blocks": [ + { + "bbox": [ + 304, + 74, + 547, + 204 + ], + "lines": [ + { + "bbox": [ + 304, + 74, + 547, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 74, + 547, + 204 + ], + "type": "image", + "image_path": "f03a900cd5ed94daddb29f1585000c813ccaa2207a4462c7b9f5c88529204ab8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 278, + 203, + 292 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 278, + 203, + 292 + ], + "spans": [ + { + "bbox": [ + 47, + 278, + 203, + 292 + ], + "type": "text", + "content": "3.2. Distillation in Feature Space" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 297, + 287, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 287, + 403 + ], + "type": "text", + "content": "Well-learned feature space for aligned images and texts enables vision-language models' strong zero-shot transfer ability. It also facilitates the learning of downstream tasks. Compared with the pre-training dataset, downstream datasets lie in a small scope in the feature space (shown in Fig. 2(b)). Direct fine-tuning of downstream tasks greatly distorts the feature distribution of out-of-distribution data, which leads to a significant drop in zero-shot prediction performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 404, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 404, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 404, + 287, + 464 + ], + "type": "text", + "content": "While the cross-entropy improves the performance by altering fine-tuned feature subspace, we need a new regularization to preserve the potential out-of-distribution feature space. The relative similarity between one image and different texts is:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 110, + 475, + 287, + 488 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 475, + 287, + 488 + ], + "spans": [ + { + "bbox": [ + 110, + 475, + 287, + 488 + ], + "type": "interline_equation", + "content": "\\boldsymbol {p} = \\operatorname {S o f t m a x} \\left(\\boldsymbol {s} _ {1}, \\dots , \\boldsymbol {s} _ {m}\\right). \\tag {2}", + "image_path": "a1c79b09d6f3e7b48e3dd5dd3255dfd781a618224312aa9ea7010d3a84556e61.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 496, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 287, + 544 + ], + "type": "text", + "content": "We hope the above similarity distribution is stable during fine-tuning for all potential images and texts. Given a teacher model " + }, + { + "bbox": [ + 46, + 496, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\overline{f}" + }, + { + "bbox": [ + 46, + 496, + 287, + 544 + ], + "type": "text", + "content": ", distillation loss can be applied to penalize changes from the original distribution:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 83, + 553, + 287, + 585 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 553, + 287, + 585 + ], + "spans": [ + { + "bbox": [ + 83, + 553, + 287, + 585 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {d i s t . i m g}} = \\operatorname {C E} (\\boldsymbol {p}, \\bar {\\boldsymbol {p}}) = - \\sum_ {j = 1} ^ {m} \\boldsymbol {p} _ {j} \\cdot \\log \\bar {\\boldsymbol {p}} _ {j}, \\tag {3}", + "image_path": "e89ada5c31932222ed3fed2adee39a31e8db322c080de061a82ad27132c53d6b.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 594, + 268, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 594, + 268, + 605 + ], + "spans": [ + { + "bbox": [ + 47, + 594, + 268, + 605 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 594, + 268, + 605 + ], + "type": "inline_equation", + "content": "\\overline{\\pmb{p}}" + }, + { + "bbox": [ + 47, + 594, + 268, + 605 + ], + "type": "text", + "content": " is the distribution given by the teacher model." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "text", + "content": "Although the distillation form has been widely used in previous methods [18, 33, 47], they are applied to continual learning from scratch. We investigate different components of the distillation loss for enhancing pre-trained vision-language models." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "Three components are discussed in this paper in detail: the data source, the teacher model, and the loss design. Sec. 5.1 shows the performance for the different choices. First, for the data source, LwF [33] uses data from the cur" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 279, + 545, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 279, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 279, + 545, + 447 + ], + "type": "text", + "content": "rent task, while iCarl [47] carefully selects data from previous tasks. However, data from downstream tasks span a small subspace and are not good enough to preserve the whole feature space. An ideal choice is the pre-training dataset. However, the CLIP pre-training dataset is private, and the size is too large to load. To solve this challenge, we introduce the reference dataset. A reference dataset is a publicly available image dataset with enough semantics. Enough semantics can be seen as random sampling in the whole feature space. The texts can be related class names, unrelated sentences, or even random tokens. This is because text semantics are easier to sample, and we need not ground truth to calculate the distance between one image to sufficient text samples spread among feature space." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 456, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 564 + ], + "type": "text", + "content": "For the teacher model, [33, 47] use the model after learning task i-1 and before learning task i as the teacher model. During the continual training of the vision-language model, the feature space deviates gradually from the initial model. Using fine-tuned models as teacher models enlarges this change. In contrast, we find using the pre-trained model as a teacher model not only preserves the zero-shot transfer ability but also takes advantage of well-learned feature space for better downstream performance." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "spans": [ + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "type": "text", + "content": "Finally, previous distillation loss is applied on traditional backbones, where a classification head gives the probability for different labels. For the vision-language model, the probability is calculated based on the relative distance between images and texts. Thus, in addition to Eq. (3), we impose regularization " + }, + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{dist\\_txt}}" + }, + { + "bbox": [ + 304, + 574, + 545, + 671 + ], + "type": "text", + "content": " on the distances from a text to a batch of images. The whole framework is shown in Fig. 2 (a) with the following training loss:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 355, + 701, + 545, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 355, + 701, + 545, + 714 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\mathrm {c e}} + \\lambda \\cdot \\left(\\mathcal {L} _ {\\mathrm {l w f . i m g}} + \\mathcal {L} _ {\\mathrm {l w f . t x t}}\\right). \\tag {4}", + "image_path": "d75a0e38fdc7568d46b6c8094d378b883afd95152e68a6aeb6e11673397fcf11.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19128" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 69, + 265, + 209 + ], + "blocks": [ + { + "bbox": [ + 70, + 69, + 265, + 209 + ], + "lines": [ + { + "bbox": [ + 70, + 69, + 265, + 209 + ], + "spans": [ + { + "bbox": [ + 70, + 69, + 265, + 209 + ], + "type": "image", + "image_path": "eb3d24a46c63689d28133592e77841b07804ba7d89e7f0c1fa29b32d5c02b588.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 216, + 289, + 273 + ], + "lines": [ + { + "bbox": [ + 46, + 216, + 289, + 273 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 289, + 273 + ], + "type": "text", + "content": "Figure 3. Models during training contain different tradeoffs between zero-shot and new task performance. Points for FT are sampled every 100 iterations, and the ones for WiSE-FT means different " + }, + { + "bbox": [ + 46, + 216, + 289, + 273 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 216, + 289, + 273 + ], + "type": "text", + "content": " choices. WE ensembles models during training and achieve better performance." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 290, + 247, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 290, + 247, + 304 + ], + "spans": [ + { + "bbox": [ + 47, + 290, + 247, + 304 + ], + "type": "text", + "content": "3.3. Weight Ensemble in Parameter Space" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 309, + 288, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 309, + 288, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 309, + 288, + 369 + ], + "type": "text", + "content": "Machine learning models integrate learned knowledge in their parameters. To mitigate the forgetting problem, a series of works [25, 62, 1] impose regularization losses on the changes of parameters. Weight consolidation (WC) [25] imposes the following loss:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 120, + 376, + 287, + 401 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 376, + 287, + 401 + ], + "spans": [ + { + "bbox": [ + 120, + 376, + 287, + 401 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {W C}} = \\sum_ {i} \\left(\\theta_ {i} - \\bar {\\theta} _ {i}\\right) ^ {2}. \\tag {5}", + "image_path": "bf6f8cbdaa42ad1a051aa9c8e274a50ee2774be08693cd7b7d4512585ab0fc2b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 409, + 287, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 287, + 457 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 287, + 457 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 409, + 287, + 457 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 409, + 287, + 457 + ], + "type": "text", + "content": " is the parameters of the current model, and " + }, + { + "bbox": [ + 46, + 409, + 287, + 457 + ], + "type": "inline_equation", + "content": "\\overline{\\theta}" + }, + { + "bbox": [ + 46, + 409, + 287, + 457 + ], + "type": "text", + "content": " is the reference ones. Although this regularization prevents forgetting, it hinders learning new tasks in a challenging CL setting." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 458, + 287, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 458, + 287, + 541 + ], + "spans": [ + { + "bbox": [ + 46, + 458, + 287, + 541 + ], + "type": "text", + "content": "Apart from regularization losses, another method in parameter space is to ensemble different model weights. Model soup [57] averages weights of multiple fine-tuned models to improve the model's robustness but introduces additional training costs. WiSE-FT [58] propose a weighted average between fine-tuned model and the original model to improve the out-of-distribution prediction robustness:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 111, + 549, + 287, + 562 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 549, + 287, + 562 + ], + "spans": [ + { + "bbox": [ + 111, + 549, + 287, + 562 + ], + "type": "interline_equation", + "content": "f (x; (1 - \\alpha) \\cdot \\theta_ {0} + \\alpha \\cdot \\theta_ {1}), \\tag {6}", + "image_path": "15dfb527d530e05ea1face79a55d39f36dcd48a361cf727270e45406f270bc52.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 570, + 287, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 630 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 630 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 570, + 287, + 630 + ], + "type": "inline_equation", + "content": "\\theta_0" + }, + { + "bbox": [ + 46, + 570, + 287, + 630 + ], + "type": "text", + "content": " is the original model and " + }, + { + "bbox": [ + 46, + 570, + 287, + 630 + ], + "type": "inline_equation", + "content": "\\theta_{1}" + }, + { + "bbox": [ + 46, + 570, + 287, + 630 + ], + "type": "text", + "content": " is the fine-tuned one. However, this method is hyper-parameter-sensitive where different " + }, + { + "bbox": [ + 46, + 570, + 287, + 630 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 570, + 287, + 630 + ], + "type": "text", + "content": " gives different tradeoffs between zero-shot transfer ability and downstream task performance (blue line in Fig. 3." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "Inspired by this, we extend the weighted average to the CL setting. The motivation for the weighted average is to prevent fine-tuning from losing too much knowledge in the original model. As training goes by (green line in Fig. 3), the model performs better on new tasks while losing accuracy on previous ones. The models among training compose a sequence of different learning-forgetting tradeoffs." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 86, + 354, + 142 + ], + "blocks": [ + { + "bbox": [ + 312, + 73, + 321, + 81 + ], + "lines": [ + { + "bbox": [ + 312, + 73, + 321, + 81 + ], + "spans": [ + { + "bbox": [ + 312, + 73, + 321, + 81 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 310, + 86, + 354, + 142 + ], + "lines": [ + { + "bbox": [ + 310, + 86, + 354, + 142 + ], + "spans": [ + { + "bbox": [ + 310, + 86, + 354, + 142 + ], + "type": "image", + "image_path": "c1c8038706070e6074aff8433598727beaf8d68f06790075ab76e09402bafbd0.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 363, + 86, + 408, + 142 + ], + "blocks": [ + { + "bbox": [ + 363, + 86, + 408, + 142 + ], + "lines": [ + { + "bbox": [ + 363, + 86, + 408, + 142 + ], + "spans": [ + { + "bbox": [ + 363, + 86, + 408, + 142 + ], + "type": "image", + "image_path": "7612a0001597f0d99113646e1932e6b9a2dfdfa5b9fc31e1b66a56d4a369c262.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 311, + 149, + 353, + 207 + ], + "blocks": [ + { + "bbox": [ + 311, + 149, + 353, + 207 + ], + "lines": [ + { + "bbox": [ + 311, + 149, + 353, + 207 + ], + "spans": [ + { + "bbox": [ + 311, + 149, + 353, + 207 + ], + "type": "image", + "image_path": "816e3786999b886a7661b676ba1153e0a0d8b60c6ea218d1e5871216e42d0f37.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 364, + 149, + 408, + 206 + ], + "blocks": [ + { + "bbox": [ + 364, + 149, + 408, + 206 + ], + "lines": [ + { + "bbox": [ + 364, + 149, + 408, + 206 + ], + "spans": [ + { + "bbox": [ + 364, + 149, + 408, + 206 + ], + "type": "image", + "image_path": "952c17a62f4e4c386253f86e5ba5a7e8676eb7209cde979b79afbd3ab84319b1.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 419, + 83, + 545, + 228 + ], + "blocks": [ + { + "bbox": [ + 419, + 73, + 428, + 81 + ], + "lines": [ + { + "bbox": [ + 419, + 73, + 428, + 81 + ], + "spans": [ + { + "bbox": [ + 419, + 73, + 428, + 81 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 419, + 83, + 545, + 228 + ], + "lines": [ + { + "bbox": [ + 419, + 83, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 419, + 83, + 545, + 228 + ], + "type": "image", + "image_path": "81e23c68abd350a661469da9d431633c4fcb113cc4ec578215ac9647b344ca15.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 236, + 547, + 270 + ], + "lines": [ + { + "bbox": [ + 305, + 236, + 547, + 270 + ], + "spans": [ + { + "bbox": [ + 305, + 236, + 547, + 270 + ], + "type": "text", + "content": "Figure 4. Fig.(a): examples of tasks from different domains in MTIL benchmark. Fig.(b): illustration of calculating metrics Transfer, Avg. and Last during continual learning." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 289, + 546, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 289, + 546, + 326 + ], + "spans": [ + { + "bbox": [ + 305, + 289, + 546, + 326 + ], + "type": "text", + "content": "Instead of interpolating only between the initial and the final model, our method weight ensemble (WE) averages the weights in the sequence during the training time:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 329, + 332, + 545, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 332, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 329, + 332, + 545, + 365 + ], + "type": "interline_equation", + "content": "\\hat {\\theta} _ {t} = \\left\\{ \\begin{array}{l l} \\theta_ {0} & t = 0 \\\\ \\frac {1}{t + 1} \\theta_ {t} + \\frac {t}{t + 1} \\cdot \\hat {\\theta} _ {t - 1} & \\text {e v e r y I i t e r a t i o n s} \\end{array} . \\right. \\tag {7}", + "image_path": "b3c51845187d90d38de07c2f1f7a7b50a989c732a7d7437f1f27c9dbc04efaae.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 372, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 372, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 305, + 372, + 545, + 491 + ], + "type": "text", + "content": "where model weight sampling happens every " + }, + { + "bbox": [ + 305, + 372, + 545, + 491 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 305, + 372, + 545, + 491 + ], + "type": "text", + "content": " iteration. The method is related to Stochastic Weight Averaging (SWA) [22], but we do not use a modified learning rate schedule here because instead of getting better generalization ability, WE aim to give an improved learning-forgetting tradeoff. As shown in Fig. 3, WE achieves better performance on downstream tasks than WiSE-FT. In addition, while WiSE-FT is sensitive to different values of " + }, + { + "bbox": [ + 305, + 372, + 545, + 491 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 372, + 545, + 491 + ], + "type": "text", + "content": ", our method is much more robust under different hyperparameter " + }, + { + "bbox": [ + 305, + 372, + 545, + 491 + ], + "type": "inline_equation", + "content": "(I)" + }, + { + "bbox": [ + 305, + 372, + 545, + 491 + ], + "type": "text", + "content": " choices." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 502, + 535, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 502, + 535, + 515 + ], + "spans": [ + { + "bbox": [ + 305, + 502, + 535, + 515 + ], + "type": "text", + "content": "4. Multi-domain Task Incremental Learning" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": "Conventional Continual Learning Benchmark. A benchmark consisting of several tasks is needed to evaluate different methods for continual learning. Most previous benchmarks are built by separating classes in a single dataset, such as MNIST [55], CIFAR100 [14], TinyImageNet [60], and ImageNet [60, 65]. We also evaluate our method with traditional benchmarks. In CIFAR100 [26], classes are separated into groups to build tasks. Suppose the dataset has " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": " classes, a " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": "-step setting means we learn " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "m / k" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": " classes in each new task. The CIFAR100 contains 100 classes, and the setting of 10, 20, and 50 steps are visited. For TinyImageNet with " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "m = 200" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": ", the first step learns 100 classes, and the rest is learned with 5, 10, and 20 steps. As for ImageNet-100, we have two settings: ImageNet-100-B0, which includes the same amount of classes for each step, and ImageNet-100-B50, which has" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19129" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 116, + 206, + 178 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "type": "text", + "content": "Table 1. Ablation experiments. Default settings are marked in gray, which uses image and text distillation loss with the initial CLIP model on 100k ImageNet images and texts generated from ImageNet classes with a simple template." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 77, + 103, + 171, + 114 + ], + "lines": [ + { + "bbox": [ + 77, + 103, + 171, + 114 + ], + "spans": [ + { + "bbox": [ + 77, + 103, + 171, + 114 + ], + "type": "text", + "content": "(a) Continual learning loss." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 116, + 206, + 178 + ], + "lines": [ + { + "bbox": [ + 53, + 116, + 206, + 178 + ], + "spans": [ + { + "bbox": [ + 53, + 116, + 206, + 178 + ], + "type": "table", + "html": "
lossTransferAvg.Last
CE only44.655.977.3
Feat. Dist.47.658.777.1
Image-only56.568.982.1
Text-only56.769.082.6
Both56.869.283.0
", + "image_path": "bd47b8cc97b89c696691abf6145c7fa7b7975a21209b7a49d0a2c12b27dbebbe.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 53, + 191, + 209, + 244 + ], + "blocks": [ + { + "bbox": [ + 92, + 179, + 157, + 188 + ], + "lines": [ + { + "bbox": [ + 92, + 179, + 157, + 188 + ], + "spans": [ + { + "bbox": [ + 92, + 179, + 157, + 188 + ], + "type": "text", + "content": "(d) Teacher model." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 191, + 209, + 244 + ], + "lines": [ + { + "bbox": [ + 53, + 191, + 209, + 244 + ], + "spans": [ + { + "bbox": [ + 53, + 191, + 209, + 244 + ], + "type": "table", + "html": "
sourceTransferAvg.Last
Initial56.869.283.0
n-153.966.680.7
WiSE(0.5)56.468.982.9
WiSE(0.8)56.267.881.3
", + "image_path": "aa1d0b2e84d0d8395d5958f4119eb749f0b5b6e3f4a5e35a6c7cbb93ff77a63a.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 225, + 117, + 380, + 178 + ], + "blocks": [ + { + "bbox": [ + 248, + 103, + 342, + 114 + ], + "lines": [ + { + "bbox": [ + 248, + 103, + 342, + 114 + ], + "spans": [ + { + "bbox": [ + 248, + 103, + 342, + 114 + ], + "type": "text", + "content": "(b) Data sources for replay." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 225, + 117, + 380, + 178 + ], + "lines": [ + { + "bbox": [ + 225, + 117, + 380, + 178 + ], + "spans": [ + { + "bbox": [ + 225, + 117, + 380, + 178 + ], + "type": "table", + "html": "
sourceTransferAvg.Last
current56.766.580.2
ImageNet56.869.283.0
CC57.268.580.9
CIFAR10055.265.980.7
Flowers54.766.080.8
", + "image_path": "e7a53235fc55eabdceac0aed247a87eb840a49f999bd06615b82055e6889be59.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 225, + 191, + 380, + 243 + ], + "blocks": [ + { + "bbox": [ + 255, + 178, + 335, + 189 + ], + "lines": [ + { + "bbox": [ + 255, + 178, + 335, + 189 + ], + "spans": [ + { + "bbox": [ + 255, + 178, + 335, + 189 + ], + "type": "text", + "content": "(e) # images for replay." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 225, + 191, + 380, + 243 + ], + "lines": [ + { + "bbox": [ + 225, + 191, + 380, + 243 + ], + "spans": [ + { + "bbox": [ + 225, + 191, + 380, + 243 + ], + "type": "table", + "html": "
#imageTransferAvg.Last
1M58.770.183.2
100k56.869.283.0
10k57.868.781.2
1k56.367.680.8
", + "image_path": "1bdffdf8de7307efbe544e64fd3f83a288a35b2bfb186dc9758440726f83378b.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 395, + 117, + 550, + 178 + ], + "blocks": [ + { + "bbox": [ + 420, + 103, + 512, + 114 + ], + "lines": [ + { + "bbox": [ + 420, + 103, + 512, + 114 + ], + "spans": [ + { + "bbox": [ + 420, + 103, + 512, + 114 + ], + "type": "text", + "content": "(c) Text sources for replay." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 395, + 117, + 550, + 178 + ], + "lines": [ + { + "bbox": [ + 395, + 117, + 550, + 178 + ], + "spans": [ + { + "bbox": [ + 395, + 117, + 550, + 178 + ], + "type": "table", + "html": "
sourceTransferAvg.Last
current51.864.982.0
prev. all54.070.283.7
1k classes (IN)56.869.283.0
13k Sent. (CC)58.970.584.0
1k Rand. Sent.58.770.283.8
", + "image_path": "89a67456fdb955935a5376d6ef17aa5c518dd36a1e1af1bfedd4d3b100627246.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 395, + 191, + 550, + 243 + ], + "blocks": [ + { + "bbox": [ + 416, + 178, + 517, + 189 + ], + "lines": [ + { + "bbox": [ + 416, + 178, + 517, + 189 + ], + "spans": [ + { + "bbox": [ + 416, + 178, + 517, + 189 + ], + "type": "text", + "content": "(f) # image classes for replay." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 395, + 191, + 550, + 243 + ], + "lines": [ + { + "bbox": [ + 395, + 191, + 550, + 243 + ], + "spans": [ + { + "bbox": [ + 395, + 191, + 550, + 243 + ], + "type": "table", + "html": "
#classTransferAvg.Last
100056.867.683.0
10056.767.382.3
1053.866.481.0
153.165.580.5
", + "image_path": "1fbef6a5fee68628c0b246ae13a2e24e77befe915ade7a66d22af3cc956111c2.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 48, + 283, + 290, + 383 + ], + "blocks": [ + { + "bbox": [ + 59, + 262, + 274, + 274 + ], + "lines": [ + { + "bbox": [ + 59, + 262, + 274, + 274 + ], + "spans": [ + { + "bbox": [ + 59, + 262, + 274, + 274 + ], + "type": "text", + "content": "Table 2. Ablation study of different components for ZSCL." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 283, + 290, + 383 + ], + "lines": [ + { + "bbox": [ + 48, + 283, + 290, + 383 + ], + "spans": [ + { + "bbox": [ + 48, + 283, + 290, + 383 + ], + "type": "table", + "html": "
MethodTransferΔAvg.ΔLastΔ
CLIP ViT-B/16@224px
Zero-shot69.40.065.30.065.30.0
Continual Learning44.6-24.855.9-9.477.3+12.0
+ Distillation58.9-10.570.5+5.283.8+18.5
+ WiSE-FT (best α)61.7-7.771.6+6.383.3+18.0
+ WE (ZSCL*)62.2-7.272.6+7.384.5+19.2
+ WC67.6-1.874.5+9.283.2+17.9
+ WiSE-FT67.7-1.774.2+8.981.9+16.6
+ WE (ZSCL)68.1-1.375.4+10.183.6+18.3
", + "image_path": "c391686ce697cfd0b0b4f8435ebbc81c674df95a2fd0850f219f8c907a0ccd04.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 403, + 288, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 288, + 452 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 288, + 452 + ], + "type": "text", + "content": "50 classes for the first step, and the remaining 50 classes are observed progressively over the next 10 stages. For ImageNet [7], we investigate a 10-step setting, which learns 100 new classes per task." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 468, + 288, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 288, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 288, + 673 + ], + "type": "text", + "content": "MTIL Benchmark. Different classes from one dataset share the common image source and a similar style [48, 17]. Thus, we propose Multi-domain Task Incremental Learning (MTIL), a cross-domain version of task incremental learning. Different tasks are collected from different domains, requiring different domain knowledge for humans to achieve high accuracy. Our MTIL benchmark consists of 11 tasks (detailed in supplementary materials), as some of the tasks illustrated in Fig. 4 (a). The MTIL benchmark is very challenging with a total number of 1,201 classes. Two orders are used for the evaluation; the first one is alphabet order (Order-I): Aircraft, Caltech101, CIFAR100, DTD, EuroSAT, Flowers, Food, MNIST, OxfordPet, StanfordCars, SUN397. And the second one is a random order (Order-II): StanfordCars, Food, MNIST, OxfordPet, Flowers, SUN397, Aircraft, Caltech101, DTD, EuroSAT, CIFAR100. Experiments are done in Order I by default." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "Evaluation Metrics. The metrics of MTIL are illustrated in Fig. 4(b), where rows represent training steps and a" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 264, + 547, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 264, + 547, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 264, + 547, + 445 + ], + "type": "text", + "content": "column shows performance for one dataset. For conventional continual learning, only scores under the diagonal are meaningful, since they cannot give zero-shot predictions on unseen tasks. In contrast, the zeros-hot transfer ability enables a vision-language model to provide predictions for all datasets. The average accuracy on all datasets among all timestamps is the \"Avg\" metric. The \"Last\" metric is the average performance of all tasks after CL. The \"Transfer\" metric is the average task performance in the upper-right triangle of the matrix. Every task's performance is first averaged to equal the weight of each dataset. It measures to what extent the zero-shot transfer ability is preserved. Before learning task " + }, + { + "bbox": [ + 304, + 264, + 547, + 445 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 264, + 547, + 445 + ], + "type": "text", + "content": ", tasks not earlier than " + }, + { + "bbox": [ + 304, + 264, + 547, + 445 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 264, + 547, + 445 + ], + "type": "text", + "content": " are not finetuned. Thus, their performance is an indicator of zero-shot transfer ability." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 456, + 388, + 470 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 456, + 388, + 470 + ], + "spans": [ + { + "bbox": [ + 306, + 456, + 388, + 470 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 476, + 547, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 476, + 547, + 573 + ], + "spans": [ + { + "bbox": [ + 304, + 476, + 547, + 573 + ], + "type": "text", + "content": "Implementation. We use CLIP [44] model with image encoder ViT-B/16 [12]. We conduct training with AdamW [37] optimizer and use a label smoothing [38] technique for a better baseline result. For multi-domain task continual learning, we train 1K iterations for each task, while for class-incremental learning, we follow the same evaluation setting in [14]. More implementation details can be found in the supplementary material." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 582, + 405, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 582, + 405, + 594 + ], + "spans": [ + { + "bbox": [ + 306, + 582, + 405, + 594 + ], + "type": "text", + "content": "5.1. Main Properties" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 600, + 545, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 600, + 545, + 637 + ], + "spans": [ + { + "bbox": [ + 304, + 600, + 545, + 637 + ], + "type": "text", + "content": "We ablate our method in feature-space in Tab. 1, and different choices for parameter-space regularization in Tab. 2. Several interesting characteristics are noted." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "Continual learning loss. In Tab. 1a, several types of loss for feature space are tested. The Feature Distance penalizing absolute distances achieves a low accuracy. Distillation loss on probability distribution regularizes relative distance in the feature space. With image-only or text-only distilla" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19130" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 72, + 149, + 163 + ], + "blocks": [ + { + "bbox": [ + 53, + 72, + 149, + 163 + ], + "lines": [ + { + "bbox": [ + 53, + 72, + 149, + 163 + ], + "spans": [ + { + "bbox": [ + 53, + 72, + 149, + 163 + ], + "type": "image", + "image_path": "486e0281799167fdc39ad25fe08f6ed1648465a543e6415e44a1f33130cf66aa.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 171, + 546, + 194 + ], + "lines": [ + { + "bbox": [ + 46, + 171, + 546, + 194 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 546, + 194 + ], + "type": "text", + "content": "Figure 5. t-SNE on five models' outputs together of Aircraft datasets after MTCL training: only our model maintains a similar feature distribution to the original CLIP ones with minor shift, while the rest significantly distort the feature space." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 152, + 72, + 248, + 163 + ], + "blocks": [ + { + "bbox": [ + 152, + 72, + 248, + 163 + ], + "lines": [ + { + "bbox": [ + 152, + 72, + 248, + 163 + ], + "spans": [ + { + "bbox": [ + 152, + 72, + 248, + 163 + ], + "type": "image", + "image_path": "7784c328f4cdf2b9bb2ed7f173c38e0d41ae1044f2237fb671b5c4c8254a9dc8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 250, + 72, + 347, + 163 + ], + "blocks": [ + { + "bbox": [ + 250, + 72, + 347, + 163 + ], + "lines": [ + { + "bbox": [ + 250, + 72, + 347, + 163 + ], + "spans": [ + { + "bbox": [ + 250, + 72, + 347, + 163 + ], + "type": "image", + "image_path": "09b430fabc5fe55f1527a5618eccc3aa9a80fbc30f1e07b877ca20d9e3d1d5a5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 350, + 72, + 446, + 163 + ], + "blocks": [ + { + "bbox": [ + 350, + 72, + 446, + 163 + ], + "lines": [ + { + "bbox": [ + 350, + 72, + 446, + 163 + ], + "spans": [ + { + "bbox": [ + 350, + 72, + 446, + 163 + ], + "type": "image", + "image_path": "eb90c5de160688afb191eadaa39b87a75136e54a5cc737262f85f987cb769e3e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 448, + 72, + 542, + 163 + ], + "blocks": [ + { + "bbox": [ + 448, + 72, + 542, + 163 + ], + "lines": [ + { + "bbox": [ + 448, + 72, + 542, + 163 + ], + "spans": [ + { + "bbox": [ + 448, + 72, + 542, + 163 + ], + "type": "image", + "image_path": "e8277e097f9a1ced82aa1b0687e58001beb7132aad61f8a706e47c69a5d84737.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 48, + 232, + 288, + 338 + ], + "blocks": [ + { + "bbox": [ + 52, + 213, + 282, + 224 + ], + "lines": [ + { + "bbox": [ + 52, + 213, + 282, + 224 + ], + "spans": [ + { + "bbox": [ + 52, + 213, + 282, + 224 + ], + "type": "text", + "content": "Table 3. Comparison of different methods on MTIL in Order I." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 232, + 288, + 338 + ], + "lines": [ + { + "bbox": [ + 48, + 232, + 288, + 338 + ], + "spans": [ + { + "bbox": [ + 48, + 232, + 288, + 338 + ], + "type": "table", + "html": "
MethodTransferΔAvg.ΔLastΔ
CLIP ViT-B/16@224px
Zero-shot69.40.065.30.065.30.0
Continual Learning44.6-24.855.9-9.477.3+12.0
LwF [33]56.9-12.564.7-0.674.6+9.0
iCaRL [47]50.4-19.065.7+0.480.1+14.8
LwF-VR [11]57.2-12.265.1-0.276.6+11.3
WiSE-FT [58]52.3-17.160.7-4.677.7+12.4
ZSCL* (Ours)62.2-7.272.6+7.384.5+19.2
ZSCL (Ours)68.1-1.375.4+10.183.6+18.3
", + "image_path": "93a36b72b943f7cd603380a954c6668578e979820d207fe6599536d19724b99c.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 357, + 287, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 287, + 393 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 287, + 393 + ], + "type": "text", + "content": "tion, the Transfer, Avg., and Last accuracy all improve. A further boost in performance occurs with both of the distillation losses." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 413, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 616 + ], + "type": "text", + "content": "Data source for replay. Tabs. 1b, 1c, 1e and 1f seek the standard for a good reference dataset. As shown in Tab. 1b, distillation on images of current tasks achieves a good Transfer score. However, it hinders the learning on new tasks and results in a low Avg. and Last score. Images in a specific domain (e.g., Flowers) are also not good choices. General images in ImageNet and Conceptual Caption (CC) datasets are examples of good reference datasets. These images are easily available by a web crawler [54]. Text with more semantics can improve performance (shown in Tab. 1c). When using sentences from the Conceptual Caption dataset [49], or even sentences randomly generated from the CLIP vocabulary, there is no ground truth target among the texts for the image from the ImageNet dataset. However, they all achieve an improvement due to more semantics. The reference image dataset does not need to be labeled, matched with the text, or seen by the CLIP model." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": "Enough semantics in the reference image dataset boosts the distillation performance. In Tabs. 1e and 1f, a smaller number of images and classes all lead to a degradation in the performance. Fewer classes of images in the reference dataset have a worse impact on the performance compared with the image numbers. To keep a reasonable memory buffer, we randomly sample " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "100\\mathrm{k}" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " images from ImageNet for MTIL and use texts from CC dataset. For class-" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 306, + 232, + 547, + 338 + ], + "blocks": [ + { + "bbox": [ + 309, + 213, + 541, + 224 + ], + "lines": [ + { + "bbox": [ + 309, + 213, + 541, + 224 + ], + "spans": [ + { + "bbox": [ + 309, + 213, + 541, + 224 + ], + "type": "text", + "content": "Table 4. Comparison of different methods on MTIL in Order II." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 232, + 547, + 338 + ], + "lines": [ + { + "bbox": [ + 306, + 232, + 547, + 338 + ], + "spans": [ + { + "bbox": [ + 306, + 232, + 547, + 338 + ], + "type": "table", + "html": "
MethodTransferΔAvg.ΔLastΔ
CLIP ViT-B/16@224px
Zero-shot65.40.065.30.065.30.0
Continual Learning46.6-18.856.2-9.167.4+2.1
LwF [33]53.2-12.262.2-5.271.9+6.6
iCaRL [47]50.9-14.556.9-8.471.6+6.3
LwF-VR [11]53.1-12.360.6-7.468.3+0.9
WiSE-FT [58]51.0-14.461.5-5.972.2+6.9
ZSCL*59.8-5.671.8+6.583.3+18.0
ZSCL64.2-1.274.5+9.283.4+18.1
", + "image_path": "a3c81c468e3153ab25efe2bc7736f185000675360c5f0818bbee81b4145c0144.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 358, + 545, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 358, + 545, + 383 + ], + "spans": [ + { + "bbox": [ + 305, + 358, + 545, + 383 + ], + "type": "text", + "content": "incremental learning, conceptual caption dataset's validation set (28k images) is used to avoid information leakage." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 398, + 546, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 398, + 546, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 398, + 546, + 518 + ], + "type": "text", + "content": "Teacher model. Tab. 1d shows the performance of distillation loss with different teacher models. Unlike conventional continual learning, the teacher model should not be the one trained on the previous task; otherwise, the deviation from the initial CLIP in the previous task may be amplified. In contrast, with the initial CLIP as the teacher model, not only is the zero-shot performance improved but the Mean and Last scores are also boosted, indicating that preserving high-quality feature space facilitates continual learning." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": "Parameter-space regularization. In Tab. 2, we experiment with three different parameter-space regularizations. We experiment with two variants of WiSE-FT [58]: the weighted average between the current model with the initial CLIP or the one at the previous task. The result shows the latter one is a better choice because keeping weight averaging with initial CLIP loses the newly learned knowledge. We experiment with different " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " choices for WiSE, and the best result is reported. While distillation loss improves the whole performance, the parameter-space regularization further protects the zero-shot transfer ability with a higher Transfer. Among the three parameter-space regularizations, only WE achieve a better Last score. WC greatly improves the Transfer scores with a lower Last score. A combination of the weight consolidation loss with weight" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19131" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 66, + 91, + 529, + 445 + ], + "blocks": [ + { + "bbox": [ + 107, + 70, + 485, + 82 + ], + "lines": [ + { + "bbox": [ + 107, + 70, + 485, + 82 + ], + "spans": [ + { + "bbox": [ + 107, + 70, + 485, + 82 + ], + "type": "text", + "content": "Table 5. Transfer, Avg., and Last scores (%) of different continue training methods on MTIL benchmark." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 91, + 529, + 445 + ], + "lines": [ + { + "bbox": [ + 66, + 91, + 529, + 445 + ], + "spans": [ + { + "bbox": [ + 66, + 91, + 529, + 445 + ], + "type": "table", + "html": "
MethodAircraftCaltech101CIFAR100DTDEuroSATFlowersFoodMNISTOxfordPetCarsSUN397
CLIP ViT-B/16@224px
Zero-shot24.388.468.244.654.971.088.559.489.064.765.2
Fine-tune62.095.189.679.598.997.592.799.694.789.681.8
Transfer
Continual-FT67.146.032.135.635.057.744.160.820.546.6
LwF [33]74.556.939.151.152.672.860.675.130.355.9
iCaRL [47]56.644.632.739.346.668.046.077.431.960.5
LwF-VR [11]77.161.040.545.354.474.647.976.736.358.6
WiSE-FT [58]73.555.635.641.547.068.353.969.326.851.9
Dist. only80.162.240.239.958.180.853.474.638.161.9
ZSCL*78.364.042.945.263.584.256.178.944.164.3
ZSCL86.067.445.450.469.187.661.886.860.166.8
Avg.
Continual-FT25.581.559.153.264.751.863.264.369.731.849.7
LwF [33]36.386.972.059.073.760.073.674.880.037.358.1
iCaRL [47]35.589.272.260.668.870.078.262.381.841.262.5
LwF-VR [11]29.687.774.459.572.463.677.066.781.243.760.7
WiSE-FT [58]26.786.564.357.165.758.771.170.575.836.954.6
Dist. only48.190.679.863.275.672.584.770.279.846.963.7
ZSCL*50.790.979.863.876.677.387.071.983.052.065.9
ZSCL45.192.080.164.379.581.689.675.288.964.768.0
Last
Continual-FT31.089.365.867.388.971.185.699.692.977.381.1
LwF [33]26.387.571.966.679.966.983.899.692.166.180.4
iCaRL [47]35.893.077.070.283.388.590.486.793.281.281.9
LwF-VR [11]20.589.872.367.685.573.885.799.693.173.380.9
WiSE-FT [58]27.290.868.068.986.974.087.699.692.677.881.3
Dist. only43.391.981.372.495.190.590.499.792.585.181.8
ZSCL*46.092.381.272.493.092.190.899.693.386.681.7
ZSCL40.692.281.370.594.890.591.998.793.985.380.2
", + "image_path": "9c645337f982c4049b97a0b2cbd146fe3651998e8ffb2db64402112ddaccf5f9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 464, + 288, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 288, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 288, + 514 + ], + "type": "text", + "content": "ensemble achieves a better tradeoff between Transfer and Last value. While " + }, + { + "bbox": [ + 46, + 464, + 288, + 514 + ], + "type": "inline_equation", + "content": "\\mathrm{ZSCL}^*" + }, + { + "bbox": [ + 46, + 464, + 288, + 514 + ], + "type": "text", + "content": ", a variant without the WC loss, obtains the highest Last score, the ZSCL with WC loss outperforms it with " + }, + { + "bbox": [ + 46, + 464, + 288, + 514 + ], + "type": "inline_equation", + "content": "2.8\\%" + }, + { + "bbox": [ + 46, + 464, + 288, + 514 + ], + "type": "text", + "content": " Avg. and " + }, + { + "bbox": [ + 46, + 464, + 288, + 514 + ], + "type": "inline_equation", + "content": "5.9\\%" + }, + { + "bbox": [ + 46, + 464, + 288, + 514 + ], + "type": "text", + "content": " Transfer scores." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 525, + 266, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 266, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 266, + 539 + ], + "type": "text", + "content": "5.2. Multi-domain Task Incremental Learning" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": "Tab. 3 displays the performance of different methods on the MTIL benchmark, and Tab. 5 presents the detailed Transfer, Avg, and Last metrics on each dataset. Zero-shot denotes the zero-shot prediction performance of the initial CLIP model, and Fine-tune means the direct fine-tuning accuracy on each dataset, which can be seen as an upperbound where no forgetting phenomenon happens. Continual learning uses cross-entropy loss to learn each dataset sequentially, where there is a significant forgetting issue on both zero-shot predictions (Transfer drops by " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "24.8\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": ") and newly learned knowledge (Last drops by " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "9.4\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": "). Previous methods improve the Last performance slightly and cannot maintain a high zero-shot prediction performance. Without WC, " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{ZSCL}^*" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": " achieves the best Last scores, outperforming" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 464, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 464, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 305, + 464, + 545, + 514 + ], + "type": "text", + "content": "the previous best one by " + }, + { + "bbox": [ + 305, + 464, + 545, + 514 + ], + "type": "inline_equation", + "content": "4.4\\%" + }, + { + "bbox": [ + 305, + 464, + 545, + 514 + ], + "type": "text", + "content": ". Our method ZSCL improves " + }, + { + "bbox": [ + 305, + 464, + 545, + 514 + ], + "type": "inline_equation", + "content": "9.1\\%" + }, + { + "bbox": [ + 305, + 464, + 545, + 514 + ], + "type": "text", + "content": " on Transfer accuracy, with only " + }, + { + "bbox": [ + 305, + 464, + 545, + 514 + ], + "type": "inline_equation", + "content": "1.3\\%" + }, + { + "bbox": [ + 305, + 464, + 545, + 514 + ], + "type": "text", + "content": " drops compared with the initial CLIP model, and achieves a " + }, + { + "bbox": [ + 305, + 464, + 545, + 514 + ], + "type": "inline_equation", + "content": "10.1\\%" + }, + { + "bbox": [ + 305, + 464, + 545, + 514 + ], + "type": "text", + "content": " gain in the Avg. accuracy." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 517, + 547, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 547, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 547, + 601 + ], + "type": "text", + "content": "Figure Fig. 5 provides a visualization of the feature space on Aircraft of the original CLIP and four methods trained at the end of MTCL (t-SNE conducted only once on all features collected). This shows our method is capable of maintaining the pretrained feature distribution with a small averaged feature distance and thus preserving zero-shot performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "The result of the MTIL method in Order-II is presented in Tab. 4. Our method surpasses previous methods in another order setting of the MTIL benchmark. A similar conclusion holds from the results of MTIL Order-II compared with MTIL Order-I. Our method ZSCL outperforms others by " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "9.2\\%" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " on the Avg. score and " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "18.1\\%" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " on the Last score with only a " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "1.2\\%" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " performance loss on the Transfer score. This shows our approach can work for different orders of the multi-domain task incremental learning. In addition," + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19132" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 102, + 288, + 272 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": "Table 6. Comparison of state-of-the-art CL methods on CIFAR100 benchmark in class-incremental setting." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 102, + 288, + 272 + ], + "lines": [ + { + "bbox": [ + 47, + 102, + 288, + 272 + ], + "spans": [ + { + "bbox": [ + 47, + 102, + 288, + 272 + ], + "type": "table", + "html": "
Methods10 steps20 steps50 steps
AvgLastAvgLastAvgLast
UCIR [19]58.6643.3958.1740.6356.8637.09
BiC [59]68.8053.5466.4847.0262.0941.04
RPSNet [46]68.6057.05----
PODNet [13]58.0341.0553.9735.0251.1932.99
DER [60]74.6464.3573.9862.5572.0559.76
DyTox+ [14]74.1062.3471.6257.4368.9051.09
CLIP [44]74.4765.9275.2065.7475.6765.94
FT65.4653.2359.6943.1339.2318.89
LwF [33]65.8648.0460.6440.5647.6932.90
iCaRL [47]79.3570.9773.3264.5571.2859.07
LwF-VR [11]78.8170.7574.5463.5471.0259.45
ZSCL (Ours)82.1573.6580.3969.5879.9267.36
Impr+7.68+7.73+5.19+3.84+3.95+1.42
", + "image_path": "d650b00a134f12b88b67cba437bcb07263b2d4a1ef65ad84a9d666ca2cd3cbb3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 300, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 361 + ], + "type": "text", + "content": "compared with Order-I, previous methods achieve a much lower Last score (e.g., for Continual-Learning, Order-I has " + }, + { + "bbox": [ + 46, + 300, + 287, + 361 + ], + "type": "inline_equation", + "content": "77.3\\%" + }, + { + "bbox": [ + 46, + 300, + 287, + 361 + ], + "type": "text", + "content": ", while Order-II has " + }, + { + "bbox": [ + 46, + 300, + 287, + 361 + ], + "type": "inline_equation", + "content": "65.3\\%" + }, + { + "bbox": [ + 46, + 300, + 287, + 361 + ], + "type": "text", + "content": "). With ZSCL, the Last score is similar (" + }, + { + "bbox": [ + 46, + 300, + 287, + 361 + ], + "type": "inline_equation", + "content": "83.6\\%" + }, + { + "bbox": [ + 46, + 300, + 287, + 361 + ], + "type": "text", + "content": " compared with " + }, + { + "bbox": [ + 46, + 300, + 287, + 361 + ], + "type": "inline_equation", + "content": "83.4\\%" + }, + { + "bbox": [ + 46, + 300, + 287, + 361 + ], + "type": "text", + "content": "). This shows our method is more robust towards different training orders." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 366, + 201, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 366, + 201, + 380 + ], + "spans": [ + { + "bbox": [ + 47, + 366, + 201, + 380 + ], + "type": "text", + "content": "5.3. Class Incremental Learning" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 384, + 288, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 288, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 288, + 552 + ], + "type": "text", + "content": "We evaluate our methods on conventional class incremental learning. Tabs. 6 and 7 display results on CIFAR100 and TinyImageNet, respectively. We re-implement some previous methods with a CLIP backbone (after CLIP in the table), while others using a special network design cannot be easily adapted. Although zero-shot CLIP prediction achieves a good result on these benchmarks, continual learning with direct fine-tuning or LwF [33] degrades the performance greatly, especially under the setting of a large step number. This demonstrates a severe catastrophic forgetting phenomenon in fine-tuning the CLIP model. Our method consistently improves the performance of the CLIP model on both Avg. and Last scores with a large gap towards previous ones." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 562, + 209, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 209, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 209, + 574 + ], + "type": "text", + "content": "6. Limitation and Future Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 653 + ], + "type": "text", + "content": "Our proposed method has a limitation that a reference dataset is needed. A promising direction of the work is to preserve the zero-shot transfer ability without the need for an outside dataset. For example, we may generate a synthetic image dataset as the reference dataset. Methods like [51] can synthesize datasets from a network." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "content": "The deep learning community tends to build large models with a huge dataset [3, 6], including vision-language models [44, 20]. As re-training cost upsurges, continual learning is an efficient approach for updating these models with custom usage." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 306, + 102, + 547, + 272 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "type": "text", + "content": "Table 7. Comparison of different methods on TinyImageNet splits in class-incremental settings with 100 base classes." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 102, + 547, + 272 + ], + "lines": [ + { + "bbox": [ + 306, + 102, + 547, + 272 + ], + "spans": [ + { + "bbox": [ + 306, + 102, + 547, + 272 + ], + "type": "table", + "html": "
Methods5 steps10 steps20 steps
AvgLastAvgLastAvgLast
EWC [25]19.016.0015.823.7912.354.73
EEIL [4]47.1735.1245.0334.6440.4129.72
UCIR [19]50.3039.4248.5837.2942.8430.85
MUC [35]32.2319.2026.6715.3321.8910.32
PASS [65]49.5441.6447.1939.2742.0132.93
DyTox [14]55.5847.2352.2642.7946.1836.21
CLIP [44]69.6265.3069.5565.5969.4965.30
FT61.5446.6657.0541.5454.6244.55
LwF [33]60.9748.7757.6044.0054.7942.26
iCaRL [47]77.0270.3973.4865.9769.6564.68
LwF-VR [11]77.5670.8974.1267.0569.9463.89
ZSCL (Ours)80.2773.5778.6171.6277.1868.30
Impr+10.65+8.27+9.06+6.03+7.69+3.00
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How to conduct this task with a reference dataset is left as future work." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 353, + 545, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 353, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 305, + 353, + 545, + 425 + ], + "type": "text", + "content": "Lately, a noticeable trend involves the creation of multimodality models utilizing large language models, showcasing encouraging outcomes in tasks such as Visual Question Answering (VQA). Expanding our approach to encompass the next token prediction task remains an avenue for future exploration and research." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 440, + 379, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 440, + 379, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 440, + 379, + 453 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "text", + "content": "In this paper, we investigate continual learning with the vision-language model. We propose a better continual learning algorithm to protect the zero-shot transfer ability in the vision-language model learned in the pre-training stage. Our algorithm mitigates the catastrophic forgetting in both feature space and parameter space. In feature space, distilling the initial model on a reference dataset significantly boosts the model's performance. In parameter space, weight ensemble among different training stages alleviates the forgetting issue. We propose a more challenging Multidomain Task Incremental Learning (MTIL) benchmark to evaluate the continual learning methods better. On both conventional and new benchmarks, our method achieves state-of-the-art performance." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 644, + 408, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 644, + 408, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 644, + 408, + 658 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 665, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 715 + ], + "type": "text", + "content": "Yang You's research group is being sponsored by the NUS startup grant (Presidential Young Professorship), Singapore MOE Tier-1 grant, ByteDance grant, ARCTIC grant, SMI grant, and Alibaba grant." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19133" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5871-5880, 2021. 2, 5, 9" + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19136" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Prior-guided Source-free Domain Adaptation for Human Pose Estimation/67d12eb1-f1e4-4b90-aba2-4771e3bf7c39_content_list.json b/2023/Prior-guided Source-free Domain Adaptation for Human Pose Estimation/67d12eb1-f1e4-4b90-aba2-4771e3bf7c39_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..53d8e857208829ddf053a456377a56de2e94bf08 --- /dev/null +++ b/2023/Prior-guided Source-free Domain Adaptation for Human Pose Estimation/67d12eb1-f1e4-4b90-aba2-4771e3bf7c39_content_list.json @@ -0,0 +1,2011 @@ +[ + { + "type": "text", + "text": "Prior-guided Source-free Domain Adaptation for Human Pose Estimation", + "text_level": 1, + "bbox": [ + 112, + 130, + 854, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dripta S. Raychaudhuri $^{1,2*}$ Calvin-Khang Ta $^{1}$ Arindam Dutta $^{1}$ Rohit Lal $^{1}$ Amit K. Roy-Chowdhury $^{1}$ $^{1}$ University of California, Riverside $^{2}$ AWS AI Labs", + "bbox": [ + 86, + 186, + 898, + 228 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{drayc001@, cta003@, adutt020@, rla1011@, amertc@ece.}ucr.edu", + "bbox": [ + 223, + 233, + 763, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 300, + 313, + 316 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Domain adaptation methods for 2D human pose estimation typically require continuous access to the source data during adaptation, which can be challenging due to privacy, memory, or computational constraints. To address this limitation, we focus on the task of source-free domain adaptation for pose estimation, where a source model must adapt to a new target domain using only unlabeled target data. Although recent advances have introduced source-free methods for classification tasks, extending them to the regression task of pose estimation is non-trivial. In this paper, we present Prior-guided Self-training (POST), a pseudolabeling approach that builds on the popular Mean Teacher framework to compensate for the distribution shift. POST leverages prediction-level and feature-level consistency between a student and teacher model against certain image transformations. In the absence of source data, POST utilizes a human pose prior that regularizes the adaptation process by directing the model to generate more accurate and anatomically plausible pose pseudo-labels. Despite being simple and intuitive, our framework can deliver significant performance gains compared to applying the source model directly to the target data, as demonstrated in our extensive experiments and ablation studies. In fact, our approach achieves comparable performance to recent state-of-the-art methods that use source data for adaptation.", + "bbox": [ + 75, + 333, + 473, + 710 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 742, + 209, + 757 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Human pose estimation is a fundamental task in computer vision that involves determining the precise locations of keypoints, such as joints, on a human body in an image or video [1]. The growing need for pose estimation in various applications such as action recognition [2], human-computer interaction [3], and video surveillance [4] has driven the rapid development of highly accurate deep learning tech", + "bbox": [ + 75, + 768, + 470, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f269fd9a6d1df8c4a7d32d89b1b306e6b1a67e8a5f63ca42de4197fc02660e7b.jpg", + "image_caption": [ + "Figure 1. Problem setup. Existing UDA methods for pose estimation rely on a labeled source dataset while adapting to an unlabeled target dataset. However, privacy concerns surrounding the use of personally identifiable information in these labeled datasets, as well as the significant storage and computational requirements, can limit access to such data. Hence, our work focuses on source-free UDA of pose estimation models." + ], + "image_footnote": [], + "bbox": [ + 504, + 285, + 890, + 512 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "niques. However, the challenge of obtaining large annotated datasets for training, compounded with the susceptibility to a performance decline in the face of data distribution shifts still poses limitations for current pose estimation models.", + "bbox": [ + 496, + 642, + 893, + 703 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To overcome these limitations, recent studies have focused on unsupervised domain adaptation (UDA) of pose estimators [5, 6]. UDA allows for transferring a pose estimation model trained on a source domain, where labeled data is available, to a target domain where labeled data is unavailable. Despite improved and robust pose estimation, the requirement of simultaneous access to both source and target domains during adaptation hinders real-world implementation. For instance, the labeled source data may not be accessible post-deployment due to privacy or proprietary issues. This is particularly relevant for human pose datasets, which contain personally identifiable information (PII) [7]. Furthermore, adaptation using the entire source data might", + "bbox": [ + 496, + 704, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 47 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Currently at AWS AI Labs. Work done while the author was at UCR.", + "bbox": [ + 98, + 886, + 467, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14996", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "be infeasible due to both memory and computational constraints. In light of these issues, we focus on source-free UDA of human pose estimation models.", + "bbox": [ + 76, + 90, + 470, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Concretely, our objective is to adapt a 2D human pose estimation model to a new target domain utilizing only its trained parameters and unlabeled target data. This presents a major challenge as the absence of source data for regularization can cause catastrophic forgetting. While recent advances have introduced methods to tackle this issue in classification tasks [8, 9, 10], extending them to the regression task of pose estimation is non-trivial. To address this challenge, we introduce Prior-guided Self-training (POST), a self-training regression framework that employs a human pose prior to effectively guide the adaptation process in the absence of source data. An overview of our problem setup is shown in Figure 1.", + "bbox": [ + 75, + 138, + 470, + 335 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our approach builds on the Mean Teacher [11] framework, which uses consistency in the prediction space of a student and teacher model to produce trustworthy pseudo-labels and learn from the unlabeled target domain. To achieve this, we create two augmented views of each target image, varying in scale, spatial context, and color statistics. Aligned pose predictions from both models in both views are then obtained, and consistency between the predictions across the different views is encouraged to facilitate prediction space adaptation. However, our empirical results show that relying solely on consistency in the output space is insufficient when supervision from the source data is lacking. To address this, we also introduce feature space adaptation, which aims to encourage consistency across features extracted from the two separate views. We adopt the Barlow Twins [12] approach to accomplish this. Specifically, we seek to make the cross-correlation matrix calculated from a pair of feature embeddings as close to the identity matrix as possible.", + "bbox": [ + 75, + 338, + 473, + 611 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In addition to the adaptation across both outputs and features, we employ a human pose prior that models the full manifold of plausible poses in some high-dimensional pose space to refine possible noisy pseudo-labels that may arise during self-training. The plausible poses are represented as points on the manifold surface, with zero distance from it, while non-plausible poses are located outside the surface, with a non-zero distance from it. This manifold is learned using a high-dimensional neural field, similar to Pose-NDF [13]. The pose prior acts as a strong regularizer, directing the model to generate more accurate pose pseudolabels on the target data and leading to improved adaptation. The learning of this prior requires an auxiliary dataset of plausible human poses, but this does not compromise the privacy aspect of our framework as the prior does not make use of RGB images. In addition, it is worth noting that the prior can be trained offline, separately from the adaptation process. This not only saves computational resources but also reduces the amount of storage required. Compared to storing entire", + "bbox": [ + 75, + 613, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "images, it is much more efficient to store pose coordinates, which requires approximately $3000 \\times$ less memory.", + "bbox": [ + 498, + 90, + 893, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Main contributions. To summarize, our primary contributions are as follows:", + "bbox": [ + 498, + 122, + 893, + 151 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We address the problem of adapting a human pose estimation model to a target domain consisting of unlabeled data, without access to the original source dataset. This ameliorates the privacy concern associated with the current domain adaptive pose estimation methods.", + "- We introduce Prior-guided Self-training (POST), a simple source-free unsupervised adaptation algorithm. POST leverages both prediction-level and feature-level consistency, in addition to a human pose prior, to drive self-training for improved adaptation to the target domain.", + "- We evaluate our method qualitatively and quantitatively on three challenging domain adaptive scenarios, demonstrating comparable performance to existing UDA methods that have access to the source data." + ], + "bbox": [ + 500, + 152, + 893, + 367 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 383, + 650, + 398 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Pose Estimation. 2D human pose estimation aims to locate human anatomical keypoints, such as the elbow and knee. Prior works can be categorized into two primary frameworks: the top-down framework and the bottom-up framework. Top-down methods [14, 15, 16, 17, 18, 19, 1] first detect each person from the image and then perform single-person pose estimation on each bounding box independently. On the other hand, bottom-up methods [20, 21, 22, 23, 24, 25, 26] predict keypoints of each person directly in an end-to-end manner. Typical bottom-up methods consist of two steps: predicting keypoint heatmaps and grouping the detected keypoints into separate poses. In this work, we focus on the bottom-up framework for efficiency purposes and adopt the Simple Baseline [18] architecture following [6] to ensure fair comparisons with prior domain adaptation algorithms.", + "bbox": [ + 498, + 409, + 893, + 636 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unsupervised Domain Adaptation. UDA methods have been extensively applied to a broad range of computer vision tasks, including image classification [27], semantic segmentation [28], object detection [29], and reinforcement learning [30] to tackle the issue of data distribution shift. Most approaches aim to align the source and target data distributions through techniques such as maximum mean discrepancy [31] and adversarial learning [32, 27]. Another line of research utilizes image translation methods to perform adaptation by transforming the source images into the target domain [33, 34]. More recently, there has been a surge of interest in adaptation using only a pre-trained source model due to privacy and memory storage concerns related to the source data. These include techniques such as information maximization [8, 9], pseudo-labeling [35, 36] and self-supervision [37]. Compared to other tasks, domain adaptation for regression tasks, such as pose estimation, remains", + "bbox": [ + 496, + 643, + 895, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14997", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "relatively unexplored.", + "bbox": [ + 76, + 90, + 223, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Domain Adaptive Pose Estimation. UDA methods for pose estimation have explored various techniques for overcoming the domain gap, including adversarial feature alignment and pseudo-labeling. RegDA [5] estimates the domain discrepancy by evaluating false predictions on the target domain and minimizes it. Mu et al. [38] proposed consistency regularization with respect to transformations and temporal consistency learning within a video. Li et al. [39] proposed a refinement module and a self-feedback loop to obtain reliable pseudo-labels. Recently, Kim et al. [6] introduced a unified framework for both human and animal keypoint detection, which aligns representations using input-level and output-level cues. Typically, these methods require access to the source data, which may raise data privacy, memory and computation concerns. In contrast, our method addresses the domain adaptation problem in a source-free setting.", + "bbox": [ + 75, + 112, + 473, + 354 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Prior-guided Self-training", + "text_level": 1, + "bbox": [ + 76, + 368, + 320, + 386 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our work investigates source-free domain adaptation for 2D human pose estimation. In the pose estimation task, given an input image $\\pmb{x} \\in \\mathbb{R}^{H \\times W \\times 3}$ , the goal is to predict the corresponding $y \\in \\mathbb{R}^{K \\times 2}$ representing the 2D coordinates of $K$ keypoints using a pose regression model $f$ . In this paper, we assume access to a pre-trained model, denoted by $f_{S}$ , as well as $N$ unlabeled images $\\mathcal{D} = \\{\\pmb{x}_i\\}_{i=1}^N$ from a target domain $\\mathcal{T}$ . Our goal is to adapt the source model to the target such that it performs better on images drawn from the target distribution than when directly using the source model on the target images.", + "bbox": [ + 75, + 393, + 470, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Overview. In the absence of source data, we propose to use self-training to adapt the source pose estimation model to the target domain. However, self-training methods are prone to error accumulation, particularly when labeled data is absent to act as regularization. Hence, we introduce POST, an enhanced self-training strategy that employs three essential ideas to prevent such errors:", + "bbox": [ + 75, + 564, + 468, + 669 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. A weight-averaged teacher model is used to generate the pseudo-labels for self-training. This ensures better retention of the source knowledge within the teacher model by reducing the effect of updating the weights via noisy pseudo-labels (Section 3.1.1).", + "2. In addition to adaptation over the output space via pseudolabels, the model is adapted in the feature space as well. For each target image, two aligned predictive views are generated via data augmentation, and consistency across features extracted from the two separate views is encouraged via a contrastive learning strategy (Section 3.1.2).", + "3. A human pose prior is used to regularize the adaptation by directing the model to generate more accurate and anatomically plausible pose pseudo-labels (Section 3.2). An overview of our framework is presented in Figure 2." + ], + "bbox": [ + 76, + 670, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Self-training via Mean Teacher", + "text_level": 1, + "bbox": [ + 500, + 90, + 774, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Motivated by research suggesting that weight-averaged models over training steps tend to perform better than the final model [6, 39], we utilize the Mean Teacher framework [11] to generate pseudo-labels for self-training. The framework involves creating two identical models, a teacher model $f_{\\mathrm{tea}}$ and a student model $f_{\\mathrm{stu}}$ , both of which are initialized with the pre-trained network $f_{S}$ at time step $t = 0$ . At each subsequent time step $t$ , the student model parameters $\\theta$ are updated by backpropagating the supervisory signals provided by the teacher model. The parameters of the teacher model $\\tilde{\\theta}$ are updated via an exponential moving average (EMA) of the student model parameters:", + "bbox": [ + 496, + 113, + 893, + 295 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\theta} _ {t} = \\alpha \\tilde {\\theta} _ {t - 1} + (1 - \\alpha) \\theta_ {t}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 305, + 893, + 325 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\alpha$ denotes the smoothing coefficient which is set to 0.999 by default. The EMA update prevents the teacher model from overfitting to noisy pseudo-labels during the initial rounds of self-training, thereby, preserving the source knowledge. This is especially advantageous in our scenario where source data is unavailable to regularize the adaptation.", + "bbox": [ + 496, + 335, + 893, + 426 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the following sections, we demonstrate how to adapt $f_{\\mathrm{stu}}$ using supervisory signals from $f_{\\mathrm{tea}}$ on both the feature space and the pose prediction space.", + "bbox": [ + 496, + 426, + 893, + 472 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1.1 Prediction Space Adaptation", + "text_level": 1, + "bbox": [ + 498, + 492, + 754, + 508 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "At each time step $t$ , we apply two different data augmentations, $\\mathcal{A}_1$ and $\\mathcal{A}_2$ , to a target image $\\pmb{x}$ to generate two views. We then obtain the keypoint heatmap corresponding to the first transformed image $\\tilde{h}^t = f_{\\mathrm{tea}}^t (\\mathcal{A}_1(\\pmb {x}))$ . Here $\\tilde{h}^t\\in \\mathbb{R}^{K\\times H'\\times W'}$ denotes the spatial likelihood of the $K$ different keypoints on each channel. The pseudolabel from the teacher model is generated by obtaining the coordinates which produce the maximum activations $\\hat{y}^t = \\operatorname{argmax}_u\\tilde{h}_{[:,u]}^t$ .", + "bbox": [ + 496, + 516, + 893, + 652 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To reduce the influence of erroneous pseudo-labels in our training process, we utilize a confidence threshold to discard potentially unreliable labels. Specifically, we only retain the keypoint activations with the top $p\\%$ maximum values among all activations and discard the rest. We set the threshold $\\tau$ accordingly to reflect this, thereby ensuring that only the most confident labels are used for training.", + "bbox": [ + 496, + 652, + 893, + 757 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Following prior work on supervised pose estimation, we first convert the pseudo-labels to normalized Gaussian heatmaps [40] and then use the mean squared error (MSE) loss to update the student model over batches of target images sampled from $\\mathcal{D}$ :", + "bbox": [ + 496, + 758, + 893, + 834 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {o u t}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {\\mathbf {x} \\in \\mathcal {B}} \\sum_ {k = 1} ^ {K} \\mathbb {1} \\left(\\hat {h} _ {k} ^ {t} \\geq \\tau\\right) \\| \\tilde {\\mathcal {A}} _ {1} \\left(\\hat {h} _ {k} ^ {t}\\right) - \\tilde {\\mathcal {A}} _ {2} \\left(h _ {k} ^ {t}\\right) \\| _ {2}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 845, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14998", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c556debaba324cdf504fd1ec865cb5e134057372a5fa29e9517f0c4813dae355.jpg", + "image_caption": [ + "Figure 2. Framework overview. Our approach builds on the Mean Teacher framework and performs adaptation both in the pose prediction space using $\\mathcal{L}_{\\mathrm{out}}$ , and the feature space using $\\mathcal{L}_{\\mathrm{feat}}$ . This is supplemented by a human pose prior $g$ that scores the predicted pseudo-labels in terms of plausibility. These scores are used to regularize the adaptation process in the absence of labeled source data via $\\mathcal{L}_{\\mathrm{prior}}$ . The student model $f_{\\mathrm{stu}}$ is trained by the combination of the three losses, while the teacher model $f_{\\mathrm{tea}}$ is updated with the exponential moving average (EMA) of the weights of the student model." + ], + "image_footnote": [], + "bbox": [ + 138, + 88, + 831, + 367 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We denote the inverse functions of the chosen augmentations $\\mathcal{A}_1$ and $\\mathcal{A}_2$ as $\\tilde{\\mathcal{A}}_1$ and $\\tilde{\\mathcal{A}}_2$ , respectively. The heatmap predicted by the student model for the $k$ -th keypoint is represented by $h_k^t = f_{\\mathrm{stu}}^t (\\mathcal{A}_2(\\pmb {x}))^k$ , while the heatmap generated from the pseudo-labels predicted by the teacher model is represented by $\\hat{h}_k^t = L(\\hat{y}^t)^k$ . Here, $L(\\cdot)$ represents the heatmap generating function and $\\mathcal{B}$ denotes a batch of target images.", + "bbox": [ + 75, + 465, + 473, + 573 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.2 Feature Apace Adaptation", + "text_level": 1, + "bbox": [ + 76, + 589, + 316, + 606 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Pose estimation models primarily rely on a high-to-low-resolution feature encoder to generate low-resolution representations, which are then used to recover high-resolution pose heatmaps [18]. Since the upsampling process is inherently noisy, providing intermediate supervision to explicitly adapt the features, in addition to adapting the output pose keypoints as shown in the previous section, can be beneficial [17]. While previous work has demonstrated the benefits of joint adaptation across the output and feature space via adversarial learning in tasks such as semantic segmentation [41], this has been exclusively focused on scenarios where source data is available. Here, we propose an alternative way to accomplish feature space adaptation in the absence of source data via contrastive learning.", + "bbox": [ + 75, + 613, + 470, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We begin by creating two different views of each target image $\\mathbf{x}$ using a pair of sampled augmentations $\\mathcal{A}_1$ and $\\mathcal{A}_2$ , as previously shown. Next, considering the pose estimation model as a composition of a feature encoder and an output regressor, i.e., $f = \\mathrm{Dec} \\circ \\mathrm{Enc}$ , we extract", + "bbox": [ + 75, + 825, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the augmentation reversed feature maps from the teacher model $\\tilde{z} = \\tilde{\\mathcal{A}}_1(\\mathrm{Enc}_{\\mathrm{tea}}(\\mathcal{A}_1(\\boldsymbol{x})))$ and the student model $z = \\tilde{\\mathcal{A}}_2(\\mathrm{Enc}_{\\mathrm{stu}}(\\mathcal{A}_2(\\boldsymbol{x})))$ . We extract pairs of features for every image in a batch, pool them along the spatial dimensions, and then normalize them along the batch dimension to ensure that each covariate has a mean of 0 over the batch. For simplicity, we overload $z,\\tilde{z}$ to represent the normalized features, and drop the time index $t$ .", + "bbox": [ + 496, + 465, + 893, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We utilize feature-level consistency between the different views in order to accomplish feature space adaptation. This is achieved via a contrastive learning strategy which encourages the cross-correlation matrix between the outputs of the two networks to be as close to the identity matrix as possible [12],", + "bbox": [ + 496, + 585, + 893, + 676 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {f e a t}} = \\sum_ {i} (1 - C _ {i i}) ^ {2} + \\gamma \\sum_ {i} \\sum_ {j \\neq i} C _ {i j} ^ {2}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 684, + 893, + 718 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We define $\\gamma$ as a positive constant that balances the importance of the first and second terms of the loss function. $C$ represents the cross-correlation matrix computed between the outputs of the student and teacher networks along the batch dimension:", + "bbox": [ + 496, + 723, + 893, + 797 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nC _ {i j} = \\frac {\\sum_ {b = 1} ^ {| \\mathcal {B} |} \\tilde {z} _ {b , i} z _ {b , j}}{\\sqrt {\\sum_ {b = 1} ^ {| \\mathcal {B} |} \\left(\\tilde {z} _ {b , i}\\right) ^ {2}} \\sqrt {\\sum_ {b = 1} ^ {| \\mathcal {B} |} \\left(z _ {b , j}\\right) ^ {2}}}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 801, + 893, + 849 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, $b$ represents the batch index, while $i$ and $j$ index the feature dimensions of the networks' outputs. We set $\\gamma = 5e - 3$ following [12].", + "bbox": [ + 496, + 854, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14999", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The first term of $\\mathcal{L}_{\\mathrm{feat}}$ encourages the consistency of pose features within the same image by equating the diagonal elements of the cross-correlation matrix to 1, effectively reversing the effects of augmentations. In contrast, the second term aims to decorrelate the different feature dimensions of the embedding by forcing the off-diagonal elements of the cross-correlation matrix to 0.", + "bbox": [ + 75, + 90, + 472, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Regularization via Pose Prior", + "text_level": 1, + "bbox": [ + 76, + 204, + 339, + 219 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Enhancing the performance of the pose estimation model on the target domain through joint adaptation over the output and feature space is undoubtedly valuable. However, this approach has its limitations, as it relies solely on general domain adaptation principles and overlooks the rich structural priors associated with human poses. To address this issue, we propose incorporating a parametric human pose prior to better adapt the pose estimation model to the target domain.", + "bbox": [ + 75, + 227, + 473, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.1 2D Human Pose Prior", + "text_level": 1, + "bbox": [ + 76, + 366, + 284, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Building upon the work of [13], we propose a human pose prior modeled as a manifold consisting of plausible 2D poses. To represent the 2D poses while ignoring aspects such as size and scale, we use a set of 2D orientation vectors that connect pairs of joints in the human skeleton, denoted by $\\mathcal{G} = \\{\\pmb {\\theta} = (\\theta_1,\\dots ,\\theta_L)\\mid \\theta_l\\in \\mathbb{R}^2,\\| \\theta_l\\| _2 = 1\\forall l\\in [L]\\}$ . We assume that plausible 2D human poses lie on a manifold embedded in this pose space $\\mathcal{G}$ . We use a function $g:\\mathcal{G}\\to$ $\\mathbb{R}^+$ , which maps a pose to a non-negative scalar, to represent the manifold of plausible poses as the zero-level set:", + "bbox": [ + 75, + 388, + 472, + 541 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} = \\{\\boldsymbol {\\theta} \\in \\mathcal {G} \\mid g (\\boldsymbol {\\theta}) = 0 \\}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 547, + 470, + 565 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $g$ represents the unsigned distance to the manifold. We construct this distance function by first encoding the pose using a hierarchical network $g_{\\mathrm{enc}}$ that encodes the human pose based on its anatomical structure [42], and subsequently, use $g_{\\mathrm{dec}}$ to predict the distance based on the pose representation.", + "bbox": [ + 75, + 571, + 472, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, for a given pose $\\theta$ , we encode it as follows,", + "bbox": [ + 94, + 648, + 465, + 662 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {v} _ {1} = g _ {\\mathrm {e n c}} ^ {1} \\left(\\theta_ {1}\\right), \\quad \\mathbf {v} _ {l} = g _ {\\mathrm {e n c}} ^ {l} \\left(\\theta_ {l}, \\mathbf {v} _ {\\Omega (l)}\\right), l \\in \\{2, \\dots , L \\}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 667, + 468, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $\\Omega(l)$ is a function that maps the index of each orientation vector to its parent orientation vector in the kinematic chain of the human skeleton. We obtain the overall pose encoding as $\\mathbf{p} = [\\mathbf{v}_1|\\ldots|\\mathbf{v}_L]$ by concatenating all the individual orientation encodings. This pose encoding is then processed by $g_{\\mathrm{dec}}: \\mathbb{R}^{d,L} \\to \\mathbb{R}^+$ , which predicts the unsigned distance for the given pose representation $\\mathbf{p}$ . A lower distance value for a pose implies that the configuration of joints is more likely to be a plausible human pose.", + "bbox": [ + 75, + 693, + 472, + 829 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.2 Pose Prior Training", + "text_level": 1, + "bbox": [ + 76, + 845, + 269, + 862 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To train the parametric prior $g$ , we rely on an auxiliary dataset of $M$ human poses $\\mathcal{D}_{\\mathrm{A}} = \\{\\pmb{\\theta}^{i}\\}_{i=1}^{N_{\\mathrm{A}}}$ , where $\\pmb{\\theta}^{i} =$", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$(\\theta_1^i,\\dots ,\\theta_L^i)$ . Importantly, these poses are not associated with their corresponding RGB images, which preserves the privacy aspect of the method. Additionally, storing only the pose coordinates instead of entire images makes data storage much more efficient and feasible.", + "bbox": [ + 496, + 90, + 890, + 165 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We adopt a supervised approach to train $g$ to predict the $L2$ distance to the plausible pose manifold for a given pose. To achieve this, we construct a dataset $\\tilde{\\mathcal{D}} = \\{(\\pmb{\\theta}_i,d_i)\\}_{i=1}^M$ , consisting of pose and distance pairs, from $\\mathcal{D}_{\\mathrm{A}}$ . As the poses from $\\mathcal{D}_{\\mathrm{A}}$ lie on the desired manifold, we assign $d = 0$ to all poses in the dataset. To diversify our training samples, we randomly generate negative samples with distance $d > 0$ by perturbing the poses from $\\mathcal{D}_{\\mathrm{A}}$ with noise.", + "bbox": [ + 496, + 167, + 893, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train the network with the standard $L1$ loss,", + "bbox": [ + 517, + 287, + 834, + 301 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {d i s t}} = \\sum_ {(\\boldsymbol {\\theta}, d) \\in \\tilde {D}} \\| g (\\boldsymbol {\\theta}) - d \\| _ {1}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 306, + 890, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "More details on the training process of the prior are provided in Section 4.2.", + "bbox": [ + 498, + 347, + 893, + 376 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.3 Adaptation using Pose Prior", + "text_level": 1, + "bbox": [ + 500, + 395, + 751, + 410 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We leverage the trained pose prior $g$ to regularize the adaptation process by incentivizing the pose estimator to generate pseudo-labels that resemble plausible human poses.", + "bbox": [ + 496, + 417, + 893, + 463 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given the heatmaps $\\{h_k^t\\}_{k=1}^K$ generated for each keypoint by the student model $f_{\\mathrm{stu}}^t$ for a target image $x$ , we calculate the corresponding orientation vectors in a differentiable manner to evaluate the plausibility of the predicted pose using the prior. First, we renormalize each heatmap to a probability distribution via spatial softmax and condense it to a point by computing the spatial expected value of the latter. For computational efficiency, we carry this out in a separable manner along the two spatial dimensions. Namely, assuming $u = (u_1, u_2)$ to be the two components of each pixel coordinate, we set", + "bbox": [ + 496, + 463, + 893, + 628 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nu _ {i} ^ {k} = \\frac {\\sum_ {u _ {i}} u _ {i} e ^ {h _ {k} ^ {t} (u _ {i})}}{\\sum_ {u _ {i}} e ^ {h _ {k} ^ {t} (u _ {i})}}, \\quad h _ {k} ^ {t} (u _ {i}) = \\sum_ {u _ {j}} h _ {k} ^ {t} (u _ {1}, u _ {2}), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 633, + 890, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $i = 1,2$ and $j = 2,1$ respectively. Next, we use the pose coordinates to determine the orientation vectors between pairs of connected keypoints. Specifically, for every pair $(a,b)$ of connected keypoints in the human skeleton (denoted by the set $\\mathcal{E}$ ), we calculate the unit vector $\\theta$ in the direction from $u^a$ to $u^b$ , where $u^a$ and $u^b$ are the estimated softmax coordinates of keypoints $a$ and $b$ , respectively, i.e.,", + "bbox": [ + 496, + 681, + 890, + 787 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\theta = \\frac {u ^ {a} - u ^ {b}}{\\| u ^ {a} - u ^ {b} \\| _ {2}}, \\quad \\forall (a, b) \\in \\mathcal {E}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 792, + 890, + 827 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we use the prior as a regularization term to minimize the distance of the current pose from our learned manifold,", + "bbox": [ + 498, + 832, + 890, + 861 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p r i o r}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {\\boldsymbol {x} \\in \\mathcal {B}} g \\left(T \\left(f _ {\\mathrm {s t u}} ^ {t} (\\boldsymbol {x})\\right)\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 867, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15000", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $T(\\cdot)$ converts the predicted heatmaps to the orientation vector format required as input by the prior.", + "bbox": [ + 76, + 90, + 468, + 122 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3. Overall Adaptation", + "text_level": 1, + "bbox": [ + 76, + 132, + 263, + 148 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The final training objective for the student model $f_{\\mathrm{stu}}$ can be expressed as:", + "bbox": [ + 76, + 155, + 468, + 186 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {f _ {\\mathrm {s t u}}} \\mathcal {L} _ {\\text {o u t}} + \\lambda_ {1} \\mathcal {L} _ {\\text {f e a t}} + \\lambda_ {2} \\mathcal {L} _ {\\text {p r i o r}}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 168, + 199, + 468, + 223 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here, $\\lambda_{1}$ and $\\lambda_{2}$ are hyper-parameters that control the influence of feature space adaptation and prior regularization, respectively. The teacher model $f_{\\mathrm{tea}}$ is updated asynchronously by computing an exponential moving average of the student model weights as shown in Equation 1.", + "bbox": [ + 76, + 234, + 470, + 310 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 325, + 209, + 343 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we demonstrate POST's ability to adapt a 2D human pose estimation model to a target domain using only unlabeled data from that domain. We conduct experiments on three domain adaptive scenarios and compare with state-of-the-art domain adaptation baselines that utilize source data during adaptation. We also conduct extensive analysis to analyze the contribution and interaction between each component in our framework.", + "bbox": [ + 76, + 349, + 468, + 472 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 483, + 179, + 497 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SURREAL: SURREAL [43] is a large-scale dataset of synthetically generated images of people rendered from 3D sequences of human motion capture data against indoor backgrounds. It contains over 6 million frames, making it one of the largest and most diverse datasets of its kind.", + "bbox": [ + 76, + 506, + 470, + 580 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Human3.6M: Human3.6M [44] is a real-world video dataset captured in indoor environments, comprising 3.6 million frames. The dataset features human subjects performing various actions. In order to reduce redundancy and computational complexity, we down-sampled the videos from 50fps to 10fps as per the approach proposed in [5]. For training, we follow the standard protocol proposed in [6] and use 5 subjects (S1, S5, S6, S7, S8), while the remaining 2 subjects (S9, S11) are reserved for testing.", + "bbox": [ + 76, + 587, + 468, + 723 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "LSP: Leeds Sports Pose (LSP) [45] is a real-world dataset that contains 2,000 images with annotated human body joint locations collected from sports activities. The images in LSP are captured in the wild, featuring a wide variety of human poses that are often challenging to detect.", + "bbox": [ + 76, + 728, + 468, + 805 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "BRIAR: BRIAR [46] is a cutting-edge biometric dataset featuring a large-scale collection of videos of human subjects captured in extremely challenging conditions. The videos are recorded at varying distances, i.e., close range, $100\\mathrm{m}$ , $200\\mathrm{m}$ , $400\\mathrm{m}$ , $500\\mathrm{m}$ , and unmanned aerial vehicles (UAV), with each video lasting around 90 seconds. We randomly", + "bbox": [ + 76, + 809, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "sample 20 frames from each sequence for each of the 158 subjects for our experiments.", + "bbox": [ + 500, + 90, + 890, + 122 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experiment Protocols", + "text_level": 1, + "bbox": [ + 500, + 130, + 702, + 146 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Pose estimation model. We adopt the Simple Baseline [18] as our pose estimation model, with the ResNet-101 [47] as the backbone. To train the model, we use the Adam optimizer [48] with a base learning rate of $1e - 4$ , scheduled to decrease to $1e - 5$ after 5 epochs and to $1e - 6$ after 20 epochs. The model is trained for 30 epochs. We use a batch size of 32 and run 500 iterations per epoch. To threshold the model predictions, we set the confidence thresholding ratio $p$ to 0.5. To augment the images during training, we follow [6] and use rotation, translation, shear, and Gaussian blur. The hyper-parameters $\\lambda_{1}$ and $\\lambda_{2}$ are set to $1e - 3$ and $1e - 6$ , respectively.", + "bbox": [ + 498, + 152, + 890, + 335 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Pose prior model. The training of the parametric prior follows a multi-stage approach that involves using different types of training samples. Initially, we use a combination of manifold poses $\\theta_{m}$ and non-manifold poses $\\theta_{nm}$ with a considerable distance from the desired manifold. Over the course of training, we gradually increase the number of non-manifold poses $\\theta_{nm}$ with a small distance from the manifold. This enables our model to first learn a smooth surface and then gradually incorporate finer details as training progresses. We create these non-manifold poses $\\theta_{nm}$ by injecting noise into the manifold poses $\\theta_{m}$ obtained from the auxiliary dataset. Specifically, we sample directional noise from the Von-Mises distribution [49] and add it to the manifold poses in order to obtain the implausible poses.", + "bbox": [ + 498, + 339, + 893, + 551 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The architecture for the encoder $g_{\\mathrm{enc}}$ consists of a 2-layer MLP with an output feature size of $d = 6$ for each orientation vector, similar to [42]. The distance field network $g_{\\mathrm{dec}}$ is implemented as a 5-layer MLP. Given its large size and diverse poses, we train the prior for our primary experiments using the SURREAL dataset.", + "bbox": [ + 498, + 551, + 890, + 642 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison with Baselines", + "text_level": 1, + "bbox": [ + 500, + 650, + 745, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. We evaluate the performance of our proposed method against several state-of-the-art domain adaptive frameworks. This includes adversarial learning-based feature alignment methods, such as DAN[31], DD[50], and RegDA[5]. Additionally, we consider approaches based on pseudo-labeling, namely CCSSL[38], and UDAPE [6]. It is worth noting that all these methods employ the source data during the adaptation process. To establish a comprehensive performance baseline, we report the results of two additional baselines: Oracle and Source only. The Oracle baseline represents the upper bound of the model's performance, achieved by training the model jointly with target 2D annotations. On the other hand, Source only represents the model's performance when it is directly applied to the target domain without any adaptation.", + "bbox": [ + 498, + 674, + 893, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15001", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8cc6403209faf3336274df573533ff128f80f2dfd107a47bc6f421cda02ba380.jpg", + "table_caption": [ + "Table 1. PCK@0.05 on SURREAL $\\rightarrow$ LSP. (Best value is in red color, while the second best value is in blue color.)" + ], + "table_footnote": [], + "table_body": "
MethodSFSld.Elb.WristHipKneeAnkleAvg.
Source only-51.565.062.968.068.767.463.9
Oracle--------
DANX52.262.958.971.068.165.163.0
DDX28.465.956.875.074.373.962.4
RegDAX62.776.771.181.080.375.374.6
CCSSLX36.866.363.959.667.370.460.7
UDAPEX69.284.983.385.584.784.382.0
POST✓66.583.981.084.683.182.680.3
", + "bbox": [ + 78, + 121, + 468, + 268 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a6fe4e1c5a1647be1f5939c567aa9b00152085a1219b1befdbf622759c82e948.jpg", + "table_caption": [ + "Table 2. PCK@0.05 on SURREAL $\\rightarrow$ Human3.6M." + ], + "table_footnote": [], + "table_body": "
MethodSFSld.Elb.WristHipKneeAnkleAvg.
Source only-69.475.466.437.977.377.767.3
Oracle-95.391.886.995.694.193.692.9
DANX68.177.562.330.478.479.466.0
DDX71.683.375.142.176.276.170.7
RegDAX73.386.472.854.882.084.475.6
CCSSLX44.368.555.222.262.357.851.7
UDAPEX78.189.681.152.685.387.179.0
POST✓81.388.577.446.183.483.476.7
", + "bbox": [ + 78, + 297, + 468, + 445 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Metrics. We adopt the evaluation metric of Percentage of Correct Keypoint (PCK) for all experiments and report PCK@0.05 that measures the ratio of correct prediction within a range of $5\\%$ with respect to the image size.", + "bbox": [ + 75, + 469, + 468, + 530 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Results", + "text_level": 1, + "bbox": [ + 76, + 539, + 171, + 554 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative results. We evaluate POST in two adaptation scenarios: SURREAL $\\rightarrow$ LSP and SURREAL $\\rightarrow$ Human3.6M, and report the quantitative results in Table 1 and Table 2, respectively. Specifically, we report the PCK@0.05 on 16 keypoints of the human body, including shoulders (sld.), elbows (elb.), wrists, hips, knees, and ankles. Our method achieves comparable results to many recent approaches that leverage source data for adaptation. Among these methods, UDAPE [6] achieves the highest performance on both cases, with our framework achieving a close second and only 2 percentage points behind on average. Notably, we outperform every other method, including the recently proposed RegDA [5] approach, by a significant margin of up to 5.7 percentage points. It is worth noting that not only do these methods require source data, but also involve additional models such as discriminators or style transfer modules, and unstable adversarial training. In contrast, our framework is lightweight, only involves pseudo-label training, and utilizes a simple prior model that can be trained offline.", + "bbox": [ + 75, + 561, + 472, + 851 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative results. In addition to quantitative results, we also present qualitative results on SURREAL $\\rightarrow$ Human3.6M in Figure 3 and on SURREAL $\\rightarrow$ LSP in Figure 4. Also,", + "bbox": [ + 75, + 854, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9ca3dd4ca1a1e28750331b7cb8a5c701cc85b54cdf7f37b743deb37214ce2ba2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 560, + 89, + 650, + 157 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6ddd8ed53a6b19b31f5e7fed23c697ea428f3503f8c8f9a11f0efe292d6a862a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 651, + 89, + 740, + 157 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/06b8c705d828873c385eadc00468c9bc2fc87a4a57b2a58acd501b61a009979f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 741, + 89, + 831, + 157 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/55035cceed5ab24a11f808a10e6e62344fe77e57fb571c064ec77e259f690089.jpg", + "image_caption": [ + "Figure 3. Qualitative results on SURREAL $\\rightarrow$ Human3.6M. We demonstrate sample results on the Human3.6M dataset. For each row, the leftmost shows the Source only prediction, the middle one shows the UDAPE [6] prediction, and the rightmost shows the prediction made POST." + ], + "image_footnote": [], + "bbox": [ + 560, + 159, + 650, + 228 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bf638cc35de63688c3f809da13d6ecca3d074a6a5776fca8ba763b09bb5c3770.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 651, + 159, + 740, + 228 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1af0c514de7f1b2d09958562f8961b6c6cb0fc0159bb2d8a0d44fdaad1875b10.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 741, + 159, + 831, + 228 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3de0508bba699e9fb9ed70599bbfe639183e0de420765c2cb29b22922db41eeb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 581, + 321, + 656, + 380 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e88c80e6e37804c9a9155a709612e3849a0aaa276c55742ab55e4428bd64f1ea.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 658, + 321, + 733, + 380 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5800a5eff490007d9f72a9f3305ce806c7c576c1725fde8c20e35ff5cef02c7b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 735, + 321, + 810, + 380 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/26f10a4c3df8781a5005c528fcf7cf87a1ea31a01fba7fe9144c0a13b57a9949.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 583, + 386, + 656, + 443 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/87d6f34fb2bad67ef3179be8f212ff38d3cc26040310bce2f12f61dbaa69e179.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 658, + 386, + 733, + 443 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/90ddfdaed2ee6ce2a5359bb92ed4d83fe00269159ce15ce6affd72347148e4ff.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 735, + 386, + 810, + 443 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/30be3e3f739364914f6ac74358e4da78e6dc356ac72f5439de9a1d16fe5168af.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 583, + 449, + 656, + 506 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a24aa9696468f014d926a23875096da8c11ed3a8297a696ef0e21d4f5ab516a3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 660, + 449, + 733, + 506 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/578aa8f70007e230899509d88df089d6989ca9c2fdd76f65830f0199b54453d9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 735, + 449, + 810, + 506 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2b917ce2bae4dc5d9ce79cef983cb4c7e5db69f2b175d78a10a9b48151f391f0.jpg", + "image_caption": [ + "Figure 4. Qualitative results on SURREAL $\\rightarrow$ LSP. We demonstrate sample results on the LSP dataset. For each row, the left-most shows the Source only prediction, the middle one shows the UDAPE [6] prediction, and the rightmost shows the prediction made POST." + ], + "image_footnote": [], + "bbox": [ + 583, + 513, + 656, + 570 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f45bf2fae60fa16dfdefd095aa7ee8e2514a82b33f48d654214f5c08b987128a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 658, + 513, + 733, + 570 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f932f0b4aa506b25c209f2b2dc069513b86eee3321aba82c71b5d750428d5b9d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 735, + 513, + 810, + 570 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "we present only visual results on the SURREAL $\\rightarrow$ BRIAR adaptation scenario since pose annotations are absent in the BRIAR dataset. Figure 5 displays the predicted human poses on images taken from six different imaging ranges in the BRIAR dataset. While using the source model directly produces completely inaccurate poses, POST can accurately localize the keypoint locations, even in the presence of occlusions and atmospheric turbulence. Our approach can also accurately reconstruct poses even when the human is imaged from an elevated perspective, resulting in a high camera angle (Figure 5.f). Notably, our approach achieves this without using any source data for adaptation. Our results are comparable to those produced by UDAPE [6], which utilizes source data for adaptation. Additional qualitative results can be found in the supplementary document.", + "bbox": [ + 496, + 672, + 895, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15002", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b488637a570423b0c61b2b920d409367b8d37de12030b61d1cfa0a0d86a0fada.jpg", + "image_caption": [ + "a) $100\\mathrm{m}$" + ], + "image_footnote": [], + "bbox": [ + 163, + 93, + 464, + 172 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6699f621e33ec7924a2e3e22e59af8268b17dc67c2b86f498bef502438207a34.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 93, + 807, + 172 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7a74b7dbf63c3c52242e7f9de6d519c459d882828be198e5e53081e5072e7488.jpg", + "image_caption": [ + "b) $200\\mathrm{m}$" + ], + "image_footnote": [], + "bbox": [ + 163, + 198, + 464, + 277 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0e423e1f372fc6d2f448b59ecf1bf54c35a70d65eccaf60269c757cd1fe5f1bd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 199, + 807, + 277 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a2d47abb81dece636654ac0a86b4cca9356074298df4759fd5136a58f4212362.jpg", + "image_caption": [ + "c) $400\\mathrm{m}$" + ], + "image_footnote": [], + "bbox": [ + 163, + 304, + 464, + 383 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4e89899667fa45cde15a39a23c01f71b2bc367063323bb7caffea4f57f7f63e0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 508, + 305, + 807, + 383 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e1eb07fe7e882dfb82fce907089730185aeea9907de1c34c662f2eadacfe2082.jpg", + "image_caption": [ + "d) $500\\mathrm{m}$" + ], + "image_footnote": [], + "bbox": [ + 163, + 410, + 464, + 488 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/117eb71616e26b7bb49299de2a2aa1031bf8907490a22a21fb563ffe508a9f3d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 508, + 411, + 807, + 488 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ae26e585dc79fcadbe7beef7631175128cb92f7806c412598d808f049f8df802.jpg", + "image_caption": [ + "e) close range" + ], + "image_footnote": [], + "bbox": [ + 165, + 516, + 464, + 594 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/20c06172a974e6383a36ad30d312c3833e0cf846cc3308210aceb24e8e687611.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 508, + 516, + 807, + 594 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f2aa48b85552239f56e0f04de58b137b6f5e654cda8884c106ba54f4b6e5fe1a.jpg", + "image_caption": [ + "f) uav" + ], + "image_footnote": [], + "bbox": [ + 165, + 622, + 464, + 700 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1c048a6e1e9309091c8b02dde1f23d8ed93272664bc72a57d8b8a03fc087ac8a.jpg", + "image_caption": [ + "Figure 5. Qualitative results on SURREAL $\\rightarrow$ BRIAR. We demonstrate sample results on BRIAR at all ranges. For each range, we display three images: the leftmost shows the Source only prediction, the middle one shows the UDAPE [6] prediction, and the rightmost shows the prediction using POST. Although POST does not use source data for adaptation, it is able to match the predictions produced by UDAPE, which uses source data." + ], + "image_footnote": [], + "bbox": [ + 508, + 622, + 807, + 700 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 801, + 240, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of auxiliary dataset. We conduct experiments to evaluate the impact of the choice of the auxiliary dataset (used to train the prior) on downstream adaptation. The results are presented in Table 3. Our findings indicate that", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "POST is robust to the choice of the auxiliary dataset, with performance differences of $\\sim 0.5$ percentage points.", + "bbox": [ + 498, + 803, + 890, + 835 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of loss terms. We conduct an experiment to evaluate the performance of each component of our framework. The results on the SURREAL $\\rightarrow$ Human3.6M adaptation scenario are presented in Table 4. Our findings indicate that in addi", + "bbox": [ + 498, + 839, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15003", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f33a9eab7d6b22371583b8a33afe270a2a874518ff5094082116c094d2114b6f.jpg", + "table_caption": [ + "Table 3. Effect of auxiliary dataset. We evaluate the effect of auxiliary dataset on downstream adaptation tasks." + ], + "table_footnote": [], + "table_body": "
SURREAL→HUMAN3.6M
Aux. datasetSld.Elb.WristHipKneeAnkleAvg.
SURREAL81.388.577.446.183.483.476.7
Human3.6M80.988.077.245.083.182.876.2
SURREAL→LSP
Aux. datasetSld.Elb.WristHipKneeAnkleAvg.
SURREAL66.583.981.084.683.182.680.3
Human3.6M66.183.680.784.483.182.580.1
", + "bbox": [ + 76, + 119, + 470, + 267 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/8647424d859b191fa3cf852da3d10e0050e9733572ba9d8ee4f46abe481e298d.jpg", + "table_caption": [ + "Table 4. Effect of each loss term. We evaluate the contribution of each loss term on SURREAL $\\rightarrow$ Human3.6M." + ], + "table_footnote": [], + "table_body": "
LoutLfeatLpriorSld.Elb.WristHipKneeAnkleAvg.
XXX69.475.466.437.977.377.767.3
✓XX77.986.773.738.883.084.374.1
✓✓X81.787.175.244.382.382.275.5
✓✓✓81.388.577.446.183.483.476.7
", + "bbox": [ + 78, + 313, + 468, + 393 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "tion to prediction space adaptation, feature space adaptation also plays a crucial role in enabling effective unsupervised learning from pseudo-labels. Moreover, we observed that the human pose prior brings additional improvements, thus validating our hypothesis that noisy pose pseudo-labels can be refined implicitly by a prior in the absence of source data. Overall, our results demonstrate the effectiveness of our framework and the importance of each of its components in achieving state-of-the-art performance.", + "bbox": [ + 75, + 422, + 468, + 556 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Cross-dataset performance of prior. We evaluate the ability of the learned prior to handle distribution shift separately from the adaptation performance. Specifically, we assess the robustness of the prior by computing pose scores across datasets, and the results are presented in Figure 6. The plot demonstrates that our prior is effective in scoring plausible (real) poses with low scores and scoring implausible poses with higher scores. Note that the bell curve shape of the noisy pose scores is due to the Von-Mises noise added to create the noisy poses.", + "bbox": [ + 75, + 564, + 468, + 715 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Effect of thresholding. We analyze the impact of the pseudo-label threshold $\\tau$ on the adaptation performance in Table 5. The results on SURREAL $\\rightarrow$ Human3.6M reveal that as we increase this ratio, the performance gradually decreases. This can be attributed to the fact that higher thresholding ratios tend to include lower confident predictions as pseudo-labels, which can negatively impact adaptation.", + "bbox": [ + 75, + 720, + 468, + 827 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 844, + 194, + 859 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We address the problem of adapting a pre-trained 2D human pose estimator to a new target domain with unlabeled", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/b26de1c511bd6d9ad94438716cb834d7a7533ad29ab73caad6ac905ee06cbb34.jpg", + "table_caption": [ + "Table 5. Effect of $\\tau$ . We evaluate adaptation performance on SURREAL $\\rightarrow$ Human3.6M as $\\tau$ is varied." + ], + "table_footnote": [], + "table_body": "
τ = 0.1τ = 0.3τ = 0.5τ = 0.7τ = 0.9
76.476.576.775.373.8
", + "bbox": [ + 540, + 118, + 851, + 284 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/fe682b04ab13c49f01819e55fd9998b7720e2fa39836b2a08ac6227d112420df.jpg", + "image_caption": [ + "(a) Human3.6M $\\rightarrow$ SURREAL", + "(b) SURREAL $\\rightarrow$ Human3.6M", + "Figure 6. Cross-dataset prior transfer. We plot the histogram of scores predicted by the prior. The prior can clearly demarcate plausible poses from implausible poses across datasets." + ], + "image_footnote": [], + "bbox": [ + 540, + 308, + 846, + 417 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "target data. To this end, we propose a self-training algorithm, POST, that leverages a Mean Teacher framework to enforce both prediction-level and feature-level consistency between a pair of student and teacher models. Our approach incorporates a human pose prior that captures the manifold of possible poses in a high-dimensional space, which helps to refine noisy pseudo-labels generated during self-training. We evaluate our method on three challenging adaptation scenarios and show that it achieves competitive performance compared to existing UDA methods that have access to source data.", + "bbox": [ + 496, + 507, + 893, + 657 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements. This research is based upon work supported in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via [2022-21102100007]. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein.", + "bbox": [ + 496, + 666, + 893, + 818 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 833, + 596, + 848 + ], + "page_idx": 8 + }, + { + "type": "ref_text", + "text": "[1] Ke Sun, Bin Xiao, Dong Liu, and Jingdong Wang. Deep high-resolution representation learning for human pose estimation. In CVPR, 2019. 1, 2", + "bbox": [ + 506, + 858, + 893, + 898 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "15004", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[2] Sijie Yan, Yuanjun Xiong, and Dahua Lin. Spatial temporal graph convolutional networks for skeleton-based action recognition. 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In ICML, 2019. 6" + ], + "bbox": [ + 501, + 90, + 893, + 272 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "15006", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Prior-guided Source-free Domain Adaptation for Human Pose Estimation/67d12eb1-f1e4-4b90-aba2-4771e3bf7c39_model.json b/2023/Prior-guided Source-free Domain Adaptation for Human Pose Estimation/67d12eb1-f1e4-4b90-aba2-4771e3bf7c39_model.json new file mode 100644 index 0000000000000000000000000000000000000000..102187bca0ae941c52ef17e8d60e6145e963b32e --- /dev/null +++ b/2023/Prior-guided Source-free Domain Adaptation for Human Pose Estimation/67d12eb1-f1e4-4b90-aba2-4771e3bf7c39_model.json @@ -0,0 +1,2631 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.048 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.131, + 0.856, + 0.154 + ], + "angle": 0, + "content": "Prior-guided Source-free Domain Adaptation for Human Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.188, + 0.899, + 0.229 + ], + "angle": 0, + "content": "Dripta S. Raychaudhuri\\(^{1,2*}\\) Calvin-Khang Ta\\(^{1}\\) Arindam Dutta\\(^{1}\\) Rohit Lal\\(^{1}\\) Amit K. Roy-Chowdhury\\(^{1}\\) \n\\(^{1}\\)University of California, Riverside \\(^{2}\\)AWS AI Labs" + }, + { + "type": "text", + "bbox": [ + 0.224, + 0.234, + 0.764, + 0.25 + ], + "angle": 0, + "content": "{drayc001@, cta003@, adutt020@, rla1011@, amertc@ece.}ucr.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.301, + 0.314, + 0.317 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.474, + 0.712 + ], + "angle": 0, + "content": "Domain adaptation methods for 2D human pose estimation typically require continuous access to the source data during adaptation, which can be challenging due to privacy, memory, or computational constraints. To address this limitation, we focus on the task of source-free domain adaptation for pose estimation, where a source model must adapt to a new target domain using only unlabeled target data. Although recent advances have introduced source-free methods for classification tasks, extending them to the regression task of pose estimation is non-trivial. In this paper, we present Prior-guided Self-training (POST), a pseudolabeling approach that builds on the popular Mean Teacher framework to compensate for the distribution shift. POST leverages prediction-level and feature-level consistency between a student and teacher model against certain image transformations. In the absence of source data, POST utilizes a human pose prior that regularizes the adaptation process by directing the model to generate more accurate and anatomically plausible pose pseudo-labels. Despite being simple and intuitive, our framework can deliver significant performance gains compared to applying the source model directly to the target data, as demonstrated in our extensive experiments and ablation studies. In fact, our approach achieves comparable performance to recent state-of-the-art methods that use source data for adaptation." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.743, + 0.21, + 0.758 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.769, + 0.471, + 0.876 + ], + "angle": 0, + "content": "Human pose estimation is a fundamental task in computer vision that involves determining the precise locations of keypoints, such as joints, on a human body in an image or video [1]. The growing need for pose estimation in various applications such as action recognition [2], human-computer interaction [3], and video surveillance [4] has driven the rapid development of highly accurate deep learning tech" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.286, + 0.891, + 0.513 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.519, + 0.895, + 0.617 + ], + "angle": 0, + "content": "Figure 1. Problem setup. Existing UDA methods for pose estimation rely on a labeled source dataset while adapting to an unlabeled target dataset. However, privacy concerns surrounding the use of personally identifiable information in these labeled datasets, as well as the significant storage and computational requirements, can limit access to such data. Hence, our work focuses on source-free UDA of pose estimation models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.894, + 0.704 + ], + "angle": 0, + "content": "niques. However, the challenge of obtaining large annotated datasets for training, compounded with the susceptibility to a performance decline in the face of data distribution shifts still poses limitations for current pose estimation models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.902 + ], + "angle": 0, + "content": "To overcome these limitations, recent studies have focused on unsupervised domain adaptation (UDA) of pose estimators [5, 6]. UDA allows for transferring a pose estimation model trained on a source domain, where labeled data is available, to a target domain where labeled data is unavailable. Despite improved and robust pose estimation, the requirement of simultaneous access to both source and target domains during adaptation hinders real-world implementation. For instance, the labeled source data may not be accessible post-deployment due to privacy or proprietary issues. This is particularly relevant for human pose datasets, which contain personally identifiable information (PII) [7]. Furthermore, adaptation using the entire source data might" + }, + { + "type": "page_footnote", + "bbox": [ + 0.099, + 0.887, + 0.468, + 0.9 + ], + "angle": 0, + "content": "* Currently at AWS AI Labs. Work done while the author was at UCR." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14996" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.471, + 0.137 + ], + "angle": 0, + "content": "be infeasible due to both memory and computational constraints. In light of these issues, we focus on source-free UDA of human pose estimation models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.14, + 0.471, + 0.337 + ], + "angle": 0, + "content": "Concretely, our objective is to adapt a 2D human pose estimation model to a new target domain utilizing only its trained parameters and unlabeled target data. This presents a major challenge as the absence of source data for regularization can cause catastrophic forgetting. While recent advances have introduced methods to tackle this issue in classification tasks [8, 9, 10], extending them to the regression task of pose estimation is non-trivial. To address this challenge, we introduce Prior-guided Self-training (POST), a self-training regression framework that employs a human pose prior to effectively guide the adaptation process in the absence of source data. An overview of our problem setup is shown in Figure 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.339, + 0.474, + 0.612 + ], + "angle": 0, + "content": "Our approach builds on the Mean Teacher [11] framework, which uses consistency in the prediction space of a student and teacher model to produce trustworthy pseudo-labels and learn from the unlabeled target domain. To achieve this, we create two augmented views of each target image, varying in scale, spatial context, and color statistics. Aligned pose predictions from both models in both views are then obtained, and consistency between the predictions across the different views is encouraged to facilitate prediction space adaptation. However, our empirical results show that relying solely on consistency in the output space is insufficient when supervision from the source data is lacking. To address this, we also introduce feature space adaptation, which aims to encourage consistency across features extracted from the two separate views. We adopt the Barlow Twins [12] approach to accomplish this. Specifically, we seek to make the cross-correlation matrix calculated from a pair of feature embeddings as close to the identity matrix as possible." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.472, + 0.902 + ], + "angle": 0, + "content": "In addition to the adaptation across both outputs and features, we employ a human pose prior that models the full manifold of plausible poses in some high-dimensional pose space to refine possible noisy pseudo-labels that may arise during self-training. The plausible poses are represented as points on the manifold surface, with zero distance from it, while non-plausible poses are located outside the surface, with a non-zero distance from it. This manifold is learned using a high-dimensional neural field, similar to Pose-NDF [13]. The pose prior acts as a strong regularizer, directing the model to generate more accurate pose pseudolabels on the target data and leading to improved adaptation. The learning of this prior requires an auxiliary dataset of plausible human poses, but this does not compromise the privacy aspect of our framework as the prior does not make use of RGB images. In addition, it is worth noting that the prior can be trained offline, separately from the adaptation process. This not only saves computational resources but also reduces the amount of storage required. Compared to storing entire" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.894, + 0.122 + ], + "angle": 0, + "content": "images, it is much more efficient to store pose coordinates, which requires approximately \\(3000 \\times\\) less memory." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.123, + 0.894, + 0.152 + ], + "angle": 0, + "content": "Main contributions. To summarize, our primary contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.153, + 0.895, + 0.229 + ], + "angle": 0, + "content": "- We address the problem of adapting a human pose estimation model to a target domain consisting of unlabeled data, without access to the original source dataset. This ameliorates the privacy concern associated with the current domain adaptive pose estimation methods." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.231, + 0.895, + 0.307 + ], + "angle": 0, + "content": "- We introduce Prior-guided Self-training (POST), a simple source-free unsupervised adaptation algorithm. POST leverages both prediction-level and feature-level consistency, in addition to a human pose prior, to drive self-training for improved adaptation to the target domain." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.309, + 0.894, + 0.368 + ], + "angle": 0, + "content": "- We evaluate our method qualitatively and quantitatively on three challenging domain adaptive scenarios, demonstrating comparable performance to existing UDA methods that have access to the source data." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.153, + 0.895, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.384, + 0.651, + 0.4 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.41, + 0.895, + 0.637 + ], + "angle": 0, + "content": "Pose Estimation. 2D human pose estimation aims to locate human anatomical keypoints, such as the elbow and knee. Prior works can be categorized into two primary frameworks: the top-down framework and the bottom-up framework. Top-down methods [14, 15, 16, 17, 18, 19, 1] first detect each person from the image and then perform single-person pose estimation on each bounding box independently. On the other hand, bottom-up methods [20, 21, 22, 23, 24, 25, 26] predict keypoints of each person directly in an end-to-end manner. Typical bottom-up methods consist of two steps: predicting keypoint heatmaps and grouping the detected keypoints into separate poses. In this work, we focus on the bottom-up framework for efficiency purposes and adopt the Simple Baseline [18] architecture following [6] to ensure fair comparisons with prior domain adaptation algorithms." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.897, + 0.902 + ], + "angle": 0, + "content": "Unsupervised Domain Adaptation. UDA methods have been extensively applied to a broad range of computer vision tasks, including image classification [27], semantic segmentation [28], object detection [29], and reinforcement learning [30] to tackle the issue of data distribution shift. Most approaches aim to align the source and target data distributions through techniques such as maximum mean discrepancy [31] and adversarial learning [32, 27]. Another line of research utilizes image translation methods to perform adaptation by transforming the source images into the target domain [33, 34]. More recently, there has been a surge of interest in adaptation using only a pre-trained source model due to privacy and memory storage concerns related to the source data. These include techniques such as information maximization [8, 9], pseudo-labeling [35, 36] and self-supervision [37]. Compared to other tasks, domain adaptation for regression tasks, such as pose estimation, remains" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14997" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.225, + 0.106 + ], + "angle": 0, + "content": "relatively unexplored." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.113, + 0.474, + 0.356 + ], + "angle": 0, + "content": "Domain Adaptive Pose Estimation. UDA methods for pose estimation have explored various techniques for overcoming the domain gap, including adversarial feature alignment and pseudo-labeling. RegDA [5] estimates the domain discrepancy by evaluating false predictions on the target domain and minimizes it. Mu et al. [38] proposed consistency regularization with respect to transformations and temporal consistency learning within a video. Li et al. [39] proposed a refinement module and a self-feedback loop to obtain reliable pseudo-labels. Recently, Kim et al. [6] introduced a unified framework for both human and animal keypoint detection, which aligns representations using input-level and output-level cues. Typically, these methods require access to the source data, which may raise data privacy, memory and computation concerns. In contrast, our method addresses the domain adaptation problem in a source-free setting." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.369, + 0.321, + 0.387 + ], + "angle": 0, + "content": "3. Prior-guided Self-training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.394, + 0.471, + 0.56 + ], + "angle": 0, + "content": "Our work investigates source-free domain adaptation for 2D human pose estimation. In the pose estimation task, given an input image \\( \\pmb{x} \\in \\mathbb{R}^{H \\times W \\times 3} \\), the goal is to predict the corresponding \\( y \\in \\mathbb{R}^{K \\times 2} \\) representing the 2D coordinates of \\( K \\) keypoints using a pose regression model \\( f \\). In this paper, we assume access to a pre-trained model, denoted by \\( f_{S} \\), as well as \\( N \\) unlabeled images \\( \\mathcal{D} = \\{\\pmb{x}_i\\}_{i=1}^N \\) from a target domain \\( \\mathcal{T} \\). Our goal is to adapt the source model to the target such that it performs better on images drawn from the target distribution than when directly using the source model on the target images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.47, + 0.67 + ], + "angle": 0, + "content": "Overview. In the absence of source data, we propose to use self-training to adapt the source pose estimation model to the target domain. However, self-training methods are prone to error accumulation, particularly when labeled data is absent to act as regularization. Hence, we introduce POST, an enhanced self-training strategy that employs three essential ideas to prevent such errors:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.671, + 0.47, + 0.746 + ], + "angle": 0, + "content": "1. A weight-averaged teacher model is used to generate the pseudo-labels for self-training. This ensures better retention of the source knowledge within the teacher model by reducing the effect of updating the weights via noisy pseudo-labels (Section 3.1.1)." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.748, + 0.472, + 0.839 + ], + "angle": 0, + "content": "2. In addition to adaptation over the output space via pseudolabels, the model is adapted in the feature space as well. For each target image, two aligned predictive views are generated via data augmentation, and consistency across features extracted from the two separate views is encouraged via a contrastive learning strategy (Section 3.1.2)." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.841, + 0.471, + 0.902 + ], + "angle": 0, + "content": "3. A human pose prior is used to regularize the adaptation by directing the model to generate more accurate and anatomically plausible pose pseudo-labels (Section 3.2). An overview of our framework is presented in Figure 2." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.671, + 0.472, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.776, + 0.108 + ], + "angle": 0, + "content": "3.1. Self-training via Mean Teacher" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.895, + 0.296 + ], + "angle": 0, + "content": "Motivated by research suggesting that weight-averaged models over training steps tend to perform better than the final model [6, 39], we utilize the Mean Teacher framework [11] to generate pseudo-labels for self-training. The framework involves creating two identical models, a teacher model \\( f_{\\mathrm{tea}} \\) and a student model \\( f_{\\mathrm{stu}} \\), both of which are initialized with the pre-trained network \\( f_{S} \\) at time step \\( t = 0 \\). At each subsequent time step \\( t \\), the student model parameters \\( \\theta \\) are updated by backpropagating the supervisory signals provided by the teacher model. The parameters of the teacher model \\( \\tilde{\\theta} \\) are updated via an exponential moving average (EMA) of the student model parameters:" + }, + { + "type": "equation", + "bbox": [ + 0.61, + 0.306, + 0.895, + 0.326 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\theta} _ {t} = \\alpha \\tilde {\\theta} _ {t - 1} + (1 - \\alpha) \\theta_ {t}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.337, + 0.895, + 0.427 + ], + "angle": 0, + "content": "where \\(\\alpha\\) denotes the smoothing coefficient which is set to 0.999 by default. The EMA update prevents the teacher model from overfitting to noisy pseudo-labels during the initial rounds of self-training, thereby, preserving the source knowledge. This is especially advantageous in our scenario where source data is unavailable to regularize the adaptation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.428, + 0.895, + 0.473 + ], + "angle": 0, + "content": "In the following sections, we demonstrate how to adapt \\( f_{\\mathrm{stu}} \\) using supervisory signals from \\( f_{\\mathrm{tea}} \\) on both the feature space and the pose prediction space." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.493, + 0.756, + 0.509 + ], + "angle": 0, + "content": "3.1.1 Prediction Space Adaptation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.517, + 0.895, + 0.653 + ], + "angle": 0, + "content": "At each time step \\(t\\), we apply two different data augmentations, \\(\\mathcal{A}_1\\) and \\(\\mathcal{A}_2\\), to a target image \\(\\pmb{x}\\) to generate two views. We then obtain the keypoint heatmap corresponding to the first transformed image \\(\\tilde{h}^t = f_{\\mathrm{tea}}^t (\\mathcal{A}_1(\\pmb {x}))\\). Here \\(\\tilde{h}^t\\in \\mathbb{R}^{K\\times H'\\times W'}\\) denotes the spatial likelihood of the \\(K\\) different keypoints on each channel. The pseudolabel from the teacher model is generated by obtaining the coordinates which produce the maximum activations \\(\\hat{y}^t = \\operatorname{argmax}_u\\tilde{h}_{[:,u]}^t\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.653, + 0.895, + 0.758 + ], + "angle": 0, + "content": "To reduce the influence of erroneous pseudo-labels in our training process, we utilize a confidence threshold to discard potentially unreliable labels. Specifically, we only retain the keypoint activations with the top \\( p\\% \\) maximum values among all activations and discard the rest. We set the threshold \\( \\tau \\) accordingly to reflect this, thereby ensuring that only the most confident labels are used for training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.759, + 0.895, + 0.835 + ], + "angle": 0, + "content": "Following prior work on supervised pose estimation, we first convert the pseudo-labels to normalized Gaussian heatmaps [40] and then use the mean squared error (MSE) loss to update the student model over batches of target images sampled from \\(\\mathcal{D}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.846, + 0.895, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {o u t}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {\\mathbf {x} \\in \\mathcal {B}} \\sum_ {k = 1} ^ {K} \\mathbb {1} \\left(\\hat {h} _ {k} ^ {t} \\geq \\tau\\right) \\| \\tilde {\\mathcal {A}} _ {1} \\left(\\hat {h} _ {k} ^ {t}\\right) - \\tilde {\\mathcal {A}} _ {2} \\left(h _ {k} ^ {t}\\right) \\| _ {2}. \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14998" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.14, + 0.089, + 0.833, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.372, + 0.895, + 0.442 + ], + "angle": 0, + "content": "Figure 2. Framework overview. Our approach builds on the Mean Teacher framework and performs adaptation both in the pose prediction space using \\(\\mathcal{L}_{\\mathrm{out}}\\), and the feature space using \\(\\mathcal{L}_{\\mathrm{feat}}\\). This is supplemented by a human pose prior \\(g\\) that scores the predicted pseudo-labels in terms of plausibility. These scores are used to regularize the adaptation process in the absence of labeled source data via \\(\\mathcal{L}_{\\mathrm{prior}}\\). The student model \\(f_{\\mathrm{stu}}\\) is trained by the combination of the three losses, while the teacher model \\(f_{\\mathrm{tea}}\\) is updated with the exponential moving average (EMA) of the weights of the student model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.467, + 0.475, + 0.574 + ], + "angle": 0, + "content": "We denote the inverse functions of the chosen augmentations \\(\\mathcal{A}_1\\) and \\(\\mathcal{A}_2\\) as \\(\\tilde{\\mathcal{A}}_1\\) and \\(\\tilde{\\mathcal{A}}_2\\), respectively. The heatmap predicted by the student model for the \\(k\\)-th keypoint is represented by \\(h_k^t = f_{\\mathrm{stu}}^t (\\mathcal{A}_2(\\pmb {x}))^k\\), while the heatmap generated from the pseudo-labels predicted by the teacher model is represented by \\(\\hat{h}_k^t = L(\\hat{y}^t)^k\\). Here, \\(L(\\cdot)\\) represents the heatmap generating function and \\(\\mathcal{B}\\) denotes a batch of target images." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.59, + 0.317, + 0.607 + ], + "angle": 0, + "content": "3.1.2 Feature Apace Adaptation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.471, + 0.825 + ], + "angle": 0, + "content": "Pose estimation models primarily rely on a high-to-low-resolution feature encoder to generate low-resolution representations, which are then used to recover high-resolution pose heatmaps [18]. Since the upsampling process is inherently noisy, providing intermediate supervision to explicitly adapt the features, in addition to adapting the output pose keypoints as shown in the previous section, can be beneficial [17]. While previous work has demonstrated the benefits of joint adaptation across the output and feature space via adversarial learning in tasks such as semantic segmentation [41], this has been exclusively focused on scenarios where source data is available. Here, we propose an alternative way to accomplish feature space adaptation in the absence of source data via contrastive learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We begin by creating two different views of each target image \\(\\mathbf{x}\\) using a pair of sampled augmentations \\(\\mathcal{A}_1\\) and \\(\\mathcal{A}_2\\), as previously shown. Next, considering the pose estimation model as a composition of a feature encoder and an output regressor, i.e., \\(f = \\mathrm{Dec} \\circ \\mathrm{Enc}\\), we extract" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.467, + 0.895, + 0.587 + ], + "angle": 0, + "content": "the augmentation reversed feature maps from the teacher model \\(\\tilde{z} = \\tilde{\\mathcal{A}}_1(\\mathrm{Enc}_{\\mathrm{tea}}(\\mathcal{A}_1(\\boldsymbol{x})))\\) and the student model \\(z = \\tilde{\\mathcal{A}}_2(\\mathrm{Enc}_{\\mathrm{stu}}(\\mathcal{A}_2(\\boldsymbol{x})))\\). We extract pairs of features for every image in a batch, pool them along the spatial dimensions, and then normalize them along the batch dimension to ensure that each covariate has a mean of 0 over the batch. For simplicity, we overload \\(z,\\tilde{z}\\) to represent the normalized features, and drop the time index \\(t\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.587, + 0.895, + 0.678 + ], + "angle": 0, + "content": "We utilize feature-level consistency between the different views in order to accomplish feature space adaptation. This is achieved via a contrastive learning strategy which encourages the cross-correlation matrix between the outputs of the two networks to be as close to the identity matrix as possible [12]," + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.685, + 0.895, + 0.719 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {f e a t}} = \\sum_ {i} (1 - C _ {i i}) ^ {2} + \\gamma \\sum_ {i} \\sum_ {j \\neq i} C _ {i j} ^ {2}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.724, + 0.895, + 0.799 + ], + "angle": 0, + "content": "We define \\(\\gamma\\) as a positive constant that balances the importance of the first and second terms of the loss function. \\(C\\) represents the cross-correlation matrix computed between the outputs of the student and teacher networks along the batch dimension:" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.803, + 0.895, + 0.851 + ], + "angle": 0, + "content": "\\[\nC _ {i j} = \\frac {\\sum_ {b = 1} ^ {| \\mathcal {B} |} \\tilde {z} _ {b , i} z _ {b , j}}{\\sqrt {\\sum_ {b = 1} ^ {| \\mathcal {B} |} \\left(\\tilde {z} _ {b , i}\\right) ^ {2}} \\sqrt {\\sum_ {b = 1} ^ {| \\mathcal {B} |} \\left(z _ {b , j}\\right) ^ {2}}}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Here, \\( b \\) represents the batch index, while \\( i \\) and \\( j \\) index the feature dimensions of the networks' outputs. We set \\( \\gamma = 5e - 3 \\) following [12]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "14999" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.198 + ], + "angle": 0, + "content": "The first term of \\(\\mathcal{L}_{\\mathrm{feat}}\\) encourages the consistency of pose features within the same image by equating the diagonal elements of the cross-correlation matrix to 1, effectively reversing the effects of augmentations. In contrast, the second term aims to decorrelate the different feature dimensions of the embedding by forcing the off-diagonal elements of the cross-correlation matrix to 0." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.205, + 0.34, + 0.22 + ], + "angle": 0, + "content": "3.2. Regularization via Pose Prior" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.474, + 0.351 + ], + "angle": 0, + "content": "Enhancing the performance of the pose estimation model on the target domain through joint adaptation over the output and feature space is undoubtedly valuable. However, this approach has its limitations, as it relies solely on general domain adaptation principles and overlooks the rich structural priors associated with human poses. To address this issue, we propose incorporating a parametric human pose prior to better adapt the pose estimation model to the target domain." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.367, + 0.285, + 0.38 + ], + "angle": 0, + "content": "3.2.1 2D Human Pose Prior" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.39, + 0.473, + 0.542 + ], + "angle": 0, + "content": "Building upon the work of [13], we propose a human pose prior modeled as a manifold consisting of plausible 2D poses. To represent the 2D poses while ignoring aspects such as size and scale, we use a set of 2D orientation vectors that connect pairs of joints in the human skeleton, denoted by \\(\\mathcal{G} = \\{\\pmb {\\theta} = (\\theta_1,\\dots ,\\theta_L)\\mid \\theta_l\\in \\mathbb{R}^2,\\| \\theta_l\\| _2 = 1\\forall l\\in [L]\\}\\). We assume that plausible 2D human poses lie on a manifold embedded in this pose space \\(\\mathcal{G}\\). We use a function \\(g:\\mathcal{G}\\to\\) \\(\\mathbb{R}^+\\), which maps a pose to a non-negative scalar, to represent the manifold of plausible poses as the zero-level set:" + }, + { + "type": "equation", + "bbox": [ + 0.186, + 0.549, + 0.471, + 0.566 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} = \\{\\boldsymbol {\\theta} \\in \\mathcal {G} \\mid g (\\boldsymbol {\\theta}) = 0 \\}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.572, + 0.473, + 0.649 + ], + "angle": 0, + "content": "where \\( g \\) represents the unsigned distance to the manifold. We construct this distance function by first encoding the pose using a hierarchical network \\( g_{\\mathrm{enc}} \\) that encodes the human pose based on its anatomical structure [42], and subsequently, use \\( g_{\\mathrm{dec}} \\) to predict the distance based on the pose representation." + }, + { + "type": "text", + "bbox": [ + 0.095, + 0.649, + 0.466, + 0.663 + ], + "angle": 0, + "content": "Specifically, for a given pose \\(\\theta\\), we encode it as follows," + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.669, + 0.47, + 0.688 + ], + "angle": 0, + "content": "\\[\n\\mathbf {v} _ {1} = g _ {\\mathrm {e n c}} ^ {1} \\left(\\theta_ {1}\\right), \\quad \\mathbf {v} _ {l} = g _ {\\mathrm {e n c}} ^ {l} \\left(\\theta_ {l}, \\mathbf {v} _ {\\Omega (l)}\\right), l \\in \\{2, \\dots , L \\}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.694, + 0.473, + 0.83 + ], + "angle": 0, + "content": "Here, \\(\\Omega(l)\\) is a function that maps the index of each orientation vector to its parent orientation vector in the kinematic chain of the human skeleton. We obtain the overall pose encoding as \\(\\mathbf{p} = [\\mathbf{v}_1|\\ldots|\\mathbf{v}_L]\\) by concatenating all the individual orientation encodings. This pose encoding is then processed by \\(g_{\\mathrm{dec}}: \\mathbb{R}^{d,L} \\to \\mathbb{R}^+\\), which predicts the unsigned distance for the given pose representation \\(\\mathbf{p}\\). A lower distance value for a pose implies that the configuration of joints is more likely to be a plausible human pose." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.27, + 0.863 + ], + "angle": 0, + "content": "3.2.2 Pose Prior Training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.472, + 0.903 + ], + "angle": 0, + "content": "To train the parametric prior \\(g\\), we rely on an auxiliary dataset of \\(M\\) human poses \\(\\mathcal{D}_{\\mathrm{A}} = \\{\\pmb{\\theta}^{i}\\}_{i=1}^{N_{\\mathrm{A}}}\\), where \\(\\pmb{\\theta}^{i} =\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.166 + ], + "angle": 0, + "content": "\\((\\theta_1^i,\\dots ,\\theta_L^i)\\). Importantly, these poses are not associated with their corresponding RGB images, which preserves the privacy aspect of the method. Additionally, storing only the pose coordinates instead of entire images makes data storage much more efficient and feasible." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.895, + 0.288 + ], + "angle": 0, + "content": "We adopt a supervised approach to train \\(g\\) to predict the \\(L2\\) distance to the plausible pose manifold for a given pose. To achieve this, we construct a dataset \\(\\tilde{\\mathcal{D}} = \\{(\\pmb{\\theta}_i,d_i)\\}_{i=1}^M\\), consisting of pose and distance pairs, from \\(\\mathcal{D}_{\\mathrm{A}}\\). As the poses from \\(\\mathcal{D}_{\\mathrm{A}}\\) lie on the desired manifold, we assign \\(d = 0\\) to all poses in the dataset. To diversify our training samples, we randomly generate negative samples with distance \\(d > 0\\) by perturbing the poses from \\(\\mathcal{D}_{\\mathrm{A}}\\) with noise." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.289, + 0.836, + 0.302 + ], + "angle": 0, + "content": "We train the network with the standard \\(L1\\) loss," + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.307, + 0.892, + 0.342 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {d i s t}} = \\sum_ {(\\boldsymbol {\\theta}, d) \\in \\tilde {D}} \\| g (\\boldsymbol {\\theta}) - d \\| _ {1}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.348, + 0.895, + 0.377 + ], + "angle": 0, + "content": "More details on the training process of the prior are provided in Section 4.2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.396, + 0.753, + 0.411 + ], + "angle": 0, + "content": "3.2.3 Adaptation using Pose Prior" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.419, + 0.894, + 0.464 + ], + "angle": 0, + "content": "We leverage the trained pose prior \\( g \\) to regularize the adaptation process by incentivizing the pose estimator to generate pseudo-labels that resemble plausible human poses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.464, + 0.895, + 0.629 + ], + "angle": 0, + "content": "Given the heatmaps \\(\\{h_k^t\\}_{k=1}^K\\) generated for each keypoint by the student model \\(f_{\\mathrm{stu}}^t\\) for a target image \\(x\\), we calculate the corresponding orientation vectors in a differentiable manner to evaluate the plausibility of the predicted pose using the prior. First, we renormalize each heatmap to a probability distribution via spatial softmax and condense it to a point by computing the spatial expected value of the latter. For computational efficiency, we carry this out in a separable manner along the two spatial dimensions. Namely, assuming \\(u = (u_1, u_2)\\) to be the two components of each pixel coordinate, we set" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.635, + 0.892, + 0.678 + ], + "angle": 0, + "content": "\\[\nu _ {i} ^ {k} = \\frac {\\sum_ {u _ {i}} u _ {i} e ^ {h _ {k} ^ {t} (u _ {i})}}{\\sum_ {u _ {i}} e ^ {h _ {k} ^ {t} (u _ {i})}}, \\quad h _ {k} ^ {t} (u _ {i}) = \\sum_ {u _ {j}} h _ {k} ^ {t} (u _ {1}, u _ {2}), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.683, + 0.892, + 0.789 + ], + "angle": 0, + "content": "where \\(i = 1,2\\) and \\(j = 2,1\\) respectively. Next, we use the pose coordinates to determine the orientation vectors between pairs of connected keypoints. Specifically, for every pair \\((a,b)\\) of connected keypoints in the human skeleton (denoted by the set \\(\\mathcal{E}\\)), we calculate the unit vector \\(\\theta\\) in the direction from \\(u^a\\) to \\(u^b\\), where \\(u^a\\) and \\(u^b\\) are the estimated softmax coordinates of keypoints \\(a\\) and \\(b\\), respectively, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.794, + 0.892, + 0.828 + ], + "angle": 0, + "content": "\\[\n\\theta = \\frac {u ^ {a} - u ^ {b}}{\\| u ^ {a} - u ^ {b} \\| _ {2}}, \\quad \\forall (a, b) \\in \\mathcal {E}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.833, + 0.892, + 0.862 + ], + "angle": 0, + "content": "Finally, we use the prior as a regularization term to minimize the distance of the current pose from our learned manifold," + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.868, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p r i o r}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {\\boldsymbol {x} \\in \\mathcal {B}} g \\left(T \\left(f _ {\\mathrm {s t u}} ^ {t} (\\boldsymbol {x})\\right)\\right), \\tag {10}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15000" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.123 + ], + "angle": 0, + "content": "where \\( T(\\cdot) \\) converts the predicted heatmaps to the orientation vector format required as input by the prior." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.133, + 0.264, + 0.15 + ], + "angle": 0, + "content": "3.3. Overall Adaptation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.156, + 0.47, + 0.187 + ], + "angle": 0, + "content": "The final training objective for the student model \\( f_{\\mathrm{stu}} \\) can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.169, + 0.2, + 0.47, + 0.224 + ], + "angle": 0, + "content": "\\[\n\\min _ {f _ {\\mathrm {s t u}}} \\mathcal {L} _ {\\text {o u t}} + \\lambda_ {1} \\mathcal {L} _ {\\text {f e a t}} + \\lambda_ {2} \\mathcal {L} _ {\\text {p r i o r}}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.235, + 0.471, + 0.311 + ], + "angle": 0, + "content": "Here, \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are hyper-parameters that control the influence of feature space adaptation and prior regularization, respectively. The teacher model \\(f_{\\mathrm{tea}}\\) is updated asynchronously by computing an exponential moving average of the student model weights as shown in Equation 1." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.326, + 0.21, + 0.344 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.351, + 0.47, + 0.473 + ], + "angle": 0, + "content": "In this section, we demonstrate POST's ability to adapt a 2D human pose estimation model to a target domain using only unlabeled data from that domain. We conduct experiments on three domain adaptive scenarios and compare with state-of-the-art domain adaptation baselines that utilize source data during adaptation. We also conduct extensive analysis to analyze the contribution and interaction between each component in our framework." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.484, + 0.18, + 0.498 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.507, + 0.472, + 0.582 + ], + "angle": 0, + "content": "SURREAL: SURREAL [43] is a large-scale dataset of synthetically generated images of people rendered from 3D sequences of human motion capture data against indoor backgrounds. It contains over 6 million frames, making it one of the largest and most diverse datasets of its kind." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.588, + 0.47, + 0.724 + ], + "angle": 0, + "content": "Human3.6M: Human3.6M [44] is a real-world video dataset captured in indoor environments, comprising 3.6 million frames. The dataset features human subjects performing various actions. In order to reduce redundancy and computational complexity, we down-sampled the videos from 50fps to 10fps as per the approach proposed in [5]. For training, we follow the standard protocol proposed in [6] and use 5 subjects (S1, S5, S6, S7, S8), while the remaining 2 subjects (S9, S11) are reserved for testing." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.729, + 0.47, + 0.806 + ], + "angle": 0, + "content": "LSP: Leeds Sports Pose (LSP) [45] is a real-world dataset that contains 2,000 images with annotated human body joint locations collected from sports activities. The images in LSP are captured in the wild, featuring a wide variety of human poses that are often challenging to detect." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.81, + 0.471, + 0.902 + ], + "angle": 0, + "content": "BRIAR: BRIAR [46] is a cutting-edge biometric dataset featuring a large-scale collection of videos of human subjects captured in extremely challenging conditions. The videos are recorded at varying distances, i.e., close range, \\(100\\mathrm{m}\\), \\(200\\mathrm{m}\\), \\(400\\mathrm{m}\\), \\(500\\mathrm{m}\\), and unmanned aerial vehicles (UAV), with each video lasting around 90 seconds. We randomly" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.123 + ], + "angle": 0, + "content": "sample 20 frames from each sequence for each of the 158 subjects for our experiments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.131, + 0.704, + 0.147 + ], + "angle": 0, + "content": "4.2. Experiment Protocols" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.154, + 0.892, + 0.336 + ], + "angle": 0, + "content": "Pose estimation model. We adopt the Simple Baseline [18] as our pose estimation model, with the ResNet-101 [47] as the backbone. To train the model, we use the Adam optimizer [48] with a base learning rate of \\( 1e - 4 \\), scheduled to decrease to \\( 1e - 5 \\) after 5 epochs and to \\( 1e - 6 \\) after 20 epochs. The model is trained for 30 epochs. We use a batch size of 32 and run 500 iterations per epoch. To threshold the model predictions, we set the confidence thresholding ratio \\( p \\) to 0.5. To augment the images during training, we follow [6] and use rotation, translation, shear, and Gaussian blur. The hyper-parameters \\( \\lambda_{1} \\) and \\( \\lambda_{2} \\) are set to \\( 1e - 3 \\) and \\( 1e - 6 \\), respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.34, + 0.895, + 0.552 + ], + "angle": 0, + "content": "Pose prior model. The training of the parametric prior follows a multi-stage approach that involves using different types of training samples. Initially, we use a combination of manifold poses \\(\\theta_{m}\\) and non-manifold poses \\(\\theta_{nm}\\) with a considerable distance from the desired manifold. Over the course of training, we gradually increase the number of non-manifold poses \\(\\theta_{nm}\\) with a small distance from the manifold. This enables our model to first learn a smooth surface and then gradually incorporate finer details as training progresses. We create these non-manifold poses \\(\\theta_{nm}\\) by injecting noise into the manifold poses \\(\\theta_{m}\\) obtained from the auxiliary dataset. Specifically, we sample directional noise from the Von-Mises distribution [49] and add it to the manifold poses in order to obtain the implausible poses." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.552, + 0.892, + 0.643 + ], + "angle": 0, + "content": "The architecture for the encoder \\( g_{\\mathrm{enc}} \\) consists of a 2-layer MLP with an output feature size of \\( d = 6 \\) for each orientation vector, similar to [42]. The distance field network \\( g_{\\mathrm{dec}} \\) is implemented as a 5-layer MLP. Given its large size and diverse poses, we train the prior for our primary experiments using the SURREAL dataset." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.746, + 0.667 + ], + "angle": 0, + "content": "4.3. Comparison with Baselines" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.675, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Baselines. We evaluate the performance of our proposed method against several state-of-the-art domain adaptive frameworks. This includes adversarial learning-based feature alignment methods, such as DAN[31], DD[50], and RegDA[5]. Additionally, we consider approaches based on pseudo-labeling, namely CCSSL[38], and UDAPE [6]. It is worth noting that all these methods employ the source data during the adaptation process. To establish a comprehensive performance baseline, we report the results of two additional baselines: Oracle and Source only. The Oracle baseline represents the upper bound of the model's performance, achieved by training the model jointly with target 2D annotations. On the other hand, Source only represents the model's performance when it is directly applied to the target domain without any adaptation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15001" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.47, + 0.116 + ], + "angle": 0, + "content": "Table 1. PCK@0.05 on SURREAL \\(\\rightarrow\\) LSP. (Best value is in red color, while the second best value is in blue color.)" + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.122, + 0.47, + 0.269 + ], + "angle": 0, + "content": "
MethodSFSld.Elb.WristHipKneeAnkleAvg.
Source only-51.565.062.968.068.767.463.9
Oracle--------
DANX52.262.958.971.068.165.163.0
DDX28.465.956.875.074.373.962.4
RegDAX62.776.771.181.080.375.374.6
CCSSLX36.866.363.959.667.370.460.7
UDAPEX69.284.983.385.584.784.382.0
POST✓66.583.981.084.683.182.680.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.111, + 0.28, + 0.435, + 0.294 + ], + "angle": 0, + "content": "Table 2. PCK@0.05 on SURREAL \\( \\rightarrow \\) Human3.6M." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.298, + 0.47, + 0.446 + ], + "angle": 0, + "content": "
MethodSFSld.Elb.WristHipKneeAnkleAvg.
Source only-69.475.466.437.977.377.767.3
Oracle-95.391.886.995.694.193.692.9
DANX68.177.562.330.478.479.466.0
DDX71.683.375.142.176.276.170.7
RegDAX73.386.472.854.882.084.475.6
CCSSLX44.368.555.222.262.357.851.7
UDAPEX78.189.681.152.685.387.179.0
POST✓81.388.577.446.183.483.476.7
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.47, + 0.47, + 0.531 + ], + "angle": 0, + "content": "Metrics. We adopt the evaluation metric of Percentage of Correct Keypoint (PCK) for all experiments and report PCK@0.05 that measures the ratio of correct prediction within a range of \\(5\\%\\) with respect to the image size." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.54, + 0.172, + 0.555 + ], + "angle": 0, + "content": "4.4. Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.563, + 0.473, + 0.852 + ], + "angle": 0, + "content": "Quantitative results. We evaluate POST in two adaptation scenarios: SURREAL \\(\\rightarrow\\) LSP and SURREAL \\(\\rightarrow\\) Human3.6M, and report the quantitative results in Table 1 and Table 2, respectively. Specifically, we report the PCK@0.05 on 16 keypoints of the human body, including shoulders (sld.), elbows (elb.), wrists, hips, knees, and ankles. Our method achieves comparable results to many recent approaches that leverage source data for adaptation. Among these methods, UDAPE [6] achieves the highest performance on both cases, with our framework achieving a close second and only 2 percentage points behind on average. Notably, we outperform every other method, including the recently proposed RegDA [5] approach, by a significant margin of up to 5.7 percentage points. It is worth noting that not only do these methods require source data, but also involve additional models such as discriminators or style transfer modules, and unstable adversarial training. In contrast, our framework is lightweight, only involves pseudo-label training, and utilizes a simple prior model that can be trained offline." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Qualitative results. In addition to quantitative results, we also present qualitative results on SURREAL \\(\\rightarrow\\) Human3.6M in Figure 3 and on SURREAL \\(\\rightarrow\\) LSP in Figure 4. Also," + }, + { + "type": "image", + "bbox": [ + 0.562, + 0.09, + 0.651, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.653, + 0.09, + 0.741, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.743, + 0.09, + 0.832, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.562, + 0.16, + 0.651, + 0.229 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.653, + 0.16, + 0.741, + 0.229 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.743, + 0.16, + 0.832, + 0.229 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.233, + 0.895, + 0.304 + ], + "angle": 0, + "content": "Figure 3. Qualitative results on SURREAL \\(\\rightarrow\\) Human3.6M. We demonstrate sample results on the Human3.6M dataset. For each row, the leftmost shows the Source only prediction, the middle one shows the UDAPE [6] prediction, and the rightmost shows the prediction made POST." + }, + { + "type": "image", + "bbox": [ + 0.583, + 0.323, + 0.658, + 0.381 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.66, + 0.323, + 0.734, + 0.381 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.736, + 0.323, + 0.811, + 0.381 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.584, + 0.387, + 0.658, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.66, + 0.387, + 0.734, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.736, + 0.387, + 0.811, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.584, + 0.45, + 0.658, + 0.507 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.661, + 0.45, + 0.734, + 0.507 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.736, + 0.45, + 0.811, + 0.507 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.584, + 0.514, + 0.658, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.66, + 0.514, + 0.734, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.736, + 0.514, + 0.811, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.577, + 0.895, + 0.647 + ], + "angle": 0, + "content": "Figure 4. Qualitative results on SURREAL \\(\\rightarrow\\) LSP. We demonstrate sample results on the LSP dataset. For each row, the left-most shows the Source only prediction, the middle one shows the UDAPE [6] prediction, and the rightmost shows the prediction made POST." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.897, + 0.903 + ], + "angle": 0, + "content": "we present only visual results on the SURREAL \\(\\rightarrow\\) BRIAR adaptation scenario since pose annotations are absent in the BRIAR dataset. Figure 5 displays the predicted human poses on images taken from six different imaging ranges in the BRIAR dataset. While using the source model directly produces completely inaccurate poses, POST can accurately localize the keypoint locations, even in the presence of occlusions and atmospheric turbulence. Our approach can also accurately reconstruct poses even when the human is imaged from an elevated perspective, resulting in a high camera angle (Figure 5.f). Notably, our approach achieves this without using any source data for adaptation. Our results are comparable to those produced by UDAPE [6], which utilizes source data for adaptation. Additional qualitative results can be found in the supplementary document." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15002" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.164, + 0.094, + 0.465, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.094, + 0.808, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.462, + 0.181, + 0.509, + 0.192 + ], + "angle": 0, + "content": "a) \\(100\\mathrm{m}\\)" + }, + { + "type": "image", + "bbox": [ + 0.164, + 0.199, + 0.465, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.2, + 0.808, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.459, + 0.286, + 0.506, + 0.297 + ], + "angle": 0, + "content": "b) \\(200\\mathrm{m}\\)" + }, + { + "type": "image", + "bbox": [ + 0.164, + 0.305, + 0.465, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.306, + 0.808, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.459, + 0.392, + 0.506, + 0.403 + ], + "angle": 0, + "content": "c) \\(400\\mathrm{m}\\)" + }, + { + "type": "image", + "bbox": [ + 0.165, + 0.411, + 0.465, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.412, + 0.808, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.462, + 0.497, + 0.509, + 0.508 + ], + "angle": 0, + "content": "d) \\(500\\mathrm{m}\\)" + }, + { + "type": "image", + "bbox": [ + 0.166, + 0.517, + 0.465, + 0.595 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.517, + 0.808, + 0.595 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.459, + 0.604, + 0.535, + 0.615 + ], + "angle": 0, + "content": "e) close range" + }, + { + "type": "image", + "bbox": [ + 0.166, + 0.623, + 0.465, + 0.701 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.623, + 0.808, + 0.701 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.459, + 0.709, + 0.493, + 0.72 + ], + "angle": 0, + "content": "f) uav" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.724, + 0.895, + 0.78 + ], + "angle": 0, + "content": "Figure 5. Qualitative results on SURREAL \\(\\rightarrow\\) BRIAR. We demonstrate sample results on BRIAR at all ranges. For each range, we display three images: the leftmost shows the Source only prediction, the middle one shows the UDAPE [6] prediction, and the rightmost shows the prediction using POST. Although POST does not use source data for adaptation, it is able to match the predictions produced by UDAPE, which uses source data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.803, + 0.241, + 0.818 + ], + "angle": 0, + "content": "4.5. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Effect of auxiliary dataset. We conduct experiments to evaluate the impact of the choice of the auxiliary dataset (used to train the prior) on downstream adaptation. The results are presented in Table 3. Our findings indicate that" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.804, + 0.892, + 0.836 + ], + "angle": 0, + "content": "POST is robust to the choice of the auxiliary dataset, with performance differences of \\(\\sim 0.5\\) percentage points." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Effect of loss terms. We conduct an experiment to evaluate the performance of each component of our framework. The results on the SURREAL \\(\\rightarrow\\) Human3.6M adaptation scenario are presented in Table 4. Our findings indicate that in addi" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15003" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.47, + 0.116 + ], + "angle": 0, + "content": "Table 3. Effect of auxiliary dataset. We evaluate the effect of auxiliary dataset on downstream adaptation tasks." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.121, + 0.472, + 0.268 + ], + "angle": 0, + "content": "
SURREAL→HUMAN3.6M
Aux. datasetSld.Elb.WristHipKneeAnkleAvg.
SURREAL81.388.577.446.183.483.476.7
Human3.6M80.988.077.245.083.182.876.2
SURREAL→LSP
Aux. datasetSld.Elb.WristHipKneeAnkleAvg.
SURREAL66.583.981.084.683.182.680.3
Human3.6M66.183.680.784.483.182.580.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.282, + 0.47, + 0.309 + ], + "angle": 0, + "content": "Table 4. Effect of each loss term. We evaluate the contribution of each loss term on SURREAL \\(\\rightarrow\\) Human3.6M." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.314, + 0.47, + 0.395 + ], + "angle": 0, + "content": "
LoutLfeatLpriorSld.Elb.WristHipKneeAnkleAvg.
XXX69.475.466.437.977.377.767.3
✓XX77.986.773.738.883.084.374.1
✓✓X81.787.175.244.382.382.275.5
✓✓✓81.388.577.446.183.483.476.7
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.423, + 0.47, + 0.558 + ], + "angle": 0, + "content": "tion to prediction space adaptation, feature space adaptation also plays a crucial role in enabling effective unsupervised learning from pseudo-labels. Moreover, we observed that the human pose prior brings additional improvements, thus validating our hypothesis that noisy pose pseudo-labels can be refined implicitly by a prior in the absence of source data. Overall, our results demonstrate the effectiveness of our framework and the importance of each of its components in achieving state-of-the-art performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.47, + 0.716 + ], + "angle": 0, + "content": "Cross-dataset performance of prior. We evaluate the ability of the learned prior to handle distribution shift separately from the adaptation performance. Specifically, we assess the robustness of the prior by computing pose scores across datasets, and the results are presented in Figure 6. The plot demonstrates that our prior is effective in scoring plausible (real) poses with low scores and scoring implausible poses with higher scores. Note that the bell curve shape of the noisy pose scores is due to the Von-Mises noise added to create the noisy poses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.722, + 0.47, + 0.828 + ], + "angle": 0, + "content": "Effect of thresholding. We analyze the impact of the pseudo-label threshold \\(\\tau\\) on the adaptation performance in Table 5. The results on SURREAL \\(\\rightarrow\\) Human3.6M reveal that as we increase this ratio, the performance gradually decreases. This can be attributed to the fact that higher thresholding ratios tend to include lower confident predictions as pseudo-labels, which can negatively impact adaptation." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.845, + 0.195, + 0.86 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We address the problem of adapting a pre-trained 2D human pose estimator to a new target domain with unlabeled" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.088, + 0.892, + 0.115 + ], + "angle": 0, + "content": "Table 5. Effect of \\(\\tau\\). We evaluate adaptation performance on SURREAL \\(\\rightarrow\\) Human3.6M as \\(\\tau\\) is varied." + }, + { + "type": "table", + "bbox": [ + 0.541, + 0.119, + 0.852, + 0.285 + ], + "angle": 0, + "content": "
τ = 0.1τ = 0.3τ = 0.5τ = 0.7τ = 0.9
76.476.576.775.373.8
" + }, + { + "type": "image_caption", + "bbox": [ + 0.641, + 0.289, + 0.805, + 0.3 + ], + "angle": 0, + "content": "(a) Human3.6M \\(\\rightarrow\\) SURREAL" + }, + { + "type": "image", + "bbox": [ + 0.542, + 0.309, + 0.848, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.641, + 0.422, + 0.804, + 0.434 + ], + "angle": 0, + "content": "(b) SURREAL \\(\\rightarrow\\) Human3.6M" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.44, + 0.892, + 0.482 + ], + "angle": 0, + "content": "Figure 6. Cross-dataset prior transfer. We plot the histogram of scores predicted by the prior. The prior can clearly demarcate plausible poses from implausible poses across datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.894, + 0.659 + ], + "angle": 0, + "content": "target data. To this end, we propose a self-training algorithm, POST, that leverages a Mean Teacher framework to enforce both prediction-level and feature-level consistency between a pair of student and teacher models. Our approach incorporates a human pose prior that captures the manifold of possible poses in a high-dimensional space, which helps to refine noisy pseudo-labels generated during self-training. We evaluate our method on three challenging adaptation scenarios and show that it achieves competitive performance compared to existing UDA methods that have access to source data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.667, + 0.895, + 0.819 + ], + "angle": 0, + "content": "Acknowledgements. This research is based upon work supported in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via [2022-21102100007]. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.834, + 0.597, + 0.849 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.859, + 0.894, + 0.9 + ], + "angle": 0, + "content": "[1] Ke Sun, Bin Xiao, Dong Liu, and Jingdong Wang. Deep high-resolution representation learning for human pose estimation. 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Raychaudhuri $^{1,2*}$ Calvin-Khang Ta $^{1}$ Arindam Dutta $^{1}$ Rohit Lal $^{1}$ Amit K. Roy-Chowdhury $^{1}$ $^{1}$ University of California, Riverside $^{2}$ AWS AI Labs + +{drayc001@, cta003@, adutt020@, rla1011@, amertc@ece.}ucr.edu + +# Abstract + +Domain adaptation methods for 2D human pose estimation typically require continuous access to the source data during adaptation, which can be challenging due to privacy, memory, or computational constraints. To address this limitation, we focus on the task of source-free domain adaptation for pose estimation, where a source model must adapt to a new target domain using only unlabeled target data. Although recent advances have introduced source-free methods for classification tasks, extending them to the regression task of pose estimation is non-trivial. In this paper, we present Prior-guided Self-training (POST), a pseudolabeling approach that builds on the popular Mean Teacher framework to compensate for the distribution shift. POST leverages prediction-level and feature-level consistency between a student and teacher model against certain image transformations. In the absence of source data, POST utilizes a human pose prior that regularizes the adaptation process by directing the model to generate more accurate and anatomically plausible pose pseudo-labels. Despite being simple and intuitive, our framework can deliver significant performance gains compared to applying the source model directly to the target data, as demonstrated in our extensive experiments and ablation studies. In fact, our approach achieves comparable performance to recent state-of-the-art methods that use source data for adaptation. + +# 1. Introduction + +Human pose estimation is a fundamental task in computer vision that involves determining the precise locations of keypoints, such as joints, on a human body in an image or video [1]. The growing need for pose estimation in various applications such as action recognition [2], human-computer interaction [3], and video surveillance [4] has driven the rapid development of highly accurate deep learning tech + +![](images/f269fd9a6d1df8c4a7d32d89b1b306e6b1a67e8a5f63ca42de4197fc02660e7b.jpg) +Figure 1. Problem setup. Existing UDA methods for pose estimation rely on a labeled source dataset while adapting to an unlabeled target dataset. However, privacy concerns surrounding the use of personally identifiable information in these labeled datasets, as well as the significant storage and computational requirements, can limit access to such data. Hence, our work focuses on source-free UDA of pose estimation models. + +niques. However, the challenge of obtaining large annotated datasets for training, compounded with the susceptibility to a performance decline in the face of data distribution shifts still poses limitations for current pose estimation models. + +To overcome these limitations, recent studies have focused on unsupervised domain adaptation (UDA) of pose estimators [5, 6]. UDA allows for transferring a pose estimation model trained on a source domain, where labeled data is available, to a target domain where labeled data is unavailable. Despite improved and robust pose estimation, the requirement of simultaneous access to both source and target domains during adaptation hinders real-world implementation. For instance, the labeled source data may not be accessible post-deployment due to privacy or proprietary issues. This is particularly relevant for human pose datasets, which contain personally identifiable information (PII) [7]. Furthermore, adaptation using the entire source data might + +be infeasible due to both memory and computational constraints. In light of these issues, we focus on source-free UDA of human pose estimation models. + +Concretely, our objective is to adapt a 2D human pose estimation model to a new target domain utilizing only its trained parameters and unlabeled target data. This presents a major challenge as the absence of source data for regularization can cause catastrophic forgetting. While recent advances have introduced methods to tackle this issue in classification tasks [8, 9, 10], extending them to the regression task of pose estimation is non-trivial. To address this challenge, we introduce Prior-guided Self-training (POST), a self-training regression framework that employs a human pose prior to effectively guide the adaptation process in the absence of source data. An overview of our problem setup is shown in Figure 1. + +Our approach builds on the Mean Teacher [11] framework, which uses consistency in the prediction space of a student and teacher model to produce trustworthy pseudo-labels and learn from the unlabeled target domain. To achieve this, we create two augmented views of each target image, varying in scale, spatial context, and color statistics. Aligned pose predictions from both models in both views are then obtained, and consistency between the predictions across the different views is encouraged to facilitate prediction space adaptation. However, our empirical results show that relying solely on consistency in the output space is insufficient when supervision from the source data is lacking. To address this, we also introduce feature space adaptation, which aims to encourage consistency across features extracted from the two separate views. We adopt the Barlow Twins [12] approach to accomplish this. Specifically, we seek to make the cross-correlation matrix calculated from a pair of feature embeddings as close to the identity matrix as possible. + +In addition to the adaptation across both outputs and features, we employ a human pose prior that models the full manifold of plausible poses in some high-dimensional pose space to refine possible noisy pseudo-labels that may arise during self-training. The plausible poses are represented as points on the manifold surface, with zero distance from it, while non-plausible poses are located outside the surface, with a non-zero distance from it. This manifold is learned using a high-dimensional neural field, similar to Pose-NDF [13]. The pose prior acts as a strong regularizer, directing the model to generate more accurate pose pseudolabels on the target data and leading to improved adaptation. The learning of this prior requires an auxiliary dataset of plausible human poses, but this does not compromise the privacy aspect of our framework as the prior does not make use of RGB images. In addition, it is worth noting that the prior can be trained offline, separately from the adaptation process. This not only saves computational resources but also reduces the amount of storage required. Compared to storing entire + +images, it is much more efficient to store pose coordinates, which requires approximately $3000 \times$ less memory. + +Main contributions. To summarize, our primary contributions are as follows: + +- We address the problem of adapting a human pose estimation model to a target domain consisting of unlabeled data, without access to the original source dataset. This ameliorates the privacy concern associated with the current domain adaptive pose estimation methods. +- We introduce Prior-guided Self-training (POST), a simple source-free unsupervised adaptation algorithm. POST leverages both prediction-level and feature-level consistency, in addition to a human pose prior, to drive self-training for improved adaptation to the target domain. +- We evaluate our method qualitatively and quantitatively on three challenging domain adaptive scenarios, demonstrating comparable performance to existing UDA methods that have access to the source data. + +# 2. Related Works + +Pose Estimation. 2D human pose estimation aims to locate human anatomical keypoints, such as the elbow and knee. Prior works can be categorized into two primary frameworks: the top-down framework and the bottom-up framework. Top-down methods [14, 15, 16, 17, 18, 19, 1] first detect each person from the image and then perform single-person pose estimation on each bounding box independently. On the other hand, bottom-up methods [20, 21, 22, 23, 24, 25, 26] predict keypoints of each person directly in an end-to-end manner. Typical bottom-up methods consist of two steps: predicting keypoint heatmaps and grouping the detected keypoints into separate poses. In this work, we focus on the bottom-up framework for efficiency purposes and adopt the Simple Baseline [18] architecture following [6] to ensure fair comparisons with prior domain adaptation algorithms. + +Unsupervised Domain Adaptation. UDA methods have been extensively applied to a broad range of computer vision tasks, including image classification [27], semantic segmentation [28], object detection [29], and reinforcement learning [30] to tackle the issue of data distribution shift. Most approaches aim to align the source and target data distributions through techniques such as maximum mean discrepancy [31] and adversarial learning [32, 27]. Another line of research utilizes image translation methods to perform adaptation by transforming the source images into the target domain [33, 34]. More recently, there has been a surge of interest in adaptation using only a pre-trained source model due to privacy and memory storage concerns related to the source data. These include techniques such as information maximization [8, 9], pseudo-labeling [35, 36] and self-supervision [37]. Compared to other tasks, domain adaptation for regression tasks, such as pose estimation, remains + +relatively unexplored. + +Domain Adaptive Pose Estimation. UDA methods for pose estimation have explored various techniques for overcoming the domain gap, including adversarial feature alignment and pseudo-labeling. RegDA [5] estimates the domain discrepancy by evaluating false predictions on the target domain and minimizes it. Mu et al. [38] proposed consistency regularization with respect to transformations and temporal consistency learning within a video. Li et al. [39] proposed a refinement module and a self-feedback loop to obtain reliable pseudo-labels. Recently, Kim et al. [6] introduced a unified framework for both human and animal keypoint detection, which aligns representations using input-level and output-level cues. Typically, these methods require access to the source data, which may raise data privacy, memory and computation concerns. In contrast, our method addresses the domain adaptation problem in a source-free setting. + +# 3. Prior-guided Self-training + +Our work investigates source-free domain adaptation for 2D human pose estimation. In the pose estimation task, given an input image $\pmb{x} \in \mathbb{R}^{H \times W \times 3}$ , the goal is to predict the corresponding $y \in \mathbb{R}^{K \times 2}$ representing the 2D coordinates of $K$ keypoints using a pose regression model $f$ . In this paper, we assume access to a pre-trained model, denoted by $f_{S}$ , as well as $N$ unlabeled images $\mathcal{D} = \{\pmb{x}_i\}_{i=1}^N$ from a target domain $\mathcal{T}$ . Our goal is to adapt the source model to the target such that it performs better on images drawn from the target distribution than when directly using the source model on the target images. + +Overview. In the absence of source data, we propose to use self-training to adapt the source pose estimation model to the target domain. However, self-training methods are prone to error accumulation, particularly when labeled data is absent to act as regularization. Hence, we introduce POST, an enhanced self-training strategy that employs three essential ideas to prevent such errors: + +1. A weight-averaged teacher model is used to generate the pseudo-labels for self-training. This ensures better retention of the source knowledge within the teacher model by reducing the effect of updating the weights via noisy pseudo-labels (Section 3.1.1). +2. In addition to adaptation over the output space via pseudolabels, the model is adapted in the feature space as well. For each target image, two aligned predictive views are generated via data augmentation, and consistency across features extracted from the two separate views is encouraged via a contrastive learning strategy (Section 3.1.2). +3. A human pose prior is used to regularize the adaptation by directing the model to generate more accurate and anatomically plausible pose pseudo-labels (Section 3.2). An overview of our framework is presented in Figure 2. + +# 3.1. Self-training via Mean Teacher + +Motivated by research suggesting that weight-averaged models over training steps tend to perform better than the final model [6, 39], we utilize the Mean Teacher framework [11] to generate pseudo-labels for self-training. The framework involves creating two identical models, a teacher model $f_{\mathrm{tea}}$ and a student model $f_{\mathrm{stu}}$ , both of which are initialized with the pre-trained network $f_{S}$ at time step $t = 0$ . At each subsequent time step $t$ , the student model parameters $\theta$ are updated by backpropagating the supervisory signals provided by the teacher model. The parameters of the teacher model $\tilde{\theta}$ are updated via an exponential moving average (EMA) of the student model parameters: + +$$ +\tilde {\theta} _ {t} = \alpha \tilde {\theta} _ {t - 1} + (1 - \alpha) \theta_ {t}, \tag {1} +$$ + +where $\alpha$ denotes the smoothing coefficient which is set to 0.999 by default. The EMA update prevents the teacher model from overfitting to noisy pseudo-labels during the initial rounds of self-training, thereby, preserving the source knowledge. This is especially advantageous in our scenario where source data is unavailable to regularize the adaptation. + +In the following sections, we demonstrate how to adapt $f_{\mathrm{stu}}$ using supervisory signals from $f_{\mathrm{tea}}$ on both the feature space and the pose prediction space. + +# 3.1.1 Prediction Space Adaptation + +At each time step $t$ , we apply two different data augmentations, $\mathcal{A}_1$ and $\mathcal{A}_2$ , to a target image $\pmb{x}$ to generate two views. We then obtain the keypoint heatmap corresponding to the first transformed image $\tilde{h}^t = f_{\mathrm{tea}}^t (\mathcal{A}_1(\pmb {x}))$ . Here $\tilde{h}^t\in \mathbb{R}^{K\times H'\times W'}$ denotes the spatial likelihood of the $K$ different keypoints on each channel. The pseudolabel from the teacher model is generated by obtaining the coordinates which produce the maximum activations $\hat{y}^t = \operatorname{argmax}_u\tilde{h}_{[:,u]}^t$ . + +To reduce the influence of erroneous pseudo-labels in our training process, we utilize a confidence threshold to discard potentially unreliable labels. Specifically, we only retain the keypoint activations with the top $p\%$ maximum values among all activations and discard the rest. We set the threshold $\tau$ accordingly to reflect this, thereby ensuring that only the most confident labels are used for training. + +Following prior work on supervised pose estimation, we first convert the pseudo-labels to normalized Gaussian heatmaps [40] and then use the mean squared error (MSE) loss to update the student model over batches of target images sampled from $\mathcal{D}$ : + +$$ +\mathcal {L} _ {\text {o u t}} = \frac {1}{| \mathcal {B} |} \sum_ {\mathbf {x} \in \mathcal {B}} \sum_ {k = 1} ^ {K} \mathbb {1} \left(\hat {h} _ {k} ^ {t} \geq \tau\right) \| \tilde {\mathcal {A}} _ {1} \left(\hat {h} _ {k} ^ {t}\right) - \tilde {\mathcal {A}} _ {2} \left(h _ {k} ^ {t}\right) \| _ {2}. \tag {2} +$$ + +![](images/c556debaba324cdf504fd1ec865cb5e134057372a5fa29e9517f0c4813dae355.jpg) +Figure 2. Framework overview. Our approach builds on the Mean Teacher framework and performs adaptation both in the pose prediction space using $\mathcal{L}_{\mathrm{out}}$ , and the feature space using $\mathcal{L}_{\mathrm{feat}}$ . This is supplemented by a human pose prior $g$ that scores the predicted pseudo-labels in terms of plausibility. These scores are used to regularize the adaptation process in the absence of labeled source data via $\mathcal{L}_{\mathrm{prior}}$ . The student model $f_{\mathrm{stu}}$ is trained by the combination of the three losses, while the teacher model $f_{\mathrm{tea}}$ is updated with the exponential moving average (EMA) of the weights of the student model. + +We denote the inverse functions of the chosen augmentations $\mathcal{A}_1$ and $\mathcal{A}_2$ as $\tilde{\mathcal{A}}_1$ and $\tilde{\mathcal{A}}_2$ , respectively. The heatmap predicted by the student model for the $k$ -th keypoint is represented by $h_k^t = f_{\mathrm{stu}}^t (\mathcal{A}_2(\pmb {x}))^k$ , while the heatmap generated from the pseudo-labels predicted by the teacher model is represented by $\hat{h}_k^t = L(\hat{y}^t)^k$ . Here, $L(\cdot)$ represents the heatmap generating function and $\mathcal{B}$ denotes a batch of target images. + +# 3.1.2 Feature Apace Adaptation + +Pose estimation models primarily rely on a high-to-low-resolution feature encoder to generate low-resolution representations, which are then used to recover high-resolution pose heatmaps [18]. Since the upsampling process is inherently noisy, providing intermediate supervision to explicitly adapt the features, in addition to adapting the output pose keypoints as shown in the previous section, can be beneficial [17]. While previous work has demonstrated the benefits of joint adaptation across the output and feature space via adversarial learning in tasks such as semantic segmentation [41], this has been exclusively focused on scenarios where source data is available. Here, we propose an alternative way to accomplish feature space adaptation in the absence of source data via contrastive learning. + +We begin by creating two different views of each target image $\mathbf{x}$ using a pair of sampled augmentations $\mathcal{A}_1$ and $\mathcal{A}_2$ , as previously shown. Next, considering the pose estimation model as a composition of a feature encoder and an output regressor, i.e., $f = \mathrm{Dec} \circ \mathrm{Enc}$ , we extract + +the augmentation reversed feature maps from the teacher model $\tilde{z} = \tilde{\mathcal{A}}_1(\mathrm{Enc}_{\mathrm{tea}}(\mathcal{A}_1(\boldsymbol{x})))$ and the student model $z = \tilde{\mathcal{A}}_2(\mathrm{Enc}_{\mathrm{stu}}(\mathcal{A}_2(\boldsymbol{x})))$ . We extract pairs of features for every image in a batch, pool them along the spatial dimensions, and then normalize them along the batch dimension to ensure that each covariate has a mean of 0 over the batch. For simplicity, we overload $z,\tilde{z}$ to represent the normalized features, and drop the time index $t$ . + +We utilize feature-level consistency between the different views in order to accomplish feature space adaptation. This is achieved via a contrastive learning strategy which encourages the cross-correlation matrix between the outputs of the two networks to be as close to the identity matrix as possible [12], + +$$ +\mathcal {L} _ {\text {f e a t}} = \sum_ {i} (1 - C _ {i i}) ^ {2} + \gamma \sum_ {i} \sum_ {j \neq i} C _ {i j} ^ {2}. \tag {3} +$$ + +We define $\gamma$ as a positive constant that balances the importance of the first and second terms of the loss function. $C$ represents the cross-correlation matrix computed between the outputs of the student and teacher networks along the batch dimension: + +$$ +C _ {i j} = \frac {\sum_ {b = 1} ^ {| \mathcal {B} |} \tilde {z} _ {b , i} z _ {b , j}}{\sqrt {\sum_ {b = 1} ^ {| \mathcal {B} |} \left(\tilde {z} _ {b , i}\right) ^ {2}} \sqrt {\sum_ {b = 1} ^ {| \mathcal {B} |} \left(z _ {b , j}\right) ^ {2}}}. \tag {4} +$$ + +Here, $b$ represents the batch index, while $i$ and $j$ index the feature dimensions of the networks' outputs. We set $\gamma = 5e - 3$ following [12]. + +The first term of $\mathcal{L}_{\mathrm{feat}}$ encourages the consistency of pose features within the same image by equating the diagonal elements of the cross-correlation matrix to 1, effectively reversing the effects of augmentations. In contrast, the second term aims to decorrelate the different feature dimensions of the embedding by forcing the off-diagonal elements of the cross-correlation matrix to 0. + +# 3.2. Regularization via Pose Prior + +Enhancing the performance of the pose estimation model on the target domain through joint adaptation over the output and feature space is undoubtedly valuable. However, this approach has its limitations, as it relies solely on general domain adaptation principles and overlooks the rich structural priors associated with human poses. To address this issue, we propose incorporating a parametric human pose prior to better adapt the pose estimation model to the target domain. + +# 3.2.1 2D Human Pose Prior + +Building upon the work of [13], we propose a human pose prior modeled as a manifold consisting of plausible 2D poses. To represent the 2D poses while ignoring aspects such as size and scale, we use a set of 2D orientation vectors that connect pairs of joints in the human skeleton, denoted by $\mathcal{G} = \{\pmb {\theta} = (\theta_1,\dots ,\theta_L)\mid \theta_l\in \mathbb{R}^2,\| \theta_l\| _2 = 1\forall l\in [L]\}$ . We assume that plausible 2D human poses lie on a manifold embedded in this pose space $\mathcal{G}$ . We use a function $g:\mathcal{G}\to$ $\mathbb{R}^+$ , which maps a pose to a non-negative scalar, to represent the manifold of plausible poses as the zero-level set: + +$$ +\mathcal {P} = \{\boldsymbol {\theta} \in \mathcal {G} \mid g (\boldsymbol {\theta}) = 0 \}, \tag {5} +$$ + +where $g$ represents the unsigned distance to the manifold. We construct this distance function by first encoding the pose using a hierarchical network $g_{\mathrm{enc}}$ that encodes the human pose based on its anatomical structure [42], and subsequently, use $g_{\mathrm{dec}}$ to predict the distance based on the pose representation. + +Specifically, for a given pose $\theta$ , we encode it as follows, + +$$ +\mathbf {v} _ {1} = g _ {\mathrm {e n c}} ^ {1} \left(\theta_ {1}\right), \quad \mathbf {v} _ {l} = g _ {\mathrm {e n c}} ^ {l} \left(\theta_ {l}, \mathbf {v} _ {\Omega (l)}\right), l \in \{2, \dots , L \}. \tag {6} +$$ + +Here, $\Omega(l)$ is a function that maps the index of each orientation vector to its parent orientation vector in the kinematic chain of the human skeleton. We obtain the overall pose encoding as $\mathbf{p} = [\mathbf{v}_1|\ldots|\mathbf{v}_L]$ by concatenating all the individual orientation encodings. This pose encoding is then processed by $g_{\mathrm{dec}}: \mathbb{R}^{d,L} \to \mathbb{R}^+$ , which predicts the unsigned distance for the given pose representation $\mathbf{p}$ . A lower distance value for a pose implies that the configuration of joints is more likely to be a plausible human pose. + +# 3.2.2 Pose Prior Training + +To train the parametric prior $g$ , we rely on an auxiliary dataset of $M$ human poses $\mathcal{D}_{\mathrm{A}} = \{\pmb{\theta}^{i}\}_{i=1}^{N_{\mathrm{A}}}$ , where $\pmb{\theta}^{i} =$ + +$(\theta_1^i,\dots ,\theta_L^i)$ . Importantly, these poses are not associated with their corresponding RGB images, which preserves the privacy aspect of the method. Additionally, storing only the pose coordinates instead of entire images makes data storage much more efficient and feasible. + +We adopt a supervised approach to train $g$ to predict the $L2$ distance to the plausible pose manifold for a given pose. To achieve this, we construct a dataset $\tilde{\mathcal{D}} = \{(\pmb{\theta}_i,d_i)\}_{i=1}^M$ , consisting of pose and distance pairs, from $\mathcal{D}_{\mathrm{A}}$ . As the poses from $\mathcal{D}_{\mathrm{A}}$ lie on the desired manifold, we assign $d = 0$ to all poses in the dataset. To diversify our training samples, we randomly generate negative samples with distance $d > 0$ by perturbing the poses from $\mathcal{D}_{\mathrm{A}}$ with noise. + +We train the network with the standard $L1$ loss, + +$$ +\mathcal {L} _ {\text {d i s t}} = \sum_ {(\boldsymbol {\theta}, d) \in \tilde {D}} \| g (\boldsymbol {\theta}) - d \| _ {1}. \tag {7} +$$ + +More details on the training process of the prior are provided in Section 4.2. + +# 3.2.3 Adaptation using Pose Prior + +We leverage the trained pose prior $g$ to regularize the adaptation process by incentivizing the pose estimator to generate pseudo-labels that resemble plausible human poses. + +Given the heatmaps $\{h_k^t\}_{k=1}^K$ generated for each keypoint by the student model $f_{\mathrm{stu}}^t$ for a target image $x$ , we calculate the corresponding orientation vectors in a differentiable manner to evaluate the plausibility of the predicted pose using the prior. First, we renormalize each heatmap to a probability distribution via spatial softmax and condense it to a point by computing the spatial expected value of the latter. For computational efficiency, we carry this out in a separable manner along the two spatial dimensions. Namely, assuming $u = (u_1, u_2)$ to be the two components of each pixel coordinate, we set + +$$ +u _ {i} ^ {k} = \frac {\sum_ {u _ {i}} u _ {i} e ^ {h _ {k} ^ {t} (u _ {i})}}{\sum_ {u _ {i}} e ^ {h _ {k} ^ {t} (u _ {i})}}, \quad h _ {k} ^ {t} (u _ {i}) = \sum_ {u _ {j}} h _ {k} ^ {t} (u _ {1}, u _ {2}), \tag {8} +$$ + +where $i = 1,2$ and $j = 2,1$ respectively. Next, we use the pose coordinates to determine the orientation vectors between pairs of connected keypoints. Specifically, for every pair $(a,b)$ of connected keypoints in the human skeleton (denoted by the set $\mathcal{E}$ ), we calculate the unit vector $\theta$ in the direction from $u^a$ to $u^b$ , where $u^a$ and $u^b$ are the estimated softmax coordinates of keypoints $a$ and $b$ , respectively, i.e., + +$$ +\theta = \frac {u ^ {a} - u ^ {b}}{\| u ^ {a} - u ^ {b} \| _ {2}}, \quad \forall (a, b) \in \mathcal {E}. \tag {9} +$$ + +Finally, we use the prior as a regularization term to minimize the distance of the current pose from our learned manifold, + +$$ +\mathcal {L} _ {\text {p r i o r}} = \frac {1}{| \mathcal {B} |} \sum_ {\boldsymbol {x} \in \mathcal {B}} g \left(T \left(f _ {\mathrm {s t u}} ^ {t} (\boldsymbol {x})\right)\right), \tag {10} +$$ + +where $T(\cdot)$ converts the predicted heatmaps to the orientation vector format required as input by the prior. + +# 3.3. Overall Adaptation + +The final training objective for the student model $f_{\mathrm{stu}}$ can be expressed as: + +$$ +\min _ {f _ {\mathrm {s t u}}} \mathcal {L} _ {\text {o u t}} + \lambda_ {1} \mathcal {L} _ {\text {f e a t}} + \lambda_ {2} \mathcal {L} _ {\text {p r i o r}}. \tag {11} +$$ + +Here, $\lambda_{1}$ and $\lambda_{2}$ are hyper-parameters that control the influence of feature space adaptation and prior regularization, respectively. The teacher model $f_{\mathrm{tea}}$ is updated asynchronously by computing an exponential moving average of the student model weights as shown in Equation 1. + +# 4. Experiments + +In this section, we demonstrate POST's ability to adapt a 2D human pose estimation model to a target domain using only unlabeled data from that domain. We conduct experiments on three domain adaptive scenarios and compare with state-of-the-art domain adaptation baselines that utilize source data during adaptation. We also conduct extensive analysis to analyze the contribution and interaction between each component in our framework. + +# 4.1. Datasets + +SURREAL: SURREAL [43] is a large-scale dataset of synthetically generated images of people rendered from 3D sequences of human motion capture data against indoor backgrounds. It contains over 6 million frames, making it one of the largest and most diverse datasets of its kind. + +Human3.6M: Human3.6M [44] is a real-world video dataset captured in indoor environments, comprising 3.6 million frames. The dataset features human subjects performing various actions. In order to reduce redundancy and computational complexity, we down-sampled the videos from 50fps to 10fps as per the approach proposed in [5]. For training, we follow the standard protocol proposed in [6] and use 5 subjects (S1, S5, S6, S7, S8), while the remaining 2 subjects (S9, S11) are reserved for testing. + +LSP: Leeds Sports Pose (LSP) [45] is a real-world dataset that contains 2,000 images with annotated human body joint locations collected from sports activities. The images in LSP are captured in the wild, featuring a wide variety of human poses that are often challenging to detect. + +BRIAR: BRIAR [46] is a cutting-edge biometric dataset featuring a large-scale collection of videos of human subjects captured in extremely challenging conditions. The videos are recorded at varying distances, i.e., close range, $100\mathrm{m}$ , $200\mathrm{m}$ , $400\mathrm{m}$ , $500\mathrm{m}$ , and unmanned aerial vehicles (UAV), with each video lasting around 90 seconds. We randomly + +sample 20 frames from each sequence for each of the 158 subjects for our experiments. + +# 4.2. Experiment Protocols + +Pose estimation model. We adopt the Simple Baseline [18] as our pose estimation model, with the ResNet-101 [47] as the backbone. To train the model, we use the Adam optimizer [48] with a base learning rate of $1e - 4$ , scheduled to decrease to $1e - 5$ after 5 epochs and to $1e - 6$ after 20 epochs. The model is trained for 30 epochs. We use a batch size of 32 and run 500 iterations per epoch. To threshold the model predictions, we set the confidence thresholding ratio $p$ to 0.5. To augment the images during training, we follow [6] and use rotation, translation, shear, and Gaussian blur. The hyper-parameters $\lambda_{1}$ and $\lambda_{2}$ are set to $1e - 3$ and $1e - 6$ , respectively. + +Pose prior model. The training of the parametric prior follows a multi-stage approach that involves using different types of training samples. Initially, we use a combination of manifold poses $\theta_{m}$ and non-manifold poses $\theta_{nm}$ with a considerable distance from the desired manifold. Over the course of training, we gradually increase the number of non-manifold poses $\theta_{nm}$ with a small distance from the manifold. This enables our model to first learn a smooth surface and then gradually incorporate finer details as training progresses. We create these non-manifold poses $\theta_{nm}$ by injecting noise into the manifold poses $\theta_{m}$ obtained from the auxiliary dataset. Specifically, we sample directional noise from the Von-Mises distribution [49] and add it to the manifold poses in order to obtain the implausible poses. + +The architecture for the encoder $g_{\mathrm{enc}}$ consists of a 2-layer MLP with an output feature size of $d = 6$ for each orientation vector, similar to [42]. The distance field network $g_{\mathrm{dec}}$ is implemented as a 5-layer MLP. Given its large size and diverse poses, we train the prior for our primary experiments using the SURREAL dataset. + +# 4.3. Comparison with Baselines + +Baselines. We evaluate the performance of our proposed method against several state-of-the-art domain adaptive frameworks. This includes adversarial learning-based feature alignment methods, such as DAN[31], DD[50], and RegDA[5]. Additionally, we consider approaches based on pseudo-labeling, namely CCSSL[38], and UDAPE [6]. It is worth noting that all these methods employ the source data during the adaptation process. To establish a comprehensive performance baseline, we report the results of two additional baselines: Oracle and Source only. The Oracle baseline represents the upper bound of the model's performance, achieved by training the model jointly with target 2D annotations. On the other hand, Source only represents the model's performance when it is directly applied to the target domain without any adaptation. + +Table 1. PCK@0.05 on SURREAL $\rightarrow$ LSP. (Best value is in red color, while the second best value is in blue color.) + +
MethodSFSld.Elb.WristHipKneeAnkleAvg.
Source only-51.565.062.968.068.767.463.9
Oracle--------
DANX52.262.958.971.068.165.163.0
DDX28.465.956.875.074.373.962.4
RegDAX62.776.771.181.080.375.374.6
CCSSLX36.866.363.959.667.370.460.7
UDAPEX69.284.983.385.584.784.382.0
POST✓66.583.981.084.683.182.680.3
+ +Table 2. PCK@0.05 on SURREAL $\rightarrow$ Human3.6M. + +
MethodSFSld.Elb.WristHipKneeAnkleAvg.
Source only-69.475.466.437.977.377.767.3
Oracle-95.391.886.995.694.193.692.9
DANX68.177.562.330.478.479.466.0
DDX71.683.375.142.176.276.170.7
RegDAX73.386.472.854.882.084.475.6
CCSSLX44.368.555.222.262.357.851.7
UDAPEX78.189.681.152.685.387.179.0
POST✓81.388.577.446.183.483.476.7
+ +Metrics. We adopt the evaluation metric of Percentage of Correct Keypoint (PCK) for all experiments and report PCK@0.05 that measures the ratio of correct prediction within a range of $5\%$ with respect to the image size. + +# 4.4. Results + +Quantitative results. We evaluate POST in two adaptation scenarios: SURREAL $\rightarrow$ LSP and SURREAL $\rightarrow$ Human3.6M, and report the quantitative results in Table 1 and Table 2, respectively. Specifically, we report the PCK@0.05 on 16 keypoints of the human body, including shoulders (sld.), elbows (elb.), wrists, hips, knees, and ankles. Our method achieves comparable results to many recent approaches that leverage source data for adaptation. Among these methods, UDAPE [6] achieves the highest performance on both cases, with our framework achieving a close second and only 2 percentage points behind on average. Notably, we outperform every other method, including the recently proposed RegDA [5] approach, by a significant margin of up to 5.7 percentage points. It is worth noting that not only do these methods require source data, but also involve additional models such as discriminators or style transfer modules, and unstable adversarial training. In contrast, our framework is lightweight, only involves pseudo-label training, and utilizes a simple prior model that can be trained offline. + +Qualitative results. In addition to quantitative results, we also present qualitative results on SURREAL $\rightarrow$ Human3.6M in Figure 3 and on SURREAL $\rightarrow$ LSP in Figure 4. Also, + +![](images/9ca3dd4ca1a1e28750331b7cb8a5c701cc85b54cdf7f37b743deb37214ce2ba2.jpg) + +![](images/6ddd8ed53a6b19b31f5e7fed23c697ea428f3503f8c8f9a11f0efe292d6a862a.jpg) + +![](images/06b8c705d828873c385eadc00468c9bc2fc87a4a57b2a58acd501b61a009979f.jpg) + +![](images/55035cceed5ab24a11f808a10e6e62344fe77e57fb571c064ec77e259f690089.jpg) +Figure 3. Qualitative results on SURREAL $\rightarrow$ Human3.6M. We demonstrate sample results on the Human3.6M dataset. For each row, the leftmost shows the Source only prediction, the middle one shows the UDAPE [6] prediction, and the rightmost shows the prediction made POST. + +![](images/bf638cc35de63688c3f809da13d6ecca3d074a6a5776fca8ba763b09bb5c3770.jpg) + +![](images/1af0c514de7f1b2d09958562f8961b6c6cb0fc0159bb2d8a0d44fdaad1875b10.jpg) + +![](images/3de0508bba699e9fb9ed70599bbfe639183e0de420765c2cb29b22922db41eeb.jpg) + +![](images/e88c80e6e37804c9a9155a709612e3849a0aaa276c55742ab55e4428bd64f1ea.jpg) + +![](images/5800a5eff490007d9f72a9f3305ce806c7c576c1725fde8c20e35ff5cef02c7b.jpg) + +![](images/26f10a4c3df8781a5005c528fcf7cf87a1ea31a01fba7fe9144c0a13b57a9949.jpg) + +![](images/87d6f34fb2bad67ef3179be8f212ff38d3cc26040310bce2f12f61dbaa69e179.jpg) + +![](images/90ddfdaed2ee6ce2a5359bb92ed4d83fe00269159ce15ce6affd72347148e4ff.jpg) + +![](images/30be3e3f739364914f6ac74358e4da78e6dc356ac72f5439de9a1d16fe5168af.jpg) + +![](images/a24aa9696468f014d926a23875096da8c11ed3a8297a696ef0e21d4f5ab516a3.jpg) + +![](images/578aa8f70007e230899509d88df089d6989ca9c2fdd76f65830f0199b54453d9.jpg) + +![](images/2b917ce2bae4dc5d9ce79cef983cb4c7e5db69f2b175d78a10a9b48151f391f0.jpg) +Figure 4. Qualitative results on SURREAL $\rightarrow$ LSP. We demonstrate sample results on the LSP dataset. For each row, the left-most shows the Source only prediction, the middle one shows the UDAPE [6] prediction, and the rightmost shows the prediction made POST. + +![](images/f45bf2fae60fa16dfdefd095aa7ee8e2514a82b33f48d654214f5c08b987128a.jpg) + +![](images/f932f0b4aa506b25c209f2b2dc069513b86eee3321aba82c71b5d750428d5b9d.jpg) + +we present only visual results on the SURREAL $\rightarrow$ BRIAR adaptation scenario since pose annotations are absent in the BRIAR dataset. Figure 5 displays the predicted human poses on images taken from six different imaging ranges in the BRIAR dataset. While using the source model directly produces completely inaccurate poses, POST can accurately localize the keypoint locations, even in the presence of occlusions and atmospheric turbulence. Our approach can also accurately reconstruct poses even when the human is imaged from an elevated perspective, resulting in a high camera angle (Figure 5.f). Notably, our approach achieves this without using any source data for adaptation. Our results are comparable to those produced by UDAPE [6], which utilizes source data for adaptation. Additional qualitative results can be found in the supplementary document. + +![](images/b488637a570423b0c61b2b920d409367b8d37de12030b61d1cfa0a0d86a0fada.jpg) +a) $100\mathrm{m}$ + +![](images/6699f621e33ec7924a2e3e22e59af8268b17dc67c2b86f498bef502438207a34.jpg) + +![](images/7a74b7dbf63c3c52242e7f9de6d519c459d882828be198e5e53081e5072e7488.jpg) +b) $200\mathrm{m}$ + +![](images/0e423e1f372fc6d2f448b59ecf1bf54c35a70d65eccaf60269c757cd1fe5f1bd.jpg) + +![](images/a2d47abb81dece636654ac0a86b4cca9356074298df4759fd5136a58f4212362.jpg) +c) $400\mathrm{m}$ + +![](images/4e89899667fa45cde15a39a23c01f71b2bc367063323bb7caffea4f57f7f63e0.jpg) + +![](images/e1eb07fe7e882dfb82fce907089730185aeea9907de1c34c662f2eadacfe2082.jpg) +d) $500\mathrm{m}$ + +![](images/117eb71616e26b7bb49299de2a2aa1031bf8907490a22a21fb563ffe508a9f3d.jpg) + +![](images/ae26e585dc79fcadbe7beef7631175128cb92f7806c412598d808f049f8df802.jpg) +e) close range + +![](images/20c06172a974e6383a36ad30d312c3833e0cf846cc3308210aceb24e8e687611.jpg) + +![](images/f2aa48b85552239f56e0f04de58b137b6f5e654cda8884c106ba54f4b6e5fe1a.jpg) +f) uav + +![](images/1c048a6e1e9309091c8b02dde1f23d8ed93272664bc72a57d8b8a03fc087ac8a.jpg) +Figure 5. Qualitative results on SURREAL $\rightarrow$ BRIAR. We demonstrate sample results on BRIAR at all ranges. For each range, we display three images: the leftmost shows the Source only prediction, the middle one shows the UDAPE [6] prediction, and the rightmost shows the prediction using POST. Although POST does not use source data for adaptation, it is able to match the predictions produced by UDAPE, which uses source data. + +# 4.5. Ablation Studies + +Effect of auxiliary dataset. We conduct experiments to evaluate the impact of the choice of the auxiliary dataset (used to train the prior) on downstream adaptation. The results are presented in Table 3. Our findings indicate that + +POST is robust to the choice of the auxiliary dataset, with performance differences of $\sim 0.5$ percentage points. + +Effect of loss terms. We conduct an experiment to evaluate the performance of each component of our framework. The results on the SURREAL $\rightarrow$ Human3.6M adaptation scenario are presented in Table 4. Our findings indicate that in addi + +Table 3. Effect of auxiliary dataset. We evaluate the effect of auxiliary dataset on downstream adaptation tasks. + +
SURREAL→HUMAN3.6M
Aux. datasetSld.Elb.WristHipKneeAnkleAvg.
SURREAL81.388.577.446.183.483.476.7
Human3.6M80.988.077.245.083.182.876.2
SURREAL→LSP
Aux. datasetSld.Elb.WristHipKneeAnkleAvg.
SURREAL66.583.981.084.683.182.680.3
Human3.6M66.183.680.784.483.182.580.1
+ +Table 4. Effect of each loss term. We evaluate the contribution of each loss term on SURREAL $\rightarrow$ Human3.6M. + +
LoutLfeatLpriorSld.Elb.WristHipKneeAnkleAvg.
XXX69.475.466.437.977.377.767.3
✓XX77.986.773.738.883.084.374.1
✓✓X81.787.175.244.382.382.275.5
✓✓✓81.388.577.446.183.483.476.7
+ +tion to prediction space adaptation, feature space adaptation also plays a crucial role in enabling effective unsupervised learning from pseudo-labels. Moreover, we observed that the human pose prior brings additional improvements, thus validating our hypothesis that noisy pose pseudo-labels can be refined implicitly by a prior in the absence of source data. Overall, our results demonstrate the effectiveness of our framework and the importance of each of its components in achieving state-of-the-art performance. + +Cross-dataset performance of prior. We evaluate the ability of the learned prior to handle distribution shift separately from the adaptation performance. Specifically, we assess the robustness of the prior by computing pose scores across datasets, and the results are presented in Figure 6. The plot demonstrates that our prior is effective in scoring plausible (real) poses with low scores and scoring implausible poses with higher scores. Note that the bell curve shape of the noisy pose scores is due to the Von-Mises noise added to create the noisy poses. + +Effect of thresholding. We analyze the impact of the pseudo-label threshold $\tau$ on the adaptation performance in Table 5. The results on SURREAL $\rightarrow$ Human3.6M reveal that as we increase this ratio, the performance gradually decreases. This can be attributed to the fact that higher thresholding ratios tend to include lower confident predictions as pseudo-labels, which can negatively impact adaptation. + +# 5. Conclusion + +We address the problem of adapting a pre-trained 2D human pose estimator to a new target domain with unlabeled + +Table 5. Effect of $\tau$ . We evaluate adaptation performance on SURREAL $\rightarrow$ Human3.6M as $\tau$ is varied. + +
τ = 0.1τ = 0.3τ = 0.5τ = 0.7τ = 0.9
76.476.576.775.373.8
+ +![](images/fe682b04ab13c49f01819e55fd9998b7720e2fa39836b2a08ac6227d112420df.jpg) +(a) Human3.6M $\rightarrow$ SURREAL +(b) SURREAL $\rightarrow$ Human3.6M +Figure 6. Cross-dataset prior transfer. We plot the histogram of scores predicted by the prior. The prior can clearly demarcate plausible poses from implausible poses across datasets. + +target data. To this end, we propose a self-training algorithm, POST, that leverages a Mean Teacher framework to enforce both prediction-level and feature-level consistency between a pair of student and teacher models. Our approach incorporates a human pose prior that captures the manifold of possible poses in a high-dimensional space, which helps to refine noisy pseudo-labels generated during self-training. We evaluate our method on three challenging adaptation scenarios and show that it achieves competitive performance compared to existing UDA methods that have access to source data. + +Acknowledgements. This research is based upon work supported in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via [2022-21102100007]. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein. + +# References + +[1] Ke Sun, Bin Xiao, Dong Liu, and Jingdong Wang. Deep high-resolution representation learning for human pose estimation. In CVPR, 2019. 1, 2 + +[2] Sijie Yan, Yuanjun Xiong, and Dahua Lin. Spatial temporal graph convolutional networks for skeleton-based action recognition. In AAAI, 2018. 1 +[3] Hai Liu, Tingting Liu, Zhaoli Zhang, Arun Kumar Sangaiah, Bing Yang, and Youfu Li. 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To address this limitation, we focus on the task of source-free domain adaptation for pose estimation, where a source model must adapt to a new target domain using only unlabeled target data. Although recent advances have introduced source-free methods for classification tasks, extending them to the regression task of pose estimation is non-trivial. In this paper, we present Prior-guided Self-training (POST), a pseudolabeling approach that builds on the popular Mean Teacher framework to compensate for the distribution shift. POST leverages prediction-level and feature-level consistency between a student and teacher model against certain image transformations. In the absence of source data, POST utilizes a human pose prior that regularizes the adaptation process by directing the model to generate more accurate and anatomically plausible pose pseudo-labels. Despite being simple and intuitive, our framework can deliver significant performance gains compared to applying the source model directly to the target data, as demonstrated in our extensive experiments and ablation studies. In fact, our approach achieves comparable performance to recent state-of-the-art methods that use source data for adaptation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 588, + 128, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 588, + 128, + 600 + ], + "spans": [ + { + "bbox": [ + 47, + 588, + 128, + 600 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 609, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 609, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 609, + 288, + 693 + ], + "type": "text", + "content": "Human pose estimation is a fundamental task in computer vision that involves determining the precise locations of keypoints, such as joints, on a human body in an image or video [1]. The growing need for pose estimation in various applications such as action recognition [2], human-computer interaction [3], and video surveillance [4] has driven the rapid development of highly accurate deep learning tech" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 226, + 545, + 406 + ], + "blocks": [ + { + "bbox": [ + 309, + 226, + 545, + 406 + ], + "lines": [ + { + "bbox": [ + 309, + 226, + 545, + 406 + ], + "spans": [ + { + "bbox": [ + 309, + 226, + 545, + 406 + ], + "type": "image", + "image_path": "f269fd9a6d1df8c4a7d32d89b1b306e6b1a67e8a5f63ca42de4197fc02660e7b.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 411, + 547, + 488 + ], + "lines": [ + { + "bbox": [ + 305, + 411, + 547, + 488 + ], + "spans": [ + { + "bbox": [ + 305, + 411, + 547, + 488 + ], + "type": "text", + "content": "Figure 1. Problem setup. Existing UDA methods for pose estimation rely on a labeled source dataset while adapting to an unlabeled target dataset. However, privacy concerns surrounding the use of personally identifiable information in these labeled datasets, as well as the significant storage and computational requirements, can limit access to such data. Hence, our work focuses on source-free UDA of pose estimation models." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 509, + 547, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 547, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 547, + 557 + ], + "type": "text", + "content": "niques. However, the challenge of obtaining large annotated datasets for training, compounded with the susceptibility to a performance decline in the face of data distribution shifts still poses limitations for current pose estimation models." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "content": "To overcome these limitations, recent studies have focused on unsupervised domain adaptation (UDA) of pose estimators [5, 6]. UDA allows for transferring a pose estimation model trained on a source domain, where labeled data is available, to a target domain where labeled data is unavailable. Despite improved and robust pose estimation, the requirement of simultaneous access to both source and target domains during adaptation hinders real-world implementation. For instance, the labeled source data may not be accessible post-deployment due to privacy or proprietary issues. This is particularly relevant for human pose datasets, which contain personally identifiable information (PII) [7]. Furthermore, adaptation using the entire source data might" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 38 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 38 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 38 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 60, + 702, + 286, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 702, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 60, + 702, + 286, + 712 + ], + "type": "text", + "content": "* Currently at AWS AI Labs. Work done while the author was at UCR." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14996" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 288, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 288, + 108 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 288, + 108 + ], + "type": "text", + "content": "be infeasible due to both memory and computational constraints. In light of these issues, we focus on source-free UDA of human pose estimation models." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 110, + 288, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 110, + 288, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 110, + 288, + 266 + ], + "type": "text", + "content": "Concretely, our objective is to adapt a 2D human pose estimation model to a new target domain utilizing only its trained parameters and unlabeled target data. This presents a major challenge as the absence of source data for regularization can cause catastrophic forgetting. While recent advances have introduced methods to tackle this issue in classification tasks [8, 9, 10], extending them to the regression task of pose estimation is non-trivial. To address this challenge, we introduce Prior-guided Self-training (POST), a self-training regression framework that employs a human pose prior to effectively guide the adaptation process in the absence of source data. An overview of our problem setup is shown in Figure 1." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 268, + 290, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 268, + 290, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 268, + 290, + 484 + ], + "type": "text", + "content": "Our approach builds on the Mean Teacher [11] framework, which uses consistency in the prediction space of a student and teacher model to produce trustworthy pseudo-labels and learn from the unlabeled target domain. To achieve this, we create two augmented views of each target image, varying in scale, spatial context, and color statistics. Aligned pose predictions from both models in both views are then obtained, and consistency between the predictions across the different views is encouraged to facilitate prediction space adaptation. However, our empirical results show that relying solely on consistency in the output space is insufficient when supervision from the source data is lacking. To address this, we also introduce feature space adaptation, which aims to encourage consistency across features extracted from the two separate views. We adopt the Barlow Twins [12] approach to accomplish this. Specifically, we seek to make the cross-correlation matrix calculated from a pair of feature embeddings as close to the identity matrix as possible." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "type": "text", + "content": "In addition to the adaptation across both outputs and features, we employ a human pose prior that models the full manifold of plausible poses in some high-dimensional pose space to refine possible noisy pseudo-labels that may arise during self-training. The plausible poses are represented as points on the manifold surface, with zero distance from it, while non-plausible poses are located outside the surface, with a non-zero distance from it. This manifold is learned using a high-dimensional neural field, similar to Pose-NDF [13]. The pose prior acts as a strong regularizer, directing the model to generate more accurate pose pseudolabels on the target data and leading to improved adaptation. The learning of this prior requires an auxiliary dataset of plausible human poses, but this does not compromise the privacy aspect of our framework as the prior does not make use of RGB images. In addition, it is worth noting that the prior can be trained offline, separately from the adaptation process. This not only saves computational resources but also reduces the amount of storage required. Compared to storing entire" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 72, + 547, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 547, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 547, + 96 + ], + "type": "text", + "content": "images, it is much more efficient to store pose coordinates, which requires approximately " + }, + { + "bbox": [ + 305, + 72, + 547, + 96 + ], + "type": "inline_equation", + "content": "3000 \\times" + }, + { + "bbox": [ + 305, + 72, + 547, + 96 + ], + "type": "text", + "content": " less memory." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 97, + 547, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 97, + 547, + 120 + ], + "spans": [ + { + "bbox": [ + 305, + 97, + 547, + 120 + ], + "type": "text", + "content": "Main contributions. To summarize, our primary contributions are as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 121, + 547, + 291 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 306, + 121, + 547, + 181 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 121, + 547, + 181 + ], + "spans": [ + { + "bbox": [ + 306, + 121, + 547, + 181 + ], + "type": "text", + "content": "- We address the problem of adapting a human pose estimation model to a target domain consisting of unlabeled data, without access to the original source dataset. This ameliorates the privacy concern associated with the current domain adaptive pose estimation methods." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 182, + 547, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 182, + 547, + 243 + ], + "spans": [ + { + "bbox": [ + 306, + 182, + 547, + 243 + ], + "type": "text", + "content": "- We introduce Prior-guided Self-training (POST), a simple source-free unsupervised adaptation algorithm. POST leverages both prediction-level and feature-level consistency, in addition to a human pose prior, to drive self-training for improved adaptation to the target domain." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 244, + 547, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 244, + 547, + 291 + ], + "spans": [ + { + "bbox": [ + 306, + 244, + 547, + 291 + ], + "type": "text", + "content": "- We evaluate our method qualitatively and quantitatively on three challenging domain adaptive scenarios, demonstrating comparable performance to existing UDA methods that have access to the source data." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 304, + 398, + 316 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 304, + 398, + 316 + ], + "spans": [ + { + "bbox": [ + 306, + 304, + 398, + 316 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 324, + 547, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 324, + 547, + 504 + ], + "spans": [ + { + "bbox": [ + 305, + 324, + 547, + 504 + ], + "type": "text", + "content": "Pose Estimation. 2D human pose estimation aims to locate human anatomical keypoints, such as the elbow and knee. Prior works can be categorized into two primary frameworks: the top-down framework and the bottom-up framework. Top-down methods [14, 15, 16, 17, 18, 19, 1] first detect each person from the image and then perform single-person pose estimation on each bounding box independently. On the other hand, bottom-up methods [20, 21, 22, 23, 24, 25, 26] predict keypoints of each person directly in an end-to-end manner. Typical bottom-up methods consist of two steps: predicting keypoint heatmaps and grouping the detected keypoints into separate poses. In this work, we focus on the bottom-up framework for efficiency purposes and adopt the Simple Baseline [18] architecture following [6] to ensure fair comparisons with prior domain adaptation algorithms." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 510, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 548, + 714 + ], + "type": "text", + "content": "Unsupervised Domain Adaptation. UDA methods have been extensively applied to a broad range of computer vision tasks, including image classification [27], semantic segmentation [28], object detection [29], and reinforcement learning [30] to tackle the issue of data distribution shift. Most approaches aim to align the source and target data distributions through techniques such as maximum mean discrepancy [31] and adversarial learning [32, 27]. Another line of research utilizes image translation methods to perform adaptation by transforming the source images into the target domain [33, 34]. More recently, there has been a surge of interest in adaptation using only a pre-trained source model due to privacy and memory storage concerns related to the source data. These include techniques such as information maximization [8, 9], pseudo-labeling [35, 36] and self-supervision [37]. Compared to other tasks, domain adaptation for regression tasks, such as pose estimation, remains" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14997" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 137, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 137, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 137, + 83 + ], + "type": "text", + "content": "relatively unexplored." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 89, + 290, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 89, + 290, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 89, + 290, + 281 + ], + "type": "text", + "content": "Domain Adaptive Pose Estimation. UDA methods for pose estimation have explored various techniques for overcoming the domain gap, including adversarial feature alignment and pseudo-labeling. RegDA [5] estimates the domain discrepancy by evaluating false predictions on the target domain and minimizes it. Mu et al. [38] proposed consistency regularization with respect to transformations and temporal consistency learning within a video. Li et al. [39] proposed a refinement module and a self-feedback loop to obtain reliable pseudo-labels. Recently, Kim et al. [6] introduced a unified framework for both human and animal keypoint detection, which aligns representations using input-level and output-level cues. Typically, these methods require access to the source data, which may raise data privacy, memory and computation concerns. In contrast, our method addresses the domain adaptation problem in a source-free setting." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 292, + 196, + 306 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 292, + 196, + 306 + ], + "spans": [ + { + "bbox": [ + 47, + 292, + 196, + 306 + ], + "type": "text", + "content": "3. Prior-guided Self-training" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "type": "text", + "content": "Our work investigates source-free domain adaptation for 2D human pose estimation. In the pose estimation task, given an input image " + }, + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "type": "inline_equation", + "content": "\\pmb{x} \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "type": "text", + "content": ", the goal is to predict the corresponding " + }, + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "type": "inline_equation", + "content": "y \\in \\mathbb{R}^{K \\times 2}" + }, + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "type": "text", + "content": " representing the 2D coordinates of " + }, + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "type": "text", + "content": " keypoints using a pose regression model " + }, + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "type": "text", + "content": ". In this paper, we assume access to a pre-trained model, denoted by " + }, + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "type": "inline_equation", + "content": "f_{S}" + }, + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "type": "text", + "content": ", as well as " + }, + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "type": "text", + "content": " unlabeled images " + }, + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{\\pmb{x}_i\\}_{i=1}^N" + }, + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "type": "text", + "content": " from a target domain " + }, + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 312, + 288, + 443 + ], + "type": "text", + "content": ". Our goal is to adapt the source model to the target such that it performs better on images drawn from the target distribution than when directly using the source model on the target images." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 447, + 287, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 287, + 530 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 287, + 530 + ], + "type": "text", + "content": "Overview. In the absence of source data, we propose to use self-training to adapt the source pose estimation model to the target domain. However, self-training methods are prone to error accumulation, particularly when labeled data is absent to act as regularization. Hence, we introduce POST, an enhanced self-training strategy that employs three essential ideas to prevent such errors:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 531, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 47, + 531, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 531, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 531, + 287, + 590 + ], + "type": "text", + "content": "1. A weight-averaged teacher model is used to generate the pseudo-labels for self-training. This ensures better retention of the source knowledge within the teacher model by reducing the effect of updating the weights via noisy pseudo-labels (Section 3.1.1)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 592, + 288, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 592, + 288, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 592, + 288, + 664 + ], + "type": "text", + "content": "2. In addition to adaptation over the output space via pseudolabels, the model is adapted in the feature space as well. For each target image, two aligned predictive views are generated via data augmentation, and consistency across features extracted from the two separate views is encouraged via a contrastive learning strategy (Section 3.1.2)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 666, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 666, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 666, + 288, + 714 + ], + "type": "text", + "content": "3. A human pose prior is used to regularize the adaptation by directing the model to generate more accurate and anatomically plausible pose pseudo-labels (Section 3.2). An overview of our framework is presented in Figure 2." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 72, + 474, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 474, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 474, + 85 + ], + "type": "text", + "content": "3.1. Self-training via Mean Teacher" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 90, + 547, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 547, + 234 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 547, + 234 + ], + "type": "text", + "content": "Motivated by research suggesting that weight-averaged models over training steps tend to perform better than the final model [6, 39], we utilize the Mean Teacher framework [11] to generate pseudo-labels for self-training. The framework involves creating two identical models, a teacher model " + }, + { + "bbox": [ + 304, + 90, + 547, + 234 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{tea}}" + }, + { + "bbox": [ + 304, + 90, + 547, + 234 + ], + "type": "text", + "content": " and a student model " + }, + { + "bbox": [ + 304, + 90, + 547, + 234 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{stu}}" + }, + { + "bbox": [ + 304, + 90, + 547, + 234 + ], + "type": "text", + "content": ", both of which are initialized with the pre-trained network " + }, + { + "bbox": [ + 304, + 90, + 547, + 234 + ], + "type": "inline_equation", + "content": "f_{S}" + }, + { + "bbox": [ + 304, + 90, + 547, + 234 + ], + "type": "text", + "content": " at time step " + }, + { + "bbox": [ + 304, + 90, + 547, + 234 + ], + "type": "inline_equation", + "content": "t = 0" + }, + { + "bbox": [ + 304, + 90, + 547, + 234 + ], + "type": "text", + "content": ". At each subsequent time step " + }, + { + "bbox": [ + 304, + 90, + 547, + 234 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 90, + 547, + 234 + ], + "type": "text", + "content": ", the student model parameters " + }, + { + "bbox": [ + 304, + 90, + 547, + 234 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 90, + 547, + 234 + ], + "type": "text", + "content": " are updated by backpropagating the supervisory signals provided by the teacher model. The parameters of the teacher model " + }, + { + "bbox": [ + 304, + 90, + 547, + 234 + ], + "type": "inline_equation", + "content": "\\tilde{\\theta}" + }, + { + "bbox": [ + 304, + 90, + 547, + 234 + ], + "type": "text", + "content": " are updated via an exponential moving average (EMA) of the student model parameters:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 373, + 242, + 547, + 258 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 242, + 547, + 258 + ], + "spans": [ + { + "bbox": [ + 373, + 242, + 547, + 258 + ], + "type": "interline_equation", + "content": "\\tilde {\\theta} _ {t} = \\alpha \\tilde {\\theta} _ {t - 1} + (1 - \\alpha) \\theta_ {t}, \\tag {1}", + "image_path": "bf534c72d72cf576388bf522541e1612723d70a70483251a0a9f8f9b430d55be.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 266, + 547, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 547, + 338 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 547, + 338 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 266, + 547, + 338 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 266, + 547, + 338 + ], + "type": "text", + "content": " denotes the smoothing coefficient which is set to 0.999 by default. The EMA update prevents the teacher model from overfitting to noisy pseudo-labels during the initial rounds of self-training, thereby, preserving the source knowledge. This is especially advantageous in our scenario where source data is unavailable to regularize the adaptation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 338, + 547, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 547, + 374 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 547, + 374 + ], + "type": "text", + "content": "In the following sections, we demonstrate how to adapt " + }, + { + "bbox": [ + 304, + 338, + 547, + 374 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{stu}}" + }, + { + "bbox": [ + 304, + 338, + 547, + 374 + ], + "type": "text", + "content": " using supervisory signals from " + }, + { + "bbox": [ + 304, + 338, + 547, + 374 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{tea}}" + }, + { + "bbox": [ + 304, + 338, + 547, + 374 + ], + "type": "text", + "content": " on both the feature space and the pose prediction space." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 390, + 462, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 390, + 462, + 403 + ], + "spans": [ + { + "bbox": [ + 305, + 390, + 462, + 403 + ], + "type": "text", + "content": "3.1.1 Prediction Space Adaptation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "type": "text", + "content": "At each time step " + }, + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "type": "text", + "content": ", we apply two different data augmentations, " + }, + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_1" + }, + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_2" + }, + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "type": "text", + "content": ", to a target image " + }, + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "type": "text", + "content": " to generate two views. We then obtain the keypoint heatmap corresponding to the first transformed image " + }, + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "type": "inline_equation", + "content": "\\tilde{h}^t = f_{\\mathrm{tea}}^t (\\mathcal{A}_1(\\pmb {x}))" + }, + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "type": "text", + "content": ". Here " + }, + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "type": "inline_equation", + "content": "\\tilde{h}^t\\in \\mathbb{R}^{K\\times H'\\times W'}" + }, + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "type": "text", + "content": " denotes the spatial likelihood of the " + }, + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "type": "text", + "content": " different keypoints on each channel. The pseudolabel from the teacher model is generated by obtaining the coordinates which produce the maximum activations " + }, + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "type": "inline_equation", + "content": "\\hat{y}^t = \\operatorname{argmax}_u\\tilde{h}_{[:,u]}^t" + }, + { + "bbox": [ + 304, + 409, + 547, + 517 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 517, + 547, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 547, + 600 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 547, + 600 + ], + "type": "text", + "content": "To reduce the influence of erroneous pseudo-labels in our training process, we utilize a confidence threshold to discard potentially unreliable labels. Specifically, we only retain the keypoint activations with the top " + }, + { + "bbox": [ + 304, + 517, + 547, + 600 + ], + "type": "inline_equation", + "content": "p\\%" + }, + { + "bbox": [ + 304, + 517, + 547, + 600 + ], + "type": "text", + "content": " maximum values among all activations and discard the rest. We set the threshold " + }, + { + "bbox": [ + 304, + 517, + 547, + 600 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 517, + 547, + 600 + ], + "type": "text", + "content": " accordingly to reflect this, thereby ensuring that only the most confident labels are used for training." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 601, + 547, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 601, + 547, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 601, + 547, + 661 + ], + "type": "text", + "content": "Following prior work on supervised pose estimation, we first convert the pseudo-labels to normalized Gaussian heatmaps [40] and then use the mean squared error (MSE) loss to update the student model over batches of target images sampled from " + }, + { + "bbox": [ + 304, + 601, + 547, + 661 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 601, + 547, + 661 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 670, + 547, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 670, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 670, + 547, + 713 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {o u t}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {\\mathbf {x} \\in \\mathcal {B}} \\sum_ {k = 1} ^ {K} \\mathbb {1} \\left(\\hat {h} _ {k} ^ {t} \\geq \\tau\\right) \\| \\tilde {\\mathcal {A}} _ {1} \\left(\\hat {h} _ {k} ^ {t}\\right) - \\tilde {\\mathcal {A}} _ {2} \\left(h _ {k} ^ {t}\\right) \\| _ {2}. \\tag {2}", + "image_path": "cc2b9244fa01c4f12dfbd0a49492ac657985e7912aab8db40a374bbc755ef93a.jpg" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14998" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 85, + 70, + 509, + 291 + ], + "blocks": [ + { + "bbox": [ + 85, + 70, + 509, + 291 + ], + "lines": [ + { + "bbox": [ + 85, + 70, + 509, + 291 + ], + "spans": [ + { + "bbox": [ + 85, + 70, + 509, + 291 + ], + "type": "image", + "image_path": "c556debaba324cdf504fd1ec865cb5e134057372a5fa29e9517f0c4813dae355.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 294, + 547, + 350 + ], + "lines": [ + { + "bbox": [ + 46, + 294, + 547, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 547, + 350 + ], + "type": "text", + "content": "Figure 2. Framework overview. Our approach builds on the Mean Teacher framework and performs adaptation both in the pose prediction space using " + }, + { + "bbox": [ + 46, + 294, + 547, + 350 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{out}}" + }, + { + "bbox": [ + 46, + 294, + 547, + 350 + ], + "type": "text", + "content": ", and the feature space using " + }, + { + "bbox": [ + 46, + 294, + 547, + 350 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{feat}}" + }, + { + "bbox": [ + 46, + 294, + 547, + 350 + ], + "type": "text", + "content": ". This is supplemented by a human pose prior " + }, + { + "bbox": [ + 46, + 294, + 547, + 350 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 294, + 547, + 350 + ], + "type": "text", + "content": " that scores the predicted pseudo-labels in terms of plausibility. These scores are used to regularize the adaptation process in the absence of labeled source data via " + }, + { + "bbox": [ + 46, + 294, + 547, + 350 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{prior}}" + }, + { + "bbox": [ + 46, + 294, + 547, + 350 + ], + "type": "text", + "content": ". The student model " + }, + { + "bbox": [ + 46, + 294, + 547, + 350 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{stu}}" + }, + { + "bbox": [ + 46, + 294, + 547, + 350 + ], + "type": "text", + "content": " is trained by the combination of the three losses, while the teacher model " + }, + { + "bbox": [ + 46, + 294, + 547, + 350 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{tea}}" + }, + { + "bbox": [ + 46, + 294, + 547, + 350 + ], + "type": "text", + "content": " is updated with the exponential moving average (EMA) of the weights of the student model." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "text", + "content": "We denote the inverse functions of the chosen augmentations " + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_1" + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_2" + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{A}}_1" + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{A}}_2" + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "text", + "content": ", respectively. The heatmap predicted by the student model for the " + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "text", + "content": "-th keypoint is represented by " + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "inline_equation", + "content": "h_k^t = f_{\\mathrm{stu}}^t (\\mathcal{A}_2(\\pmb {x}))^k" + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "text", + "content": ", while the heatmap generated from the pseudo-labels predicted by the teacher model is represented by " + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "inline_equation", + "content": "\\hat{h}_k^t = L(\\hat{y}^t)^k" + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "inline_equation", + "content": "L(\\cdot)" + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "text", + "content": " represents the heatmap generating function and " + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 369, + 290, + 454 + ], + "type": "text", + "content": " denotes a batch of target images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 467, + 194, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 467, + 194, + 480 + ], + "spans": [ + { + "bbox": [ + 47, + 467, + 194, + 480 + ], + "type": "text", + "content": "3.1.2 Feature Apace Adaptation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 486, + 288, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 288, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 288, + 653 + ], + "type": "text", + "content": "Pose estimation models primarily rely on a high-to-low-resolution feature encoder to generate low-resolution representations, which are then used to recover high-resolution pose heatmaps [18]. Since the upsampling process is inherently noisy, providing intermediate supervision to explicitly adapt the features, in addition to adapting the output pose keypoints as shown in the previous section, can be beneficial [17]. While previous work has demonstrated the benefits of joint adaptation across the output and feature space via adversarial learning in tasks such as semantic segmentation [41], this has been exclusively focused on scenarios where source data is available. Here, we propose an alternative way to accomplish feature space adaptation in the absence of source data via contrastive learning." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "text", + "content": "We begin by creating two different views of each target image " + }, + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "text", + "content": " using a pair of sampled augmentations " + }, + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_1" + }, + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_2" + }, + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "text", + "content": ", as previously shown. Next, considering the pose estimation model as a composition of a feature encoder and an output regressor, i.e., " + }, + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "inline_equation", + "content": "f = \\mathrm{Dec} \\circ \\mathrm{Enc}" + }, + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "text", + "content": ", we extract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 369, + 547, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 547, + 464 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 547, + 464 + ], + "type": "text", + "content": "the augmentation reversed feature maps from the teacher model " + }, + { + "bbox": [ + 304, + 369, + 547, + 464 + ], + "type": "inline_equation", + "content": "\\tilde{z} = \\tilde{\\mathcal{A}}_1(\\mathrm{Enc}_{\\mathrm{tea}}(\\mathcal{A}_1(\\boldsymbol{x})))" + }, + { + "bbox": [ + 304, + 369, + 547, + 464 + ], + "type": "text", + "content": " and the student model " + }, + { + "bbox": [ + 304, + 369, + 547, + 464 + ], + "type": "inline_equation", + "content": "z = \\tilde{\\mathcal{A}}_2(\\mathrm{Enc}_{\\mathrm{stu}}(\\mathcal{A}_2(\\boldsymbol{x})))" + }, + { + "bbox": [ + 304, + 369, + 547, + 464 + ], + "type": "text", + "content": ". We extract pairs of features for every image in a batch, pool them along the spatial dimensions, and then normalize them along the batch dimension to ensure that each covariate has a mean of 0 over the batch. For simplicity, we overload " + }, + { + "bbox": [ + 304, + 369, + 547, + 464 + ], + "type": "inline_equation", + "content": "z,\\tilde{z}" + }, + { + "bbox": [ + 304, + 369, + 547, + 464 + ], + "type": "text", + "content": " to represent the normalized features, and drop the time index " + }, + { + "bbox": [ + 304, + 369, + 547, + 464 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 369, + 547, + 464 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 464, + 547, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 464, + 547, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 464, + 547, + 536 + ], + "type": "text", + "content": "We utilize feature-level consistency between the different views in order to accomplish feature space adaptation. This is achieved via a contrastive learning strategy which encourages the cross-correlation matrix between the outputs of the two networks to be as close to the identity matrix as possible [12]," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 343, + 542, + 547, + 569 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 542, + 547, + 569 + ], + "spans": [ + { + "bbox": [ + 343, + 542, + 547, + 569 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {f e a t}} = \\sum_ {i} (1 - C _ {i i}) ^ {2} + \\gamma \\sum_ {i} \\sum_ {j \\neq i} C _ {i j} ^ {2}. \\tag {3}", + "image_path": "a02cc8bac57c5f848919bd09e864c6a36086844dd6e0176d97cb6c3a4d4e0c87.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 573, + 547, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 573, + 547, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 573, + 547, + 632 + ], + "type": "text", + "content": "We define " + }, + { + "bbox": [ + 304, + 573, + 547, + 632 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 573, + 547, + 632 + ], + "type": "text", + "content": " as a positive constant that balances the importance of the first and second terms of the loss function. " + }, + { + "bbox": [ + 304, + 573, + 547, + 632 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 573, + 547, + 632 + ], + "type": "text", + "content": " represents the cross-correlation matrix computed between the outputs of the student and teacher networks along the batch dimension:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 344, + 635, + 547, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 635, + 547, + 673 + ], + "spans": [ + { + "bbox": [ + 344, + 635, + 547, + 673 + ], + "type": "interline_equation", + "content": "C _ {i j} = \\frac {\\sum_ {b = 1} ^ {| \\mathcal {B} |} \\tilde {z} _ {b , i} z _ {b , j}}{\\sqrt {\\sum_ {b = 1} ^ {| \\mathcal {B} |} \\left(\\tilde {z} _ {b , i}\\right) ^ {2}} \\sqrt {\\sum_ {b = 1} ^ {| \\mathcal {B} |} \\left(z _ {b , j}\\right) ^ {2}}}. \\tag {4}", + "image_path": "aa32dd747ce708f8412e73fbed3491444ac58ae3a5975ea2311c025f41b9105d.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "content": " represents the batch index, while " + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "content": " index the feature dimensions of the networks' outputs. We set " + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\gamma = 5e - 3" + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "content": " following [12]." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "14999" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": "The first term of " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{feat}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " encourages the consistency of pose features within the same image by equating the diagonal elements of the cross-correlation matrix to 1, effectively reversing the effects of augmentations. In contrast, the second term aims to decorrelate the different feature dimensions of the embedding by forcing the off-diagonal elements of the cross-correlation matrix to 0." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 162, + 208, + 174 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 162, + 208, + 174 + ], + "spans": [ + { + "bbox": [ + 47, + 162, + 208, + 174 + ], + "type": "text", + "content": "3.2. Regularization via Pose Prior" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 180, + 290, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 290, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 290, + 277 + ], + "type": "text", + "content": "Enhancing the performance of the pose estimation model on the target domain through joint adaptation over the output and feature space is undoubtedly valuable. However, this approach has its limitations, as it relies solely on general domain adaptation principles and overlooks the rich structural priors associated with human poses. To address this issue, we propose incorporating a parametric human pose prior to better adapt the pose estimation model to the target domain." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 290, + 174, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 290, + 174, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 290, + 174, + 300 + ], + "type": "text", + "content": "3.2.1 2D Human Pose Prior" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 308, + 289, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 289, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 289, + 429 + ], + "type": "text", + "content": "Building upon the work of [13], we propose a human pose prior modeled as a manifold consisting of plausible 2D poses. To represent the 2D poses while ignoring aspects such as size and scale, we use a set of 2D orientation vectors that connect pairs of joints in the human skeleton, denoted by " + }, + { + "bbox": [ + 46, + 308, + 289, + 429 + ], + "type": "inline_equation", + "content": "\\mathcal{G} = \\{\\pmb {\\theta} = (\\theta_1,\\dots ,\\theta_L)\\mid \\theta_l\\in \\mathbb{R}^2,\\| \\theta_l\\| _2 = 1\\forall l\\in [L]\\}" + }, + { + "bbox": [ + 46, + 308, + 289, + 429 + ], + "type": "text", + "content": ". We assume that plausible 2D human poses lie on a manifold embedded in this pose space " + }, + { + "bbox": [ + 46, + 308, + 289, + 429 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 308, + 289, + 429 + ], + "type": "text", + "content": ". We use a function " + }, + { + "bbox": [ + 46, + 308, + 289, + 429 + ], + "type": "inline_equation", + "content": "g:\\mathcal{G}\\to" + }, + { + "bbox": [ + 46, + 308, + 289, + 429 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^+" + }, + { + "bbox": [ + 46, + 308, + 289, + 429 + ], + "type": "text", + "content": ", which maps a pose to a non-negative scalar, to represent the manifold of plausible poses as the zero-level set:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 113, + 434, + 288, + 448 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 434, + 288, + 448 + ], + "spans": [ + { + "bbox": [ + 113, + 434, + 288, + 448 + ], + "type": "interline_equation", + "content": "\\mathcal {P} = \\{\\boldsymbol {\\theta} \\in \\mathcal {G} \\mid g (\\boldsymbol {\\theta}) = 0 \\}, \\tag {5}", + "image_path": "fd17dfc614e18ec2b6133a0b7144f887cb286e68efb9413d8132a45e1480b46c.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 453, + 289, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 453, + 289, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 453, + 289, + 514 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 453, + 289, + 514 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 453, + 289, + 514 + ], + "type": "text", + "content": " represents the unsigned distance to the manifold. We construct this distance function by first encoding the pose using a hierarchical network " + }, + { + "bbox": [ + 46, + 453, + 289, + 514 + ], + "type": "inline_equation", + "content": "g_{\\mathrm{enc}}" + }, + { + "bbox": [ + 46, + 453, + 289, + 514 + ], + "type": "text", + "content": " that encodes the human pose based on its anatomical structure [42], and subsequently, use " + }, + { + "bbox": [ + 46, + 453, + 289, + 514 + ], + "type": "inline_equation", + "content": "g_{\\mathrm{dec}}" + }, + { + "bbox": [ + 46, + 453, + 289, + 514 + ], + "type": "text", + "content": " to predict the distance based on the pose representation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 514, + 285, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 514, + 285, + 525 + ], + "spans": [ + { + "bbox": [ + 58, + 514, + 285, + 525 + ], + "type": "text", + "content": "Specifically, for a given pose " + }, + { + "bbox": [ + 58, + 514, + 285, + 525 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 58, + 514, + 285, + 525 + ], + "type": "text", + "content": ", we encode it as follows," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 52, + 529, + 287, + 544 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 529, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 52, + 529, + 287, + 544 + ], + "type": "interline_equation", + "content": "\\mathbf {v} _ {1} = g _ {\\mathrm {e n c}} ^ {1} \\left(\\theta_ {1}\\right), \\quad \\mathbf {v} _ {l} = g _ {\\mathrm {e n c}} ^ {l} \\left(\\theta_ {l}, \\mathbf {v} _ {\\Omega (l)}\\right), l \\in \\{2, \\dots , L \\}. \\tag {6}", + "image_path": "53a8640019451c9347992fd96eef190cc926d9eb86f80b42413633b3dc7a3e8b.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 549, + 289, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 549, + 289, + 657 + ], + "spans": [ + { + "bbox": [ + 46, + 549, + 289, + 657 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 46, + 549, + 289, + 657 + ], + "type": "inline_equation", + "content": "\\Omega(l)" + }, + { + "bbox": [ + 46, + 549, + 289, + 657 + ], + "type": "text", + "content": " is a function that maps the index of each orientation vector to its parent orientation vector in the kinematic chain of the human skeleton. We obtain the overall pose encoding as " + }, + { + "bbox": [ + 46, + 549, + 289, + 657 + ], + "type": "inline_equation", + "content": "\\mathbf{p} = [\\mathbf{v}_1|\\ldots|\\mathbf{v}_L]" + }, + { + "bbox": [ + 46, + 549, + 289, + 657 + ], + "type": "text", + "content": " by concatenating all the individual orientation encodings. This pose encoding is then processed by " + }, + { + "bbox": [ + 46, + 549, + 289, + 657 + ], + "type": "inline_equation", + "content": "g_{\\mathrm{dec}}: \\mathbb{R}^{d,L} \\to \\mathbb{R}^+" + }, + { + "bbox": [ + 46, + 549, + 289, + 657 + ], + "type": "text", + "content": ", which predicts the unsigned distance for the given pose representation " + }, + { + "bbox": [ + 46, + 549, + 289, + 657 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 549, + 289, + 657 + ], + "type": "text", + "content": ". A lower distance value for a pose implies that the configuration of joints is more likely to be a plausible human pose." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 670, + 165, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 165, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 165, + 683 + ], + "type": "text", + "content": "3.2.2 Pose Prior Training" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "To train the parametric prior " + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": ", we rely on an auxiliary dataset of " + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": " human poses " + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{A}} = \\{\\pmb{\\theta}^{i}\\}_{i=1}^{N_{\\mathrm{A}}}" + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}^{i} =" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "inline_equation", + "content": "(\\theta_1^i,\\dots ,\\theta_L^i)" + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "content": ". Importantly, these poses are not associated with their corresponding RGB images, which preserves the privacy aspect of the method. Additionally, storing only the pose coordinates instead of entire images makes data storage much more efficient and feasible." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "type": "text", + "content": "We adopt a supervised approach to train " + }, + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "type": "text", + "content": " to predict the " + }, + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "type": "inline_equation", + "content": "L2" + }, + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "type": "text", + "content": " distance to the plausible pose manifold for a given pose. To achieve this, we construct a dataset " + }, + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{D}} = \\{(\\pmb{\\theta}_i,d_i)\\}_{i=1}^M" + }, + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "type": "text", + "content": ", consisting of pose and distance pairs, from " + }, + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{A}}" + }, + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "type": "text", + "content": ". As the poses from " + }, + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{A}}" + }, + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "type": "text", + "content": " lie on the desired manifold, we assign " + }, + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "type": "inline_equation", + "content": "d = 0" + }, + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "type": "text", + "content": " to all poses in the dataset. To diversify our training samples, we randomly generate negative samples with distance " + }, + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "type": "inline_equation", + "content": "d > 0" + }, + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "type": "text", + "content": " by perturbing the poses from " + }, + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{A}}" + }, + { + "bbox": [ + 304, + 133, + 547, + 228 + ], + "type": "text", + "content": " with noise." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 317, + 228, + 511, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 228, + 511, + 239 + ], + "spans": [ + { + "bbox": [ + 317, + 228, + 511, + 239 + ], + "type": "text", + "content": "We train the network with the standard " + }, + { + "bbox": [ + 317, + 228, + 511, + 239 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 317, + 228, + 511, + 239 + ], + "type": "text", + "content": " loss," + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 366, + 243, + 545, + 270 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 243, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 366, + 243, + 545, + 270 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {d i s t}} = \\sum_ {(\\boldsymbol {\\theta}, d) \\in \\tilde {D}} \\| g (\\boldsymbol {\\theta}) - d \\| _ {1}. \\tag {7}", + "image_path": "5e59fa9a965555b43cb5dd7e614e87839712b9a67ca3477d1ab2d23721415c1c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 275, + 547, + 298 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 275, + 547, + 298 + ], + "spans": [ + { + "bbox": [ + 305, + 275, + 547, + 298 + ], + "type": "text", + "content": "More details on the training process of the prior are provided in Section 4.2." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 313, + 460, + 325 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 313, + 460, + 325 + ], + "spans": [ + { + "bbox": [ + 306, + 313, + 460, + 325 + ], + "type": "text", + "content": "3.2.3 Adaptation using Pose Prior" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 331, + 547, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 547, + 367 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 547, + 367 + ], + "type": "text", + "content": "We leverage the trained pose prior " + }, + { + "bbox": [ + 304, + 331, + 547, + 367 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 331, + 547, + 367 + ], + "type": "text", + "content": " to regularize the adaptation process by incentivizing the pose estimator to generate pseudo-labels that resemble plausible human poses." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 367, + 547, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 367, + 547, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 367, + 547, + 498 + ], + "type": "text", + "content": "Given the heatmaps " + }, + { + "bbox": [ + 304, + 367, + 547, + 498 + ], + "type": "inline_equation", + "content": "\\{h_k^t\\}_{k=1}^K" + }, + { + "bbox": [ + 304, + 367, + 547, + 498 + ], + "type": "text", + "content": " generated for each keypoint by the student model " + }, + { + "bbox": [ + 304, + 367, + 547, + 498 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{stu}}^t" + }, + { + "bbox": [ + 304, + 367, + 547, + 498 + ], + "type": "text", + "content": " for a target image " + }, + { + "bbox": [ + 304, + 367, + 547, + 498 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 367, + 547, + 498 + ], + "type": "text", + "content": ", we calculate the corresponding orientation vectors in a differentiable manner to evaluate the plausibility of the predicted pose using the prior. First, we renormalize each heatmap to a probability distribution via spatial softmax and condense it to a point by computing the spatial expected value of the latter. For computational efficiency, we carry this out in a separable manner along the two spatial dimensions. Namely, assuming " + }, + { + "bbox": [ + 304, + 367, + 547, + 498 + ], + "type": "inline_equation", + "content": "u = (u_1, u_2)" + }, + { + "bbox": [ + 304, + 367, + 547, + 498 + ], + "type": "text", + "content": " to be the two components of each pixel coordinate, we set" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 318, + 502, + 545, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 502, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 318, + 502, + 545, + 536 + ], + "type": "interline_equation", + "content": "u _ {i} ^ {k} = \\frac {\\sum_ {u _ {i}} u _ {i} e ^ {h _ {k} ^ {t} (u _ {i})}}{\\sum_ {u _ {i}} e ^ {h _ {k} ^ {t} (u _ {i})}}, \\quad h _ {k} ^ {t} (u _ {i}) = \\sum_ {u _ {j}} h _ {k} ^ {t} (u _ {1}, u _ {2}), \\tag {8}", + "image_path": "6a72a555c9ecea630ac34c4b62f8083555f8e65bbc55198da00261de769d4865.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "inline_equation", + "content": "i = 1,2" + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "inline_equation", + "content": "j = 2,1" + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "text", + "content": " respectively. Next, we use the pose coordinates to determine the orientation vectors between pairs of connected keypoints. Specifically, for every pair " + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "inline_equation", + "content": "(a,b)" + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "text", + "content": " of connected keypoints in the human skeleton (denoted by the set " + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "text", + "content": "), we calculate the unit vector " + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "text", + "content": " in the direction from " + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "inline_equation", + "content": "u^a" + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "inline_equation", + "content": "u^b" + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "inline_equation", + "content": "u^a" + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "inline_equation", + "content": "u^b" + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "text", + "content": " are the estimated softmax coordinates of keypoints " + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 540, + 545, + 624 + ], + "type": "text", + "content": ", respectively, i.e.," + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 358, + 628, + 545, + 655 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 628, + 545, + 655 + ], + "spans": [ + { + "bbox": [ + 358, + 628, + 545, + 655 + ], + "type": "interline_equation", + "content": "\\theta = \\frac {u ^ {a} - u ^ {b}}{\\| u ^ {a} - u ^ {b} \\| _ {2}}, \\quad \\forall (a, b) \\in \\mathcal {E}. \\tag {9}", + "image_path": "35ac90309c96dd6734c1365a05b9760cf143fa96e4b23fa2294b2c82eaffb110.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 659, + 545, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 659, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 305, + 659, + 545, + 682 + ], + "type": "text", + "content": "Finally, we use the prior as a regularization term to minimize the distance of the current pose from our learned manifold," + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 361, + 687, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 687, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 361, + 687, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p r i o r}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {\\boldsymbol {x} \\in \\mathcal {B}} g \\left(T \\left(f _ {\\mathrm {s t u}} ^ {t} (\\boldsymbol {x})\\right)\\right), \\tag {10}", + "image_path": "528ef40c7c9b3609d16a8f74dc6a49e8181f5bb08268737673eeaaa80d7f7961.jpg" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15000" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "inline_equation", + "content": "T(\\cdot)" + }, + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "content": " converts the predicted heatmaps to the orientation vector format required as input by the prior." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 105, + 161, + 118 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 105, + 161, + 118 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 161, + 118 + ], + "type": "text", + "content": "3.3. Overall Adaptation" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 123, + 287, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 123, + 287, + 148 + ], + "spans": [ + { + "bbox": [ + 47, + 123, + 287, + 148 + ], + "type": "text", + "content": "The final training objective for the student model " + }, + { + "bbox": [ + 47, + 123, + 287, + 148 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{stu}}" + }, + { + "bbox": [ + 47, + 123, + 287, + 148 + ], + "type": "text", + "content": " can be expressed as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 103, + 158, + 287, + 177 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 103, + 158, + 287, + 177 + ], + "spans": [ + { + "bbox": [ + 103, + 158, + 287, + 177 + ], + "type": "interline_equation", + "content": "\\min _ {f _ {\\mathrm {s t u}}} \\mathcal {L} _ {\\text {o u t}} + \\lambda_ {1} \\mathcal {L} _ {\\text {f e a t}} + \\lambda_ {2} \\mathcal {L} _ {\\text {p r i o r}}. \\tag {11}", + "image_path": "f5833442dd268b1804af2e7accc6e98aa4822bbd9ccbed76cf1d6bde753bd387.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 186, + 288, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 186, + 288, + 246 + ], + "spans": [ + { + "bbox": [ + 47, + 186, + 288, + 246 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 47, + 186, + 288, + 246 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 47, + 186, + 288, + 246 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 186, + 288, + 246 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 47, + 186, + 288, + 246 + ], + "type": "text", + "content": " are hyper-parameters that control the influence of feature space adaptation and prior regularization, respectively. The teacher model " + }, + { + "bbox": [ + 47, + 186, + 288, + 246 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{tea}}" + }, + { + "bbox": [ + 47, + 186, + 288, + 246 + ], + "type": "text", + "content": " is updated asynchronously by computing an exponential moving average of the student model weights as shown in Equation 1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 258, + 128, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 258, + 128, + 272 + ], + "spans": [ + { + "bbox": [ + 47, + 258, + 128, + 272 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 277, + 287, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 277, + 287, + 374 + ], + "spans": [ + { + "bbox": [ + 47, + 277, + 287, + 374 + ], + "type": "text", + "content": "In this section, we demonstrate POST's ability to adapt a 2D human pose estimation model to a target domain using only unlabeled data from that domain. We conduct experiments on three domain adaptive scenarios and compare with state-of-the-art domain adaptation baselines that utilize source data during adaptation. We also conduct extensive analysis to analyze the contribution and interaction between each component in our framework." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 383, + 110, + 394 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 383, + 110, + 394 + ], + "spans": [ + { + "bbox": [ + 47, + 383, + 110, + 394 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 401, + 288, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 401, + 288, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 401, + 288, + 460 + ], + "type": "text", + "content": "SURREAL: SURREAL [43] is a large-scale dataset of synthetically generated images of people rendered from 3D sequences of human motion capture data against indoor backgrounds. It contains over 6 million frames, making it one of the largest and most diverse datasets of its kind." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 465, + 287, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 465, + 287, + 573 + ], + "spans": [ + { + "bbox": [ + 47, + 465, + 287, + 573 + ], + "type": "text", + "content": "Human3.6M: Human3.6M [44] is a real-world video dataset captured in indoor environments, comprising 3.6 million frames. The dataset features human subjects performing various actions. In order to reduce redundancy and computational complexity, we down-sampled the videos from 50fps to 10fps as per the approach proposed in [5]. For training, we follow the standard protocol proposed in [6] and use 5 subjects (S1, S5, S6, S7, S8), while the remaining 2 subjects (S9, S11) are reserved for testing." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 577, + 287, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 577, + 287, + 638 + ], + "spans": [ + { + "bbox": [ + 47, + 577, + 287, + 638 + ], + "type": "text", + "content": "LSP: Leeds Sports Pose (LSP) [45] is a real-world dataset that contains 2,000 images with annotated human body joint locations collected from sports activities. The images in LSP are captured in the wild, featuring a wide variety of human poses that are often challenging to detect." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "text", + "content": "BRIAR: BRIAR [46] is a cutting-edge biometric dataset featuring a large-scale collection of videos of human subjects captured in extremely challenging conditions. The videos are recorded at varying distances, i.e., close range, " + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "100\\mathrm{m}" + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "200\\mathrm{m}" + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "400\\mathrm{m}" + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "500\\mathrm{m}" + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "text", + "content": ", and unmanned aerial vehicles (UAV), with each video lasting around 90 seconds. We randomly" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "content": "sample 20 frames from each sequence for each of the 158 subjects for our experiments." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 103, + 430, + 116 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 103, + 430, + 116 + ], + "spans": [ + { + "bbox": [ + 306, + 103, + 430, + 116 + ], + "type": "text", + "content": "4.2. Experiment Protocols" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "type": "text", + "content": "Pose estimation model. We adopt the Simple Baseline [18] as our pose estimation model, with the ResNet-101 [47] as the backbone. To train the model, we use the Adam optimizer [48] with a base learning rate of " + }, + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "type": "inline_equation", + "content": "1e - 4" + }, + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "type": "text", + "content": ", scheduled to decrease to " + }, + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "type": "inline_equation", + "content": "1e - 5" + }, + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "type": "text", + "content": " after 5 epochs and to " + }, + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "type": "inline_equation", + "content": "1e - 6" + }, + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "type": "text", + "content": " after 20 epochs. The model is trained for 30 epochs. We use a batch size of 32 and run 500 iterations per epoch. To threshold the model predictions, we set the confidence thresholding ratio " + }, + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "type": "text", + "content": " to 0.5. To augment the images during training, we follow [6] and use rotation, translation, shear, and Gaussian blur. The hyper-parameters " + }, + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "type": "text", + "content": " are set to " + }, + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "type": "inline_equation", + "content": "1e - 3" + }, + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "type": "inline_equation", + "content": "1e - 6" + }, + { + "bbox": [ + 305, + 121, + 545, + 266 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 269, + 547, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 269, + 547, + 437 + ], + "spans": [ + { + "bbox": [ + 305, + 269, + 547, + 437 + ], + "type": "text", + "content": "Pose prior model. The training of the parametric prior follows a multi-stage approach that involves using different types of training samples. Initially, we use a combination of manifold poses " + }, + { + "bbox": [ + 305, + 269, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\theta_{m}" + }, + { + "bbox": [ + 305, + 269, + 547, + 437 + ], + "type": "text", + "content": " and non-manifold poses " + }, + { + "bbox": [ + 305, + 269, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\theta_{nm}" + }, + { + "bbox": [ + 305, + 269, + 547, + 437 + ], + "type": "text", + "content": " with a considerable distance from the desired manifold. Over the course of training, we gradually increase the number of non-manifold poses " + }, + { + "bbox": [ + 305, + 269, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\theta_{nm}" + }, + { + "bbox": [ + 305, + 269, + 547, + 437 + ], + "type": "text", + "content": " with a small distance from the manifold. This enables our model to first learn a smooth surface and then gradually incorporate finer details as training progresses. We create these non-manifold poses " + }, + { + "bbox": [ + 305, + 269, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\theta_{nm}" + }, + { + "bbox": [ + 305, + 269, + 547, + 437 + ], + "type": "text", + "content": " by injecting noise into the manifold poses " + }, + { + "bbox": [ + 305, + 269, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\theta_{m}" + }, + { + "bbox": [ + 305, + 269, + 547, + 437 + ], + "type": "text", + "content": " obtained from the auxiliary dataset. Specifically, we sample directional noise from the Von-Mises distribution [49] and add it to the manifold poses in order to obtain the implausible poses." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 437, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 437, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 305, + 437, + 545, + 509 + ], + "type": "text", + "content": "The architecture for the encoder " + }, + { + "bbox": [ + 305, + 437, + 545, + 509 + ], + "type": "inline_equation", + "content": "g_{\\mathrm{enc}}" + }, + { + "bbox": [ + 305, + 437, + 545, + 509 + ], + "type": "text", + "content": " consists of a 2-layer MLP with an output feature size of " + }, + { + "bbox": [ + 305, + 437, + 545, + 509 + ], + "type": "inline_equation", + "content": "d = 6" + }, + { + "bbox": [ + 305, + 437, + 545, + 509 + ], + "type": "text", + "content": " for each orientation vector, similar to [42]. The distance field network " + }, + { + "bbox": [ + 305, + 437, + 545, + 509 + ], + "type": "inline_equation", + "content": "g_{\\mathrm{dec}}" + }, + { + "bbox": [ + 305, + 437, + 545, + 509 + ], + "type": "text", + "content": " is implemented as a 5-layer MLP. Given its large size and diverse poses, we train the prior for our primary experiments using the SURREAL dataset." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 515, + 456, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 456, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 456, + 528 + ], + "type": "text", + "content": "4.3. Comparison with Baselines" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 534, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 534, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 534, + 547, + 714 + ], + "type": "text", + "content": "Baselines. We evaluate the performance of our proposed method against several state-of-the-art domain adaptive frameworks. This includes adversarial learning-based feature alignment methods, such as DAN[31], DD[50], and RegDA[5]. Additionally, we consider approaches based on pseudo-labeling, namely CCSSL[38], and UDAPE [6]. It is worth noting that all these methods employ the source data during the adaptation process. To establish a comprehensive performance baseline, we report the results of two additional baselines: Oracle and Source only. The Oracle baseline represents the upper bound of the model's performance, achieved by training the model jointly with target 2D annotations. On the other hand, Source only represents the model's performance when it is directly applied to the target domain without any adaptation." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15001" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 96, + 287, + 213 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 287, + 91 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 287, + 91 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 287, + 91 + ], + "type": "text", + "content": "Table 1. PCK@0.05 on SURREAL " + }, + { + "bbox": [ + 47, + 69, + 287, + 91 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 47, + 69, + 287, + 91 + ], + "type": "text", + "content": " LSP. (Best value is in red color, while the second best value is in blue color.)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 96, + 287, + 213 + ], + "lines": [ + { + "bbox": [ + 48, + 96, + 287, + 213 + ], + "spans": [ + { + "bbox": [ + 48, + 96, + 287, + 213 + ], + "type": "table", + "html": "
MethodSFSld.Elb.WristHipKneeAnkleAvg.
Source only-51.565.062.968.068.767.463.9
Oracle--------
DANX52.262.958.971.068.165.163.0
DDX28.465.956.875.074.373.962.4
RegDAX62.776.771.181.080.375.374.6
CCSSLX36.866.363.959.667.370.460.7
UDAPEX69.284.983.385.584.784.382.0
POST✓66.583.981.084.683.182.680.3
", + "image_path": "8cc6403209faf3336274df573533ff128f80f2dfd107a47bc6f421cda02ba380.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 236, + 287, + 353 + ], + "blocks": [ + { + "bbox": [ + 67, + 221, + 266, + 232 + ], + "lines": [ + { + "bbox": [ + 67, + 221, + 266, + 232 + ], + "spans": [ + { + "bbox": [ + 67, + 221, + 266, + 232 + ], + "type": "text", + "content": "Table 2. PCK@0.05 on SURREAL " + }, + { + "bbox": [ + 67, + 221, + 266, + 232 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 67, + 221, + 266, + 232 + ], + "type": "text", + "content": " Human3.6M." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 236, + 287, + 353 + ], + "lines": [ + { + "bbox": [ + 48, + 236, + 287, + 353 + ], + "spans": [ + { + "bbox": [ + 48, + 236, + 287, + 353 + ], + "type": "table", + "html": "
MethodSFSld.Elb.WristHipKneeAnkleAvg.
Source only-69.475.466.437.977.377.767.3
Oracle-95.391.886.995.694.193.692.9
DANX68.177.562.330.478.479.466.0
DDX71.683.375.142.176.276.170.7
RegDAX73.386.472.854.882.084.475.6
CCSSLX44.368.555.222.262.357.851.7
UDAPEX78.189.681.152.685.387.179.0
POST✓81.388.577.446.183.483.476.7
", + "image_path": "a6fe4e1c5a1647be1f5939c567aa9b00152085a1219b1befdbf622759c82e948.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 372, + 287, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 372, + 287, + 420 + ], + "spans": [ + { + "bbox": [ + 46, + 372, + 287, + 420 + ], + "type": "text", + "content": "Metrics. We adopt the evaluation metric of Percentage of Correct Keypoint (PCK) for all experiments and report PCK@0.05 that measures the ratio of correct prediction within a range of " + }, + { + "bbox": [ + 46, + 372, + 287, + 420 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 372, + 287, + 420 + ], + "type": "text", + "content": " with respect to the image size." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 427, + 105, + 439 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 427, + 105, + 439 + ], + "spans": [ + { + "bbox": [ + 47, + 427, + 105, + 439 + ], + "type": "text", + "content": "4.4. Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 445, + 289, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 289, + 674 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 289, + 674 + ], + "type": "text", + "content": "Quantitative results. We evaluate POST in two adaptation scenarios: SURREAL " + }, + { + "bbox": [ + 46, + 445, + 289, + 674 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 445, + 289, + 674 + ], + "type": "text", + "content": " LSP and SURREAL " + }, + { + "bbox": [ + 46, + 445, + 289, + 674 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 445, + 289, + 674 + ], + "type": "text", + "content": " Human3.6M, and report the quantitative results in Table 1 and Table 2, respectively. Specifically, we report the PCK@0.05 on 16 keypoints of the human body, including shoulders (sld.), elbows (elb.), wrists, hips, knees, and ankles. Our method achieves comparable results to many recent approaches that leverage source data for adaptation. Among these methods, UDAPE [6] achieves the highest performance on both cases, with our framework achieving a close second and only 2 percentage points behind on average. Notably, we outperform every other method, including the recently proposed RegDA [5] approach, by a significant margin of up to 5.7 percentage points. It is worth noting that not only do these methods require source data, but also involve additional models such as discriminators or style transfer modules, and unstable adversarial training. In contrast, our framework is lightweight, only involves pseudo-label training, and utilizes a simple prior model that can be trained offline." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": "Qualitative results. In addition to quantitative results, we also present qualitative results on SURREAL " + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": " Human3.6M in Figure 3 and on SURREAL " + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": " LSP in Figure 4. 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Figure 5 displays the predicted human poses on images taken from six different imaging ranges in the BRIAR dataset. While using the source model directly produces completely inaccurate poses, POST can accurately localize the keypoint locations, even in the presence of occlusions and atmospheric turbulence. Our approach can also accurately reconstruct poses even when the human is imaged from an elevated perspective, resulting in a high camera angle (Figure 5.f). Notably, our approach achieves this without using any source data for adaptation. Our results are comparable to those produced by UDAPE [6], which utilizes source data for adaptation. 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Qualitative results on SURREAL " + }, + { + "bbox": [ + 45, + 573, + 547, + 617 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 45, + 573, + 547, + 617 + ], + "type": "text", + "content": " BRIAR. We demonstrate sample results on BRIAR at all ranges. For each range, we display three images: the leftmost shows the Source only prediction, the middle one shows the UDAPE [6] prediction, and the rightmost shows the prediction using POST. Although POST does not use source data for adaptation, it is able to match the predictions produced by UDAPE, which uses source data." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 635, + 147, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 147, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 147, + 647 + ], + "type": "text", + "content": "4.5. Ablation Studies" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Effect of auxiliary dataset. We conduct experiments to evaluate the impact of the choice of the auxiliary dataset (used to train the prior) on downstream adaptation. The results are presented in Table 3. Our findings indicate that" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 636, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 636, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 305, + 636, + 545, + 662 + ], + "type": "text", + "content": "POST is robust to the choice of the auxiliary dataset, with performance differences of " + }, + { + "bbox": [ + 305, + 636, + 545, + 662 + ], + "type": "inline_equation", + "content": "\\sim 0.5" + }, + { + "bbox": [ + 305, + 636, + 545, + 662 + ], + "type": "text", + "content": " percentage points." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": "Effect of loss terms. We conduct an experiment to evaluate the performance of each component of our framework. The results on the SURREAL " + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": " Human3.6M adaptation scenario are presented in Table 4. Our findings indicate that in addi" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15003" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 95, + 288, + 212 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 287, + 91 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 287, + 91 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 287, + 91 + ], + "type": "text", + "content": "Table 3. Effect of auxiliary dataset. We evaluate the effect of auxiliary dataset on downstream adaptation tasks." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 95, + 288, + 212 + ], + "lines": [ + { + "bbox": [ + 47, + 95, + 288, + 212 + ], + "spans": [ + { + "bbox": [ + 47, + 95, + 288, + 212 + ], + "type": "table", + "html": "
SURREAL→HUMAN3.6M
Aux. datasetSld.Elb.WristHipKneeAnkleAvg.
SURREAL81.388.577.446.183.483.476.7
Human3.6M80.988.077.245.083.182.876.2
SURREAL→LSP
Aux. datasetSld.Elb.WristHipKneeAnkleAvg.
SURREAL66.583.981.084.683.182.680.3
Human3.6M66.183.680.784.483.182.580.1
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LoutLfeatLpriorSld.Elb.WristHipKneeAnkleAvg.
XXX69.475.466.437.977.377.767.3
✓XX77.986.773.738.883.084.374.1
✓✓X81.787.175.244.382.382.275.5
✓✓✓81.388.577.446.183.483.476.7
", + "image_path": "8647424d859b191fa3cf852da3d10e0050e9733572ba9d8ee4f46abe481e298d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "type": "text", + "content": "tion to prediction space adaptation, feature space adaptation also plays a crucial role in enabling effective unsupervised learning from pseudo-labels. Moreover, we observed that the human pose prior brings additional improvements, thus validating our hypothesis that noisy pose pseudo-labels can be refined implicitly by a prior in the absence of source data. Overall, our results demonstrate the effectiveness of our framework and the importance of each of its components in achieving state-of-the-art performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 447, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 287, + 567 + ], + "type": "text", + "content": "Cross-dataset performance of prior. We evaluate the ability of the learned prior to handle distribution shift separately from the adaptation performance. Specifically, we assess the robustness of the prior by computing pose scores across datasets, and the results are presented in Figure 6. The plot demonstrates that our prior is effective in scoring plausible (real) poses with low scores and scoring implausible poses with higher scores. Note that the bell curve shape of the noisy pose scores is due to the Von-Mises noise added to create the noisy poses." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 571, + 287, + 655 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 571, + 287, + 655 + ], + "spans": [ + { + "bbox": [ + 46, + 571, + 287, + 655 + ], + "type": "text", + "content": "Effect of thresholding. We analyze the impact of the pseudo-label threshold " + }, + { + "bbox": [ + 46, + 571, + 287, + 655 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 571, + 287, + 655 + ], + "type": "text", + "content": " on the adaptation performance in Table 5. The results on SURREAL " + }, + { + "bbox": [ + 46, + 571, + 287, + 655 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 571, + 287, + 655 + ], + "type": "text", + "content": " Human3.6M reveal that as we increase this ratio, the performance gradually decreases. This can be attributed to the fact that higher thresholding ratios tend to include lower confident predictions as pseudo-labels, which can negatively impact adaptation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 669, + 119, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 119, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 119, + 681 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "We address the problem of adapting a pre-trained 2D human pose estimator to a new target domain with unlabeled" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 331, + 94, + 521, + 225 + ], + "blocks": [ + { + "bbox": [ + 306, + 69, + 545, + 91 + ], + "lines": [ + { + "bbox": [ + 306, + 69, + 545, + 91 + ], + "spans": [ + { + "bbox": [ + 306, + 69, + 545, + 91 + ], + "type": "text", + "content": "Table 5. Effect of " + }, + { + "bbox": [ + 306, + 69, + 545, + 91 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 306, + 69, + 545, + 91 + ], + "type": "text", + "content": ". We evaluate adaptation performance on SURREAL " + }, + { + "bbox": [ + 306, + 69, + 545, + 91 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 306, + 69, + 545, + 91 + ], + "type": "text", + "content": " Human3.6M as " + }, + { + "bbox": [ + 306, + 69, + 545, + 91 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 306, + 69, + 545, + 91 + ], + "type": "text", + "content": " is varied." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 331, + 94, + 521, + 225 + ], + "lines": [ + { + "bbox": [ + 331, + 94, + 521, + 225 + ], + "spans": [ + { + "bbox": [ + 331, + 94, + 521, + 225 + ], + "type": "table", + "html": "
τ = 0.1τ = 0.3τ = 0.5τ = 0.7τ = 0.9
76.476.576.775.373.8
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Cross-dataset prior transfer. We plot the histogram of scores predicted by the prior. The prior can clearly demarcate plausible poses from implausible poses across datasets." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 402, + 547, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 547, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 547, + 521 + ], + "type": "text", + "content": "target data. To this end, we propose a self-training algorithm, POST, that leverages a Mean Teacher framework to enforce both prediction-level and feature-level consistency between a pair of student and teacher models. Our approach incorporates a human pose prior that captures the manifold of possible poses in a high-dimensional space, which helps to refine noisy pseudo-labels generated during self-training. We evaluate our method on three challenging adaptation scenarios and show that it achieves competitive performance compared to existing UDA methods that have access to source data." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 528, + 547, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 528, + 547, + 648 + ], + "spans": [ + { + "bbox": [ + 304, + 528, + 547, + 648 + ], + "type": "text", + "content": "Acknowledgements. This research is based upon work supported in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via [2022-21102100007]. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, IARPA, or the U.S. Government. 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In ICML, 2019. 6" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "15006" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Priority-Centric Human Motion Generation in Discrete Latent Space/58c7e478-f288-424e-a702-051324564633_content_list.json b/2023/Priority-Centric Human Motion Generation in Discrete Latent Space/58c7e478-f288-424e-a702-051324564633_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..1e7840693248e9982816405f59b9160d6efbad27 --- /dev/null +++ b/2023/Priority-Centric Human Motion Generation in Discrete Latent Space/58c7e478-f288-424e-a702-051324564633_content_list.json @@ -0,0 +1,1733 @@ +[ + { + "type": "text", + "text": "Priority-Centric Human Motion Generation in Discrete Latent Space", + "text_level": 1, + "bbox": [ + 135, + 130, + 833, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hanyang Kong $^{1}$ , Kehong Gong $^{1}$ , Dongze Lian $^{1}$ , Michael Bi Mi $^{2}$ , Xinchao Wang $^{1*}$", + "bbox": [ + 158, + 179, + 810, + 200 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ National University of Singapore $^{2}$ Huawei International Pte Ltd", + "bbox": [ + 218, + 204, + 750, + 223 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{hanyang.k, gongkehong}@u.nus.edu {dongze, xinchao}@nus.edu.sg", + "bbox": [ + 205, + 224, + 764, + 241 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 275, + 313, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Text-to-motion generation is a formidable task, aiming to produce human motions that align with the input text while also adhering to human capabilities and physical laws. While there have been advancements in diffusion models, their application in discrete spaces remains underexplored. Current methods often overlook the varying significance of different motions, treating them uniformly. It is essential to recognize that not all motions hold the same relevance to a particular textual description. Some motions, being more salient and informative, should be given precedence during generation. In response, we introduce a Priority-Centric Motion Discrete Diffusion Model (M2DM), which utilizes a Transformer-based VQ-VAE to derive a concise, discrete motion representation, incorporating a global self-attention mechanism and a regularization term to counteract code collapse. We also present a motion discrete diffusion model that employs an innovative noise schedule, determined by the significance of each motion token within the entire motion sequence. This approach retains the most salient motions during the reverse diffusion process, leading to more semantically rich and varied motions. Additionally, we formulate two strategies to gauge the importance of motion tokens, drawing from both textual and visual indicators. Comprehensive experiments on the HumanML3D and KIT-ML datasets confirm that our model surpasses existing techniques in fidelity and diversity, particularly for intricate textual descriptions.", + "bbox": [ + 76, + 306, + 473, + 717 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 744, + 209, + 762 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Generating realistic and diverse 3D human motions under various conditions e.g., action labels [34, 18], natural language descriptions [55, 17, 5, 56], and musical cues [27, 28, 29], presents a significant challenge across multiple domains, including gaming, filmmaking, and robotic animation. Notably, motion generation based on language descriptions has garnered substantial interest, given its promise", + "bbox": [ + 75, + 770, + 470, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "for enhancing realism and broadening practical applications.", + "bbox": [ + 500, + 277, + 893, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, generating a high-quality motion is not trivial due to the inherent modality gap and the complex mapping between text and motion modalities. Previous works [35, 43] align the latent feature space between text and motion modalities. For instance, TEMOS [35] aligns the text and motion feature by learning text and motion encoders. MotionClip [43] aligns the human motion manifold to CLIP [37] space for infusing semantic knowledge of CLIP into the motion extractor. Despite these advancements, they might encounter performance degradation when dealing with complex textual descriptions.", + "bbox": [ + 496, + 292, + 893, + 459 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To process these complex textual descriptions, some text-to-motion methods are proposed. State-of-the-art approaches such as TM2T [17] and T2M-GPT [55] use vector-quantized autoencoder (VQ-VAE) [46] to learn a discrete and compact motion representation, followed by a translation model [38, 47] to map the text modality to the motion modality. With the popularity and the superior performance in the generation tasks of diffusion models [20], MDM [44] and MLD [5] are proposed to learn conditioned diffusion models on the raw motion representation space and the latent feature space, respectively.", + "bbox": [ + 496, + 460, + 895, + 626 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While there have been promising advancements, two primary issues remain unresolved: i) The aforementioned diffusion methods, namely MDM [44] and MLD [5], predominantly address the latent feature within a continuous space. Although VQ-VAE-inspired architectures have made considerable strides in motion generation [55, 17], particularly with the support of discrete and compact motion representations, the integration of the diffusion model into a discrete space remains inadequately explored. ii) Discrete diffusion models employed in prior studies [15, 14, 22] treat all tokens uniformly. This approach presupposes that every token conveys an equivalent amount of information, neglecting the inherent disparities among tokens within a sequence. A more intuitive generative approach for humans would involve a progressive hierarchy, commencing with overarching concepts and gradually delving into finer details.", + "bbox": [ + 496, + 627, + 895, + 868 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address the aforementioned challenges, we introduce a priority-centric motion discrete diffusion model (M2DM)", + "bbox": [ + 500, + 869, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 805, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author: xinchao@nus.edu.sg", + "bbox": [ + 94, + 886, + 336, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14806", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b439b8314da8a8ceb3326548da576200317184eb052eb4f23a161258ea0bf35f.jpg", + "image_caption": [ + "a person steps forward with left leg walking in a circle counterclockwise motion swinging arms and returns back." + ], + "image_footnote": [], + "bbox": [ + 91, + 90, + 267, + 198 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9d0c251455da47bd3d24f66b71118aebf0d37946e80a8daacde1e958f2e04810.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 276, + 90, + 439, + 198 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c8ea4c1f7282c3d12e82f475d439ce5e00a7a9482b33fc27749fca5bf60e559b.jpg", + "image_caption": [ + "a person runs forward, then turns around and walks in the opposite direction while swinging their right arm." + ], + "image_footnote": [], + "bbox": [ + 83, + 233, + 251, + 345 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c859db1c1545f793b8cdf537f4e5ba72913f0744a729ef102d8e27a747e06912.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 269, + 236, + 447, + 347 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ed8e60537fcd7457573289571d364e02360b7d0c102a0ab97a985dc78d08cfc3.jpg", + "image_caption": [ + "a man gets up from the ground, walks around in a circle and then sits down on the ground again." + ], + "image_footnote": [], + "bbox": [ + 509, + 88, + 875, + 200 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/85861fed1c799c75fb9e0e963334011b3432907a77306bb750bfcea593abbd37.jpg", + "image_caption": [ + "a man postures his arms like holding a dance partner and dances the waltz from the right hand side to the left hand side." + ], + "image_footnote": [], + "bbox": [ + 532, + 247, + 694, + 347 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a8b75794bd13b135797c0134ed741dcf543f0c5d0c7087ad0abad9fa0f0f1441.jpg", + "image_caption": [ + "Figure 1: Our Priority-Centric Motion Discrete Diffusion Model (M2DM) generates diverse and precise human motions given complex textual descriptions. The color of human mesh goes from light to dark over time." + ], + "image_footnote": [], + "bbox": [ + 709, + 244, + 861, + 348 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "designed to generate motion sequences from textual descriptions, progressing in a primary to secondary manner. Initially, we employ a Transformer-based VQ-VAE, which is adept at learning a concise, discrete motion representation through the global self-attention mechanism. To circumvent code collapse and guarantee the optimal utilization of each motion token within the codebook, a regularization term is incorporated during the VQ-VAE training phase. Furthermore, we craft a noise schedule wherein individual tokens within a sequence are allocated varying corruption probabilities, contingent on their respective priorities during the forward process. Specifically, tokens of higher priority are slated for corruption towards the latter stages of the forward process. This ensures that the subsequent learnable reverse process adheres to a primary-to-secondary sequence, with top-priority tokens being reinstated foremost.", + "bbox": [ + 75, + 446, + 472, + 688 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To discern the significance of motion tokens within a sequence, we introduce two evaluative strategies: static assessment and dynamic assessment. 1) Static assessment: Drawing inspiration from the neural language domain, where the significance of individual words is gauged by their entropy across datasets, we calculate the entropy of each motion token across the entire motion dataset. 2) Dynamic assessment: We cultivate an agent specifically to dynamically gauge the importance of tokens within a sequence. Given a discrete motion token sequence, the agent masks one token at each iteration. These masked token sequences are then fed into the VQ decoder for continuous motion reconstruction. The agent's objective is to curtail the cumulative reconstruction discrepancy between the original and the reconstructed mo", + "bbox": [ + 75, + 688, + 472, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tions at every phase. This is achieved using a reinforcement learning [23] (RL) strategy, facilitating the agent's identification of motion tokens that convey minimal information within a sequence—a process we term dynamic analysis. Our priority-centric discrete diffusion model has showcased commendable generative prowess, especially when dealing with intricate textual descriptions. Through rigorous testing, our method has proven its mettle, consistently matching or surpassing the performance of prevailing text-to-motion generation techniques on the HumanML3D and KIT-ML datasets.", + "bbox": [ + 496, + 446, + 893, + 611 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We summarize our contributions as follows:", + "bbox": [ + 519, + 613, + 812, + 627 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- To capture long-range dependencies in the motion sequences, we apply Transformer as the architecture of VQ-VAE. Besides, a regularization term is applied to increase the usage of tokens in the codebook.", + "- We design a priority-centric scheme for human motion generation in the discrete latent space. To enhance the performance given complex descriptions, we design a novel priority-centric scheme for the discrete diffusion model.", + "- Our proposed priority-centric M2DM achieves state-of-the-art performance on the HumanML3D [16] and KIT-ML [36] datasets." + ], + "bbox": [ + 519, + 635, + 893, + 832 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 844, + 640, + 859 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "VQ-VAE. Vector Quantized Variational Autoencoder (VQ-VAE) [46] aims to minimize reconstruction error with dis", + "bbox": [ + 500, + 869, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14807", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "crete representations by training a variational autoencoder. VQ-VAE achieves promising performance on generative tasks, such as text-to-image generation [39, 52], music generation [7], unconditional image synthesis [9], etc. For motion generation tasks, most of the methods [17, 55] tokenize the continuous motion representation by the 1D-CNN network. Since the motion style varies from person to person and the number of action combinations is almost infinite, it is essential to extract discriminative and distinctive motion features from the raw motion representations. Moreover, raw motion representation is much more redundant compared with neural language, it is feasible to represent a motion sequence using few motion tokens from a global perspective. To this end, we introduce a transformer-based VQ-VAE and several techniques are applied to balance the usage of each motion token in the codebook and prevent the codebook from collapsing, i.e., only a small proportion of codes in the codebook are activated.", + "bbox": [ + 75, + 90, + 472, + 363 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models. Diffusion generative models are first proposed in [42] and achieve promising results on image generation [8, 33, 21, 20, 50, 48, 53, 11, 10]. Discrete diffusion model is first proposed by [42] and several works [22, 14] apply the discrete diffusion model for text generation. D3PM [3] then applies the discrete diffusion model to the image generation task. For motion generation tasks, several works [24, 56, 44, 5] introduce diffusion models to generate diverse motion sequences from textual descriptions. In this work, we first introduce the discrete diffusion model for text-to-motion generation tasks which achieves promising results, especially for long text descriptions with several action commands.", + "bbox": [ + 75, + 382, + 472, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Conditional human motion synthesis Compared with unconditional Human motion synthesis, human motion synthesis conditioned on various conditions, such as textual description [55, 17, 5, 56], music [27, 28, 29, 13], and actions [34, 18] is more challenging due to the huge gap between two different domains. A common strategy of conditioned human motion synthesis is to employ generative models, for instance, conditional VAE [26], and learn a latent motion representation. Text-to-motion task is more challenging because neural language is a type of information highly refined by human beings, whereas human motion is much more redundant. Most recently, several promising works [5, 16, 17, 56, 55] are proposed for text-to-motion tasks. T2M-GPT [55] and TM2T [17] regard the text-to-motion task as a translation problem. They first train a VQ-VAE [46] to tokenize the motion sequences into motion tokens, and Recurrent Neural Networks (RNN) [32], Transformer [47, 51, 49, 41, 40, 54], or GPT-like [38] models are further applied to 'translate' textual descriptions to motions. Moreover, diffusion-based [20] models are introduced for", + "bbox": [ + 75, + 598, + 472, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "text-to-motion generation by [56, 6, 44, 5] in the contentious space. In this work, to the best of our knowledge, we are the first ones to diffuse the motion representation in the discrete latent space. Moreover, we notice that different motion clips in a whole motion sequence play various roles, for instance, stepping forward is more important than swinging arms for a running motion. We further design a diffuse schedule such that the generation process follows a from-primary-to-secondary manner.", + "bbox": [ + 496, + 90, + 893, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 242, + 591, + 258 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Motion Tokenizer", + "text_level": 1, + "bbox": [ + 500, + 267, + 671, + 282 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The motion tokenizer aims to learn a codebook that can represent a wide range of motion sequences with the priority awareness of motion tokens. To achieve this, we propose a transformer-based VQ-VAE that leverages self-attention to capture long-range dependencies between motion frames and learns a stable and diverse codebook.", + "bbox": [ + 496, + 291, + 890, + 381 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fig. 2 shows the overview of our motion tokenizer. Given a motion sequence $X \\in \\mathbb{R}^{T \\times d}$ with $T$ frames and $d$ dimensional motion representation, we reconstruct the motion sequence using a transformer autoencoder and learn an informative codebook $Z = \\{z_k\\}_{k=1}^K$ with $K$ entries. We use the transformer encoder $E$ to compute the latent motion features $\\boldsymbol{b} = \\{b_t\\}_{t=1}^T \\in \\mathbb{R}^{T \\times d}$ , where $d$ is the dimension of the latent features. Then for each feature $b_t$ , we query the codebook $Z$ by measuring the distance between feature $b_t$ and each entry in the codebook $Z$ . To improve the codebook usage and avoid dead codes, we first normalize $b_t$ and $z_t$ and then measure the Euclidean distance between two normalized vectors in the unit sphere coordinate, which is formulated as:", + "bbox": [ + 496, + 383, + 893, + 580 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {b} _ {t} = \\underset {b _ {t} \\in \\boldsymbol {b}} {\\arg \\min } \\| \\ell_ {2} (b _ {t}) - \\ell_ {2} \\left(z _ {k}\\right) \\| _ {2} ^ {2}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 594, + 890, + 622 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\ell_2$ is the $l_{2}$ normalized function.", + "bbox": [ + 498, + 628, + 756, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The standard optimization goal consists of three parts: the reconstruction loss, the embedding loss, and the commitment loss, which is formulated as", + "bbox": [ + 496, + 645, + 893, + 690 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {v q} = \\left\\| X - \\tilde {X} \\right\\| _ {2} ^ {2} + \\left\\| Z - s g [ \\hat {Z} ] \\right\\| _ {2} ^ {2} \\tag {2} \\\\ + \\eta | | s g [ Z ] - \\hat {Z} | | _ {2} ^ {2}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 700, + 890, + 752 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Moreover, to achieve an informative codebook with diverse and high usage of its entries, we apply an orthogonal regularization. Specifically, we calculate the distance between each pair of codebook entries to enforce orthogonality among all the codebook entries:", + "bbox": [ + 496, + 763, + 893, + 839 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {o r t h}} (Z) = \\left\\| \\ell_ {2} (Z) ^ {\\top} \\ell_ {2} (Z) - I _ {K} \\right\\| _ {2} ^ {2}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 851, + 890, + 875 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_2$ is the $l_{2}$ normalized function.", + "bbox": [ + 500, + 885, + 761, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14808", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5b14b9f440f563c742bd7350990b93a1daf121fbfd30f65ec94ca918acd80905.jpg", + "image_caption": [ + "Figure 2: Overview of our framework for our Motion Discrete Diffusion Model (M2DM). M2DM consists of a Transformer-based VQ-VAE (Sec. 3.1) and a discrete diffusion model (Sec. 3.2). Firstly, the Transformer-based motion tokenizer is learned to discretize motion sequences into tokens and reconstruct original motion sequences from tokens queried from the learnable codebook. Then the discrete diffusion model is learned to generate diverse motions conditioned on the textual descriptions. Two priority assessment strategies (Sec. 3.3) are applied to mask or replace motion tokens with less information at the beginning of the forward diffusion process and the most important motion tokens are corrupted in the last few diffusion steps. The diffusion model learns to restore the original motion token index conditioned on the given textual descriptions." + ], + "image_footnote": [], + "bbox": [ + 98, + 88, + 880, + 308 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Therefore, the overall training objective of vector quantization is defined as follows:", + "bbox": [ + 76, + 450, + 472, + 479 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {v q} = \\left\\| X - \\tilde {X} \\right\\| _ {2} ^ {2} + \\| Z - s g [ \\hat {Z} ] \\| _ {2} ^ {2} \\tag {4} \\\\ + \\eta | | s g [ Z ] - \\hat {Z} | | _ {2} ^ {2} + \\delta \\mathcal {L} _ {\\text {o r t h}} (Z), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 502, + 468, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tilde{X} = D(\\pmb {b})$ $D$ is the decoder, $sg[\\cdot ]$ denotes the stopgradient operation, $\\eta$ and $\\delta$ are the weighting scalars.", + "bbox": [ + 76, + 580, + 470, + 612 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Discrete Diffusion Models", + "text_level": 1, + "bbox": [ + 76, + 643, + 312, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Generally speaking, the forward discrete diffusion process corrupts each element $x_{t}$ at timestep $t$ with $K$ categories via fixed Markov chain $q(x_{t}|x_{t - 1})$ , for instance, replace some tokens of $x_{t - 1}$ or mask the token directly. After a fixed number of $T$ timesteps, the forward process yields a sequence of increasingly noisy discrete tokens $z_{1},\\ldots ,z_{T}$ of the same dimension of $z_{0}$ and $z_{T}$ becomes pure noise token. For the denoising procedure, the real $x_0$ is restored sequentially based on the pure noisy token $z_{T}$ . To be specific, for scalar random variable with $K$ categories $x_{t},x_{t - 1}\\in 1,\\dots K$ , the forward transition probabilities can be represented by the transition matrices $[Q_{t}]_{ij} = q(x_{t} = i|x_{t - 1} = j)\\in \\mathbb{R}^{(K + 1)\\times (K + 1)}$ . $[Q_{t}]_{i,j}$ is the Markov transition matrix from state $t$ to state $t - 1$ that is applied to each token in the sequence independently, which", + "bbox": [ + 76, + 674, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "can be written as:", + "bbox": [ + 500, + 450, + 619, + 463 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {Q} _ {t} = \\left[ \\begin{array}{c c c c c} \\alpha_ {t} + \\beta_ {t} & \\beta_ {t} & \\beta_ {t} & \\dots & 0 \\\\ \\beta_ {t} & \\alpha_ {t} + \\beta_ {t} & \\beta_ {t} & \\dots & 0 \\\\ \\beta_ {t} & \\beta_ {t} & \\alpha_ {t} + \\beta_ {t} & \\dots & 0 \\\\ \\vdots & \\vdots & \\vdots & & \\vdots \\\\ \\gamma_ {t} & \\gamma_ {t} & \\gamma_ {t} & \\dots & 1 \\end{array} \\right], \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 534, + 472, + 892, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha_{t} \\in [0,1]$ is the probability of retaining the token, $\\gamma_{t}$ is the probability of replacing the original token to [MASK] token, leaving the probability $\\beta_{t} = (1 - \\alpha_{t} - \\gamma_{t}) / K$ to be diffused. The forward Markov diffusion process for the whole token sequence is written as,", + "bbox": [ + 496, + 571, + 892, + 647 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\boldsymbol {x} _ {t} \\mid \\boldsymbol {x} _ {t - 1}\\right) = \\operatorname {C a t} (\\boldsymbol {x}; \\boldsymbol {p} = \\boldsymbol {x} _ {t - 1} \\boldsymbol {Q} _ {t}) = \\boldsymbol {x} _ {t} \\boldsymbol {Q} _ {t} \\boldsymbol {x} _ {t - 1}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 659, + 892, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\pmb{x}$ is the one-hot row vector identifying the token index and $\\operatorname{Cat}(\\pmb{x};\\pmb{p})$ is a categorical distribution over the one-hot vector $\\pmb{x}_t$ with probabilities $\\pmb{p}$ .", + "bbox": [ + 496, + 686, + 890, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Starting from the initial step $x_0$ , the posterior diffusion process is formulated as:", + "bbox": [ + 496, + 733, + 890, + 762 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} q \\left(\\boldsymbol {x} _ {t - 1} \\mid \\boldsymbol {x} _ {t}, \\boldsymbol {x} _ {0}\\right) = \\frac {q \\left(\\boldsymbol {x} _ {t} \\mid \\boldsymbol {x} _ {t - 1} , \\boldsymbol {x} _ {0}\\right) q \\left(\\boldsymbol {x} _ {t - 1} , \\boldsymbol {x} _ {0}\\right)}{q \\left(\\boldsymbol {x} _ {t} \\mid \\boldsymbol {x} _ {0}\\right)} (7) \\\\ = \\frac {\\left(\\boldsymbol {x} ^ {\\top} \\boldsymbol {Q} _ {t} \\boldsymbol {x} _ {t - 1}\\right) \\left(\\boldsymbol {x} _ {t - 1} ^ {T} \\bar {\\boldsymbol {Q}} _ {t - 1} \\boldsymbol {x} _ {0}\\right)}{\\boldsymbol {x} _ {t} ^ {\\top} \\bar {\\boldsymbol {Q}} _ {t} \\boldsymbol {x} _ {0}} (7) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 773, + 890, + 844 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with $\\bar{Q} = Q_{1}Q_{2}\\dots Q_{t}$", + "bbox": [ + 498, + 854, + 663, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Recording to Markov chain, the intermediate step can be marginalized out and the derivation of the probability of $\\boldsymbol{x}_t$", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14809", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "at arbitrary timestep directly from $\\pmb{x}_0$ can be formulated by", + "bbox": [ + 76, + 90, + 465, + 107 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\boldsymbol {x} _ {t} \\mid \\boldsymbol {x} _ {0}\\right) = \\boldsymbol {x} _ {t} ^ {\\top} \\bar {\\boldsymbol {Q}} \\boldsymbol {x} _ {0}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 199, + 116, + 468, + 135 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The cumulative transition matrix $\\bar{Q}$ and the probability $q(\\pmb{x}_t|\\pmb{x}_0)$ are then computed as", + "bbox": [ + 76, + 146, + 468, + 179 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {Q} \\boldsymbol {x} _ {0} = \\bar {\\alpha} _ {t} \\boldsymbol {x} _ {0} + (\\bar {\\gamma} - \\bar {\\beta} _ {t}) \\boldsymbol {m} + \\bar {\\beta} _ {t} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 186, + 468, + 207 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $m$ is the one-hot vector for [MASK] and [PAD], $\\bar{\\alpha}_t = \\prod_{i=1}^t \\alpha_i$ , $\\bar{\\gamma}_t = 1 - \\prod_{i=1}^t (1 - \\gamma_i)$ , and $\\bar{\\beta}_t = (1 - \\bar{\\alpha}_t - \\bar{\\gamma}_t) / K$ .", + "bbox": [ + 76, + 217, + 468, + 250 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Regarding the reverse diffusion process, we train a transformer-like [47] denoising network $p_{\\theta}(\\pmb{x}_{t-1}|\\pmb{x}_t,\\pmb{y})$ to estimate the posterior transition distribution $q(\\pmb{x}_{t-1}|\\pmb{x}_t,\\pmb{x}_0)$ . The network is trained to minimize the variational lower bound (VLB) [42]:", + "bbox": [ + 75, + 250, + 470, + 325 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {V L B} = \\mathbb {E} _ {q} \\left[ D _ {K L} \\left(q \\left(\\boldsymbol {x} _ {T} \\mid \\boldsymbol {x} _ {0}\\right) \\| p _ {\\theta} \\left(\\boldsymbol {x} _ {T}\\right)\\right) \\right] \\\\ + \\mathbb {E} _ {q} [ \\sum_ {t = 2} ^ {T} D _ {K L} (q (\\boldsymbol {x} _ {t - 1} | \\boldsymbol {x} _ {t}, \\boldsymbol {x} _ {0}) \\| p _ {\\theta} (\\boldsymbol {x} _ {t - 1} | \\boldsymbol {x} _ {t}, t)) ] \\\\ - \\log p _ {\\theta} \\left(\\boldsymbol {x} _ {0} \\mid \\boldsymbol {x} _ {1}\\right) \\tag {10} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 334, + 473, + 428 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbb{E}_q[\\cdot ]$ denotes the expectation over the joint distribution $q(\\pmb{x}_{0:T})$ .", + "bbox": [ + 75, + 429, + 470, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Priority-Centric Denoising Process", + "text_level": 1, + "bbox": [ + 76, + 468, + 380, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The designation of the noise schedule in the continuous domain, for instance, the linear schedule [20] and the cosine schedule [33], achieves the excellent performance of diffusion models. The noise can be easily controlled by the variation of Gaussian noise. For the discrete diffusion models, several noise schedules [22, 3] have been explored to control the data corruption and denoise the reverse process by choosing the transition matrix $Q_{t}$ . For text-to-motion generation, however, such a schedule assumes all motion tokens carry the same amount of information and do not consider the difference among the discrete tokens extracted from the continuous motion sequence. Intuitively, the motion generation process would be in a progressive manner, where the most important motion tokens should appear in earlier steps for laying a solid foundation when denoising the noise in the discrete domain.", + "bbox": [ + 73, + 492, + 468, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, we apply the mask-and-replace strategy in Eq. (5) to corrupt each ordinary discrete token with a probability of $\\gamma_{t}$ for masking [MASK] token and a probability of $\\beta_{t}$ for uniform diffusion to a random token $x_{k}$ , resulting in a remaining probability of $\\alpha_{t} = 1 - K\\beta_{t} - \\gamma_{t}$ for retention. When corrupting across the forward process in the discrete domain, we expect that $\\bar{\\alpha}_{t}^{i} < \\bar{\\alpha}_{t}^{j}$ if token $x_{i}$ is more informative than $x_{j}$ such that the tokens with high information emerge earlier than less informative motion tokens in the reverse process. Instead of using a normal corruption strategy with linearly increasing $\\bar{\\gamma}_{t}$ and $\\bar{\\beta}_{t}$ , we propose a", + "bbox": [ + 75, + 734, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "priority-score function $F$ to assess the relative importance of information for a motion token sequence, which enables the recovery of the most informative tokens during the reverse process.", + "bbox": [ + 496, + 90, + 892, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given an original motion token sequences $\\pmb{x}_0$ at timestep 0 with length $N$ , we aim to analyze the importance of each token $x_0^i$ in $\\pmb{x}_0$ . Based on the information entropy theory, we calculate the information entropy for each motion token $x_0^i$ as the importance score", + "bbox": [ + 496, + 152, + 893, + 227 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF \\left(x _ {0} ^ {i}\\right) = \\frac {N H \\left(x _ {0} ^ {i}\\right)}{\\sum_ {j = 1} ^ {N} H \\left(x _ {0} ^ {j}\\right)}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 239, + 892, + 280 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 500, + 291, + 544, + 303 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nH (x) = - \\sum_ {i = 1} ^ {K} p \\left(x _ {i}\\right) \\log p \\left(x _ {i}\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 304, + 892, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and $K$ denotes the number of categories belonging to $x_{i}$", + "bbox": [ + 498, + 353, + 874, + 369 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After obtaining the importance score function and setting linearly increasing schedule $\\bar{\\gamma}_t^i$ and $\\bar{\\beta}_t^i$ for all tokens, $\\bar{\\gamma}_t^i$ and $\\bar{\\beta}_t^i$ for specific token $x_0^i$ can be further updated by", + "bbox": [ + 498, + 369, + 890, + 415 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\gamma} _ {t} ^ {i} \\Leftarrow \\bar {\\gamma} _ {t} ^ {i} \\cdot \\sin \\frac {t \\pi}{T} \\cdot F \\left(x _ {0} ^ {i}\\right), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 426, + 892, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and", + "bbox": [ + 500, + 468, + 529, + 479 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\beta} ^ {i} \\Leftarrow \\bar {\\beta} ^ {i} \\cdot \\sin \\frac {t \\pi}{T} \\cdot F \\left(x _ {0} ^ {i}\\right), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 479, + 892, + 508 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $x_0^i$ is the $i$ -th token at timestep 0.", + "bbox": [ + 498, + 517, + 764, + 532 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Now we introduce two solutions for obtaining $p(x_{i})$ .", + "bbox": [ + 517, + 532, + 867, + 549 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Static assessment. Analogously to computing the entropy for each word in natural language processing, we estimate the probability $p(x_{i})$ for each motion token by counting its frequency in the quantized motion sequences over the entire dataset.", + "bbox": [ + 496, + 571, + 892, + 646 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3d0befa6afe7389516bbd25840dc6cd2e93ada0b6bc000589e1a52883fd2441f.jpg", + "image_caption": [ + "Figure 3: Illustration for dynamic assessment strategy. The gray blocks are masked tokens and other colorful blocks are motion tokens." + ], + "image_footnote": [], + "bbox": [ + 566, + 660, + 826, + 823 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14810", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dynamic assessment. Rather than counting motion token frequency and calculating the importance of each token, we further propose to learn an agent to estimate the importance of each token in the token sequences by reinforcement learning strategy. As shown in Fig. 3, given a series of complete motion tokens $\\boldsymbol{x} = \\{x_{n}\\}_{n=1}^{N}$ that are queried from the codebook at current state $s_{t} \\in S$ , the scorer samples the motion tokens $\\tilde{\\boldsymbol{x}} = \\{x_{n}\\}_{n=1}^{N'}$ and tries to minimize the reconstruction error between the original motion sequences $\\boldsymbol{m}$ and the motion sequences decoded from the sampled tokens $\\tilde{\\boldsymbol{m}}$ .", + "bbox": [ + 75, + 90, + 472, + 244 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "State includes the currently selected motion tokens $\\tilde{\\pmb{x}} = \\{x_{n}\\}_{n = 1}^{N^{\\prime}}$ , the complete motion tokens $\\pmb {x} = \\{x_{n}\\}_{n = 1}^{N}$ , and the corresponding reconstructed continuous motions $\\tilde{m}$ and $m$ . The reconstructed continuous motion sequences $\\tilde{m}$ and $m$ are obtained by decoding the motion tokens by VQ decoder. The action is to sample one motion token from the complete motion token sequence at each stage. To be specific, given a motion token sequence, the agent $\\pi_{\\theta}(a_t|s_t)$ tries to sample a motion token that can recover the continuous motion sequences with the minimum reconstruction error. The reward measures the reconstruction difference between $\\tilde{m}$ and $m$ with the minimum sample times.", + "bbox": [ + 75, + 251, + 472, + 435 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/64487833a06942ff58a25558356f6c19cec3d49745c206c3d6a61b15fa11e306.jpg", + "image_caption": [ + "Figure 4: Priority-centric denoising schedule for motion tokens." + ], + "image_footnote": [], + "bbox": [ + 89, + 460, + 455, + 588 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "After the agent is well-trained, we calculate and restore the sampling order for each motion token sequence by the agent $\\pi_{\\theta}(a_t|s_t)$ and compute the noise schedule for each motion token in the codebook by Eq. (13) and (14). Fig. 4 shows the noise schedule for different motion tokens w.r.t. the corresponding priorities. As shown in Fig. 4, high-priority tokens (orange and green curves) are encouraged to be corrupted at the end of the forward process such that the learnable reverse process follows a primary-to-secondary manner and high-priority tokens will be restored first. It is worth noting that both strategies are applied to design noise schedules for each token, which can be calculated and stored in advance such that the agent will not join the forward and reverse diffusion processes. Thus, there is no extra computational cost for the diffusion model during the training and inference stages.", + "bbox": [ + 75, + 659, + 472, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 90, + 633, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets and Evaluation Metrics", + "text_level": 1, + "bbox": [ + 500, + 114, + 785, + 130 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our experiments are conducted on two standard text-to-motion datasets for text-to-motion generation: HumanML3D [16] and KIT-ML [36]. We follow the evaluation metrics provided in [16].", + "bbox": [ + 498, + 138, + 893, + 199 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "HumanML3D. HumanML3D [16] is currently the largest 3D human motion dataset that covers a broad range of daily human actions, for instance, exercising and dancing. The dataset contains 14,616 motion sequences and 44970 text descriptions. The motion sequences are processed to 20 frame-per-second (FPS) and cropped to 10 seconds if the motion sequences are longer than 10 seconds, resulting in duration ranges from 2 to 10 seconds. For each motion clip, the corresponding number of descriptions is at least three.", + "bbox": [ + 496, + 219, + 893, + 354 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "KIT Motion-Language (KIT-ML). KIT-ML dataset [36] contains 3,911 3D human motion clips with 6,278 text descriptions. For each motion clip, one to four textual descriptions are provided. The motion sequences are collected from the KIT dataset [31] and the CMU dataset [1] with the down-sampled 12.5 FPS.", + "bbox": [ + 496, + 375, + 893, + 465 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Both of the aforementioned datasets are split into training, validation, and testing datasets with the proportions of $80\\%$ , $5\\%$ , and $15\\%$ .", + "bbox": [ + 498, + 465, + 893, + 511 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. Both our VQ-encoder and decoder consist of 4 transformer layers with 8 heads and the dimension is 512. For the HumanML3D [16] and KIT-ML [36] datasets, the motion sequences are cropped to 64 frames for training. We apply Adam with $\\beta_{1} = 0.9$ , $\\beta_{2} = 0.999$ , weight decay is 1e-4. The learning rate is 1e-4 after warmup linearly for 5 epochs. The number of tokens in the codebook is 8192. We train our VQ-VAE with a batch size of 1024 across 8 Tesla T4 for a total 100 training epochs for 8 hours.", + "bbox": [ + 496, + 532, + 893, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the discrete diffusion model, we set timesteps $T = 100$ and the network is trained using Adam [25] with $\\beta_{1} = 0.9$ , $\\beta_{2} = 0.999$ . The learning rate reaches 2e-4 after 2000 iterations of a linear warmup schedule. The transformer-based discrete diffusion model consists of 12 transformer layers with 8 heads, and the dimension is 512. The text features are extracted by pre-trained CLIP [37] model. The diffusion model is trained with a batch size of 64 across 8 Tesla T4 for 100k iterations for 36 hours.", + "bbox": [ + 496, + 667, + 893, + 804 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics. Following the evaluation protocols provided in previous works [16, 55, 44, 5], we evaluate the correspondences between motion and language using deep multimodal features with the pre-trained models in [16] by the following metrics: 1) Generation diversity: We randomly", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14811", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f9cd13004f2232ed68f65266461c6c6dc29584485240cf341a67533677a4ea85.jpg", + "table_caption": [], + "table_footnote": [ + "${}^{8}$ reports results using ground-truth motion length." + ], + "table_body": "
MethodsR-Precision ↑FID ↓MM-Dist ↓Diversity →MModality ↑
Top-1Top-2Top-3
Real motion0.511±.0030.703±.0030.797±.0020.002±.0002.974±.0089.503±.065-
Our VQ-VAE0.508±.0020.691±.0020.791±.0030.63±.0013.015±.0109.577±.081-
Our VQ-VAE w/o l20.494±.0030.685±.0020.772±.0030.70±.0013.251±.0089.525±.092-
Our VQ-VAE w/o l2, Lorth0.485±.0020.671±.0030.752±.0030.79±.0013.378±.0129.511±.095-
Seq2Seq [30]0.180±.0020.300±.0020.396±.00211.75±.0355.529±.0076.223±.061-
Language2Pose [2]0.246±.0020.387±.0020.486±.00211.02±.0465.296±.0087.676±.058-
Text2Gesture [4]0.165±.0010.267±.0020.345±.0025.012±.0306.030±.0086.409±.071-
Hier [12]0.301±.0020.425±.0020.552±.0046.532±.0245.012±.0188.332±.042-
MoCoGAN [45]0.037±.0000.072±.0010.106±.00194.41±.0219.643±.0060.462±.0080.019±.000
Dance2Music [27]0.033±.0000.065±.0010.097±.00166.98±.0168.116±.0060.725±.0110.043±.001
TM2T [17]0.424±.0030.618±.0030.729±.0021.501±.0173.467±.0118.589±.0762.424±.093
Guo et al. [16]0.455±.0030.636±.0030.736±.0021.087±.0213.347±.0089.175±.0832.219±.074
MDM [44]$--0.611±.0070.544±.0445.566±.0279.559±.0862.799±.072
MotionDiffuse [56]$0.491±.0010.681±.0010.782±.0010.630±.0013.113±.0019.410±.0491.553±.042
T2M-GPT [55]0.492±.0030.679±.0020.775±.0020.141±.0053.121±.0099.722±.0821.831±.048
MLD [5]0.481±.0030.673±.0030.772±.0020.473±.0133.196±.0109.724±.0822.413±.079
M2DM (Ours) w. linear schedule0.452±.0030.678±.0020.752±.0030.417±.0043.167±.0089.972±.0893.562±.071
M2DM (Ours) w. static assessment0.492±.0030.671±.0030.775±.0030.395±.0053.116±.0089.937±.0753.413±.035
M2DM (Ours) w. dynamic assessment0.497±.0030.682±.0020.763±.0030.352±.0053.134±.0109.926±.0733.587±.072
", + "bbox": [ + 84, + 88, + 885, + 383 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1: Comparison with the state-of-the-art methods on HumanML3D [16] test set. The evaluation metrics are evaluated by the motion encoder from Guo et al. [16]. The right row $\\rightarrow$ means the closer to the real motion the better.", + "bbox": [ + 75, + 397, + 890, + 428 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "sample 300 pairs of motions from the motion pool and extracted the selected motion features by the extractor provided by [16]. Euclidean distances of the motion pairs are computed for measuring the motion diversity. 2) R-Precision: Provided one motion representation and 32 textual descriptions, the Euclidean distances between the description feature and each motion feature in the candidates are calculated and ranked. Top-k $(k = 1,2,3)$ average accuracy of motion-to-text retrieval is reported. 3) Frechet Inception Distance (FID) [19]: FID is the principal metric to evaluate the feature descriptions between the generated motions and the ground-truth motions by the feature extractor [16]. 4) Multimodal Distance (MM-Dist): MM-Dist measures the average Euclidean distances between each text feature and the generated motion feature. 5) MModality measures the generation diversity within the same textual descriptions. Please refer to the supplementary material for a detailed introduction.", + "bbox": [ + 75, + 454, + 472, + 710 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Comparisons with state-of-the-art approaches", + "text_level": 1, + "bbox": [ + 76, + 720, + 465, + 738 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our methods with other state-of-the-art methods [30, 2, 4, 12, 45, 27, 17, 16, 44, 56, 55, 5] on the HumanML3D [16] and KIT-ML [36] datasets.", + "bbox": [ + 75, + 744, + 470, + 789 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative comparisons. For each metric, we repeat the evaluation 20 times and report the average with $95\\%$ confidence interval, followed by [16]. Most of the results are borrowed from [55]. Tab. 1 and Tab. 2 summarize the comparison results on the HumanML3D [16] and the KIT-ML [36] datasets, respectively. Firstly, the metrics scores for", + "bbox": [ + 75, + 810, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "our reconstruction motion achieve close performance compared with real motion, which suggests the distinctive and high-quality discrete motion tokens in the codebook learned by our Transformer-based VQ-VAE. The performance of our VQ-VAE degrades when the normalized function $\\ell_2$ and the orthogonal regularization term $\\mathcal{L}_{\\mathrm{orth}}$ are removed. For text-to-motion generation, our approach achieves compatible performance (R-Precision, FID, and MModality) compared to other state-of-the-art methods. Moreover, compared with MDM [44] and MotionDiffuse [56] which evaluate their performance with the ground-truth motion lengths, our model can generate motion sequences with arbitrary lengths conditioned on the given textual descriptions since the [MASK] and [PAD] tokens are introduced in the discrete diffusion process.", + "bbox": [ + 496, + 454, + 893, + 680 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Furthermore, we conduct more experiments to evaluate the generation performance conditioned on different lengths of textual descriptions. The testing dataset is split into three parts according to the length of the textual descriptions: less than 15 words, between 15 words and 30 words, and more than 30 words. Tab. 3 shows the quantitative results on the aforementioned three sub-sets. Both TM2T [17] and MLD [5] suffer degradation when the textual descriptions are long and complex, especially the descriptions are more than 30 words. Our method significantly outperforms the other two methods with various metrics and there is not much degradation when the descriptions are more complex. The quantitative results demonstrate the effectiveness of our proposed primary-to-secondary diffusion manner.", + "bbox": [ + 496, + 689, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14812", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ae6150a8e1c2a9bdf849573f0306b72d6a23f0def0aaa4aaa7b5b1caea5b8038.jpg", + "table_caption": [], + "table_footnote": [ + "${}^{8}$ reports results using ground-truth motion length." + ], + "table_body": "
MethodsR-Precision ↑FID ↓MM-Dist ↓Diversity →MModality ↑
Top-1Top-2Top-3
Real motion0.424±.0050.649±.0060.779±.0060.031±.0042.788±.01211.08±.097-
Our VQ-VAE (Recons.)0.417±.0040.621±.0030.741±.0060.413±.0092.772±.01810.851±.105-
Seq2Seq [30]0.103±.0030.178±.0050.241±.00624.86±.3487.960±.0316.744±.106-
Language2Pose [2]0.221±.0050.373±.0040.483±.0056.545±.0725.147±.0309.073±.100-
Text2Gesture [4]0.156±.0040.255±.0040.338±.00512.12±.1836.964±.0299.334±.079-
Hier [12]0.255±.0060.432±.0070.531±.0075.203±.1074.986±.0279.563±.072-
MoCoGAN [45]0.022±.0020.042±.0030.063±.00382.69±.24210.47±.0123.091±.0430.250±.009
Dance2Music [27]0.031±.0020.058±.0020.086±.003115.4±.24010.40±.0160.241±.0040.062±.002
TM2T [17]0.280±.0050.463±.0060.587±.0053.599±.1534.591±.0269.473±.1173.292±.081
Guo et al. [16]0.361±.0060.559±.0070.681±.0073.022±.1073.488±.02810.72±.1452.052±.107
MDM [44]$--0.396±.0040.497±.0219.191±.02210.847±.1091.907±.214
MotionDiffuse [56]$0.417±.0040.621±.0040.739±.0041.954±.0622.958±.00511.10±.1430.730±.013
T2M-GPT [55]0.416±.0060.627±.0060.745±.0060.514±.0293.007±.02310.921±.1081.570±.039
MLD [5]0.390±.0030.609±.0030.734±.0020.404±.0133.204±.01010.8±.0822.192±.079
M2DM (Ours) w. linear schedule0.405±.0030.629±.0050.739±.0040.502±.0493.012±.01511.375±.0793.273±.045
M2DM (Ours) w. static assessment0.417±.0060.625±.0030.741±.0060.521±.0413.024±.01811.373±.0813.317±.031
M2DM (Ours) w. dynamic assessment0.416±.0040.628±.0040.743±.0040.515±.0293.015±.01711.417±.973.325±.37
", + "bbox": [ + 84, + 88, + 885, + 358 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/df198118ee40c61ad1c53f774873c14103d6ce10cad67b2ec089f41744a4eff8.jpg", + "table_caption": [ + "Table 2: Comparison with the state-of-the-art methods on KIT-ML [36] test set. The evaluation metrics are evaluated by the motion encoder from Guo et al. [16]. The right row $\\rightarrow$ means the closer to the real motion the better." + ], + "table_footnote": [], + "table_body": "
TM2TMDMT2M-GPTMLDOurs
a person grabs something, turns around, walks forward, squats, stands up, walks forward, squats and stands up again.
a person puts both hands by their face in a defensive stance, then kicks with their right foot.
a person jumps and turns around in the air to face behind him.
a person walks forward briskly, crouches and lifts an object with both hands, puts the object down in a higher position, then stands up and turn right.
a person takes something, put it down and throws something.
", + "bbox": [ + 84, + 417, + 888, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 5: Qualitative comparison of the state-of-the-art methods on the HumanML3D [16] dataset. We compare our generations with TM2T [17], MDM [44], T2M-GPT [55], and MLD [5]. The color of human mesh goes from light to dark over time.", + "bbox": [ + 75, + 789, + 892, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative comparisons. Fig. 5 qualitatively compares the generated motions from the same textual descriptions. Most of the methods suffer from motion freezing if the tex", + "bbox": [ + 75, + 845, + 472, + 892 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tual descriptions consist of several complex commands. For example, the first row in Fig. 5 shows the generation results from a long textual description with various duplicate action", + "bbox": [ + 498, + 845, + 893, + 892 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14813", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/420cc7244abe45a33681b07f0d5cdf88593415861b117205df0de0cf0fd1f147.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Text LengthMethodsR-Precision ↑FID ↓MM-Dist ↓Diversity →MModality ↑
Top-1Top-2Top-3
AllTM2T [17]0.424±0.0030.618±0.0030.729±0.0021.501±0.0173.467±0.0118.580±0.0762.424±0.093
MLD [5]0.481±0.0030.673±0.0030.772±0.0020.473±0.0133.196±0.0109.724±0.0822.413±0.079
M2DM (Ours)0.497±0.0030.689±0.0020.763±0.0030.352±0.0053.134±0.0109.926±0.0733.587±0.072
< 15 wordsTM2T [17]0.433±0.0030.627±0.0030.738±0.0031.592±0.0173.446±0.0088.677±0.0772.520±0.051
MLD [5]0.492±0.0030.680±0.0040.779±0.0040.469±0.0143.191±0.0119.770±0.0102.586±0.086
M2DM (Ours)0.508±0.0030.685±0.0030.767±0.0040.347±0.0153.129±0.0139.915±0.0683.594±0.077
15-30 wordsTM2T [17]0.406±0.0030.596±0.0020.708±0.0021.425±0.0143.528±0.0078.000±0.0512.477±0.057
MLD [5]0.406±0.0050.592±0.0050.701±0.0060.480±0.0203.591±0.0209.089±0.0832.727±0.094
M2DM (Ours)0.493±0.0030.681±0.0040.761±0.0040.353±0.0313.135±0.0149.926±0.0733.588±0.081
>30 wordsTM2T [17]0.353±0.0090.536±0.0090.650±0.0071.779±0.0613.577±0.0247.411±0.0712.612±0.055
MLD [5]0.289±0.0100.466±0.0120.581±0.0150.947±0.0663.870±0.0398.347±0.1002.916±0.063
M2DM (Ours)0.491±0.0040.677±0.0040.758±0.0040.356±0.0383.138±0.0259.930±0.0883.585±0.071
", + "bbox": [ + 80, + 88, + 480, + 202 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 3: Comparison with the state-of-the-art methods on HumanML3D [16] test set. The evaluation metrics are evaluated by the motion encoder from Guo et al. [16]. The right row $\\rightarrow$ means the closer to the real motion the better. The first three rows are the evaluation results on the whole testing dataset. The rest are the evaluation results from textual descriptions with different lengths.", + "bbox": [ + 75, + 212, + 473, + 319 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "commands. MDM [44] and MLD [5] generate fewer semantic motions compared with the given description. With the help of compact discrete motion tokens, TM2T [17] and T2M-GPT [55] achieve better results compared with MDM [44] and MLD [5]. Our motion generation results conform to the textual descriptions and exhibit a high degree of diversity compared with other state-of-the-art methods, which validates the efficacy of our proposed method.", + "bbox": [ + 75, + 344, + 472, + 467 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.3. Ablation studies", + "text_level": 1, + "bbox": [ + 76, + 474, + 238, + 491 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We delved into the significance of various quantization techniques, as delineated in the initial four rows of Tab.1. The findings indicate that a rudimentary Transformer-based VQ-VAE struggles to reconstruct credible motion sequences, primarily due to the limited efficacy of the codebook. However, the incorporation of the $\\ell_2$ norm and $\\mathcal{L}_{\\mathrm{orth}}$ ensures that each motion token acquires a distinct motion representation. We further scrutinized the utilization of each motion token on the HumanML3D [16] test set, with the outcomes depicted in Fig.6. As evidenced by Fig.6a and 6b, both the vanilla CNN-based VQ-VAE and Transformer-based VQ-VAE grapple with sub-optimal codebook usage. This is because the tokens in the codebook aren't inherently driven to develop a distinguishing motion representation. Yet, with the aid of the $\\ell_2$ norm and $\\mathcal{L}_{\\mathrm{orth}}$ , there's a marked surge in the codebook token utilization. Moreover, when juxtaposing the codebook usage in Fig.6c with that in Fig.6d, the latter exhibits a more equitably distributed frequency, attributable to the orthogonal regularization term $\\mathcal{L}_{\\mathrm{orth}}$ .", + "bbox": [ + 75, + 498, + 473, + 787 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 799, + 196, + 814 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this study, we introduced the priority-centric motion discrete diffusion model (M2DM) tailored for text-to-motion generation. Our model excels in producing varied and life-like human motions, aligning seamlessly with the input text. This is achieved by mastering a discrete motion representa", + "bbox": [ + 75, + 824, + 472, + 902 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/fc329d554b712ebab8445885af79b588165483f118280db747c3031a33d97614.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 88, + 694, + 183 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/28883f5084cde44709e4afc09a8ae2903a48ef63c332b77913d0e163e9082e7b.jpg", + "image_caption": [ + "(a) 1D-CNN VQ-VAE.", + "Figure 6: Codebook usage for different training strategies on HumanML3D [16] test set. We train our VQ-VAE (Reconstruction) with different training strategy on the HumanML3D [16] dataset." + ], + "image_footnote": [], + "bbox": [ + 500, + 205, + 694, + 299 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/c0e1017151f31bbe46a5760b61b3892cd922ab459b8f8b4271862dbc78c61cd1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 94, + 890, + 183 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/e99bc9909e6b52f64dded8cc3908bfbee41524111947c4e675d4ffad96c19899.jpg", + "image_caption": [ + "(c) Our VQ-VAE w. $\\ell_2$ norm.", + "(b) Our VQ-VAE.", + "(d) Our VQ-VAE w. $\\ell_2$ and $\\mathcal{L}_{\\mathrm{orth}}$" + ], + "image_footnote": [], + "bbox": [ + 697, + 205, + 890, + 297 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "tion through a Transformer-based VQ-VAE and implementing a priority-informed noise schedule within the motion discrete diffusion framework. Additionally, we unveiled two innovative techniques for gauging the priority or significance of each motion token. Experimental evaluations across two datasets underscore our model's competitive edge, outpacing existing methodologies in R-Precision and diversity, particularly with intricate textual narratives.", + "bbox": [ + 496, + 419, + 895, + 541 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 556, + 660, + 574 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This project is supported by the Ministry of Education, Singapore, under its Academic Research Fund Tier 2 (Award Number: MOE-T2EP20122-0006).", + "bbox": [ + 498, + 584, + 893, + 628 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 645, + 596, + 660 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Cmu graphics lab motion capture database. http://mocap.cs.cmu.edu/.6", + "[2] Chaitanya Ahuja and Louis-Philippe Morency. 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Motiondiffuse: Text-driven human motion generation with diffusion model. arXiv preprint arXiv:2208.15001, 2022. 1, 3, 7, 8" + ], + "bbox": [ + 501, + 92, + 892, + 686 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "14816", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Priority-Centric Human Motion Generation in Discrete Latent Space/58c7e478-f288-424e-a702-051324564633_model.json b/2023/Priority-Centric Human Motion Generation in Discrete Latent Space/58c7e478-f288-424e-a702-051324564633_model.json new file mode 100644 index 0000000000000000000000000000000000000000..db128de773b9b703593615ff92c790e8a974f286 --- /dev/null +++ b/2023/Priority-Centric Human Motion Generation in Discrete Latent Space/58c7e478-f288-424e-a702-051324564633_model.json @@ -0,0 +1,2411 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.807, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.137, + 0.131, + 0.834, + 0.154 + ], + "angle": 0, + "content": "Priority-Centric Human Motion Generation in Discrete Latent Space" + }, + { + "type": "text", + "bbox": [ + 0.16, + 0.18, + 0.812, + 0.201 + ], + "angle": 0, + "content": "Hanyang Kong\\(^{1}\\), Kehong Gong\\(^{1}\\), Dongze Lian\\(^{1}\\), Michael Bi Mi\\(^{2}\\), Xinchao Wang\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.22, + 0.205, + 0.751, + 0.224 + ], + "angle": 0, + "content": "\\(^{1}\\)National University of Singapore \\(^{2}\\)Huawei International Pte Ltd" + }, + { + "type": "text", + "bbox": [ + 0.207, + 0.226, + 0.765, + 0.242 + ], + "angle": 0, + "content": "{hanyang.k, gongkehong}@u.nus.edu {dongze, xinchao}@nus.edu.sg" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.276, + 0.314, + 0.293 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.308, + 0.474, + 0.718 + ], + "angle": 0, + "content": "Text-to-motion generation is a formidable task, aiming to produce human motions that align with the input text while also adhering to human capabilities and physical laws. While there have been advancements in diffusion models, their application in discrete spaces remains underexplored. Current methods often overlook the varying significance of different motions, treating them uniformly. It is essential to recognize that not all motions hold the same relevance to a particular textual description. Some motions, being more salient and informative, should be given precedence during generation. In response, we introduce a Priority-Centric Motion Discrete Diffusion Model (M2DM), which utilizes a Transformer-based VQ-VAE to derive a concise, discrete motion representation, incorporating a global self-attention mechanism and a regularization term to counteract code collapse. We also present a motion discrete diffusion model that employs an innovative noise schedule, determined by the significance of each motion token within the entire motion sequence. This approach retains the most salient motions during the reverse diffusion process, leading to more semantically rich and varied motions. Additionally, we formulate two strategies to gauge the importance of motion tokens, drawing from both textual and visual indicators. Comprehensive experiments on the HumanML3D and KIT-ML datasets confirm that our model surpasses existing techniques in fidelity and diversity, particularly for intricate textual descriptions." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.746, + 0.21, + 0.763 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.771, + 0.471, + 0.879 + ], + "angle": 0, + "content": "Generating realistic and diverse 3D human motions under various conditions e.g., action labels [34, 18], natural language descriptions [55, 17, 5, 56], and musical cues [27, 28, 29], presents a significant challenge across multiple domains, including gaming, filmmaking, and robotic animation. Notably, motion generation based on language descriptions has garnered substantial interest, given its promise" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.278, + 0.895, + 0.293 + ], + "angle": 0, + "content": "for enhancing realism and broadening practical applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.294, + 0.895, + 0.46 + ], + "angle": 0, + "content": "However, generating a high-quality motion is not trivial due to the inherent modality gap and the complex mapping between text and motion modalities. Previous works [35, 43] align the latent feature space between text and motion modalities. For instance, TEMOS [35] aligns the text and motion feature by learning text and motion encoders. MotionClip [43] aligns the human motion manifold to CLIP [37] space for infusing semantic knowledge of CLIP into the motion extractor. Despite these advancements, they might encounter performance degradation when dealing with complex textual descriptions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.896, + 0.627 + ], + "angle": 0, + "content": "To process these complex textual descriptions, some text-to-motion methods are proposed. State-of-the-art approaches such as TM2T [17] and T2M-GPT [55] use vector-quantized autoencoder (VQ-VAE) [46] to learn a discrete and compact motion representation, followed by a translation model [38, 47] to map the text modality to the motion modality. With the popularity and the superior performance in the generation tasks of diffusion models [20], MDM [44] and MLD [5] are proposed to learn conditioned diffusion models on the raw motion representation space and the latent feature space, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.897, + 0.869 + ], + "angle": 0, + "content": "While there have been promising advancements, two primary issues remain unresolved: i) The aforementioned diffusion methods, namely MDM [44] and MLD [5], predominantly address the latent feature within a continuous space. Although VQ-VAE-inspired architectures have made considerable strides in motion generation [55, 17], particularly with the support of discrete and compact motion representations, the integration of the diffusion model into a discrete space remains inadequately explored. ii) Discrete diffusion models employed in prior studies [15, 14, 22] treat all tokens uniformly. This approach presupposes that every token conveys an equivalent amount of information, neglecting the inherent disparities among tokens within a sequence. A more intuitive generative approach for humans would involve a progressive hierarchy, commencing with overarching concepts and gradually delving into finer details." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.895, + 0.902 + ], + "angle": 0, + "content": "To address the aforementioned challenges, we introduce a priority-centric motion discrete diffusion model (M2DM)" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.338, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author: xinchao@nus.edu.sg" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "14806" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.092, + 0.268, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.092, + 0.44, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.204, + 0.446, + 0.23 + ], + "angle": 0, + "content": "a person steps forward with left leg walking in a circle counterclockwise motion swinging arms and returns back." + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.234, + 0.252, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.271, + 0.237, + 0.449, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.085, + 0.351, + 0.448, + 0.378 + ], + "angle": 0, + "content": "a person runs forward, then turns around and walks in the opposite direction while swinging their right arm." + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.089, + 0.877, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.505, + 0.204, + 0.854, + 0.23 + ], + "angle": 0, + "content": "a man gets up from the ground, walks around in a circle and then sits down on the ground again." + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.248, + 0.696, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.246, + 0.862, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.351, + 0.889, + 0.377 + ], + "angle": 0, + "content": "a man postures his arms like holding a dance partner and dances the waltz from the right hand side to the left hand side." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.39, + 0.893, + 0.421 + ], + "angle": 0, + "content": "Figure 1: Our Priority-Centric Motion Discrete Diffusion Model (M2DM) generates diverse and precise human motions given complex textual descriptions. The color of human mesh goes from light to dark over time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.448, + 0.473, + 0.689 + ], + "angle": 0, + "content": "designed to generate motion sequences from textual descriptions, progressing in a primary to secondary manner. Initially, we employ a Transformer-based VQ-VAE, which is adept at learning a concise, discrete motion representation through the global self-attention mechanism. To circumvent code collapse and guarantee the optimal utilization of each motion token within the codebook, a regularization term is incorporated during the VQ-VAE training phase. Furthermore, we craft a noise schedule wherein individual tokens within a sequence are allocated varying corruption probabilities, contingent on their respective priorities during the forward process. Specifically, tokens of higher priority are slated for corruption towards the latter stages of the forward process. This ensures that the subsequent learnable reverse process adheres to a primary-to-secondary sequence, with top-priority tokens being reinstated foremost." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.473, + 0.901 + ], + "angle": 0, + "content": "To discern the significance of motion tokens within a sequence, we introduce two evaluative strategies: static assessment and dynamic assessment. 1) Static assessment: Drawing inspiration from the neural language domain, where the significance of individual words is gauged by their entropy across datasets, we calculate the entropy of each motion token across the entire motion dataset. 2) Dynamic assessment: We cultivate an agent specifically to dynamically gauge the importance of tokens within a sequence. Given a discrete motion token sequence, the agent masks one token at each iteration. These masked token sequences are then fed into the VQ decoder for continuous motion reconstruction. The agent's objective is to curtail the cumulative reconstruction discrepancy between the original and the reconstructed mo" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.895, + 0.612 + ], + "angle": 0, + "content": "tions at every phase. This is achieved using a reinforcement learning [23] (RL) strategy, facilitating the agent's identification of motion tokens that convey minimal information within a sequence—a process we term dynamic analysis. Our priority-centric discrete diffusion model has showcased commendable generative prowess, especially when dealing with intricate textual descriptions. Through rigorous testing, our method has proven its mettle, consistently matching or surpassing the performance of prevailing text-to-motion generation techniques on the HumanML3D and KIT-ML datasets." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.614, + 0.813, + 0.628 + ], + "angle": 0, + "content": "We summarize our contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.636, + 0.894, + 0.696 + ], + "angle": 0, + "content": "- To capture long-range dependencies in the motion sequences, we apply Transformer as the architecture of VQ-VAE. Besides, a regularization term is applied to increase the usage of tokens in the codebook." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.705, + 0.894, + 0.779 + ], + "angle": 0, + "content": "- We design a priority-centric scheme for human motion generation in the discrete latent space. To enhance the performance given complex descriptions, we design a novel priority-centric scheme for the discrete diffusion model." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.788, + 0.894, + 0.833 + ], + "angle": 0, + "content": "- Our proposed priority-centric M2DM achieves state-of-the-art performance on the HumanML3D [16] and KIT-ML [36] datasets." + }, + { + "type": "list", + "bbox": [ + 0.52, + 0.636, + 0.894, + 0.833 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.845, + 0.642, + 0.861 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.895, + 0.901 + ], + "angle": 0, + "content": "VQ-VAE. Vector Quantized Variational Autoencoder (VQ-VAE) [46] aims to minimize reconstruction error with dis" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14807" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.364 + ], + "angle": 0, + "content": "crete representations by training a variational autoencoder. VQ-VAE achieves promising performance on generative tasks, such as text-to-image generation [39, 52], music generation [7], unconditional image synthesis [9], etc. For motion generation tasks, most of the methods [17, 55] tokenize the continuous motion representation by the 1D-CNN network. Since the motion style varies from person to person and the number of action combinations is almost infinite, it is essential to extract discriminative and distinctive motion features from the raw motion representations. Moreover, raw motion representation is much more redundant compared with neural language, it is feasible to represent a motion sequence using few motion tokens from a global perspective. To this end, we introduce a transformer-based VQ-VAE and several techniques are applied to balance the usage of each motion token in the codebook and prevent the codebook from collapsing, i.e., only a small proportion of codes in the codebook are activated." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.383, + 0.473, + 0.581 + ], + "angle": 0, + "content": "Diffusion models. Diffusion generative models are first proposed in [42] and achieve promising results on image generation [8, 33, 21, 20, 50, 48, 53, 11, 10]. Discrete diffusion model is first proposed by [42] and several works [22, 14] apply the discrete diffusion model for text generation. D3PM [3] then applies the discrete diffusion model to the image generation task. For motion generation tasks, several works [24, 56, 44, 5] introduce diffusion models to generate diverse motion sequences from textual descriptions. In this work, we first introduce the discrete diffusion model for text-to-motion generation tasks which achieves promising results, especially for long text descriptions with several action commands." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.473, + 0.901 + ], + "angle": 0, + "content": "Conditional human motion synthesis Compared with unconditional Human motion synthesis, human motion synthesis conditioned on various conditions, such as textual description [55, 17, 5, 56], music [27, 28, 29, 13], and actions [34, 18] is more challenging due to the huge gap between two different domains. A common strategy of conditioned human motion synthesis is to employ generative models, for instance, conditional VAE [26], and learn a latent motion representation. Text-to-motion task is more challenging because neural language is a type of information highly refined by human beings, whereas human motion is much more redundant. Most recently, several promising works [5, 16, 17, 56, 55] are proposed for text-to-motion tasks. T2M-GPT [55] and TM2T [17] regard the text-to-motion task as a translation problem. They first train a VQ-VAE [46] to tokenize the motion sequences into motion tokens, and Recurrent Neural Networks (RNN) [32], Transformer [47, 51, 49, 41, 40, 54], or GPT-like [38] models are further applied to 'translate' textual descriptions to motions. Moreover, diffusion-based [20] models are introduced for" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.228 + ], + "angle": 0, + "content": "text-to-motion generation by [56, 6, 44, 5] in the contentious space. In this work, to the best of our knowledge, we are the first ones to diffuse the motion representation in the discrete latent space. Moreover, we notice that different motion clips in a whole motion sequence play various roles, for instance, stepping forward is more important than swinging arms for a running motion. We further design a diffuse schedule such that the generation process follows a from-primary-to-secondary manner." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.243, + 0.593, + 0.259 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.268, + 0.673, + 0.283 + ], + "angle": 0, + "content": "3.1. Motion Tokenizer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.292, + 0.892, + 0.382 + ], + "angle": 0, + "content": "The motion tokenizer aims to learn a codebook that can represent a wide range of motion sequences with the priority awareness of motion tokens. To achieve this, we propose a transformer-based VQ-VAE that leverages self-attention to capture long-range dependencies between motion frames and learns a stable and diverse codebook." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.384, + 0.895, + 0.581 + ], + "angle": 0, + "content": "Fig. 2 shows the overview of our motion tokenizer. Given a motion sequence \\( X \\in \\mathbb{R}^{T \\times d} \\) with \\( T \\) frames and \\( d \\) dimensional motion representation, we reconstruct the motion sequence using a transformer autoencoder and learn an informative codebook \\( Z = \\{z_k\\}_{k=1}^K \\) with \\( K \\) entries. We use the transformer encoder \\( E \\) to compute the latent motion features \\( \\boldsymbol{b} = \\{b_t\\}_{t=1}^T \\in \\mathbb{R}^{T \\times d} \\), where \\( d \\) is the dimension of the latent features. Then for each feature \\( b_t \\), we query the codebook \\( Z \\) by measuring the distance between feature \\( b_t \\) and each entry in the codebook \\( Z \\). To improve the codebook usage and avoid dead codes, we first normalize \\( b_t \\) and \\( z_t \\) and then measure the Euclidean distance between two normalized vectors in the unit sphere coordinate, which is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.595, + 0.892, + 0.623 + ], + "angle": 0, + "content": "\\[\n\\hat {b} _ {t} = \\underset {b _ {t} \\in \\boldsymbol {b}} {\\arg \\min } \\| \\ell_ {2} (b _ {t}) - \\ell_ {2} \\left(z _ {k}\\right) \\| _ {2} ^ {2}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.63, + 0.757, + 0.645 + ], + "angle": 0, + "content": "where \\(\\ell_2\\) is the \\(l_{2}\\) normalized function." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.646, + 0.894, + 0.691 + ], + "angle": 0, + "content": "The standard optimization goal consists of three parts: the reconstruction loss, the embedding loss, and the commitment loss, which is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.702, + 0.892, + 0.753 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {v q} = \\left\\| X - \\tilde {X} \\right\\| _ {2} ^ {2} + \\left\\| Z - s g [ \\hat {Z} ] \\right\\| _ {2} ^ {2} \\tag {2} \\\\ + \\eta | | s g [ Z ] - \\hat {Z} | | _ {2} ^ {2}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.84 + ], + "angle": 0, + "content": "Moreover, to achieve an informative codebook with diverse and high usage of its entries, we apply an orthogonal regularization. Specifically, we calculate the distance between each pair of codebook entries to enforce orthogonality among all the codebook entries:" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.852, + 0.892, + 0.876 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {o r t h}} (Z) = \\left\\| \\ell_ {2} (Z) ^ {\\top} \\ell_ {2} (Z) - I _ {K} \\right\\| _ {2} ^ {2}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.763, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_2\\) is the \\(l_{2}\\) normalized function." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14808" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.089, + 0.881, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.318, + 0.896, + 0.427 + ], + "angle": 0, + "content": "Figure 2: Overview of our framework for our Motion Discrete Diffusion Model (M2DM). M2DM consists of a Transformer-based VQ-VAE (Sec. 3.1) and a discrete diffusion model (Sec. 3.2). Firstly, the Transformer-based motion tokenizer is learned to discretize motion sequences into tokens and reconstruct original motion sequences from tokens queried from the learnable codebook. Then the discrete diffusion model is learned to generate diverse motions conditioned on the textual descriptions. Two priority assessment strategies (Sec. 3.3) are applied to mask or replace motion tokens with less information at the beginning of the forward diffusion process and the most important motion tokens are corrupted in the last few diffusion steps. The diffusion model learns to restore the original motion token index conditioned on the given textual descriptions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.451, + 0.473, + 0.48 + ], + "angle": 0, + "content": "Therefore, the overall training objective of vector quantization is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.503, + 0.47, + 0.553 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {v q} = \\left\\| X - \\tilde {X} \\right\\| _ {2} ^ {2} + \\| Z - s g [ \\hat {Z} ] \\| _ {2} ^ {2} \\tag {4} \\\\ + \\eta | | s g [ Z ] - \\hat {Z} | | _ {2} ^ {2} + \\delta \\mathcal {L} _ {\\text {o r t h}} (Z), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.581, + 0.472, + 0.613 + ], + "angle": 0, + "content": "where \\(\\tilde{X} = D(\\pmb {b})\\) \\(D\\) is the decoder, \\(sg[\\cdot ]\\) denotes the stopgradient operation, \\(\\eta\\) and \\(\\delta\\) are the weighting scalars." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.644, + 0.313, + 0.658 + ], + "angle": 0, + "content": "3.2. Discrete Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.675, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Generally speaking, the forward discrete diffusion process corrupts each element \\( x_{t} \\) at timestep \\( t \\) with \\( K \\) categories via fixed Markov chain \\( q(x_{t}|x_{t - 1}) \\), for instance, replace some tokens of \\( x_{t - 1} \\) or mask the token directly. After a fixed number of \\( T \\) timesteps, the forward process yields a sequence of increasingly noisy discrete tokens \\( z_{1},\\ldots ,z_{T} \\) of the same dimension of \\( z_{0} \\) and \\( z_{T} \\) becomes pure noise token. For the denoising procedure, the real \\( x_0 \\) is restored sequentially based on the pure noisy token \\( z_{T} \\). To be specific, for scalar random variable with \\( K \\) categories \\( x_{t},x_{t - 1}\\in 1,\\dots K \\), the forward transition probabilities can be represented by the transition matrices \\( [Q_{t}]_{ij} = q(x_{t} = i|x_{t - 1} = j)\\in \\mathbb{R}^{(K + 1)\\times (K + 1)} \\). \\( [Q_{t}]_{i,j} \\) is the Markov transition matrix from state \\( t \\) to state \\( t - 1 \\) that is applied to each token in the sequence independently, which" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.451, + 0.62, + 0.464 + ], + "angle": 0, + "content": "can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.535, + 0.473, + 0.893, + 0.562 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {Q} _ {t} = \\left[ \\begin{array}{c c c c c} \\alpha_ {t} + \\beta_ {t} & \\beta_ {t} & \\beta_ {t} & \\dots & 0 \\\\ \\beta_ {t} & \\alpha_ {t} + \\beta_ {t} & \\beta_ {t} & \\dots & 0 \\\\ \\beta_ {t} & \\beta_ {t} & \\alpha_ {t} + \\beta_ {t} & \\dots & 0 \\\\ \\vdots & \\vdots & \\vdots & & \\vdots \\\\ \\gamma_ {t} & \\gamma_ {t} & \\gamma_ {t} & \\dots & 1 \\end{array} \\right], \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.572, + 0.893, + 0.648 + ], + "angle": 0, + "content": "where \\(\\alpha_{t} \\in [0,1]\\) is the probability of retaining the token, \\(\\gamma_{t}\\) is the probability of replacing the original token to [MASK] token, leaving the probability \\(\\beta_{t} = (1 - \\alpha_{t} - \\gamma_{t}) / K\\) to be diffused. The forward Markov diffusion process for the whole token sequence is written as," + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.66, + 0.893, + 0.677 + ], + "angle": 0, + "content": "\\[\nq \\left(\\boldsymbol {x} _ {t} \\mid \\boldsymbol {x} _ {t - 1}\\right) = \\operatorname {C a t} (\\boldsymbol {x}; \\boldsymbol {p} = \\boldsymbol {x} _ {t - 1} \\boldsymbol {Q} _ {t}) = \\boldsymbol {x} _ {t} \\boldsymbol {Q} _ {t} \\boldsymbol {x} _ {t - 1}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.734 + ], + "angle": 0, + "content": "where \\(\\pmb{x}\\) is the one-hot row vector identifying the token index and \\(\\operatorname{Cat}(\\pmb{x};\\pmb{p})\\) is a categorical distribution over the one-hot vector \\(\\pmb{x}_t\\) with probabilities \\(\\pmb{p}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.734, + 0.892, + 0.763 + ], + "angle": 0, + "content": "Starting from the initial step \\( x_0 \\), the posterior diffusion process is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.774, + 0.892, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} q \\left(\\boldsymbol {x} _ {t - 1} \\mid \\boldsymbol {x} _ {t}, \\boldsymbol {x} _ {0}\\right) = \\frac {q \\left(\\boldsymbol {x} _ {t} \\mid \\boldsymbol {x} _ {t - 1} , \\boldsymbol {x} _ {0}\\right) q \\left(\\boldsymbol {x} _ {t - 1} , \\boldsymbol {x} _ {0}\\right)}{q \\left(\\boldsymbol {x} _ {t} \\mid \\boldsymbol {x} _ {0}\\right)} (7) \\\\ = \\frac {\\left(\\boldsymbol {x} ^ {\\top} \\boldsymbol {Q} _ {t} \\boldsymbol {x} _ {t - 1}\\right) \\left(\\boldsymbol {x} _ {t - 1} ^ {T} \\bar {\\boldsymbol {Q}} _ {t - 1} \\boldsymbol {x} _ {0}\\right)}{\\boldsymbol {x} _ {t} ^ {\\top} \\bar {\\boldsymbol {Q}} _ {t} \\boldsymbol {x} _ {0}} (7) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.855, + 0.665, + 0.871 + ], + "angle": 0, + "content": "with \\(\\bar{Q} = Q_{1}Q_{2}\\dots Q_{t}\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Recording to Markov chain, the intermediate step can be marginalized out and the derivation of the probability of \\( \\boldsymbol{x}_t \\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14809" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.467, + 0.108 + ], + "angle": 0, + "content": "at arbitrary timestep directly from \\( \\pmb{x}_0 \\) can be formulated by" + }, + { + "type": "equation", + "bbox": [ + 0.2, + 0.117, + 0.47, + 0.136 + ], + "angle": 0, + "content": "\\[\nq \\left(\\boldsymbol {x} _ {t} \\mid \\boldsymbol {x} _ {0}\\right) = \\boldsymbol {x} _ {t} ^ {\\top} \\bar {\\boldsymbol {Q}} \\boldsymbol {x} _ {0}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.147, + 0.47, + 0.18 + ], + "angle": 0, + "content": "The cumulative transition matrix \\(\\bar{Q}\\) and the probability \\(q(\\pmb{x}_t|\\pmb{x}_0)\\) are then computed as" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.188, + 0.47, + 0.208 + ], + "angle": 0, + "content": "\\[\n\\bar {Q} \\boldsymbol {x} _ {0} = \\bar {\\alpha} _ {t} \\boldsymbol {x} _ {0} + (\\bar {\\gamma} - \\bar {\\beta} _ {t}) \\boldsymbol {m} + \\bar {\\beta} _ {t} \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.218, + 0.47, + 0.25 + ], + "angle": 0, + "content": "where \\(m\\) is the one-hot vector for [MASK] and [PAD], \\(\\bar{\\alpha}_t = \\prod_{i=1}^t \\alpha_i\\), \\(\\bar{\\gamma}_t = 1 - \\prod_{i=1}^t (1 - \\gamma_i)\\), and \\(\\bar{\\beta}_t = (1 - \\bar{\\alpha}_t - \\bar{\\gamma}_t) / K\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.25, + 0.471, + 0.326 + ], + "angle": 0, + "content": "Regarding the reverse diffusion process, we train a transformer-like [47] denoising network \\( p_{\\theta}(\\pmb{x}_{t-1}|\\pmb{x}_t,\\pmb{y}) \\) to estimate the posterior transition distribution \\( q(\\pmb{x}_{t-1}|\\pmb{x}_t,\\pmb{x}_0) \\). The network is trained to minimize the variational lower bound (VLB) [42]:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.335, + 0.474, + 0.429 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {V L B} = \\mathbb {E} _ {q} \\left[ D _ {K L} \\left(q \\left(\\boldsymbol {x} _ {T} \\mid \\boldsymbol {x} _ {0}\\right) \\| p _ {\\theta} \\left(\\boldsymbol {x} _ {T}\\right)\\right) \\right] \\\\ + \\mathbb {E} _ {q} [ \\sum_ {t = 2} ^ {T} D _ {K L} (q (\\boldsymbol {x} _ {t - 1} | \\boldsymbol {x} _ {t}, \\boldsymbol {x} _ {0}) \\| p _ {\\theta} (\\boldsymbol {x} _ {t - 1} | \\boldsymbol {x} _ {t}, t)) ] \\\\ - \\log p _ {\\theta} \\left(\\boldsymbol {x} _ {0} \\mid \\boldsymbol {x} _ {1}\\right) \\tag {10} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.472, + 0.462 + ], + "angle": 0, + "content": "where \\(\\mathbb{E}_q[\\cdot ]\\) denotes the expectation over the joint distribution \\(q(\\pmb{x}_{0:T})\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.469, + 0.382, + 0.486 + ], + "angle": 0, + "content": "3.3. Priority-Centric Denoising Process" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.493, + 0.47, + 0.734 + ], + "angle": 0, + "content": "The designation of the noise schedule in the continuous domain, for instance, the linear schedule [20] and the cosine schedule [33], achieves the excellent performance of diffusion models. The noise can be easily controlled by the variation of Gaussian noise. For the discrete diffusion models, several noise schedules [22, 3] have been explored to control the data corruption and denoise the reverse process by choosing the transition matrix \\( Q_{t} \\). For text-to-motion generation, however, such a schedule assumes all motion tokens carry the same amount of information and do not consider the difference among the discrete tokens extracted from the continuous motion sequence. Intuitively, the motion generation process would be in a progressive manner, where the most important motion tokens should appear in earlier steps for laying a solid foundation when denoising the noise in the discrete domain." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Specifically, we apply the mask-and-replace strategy in Eq. (5) to corrupt each ordinary discrete token with a probability of \\(\\gamma_{t}\\) for masking [MASK] token and a probability of \\(\\beta_{t}\\) for uniform diffusion to a random token \\(x_{k}\\), resulting in a remaining probability of \\(\\alpha_{t} = 1 - K\\beta_{t} - \\gamma_{t}\\) for retention. When corrupting across the forward process in the discrete domain, we expect that \\(\\bar{\\alpha}_{t}^{i} < \\bar{\\alpha}_{t}^{j}\\) if token \\(x_{i}\\) is more informative than \\(x_{j}\\) such that the tokens with high information emerge earlier than less informative motion tokens in the reverse process. Instead of using a normal corruption strategy with linearly increasing \\(\\bar{\\gamma}_{t}\\) and \\(\\bar{\\beta}_{t}\\), we propose a" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.893, + 0.152 + ], + "angle": 0, + "content": "priority-score function \\( F \\) to assess the relative importance of information for a motion token sequence, which enables the recovery of the most informative tokens during the reverse process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.153, + 0.894, + 0.228 + ], + "angle": 0, + "content": "Given an original motion token sequences \\( \\pmb{x}_0 \\) at timestep 0 with length \\( N \\), we aim to analyze the importance of each token \\( x_0^i \\) in \\( \\pmb{x}_0 \\). Based on the information entropy theory, we calculate the information entropy for each motion token \\( x_0^i \\) as the importance score" + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.241, + 0.893, + 0.281 + ], + "angle": 0, + "content": "\\[\nF \\left(x _ {0} ^ {i}\\right) = \\frac {N H \\left(x _ {0} ^ {i}\\right)}{\\sum_ {j = 1} ^ {N} H \\left(x _ {0} ^ {j}\\right)}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.292, + 0.545, + 0.304 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.593, + 0.305, + 0.893, + 0.346 + ], + "angle": 0, + "content": "\\[\nH (x) = - \\sum_ {i = 1} ^ {K} p \\left(x _ {i}\\right) \\log p \\left(x _ {i}\\right), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.354, + 0.875, + 0.37 + ], + "angle": 0, + "content": "and \\(K\\) denotes the number of categories belonging to \\(x_{i}\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.37, + 0.892, + 0.416 + ], + "angle": 0, + "content": "After obtaining the importance score function and setting linearly increasing schedule \\(\\bar{\\gamma}_t^i\\) and \\(\\bar{\\beta}_t^i\\) for all tokens, \\(\\bar{\\gamma}_t^i\\) and \\(\\bar{\\beta}_t^i\\) for specific token \\(x_0^i\\) can be further updated by" + }, + { + "type": "equation", + "bbox": [ + 0.609, + 0.428, + 0.893, + 0.457 + ], + "angle": 0, + "content": "\\[\n\\bar {\\gamma} _ {t} ^ {i} \\Leftarrow \\bar {\\gamma} _ {t} ^ {i} \\cdot \\sin \\frac {t \\pi}{T} \\cdot F \\left(x _ {0} ^ {i}\\right), \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.469, + 0.53, + 0.481 + ], + "angle": 0, + "content": "and" + }, + { + "type": "equation", + "bbox": [ + 0.609, + 0.481, + 0.893, + 0.51 + ], + "angle": 0, + "content": "\\[\n\\bar {\\beta} ^ {i} \\Leftarrow \\bar {\\beta} ^ {i} \\cdot \\sin \\frac {t \\pi}{T} \\cdot F \\left(x _ {0} ^ {i}\\right), \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.518, + 0.766, + 0.534 + ], + "angle": 0, + "content": "where \\(x_0^i\\) is the \\(i\\)-th token at timestep 0." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.534, + 0.868, + 0.55 + ], + "angle": 0, + "content": "Now we introduce two solutions for obtaining \\( p(x_{i}) \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.572, + 0.893, + 0.647 + ], + "angle": 0, + "content": "Static assessment. Analogously to computing the entropy for each word in natural language processing, we estimate the probability \\( p(x_{i}) \\) for each motion token by counting its frequency in the quantized motion sequences over the entire dataset." + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.661, + 0.827, + 0.824 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.836, + 0.893, + 0.88 + ], + "angle": 0, + "content": "Figure 3: Illustration for dynamic assessment strategy. The gray blocks are masked tokens and other colorful blocks are motion tokens." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14810" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.246 + ], + "angle": 0, + "content": "Dynamic assessment. Rather than counting motion token frequency and calculating the importance of each token, we further propose to learn an agent to estimate the importance of each token in the token sequences by reinforcement learning strategy. As shown in Fig. 3, given a series of complete motion tokens \\( \\boldsymbol{x} = \\{x_{n}\\}_{n=1}^{N} \\) that are queried from the codebook at current state \\( s_{t} \\in S \\), the scorer samples the motion tokens \\( \\tilde{\\boldsymbol{x}} = \\{x_{n}\\}_{n=1}^{N'} \\) and tries to minimize the reconstruction error between the original motion sequences \\( \\boldsymbol{m} \\) and the motion sequences decoded from the sampled tokens \\( \\tilde{\\boldsymbol{m}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.252, + 0.473, + 0.436 + ], + "angle": 0, + "content": "State includes the currently selected motion tokens \\(\\tilde{\\pmb{x}} = \\{x_{n}\\}_{n = 1}^{N^{\\prime}}\\), the complete motion tokens \\(\\pmb {x} = \\{x_{n}\\}_{n = 1}^{N}\\), and the corresponding reconstructed continuous motions \\(\\tilde{m}\\) and \\(m\\). The reconstructed continuous motion sequences \\(\\tilde{m}\\) and \\(m\\) are obtained by decoding the motion tokens by VQ decoder. The action is to sample one motion token from the complete motion token sequence at each stage. To be specific, given a motion token sequence, the agent \\(\\pi_{\\theta}(a_t|s_t)\\) tries to sample a motion token that can recover the continuous motion sequences with the minimum reconstruction error. The reward measures the reconstruction difference between \\(\\tilde{m}\\) and \\(m\\) with the minimum sample times." + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.461, + 0.456, + 0.589 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.63 + ], + "angle": 0, + "content": "Figure 4: Priority-centric denoising schedule for motion tokens." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.473, + 0.902 + ], + "angle": 0, + "content": "After the agent is well-trained, we calculate and restore the sampling order for each motion token sequence by the agent \\(\\pi_{\\theta}(a_t|s_t)\\) and compute the noise schedule for each motion token in the codebook by Eq. (13) and (14). Fig. 4 shows the noise schedule for different motion tokens w.r.t. the corresponding priorities. As shown in Fig. 4, high-priority tokens (orange and green curves) are encouraged to be corrupted at the end of the forward process such that the learnable reverse process follows a primary-to-secondary manner and high-priority tokens will be restored first. It is worth noting that both strategies are applied to design noise schedules for each token, which can be calculated and stored in advance such that the agent will not join the forward and reverse diffusion processes. Thus, there is no extra computational cost for the diffusion model during the training and inference stages." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.634, + 0.108 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.115, + 0.787, + 0.131 + ], + "angle": 0, + "content": "4.1. Datasets and Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.139, + 0.895, + 0.2 + ], + "angle": 0, + "content": "Our experiments are conducted on two standard text-to-motion datasets for text-to-motion generation: HumanML3D [16] and KIT-ML [36]. We follow the evaluation metrics provided in [16]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.22, + 0.895, + 0.356 + ], + "angle": 0, + "content": "HumanML3D. HumanML3D [16] is currently the largest 3D human motion dataset that covers a broad range of daily human actions, for instance, exercising and dancing. The dataset contains 14,616 motion sequences and 44970 text descriptions. The motion sequences are processed to 20 frame-per-second (FPS) and cropped to 10 seconds if the motion sequences are longer than 10 seconds, resulting in duration ranges from 2 to 10 seconds. For each motion clip, the corresponding number of descriptions is at least three." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.376, + 0.895, + 0.466 + ], + "angle": 0, + "content": "KIT Motion-Language (KIT-ML). KIT-ML dataset [36] contains 3,911 3D human motion clips with 6,278 text descriptions. For each motion clip, one to four textual descriptions are provided. The motion sequences are collected from the KIT dataset [31] and the CMU dataset [1] with the down-sampled 12.5 FPS." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.467, + 0.895, + 0.512 + ], + "angle": 0, + "content": "Both of the aforementioned datasets are split into training, validation, and testing datasets with the proportions of \\(80\\%\\), \\(5\\%\\), and \\(15\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.533, + 0.895, + 0.669 + ], + "angle": 0, + "content": "Implementation details. Both our VQ-encoder and decoder consist of 4 transformer layers with 8 heads and the dimension is 512. For the HumanML3D [16] and KIT-ML [36] datasets, the motion sequences are cropped to 64 frames for training. We apply Adam with \\(\\beta_{1} = 0.9\\), \\(\\beta_{2} = 0.999\\), weight decay is 1e-4. The learning rate is 1e-4 after warmup linearly for 5 epochs. The number of tokens in the codebook is 8192. We train our VQ-VAE with a batch size of 1024 across 8 Tesla T4 for a total 100 training epochs for 8 hours." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.669, + 0.895, + 0.805 + ], + "angle": 0, + "content": "For the discrete diffusion model, we set timesteps \\( T = 100 \\) and the network is trained using Adam [25] with \\( \\beta_{1} = 0.9 \\), \\( \\beta_{2} = 0.999 \\). The learning rate reaches 2e-4 after 2000 iterations of a linear warmup schedule. The transformer-based discrete diffusion model consists of 12 transformer layers with 8 heads, and the dimension is 512. The text features are extracted by pre-trained CLIP [37] model. The diffusion model is trained with a batch size of 64 across 8 Tesla T4 for 100k iterations for 36 hours." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Evaluation metrics. Following the evaluation protocols provided in previous works [16, 55, 44, 5], we evaluate the correspondences between motion and language using deep multimodal features with the pre-trained models in [16] by the following metrics: 1) Generation diversity: We randomly" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14811" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.086, + 0.089, + 0.887, + 0.385 + ], + "angle": 0, + "content": "
MethodsR-Precision ↑FID ↓MM-Dist ↓Diversity →MModality ↑
Top-1Top-2Top-3
Real motion0.511±.0030.703±.0030.797±.0020.002±.0002.974±.0089.503±.065-
Our VQ-VAE0.508±.0020.691±.0020.791±.0030.63±.0013.015±.0109.577±.081-
Our VQ-VAE w/o l20.494±.0030.685±.0020.772±.0030.70±.0013.251±.0089.525±.092-
Our VQ-VAE w/o l2, Lorth0.485±.0020.671±.0030.752±.0030.79±.0013.378±.0129.511±.095-
Seq2Seq [30]0.180±.0020.300±.0020.396±.00211.75±.0355.529±.0076.223±.061-
Language2Pose [2]0.246±.0020.387±.0020.486±.00211.02±.0465.296±.0087.676±.058-
Text2Gesture [4]0.165±.0010.267±.0020.345±.0025.012±.0306.030±.0086.409±.071-
Hier [12]0.301±.0020.425±.0020.552±.0046.532±.0245.012±.0188.332±.042-
MoCoGAN [45]0.037±.0000.072±.0010.106±.00194.41±.0219.643±.0060.462±.0080.019±.000
Dance2Music [27]0.033±.0000.065±.0010.097±.00166.98±.0168.116±.0060.725±.0110.043±.001
TM2T [17]0.424±.0030.618±.0030.729±.0021.501±.0173.467±.0118.589±.0762.424±.093
Guo et al. [16]0.455±.0030.636±.0030.736±.0021.087±.0213.347±.0089.175±.0832.219±.074
MDM [44]$--0.611±.0070.544±.0445.566±.0279.559±.0862.799±.072
MotionDiffuse [56]$0.491±.0010.681±.0010.782±.0010.630±.0013.113±.0019.410±.0491.553±.042
T2M-GPT [55]0.492±.0030.679±.0020.775±.0020.141±.0053.121±.0099.722±.0821.831±.048
MLD [5]0.481±.0030.673±.0030.772±.0020.473±.0133.196±.0109.724±.0822.413±.079
M2DM (Ours) w. linear schedule0.452±.0030.678±.0020.752±.0030.417±.0043.167±.0089.972±.0893.562±.071
M2DM (Ours) w. static assessment0.492±.0030.671±.0030.775±.0030.395±.0053.116±.0089.937±.0753.413±.035
M2DM (Ours) w. dynamic assessment0.497±.0030.682±.0020.763±.0030.352±.0053.134±.0109.926±.0733.587±.072
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.35, + 0.385, + 0.616, + 0.397 + ], + "angle": 0, + "content": "\\( {}^{8} \\) reports results using ground-truth motion length." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.398, + 0.892, + 0.429 + ], + "angle": 0, + "content": "Table 1: Comparison with the state-of-the-art methods on HumanML3D [16] test set. The evaluation metrics are evaluated by the motion encoder from Guo et al. [16]. The right row \\(\\rightarrow\\) means the closer to the real motion the better." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.473, + 0.712 + ], + "angle": 0, + "content": "sample 300 pairs of motions from the motion pool and extracted the selected motion features by the extractor provided by [16]. Euclidean distances of the motion pairs are computed for measuring the motion diversity. 2) R-Precision: Provided one motion representation and 32 textual descriptions, the Euclidean distances between the description feature and each motion feature in the candidates are calculated and ranked. Top-k \\((k = 1,2,3)\\) average accuracy of motion-to-text retrieval is reported. 3) Frechet Inception Distance (FID) [19]: FID is the principal metric to evaluate the feature descriptions between the generated motions and the ground-truth motions by the feature extractor [16]. 4) Multimodal Distance (MM-Dist): MM-Dist measures the average Euclidean distances between each text feature and the generated motion feature. 5) MModality measures the generation diversity within the same textual descriptions. Please refer to the supplementary material for a detailed introduction." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.722, + 0.466, + 0.739 + ], + "angle": 0, + "content": "4.2. Comparisons with state-of-the-art approaches" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.471, + 0.79 + ], + "angle": 0, + "content": "We compare our methods with other state-of-the-art methods [30, 2, 4, 12, 45, 27, 17, 16, 44, 56, 55, 5] on the HumanML3D [16] and KIT-ML [36] datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Quantitative comparisons. For each metric, we repeat the evaluation 20 times and report the average with \\(95\\%\\) confidence interval, followed by [16]. Most of the results are borrowed from [55]. Tab. 1 and Tab. 2 summarize the comparison results on the HumanML3D [16] and the KIT-ML [36] datasets, respectively. Firstly, the metrics scores for" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.455, + 0.895, + 0.681 + ], + "angle": 0, + "content": "our reconstruction motion achieve close performance compared with real motion, which suggests the distinctive and high-quality discrete motion tokens in the codebook learned by our Transformer-based VQ-VAE. The performance of our VQ-VAE degrades when the normalized function \\(\\ell_2\\) and the orthogonal regularization term \\(\\mathcal{L}_{\\mathrm{orth}}\\) are removed. For text-to-motion generation, our approach achieves compatible performance (R-Precision, FID, and MModality) compared to other state-of-the-art methods. Moreover, compared with MDM [44] and MotionDiffuse [56] which evaluate their performance with the ground-truth motion lengths, our model can generate motion sequences with arbitrary lengths conditioned on the given textual descriptions since the [MASK] and [PAD] tokens are introduced in the discrete diffusion process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Furthermore, we conduct more experiments to evaluate the generation performance conditioned on different lengths of textual descriptions. The testing dataset is split into three parts according to the length of the textual descriptions: less than 15 words, between 15 words and 30 words, and more than 30 words. Tab. 3 shows the quantitative results on the aforementioned three sub-sets. Both TM2T [17] and MLD [5] suffer degradation when the textual descriptions are long and complex, especially the descriptions are more than 30 words. Our method significantly outperforms the other two methods with various metrics and there is not much degradation when the descriptions are more complex. The quantitative results demonstrate the effectiveness of our proposed primary-to-secondary diffusion manner." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14812" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.086, + 0.089, + 0.887, + 0.359 + ], + "angle": 0, + "content": "
MethodsR-Precision ↑FID ↓MM-Dist ↓Diversity →MModality ↑
Top-1Top-2Top-3
Real motion0.424±.0050.649±.0060.779±.0060.031±.0042.788±.01211.08±.097-
Our VQ-VAE (Recons.)0.417±.0040.621±.0030.741±.0060.413±.0092.772±.01810.851±.105-
Seq2Seq [30]0.103±.0030.178±.0050.241±.00624.86±.3487.960±.0316.744±.106-
Language2Pose [2]0.221±.0050.373±.0040.483±.0056.545±.0725.147±.0309.073±.100-
Text2Gesture [4]0.156±.0040.255±.0040.338±.00512.12±.1836.964±.0299.334±.079-
Hier [12]0.255±.0060.432±.0070.531±.0075.203±.1074.986±.0279.563±.072-
MoCoGAN [45]0.022±.0020.042±.0030.063±.00382.69±.24210.47±.0123.091±.0430.250±.009
Dance2Music [27]0.031±.0020.058±.0020.086±.003115.4±.24010.40±.0160.241±.0040.062±.002
TM2T [17]0.280±.0050.463±.0060.587±.0053.599±.1534.591±.0269.473±.1173.292±.081
Guo et al. [16]0.361±.0060.559±.0070.681±.0073.022±.1073.488±.02810.72±.1452.052±.107
MDM [44]$--0.396±.0040.497±.0219.191±.02210.847±.1091.907±.214
MotionDiffuse [56]$0.417±.0040.621±.0040.739±.0041.954±.0622.958±.00511.10±.1430.730±.013
T2M-GPT [55]0.416±.0060.627±.0060.745±.0060.514±.0293.007±.02310.921±.1081.570±.039
MLD [5]0.390±.0030.609±.0030.734±.0020.404±.0133.204±.01010.8±.0822.192±.079
M2DM (Ours) w. linear schedule0.405±.0030.629±.0050.739±.0040.502±.0493.012±.01511.375±.0793.273±.045
M2DM (Ours) w. static assessment0.417±.0060.625±.0030.741±.0060.521±.0413.024±.01811.373±.0813.317±.031
M2DM (Ours) w. dynamic assessment0.416±.0040.628±.0040.743±.0040.515±.0293.015±.01711.417±.973.325±.37
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.35, + 0.36, + 0.615, + 0.372 + ], + "angle": 0, + "content": "\\( {}^{8} \\) reports results using ground-truth motion length." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.372, + 0.893, + 0.403 + ], + "angle": 0, + "content": "Table 2: Comparison with the state-of-the-art methods on KIT-ML [36] test set. The evaluation metrics are evaluated by the motion encoder from Guo et al. [16]. The right row \\(\\rightarrow\\) means the closer to the real motion the better." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.418, + 0.889, + 0.778 + ], + "angle": 0, + "content": "
TM2TMDMT2M-GPTMLDOurs
a person grabs something, turns around, walks forward, squats, stands up, walks forward, squats and stands up again.
a person puts both hands by their face in a defensive stance, then kicks with their right foot.
a person jumps and turns around in the air to face behind him.
a person walks forward briskly, crouches and lifts an object with both hands, puts the object down in a higher position, then stands up and turn right.
a person takes something, put it down and throws something.
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.79, + 0.893, + 0.822 + ], + "angle": 0, + "content": "Figure 5: Qualitative comparison of the state-of-the-art methods on the HumanML3D [16] dataset. We compare our generations with TM2T [17], MDM [44], T2M-GPT [55], and MLD [5]. The color of human mesh goes from light to dark over time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.847, + 0.473, + 0.893 + ], + "angle": 0, + "content": "Qualitative comparisons. Fig. 5 qualitatively compares the generated motions from the same textual descriptions. Most of the methods suffer from motion freezing if the tex" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.847, + 0.894, + 0.893 + ], + "angle": 0, + "content": "tual descriptions consist of several complex commands. For example, the first row in Fig. 5 shows the generation results from a long textual description with various duplicate action" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14813" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.089, + 0.482, + 0.203 + ], + "angle": 0, + "content": "
Text LengthMethodsR-Precision ↑FID ↓MM-Dist ↓Diversity →MModality ↑
Top-1Top-2Top-3
AllTM2T [17]0.424±0.0030.618±0.0030.729±0.0021.501±0.0173.467±0.0118.580±0.0762.424±0.093
MLD [5]0.481±0.0030.673±0.0030.772±0.0020.473±0.0133.196±0.0109.724±0.0822.413±0.079
M2DM (Ours)0.497±0.0030.689±0.0020.763±0.0030.352±0.0053.134±0.0109.926±0.0733.587±0.072
< 15 wordsTM2T [17]0.433±0.0030.627±0.0030.738±0.0031.592±0.0173.446±0.0088.677±0.0772.520±0.051
MLD [5]0.492±0.0030.680±0.0040.779±0.0040.469±0.0143.191±0.0119.770±0.0102.586±0.086
M2DM (Ours)0.508±0.0030.685±0.0030.767±0.0040.347±0.0153.129±0.0139.915±0.0683.594±0.077
15-30 wordsTM2T [17]0.406±0.0030.596±0.0020.708±0.0021.425±0.0143.528±0.0078.000±0.0512.477±0.057
MLD [5]0.406±0.0050.592±0.0050.701±0.0060.480±0.0203.591±0.0209.089±0.0832.727±0.094
M2DM (Ours)0.493±0.0030.681±0.0040.761±0.0040.353±0.0313.135±0.0149.926±0.0733.588±0.081
>30 wordsTM2T [17]0.353±0.0090.536±0.0090.650±0.0071.779±0.0613.577±0.0247.411±0.0712.612±0.055
MLD [5]0.289±0.0100.466±0.0120.581±0.0150.947±0.0663.870±0.0398.347±0.1002.916±0.063
M2DM (Ours)0.491±0.0040.677±0.0040.758±0.0040.356±0.0383.138±0.0259.930±0.0883.585±0.071
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.213, + 0.474, + 0.32 + ], + "angle": 0, + "content": "Table 3: Comparison with the state-of-the-art methods on HumanML3D [16] test set. The evaluation metrics are evaluated by the motion encoder from Guo et al. [16]. The right row \\(\\rightarrow\\) means the closer to the real motion the better. The first three rows are the evaluation results on the whole testing dataset. The rest are the evaluation results from textual descriptions with different lengths." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.345, + 0.473, + 0.468 + ], + "angle": 0, + "content": "commands. MDM [44] and MLD [5] generate fewer semantic motions compared with the given description. With the help of compact discrete motion tokens, TM2T [17] and T2M-GPT [55] achieve better results compared with MDM [44] and MLD [5]. Our motion generation results conform to the textual descriptions and exhibit a high degree of diversity compared with other state-of-the-art methods, which validates the efficacy of our proposed method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.476, + 0.24, + 0.492 + ], + "angle": 0, + "content": "4.3. Ablation studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.499, + 0.474, + 0.788 + ], + "angle": 0, + "content": "We delved into the significance of various quantization techniques, as delineated in the initial four rows of Tab.1. The findings indicate that a rudimentary Transformer-based VQ-VAE struggles to reconstruct credible motion sequences, primarily due to the limited efficacy of the codebook. However, the incorporation of the \\(\\ell_2\\) norm and \\(\\mathcal{L}_{\\mathrm{orth}}\\) ensures that each motion token acquires a distinct motion representation. We further scrutinized the utilization of each motion token on the HumanML3D [16] test set, with the outcomes depicted in Fig.6. As evidenced by Fig.6a and 6b, both the vanilla CNN-based VQ-VAE and Transformer-based VQ-VAE grapple with sub-optimal codebook usage. This is because the tokens in the codebook aren't inherently driven to develop a distinguishing motion representation. Yet, with the aid of the \\(\\ell_2\\) norm and \\(\\mathcal{L}_{\\mathrm{orth}}\\), there's a marked surge in the codebook token utilization. Moreover, when juxtaposing the codebook usage in Fig.6c with that in Fig.6d, the latter exhibits a more equitably distributed frequency, attributable to the orthogonal regularization term \\(\\mathcal{L}_{\\mathrm{orth}}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.8, + 0.197, + 0.815 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In this study, we introduced the priority-centric motion discrete diffusion model (M2DM) tailored for text-to-motion generation. Our model excels in producing varied and life-like human motions, aligning seamlessly with the input text. This is achieved by mastering a discrete motion representa" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.089, + 0.695, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.536, + 0.192, + 0.66, + 0.204 + ], + "angle": 0, + "content": "(a) 1D-CNN VQ-VAE." + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.206, + 0.695, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.518, + 0.306, + 0.678, + 0.319 + ], + "angle": 0, + "content": "(c) Our VQ-VAE w. \\(\\ell_2\\) norm." + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.095, + 0.891, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.746, + 0.192, + 0.845, + 0.204 + ], + "angle": 0, + "content": "(b) Our VQ-VAE." + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.206, + 0.891, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.701, + 0.306, + 0.888, + 0.32 + ], + "angle": 0, + "content": "(d) Our VQ-VAE w. \\(\\ell_2\\) and \\(\\mathcal{L}_{\\mathrm{orth}}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.331, + 0.896, + 0.392 + ], + "angle": 0, + "content": "Figure 6: Codebook usage for different training strategies on HumanML3D [16] test set. We train our VQ-VAE (Reconstruction) with different training strategy on the HumanML3D [16] dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.42, + 0.896, + 0.542 + ], + "angle": 0, + "content": "tion through a Transformer-based VQ-VAE and implementing a priority-informed noise schedule within the motion discrete diffusion framework. Additionally, we unveiled two innovative techniques for gauging the priority or significance of each motion token. Experimental evaluations across two datasets underscore our model's competitive edge, outpacing existing methodologies in R-Precision and diversity, particularly with intricate textual narratives." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.558, + 0.661, + 0.575 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.585, + 0.894, + 0.63 + ], + "angle": 0, + "content": "This project is supported by the Ministry of Education, Singapore, under its Academic Research Fund Tier 2 (Award Number: MOE-T2EP20122-0006)." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.646, + 0.597, + 0.661 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.672, + 0.894, + 0.699 + ], + "angle": 0, + "content": "[1] Cmu graphics lab motion capture database. http://mocap.cs.cmu.edu/.6" + }, + { + "type": "ref_text", + "bbox": [ + 0.509, + 0.702, + 0.895, + 0.757 + ], + "angle": 0, + "content": "[2] Chaitanya Ahuja and Louis-Philippe Morency. 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Motiondiffuse: Text-driven human motion generation with diffusion model. arXiv preprint arXiv:2208.15001, 2022. 1, 3, 7, 8" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.893, + 0.687 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14816" + } + ] +] \ No newline at end of file diff --git a/2023/Priority-Centric Human Motion Generation in Discrete Latent Space/58c7e478-f288-424e-a702-051324564633_origin.pdf b/2023/Priority-Centric Human Motion Generation in Discrete Latent Space/58c7e478-f288-424e-a702-051324564633_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a82654af46e07b7fc377bc46c948cab23b622bba --- /dev/null +++ b/2023/Priority-Centric Human Motion Generation in Discrete Latent Space/58c7e478-f288-424e-a702-051324564633_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fae5046f9be915ad0f6e7b3fb9813137b4249af6a135f5d498ad59b8a90e2724 +size 5824223 diff --git a/2023/Priority-Centric Human Motion Generation in Discrete Latent Space/full.md b/2023/Priority-Centric Human Motion Generation in Discrete Latent Space/full.md new file mode 100644 index 0000000000000000000000000000000000000000..22a4211be850b071240c0f939bcb9f9940e36e2f --- /dev/null +++ b/2023/Priority-Centric Human Motion Generation in Discrete Latent Space/full.md @@ -0,0 +1,355 @@ +# Priority-Centric Human Motion Generation in Discrete Latent Space + +Hanyang Kong $^{1}$ , Kehong Gong $^{1}$ , Dongze Lian $^{1}$ , Michael Bi Mi $^{2}$ , Xinchao Wang $^{1*}$ + +$^{1}$ National University of Singapore $^{2}$ Huawei International Pte Ltd + +{hanyang.k, gongkehong}@u.nus.edu {dongze, xinchao}@nus.edu.sg + +# Abstract + +Text-to-motion generation is a formidable task, aiming to produce human motions that align with the input text while also adhering to human capabilities and physical laws. While there have been advancements in diffusion models, their application in discrete spaces remains underexplored. Current methods often overlook the varying significance of different motions, treating them uniformly. It is essential to recognize that not all motions hold the same relevance to a particular textual description. Some motions, being more salient and informative, should be given precedence during generation. In response, we introduce a Priority-Centric Motion Discrete Diffusion Model (M2DM), which utilizes a Transformer-based VQ-VAE to derive a concise, discrete motion representation, incorporating a global self-attention mechanism and a regularization term to counteract code collapse. We also present a motion discrete diffusion model that employs an innovative noise schedule, determined by the significance of each motion token within the entire motion sequence. This approach retains the most salient motions during the reverse diffusion process, leading to more semantically rich and varied motions. Additionally, we formulate two strategies to gauge the importance of motion tokens, drawing from both textual and visual indicators. Comprehensive experiments on the HumanML3D and KIT-ML datasets confirm that our model surpasses existing techniques in fidelity and diversity, particularly for intricate textual descriptions. + +# 1. Introduction + +Generating realistic and diverse 3D human motions under various conditions e.g., action labels [34, 18], natural language descriptions [55, 17, 5, 56], and musical cues [27, 28, 29], presents a significant challenge across multiple domains, including gaming, filmmaking, and robotic animation. Notably, motion generation based on language descriptions has garnered substantial interest, given its promise + +for enhancing realism and broadening practical applications. + +However, generating a high-quality motion is not trivial due to the inherent modality gap and the complex mapping between text and motion modalities. Previous works [35, 43] align the latent feature space between text and motion modalities. For instance, TEMOS [35] aligns the text and motion feature by learning text and motion encoders. MotionClip [43] aligns the human motion manifold to CLIP [37] space for infusing semantic knowledge of CLIP into the motion extractor. Despite these advancements, they might encounter performance degradation when dealing with complex textual descriptions. + +To process these complex textual descriptions, some text-to-motion methods are proposed. State-of-the-art approaches such as TM2T [17] and T2M-GPT [55] use vector-quantized autoencoder (VQ-VAE) [46] to learn a discrete and compact motion representation, followed by a translation model [38, 47] to map the text modality to the motion modality. With the popularity and the superior performance in the generation tasks of diffusion models [20], MDM [44] and MLD [5] are proposed to learn conditioned diffusion models on the raw motion representation space and the latent feature space, respectively. + +While there have been promising advancements, two primary issues remain unresolved: i) The aforementioned diffusion methods, namely MDM [44] and MLD [5], predominantly address the latent feature within a continuous space. Although VQ-VAE-inspired architectures have made considerable strides in motion generation [55, 17], particularly with the support of discrete and compact motion representations, the integration of the diffusion model into a discrete space remains inadequately explored. ii) Discrete diffusion models employed in prior studies [15, 14, 22] treat all tokens uniformly. This approach presupposes that every token conveys an equivalent amount of information, neglecting the inherent disparities among tokens within a sequence. A more intuitive generative approach for humans would involve a progressive hierarchy, commencing with overarching concepts and gradually delving into finer details. + +To address the aforementioned challenges, we introduce a priority-centric motion discrete diffusion model (M2DM) + +![](images/b439b8314da8a8ceb3326548da576200317184eb052eb4f23a161258ea0bf35f.jpg) +a person steps forward with left leg walking in a circle counterclockwise motion swinging arms and returns back. + +![](images/9d0c251455da47bd3d24f66b71118aebf0d37946e80a8daacde1e958f2e04810.jpg) + +![](images/c8ea4c1f7282c3d12e82f475d439ce5e00a7a9482b33fc27749fca5bf60e559b.jpg) +a person runs forward, then turns around and walks in the opposite direction while swinging their right arm. + +![](images/c859db1c1545f793b8cdf537f4e5ba72913f0744a729ef102d8e27a747e06912.jpg) + +![](images/ed8e60537fcd7457573289571d364e02360b7d0c102a0ab97a985dc78d08cfc3.jpg) +a man gets up from the ground, walks around in a circle and then sits down on the ground again. + +![](images/85861fed1c799c75fb9e0e963334011b3432907a77306bb750bfcea593abbd37.jpg) +a man postures his arms like holding a dance partner and dances the waltz from the right hand side to the left hand side. + +![](images/a8b75794bd13b135797c0134ed741dcf543f0c5d0c7087ad0abad9fa0f0f1441.jpg) +Figure 1: Our Priority-Centric Motion Discrete Diffusion Model (M2DM) generates diverse and precise human motions given complex textual descriptions. The color of human mesh goes from light to dark over time. + +designed to generate motion sequences from textual descriptions, progressing in a primary to secondary manner. Initially, we employ a Transformer-based VQ-VAE, which is adept at learning a concise, discrete motion representation through the global self-attention mechanism. To circumvent code collapse and guarantee the optimal utilization of each motion token within the codebook, a regularization term is incorporated during the VQ-VAE training phase. Furthermore, we craft a noise schedule wherein individual tokens within a sequence are allocated varying corruption probabilities, contingent on their respective priorities during the forward process. Specifically, tokens of higher priority are slated for corruption towards the latter stages of the forward process. This ensures that the subsequent learnable reverse process adheres to a primary-to-secondary sequence, with top-priority tokens being reinstated foremost. + +To discern the significance of motion tokens within a sequence, we introduce two evaluative strategies: static assessment and dynamic assessment. 1) Static assessment: Drawing inspiration from the neural language domain, where the significance of individual words is gauged by their entropy across datasets, we calculate the entropy of each motion token across the entire motion dataset. 2) Dynamic assessment: We cultivate an agent specifically to dynamically gauge the importance of tokens within a sequence. Given a discrete motion token sequence, the agent masks one token at each iteration. These masked token sequences are then fed into the VQ decoder for continuous motion reconstruction. The agent's objective is to curtail the cumulative reconstruction discrepancy between the original and the reconstructed mo + +tions at every phase. This is achieved using a reinforcement learning [23] (RL) strategy, facilitating the agent's identification of motion tokens that convey minimal information within a sequence—a process we term dynamic analysis. Our priority-centric discrete diffusion model has showcased commendable generative prowess, especially when dealing with intricate textual descriptions. Through rigorous testing, our method has proven its mettle, consistently matching or surpassing the performance of prevailing text-to-motion generation techniques on the HumanML3D and KIT-ML datasets. + +We summarize our contributions as follows: + +- To capture long-range dependencies in the motion sequences, we apply Transformer as the architecture of VQ-VAE. Besides, a regularization term is applied to increase the usage of tokens in the codebook. +- We design a priority-centric scheme for human motion generation in the discrete latent space. To enhance the performance given complex descriptions, we design a novel priority-centric scheme for the discrete diffusion model. +- Our proposed priority-centric M2DM achieves state-of-the-art performance on the HumanML3D [16] and KIT-ML [36] datasets. + +# 2. Related Work + +VQ-VAE. Vector Quantized Variational Autoencoder (VQ-VAE) [46] aims to minimize reconstruction error with dis + +crete representations by training a variational autoencoder. VQ-VAE achieves promising performance on generative tasks, such as text-to-image generation [39, 52], music generation [7], unconditional image synthesis [9], etc. For motion generation tasks, most of the methods [17, 55] tokenize the continuous motion representation by the 1D-CNN network. Since the motion style varies from person to person and the number of action combinations is almost infinite, it is essential to extract discriminative and distinctive motion features from the raw motion representations. Moreover, raw motion representation is much more redundant compared with neural language, it is feasible to represent a motion sequence using few motion tokens from a global perspective. To this end, we introduce a transformer-based VQ-VAE and several techniques are applied to balance the usage of each motion token in the codebook and prevent the codebook from collapsing, i.e., only a small proportion of codes in the codebook are activated. + +Diffusion models. Diffusion generative models are first proposed in [42] and achieve promising results on image generation [8, 33, 21, 20, 50, 48, 53, 11, 10]. Discrete diffusion model is first proposed by [42] and several works [22, 14] apply the discrete diffusion model for text generation. D3PM [3] then applies the discrete diffusion model to the image generation task. For motion generation tasks, several works [24, 56, 44, 5] introduce diffusion models to generate diverse motion sequences from textual descriptions. In this work, we first introduce the discrete diffusion model for text-to-motion generation tasks which achieves promising results, especially for long text descriptions with several action commands. + +Conditional human motion synthesis Compared with unconditional Human motion synthesis, human motion synthesis conditioned on various conditions, such as textual description [55, 17, 5, 56], music [27, 28, 29, 13], and actions [34, 18] is more challenging due to the huge gap between two different domains. A common strategy of conditioned human motion synthesis is to employ generative models, for instance, conditional VAE [26], and learn a latent motion representation. Text-to-motion task is more challenging because neural language is a type of information highly refined by human beings, whereas human motion is much more redundant. Most recently, several promising works [5, 16, 17, 56, 55] are proposed for text-to-motion tasks. T2M-GPT [55] and TM2T [17] regard the text-to-motion task as a translation problem. They first train a VQ-VAE [46] to tokenize the motion sequences into motion tokens, and Recurrent Neural Networks (RNN) [32], Transformer [47, 51, 49, 41, 40, 54], or GPT-like [38] models are further applied to 'translate' textual descriptions to motions. Moreover, diffusion-based [20] models are introduced for + +text-to-motion generation by [56, 6, 44, 5] in the contentious space. In this work, to the best of our knowledge, we are the first ones to diffuse the motion representation in the discrete latent space. Moreover, we notice that different motion clips in a whole motion sequence play various roles, for instance, stepping forward is more important than swinging arms for a running motion. We further design a diffuse schedule such that the generation process follows a from-primary-to-secondary manner. + +# 3. Method + +# 3.1. Motion Tokenizer + +The motion tokenizer aims to learn a codebook that can represent a wide range of motion sequences with the priority awareness of motion tokens. To achieve this, we propose a transformer-based VQ-VAE that leverages self-attention to capture long-range dependencies between motion frames and learns a stable and diverse codebook. + +Fig. 2 shows the overview of our motion tokenizer. Given a motion sequence $X \in \mathbb{R}^{T \times d}$ with $T$ frames and $d$ dimensional motion representation, we reconstruct the motion sequence using a transformer autoencoder and learn an informative codebook $Z = \{z_k\}_{k=1}^K$ with $K$ entries. We use the transformer encoder $E$ to compute the latent motion features $\boldsymbol{b} = \{b_t\}_{t=1}^T \in \mathbb{R}^{T \times d}$ , where $d$ is the dimension of the latent features. Then for each feature $b_t$ , we query the codebook $Z$ by measuring the distance between feature $b_t$ and each entry in the codebook $Z$ . To improve the codebook usage and avoid dead codes, we first normalize $b_t$ and $z_t$ and then measure the Euclidean distance between two normalized vectors in the unit sphere coordinate, which is formulated as: + +$$ +\hat {b} _ {t} = \underset {b _ {t} \in \boldsymbol {b}} {\arg \min } \| \ell_ {2} (b _ {t}) - \ell_ {2} \left(z _ {k}\right) \| _ {2} ^ {2}, \tag {1} +$$ + +where $\ell_2$ is the $l_{2}$ normalized function. + +The standard optimization goal consists of three parts: the reconstruction loss, the embedding loss, and the commitment loss, which is formulated as + +$$ +\begin{array}{l} \mathcal {L} _ {v q} = \left\| X - \tilde {X} \right\| _ {2} ^ {2} + \left\| Z - s g [ \hat {Z} ] \right\| _ {2} ^ {2} \tag {2} \\ + \eta | | s g [ Z ] - \hat {Z} | | _ {2} ^ {2}. \\ \end{array} +$$ + +Moreover, to achieve an informative codebook with diverse and high usage of its entries, we apply an orthogonal regularization. Specifically, we calculate the distance between each pair of codebook entries to enforce orthogonality among all the codebook entries: + +$$ +\mathcal {L} _ {\text {o r t h}} (Z) = \left\| \ell_ {2} (Z) ^ {\top} \ell_ {2} (Z) - I _ {K} \right\| _ {2} ^ {2}, \tag {3} +$$ + +where $\mathcal{L}_2$ is the $l_{2}$ normalized function. + +![](images/5b14b9f440f563c742bd7350990b93a1daf121fbfd30f65ec94ca918acd80905.jpg) +Figure 2: Overview of our framework for our Motion Discrete Diffusion Model (M2DM). M2DM consists of a Transformer-based VQ-VAE (Sec. 3.1) and a discrete diffusion model (Sec. 3.2). Firstly, the Transformer-based motion tokenizer is learned to discretize motion sequences into tokens and reconstruct original motion sequences from tokens queried from the learnable codebook. Then the discrete diffusion model is learned to generate diverse motions conditioned on the textual descriptions. Two priority assessment strategies (Sec. 3.3) are applied to mask or replace motion tokens with less information at the beginning of the forward diffusion process and the most important motion tokens are corrupted in the last few diffusion steps. The diffusion model learns to restore the original motion token index conditioned on the given textual descriptions. + +Therefore, the overall training objective of vector quantization is defined as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {v q} = \left\| X - \tilde {X} \right\| _ {2} ^ {2} + \| Z - s g [ \hat {Z} ] \| _ {2} ^ {2} \tag {4} \\ + \eta | | s g [ Z ] - \hat {Z} | | _ {2} ^ {2} + \delta \mathcal {L} _ {\text {o r t h}} (Z), \\ \end{array} +$$ + +where $\tilde{X} = D(\pmb {b})$ $D$ is the decoder, $sg[\cdot ]$ denotes the stopgradient operation, $\eta$ and $\delta$ are the weighting scalars. + +# 3.2. Discrete Diffusion Models + +Generally speaking, the forward discrete diffusion process corrupts each element $x_{t}$ at timestep $t$ with $K$ categories via fixed Markov chain $q(x_{t}|x_{t - 1})$ , for instance, replace some tokens of $x_{t - 1}$ or mask the token directly. After a fixed number of $T$ timesteps, the forward process yields a sequence of increasingly noisy discrete tokens $z_{1},\ldots ,z_{T}$ of the same dimension of $z_{0}$ and $z_{T}$ becomes pure noise token. For the denoising procedure, the real $x_0$ is restored sequentially based on the pure noisy token $z_{T}$ . To be specific, for scalar random variable with $K$ categories $x_{t},x_{t - 1}\in 1,\dots K$ , the forward transition probabilities can be represented by the transition matrices $[Q_{t}]_{ij} = q(x_{t} = i|x_{t - 1} = j)\in \mathbb{R}^{(K + 1)\times (K + 1)}$ . $[Q_{t}]_{i,j}$ is the Markov transition matrix from state $t$ to state $t - 1$ that is applied to each token in the sequence independently, which + +can be written as: + +$$ +\boldsymbol {Q} _ {t} = \left[ \begin{array}{c c c c c} \alpha_ {t} + \beta_ {t} & \beta_ {t} & \beta_ {t} & \dots & 0 \\ \beta_ {t} & \alpha_ {t} + \beta_ {t} & \beta_ {t} & \dots & 0 \\ \beta_ {t} & \beta_ {t} & \alpha_ {t} + \beta_ {t} & \dots & 0 \\ \vdots & \vdots & \vdots & & \vdots \\ \gamma_ {t} & \gamma_ {t} & \gamma_ {t} & \dots & 1 \end{array} \right], \tag {5} +$$ + +where $\alpha_{t} \in [0,1]$ is the probability of retaining the token, $\gamma_{t}$ is the probability of replacing the original token to [MASK] token, leaving the probability $\beta_{t} = (1 - \alpha_{t} - \gamma_{t}) / K$ to be diffused. The forward Markov diffusion process for the whole token sequence is written as, + +$$ +q \left(\boldsymbol {x} _ {t} \mid \boldsymbol {x} _ {t - 1}\right) = \operatorname {C a t} (\boldsymbol {x}; \boldsymbol {p} = \boldsymbol {x} _ {t - 1} \boldsymbol {Q} _ {t}) = \boldsymbol {x} _ {t} \boldsymbol {Q} _ {t} \boldsymbol {x} _ {t - 1}, \tag {6} +$$ + +where $\pmb{x}$ is the one-hot row vector identifying the token index and $\operatorname{Cat}(\pmb{x};\pmb{p})$ is a categorical distribution over the one-hot vector $\pmb{x}_t$ with probabilities $\pmb{p}$ . + +Starting from the initial step $x_0$ , the posterior diffusion process is formulated as: + +$$ +\begin{array}{l} q \left(\boldsymbol {x} _ {t - 1} \mid \boldsymbol {x} _ {t}, \boldsymbol {x} _ {0}\right) = \frac {q \left(\boldsymbol {x} _ {t} \mid \boldsymbol {x} _ {t - 1} , \boldsymbol {x} _ {0}\right) q \left(\boldsymbol {x} _ {t - 1} , \boldsymbol {x} _ {0}\right)}{q \left(\boldsymbol {x} _ {t} \mid \boldsymbol {x} _ {0}\right)} (7) \\ = \frac {\left(\boldsymbol {x} ^ {\top} \boldsymbol {Q} _ {t} \boldsymbol {x} _ {t - 1}\right) \left(\boldsymbol {x} _ {t - 1} ^ {T} \bar {\boldsymbol {Q}} _ {t - 1} \boldsymbol {x} _ {0}\right)}{\boldsymbol {x} _ {t} ^ {\top} \bar {\boldsymbol {Q}} _ {t} \boldsymbol {x} _ {0}} (7) \\ \end{array} +$$ + +with $\bar{Q} = Q_{1}Q_{2}\dots Q_{t}$ + +Recording to Markov chain, the intermediate step can be marginalized out and the derivation of the probability of $\boldsymbol{x}_t$ + +at arbitrary timestep directly from $\pmb{x}_0$ can be formulated by + +$$ +q \left(\boldsymbol {x} _ {t} \mid \boldsymbol {x} _ {0}\right) = \boldsymbol {x} _ {t} ^ {\top} \bar {\boldsymbol {Q}} \boldsymbol {x} _ {0}. \tag {8} +$$ + +The cumulative transition matrix $\bar{Q}$ and the probability $q(\pmb{x}_t|\pmb{x}_0)$ are then computed as + +$$ +\bar {Q} \boldsymbol {x} _ {0} = \bar {\alpha} _ {t} \boldsymbol {x} _ {0} + (\bar {\gamma} - \bar {\beta} _ {t}) \boldsymbol {m} + \bar {\beta} _ {t} \tag {9} +$$ + +where $m$ is the one-hot vector for [MASK] and [PAD], $\bar{\alpha}_t = \prod_{i=1}^t \alpha_i$ , $\bar{\gamma}_t = 1 - \prod_{i=1}^t (1 - \gamma_i)$ , and $\bar{\beta}_t = (1 - \bar{\alpha}_t - \bar{\gamma}_t) / K$ . + +Regarding the reverse diffusion process, we train a transformer-like [47] denoising network $p_{\theta}(\pmb{x}_{t-1}|\pmb{x}_t,\pmb{y})$ to estimate the posterior transition distribution $q(\pmb{x}_{t-1}|\pmb{x}_t,\pmb{x}_0)$ . The network is trained to minimize the variational lower bound (VLB) [42]: + +$$ +\begin{array}{l} \mathcal {L} _ {V L B} = \mathbb {E} _ {q} \left[ D _ {K L} \left(q \left(\boldsymbol {x} _ {T} \mid \boldsymbol {x} _ {0}\right) \| p _ {\theta} \left(\boldsymbol {x} _ {T}\right)\right) \right] \\ + \mathbb {E} _ {q} [ \sum_ {t = 2} ^ {T} D _ {K L} (q (\boldsymbol {x} _ {t - 1} | \boldsymbol {x} _ {t}, \boldsymbol {x} _ {0}) \| p _ {\theta} (\boldsymbol {x} _ {t - 1} | \boldsymbol {x} _ {t}, t)) ] \\ - \log p _ {\theta} \left(\boldsymbol {x} _ {0} \mid \boldsymbol {x} _ {1}\right) \tag {10} \\ \end{array} +$$ + +where $\mathbb{E}_q[\cdot ]$ denotes the expectation over the joint distribution $q(\pmb{x}_{0:T})$ . + +# 3.3. Priority-Centric Denoising Process + +The designation of the noise schedule in the continuous domain, for instance, the linear schedule [20] and the cosine schedule [33], achieves the excellent performance of diffusion models. The noise can be easily controlled by the variation of Gaussian noise. For the discrete diffusion models, several noise schedules [22, 3] have been explored to control the data corruption and denoise the reverse process by choosing the transition matrix $Q_{t}$ . For text-to-motion generation, however, such a schedule assumes all motion tokens carry the same amount of information and do not consider the difference among the discrete tokens extracted from the continuous motion sequence. Intuitively, the motion generation process would be in a progressive manner, where the most important motion tokens should appear in earlier steps for laying a solid foundation when denoising the noise in the discrete domain. + +Specifically, we apply the mask-and-replace strategy in Eq. (5) to corrupt each ordinary discrete token with a probability of $\gamma_{t}$ for masking [MASK] token and a probability of $\beta_{t}$ for uniform diffusion to a random token $x_{k}$ , resulting in a remaining probability of $\alpha_{t} = 1 - K\beta_{t} - \gamma_{t}$ for retention. When corrupting across the forward process in the discrete domain, we expect that $\bar{\alpha}_{t}^{i} < \bar{\alpha}_{t}^{j}$ if token $x_{i}$ is more informative than $x_{j}$ such that the tokens with high information emerge earlier than less informative motion tokens in the reverse process. Instead of using a normal corruption strategy with linearly increasing $\bar{\gamma}_{t}$ and $\bar{\beta}_{t}$ , we propose a + +priority-score function $F$ to assess the relative importance of information for a motion token sequence, which enables the recovery of the most informative tokens during the reverse process. + +Given an original motion token sequences $\pmb{x}_0$ at timestep 0 with length $N$ , we aim to analyze the importance of each token $x_0^i$ in $\pmb{x}_0$ . Based on the information entropy theory, we calculate the information entropy for each motion token $x_0^i$ as the importance score + +$$ +F \left(x _ {0} ^ {i}\right) = \frac {N H \left(x _ {0} ^ {i}\right)}{\sum_ {j = 1} ^ {N} H \left(x _ {0} ^ {j}\right)}, \tag {11} +$$ + +where + +$$ +H (x) = - \sum_ {i = 1} ^ {K} p \left(x _ {i}\right) \log p \left(x _ {i}\right), \tag {12} +$$ + +and $K$ denotes the number of categories belonging to $x_{i}$ + +After obtaining the importance score function and setting linearly increasing schedule $\bar{\gamma}_t^i$ and $\bar{\beta}_t^i$ for all tokens, $\bar{\gamma}_t^i$ and $\bar{\beta}_t^i$ for specific token $x_0^i$ can be further updated by + +$$ +\bar {\gamma} _ {t} ^ {i} \Leftarrow \bar {\gamma} _ {t} ^ {i} \cdot \sin \frac {t \pi}{T} \cdot F \left(x _ {0} ^ {i}\right), \tag {13} +$$ + +and + +$$ +\bar {\beta} ^ {i} \Leftarrow \bar {\beta} ^ {i} \cdot \sin \frac {t \pi}{T} \cdot F \left(x _ {0} ^ {i}\right), \tag {14} +$$ + +where $x_0^i$ is the $i$ -th token at timestep 0. + +Now we introduce two solutions for obtaining $p(x_{i})$ . + +Static assessment. Analogously to computing the entropy for each word in natural language processing, we estimate the probability $p(x_{i})$ for each motion token by counting its frequency in the quantized motion sequences over the entire dataset. + +![](images/3d0befa6afe7389516bbd25840dc6cd2e93ada0b6bc000589e1a52883fd2441f.jpg) +Figure 3: Illustration for dynamic assessment strategy. The gray blocks are masked tokens and other colorful blocks are motion tokens. + +Dynamic assessment. Rather than counting motion token frequency and calculating the importance of each token, we further propose to learn an agent to estimate the importance of each token in the token sequences by reinforcement learning strategy. As shown in Fig. 3, given a series of complete motion tokens $\boldsymbol{x} = \{x_{n}\}_{n=1}^{N}$ that are queried from the codebook at current state $s_{t} \in S$ , the scorer samples the motion tokens $\tilde{\boldsymbol{x}} = \{x_{n}\}_{n=1}^{N'}$ and tries to minimize the reconstruction error between the original motion sequences $\boldsymbol{m}$ and the motion sequences decoded from the sampled tokens $\tilde{\boldsymbol{m}}$ . + +State includes the currently selected motion tokens $\tilde{\pmb{x}} = \{x_{n}\}_{n = 1}^{N^{\prime}}$ , the complete motion tokens $\pmb {x} = \{x_{n}\}_{n = 1}^{N}$ , and the corresponding reconstructed continuous motions $\tilde{m}$ and $m$ . The reconstructed continuous motion sequences $\tilde{m}$ and $m$ are obtained by decoding the motion tokens by VQ decoder. The action is to sample one motion token from the complete motion token sequence at each stage. To be specific, given a motion token sequence, the agent $\pi_{\theta}(a_t|s_t)$ tries to sample a motion token that can recover the continuous motion sequences with the minimum reconstruction error. The reward measures the reconstruction difference between $\tilde{m}$ and $m$ with the minimum sample times. + +![](images/64487833a06942ff58a25558356f6c19cec3d49745c206c3d6a61b15fa11e306.jpg) +Figure 4: Priority-centric denoising schedule for motion tokens. + +After the agent is well-trained, we calculate and restore the sampling order for each motion token sequence by the agent $\pi_{\theta}(a_t|s_t)$ and compute the noise schedule for each motion token in the codebook by Eq. (13) and (14). Fig. 4 shows the noise schedule for different motion tokens w.r.t. the corresponding priorities. As shown in Fig. 4, high-priority tokens (orange and green curves) are encouraged to be corrupted at the end of the forward process such that the learnable reverse process follows a primary-to-secondary manner and high-priority tokens will be restored first. It is worth noting that both strategies are applied to design noise schedules for each token, which can be calculated and stored in advance such that the agent will not join the forward and reverse diffusion processes. Thus, there is no extra computational cost for the diffusion model during the training and inference stages. + +# 4. Experiments + +# 4.1. Datasets and Evaluation Metrics + +Our experiments are conducted on two standard text-to-motion datasets for text-to-motion generation: HumanML3D [16] and KIT-ML [36]. We follow the evaluation metrics provided in [16]. + +HumanML3D. HumanML3D [16] is currently the largest 3D human motion dataset that covers a broad range of daily human actions, for instance, exercising and dancing. The dataset contains 14,616 motion sequences and 44970 text descriptions. The motion sequences are processed to 20 frame-per-second (FPS) and cropped to 10 seconds if the motion sequences are longer than 10 seconds, resulting in duration ranges from 2 to 10 seconds. For each motion clip, the corresponding number of descriptions is at least three. + +KIT Motion-Language (KIT-ML). KIT-ML dataset [36] contains 3,911 3D human motion clips with 6,278 text descriptions. For each motion clip, one to four textual descriptions are provided. The motion sequences are collected from the KIT dataset [31] and the CMU dataset [1] with the down-sampled 12.5 FPS. + +Both of the aforementioned datasets are split into training, validation, and testing datasets with the proportions of $80\%$ , $5\%$ , and $15\%$ . + +Implementation details. Both our VQ-encoder and decoder consist of 4 transformer layers with 8 heads and the dimension is 512. For the HumanML3D [16] and KIT-ML [36] datasets, the motion sequences are cropped to 64 frames for training. We apply Adam with $\beta_{1} = 0.9$ , $\beta_{2} = 0.999$ , weight decay is 1e-4. The learning rate is 1e-4 after warmup linearly for 5 epochs. The number of tokens in the codebook is 8192. We train our VQ-VAE with a batch size of 1024 across 8 Tesla T4 for a total 100 training epochs for 8 hours. + +For the discrete diffusion model, we set timesteps $T = 100$ and the network is trained using Adam [25] with $\beta_{1} = 0.9$ , $\beta_{2} = 0.999$ . The learning rate reaches 2e-4 after 2000 iterations of a linear warmup schedule. The transformer-based discrete diffusion model consists of 12 transformer layers with 8 heads, and the dimension is 512. The text features are extracted by pre-trained CLIP [37] model. The diffusion model is trained with a batch size of 64 across 8 Tesla T4 for 100k iterations for 36 hours. + +Evaluation metrics. Following the evaluation protocols provided in previous works [16, 55, 44, 5], we evaluate the correspondences between motion and language using deep multimodal features with the pre-trained models in [16] by the following metrics: 1) Generation diversity: We randomly + +
MethodsR-Precision ↑FID ↓MM-Dist ↓Diversity →MModality ↑
Top-1Top-2Top-3
Real motion0.511±.0030.703±.0030.797±.0020.002±.0002.974±.0089.503±.065-
Our VQ-VAE0.508±.0020.691±.0020.791±.0030.63±.0013.015±.0109.577±.081-
Our VQ-VAE w/o l20.494±.0030.685±.0020.772±.0030.70±.0013.251±.0089.525±.092-
Our VQ-VAE w/o l2, Lorth0.485±.0020.671±.0030.752±.0030.79±.0013.378±.0129.511±.095-
Seq2Seq [30]0.180±.0020.300±.0020.396±.00211.75±.0355.529±.0076.223±.061-
Language2Pose [2]0.246±.0020.387±.0020.486±.00211.02±.0465.296±.0087.676±.058-
Text2Gesture [4]0.165±.0010.267±.0020.345±.0025.012±.0306.030±.0086.409±.071-
Hier [12]0.301±.0020.425±.0020.552±.0046.532±.0245.012±.0188.332±.042-
MoCoGAN [45]0.037±.0000.072±.0010.106±.00194.41±.0219.643±.0060.462±.0080.019±.000
Dance2Music [27]0.033±.0000.065±.0010.097±.00166.98±.0168.116±.0060.725±.0110.043±.001
TM2T [17]0.424±.0030.618±.0030.729±.0021.501±.0173.467±.0118.589±.0762.424±.093
Guo et al. [16]0.455±.0030.636±.0030.736±.0021.087±.0213.347±.0089.175±.0832.219±.074
MDM [44]$--0.611±.0070.544±.0445.566±.0279.559±.0862.799±.072
MotionDiffuse [56]$0.491±.0010.681±.0010.782±.0010.630±.0013.113±.0019.410±.0491.553±.042
T2M-GPT [55]0.492±.0030.679±.0020.775±.0020.141±.0053.121±.0099.722±.0821.831±.048
MLD [5]0.481±.0030.673±.0030.772±.0020.473±.0133.196±.0109.724±.0822.413±.079
M2DM (Ours) w. linear schedule0.452±.0030.678±.0020.752±.0030.417±.0043.167±.0089.972±.0893.562±.071
M2DM (Ours) w. static assessment0.492±.0030.671±.0030.775±.0030.395±.0053.116±.0089.937±.0753.413±.035
M2DM (Ours) w. dynamic assessment0.497±.0030.682±.0020.763±.0030.352±.0053.134±.0109.926±.0733.587±.072
+ +${}^{8}$ reports results using ground-truth motion length. + +Table 1: Comparison with the state-of-the-art methods on HumanML3D [16] test set. The evaluation metrics are evaluated by the motion encoder from Guo et al. [16]. The right row $\rightarrow$ means the closer to the real motion the better. + +sample 300 pairs of motions from the motion pool and extracted the selected motion features by the extractor provided by [16]. Euclidean distances of the motion pairs are computed for measuring the motion diversity. 2) R-Precision: Provided one motion representation and 32 textual descriptions, the Euclidean distances between the description feature and each motion feature in the candidates are calculated and ranked. Top-k $(k = 1,2,3)$ average accuracy of motion-to-text retrieval is reported. 3) Frechet Inception Distance (FID) [19]: FID is the principal metric to evaluate the feature descriptions between the generated motions and the ground-truth motions by the feature extractor [16]. 4) Multimodal Distance (MM-Dist): MM-Dist measures the average Euclidean distances between each text feature and the generated motion feature. 5) MModality measures the generation diversity within the same textual descriptions. Please refer to the supplementary material for a detailed introduction. + +# 4.2. Comparisons with state-of-the-art approaches + +We compare our methods with other state-of-the-art methods [30, 2, 4, 12, 45, 27, 17, 16, 44, 56, 55, 5] on the HumanML3D [16] and KIT-ML [36] datasets. + +Quantitative comparisons. For each metric, we repeat the evaluation 20 times and report the average with $95\%$ confidence interval, followed by [16]. Most of the results are borrowed from [55]. Tab. 1 and Tab. 2 summarize the comparison results on the HumanML3D [16] and the KIT-ML [36] datasets, respectively. Firstly, the metrics scores for + +our reconstruction motion achieve close performance compared with real motion, which suggests the distinctive and high-quality discrete motion tokens in the codebook learned by our Transformer-based VQ-VAE. The performance of our VQ-VAE degrades when the normalized function $\ell_2$ and the orthogonal regularization term $\mathcal{L}_{\mathrm{orth}}$ are removed. For text-to-motion generation, our approach achieves compatible performance (R-Precision, FID, and MModality) compared to other state-of-the-art methods. Moreover, compared with MDM [44] and MotionDiffuse [56] which evaluate their performance with the ground-truth motion lengths, our model can generate motion sequences with arbitrary lengths conditioned on the given textual descriptions since the [MASK] and [PAD] tokens are introduced in the discrete diffusion process. + +Furthermore, we conduct more experiments to evaluate the generation performance conditioned on different lengths of textual descriptions. The testing dataset is split into three parts according to the length of the textual descriptions: less than 15 words, between 15 words and 30 words, and more than 30 words. Tab. 3 shows the quantitative results on the aforementioned three sub-sets. Both TM2T [17] and MLD [5] suffer degradation when the textual descriptions are long and complex, especially the descriptions are more than 30 words. Our method significantly outperforms the other two methods with various metrics and there is not much degradation when the descriptions are more complex. The quantitative results demonstrate the effectiveness of our proposed primary-to-secondary diffusion manner. + +
MethodsR-Precision ↑FID ↓MM-Dist ↓Diversity →MModality ↑
Top-1Top-2Top-3
Real motion0.424±.0050.649±.0060.779±.0060.031±.0042.788±.01211.08±.097-
Our VQ-VAE (Recons.)0.417±.0040.621±.0030.741±.0060.413±.0092.772±.01810.851±.105-
Seq2Seq [30]0.103±.0030.178±.0050.241±.00624.86±.3487.960±.0316.744±.106-
Language2Pose [2]0.221±.0050.373±.0040.483±.0056.545±.0725.147±.0309.073±.100-
Text2Gesture [4]0.156±.0040.255±.0040.338±.00512.12±.1836.964±.0299.334±.079-
Hier [12]0.255±.0060.432±.0070.531±.0075.203±.1074.986±.0279.563±.072-
MoCoGAN [45]0.022±.0020.042±.0030.063±.00382.69±.24210.47±.0123.091±.0430.250±.009
Dance2Music [27]0.031±.0020.058±.0020.086±.003115.4±.24010.40±.0160.241±.0040.062±.002
TM2T [17]0.280±.0050.463±.0060.587±.0053.599±.1534.591±.0269.473±.1173.292±.081
Guo et al. [16]0.361±.0060.559±.0070.681±.0073.022±.1073.488±.02810.72±.1452.052±.107
MDM [44]$--0.396±.0040.497±.0219.191±.02210.847±.1091.907±.214
MotionDiffuse [56]$0.417±.0040.621±.0040.739±.0041.954±.0622.958±.00511.10±.1430.730±.013
T2M-GPT [55]0.416±.0060.627±.0060.745±.0060.514±.0293.007±.02310.921±.1081.570±.039
MLD [5]0.390±.0030.609±.0030.734±.0020.404±.0133.204±.01010.8±.0822.192±.079
M2DM (Ours) w. linear schedule0.405±.0030.629±.0050.739±.0040.502±.0493.012±.01511.375±.0793.273±.045
M2DM (Ours) w. static assessment0.417±.0060.625±.0030.741±.0060.521±.0413.024±.01811.373±.0813.317±.031
M2DM (Ours) w. dynamic assessment0.416±.0040.628±.0040.743±.0040.515±.0293.015±.01711.417±.973.325±.37
+ +${}^{8}$ reports results using ground-truth motion length. + +Table 2: Comparison with the state-of-the-art methods on KIT-ML [36] test set. The evaluation metrics are evaluated by the motion encoder from Guo et al. [16]. The right row $\rightarrow$ means the closer to the real motion the better. + +
TM2TMDMT2M-GPTMLDOurs
a person grabs something, turns around, walks forward, squats, stands up, walks forward, squats and stands up again.
a person puts both hands by their face in a defensive stance, then kicks with their right foot.
a person jumps and turns around in the air to face behind him.
a person walks forward briskly, crouches and lifts an object with both hands, puts the object down in a higher position, then stands up and turn right.
a person takes something, put it down and throws something.
+ +Figure 5: Qualitative comparison of the state-of-the-art methods on the HumanML3D [16] dataset. We compare our generations with TM2T [17], MDM [44], T2M-GPT [55], and MLD [5]. The color of human mesh goes from light to dark over time. + +Qualitative comparisons. Fig. 5 qualitatively compares the generated motions from the same textual descriptions. Most of the methods suffer from motion freezing if the tex + +tual descriptions consist of several complex commands. For example, the first row in Fig. 5 shows the generation results from a long textual description with various duplicate action + +
Text LengthMethodsR-Precision ↑FID ↓MM-Dist ↓Diversity →MModality ↑
Top-1Top-2Top-3
AllTM2T [17]0.424±0.0030.618±0.0030.729±0.0021.501±0.0173.467±0.0118.580±0.0762.424±0.093
MLD [5]0.481±0.0030.673±0.0030.772±0.0020.473±0.0133.196±0.0109.724±0.0822.413±0.079
M2DM (Ours)0.497±0.0030.689±0.0020.763±0.0030.352±0.0053.134±0.0109.926±0.0733.587±0.072
< 15 wordsTM2T [17]0.433±0.0030.627±0.0030.738±0.0031.592±0.0173.446±0.0088.677±0.0772.520±0.051
MLD [5]0.492±0.0030.680±0.0040.779±0.0040.469±0.0143.191±0.0119.770±0.0102.586±0.086
M2DM (Ours)0.508±0.0030.685±0.0030.767±0.0040.347±0.0153.129±0.0139.915±0.0683.594±0.077
15-30 wordsTM2T [17]0.406±0.0030.596±0.0020.708±0.0021.425±0.0143.528±0.0078.000±0.0512.477±0.057
MLD [5]0.406±0.0050.592±0.0050.701±0.0060.480±0.0203.591±0.0209.089±0.0832.727±0.094
M2DM (Ours)0.493±0.0030.681±0.0040.761±0.0040.353±0.0313.135±0.0149.926±0.0733.588±0.081
>30 wordsTM2T [17]0.353±0.0090.536±0.0090.650±0.0071.779±0.0613.577±0.0247.411±0.0712.612±0.055
MLD [5]0.289±0.0100.466±0.0120.581±0.0150.947±0.0663.870±0.0398.347±0.1002.916±0.063
M2DM (Ours)0.491±0.0040.677±0.0040.758±0.0040.356±0.0383.138±0.0259.930±0.0883.585±0.071
+ +Table 3: Comparison with the state-of-the-art methods on HumanML3D [16] test set. The evaluation metrics are evaluated by the motion encoder from Guo et al. [16]. The right row $\rightarrow$ means the closer to the real motion the better. The first three rows are the evaluation results on the whole testing dataset. The rest are the evaluation results from textual descriptions with different lengths. + +commands. MDM [44] and MLD [5] generate fewer semantic motions compared with the given description. With the help of compact discrete motion tokens, TM2T [17] and T2M-GPT [55] achieve better results compared with MDM [44] and MLD [5]. Our motion generation results conform to the textual descriptions and exhibit a high degree of diversity compared with other state-of-the-art methods, which validates the efficacy of our proposed method. + +# 4.3. Ablation studies + +We delved into the significance of various quantization techniques, as delineated in the initial four rows of Tab.1. The findings indicate that a rudimentary Transformer-based VQ-VAE struggles to reconstruct credible motion sequences, primarily due to the limited efficacy of the codebook. However, the incorporation of the $\ell_2$ norm and $\mathcal{L}_{\mathrm{orth}}$ ensures that each motion token acquires a distinct motion representation. We further scrutinized the utilization of each motion token on the HumanML3D [16] test set, with the outcomes depicted in Fig.6. As evidenced by Fig.6a and 6b, both the vanilla CNN-based VQ-VAE and Transformer-based VQ-VAE grapple with sub-optimal codebook usage. This is because the tokens in the codebook aren't inherently driven to develop a distinguishing motion representation. Yet, with the aid of the $\ell_2$ norm and $\mathcal{L}_{\mathrm{orth}}$ , there's a marked surge in the codebook token utilization. Moreover, when juxtaposing the codebook usage in Fig.6c with that in Fig.6d, the latter exhibits a more equitably distributed frequency, attributable to the orthogonal regularization term $\mathcal{L}_{\mathrm{orth}}$ . + +# 5. Conclusion + +In this study, we introduced the priority-centric motion discrete diffusion model (M2DM) tailored for text-to-motion generation. Our model excels in producing varied and life-like human motions, aligning seamlessly with the input text. This is achieved by mastering a discrete motion representa + +![](images/fc329d554b712ebab8445885af79b588165483f118280db747c3031a33d97614.jpg) + +![](images/28883f5084cde44709e4afc09a8ae2903a48ef63c332b77913d0e163e9082e7b.jpg) +(a) 1D-CNN VQ-VAE. +Figure 6: Codebook usage for different training strategies on HumanML3D [16] test set. We train our VQ-VAE (Reconstruction) with different training strategy on the HumanML3D [16] dataset. + +![](images/c0e1017151f31bbe46a5760b61b3892cd922ab459b8f8b4271862dbc78c61cd1.jpg) + +![](images/e99bc9909e6b52f64dded8cc3908bfbee41524111947c4e675d4ffad96c19899.jpg) +(c) Our VQ-VAE w. $\ell_2$ norm. +(b) Our VQ-VAE. +(d) Our VQ-VAE w. $\ell_2$ and $\mathcal{L}_{\mathrm{orth}}$ + +tion through a Transformer-based VQ-VAE and implementing a priority-informed noise schedule within the motion discrete diffusion framework. Additionally, we unveiled two innovative techniques for gauging the priority or significance of each motion token. Experimental evaluations across two datasets underscore our model's competitive edge, outpacing existing methodologies in R-Precision and diversity, particularly with intricate textual narratives. + +# Acknowledgement + +This project is supported by the Ministry of Education, Singapore, under its Academic Research Fund Tier 2 (Award Number: MOE-T2EP20122-0006). + +# References + +[1] Cmu graphics lab motion capture database. http://mocap.cs.cmu.edu/.6 +[2] Chaitanya Ahuja and Louis-Philippe Morency. Language2pose: Natural language grounded pose forecasting. In 2019 International Conference on 3D Vision (3DV), pages 719-728. IEEE, 2019. 7, 8 +[3] Jacob Austin, Daniel D Johnson, Jonathan Ho, Daniel Tarlow, and Rianne van den Berg. Structured denoising diffusion models in discrete state-spaces. Advances in Neural Information Processing Systems, 34:17981-17993, 2021. 3, 5 +[4] Uttaran Bhattacharya, Nicholas Rewkowski, Abhishek Banerjee, Pooja Guhan, Aniket Bera, and Dinesh Manocha. 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In European Conference on Computer Vision, 2022. 3 +[50] Xingyi Yang, Daquan Zhou, Jiashi Feng, and Xinchao Wang. Diffusion Probabilistic Model Made Slim. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2023. 3 +[51] Xingyi Yang, Daquan Zhou, Songhua Liu, Jingwen Ye, and Xinchao Wang. Deep model reassembly. In Advances in neural information processing systems, 2022. 3 +[52] Jiahui Yu, Yuanzhong Xu, Jing Yu Koh, Thang Luong, Gunjan Baid, Zirui Wang, Vijay Vasudevan, Alexander Ku, Yinfei Yang, Burcu Karagol Ayan, et al. Scaling autoregressive models for content-rich text-to-image generation. arXiv preprint arXiv:2206.10789, 2022. 3 +[53] Runpeng Yu, Songhua Liu, Xingyi Yang, and Xinchao Wang. Distribution Shift Inversion for Out-of-Distribution Prediction. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2023. 3 +[54] Weihao Yu, Chenyang Si, Pan Zhou, Mi Luo, Yichen Zhou, Jiashi Feng, Shuicheng Yan, and Xinchao Wang. Metaformer Baselines for Vision. arXiv preprint arXiv:2210.13452, 2022. 3 +[55] Jianrong Zhang, Yangsong Zhang, Xiaodong Cun, Shaoli Huang, Yong Zhang, Hongwei Zhao, Hongtao Lu, and Xi Shen. T2m-gpt: Generating human motion from textual descriptions with discrete representations. arXiv preprint arXiv:2301.06052, 2023. 1, 3, 6, 7, 8, 9 +[56] Mingyuan Zhang, Zhongang Cai, Liang Pan, Fangzhou Hong, Xinying Guo, Lei Yang, and Ziwei Liu. Motiondiffuse: Text-driven human motion generation with diffusion model. arXiv preprint arXiv:2208.15001, 2022. 1, 3, 7, 8 \ No newline at end of file diff --git a/2023/Priority-Centric Human Motion Generation in Discrete Latent Space/images.zip b/2023/Priority-Centric Human Motion Generation in Discrete Latent Space/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..4a39fdce465a94571038864ad08690ec2b54a511 --- /dev/null +++ b/2023/Priority-Centric Human Motion Generation in Discrete Latent Space/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c4e724f4f6e517ae72a4402bea866272999e20389bfb57145bfdbf5eb4d43751 +size 814208 diff --git a/2023/Priority-Centric Human Motion Generation in Discrete Latent Space/layout.json b/2023/Priority-Centric Human Motion Generation in Discrete Latent Space/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..91756ff6a07a358281ecf1e6ea793a41e1dd6219 --- /dev/null +++ b/2023/Priority-Centric Human Motion Generation in Discrete Latent Space/layout.json @@ -0,0 +1,10018 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 83, + 103, + 510, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 103, + 510, + 121 + ], + "spans": [ + { + "bbox": [ + 83, + 103, + 510, + 121 + ], + "type": "text", + "content": "Priority-Centric Human Motion Generation in Discrete Latent Space" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 97, + 142, + 496, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 142, + 496, + 159 + ], + "spans": [ + { + "bbox": [ + 97, + 142, + 496, + 159 + ], + "type": "text", + "content": "Hanyang Kong" + }, + { + "bbox": [ + 97, + 142, + 496, + 159 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 97, + 142, + 496, + 159 + ], + "type": "text", + "content": ", Kehong Gong" + }, + { + "bbox": [ + 97, + 142, + 496, + 159 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 97, + 142, + 496, + 159 + ], + "type": "text", + "content": ", Dongze Lian" + }, + { + "bbox": [ + 97, + 142, + 496, + 159 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 97, + 142, + 496, + 159 + ], + "type": "text", + "content": ", Michael Bi Mi" + }, + { + "bbox": [ + 97, + 142, + 496, + 159 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 97, + 142, + 496, + 159 + ], + "type": "text", + "content": ", Xinchao Wang" + }, + { + "bbox": [ + 97, + 142, + 496, + 159 + ], + "type": "inline_equation", + "content": "^{1*}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 134, + 162, + 459, + 177 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 162, + 459, + 177 + ], + "spans": [ + { + "bbox": [ + 134, + 162, + 459, + 177 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 134, + 162, + 459, + 177 + ], + "type": "text", + "content": "National University of Singapore " + }, + { + "bbox": [ + 134, + 162, + 459, + 177 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 134, + 162, + 459, + 177 + ], + "type": "text", + "content": "Huawei International Pte Ltd" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 126, + 178, + 468, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 178, + 468, + 191 + ], + "spans": [ + { + "bbox": [ + 126, + 178, + 468, + 191 + ], + "type": "text", + "content": "{hanyang.k, gongkehong}@u.nus.edu {dongze, xinchao}@nus.edu.sg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 218, + 192, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 218, + 192, + 232 + ], + "spans": [ + { + "bbox": [ + 143, + 218, + 192, + 232 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 243, + 290, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 243, + 290, + 568 + ], + "spans": [ + { + "bbox": [ + 47, + 243, + 290, + 568 + ], + "type": "text", + "content": "Text-to-motion generation is a formidable task, aiming to produce human motions that align with the input text while also adhering to human capabilities and physical laws. While there have been advancements in diffusion models, their application in discrete spaces remains underexplored. Current methods often overlook the varying significance of different motions, treating them uniformly. It is essential to recognize that not all motions hold the same relevance to a particular textual description. Some motions, being more salient and informative, should be given precedence during generation. In response, we introduce a Priority-Centric Motion Discrete Diffusion Model (M2DM), which utilizes a Transformer-based VQ-VAE to derive a concise, discrete motion representation, incorporating a global self-attention mechanism and a regularization term to counteract code collapse. We also present a motion discrete diffusion model that employs an innovative noise schedule, determined by the significance of each motion token within the entire motion sequence. This approach retains the most salient motions during the reverse diffusion process, leading to more semantically rich and varied motions. Additionally, we formulate two strategies to gauge the importance of motion tokens, drawing from both textual and visual indicators. Comprehensive experiments on the HumanML3D and KIT-ML datasets confirm that our model surpasses existing techniques in fidelity and diversity, particularly for intricate textual descriptions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 590, + 128, + 604 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 590, + 128, + 604 + ], + "spans": [ + { + "bbox": [ + 47, + 590, + 128, + 604 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 610, + 288, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 610, + 288, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 610, + 288, + 696 + ], + "type": "text", + "content": "Generating realistic and diverse 3D human motions under various conditions e.g., action labels [34, 18], natural language descriptions [55, 17, 5, 56], and musical cues [27, 28, 29], presents a significant challenge across multiple domains, including gaming, filmmaking, and robotic animation. Notably, motion generation based on language descriptions has garnered substantial interest, given its promise" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 220, + 547, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 220, + 547, + 232 + ], + "spans": [ + { + "bbox": [ + 306, + 220, + 547, + 232 + ], + "type": "text", + "content": "for enhancing realism and broadening practical applications." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 232, + 547, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 547, + 364 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 547, + 364 + ], + "type": "text", + "content": "However, generating a high-quality motion is not trivial due to the inherent modality gap and the complex mapping between text and motion modalities. Previous works [35, 43] align the latent feature space between text and motion modalities. For instance, TEMOS [35] aligns the text and motion feature by learning text and motion encoders. MotionClip [43] aligns the human motion manifold to CLIP [37] space for infusing semantic knowledge of CLIP into the motion extractor. Despite these advancements, they might encounter performance degradation when dealing with complex textual descriptions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 365, + 548, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 548, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 548, + 496 + ], + "type": "text", + "content": "To process these complex textual descriptions, some text-to-motion methods are proposed. State-of-the-art approaches such as TM2T [17] and T2M-GPT [55] use vector-quantized autoencoder (VQ-VAE) [46] to learn a discrete and compact motion representation, followed by a translation model [38, 47] to map the text modality to the motion modality. With the popularity and the superior performance in the generation tasks of diffusion models [20], MDM [44] and MLD [5] are proposed to learn conditioned diffusion models on the raw motion representation space and the latent feature space, respectively." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 497, + 548, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 548, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 548, + 688 + ], + "type": "text", + "content": "While there have been promising advancements, two primary issues remain unresolved: i) The aforementioned diffusion methods, namely MDM [44] and MLD [5], predominantly address the latent feature within a continuous space. Although VQ-VAE-inspired architectures have made considerable strides in motion generation [55, 17], particularly with the support of discrete and compact motion representations, the integration of the diffusion model into a discrete space remains inadequately explored. ii) Discrete diffusion models employed in prior studies [15, 14, 22] treat all tokens uniformly. This approach presupposes that every token conveys an equivalent amount of information, neglecting the inherent disparities among tokens within a sequence. A more intuitive generative approach for humans would involve a progressive hierarchy, commencing with overarching concepts and gradually delving into finer details." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "content": "To address the aforementioned challenges, we introduce a priority-centric motion discrete diffusion model (M2DM)" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. 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side to the left hand side." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 434, + 194, + 527, + 276 + ], + "blocks": [ + { + "bbox": [ + 434, + 194, + 527, + 276 + ], + "lines": [ + { + "bbox": [ + 434, + 194, + 527, + 276 + ], + "spans": [ + { + "bbox": [ + 434, + 194, + 527, + 276 + ], + "type": "image", + "image_path": "a8b75794bd13b135797c0134ed741dcf543f0c5d0c7087ad0abad9fa0f0f1441.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 308, + 546, + 333 + ], + "lines": [ + { + "bbox": [ + 46, + 308, + 546, + 333 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 546, + 333 + ], + "type": "text", + "content": "Figure 1: Our Priority-Centric Motion Discrete Diffusion Model (M2DM) generates diverse and precise human motions given complex textual descriptions. The color of human mesh goes from light to dark over time." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 354, + 289, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 289, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 289, + 545 + ], + "type": "text", + "content": "designed to generate motion sequences from textual descriptions, progressing in a primary to secondary manner. Initially, we employ a Transformer-based VQ-VAE, which is adept at learning a concise, discrete motion representation through the global self-attention mechanism. To circumvent code collapse and guarantee the optimal utilization of each motion token within the codebook, a regularization term is incorporated during the VQ-VAE training phase. Furthermore, we craft a noise schedule wherein individual tokens within a sequence are allocated varying corruption probabilities, contingent on their respective priorities during the forward process. Specifically, tokens of higher priority are slated for corruption towards the latter stages of the forward process. This ensures that the subsequent learnable reverse process adheres to a primary-to-secondary sequence, with top-priority tokens being reinstated foremost." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 545, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 289, + 713 + ], + "type": "text", + "content": "To discern the significance of motion tokens within a sequence, we introduce two evaluative strategies: static assessment and dynamic assessment. 1) Static assessment: Drawing inspiration from the neural language domain, where the significance of individual words is gauged by their entropy across datasets, we calculate the entropy of each motion token across the entire motion dataset. 2) Dynamic assessment: We cultivate an agent specifically to dynamically gauge the importance of tokens within a sequence. Given a discrete motion token sequence, the agent masks one token at each iteration. These masked token sequences are then fed into the VQ decoder for continuous motion reconstruction. The agent's objective is to curtail the cumulative reconstruction discrepancy between the original and the reconstructed mo" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 354, + 547, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 547, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 547, + 484 + ], + "type": "text", + "content": "tions at every phase. This is achieved using a reinforcement learning [23] (RL) strategy, facilitating the agent's identification of motion tokens that convey minimal information within a sequence—a process we term dynamic analysis. Our priority-centric discrete diffusion model has showcased commendable generative prowess, especially when dealing with intricate textual descriptions. Through rigorous testing, our method has proven its mettle, consistently matching or surpassing the performance of prevailing text-to-motion generation techniques on the HumanML3D and KIT-ML datasets." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 318, + 486, + 497, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 486, + 497, + 497 + ], + "spans": [ + { + "bbox": [ + 318, + 486, + 497, + 497 + ], + "type": "text", + "content": "We summarize our contributions as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 318, + 503, + 547, + 659 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 318, + 503, + 547, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 503, + 547, + 551 + ], + "spans": [ + { + "bbox": [ + 318, + 503, + 547, + 551 + ], + "type": "text", + "content": "- To capture long-range dependencies in the motion sequences, we apply Transformer as the architecture of VQ-VAE. Besides, a regularization term is applied to increase the usage of tokens in the codebook." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 318, + 558, + 547, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 558, + 547, + 616 + ], + "spans": [ + { + "bbox": [ + 318, + 558, + 547, + 616 + ], + "type": "text", + "content": "- We design a priority-centric scheme for human motion generation in the discrete latent space. To enhance the performance given complex descriptions, we design a novel priority-centric scheme for the discrete diffusion model." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 318, + 624, + 547, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 624, + 547, + 659 + ], + "spans": [ + { + "bbox": [ + 318, + 624, + 547, + 659 + ], + "type": "text", + "content": "- Our proposed priority-centric M2DM achieves state-of-the-art performance on the HumanML3D [16] and KIT-ML [36] datasets." + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 669, + 392, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 392, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 392, + 681 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "type": "text", + "content": "VQ-VAE. Vector Quantized Variational Autoencoder (VQ-VAE) [46] aims to minimize reconstruction error with dis" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14807" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 288 + ], + "type": "text", + "content": "crete representations by training a variational autoencoder. VQ-VAE achieves promising performance on generative tasks, such as text-to-image generation [39, 52], music generation [7], unconditional image synthesis [9], etc. For motion generation tasks, most of the methods [17, 55] tokenize the continuous motion representation by the 1D-CNN network. Since the motion style varies from person to person and the number of action combinations is almost infinite, it is essential to extract discriminative and distinctive motion features from the raw motion representations. Moreover, raw motion representation is much more redundant compared with neural language, it is feasible to represent a motion sequence using few motion tokens from a global perspective. To this end, we introduce a transformer-based VQ-VAE and several techniques are applied to balance the usage of each motion token in the codebook and prevent the codebook from collapsing, i.e., only a small proportion of codes in the codebook are activated." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 303, + 289, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 303, + 289, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 289, + 460 + ], + "type": "text", + "content": "Diffusion models. Diffusion generative models are first proposed in [42] and achieve promising results on image generation [8, 33, 21, 20, 50, 48, 53, 11, 10]. Discrete diffusion model is first proposed by [42] and several works [22, 14] apply the discrete diffusion model for text generation. D3PM [3] then applies the discrete diffusion model to the image generation task. For motion generation tasks, several works [24, 56, 44, 5] introduce diffusion models to generate diverse motion sequences from textual descriptions. In this work, we first introduce the discrete diffusion model for text-to-motion generation tasks which achieves promising results, especially for long text descriptions with several action commands." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 474, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 289, + 713 + ], + "type": "text", + "content": "Conditional human motion synthesis Compared with unconditional Human motion synthesis, human motion synthesis conditioned on various conditions, such as textual description [55, 17, 5, 56], music [27, 28, 29, 13], and actions [34, 18] is more challenging due to the huge gap between two different domains. A common strategy of conditioned human motion synthesis is to employ generative models, for instance, conditional VAE [26], and learn a latent motion representation. Text-to-motion task is more challenging because neural language is a type of information highly refined by human beings, whereas human motion is much more redundant. Most recently, several promising works [5, 16, 17, 56, 55] are proposed for text-to-motion tasks. T2M-GPT [55] and TM2T [17] regard the text-to-motion task as a translation problem. They first train a VQ-VAE [46] to tokenize the motion sequences into motion tokens, and Recurrent Neural Networks (RNN) [32], Transformer [47, 51, 49, 41, 40, 54], or GPT-like [38] models are further applied to 'translate' textual descriptions to motions. Moreover, diffusion-based [20] models are introduced for" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": "text-to-motion generation by [56, 6, 44, 5] in the contentious space. In this work, to the best of our knowledge, we are the first ones to diffuse the motion representation in the discrete latent space. Moreover, we notice that different motion clips in a whole motion sequence play various roles, for instance, stepping forward is more important than swinging arms for a running motion. We further design a diffuse schedule such that the generation process follows a from-primary-to-secondary manner." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 192, + 362, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 192, + 362, + 205 + ], + "spans": [ + { + "bbox": [ + 306, + 192, + 362, + 205 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 212, + 411, + 224 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 212, + 411, + 224 + ], + "spans": [ + { + "bbox": [ + 306, + 212, + 411, + 224 + ], + "type": "text", + "content": "3.1. Motion Tokenizer" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 231, + 545, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 231, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 304, + 231, + 545, + 302 + ], + "type": "text", + "content": "The motion tokenizer aims to learn a codebook that can represent a wide range of motion sequences with the priority awareness of motion tokens. To achieve this, we propose a transformer-based VQ-VAE that leverages self-attention to capture long-range dependencies between motion frames and learns a stable and diverse codebook." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "text", + "content": "Fig. 2 shows the overview of our motion tokenizer. Given a motion sequence " + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "inline_equation", + "content": "X \\in \\mathbb{R}^{T \\times d}" + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "text", + "content": " frames and " + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "text", + "content": " dimensional motion representation, we reconstruct the motion sequence using a transformer autoencoder and learn an informative codebook " + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "inline_equation", + "content": "Z = \\{z_k\\}_{k=1}^K" + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "text", + "content": " entries. We use the transformer encoder " + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "text", + "content": " to compute the latent motion features " + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "inline_equation", + "content": "\\boldsymbol{b} = \\{b_t\\}_{t=1}^T \\in \\mathbb{R}^{T \\times d}" + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "text", + "content": " is the dimension of the latent features. Then for each feature " + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "inline_equation", + "content": "b_t" + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "text", + "content": ", we query the codebook " + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "text", + "content": " by measuring the distance between feature " + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "inline_equation", + "content": "b_t" + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "text", + "content": " and each entry in the codebook " + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "text", + "content": ". To improve the codebook usage and avoid dead codes, we first normalize " + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "inline_equation", + "content": "b_t" + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "inline_equation", + "content": "z_t" + }, + { + "bbox": [ + 304, + 304, + 547, + 460 + ], + "type": "text", + "content": " and then measure the Euclidean distance between two normalized vectors in the unit sphere coordinate, which is formulated as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 354, + 471, + 545, + 493 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 471, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 354, + 471, + 545, + 493 + ], + "type": "interline_equation", + "content": "\\hat {b} _ {t} = \\underset {b _ {t} \\in \\boldsymbol {b}} {\\arg \\min } \\| \\ell_ {2} (b _ {t}) - \\ell_ {2} \\left(z _ {k}\\right) \\| _ {2} ^ {2}, \\tag {1}", + "image_path": "be1f89c578674cca94001a0924b72997fa1440c9eabd1a0f10851a75f9a84334.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 498, + 463, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 498, + 463, + 510 + ], + "spans": [ + { + "bbox": [ + 305, + 498, + 463, + 510 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 498, + 463, + 510 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 305, + 498, + 463, + 510 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 305, + 498, + 463, + 510 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 305, + 498, + 463, + 510 + ], + "type": "text", + "content": " normalized function." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 511, + 547, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 511, + 547, + 547 + ], + "spans": [ + { + "bbox": [ + 304, + 511, + 547, + 547 + ], + "type": "text", + "content": "The standard optimization goal consists of three parts: the reconstruction loss, the embedding loss, and the commitment loss, which is formulated as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 351, + 555, + 545, + 596 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 555, + 545, + 596 + ], + "spans": [ + { + "bbox": [ + 351, + 555, + 545, + 596 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {v q} = \\left\\| X - \\tilde {X} \\right\\| _ {2} ^ {2} + \\left\\| Z - s g [ \\hat {Z} ] \\right\\| _ {2} ^ {2} \\tag {2} \\\\ + \\eta | | s g [ Z ] - \\hat {Z} | | _ {2} ^ {2}. \\\\ \\end{array}", + "image_path": "f08592ca6cf9ffb4d5c585dcd6441245ca0648eeadd74b174b8a8b8eda7b207e.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 605, + 547, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 665 + ], + "type": "text", + "content": "Moreover, to achieve an informative codebook with diverse and high usage of its entries, we apply an orthogonal regularization. Specifically, we calculate the distance between each pair of codebook entries to enforce orthogonality among all the codebook entries:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 348, + 674, + 545, + 693 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 674, + 545, + 693 + ], + "spans": [ + { + "bbox": [ + 348, + 674, + 545, + 693 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {o r t h}} (Z) = \\left\\| \\ell_ {2} (Z) ^ {\\top} \\ell_ {2} (Z) - I _ {K} \\right\\| _ {2} ^ {2}, \\tag {3}", + "image_path": "f032fe4ccbd6f768dde4060910767adfea66a4e3b60b7e4cb454ae9b2292d612.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 701, + 466, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 466, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 466, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 701, + 466, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2" + }, + { + "bbox": [ + 306, + 701, + 466, + 713 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 306, + 701, + 466, + 713 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 306, + 701, + 466, + 713 + ], + "type": "text", + "content": " normalized function." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14808" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 70, + 539, + 244 + ], + "blocks": [ + { + "bbox": [ + 60, + 70, + 539, + 244 + ], + "lines": [ + { + "bbox": [ + 60, + 70, + 539, + 244 + ], + "spans": [ + { + "bbox": [ + 60, + 70, + 539, + 244 + ], + "type": "image", + "image_path": "5b14b9f440f563c742bd7350990b93a1daf121fbfd30f65ec94ca918acd80905.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 251, + 548, + 338 + ], + "lines": [ + { + "bbox": [ + 46, + 251, + 548, + 338 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 548, + 338 + ], + "type": "text", + "content": "Figure 2: Overview of our framework for our Motion Discrete Diffusion Model (M2DM). M2DM consists of a Transformer-based VQ-VAE (Sec. 3.1) and a discrete diffusion model (Sec. 3.2). Firstly, the Transformer-based motion tokenizer is learned to discretize motion sequences into tokens and reconstruct original motion sequences from tokens queried from the learnable codebook. Then the discrete diffusion model is learned to generate diverse motions conditioned on the textual descriptions. Two priority assessment strategies (Sec. 3.3) are applied to mask or replace motion tokens with less information at the beginning of the forward diffusion process and the most important motion tokens are corrupted in the last few diffusion steps. The diffusion model learns to restore the original motion token index conditioned on the given textual descriptions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 357, + 289, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 357, + 289, + 380 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 289, + 380 + ], + "type": "text", + "content": "Therefore, the overall training objective of vector quantization is defined as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 90, + 398, + 287, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 398, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 90, + 398, + 287, + 437 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {v q} = \\left\\| X - \\tilde {X} \\right\\| _ {2} ^ {2} + \\| Z - s g [ \\hat {Z} ] \\| _ {2} ^ {2} \\tag {4} \\\\ + \\eta | | s g [ Z ] - \\hat {Z} | | _ {2} ^ {2} + \\delta \\mathcal {L} _ {\\text {o r t h}} (Z), \\\\ \\end{array}", + "image_path": "31b04b8d0074d11fa0417a03180d7a5b735346281f5196ab3f72705d5cc5d2a6.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 460, + 288, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 460, + 288, + 485 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 288, + 485 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 460, + 288, + 485 + ], + "type": "inline_equation", + "content": "\\tilde{X} = D(\\pmb {b})" + }, + { + "bbox": [ + 47, + 460, + 288, + 485 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 460, + 288, + 485 + ], + "type": "text", + "content": " is the decoder, " + }, + { + "bbox": [ + 47, + 460, + 288, + 485 + ], + "type": "inline_equation", + "content": "sg[\\cdot ]" + }, + { + "bbox": [ + 47, + 460, + 288, + 485 + ], + "type": "text", + "content": " denotes the stopgradient operation, " + }, + { + "bbox": [ + 47, + 460, + 288, + 485 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 47, + 460, + 288, + 485 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 460, + 288, + 485 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 47, + 460, + 288, + 485 + ], + "type": "text", + "content": " are the weighting scalars." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 510, + 191, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 510, + 191, + 521 + ], + "spans": [ + { + "bbox": [ + 47, + 510, + 191, + 521 + ], + "type": "text", + "content": "3.2. 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For the denoising procedure, the real " + }, + { + "bbox": [ + 47, + 534, + 289, + 715 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 47, + 534, + 289, + 715 + ], + "type": "text", + "content": " is restored sequentially based on the pure noisy token " + }, + { + "bbox": [ + 47, + 534, + 289, + 715 + ], + "type": "inline_equation", + "content": "z_{T}" + }, + { + "bbox": [ + 47, + 534, + 289, + 715 + ], + "type": "text", + "content": ". 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" + }, + { + "bbox": [ + 47, + 534, + 289, + 715 + ], + "type": "inline_equation", + "content": "[Q_{t}]_{i,j}" + }, + { + "bbox": [ + 47, + 534, + 289, + 715 + ], + "type": "text", + "content": " is the Markov transition matrix from state " + }, + { + "bbox": [ + 47, + 534, + 289, + 715 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 534, + 289, + 715 + ], + "type": "text", + "content": " to state " + }, + { + "bbox": [ + 47, + 534, + 289, + 715 + ], + "type": "inline_equation", + "content": "t - 1" + }, + { + "bbox": [ + 47, + 534, + 289, + 715 + ], + "type": "text", + "content": " that is applied to each token in the sequence independently, which" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 357, + 379, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 357, + 379, + 367 + ], + "spans": [ + { + "bbox": [ + 306, + 357, + 379, + 367 + ], + "type": "text", + "content": "can be written as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 327, + 374, + 546, + 445 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 327, + 374, + 546, + 445 + ], + "spans": [ + { + "bbox": [ + 327, + 374, + 546, + 445 + ], + "type": "interline_equation", + "content": "\\boldsymbol {Q} _ {t} = \\left[ \\begin{array}{c c c c c} \\alpha_ {t} + \\beta_ {t} & \\beta_ {t} & \\beta_ {t} & \\dots & 0 \\\\ \\beta_ {t} & \\alpha_ {t} + \\beta_ {t} & \\beta_ {t} & \\dots & 0 \\\\ \\beta_ {t} & \\beta_ {t} & \\alpha_ {t} + \\beta_ {t} & \\dots & 0 \\\\ \\vdots & \\vdots & \\vdots & & \\vdots \\\\ \\gamma_ {t} & \\gamma_ {t} & \\gamma_ {t} & \\dots & 1 \\end{array} \\right], \\tag {5}", + "image_path": "eda12d2203cc5358199bc0715f6b18f0e2969414e7106537eed935dfe97f70b4.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 453, + 546, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 546, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 546, + 513 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 453, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\alpha_{t} \\in [0,1]" + }, + { + "bbox": [ + 304, + 453, + 546, + 513 + ], + "type": "text", + "content": " is the probability of retaining the token, " + }, + { + "bbox": [ + 304, + 453, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\gamma_{t}" + }, + { + "bbox": [ + 304, + 453, + 546, + 513 + ], + "type": "text", + "content": " is the probability of replacing the original token to [MASK] token, leaving the probability " + }, + { + "bbox": [ + 304, + 453, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\beta_{t} = (1 - \\alpha_{t} - \\gamma_{t}) / K" + }, + { + "bbox": [ + 304, + 453, + 546, + 513 + ], + "type": "text", + "content": " to be diffused. The forward Markov diffusion process for the whole token sequence is written as," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 316, + 522, + 546, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 522, + 546, + 536 + ], + "spans": [ + { + "bbox": [ + 316, + 522, + 546, + 536 + ], + "type": "interline_equation", + "content": "q \\left(\\boldsymbol {x} _ {t} \\mid \\boldsymbol {x} _ {t - 1}\\right) = \\operatorname {C a t} (\\boldsymbol {x}; \\boldsymbol {p} = \\boldsymbol {x} _ {t - 1} \\boldsymbol {Q} _ {t}) = \\boldsymbol {x} _ {t} \\boldsymbol {Q} _ {t} \\boldsymbol {x} _ {t - 1}, \\tag {6}", + "image_path": "705ec05c2573208742937af852dc79bee756c2a69d2206bd08879378bf7048a6.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 544, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 581 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 544, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 304, + 544, + 545, + 581 + ], + "type": "text", + "content": " is the one-hot row vector identifying the token index and " + }, + { + "bbox": [ + 304, + 544, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\operatorname{Cat}(\\pmb{x};\\pmb{p})" + }, + { + "bbox": [ + 304, + 544, + 545, + 581 + ], + "type": "text", + "content": " is a categorical distribution over the one-hot vector " + }, + { + "bbox": [ + 304, + 544, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\pmb{x}_t" + }, + { + "bbox": [ + 304, + 544, + 545, + 581 + ], + "type": "text", + "content": " with probabilities " + }, + { + "bbox": [ + 304, + 544, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\pmb{p}" + }, + { + "bbox": [ + 304, + 544, + 545, + 581 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 581, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 581, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 545, + 604 + ], + "type": "text", + "content": "Starting from the initial step " + }, + { + "bbox": [ + 304, + 581, + 545, + 604 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 304, + 581, + 545, + 604 + ], + "type": "text", + "content": ", the posterior diffusion process is formulated as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 328, + 613, + 545, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 613, + 545, + 669 + ], + "spans": [ + { + "bbox": [ + 328, + 613, + 545, + 669 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} q \\left(\\boldsymbol {x} _ {t - 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\\bar {\\beta} _ {t}) \\boldsymbol {m} + \\bar {\\beta} _ {t} \\tag {9}", + "image_path": "b09d7e34ae07d83180c23740960203c160a7b5206f540a1ede96e79057be709c.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 172, + 287, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 172, + 287, + 198 + ], + "spans": [ + { + "bbox": [ + 47, + 172, + 287, + 198 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 172, + 287, + 198 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 172, + 287, + 198 + ], + "type": "text", + "content": " is the one-hot vector for [MASK] and [PAD], " + }, + { + "bbox": [ + 47, + 172, + 287, + 198 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_t = \\prod_{i=1}^t \\alpha_i" + }, + { + "bbox": [ + 47, + 172, + 287, + 198 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 172, + 287, + 198 + ], + "type": "inline_equation", + "content": "\\bar{\\gamma}_t = 1 - \\prod_{i=1}^t (1 - \\gamma_i)" + }, + { + "bbox": [ + 47, + 172, + 287, + 198 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 172, + 287, + 198 + ], + "type": "inline_equation", + "content": "\\bar{\\beta}_t = (1 - \\bar{\\alpha}_t - \\bar{\\gamma}_t) / K" + }, + { + "bbox": [ + 47, + 172, + 287, + 198 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 198, + 288, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 198, + 288, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 288, + 258 + ], + "type": "text", + "content": "Regarding the reverse diffusion process, we train a transformer-like [47] denoising network " + }, + { + "bbox": [ + 46, + 198, + 288, + 258 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\pmb{x}_{t-1}|\\pmb{x}_t,\\pmb{y})" + }, + { + "bbox": [ + 46, + 198, + 288, + 258 + ], + "type": "text", + "content": " to estimate the posterior transition distribution " + }, + { + "bbox": [ + 46, + 198, + 288, + 258 + ], + "type": "inline_equation", + "content": "q(\\pmb{x}_{t-1}|\\pmb{x}_t,\\pmb{x}_0)" + }, + { + "bbox": [ + 46, + 198, + 288, + 258 + ], + "type": "text", + "content": ". The network is trained to minimize the variational lower bound (VLB) [42]:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 265, + 290, + 339 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 265, + 290, + 339 + ], + "spans": [ + { + "bbox": [ + 47, + 265, + 290, + 339 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {V L B} = \\mathbb {E} _ {q} \\left[ D _ {K L} \\left(q \\left(\\boldsymbol {x} _ {T} \\mid \\boldsymbol {x} _ {0}\\right) \\| p _ {\\theta} \\left(\\boldsymbol {x} _ {T}\\right)\\right) \\right] \\\\ + \\mathbb {E} _ {q} [ \\sum_ {t = 2} ^ {T} D _ {K L} (q (\\boldsymbol {x} _ {t - 1} | \\boldsymbol {x} _ {t}, \\boldsymbol {x} _ {0}) \\| p _ {\\theta} (\\boldsymbol {x} _ {t - 1} | \\boldsymbol {x} _ {t}, t)) ] \\\\ - \\log p _ {\\theta} \\left(\\boldsymbol {x} _ {0} \\mid \\boldsymbol {x} _ {1}\\right) \\tag {10} \\\\ \\end{array}", + "image_path": "a96deb84d5c2fb544516a1c29e0b936a4e5840963dcc24de35b3e197bf0429f2.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 340, + 288, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 288, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 288, + 365 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 340, + 288, + 365 + ], + "type": "inline_equation", + "content": "\\mathbb{E}_q[\\cdot ]" + }, + { + "bbox": [ + 46, + 340, + 288, + 365 + ], + "type": "text", + "content": " denotes the expectation over the joint distribution " + }, + { + "bbox": [ + 46, + 340, + 288, + 365 + ], + "type": "inline_equation", + "content": "q(\\pmb{x}_{0:T})" + }, + { + "bbox": [ + 46, + 340, + 288, + 365 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 371, + 233, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 371, + 233, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 371, + 233, + 384 + ], + "type": "text", + "content": "3.3. Priority-Centric Denoising Process" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 390, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 390, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 45, + 390, + 287, + 581 + ], + "type": "text", + "content": "The designation of the noise schedule in the continuous domain, for instance, the linear schedule [20] and the cosine schedule [33], achieves the excellent performance of diffusion models. The noise can be easily controlled by the variation of Gaussian noise. For the discrete diffusion models, several noise schedules [22, 3] have been explored to control the data corruption and denoise the reverse process by choosing the transition matrix " + }, + { + "bbox": [ + 45, + 390, + 287, + 581 + ], + "type": "inline_equation", + "content": "Q_{t}" + }, + { + "bbox": [ + 45, + 390, + 287, + 581 + ], + "type": "text", + "content": ". For text-to-motion generation, however, such a schedule assumes all motion tokens carry the same amount of information and do not consider the difference among the discrete tokens extracted from the continuous motion sequence. Intuitively, the motion generation process would be in a progressive manner, where the most important motion tokens should appear in earlier steps for laying a solid foundation when denoising the noise in the discrete domain." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": "Specifically, we apply the mask-and-replace strategy in Eq. (5) to corrupt each ordinary discrete token with a probability of " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\gamma_{t}" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": " for masking [MASK] token and a probability of " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": " for uniform diffusion to a random token " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "x_{k}" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": ", resulting in a remaining probability of " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\alpha_{t} = 1 - K\\beta_{t} - \\gamma_{t}" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": " for retention. When corrupting across the forward process in the discrete domain, we expect that " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_{t}^{i} < \\bar{\\alpha}_{t}^{j}" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": " if token " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": " is more informative than " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "x_{j}" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": " such that the tokens with high information emerge earlier than less informative motion tokens in the reverse process. Instead of using a normal corruption strategy with linearly increasing " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\bar{\\gamma}_{t}" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\bar{\\beta}_{t}" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": ", we propose a" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 546, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 546, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 546, + 120 + ], + "type": "text", + "content": "priority-score function " + }, + { + "bbox": [ + 304, + 72, + 546, + 120 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 72, + 546, + 120 + ], + "type": "text", + "content": " to assess the relative importance of information for a motion token sequence, which enables the recovery of the most informative tokens during the reverse process." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 121, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 121, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 121, + 547, + 180 + ], + "type": "text", + "content": "Given an original motion token sequences " + }, + { + "bbox": [ + 304, + 121, + 547, + 180 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0" + }, + { + "bbox": [ + 304, + 121, + 547, + 180 + ], + "type": "text", + "content": " at timestep 0 with length " + }, + { + "bbox": [ + 304, + 121, + 547, + 180 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 121, + 547, + 180 + ], + "type": "text", + "content": ", we aim to analyze the importance of each token " + }, + { + "bbox": [ + 304, + 121, + 547, + 180 + ], + "type": "inline_equation", + "content": "x_0^i" + }, + { + "bbox": [ + 304, + 121, + 547, + 180 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 121, + 547, + 180 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0" + }, + { + "bbox": [ + 304, + 121, + 547, + 180 + ], + "type": "text", + "content": ". Based on the information entropy theory, we calculate the information entropy for each motion token " + }, + { + "bbox": [ + 304, + 121, + 547, + 180 + ], + "type": "inline_equation", + "content": "x_0^i" + }, + { + "bbox": [ + 304, + 121, + 547, + 180 + ], + "type": "text", + "content": " as the importance score" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 375, + 190, + 546, + 222 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 190, + 546, + 222 + ], + "spans": [ + { + "bbox": [ + 375, + 190, + 546, + 222 + ], + "type": "interline_equation", + "content": "F \\left(x _ {0} ^ {i}\\right) = \\frac {N H \\left(x _ {0} ^ {i}\\right)}{\\sum_ {j = 1} ^ {N} H \\left(x _ {0} ^ {j}\\right)}, \\tag {11}", + "image_path": "8cca4785ced07527d548e4a5be1af4f9c01e3af28ba225c2c8a09e13f61683b1.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 231, + 333, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 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"bbox": [ + 305, + 280, + 535, + 293 + ], + "type": "text", + "content": " denotes the number of categories belonging to " + }, + { + "bbox": [ + 305, + 280, + 535, + 293 + ], + "type": "inline_equation", + "content": "x_{i}" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 293, + 545, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 293, + 545, + 329 + ], + "spans": [ + { + "bbox": [ + 305, + 293, + 545, + 329 + ], + "type": "text", + "content": "After obtaining the importance score function and setting linearly increasing schedule " + }, + { + "bbox": [ + 305, + 293, + 545, + 329 + ], + "type": "inline_equation", + "content": "\\bar{\\gamma}_t^i" + }, + { + "bbox": [ + 305, + 293, + 545, + 329 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 293, + 545, + 329 + ], + "type": "inline_equation", + "content": "\\bar{\\beta}_t^i" + }, + { + "bbox": [ + 305, + 293, + 545, + 329 + ], + "type": "text", + "content": " for all tokens, " + }, + { + "bbox": [ + 305, + 293, + 545, + 329 + ], + "type": "inline_equation", + "content": "\\bar{\\gamma}_t^i" + }, + { + "bbox": [ + 305, + 293, + 545, + 329 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 293, + 545, + 329 + ], + "type": "inline_equation", + "content": "\\bar{\\beta}_t^i" + }, + { + "bbox": [ + 305, + 293, + 545, + 329 + ], + "type": "text", + "content": " for specific token " + }, + { + "bbox": [ + 305, + 293, + 545, + 329 + ], + "type": "inline_equation", + "content": "x_0^i" + }, + { + "bbox": [ + 305, + 293, + 545, + 329 + ], + "type": "text", + "content": " can be further updated by" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 372, + 338, + 546, + 361 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 338, + 546, + 361 + ], + "spans": [ + { + "bbox": [ + 372, + 338, + 546, + 361 + ], + "type": "interline_equation", + "content": "\\bar {\\gamma} _ {t} ^ {i} \\Leftarrow \\bar {\\gamma} _ {t} ^ {i} \\cdot \\sin \\frac {t \\pi}{T} \\cdot F \\left(x _ {0} ^ {i}\\right), \\tag {13}", + "image_path": "c041ca22f57815f749066605dc8de60de8ac76b90e3085d87f88f25cd1616a5c.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 371, + 324, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 371, + 324, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 371, + 324, + 380 + ], + "type": "text", + "content": "and" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 372, + 380, + 546, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 380, + 546, + 403 + ], + "spans": [ + { + "bbox": [ + 372, + 380, + 546, + 403 + ], + "type": "interline_equation", + "content": "\\bar {\\beta} ^ {i} \\Leftarrow \\bar {\\beta} ^ {i} \\cdot \\sin \\frac {t \\pi}{T} \\cdot F \\left(x _ {0} ^ {i}\\right), \\tag {14}", + "image_path": "e8306b5c2effedcb2ff526555fd3c9b28f4e0a54a74c1947f444a9daded5c243.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 410, + 468, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 410, + 468, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 410, + 468, + 422 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 410, + 468, + 422 + ], + "type": "inline_equation", + "content": "x_0^i" + }, + { + "bbox": [ + 305, + 410, + 468, + 422 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 305, + 410, + 468, + 422 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 410, + 468, + 422 + ], + "type": "text", + "content": "-th token at timestep 0." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 317, + 422, + 531, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 422, + 531, + 435 + ], + "spans": [ + { + "bbox": [ + 317, + 422, + 531, + 435 + ], + "type": "text", + "content": "Now we introduce two solutions for obtaining " + }, + { + "bbox": [ + 317, + 422, + 531, + 435 + ], + "type": "inline_equation", + "content": "p(x_{i})" + }, + { + "bbox": [ + 317, + 422, + 531, + 435 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 453, + 546, + 512 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 546, + 512 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 546, + 512 + ], + "type": "text", + "content": "Static assessment. Analogously to computing the entropy for each word in natural language processing, we estimate the probability " + }, + { + "bbox": [ + 304, + 453, + 546, + 512 + ], + "type": "inline_equation", + "content": "p(x_{i})" + }, + { + "bbox": [ + 304, + 453, + 546, + 512 + ], + "type": "text", + "content": " for each motion token by counting its frequency in the quantized motion sequences over the entire dataset." + } + ] + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 347, + 523, + 506, + 652 + ], + "blocks": [ + { + "bbox": [ + 347, + 523, + 506, + 652 + ], + "lines": [ + { + "bbox": [ + 347, + 523, + 506, + 652 + ], + "spans": [ + { + "bbox": [ + 347, + 523, + 506, + 652 + ], + "type": "image", + "image_path": "3d0befa6afe7389516bbd25840dc6cd2e93ada0b6bc000589e1a52883fd2441f.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 662, + 546, + 696 + ], + "lines": [ + { + "bbox": [ + 304, + 662, + 546, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 662, + 546, + 696 + ], + "type": "text", + "content": "Figure 3: Illustration for dynamic assessment strategy. The gray blocks are masked tokens and other colorful blocks are motion tokens." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14810" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 194 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 194 + ], + "type": "text", + "content": "Dynamic assessment. Rather than counting motion token frequency and calculating the importance of each token, we further propose to learn an agent to estimate the importance of each token in the token sequences by reinforcement learning strategy. As shown in Fig. 3, given a series of complete motion tokens " + }, + { + "bbox": [ + 46, + 72, + 289, + 194 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x} = \\{x_{n}\\}_{n=1}^{N}" + }, + { + "bbox": [ + 46, + 72, + 289, + 194 + ], + "type": "text", + "content": " that are queried from the codebook at current state " + }, + { + "bbox": [ + 46, + 72, + 289, + 194 + ], + "type": "inline_equation", + "content": "s_{t} \\in S" + }, + { + "bbox": [ + 46, + 72, + 289, + 194 + ], + "type": "text", + "content": ", the scorer samples the motion tokens " + }, + { + "bbox": [ + 46, + 72, + 289, + 194 + ], + "type": "inline_equation", + "content": "\\tilde{\\boldsymbol{x}} = \\{x_{n}\\}_{n=1}^{N'}" + }, + { + "bbox": [ + 46, + 72, + 289, + 194 + ], + "type": "text", + "content": " and tries to minimize the reconstruction error between the original motion sequences " + }, + { + "bbox": [ + 46, + 72, + 289, + 194 + ], + "type": "inline_equation", + "content": "\\boldsymbol{m}" + }, + { + "bbox": [ + 46, + 72, + 289, + 194 + ], + "type": "text", + "content": " and the motion sequences decoded from the sampled tokens " + }, + { + "bbox": [ + 46, + 72, + 289, + 194 + ], + "type": "inline_equation", + "content": "\\tilde{\\boldsymbol{m}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 194 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "spans": [ + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "text", + "content": "State includes the currently selected motion tokens " + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{x}} = \\{x_{n}\\}_{n = 1}^{N^{\\prime}}" + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "text", + "content": ", the complete motion tokens " + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "inline_equation", + "content": "\\pmb {x} = \\{x_{n}\\}_{n = 1}^{N}" + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "text", + "content": ", and the corresponding reconstructed continuous motions " + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "inline_equation", + "content": "\\tilde{m}" + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "text", + "content": ". The reconstructed continuous motion sequences " + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "inline_equation", + "content": "\\tilde{m}" + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "text", + "content": " are obtained by decoding the motion tokens by VQ decoder. The action is to sample one motion token from the complete motion token sequence at each stage. To be specific, given a motion token sequence, the agent " + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "inline_equation", + "content": "\\pi_{\\theta}(a_t|s_t)" + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "text", + "content": " tries to sample a motion token that can recover the continuous motion sequences with the minimum reconstruction error. The reward measures the reconstruction difference between " + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "inline_equation", + "content": "\\tilde{m}" + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 199, + 289, + 345 + ], + "type": "text", + "content": " with the minimum sample times." + } + ] + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 55, + 365, + 279, + 466 + ], + "blocks": [ + { + "bbox": [ + 55, + 365, + 279, + 466 + ], + "lines": [ + { + "bbox": [ + 55, + 365, + 279, + 466 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 279, + 466 + ], + "type": "image", + "image_path": "64487833a06942ff58a25558356f6c19cec3d49745c206c3d6a61b15fa11e306.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 474, + 287, + 498 + ], + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 498 + ], + "type": "text", + "content": "Figure 4: Priority-centric denoising schedule for motion tokens." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "text", + "content": "After the agent is well-trained, we calculate and restore the sampling order for each motion token sequence by the agent " + }, + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\pi_{\\theta}(a_t|s_t)" + }, + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "text", + "content": " and compute the noise schedule for each motion token in the codebook by Eq. (13) and (14). Fig. 4 shows the noise schedule for different motion tokens w.r.t. the corresponding priorities. As shown in Fig. 4, high-priority tokens (orange and green curves) are encouraged to be corrupted at the end of the forward process such that the learnable reverse process follows a primary-to-secondary manner and high-priority tokens will be restored first. It is worth noting that both strategies are applied to design noise schedules for each token, which can be calculated and stored in advance such that the agent will not join the forward and reverse diffusion processes. Thus, there is no extra computational cost for the diffusion model during the training and inference stages." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 72, + 388, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 388, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 388, + 85 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 91, + 481, + 103 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 91, + 481, + 103 + ], + "spans": [ + { + "bbox": [ + 306, + 91, + 481, + 103 + ], + "type": "text", + "content": "4.1. Datasets and Evaluation Metrics" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 110, + 547, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 110, + 547, + 158 + ], + "spans": [ + { + "bbox": [ + 305, + 110, + 547, + 158 + ], + "type": "text", + "content": "Our experiments are conducted on two standard text-to-motion datasets for text-to-motion generation: HumanML3D [16] and KIT-ML [36]. We follow the evaluation metrics provided in [16]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 174, + 547, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 174, + 547, + 281 + ], + "spans": [ + { + "bbox": [ + 304, + 174, + 547, + 281 + ], + "type": "text", + "content": "HumanML3D. HumanML3D [16] is currently the largest 3D human motion dataset that covers a broad range of daily human actions, for instance, exercising and dancing. The dataset contains 14,616 motion sequences and 44970 text descriptions. The motion sequences are processed to 20 frame-per-second (FPS) and cropped to 10 seconds if the motion sequences are longer than 10 seconds, resulting in duration ranges from 2 to 10 seconds. For each motion clip, the corresponding number of descriptions is at least three." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 297, + 547, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 547, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 547, + 369 + ], + "type": "text", + "content": "KIT Motion-Language (KIT-ML). KIT-ML dataset [36] contains 3,911 3D human motion clips with 6,278 text descriptions. For each motion clip, one to four textual descriptions are provided. The motion sequences are collected from the KIT dataset [31] and the CMU dataset [1] with the down-sampled 12.5 FPS." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 369, + 547, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 369, + 547, + 405 + ], + "spans": [ + { + "bbox": [ + 305, + 369, + 547, + 405 + ], + "type": "text", + "content": "Both of the aforementioned datasets are split into training, validation, and testing datasets with the proportions of " + }, + { + "bbox": [ + 305, + 369, + 547, + 405 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 305, + 369, + 547, + 405 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 369, + 547, + 405 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 305, + 369, + 547, + 405 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 369, + 547, + 405 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 305, + 369, + 547, + 405 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 422, + 547, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 547, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 547, + 529 + ], + "type": "text", + "content": "Implementation details. Both our VQ-encoder and decoder consist of 4 transformer layers with 8 heads and the dimension is 512. For the HumanML3D [16] and KIT-ML [36] datasets, the motion sequences are cropped to 64 frames for training. We apply Adam with " + }, + { + "bbox": [ + 304, + 422, + 547, + 529 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 304, + 422, + 547, + 529 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 422, + 547, + 529 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 304, + 422, + 547, + 529 + ], + "type": "text", + "content": ", weight decay is 1e-4. The learning rate is 1e-4 after warmup linearly for 5 epochs. The number of tokens in the codebook is 8192. We train our VQ-VAE with a batch size of 1024 across 8 Tesla T4 for a total 100 training epochs for 8 hours." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 529, + 547, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 547, + 637 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 547, + 637 + ], + "type": "text", + "content": "For the discrete diffusion model, we set timesteps " + }, + { + "bbox": [ + 304, + 529, + 547, + 637 + ], + "type": "inline_equation", + "content": "T = 100" + }, + { + "bbox": [ + 304, + 529, + 547, + 637 + ], + "type": "text", + "content": " and the network is trained using Adam [25] with " + }, + { + "bbox": [ + 304, + 529, + 547, + 637 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 304, + 529, + 547, + 637 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 529, + 547, + 637 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 304, + 529, + 547, + 637 + ], + "type": "text", + "content": ". The learning rate reaches 2e-4 after 2000 iterations of a linear warmup schedule. The transformer-based discrete diffusion model consists of 12 transformer layers with 8 heads, and the dimension is 512. The text features are extracted by pre-trained CLIP [37] model. The diffusion model is trained with a batch size of 64 across 8 Tesla T4 for 100k iterations for 36 hours." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "Evaluation metrics. Following the evaluation protocols provided in previous works [16, 55, 44, 5], we evaluate the correspondences between motion and language using deep multimodal features with the pre-trained models in [16] by the following metrics: 1) Generation diversity: We randomly" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14811" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 70, + 542, + 304 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 542, + 304 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 542, + 304 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 542, + 304 + ], + "type": "table", + "html": "
MethodsR-Precision ↑FID ↓MM-Dist ↓Diversity →MModality ↑
Top-1Top-2Top-3
Real motion0.511±.0030.703±.0030.797±.0020.002±.0002.974±.0089.503±.065-
Our VQ-VAE0.508±.0020.691±.0020.791±.0030.63±.0013.015±.0109.577±.081-
Our VQ-VAE w/o l20.494±.0030.685±.0020.772±.0030.70±.0013.251±.0089.525±.092-
Our VQ-VAE w/o l2, Lorth0.485±.0020.671±.0030.752±.0030.79±.0013.378±.0129.511±.095-
Seq2Seq [30]0.180±.0020.300±.0020.396±.00211.75±.0355.529±.0076.223±.061-
Language2Pose [2]0.246±.0020.387±.0020.486±.00211.02±.0465.296±.0087.676±.058-
Text2Gesture [4]0.165±.0010.267±.0020.345±.0025.012±.0306.030±.0086.409±.071-
Hier [12]0.301±.0020.425±.0020.552±.0046.532±.0245.012±.0188.332±.042-
MoCoGAN [45]0.037±.0000.072±.0010.106±.00194.41±.0219.643±.0060.462±.0080.019±.000
Dance2Music [27]0.033±.0000.065±.0010.097±.00166.98±.0168.116±.0060.725±.0110.043±.001
TM2T [17]0.424±.0030.618±.0030.729±.0021.501±.0173.467±.0118.589±.0762.424±.093
Guo et al. [16]0.455±.0030.636±.0030.736±.0021.087±.0213.347±.0089.175±.0832.219±.074
MDM [44]$--0.611±.0070.544±.0445.566±.0279.559±.0862.799±.072
MotionDiffuse [56]$0.491±.0010.681±.0010.782±.0010.630±.0013.113±.0019.410±.0491.553±.042
T2M-GPT [55]0.492±.0030.679±.0020.775±.0020.141±.0053.121±.0099.722±.0821.831±.048
MLD [5]0.481±.0030.673±.0030.772±.0020.473±.0133.196±.0109.724±.0822.413±.079
M2DM (Ours) w. linear schedule0.452±.0030.678±.0020.752±.0030.417±.0043.167±.0089.972±.0893.562±.071
M2DM (Ours) w. static assessment0.492±.0030.671±.0030.775±.0030.395±.0053.116±.0089.937±.0753.413±.035
M2DM (Ours) w. dynamic assessment0.497±.0030.682±.0020.763±.0030.352±.0053.134±.0109.926±.0733.587±.072
", + "image_path": "f9cd13004f2232ed68f65266461c6c6dc29584485240cf341a67533677a4ea85.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 214, + 304, + 376, + 314 + ], + "lines": [ + { + "bbox": [ + 214, + 304, + 376, + 314 + ], + "spans": [ + { + "bbox": [ + 214, + 304, + 376, + 314 + ], + "type": "inline_equation", + "content": "{}^{8}" + }, + { + "bbox": [ + 214, + 304, + 376, + 314 + ], + "type": "text", + "content": " reports results using ground-truth motion length." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 315, + 545, + 339 + ], + "lines": [ + { + "bbox": [ + 46, + 315, + 545, + 339 + ], + "spans": [ + { + "bbox": [ + 46, + 315, + 545, + 339 + ], + "type": "text", + "content": "Table 1: Comparison with the state-of-the-art methods on HumanML3D [16] test set. The evaluation metrics are evaluated by the motion encoder from Guo et al. [16]. The right row " + }, + { + "bbox": [ + 46, + 315, + 545, + 339 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 315, + 545, + 339 + ], + "type": "text", + "content": " means the closer to the real motion the better." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 360, + 289, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 289, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 289, + 563 + ], + "type": "text", + "content": "sample 300 pairs of motions from the motion pool and extracted the selected motion features by the extractor provided by [16]. Euclidean distances of the motion pairs are computed for measuring the motion diversity. 2) R-Precision: Provided one motion representation and 32 textual descriptions, the Euclidean distances between the description feature and each motion feature in the candidates are calculated and ranked. Top-k " + }, + { + "bbox": [ + 46, + 360, + 289, + 563 + ], + "type": "inline_equation", + "content": "(k = 1,2,3)" + }, + { + "bbox": [ + 46, + 360, + 289, + 563 + ], + "type": "text", + "content": " average accuracy of motion-to-text retrieval is reported. 3) Frechet Inception Distance (FID) [19]: FID is the principal metric to evaluate the feature descriptions between the generated motions and the ground-truth motions by the feature extractor [16]. 4) Multimodal Distance (MM-Dist): MM-Dist measures the average Euclidean distances between each text feature and the generated motion feature. 5) MModality measures the generation diversity within the same textual descriptions. Please refer to the supplementary material for a detailed introduction." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 571, + 285, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 285, + 585 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 285, + 585 + ], + "type": "text", + "content": "4.2. Comparisons with state-of-the-art approaches" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 590, + 288, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 288, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 288, + 625 + ], + "type": "text", + "content": "We compare our methods with other state-of-the-art methods [30, 2, 4, 12, 45, 27, 17, 16, 44, 56, 55, 5] on the HumanML3D [16] and KIT-ML [36] datasets." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "type": "text", + "content": "Quantitative comparisons. For each metric, we repeat the evaluation 20 times and report the average with " + }, + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "type": "text", + "content": " confidence interval, followed by [16]. Most of the results are borrowed from [55]. Tab. 1 and Tab. 2 summarize the comparison results on the HumanML3D [16] and the KIT-ML [36] datasets, respectively. Firstly, the metrics scores for" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 360, + 547, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 360, + 547, + 539 + ], + "spans": [ + { + "bbox": [ + 304, + 360, + 547, + 539 + ], + "type": "text", + "content": "our reconstruction motion achieve close performance compared with real motion, which suggests the distinctive and high-quality discrete motion tokens in the codebook learned by our Transformer-based VQ-VAE. The performance of our VQ-VAE degrades when the normalized function " + }, + { + "bbox": [ + 304, + 360, + 547, + 539 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 304, + 360, + 547, + 539 + ], + "type": "text", + "content": " and the orthogonal regularization term " + }, + { + "bbox": [ + 304, + 360, + 547, + 539 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{orth}}" + }, + { + "bbox": [ + 304, + 360, + 547, + 539 + ], + "type": "text", + "content": " are removed. For text-to-motion generation, our approach achieves compatible performance (R-Precision, FID, and MModality) compared to other state-of-the-art methods. Moreover, compared with MDM [44] and MotionDiffuse [56] which evaluate their performance with the ground-truth motion lengths, our model can generate motion sequences with arbitrary lengths conditioned on the given textual descriptions since the [MASK] and [PAD] tokens are introduced in the discrete diffusion process." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": "Furthermore, we conduct more experiments to evaluate the generation performance conditioned on different lengths of textual descriptions. The testing dataset is split into three parts according to the length of the textual descriptions: less than 15 words, between 15 words and 30 words, and more than 30 words. Tab. 3 shows the quantitative results on the aforementioned three sub-sets. Both TM2T [17] and MLD [5] suffer degradation when the textual descriptions are long and complex, especially the descriptions are more than 30 words. Our method significantly outperforms the other two methods with various metrics and there is not much degradation when the descriptions are more complex. The quantitative results demonstrate the effectiveness of our proposed primary-to-secondary diffusion manner." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14812" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 70, + 542, + 284 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 542, + 284 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 542, + 284 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 542, + 284 + ], + "type": "table", + "html": "
MethodsR-Precision ↑FID ↓MM-Dist ↓Diversity →MModality ↑
Top-1Top-2Top-3
Real motion0.424±.0050.649±.0060.779±.0060.031±.0042.788±.01211.08±.097-
Our VQ-VAE (Recons.)0.417±.0040.621±.0030.741±.0060.413±.0092.772±.01810.851±.105-
Seq2Seq [30]0.103±.0030.178±.0050.241±.00624.86±.3487.960±.0316.744±.106-
Language2Pose [2]0.221±.0050.373±.0040.483±.0056.545±.0725.147±.0309.073±.100-
Text2Gesture [4]0.156±.0040.255±.0040.338±.00512.12±.1836.964±.0299.334±.079-
Hier [12]0.255±.0060.432±.0070.531±.0075.203±.1074.986±.0279.563±.072-
MoCoGAN [45]0.022±.0020.042±.0030.063±.00382.69±.24210.47±.0123.091±.0430.250±.009
Dance2Music [27]0.031±.0020.058±.0020.086±.003115.4±.24010.40±.0160.241±.0040.062±.002
TM2T [17]0.280±.0050.463±.0060.587±.0053.599±.1534.591±.0269.473±.1173.292±.081
Guo et al. [16]0.361±.0060.559±.0070.681±.0073.022±.1073.488±.02810.72±.1452.052±.107
MDM [44]$--0.396±.0040.497±.0219.191±.02210.847±.1091.907±.214
MotionDiffuse [56]$0.417±.0040.621±.0040.739±.0041.954±.0622.958±.00511.10±.1430.730±.013
T2M-GPT [55]0.416±.0060.627±.0060.745±.0060.514±.0293.007±.02310.921±.1081.570±.039
MLD [5]0.390±.0030.609±.0030.734±.0020.404±.0133.204±.01010.8±.0822.192±.079
M2DM (Ours) w. linear schedule0.405±.0030.629±.0050.739±.0040.502±.0493.012±.01511.375±.0793.273±.045
M2DM (Ours) w. static assessment0.417±.0060.625±.0030.741±.0060.521±.0413.024±.01811.373±.0813.317±.031
M2DM (Ours) w. dynamic assessment0.416±.0040.628±.0040.743±.0040.515±.0293.015±.01711.417±.973.325±.37
", + "image_path": "ae6150a8e1c2a9bdf849573f0306b72d6a23f0def0aaa4aaa7b5b1caea5b8038.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 214, + 285, + 376, + 294 + ], + "lines": [ + { + "bbox": [ + 214, + 285, + 376, + 294 + ], + "spans": [ + { + "bbox": [ + 214, + 285, + 376, + 294 + ], + "type": "inline_equation", + "content": "{}^{8}" + }, + { + "bbox": [ + 214, + 285, + 376, + 294 + ], + "type": "text", + "content": " reports results using ground-truth motion length." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 52, + 331, + 544, + 616 + ], + "blocks": [ + { + "bbox": [ + 46, + 294, + 546, + 319 + ], + "lines": [ + { + "bbox": [ + 46, + 294, + 546, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 546, + 319 + ], + "type": "text", + "content": "Table 2: Comparison with the state-of-the-art methods on KIT-ML [36] test set. The evaluation metrics are evaluated by the motion encoder from Guo et al. [16]. The right row " + }, + { + "bbox": [ + 46, + 294, + 546, + 319 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 294, + 546, + 319 + ], + "type": "text", + "content": " means the closer to the real motion the better." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 331, + 544, + 616 + ], + "lines": [ + { + "bbox": [ + 52, + 331, + 544, + 616 + ], + "spans": [ + { + "bbox": [ + 52, + 331, + 544, + 616 + ], + "type": "table", + "html": "
TM2TMDMT2M-GPTMLDOurs
a person grabs something, turns around, walks forward, squats, stands up, walks forward, squats and stands up again.
a person puts both hands by their face in a defensive stance, then kicks with their right foot.
a person jumps and turns around in the air to face behind him.
a person walks forward briskly, crouches and lifts an object with both hands, puts the object down in a higher position, then stands up and turn right.
a person takes something, put it down and throws something.
", + "image_path": "df198118ee40c61ad1c53f774873c14103d6ce10cad67b2ec089f41744a4eff8.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 625, + 546, + 651 + ], + "lines": [ + { + "bbox": [ + 46, + 625, + 546, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 625, + 546, + 651 + ], + "type": "text", + "content": "Figure 5: Qualitative comparison of the state-of-the-art methods on the HumanML3D [16] dataset. We compare our generations with TM2T [17], MDM [44], T2M-GPT [55], and MLD [5]. The color of human mesh goes from light to dark over time." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 670, + 289, + 707 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 670, + 289, + 707 + ], + "spans": [ + { + "bbox": [ + 46, + 670, + 289, + 707 + ], + "type": "text", + "content": "Qualitative comparisons. Fig. 5 qualitatively compares the generated motions from the same textual descriptions. Most of the methods suffer from motion freezing if the tex" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 670, + 547, + 707 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 670, + 547, + 707 + ], + "spans": [ + { + "bbox": [ + 305, + 670, + 547, + 707 + ], + "type": "text", + "content": "tual descriptions consist of several complex commands. For example, the first row in Fig. 5 shows the generation results from a long textual description with various duplicate action" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14813" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 70, + 294, + 160 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 294, + 160 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 294, + 160 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 294, + 160 + ], + "type": "table", + "html": "
Text LengthMethodsR-Precision ↑FID ↓MM-Dist ↓Diversity →MModality ↑
Top-1Top-2Top-3
AllTM2T [17]0.424±0.0030.618±0.0030.729±0.0021.501±0.0173.467±0.0118.580±0.0762.424±0.093
MLD [5]0.481±0.0030.673±0.0030.772±0.0020.473±0.0133.196±0.0109.724±0.0822.413±0.079
M2DM (Ours)0.497±0.0030.689±0.0020.763±0.0030.352±0.0053.134±0.0109.926±0.0733.587±0.072
< 15 wordsTM2T [17]0.433±0.0030.627±0.0030.738±0.0031.592±0.0173.446±0.0088.677±0.0772.520±0.051
MLD [5]0.492±0.0030.680±0.0040.779±0.0040.469±0.0143.191±0.0119.770±0.0102.586±0.086
M2DM (Ours)0.508±0.0030.685±0.0030.767±0.0040.347±0.0153.129±0.0139.915±0.0683.594±0.077
15-30 wordsTM2T [17]0.406±0.0030.596±0.0020.708±0.0021.425±0.0143.528±0.0078.000±0.0512.477±0.057
MLD [5]0.406±0.0050.592±0.0050.701±0.0060.480±0.0203.591±0.0209.089±0.0832.727±0.094
M2DM (Ours)0.493±0.0030.681±0.0040.761±0.0040.353±0.0313.135±0.0149.926±0.0733.588±0.081
>30 wordsTM2T [17]0.353±0.0090.536±0.0090.650±0.0071.779±0.0613.577±0.0247.411±0.0712.612±0.055
MLD [5]0.289±0.0100.466±0.0120.581±0.0150.947±0.0663.870±0.0398.347±0.1002.916±0.063
M2DM (Ours)0.491±0.0040.677±0.0040.758±0.0040.356±0.0383.138±0.0259.930±0.0883.585±0.071
", + "image_path": "420cc7244abe45a33681b07f0d5cdf88593415861b117205df0de0cf0fd1f147.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 290, + 253 + ], + "lines": [ + { + "bbox": [ + 46, + 168, + 290, + 253 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 290, + 253 + ], + "type": "text", + "content": "Table 3: Comparison with the state-of-the-art methods on HumanML3D [16] test set. The evaluation metrics are evaluated by the motion encoder from Guo et al. [16]. The right row " + }, + { + "bbox": [ + 46, + 168, + 290, + 253 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 168, + 290, + 253 + ], + "type": "text", + "content": " means the closer to the real motion the better. The first three rows are the evaluation results on the whole testing dataset. The rest are the evaluation results from textual descriptions with different lengths." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 273, + 289, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 273, + 289, + 370 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 289, + 370 + ], + "type": "text", + "content": "commands. MDM [44] and MLD [5] generate fewer semantic motions compared with the given description. With the help of compact discrete motion tokens, TM2T [17] and T2M-GPT [55] achieve better results compared with MDM [44] and MLD [5]. Our motion generation results conform to the textual descriptions and exhibit a high degree of diversity compared with other state-of-the-art methods, which validates the efficacy of our proposed method." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 376, + 146, + 389 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 146, + 389 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 146, + 389 + ], + "type": "text", + "content": "4.3. Ablation studies" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 395, + 290, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 395, + 290, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 395, + 290, + 624 + ], + "type": "text", + "content": "We delved into the significance of various quantization techniques, as delineated in the initial four rows of Tab.1. The findings indicate that a rudimentary Transformer-based VQ-VAE struggles to reconstruct credible motion sequences, primarily due to the limited efficacy of the codebook. However, the incorporation of the " + }, + { + "bbox": [ + 46, + 395, + 290, + 624 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 46, + 395, + 290, + 624 + ], + "type": "text", + "content": " norm and " + }, + { + "bbox": [ + 46, + 395, + 290, + 624 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{orth}}" + }, + { + "bbox": [ + 46, + 395, + 290, + 624 + ], + "type": "text", + "content": " ensures that each motion token acquires a distinct motion representation. We further scrutinized the utilization of each motion token on the HumanML3D [16] test set, with the outcomes depicted in Fig.6. As evidenced by Fig.6a and 6b, both the vanilla CNN-based VQ-VAE and Transformer-based VQ-VAE grapple with sub-optimal codebook usage. This is because the tokens in the codebook aren't inherently driven to develop a distinguishing motion representation. Yet, with the aid of the " + }, + { + "bbox": [ + 46, + 395, + 290, + 624 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 46, + 395, + 290, + 624 + ], + "type": "text", + "content": " norm and " + }, + { + "bbox": [ + 46, + 395, + 290, + 624 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{orth}}" + }, + { + "bbox": [ + 46, + 395, + 290, + 624 + ], + "type": "text", + "content": ", there's a marked surge in the codebook token utilization. Moreover, when juxtaposing the codebook usage in Fig.6c with that in Fig.6d, the latter exhibits a more equitably distributed frequency, attributable to the orthogonal regularization term " + }, + { + "bbox": [ + 46, + 395, + 290, + 624 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{orth}}" + }, + { + "bbox": [ + 46, + 395, + 290, + 624 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 633, + 120, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 633, + 120, + 645 + ], + "spans": [ + { + "bbox": [ + 47, + 633, + 120, + 645 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "content": "In this study, we introduced the priority-centric motion discrete diffusion model (M2DM) tailored for text-to-motion generation. Our model excels in producing varied and life-like human motions, aligning seamlessly with the input text. This is achieved by mastering a discrete motion representa" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 306, + 70, + 425, + 145 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 425, + 145 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 425, + 145 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 425, + 145 + ], + "type": "image", + "image_path": "fc329d554b712ebab8445885af79b588165483f118280db747c3031a33d97614.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 306, + 163, + 425, + 237 + ], + "blocks": [ + { + "bbox": [ + 328, + 152, + 403, + 161 + ], + "lines": [ + { + "bbox": [ + 328, + 152, + 403, + 161 + ], + "spans": [ + { + "bbox": [ + 328, + 152, + 403, + 161 + ], + "type": "text", + "content": "(a) 1D-CNN VQ-VAE." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 163, + 425, + 237 + ], + "lines": [ + { + "bbox": [ + 306, + 163, + 425, + 237 + ], + "spans": [ + { + "bbox": [ + 306, + 163, + 425, + 237 + ], + "type": "image", + "image_path": "28883f5084cde44709e4afc09a8ae2903a48ef63c332b77913d0e163e9082e7b.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 262, + 548, + 310 + ], + "lines": [ + { + "bbox": [ + 305, + 262, + 548, + 310 + ], + "spans": [ + { + "bbox": [ + 305, + 262, + 548, + 310 + ], + "type": "text", + "content": "Figure 6: Codebook usage for different training strategies on HumanML3D [16] test set. We train our VQ-VAE (Reconstruction) with different training strategy on the HumanML3D [16] dataset." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 427, + 75, + 545, + 145 + ], + "blocks": [ + { + "bbox": [ + 427, + 75, + 545, + 145 + ], + "lines": [ + { + "bbox": [ + 427, + 75, + 545, + 145 + ], + "spans": [ + { + "bbox": [ + 427, + 75, + 545, + 145 + ], + "type": "image", + "image_path": "c0e1017151f31bbe46a5760b61b3892cd922ab459b8f8b4271862dbc78c61cd1.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 427, + 163, + 545, + 236 + ], + "blocks": [ + { + "bbox": [ + 317, + 242, + 414, + 252 + ], + "lines": [ + { + "bbox": [ + 317, + 242, + 414, + 252 + ], + "spans": [ + { + "bbox": [ + 317, + 242, + 414, + 252 + ], + "type": "text", + "content": "(c) Our VQ-VAE w. " + }, + { + "bbox": [ + 317, + 242, + 414, + 252 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 317, + 242, + 414, + 252 + ], + "type": "text", + "content": " norm." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 456, + 152, + 517, + 161 + ], + "lines": [ + { + "bbox": [ + 456, + 152, + 517, + 161 + ], + "spans": [ + { + "bbox": [ + 456, + 152, + 517, + 161 + ], + "type": "text", + "content": "(b) Our VQ-VAE." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 427, + 163, + 545, + 236 + ], + "lines": [ + { + "bbox": [ + 427, + 163, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 427, + 163, + 545, + 236 + ], + "type": "image", + "image_path": "e99bc9909e6b52f64dded8cc3908bfbee41524111947c4e675d4ffad96c19899.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 429, + 242, + 543, + 253 + ], + "lines": [ + { + "bbox": [ + 429, + 242, + 543, + 253 + ], + "spans": [ + { + "bbox": [ + 429, + 242, + 543, + 253 + ], + "type": "text", + "content": "(d) Our VQ-VAE w. " + }, + { + "bbox": [ + 429, + 242, + 543, + 253 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 429, + 242, + 543, + 253 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 429, + 242, + 543, + 253 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{orth}}" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 332, + 548, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 332, + 548, + 429 + ], + "spans": [ + { + "bbox": [ + 304, + 332, + 548, + 429 + ], + "type": "text", + "content": "tion through a Transformer-based VQ-VAE and implementing a priority-informed noise schedule within the motion discrete diffusion framework. Additionally, we unveiled two innovative techniques for gauging the priority or significance of each motion token. Experimental evaluations across two datasets underscore our model's competitive edge, outpacing existing methodologies in R-Precision and diversity, particularly with intricate textual narratives." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 441, + 404, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 404, + 455 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 404, + 455 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 463, + 547, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 463, + 547, + 498 + ], + "spans": [ + { + "bbox": [ + 305, + 463, + 547, + 498 + ], + "type": "text", + "content": "This project is supported by the Ministry of Education, Singapore, under its Academic Research Fund Tier 2 (Award Number: MOE-T2EP20122-0006)." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 511, + 365, + 523 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 511, + 365, + 523 + ], + "spans": [ + { + "bbox": [ + 306, + 511, + 365, + 523 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 310, + 532, + 548, + 712 + ], + "type": "list", + "angle": 0, + "index": 24, + "blocks": [ + { + "bbox": [ + 310, + 532, + 547, + 553 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 532, + 547, + 553 + ], + "spans": [ + { + "bbox": [ + 310, + 532, + 547, + 553 + ], + "type": "text", + "content": "[1] Cmu graphics lab motion capture database. http://mocap.cs.cmu.edu/.6" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 311, + 555, + 547, + 599 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 555, + 547, + 599 + ], + "spans": [ + { + "bbox": [ + 311, + 555, + 547, + 599 + ], + "type": "text", + "content": "[2] Chaitanya Ahuja and Louis-Philippe Morency. 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Schonberger2 Viktor Larsson3 Marc Pollefeys1,2 ETH Zurich Microsoft Lund University", + "bbox": [ + 163, + 179, + 844, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1{linfei.pan,marc.pollefeys}@inf.ethz.ch,2joschonb@microsoft.com,3viktor.larsson@math.lth.se", + "bbox": [ + 84, + 215, + 919, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent methods on privacy-preserving image-based localization use a random line parameterization to protect the privacy of query images and database maps. The lifting of points to lines effectively drops one of the two geometric constraints traditionally used with point-to-point correspondences in structure-based localization. This leads to a significant loss of accuracy for the privacy-preserving methods. In this paper, we overcome this limitation by devising a coordinate permutation scheme that allows for recovering the original point positions during pose estimation. The recovered points provide the full 2D geometric constraints and enable us to close the gap between privacy-preserving and traditional methods in terms of accuracy. Another limitation of random line methods is their vulnerability to density based 3D line cloud inversion attacks. Our method not only provides better accuracy than the original random line based approach but also provides stronger privacy guarantees against these recently proposed attacks. Extensive experiments on standard benchmark datasets demonstrate these improvements consistently across both scenarios of protecting the privacy of query images as well as the database map.", + "bbox": [ + 75, + 301, + 473, + 633 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 662, + 209, + 679 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The interest in commercial solutions for cloud-based localization and mapping in mixed reality and robotics (e.g., Google VPS [34], Microsoft Azure Spatial Anchors [21], or Facebook LiveMaps [1]) has raised a host of privacy concerns [24, 31, 35, 51]. Recently, several approaches have been introduced by the research community to address these concerns [14, 17-19, 25, 45-47]. The common theme underlying these methods is based on the principle of lifting traditional point-based features to randomly oriented lines to conceal the appearance of query images and database maps.", + "bbox": [ + 75, + 688, + 468, + 840 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While this family of approaches is successful in enabling privacy preserving image-based localization and mapping, it comes at significant trade-offs in terms of accuracy and recall. These trade-offs are primarily caused by the fact that", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/524c6b154c2a14c46cacf05b0c2a3aa503f66a41bac75c032d1d12660794369b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 270, + 696, + 416 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d2399fcb7658fe3c79a7ec4e74dd914c3cacf990cf989a1d6588aca9083aa944.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 522, + 431, + 696, + 536 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e1b5aada20d4f28e8c3633c703f0a32d355ad8acbd868d1aef5abaa15185b738.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 277, + 888, + 415 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f95403eda44190c1f50465ad34d41ad45cafe1ca676559edecc618a2a2c298e6.jpg", + "image_caption": [ + "Figure 1: Privacy-preserving localization. Top Left: The client extracts keypoints and descriptors from the query image. Top Right: The client secretly pairs keypoints and permutes their coordinates; hiding their true position from the server. Bottom Left: Server performs localization using the permuted points and recovers the original 2D positions for points that exist in both query and map. Bottom Right: Feature inversion on the set of recovered points only reveals objects that are already present in the map." + ], + "image_footnote": [], + "bbox": [ + 697, + 420, + 887, + 566 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the privacy preserving line-to-point or point-to-line correspondences provide weaker geometric constraints than the traditional point-to-point correspondences [46]. When concealing the content of images or maps, the number of constraints is effectively halved, as each point-to-line or line-to-point reprojection only contributes a 1D geometric constraint compared to the 2D constraint from a point-to-point reprojection. Especially for the hard to localize images, where only few correspondences can be recovered during feature matching, this limitation makes a significant difference in terms of accuracy and recall.", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18174", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Furthermore, without careful construction of random line maps, density based attacks have been shown to be effective in uncovering information from the privacy preserving representations, which was already mentioned as a limitation by Speciale et al. [46]. The main idea behind density based attacks exploits the fact that pairs of randomly oriented lines have a relatively higher chance of intersecting near the true surface as compared to empty or unobserved space. As such, a naive attack could simply gather statistics from pairwise intersections of random lines and assume the true surface in dense regions of the intersected space. More sophisticated attacks based on this idea can yield realistic image renderings from 3D line maps when attacking naively constructed line maps [9].", + "bbox": [ + 75, + 90, + 472, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we revisit the approach of lifting points to lines in order to improve upon these two main limitations. In contrast to the original approach, we introduce a coordinate permutation scheme by which we effectively construct axis-aligned lines. During the pose estimation routine, the permutation scheme enables us to recover the original points for a large fraction of the inlier correspondences. Therefore, we can use the same 2D geometric constraints as in the traditional setup. This significantly improves the accuracy of the localization results. Moreover, when applying our approach for hiding the 3D map, we drastically increase the combinatorial complexity for density based attacks as well as reduce the chance for line intersections due to constructing axis-aligned lines. Counter-intuitively, our proposed method therefore not only leads to better accuracy but also provides a stronger level of privacy preservation. We experimentally demonstrate these improvements on standard benchmark datasets and by attacking our axis-aligned line maps using the approach by Chelani et al. [9]. In summary, we make the following contributions:", + "bbox": [ + 75, + 301, + 472, + 604 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Propose a new privacy-preserving lifting approach, applicable to protecting the map and query.", + "- Attacking the lifted representation has a higher combinatorial complexity compared to random lifting, rendering previous density based attacks ineffective.", + "- In contrast to previous work, we can recover the original 2D or 3D points, allowing for stronger geometric constraints and more accurate poses.", + "- Experimentally, we show significant improvements over previous privacy preserving work, closing the gap to traditional point-based non-private methods." + ], + "bbox": [ + 96, + 613, + 467, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 829, + 218, + 845 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image-based Localization Methods in image-based localization have made tremendous progress. Over the years, the methods have been scaled for robust localization in", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "large-scale scenes [27,38,40,54] with compressed map representations [8,15], while some of the methods can even run in real-time on mobile devices [4,20,22,27,28,39]. Some of the recent works focus on improving the robustness to drastic environmental changes [3,42,50] or enabling crossdevice localization and mapping scenarios [13]. The developed approaches are generally divided into structure-based methods [20, 38-40] using on an explicit geometric map representation or learning-based methods [7,22,44] with an implicit map representation.", + "bbox": [ + 496, + 90, + 890, + 243 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Privacy Risks Image-based localization is subject to privacy risks due to requiring images as an input [24, 31, 35, 51]. For example, in a cloud-based localization system, users may be concerned about sharing images of private spaces with the service provider. In a practical setting, the clients could only send local image features to the cloud to avoid these risks. However, recent inversion attacks have proven extremely effective in recovering the original images from only sparse local image features [12, 30, 32]. Recently, Chelani et al. proposed a method to query a localization service with a database of objects to recover information about scene contents [10].", + "bbox": [ + 496, + 261, + 890, + 443 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Privacy Preservation To protect against these risks, several methods have been developed recently. The first work on this topic [46, 47] proposed a solution to preserve the privacy of 2D image or 3D map points in image-based localization. Their main idea was to lift 2D or 3D points to random lines by dropping one of the two geometric constraints during the pose estimation problem. Based on the same idea, a number of works followed up to address the problems of structure-from-motion [18, 19] and real-time SLAM [45], or to directly protect the high-dimensional feature representations instead of the geometry [14].", + "bbox": [ + 496, + 462, + 890, + 628 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Underlying all these approaches, there are two fundamental limitations that were already observed by the original work [47]. First, by dropping one geometric constraint per correspondence for pose estimation, the accuracy of these approaches is significantly lowered, especially in the challenging cases with few matches between query and database. Second, without careful sparsification of the 3D map, density based attacks can recover information from 3D line clouds [9]. Sparsification of the map is an effective protection against density based attacks but comes with a further reduction of accuracy as well as recall.", + "bbox": [ + 496, + 628, + 890, + 794 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To protect in a more principled manner against these attacks, Geppert et al. [17] proposed to decompose the full 3D map into 1D partial maps, which are distributed across different servers. Each server then solves a partial localization problem and sends back the answer to the client, which can assemble a full 6-DoF localization result from the partial answers. Despite being effective against density based at", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18175", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/4cf0f0d1a72c8c2e4aa121a4a6dd209e9abbe199ab036ac03a486d34397c0373.jpg", + "image_caption": [ + "Figure 2: Method overview for localization with private queries. The client extracts keypoints in the query image and secretly pairs them to swap one of their coordinates. The server only receives the permuted points, which can be considered as axis-aligned lines. The secretly paired points form rectangles, which can be leveraged during RANSAC to efficiently recover the original point positions for pairs that are both inliers. The scoring of candidate poses and the final non-linear pose refinement jointly leverage the stronger 2D constraints for recovered points and otherwise the weaker 1D constraints." + ], + "image_footnote": [], + "bbox": [ + 117, + 87, + 410, + 215 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9723d42c230ae8c976a9a35e81051ea175c704f4c571dc3ced2864ac61d4fe8e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 416, + 88, + 846, + 215 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tacks, the system is complex and it comes with further accuracy and recall trade-offs. In contrast, our method does not require a complex multi-server setup and we improve upon the two main limitations of the random lifting approaches simultaneously. Our method provides both stronger privacy guarantees while also closing the accuracy gap to traditional localization approaches.", + "bbox": [ + 75, + 310, + 472, + 416 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 440, + 168, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We now present our method for privacy-preserving localization. We address both the scenario of protecting the client's 2D image points in the localization query (Section 3.2) as well as protecting the service's 3D points in the database map (Section 3.3).", + "bbox": [ + 75, + 470, + 468, + 546 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our approach follows the main idea in Speciale et al. [46, 47], where the exact 2D or 3D point positions are hidden by introducing ambiguity in the coordinates. In the original works, this is done by lifting each point to a random line. The line representation still enables localization, using line-to-point instead of point-to-point correspondences, but makes it difficult to identify potentially sensitive image or map content. Similar to the original idea [46], we also obscure the true position of the point. However, instead of replacing it with a random line, we select a subset of the point coordinates and corrupt them. This is done by secretly forming pairs of points and swapping their coordinates at random. Since the list of pairs is not known to an attacker, it is practically intractable to recover the original point positions. As we will later show, for point-pairs that exist in both the query and the map, we can devise a scheme to recover the true positions, allowing us to use the full 2D-3D geometric constraints for accurate pose refinement.", + "bbox": [ + 75, + 549, + 470, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An overview of our pipeline can be found in Figure 2 and we detail the steps of our method in the following sections. For ease of presentation, we first review the traditional setup and then explain the 2D setting that hides the query, but the same principle generalizes to the 3D setting as well.", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Review of Traditional Localization", + "text_level": 1, + "bbox": [ + 498, + 309, + 802, + 324 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Traditionally, localization is performed by establishing a set of tentative 2D-3D point correspondences between the query image and the database map. Each correspondence $(\\pmb{x},\\pmb{X})\\in \\mathbb{R}^2\\times \\mathbb{R}^3$ yields two geometric constraints on the unknown camera pose $(R,t)\\in \\mathrm{SE}(3)$ as", + "bbox": [ + 496, + 332, + 890, + 409 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\lambda \\bar {\\boldsymbol {x}} = R \\boldsymbol {X} + \\boldsymbol {t}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 637, + 417, + 890, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where we let $\\bar{x}$ denote the homogeneous 2D point in the normalized image plane (after removing the intrinsic calibration), and $\\lambda$ represents the unknown depth. To identify outlier matches and estimate an initial pose, the standard approach is to use hypothesize-and-test frameworks, such as RANSAC [16], in order to generate multiple pose candidates by fitting $(R,t)$ to minimal subsets of the points, followed by measuring the consensus among the rest of the matches. The consistency between a candidate pose and a 2D-3D match is computed using the 2D reprojection error", + "bbox": [ + 496, + 440, + 892, + 592 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nd _ {p} = \\| \\boldsymbol {x} - \\pi (R \\boldsymbol {X} + t) \\|, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 599, + 890, + 618 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\pi : \\mathbb{R}^3 \\to \\mathbb{R}^2$ is the projection mapping. Once a candidate pose, together with the inlier matches, have been established, it is refined by minimizing the reprojection errors for all inliers jointly.", + "bbox": [ + 496, + 625, + 890, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Localization with Private Queries", + "text_level": 1, + "bbox": [ + 500, + 693, + 794, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The traditional method relies on the availability of the original 2D image points, and is thus not privacy preserving. To preserve the privacy of the image, Speciale et al. [47] proposed to lift 2D image points into random 2D lines. Our method also builds upon 2D lines but aligns them with the coordinate axes through a random coordinate permutation scheme. The following paragraphs first establish notation by reviewing (random) line constraints for localization and then explain our permutation scheme in detail.", + "bbox": [ + 496, + 715, + 890, + 852 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Random Line Constraints In Speciale et al. [47], each 2D line $\\ell$ back-projects into a 3D plane $\\Pi_i = P^\\top \\ell_i$ passing", + "bbox": [ + 500, + 869, + 892, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18176", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1bbdcd6bee67e2cee3b5d12cf251658bcbefee1565373d3daa6b45f8cfb3caa5.jpg", + "image_caption": [ + "Figure 3: Illustration of geometric constraints induced by coordinate permutation and point recovery mechanism in the scenario of private queries. Red image points are secretly permuted. Black points are 3D map points. Blue points are the recovered, original image points obtained by back-swapping and form a rectangle together with their respective permuted points." + ], + "image_footnote": [], + "bbox": [ + 155, + 87, + 395, + 218 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "through camera projection center and the line in the image plane. The corresponding 3D point $\\mathbf{X}$ is expected to lie on this plane, which constrains the pose as", + "bbox": [ + 75, + 345, + 470, + 392 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\ell} ^ {\\top} \\left(R \\boldsymbol {X} + \\boldsymbol {t}\\right) = 0. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 402, + 468, + 422 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that this only yields a single geometric constraint instead of two as in Equation (1). In this case, it is still possible to estimate the pose, though the minimal problem now requires 6 instead of 3 correspondences. The minimal solver for this problem is known as $p6LP$ [33] and was used in [47]. Further, to validate a match, we can only measure the distance between the 2D line and the projected 3D point", + "bbox": [ + 75, + 435, + 468, + 541 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nd _ {l} = \\frac {\\left| \\boldsymbol {\\ell} ^ {\\top} \\bar {\\pi} (\\boldsymbol {R} \\boldsymbol {X} + \\boldsymbol {t}) \\right|}{\\sqrt {l _ {1} ^ {2} + l _ {2} ^ {2}}} , \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 553, + 468, + 592 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\ell = [l_1, l_2, l_3]^\\top$ and $\\bar{\\pi}$ is the homogeneous projected 2D point. This is a weaker constraint compared to the 2D error measured in Equation (2) and thus explains the observed loss in accuracy by this approach.", + "bbox": [ + 75, + 604, + 468, + 666 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Coordinate Permutation Constraints In our case, we have 2D image points, where we know that only one of the two coordinates is correct because of the a priori secret permutation (illustrated in Figures 2 and 3). In the context of the line-based framework from Speciale et al. [47], this can be considered as, instead of having a random line, having two axis-aligned lines passing through the given point. The original point will share one of the coordinates, and thus lie on one of these two lines. Mathematically, each point $\\pmb{x} = [x_1,x_2]^\\top$ gives rise to two axis-aligned lines $\\ell_1,\\ell_2$ , where $\\ell_{1} = [1,0, - x_{1}]^{\\top}$ $\\ell_{2} = [0,1, - x_{2}]^{\\top}$ . Each correspondence then gives us the following constraint", + "bbox": [ + 75, + 689, + 470, + 872 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {1} ^ {\\top} (R \\boldsymbol {X} + \\boldsymbol {t}) = 0 \\quad \\vee \\quad \\ell_ {2} ^ {\\top} (R \\boldsymbol {X} + \\boldsymbol {t}) = 0, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 883, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where we only know that one of the two constraints should be satisfied. For $n$ point correspondences, we thus have $2^{n}$ possible combinations of constraints to choose from.", + "bbox": [ + 496, + 90, + 890, + 135 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While considering all $n$ points leads to a combinatorial explosion and would be computationally intractable, we only need to consider small subsets of matches to hypothesize candidate poses inside RANSAC. For a minimal sample of 6 correspondences, there exist $2^6 = 64$ different combinations of lines in Equation (5). One of these combinations will correspond to having the true (uncorrupted) coordinate in all 6 lines, and should give a correct camera pose for an all-inlier minimal sample. So, to find a camera pose, we can simply iterate exhaustively over all $2^6 = 64$ combinations. Each of these combinations corresponds to a $p6LP$ minimal estimation problem, which can be efficiently solved. If gravity is known, we can efficiently solve the minimal $up4LP$ problem [33] from $2^4 = 16$ combinations.", + "bbox": [ + 496, + 137, + 892, + 348 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The key observation is now that, if we have a candidate pose, then for any inlier correspondence, we can easily resolve which of the two axis-aligned lines (i.e., coordinates) is the correct one by simply projecting the 3D points to the image and taking the one with the smaller 1D residual $d_{l}$ . By determining the inlier coordinates $\\mathcal{I}$ within the threshold (i.e., $d_{l} < \\varepsilon$ ), we can score candidate poses and thereby embed our method into a standard RANSAC loop to robustly estimate a camera pose. This approach still uses the weaker 1D constraints. The next paragraph explains how we can efficiently recover the original 2D points in this framework to benefit from stronger 2D constraints.", + "bbox": [ + 496, + 349, + 893, + 530 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Original Point Recovery After finding a candidate pose using RANSAC, we devise an efficient scheme for recovering the original points $\\pmb{x}$ from the set of inliers $\\mathcal{I}$ . Note that our scheme can only recover the positions for points that are visible in both the query and the map. As such, recovering the original points is not a concern for privacy, as they are known to both client and server.", + "bbox": [ + 496, + 551, + 890, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let's recall that we randomly picked pairs of points and swapped one of their coordinates to preserve their privacy. To recover the original points, we need to rely on the projected points and the property that the swapped back points should be close to the projected points (within $\\varepsilon$ distance) if it is an inlier. As for outliers points, there is no proper mechanism to distinguish a correct pair from an incorrect one, thus they remain unrecoverable.", + "bbox": [ + 496, + 657, + 890, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "One way of recovering points is to iterate through all pairwise combinations of inlier correspondences and choose a configuration with the most swapped back points close to the projected points. However, this method has a squared complexity in the number of correspondences and is thus computationally expensive to execute inside a RANSAC loop. To achieve a better complexity, it is helpful to notice that each pair of points, that are selected for", + "bbox": [ + 496, + 780, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18177", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "coordinate permutation, their original points and the permuted points form a 2D rectangle in the image (c.f. Figures 2 and 3). Using this observation, we can devise a more efficient recovery algorithm. For bookkeeping of recovered point coordinates, we first define the two sets", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS _ {j} = \\left\\{\\left(x _ {k j}, k\\right) \\mid \\hat {\\boldsymbol {x}} _ {k} = \\left[ x _ {k 1} \\quad x _ {k 2} \\right] ^ {\\top} \\right\\}, \\quad j = \\{1, 2 \\} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 176, + 468, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Each element in the sets consists of a single coordinate $(x_{1}$ or $x_{2})$ and its index $k$ in the ordered list of points. The index uniquely identifies coordinates to enable swapping of point pairs. For example, if the query image has 3 points $\\{\\hat{x}_1 = [0,10]^\\top ,\\hat{x}_2 = [20,30]^\\top ,\\hat{x}_3 = [40,50]^\\top \\}$ , then $S_{1} = \\{(0,1),(20,2),(40,3)\\}$ , $S_{2} = \\{(10,1),(30,2),(50,3)\\}$ . For each projected image point $\\tilde{x}$ , we first decide which coordinate could be the original one by comparing $\\tilde{x}$ and the permuted image point $\\hat{x}$ . We label coordinate $j$ as correct if the $j$ -th coordinate is within $\\varepsilon$ from the projected point, that is $|\\hat{x}_j - \\tilde{x}_j| < \\varepsilon$ . Denoting the other coordinate as $j'$ , we collect the possible swapped point candidates $C$ by looking in the set $S_{j'}$ , and finding points with the respective coordinate close to the projected point", + "bbox": [ + 75, + 205, + 470, + 417 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nC = \\left\\{k \\mid \\left| x _ {k j ^ {\\prime}} - \\tilde {x} _ {j ^ {\\prime}} \\right| < \\varepsilon , \\left(x _ {k j ^ {\\prime}}, k\\right) \\in S _ {j ^ {\\prime}} \\right\\} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 428, + 468, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since this set likely contains multiple candidates for each point (having a similar $x_{1}$ or $x_{2}$ coordinate), and the candidate points after swapping back can be distant from their projected points, we use a symmetric swapping error to filter out the coincident candidates", + "bbox": [ + 75, + 455, + 468, + 531 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\varepsilon_ {s y m} = \\left\\| \\tilde {\\boldsymbol {x}} - \\left[ \\begin{array}{l l} x _ {j} & x _ {k j ^ {\\prime}} \\end{array} \\right] ^ {\\top} \\right\\| _ {2} + \\left\\| \\tilde {\\boldsymbol {x}} _ {k} - \\left[ \\begin{array}{l l} x _ {k j} & x _ {j ^ {\\prime}} \\end{array} \\right] ^ {\\top} \\right\\| _ {2} (8)\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 541, + 468, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We only consider a candidate to be valid, if both points are close to the respective reprojected image points after swapping them back. If multiple candidates are valid, we keep the one with the smallest $\\varepsilon_{sym}$ . Notice that, with such a selection mechanism, the recovered original points may not be symmetric. However, we have not found any drawbacks from this asymmetry in our experiments.", + "bbox": [ + 75, + 571, + 468, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By implementing the sets $S_{j}$ using hashing, we achieve amortized linear runtime complexity on average w.r.t. the number of correspondences for our recovery scheme. More details can be found in the suppl. material.", + "bbox": [ + 75, + 676, + 468, + 738 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pose Refinement To further improve the accuracy of our pose estimates, we conduct a non-linear refinement over all inliers using the stronger 2D constraints from Equation (2) for recovered points $\\mathcal{I}_p$ and the weaker 1D constraints from Equation (4) for coordinates $\\mathcal{I}_l$ that could not be swapped back. The overall cost function is defined as", + "bbox": [ + 75, + 755, + 468, + 845 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\sum_ {k \\in \\mathcal {I} _ {p}} \\rho \\left(d _ {p} \\left(\\boldsymbol {x} _ {k}, P \\bar {\\boldsymbol {X}} _ {k}\\right)\\right) + \\sum_ {k \\in \\mathcal {I} _ {\\ell}} \\rho \\left(\\underset {i \\in \\{1, 2 \\}} {\\operatorname {s o f t m i n}} \\left(d _ {l} \\left(\\boldsymbol {\\ell} _ {k i}, P \\bar {\\boldsymbol {X}} _ {k}\\right)\\right)\\right) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 852, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2dbf1298f0c8dbce52b528f0c2f52a9a9c516458f56de08ce214d7bce1591ee1.jpg", + "image_caption": [ + "Figure 4: Illustration of point recovery mechanism in the 3D scenario with private maps, where the permuted red points form a cuboid in 3D. The reprojection of the 3D points is used for thresholding of errors in image space." + ], + "image_footnote": [], + "bbox": [ + 576, + 87, + 818, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\rho$ is a robustifier. To smoothly select between the two possible axis-aligned lines, we use the (Boltzmann) soft-min operator [5], defined as $\\operatorname*{softmin}_{i}\\{d_{i}\\} = (\\sum_{i}d_{i}e^{-d_{i}}) / (\\sum_{i}e^{-d_{i}})$ . We incorporate this non-linear refinement into LO-RANSAC [11] using the Arctan loss as $\\rho$ inside the RANSAC loop and Cauchy as the robust loss for the final pose refinement.", + "bbox": [ + 498, + 292, + 892, + 404 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Degenerate Configurations Note that when all $\\ell_{i}$ lines are parallel (i.e., originating from the same coordinate), the configuration becomes degenerate as the full 6-DoF of the pose cannot be recovered. This happens for 2 out of 64 configurations that we can trivially discard. For the two degenerate cases, it would be possible to solve for the rotation and two translation parameters using 5 correspondences. We initially explored this direction as well yet found the solutions to be less stable, as they provide less accurate pose estimates, so we do not include them in our final method.", + "bbox": [ + 498, + 422, + 890, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Localization with Private Maps", + "text_level": 1, + "bbox": [ + 500, + 580, + 777, + 598 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the previous section, we described our coordinate permutation scheme for 2D image points to preserve the privacy of localization queries. Similar to the 2D case, we can also permute coordinates of 3D points to hide the contents of private maps. This is a scenario that was originally addressed by Speciale et al. [46] using lifting to random 3D lines. We denote a random 3D line $L$ as", + "bbox": [ + 498, + 604, + 890, + 709 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {L} = \\left[ \\begin{array}{l} \\boldsymbol {p} \\\\ \\boldsymbol {d} \\end{array} \\right] \\in \\mathbb {R} ^ {3} \\times \\mathbb {P} ^ {2}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 717, + 890, + 751 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $p$ and $q$ are 3D points on $L$ subject to $d = \\frac{p - q}{\\|p - q\\|_2}$ and such that the line passes through the original 3D point $X$ . The reprojection of the 3D line to the image defines a 1D geometric constraint", + "bbox": [ + 498, + 761, + 890, + 833 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n0 = \\hat {\\boldsymbol {L}} _ {i} ^ {\\top} \\bar {\\boldsymbol {x}} = \\left(\\left[ \\boldsymbol {R} \\boldsymbol {d} _ {i} \\right] _ {\\times} \\boldsymbol {P} \\bar {\\boldsymbol {p}} _ {i}\\right) ^ {\\top} \\bar {\\boldsymbol {x}} \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 840, + 890, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "that can be used for privacy-preserving pose estimation. To solve for the full 6-DoF pose, at least 6 correspondences are", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18178", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "needed to solve the minimal $p6L$ problem [48] in RANSAC. If gravity is known, only 4 correspondences are needed to solve the up4L problem [49].", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Instead of lifting to random 3D lines, we construct axis-aligned 3D lines by coordinate permutation of randomly selected pairs of 3D points. Analogous to the 2D case, we can hypothesize pose candidates in RANSAC by generating the different $3^{6} = 729$ combinations of line constraints, and we can also recover the original 3D point positions by back-swapping with sets $S_{j=1,2,3}$ . Notice that the original 3D point may lie on any of the three axis-aligned lines and the randomly selected point pairs form a cuboid in 3D (see Figure 4). To robustify the back-swapping algorithm against non-isotropic noise on the (triangulated) 3D points, we define the error $\\varepsilon_{sym}$ in image space through reprojection. Moreover, if runtime is a concern for the final application, we can also choose to expose one of the 3 coordinates, so the number of line combinations would be $2^{6} = 64$ .", + "bbox": [ + 75, + 136, + 470, + 363 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Pose Refinement For pose refinement in the 3D case, we again add constraints from two sources: the ones from inlier lines $\\mathcal{I}_L$ and the ones from recovered inlier points $\\mathcal{I}_p$ . The overall cost function is defined as", + "bbox": [ + 75, + 380, + 468, + 439 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\sum_ {k \\in \\mathcal {I} _ {p}} \\rho (d _ {p} (\\boldsymbol {x} _ {k}, P \\bar {\\boldsymbol {X}} _ {k})) + \\sum_ {k \\in \\mathcal {I} _ {L}} \\rho (\\underset {i \\in \\{1, 2 \\}} {\\operatorname {s o f t m i n}} (d _ {L} (\\boldsymbol {x} _ {k}, \\hat {\\boldsymbol {L}} _ {k i}))\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 441, + 454, + 478 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\text {w h e r e} d _ {L} = \\frac {\\left| \\hat {\\boldsymbol {L}} _ {k i} ^ {\\top} \\bar {\\boldsymbol {x}} _ {k} \\right|}{\\sqrt {\\hat {L} _ {k i 1} ^ {2} + \\hat {L} _ {k i 2} ^ {2}}} \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 481, + 468, + 532 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and we use the same setup of LO-RANSAC and choice of robustifiers as in the 2D scenario.", + "bbox": [ + 75, + 532, + 468, + 563 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 575, + 209, + 590 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In our experiments, we first focus on demonstrating the effectiveness of our proposed point recovery mechanism using an ablation study. We then compare our method against the traditional non-privacy preserving approach (PnP) and the original privacy-preserving approach based on random lines. Results are reported on existing benchmark datasets [23,46,52] for image-based localization, evaluated for the two scenarios of private localization queries (PnLP) and maps (PnL). All results assume unknown gravity and we show further results with known gravity in the supplementary material. Finally, we show image inversion results using the density-based attack by Chelani et al. [9].", + "bbox": [ + 75, + 599, + 470, + 782 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details We embed our method into LO-RANSAC [11] with Levenberg-Marquardt [2, 26] as nonlinear optimizer for pose refinement. Inlier reprojection thresholds on 2D points are set to $12px$ for the Cambridge dataset [23] and to $4px$ otherwise. Reprojection thresholds on lines are chosen as $\\frac{12px}{\\sqrt{2}}$ and $\\frac{4px}{\\sqrt{2}}$ , respectively.", + "bbox": [ + 75, + 799, + 468, + 904 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fcfdda0c24f7add157c62919900c928caae6e6cf651a9c77f77fd29735bad04c.jpg", + "image_caption": [ + "Figure 5: Ablation study on King's college sequence [23] w.r.t. the number of correspondences. Our method closes the performance gap, that is especially pronounced in difficult cases with few correspondences." + ], + "image_footnote": [], + "bbox": [ + 504, + 90, + 700, + 217 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f9b3f6097d3455aa7522fe3b6bc4d97e2303d939e895b7637f10002ab5974189.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 704, + 90, + 888, + 217 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We re-implement all methods in the same framework for a fair comparison of accuracy, recall, and runtime. All point clouds are triangulated using COLMAP [41, 43].", + "bbox": [ + 496, + 295, + 892, + 340 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Ablation Study", + "text_level": 1, + "bbox": [ + 498, + 351, + 653, + 368 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1.1 Impact of Number of Correspondences", + "text_level": 1, + "bbox": [ + 498, + 375, + 825, + 391 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As argued in previous sections, the reduced accuracy and recall in privacy-preserving localization methods based on random lines is largely attributed to the weaker geometric constraints. To showcase this performance gap, we conduct an experiment on the King's College sequence in the Cambridge dataset [23]. Localization performance is tested on varying number of correspondences per query image by randomly dropping input matches. Cases with few correspondences typically depict the challenging localization scenarios, where feature matching only yields few matches and only few constraints can be used for pose estimation. The results of this experiment are summarized in Figure 5. First, we observe that the performance gap between the privacy-preserving and traditional approach is especially pronounced for low number of matches, which in turn suggests that the impact of the number of constraints on the localization accuracy saturates eventually. We also see that our method closes the accuracy gap to the traditional approach across the board.", + "bbox": [ + 496, + 400, + 890, + 688 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1.2 Impact of Point Recovery Mechanism", + "text_level": 1, + "bbox": [ + 498, + 709, + 815, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To analyze the effectiveness of the proposed point recovery mechanism, we conduct experiments on HoloLens data [47] with our method in different settings: with only line constraints, with recovered point constraints, and with the true recovered points using an oracle that has access to groundtruth information. This dataset contains images with a large variance on the inlier ratio, which makes it suitable for this ablation study, as the point recovery mechanism is strongly influenced by it. Results are summarized in Figure 6, which shows a significant improvement in accuracy for our method when using the stronger 2D constraints from", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18179", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/14eebd814c76fc5b5200e557d5bdc68f0f072e276edf43984cfcf95cb849b390.jpg", + "image_caption": [ + "Figure 6: Ablation study on HoloLens data from [47] to measure the effectiveness of our point recovery mechanism." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 285, + 218 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2e74e1d0727393db298b76a34c2d0c4f550394adde9bc3a584292f974f9ea90a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 89, + 467, + 217 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/03bb19e9f7286bd9f392c3f6c0693956d0e5f30e5362b5516d9af07430396d66.jpg", + "image_caption": [ + "Figure 7: Ablation study on HoloLens data from [47] that shows effective point recovery across all outlier ratios and overall low error rates on the recovered points." + ], + "image_footnote": [], + "bbox": [ + 81, + 270, + 269, + 387 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ebb9e667a9b4211c02f21788eac833da46a54bbd88fcd7d8e77b84786fb0ad3e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 272, + 464, + 388 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d5705481af6e29edd51ab27014749c570972495691838be58e84959d8286c4cd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MED (°)AUC@1°MED (cm)AUC@10cm(1°, 10 cm)Time (s)
PnLP [47]0.0884.790.6388.8897.800.07
Proposed0.0786.690.5690.1298.410.36
PnP0.0787.920.5190.8598.800.05
", + "bbox": [ + 78, + 457, + 467, + 507 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "recovered points. In comparison to the oracle that defines a theoretical upper bound for our method, there is no significant difference in performance.", + "bbox": [ + 75, + 561, + 468, + 606 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Furthermore, we also report the correlation between the outlier ratio and the ratio of recovered points in Figure 7. The expected number is calculated as $p^2$ where $p$ is the inlier ratio. From the figure we can see that the ratios of correctly recovered points matches the expected number across all outlier ratios. The ratio of mismatched points stays low in this dataset even when the inlier ratio is as low as $20\\%$ . Those observations combined provide strong evidence that the recovering mechanism is effective.", + "bbox": [ + 75, + 608, + 468, + 743 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Localization with Private Queries", + "text_level": 1, + "bbox": [ + 76, + 755, + 372, + 771 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "HoloLens [47] This dataset features mostly small-scale scenes and unconstrained motion trajectories from a headworn augmented reality device with VGA-resolution cameras. Equivalent to the original dataset, we use COLMAP for reconstruction of the full image sequence while limiting the number of SIFT features per image to at most 500. There are 3325 query images in total and each query has on average 320 correspondences. After reconstructing the full", + "bbox": [ + 75, + 779, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/fa3f599bcb1979fcf78caaa3e9c785abeea0f2cdb230f41a39f55d48ff6e1205.jpg", + "table_caption": [ + "Table 1: Localization performance on HoloLens dataset [47] with indoor and outdoor scenes." + ], + "table_footnote": [], + "table_body": "
MED (°)AUC@1°MED (cm)AUC@10cm(1°, 10 cm)Time (s)
PnLP [47]0.1871.5912.1318.3841.290.36
Proposed0.1872.6111.7320.0344.262.31
PnP0.1773.0911.6620.2243.950.20
", + "bbox": [ + 501, + 88, + 890, + 137 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/11ca6fa186ad75b9cb2b80c4a3d785898f2c78cd5836473dd96becbd430700fa.jpg", + "table_caption": [ + "Table 2: Localization performance on Cambridge dataset [23] with handheld videos in an outdoor scene." + ], + "table_footnote": [], + "table_body": "
MED (°)AUC@1°MED (cm)AUC@10cm(1°, 10 cm)Time (s)
PnLP [47]0.0288.322.2459.5778.230.09
Proposed0.0289.671.9263.6281.330.68
PnP0.0290.741.8564.5882.620.08
", + "bbox": [ + 503, + 186, + 890, + 237 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/40d5dc88f55da7c587fdc4c15498dd877fd8fcbf0ac336b1401460227a8cf8fa.jpg", + "table_caption": [ + "Table 3: Localization performance on crowd-sourced Internet photo collections [29, 53]." + ], + "table_footnote": [], + "table_body": "
MED (°)AUC@1°MED (cm)AUC@10cm(1°, 10 cm)Time (s)
PnL [46]0.0884.710.6488.6697.711.16
Proposed0.0786.310.5689.7197.926.61
PnP0.0787.850.5190.8498.830.07
", + "bbox": [ + 501, + 287, + 890, + 335 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4: Localization performance on HoloLens dataset [47] in the private map scenario.", + "bbox": [ + 500, + 337, + 890, + 367 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "sequence, we hold out every 5-th image as a query, remove any point correspondences associated to these images from the reconstruction, and retriangulate the remaining database images. The pose of the query images in the full reconstruction serve as the groundtruth for evaluation. The results are summarized in Table 1, where we can see that our method performs almost on par with the traditional non-privacy preserving case in terms of accuracy and recall. The additional combinatorial overhead of evaluating more pose candidates leads to a roughly 5-fold runtime increase for our method.", + "bbox": [ + 496, + 378, + 890, + 531 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Cambridge [23] This localization benchmark dataset contains handheld HD-resolution videos taken around Cambridge University in an outdoor setting. We use the same reference reconstruction as in [6] for the database map and extract SuperPoint+SuperGlue feature correspondences using the hloc toolbox [36, 37]. The dataset has a total of 1918 query images and an average of around 2850 2D-3D correspondences per image. Results are summarized in Table 2 and the performance trend for accuracy, recall, and runtime are all consistent with the results on the lower-resolution HoloLens dataset. This underlines the robustness of our approach against different sensors, scene types, as well as feature detection and matching algorithm characteristics.", + "bbox": [ + 496, + 549, + 892, + 746 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Internet Photo Collections [29, 53] This collection of datasets is crowd-sourced from the internet and comprises a large variety in image resolution and quality, lighting conditions, etc. We conduct experiments on the Dubrovnik6k, Gendarmenmarkt, Roman Forum, and Trafalgar locations with equivalent settings as used by Speciale et al. [47] for generating pseudo-groundtruth and establishing feature correspondences using COLMAP. On average, there are around 1000 SIFT correspondences per image with a total", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18180", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b2d44ac88d4801cda4a69e67eff0099aa6ac971d574fc65992836e440b62a3e1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 76, + 88, + 285, + 207 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9e551d266bf5c6131ff9f1420b864b965c16cf4c23f9347fe6f2c9c3737b0751.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 92, + 486, + 207 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5ce5c8a2a75b9c85a500d9449ddf849627a70ba93664f8742a97889ad1cdab2e.jpg", + "image_caption": [ + "(a) Original" + ], + "image_footnote": [], + "bbox": [ + 80, + 209, + 179, + 285 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ef8e893c68bd4aca50b8e99e1d847e6ee9d40e13e87894723d44644cffd77ef9.jpg", + "image_caption": [ + "Figure 8: Privacy attack on (private) maps using a combination of 3D image inversion [32] and the density based attack method Line2Point [9]. The top row shows the 3D map that is recovered using Line2Point for all but the leftmost result. The 3D map is used as an input for rendering synthesized images shown at two different viewpoints in the bottom row. From left to right: (a) Results on original, non-privacy preserving point cloud. (b) Results on random line cloud. (c) Results on our method with an attacker that gained access to swapped coordinates. (d) Results on our method with permuted coordinates." + ], + "image_footnote": [], + "bbox": [ + 179, + 209, + 279, + 285 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0233f679175491a3c125b02efcaf46f3165233349eaf8f6c03ec55f701754edd.jpg", + "image_caption": [ + "(b) Random line" + ], + "image_footnote": [], + "bbox": [ + 285, + 209, + 383, + 285 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c59a2479938f7529e748de30739078938d93956484356f4f46a8c62e3aedb6b8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 383, + 209, + 482, + 285 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ca60b5e169f291d2dc35afd49444e32767fdeea66416909f0708ad60724ac263.jpg", + "image_caption": [ + "(c) Oracle" + ], + "image_footnote": [], + "bbox": [ + 486, + 209, + 586, + 285 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/38e85b2d1cf80a6ef1f57c80a35ff301f74873b4b134a5eba57d8db2b52ca315.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 586, + 209, + 684, + 285 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fb1986a0c95d80e0536062c8f1af82e57bb9d9ad03280206dd6acdc9175ef71b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 88, + 890, + 207 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a1d8eb92aad51fb1caf5f23b5f0ea870cc03274335a0a97f00fe4940b677823a.jpg", + "image_caption": [ + "(d) Proposed" + ], + "image_footnote": [], + "bbox": [ + 689, + 209, + 787, + 285 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fb2b36e85cb9bceaf814a9c5b6ebfc224acad267e2d8ef4bcd0ab15679a7b6a4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 790, + 209, + 888, + 285 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of 2416 query images. Results are summarized in Table 3. The accuracy of all methods on this dataset is surprisingly high, yet we can still observe significant improvements.", + "bbox": [ + 75, + 393, + 468, + 441 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Localization with a Private Map", + "text_level": 1, + "bbox": [ + 76, + 450, + 359, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To evaluate localization scenario with a private map, we conduct experiments on HoloLens data [47] using the same setup as in the private query scenario described in the previous section. We adopt the setting of exposing one correct coordinate in Table 4 and provide results for the computationally more expensive case with 729 combinations in the supplementary material. Like in the private query scenario, we are able to significantly close the accuracy gap but increase run-time by a factor of around six.", + "bbox": [ + 75, + 474, + 468, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Inversion Attack on Line Cloud", + "text_level": 1, + "bbox": [ + 76, + 619, + 354, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this section, we analyze and compare the level of privacy protection for the map representation. We perform this analysis by attacking the 3D point maps using image inversion techniques, as proposed by Pittaluga et al. [32]. To render images from the privacy preserving 3D line maps, we first execute a density based attack on the map representations using the Line2Point [9] method and then run image inversion on the recovered point cloud. Figure 8 shows results for this experiment, where inverted images from the non-privacy preserving map are nearly indistinguishable from original images of the scene. This again highlights the importance of research on privacy preserving methods for image-based localization. Images rendered from naively constructed random line clouds without sparsification closely resemble the original images as well and thus are not sufficient to protect private information in the map. The results of the attack on our method in column (d)", + "bbox": [ + 75, + 643, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "shows mostly recognizable images and demonstrates the increased level of privacy that our method provides. Even if an attacker had access to an oracle that knows about which of the coordinates is correct, the rendered images (c) are less recognizable than the ones from a random line cloud. It is important to note that this information is not available to an attacker in practice, but it allows us to understand the relative impact on the increased level of privacy. On the one hand, our method constructs axis-aligned lines, which, by construction, cannot be intersected in a density based attack. On the other hand, we increase the combinatorial complexity of executing a density based attack, as significantly more coordinate pairs must be tried to find a valid intersection. In the supplementary material we provide additional inversion results and more discussion regarding potential attacks.", + "bbox": [ + 496, + 393, + 890, + 621 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 638, + 617, + 654 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present a significant improvement over existing privacy-preserving image-based localization approaches. Our method improves upon the accuracy limitation of random line based approaches and closes the gap to traditional non-privacy preserving methods. At the same time, our method proves as robust against recently presented density attacks on random 3D line clouds. An interesting avenue for future work could be in addressing the increased runtime of our method. One promising idea involves voting for correct coordinate swaps during RANSAC and progressively sampling from more likely lines.", + "bbox": [ + 496, + 666, + 890, + 832 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments We would like to thank Marcel Geppert for reviewing this paper, for the insightful discussions, and his help in the supp. material, as well as Torsten Sattler and Kunal Chelani for the code and data of line cloud inversion experiments. Viktor Larsson was supported by ELLIIT.", + "bbox": [ + 496, + 840, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18181", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Inside Facebook Reality Labs: Research updates and the future of social connection. https://tech.fb.com/inside-facebook-reality-labs-research-updates-and-the-future-of-social-connection/, 2019. 1", + "[2] Sameer Agarwal, Keir Mierle, and The Ceres Solver Team. Ceres Solver, 3 2022. 6", + "[3] Relja Arandjelovic, Petr Gronat, Akihiko Torii, Tomas Pajdla, and Josef Sivic. NetVLAD: CNN architecture for weakly supervised place recognition. 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In International Conference on Computer Vision (ICCV), 2019. 1, 2, 3, 4, 6, 7, 8", + "[48] Henrik Stewénius, David Nister, Magnus Oskarsson, and Kalle Astrom. Solutions to minimal generalized relative pose problems. In Workshop on omnidirectional vision, 2005. 6", + "[49] Chris Sweeney, John Flynn, and Matthew Turk. Solving for relative pose with a partially known rotation is a quadratic eigenvalue problem. In International Conference on 3D Vision (3DV), 2014. 6", + "[50] Carl Toft, Will Maddern, Akihiko Torii, Lars Hammarstrand, Erik Stenberg, Daniel Safari, Masatoshi Okutomi, Marc Pollefeys, Josef Sivic, Tomas Pajdla, et al. Long-term visual localization revisited. Trans. Pattern Analysis and Machine Intelligence (PAMI), 2020. 2", + "[51] Jan-Erik Vinje. Privacy Manifesto for AR Cloud Solutions. https://medium.com/openarcloud/privacy-manifesto-for-ar-cloud-solutions-9507543f50b6, 2018. 1, 2", + "[52] Kyle Wilson and Noah Snavely. Robust global translations with 1DSFM. 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In International Conference on Computer Vision (ICCV), 2015. 2" + ], + "bbox": [ + 501, + 90, + 890, + 613 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "18183", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Privacy Preserving Localization via Coordinate Permutations/f992eeb4-2e60-42f9-9e28-abc98f428b2a_model.json b/2023/Privacy Preserving Localization via Coordinate Permutations/f992eeb4-2e60-42f9-9e28-abc98f428b2a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..485f29e7c87aebcf73da0a0423ef609b9686451c --- /dev/null +++ b/2023/Privacy Preserving Localization via Coordinate Permutations/f992eeb4-2e60-42f9-9e28-abc98f428b2a_model.json @@ -0,0 +1,2387 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.175, + 0.131, + 0.797, + 0.154 + ], + "angle": 0, + "content": "Privacy Preserving Localization via Coordinate Permutations" + }, + { + "type": "text", + "bbox": [ + 0.164, + 0.18, + 0.845, + 0.217 + ], + "angle": 0, + "content": "Linfei Pan1 Johannes L. Schonberger2 Viktor Larsson3 Marc Pollefeys1,2 ETH Zurich Microsoft Lund University" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.217, + 0.921, + 0.235 + ], + "angle": 0, + "content": "1{linfei.pan,marc.pollefeys}@inf.ethz.ch,2joschonb@microsoft.com,3viktor.larsson@math.lth.se" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.474, + 0.635 + ], + "angle": 0, + "content": "Recent methods on privacy-preserving image-based localization use a random line parameterization to protect the privacy of query images and database maps. The lifting of points to lines effectively drops one of the two geometric constraints traditionally used with point-to-point correspondences in structure-based localization. This leads to a significant loss of accuracy for the privacy-preserving methods. In this paper, we overcome this limitation by devising a coordinate permutation scheme that allows for recovering the original point positions during pose estimation. The recovered points provide the full 2D geometric constraints and enable us to close the gap between privacy-preserving and traditional methods in terms of accuracy. Another limitation of random line methods is their vulnerability to density based 3D line cloud inversion attacks. Our method not only provides better accuracy than the original random line based approach but also provides stronger privacy guarantees against these recently proposed attacks. Extensive experiments on standard benchmark datasets demonstrate these improvements consistently across both scenarios of protecting the privacy of query images as well as the database map." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.663, + 0.21, + 0.68 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.841 + ], + "angle": 0, + "content": "The interest in commercial solutions for cloud-based localization and mapping in mixed reality and robotics (e.g., Google VPS [34], Microsoft Azure Spatial Anchors [21], or Facebook LiveMaps [1]) has raised a host of privacy concerns [24, 31, 35, 51]. Recently, several approaches have been introduced by the research community to address these concerns [14, 17-19, 25, 45-47]. The common theme underlying these methods is based on the principle of lifting traditional point-based features to randomly oriented lines to conceal the appearance of query images and database maps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "While this family of approaches is successful in enabling privacy preserving image-based localization and mapping, it comes at significant trade-offs in terms of accuracy and recall. These trade-offs are primarily caused by the fact that" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.271, + 0.697, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.432, + 0.697, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.278, + 0.89, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.421, + 0.888, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.58, + 0.895, + 0.718 + ], + "angle": 0, + "content": "Figure 1: Privacy-preserving localization. Top Left: The client extracts keypoints and descriptors from the query image. Top Right: The client secretly pairs keypoints and permutes their coordinates; hiding their true position from the server. Bottom Left: Server performs localization using the permuted points and recovers the original 2D positions for points that exist in both query and map. Bottom Right: Feature inversion on the set of recovered points only reveals objects that are already present in the map." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "the privacy preserving line-to-point or point-to-line correspondences provide weaker geometric constraints than the traditional point-to-point correspondences [46]. When concealing the content of images or maps, the number of constraints is effectively halved, as each point-to-line or line-to-point reprojection only contributes a 1D geometric constraint compared to the 2D constraint from a point-to-point reprojection. Especially for the hard to localize images, where only few correspondences can be recovered during feature matching, this limitation makes a significant difference in terms of accuracy and recall." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18174" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.302 + ], + "angle": 0, + "content": "Furthermore, without careful construction of random line maps, density based attacks have been shown to be effective in uncovering information from the privacy preserving representations, which was already mentioned as a limitation by Speciale et al. [46]. The main idea behind density based attacks exploits the fact that pairs of randomly oriented lines have a relatively higher chance of intersecting near the true surface as compared to empty or unobserved space. As such, a naive attack could simply gather statistics from pairwise intersections of random lines and assume the true surface in dense regions of the intersected space. More sophisticated attacks based on this idea can yield realistic image renderings from 3D line maps when attacking naively constructed line maps [9]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.473, + 0.606 + ], + "angle": 0, + "content": "In this work, we revisit the approach of lifting points to lines in order to improve upon these two main limitations. In contrast to the original approach, we introduce a coordinate permutation scheme by which we effectively construct axis-aligned lines. During the pose estimation routine, the permutation scheme enables us to recover the original points for a large fraction of the inlier correspondences. Therefore, we can use the same 2D geometric constraints as in the traditional setup. This significantly improves the accuracy of the localization results. Moreover, when applying our approach for hiding the 3D map, we drastically increase the combinatorial complexity for density based attacks as well as reduce the chance for line intersections due to constructing axis-aligned lines. Counter-intuitively, our proposed method therefore not only leads to better accuracy but also provides a stronger level of privacy preservation. We experimentally demonstrate these improvements on standard benchmark datasets and by attacking our axis-aligned line maps using the approach by Chelani et al. [9]. In summary, we make the following contributions:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.614, + 0.468, + 0.645 + ], + "angle": 0, + "content": "- Propose a new privacy-preserving lifting approach, applicable to protecting the map and query." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.654, + 0.468, + 0.699 + ], + "angle": 0, + "content": "- Attacking the lifted representation has a higher combinatorial complexity compared to random lifting, rendering previous density based attacks ineffective." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.709, + 0.468, + 0.754 + ], + "angle": 0, + "content": "- In contrast to previous work, we can recover the original 2D or 3D points, allowing for stronger geometric constraints and more accurate poses." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.763, + 0.468, + 0.809 + ], + "angle": 0, + "content": "- Experimentally, we show significant improvements over previous privacy preserving work, closing the gap to traditional point-based non-private methods." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.614, + 0.468, + 0.809 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.83, + 0.22, + 0.846 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Image-based Localization Methods in image-based localization have made tremendous progress. Over the years, the methods have been scaled for robust localization in" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.244 + ], + "angle": 0, + "content": "large-scale scenes [27,38,40,54] with compressed map representations [8,15], while some of the methods can even run in real-time on mobile devices [4,20,22,27,28,39]. Some of the recent works focus on improving the robustness to drastic environmental changes [3,42,50] or enabling crossdevice localization and mapping scenarios [13]. The developed approaches are generally divided into structure-based methods [20, 38-40] using on an explicit geometric map representation or learning-based methods [7,22,44] with an implicit map representation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.262, + 0.892, + 0.444 + ], + "angle": 0, + "content": "Privacy Risks Image-based localization is subject to privacy risks due to requiring images as an input [24, 31, 35, 51]. For example, in a cloud-based localization system, users may be concerned about sharing images of private spaces with the service provider. In a practical setting, the clients could only send local image features to the cloud to avoid these risks. However, recent inversion attacks have proven extremely effective in recovering the original images from only sparse local image features [12, 30, 32]. Recently, Chelani et al. proposed a method to query a localization service with a database of objects to recover information about scene contents [10]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.892, + 0.629 + ], + "angle": 0, + "content": "Privacy Preservation To protect against these risks, several methods have been developed recently. The first work on this topic [46, 47] proposed a solution to preserve the privacy of 2D image or 3D map points in image-based localization. Their main idea was to lift 2D or 3D points to random lines by dropping one of the two geometric constraints during the pose estimation problem. Based on the same idea, a number of works followed up to address the problems of structure-from-motion [18, 19] and real-time SLAM [45], or to directly protect the high-dimensional feature representations instead of the geometry [14]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.892, + 0.795 + ], + "angle": 0, + "content": "Underlying all these approaches, there are two fundamental limitations that were already observed by the original work [47]. First, by dropping one geometric constraint per correspondence for pose estimation, the accuracy of these approaches is significantly lowered, especially in the challenging cases with few matches between query and database. Second, without careful sparsification of the 3D map, density based attacks can recover information from 3D line clouds [9]. Sparsification of the map is an effective protection against density based attacks but comes with a further reduction of accuracy as well as recall." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To protect in a more principled manner against these attacks, Geppert et al. [17] proposed to decompose the full 3D map into 1D partial maps, which are distributed across different servers. Each server then solves a partial localization problem and sends back the answer to the client, which can assemble a full 6-DoF localization result from the partial answers. Despite being effective against density based at" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18175" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.088, + 0.411, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.089, + 0.847, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.223, + 0.894, + 0.3 + ], + "angle": 0, + "content": "Figure 2: Method overview for localization with private queries. The client extracts keypoints in the query image and secretly pairs them to swap one of their coordinates. The server only receives the permuted points, which can be considered as axis-aligned lines. The secretly paired points form rectangles, which can be leveraged during RANSAC to efficiently recover the original point positions for pairs that are both inliers. The scoring of candidate poses and the final non-linear pose refinement jointly leverage the stronger 2D constraints for recovered points and otherwise the weaker 1D constraints." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.311, + 0.473, + 0.417 + ], + "angle": 0, + "content": "tacks, the system is complex and it comes with further accuracy and recall trade-offs. In contrast, our method does not require a complex multi-server setup and we improve upon the two main limitations of the random lifting approaches simultaneously. Our method provides both stronger privacy guarantees while also closing the accuracy gap to traditional localization approaches." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.441, + 0.169, + 0.457 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.471, + 0.47, + 0.547 + ], + "angle": 0, + "content": "We now present our method for privacy-preserving localization. We address both the scenario of protecting the client's 2D image points in the localization query (Section 3.2) as well as protecting the service's 3D points in the database map (Section 3.3)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.471, + 0.822 + ], + "angle": 0, + "content": "Our approach follows the main idea in Speciale et al. [46, 47], where the exact 2D or 3D point positions are hidden by introducing ambiguity in the coordinates. In the original works, this is done by lifting each point to a random line. The line representation still enables localization, using line-to-point instead of point-to-point correspondences, but makes it difficult to identify potentially sensitive image or map content. Similar to the original idea [46], we also obscure the true position of the point. However, instead of replacing it with a random line, we select a subset of the point coordinates and corrupt them. This is done by secretly forming pairs of points and swapping their coordinates at random. Since the list of pairs is not known to an attacker, it is practically intractable to recover the original point positions. As we will later show, for point-pairs that exist in both the query and the map, we can devise a scheme to recover the true positions, allowing us to use the full 2D-3D geometric constraints for accurate pose refinement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "An overview of our pipeline can be found in Figure 2 and we detail the steps of our method in the following sections. For ease of presentation, we first review the traditional setup and then explain the 2D setting that hides the query, but the same principle generalizes to the 3D setting as well." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.31, + 0.803, + 0.325 + ], + "angle": 0, + "content": "3.1. Review of Traditional Localization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.333, + 0.892, + 0.41 + ], + "angle": 0, + "content": "Traditionally, localization is performed by establishing a set of tentative 2D-3D point correspondences between the query image and the database map. Each correspondence \\((\\pmb{x},\\pmb{X})\\in \\mathbb{R}^2\\times \\mathbb{R}^3\\) yields two geometric constraints on the unknown camera pose \\((R,t)\\in \\mathrm{SE}(3)\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.638, + 0.418, + 0.892, + 0.433 + ], + "angle": 0, + "content": "\\[\n\\lambda \\bar {\\boldsymbol {x}} = R \\boldsymbol {X} + \\boldsymbol {t}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.441, + 0.893, + 0.593 + ], + "angle": 0, + "content": "where we let \\(\\bar{x}\\) denote the homogeneous 2D point in the normalized image plane (after removing the intrinsic calibration), and \\(\\lambda\\) represents the unknown depth. To identify outlier matches and estimate an initial pose, the standard approach is to use hypothesize-and-test frameworks, such as RANSAC [16], in order to generate multiple pose candidates by fitting \\((R,t)\\) to minimal subsets of the points, followed by measuring the consensus among the rest of the matches. The consistency between a candidate pose and a 2D-3D match is computed using the 2D reprojection error" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.601, + 0.892, + 0.619 + ], + "angle": 0, + "content": "\\[\nd _ {p} = \\| \\boldsymbol {x} - \\pi (R \\boldsymbol {X} + t) \\|, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.892, + 0.687 + ], + "angle": 0, + "content": "where \\(\\pi : \\mathbb{R}^3 \\to \\mathbb{R}^2\\) is the projection mapping. Once a candidate pose, together with the inlier matches, have been established, it is refined by minimizing the reprojection errors for all inliers jointly." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.694, + 0.795, + 0.71 + ], + "angle": 0, + "content": "3.2. Localization with Private Queries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.717, + 0.892, + 0.853 + ], + "angle": 0, + "content": "The traditional method relies on the availability of the original 2D image points, and is thus not privacy preserving. To preserve the privacy of the image, Speciale et al. [47] proposed to lift 2D image points into random 2D lines. Our method also builds upon 2D lines but aligns them with the coordinate axes through a random coordinate permutation scheme. The following paragraphs first establish notation by reviewing (random) line constraints for localization and then explain our permutation scheme in detail." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Random Line Constraints In Speciale et al. [47], each 2D line \\(\\ell\\) back-projects into a 3D plane \\(\\Pi_i = P^\\top \\ell_i\\) passing" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18176" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.156, + 0.088, + 0.396, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.227, + 0.473, + 0.334 + ], + "angle": 0, + "content": "Figure 3: Illustration of geometric constraints induced by coordinate permutation and point recovery mechanism in the scenario of private queries. Red image points are secretly permuted. Black points are 3D map points. Blue points are the recovered, original image points obtained by back-swapping and form a rectangle together with their respective permuted points." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.347, + 0.471, + 0.393 + ], + "angle": 0, + "content": "through camera projection center and the line in the image plane. The corresponding 3D point \\( \\mathbf{X} \\) is expected to lie on this plane, which constrains the pose as" + }, + { + "type": "equation", + "bbox": [ + 0.203, + 0.404, + 0.47, + 0.423 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\ell} ^ {\\top} \\left(R \\boldsymbol {X} + \\boldsymbol {t}\\right) = 0. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.436, + 0.47, + 0.542 + ], + "angle": 0, + "content": "Note that this only yields a single geometric constraint instead of two as in Equation (1). In this case, it is still possible to estimate the pose, though the minimal problem now requires 6 instead of 3 correspondences. The minimal solver for this problem is known as \\( p6LP \\) [33] and was used in [47]. Further, to validate a match, we can only measure the distance between the 2D line and the projected 3D point" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.554, + 0.47, + 0.593 + ], + "angle": 0, + "content": "\\[\nd _ {l} = \\frac {\\left| \\boldsymbol {\\ell} ^ {\\top} \\bar {\\pi} (\\boldsymbol {R} \\boldsymbol {X} + \\boldsymbol {t}) \\right|}{\\sqrt {l _ {1} ^ {2} + l _ {2} ^ {2}}} , \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.605, + 0.47, + 0.667 + ], + "angle": 0, + "content": "where \\(\\ell = [l_1, l_2, l_3]^\\top\\) and \\(\\bar{\\pi}\\) is the homogeneous projected 2D point. This is a weaker constraint compared to the 2D error measured in Equation (2) and thus explains the observed loss in accuracy by this approach." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.471, + 0.873 + ], + "angle": 0, + "content": "Coordinate Permutation Constraints In our case, we have 2D image points, where we know that only one of the two coordinates is correct because of the a priori secret permutation (illustrated in Figures 2 and 3). In the context of the line-based framework from Speciale et al. [47], this can be considered as, instead of having a random line, having two axis-aligned lines passing through the given point. The original point will share one of the coordinates, and thus lie on one of these two lines. Mathematically, each point \\(\\pmb{x} = [x_1,x_2]^\\top\\) gives rise to two axis-aligned lines \\(\\ell_1,\\ell_2\\), where \\(\\ell_{1} = [1,0, - x_{1}]^{\\top}\\) \\(\\ell_{2} = [0,1, - x_{2}]^{\\top}\\). Each correspondence then gives us the following constraint" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.884, + 0.47, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\ell_ {1} ^ {\\top} (R \\boldsymbol {X} + \\boldsymbol {t}) = 0 \\quad \\vee \\quad \\ell_ {2} ^ {\\top} (R \\boldsymbol {X} + \\boldsymbol {t}) = 0, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "where we only know that one of the two constraints should be satisfied. For \\( n \\) point correspondences, we thus have \\( 2^{n} \\) possible combinations of constraints to choose from." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.138, + 0.893, + 0.349 + ], + "angle": 0, + "content": "While considering all \\( n \\) points leads to a combinatorial explosion and would be computationally intractable, we only need to consider small subsets of matches to hypothesize candidate poses inside RANSAC. For a minimal sample of 6 correspondences, there exist \\( 2^6 = 64 \\) different combinations of lines in Equation (5). One of these combinations will correspond to having the true (uncorrupted) coordinate in all 6 lines, and should give a correct camera pose for an all-inlier minimal sample. So, to find a camera pose, we can simply iterate exhaustively over all \\( 2^6 = 64 \\) combinations. Each of these combinations corresponds to a \\( p6LP \\) minimal estimation problem, which can be efficiently solved. If gravity is known, we can efficiently solve the minimal \\( up4LP \\) problem [33] from \\( 2^4 = 16 \\) combinations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.35, + 0.894, + 0.531 + ], + "angle": 0, + "content": "The key observation is now that, if we have a candidate pose, then for any inlier correspondence, we can easily resolve which of the two axis-aligned lines (i.e., coordinates) is the correct one by simply projecting the 3D points to the image and taking the one with the smaller 1D residual \\( d_{l} \\). By determining the inlier coordinates \\( \\mathcal{I} \\) within the threshold (i.e., \\( d_{l} < \\varepsilon \\)), we can score candidate poses and thereby embed our method into a standard RANSAC loop to robustly estimate a camera pose. This approach still uses the weaker 1D constraints. The next paragraph explains how we can efficiently recover the original 2D points in this framework to benefit from stronger 2D constraints." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.657 + ], + "angle": 0, + "content": "Original Point Recovery After finding a candidate pose using RANSAC, we devise an efficient scheme for recovering the original points \\( \\pmb{x} \\) from the set of inliers \\( \\mathcal{I} \\). Note that our scheme can only recover the positions for points that are visible in both the query and the map. As such, recovering the original points is not a concern for privacy, as they are known to both client and server." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.78 + ], + "angle": 0, + "content": "Let's recall that we randomly picked pairs of points and swapped one of their coordinates to preserve their privacy. To recover the original points, we need to rely on the projected points and the property that the swapped back points should be close to the projected points (within \\(\\varepsilon\\) distance) if it is an inlier. As for outliers points, there is no proper mechanism to distinguish a correct pair from an incorrect one, thus they remain unrecoverable." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.893, + 0.901 + ], + "angle": 0, + "content": "One way of recovering points is to iterate through all pairwise combinations of inlier correspondences and choose a configuration with the most swapped back points close to the projected points. However, this method has a squared complexity in the number of correspondences and is thus computationally expensive to execute inside a RANSAC loop. To achieve a better complexity, it is helpful to notice that each pair of points, that are selected for" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18177" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "coordinate permutation, their original points and the permuted points form a 2D rectangle in the image (c.f. Figures 2 and 3). Using this observation, we can devise a more efficient recovery algorithm. For bookkeeping of recovered point coordinates, we first define the two sets" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.177, + 0.47, + 0.197 + ], + "angle": 0, + "content": "\\[\nS _ {j} = \\left\\{\\left(x _ {k j}, k\\right) \\mid \\hat {\\boldsymbol {x}} _ {k} = \\left[ x _ {k 1} \\quad x _ {k 2} \\right] ^ {\\top} \\right\\}, \\quad j = \\{1, 2 \\} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.206, + 0.471, + 0.419 + ], + "angle": 0, + "content": "Each element in the sets consists of a single coordinate \\((x_{1}\\) or \\(x_{2})\\) and its index \\(k\\) in the ordered list of points. The index uniquely identifies coordinates to enable swapping of point pairs. For example, if the query image has 3 points \\(\\{\\hat{x}_1 = [0,10]^\\top ,\\hat{x}_2 = [20,30]^\\top ,\\hat{x}_3 = [40,50]^\\top \\}\\), then \\(S_{1} = \\{(0,1),(20,2),(40,3)\\}\\), \\(S_{2} = \\{(10,1),(30,2),(50,3)\\}\\). For each projected image point \\(\\tilde{x}\\), we first decide which coordinate could be the original one by comparing \\(\\tilde{x}\\) and the permuted image point \\(\\hat{x}\\). We label coordinate \\(j\\) as correct if the \\(j\\)-th coordinate is within \\(\\varepsilon\\) from the projected point, that is \\(|\\hat{x}_j - \\tilde{x}_j| < \\varepsilon\\). Denoting the other coordinate as \\(j'\\), we collect the possible swapped point candidates \\(C\\) by looking in the set \\(S_{j'}\\), and finding points with the respective coordinate close to the projected point" + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.429, + 0.47, + 0.448 + ], + "angle": 0, + "content": "\\[\nC = \\left\\{k \\mid \\left| x _ {k j ^ {\\prime}} - \\tilde {x} _ {j ^ {\\prime}} \\right| < \\varepsilon , \\left(x _ {k j ^ {\\prime}}, k\\right) \\in S _ {j ^ {\\prime}} \\right\\} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.457, + 0.47, + 0.532 + ], + "angle": 0, + "content": "Since this set likely contains multiple candidates for each point (having a similar \\( x_{1} \\) or \\( x_{2} \\) coordinate), and the candidate points after swapping back can be distant from their projected points, we use a symmetric swapping error to filter out the coincident candidates" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.542, + 0.47, + 0.563 + ], + "angle": 0, + "content": "\\[\n\\varepsilon_ {s y m} = \\left\\| \\tilde {\\boldsymbol {x}} - \\left[ \\begin{array}{l l} x _ {j} & x _ {k j ^ {\\prime}} \\end{array} \\right] ^ {\\top} \\right\\| _ {2} + \\left\\| \\tilde {\\boldsymbol {x}} _ {k} - \\left[ \\begin{array}{l l} x _ {k j} & x _ {j ^ {\\prime}} \\end{array} \\right] ^ {\\top} \\right\\| _ {2} (8)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.572, + 0.469, + 0.677 + ], + "angle": 0, + "content": "We only consider a candidate to be valid, if both points are close to the respective reprojected image points after swapping them back. If multiple candidates are valid, we keep the one with the smallest \\(\\varepsilon_{sym}\\). Notice that, with such a selection mechanism, the recovered original points may not be symmetric. However, we have not found any drawbacks from this asymmetry in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.678, + 0.47, + 0.739 + ], + "angle": 0, + "content": "By implementing the sets \\( S_{j} \\) using hashing, we achieve amortized linear runtime complexity on average w.r.t. the number of correspondences for our recovery scheme. More details can be found in the suppl. material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.756, + 0.47, + 0.846 + ], + "angle": 0, + "content": "Pose Refinement To further improve the accuracy of our pose estimates, we conduct a non-linear refinement over all inliers using the stronger 2D constraints from Equation (2) for recovered points \\(\\mathcal{I}_p\\) and the weaker 1D constraints from Equation (4) for coordinates \\(\\mathcal{I}_l\\) that could not be swapped back. The overall cost function is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.853, + 0.47, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\sum_ {k \\in \\mathcal {I} _ {p}} \\rho \\left(d _ {p} \\left(\\boldsymbol {x} _ {k}, P \\bar {\\boldsymbol {X}} _ {k}\\right)\\right) + \\sum_ {k \\in \\mathcal {I} _ {\\ell}} \\rho \\left(\\underset {i \\in \\{1, 2 \\}} {\\operatorname {s o f t m i n}} \\left(d _ {l} \\left(\\boldsymbol {\\ell} _ {k i}, P \\bar {\\boldsymbol {X}} _ {k}\\right)\\right)\\right) \\tag {9}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.578, + 0.088, + 0.819, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.22, + 0.892, + 0.282 + ], + "angle": 0, + "content": "Figure 4: Illustration of point recovery mechanism in the 3D scenario with private maps, where the permuted red points form a cuboid in 3D. The reprojection of the 3D points is used for thresholding of errors in image space." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.293, + 0.893, + 0.405 + ], + "angle": 0, + "content": "where \\(\\rho\\) is a robustifier. To smoothly select between the two possible axis-aligned lines, we use the (Boltzmann) soft-min operator [5], defined as \\(\\operatorname*{softmin}_{i}\\{d_{i}\\} = (\\sum_{i}d_{i}e^{-d_{i}}) / (\\sum_{i}e^{-d_{i}})\\). We incorporate this non-linear refinement into LO-RANSAC [11] using the Arctan loss as \\(\\rho\\) inside the RANSAC loop and Cauchy as the robust loss for the final pose refinement." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.423, + 0.892, + 0.573 + ], + "angle": 0, + "content": "Degenerate Configurations Note that when all \\(\\ell_{i}\\) lines are parallel (i.e., originating from the same coordinate), the configuration becomes degenerate as the full 6-DoF of the pose cannot be recovered. This happens for 2 out of 64 configurations that we can trivially discard. For the two degenerate cases, it would be possible to solve for the rotation and two translation parameters using 5 correspondences. We initially explored this direction as well yet found the solutions to be less stable, as they provide less accurate pose estimates, so we do not include them in our final method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.582, + 0.779, + 0.599 + ], + "angle": 0, + "content": "3.3. Localization with Private Maps" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.606, + 0.892, + 0.71 + ], + "angle": 0, + "content": "In the previous section, we described our coordinate permutation scheme for 2D image points to preserve the privacy of localization queries. Similar to the 2D case, we can also permute coordinates of 3D points to hide the contents of private maps. This is a scenario that was originally addressed by Speciale et al. [46] using lifting to random 3D lines. We denote a random 3D line \\(L\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.718, + 0.892, + 0.752 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {L} = \\left[ \\begin{array}{l} \\boldsymbol {p} \\\\ \\boldsymbol {d} \\end{array} \\right] \\in \\mathbb {R} ^ {3} \\times \\mathbb {P} ^ {2}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.762, + 0.892, + 0.834 + ], + "angle": 0, + "content": "where \\( p \\) and \\( q \\) are 3D points on \\( L \\) subject to \\( d = \\frac{p - q}{\\|p - q\\|_2} \\) and such that the line passes through the original 3D point \\( X \\). The reprojection of the 3D line to the image defines a 1D geometric constraint" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.842, + 0.892, + 0.862 + ], + "angle": 0, + "content": "\\[\n0 = \\hat {\\boldsymbol {L}} _ {i} ^ {\\top} \\bar {\\boldsymbol {x}} = \\left(\\left[ \\boldsymbol {R} \\boldsymbol {d} _ {i} \\right] _ {\\times} \\boldsymbol {P} \\bar {\\boldsymbol {p}} _ {i}\\right) ^ {\\top} \\bar {\\boldsymbol {x}} \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "that can be used for privacy-preserving pose estimation. To solve for the full 6-DoF pose, at least 6 correspondences are" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18178" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.137 + ], + "angle": 0, + "content": "needed to solve the minimal \\( p6L \\) problem [48] in RANSAC. If gravity is known, only 4 correspondences are needed to solve the up4L problem [49]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.471, + 0.364 + ], + "angle": 0, + "content": "Instead of lifting to random 3D lines, we construct axis-aligned 3D lines by coordinate permutation of randomly selected pairs of 3D points. Analogous to the 2D case, we can hypothesize pose candidates in RANSAC by generating the different \\(3^{6} = 729\\) combinations of line constraints, and we can also recover the original 3D point positions by back-swapping with sets \\(S_{j=1,2,3}\\). Notice that the original 3D point may lie on any of the three axis-aligned lines and the randomly selected point pairs form a cuboid in 3D (see Figure 4). To robustify the back-swapping algorithm against non-isotropic noise on the (triangulated) 3D points, we define the error \\(\\varepsilon_{sym}\\) in image space through reprojection. Moreover, if runtime is a concern for the final application, we can also choose to expose one of the 3 coordinates, so the number of line combinations would be \\(2^{6} = 64\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.47, + 0.44 + ], + "angle": 0, + "content": "Pose Refinement For pose refinement in the 3D case, we again add constraints from two sources: the ones from inlier lines \\(\\mathcal{I}_L\\) and the ones from recovered inlier points \\(\\mathcal{I}_p\\). The overall cost function is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.443, + 0.455, + 0.479 + ], + "angle": 0, + "content": "\\[\n\\sum_ {k \\in \\mathcal {I} _ {p}} \\rho (d _ {p} (\\boldsymbol {x} _ {k}, P \\bar {\\boldsymbol {X}} _ {k})) + \\sum_ {k \\in \\mathcal {I} _ {L}} \\rho (\\underset {i \\in \\{1, 2 \\}} {\\operatorname {s o f t m i n}} (d _ {L} (\\boldsymbol {x} _ {k}, \\hat {\\boldsymbol {L}} _ {k i}))\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.482, + 0.47, + 0.533 + ], + "angle": 0, + "content": "\\[\n\\text {w h e r e} d _ {L} = \\frac {\\left| \\hat {\\boldsymbol {L}} _ {k i} ^ {\\top} \\bar {\\boldsymbol {x}} _ {k} \\right|}{\\sqrt {\\hat {L} _ {k i 1} ^ {2} + \\hat {L} _ {k i 2} ^ {2}}} \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.534, + 0.47, + 0.564 + ], + "angle": 0, + "content": "and we use the same setup of LO-RANSAC and choice of robustifiers as in the 2D scenario." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.576, + 0.21, + 0.592 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.601, + 0.471, + 0.783 + ], + "angle": 0, + "content": "In our experiments, we first focus on demonstrating the effectiveness of our proposed point recovery mechanism using an ablation study. We then compare our method against the traditional non-privacy preserving approach (PnP) and the original privacy-preserving approach based on random lines. Results are reported on existing benchmark datasets [23,46,52] for image-based localization, evaluated for the two scenarios of private localization queries (PnLP) and maps (PnL). All results assume unknown gravity and we show further results with known gravity in the supplementary material. Finally, we show image inversion results using the density-based attack by Chelani et al. [9]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.8, + 0.47, + 0.905 + ], + "angle": 0, + "content": "Implementation Details We embed our method into LO-RANSAC [11] with Levenberg-Marquardt [2, 26] as nonlinear optimizer for pose refinement. Inlier reprojection thresholds on 2D points are set to \\(12px\\) for the Cambridge dataset [23] and to \\(4px\\) otherwise. Reprojection thresholds on lines are chosen as \\(\\frac{12px}{\\sqrt{2}}\\) and \\(\\frac{4px}{\\sqrt{2}}\\), respectively." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.091, + 0.701, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.705, + 0.092, + 0.889, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.228, + 0.892, + 0.289 + ], + "angle": 0, + "content": "Figure 5: Ablation study on King's college sequence [23] w.r.t. the number of correspondences. Our method closes the performance gap, that is especially pronounced in difficult cases with few correspondences." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.296, + 0.893, + 0.342 + ], + "angle": 0, + "content": "We re-implement all methods in the same framework for a fair comparison of accuracy, recall, and runtime. All point clouds are triangulated using COLMAP [41, 43]." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.352, + 0.654, + 0.369 + ], + "angle": 0, + "content": "4.1. Ablation Study" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.376, + 0.826, + 0.392 + ], + "angle": 0, + "content": "4.1.1 Impact of Number of Correspondences" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.892, + 0.689 + ], + "angle": 0, + "content": "As argued in previous sections, the reduced accuracy and recall in privacy-preserving localization methods based on random lines is largely attributed to the weaker geometric constraints. To showcase this performance gap, we conduct an experiment on the King's College sequence in the Cambridge dataset [23]. Localization performance is tested on varying number of correspondences per query image by randomly dropping input matches. Cases with few correspondences typically depict the challenging localization scenarios, where feature matching only yields few matches and only few constraints can be used for pose estimation. The results of this experiment are summarized in Figure 5. First, we observe that the performance gap between the privacy-preserving and traditional approach is especially pronounced for low number of matches, which in turn suggests that the impact of the number of constraints on the localization accuracy saturates eventually. We also see that our method closes the accuracy gap to the traditional approach across the board." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.71, + 0.816, + 0.726 + ], + "angle": 0, + "content": "4.1.2 Impact of Point Recovery Mechanism" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To analyze the effectiveness of the proposed point recovery mechanism, we conduct experiments on HoloLens data [47] with our method in different settings: with only line constraints, with recovered point constraints, and with the true recovered points using an oracle that has access to groundtruth information. This dataset contains images with a large variance on the inlier ratio, which makes it suitable for this ablation study, as the point recovery mechanism is strongly influenced by it. Results are summarized in Figure 6, which shows a significant improvement in accuracy for our method when using the stronger 2D constraints from" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18179" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.287, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.09, + 0.468, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.228, + 0.47, + 0.259 + ], + "angle": 0, + "content": "Figure 6: Ablation study on HoloLens data from [47] to measure the effectiveness of our point recovery mechanism." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.271, + 0.271, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.273, + 0.465, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.402, + 0.47, + 0.448 + ], + "angle": 0, + "content": "Figure 7: Ablation study on HoloLens data from [47] that shows effective point recovery across all outlier ratios and overall low error rates on the recovered points." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.458, + 0.468, + 0.508 + ], + "angle": 0, + "content": "
MED (°)AUC@1°MED (cm)AUC@10cm(1°, 10 cm)Time (s)
PnLP [47]0.0884.790.6388.8897.800.07
Proposed0.0786.690.5690.1298.410.36
PnP0.0787.920.5190.8598.800.05
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.519, + 0.47, + 0.549 + ], + "angle": 0, + "content": "Table 1: Localization performance on HoloLens dataset [47] with indoor and outdoor scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.562, + 0.469, + 0.607 + ], + "angle": 0, + "content": "recovered points. In comparison to the oracle that defines a theoretical upper bound for our method, there is no significant difference in performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.609, + 0.47, + 0.744 + ], + "angle": 0, + "content": "Furthermore, we also report the correlation between the outlier ratio and the ratio of recovered points in Figure 7. The expected number is calculated as \\( p^2 \\) where \\( p \\) is the inlier ratio. From the figure we can see that the ratios of correctly recovered points matches the expected number across all outlier ratios. The ratio of mismatched points stays low in this dataset even when the inlier ratio is as low as \\( 20\\% \\). Those observations combined provide strong evidence that the recovering mechanism is effective." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.756, + 0.373, + 0.772 + ], + "angle": 0, + "content": "4.2. Localization with Private Queries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.902 + ], + "angle": 0, + "content": "HoloLens [47] This dataset features mostly small-scale scenes and unconstrained motion trajectories from a headworn augmented reality device with VGA-resolution cameras. Equivalent to the original dataset, we use COLMAP for reconstruction of the full image sequence while limiting the number of SIFT features per image to at most 500. There are 3325 query images in total and each query has on average 320 correspondences. After reconstructing the full" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.089, + 0.891, + 0.138 + ], + "angle": 0, + "content": "
MED (°)AUC@1°MED (cm)AUC@10cm(1°, 10 cm)Time (s)
PnLP [47]0.1871.5912.1318.3841.290.36
Proposed0.1872.6111.7320.0344.262.31
PnP0.1773.0911.6620.2243.950.20
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.149, + 0.892, + 0.18 + ], + "angle": 0, + "content": "Table 2: Localization performance on Cambridge dataset [23] with handheld videos in an outdoor scene." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.188, + 0.891, + 0.238 + ], + "angle": 0, + "content": "
MED (°)AUC@1°MED (cm)AUC@10cm(1°, 10 cm)Time (s)
PnLP [47]0.0288.322.2459.5778.230.09
Proposed0.0289.671.9263.6281.330.68
PnP0.0290.741.8564.5882.620.08
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.249, + 0.892, + 0.279 + ], + "angle": 0, + "content": "Table 3: Localization performance on crowd-sourced Internet photo collections [29, 53]." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.288, + 0.891, + 0.336 + ], + "angle": 0, + "content": "
MED (°)AUC@1°MED (cm)AUC@10cm(1°, 10 cm)Time (s)
PnL [46]0.0884.710.6488.6697.711.16
Proposed0.0786.310.5689.7197.926.61
PnP0.0787.850.5190.8498.830.07
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.338, + 0.892, + 0.368 + ], + "angle": 0, + "content": "Table 4: Localization performance on HoloLens dataset [47] in the private map scenario." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.38, + 0.892, + 0.532 + ], + "angle": 0, + "content": "sequence, we hold out every 5-th image as a query, remove any point correspondences associated to these images from the reconstruction, and retriangulate the remaining database images. The pose of the query images in the full reconstruction serve as the groundtruth for evaluation. The results are summarized in Table 1, where we can see that our method performs almost on par with the traditional non-privacy preserving case in terms of accuracy and recall. The additional combinatorial overhead of evaluating more pose candidates leads to a roughly 5-fold runtime increase for our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.893, + 0.747 + ], + "angle": 0, + "content": "Cambridge [23] This localization benchmark dataset contains handheld HD-resolution videos taken around Cambridge University in an outdoor setting. We use the same reference reconstruction as in [6] for the database map and extract SuperPoint+SuperGlue feature correspondences using the hloc toolbox [36, 37]. The dataset has a total of 1918 query images and an average of around 2850 2D-3D correspondences per image. Results are summarized in Table 2 and the performance trend for accuracy, recall, and runtime are all consistent with the results on the lower-resolution HoloLens dataset. This underlines the robustness of our approach against different sensors, scene types, as well as feature detection and matching algorithm characteristics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Internet Photo Collections [29, 53] This collection of datasets is crowd-sourced from the internet and comprises a large variety in image resolution and quality, lighting conditions, etc. We conduct experiments on the Dubrovnik6k, Gendarmenmarkt, Roman Forum, and Trafalgar locations with equivalent settings as used by Speciale et al. [47] for generating pseudo-groundtruth and establishing feature correspondences using COLMAP. On average, there are around 1000 SIFT correspondences per image with a total" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18180" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.287, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.093, + 0.488, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.21, + 0.181, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.181, + 0.21, + 0.28, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.145, + 0.292, + 0.216, + 0.306 + ], + "angle": 0, + "content": "(a) Original" + }, + { + "type": "image", + "bbox": [ + 0.286, + 0.21, + 0.384, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.385, + 0.21, + 0.483, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.335, + 0.292, + 0.434, + 0.305 + ], + "angle": 0, + "content": "(b) Random line" + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.21, + 0.587, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.588, + 0.21, + 0.686, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.557, + 0.293, + 0.617, + 0.305 + ], + "angle": 0, + "content": "(c) Oracle" + }, + { + "type": "image", + "bbox": [ + 0.689, + 0.089, + 0.892, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.691, + 0.21, + 0.789, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.791, + 0.21, + 0.889, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.752, + 0.293, + 0.829, + 0.306 + ], + "angle": 0, + "content": "(d) Proposed" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.308, + 0.894, + 0.384 + ], + "angle": 0, + "content": "Figure 8: Privacy attack on (private) maps using a combination of 3D image inversion [32] and the density based attack method Line2Point [9]. The top row shows the 3D map that is recovered using Line2Point for all but the leftmost result. The 3D map is used as an input for rendering synthesized images shown at two different viewpoints in the bottom row. From left to right: (a) Results on original, non-privacy preserving point cloud. (b) Results on random line cloud. (c) Results on our method with an attacker that gained access to swapped coordinates. (d) Results on our method with permuted coordinates." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.469, + 0.442 + ], + "angle": 0, + "content": "of 2416 query images. Results are summarized in Table 3. The accuracy of all methods on this dataset is surprisingly high, yet we can still observe significant improvements." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.451, + 0.361, + 0.467 + ], + "angle": 0, + "content": "4.3. Localization with a Private Map" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.475, + 0.469, + 0.61 + ], + "angle": 0, + "content": "To evaluate localization scenario with a private map, we conduct experiments on HoloLens data [47] using the same setup as in the private query scenario described in the previous section. We adopt the setting of exposing one correct coordinate in Table 4 and provide results for the computationally more expensive case with 729 combinations in the supplementary material. Like in the private query scenario, we are able to significantly close the accuracy gap but increase run-time by a factor of around six." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.621, + 0.356, + 0.635 + ], + "angle": 0, + "content": "4.4. Inversion Attack on Line Cloud" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In this section, we analyze and compare the level of privacy protection for the map representation. We perform this analysis by attacking the 3D point maps using image inversion techniques, as proposed by Pittaluga et al. [32]. To render images from the privacy preserving 3D line maps, we first execute a density based attack on the map representations using the Line2Point [9] method and then run image inversion on the recovered point cloud. Figure 8 shows results for this experiment, where inverted images from the non-privacy preserving map are nearly indistinguishable from original images of the scene. This again highlights the importance of research on privacy preserving methods for image-based localization. Images rendered from naively constructed random line clouds without sparsification closely resemble the original images as well and thus are not sufficient to protect private information in the map. The results of the attack on our method in column (d)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.395, + 0.892, + 0.622 + ], + "angle": 0, + "content": "shows mostly recognizable images and demonstrates the increased level of privacy that our method provides. Even if an attacker had access to an oracle that knows about which of the coordinates is correct, the rendered images (c) are less recognizable than the ones from a random line cloud. It is important to note that this information is not available to an attacker in practice, but it allows us to understand the relative impact on the increased level of privacy. On the one hand, our method constructs axis-aligned lines, which, by construction, cannot be intersected in a density based attack. On the other hand, we increase the combinatorial complexity of executing a density based attack, as significantly more coordinate pairs must be tried to find a valid intersection. In the supplementary material we provide additional inversion results and more discussion regarding potential attacks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.64, + 0.618, + 0.655 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.667, + 0.892, + 0.833 + ], + "angle": 0, + "content": "In this paper, we present a significant improvement over existing privacy-preserving image-based localization approaches. Our method improves upon the accuracy limitation of random line based approaches and closes the gap to traditional non-privacy preserving methods. At the same time, our method proves as robust against recently presented density attacks on random 3D line clouds. An interesting avenue for future work could be in addressing the increased runtime of our method. One promising idea involves voting for correct coordinate swaps during RANSAC and progressively sampling from more likely lines." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.842, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments We would like to thank Marcel Geppert for reviewing this paper, for the insightful discussions, and his help in the supp. material, as well as Torsten Sattler and Kunal Chelani for the code and data of line cloud inversion experiments. Viktor Larsson was supported by ELLIIT." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18181" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Inside Facebook Reality Labs: Research updates and the future of social connection. https://tech.fb.com/inside-facebook-reality-labs-research-updates-and-the-future-of-social-connection/, 2019. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.172, + 0.468, + 0.198 + ], + "angle": 0, + "content": "[2] Sameer Agarwal, Keir Mierle, and The Ceres Solver Team. Ceres Solver, 3 2022. 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.088, + 0.2, + 0.469, + 0.255 + ], + "angle": 0, + "content": "[3] Relja Arandjelovic, Petr Gronat, Akihiko Torii, Tomas Pajdla, and Josef Sivic. 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In International Conference on Computer Vision (ICCV), 2015. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.892, + 0.614 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "18183" + } + ] +] \ No newline at end of file diff --git a/2023/Privacy Preserving Localization via Coordinate Permutations/f992eeb4-2e60-42f9-9e28-abc98f428b2a_origin.pdf b/2023/Privacy Preserving Localization via Coordinate Permutations/f992eeb4-2e60-42f9-9e28-abc98f428b2a_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..63e69c3e307ea15d6df2d8c21927a9efbbe3824a --- /dev/null +++ b/2023/Privacy Preserving Localization via Coordinate Permutations/f992eeb4-2e60-42f9-9e28-abc98f428b2a_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9317b011ecaf6e2e057ac28e707321977edf5e08b6e4893a6c4cd834c6d96998 +size 6553982 diff --git a/2023/Privacy Preserving Localization via Coordinate Permutations/full.md b/2023/Privacy Preserving Localization via Coordinate Permutations/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a2eb8672d2be58ca41a4645b1ffe0949d11094c8 --- /dev/null +++ b/2023/Privacy Preserving Localization via Coordinate Permutations/full.md @@ -0,0 +1,356 @@ +# Privacy Preserving Localization via Coordinate Permutations + +Linfei Pan1 Johannes L. Schonberger2 Viktor Larsson3 Marc Pollefeys1,2 ETH Zurich Microsoft Lund University + +1{linfei.pan,marc.pollefeys}@inf.ethz.ch,2joschonb@microsoft.com,3viktor.larsson@math.lth.se + +# Abstract + +Recent methods on privacy-preserving image-based localization use a random line parameterization to protect the privacy of query images and database maps. The lifting of points to lines effectively drops one of the two geometric constraints traditionally used with point-to-point correspondences in structure-based localization. This leads to a significant loss of accuracy for the privacy-preserving methods. In this paper, we overcome this limitation by devising a coordinate permutation scheme that allows for recovering the original point positions during pose estimation. The recovered points provide the full 2D geometric constraints and enable us to close the gap between privacy-preserving and traditional methods in terms of accuracy. Another limitation of random line methods is their vulnerability to density based 3D line cloud inversion attacks. Our method not only provides better accuracy than the original random line based approach but also provides stronger privacy guarantees against these recently proposed attacks. Extensive experiments on standard benchmark datasets demonstrate these improvements consistently across both scenarios of protecting the privacy of query images as well as the database map. + +# 1. Introduction + +The interest in commercial solutions for cloud-based localization and mapping in mixed reality and robotics (e.g., Google VPS [34], Microsoft Azure Spatial Anchors [21], or Facebook LiveMaps [1]) has raised a host of privacy concerns [24, 31, 35, 51]. Recently, several approaches have been introduced by the research community to address these concerns [14, 17-19, 25, 45-47]. The common theme underlying these methods is based on the principle of lifting traditional point-based features to randomly oriented lines to conceal the appearance of query images and database maps. + +While this family of approaches is successful in enabling privacy preserving image-based localization and mapping, it comes at significant trade-offs in terms of accuracy and recall. These trade-offs are primarily caused by the fact that + +![](images/524c6b154c2a14c46cacf05b0c2a3aa503f66a41bac75c032d1d12660794369b.jpg) + +![](images/d2399fcb7658fe3c79a7ec4e74dd914c3cacf990cf989a1d6588aca9083aa944.jpg) + +![](images/e1b5aada20d4f28e8c3633c703f0a32d355ad8acbd868d1aef5abaa15185b738.jpg) + +![](images/f95403eda44190c1f50465ad34d41ad45cafe1ca676559edecc618a2a2c298e6.jpg) +Figure 1: Privacy-preserving localization. Top Left: The client extracts keypoints and descriptors from the query image. Top Right: The client secretly pairs keypoints and permutes their coordinates; hiding their true position from the server. Bottom Left: Server performs localization using the permuted points and recovers the original 2D positions for points that exist in both query and map. Bottom Right: Feature inversion on the set of recovered points only reveals objects that are already present in the map. + +the privacy preserving line-to-point or point-to-line correspondences provide weaker geometric constraints than the traditional point-to-point correspondences [46]. When concealing the content of images or maps, the number of constraints is effectively halved, as each point-to-line or line-to-point reprojection only contributes a 1D geometric constraint compared to the 2D constraint from a point-to-point reprojection. Especially for the hard to localize images, where only few correspondences can be recovered during feature matching, this limitation makes a significant difference in terms of accuracy and recall. + +Furthermore, without careful construction of random line maps, density based attacks have been shown to be effective in uncovering information from the privacy preserving representations, which was already mentioned as a limitation by Speciale et al. [46]. The main idea behind density based attacks exploits the fact that pairs of randomly oriented lines have a relatively higher chance of intersecting near the true surface as compared to empty or unobserved space. As such, a naive attack could simply gather statistics from pairwise intersections of random lines and assume the true surface in dense regions of the intersected space. More sophisticated attacks based on this idea can yield realistic image renderings from 3D line maps when attacking naively constructed line maps [9]. + +In this work, we revisit the approach of lifting points to lines in order to improve upon these two main limitations. In contrast to the original approach, we introduce a coordinate permutation scheme by which we effectively construct axis-aligned lines. During the pose estimation routine, the permutation scheme enables us to recover the original points for a large fraction of the inlier correspondences. Therefore, we can use the same 2D geometric constraints as in the traditional setup. This significantly improves the accuracy of the localization results. Moreover, when applying our approach for hiding the 3D map, we drastically increase the combinatorial complexity for density based attacks as well as reduce the chance for line intersections due to constructing axis-aligned lines. Counter-intuitively, our proposed method therefore not only leads to better accuracy but also provides a stronger level of privacy preservation. We experimentally demonstrate these improvements on standard benchmark datasets and by attacking our axis-aligned line maps using the approach by Chelani et al. [9]. In summary, we make the following contributions: + +- Propose a new privacy-preserving lifting approach, applicable to protecting the map and query. +- Attacking the lifted representation has a higher combinatorial complexity compared to random lifting, rendering previous density based attacks ineffective. +- In contrast to previous work, we can recover the original 2D or 3D points, allowing for stronger geometric constraints and more accurate poses. +- Experimentally, we show significant improvements over previous privacy preserving work, closing the gap to traditional point-based non-private methods. + +# 2. Related Work + +Image-based Localization Methods in image-based localization have made tremendous progress. Over the years, the methods have been scaled for robust localization in + +large-scale scenes [27,38,40,54] with compressed map representations [8,15], while some of the methods can even run in real-time on mobile devices [4,20,22,27,28,39]. Some of the recent works focus on improving the robustness to drastic environmental changes [3,42,50] or enabling crossdevice localization and mapping scenarios [13]. The developed approaches are generally divided into structure-based methods [20, 38-40] using on an explicit geometric map representation or learning-based methods [7,22,44] with an implicit map representation. + +Privacy Risks Image-based localization is subject to privacy risks due to requiring images as an input [24, 31, 35, 51]. For example, in a cloud-based localization system, users may be concerned about sharing images of private spaces with the service provider. In a practical setting, the clients could only send local image features to the cloud to avoid these risks. However, recent inversion attacks have proven extremely effective in recovering the original images from only sparse local image features [12, 30, 32]. Recently, Chelani et al. proposed a method to query a localization service with a database of objects to recover information about scene contents [10]. + +Privacy Preservation To protect against these risks, several methods have been developed recently. The first work on this topic [46, 47] proposed a solution to preserve the privacy of 2D image or 3D map points in image-based localization. Their main idea was to lift 2D or 3D points to random lines by dropping one of the two geometric constraints during the pose estimation problem. Based on the same idea, a number of works followed up to address the problems of structure-from-motion [18, 19] and real-time SLAM [45], or to directly protect the high-dimensional feature representations instead of the geometry [14]. + +Underlying all these approaches, there are two fundamental limitations that were already observed by the original work [47]. First, by dropping one geometric constraint per correspondence for pose estimation, the accuracy of these approaches is significantly lowered, especially in the challenging cases with few matches between query and database. Second, without careful sparsification of the 3D map, density based attacks can recover information from 3D line clouds [9]. Sparsification of the map is an effective protection against density based attacks but comes with a further reduction of accuracy as well as recall. + +To protect in a more principled manner against these attacks, Geppert et al. [17] proposed to decompose the full 3D map into 1D partial maps, which are distributed across different servers. Each server then solves a partial localization problem and sends back the answer to the client, which can assemble a full 6-DoF localization result from the partial answers. Despite being effective against density based at + +![](images/4cf0f0d1a72c8c2e4aa121a4a6dd209e9abbe199ab036ac03a486d34397c0373.jpg) +Figure 2: Method overview for localization with private queries. The client extracts keypoints in the query image and secretly pairs them to swap one of their coordinates. The server only receives the permuted points, which can be considered as axis-aligned lines. The secretly paired points form rectangles, which can be leveraged during RANSAC to efficiently recover the original point positions for pairs that are both inliers. The scoring of candidate poses and the final non-linear pose refinement jointly leverage the stronger 2D constraints for recovered points and otherwise the weaker 1D constraints. + +![](images/9723d42c230ae8c976a9a35e81051ea175c704f4c571dc3ced2864ac61d4fe8e.jpg) + +tacks, the system is complex and it comes with further accuracy and recall trade-offs. In contrast, our method does not require a complex multi-server setup and we improve upon the two main limitations of the random lifting approaches simultaneously. Our method provides both stronger privacy guarantees while also closing the accuracy gap to traditional localization approaches. + +# 3. Method + +We now present our method for privacy-preserving localization. We address both the scenario of protecting the client's 2D image points in the localization query (Section 3.2) as well as protecting the service's 3D points in the database map (Section 3.3). + +Our approach follows the main idea in Speciale et al. [46, 47], where the exact 2D or 3D point positions are hidden by introducing ambiguity in the coordinates. In the original works, this is done by lifting each point to a random line. The line representation still enables localization, using line-to-point instead of point-to-point correspondences, but makes it difficult to identify potentially sensitive image or map content. Similar to the original idea [46], we also obscure the true position of the point. However, instead of replacing it with a random line, we select a subset of the point coordinates and corrupt them. This is done by secretly forming pairs of points and swapping their coordinates at random. Since the list of pairs is not known to an attacker, it is practically intractable to recover the original point positions. As we will later show, for point-pairs that exist in both the query and the map, we can devise a scheme to recover the true positions, allowing us to use the full 2D-3D geometric constraints for accurate pose refinement. + +An overview of our pipeline can be found in Figure 2 and we detail the steps of our method in the following sections. For ease of presentation, we first review the traditional setup and then explain the 2D setting that hides the query, but the same principle generalizes to the 3D setting as well. + +# 3.1. Review of Traditional Localization + +Traditionally, localization is performed by establishing a set of tentative 2D-3D point correspondences between the query image and the database map. Each correspondence $(\pmb{x},\pmb{X})\in \mathbb{R}^2\times \mathbb{R}^3$ yields two geometric constraints on the unknown camera pose $(R,t)\in \mathrm{SE}(3)$ as + +$$ +\lambda \bar {\boldsymbol {x}} = R \boldsymbol {X} + \boldsymbol {t}, \tag {1} +$$ + +where we let $\bar{x}$ denote the homogeneous 2D point in the normalized image plane (after removing the intrinsic calibration), and $\lambda$ represents the unknown depth. To identify outlier matches and estimate an initial pose, the standard approach is to use hypothesize-and-test frameworks, such as RANSAC [16], in order to generate multiple pose candidates by fitting $(R,t)$ to minimal subsets of the points, followed by measuring the consensus among the rest of the matches. The consistency between a candidate pose and a 2D-3D match is computed using the 2D reprojection error + +$$ +d _ {p} = \| \boldsymbol {x} - \pi (R \boldsymbol {X} + t) \|, \tag {2} +$$ + +where $\pi : \mathbb{R}^3 \to \mathbb{R}^2$ is the projection mapping. Once a candidate pose, together with the inlier matches, have been established, it is refined by minimizing the reprojection errors for all inliers jointly. + +# 3.2. Localization with Private Queries + +The traditional method relies on the availability of the original 2D image points, and is thus not privacy preserving. To preserve the privacy of the image, Speciale et al. [47] proposed to lift 2D image points into random 2D lines. Our method also builds upon 2D lines but aligns them with the coordinate axes through a random coordinate permutation scheme. The following paragraphs first establish notation by reviewing (random) line constraints for localization and then explain our permutation scheme in detail. + +Random Line Constraints In Speciale et al. [47], each 2D line $\ell$ back-projects into a 3D plane $\Pi_i = P^\top \ell_i$ passing + +![](images/1bbdcd6bee67e2cee3b5d12cf251658bcbefee1565373d3daa6b45f8cfb3caa5.jpg) +Figure 3: Illustration of geometric constraints induced by coordinate permutation and point recovery mechanism in the scenario of private queries. Red image points are secretly permuted. Black points are 3D map points. Blue points are the recovered, original image points obtained by back-swapping and form a rectangle together with their respective permuted points. + +through camera projection center and the line in the image plane. The corresponding 3D point $\mathbf{X}$ is expected to lie on this plane, which constrains the pose as + +$$ +\boldsymbol {\ell} ^ {\top} \left(R \boldsymbol {X} + \boldsymbol {t}\right) = 0. \tag {3} +$$ + +Note that this only yields a single geometric constraint instead of two as in Equation (1). In this case, it is still possible to estimate the pose, though the minimal problem now requires 6 instead of 3 correspondences. The minimal solver for this problem is known as $p6LP$ [33] and was used in [47]. Further, to validate a match, we can only measure the distance between the 2D line and the projected 3D point + +$$ +d _ {l} = \frac {\left| \boldsymbol {\ell} ^ {\top} \bar {\pi} (\boldsymbol {R} \boldsymbol {X} + \boldsymbol {t}) \right|}{\sqrt {l _ {1} ^ {2} + l _ {2} ^ {2}}} , \tag {4} +$$ + +where $\ell = [l_1, l_2, l_3]^\top$ and $\bar{\pi}$ is the homogeneous projected 2D point. This is a weaker constraint compared to the 2D error measured in Equation (2) and thus explains the observed loss in accuracy by this approach. + +Coordinate Permutation Constraints In our case, we have 2D image points, where we know that only one of the two coordinates is correct because of the a priori secret permutation (illustrated in Figures 2 and 3). In the context of the line-based framework from Speciale et al. [47], this can be considered as, instead of having a random line, having two axis-aligned lines passing through the given point. The original point will share one of the coordinates, and thus lie on one of these two lines. Mathematically, each point $\pmb{x} = [x_1,x_2]^\top$ gives rise to two axis-aligned lines $\ell_1,\ell_2$ , where $\ell_{1} = [1,0, - x_{1}]^{\top}$ $\ell_{2} = [0,1, - x_{2}]^{\top}$ . Each correspondence then gives us the following constraint + +$$ +\ell_ {1} ^ {\top} (R \boldsymbol {X} + \boldsymbol {t}) = 0 \quad \vee \quad \ell_ {2} ^ {\top} (R \boldsymbol {X} + \boldsymbol {t}) = 0, \tag {5} +$$ + +where we only know that one of the two constraints should be satisfied. For $n$ point correspondences, we thus have $2^{n}$ possible combinations of constraints to choose from. + +While considering all $n$ points leads to a combinatorial explosion and would be computationally intractable, we only need to consider small subsets of matches to hypothesize candidate poses inside RANSAC. For a minimal sample of 6 correspondences, there exist $2^6 = 64$ different combinations of lines in Equation (5). One of these combinations will correspond to having the true (uncorrupted) coordinate in all 6 lines, and should give a correct camera pose for an all-inlier minimal sample. So, to find a camera pose, we can simply iterate exhaustively over all $2^6 = 64$ combinations. Each of these combinations corresponds to a $p6LP$ minimal estimation problem, which can be efficiently solved. If gravity is known, we can efficiently solve the minimal $up4LP$ problem [33] from $2^4 = 16$ combinations. + +The key observation is now that, if we have a candidate pose, then for any inlier correspondence, we can easily resolve which of the two axis-aligned lines (i.e., coordinates) is the correct one by simply projecting the 3D points to the image and taking the one with the smaller 1D residual $d_{l}$ . By determining the inlier coordinates $\mathcal{I}$ within the threshold (i.e., $d_{l} < \varepsilon$ ), we can score candidate poses and thereby embed our method into a standard RANSAC loop to robustly estimate a camera pose. This approach still uses the weaker 1D constraints. The next paragraph explains how we can efficiently recover the original 2D points in this framework to benefit from stronger 2D constraints. + +Original Point Recovery After finding a candidate pose using RANSAC, we devise an efficient scheme for recovering the original points $\pmb{x}$ from the set of inliers $\mathcal{I}$ . Note that our scheme can only recover the positions for points that are visible in both the query and the map. As such, recovering the original points is not a concern for privacy, as they are known to both client and server. + +Let's recall that we randomly picked pairs of points and swapped one of their coordinates to preserve their privacy. To recover the original points, we need to rely on the projected points and the property that the swapped back points should be close to the projected points (within $\varepsilon$ distance) if it is an inlier. As for outliers points, there is no proper mechanism to distinguish a correct pair from an incorrect one, thus they remain unrecoverable. + +One way of recovering points is to iterate through all pairwise combinations of inlier correspondences and choose a configuration with the most swapped back points close to the projected points. However, this method has a squared complexity in the number of correspondences and is thus computationally expensive to execute inside a RANSAC loop. To achieve a better complexity, it is helpful to notice that each pair of points, that are selected for + +coordinate permutation, their original points and the permuted points form a 2D rectangle in the image (c.f. Figures 2 and 3). Using this observation, we can devise a more efficient recovery algorithm. For bookkeeping of recovered point coordinates, we first define the two sets + +$$ +S _ {j} = \left\{\left(x _ {k j}, k\right) \mid \hat {\boldsymbol {x}} _ {k} = \left[ x _ {k 1} \quad x _ {k 2} \right] ^ {\top} \right\}, \quad j = \{1, 2 \} \tag {6} +$$ + +Each element in the sets consists of a single coordinate $(x_{1}$ or $x_{2})$ and its index $k$ in the ordered list of points. The index uniquely identifies coordinates to enable swapping of point pairs. For example, if the query image has 3 points $\{\hat{x}_1 = [0,10]^\top ,\hat{x}_2 = [20,30]^\top ,\hat{x}_3 = [40,50]^\top \}$ , then $S_{1} = \{(0,1),(20,2),(40,3)\}$ , $S_{2} = \{(10,1),(30,2),(50,3)\}$ . For each projected image point $\tilde{x}$ , we first decide which coordinate could be the original one by comparing $\tilde{x}$ and the permuted image point $\hat{x}$ . We label coordinate $j$ as correct if the $j$ -th coordinate is within $\varepsilon$ from the projected point, that is $|\hat{x}_j - \tilde{x}_j| < \varepsilon$ . Denoting the other coordinate as $j'$ , we collect the possible swapped point candidates $C$ by looking in the set $S_{j'}$ , and finding points with the respective coordinate close to the projected point + +$$ +C = \left\{k \mid \left| x _ {k j ^ {\prime}} - \tilde {x} _ {j ^ {\prime}} \right| < \varepsilon , \left(x _ {k j ^ {\prime}}, k\right) \in S _ {j ^ {\prime}} \right\} \tag {7} +$$ + +Since this set likely contains multiple candidates for each point (having a similar $x_{1}$ or $x_{2}$ coordinate), and the candidate points after swapping back can be distant from their projected points, we use a symmetric swapping error to filter out the coincident candidates + +$$ +\varepsilon_ {s y m} = \left\| \tilde {\boldsymbol {x}} - \left[ \begin{array}{l l} x _ {j} & x _ {k j ^ {\prime}} \end{array} \right] ^ {\top} \right\| _ {2} + \left\| \tilde {\boldsymbol {x}} _ {k} - \left[ \begin{array}{l l} x _ {k j} & x _ {j ^ {\prime}} \end{array} \right] ^ {\top} \right\| _ {2} (8) +$$ + +We only consider a candidate to be valid, if both points are close to the respective reprojected image points after swapping them back. If multiple candidates are valid, we keep the one with the smallest $\varepsilon_{sym}$ . Notice that, with such a selection mechanism, the recovered original points may not be symmetric. However, we have not found any drawbacks from this asymmetry in our experiments. + +By implementing the sets $S_{j}$ using hashing, we achieve amortized linear runtime complexity on average w.r.t. the number of correspondences for our recovery scheme. More details can be found in the suppl. material. + +Pose Refinement To further improve the accuracy of our pose estimates, we conduct a non-linear refinement over all inliers using the stronger 2D constraints from Equation (2) for recovered points $\mathcal{I}_p$ and the weaker 1D constraints from Equation (4) for coordinates $\mathcal{I}_l$ that could not be swapped back. The overall cost function is defined as + +$$ +\sum_ {k \in \mathcal {I} _ {p}} \rho \left(d _ {p} \left(\boldsymbol {x} _ {k}, P \bar {\boldsymbol {X}} _ {k}\right)\right) + \sum_ {k \in \mathcal {I} _ {\ell}} \rho \left(\underset {i \in \{1, 2 \}} {\operatorname {s o f t m i n}} \left(d _ {l} \left(\boldsymbol {\ell} _ {k i}, P \bar {\boldsymbol {X}} _ {k}\right)\right)\right) \tag {9} +$$ + +![](images/2dbf1298f0c8dbce52b528f0c2f52a9a9c516458f56de08ce214d7bce1591ee1.jpg) +Figure 4: Illustration of point recovery mechanism in the 3D scenario with private maps, where the permuted red points form a cuboid in 3D. The reprojection of the 3D points is used for thresholding of errors in image space. + +where $\rho$ is a robustifier. To smoothly select between the two possible axis-aligned lines, we use the (Boltzmann) soft-min operator [5], defined as $\operatorname*{softmin}_{i}\{d_{i}\} = (\sum_{i}d_{i}e^{-d_{i}}) / (\sum_{i}e^{-d_{i}})$ . We incorporate this non-linear refinement into LO-RANSAC [11] using the Arctan loss as $\rho$ inside the RANSAC loop and Cauchy as the robust loss for the final pose refinement. + +Degenerate Configurations Note that when all $\ell_{i}$ lines are parallel (i.e., originating from the same coordinate), the configuration becomes degenerate as the full 6-DoF of the pose cannot be recovered. This happens for 2 out of 64 configurations that we can trivially discard. For the two degenerate cases, it would be possible to solve for the rotation and two translation parameters using 5 correspondences. We initially explored this direction as well yet found the solutions to be less stable, as they provide less accurate pose estimates, so we do not include them in our final method. + +# 3.3. Localization with Private Maps + +In the previous section, we described our coordinate permutation scheme for 2D image points to preserve the privacy of localization queries. Similar to the 2D case, we can also permute coordinates of 3D points to hide the contents of private maps. This is a scenario that was originally addressed by Speciale et al. [46] using lifting to random 3D lines. We denote a random 3D line $L$ as + +$$ +\boldsymbol {L} = \left[ \begin{array}{l} \boldsymbol {p} \\ \boldsymbol {d} \end{array} \right] \in \mathbb {R} ^ {3} \times \mathbb {P} ^ {2}, \tag {10} +$$ + +where $p$ and $q$ are 3D points on $L$ subject to $d = \frac{p - q}{\|p - q\|_2}$ and such that the line passes through the original 3D point $X$ . The reprojection of the 3D line to the image defines a 1D geometric constraint + +$$ +0 = \hat {\boldsymbol {L}} _ {i} ^ {\top} \bar {\boldsymbol {x}} = \left(\left[ \boldsymbol {R} \boldsymbol {d} _ {i} \right] _ {\times} \boldsymbol {P} \bar {\boldsymbol {p}} _ {i}\right) ^ {\top} \bar {\boldsymbol {x}} \tag {11} +$$ + +that can be used for privacy-preserving pose estimation. To solve for the full 6-DoF pose, at least 6 correspondences are + +needed to solve the minimal $p6L$ problem [48] in RANSAC. If gravity is known, only 4 correspondences are needed to solve the up4L problem [49]. + +Instead of lifting to random 3D lines, we construct axis-aligned 3D lines by coordinate permutation of randomly selected pairs of 3D points. Analogous to the 2D case, we can hypothesize pose candidates in RANSAC by generating the different $3^{6} = 729$ combinations of line constraints, and we can also recover the original 3D point positions by back-swapping with sets $S_{j=1,2,3}$ . Notice that the original 3D point may lie on any of the three axis-aligned lines and the randomly selected point pairs form a cuboid in 3D (see Figure 4). To robustify the back-swapping algorithm against non-isotropic noise on the (triangulated) 3D points, we define the error $\varepsilon_{sym}$ in image space through reprojection. Moreover, if runtime is a concern for the final application, we can also choose to expose one of the 3 coordinates, so the number of line combinations would be $2^{6} = 64$ . + +Pose Refinement For pose refinement in the 3D case, we again add constraints from two sources: the ones from inlier lines $\mathcal{I}_L$ and the ones from recovered inlier points $\mathcal{I}_p$ . The overall cost function is defined as + +$$ +\sum_ {k \in \mathcal {I} _ {p}} \rho (d _ {p} (\boldsymbol {x} _ {k}, P \bar {\boldsymbol {X}} _ {k})) + \sum_ {k \in \mathcal {I} _ {L}} \rho (\underset {i \in \{1, 2 \}} {\operatorname {s o f t m i n}} (d _ {L} (\boldsymbol {x} _ {k}, \hat {\boldsymbol {L}} _ {k i})) +$$ + +$$ +\text {w h e r e} d _ {L} = \frac {\left| \hat {\boldsymbol {L}} _ {k i} ^ {\top} \bar {\boldsymbol {x}} _ {k} \right|}{\sqrt {\hat {L} _ {k i 1} ^ {2} + \hat {L} _ {k i 2} ^ {2}}} \tag {12} +$$ + +and we use the same setup of LO-RANSAC and choice of robustifiers as in the 2D scenario. + +# 4. Experiments + +In our experiments, we first focus on demonstrating the effectiveness of our proposed point recovery mechanism using an ablation study. We then compare our method against the traditional non-privacy preserving approach (PnP) and the original privacy-preserving approach based on random lines. Results are reported on existing benchmark datasets [23,46,52] for image-based localization, evaluated for the two scenarios of private localization queries (PnLP) and maps (PnL). All results assume unknown gravity and we show further results with known gravity in the supplementary material. Finally, we show image inversion results using the density-based attack by Chelani et al. [9]. + +Implementation Details We embed our method into LO-RANSAC [11] with Levenberg-Marquardt [2, 26] as nonlinear optimizer for pose refinement. Inlier reprojection thresholds on 2D points are set to $12px$ for the Cambridge dataset [23] and to $4px$ otherwise. Reprojection thresholds on lines are chosen as $\frac{12px}{\sqrt{2}}$ and $\frac{4px}{\sqrt{2}}$ , respectively. + +![](images/fcfdda0c24f7add157c62919900c928caae6e6cf651a9c77f77fd29735bad04c.jpg) +Figure 5: Ablation study on King's college sequence [23] w.r.t. the number of correspondences. Our method closes the performance gap, that is especially pronounced in difficult cases with few correspondences. + +![](images/f9b3f6097d3455aa7522fe3b6bc4d97e2303d939e895b7637f10002ab5974189.jpg) + +We re-implement all methods in the same framework for a fair comparison of accuracy, recall, and runtime. All point clouds are triangulated using COLMAP [41, 43]. + +# 4.1. Ablation Study + +# 4.1.1 Impact of Number of Correspondences + +As argued in previous sections, the reduced accuracy and recall in privacy-preserving localization methods based on random lines is largely attributed to the weaker geometric constraints. To showcase this performance gap, we conduct an experiment on the King's College sequence in the Cambridge dataset [23]. Localization performance is tested on varying number of correspondences per query image by randomly dropping input matches. Cases with few correspondences typically depict the challenging localization scenarios, where feature matching only yields few matches and only few constraints can be used for pose estimation. The results of this experiment are summarized in Figure 5. First, we observe that the performance gap between the privacy-preserving and traditional approach is especially pronounced for low number of matches, which in turn suggests that the impact of the number of constraints on the localization accuracy saturates eventually. We also see that our method closes the accuracy gap to the traditional approach across the board. + +# 4.1.2 Impact of Point Recovery Mechanism + +To analyze the effectiveness of the proposed point recovery mechanism, we conduct experiments on HoloLens data [47] with our method in different settings: with only line constraints, with recovered point constraints, and with the true recovered points using an oracle that has access to groundtruth information. This dataset contains images with a large variance on the inlier ratio, which makes it suitable for this ablation study, as the point recovery mechanism is strongly influenced by it. Results are summarized in Figure 6, which shows a significant improvement in accuracy for our method when using the stronger 2D constraints from + +![](images/14eebd814c76fc5b5200e557d5bdc68f0f072e276edf43984cfcf95cb849b390.jpg) +Figure 6: Ablation study on HoloLens data from [47] to measure the effectiveness of our point recovery mechanism. + +![](images/2e74e1d0727393db298b76a34c2d0c4f550394adde9bc3a584292f974f9ea90a.jpg) + +![](images/03bb19e9f7286bd9f392c3f6c0693956d0e5f30e5362b5516d9af07430396d66.jpg) +Figure 7: Ablation study on HoloLens data from [47] that shows effective point recovery across all outlier ratios and overall low error rates on the recovered points. + +![](images/ebb9e667a9b4211c02f21788eac833da46a54bbd88fcd7d8e77b84786fb0ad3e.jpg) + +
MED (°)AUC@1°MED (cm)AUC@10cm(1°, 10 cm)Time (s)
PnLP [47]0.0884.790.6388.8897.800.07
Proposed0.0786.690.5690.1298.410.36
PnP0.0787.920.5190.8598.800.05
+ +recovered points. In comparison to the oracle that defines a theoretical upper bound for our method, there is no significant difference in performance. + +Furthermore, we also report the correlation between the outlier ratio and the ratio of recovered points in Figure 7. The expected number is calculated as $p^2$ where $p$ is the inlier ratio. From the figure we can see that the ratios of correctly recovered points matches the expected number across all outlier ratios. The ratio of mismatched points stays low in this dataset even when the inlier ratio is as low as $20\%$ . Those observations combined provide strong evidence that the recovering mechanism is effective. + +# 4.2. Localization with Private Queries + +HoloLens [47] This dataset features mostly small-scale scenes and unconstrained motion trajectories from a headworn augmented reality device with VGA-resolution cameras. Equivalent to the original dataset, we use COLMAP for reconstruction of the full image sequence while limiting the number of SIFT features per image to at most 500. There are 3325 query images in total and each query has on average 320 correspondences. After reconstructing the full + +Table 1: Localization performance on HoloLens dataset [47] with indoor and outdoor scenes. + +
MED (°)AUC@1°MED (cm)AUC@10cm(1°, 10 cm)Time (s)
PnLP [47]0.1871.5912.1318.3841.290.36
Proposed0.1872.6111.7320.0344.262.31
PnP0.1773.0911.6620.2243.950.20
+ +Table 2: Localization performance on Cambridge dataset [23] with handheld videos in an outdoor scene. + +
MED (°)AUC@1°MED (cm)AUC@10cm(1°, 10 cm)Time (s)
PnLP [47]0.0288.322.2459.5778.230.09
Proposed0.0289.671.9263.6281.330.68
PnP0.0290.741.8564.5882.620.08
+ +Table 3: Localization performance on crowd-sourced Internet photo collections [29, 53]. + +
MED (°)AUC@1°MED (cm)AUC@10cm(1°, 10 cm)Time (s)
PnL [46]0.0884.710.6488.6697.711.16
Proposed0.0786.310.5689.7197.926.61
PnP0.0787.850.5190.8498.830.07
+ +Table 4: Localization performance on HoloLens dataset [47] in the private map scenario. + +sequence, we hold out every 5-th image as a query, remove any point correspondences associated to these images from the reconstruction, and retriangulate the remaining database images. The pose of the query images in the full reconstruction serve as the groundtruth for evaluation. The results are summarized in Table 1, where we can see that our method performs almost on par with the traditional non-privacy preserving case in terms of accuracy and recall. The additional combinatorial overhead of evaluating more pose candidates leads to a roughly 5-fold runtime increase for our method. + +Cambridge [23] This localization benchmark dataset contains handheld HD-resolution videos taken around Cambridge University in an outdoor setting. We use the same reference reconstruction as in [6] for the database map and extract SuperPoint+SuperGlue feature correspondences using the hloc toolbox [36, 37]. The dataset has a total of 1918 query images and an average of around 2850 2D-3D correspondences per image. Results are summarized in Table 2 and the performance trend for accuracy, recall, and runtime are all consistent with the results on the lower-resolution HoloLens dataset. This underlines the robustness of our approach against different sensors, scene types, as well as feature detection and matching algorithm characteristics. + +Internet Photo Collections [29, 53] This collection of datasets is crowd-sourced from the internet and comprises a large variety in image resolution and quality, lighting conditions, etc. We conduct experiments on the Dubrovnik6k, Gendarmenmarkt, Roman Forum, and Trafalgar locations with equivalent settings as used by Speciale et al. [47] for generating pseudo-groundtruth and establishing feature correspondences using COLMAP. On average, there are around 1000 SIFT correspondences per image with a total + +![](images/b2d44ac88d4801cda4a69e67eff0099aa6ac971d574fc65992836e440b62a3e1.jpg) + +![](images/9e551d266bf5c6131ff9f1420b864b965c16cf4c23f9347fe6f2c9c3737b0751.jpg) + +![](images/5ce5c8a2a75b9c85a500d9449ddf849627a70ba93664f8742a97889ad1cdab2e.jpg) +(a) Original + +![](images/ef8e893c68bd4aca50b8e99e1d847e6ee9d40e13e87894723d44644cffd77ef9.jpg) +Figure 8: Privacy attack on (private) maps using a combination of 3D image inversion [32] and the density based attack method Line2Point [9]. The top row shows the 3D map that is recovered using Line2Point for all but the leftmost result. The 3D map is used as an input for rendering synthesized images shown at two different viewpoints in the bottom row. From left to right: (a) Results on original, non-privacy preserving point cloud. (b) Results on random line cloud. (c) Results on our method with an attacker that gained access to swapped coordinates. (d) Results on our method with permuted coordinates. + +![](images/0233f679175491a3c125b02efcaf46f3165233349eaf8f6c03ec55f701754edd.jpg) +(b) Random line + +![](images/c59a2479938f7529e748de30739078938d93956484356f4f46a8c62e3aedb6b8.jpg) + +![](images/ca60b5e169f291d2dc35afd49444e32767fdeea66416909f0708ad60724ac263.jpg) +(c) Oracle + +![](images/38e85b2d1cf80a6ef1f57c80a35ff301f74873b4b134a5eba57d8db2b52ca315.jpg) + +![](images/fb1986a0c95d80e0536062c8f1af82e57bb9d9ad03280206dd6acdc9175ef71b.jpg) + +![](images/a1d8eb92aad51fb1caf5f23b5f0ea870cc03274335a0a97f00fe4940b677823a.jpg) +(d) Proposed + +![](images/fb2b36e85cb9bceaf814a9c5b6ebfc224acad267e2d8ef4bcd0ab15679a7b6a4.jpg) + +of 2416 query images. Results are summarized in Table 3. The accuracy of all methods on this dataset is surprisingly high, yet we can still observe significant improvements. + +# 4.3. Localization with a Private Map + +To evaluate localization scenario with a private map, we conduct experiments on HoloLens data [47] using the same setup as in the private query scenario described in the previous section. We adopt the setting of exposing one correct coordinate in Table 4 and provide results for the computationally more expensive case with 729 combinations in the supplementary material. Like in the private query scenario, we are able to significantly close the accuracy gap but increase run-time by a factor of around six. + +# 4.4. Inversion Attack on Line Cloud + +In this section, we analyze and compare the level of privacy protection for the map representation. We perform this analysis by attacking the 3D point maps using image inversion techniques, as proposed by Pittaluga et al. [32]. To render images from the privacy preserving 3D line maps, we first execute a density based attack on the map representations using the Line2Point [9] method and then run image inversion on the recovered point cloud. Figure 8 shows results for this experiment, where inverted images from the non-privacy preserving map are nearly indistinguishable from original images of the scene. This again highlights the importance of research on privacy preserving methods for image-based localization. Images rendered from naively constructed random line clouds without sparsification closely resemble the original images as well and thus are not sufficient to protect private information in the map. The results of the attack on our method in column (d) + +shows mostly recognizable images and demonstrates the increased level of privacy that our method provides. Even if an attacker had access to an oracle that knows about which of the coordinates is correct, the rendered images (c) are less recognizable than the ones from a random line cloud. It is important to note that this information is not available to an attacker in practice, but it allows us to understand the relative impact on the increased level of privacy. On the one hand, our method constructs axis-aligned lines, which, by construction, cannot be intersected in a density based attack. On the other hand, we increase the combinatorial complexity of executing a density based attack, as significantly more coordinate pairs must be tried to find a valid intersection. In the supplementary material we provide additional inversion results and more discussion regarding potential attacks. + +# 5. Conclusion + +In this paper, we present a significant improvement over existing privacy-preserving image-based localization approaches. Our method improves upon the accuracy limitation of random line based approaches and closes the gap to traditional non-privacy preserving methods. At the same time, our method proves as robust against recently presented density attacks on random 3D line clouds. An interesting avenue for future work could be in addressing the increased runtime of our method. One promising idea involves voting for correct coordinate swaps during RANSAC and progressively sampling from more likely lines. + +Acknowledgments We would like to thank Marcel Geppert for reviewing this paper, for the insightful discussions, and his help in the supp. material, as well as Torsten Sattler and Kunal Chelani for the code and data of line cloud inversion experiments. 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Schonberger2 Viktor Larsson3 Marc Pollefeys1,2 ETH Zurich Microsoft Lund University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 52, + 171, + 563, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 171, + 563, + 186 + ], + "spans": [ + { + "bbox": [ + 52, + 171, + 563, + 186 + ], + "type": "text", + "content": "1{linfei.pan,marc.pollefeys}@inf.ethz.ch,2joschonb@microsoft.com,3viktor.larsson@math.lth.se" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 239, + 290, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 290, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 290, + 502 + ], + "type": "text", + "content": "Recent methods on privacy-preserving image-based localization use a random line parameterization to protect the privacy of query images and database maps. The lifting of points to lines effectively drops one of the two geometric constraints traditionally used with point-to-point correspondences in structure-based localization. This leads to a significant loss of accuracy for the privacy-preserving methods. In this paper, we overcome this limitation by devising a coordinate permutation scheme that allows for recovering the original point positions during pose estimation. The recovered points provide the full 2D geometric constraints and enable us to close the gap between privacy-preserving and traditional methods in terms of accuracy. Another limitation of random line methods is their vulnerability to density based 3D line cloud inversion attacks. Our method not only provides better accuracy than the original random line based approach but also provides stronger privacy guarantees against these recently proposed attacks. Extensive experiments on standard benchmark datasets demonstrate these improvements consistently across both scenarios of protecting the privacy of query images as well as the database map." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 525, + 128, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 128, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 128, + 538 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 545, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 666 + ], + "type": "text", + "content": "The interest in commercial solutions for cloud-based localization and mapping in mixed reality and robotics (e.g., Google VPS [34], Microsoft Azure Spatial Anchors [21], or Facebook LiveMaps [1]) has raised a host of privacy concerns [24, 31, 35, 51]. Recently, several approaches have been introduced by the research community to address these concerns [14, 17-19, 25, 45-47]. The common theme underlying these methods is based on the principle of lifting traditional point-based features to randomly oriented lines to conceal the appearance of query images and database maps." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "While this family of approaches is successful in enabling privacy preserving image-based localization and mapping, it comes at significant trade-offs in terms of accuracy and recall. These trade-offs are primarily caused by the fact that" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 214, + 426, + 330 + ], + "blocks": [ + { + "bbox": [ + 310, + 214, + 426, + 330 + ], + "lines": [ + { + "bbox": [ + 310, + 214, + 426, + 330 + ], + "spans": [ + { + "bbox": [ + 310, + 214, + 426, + 330 + ], + "type": "image", + "image_path": "524c6b154c2a14c46cacf05b0c2a3aa503f66a41bac75c032d1d12660794369b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 320, + 342, + 426, + 425 + ], + "blocks": [ + { + "bbox": [ + 320, + 342, + 426, + 425 + ], + "lines": [ + { + "bbox": [ + 320, + 342, + 426, + 425 + ], + "spans": [ + { + "bbox": [ + 320, + 342, + 426, + 425 + ], + "type": "image", + "image_path": "d2399fcb7658fe3c79a7ec4e74dd914c3cacf990cf989a1d6588aca9083aa944.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 427, + 220, + 544, + 329 + ], + "blocks": [ + { + "bbox": [ + 427, + 220, + 544, + 329 + ], + "lines": [ + { + "bbox": [ + 427, + 220, + 544, + 329 + ], + "spans": [ + { + "bbox": [ + 427, + 220, + 544, + 329 + ], + "type": "image", + "image_path": "e1b5aada20d4f28e8c3633c703f0a32d355ad8acbd868d1aef5abaa15185b738.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 427, + 333, + 543, + 449 + ], + "blocks": [ + { + "bbox": [ + 427, + 333, + 543, + 449 + ], + "lines": [ + { + "bbox": [ + 427, + 333, + 543, + 449 + ], + "spans": [ + { + "bbox": [ + 427, + 333, + 543, + 449 + ], + "type": "image", + "image_path": "f95403eda44190c1f50465ad34d41ad45cafe1ca676559edecc618a2a2c298e6.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 459, + 547, + 568 + ], + "lines": [ + { + "bbox": [ + 304, + 459, + 547, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 547, + 568 + ], + "type": "text", + "content": "Figure 1: Privacy-preserving localization. Top Left: The client extracts keypoints and descriptors from the query image. Top Right: The client secretly pairs keypoints and permutes their coordinates; hiding their true position from the server. Bottom Left: Server performs localization using the permuted points and recovers the original 2D positions for points that exist in both query and map. Bottom Right: Feature inversion on the set of recovered points only reveals objects that are already present in the map." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "the privacy preserving line-to-point or point-to-line correspondences provide weaker geometric constraints than the traditional point-to-point correspondences [46]. When concealing the content of images or maps, the number of constraints is effectively halved, as each point-to-line or line-to-point reprojection only contributes a 1D geometric constraint compared to the 2D constraint from a point-to-point reprojection. Especially for the hard to localize images, where only few correspondences can be recovered during feature matching, this limitation makes a significant difference in terms of accuracy and recall." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18174" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "content": "Furthermore, without careful construction of random line maps, density based attacks have been shown to be effective in uncovering information from the privacy preserving representations, which was already mentioned as a limitation by Speciale et al. [46]. The main idea behind density based attacks exploits the fact that pairs of randomly oriented lines have a relatively higher chance of intersecting near the true surface as compared to empty or unobserved space. As such, a naive attack could simply gather statistics from pairwise intersections of random lines and assume the true surface in dense regions of the intersected space. More sophisticated attacks based on this idea can yield realistic image renderings from 3D line maps when attacking naively constructed line maps [9]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 239, + 289, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 289, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 289, + 479 + ], + "type": "text", + "content": "In this work, we revisit the approach of lifting points to lines in order to improve upon these two main limitations. In contrast to the original approach, we introduce a coordinate permutation scheme by which we effectively construct axis-aligned lines. During the pose estimation routine, the permutation scheme enables us to recover the original points for a large fraction of the inlier correspondences. Therefore, we can use the same 2D geometric constraints as in the traditional setup. This significantly improves the accuracy of the localization results. Moreover, when applying our approach for hiding the 3D map, we drastically increase the combinatorial complexity for density based attacks as well as reduce the chance for line intersections due to constructing axis-aligned lines. Counter-intuitively, our proposed method therefore not only leads to better accuracy but also provides a stronger level of privacy preservation. We experimentally demonstrate these improvements on standard benchmark datasets and by attacking our axis-aligned line maps using the approach by Chelani et al. [9]. In summary, we make the following contributions:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 486, + 286, + 640 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 59, + 486, + 286, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 486, + 286, + 510 + ], + "spans": [ + { + "bbox": [ + 59, + 486, + 286, + 510 + ], + "type": "text", + "content": "- Propose a new privacy-preserving lifting approach, applicable to protecting the map and query." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 517, + 286, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 517, + 286, + 553 + ], + "spans": [ + { + "bbox": [ + 59, + 517, + 286, + 553 + ], + "type": "text", + "content": "- Attacking the lifted representation has a higher combinatorial complexity compared to random lifting, rendering previous density based attacks ineffective." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 561, + 286, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 561, + 286, + 597 + ], + "spans": [ + { + "bbox": [ + 59, + 561, + 286, + 597 + ], + "type": "text", + "content": "- In contrast to previous work, we can recover the original 2D or 3D points, allowing for stronger geometric constraints and more accurate poses." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 604, + 286, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 604, + 286, + 640 + ], + "spans": [ + { + "bbox": [ + 59, + 604, + 286, + 640 + ], + "type": "text", + "content": "- Experimentally, we show significant improvements over previous privacy preserving work, closing the gap to traditional point-based non-private methods." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 657, + 134, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 134, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 134, + 670 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Image-based Localization Methods in image-based localization have made tremendous progress. Over the years, the methods have been scaled for robust localization in" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "type": "text", + "content": "large-scale scenes [27,38,40,54] with compressed map representations [8,15], while some of the methods can even run in real-time on mobile devices [4,20,22,27,28,39]. Some of the recent works focus on improving the robustness to drastic environmental changes [3,42,50] or enabling crossdevice localization and mapping scenarios [13]. The developed approaches are generally divided into structure-based methods [20, 38-40] using on an explicit geometric map representation or learning-based methods [7,22,44] with an implicit map representation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 207, + 545, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 207, + 545, + 351 + ], + "spans": [ + { + "bbox": [ + 304, + 207, + 545, + 351 + ], + "type": "text", + "content": "Privacy Risks Image-based localization is subject to privacy risks due to requiring images as an input [24, 31, 35, 51]. For example, in a cloud-based localization system, users may be concerned about sharing images of private spaces with the service provider. In a practical setting, the clients could only send local image features to the cloud to avoid these risks. However, recent inversion attacks have proven extremely effective in recovering the original images from only sparse local image features [12, 30, 32]. Recently, Chelani et al. proposed a method to query a localization service with a database of objects to recover information about scene contents [10]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 366, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 545, + 498 + ], + "type": "text", + "content": "Privacy Preservation To protect against these risks, several methods have been developed recently. The first work on this topic [46, 47] proposed a solution to preserve the privacy of 2D image or 3D map points in image-based localization. Their main idea was to lift 2D or 3D points to random lines by dropping one of the two geometric constraints during the pose estimation problem. Based on the same idea, a number of works followed up to address the problems of structure-from-motion [18, 19] and real-time SLAM [45], or to directly protect the high-dimensional feature representations instead of the geometry [14]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 498, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 629 + ], + "type": "text", + "content": "Underlying all these approaches, there are two fundamental limitations that were already observed by the original work [47]. First, by dropping one geometric constraint per correspondence for pose estimation, the accuracy of these approaches is significantly lowered, especially in the challenging cases with few matches between query and database. Second, without careful sparsification of the 3D map, density based attacks can recover information from 3D line clouds [9]. Sparsification of the map is an effective protection against density based attacks but comes with a further reduction of accuracy as well as recall." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "To protect in a more principled manner against these attacks, Geppert et al. [17] proposed to decompose the full 3D map into 1D partial maps, which are distributed across different servers. Each server then solves a partial localization problem and sends back the answer to the client, which can assemble a full 6-DoF localization result from the partial answers. Despite being effective against density based at" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18175" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 69, + 251, + 171 + ], + "blocks": [ + { + "bbox": [ + 72, + 69, + 251, + 171 + ], + "lines": [ + { + "bbox": [ + 72, + 69, + 251, + 171 + ], + "spans": [ + { + "bbox": [ + 72, + 69, + 251, + 171 + ], + "type": "image", + "image_path": "4cf0f0d1a72c8c2e4aa121a4a6dd209e9abbe199ab036ac03a486d34397c0373.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 176, + 547, + 237 + ], + "lines": [ + { + "bbox": [ + 45, + 176, + 547, + 237 + ], + "spans": [ + { + "bbox": [ + 45, + 176, + 547, + 237 + ], + "type": "text", + "content": "Figure 2: Method overview for localization with private queries. The client extracts keypoints in the query image and secretly pairs them to swap one of their coordinates. The server only receives the permuted points, which can be considered as axis-aligned lines. The secretly paired points form rectangles, which can be leveraged during RANSAC to efficiently recover the original point positions for pairs that are both inliers. The scoring of candidate poses and the final non-linear pose refinement jointly leverage the stronger 2D constraints for recovered points and otherwise the weaker 1D constraints." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 255, + 70, + 518, + 171 + ], + "blocks": [ + { + "bbox": [ + 255, + 70, + 518, + 171 + ], + "lines": [ + { + "bbox": [ + 255, + 70, + 518, + 171 + ], + "spans": [ + { + "bbox": [ + 255, + 70, + 518, + 171 + ], + "type": "image", + "image_path": "9723d42c230ae8c976a9a35e81051ea175c704f4c571dc3ced2864ac61d4fe8e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 246, + 289, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 246, + 289, + 330 + ], + "spans": [ + { + "bbox": [ + 46, + 246, + 289, + 330 + ], + "type": "text", + "content": "tacks, the system is complex and it comes with further accuracy and recall trade-offs. In contrast, our method does not require a complex multi-server setup and we improve upon the two main limitations of the random lifting approaches simultaneously. Our method provides both stronger privacy guarantees while also closing the accuracy gap to traditional localization approaches." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 349, + 103, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 349, + 103, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 349, + 103, + 361 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 373, + 287, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 287, + 433 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 287, + 433 + ], + "type": "text", + "content": "We now present our method for privacy-preserving localization. We address both the scenario of protecting the client's 2D image points in the localization query (Section 3.2) as well as protecting the service's 3D points in the database map (Section 3.3)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 435, + 288, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 288, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 288, + 651 + ], + "type": "text", + "content": "Our approach follows the main idea in Speciale et al. [46, 47], where the exact 2D or 3D point positions are hidden by introducing ambiguity in the coordinates. In the original works, this is done by lifting each point to a random line. The line representation still enables localization, using line-to-point instead of point-to-point correspondences, but makes it difficult to identify potentially sensitive image or map content. Similar to the original idea [46], we also obscure the true position of the point. However, instead of replacing it with a random line, we select a subset of the point coordinates and corrupt them. This is done by secretly forming pairs of points and swapping their coordinates at random. Since the list of pairs is not known to an attacker, it is practically intractable to recover the original point positions. As we will later show, for point-pairs that exist in both the query and the map, we can devise a scheme to recover the true positions, allowing us to use the full 2D-3D geometric constraints for accurate pose refinement." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "An overview of our pipeline can be found in Figure 2 and we detail the steps of our method in the following sections. For ease of presentation, we first review the traditional setup and then explain the 2D setting that hides the query, but the same principle generalizes to the 3D setting as well." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 245, + 491, + 257 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 245, + 491, + 257 + ], + "spans": [ + { + "bbox": [ + 305, + 245, + 491, + 257 + ], + "type": "text", + "content": "3.1. Review of Traditional Localization" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 263, + 545, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 263, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 263, + 545, + 324 + ], + "type": "text", + "content": "Traditionally, localization is performed by establishing a set of tentative 2D-3D point correspondences between the query image and the database map. Each correspondence " + }, + { + "bbox": [ + 304, + 263, + 545, + 324 + ], + "type": "inline_equation", + "content": "(\\pmb{x},\\pmb{X})\\in \\mathbb{R}^2\\times \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 263, + 545, + 324 + ], + "type": "text", + "content": " yields two geometric constraints on the unknown camera pose " + }, + { + "bbox": [ + 304, + 263, + 545, + 324 + ], + "type": "inline_equation", + "content": "(R,t)\\in \\mathrm{SE}(3)" + }, + { + "bbox": [ + 304, + 263, + 545, + 324 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 390, + 331, + 545, + 342 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 390, + 331, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 390, + 331, + 545, + 342 + ], + "type": "interline_equation", + "content": "\\lambda \\bar {\\boldsymbol {x}} = R \\boldsymbol {X} + \\boldsymbol {t}, \\tag {1}", + "image_path": "874eebf1ea461fbab7d05e3e1f15ac6653025aeed5a78ccd522be66ce92e5430.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 349, + 546, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 349, + 546, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 349, + 546, + 469 + ], + "type": "text", + "content": "where we let " + }, + { + "bbox": [ + 304, + 349, + 546, + 469 + ], + "type": "inline_equation", + "content": "\\bar{x}" + }, + { + "bbox": [ + 304, + 349, + 546, + 469 + ], + "type": "text", + "content": " denote the homogeneous 2D point in the normalized image plane (after removing the intrinsic calibration), and " + }, + { + "bbox": [ + 304, + 349, + 546, + 469 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 349, + 546, + 469 + ], + "type": "text", + "content": " represents the unknown depth. To identify outlier matches and estimate an initial pose, the standard approach is to use hypothesize-and-test frameworks, such as RANSAC [16], in order to generate multiple pose candidates by fitting " + }, + { + "bbox": [ + 304, + 349, + 546, + 469 + ], + "type": "inline_equation", + "content": "(R,t)" + }, + { + "bbox": [ + 304, + 349, + 546, + 469 + ], + "type": "text", + "content": " to minimal subsets of the points, followed by measuring the consensus among the rest of the matches. The consistency between a candidate pose and a 2D-3D match is computed using the 2D reprojection error" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 370, + 475, + 545, + 490 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 475, + 545, + 490 + ], + "spans": [ + { + "bbox": [ + 370, + 475, + 545, + 490 + ], + "type": "interline_equation", + "content": "d _ {p} = \\| \\boldsymbol {x} - \\pi (R \\boldsymbol {X} + t) \\|, \\tag {2}", + "image_path": "9a80a4154cb25808f03890e097b9e4a382fc7945fb466e818f3a9a9d3d725b5e.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 495, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 544 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 495, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\pi : \\mathbb{R}^3 \\to \\mathbb{R}^2" + }, + { + "bbox": [ + 304, + 495, + 545, + 544 + ], + "type": "text", + "content": " is the projection mapping. Once a candidate pose, together with the inlier matches, have been established, it is refined by minimizing the reprojection errors for all inliers jointly." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 549, + 486, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 549, + 486, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 549, + 486, + 562 + ], + "type": "text", + "content": "3.2. Localization with Private Queries" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 567, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 545, + 675 + ], + "type": "text", + "content": "The traditional method relies on the availability of the original 2D image points, and is thus not privacy preserving. To preserve the privacy of the image, Speciale et al. [47] proposed to lift 2D image points into random 2D lines. Our method also builds upon 2D lines but aligns them with the coordinate axes through a random coordinate permutation scheme. The following paragraphs first establish notation by reviewing (random) line constraints for localization and then explain our permutation scheme in detail." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "type": "text", + "content": "Random Line Constraints In Speciale et al. [47], each 2D line " + }, + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\ell" + }, + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "type": "text", + "content": " back-projects into a 3D plane " + }, + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\Pi_i = P^\\top \\ell_i" + }, + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "type": "text", + "content": " passing" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18176" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 95, + 69, + 242, + 173 + ], + "blocks": [ + { + "bbox": [ + 95, + 69, + 242, + 173 + ], + "lines": [ + { + "bbox": [ + 95, + 69, + 242, + 173 + ], + "spans": [ + { + "bbox": [ + 95, + 69, + 242, + 173 + ], + "type": "image", + "image_path": "1bbdcd6bee67e2cee3b5d12cf251658bcbefee1565373d3daa6b45f8cfb3caa5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 179, + 289, + 264 + ], + "lines": [ + { + "bbox": [ + 46, + 179, + 289, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 179, + 289, + 264 + ], + "type": "text", + "content": "Figure 3: Illustration of geometric constraints induced by coordinate permutation and point recovery mechanism in the scenario of private queries. Red image points are secretly permuted. Black points are 3D map points. Blue points are the recovered, original image points obtained by back-swapping and form a rectangle together with their respective permuted points." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 274, + 288, + 311 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 274, + 288, + 311 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 288, + 311 + ], + "type": "text", + "content": "through camera projection center and the line in the image plane. The corresponding 3D point " + }, + { + "bbox": [ + 46, + 274, + 288, + 311 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 274, + 288, + 311 + ], + "type": "text", + "content": " is expected to lie on this plane, which constrains the pose as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 124, + 319, + 287, + 335 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 319, + 287, + 335 + ], + "spans": [ + { + "bbox": [ + 124, + 319, + 287, + 335 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\ell} ^ {\\top} \\left(R \\boldsymbol {X} + \\boldsymbol {t}\\right) = 0. \\tag {3}", + "image_path": "ddd2af3888f84b65d4b5a1ad9e79f3d3440053e8477a1e51882244e71eaad84a.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 345, + 287, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 345, + 287, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 345, + 287, + 429 + ], + "type": "text", + "content": "Note that this only yields a single geometric constraint instead of two as in Equation (1). In this case, it is still possible to estimate the pose, though the minimal problem now requires 6 instead of 3 correspondences. The minimal solver for this problem is known as " + }, + { + "bbox": [ + 46, + 345, + 287, + 429 + ], + "type": "inline_equation", + "content": "p6LP" + }, + { + "bbox": [ + 46, + 345, + 287, + 429 + ], + "type": "text", + "content": " [33] and was used in [47]. Further, to validate a match, we can only measure the distance between the 2D line and the projected 3D point" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 116, + 438, + 287, + 469 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 438, + 287, + 469 + ], + "spans": [ + { + "bbox": [ + 116, + 438, + 287, + 469 + ], + "type": "interline_equation", + "content": "d _ {l} = \\frac {\\left| \\boldsymbol {\\ell} ^ {\\top} \\bar {\\pi} (\\boldsymbol {R} \\boldsymbol {X} + \\boldsymbol {t}) \\right|}{\\sqrt {l _ {1} ^ {2} + l _ {2} ^ {2}}} , \\tag {4}", + "image_path": "bc4d6267c55e332528352c0c43d09f9499d946783111922ef27befcac222078a.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 479, + 287, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 287, + 528 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 287, + 528 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 479, + 287, + 528 + ], + "type": "inline_equation", + "content": "\\ell = [l_1, l_2, l_3]^\\top" + }, + { + "bbox": [ + 46, + 479, + 287, + 528 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 479, + 287, + 528 + ], + "type": "inline_equation", + "content": "\\bar{\\pi}" + }, + { + "bbox": [ + 46, + 479, + 287, + 528 + ], + "type": "text", + "content": " is the homogeneous projected 2D point. This is a weaker constraint compared to the 2D error measured in Equation (2) and thus explains the observed loss in accuracy by this approach." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 546, + 288, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 288, + 691 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 288, + 691 + ], + "type": "text", + "content": "Coordinate Permutation Constraints In our case, we have 2D image points, where we know that only one of the two coordinates is correct because of the a priori secret permutation (illustrated in Figures 2 and 3). In the context of the line-based framework from Speciale et al. [47], this can be considered as, instead of having a random line, having two axis-aligned lines passing through the given point. The original point will share one of the coordinates, and thus lie on one of these two lines. Mathematically, each point " + }, + { + "bbox": [ + 46, + 546, + 288, + 691 + ], + "type": "inline_equation", + "content": "\\pmb{x} = [x_1,x_2]^\\top" + }, + { + "bbox": [ + 46, + 546, + 288, + 691 + ], + "type": "text", + "content": " gives rise to two axis-aligned lines " + }, + { + "bbox": [ + 46, + 546, + 288, + 691 + ], + "type": "inline_equation", + "content": "\\ell_1,\\ell_2" + }, + { + "bbox": [ + 46, + 546, + 288, + 691 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 546, + 288, + 691 + ], + "type": "inline_equation", + "content": "\\ell_{1} = [1,0, - x_{1}]^{\\top}" + }, + { + "bbox": [ + 46, + 546, + 288, + 691 + ], + "type": "inline_equation", + "content": "\\ell_{2} = [0,1, - x_{2}]^{\\top}" + }, + { + "bbox": [ + 46, + 546, + 288, + 691 + ], + "type": "text", + "content": ". Each correspondence then gives us the following constraint" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 71, + 700, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 700, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 71, + 700, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\ell_ {1} ^ {\\top} (R \\boldsymbol {X} + \\boldsymbol {t}) = 0 \\quad \\vee \\quad \\ell_ {2} ^ {\\top} (R \\boldsymbol {X} + \\boldsymbol {t}) = 0, \\tag {5}", + "image_path": "c2483803ccc649cbad57e062d9c14bafdef07fe40d0ed71d11cb384452bf6c50.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "content": "where we only know that one of the two constraints should be satisfied. For " + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "content": " point correspondences, we thus have " + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "inline_equation", + "content": "2^{n}" + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "content": " possible combinations of constraints to choose from." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 109, + 546, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 109, + 546, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 109, + 546, + 276 + ], + "type": "text", + "content": "While considering all " + }, + { + "bbox": [ + 304, + 109, + 546, + 276 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 109, + 546, + 276 + ], + "type": "text", + "content": " points leads to a combinatorial explosion and would be computationally intractable, we only need to consider small subsets of matches to hypothesize candidate poses inside RANSAC. For a minimal sample of 6 correspondences, there exist " + }, + { + "bbox": [ + 304, + 109, + 546, + 276 + ], + "type": "inline_equation", + "content": "2^6 = 64" + }, + { + "bbox": [ + 304, + 109, + 546, + 276 + ], + "type": "text", + "content": " different combinations of lines in Equation (5). One of these combinations will correspond to having the true (uncorrupted) coordinate in all 6 lines, and should give a correct camera pose for an all-inlier minimal sample. So, to find a camera pose, we can simply iterate exhaustively over all " + }, + { + "bbox": [ + 304, + 109, + 546, + 276 + ], + "type": "inline_equation", + "content": "2^6 = 64" + }, + { + "bbox": [ + 304, + 109, + 546, + 276 + ], + "type": "text", + "content": " combinations. Each of these combinations corresponds to a " + }, + { + "bbox": [ + 304, + 109, + 546, + 276 + ], + "type": "inline_equation", + "content": "p6LP" + }, + { + "bbox": [ + 304, + 109, + 546, + 276 + ], + "type": "text", + "content": " minimal estimation problem, which can be efficiently solved. If gravity is known, we can efficiently solve the minimal " + }, + { + "bbox": [ + 304, + 109, + 546, + 276 + ], + "type": "inline_equation", + "content": "up4LP" + }, + { + "bbox": [ + 304, + 109, + 546, + 276 + ], + "type": "text", + "content": " problem [33] from " + }, + { + "bbox": [ + 304, + 109, + 546, + 276 + ], + "type": "inline_equation", + "content": "2^4 = 16" + }, + { + "bbox": [ + 304, + 109, + 546, + 276 + ], + "type": "text", + "content": " combinations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 277, + 547, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 547, + 420 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 547, + 420 + ], + "type": "text", + "content": "The key observation is now that, if we have a candidate pose, then for any inlier correspondence, we can easily resolve which of the two axis-aligned lines (i.e., coordinates) is the correct one by simply projecting the 3D points to the image and taking the one with the smaller 1D residual " + }, + { + "bbox": [ + 304, + 277, + 547, + 420 + ], + "type": "inline_equation", + "content": "d_{l}" + }, + { + "bbox": [ + 304, + 277, + 547, + 420 + ], + "type": "text", + "content": ". By determining the inlier coordinates " + }, + { + "bbox": [ + 304, + 277, + 547, + 420 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 277, + 547, + 420 + ], + "type": "text", + "content": " within the threshold (i.e., " + }, + { + "bbox": [ + 304, + 277, + 547, + 420 + ], + "type": "inline_equation", + "content": "d_{l} < \\varepsilon" + }, + { + "bbox": [ + 304, + 277, + 547, + 420 + ], + "type": "text", + "content": "), we can score candidate poses and thereby embed our method into a standard RANSAC loop to robustly estimate a camera pose. This approach still uses the weaker 1D constraints. The next paragraph explains how we can efficiently recover the original 2D points in this framework to benefit from stronger 2D constraints." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 437, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 520 + ], + "type": "text", + "content": "Original Point Recovery After finding a candidate pose using RANSAC, we devise an efficient scheme for recovering the original points " + }, + { + "bbox": [ + 304, + 437, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 304, + 437, + 545, + 520 + ], + "type": "text", + "content": " from the set of inliers " + }, + { + "bbox": [ + 304, + 437, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 437, + 545, + 520 + ], + "type": "text", + "content": ". Note that our scheme can only recover the positions for points that are visible in both the query and the map. As such, recovering the original points is not a concern for privacy, as they are known to both client and server." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "text", + "content": "Let's recall that we randomly picked pairs of points and swapped one of their coordinates to preserve their privacy. To recover the original points, we need to rely on the projected points and the property that the swapped back points should be close to the projected points (within " + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "text", + "content": " distance) if it is an inlier. As for outliers points, there is no proper mechanism to distinguish a correct pair from an incorrect one, thus they remain unrecoverable." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 618, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 546, + 713 + ], + "type": "text", + "content": "One way of recovering points is to iterate through all pairwise combinations of inlier correspondences and choose a configuration with the most swapped back points close to the projected points. However, this method has a squared complexity in the number of correspondences and is thus computationally expensive to execute inside a RANSAC loop. To achieve a better complexity, it is helpful to notice that each pair of points, that are selected for" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18177" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "coordinate permutation, their original points and the permuted points form a 2D rectangle in the image (c.f. Figures 2 and 3). Using this observation, we can devise a more efficient recovery algorithm. For bookkeeping of recovered point coordinates, we first define the two sets" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 140, + 287, + 156 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 140, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 140, + 287, + 156 + ], + "type": "interline_equation", + "content": "S _ {j} = \\left\\{\\left(x _ {k j}, k\\right) \\mid \\hat {\\boldsymbol {x}} _ {k} = \\left[ x _ {k 1} \\quad x _ {k 2} \\right] ^ {\\top} \\right\\}, \\quad j = \\{1, 2 \\} \\tag {6}", + "image_path": "a06822e08f1869f21932ed30d707959f45195c04803c54809ea3082b9bdd0447.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "text", + "content": "Each element in the sets consists of a single coordinate " + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "inline_equation", + "content": "(x_{1}" + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "inline_equation", + "content": "x_{2})" + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "text", + "content": " and its index " + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "text", + "content": " in the ordered list of points. The index uniquely identifies coordinates to enable swapping of point pairs. For example, if the query image has 3 points " + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "inline_equation", + "content": "\\{\\hat{x}_1 = [0,10]^\\top ,\\hat{x}_2 = [20,30]^\\top ,\\hat{x}_3 = [40,50]^\\top \\}" + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "text", + "content": ", then " + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "inline_equation", + "content": "S_{1} = \\{(0,1),(20,2),(40,3)\\}" + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "inline_equation", + "content": "S_{2} = \\{(10,1),(30,2),(50,3)\\}" + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "text", + "content": ". For each projected image point " + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "inline_equation", + "content": "\\tilde{x}" + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "text", + "content": ", we first decide which coordinate could be the original one by comparing " + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "inline_equation", + "content": "\\tilde{x}" + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "text", + "content": " and the permuted image point " + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "inline_equation", + "content": "\\hat{x}" + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "text", + "content": ". We label coordinate " + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "text", + "content": " as correct if the " + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "text", + "content": "-th coordinate is within " + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "text", + "content": " from the projected point, that is " + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "inline_equation", + "content": "|\\hat{x}_j - \\tilde{x}_j| < \\varepsilon" + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "text", + "content": ". Denoting the other coordinate as " + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "inline_equation", + "content": "j'" + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "text", + "content": ", we collect the possible swapped point candidates " + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "text", + "content": " by looking in the set " + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "inline_equation", + "content": "S_{j'}" + }, + { + "bbox": [ + 46, + 163, + 288, + 331 + ], + "type": "text", + "content": ", and finding points with the respective coordinate close to the projected point" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 77, + 339, + 287, + 354 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 339, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 77, + 339, + 287, + 354 + ], + "type": "interline_equation", + "content": "C = \\left\\{k \\mid \\left| x _ {k j ^ {\\prime}} - \\tilde {x} _ {j ^ {\\prime}} \\right| < \\varepsilon , \\left(x _ {k j ^ {\\prime}}, k\\right) \\in S _ {j ^ {\\prime}} \\right\\} \\tag {7}", + "image_path": "5925477ef3906baf5d48380fb7d2f1d0ca00e8386fd9790fed6619b937789b36.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 361, + 287, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 287, + 421 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 287, + 421 + ], + "type": "text", + "content": "Since this set likely contains multiple candidates for each point (having a similar " + }, + { + "bbox": [ + 46, + 361, + 287, + 421 + ], + "type": "inline_equation", + "content": "x_{1}" + }, + { + "bbox": [ + 46, + 361, + 287, + 421 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 361, + 287, + 421 + ], + "type": "inline_equation", + "content": "x_{2}" + }, + { + "bbox": [ + 46, + 361, + 287, + 421 + ], + "type": "text", + "content": " coordinate), and the candidate points after swapping back can be distant from their projected points, we use a symmetric swapping error to filter out the coincident candidates" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 52, + 429, + 287, + 445 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 429, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 52, + 429, + 287, + 445 + ], + "type": "interline_equation", + "content": "\\varepsilon_ {s y m} = \\left\\| \\tilde {\\boldsymbol {x}} - \\left[ \\begin{array}{l l} x _ {j} & x _ {k j ^ {\\prime}} \\end{array} \\right] ^ {\\top} \\right\\| _ {2} + \\left\\| \\tilde {\\boldsymbol {x}} _ {k} - \\left[ \\begin{array}{l l} x _ {k j} & x _ {j ^ {\\prime}} \\end{array} \\right] ^ {\\top} \\right\\| _ {2} (8)", + "image_path": "28bd093cd590b02b0de21f4447000bd5e3e466d91f52d4c07597e036eda57324.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 453, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 453, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 453, + 287, + 536 + ], + "type": "text", + "content": "We only consider a candidate to be valid, if both points are close to the respective reprojected image points after swapping them back. If multiple candidates are valid, we keep the one with the smallest " + }, + { + "bbox": [ + 46, + 453, + 287, + 536 + ], + "type": "inline_equation", + "content": "\\varepsilon_{sym}" + }, + { + "bbox": [ + 46, + 453, + 287, + 536 + ], + "type": "text", + "content": ". Notice that, with such a selection mechanism, the recovered original points may not be symmetric. However, we have not found any drawbacks from this asymmetry in our experiments." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 536, + 287, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 287, + 585 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 287, + 585 + ], + "type": "text", + "content": "By implementing the sets " + }, + { + "bbox": [ + 46, + 536, + 287, + 585 + ], + "type": "inline_equation", + "content": "S_{j}" + }, + { + "bbox": [ + 46, + 536, + 287, + 585 + ], + "type": "text", + "content": " using hashing, we achieve amortized linear runtime complexity on average w.r.t. the number of correspondences for our recovery scheme. More details can be found in the suppl. material." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 598, + 287, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 598, + 287, + 670 + ], + "spans": [ + { + "bbox": [ + 46, + 598, + 287, + 670 + ], + "type": "text", + "content": "Pose Refinement To further improve the accuracy of our pose estimates, we conduct a non-linear refinement over all inliers using the stronger 2D constraints from Equation (2) for recovered points " + }, + { + "bbox": [ + 46, + 598, + 287, + 670 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_p" + }, + { + "bbox": [ + 46, + 598, + 287, + 670 + ], + "type": "text", + "content": " and the weaker 1D constraints from Equation (4) for coordinates " + }, + { + "bbox": [ + 46, + 598, + 287, + 670 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_l" + }, + { + "bbox": [ + 46, + 598, + 287, + 670 + ], + "type": "text", + "content": " that could not be swapped back. The overall cost function is defined as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 53, + 675, + 287, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 675, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 53, + 675, + 287, + 714 + ], + "type": "interline_equation", + "content": "\\sum_ {k \\in \\mathcal {I} _ {p}} \\rho \\left(d _ {p} \\left(\\boldsymbol {x} _ {k}, P \\bar {\\boldsymbol {X}} _ {k}\\right)\\right) + \\sum_ {k \\in \\mathcal {I} _ {\\ell}} \\rho \\left(\\underset {i \\in \\{1, 2 \\}} {\\operatorname {s o f t m i n}} \\left(d _ {l} \\left(\\boldsymbol {\\ell} _ {k i}, P \\bar {\\boldsymbol {X}} _ {k}\\right)\\right)\\right) \\tag {9}", + "image_path": "78c1440782333d182309cc731d36660a620654a60fdd171b06a6ac77b81b2e96.jpg" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 353, + 69, + 501, + 167 + ], + "blocks": [ + { + "bbox": [ + 353, + 69, + 501, + 167 + ], + "lines": [ + { + "bbox": [ + 353, + 69, + 501, + 167 + ], + "spans": [ + { + "bbox": [ + 353, + 69, + 501, + 167 + ], + "type": "image", + "image_path": "2dbf1298f0c8dbce52b528f0c2f52a9a9c516458f56de08ce214d7bce1591ee1.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 174, + 545, + 223 + ], + "lines": [ + { + "bbox": [ + 305, + 174, + 545, + 223 + ], + "spans": [ + { + "bbox": [ + 305, + 174, + 545, + 223 + ], + "type": "text", + "content": "Figure 4: Illustration of point recovery mechanism in the 3D scenario with private maps, where the permuted red points form a cuboid in 3D. The reprojection of the 3D points is used for thresholding of errors in image space." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 232, + 546, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 232, + 546, + 320 + ], + "spans": [ + { + "bbox": [ + 305, + 232, + 546, + 320 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 232, + 546, + 320 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 305, + 232, + 546, + 320 + ], + "type": "text", + "content": " is a robustifier. To smoothly select between the two possible axis-aligned lines, we use the (Boltzmann) soft-min operator [5], defined as " + }, + { + "bbox": [ + 305, + 232, + 546, + 320 + ], + "type": "inline_equation", + "content": "\\operatorname*{softmin}_{i}\\{d_{i}\\} = (\\sum_{i}d_{i}e^{-d_{i}}) / (\\sum_{i}e^{-d_{i}})" + }, + { + "bbox": [ + 305, + 232, + 546, + 320 + ], + "type": "text", + "content": ". We incorporate this non-linear refinement into LO-RANSAC [11] using the Arctan loss as " + }, + { + "bbox": [ + 305, + 232, + 546, + 320 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 305, + 232, + 546, + 320 + ], + "type": "text", + "content": " inside the RANSAC loop and Cauchy as the robust loss for the final pose refinement." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 335, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 335, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 305, + 335, + 545, + 453 + ], + "type": "text", + "content": "Degenerate Configurations Note that when all " + }, + { + "bbox": [ + 305, + 335, + 545, + 453 + ], + "type": "inline_equation", + "content": "\\ell_{i}" + }, + { + "bbox": [ + 305, + 335, + 545, + 453 + ], + "type": "text", + "content": " lines are parallel (i.e., originating from the same coordinate), the configuration becomes degenerate as the full 6-DoF of the pose cannot be recovered. This happens for 2 out of 64 configurations that we can trivially discard. For the two degenerate cases, it would be possible to solve for the rotation and two translation parameters using 5 correspondences. We initially explored this direction as well yet found the solutions to be less stable, as they provide less accurate pose estimates, so we do not include them in our final method." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 460, + 476, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 460, + 476, + 474 + ], + "spans": [ + { + "bbox": [ + 306, + 460, + 476, + 474 + ], + "type": "text", + "content": "3.3. Localization with Private Maps" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 479, + 545, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 479, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 305, + 479, + 545, + 562 + ], + "type": "text", + "content": "In the previous section, we described our coordinate permutation scheme for 2D image points to preserve the privacy of localization queries. Similar to the 2D case, we can also permute coordinates of 3D points to hide the contents of private maps. This is a scenario that was originally addressed by Speciale et al. [46] using lifting to random 3D lines. We denote a random 3D line " + }, + { + "bbox": [ + 305, + 479, + 545, + 562 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 305, + 479, + 545, + 562 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 378, + 568, + 545, + 595 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 568, + 545, + 595 + ], + "spans": [ + { + "bbox": [ + 378, + 568, + 545, + 595 + ], + "type": "interline_equation", + "content": "\\boldsymbol {L} = \\left[ \\begin{array}{l} \\boldsymbol {p} \\\\ \\boldsymbol {d} \\end{array} \\right] \\in \\mathbb {R} ^ {3} \\times \\mathbb {P} ^ {2}, \\tag {10}", + "image_path": "dd0cb6df2516a9baeb2ed3357c6331ef8561561923ea5e2eb9ea022566eda96c.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 603, + 545, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 603, + 545, + 660 + ], + "spans": [ + { + "bbox": [ + 305, + 603, + 545, + 660 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 603, + 545, + 660 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 305, + 603, + 545, + 660 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 603, + 545, + 660 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 305, + 603, + 545, + 660 + ], + "type": "text", + "content": " are 3D points on " + }, + { + "bbox": [ + 305, + 603, + 545, + 660 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 305, + 603, + 545, + 660 + ], + "type": "text", + "content": " subject to " + }, + { + "bbox": [ + 305, + 603, + 545, + 660 + ], + "type": "inline_equation", + "content": "d = \\frac{p - q}{\\|p - q\\|_2}" + }, + { + "bbox": [ + 305, + 603, + 545, + 660 + ], + "type": "text", + "content": " and such that the line passes through the original 3D point " + }, + { + "bbox": [ + 305, + 603, + 545, + 660 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 305, + 603, + 545, + 660 + ], + "type": "text", + "content": ". The reprojection of the 3D line to the image defines a 1D geometric constraint" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 362, + 666, + 545, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 666, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 362, + 666, + 545, + 682 + ], + "type": "interline_equation", + "content": "0 = \\hat {\\boldsymbol {L}} _ {i} ^ {\\top} \\bar {\\boldsymbol {x}} = \\left(\\left[ \\boldsymbol {R} \\boldsymbol {d} _ {i} \\right] _ {\\times} \\boldsymbol {P} \\bar {\\boldsymbol {p}} _ {i}\\right) ^ {\\top} \\bar {\\boldsymbol {x}} \\tag {11}", + "image_path": "f53df2be4f4fba3041ea709c8deb9c2ed9aa7b1fe48024be960a0ed072ce6995.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "that can be used for privacy-preserving pose estimation. To solve for the full 6-DoF pose, at least 6 correspondences are" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18178" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "needed to solve the minimal " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "p6L" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " problem [48] in RANSAC. If gravity is known, only 4 correspondences are needed to solve the up4L problem [49]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 288, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 288, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 288, + 288 + ], + "type": "text", + "content": "Instead of lifting to random 3D lines, we construct axis-aligned 3D lines by coordinate permutation of randomly selected pairs of 3D points. Analogous to the 2D case, we can hypothesize pose candidates in RANSAC by generating the different " + }, + { + "bbox": [ + 46, + 108, + 288, + 288 + ], + "type": "inline_equation", + "content": "3^{6} = 729" + }, + { + "bbox": [ + 46, + 108, + 288, + 288 + ], + "type": "text", + "content": " combinations of line constraints, and we can also recover the original 3D point positions by back-swapping with sets " + }, + { + "bbox": [ + 46, + 108, + 288, + 288 + ], + "type": "inline_equation", + "content": "S_{j=1,2,3}" + }, + { + "bbox": [ + 46, + 108, + 288, + 288 + ], + "type": "text", + "content": ". Notice that the original 3D point may lie on any of the three axis-aligned lines and the randomly selected point pairs form a cuboid in 3D (see Figure 4). To robustify the back-swapping algorithm against non-isotropic noise on the (triangulated) 3D points, we define the error " + }, + { + "bbox": [ + 46, + 108, + 288, + 288 + ], + "type": "inline_equation", + "content": "\\varepsilon_{sym}" + }, + { + "bbox": [ + 46, + 108, + 288, + 288 + ], + "type": "text", + "content": " in image space through reprojection. Moreover, if runtime is a concern for the final application, we can also choose to expose one of the 3 coordinates, so the number of line combinations would be " + }, + { + "bbox": [ + 46, + 108, + 288, + 288 + ], + "type": "inline_equation", + "content": "2^{6} = 64" + }, + { + "bbox": [ + 46, + 108, + 288, + 288 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 301, + 287, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 287, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 287, + 348 + ], + "type": "text", + "content": "Pose Refinement For pose refinement in the 3D case, we again add constraints from two sources: the ones from inlier lines " + }, + { + "bbox": [ + 46, + 301, + 287, + 348 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_L" + }, + { + "bbox": [ + 46, + 301, + 287, + 348 + ], + "type": "text", + "content": " and the ones from recovered inlier points " + }, + { + "bbox": [ + 46, + 301, + 287, + 348 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_p" + }, + { + "bbox": [ + 46, + 301, + 287, + 348 + ], + "type": "text", + "content": ". The overall cost function is defined as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 350, + 278, + 379 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 350, + 278, + 379 + ], + "spans": [ + { + "bbox": [ + 53, + 350, + 278, + 379 + ], + "type": "interline_equation", + "content": "\\sum_ {k \\in \\mathcal {I} _ {p}} \\rho (d _ {p} (\\boldsymbol {x} _ {k}, P \\bar {\\boldsymbol {X}} _ {k})) + \\sum_ {k \\in \\mathcal {I} _ {L}} \\rho (\\underset {i \\in \\{1, 2 \\}} {\\operatorname {s o f t m i n}} (d _ {L} (\\boldsymbol {x} _ {k}, \\hat {\\boldsymbol {L}} _ {k i}))", + "image_path": "5d69cb4ff309c05803aa2f53103e5277894b2b151e45dcd948b29d996da4f46c.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 110, + 381, + 287, + 422 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 381, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 110, + 381, + 287, + 422 + ], + "type": "interline_equation", + "content": "\\text {w h e r e} d _ {L} = \\frac {\\left| \\hat {\\boldsymbol {L}} _ {k i} ^ {\\top} \\bar {\\boldsymbol {x}} _ {k} \\right|}{\\sqrt {\\hat {L} _ {k i 1} ^ {2} + \\hat {L} _ {k i 2} ^ {2}}} \\tag {12}", + "image_path": "f390bccae0f59f02acc75fb9f5686ec17209a879bd66c9d487e484c6d57bac19.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 422, + 287, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 446 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 446 + ], + "type": "text", + "content": "and we use the same setup of LO-RANSAC and choice of robustifiers as in the 2D scenario." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 456, + 128, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 128, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 128, + 468 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 475, + 288, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 288, + 620 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 288, + 620 + ], + "type": "text", + "content": "In our experiments, we first focus on demonstrating the effectiveness of our proposed point recovery mechanism using an ablation study. We then compare our method against the traditional non-privacy preserving approach (PnP) and the original privacy-preserving approach based on random lines. Results are reported on existing benchmark datasets [23,46,52] for image-based localization, evaluated for the two scenarios of private localization queries (PnLP) and maps (PnL). All results assume unknown gravity and we show further results with known gravity in the supplementary material. Finally, we show image inversion results using the density-based attack by Chelani et al. [9]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 633, + 287, + 716 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 633, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 46, + 633, + 287, + 716 + ], + "type": "text", + "content": "Implementation Details We embed our method into LO-RANSAC [11] with Levenberg-Marquardt [2, 26] as nonlinear optimizer for pose refinement. Inlier reprojection thresholds on 2D points are set to " + }, + { + "bbox": [ + 46, + 633, + 287, + 716 + ], + "type": "inline_equation", + "content": "12px" + }, + { + "bbox": [ + 46, + 633, + 287, + 716 + ], + "type": "text", + "content": " for the Cambridge dataset [23] and to " + }, + { + "bbox": [ + 46, + 633, + 287, + 716 + ], + "type": "inline_equation", + "content": "4px" + }, + { + "bbox": [ + 46, + 633, + 287, + 716 + ], + "type": "text", + "content": " otherwise. Reprojection thresholds on lines are chosen as " + }, + { + "bbox": [ + 46, + 633, + 287, + 716 + ], + "type": "inline_equation", + "content": "\\frac{12px}{\\sqrt{2}}" + }, + { + "bbox": [ + 46, + 633, + 287, + 716 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 633, + 287, + 716 + ], + "type": "inline_equation", + "content": "\\frac{4px}{\\sqrt{2}}" + }, + { + "bbox": [ + 46, + 633, + 287, + 716 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 72, + 429, + 172 + ], + "blocks": [ + { + "bbox": [ + 309, + 72, + 429, + 172 + ], + "lines": [ + { + "bbox": [ + 309, + 72, + 429, + 172 + ], + "spans": [ + { + "bbox": [ + 309, + 72, + 429, + 172 + ], + "type": "image", + "image_path": "fcfdda0c24f7add157c62919900c928caae6e6cf651a9c77f77fd29735bad04c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 180, + 545, + 228 + ], + "lines": [ + { + "bbox": [ + 304, + 180, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 545, + 228 + ], + "type": "text", + "content": "Figure 5: Ablation study on King's college sequence [23] w.r.t. the number of correspondences. Our method closes the performance gap, that is especially pronounced in difficult cases with few correspondences." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 431, + 72, + 544, + 172 + ], + "blocks": [ + { + "bbox": [ + 431, + 72, + 544, + 172 + ], + "lines": [ + { + "bbox": [ + 431, + 72, + 544, + 172 + ], + "spans": [ + { + "bbox": [ + 431, + 72, + 544, + 172 + ], + "type": "image", + "image_path": "f9b3f6097d3455aa7522fe3b6bc4d97e2303d939e895b7637f10002ab5974189.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 234, + 546, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 234, + 546, + 270 + ], + "spans": [ + { + "bbox": [ + 304, + 234, + 546, + 270 + ], + "type": "text", + "content": "We re-implement all methods in the same framework for a fair comparison of accuracy, recall, and runtime. All point clouds are triangulated using COLMAP [41, 43]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 278, + 400, + 292 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 278, + 400, + 292 + ], + "spans": [ + { + "bbox": [ + 305, + 278, + 400, + 292 + ], + "type": "text", + "content": "4.1. Ablation Study" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 297, + 505, + 310 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 297, + 505, + 310 + ], + "spans": [ + { + "bbox": [ + 305, + 297, + 505, + 310 + ], + "type": "text", + "content": "4.1.1 Impact of Number of Correspondences" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 317, + 545, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 545, + 545 + ], + "type": "text", + "content": "As argued in previous sections, the reduced accuracy and recall in privacy-preserving localization methods based on random lines is largely attributed to the weaker geometric constraints. To showcase this performance gap, we conduct an experiment on the King's College sequence in the Cambridge dataset [23]. Localization performance is tested on varying number of correspondences per query image by randomly dropping input matches. Cases with few correspondences typically depict the challenging localization scenarios, where feature matching only yields few matches and only few constraints can be used for pose estimation. The results of this experiment are summarized in Figure 5. First, we observe that the performance gap between the privacy-preserving and traditional approach is especially pronounced for low number of matches, which in turn suggests that the impact of the number of constraints on the localization accuracy saturates eventually. We also see that our method closes the accuracy gap to the traditional approach across the board." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 562, + 499, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 562, + 499, + 574 + ], + "spans": [ + { + "bbox": [ + 305, + 562, + 499, + 574 + ], + "type": "text", + "content": "4.1.2 Impact of Point Recovery Mechanism" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "To analyze the effectiveness of the proposed point recovery mechanism, we conduct experiments on HoloLens data [47] with our method in different settings: with only line constraints, with recovered point constraints, and with the true recovered points using an oracle that has access to groundtruth information. This dataset contains images with a large variance on the inlier ratio, which makes it suitable for this ablation study, as the point recovery mechanism is strongly influenced by it. Results are summarized in Figure 6, which shows a significant improvement in accuracy for our method when using the stronger 2D constraints from" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18179" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 175, + 173 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 175, + 173 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 175, + 173 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 175, + 173 + ], + "type": "image", + "image_path": "14eebd814c76fc5b5200e557d5bdc68f0f072e276edf43984cfcf95cb849b390.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 180, + 287, + 205 + ], + "lines": [ + { + "bbox": [ + 47, + 180, + 287, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 180, + 287, + 205 + ], + "type": "text", + "content": "Figure 6: Ablation study on HoloLens data from [47] to measure the effectiveness of our point recovery mechanism." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 178, + 71, + 286, + 172 + ], + "blocks": [ + { + "bbox": [ + 178, + 71, + 286, + 172 + ], + "lines": [ + { + "bbox": [ + 178, + 71, + 286, + 172 + ], + "spans": [ + { + "bbox": [ + 178, + 71, + 286, + 172 + ], + "type": "image", + "image_path": "2e74e1d0727393db298b76a34c2d0c4f550394adde9bc3a584292f974f9ea90a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 50, + 214, + 165, + 307 + ], + "blocks": [ + { + "bbox": [ + 50, + 214, + 165, + 307 + ], + "lines": [ + { + "bbox": [ + 50, + 214, + 165, + 307 + ], + "spans": [ + { + "bbox": [ + 50, + 214, + 165, + 307 + ], + "type": "image", + "image_path": "03bb19e9f7286bd9f392c3f6c0693956d0e5f30e5362b5516d9af07430396d66.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 318, + 287, + 354 + ], + "lines": [ + { + "bbox": [ + 46, + 318, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 318, + 287, + 354 + ], + "type": "text", + "content": "Figure 7: Ablation study on HoloLens data from [47] that shows effective point recovery across all outlier ratios and overall low error rates on the recovered points." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 168, + 216, + 284, + 308 + ], + "blocks": [ + { + "bbox": [ + 168, + 216, + 284, + 308 + ], + "lines": [ + { + "bbox": [ + 168, + 216, + 284, + 308 + ], + "spans": [ + { + "bbox": [ + 168, + 216, + 284, + 308 + ], + "type": "image", + "image_path": "ebb9e667a9b4211c02f21788eac833da46a54bbd88fcd7d8e77b84786fb0ad3e.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 48, + 362, + 286, + 402 + ], + "blocks": [ + { + "bbox": [ + 48, + 362, + 286, + 402 + ], + "lines": [ + { + "bbox": [ + 48, + 362, + 286, + 402 + ], + "spans": [ + { + "bbox": [ + 48, + 362, + 286, + 402 + ], + "type": "table", + "html": "
MED (°)AUC@1°MED (cm)AUC@10cm(1°, 10 cm)Time (s)
PnLP [47]0.0884.790.6388.8897.800.07
Proposed0.0786.690.5690.1298.410.36
PnP0.0787.920.5190.8598.800.05
", + "image_path": "d5705481af6e29edd51ab27014749c570972495691838be58e84959d8286c4cd.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 445, + 287, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 480 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 480 + ], + "type": "text", + "content": "recovered points. In comparison to the oracle that defines a theoretical upper bound for our method, there is no significant difference in performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 482, + 287, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 482, + 287, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 482, + 287, + 589 + ], + "type": "text", + "content": "Furthermore, we also report the correlation between the outlier ratio and the ratio of recovered points in Figure 7. The expected number is calculated as " + }, + { + "bbox": [ + 46, + 482, + 287, + 589 + ], + "type": "inline_equation", + "content": "p^2" + }, + { + "bbox": [ + 46, + 482, + 287, + 589 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 482, + 287, + 589 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 482, + 287, + 589 + ], + "type": "text", + "content": " is the inlier ratio. From the figure we can see that the ratios of correctly recovered points matches the expected number across all outlier ratios. The ratio of mismatched points stays low in this dataset even when the inlier ratio is as low as " + }, + { + "bbox": [ + 46, + 482, + 287, + 589 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 482, + 287, + 589 + ], + "type": "text", + "content": ". Those observations combined provide strong evidence that the recovering mechanism is effective." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 598, + 228, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 598, + 228, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 598, + 228, + 611 + ], + "type": "text", + "content": "4.2. Localization with Private Queries" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": "HoloLens [47] This dataset features mostly small-scale scenes and unconstrained motion trajectories from a headworn augmented reality device with VGA-resolution cameras. Equivalent to the original dataset, we use COLMAP for reconstruction of the full image sequence while limiting the number of SIFT features per image to at most 500. There are 3325 query images in total and each query has on average 320 correspondences. After reconstructing the full" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 307, + 70, + 545, + 109 + ], + "blocks": [ + { + "bbox": [ + 46, + 411, + 287, + 434 + ], + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 434 + ], + "type": "text", + "content": "Table 1: Localization performance on HoloLens dataset [47] with indoor and outdoor scenes." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 70, + 545, + 109 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 109 + ], + "type": "table", + "html": "
MED (°)AUC@1°MED (cm)AUC@10cm(1°, 10 cm)Time (s)
PnLP [47]0.1871.5912.1318.3841.290.36
Proposed0.1872.6111.7320.0344.262.31
PnP0.1773.0911.6620.2243.950.20
", + "image_path": "fa3f599bcb1979fcf78caaa3e9c785abeea0f2cdb230f41a39f55d48ff6e1205.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 308, + 148, + 545, + 188 + ], + "blocks": [ + { + "bbox": [ + 305, + 118, + 545, + 142 + ], + "lines": [ + { + "bbox": [ + 305, + 118, + 545, + 142 + ], + "spans": [ + { + "bbox": [ + 305, + 118, + 545, + 142 + ], + "type": "text", + "content": "Table 2: Localization performance on Cambridge dataset [23] with handheld videos in an outdoor scene." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 148, + 545, + 188 + ], + "lines": [ + { + "bbox": [ + 308, + 148, + 545, + 188 + ], + "spans": [ + { + "bbox": [ + 308, + 148, + 545, + 188 + ], + "type": "table", + "html": "
MED (°)AUC@1°MED (cm)AUC@10cm(1°, 10 cm)Time (s)
PnLP [47]0.0288.322.2459.5778.230.09
Proposed0.0289.671.9263.6281.330.68
PnP0.0290.741.8564.5882.620.08
", + "image_path": "11ca6fa186ad75b9cb2b80c4a3d785898f2c78cd5836473dd96becbd430700fa.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 307, + 228, + 545, + 266 + ], + "blocks": [ + { + "bbox": [ + 305, + 197, + 545, + 220 + ], + "lines": [ + { + "bbox": [ + 305, + 197, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 305, + 197, + 545, + 220 + ], + "type": "text", + "content": "Table 3: Localization performance on crowd-sourced Internet photo collections [29, 53]." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 228, + 545, + 266 + ], + "lines": [ + { + "bbox": [ + 307, + 228, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 307, + 228, + 545, + 266 + ], + "type": "table", + "html": "
MED (°)AUC@1°MED (cm)AUC@10cm(1°, 10 cm)Time (s)
PnL [46]0.0884.710.6488.6697.711.16
Proposed0.0786.310.5689.7197.926.61
PnP0.0787.850.5190.8498.830.07
", + "image_path": "40d5dc88f55da7c587fdc4c15498dd877fd8fcbf0ac336b1401460227a8cf8fa.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 267, + 545, + 291 + ], + "lines": [ + { + "bbox": [ + 306, + 267, + 545, + 291 + ], + "spans": [ + { + "bbox": [ + 306, + 267, + 545, + 291 + ], + "type": "text", + "content": "Table 4: Localization performance on HoloLens dataset [47] in the private map scenario." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 300, + 545, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 545, + 421 + ], + "type": "text", + "content": "sequence, we hold out every 5-th image as a query, remove any point correspondences associated to these images from the reconstruction, and retriangulate the remaining database images. The pose of the query images in the full reconstruction serve as the groundtruth for evaluation. The results are summarized in Table 1, where we can see that our method performs almost on par with the traditional non-privacy preserving case in terms of accuracy and recall. The additional combinatorial overhead of evaluating more pose candidates leads to a roughly 5-fold runtime increase for our method." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 435, + 546, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 546, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 546, + 591 + ], + "type": "text", + "content": "Cambridge [23] This localization benchmark dataset contains handheld HD-resolution videos taken around Cambridge University in an outdoor setting. We use the same reference reconstruction as in [6] for the database map and extract SuperPoint+SuperGlue feature correspondences using the hloc toolbox [36, 37]. The dataset has a total of 1918 query images and an average of around 2850 2D-3D correspondences per image. Results are summarized in Table 2 and the performance trend for accuracy, recall, and runtime are all consistent with the results on the lower-resolution HoloLens dataset. This underlines the robustness of our approach against different sensors, scene types, as well as feature detection and matching algorithm characteristics." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "Internet Photo Collections [29, 53] This collection of datasets is crowd-sourced from the internet and comprises a large variety in image resolution and quality, lighting conditions, etc. We conduct experiments on the Dubrovnik6k, Gendarmenmarkt, Roman Forum, and Trafalgar locations with equivalent settings as used by Speciale et al. [47] for generating pseudo-groundtruth and establishing feature correspondences using COLMAP. On average, there are around 1000 SIFT correspondences per image with a total" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18180" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 175, + 164 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 175, + 164 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 175, + 164 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 175, + 164 + ], + "type": "image", + "image_path": "b2d44ac88d4801cda4a69e67eff0099aa6ac971d574fc65992836e440b62a3e1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 175, + 73, + 298, + 164 + ], + "blocks": [ + { + "bbox": [ + 175, + 73, + 298, + 164 + ], + "lines": [ + { + "bbox": [ + 175, + 73, + 298, + 164 + ], + "spans": [ + { + "bbox": [ + 175, + 73, + 298, + 164 + ], + "type": "image", + "image_path": "9e551d266bf5c6131ff9f1420b864b965c16cf4c23f9347fe6f2c9c3737b0751.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 49, + 166, + 110, + 226 + ], + "blocks": [ + { + "bbox": [ + 49, + 166, + 110, + 226 + ], + "lines": [ + { + "bbox": [ + 49, + 166, + 110, + 226 + ], + "spans": [ + { + "bbox": [ + 49, + 166, + 110, + 226 + ], + "type": "image", + "image_path": "5ce5c8a2a75b9c85a500d9449ddf849627a70ba93664f8742a97889ad1cdab2e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 88, + 231, + 132, + 242 + ], + "lines": [ + { + "bbox": [ + 88, + 231, + 132, + 242 + ], + "spans": [ + { + "bbox": [ + 88, + 231, + 132, + 242 + ], + "type": "text", + "content": "(a) Original" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 110, + 166, + 171, + 226 + ], + "blocks": [ + { + "bbox": [ + 110, + 166, + 171, + 226 + ], + "lines": [ + { + "bbox": [ + 110, + 166, + 171, + 226 + ], + "spans": [ + { + "bbox": [ + 110, + 166, + 171, + 226 + ], + "type": "image", + "image_path": "ef8e893c68bd4aca50b8e99e1d847e6ee9d40e13e87894723d44644cffd77ef9.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 243, + 547, + 304 + ], + "lines": [ + { + "bbox": [ + 46, + 243, + 547, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 547, + 304 + ], + "type": "text", + "content": "Figure 8: Privacy attack on (private) maps using a combination of 3D image inversion [32] and the density based attack method Line2Point [9]. The top row shows the 3D map that is recovered using Line2Point for all but the leftmost result. The 3D map is used as an input for rendering synthesized images shown at two different viewpoints in the bottom row. From left to right: (a) Results on original, non-privacy preserving point cloud. (b) Results on random line cloud. (c) Results on our method with an attacker that gained access to swapped coordinates. (d) Results on our method with permuted coordinates." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 175, + 166, + 235, + 226 + ], + "blocks": [ + { + "bbox": [ + 175, + 166, + 235, + 226 + ], + "lines": [ + { + "bbox": [ + 175, + 166, + 235, + 226 + ], + "spans": [ + { + "bbox": [ + 175, + 166, + 235, + 226 + ], + "type": "image", + "image_path": "0233f679175491a3c125b02efcaf46f3165233349eaf8f6c03ec55f701754edd.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 205, + 231, + 265, + 241 + ], + "lines": [ + { + "bbox": [ + 205, + 231, + 265, + 241 + ], + "spans": [ + { + "bbox": [ + 205, + 231, + 265, + 241 + ], + "type": "text", + "content": "(b) Random line" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 235, + 166, + 295, + 226 + ], + "blocks": [ + { + "bbox": [ + 235, + 166, + 295, + 226 + ], + "lines": [ + { + "bbox": [ + 235, + 166, + 295, + 226 + ], + "spans": [ + { + "bbox": [ + 235, + 166, + 295, + 226 + ], + "type": "image", + "image_path": "c59a2479938f7529e748de30739078938d93956484356f4f46a8c62e3aedb6b8.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 298, + 166, + 359, + 226 + ], + "blocks": [ + { + "bbox": [ + 298, + 166, + 359, + 226 + ], + "lines": [ + { + "bbox": [ + 298, + 166, + 359, + 226 + ], + "spans": [ + { + "bbox": [ + 298, + 166, + 359, + 226 + ], + "type": "image", + "image_path": "ca60b5e169f291d2dc35afd49444e32767fdeea66416909f0708ad60724ac263.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 340, + 232, + 377, + 241 + ], + "lines": [ + { + "bbox": [ + 340, + 232, + 377, + 241 + ], + "spans": [ + { + "bbox": [ + 340, + 232, + 377, + 241 + ], + "type": "text", + "content": "(c) Oracle" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 359, + 166, + 419, + 226 + ], + "blocks": [ + { + "bbox": [ + 359, + 166, + 419, + 226 + ], + "lines": [ + { + "bbox": [ + 359, + 166, + 419, + 226 + ], + "spans": [ + { + "bbox": [ + 359, + 166, + 419, + 226 + ], + "type": "image", + "image_path": "38e85b2d1cf80a6ef1f57c80a35ff301f74873b4b134a5eba57d8db2b52ca315.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 421, + 70, + 545, + 164 + ], + "blocks": [ + { + "bbox": [ + 421, + 70, + 545, + 164 + ], + "lines": [ + { + "bbox": [ + 421, + 70, + 545, + 164 + ], + "spans": [ + { + "bbox": [ + 421, + 70, + 545, + 164 + ], + "type": "image", + "image_path": "fb1986a0c95d80e0536062c8f1af82e57bb9d9ad03280206dd6acdc9175ef71b.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 422, + 166, + 482, + 226 + ], + "blocks": [ + { + "bbox": [ + 422, + 166, + 482, + 226 + ], + "lines": [ + { + "bbox": [ + 422, + 166, + 482, + 226 + ], + "spans": [ + { + "bbox": [ + 422, + 166, + 482, + 226 + ], + "type": "image", + "image_path": "a1d8eb92aad51fb1caf5f23b5f0ea870cc03274335a0a97f00fe4940b677823a.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 460, + 232, + 507, + 242 + ], + "lines": [ + { + "bbox": [ + 460, + 232, + 507, + 242 + ], + "spans": [ + { + "bbox": [ + 460, + 232, + 507, + 242 + ], + "type": "text", + "content": "(d) Proposed" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 484, + 166, + 544, + 226 + ], + "blocks": [ + { + "bbox": [ + 484, + 166, + 544, + 226 + ], + "lines": [ + { + "bbox": [ + 484, + 166, + 544, + 226 + ], + "spans": [ + { + "bbox": [ + 484, + 166, + 544, + 226 + ], + "type": "image", + "image_path": "fb2b36e85cb9bceaf814a9c5b6ebfc224acad267e2d8ef4bcd0ab15679a7b6a4.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 312, + 287, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 287, + 350 + ], + "type": "text", + "content": "of 2416 query images. Results are summarized in Table 3. The accuracy of all methods on this dataset is surprisingly high, yet we can still observe significant improvements." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 357, + 220, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 357, + 220, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 220, + 369 + ], + "type": "text", + "content": "4.3. Localization with a Private Map" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 376, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 287, + 483 + ], + "type": "text", + "content": "To evaluate localization scenario with a private map, we conduct experiments on HoloLens data [47] using the same setup as in the private query scenario described in the previous section. We adopt the setting of exposing one correct coordinate in Table 4 and provide results for the computationally more expensive case with 729 combinations in the supplementary material. Like in the private query scenario, we are able to significantly close the accuracy gap but increase run-time by a factor of around six." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 47, + 491, + 217, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 217, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 217, + 502 + ], + "type": "text", + "content": "4.4. Inversion Attack on Line Cloud" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "text", + "content": "In this section, we analyze and compare the level of privacy protection for the map representation. We perform this analysis by attacking the 3D point maps using image inversion techniques, as proposed by Pittaluga et al. [32]. To render images from the privacy preserving 3D line maps, we first execute a density based attack on the map representations using the Line2Point [9] method and then run image inversion on the recovered point cloud. Figure 8 shows results for this experiment, where inverted images from the non-privacy preserving map are nearly indistinguishable from original images of the scene. This again highlights the importance of research on privacy preserving methods for image-based localization. Images rendered from naively constructed random line clouds without sparsification closely resemble the original images as well and thus are not sufficient to protect private information in the map. The results of the attack on our method in column (d)" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 312, + 545, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 545, + 492 + ], + "type": "text", + "content": "shows mostly recognizable images and demonstrates the increased level of privacy that our method provides. Even if an attacker had access to an oracle that knows about which of the coordinates is correct, the rendered images (c) are less recognizable than the ones from a random line cloud. It is important to note that this information is not available to an attacker in practice, but it allows us to understand the relative impact on the increased level of privacy. On the one hand, our method constructs axis-aligned lines, which, by construction, cannot be intersected in a density based attack. On the other hand, we increase the combinatorial complexity of executing a density based attack, as significantly more coordinate pairs must be tried to find a valid intersection. In the supplementary material we provide additional inversion results and more discussion regarding potential attacks." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 506, + 378, + 518 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 506, + 378, + 518 + ], + "spans": [ + { + "bbox": [ + 306, + 506, + 378, + 518 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 528, + 545, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 528, + 545, + 659 + ], + "spans": [ + { + "bbox": [ + 304, + 528, + 545, + 659 + ], + "type": "text", + "content": "In this paper, we present a significant improvement over existing privacy-preserving image-based localization approaches. Our method improves upon the accuracy limitation of random line based approaches and closes the gap to traditional non-privacy preserving methods. At the same time, our method proves as robust against recently presented density attacks on random 3D line clouds. An interesting avenue for future work could be in addressing the increased runtime of our method. One promising idea involves voting for correct coordinate swaps during RANSAC and progressively sampling from more likely lines." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgments We would like to thank Marcel Geppert for reviewing this paper, for the insightful discussions, and his help in the supp. material, as well as Torsten Sattler and Kunal Chelani for the code and data of line cloud inversion experiments. Viktor Larsson was supported by ELLIIT." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18181" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Inside Facebook Reality Labs: Research updates and the future of social connection. https://tech.fb.com/inside-facebook-reality-labs-research-updates-and-the-future-of-social-connection/, 2019. 1" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 136, + 286, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 136, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 136, + 286, + 156 + ], + "type": "text", + "content": "[2] Sameer Agarwal, Keir Mierle, and The Ceres Solver Team. 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In International Conference on Computer Vision (ICCV), 2015. 2" + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18183" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Privacy-Preserving Face Recognition Using Random Frequency Components/3da3fc63-806e-4e3e-99b2-e2f33c132bad_content_list.json b/2023/Privacy-Preserving Face Recognition Using Random Frequency Components/3da3fc63-806e-4e3e-99b2-e2f33c132bad_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..d5fcd3e59a002928e7eae47b923a31d59711e2fd --- /dev/null +++ b/2023/Privacy-Preserving Face Recognition Using Random Frequency Components/3da3fc63-806e-4e3e-99b2-e2f33c132bad_content_list.json @@ -0,0 +1,2005 @@ +[ + { + "type": "text", + "text": "Privacy-Preserving Face Recognition Using Random Frequency Components", + "text_level": 1, + "bbox": [ + 98, + 130, + 870, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yuxi Mi $^{1*}$ Yuge Huang $^{2*}$ Jiazhen Ji $^{2}$ Minyi Zhao $^{1}$ \nJiaxiang Wu $^{2}$ Xingkun Xu $^{2}$ Shouhong Ding $^{2}$ Shuigeng Zhou $^{1\\dagger}$ $^{1}$ Fudan University $^{2}$ Tencent Youtu Lab \n{yxmi20, zhaomy20, sgzhou}@fudan.edu.cn \n{yugehuang, royji, willjxwu, xingkunxu, ericshding}@tencent.com", + "bbox": [ + 209, + 179, + 756, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 304, + 312, + 319 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The ubiquitous use of face recognition has sparked increasing privacy concerns, as unauthorized access to sensitive face images could compromise the information of individuals. This paper presents an in-depth study of the privacy protection of face images' visual information and against recovery. Drawing on the perceptual disparity between humans and models, we propose to conceal visual information by pruning human-perceivable low-frequency components. For impeding recovery, we first elucidate the seeming paradox between reducing model-exploitable information and retaining high recognition accuracy. Based on recent theoretical insights and our observation on model attention, we propose a solution to the dilemma, by advocating for the training and inference of recognition models on randomly selected frequency components. We distill our findings into a novel privacy-preserving face recognition method, PartialFace. Extensive experiments demonstrate that PartialFace effectively balances privacy protection goals and recognition accuracy. Code is available at: https://github.com/Tencent/TFace.", + "bbox": [ + 75, + 335, + 473, + 638 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 670, + 207, + 684 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Face recognition (FR) is a landmark biometric technique that enables a person to be identified or verified by face. It has seen remarkable methodological breakthroughs and rising adoptions in recent years. Currently, considerable applications of face recognition are carried out online to bypass local resource constraints and to attain high accuracy [19]: Face images are collected by local devices such as cell phones or webcams, then outsourced to a service provider, that uses large convolutional neural networks (CNN) to extract the faces' identity-representative templates and matches them with records in its database.", + "bbox": [ + 75, + 696, + 468, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ab0f35fb5afe1dbd1a1b9f0d4eaafbf36474695ada0837df775f241a07693548.jpg", + "image_caption": [ + "Figure 1. Paradigm comparison among other frequency-based methodologies and PartialFace. (a) Pruning low-frequency channels can conceal visual information but stop no recovery. (b) A vanilla method that uses fixed channel subsets to impede recovery suffers downgraded accuracy. (c) PartialFace addresses the dilemma by training and inferring from random channels." + ], + "image_footnote": [], + "bbox": [ + 511, + 301, + 879, + 460 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "During the process, the original face images are often considered sensitive data under regulatory demands that are unwise to share without privacy protection. This fosters the studies of privacy-preserving face recognition (PPFR), where cryptographic [7,8,14,17,21,33,44,47] and perturbation-based [3, 12, 18, 28-30, 46, 48] measures are taken to prevent face images from unauthorized access of, e.g., wiretapping third parties. Face images are converted to protective representations that their visual information is both concealed and cannot be easily recovered [2].", + "bbox": [ + 496, + 577, + 890, + 728 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This paper advocates a novel PPFR scheme, to learn face images from random combinations of their partial frequency components. Our proposed PartialFace can protect face images' visual information and prevent recovery while maintaining the high distinguishability of their identities.", + "bbox": [ + 496, + 731, + 890, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We start with the disparity in how humans and models perceive images. Recent image classification studies suggest that models' predictions are determined mainly by the images' high-frequency components [39, 45], which carry negligible visual information and are barely picked up by humans. We extend the theory to face recognition from a", + "bbox": [ + 496, + 810, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contributions.", + "bbox": [ + 94, + 875, + 222, + 886 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 96, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19673", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "privacy perspective, to train and infer the model on pruned frequency inputs: As depicted in Fig. 1(a), we decouple the face images' frequency compositions via discrete cosine transform (DCT), which breakdown every spatial domain into a certain number of (typically 64) constituent bands, i.e., frequency channels. We prune the human-perceivable low-frequency channels and exploit the remaining. We find the processed face images become almost visually indiscernible, and the model still works accurately.", + "bbox": [ + 75, + 90, + 472, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Pruning notably conceals visual information. However, to what degree can it impede recovery? We define recovery as the general attempts to reveal the faces' visual appearances from shared protected features using trained attack models. Notice we may prune very few (say, about 10) channels, if according to human perception. At the same time, the remaining high-frequency channels being shared, hence exposed, are quite numerous and carry a wealth of model-perceivable features. While the information abundance can benefit a recognition model, it is also exploitable by a model carrying out attacks, as both may share similar perceptions. Therefore, as we later experimentally show, the attacker can recover visual features from high-frequency channels with ease in the absence of additional safeguards, rendering privacy protection useless.", + "bbox": [ + 75, + 229, + 472, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "An intuitive tactic to reinstate protection is to reduce the attacker's exploitable features by training on a small portion of fixed channels, as shown in Fig. 1(b). However, we find the reduction also severely impairs the accuracy of trained recognition models. Evidence on the models' attention, as later shown, attributes their utility downgrade to being incapable of learning a complete set of facial features, as vital channels describing some local features may be pruned.", + "bbox": [ + 75, + 458, + 472, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Training on subsets of channels hence seems contradictory to the privacy-accuracy equilibrium. Fortunately, we can offer a reconciliation getting inspired by a recent timeseries study [51]. It proves under mild conditions, models trained on random frequency components can preserve more entirety's information than on fixed ones, plausibly by alternately learning from complementary features. We hence propose a novel address to the equilibrium based on its theoretical findings and our observation on model attention: For any incoming face image, we arbitrarily pick a small subset of its high-frequency channels. Therefore, our recognition model is let trained and inferred from image-wise random chosen channels, illustrated in Fig. 1(c).", + "bbox": [ + 75, + 580, + 472, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We further show that randomness can be adjusted to a moderate level, by choosing channels from pre-specified combinations and perturbations called ranks, to keep privacy protection while reconciling technical constraints to ease training. At first glance, our randomized approach may seem counter-intuitive as it is common wisdom that models require consistent forms of inputs to learn stably. However, since DCT produces spatially correlated frequency channels", + "bbox": [ + 75, + 779, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "that preserve the face's structural information, as later illustrated in Fig. 3, it turns out the model generalizes quite naturally. Experimental analyses show our PartialFace well balances privacy and accuracy.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions of our paper are three-fold:", + "bbox": [ + 517, + 152, + 820, + 167 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We present an in-depth study of the privacy protection of face images, regarding the privacy goals of concealing visual information and impeding recovery.", + "2. We propose two methodological advances to fulfill the privacy goals, pruning low-frequency components and using randomly selected channels, based on the observation of model perception and learning behavior.", + "3. We distill our findings into a novel PPFR method, PartialFace. We demonstrate by extensive experiments that our proposed method effectively safeguards privacy and maintains satisfactory recognition accuracy." + ], + "bbox": [ + 511, + 175, + 890, + 361 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 382, + 637, + 398 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Face recognition", + "text_level": 1, + "bbox": [ + 500, + 407, + 663, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The current method of choice for face recognition is CNN-based embedding. The service provider trains a CNN with a softmax-based loss to map face images into one-dimensional embedding features which achieve large interidentity and small intra-identity discrepancies. While the state-of-the-art (SOTA) FR methods [6, 20, 38] achieve impressive task utility in real-world applications, their attention to privacy protection could be deficient.", + "bbox": [ + 496, + 430, + 890, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Privacy-preserving face recognition", + "text_level": 1, + "bbox": [ + 500, + 560, + 808, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The past decade witnessed significant advances in privacy-preserving face recognition [24,25,41]. We roughly categorize the related arts into two branches:", + "bbox": [ + 496, + 584, + 890, + 628 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Cryptographic methods perform recognition on encrypted images, or by executing dedicated security protocols. Many pioneering works fall under the category of homomorphic encryption (HE) [8,14,33] or secure multiparty computation (MPC) [21, 44, 47], to securely carry out necessary computations such as model's feature extraction. Some methods also employ various crypto-primitives including one-time-pad [7], matrix encryption [17], and functional encryption [1]. The major pain points of these methods are generally high latency and expensive computational costs.", + "bbox": [ + 496, + 628, + 890, + 779 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Perturbation-based methods transform face images into protected representations that are difficult for unauthorized parties to discern or recover. Many methods leverage differential privacy (DP) [3, 18, 22, 48], in which face images are obfuscated by a noise mechanism. Some use autoencoders [28] or adversarial generative networks (GAN) [18, 29] to recreate visually distinct faces that maintain a constant identity. Others compress the original images into", + "bbox": [ + 496, + 780, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19674", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c060aad62d664fd1c861a46e711802f260a985a212a712fb99ea67098160c1dd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 89, + 890, + 258 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/52ba281a90bada064160f9149dcefc64a96ce167b441101729c335793ebd21c9.jpg", + "image_caption": [ + "Training/Trained Model" + ], + "image_footnote": [], + "bbox": [ + 80, + 260, + 106, + 282 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3e7cb37aa48efa178868182c0f5a5b3ef2ab8336f7a423f98549bc4ae491ec21.jpg", + "image_caption": [ + "Server", + "Figure 2. Pipeline of PartialFace. DCT turns face images into the frequency domain, where low-frequency channels are first pruned to remove the human perception. A small subset of channels is selected and permuted at random according to pre-specified combinations $\\{\\mathbf{S},\\mathbf{P}\\}$ , or ranks. The model is trained and inferred from random subsets to address the equilibrium between accuracy and privacy." + ], + "image_footnote": [], + "bbox": [ + 199, + 263, + 223, + 281 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c3e695b6a5b13b5c73cf1915c1c7aaeb732edee5786529842b57073e0f252087.jpg", + "image_caption": [ + "Client" + ], + "image_footnote": [], + "bbox": [ + 258, + 263, + 274, + 281 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5786298c1d99699ae56be04ec3b85efdedf83d2a54ceb827e145350105fbae3a.jpg", + "image_caption": [ + "Face Image" + ], + "image_footnote": [], + "bbox": [ + 302, + 263, + 325, + 281 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5916d093c29f83c57f22ce3e95c885a9ddf18491d870697c1de87b71e7ea41d1.jpg", + "image_caption": [ + "Recognition" + ], + "image_footnote": [], + "bbox": [ + 375, + 263, + 392, + 281 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/24ce2f3765079964805fbd69aae20fd93e7112d674a21748cd186f67a7378b46.jpg", + "image_caption": [ + "Trainin" + ], + "image_footnote": [], + "bbox": [ + 450, + 263, + 473, + 281 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e3ef3357a52ac41ff5ba7b4af423d6ec825a4bca1e394dcc9a68ef17e22c47c6.jpg", + "image_caption": [ + "面" + ], + "image_footnote": [], + "bbox": [ + 501, + 263, + 527, + 281 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/62017f6a1ddd8c07224dd6e02aac011d2fe65a1aef03c35d4531c0440f99cf5d.jpg", + "image_caption": [ + "d LF Channels" + ], + "image_footnote": [], + "bbox": [ + 557, + 263, + 578, + 281 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4d934a41c694222ed27e034f0c627c0b27f02226ea7e9bb18fe2b37befa740ca.jpg", + "image_caption": [ + "Sample Combinations" + ], + "image_footnote": [], + "bbox": [ + 638, + 263, + 661, + 281 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c60e5e59f6e7da39ac3b9acfb979ac8da7519049e0f1a66249c2634898956afc.jpg", + "image_caption": [ + "Randomly Sample Subset(s)" + ], + "image_footnote": [], + "bbox": [ + 754, + 263, + 776, + 280 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "compact representations by mapping discriminative components into subspaces [4, 16, 27], or anonymize the images by clustering their features [12]. These methods face a common bottleneck of task utility: As the techniques they employ essentially distort the original images, their protection often impairs recognition accuracy.", + "bbox": [ + 75, + 354, + 467, + 445 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Learning in the frequency domain", + "text_level": 1, + "bbox": [ + 76, + 455, + 375, + 472 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Converting spatial or temporal data into the frequency domain provides a powerful way to extract interesting signals. For instance, the Fourier-based discrete cosine transform [5] is used by the JPEG standard [37] to enable image compression. Researches in deep learning [9, 45] suggest models trained on images' frequency components can perform as well as trained on the original images. Advance [39] further reveals humans and models perceive low- and high-frequency components differently. In the realm of PPFR, three recent methods [15, 26, 42] are closely related to ours as we all conceal visual information by exploiting the split in human and model perceptions. However, these methods bear inadequacy in defending recovery, according to our previous discussion of channel redundancy and later testified in experiments.", + "bbox": [ + 73, + 479, + 468, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 720, + 210, + 736 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This section discusses the motivation and technical details behind PartialFace. PartialFace is named after its key protection mechanism, where the model only exploits face images' partial frequency components to reduce information exposure. Figure 2 describes its framework.", + "bbox": [ + 75, + 744, + 467, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 76, + 830, + 186, + 845 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recall our privacy goals are to conceal the face images' visual information and to prevent recovery attacks on them. They respectively target the adversarial capability of hu", + "bbox": [ + 75, + 854, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "mans and models. We naturally concretize them into two technical aims, on how to eliminate human perception, and, on how to reduce exploitable information for attack models.", + "bbox": [ + 496, + 354, + 890, + 400 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To eliminate human perception, we leverage the finding that models' utility can be maintained almost in full on the images' high-frequency channels [39]. Contrarily, humans mostly perceive the images' low-frequency channels, as only they carry signals of conspicuous amplitude for human eyes to discern. Whereby spatial-frequency transforms, these channels can be easily located and pruned from raw images. We concretely opt for DCT as our transform as it facilitates the calculation of energy, to serve as the quantification for human perceivable information. Experimentally, we can prune a very small portion of channels to eliminate $95\\%$ of total energy, hence satisfying our aim.", + "bbox": [ + 496, + 401, + 890, + 582 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Reducing the attacker's exploitable information requires further pruning of high-frequency channels, as previously discussed. However, it is equally crucial to maintain the recognition model's accuracy, which presents a seeming dilemma, as the training features utilizable by recognition and attack models are tightly interwoven in these channels. We offer a viable way as our major contribution: We notice different channel subsets each carrying certain local facial features. Hence, we feed the model with a random subset from each face image, with the hope to let the model learn the entire face's impression from different images' complementary local feature partitions. This approach is proved feasible by recent theoretical studies [51] and demonstrated by our experiments. Therefore, information exposure is minimized as only each image's chosen subset is exposed, and the model still performs surprisingly well.", + "bbox": [ + 496, + 583, + 890, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Despite being well justified by theory, we find sampling channels under complete randomness could under-perform in actual training due to two technical limitations: the inadequacy in training samples and the biased sampling within mini-batches. We propose two targeted fixes to reconcile", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19675", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a2eabe9499f00ea53245db1238873ee5595c157f1bddd4cf2a531fbca442054d.jpg", + "image_caption": [ + "Figure 3. The DCT process. The produced (d) frequency channels keep the spatial structure to (a) the original image, though only low-frequency channels are discernible bu humans. We use (c) 2D grids to describe the frequency spectrum. Each cell in the grid represents one frequency channel of $H \\times W$ ." + ], + "image_footnote": [], + "bbox": [ + 84, + 89, + 467, + 175 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the constraints, by augmenting samples and seeking a moderate level of randomness. We find the modified approach satisfactorily addresses the privacy-accuracy equilibrium.", + "bbox": [ + 75, + 276, + 468, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Conceal visual information", + "text_level": 1, + "bbox": [ + 76, + 334, + 320, + 348 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first set up some basic notions: $\\langle X, y \\rangle$ denotes a data sample of a face image and its corresponding label. $x$ denotes the frequency composition of $X$ and $x_i$ denotes its individual frequency channels. $f(\\cdot; \\theta)$ denotes the recognition model parameterized by $\\theta$ . $l(\\cdot, \\cdot)$ denotes a generic loss function (e.g., ArcFace). $\\mathcal{T}(\\cdot)$ denotes the discrete cosine transform and $\\mathcal{T}^{-1}(\\cdot)$ denotes its inverse transform.", + "bbox": [ + 75, + 358, + 468, + 463 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To conceal visual information, recall humans and models mainly perceive low- and high-frequency components, respectively. Therefore, we need to find a frequency decomposition of $X = \\{\\mathbf{x}_l, \\mathbf{x}_h\\}$ , where $\\mathbf{x}_l, \\mathbf{x}_h$ are the respective low- and high-frequency channels, then prune $\\mathbf{x}_l$ .", + "bbox": [ + 75, + 465, + 468, + 541 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We presume $X$ is with the shape of $(H, W)$ . We employ DCT to transform $X$ 's spatial channels into a frequency spectrum. While an RGB image typically has 3 spatial channels, we pick one for simplicity. We perform an 8-fold up-sampling ahead to turn $X$ into $(8H, 8W)$ . As DCT later divides $H$ and $W$ by 8, this makes sure the resulting frequency channels can be fed into the model as usual. Figure 3 illustrates the process of DCT, where $\\mathbf{x} = \\mathcal{T}(X)$ . Concretely, $X$ is divided into (8, 8)-pixel blocks. DCT turns each block into a 1D array of 64 frequency coefficients and reorganizes all coefficients from the same frequency across blocks into an $(H, W)$ frequency channel (there are 64 of them), that is spatially correlated to the original $X$ . As a result, $X$ is turned into $\\mathbf{x}$ of $(64, H, W)$ .", + "bbox": [ + 75, + 541, + 468, + 752 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We then decouple $\\mathbf{x}$ into $\\{\\mathbf{x}_l, \\mathbf{x}_h\\}$ . Notice that human-perceivable low-frequency channels should meanwhile be those with higher amplitude, as humans preferentially identify signals with conspicuous value changes. We measure a channel's amplitude by its channel energy $e(\\cdot)$ , which is the mean of amplitudes of all its elements:", + "bbox": [ + 75, + 753, + 468, + 844 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ne (x) = \\frac {1}{H W} \\sum_ {i = 0} ^ {H - 1} \\sum_ {j = 0} ^ {W - 1} | x ^ {i, j} |. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 859, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/44b4ceb330dc99d2c71d4df6c3e28ec9162fb3983ab0986a8ef11b133e12866a.jpg", + "image_caption": [ + "Figure 4. The visual appearance and recovery of an example image of (a) after pruning, (b) a fixed subset, and (c) a random subset. This shows protection is enhanced by removing human perception, reducing the number of channels, and randomness, respectively." + ], + "image_footnote": [], + "bbox": [ + 517, + 90, + 880, + 233 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We choose $\\sigma = 10$ highest-energy channels as $\\mathbf{x}_l$ to be pruned and the rest as $\\mathbf{x}_h$ to be available to models. We experimentally find $\\sum_{x\\in \\mathbf{x}_l}e(x)\\geq 0.95\\sum_{x\\in \\mathbf{x}}e(x)$ , and a model trained with $\\arg \\min_{\\theta}l(f(\\mathbf{x}_h,\\theta),y)$ obtain close accuracy to one trained with $\\arg \\min_{\\theta}l(f(\\mathbf{x},\\theta),y)$ . For privacy, example of a channel-pruned image in Fig. 4(a) show that most visual information is concealed. While its recovery is still carried out quite successfully, we are to address the issue in the following.", + "bbox": [ + 496, + 319, + 890, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Impede easy recovery", + "text_level": 1, + "bbox": [ + 500, + 467, + 700, + 483 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To elucidate the seeming dilemma between reducing model-available channels and retaining high recognition accuracy, we first introduce an intuitive protection, referred to as the vanilla method. It trains models on a fixed small subset of channels straightforwardly: Concretely for every $X$ , the model pick $s < d$ channels $\\mathbf{x}_s = (x_{a_1},\\dots,x_{a_s})$ from its high-frequency $\\mathbf{x}_h = (x_1,\\dots,x_d)$ , where $a_1 < a_2 < \\dots < a_s$ are fixed indices. We benchmark the trained model on IJB-B/C with $s = 9,18,36$ and $d = 54$ , and verify its privacy.", + "bbox": [ + 496, + 491, + 890, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The model indeed effectively prevents recovery, as in Fig. 4(b) its recovered image is very blurred. However, the benchmark in Fig. 5(a-b) suggests its accuracy dropped by at most $9\\%$ . To find out why is the model's performance impaired, we inspect its attention via Grad-CAM [34]. Results are exemplified in Fig. 5(c-d), which we note show similar patterns among different face images. We derive two observations: (1) Unlike high-utility models that typically have attention to the full face, this model only gains attention to certain local features, which suggests some vital face-describing information is missing in $\\mathbf{x}_s$ ; (2) By training vanilla models on different $\\mathbf{x}_s$ , we find it can acquire distinct information from different channels, suggesting its attention is correlated to the specific choices of $\\mathbf{x}_s$ .", + "bbox": [ + 496, + 628, + 890, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The first observation suggests the cause of the accuracy downgrade. Meanwhile, the second pursues us to consider a viable bypass: We can gather complementary local features from different images and initiate mixed training, to let the", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19676", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/51f9230e1919a086e153bf2620c135a13bb7d544139c1ac5e185436130f38738.jpg", + "image_caption": [ + "Figure 5. The privacy and accuracy dilemma. (a-b) The vanilla model trained on fixed channels under-performs on IJB-B/C (orange), compared to the unprotected baseline (blue) and PartialFace (green). (c-d) The model gains local attention on foreheads and cheeks, suggesting missing face-describing information. The attention varies by the specific choice of $\\mathbf{x}_s$ ." + ], + "image_footnote": [], + "bbox": [ + 91, + 89, + 187, + 165 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3642c4c288e228dcc526ebb0b5927257f8bde6bb246a0fd22acd47852f87bf5d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 189, + 89, + 277, + 165 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/fd1595fb6414c733c4cc01ea382720654b022e1e5b4eef574661461995eb4eda.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 287, + 90, + 366, + 165 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2e5084efa6247027a319eb36e0b42f957c4feb1170cc2db432d6becd9682e3f5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 375, + 90, + 454, + 165 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "model learn a holistic impression of the entirety while keeping the individual information exposure minimized. Our idea is corroborated by [51], which proves in time-series, training models on random frequency components can preserve more information compared to training on fixed ones.", + "bbox": [ + 75, + 277, + 467, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We concrete our theory into a randomized strategy, by advocating training and inferring the recognition model on image-wise randomly chosen channels. Formally, we construct matrix $S \\in \\{0,1\\}^{d \\times s}$ , with $s_{ij} = 1$ if $i = a_j$ and $s_{ij} = 0$ if otherwise. We also construct permutation matrix $P \\in \\{0,1\\}^{s \\times s}$ . For each $X$ , we draw $(a_1, \\ldots, a_s)$ (therefore $S$ ) and $P$ uniformly at random, and calculate", + "bbox": [ + 76, + 354, + 467, + 460 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {s} = \\mathbf {x} _ {h} \\cdot S \\cdot P. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 478, + 468, + 494 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $S$ randomly pick $s$ channels out of $\\mathbf{x}_h$ , then their order is permuted by $P$ . We introduce $P$ to further impede recovery, as later discussed in Sec. 3.5. The model is trained in the same way as standard FR using $\\langle \\mathbf{x}_s, y \\rangle$ . However, it does not require to know the sample-wise specific $\\{S, P\\}$ , which is favorable for privacy. The approach sounds a bit counter-intuitive since receiving random inputs seems to mess with the model's understanding. However, recall that the DCT frequency channels are spatially correlated to $X$ and each other. The randomness only pertains to the frequency spectrum while the face's structural information is preserved and unaltered. The model, therefore, can associate different $\\mathbf{x}_s$ to the same $X$ quite naturally.", + "bbox": [ + 75, + 503, + 468, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Reconcile technical constraints", + "text_level": 1, + "bbox": [ + 76, + 710, + 349, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Equation (2) distills our core idea to sampling $\\mathbf{x}_s$ at complete random. However, for practical training, there need to further reconcile two technical constraints to achieve satisfying model performance: First to note that $\\langle \\mathbf{x}_s, y \\rangle$ are more varied in feature representations than the unprotected $\\langle X, y \\rangle$ , owing to the randomized frequency. It hence could plausibly take the model with more training samples and a longer training time to approach a well-generalized convergence. Second, ideally, channels at random should be sampled with equal probability to ensure balanced learning of different local features. However, when the training data", + "bbox": [ + 75, + 734, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "is partitioned into small mini-batches, sampling is often less unbiased batch-wise so the occurrence of different channel combinations may vary greatly, which we find could undermine the training stability.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Targeting the constraints, we slightly adjust our established approach in two ways. We first augment the training dataset by picking multiple $\\mathbf{x}_s$ each time from a face image $X$ : From $X$ we sample $\\{\\mathbf{x}_s^1,\\ldots ,\\mathbf{x}_s^r\\}$ , where $r$ determines the degree of augmentation. Each $\\mathbf{x}_s^i$ is independently drawn and appended to the training dataset as individual training samples. The dataset is then fully shuffled so that $\\mathbf{x}_s^i$ corresponding to the same face image cannot be easily associated.", + "bbox": [ + 496, + 152, + 890, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We also control the randomness to a moderate level by specifying the possible combinations of $S, P$ in advance. Concretely, we opt for choosing one $S, P$ from $\\mathbf{S} = \\{S_1, \\dots, S_m\\}$ and $\\mathbf{P} = \\{P_1, \\dots, P_n\\}$ respectively, where $\\mathbf{S}, \\mathbf{P}$ are determined by the service provider. We specifically require $\\{S_1, \\dots, S_n\\}$ to be a non-overlapping partition of channels from $\\mathbf{x}_h$ (i.e., divide $\\mathbf{x}_h$ into equal-length subsets) to maximize the use of $\\mathbf{x}_h$ and reduce model bias. Therefore, each $\\mathbf{x}_s^i$ is picked from one of $m \\times n$ fixed combinations of channels, called ranks. This allows us to facilitate the training and overcome sampling biases. The service provider shares $\\{\\mathbf{S}, \\mathbf{P}\\}$ with all local devices, so the latter can generate their query $\\mathbf{x}_s$ accordingly. During inference, the model is expected to provide consistent results of the same query $X$ regardless of the choice of rank, since it learned about a mapping from local features to the face's entirety. We later testify to it in Sec. 4.3. Meanwhile, the model is still unaware of the sample-wise specific choice of $\\{S, P\\}$ as the recognition relies on nothing else but $\\mathbf{x}_s$ alone. Hence privacy is maintained.", + "bbox": [ + 496, + 287, + 892, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To conclude, we present PartialFace that train and infer the recognition model with $\\arg \\min_{\\theta} l(f(\\mathbf{x}_s^i, \\theta), y)$ , where $X = \\{\\mathbf{x}_l, \\mathbf{x}_h\\}$ and $\\mathbf{x}_s^i = \\mathbf{x}_h \\cdot S \\cdot P$ in random, parameterized by $\\{\\mathbf{S}, \\mathbf{P}\\}$ and $(\\sigma, s, r, m, n)$ . Later analyses in Secs. 4.2 and 4.3 show PartialFace overcomes the drawback of the vanilla method, plus outperforms most prior arts, to achieve satisfactory recognition accuracy.", + "bbox": [ + 496, + 590, + 890, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Enhance privacy with randomness", + "text_level": 1, + "bbox": [ + 500, + 709, + 802, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The benefit of randomness is multi-fold. We have discussed it for now on helping address the accuracy and privacy balance and enhance recognition performance. In retrospect, we briefly elaborate on how randomness further safeguards privacy to a large extent.", + "bbox": [ + 496, + 733, + 890, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Recall we remove visual information by pruning $\\mathbf{x}_l$ and impede recovery by choosing a subset of $\\mathbf{x}_s$ . After that, randomness further obstructs recovery: To impose recovery, the attacker exploits not only the channels' information but also their relative orders and positions in the frequency spectrum. We introduce $P$ to distort the order of channels to", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19677", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "this end. As the recognition model does not require samplewise $\\{S,P\\}$ , they won't be exposed to the attacker. Figure 4(c) shows the improvement against recovery if the attacker doesn't know the specific choice of subsets.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 166, + 209, + 183 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental settings", + "text_level": 1, + "bbox": [ + 76, + 191, + 279, + 208 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare PartialFace with the unprotected baseline and prior PPFR methods on three criteria: recognition performance, privacy protection of visual information, and that against recovery attack. We further study the computation and cost of PartialFace. We mainly employ an IR-50 [11] trained on the MS1Mv2 [10] dataset as our FR model, while also using a smaller combination of IR-18 and the BUPT [40] dataset on some resource-consuming experiments. We set $(\\sigma, s, r, m, n) = (10, 9, 18, 6, 6)$ and use fixed $\\{\\mathbf{S}, \\mathbf{P}\\}$ , if not else specified. Benchmarks are carried out on 5 widely used, regular-size datasets, LFW [13], CFP-FP [35], AgeDB [31], CPLFW [49] and CALFW [50], and 2 large-scale datasets, IJB-B [43] and IJB-C [23].", + "bbox": [ + 75, + 214, + 470, + 411 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Benchmarks on recognition accuracy", + "text_level": 1, + "bbox": [ + 76, + 421, + 398, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compared methods. We compare PartialFace with 2 unprotected baselines, 4 perturbation-based PPFR methods, and 3 methods base on the frequency domain that share close relation to us. Results are summarized in Tab. 1. Here, (1) ArcFace [6] denotes the unprotected SOTA trained directly on RGB images; (2) ArcFace-FD [45] is the ArcFace trained on the image's all frequency channels; (3) PEEP [3] is a differential-privacy-based method with a privacy budget $\\epsilon = 5$ ; (4) Cloak [27] perturbs and compresses its input feature space. Its accuracy-privacy trade-off parameter is set to 100; (5) InstaHide [14] mixes up $k = 2$ images and performs a distributed encryption; (6) CPGAN [36] generates compressed protected representation by a joint effort of GAN and differential privacy; (7) PPFR-FD1 [42] adopts a channel-wise shuffle-and-mix strategy in the frequency domain; (8) DCTDP [15] perturbs the frequency components by a noise disturbance mask with learnable privacy budget, where we set $\\epsilon = 1$ ; (9) DuetFace [26] is a two-party framework that employs channel splitting and attention transfer.", + "bbox": [ + 75, + 444, + 468, + 731 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Performance. Results are reported on LFW, CFP-FP, AgeDB, CPLFW, and CALFW by accuracy, and on IJB-B and IJB-C by TPR@FPR(1e-4). Table 1 shows PartialFace achieves close performance to the unprotected baseline, with a small accuracy gap of $\\leq 0.8\\%$ . In comparison, perturbation-based methods all generalize unsatisfactorily on large-scale benchmarks. PartialFace outperforms all PPFR prior arts but DuetFace. While DuetFace achieves", + "bbox": [ + 75, + 732, + 468, + 852 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "1The results of PPFR-FD on IJB-B is unattainable due its non-disclosure of source code. The rest is quoted from its paper [42]. Please note its experimental condition may have slight inconsistency with ours.", + "bbox": [ + 75, + 862, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4be29bb14fefddc554c294db7c50ba56734f4bce6f2b41ec480aba7e69bd3c55.jpg", + "image_caption": [ + "Figure 6. Visualization of model attention via Grad-CAM. (a) PartialFace (1st row) compared with vanilla models (2nd row) on each of 6 different ranks. (b) Integrated attention of all ranks." + ], + "image_footnote": [], + "bbox": [ + 511, + 88, + 882, + 188 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "slightly higher accuracy, its protection is inferior to ours as it only covers the inference phase and can be easily nullified by recovery attacks, later see Secs. 4.4 and 4.5.", + "bbox": [ + 498, + 258, + 890, + 305 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison with the vanilla method", + "text_level": 1, + "bbox": [ + 500, + 316, + 815, + 332 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We elaborate that randomized PartialFace outperforms the vanilla method that fixes channels in not only recognition accuracy but also robustness. As PartialFace employs data augmentation, for a fair comparison regarding the volume of training data, we consider two experimental settings: the standard PartialFace and one without augmentation $(r = 1)$ . We also set $n = 1$ to rule out permutation: $P$ is introduced for privacy and is out of our interest here. There are therefore $m \\times n = 6$ combinations of channels, or ranks. As channels from different ranks carry distinct information that may affect the performance, we train one vanilla model on each rank and average their test accuracy, with the range marked in parentheses. Though PartialFace is able to infer from arbitrary rank, we evaluate its robustness by inferring from each fixed rank separately. The model is robust if it performs on different ranks consistently (small range). Results are reported on IJB-B/C by TPR@FPR(1e-4) in Tab. 2. Performance. PartialFace achieves an average accuracy gain of $7.53\\%$ and $7.75\\%$ on IJB-B/C, respectively, compared to the vanilla. The performance is close to the unprotected baseline, showing that the privacy-accuracy trade-off of PartialFace is highly efficient. Even PartialFace without augmentation outperforms the vanilla for about $3\\%$ . We further note: (1) The range shows PartialFace is more robust than the vanilla under different $S_{i}$ . (2) PartialFace outperforms the vanilla for all individual $S_{i}$ . This suggests that randomness empowers PartialFace with the knowledge of the entirety instead of that of certain informative ranks.", + "bbox": [ + 496, + 340, + 890, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Visualization. We visualize the rank-wise attention of PartialFace and the vanilla via Grad-CAM [34], see Fig. 6(a). The attention of each vanilla model is restrained to local facial features, which indicates the inadequate learning of the entirety features. PartialFace generate accurate attention on the entire face regardless the rank. We integrated the attention across all ranks in Fig. 6(b). All vanilla models' attention combined gains attention on the entire face, which testifies to our \"learn-entropy-from-local\" theory. Also to", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19678", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9229b85a363fdfc0cb65b863654e150369e519ad6689bbbf421e62e3cf593db6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodPPFRLFWCFP-FPAgeDBCPLFWCALFWIJB-BIJB-C
ArcFace [6]No99.7798.3097.8892.7796.0594.1395.60
ArcFace-FD [45]No99.7898.0498.1092.4896.0394.0895.64
PEEP [3]Yes98.4174.4787.4779.5890.065.826.02
Cloak [27]Yes98.9187.9792.6083.4392.1833.5833.82
InstaHide [14]Yes96.5383.2079.5881.0386.2461.8869.02
CPGAN [36]Yes98.8794.6196.9890.4394.7992.6794.31
PPFR-FD [42]Yes99.6895.0497.3790.7895.72/94.10
DCTDP [15]Yes99.7796.9797.7291.3796.0593.2994.43
DuetFace [26]Yes99.8297.7997.9392.3596.1093.6695.30
PartialFace (ours)Yes99.8097.6397.7992.0396.0793.6494.93
", + "bbox": [ + 138, + 88, + 831, + 281 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3ca4b231a95ab3f987e6c4f482d53e3ee1d2efd320b2002e813a0f74ee47ed74.jpg", + "table_caption": [ + "Table 1. Benchmarks on recognition accuracy. PartialFace is compared with the unprotected baselines and PPFR SOTAs." + ], + "table_footnote": [ + "Table 2. Comparison with the vanilla method by accuracy and robustness. Experiments are conducted on IR-18 + BUPT. \"PF w/o aug.\" indicates PartialFace without augmentation." + ], + "table_body": "
MethodIJB-B (range)IJB-C (range)
ArcFace86.8390.35
Vanilla78.24 (-14.49/7.36)80.73 (-16.37/7.45)
PF w/o aug.81.43 (-4.19/2.88)82.81 (-4.29/2.79)
PartialFace85.77 (-1.95/1.25)88.48 (-1.71/1.18)
", + "bbox": [ + 83, + 316, + 460, + 405 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "note that PartialFace has similar attention across all ranks. This allows it to recognize $X$ using arbitrary rank, as they produce aligned outcomes.", + "bbox": [ + 76, + 474, + 468, + 518 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Protection of visual information", + "text_level": 1, + "bbox": [ + 76, + 530, + 357, + 542 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We investigate PartialFace's protection of privacy. We reiterate that the first privacy goal is to conceal the visual information of face images. We compare ParitalFace with 3 PPFR SOTAs using the frequency domain: PPFR-FD [42], DCTDP [15], and DuetFace [26]. These prior arts are closely related to ours since we all leverage the perceptual difference between humans and models as means of protection. However, they differ in the processing of frequency components: Both PPFR-FD and DCTDP remove the component with the highest energy (the DC component). To obfuscate the remaining components, PPFR-FD employs mix-and-shuffle and DCTDP applies a noise mechanism. DuetFace is the most related method in the pruning of low-frequency components. We note in special that they retain 36, 63, and 54 high-frequency channels, respectively, while PartialFace retains 9. We now demonstrate the methodological differences and varied number of channels result in contrasting privacy protection capacities.", + "bbox": [ + 75, + 551, + 468, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 7 exemplifies face images processed (therefore are supposed to be protective) by each compared method. As all methods carry out protection in the frequency domain, we convert images back by padding any removed frequency components with zero and applying an inverse", + "bbox": [ + 75, + 825, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4c9f094437d115070dee2563daa4d1aae5335c6c56ab7084b7a34ba40d8933e7.jpg", + "image_caption": [ + "Figure 7. Example face images of (a) unprotected ArcFace, (b-d) compared SOTAs, and (e) PartialFace, during both training and inference phase. PartialFace best conceals visual information." + ], + "image_footnote": [], + "bbox": [ + 511, + 318, + 879, + 440 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "transform. PartialFace, e.g., has $X' = \\mathcal{T}^{-1}(\\{\\mathbf{0}, \\mathbf{x}_h\\})$ . We visualize the training and inference phases separately, as the compared methods' processing on them may vary: During inference, we argue PPFR-FD and DuetFace (Fig. 7(b)(d)) provide inadequate protection, as one can still discern the face quite clearly in their processed images. DCTDP effectively conceals visual information after obfuscating the channels with its proposed noise mask (Fig. 7(c)). However, its protection during training is impaired, as it requires access to abundant non-obfuscated components to learn the mask. DuetFace manifests a similar weakness as it relies on original images to rectify the model's attention (Fig. 7(d)).", + "bbox": [ + 496, + 512, + 890, + 694 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "PartialFace first discards most visual information by pruning $\\mathbf{x}_l$ . The rest is further partitioned when sampling $\\mathbf{x}_s$ from $\\mathbf{x}_h$ . By energy, each $\\mathbf{x}_s$ carries less than $1\\%$ of visual information compared to the original $X$ . As a result, Fig. 7(e) shows PartialFace provides better protection on visual information than related SOTAs in both phases.", + "bbox": [ + 496, + 695, + 890, + 786 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Protection against recovery", + "text_level": 1, + "bbox": [ + 500, + 800, + 745, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We here provide an in-depth analysis of how Partial-Face impedes recovery. Our primary aiming is to show how the removal of model-exploitable information and the randomness of channels contribute to the defense. Assume the recovery attacker possesses a collection of face im", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19679", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b36414754013647d0b1b57b22ac11e3fb44dbbff5a221102a9d96d139fe7e62b.jpg", + "image_caption": [ + "(a) black-box" + ], + "image_footnote": [], + "bbox": [ + 89, + 89, + 205, + 179 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9f6e40b8c24f97d1466a4b74688cf7a16b625c1b15c577a45c960408751d2fab.jpg", + "image_caption": [ + "(b) white-box", + "Figure 8. Examples of recovered face images of PartialFace under attackers with varied capabilities: (a) a black-box, (b) a white-box, and (c) an enhanced white-box attacker. PartialFace effectively prevents recovery as all images are blurry and hardly identifiable." + ], + "image_footnote": [], + "bbox": [ + 215, + 90, + 330, + 179 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2ec6786deb502db39b178c922a73e859ca5cb920c736b2580c067ecce1d799dc.jpg", + "image_caption": [ + "(c) enhanced white-box" + ], + "image_footnote": [], + "bbox": [ + 341, + 90, + 454, + 179 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5246ab7aa1628fc9357eac73cf5316375c94ed717803f0d9b9ae55385f3f8e70.jpg", + "image_caption": [ + "(a) PPFR-FD", + "Figure 9. Recovered images from (a-c) compared SOTAs and (d) PartialFace. PartialFace impedes recovery better than the rest." + ], + "image_footnote": [], + "bbox": [ + 109, + 265, + 186, + 325 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/75a31fec39f98ee594aefc2423a92a13a4582695fb84586e268e9e86a555d9f1.jpg", + "image_caption": [ + "(b) DCTDP" + ], + "image_footnote": [], + "bbox": [ + 192, + 266, + 269, + 325 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dd07ffcce9771c0220ec9fa756795eaba24c2aaf885946d305b10788d435de63.jpg", + "image_caption": [ + "(c) DuetFace" + ], + "image_footnote": [], + "bbox": [ + 274, + 266, + 352, + 325 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/79f085360aba579d4f5feb441c65b5d9d05b64e4e87a7caca0788730de77e3d2.jpg", + "image_caption": [ + "(d) ours" + ], + "image_footnote": [], + "bbox": [ + 359, + 266, + 436, + 325 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ages $\\{X\\}$ and is aware of the protection mechanism. It can locally generate protected representations $X^{\\prime}$ $(\\mathbf{x}_h$ in our case) from $X$ , then train a malicious model $g(\\cdot)$ with $\\arg \\min_{\\delta}l^{\\prime}(g(X^{\\prime},\\delta),X)$ , with the aiming to inversely fit $X$ from $X^{\\prime}$ . Having intercepted a recognition query, the attacker leverages $g(\\cdot)$ to recover the concealed visual information. Upon the knowledge it possesses, a black-box attacker is one unknowing of necessary parameters ( $\\{\\mathbf{S},\\mathbf{P}\\}$ in our case), whilst a white-box attacker possesses such knowledge. We also study the capability of PPFR-FD, DCTDP, and DuetFace against the white-box attacker. We further investigate an enhanced white-box attacker, who imposes threats dedicated to the randomness of PartialFace.", + "bbox": [ + 75, + 397, + 467, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Black-box attacker. It is concretized as a malicious third party, uninvolved in the recognition yet eager to wiretap the transmission. For each attacker, We employ a full-scale U-Net [32] as the recovery model and train it on BUPT. Unknown of $\\{\\mathbf{S},\\mathbf{P}\\}$ , it must produce $X^{\\prime}$ based on its own conjectured $\\{\\mathbf{S}^{\\prime},\\mathbf{P}^{\\prime}\\}$ , which is believably inconsistent with that applied to the recognition model. Thus produced $X^{\\prime}$ are invalid samples and training $g(\\cdot)$ on them will nullify the recovery, as shown in Fig. 8(a).", + "bbox": [ + 75, + 595, + 467, + 731 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "White-box attacker. The candidate combinations $\\{\\mathbf{S},\\mathbf{P}\\}$ is known by any party participates in the recognition, e.g., an honest-but-curious server. Such an attacker can generate $X^{\\prime}$ correctly. However, receiving a query $\\mathbf{x}_s$ , the attacker is unknowing of its channels' position and order, since the specific $\\{S,P\\}$ doesn't come with $\\mathbf{x}_s$ . The missing information is vital to recovery. Consequently, the attack is obstructed by $\\mathbf{x}_s$ 's randomness in Fig. 8(b): The recovered image is blurry and hardly identifiable.", + "bbox": [ + 75, + 732, + 467, + 867 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We plus compare with PPFR-FD, DCTDP and Duet-Face under the white-box settings. Among them, Duet", + "bbox": [ + 76, + 869, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/25920325fd36a4bf9ae58c52990b2006e62a0870946815e94e02e176b5de73f7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodSSIM (↓)PSNR (↓)Accuracy (↓)
PPFR-FD0.71315.6683.73
DCTDP0.68715.4279.60
DuetFace0.86619.8896.52
PartialFace0.59113.7065.35
", + "bbox": [ + 500, + 88, + 875, + 178 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Quantitative analyses of the recovery quality. Lower SSIM, PSNR and accuracy suggest better protection. Here, we remind the accuracy of verification is lower bounded by 50.00.", + "bbox": [ + 498, + 179, + 890, + 219 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/06238690f2f1ea7ed00a3cbef62416ebf8fc4ed54f3518aa8e4738eda95cb857.jpg", + "image_caption": [ + "Figure 10. Recovered images from extracted identity templates, that are blurry and can hardly be inferred by humans or models." + ], + "image_footnote": [], + "bbox": [ + 532, + 234, + 609, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8ebeb2b1f03ded30bf944efa3bed36eddf883b66e7352449b1ec3ec4b5d206dc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 616, + 234, + 692, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b2aefcfc9eb18c603470c9f72e01dbbe729f7a2bfc463b67a7f5f61c2787f847.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 234, + 774, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/aab93b1ffd9cfdc2529b203d64066811abfdc487694f7f0a92f0c610e423973e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 782, + 234, + 857, + 292 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Face shows almost no resistance to recovery (Fig. 9(c)). PPFR-FD and DCTDP provide inadequate protection, as images recovered from them (Fig. 9(a-b)) are blurred yet still clearly identifiable. The protection is impaired as their processed images retain most high-frequency components, and the excessive perceivable information is learned by the recovery model. In comparison, PartialFace (Fig. 9(d)) offers significantly outperformed protection.", + "bbox": [ + 496, + 352, + 890, + 472 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Enhanced white-box attacker. A resource-unbounded attacker may brute-forcibly break the randomness of Partial-Face leveraging a more sophisticated attack: it trains a series of attack models, one for each candidate $\\{S,P\\}$ . Receiving $\\mathbf{x}_s$ , the attacker feeds it into every model to try every combination of $\\{S,P\\}$ , until one produces the best recovery. The vague face images in Fig. 8(c) imply the attempted recovery is unsuccessful, even if the attacker finds the correct $\\{S,P\\}$ . This is attributed to the reduction of model-exploitable channels.", + "bbox": [ + 496, + 473, + 890, + 623 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Quantitative comparison. To quantitatively assess the recovery quality, we measure the average structural similarity index (SSIM) and peak signal-to-noise ratio (PSNR) of the recovered images. Additionally, to study if the attacker can exploit its outcome for recognition proposes, we feed the images into a pre-trained model and measure verification accuracy. Lower SSIM, PSNR, and recognition accuracy suggest deficient recovery, thus indicating a higher level of protection. The results in Tab. 3 suggest PartialFace outperforms its competitors in all three evaluated metrics.", + "bbox": [ + 496, + 625, + 890, + 775 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Protection against recovery from templates", + "text_level": 1, + "bbox": [ + 500, + 786, + 864, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "By the principle of FR, all $\\mathbf{x}_s$ of face image $X$ are later extracted to very similar identity templates, so the recognition on them produces aligned results. Here, one would arise concern that recovery can also be carried out on the extracted templates, which theoretically contain the faces' full identity information, to realize better inversion of im", + "bbox": [ + 496, + 809, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19680", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8e7745c237f63c53c557a904242692934196ed237e424471aff5444c3cc3a6ee.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SettingsLFWCFP-FPAgeDBCPLFWCALFW
ArcFace99.3892.3194.6589.4194.78
r3699.5191.2794.4488.9394.81
698.6986.7990.6584.5092.67
m399.4291.6893.9588.7094.69
999.3290.7493.5687.3094.36
n199.3791.5594.2588.7394.70
1299.3589.2193.1787.1994.26
Default99.3891.2093.7288.1194.42
", + "bbox": [ + 78, + 89, + 468, + 263 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/83582d532c5902120596209d9bab4adc7a60d7de43f4a303d711a3765a2bcc1a.jpg", + "table_caption": [ + "Table 4. Ablation study on combinations of hyperparameters. Experiments are carried out on IR-18 + BUPT. When changing one of them, we keep the rest to default values, i.e., $(r,m,n) = (18,6,6)$ ." + ], + "table_footnote": [], + "table_body": "
SettingsLFWCFP-FPAgeDBCPLFW
CosFace99.5392.8995.1589.52
PartialFace99.3589.5493.9787.90
", + "bbox": [ + 80, + 316, + 465, + 377 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 5. Compatibility of PartialFace. FR models are trained using CosFace on IR-18 + BUPT. Combining PartialFace with CosFace also demonstrates high utility, compared to its baseline.", + "bbox": [ + 76, + 378, + 467, + 417 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "ages. We demonstrate that such a proposed attack is also ineffective to PartialFace.", + "bbox": [ + 76, + 443, + 467, + 470 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Although there could be dedicated attacks on templates, in practice, high-quality recovery from them is difficult as templates are far more compact representations than images and channel subsets. In Fig. 10, the recovered images are highly blurred, and can hardly be inferred by humans or models, hence won't impose an effective threat.", + "bbox": [ + 75, + 473, + 468, + 563 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.7. Ablation study", + "text_level": 1, + "bbox": [ + 76, + 573, + 225, + 588 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "PartialFace is parameterized by $(\\sigma, s, r, m, n)$ . Among them, we note $\\sigma$ is chosen according to channel energy, and $s$ is determined by $(\\sigma, m)$ . Table 4 analyzes the choice of the remaining parameters. Results show augmentation $(r)$ enhances the model's performance, at the cost of taking longer time to train. $m$ affects the performance mainly by its influence on $s$ , as larger $m$ leading to fewer channels in each $\\mathbf{x}_s$ . We introduce $P$ solely for privacy purposes. Results on $n$ indicate a trade-off between accuracy and privacy. Generally, PartialFace is robust to the choice of parameters.", + "bbox": [ + 75, + 595, + 468, + 746 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.8. Complexity and compatibility", + "text_level": 1, + "bbox": [ + 76, + 756, + 341, + 772 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Though PartialFace is proposed by studying the model's behavior, privacy protection is solely realized by processing the face images. The decoupling with model architecture and training tactics benefits resources and compatibility.", + "bbox": [ + 75, + 779, + 468, + 839 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "PartialFace is resource-efficient. Compared to the unprotected baseline, PartialFace doesn't increment model size as they share identical model architectures. Training does take more $(r)$ time and storage due to augmentation, while we", + "bbox": [ + 75, + 839, + 468, + 898 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "argue it is acceptable for the service provider. The crucial inference time remains the same as the baseline, as DCT and sampling $\\mathbf{x}_s$ only increase negligible computation costs.", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "PartialFace is well compatible. The decoupling of preprocessing and training also allows PartialFace to serve as a convenient plug-in: PartialFace can be integrated with SOTA FR methods to enjoy enhanced privacy protection. Specifically, we demonstrate the recognition accuracy on CosFace [38], a major competitor of ArcFace, in Tab. 5. Combining PartialFace with CosFace also results in high utility, as compared to its baseline.", + "bbox": [ + 496, + 136, + 890, + 257 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 268, + 617, + 284 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This paper presents an in-depth study of the privacy protection of face images. Based on the observations on model perception and training behavior, we present two methodological advances, pruning low-frequency components and using randomly selected channels, to address the privacy goal of concealing visual information and impeding recovery. We distill our findings into a novel privacy-preserving face recognition method, PartialFace. 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PMLR, 2022. 2, 3, 5" + ], + "bbox": [ + 78, + 90, + 468, + 582 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "19684", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Privacy-Preserving Face Recognition Using Random Frequency Components/3da3fc63-806e-4e3e-99b2-e2f33c132bad_model.json b/2023/Privacy-Preserving Face Recognition Using Random Frequency Components/3da3fc63-806e-4e3e-99b2-e2f33c132bad_model.json new file mode 100644 index 0000000000000000000000000000000000000000..78c6ed24d40337b6641e22650fed71d4efc174e0 --- /dev/null +++ b/2023/Privacy-Preserving Face Recognition Using Random Frequency Components/3da3fc63-806e-4e3e-99b2-e2f33c132bad_model.json @@ -0,0 +1,2776 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.099, + 0.131, + 0.872, + 0.153 + ], + "angle": 0, + "content": "Privacy-Preserving Face Recognition Using Random Frequency Components" + }, + { + "type": "text", + "bbox": [ + 0.21, + 0.18, + 0.758, + 0.27 + ], + "angle": 0, + "content": "Yuxi Mi\\(^{1*}\\) Yuge Huang\\(^{2*}\\) Jiazhen Ji\\(^{2}\\) Minyi Zhao\\(^{1}\\) \nJiaxiang Wu\\(^{2}\\) Xingkun Xu\\(^{2}\\) Shouhong Ding\\(^{2}\\) Shuigeng Zhou\\(^{1\\dagger}\\) \n\\(^{1}\\)Fudan University \\(^{2}\\)Tencent Youtu Lab \n{yxmi20, zhaomy20, sgzhou}@fudan.edu.cn \n{yugehuang, royji, willjxwu, xingkunxu, ericshding}@tencent.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.313, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.474, + 0.64 + ], + "angle": 0, + "content": "The ubiquitous use of face recognition has sparked increasing privacy concerns, as unauthorized access to sensitive face images could compromise the information of individuals. This paper presents an in-depth study of the privacy protection of face images' visual information and against recovery. Drawing on the perceptual disparity between humans and models, we propose to conceal visual information by pruning human-perceivable low-frequency components. For impeding recovery, we first elucidate the seeming paradox between reducing model-exploitable information and retaining high recognition accuracy. Based on recent theoretical insights and our observation on model attention, we propose a solution to the dilemma, by advocating for the training and inference of recognition models on randomly selected frequency components. We distill our findings into a novel privacy-preserving face recognition method, PartialFace. Extensive experiments demonstrate that PartialFace effectively balances privacy protection goals and recognition accuracy. Code is available at: https://github.com/Tencent/TFace." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.671, + 0.208, + 0.685 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.697, + 0.47, + 0.864 + ], + "angle": 0, + "content": "Face recognition (FR) is a landmark biometric technique that enables a person to be identified or verified by face. It has seen remarkable methodological breakthroughs and rising adoptions in recent years. Currently, considerable applications of face recognition are carried out online to bypass local resource constraints and to attain high accuracy [19]: Face images are collected by local devices such as cell phones or webcams, then outsourced to a service provider, that uses large convolutional neural networks (CNN) to extract the faces' identity-representative templates and matches them with records in its database." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.303, + 0.88, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.464, + 0.892, + 0.547 + ], + "angle": 0, + "content": "Figure 1. Paradigm comparison among other frequency-based methodologies and PartialFace. (a) Pruning low-frequency channels can conceal visual information but stop no recovery. (b) A vanilla method that uses fixed channel subsets to impede recovery suffers downgraded accuracy. (c) PartialFace addresses the dilemma by training and inferring from random channels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.578, + 0.892, + 0.729 + ], + "angle": 0, + "content": "During the process, the original face images are often considered sensitive data under regulatory demands that are unwise to share without privacy protection. This fosters the studies of privacy-preserving face recognition (PPFR), where cryptographic [7,8,14,17,21,33,44,47] and perturbation-based [3, 12, 18, 28-30, 46, 48] measures are taken to prevent face images from unauthorized access of, e.g., wiretapping third parties. Face images are converted to protective representations that their visual information is both concealed and cannot be easily recovered [2]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.732, + 0.892, + 0.807 + ], + "angle": 0, + "content": "This paper advocates a novel PPFR scheme, to learn face images from random combinations of their partial frequency components. Our proposed PartialFace can protect face images' visual information and prevent recovery while maintaining the high distinguishability of their identities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.893, + 0.901 + ], + "angle": 0, + "content": "We start with the disparity in how humans and models perceive images. Recent image classification studies suggest that models' predictions are determined mainly by the images' high-frequency components [39, 45], which carry negligible visual information and are barely picked up by humans. We extend the theory to face recognition from a" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.223, + 0.887 + ], + "angle": 0, + "content": "*Equal contributions." + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.223, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19673" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.228 + ], + "angle": 0, + "content": "privacy perspective, to train and infer the model on pruned frequency inputs: As depicted in Fig. 1(a), we decouple the face images' frequency compositions via discrete cosine transform (DCT), which breakdown every spatial domain into a certain number of (typically 64) constituent bands, i.e., frequency channels. We prune the human-perceivable low-frequency channels and exploit the remaining. We find the processed face images become almost visually indiscernible, and the model still works accurately." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.23, + 0.473, + 0.456 + ], + "angle": 0, + "content": "Pruning notably conceals visual information. However, to what degree can it impede recovery? We define recovery as the general attempts to reveal the faces' visual appearances from shared protected features using trained attack models. Notice we may prune very few (say, about 10) channels, if according to human perception. At the same time, the remaining high-frequency channels being shared, hence exposed, are quite numerous and carry a wealth of model-perceivable features. While the information abundance can benefit a recognition model, it is also exploitable by a model carrying out attacks, as both may share similar perceptions. Therefore, as we later experimentally show, the attacker can recover visual features from high-frequency channels with ease in the absence of additional safeguards, rendering privacy protection useless." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.473, + 0.581 + ], + "angle": 0, + "content": "An intuitive tactic to reinstate protection is to reduce the attacker's exploitable features by training on a small portion of fixed channels, as shown in Fig. 1(b). However, we find the reduction also severely impairs the accuracy of trained recognition models. Evidence on the models' attention, as later shown, attributes their utility downgrade to being incapable of learning a complete set of facial features, as vital channels describing some local features may be pruned." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.582, + 0.473, + 0.779 + ], + "angle": 0, + "content": "Training on subsets of channels hence seems contradictory to the privacy-accuracy equilibrium. Fortunately, we can offer a reconciliation getting inspired by a recent timeseries study [51]. It proves under mild conditions, models trained on random frequency components can preserve more entirety's information than on fixed ones, plausibly by alternately learning from complementary features. We hence propose a novel address to the equilibrium based on its theoretical findings and our observation on model attention: For any incoming face image, we arbitrarily pick a small subset of its high-frequency channels. Therefore, our recognition model is let trained and inferred from image-wise random chosen channels, illustrated in Fig. 1(c)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We further show that randomness can be adjusted to a moderate level, by choosing channels from pre-specified combinations and perturbations called ranks, to keep privacy protection while reconciling technical constraints to ease training. At first glance, our randomized approach may seem counter-intuitive as it is common wisdom that models require consistent forms of inputs to learn stably. However, since DCT produces spatially correlated frequency channels" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "that preserve the face's structural information, as later illustrated in Fig. 3, it turns out the model generalizes quite naturally. Experimental analyses show our PartialFace well balances privacy and accuracy." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.153, + 0.821, + 0.168 + ], + "angle": 0, + "content": "The contributions of our paper are three-fold:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.176, + 0.892, + 0.223 + ], + "angle": 0, + "content": "1. We present an in-depth study of the privacy protection of face images, regarding the privacy goals of concealing visual information and impeding recovery." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.231, + 0.892, + 0.292 + ], + "angle": 0, + "content": "2. We propose two methodological advances to fulfill the privacy goals, pruning low-frequency components and using randomly selected channels, based on the observation of model perception and learning behavior." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.301, + 0.892, + 0.362 + ], + "angle": 0, + "content": "3. We distill our findings into a novel PPFR method, PartialFace. We demonstrate by extensive experiments that our proposed method effectively safeguards privacy and maintains satisfactory recognition accuracy." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.176, + 0.892, + 0.362 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.383, + 0.638, + 0.399 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.408, + 0.664, + 0.424 + ], + "angle": 0, + "content": "2.1. Face recognition" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.431, + 0.892, + 0.553 + ], + "angle": 0, + "content": "The current method of choice for face recognition is CNN-based embedding. The service provider trains a CNN with a softmax-based loss to map face images into one-dimensional embedding features which achieve large interidentity and small intra-identity discrepancies. While the state-of-the-art (SOTA) FR methods [6, 20, 38] achieve impressive task utility in real-world applications, their attention to privacy protection could be deficient." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.561, + 0.809, + 0.577 + ], + "angle": 0, + "content": "2.2. Privacy-preserving face recognition" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.585, + 0.892, + 0.629 + ], + "angle": 0, + "content": "The past decade witnessed significant advances in privacy-preserving face recognition [24,25,41]. We roughly categorize the related arts into two branches:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.892, + 0.78 + ], + "angle": 0, + "content": "Cryptographic methods perform recognition on encrypted images, or by executing dedicated security protocols. Many pioneering works fall under the category of homomorphic encryption (HE) [8,14,33] or secure multiparty computation (MPC) [21, 44, 47], to securely carry out necessary computations such as model's feature extraction. Some methods also employ various crypto-primitives including one-time-pad [7], matrix encryption [17], and functional encryption [1]. The major pain points of these methods are generally high latency and expensive computational costs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Perturbation-based methods transform face images into protected representations that are difficult for unauthorized parties to discern or recover. Many methods leverage differential privacy (DP) [3, 18, 22, 48], in which face images are obfuscated by a noise mechanism. Some use autoencoders [28] or adversarial generative networks (GAN) [18, 29] to recreate visually distinct faces that maintain a constant identity. Others compress the original images into" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19674" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.891, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.261, + 0.107, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.108, + 0.267, + 0.195, + 0.277 + ], + "angle": 0, + "content": "Training/Trained Model" + }, + { + "type": "image", + "bbox": [ + 0.2, + 0.264, + 0.225, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.227, + 0.267, + 0.252, + 0.277 + ], + "angle": 0, + "content": "Server" + }, + { + "type": "image", + "bbox": [ + 0.259, + 0.264, + 0.275, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.267, + 0.3, + 0.277 + ], + "angle": 0, + "content": "Client" + }, + { + "type": "image", + "bbox": [ + 0.303, + 0.265, + 0.326, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.328, + 0.267, + 0.373, + 0.277 + ], + "angle": 0, + "content": "Face Image" + }, + { + "type": "image", + "bbox": [ + 0.377, + 0.265, + 0.393, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.395, + 0.267, + 0.447, + 0.277 + ], + "angle": 0, + "content": "Recognition" + }, + { + "type": "image", + "bbox": [ + 0.452, + 0.265, + 0.475, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.477, + 0.267, + 0.498, + 0.277 + ], + "angle": 0, + "content": "Trainin" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.265, + 0.528, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.531, + 0.267, + 0.553, + 0.277 + ], + "angle": 0, + "content": "面" + }, + { + "type": "image", + "bbox": [ + 0.558, + 0.265, + 0.579, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.581, + 0.267, + 0.635, + 0.277 + ], + "angle": 0, + "content": "d LF Channels" + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.265, + 0.663, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.665, + 0.267, + 0.747, + 0.277 + ], + "angle": 0, + "content": "Sample Combinations" + }, + { + "type": "image", + "bbox": [ + 0.756, + 0.265, + 0.777, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.78, + 0.267, + 0.888, + 0.277 + ], + "angle": 0, + "content": "Randomly Sample Subset(s)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.288, + 0.893, + 0.331 + ], + "angle": 0, + "content": "Figure 2. Pipeline of PartialFace. DCT turns face images into the frequency domain, where low-frequency channels are first pruned to remove the human perception. A small subset of channels is selected and permuted at random according to pre-specified combinations \\(\\{\\mathbf{S},\\mathbf{P}\\}\\), or ranks. The model is trained and inferred from random subsets to address the equilibrium between accuracy and privacy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.356, + 0.468, + 0.446 + ], + "angle": 0, + "content": "compact representations by mapping discriminative components into subspaces [4, 16, 27], or anonymize the images by clustering their features [12]. These methods face a common bottleneck of task utility: As the techniques they employ essentially distort the original images, their protection often impairs recognition accuracy." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.457, + 0.376, + 0.473 + ], + "angle": 0, + "content": "2.3. Learning in the frequency domain" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.48, + 0.47, + 0.707 + ], + "angle": 0, + "content": "Converting spatial or temporal data into the frequency domain provides a powerful way to extract interesting signals. For instance, the Fourier-based discrete cosine transform [5] is used by the JPEG standard [37] to enable image compression. Researches in deep learning [9, 45] suggest models trained on images' frequency components can perform as well as trained on the original images. Advance [39] further reveals humans and models perceive low- and high-frequency components differently. In the realm of PPFR, three recent methods [15, 26, 42] are closely related to ours as we all conceal visual information by exploiting the split in human and model perceptions. However, these methods bear inadequacy in defending recovery, according to our previous discussion of channel redundancy and later testified in experiments." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.721, + 0.212, + 0.737 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.468, + 0.822 + ], + "angle": 0, + "content": "This section discusses the motivation and technical details behind PartialFace. PartialFace is named after its key protection mechanism, where the model only exploits face images' partial frequency components to reduce information exposure. Figure 2 describes its framework." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.187, + 0.846 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Recall our privacy goals are to conceal the face images' visual information and to prevent recovery attacks on them. They respectively target the adversarial capability of hu" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.356, + 0.892, + 0.401 + ], + "angle": 0, + "content": "mans and models. We naturally concretize them into two technical aims, on how to eliminate human perception, and, on how to reduce exploitable information for attack models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.402, + 0.892, + 0.583 + ], + "angle": 0, + "content": "To eliminate human perception, we leverage the finding that models' utility can be maintained almost in full on the images' high-frequency channels [39]. Contrarily, humans mostly perceive the images' low-frequency channels, as only they carry signals of conspicuous amplitude for human eyes to discern. Whereby spatial-frequency transforms, these channels can be easily located and pruned from raw images. We concretely opt for DCT as our transform as it facilitates the calculation of energy, to serve as the quantification for human perceivable information. Experimentally, we can prune a very small portion of channels to eliminate \\(95\\%\\) of total energy, hence satisfying our aim." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.825 + ], + "angle": 0, + "content": "Reducing the attacker's exploitable information requires further pruning of high-frequency channels, as previously discussed. However, it is equally crucial to maintain the recognition model's accuracy, which presents a seeming dilemma, as the training features utilizable by recognition and attack models are tightly interwoven in these channels. We offer a viable way as our major contribution: We notice different channel subsets each carrying certain local facial features. Hence, we feed the model with a random subset from each face image, with the hope to let the model learn the entire face's impression from different images' complementary local feature partitions. This approach is proved feasible by recent theoretical studies [51] and demonstrated by our experiments. Therefore, information exposure is minimized as only each image's chosen subset is exposed, and the model still performs surprisingly well." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Despite being well justified by theory, we find sampling channels under complete randomness could under-perform in actual training due to two technical limitations: the inadequacy in training samples and the biased sampling within mini-batches. We propose two targeted fixes to reconcile" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19675" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.09, + 0.468, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.18, + 0.47, + 0.249 + ], + "angle": 0, + "content": "Figure 3. The DCT process. The produced (d) frequency channels keep the spatial structure to (a) the original image, though only low-frequency channels are discernible bu humans. We use (c) 2D grids to describe the frequency spectrum. Each cell in the grid represents one frequency channel of \\( H \\times W \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.277, + 0.469, + 0.322 + ], + "angle": 0, + "content": "the constraints, by augmenting samples and seeking a moderate level of randomness. We find the modified approach satisfactorily addresses the privacy-accuracy equilibrium." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.335, + 0.321, + 0.349 + ], + "angle": 0, + "content": "3.2. Conceal visual information" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.359, + 0.469, + 0.464 + ], + "angle": 0, + "content": "We first set up some basic notions: \\(\\langle X, y \\rangle\\) denotes a data sample of a face image and its corresponding label. \\(x\\) denotes the frequency composition of \\(X\\) and \\(x_i\\) denotes its individual frequency channels. \\(f(\\cdot; \\theta)\\) denotes the recognition model parameterized by \\(\\theta\\). \\(l(\\cdot, \\cdot)\\) denotes a generic loss function (e.g., ArcFace). \\(\\mathcal{T}(\\cdot)\\) denotes the discrete cosine transform and \\(\\mathcal{T}^{-1}(\\cdot)\\) denotes its inverse transform." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.469, + 0.542 + ], + "angle": 0, + "content": "To conceal visual information, recall humans and models mainly perceive low- and high-frequency components, respectively. Therefore, we need to find a frequency decomposition of \\( X = \\{\\mathbf{x}_l, \\mathbf{x}_h\\} \\), where \\( \\mathbf{x}_l, \\mathbf{x}_h \\) are the respective low- and high-frequency channels, then prune \\( \\mathbf{x}_l \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.542, + 0.469, + 0.753 + ], + "angle": 0, + "content": "We presume \\( X \\) is with the shape of \\( (H, W) \\). We employ DCT to transform \\( X \\)'s spatial channels into a frequency spectrum. While an RGB image typically has 3 spatial channels, we pick one for simplicity. We perform an 8-fold up-sampling ahead to turn \\( X \\) into \\( (8H, 8W) \\). As DCT later divides \\( H \\) and \\( W \\) by 8, this makes sure the resulting frequency channels can be fed into the model as usual. Figure 3 illustrates the process of DCT, where \\( \\mathbf{x} = \\mathcal{T}(X) \\). Concretely, \\( X \\) is divided into (8, 8)-pixel blocks. DCT turns each block into a 1D array of 64 frequency coefficients and reorganizes all coefficients from the same frequency across blocks into an \\( (H, W) \\) frequency channel (there are 64 of them), that is spatially correlated to the original \\( X \\). As a result, \\( X \\) is turned into \\( \\mathbf{x} \\) of \\( (64, H, W) \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.755, + 0.469, + 0.845 + ], + "angle": 0, + "content": "We then decouple \\(\\mathbf{x}\\) into \\(\\{\\mathbf{x}_l, \\mathbf{x}_h\\}\\). Notice that human-perceivable low-frequency channels should meanwhile be those with higher amplitude, as humans preferentially identify signals with conspicuous value changes. We measure a channel's amplitude by its channel energy \\(e(\\cdot)\\), which is the mean of amplitudes of all its elements:" + }, + { + "type": "equation", + "bbox": [ + 0.173, + 0.861, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\ne (x) = \\frac {1}{H W} \\sum_ {i = 0} ^ {H - 1} \\sum_ {j = 0} ^ {W - 1} | x ^ {i, j} |. \\tag {1}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.091, + 0.882, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.237, + 0.892, + 0.293 + ], + "angle": 0, + "content": "Figure 4. The visual appearance and recovery of an example image of (a) after pruning, (b) a fixed subset, and (c) a random subset. This shows protection is enhanced by removing human perception, reducing the number of channels, and randomness, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.32, + 0.892, + 0.456 + ], + "angle": 0, + "content": "We choose \\(\\sigma = 10\\) highest-energy channels as \\(\\mathbf{x}_l\\) to be pruned and the rest as \\(\\mathbf{x}_h\\) to be available to models. We experimentally find \\(\\sum_{x\\in \\mathbf{x}_l}e(x)\\geq 0.95\\sum_{x\\in \\mathbf{x}}e(x)\\), and a model trained with \\(\\arg \\min_{\\theta}l(f(\\mathbf{x}_h,\\theta),y)\\) obtain close accuracy to one trained with \\(\\arg \\min_{\\theta}l(f(\\mathbf{x},\\theta),y)\\). For privacy, example of a channel-pruned image in Fig. 4(a) show that most visual information is concealed. While its recovery is still carried out quite successfully, we are to address the issue in the following." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.468, + 0.702, + 0.484 + ], + "angle": 0, + "content": "3.3. Impede easy recovery" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.892, + 0.627 + ], + "angle": 0, + "content": "To elucidate the seeming dilemma between reducing model-available channels and retaining high recognition accuracy, we first introduce an intuitive protection, referred to as the vanilla method. It trains models on a fixed small subset of channels straightforwardly: Concretely for every \\( X \\), the model pick \\( s < d \\) channels \\( \\mathbf{x}_s = (x_{a_1},\\dots,x_{a_s}) \\) from its high-frequency \\( \\mathbf{x}_h = (x_1,\\dots,x_d) \\), where \\( a_1 < a_2 < \\dots < a_s \\) are fixed indices. We benchmark the trained model on IJB-B/C with \\( s = 9,18,36 \\) and \\( d = 54 \\), and verify its privacy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.839 + ], + "angle": 0, + "content": "The model indeed effectively prevents recovery, as in Fig. 4(b) its recovered image is very blurred. However, the benchmark in Fig. 5(a-b) suggests its accuracy dropped by at most \\(9\\%\\). To find out why is the model's performance impaired, we inspect its attention via Grad-CAM [34]. Results are exemplified in Fig. 5(c-d), which we note show similar patterns among different face images. We derive two observations: (1) Unlike high-utility models that typically have attention to the full face, this model only gains attention to certain local features, which suggests some vital face-describing information is missing in \\(\\mathbf{x}_s\\); (2) By training vanilla models on different \\(\\mathbf{x}_s\\), we find it can acquire distinct information from different channels, suggesting its attention is correlated to the specific choices of \\(\\mathbf{x}_s\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The first observation suggests the cause of the accuracy downgrade. Meanwhile, the second pursues us to consider a viable bypass: We can gather complementary local features from different images and initiate mixed training, to let the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19676" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.09, + 0.188, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.19, + 0.09, + 0.278, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.288, + 0.091, + 0.367, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.377, + 0.091, + 0.455, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.17, + 0.47, + 0.253 + ], + "angle": 0, + "content": "Figure 5. The privacy and accuracy dilemma. (a-b) The vanilla model trained on fixed channels under-performs on IJB-B/C (orange), compared to the unprotected baseline (blue) and PartialFace (green). (c-d) The model gains local attention on foreheads and cheeks, suggesting missing face-describing information. The attention varies by the specific choice of \\(\\mathbf{x}_s\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.279, + 0.468, + 0.355 + ], + "angle": 0, + "content": "model learn a holistic impression of the entirety while keeping the individual information exposure minimized. Our idea is corroborated by [51], which proves in time-series, training models on random frequency components can preserve more information compared to training on fixed ones." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.356, + 0.468, + 0.461 + ], + "angle": 0, + "content": "We concrete our theory into a randomized strategy, by advocating training and inferring the recognition model on image-wise randomly chosen channels. Formally, we construct matrix \\( S \\in \\{0,1\\}^{d \\times s} \\), with \\( s_{ij} = 1 \\) if \\( i = a_j \\) and \\( s_{ij} = 0 \\) if otherwise. We also construct permutation matrix \\( P \\in \\{0,1\\}^{s \\times s} \\). For each \\( X \\), we draw \\( (a_1, \\ldots, a_s) \\) (therefore \\( S \\)) and \\( P \\) uniformly at random, and calculate" + }, + { + "type": "equation", + "bbox": [ + 0.217, + 0.479, + 0.469, + 0.495 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {s} = \\mathbf {x} _ {h} \\cdot S \\cdot P. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.469, + 0.701 + ], + "angle": 0, + "content": "Here, \\( S \\) randomly pick \\( s \\) channels out of \\( \\mathbf{x}_h \\), then their order is permuted by \\( P \\). We introduce \\( P \\) to further impede recovery, as later discussed in Sec. 3.5. The model is trained in the same way as standard FR using \\( \\langle \\mathbf{x}_s, y \\rangle \\). However, it does not require to know the sample-wise specific \\( \\{S, P\\} \\), which is favorable for privacy. The approach sounds a bit counter-intuitive since receiving random inputs seems to mess with the model's understanding. However, recall that the DCT frequency channels are spatially correlated to \\( X \\) and each other. The randomness only pertains to the frequency spectrum while the face's structural information is preserved and unaltered. The model, therefore, can associate different \\( \\mathbf{x}_s \\) to the same \\( X \\) quite naturally." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.711, + 0.351, + 0.726 + ], + "angle": 0, + "content": "3.4. Reconcile technical constraints" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Equation (2) distills our core idea to sampling \\(\\mathbf{x}_s\\) at complete random. However, for practical training, there need to further reconcile two technical constraints to achieve satisfying model performance: First to note that \\(\\langle \\mathbf{x}_s, y \\rangle\\) are more varied in feature representations than the unprotected \\(\\langle X, y \\rangle\\), owing to the randomized frequency. It hence could plausibly take the model with more training samples and a longer training time to approach a well-generalized convergence. Second, ideally, channels at random should be sampled with equal probability to ensure balanced learning of different local features. However, when the training data" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "is partitioned into small mini-batches, sampling is often less unbiased batch-wise so the occurrence of different channel combinations may vary greatly, which we find could undermine the training stability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.153, + 0.892, + 0.288 + ], + "angle": 0, + "content": "Targeting the constraints, we slightly adjust our established approach in two ways. We first augment the training dataset by picking multiple \\(\\mathbf{x}_s\\) each time from a face image \\(X\\): From \\(X\\) we sample \\(\\{\\mathbf{x}_s^1,\\ldots ,\\mathbf{x}_s^r\\}\\), where \\(r\\) determines the degree of augmentation. Each \\(\\mathbf{x}_s^i\\) is independently drawn and appended to the training dataset as individual training samples. The dataset is then fully shuffled so that \\(\\mathbf{x}_s^i\\) corresponding to the same face image cannot be easily associated." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.893, + 0.591 + ], + "angle": 0, + "content": "We also control the randomness to a moderate level by specifying the possible combinations of \\( S, P \\) in advance. Concretely, we opt for choosing one \\( S, P \\) from \\( \\mathbf{S} = \\{S_1, \\dots, S_m\\} \\) and \\( \\mathbf{P} = \\{P_1, \\dots, P_n\\} \\) respectively, where \\( \\mathbf{S}, \\mathbf{P} \\) are determined by the service provider. We specifically require \\( \\{S_1, \\dots, S_n\\} \\) to be a non-overlapping partition of channels from \\( \\mathbf{x}_h \\) (i.e., divide \\( \\mathbf{x}_h \\) into equal-length subsets) to maximize the use of \\( \\mathbf{x}_h \\) and reduce model bias. Therefore, each \\( \\mathbf{x}_s^i \\) is picked from one of \\( m \\times n \\) fixed combinations of channels, called ranks. This allows us to facilitate the training and overcome sampling biases. The service provider shares \\( \\{\\mathbf{S}, \\mathbf{P}\\} \\) with all local devices, so the latter can generate their query \\( \\mathbf{x}_s \\) accordingly. During inference, the model is expected to provide consistent results of the same query \\( X \\) regardless of the choice of rank, since it learned about a mapping from local features to the face's entirety. We later testify to it in Sec. 4.3. Meanwhile, the model is still unaware of the sample-wise specific choice of \\( \\{S, P\\} \\) as the recognition relies on nothing else but \\( \\mathbf{x}_s \\) alone. Hence privacy is maintained." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.592, + 0.892, + 0.699 + ], + "angle": 0, + "content": "To conclude, we present PartialFace that train and infer the recognition model with \\(\\arg \\min_{\\theta} l(f(\\mathbf{x}_s^i, \\theta), y)\\), where \\(X = \\{\\mathbf{x}_l, \\mathbf{x}_h\\}\\) and \\(\\mathbf{x}_s^i = \\mathbf{x}_h \\cdot S \\cdot P\\) in random, parameterized by \\(\\{\\mathbf{S}, \\mathbf{P}\\}\\) and \\((\\sigma, s, r, m, n)\\). Later analyses in Secs. 4.2 and 4.3 show PartialFace overcomes the drawback of the vanilla method, plus outperforms most prior arts, to achieve satisfactory recognition accuracy." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.71, + 0.803, + 0.726 + ], + "angle": 0, + "content": "3.5. Enhance privacy with randomness" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.734, + 0.892, + 0.809 + ], + "angle": 0, + "content": "The benefit of randomness is multi-fold. We have discussed it for now on helping address the accuracy and privacy balance and enhance recognition performance. In retrospect, we briefly elaborate on how randomness further safeguards privacy to a large extent." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Recall we remove visual information by pruning \\(\\mathbf{x}_l\\) and impede recovery by choosing a subset of \\(\\mathbf{x}_s\\). After that, randomness further obstructs recovery: To impose recovery, the attacker exploits not only the channels' information but also their relative orders and positions in the frequency spectrum. We introduce \\(P\\) to distort the order of channels to" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19677" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "this end. As the recognition model does not require samplewise \\(\\{S,P\\}\\), they won't be exposed to the attacker. Figure 4(c) shows the improvement against recovery if the attacker doesn't know the specific choice of subsets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.167, + 0.21, + 0.184 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.192, + 0.281, + 0.209 + ], + "angle": 0, + "content": "4.1. Experimental settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.215, + 0.471, + 0.412 + ], + "angle": 0, + "content": "We compare PartialFace with the unprotected baseline and prior PPFR methods on three criteria: recognition performance, privacy protection of visual information, and that against recovery attack. We further study the computation and cost of PartialFace. We mainly employ an IR-50 [11] trained on the MS1Mv2 [10] dataset as our FR model, while also using a smaller combination of IR-18 and the BUPT [40] dataset on some resource-consuming experiments. We set \\((\\sigma, s, r, m, n) = (10, 9, 18, 6, 6)\\) and use fixed \\(\\{\\mathbf{S}, \\mathbf{P}\\}\\), if not else specified. Benchmarks are carried out on 5 widely used, regular-size datasets, LFW [13], CFP-FP [35], AgeDB [31], CPLFW [49] and CALFW [50], and 2 large-scale datasets, IJB-B [43] and IJB-C [23]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.422, + 0.399, + 0.437 + ], + "angle": 0, + "content": "4.2. Benchmarks on recognition accuracy" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.47, + 0.732 + ], + "angle": 0, + "content": "Compared methods. We compare PartialFace with 2 unprotected baselines, 4 perturbation-based PPFR methods, and 3 methods base on the frequency domain that share close relation to us. Results are summarized in Tab. 1. Here, (1) ArcFace [6] denotes the unprotected SOTA trained directly on RGB images; (2) ArcFace-FD [45] is the ArcFace trained on the image's all frequency channels; (3) PEEP [3] is a differential-privacy-based method with a privacy budget \\(\\epsilon = 5\\); (4) Cloak [27] perturbs and compresses its input feature space. Its accuracy-privacy trade-off parameter is set to 100; (5) InstaHide [14] mixes up \\(k = 2\\) images and performs a distributed encryption; (6) CPGAN [36] generates compressed protected representation by a joint effort of GAN and differential privacy; (7) PPFR-FD1 [42] adopts a channel-wise shuffle-and-mix strategy in the frequency domain; (8) DCTDP [15] perturbs the frequency components by a noise disturbance mask with learnable privacy budget, where we set \\(\\epsilon = 1\\); (9) DuetFace [26] is a two-party framework that employs channel splitting and attention transfer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.47, + 0.853 + ], + "angle": 0, + "content": "Performance. Results are reported on LFW, CFP-FP, AgeDB, CPLFW, and CALFW by accuracy, and on IJB-B and IJB-C by TPR@FPR(1e-4). Table 1 shows PartialFace achieves close performance to the unprotected baseline, with a small accuracy gap of \\(\\leq 0.8\\%\\). In comparison, perturbation-based methods all generalize unsatisfactorily on large-scale benchmarks. PartialFace outperforms all PPFR prior arts but DuetFace. While DuetFace achieves" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.863, + 0.469, + 0.901 + ], + "angle": 0, + "content": "1The results of PPFR-FD on IJB-B is unattainable due its non-disclosure of source code. The rest is quoted from its paper [42]. Please note its experimental condition may have slight inconsistency with ours." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.089, + 0.883, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.192, + 0.892, + 0.234 + ], + "angle": 0, + "content": "Figure 6. Visualization of model attention via Grad-CAM. (a) PartialFace (1st row) compared with vanilla models (2nd row) on each of 6 different ranks. (b) Integrated attention of all ranks." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.26, + 0.892, + 0.306 + ], + "angle": 0, + "content": "slightly higher accuracy, its protection is inferior to ours as it only covers the inference phase and can be easily nullified by recovery attacks, later see Secs. 4.4 and 4.5." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.317, + 0.816, + 0.333 + ], + "angle": 0, + "content": "4.3. Comparison with the vanilla method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.341, + 0.892, + 0.763 + ], + "angle": 0, + "content": "We elaborate that randomized PartialFace outperforms the vanilla method that fixes channels in not only recognition accuracy but also robustness. As PartialFace employs data augmentation, for a fair comparison regarding the volume of training data, we consider two experimental settings: the standard PartialFace and one without augmentation \\((r = 1)\\). We also set \\(n = 1\\) to rule out permutation: \\(P\\) is introduced for privacy and is out of our interest here. There are therefore \\(m \\times n = 6\\) combinations of channels, or ranks. As channels from different ranks carry distinct information that may affect the performance, we train one vanilla model on each rank and average their test accuracy, with the range marked in parentheses. Though PartialFace is able to infer from arbitrary rank, we evaluate its robustness by inferring from each fixed rank separately. The model is robust if it performs on different ranks consistently (small range). Results are reported on IJB-B/C by TPR@FPR(1e-4) in Tab. 2. Performance. PartialFace achieves an average accuracy gain of \\(7.53\\%\\) and \\(7.75\\%\\) on IJB-B/C, respectively, compared to the vanilla. The performance is close to the unprotected baseline, showing that the privacy-accuracy trade-off of PartialFace is highly efficient. Even PartialFace without augmentation outperforms the vanilla for about \\(3\\%\\). We further note: (1) The range shows PartialFace is more robust than the vanilla under different \\(S_{i}\\). (2) PartialFace outperforms the vanilla for all individual \\(S_{i}\\). This suggests that randomness empowers PartialFace with the knowledge of the entirety instead of that of certain informative ranks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Visualization. We visualize the rank-wise attention of PartialFace and the vanilla via Grad-CAM [34], see Fig. 6(a). The attention of each vanilla model is restrained to local facial features, which indicates the inadequate learning of the entirety features. PartialFace generate accurate attention on the entire face regardless the rank. We integrated the attention across all ranks in Fig. 6(b). All vanilla models' attention combined gains attention on the entire face, which testifies to our \"learn-entropy-from-local\" theory. Also to" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19678" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.139, + 0.089, + 0.833, + 0.282 + ], + "angle": 0, + "content": "
MethodPPFRLFWCFP-FPAgeDBCPLFWCALFWIJB-BIJB-C
ArcFace [6]No99.7798.3097.8892.7796.0594.1395.60
ArcFace-FD [45]No99.7898.0498.1092.4896.0394.0895.64
PEEP [3]Yes98.4174.4787.4779.5890.065.826.02
Cloak [27]Yes98.9187.9792.6083.4392.1833.5833.82
InstaHide [14]Yes96.5383.2079.5881.0386.2461.8869.02
CPGAN [36]Yes98.8794.6196.9890.4394.7992.6794.31
PPFR-FD [42]Yes99.6895.0497.3790.7895.72/94.10
DCTDP [15]Yes99.7796.9797.7291.3796.0593.2994.43
DuetFace [26]Yes99.8297.7997.9392.3596.1093.6695.30
PartialFace (ours)Yes99.8097.6397.7992.0396.0793.6494.93
" + }, + { + "type": "table_caption", + "bbox": [ + 0.128, + 0.282, + 0.841, + 0.296 + ], + "angle": 0, + "content": "Table 1. Benchmarks on recognition accuracy. PartialFace is compared with the unprotected baselines and PPFR SOTAs." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.318, + 0.462, + 0.406 + ], + "angle": 0, + "content": "
MethodIJB-B (range)IJB-C (range)
ArcFace86.8390.35
Vanilla78.24 (-14.49/7.36)80.73 (-16.37/7.45)
PF w/o aug.81.43 (-4.19/2.88)82.81 (-4.29/2.79)
PartialFace85.77 (-1.95/1.25)88.48 (-1.71/1.18)
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.077, + 0.408, + 0.469, + 0.45 + ], + "angle": 0, + "content": "Table 2. Comparison with the vanilla method by accuracy and robustness. Experiments are conducted on IR-18 + BUPT. \"PF w/o aug.\" indicates PartialFace without augmentation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.475, + 0.469, + 0.52 + ], + "angle": 0, + "content": "note that PartialFace has similar attention across all ranks. This allows it to recognize \\( X \\) using arbitrary rank, as they produce aligned outcomes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.531, + 0.358, + 0.544 + ], + "angle": 0, + "content": "4.4. Protection of visual information" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.47, + 0.825 + ], + "angle": 0, + "content": "We investigate PartialFace's protection of privacy. We reiterate that the first privacy goal is to conceal the visual information of face images. We compare ParitalFace with 3 PPFR SOTAs using the frequency domain: PPFR-FD [42], DCTDP [15], and DuetFace [26]. These prior arts are closely related to ours since we all leverage the perceptual difference between humans and models as means of protection. However, they differ in the processing of frequency components: Both PPFR-FD and DCTDP remove the component with the highest energy (the DC component). To obfuscate the remaining components, PPFR-FD employs mix-and-shuffle and DCTDP applies a noise mechanism. DuetFace is the most related method in the pruning of low-frequency components. We note in special that they retain 36, 63, and 54 high-frequency channels, respectively, while PartialFace retains 9. We now demonstrate the methodological differences and varied number of channels result in contrasting privacy protection capacities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Figure 7 exemplifies face images processed (therefore are supposed to be protective) by each compared method. As all methods carry out protection in the frequency domain, we convert images back by padding any removed frequency components with zero and applying an inverse" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.319, + 0.88, + 0.441 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.443, + 0.892, + 0.485 + ], + "angle": 0, + "content": "Figure 7. Example face images of (a) unprotected ArcFace, (b-d) compared SOTAs, and (e) PartialFace, during both training and inference phase. PartialFace best conceals visual information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.513, + 0.892, + 0.695 + ], + "angle": 0, + "content": "transform. PartialFace, e.g., has \\( X' = \\mathcal{T}^{-1}(\\{\\mathbf{0}, \\mathbf{x}_h\\}) \\). We visualize the training and inference phases separately, as the compared methods' processing on them may vary: During inference, we argue PPFR-FD and DuetFace (Fig. 7(b)(d)) provide inadequate protection, as one can still discern the face quite clearly in their processed images. DCTDP effectively conceals visual information after obfuscating the channels with its proposed noise mask (Fig. 7(c)). However, its protection during training is impaired, as it requires access to abundant non-obfuscated components to learn the mask. DuetFace manifests a similar weakness as it relies on original images to rectify the model's attention (Fig. 7(d))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.696, + 0.892, + 0.787 + ], + "angle": 0, + "content": "PartialFace first discards most visual information by pruning \\(\\mathbf{x}_l\\). The rest is further partitioned when sampling \\(\\mathbf{x}_s\\) from \\(\\mathbf{x}_h\\). By energy, each \\(\\mathbf{x}_s\\) carries less than \\(1\\%\\) of visual information compared to the original \\(X\\). As a result, Fig. 7(e) shows PartialFace provides better protection on visual information than related SOTAs in both phases." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.801, + 0.746, + 0.817 + ], + "angle": 0, + "content": "4.5. Protection against recovery" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We here provide an in-depth analysis of how Partial-Face impedes recovery. Our primary aiming is to show how the removal of model-exploitable information and the randomness of channels contribute to the defense. Assume the recovery attacker possesses a collection of face im" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19679" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.09, + 0.207, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.181, + 0.182, + 0.191 + ], + "angle": 0, + "content": "(a) black-box" + }, + { + "type": "image", + "bbox": [ + 0.216, + 0.091, + 0.331, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.241, + 0.181, + 0.306, + 0.191 + ], + "angle": 0, + "content": "(b) white-box" + }, + { + "type": "image", + "bbox": [ + 0.342, + 0.091, + 0.455, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.341, + 0.181, + 0.457, + 0.19 + ], + "angle": 0, + "content": "(c) enhanced white-box" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.195, + 0.468, + 0.251 + ], + "angle": 0, + "content": "Figure 8. Examples of recovered face images of PartialFace under attackers with varied capabilities: (a) a black-box, (b) a white-box, and (c) an enhanced white-box attacker. PartialFace effectively prevents recovery as all images are blurry and hardly identifiable." + }, + { + "type": "image", + "bbox": [ + 0.11, + 0.266, + 0.187, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.121, + 0.329, + 0.176, + 0.338 + ], + "angle": 0, + "content": "(a) PPFR-FD" + }, + { + "type": "image", + "bbox": [ + 0.194, + 0.267, + 0.271, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.209, + 0.329, + 0.255, + 0.338 + ], + "angle": 0, + "content": "(b) DCTDP" + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.267, + 0.354, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.287, + 0.329, + 0.343, + 0.338 + ], + "angle": 0, + "content": "(c) DuetFace" + }, + { + "type": "image", + "bbox": [ + 0.36, + 0.267, + 0.437, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.381, + 0.329, + 0.416, + 0.338 + ], + "angle": 0, + "content": "(d) ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.341, + 0.468, + 0.369 + ], + "angle": 0, + "content": "Figure 9. Recovered images from (a-c) compared SOTAs and (d) PartialFace. PartialFace impedes recovery better than the rest." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.398, + 0.468, + 0.593 + ], + "angle": 0, + "content": "ages \\(\\{X\\}\\) and is aware of the protection mechanism. It can locally generate protected representations \\(X^{\\prime}\\) \\((\\mathbf{x}_h\\) in our case) from \\(X\\), then train a malicious model \\(g(\\cdot)\\) with \\(\\arg \\min_{\\delta}l^{\\prime}(g(X^{\\prime},\\delta),X)\\), with the aiming to inversely fit \\(X\\) from \\(X^{\\prime}\\). Having intercepted a recognition query, the attacker leverages \\(g(\\cdot)\\) to recover the concealed visual information. Upon the knowledge it possesses, a black-box attacker is one unknowing of necessary parameters (\\(\\{\\mathbf{S},\\mathbf{P}\\}\\) in our case), whilst a white-box attacker possesses such knowledge. We also study the capability of PPFR-FD, DCTDP, and DuetFace against the white-box attacker. We further investigate an enhanced white-box attacker, who imposes threats dedicated to the randomness of PartialFace." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.596, + 0.468, + 0.732 + ], + "angle": 0, + "content": "Black-box attacker. It is concretized as a malicious third party, uninvolved in the recognition yet eager to wiretap the transmission. For each attacker, We employ a full-scale U-Net [32] as the recovery model and train it on BUPT. Unknown of \\(\\{\\mathbf{S},\\mathbf{P}\\}\\), it must produce \\(X^{\\prime}\\) based on its own conjectured \\(\\{\\mathbf{S}^{\\prime},\\mathbf{P}^{\\prime}\\}\\), which is believably inconsistent with that applied to the recognition model. Thus produced \\(X^{\\prime}\\) are invalid samples and training \\(g(\\cdot)\\) on them will nullify the recovery, as shown in Fig. 8(a)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.468, + 0.868 + ], + "angle": 0, + "content": "White-box attacker. The candidate combinations \\(\\{\\mathbf{S},\\mathbf{P}\\}\\) is known by any party participates in the recognition, e.g., an honest-but-curious server. Such an attacker can generate \\(X^{\\prime}\\) correctly. However, receiving a query \\(\\mathbf{x}_s\\), the attacker is unknowing of its channels' position and order, since the specific \\(\\{S,P\\}\\) doesn't come with \\(\\mathbf{x}_s\\). The missing information is vital to recovery. Consequently, the attack is obstructed by \\(\\mathbf{x}_s\\) 's randomness in Fig. 8(b): The recovered image is blurry and hardly identifiable." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We plus compare with PPFR-FD, DCTDP and Duet-Face under the white-box settings. Among them, Duet" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.089, + 0.877, + 0.179 + ], + "angle": 0, + "content": "
MethodSSIM (↓)PSNR (↓)Accuracy (↓)
PPFR-FD0.71315.6683.73
DCTDP0.68715.4279.60
DuetFace0.86619.8896.52
PartialFace0.59113.7065.35
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.18, + 0.892, + 0.22 + ], + "angle": 0, + "content": "Table 3. Quantitative analyses of the recovery quality. Lower SSIM, PSNR and accuracy suggest better protection. Here, we remind the accuracy of verification is lower bounded by 50.00." + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.235, + 0.611, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.235, + 0.693, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.235, + 0.776, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.784, + 0.235, + 0.859, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.299, + 0.89, + 0.327 + ], + "angle": 0, + "content": "Figure 10. Recovered images from extracted identity templates, that are blurry and can hardly be inferred by humans or models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.353, + 0.892, + 0.473 + ], + "angle": 0, + "content": "Face shows almost no resistance to recovery (Fig. 9(c)). PPFR-FD and DCTDP provide inadequate protection, as images recovered from them (Fig. 9(a-b)) are blurred yet still clearly identifiable. The protection is impaired as their processed images retain most high-frequency components, and the excessive perceivable information is learned by the recovery model. In comparison, PartialFace (Fig. 9(d)) offers significantly outperformed protection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.892, + 0.624 + ], + "angle": 0, + "content": "Enhanced white-box attacker. A resource-unbounded attacker may brute-forcibly break the randomness of Partial-Face leveraging a more sophisticated attack: it trains a series of attack models, one for each candidate \\(\\{S,P\\}\\). Receiving \\(\\mathbf{x}_s\\), the attacker feeds it into every model to try every combination of \\(\\{S,P\\}\\), until one produces the best recovery. The vague face images in Fig. 8(c) imply the attempted recovery is unsuccessful, even if the attacker finds the correct \\(\\{S,P\\}\\). This is attributed to the reduction of model-exploitable channels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.892, + 0.776 + ], + "angle": 0, + "content": "Quantitative comparison. To quantitatively assess the recovery quality, we measure the average structural similarity index (SSIM) and peak signal-to-noise ratio (PSNR) of the recovered images. Additionally, to study if the attacker can exploit its outcome for recognition proposes, we feed the images into a pre-trained model and measure verification accuracy. Lower SSIM, PSNR, and recognition accuracy suggest deficient recovery, thus indicating a higher level of protection. The results in Tab. 3 suggest PartialFace outperforms its competitors in all three evaluated metrics." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.866, + 0.803 + ], + "angle": 0, + "content": "4.6. Protection against recovery from templates" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.9 + ], + "angle": 0, + "content": "By the principle of FR, all \\(\\mathbf{x}_s\\) of face image \\(X\\) are later extracted to very similar identity templates, so the recognition on them produces aligned results. Here, one would arise concern that recovery can also be carried out on the extracted templates, which theoretically contain the faces' full identity information, to realize better inversion of im" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19680" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.09, + 0.47, + 0.265 + ], + "angle": 0, + "content": "
SettingsLFWCFP-FPAgeDBCPLFWCALFW
ArcFace99.3892.3194.6589.4194.78
r3699.5191.2794.4488.9394.81
698.6986.7990.6584.5092.67
m399.4291.6893.9588.7094.69
999.3290.7493.5687.3094.36
n199.3791.5594.2588.7394.70
1299.3589.2193.1787.1994.26
Default99.3891.2093.7288.1194.42
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.266, + 0.47, + 0.307 + ], + "angle": 0, + "content": "Table 4. Ablation study on combinations of hyperparameters. Experiments are carried out on IR-18 + BUPT. When changing one of them, we keep the rest to default values, i.e., \\((r,m,n) = (18,6,6)\\)." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.318, + 0.466, + 0.378 + ], + "angle": 0, + "content": "
SettingsLFWCFP-FPAgeDBCPLFW
CosFace99.5392.8995.1589.52
PartialFace99.3589.5493.9787.90
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.379, + 0.468, + 0.419 + ], + "angle": 0, + "content": "Table 5. Compatibility of PartialFace. FR models are trained using CosFace on IR-18 + BUPT. Combining PartialFace with CosFace also demonstrates high utility, compared to its baseline." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.444, + 0.468, + 0.472 + ], + "angle": 0, + "content": "ages. We demonstrate that such a proposed attack is also ineffective to PartialFace." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.469, + 0.564 + ], + "angle": 0, + "content": "Although there could be dedicated attacks on templates, in practice, high-quality recovery from them is difficult as templates are far more compact representations than images and channel subsets. In Fig. 10, the recovered images are highly blurred, and can hardly be inferred by humans or models, hence won't impose an effective threat." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.574, + 0.227, + 0.589 + ], + "angle": 0, + "content": "4.7. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.469, + 0.747 + ], + "angle": 0, + "content": "PartialFace is parameterized by \\((\\sigma, s, r, m, n)\\). Among them, we note \\(\\sigma\\) is chosen according to channel energy, and \\(s\\) is determined by \\((\\sigma, m)\\). Table 4 analyzes the choice of the remaining parameters. Results show augmentation \\((r)\\) enhances the model's performance, at the cost of taking longer time to train. \\(m\\) affects the performance mainly by its influence on \\(s\\), as larger \\(m\\) leading to fewer channels in each \\(\\mathbf{x}_s\\). We introduce \\(P\\) solely for privacy purposes. Results on \\(n\\) indicate a trade-off between accuracy and privacy. Generally, PartialFace is robust to the choice of parameters." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.342, + 0.773 + ], + "angle": 0, + "content": "4.8. Complexity and compatibility" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.84 + ], + "angle": 0, + "content": "Though PartialFace is proposed by studying the model's behavior, privacy protection is solely realized by processing the face images. The decoupling with model architecture and training tactics benefits resources and compatibility." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.9 + ], + "angle": 0, + "content": "PartialFace is resource-efficient. Compared to the unprotected baseline, PartialFace doesn't increment model size as they share identical model architectures. Training does take more \\((r)\\) time and storage due to augmentation, while we" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "argue it is acceptable for the service provider. The crucial inference time remains the same as the baseline, as DCT and sampling \\(\\mathbf{x}_s\\) only increase negligible computation costs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.892, + 0.258 + ], + "angle": 0, + "content": "PartialFace is well compatible. The decoupling of preprocessing and training also allows PartialFace to serve as a convenient plug-in: PartialFace can be integrated with SOTA FR methods to enjoy enhanced privacy protection. Specifically, we demonstrate the recognition accuracy on CosFace [38], a major competitor of ArcFace, in Tab. 5. Combining PartialFace with CosFace also results in high utility, as compared to its baseline." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.27, + 0.618, + 0.285 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.295, + 0.892, + 0.446 + ], + "angle": 0, + "content": "This paper presents an in-depth study of the privacy protection of face images. Based on the observations on model perception and training behavior, we present two methodological advances, pruning low-frequency components and using randomly selected channels, to address the privacy goal of concealing visual information and impeding recovery. We distill our findings into a novel privacy-preserving face recognition method, PartialFace. 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This paper presents an in-depth study of the privacy protection of face images' visual information and against recovery. Drawing on the perceptual disparity between humans and models, we propose to conceal visual information by pruning human-perceivable low-frequency components. For impeding recovery, we first elucidate the seeming paradox between reducing model-exploitable information and retaining high recognition accuracy. Based on recent theoretical insights and our observation on model attention, we propose a solution to the dilemma, by advocating for the training and inference of recognition models on randomly selected frequency components. We distill our findings into a novel privacy-preserving face recognition method, PartialFace. Extensive experiments demonstrate that PartialFace effectively balances privacy protection goals and recognition accuracy. Code is available at: https://github.com/Tencent/TFace. + +# 1. Introduction + +Face recognition (FR) is a landmark biometric technique that enables a person to be identified or verified by face. It has seen remarkable methodological breakthroughs and rising adoptions in recent years. Currently, considerable applications of face recognition are carried out online to bypass local resource constraints and to attain high accuracy [19]: Face images are collected by local devices such as cell phones or webcams, then outsourced to a service provider, that uses large convolutional neural networks (CNN) to extract the faces' identity-representative templates and matches them with records in its database. + +![](images/ab0f35fb5afe1dbd1a1b9f0d4eaafbf36474695ada0837df775f241a07693548.jpg) +Figure 1. Paradigm comparison among other frequency-based methodologies and PartialFace. (a) Pruning low-frequency channels can conceal visual information but stop no recovery. (b) A vanilla method that uses fixed channel subsets to impede recovery suffers downgraded accuracy. (c) PartialFace addresses the dilemma by training and inferring from random channels. + +During the process, the original face images are often considered sensitive data under regulatory demands that are unwise to share without privacy protection. This fosters the studies of privacy-preserving face recognition (PPFR), where cryptographic [7,8,14,17,21,33,44,47] and perturbation-based [3, 12, 18, 28-30, 46, 48] measures are taken to prevent face images from unauthorized access of, e.g., wiretapping third parties. Face images are converted to protective representations that their visual information is both concealed and cannot be easily recovered [2]. + +This paper advocates a novel PPFR scheme, to learn face images from random combinations of their partial frequency components. Our proposed PartialFace can protect face images' visual information and prevent recovery while maintaining the high distinguishability of their identities. + +We start with the disparity in how humans and models perceive images. Recent image classification studies suggest that models' predictions are determined mainly by the images' high-frequency components [39, 45], which carry negligible visual information and are barely picked up by humans. We extend the theory to face recognition from a + +privacy perspective, to train and infer the model on pruned frequency inputs: As depicted in Fig. 1(a), we decouple the face images' frequency compositions via discrete cosine transform (DCT), which breakdown every spatial domain into a certain number of (typically 64) constituent bands, i.e., frequency channels. We prune the human-perceivable low-frequency channels and exploit the remaining. We find the processed face images become almost visually indiscernible, and the model still works accurately. + +Pruning notably conceals visual information. However, to what degree can it impede recovery? We define recovery as the general attempts to reveal the faces' visual appearances from shared protected features using trained attack models. Notice we may prune very few (say, about 10) channels, if according to human perception. At the same time, the remaining high-frequency channels being shared, hence exposed, are quite numerous and carry a wealth of model-perceivable features. While the information abundance can benefit a recognition model, it is also exploitable by a model carrying out attacks, as both may share similar perceptions. Therefore, as we later experimentally show, the attacker can recover visual features from high-frequency channels with ease in the absence of additional safeguards, rendering privacy protection useless. + +An intuitive tactic to reinstate protection is to reduce the attacker's exploitable features by training on a small portion of fixed channels, as shown in Fig. 1(b). However, we find the reduction also severely impairs the accuracy of trained recognition models. Evidence on the models' attention, as later shown, attributes their utility downgrade to being incapable of learning a complete set of facial features, as vital channels describing some local features may be pruned. + +Training on subsets of channels hence seems contradictory to the privacy-accuracy equilibrium. Fortunately, we can offer a reconciliation getting inspired by a recent timeseries study [51]. It proves under mild conditions, models trained on random frequency components can preserve more entirety's information than on fixed ones, plausibly by alternately learning from complementary features. We hence propose a novel address to the equilibrium based on its theoretical findings and our observation on model attention: For any incoming face image, we arbitrarily pick a small subset of its high-frequency channels. Therefore, our recognition model is let trained and inferred from image-wise random chosen channels, illustrated in Fig. 1(c). + +We further show that randomness can be adjusted to a moderate level, by choosing channels from pre-specified combinations and perturbations called ranks, to keep privacy protection while reconciling technical constraints to ease training. At first glance, our randomized approach may seem counter-intuitive as it is common wisdom that models require consistent forms of inputs to learn stably. However, since DCT produces spatially correlated frequency channels + +that preserve the face's structural information, as later illustrated in Fig. 3, it turns out the model generalizes quite naturally. Experimental analyses show our PartialFace well balances privacy and accuracy. + +The contributions of our paper are three-fold: + +1. We present an in-depth study of the privacy protection of face images, regarding the privacy goals of concealing visual information and impeding recovery. +2. We propose two methodological advances to fulfill the privacy goals, pruning low-frequency components and using randomly selected channels, based on the observation of model perception and learning behavior. +3. We distill our findings into a novel PPFR method, PartialFace. We demonstrate by extensive experiments that our proposed method effectively safeguards privacy and maintains satisfactory recognition accuracy. + +# 2. Related work + +# 2.1. Face recognition + +The current method of choice for face recognition is CNN-based embedding. The service provider trains a CNN with a softmax-based loss to map face images into one-dimensional embedding features which achieve large interidentity and small intra-identity discrepancies. While the state-of-the-art (SOTA) FR methods [6, 20, 38] achieve impressive task utility in real-world applications, their attention to privacy protection could be deficient. + +# 2.2. Privacy-preserving face recognition + +The past decade witnessed significant advances in privacy-preserving face recognition [24,25,41]. We roughly categorize the related arts into two branches: + +Cryptographic methods perform recognition on encrypted images, or by executing dedicated security protocols. Many pioneering works fall under the category of homomorphic encryption (HE) [8,14,33] or secure multiparty computation (MPC) [21, 44, 47], to securely carry out necessary computations such as model's feature extraction. Some methods also employ various crypto-primitives including one-time-pad [7], matrix encryption [17], and functional encryption [1]. The major pain points of these methods are generally high latency and expensive computational costs. + +Perturbation-based methods transform face images into protected representations that are difficult for unauthorized parties to discern or recover. Many methods leverage differential privacy (DP) [3, 18, 22, 48], in which face images are obfuscated by a noise mechanism. Some use autoencoders [28] or adversarial generative networks (GAN) [18, 29] to recreate visually distinct faces that maintain a constant identity. Others compress the original images into + +![](images/c060aad62d664fd1c861a46e711802f260a985a212a712fb99ea67098160c1dd.jpg) + +![](images/52ba281a90bada064160f9149dcefc64a96ce167b441101729c335793ebd21c9.jpg) +Training/Trained Model + +![](images/3e7cb37aa48efa178868182c0f5a5b3ef2ab8336f7a423f98549bc4ae491ec21.jpg) +Server +Figure 2. Pipeline of PartialFace. DCT turns face images into the frequency domain, where low-frequency channels are first pruned to remove the human perception. A small subset of channels is selected and permuted at random according to pre-specified combinations $\{\mathbf{S},\mathbf{P}\}$ , or ranks. The model is trained and inferred from random subsets to address the equilibrium between accuracy and privacy. + +![](images/c3e695b6a5b13b5c73cf1915c1c7aaeb732edee5786529842b57073e0f252087.jpg) +Client + +![](images/5786298c1d99699ae56be04ec3b85efdedf83d2a54ceb827e145350105fbae3a.jpg) +Face Image + +![](images/5916d093c29f83c57f22ce3e95c885a9ddf18491d870697c1de87b71e7ea41d1.jpg) +Recognition + +![](images/24ce2f3765079964805fbd69aae20fd93e7112d674a21748cd186f67a7378b46.jpg) +Trainin + +![](images/e3ef3357a52ac41ff5ba7b4af423d6ec825a4bca1e394dcc9a68ef17e22c47c6.jpg) +面 + +![](images/62017f6a1ddd8c07224dd6e02aac011d2fe65a1aef03c35d4531c0440f99cf5d.jpg) +d LF Channels + +![](images/4d934a41c694222ed27e034f0c627c0b27f02226ea7e9bb18fe2b37befa740ca.jpg) +Sample Combinations + +![](images/c60e5e59f6e7da39ac3b9acfb979ac8da7519049e0f1a66249c2634898956afc.jpg) +Randomly Sample Subset(s) + +compact representations by mapping discriminative components into subspaces [4, 16, 27], or anonymize the images by clustering their features [12]. These methods face a common bottleneck of task utility: As the techniques they employ essentially distort the original images, their protection often impairs recognition accuracy. + +# 2.3. Learning in the frequency domain + +Converting spatial or temporal data into the frequency domain provides a powerful way to extract interesting signals. For instance, the Fourier-based discrete cosine transform [5] is used by the JPEG standard [37] to enable image compression. Researches in deep learning [9, 45] suggest models trained on images' frequency components can perform as well as trained on the original images. Advance [39] further reveals humans and models perceive low- and high-frequency components differently. In the realm of PPFR, three recent methods [15, 26, 42] are closely related to ours as we all conceal visual information by exploiting the split in human and model perceptions. However, these methods bear inadequacy in defending recovery, according to our previous discussion of channel redundancy and later testified in experiments. + +# 3. Methodology + +This section discusses the motivation and technical details behind PartialFace. PartialFace is named after its key protection mechanism, where the model only exploits face images' partial frequency components to reduce information exposure. Figure 2 describes its framework. + +# 3.1. Overview + +Recall our privacy goals are to conceal the face images' visual information and to prevent recovery attacks on them. They respectively target the adversarial capability of hu + +mans and models. We naturally concretize them into two technical aims, on how to eliminate human perception, and, on how to reduce exploitable information for attack models. + +To eliminate human perception, we leverage the finding that models' utility can be maintained almost in full on the images' high-frequency channels [39]. Contrarily, humans mostly perceive the images' low-frequency channels, as only they carry signals of conspicuous amplitude for human eyes to discern. Whereby spatial-frequency transforms, these channels can be easily located and pruned from raw images. We concretely opt for DCT as our transform as it facilitates the calculation of energy, to serve as the quantification for human perceivable information. Experimentally, we can prune a very small portion of channels to eliminate $95\%$ of total energy, hence satisfying our aim. + +Reducing the attacker's exploitable information requires further pruning of high-frequency channels, as previously discussed. However, it is equally crucial to maintain the recognition model's accuracy, which presents a seeming dilemma, as the training features utilizable by recognition and attack models are tightly interwoven in these channels. We offer a viable way as our major contribution: We notice different channel subsets each carrying certain local facial features. Hence, we feed the model with a random subset from each face image, with the hope to let the model learn the entire face's impression from different images' complementary local feature partitions. This approach is proved feasible by recent theoretical studies [51] and demonstrated by our experiments. Therefore, information exposure is minimized as only each image's chosen subset is exposed, and the model still performs surprisingly well. + +Despite being well justified by theory, we find sampling channels under complete randomness could under-perform in actual training due to two technical limitations: the inadequacy in training samples and the biased sampling within mini-batches. We propose two targeted fixes to reconcile + +![](images/a2eabe9499f00ea53245db1238873ee5595c157f1bddd4cf2a531fbca442054d.jpg) +Figure 3. The DCT process. The produced (d) frequency channels keep the spatial structure to (a) the original image, though only low-frequency channels are discernible bu humans. We use (c) 2D grids to describe the frequency spectrum. Each cell in the grid represents one frequency channel of $H \times W$ . + +the constraints, by augmenting samples and seeking a moderate level of randomness. We find the modified approach satisfactorily addresses the privacy-accuracy equilibrium. + +# 3.2. Conceal visual information + +We first set up some basic notions: $\langle X, y \rangle$ denotes a data sample of a face image and its corresponding label. $x$ denotes the frequency composition of $X$ and $x_i$ denotes its individual frequency channels. $f(\cdot; \theta)$ denotes the recognition model parameterized by $\theta$ . $l(\cdot, \cdot)$ denotes a generic loss function (e.g., ArcFace). $\mathcal{T}(\cdot)$ denotes the discrete cosine transform and $\mathcal{T}^{-1}(\cdot)$ denotes its inverse transform. + +To conceal visual information, recall humans and models mainly perceive low- and high-frequency components, respectively. Therefore, we need to find a frequency decomposition of $X = \{\mathbf{x}_l, \mathbf{x}_h\}$ , where $\mathbf{x}_l, \mathbf{x}_h$ are the respective low- and high-frequency channels, then prune $\mathbf{x}_l$ . + +We presume $X$ is with the shape of $(H, W)$ . We employ DCT to transform $X$ 's spatial channels into a frequency spectrum. While an RGB image typically has 3 spatial channels, we pick one for simplicity. We perform an 8-fold up-sampling ahead to turn $X$ into $(8H, 8W)$ . As DCT later divides $H$ and $W$ by 8, this makes sure the resulting frequency channels can be fed into the model as usual. Figure 3 illustrates the process of DCT, where $\mathbf{x} = \mathcal{T}(X)$ . Concretely, $X$ is divided into (8, 8)-pixel blocks. DCT turns each block into a 1D array of 64 frequency coefficients and reorganizes all coefficients from the same frequency across blocks into an $(H, W)$ frequency channel (there are 64 of them), that is spatially correlated to the original $X$ . As a result, $X$ is turned into $\mathbf{x}$ of $(64, H, W)$ . + +We then decouple $\mathbf{x}$ into $\{\mathbf{x}_l, \mathbf{x}_h\}$ . Notice that human-perceivable low-frequency channels should meanwhile be those with higher amplitude, as humans preferentially identify signals with conspicuous value changes. We measure a channel's amplitude by its channel energy $e(\cdot)$ , which is the mean of amplitudes of all its elements: + +$$ +e (x) = \frac {1}{H W} \sum_ {i = 0} ^ {H - 1} \sum_ {j = 0} ^ {W - 1} | x ^ {i, j} |. \tag {1} +$$ + +![](images/44b4ceb330dc99d2c71d4df6c3e28ec9162fb3983ab0986a8ef11b133e12866a.jpg) +Figure 4. The visual appearance and recovery of an example image of (a) after pruning, (b) a fixed subset, and (c) a random subset. This shows protection is enhanced by removing human perception, reducing the number of channels, and randomness, respectively. + +We choose $\sigma = 10$ highest-energy channels as $\mathbf{x}_l$ to be pruned and the rest as $\mathbf{x}_h$ to be available to models. We experimentally find $\sum_{x\in \mathbf{x}_l}e(x)\geq 0.95\sum_{x\in \mathbf{x}}e(x)$ , and a model trained with $\arg \min_{\theta}l(f(\mathbf{x}_h,\theta),y)$ obtain close accuracy to one trained with $\arg \min_{\theta}l(f(\mathbf{x},\theta),y)$ . For privacy, example of a channel-pruned image in Fig. 4(a) show that most visual information is concealed. While its recovery is still carried out quite successfully, we are to address the issue in the following. + +# 3.3. Impede easy recovery + +To elucidate the seeming dilemma between reducing model-available channels and retaining high recognition accuracy, we first introduce an intuitive protection, referred to as the vanilla method. It trains models on a fixed small subset of channels straightforwardly: Concretely for every $X$ , the model pick $s < d$ channels $\mathbf{x}_s = (x_{a_1},\dots,x_{a_s})$ from its high-frequency $\mathbf{x}_h = (x_1,\dots,x_d)$ , where $a_1 < a_2 < \dots < a_s$ are fixed indices. We benchmark the trained model on IJB-B/C with $s = 9,18,36$ and $d = 54$ , and verify its privacy. + +The model indeed effectively prevents recovery, as in Fig. 4(b) its recovered image is very blurred. However, the benchmark in Fig. 5(a-b) suggests its accuracy dropped by at most $9\%$ . To find out why is the model's performance impaired, we inspect its attention via Grad-CAM [34]. Results are exemplified in Fig. 5(c-d), which we note show similar patterns among different face images. We derive two observations: (1) Unlike high-utility models that typically have attention to the full face, this model only gains attention to certain local features, which suggests some vital face-describing information is missing in $\mathbf{x}_s$ ; (2) By training vanilla models on different $\mathbf{x}_s$ , we find it can acquire distinct information from different channels, suggesting its attention is correlated to the specific choices of $\mathbf{x}_s$ . + +The first observation suggests the cause of the accuracy downgrade. Meanwhile, the second pursues us to consider a viable bypass: We can gather complementary local features from different images and initiate mixed training, to let the + +![](images/51f9230e1919a086e153bf2620c135a13bb7d544139c1ac5e185436130f38738.jpg) +Figure 5. The privacy and accuracy dilemma. (a-b) The vanilla model trained on fixed channels under-performs on IJB-B/C (orange), compared to the unprotected baseline (blue) and PartialFace (green). (c-d) The model gains local attention on foreheads and cheeks, suggesting missing face-describing information. The attention varies by the specific choice of $\mathbf{x}_s$ . + +![](images/3642c4c288e228dcc526ebb0b5927257f8bde6bb246a0fd22acd47852f87bf5d.jpg) + +![](images/fd1595fb6414c733c4cc01ea382720654b022e1e5b4eef574661461995eb4eda.jpg) + +![](images/2e5084efa6247027a319eb36e0b42f957c4feb1170cc2db432d6becd9682e3f5.jpg) + +model learn a holistic impression of the entirety while keeping the individual information exposure minimized. Our idea is corroborated by [51], which proves in time-series, training models on random frequency components can preserve more information compared to training on fixed ones. + +We concrete our theory into a randomized strategy, by advocating training and inferring the recognition model on image-wise randomly chosen channels. Formally, we construct matrix $S \in \{0,1\}^{d \times s}$ , with $s_{ij} = 1$ if $i = a_j$ and $s_{ij} = 0$ if otherwise. We also construct permutation matrix $P \in \{0,1\}^{s \times s}$ . For each $X$ , we draw $(a_1, \ldots, a_s)$ (therefore $S$ ) and $P$ uniformly at random, and calculate + +$$ +\mathbf {x} _ {s} = \mathbf {x} _ {h} \cdot S \cdot P. \tag {2} +$$ + +Here, $S$ randomly pick $s$ channels out of $\mathbf{x}_h$ , then their order is permuted by $P$ . We introduce $P$ to further impede recovery, as later discussed in Sec. 3.5. The model is trained in the same way as standard FR using $\langle \mathbf{x}_s, y \rangle$ . However, it does not require to know the sample-wise specific $\{S, P\}$ , which is favorable for privacy. The approach sounds a bit counter-intuitive since receiving random inputs seems to mess with the model's understanding. However, recall that the DCT frequency channels are spatially correlated to $X$ and each other. The randomness only pertains to the frequency spectrum while the face's structural information is preserved and unaltered. The model, therefore, can associate different $\mathbf{x}_s$ to the same $X$ quite naturally. + +# 3.4. Reconcile technical constraints + +Equation (2) distills our core idea to sampling $\mathbf{x}_s$ at complete random. However, for practical training, there need to further reconcile two technical constraints to achieve satisfying model performance: First to note that $\langle \mathbf{x}_s, y \rangle$ are more varied in feature representations than the unprotected $\langle X, y \rangle$ , owing to the randomized frequency. It hence could plausibly take the model with more training samples and a longer training time to approach a well-generalized convergence. Second, ideally, channels at random should be sampled with equal probability to ensure balanced learning of different local features. However, when the training data + +is partitioned into small mini-batches, sampling is often less unbiased batch-wise so the occurrence of different channel combinations may vary greatly, which we find could undermine the training stability. + +Targeting the constraints, we slightly adjust our established approach in two ways. We first augment the training dataset by picking multiple $\mathbf{x}_s$ each time from a face image $X$ : From $X$ we sample $\{\mathbf{x}_s^1,\ldots ,\mathbf{x}_s^r\}$ , where $r$ determines the degree of augmentation. Each $\mathbf{x}_s^i$ is independently drawn and appended to the training dataset as individual training samples. The dataset is then fully shuffled so that $\mathbf{x}_s^i$ corresponding to the same face image cannot be easily associated. + +We also control the randomness to a moderate level by specifying the possible combinations of $S, P$ in advance. Concretely, we opt for choosing one $S, P$ from $\mathbf{S} = \{S_1, \dots, S_m\}$ and $\mathbf{P} = \{P_1, \dots, P_n\}$ respectively, where $\mathbf{S}, \mathbf{P}$ are determined by the service provider. We specifically require $\{S_1, \dots, S_n\}$ to be a non-overlapping partition of channels from $\mathbf{x}_h$ (i.e., divide $\mathbf{x}_h$ into equal-length subsets) to maximize the use of $\mathbf{x}_h$ and reduce model bias. Therefore, each $\mathbf{x}_s^i$ is picked from one of $m \times n$ fixed combinations of channels, called ranks. This allows us to facilitate the training and overcome sampling biases. The service provider shares $\{\mathbf{S}, \mathbf{P}\}$ with all local devices, so the latter can generate their query $\mathbf{x}_s$ accordingly. During inference, the model is expected to provide consistent results of the same query $X$ regardless of the choice of rank, since it learned about a mapping from local features to the face's entirety. We later testify to it in Sec. 4.3. Meanwhile, the model is still unaware of the sample-wise specific choice of $\{S, P\}$ as the recognition relies on nothing else but $\mathbf{x}_s$ alone. Hence privacy is maintained. + +To conclude, we present PartialFace that train and infer the recognition model with $\arg \min_{\theta} l(f(\mathbf{x}_s^i, \theta), y)$ , where $X = \{\mathbf{x}_l, \mathbf{x}_h\}$ and $\mathbf{x}_s^i = \mathbf{x}_h \cdot S \cdot P$ in random, parameterized by $\{\mathbf{S}, \mathbf{P}\}$ and $(\sigma, s, r, m, n)$ . Later analyses in Secs. 4.2 and 4.3 show PartialFace overcomes the drawback of the vanilla method, plus outperforms most prior arts, to achieve satisfactory recognition accuracy. + +# 3.5. Enhance privacy with randomness + +The benefit of randomness is multi-fold. We have discussed it for now on helping address the accuracy and privacy balance and enhance recognition performance. In retrospect, we briefly elaborate on how randomness further safeguards privacy to a large extent. + +Recall we remove visual information by pruning $\mathbf{x}_l$ and impede recovery by choosing a subset of $\mathbf{x}_s$ . After that, randomness further obstructs recovery: To impose recovery, the attacker exploits not only the channels' information but also their relative orders and positions in the frequency spectrum. We introduce $P$ to distort the order of channels to + +this end. As the recognition model does not require samplewise $\{S,P\}$ , they won't be exposed to the attacker. Figure 4(c) shows the improvement against recovery if the attacker doesn't know the specific choice of subsets. + +# 4. Experiments + +# 4.1. Experimental settings + +We compare PartialFace with the unprotected baseline and prior PPFR methods on three criteria: recognition performance, privacy protection of visual information, and that against recovery attack. We further study the computation and cost of PartialFace. We mainly employ an IR-50 [11] trained on the MS1Mv2 [10] dataset as our FR model, while also using a smaller combination of IR-18 and the BUPT [40] dataset on some resource-consuming experiments. We set $(\sigma, s, r, m, n) = (10, 9, 18, 6, 6)$ and use fixed $\{\mathbf{S}, \mathbf{P}\}$ , if not else specified. Benchmarks are carried out on 5 widely used, regular-size datasets, LFW [13], CFP-FP [35], AgeDB [31], CPLFW [49] and CALFW [50], and 2 large-scale datasets, IJB-B [43] and IJB-C [23]. + +# 4.2. Benchmarks on recognition accuracy + +Compared methods. We compare PartialFace with 2 unprotected baselines, 4 perturbation-based PPFR methods, and 3 methods base on the frequency domain that share close relation to us. Results are summarized in Tab. 1. Here, (1) ArcFace [6] denotes the unprotected SOTA trained directly on RGB images; (2) ArcFace-FD [45] is the ArcFace trained on the image's all frequency channels; (3) PEEP [3] is a differential-privacy-based method with a privacy budget $\epsilon = 5$ ; (4) Cloak [27] perturbs and compresses its input feature space. Its accuracy-privacy trade-off parameter is set to 100; (5) InstaHide [14] mixes up $k = 2$ images and performs a distributed encryption; (6) CPGAN [36] generates compressed protected representation by a joint effort of GAN and differential privacy; (7) PPFR-FD1 [42] adopts a channel-wise shuffle-and-mix strategy in the frequency domain; (8) DCTDP [15] perturbs the frequency components by a noise disturbance mask with learnable privacy budget, where we set $\epsilon = 1$ ; (9) DuetFace [26] is a two-party framework that employs channel splitting and attention transfer. + +Performance. Results are reported on LFW, CFP-FP, AgeDB, CPLFW, and CALFW by accuracy, and on IJB-B and IJB-C by TPR@FPR(1e-4). Table 1 shows PartialFace achieves close performance to the unprotected baseline, with a small accuracy gap of $\leq 0.8\%$ . In comparison, perturbation-based methods all generalize unsatisfactorily on large-scale benchmarks. PartialFace outperforms all PPFR prior arts but DuetFace. While DuetFace achieves + +1The results of PPFR-FD on IJB-B is unattainable due its non-disclosure of source code. The rest is quoted from its paper [42]. Please note its experimental condition may have slight inconsistency with ours. + +![](images/4be29bb14fefddc554c294db7c50ba56734f4bce6f2b41ec480aba7e69bd3c55.jpg) +Figure 6. Visualization of model attention via Grad-CAM. (a) PartialFace (1st row) compared with vanilla models (2nd row) on each of 6 different ranks. (b) Integrated attention of all ranks. + +slightly higher accuracy, its protection is inferior to ours as it only covers the inference phase and can be easily nullified by recovery attacks, later see Secs. 4.4 and 4.5. + +# 4.3. Comparison with the vanilla method + +We elaborate that randomized PartialFace outperforms the vanilla method that fixes channels in not only recognition accuracy but also robustness. As PartialFace employs data augmentation, for a fair comparison regarding the volume of training data, we consider two experimental settings: the standard PartialFace and one without augmentation $(r = 1)$ . We also set $n = 1$ to rule out permutation: $P$ is introduced for privacy and is out of our interest here. There are therefore $m \times n = 6$ combinations of channels, or ranks. As channels from different ranks carry distinct information that may affect the performance, we train one vanilla model on each rank and average their test accuracy, with the range marked in parentheses. Though PartialFace is able to infer from arbitrary rank, we evaluate its robustness by inferring from each fixed rank separately. The model is robust if it performs on different ranks consistently (small range). Results are reported on IJB-B/C by TPR@FPR(1e-4) in Tab. 2. Performance. PartialFace achieves an average accuracy gain of $7.53\%$ and $7.75\%$ on IJB-B/C, respectively, compared to the vanilla. The performance is close to the unprotected baseline, showing that the privacy-accuracy trade-off of PartialFace is highly efficient. Even PartialFace without augmentation outperforms the vanilla for about $3\%$ . We further note: (1) The range shows PartialFace is more robust than the vanilla under different $S_{i}$ . (2) PartialFace outperforms the vanilla for all individual $S_{i}$ . This suggests that randomness empowers PartialFace with the knowledge of the entirety instead of that of certain informative ranks. + +Visualization. We visualize the rank-wise attention of PartialFace and the vanilla via Grad-CAM [34], see Fig. 6(a). The attention of each vanilla model is restrained to local facial features, which indicates the inadequate learning of the entirety features. PartialFace generate accurate attention on the entire face regardless the rank. We integrated the attention across all ranks in Fig. 6(b). All vanilla models' attention combined gains attention on the entire face, which testifies to our "learn-entropy-from-local" theory. Also to + +
MethodPPFRLFWCFP-FPAgeDBCPLFWCALFWIJB-BIJB-C
ArcFace [6]No99.7798.3097.8892.7796.0594.1395.60
ArcFace-FD [45]No99.7898.0498.1092.4896.0394.0895.64
PEEP [3]Yes98.4174.4787.4779.5890.065.826.02
Cloak [27]Yes98.9187.9792.6083.4392.1833.5833.82
InstaHide [14]Yes96.5383.2079.5881.0386.2461.8869.02
CPGAN [36]Yes98.8794.6196.9890.4394.7992.6794.31
PPFR-FD [42]Yes99.6895.0497.3790.7895.72/94.10
DCTDP [15]Yes99.7796.9797.7291.3796.0593.2994.43
DuetFace [26]Yes99.8297.7997.9392.3596.1093.6695.30
PartialFace (ours)Yes99.8097.6397.7992.0396.0793.6494.93
+ +Table 1. Benchmarks on recognition accuracy. PartialFace is compared with the unprotected baselines and PPFR SOTAs. + +
MethodIJB-B (range)IJB-C (range)
ArcFace86.8390.35
Vanilla78.24 (-14.49/7.36)80.73 (-16.37/7.45)
PF w/o aug.81.43 (-4.19/2.88)82.81 (-4.29/2.79)
PartialFace85.77 (-1.95/1.25)88.48 (-1.71/1.18)
+ +Table 2. Comparison with the vanilla method by accuracy and robustness. Experiments are conducted on IR-18 + BUPT. "PF w/o aug." indicates PartialFace without augmentation. + +note that PartialFace has similar attention across all ranks. This allows it to recognize $X$ using arbitrary rank, as they produce aligned outcomes. + +# 4.4. Protection of visual information + +We investigate PartialFace's protection of privacy. We reiterate that the first privacy goal is to conceal the visual information of face images. We compare ParitalFace with 3 PPFR SOTAs using the frequency domain: PPFR-FD [42], DCTDP [15], and DuetFace [26]. These prior arts are closely related to ours since we all leverage the perceptual difference between humans and models as means of protection. However, they differ in the processing of frequency components: Both PPFR-FD and DCTDP remove the component with the highest energy (the DC component). To obfuscate the remaining components, PPFR-FD employs mix-and-shuffle and DCTDP applies a noise mechanism. DuetFace is the most related method in the pruning of low-frequency components. We note in special that they retain 36, 63, and 54 high-frequency channels, respectively, while PartialFace retains 9. We now demonstrate the methodological differences and varied number of channels result in contrasting privacy protection capacities. + +Figure 7 exemplifies face images processed (therefore are supposed to be protective) by each compared method. As all methods carry out protection in the frequency domain, we convert images back by padding any removed frequency components with zero and applying an inverse + +![](images/4c9f094437d115070dee2563daa4d1aae5335c6c56ab7084b7a34ba40d8933e7.jpg) +Figure 7. Example face images of (a) unprotected ArcFace, (b-d) compared SOTAs, and (e) PartialFace, during both training and inference phase. PartialFace best conceals visual information. + +transform. PartialFace, e.g., has $X' = \mathcal{T}^{-1}(\{\mathbf{0}, \mathbf{x}_h\})$ . We visualize the training and inference phases separately, as the compared methods' processing on them may vary: During inference, we argue PPFR-FD and DuetFace (Fig. 7(b)(d)) provide inadequate protection, as one can still discern the face quite clearly in their processed images. DCTDP effectively conceals visual information after obfuscating the channels with its proposed noise mask (Fig. 7(c)). However, its protection during training is impaired, as it requires access to abundant non-obfuscated components to learn the mask. DuetFace manifests a similar weakness as it relies on original images to rectify the model's attention (Fig. 7(d)). + +PartialFace first discards most visual information by pruning $\mathbf{x}_l$ . The rest is further partitioned when sampling $\mathbf{x}_s$ from $\mathbf{x}_h$ . By energy, each $\mathbf{x}_s$ carries less than $1\%$ of visual information compared to the original $X$ . As a result, Fig. 7(e) shows PartialFace provides better protection on visual information than related SOTAs in both phases. + +# 4.5. Protection against recovery + +We here provide an in-depth analysis of how Partial-Face impedes recovery. Our primary aiming is to show how the removal of model-exploitable information and the randomness of channels contribute to the defense. Assume the recovery attacker possesses a collection of face im + +![](images/b36414754013647d0b1b57b22ac11e3fb44dbbff5a221102a9d96d139fe7e62b.jpg) +(a) black-box + +![](images/9f6e40b8c24f97d1466a4b74688cf7a16b625c1b15c577a45c960408751d2fab.jpg) +(b) white-box +Figure 8. Examples of recovered face images of PartialFace under attackers with varied capabilities: (a) a black-box, (b) a white-box, and (c) an enhanced white-box attacker. PartialFace effectively prevents recovery as all images are blurry and hardly identifiable. + +![](images/2ec6786deb502db39b178c922a73e859ca5cb920c736b2580c067ecce1d799dc.jpg) +(c) enhanced white-box + +![](images/5246ab7aa1628fc9357eac73cf5316375c94ed717803f0d9b9ae55385f3f8e70.jpg) +(a) PPFR-FD +Figure 9. Recovered images from (a-c) compared SOTAs and (d) PartialFace. PartialFace impedes recovery better than the rest. + +![](images/75a31fec39f98ee594aefc2423a92a13a4582695fb84586e268e9e86a555d9f1.jpg) +(b) DCTDP + +![](images/dd07ffcce9771c0220ec9fa756795eaba24c2aaf885946d305b10788d435de63.jpg) +(c) DuetFace + +![](images/79f085360aba579d4f5feb441c65b5d9d05b64e4e87a7caca0788730de77e3d2.jpg) +(d) ours + +ages $\{X\}$ and is aware of the protection mechanism. It can locally generate protected representations $X^{\prime}$ $(\mathbf{x}_h$ in our case) from $X$ , then train a malicious model $g(\cdot)$ with $\arg \min_{\delta}l^{\prime}(g(X^{\prime},\delta),X)$ , with the aiming to inversely fit $X$ from $X^{\prime}$ . Having intercepted a recognition query, the attacker leverages $g(\cdot)$ to recover the concealed visual information. Upon the knowledge it possesses, a black-box attacker is one unknowing of necessary parameters ( $\{\mathbf{S},\mathbf{P}\}$ in our case), whilst a white-box attacker possesses such knowledge. We also study the capability of PPFR-FD, DCTDP, and DuetFace against the white-box attacker. We further investigate an enhanced white-box attacker, who imposes threats dedicated to the randomness of PartialFace. + +Black-box attacker. It is concretized as a malicious third party, uninvolved in the recognition yet eager to wiretap the transmission. For each attacker, We employ a full-scale U-Net [32] as the recovery model and train it on BUPT. Unknown of $\{\mathbf{S},\mathbf{P}\}$ , it must produce $X^{\prime}$ based on its own conjectured $\{\mathbf{S}^{\prime},\mathbf{P}^{\prime}\}$ , which is believably inconsistent with that applied to the recognition model. Thus produced $X^{\prime}$ are invalid samples and training $g(\cdot)$ on them will nullify the recovery, as shown in Fig. 8(a). + +White-box attacker. The candidate combinations $\{\mathbf{S},\mathbf{P}\}$ is known by any party participates in the recognition, e.g., an honest-but-curious server. Such an attacker can generate $X^{\prime}$ correctly. However, receiving a query $\mathbf{x}_s$ , the attacker is unknowing of its channels' position and order, since the specific $\{S,P\}$ doesn't come with $\mathbf{x}_s$ . The missing information is vital to recovery. Consequently, the attack is obstructed by $\mathbf{x}_s$ 's randomness in Fig. 8(b): The recovered image is blurry and hardly identifiable. + +We plus compare with PPFR-FD, DCTDP and Duet-Face under the white-box settings. Among them, Duet + +
MethodSSIM (↓)PSNR (↓)Accuracy (↓)
PPFR-FD0.71315.6683.73
DCTDP0.68715.4279.60
DuetFace0.86619.8896.52
PartialFace0.59113.7065.35
+ +Table 3. Quantitative analyses of the recovery quality. Lower SSIM, PSNR and accuracy suggest better protection. Here, we remind the accuracy of verification is lower bounded by 50.00. + +![](images/06238690f2f1ea7ed00a3cbef62416ebf8fc4ed54f3518aa8e4738eda95cb857.jpg) +Figure 10. Recovered images from extracted identity templates, that are blurry and can hardly be inferred by humans or models. + +![](images/8ebeb2b1f03ded30bf944efa3bed36eddf883b66e7352449b1ec3ec4b5d206dc.jpg) + +![](images/b2aefcfc9eb18c603470c9f72e01dbbe729f7a2bfc463b67a7f5f61c2787f847.jpg) + +![](images/aab93b1ffd9cfdc2529b203d64066811abfdc487694f7f0a92f0c610e423973e.jpg) + +Face shows almost no resistance to recovery (Fig. 9(c)). PPFR-FD and DCTDP provide inadequate protection, as images recovered from them (Fig. 9(a-b)) are blurred yet still clearly identifiable. The protection is impaired as their processed images retain most high-frequency components, and the excessive perceivable information is learned by the recovery model. In comparison, PartialFace (Fig. 9(d)) offers significantly outperformed protection. + +Enhanced white-box attacker. A resource-unbounded attacker may brute-forcibly break the randomness of Partial-Face leveraging a more sophisticated attack: it trains a series of attack models, one for each candidate $\{S,P\}$ . Receiving $\mathbf{x}_s$ , the attacker feeds it into every model to try every combination of $\{S,P\}$ , until one produces the best recovery. The vague face images in Fig. 8(c) imply the attempted recovery is unsuccessful, even if the attacker finds the correct $\{S,P\}$ . This is attributed to the reduction of model-exploitable channels. + +Quantitative comparison. To quantitatively assess the recovery quality, we measure the average structural similarity index (SSIM) and peak signal-to-noise ratio (PSNR) of the recovered images. Additionally, to study if the attacker can exploit its outcome for recognition proposes, we feed the images into a pre-trained model and measure verification accuracy. Lower SSIM, PSNR, and recognition accuracy suggest deficient recovery, thus indicating a higher level of protection. The results in Tab. 3 suggest PartialFace outperforms its competitors in all three evaluated metrics. + +# 4.6. Protection against recovery from templates + +By the principle of FR, all $\mathbf{x}_s$ of face image $X$ are later extracted to very similar identity templates, so the recognition on them produces aligned results. Here, one would arise concern that recovery can also be carried out on the extracted templates, which theoretically contain the faces' full identity information, to realize better inversion of im + +
SettingsLFWCFP-FPAgeDBCPLFWCALFW
ArcFace99.3892.3194.6589.4194.78
r3699.5191.2794.4488.9394.81
698.6986.7990.6584.5092.67
m399.4291.6893.9588.7094.69
999.3290.7493.5687.3094.36
n199.3791.5594.2588.7394.70
1299.3589.2193.1787.1994.26
Default99.3891.2093.7288.1194.42
+ +Table 4. Ablation study on combinations of hyperparameters. Experiments are carried out on IR-18 + BUPT. When changing one of them, we keep the rest to default values, i.e., $(r,m,n) = (18,6,6)$ . + +
SettingsLFWCFP-FPAgeDBCPLFW
CosFace99.5392.8995.1589.52
PartialFace99.3589.5493.9787.90
+ +Table 5. Compatibility of PartialFace. FR models are trained using CosFace on IR-18 + BUPT. Combining PartialFace with CosFace also demonstrates high utility, compared to its baseline. + +ages. We demonstrate that such a proposed attack is also ineffective to PartialFace. + +Although there could be dedicated attacks on templates, in practice, high-quality recovery from them is difficult as templates are far more compact representations than images and channel subsets. In Fig. 10, the recovered images are highly blurred, and can hardly be inferred by humans or models, hence won't impose an effective threat. + +# 4.7. Ablation study + +PartialFace is parameterized by $(\sigma, s, r, m, n)$ . Among them, we note $\sigma$ is chosen according to channel energy, and $s$ is determined by $(\sigma, m)$ . Table 4 analyzes the choice of the remaining parameters. Results show augmentation $(r)$ enhances the model's performance, at the cost of taking longer time to train. $m$ affects the performance mainly by its influence on $s$ , as larger $m$ leading to fewer channels in each $\mathbf{x}_s$ . We introduce $P$ solely for privacy purposes. Results on $n$ indicate a trade-off between accuracy and privacy. Generally, PartialFace is robust to the choice of parameters. + +# 4.8. Complexity and compatibility + +Though PartialFace is proposed by studying the model's behavior, privacy protection is solely realized by processing the face images. The decoupling with model architecture and training tactics benefits resources and compatibility. + +PartialFace is resource-efficient. Compared to the unprotected baseline, PartialFace doesn't increment model size as they share identical model architectures. Training does take more $(r)$ time and storage due to augmentation, while we + +argue it is acceptable for the service provider. The crucial inference time remains the same as the baseline, as DCT and sampling $\mathbf{x}_s$ only increase negligible computation costs. + +PartialFace is well compatible. The decoupling of preprocessing and training also allows PartialFace to serve as a convenient plug-in: PartialFace can be integrated with SOTA FR methods to enjoy enhanced privacy protection. Specifically, we demonstrate the recognition accuracy on CosFace [38], a major competitor of ArcFace, in Tab. 5. Combining PartialFace with CosFace also results in high utility, as compared to its baseline. + +# 5. Conclusion + +This paper presents an in-depth study of the privacy protection of face images. Based on the observations on model perception and training behavior, we present two methodological advances, pruning low-frequency components and using randomly selected channels, to address the privacy goal of concealing visual information and impeding recovery. 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This paper presents an in-depth study of the privacy protection of face images' visual information and against recovery. Drawing on the perceptual disparity between humans and models, we propose to conceal visual information by pruning human-perceivable low-frequency components. For impeding recovery, we first elucidate the seeming paradox between reducing model-exploitable information and retaining high recognition accuracy. Based on recent theoretical insights and our observation on model attention, we propose a solution to the dilemma, by advocating for the training and inference of recognition models on randomly selected frequency components. We distill our findings into a novel privacy-preserving face recognition method, PartialFace. Extensive experiments demonstrate that PartialFace effectively balances privacy protection goals and recognition accuracy. 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Currently, considerable applications of face recognition are carried out online to bypass local resource constraints and to attain high accuracy [19]: Face images are collected by local devices such as cell phones or webcams, then outsourced to a service provider, that uses large convolutional neural networks (CNN) to extract the faces' identity-representative templates and matches them with records in its database." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 313, + 239, + 538, + 365 + ], + "blocks": [ + { + "bbox": [ + 313, + 239, + 538, + 365 + ], + "lines": [ + { + "bbox": [ + 313, + 239, + 538, + 365 + ], + "spans": [ + { + "bbox": [ + 313, + 239, + 538, + 365 + ], + "type": "image", + "image_path": "ab0f35fb5afe1dbd1a1b9f0d4eaafbf36474695ada0837df775f241a07693548.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 367, + 545, + 433 + ], + "lines": [ + { + "bbox": [ + 305, + 367, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 305, + 367, + 545, + 433 + ], + "type": "text", + "content": "Figure 1. Paradigm comparison among other frequency-based methodologies and PartialFace. (a) Pruning low-frequency channels can conceal visual information but stop no recovery. (b) A vanilla method that uses fixed channel subsets to impede recovery suffers downgraded accuracy. (c) PartialFace addresses the dilemma by training and inferring from random channels." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 457, + 545, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 457, + 545, + 577 + ], + "spans": [ + { + "bbox": [ + 304, + 457, + 545, + 577 + ], + "type": "text", + "content": "During the process, the original face images are often considered sensitive data under regulatory demands that are unwise to share without privacy protection. This fosters the studies of privacy-preserving face recognition (PPFR), where cryptographic [7,8,14,17,21,33,44,47] and perturbation-based [3, 12, 18, 28-30, 46, 48] measures are taken to prevent face images from unauthorized access of, e.g., wiretapping third parties. Face images are converted to protective representations that their visual information is both concealed and cannot be easily recovered [2]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 579, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 579, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 579, + 545, + 639 + ], + "type": "text", + "content": "This paper advocates a novel PPFR scheme, to learn face images from random combinations of their partial frequency components. Our proposed PartialFace can protect face images' visual information and prevent recovery while maintaining the high distinguishability of their identities." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "text", + "content": "We start with the disparity in how humans and models perceive images. Recent image classification studies suggest that models' predictions are determined mainly by the images' high-frequency components [39, 45], which carry negligible visual information and are barely picked up by humans. We extend the theory to face recognition from a" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 136, + 702 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 136, + 702 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 136, + 702 + ], + "type": "text", + "content": "*Equal contributions." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19673" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": "privacy perspective, to train and infer the model on pruned frequency inputs: As depicted in Fig. 1(a), we decouple the face images' frequency compositions via discrete cosine transform (DCT), which breakdown every spatial domain into a certain number of (typically 64) constituent bands, i.e., frequency channels. We prune the human-perceivable low-frequency channels and exploit the remaining. We find the processed face images become almost visually indiscernible, and the model still works accurately." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 182, + 289, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 289, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 289, + 361 + ], + "type": "text", + "content": "Pruning notably conceals visual information. However, to what degree can it impede recovery? We define recovery as the general attempts to reveal the faces' visual appearances from shared protected features using trained attack models. Notice we may prune very few (say, about 10) channels, if according to human perception. At the same time, the remaining high-frequency channels being shared, hence exposed, are quite numerous and carry a wealth of model-perceivable features. While the information abundance can benefit a recognition model, it is also exploitable by a model carrying out attacks, as both may share similar perceptions. Therefore, as we later experimentally show, the attacker can recover visual features from high-frequency channels with ease in the absence of additional safeguards, rendering privacy protection useless." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 363, + 289, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 289, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 289, + 460 + ], + "type": "text", + "content": "An intuitive tactic to reinstate protection is to reduce the attacker's exploitable features by training on a small portion of fixed channels, as shown in Fig. 1(b). However, we find the reduction also severely impairs the accuracy of trained recognition models. Evidence on the models' attention, as later shown, attributes their utility downgrade to being incapable of learning a complete set of facial features, as vital channels describing some local features may be pruned." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 460, + 289, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 289, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 289, + 616 + ], + "type": "text", + "content": "Training on subsets of channels hence seems contradictory to the privacy-accuracy equilibrium. Fortunately, we can offer a reconciliation getting inspired by a recent timeseries study [51]. It proves under mild conditions, models trained on random frequency components can preserve more entirety's information than on fixed ones, plausibly by alternately learning from complementary features. We hence propose a novel address to the equilibrium based on its theoretical findings and our observation on model attention: For any incoming face image, we arbitrarily pick a small subset of its high-frequency channels. Therefore, our recognition model is let trained and inferred from image-wise random chosen channels, illustrated in Fig. 1(c)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": "We further show that randomness can be adjusted to a moderate level, by choosing channels from pre-specified combinations and perturbations called ranks, to keep privacy protection while reconciling technical constraints to ease training. At first glance, our randomized approach may seem counter-intuitive as it is common wisdom that models require consistent forms of inputs to learn stably. However, since DCT produces spatially correlated frequency channels" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "that preserve the face's structural information, as later illustrated in Fig. 3, it turns out the model generalizes quite naturally. Experimental analyses show our PartialFace well balances privacy and accuracy." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 121, + 502, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 121, + 502, + 133 + ], + "spans": [ + { + "bbox": [ + 317, + 121, + 502, + 133 + ], + "type": "text", + "content": "The contributions of our paper are three-fold:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 139, + 545, + 286 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 314, + 139, + 545, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 139, + 545, + 176 + ], + "spans": [ + { + "bbox": [ + 314, + 139, + 545, + 176 + ], + "type": "text", + "content": "1. We present an in-depth study of the privacy protection of face images, regarding the privacy goals of concealing visual information and impeding recovery." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 182, + 545, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 182, + 545, + 231 + ], + "spans": [ + { + "bbox": [ + 313, + 182, + 545, + 231 + ], + "type": "text", + "content": "2. We propose two methodological advances to fulfill the privacy goals, pruning low-frequency components and using randomly selected channels, based on the observation of model perception and learning behavior." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 238, + 545, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 238, + 545, + 286 + ], + "spans": [ + { + "bbox": [ + 313, + 238, + 545, + 286 + ], + "type": "text", + "content": "3. We distill our findings into a novel PPFR method, PartialFace. We demonstrate by extensive experiments that our proposed method effectively safeguards privacy and maintains satisfactory recognition accuracy." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 303, + 390, + 316 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 303, + 390, + 316 + ], + "spans": [ + { + "bbox": [ + 306, + 303, + 390, + 316 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 323, + 406, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 323, + 406, + 335 + ], + "spans": [ + { + "bbox": [ + 306, + 323, + 406, + 335 + ], + "type": "text", + "content": "2.1. Face recognition" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 341, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 341, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 341, + 545, + 437 + ], + "type": "text", + "content": "The current method of choice for face recognition is CNN-based embedding. The service provider trains a CNN with a softmax-based loss to map face images into one-dimensional embedding features which achieve large interidentity and small intra-identity discrepancies. While the state-of-the-art (SOTA) FR methods [6, 20, 38] achieve impressive task utility in real-world applications, their attention to privacy protection could be deficient." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 444, + 495, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 444, + 495, + 456 + ], + "spans": [ + { + "bbox": [ + 306, + 444, + 495, + 456 + ], + "type": "text", + "content": "2.2. Privacy-preserving face recognition" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 463, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 463, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 463, + 545, + 498 + ], + "type": "text", + "content": "The past decade witnessed significant advances in privacy-preserving face recognition [24,25,41]. We roughly categorize the related arts into two branches:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 498, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 617 + ], + "type": "text", + "content": "Cryptographic methods perform recognition on encrypted images, or by executing dedicated security protocols. Many pioneering works fall under the category of homomorphic encryption (HE) [8,14,33] or secure multiparty computation (MPC) [21, 44, 47], to securely carry out necessary computations such as model's feature extraction. Some methods also employ various crypto-primitives including one-time-pad [7], matrix encryption [17], and functional encryption [1]. The major pain points of these methods are generally high latency and expensive computational costs." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 618, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 714 + ], + "type": "text", + "content": "Perturbation-based methods transform face images into protected representations that are difficult for unauthorized parties to discern or recover. Many methods leverage differential privacy (DP) [3, 18, 22, 48], in which face images are obfuscated by a noise mechanism. Some use autoencoders [28] or adversarial generative networks (GAN) [18, 29] to recreate visually distinct faces that maintain a constant identity. 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219 + ], + "spans": [ + { + "bbox": [ + 477, + 211, + 543, + 219 + ], + "type": "text", + "content": "Randomly Sample Subset(s)" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 281, + 286, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 286, + 353 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 286, + 353 + ], + "type": "text", + "content": "compact representations by mapping discriminative components into subspaces [4, 16, 27], or anonymize the images by clustering their features [12]. These methods face a common bottleneck of task utility: As the techniques they employ essentially distort the original images, their protection often impairs recognition accuracy." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 47, + 361, + 230, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 361, + 230, + 374 + ], + "spans": [ + { + "bbox": [ + 47, + 361, + 230, + 374 + ], + "type": "text", + "content": "2.3. Learning in the frequency domain" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 45, + 380, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 380, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 45, + 380, + 287, + 559 + ], + "type": "text", + "content": "Converting spatial or temporal data into the frequency domain provides a powerful way to extract interesting signals. For instance, the Fourier-based discrete cosine transform [5] is used by the JPEG standard [37] to enable image compression. Researches in deep learning [9, 45] suggest models trained on images' frequency components can perform as well as trained on the original images. Advance [39] further reveals humans and models perceive low- and high-frequency components differently. In the realm of PPFR, three recent methods [15, 26, 42] are closely related to ours as we all conceal visual information by exploiting the split in human and model perceptions. However, these methods bear inadequacy in defending recovery, according to our previous discussion of channel redundancy and later testified in experiments." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 47, + 571, + 129, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 129, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 129, + 583 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 590, + 286, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 286, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 286, + 651 + ], + "type": "text", + "content": "This section discusses the motivation and technical details behind PartialFace. PartialFace is named after its key protection mechanism, where the model only exploits face images' partial frequency components to reduce information exposure. Figure 2 describes its framework." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 47, + 658, + 114, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 114, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 114, + 670 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": "Recall our privacy goals are to conceal the face images' visual information and to prevent recovery attacks on them. They respectively target the adversarial capability of hu" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 281, + 545, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 545, + 317 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 545, + 317 + ], + "type": "text", + "content": "mans and models. We naturally concretize them into two technical aims, on how to eliminate human perception, and, on how to reduce exploitable information for attack models." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 318, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 318, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 318, + 545, + 461 + ], + "type": "text", + "content": "To eliminate human perception, we leverage the finding that models' utility can be maintained almost in full on the images' high-frequency channels [39]. Contrarily, humans mostly perceive the images' low-frequency channels, as only they carry signals of conspicuous amplitude for human eyes to discern. Whereby spatial-frequency transforms, these channels can be easily located and pruned from raw images. We concretely opt for DCT as our transform as it facilitates the calculation of energy, to serve as the quantification for human perceivable information. Experimentally, we can prune a very small portion of channels to eliminate " + }, + { + "bbox": [ + 304, + 318, + 545, + 461 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 304, + 318, + 545, + 461 + ], + "type": "text", + "content": " of total energy, hence satisfying our aim." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 462, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 653 + ], + "type": "text", + "content": "Reducing the attacker's exploitable information requires further pruning of high-frequency channels, as previously discussed. However, it is equally crucial to maintain the recognition model's accuracy, which presents a seeming dilemma, as the training features utilizable by recognition and attack models are tightly interwoven in these channels. We offer a viable way as our major contribution: We notice different channel subsets each carrying certain local facial features. Hence, we feed the model with a random subset from each face image, with the hope to let the model learn the entire face's impression from different images' complementary local feature partitions. This approach is proved feasible by recent theoretical studies [51] and demonstrated by our experiments. Therefore, information exposure is minimized as only each image's chosen subset is exposed, and the model still performs surprisingly well." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Despite being well justified by theory, we find sampling channels under complete randomness could under-perform in actual training due to two technical limitations: the inadequacy in training samples and the biased sampling within mini-batches. We propose two targeted fixes to reconcile" + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19675" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 71, + 286, + 139 + ], + "blocks": [ + { + "bbox": [ + 52, + 71, + 286, + 139 + ], + "lines": [ + { + "bbox": [ + 52, + 71, + 286, + 139 + ], + "spans": [ + { + "bbox": [ + 52, + 71, + 286, + 139 + ], + "type": "image", + "image_path": "a2eabe9499f00ea53245db1238873ee5595c157f1bddd4cf2a531fbca442054d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 142, + 287, + 197 + ], + "lines": [ + { + "bbox": [ + 46, + 142, + 287, + 197 + ], + "spans": [ + { + "bbox": [ + 46, + 142, + 287, + 197 + ], + "type": "text", + "content": "Figure 3. The DCT process. The produced (d) frequency channels keep the spatial structure to (a) the original image, though only low-frequency channels are discernible bu humans. We use (c) 2D grids to describe the frequency spectrum. Each cell in the grid represents one frequency channel of " + }, + { + "bbox": [ + 46, + 142, + 287, + 197 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 46, + 142, + 287, + 197 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 219, + 287, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 219, + 287, + 255 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 287, + 255 + ], + "type": "text", + "content": "the constraints, by augmenting samples and seeking a moderate level of randomness. We find the modified approach satisfactorily addresses the privacy-accuracy equilibrium." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 265, + 196, + 276 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 265, + 196, + 276 + ], + "spans": [ + { + "bbox": [ + 47, + 265, + 196, + 276 + ], + "type": "text", + "content": "3.2. Conceal visual information" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "text", + "content": "We first set up some basic notions: " + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "inline_equation", + "content": "\\langle X, y \\rangle" + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "text", + "content": " denotes a data sample of a face image and its corresponding label. " + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "text", + "content": " denotes the frequency composition of " + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "text", + "content": " denotes its individual frequency channels. " + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "inline_equation", + "content": "f(\\cdot; \\theta)" + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "text", + "content": " denotes the recognition model parameterized by " + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "inline_equation", + "content": "l(\\cdot, \\cdot)" + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "text", + "content": " denotes a generic loss function (e.g., ArcFace). " + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "inline_equation", + "content": "\\mathcal{T}(\\cdot)" + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "text", + "content": " denotes the discrete cosine transform and " + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^{-1}(\\cdot)" + }, + { + "bbox": [ + 46, + 284, + 287, + 367 + ], + "type": "text", + "content": " denotes its inverse transform." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 369, + 287, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 287, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 287, + 429 + ], + "type": "text", + "content": "To conceal visual information, recall humans and models mainly perceive low- and high-frequency components, respectively. Therefore, we need to find a frequency decomposition of " + }, + { + "bbox": [ + 46, + 369, + 287, + 429 + ], + "type": "inline_equation", + "content": "X = \\{\\mathbf{x}_l, \\mathbf{x}_h\\}" + }, + { + "bbox": [ + 46, + 369, + 287, + 429 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 369, + 287, + 429 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_l, \\mathbf{x}_h" + }, + { + "bbox": [ + 46, + 369, + 287, + 429 + ], + "type": "text", + "content": " are the respective low- and high-frequency channels, then prune " + }, + { + "bbox": [ + 46, + 369, + 287, + 429 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_l" + }, + { + "bbox": [ + 46, + 369, + 287, + 429 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "spans": [ + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "content": "We presume " + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "content": " is with the shape of " + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "inline_equation", + "content": "(H, W)" + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "content": ". We employ DCT to transform " + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "content": "'s spatial channels into a frequency spectrum. While an RGB image typically has 3 spatial channels, we pick one for simplicity. We perform an 8-fold up-sampling ahead to turn " + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "inline_equation", + "content": "(8H, 8W)" + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "content": ". As DCT later divides " + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "content": " by 8, this makes sure the resulting frequency channels can be fed into the model as usual. Figure 3 illustrates the process of DCT, where " + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = \\mathcal{T}(X)" + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "content": ". Concretely, " + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "content": " is divided into (8, 8)-pixel blocks. DCT turns each block into a 1D array of 64 frequency coefficients and reorganizes all coefficients from the same frequency across blocks into an " + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "inline_equation", + "content": "(H, W)" + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "content": " frequency channel (there are 64 of them), that is spatially correlated to the original " + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "content": ". As a result, " + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "content": " is turned into " + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "inline_equation", + "content": "(64, H, W)" + }, + { + "bbox": [ + 46, + 429, + 287, + 596 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 597, + 287, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 287, + 669 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 287, + 669 + ], + "type": "text", + "content": "We then decouple " + }, + { + "bbox": [ + 46, + 597, + 287, + 669 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 597, + 287, + 669 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 46, + 597, + 287, + 669 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}_l, \\mathbf{x}_h\\}" + }, + { + "bbox": [ + 46, + 597, + 287, + 669 + ], + "type": "text", + "content": ". Notice that human-perceivable low-frequency channels should meanwhile be those with higher amplitude, as humans preferentially identify signals with conspicuous value changes. We measure a channel's amplitude by its channel energy " + }, + { + "bbox": [ + 46, + 597, + 287, + 669 + ], + "type": "inline_equation", + "content": "e(\\cdot)" + }, + { + "bbox": [ + 46, + 597, + 287, + 669 + ], + "type": "text", + "content": ", which is the mean of amplitudes of all its elements:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 681, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 681, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 287, + 715 + ], + "type": "interline_equation", + "content": "e (x) = \\frac {1}{H W} \\sum_ {i = 0} ^ {H - 1} \\sum_ {j = 0} ^ {W - 1} | x ^ {i, j} |. \\tag {1}", + "image_path": "e8007af8e12e28c61053a40c7127066a8d3af3f16c68581dc93f4ec735312137.jpg" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 317, + 72, + 539, + 185 + ], + "blocks": [ + { + "bbox": [ + 317, + 72, + 539, + 185 + ], + "lines": [ + { + "bbox": [ + 317, + 72, + 539, + 185 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 539, + 185 + ], + "type": "image", + "image_path": "44b4ceb330dc99d2c71d4df6c3e28ec9162fb3983ab0986a8ef11b133e12866a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 187, + 545, + 232 + ], + "lines": [ + { + "bbox": [ + 305, + 187, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 305, + 187, + 545, + 232 + ], + "type": "text", + "content": "Figure 4. The visual appearance and recovery of an example image of (a) after pruning, (b) a fixed subset, and (c) a random subset. This shows protection is enhanced by removing human perception, reducing the number of channels, and randomness, respectively." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 253, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 253, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 253, + 545, + 361 + ], + "type": "text", + "content": "We choose " + }, + { + "bbox": [ + 304, + 253, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\sigma = 10" + }, + { + "bbox": [ + 304, + 253, + 545, + 361 + ], + "type": "text", + "content": " highest-energy channels as " + }, + { + "bbox": [ + 304, + 253, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_l" + }, + { + "bbox": [ + 304, + 253, + 545, + 361 + ], + "type": "text", + "content": " to be pruned and the rest as " + }, + { + "bbox": [ + 304, + 253, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_h" + }, + { + "bbox": [ + 304, + 253, + 545, + 361 + ], + "type": "text", + "content": " to be available to models. We experimentally find " + }, + { + "bbox": [ + 304, + 253, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\sum_{x\\in \\mathbf{x}_l}e(x)\\geq 0.95\\sum_{x\\in \\mathbf{x}}e(x)" + }, + { + "bbox": [ + 304, + 253, + 545, + 361 + ], + "type": "text", + "content": ", and a model trained with " + }, + { + "bbox": [ + 304, + 253, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\arg \\min_{\\theta}l(f(\\mathbf{x}_h,\\theta),y)" + }, + { + "bbox": [ + 304, + 253, + 545, + 361 + ], + "type": "text", + "content": " obtain close accuracy to one trained with " + }, + { + "bbox": [ + 304, + 253, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\arg \\min_{\\theta}l(f(\\mathbf{x},\\theta),y)" + }, + { + "bbox": [ + 304, + 253, + 545, + 361 + ], + "type": "text", + "content": ". For privacy, example of a channel-pruned image in Fig. 4(a) show that most visual information is concealed. While its recovery is still carried out quite successfully, we are to address the issue in the following." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 370, + 429, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 370, + 429, + 383 + ], + "spans": [ + { + "bbox": [ + 306, + 370, + 429, + 383 + ], + "type": "text", + "content": "3.3. Impede easy recovery" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 389, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 545, + 496 + ], + "type": "text", + "content": "To elucidate the seeming dilemma between reducing model-available channels and retaining high recognition accuracy, we first introduce an intuitive protection, referred to as the vanilla method. It trains models on a fixed small subset of channels straightforwardly: Concretely for every " + }, + { + "bbox": [ + 304, + 389, + 545, + 496 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 389, + 545, + 496 + ], + "type": "text", + "content": ", the model pick " + }, + { + "bbox": [ + 304, + 389, + 545, + 496 + ], + "type": "inline_equation", + "content": "s < d" + }, + { + "bbox": [ + 304, + 389, + 545, + 496 + ], + "type": "text", + "content": " channels " + }, + { + "bbox": [ + 304, + 389, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s = (x_{a_1},\\dots,x_{a_s})" + }, + { + "bbox": [ + 304, + 389, + 545, + 496 + ], + "type": "text", + "content": " from its high-frequency " + }, + { + "bbox": [ + 304, + 389, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_h = (x_1,\\dots,x_d)" + }, + { + "bbox": [ + 304, + 389, + 545, + 496 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 389, + 545, + 496 + ], + "type": "inline_equation", + "content": "a_1 < a_2 < \\dots < a_s" + }, + { + "bbox": [ + 304, + 389, + 545, + 496 + ], + "type": "text", + "content": " are fixed indices. We benchmark the trained model on IJB-B/C with " + }, + { + "bbox": [ + 304, + 389, + 545, + 496 + ], + "type": "inline_equation", + "content": "s = 9,18,36" + }, + { + "bbox": [ + 304, + 389, + 545, + 496 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 389, + 545, + 496 + ], + "type": "inline_equation", + "content": "d = 54" + }, + { + "bbox": [ + 304, + 389, + 545, + 496 + ], + "type": "text", + "content": ", and verify its privacy." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 498, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 664 + ], + "type": "text", + "content": "The model indeed effectively prevents recovery, as in Fig. 4(b) its recovered image is very blurred. However, the benchmark in Fig. 5(a-b) suggests its accuracy dropped by at most " + }, + { + "bbox": [ + 304, + 498, + 545, + 664 + ], + "type": "inline_equation", + "content": "9\\%" + }, + { + "bbox": [ + 304, + 498, + 545, + 664 + ], + "type": "text", + "content": ". To find out why is the model's performance impaired, we inspect its attention via Grad-CAM [34]. Results are exemplified in Fig. 5(c-d), which we note show similar patterns among different face images. We derive two observations: (1) Unlike high-utility models that typically have attention to the full face, this model only gains attention to certain local features, which suggests some vital face-describing information is missing in " + }, + { + "bbox": [ + 304, + 498, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 304, + 498, + 545, + 664 + ], + "type": "text", + "content": "; (2) By training vanilla models on different " + }, + { + "bbox": [ + 304, + 498, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 304, + 498, + 545, + 664 + ], + "type": "text", + "content": ", we find it can acquire distinct information from different channels, suggesting its attention is correlated to the specific choices of " + }, + { + "bbox": [ + 304, + 498, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 304, + 498, + 545, + 664 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "The first observation suggests the cause of the accuracy downgrade. Meanwhile, the second pursues us to consider a viable bypass: We can gather complementary local features from different images and initiate mixed training, to let the" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19676" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 71, + 115, + 131 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 115, + 131 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 115, + 131 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 115, + 131 + ], + "type": "image", + "image_path": "51f9230e1919a086e153bf2620c135a13bb7d544139c1ac5e185436130f38738.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 134, + 287, + 200 + ], + "lines": [ + { + "bbox": [ + 46, + 134, + 287, + 200 + ], + "spans": [ + { + "bbox": [ + 46, + 134, + 287, + 200 + ], + "type": "text", + "content": "Figure 5. The privacy and accuracy dilemma. (a-b) The vanilla model trained on fixed channels under-performs on IJB-B/C (orange), compared to the unprotected baseline (blue) and PartialFace (green). (c-d) The model gains local attention on foreheads and cheeks, suggesting missing face-describing information. The attention varies by the specific choice of " + }, + { + "bbox": [ + 46, + 134, + 287, + 200 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 46, + 134, + 287, + 200 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 116, + 71, + 170, + 131 + ], + "blocks": [ + { + "bbox": [ + 116, + 71, + 170, + 131 + ], + "lines": [ + { + "bbox": [ + 116, + 71, + 170, + 131 + ], + "spans": [ + { + "bbox": [ + 116, + 71, + 170, + 131 + ], + "type": "image", + "image_path": "3642c4c288e228dcc526ebb0b5927257f8bde6bb246a0fd22acd47852f87bf5d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 176, + 72, + 224, + 131 + ], + "blocks": [ + { + "bbox": [ + 176, + 72, + 224, + 131 + ], + "lines": [ + { + "bbox": [ + 176, + 72, + 224, + 131 + ], + "spans": [ + { + "bbox": [ + 176, + 72, + 224, + 131 + ], + "type": "image", + "image_path": "fd1595fb6414c733c4cc01ea382720654b022e1e5b4eef574661461995eb4eda.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 230, + 72, + 278, + 131 + ], + "blocks": [ + { + "bbox": [ + 230, + 72, + 278, + 131 + ], + "lines": [ + { + "bbox": [ + 230, + 72, + 278, + 131 + ], + "spans": [ + { + "bbox": [ + 230, + 72, + 278, + 131 + ], + "type": "image", + "image_path": "2e5084efa6247027a319eb36e0b42f957c4feb1170cc2db432d6becd9682e3f5.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 220, + 286, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 220, + 286, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 286, + 281 + ], + "type": "text", + "content": "model learn a holistic impression of the entirety while keeping the individual information exposure minimized. Our idea is corroborated by [51], which proves in time-series, training models on random frequency components can preserve more information compared to training on fixed ones." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "spans": [ + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "text", + "content": "We concrete our theory into a randomized strategy, by advocating training and inferring the recognition model on image-wise randomly chosen channels. Formally, we construct matrix " + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "inline_equation", + "content": "S \\in \\{0,1\\}^{d \\times s}" + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "inline_equation", + "content": "s_{ij} = 1" + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "inline_equation", + "content": "i = a_j" + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "inline_equation", + "content": "s_{ij} = 0" + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "text", + "content": " if otherwise. We also construct permutation matrix " + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "inline_equation", + "content": "P \\in \\{0,1\\}^{s \\times s}" + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "text", + "content": ". For each " + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "text", + "content": ", we draw " + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "inline_equation", + "content": "(a_1, \\ldots, a_s)" + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "text", + "content": " (therefore " + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "text", + "content": ") and " + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 47, + 281, + 286, + 365 + ], + "type": "text", + "content": " uniformly at random, and calculate" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 132, + 379, + 287, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 379, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 132, + 379, + 287, + 392 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {s} = \\mathbf {x} _ {h} \\cdot S \\cdot P. \\tag {2}", + "image_path": "82d20bae4e9553b4f089837184ad317c571d9df01598eefed0c98896798df382.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "text", + "content": " randomly pick " + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "text", + "content": " channels out of " + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_h" + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "text", + "content": ", then their order is permuted by " + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "text", + "content": ". We introduce " + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "text", + "content": " to further impede recovery, as later discussed in Sec. 3.5. The model is trained in the same way as standard FR using " + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{x}_s, y \\rangle" + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "text", + "content": ". However, it does not require to know the sample-wise specific " + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\{S, P\\}" + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "text", + "content": ", which is favorable for privacy. The approach sounds a bit counter-intuitive since receiving random inputs seems to mess with the model's understanding. However, recall that the DCT frequency channels are spatially correlated to " + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "text", + "content": " and each other. The randomness only pertains to the frequency spectrum while the face's structural information is preserved and unaltered. The model, therefore, can associate different " + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "text", + "content": " to the same " + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 399, + 287, + 555 + ], + "type": "text", + "content": " quite naturally." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 563, + 214, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 214, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 214, + 574 + ], + "type": "text", + "content": "3.4. Reconcile technical constraints" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": "Equation (2) distills our core idea to sampling " + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": " at complete random. However, for practical training, there need to further reconcile two technical constraints to achieve satisfying model performance: First to note that " + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\langle \\mathbf{x}_s, y \\rangle" + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": " are more varied in feature representations than the unprotected " + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\langle X, y \\rangle" + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": ", owing to the randomized frequency. It hence could plausibly take the model with more training samples and a longer training time to approach a well-generalized convergence. Second, ideally, channels at random should be sampled with equal probability to ensure balanced learning of different local features. However, when the training data" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "is partitioned into small mini-batches, sampling is often less unbiased batch-wise so the occurrence of different channel combinations may vary greatly, which we find could undermine the training stability." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "type": "text", + "content": "Targeting the constraints, we slightly adjust our established approach in two ways. We first augment the training dataset by picking multiple " + }, + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "type": "text", + "content": " each time from a face image " + }, + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "type": "text", + "content": ": From " + }, + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "type": "text", + "content": " we sample " + }, + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}_s^1,\\ldots ,\\mathbf{x}_s^r\\}" + }, + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "type": "text", + "content": " determines the degree of augmentation. Each " + }, + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s^i" + }, + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "type": "text", + "content": " is independently drawn and appended to the training dataset as individual training samples. The dataset is then fully shuffled so that " + }, + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s^i" + }, + { + "bbox": [ + 304, + 121, + 545, + 228 + ], + "type": "text", + "content": " corresponding to the same face image cannot be easily associated." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "text", + "content": "We also control the randomness to a moderate level by specifying the possible combinations of " + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "inline_equation", + "content": "S, P" + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "text", + "content": " in advance. Concretely, we opt for choosing one " + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "inline_equation", + "content": "S, P" + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "inline_equation", + "content": "\\mathbf{S} = \\{S_1, \\dots, S_m\\}" + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "inline_equation", + "content": "\\mathbf{P} = \\{P_1, \\dots, P_n\\}" + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "text", + "content": " respectively, where " + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "inline_equation", + "content": "\\mathbf{S}, \\mathbf{P}" + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "text", + "content": " are determined by the service provider. We specifically require " + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "inline_equation", + "content": "\\{S_1, \\dots, S_n\\}" + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "text", + "content": " to be a non-overlapping partition of channels from " + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_h" + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "text", + "content": " (i.e., divide " + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_h" + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "text", + "content": " into equal-length subsets) to maximize the use of " + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_h" + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "text", + "content": " and reduce model bias. Therefore, each " + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s^i" + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "text", + "content": " is picked from one of " + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "inline_equation", + "content": "m \\times n" + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "text", + "content": " fixed combinations of channels, called ranks. This allows us to facilitate the training and overcome sampling biases. The service provider shares " + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{S}, \\mathbf{P}\\}" + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "text", + "content": " with all local devices, so the latter can generate their query " + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "text", + "content": " accordingly. During inference, the model is expected to provide consistent results of the same query " + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "text", + "content": " regardless of the choice of rank, since it learned about a mapping from local features to the face's entirety. We later testify to it in Sec. 4.3. Meanwhile, the model is still unaware of the sample-wise specific choice of " + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "inline_equation", + "content": "\\{S, P\\}" + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "text", + "content": " as the recognition relies on nothing else but " + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 304, + 228, + 546, + 468 + ], + "type": "text", + "content": " alone. Hence privacy is maintained." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 468, + 545, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 545, + 553 + ], + "type": "text", + "content": "To conclude, we present PartialFace that train and infer the recognition model with " + }, + { + "bbox": [ + 304, + 468, + 545, + 553 + ], + "type": "inline_equation", + "content": "\\arg \\min_{\\theta} l(f(\\mathbf{x}_s^i, \\theta), y)" + }, + { + "bbox": [ + 304, + 468, + 545, + 553 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 468, + 545, + 553 + ], + "type": "inline_equation", + "content": "X = \\{\\mathbf{x}_l, \\mathbf{x}_h\\}" + }, + { + "bbox": [ + 304, + 468, + 545, + 553 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 468, + 545, + 553 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s^i = \\mathbf{x}_h \\cdot S \\cdot P" + }, + { + "bbox": [ + 304, + 468, + 545, + 553 + ], + "type": "text", + "content": " in random, parameterized by " + }, + { + "bbox": [ + 304, + 468, + 545, + 553 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{S}, \\mathbf{P}\\}" + }, + { + "bbox": [ + 304, + 468, + 545, + 553 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 468, + 545, + 553 + ], + "type": "inline_equation", + "content": "(\\sigma, s, r, m, n)" + }, + { + "bbox": [ + 304, + 468, + 545, + 553 + ], + "type": "text", + "content": ". Later analyses in Secs. 4.2 and 4.3 show PartialFace overcomes the drawback of the vanilla method, plus outperforms most prior arts, to achieve satisfactory recognition accuracy." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 562, + 491, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 562, + 491, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 562, + 491, + 574 + ], + "type": "text", + "content": "3.5. Enhance privacy with randomness" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 581, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 581, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 545, + 640 + ], + "type": "text", + "content": "The benefit of randomness is multi-fold. We have discussed it for now on helping address the accuracy and privacy balance and enhance recognition performance. In retrospect, we briefly elaborate on how randomness further safeguards privacy to a large extent." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Recall we remove visual information by pruning " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_l" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " and impede recovery by choosing a subset of " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": ". After that, randomness further obstructs recovery: To impose recovery, the attacker exploits not only the channels' information but also their relative orders and positions in the frequency spectrum. We introduce " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " to distort the order of channels to" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19677" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "this end. As the recognition model does not require samplewise " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "\\{S,P\\}" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": ", they won't be exposed to the attacker. Figure 4(c) shows the improvement against recovery if the attacker doesn't know the specific choice of subsets." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 132, + 128, + 145 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 132, + 128, + 145 + ], + "spans": [ + { + "bbox": [ + 47, + 132, + 128, + 145 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 152, + 171, + 165 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 152, + 171, + 165 + ], + "spans": [ + { + "bbox": [ + 47, + 152, + 171, + 165 + ], + "type": "text", + "content": "4.1. Experimental settings" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 170, + 288, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 170, + 288, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 170, + 288, + 326 + ], + "type": "text", + "content": "We compare PartialFace with the unprotected baseline and prior PPFR methods on three criteria: recognition performance, privacy protection of visual information, and that against recovery attack. We further study the computation and cost of PartialFace. We mainly employ an IR-50 [11] trained on the MS1Mv2 [10] dataset as our FR model, while also using a smaller combination of IR-18 and the BUPT [40] dataset on some resource-consuming experiments. We set " + }, + { + "bbox": [ + 46, + 170, + 288, + 326 + ], + "type": "inline_equation", + "content": "(\\sigma, s, r, m, n) = (10, 9, 18, 6, 6)" + }, + { + "bbox": [ + 46, + 170, + 288, + 326 + ], + "type": "text", + "content": " and use fixed " + }, + { + "bbox": [ + 46, + 170, + 288, + 326 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{S}, \\mathbf{P}\\}" + }, + { + "bbox": [ + 46, + 170, + 288, + 326 + ], + "type": "text", + "content": ", if not else specified. Benchmarks are carried out on 5 widely used, regular-size datasets, LFW [13], CFP-FP [35], AgeDB [31], CPLFW [49] and CALFW [50], and 2 large-scale datasets, IJB-B [43] and IJB-C [23]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 334, + 244, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 334, + 244, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 334, + 244, + 346 + ], + "type": "text", + "content": "4.2. Benchmarks on recognition accuracy" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 352, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 287, + 579 + ], + "type": "text", + "content": "Compared methods. We compare PartialFace with 2 unprotected baselines, 4 perturbation-based PPFR methods, and 3 methods base on the frequency domain that share close relation to us. Results are summarized in Tab. 1. Here, (1) ArcFace [6] denotes the unprotected SOTA trained directly on RGB images; (2) ArcFace-FD [45] is the ArcFace trained on the image's all frequency channels; (3) PEEP [3] is a differential-privacy-based method with a privacy budget " + }, + { + "bbox": [ + 46, + 352, + 287, + 579 + ], + "type": "inline_equation", + "content": "\\epsilon = 5" + }, + { + "bbox": [ + 46, + 352, + 287, + 579 + ], + "type": "text", + "content": "; (4) Cloak [27] perturbs and compresses its input feature space. Its accuracy-privacy trade-off parameter is set to 100; (5) InstaHide [14] mixes up " + }, + { + "bbox": [ + 46, + 352, + 287, + 579 + ], + "type": "inline_equation", + "content": "k = 2" + }, + { + "bbox": [ + 46, + 352, + 287, + 579 + ], + "type": "text", + "content": " images and performs a distributed encryption; (6) CPGAN [36] generates compressed protected representation by a joint effort of GAN and differential privacy; (7) PPFR-FD1 [42] adopts a channel-wise shuffle-and-mix strategy in the frequency domain; (8) DCTDP [15] perturbs the frequency components by a noise disturbance mask with learnable privacy budget, where we set " + }, + { + "bbox": [ + 46, + 352, + 287, + 579 + ], + "type": "inline_equation", + "content": "\\epsilon = 1" + }, + { + "bbox": [ + 46, + 352, + 287, + 579 + ], + "type": "text", + "content": "; (9) DuetFace [26] is a two-party framework that employs channel splitting and attention transfer." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 580, + 287, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 287, + 675 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 287, + 675 + ], + "type": "text", + "content": "Performance. Results are reported on LFW, CFP-FP, AgeDB, CPLFW, and CALFW by accuracy, and on IJB-B and IJB-C by TPR@FPR(1e-4). Table 1 shows PartialFace achieves close performance to the unprotected baseline, with a small accuracy gap of " + }, + { + "bbox": [ + 46, + 580, + 287, + 675 + ], + "type": "inline_equation", + "content": "\\leq 0.8\\%" + }, + { + "bbox": [ + 46, + 580, + 287, + 675 + ], + "type": "text", + "content": ". In comparison, perturbation-based methods all generalize unsatisfactorily on large-scale benchmarks. PartialFace outperforms all PPFR prior arts but DuetFace. While DuetFace achieves" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "text", + "content": "1The results of PPFR-FD on IJB-B is unattainable due its non-disclosure of source code. The rest is quoted from its paper [42]. Please note its experimental condition may have slight inconsistency with ours." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 313, + 70, + 540, + 149 + ], + "blocks": [ + { + "bbox": [ + 313, + 70, + 540, + 149 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 540, + 149 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 540, + 149 + ], + "type": "image", + "image_path": "4be29bb14fefddc554c294db7c50ba56734f4bce6f2b41ec480aba7e69bd3c55.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 152, + 545, + 185 + ], + "lines": [ + { + "bbox": [ + 305, + 152, + 545, + 185 + ], + "spans": [ + { + "bbox": [ + 305, + 152, + 545, + 185 + ], + "type": "text", + "content": "Figure 6. Visualization of model attention via Grad-CAM. (a) PartialFace (1st row) compared with vanilla models (2nd row) on each of 6 different ranks. (b) Integrated attention of all ranks." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 205, + 545, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 205, + 545, + 242 + ], + "spans": [ + { + "bbox": [ + 305, + 205, + 545, + 242 + ], + "type": "text", + "content": "slightly higher accuracy, its protection is inferior to ours as it only covers the inference phase and can be easily nullified by recovery attacks, later see Secs. 4.4 and 4.5." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 251, + 499, + 263 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 251, + 499, + 263 + ], + "spans": [ + { + "bbox": [ + 306, + 251, + 499, + 263 + ], + "type": "text", + "content": "4.3. Comparison with the vanilla method" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "text", + "content": "We elaborate that randomized PartialFace outperforms the vanilla method that fixes channels in not only recognition accuracy but also robustness. As PartialFace employs data augmentation, for a fair comparison regarding the volume of training data, we consider two experimental settings: the standard PartialFace and one without augmentation " + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "inline_equation", + "content": "(r = 1)" + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "text", + "content": ". We also set " + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "inline_equation", + "content": "n = 1" + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "text", + "content": " to rule out permutation: " + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "text", + "content": " is introduced for privacy and is out of our interest here. There are therefore " + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "inline_equation", + "content": "m \\times n = 6" + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "text", + "content": " combinations of channels, or ranks. As channels from different ranks carry distinct information that may affect the performance, we train one vanilla model on each rank and average their test accuracy, with the range marked in parentheses. Though PartialFace is able to infer from arbitrary rank, we evaluate its robustness by inferring from each fixed rank separately. The model is robust if it performs on different ranks consistently (small range). Results are reported on IJB-B/C by TPR@FPR(1e-4) in Tab. 2. Performance. PartialFace achieves an average accuracy gain of " + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "inline_equation", + "content": "7.53\\%" + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "inline_equation", + "content": "7.75\\%" + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "text", + "content": " on IJB-B/C, respectively, compared to the vanilla. The performance is close to the unprotected baseline, showing that the privacy-accuracy trade-off of PartialFace is highly efficient. Even PartialFace without augmentation outperforms the vanilla for about " + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "text", + "content": ". We further note: (1) The range shows PartialFace is more robust than the vanilla under different " + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "text", + "content": ". (2) PartialFace outperforms the vanilla for all individual " + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 304, + 270, + 545, + 604 + ], + "type": "text", + "content": ". This suggests that randomness empowers PartialFace with the knowledge of the entirety instead of that of certain informative ranks." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Visualization. We visualize the rank-wise attention of PartialFace and the vanilla via Grad-CAM [34], see Fig. 6(a). The attention of each vanilla model is restrained to local facial features, which indicates the inadequate learning of the entirety features. PartialFace generate accurate attention on the entire face regardless the rank. We integrated the attention across all ranks in Fig. 6(b). All vanilla models' attention combined gains attention on the entire face, which testifies to our \"learn-entropy-from-local\" theory. Also to" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19678" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 85, + 70, + 509, + 223 + ], + "blocks": [ + { + "bbox": [ + 85, + 70, + 509, + 223 + ], + "lines": [ + { + "bbox": [ + 85, + 70, + 509, + 223 + ], + "spans": [ + { + "bbox": [ + 85, + 70, + 509, + 223 + ], + "type": "table", + "html": "
MethodPPFRLFWCFP-FPAgeDBCPLFWCALFWIJB-BIJB-C
ArcFace [6]No99.7798.3097.8892.7796.0594.1395.60
ArcFace-FD [45]No99.7898.0498.1092.4896.0394.0895.64
PEEP [3]Yes98.4174.4787.4779.5890.065.826.02
Cloak [27]Yes98.9187.9792.6083.4392.1833.5833.82
InstaHide [14]Yes96.5383.2079.5881.0386.2461.8869.02
CPGAN [36]Yes98.8794.6196.9890.4394.7992.6794.31
PPFR-FD [42]Yes99.6895.0497.3790.7895.72/94.10
DCTDP [15]Yes99.7796.9797.7291.3796.0593.2994.43
DuetFace [26]Yes99.8297.7997.9392.3596.1093.6695.30
PartialFace (ours)Yes99.8097.6397.7992.0396.0793.6494.93
", + "image_path": "9229b85a363fdfc0cb65b863654e150369e519ad6689bbbf421e62e3cf593db6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 51, + 251, + 282, + 321 + ], + "blocks": [ + { + "bbox": [ + 78, + 223, + 514, + 234 + ], + "lines": [ + { + "bbox": [ + 78, + 223, + 514, + 234 + ], + "spans": [ + { + "bbox": [ + 78, + 223, + 514, + 234 + ], + "type": "text", + "content": "Table 1. Benchmarks on recognition accuracy. PartialFace is compared with the unprotected baselines and PPFR SOTAs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 251, + 282, + 321 + ], + "lines": [ + { + "bbox": [ + 51, + 251, + 282, + 321 + ], + "spans": [ + { + "bbox": [ + 51, + 251, + 282, + 321 + ], + "type": "table", + "html": "
MethodIJB-B (range)IJB-C (range)
ArcFace86.8390.35
Vanilla78.24 (-14.49/7.36)80.73 (-16.37/7.45)
PF w/o aug.81.43 (-4.19/2.88)82.81 (-4.29/2.79)
PartialFace85.77 (-1.95/1.25)88.48 (-1.71/1.18)
", + "image_path": "3ca4b231a95ab3f987e6c4f482d53e3ee1d2efd320b2002e813a0f74ee47ed74.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 47, + 323, + 287, + 356 + ], + "lines": [ + { + "bbox": [ + 47, + 323, + 287, + 356 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 287, + 356 + ], + "type": "text", + "content": "Table 2. Comparison with the vanilla method by accuracy and robustness. Experiments are conducted on IR-18 + BUPT. \"PF w/o aug.\" indicates PartialFace without augmentation." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 376, + 287, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 287, + 411 + ], + "type": "text", + "content": "note that PartialFace has similar attention across all ranks. This allows it to recognize " + }, + { + "bbox": [ + 47, + 376, + 287, + 411 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 47, + 376, + 287, + 411 + ], + "type": "text", + "content": " using arbitrary rank, as they produce aligned outcomes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 420, + 219, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 420, + 219, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 420, + 219, + 430 + ], + "type": "text", + "content": "4.4. Protection of visual information" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 437, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 653 + ], + "type": "text", + "content": "We investigate PartialFace's protection of privacy. We reiterate that the first privacy goal is to conceal the visual information of face images. We compare ParitalFace with 3 PPFR SOTAs using the frequency domain: PPFR-FD [42], DCTDP [15], and DuetFace [26]. These prior arts are closely related to ours since we all leverage the perceptual difference between humans and models as means of protection. However, they differ in the processing of frequency components: Both PPFR-FD and DCTDP remove the component with the highest energy (the DC component). To obfuscate the remaining components, PPFR-FD employs mix-and-shuffle and DCTDP applies a noise mechanism. DuetFace is the most related method in the pruning of low-frequency components. We note in special that they retain 36, 63, and 54 high-frequency channels, respectively, while PartialFace retains 9. We now demonstrate the methodological differences and varied number of channels result in contrasting privacy protection capacities." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": "Figure 7 exemplifies face images processed (therefore are supposed to be protective) by each compared method. As all methods carry out protection in the frequency domain, we convert images back by padding any removed frequency components with zero and applying an inverse" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 313, + 252, + 538, + 349 + ], + "blocks": [ + { + "bbox": [ + 313, + 252, + 538, + 349 + ], + "lines": [ + { + "bbox": [ + 313, + 252, + 538, + 349 + ], + "spans": [ + { + "bbox": [ + 313, + 252, + 538, + 349 + ], + "type": "image", + "image_path": "4c9f094437d115070dee2563daa4d1aae5335c6c56ab7084b7a34ba40d8933e7.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 350, + 545, + 384 + ], + "lines": [ + { + "bbox": [ + 305, + 350, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 305, + 350, + 545, + 384 + ], + "type": "text", + "content": "Figure 7. Example face images of (a) unprotected ArcFace, (b-d) compared SOTAs, and (e) PartialFace, during both training and inference phase. PartialFace best conceals visual information." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 406, + 545, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 406, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 406, + 545, + 550 + ], + "type": "text", + "content": "transform. PartialFace, e.g., has " + }, + { + "bbox": [ + 304, + 406, + 545, + 550 + ], + "type": "inline_equation", + "content": "X' = \\mathcal{T}^{-1}(\\{\\mathbf{0}, \\mathbf{x}_h\\})" + }, + { + "bbox": [ + 304, + 406, + 545, + 550 + ], + "type": "text", + "content": ". We visualize the training and inference phases separately, as the compared methods' processing on them may vary: During inference, we argue PPFR-FD and DuetFace (Fig. 7(b)(d)) provide inadequate protection, as one can still discern the face quite clearly in their processed images. DCTDP effectively conceals visual information after obfuscating the channels with its proposed noise mask (Fig. 7(c)). However, its protection during training is impaired, as it requires access to abundant non-obfuscated components to learn the mask. DuetFace manifests a similar weakness as it relies on original images to rectify the model's attention (Fig. 7(d))." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 551, + 545, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 551, + 545, + 623 + ], + "spans": [ + { + "bbox": [ + 304, + 551, + 545, + 623 + ], + "type": "text", + "content": "PartialFace first discards most visual information by pruning " + }, + { + "bbox": [ + 304, + 551, + 545, + 623 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_l" + }, + { + "bbox": [ + 304, + 551, + 545, + 623 + ], + "type": "text", + "content": ". The rest is further partitioned when sampling " + }, + { + "bbox": [ + 304, + 551, + 545, + 623 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 304, + 551, + 545, + 623 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 551, + 545, + 623 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_h" + }, + { + "bbox": [ + 304, + 551, + 545, + 623 + ], + "type": "text", + "content": ". By energy, each " + }, + { + "bbox": [ + 304, + 551, + 545, + 623 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 304, + 551, + 545, + 623 + ], + "type": "text", + "content": " carries less than " + }, + { + "bbox": [ + 304, + 551, + 545, + 623 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 551, + 545, + 623 + ], + "type": "text", + "content": " of visual information compared to the original " + }, + { + "bbox": [ + 304, + 551, + 545, + 623 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 551, + 545, + 623 + ], + "type": "text", + "content": ". As a result, Fig. 7(e) shows PartialFace provides better protection on visual information than related SOTAs in both phases." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 634, + 456, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 634, + 456, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 634, + 456, + 647 + ], + "type": "text", + "content": "4.5. Protection against recovery" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "We here provide an in-depth analysis of how Partial-Face impedes recovery. Our primary aiming is to show how the removal of model-exploitable information and the randomness of channels contribute to the defense. Assume the recovery attacker possesses a collection of face im" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19679" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 71, + 126, + 142 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 126, + 142 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 126, + 142 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 126, + 142 + ], + "type": "image", + "image_path": "b36414754013647d0b1b57b22ac11e3fb44dbbff5a221102a9d96d139fe7e62b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 71, + 143, + 111, + 151 + ], + "lines": [ + { + "bbox": [ + 71, + 143, + 111, + 151 + ], + "spans": [ + { + "bbox": [ + 71, + 143, + 111, + 151 + ], + "type": "text", + "content": "(a) black-box" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 132, + 72, + 202, + 142 + ], + "blocks": [ + { + "bbox": [ + 132, + 72, + 202, + 142 + ], + "lines": [ + { + "bbox": [ + 132, + 72, + 202, + 142 + ], + "spans": [ + { + "bbox": [ + 132, + 72, + 202, + 142 + ], + "type": "image", + "image_path": "9f6e40b8c24f97d1466a4b74688cf7a16b625c1b15c577a45c960408751d2fab.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 147, + 143, + 187, + 151 + ], + "lines": [ + { + "bbox": [ + 147, + 143, + 187, + 151 + ], + "spans": [ + { + "bbox": [ + 147, + 143, + 187, + 151 + ], + "type": "text", + "content": "(b) white-box" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 154, + 286, + 198 + ], + "lines": [ + { + "bbox": [ + 46, + 154, + 286, + 198 + ], + "spans": [ + { + "bbox": [ + 46, + 154, + 286, + 198 + ], + "type": "text", + "content": "Figure 8. Examples of recovered face images of PartialFace under attackers with varied capabilities: (a) a black-box, (b) a white-box, and (c) an enhanced white-box attacker. PartialFace effectively prevents recovery as all images are blurry and hardly identifiable." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 209, + 72, + 278, + 142 + ], + "blocks": [ + { + "bbox": [ + 209, + 72, + 278, + 142 + ], + "lines": [ + { + "bbox": [ + 209, + 72, + 278, + 142 + ], + "spans": [ + { + "bbox": [ + 209, + 72, + 278, + 142 + ], + "type": "image", + "image_path": "2ec6786deb502db39b178c922a73e859ca5cb920c736b2580c067ecce1d799dc.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 208, + 143, + 279, + 150 + ], + "lines": [ + { + "bbox": [ + 208, + 143, + 279, + 150 + ], + "spans": [ + { + "bbox": [ + 208, + 143, + 279, + 150 + ], + "type": "text", + "content": "(c) enhanced white-box" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 67, + 210, + 114, + 258 + ], + "blocks": [ + { + "bbox": [ + 67, + 210, + 114, + 258 + ], + "lines": [ + { + "bbox": [ + 67, + 210, + 114, + 258 + ], + "spans": [ + { + "bbox": [ + 67, + 210, + 114, + 258 + ], + "type": "image", + "image_path": "5246ab7aa1628fc9357eac73cf5316375c94ed717803f0d9b9ae55385f3f8e70.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 74, + 260, + 107, + 267 + ], + "lines": [ + { + "bbox": [ + 74, + 260, + 107, + 267 + ], + "spans": [ + { + "bbox": [ + 74, + 260, + 107, + 267 + ], + "type": "text", + "content": "(a) PPFR-FD" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 270, + 286, + 292 + ], + "lines": [ + { + "bbox": [ + 47, + 270, + 286, + 292 + ], + "spans": [ + { + "bbox": [ + 47, + 270, + 286, + 292 + ], + "type": "text", + "content": "Figure 9. Recovered images from (a-c) compared SOTAs and (d) PartialFace. PartialFace impedes recovery better than the rest." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 118, + 211, + 165, + 258 + ], + "blocks": [ + { + "bbox": [ + 118, + 211, + 165, + 258 + ], + "lines": [ + { + "bbox": [ + 118, + 211, + 165, + 258 + ], + "spans": [ + { + "bbox": [ + 118, + 211, + 165, + 258 + ], + "type": "image", + "image_path": "75a31fec39f98ee594aefc2423a92a13a4582695fb84586e268e9e86a555d9f1.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 127, + 260, + 156, + 267 + ], + "lines": [ + { + "bbox": [ + 127, + 260, + 156, + 267 + ], + "spans": [ + { + "bbox": [ + 127, + 260, + 156, + 267 + ], + "type": "text", + "content": "(b) DCTDP" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 168, + 211, + 216, + 258 + ], + "blocks": [ + { + "bbox": [ + 168, + 211, + 216, + 258 + ], + "lines": [ + { + "bbox": [ + 168, + 211, + 216, + 258 + ], + "spans": [ + { + "bbox": [ + 168, + 211, + 216, + 258 + ], + "type": "image", + "image_path": "dd07ffcce9771c0220ec9fa756795eaba24c2aaf885946d305b10788d435de63.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 175, + 260, + 209, + 267 + ], + "lines": [ + { + "bbox": [ + 175, + 260, + 209, + 267 + ], + "spans": [ + { + "bbox": [ + 175, + 260, + 209, + 267 + ], + "type": "text", + "content": "(c) DuetFace" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 220, + 211, + 267, + 258 + ], + "blocks": [ + { + "bbox": [ + 220, + 211, + 267, + 258 + ], + "lines": [ + { + "bbox": [ + 220, + 211, + 267, + 258 + ], + "spans": [ + { + "bbox": [ + 220, + 211, + 267, + 258 + ], + "type": "image", + "image_path": "79f085360aba579d4f5feb441c65b5d9d05b64e4e87a7caca0788730de77e3d2.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 233, + 260, + 254, + 267 + ], + "lines": [ + { + "bbox": [ + 233, + 260, + 254, + 267 + ], + "spans": [ + { + "bbox": [ + 233, + 260, + 254, + 267 + ], + "type": "text", + "content": "(d) ours" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "text", + "content": "ages " + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "inline_equation", + "content": "\\{X\\}" + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "text", + "content": " and is aware of the protection mechanism. It can locally generate protected representations " + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "inline_equation", + "content": "X^{\\prime}" + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}_h" + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "text", + "content": " in our case) from " + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "text", + "content": ", then train a malicious model " + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "inline_equation", + "content": "\\arg \\min_{\\delta}l^{\\prime}(g(X^{\\prime},\\delta),X)" + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "text", + "content": ", with the aiming to inversely fit " + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "inline_equation", + "content": "X^{\\prime}" + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "text", + "content": ". Having intercepted a recognition query, the attacker leverages " + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "text", + "content": " to recover the concealed visual information. Upon the knowledge it possesses, a black-box attacker is one unknowing of necessary parameters (" + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{S},\\mathbf{P}\\}" + }, + { + "bbox": [ + 46, + 315, + 286, + 469 + ], + "type": "text", + "content": " in our case), whilst a white-box attacker possesses such knowledge. We also study the capability of PPFR-FD, DCTDP, and DuetFace against the white-box attacker. We further investigate an enhanced white-box attacker, who imposes threats dedicated to the randomness of PartialFace." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 472, + 286, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 286, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 286, + 579 + ], + "type": "text", + "content": "Black-box attacker. It is concretized as a malicious third party, uninvolved in the recognition yet eager to wiretap the transmission. For each attacker, We employ a full-scale U-Net [32] as the recovery model and train it on BUPT. Unknown of " + }, + { + "bbox": [ + 46, + 472, + 286, + 579 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{S},\\mathbf{P}\\}" + }, + { + "bbox": [ + 46, + 472, + 286, + 579 + ], + "type": "text", + "content": ", it must produce " + }, + { + "bbox": [ + 46, + 472, + 286, + 579 + ], + "type": "inline_equation", + "content": "X^{\\prime}" + }, + { + "bbox": [ + 46, + 472, + 286, + 579 + ], + "type": "text", + "content": " based on its own conjectured " + }, + { + "bbox": [ + 46, + 472, + 286, + 579 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{S}^{\\prime},\\mathbf{P}^{\\prime}\\}" + }, + { + "bbox": [ + 46, + 472, + 286, + 579 + ], + "type": "text", + "content": ", which is believably inconsistent with that applied to the recognition model. Thus produced " + }, + { + "bbox": [ + 46, + 472, + 286, + 579 + ], + "type": "inline_equation", + "content": "X^{\\prime}" + }, + { + "bbox": [ + 46, + 472, + 286, + 579 + ], + "type": "text", + "content": " are invalid samples and training " + }, + { + "bbox": [ + 46, + 472, + 286, + 579 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 46, + 472, + 286, + 579 + ], + "type": "text", + "content": " on them will nullify the recovery, as shown in Fig. 8(a)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 580, + 286, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 286, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 286, + 687 + ], + "type": "text", + "content": "White-box attacker. The candidate combinations " + }, + { + "bbox": [ + 46, + 580, + 286, + 687 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{S},\\mathbf{P}\\}" + }, + { + "bbox": [ + 46, + 580, + 286, + 687 + ], + "type": "text", + "content": " is known by any party participates in the recognition, e.g., an honest-but-curious server. Such an attacker can generate " + }, + { + "bbox": [ + 46, + 580, + 286, + 687 + ], + "type": "inline_equation", + "content": "X^{\\prime}" + }, + { + "bbox": [ + 46, + 580, + 286, + 687 + ], + "type": "text", + "content": " correctly. However, receiving a query " + }, + { + "bbox": [ + 46, + 580, + 286, + 687 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 46, + 580, + 286, + 687 + ], + "type": "text", + "content": ", the attacker is unknowing of its channels' position and order, since the specific " + }, + { + "bbox": [ + 46, + 580, + 286, + 687 + ], + "type": "inline_equation", + "content": "\\{S,P\\}" + }, + { + "bbox": [ + 46, + 580, + 286, + 687 + ], + "type": "text", + "content": " doesn't come with " + }, + { + "bbox": [ + 46, + 580, + 286, + 687 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 46, + 580, + 286, + 687 + ], + "type": "text", + "content": ". The missing information is vital to recovery. Consequently, the attack is obstructed by " + }, + { + "bbox": [ + 46, + 580, + 286, + 687 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 46, + 580, + 286, + 687 + ], + "type": "text", + "content": " 's randomness in Fig. 8(b): The recovered image is blurry and hardly identifiable." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": "We plus compare with PPFR-FD, DCTDP and Duet-Face under the white-box settings. Among them, Duet" + } + ] + } + ], + "index": 19 + }, + { + "type": "table", + "bbox": [ + 306, + 70, + 536, + 141 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 536, + 141 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 536, + 141 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 536, + 141 + ], + "type": "table", + "html": "
MethodSSIM (↓)PSNR (↓)Accuracy (↓)
PPFR-FD0.71315.6683.73
DCTDP0.68715.4279.60
DuetFace0.86619.8896.52
PartialFace0.59113.7065.35
", + "image_path": "25920325fd36a4bf9ae58c52990b2006e62a0870946815e94e02e176b5de73f7.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "table_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 142, + 545, + 174 + ], + "lines": [ + { + "bbox": [ + 305, + 142, + 545, + 174 + ], + "spans": [ + { + "bbox": [ + 305, + 142, + 545, + 174 + ], + "type": "text", + "content": "Table 3. Quantitative analyses of the recovery quality. Lower SSIM, PSNR and accuracy suggest better protection. Here, we remind the accuracy of verification is lower bounded by 50.00." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 326, + 186, + 373, + 232 + ], + "blocks": [ + { + "bbox": [ + 326, + 186, + 373, + 232 + ], + "lines": [ + { + "bbox": [ + 326, + 186, + 373, + 232 + ], + "spans": [ + { + "bbox": [ + 326, + 186, + 373, + 232 + ], + "type": "image", + "image_path": "06238690f2f1ea7ed00a3cbef62416ebf8fc4ed54f3518aa8e4738eda95cb857.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 236, + 544, + 258 + ], + "lines": [ + { + "bbox": [ + 306, + 236, + 544, + 258 + ], + "spans": [ + { + "bbox": [ + 306, + 236, + 544, + 258 + ], + "type": "text", + "content": "Figure 10. Recovered images from extracted identity templates, that are blurry and can hardly be inferred by humans or models." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 377, + 186, + 424, + 232 + ], + "blocks": [ + { + "bbox": [ + 377, + 186, + 424, + 232 + ], + "lines": [ + { + "bbox": [ + 377, + 186, + 424, + 232 + ], + "spans": [ + { + "bbox": [ + 377, + 186, + 424, + 232 + ], + "type": "image", + "image_path": "8ebeb2b1f03ded30bf944efa3bed36eddf883b66e7352449b1ec3ec4b5d206dc.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 428, + 186, + 474, + 232 + ], + "blocks": [ + { + "bbox": [ + 428, + 186, + 474, + 232 + ], + "lines": [ + { + "bbox": [ + 428, + 186, + 474, + 232 + ], + "spans": [ + { + "bbox": [ + 428, + 186, + 474, + 232 + ], + "type": "image", + "image_path": "b2aefcfc9eb18c603470c9f72e01dbbe729f7a2bfc463b67a7f5f61c2787f847.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 479, + 186, + 525, + 232 + ], + "blocks": [ + { + "bbox": [ + 479, + 186, + 525, + 232 + ], + "lines": [ + { + "bbox": [ + 479, + 186, + 525, + 232 + ], + "spans": [ + { + "bbox": [ + 479, + 186, + 525, + 232 + ], + "type": "image", + "image_path": "aab93b1ffd9cfdc2529b203d64066811abfdc487694f7f0a92f0c610e423973e.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 279, + 545, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 279, + 545, + 374 + ], + "spans": [ + { + "bbox": [ + 304, + 279, + 545, + 374 + ], + "type": "text", + "content": "Face shows almost no resistance to recovery (Fig. 9(c)). PPFR-FD and DCTDP provide inadequate protection, as images recovered from them (Fig. 9(a-b)) are blurred yet still clearly identifiable. The protection is impaired as their processed images retain most high-frequency components, and the excessive perceivable information is learned by the recovery model. In comparison, PartialFace (Fig. 9(d)) offers significantly outperformed protection." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "text", + "content": "Enhanced white-box attacker. A resource-unbounded attacker may brute-forcibly break the randomness of Partial-Face leveraging a more sophisticated attack: it trains a series of attack models, one for each candidate " + }, + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "inline_equation", + "content": "\\{S,P\\}" + }, + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "text", + "content": ". Receiving " + }, + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "text", + "content": ", the attacker feeds it into every model to try every combination of " + }, + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "inline_equation", + "content": "\\{S,P\\}" + }, + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "text", + "content": ", until one produces the best recovery. The vague face images in Fig. 8(c) imply the attempted recovery is unsuccessful, even if the attacker finds the correct " + }, + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "inline_equation", + "content": "\\{S,P\\}" + }, + { + "bbox": [ + 304, + 375, + 545, + 494 + ], + "type": "text", + "content": ". This is attributed to the reduction of model-exploitable channels." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 495, + 545, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 614 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 614 + ], + "type": "text", + "content": "Quantitative comparison. To quantitatively assess the recovery quality, we measure the average structural similarity index (SSIM) and peak signal-to-noise ratio (PSNR) of the recovered images. Additionally, to study if the attacker can exploit its outcome for recognition proposes, we feed the images into a pre-trained model and measure verification accuracy. Lower SSIM, PSNR, and recognition accuracy suggest deficient recovery, thus indicating a higher level of protection. The results in Tab. 3 suggest PartialFace outperforms its competitors in all three evaluated metrics." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 623, + 529, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 529, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 529, + 635 + ], + "type": "text", + "content": "4.6. Protection against recovery from templates" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "content": "By the principle of FR, all " + }, + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "content": " of face image " + }, + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "content": " are later extracted to very similar identity templates, so the recognition on them produces aligned results. Here, one would arise concern that recovery can also be carried out on the extracted templates, which theoretically contain the faces' full identity information, to realize better inversion of im" + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19680" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 71, + 287, + 209 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 287, + 209 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 287, + 209 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 287, + 209 + ], + "type": "table", + "html": "
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", + "image_path": "8e7745c237f63c53c557a904242692934196ed237e424471aff5444c3cc3a6ee.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 49, + 251, + 285, + 299 + ], + "blocks": [ + { + "bbox": [ + 47, + 210, + 287, + 243 + ], + "lines": [ + { + "bbox": [ + 47, + 210, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 210, + 287, + 243 + ], + "type": "text", + "content": "Table 4. Ablation study on combinations of hyperparameters. Experiments are carried out on IR-18 + BUPT. When changing one of them, we keep the rest to default values, i.e., " + }, + { + "bbox": [ + 47, + 210, + 287, + 243 + ], + "type": "inline_equation", + "content": "(r,m,n) = (18,6,6)" + }, + { + "bbox": [ + 47, + 210, + 287, + 243 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 251, + 285, + 299 + ], + "lines": [ + { + "bbox": [ + 49, + 251, + 285, + 299 + ], + "spans": [ + { + "bbox": [ + 49, + 251, + 285, + 299 + ], + "type": "table", + "html": "
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", + "image_path": "83582d532c5902120596209d9bab4adc7a60d7de43f4a303d711a3765a2bcc1a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 300, + 286, + 331 + ], + "lines": [ + { + "bbox": [ + 47, + 300, + 286, + 331 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 286, + 331 + ], + "type": "text", + "content": "Table 5. Compatibility of PartialFace. FR models are trained using CosFace on IR-18 + BUPT. Combining PartialFace with CosFace also demonstrates high utility, compared to its baseline." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 351, + 286, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 351, + 286, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 351, + 286, + 373 + ], + "type": "text", + "content": "ages. We demonstrate that such a proposed attack is also ineffective to PartialFace." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 375, + 287, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 375, + 287, + 446 + ], + "spans": [ + { + "bbox": [ + 46, + 375, + 287, + 446 + ], + "type": "text", + "content": "Although there could be dedicated attacks on templates, in practice, high-quality recovery from them is difficult as templates are far more compact representations than images and channel subsets. In Fig. 10, the recovered images are highly blurred, and can hardly be inferred by humans or models, hence won't impose an effective threat." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 454, + 138, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 454, + 138, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 454, + 138, + 466 + ], + "type": "text", + "content": "4.7. Ablation study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "text", + "content": "PartialFace is parameterized by " + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "inline_equation", + "content": "(\\sigma, s, r, m, n)" + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "text", + "content": ". Among them, we note " + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "text", + "content": " is chosen according to channel energy, and " + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "text", + "content": " is determined by " + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "inline_equation", + "content": "(\\sigma, m)" + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "text", + "content": ". Table 4 analyzes the choice of the remaining parameters. Results show augmentation " + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "inline_equation", + "content": "(r)" + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "text", + "content": " enhances the model's performance, at the cost of taking longer time to train. " + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "text", + "content": " affects the performance mainly by its influence on " + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "text", + "content": ", as larger " + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "text", + "content": " leading to fewer channels in each " + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "text", + "content": ". We introduce " + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "text", + "content": " solely for privacy purposes. Results on " + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 472, + 287, + 591 + ], + "type": "text", + "content": " indicate a trade-off between accuracy and privacy. Generally, PartialFace is robust to the choice of parameters." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 599, + 209, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 209, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 209, + 612 + ], + "type": "text", + "content": "4.8. Complexity and compatibility" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 617, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 665 + ], + "type": "text", + "content": "Though PartialFace is proposed by studying the model's behavior, privacy protection is solely realized by processing the face images. The decoupling with model architecture and training tactics benefits resources and compatibility." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "content": "PartialFace is resource-efficient. Compared to the unprotected baseline, PartialFace doesn't increment model size as they share identical model architectures. Training does take more " + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "inline_equation", + "content": "(r)" + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "content": " time and storage due to augmentation, while we" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "argue it is acceptable for the service provider. The crucial inference time remains the same as the baseline, as DCT and sampling " + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": " only increase negligible computation costs." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 108, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 545, + 204 + ], + "type": "text", + "content": "PartialFace is well compatible. The decoupling of preprocessing and training also allows PartialFace to serve as a convenient plug-in: PartialFace can be integrated with SOTA FR methods to enjoy enhanced privacy protection. Specifically, we demonstrate the recognition accuracy on CosFace [38], a major competitor of ArcFace, in Tab. 5. Combining PartialFace with CosFace also results in high utility, as compared to its baseline." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 213, + 378, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 213, + 378, + 225 + ], + "spans": [ + { + "bbox": [ + 306, + 213, + 378, + 225 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 233, + 545, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 233, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 304, + 233, + 545, + 353 + ], + "type": "text", + "content": "This paper presents an in-depth study of the privacy protection of face images. Based on the observations on model perception and training behavior, we present two methodological advances, pruning low-frequency components and using randomly selected channels, to address the privacy goal of concealing visual information and impeding recovery. We distill our findings into a novel privacy-preserving face recognition method, PartialFace. Extensive experiments demonstrate that PartialFace effectively balances privacy protection goals and recognition accuracy." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 362, + 365, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 362, + 365, + 374 + ], + "spans": [ + { + "bbox": [ + 306, + 362, + 365, + 374 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 310, + 382, + 545, + 712 + ], + "type": "list", + "angle": 0, + "index": 22, + "blocks": [ + { + "bbox": [ + 310, + 382, + 545, + 470 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 382, + 545, + 470 + ], + "spans": [ + { + "bbox": [ + 310, + 382, + 545, + 470 + ], + "type": "text", + "content": "[1] Michel Abdalla, Florian Bourse, Angelo De Caro, and David Pointcheval. 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PMLR, 2022. 2, 3, 5" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "19684" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/ProPainter_ Improving Propagation and Transformer for Video Inpainting/447df786-8aae-4bc4-b7d5-1e90caa96cc1_content_list.json b/2023/ProPainter_ Improving Propagation and Transformer for Video Inpainting/447df786-8aae-4bc4-b7d5-1e90caa96cc1_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..b7fe2ded2a0d9d50e105966835e5d21fd2710a17 --- /dev/null +++ b/2023/ProPainter_ Improving Propagation and Transformer for Video Inpainting/447df786-8aae-4bc4-b7d5-1e90caa96cc1_content_list.json @@ -0,0 +1,1759 @@ +[ + { + "type": "text", + "text": "ProPainter: Improving Propagation and Transformer for Video Inpainting", + "text_level": 1, + "bbox": [ + 107, + 130, + 861, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shangchen Zhou Chongyi Li Kelvin C.K. Chan Chen Change Loy S-Lab, Nanyang Technological University", + "bbox": [ + 192, + 180, + 776, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{s200094，chongyi.li，chan0899，ccloy}@ntu.edu.sg", + "bbox": [ + 267, + 219, + 702, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://shangchenzhou.com/projects/ProPainter", + "bbox": [ + 284, + 236, + 683, + 250 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b732b1c0f3aa605872f94707e23d8c4302a19932fb9150ed7b74e9f0a48f6f3e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 279, + 299, + 404 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/578a78b77f2286d96a2cd0d5905ee5e460639d0d84352b08a580c227d1363994.jpg", + "image_caption": [ + "Sparse Query Space (masked window)" + ], + "image_footnote": [], + "bbox": [ + 336, + 282, + 459, + 369 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c8e256b499cb885f38ccba6bcfc4059c8c7d886d6c8369ff3007b69b347df166.jpg", + "image_caption": [ + "Sparse Key/Value Space (temporal strided window)" + ], + "image_footnote": [], + "bbox": [ + 467, + 282, + 584, + 369 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fdaa637903020c68b32926e26378ae3a3290bedb649a8e6a636dcb099b891a08.jpg", + "image_caption": [ + "(a) Dual-domain Propagation", + "(d) Input with object mask", + "Figure 1: (a) Dual-domain propagation enables more effective propagation due to its global and reliable nature. (b) Mask-guided sparse video Transformer achieves high efficiency by discarding unnecessary and redundant windows. (c) ProPainter outperforms prior methods while maintaining efficiency. (d-h) In visual comparisons with FuseFormer [22], FGT [42], and $\\mathrm{E}^2\\mathrm{FGVI}$ [19], our ProPainter exhibits superiority in filling complete and rich textures." + ], + "image_footnote": [], + "bbox": [ + 83, + 422, + 241, + 492 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6f6e279f101171584bab1bc53f1b9c9c82fb91cd2af74cebebb3b74b4b6dae1d.jpg", + "image_caption": [ + "(b) Mask-guided Sparse Video Transformer", + "(e) FuseFormer" + ], + "image_footnote": [], + "bbox": [ + 243, + 422, + 401, + 492 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/750da2b152646942cdd527a3e2235bc0bfc713406d2026574c2ba478235a4680.jpg", + "image_caption": [ + "(f) FGT" + ], + "image_footnote": [], + "bbox": [ + 403, + 422, + 562, + 492 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/906419075af44cbc8420f292582f7ee59bf7506739eb66a18517651f888e9255.jpg", + "image_caption": [ + "(c) Performance Gain" + ], + "image_footnote": [], + "bbox": [ + 620, + 270, + 883, + 407 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/000eccb62274be3e14d5500451d3145d325efd73faf294aab5dc4e13a1cfa9a5.jpg", + "image_caption": [ + "(g) $\\mathrm{E}^2\\mathrm{FGVI}$" + ], + "image_footnote": [], + "bbox": [ + 563, + 422, + 720, + 492 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6c22027452f062af6ec82b7e7241bb75e33ec2a752716b2f80f7e3c2d1e352fa.jpg", + "image_caption": [ + "(h) ProPainter (ours)" + ], + "image_footnote": [], + "bbox": [ + 723, + 422, + 883, + 492 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 592, + 312, + 608 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Flow-based propagation and spatiotemporal Transformer are two mainstream mechanisms in video inpainting (VI). Despite the effectiveness of these components, they still suffer from some limitations that affect their performance. Previous propagation-based approaches are performed separately either in the image or feature domain. Global image propagation isolated from learning may cause spatial misalignment due to inaccurate optical flow. Moreover, memory or computational constraints limit the temporal range of feature propagation and video Transformer, preventing exploration of correspondence information from distant frames. To address these issues, we propose an improved framework, called ProPainter, which involves enhanced ProPagation and an efficient Transformer. Specifically, we introduce dual-domain propagation that combines the advantages of image and feature warping, exploiting global correspondences reliably. We also propose a mask-guided sparse video Transformer, which achieves high efficiency by discarding unnecessary", + "bbox": [ + 73, + 628, + 473, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "and redundant tokens. With these components, ProPainter outperforms prior arts by a large margin of 1.46 dB in PSNR while maintaining appealing efficiency.", + "bbox": [ + 498, + 594, + 892, + 640 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 662, + 632, + 678 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Video inpainting (VI) aims to fill gaps or missing regions in a video with visually consistent content while ensuring spatial and temporal coherence. This technique has broad applications, including video completion [10], object removal [9, 37], video restoration [31], watermark, and logo removal [19]. VI is challenging because it requires establishing accurate correspondence across distant frames for information aggregation. To address this challenge, various mechanisms have been explored, such as 3D CNN [6, 11], video internal learning [41, 27], flow-guided propagation [37, 10, 43, 42, 19], and video Transformer [22, 42, 19]. Among these mechanisms, flow-guided propagation and video Transformer have become mainstream choices for VI due to their promising performance.", + "bbox": [ + 496, + 688, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10477", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Propagation-based methods in VI can be divided into two categories: image propagation and feature propagation. The former employs bidirectional global propagation in the image domain with a pre-completed flow field. While this approach can fill the majority of holes in a corrupted video, it requires an additional image or video inpainting network after propagation to hallucinate the remaining missing regions. This isolated two-step process can result in unpleasant artifacts and texture misalignment due to inaccurate flow, as shown in Figure 1(f). To address this issue, a recent approach called $\\mathrm{E}^2\\mathrm{FGVI}$ [19] implements propagation in the feature domain, incorporating flow completion and content hallucination modules in an end-to-end framework. With the learnable warping module, the feature propagation module relieves the pressure of having inaccurate flow. However, $\\mathrm{E}^2\\mathrm{FGVI}$ employs a downsampled flow field to match the spatial size of the feature domain, limiting the precision of spatial warping and the efficacy of propagation, potentially resulting in blurry results. Moreover, feature propagation can only be performed within a short range of video sequences due to memory and computational constraints, hindering propagation from distant frames and leading to missing texture, as shown in Figure 1(g).", + "bbox": [ + 76, + 90, + 472, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Both image- and feature-based propagation have their pros and cons. In this study, we carefully revisit the VI problem and investigate the possibility of combining the strengths of both techniques. We demonstrate that with systematic redesigns and adaptation of best practices in the literature, we can achieve dual-domain propagation, as illustrated in Figure 1(a). To achieve reliable and efficient information propagation across a video, we identify several essential components: i) Efficient GPU-based propagation with reliability check – Unlike previous methods that rely on complex and time-consuming CPU-centric operations, such as indexing flow trajectories, we perform global image propagation on GPU with flow consistency check. This implementation can be inserted at the beginning of the inpainting network and jointly trained with the other modules. Thus, subsequent modules are able to correct any propagation errors and benefit from the long-range correspondence information provided by the global propagation, resulting in a significant performance improvement. ii) Improved feature propagation – Our implementation of feature propagation leverages flow-based deformable alignment [3], which improves robustness to occlusion and inaccurate flow completion compared to $\\mathrm{E}^2\\mathrm{FGVI}$ [19]. iii) Efficient flow completion – We design a highly efficient recurrent network to complete flows for dual-domain propagation, which is over 40 times ( $\\sim 192$ fps $^1$ ) faster than SOTA method [43] while maintaining comparable performance. We demonstrate that these designs are essential to achieve efficient propagation of global and local information without texture misalignment or blurring in the", + "bbox": [ + 76, + 439, + 472, + 877 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "filling results. An example is shown in Figure 1(h).", + "bbox": [ + 500, + 90, + 838, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In addition to dual-domain propagation, we introduce an efficient mask-guided sparse video Transformer tailored for the VI task. The classic spatiotemporal Transformer is computationally intensive due to the quadratic number of interactions between video tokens, making it intractable for high-resolution and long temporal-length videos. For instance, contemporary Transformer-based methods, FuseFormer [22] and FGT [42], are unable to handle 480p videos with a $32\\mathrm{G}$ GPU due to excessive memory demands. However, we observe that the inpainting mask usually covers only a small local region, such as the object area. Moreover, adjacent frames contain highly redundant textures. These observations suggest that spatiotemporal attention is unnecessary for most unmasked areas, and it is adequate to consider only alternating interval frames in attention computation. Motivated by these observations, we redesign the Transformer by discarding unnecessary and redundant windows in the query and key/value space, respectively, significantly reducing computational complexity and memory without compromising inpainting performance.", + "bbox": [ + 496, + 107, + 893, + 409 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contribution of this work is to provide a systematic study into the core problem of VI and offer a practical solution that is both effective and efficient. Propagating information in two distinct image and feature domains and combining them in a unified framework with fast GPU implementation is new for VI task. The mask-guided sparse video Transformer also offers practical insights into designing efficient spatiotemporal attention for VI task. Compared to the state-of-the-art methods, our model achieves superior performance with a large margin of $1.46\\mathrm{dB}$ in PSNR, while also significantly reducing memory consumption.", + "bbox": [ + 496, + 409, + 893, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 590, + 640, + 606 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Numerous deep networks with different modules and propagation strategies have achieved significant success in video inpainting. These approaches can be broadly categorized into four categories:", + "bbox": [ + 496, + 616, + 893, + 676 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D convolution. Earlier video inpainting networks typically employed 3D CNNs [6, 33, 11] or temporal shift [7] to aggregate spatiotemporal information. These methods often suffer from limited receptive fields in both temporal and spatial dimensions and misalignment between adjacent frames. As a result, they are less effective in exploring distant content.", + "bbox": [ + 496, + 678, + 893, + 768 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Internal learning. To fully exploit content of a video, some studies [41, 27, 30] adopt internal learning to encode and memorize the appearance and motion of the video through deep networks. However, these methods require individual training for each test video, limiting their practical use.", + "bbox": [ + 496, + 768, + 890, + 844 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Flow-guided propagation. Optical flow [13, 18, 46] and homography [17, 1] are commonly used in video inpainting", + "bbox": [ + 496, + 844, + 890, + 875 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1Tested on a single NVIDIA Tesla V100 GPU (32G).", + "bbox": [ + 94, + 886, + 377, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "${}^{2}$ Object regions account for only 13.6% of the DAVIS [28] dataset.", + "bbox": [ + 514, + 886, + 872, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10478", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "networks to align neighboring reference frames to enhance temporal coherence and aggregation. However, incomplete optical flow may not provide valid propagation for completing missing regions. To address this issue, recent flow-based methods [37, 10, 12, 43, 42] focus on first completing the flow and then use it as a guidance for pixel-domain propagation. This approach simplifies RGB pixel inpainting by completing a less complex flow field. However, this offline propagation is independent of the subsequent learnable refinement module, making it difficult to correct content distortion caused by inaccurate propagation. Inspired by flow-guided recurrent networks [2, 3], Li et al. [19] proposed an end-to-end framework that jointly learns flow completion and feature propagation in the downsampled feature domain. However, downsampled flow reduces its ability to provide spatially precise warping. To overcome this limitation, we propose more faithful propagation by performing both pixel and feature propagation with flow consistency checks.", + "bbox": [ + 75, + 90, + 472, + 362 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Video Transformer. Attention [17, 26, 11, 18] and Transformer [40, 21, 22, 1, 19, 42] blocks adopt spatiotemporal attention to explore recurrent textures in a video. This enables them to retrieve and aggregate tokens with similar texture or context for filling in missing regions. Liu et al. [22] present a fine-grained fusion Transformer based on the soft split and composition operations, which further boosts video inpainting performance. However, these methods are computationally and memory intensive. To address this issue, some Transformers [21, 1, 42] decouple the spatiotemporal attention by performing spatial and temporal attention alternately, while others [19, 42] adopt window-based Transformers [23, 38] to reduce the spatial range for efficient video attention. However, these approaches still involve redundant or unnecessary tokens. Inspired by token pruning for adaptive attention [29, 39, 25, 20, 15] in high-level tasks, our study proposes a more efficient and faster video Transformer with sparse spatiotemporal attention and a largely reduced token space while maintaining inpainting performance.", + "bbox": [ + 75, + 363, + 472, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recent studies [18, 19, 42] have demonstrated the effectiveness of combining flow-guided propagation with Transformer in VI. However, the high memory requirement of the Transformer limits the propagation range during both training and inference, severely hindering the ability to propagate temporally distant content. In this paper, we also adopt this combination strategy but propose a reliable propagation scheme, along with an efficient Transformer model that fully exploits the benefits of long-range propagation and attention. This results in superior inpainting performance while maintaining computational efficiency.", + "bbox": [ + 75, + 650, + 472, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 830, + 210, + 847 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a masked video sequence $X = \\{X_{t} \\in \\mathbb{R}^{H \\times W \\times 3}\\}_{t=1}^{T}$ , which has a sequence length of $T$ , along with corresponding mask sequence $M = \\{M_{t} \\in$", + "bbox": [ + 76, + 854, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\mathbb{R}^{H\\times W\\times 1}\\}_{t = 1}^{T}$ , the objective of video inpainting is to generate visually consistent and coherent content within the corrupted or missing regions. ProPainter, as shown in Figure 2, is composed of three key components: Recurrent Flow Completion (RFC), Dual-Domain Propagation (DDP), and Mask-guided Sparse Video Transformer (MSVT). Before feeding the sequence into ProPainter, we extract the forward and backward optical flows, denoted as $F^f = \\{F_t^f = F_{t\\to t + 1}\\in \\mathbb{R}^{H\\times W\\times 2}\\}_{t = 1}^{T - 1}$ and $F^b = \\{F_t^b = F_{t + 1\\to t}\\in \\mathbb{R}^{H\\times W\\times 2}\\}_{t = 1}^{T - 1}$ from a given video $X$ . We first use RFC to complete the corrupted flow fields. Guided by the completed flows, we then perform global image propagation and local feature propagation sequentially. Finally, we employ multiple MSVT blocks to refine propagation features and a decoder to reconstruct the final video sequence $\\hat{Y} = \\{\\hat{Y}_t\\in \\mathbb{R}^{H\\times W\\times 3}\\}_{t = 1}^T$ . We introduce the specific design of each component below.", + "bbox": [ + 496, + 89, + 893, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Recurrent Flow Completion", + "text_level": 1, + "bbox": [ + 500, + 359, + 751, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Pre-trained flow completion modules are commonly used in video inpainting networks [37, 10, 43, 42]. The rationale behind this approach is that it is simpler to complete missing flow than to directly fill in complex RGB content [37]. Furthermore, using completed flow to propagate pixels reduces the pressure of video inpainting and better maintains temporal coherence. $\\mathrm{E}^2\\mathrm{FGVI}$ [19] proposes to insert the flow completion module into an end-to-end framework, which simplifies the inpainting pipeline. However, flow completion modules that are learned together with inpainting-oriented losses can result in a suboptimal learning process and less accurate completed flow. Moreover, the downsampled flow may limit the precision of spatial warping and the efficacy of propagation, which can result in blurred and incomplete filling content, as shown in Figure 1(g). Therefore, an independent flow completion model is not only important but also necessary for video inpainting.", + "bbox": [ + 496, + 383, + 893, + 641 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To maintain temporal coherence while completing flows, previous methods [37, 42] adopt sliding-window-based networks to aggregate optical flow information from adjacent frames, which are highly correlated. However, these methods can be computationally expensive as repeated inferences are required in the overlapping frames. To improve efficiency and enhance flow coherence further, we adopt a recurrent network [2, 3] for flow completion, which provides precise optical flow fields for subsequent propagation modules.", + "bbox": [ + 496, + 642, + 893, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We complete forward and backward flows using the same process, thus we denote $F^f$ and $F^b$ as $F$ for simplicity. We first encode the flows $F_t$ into a downsampled feature $f_t$ with a downsampling ratio of 8. Next, we employ deformable alignment [3] that is based on deformable convolution (DCN) [8, 45], to bidirectionally propagate the flow information from nearby frames for flow completion. For simplicity, we only describe the backward propagation", + "bbox": [ + 496, + 779, + 895, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10479", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/bd7f9fc1852304742d261be2133dae94328f6fdadb074bc7503bccbb66973551.jpg", + "image_caption": [ + "Figure 2: ProPainter comprises three key components: recurrent flow completion, dual-domain propagation, and mask-guided sparse Transformer. First, we employ a highly efficient recurrent flow completion network to complete the corrupted flow fields. We then perform propagation in both image and feature domains, which are jointly trained. This approach enables us to explore correspondences from both global and local temporal frames, resulting in more reliable and effective propagation. The subsequent mask-guided sparse Transformer blocks refine the propagated features using spatiotemporal attention, aided by a sparse strategy that considers only a subset of the tokens. This enhances efficiency and reduces memory consumption, while maintaining performance." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 893, + 244 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "process here. Taking the concatenated feature $c(f_t, \\hat{f}_{t+1})$ , where $\\hat{f}_{t+1}$ is the propagation feature of the $t+1$ -th frame, as input a lightweight network with a stack of convolutions is employed to compute DCN offsets $o_{t \\to t+1}$ and modulation masks $m_{t \\to t+1}$ . DCN alignment propagation can be expressed as:", + "bbox": [ + 75, + 380, + 473, + 474 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {f} _ {t} = \\mathcal {R} \\big (\\mathcal {D} \\big (\\hat {f} _ {t + 1}; o _ {t \\rightarrow t + 1}, m _ {t \\rightarrow t + 1}), f _ {t} \\big), \\qquad (1)\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 491, + 470, + 512 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{D}(\\cdot)$ denotes deformable convolution, and $\\mathcal{R}(\\cdot)$ denotes the convolution layers that fuse the aligned and current features. In this way, information of $(t + 1)$ -th flow can be adaptively transferred to the current $t$ -th flow. Finally, a decoder is used to reconstruct the completed flows $\\hat{F}_t$ . For clarity, an illustration of deformable alignment is provided in the supplementary material.", + "bbox": [ + 75, + 529, + 472, + 638 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Dual-domain Propagation", + "text_level": 1, + "bbox": [ + 76, + 657, + 313, + 674 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After completing the flow, we perform global and local propagation in the image and feature domains, respectively. We employ distinct alignment operations and strategies for each domain. Both domains involve bidirectional propagation in the forward and backward directions. Here, we elaborate on the backward propagation since the forward propagation follows the same process.", + "bbox": [ + 75, + 684, + 470, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Image propagation. To maintain efficiency and simplicity, we adopt flow-based warping for image propagation, along with a simple reliability check strategy. This process does not involve any learnable operation. In the case of a video sequence $X$ with binary masks $M$ (a pixel with value 1 represents masked region) and completed flows $\\hat{F}$ , we first check the validity of completed flow based on forward-backward", + "bbox": [ + 75, + 794, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "consistency error [37, 10]:", + "bbox": [ + 500, + 382, + 676, + 398 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {E} _ {t \\rightarrow t + 1} (p) = \\left\\| \\hat {F} _ {t \\rightarrow t + 1} (p) + \\hat {F} _ {t + 1 \\rightarrow t} (p + \\hat {F} _ {t \\rightarrow t + 1} (p)) \\right\\| _ {2} ^ {2}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 407, + 892, + 448 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $p$ denotes a pixel position of the current frame. Only pixels with a small consistency error will be propagated, i.e., $C_1: \\mathcal{E}_{t \\to t + 1}(p) < \\epsilon$ , where $\\epsilon$ is a threshold and set to 5. Furthermore, we only consider the masked areas of the current frame $X_t$ that needs to be filled, i.e., $C_2: M_t(p) = 1$ , and we only propagate the unmasked areas from neighboring frame $X_{t + 1}$ , i.e., $C_3: M_{t + 1}(p + \\hat{F}_{t \\to t + 1}(p)) = 0$ . By enforcing the three constraints, a reliable propagation area $A_r$ is identified as:", + "bbox": [ + 496, + 449, + 893, + 584 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA _ {r} (p) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} p \\in C _ {1} \\cap C _ {2} \\cap C _ {3}, \\\\ 0 & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 594, + 892, + 636 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The process of image propagation is expressed as:", + "bbox": [ + 500, + 646, + 831, + 662 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {X} _ {t} = \\mathcal {W} \\left(X _ {t + 1}, \\hat {F} _ {t \\rightarrow t + 1}\\right) * A _ {r} + X _ {t} * \\left(1 - A _ {r}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 672, + 893, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{W}(\\cdot)$ denotes warping operation. To ensure continuous propagation, we promptly update the mask $M_{t}$ of the current frame and convert the propagated area to the un-masked status by updating masks via $\\dot{M}_t = M_t - A_r$ . After global image propagation, we obtain a partially filled video sequence $\\tilde{X}$ , which greatly eases the learning process for subsequent modules.", + "bbox": [ + 496, + 700, + 893, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Feature propagation. We use an image encoder with the same structure as previous works [22, 19] to extract features from a local sequence $\\hat{X}_{t=1}^{T_l}$ , denoted as $\\{e_t \\in \\mathbb{R}^{\\frac{H}{4} \\times \\frac{W}{4} \\times C}\\}_{t=1}^{T_l}$ . Similar to E²FGVI [19], we also adopt flow-guided deformable alignment module [3] for feature propagation, which has demonstrated remarkable benefits", + "bbox": [ + 496, + 808, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10480", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/80c09d94207daea57d5a8bc24ff28e14791bd063d4b4cc0e88bb0f51445376c6.jpg", + "image_caption": [ + "Figure 3: Flow-guided deformable alignment is effective by taking reliable completed flows and mask-aware conditions. We concatenate the validated flow map, original mask, and updated mask into conditions to produce DCN offsets (residue to optical flow). A DCN is then applied to align the propagation feature from the previous frame. Finally, a CNN block is employed to fuse the current and aligned features, achieving the propagation feature of the current frame." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 467, + 232 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in various low-level video tasks [5, 4, 44]. Unlike the deformable alignment used in Sec. 3.1 that directly learns DCN offsets, flow-guided deformable alignment employs the completed flow as a base offset and refines it by learning offset residue. However, our design differs from $\\mathrm{E}^2\\mathrm{FGVI}$ in that we offer richer conditions for learning DCN offsets. As illustrated in Figure 3, apart from the current feature $e_t$ , warped propagation feature $\\mathcal{W}(\\hat{e}_{t + 1},\\hat{F}_{t\\rightarrow t + 1}^{\\downarrow})$ , and completed flows $\\hat{F}_{t\\rightarrow t + 1}^{\\downarrow}$ , we additionally introduce the flow valid map $V_{t + 1\\to t}$ calculated by consistency check (Eq. 2), as well as the original mask $M_t^\\downarrow$ , and updated mask $\\hat{M}_t^\\downarrow$ after image propagation. With these conditions, a stack of convolutions is employed to predict the DCN offset residue $\\widetilde{o}_{t\\rightarrow t + 1}$ and modulation masks $m_{t\\rightarrow t + 1}$ . The flow-guided DCN alignment propagation is expressed as:", + "bbox": [ + 75, + 390, + 472, + 621 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {e} _ {t} = \\mathcal {R} \\big (\\mathcal {D} \\big (\\hat {e} _ {t + 1}; \\hat {F} _ {t \\rightarrow t + 1} ^ {\\downarrow} + \\widetilde {o} _ {t \\rightarrow t + 1}, m _ {t \\rightarrow t + 1}), f _ {t} \\big), \\quad (5)\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 628, + 470, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\downarrow$ denotes downsampling. The improved reliability of flow and the additional awareness of mask as a condition make our flow-guided deformable alignment module more stable to learn than previous designs [3, 19]. The current step is able to focus more on truly challenging regions where flow is invalid and former image propagation is unreliable.", + "bbox": [ + 75, + 657, + 468, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Mask-Guided Sparse Video Transformer", + "text_level": 1, + "bbox": [ + 76, + 756, + 426, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While video Transformers have achieved excellent performance in video inpainting, they can be computationally and memory intensive, posing a challenge to their practical application. $\\mathrm{E}^2\\mathrm{FGVI}$ and FGT have addressed this issue by using window-based Transformer blocks, but they still have some efficiency limitations. To overcome this, we propose a novel sparse video Transformer that builds on the window-based approach. Given a video sequence feature", + "bbox": [ + 75, + 780, + 472, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/93c4a07f8bdc940a274970239c1836076b54b3b8ae53c050013af3af5ed939f9.jpg", + "image_caption": [ + "Figure 4: Mask-guided sparse video Transformer. To reduce computational complexity and memory usage, our mask-guided sparse Transformer filters out unnecessary and redundant windows in the query and key/value space, respectively, before applying self-attention. To enlarge spatial interrelation range, we also adopt the window expand strategy [38] and pooling global tokens [42, 19]." + ], + "image_footnote": [], + "bbox": [ + 504, + 88, + 890, + 232 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$E_{l} \\in \\mathbb{R}^{T_{l} \\times \\frac{H}{4} \\times \\frac{W}{4} \\times C}$ , we use the soft split operation [22] to generate patch embeddings $Z \\in \\mathbb{R}^{T_{l} \\times M \\times N \\times C_{z}}$ . We partition $Z$ into $m \\times n$ non-overlapping windows, resulting in partitioned features $Z_{w} \\in \\mathbb{R}^{T_{l} \\times m \\times n \\times h \\times w \\times C_{z}}$ , where $m \\times n$ and $h \\times w$ are the number and size of the windows, respectively. We obtain the query $Q$ , key $K$ , and value $V$ from $Z_{w}$ through linear layers. We design sparse strategies for both query and key/value spaces separately. Note that we also apply the window expand strategy [22] and integrate global tokens [42] into key and value, enabling us to use a small window size of $5 \\times 9$ in our experiments. We omit them from the following discussion since they do not affect our sparse strategy designs.", + "bbox": [ + 496, + 375, + 893, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sparse Query Space. We observe that mask regions often occupy only a small area of the video, such as in the case of object removal in the DAVIS [28] dataset, where the proportion of object regions is only $13.6\\%$ . This indicates that spatiotemporal attention may not be necessary for all query windows. To exploit this observation, we selectively apply attention to query windows that intersect with the mask regions. Specifically, we first use nearest neighbor interpolation to downsample the mask sequence $M \\in \\mathbb{R}^{T_l \\times H \\times W}$ to $M^{\\downarrow} \\in \\mathbb{R}^{T_l \\times m \\times n}$ , where $m \\times n$ is the number of non-overlapping windows after partitioning. We then sum it up in the temporal dimension and obtain sparse mask $S_Q \\in \\mathbb{R}^{m \\times n}$ for query cubes following the equation:", + "bbox": [ + 496, + 575, + 893, + 772 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS _ {Q} = \\operatorname {C l i p} \\left(\\sum_ {t = 1} ^ {T _ {l}} M _ {t} ^ {\\downarrow}, 1\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 784, + 893, + 811 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $Clip$ represents a clipping function that set $S_{Q}$ to 1 if $\\sum_{t=1}^{T_l} M_t^{\\downarrow} > 0$ . In other words, if the query cube at a window $(i,j)$ has never contained any mask region in the past frames, then $S_{Q}(i,j) = 0$ , indicating that spatiotemporal attention within this window can be skipped.", + "bbox": [ + 496, + 821, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10481", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/a0f1c6279bd90eaf0d5fe930efc0e984ecd78460af9db980377041a255d686d5.jpg", + "table_caption": [ + "Table 1: Quantitative comparisons on YouTube-VOS [36] and DAVIS [28] datasets. The best and second performances are marked in red and blue, respectively. $E_{\\text{warp}}^*$ denotes $E_{\\text{warp}} (\\times 10^{-3})$ . All methods are evaluated following their default settings. Since DFVI, FGVC, ISVI, and FGT involve several CPU processes, their FLOPs cannot be accurately projected." + ], + "table_footnote": [], + "table_body": "
AccuracyEfficiency
YouTube-VOSDAVISFLOPs (10 frames)Runtime (s/frame)
ModelsPSNR ↑SSIM ↑VFID ↓E* \\( _{warp} \\) ↓PSNR ↑SSIM ↑VFID ↓E* \\( _{warp} \\) ↓
DFVI [37]29.160.94290.0661.65128.810.94040.1871.596-0.837
CPNet [17]31.580.96070.0711.62230.280.95210.1821.5211407G0.316
FGVC [10]29.670.94030.0641.16330.800.94970.1651.571-1.795
STTN [40]32.340.96550.0531.06130.610.95600.1491.4381315G0.051
TSAM [46]30.220.94680.0701.01430.670.95480.1461.2351001G0.068
FuseFormer [22]33.320.96810.0531.05332.590.97010.1371.3491025G0.114
ISVI [43]30.340.94580.0771.00832.170.95880.1891.291-1.594
FGT [42]32.170.95990.0541.02532.860.96500.1291.323-1.828
E2FGVI [19]33.710.97000.0461.01333.010.97210.1161.289986G0.085
ProPainter (Ours)34.430.97350.0420.97434.470.97760.0981.187808G0.083
", + "bbox": [ + 80, + 141, + 890, + 356 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Sparse Key/Value Space. Due to the highly redundant and repetitive textures in adjacent frames, it is unnecessary to include all frames as key/value tokens in each Transformer block. Instead, we will only include stripped temporal frames alternately, with a temporal stride of 2 in our design. That is, in each odd-numbered Transformer block, only odd-number frames are activated to participate in self-attention with their key and value, while even-number blocks include only even-number frames. By doing so, the key and value space is reduced by half, effectively reducing the computation and memory cost of the Transformer module. After filtering out unnecessary and redundant windows based on our sparse strategy, we perform self-attention on the remaining windows to extract refined features. These features are then gathered using a soft composition operation [22] for subsequent modules. Experimental results suggest that our design significantly reduces the computational cost of video Transformers while maintaining performance for video inpainting.", + "bbox": [ + 75, + 377, + 473, + 650 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. Training Objectives", + "text_level": 1, + "bbox": [ + 76, + 657, + 266, + 674 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Flow Completion. We utilize L1 loss as the reconstruction loss and a second-order smoothness constraint on the flow field [24] to promote the collinearity of neighboring flows and thus enhance the smoothness of the completed flow field. Video Inpainting. We adopt L1 loss as the reconstruction loss for all pixels. To enhance the realistic and temporal consistency of video inpainting results, we also employ an adversarial loss that is measured using a T-PatchGAN [6] discriminator. The details and formulation of these losses are provided in the supplementary material.", + "bbox": [ + 75, + 680, + 470, + 833 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 845, + 210, + 862 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We use the training set of YouTube-VOS [36] with 3471 video sequences to train our networks. Two widely-", + "bbox": [ + 76, + 869, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "used test sets are adopted for evaluation: YouTube-VOS [36] and DAVIS [28], which consist of 508 and 90 video sequences, respectively. For the DAVIS test set, following FuseFormer [22] and $\\mathrm{E}^2\\mathrm{FGVI}$ [19], we use 50 video clips for evaluations. During training, we follow [13, 17, 22, 19] and generate stationary and object masks in a random fashion to simulate the masks in video completion and object removal tasks. As for evaluation, we adopt the stationary masks provided in [19] to calculate quantitative scores, and the object masks are extracted from their segmentation labels for qualitative comparisons. Video frames are sized to $432\\times 240$ for training and evaluation.", + "bbox": [ + 496, + 377, + 893, + 559 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training Details and Metrics. We use RAFT [32] to extract optical flow in our approach. For training the RFC network, we set the flow sequence length to 10 and perform deformable propagation on feature maps that are downsampled by a factor of 8 for faster processing. We adopt 8 Transformer blocks for the inpainting modules and use a local video sequence of length 10. The Transformer window size is $5 \\times 9$ , and the extended size is half of the window size. We train both the RFC and inpainting modules using the Adam [14] optimizer with a batch size of 8, setting the initial learning rate to $10^{-4}$ and running 700k iterations for each. We implement our method using the PyTorch framework and train it on 8 NVIDIA Tesla V100 (32G) GPUs.", + "bbox": [ + 496, + 561, + 895, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We employ the widely used PSNR and SSIM metrics [35] to evaluate the reconstruction performance and VFID [34] scores to measure the perceptual similarity between input videos and outputs, as used in recent video inpainting studies [22, 19]. Additionally, we report the flow warping error $E_{\\text{warp}}$ [16] to assess the temporal consistency and smoothness of the resulting video sequences.", + "bbox": [ + 496, + 760, + 893, + 867 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "3We set 450k training iterations for ablation study.", + "bbox": [ + 514, + 886, + 785, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10482", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/32be32cdf697b876bb62f0e2d165f50b35cf9cca2ae0f7f7c000d6ea64358ab8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 90, + 241, + 159 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/48ddc568f3349fea0865aa0a8359a9537db0af9b1c5a960da99ad50e0f95ff1c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 243, + 90, + 401, + 159 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3864b9333a5d884e10789d3d921d2721b0005412c8018343fb1ef70cda69189b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 401, + 90, + 560, + 159 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fbb63eb01c40d0763a2df11f80d96aac567c8ea3eb9ac85d75294c69836a5c40.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 562, + 90, + 720, + 159 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b3a1f800c95f71ffe6e0ab625f508440bce92a04bcc03a1e1647e49dde1d5033.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 723, + 90, + 880, + 159 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/69e79e925fafc6b9e36c02aaf05f0d9739eb424fed9907c439be664927f9b22c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 160, + 241, + 229 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/311aa1a5114eaa580e65a8f742b2857b0fbd2e64d2e41464ae66f98e011b31a2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 243, + 160, + 401, + 229 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a2058423efc80ad3f19a0ebde4722c4971e11450212d121dab0fadca2f695473.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 401, + 160, + 560, + 229 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/52f7421f5a7ca2ecb26faf7c2ef4becb68252e440ec60a6ff073ed42c77ec482.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 562, + 160, + 720, + 229 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4d6cc73722e26daf42d983f4133f17ee6b313f6febb82fc385f32423db7a919e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 723, + 160, + 880, + 229 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f217084ed22d5bed4bfe2ca7f4b97ab90db224d73cea54cbac4c52a2464e2d73.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 231, + 241, + 301 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4fa794b22642fd69969e4b1df52552cebb553258bf67f8c3abffd0e66be641a6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 243, + 231, + 401, + 301 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8bf3b1ff4bf54923fe48770a1a017845d15dec87d520afb7791788a96bc09255.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 401, + 231, + 560, + 301 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dbb502ad9069e181d2d0929d6a7b85d646a9fe5b3996a8a9c280b1656f6fbda0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 562, + 231, + 720, + 301 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6e23f8a2b46153381a223d15fccfc7c73f1965cfe384cafca902e198aad3b299.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 723, + 231, + 880, + 301 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/63b3d42ff3db985f839faf3dc8c36cb9e23b18dc226362def74a94deb5d7938f.jpg", + "image_caption": [ + "Masked Frames" + ], + "image_footnote": [], + "bbox": [ + 83, + 301, + 241, + 371 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/987a78a4c34bfc0db1dbd966928f9a24adad4ea817c9c367fddb424814d66435.jpg", + "image_caption": [ + "FuseFormer" + ], + "image_footnote": [], + "bbox": [ + 243, + 301, + 401, + 371 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b10b60d0f4e257ed730b73a05e252fbaed59846768c42c8fe74df7b62efb03c3.jpg", + "image_caption": [ + "FGT", + "Figure 5: Qualitative comparisons on both video completion and object removal. Our ProPainter exhibits superiority in producing complete and faithful textures, resulting in enhanced spatiotemporal coherence for video inpainting." + ], + "image_footnote": [], + "bbox": [ + 401, + 301, + 560, + 371 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/59aee458a23089a7d47194aa22edb3e403d467aa060bfa86a5f9ebd11bb760fa.jpg", + "image_caption": [ + "$\\mathrm{E}^2\\mathrm{FGVI}$" + ], + "image_footnote": [], + "bbox": [ + 562, + 301, + 720, + 371 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cceb1c7f4f0b504a026c4edafdaa0b047e213c7b7176aff181ed7036130e10fd.jpg", + "image_caption": [ + "ProPainter (Ours)" + ], + "image_footnote": [], + "bbox": [ + 723, + 301, + 880, + 371 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1. Comparisons", + "text_level": 1, + "bbox": [ + 76, + 444, + 215, + 460 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative Evaluation. We compare ProPainter with nine state-of-the-art methods including DFVI [37], CPNet [17], FGVC [10], STTN [40], TSAM [46], Fuseformer [22], ISVI [43], FGT [42], and $\\mathrm{E}^2\\mathrm{FGVI}$ [19] on both YouTube-VOS [36] and DAVIS [28]. Thanks to the efficient design, ProPainter uses a temporal length of 20 for inference. Table 1 shows that ProPainter outperforms other methods in all quantitative metrics, especially on the DAVIS dataset, where our method surpasses the state-of-the-art method by $1.14\\mathrm{dB}$ in PSNR. The results suggest that our method has superior inpainting capability, enabling it to produce higher-quality, faithful, and seamless videos.", + "bbox": [ + 75, + 470, + 472, + 651 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative Evaluation. For the visual comparison, we compare our method with FuseFormer [22], FGT [42], and $\\mathrm{E}^2\\mathrm{FGVI}$ [19], which are representative methods of Transformer-, image propagation-, and feature propagation-based approaches, respectively. Figure 5 presents four comparison results for video completion and object removal. Our method uses dual-domain propagation to ensure reliable and long-range propagation. It completes missing regions with coherence and clear contents, while other compared methods tend to fail or produce unpleasant inpainting results such as texture distortions and black hazy region in FGT [42] results, as well as artifacts in FuseFormer [22] and $\\mathrm{E}^2\\mathrm{FGVI}$ [19].", + "bbox": [ + 75, + 656, + 470, + 837 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Efficiency Comparison. Table 1 presents the efficiency comparisons between all methods in terms of FLOPs and running time. The FLOPs of all methods are computed based on a temporal length of 10. We consider all learn-", + "bbox": [ + 75, + 839, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e0f29bdffe3c17b7f91b14a054a249b642ce236a7acd4b29ef5fb200c8327602.jpg", + "table_caption": [ + "Table 2: Comparisons of flow completion networks. Our network offers a dual benefit with high accuracy and efficiency." + ], + "table_footnote": [], + "table_body": "
EPE ↓DFVI [37]FGVC [10]FGT [42]ISVI [43]Ours
YouTube-VOS0.0460.0320.0210.0190.020
DAVIS0.1070.0820.0520.0510.051
Runtime (s/frame)0.1301.1250.3120.2310.005
", + "bbox": [ + 511, + 477, + 888, + 550 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "able modules (including the recurrent flow completion) in our ProPainter to calculate the FLOPs. The running time records the time of all processes in each method, including inpainting, as well as flow calculation and flow completion if involved. To keep efficiency, we use only five iterations of the RAFT network to calculate optical flow.", + "bbox": [ + 496, + 560, + 893, + 651 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Flow Completion Comparisons. We compare our recurrent flow network with previous approaches [37, 10, 43] on both YouTube-VOS and DAVIS datasets. Table 2 presents the end-point-error (EPE) of flow completion and running time of each method. Our recurrent network offers a dual benefit with high accuracy and efficiency. Compared to previous methods, our network is approximately 40 times faster while maintaining a comparable flow completion accuracy to the state-of-the-art methods.", + "bbox": [ + 496, + 652, + 893, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 800, + 653, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Image Propagation. Table 3 shows that Exp. (a) experiences a significant performance drop when image propagation is removed. Moreover, the model's propagation ability is reduced without image propagation, as presented in Figure 7, causing it to fail to complete missing", + "bbox": [ + 496, + 824, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10483", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f3d03675ff625420a61fead781abc7ea8daa740a91105a0734b067c5a1038b54.jpg", + "table_caption": [ + "Table 3: Ablation study of dual-main propagation and sparse Transformer." + ], + "table_footnote": [], + "table_body": "
Exp.(a) w/o Img Prop.(b) w/ Img Prop. in FGVC(c) w/o Feat Prop.(d) w/ Feat Prop. in E²FGVI(f) Full TokensProPainter
PSNR33.0532.9133.1733.9434.1834.15
SSIM0.97240.96870.97320.97560.97650.9764
", + "bbox": [ + 81, + 109, + 883, + 167 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/97374e4fc53c1b7ce479bf1281ef10f65e87ab5f6930694b9cbe0edd51ce80bb.jpg", + "image_caption": [ + "Masked Frame" + ], + "image_footnote": [], + "bbox": [ + 83, + 176, + 241, + 248 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7963d766debcf0daa773698e419aea55b13699f270cacd559f274f606c45729e.jpg", + "image_caption": [ + "Img Prop. of FGVC" + ], + "image_footnote": [], + "bbox": [ + 243, + 178, + 401, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/04c70c26b5d78e07c1e517d2b6eade402dc0cad8aecf76f74652665bd08394cd.jpg", + "image_caption": [ + "w/Img Prop.of FGVC (Exp.b)" + ], + "image_footnote": [], + "bbox": [ + 401, + 178, + 562, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/53070cdda0f534ce7823c99ee930151befd318d4ad05f7b12aaf77bd35db5ec0.jpg", + "image_caption": [ + "Img Prop. (Ours)" + ], + "image_footnote": [], + "bbox": [ + 563, + 178, + 722, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c7102e99c5c8114e4fdcb4bea52a038b55d71171538a7a23e827359b356b47d1.jpg", + "image_caption": [ + "ProPainter (Ours)" + ], + "image_footnote": [], + "bbox": [ + 723, + 178, + 883, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e232ab15bd04c85308d8e3b36424fbe681de8043122865e80c2d0b6d9f6857f0.jpg", + "image_caption": [ + "Masked Frames" + ], + "image_footnote": [], + "bbox": [ + 81, + 297, + 207, + 407 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a0f0bbb34ee6d8fbfa92eb5679cc1ded1de676c1f4ecf47ace9957baed6c35e3.jpg", + "image_caption": [ + "w/o Img Prop. (Exp. a)" + ], + "image_footnote": [], + "bbox": [ + 210, + 297, + 336, + 407 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/acacbf713191d549a09bcb8ebe14e4f750b162d43f3721dc631b4a20d93aef03.jpg", + "image_caption": [ + "w/ImgProp." + ], + "image_footnote": [], + "bbox": [ + 339, + 297, + 465, + 409 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "content with details. To verify the effectiveness of our reliability check strategy in image propagation, we replaced our design with the FGVC image propagation module in Exp. (b) (without retraining), resulting in a noticeable decrease in PSNR. This is because the FGVC image propagation method is prone to being affected by incorrect optical flow, leading to severe texture distortion that subsequent modules cannot correct. Our model can effectively aware and stop unreliable propagation areas using a simple reliability check via Eq.2, and generate more faithful inpainting results.", + "bbox": [ + 75, + 458, + 468, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of Feature Propagation. Similarly, we observe a slight decrease in performance by either removing feature propagation, i.e., Exp. (c), or replacing it with the Feature propagation of $\\mathrm{E}^2\\mathrm{FGVI}$ , i.e., Exp. (d), indicating the effectiveness of the feature propagation modules and our reliability mask-aware conditions. This suggests that our design, which learns reliable DCN offsets in the feature domain, can further complement and enhance the propagation ability in the image domain.", + "bbox": [ + 75, + 611, + 470, + 747 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of Sparse Transformer. In theory, our strategy of using masks to guide sparsity only eliminates redundant and unnecessary tokens (windows), while preserving essential information. This means that there should be no adverse effect on performance. To confirm this, we conducted Exp. (d), comparing our approach to standard self-attention without sparse filtering. Our results indicate that our sparse Transformer block performs almost as well as the standard one, indicating that it can achieve high efficiency without sacrificing performance.", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a833ee63db660f7ba011c8e7a32a81a190130014c91f677114fb7d56b803e08d.jpg", + "image_caption": [ + "Figure 7: Comparison of w/ and w/o image propagation.", + "Figure 8: FLOPs cures of different Transformer blocks." + ], + "image_footnote": [], + "bbox": [ + 498, + 297, + 689, + 417 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/32b125153ca9a705c43cd44cee1fb562e9f91950814bcca2f0f71588fda4dc85.jpg", + "image_caption": [ + "Figure 6: Visual comparison on image propagation methods of FGVC [10] and ours." + ], + "image_footnote": [], + "bbox": [ + 694, + 296, + 883, + 417 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Efficiency of Sparse Transformer. In Figure 8, we compare the FLOPs of different Transformer blocks with respect to temporal length and spatial resolution, including those used in FuseFormer [22], FGT [42], and $\\mathrm{E}^2\\mathrm{FGVI}$ [19]. We use a mask with a missing region ratio of $1/6$ (higher than the average object ratio of $13.6\\%$ in DAVIS) to calculate the FLOPs of our mask-guided sparse Transformer. The curves indicate that the efficiency advantage of our sparse Transformer becomes more prominent as the temporal length and video resolution increase, indicating great potential for developing longer-range spatiotemporal attention and applying it to larger resolution videos.", + "bbox": [ + 496, + 457, + 893, + 638 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 652, + 617, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This study introduces a novel and improved video inpainting framework called ProPainter. It incorporates an enhanced dual-domain propagation and an efficient mask-guided sparse video Transformer. Thanks to the two modules, our ProPainter exhibits reliable and precise propagation capabilities over long distances, significantly improving the performance of video inpainting while maintaining high efficiency in terms of running time and computational complexity. We believe that the designs in ProPainter will provide valuable insights to the video inpainting community.", + "bbox": [ + 496, + 676, + 893, + 829 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This study is supported under the RIE2020 Industry Alignment Fund Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s).", + "bbox": [ + 496, + 835, + 893, + 897 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10484", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jiayin Cai, Changlin Li, Xin Tao, Chun Yuan, and Yu-Wing Tai. DeViT: Deformed vision transformers in video inpainting. In ACM MM, 2022. 2, 3", + "[2] Kelvin CK Chan, Xintao Wang, Ke Yu, Chao Dong, and Chen Change Loy. BasicVSR: The search for essential components in video super-resolution and beyond. In CVPR, 2021. 3", + "[3] Kelvin CK Chan, Shangchen Zhou, Xiangyu Xu, and Chen Change Loy. 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In NeurIPS, 2018. 6" + ], + "bbox": [ + 501, + 92, + 893, + 900 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "10485", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[35] Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli. Image quality assessment: from error visibility to structural similarity. TIP, 2004. 6", + "[36] Ning Xu, Linjie Yang, Yuchen Fan, Jianchao Yang, Dingcheng Yue, Yuchen Liang, Brian Price, Scott Cohen, and Thomas Huang. YouTube-VOS: Sequence-to-sequence video object segmentation. In ECCV, 2018. 6, 7", + "[37] Rui Xu, Xiaoxiao Li, Bolei Zhou, and Chen Change Loy. Deep flow-guided video inpainting. In CVPR, 2019. 1, 3, 4, 6, 7", + "[38] Jianwei Yang, Chunyuan Li, Pengchuan Zhang, Xiyang Dai, Bin Xiao, Lu Yuan, and Jianfeng Gao. Focal attention for long-range interactions in vision transformers. 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In CVPR, 2021. 2, 6, 7" + ], + "bbox": [ + 78, + 90, + 470, + 631 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10486", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/ProPainter_ Improving Propagation and Transformer for Video Inpainting/447df786-8aae-4bc4-b7d5-1e90caa96cc1_model.json b/2023/ProPainter_ Improving Propagation and Transformer for Video Inpainting/447df786-8aae-4bc4-b7d5-1e90caa96cc1_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e84f614a58c7c97c3075171311be9a3d639faf3c --- /dev/null +++ b/2023/ProPainter_ Improving Propagation and Transformer for Video Inpainting/447df786-8aae-4bc4-b7d5-1e90caa96cc1_model.json @@ -0,0 +1,2431 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.109, + 0.131, + 0.862, + 0.154 + ], + "angle": 0, + "content": "ProPainter: Improving Propagation and Transformer for Video Inpainting" + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.181, + 0.777, + 0.218 + ], + "angle": 0, + "content": "Shangchen Zhou Chongyi Li Kelvin C.K. Chan Chen Change Loy S-Lab, Nanyang Technological University" + }, + { + "type": "text", + "bbox": [ + 0.269, + 0.22, + 0.704, + 0.235 + ], + "angle": 0, + "content": "{s200094，chongyi.li，chan0899，ccloy}@ntu.edu.sg" + }, + { + "type": "text", + "bbox": [ + 0.285, + 0.237, + 0.684, + 0.251 + ], + "angle": 0, + "content": "https://shangchenzhou.com/projects/ProPainter" + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.28, + 0.3, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.115, + 0.41, + 0.262, + 0.422 + ], + "angle": 0, + "content": "(a) Dual-domain Propagation" + }, + { + "type": "image", + "bbox": [ + 0.338, + 0.284, + 0.46, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.353, + 0.379, + 0.434, + 0.397 + ], + "angle": 0, + "content": "Sparse Query Space (masked window)" + }, + { + "type": "image", + "bbox": [ + 0.468, + 0.283, + 0.585, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.467, + 0.379, + 0.571, + 0.397 + ], + "angle": 0, + "content": "Sparse Key/Value Space (temporal strided window)" + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.41, + 0.567, + 0.421 + ], + "angle": 0, + "content": "(b) Mask-guided Sparse Video Transformer" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.424, + 0.242, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.495, + 0.23, + 0.506 + ], + "angle": 0, + "content": "(d) Input with object mask" + }, + { + "type": "image", + "bbox": [ + 0.245, + 0.424, + 0.402, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.286, + 0.495, + 0.364, + 0.506 + ], + "angle": 0, + "content": "(e) FuseFormer" + }, + { + "type": "image", + "bbox": [ + 0.405, + 0.424, + 0.563, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.462, + 0.495, + 0.503, + 0.506 + ], + "angle": 0, + "content": "(f) FGT" + }, + { + "type": "image", + "bbox": [ + 0.622, + 0.271, + 0.885, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.704, + 0.41, + 0.812, + 0.42 + ], + "angle": 0, + "content": "(c) Performance Gain" + }, + { + "type": "image", + "bbox": [ + 0.565, + 0.424, + 0.722, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.614, + 0.495, + 0.673, + 0.506 + ], + "angle": 0, + "content": "(g) \\(\\mathrm{E}^2\\mathrm{FGVI}\\)" + }, + { + "type": "image", + "bbox": [ + 0.725, + 0.424, + 0.884, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.752, + 0.495, + 0.855, + 0.506 + ], + "angle": 0, + "content": "(h) ProPainter (ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.516, + 0.895, + 0.577 + ], + "angle": 0, + "content": "Figure 1: (a) Dual-domain propagation enables more effective propagation due to its global and reliable nature. (b) Mask-guided sparse video Transformer achieves high efficiency by discarding unnecessary and redundant windows. (c) ProPainter outperforms prior methods while maintaining efficiency. (d-h) In visual comparisons with FuseFormer [22], FGT [42], and \\(\\mathrm{E}^2\\mathrm{FGVI}\\) [19], our ProPainter exhibits superiority in filling complete and rich textures." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.593, + 0.313, + 0.609 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.629, + 0.474, + 0.903 + ], + "angle": 0, + "content": "Flow-based propagation and spatiotemporal Transformer are two mainstream mechanisms in video inpainting (VI). Despite the effectiveness of these components, they still suffer from some limitations that affect their performance. Previous propagation-based approaches are performed separately either in the image or feature domain. Global image propagation isolated from learning may cause spatial misalignment due to inaccurate optical flow. Moreover, memory or computational constraints limit the temporal range of feature propagation and video Transformer, preventing exploration of correspondence information from distant frames. To address these issues, we propose an improved framework, called ProPainter, which involves enhanced ProPagation and an efficient Transformer. Specifically, we introduce dual-domain propagation that combines the advantages of image and feature warping, exploiting global correspondences reliably. We also propose a mask-guided sparse video Transformer, which achieves high efficiency by discarding unnecessary" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.595, + 0.893, + 0.641 + ], + "angle": 0, + "content": "and redundant tokens. With these components, ProPainter outperforms prior arts by a large margin of 1.46 dB in PSNR while maintaining appealing efficiency." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.663, + 0.633, + 0.679 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.896, + 0.902 + ], + "angle": 0, + "content": "Video inpainting (VI) aims to fill gaps or missing regions in a video with visually consistent content while ensuring spatial and temporal coherence. This technique has broad applications, including video completion [10], object removal [9, 37], video restoration [31], watermark, and logo removal [19]. VI is challenging because it requires establishing accurate correspondence across distant frames for information aggregation. To address this challenge, various mechanisms have been explored, such as 3D CNN [6, 11], video internal learning [41, 27], flow-guided propagation [37, 10, 43, 42, 19], and video Transformer [22, 42, 19]. Among these mechanisms, flow-guided propagation and video Transformer have become mainstream choices for VI due to their promising performance." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10477" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.438 + ], + "angle": 0, + "content": "Propagation-based methods in VI can be divided into two categories: image propagation and feature propagation. The former employs bidirectional global propagation in the image domain with a pre-completed flow field. While this approach can fill the majority of holes in a corrupted video, it requires an additional image or video inpainting network after propagation to hallucinate the remaining missing regions. This isolated two-step process can result in unpleasant artifacts and texture misalignment due to inaccurate flow, as shown in Figure 1(f). To address this issue, a recent approach called \\(\\mathrm{E}^2\\mathrm{FGVI}\\) [19] implements propagation in the feature domain, incorporating flow completion and content hallucination modules in an end-to-end framework. With the learnable warping module, the feature propagation module relieves the pressure of having inaccurate flow. However, \\(\\mathrm{E}^2\\mathrm{FGVI}\\) employs a downsampled flow field to match the spatial size of the feature domain, limiting the precision of spatial warping and the efficacy of propagation, potentially resulting in blurry results. Moreover, feature propagation can only be performed within a short range of video sequences due to memory and computational constraints, hindering propagation from distant frames and leading to missing texture, as shown in Figure 1(g)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.44, + 0.473, + 0.878 + ], + "angle": 0, + "content": "Both image- and feature-based propagation have their pros and cons. In this study, we carefully revisit the VI problem and investigate the possibility of combining the strengths of both techniques. We demonstrate that with systematic redesigns and adaptation of best practices in the literature, we can achieve dual-domain propagation, as illustrated in Figure 1(a). To achieve reliable and efficient information propagation across a video, we identify several essential components: i) Efficient GPU-based propagation with reliability check – Unlike previous methods that rely on complex and time-consuming CPU-centric operations, such as indexing flow trajectories, we perform global image propagation on GPU with flow consistency check. This implementation can be inserted at the beginning of the inpainting network and jointly trained with the other modules. Thus, subsequent modules are able to correct any propagation errors and benefit from the long-range correspondence information provided by the global propagation, resulting in a significant performance improvement. ii) Improved feature propagation – Our implementation of feature propagation leverages flow-based deformable alignment [3], which improves robustness to occlusion and inaccurate flow completion compared to \\(\\mathrm{E}^2\\mathrm{FGVI}\\) [19]. iii) Efficient flow completion – We design a highly efficient recurrent network to complete flows for dual-domain propagation, which is over 40 times (\\(\\sim 192\\) fps\\(^1\\)) faster than SOTA method [43] while maintaining comparable performance. We demonstrate that these designs are essential to achieve efficient propagation of global and local information without texture misalignment or blurring in the" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.839, + 0.107 + ], + "angle": 0, + "content": "filling results. An example is shown in Figure 1(h)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.108, + 0.895, + 0.41 + ], + "angle": 0, + "content": "In addition to dual-domain propagation, we introduce an efficient mask-guided sparse video Transformer tailored for the VI task. The classic spatiotemporal Transformer is computationally intensive due to the quadratic number of interactions between video tokens, making it intractable for high-resolution and long temporal-length videos. For instance, contemporary Transformer-based methods, FuseFormer [22] and FGT [42], are unable to handle 480p videos with a \\(32\\mathrm{G}\\) GPU due to excessive memory demands. However, we observe that the inpainting mask usually covers only a small local region, such as the object area. Moreover, adjacent frames contain highly redundant textures. These observations suggest that spatiotemporal attention is unnecessary for most unmasked areas, and it is adequate to consider only alternating interval frames in attention computation. Motivated by these observations, we redesign the Transformer by discarding unnecessary and redundant windows in the query and key/value space, respectively, significantly reducing computational complexity and memory without compromising inpainting performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.895, + 0.577 + ], + "angle": 0, + "content": "The main contribution of this work is to provide a systematic study into the core problem of VI and offer a practical solution that is both effective and efficient. Propagating information in two distinct image and feature domains and combining them in a unified framework with fast GPU implementation is new for VI task. The mask-guided sparse video Transformer also offers practical insights into designing efficient spatiotemporal attention for VI task. Compared to the state-of-the-art methods, our model achieves superior performance with a large margin of \\(1.46\\mathrm{dB}\\) in PSNR, while also significantly reducing memory consumption." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.591, + 0.642, + 0.607 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.617, + 0.895, + 0.678 + ], + "angle": 0, + "content": "Numerous deep networks with different modules and propagation strategies have achieved significant success in video inpainting. These approaches can be broadly categorized into four categories:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.679, + 0.895, + 0.769 + ], + "angle": 0, + "content": "3D convolution. Earlier video inpainting networks typically employed 3D CNNs [6, 33, 11] or temporal shift [7] to aggregate spatiotemporal information. These methods often suffer from limited receptive fields in both temporal and spatial dimensions and misalignment between adjacent frames. As a result, they are less effective in exploring distant content." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.77, + 0.892, + 0.845 + ], + "angle": 0, + "content": "Internal learning. To fully exploit content of a video, some studies [41, 27, 30] adopt internal learning to encode and memorize the appearance and motion of the video through deep networks. However, these methods require individual training for each test video, limiting their practical use." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.845, + 0.892, + 0.876 + ], + "angle": 0, + "content": "Flow-guided propagation. Optical flow [13, 18, 46] and homography [17, 1] are commonly used in video inpainting" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.378, + 0.9 + ], + "angle": 0, + "content": "1Tested on a single NVIDIA Tesla V100 GPU (32G)." + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.887, + 0.874, + 0.901 + ], + "angle": 0, + "content": "\\( {}^{2} \\) Object regions account for only 13.6% of the DAVIS [28] dataset." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10478" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.363 + ], + "angle": 0, + "content": "networks to align neighboring reference frames to enhance temporal coherence and aggregation. However, incomplete optical flow may not provide valid propagation for completing missing regions. To address this issue, recent flow-based methods [37, 10, 12, 43, 42] focus on first completing the flow and then use it as a guidance for pixel-domain propagation. This approach simplifies RGB pixel inpainting by completing a less complex flow field. However, this offline propagation is independent of the subsequent learnable refinement module, making it difficult to correct content distortion caused by inaccurate propagation. Inspired by flow-guided recurrent networks [2, 3], Li et al. [19] proposed an end-to-end framework that jointly learns flow completion and feature propagation in the downsampled feature domain. However, downsampled flow reduces its ability to provide spatially precise warping. To overcome this limitation, we propose more faithful propagation by performing both pixel and feature propagation with flow consistency checks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.473, + 0.65 + ], + "angle": 0, + "content": "Video Transformer. Attention [17, 26, 11, 18] and Transformer [40, 21, 22, 1, 19, 42] blocks adopt spatiotemporal attention to explore recurrent textures in a video. This enables them to retrieve and aggregate tokens with similar texture or context for filling in missing regions. Liu et al. [22] present a fine-grained fusion Transformer based on the soft split and composition operations, which further boosts video inpainting performance. However, these methods are computationally and memory intensive. To address this issue, some Transformers [21, 1, 42] decouple the spatiotemporal attention by performing spatial and temporal attention alternately, while others [19, 42] adopt window-based Transformers [23, 38] to reduce the spatial range for efficient video attention. However, these approaches still involve redundant or unnecessary tokens. Inspired by token pruning for adaptive attention [29, 39, 25, 20, 15] in high-level tasks, our study proposes a more efficient and faster video Transformer with sparse spatiotemporal attention and a largely reduced token space while maintaining inpainting performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.651, + 0.473, + 0.817 + ], + "angle": 0, + "content": "Recent studies [18, 19, 42] have demonstrated the effectiveness of combining flow-guided propagation with Transformer in VI. However, the high memory requirement of the Transformer limits the propagation range during both training and inference, severely hindering the ability to propagate temporally distant content. In this paper, we also adopt this combination strategy but propose a reliable propagation scheme, along with an efficient Transformer model that fully exploits the benefits of long-range propagation and attention. This results in superior inpainting performance while maintaining computational efficiency." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.831, + 0.212, + 0.848 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Given a masked video sequence \\(X = \\{X_{t} \\in \\mathbb{R}^{H \\times W \\times 3}\\}_{t=1}^{T}\\), which has a sequence length of \\(T\\), along with corresponding mask sequence \\(M = \\{M_{t} \\in\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.09, + 0.895, + 0.35 + ], + "angle": 0, + "content": "\\(\\mathbb{R}^{H\\times W\\times 1}\\}_{t = 1}^{T}\\), the objective of video inpainting is to generate visually consistent and coherent content within the corrupted or missing regions. ProPainter, as shown in Figure 2, is composed of three key components: Recurrent Flow Completion (RFC), Dual-Domain Propagation (DDP), and Mask-guided Sparse Video Transformer (MSVT). Before feeding the sequence into ProPainter, we extract the forward and backward optical flows, denoted as \\(F^f = \\{F_t^f = F_{t\\to t + 1}\\in \\mathbb{R}^{H\\times W\\times 2}\\}_{t = 1}^{T - 1}\\) and \\(F^b = \\{F_t^b = F_{t + 1\\to t}\\in \\mathbb{R}^{H\\times W\\times 2}\\}_{t = 1}^{T - 1}\\) from a given video \\(X\\). We first use RFC to complete the corrupted flow fields. Guided by the completed flows, we then perform global image propagation and local feature propagation sequentially. Finally, we employ multiple MSVT blocks to refine propagation features and a decoder to reconstruct the final video sequence \\(\\hat{Y} = \\{\\hat{Y}_t\\in \\mathbb{R}^{H\\times W\\times 3}\\}_{t = 1}^T\\). We introduce the specific design of each component below." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.361, + 0.753, + 0.379 + ], + "angle": 0, + "content": "3.1. Recurrent Flow Completion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.895, + 0.642 + ], + "angle": 0, + "content": "Pre-trained flow completion modules are commonly used in video inpainting networks [37, 10, 43, 42]. The rationale behind this approach is that it is simpler to complete missing flow than to directly fill in complex RGB content [37]. Furthermore, using completed flow to propagate pixels reduces the pressure of video inpainting and better maintains temporal coherence. \\(\\mathrm{E}^2\\mathrm{FGVI}\\) [19] proposes to insert the flow completion module into an end-to-end framework, which simplifies the inpainting pipeline. However, flow completion modules that are learned together with inpainting-oriented losses can result in a suboptimal learning process and less accurate completed flow. Moreover, the downsampled flow may limit the precision of spatial warping and the efficacy of propagation, which can result in blurred and incomplete filling content, as shown in Figure 1(g). Therefore, an independent flow completion model is not only important but also necessary for video inpainting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.895, + 0.78 + ], + "angle": 0, + "content": "To maintain temporal coherence while completing flows, previous methods [37, 42] adopt sliding-window-based networks to aggregate optical flow information from adjacent frames, which are highly correlated. However, these methods can be computationally expensive as repeated inferences are required in the overlapping frames. To improve efficiency and enhance flow coherence further, we adopt a recurrent network [2, 3] for flow completion, which provides precise optical flow fields for subsequent propagation modules." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.897, + 0.902 + ], + "angle": 0, + "content": "We complete forward and backward flows using the same process, thus we denote \\( F^f \\) and \\( F^b \\) as \\( F \\) for simplicity. We first encode the flows \\( F_t \\) into a downsampled feature \\( f_t \\) with a downsampling ratio of 8. Next, we employ deformable alignment [3] that is based on deformable convolution (DCN) [8, 45], to bidirectionally propagate the flow information from nearby frames for flow completion. For simplicity, we only describe the backward propagation" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10479" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.895, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.258, + 0.895, + 0.366 + ], + "angle": 0, + "content": "Figure 2: ProPainter comprises three key components: recurrent flow completion, dual-domain propagation, and mask-guided sparse Transformer. First, we employ a highly efficient recurrent flow completion network to complete the corrupted flow fields. We then perform propagation in both image and feature domains, which are jointly trained. This approach enables us to explore correspondences from both global and local temporal frames, resulting in more reliable and effective propagation. The subsequent mask-guided sparse Transformer blocks refine the propagated features using spatiotemporal attention, aided by a sparse strategy that considers only a subset of the tokens. This enhances efficiency and reduces memory consumption, while maintaining performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.475, + 0.475 + ], + "angle": 0, + "content": "process here. Taking the concatenated feature \\( c(f_t, \\hat{f}_{t+1}) \\), where \\( \\hat{f}_{t+1} \\) is the propagation feature of the \\( t+1 \\)-th frame, as input a lightweight network with a stack of convolutions is employed to compute DCN offsets \\( o_{t \\to t+1} \\) and modulation masks \\( m_{t \\to t+1} \\). DCN alignment propagation can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.492, + 0.471, + 0.513 + ], + "angle": 0, + "content": "\\[\n\\hat {f} _ {t} = \\mathcal {R} \\big (\\mathcal {D} \\big (\\hat {f} _ {t + 1}; o _ {t \\rightarrow t + 1}, m _ {t \\rightarrow t + 1}), f _ {t} \\big), \\qquad (1)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.473, + 0.639 + ], + "angle": 0, + "content": "where \\(\\mathcal{D}(\\cdot)\\) denotes deformable convolution, and \\(\\mathcal{R}(\\cdot)\\) denotes the convolution layers that fuse the aligned and current features. In this way, information of \\((t + 1)\\)-th flow can be adaptively transferred to the current \\(t\\)-th flow. Finally, a decoder is used to reconstruct the completed flows \\(\\hat{F}_t\\). For clarity, an illustration of deformable alignment is provided in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.658, + 0.315, + 0.675 + ], + "angle": 0, + "content": "3.2. Dual-domain Propagation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.685, + 0.471, + 0.793 + ], + "angle": 0, + "content": "After completing the flow, we perform global and local propagation in the image and feature domains, respectively. We employ distinct alignment operations and strategies for each domain. Both domains involve bidirectional propagation in the forward and backward directions. Here, we elaborate on the backward propagation since the forward propagation follows the same process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Image propagation. To maintain efficiency and simplicity, we adopt flow-based warping for image propagation, along with a simple reliability check strategy. This process does not involve any learnable operation. In the case of a video sequence \\( X \\) with binary masks \\( M \\) (a pixel with value 1 represents masked region) and completed flows \\( \\hat{F} \\), we first check the validity of completed flow based on forward-backward" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.383, + 0.678, + 0.399 + ], + "angle": 0, + "content": "consistency error [37, 10]:" + }, + { + "type": "equation", + "bbox": [ + 0.501, + 0.409, + 0.893, + 0.449 + ], + "angle": 0, + "content": "\\[\n\\mathcal {E} _ {t \\rightarrow t + 1} (p) = \\left\\| \\hat {F} _ {t \\rightarrow t + 1} (p) + \\hat {F} _ {t + 1 \\rightarrow t} (p + \\hat {F} _ {t \\rightarrow t + 1} (p)) \\right\\| _ {2} ^ {2}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.45, + 0.895, + 0.585 + ], + "angle": 0, + "content": "where \\(p\\) denotes a pixel position of the current frame. Only pixels with a small consistency error will be propagated, i.e., \\(C_1: \\mathcal{E}_{t \\to t + 1}(p) < \\epsilon\\), where \\(\\epsilon\\) is a threshold and set to 5. Furthermore, we only consider the masked areas of the current frame \\(X_t\\) that needs to be filled, i.e., \\(C_2: M_t(p) = 1\\), and we only propagate the unmasked areas from neighboring frame \\(X_{t + 1}\\), i.e., \\(C_3: M_{t + 1}(p + \\hat{F}_{t \\to t + 1}(p)) = 0\\). By enforcing the three constraints, a reliable propagation area \\(A_r\\) is identified as:" + }, + { + "type": "equation", + "bbox": [ + 0.572, + 0.595, + 0.893, + 0.637 + ], + "angle": 0, + "content": "\\[\nA _ {r} (p) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} p \\in C _ {1} \\cap C _ {2} \\cap C _ {3}, \\\\ 0 & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.647, + 0.833, + 0.663 + ], + "angle": 0, + "content": "The process of image propagation is expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.673, + 0.894, + 0.693 + ], + "angle": 0, + "content": "\\[\n\\hat {X} _ {t} = \\mathcal {W} \\left(X _ {t + 1}, \\hat {F} _ {t \\rightarrow t + 1}\\right) * A _ {r} + X _ {t} * \\left(1 - A _ {r}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.702, + 0.895, + 0.808 + ], + "angle": 0, + "content": "where \\(\\mathcal{W}(\\cdot)\\) denotes warping operation. To ensure continuous propagation, we promptly update the mask \\(M_{t}\\) of the current frame and convert the propagated area to the un-masked status by updating masks via \\(\\dot{M}_t = M_t - A_r\\). After global image propagation, we obtain a partially filled video sequence \\(\\tilde{X}\\), which greatly eases the learning process for subsequent modules." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.809, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Feature propagation. We use an image encoder with the same structure as previous works [22, 19] to extract features from a local sequence \\(\\hat{X}_{t=1}^{T_l}\\), denoted as \\(\\{e_t \\in \\mathbb{R}^{\\frac{H}{4} \\times \\frac{W}{4} \\times C}\\}_{t=1}^{T_l}\\). Similar to E²FGVI [19], we also adopt flow-guided deformable alignment module [3] for feature propagation, which has demonstrated remarkable benefits" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10480" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.468, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.243, + 0.473, + 0.364 + ], + "angle": 0, + "content": "Figure 3: Flow-guided deformable alignment is effective by taking reliable completed flows and mask-aware conditions. We concatenate the validated flow map, original mask, and updated mask into conditions to produce DCN offsets (residue to optical flow). A DCN is then applied to align the propagation feature from the previous frame. Finally, a CNN block is employed to fuse the current and aligned features, achieving the propagation feature of the current frame." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.391, + 0.473, + 0.622 + ], + "angle": 0, + "content": "in various low-level video tasks [5, 4, 44]. Unlike the deformable alignment used in Sec. 3.1 that directly learns DCN offsets, flow-guided deformable alignment employs the completed flow as a base offset and refines it by learning offset residue. However, our design differs from \\(\\mathrm{E}^2\\mathrm{FGVI}\\) in that we offer richer conditions for learning DCN offsets. As illustrated in Figure 3, apart from the current feature \\(e_t\\), warped propagation feature \\(\\mathcal{W}(\\hat{e}_{t + 1},\\hat{F}_{t\\rightarrow t + 1}^{\\downarrow})\\), and completed flows \\(\\hat{F}_{t\\rightarrow t + 1}^{\\downarrow}\\), we additionally introduce the flow valid map \\(V_{t + 1\\to t}\\) calculated by consistency check (Eq. 2), as well as the original mask \\(M_t^\\downarrow\\), and updated mask \\(\\hat{M}_t^\\downarrow\\) after image propagation. With these conditions, a stack of convolutions is employed to predict the DCN offset residue \\(\\widetilde{o}_{t\\rightarrow t + 1}\\) and modulation masks \\(m_{t\\rightarrow t + 1}\\). The flow-guided DCN alignment propagation is expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.629, + 0.471, + 0.65 + ], + "angle": 0, + "content": "\\[\n\\hat {e} _ {t} = \\mathcal {R} \\big (\\mathcal {D} \\big (\\hat {e} _ {t + 1}; \\hat {F} _ {t \\rightarrow t + 1} ^ {\\downarrow} + \\widetilde {o} _ {t \\rightarrow t + 1}, m _ {t \\rightarrow t + 1}), f _ {t} \\big), \\quad (5)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.47, + 0.749 + ], + "angle": 0, + "content": "where \\(\\downarrow\\) denotes downsampling. The improved reliability of flow and the additional awareness of mask as a condition make our flow-guided deformable alignment module more stable to learn than previous designs [3, 19]. The current step is able to focus more on truly challenging regions where flow is invalid and former image propagation is unreliable." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.427, + 0.773 + ], + "angle": 0, + "content": "3.3. Mask-Guided Sparse Video Transformer" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.473, + 0.901 + ], + "angle": 0, + "content": "While video Transformers have achieved excellent performance in video inpainting, they can be computationally and memory intensive, posing a challenge to their practical application. \\(\\mathrm{E}^2\\mathrm{FGVI}\\) and FGT have addressed this issue by using window-based Transformer blocks, but they still have some efficiency limitations. To overcome this, we propose a novel sparse video Transformer that builds on the window-based approach. Given a video sequence feature" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.089, + 0.891, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.242, + 0.895, + 0.349 + ], + "angle": 0, + "content": "Figure 4: Mask-guided sparse video Transformer. To reduce computational complexity and memory usage, our mask-guided sparse Transformer filters out unnecessary and redundant windows in the query and key/value space, respectively, before applying self-attention. To enlarge spatial interrelation range, we also adopt the window expand strategy [38] and pooling global tokens [42, 19]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.376, + 0.895, + 0.575 + ], + "angle": 0, + "content": "\\(E_{l} \\in \\mathbb{R}^{T_{l} \\times \\frac{H}{4} \\times \\frac{W}{4} \\times C}\\), we use the soft split operation [22] to generate patch embeddings \\(Z \\in \\mathbb{R}^{T_{l} \\times M \\times N \\times C_{z}}\\). We partition \\(Z\\) into \\(m \\times n\\) non-overlapping windows, resulting in partitioned features \\(Z_{w} \\in \\mathbb{R}^{T_{l} \\times m \\times n \\times h \\times w \\times C_{z}}\\), where \\(m \\times n\\) and \\(h \\times w\\) are the number and size of the windows, respectively. We obtain the query \\(Q\\), key \\(K\\), and value \\(V\\) from \\(Z_{w}\\) through linear layers. We design sparse strategies for both query and key/value spaces separately. Note that we also apply the window expand strategy [22] and integrate global tokens [42] into key and value, enabling us to use a small window size of \\(5 \\times 9\\) in our experiments. We omit them from the following discussion since they do not affect our sparse strategy designs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.576, + 0.895, + 0.773 + ], + "angle": 0, + "content": "Sparse Query Space. We observe that mask regions often occupy only a small area of the video, such as in the case of object removal in the DAVIS [28] dataset, where the proportion of object regions is only \\(13.6\\%\\). This indicates that spatiotemporal attention may not be necessary for all query windows. To exploit this observation, we selectively apply attention to query windows that intersect with the mask regions. Specifically, we first use nearest neighbor interpolation to downsample the mask sequence \\(M \\in \\mathbb{R}^{T_l \\times H \\times W}\\) to \\(M^{\\downarrow} \\in \\mathbb{R}^{T_l \\times m \\times n}\\), where \\(m \\times n\\) is the number of non-overlapping windows after partitioning. We then sum it up in the temporal dimension and obtain sparse mask \\(S_Q \\in \\mathbb{R}^{m \\times n}\\) for query cubes following the equation:" + }, + { + "type": "equation", + "bbox": [ + 0.593, + 0.785, + 0.894, + 0.813 + ], + "angle": 0, + "content": "\\[\nS _ {Q} = \\operatorname {C l i p} \\left(\\sum_ {t = 1} ^ {T _ {l}} M _ {t} ^ {\\downarrow}, 1\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.823, + 0.894, + 0.901 + ], + "angle": 0, + "content": "where \\(Clip\\) represents a clipping function that set \\(S_{Q}\\) to 1 if \\(\\sum_{t=1}^{T_l} M_t^{\\downarrow} > 0\\). In other words, if the query cube at a window \\((i,j)\\) has never contained any mask region in the past frames, then \\(S_{Q}(i,j) = 0\\), indicating that spatiotemporal attention within this window can be skipped." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10481" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.138 + ], + "angle": 0, + "content": "Table 1: Quantitative comparisons on YouTube-VOS [36] and DAVIS [28] datasets. The best and second performances are marked in red and blue, respectively. \\( E_{\\text{warp}}^* \\) denotes \\( E_{\\text{warp}} (\\times 10^{-3}) \\). All methods are evaluated following their default settings. Since DFVI, FGVC, ISVI, and FGT involve several CPU processes, their FLOPs cannot be accurately projected." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.142, + 0.892, + 0.357 + ], + "angle": 0, + "content": "
AccuracyEfficiency
YouTube-VOSDAVISFLOPs (10 frames)Runtime (s/frame)
ModelsPSNR ↑SSIM ↑VFID ↓E* \\( _{warp} \\) ↓PSNR ↑SSIM ↑VFID ↓E* \\( _{warp} \\) ↓
DFVI [37]29.160.94290.0661.65128.810.94040.1871.596-0.837
CPNet [17]31.580.96070.0711.62230.280.95210.1821.5211407G0.316
FGVC [10]29.670.94030.0641.16330.800.94970.1651.571-1.795
STTN [40]32.340.96550.0531.06130.610.95600.1491.4381315G0.051
TSAM [46]30.220.94680.0701.01430.670.95480.1461.2351001G0.068
FuseFormer [22]33.320.96810.0531.05332.590.97010.1371.3491025G0.114
ISVI [43]30.340.94580.0771.00832.170.95880.1891.291-1.594
FGT [42]32.170.95990.0541.02532.860.96500.1291.323-1.828
E2FGVI [19]33.710.97000.0461.01333.010.97210.1161.289986G0.085
ProPainter (Ours)34.430.97350.0420.97434.470.97760.0981.187808G0.083
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.378, + 0.475, + 0.651 + ], + "angle": 0, + "content": "Sparse Key/Value Space. Due to the highly redundant and repetitive textures in adjacent frames, it is unnecessary to include all frames as key/value tokens in each Transformer block. Instead, we will only include stripped temporal frames alternately, with a temporal stride of 2 in our design. That is, in each odd-numbered Transformer block, only odd-number frames are activated to participate in self-attention with their key and value, while even-number blocks include only even-number frames. By doing so, the key and value space is reduced by half, effectively reducing the computation and memory cost of the Transformer module. After filtering out unnecessary and redundant windows based on our sparse strategy, we perform self-attention on the remaining windows to extract refined features. These features are then gathered using a soft composition operation [22] for subsequent modules. Experimental results suggest that our design significantly reduces the computational cost of video Transformers while maintaining performance for video inpainting." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.659, + 0.267, + 0.675 + ], + "angle": 0, + "content": "3.4. Training Objectives" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.681, + 0.472, + 0.834 + ], + "angle": 0, + "content": "Flow Completion. We utilize L1 loss as the reconstruction loss and a second-order smoothness constraint on the flow field [24] to promote the collinearity of neighboring flows and thus enhance the smoothness of the completed flow field. Video Inpainting. We adopt L1 loss as the reconstruction loss for all pixels. To enhance the realistic and temporal consistency of video inpainting results, we also employ an adversarial loss that is measured using a T-PatchGAN [6] discriminator. The details and formulation of these losses are provided in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.846, + 0.212, + 0.863 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Datasets. We use the training set of YouTube-VOS [36] with 3471 video sequences to train our networks. Two widely-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.378, + 0.895, + 0.56 + ], + "angle": 0, + "content": "used test sets are adopted for evaluation: YouTube-VOS [36] and DAVIS [28], which consist of 508 and 90 video sequences, respectively. For the DAVIS test set, following FuseFormer [22] and \\(\\mathrm{E}^2\\mathrm{FGVI}\\) [19], we use 50 video clips for evaluations. During training, we follow [13, 17, 22, 19] and generate stationary and object masks in a random fashion to simulate the masks in video completion and object removal tasks. As for evaluation, we adopt the stationary masks provided in [19] to calculate quantitative scores, and the object masks are extracted from their segmentation labels for qualitative comparisons. Video frames are sized to \\(432\\times 240\\) for training and evaluation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.562, + 0.897, + 0.759 + ], + "angle": 0, + "content": "Training Details and Metrics. We use RAFT [32] to extract optical flow in our approach. For training the RFC network, we set the flow sequence length to 10 and perform deformable propagation on feature maps that are downsampled by a factor of 8 for faster processing. We adopt 8 Transformer blocks for the inpainting modules and use a local video sequence of length 10. The Transformer window size is \\(5 \\times 9\\), and the extended size is half of the window size. We train both the RFC and inpainting modules using the Adam [14] optimizer with a batch size of 8, setting the initial learning rate to \\(10^{-4}\\) and running 700k iterations for each. We implement our method using the PyTorch framework and train it on 8 NVIDIA Tesla V100 (32G) GPUs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.761, + 0.895, + 0.868 + ], + "angle": 0, + "content": "We employ the widely used PSNR and SSIM metrics [35] to evaluate the reconstruction performance and VFID [34] scores to measure the perceptual similarity between input videos and outputs, as used in recent video inpainting studies [22, 19]. Additionally, we report the flow warping error \\( E_{\\text{warp}} \\) [16] to assess the temporal consistency and smoothness of the resulting video sequences." + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.887, + 0.786, + 0.902 + ], + "angle": 0, + "content": "3We set 450k training iterations for ablation study." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10482" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.091, + 0.242, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.245, + 0.091, + 0.402, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.403, + 0.091, + 0.561, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.563, + 0.091, + 0.722, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.724, + 0.091, + 0.882, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.161, + 0.242, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.244, + 0.161, + 0.402, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.403, + 0.161, + 0.561, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.563, + 0.161, + 0.722, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.724, + 0.161, + 0.882, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.232, + 0.242, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.244, + 0.232, + 0.402, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.403, + 0.232, + 0.561, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.563, + 0.232, + 0.722, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.724, + 0.232, + 0.882, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.303, + 0.242, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.119, + 0.374, + 0.208, + 0.385 + ], + "angle": 0, + "content": "Masked Frames" + }, + { + "type": "image", + "bbox": [ + 0.244, + 0.303, + 0.402, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.289, + 0.374, + 0.358, + 0.384 + ], + "angle": 0, + "content": "FuseFormer" + }, + { + "type": "image", + "bbox": [ + 0.403, + 0.303, + 0.561, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.469, + 0.374, + 0.498, + 0.384 + ], + "angle": 0, + "content": "FGT" + }, + { + "type": "image", + "bbox": [ + 0.563, + 0.303, + 0.722, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.62, + 0.374, + 0.667, + 0.385 + ], + "angle": 0, + "content": "\\(\\mathrm{E}^2\\mathrm{FGVI}\\)" + }, + { + "type": "image", + "bbox": [ + 0.724, + 0.303, + 0.882, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.754, + 0.374, + 0.852, + 0.385 + ], + "angle": 0, + "content": "ProPainter (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.394, + 0.893, + 0.425 + ], + "angle": 0, + "content": "Figure 5: Qualitative comparisons on both video completion and object removal. Our ProPainter exhibits superiority in producing complete and faithful textures, resulting in enhanced spatiotemporal coherence for video inpainting." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.445, + 0.216, + 0.461 + ], + "angle": 0, + "content": "4.1. Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.472, + 0.473, + 0.652 + ], + "angle": 0, + "content": "Quantitative Evaluation. We compare ProPainter with nine state-of-the-art methods including DFVI [37], CPNet [17], FGVC [10], STTN [40], TSAM [46], Fuseformer [22], ISVI [43], FGT [42], and \\(\\mathrm{E}^2\\mathrm{FGVI}\\) [19] on both YouTube-VOS [36] and DAVIS [28]. Thanks to the efficient design, ProPainter uses a temporal length of 20 for inference. Table 1 shows that ProPainter outperforms other methods in all quantitative metrics, especially on the DAVIS dataset, where our method surpasses the state-of-the-art method by \\(1.14\\mathrm{dB}\\) in PSNR. The results suggest that our method has superior inpainting capability, enabling it to produce higher-quality, faithful, and seamless videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.472, + 0.838 + ], + "angle": 0, + "content": "Qualitative Evaluation. For the visual comparison, we compare our method with FuseFormer [22], FGT [42], and \\(\\mathrm{E}^2\\mathrm{FGVI}\\) [19], which are representative methods of Transformer-, image propagation-, and feature propagation-based approaches, respectively. Figure 5 presents four comparison results for video completion and object removal. Our method uses dual-domain propagation to ensure reliable and long-range propagation. It completes missing regions with coherence and clear contents, while other compared methods tend to fail or produce unpleasant inpainting results such as texture distortions and black hazy region in FGT [42] results, as well as artifacts in FuseFormer [22] and \\(\\mathrm{E}^2\\mathrm{FGVI}\\) [19]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.472, + 0.901 + ], + "angle": 0, + "content": "Efficiency Comparison. Table 1 presents the efficiency comparisons between all methods in terms of FLOPs and running time. The FLOPs of all methods are computed based on a temporal length of 10. We consider all learn-" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.444, + 0.894, + 0.474 + ], + "angle": 0, + "content": "Table 2: Comparisons of flow completion networks. Our network offers a dual benefit with high accuracy and efficiency." + }, + { + "type": "table", + "bbox": [ + 0.512, + 0.478, + 0.889, + 0.551 + ], + "angle": 0, + "content": "
EPE ↓DFVI [37]FGVC [10]FGT [42]ISVI [43]Ours
YouTube-VOS0.0460.0320.0210.0190.020
DAVIS0.1070.0820.0520.0510.051
Runtime (s/frame)0.1301.1250.3120.2310.005
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.894, + 0.652 + ], + "angle": 0, + "content": "able modules (including the recurrent flow completion) in our ProPainter to calculate the FLOPs. The running time records the time of all processes in each method, including inpainting, as well as flow calculation and flow completion if involved. To keep efficiency, we use only five iterations of the RAFT network to calculate optical flow." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.653, + 0.894, + 0.788 + ], + "angle": 0, + "content": "Flow Completion Comparisons. We compare our recurrent flow network with previous approaches [37, 10, 43] on both YouTube-VOS and DAVIS datasets. Table 2 presents the end-point-error (EPE) of flow completion and running time of each method. Our recurrent network offers a dual benefit with high accuracy and efficiency. Compared to previous methods, our network is approximately 40 times faster while maintaining a comparable flow completion accuracy to the state-of-the-art methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.801, + 0.655, + 0.817 + ], + "angle": 0, + "content": "4.2. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Effectiveness of Image Propagation. Table 3 shows that Exp. (a) experiences a significant performance drop when image propagation is removed. Moreover, the model's propagation ability is reduced without image propagation, as presented in Figure 7, causing it to fail to complete missing" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10483" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.24, + 0.09, + 0.729, + 0.105 + ], + "angle": 0, + "content": "Table 3: Ablation study of dual-main propagation and sparse Transformer." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.11, + 0.885, + 0.169 + ], + "angle": 0, + "content": "
Exp.(a) w/o Img Prop.(b) w/ Img Prop. in FGVC(c) w/o Feat Prop.(d) w/ Feat Prop. in E²FGVI(f) Full TokensProPainter
PSNR33.0532.9133.1733.9434.1834.15
SSIM0.97240.96870.97320.97560.97650.9764
" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.178, + 0.242, + 0.249 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.128, + 0.251, + 0.201, + 0.26 + ], + "angle": 0, + "content": "Masked Frame" + }, + { + "type": "image", + "bbox": [ + 0.244, + 0.179, + 0.403, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.275, + 0.251, + 0.372, + 0.261 + ], + "angle": 0, + "content": "Img Prop. of FGVC" + }, + { + "type": "image", + "bbox": [ + 0.403, + 0.179, + 0.563, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.405, + 0.251, + 0.559, + 0.262 + ], + "angle": 0, + "content": "w/Img Prop.of FGVC (Exp.b)" + }, + { + "type": "image", + "bbox": [ + 0.565, + 0.179, + 0.723, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.604, + 0.251, + 0.688, + 0.261 + ], + "angle": 0, + "content": "Img Prop. (Ours)" + }, + { + "type": "image", + "bbox": [ + 0.725, + 0.179, + 0.884, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.761, + 0.251, + 0.846, + 0.261 + ], + "angle": 0, + "content": "ProPainter (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.205, + 0.268, + 0.761, + 0.283 + ], + "angle": 0, + "content": "Figure 6: Visual comparison on image propagation methods of FGVC [10] and ours." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.299, + 0.209, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.106, + 0.413, + 0.186, + 0.423 + ], + "angle": 0, + "content": "Masked Frames" + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.299, + 0.338, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.216, + 0.413, + 0.331, + 0.425 + ], + "angle": 0, + "content": "w/o Img Prop. (Exp. a)" + }, + { + "type": "image", + "bbox": [ + 0.34, + 0.299, + 0.466, + 0.41 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.37, + 0.413, + 0.435, + 0.424 + ], + "angle": 0, + "content": "w/ImgProp." + }, + { + "type": "image_caption", + "bbox": [ + 0.086, + 0.432, + 0.458, + 0.447 + ], + "angle": 0, + "content": "Figure 7: Comparison of w/ and w/o image propagation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.47, + 0.61 + ], + "angle": 0, + "content": "content with details. To verify the effectiveness of our reliability check strategy in image propagation, we replaced our design with the FGVC image propagation module in Exp. (b) (without retraining), resulting in a noticeable decrease in PSNR. This is because the FGVC image propagation method is prone to being affected by incorrect optical flow, leading to severe texture distortion that subsequent modules cannot correct. Our model can effectively aware and stop unreliable propagation areas using a simple reliability check via Eq.2, and generate more faithful inpainting results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.471, + 0.748 + ], + "angle": 0, + "content": "Effectiveness of Feature Propagation. Similarly, we observe a slight decrease in performance by either removing feature propagation, i.e., Exp. (c), or replacing it with the Feature propagation of \\(\\mathrm{E}^2\\mathrm{FGVI}\\), i.e., Exp. (d), indicating the effectiveness of the feature propagation modules and our reliability mask-aware conditions. This suggests that our design, which learns reliable DCN offsets in the feature domain, can further complement and enhance the propagation ability in the image domain." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Effectiveness of Sparse Transformer. In theory, our strategy of using masks to guide sparsity only eliminates redundant and unnecessary tokens (windows), while preserving essential information. This means that there should be no adverse effect on performance. To confirm this, we conducted Exp. (d), comparing our approach to standard self-attention without sparse filtering. Our results indicate that our sparse Transformer block performs almost as well as the standard one, indicating that it can achieve high efficiency without sacrificing performance." + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.298, + 0.691, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.297, + 0.885, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.511, + 0.427, + 0.879, + 0.441 + ], + "angle": 0, + "content": "Figure 8: FLOPs cures of different Transformer blocks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.458, + 0.895, + 0.639 + ], + "angle": 0, + "content": "Efficiency of Sparse Transformer. In Figure 8, we compare the FLOPs of different Transformer blocks with respect to temporal length and spatial resolution, including those used in FuseFormer [22], FGT [42], and \\(\\mathrm{E}^2\\mathrm{FGVI}\\) [19]. We use a mask with a missing region ratio of \\(1/6\\) (higher than the average object ratio of \\(13.6\\%\\) in DAVIS) to calculate the FLOPs of our mask-guided sparse Transformer. The curves indicate that the efficiency advantage of our sparse Transformer becomes more prominent as the temporal length and video resolution increase, indicating great potential for developing longer-range spatiotemporal attention and applying it to larger resolution videos." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.653, + 0.619, + 0.669 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.678, + 0.895, + 0.83 + ], + "angle": 0, + "content": "This study introduces a novel and improved video inpainting framework called ProPainter. It incorporates an enhanced dual-domain propagation and an efficient mask-guided sparse video Transformer. Thanks to the two modules, our ProPainter exhibits reliable and precise propagation capabilities over long distances, significantly improving the performance of video inpainting while maintaining high efficiency in terms of running time and computational complexity. We believe that the designs in ProPainter will provide valuable insights to the video inpainting community." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.836, + 0.894, + 0.898 + ], + "angle": 0, + "content": "Acknowledgement. This study is supported under the RIE2020 Industry Alignment Fund Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10484" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Jiayin Cai, Changlin Li, Xin Tao, Chun Yuan, and Yu-Wing Tai. DeViT: Deformed vision transformers in video inpainting. In ACM MM, 2022. 2, 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.472, + 0.212 + ], + "angle": 0, + "content": "[2] Kelvin CK Chan, Xintao Wang, Ke Yu, Chao Dong, and Chen Change Loy. BasicVSR: The search for essential components in video super-resolution and beyond. 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Chan Chen Change Loy S-Lab, Nanyang Technological University + +{s200094，chongyi.li，chan0899，ccloy}@ntu.edu.sg + +https://shangchenzhou.com/projects/ProPainter + +![](images/b732b1c0f3aa605872f94707e23d8c4302a19932fb9150ed7b74e9f0a48f6f3e.jpg) + +![](images/578a78b77f2286d96a2cd0d5905ee5e460639d0d84352b08a580c227d1363994.jpg) +Sparse Query Space (masked window) + +![](images/c8e256b499cb885f38ccba6bcfc4059c8c7d886d6c8369ff3007b69b347df166.jpg) +Sparse Key/Value Space (temporal strided window) + +![](images/fdaa637903020c68b32926e26378ae3a3290bedb649a8e6a636dcb099b891a08.jpg) +(a) Dual-domain Propagation +(d) Input with object mask +Figure 1: (a) Dual-domain propagation enables more effective propagation due to its global and reliable nature. (b) Mask-guided sparse video Transformer achieves high efficiency by discarding unnecessary and redundant windows. (c) ProPainter outperforms prior methods while maintaining efficiency. (d-h) In visual comparisons with FuseFormer [22], FGT [42], and $\mathrm{E}^2\mathrm{FGVI}$ [19], our ProPainter exhibits superiority in filling complete and rich textures. + +![](images/6f6e279f101171584bab1bc53f1b9c9c82fb91cd2af74cebebb3b74b4b6dae1d.jpg) +(b) Mask-guided Sparse Video Transformer +(e) FuseFormer + +![](images/750da2b152646942cdd527a3e2235bc0bfc713406d2026574c2ba478235a4680.jpg) +(f) FGT + +![](images/906419075af44cbc8420f292582f7ee59bf7506739eb66a18517651f888e9255.jpg) +(c) Performance Gain + +![](images/000eccb62274be3e14d5500451d3145d325efd73faf294aab5dc4e13a1cfa9a5.jpg) +(g) $\mathrm{E}^2\mathrm{FGVI}$ + +![](images/6c22027452f062af6ec82b7e7241bb75e33ec2a752716b2f80f7e3c2d1e352fa.jpg) +(h) ProPainter (ours) + +# Abstract + +Flow-based propagation and spatiotemporal Transformer are two mainstream mechanisms in video inpainting (VI). Despite the effectiveness of these components, they still suffer from some limitations that affect their performance. Previous propagation-based approaches are performed separately either in the image or feature domain. Global image propagation isolated from learning may cause spatial misalignment due to inaccurate optical flow. Moreover, memory or computational constraints limit the temporal range of feature propagation and video Transformer, preventing exploration of correspondence information from distant frames. To address these issues, we propose an improved framework, called ProPainter, which involves enhanced ProPagation and an efficient Transformer. Specifically, we introduce dual-domain propagation that combines the advantages of image and feature warping, exploiting global correspondences reliably. We also propose a mask-guided sparse video Transformer, which achieves high efficiency by discarding unnecessary + +and redundant tokens. With these components, ProPainter outperforms prior arts by a large margin of 1.46 dB in PSNR while maintaining appealing efficiency. + +# 1. Introduction + +Video inpainting (VI) aims to fill gaps or missing regions in a video with visually consistent content while ensuring spatial and temporal coherence. This technique has broad applications, including video completion [10], object removal [9, 37], video restoration [31], watermark, and logo removal [19]. VI is challenging because it requires establishing accurate correspondence across distant frames for information aggregation. To address this challenge, various mechanisms have been explored, such as 3D CNN [6, 11], video internal learning [41, 27], flow-guided propagation [37, 10, 43, 42, 19], and video Transformer [22, 42, 19]. Among these mechanisms, flow-guided propagation and video Transformer have become mainstream choices for VI due to their promising performance. + +Propagation-based methods in VI can be divided into two categories: image propagation and feature propagation. The former employs bidirectional global propagation in the image domain with a pre-completed flow field. While this approach can fill the majority of holes in a corrupted video, it requires an additional image or video inpainting network after propagation to hallucinate the remaining missing regions. This isolated two-step process can result in unpleasant artifacts and texture misalignment due to inaccurate flow, as shown in Figure 1(f). To address this issue, a recent approach called $\mathrm{E}^2\mathrm{FGVI}$ [19] implements propagation in the feature domain, incorporating flow completion and content hallucination modules in an end-to-end framework. With the learnable warping module, the feature propagation module relieves the pressure of having inaccurate flow. However, $\mathrm{E}^2\mathrm{FGVI}$ employs a downsampled flow field to match the spatial size of the feature domain, limiting the precision of spatial warping and the efficacy of propagation, potentially resulting in blurry results. Moreover, feature propagation can only be performed within a short range of video sequences due to memory and computational constraints, hindering propagation from distant frames and leading to missing texture, as shown in Figure 1(g). + +Both image- and feature-based propagation have their pros and cons. In this study, we carefully revisit the VI problem and investigate the possibility of combining the strengths of both techniques. We demonstrate that with systematic redesigns and adaptation of best practices in the literature, we can achieve dual-domain propagation, as illustrated in Figure 1(a). To achieve reliable and efficient information propagation across a video, we identify several essential components: i) Efficient GPU-based propagation with reliability check – Unlike previous methods that rely on complex and time-consuming CPU-centric operations, such as indexing flow trajectories, we perform global image propagation on GPU with flow consistency check. This implementation can be inserted at the beginning of the inpainting network and jointly trained with the other modules. Thus, subsequent modules are able to correct any propagation errors and benefit from the long-range correspondence information provided by the global propagation, resulting in a significant performance improvement. ii) Improved feature propagation – Our implementation of feature propagation leverages flow-based deformable alignment [3], which improves robustness to occlusion and inaccurate flow completion compared to $\mathrm{E}^2\mathrm{FGVI}$ [19]. iii) Efficient flow completion – We design a highly efficient recurrent network to complete flows for dual-domain propagation, which is over 40 times ( $\sim 192$ fps $^1$ ) faster than SOTA method [43] while maintaining comparable performance. We demonstrate that these designs are essential to achieve efficient propagation of global and local information without texture misalignment or blurring in the + +filling results. An example is shown in Figure 1(h). + +In addition to dual-domain propagation, we introduce an efficient mask-guided sparse video Transformer tailored for the VI task. The classic spatiotemporal Transformer is computationally intensive due to the quadratic number of interactions between video tokens, making it intractable for high-resolution and long temporal-length videos. For instance, contemporary Transformer-based methods, FuseFormer [22] and FGT [42], are unable to handle 480p videos with a $32\mathrm{G}$ GPU due to excessive memory demands. However, we observe that the inpainting mask usually covers only a small local region, such as the object area. Moreover, adjacent frames contain highly redundant textures. These observations suggest that spatiotemporal attention is unnecessary for most unmasked areas, and it is adequate to consider only alternating interval frames in attention computation. Motivated by these observations, we redesign the Transformer by discarding unnecessary and redundant windows in the query and key/value space, respectively, significantly reducing computational complexity and memory without compromising inpainting performance. + +The main contribution of this work is to provide a systematic study into the core problem of VI and offer a practical solution that is both effective and efficient. Propagating information in two distinct image and feature domains and combining them in a unified framework with fast GPU implementation is new for VI task. The mask-guided sparse video Transformer also offers practical insights into designing efficient spatiotemporal attention for VI task. Compared to the state-of-the-art methods, our model achieves superior performance with a large margin of $1.46\mathrm{dB}$ in PSNR, while also significantly reducing memory consumption. + +# 2. Related Work + +Numerous deep networks with different modules and propagation strategies have achieved significant success in video inpainting. These approaches can be broadly categorized into four categories: + +3D convolution. Earlier video inpainting networks typically employed 3D CNNs [6, 33, 11] or temporal shift [7] to aggregate spatiotemporal information. These methods often suffer from limited receptive fields in both temporal and spatial dimensions and misalignment between adjacent frames. As a result, they are less effective in exploring distant content. + +Internal learning. To fully exploit content of a video, some studies [41, 27, 30] adopt internal learning to encode and memorize the appearance and motion of the video through deep networks. However, these methods require individual training for each test video, limiting their practical use. + +Flow-guided propagation. Optical flow [13, 18, 46] and homography [17, 1] are commonly used in video inpainting + +networks to align neighboring reference frames to enhance temporal coherence and aggregation. However, incomplete optical flow may not provide valid propagation for completing missing regions. To address this issue, recent flow-based methods [37, 10, 12, 43, 42] focus on first completing the flow and then use it as a guidance for pixel-domain propagation. This approach simplifies RGB pixel inpainting by completing a less complex flow field. However, this offline propagation is independent of the subsequent learnable refinement module, making it difficult to correct content distortion caused by inaccurate propagation. Inspired by flow-guided recurrent networks [2, 3], Li et al. [19] proposed an end-to-end framework that jointly learns flow completion and feature propagation in the downsampled feature domain. However, downsampled flow reduces its ability to provide spatially precise warping. To overcome this limitation, we propose more faithful propagation by performing both pixel and feature propagation with flow consistency checks. + +Video Transformer. Attention [17, 26, 11, 18] and Transformer [40, 21, 22, 1, 19, 42] blocks adopt spatiotemporal attention to explore recurrent textures in a video. This enables them to retrieve and aggregate tokens with similar texture or context for filling in missing regions. Liu et al. [22] present a fine-grained fusion Transformer based on the soft split and composition operations, which further boosts video inpainting performance. However, these methods are computationally and memory intensive. To address this issue, some Transformers [21, 1, 42] decouple the spatiotemporal attention by performing spatial and temporal attention alternately, while others [19, 42] adopt window-based Transformers [23, 38] to reduce the spatial range for efficient video attention. However, these approaches still involve redundant or unnecessary tokens. Inspired by token pruning for adaptive attention [29, 39, 25, 20, 15] in high-level tasks, our study proposes a more efficient and faster video Transformer with sparse spatiotemporal attention and a largely reduced token space while maintaining inpainting performance. + +Recent studies [18, 19, 42] have demonstrated the effectiveness of combining flow-guided propagation with Transformer in VI. However, the high memory requirement of the Transformer limits the propagation range during both training and inference, severely hindering the ability to propagate temporally distant content. In this paper, we also adopt this combination strategy but propose a reliable propagation scheme, along with an efficient Transformer model that fully exploits the benefits of long-range propagation and attention. This results in superior inpainting performance while maintaining computational efficiency. + +# 3. Methodology + +Given a masked video sequence $X = \{X_{t} \in \mathbb{R}^{H \times W \times 3}\}_{t=1}^{T}$ , which has a sequence length of $T$ , along with corresponding mask sequence $M = \{M_{t} \in$ + +$\mathbb{R}^{H\times W\times 1}\}_{t = 1}^{T}$ , the objective of video inpainting is to generate visually consistent and coherent content within the corrupted or missing regions. ProPainter, as shown in Figure 2, is composed of three key components: Recurrent Flow Completion (RFC), Dual-Domain Propagation (DDP), and Mask-guided Sparse Video Transformer (MSVT). Before feeding the sequence into ProPainter, we extract the forward and backward optical flows, denoted as $F^f = \{F_t^f = F_{t\to t + 1}\in \mathbb{R}^{H\times W\times 2}\}_{t = 1}^{T - 1}$ and $F^b = \{F_t^b = F_{t + 1\to t}\in \mathbb{R}^{H\times W\times 2}\}_{t = 1}^{T - 1}$ from a given video $X$ . We first use RFC to complete the corrupted flow fields. Guided by the completed flows, we then perform global image propagation and local feature propagation sequentially. Finally, we employ multiple MSVT blocks to refine propagation features and a decoder to reconstruct the final video sequence $\hat{Y} = \{\hat{Y}_t\in \mathbb{R}^{H\times W\times 3}\}_{t = 1}^T$ . We introduce the specific design of each component below. + +# 3.1. Recurrent Flow Completion + +Pre-trained flow completion modules are commonly used in video inpainting networks [37, 10, 43, 42]. The rationale behind this approach is that it is simpler to complete missing flow than to directly fill in complex RGB content [37]. Furthermore, using completed flow to propagate pixels reduces the pressure of video inpainting and better maintains temporal coherence. $\mathrm{E}^2\mathrm{FGVI}$ [19] proposes to insert the flow completion module into an end-to-end framework, which simplifies the inpainting pipeline. However, flow completion modules that are learned together with inpainting-oriented losses can result in a suboptimal learning process and less accurate completed flow. Moreover, the downsampled flow may limit the precision of spatial warping and the efficacy of propagation, which can result in blurred and incomplete filling content, as shown in Figure 1(g). Therefore, an independent flow completion model is not only important but also necessary for video inpainting. + +To maintain temporal coherence while completing flows, previous methods [37, 42] adopt sliding-window-based networks to aggregate optical flow information from adjacent frames, which are highly correlated. However, these methods can be computationally expensive as repeated inferences are required in the overlapping frames. To improve efficiency and enhance flow coherence further, we adopt a recurrent network [2, 3] for flow completion, which provides precise optical flow fields for subsequent propagation modules. + +We complete forward and backward flows using the same process, thus we denote $F^f$ and $F^b$ as $F$ for simplicity. We first encode the flows $F_t$ into a downsampled feature $f_t$ with a downsampling ratio of 8. Next, we employ deformable alignment [3] that is based on deformable convolution (DCN) [8, 45], to bidirectionally propagate the flow information from nearby frames for flow completion. For simplicity, we only describe the backward propagation + +![](images/bd7f9fc1852304742d261be2133dae94328f6fdadb074bc7503bccbb66973551.jpg) +Figure 2: ProPainter comprises three key components: recurrent flow completion, dual-domain propagation, and mask-guided sparse Transformer. First, we employ a highly efficient recurrent flow completion network to complete the corrupted flow fields. We then perform propagation in both image and feature domains, which are jointly trained. This approach enables us to explore correspondences from both global and local temporal frames, resulting in more reliable and effective propagation. The subsequent mask-guided sparse Transformer blocks refine the propagated features using spatiotemporal attention, aided by a sparse strategy that considers only a subset of the tokens. This enhances efficiency and reduces memory consumption, while maintaining performance. + +process here. Taking the concatenated feature $c(f_t, \hat{f}_{t+1})$ , where $\hat{f}_{t+1}$ is the propagation feature of the $t+1$ -th frame, as input a lightweight network with a stack of convolutions is employed to compute DCN offsets $o_{t \to t+1}$ and modulation masks $m_{t \to t+1}$ . DCN alignment propagation can be expressed as: + +$$ +\hat {f} _ {t} = \mathcal {R} \big (\mathcal {D} \big (\hat {f} _ {t + 1}; o _ {t \rightarrow t + 1}, m _ {t \rightarrow t + 1}), f _ {t} \big), \qquad (1) +$$ + +where $\mathcal{D}(\cdot)$ denotes deformable convolution, and $\mathcal{R}(\cdot)$ denotes the convolution layers that fuse the aligned and current features. In this way, information of $(t + 1)$ -th flow can be adaptively transferred to the current $t$ -th flow. Finally, a decoder is used to reconstruct the completed flows $\hat{F}_t$ . For clarity, an illustration of deformable alignment is provided in the supplementary material. + +# 3.2. Dual-domain Propagation + +After completing the flow, we perform global and local propagation in the image and feature domains, respectively. We employ distinct alignment operations and strategies for each domain. Both domains involve bidirectional propagation in the forward and backward directions. Here, we elaborate on the backward propagation since the forward propagation follows the same process. + +Image propagation. To maintain efficiency and simplicity, we adopt flow-based warping for image propagation, along with a simple reliability check strategy. This process does not involve any learnable operation. In the case of a video sequence $X$ with binary masks $M$ (a pixel with value 1 represents masked region) and completed flows $\hat{F}$ , we first check the validity of completed flow based on forward-backward + +consistency error [37, 10]: + +$$ +\mathcal {E} _ {t \rightarrow t + 1} (p) = \left\| \hat {F} _ {t \rightarrow t + 1} (p) + \hat {F} _ {t + 1 \rightarrow t} (p + \hat {F} _ {t \rightarrow t + 1} (p)) \right\| _ {2} ^ {2}, \tag {2} +$$ + +where $p$ denotes a pixel position of the current frame. Only pixels with a small consistency error will be propagated, i.e., $C_1: \mathcal{E}_{t \to t + 1}(p) < \epsilon$ , where $\epsilon$ is a threshold and set to 5. Furthermore, we only consider the masked areas of the current frame $X_t$ that needs to be filled, i.e., $C_2: M_t(p) = 1$ , and we only propagate the unmasked areas from neighboring frame $X_{t + 1}$ , i.e., $C_3: M_{t + 1}(p + \hat{F}_{t \to t + 1}(p)) = 0$ . By enforcing the three constraints, a reliable propagation area $A_r$ is identified as: + +$$ +A _ {r} (p) = \left\{ \begin{array}{l l} 1 & \text {i f} p \in C _ {1} \cap C _ {2} \cap C _ {3}, \\ 0 & \text {o t h e r w i s e .} \end{array} \right. \tag {3} +$$ + +The process of image propagation is expressed as: + +$$ +\hat {X} _ {t} = \mathcal {W} \left(X _ {t + 1}, \hat {F} _ {t \rightarrow t + 1}\right) * A _ {r} + X _ {t} * \left(1 - A _ {r}\right), \tag {4} +$$ + +where $\mathcal{W}(\cdot)$ denotes warping operation. To ensure continuous propagation, we promptly update the mask $M_{t}$ of the current frame and convert the propagated area to the un-masked status by updating masks via $\dot{M}_t = M_t - A_r$ . After global image propagation, we obtain a partially filled video sequence $\tilde{X}$ , which greatly eases the learning process for subsequent modules. + +Feature propagation. We use an image encoder with the same structure as previous works [22, 19] to extract features from a local sequence $\hat{X}_{t=1}^{T_l}$ , denoted as $\{e_t \in \mathbb{R}^{\frac{H}{4} \times \frac{W}{4} \times C}\}_{t=1}^{T_l}$ . Similar to E²FGVI [19], we also adopt flow-guided deformable alignment module [3] for feature propagation, which has demonstrated remarkable benefits + +![](images/80c09d94207daea57d5a8bc24ff28e14791bd063d4b4cc0e88bb0f51445376c6.jpg) +Figure 3: Flow-guided deformable alignment is effective by taking reliable completed flows and mask-aware conditions. We concatenate the validated flow map, original mask, and updated mask into conditions to produce DCN offsets (residue to optical flow). A DCN is then applied to align the propagation feature from the previous frame. Finally, a CNN block is employed to fuse the current and aligned features, achieving the propagation feature of the current frame. + +in various low-level video tasks [5, 4, 44]. Unlike the deformable alignment used in Sec. 3.1 that directly learns DCN offsets, flow-guided deformable alignment employs the completed flow as a base offset and refines it by learning offset residue. However, our design differs from $\mathrm{E}^2\mathrm{FGVI}$ in that we offer richer conditions for learning DCN offsets. As illustrated in Figure 3, apart from the current feature $e_t$ , warped propagation feature $\mathcal{W}(\hat{e}_{t + 1},\hat{F}_{t\rightarrow t + 1}^{\downarrow})$ , and completed flows $\hat{F}_{t\rightarrow t + 1}^{\downarrow}$ , we additionally introduce the flow valid map $V_{t + 1\to t}$ calculated by consistency check (Eq. 2), as well as the original mask $M_t^\downarrow$ , and updated mask $\hat{M}_t^\downarrow$ after image propagation. With these conditions, a stack of convolutions is employed to predict the DCN offset residue $\widetilde{o}_{t\rightarrow t + 1}$ and modulation masks $m_{t\rightarrow t + 1}$ . The flow-guided DCN alignment propagation is expressed as: + +$$ +\hat {e} _ {t} = \mathcal {R} \big (\mathcal {D} \big (\hat {e} _ {t + 1}; \hat {F} _ {t \rightarrow t + 1} ^ {\downarrow} + \widetilde {o} _ {t \rightarrow t + 1}, m _ {t \rightarrow t + 1}), f _ {t} \big), \quad (5) +$$ + +where $\downarrow$ denotes downsampling. The improved reliability of flow and the additional awareness of mask as a condition make our flow-guided deformable alignment module more stable to learn than previous designs [3, 19]. The current step is able to focus more on truly challenging regions where flow is invalid and former image propagation is unreliable. + +# 3.3. Mask-Guided Sparse Video Transformer + +While video Transformers have achieved excellent performance in video inpainting, they can be computationally and memory intensive, posing a challenge to their practical application. $\mathrm{E}^2\mathrm{FGVI}$ and FGT have addressed this issue by using window-based Transformer blocks, but they still have some efficiency limitations. To overcome this, we propose a novel sparse video Transformer that builds on the window-based approach. Given a video sequence feature + +![](images/93c4a07f8bdc940a274970239c1836076b54b3b8ae53c050013af3af5ed939f9.jpg) +Figure 4: Mask-guided sparse video Transformer. To reduce computational complexity and memory usage, our mask-guided sparse Transformer filters out unnecessary and redundant windows in the query and key/value space, respectively, before applying self-attention. To enlarge spatial interrelation range, we also adopt the window expand strategy [38] and pooling global tokens [42, 19]. + +$E_{l} \in \mathbb{R}^{T_{l} \times \frac{H}{4} \times \frac{W}{4} \times C}$ , we use the soft split operation [22] to generate patch embeddings $Z \in \mathbb{R}^{T_{l} \times M \times N \times C_{z}}$ . We partition $Z$ into $m \times n$ non-overlapping windows, resulting in partitioned features $Z_{w} \in \mathbb{R}^{T_{l} \times m \times n \times h \times w \times C_{z}}$ , where $m \times n$ and $h \times w$ are the number and size of the windows, respectively. We obtain the query $Q$ , key $K$ , and value $V$ from $Z_{w}$ through linear layers. We design sparse strategies for both query and key/value spaces separately. Note that we also apply the window expand strategy [22] and integrate global tokens [42] into key and value, enabling us to use a small window size of $5 \times 9$ in our experiments. We omit them from the following discussion since they do not affect our sparse strategy designs. + +Sparse Query Space. We observe that mask regions often occupy only a small area of the video, such as in the case of object removal in the DAVIS [28] dataset, where the proportion of object regions is only $13.6\%$ . This indicates that spatiotemporal attention may not be necessary for all query windows. To exploit this observation, we selectively apply attention to query windows that intersect with the mask regions. Specifically, we first use nearest neighbor interpolation to downsample the mask sequence $M \in \mathbb{R}^{T_l \times H \times W}$ to $M^{\downarrow} \in \mathbb{R}^{T_l \times m \times n}$ , where $m \times n$ is the number of non-overlapping windows after partitioning. We then sum it up in the temporal dimension and obtain sparse mask $S_Q \in \mathbb{R}^{m \times n}$ for query cubes following the equation: + +$$ +S _ {Q} = \operatorname {C l i p} \left(\sum_ {t = 1} ^ {T _ {l}} M _ {t} ^ {\downarrow}, 1\right), \tag {6} +$$ + +where $Clip$ represents a clipping function that set $S_{Q}$ to 1 if $\sum_{t=1}^{T_l} M_t^{\downarrow} > 0$ . In other words, if the query cube at a window $(i,j)$ has never contained any mask region in the past frames, then $S_{Q}(i,j) = 0$ , indicating that spatiotemporal attention within this window can be skipped. + +Table 1: Quantitative comparisons on YouTube-VOS [36] and DAVIS [28] datasets. The best and second performances are marked in red and blue, respectively. $E_{\text{warp}}^*$ denotes $E_{\text{warp}} (\times 10^{-3})$ . All methods are evaluated following their default settings. Since DFVI, FGVC, ISVI, and FGT involve several CPU processes, their FLOPs cannot be accurately projected. + +
AccuracyEfficiency
YouTube-VOSDAVISFLOPs (10 frames)Runtime (s/frame)
ModelsPSNR ↑SSIM ↑VFID ↓E* \( _{warp} \) ↓PSNR ↑SSIM ↑VFID ↓E* \( _{warp} \) ↓
DFVI [37]29.160.94290.0661.65128.810.94040.1871.596-0.837
CPNet [17]31.580.96070.0711.62230.280.95210.1821.5211407G0.316
FGVC [10]29.670.94030.0641.16330.800.94970.1651.571-1.795
STTN [40]32.340.96550.0531.06130.610.95600.1491.4381315G0.051
TSAM [46]30.220.94680.0701.01430.670.95480.1461.2351001G0.068
FuseFormer [22]33.320.96810.0531.05332.590.97010.1371.3491025G0.114
ISVI [43]30.340.94580.0771.00832.170.95880.1891.291-1.594
FGT [42]32.170.95990.0541.02532.860.96500.1291.323-1.828
E2FGVI [19]33.710.97000.0461.01333.010.97210.1161.289986G0.085
ProPainter (Ours)34.430.97350.0420.97434.470.97760.0981.187808G0.083
+ +Sparse Key/Value Space. Due to the highly redundant and repetitive textures in adjacent frames, it is unnecessary to include all frames as key/value tokens in each Transformer block. Instead, we will only include stripped temporal frames alternately, with a temporal stride of 2 in our design. That is, in each odd-numbered Transformer block, only odd-number frames are activated to participate in self-attention with their key and value, while even-number blocks include only even-number frames. By doing so, the key and value space is reduced by half, effectively reducing the computation and memory cost of the Transformer module. After filtering out unnecessary and redundant windows based on our sparse strategy, we perform self-attention on the remaining windows to extract refined features. These features are then gathered using a soft composition operation [22] for subsequent modules. Experimental results suggest that our design significantly reduces the computational cost of video Transformers while maintaining performance for video inpainting. + +# 3.4. Training Objectives + +Flow Completion. We utilize L1 loss as the reconstruction loss and a second-order smoothness constraint on the flow field [24] to promote the collinearity of neighboring flows and thus enhance the smoothness of the completed flow field. Video Inpainting. We adopt L1 loss as the reconstruction loss for all pixels. To enhance the realistic and temporal consistency of video inpainting results, we also employ an adversarial loss that is measured using a T-PatchGAN [6] discriminator. The details and formulation of these losses are provided in the supplementary material. + +# 4. Experiments + +Datasets. We use the training set of YouTube-VOS [36] with 3471 video sequences to train our networks. Two widely- + +used test sets are adopted for evaluation: YouTube-VOS [36] and DAVIS [28], which consist of 508 and 90 video sequences, respectively. For the DAVIS test set, following FuseFormer [22] and $\mathrm{E}^2\mathrm{FGVI}$ [19], we use 50 video clips for evaluations. During training, we follow [13, 17, 22, 19] and generate stationary and object masks in a random fashion to simulate the masks in video completion and object removal tasks. As for evaluation, we adopt the stationary masks provided in [19] to calculate quantitative scores, and the object masks are extracted from their segmentation labels for qualitative comparisons. Video frames are sized to $432\times 240$ for training and evaluation. + +Training Details and Metrics. We use RAFT [32] to extract optical flow in our approach. For training the RFC network, we set the flow sequence length to 10 and perform deformable propagation on feature maps that are downsampled by a factor of 8 for faster processing. We adopt 8 Transformer blocks for the inpainting modules and use a local video sequence of length 10. The Transformer window size is $5 \times 9$ , and the extended size is half of the window size. We train both the RFC and inpainting modules using the Adam [14] optimizer with a batch size of 8, setting the initial learning rate to $10^{-4}$ and running 700k iterations for each. We implement our method using the PyTorch framework and train it on 8 NVIDIA Tesla V100 (32G) GPUs. + +We employ the widely used PSNR and SSIM metrics [35] to evaluate the reconstruction performance and VFID [34] scores to measure the perceptual similarity between input videos and outputs, as used in recent video inpainting studies [22, 19]. Additionally, we report the flow warping error $E_{\text{warp}}$ [16] to assess the temporal consistency and smoothness of the resulting video sequences. + +![](images/32be32cdf697b876bb62f0e2d165f50b35cf9cca2ae0f7f7c000d6ea64358ab8.jpg) + +![](images/48ddc568f3349fea0865aa0a8359a9537db0af9b1c5a960da99ad50e0f95ff1c.jpg) + +![](images/3864b9333a5d884e10789d3d921d2721b0005412c8018343fb1ef70cda69189b.jpg) + +![](images/fbb63eb01c40d0763a2df11f80d96aac567c8ea3eb9ac85d75294c69836a5c40.jpg) + +![](images/b3a1f800c95f71ffe6e0ab625f508440bce92a04bcc03a1e1647e49dde1d5033.jpg) + +![](images/69e79e925fafc6b9e36c02aaf05f0d9739eb424fed9907c439be664927f9b22c.jpg) + +![](images/311aa1a5114eaa580e65a8f742b2857b0fbd2e64d2e41464ae66f98e011b31a2.jpg) + +![](images/a2058423efc80ad3f19a0ebde4722c4971e11450212d121dab0fadca2f695473.jpg) + +![](images/52f7421f5a7ca2ecb26faf7c2ef4becb68252e440ec60a6ff073ed42c77ec482.jpg) + +![](images/4d6cc73722e26daf42d983f4133f17ee6b313f6febb82fc385f32423db7a919e.jpg) + +![](images/f217084ed22d5bed4bfe2ca7f4b97ab90db224d73cea54cbac4c52a2464e2d73.jpg) + +![](images/4fa794b22642fd69969e4b1df52552cebb553258bf67f8c3abffd0e66be641a6.jpg) + +![](images/8bf3b1ff4bf54923fe48770a1a017845d15dec87d520afb7791788a96bc09255.jpg) + +![](images/dbb502ad9069e181d2d0929d6a7b85d646a9fe5b3996a8a9c280b1656f6fbda0.jpg) + +![](images/6e23f8a2b46153381a223d15fccfc7c73f1965cfe384cafca902e198aad3b299.jpg) + +![](images/63b3d42ff3db985f839faf3dc8c36cb9e23b18dc226362def74a94deb5d7938f.jpg) +Masked Frames + +![](images/987a78a4c34bfc0db1dbd966928f9a24adad4ea817c9c367fddb424814d66435.jpg) +FuseFormer + +![](images/b10b60d0f4e257ed730b73a05e252fbaed59846768c42c8fe74df7b62efb03c3.jpg) +FGT +Figure 5: Qualitative comparisons on both video completion and object removal. Our ProPainter exhibits superiority in producing complete and faithful textures, resulting in enhanced spatiotemporal coherence for video inpainting. + +![](images/59aee458a23089a7d47194aa22edb3e403d467aa060bfa86a5f9ebd11bb760fa.jpg) +$\mathrm{E}^2\mathrm{FGVI}$ + +![](images/cceb1c7f4f0b504a026c4edafdaa0b047e213c7b7176aff181ed7036130e10fd.jpg) +ProPainter (Ours) + +# 4.1. Comparisons + +Quantitative Evaluation. We compare ProPainter with nine state-of-the-art methods including DFVI [37], CPNet [17], FGVC [10], STTN [40], TSAM [46], Fuseformer [22], ISVI [43], FGT [42], and $\mathrm{E}^2\mathrm{FGVI}$ [19] on both YouTube-VOS [36] and DAVIS [28]. Thanks to the efficient design, ProPainter uses a temporal length of 20 for inference. Table 1 shows that ProPainter outperforms other methods in all quantitative metrics, especially on the DAVIS dataset, where our method surpasses the state-of-the-art method by $1.14\mathrm{dB}$ in PSNR. The results suggest that our method has superior inpainting capability, enabling it to produce higher-quality, faithful, and seamless videos. + +Qualitative Evaluation. For the visual comparison, we compare our method with FuseFormer [22], FGT [42], and $\mathrm{E}^2\mathrm{FGVI}$ [19], which are representative methods of Transformer-, image propagation-, and feature propagation-based approaches, respectively. Figure 5 presents four comparison results for video completion and object removal. Our method uses dual-domain propagation to ensure reliable and long-range propagation. It completes missing regions with coherence and clear contents, while other compared methods tend to fail or produce unpleasant inpainting results such as texture distortions and black hazy region in FGT [42] results, as well as artifacts in FuseFormer [22] and $\mathrm{E}^2\mathrm{FGVI}$ [19]. + +Efficiency Comparison. Table 1 presents the efficiency comparisons between all methods in terms of FLOPs and running time. The FLOPs of all methods are computed based on a temporal length of 10. We consider all learn- + +Table 2: Comparisons of flow completion networks. Our network offers a dual benefit with high accuracy and efficiency. + +
EPE ↓DFVI [37]FGVC [10]FGT [42]ISVI [43]Ours
YouTube-VOS0.0460.0320.0210.0190.020
DAVIS0.1070.0820.0520.0510.051
Runtime (s/frame)0.1301.1250.3120.2310.005
+ +able modules (including the recurrent flow completion) in our ProPainter to calculate the FLOPs. The running time records the time of all processes in each method, including inpainting, as well as flow calculation and flow completion if involved. To keep efficiency, we use only five iterations of the RAFT network to calculate optical flow. + +Flow Completion Comparisons. We compare our recurrent flow network with previous approaches [37, 10, 43] on both YouTube-VOS and DAVIS datasets. Table 2 presents the end-point-error (EPE) of flow completion and running time of each method. Our recurrent network offers a dual benefit with high accuracy and efficiency. Compared to previous methods, our network is approximately 40 times faster while maintaining a comparable flow completion accuracy to the state-of-the-art methods. + +# 4.2. Ablation Study + +Effectiveness of Image Propagation. Table 3 shows that Exp. (a) experiences a significant performance drop when image propagation is removed. Moreover, the model's propagation ability is reduced without image propagation, as presented in Figure 7, causing it to fail to complete missing + +Table 3: Ablation study of dual-main propagation and sparse Transformer. + +
Exp.(a) w/o Img Prop.(b) w/ Img Prop. in FGVC(c) w/o Feat Prop.(d) w/ Feat Prop. in E²FGVI(f) Full TokensProPainter
PSNR33.0532.9133.1733.9434.1834.15
SSIM0.97240.96870.97320.97560.97650.9764
+ +![](images/97374e4fc53c1b7ce479bf1281ef10f65e87ab5f6930694b9cbe0edd51ce80bb.jpg) +Masked Frame + +![](images/7963d766debcf0daa773698e419aea55b13699f270cacd559f274f606c45729e.jpg) +Img Prop. of FGVC + +![](images/04c70c26b5d78e07c1e517d2b6eade402dc0cad8aecf76f74652665bd08394cd.jpg) +w/Img Prop.of FGVC (Exp.b) + +![](images/53070cdda0f534ce7823c99ee930151befd318d4ad05f7b12aaf77bd35db5ec0.jpg) +Img Prop. (Ours) + +![](images/c7102e99c5c8114e4fdcb4bea52a038b55d71171538a7a23e827359b356b47d1.jpg) +ProPainter (Ours) + +![](images/e232ab15bd04c85308d8e3b36424fbe681de8043122865e80c2d0b6d9f6857f0.jpg) +Masked Frames + +![](images/a0f0bbb34ee6d8fbfa92eb5679cc1ded1de676c1f4ecf47ace9957baed6c35e3.jpg) +w/o Img Prop. (Exp. a) + +![](images/acacbf713191d549a09bcb8ebe14e4f750b162d43f3721dc631b4a20d93aef03.jpg) +w/ImgProp. + +content with details. To verify the effectiveness of our reliability check strategy in image propagation, we replaced our design with the FGVC image propagation module in Exp. (b) (without retraining), resulting in a noticeable decrease in PSNR. This is because the FGVC image propagation method is prone to being affected by incorrect optical flow, leading to severe texture distortion that subsequent modules cannot correct. Our model can effectively aware and stop unreliable propagation areas using a simple reliability check via Eq.2, and generate more faithful inpainting results. + +Effectiveness of Feature Propagation. Similarly, we observe a slight decrease in performance by either removing feature propagation, i.e., Exp. (c), or replacing it with the Feature propagation of $\mathrm{E}^2\mathrm{FGVI}$ , i.e., Exp. (d), indicating the effectiveness of the feature propagation modules and our reliability mask-aware conditions. This suggests that our design, which learns reliable DCN offsets in the feature domain, can further complement and enhance the propagation ability in the image domain. + +Effectiveness of Sparse Transformer. In theory, our strategy of using masks to guide sparsity only eliminates redundant and unnecessary tokens (windows), while preserving essential information. This means that there should be no adverse effect on performance. To confirm this, we conducted Exp. (d), comparing our approach to standard self-attention without sparse filtering. Our results indicate that our sparse Transformer block performs almost as well as the standard one, indicating that it can achieve high efficiency without sacrificing performance. + +![](images/a833ee63db660f7ba011c8e7a32a81a190130014c91f677114fb7d56b803e08d.jpg) +Figure 7: Comparison of w/ and w/o image propagation. +Figure 8: FLOPs cures of different Transformer blocks. + +![](images/32b125153ca9a705c43cd44cee1fb562e9f91950814bcca2f0f71588fda4dc85.jpg) +Figure 6: Visual comparison on image propagation methods of FGVC [10] and ours. + +Efficiency of Sparse Transformer. In Figure 8, we compare the FLOPs of different Transformer blocks with respect to temporal length and spatial resolution, including those used in FuseFormer [22], FGT [42], and $\mathrm{E}^2\mathrm{FGVI}$ [19]. We use a mask with a missing region ratio of $1/6$ (higher than the average object ratio of $13.6\%$ in DAVIS) to calculate the FLOPs of our mask-guided sparse Transformer. The curves indicate that the efficiency advantage of our sparse Transformer becomes more prominent as the temporal length and video resolution increase, indicating great potential for developing longer-range spatiotemporal attention and applying it to larger resolution videos. + +# 5. Conclusion + +This study introduces a novel and improved video inpainting framework called ProPainter. It incorporates an enhanced dual-domain propagation and an efficient mask-guided sparse video Transformer. Thanks to the two modules, our ProPainter exhibits reliable and precise propagation capabilities over long distances, significantly improving the performance of video inpainting while maintaining high efficiency in terms of running time and computational complexity. We believe that the designs in ProPainter will provide valuable insights to the video inpainting community. + +Acknowledgement. This study is supported under the RIE2020 Industry Alignment Fund Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s). + +# References + +[1] Jiayin Cai, Changlin Li, Xin Tao, Chun Yuan, and Yu-Wing Tai. DeViT: Deformed vision transformers in video inpainting. In ACM MM, 2022. 2, 3 +[2] Kelvin CK Chan, Xintao Wang, Ke Yu, Chao Dong, and Chen Change Loy. BasicVSR: The search for essential components in video super-resolution and beyond. 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Despite the effectiveness of these components, they still suffer from some limitations that affect their performance. Previous propagation-based approaches are performed separately either in the image or feature domain. Global image propagation isolated from learning may cause spatial misalignment due to inaccurate optical flow. Moreover, memory or computational constraints limit the temporal range of feature propagation and video Transformer, preventing exploration of correspondence information from distant frames. To address these issues, we propose an improved framework, called ProPainter, which involves enhanced ProPagation and an efficient Transformer. Specifically, we introduce dual-domain propagation that combines the advantages of image and feature warping, exploiting global correspondences reliably. We also propose a mask-guided sparse video Transformer, which achieves high efficiency by discarding unnecessary" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 471, + 546, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 471, + 546, + 507 + ], + "spans": [ + { + "bbox": [ + 305, + 471, + 546, + 507 + ], + "type": "text", + "content": "and redundant tokens. With these components, ProPainter outperforms prior arts by a large margin of 1.46 dB in PSNR while maintaining appealing efficiency." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 525, + 387, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 525, + 387, + 537 + ], + "spans": [ + { + "bbox": [ + 306, + 525, + 387, + 537 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 545, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 548, + 714 + ], + "type": "text", + "content": "Video inpainting (VI) aims to fill gaps or missing regions in a video with visually consistent content while ensuring spatial and temporal coherence. This technique has broad applications, including video completion [10], object removal [9, 37], video restoration [31], watermark, and logo removal [19]. VI is challenging because it requires establishing accurate correspondence across distant frames for information aggregation. To address this challenge, various mechanisms have been explored, such as 3D CNN [6, 11], video internal learning [41, 27], flow-guided propagation [37, 10, 43, 42, 19], and video Transformer [22, 42, 19]. Among these mechanisms, flow-guided propagation and video Transformer have become mainstream choices for VI due to their promising performance." + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10477" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "text", + "content": "Propagation-based methods in VI can be divided into two categories: image propagation and feature propagation. The former employs bidirectional global propagation in the image domain with a pre-completed flow field. While this approach can fill the majority of holes in a corrupted video, it requires an additional image or video inpainting network after propagation to hallucinate the remaining missing regions. This isolated two-step process can result in unpleasant artifacts and texture misalignment due to inaccurate flow, as shown in Figure 1(f). To address this issue, a recent approach called " + }, + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "inline_equation", + "content": "\\mathrm{E}^2\\mathrm{FGVI}" + }, + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "text", + "content": " [19] implements propagation in the feature domain, incorporating flow completion and content hallucination modules in an end-to-end framework. With the learnable warping module, the feature propagation module relieves the pressure of having inaccurate flow. However, " + }, + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "inline_equation", + "content": "\\mathrm{E}^2\\mathrm{FGVI}" + }, + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "text", + "content": " employs a downsampled flow field to match the spatial size of the feature domain, limiting the precision of spatial warping and the efficacy of propagation, potentially resulting in blurry results. Moreover, feature propagation can only be performed within a short range of video sequences due to memory and computational constraints, hindering propagation from distant frames and leading to missing texture, as shown in Figure 1(g)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 348, + 289, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 348, + 289, + 695 + ], + "spans": [ + { + "bbox": [ + 47, + 348, + 289, + 695 + ], + "type": "text", + "content": "Both image- and feature-based propagation have their pros and cons. In this study, we carefully revisit the VI problem and investigate the possibility of combining the strengths of both techniques. We demonstrate that with systematic redesigns and adaptation of best practices in the literature, we can achieve dual-domain propagation, as illustrated in Figure 1(a). To achieve reliable and efficient information propagation across a video, we identify several essential components: i) Efficient GPU-based propagation with reliability check – Unlike previous methods that rely on complex and time-consuming CPU-centric operations, such as indexing flow trajectories, we perform global image propagation on GPU with flow consistency check. This implementation can be inserted at the beginning of the inpainting network and jointly trained with the other modules. Thus, subsequent modules are able to correct any propagation errors and benefit from the long-range correspondence information provided by the global propagation, resulting in a significant performance improvement. ii) Improved feature propagation – Our implementation of feature propagation leverages flow-based deformable alignment [3], which improves robustness to occlusion and inaccurate flow completion compared to " + }, + { + "bbox": [ + 47, + 348, + 289, + 695 + ], + "type": "inline_equation", + "content": "\\mathrm{E}^2\\mathrm{FGVI}" + }, + { + "bbox": [ + 47, + 348, + 289, + 695 + ], + "type": "text", + "content": " [19]. iii) Efficient flow completion – We design a highly efficient recurrent network to complete flows for dual-domain propagation, which is over 40 times (" + }, + { + "bbox": [ + 47, + 348, + 289, + 695 + ], + "type": "inline_equation", + "content": "\\sim 192" + }, + { + "bbox": [ + 47, + 348, + 289, + 695 + ], + "type": "text", + "content": " fps" + }, + { + "bbox": [ + 47, + 348, + 289, + 695 + ], + "type": "inline_equation", + "content": "^1" + }, + { + "bbox": [ + 47, + 348, + 289, + 695 + ], + "type": "text", + "content": ") faster than SOTA method [43] while maintaining comparable performance. We demonstrate that these designs are essential to achieve efficient propagation of global and local information without texture misalignment or blurring in the" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 306, + 72, + 513, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 513, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 513, + 84 + ], + "type": "text", + "content": "filling results. An example is shown in Figure 1(h)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 85, + 547, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 85, + 547, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 85, + 547, + 324 + ], + "type": "text", + "content": "In addition to dual-domain propagation, we introduce an efficient mask-guided sparse video Transformer tailored for the VI task. The classic spatiotemporal Transformer is computationally intensive due to the quadratic number of interactions between video tokens, making it intractable for high-resolution and long temporal-length videos. For instance, contemporary Transformer-based methods, FuseFormer [22] and FGT [42], are unable to handle 480p videos with a " + }, + { + "bbox": [ + 304, + 85, + 547, + 324 + ], + "type": "inline_equation", + "content": "32\\mathrm{G}" + }, + { + "bbox": [ + 304, + 85, + 547, + 324 + ], + "type": "text", + "content": " GPU due to excessive memory demands. However, we observe that the inpainting mask usually covers only a small local region, such as the object area. Moreover, adjacent frames contain highly redundant textures. These observations suggest that spatiotemporal attention is unnecessary for most unmasked areas, and it is adequate to consider only alternating interval frames in attention computation. Motivated by these observations, we redesign the Transformer by discarding unnecessary and redundant windows in the query and key/value space, respectively, significantly reducing computational complexity and memory without compromising inpainting performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 324, + 547, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 547, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 547, + 456 + ], + "type": "text", + "content": "The main contribution of this work is to provide a systematic study into the core problem of VI and offer a practical solution that is both effective and efficient. Propagating information in two distinct image and feature domains and combining them in a unified framework with fast GPU implementation is new for VI task. The mask-guided sparse video Transformer also offers practical insights into designing efficient spatiotemporal attention for VI task. Compared to the state-of-the-art methods, our model achieves superior performance with a large margin of " + }, + { + "bbox": [ + 304, + 324, + 547, + 456 + ], + "type": "inline_equation", + "content": "1.46\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 324, + 547, + 456 + ], + "type": "text", + "content": " in PSNR, while also significantly reducing memory consumption." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 468, + 392, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 468, + 392, + 480 + ], + "spans": [ + { + "bbox": [ + 306, + 468, + 392, + 480 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 488, + 547, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 488, + 547, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 488, + 547, + 536 + ], + "type": "text", + "content": "Numerous deep networks with different modules and propagation strategies have achieved significant success in video inpainting. These approaches can be broadly categorized into four categories:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 537, + 547, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 537, + 547, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 537, + 547, + 609 + ], + "type": "text", + "content": "3D convolution. Earlier video inpainting networks typically employed 3D CNNs [6, 33, 11] or temporal shift [7] to aggregate spatiotemporal information. These methods often suffer from limited receptive fields in both temporal and spatial dimensions and misalignment between adjacent frames. As a result, they are less effective in exploring distant content." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 609, + 545, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 609, + 545, + 669 + ], + "spans": [ + { + "bbox": [ + 304, + 609, + 545, + 669 + ], + "type": "text", + "content": "Internal learning. To fully exploit content of a video, some studies [41, 27, 30] adopt internal learning to encode and memorize the appearance and motion of the video through deep networks. However, these methods require individual training for each test video, limiting their practical use." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 669, + 545, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 669, + 545, + 693 + ], + "spans": [ + { + "bbox": [ + 304, + 669, + 545, + 693 + ], + "type": "text", + "content": "Flow-guided propagation. Optical flow [13, 18, 46] and homography [17, 1] are commonly used in video inpainting" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 231, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 231, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 231, + 712 + ], + "type": "text", + "content": "1Tested on a single NVIDIA Tesla V100 GPU (32G)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 315, + 702, + 534, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 702, + 534, + 713 + ], + "spans": [ + { + "bbox": [ + 315, + 702, + 534, + 713 + ], + "type": "inline_equation", + "content": "{}^{2}" + }, + { + "bbox": [ + 315, + 702, + 534, + 713 + ], + "type": "text", + "content": " Object regions account for only 13.6% of the DAVIS [28] dataset." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10478" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": "networks to align neighboring reference frames to enhance temporal coherence and aggregation. However, incomplete optical flow may not provide valid propagation for completing missing regions. To address this issue, recent flow-based methods [37, 10, 12, 43, 42] focus on first completing the flow and then use it as a guidance for pixel-domain propagation. This approach simplifies RGB pixel inpainting by completing a less complex flow field. However, this offline propagation is independent of the subsequent learnable refinement module, making it difficult to correct content distortion caused by inaccurate propagation. Inspired by flow-guided recurrent networks [2, 3], Li et al. [19] proposed an end-to-end framework that jointly learns flow completion and feature propagation in the downsampled feature domain. However, downsampled flow reduces its ability to provide spatially precise warping. To overcome this limitation, we propose more faithful propagation by performing both pixel and feature propagation with flow consistency checks." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 288, + 289, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 289, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 289, + 514 + ], + "type": "text", + "content": "Video Transformer. Attention [17, 26, 11, 18] and Transformer [40, 21, 22, 1, 19, 42] blocks adopt spatiotemporal attention to explore recurrent textures in a video. This enables them to retrieve and aggregate tokens with similar texture or context for filling in missing regions. Liu et al. [22] present a fine-grained fusion Transformer based on the soft split and composition operations, which further boosts video inpainting performance. However, these methods are computationally and memory intensive. To address this issue, some Transformers [21, 1, 42] decouple the spatiotemporal attention by performing spatial and temporal attention alternately, while others [19, 42] adopt window-based Transformers [23, 38] to reduce the spatial range for efficient video attention. However, these approaches still involve redundant or unnecessary tokens. Inspired by token pruning for adaptive attention [29, 39, 25, 20, 15] in high-level tasks, our study proposes a more efficient and faster video Transformer with sparse spatiotemporal attention and a largely reduced token space while maintaining inpainting performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 515, + 289, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 515, + 289, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 515, + 289, + 647 + ], + "type": "text", + "content": "Recent studies [18, 19, 42] have demonstrated the effectiveness of combining flow-guided propagation with Transformer in VI. However, the high memory requirement of the Transformer limits the propagation range during both training and inference, severely hindering the ability to propagate temporally distant content. In this paper, we also adopt this combination strategy but propose a reliable propagation scheme, along with an efficient Transformer model that fully exploits the benefits of long-range propagation and attention. This results in superior inpainting performance while maintaining computational efficiency." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 658, + 129, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 129, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 129, + 671 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": "Given a masked video sequence " + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "X = \\{X_{t} \\in \\mathbb{R}^{H \\times W \\times 3}\\}_{t=1}^{T}" + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": ", which has a sequence length of " + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": ", along with corresponding mask sequence " + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "M = \\{M_{t} \\in" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 71, + 547, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 71, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 71, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{H\\times W\\times 1}\\}_{t = 1}^{T}" + }, + { + "bbox": [ + 304, + 71, + 547, + 277 + ], + "type": "text", + "content": ", the objective of video inpainting is to generate visually consistent and coherent content within the corrupted or missing regions. ProPainter, as shown in Figure 2, is composed of three key components: Recurrent Flow Completion (RFC), Dual-Domain Propagation (DDP), and Mask-guided Sparse Video Transformer (MSVT). Before feeding the sequence into ProPainter, we extract the forward and backward optical flows, denoted as " + }, + { + "bbox": [ + 304, + 71, + 547, + 277 + ], + "type": "inline_equation", + "content": "F^f = \\{F_t^f = F_{t\\to t + 1}\\in \\mathbb{R}^{H\\times W\\times 2}\\}_{t = 1}^{T - 1}" + }, + { + "bbox": [ + 304, + 71, + 547, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 71, + 547, + 277 + ], + "type": "inline_equation", + "content": "F^b = \\{F_t^b = F_{t + 1\\to t}\\in \\mathbb{R}^{H\\times W\\times 2}\\}_{t = 1}^{T - 1}" + }, + { + "bbox": [ + 304, + 71, + 547, + 277 + ], + "type": "text", + "content": " from a given video " + }, + { + "bbox": [ + 304, + 71, + 547, + 277 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 71, + 547, + 277 + ], + "type": "text", + "content": ". We first use RFC to complete the corrupted flow fields. Guided by the completed flows, we then perform global image propagation and local feature propagation sequentially. Finally, we employ multiple MSVT blocks to refine propagation features and a decoder to reconstruct the final video sequence " + }, + { + "bbox": [ + 304, + 71, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\hat{Y} = \\{\\hat{Y}_t\\in \\mathbb{R}^{H\\times W\\times 3}\\}_{t = 1}^T" + }, + { + "bbox": [ + 304, + 71, + 547, + 277 + ], + "type": "text", + "content": ". We introduce the specific design of each component below." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 285, + 460, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 285, + 460, + 300 + ], + "spans": [ + { + "bbox": [ + 306, + 285, + 460, + 300 + ], + "type": "text", + "content": "3.1. Recurrent Flow Completion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 304, + 547, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 547, + 508 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 547, + 508 + ], + "type": "text", + "content": "Pre-trained flow completion modules are commonly used in video inpainting networks [37, 10, 43, 42]. The rationale behind this approach is that it is simpler to complete missing flow than to directly fill in complex RGB content [37]. Furthermore, using completed flow to propagate pixels reduces the pressure of video inpainting and better maintains temporal coherence. " + }, + { + "bbox": [ + 304, + 304, + 547, + 508 + ], + "type": "inline_equation", + "content": "\\mathrm{E}^2\\mathrm{FGVI}" + }, + { + "bbox": [ + 304, + 304, + 547, + 508 + ], + "type": "text", + "content": " [19] proposes to insert the flow completion module into an end-to-end framework, which simplifies the inpainting pipeline. However, flow completion modules that are learned together with inpainting-oriented losses can result in a suboptimal learning process and less accurate completed flow. Moreover, the downsampled flow may limit the precision of spatial warping and the efficacy of propagation, which can result in blurred and incomplete filling content, as shown in Figure 1(g). Therefore, an independent flow completion model is not only important but also necessary for video inpainting." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 509, + 547, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 547, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 547, + 617 + ], + "type": "text", + "content": "To maintain temporal coherence while completing flows, previous methods [37, 42] adopt sliding-window-based networks to aggregate optical flow information from adjacent frames, which are highly correlated. However, these methods can be computationally expensive as repeated inferences are required in the overlapping frames. To improve efficiency and enhance flow coherence further, we adopt a recurrent network [2, 3] for flow completion, which provides precise optical flow fields for subsequent propagation modules." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": "We complete forward and backward flows using the same process, thus we denote " + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "inline_equation", + "content": "F^f" + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "inline_equation", + "content": "F^b" + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": " for simplicity. We first encode the flows " + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "inline_equation", + "content": "F_t" + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": " into a downsampled feature " + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "inline_equation", + "content": "f_t" + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": " with a downsampling ratio of 8. Next, we employ deformable alignment [3] that is based on deformable convolution (DCN) [8, 45], to bidirectionally propagate the flow information from nearby frames for flow completion. For simplicity, we only describe the backward propagation" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10479" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 547, + 194 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 547, + 194 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 547, + 194 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 547, + 194 + ], + "type": "image", + "image_path": "bd7f9fc1852304742d261be2133dae94328f6fdadb074bc7503bccbb66973551.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 204, + 547, + 289 + ], + "lines": [ + { + "bbox": [ + 46, + 204, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 547, + 289 + ], + "type": "text", + "content": "Figure 2: ProPainter comprises three key components: recurrent flow completion, dual-domain propagation, and mask-guided sparse Transformer. First, we employ a highly efficient recurrent flow completion network to complete the corrupted flow fields. We then perform propagation in both image and feature domains, which are jointly trained. This approach enables us to explore correspondences from both global and local temporal frames, resulting in more reliable and effective propagation. The subsequent mask-guided sparse Transformer blocks refine the propagated features using spatiotemporal attention, aided by a sparse strategy that considers only a subset of the tokens. This enhances efficiency and reduces memory consumption, while maintaining performance." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 301, + 290, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 290, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 290, + 376 + ], + "type": "text", + "content": "process here. Taking the concatenated feature " + }, + { + "bbox": [ + 46, + 301, + 290, + 376 + ], + "type": "inline_equation", + "content": "c(f_t, \\hat{f}_{t+1})" + }, + { + "bbox": [ + 46, + 301, + 290, + 376 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 301, + 290, + 376 + ], + "type": "inline_equation", + "content": "\\hat{f}_{t+1}" + }, + { + "bbox": [ + 46, + 301, + 290, + 376 + ], + "type": "text", + "content": " is the propagation feature of the " + }, + { + "bbox": [ + 46, + 301, + 290, + 376 + ], + "type": "inline_equation", + "content": "t+1" + }, + { + "bbox": [ + 46, + 301, + 290, + 376 + ], + "type": "text", + "content": "-th frame, as input a lightweight network with a stack of convolutions is employed to compute DCN offsets " + }, + { + "bbox": [ + 46, + 301, + 290, + 376 + ], + "type": "inline_equation", + "content": "o_{t \\to t+1}" + }, + { + "bbox": [ + 46, + 301, + 290, + 376 + ], + "type": "text", + "content": " and modulation masks " + }, + { + "bbox": [ + 46, + 301, + 290, + 376 + ], + "type": "inline_equation", + "content": "m_{t \\to t+1}" + }, + { + "bbox": [ + 46, + 301, + 290, + 376 + ], + "type": "text", + "content": ". DCN alignment propagation can be expressed as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 85, + 389, + 288, + 406 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 389, + 288, + 406 + ], + "spans": [ + { + "bbox": [ + 85, + 389, + 288, + 406 + ], + "type": "interline_equation", + "content": "\\hat {f} _ {t} = \\mathcal {R} \\big (\\mathcal {D} \\big (\\hat {f} _ {t + 1}; o _ {t \\rightarrow t + 1}, m _ {t \\rightarrow t + 1}), f _ {t} \\big), \\qquad (1)", + "image_path": "c17f358d0b243e314846d47b0c3dfaeb1fe12b8ffb7f58f896f2b566e65832e5.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 419, + 289, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 419, + 289, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 289, + 506 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 419, + 289, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\cdot)" + }, + { + "bbox": [ + 46, + 419, + 289, + 506 + ], + "type": "text", + "content": " denotes deformable convolution, and " + }, + { + "bbox": [ + 46, + 419, + 289, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{R}(\\cdot)" + }, + { + "bbox": [ + 46, + 419, + 289, + 506 + ], + "type": "text", + "content": " denotes the convolution layers that fuse the aligned and current features. In this way, information of " + }, + { + "bbox": [ + 46, + 419, + 289, + 506 + ], + "type": "inline_equation", + "content": "(t + 1)" + }, + { + "bbox": [ + 46, + 419, + 289, + 506 + ], + "type": "text", + "content": "-th flow can be adaptively transferred to the current " + }, + { + "bbox": [ + 46, + 419, + 289, + 506 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 419, + 289, + 506 + ], + "type": "text", + "content": "-th flow. Finally, a decoder is used to reconstruct the completed flows " + }, + { + "bbox": [ + 46, + 419, + 289, + 506 + ], + "type": "inline_equation", + "content": "\\hat{F}_t" + }, + { + "bbox": [ + 46, + 419, + 289, + 506 + ], + "type": "text", + "content": ". For clarity, an illustration of deformable alignment is provided in the supplementary material." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 521, + 192, + 534 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 192, + 534 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 192, + 534 + ], + "type": "text", + "content": "3.2. Dual-domain Propagation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 542, + 288, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 542, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 542, + 288, + 628 + ], + "type": "text", + "content": "After completing the flow, we perform global and local propagation in the image and feature domains, respectively. We employ distinct alignment operations and strategies for each domain. Both domains involve bidirectional propagation in the forward and backward directions. Here, we elaborate on the backward propagation since the forward propagation follows the same process." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "type": "text", + "content": "Image propagation. To maintain efficiency and simplicity, we adopt flow-based warping for image propagation, along with a simple reliability check strategy. This process does not involve any learnable operation. In the case of a video sequence " + }, + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "type": "text", + "content": " with binary masks " + }, + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "type": "text", + "content": " (a pixel with value 1 represents masked region) and completed flows " + }, + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\hat{F}" + }, + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "type": "text", + "content": ", we first check the validity of completed flow based on forward-backward" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 303, + 414, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 303, + 414, + 316 + ], + "spans": [ + { + "bbox": [ + 306, + 303, + 414, + 316 + ], + "type": "text", + "content": "consistency error [37, 10]:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 323, + 546, + 355 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 323, + 546, + 355 + ], + "spans": [ + { + "bbox": [ + 306, + 323, + 546, + 355 + ], + "type": "interline_equation", + "content": "\\mathcal {E} _ {t \\rightarrow t + 1} (p) = \\left\\| \\hat {F} _ {t \\rightarrow t + 1} (p) + \\hat {F} _ {t + 1 \\rightarrow t} (p + \\hat {F} _ {t \\rightarrow t + 1} (p)) \\right\\| _ {2} ^ {2}, \\tag {2}", + "image_path": "909c17209abc0cf5a0d189e3fd898efcca4e3f021e57906218b8714582f1f576.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "spans": [ + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "type": "text", + "content": " denotes a pixel position of the current frame. Only pixels with a small consistency error will be propagated, i.e., " + }, + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "type": "inline_equation", + "content": "C_1: \\mathcal{E}_{t \\to t + 1}(p) < \\epsilon" + }, + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "type": "text", + "content": " is a threshold and set to 5. Furthermore, we only consider the masked areas of the current frame " + }, + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "type": "inline_equation", + "content": "X_t" + }, + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "type": "text", + "content": " that needs to be filled, i.e., " + }, + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "type": "inline_equation", + "content": "C_2: M_t(p) = 1" + }, + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "type": "text", + "content": ", and we only propagate the unmasked areas from neighboring frame " + }, + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "type": "inline_equation", + "content": "X_{t + 1}" + }, + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "type": "inline_equation", + "content": "C_3: M_{t + 1}(p + \\hat{F}_{t \\to t + 1}(p)) = 0" + }, + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "type": "text", + "content": ". By enforcing the three constraints, a reliable propagation area " + }, + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "type": "inline_equation", + "content": "A_r" + }, + { + "bbox": [ + 304, + 356, + 547, + 463 + ], + "type": "text", + "content": " is identified as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 350, + 471, + 546, + 504 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 471, + 546, + 504 + ], + "spans": [ + { + "bbox": [ + 350, + 471, + 546, + 504 + ], + "type": "interline_equation", + "content": "A _ {r} (p) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} p \\in C _ {1} \\cap C _ {2} \\cap C _ {3}, \\\\ 0 & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {3}", + "image_path": "08c03c901a97dbb4504f72eb07c27dd4ee4e4f7d0aafc42741942e908017ffa4.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 512, + 509, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 512, + 509, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 512, + 509, + 525 + ], + "type": "text", + "content": "The process of image propagation is expressed as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 319, + 533, + 547, + 548 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 533, + 547, + 548 + ], + "spans": [ + { + "bbox": [ + 319, + 533, + 547, + 548 + ], + "type": "interline_equation", + "content": "\\hat {X} _ {t} = \\mathcal {W} \\left(X _ {t + 1}, \\hat {F} _ {t \\rightarrow t + 1}\\right) * A _ {r} + X _ {t} * \\left(1 - A _ {r}\\right), \\tag {4}", + "image_path": "cc20b9119baaa949f69c25012b6238769842d11fb9fa44255ec23f9a3dbac0df.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 555, + 547, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 547, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 547, + 639 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 555, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{W}(\\cdot)" + }, + { + "bbox": [ + 304, + 555, + 547, + 639 + ], + "type": "text", + "content": " denotes warping operation. To ensure continuous propagation, we promptly update the mask " + }, + { + "bbox": [ + 304, + 555, + 547, + 639 + ], + "type": "inline_equation", + "content": "M_{t}" + }, + { + "bbox": [ + 304, + 555, + 547, + 639 + ], + "type": "text", + "content": " of the current frame and convert the propagated area to the un-masked status by updating masks via " + }, + { + "bbox": [ + 304, + 555, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\dot{M}_t = M_t - A_r" + }, + { + "bbox": [ + 304, + 555, + 547, + 639 + ], + "type": "text", + "content": ". After global image propagation, we obtain a partially filled video sequence " + }, + { + "bbox": [ + 304, + 555, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\tilde{X}" + }, + { + "bbox": [ + 304, + 555, + 547, + 639 + ], + "type": "text", + "content": ", which greatly eases the learning process for subsequent modules." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 640, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 640, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 640, + 547, + 715 + ], + "type": "text", + "content": "Feature propagation. We use an image encoder with the same structure as previous works [22, 19] to extract features from a local sequence " + }, + { + "bbox": [ + 304, + 640, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\hat{X}_{t=1}^{T_l}" + }, + { + "bbox": [ + 304, + 640, + 547, + 715 + ], + "type": "text", + "content": ", denoted as " + }, + { + "bbox": [ + 304, + 640, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\{e_t \\in \\mathbb{R}^{\\frac{H}{4} \\times \\frac{W}{4} \\times C}\\}_{t=1}^{T_l}" + }, + { + "bbox": [ + 304, + 640, + 547, + 715 + ], + "type": "text", + "content": ". Similar to E²FGVI [19], we also adopt flow-guided deformable alignment module [3] for feature propagation, which has demonstrated remarkable benefits" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10480" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 286, + 184 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 286, + 184 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 286, + 184 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 286, + 184 + ], + "type": "image", + "image_path": "80c09d94207daea57d5a8bc24ff28e14791bd063d4b4cc0e88bb0f51445376c6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 192, + 289, + 288 + ], + "lines": [ + { + "bbox": [ + 46, + 192, + 289, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 289, + 288 + ], + "type": "text", + "content": "Figure 3: Flow-guided deformable alignment is effective by taking reliable completed flows and mask-aware conditions. We concatenate the validated flow map, original mask, and updated mask into conditions to produce DCN offsets (residue to optical flow). A DCN is then applied to align the propagation feature from the previous frame. Finally, a CNN block is employed to fuse the current and aligned features, achieving the propagation feature of the current frame." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "text", + "content": "in various low-level video tasks [5, 4, 44]. Unlike the deformable alignment used in Sec. 3.1 that directly learns DCN offsets, flow-guided deformable alignment employs the completed flow as a base offset and refines it by learning offset residue. However, our design differs from " + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "inline_equation", + "content": "\\mathrm{E}^2\\mathrm{FGVI}" + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "text", + "content": " in that we offer richer conditions for learning DCN offsets. As illustrated in Figure 3, apart from the current feature " + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "inline_equation", + "content": "e_t" + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "text", + "content": ", warped propagation feature " + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "inline_equation", + "content": "\\mathcal{W}(\\hat{e}_{t + 1},\\hat{F}_{t\\rightarrow t + 1}^{\\downarrow})" + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "text", + "content": ", and completed flows " + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "inline_equation", + "content": "\\hat{F}_{t\\rightarrow t + 1}^{\\downarrow}" + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "text", + "content": ", we additionally introduce the flow valid map " + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "inline_equation", + "content": "V_{t + 1\\to t}" + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "text", + "content": " calculated by consistency check (Eq. 2), as well as the original mask " + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "inline_equation", + "content": "M_t^\\downarrow" + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "text", + "content": ", and updated mask " + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "inline_equation", + "content": "\\hat{M}_t^\\downarrow" + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "text", + "content": " after image propagation. With these conditions, a stack of convolutions is employed to predict the DCN offset residue " + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "inline_equation", + "content": "\\widetilde{o}_{t\\rightarrow t + 1}" + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "text", + "content": " and modulation masks " + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "inline_equation", + "content": "m_{t\\rightarrow t + 1}" + }, + { + "bbox": [ + 46, + 309, + 289, + 492 + ], + "type": "text", + "content": ". The flow-guided DCN alignment propagation is expressed as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 498, + 288, + 514 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 498, + 288, + 514 + ], + "spans": [ + { + "bbox": [ + 58, + 498, + 288, + 514 + ], + "type": "interline_equation", + "content": "\\hat {e} _ {t} = \\mathcal {R} \\big (\\mathcal {D} \\big (\\hat {e} _ {t + 1}; \\hat {F} _ {t \\rightarrow t + 1} ^ {\\downarrow} + \\widetilde {o} _ {t \\rightarrow t + 1}, m _ {t \\rightarrow t + 1}), f _ {t} \\big), \\quad (5)", + "image_path": "f38ef62d2bd1f304104966e64b7a83270e9bb7edd07ee4c1707b7026189ca568.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 521, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 593 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 521, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 521, + 287, + 593 + ], + "type": "text", + "content": " denotes downsampling. The improved reliability of flow and the additional awareness of mask as a condition make our flow-guided deformable alignment module more stable to learn than previous designs [3, 19]. The current step is able to focus more on truly challenging regions where flow is invalid and former image propagation is unreliable." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 599, + 261, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 261, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 261, + 612 + ], + "type": "text", + "content": "3.3. Mask-Guided Sparse Video Transformer" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 618, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 289, + 713 + ], + "type": "text", + "content": "While video Transformers have achieved excellent performance in video inpainting, they can be computationally and memory intensive, posing a challenge to their practical application. " + }, + { + "bbox": [ + 46, + 618, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{E}^2\\mathrm{FGVI}" + }, + { + "bbox": [ + 46, + 618, + 289, + 713 + ], + "type": "text", + "content": " and FGT have addressed this issue by using window-based Transformer blocks, but they still have some efficiency limitations. To overcome this, we propose a novel sparse video Transformer that builds on the window-based approach. Given a video sequence feature" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 309, + 70, + 545, + 184 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 545, + 184 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 545, + 184 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 545, + 184 + ], + "type": "image", + "image_path": "93c4a07f8bdc940a274970239c1836076b54b3b8ae53c050013af3af5ed939f9.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 191, + 547, + 276 + ], + "lines": [ + { + "bbox": [ + 304, + 191, + 547, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 191, + 547, + 276 + ], + "type": "text", + "content": "Figure 4: Mask-guided sparse video Transformer. To reduce computational complexity and memory usage, our mask-guided sparse Transformer filters out unnecessary and redundant windows in the query and key/value space, respectively, before applying self-attention. To enlarge spatial interrelation range, we also adopt the window expand strategy [38] and pooling global tokens [42, 19]." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "inline_equation", + "content": "E_{l} \\in \\mathbb{R}^{T_{l} \\times \\frac{H}{4} \\times \\frac{W}{4} \\times C}" + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "text", + "content": ", we use the soft split operation [22] to generate patch embeddings " + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "inline_equation", + "content": "Z \\in \\mathbb{R}^{T_{l} \\times M \\times N \\times C_{z}}" + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "text", + "content": ". We partition " + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "inline_equation", + "content": "m \\times n" + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "text", + "content": " non-overlapping windows, resulting in partitioned features " + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "inline_equation", + "content": "Z_{w} \\in \\mathbb{R}^{T_{l} \\times m \\times n \\times h \\times w \\times C_{z}}" + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "inline_equation", + "content": "m \\times n" + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "inline_equation", + "content": "h \\times w" + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "text", + "content": " are the number and size of the windows, respectively. We obtain the query " + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "text", + "content": ", key " + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "text", + "content": ", and value " + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "inline_equation", + "content": "Z_{w}" + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "text", + "content": " through linear layers. We design sparse strategies for both query and key/value spaces separately. Note that we also apply the window expand strategy [22] and integrate global tokens [42] into key and value, enabling us to use a small window size of " + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "inline_equation", + "content": "5 \\times 9" + }, + { + "bbox": [ + 304, + 297, + 547, + 455 + ], + "type": "text", + "content": " in our experiments. We omit them from the following discussion since they do not affect our sparse strategy designs." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 456, + 547, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 547, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 547, + 612 + ], + "type": "text", + "content": "Sparse Query Space. We observe that mask regions often occupy only a small area of the video, such as in the case of object removal in the DAVIS [28] dataset, where the proportion of object regions is only " + }, + { + "bbox": [ + 304, + 456, + 547, + 612 + ], + "type": "inline_equation", + "content": "13.6\\%" + }, + { + "bbox": [ + 304, + 456, + 547, + 612 + ], + "type": "text", + "content": ". This indicates that spatiotemporal attention may not be necessary for all query windows. To exploit this observation, we selectively apply attention to query windows that intersect with the mask regions. Specifically, we first use nearest neighbor interpolation to downsample the mask sequence " + }, + { + "bbox": [ + 304, + 456, + 547, + 612 + ], + "type": "inline_equation", + "content": "M \\in \\mathbb{R}^{T_l \\times H \\times W}" + }, + { + "bbox": [ + 304, + 456, + 547, + 612 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 456, + 547, + 612 + ], + "type": "inline_equation", + "content": "M^{\\downarrow} \\in \\mathbb{R}^{T_l \\times m \\times n}" + }, + { + "bbox": [ + 304, + 456, + 547, + 612 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 456, + 547, + 612 + ], + "type": "inline_equation", + "content": "m \\times n" + }, + { + "bbox": [ + 304, + 456, + 547, + 612 + ], + "type": "text", + "content": " is the number of non-overlapping windows after partitioning. We then sum it up in the temporal dimension and obtain sparse mask " + }, + { + "bbox": [ + 304, + 456, + 547, + 612 + ], + "type": "inline_equation", + "content": "S_Q \\in \\mathbb{R}^{m \\times n}" + }, + { + "bbox": [ + 304, + 456, + 547, + 612 + ], + "type": "text", + "content": " for query cubes following the equation:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 362, + 621, + 547, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 621, + 547, + 643 + ], + "spans": [ + { + "bbox": [ + 362, + 621, + 547, + 643 + ], + "type": "interline_equation", + "content": "S _ {Q} = \\operatorname {C l i p} \\left(\\sum_ {t = 1} ^ {T _ {l}} M _ {t} ^ {\\downarrow}, 1\\right), \\tag {6}", + "image_path": "05cc03b9c36460d8fc1d15d8348541ba7213972946c22cfaf338bcee707cd261.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "inline_equation", + "content": "Clip" + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "text", + "content": " represents a clipping function that set " + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "inline_equation", + "content": "S_{Q}" + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "text", + "content": " to 1 if " + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\sum_{t=1}^{T_l} M_t^{\\downarrow} > 0" + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "text", + "content": ". In other words, if the query cube at a window " + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "text", + "content": " has never contained any mask region in the past frames, then " + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "inline_equation", + "content": "S_{Q}(i,j) = 0" + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "text", + "content": ", indicating that spatiotemporal attention within this window can be skipped." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10481" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 112, + 545, + 282 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 109 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 109 + ], + "type": "text", + "content": "Table 1: Quantitative comparisons on YouTube-VOS [36] and DAVIS [28] datasets. The best and second performances are marked in red and blue, respectively. " + }, + { + "bbox": [ + 46, + 70, + 547, + 109 + ], + "type": "inline_equation", + "content": "E_{\\text{warp}}^*" + }, + { + "bbox": [ + 46, + 70, + 547, + 109 + ], + "type": "text", + "content": " denotes " + }, + { + "bbox": [ + 46, + 70, + 547, + 109 + ], + "type": "inline_equation", + "content": "E_{\\text{warp}} (\\times 10^{-3})" + }, + { + "bbox": [ + 46, + 70, + 547, + 109 + ], + "type": "text", + "content": ". All methods are evaluated following their default settings. Since DFVI, FGVC, ISVI, and FGT involve several CPU processes, their FLOPs cannot be accurately projected." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 112, + 545, + 282 + ], + "lines": [ + { + "bbox": [ + 49, + 112, + 545, + 282 + ], + "spans": [ + { + "bbox": [ + 49, + 112, + 545, + 282 + ], + "type": "table", + "html": "
AccuracyEfficiency
YouTube-VOSDAVISFLOPs (10 frames)Runtime (s/frame)
ModelsPSNR ↑SSIM ↑VFID ↓E* \\( _{warp} \\) ↓PSNR ↑SSIM ↑VFID ↓E* \\( _{warp} \\) ↓
DFVI [37]29.160.94290.0661.65128.810.94040.1871.596-0.837
CPNet [17]31.580.96070.0711.62230.280.95210.1821.5211407G0.316
FGVC [10]29.670.94030.0641.16330.800.94970.1651.571-1.795
STTN [40]32.340.96550.0531.06130.610.95600.1491.4381315G0.051
TSAM [46]30.220.94680.0701.01430.670.95480.1461.2351001G0.068
FuseFormer [22]33.320.96810.0531.05332.590.97010.1371.3491025G0.114
ISVI [43]30.340.94580.0771.00832.170.95880.1891.291-1.594
FGT [42]32.170.95990.0541.02532.860.96500.1291.323-1.828
E2FGVI [19]33.710.97000.0461.01333.010.97210.1161.289986G0.085
ProPainter (Ours)34.430.97350.0420.97434.470.97760.0981.187808G0.083
", + "image_path": "a0f1c6279bd90eaf0d5fe930efc0e984ecd78460af9db980377041a255d686d5.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 299, + 290, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 299, + 290, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 299, + 290, + 515 + ], + "type": "text", + "content": "Sparse Key/Value Space. Due to the highly redundant and repetitive textures in adjacent frames, it is unnecessary to include all frames as key/value tokens in each Transformer block. Instead, we will only include stripped temporal frames alternately, with a temporal stride of 2 in our design. That is, in each odd-numbered Transformer block, only odd-number frames are activated to participate in self-attention with their key and value, while even-number blocks include only even-number frames. By doing so, the key and value space is reduced by half, effectively reducing the computation and memory cost of the Transformer module. After filtering out unnecessary and redundant windows based on our sparse strategy, we perform self-attention on the remaining windows to extract refined features. These features are then gathered using a soft composition operation [22] for subsequent modules. Experimental results suggest that our design significantly reduces the computational cost of video Transformers while maintaining performance for video inpainting." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 521, + 163, + 534 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 163, + 534 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 163, + 534 + ], + "type": "text", + "content": "3.4. Training Objectives" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 539, + 288, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 539, + 288, + 660 + ], + "spans": [ + { + "bbox": [ + 46, + 539, + 288, + 660 + ], + "type": "text", + "content": "Flow Completion. We utilize L1 loss as the reconstruction loss and a second-order smoothness constraint on the flow field [24] to promote the collinearity of neighboring flows and thus enhance the smoothness of the completed flow field. Video Inpainting. We adopt L1 loss as the reconstruction loss for all pixels. To enhance the realistic and temporal consistency of video inpainting results, we also employ an adversarial loss that is measured using a T-PatchGAN [6] discriminator. The details and formulation of these losses are provided in the supplementary material." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 670, + 129, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 129, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 129, + 683 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 289, + 715 + ], + "type": "text", + "content": "Datasets. We use the training set of YouTube-VOS [36] with 3471 video sequences to train our networks. Two widely-" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 299, + 547, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 299, + 547, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 299, + 547, + 443 + ], + "type": "text", + "content": "used test sets are adopted for evaluation: YouTube-VOS [36] and DAVIS [28], which consist of 508 and 90 video sequences, respectively. For the DAVIS test set, following FuseFormer [22] and " + }, + { + "bbox": [ + 304, + 299, + 547, + 443 + ], + "type": "inline_equation", + "content": "\\mathrm{E}^2\\mathrm{FGVI}" + }, + { + "bbox": [ + 304, + 299, + 547, + 443 + ], + "type": "text", + "content": " [19], we use 50 video clips for evaluations. During training, we follow [13, 17, 22, 19] and generate stationary and object masks in a random fashion to simulate the masks in video completion and object removal tasks. As for evaluation, we adopt the stationary masks provided in [19] to calculate quantitative scores, and the object masks are extracted from their segmentation labels for qualitative comparisons. Video frames are sized to " + }, + { + "bbox": [ + 304, + 299, + 547, + 443 + ], + "type": "inline_equation", + "content": "432\\times 240" + }, + { + "bbox": [ + 304, + 299, + 547, + 443 + ], + "type": "text", + "content": " for training and evaluation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 445, + 548, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 548, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 548, + 601 + ], + "type": "text", + "content": "Training Details and Metrics. We use RAFT [32] to extract optical flow in our approach. For training the RFC network, we set the flow sequence length to 10 and perform deformable propagation on feature maps that are downsampled by a factor of 8 for faster processing. We adopt 8 Transformer blocks for the inpainting modules and use a local video sequence of length 10. The Transformer window size is " + }, + { + "bbox": [ + 304, + 445, + 548, + 601 + ], + "type": "inline_equation", + "content": "5 \\times 9" + }, + { + "bbox": [ + 304, + 445, + 548, + 601 + ], + "type": "text", + "content": ", and the extended size is half of the window size. We train both the RFC and inpainting modules using the Adam [14] optimizer with a batch size of 8, setting the initial learning rate to " + }, + { + "bbox": [ + 304, + 445, + 548, + 601 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 304, + 445, + 548, + 601 + ], + "type": "text", + "content": " and running 700k iterations for each. We implement our method using the PyTorch framework and train it on 8 NVIDIA Tesla V100 (32G) GPUs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 602, + 547, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 602, + 547, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 602, + 547, + 687 + ], + "type": "text", + "content": "We employ the widely used PSNR and SSIM metrics [35] to evaluate the reconstruction performance and VFID [34] scores to measure the perceptual similarity between input videos and outputs, as used in recent video inpainting studies [22, 19]. Additionally, we report the flow warping error " + }, + { + "bbox": [ + 304, + 602, + 547, + 687 + ], + "type": "inline_equation", + "content": "E_{\\text{warp}}" + }, + { + "bbox": [ + 304, + 602, + 547, + 687 + ], + "type": "text", + "content": " [16] to assess the temporal consistency and smoothness of the resulting video sequences." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 315, + 702, + 481, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 702, + 481, + 714 + ], + "spans": [ + { + "bbox": [ + 315, + 702, + 481, + 714 + ], + "type": "text", + "content": "3We set 450k training iterations for ablation study." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10482" + } + ] + } + ], 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Our ProPainter exhibits superiority in producing complete and faithful textures, resulting in enhanced spatiotemporal coherence for video inpainting." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 344, + 239, + 441, + 294 + ], + "blocks": [ + { + "bbox": [ + 344, + 239, + 441, + 294 + ], + "lines": [ + { + "bbox": [ + 344, + 239, + 441, + 294 + ], + "spans": [ + { + "bbox": [ + 344, + 239, + 441, + 294 + ], + "type": "image", + "image_path": "59aee458a23089a7d47194aa22edb3e403d467aa060bfa86a5f9ebd11bb760fa.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 379, + 296, + 408, + 304 + ], + "lines": [ + { + "bbox": [ + 379, + 296, + 408, + 304 + ], + "spans": [ + { + "bbox": [ + 379, + 296, + 408, + 304 + ], + "type": "inline_equation", + "content": "\\mathrm{E}^2\\mathrm{FGVI}" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 443, + 239, + 539, + 294 + ], + "blocks": [ + { + "bbox": [ + 443, + 239, + 539, + 294 + ], + "lines": [ + { + "bbox": [ + 443, + 239, + 539, + 294 + ], + "spans": [ + { + "bbox": [ + 443, + 239, + 539, + 294 + ], + "type": "image", + "image_path": "cceb1c7f4f0b504a026c4edafdaa0b047e213c7b7176aff181ed7036130e10fd.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 461, + 296, + 521, + 304 + ], + "lines": [ + { + "bbox": [ + 461, + 296, + 521, + 304 + ], + "spans": [ + { + "bbox": [ + 461, + 296, + 521, + 304 + ], + "type": "text", + "content": "ProPainter (Ours)" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "bbox": [ + 47, + 352, + 132, + 365 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 352, + 132, + 365 + ], + "spans": [ + { + "bbox": [ + 47, + 352, + 132, + 365 + ], + "type": "text", + "content": "4.1. Comparisons" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 46, + 373, + 289, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 289, + 516 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 289, + 516 + ], + "type": "text", + "content": "Quantitative Evaluation. We compare ProPainter with nine state-of-the-art methods including DFVI [37], CPNet [17], FGVC [10], STTN [40], TSAM [46], Fuseformer [22], ISVI [43], FGT [42], and " + }, + { + "bbox": [ + 46, + 373, + 289, + 516 + ], + "type": "inline_equation", + "content": "\\mathrm{E}^2\\mathrm{FGVI}" + }, + { + "bbox": [ + 46, + 373, + 289, + 516 + ], + "type": "text", + "content": " [19] on both YouTube-VOS [36] and DAVIS [28]. Thanks to the efficient design, ProPainter uses a temporal length of 20 for inference. Table 1 shows that ProPainter outperforms other methods in all quantitative metrics, especially on the DAVIS dataset, where our method surpasses the state-of-the-art method by " + }, + { + "bbox": [ + 46, + 373, + 289, + 516 + ], + "type": "inline_equation", + "content": "1.14\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 373, + 289, + 516 + ], + "type": "text", + "content": " in PSNR. The results suggest that our method has superior inpainting capability, enabling it to produce higher-quality, faithful, and seamless videos." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 46, + 520, + 288, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 288, + 663 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 288, + 663 + ], + "type": "text", + "content": "Qualitative Evaluation. For the visual comparison, we compare our method with FuseFormer [22], FGT [42], and " + }, + { + "bbox": [ + 46, + 520, + 288, + 663 + ], + "type": "inline_equation", + "content": "\\mathrm{E}^2\\mathrm{FGVI}" + }, + { + "bbox": [ + 46, + 520, + 288, + 663 + ], + "type": "text", + "content": " [19], which are representative methods of Transformer-, image propagation-, and feature propagation-based approaches, respectively. Figure 5 presents four comparison results for video completion and object removal. Our method uses dual-domain propagation to ensure reliable and long-range propagation. It completes missing regions with coherence and clear contents, while other compared methods tend to fail or produce unpleasant inpainting results such as texture distortions and black hazy region in FGT [42] results, as well as artifacts in FuseFormer [22] and " + }, + { + "bbox": [ + 46, + 520, + 288, + 663 + ], + "type": "inline_equation", + "content": "\\mathrm{E}^2\\mathrm{FGVI}" + }, + { + "bbox": [ + 46, + 520, + 288, + 663 + ], + "type": "text", + "content": " [19]." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "content": "Efficiency Comparison. Table 1 presents the efficiency comparisons between all methods in terms of FLOPs and running time. The FLOPs of all methods are computed based on a temporal length of 10. We consider all learn-" + } + ] + } + ], + "index": 29 + }, + { + "type": "table", + "bbox": [ + 313, + 378, + 544, + 436 + ], + "blocks": [ + { + "bbox": [ + 305, + 351, + 547, + 375 + ], + "lines": [ + { + "bbox": [ + 305, + 351, + 547, + 375 + ], + "spans": [ + { + "bbox": [ + 305, + 351, + 547, + 375 + ], + "type": "text", + "content": "Table 2: Comparisons of flow completion networks. Our network offers a dual benefit with high accuracy and efficiency." + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 378, + 544, + 436 + ], + "lines": [ + { + "bbox": [ + 313, + 378, + 544, + 436 + ], + "spans": [ + { + "bbox": [ + 313, + 378, + 544, + 436 + ], + "type": "table", + "html": "
EPE ↓DFVI [37]FGVC [10]FGT [42]ISVI [43]Ours
YouTube-VOS0.0460.0320.0210.0190.020
DAVIS0.1070.0820.0520.0510.051
Runtime (s/frame)0.1301.1250.3120.2310.005
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Exp.(a) w/o Img Prop.(b) w/ Img Prop. in FGVC(c) w/o Feat Prop.(d) w/ Feat Prop. in E²FGVI(f) Full TokensProPainter
PSNR33.0532.9133.1733.9434.1834.15
SSIM0.97240.96870.97320.97560.97650.9764
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(Exp. a)" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 208, + 236, + 285, + 324 + ], + "blocks": [ + { + "bbox": [ + 208, + 236, + 285, + 324 + ], + "lines": [ + { + "bbox": [ + 208, + 236, + 285, + 324 + ], + "spans": [ + { + "bbox": [ + 208, + 236, + 285, + 324 + ], + "type": "image", + "image_path": "acacbf713191d549a09bcb8ebe14e4f750b162d43f3721dc631b4a20d93aef03.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 226, + 327, + 266, + 335 + ], + "lines": [ + { + "bbox": [ + 226, + 327, + 266, + 335 + ], + "spans": [ + { + "bbox": [ + 226, + 327, + 266, + 335 + ], + "type": "text", + "content": "w/ImgProp." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 363, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 287, + 483 + ], + "type": "text", + "content": "content with details. To verify the effectiveness of our reliability check strategy in image propagation, we replaced our design with the FGVC image propagation module in Exp. (b) (without retraining), resulting in a noticeable decrease in PSNR. This is because the FGVC image propagation method is prone to being affected by incorrect optical flow, leading to severe texture distortion that subsequent modules cannot correct. Our model can effectively aware and stop unreliable propagation areas using a simple reliability check via Eq.2, and generate more faithful inpainting results." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 484, + 288, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 288, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 288, + 592 + ], + "type": "text", + "content": "Effectiveness of Feature Propagation. Similarly, we observe a slight decrease in performance by either removing feature propagation, i.e., Exp. (c), or replacing it with the Feature propagation of " + }, + { + "bbox": [ + 46, + 484, + 288, + 592 + ], + "type": "inline_equation", + "content": "\\mathrm{E}^2\\mathrm{FGVI}" + }, + { + "bbox": [ + 46, + 484, + 288, + 592 + ], + "type": "text", + "content": ", i.e., Exp. (d), indicating the effectiveness of the feature propagation modules and our reliability mask-aware conditions. This suggests that our design, which learns reliable DCN offsets in the feature domain, can further complement and enhance the propagation ability in the image domain." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "Effectiveness of Sparse Transformer. In theory, our strategy of using masks to guide sparsity only eliminates redundant and unnecessary tokens (windows), while preserving essential information. This means that there should be no adverse effect on performance. To confirm this, we conducted Exp. (d), comparing our approach to standard self-attention without sparse filtering. Our results indicate that our sparse Transformer block performs almost as well as the standard one, indicating that it can achieve high efficiency without sacrificing performance." + } + ] + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 305, + 236, + 422, + 331 + ], + "blocks": [ + { + "bbox": [ + 52, + 342, + 280, + 354 + ], + "lines": [ + { + "bbox": [ + 52, + 342, + 280, + 354 + ], + "spans": [ + { + "bbox": [ + 52, + 342, + 280, + 354 + ], + "type": "text", + "content": "Figure 7: Comparison of w/ and w/o image propagation." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 236, + 422, + 331 + ], + "lines": [ + { + "bbox": [ + 305, + 236, + 422, + 331 + ], + "spans": [ + { + "bbox": [ + 305, + 236, + 422, + 331 + ], + "type": "image", + "image_path": "a833ee63db660f7ba011c8e7a32a81a190130014c91f677114fb7d56b803e08d.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 312, + 338, + 537, + 349 + ], + "lines": [ + { + "bbox": [ + 312, + 338, + 537, + 349 + ], + "spans": [ + { + "bbox": [ + 312, + 338, + 537, + 349 + ], + "type": "text", + "content": "Figure 8: FLOPs cures of different Transformer blocks." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 425, + 235, + 541, + 331 + ], + "blocks": [ + { + "bbox": [ + 125, + 212, + 465, + 224 + ], + "lines": [ + { + "bbox": [ + 125, + 212, + 465, + 224 + ], + "spans": [ + { + "bbox": [ + 125, + 212, + 465, + 224 + ], + "type": "text", + "content": "Figure 6: Visual comparison on image propagation methods of FGVC [10] and ours." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 425, + 235, + 541, + 331 + ], + "lines": [ + { + "bbox": [ + 425, + 235, + 541, + 331 + ], + "spans": [ + { + "bbox": [ + 425, + 235, + 541, + 331 + ], + "type": "image", + "image_path": "32b125153ca9a705c43cd44cee1fb562e9f91950814bcca2f0f71588fda4dc85.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 362, + 547, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 362, + 547, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 362, + 547, + 506 + ], + "type": "text", + "content": "Efficiency of Sparse Transformer. In Figure 8, we compare the FLOPs of different Transformer blocks with respect to temporal length and spatial resolution, including those used in FuseFormer [22], FGT [42], and " + }, + { + "bbox": [ + 304, + 362, + 547, + 506 + ], + "type": "inline_equation", + "content": "\\mathrm{E}^2\\mathrm{FGVI}" + }, + { + "bbox": [ + 304, + 362, + 547, + 506 + ], + "type": "text", + "content": " [19]. We use a mask with a missing region ratio of " + }, + { + "bbox": [ + 304, + 362, + 547, + 506 + ], + "type": "inline_equation", + "content": "1/6" + }, + { + "bbox": [ + 304, + 362, + 547, + 506 + ], + "type": "text", + "content": " (higher than the average object ratio of " + }, + { + "bbox": [ + 304, + 362, + 547, + 506 + ], + "type": "inline_equation", + "content": "13.6\\%" + }, + { + "bbox": [ + 304, + 362, + 547, + 506 + ], + "type": "text", + "content": " in DAVIS) to calculate the FLOPs of our mask-guided sparse Transformer. The curves indicate that the efficiency advantage of our sparse Transformer becomes more prominent as the temporal length and video resolution increase, indicating great potential for developing longer-range spatiotemporal attention and applying it to larger resolution videos." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 517, + 378, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 517, + 378, + 529 + ], + "spans": [ + { + "bbox": [ + 306, + 517, + 378, + 529 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 536, + 547, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 536, + 547, + 657 + ], + "spans": [ + { + "bbox": [ + 304, + 536, + 547, + 657 + ], + "type": "text", + "content": "This study introduces a novel and improved video inpainting framework called ProPainter. It incorporates an enhanced dual-domain propagation and an efficient mask-guided sparse video Transformer. Thanks to the two modules, our ProPainter exhibits reliable and precise propagation capabilities over long distances, significantly improving the performance of video inpainting while maintaining high efficiency in terms of running time and computational complexity. We believe that the designs in ProPainter will provide valuable insights to the video inpainting community." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 662, + 547, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 662, + 547, + 711 + ], + "spans": [ + { + "bbox": [ + 304, + 662, + 547, + 711 + ], + "type": "text", + "content": "Acknowledgement. This study is supported under the RIE2020 Industry Alignment Fund Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s)." + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10484" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Jiayin Cai, Changlin Li, Xin Tao, Chun Yuan, and Yu-Wing Tai. 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In CVPR, 2021. 2, 6, 7" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10486" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/ProbVLM_ Probabilistic Adapter for Frozen Vison-Language Models/52935457-f9bc-4c99-866c-671f6012153b_content_list.json b/2023/ProbVLM_ Probabilistic Adapter for Frozen Vison-Language Models/52935457-f9bc-4c99-866c-671f6012153b_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..073ba84158e42281641d5e356ae8934e843a69c6 --- /dev/null +++ b/2023/ProbVLM_ Probabilistic Adapter for Frozen Vison-Language Models/52935457-f9bc-4c99-866c-671f6012153b_content_list.json @@ -0,0 +1,1503 @@ +[ + { + "type": "text", + "text": "ProbVLM: Probabilistic Adapter for Frozen Vison-Language Models", + "text_level": 1, + "bbox": [ + 137, + 130, + 831, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Uddeshya Upadhyay*,1 Shyamgopal Karthik*,1 Massimiliano Mancini2 Zeynep Akata $^{1,3}$", + "bbox": [ + 117, + 179, + 854, + 200 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1University of Tübingen 2University of Trento 3MPI for Intelligent Systems", + "bbox": [ + 173, + 205, + 800, + 224 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 258, + 313, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Large-scale vision-language models (VLMs) like CLIP successfully find correspondences between images and text. Through the standard deterministic mapping process, an image or a text sample is mapped to a single vector in the embedding space. This is problematic: as multiple samples (images or text) can abstract the same concept in the physical world, deterministic embeddings do not reflect the inherent ambiguity in the embedding space. We propose ProbVLM, a probabilistic adapter that estimates probability distributions for the embeddings of pre-trained VLMs via inter/intra-modal alignment in a post-hoc manner without needing large-scale datasets or computing. On four challenging datasets, i.e., COCO, Flickr, CUB, and Oxford-flowers, we estimate the multi-modal embedding uncertainties for two VLMs, i.e., CLIP and BLIP, quantify the calibration of embedding uncertainties in retrieval tasks and show that ProbVLM outperforms other methods. Furthermore, we propose active learning and model selection as two real-world downstream tasks for VLMs and show that the estimated uncertainty aids both tasks. Lastly, we present a novel technique for visualizing the embedding distributions using a large-scale pre-trained latent diffusion model. Code is available at https://github.com/ExplainableML/ProbVLM", + "bbox": [ + 75, + 290, + 473, + 654 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 683, + 209, + 698 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, large vision-language models (VLMs) [62, 51, 45, 74, 1, 35] have become exceedingly popular due to their ability to align images and text. These models such as CLIP [62] and BLIP [45] are trained on large-scale datasets such as LAION-400M [70] and YFCC-100M [79] and have shown strong performance when evaluated in a zero-shot fashion (i.e without requiring fine-tuning on specific datasets) for a variety of downstream tasks. One of the most popular applications of VLMs is cross-modal retrieval [86, 88] i.e retrieving images (text) for a queried text (images). However, image-to-text matching (and vice", + "bbox": [ + 75, + 709, + 468, + 876 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1c61ba78ab3c25afd80acda7c5326db9f89787588a23993bdcf5b94938ea196c.jpg", + "image_caption": [ + "Figure 1: We provide probabilistic embeddings for deterministic pre-trained vision-language models that are frozen. By capturing the ambiguity inherently present in the inputs, we obtain well-calibrated uncertainty estimates." + ], + "image_footnote": [], + "bbox": [ + 504, + 258, + 890, + 364 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "versa) is fundamentally ill-posed due to the inherent ambiguity in either modality [97], i.e. the same caption (or image) can be valid for multiple images (or captions). Therefore, it becomes essential to model the ambiguity inherently present in the various modalities, and combinations thereof.", + "bbox": [ + 496, + 455, + 892, + 531 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Instead of mapping inputs to embeddings, probabilistic embedding methods [57, 10] learn to map input samples to distributions. This is achieved by parameterizing the distributions of the embeddings and training a deep neural network to maximize its likelihood. Although they model ambiguities in the embedding space, such probabilistic models require training deep networks from scratch. This requires access to the large-scale datasets and the computational resources of the recent VLMs [62, 35, 51, 74, 45].", + "bbox": [ + 496, + 532, + 893, + 669 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We propose ProbVLM, a post-hoc probabilistic adapter, the first method to convert the deterministic embeddings provided by a frozen large-scale vision-language models into probabilistic ones, as shown in Figure 1. This enables us to efficiently retain the benefits of large-scale pre-training while learning distributions that model the inherent ambiguities in the different modalities. Our ProbVLM models the embedding distribution as a heteroscedastic probability distribution and is trained using a combination of intra-modal and cross-modal alignment objectives and provides well-calibrated uncertainty estimates, useful for several tasks.", + "bbox": [ + 496, + 671, + 893, + 837 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We demonstrate on two large vision-language datasets, i.e., COCO [46] and Flickr [60], and on two fine-grained image datasets, i.e., CUB [85] and Oxford-Flowers [55] with sentences from [66], that ProbVLM learns calibrated", + "bbox": [ + 498, + 839, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Authors contributed equally.", + "bbox": [ + 99, + 887, + 261, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1899", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "uncertainties without requiring large-scale models to be trained from scratch. This sharply contrasts previous works on probabilistic embeddings [57, 10] that train new models from scratch. We perform a series of analyses to understand the impact of the training objective and to study the properties of the resulting uncertainties. Furthermore, we demonstrate that our uncertainty estimates can be used to select the optimal model from a set of finetuned vision-language models on an unlabeled target dataset. They can also be used to choose the most suitable samples for fine-tuning the model in an active learning setup. Finally, with the help of a pretrained latent diffusion model [67], i.e., Stable Diffusion, we decode sampled embeddings from predicted distribution to visualize the predicted embedding distributions. We show that the predicted embedding distributions indeed capture meaningful modes of variation, that may be interpretable.", + "bbox": [ + 75, + 90, + 472, + 333 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 344, + 218, + 359 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Vision-Language Models. Such models [62, 51, 74, 1, 45, 47, 44, 100, 101, 90] have become ubiquitous in recent times due to their various applications in image classification [105, 21, 106, 50], cross-modal retrieval [4], as well as open-vocabulary semantic segmentation [24, 96]. The most notable among these is CLIP [62], which consists of an image and text encoder trained on 400M image-text pairs with a contrastive objective [28, 58]. As a result, the model is able to project images and text to a shared embedding space. In this paper, we focus on using the shared embedding space for the task of cross-modal retrieval [60, 46]. Recent works have predominantly relied on large-scale pre-training [62, 51, 74, 1, 104, 70, 69] to project images and text to the same metric space. However, it is essential to note that all of these vision-language models [62, 51, 45, 74, 1] provide deterministic mappings that do not model the inherent ambiguity in the inputs. In this work, we turn a deterministic model (i.e., CLIP) into a probabilistic one, without the need of a large-scale dataset.", + "bbox": [ + 75, + 369, + 472, + 657 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Probabilistic Embeddings. These methods [57, 10, 43] provide an elegant solution to estimate the ambiguity present in the inputs [37]. The key idea here is to map inputs to probability distributions in the embedding space, as opposed to point estimates, thereby modeling the inherent ambiguity present in the input. In the context of cross-modal retrieval, this was done by optimizing a probabilistic analog of the contrastive objective to learn distributions for the image and text inputs [10]. Other works have further improved the performance [43, 59, 34], extended this formulation to achieve compositional retrieval [54], and have applied it to other tasks such as video retrieval [59, 17] and tasks like pose estimation [78]. However, most of these works focus on training a model from scratch, thereby not leveraging the power of the pre-trained models that are widely present. The notable exception to this is Probabilistic Face Embed", + "bbox": [ + 75, + 659, + 472, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ding (PFE) [73] that proposed to learn a probabilistic embedding while retaining a deterministic pre-trained model for the task of learning face embeddings. However, this was done in a unimodal setting using only images. In this work, we aim to utilize pre-trained vision-language models while providing probabilistic embeddings for both modalities. The probabilistic embeddings derived from our proposed ProbVLM are consistent with cross-modal learning at the core of pretrained vision-language models.", + "bbox": [ + 496, + 90, + 893, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Uncertainty Estimation. These techniques have been widely explored for different tasks in computer vision [36, 7, 41, 42, 56, 102, 83, 53, 80, 27, 68, 103, 65, 81, 77, 82]. Uncertainties can be broadly categorized into aleatoric [36, 23, 3, 89, 12, 2, 87, 56, 95] and epistemic [25, 7, 41, 91, 20, 33, 19, 18] uncertainties. Uncertainty estimation has been used for a variety of tasks, such as identifying model failure [15, 5, 6, 92] and is extensively used in active learning to select the best samples to train the model [71, 38, 64, 72, 99, 98, 61, 52]. While several of these methods focus on training a new Bayesian model from scratch for quantifying the uncertainties in the prediction, some recent works like [83, 102, 29] have proposed methods to estimate the uncertainties for the pre-trained frozen models. However, these works tackle data from a single modality. This work efficiently estimates the uncertainty for the pre-trained frozen large-scale vision-language model.", + "bbox": [ + 496, + 228, + 895, + 486 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 496, + 591, + 512 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We first describe the problem formulation in Section 3.1. In Section 3.2, we describe our proposed method ProbVLM that estimates the complex probability distributions for the embeddings of the frozen deterministic vision-langue encoders, quantifying the uncertainties for their predictions.", + "bbox": [ + 496, + 522, + 893, + 599 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 500, + 604, + 702, + 619 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Let $\\mathcal{D} = (\\mathcal{I},\\mathcal{C})$ denote a vision and language dataset, where $\\mathcal{I}$ is a set of images and $\\mathcal{C}$ a set of captions. The two sets are connected via ground-truth matches where multiplicity is plausible. For a caption $c\\in \\mathcal{C}$ (respectively an image $i\\in \\mathcal{I}$ ), the set of corresponding images (respectively captions) is given by $\\kappa (c)\\subseteq \\mathcal{I}$ (respectively $\\kappa (i)\\subseteq \\mathcal{C}$ ). Recent advances in cross-modal vision-language models [62, 51, 74] often involve learning a shared embedding space, $\\mathcal{Z}\\subseteq \\mathbb{R}^{D}$ ( $D$ -dimensional space), for images and texts. This allows quantifying the similarity between cross-modal elements based on their distances in the shared embedding space. The shared embedding space is learned via a set of two encoders: $\\Phi_{\\mathcal{V}}(\\cdot ;\\theta_{\\mathcal{V}}):\\mathcal{I}\\to \\mathcal{Z}$ for the images and $\\Phi_{\\mathcal{T}}(\\cdot ;\\theta_{\\mathcal{T}}):\\mathcal{C}\\rightarrow \\mathcal{Z}$ for the texts, where $\\theta_{\\mathcal{V}}$ and $\\theta_{\\mathcal{T}}$ are the parameters for the respective mapping functions.", + "bbox": [ + 496, + 628, + 893, + 854 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We consider a real-world scenario where the above set of encoders have already been trained on vast datasets using large models with high computational cost, e.g., CLIP [62],", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1900", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/275641a36a92f5f83bd7720fadceb74c29f10d33b427866121d2f42615eb5ab3.jpg", + "image_caption": [ + "Figure 2: Proposed framework (ProbVLM) takes an existing vision-language model and introduces a probabilistic adapter over the image and text encoders. These adapters predict the parameters of a parameterized distribution for a given embedding. Models are trained by minimizing an objective consisting of intra/cross-modal supervision as detailed in Section 3." + ], + "image_footnote": [], + "bbox": [ + 86, + 90, + 883, + 404 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SLIP [51], Flava [74] and BLIP [45], are in frozen state, i.e., we have $\\Phi_{\\mathcal{V}}(\\cdot;\\theta_{\\mathcal{V}}^{*})$ and $\\Phi_{\\mathcal{T}}(\\cdot;\\theta_{\\mathcal{T}}^{*})$ , where $\\theta_{\\mathcal{V}}^{*},\\theta_{\\mathcal{T}}^{*}$ represents the parameters of the pretrained frozen encoders. These encoders are deterministic and map an image/text to vectors in the shared space, i.e., given a sample image $\\mathbf{x}_{\\mathcal{V}}$ (and similarly sample text $\\mathbf{x}_{\\mathcal{T}}$ ), the encoder provides an embedding $\\mathbf{z}_{\\mathcal{V}} := \\Phi_{\\mathcal{V}}(\\mathbf{x}_{\\mathcal{V}};\\theta_{\\mathcal{V}}^{*})$ (and similarly, $\\mathbf{z}_{\\mathcal{T}} := \\Phi_{\\mathcal{T}}(\\mathbf{x}_{\\mathcal{T}};\\theta_{\\mathcal{T}}^{*}))$ ). However, the point estimates, $\\mathbf{z}$ , do not capture the ambiguity inherent to these embeddings [57, 10, 17] that are better represented by the probability distribution $P_{\\mathbf{z}|\\mathbf{x}}$ . Therefore, we propose to estimate $P_{\\mathbf{z}|\\mathbf{x}}$ for the pretrained model efficiently, using ProbVLM, quantifying the uncertainties of the output without re-training the encoders.", + "bbox": [ + 75, + 468, + 472, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Building ProbVLM", + "text_level": 1, + "bbox": [ + 76, + 674, + 253, + 690 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Despite being deterministic, large-scale frozen encoders already provide high-quality point estimates. Our proposed method leverages this fact, using the embeddings $\\mathbf{z}$ as estimates for the mean of the desired distribution $P_{\\mathbf{z}|\\mathbf{x}}$ , and estimating the remaining parameters. $P_{\\mathbf{z}|\\mathbf{x}}$ can be modeled as a parametric distribution $P_{\\mathbf{z}|\\mathbf{x}}(\\mathbf{z}|\\{\\hat{\\mathbf{z}},\\hat{\\nu}\\dots \\hat{\\rho}\\})$ where the parameters can be estimated using a deep neural network [20, 36, 41]. Therefore, we introduce ProbVLM,", + "bbox": [ + 75, + 696, + 468, + 818 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\Psi (\\cdot ; \\zeta) := \\left(\\Psi_ {\\mathcal {V}} (\\cdot ; \\zeta_ {\\mathcal {V}}), \\Psi_ {\\mathcal {T}} (\\cdot ; \\zeta_ {\\mathcal {T}})\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 828, + 468, + 845 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\Psi_{\\mathcal{V}}$ and $\\Psi_{\\mathcal{T}}$ represents the vision and text encoders parameterized by $\\zeta_{\\nu}$ and $\\zeta_{\\tau}$ , respectively. Also, $\\zeta := \\zeta_{\\nu} \\cup \\zeta_{\\mathcal{T}}$ represents the overall parameters for ProbVLM.", + "bbox": [ + 76, + 854, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "that learns to estimate the parameters $\\{\\hat{\\mathbf{z}},\\hat{\\nu}\\dots \\hat{\\rho}\\}$ with the help of frozen encoders $\\Phi_{\\mathcal{V}}(\\cdot ;\\theta_{\\mathcal{V}}^{*})$ and $\\Phi_{\\mathcal{T}}(\\cdot ;\\theta_{\\mathcal{T}}^{*})$ . The functions $\\Psi_{\\mathcal{V}}(\\cdot ;\\zeta_{\\mathcal{V}})$ and $\\Psi_{\\mathcal{T}}(\\cdot ;\\zeta_{\\mathcal{T}})$ operate on image and text embeddings respectively, but during training depend on both modalities, as discussed later. We design the learning scheme for $\\Psi (\\cdot ;\\zeta)$ such that: (i) Estimated parameter $\\hat{\\mathbf{z}}$ should remain faithful to the original unimodal embedding $\\mathbf{z}$ (intra-modal alignment), this makes the uncertainty of the ProbVLM serve as a good proxy for the uncertainty of frozen encoders. (ii) Estimated parameters $\\{\\hat{\\nu}\\dots \\hat{\\rho}\\}$ should capture the ambiguities and uncertainties present within and across modalities (cross-modal alignment). Figure 2 depicts ProbVLM in tandem with the frozen VLM.", + "bbox": [ + 496, + 468, + 893, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Intra-modal Alignment. To ensure that the mean of the distribution estimated by $\\Psi (\\cdot ;\\zeta)$ reflects the point estimates provided by the frozen encoders, we set up a probabilistic reconstruction problem for the embeddings within the modalities. That is, for a given sample $\\mathbf{x}$ (either from image or text modality), we obtain the embedding from the frozen encoder $\\mathbf{z} = \\Phi (\\mathbf{x};\\theta)$ (using the appropriate encoder), then the modality-specific component of $\\Psi (\\cdot ;\\zeta)$ learns to reconstruct the $\\mathbf{z}$ (let the reconstruction be called $\\hat{\\mathbf{z}}$ ). The modality-specific component of $\\Psi (\\cdot ;\\zeta)$ is designed to (i) relax the i.i.d constraints by assuming independent but not identically distributed residuals and (ii) learn the heteroscedasticity for the residuals at the time of reconstruction that may follow the heavy-tailed distributions [83, 84, 40, 39, 30]. The modality-specific component", + "bbox": [ + 496, + 674, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1901", + "bbox": [ + 483, + 944, + 513, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "is learned by maximizing the likelihood, $\\mathcal{L}(\\zeta ;\\{\\mathbf{z}_i\\}_{i = 1}^N)$ for the embeddings of $N$ samples in the datasets. That is, the modality-specific optimal parameters are given by,", + "bbox": [ + 75, + 90, + 468, + 137 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\zeta^ {*} := \\underset {\\zeta} {\\operatorname {a r g m a x}} \\mathcal {L} (\\zeta ; \\left\\{\\mathbf {z} _ {i} \\right\\} _ {i = 1} ^ {N}) = \\prod_ {i = 1} ^ {N} \\frac {\\hat {\\beta} _ {i} e ^ {- \\left(\\left| \\bar {\\mathbf {z}} _ {i} - \\mathbf {z} _ {i} \\right| / \\hat {\\alpha} _ {i}\\right) ^ {\\hat {\\beta} _ {i}}}}{2 \\hat {\\alpha} _ {i} \\Gamma \\left(1 / \\hat {\\beta} _ {i}\\right)} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 148, + 468, + 205 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the above equation, $\\frac{\\hat{\\beta}_i e^{-(|\\hat{\\mathbf{z}}_i - \\mathbf{z}_i| / \\hat{\\alpha}_i)^{\\hat{\\beta}_i}}{2\\hat{\\alpha}_i \\Gamma(1 / \\hat{\\beta}_i)}$ represents the generalized Gaussian distribution (GGD, represented by $\\mathcal{G}$ ) that is capable of modeling heavy-tailed distributions (note the Gaussian and Laplace are special cases of $\\mathcal{G}$ with $\\alpha = 1, \\beta = 2$ and $\\alpha = 1, \\beta = 1$ , respectively). The variables $\\hat{\\mathbf{z}}_i, \\hat{\\alpha}_i, \\hat{\\beta}_i$ are the predicted mean, scale, and shape parameters of $\\mathcal{G}$ from our modality-specific components for the given input $\\mathbf{z}_i$ . We obtain modality-specific optimal parameters by minimizing negative log-likelihood (equivalent to Equation 2). Given $\\mathbf{z}$ and predicted $\\hat{\\mathbf{z}}, \\hat{\\alpha}, \\hat{\\beta}$ , loss is given by,", + "bbox": [ + 75, + 223, + 470, + 387 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {r e c}} (\\zeta) := \\left(\\frac {| \\hat {\\mathbf {z}} - \\mathbf {z} |}{\\hat {\\alpha}}\\right) ^ {\\hat {\\beta}} - \\log \\frac {\\hat {\\beta}}{\\hat {\\alpha}} + \\log \\Gamma \\left(\\frac {1}{\\hat {\\beta}}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 411, + 468, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Therefore, the vision-specific component of ProbVLM, $\\Psi (\\cdot ;\\zeta_{\\nu}))$ , is trained by minimizing the Equation 3 using image embeddings, we denote this loss as $L_{\\mathrm{rec}}^{\\mathcal{V}}(\\zeta_V)$ . Similarly the text-specific component, $\\Psi (\\cdot ;\\zeta_T)$ , is trained by minimizing $L_{\\mathrm{rec}}^{\\mathcal{T}}(\\zeta_T)$ . As discussed next, we also enforce cross-modal alignment so that the predicted distribution of ProbVLM captures the uncertainties across modalities from one-to-many correspondences for an embedding.", + "bbox": [ + 75, + 464, + 468, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Cross-modal Alignment. While the intra-modal alignment seeks to match the means of the output distribution from ProbVLM to the embeddings derived from frozen vision-language encoders, we also enforce the image and text embedding output distribution (from ProbVLM) belonging to similar concepts to remain close to each other. That is, given an image and text embedding pair $(\\mathbf{z}_{\\mathcal{V}},\\mathbf{z}_{\\mathcal{T}})$ (from frozen model) representing similar concepts, the output distributions from $\\Psi (\\cdot ;\\zeta),\\mathcal{G}(\\mathbf{z};\\hat{\\mathbf{z}}_{\\mathcal{V}},\\hat{\\alpha}_{\\mathcal{V}},\\hat{\\beta}_{\\mathcal{V}})$ and $\\mathcal{G}(\\mathbf{z};\\hat{\\mathbf{z}}_{\\mathcal{T}},\\hat{\\alpha}_{\\mathcal{T}},\\hat{\\beta}_{\\mathcal{T}})$ (later referred to as $\\mathcal{G}_{\\mathcal{V}}(\\mathbf{z}))$ and $\\mathcal{G}_{\\mathcal{T}}(\\mathbf{z}))$ should match. This can be measured directly from the likelihood as, $p(\\mathbf{z}_v = \\mathbf{z}_u)$ , where $\\mathbf{z}_v\\sim \\mathcal{G}_{\\mathcal{V}}(\\mathbf{z})$ and $\\mathbf{z}_u\\sim \\mathcal{G}_{\\mathcal{T}}(\\mathbf{z})$ as in [73], i.e.,", + "bbox": [ + 75, + 587, + 470, + 771 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np \\left(\\mathbf {z} _ {v} = \\mathbf {z} _ {u}\\right) := \\iint \\mathcal {G} _ {\\mathcal {Y}} \\left(\\mathbf {z} _ {v}\\right) \\mathcal {G} _ {\\mathcal {T}} \\left(\\mathbf {z} _ {u}\\right) \\delta \\left(\\mathbf {z} _ {v} - \\mathbf {z} _ {u}\\right) d \\mathbf {z} _ {v} d \\mathbf {z} _ {u} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 794, + 468, + 825 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\delta (\\cdot)$ refers to the Dirac-delta distribution. The above integral can be simplified further by defining $\\Delta \\mathbf{z} = \\mathbf{z}_v - \\mathbf{z}_u$ and seeking $p(\\Delta \\mathbf{z}) = 0$ . As both $\\mathbf{z}_v$ and $\\mathbf{z}_u$ are GGD random variables, $\\Delta \\mathbf{z}$ follows the distribution based on the", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Bivariate Fox H-function [76, 48, 49] given by,", + "bbox": [ + 500, + 90, + 812, + 106 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta z \\sim \\frac {1}{2 \\Gamma (1 / \\hat {\\beta} _ {\\mathcal {V}}) , \\Gamma (1 / \\hat {\\beta} _ {\\mathcal {T}})} \\times\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 114, + 774, + 137 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\int \\mathcal {H} _ {1, 2} ^ {1, 1} \\left[ A t ^ {2} \\left| \\begin{array}{l} \\left(1 - \\frac {1}{\\bar {\\mathbf {z}} _ {\\mathcal {V}}}, \\frac {1}{\\bar {\\mathbf {z}} _ {\\mathcal {T}}}\\right) \\\\ (0, 1) \\left(\\frac {1}{2}, 1\\right) \\end{array} \\right. \\right] \\mathcal {H} _ {1, 2} ^ {1, 1} \\left[ B t ^ {2} \\left| \\begin{array}{l} \\left(1 - \\frac {1}{\\bar {\\mathbf {z}} _ {\\mathcal {T}}}, \\frac {1}{\\bar {\\mathbf {z}} _ {\\mathcal {T}}}\\right) \\\\ (0, 1) \\left(\\frac {1}{2}, 1\\right) \\end{array} \\right. \\right] \\cos t (\\mu - z) d t \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 138, + 890, + 184 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Where $A = \\frac{\\hat{\\alpha}_{\\mathcal{V}}^2\\Gamma(1 / \\hat{\\beta}_{\\mathcal{V}})}{4\\Gamma(3 / \\hat{\\beta}_{\\mathcal{V}})}$ , $B = \\frac{\\hat{\\alpha}_{\\mathcal{T}}^2\\Gamma(1 / \\hat{\\beta}_{\\mathcal{T}})}{4\\Gamma(3 / \\hat{\\beta}_{\\mathcal{T}})}$ , $\\mu = \\hat{\\mathbf{z}}_v - \\hat{\\mathbf{z}}_u$ , and $\\mathcal{H}$ is the Fox $H$ function [76, 48, 49]. Equation 5 does not provide a scalable objective function suitable for training deep neural networks. Hence, we propose an approximation that is easily scalable for deep-learning models given by,", + "bbox": [ + 498, + 195, + 890, + 279 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} p (\\mathbf {z} _ {v} = \\mathbf {z} _ {u}) = \\iint \\mathcal {G} _ {\\mathcal {V}} (\\mathbf {z} _ {v}) \\mathcal {G} _ {\\mathcal {T}} (\\mathbf {z} _ {u}) \\delta (\\mathbf {z} _ {v} - \\mathbf {z} _ {u}) d \\mathbf {z} _ {v} d \\mathbf {z} _ {u} \\\\ \\approx \\int \\frac {1}{2} \\left(\\mathcal {G} _ {\\mathcal {V}} (\\mathbf {z}) \\delta (\\mathbf {z} - \\mathbf {z} _ {\\mathcal {T}}) + \\mathcal {G} _ {\\mathcal {T}} (\\mathbf {z}) \\delta (\\mathbf {z} - \\mathbf {z} _ {\\mathcal {V}})\\right) d \\mathbf {z} \\tag {6} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 300, + 890, + 364 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The appendix shows details of the above equation. The first term in the integral, $\\int \\mathcal{G}_{\\mathcal{V}}(\\mathbf{z})\\delta (\\mathbf{z} - \\mathbf{z}_{\\mathcal{T}})d\\mathbf{z}$ , is the likelihood of the text embedding $\\mathbf{z}_{\\mathcal{T}}$ under the predicted distribution, $\\mathcal{G}_{\\mathcal{V}}(\\mathbf{z})$ , for the visual embedding. Similarly, the second term is the likelihood of the visual embedding $\\mathbf{z}_{\\mathcal{V}}$ under the predicted distribution, $\\mathcal{G}_{\\mathcal{T}}(\\mathbf{z})$ , for the text embedding. Negative log of Equation 6 leads to a scalable objective function that can be used to learn the optimal parameters for vision and text components of ProbVLM $(\\Psi_{\\mathcal{V}}(\\cdot ;\\zeta_{\\mathcal{V}})$ and $\\Psi_{\\mathcal{T}}(\\cdot ;\\zeta_{\\mathcal{T}}))$", + "bbox": [ + 498, + 372, + 890, + 508 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {\\text {c r o s s}} (\\zeta_ {\\mathcal {V}}, \\zeta_ {\\mathcal {T}}) := \\underbrace {\\left(\\frac {| \\hat {\\mathbf {z}} _ {\\mathcal {V}} - \\mathbf {z} _ {\\mathcal {T}} |}{\\hat {\\alpha} _ {\\mathcal {V}}}\\right) ^ {\\hat {\\beta} _ {\\mathcal {V}}} - \\log \\frac {\\hat {\\beta} _ {\\mathcal {V}}}{\\hat {\\alpha} _ {\\mathcal {V}}} + \\log \\Gamma \\left(\\frac {1}{\\hat {\\beta} _ {\\mathcal {V}}}\\right)} _ {\\text {C r o s s - m o d a l : v i s i o n} \\rightarrow \\text {t e x t}} + \\\\ \\underbrace {\\left(\\frac {| \\hat {\\mathbf {z}} _ {\\mathcal {T}} - \\mathbf {z} _ {\\mathcal {V}} |}{\\hat {\\alpha} _ {\\mathcal {T}}}\\right) ^ {\\hat {\\beta} _ {\\mathcal {T}}} - \\log \\frac {\\hat {\\beta} _ {\\mathcal {T}}}{\\hat {\\alpha} _ {\\mathcal {T}}} + \\log \\Gamma \\left(\\frac {1}{\\hat {\\beta} _ {\\mathcal {T}}}\\right)} _ {\\text {C r o s s - m o d a l : t e x t} \\rightarrow \\text {v i s i o n}} \\tag {7} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 530, + 890, + 637 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The overall objective used for ProbVLM is designed to be,", + "bbox": [ + 500, + 645, + 888, + 661 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {P r o b V L M}} \\left(\\zeta_ {\\mathcal {V}}, \\zeta_ {\\mathcal {T}}\\right) = L _ {\\text {r e c}} ^ {\\mathcal {V}} \\left(\\zeta_ {\\mathcal {V}}\\right) + L _ {\\text {r e c}} ^ {\\mathcal {T}} \\left(\\zeta_ {\\mathcal {T}}\\right) + \\lambda_ {\\text {c r o s s}} L _ {\\text {c r o s s}} \\left(\\zeta_ {\\mathcal {V}}, \\zeta_ {\\mathcal {T}}\\right) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 685, + 890, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda_{cross}$ is a hyperparameter controlling the relative contribution of inter-intra modality terms.", + "bbox": [ + 498, + 727, + 888, + 756 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Uncertainty Quantification. Given embedding $\\mathbf{z}$ from a frozen encoder, predicted distributions from the trained ProbVLM (output from the appropriate component) allows aleatoric uncertainty estimation as $\\hat{\\sigma}_{\\mathrm{aleatoric}}^2 = \\frac{\\hat{\\alpha}^2\\Gamma(3 / \\hat{\\beta})}{\\Gamma(1 / \\hat{\\beta})}$ . Moreover, we design both $\\Psi_{\\mathcal{V}}$ and $\\Psi_{\\mathcal{T}}$ to be simple 3-layer MLPs with dropout layers (with dropout probability set to 0.1 during training). Activating dropouts during inference, with multiple forward passes (say $M$ ), allows estimating the epistemic uncertainty, $\\hat{\\sigma}_{\\mathrm{epistemic}}^2 = \\frac{1}{M}\\sum_{m = 1}^{M}(\\hat{\\mathbf{z}}_m - \\hat{\\mathbf{z}}_m)$ .", + "bbox": [ + 498, + 758, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1902", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/dd1fa4cba0b3d41f9705ef3b250b6d128d630ee9b7b2bb24ce589fc600aeabf8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 106, + 88, + 862, + 308 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e064d97907fb223a5aa4c8799ec4fccd4d0b3f6a60db46e50991bcc93f31b41b.jpg", + "image_caption": [ + "Figure 3: Measuring the calibration with various post-hoc method for Image-to-Text and Text-to-Image retrieval when trained on (top) CUB and (bottom) COCO, and evaluated on CUB, COCO, Flickr, FLO." + ], + "image_footnote": [], + "bbox": [ + 106, + 309, + 862, + 515 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\frac{1}{M}\\sum_{j = 1}^{M}\\hat{\\mathbf{z}}_j)^2$ We estimate total uncertainty as,", + "bbox": [ + 76, + 551, + 393, + 571 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\sigma} _ {\\text {t o t a l}} ^ {2} = \\hat {\\sigma} _ {\\text {e p i s t e m i c}} ^ {2} + \\hat {\\sigma} _ {\\text {a l e a t o r i c}} ^ {2} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 583, + 468, + 603 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Latent Diffusion for Probabilistic Embeddings", + "text_level": 1, + "bbox": [ + 76, + 613, + 468, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For a given text embedding $\\mathbf{z}_{\\mathcal{T}}$ , the distribution estimated via ProbVLM, $\\mathcal{G}(\\mathbf{z};\\hat{\\mathbf{z}}_{\\mathcal{T}},\\hat{\\alpha}_{\\mathcal{T}},\\hat{\\beta}_{\\mathcal{T}})$ can be visualized by drawing samples from the predicted distribution of vectors (say, $\\{\\hat{\\mathbf{z}}_{\\mathcal{T},i}\\}_{i = 1}^{Q}$ ) and passing them through a latent diffusion model, e.g., Stable Diffusion (say, $\\Omega (\\cdot ;\\theta_{\\Omega}^{*}))$ using CLIP text encoder, to synthesize the set of samples (say, $J$ ) from the corresponding distribution of images, i.e.,", + "bbox": [ + 75, + 637, + 468, + 743 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nJ := \\left\\{\\boldsymbol {\\Omega} \\left(\\hat {\\mathbf {z}} _ {i}; \\theta_ {\\Omega}\\right) \\right\\} _ {i = 1} ^ {Q} \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 753, + 468, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Section 4.4 uses this to visualize the predicted distributions.", + "bbox": [ + 76, + 784, + 467, + 799 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments and Results", + "text_level": 1, + "bbox": [ + 76, + 814, + 310, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We start by highlighting our tasks, datasets, and evaluation metrics. We also compare our model to various state-of-the-art methods quantitatively and qualitatively in Section 4.1. In Section 4.2, we provide an ablation analysis,", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and Section 4.3 demonstrates some real-world applications of ProbVLM for model selection and active learning.", + "bbox": [ + 498, + 554, + 890, + 585 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets, Metrics, and Baselines. We use the MS-COCO [46], Flickr-30k [60], and the CUB [85] as they are widely used for cross-modal retrieval [10, 16, 75]. Furthermore, we adapt the Oxford-Flowers 102 (FLO) dataset [55] similar to [10] as an additional benchmark for cross-modal retrieval in a fine-grained setting. We evaluate the performance of both Image-to-Text retrieval and Text-to-Image Retrieval using the Recall@k (R@k) metric. To evaluate the calibration of the uncertainty estimates, we define uncertainty levels [10] and use the Spearman rank correlation (denoted by $S$ ) between the uncertainty level and the Recall@k for retrieval. For an ideal model, performance would decrease monotonically with increasing uncertainty levels, leading to a score of -1. We also compute the $R^2$ for the regression fit between the uncertainty levels and R@1 performances to measure if the drop in performance follows a linear trend. Finally, we also measure the product of these two scores (as a unified metric), i.e., $-SR^2$ , which should be 1.0 for an ideal model. Since there is no prior work to estimate probabilistic embeddings from a deterministic model", + "bbox": [ + 496, + 598, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1903", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/1b77bdfa1162b48e15897f3912374d73744f1148e2203d5b5442d0e496fcaa38.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
VLMMetricsi2tt2i
COCOFlickrFLOCUBCOCOFlickrFLOCUB
CLIPS↓-0.99-0.70-0.90-0.60-0.30-0.70-0.99-0.89
R2↑0.930.710.620.670.350.500.990.70
-SR2↑0.930.490.560.400.100.350.990.63
S↓-0.79-0.190.60-0.600.790.30-0.89-0.10
R2↑0.590.010.300.280.740.440.520.00
-SR2↑0.470.00-0.180.17-0.59-0.130.47-0.00
S↓-0.89-0.30-0.30-0.600.300.09-0.700.30
R2↑0.750.070.070.200.160.010.570.01
-SR2↑0.680.020.020.12-0.05-0.000.40-0.00
S↓-0.79-0.300.00-0.60-0.10-0.19-0.89-0.50
R2↑0.690.090.000.410.260.0710.800.15
-SR2↑0.550.030.000.240.000.010.730.07
BLIPS↓-0.87-0.79-0.74-0.66-0.43-0.38-0.31-0.22
R2↑0.920.830.680.610.520.480.450.38
-SR2↑0.800.660.500.400.220.180.140.08
S↓-0.82-0.74-0.63-0.63-0.39-0.32-0.28-0.18
R2↑0.720.760.620.440.480.380.390.37
-SR2↑0.580.570.390.270.190.120.110.07
S↓-0.76-0.53-0.60-0.44-0.28-0.26-0.28-0.21
R2↑0.810.560.600.530.500.340.440.36
-SR2↑0.620.290.360.230.140.090.120.08
S↓-0.44-0.33-0.74-0.60-0.19-0.26-0.21-0.21
R2↑0.660.560.420.550.490.230.350.36
-SR2↑0.290.180.310.330.100.060.070.08
", + "bbox": [ + 81, + 90, + 470, + 540 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1: Metrics to evaluate the calibration of the uncertainty estimates for both CLIP [62] and BLIP [45] Vision-Language models for all considered methods, trained on COCO and evaluated on COCO, Flickr, CUB, and FLO.", + "bbox": [ + 75, + 550, + 468, + 612 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "in a cross-modal setting, we adapt a few existing ideas for the task. The first baseline is adapted from PFE [73], where we learn the covariances for the heteroscedastic Gaussian distribution while keeping the mean fixed to the embeddings derived from the frozen encoders in each modality. The second is to use the soft-contrastive objective of PCME[10] to train a probabilistic adapter in a post-hoc fashion. Finally, we also have a baseline that performs Test-Time Data Augmentation (TTDA) on the inputs [2, 87]. This is done by perturbing the images and masking out words in the text. While TTDA does not require additional training, we train our ProbVLM and other baselines on datasets like COCO, Flickr, CUB, and FLO.", + "bbox": [ + 75, + 637, + 468, + 834 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. Our ProbVLM consists of a Multi-Layer Perceptron (MLP) for both the image and text encoder, each consisting of an input layer going from embedding dimension to 256, a hidden layer of size 256, and", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "an output layer going from 256 to embedding dimensions. This is trained for 100 epochs with a learning rate of $1e^{-4}$ . More details are available in the supplementary.", + "bbox": [ + 498, + 90, + 890, + 137 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Calibrated Uncertainty via ProbVLM", + "text_level": 1, + "bbox": [ + 498, + 167, + 816, + 184 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We investigate the calibration of the uncertainty derived from ProbVLM for the cross-modal retrieval task. All models trained on CUB and COCO were evaluated on all four datasets. Calibration plots are illustrated in Figure 3. We observe that the R@1 performance consistently drops for ProbVLM as we increase the uncertainty levels, whereas the baselines rarely see a monotonic drop in performance. We quantify this performance in Table 1. The highest score of 0.93 for $-SR^2$ (i2t) on the COCO dataset indicates a decreasing performance trend with increasing uncertainty. Notably, the uncertainty estimates indicate the average performance in different bins even when ProbVLM is evaluated on datasets that are different from the train set. In some cases, we see that ProbVLM even achieves a nearly perfect score $(-SR^2$ of 0.99, with CLIP VLM on FLO, after training on COCO for Image-to-Text Retrieval). On the contrary, we find that the baselines often achieve poor scores. It is important to note that all these models use the same underlying embeddings and achieve the same performance on the retrieval task. Of all the considered methods, ProbVLM provides the most calibrated uncertainty estimates. We see similar trends for ProbVLM with BLIP [45], where ProbVLM achieves a $-SR^2$ of 0.80, when trained on COCO and evaluated on COCO, compared to other methods like PFE\\* (0.58), PCME\\* (0.62), and TTDA (0.29).", + "bbox": [ + 496, + 198, + 890, + 575 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 4-(Top) visualizes the ambiguities captured by ProbVLM on the visual embeddings. We take a bird image (source) from the CUB dataset and obtain the probability distribution for the visual embedding of that sample; we then compute the likelihood of the visual embeddings (i.e., point estimates derived from CLIP) for the other samples of CUB and COCO datasets, under the source distribution. We notice that within the CUB dataset, the bird images similar to the source image have a higher likelihood compared to other bird images. Also, the images from the COCO dataset tend to have a lower likelihood. However, some images from the COCO dataset have a likelihood similar to the samples from CUB. We visualize these samples and discover them to be bird images. Moreover, the overlapping region between CUB and COCO has samples from the COCO dataset that are ambiguous and related to bird images as they have similar backgrounds, etc. On the contrary, when a similar analysis is performed using the CLIP (by measuring the distance between the embeddings instead of likelihood, Figure 4-(Bottom)), we notice that the two datasets are well separated and ambiguities are not captured.", + "bbox": [ + 496, + 583, + 892, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1904", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3ab0254dfbaf805c5c039debed3b6d06fb1f934714e6af4d7c9c32401ba36ee2.jpg", + "image_caption": [ + "Figure 4: Visualizing the uncertainties of the vision encoder captured by ProbVLM. Fixing an image from CUB, we obtain the predicted embedding distribution and compute the likelihood of all other samples in CUB and COCO. We observe that the images in COCO are similar/ambiguous to CUB overlap (Top). However, deterministic embeddings lead to a separation between the two datasets (Bottom)." + ], + "image_footnote": [], + "bbox": [ + 84, + 88, + 467, + 335 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8bd425a32f6e9ed765ef783551338c2d3a699a85f2ebdbd66845e30246fd6596.jpg", + "image_caption": [ + "Figure 5: Plot indicating (left) necessity of the cross-modal alignment and (right) data required to train ProbVLM." + ], + "image_footnote": [], + "bbox": [ + 78, + 468, + 274, + 608 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a7302e1bd2fcfb0f397635edae76fe5e697b635ea37ce994e893aea1955c2c4b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 281, + 468, + 472, + 609 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/03282f7e403dc14d26cd0fd911bb2ef42a5b2d2a215861b1f0914c319883157c.jpg", + "image_caption": [ + "Figure 6: Uncertainty increases with increased masking of the input images (Left) and texts (Right). Results with three vision encoders and one language encoder from CLIP." + ], + "image_footnote": [], + "bbox": [ + 78, + 666, + 276, + 811 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ed8587106abc2759ed78ea8382486bc4711dd00dc5d90fa45be954d2cd705089.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 276, + 667, + 470, + 811 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/719289f05fe280d6e183887a2199a8d7d78dd4271dd74df3ba1b73de8a94d3dd.jpg", + "image_caption": [ + "Figure 7: Results for active learning, with different vision encoders and varying training budgets. For a given encoder, uncertainty-based sampling outperforms random sampling." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 893, + 300 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Ablations", + "text_level": 1, + "bbox": [ + 500, + 369, + 609, + 383 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We ablate different components of our proposed ProbVLM, to provide a deeper understanding of its workings. First, we perform a sensitivity analysis on the cross-modal reconstruction objective, as shown in Figure 5-(Left), for ProbVLM on BLIP using the COCO dataset. We need a non-zero coefficient of the cross-modal loss to ensure that ProbVLM learns meaningful uncertainties that capture the ambiguities across modalities and are well-correlated with its performance on the downstream retrieval task. Similarly, having a large co-efficient for the cross-modal loss could hinder learning a faithful identity reconstruction, thereby hampering the performance of the downstream evaluation. Next, we investigate the amount of data that is required to train ProbVLM in Figure 5-(Right). We get satisfactory calibration of the uncertainty estimates while using only $50\\%$ of the dataset (shown for ProbVLM on BLIP using COCO), indicating that ProbVLM is highly data-efficient.", + "bbox": [ + 496, + 393, + 892, + 651 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Further, we investigate the uncertainties by masking out increasing portions of the input image/text in Figure 6. We use three different CLIP backbones for the images, ViT-B/32, ViT-B/16, ResNet50, and GPT-based language encoder from CLIP [62, 63]. The mean uncertainty steadily increases as we mask increasing amounts of input.", + "bbox": [ + 496, + 651, + 890, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Applications", + "text_level": 1, + "bbox": [ + 500, + 753, + 633, + 768 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We study the utility of the uncertainty estimates derived from ProbVLM on two critical applications not well reviewed for VLMs: active learning and model selection.", + "bbox": [ + 496, + 777, + 890, + 823 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Active Learning. Here, we choose a small subset of the unlabeled dataset to fine-tune the model [11]. In this case, we wish to finetune the CLIP model on the FLO dataset while using a limited amount of labeled data. To achieve this, we estimate the uncertainty of the image embeddings us", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1905", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b488cda5401dfc2a146c54173cab431149259b6dd9f630f094a14b9b4f27c708.jpg", + "image_caption": [ + "Figure 8: Visualizing the predicted embedding distributions from ProbVLM using a large-scale pre-trained diffusion model, i.e., Stable Diffusion. The example is shown for two different captions from CUB dataset, for which the point-estimate embedding vector is obtained via CLIP, and the distribution is obtained via ProbVLM." + ], + "image_footnote": [], + "bbox": [ + 81, + 85, + 888, + 262 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d63eeecb45416afdf5808264cc5b4d1bf3ad2aa15ffd455d18d53bdf10c41547.jpg", + "table_caption": [ + "Metrics" + ], + "table_footnote": [], + "table_body": "
DModelsUncertainty scoreR@1R@5R@10
CUBCLIP-ViT32-COCO11.9231.561.075.8
CLIP-ViT32-Flickr9.3732.464.276.9
CLIP-ViT32-FLO15.4322.849.864.9
FLOCLIP-ViT32-COCO11.8347.979.288.5
CLIP-ViT32-Flickr13.5549.584.693.9
CLIP-ViT32-CUB18.3937.769.482.8
FlickrCLIP-ViT32-COCO9.6188.897.899.8
CLIP-ViT32-CUB16.4925.847.455.6
CLIP-ViT32-FLO13.6752.877.885.2
COCOCLIP-ViT32-Flickr7.2858.180.988.2
CLIP-ViT32-CUB15.378.821.729.8
CLIP-ViT32-FLO12.4423.946.658.8
", + "bbox": [ + 81, + 338, + 468, + 549 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2: Results for the model selection experiment. ProbVLM accurately identifies the best performing source model using only unlabeled samples of the target dataset.", + "bbox": [ + 75, + 553, + 468, + 599 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing ProbVLM (trained using a diverse dataset like COCO). We then select the top-k samples sorted by their mean uncertainty in the visual embeddings and fine-tune the CLIP model using them with a contrastive objective [62]. Results with varying budgets are shown in Figure 7. Selecting samples based on uncertainty scores significantly outperforms random sampling for all considered visual backbones.", + "bbox": [ + 75, + 609, + 468, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Pretrained Model Selection. We are given a set of models trained on different data distributions. We aim to select the best model for the target distribution for which we have unlabeled samples. This has been explored mostly in the context of classification previously [22, 26, 8, 9, 13, 14].", + "bbox": [ + 75, + 718, + 468, + 794 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We consider the specific case of having the CLIP models fine-tuned on three datasets, and the fourth dataset is held out, for which we only have the images. We compute the mean uncertainty on these images using ProbVLM whose weights are interpolated from all the source datasets [93, 94, 32, 31]. This is to ensure that the uncertainties on all these models are comparable. The results for this experiment are", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "shown in Table 2. On CUB, Flickr, and COCO, the source model with the lowest uncertainty has the best performance on the target dataset, and on FLO dataset, the model with the least uncertainty has the 2nd best performance (R@1 of 47.9 vs 49.5 for the best model). This indicates that the uncertainties provided by ProbVLM can be used as a signal to predict the performance on unlabelled samples for retrieval.", + "bbox": [ + 496, + 324, + 893, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Latent Diffusion for Embedding Uncertainty", + "text_level": 1, + "bbox": [ + 498, + 441, + 879, + 458 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To further understand the semantics of the predicted embedding distributions from the ProbVLM, we visualize the text embedding distributions by sampling the embedding vectors from the predicted distribution for a caption (converted to embedding vector using CLIP) and passing it through the pre-trained latent diffusion model using CLIPs text encoder, stable diffusion, as shown in Figure 8 and described in details in Section 3.3. We observe from Figure 8 that the samples obtained closer to the mean (i.e., sampled embedding vector similar to the one generated by CLIP for the caption) lead to meaningful variations in the generated images, e.g., for the left caption, close to the mean of the distribution, the generated samples show variations in the shape and colour of the beak, wings, and feet. Whereas far away from the mean of the distributions, i.e., on the tails, we start seeing images with strong artifacts that no longer preserves the semantics of the caption. We observe this for another example as well shown in Figure 8-(Right). More results are available in the supplementary.", + "bbox": [ + 496, + 465, + 893, + 755 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 768, + 619, + 784 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduce ProbVLM, a post-hoc method for estimating the embedding distribution for a frozen large-scale deterministic vision-language model. We efficiently estimate calibrated uncertainties using our framework and show that such calibrated estimates have a variety of applications in downstream tasks such as model selection and active learning. Furthermore, we perform experiments to interpret em", + "bbox": [ + 496, + 795, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1906", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "bedding distribution predicted by ProbVLM using a large-scale pre-trained latent diffusion model (i.e., Stable Diffusion). We hope our work highlights and inspires future work on efficient methods for probabilistic embeddings.", + "bbox": [ + 76, + 90, + 468, + 151 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported by DFG project number 276693517, by BMBF FKZ: 01IS18039A, by the ERC (853489 - DEXIM), by EXC number 2064/1 - project number 390727645, and by the MUR PNRR project FAIR - Future AI Research (PE00000013) funded by NextGenerationEU. 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IJCV, 2022. 2", + "bbox": [ + 501, + 90, + 890, + 133 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "1910", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/ProbVLM_ Probabilistic Adapter for Frozen Vison-Language Models/52935457-f9bc-4c99-866c-671f6012153b_model.json b/2023/ProbVLM_ Probabilistic Adapter for Frozen Vison-Language Models/52935457-f9bc-4c99-866c-671f6012153b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b863ddc73be9c138af120485a2217125a0bea23c --- /dev/null +++ b/2023/ProbVLM_ Probabilistic Adapter for Frozen Vison-Language Models/52935457-f9bc-4c99-866c-671f6012153b_model.json @@ -0,0 +1,2600 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.138, + 0.131, + 0.833, + 0.154 + ], + "angle": 0, + "content": "ProbVLM: Probabilistic Adapter for Frozen Vison-Language Models" + }, + { + "type": "text", + "bbox": [ + 0.118, + 0.18, + 0.856, + 0.201 + ], + "angle": 0, + "content": "Uddeshya Upadhyay*,1 Shyamgopal Karthik*,1 Massimiliano Mancini2 Zeynep Akata\\(^{1,3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.206, + 0.802, + 0.226 + ], + "angle": 0, + "content": "1University of Tübingen 2University of Trento 3MPI for Intelligent Systems" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.259, + 0.314, + 0.275 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.291, + 0.474, + 0.655 + ], + "angle": 0, + "content": "Large-scale vision-language models (VLMs) like CLIP successfully find correspondences between images and text. Through the standard deterministic mapping process, an image or a text sample is mapped to a single vector in the embedding space. This is problematic: as multiple samples (images or text) can abstract the same concept in the physical world, deterministic embeddings do not reflect the inherent ambiguity in the embedding space. We propose ProbVLM, a probabilistic adapter that estimates probability distributions for the embeddings of pre-trained VLMs via inter/intra-modal alignment in a post-hoc manner without needing large-scale datasets or computing. On four challenging datasets, i.e., COCO, Flickr, CUB, and Oxford-flowers, we estimate the multi-modal embedding uncertainties for two VLMs, i.e., CLIP and BLIP, quantify the calibration of embedding uncertainties in retrieval tasks and show that ProbVLM outperforms other methods. Furthermore, we propose active learning and model selection as two real-world downstream tasks for VLMs and show that the estimated uncertainty aids both tasks. Lastly, we present a novel technique for visualizing the embedding distributions using a large-scale pre-trained latent diffusion model. Code is available at https://github.com/ExplainableML/ProbVLM" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.684, + 0.21, + 0.699 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.71, + 0.47, + 0.877 + ], + "angle": 0, + "content": "Recently, large vision-language models (VLMs) [62, 51, 45, 74, 1, 35] have become exceedingly popular due to their ability to align images and text. These models such as CLIP [62] and BLIP [45] are trained on large-scale datasets such as LAION-400M [70] and YFCC-100M [79] and have shown strong performance when evaluated in a zero-shot fashion (i.e without requiring fine-tuning on specific datasets) for a variety of downstream tasks. One of the most popular applications of VLMs is cross-modal retrieval [86, 88] i.e retrieving images (text) for a queried text (images). However, image-to-text matching (and vice" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.259, + 0.891, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.377, + 0.893, + 0.438 + ], + "angle": 0, + "content": "Figure 1: We provide probabilistic embeddings for deterministic pre-trained vision-language models that are frozen. By capturing the ambiguity inherently present in the inputs, we obtain well-calibrated uncertainty estimates." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.893, + 0.532 + ], + "angle": 0, + "content": "versa) is fundamentally ill-posed due to the inherent ambiguity in either modality [97], i.e. the same caption (or image) can be valid for multiple images (or captions). Therefore, it becomes essential to model the ambiguity inherently present in the various modalities, and combinations thereof." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.534, + 0.895, + 0.67 + ], + "angle": 0, + "content": "Instead of mapping inputs to embeddings, probabilistic embedding methods [57, 10] learn to map input samples to distributions. This is achieved by parameterizing the distributions of the embeddings and training a deep neural network to maximize its likelihood. Although they model ambiguities in the embedding space, such probabilistic models require training deep networks from scratch. This requires access to the large-scale datasets and the computational resources of the recent VLMs [62, 35, 51, 74, 45]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.895, + 0.838 + ], + "angle": 0, + "content": "We propose ProbVLM, a post-hoc probabilistic adapter, the first method to convert the deterministic embeddings provided by a frozen large-scale vision-language models into probabilistic ones, as shown in Figure 1. This enables us to efficiently retain the benefits of large-scale pre-training while learning distributions that model the inherent ambiguities in the different modalities. Our ProbVLM models the embedding distribution as a heteroscedastic probability distribution and is trained using a combination of intra-modal and cross-modal alignment objectives and provides well-calibrated uncertainty estimates, useful for several tasks." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "We demonstrate on two large vision-language datasets, i.e., COCO [46] and Flickr [60], and on two fine-grained image datasets, i.e., CUB [85] and Oxford-Flowers [55] with sentences from [66], that ProbVLM learns calibrated" + }, + { + "type": "page_footnote", + "bbox": [ + 0.101, + 0.888, + 0.262, + 0.901 + ], + "angle": 0, + "content": "*Authors contributed equally." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1899" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.334 + ], + "angle": 0, + "content": "uncertainties without requiring large-scale models to be trained from scratch. This sharply contrasts previous works on probabilistic embeddings [57, 10] that train new models from scratch. We perform a series of analyses to understand the impact of the training objective and to study the properties of the resulting uncertainties. Furthermore, we demonstrate that our uncertainty estimates can be used to select the optimal model from a set of finetuned vision-language models on an unlabeled target dataset. They can also be used to choose the most suitable samples for fine-tuning the model in an active learning setup. Finally, with the help of a pretrained latent diffusion model [67], i.e., Stable Diffusion, we decode sampled embeddings from predicted distribution to visualize the predicted embedding distributions. We show that the predicted embedding distributions indeed capture meaningful modes of variation, that may be interpretable." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.345, + 0.22, + 0.36 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.371, + 0.473, + 0.658 + ], + "angle": 0, + "content": "Vision-Language Models. Such models [62, 51, 74, 1, 45, 47, 44, 100, 101, 90] have become ubiquitous in recent times due to their various applications in image classification [105, 21, 106, 50], cross-modal retrieval [4], as well as open-vocabulary semantic segmentation [24, 96]. The most notable among these is CLIP [62], which consists of an image and text encoder trained on 400M image-text pairs with a contrastive objective [28, 58]. As a result, the model is able to project images and text to a shared embedding space. In this paper, we focus on using the shared embedding space for the task of cross-modal retrieval [60, 46]. Recent works have predominantly relied on large-scale pre-training [62, 51, 74, 1, 104, 70, 69] to project images and text to the same metric space. However, it is essential to note that all of these vision-language models [62, 51, 45, 74, 1] provide deterministic mappings that do not model the inherent ambiguity in the inputs. In this work, we turn a deterministic model (i.e., CLIP) into a probabilistic one, without the need of a large-scale dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Probabilistic Embeddings. These methods [57, 10, 43] provide an elegant solution to estimate the ambiguity present in the inputs [37]. The key idea here is to map inputs to probability distributions in the embedding space, as opposed to point estimates, thereby modeling the inherent ambiguity present in the input. In the context of cross-modal retrieval, this was done by optimizing a probabilistic analog of the contrastive objective to learn distributions for the image and text inputs [10]. Other works have further improved the performance [43, 59, 34], extended this formulation to achieve compositional retrieval [54], and have applied it to other tasks such as video retrieval [59, 17] and tasks like pose estimation [78]. However, most of these works focus on training a model from scratch, thereby not leveraging the power of the pre-trained models that are widely present. The notable exception to this is Probabilistic Face Embed" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.228 + ], + "angle": 0, + "content": "ding (PFE) [73] that proposed to learn a probabilistic embedding while retaining a deterministic pre-trained model for the task of learning face embeddings. However, this was done in a unimodal setting using only images. In this work, we aim to utilize pre-trained vision-language models while providing probabilistic embeddings for both modalities. The probabilistic embeddings derived from our proposed ProbVLM are consistent with cross-modal learning at the core of pretrained vision-language models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.229, + 0.897, + 0.487 + ], + "angle": 0, + "content": "Uncertainty Estimation. These techniques have been widely explored for different tasks in computer vision [36, 7, 41, 42, 56, 102, 83, 53, 80, 27, 68, 103, 65, 81, 77, 82]. Uncertainties can be broadly categorized into aleatoric [36, 23, 3, 89, 12, 2, 87, 56, 95] and epistemic [25, 7, 41, 91, 20, 33, 19, 18] uncertainties. Uncertainty estimation has been used for a variety of tasks, such as identifying model failure [15, 5, 6, 92] and is extensively used in active learning to select the best samples to train the model [71, 38, 64, 72, 99, 98, 61, 52]. While several of these methods focus on training a new Bayesian model from scratch for quantifying the uncertainties in the prediction, some recent works like [83, 102, 29] have proposed methods to estimate the uncertainties for the pre-trained frozen models. However, these works tackle data from a single modality. This work efficiently estimates the uncertainty for the pre-trained frozen large-scale vision-language model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.497, + 0.593, + 0.513 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.895, + 0.6 + ], + "angle": 0, + "content": "We first describe the problem formulation in Section 3.1. In Section 3.2, we describe our proposed method ProbVLM that estimates the complex probability distributions for the embeddings of the frozen deterministic vision-langue encoders, quantifying the uncertainties for their predictions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.606, + 0.704, + 0.621 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.895, + 0.856 + ], + "angle": 0, + "content": "Let \\(\\mathcal{D} = (\\mathcal{I},\\mathcal{C})\\) denote a vision and language dataset, where \\(\\mathcal{I}\\) is a set of images and \\(\\mathcal{C}\\) a set of captions. The two sets are connected via ground-truth matches where multiplicity is plausible. For a caption \\(c\\in \\mathcal{C}\\) (respectively an image \\(i\\in \\mathcal{I}\\)), the set of corresponding images (respectively captions) is given by \\(\\kappa (c)\\subseteq \\mathcal{I}\\) (respectively \\(\\kappa (i)\\subseteq \\mathcal{C}\\)). Recent advances in cross-modal vision-language models [62, 51, 74] often involve learning a shared embedding space, \\(\\mathcal{Z}\\subseteq \\mathbb{R}^{D}\\) (\\(D\\)-dimensional space), for images and texts. This allows quantifying the similarity between cross-modal elements based on their distances in the shared embedding space. The shared embedding space is learned via a set of two encoders: \\(\\Phi_{\\mathcal{V}}(\\cdot ;\\theta_{\\mathcal{V}}):\\mathcal{I}\\to \\mathcal{Z}\\) for the images and \\(\\Phi_{\\mathcal{T}}(\\cdot ;\\theta_{\\mathcal{T}}):\\mathcal{C}\\rightarrow \\mathcal{Z}\\) for the texts, where \\(\\theta_{\\mathcal{V}}\\) and \\(\\theta_{\\mathcal{T}}\\) are the parameters for the respective mapping functions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We consider a real-world scenario where the above set of encoders have already been trained on vast datasets using large models with high computational cost, e.g., CLIP [62]," + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1900" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.092, + 0.885, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.41, + 0.895, + 0.457 + ], + "angle": 0, + "content": "Figure 2: Proposed framework (ProbVLM) takes an existing vision-language model and introduces a probabilistic adapter over the image and text encoders. These adapters predict the parameters of a parameterized distribution for a given embedding. Models are trained by minimizing an objective consisting of intra/cross-modal supervision as detailed in Section 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.469, + 0.473, + 0.668 + ], + "angle": 0, + "content": "SLIP [51], Flava [74] and BLIP [45], are in frozen state, i.e., we have \\(\\Phi_{\\mathcal{V}}(\\cdot;\\theta_{\\mathcal{V}}^{*})\\) and \\(\\Phi_{\\mathcal{T}}(\\cdot;\\theta_{\\mathcal{T}}^{*})\\), where \\(\\theta_{\\mathcal{V}}^{*},\\theta_{\\mathcal{T}}^{*}\\) represents the parameters of the pretrained frozen encoders. These encoders are deterministic and map an image/text to vectors in the shared space, i.e., given a sample image \\(\\mathbf{x}_{\\mathcal{V}}\\) (and similarly sample text \\(\\mathbf{x}_{\\mathcal{T}}\\)), the encoder provides an embedding \\(\\mathbf{z}_{\\mathcal{V}} := \\Phi_{\\mathcal{V}}(\\mathbf{x}_{\\mathcal{V}};\\theta_{\\mathcal{V}}^{*})\\) (and similarly, \\(\\mathbf{z}_{\\mathcal{T}} := \\Phi_{\\mathcal{T}}(\\mathbf{x}_{\\mathcal{T}};\\theta_{\\mathcal{T}}^{*}))\\)). However, the point estimates, \\(\\mathbf{z}\\), do not capture the ambiguity inherent to these embeddings [57, 10, 17] that are better represented by the probability distribution \\(P_{\\mathbf{z}|\\mathbf{x}}\\). Therefore, we propose to estimate \\(P_{\\mathbf{z}|\\mathbf{x}}\\) for the pretrained model efficiently, using ProbVLM, quantifying the uncertainties of the output without re-training the encoders." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.675, + 0.254, + 0.691 + ], + "angle": 0, + "content": "3.2. Building ProbVLM" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.698, + 0.47, + 0.819 + ], + "angle": 0, + "content": "Despite being deterministic, large-scale frozen encoders already provide high-quality point estimates. Our proposed method leverages this fact, using the embeddings \\(\\mathbf{z}\\) as estimates for the mean of the desired distribution \\(P_{\\mathbf{z}|\\mathbf{x}}\\), and estimating the remaining parameters. \\(P_{\\mathbf{z}|\\mathbf{x}}\\) can be modeled as a parametric distribution \\(P_{\\mathbf{z}|\\mathbf{x}}(\\mathbf{z}|\\{\\hat{\\mathbf{z}},\\hat{\\nu}\\dots \\hat{\\rho}\\})\\) where the parameters can be estimated using a deep neural network [20, 36, 41]. Therefore, we introduce ProbVLM," + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.829, + 0.47, + 0.847 + ], + "angle": 0, + "content": "\\[\n\\Psi (\\cdot ; \\zeta) := \\left(\\Psi_ {\\mathcal {V}} (\\cdot ; \\zeta_ {\\mathcal {V}}), \\Psi_ {\\mathcal {T}} (\\cdot ; \\zeta_ {\\mathcal {T}})\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "where \\(\\Psi_{\\mathcal{V}}\\) and \\(\\Psi_{\\mathcal{T}}\\) represents the vision and text encoders parameterized by \\(\\zeta_{\\nu}\\) and \\(\\zeta_{\\tau}\\), respectively. Also, \\(\\zeta := \\zeta_{\\nu} \\cup \\zeta_{\\mathcal{T}}\\) represents the overall parameters for ProbVLM." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.469, + 0.895, + 0.665 + ], + "angle": 0, + "content": "that learns to estimate the parameters \\(\\{\\hat{\\mathbf{z}},\\hat{\\nu}\\dots \\hat{\\rho}\\}\\) with the help of frozen encoders \\(\\Phi_{\\mathcal{V}}(\\cdot ;\\theta_{\\mathcal{V}}^{*})\\) and \\(\\Phi_{\\mathcal{T}}(\\cdot ;\\theta_{\\mathcal{T}}^{*})\\) . The functions \\(\\Psi_{\\mathcal{V}}(\\cdot ;\\zeta_{\\mathcal{V}})\\) and \\(\\Psi_{\\mathcal{T}}(\\cdot ;\\zeta_{\\mathcal{T}})\\) operate on image and text embeddings respectively, but during training depend on both modalities, as discussed later. We design the learning scheme for \\(\\Psi (\\cdot ;\\zeta)\\) such that: (i) Estimated parameter \\(\\hat{\\mathbf{z}}\\) should remain faithful to the original unimodal embedding \\(\\mathbf{z}\\) (intra-modal alignment), this makes the uncertainty of the ProbVLM serve as a good proxy for the uncertainty of frozen encoders. (ii) Estimated parameters \\(\\{\\hat{\\nu}\\dots \\hat{\\rho}\\}\\) should capture the ambiguities and uncertainties present within and across modalities (cross-modal alignment). Figure 2 depicts ProbVLM in tandem with the frozen VLM." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Intra-modal Alignment. To ensure that the mean of the distribution estimated by \\(\\Psi (\\cdot ;\\zeta)\\) reflects the point estimates provided by the frozen encoders, we set up a probabilistic reconstruction problem for the embeddings within the modalities. That is, for a given sample \\(\\mathbf{x}\\) (either from image or text modality), we obtain the embedding from the frozen encoder \\(\\mathbf{z} = \\Phi (\\mathbf{x};\\theta)\\) (using the appropriate encoder), then the modality-specific component of \\(\\Psi (\\cdot ;\\zeta)\\) learns to reconstruct the \\(\\mathbf{z}\\) (let the reconstruction be called \\(\\hat{\\mathbf{z}}\\)). The modality-specific component of \\(\\Psi (\\cdot ;\\zeta)\\) is designed to (i) relax the i.i.d constraints by assuming independent but not identically distributed residuals and (ii) learn the heteroscedasticity for the residuals at the time of reconstruction that may follow the heavy-tailed distributions [83, 84, 40, 39, 30]. The modality-specific component" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.514, + 0.958 + ], + "angle": 0, + "content": "1901" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.138 + ], + "angle": 0, + "content": "is learned by maximizing the likelihood, \\(\\mathcal{L}(\\zeta ;\\{\\mathbf{z}_i\\}_{i = 1}^N)\\) for the embeddings of \\(N\\) samples in the datasets. That is, the modality-specific optimal parameters are given by," + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.15, + 0.47, + 0.207 + ], + "angle": 0, + "content": "\\[\n\\zeta^ {*} := \\underset {\\zeta} {\\operatorname {a r g m a x}} \\mathcal {L} (\\zeta ; \\left\\{\\mathbf {z} _ {i} \\right\\} _ {i = 1} ^ {N}) = \\prod_ {i = 1} ^ {N} \\frac {\\hat {\\beta} _ {i} e ^ {- \\left(\\left| \\bar {\\mathbf {z}} _ {i} - \\mathbf {z} _ {i} \\right| / \\hat {\\alpha} _ {i}\\right) ^ {\\hat {\\beta} _ {i}}}}{2 \\hat {\\alpha} _ {i} \\Gamma \\left(1 / \\hat {\\beta} _ {i}\\right)} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.224, + 0.471, + 0.388 + ], + "angle": 0, + "content": "In the above equation, \\(\\frac{\\hat{\\beta}_i e^{-(|\\hat{\\mathbf{z}}_i - \\mathbf{z}_i| / \\hat{\\alpha}_i)^{\\hat{\\beta}_i}}{2\\hat{\\alpha}_i \\Gamma(1 / \\hat{\\beta}_i)}\\) represents the generalized Gaussian distribution (GGD, represented by \\(\\mathcal{G}\\)) that is capable of modeling heavy-tailed distributions (note the Gaussian and Laplace are special cases of \\(\\mathcal{G}\\) with \\(\\alpha = 1, \\beta = 2\\) and \\(\\alpha = 1, \\beta = 1\\), respectively). The variables \\(\\hat{\\mathbf{z}}_i, \\hat{\\alpha}_i, \\hat{\\beta}_i\\) are the predicted mean, scale, and shape parameters of \\(\\mathcal{G}\\) from our modality-specific components for the given input \\(\\mathbf{z}_i\\). We obtain modality-specific optimal parameters by minimizing negative log-likelihood (equivalent to Equation 2). Given \\(\\mathbf{z}\\) and predicted \\(\\hat{\\mathbf{z}}, \\hat{\\alpha}, \\hat{\\beta}\\), loss is given by," + }, + { + "type": "equation", + "bbox": [ + 0.124, + 0.412, + 0.47, + 0.452 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {r e c}} (\\zeta) := \\left(\\frac {| \\hat {\\mathbf {z}} - \\mathbf {z} |}{\\hat {\\alpha}}\\right) ^ {\\hat {\\beta}} - \\log \\frac {\\hat {\\beta}}{\\hat {\\alpha}} + \\log \\Gamma \\left(\\frac {1}{\\hat {\\beta}}\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.465, + 0.47, + 0.586 + ], + "angle": 0, + "content": "Therefore, the vision-specific component of ProbVLM, \\(\\Psi (\\cdot ;\\zeta_{\\nu}))\\), is trained by minimizing the Equation 3 using image embeddings, we denote this loss as \\(L_{\\mathrm{rec}}^{\\mathcal{V}}(\\zeta_V)\\). Similarly the text-specific component, \\(\\Psi (\\cdot ;\\zeta_T)\\), is trained by minimizing \\(L_{\\mathrm{rec}}^{\\mathcal{T}}(\\zeta_T)\\). As discussed next, we also enforce cross-modal alignment so that the predicted distribution of ProbVLM captures the uncertainties across modalities from one-to-many correspondences for an embedding." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.588, + 0.471, + 0.772 + ], + "angle": 0, + "content": "Cross-modal Alignment. While the intra-modal alignment seeks to match the means of the output distribution from ProbVLM to the embeddings derived from frozen vision-language encoders, we also enforce the image and text embedding output distribution (from ProbVLM) belonging to similar concepts to remain close to each other. That is, given an image and text embedding pair \\((\\mathbf{z}_{\\mathcal{V}},\\mathbf{z}_{\\mathcal{T}})\\) (from frozen model) representing similar concepts, the output distributions from \\(\\Psi (\\cdot ;\\zeta),\\mathcal{G}(\\mathbf{z};\\hat{\\mathbf{z}}_{\\mathcal{V}},\\hat{\\alpha}_{\\mathcal{V}},\\hat{\\beta}_{\\mathcal{V}})\\) and \\(\\mathcal{G}(\\mathbf{z};\\hat{\\mathbf{z}}_{\\mathcal{T}},\\hat{\\alpha}_{\\mathcal{T}},\\hat{\\beta}_{\\mathcal{T}})\\) (later referred to as \\(\\mathcal{G}_{\\mathcal{V}}(\\mathbf{z}))\\) and \\(\\mathcal{G}_{\\mathcal{T}}(\\mathbf{z}))\\) should match. This can be measured directly from the likelihood as, \\(p(\\mathbf{z}_v = \\mathbf{z}_u)\\), where \\(\\mathbf{z}_v\\sim \\mathcal{G}_{\\mathcal{V}}(\\mathbf{z})\\) and \\(\\mathbf{z}_u\\sim \\mathcal{G}_{\\mathcal{T}}(\\mathbf{z})\\) as in [73], i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.795, + 0.47, + 0.827 + ], + "angle": 0, + "content": "\\[\np \\left(\\mathbf {z} _ {v} = \\mathbf {z} _ {u}\\right) := \\iint \\mathcal {G} _ {\\mathcal {Y}} \\left(\\mathbf {z} _ {v}\\right) \\mathcal {G} _ {\\mathcal {T}} \\left(\\mathbf {z} _ {u}\\right) \\delta \\left(\\mathbf {z} _ {v} - \\mathbf {z} _ {u}\\right) d \\mathbf {z} _ {v} d \\mathbf {z} _ {u} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.901 + ], + "angle": 0, + "content": "where \\(\\delta (\\cdot)\\) refers to the Dirac-delta distribution. The above integral can be simplified further by defining \\(\\Delta \\mathbf{z} = \\mathbf{z}_v - \\mathbf{z}_u\\) and seeking \\(p(\\Delta \\mathbf{z}) = 0\\). As both \\(\\mathbf{z}_v\\) and \\(\\mathbf{z}_u\\) are GGD random variables, \\(\\Delta \\mathbf{z}\\) follows the distribution based on the" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.813, + 0.107 + ], + "angle": 0, + "content": "Bivariate Fox H-function [76, 48, 49] given by," + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.116, + 0.776, + 0.138 + ], + "angle": 0, + "content": "\\[\n\\Delta z \\sim \\frac {1}{2 \\Gamma (1 / \\hat {\\beta} _ {\\mathcal {V}}) , \\Gamma (1 / \\hat {\\beta} _ {\\mathcal {T}})} \\times\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.506, + 0.14, + 0.892, + 0.185 + ], + "angle": 0, + "content": "\\[\n\\int \\mathcal {H} _ {1, 2} ^ {1, 1} \\left[ A t ^ {2} \\left| \\begin{array}{l} \\left(1 - \\frac {1}{\\bar {\\mathbf {z}} _ {\\mathcal {V}}}, \\frac {1}{\\bar {\\mathbf {z}} _ {\\mathcal {T}}}\\right) \\\\ (0, 1) \\left(\\frac {1}{2}, 1\\right) \\end{array} \\right. \\right] \\mathcal {H} _ {1, 2} ^ {1, 1} \\left[ B t ^ {2} \\left| \\begin{array}{l} \\left(1 - \\frac {1}{\\bar {\\mathbf {z}} _ {\\mathcal {T}}}, \\frac {1}{\\bar {\\mathbf {z}} _ {\\mathcal {T}}}\\right) \\\\ (0, 1) \\left(\\frac {1}{2}, 1\\right) \\end{array} \\right. \\right] \\cos t (\\mu - z) d t \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.196, + 0.892, + 0.28 + ], + "angle": 0, + "content": "Where \\(A = \\frac{\\hat{\\alpha}_{\\mathcal{V}}^2\\Gamma(1 / \\hat{\\beta}_{\\mathcal{V}})}{4\\Gamma(3 / \\hat{\\beta}_{\\mathcal{V}})}\\), \\(B = \\frac{\\hat{\\alpha}_{\\mathcal{T}}^2\\Gamma(1 / \\hat{\\beta}_{\\mathcal{T}})}{4\\Gamma(3 / \\hat{\\beta}_{\\mathcal{T}})}\\), \\(\\mu = \\hat{\\mathbf{z}}_v - \\hat{\\mathbf{z}}_u\\), and \\(\\mathcal{H}\\) is the Fox \\(H\\) function [76, 48, 49]. Equation 5 does not provide a scalable objective function suitable for training deep neural networks. Hence, we propose an approximation that is easily scalable for deep-learning models given by," + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.301, + 0.892, + 0.366 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} p (\\mathbf {z} _ {v} = \\mathbf {z} _ {u}) = \\iint \\mathcal {G} _ {\\mathcal {V}} (\\mathbf {z} _ {v}) \\mathcal {G} _ {\\mathcal {T}} (\\mathbf {z} _ {u}) \\delta (\\mathbf {z} _ {v} - \\mathbf {z} _ {u}) d \\mathbf {z} _ {v} d \\mathbf {z} _ {u} \\\\ \\approx \\int \\frac {1}{2} \\left(\\mathcal {G} _ {\\mathcal {V}} (\\mathbf {z}) \\delta (\\mathbf {z} - \\mathbf {z} _ {\\mathcal {T}}) + \\mathcal {G} _ {\\mathcal {T}} (\\mathbf {z}) \\delta (\\mathbf {z} - \\mathbf {z} _ {\\mathcal {V}})\\right) d \\mathbf {z} \\tag {6} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.373, + 0.892, + 0.51 + ], + "angle": 0, + "content": "The appendix shows details of the above equation. The first term in the integral, \\(\\int \\mathcal{G}_{\\mathcal{V}}(\\mathbf{z})\\delta (\\mathbf{z} - \\mathbf{z}_{\\mathcal{T}})d\\mathbf{z}\\), is the likelihood of the text embedding \\(\\mathbf{z}_{\\mathcal{T}}\\) under the predicted distribution, \\(\\mathcal{G}_{\\mathcal{V}}(\\mathbf{z})\\), for the visual embedding. Similarly, the second term is the likelihood of the visual embedding \\(\\mathbf{z}_{\\mathcal{V}}\\) under the predicted distribution, \\(\\mathcal{G}_{\\mathcal{T}}(\\mathbf{z})\\), for the text embedding. Negative log of Equation 6 leads to a scalable objective function that can be used to learn the optimal parameters for vision and text components of ProbVLM \\((\\Psi_{\\mathcal{V}}(\\cdot ;\\zeta_{\\mathcal{V}})\\) and \\(\\Psi_{\\mathcal{T}}(\\cdot ;\\zeta_{\\mathcal{T}}))\\)" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.531, + 0.892, + 0.638 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {\\text {c r o s s}} (\\zeta_ {\\mathcal {V}}, \\zeta_ {\\mathcal {T}}) := \\underbrace {\\left(\\frac {| \\hat {\\mathbf {z}} _ {\\mathcal {V}} - \\mathbf {z} _ {\\mathcal {T}} |}{\\hat {\\alpha} _ {\\mathcal {V}}}\\right) ^ {\\hat {\\beta} _ {\\mathcal {V}}} - \\log \\frac {\\hat {\\beta} _ {\\mathcal {V}}}{\\hat {\\alpha} _ {\\mathcal {V}}} + \\log \\Gamma \\left(\\frac {1}{\\hat {\\beta} _ {\\mathcal {V}}}\\right)} _ {\\text {C r o s s - m o d a l : v i s i o n} \\rightarrow \\text {t e x t}} + \\\\ \\underbrace {\\left(\\frac {| \\hat {\\mathbf {z}} _ {\\mathcal {T}} - \\mathbf {z} _ {\\mathcal {V}} |}{\\hat {\\alpha} _ {\\mathcal {T}}}\\right) ^ {\\hat {\\beta} _ {\\mathcal {T}}} - \\log \\frac {\\hat {\\beta} _ {\\mathcal {T}}}{\\hat {\\alpha} _ {\\mathcal {T}}} + \\log \\Gamma \\left(\\frac {1}{\\hat {\\beta} _ {\\mathcal {T}}}\\right)} _ {\\text {C r o s s - m o d a l : t e x t} \\rightarrow \\text {v i s i o n}} \\tag {7} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.646, + 0.89, + 0.662 + ], + "angle": 0, + "content": "The overall objective used for ProbVLM is designed to be," + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.686, + 0.891, + 0.717 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {P r o b V L M}} \\left(\\zeta_ {\\mathcal {V}}, \\zeta_ {\\mathcal {T}}\\right) = L _ {\\text {r e c}} ^ {\\mathcal {V}} \\left(\\zeta_ {\\mathcal {V}}\\right) + L _ {\\text {r e c}} ^ {\\mathcal {T}} \\left(\\zeta_ {\\mathcal {T}}\\right) + \\lambda_ {\\text {c r o s s}} L _ {\\text {c r o s s}} \\left(\\zeta_ {\\mathcal {V}}, \\zeta_ {\\mathcal {T}}\\right) \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.728, + 0.89, + 0.757 + ], + "angle": 0, + "content": "where \\(\\lambda_{cross}\\) is a hyperparameter controlling the relative contribution of inter-intra modality terms." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.759, + 0.892, + 0.904 + ], + "angle": 0, + "content": "Uncertainty Quantification. Given embedding \\(\\mathbf{z}\\) from a frozen encoder, predicted distributions from the trained ProbVLM (output from the appropriate component) allows aleatoric uncertainty estimation as \\(\\hat{\\sigma}_{\\mathrm{aleatoric}}^2 = \\frac{\\hat{\\alpha}^2\\Gamma(3 / \\hat{\\beta})}{\\Gamma(1 / \\hat{\\beta})}\\). Moreover, we design both \\(\\Psi_{\\mathcal{V}}\\) and \\(\\Psi_{\\mathcal{T}}\\) to be simple 3-layer MLPs with dropout layers (with dropout probability set to 0.1 during training). Activating dropouts during inference, with multiple forward passes (say \\(M\\)), allows estimating the epistemic uncertainty, \\(\\hat{\\sigma}_{\\mathrm{epistemic}}^2 = \\frac{1}{M}\\sum_{m = 1}^{M}(\\hat{\\mathbf{z}}_m - \\hat{\\mathbf{z}}_m)\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1902" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.089, + 0.863, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.31, + 0.863, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.517, + 0.893, + 0.547 + ], + "angle": 0, + "content": "Figure 3: Measuring the calibration with various post-hoc method for Image-to-Text and Text-to-Image retrieval when trained on (top) CUB and (bottom) COCO, and evaluated on CUB, COCO, Flickr, FLO." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.552, + 0.395, + 0.573 + ], + "angle": 0, + "content": "\\(\\frac{1}{M}\\sum_{j = 1}^{M}\\hat{\\mathbf{z}}_j)^2\\) We estimate total uncertainty as," + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.584, + 0.47, + 0.604 + ], + "angle": 0, + "content": "\\[\n\\hat {\\sigma} _ {\\text {t o t a l}} ^ {2} = \\hat {\\sigma} _ {\\text {e p i s t e m i c}} ^ {2} + \\hat {\\sigma} _ {\\text {a l e a t o r i c}} ^ {2} \\tag {9}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.614, + 0.47, + 0.63 + ], + "angle": 0, + "content": "3.3. Latent Diffusion for Probabilistic Embeddings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.47, + 0.744 + ], + "angle": 0, + "content": "For a given text embedding \\(\\mathbf{z}_{\\mathcal{T}}\\), the distribution estimated via ProbVLM, \\(\\mathcal{G}(\\mathbf{z};\\hat{\\mathbf{z}}_{\\mathcal{T}},\\hat{\\alpha}_{\\mathcal{T}},\\hat{\\beta}_{\\mathcal{T}})\\) can be visualized by drawing samples from the predicted distribution of vectors (say, \\(\\{\\hat{\\mathbf{z}}_{\\mathcal{T},i}\\}_{i = 1}^{Q}\\)) and passing them through a latent diffusion model, e.g., Stable Diffusion (say, \\(\\Omega (\\cdot ;\\theta_{\\Omega}^{*}))\\) using CLIP text encoder, to synthesize the set of samples (say, \\(J\\)) from the corresponding distribution of images, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.201, + 0.754, + 0.469, + 0.773 + ], + "angle": 0, + "content": "\\[\nJ := \\left\\{\\boldsymbol {\\Omega} \\left(\\hat {\\mathbf {z}} _ {i}; \\theta_ {\\Omega}\\right) \\right\\} _ {i = 1} ^ {Q} \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.785, + 0.468, + 0.8 + ], + "angle": 0, + "content": "Section 4.4 uses this to visualize the predicted distributions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.815, + 0.312, + 0.832 + ], + "angle": 0, + "content": "4. Experiments and Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "We start by highlighting our tasks, datasets, and evaluation metrics. We also compare our model to various state-of-the-art methods quantitatively and qualitatively in Section 4.1. In Section 4.2, we provide an ablation analysis," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.555, + 0.892, + 0.586 + ], + "angle": 0, + "content": "and Section 4.3 demonstrates some real-world applications of ProbVLM for model selection and active learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Datasets, Metrics, and Baselines. We use the MS-COCO [46], Flickr-30k [60], and the CUB [85] as they are widely used for cross-modal retrieval [10, 16, 75]. Furthermore, we adapt the Oxford-Flowers 102 (FLO) dataset [55] similar to [10] as an additional benchmark for cross-modal retrieval in a fine-grained setting. We evaluate the performance of both Image-to-Text retrieval and Text-to-Image Retrieval using the Recall@k (R@k) metric. To evaluate the calibration of the uncertainty estimates, we define uncertainty levels [10] and use the Spearman rank correlation (denoted by \\( S \\)) between the uncertainty level and the Recall@k for retrieval. For an ideal model, performance would decrease monotonically with increasing uncertainty levels, leading to a score of -1. We also compute the \\( R^2 \\) for the regression fit between the uncertainty levels and R@1 performances to measure if the drop in performance follows a linear trend. Finally, we also measure the product of these two scores (as a unified metric), i.e., \\( -SR^2 \\), which should be 1.0 for an ideal model. Since there is no prior work to estimate probabilistic embeddings from a deterministic model" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1903" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.092, + 0.472, + 0.541 + ], + "angle": 0, + "content": "
VLMMetricsi2tt2i
COCOFlickrFLOCUBCOCOFlickrFLOCUB
CLIPS↓-0.99-0.70-0.90-0.60-0.30-0.70-0.99-0.89
R2↑0.930.710.620.670.350.500.990.70
-SR2↑0.930.490.560.400.100.350.990.63
S↓-0.79-0.190.60-0.600.790.30-0.89-0.10
R2↑0.590.010.300.280.740.440.520.00
-SR2↑0.470.00-0.180.17-0.59-0.130.47-0.00
S↓-0.89-0.30-0.30-0.600.300.09-0.700.30
R2↑0.750.070.070.200.160.010.570.01
-SR2↑0.680.020.020.12-0.05-0.000.40-0.00
S↓-0.79-0.300.00-0.60-0.10-0.19-0.89-0.50
R2↑0.690.090.000.410.260.0710.800.15
-SR2↑0.550.030.000.240.000.010.730.07
BLIPS↓-0.87-0.79-0.74-0.66-0.43-0.38-0.31-0.22
R2↑0.920.830.680.610.520.480.450.38
-SR2↑0.800.660.500.400.220.180.140.08
S↓-0.82-0.74-0.63-0.63-0.39-0.32-0.28-0.18
R2↑0.720.760.620.440.480.380.390.37
-SR2↑0.580.570.390.270.190.120.110.07
S↓-0.76-0.53-0.60-0.44-0.28-0.26-0.28-0.21
R2↑0.810.560.600.530.500.340.440.36
-SR2↑0.620.290.360.230.140.090.120.08
S↓-0.44-0.33-0.74-0.60-0.19-0.26-0.21-0.21
R2↑0.660.560.420.550.490.230.350.36
-SR2↑0.290.180.310.330.100.060.070.08
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.551, + 0.47, + 0.613 + ], + "angle": 0, + "content": "Table 1: Metrics to evaluate the calibration of the uncertainty estimates for both CLIP [62] and BLIP [45] Vision-Language models for all considered methods, trained on COCO and evaluated on COCO, Flickr, CUB, and FLO." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.47, + 0.835 + ], + "angle": 0, + "content": "in a cross-modal setting, we adapt a few existing ideas for the task. The first baseline is adapted from PFE [73], where we learn the covariances for the heteroscedastic Gaussian distribution while keeping the mean fixed to the embeddings derived from the frozen encoders in each modality. The second is to use the soft-contrastive objective of PCME[10] to train a probabilistic adapter in a post-hoc fashion. Finally, we also have a baseline that performs Test-Time Data Augmentation (TTDA) on the inputs [2, 87]. This is done by perturbing the images and masking out words in the text. While TTDA does not require additional training, we train our ProbVLM and other baselines on datasets like COCO, Flickr, CUB, and FLO." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Implementation Details. Our ProbVLM consists of a Multi-Layer Perceptron (MLP) for both the image and text encoder, each consisting of an input layer going from embedding dimension to 256, a hidden layer of size 256, and" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "an output layer going from 256 to embedding dimensions. This is trained for 100 epochs with a learning rate of \\( 1e^{-4} \\). More details are available in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.168, + 0.818, + 0.185 + ], + "angle": 0, + "content": "4.1. Calibrated Uncertainty via ProbVLM" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.199, + 0.892, + 0.577 + ], + "angle": 0, + "content": "We investigate the calibration of the uncertainty derived from ProbVLM for the cross-modal retrieval task. All models trained on CUB and COCO were evaluated on all four datasets. Calibration plots are illustrated in Figure 3. We observe that the R@1 performance consistently drops for ProbVLM as we increase the uncertainty levels, whereas the baselines rarely see a monotonic drop in performance. We quantify this performance in Table 1. The highest score of 0.93 for \\(-SR^2\\) (i2t) on the COCO dataset indicates a decreasing performance trend with increasing uncertainty. Notably, the uncertainty estimates indicate the average performance in different bins even when ProbVLM is evaluated on datasets that are different from the train set. In some cases, we see that ProbVLM even achieves a nearly perfect score \\((-SR^2\\) of 0.99, with CLIP VLM on FLO, after training on COCO for Image-to-Text Retrieval). On the contrary, we find that the baselines often achieve poor scores. It is important to note that all these models use the same underlying embeddings and achieve the same performance on the retrieval task. Of all the considered methods, ProbVLM provides the most calibrated uncertainty estimates. We see similar trends for ProbVLM with BLIP [45], where ProbVLM achieves a \\(-SR^2\\) of 0.80, when trained on COCO and evaluated on COCO, compared to other methods like PFE\\* (0.58), PCME\\* (0.62), and TTDA (0.29)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Figure 4-(Top) visualizes the ambiguities captured by ProbVLM on the visual embeddings. We take a bird image (source) from the CUB dataset and obtain the probability distribution for the visual embedding of that sample; we then compute the likelihood of the visual embeddings (i.e., point estimates derived from CLIP) for the other samples of CUB and COCO datasets, under the source distribution. We notice that within the CUB dataset, the bird images similar to the source image have a higher likelihood compared to other bird images. Also, the images from the COCO dataset tend to have a lower likelihood. However, some images from the COCO dataset have a likelihood similar to the samples from CUB. We visualize these samples and discover them to be bird images. Moreover, the overlapping region between CUB and COCO has samples from the COCO dataset that are ambiguous and related to bird images as they have similar backgrounds, etc. On the contrary, when a similar analysis is performed using the CLIP (by measuring the distance between the embeddings instead of likelihood, Figure 4-(Bottom)), we notice that the two datasets are well separated and ambiguities are not captured." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1904" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.089, + 0.468, + 0.337 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.347, + 0.473, + 0.455 + ], + "angle": 0, + "content": "Figure 4: Visualizing the uncertainties of the vision encoder captured by ProbVLM. Fixing an image from CUB, we obtain the predicted embedding distribution and compute the likelihood of all other samples in CUB and COCO. We observe that the images in COCO are similar/ambiguous to CUB overlap (Top). However, deterministic embeddings lead to a separation between the two datasets (Bottom)." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.469, + 0.275, + 0.609 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.282, + 0.469, + 0.473, + 0.61 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.619, + 0.47, + 0.651 + ], + "angle": 0, + "content": "Figure 5: Plot indicating (left) necessity of the cross-modal alignment and (right) data required to train ProbVLM." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.667, + 0.277, + 0.813 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.668, + 0.471, + 0.813 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.823, + 0.471, + 0.869 + ], + "angle": 0, + "content": "Figure 6: Uncertainty increases with increased masking of the input images (Left) and texts (Right). Results with three vision encoders and one language encoder from CLIP." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.895, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.309, + 0.893, + 0.356 + ], + "angle": 0, + "content": "Figure 7: Results for active learning, with different vision encoders and varying training budgets. For a given encoder, uncertainty-based sampling outperforms random sampling." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.37, + 0.611, + 0.385 + ], + "angle": 0, + "content": "4.2. Ablations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.394, + 0.893, + 0.652 + ], + "angle": 0, + "content": "We ablate different components of our proposed ProbVLM, to provide a deeper understanding of its workings. First, we perform a sensitivity analysis on the cross-modal reconstruction objective, as shown in Figure 5-(Left), for ProbVLM on BLIP using the COCO dataset. We need a non-zero coefficient of the cross-modal loss to ensure that ProbVLM learns meaningful uncertainties that capture the ambiguities across modalities and are well-correlated with its performance on the downstream retrieval task. Similarly, having a large co-efficient for the cross-modal loss could hinder learning a faithful identity reconstruction, thereby hampering the performance of the downstream evaluation. Next, we investigate the amount of data that is required to train ProbVLM in Figure 5-(Right). We get satisfactory calibration of the uncertainty estimates while using only \\(50\\%\\) of the dataset (shown for ProbVLM on BLIP using COCO), indicating that ProbVLM is highly data-efficient." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.652, + 0.892, + 0.743 + ], + "angle": 0, + "content": "Further, we investigate the uncertainties by masking out increasing portions of the input image/text in Figure 6. We use three different CLIP backbones for the images, ViT-B/32, ViT-B/16, ResNet50, and GPT-based language encoder from CLIP [62, 63]. The mean uncertainty steadily increases as we mask increasing amounts of input." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.754, + 0.634, + 0.77 + ], + "angle": 0, + "content": "4.3. Applications" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.778, + 0.892, + 0.824 + ], + "angle": 0, + "content": "We study the utility of the uncertainty estimates derived from ProbVLM on two critical applications not well reviewed for VLMs: active learning and model selection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Active Learning. Here, we choose a small subset of the unlabeled dataset to fine-tune the model [11]. In this case, we wish to finetune the CLIP model on the FLO dataset while using a limited amount of labeled data. To achieve this, we estimate the uncertainty of the image embeddings us" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1905" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.086, + 0.889, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.266, + 0.895, + 0.312 + ], + "angle": 0, + "content": "Figure 8: Visualizing the predicted embedding distributions from ProbVLM using a large-scale pre-trained diffusion model, i.e., Stable Diffusion. The example is shown for two different captions from CUB dataset, for which the point-estimate embedding vector is obtained via CLIP, and the distribution is obtained via ProbVLM." + }, + { + "type": "table_caption", + "bbox": [ + 0.324, + 0.326, + 0.37, + 0.337 + ], + "angle": 0, + "content": "Metrics" + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.339, + 0.47, + 0.55 + ], + "angle": 0, + "content": "
DModelsUncertainty scoreR@1R@5R@10
CUBCLIP-ViT32-COCO11.9231.561.075.8
CLIP-ViT32-Flickr9.3732.464.276.9
CLIP-ViT32-FLO15.4322.849.864.9
FLOCLIP-ViT32-COCO11.8347.979.288.5
CLIP-ViT32-Flickr13.5549.584.693.9
CLIP-ViT32-CUB18.3937.769.482.8
FlickrCLIP-ViT32-COCO9.6188.897.899.8
CLIP-ViT32-CUB16.4925.847.455.6
CLIP-ViT32-FLO13.6752.877.885.2
COCOCLIP-ViT32-Flickr7.2858.180.988.2
CLIP-ViT32-CUB15.378.821.729.8
CLIP-ViT32-FLO12.4423.946.658.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.554, + 0.47, + 0.601 + ], + "angle": 0, + "content": "Table 2: Results for the model selection experiment. ProbVLM accurately identifies the best performing source model using only unlabeled samples of the target dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.61, + 0.47, + 0.716 + ], + "angle": 0, + "content": "ing ProbVLM (trained using a diverse dataset like COCO). We then select the top-k samples sorted by their mean uncertainty in the visual embeddings and fine-tune the CLIP model using them with a contrastive objective [62]. Results with varying budgets are shown in Figure 7. Selecting samples based on uncertainty scores significantly outperforms random sampling for all considered visual backbones." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.719, + 0.47, + 0.795 + ], + "angle": 0, + "content": "Pretrained Model Selection. We are given a set of models trained on different data distributions. We aim to select the best model for the target distribution for which we have unlabeled samples. This has been explored mostly in the context of classification previously [22, 26, 8, 9, 13, 14]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We consider the specific case of having the CLIP models fine-tuned on three datasets, and the fourth dataset is held out, for which we only have the images. We compute the mean uncertainty on these images using ProbVLM whose weights are interpolated from all the source datasets [93, 94, 32, 31]. This is to ensure that the uncertainties on all these models are comparable. The results for this experiment are" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.325, + 0.895, + 0.433 + ], + "angle": 0, + "content": "shown in Table 2. On CUB, Flickr, and COCO, the source model with the lowest uncertainty has the best performance on the target dataset, and on FLO dataset, the model with the least uncertainty has the 2nd best performance (R@1 of 47.9 vs 49.5 for the best model). This indicates that the uncertainties provided by ProbVLM can be used as a signal to predict the performance on unlabelled samples for retrieval." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.442, + 0.88, + 0.459 + ], + "angle": 0, + "content": "4.4. Latent Diffusion for Embedding Uncertainty" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.467, + 0.895, + 0.756 + ], + "angle": 0, + "content": "To further understand the semantics of the predicted embedding distributions from the ProbVLM, we visualize the text embedding distributions by sampling the embedding vectors from the predicted distribution for a caption (converted to embedding vector using CLIP) and passing it through the pre-trained latent diffusion model using CLIPs text encoder, stable diffusion, as shown in Figure 8 and described in details in Section 3.3. We observe from Figure 8 that the samples obtained closer to the mean (i.e., sampled embedding vector similar to the one generated by CLIP for the caption) lead to meaningful variations in the generated images, e.g., for the left caption, close to the mean of the distribution, the generated samples show variations in the shape and colour of the beak, wings, and feet. Whereas far away from the mean of the distributions, i.e., on the tails, we start seeing images with strong artifacts that no longer preserves the semantics of the caption. We observe this for another example as well shown in Figure 8-(Right). More results are available in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.77, + 0.62, + 0.785 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We introduce ProbVLM, a post-hoc method for estimating the embedding distribution for a frozen large-scale deterministic vision-language model. We efficiently estimate calibrated uncertainties using our framework and show that such calibrated estimates have a variety of applications in downstream tasks such as model selection and active learning. Furthermore, we perform experiments to interpret em" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1906" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "bedding distribution predicted by ProbVLM using a large-scale pre-trained latent diffusion model (i.e., Stable Diffusion). We hope our work highlights and inspires future work on efficient methods for probabilistic embeddings." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.154, + 0.473, + 0.29 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported by DFG project number 276693517, by BMBF FKZ: 01IS18039A, by the ERC (853489 - DEXIM), by EXC number 2064/1 - project number 390727645, and by the MUR PNRR project FAIR - Future AI Research (PE00000013) funded by NextGenerationEU. 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Through the standard deterministic mapping process, an image or a text sample is mapped to a single vector in the embedding space. This is problematic: as multiple samples (images or text) can abstract the same concept in the physical world, deterministic embeddings do not reflect the inherent ambiguity in the embedding space. We propose ProbVLM, a probabilistic adapter that estimates probability distributions for the embeddings of pre-trained VLMs via inter/intra-modal alignment in a post-hoc manner without needing large-scale datasets or computing. On four challenging datasets, i.e., COCO, Flickr, CUB, and Oxford-flowers, we estimate the multi-modal embedding uncertainties for two VLMs, i.e., CLIP and BLIP, quantify the calibration of embedding uncertainties in retrieval tasks and show that ProbVLM outperforms other methods. Furthermore, we propose active learning and model selection as two real-world downstream tasks for VLMs and show that the estimated uncertainty aids both tasks. Lastly, we present a novel technique for visualizing the embedding distributions using a large-scale pre-trained latent diffusion model. Code is available at https://github.com/ExplainableML/ProbVLM + +# 1. Introduction + +Recently, large vision-language models (VLMs) [62, 51, 45, 74, 1, 35] have become exceedingly popular due to their ability to align images and text. These models such as CLIP [62] and BLIP [45] are trained on large-scale datasets such as LAION-400M [70] and YFCC-100M [79] and have shown strong performance when evaluated in a zero-shot fashion (i.e without requiring fine-tuning on specific datasets) for a variety of downstream tasks. One of the most popular applications of VLMs is cross-modal retrieval [86, 88] i.e retrieving images (text) for a queried text (images). However, image-to-text matching (and vice + +![](images/1c61ba78ab3c25afd80acda7c5326db9f89787588a23993bdcf5b94938ea196c.jpg) +Figure 1: We provide probabilistic embeddings for deterministic pre-trained vision-language models that are frozen. By capturing the ambiguity inherently present in the inputs, we obtain well-calibrated uncertainty estimates. + +versa) is fundamentally ill-posed due to the inherent ambiguity in either modality [97], i.e. the same caption (or image) can be valid for multiple images (or captions). Therefore, it becomes essential to model the ambiguity inherently present in the various modalities, and combinations thereof. + +Instead of mapping inputs to embeddings, probabilistic embedding methods [57, 10] learn to map input samples to distributions. This is achieved by parameterizing the distributions of the embeddings and training a deep neural network to maximize its likelihood. Although they model ambiguities in the embedding space, such probabilistic models require training deep networks from scratch. This requires access to the large-scale datasets and the computational resources of the recent VLMs [62, 35, 51, 74, 45]. + +We propose ProbVLM, a post-hoc probabilistic adapter, the first method to convert the deterministic embeddings provided by a frozen large-scale vision-language models into probabilistic ones, as shown in Figure 1. This enables us to efficiently retain the benefits of large-scale pre-training while learning distributions that model the inherent ambiguities in the different modalities. Our ProbVLM models the embedding distribution as a heteroscedastic probability distribution and is trained using a combination of intra-modal and cross-modal alignment objectives and provides well-calibrated uncertainty estimates, useful for several tasks. + +We demonstrate on two large vision-language datasets, i.e., COCO [46] and Flickr [60], and on two fine-grained image datasets, i.e., CUB [85] and Oxford-Flowers [55] with sentences from [66], that ProbVLM learns calibrated + +uncertainties without requiring large-scale models to be trained from scratch. This sharply contrasts previous works on probabilistic embeddings [57, 10] that train new models from scratch. We perform a series of analyses to understand the impact of the training objective and to study the properties of the resulting uncertainties. Furthermore, we demonstrate that our uncertainty estimates can be used to select the optimal model from a set of finetuned vision-language models on an unlabeled target dataset. They can also be used to choose the most suitable samples for fine-tuning the model in an active learning setup. Finally, with the help of a pretrained latent diffusion model [67], i.e., Stable Diffusion, we decode sampled embeddings from predicted distribution to visualize the predicted embedding distributions. We show that the predicted embedding distributions indeed capture meaningful modes of variation, that may be interpretable. + +# 2. Related Work + +Vision-Language Models. Such models [62, 51, 74, 1, 45, 47, 44, 100, 101, 90] have become ubiquitous in recent times due to their various applications in image classification [105, 21, 106, 50], cross-modal retrieval [4], as well as open-vocabulary semantic segmentation [24, 96]. The most notable among these is CLIP [62], which consists of an image and text encoder trained on 400M image-text pairs with a contrastive objective [28, 58]. As a result, the model is able to project images and text to a shared embedding space. In this paper, we focus on using the shared embedding space for the task of cross-modal retrieval [60, 46]. Recent works have predominantly relied on large-scale pre-training [62, 51, 74, 1, 104, 70, 69] to project images and text to the same metric space. However, it is essential to note that all of these vision-language models [62, 51, 45, 74, 1] provide deterministic mappings that do not model the inherent ambiguity in the inputs. In this work, we turn a deterministic model (i.e., CLIP) into a probabilistic one, without the need of a large-scale dataset. + +Probabilistic Embeddings. These methods [57, 10, 43] provide an elegant solution to estimate the ambiguity present in the inputs [37]. The key idea here is to map inputs to probability distributions in the embedding space, as opposed to point estimates, thereby modeling the inherent ambiguity present in the input. In the context of cross-modal retrieval, this was done by optimizing a probabilistic analog of the contrastive objective to learn distributions for the image and text inputs [10]. Other works have further improved the performance [43, 59, 34], extended this formulation to achieve compositional retrieval [54], and have applied it to other tasks such as video retrieval [59, 17] and tasks like pose estimation [78]. However, most of these works focus on training a model from scratch, thereby not leveraging the power of the pre-trained models that are widely present. The notable exception to this is Probabilistic Face Embed + +ding (PFE) [73] that proposed to learn a probabilistic embedding while retaining a deterministic pre-trained model for the task of learning face embeddings. However, this was done in a unimodal setting using only images. In this work, we aim to utilize pre-trained vision-language models while providing probabilistic embeddings for both modalities. The probabilistic embeddings derived from our proposed ProbVLM are consistent with cross-modal learning at the core of pretrained vision-language models. + +Uncertainty Estimation. These techniques have been widely explored for different tasks in computer vision [36, 7, 41, 42, 56, 102, 83, 53, 80, 27, 68, 103, 65, 81, 77, 82]. Uncertainties can be broadly categorized into aleatoric [36, 23, 3, 89, 12, 2, 87, 56, 95] and epistemic [25, 7, 41, 91, 20, 33, 19, 18] uncertainties. Uncertainty estimation has been used for a variety of tasks, such as identifying model failure [15, 5, 6, 92] and is extensively used in active learning to select the best samples to train the model [71, 38, 64, 72, 99, 98, 61, 52]. While several of these methods focus on training a new Bayesian model from scratch for quantifying the uncertainties in the prediction, some recent works like [83, 102, 29] have proposed methods to estimate the uncertainties for the pre-trained frozen models. However, these works tackle data from a single modality. This work efficiently estimates the uncertainty for the pre-trained frozen large-scale vision-language model. + +# 3. Method + +We first describe the problem formulation in Section 3.1. In Section 3.2, we describe our proposed method ProbVLM that estimates the complex probability distributions for the embeddings of the frozen deterministic vision-langue encoders, quantifying the uncertainties for their predictions. + +# 3.1. Problem Formulation + +Let $\mathcal{D} = (\mathcal{I},\mathcal{C})$ denote a vision and language dataset, where $\mathcal{I}$ is a set of images and $\mathcal{C}$ a set of captions. The two sets are connected via ground-truth matches where multiplicity is plausible. For a caption $c\in \mathcal{C}$ (respectively an image $i\in \mathcal{I}$ ), the set of corresponding images (respectively captions) is given by $\kappa (c)\subseteq \mathcal{I}$ (respectively $\kappa (i)\subseteq \mathcal{C}$ ). Recent advances in cross-modal vision-language models [62, 51, 74] often involve learning a shared embedding space, $\mathcal{Z}\subseteq \mathbb{R}^{D}$ ( $D$ -dimensional space), for images and texts. This allows quantifying the similarity between cross-modal elements based on their distances in the shared embedding space. The shared embedding space is learned via a set of two encoders: $\Phi_{\mathcal{V}}(\cdot ;\theta_{\mathcal{V}}):\mathcal{I}\to \mathcal{Z}$ for the images and $\Phi_{\mathcal{T}}(\cdot ;\theta_{\mathcal{T}}):\mathcal{C}\rightarrow \mathcal{Z}$ for the texts, where $\theta_{\mathcal{V}}$ and $\theta_{\mathcal{T}}$ are the parameters for the respective mapping functions. + +We consider a real-world scenario where the above set of encoders have already been trained on vast datasets using large models with high computational cost, e.g., CLIP [62], + +![](images/275641a36a92f5f83bd7720fadceb74c29f10d33b427866121d2f42615eb5ab3.jpg) +Figure 2: Proposed framework (ProbVLM) takes an existing vision-language model and introduces a probabilistic adapter over the image and text encoders. These adapters predict the parameters of a parameterized distribution for a given embedding. Models are trained by minimizing an objective consisting of intra/cross-modal supervision as detailed in Section 3. + +SLIP [51], Flava [74] and BLIP [45], are in frozen state, i.e., we have $\Phi_{\mathcal{V}}(\cdot;\theta_{\mathcal{V}}^{*})$ and $\Phi_{\mathcal{T}}(\cdot;\theta_{\mathcal{T}}^{*})$ , where $\theta_{\mathcal{V}}^{*},\theta_{\mathcal{T}}^{*}$ represents the parameters of the pretrained frozen encoders. These encoders are deterministic and map an image/text to vectors in the shared space, i.e., given a sample image $\mathbf{x}_{\mathcal{V}}$ (and similarly sample text $\mathbf{x}_{\mathcal{T}}$ ), the encoder provides an embedding $\mathbf{z}_{\mathcal{V}} := \Phi_{\mathcal{V}}(\mathbf{x}_{\mathcal{V}};\theta_{\mathcal{V}}^{*})$ (and similarly, $\mathbf{z}_{\mathcal{T}} := \Phi_{\mathcal{T}}(\mathbf{x}_{\mathcal{T}};\theta_{\mathcal{T}}^{*}))$ ). However, the point estimates, $\mathbf{z}$ , do not capture the ambiguity inherent to these embeddings [57, 10, 17] that are better represented by the probability distribution $P_{\mathbf{z}|\mathbf{x}}$ . Therefore, we propose to estimate $P_{\mathbf{z}|\mathbf{x}}$ for the pretrained model efficiently, using ProbVLM, quantifying the uncertainties of the output without re-training the encoders. + +# 3.2. Building ProbVLM + +Despite being deterministic, large-scale frozen encoders already provide high-quality point estimates. Our proposed method leverages this fact, using the embeddings $\mathbf{z}$ as estimates for the mean of the desired distribution $P_{\mathbf{z}|\mathbf{x}}$ , and estimating the remaining parameters. $P_{\mathbf{z}|\mathbf{x}}$ can be modeled as a parametric distribution $P_{\mathbf{z}|\mathbf{x}}(\mathbf{z}|\{\hat{\mathbf{z}},\hat{\nu}\dots \hat{\rho}\})$ where the parameters can be estimated using a deep neural network [20, 36, 41]. Therefore, we introduce ProbVLM, + +$$ +\Psi (\cdot ; \zeta) := \left(\Psi_ {\mathcal {V}} (\cdot ; \zeta_ {\mathcal {V}}), \Psi_ {\mathcal {T}} (\cdot ; \zeta_ {\mathcal {T}})\right) \tag {1} +$$ + +where $\Psi_{\mathcal{V}}$ and $\Psi_{\mathcal{T}}$ represents the vision and text encoders parameterized by $\zeta_{\nu}$ and $\zeta_{\tau}$ , respectively. Also, $\zeta := \zeta_{\nu} \cup \zeta_{\mathcal{T}}$ represents the overall parameters for ProbVLM. + +that learns to estimate the parameters $\{\hat{\mathbf{z}},\hat{\nu}\dots \hat{\rho}\}$ with the help of frozen encoders $\Phi_{\mathcal{V}}(\cdot ;\theta_{\mathcal{V}}^{*})$ and $\Phi_{\mathcal{T}}(\cdot ;\theta_{\mathcal{T}}^{*})$ . The functions $\Psi_{\mathcal{V}}(\cdot ;\zeta_{\mathcal{V}})$ and $\Psi_{\mathcal{T}}(\cdot ;\zeta_{\mathcal{T}})$ operate on image and text embeddings respectively, but during training depend on both modalities, as discussed later. We design the learning scheme for $\Psi (\cdot ;\zeta)$ such that: (i) Estimated parameter $\hat{\mathbf{z}}$ should remain faithful to the original unimodal embedding $\mathbf{z}$ (intra-modal alignment), this makes the uncertainty of the ProbVLM serve as a good proxy for the uncertainty of frozen encoders. (ii) Estimated parameters $\{\hat{\nu}\dots \hat{\rho}\}$ should capture the ambiguities and uncertainties present within and across modalities (cross-modal alignment). Figure 2 depicts ProbVLM in tandem with the frozen VLM. + +Intra-modal Alignment. To ensure that the mean of the distribution estimated by $\Psi (\cdot ;\zeta)$ reflects the point estimates provided by the frozen encoders, we set up a probabilistic reconstruction problem for the embeddings within the modalities. That is, for a given sample $\mathbf{x}$ (either from image or text modality), we obtain the embedding from the frozen encoder $\mathbf{z} = \Phi (\mathbf{x};\theta)$ (using the appropriate encoder), then the modality-specific component of $\Psi (\cdot ;\zeta)$ learns to reconstruct the $\mathbf{z}$ (let the reconstruction be called $\hat{\mathbf{z}}$ ). The modality-specific component of $\Psi (\cdot ;\zeta)$ is designed to (i) relax the i.i.d constraints by assuming independent but not identically distributed residuals and (ii) learn the heteroscedasticity for the residuals at the time of reconstruction that may follow the heavy-tailed distributions [83, 84, 40, 39, 30]. The modality-specific component + +is learned by maximizing the likelihood, $\mathcal{L}(\zeta ;\{\mathbf{z}_i\}_{i = 1}^N)$ for the embeddings of $N$ samples in the datasets. That is, the modality-specific optimal parameters are given by, + +$$ +\zeta^ {*} := \underset {\zeta} {\operatorname {a r g m a x}} \mathcal {L} (\zeta ; \left\{\mathbf {z} _ {i} \right\} _ {i = 1} ^ {N}) = \prod_ {i = 1} ^ {N} \frac {\hat {\beta} _ {i} e ^ {- \left(\left| \bar {\mathbf {z}} _ {i} - \mathbf {z} _ {i} \right| / \hat {\alpha} _ {i}\right) ^ {\hat {\beta} _ {i}}}}{2 \hat {\alpha} _ {i} \Gamma \left(1 / \hat {\beta} _ {i}\right)} \tag {2} +$$ + +In the above equation, $\frac{\hat{\beta}_i e^{-(|\hat{\mathbf{z}}_i - \mathbf{z}_i| / \hat{\alpha}_i)^{\hat{\beta}_i}}{2\hat{\alpha}_i \Gamma(1 / \hat{\beta}_i)}$ represents the generalized Gaussian distribution (GGD, represented by $\mathcal{G}$ ) that is capable of modeling heavy-tailed distributions (note the Gaussian and Laplace are special cases of $\mathcal{G}$ with $\alpha = 1, \beta = 2$ and $\alpha = 1, \beta = 1$ , respectively). The variables $\hat{\mathbf{z}}_i, \hat{\alpha}_i, \hat{\beta}_i$ are the predicted mean, scale, and shape parameters of $\mathcal{G}$ from our modality-specific components for the given input $\mathbf{z}_i$ . We obtain modality-specific optimal parameters by minimizing negative log-likelihood (equivalent to Equation 2). Given $\mathbf{z}$ and predicted $\hat{\mathbf{z}}, \hat{\alpha}, \hat{\beta}$ , loss is given by, + +$$ +L _ {\mathrm {r e c}} (\zeta) := \left(\frac {| \hat {\mathbf {z}} - \mathbf {z} |}{\hat {\alpha}}\right) ^ {\hat {\beta}} - \log \frac {\hat {\beta}}{\hat {\alpha}} + \log \Gamma \left(\frac {1}{\hat {\beta}}\right) \tag {3} +$$ + +Therefore, the vision-specific component of ProbVLM, $\Psi (\cdot ;\zeta_{\nu}))$ , is trained by minimizing the Equation 3 using image embeddings, we denote this loss as $L_{\mathrm{rec}}^{\mathcal{V}}(\zeta_V)$ . Similarly the text-specific component, $\Psi (\cdot ;\zeta_T)$ , is trained by minimizing $L_{\mathrm{rec}}^{\mathcal{T}}(\zeta_T)$ . As discussed next, we also enforce cross-modal alignment so that the predicted distribution of ProbVLM captures the uncertainties across modalities from one-to-many correspondences for an embedding. + +Cross-modal Alignment. While the intra-modal alignment seeks to match the means of the output distribution from ProbVLM to the embeddings derived from frozen vision-language encoders, we also enforce the image and text embedding output distribution (from ProbVLM) belonging to similar concepts to remain close to each other. That is, given an image and text embedding pair $(\mathbf{z}_{\mathcal{V}},\mathbf{z}_{\mathcal{T}})$ (from frozen model) representing similar concepts, the output distributions from $\Psi (\cdot ;\zeta),\mathcal{G}(\mathbf{z};\hat{\mathbf{z}}_{\mathcal{V}},\hat{\alpha}_{\mathcal{V}},\hat{\beta}_{\mathcal{V}})$ and $\mathcal{G}(\mathbf{z};\hat{\mathbf{z}}_{\mathcal{T}},\hat{\alpha}_{\mathcal{T}},\hat{\beta}_{\mathcal{T}})$ (later referred to as $\mathcal{G}_{\mathcal{V}}(\mathbf{z}))$ and $\mathcal{G}_{\mathcal{T}}(\mathbf{z}))$ should match. This can be measured directly from the likelihood as, $p(\mathbf{z}_v = \mathbf{z}_u)$ , where $\mathbf{z}_v\sim \mathcal{G}_{\mathcal{V}}(\mathbf{z})$ and $\mathbf{z}_u\sim \mathcal{G}_{\mathcal{T}}(\mathbf{z})$ as in [73], i.e., + +$$ +p \left(\mathbf {z} _ {v} = \mathbf {z} _ {u}\right) := \iint \mathcal {G} _ {\mathcal {Y}} \left(\mathbf {z} _ {v}\right) \mathcal {G} _ {\mathcal {T}} \left(\mathbf {z} _ {u}\right) \delta \left(\mathbf {z} _ {v} - \mathbf {z} _ {u}\right) d \mathbf {z} _ {v} d \mathbf {z} _ {u} \tag {4} +$$ + +where $\delta (\cdot)$ refers to the Dirac-delta distribution. The above integral can be simplified further by defining $\Delta \mathbf{z} = \mathbf{z}_v - \mathbf{z}_u$ and seeking $p(\Delta \mathbf{z}) = 0$ . As both $\mathbf{z}_v$ and $\mathbf{z}_u$ are GGD random variables, $\Delta \mathbf{z}$ follows the distribution based on the + +Bivariate Fox H-function [76, 48, 49] given by, + +$$ +\Delta z \sim \frac {1}{2 \Gamma (1 / \hat {\beta} _ {\mathcal {V}}) , \Gamma (1 / \hat {\beta} _ {\mathcal {T}})} \times +$$ + +$$ +\int \mathcal {H} _ {1, 2} ^ {1, 1} \left[ A t ^ {2} \left| \begin{array}{l} \left(1 - \frac {1}{\bar {\mathbf {z}} _ {\mathcal {V}}}, \frac {1}{\bar {\mathbf {z}} _ {\mathcal {T}}}\right) \\ (0, 1) \left(\frac {1}{2}, 1\right) \end{array} \right. \right] \mathcal {H} _ {1, 2} ^ {1, 1} \left[ B t ^ {2} \left| \begin{array}{l} \left(1 - \frac {1}{\bar {\mathbf {z}} _ {\mathcal {T}}}, \frac {1}{\bar {\mathbf {z}} _ {\mathcal {T}}}\right) \\ (0, 1) \left(\frac {1}{2}, 1\right) \end{array} \right. \right] \cos t (\mu - z) d t \tag {5} +$$ + +Where $A = \frac{\hat{\alpha}_{\mathcal{V}}^2\Gamma(1 / \hat{\beta}_{\mathcal{V}})}{4\Gamma(3 / \hat{\beta}_{\mathcal{V}})}$ , $B = \frac{\hat{\alpha}_{\mathcal{T}}^2\Gamma(1 / \hat{\beta}_{\mathcal{T}})}{4\Gamma(3 / \hat{\beta}_{\mathcal{T}})}$ , $\mu = \hat{\mathbf{z}}_v - \hat{\mathbf{z}}_u$ , and $\mathcal{H}$ is the Fox $H$ function [76, 48, 49]. Equation 5 does not provide a scalable objective function suitable for training deep neural networks. Hence, we propose an approximation that is easily scalable for deep-learning models given by, + +$$ +\begin{array}{l} p (\mathbf {z} _ {v} = \mathbf {z} _ {u}) = \iint \mathcal {G} _ {\mathcal {V}} (\mathbf {z} _ {v}) \mathcal {G} _ {\mathcal {T}} (\mathbf {z} _ {u}) \delta (\mathbf {z} _ {v} - \mathbf {z} _ {u}) d \mathbf {z} _ {v} d \mathbf {z} _ {u} \\ \approx \int \frac {1}{2} \left(\mathcal {G} _ {\mathcal {V}} (\mathbf {z}) \delta (\mathbf {z} - \mathbf {z} _ {\mathcal {T}}) + \mathcal {G} _ {\mathcal {T}} (\mathbf {z}) \delta (\mathbf {z} - \mathbf {z} _ {\mathcal {V}})\right) d \mathbf {z} \tag {6} \\ \end{array} +$$ + +The appendix shows details of the above equation. The first term in the integral, $\int \mathcal{G}_{\mathcal{V}}(\mathbf{z})\delta (\mathbf{z} - \mathbf{z}_{\mathcal{T}})d\mathbf{z}$ , is the likelihood of the text embedding $\mathbf{z}_{\mathcal{T}}$ under the predicted distribution, $\mathcal{G}_{\mathcal{V}}(\mathbf{z})$ , for the visual embedding. Similarly, the second term is the likelihood of the visual embedding $\mathbf{z}_{\mathcal{V}}$ under the predicted distribution, $\mathcal{G}_{\mathcal{T}}(\mathbf{z})$ , for the text embedding. Negative log of Equation 6 leads to a scalable objective function that can be used to learn the optimal parameters for vision and text components of ProbVLM $(\Psi_{\mathcal{V}}(\cdot ;\zeta_{\mathcal{V}})$ and $\Psi_{\mathcal{T}}(\cdot ;\zeta_{\mathcal{T}}))$ + +$$ +\begin{array}{l} L _ {\text {c r o s s}} (\zeta_ {\mathcal {V}}, \zeta_ {\mathcal {T}}) := \underbrace {\left(\frac {| \hat {\mathbf {z}} _ {\mathcal {V}} - \mathbf {z} _ {\mathcal {T}} |}{\hat {\alpha} _ {\mathcal {V}}}\right) ^ {\hat {\beta} _ {\mathcal {V}}} - \log \frac {\hat {\beta} _ {\mathcal {V}}}{\hat {\alpha} _ {\mathcal {V}}} + \log \Gamma \left(\frac {1}{\hat {\beta} _ {\mathcal {V}}}\right)} _ {\text {C r o s s - m o d a l : v i s i o n} \rightarrow \text {t e x t}} + \\ \underbrace {\left(\frac {| \hat {\mathbf {z}} _ {\mathcal {T}} - \mathbf {z} _ {\mathcal {V}} |}{\hat {\alpha} _ {\mathcal {T}}}\right) ^ {\hat {\beta} _ {\mathcal {T}}} - \log \frac {\hat {\beta} _ {\mathcal {T}}}{\hat {\alpha} _ {\mathcal {T}}} + \log \Gamma \left(\frac {1}{\hat {\beta} _ {\mathcal {T}}}\right)} _ {\text {C r o s s - m o d a l : t e x t} \rightarrow \text {v i s i o n}} \tag {7} \\ \end{array} +$$ + +The overall objective used for ProbVLM is designed to be, + +$$ +L _ {\text {P r o b V L M}} \left(\zeta_ {\mathcal {V}}, \zeta_ {\mathcal {T}}\right) = L _ {\text {r e c}} ^ {\mathcal {V}} \left(\zeta_ {\mathcal {V}}\right) + L _ {\text {r e c}} ^ {\mathcal {T}} \left(\zeta_ {\mathcal {T}}\right) + \lambda_ {\text {c r o s s}} L _ {\text {c r o s s}} \left(\zeta_ {\mathcal {V}}, \zeta_ {\mathcal {T}}\right) \tag {8} +$$ + +where $\lambda_{cross}$ is a hyperparameter controlling the relative contribution of inter-intra modality terms. + +Uncertainty Quantification. Given embedding $\mathbf{z}$ from a frozen encoder, predicted distributions from the trained ProbVLM (output from the appropriate component) allows aleatoric uncertainty estimation as $\hat{\sigma}_{\mathrm{aleatoric}}^2 = \frac{\hat{\alpha}^2\Gamma(3 / \hat{\beta})}{\Gamma(1 / \hat{\beta})}$ . Moreover, we design both $\Psi_{\mathcal{V}}$ and $\Psi_{\mathcal{T}}$ to be simple 3-layer MLPs with dropout layers (with dropout probability set to 0.1 during training). Activating dropouts during inference, with multiple forward passes (say $M$ ), allows estimating the epistemic uncertainty, $\hat{\sigma}_{\mathrm{epistemic}}^2 = \frac{1}{M}\sum_{m = 1}^{M}(\hat{\mathbf{z}}_m - \hat{\mathbf{z}}_m)$ . + +![](images/dd1fa4cba0b3d41f9705ef3b250b6d128d630ee9b7b2bb24ce589fc600aeabf8.jpg) + +![](images/e064d97907fb223a5aa4c8799ec4fccd4d0b3f6a60db46e50991bcc93f31b41b.jpg) +Figure 3: Measuring the calibration with various post-hoc method for Image-to-Text and Text-to-Image retrieval when trained on (top) CUB and (bottom) COCO, and evaluated on CUB, COCO, Flickr, FLO. + +$\frac{1}{M}\sum_{j = 1}^{M}\hat{\mathbf{z}}_j)^2$ We estimate total uncertainty as, + +$$ +\hat {\sigma} _ {\text {t o t a l}} ^ {2} = \hat {\sigma} _ {\text {e p i s t e m i c}} ^ {2} + \hat {\sigma} _ {\text {a l e a t o r i c}} ^ {2} \tag {9} +$$ + +# 3.3. Latent Diffusion for Probabilistic Embeddings + +For a given text embedding $\mathbf{z}_{\mathcal{T}}$ , the distribution estimated via ProbVLM, $\mathcal{G}(\mathbf{z};\hat{\mathbf{z}}_{\mathcal{T}},\hat{\alpha}_{\mathcal{T}},\hat{\beta}_{\mathcal{T}})$ can be visualized by drawing samples from the predicted distribution of vectors (say, $\{\hat{\mathbf{z}}_{\mathcal{T},i}\}_{i = 1}^{Q}$ ) and passing them through a latent diffusion model, e.g., Stable Diffusion (say, $\Omega (\cdot ;\theta_{\Omega}^{*}))$ using CLIP text encoder, to synthesize the set of samples (say, $J$ ) from the corresponding distribution of images, i.e., + +$$ +J := \left\{\boldsymbol {\Omega} \left(\hat {\mathbf {z}} _ {i}; \theta_ {\Omega}\right) \right\} _ {i = 1} ^ {Q} \tag {10} +$$ + +Section 4.4 uses this to visualize the predicted distributions. + +# 4. Experiments and Results + +We start by highlighting our tasks, datasets, and evaluation metrics. We also compare our model to various state-of-the-art methods quantitatively and qualitatively in Section 4.1. In Section 4.2, we provide an ablation analysis, + +and Section 4.3 demonstrates some real-world applications of ProbVLM for model selection and active learning. + +Datasets, Metrics, and Baselines. We use the MS-COCO [46], Flickr-30k [60], and the CUB [85] as they are widely used for cross-modal retrieval [10, 16, 75]. Furthermore, we adapt the Oxford-Flowers 102 (FLO) dataset [55] similar to [10] as an additional benchmark for cross-modal retrieval in a fine-grained setting. We evaluate the performance of both Image-to-Text retrieval and Text-to-Image Retrieval using the Recall@k (R@k) metric. To evaluate the calibration of the uncertainty estimates, we define uncertainty levels [10] and use the Spearman rank correlation (denoted by $S$ ) between the uncertainty level and the Recall@k for retrieval. For an ideal model, performance would decrease monotonically with increasing uncertainty levels, leading to a score of -1. We also compute the $R^2$ for the regression fit between the uncertainty levels and R@1 performances to measure if the drop in performance follows a linear trend. Finally, we also measure the product of these two scores (as a unified metric), i.e., $-SR^2$ , which should be 1.0 for an ideal model. Since there is no prior work to estimate probabilistic embeddings from a deterministic model + +
VLMMetricsi2tt2i
COCOFlickrFLOCUBCOCOFlickrFLOCUB
CLIPS↓-0.99-0.70-0.90-0.60-0.30-0.70-0.99-0.89
R2↑0.930.710.620.670.350.500.990.70
-SR2↑0.930.490.560.400.100.350.990.63
S↓-0.79-0.190.60-0.600.790.30-0.89-0.10
R2↑0.590.010.300.280.740.440.520.00
-SR2↑0.470.00-0.180.17-0.59-0.130.47-0.00
S↓-0.89-0.30-0.30-0.600.300.09-0.700.30
R2↑0.750.070.070.200.160.010.570.01
-SR2↑0.680.020.020.12-0.05-0.000.40-0.00
S↓-0.79-0.300.00-0.60-0.10-0.19-0.89-0.50
R2↑0.690.090.000.410.260.0710.800.15
-SR2↑0.550.030.000.240.000.010.730.07
BLIPS↓-0.87-0.79-0.74-0.66-0.43-0.38-0.31-0.22
R2↑0.920.830.680.610.520.480.450.38
-SR2↑0.800.660.500.400.220.180.140.08
S↓-0.82-0.74-0.63-0.63-0.39-0.32-0.28-0.18
R2↑0.720.760.620.440.480.380.390.37
-SR2↑0.580.570.390.270.190.120.110.07
S↓-0.76-0.53-0.60-0.44-0.28-0.26-0.28-0.21
R2↑0.810.560.600.530.500.340.440.36
-SR2↑0.620.290.360.230.140.090.120.08
S↓-0.44-0.33-0.74-0.60-0.19-0.26-0.21-0.21
R2↑0.660.560.420.550.490.230.350.36
-SR2↑0.290.180.310.330.100.060.070.08
+ +Table 1: Metrics to evaluate the calibration of the uncertainty estimates for both CLIP [62] and BLIP [45] Vision-Language models for all considered methods, trained on COCO and evaluated on COCO, Flickr, CUB, and FLO. + +in a cross-modal setting, we adapt a few existing ideas for the task. The first baseline is adapted from PFE [73], where we learn the covariances for the heteroscedastic Gaussian distribution while keeping the mean fixed to the embeddings derived from the frozen encoders in each modality. The second is to use the soft-contrastive objective of PCME[10] to train a probabilistic adapter in a post-hoc fashion. Finally, we also have a baseline that performs Test-Time Data Augmentation (TTDA) on the inputs [2, 87]. This is done by perturbing the images and masking out words in the text. While TTDA does not require additional training, we train our ProbVLM and other baselines on datasets like COCO, Flickr, CUB, and FLO. + +Implementation Details. Our ProbVLM consists of a Multi-Layer Perceptron (MLP) for both the image and text encoder, each consisting of an input layer going from embedding dimension to 256, a hidden layer of size 256, and + +an output layer going from 256 to embedding dimensions. This is trained for 100 epochs with a learning rate of $1e^{-4}$ . More details are available in the supplementary. + +# 4.1. Calibrated Uncertainty via ProbVLM + +We investigate the calibration of the uncertainty derived from ProbVLM for the cross-modal retrieval task. All models trained on CUB and COCO were evaluated on all four datasets. Calibration plots are illustrated in Figure 3. We observe that the R@1 performance consistently drops for ProbVLM as we increase the uncertainty levels, whereas the baselines rarely see a monotonic drop in performance. We quantify this performance in Table 1. The highest score of 0.93 for $-SR^2$ (i2t) on the COCO dataset indicates a decreasing performance trend with increasing uncertainty. Notably, the uncertainty estimates indicate the average performance in different bins even when ProbVLM is evaluated on datasets that are different from the train set. In some cases, we see that ProbVLM even achieves a nearly perfect score $(-SR^2$ of 0.99, with CLIP VLM on FLO, after training on COCO for Image-to-Text Retrieval). On the contrary, we find that the baselines often achieve poor scores. It is important to note that all these models use the same underlying embeddings and achieve the same performance on the retrieval task. Of all the considered methods, ProbVLM provides the most calibrated uncertainty estimates. We see similar trends for ProbVLM with BLIP [45], where ProbVLM achieves a $-SR^2$ of 0.80, when trained on COCO and evaluated on COCO, compared to other methods like PFE\* (0.58), PCME\* (0.62), and TTDA (0.29). + +Figure 4-(Top) visualizes the ambiguities captured by ProbVLM on the visual embeddings. We take a bird image (source) from the CUB dataset and obtain the probability distribution for the visual embedding of that sample; we then compute the likelihood of the visual embeddings (i.e., point estimates derived from CLIP) for the other samples of CUB and COCO datasets, under the source distribution. We notice that within the CUB dataset, the bird images similar to the source image have a higher likelihood compared to other bird images. Also, the images from the COCO dataset tend to have a lower likelihood. However, some images from the COCO dataset have a likelihood similar to the samples from CUB. We visualize these samples and discover them to be bird images. Moreover, the overlapping region between CUB and COCO has samples from the COCO dataset that are ambiguous and related to bird images as they have similar backgrounds, etc. On the contrary, when a similar analysis is performed using the CLIP (by measuring the distance between the embeddings instead of likelihood, Figure 4-(Bottom)), we notice that the two datasets are well separated and ambiguities are not captured. + +![](images/3ab0254dfbaf805c5c039debed3b6d06fb1f934714e6af4d7c9c32401ba36ee2.jpg) +Figure 4: Visualizing the uncertainties of the vision encoder captured by ProbVLM. Fixing an image from CUB, we obtain the predicted embedding distribution and compute the likelihood of all other samples in CUB and COCO. We observe that the images in COCO are similar/ambiguous to CUB overlap (Top). However, deterministic embeddings lead to a separation between the two datasets (Bottom). + +![](images/8bd425a32f6e9ed765ef783551338c2d3a699a85f2ebdbd66845e30246fd6596.jpg) +Figure 5: Plot indicating (left) necessity of the cross-modal alignment and (right) data required to train ProbVLM. + +![](images/a7302e1bd2fcfb0f397635edae76fe5e697b635ea37ce994e893aea1955c2c4b.jpg) + +![](images/03282f7e403dc14d26cd0fd911bb2ef42a5b2d2a215861b1f0914c319883157c.jpg) +Figure 6: Uncertainty increases with increased masking of the input images (Left) and texts (Right). Results with three vision encoders and one language encoder from CLIP. + +![](images/ed8587106abc2759ed78ea8382486bc4711dd00dc5d90fa45be954d2cd705089.jpg) + +![](images/719289f05fe280d6e183887a2199a8d7d78dd4271dd74df3ba1b73de8a94d3dd.jpg) +Figure 7: Results for active learning, with different vision encoders and varying training budgets. For a given encoder, uncertainty-based sampling outperforms random sampling. + +# 4.2. Ablations + +We ablate different components of our proposed ProbVLM, to provide a deeper understanding of its workings. First, we perform a sensitivity analysis on the cross-modal reconstruction objective, as shown in Figure 5-(Left), for ProbVLM on BLIP using the COCO dataset. We need a non-zero coefficient of the cross-modal loss to ensure that ProbVLM learns meaningful uncertainties that capture the ambiguities across modalities and are well-correlated with its performance on the downstream retrieval task. Similarly, having a large co-efficient for the cross-modal loss could hinder learning a faithful identity reconstruction, thereby hampering the performance of the downstream evaluation. Next, we investigate the amount of data that is required to train ProbVLM in Figure 5-(Right). We get satisfactory calibration of the uncertainty estimates while using only $50\%$ of the dataset (shown for ProbVLM on BLIP using COCO), indicating that ProbVLM is highly data-efficient. + +Further, we investigate the uncertainties by masking out increasing portions of the input image/text in Figure 6. We use three different CLIP backbones for the images, ViT-B/32, ViT-B/16, ResNet50, and GPT-based language encoder from CLIP [62, 63]. The mean uncertainty steadily increases as we mask increasing amounts of input. + +# 4.3. Applications + +We study the utility of the uncertainty estimates derived from ProbVLM on two critical applications not well reviewed for VLMs: active learning and model selection. + +Active Learning. Here, we choose a small subset of the unlabeled dataset to fine-tune the model [11]. In this case, we wish to finetune the CLIP model on the FLO dataset while using a limited amount of labeled data. To achieve this, we estimate the uncertainty of the image embeddings us + +![](images/b488cda5401dfc2a146c54173cab431149259b6dd9f630f094a14b9b4f27c708.jpg) +Figure 8: Visualizing the predicted embedding distributions from ProbVLM using a large-scale pre-trained diffusion model, i.e., Stable Diffusion. The example is shown for two different captions from CUB dataset, for which the point-estimate embedding vector is obtained via CLIP, and the distribution is obtained via ProbVLM. + +Metrics + +
DModelsUncertainty scoreR@1R@5R@10
CUBCLIP-ViT32-COCO11.9231.561.075.8
CLIP-ViT32-Flickr9.3732.464.276.9
CLIP-ViT32-FLO15.4322.849.864.9
FLOCLIP-ViT32-COCO11.8347.979.288.5
CLIP-ViT32-Flickr13.5549.584.693.9
CLIP-ViT32-CUB18.3937.769.482.8
FlickrCLIP-ViT32-COCO9.6188.897.899.8
CLIP-ViT32-CUB16.4925.847.455.6
CLIP-ViT32-FLO13.6752.877.885.2
COCOCLIP-ViT32-Flickr7.2858.180.988.2
CLIP-ViT32-CUB15.378.821.729.8
CLIP-ViT32-FLO12.4423.946.658.8
+ +Table 2: Results for the model selection experiment. ProbVLM accurately identifies the best performing source model using only unlabeled samples of the target dataset. + +ing ProbVLM (trained using a diverse dataset like COCO). We then select the top-k samples sorted by their mean uncertainty in the visual embeddings and fine-tune the CLIP model using them with a contrastive objective [62]. Results with varying budgets are shown in Figure 7. Selecting samples based on uncertainty scores significantly outperforms random sampling for all considered visual backbones. + +Pretrained Model Selection. We are given a set of models trained on different data distributions. We aim to select the best model for the target distribution for which we have unlabeled samples. This has been explored mostly in the context of classification previously [22, 26, 8, 9, 13, 14]. + +We consider the specific case of having the CLIP models fine-tuned on three datasets, and the fourth dataset is held out, for which we only have the images. We compute the mean uncertainty on these images using ProbVLM whose weights are interpolated from all the source datasets [93, 94, 32, 31]. This is to ensure that the uncertainties on all these models are comparable. The results for this experiment are + +shown in Table 2. On CUB, Flickr, and COCO, the source model with the lowest uncertainty has the best performance on the target dataset, and on FLO dataset, the model with the least uncertainty has the 2nd best performance (R@1 of 47.9 vs 49.5 for the best model). This indicates that the uncertainties provided by ProbVLM can be used as a signal to predict the performance on unlabelled samples for retrieval. + +# 4.4. Latent Diffusion for Embedding Uncertainty + +To further understand the semantics of the predicted embedding distributions from the ProbVLM, we visualize the text embedding distributions by sampling the embedding vectors from the predicted distribution for a caption (converted to embedding vector using CLIP) and passing it through the pre-trained latent diffusion model using CLIPs text encoder, stable diffusion, as shown in Figure 8 and described in details in Section 3.3. We observe from Figure 8 that the samples obtained closer to the mean (i.e., sampled embedding vector similar to the one generated by CLIP for the caption) lead to meaningful variations in the generated images, e.g., for the left caption, close to the mean of the distribution, the generated samples show variations in the shape and colour of the beak, wings, and feet. Whereas far away from the mean of the distributions, i.e., on the tails, we start seeing images with strong artifacts that no longer preserves the semantics of the caption. We observe this for another example as well shown in Figure 8-(Right). More results are available in the supplementary. + +# 5. Conclusion + +We introduce ProbVLM, a post-hoc method for estimating the embedding distribution for a frozen large-scale deterministic vision-language model. We efficiently estimate calibrated uncertainties using our framework and show that such calibrated estimates have a variety of applications in downstream tasks such as model selection and active learning. Furthermore, we perform experiments to interpret em + +bedding distribution predicted by ProbVLM using a large-scale pre-trained latent diffusion model (i.e., Stable Diffusion). We hope our work highlights and inspires future work on efficient methods for probabilistic embeddings. + +Acknowledgements. This work was supported by DFG project number 276693517, by BMBF FKZ: 01IS18039A, by the ERC (853489 - DEXIM), by EXC number 2064/1 - project number 390727645, and by the MUR PNRR project FAIR - Future AI Research (PE00000013) funded by NextGenerationEU. The authors thank the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting Uddeshya Upadhyay and Shyamgopal Karthik. + +# References + +[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, et al. Flamingo: a visual language model for few-shot learning. arXiv preprint arXiv:2204.14198, 2022. 1, 2 +[2] Murat Seckin Ayhan and Philipp Berens. Test-time data augmentation for estimation of heteroscedastic aleatoric uncertainty in deep neural networks. In MIDL, 2018. 2, 6 +[3] Gwangbin Bae, Ignas Budvytis, and Roberto Cipolla. 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Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time. In ICML, 2022. 8 +[94] Mitchell Wortsman, Gabriel Ilharco, Jong Wook Kim, Mike Li, Simon Kornblith, Rebecca Roelofs, Raphael Gontijo Lopes, Hannaneh Hajishirzi, Ali Farhadi, Hongseok Namkoong, et al. Robust fine-tuning of zero-shot models. In CVPR, 2022. 8 +[95] Binhui Xie, Longhui Yuan, Shuang Li, Chi Harold Liu, and Xinjing Cheng. Towards fewer annotations: Active learning via region impurity and prediction uncertainty for domain adaptive semantic segmentation. In CVPR, 2022. 2 +[96] Mengde Xu, Zheng Zhang, Fangyun Wei, Yutong Lin, Yue Cao, Han Hu, and Xiang Bai. A simple baseline for zero-shot semantic segmentation with pre-trained vision-language model. arXiv preprint arXiv:2112.14757, 2021. 2 +[97] Gengcong Yang, Jingyi Zhang, Yong Zhang, Baoyuan Wu, and Yujiu Yang. Probabilistic modeling of semantic ambiguity for scene graph generation. 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Learning uncertainty for unknown domains with zero-target-assumption. In ICLR, 2023. 2 +[104] Pengchuan Zhang, Xiujun Li, Xiaowei Hu, Jianwei Yang, Lei Zhang, Lijuan Wang, Yejin Choi, and Jianfeng Gao. Vinvl: Revisiting visual representations in vision-language models. In CVPR, 2021. 2 +[105] Kaiyang Zhou, Jingkang Yang, Chen Change Loy, and Zwei Liu. Conditional prompt learning for vision-language models. In CVPR, 2022. 2 + +[106] Kaiyang Zhou, Jingkang Yang, Chen Change Loy, and Zwei Liu. Learning to prompt for vision-language models. IJCV, 2022. 2 \ No newline at end of file diff --git a/2023/ProbVLM_ Probabilistic Adapter for Frozen Vison-Language Models/images.zip b/2023/ProbVLM_ Probabilistic Adapter for Frozen Vison-Language Models/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..e1d7eb439ce95d87ae4a5702189192d19913ae82 --- /dev/null +++ b/2023/ProbVLM_ Probabilistic Adapter for Frozen Vison-Language Models/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6eb0a5e05f332047c013ac09da1bee68dbe89cdc23e8a21a57e7428f442e4d77 +size 749448 diff --git a/2023/ProbVLM_ Probabilistic Adapter for Frozen Vison-Language Models/layout.json b/2023/ProbVLM_ Probabilistic Adapter for Frozen Vison-Language Models/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..498ab03ea0fa35c6d2e1659ad8c074a8699e60ed --- /dev/null +++ b/2023/ProbVLM_ Probabilistic Adapter for Frozen Vison-Language Models/layout.json @@ -0,0 +1,10106 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 84, + 103, + 509, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 103, + 509, + 121 + ], + "spans": [ + { + "bbox": [ + 84, + 103, + 509, + 121 + ], + "type": "text", + "content": "ProbVLM: Probabilistic Adapter for Frozen Vison-Language Models" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 72, + 142, + 523, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 142, + 523, + 159 + ], + "spans": [ + { + "bbox": [ + 72, + 142, + 523, + 159 + ], + "type": "text", + "content": "Uddeshya Upadhyay*,1 Shyamgopal Karthik*,1 Massimiliano Mancini2 Zeynep Akata" + }, + { + "bbox": [ + 72, + 142, + 523, + 159 + ], + "type": "inline_equation", + "content": "^{1,3}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 163, + 490, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 163, + 490, + 178 + ], + "spans": [ + { + "bbox": [ + 106, + 163, + 490, + 178 + ], + "type": "text", + "content": "1University of Tübingen 2University of Trento 3MPI for Intelligent Systems" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 205, + 192, + 217 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 205, + 192, + 217 + ], + "spans": [ + { + "bbox": [ + 143, + 205, + 192, + 217 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 230, + 290, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 230, + 290, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 290, + 518 + ], + "type": "text", + "content": "Large-scale vision-language models (VLMs) like CLIP successfully find correspondences between images and text. Through the standard deterministic mapping process, an image or a text sample is mapped to a single vector in the embedding space. This is problematic: as multiple samples (images or text) can abstract the same concept in the physical world, deterministic embeddings do not reflect the inherent ambiguity in the embedding space. We propose ProbVLM, a probabilistic adapter that estimates probability distributions for the embeddings of pre-trained VLMs via inter/intra-modal alignment in a post-hoc manner without needing large-scale datasets or computing. On four challenging datasets, i.e., COCO, Flickr, CUB, and Oxford-flowers, we estimate the multi-modal embedding uncertainties for two VLMs, i.e., CLIP and BLIP, quantify the calibration of embedding uncertainties in retrieval tasks and show that ProbVLM outperforms other methods. Furthermore, we propose active learning and model selection as two real-world downstream tasks for VLMs and show that the estimated uncertainty aids both tasks. Lastly, we present a novel technique for visualizing the embedding distributions using a large-scale pre-trained latent diffusion model. Code is available at https://github.com/ExplainableML/ProbVLM" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 541, + 128, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 541, + 128, + 553 + ], + "spans": [ + { + "bbox": [ + 47, + 541, + 128, + 553 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 562, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 562, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 562, + 287, + 694 + ], + "type": "text", + "content": "Recently, large vision-language models (VLMs) [62, 51, 45, 74, 1, 35] have become exceedingly popular due to their ability to align images and text. These models such as CLIP [62] and BLIP [45] are trained on large-scale datasets such as LAION-400M [70] and YFCC-100M [79] and have shown strong performance when evaluated in a zero-shot fashion (i.e without requiring fine-tuning on specific datasets) for a variety of downstream tasks. One of the most popular applications of VLMs is cross-modal retrieval [86, 88] i.e retrieving images (text) for a queried text (images). However, image-to-text matching (and vice" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 205, + 545, + 289 + ], + "blocks": [ + { + "bbox": [ + 309, + 205, + 545, + 289 + ], + "lines": [ + { + "bbox": [ + 309, + 205, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 309, + 205, + 545, + 289 + ], + "type": "image", + "image_path": "1c61ba78ab3c25afd80acda7c5326db9f89787588a23993bdcf5b94938ea196c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 298, + 546, + 346 + ], + "lines": [ + { + "bbox": [ + 305, + 298, + 546, + 346 + ], + "spans": [ + { + "bbox": [ + 305, + 298, + 546, + 346 + ], + "type": "text", + "content": "Figure 1: We provide probabilistic embeddings for deterministic pre-trained vision-language models that are frozen. By capturing the ambiguity inherently present in the inputs, we obtain well-calibrated uncertainty estimates." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 361, + 546, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 546, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 546, + 421 + ], + "type": "text", + "content": "versa) is fundamentally ill-posed due to the inherent ambiguity in either modality [97], i.e. the same caption (or image) can be valid for multiple images (or captions). Therefore, it becomes essential to model the ambiguity inherently present in the various modalities, and combinations thereof." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 422, + 547, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 547, + 530 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 547, + 530 + ], + "type": "text", + "content": "Instead of mapping inputs to embeddings, probabilistic embedding methods [57, 10] learn to map input samples to distributions. This is achieved by parameterizing the distributions of the embeddings and training a deep neural network to maximize its likelihood. Although they model ambiguities in the embedding space, such probabilistic models require training deep networks from scratch. This requires access to the large-scale datasets and the computational resources of the recent VLMs [62, 35, 51, 74, 45]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 532, + 547, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 547, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 547, + 663 + ], + "type": "text", + "content": "We propose ProbVLM, a post-hoc probabilistic adapter, the first method to convert the deterministic embeddings provided by a frozen large-scale vision-language models into probabilistic ones, as shown in Figure 1. This enables us to efficiently retain the benefits of large-scale pre-training while learning distributions that model the inherent ambiguities in the different modalities. Our ProbVLM models the embedding distribution as a heteroscedastic probability distribution and is trained using a combination of intra-modal and cross-modal alignment objectives and provides well-calibrated uncertainty estimates, useful for several tasks." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "type": "text", + "content": "We demonstrate on two large vision-language datasets, i.e., COCO [46] and Flickr [60], and on two fine-grained image datasets, i.e., CUB [85] and Oxford-Flowers [55] with sentences from [66], that ProbVLM learns calibrated" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 703, + 160, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 703, + 160, + 713 + ], + "spans": [ + { + "bbox": [ + 61, + 703, + 160, + 713 + ], + "type": "text", + "content": "*Authors contributed equally." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1899" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 264 + ], + "type": "text", + "content": "uncertainties without requiring large-scale models to be trained from scratch. This sharply contrasts previous works on probabilistic embeddings [57, 10] that train new models from scratch. We perform a series of analyses to understand the impact of the training objective and to study the properties of the resulting uncertainties. Furthermore, we demonstrate that our uncertainty estimates can be used to select the optimal model from a set of finetuned vision-language models on an unlabeled target dataset. They can also be used to choose the most suitable samples for fine-tuning the model in an active learning setup. Finally, with the help of a pretrained latent diffusion model [67], i.e., Stable Diffusion, we decode sampled embeddings from predicted distribution to visualize the predicted embedding distributions. We show that the predicted embedding distributions indeed capture meaningful modes of variation, that may be interpretable." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 273, + 134, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 273, + 134, + 285 + ], + "spans": [ + { + "bbox": [ + 47, + 273, + 134, + 285 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 293, + 289, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 289, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 289, + 521 + ], + "type": "text", + "content": "Vision-Language Models. Such models [62, 51, 74, 1, 45, 47, 44, 100, 101, 90] have become ubiquitous in recent times due to their various applications in image classification [105, 21, 106, 50], cross-modal retrieval [4], as well as open-vocabulary semantic segmentation [24, 96]. The most notable among these is CLIP [62], which consists of an image and text encoder trained on 400M image-text pairs with a contrastive objective [28, 58]. As a result, the model is able to project images and text to a shared embedding space. In this paper, we focus on using the shared embedding space for the task of cross-modal retrieval [60, 46]. Recent works have predominantly relied on large-scale pre-training [62, 51, 74, 1, 104, 70, 69] to project images and text to the same metric space. However, it is essential to note that all of these vision-language models [62, 51, 45, 74, 1] provide deterministic mappings that do not model the inherent ambiguity in the inputs. In this work, we turn a deterministic model (i.e., CLIP) into a probabilistic one, without the need of a large-scale dataset." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "text", + "content": "Probabilistic Embeddings. These methods [57, 10, 43] provide an elegant solution to estimate the ambiguity present in the inputs [37]. The key idea here is to map inputs to probability distributions in the embedding space, as opposed to point estimates, thereby modeling the inherent ambiguity present in the input. In the context of cross-modal retrieval, this was done by optimizing a probabilistic analog of the contrastive objective to learn distributions for the image and text inputs [10]. Other works have further improved the performance [43, 59, 34], extended this formulation to achieve compositional retrieval [54], and have applied it to other tasks such as video retrieval [59, 17] and tasks like pose estimation [78]. However, most of these works focus on training a model from scratch, thereby not leveraging the power of the pre-trained models that are widely present. The notable exception to this is Probabilistic Face Embed" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": "ding (PFE) [73] that proposed to learn a probabilistic embedding while retaining a deterministic pre-trained model for the task of learning face embeddings. However, this was done in a unimodal setting using only images. In this work, we aim to utilize pre-trained vision-language models while providing probabilistic embeddings for both modalities. The probabilistic embeddings derived from our proposed ProbVLM are consistent with cross-modal learning at the core of pretrained vision-language models." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 181, + 548, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 181, + 548, + 385 + ], + "spans": [ + { + "bbox": [ + 304, + 181, + 548, + 385 + ], + "type": "text", + "content": "Uncertainty Estimation. These techniques have been widely explored for different tasks in computer vision [36, 7, 41, 42, 56, 102, 83, 53, 80, 27, 68, 103, 65, 81, 77, 82]. Uncertainties can be broadly categorized into aleatoric [36, 23, 3, 89, 12, 2, 87, 56, 95] and epistemic [25, 7, 41, 91, 20, 33, 19, 18] uncertainties. Uncertainty estimation has been used for a variety of tasks, such as identifying model failure [15, 5, 6, 92] and is extensively used in active learning to select the best samples to train the model [71, 38, 64, 72, 99, 98, 61, 52]. While several of these methods focus on training a new Bayesian model from scratch for quantifying the uncertainties in the prediction, some recent works like [83, 102, 29] have proposed methods to estimate the uncertainties for the pre-trained frozen models. However, these works tackle data from a single modality. This work efficiently estimates the uncertainty for the pre-trained frozen large-scale vision-language model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 393, + 362, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 393, + 362, + 406 + ], + "spans": [ + { + "bbox": [ + 306, + 393, + 362, + 406 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 414, + 547, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 547, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 547, + 475 + ], + "type": "text", + "content": "We first describe the problem formulation in Section 3.1. In Section 3.2, we describe our proposed method ProbVLM that estimates the complex probability distributions for the embeddings of the frozen deterministic vision-langue encoders, quantifying the uncertainties for their predictions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 479, + 430, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 430, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 430, + 491 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = (\\mathcal{I},\\mathcal{C})" + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "text", + "content": " denote a vision and language dataset, where " + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "text", + "content": " is a set of images and " + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "text", + "content": " a set of captions. The two sets are connected via ground-truth matches where multiplicity is plausible. For a caption " + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "inline_equation", + "content": "c\\in \\mathcal{C}" + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "text", + "content": " (respectively an image " + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "inline_equation", + "content": "i\\in \\mathcal{I}" + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "text", + "content": "), the set of corresponding images (respectively captions) is given by " + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\kappa (c)\\subseteq \\mathcal{I}" + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "text", + "content": " (respectively " + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\kappa (i)\\subseteq \\mathcal{C}" + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "text", + "content": "). Recent advances in cross-modal vision-language models [62, 51, 74] often involve learning a shared embedding space, " + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}\\subseteq \\mathbb{R}^{D}" + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "text", + "content": "-dimensional space), for images and texts. This allows quantifying the similarity between cross-modal elements based on their distances in the shared embedding space. The shared embedding space is learned via a set of two encoders: " + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\Phi_{\\mathcal{V}}(\\cdot ;\\theta_{\\mathcal{V}}):\\mathcal{I}\\to \\mathcal{Z}" + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "text", + "content": " for the images and " + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\Phi_{\\mathcal{T}}(\\cdot ;\\theta_{\\mathcal{T}}):\\mathcal{C}\\rightarrow \\mathcal{Z}" + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "text", + "content": " for the texts, where " + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\theta_{\\mathcal{V}}" + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\theta_{\\mathcal{T}}" + }, + { + "bbox": [ + 304, + 498, + 547, + 677 + ], + "type": "text", + "content": " are the parameters for the respective mapping functions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "We consider a real-world scenario where the above set of encoders have already been trained on vast datasets using large models with high computational cost, e.g., CLIP [62]," + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1900" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 72, + 541, + 320 + ], + "blocks": [ + { + "bbox": [ + 53, + 72, + 541, + 320 + ], + "lines": [ + { + "bbox": [ + 53, + 72, + 541, + 320 + ], + "spans": [ + { + "bbox": [ + 53, + 72, + 541, + 320 + ], + "type": "image", + "image_path": "275641a36a92f5f83bd7720fadceb74c29f10d33b427866121d2f42615eb5ab3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 324, + 547, + 361 + ], + "lines": [ + { + "bbox": [ + 46, + 324, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 547, + 361 + ], + "type": "text", + "content": "Figure 2: Proposed framework (ProbVLM) takes an existing vision-language model and introduces a probabilistic adapter over the image and text encoders. These adapters predict the parameters of a parameterized distribution for a given embedding. Models are trained by minimizing an objective consisting of intra/cross-modal supervision as detailed in Section 3." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "text", + "content": "SLIP [51], Flava [74] and BLIP [45], are in frozen state, i.e., we have " + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "inline_equation", + "content": "\\Phi_{\\mathcal{V}}(\\cdot;\\theta_{\\mathcal{V}}^{*})" + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "inline_equation", + "content": "\\Phi_{\\mathcal{T}}(\\cdot;\\theta_{\\mathcal{T}}^{*})" + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "inline_equation", + "content": "\\theta_{\\mathcal{V}}^{*},\\theta_{\\mathcal{T}}^{*}" + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "text", + "content": " represents the parameters of the pretrained frozen encoders. These encoders are deterministic and map an image/text to vectors in the shared space, i.e., given a sample image " + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathcal{V}}" + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "text", + "content": " (and similarly sample text " + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathcal{T}}" + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "text", + "content": "), the encoder provides an embedding " + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathcal{V}} := \\Phi_{\\mathcal{V}}(\\mathbf{x}_{\\mathcal{V}};\\theta_{\\mathcal{V}}^{*})" + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "text", + "content": " (and similarly, " + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathcal{T}} := \\Phi_{\\mathcal{T}}(\\mathbf{x}_{\\mathcal{T}};\\theta_{\\mathcal{T}}^{*}))" + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "text", + "content": "). However, the point estimates, " + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "text", + "content": ", do not capture the ambiguity inherent to these embeddings [57, 10, 17] that are better represented by the probability distribution " + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "inline_equation", + "content": "P_{\\mathbf{z}|\\mathbf{x}}" + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "text", + "content": ". Therefore, we propose to estimate " + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "inline_equation", + "content": "P_{\\mathbf{z}|\\mathbf{x}}" + }, + { + "bbox": [ + 46, + 371, + 289, + 529 + ], + "type": "text", + "content": " for the pretrained model efficiently, using ProbVLM, quantifying the uncertainties of the output without re-training the encoders." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 534, + 155, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 534, + 155, + 547 + ], + "spans": [ + { + "bbox": [ + 47, + 534, + 155, + 547 + ], + "type": "text", + "content": "3.2. Building ProbVLM" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 552, + 287, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 287, + 648 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 287, + 648 + ], + "type": "text", + "content": "Despite being deterministic, large-scale frozen encoders already provide high-quality point estimates. Our proposed method leverages this fact, using the embeddings " + }, + { + "bbox": [ + 46, + 552, + 287, + 648 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 552, + 287, + 648 + ], + "type": "text", + "content": " as estimates for the mean of the desired distribution " + }, + { + "bbox": [ + 46, + 552, + 287, + 648 + ], + "type": "inline_equation", + "content": "P_{\\mathbf{z}|\\mathbf{x}}" + }, + { + "bbox": [ + 46, + 552, + 287, + 648 + ], + "type": "text", + "content": ", and estimating the remaining parameters. " + }, + { + "bbox": [ + 46, + 552, + 287, + 648 + ], + "type": "inline_equation", + "content": "P_{\\mathbf{z}|\\mathbf{x}}" + }, + { + "bbox": [ + 46, + 552, + 287, + 648 + ], + "type": "text", + "content": " can be modeled as a parametric distribution " + }, + { + "bbox": [ + 46, + 552, + 287, + 648 + ], + "type": "inline_equation", + "content": "P_{\\mathbf{z}|\\mathbf{x}}(\\mathbf{z}|\\{\\hat{\\mathbf{z}},\\hat{\\nu}\\dots \\hat{\\rho}\\})" + }, + { + "bbox": [ + 46, + 552, + 287, + 648 + ], + "type": "text", + "content": " where the parameters can be estimated using a deep neural network [20, 36, 41]. Therefore, we introduce ProbVLM," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 96, + 656, + 287, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 656, + 287, + 670 + ], + "spans": [ + { + "bbox": [ + 96, + 656, + 287, + 670 + ], + "type": "interline_equation", + "content": "\\Psi (\\cdot ; \\zeta) := \\left(\\Psi_ {\\mathcal {V}} (\\cdot ; \\zeta_ {\\mathcal {V}}), \\Psi_ {\\mathcal {T}} (\\cdot ; \\zeta_ {\\mathcal {T}})\\right) \\tag {1}", + "image_path": "204c0ac6353879cdd8f1309843d805947918313719ecbbc19ace179da83a3c2e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\Psi_{\\mathcal{V}}" + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\Psi_{\\mathcal{T}}" + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": " represents the vision and text encoders parameterized by " + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\zeta_{\\nu}" + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\zeta_{\\tau}" + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": ", respectively. Also, " + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\zeta := \\zeta_{\\nu} \\cup \\zeta_{\\mathcal{T}}" + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": " represents the overall parameters for ProbVLM." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "text", + "content": "that learns to estimate the parameters " + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "inline_equation", + "content": "\\{\\hat{\\mathbf{z}},\\hat{\\nu}\\dots \\hat{\\rho}\\}" + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "text", + "content": " with the help of frozen encoders " + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "inline_equation", + "content": "\\Phi_{\\mathcal{V}}(\\cdot ;\\theta_{\\mathcal{V}}^{*})" + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "inline_equation", + "content": "\\Phi_{\\mathcal{T}}(\\cdot ;\\theta_{\\mathcal{T}}^{*})" + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "text", + "content": " . The functions " + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "inline_equation", + "content": "\\Psi_{\\mathcal{V}}(\\cdot ;\\zeta_{\\mathcal{V}})" + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "inline_equation", + "content": "\\Psi_{\\mathcal{T}}(\\cdot ;\\zeta_{\\mathcal{T}})" + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "text", + "content": " operate on image and text embeddings respectively, but during training depend on both modalities, as discussed later. We design the learning scheme for " + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "inline_equation", + "content": "\\Psi (\\cdot ;\\zeta)" + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "text", + "content": " such that: (i) Estimated parameter " + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}" + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "text", + "content": " should remain faithful to the original unimodal embedding " + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "text", + "content": " (intra-modal alignment), this makes the uncertainty of the ProbVLM serve as a good proxy for the uncertainty of frozen encoders. (ii) Estimated parameters " + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "inline_equation", + "content": "\\{\\hat{\\nu}\\dots \\hat{\\rho}\\}" + }, + { + "bbox": [ + 304, + 371, + 547, + 526 + ], + "type": "text", + "content": " should capture the ambiguities and uncertainties present within and across modalities (cross-modal alignment). Figure 2 depicts ProbVLM in tandem with the frozen VLM." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": "Intra-modal Alignment. To ensure that the mean of the distribution estimated by " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\Psi (\\cdot ;\\zeta)" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " reflects the point estimates provided by the frozen encoders, we set up a probabilistic reconstruction problem for the embeddings within the modalities. That is, for a given sample " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " (either from image or text modality), we obtain the embedding from the frozen encoder " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = \\Phi (\\mathbf{x};\\theta)" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " (using the appropriate encoder), then the modality-specific component of " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\Psi (\\cdot ;\\zeta)" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " learns to reconstruct the " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " (let the reconstruction be called " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": "). The modality-specific component of " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\Psi (\\cdot ;\\zeta)" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " is designed to (i) relax the i.i.d constraints by assuming independent but not identically distributed residuals and (ii) learn the heteroscedasticity for the residuals at the time of reconstruction that may follow the heavy-tailed distributions [83, 84, 40, 39, 30]. The modality-specific component" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 314, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 314, + 758 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 314, + 758 + ], + "type": "text", + "content": "1901" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": "is learned by maximizing the likelihood, " + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\zeta ;\\{\\mathbf{z}_i\\}_{i = 1}^N)" + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": " for the embeddings of " + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": " samples in the datasets. That is, the modality-specific optimal parameters are given by," + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 118, + 287, + 163 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 118, + 287, + 163 + ], + "spans": [ + { + "bbox": [ + 56, + 118, + 287, + 163 + ], + "type": "interline_equation", + "content": "\\zeta^ {*} := \\underset {\\zeta} {\\operatorname {a r g m a x}} \\mathcal {L} (\\zeta ; \\left\\{\\mathbf {z} _ {i} \\right\\} _ {i = 1} ^ {N}) = \\prod_ {i = 1} ^ {N} \\frac {\\hat {\\beta} _ {i} e ^ {- \\left(\\left| \\bar {\\mathbf {z}} _ {i} - \\mathbf {z} _ {i} \\right| / \\hat {\\alpha} _ {i}\\right) ^ {\\hat {\\beta} _ {i}}}}{2 \\hat {\\alpha} _ {i} \\Gamma \\left(1 / \\hat {\\beta} _ {i}\\right)} \\tag {2}", + "image_path": "16dbc04ba7b3ca77a6807c42269700235503856e568ac8318292999beb7d73ca.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "text", + "content": "In the above equation, " + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "inline_equation", + "content": "\\frac{\\hat{\\beta}_i e^{-(|\\hat{\\mathbf{z}}_i - \\mathbf{z}_i| / \\hat{\\alpha}_i)^{\\hat{\\beta}_i}}{2\\hat{\\alpha}_i \\Gamma(1 / \\hat{\\beta}_i)}" + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "text", + "content": " represents the generalized Gaussian distribution (GGD, represented by " + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "text", + "content": ") that is capable of modeling heavy-tailed distributions (note the Gaussian and Laplace are special cases of " + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "inline_equation", + "content": "\\alpha = 1, \\beta = 2" + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "inline_equation", + "content": "\\alpha = 1, \\beta = 1" + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "text", + "content": ", respectively). The variables " + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_i, \\hat{\\alpha}_i, \\hat{\\beta}_i" + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "text", + "content": " are the predicted mean, scale, and shape parameters of " + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "text", + "content": " from our modality-specific components for the given input " + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "text", + "content": ". We obtain modality-specific optimal parameters by minimizing negative log-likelihood (equivalent to Equation 2). Given " + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "text", + "content": " and predicted " + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}, \\hat{\\alpha}, \\hat{\\beta}" + }, + { + "bbox": [ + 46, + 177, + 288, + 307 + ], + "type": "text", + "content": ", loss is given by," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 75, + 326, + 287, + 357 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 326, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 75, + 326, + 287, + 357 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {r e c}} (\\zeta) := \\left(\\frac {| \\hat {\\mathbf {z}} - \\mathbf {z} |}{\\hat {\\alpha}}\\right) ^ {\\hat {\\beta}} - \\log \\frac {\\hat {\\beta}}{\\hat {\\alpha}} + \\log \\Gamma \\left(\\frac {1}{\\hat {\\beta}}\\right) \\tag {3}", + "image_path": "53810e043bffc85a39405e9ca90d4b5d2778725585ad4d62830bb6bbf0ab8a5a.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 368, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 368, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 368, + 287, + 464 + ], + "type": "text", + "content": "Therefore, the vision-specific component of ProbVLM, " + }, + { + "bbox": [ + 46, + 368, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\Psi (\\cdot ;\\zeta_{\\nu}))" + }, + { + "bbox": [ + 46, + 368, + 287, + 464 + ], + "type": "text", + "content": ", is trained by minimizing the Equation 3 using image embeddings, we denote this loss as " + }, + { + "bbox": [ + 46, + 368, + 287, + 464 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{rec}}^{\\mathcal{V}}(\\zeta_V)" + }, + { + "bbox": [ + 46, + 368, + 287, + 464 + ], + "type": "text", + "content": ". Similarly the text-specific component, " + }, + { + "bbox": [ + 46, + 368, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\Psi (\\cdot ;\\zeta_T)" + }, + { + "bbox": [ + 46, + 368, + 287, + 464 + ], + "type": "text", + "content": ", is trained by minimizing " + }, + { + "bbox": [ + 46, + 368, + 287, + 464 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{rec}}^{\\mathcal{T}}(\\zeta_T)" + }, + { + "bbox": [ + 46, + 368, + 287, + 464 + ], + "type": "text", + "content": ". As discussed next, we also enforce cross-modal alignment so that the predicted distribution of ProbVLM captures the uncertainties across modalities from one-to-many correspondences for an embedding." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "spans": [ + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "type": "text", + "content": "Cross-modal Alignment. While the intra-modal alignment seeks to match the means of the output distribution from ProbVLM to the embeddings derived from frozen vision-language encoders, we also enforce the image and text embedding output distribution (from ProbVLM) belonging to similar concepts to remain close to each other. That is, given an image and text embedding pair " + }, + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "type": "inline_equation", + "content": "(\\mathbf{z}_{\\mathcal{V}},\\mathbf{z}_{\\mathcal{T}})" + }, + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "type": "text", + "content": " (from frozen model) representing similar concepts, the output distributions from " + }, + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "type": "inline_equation", + "content": "\\Psi (\\cdot ;\\zeta),\\mathcal{G}(\\mathbf{z};\\hat{\\mathbf{z}}_{\\mathcal{V}},\\hat{\\alpha}_{\\mathcal{V}},\\hat{\\beta}_{\\mathcal{V}})" + }, + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(\\mathbf{z};\\hat{\\mathbf{z}}_{\\mathcal{T}},\\hat{\\alpha}_{\\mathcal{T}},\\hat{\\beta}_{\\mathcal{T}})" + }, + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "type": "text", + "content": " (later referred to as " + }, + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\mathcal{V}}(\\mathbf{z}))" + }, + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\mathcal{T}}(\\mathbf{z}))" + }, + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "type": "text", + "content": " should match. This can be measured directly from the likelihood as, " + }, + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "type": "inline_equation", + "content": "p(\\mathbf{z}_v = \\mathbf{z}_u)" + }, + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_v\\sim \\mathcal{G}_{\\mathcal{V}}(\\mathbf{z})" + }, + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_u\\sim \\mathcal{G}_{\\mathcal{T}}(\\mathbf{z})" + }, + { + "bbox": [ + 46, + 465, + 288, + 611 + ], + "type": "text", + "content": " as in [73], i.e.," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 629, + 287, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 629, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 52, + 629, + 287, + 654 + ], + "type": "interline_equation", + "content": "p \\left(\\mathbf {z} _ {v} = \\mathbf {z} _ {u}\\right) := \\iint \\mathcal {G} _ {\\mathcal {Y}} \\left(\\mathbf {z} _ {v}\\right) \\mathcal {G} _ {\\mathcal {T}} \\left(\\mathbf {z} _ {u}\\right) \\delta \\left(\\mathbf {z} _ {v} - \\mathbf {z} _ {u}\\right) d \\mathbf {z} _ {v} d \\mathbf {z} _ {u} \\tag {4}", + "image_path": "90389d759aa7da6aed14e777243d0e6007f6ca41235bd0e4183c798ea589c55c.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\delta (\\cdot)" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": " refers to the Dirac-delta distribution. The above integral can be simplified further by defining " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\Delta \\mathbf{z} = \\mathbf{z}_v - \\mathbf{z}_u" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": " and seeking " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "p(\\Delta \\mathbf{z}) = 0" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": ". As both " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_v" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_u" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": " are GGD random variables, " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\Delta \\mathbf{z}" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": " follows the distribution based on the" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 72, + 497, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 497, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 497, + 84 + ], + "type": "text", + "content": "Bivariate Fox H-function [76, 48, 49] given by," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 376, + 91, + 474, + 109 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 91, + 474, + 109 + ], + "spans": [ + { + "bbox": [ + 376, + 91, + 474, + 109 + ], + "type": "interline_equation", + "content": "\\Delta z \\sim \\frac {1}{2 \\Gamma (1 / \\hat {\\beta} _ {\\mathcal {V}}) , \\Gamma (1 / \\hat {\\beta} _ {\\mathcal {T}})} \\times", + "image_path": "f65bad5b8a92f5266df4967d3d5a140d60762c6355b975fde455c6b3e0d029af.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 309, + 110, + 545, + 146 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 110, + 545, + 146 + ], + "spans": [ + { + "bbox": [ + 309, + 110, + 545, + 146 + ], + "type": "interline_equation", + "content": "\\int \\mathcal {H} _ {1, 2} ^ {1, 1} \\left[ A t ^ {2} \\left| \\begin{array}{l} \\left(1 - \\frac {1}{\\bar {\\mathbf {z}} _ {\\mathcal {V}}}, \\frac {1}{\\bar {\\mathbf {z}} _ {\\mathcal {T}}}\\right) \\\\ (0, 1) \\left(\\frac {1}{2}, 1\\right) \\end{array} \\right. \\right] \\mathcal {H} _ {1, 2} ^ {1, 1} \\left[ B t ^ {2} \\left| \\begin{array}{l} \\left(1 - \\frac {1}{\\bar {\\mathbf {z}} _ {\\mathcal {T}}}, \\frac {1}{\\bar {\\mathbf {z}} _ {\\mathcal {T}}}\\right) \\\\ (0, 1) \\left(\\frac {1}{2}, 1\\right) \\end{array} \\right. \\right] \\cos t (\\mu - z) d t \\tag {5}", + "image_path": "95419e34cab610a7723842d03c346568d71210f1110da196550123bee6b1d2f0.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 155, + 545, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 155, + 545, + 221 + ], + "spans": [ + { + "bbox": [ + 305, + 155, + 545, + 221 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 305, + 155, + 545, + 221 + ], + "type": "inline_equation", + "content": "A = \\frac{\\hat{\\alpha}_{\\mathcal{V}}^2\\Gamma(1 / \\hat{\\beta}_{\\mathcal{V}})}{4\\Gamma(3 / \\hat{\\beta}_{\\mathcal{V}})}" + }, + { + "bbox": [ + 305, + 155, + 545, + 221 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 155, + 545, + 221 + ], + "type": "inline_equation", + "content": "B = \\frac{\\hat{\\alpha}_{\\mathcal{T}}^2\\Gamma(1 / \\hat{\\beta}_{\\mathcal{T}})}{4\\Gamma(3 / \\hat{\\beta}_{\\mathcal{T}})}" + }, + { + "bbox": [ + 305, + 155, + 545, + 221 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 155, + 545, + 221 + ], + "type": "inline_equation", + "content": "\\mu = \\hat{\\mathbf{z}}_v - \\hat{\\mathbf{z}}_u" + }, + { + "bbox": [ + 305, + 155, + 545, + 221 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 155, + 545, + 221 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 305, + 155, + 545, + 221 + ], + "type": "text", + "content": " is the Fox " + }, + { + "bbox": [ + 305, + 155, + 545, + 221 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 305, + 155, + 545, + 221 + ], + "type": "text", + "content": " function [76, 48, 49]. Equation 5 does not provide a scalable objective function suitable for training deep neural networks. Hence, we propose an approximation that is easily scalable for deep-learning models given by," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 238, + 545, + 289 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 238, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 317, + 238, + 545, + 289 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} p (\\mathbf {z} _ {v} = \\mathbf {z} _ {u}) = \\iint \\mathcal {G} _ {\\mathcal {V}} (\\mathbf {z} _ {v}) \\mathcal {G} _ {\\mathcal {T}} (\\mathbf {z} _ {u}) \\delta (\\mathbf {z} _ {v} - \\mathbf {z} _ {u}) d \\mathbf {z} _ {v} d \\mathbf {z} _ {u} \\\\ \\approx \\int \\frac {1}{2} \\left(\\mathcal {G} _ {\\mathcal {V}} (\\mathbf {z}) \\delta (\\mathbf {z} - \\mathbf {z} _ {\\mathcal {T}}) + \\mathcal {G} _ {\\mathcal {T}} (\\mathbf {z}) \\delta (\\mathbf {z} - \\mathbf {z} _ {\\mathcal {V}})\\right) d \\mathbf {z} \\tag {6} \\\\ \\end{array}", + "image_path": "786e34345c40390819ec889855f6f1a5ff917fd72adba41ab92a73270fbbaff8.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 295, + 545, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 295, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 305, + 295, + 545, + 403 + ], + "type": "text", + "content": "The appendix shows details of the above equation. The first term in the integral, " + }, + { + "bbox": [ + 305, + 295, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\int \\mathcal{G}_{\\mathcal{V}}(\\mathbf{z})\\delta (\\mathbf{z} - \\mathbf{z}_{\\mathcal{T}})d\\mathbf{z}" + }, + { + "bbox": [ + 305, + 295, + 545, + 403 + ], + "type": "text", + "content": ", is the likelihood of the text embedding " + }, + { + "bbox": [ + 305, + 295, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathcal{T}}" + }, + { + "bbox": [ + 305, + 295, + 545, + 403 + ], + "type": "text", + "content": " under the predicted distribution, " + }, + { + "bbox": [ + 305, + 295, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\mathcal{V}}(\\mathbf{z})" + }, + { + "bbox": [ + 305, + 295, + 545, + 403 + ], + "type": "text", + "content": ", for the visual embedding. Similarly, the second term is the likelihood of the visual embedding " + }, + { + "bbox": [ + 305, + 295, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathcal{V}}" + }, + { + "bbox": [ + 305, + 295, + 545, + 403 + ], + "type": "text", + "content": " under the predicted distribution, " + }, + { + "bbox": [ + 305, + 295, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\mathcal{T}}(\\mathbf{z})" + }, + { + "bbox": [ + 305, + 295, + 545, + 403 + ], + "type": "text", + "content": ", for the text embedding. Negative log of Equation 6 leads to a scalable objective function that can be used to learn the optimal parameters for vision and text components of ProbVLM " + }, + { + "bbox": [ + 305, + 295, + 545, + 403 + ], + "type": "inline_equation", + "content": "(\\Psi_{\\mathcal{V}}(\\cdot ;\\zeta_{\\mathcal{V}})" + }, + { + "bbox": [ + 305, + 295, + 545, + 403 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 295, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\Psi_{\\mathcal{T}}(\\cdot ;\\zeta_{\\mathcal{T}}))" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 310, + 420, + 545, + 505 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 420, + 545, + 505 + ], + "spans": [ + { + "bbox": [ + 310, + 420, + 545, + 505 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {\\text {c r o s s}} (\\zeta_ {\\mathcal {V}}, \\zeta_ {\\mathcal {T}}) := \\underbrace {\\left(\\frac {| \\hat {\\mathbf {z}} _ {\\mathcal {V}} - \\mathbf {z} _ {\\mathcal {T}} |}{\\hat {\\alpha} _ {\\mathcal {V}}}\\right) ^ {\\hat {\\beta} _ {\\mathcal {V}}} - \\log \\frac {\\hat {\\beta} _ {\\mathcal {V}}}{\\hat {\\alpha} _ {\\mathcal {V}}} + \\log \\Gamma \\left(\\frac {1}{\\hat {\\beta} _ {\\mathcal {V}}}\\right)} _ {\\text {C r o s s - m o d a l : v i s i o n} \\rightarrow \\text {t e x t}} + \\\\ \\underbrace {\\left(\\frac {| \\hat {\\mathbf {z}} _ {\\mathcal {T}} - \\mathbf {z} _ {\\mathcal {V}} |}{\\hat {\\alpha} _ {\\mathcal {T}}}\\right) ^ {\\hat {\\beta} _ {\\mathcal {T}}} - \\log \\frac {\\hat {\\beta} _ {\\mathcal {T}}}{\\hat {\\alpha} _ {\\mathcal {T}}} + \\log \\Gamma \\left(\\frac {1}{\\hat {\\beta} _ {\\mathcal {T}}}\\right)} _ {\\text {C r o s s - m o d a l : t e x t} \\rightarrow \\text {v i s i o n}} \\tag {7} \\\\ \\end{array}", + "image_path": "2ec569be467f4f47b499181dc4c92ba356457af2b496e1d41fafeb155098360b.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 511, + 544, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 511, + 544, + 524 + ], + "spans": [ + { + "bbox": [ + 306, + 511, + 544, + 524 + ], + "type": "text", + "content": "The overall objective used for ProbVLM is designed to be," + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 543, + 545, + 567 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 543, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 313, + 543, + 545, + 567 + ], + "type": "interline_equation", + "content": "L _ {\\text {P r o b V L M}} \\left(\\zeta_ {\\mathcal {V}}, \\zeta_ {\\mathcal {T}}\\right) = L _ {\\text {r e c}} ^ {\\mathcal {V}} \\left(\\zeta_ {\\mathcal {V}}\\right) + L _ {\\text {r e c}} ^ {\\mathcal {T}} \\left(\\zeta_ {\\mathcal {T}}\\right) + \\lambda_ {\\text {c r o s s}} L _ {\\text {c r o s s}} \\left(\\zeta_ {\\mathcal {V}}, \\zeta_ {\\mathcal {T}}\\right) \\tag {8}", + "image_path": "e50e2d17a2f129259dc174012ae36518425f235c8fd31ea45a6008b91a8a910d.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 576, + 544, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 576, + 544, + 599 + ], + "spans": [ + { + "bbox": [ + 305, + 576, + 544, + 599 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 576, + 544, + 599 + ], + "type": "inline_equation", + "content": "\\lambda_{cross}" + }, + { + "bbox": [ + 305, + 576, + 544, + 599 + ], + "type": "text", + "content": " is a hyperparameter controlling the relative contribution of inter-intra modality terms." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 601, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 601, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 601, + 545, + 715 + ], + "type": "text", + "content": "Uncertainty Quantification. Given embedding " + }, + { + "bbox": [ + 305, + 601, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 305, + 601, + 545, + 715 + ], + "type": "text", + "content": " from a frozen encoder, predicted distributions from the trained ProbVLM (output from the appropriate component) allows aleatoric uncertainty estimation as " + }, + { + "bbox": [ + 305, + 601, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\hat{\\sigma}_{\\mathrm{aleatoric}}^2 = \\frac{\\hat{\\alpha}^2\\Gamma(3 / \\hat{\\beta})}{\\Gamma(1 / \\hat{\\beta})}" + }, + { + "bbox": [ + 305, + 601, + 545, + 715 + ], + "type": "text", + "content": ". Moreover, we design both " + }, + { + "bbox": [ + 305, + 601, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\Psi_{\\mathcal{V}}" + }, + { + "bbox": [ + 305, + 601, + 545, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 601, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\Psi_{\\mathcal{T}}" + }, + { + "bbox": [ + 305, + 601, + 545, + 715 + ], + "type": "text", + "content": " to be simple 3-layer MLPs with dropout layers (with dropout probability set to 0.1 during training). Activating dropouts during inference, with multiple forward passes (say " + }, + { + "bbox": [ + 305, + 601, + 545, + 715 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 601, + 545, + 715 + ], + "type": "text", + "content": "), allows estimating the epistemic uncertainty, " + }, + { + "bbox": [ + 305, + 601, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\hat{\\sigma}_{\\mathrm{epistemic}}^2 = \\frac{1}{M}\\sum_{m = 1}^{M}(\\hat{\\mathbf{z}}_m - \\hat{\\mathbf{z}}_m)" + }, + { + "bbox": [ + 305, + 601, + 545, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1902" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 70, + 528, + 244 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 528, + 244 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 528, + 244 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 528, + 244 + ], + "type": "image", + "image_path": "dd1fa4cba0b3d41f9705ef3b250b6d128d630ee9b7b2bb24ce589fc600aeabf8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 65, + 245, + 528, + 408 + ], + "blocks": [ + { + "bbox": [ + 65, + 245, + 528, + 408 + ], + "lines": [ + { + "bbox": [ + 65, + 245, + 528, + 408 + ], + "spans": [ + { + "bbox": [ + 65, + 245, + 528, + 408 + ], + "type": "image", + "image_path": "e064d97907fb223a5aa4c8799ec4fccd4d0b3f6a60db46e50991bcc93f31b41b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 409, + 546, + 433 + ], + "lines": [ + { + "bbox": [ + 46, + 409, + 546, + 433 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 546, + 433 + ], + "type": "text", + "content": "Figure 3: Measuring the calibration with various post-hoc method for Image-to-Text and Text-to-Image retrieval when trained on (top) CUB and (bottom) COCO, and evaluated on CUB, COCO, Flickr, FLO." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 437, + 241, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 437, + 241, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 437, + 241, + 453 + ], + "type": "inline_equation", + "content": "\\frac{1}{M}\\sum_{j = 1}^{M}\\hat{\\mathbf{z}}_j)^2" + }, + { + "bbox": [ + 47, + 437, + 241, + 453 + ], + "type": "text", + "content": " We estimate total uncertainty as," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 111, + 462, + 287, + 478 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 462, + 287, + 478 + ], + "spans": [ + { + "bbox": [ + 111, + 462, + 287, + 478 + ], + "type": "interline_equation", + "content": "\\hat {\\sigma} _ {\\text {t o t a l}} ^ {2} = \\hat {\\sigma} _ {\\text {e p i s t e m i c}} ^ {2} + \\hat {\\sigma} _ {\\text {a l e a t o r i c}} ^ {2} \\tag {9}", + "image_path": "347dc415b78fe2abe4fdd1d0d04f28de7f4988031fd452c30460d6d6489859b1.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 486, + 287, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 486, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 47, + 486, + 287, + 498 + ], + "type": "text", + "content": "3.3. Latent Diffusion for Probabilistic Embeddings" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 505, + 287, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 589 + ], + "type": "text", + "content": "For a given text embedding " + }, + { + "bbox": [ + 46, + 505, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathcal{T}}" + }, + { + "bbox": [ + 46, + 505, + 287, + 589 + ], + "type": "text", + "content": ", the distribution estimated via ProbVLM, " + }, + { + "bbox": [ + 46, + 505, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(\\mathbf{z};\\hat{\\mathbf{z}}_{\\mathcal{T}},\\hat{\\alpha}_{\\mathcal{T}},\\hat{\\beta}_{\\mathcal{T}})" + }, + { + "bbox": [ + 46, + 505, + 287, + 589 + ], + "type": "text", + "content": " can be visualized by drawing samples from the predicted distribution of vectors (say, " + }, + { + "bbox": [ + 46, + 505, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\{\\hat{\\mathbf{z}}_{\\mathcal{T},i}\\}_{i = 1}^{Q}" + }, + { + "bbox": [ + 46, + 505, + 287, + 589 + ], + "type": "text", + "content": ") and passing them through a latent diffusion model, e.g., Stable Diffusion (say, " + }, + { + "bbox": [ + 46, + 505, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\Omega (\\cdot ;\\theta_{\\Omega}^{*}))" + }, + { + "bbox": [ + 46, + 505, + 287, + 589 + ], + "type": "text", + "content": " using CLIP text encoder, to synthesize the set of samples (say, " + }, + { + "bbox": [ + 46, + 505, + 287, + 589 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 46, + 505, + 287, + 589 + ], + "type": "text", + "content": ") from the corresponding distribution of images, i.e.," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 123, + 597, + 287, + 612 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 597, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 123, + 597, + 287, + 612 + ], + "type": "interline_equation", + "content": "J := \\left\\{\\boldsymbol {\\Omega} \\left(\\hat {\\mathbf {z}} _ {i}; \\theta_ {\\Omega}\\right) \\right\\} _ {i = 1} ^ {Q} \\tag {10}", + "image_path": "9cb9043cba3946917681bb75ebc24518077b5568fb70e4acac269660cf925051.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 621, + 286, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 286, + 633 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 286, + 633 + ], + "type": "text", + "content": "Section 4.4 uses this to visualize the predicted distributions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 645, + 190, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 190, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 190, + 658 + ], + "type": "text", + "content": "4. Experiments and Results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "We start by highlighting our tasks, datasets, and evaluation metrics. We also compare our model to various state-of-the-art methods quantitatively and qualitatively in Section 4.1. In Section 4.2, we provide an ablation analysis," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 439, + 545, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 439, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 305, + 439, + 545, + 464 + ], + "type": "text", + "content": "and Section 4.3 demonstrates some real-world applications of ProbVLM for model selection and active learning." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "content": "Datasets, Metrics, and Baselines. We use the MS-COCO [46], Flickr-30k [60], and the CUB [85] as they are widely used for cross-modal retrieval [10, 16, 75]. Furthermore, we adapt the Oxford-Flowers 102 (FLO) dataset [55] similar to [10] as an additional benchmark for cross-modal retrieval in a fine-grained setting. We evaluate the performance of both Image-to-Text retrieval and Text-to-Image Retrieval using the Recall@k (R@k) metric. To evaluate the calibration of the uncertainty estimates, we define uncertainty levels [10] and use the Spearman rank correlation (denoted by " + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "content": ") between the uncertainty level and the Recall@k for retrieval. For an ideal model, performance would decrease monotonically with increasing uncertainty levels, leading to a score of -1. We also compute the " + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "inline_equation", + "content": "R^2" + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "content": " for the regression fit between the uncertainty levels and R@1 performances to measure if the drop in performance follows a linear trend. Finally, we also measure the product of these two scores (as a unified metric), i.e., " + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "inline_equation", + "content": "-SR^2" + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "content": ", which should be 1.0 for an ideal model. Since there is no prior work to estimate probabilistic embeddings from a deterministic model" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1903" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 72, + 288, + 428 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 288, + 428 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 288, + 428 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 288, + 428 + ], + "type": "table", + "html": "
VLMMetricsi2tt2i
COCOFlickrFLOCUBCOCOFlickrFLOCUB
CLIPS↓-0.99-0.70-0.90-0.60-0.30-0.70-0.99-0.89
R2↑0.930.710.620.670.350.500.990.70
-SR2↑0.930.490.560.400.100.350.990.63
S↓-0.79-0.190.60-0.600.790.30-0.89-0.10
R2↑0.590.010.300.280.740.440.520.00
-SR2↑0.470.00-0.180.17-0.59-0.130.47-0.00
S↓-0.89-0.30-0.30-0.600.300.09-0.700.30
R2↑0.750.070.070.200.160.010.570.01
-SR2↑0.680.020.020.12-0.05-0.000.40-0.00
S↓-0.79-0.300.00-0.60-0.10-0.19-0.89-0.50
R2↑0.690.090.000.410.260.0710.800.15
-SR2↑0.550.030.000.240.000.010.730.07
BLIPS↓-0.87-0.79-0.74-0.66-0.43-0.38-0.31-0.22
R2↑0.920.830.680.610.520.480.450.38
-SR2↑0.800.660.500.400.220.180.140.08
S↓-0.82-0.74-0.63-0.63-0.39-0.32-0.28-0.18
R2↑0.720.760.620.440.480.380.390.37
-SR2↑0.580.570.390.270.190.120.110.07
S↓-0.76-0.53-0.60-0.44-0.28-0.26-0.28-0.21
R2↑0.810.560.600.530.500.340.440.36
-SR2↑0.620.290.360.230.140.090.120.08
S↓-0.44-0.33-0.74-0.60-0.19-0.26-0.21-0.21
R2↑0.660.560.420.550.490.230.350.36
-SR2↑0.290.180.310.330.100.060.070.08
", + "image_path": "1b77bdfa1162b48e15897f3912374d73744f1148e2203d5b5442d0e496fcaa38.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 436, + 287, + 485 + ], + "lines": [ + { + "bbox": [ + 46, + 436, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 287, + 485 + ], + "type": "text", + "content": "Table 1: Metrics to evaluate the calibration of the uncertainty estimates for both CLIP [62] and BLIP [45] Vision-Language models for all considered methods, trained on COCO and evaluated on COCO, Flickr, CUB, and FLO." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 505, + 287, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 661 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 661 + ], + "type": "text", + "content": "in a cross-modal setting, we adapt a few existing ideas for the task. The first baseline is adapted from PFE [73], where we learn the covariances for the heteroscedastic Gaussian distribution while keeping the mean fixed to the embeddings derived from the frozen encoders in each modality. The second is to use the soft-contrastive objective of PCME[10] to train a probabilistic adapter in a post-hoc fashion. Finally, we also have a baseline that performs Test-Time Data Augmentation (TTDA) on the inputs [2, 87]. This is done by perturbing the images and masking out words in the text. While TTDA does not require additional training, we train our ProbVLM and other baselines on datasets like COCO, Flickr, CUB, and FLO." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Implementation Details. Our ProbVLM consists of a Multi-Layer Perceptron (MLP) for both the image and text encoder, each consisting of an input layer going from embedding dimension to 256, a hidden layer of size 256, and" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "an output layer going from 256 to embedding dimensions. This is trained for 100 epochs with a learning rate of " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "1e^{-4}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": ". More details are available in the supplementary." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 133, + 500, + 146 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 133, + 500, + 146 + ], + "spans": [ + { + "bbox": [ + 305, + 133, + 500, + 146 + ], + "type": "text", + "content": "4.1. Calibrated Uncertainty via ProbVLM" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 157, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 157, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 157, + 545, + 456 + ], + "type": "text", + "content": "We investigate the calibration of the uncertainty derived from ProbVLM for the cross-modal retrieval task. All models trained on CUB and COCO were evaluated on all four datasets. Calibration plots are illustrated in Figure 3. We observe that the R@1 performance consistently drops for ProbVLM as we increase the uncertainty levels, whereas the baselines rarely see a monotonic drop in performance. We quantify this performance in Table 1. The highest score of 0.93 for " + }, + { + "bbox": [ + 304, + 157, + 545, + 456 + ], + "type": "inline_equation", + "content": "-SR^2" + }, + { + "bbox": [ + 304, + 157, + 545, + 456 + ], + "type": "text", + "content": " (i2t) on the COCO dataset indicates a decreasing performance trend with increasing uncertainty. Notably, the uncertainty estimates indicate the average performance in different bins even when ProbVLM is evaluated on datasets that are different from the train set. In some cases, we see that ProbVLM even achieves a nearly perfect score " + }, + { + "bbox": [ + 304, + 157, + 545, + 456 + ], + "type": "inline_equation", + "content": "(-SR^2" + }, + { + "bbox": [ + 304, + 157, + 545, + 456 + ], + "type": "text", + "content": " of 0.99, with CLIP VLM on FLO, after training on COCO for Image-to-Text Retrieval). On the contrary, we find that the baselines often achieve poor scores. It is important to note that all these models use the same underlying embeddings and achieve the same performance on the retrieval task. Of all the considered methods, ProbVLM provides the most calibrated uncertainty estimates. We see similar trends for ProbVLM with BLIP [45], where ProbVLM achieves a " + }, + { + "bbox": [ + 304, + 157, + 545, + 456 + ], + "type": "inline_equation", + "content": "-SR^2" + }, + { + "bbox": [ + 304, + 157, + 545, + 456 + ], + "type": "text", + "content": " of 0.80, when trained on COCO and evaluated on COCO, compared to other methods like PFE\\* (0.58), PCME\\* (0.62), and TTDA (0.29)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": "Figure 4-(Top) visualizes the ambiguities captured by ProbVLM on the visual embeddings. We take a bird image (source) from the CUB dataset and obtain the probability distribution for the visual embedding of that sample; we then compute the likelihood of the visual embeddings (i.e., point estimates derived from CLIP) for the other samples of CUB and COCO datasets, under the source distribution. We notice that within the CUB dataset, the bird images similar to the source image have a higher likelihood compared to other bird images. Also, the images from the COCO dataset tend to have a lower likelihood. However, some images from the COCO dataset have a likelihood similar to the samples from CUB. We visualize these samples and discover them to be bird images. Moreover, the overlapping region between CUB and COCO has samples from the COCO dataset that are ambiguous and related to bird images as they have similar backgrounds, etc. On the contrary, when a similar analysis is performed using the CLIP (by measuring the distance between the embeddings instead of likelihood, Figure 4-(Bottom)), we notice that the two datasets are well separated and ambiguities are not captured." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1904" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 70, + 286, + 266 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 286, + 266 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 286, + 266 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 286, + 266 + ], + "type": "image", + "image_path": "3ab0254dfbaf805c5c039debed3b6d06fb1f934714e6af4d7c9c32401ba36ee2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 274, + 289, + 360 + ], + "lines": [ + { + "bbox": [ + 46, + 274, + 289, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 289, + 360 + ], + "type": "text", + "content": "Figure 4: Visualizing the uncertainties of the vision encoder captured by ProbVLM. Fixing an image from CUB, we obtain the predicted embedding distribution and compute the likelihood of all other samples in CUB and COCO. We observe that the images in COCO are similar/ambiguous to CUB overlap (Top). However, deterministic embeddings lead to a separation between the two datasets (Bottom)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 371, + 168, + 482 + ], + "blocks": [ + { + "bbox": [ + 48, + 371, + 168, + 482 + ], + "lines": [ + { + "bbox": [ + 48, + 371, + 168, + 482 + ], + "spans": [ + { + "bbox": [ + 48, + 371, + 168, + 482 + ], + "type": "image", + "image_path": "8bd425a32f6e9ed765ef783551338c2d3a699a85f2ebdbd66845e30246fd6596.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 490, + 287, + 515 + ], + "lines": [ + { + "bbox": [ + 46, + 490, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 490, + 287, + 515 + ], + "type": "text", + "content": "Figure 5: Plot indicating (left) necessity of the cross-modal alignment and (right) data required to train ProbVLM." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 172, + 371, + 289, + 483 + ], + "blocks": [ + { + "bbox": [ + 172, + 371, + 289, + 483 + ], + "lines": [ + { + "bbox": [ + 172, + 371, + 289, + 483 + ], + "spans": [ + { + "bbox": [ + 172, + 371, + 289, + 483 + ], + "type": "image", + "image_path": "a7302e1bd2fcfb0f397635edae76fe5e697b635ea37ce994e893aea1955c2c4b.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 48, + 528, + 169, + 643 + ], + "blocks": [ + { + "bbox": [ + 48, + 528, + 169, + 643 + ], + "lines": [ + { + "bbox": [ + 48, + 528, + 169, + 643 + ], + "spans": [ + { + "bbox": [ + 48, + 528, + 169, + 643 + ], + "type": "image", + "image_path": "03282f7e403dc14d26cd0fd911bb2ef42a5b2d2a215861b1f0914c319883157c.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 651, + 288, + 688 + ], + "lines": [ + { + "bbox": [ + 46, + 651, + 288, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 651, + 288, + 688 + ], + "type": "text", + "content": "Figure 6: Uncertainty increases with increased masking of the input images (Left) and texts (Right). Results with three vision encoders and one language encoder from CLIP." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 169, + 529, + 288, + 643 + ], + "blocks": [ + { + "bbox": [ + 169, + 529, + 288, + 643 + ], + "lines": [ + { + "bbox": [ + 169, + 529, + 288, + 643 + ], + "spans": [ + { + "bbox": [ + 169, + 529, + 288, + 643 + ], + "type": "image", + "image_path": "ed8587106abc2759ed78ea8382486bc4711dd00dc5d90fa45be954d2cd705089.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 547, + 238 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 547, + 238 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 547, + 238 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 547, + 238 + ], + "type": "image", + "image_path": "719289f05fe280d6e183887a2199a8d7d78dd4271dd74df3ba1b73de8a94d3dd.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 244, + 546, + 281 + ], + "lines": [ + { + "bbox": [ + 304, + 244, + 546, + 281 + ], + "spans": [ + { + "bbox": [ + 304, + 244, + 546, + 281 + ], + "type": "text", + "content": "Figure 7: Results for active learning, with different vision encoders and varying training budgets. For a given encoder, uncertainty-based sampling outperforms random sampling." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 293, + 373, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 293, + 373, + 304 + ], + "spans": [ + { + "bbox": [ + 306, + 293, + 373, + 304 + ], + "type": "text", + "content": "4.2. Ablations" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 312, + 546, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 546, + 516 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 546, + 516 + ], + "type": "text", + "content": "We ablate different components of our proposed ProbVLM, to provide a deeper understanding of its workings. First, we perform a sensitivity analysis on the cross-modal reconstruction objective, as shown in Figure 5-(Left), for ProbVLM on BLIP using the COCO dataset. We need a non-zero coefficient of the cross-modal loss to ensure that ProbVLM learns meaningful uncertainties that capture the ambiguities across modalities and are well-correlated with its performance on the downstream retrieval task. Similarly, having a large co-efficient for the cross-modal loss could hinder learning a faithful identity reconstruction, thereby hampering the performance of the downstream evaluation. Next, we investigate the amount of data that is required to train ProbVLM in Figure 5-(Right). We get satisfactory calibration of the uncertainty estimates while using only " + }, + { + "bbox": [ + 304, + 312, + 546, + 516 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 312, + 546, + 516 + ], + "type": "text", + "content": " of the dataset (shown for ProbVLM on BLIP using COCO), indicating that ProbVLM is highly data-efficient." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 516, + 545, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 516, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 304, + 516, + 545, + 588 + ], + "type": "text", + "content": "Further, we investigate the uncertainties by masking out increasing portions of the input image/text in Figure 6. We use three different CLIP backbones for the images, ViT-B/32, ViT-B/16, ResNet50, and GPT-based language encoder from CLIP [62, 63]. The mean uncertainty steadily increases as we mask increasing amounts of input." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 597, + 388, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 388, + 609 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 388, + 609 + ], + "type": "text", + "content": "4.3. Applications" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 616, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 616, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 616, + 545, + 652 + ], + "type": "text", + "content": "We study the utility of the uncertainty estimates derived from ProbVLM on two critical applications not well reviewed for VLMs: active learning and model selection." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Active Learning. Here, we choose a small subset of the unlabeled dataset to fine-tune the model [11]. In this case, we wish to finetune the CLIP model on the FLO dataset while using a limited amount of labeled data. To achieve this, we estimate the uncertainty of the image embeddings us" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1905" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 68, + 544, + 208 + ], + "blocks": [ + { + "bbox": [ + 50, + 68, + 544, + 208 + ], + "lines": [ + { + "bbox": [ + 50, + 68, + 544, + 208 + ], + "spans": [ + { + "bbox": [ + 50, + 68, + 544, + 208 + ], + "type": "image", + "image_path": "b488cda5401dfc2a146c54173cab431149259b6dd9f630f094a14b9b4f27c708.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 210, + 547, + 247 + ], + "lines": [ + { + "bbox": [ + 46, + 210, + 547, + 247 + ], + "spans": [ + { + "bbox": [ + 46, + 210, + 547, + 247 + ], + "type": "text", + "content": "Figure 8: Visualizing the predicted embedding distributions from ProbVLM using a large-scale pre-trained diffusion model, i.e., Stable Diffusion. The example is shown for two different captions from CUB dataset, for which the point-estimate embedding vector is obtained via CLIP, and the distribution is obtained via ProbVLM." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 268, + 287, + 435 + ], + "blocks": [ + { + "bbox": [ + 198, + 258, + 226, + 266 + ], + "lines": [ + { + "bbox": [ + 198, + 258, + 226, + 266 + ], + "spans": [ + { + "bbox": [ + 198, + 258, + 226, + 266 + ], + "type": "text", + "content": "Metrics" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 268, + 287, + 435 + ], + "lines": [ + { + "bbox": [ + 50, + 268, + 287, + 435 + ], + "spans": [ + { + "bbox": [ + 50, + 268, + 287, + 435 + ], + "type": "table", + "html": "
DModelsUncertainty scoreR@1R@5R@10
CUBCLIP-ViT32-COCO11.9231.561.075.8
CLIP-ViT32-Flickr9.3732.464.276.9
CLIP-ViT32-FLO15.4322.849.864.9
FLOCLIP-ViT32-COCO11.8347.979.288.5
CLIP-ViT32-Flickr13.5549.584.693.9
CLIP-ViT32-CUB18.3937.769.482.8
FlickrCLIP-ViT32-COCO9.6188.897.899.8
CLIP-ViT32-CUB16.4925.847.455.6
CLIP-ViT32-FLO13.6752.877.885.2
COCOCLIP-ViT32-Flickr7.2858.180.988.2
CLIP-ViT32-CUB15.378.821.729.8
CLIP-ViT32-FLO12.4423.946.658.8
", + "image_path": "d63eeecb45416afdf5808264cc5b4d1bf3ad2aa15ffd455d18d53bdf10c41547.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 438, + 287, + 475 + ], + "lines": [ + { + "bbox": [ + 46, + 438, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 287, + 475 + ], + "type": "text", + "content": "Table 2: Results for the model selection experiment. ProbVLM accurately identifies the best performing source model using only unlabeled samples of the target dataset." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 483, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 287, + 567 + ], + "type": "text", + "content": "ing ProbVLM (trained using a diverse dataset like COCO). We then select the top-k samples sorted by their mean uncertainty in the visual embeddings and fine-tune the CLIP model using them with a contrastive objective [62]. Results with varying budgets are shown in Figure 7. Selecting samples based on uncertainty scores significantly outperforms random sampling for all considered visual backbones." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 569, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 569, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 569, + 287, + 629 + ], + "type": "text", + "content": "Pretrained Model Selection. We are given a set of models trained on different data distributions. We aim to select the best model for the target distribution for which we have unlabeled samples. This has been explored mostly in the context of classification previously [22, 26, 8, 9, 13, 14]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "We consider the specific case of having the CLIP models fine-tuned on three datasets, and the fourth dataset is held out, for which we only have the images. We compute the mean uncertainty on these images using ProbVLM whose weights are interpolated from all the source datasets [93, 94, 32, 31]. This is to ensure that the uncertainties on all these models are comparable. The results for this experiment are" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 257, + 547, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 257, + 547, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 257, + 547, + 342 + ], + "type": "text", + "content": "shown in Table 2. On CUB, Flickr, and COCO, the source model with the lowest uncertainty has the best performance on the target dataset, and on FLO dataset, the model with the least uncertainty has the 2nd best performance (R@1 of 47.9 vs 49.5 for the best model). This indicates that the uncertainties provided by ProbVLM can be used as a signal to predict the performance on unlabelled samples for retrieval." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 350, + 538, + 363 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 350, + 538, + 363 + ], + "spans": [ + { + "bbox": [ + 305, + 350, + 538, + 363 + ], + "type": "text", + "content": "4.4. Latent Diffusion for Embedding Uncertainty" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 369, + 547, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 547, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 547, + 598 + ], + "type": "text", + "content": "To further understand the semantics of the predicted embedding distributions from the ProbVLM, we visualize the text embedding distributions by sampling the embedding vectors from the predicted distribution for a caption (converted to embedding vector using CLIP) and passing it through the pre-trained latent diffusion model using CLIPs text encoder, stable diffusion, as shown in Figure 8 and described in details in Section 3.3. We observe from Figure 8 that the samples obtained closer to the mean (i.e., sampled embedding vector similar to the one generated by CLIP for the caption) lead to meaningful variations in the generated images, e.g., for the left caption, close to the mean of the distribution, the generated samples show variations in the shape and colour of the beak, wings, and feet. Whereas far away from the mean of the distributions, i.e., on the tails, we start seeing images with strong artifacts that no longer preserves the semantics of the caption. We observe this for another example as well shown in Figure 8-(Right). More results are available in the supplementary." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 609, + 379, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 379, + 621 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 379, + 621 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": "We introduce ProbVLM, a post-hoc method for estimating the embedding distribution for a frozen large-scale deterministic vision-language model. We efficiently estimate calibrated uncertainties using our framework and show that such calibrated estimates have a variety of applications in downstream tasks such as model selection and active learning. Furthermore, we perform experiments to interpret em" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1906" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": "bedding distribution predicted by ProbVLM using a large-scale pre-trained latent diffusion model (i.e., Stable Diffusion). We hope our work highlights and inspires future work on efficient methods for probabilistic embeddings." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 121, + 289, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 121, + 289, + 229 + ], + "spans": [ + { + "bbox": [ + 47, + 121, + 289, + 229 + ], + "type": "text", + "content": "Acknowledgements. This work was supported by DFG project number 276693517, by BMBF FKZ: 01IS18039A, by the ERC (853489 - DEXIM), by EXC number 2064/1 - project number 390727645, and by the MUR PNRR project FAIR - Future AI Research (PE00000013) funded by NextGenerationEU. 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EgoHMR efficiently leverages the scene geometry and achieves significantly more plausible human-scene interactions compared to baseline methods, ProHMR [32] and the extended ProHMR-scene (Sec. 5.3), even with severe body truncations." + ], + "image_footnote": [], + "bbox": [ + 122, + 327, + 261, + 404 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/99fa2f6fc657b5f73a4249c6d203aa108e28a1130f64ee332f494cda7766d053.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 299, + 255, + 478, + 325 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/74df6eea3b87bc8c5264d2bd61bc6b0aac966866760fad65e40eff3e922d7e89.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 271, + 325, + 470, + 404 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/808e491adb646f56082d00e64ba53e313db206869ae3e828ce4e780fc146cda2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 493, + 255, + 671, + 325 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9f4311148457c4d2094bad571b0e6030dcd418b45faa7536200a4c021e946a39.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 470, + 325, + 669, + 404 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/21be33b5f7f907620c67f306b8a954a8a1b694efaa4152287a153380e290c64b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 663, + 255, + 862, + 325 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3622831795701a0d6b7e26de6b66940c7027dab7a71eaa3ff386329414340cfb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 665, + 325, + 862, + 404 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 501, + 313, + 516 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Automatic perception of human behaviors during social interactions is crucial for AR/VR applications, and an essential component is estimation of plausible 3D human pose and shape of our social partners from the egocentric view. One of the biggest challenges of this task is severe body truncation due to close social distances in egocentric scenarios, which brings large pose ambiguities for unseen body parts. To tackle this challenge, we propose a novel scene-conditioned diffusion method to model the body pose distribution. Conditioned on the 3D scene geometry, the diffusion model generates bodies in plausible human-scene interactions, with the sampling guided by a physics-based collision score to further resolve human-scene interpenetrations. The classifier-free training enables flexible sampling with different conditions and enhanced diversity. A visibility-aware graph convolution model guided by per-joint visibility serves as the diffusion denoiser to incorporate inter-joint dependencies and per-body-part control. Extensive evaluations show that our method generates bodies in plausible interactions with 3D scenes, achieving both superior accuracy for visible joints and diversity for invisible body parts. The code is available at https:// sanweiliti.github.io/egohmr/egohmr.html.", + "bbox": [ + 75, + 536, + 472, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 501, + 630, + 516 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the rapid development of Augmented and Virtual Reality (AR/VR) devices, understanding human actions, behaviors and interactions of our social partners (\"inter-actee\") from the egocentric view is a vital component for head-mounted devices (HMDs) to truly become a virtual companion for humans. The first step towards the automatic perception of human behaviors and interactions for HMDs is to estimate 3D human pose and shape (i.e. human mesh recovery) of the interactee from egocentric view images.", + "bbox": [ + 496, + 531, + 890, + 667 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The research community has extensively studied human mesh recovery (HMR) from a single RGB image (usually captured with third-person view cameras) by predicting SMPL [39, 50] parameters from global image features [8, 24, 27, 30, 45]. However, their performance degrades significantly in egocentric images [78]. A major challenge presented in egocentric scenarios is frequent body truncation [38, 78], when individuals interact with each other within close proximity, while the HMD camera has a limited field-of-view. Since human poses are highly reliant on the surrounding environment, 3D scene structures can potentially provide strong cues to infer invisible body parts, which is crucial for precise understanding of human behaviors: sitting on a chair and standing on the ground may indicate distinct intentions and future behaviors. Following", + "bbox": [ + 496, + 674, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7989", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "PROX [15], we assume a rough 3D scene structure is available, as such information nowadays can be easily obtained with commodity sensors. Furthermore, visual localization and mapping, one of the extensively studied topics in computer vision, is progressing rapidly for head-mounted devices [52]. Therefore, we make the assumption that a coarse 3D model of the scene and the localization of the egocentric camera are readily available (e.g. in HoloLens2 [1]). In this paper, we focus on the challenging problem of estimating 3D human bodies that are heavily truncated from egocentric views due to the proximity between people and the motion of embodied cameras.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given an egocentric image and the corresponding 3D environment, what should an ideal human mesh recovery method achieve? In contrast to previous studies that mostly pursue full-body pose accuracy, we argue the following properties are desired in the egocentric scenario: (1) natural and plausible human-scene interactions; (2) accurate body pose estimations consistent with image observations for visible joints; (3) a comprehensive conditional distribution to generate diverse and plausible poses for unobserved body parts. Several recent studies have attempted to tackle pose ambiguities caused by occlusions and body truncations. However, some methods can only produce a discrete number of body poses [3, 34, 48], ignoring the continuous nature of the pose manifold. Other approaches model the continuous body pose distribution via conditional variational autoencoder [53] or normalizing flows [32, 68], but with limited expressiveness. Furthermore, the 3D environment is often ignored although it provides strong cues for inferring missing body parts in the image. Existing works for human pose estimation [54, 55, 79] or generation [14, 80-82] in 3D scenes typically cannot deal with truncated bodies in images.", + "bbox": [ + 75, + 276, + 472, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these issues, we introduce a novel scene-conditioned probabilistic approach, the first method to recover human mesh in 3D scenes from the egocentric view image. Inspired by the recent diffusion models that can generate high fidelity images [9, 17, 18, 59] and human motions [6, 25, 41, 63, 77] with flexible conditioning, our model is trained with a conditional diffusion framework, leveraging both the classifier-free guidance [18] and the classifier-guided diffusion sampling [9, 57, 60] for efficient scene conditioning. By training the model conditioning on a human-centric scene encoding, the diffusion denoiser can generate body poses with plausible human-scene interactions even with highly truncated bodies (see Fig. 1). The classifier-free training enables flexible sampling from models with or without image conditions, achieving accurate estimations of visible body parts while generating diverse plausible results for unseen body parts. On top of that, the diffusion sampling process is guided by the gradients of a physics-based collision score guidance in the classifier-", + "bbox": [ + 75, + 613, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "guided sampling manner, which further resolves human-scene inter-penetrations without requiring additional time-consuming postprocessing.", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To facilitate the learning of the multimodal distributions of the invisible body parts, we introduce a visibility-aware graph convolution model as the diffusion denoiser network, to explicitly guide the network to learn more expressive distribution for invisible body parts. Unlike existing methods [24, 32, 36, 68] that simply condition the full body pose on a global image feature, we condition the pose diffusion of each body joint on the joint visibility mask and the 3D scene feature, in addition to the image feature. With such explicit visibility guidance, the model learns to estimate accurate body pose for visible joints while encouraging diversity for truncated body parts. We adopt a graph convolution network (GCN) [26, 75, 84] to better incorporate local dependencies between highly-relevant body parts (e.g. knee-foot) according to the human kinematic tree.", + "bbox": [ + 496, + 136, + 892, + 362 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are: 1) a novel scene-conditioned diffusion model for probabilistic human mesh recovery in the 3D environment from egocentric images; 2) a physics-based collision score that guides the diffusion sampling process to further resolve human-scene interpenetrations; 3) a visibility-aware GCN architecture that incorporates inter-joint dependencies for the pose diffusion, and enables per-body-part control via the per-joint visibility conditioning. With extensive evaluations, the proposed method demonstrates superior accuracy and diversity of generated human bodies from egocentric images, in natural and plausible interactions with the 3D environment.", + "bbox": [ + 496, + 363, + 893, + 544 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 558, + 640, + 573 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Human mesh recovery from a single image. Given a single RGB image, the task of deterministic 3D human mesh recovery has been widely studied in the literature, with regression-based methods [7, 8, 11, 24, 27, 28, 30, 31, 35-37, 45, 49, 62, 71, 76, 83], optimization-based methods [4, 10, 33, 50, 69] or hybrid methods [23, 29, 58], mostly adopting parametric 3D body models [4, 70] to represent the 3D human mesh. Most of recent regression-based methods train neural networks to regress SMPL [4] parameters from images [11, 24, 28, 36, 51]. Model-free methods [7, 8, 37, 45] regress human mesh vertices without relying on parametric body models. Optimization-based methods iteratively optimize the body model parameters to fit 2D keypoints, human silhouettes, etc. Some resort to self-contact [46], scene [15, 69] or object [61] constraints to model interactions. Hybrid methods seek to combine the strengths of both regression and optimization, for instance, SPIN [29], which integrates an optimization loop into the deep learning framework. However, these methods often lack robustness when dealing with truncated bodies, a typical challenge in egocentric scenarios, and cannot", + "bbox": [ + 496, + 583, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7990", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "model the diverse nature of plausible missing body parts. 3D scene information is mostly disregarded, resulting in unrealistic human-scene interactions. In this work, we address these challenges by proposing a scene-conditioned generative model for human mesh recovery in 3D scenes.", + "bbox": [ + 75, + 90, + 467, + 165 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multi-hypothesis for 3D human pose estimation. Due to the limited image observation and depth ambiguity, estimating 3D human pose from a single image can have multiple potential solutions, especially when body truncation is presented. Recent works seek to model this task as a generative process or predict multiple hypothesis of possible poses. A discrete number of hypotheses are generated in [3, 21, 34, 48]. To learn the continuous distribution of possible body poses, conditional variational autoencoders [53] or conditional normalizing flows [32, 68] are adopted to generate unlimited number of hypotheses, but relying on additional scoring functions for pose selection [53], or discriminators to stabilize the training [32, 68]. Nevertheless, the 3D scene constraint is usually not taken into account in this line of works. We leverage the diffusion process to model the inherent pose ambiguity, with flexible scene-conditioning strategies.", + "bbox": [ + 75, + 167, + 467, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Egocentric human pose estimation. Most of existing works in egocentric human pose estimation targets the camera wearer's 3D pose [13, 22, 40, 56, 64, 65, 73]. 3D pose estimation for a social partner from the egocentric view has been receiving growing attention [38, 47, 72]. However, the 3D scene geometry is neglected in [47, 72], while [38] employs the time-consuming optimization, without modelling the probabilistic distribution of unseen body parts.", + "bbox": [ + 75, + 424, + 467, + 542 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models for human motion/pose generation. Denoising Diffusion Models [17, 57, 59, 60] are becoming a popular choice for human motion generative models. Typically trained with the DDPM formulation [17] and based on Transformer-backbones, different methods vary on their choice of motion representation (e.g. skeletons [41, 77], joint rotations [2, 25, 66] or latent variables [6]) and downstream tasks. To generate plausible human-scene interactions, SceneDiffuser [19] condition the motion/pose diffusion model on 3D scenes and further guide the model with physics-based objectives at inference time. In a similar fashion, PhysDiff [74] incorporates a physics-based motion projection module in the inference loop to resolve typical flaws in motion synthesis such as foot-ground penetrations. While these methods all target human action synthesis, we take a different perspective and leverage Diffusion Models for a perception task — as a multi-proposal formulation to address the ambiguity in the egocentric pose estimation.", + "bbox": [ + 75, + 544, + 467, + 815 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 829, + 215, + 845 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SMPL body model [39]. We model the human mesh with the parametric SMPL body model. SMPL parametrizes a body as a function $\\mathcal{M}_b(\\gamma, \\beta, \\theta)$ of the global transla", + "bbox": [ + 75, + 854, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tion $\\gamma \\in \\mathbb{R}^3$ , body shape $\\beta \\in \\mathbb{R}^{10}$ , and full body pose $\\theta \\in \\mathbb{R}^{24\\times 3}$ of 23 body joints, plus the global orientation, returning a mesh $\\mathcal{M}_b$ with 6890 vertices.", + "bbox": [ + 496, + 90, + 890, + 135 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Conditional Diffusion Model. We use DDPM [17] as our formulation of pose diffusion model. DDPM learns a distribution of body poses $\\pmb{\\theta}$ through a forward diffusion process and an inverse denoising (sampling) process. The forward diffusion process is a Markov chain of added Gaussian noise over $t\\in \\{1,\\dots ,T\\}$ steps:", + "bbox": [ + 496, + 136, + 890, + 227 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\boldsymbol {\\theta} _ {t} \\mid \\boldsymbol {\\theta} _ {t - 1}\\right) = \\mathcal {N} \\left(\\boldsymbol {\\theta} _ {t}; \\sqrt {\\alpha_ {t}} \\boldsymbol {\\theta} _ {t - 1}, (1 - \\alpha_ {t}) \\mathbf {I}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 239, + 890, + 256 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the variance $1 - \\alpha_{t} \\in (0, 1]$ increases with $t$ according to a pre-defined schedule, and $T$ is the total number of noise corruption steps.", + "bbox": [ + 496, + 267, + 890, + 311 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "At the core of the inverse process is a denoiser neural network $D(\\cdot)$ , which is trained to remove the added Gaussian noise based on condition signal $c$ at each step $t$ . Following the design of recent motion diffusion models [63], the denoiser predicts the clean signal itself: $\\hat{\\pmb{\\theta}}_0 = D(\\pmb{\\theta}_t, t, c)$ .", + "bbox": [ + 496, + 313, + 890, + 387 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The Gaussian forward diffusion process has a special property that allows directly sampling $\\theta_{t}$ from $\\theta_0$ :", + "bbox": [ + 496, + 388, + 890, + 417 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\theta} _ {t} = \\sqrt {\\alpha_ {t}} \\boldsymbol {\\theta} _ {0} + \\sqrt {1 - \\alpha_ {t}} \\boldsymbol {\\epsilon}, \\text {w h e r e} \\boldsymbol {\\epsilon} \\sim \\mathcal {N} (0, \\mathbf {I}). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 430, + 890, + 446 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "With this, training the denoiser amounts to sampling a random $t \\in \\{0, \\dots, T - 1\\}$ , adding noise according to Eq. (2), and optimizing the simple objective [17]:", + "bbox": [ + 496, + 458, + 890, + 503 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s i m p l e}} = E _ {\\boldsymbol {\\theta} _ {0} \\sim q (\\boldsymbol {\\theta} _ {0} | \\boldsymbol {c}), t \\sim [ 1, T ]} \\left[ \\| \\boldsymbol {\\theta} _ {0} - D (\\boldsymbol {\\theta} _ {t}, t, \\boldsymbol {c}) \\| _ {2} ^ {2} \\right]. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 515, + 890, + 534 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper we use the subscript $t$ to denote the diffusion timestep and superscript $j$ for the body joint index.", + "bbox": [ + 496, + 544, + 890, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 500, + 588, + 589, + 603 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We introduce a novel scene-conditioned diffusion method to recover the human mesh in 3D environments from the egocentric image. Fig. 2 shows the overview of our model. Given an egocentric image $\\mathcal{I}$ with a truncated body, the camera intrinsics $\\mathcal{K} = (f, c_x, c_y)$ , and the 3D scene point cloud $S \\in \\mathbb{R}^{N \\times 3}$ with $N$ points, our goal is to learn the conditional distribution of body poses $p(\\boldsymbol{\\theta} | \\mathcal{I}, S, \\mathcal{K})$ , with the objective of generating humans that naturally interact with the scene while being aligned with the image observation. The body translation $\\gamma$ and shape $\\beta$ are learnt in a deterministic way following [32]. Here $f$ and $(c_x, c_y)$ denote the focal length and the camera center, respectively.", + "bbox": [ + 496, + 613, + 890, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The diffusion denoising process (Sec. 3) is modeled by a visibility-aware graph convolution network (GCN), which achieves per-body-part control with the per-joint conditioning on the input image, scene geometry and joint visibility (Sec. 4.1). The diffusion model is trained in a classifier-free manner [18], enabling flexible sampling from both models", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7991", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/990be32fc501583ba472a7bdd5ff40d66a2f489fe6bc81dd0395efb5b2471e14.jpg", + "image_caption": [ + "Figure 2: Method overview. Given an egocentric image $\\mathcal{I}$ containing a partially visible body and the 3D scene geometry $S$ , the proposed model generates a SMPL mesh with plausible human-scene interactions and conforming to the image observation. The model comprises a Scene Conditioning module to estimate the body translation $\\hat{\\gamma}$ and encode the local scene features, an Image Conditioning module to encode image features, a GCN-based Diffusion Denoiser to predict the clean body pose $\\hat{\\theta}_0$ from noisy pose $\\theta_t$ with Per-joint Conditioning, and a Shape Estimator to estimate body shape $\\hat{\\beta}$ ." + ], + "image_footnote": [], + "bbox": [ + 86, + 89, + 885, + 313 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "that include or exclude image conditions to enhance diversity and expressiveness for truncated body parts. Guided by the gradients of a physics-based human-scene collision score, we further resolve human-scene inter-penetrations during the diffusion sampling (Sec. 4.2). The training objectives are explained in Sec. 4.3.", + "bbox": [ + 75, + 407, + 470, + 498 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Scene-conditioned Pose Diffusion Model", + "text_level": 1, + "bbox": [ + 76, + 511, + 421, + 527 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3D scene conditioning. To model fine-grained human-scene interactions, only a small region of the scene surrounding the human is relevant. An accurate global body translation provides better reasoning about local scene geometries, thus crucial for accurate and scene-plausible local body pose modelling. To this end, we propose a body translation estimator (see Fig. 2) to estimate the translation $\\hat{\\gamma}$ by extracting features from $\\mathcal{I}$ and the full 3D scene point cloud $S$ . The global scene features alleviate the scale ambiguity and localize the body in the 3D environment accurately (please refer to Supp. Mat. for more details). Given the estimated body translation $\\hat{\\gamma}$ , scene vertices in a $2 \\times 2m$ region around the human are selected and considered as the scene conditioning for the diffusion denoising process. Furthermore, the selected scene vertices are translated by $\\hat{\\gamma}$ such that the scene vertex origin is around the body pelvis. The translated scene point cloud is encoded by a scene encoder $E_{S}$ into a localized human-centric scene feature $E_{S}(S, \\hat{\\gamma})$ for modelling detailed interactions between the body and the 3D scene.", + "bbox": [ + 75, + 536, + 468, + 837 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Per-joint conditioning. A ResNet50 backbone [16] $E_{\\mathcal{I}}$ is used to encode the cropped input image $I$ into a latent feature $E_{\\mathcal{I}}(\\mathcal{I}) \\in \\mathbb{R}^{2048}$ as the image conditioning. However, regressing the full body pose directly from the global im", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "age feature as in previous works [24, 29, 32] loses the explicit joint visibility information. With the body truncated in the image, different properties are desired for different body parts: the model should achieve pose accuracy for observed body joints, and pose expressiveness for truncated body parts. To achieve the per-body-part control, the 2D joint visibility mask $\\mathcal{V} = (v^0,\\dots,v^j,\\dots,v^{J - 1})\\in \\mathbb{R}^J$ is extracted from the image via OpenPose [5] 2D joint detections, and passed to the diffusion model as the visibility condition. Here $J$ denotes the joint number; and $v^{j}$ equals to 1 if the $j$ -th joint is visible in $\\mathcal{I}$ , otherwise 0.", + "bbox": [ + 496, + 407, + 890, + 573 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Apart from above conditions, the bounding box information $\\mathcal{B}$ is additionally fed to the network inspired by [36], serving as a global-location-aware feature to better model global information:", + "bbox": [ + 496, + 574, + 890, + 633 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {B} = \\left(b _ {x}, b _ {y}, b\\right) / f, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 643, + 890, + 660 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $b_{x}, b_{y}, b$ denote the bounding box center coordinates and bounding box size in the full image, respectively.", + "bbox": [ + 496, + 667, + 890, + 699 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The full condition $c^j$ for $j$ -th joint is formulated as the concatenation of: the image feature (masked out by $v^j$ if the joint is not visible), 3D scene feature, estimated body translation, bounding box feature, camera intrinsics and the diffusion timestep $t$ :", + "bbox": [ + 496, + 699, + 890, + 775 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {c} ^ {j} = \\left(E _ {\\mathcal {I}} (\\mathcal {I}) \\cdot v ^ {j}, E _ {\\mathcal {S}} (\\mathcal {S}, \\hat {\\gamma}), \\hat {\\gamma}, \\mathcal {B}, \\mathcal {K}, t\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 784, + 890, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By conditioning on a per-joint basis, the model achieves flexible control over each body part according to the joint visibility. This allows for both accurate pose estimation of visible body parts, and flexibility for invisible body parts.", + "bbox": [ + 496, + 810, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Diffusion denoiser architecture. At diffusion timestep $t$ , for the noisy body pose parameters $\\theta_{t}$ , the diffusion de", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7992", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "noiser $D$ predicts the clean pose parameter $\\hat{\\theta}_0$ conditioned on $c$ . Previous works either use a single MLP for the full body pose [24, 32, 36, 68] with redundant dependencies between irrelevant joints, or employ a separate MLP for each joint [27] which fully ignores joint dependencies. Instead, we adopt a graph convolution network (GCN) [26, 84] as the denoising function $D$ . Given the predefined human kinematic tree, GCN models inter-joint dependencies by treating the human skeleton as a graph, where each node corresponds to a body joint. Specifically, for each joint $j$ , the noisy pose parameters $\\theta_t^j$ is embedded and concatenated with the per-joint conditioning $c^j$ as the feature for node $j$ in the GCN (see Fig. 2). We adopt the modulated GCN [84] for the implementation. Different from vanilla GCN [26], the modulated GCN learns node-specific modulation vectors to disentangle joint feature transformations, such that different relations can be learnt between joints. It also modulates the affinity matrix with learnable parameters to model additional edges beyond the human skeleton [84]. Please refer to Supp. Mat. for implementation details.", + "bbox": [ + 75, + 89, + 472, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Shape estimator. As the body shape $\\beta$ is a global feature and more robust to body truncations, an MLP branch (the body shape estimator in Fig. 2) predicts $\\hat{\\beta}$ from the conditions $(E_{\\mathcal{I}}(\\mathcal{I}), E_S(S, \\hat{\\gamma}), \\hat{\\gamma}, \\mathcal{B}, \\mathcal{K})$ in a deterministic way.", + "bbox": [ + 76, + 393, + 470, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Scene-guided Sampling", + "text_level": 1, + "bbox": [ + 76, + 463, + 294, + 479 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use the DDPM [17] sampler at inference time. At each sampling step $t$ , the denoiser predicts $\\hat{\\theta}_0 = D(\\theta_t, t, c)$ , which is noised back to $\\theta_{t-1}$ by sampling from the Gaussian distribution:", + "bbox": [ + 76, + 486, + 468, + 546 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\theta} _ {t - 1} \\sim \\mathcal {N} \\left(\\mu_ {t} \\left(\\boldsymbol {\\theta} _ {t}, \\hat {\\boldsymbol {\\theta}} _ {0}\\right), \\Sigma_ {t}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 556, + 468, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mu_t(\\pmb{\\theta}_t, \\hat{\\pmb{\\theta}}_0)$ is a linear combination of $\\pmb{\\theta}_t$ and $\\hat{\\pmb{\\theta}}_0$ , and $\\Sigma_t$ is a scheduled Gaussian distribution as in [17]. The sampling is iteratively repeated from $t = T - 1$ until $t = 0$ .", + "bbox": [ + 76, + 587, + 468, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Classifier-free guidance. The diffusion model $D$ is trained with classifier-free guidance [18] by randomly masking out the image feature $E_{\\mathcal{I}}(\\mathcal{I})$ for all joints with a probability of $5\\%$ during training, such that the model also learns the pose distribution independent from the image, enabling flexible sampling. By combining the poses of visible joints sampled from the full-conditioned model and the poses of invisible joints sampled from the model excluding image conditions:", + "bbox": [ + 75, + 633, + 470, + 755 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {\\theta}} _ {0} = D \\left(\\boldsymbol {\\theta} _ {t}, t, \\boldsymbol {c}\\right) \\odot \\mathcal {V} + D \\left(\\boldsymbol {\\theta} _ {t}, t, \\boldsymbol {c} _ {\\phi}\\right) \\odot (1 - \\mathcal {V}), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 780, + 468, + 799 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "we achieve better per-body-part control, with enhanced diversity for invisible body parts while maintaining the accuracy of visible body parts (see Sec. 5.5 for the ablation study). Here $\\odot$ denotes multiplying the joint visibility mask with the pose of each joint, and $c_{\\phi}$ is the condition excluding image features.", + "bbox": [ + 76, + 809, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Collision score guided sampling. The proposed scene encoding in Sec. 4.1 implicitly incorporates the 3D environment constraint into the diffusion conditioning. However, the network cannot fully resolve the human-scene collisions in a fine-grained way. Another way to incorporate conditions into the diffusion model is the score-function based guidance. As shown in previous works [9, 57, 60], a pretrained classifier can be adopted to provide class information by adding the gradients of the classifier at each sampling step to the diffusion model, to guide the sampling process towards the class label. Inspired by this, we propose a collision score guided sampling strategy to further resolve implausible human-scene inter-penetrations, by leveraging implicit body representations [43, 44]. We use COAP [43] to model neural articulated occupancy of human bodies as the zero-level set $f_{\\Theta}(q|\\mathcal{G}) = 0$ , where $q$ is the input query point and $\\mathcal{G}(\\theta ,\\beta)$ is the input bone transformations. By querying each scene vertex near the body to see if it is inside of the human volume, the collision score is defined as:", + "bbox": [ + 496, + 90, + 890, + 378 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {J} (\\boldsymbol {\\theta}) = \\frac {1}{| \\mathcal {S} |} \\sum_ {q \\in \\mathcal {S}} \\sigma \\left(f _ {\\Theta} (q \\mid \\mathcal {G})\\right) \\mathbb {I} _ {f _ {\\Theta} (s \\mid \\mathcal {G}) > 0}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 388, + 890, + 421 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\sigma(\\cdot)$ stands for the sigmoid function. The gradient $\\nabla \\mathcal{J}(\\boldsymbol{\\theta})$ efficiently guides the diffusion sampling process to further alleviate the human-scene collisions (see Sec. 5.5 for the ablation study) by modifying Eq. (6) to:", + "bbox": [ + 498, + 426, + 893, + 488 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\theta} _ {t - 1} \\sim \\mathcal {N} \\left(\\mu_ {t} \\left(\\boldsymbol {\\theta} _ {t}, \\hat {\\boldsymbol {\\theta}} _ {0}\\right) + a \\Sigma_ {t} \\nabla \\mathcal {J} \\left(\\boldsymbol {\\theta} _ {t}\\right), \\Sigma_ {t}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 498, + 890, + 516 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the guidance is modulated by $\\Sigma_{t}$ and a scale factor $a$ .", + "bbox": [ + 500, + 527, + 890, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Training Objectives", + "text_level": 1, + "bbox": [ + 500, + 551, + 689, + 569 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The diffusion model is trained with $\\mathcal{L}_{\\mathrm{simple}}$ in Eq. (3) for body pose $\\hat{\\theta}_0$ , together with the 3D joint loss $\\mathcal{L}_{\\mathrm{3D}}$ , the 2D keypoint re-projection loss $\\mathcal{L}_{\\mathrm{2D}}$ calculated in the full image frame, and the shape loss $\\mathcal{L}_{\\beta}$ :", + "bbox": [ + 498, + 575, + 890, + 640 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {3 D}} = \\left\\| F K (\\hat {\\boldsymbol {\\theta}} _ {0}, \\hat {\\boldsymbol {\\beta}}) - F K (\\boldsymbol {\\theta} _ {0}, \\boldsymbol {\\beta}) \\right\\| ^ {2},\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 651, + 821, + 670 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {2 D}} = \\left\\| \\Pi_ {\\mathcal {K}} \\left(J _ {\\mathrm {3 D}} + \\hat {\\gamma}\\right) - J _ {\\mathrm {e s t}} \\right\\| ^ {2}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 672, + 890, + 690 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\beta} = \\left\\| \\hat {\\boldsymbol {\\beta}} - \\boldsymbol {\\beta} \\right\\| ^ {2}.\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 693, + 692, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here $FK(\\cdot)$ denotes the SMPL joint regressor to obtain 3D joint coordinates. $J_{\\mathrm{est}}$ is the 2D body keypoint detections, and $\\Pi_{\\mathcal{K}}$ denotes the 3D to 2D projection in the full image with camera intrinsics $\\mathcal{K}$ . The overall loss is defined as:", + "bbox": [ + 498, + 723, + 890, + 782 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\text {s i m p l e}} + \\lambda_ {3 \\mathrm {D}} \\mathcal {L} _ {3 \\mathrm {D}} + \\lambda_ {2 \\mathrm {D}} \\mathcal {L} _ {2 \\mathrm {D}} + \\lambda_ {\\beta} \\mathcal {L} _ {\\beta} \\tag {11} \\\\ + \\lambda_ {\\text {c o l l}} \\mathcal {L} _ {\\text {c o l l}} + \\lambda_ {\\text {o r t h}} \\mathcal {L} _ {\\text {o r t h}}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 792, + 890, + 829 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\mathrm{orth}}$ is a regularizer to force the generated 6D pose rotation representation to be orthonormal, $\\mathcal{L}_{\\mathrm{coll}}$ is the scene collision loss the same as defined in Eq. (8), and $\\lambda s$ are the corresponding weight factors for each loss term.", + "bbox": [ + 498, + 839, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7993", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 89, + 209, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Dataset", + "text_level": 1, + "bbox": [ + 76, + 114, + 171, + 128 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Most of existing datasets for 3D human pose evaluation are either captured from the third-person view with the full body visible [15, 20, 42, 67], or do not contain the 3D environment [47]. The most relevant dataset is EgoBody [78], a large-scale egocentric dataset capturing 3D human motions during social interactions in 3D scenes. Each sequence involves two people interacting with each other in 3D environments, and one subject wears a head-mounted camera to capture the egocentric images containing the other interactee. Due to the close social interaction distance, the captured egocentric images typically exhibit strong body truncations for the interactee. We use the official train / test splits for training and evaluation, which include 90,120 / 62,140 frames, respectively.", + "bbox": [ + 75, + 138, + 472, + 351 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Evaluation Metrics", + "text_level": 1, + "bbox": [ + 76, + 361, + 261, + 376 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Strong body truncations pose inherent ambiguity for invisible body parts, while the visible body parts are relatively deterministic given the image observations, thus evaluating the accuracy of full body joints together as in [3, 32] is not suitable for such tasks. We propose to evaluate the proposed method from the following aspects.", + "bbox": [ + 75, + 385, + 468, + 476 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Accuracy. We employ Mean Per-Joint Position Error (MPJPE) and Vertex-to-Vertex (V2V) errors in $mm$ to evaluate the accuracy of estimated body pose and shape. For MPJPE, we report different variations: G-MPJPE as the joint error in the global coordinate; MPJPE as the pelvis-aligned joint errors, and PA-MPJPE as the joint errors after Procrustes Alignment [12]. We report mean MPJPE and V2V metrics over $n$ samples for visible joints. Nevertheless, such evaluation protocol assumes a single correct ground truth prediction, which does not hold for invisible joints. Instead of the mean error, we report min-of- $n$ MPJPE for invisible body parts following [3]. To be specific, among the generated $n$ samples for each input image, we select the one with the minimum MPJPE for all evaluated methods.", + "bbox": [ + 75, + 477, + 468, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Physical plausibility. We evaluate the collision and contact scores between the body mesh and the 3D scene. As the clean scene signed distance field (SDF) is not available in EgoBody, we define the collision score as the ratio of the number of scene vertices inside of the body mesh to the number of all scene vertices. Note that the absolute scale of the collision score may vary with different size of the 3D scene, but within the same scene surface, the relative comparison between different methods indicates different collision levels. We use the cropped scene as described in Sec. 4.1 for evaluation (with a fixed size of 20,000 vertices). Following [19], the contact score is defined as 1 if the body contacts with the scene in a distance within a threshold (2 cm), otherwise 0. We report the mean collision score and", + "bbox": [ + 75, + 688, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "contact score over all test samples. Note that a model with better physical plausibility should achieve both a lower collision score and a higher contact score.", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Diversity. Diversity is evaluated for invisible body parts to demonstrate the expressiveness of the methods, by calculating the standard deviation (std) and Average Pairwise Distance (APD) of invisible body joints [19]. A higher diversity is desired, yet there is usually a trade-off between diversity and accuracy/plausibility. An ideal model should predict diverse poses for invisible body parts, with accurate visible body poses and plausible human-scene interactions.", + "bbox": [ + 496, + 136, + 893, + 258 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Baselines and Our Method", + "text_level": 1, + "bbox": [ + 498, + 268, + 741, + 282 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As there is no existing work for our task, we compare our method with the following baselines: (1) ProHMR [32], the state-of-the-art method for probabilistic human mesh recovery from a single image based on conditional normalizing flows; (2) ProHMR-scene, in which we enhance the ProHMR framework by incorporating the scene geometry $S$ with a global scene feature encoder. The ProHMR framework is trained with 2D and 3D supervisions for the sample drawn from $z = 0$ (referred as the 'mode'), such that the 'mode' can be used as a predictive model (see [32] for details). Different training weights for the samples drawn from $z \\neq 0$ yields a trade-off between the accuracy and diversity for the generated multiple hypotheses. Here $z$ denotes the latent space of the normalizing flow. To demonstrate this trade-off, we train the ProHMR-scene baseline with different training configurations. For samples drawn from $z \\neq 0$ , we supervise with: 1) only 2D re-projection loss (the same as in [32]), denoted as -orig; 2) 3D supervision with small weights, denoted as -weak-3D; 3) 3D supervision with large weights, denoted as -strong-3D. Here the 3D supervision refers to the loss on 3D body joints and SMPL parameters. Please refer to Supp. Mat. for details of the baseline models.", + "bbox": [ + 496, + 292, + 893, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.4. Results", + "text_level": 1, + "bbox": [ + 500, + 650, + 591, + 664 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tab. 1 shows the quantitative results. Compared to the baselines, our method achieves the best G-MPJPE, MPJPE and V2V metrics for visible joints, demonstrating accurate estimations of the global translation, local body pose for visible joints and body shape. For truncated body joints, our method obtains the best min-of-n MPJPE, indicating that our generated results better covers the ground truth distribution for truncated body parts than baselines, thanks to the efficient scene conditioning. Our method also outperforms the baselines with the higher contact ratios and significantly better collision scores. In particular, our collision score decreased $45\\%$ compared with ProHMR, and $37\\%$ compared with the best ProHMR-scene model. This indicates that the proposed method can effectively leverage the scene conditions and resolve body-scene inter-penetrations,", + "bbox": [ + 496, + 674, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7994", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d6d088a10ebfe8e77094511e84a73445b58bf6eed82efcbfce403b6c92760878.jpg", + "table_caption": [ + "Table 1: Evaluation for accuracy, physical plausibility and diversity on EgoBody. Here -vis and -invis denote visible and invisible joints, respectively. 'coll' and 'contact' refer to the collision and contact scores, respectively. The percentage for the collision score denotes how much improvement the corresponding method has achieved compared with the ProHMR baseline. The best results are in boldface." + ], + "table_footnote": [], + "table_body": "
nMethodG-MPJPE ↓ -visMPJPE ↓ -visPA-MPJPE ↓ -visV2V ↓ -vismin-of-n MPJPE ↓ -inviscoll ↓contact ↑std ↑ -invisAPD ↑ -invis
5ProHMR [32]181.3372.9246.5790.88128.560.00346 (-)0.9426.5332.95
ProHMR-scene-orig133.7273.1348.8791.59117.880.00305 (12%)0.9635.4244.02
Ours128.6265.7047.1782.93107.770.00191 (45%)0.9929.5935.15
10ProHMR [32]181.7073.6547.0691.84121.670.00346 (-)0.9429.2635.06
ProHMR-scene-orig134.5774.4249.6393.21110.640.00305 (12%)0.9639.0746.86
Ours128.6065.6947.2082.94100.750.00191 (45%)0.9929.5935.15
20ProHMR [32]181.8773.9947.2992.28115.480.00346 (-)0.9330.5536.14
ProHMR-scene-orig134.9775.0349.9893.98103.810.00306 (12%)0.9640.8248.32
ProHMR-scene-weak-3D131.5167.8146.9485.05111.680.00313 (10%)0.9621.7925.67
ProHMR-scene-strong-3D134.4066.4245.9682.99123.340.00316 (9%)0.9713.0115.23
Ours128.6065.6947.1982.9494.960.00191(45%)0.9930.2335.14
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The left part shows the comparison between the baseline methods and our proposed method. The right part demonstrates the effectiveness of our proposed scene collision score guidance $\\mathcal{I}_{\\theta}$ to further resolve human-scene inter-penetrations. Red circles point to human-scene collisions." + ], + "image_footnote": [], + "bbox": [ + 89, + 751, + 184, + 808 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/989482f0b2936993d6cedbf900ec248c9a0389cb6778fb11873c86e58b013501.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 204, + 667, + 305, + 742 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/130d2bc6f51cd16234317ff070598f7f9e4216255f3a083786e3bd08c21eee11.jpg", + "image_caption": [ + "ProHMR" + ], + "image_footnote": [], + "bbox": [ + 204, + 742, + 305, + 813 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8c17ef90e897c471efc92edcf5335b41acf34c8fc1c635da6c4d9f6143bef8e8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 312, + 667, + 413, + 741 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9129a211b39f312cd43595f3147ad842f2639241706714ee39ff7e9fd97952f0.jpg", + "image_caption": [ + "ProHMR-scene" + ], + 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"table_caption": [ + "Table 2: Ablation study. $\\mathcal{I}_{\\theta}$ and CF denote the collision score guidance and classifier-free guidance during the diffusion sampling (Sec 4.2). $\\mathcal{L}_{\\mathrm{coll}}$ denotes the collision loss for training (Eq. (11)). All results are reported for $n = 20$ ." + ], + "table_footnote": [], + "table_body": "
MethodMPJPE ↓ -vismin-of-n MPJPE ↓ -inviscoll ↓contact ↑std ↑ -invisAPD ↑ -invis
Ours65.6994.960.001910.9930.2335.14
Ours w/o Jθ65.0997.200.002250.9921.5325.32
Ours w/o Jθ w/o CF64.5898.820.002290.9915.7519.56
Ours w/o Jθ w/o CF w/o Lcoll64.9196.260.003020.9922.9421.79
", + "bbox": [ + 183, + 130, + 789, + 219 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6252da45fd1577930c784b04638594ef730d4690db132cd775c4810269686dbf.jpg", + "image_caption": [ + "Figure 4: Multiple samples. Given the same input, our method can generate diverse poses for invisible body parts." + ], + "image_footnote": [], + "bbox": [ + 122, + 224, + 848, + 348 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "while achieving better contact relations between the body and the 3D environment. Fig. 3 (left) shows the qualitative results and the comparison with the baseline method.", + "bbox": [ + 75, + 388, + 470, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "From the results among different ProHMR-scene baselines $(n = 20)$ in Tab. 1, we can clearly see a trade-off between the accuracy and diversity: stronger 3D supervision (ProHMR-scene-strong-3D) has better accuracy for visible body parts (MPJPE-vis), yet lower diversity (std-invis and APD-invis) for invisible joints. The reason behind this is that the ProHMR framework, like many other existing works, condition the generative process of full body pose only on the global image feature. In contrast, our method leverages the joint visibility and the GCN architecture, achieving the best MPJPE for visible joints, diverse poses for invisible joints, and natural human-scene interactions (see Fig. 4), while the baseline with a similar diversity level (ProHMR) and the baseline with the highest diversity (ProHMR-scene-orig) exhibit much higher MPJPE errors and more severe human-scene collisions. There is a very slight increase for PA-MPJPE of our model compared to the ProHMR-scene-strong/weak-3D baselines, while we obtain a much higher diversity for invisible body joints. This reveals that our method achieves flexible per-body-part control to balance between the accuracy and diversity for different body parts.", + "bbox": [ + 75, + 440, + 468, + 773 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To validate the reconstruction accuracy, the full-body accuracy of the proposed method is also evaluated and compared against existing deterministic baselines on EgoBody dataset. The results show that our method even achieves higher full-body accuracy than deterministic methods, which demonstrates that the proposed model achieves diversity without sacrificing the reconstruction accuracy. In addition, the proposed method is also evaluated on PROX [15]", + "bbox": [ + 75, + 779, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "dataset, a monocular RGB-based third-person view dataset with human-scene interactions, and our method outperforms the baseline methods in terms of pose accuracy, human-scene interaction plausibility and pose diversity. Please refer to Supp. Mat. for detailed results of evaluations on PROX and comparison with deterministic methods on EgoBody.", + "bbox": [ + 496, + 388, + 893, + 494 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 510, + 653, + 526 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To investigate the influences of different training and sampling schemes for the diffusion model, we perform an ablation study and the results are shown in Tab. 2. The scene collision score efficiently resolves the human-scene interpenetrations from two different perspectives: via the collision loss $\\mathcal{L}_{\\mathrm{coll}}$ during training and via the explicit collision score guidance $\\mathcal{I}_{\\theta}$ during the diffusion sampling (Eq. (9)). Fig. 3 (right) shows that the collision score guidance $\\mathcal{I}_{\\theta}$ improves the human-scene interaction relationships. The classifier-free guidance during the diffusion sampling in Eq. (7) significantly improves the sample diversity, by leveraging the invisible joints sampled from the model trained excluding the image conditions. It is worth mentioning that the collision score guidance $\\mathcal{I}_{\\theta}$ also contributes to the sample diversity. This is not surprising as the gradients of $\\mathcal{I}_{\\theta}$ can potentially optimize the body pose to different directions given different initial body poses.", + "bbox": [ + 496, + 535, + 890, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Compared with the trade-off in the ProHMR-based methods where the accuracy sacrifices a lot for diversity (and vice versa), the classifier-free guidance and the collision score guidance in our model only bring marginal changes for the MPJPE of visible body parts, in the trade-off for significantly enhanced physical plausibility, sample diversity and better min-of-n MPJPE for unobserved joints.", + "bbox": [ + 496, + 794, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7996", + "bbox": [ + 482, + 944, + 516, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 90, + 194, + 104 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This paper introduces a novel scene-conditioned probabilistic approach for human mesh recovery from the egocentric image given the 3D scene geometry. The proposed diffusion model efficiently leverages the scene conditions and joint visibility to achieve per-body-part control and model human-scene interactions. The classifier-free guidance and the collision score guidance enables flexible sampling process with further enhanced diversity and physical plausibility. We demonstrate that our model generates human bodies in realistic interactions with the 3D environment, with diverse poses for invisible body parts while conforming to the image observation. Nevertheless, the current method also has limitations. For example, currently only a single frame is considered as the input. A promising future direction is to further exploit temporal information to reconstruct temporally consistent human motions from the egocentric view. Acknowledgements. This work was supported by Microsoft Mixed Reality & AI Zurich Lab PhD scholarship. Qianli Ma is partially funded by the Max Planck ETH Center for Learning Systems. We sincerely thank Korrawe Karunratanakul, Marko Mihajlovic and Shaofei Wang for the fruitful discussions.", + "bbox": [ + 76, + 111, + 472, + 443 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 454, + 174, + 469 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Microsoft Hololens2. https://www.microsoft.com/en-us/hololens.2", + "[2] Simon Alexanderson, Rajmund Nagy, Jonas Beskow, and Gustav Eje Henter. Listen, denoise, action! audio-driven motion synthesis with diffusion models. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 11477-11487, 2021. 2, 5" + ], + "bbox": [ + 78, + 104, + 467, + 756 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "8000", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Probabilistic Human Mesh Recovery in 3D Scenes from Egocentric Views/c490ef67-0a1e-4595-8f34-5035e971ee89_model.json b/2023/Probabilistic Human Mesh Recovery in 3D Scenes from Egocentric Views/c490ef67-0a1e-4595-8f34-5035e971ee89_model.json new file mode 100644 index 0000000000000000000000000000000000000000..be80bd4380f73444ecb2c80a93a058d6b6d6ce17 --- /dev/null +++ b/2023/Probabilistic Human Mesh Recovery in 3D Scenes from Egocentric Views/c490ef67-0a1e-4595-8f34-5035e971ee89_model.json @@ -0,0 +1,2985 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.131, + 0.856, + 0.154 + ], + "angle": 0, + "content": "Probabilistic Human Mesh Recovery in 3D Scenes from Egocentric Views" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.179, + 0.88, + 0.217 + ], + "angle": 0, + "content": "Siwei Zhang\\(^{1}\\) Qianli Ma\\(^{1,3}\\) Yan Zhang\\(^{1}\\) Sadegh Aliakbarian\\(^{2}\\) Darren Cosker\\(^{2}\\) Siyu Tang\\(^{1}\\) ETH Zürich\\(^{2}\\) Microsoft\\(^{3}\\) Max Planck Institute for Intelligent Systems" + }, + { + "type": "text", + "bbox": [ + 0.228, + 0.219, + 0.741, + 0.234 + ], + "angle": 0, + "content": "{siwei.zhang, qianli.ma, yan.zhang, siyu.tang}@inf.ethz.ch" + }, + { + "type": "text", + "bbox": [ + 0.301, + 0.237, + 0.672, + 0.251 + ], + "angle": 0, + "content": "{coskerdarren, saliakbarian}@microsoft.com" + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.256, + 0.287, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.123, + 0.328, + 0.262, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.3, + 0.256, + 0.479, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.272, + 0.326, + 0.472, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.256, + 0.672, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.472, + 0.326, + 0.671, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.665, + 0.256, + 0.864, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.666, + 0.326, + 0.864, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.417, + 0.895, + 0.478 + ], + "angle": 0, + "content": "Figure 1: We propose EgoHMR, a novel scene-conditioned probabilistic method to recover the human mesh from an ego-centric view image (typically with the body truncated) given the 3D environment. EgoHMR efficiently leverages the scene geometry and achieves significantly more plausible human-scene interactions compared to baseline methods, ProHMR [32] and the extended ProHMR-scene (Sec. 5.3), even with severe body truncations." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.502, + 0.314, + 0.517 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.473, + 0.884 + ], + "angle": 0, + "content": "Automatic perception of human behaviors during social interactions is crucial for AR/VR applications, and an essential component is estimation of plausible 3D human pose and shape of our social partners from the egocentric view. One of the biggest challenges of this task is severe body truncation due to close social distances in egocentric scenarios, which brings large pose ambiguities for unseen body parts. To tackle this challenge, we propose a novel scene-conditioned diffusion method to model the body pose distribution. Conditioned on the 3D scene geometry, the diffusion model generates bodies in plausible human-scene interactions, with the sampling guided by a physics-based collision score to further resolve human-scene interpenetrations. The classifier-free training enables flexible sampling with different conditions and enhanced diversity. A visibility-aware graph convolution model guided by per-joint visibility serves as the diffusion denoiser to incorporate inter-joint dependencies and per-body-part control. Extensive evaluations show that our method generates bodies in plausible interactions with 3D scenes, achieving both superior accuracy for visible joints and diversity for invisible body parts. The code is available at https:// sanweiliti.github.io/egohmr/egohmr.html." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.502, + 0.631, + 0.517 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.532, + 0.892, + 0.669 + ], + "angle": 0, + "content": "With the rapid development of Augmented and Virtual Reality (AR/VR) devices, understanding human actions, behaviors and interactions of our social partners (\"inter-actee\") from the egocentric view is a vital component for head-mounted devices (HMDs) to truly become a virtual companion for humans. The first step towards the automatic perception of human behaviors and interactions for HMDs is to estimate 3D human pose and shape (i.e. human mesh recovery) of the interactee from egocentric view images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.893, + 0.901 + ], + "angle": 0, + "content": "The research community has extensively studied human mesh recovery (HMR) from a single RGB image (usually captured with third-person view cameras) by predicting SMPL [39, 50] parameters from global image features [8, 24, 27, 30, 45]. However, their performance degrades significantly in egocentric images [78]. A major challenge presented in egocentric scenarios is frequent body truncation [38, 78], when individuals interact with each other within close proximity, while the HMD camera has a limited field-of-view. Since human poses are highly reliant on the surrounding environment, 3D scene structures can potentially provide strong cues to infer invisible body parts, which is crucial for precise understanding of human behaviors: sitting on a chair and standing on the ground may indicate distinct intentions and future behaviors. Following" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7989" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "PROX [15], we assume a rough 3D scene structure is available, as such information nowadays can be easily obtained with commodity sensors. Furthermore, visual localization and mapping, one of the extensively studied topics in computer vision, is progressing rapidly for head-mounted devices [52]. Therefore, we make the assumption that a coarse 3D model of the scene and the localization of the egocentric camera are readily available (e.g. in HoloLens2 [1]). In this paper, we focus on the challenging problem of estimating 3D human bodies that are heavily truncated from egocentric views due to the proximity between people and the motion of embodied cameras." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.277, + 0.473, + 0.61 + ], + "angle": 0, + "content": "Given an egocentric image and the corresponding 3D environment, what should an ideal human mesh recovery method achieve? In contrast to previous studies that mostly pursue full-body pose accuracy, we argue the following properties are desired in the egocentric scenario: (1) natural and plausible human-scene interactions; (2) accurate body pose estimations consistent with image observations for visible joints; (3) a comprehensive conditional distribution to generate diverse and plausible poses for unobserved body parts. Several recent studies have attempted to tackle pose ambiguities caused by occlusions and body truncations. However, some methods can only produce a discrete number of body poses [3, 34, 48], ignoring the continuous nature of the pose manifold. Other approaches model the continuous body pose distribution via conditional variational autoencoder [53] or normalizing flows [32, 68], but with limited expressiveness. Furthermore, the 3D environment is often ignored although it provides strong cues for inferring missing body parts in the image. Existing works for human pose estimation [54, 55, 79] or generation [14, 80-82] in 3D scenes typically cannot deal with truncated bodies in images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.473, + 0.903 + ], + "angle": 0, + "content": "To address these issues, we introduce a novel scene-conditioned probabilistic approach, the first method to recover human mesh in 3D scenes from the egocentric view image. Inspired by the recent diffusion models that can generate high fidelity images [9, 17, 18, 59] and human motions [6, 25, 41, 63, 77] with flexible conditioning, our model is trained with a conditional diffusion framework, leveraging both the classifier-free guidance [18] and the classifier-guided diffusion sampling [9, 57, 60] for efficient scene conditioning. By training the model conditioning on a human-centric scene encoding, the diffusion denoiser can generate body poses with plausible human-scene interactions even with highly truncated bodies (see Fig. 1). The classifier-free training enables flexible sampling from models with or without image conditions, achieving accurate estimations of visible body parts while generating diverse plausible results for unseen body parts. On top of that, the diffusion sampling process is guided by the gradients of a physics-based collision score guidance in the classifier-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "guided sampling manner, which further resolves human-scene inter-penetrations without requiring additional time-consuming postprocessing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.893, + 0.363 + ], + "angle": 0, + "content": "To facilitate the learning of the multimodal distributions of the invisible body parts, we introduce a visibility-aware graph convolution model as the diffusion denoiser network, to explicitly guide the network to learn more expressive distribution for invisible body parts. Unlike existing methods [24, 32, 36, 68] that simply condition the full body pose on a global image feature, we condition the pose diffusion of each body joint on the joint visibility mask and the 3D scene feature, in addition to the image feature. With such explicit visibility guidance, the model learns to estimate accurate body pose for visible joints while encouraging diversity for truncated body parts. We adopt a graph convolution network (GCN) [26, 75, 84] to better incorporate local dependencies between highly-relevant body parts (e.g. knee-foot) according to the human kinematic tree." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.364, + 0.895, + 0.545 + ], + "angle": 0, + "content": "In summary, our contributions are: 1) a novel scene-conditioned diffusion model for probabilistic human mesh recovery in the 3D environment from egocentric images; 2) a physics-based collision score that guides the diffusion sampling process to further resolve human-scene interpenetrations; 3) a visibility-aware GCN architecture that incorporates inter-joint dependencies for the pose diffusion, and enables per-body-part control via the per-joint visibility conditioning. With extensive evaluations, the proposed method demonstrates superior accuracy and diversity of generated human bodies from egocentric images, in natural and plausible interactions with the 3D environment." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.559, + 0.642, + 0.574 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Human mesh recovery from a single image. Given a single RGB image, the task of deterministic 3D human mesh recovery has been widely studied in the literature, with regression-based methods [7, 8, 11, 24, 27, 28, 30, 31, 35-37, 45, 49, 62, 71, 76, 83], optimization-based methods [4, 10, 33, 50, 69] or hybrid methods [23, 29, 58], mostly adopting parametric 3D body models [4, 70] to represent the 3D human mesh. Most of recent regression-based methods train neural networks to regress SMPL [4] parameters from images [11, 24, 28, 36, 51]. Model-free methods [7, 8, 37, 45] regress human mesh vertices without relying on parametric body models. Optimization-based methods iteratively optimize the body model parameters to fit 2D keypoints, human silhouettes, etc. Some resort to self-contact [46], scene [15, 69] or object [61] constraints to model interactions. Hybrid methods seek to combine the strengths of both regression and optimization, for instance, SPIN [29], which integrates an optimization loop into the deep learning framework. However, these methods often lack robustness when dealing with truncated bodies, a typical challenge in egocentric scenarios, and cannot" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7990" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.166 + ], + "angle": 0, + "content": "model the diverse nature of plausible missing body parts. 3D scene information is mostly disregarded, resulting in unrealistic human-scene interactions. In this work, we address these challenges by proposing a scene-conditioned generative model for human mesh recovery in 3D scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.468, + 0.424 + ], + "angle": 0, + "content": "Multi-hypothesis for 3D human pose estimation. Due to the limited image observation and depth ambiguity, estimating 3D human pose from a single image can have multiple potential solutions, especially when body truncation is presented. Recent works seek to model this task as a generative process or predict multiple hypothesis of possible poses. A discrete number of hypotheses are generated in [3, 21, 34, 48]. To learn the continuous distribution of possible body poses, conditional variational autoencoders [53] or conditional normalizing flows [32, 68] are adopted to generate unlimited number of hypotheses, but relying on additional scoring functions for pose selection [53], or discriminators to stabilize the training [32, 68]. Nevertheless, the 3D scene constraint is usually not taken into account in this line of works. We leverage the diffusion process to model the inherent pose ambiguity, with flexible scene-conditioning strategies." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.425, + 0.468, + 0.544 + ], + "angle": 0, + "content": "Egocentric human pose estimation. Most of existing works in egocentric human pose estimation targets the camera wearer's 3D pose [13, 22, 40, 56, 64, 65, 73]. 3D pose estimation for a social partner from the egocentric view has been receiving growing attention [38, 47, 72]. However, the 3D scene geometry is neglected in [47, 72], while [38] employs the time-consuming optimization, without modelling the probabilistic distribution of unseen body parts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.545, + 0.468, + 0.816 + ], + "angle": 0, + "content": "Diffusion models for human motion/pose generation. Denoising Diffusion Models [17, 57, 59, 60] are becoming a popular choice for human motion generative models. Typically trained with the DDPM formulation [17] and based on Transformer-backbones, different methods vary on their choice of motion representation (e.g. skeletons [41, 77], joint rotations [2, 25, 66] or latent variables [6]) and downstream tasks. To generate plausible human-scene interactions, SceneDiffuser [19] condition the motion/pose diffusion model on 3D scenes and further guide the model with physics-based objectives at inference time. In a similar fashion, PhysDiff [74] incorporates a physics-based motion projection module in the inference loop to resolve typical flaws in motion synthesis such as foot-ground penetrations. While these methods all target human action synthesis, we take a different perspective and leverage Diffusion Models for a perception task — as a multi-proposal formulation to address the ambiguity in the egocentric pose estimation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.83, + 0.216, + 0.846 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "SMPL body model [39]. We model the human mesh with the parametric SMPL body model. SMPL parametrizes a body as a function \\(\\mathcal{M}_b(\\gamma, \\beta, \\theta)\\) of the global transla" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.891, + 0.136 + ], + "angle": 0, + "content": "tion \\(\\gamma \\in \\mathbb{R}^3\\), body shape \\(\\beta \\in \\mathbb{R}^{10}\\), and full body pose \\(\\theta \\in \\mathbb{R}^{24\\times 3}\\) of 23 body joints, plus the global orientation, returning a mesh \\(\\mathcal{M}_b\\) with 6890 vertices." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.892, + 0.228 + ], + "angle": 0, + "content": "Conditional Diffusion Model. We use DDPM [17] as our formulation of pose diffusion model. DDPM learns a distribution of body poses \\(\\pmb{\\theta}\\) through a forward diffusion process and an inverse denoising (sampling) process. The forward diffusion process is a Markov chain of added Gaussian noise over \\(t\\in \\{1,\\dots ,T\\}\\) steps:" + }, + { + "type": "equation", + "bbox": [ + 0.552, + 0.24, + 0.892, + 0.257 + ], + "angle": 0, + "content": "\\[\nq \\left(\\boldsymbol {\\theta} _ {t} \\mid \\boldsymbol {\\theta} _ {t - 1}\\right) = \\mathcal {N} \\left(\\boldsymbol {\\theta} _ {t}; \\sqrt {\\alpha_ {t}} \\boldsymbol {\\theta} _ {t - 1}, (1 - \\alpha_ {t}) \\mathbf {I}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.268, + 0.891, + 0.313 + ], + "angle": 0, + "content": "where the variance \\(1 - \\alpha_{t} \\in (0, 1]\\) increases with \\(t\\) according to a pre-defined schedule, and \\(T\\) is the total number of noise corruption steps." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.314, + 0.891, + 0.388 + ], + "angle": 0, + "content": "At the core of the inverse process is a denoiser neural network \\(D(\\cdot)\\), which is trained to remove the added Gaussian noise based on condition signal \\(c\\) at each step \\(t\\). Following the design of recent motion diffusion models [63], the denoiser predicts the clean signal itself: \\(\\hat{\\pmb{\\theta}}_0 = D(\\pmb{\\theta}_t, t, c)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.389, + 0.891, + 0.419 + ], + "angle": 0, + "content": "The Gaussian forward diffusion process has a special property that allows directly sampling \\(\\theta_{t}\\) from \\(\\theta_0\\):" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.431, + 0.891, + 0.448 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\theta} _ {t} = \\sqrt {\\alpha_ {t}} \\boldsymbol {\\theta} _ {0} + \\sqrt {1 - \\alpha_ {t}} \\boldsymbol {\\epsilon}, \\text {w h e r e} \\boldsymbol {\\epsilon} \\sim \\mathcal {N} (0, \\mathbf {I}). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.891, + 0.505 + ], + "angle": 0, + "content": "With this, training the denoiser amounts to sampling a random \\( t \\in \\{0, \\dots, T - 1\\} \\), adding noise according to Eq. (2), and optimizing the simple objective [17]:" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.516, + 0.891, + 0.535 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s i m p l e}} = E _ {\\boldsymbol {\\theta} _ {0} \\sim q (\\boldsymbol {\\theta} _ {0} | \\boldsymbol {c}), t \\sim [ 1, T ]} \\left[ \\| \\boldsymbol {\\theta} _ {0} - D (\\boldsymbol {\\theta} _ {t}, t, \\boldsymbol {c}) \\| _ {2} ^ {2} \\right]. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.545, + 0.891, + 0.576 + ], + "angle": 0, + "content": "In this paper we use the subscript \\( t \\) to denote the diffusion timestep and superscript \\( j \\) for the body joint index." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.589, + 0.59, + 0.604 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.81 + ], + "angle": 0, + "content": "We introduce a novel scene-conditioned diffusion method to recover the human mesh in 3D environments from the egocentric image. Fig. 2 shows the overview of our model. Given an egocentric image \\(\\mathcal{I}\\) with a truncated body, the camera intrinsics \\(\\mathcal{K} = (f, c_x, c_y)\\), and the 3D scene point cloud \\(S \\in \\mathbb{R}^{N \\times 3}\\) with \\(N\\) points, our goal is to learn the conditional distribution of body poses \\(p(\\boldsymbol{\\theta} | \\mathcal{I}, S, \\mathcal{K})\\), with the objective of generating humans that naturally interact with the scene while being aligned with the image observation. The body translation \\(\\gamma\\) and shape \\(\\beta\\) are learnt in a deterministic way following [32]. Here \\(f\\) and \\((c_x, c_y)\\) denote the focal length and the camera center, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The diffusion denoising process (Sec. 3) is modeled by a visibility-aware graph convolution network (GCN), which achieves per-body-part control with the per-joint conditioning on the input image, scene geometry and joint visibility (Sec. 4.1). The diffusion model is trained in a classifier-free manner [18], enabling flexible sampling from both models" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "7991" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.09, + 0.887, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.324, + 0.895, + 0.402 + ], + "angle": 0, + "content": "Figure 2: Method overview. Given an egocentric image \\(\\mathcal{I}\\) containing a partially visible body and the 3D scene geometry \\(S\\), the proposed model generates a SMPL mesh with plausible human-scene interactions and conforming to the image observation. The model comprises a Scene Conditioning module to estimate the body translation \\(\\hat{\\gamma}\\) and encode the local scene features, an Image Conditioning module to encode image features, a GCN-based Diffusion Denoiser to predict the clean body pose \\(\\hat{\\theta}_0\\) from noisy pose \\(\\theta_t\\) with Per-joint Conditioning, and a Shape Estimator to estimate body shape \\(\\hat{\\beta}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.408, + 0.471, + 0.499 + ], + "angle": 0, + "content": "that include or exclude image conditions to enhance diversity and expressiveness for truncated body parts. Guided by the gradients of a physics-based human-scene collision score, we further resolve human-scene inter-penetrations during the diffusion sampling (Sec. 4.2). The training objectives are explained in Sec. 4.3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.512, + 0.422, + 0.528 + ], + "angle": 0, + "content": "4.1. Scene-conditioned Pose Diffusion Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.47, + 0.838 + ], + "angle": 0, + "content": "3D scene conditioning. To model fine-grained human-scene interactions, only a small region of the scene surrounding the human is relevant. An accurate global body translation provides better reasoning about local scene geometries, thus crucial for accurate and scene-plausible local body pose modelling. To this end, we propose a body translation estimator (see Fig. 2) to estimate the translation \\(\\hat{\\gamma}\\) by extracting features from \\(\\mathcal{I}\\) and the full 3D scene point cloud \\(S\\). The global scene features alleviate the scale ambiguity and localize the body in the 3D environment accurately (please refer to Supp. Mat. for more details). Given the estimated body translation \\(\\hat{\\gamma}\\), scene vertices in a \\(2 \\times 2m\\) region around the human are selected and considered as the scene conditioning for the diffusion denoising process. Furthermore, the selected scene vertices are translated by \\(\\hat{\\gamma}\\) such that the scene vertex origin is around the body pelvis. The translated scene point cloud is encoded by a scene encoder \\(E_{S}\\) into a localized human-centric scene feature \\(E_{S}(S, \\hat{\\gamma})\\) for modelling detailed interactions between the body and the 3D scene." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Per-joint conditioning. A ResNet50 backbone [16] \\(E_{\\mathcal{I}}\\) is used to encode the cropped input image \\(I\\) into a latent feature \\(E_{\\mathcal{I}}(\\mathcal{I}) \\in \\mathbb{R}^{2048}\\) as the image conditioning. However, regressing the full body pose directly from the global im" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.408, + 0.892, + 0.574 + ], + "angle": 0, + "content": "age feature as in previous works [24, 29, 32] loses the explicit joint visibility information. With the body truncated in the image, different properties are desired for different body parts: the model should achieve pose accuracy for observed body joints, and pose expressiveness for truncated body parts. To achieve the per-body-part control, the 2D joint visibility mask \\(\\mathcal{V} = (v^0,\\dots,v^j,\\dots,v^{J - 1})\\in \\mathbb{R}^J\\) is extracted from the image via OpenPose [5] 2D joint detections, and passed to the diffusion model as the visibility condition. Here \\(J\\) denotes the joint number; and \\(v^{j}\\) equals to 1 if the \\(j\\)-th joint is visible in \\(\\mathcal{I}\\), otherwise 0." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.575, + 0.892, + 0.635 + ], + "angle": 0, + "content": "Apart from above conditions, the bounding box information \\(\\mathcal{B}\\) is additionally fed to the network inspired by [36], serving as a global-location-aware feature to better model global information:" + }, + { + "type": "equation", + "bbox": [ + 0.634, + 0.644, + 0.892, + 0.661 + ], + "angle": 0, + "content": "\\[\n\\mathcal {B} = \\left(b _ {x}, b _ {y}, b\\right) / f, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.669, + 0.891, + 0.7 + ], + "angle": 0, + "content": "where \\( b_{x}, b_{y}, b \\) denote the bounding box center coordinates and bounding box size in the full image, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.892, + 0.776 + ], + "angle": 0, + "content": "The full condition \\( c^j \\) for \\( j \\)-th joint is formulated as the concatenation of: the image feature (masked out by \\( v^j \\) if the joint is not visible), 3D scene feature, estimated body translation, bounding box feature, camera intrinsics and the diffusion timestep \\( t \\):" + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.785, + 0.892, + 0.802 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {c} ^ {j} = \\left(E _ {\\mathcal {I}} (\\mathcal {I}) \\cdot v ^ {j}, E _ {\\mathcal {S}} (\\mathcal {S}, \\hat {\\gamma}), \\hat {\\gamma}, \\mathcal {B}, \\mathcal {K}, t\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.871 + ], + "angle": 0, + "content": "By conditioning on a per-joint basis, the model achieves flexible control over each body part according to the joint visibility. This allows for both accurate pose estimation of visible body parts, and flexibility for invisible body parts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Diffusion denoiser architecture. At diffusion timestep \\(t\\), for the noisy body pose parameters \\(\\theta_{t}\\), the diffusion de" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "7992" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.09, + 0.473, + 0.394 + ], + "angle": 0, + "content": "noiser \\(D\\) predicts the clean pose parameter \\(\\hat{\\theta}_0\\) conditioned on \\(c\\). Previous works either use a single MLP for the full body pose [24, 32, 36, 68] with redundant dependencies between irrelevant joints, or employ a separate MLP for each joint [27] which fully ignores joint dependencies. Instead, we adopt a graph convolution network (GCN) [26, 84] as the denoising function \\(D\\). Given the predefined human kinematic tree, GCN models inter-joint dependencies by treating the human skeleton as a graph, where each node corresponds to a body joint. Specifically, for each joint \\(j\\), the noisy pose parameters \\(\\theta_t^j\\) is embedded and concatenated with the per-joint conditioning \\(c^j\\) as the feature for node \\(j\\) in the GCN (see Fig. 2). We adopt the modulated GCN [84] for the implementation. Different from vanilla GCN [26], the modulated GCN learns node-specific modulation vectors to disentangle joint feature transformations, such that different relations can be learnt between joints. It also modulates the affinity matrix with learnable parameters to model additional edges beyond the human skeleton [84]. Please refer to Supp. Mat. for implementation details." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.394, + 0.471, + 0.456 + ], + "angle": 0, + "content": "Shape estimator. As the body shape \\(\\beta\\) is a global feature and more robust to body truncations, an MLP branch (the body shape estimator in Fig. 2) predicts \\(\\hat{\\beta}\\) from the conditions \\((E_{\\mathcal{I}}(\\mathcal{I}), E_S(S, \\hat{\\gamma}), \\hat{\\gamma}, \\mathcal{B}, \\mathcal{K})\\) in a deterministic way." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.464, + 0.295, + 0.48 + ], + "angle": 0, + "content": "4.2. Scene-guided Sampling" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.487, + 0.47, + 0.547 + ], + "angle": 0, + "content": "We use the DDPM [17] sampler at inference time. At each sampling step \\( t \\), the denoiser predicts \\( \\hat{\\theta}_0 = D(\\theta_t, t, c) \\), which is noised back to \\( \\theta_{t-1} \\) by sampling from the Gaussian distribution:" + }, + { + "type": "equation", + "bbox": [ + 0.181, + 0.558, + 0.47, + 0.577 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\theta} _ {t - 1} \\sim \\mathcal {N} \\left(\\mu_ {t} \\left(\\boldsymbol {\\theta} _ {t}, \\hat {\\boldsymbol {\\theta}} _ {0}\\right), \\Sigma_ {t}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.588, + 0.47, + 0.634 + ], + "angle": 0, + "content": "where \\(\\mu_t(\\pmb{\\theta}_t, \\hat{\\pmb{\\theta}}_0)\\) is a linear combination of \\(\\pmb{\\theta}_t\\) and \\(\\hat{\\pmb{\\theta}}_0\\), and \\(\\Sigma_t\\) is a scheduled Gaussian distribution as in [17]. The sampling is iteratively repeated from \\(t = T - 1\\) until \\(t = 0\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.634, + 0.471, + 0.756 + ], + "angle": 0, + "content": "Classifier-free guidance. The diffusion model \\(D\\) is trained with classifier-free guidance [18] by randomly masking out the image feature \\(E_{\\mathcal{I}}(\\mathcal{I})\\) for all joints with a probability of \\(5\\%\\) during training, such that the model also learns the pose distribution independent from the image, enabling flexible sampling. By combining the poses of visible joints sampled from the full-conditioned model and the poses of invisible joints sampled from the model excluding image conditions:" + }, + { + "type": "equation", + "bbox": [ + 0.103, + 0.781, + 0.469, + 0.8 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {\\theta}} _ {0} = D \\left(\\boldsymbol {\\theta} _ {t}, t, \\boldsymbol {c}\\right) \\odot \\mathcal {V} + D \\left(\\boldsymbol {\\theta} _ {t}, t, \\boldsymbol {c} _ {\\phi}\\right) \\odot (1 - \\mathcal {V}), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.81, + 0.47, + 0.902 + ], + "angle": 0, + "content": "we achieve better per-body-part control, with enhanced diversity for invisible body parts while maintaining the accuracy of visible body parts (see Sec. 5.5 for the ablation study). Here \\(\\odot\\) denotes multiplying the joint visibility mask with the pose of each joint, and \\(c_{\\phi}\\) is the condition excluding image features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.379 + ], + "angle": 0, + "content": "Collision score guided sampling. The proposed scene encoding in Sec. 4.1 implicitly incorporates the 3D environment constraint into the diffusion conditioning. However, the network cannot fully resolve the human-scene collisions in a fine-grained way. Another way to incorporate conditions into the diffusion model is the score-function based guidance. As shown in previous works [9, 57, 60], a pretrained classifier can be adopted to provide class information by adding the gradients of the classifier at each sampling step to the diffusion model, to guide the sampling process towards the class label. Inspired by this, we propose a collision score guided sampling strategy to further resolve implausible human-scene inter-penetrations, by leveraging implicit body representations [43, 44]. We use COAP [43] to model neural articulated occupancy of human bodies as the zero-level set \\( f_{\\Theta}(q|\\mathcal{G}) = 0 \\), where \\( q \\) is the input query point and \\( \\mathcal{G}(\\theta ,\\beta) \\) is the input bone transformations. By querying each scene vertex near the body to see if it is inside of the human volume, the collision score is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.389, + 0.892, + 0.422 + ], + "angle": 0, + "content": "\\[\n\\mathcal {J} (\\boldsymbol {\\theta}) = \\frac {1}{| \\mathcal {S} |} \\sum_ {q \\in \\mathcal {S}} \\sigma \\left(f _ {\\Theta} (q \\mid \\mathcal {G})\\right) \\mathbb {I} _ {f _ {\\Theta} (s \\mid \\mathcal {G}) > 0}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.427, + 0.894, + 0.489 + ], + "angle": 0, + "content": "where \\(\\sigma(\\cdot)\\) stands for the sigmoid function. The gradient \\(\\nabla \\mathcal{J}(\\boldsymbol{\\theta})\\) efficiently guides the diffusion sampling process to further alleviate the human-scene collisions (see Sec. 5.5 for the ablation study) by modifying Eq. (6) to:" + }, + { + "type": "equation", + "bbox": [ + 0.552, + 0.499, + 0.892, + 0.517 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\theta} _ {t - 1} \\sim \\mathcal {N} \\left(\\mu_ {t} \\left(\\boldsymbol {\\theta} _ {t}, \\hat {\\boldsymbol {\\theta}} _ {0}\\right) + a \\Sigma_ {t} \\nabla \\mathcal {J} \\left(\\boldsymbol {\\theta} _ {t}\\right), \\Sigma_ {t}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.529, + 0.892, + 0.544 + ], + "angle": 0, + "content": "where the guidance is modulated by \\(\\Sigma_{t}\\) and a scale factor \\(a\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.553, + 0.691, + 0.57 + ], + "angle": 0, + "content": "4.3. Training Objectives" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.577, + 0.892, + 0.641 + ], + "angle": 0, + "content": "The diffusion model is trained with \\(\\mathcal{L}_{\\mathrm{simple}}\\) in Eq. (3) for body pose \\(\\hat{\\theta}_0\\), together with the 3D joint loss \\(\\mathcal{L}_{\\mathrm{3D}}\\), the 2D keypoint re-projection loss \\(\\mathcal{L}_{\\mathrm{2D}}\\) calculated in the full image frame, and the shape loss \\(\\mathcal{L}_{\\beta}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.652, + 0.822, + 0.671 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {3 D}} = \\left\\| F K (\\hat {\\boldsymbol {\\theta}} _ {0}, \\hat {\\boldsymbol {\\beta}}) - F K (\\boldsymbol {\\theta} _ {0}, \\boldsymbol {\\beta}) \\right\\| ^ {2},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.673, + 0.892, + 0.691 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {2 D}} = \\left\\| \\Pi_ {\\mathcal {K}} \\left(J _ {\\mathrm {3 D}} + \\hat {\\gamma}\\right) - J _ {\\mathrm {e s t}} \\right\\| ^ {2}, \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.694, + 0.693, + 0.712 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\beta} = \\left\\| \\hat {\\boldsymbol {\\beta}} - \\boldsymbol {\\beta} \\right\\| ^ {2}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.724, + 0.892, + 0.784 + ], + "angle": 0, + "content": "Here \\( FK(\\cdot) \\) denotes the SMPL joint regressor to obtain 3D joint coordinates. \\( J_{\\mathrm{est}} \\) is the 2D body keypoint detections, and \\( \\Pi_{\\mathcal{K}} \\) denotes the 3D to 2D projection in the full image with camera intrinsics \\( \\mathcal{K} \\). The overall loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.794, + 0.891, + 0.83 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\text {s i m p l e}} + \\lambda_ {3 \\mathrm {D}} \\mathcal {L} _ {3 \\mathrm {D}} + \\lambda_ {2 \\mathrm {D}} \\mathcal {L} _ {2 \\mathrm {D}} + \\lambda_ {\\beta} \\mathcal {L} _ {\\beta} \\tag {11} \\\\ + \\lambda_ {\\text {c o l l}} \\mathcal {L} _ {\\text {c o l l}} + \\lambda_ {\\text {o r t h}} \\mathcal {L} _ {\\text {o r t h}}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\mathrm{orth}}\\) is a regularizer to force the generated 6D pose rotation representation to be orthonormal, \\(\\mathcal{L}_{\\mathrm{coll}}\\) is the scene collision loss the same as defined in Eq. (8), and \\(\\lambda s\\) are the corresponding weight factors for each loss term." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7993" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.21, + 0.108 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.115, + 0.173, + 0.13 + ], + "angle": 0, + "content": "5.1. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.139, + 0.473, + 0.352 + ], + "angle": 0, + "content": "Most of existing datasets for 3D human pose evaluation are either captured from the third-person view with the full body visible [15, 20, 42, 67], or do not contain the 3D environment [47]. The most relevant dataset is EgoBody [78], a large-scale egocentric dataset capturing 3D human motions during social interactions in 3D scenes. Each sequence involves two people interacting with each other in 3D environments, and one subject wears a head-mounted camera to capture the egocentric images containing the other interactee. Due to the close social interaction distance, the captured egocentric images typically exhibit strong body truncations for the interactee. We use the official train / test splits for training and evaluation, which include 90,120 / 62,140 frames, respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.362, + 0.263, + 0.377 + ], + "angle": 0, + "content": "5.2. Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.386, + 0.47, + 0.477 + ], + "angle": 0, + "content": "Strong body truncations pose inherent ambiguity for invisible body parts, while the visible body parts are relatively deterministic given the image observations, thus evaluating the accuracy of full body joints together as in [3, 32] is not suitable for such tasks. We propose to evaluate the proposed method from the following aspects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.47, + 0.688 + ], + "angle": 0, + "content": "Accuracy. We employ Mean Per-Joint Position Error (MPJPE) and Vertex-to-Vertex (V2V) errors in \\( mm \\) to evaluate the accuracy of estimated body pose and shape. For MPJPE, we report different variations: G-MPJPE as the joint error in the global coordinate; MPJPE as the pelvis-aligned joint errors, and PA-MPJPE as the joint errors after Procrustes Alignment [12]. We report mean MPJPE and V2V metrics over \\( n \\) samples for visible joints. Nevertheless, such evaluation protocol assumes a single correct ground truth prediction, which does not hold for invisible joints. Instead of the mean error, we report min-of- \\( n \\) MPJPE for invisible body parts following [3]. To be specific, among the generated \\( n \\) samples for each input image, we select the one with the minimum MPJPE for all evaluated methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Physical plausibility. We evaluate the collision and contact scores between the body mesh and the 3D scene. As the clean scene signed distance field (SDF) is not available in EgoBody, we define the collision score as the ratio of the number of scene vertices inside of the body mesh to the number of all scene vertices. Note that the absolute scale of the collision score may vary with different size of the 3D scene, but within the same scene surface, the relative comparison between different methods indicates different collision levels. We use the cropped scene as described in Sec. 4.1 for evaluation (with a fixed size of 20,000 vertices). Following [19], the contact score is defined as 1 if the body contacts with the scene in a distance within a threshold (2 cm), otherwise 0. We report the mean collision score and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "contact score over all test samples. Note that a model with better physical plausibility should achieve both a lower collision score and a higher contact score." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.894, + 0.259 + ], + "angle": 0, + "content": "Diversity. Diversity is evaluated for invisible body parts to demonstrate the expressiveness of the methods, by calculating the standard deviation (std) and Average Pairwise Distance (APD) of invisible body joints [19]. A higher diversity is desired, yet there is usually a trade-off between diversity and accuracy/plausibility. An ideal model should predict diverse poses for invisible body parts, with accurate visible body poses and plausible human-scene interactions." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.269, + 0.742, + 0.284 + ], + "angle": 0, + "content": "5.3. Baselines and Our Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.293, + 0.895, + 0.64 + ], + "angle": 0, + "content": "As there is no existing work for our task, we compare our method with the following baselines: (1) ProHMR [32], the state-of-the-art method for probabilistic human mesh recovery from a single image based on conditional normalizing flows; (2) ProHMR-scene, in which we enhance the ProHMR framework by incorporating the scene geometry \\( S \\) with a global scene feature encoder. The ProHMR framework is trained with 2D and 3D supervisions for the sample drawn from \\( z = 0 \\) (referred as the 'mode'), such that the 'mode' can be used as a predictive model (see [32] for details). Different training weights for the samples drawn from \\( z \\neq 0 \\) yields a trade-off between the accuracy and diversity for the generated multiple hypotheses. Here \\( z \\) denotes the latent space of the normalizing flow. To demonstrate this trade-off, we train the ProHMR-scene baseline with different training configurations. For samples drawn from \\( z \\neq 0 \\), we supervise with: 1) only 2D re-projection loss (the same as in [32]), denoted as -orig; 2) 3D supervision with small weights, denoted as -weak-3D; 3) 3D supervision with large weights, denoted as -strong-3D. Here the 3D supervision refers to the loss on 3D body joints and SMPL parameters. Please refer to Supp. Mat. for details of the baseline models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.593, + 0.665 + ], + "angle": 0, + "content": "5.4. Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Tab. 1 shows the quantitative results. Compared to the baselines, our method achieves the best G-MPJPE, MPJPE and V2V metrics for visible joints, demonstrating accurate estimations of the global translation, local body pose for visible joints and body shape. For truncated body joints, our method obtains the best min-of-n MPJPE, indicating that our generated results better covers the ground truth distribution for truncated body parts than baselines, thanks to the efficient scene conditioning. Our method also outperforms the baselines with the higher contact ratios and significantly better collision scores. In particular, our collision score decreased \\(45\\%\\) compared with ProHMR, and \\(37\\%\\) compared with the best ProHMR-scene model. This indicates that the proposed method can effectively leverage the scene conditions and resolve body-scene inter-penetrations," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7994" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.15 + ], + "angle": 0, + "content": "Table 1: Evaluation for accuracy, physical plausibility and diversity on EgoBody. Here -vis and -invis denote visible and invisible joints, respectively. 'coll' and 'contact' refer to the collision and contact scores, respectively. The percentage for the collision score denotes how much improvement the corresponding method has achieved compared with the ProHMR baseline. The best results are in boldface." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.162, + 0.892, + 0.334 + ], + "angle": 0, + "content": "
nMethodG-MPJPE ↓ -visMPJPE ↓ -visPA-MPJPE ↓ -visV2V ↓ -vismin-of-n MPJPE ↓ -inviscoll ↓contact ↑std ↑ -invisAPD ↑ -invis
5ProHMR [32]181.3372.9246.5790.88128.560.00346 (-)0.9426.5332.95
ProHMR-scene-orig133.7273.1348.8791.59117.880.00305 (12%)0.9635.4244.02
Ours128.6265.7047.1782.93107.770.00191 (45%)0.9929.5935.15
10ProHMR [32]181.7073.6547.0691.84121.670.00346 (-)0.9429.2635.06
ProHMR-scene-orig134.5774.4249.6393.21110.640.00305 (12%)0.9639.0746.86
Ours128.6065.6947.2082.94100.750.00191 (45%)0.9929.5935.15
20ProHMR [32]181.8773.9947.2992.28115.480.00346 (-)0.9330.5536.14
ProHMR-scene-orig134.9775.0349.9893.98103.810.00306 (12%)0.9640.8248.32
ProHMR-scene-weak-3D131.5167.8146.9485.05111.680.00313 (10%)0.9621.7925.67
ProHMR-scene-strong-3D134.4066.4245.9682.99123.340.00316 (9%)0.9713.0115.23
Ours128.6065.6947.1982.9494.960.00191(45%)0.9930.2335.14
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0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.205, + 0.668, + 0.307, + 0.743 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.205, + 0.743, + 0.307, + 0.814 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.232, + 0.815, + 0.288, + 0.826 + ], + "angle": 0, + "content": "ProHMR" + }, + { + "type": "image", + "bbox": [ + 0.313, + 0.668, + 0.415, + 0.742 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.313, + 0.743, + 0.415, + 0.814 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.327, + 0.815, + 0.418, + 0.826 + ], + "angle": 0, + "content": "ProHMR-scene" + }, + { + "type": "image", + "bbox": [ + 0.42, + 0.668, + 0.523, + 0.742 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.42, + 0.743, + 0.522, + 0.814 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 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\\(\\mathcal{J}_{\\pmb{\\theta}}\\)" + }, + { + "type": "image", + "bbox": [ + 0.781, + 0.668, + 0.884, + 0.742 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.781, + 0.742, + 0.884, + 0.814 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.817, + 0.815, + 0.848, + 0.826 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.841, + 0.895, + 0.887 + ], + "angle": 0, + "content": "Figure 3: Qualitative results on EgoBody dataset. The left part shows the comparison between the baseline methods and our proposed method. The right part demonstrates the effectiveness of our proposed scene collision score guidance \\(\\mathcal{I}_{\\theta}\\) to further resolve human-scene inter-penetrations. Red circles point to human-scene collisions." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7995" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.121 + ], + "angle": 0, + "content": "Table 2: Ablation study. \\( \\mathcal{I}_{\\theta} \\) and CF denote the collision score guidance and classifier-free guidance during the diffusion sampling (Sec 4.2). \\( \\mathcal{L}_{\\mathrm{coll}} \\) denotes the collision loss for training (Eq. (11)). All results are reported for \\( n = 20 \\)." + }, + { + "type": "table", + "bbox": [ + 0.184, + 0.131, + 0.79, + 0.22 + ], + "angle": 0, + "content": "
MethodMPJPE ↓ -vismin-of-n MPJPE ↓ -inviscoll ↓contact ↑std ↑ -invisAPD ↑ -invis
Ours65.6994.960.001910.9930.2335.14
Ours w/o Jθ65.0997.200.002250.9921.5325.32
Ours w/o Jθ w/o CF64.5898.820.002290.9915.7519.56
Ours w/o Jθ w/o CF w/o Lcoll64.9196.260.003020.9922.9421.79
" + }, + { + "type": "image", + "bbox": [ + 0.123, + 0.225, + 0.849, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.106, + 0.359, + 0.862, + 0.377 + ], + "angle": 0, + "content": "Figure 4: Multiple samples. Given the same input, our method can generate diverse poses for invisible body parts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.39, + 0.471, + 0.435 + ], + "angle": 0, + "content": "while achieving better contact relations between the body and the 3D environment. Fig. 3 (left) shows the qualitative results and the comparison with the baseline method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.441, + 0.47, + 0.775 + ], + "angle": 0, + "content": "From the results among different ProHMR-scene baselines \\((n = 20)\\) in Tab. 1, we can clearly see a trade-off between the accuracy and diversity: stronger 3D supervision (ProHMR-scene-strong-3D) has better accuracy for visible body parts (MPJPE-vis), yet lower diversity (std-invis and APD-invis) for invisible joints. The reason behind this is that the ProHMR framework, like many other existing works, condition the generative process of full body pose only on the global image feature. In contrast, our method leverages the joint visibility and the GCN architecture, achieving the best MPJPE for visible joints, diverse poses for invisible joints, and natural human-scene interactions (see Fig. 4), while the baseline with a similar diversity level (ProHMR) and the baseline with the highest diversity (ProHMR-scene-orig) exhibit much higher MPJPE errors and more severe human-scene collisions. There is a very slight increase for PA-MPJPE of our model compared to the ProHMR-scene-strong/weak-3D baselines, while we obtain a much higher diversity for invisible body joints. This reveals that our method achieves flexible per-body-part control to balance between the accuracy and diversity for different body parts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To validate the reconstruction accuracy, the full-body accuracy of the proposed method is also evaluated and compared against existing deterministic baselines on EgoBody dataset. The results show that our method even achieves higher full-body accuracy than deterministic methods, which demonstrates that the proposed model achieves diversity without sacrificing the reconstruction accuracy. In addition, the proposed method is also evaluated on PROX [15]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.39, + 0.895, + 0.496 + ], + "angle": 0, + "content": "dataset, a monocular RGB-based third-person view dataset with human-scene interactions, and our method outperforms the baseline methods in terms of pose accuracy, human-scene interaction plausibility and pose diversity. Please refer to Supp. Mat. for detailed results of evaluations on PROX and comparison with deterministic methods on EgoBody." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.511, + 0.655, + 0.527 + ], + "angle": 0, + "content": "5.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.536, + 0.892, + 0.793 + ], + "angle": 0, + "content": "To investigate the influences of different training and sampling schemes for the diffusion model, we perform an ablation study and the results are shown in Tab. 2. The scene collision score efficiently resolves the human-scene interpenetrations from two different perspectives: via the collision loss \\(\\mathcal{L}_{\\mathrm{coll}}\\) during training and via the explicit collision score guidance \\(\\mathcal{I}_{\\theta}\\) during the diffusion sampling (Eq. (9)). Fig. 3 (right) shows that the collision score guidance \\(\\mathcal{I}_{\\theta}\\) improves the human-scene interaction relationships. The classifier-free guidance during the diffusion sampling in Eq. (7) significantly improves the sample diversity, by leveraging the invisible joints sampled from the model trained excluding the image conditions. It is worth mentioning that the collision score guidance \\(\\mathcal{I}_{\\theta}\\) also contributes to the sample diversity. This is not surprising as the gradients of \\(\\mathcal{I}_{\\theta}\\) can potentially optimize the body pose to different directions given different initial body poses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Compared with the trade-off in the ProHMR-based methods where the accuracy sacrifices a lot for diversity (and vice versa), the classifier-free guidance and the collision score guidance in our model only bring marginal changes for the MPJPE of visible body parts, in the trade-off for significantly enhanced physical plausibility, sample diversity and better min-of-n MPJPE for unobserved joints." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.958 + ], + "angle": 0, + "content": "7996" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.196, + 0.106 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.112, + 0.473, + 0.444 + ], + "angle": 0, + "content": "This paper introduces a novel scene-conditioned probabilistic approach for human mesh recovery from the egocentric image given the 3D scene geometry. The proposed diffusion model efficiently leverages the scene conditions and joint visibility to achieve per-body-part control and model human-scene interactions. The classifier-free guidance and the collision score guidance enables flexible sampling process with further enhanced diversity and physical plausibility. We demonstrate that our model generates human bodies in realistic interactions with the 3D environment, with diverse poses for invisible body parts while conforming to the image observation. Nevertheless, the current method also has limitations. For example, currently only a single frame is considered as the input. A promising future direction is to further exploit temporal information to reconstruct temporally consistent human motions from the egocentric view. Acknowledgements. This work was supported by Microsoft Mixed Reality & AI Zurich Lab PhD scholarship. Qianli Ma is partially funded by the Max Planck ETH Center for Learning Systems. We sincerely thank Korrawe Karunratanakul, Marko Mihajlovic and Shaofei Wang for the fruitful discussions." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.455, + 0.175, + 0.47 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.481, + 0.466, + 0.508 + ], + "angle": 0, + "content": "[1] Microsoft Hololens2. https://www.microsoft.com/en-us/hololens.2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.509, + 0.47, + 0.562 + ], + "angle": 0, + "content": "[2] Simon Alexanderson, Rajmund Nagy, Jonas Beskow, and Gustav Eje Henter. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 11477-11487, 2021. 2, 5" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.106, + 0.468, + 0.757 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "8000" + } + ] +] \ No newline at end of file diff --git a/2023/Probabilistic Human Mesh Recovery in 3D Scenes from Egocentric Views/c490ef67-0a1e-4595-8f34-5035e971ee89_origin.pdf b/2023/Probabilistic Human Mesh Recovery in 3D Scenes from Egocentric Views/c490ef67-0a1e-4595-8f34-5035e971ee89_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1868dc7d012d56e49e2b41c42907a1511461e3cb --- /dev/null +++ b/2023/Probabilistic Human Mesh Recovery in 3D Scenes from Egocentric Views/c490ef67-0a1e-4595-8f34-5035e971ee89_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:79a2d6ce005217fb41987e57415ea783498aac78aac5cefd80247873fc2a733f +size 8674594 diff --git a/2023/Probabilistic Human Mesh Recovery in 3D Scenes from Egocentric Views/full.md b/2023/Probabilistic Human Mesh Recovery in 3D Scenes from Egocentric Views/full.md new file mode 100644 index 0000000000000000000000000000000000000000..4592fe06d885ee6f189edbbdeae8e5e281a853ab --- /dev/null +++ b/2023/Probabilistic Human Mesh Recovery in 3D Scenes from Egocentric Views/full.md @@ -0,0 +1,430 @@ +# Probabilistic Human Mesh Recovery in 3D Scenes from Egocentric Views + +Siwei Zhang $^{1}$ Qianli Ma $^{1,3}$ Yan Zhang $^{1}$ Sadegh Aliakbarian $^{2}$ Darren Cosker $^{2}$ Siyu Tang $^{1}$ ETH Zürich $^{2}$ Microsoft $^{3}$ Max Planck Institute for Intelligent Systems + +{siwei.zhang, qianli.ma, yan.zhang, siyu.tang}@inf.ethz.ch + +{coskerdarren, saliakbarian}@microsoft.com + +![](images/0beb5c40b8ea1c094325a28b1b15f3e4ee449bded8df7e74187ee06a2a4176df.jpg) + +![](images/28ca88f67bf3e664fced7d4e9be53c91c1c3297867b5dc42db2dbb3894e88d0f.jpg) +Figure 1: We propose EgoHMR, a novel scene-conditioned probabilistic method to recover the human mesh from an ego-centric view image (typically with the body truncated) given the 3D environment. EgoHMR efficiently leverages the scene geometry and achieves significantly more plausible human-scene interactions compared to baseline methods, ProHMR [32] and the extended ProHMR-scene (Sec. 5.3), even with severe body truncations. + +![](images/99fa2f6fc657b5f73a4249c6d203aa108e28a1130f64ee332f494cda7766d053.jpg) + +![](images/74df6eea3b87bc8c5264d2bd61bc6b0aac966866760fad65e40eff3e922d7e89.jpg) + +![](images/808e491adb646f56082d00e64ba53e313db206869ae3e828ce4e780fc146cda2.jpg) + +![](images/9f4311148457c4d2094bad571b0e6030dcd418b45faa7536200a4c021e946a39.jpg) + +![](images/21be33b5f7f907620c67f306b8a954a8a1b694efaa4152287a153380e290c64b.jpg) + +![](images/3622831795701a0d6b7e26de6b66940c7027dab7a71eaa3ff386329414340cfb.jpg) + +# Abstract + +Automatic perception of human behaviors during social interactions is crucial for AR/VR applications, and an essential component is estimation of plausible 3D human pose and shape of our social partners from the egocentric view. One of the biggest challenges of this task is severe body truncation due to close social distances in egocentric scenarios, which brings large pose ambiguities for unseen body parts. To tackle this challenge, we propose a novel scene-conditioned diffusion method to model the body pose distribution. Conditioned on the 3D scene geometry, the diffusion model generates bodies in plausible human-scene interactions, with the sampling guided by a physics-based collision score to further resolve human-scene interpenetrations. The classifier-free training enables flexible sampling with different conditions and enhanced diversity. A visibility-aware graph convolution model guided by per-joint visibility serves as the diffusion denoiser to incorporate inter-joint dependencies and per-body-part control. Extensive evaluations show that our method generates bodies in plausible interactions with 3D scenes, achieving both superior accuracy for visible joints and diversity for invisible body parts. The code is available at https:// sanweiliti.github.io/egohmr/egohmr.html. + +# 1. Introduction + +With the rapid development of Augmented and Virtual Reality (AR/VR) devices, understanding human actions, behaviors and interactions of our social partners ("inter-actee") from the egocentric view is a vital component for head-mounted devices (HMDs) to truly become a virtual companion for humans. The first step towards the automatic perception of human behaviors and interactions for HMDs is to estimate 3D human pose and shape (i.e. human mesh recovery) of the interactee from egocentric view images. + +The research community has extensively studied human mesh recovery (HMR) from a single RGB image (usually captured with third-person view cameras) by predicting SMPL [39, 50] parameters from global image features [8, 24, 27, 30, 45]. However, their performance degrades significantly in egocentric images [78]. A major challenge presented in egocentric scenarios is frequent body truncation [38, 78], when individuals interact with each other within close proximity, while the HMD camera has a limited field-of-view. Since human poses are highly reliant on the surrounding environment, 3D scene structures can potentially provide strong cues to infer invisible body parts, which is crucial for precise understanding of human behaviors: sitting on a chair and standing on the ground may indicate distinct intentions and future behaviors. Following + +PROX [15], we assume a rough 3D scene structure is available, as such information nowadays can be easily obtained with commodity sensors. Furthermore, visual localization and mapping, one of the extensively studied topics in computer vision, is progressing rapidly for head-mounted devices [52]. Therefore, we make the assumption that a coarse 3D model of the scene and the localization of the egocentric camera are readily available (e.g. in HoloLens2 [1]). In this paper, we focus on the challenging problem of estimating 3D human bodies that are heavily truncated from egocentric views due to the proximity between people and the motion of embodied cameras. + +Given an egocentric image and the corresponding 3D environment, what should an ideal human mesh recovery method achieve? In contrast to previous studies that mostly pursue full-body pose accuracy, we argue the following properties are desired in the egocentric scenario: (1) natural and plausible human-scene interactions; (2) accurate body pose estimations consistent with image observations for visible joints; (3) a comprehensive conditional distribution to generate diverse and plausible poses for unobserved body parts. Several recent studies have attempted to tackle pose ambiguities caused by occlusions and body truncations. However, some methods can only produce a discrete number of body poses [3, 34, 48], ignoring the continuous nature of the pose manifold. Other approaches model the continuous body pose distribution via conditional variational autoencoder [53] or normalizing flows [32, 68], but with limited expressiveness. Furthermore, the 3D environment is often ignored although it provides strong cues for inferring missing body parts in the image. Existing works for human pose estimation [54, 55, 79] or generation [14, 80-82] in 3D scenes typically cannot deal with truncated bodies in images. + +To address these issues, we introduce a novel scene-conditioned probabilistic approach, the first method to recover human mesh in 3D scenes from the egocentric view image. Inspired by the recent diffusion models that can generate high fidelity images [9, 17, 18, 59] and human motions [6, 25, 41, 63, 77] with flexible conditioning, our model is trained with a conditional diffusion framework, leveraging both the classifier-free guidance [18] and the classifier-guided diffusion sampling [9, 57, 60] for efficient scene conditioning. By training the model conditioning on a human-centric scene encoding, the diffusion denoiser can generate body poses with plausible human-scene interactions even with highly truncated bodies (see Fig. 1). The classifier-free training enables flexible sampling from models with or without image conditions, achieving accurate estimations of visible body parts while generating diverse plausible results for unseen body parts. On top of that, the diffusion sampling process is guided by the gradients of a physics-based collision score guidance in the classifier- + +guided sampling manner, which further resolves human-scene inter-penetrations without requiring additional time-consuming postprocessing. + +To facilitate the learning of the multimodal distributions of the invisible body parts, we introduce a visibility-aware graph convolution model as the diffusion denoiser network, to explicitly guide the network to learn more expressive distribution for invisible body parts. Unlike existing methods [24, 32, 36, 68] that simply condition the full body pose on a global image feature, we condition the pose diffusion of each body joint on the joint visibility mask and the 3D scene feature, in addition to the image feature. With such explicit visibility guidance, the model learns to estimate accurate body pose for visible joints while encouraging diversity for truncated body parts. We adopt a graph convolution network (GCN) [26, 75, 84] to better incorporate local dependencies between highly-relevant body parts (e.g. knee-foot) according to the human kinematic tree. + +In summary, our contributions are: 1) a novel scene-conditioned diffusion model for probabilistic human mesh recovery in the 3D environment from egocentric images; 2) a physics-based collision score that guides the diffusion sampling process to further resolve human-scene interpenetrations; 3) a visibility-aware GCN architecture that incorporates inter-joint dependencies for the pose diffusion, and enables per-body-part control via the per-joint visibility conditioning. With extensive evaluations, the proposed method demonstrates superior accuracy and diversity of generated human bodies from egocentric images, in natural and plausible interactions with the 3D environment. + +# 2. Related Work + +Human mesh recovery from a single image. Given a single RGB image, the task of deterministic 3D human mesh recovery has been widely studied in the literature, with regression-based methods [7, 8, 11, 24, 27, 28, 30, 31, 35-37, 45, 49, 62, 71, 76, 83], optimization-based methods [4, 10, 33, 50, 69] or hybrid methods [23, 29, 58], mostly adopting parametric 3D body models [4, 70] to represent the 3D human mesh. Most of recent regression-based methods train neural networks to regress SMPL [4] parameters from images [11, 24, 28, 36, 51]. Model-free methods [7, 8, 37, 45] regress human mesh vertices without relying on parametric body models. Optimization-based methods iteratively optimize the body model parameters to fit 2D keypoints, human silhouettes, etc. Some resort to self-contact [46], scene [15, 69] or object [61] constraints to model interactions. Hybrid methods seek to combine the strengths of both regression and optimization, for instance, SPIN [29], which integrates an optimization loop into the deep learning framework. However, these methods often lack robustness when dealing with truncated bodies, a typical challenge in egocentric scenarios, and cannot + +model the diverse nature of plausible missing body parts. 3D scene information is mostly disregarded, resulting in unrealistic human-scene interactions. In this work, we address these challenges by proposing a scene-conditioned generative model for human mesh recovery in 3D scenes. + +Multi-hypothesis for 3D human pose estimation. Due to the limited image observation and depth ambiguity, estimating 3D human pose from a single image can have multiple potential solutions, especially when body truncation is presented. Recent works seek to model this task as a generative process or predict multiple hypothesis of possible poses. A discrete number of hypotheses are generated in [3, 21, 34, 48]. To learn the continuous distribution of possible body poses, conditional variational autoencoders [53] or conditional normalizing flows [32, 68] are adopted to generate unlimited number of hypotheses, but relying on additional scoring functions for pose selection [53], or discriminators to stabilize the training [32, 68]. Nevertheless, the 3D scene constraint is usually not taken into account in this line of works. We leverage the diffusion process to model the inherent pose ambiguity, with flexible scene-conditioning strategies. + +Egocentric human pose estimation. Most of existing works in egocentric human pose estimation targets the camera wearer's 3D pose [13, 22, 40, 56, 64, 65, 73]. 3D pose estimation for a social partner from the egocentric view has been receiving growing attention [38, 47, 72]. However, the 3D scene geometry is neglected in [47, 72], while [38] employs the time-consuming optimization, without modelling the probabilistic distribution of unseen body parts. + +Diffusion models for human motion/pose generation. Denoising Diffusion Models [17, 57, 59, 60] are becoming a popular choice for human motion generative models. Typically trained with the DDPM formulation [17] and based on Transformer-backbones, different methods vary on their choice of motion representation (e.g. skeletons [41, 77], joint rotations [2, 25, 66] or latent variables [6]) and downstream tasks. To generate plausible human-scene interactions, SceneDiffuser [19] condition the motion/pose diffusion model on 3D scenes and further guide the model with physics-based objectives at inference time. In a similar fashion, PhysDiff [74] incorporates a physics-based motion projection module in the inference loop to resolve typical flaws in motion synthesis such as foot-ground penetrations. While these methods all target human action synthesis, we take a different perspective and leverage Diffusion Models for a perception task — as a multi-proposal formulation to address the ambiguity in the egocentric pose estimation. + +# 3. Preliminaries + +SMPL body model [39]. We model the human mesh with the parametric SMPL body model. SMPL parametrizes a body as a function $\mathcal{M}_b(\gamma, \beta, \theta)$ of the global transla + +tion $\gamma \in \mathbb{R}^3$ , body shape $\beta \in \mathbb{R}^{10}$ , and full body pose $\theta \in \mathbb{R}^{24\times 3}$ of 23 body joints, plus the global orientation, returning a mesh $\mathcal{M}_b$ with 6890 vertices. + +Conditional Diffusion Model. We use DDPM [17] as our formulation of pose diffusion model. DDPM learns a distribution of body poses $\pmb{\theta}$ through a forward diffusion process and an inverse denoising (sampling) process. The forward diffusion process is a Markov chain of added Gaussian noise over $t\in \{1,\dots ,T\}$ steps: + +$$ +q \left(\boldsymbol {\theta} _ {t} \mid \boldsymbol {\theta} _ {t - 1}\right) = \mathcal {N} \left(\boldsymbol {\theta} _ {t}; \sqrt {\alpha_ {t}} \boldsymbol {\theta} _ {t - 1}, (1 - \alpha_ {t}) \mathbf {I}\right), \tag {1} +$$ + +where the variance $1 - \alpha_{t} \in (0, 1]$ increases with $t$ according to a pre-defined schedule, and $T$ is the total number of noise corruption steps. + +At the core of the inverse process is a denoiser neural network $D(\cdot)$ , which is trained to remove the added Gaussian noise based on condition signal $c$ at each step $t$ . Following the design of recent motion diffusion models [63], the denoiser predicts the clean signal itself: $\hat{\pmb{\theta}}_0 = D(\pmb{\theta}_t, t, c)$ . + +The Gaussian forward diffusion process has a special property that allows directly sampling $\theta_{t}$ from $\theta_0$ : + +$$ +\boldsymbol {\theta} _ {t} = \sqrt {\alpha_ {t}} \boldsymbol {\theta} _ {0} + \sqrt {1 - \alpha_ {t}} \boldsymbol {\epsilon}, \text {w h e r e} \boldsymbol {\epsilon} \sim \mathcal {N} (0, \mathbf {I}). \tag {2} +$$ + +With this, training the denoiser amounts to sampling a random $t \in \{0, \dots, T - 1\}$ , adding noise according to Eq. (2), and optimizing the simple objective [17]: + +$$ +\mathcal {L} _ {\text {s i m p l e}} = E _ {\boldsymbol {\theta} _ {0} \sim q (\boldsymbol {\theta} _ {0} | \boldsymbol {c}), t \sim [ 1, T ]} \left[ \| \boldsymbol {\theta} _ {0} - D (\boldsymbol {\theta} _ {t}, t, \boldsymbol {c}) \| _ {2} ^ {2} \right]. \tag {3} +$$ + +In this paper we use the subscript $t$ to denote the diffusion timestep and superscript $j$ for the body joint index. + +# 4. Method + +We introduce a novel scene-conditioned diffusion method to recover the human mesh in 3D environments from the egocentric image. Fig. 2 shows the overview of our model. Given an egocentric image $\mathcal{I}$ with a truncated body, the camera intrinsics $\mathcal{K} = (f, c_x, c_y)$ , and the 3D scene point cloud $S \in \mathbb{R}^{N \times 3}$ with $N$ points, our goal is to learn the conditional distribution of body poses $p(\boldsymbol{\theta} | \mathcal{I}, S, \mathcal{K})$ , with the objective of generating humans that naturally interact with the scene while being aligned with the image observation. The body translation $\gamma$ and shape $\beta$ are learnt in a deterministic way following [32]. Here $f$ and $(c_x, c_y)$ denote the focal length and the camera center, respectively. + +The diffusion denoising process (Sec. 3) is modeled by a visibility-aware graph convolution network (GCN), which achieves per-body-part control with the per-joint conditioning on the input image, scene geometry and joint visibility (Sec. 4.1). The diffusion model is trained in a classifier-free manner [18], enabling flexible sampling from both models + +![](images/990be32fc501583ba472a7bdd5ff40d66a2f489fe6bc81dd0395efb5b2471e14.jpg) +Figure 2: Method overview. Given an egocentric image $\mathcal{I}$ containing a partially visible body and the 3D scene geometry $S$ , the proposed model generates a SMPL mesh with plausible human-scene interactions and conforming to the image observation. The model comprises a Scene Conditioning module to estimate the body translation $\hat{\gamma}$ and encode the local scene features, an Image Conditioning module to encode image features, a GCN-based Diffusion Denoiser to predict the clean body pose $\hat{\theta}_0$ from noisy pose $\theta_t$ with Per-joint Conditioning, and a Shape Estimator to estimate body shape $\hat{\beta}$ . + +that include or exclude image conditions to enhance diversity and expressiveness for truncated body parts. Guided by the gradients of a physics-based human-scene collision score, we further resolve human-scene inter-penetrations during the diffusion sampling (Sec. 4.2). The training objectives are explained in Sec. 4.3. + +# 4.1. Scene-conditioned Pose Diffusion Model + +3D scene conditioning. To model fine-grained human-scene interactions, only a small region of the scene surrounding the human is relevant. An accurate global body translation provides better reasoning about local scene geometries, thus crucial for accurate and scene-plausible local body pose modelling. To this end, we propose a body translation estimator (see Fig. 2) to estimate the translation $\hat{\gamma}$ by extracting features from $\mathcal{I}$ and the full 3D scene point cloud $S$ . The global scene features alleviate the scale ambiguity and localize the body in the 3D environment accurately (please refer to Supp. Mat. for more details). Given the estimated body translation $\hat{\gamma}$ , scene vertices in a $2 \times 2m$ region around the human are selected and considered as the scene conditioning for the diffusion denoising process. Furthermore, the selected scene vertices are translated by $\hat{\gamma}$ such that the scene vertex origin is around the body pelvis. The translated scene point cloud is encoded by a scene encoder $E_{S}$ into a localized human-centric scene feature $E_{S}(S, \hat{\gamma})$ for modelling detailed interactions between the body and the 3D scene. + +Per-joint conditioning. A ResNet50 backbone [16] $E_{\mathcal{I}}$ is used to encode the cropped input image $I$ into a latent feature $E_{\mathcal{I}}(\mathcal{I}) \in \mathbb{R}^{2048}$ as the image conditioning. However, regressing the full body pose directly from the global im + +age feature as in previous works [24, 29, 32] loses the explicit joint visibility information. With the body truncated in the image, different properties are desired for different body parts: the model should achieve pose accuracy for observed body joints, and pose expressiveness for truncated body parts. To achieve the per-body-part control, the 2D joint visibility mask $\mathcal{V} = (v^0,\dots,v^j,\dots,v^{J - 1})\in \mathbb{R}^J$ is extracted from the image via OpenPose [5] 2D joint detections, and passed to the diffusion model as the visibility condition. Here $J$ denotes the joint number; and $v^{j}$ equals to 1 if the $j$ -th joint is visible in $\mathcal{I}$ , otherwise 0. + +Apart from above conditions, the bounding box information $\mathcal{B}$ is additionally fed to the network inspired by [36], serving as a global-location-aware feature to better model global information: + +$$ +\mathcal {B} = \left(b _ {x}, b _ {y}, b\right) / f, \tag {4} +$$ + +where $b_{x}, b_{y}, b$ denote the bounding box center coordinates and bounding box size in the full image, respectively. + +The full condition $c^j$ for $j$ -th joint is formulated as the concatenation of: the image feature (masked out by $v^j$ if the joint is not visible), 3D scene feature, estimated body translation, bounding box feature, camera intrinsics and the diffusion timestep $t$ : + +$$ +\boldsymbol {c} ^ {j} = \left(E _ {\mathcal {I}} (\mathcal {I}) \cdot v ^ {j}, E _ {\mathcal {S}} (\mathcal {S}, \hat {\gamma}), \hat {\gamma}, \mathcal {B}, \mathcal {K}, t\right). \tag {5} +$$ + +By conditioning on a per-joint basis, the model achieves flexible control over each body part according to the joint visibility. This allows for both accurate pose estimation of visible body parts, and flexibility for invisible body parts. + +Diffusion denoiser architecture. At diffusion timestep $t$ , for the noisy body pose parameters $\theta_{t}$ , the diffusion de + +noiser $D$ predicts the clean pose parameter $\hat{\theta}_0$ conditioned on $c$ . Previous works either use a single MLP for the full body pose [24, 32, 36, 68] with redundant dependencies between irrelevant joints, or employ a separate MLP for each joint [27] which fully ignores joint dependencies. Instead, we adopt a graph convolution network (GCN) [26, 84] as the denoising function $D$ . Given the predefined human kinematic tree, GCN models inter-joint dependencies by treating the human skeleton as a graph, where each node corresponds to a body joint. Specifically, for each joint $j$ , the noisy pose parameters $\theta_t^j$ is embedded and concatenated with the per-joint conditioning $c^j$ as the feature for node $j$ in the GCN (see Fig. 2). We adopt the modulated GCN [84] for the implementation. Different from vanilla GCN [26], the modulated GCN learns node-specific modulation vectors to disentangle joint feature transformations, such that different relations can be learnt between joints. It also modulates the affinity matrix with learnable parameters to model additional edges beyond the human skeleton [84]. Please refer to Supp. Mat. for implementation details. + +Shape estimator. As the body shape $\beta$ is a global feature and more robust to body truncations, an MLP branch (the body shape estimator in Fig. 2) predicts $\hat{\beta}$ from the conditions $(E_{\mathcal{I}}(\mathcal{I}), E_S(S, \hat{\gamma}), \hat{\gamma}, \mathcal{B}, \mathcal{K})$ in a deterministic way. + +# 4.2. Scene-guided Sampling + +We use the DDPM [17] sampler at inference time. At each sampling step $t$ , the denoiser predicts $\hat{\theta}_0 = D(\theta_t, t, c)$ , which is noised back to $\theta_{t-1}$ by sampling from the Gaussian distribution: + +$$ +\boldsymbol {\theta} _ {t - 1} \sim \mathcal {N} \left(\mu_ {t} \left(\boldsymbol {\theta} _ {t}, \hat {\boldsymbol {\theta}} _ {0}\right), \Sigma_ {t}\right), \tag {6} +$$ + +where $\mu_t(\pmb{\theta}_t, \hat{\pmb{\theta}}_0)$ is a linear combination of $\pmb{\theta}_t$ and $\hat{\pmb{\theta}}_0$ , and $\Sigma_t$ is a scheduled Gaussian distribution as in [17]. The sampling is iteratively repeated from $t = T - 1$ until $t = 0$ . + +Classifier-free guidance. The diffusion model $D$ is trained with classifier-free guidance [18] by randomly masking out the image feature $E_{\mathcal{I}}(\mathcal{I})$ for all joints with a probability of $5\%$ during training, such that the model also learns the pose distribution independent from the image, enabling flexible sampling. By combining the poses of visible joints sampled from the full-conditioned model and the poses of invisible joints sampled from the model excluding image conditions: + +$$ +\hat {\boldsymbol {\theta}} _ {0} = D \left(\boldsymbol {\theta} _ {t}, t, \boldsymbol {c}\right) \odot \mathcal {V} + D \left(\boldsymbol {\theta} _ {t}, t, \boldsymbol {c} _ {\phi}\right) \odot (1 - \mathcal {V}), \tag {7} +$$ + +we achieve better per-body-part control, with enhanced diversity for invisible body parts while maintaining the accuracy of visible body parts (see Sec. 5.5 for the ablation study). Here $\odot$ denotes multiplying the joint visibility mask with the pose of each joint, and $c_{\phi}$ is the condition excluding image features. + +Collision score guided sampling. The proposed scene encoding in Sec. 4.1 implicitly incorporates the 3D environment constraint into the diffusion conditioning. However, the network cannot fully resolve the human-scene collisions in a fine-grained way. Another way to incorporate conditions into the diffusion model is the score-function based guidance. As shown in previous works [9, 57, 60], a pretrained classifier can be adopted to provide class information by adding the gradients of the classifier at each sampling step to the diffusion model, to guide the sampling process towards the class label. Inspired by this, we propose a collision score guided sampling strategy to further resolve implausible human-scene inter-penetrations, by leveraging implicit body representations [43, 44]. We use COAP [43] to model neural articulated occupancy of human bodies as the zero-level set $f_{\Theta}(q|\mathcal{G}) = 0$ , where $q$ is the input query point and $\mathcal{G}(\theta ,\beta)$ is the input bone transformations. By querying each scene vertex near the body to see if it is inside of the human volume, the collision score is defined as: + +$$ +\mathcal {J} (\boldsymbol {\theta}) = \frac {1}{| \mathcal {S} |} \sum_ {q \in \mathcal {S}} \sigma \left(f _ {\Theta} (q \mid \mathcal {G})\right) \mathbb {I} _ {f _ {\Theta} (s \mid \mathcal {G}) > 0}, \tag {8} +$$ + +where $\sigma(\cdot)$ stands for the sigmoid function. The gradient $\nabla \mathcal{J}(\boldsymbol{\theta})$ efficiently guides the diffusion sampling process to further alleviate the human-scene collisions (see Sec. 5.5 for the ablation study) by modifying Eq. (6) to: + +$$ +\boldsymbol {\theta} _ {t - 1} \sim \mathcal {N} \left(\mu_ {t} \left(\boldsymbol {\theta} _ {t}, \hat {\boldsymbol {\theta}} _ {0}\right) + a \Sigma_ {t} \nabla \mathcal {J} \left(\boldsymbol {\theta} _ {t}\right), \Sigma_ {t}\right), \tag {9} +$$ + +where the guidance is modulated by $\Sigma_{t}$ and a scale factor $a$ . + +# 4.3. Training Objectives + +The diffusion model is trained with $\mathcal{L}_{\mathrm{simple}}$ in Eq. (3) for body pose $\hat{\theta}_0$ , together with the 3D joint loss $\mathcal{L}_{\mathrm{3D}}$ , the 2D keypoint re-projection loss $\mathcal{L}_{\mathrm{2D}}$ calculated in the full image frame, and the shape loss $\mathcal{L}_{\beta}$ : + +$$ +\mathcal {L} _ {\mathrm {3 D}} = \left\| F K (\hat {\boldsymbol {\theta}} _ {0}, \hat {\boldsymbol {\beta}}) - F K (\boldsymbol {\theta} _ {0}, \boldsymbol {\beta}) \right\| ^ {2}, +$$ + +$$ +\mathcal {L} _ {\mathrm {2 D}} = \left\| \Pi_ {\mathcal {K}} \left(J _ {\mathrm {3 D}} + \hat {\gamma}\right) - J _ {\mathrm {e s t}} \right\| ^ {2}, \tag {10} +$$ + +$$ +\mathcal {L} _ {\beta} = \left\| \hat {\boldsymbol {\beta}} - \boldsymbol {\beta} \right\| ^ {2}. +$$ + +Here $FK(\cdot)$ denotes the SMPL joint regressor to obtain 3D joint coordinates. $J_{\mathrm{est}}$ is the 2D body keypoint detections, and $\Pi_{\mathcal{K}}$ denotes the 3D to 2D projection in the full image with camera intrinsics $\mathcal{K}$ . The overall loss is defined as: + +$$ +\begin{array}{l} \mathcal {L} = \mathcal {L} _ {\text {s i m p l e}} + \lambda_ {3 \mathrm {D}} \mathcal {L} _ {3 \mathrm {D}} + \lambda_ {2 \mathrm {D}} \mathcal {L} _ {2 \mathrm {D}} + \lambda_ {\beta} \mathcal {L} _ {\beta} \tag {11} \\ + \lambda_ {\text {c o l l}} \mathcal {L} _ {\text {c o l l}} + \lambda_ {\text {o r t h}} \mathcal {L} _ {\text {o r t h}}, \\ \end{array} +$$ + +where $\mathcal{L}_{\mathrm{orth}}$ is a regularizer to force the generated 6D pose rotation representation to be orthonormal, $\mathcal{L}_{\mathrm{coll}}$ is the scene collision loss the same as defined in Eq. (8), and $\lambda s$ are the corresponding weight factors for each loss term. + +# 5. Experiments + +# 5.1. Dataset + +Most of existing datasets for 3D human pose evaluation are either captured from the third-person view with the full body visible [15, 20, 42, 67], or do not contain the 3D environment [47]. The most relevant dataset is EgoBody [78], a large-scale egocentric dataset capturing 3D human motions during social interactions in 3D scenes. Each sequence involves two people interacting with each other in 3D environments, and one subject wears a head-mounted camera to capture the egocentric images containing the other interactee. Due to the close social interaction distance, the captured egocentric images typically exhibit strong body truncations for the interactee. We use the official train / test splits for training and evaluation, which include 90,120 / 62,140 frames, respectively. + +# 5.2. Evaluation Metrics + +Strong body truncations pose inherent ambiguity for invisible body parts, while the visible body parts are relatively deterministic given the image observations, thus evaluating the accuracy of full body joints together as in [3, 32] is not suitable for such tasks. We propose to evaluate the proposed method from the following aspects. + +Accuracy. We employ Mean Per-Joint Position Error (MPJPE) and Vertex-to-Vertex (V2V) errors in $mm$ to evaluate the accuracy of estimated body pose and shape. For MPJPE, we report different variations: G-MPJPE as the joint error in the global coordinate; MPJPE as the pelvis-aligned joint errors, and PA-MPJPE as the joint errors after Procrustes Alignment [12]. We report mean MPJPE and V2V metrics over $n$ samples for visible joints. Nevertheless, such evaluation protocol assumes a single correct ground truth prediction, which does not hold for invisible joints. Instead of the mean error, we report min-of- $n$ MPJPE for invisible body parts following [3]. To be specific, among the generated $n$ samples for each input image, we select the one with the minimum MPJPE for all evaluated methods. + +Physical plausibility. We evaluate the collision and contact scores between the body mesh and the 3D scene. As the clean scene signed distance field (SDF) is not available in EgoBody, we define the collision score as the ratio of the number of scene vertices inside of the body mesh to the number of all scene vertices. Note that the absolute scale of the collision score may vary with different size of the 3D scene, but within the same scene surface, the relative comparison between different methods indicates different collision levels. We use the cropped scene as described in Sec. 4.1 for evaluation (with a fixed size of 20,000 vertices). Following [19], the contact score is defined as 1 if the body contacts with the scene in a distance within a threshold (2 cm), otherwise 0. We report the mean collision score and + +contact score over all test samples. Note that a model with better physical plausibility should achieve both a lower collision score and a higher contact score. + +Diversity. Diversity is evaluated for invisible body parts to demonstrate the expressiveness of the methods, by calculating the standard deviation (std) and Average Pairwise Distance (APD) of invisible body joints [19]. A higher diversity is desired, yet there is usually a trade-off between diversity and accuracy/plausibility. An ideal model should predict diverse poses for invisible body parts, with accurate visible body poses and plausible human-scene interactions. + +# 5.3. Baselines and Our Method + +As there is no existing work for our task, we compare our method with the following baselines: (1) ProHMR [32], the state-of-the-art method for probabilistic human mesh recovery from a single image based on conditional normalizing flows; (2) ProHMR-scene, in which we enhance the ProHMR framework by incorporating the scene geometry $S$ with a global scene feature encoder. The ProHMR framework is trained with 2D and 3D supervisions for the sample drawn from $z = 0$ (referred as the 'mode'), such that the 'mode' can be used as a predictive model (see [32] for details). Different training weights for the samples drawn from $z \neq 0$ yields a trade-off between the accuracy and diversity for the generated multiple hypotheses. Here $z$ denotes the latent space of the normalizing flow. To demonstrate this trade-off, we train the ProHMR-scene baseline with different training configurations. For samples drawn from $z \neq 0$ , we supervise with: 1) only 2D re-projection loss (the same as in [32]), denoted as -orig; 2) 3D supervision with small weights, denoted as -weak-3D; 3) 3D supervision with large weights, denoted as -strong-3D. Here the 3D supervision refers to the loss on 3D body joints and SMPL parameters. Please refer to Supp. Mat. for details of the baseline models. + +# 5.4. Results + +Tab. 1 shows the quantitative results. Compared to the baselines, our method achieves the best G-MPJPE, MPJPE and V2V metrics for visible joints, demonstrating accurate estimations of the global translation, local body pose for visible joints and body shape. For truncated body joints, our method obtains the best min-of-n MPJPE, indicating that our generated results better covers the ground truth distribution for truncated body parts than baselines, thanks to the efficient scene conditioning. Our method also outperforms the baselines with the higher contact ratios and significantly better collision scores. In particular, our collision score decreased $45\%$ compared with ProHMR, and $37\%$ compared with the best ProHMR-scene model. This indicates that the proposed method can effectively leverage the scene conditions and resolve body-scene inter-penetrations, + +Table 1: Evaluation for accuracy, physical plausibility and diversity on EgoBody. Here -vis and -invis denote visible and invisible joints, respectively. 'coll' and 'contact' refer to the collision and contact scores, respectively. The percentage for the collision score denotes how much improvement the corresponding method has achieved compared with the ProHMR baseline. The best results are in boldface. + +
nMethodG-MPJPE ↓ -visMPJPE ↓ -visPA-MPJPE ↓ -visV2V ↓ -vismin-of-n MPJPE ↓ -inviscoll ↓contact ↑std ↑ -invisAPD ↑ -invis
5ProHMR [32]181.3372.9246.5790.88128.560.00346 (-)0.9426.5332.95
ProHMR-scene-orig133.7273.1348.8791.59117.880.00305 (12%)0.9635.4244.02
Ours128.6265.7047.1782.93107.770.00191 (45%)0.9929.5935.15
10ProHMR [32]181.7073.6547.0691.84121.670.00346 (-)0.9429.2635.06
ProHMR-scene-orig134.5774.4249.6393.21110.640.00305 (12%)0.9639.0746.86
Ours128.6065.6947.2082.94100.750.00191 (45%)0.9929.5935.15
20ProHMR [32]181.8773.9947.2992.28115.480.00346 (-)0.9330.5536.14
ProHMR-scene-orig134.9775.0349.9893.98103.810.00306 (12%)0.9640.8248.32
ProHMR-scene-weak-3D131.5167.8146.9485.05111.680.00313 (10%)0.9621.7925.67
ProHMR-scene-strong-3D134.4066.4245.9682.99123.340.00316 (9%)0.9713.0115.23
Ours128.6065.6947.1982.9494.960.00191(45%)0.9930.2335.14
+ +![](images/b6244737a3714ab6171c6e7146402eb30e454586fdf5bc5d852c8cc4bba1f9f3.jpg) + +![](images/d8e0a30074e26b3611eb38fc91fa25df8fabe85709ee992fe64c7169d3a323fd.jpg) + +![](images/18079945d48da22be4c675d7897bc4b5b07ea47115ce91561289e88a782d9b18.jpg) + +![](images/2c66372178b4c010703d5d680f2764ce1bbf8021ea2ce8dfbf6a756420f014ae.jpg) + +![](images/5a4fe680dfca5d9d64d616deef7a4845d121b0cd38004f27605a3af465151b6b.jpg) + +![](images/1462b228e92ca2153ef6cfe7dec1feed2fb3dc261a85da8b9f4a04ea283d4fc6.jpg) + +![](images/42f842e905d255d806aff59b91a77483e2cd2ffd8e98dff02c48507e26d52960.jpg) + +![](images/805f2368cc6ec84983a1266b30fd0537aae69a41a98c612ad9328d5f1587b06d.jpg) + +![](images/8b8e278373957a617f1bc0591e00ddd4f7f5a7cac24408d110d47376910b235b.jpg) + +![](images/64a0acafd60c31d38635ac8c0897c8fb1d36142e73d2e6f5c12563c664b8dcc6.jpg) + +![](images/3800f5ca72e7b5ad933dd4f332a32917203acb04e179a413287fe7e02306bf12.jpg) + +![](images/74f307403d79050af07bbe749bd78e9c91249a6e16fd2974cb578bebc6182f3d.jpg) + +![](images/42f70a440b24950b3127e674cd557ca7279aedca821cc50ae1d0caaacdbe6a3c.jpg) + +![](images/6e5773a3629061f13c44f7dc0890ac254104a25d1244e6eea4f589a687e2694f.jpg) + +![](images/0a8b4f41cca89f4d021e94d4054dc032472536173aedf2248ccad7f79cca0343.jpg) + +![](images/43d63c714dc49c2ee72a8de6ba9fd8681f77ca2710c98d3d4d1c618166f4a546.jpg) + +![](images/2b91446615ac4fc65db8b06e5eeec632bb2778ffa8a24c6e4b2fa264d26c3aaf.jpg) + +![](images/5f238d31c531c203dafb699e87d989725c4f7132360be979b849aa913bf4e2a5.jpg) +Figure 3: Qualitative results on EgoBody dataset. The left part shows the comparison between the baseline methods and our proposed method. The right part demonstrates the effectiveness of our proposed scene collision score guidance $\mathcal{I}_{\theta}$ to further resolve human-scene inter-penetrations. Red circles point to human-scene collisions. + +![](images/989482f0b2936993d6cedbf900ec248c9a0389cb6778fb11873c86e58b013501.jpg) + +![](images/130d2bc6f51cd16234317ff070598f7f9e4216255f3a083786e3bd08c21eee11.jpg) +ProHMR + +![](images/8c17ef90e897c471efc92edcf5335b41acf34c8fc1c635da6c4d9f6143bef8e8.jpg) + +![](images/9129a211b39f312cd43595f3147ad842f2639241706714ee39ff7e9fd97952f0.jpg) +ProHMR-scene + +![](images/21a95fd957cc9f3f544e0c16944779202eef5796160141228d6db11a69a9af40.jpg) + +![](images/402c81e10b4a14ae9ec6221b7c367ead78c387a97ed3ab2d4c84dd3297295534.jpg) +Ours + +![](images/2cbf0bde56ba574c211f2166a3eeba935f0b1fa7ac1129e99f8c546ba8caf214.jpg) + +![](images/769d560650a840c6a1a7bd18ff965b978e1b059a7e42d0379b06548a76860a21.jpg) + +![](images/c2389c971c30964203b2c0b2ccd30a098c7576c92e14c750cfac20b9d880cb25.jpg) + +![](images/e480f85c4fa60d8afa9d65fb26300091e089858c369dea3d468d025ecc056107.jpg) + +![](images/859d05a117a8ffa240b0ab197fa0aa7d10ee7c6710bf9c9a3ecfa8d8fc680617.jpg) + +![](images/d0a360f20d2168a9549732498b14cfe23029f10d6b1f7a93fa9f30b0b03da3d2.jpg) + +![](images/cc4beb2b5f86f675395cfb987fcb6ef4ca1fbd0bb8b93ab36011f758805e15b1.jpg) + +![](images/e56f3fc2919b67f112627782a01959035d6b89cd6c5c6663969da20b88706b7b.jpg) + +![](images/ca578074f1cd4febc9023e8ac9b072e37e79f8f7dd72bd75df5a7fc382809341.jpg) + +![](images/9518dff47a593e3c12144771b57887b32c49fb5763577337cd841b3bc1fd745e.jpg) + +![](images/6f57fa63bf58fb8174ae81b1e7a7af765fd12054bcb18d1467cc66640ad41cf2.jpg) + +![](images/59a821750e87a0df9bba929d59ff71d22d01f4c7528f2f8d8bf6d4e2abc586bb.jpg) + +![](images/29f5a1bfc07e36a5501f993f109d01cd670a54abb0cc5b544bab2f0378a9b031.jpg) + +![](images/f5b5ca6051b3404a2f042c71bbf2b0a4e273210cfe8445b20a8bbe74672ead06.jpg) + +![](images/5541cc93a96263f5cbbf91715a01eb684f759aca3af46a3bdd8a02304de3f28d.jpg) + +![](images/cd2634b90fa275fa25040c8bd434244e790799c4c3e625f29d717f71534a15d5.jpg) +Ours w/o $\mathcal{J}_{\pmb{\theta}}$ + +![](images/a3c27f067a9dca2465ab828bd8fdf964deb3cc57a05317cdfce70b11e38b5a5b.jpg) + +![](images/81d5a1eb37cc5db8c075d5282fa98cbc64d8eca711f78096dd489276cb17f8b4.jpg) +Ours + +Table 2: Ablation study. $\mathcal{I}_{\theta}$ and CF denote the collision score guidance and classifier-free guidance during the diffusion sampling (Sec 4.2). $\mathcal{L}_{\mathrm{coll}}$ denotes the collision loss for training (Eq. (11)). All results are reported for $n = 20$ . + +
MethodMPJPE ↓ -vismin-of-n MPJPE ↓ -inviscoll ↓contact ↑std ↑ -invisAPD ↑ -invis
Ours65.6994.960.001910.9930.2335.14
Ours w/o Jθ65.0997.200.002250.9921.5325.32
Ours w/o Jθ w/o CF64.5898.820.002290.9915.7519.56
Ours w/o Jθ w/o CF w/o Lcoll64.9196.260.003020.9922.9421.79
+ +![](images/6252da45fd1577930c784b04638594ef730d4690db132cd775c4810269686dbf.jpg) +Figure 4: Multiple samples. Given the same input, our method can generate diverse poses for invisible body parts. + +while achieving better contact relations between the body and the 3D environment. Fig. 3 (left) shows the qualitative results and the comparison with the baseline method. + +From the results among different ProHMR-scene baselines $(n = 20)$ in Tab. 1, we can clearly see a trade-off between the accuracy and diversity: stronger 3D supervision (ProHMR-scene-strong-3D) has better accuracy for visible body parts (MPJPE-vis), yet lower diversity (std-invis and APD-invis) for invisible joints. The reason behind this is that the ProHMR framework, like many other existing works, condition the generative process of full body pose only on the global image feature. In contrast, our method leverages the joint visibility and the GCN architecture, achieving the best MPJPE for visible joints, diverse poses for invisible joints, and natural human-scene interactions (see Fig. 4), while the baseline with a similar diversity level (ProHMR) and the baseline with the highest diversity (ProHMR-scene-orig) exhibit much higher MPJPE errors and more severe human-scene collisions. There is a very slight increase for PA-MPJPE of our model compared to the ProHMR-scene-strong/weak-3D baselines, while we obtain a much higher diversity for invisible body joints. This reveals that our method achieves flexible per-body-part control to balance between the accuracy and diversity for different body parts. + +To validate the reconstruction accuracy, the full-body accuracy of the proposed method is also evaluated and compared against existing deterministic baselines on EgoBody dataset. The results show that our method even achieves higher full-body accuracy than deterministic methods, which demonstrates that the proposed model achieves diversity without sacrificing the reconstruction accuracy. In addition, the proposed method is also evaluated on PROX [15] + +dataset, a monocular RGB-based third-person view dataset with human-scene interactions, and our method outperforms the baseline methods in terms of pose accuracy, human-scene interaction plausibility and pose diversity. Please refer to Supp. Mat. for detailed results of evaluations on PROX and comparison with deterministic methods on EgoBody. + +# 5.5. Ablation Study + +To investigate the influences of different training and sampling schemes for the diffusion model, we perform an ablation study and the results are shown in Tab. 2. The scene collision score efficiently resolves the human-scene interpenetrations from two different perspectives: via the collision loss $\mathcal{L}_{\mathrm{coll}}$ during training and via the explicit collision score guidance $\mathcal{I}_{\theta}$ during the diffusion sampling (Eq. (9)). Fig. 3 (right) shows that the collision score guidance $\mathcal{I}_{\theta}$ improves the human-scene interaction relationships. The classifier-free guidance during the diffusion sampling in Eq. (7) significantly improves the sample diversity, by leveraging the invisible joints sampled from the model trained excluding the image conditions. It is worth mentioning that the collision score guidance $\mathcal{I}_{\theta}$ also contributes to the sample diversity. This is not surprising as the gradients of $\mathcal{I}_{\theta}$ can potentially optimize the body pose to different directions given different initial body poses. + +Compared with the trade-off in the ProHMR-based methods where the accuracy sacrifices a lot for diversity (and vice versa), the classifier-free guidance and the collision score guidance in our model only bring marginal changes for the MPJPE of visible body parts, in the trade-off for significantly enhanced physical plausibility, sample diversity and better min-of-n MPJPE for unobserved joints. + +# 6. Conclusion + +This paper introduces a novel scene-conditioned probabilistic approach for human mesh recovery from the egocentric image given the 3D scene geometry. The proposed diffusion model efficiently leverages the scene conditions and joint visibility to achieve per-body-part control and model human-scene interactions. The classifier-free guidance and the collision score guidance enables flexible sampling process with further enhanced diversity and physical plausibility. We demonstrate that our model generates human bodies in realistic interactions with the 3D environment, with diverse poses for invisible body parts while conforming to the image observation. Nevertheless, the current method also has limitations. For example, currently only a single frame is considered as the input. A promising future direction is to further exploit temporal information to reconstruct temporally consistent human motions from the egocentric view. Acknowledgements. This work was supported by Microsoft Mixed Reality & AI Zurich Lab PhD scholarship. Qianli Ma is partially funded by the Max Planck ETH Center for Learning Systems. We sincerely thank Korrawe Karunratanakul, Marko Mihajlovic and Shaofei Wang for the fruitful discussions. + +# References + +[1] Microsoft Hololens2. https://www.microsoft.com/en-us/hololens.2 +[2] Simon Alexanderson, Rajmund Nagy, Jonas Beskow, and Gustav Eje Henter. Listen, denoise, action! audio-driven motion synthesis with diffusion models. ACM Transactions on Graphics (TOG), 42(4):1-20, 2023. 3 +[3] Benjamin Biggs, David Novotny, Sebastien Ehrhardt, Hanbyul Joo, Ben Graham, and Andrea Vedaldi. 3D multibodies: Fitting sets of plausible 3D human models to ambiguous image data. Advances in Neural Information Processing Systems, 33:20496-20507, 2020. 2, 3, 6 +[4] Federica Bogo, Angjoo Kanazawa, Christoph Lassner, Peter Gehler, Javier Romero, and Michael J. Black. Keep it SMPL: Automatic estimation of 3D human pose and shape from a single image. In European Conference on Computer Vision, pages 561-578, 2016. 2 +[5] Z. Cao, G. Hidalgo Martinez, T. Simon, S. Wei, and Y. A. Sheikh. 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{ + "bbox": [ + 46, + 330, + 547, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 330, + 547, + 378 + ], + "type": "text", + "content": "Figure 1: We propose EgoHMR, a novel scene-conditioned probabilistic method to recover the human mesh from an ego-centric view image (typically with the body truncated) given the 3D environment. EgoHMR efficiently leverages the scene geometry and achieves significantly more plausible human-scene interactions compared to baseline methods, ProHMR [32] and the extended ProHMR-scene (Sec. 5.3), even with severe body truncations." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 183, + 202, + 293, + 258 + ], + "blocks": [ + { + "bbox": [ + 183, + 202, + 293, + 258 + ], + "lines": [ + { + "bbox": [ + 183, + 202, + 293, + 258 + ], + "spans": [ + { + "bbox": [ + 183, + 202, + 293, + 258 + ], + "type": "image", + "image_path": "99fa2f6fc657b5f73a4249c6d203aa108e28a1130f64ee332f494cda7766d053.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 166, + 258, + 288, + 320 + ], + "blocks": [ + { + "bbox": [ + 166, + 258, + 288, + 320 + ], + "lines": [ + { + "bbox": [ + 166, + 258, + 288, + 320 + ], + "spans": [ + { + "bbox": [ + 166, + 258, + 288, + 320 + ], + "type": "image", + "image_path": "74df6eea3b87bc8c5264d2bd61bc6b0aac966866760fad65e40eff3e922d7e89.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 302, + 202, + 411, + 258 + ], + "blocks": [ + { + "bbox": [ + 302, + 202, + 411, + 258 + ], + "lines": [ + { + "bbox": [ + 302, + 202, + 411, + 258 + ], + "spans": [ + { + "bbox": [ + 302, + 202, + 411, + 258 + ], + "type": "image", + "image_path": "808e491adb646f56082d00e64ba53e313db206869ae3e828ce4e780fc146cda2.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 288, + 258, + 410, + 320 + ], + "blocks": [ + { + "bbox": [ + 288, + 258, + 410, + 320 + ], + "lines": [ + { + "bbox": [ + 288, + 258, + 410, + 320 + ], + "spans": [ + { + "bbox": [ + 288, + 258, + 410, + 320 + ], + "type": "image", + "image_path": "9f4311148457c4d2094bad571b0e6030dcd418b45faa7536200a4c021e946a39.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 406, + 202, + 528, + 258 + ], + "blocks": [ + { + "bbox": [ + 406, + 202, + 528, + 258 + ], + "lines": [ + { + "bbox": [ + 406, + 202, + 528, + 258 + ], + "spans": [ + { + "bbox": [ + 406, + 202, + 528, + 258 + ], + "type": "image", + "image_path": "21be33b5f7f907620c67f306b8a954a8a1b694efaa4152287a153380e290c64b.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 407, + 258, + 528, + 320 + ], + "blocks": [ + { + "bbox": [ + 407, + 258, + 528, + 320 + ], + "lines": [ + { + "bbox": [ + 407, + 258, + 528, + 320 + ], + "spans": [ + { + "bbox": [ + 407, + 258, + 528, + 320 + ], + "type": "image", + "image_path": "3622831795701a0d6b7e26de6b66940c7027dab7a71eaa3ff386329414340cfb.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 143, + 397, + 192, + 409 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 397, + 192, + 409 + ], + "spans": [ + { + "bbox": [ + 143, + 397, + 192, + 409 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 425, + 289, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 289, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 289, + 700 + ], + "type": "text", + "content": "Automatic perception of human behaviors during social interactions is crucial for AR/VR applications, and an essential component is estimation of plausible 3D human pose and shape of our social partners from the egocentric view. One of the biggest challenges of this task is severe body truncation due to close social distances in egocentric scenarios, which brings large pose ambiguities for unseen body parts. To tackle this challenge, we propose a novel scene-conditioned diffusion method to model the body pose distribution. Conditioned on the 3D scene geometry, the diffusion model generates bodies in plausible human-scene interactions, with the sampling guided by a physics-based collision score to further resolve human-scene interpenetrations. The classifier-free training enables flexible sampling with different conditions and enhanced diversity. A visibility-aware graph convolution model guided by per-joint visibility serves as the diffusion denoiser to incorporate inter-joint dependencies and per-body-part control. Extensive evaluations show that our method generates bodies in plausible interactions with 3D scenes, achieving both superior accuracy for visible joints and diversity for invisible body parts. The code is available at https:// sanweiliti.github.io/egohmr/egohmr.html." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 307, + 397, + 386, + 409 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 397, + 386, + 409 + ], + "spans": [ + { + "bbox": [ + 307, + 397, + 386, + 409 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "type": "text", + "content": "With the rapid development of Augmented and Virtual Reality (AR/VR) devices, understanding human actions, behaviors and interactions of our social partners (\"inter-actee\") from the egocentric view is a vital component for head-mounted devices (HMDs) to truly become a virtual companion for humans. The first step towards the automatic perception of human behaviors and interactions for HMDs is to estimate 3D human pose and shape (i.e. human mesh recovery) of the interactee from egocentric view images." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": "The research community has extensively studied human mesh recovery (HMR) from a single RGB image (usually captured with third-person view cameras) by predicting SMPL [39, 50] parameters from global image features [8, 24, 27, 30, 45]. However, their performance degrades significantly in egocentric images [78]. A major challenge presented in egocentric scenarios is frequent body truncation [38, 78], when individuals interact with each other within close proximity, while the HMD camera has a limited field-of-view. Since human poses are highly reliant on the surrounding environment, 3D scene structures can potentially provide strong cues to infer invisible body parts, which is crucial for precise understanding of human behaviors: sitting on a chair and standing on the ground may indicate distinct intentions and future behaviors. Following" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7989" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "PROX [15], we assume a rough 3D scene structure is available, as such information nowadays can be easily obtained with commodity sensors. Furthermore, visual localization and mapping, one of the extensively studied topics in computer vision, is progressing rapidly for head-mounted devices [52]. Therefore, we make the assumption that a coarse 3D model of the scene and the localization of the egocentric camera are readily available (e.g. in HoloLens2 [1]). In this paper, we focus on the challenging problem of estimating 3D human bodies that are heavily truncated from egocentric views due to the proximity between people and the motion of embodied cameras." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 219, + 289, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 219, + 289, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 289, + 483 + ], + "type": "text", + "content": "Given an egocentric image and the corresponding 3D environment, what should an ideal human mesh recovery method achieve? In contrast to previous studies that mostly pursue full-body pose accuracy, we argue the following properties are desired in the egocentric scenario: (1) natural and plausible human-scene interactions; (2) accurate body pose estimations consistent with image observations for visible joints; (3) a comprehensive conditional distribution to generate diverse and plausible poses for unobserved body parts. Several recent studies have attempted to tackle pose ambiguities caused by occlusions and body truncations. However, some methods can only produce a discrete number of body poses [3, 34, 48], ignoring the continuous nature of the pose manifold. Other approaches model the continuous body pose distribution via conditional variational autoencoder [53] or normalizing flows [32, 68], but with limited expressiveness. Furthermore, the 3D environment is often ignored although it provides strong cues for inferring missing body parts in the image. Existing works for human pose estimation [54, 55, 79] or generation [14, 80-82] in 3D scenes typically cannot deal with truncated bodies in images." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "type": "text", + "content": "To address these issues, we introduce a novel scene-conditioned probabilistic approach, the first method to recover human mesh in 3D scenes from the egocentric view image. Inspired by the recent diffusion models that can generate high fidelity images [9, 17, 18, 59] and human motions [6, 25, 41, 63, 77] with flexible conditioning, our model is trained with a conditional diffusion framework, leveraging both the classifier-free guidance [18] and the classifier-guided diffusion sampling [9, 57, 60] for efficient scene conditioning. By training the model conditioning on a human-centric scene encoding, the diffusion denoiser can generate body poses with plausible human-scene interactions even with highly truncated bodies (see Fig. 1). The classifier-free training enables flexible sampling from models with or without image conditions, achieving accurate estimations of visible body parts while generating diverse plausible results for unseen body parts. On top of that, the diffusion sampling process is guided by the gradients of a physics-based collision score guidance in the classifier-" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "guided sampling manner, which further resolves human-scene inter-penetrations without requiring additional time-consuming postprocessing." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 108, + 546, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 546, + 287 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 546, + 287 + ], + "type": "text", + "content": "To facilitate the learning of the multimodal distributions of the invisible body parts, we introduce a visibility-aware graph convolution model as the diffusion denoiser network, to explicitly guide the network to learn more expressive distribution for invisible body parts. Unlike existing methods [24, 32, 36, 68] that simply condition the full body pose on a global image feature, we condition the pose diffusion of each body joint on the joint visibility mask and the 3D scene feature, in addition to the image feature. With such explicit visibility guidance, the model learns to estimate accurate body pose for visible joints while encouraging diversity for truncated body parts. We adopt a graph convolution network (GCN) [26, 75, 84] to better incorporate local dependencies between highly-relevant body parts (e.g. knee-foot) according to the human kinematic tree." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 288, + 547, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 288, + 547, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 288, + 547, + 431 + ], + "type": "text", + "content": "In summary, our contributions are: 1) a novel scene-conditioned diffusion model for probabilistic human mesh recovery in the 3D environment from egocentric images; 2) a physics-based collision score that guides the diffusion sampling process to further resolve human-scene interpenetrations; 3) a visibility-aware GCN architecture that incorporates inter-joint dependencies for the pose diffusion, and enables per-body-part control via the per-joint visibility conditioning. With extensive evaluations, the proposed method demonstrates superior accuracy and diversity of generated human bodies from egocentric images, in natural and plausible interactions with the 3D environment." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 442, + 392, + 454 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 442, + 392, + 454 + ], + "spans": [ + { + "bbox": [ + 306, + 442, + 392, + 454 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": "Human mesh recovery from a single image. Given a single RGB image, the task of deterministic 3D human mesh recovery has been widely studied in the literature, with regression-based methods [7, 8, 11, 24, 27, 28, 30, 31, 35-37, 45, 49, 62, 71, 76, 83], optimization-based methods [4, 10, 33, 50, 69] or hybrid methods [23, 29, 58], mostly adopting parametric 3D body models [4, 70] to represent the 3D human mesh. Most of recent regression-based methods train neural networks to regress SMPL [4] parameters from images [11, 24, 28, 36, 51]. Model-free methods [7, 8, 37, 45] regress human mesh vertices without relying on parametric body models. Optimization-based methods iteratively optimize the body model parameters to fit 2D keypoints, human silhouettes, etc. Some resort to self-contact [46], scene [15, 69] or object [61] constraints to model interactions. Hybrid methods seek to combine the strengths of both regression and optimization, for instance, SPIN [29], which integrates an optimization loop into the deep learning framework. However, these methods often lack robustness when dealing with truncated bodies, a typical challenge in egocentric scenarios, and cannot" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7990" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 131 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 131 + ], + "type": "text", + "content": "model the diverse nature of plausible missing body parts. 3D scene information is mostly disregarded, resulting in unrealistic human-scene interactions. In this work, we address these challenges by proposing a scene-conditioned generative model for human mesh recovery in 3D scenes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 286, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 286, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 286, + 335 + ], + "type": "text", + "content": "Multi-hypothesis for 3D human pose estimation. Due to the limited image observation and depth ambiguity, estimating 3D human pose from a single image can have multiple potential solutions, especially when body truncation is presented. Recent works seek to model this task as a generative process or predict multiple hypothesis of possible poses. A discrete number of hypotheses are generated in [3, 21, 34, 48]. To learn the continuous distribution of possible body poses, conditional variational autoencoders [53] or conditional normalizing flows [32, 68] are adopted to generate unlimited number of hypotheses, but relying on additional scoring functions for pose selection [53], or discriminators to stabilize the training [32, 68]. Nevertheless, the 3D scene constraint is usually not taken into account in this line of works. We leverage the diffusion process to model the inherent pose ambiguity, with flexible scene-conditioning strategies." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 336, + 286, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 336, + 286, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 336, + 286, + 430 + ], + "type": "text", + "content": "Egocentric human pose estimation. Most of existing works in egocentric human pose estimation targets the camera wearer's 3D pose [13, 22, 40, 56, 64, 65, 73]. 3D pose estimation for a social partner from the egocentric view has been receiving growing attention [38, 47, 72]. However, the 3D scene geometry is neglected in [47, 72], while [38] employs the time-consuming optimization, without modelling the probabilistic distribution of unseen body parts." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 431, + 286, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 431, + 286, + 646 + ], + "spans": [ + { + "bbox": [ + 46, + 431, + 286, + 646 + ], + "type": "text", + "content": "Diffusion models for human motion/pose generation. Denoising Diffusion Models [17, 57, 59, 60] are becoming a popular choice for human motion generative models. Typically trained with the DDPM formulation [17] and based on Transformer-backbones, different methods vary on their choice of motion representation (e.g. skeletons [41, 77], joint rotations [2, 25, 66] or latent variables [6]) and downstream tasks. To generate plausible human-scene interactions, SceneDiffuser [19] condition the motion/pose diffusion model on 3D scenes and further guide the model with physics-based objectives at inference time. In a similar fashion, PhysDiff [74] incorporates a physics-based motion projection module in the inference loop to resolve typical flaws in motion synthesis such as foot-ground penetrations. While these methods all target human action synthesis, we take a different perspective and leverage Diffusion Models for a perception task — as a multi-proposal formulation to address the ambiguity in the egocentric pose estimation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 657, + 132, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 132, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 132, + 670 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": "SMPL body model [39]. We model the human mesh with the parametric SMPL body model. SMPL parametrizes a body as a function " + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_b(\\gamma, \\beta, \\theta)" + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": " of the global transla" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "content": "tion " + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "inline_equation", + "content": "\\gamma \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "content": ", body shape " + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "inline_equation", + "content": "\\beta \\in \\mathbb{R}^{10}" + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "content": ", and full body pose " + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "inline_equation", + "content": "\\theta \\in \\mathbb{R}^{24\\times 3}" + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "content": " of 23 body joints, plus the global orientation, returning a mesh " + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_b" + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "content": " with 6890 vertices." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 108, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 545, + 180 + ], + "type": "text", + "content": "Conditional Diffusion Model. We use DDPM [17] as our formulation of pose diffusion model. DDPM learns a distribution of body poses " + }, + { + "bbox": [ + 304, + 108, + 545, + 180 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}" + }, + { + "bbox": [ + 304, + 108, + 545, + 180 + ], + "type": "text", + "content": " through a forward diffusion process and an inverse denoising (sampling) process. The forward diffusion process is a Markov chain of added Gaussian noise over " + }, + { + "bbox": [ + 304, + 108, + 545, + 180 + ], + "type": "inline_equation", + "content": "t\\in \\{1,\\dots ,T\\}" + }, + { + "bbox": [ + 304, + 108, + 545, + 180 + ], + "type": "text", + "content": " steps:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 337, + 190, + 545, + 203 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 190, + 545, + 203 + ], + "spans": [ + { + "bbox": [ + 337, + 190, + 545, + 203 + ], + "type": "interline_equation", + "content": "q \\left(\\boldsymbol {\\theta} _ {t} \\mid \\boldsymbol {\\theta} _ {t - 1}\\right) = \\mathcal {N} \\left(\\boldsymbol {\\theta} _ {t}; \\sqrt {\\alpha_ {t}} \\boldsymbol {\\theta} _ {t - 1}, (1 - \\alpha_ {t}) \\mathbf {I}\\right), \\tag {1}", + "image_path": "393182e18d38a333ae3d41d08c23aafe08665fc4259a847a8760c6a94b03adb9.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 212, + 545, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 212, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 304, + 212, + 545, + 247 + ], + "type": "text", + "content": "where the variance " + }, + { + "bbox": [ + 304, + 212, + 545, + 247 + ], + "type": "inline_equation", + "content": "1 - \\alpha_{t} \\in (0, 1]" + }, + { + "bbox": [ + 304, + 212, + 545, + 247 + ], + "type": "text", + "content": " increases with " + }, + { + "bbox": [ + 304, + 212, + 545, + 247 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 212, + 545, + 247 + ], + "type": "text", + "content": " according to a pre-defined schedule, and " + }, + { + "bbox": [ + 304, + 212, + 545, + 247 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 212, + 545, + 247 + ], + "type": "text", + "content": " is the total number of noise corruption steps." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 248, + 545, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 248, + 545, + 307 + ], + "spans": [ + { + "bbox": [ + 304, + 248, + 545, + 307 + ], + "type": "text", + "content": "At the core of the inverse process is a denoiser neural network " + }, + { + "bbox": [ + 304, + 248, + 545, + 307 + ], + "type": "inline_equation", + "content": "D(\\cdot)" + }, + { + "bbox": [ + 304, + 248, + 545, + 307 + ], + "type": "text", + "content": ", which is trained to remove the added Gaussian noise based on condition signal " + }, + { + "bbox": [ + 304, + 248, + 545, + 307 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 248, + 545, + 307 + ], + "type": "text", + "content": " at each step " + }, + { + "bbox": [ + 304, + 248, + 545, + 307 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 248, + 545, + 307 + ], + "type": "text", + "content": ". Following the design of recent motion diffusion models [63], the denoiser predicts the clean signal itself: " + }, + { + "bbox": [ + 304, + 248, + 545, + 307 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{\\theta}}_0 = D(\\pmb{\\theta}_t, t, c)" + }, + { + "bbox": [ + 304, + 248, + 545, + 307 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 308, + 545, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 545, + 331 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 545, + 331 + ], + "type": "text", + "content": "The Gaussian forward diffusion process has a special property that allows directly sampling " + }, + { + "bbox": [ + 304, + 308, + 545, + 331 + ], + "type": "inline_equation", + "content": "\\theta_{t}" + }, + { + "bbox": [ + 304, + 308, + 545, + 331 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 308, + 545, + 331 + ], + "type": "inline_equation", + "content": "\\theta_0" + }, + { + "bbox": [ + 304, + 308, + 545, + 331 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 329, + 341, + 545, + 354 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 341, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 329, + 341, + 545, + 354 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\theta} _ {t} = \\sqrt {\\alpha_ {t}} \\boldsymbol {\\theta} _ {0} + \\sqrt {1 - \\alpha_ {t}} \\boldsymbol {\\epsilon}, \\text {w h e r e} \\boldsymbol {\\epsilon} \\sim \\mathcal {N} (0, \\mathbf {I}). \\tag {2}", + "image_path": "7dd23bedbf9aec136cb9b822a0066fafccd3c333ffa23045e606fe8ea5517f98.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 363, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 545, + 399 + ], + "type": "text", + "content": "With this, training the denoiser amounts to sampling a random " + }, + { + "bbox": [ + 304, + 363, + 545, + 399 + ], + "type": "inline_equation", + "content": "t \\in \\{0, \\dots, T - 1\\}" + }, + { + "bbox": [ + 304, + 363, + 545, + 399 + ], + "type": "text", + "content": ", adding noise according to Eq. (2), and optimizing the simple objective [17]:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 314, + 408, + 545, + 423 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 408, + 545, + 423 + ], + "spans": [ + { + "bbox": [ + 314, + 408, + 545, + 423 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s i m p l e}} = E _ {\\boldsymbol {\\theta} _ {0} \\sim q (\\boldsymbol {\\theta} _ {0} | \\boldsymbol {c}), t \\sim [ 1, T ]} \\left[ \\| \\boldsymbol {\\theta} _ {0} - D (\\boldsymbol {\\theta} _ {t}, t, \\boldsymbol {c}) \\| _ {2} ^ {2} \\right]. \\tag {3}", + "image_path": "c84ba19d628e288f5714629ba88bccfc8c623a905ed92d70db115b6c0b9fb376.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 431, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 431, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 431, + 545, + 456 + ], + "type": "text", + "content": "In this paper we use the subscript " + }, + { + "bbox": [ + 304, + 431, + 545, + 456 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 431, + 545, + 456 + ], + "type": "text", + "content": " to denote the diffusion timestep and superscript " + }, + { + "bbox": [ + 304, + 431, + 545, + 456 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 431, + 545, + 456 + ], + "type": "text", + "content": " for the body joint index." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 466, + 361, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 466, + 361, + 478 + ], + "spans": [ + { + "bbox": [ + 306, + 466, + 361, + 478 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": "We introduce a novel scene-conditioned diffusion method to recover the human mesh in 3D environments from the egocentric image. Fig. 2 shows the overview of our model. Given an egocentric image " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": " with a truncated body, the camera intrinsics " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{K} = (f, c_x, c_y)" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": ", and the 3D scene point cloud " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "S \\in \\mathbb{R}^{N \\times 3}" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": " points, our goal is to learn the conditional distribution of body poses " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "p(\\boldsymbol{\\theta} | \\mathcal{I}, S, \\mathcal{K})" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": ", with the objective of generating humans that naturally interact with the scene while being aligned with the image observation. The body translation " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": " and shape " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": " are learnt in a deterministic way following [32]. Here " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "(c_x, c_y)" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": " denote the focal length and the camera center, respectively." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "The diffusion denoising process (Sec. 3) is modeled by a visibility-aware graph convolution network (GCN), which achieves per-body-part control with the per-joint conditioning on the input image, scene geometry and joint visibility (Sec. 4.1). The diffusion model is trained in a classifier-free manner [18], enabling flexible sampling from both models" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "7991" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 71, + 542, + 248 + ], + "blocks": [ + { + "bbox": [ + 53, + 71, + 542, + 248 + ], + "lines": [ + { + "bbox": [ + 53, + 71, + 542, + 248 + ], + "spans": [ + { + "bbox": [ + 53, + 71, + 542, + 248 + ], + "type": "image", + "image_path": "990be32fc501583ba472a7bdd5ff40d66a2f489fe6bc81dd0395efb5b2471e14.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 256, + 547, + 318 + ], + "lines": [ + { + "bbox": [ + 46, + 256, + 547, + 318 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 547, + 318 + ], + "type": "text", + "content": "Figure 2: Method overview. Given an egocentric image " + }, + { + "bbox": [ + 46, + 256, + 547, + 318 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 46, + 256, + 547, + 318 + ], + "type": "text", + "content": " containing a partially visible body and the 3D scene geometry " + }, + { + "bbox": [ + 46, + 256, + 547, + 318 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 256, + 547, + 318 + ], + "type": "text", + "content": ", the proposed model generates a SMPL mesh with plausible human-scene interactions and conforming to the image observation. The model comprises a Scene Conditioning module to estimate the body translation " + }, + { + "bbox": [ + 46, + 256, + 547, + 318 + ], + "type": "inline_equation", + "content": "\\hat{\\gamma}" + }, + { + "bbox": [ + 46, + 256, + 547, + 318 + ], + "type": "text", + "content": " and encode the local scene features, an Image Conditioning module to encode image features, a GCN-based Diffusion Denoiser to predict the clean body pose " + }, + { + "bbox": [ + 46, + 256, + 547, + 318 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}_0" + }, + { + "bbox": [ + 46, + 256, + 547, + 318 + ], + "type": "text", + "content": " from noisy pose " + }, + { + "bbox": [ + 46, + 256, + 547, + 318 + ], + "type": "inline_equation", + "content": "\\theta_t" + }, + { + "bbox": [ + 46, + 256, + 547, + 318 + ], + "type": "text", + "content": " with Per-joint Conditioning, and a Shape Estimator to estimate body shape " + }, + { + "bbox": [ + 46, + 256, + 547, + 318 + ], + "type": "inline_equation", + "content": "\\hat{\\beta}" + }, + { + "bbox": [ + 46, + 256, + 547, + 318 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 323, + 288, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 288, + 395 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 288, + 395 + ], + "type": "text", + "content": "that include or exclude image conditions to enhance diversity and expressiveness for truncated body parts. Guided by the gradients of a physics-based human-scene collision score, we further resolve human-scene inter-penetrations during the diffusion sampling (Sec. 4.2). The training objectives are explained in Sec. 4.3." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 405, + 258, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 405, + 258, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 405, + 258, + 418 + ], + "type": "text", + "content": "4.1. Scene-conditioned Pose Diffusion Model" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "type": "text", + "content": "3D scene conditioning. To model fine-grained human-scene interactions, only a small region of the scene surrounding the human is relevant. An accurate global body translation provides better reasoning about local scene geometries, thus crucial for accurate and scene-plausible local body pose modelling. To this end, we propose a body translation estimator (see Fig. 2) to estimate the translation " + }, + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "type": "inline_equation", + "content": "\\hat{\\gamma}" + }, + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "type": "text", + "content": " by extracting features from " + }, + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "type": "text", + "content": " and the full 3D scene point cloud " + }, + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "type": "text", + "content": ". The global scene features alleviate the scale ambiguity and localize the body in the 3D environment accurately (please refer to Supp. Mat. for more details). Given the estimated body translation " + }, + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "type": "inline_equation", + "content": "\\hat{\\gamma}" + }, + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "type": "text", + "content": ", scene vertices in a " + }, + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "type": "inline_equation", + "content": "2 \\times 2m" + }, + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "type": "text", + "content": " region around the human are selected and considered as the scene conditioning for the diffusion denoising process. Furthermore, the selected scene vertices are translated by " + }, + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "type": "inline_equation", + "content": "\\hat{\\gamma}" + }, + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "type": "text", + "content": " such that the scene vertex origin is around the body pelvis. The translated scene point cloud is encoded by a scene encoder " + }, + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "type": "inline_equation", + "content": "E_{S}" + }, + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "type": "text", + "content": " into a localized human-centric scene feature " + }, + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "type": "inline_equation", + "content": "E_{S}(S, \\hat{\\gamma})" + }, + { + "bbox": [ + 46, + 425, + 287, + 663 + ], + "type": "text", + "content": " for modelling detailed interactions between the body and the 3D scene." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Per-joint conditioning. A ResNet50 backbone [16] " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "E_{\\mathcal{I}}" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " is used to encode the cropped input image " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " into a latent feature " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "E_{\\mathcal{I}}(\\mathcal{I}) \\in \\mathbb{R}^{2048}" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " as the image conditioning. However, regressing the full body pose directly from the global im" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 323, + 545, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 323, + 545, + 454 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 545, + 454 + ], + "type": "text", + "content": "age feature as in previous works [24, 29, 32] loses the explicit joint visibility information. With the body truncated in the image, different properties are desired for different body parts: the model should achieve pose accuracy for observed body joints, and pose expressiveness for truncated body parts. To achieve the per-body-part control, the 2D joint visibility mask " + }, + { + "bbox": [ + 304, + 323, + 545, + 454 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = (v^0,\\dots,v^j,\\dots,v^{J - 1})\\in \\mathbb{R}^J" + }, + { + "bbox": [ + 304, + 323, + 545, + 454 + ], + "type": "text", + "content": " is extracted from the image via OpenPose [5] 2D joint detections, and passed to the diffusion model as the visibility condition. Here " + }, + { + "bbox": [ + 304, + 323, + 545, + 454 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 304, + 323, + 545, + 454 + ], + "type": "text", + "content": " denotes the joint number; and " + }, + { + "bbox": [ + 304, + 323, + 545, + 454 + ], + "type": "inline_equation", + "content": "v^{j}" + }, + { + "bbox": [ + 304, + 323, + 545, + 454 + ], + "type": "text", + "content": " equals to 1 if the " + }, + { + "bbox": [ + 304, + 323, + 545, + 454 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 323, + 545, + 454 + ], + "type": "text", + "content": "-th joint is visible in " + }, + { + "bbox": [ + 304, + 323, + 545, + 454 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 323, + 545, + 454 + ], + "type": "text", + "content": ", otherwise 0." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 455, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 455, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 455, + 545, + 502 + ], + "type": "text", + "content": "Apart from above conditions, the bounding box information " + }, + { + "bbox": [ + 304, + 455, + 545, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 304, + 455, + 545, + 502 + ], + "type": "text", + "content": " is additionally fed to the network inspired by [36], serving as a global-location-aware feature to better model global information:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 388, + 510, + 545, + 523 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 510, + 545, + 523 + ], + "spans": [ + { + "bbox": [ + 388, + 510, + 545, + 523 + ], + "type": "interline_equation", + "content": "\\mathcal {B} = \\left(b _ {x}, b _ {y}, b\\right) / f, \\tag {4}", + "image_path": "adda323cdd26eb7b587ce38bbf9b209fb5acccede0219e3d24979b7f23910ccd.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 529, + 545, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 545, + 554 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 545, + 554 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 529, + 545, + 554 + ], + "type": "inline_equation", + "content": "b_{x}, b_{y}, b" + }, + { + "bbox": [ + 304, + 529, + 545, + 554 + ], + "type": "text", + "content": " denote the bounding box center coordinates and bounding box size in the full image, respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 554, + 545, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 554, + 545, + 614 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 545, + 614 + ], + "type": "text", + "content": "The full condition " + }, + { + "bbox": [ + 304, + 554, + 545, + 614 + ], + "type": "inline_equation", + "content": "c^j" + }, + { + "bbox": [ + 304, + 554, + 545, + 614 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 554, + 545, + 614 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 554, + 545, + 614 + ], + "type": "text", + "content": "-th joint is formulated as the concatenation of: the image feature (masked out by " + }, + { + "bbox": [ + 304, + 554, + 545, + 614 + ], + "type": "inline_equation", + "content": "v^j" + }, + { + "bbox": [ + 304, + 554, + 545, + 614 + ], + "type": "text", + "content": " if the joint is not visible), 3D scene feature, estimated body translation, bounding box feature, camera intrinsics and the diffusion timestep " + }, + { + "bbox": [ + 304, + 554, + 545, + 614 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 554, + 545, + 614 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 342, + 621, + 545, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 621, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 342, + 621, + 545, + 635 + ], + "type": "interline_equation", + "content": "\\boldsymbol {c} ^ {j} = \\left(E _ {\\mathcal {I}} (\\mathcal {I}) \\cdot v ^ {j}, E _ {\\mathcal {S}} (\\mathcal {S}, \\hat {\\gamma}), \\hat {\\gamma}, \\mathcal {B}, \\mathcal {K}, t\\right). \\tag {5}", + "image_path": "bde27ef39fd3518775f7fc3234e43ccd1fe47350e2846e2b61fbbb16b27762be.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": "By conditioning on a per-joint basis, the model achieves flexible control over each body part according to the joint visibility. This allows for both accurate pose estimation of visible body parts, and flexibility for invisible body parts." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "Diffusion denoiser architecture. At diffusion timestep " + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": ", for the noisy body pose parameters " + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\theta_{t}" + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": ", the diffusion de" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "7992" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "type": "text", + "content": "noiser " + }, + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "type": "text", + "content": " predicts the clean pose parameter " + }, + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}_0" + }, + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "type": "text", + "content": " conditioned on " + }, + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "type": "text", + "content": ". Previous works either use a single MLP for the full body pose [24, 32, 36, 68] with redundant dependencies between irrelevant joints, or employ a separate MLP for each joint [27] which fully ignores joint dependencies. Instead, we adopt a graph convolution network (GCN) [26, 84] as the denoising function " + }, + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "type": "text", + "content": ". Given the predefined human kinematic tree, GCN models inter-joint dependencies by treating the human skeleton as a graph, where each node corresponds to a body joint. Specifically, for each joint " + }, + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "type": "text", + "content": ", the noisy pose parameters " + }, + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "type": "inline_equation", + "content": "\\theta_t^j" + }, + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "type": "text", + "content": " is embedded and concatenated with the per-joint conditioning " + }, + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "type": "inline_equation", + "content": "c^j" + }, + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "type": "text", + "content": " as the feature for node " + }, + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 71, + 289, + 312 + ], + "type": "text", + "content": " in the GCN (see Fig. 2). We adopt the modulated GCN [84] for the implementation. Different from vanilla GCN [26], the modulated GCN learns node-specific modulation vectors to disentangle joint feature transformations, such that different relations can be learnt between joints. It also modulates the affinity matrix with learnable parameters to model additional edges beyond the human skeleton [84]. Please refer to Supp. Mat. for implementation details." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 312, + 288, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 312, + 288, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 288, + 361 + ], + "type": "text", + "content": "Shape estimator. As the body shape " + }, + { + "bbox": [ + 47, + 312, + 288, + 361 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 312, + 288, + 361 + ], + "type": "text", + "content": " is a global feature and more robust to body truncations, an MLP branch (the body shape estimator in Fig. 2) predicts " + }, + { + "bbox": [ + 47, + 312, + 288, + 361 + ], + "type": "inline_equation", + "content": "\\hat{\\beta}" + }, + { + "bbox": [ + 47, + 312, + 288, + 361 + ], + "type": "text", + "content": " from the conditions " + }, + { + "bbox": [ + 47, + 312, + 288, + 361 + ], + "type": "inline_equation", + "content": "(E_{\\mathcal{I}}(\\mathcal{I}), E_S(S, \\hat{\\gamma}), \\hat{\\gamma}, \\mathcal{B}, \\mathcal{K})" + }, + { + "bbox": [ + 47, + 312, + 288, + 361 + ], + "type": "text", + "content": " in a deterministic way." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 367, + 180, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 367, + 180, + 380 + ], + "spans": [ + { + "bbox": [ + 47, + 367, + 180, + 380 + ], + "type": "text", + "content": "4.2. Scene-guided Sampling" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 385, + 287, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 385, + 287, + 433 + ], + "spans": [ + { + "bbox": [ + 47, + 385, + 287, + 433 + ], + "type": "text", + "content": "We use the DDPM [17] sampler at inference time. At each sampling step " + }, + { + "bbox": [ + 47, + 385, + 287, + 433 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 385, + 287, + 433 + ], + "type": "text", + "content": ", the denoiser predicts " + }, + { + "bbox": [ + 47, + 385, + 287, + 433 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}_0 = D(\\theta_t, t, c)" + }, + { + "bbox": [ + 47, + 385, + 287, + 433 + ], + "type": "text", + "content": ", which is noised back to " + }, + { + "bbox": [ + 47, + 385, + 287, + 433 + ], + "type": "inline_equation", + "content": "\\theta_{t-1}" + }, + { + "bbox": [ + 47, + 385, + 287, + 433 + ], + "type": "text", + "content": " by sampling from the Gaussian distribution:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 110, + 441, + 287, + 456 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 441, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 110, + 441, + 287, + 456 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\theta} _ {t - 1} \\sim \\mathcal {N} \\left(\\mu_ {t} \\left(\\boldsymbol {\\theta} _ {t}, \\hat {\\boldsymbol {\\theta}} _ {0}\\right), \\Sigma_ {t}\\right), \\tag {6}", + "image_path": "b9f63d6a94bc075377c45d1547a8d113b35b7a4c4a239cb7ba398b2d760073a7.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 465, + 287, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 465, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 465, + 287, + 502 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 465, + 287, + 502 + ], + "type": "inline_equation", + "content": "\\mu_t(\\pmb{\\theta}_t, \\hat{\\pmb{\\theta}}_0)" + }, + { + "bbox": [ + 47, + 465, + 287, + 502 + ], + "type": "text", + "content": " is a linear combination of " + }, + { + "bbox": [ + 47, + 465, + 287, + 502 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}_t" + }, + { + "bbox": [ + 47, + 465, + 287, + 502 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 465, + 287, + 502 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{\\theta}}_0" + }, + { + "bbox": [ + 47, + 465, + 287, + 502 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 465, + 287, + 502 + ], + "type": "inline_equation", + "content": "\\Sigma_t" + }, + { + "bbox": [ + 47, + 465, + 287, + 502 + ], + "type": "text", + "content": " is a scheduled Gaussian distribution as in [17]. The sampling is iteratively repeated from " + }, + { + "bbox": [ + 47, + 465, + 287, + 502 + ], + "type": "inline_equation", + "content": "t = T - 1" + }, + { + "bbox": [ + 47, + 465, + 287, + 502 + ], + "type": "text", + "content": " until " + }, + { + "bbox": [ + 47, + 465, + 287, + 502 + ], + "type": "inline_equation", + "content": "t = 0" + }, + { + "bbox": [ + 47, + 465, + 287, + 502 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 502, + 288, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 502, + 288, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 502, + 288, + 598 + ], + "type": "text", + "content": "Classifier-free guidance. The diffusion model " + }, + { + "bbox": [ + 46, + 502, + 288, + 598 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 502, + 288, + 598 + ], + "type": "text", + "content": " is trained with classifier-free guidance [18] by randomly masking out the image feature " + }, + { + "bbox": [ + 46, + 502, + 288, + 598 + ], + "type": "inline_equation", + "content": "E_{\\mathcal{I}}(\\mathcal{I})" + }, + { + "bbox": [ + 46, + 502, + 288, + 598 + ], + "type": "text", + "content": " for all joints with a probability of " + }, + { + "bbox": [ + 46, + 502, + 288, + 598 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 502, + 288, + 598 + ], + "type": "text", + "content": " during training, such that the model also learns the pose distribution independent from the image, enabling flexible sampling. By combining the poses of visible joints sampled from the full-conditioned model and the poses of invisible joints sampled from the model excluding image conditions:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 63, + 618, + 287, + 633 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 618, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 63, + 618, + 287, + 633 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {\\theta}} _ {0} = D \\left(\\boldsymbol {\\theta} _ {t}, t, \\boldsymbol {c}\\right) \\odot \\mathcal {V} + D \\left(\\boldsymbol {\\theta} _ {t}, t, \\boldsymbol {c} _ {\\phi}\\right) \\odot (1 - \\mathcal {V}), \\tag {7}", + "image_path": "6c9f89d7f57b9533c59753baab51e64fee19327164406f92cf08e56115aef0d8.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 641, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 641, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 641, + 287, + 714 + ], + "type": "text", + "content": "we achieve better per-body-part control, with enhanced diversity for invisible body parts while maintaining the accuracy of visible body parts (see Sec. 5.5 for the ablation study). Here " + }, + { + "bbox": [ + 47, + 641, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 47, + 641, + 287, + 714 + ], + "type": "text", + "content": " denotes multiplying the joint visibility mask with the pose of each joint, and " + }, + { + "bbox": [ + 47, + 641, + 287, + 714 + ], + "type": "inline_equation", + "content": "c_{\\phi}" + }, + { + "bbox": [ + 47, + 641, + 287, + 714 + ], + "type": "text", + "content": " is the condition excluding image features." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "content": "Collision score guided sampling. The proposed scene encoding in Sec. 4.1 implicitly incorporates the 3D environment constraint into the diffusion conditioning. However, the network cannot fully resolve the human-scene collisions in a fine-grained way. Another way to incorporate conditions into the diffusion model is the score-function based guidance. As shown in previous works [9, 57, 60], a pretrained classifier can be adopted to provide class information by adding the gradients of the classifier at each sampling step to the diffusion model, to guide the sampling process towards the class label. Inspired by this, we propose a collision score guided sampling strategy to further resolve implausible human-scene inter-penetrations, by leveraging implicit body representations [43, 44]. We use COAP [43] to model neural articulated occupancy of human bodies as the zero-level set " + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "inline_equation", + "content": "f_{\\Theta}(q|\\mathcal{G}) = 0" + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "content": " is the input query point and " + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(\\theta ,\\beta)" + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "content": " is the input bone transformations. By querying each scene vertex near the body to see if it is inside of the human volume, the collision score is defined as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 336, + 308, + 545, + 334 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 308, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 336, + 308, + 545, + 334 + ], + "type": "interline_equation", + "content": "\\mathcal {J} (\\boldsymbol {\\theta}) = \\frac {1}{| \\mathcal {S} |} \\sum_ {q \\in \\mathcal {S}} \\sigma \\left(f _ {\\Theta} (q \\mid \\mathcal {G})\\right) \\mathbb {I} _ {f _ {\\Theta} (s \\mid \\mathcal {G}) > 0}, \\tag {8}", + "image_path": "7ef7a319dd45349485427f2a36e4d8fb007784acea7f4adbaa7c218ff25cc7fd.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 338, + 547, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 338, + 547, + 387 + ], + "spans": [ + { + "bbox": [ + 305, + 338, + 547, + 387 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 338, + 547, + 387 + ], + "type": "inline_equation", + "content": "\\sigma(\\cdot)" + }, + { + "bbox": [ + 305, + 338, + 547, + 387 + ], + "type": "text", + "content": " stands for the sigmoid function. The gradient " + }, + { + "bbox": [ + 305, + 338, + 547, + 387 + ], + "type": "inline_equation", + "content": "\\nabla \\mathcal{J}(\\boldsymbol{\\theta})" + }, + { + "bbox": [ + 305, + 338, + 547, + 387 + ], + "type": "text", + "content": " efficiently guides the diffusion sampling process to further alleviate the human-scene collisions (see Sec. 5.5 for the ablation study) by modifying Eq. (6) to:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 337, + 395, + 545, + 409 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 395, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 337, + 395, + 545, + 409 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\theta} _ {t - 1} \\sim \\mathcal {N} \\left(\\mu_ {t} \\left(\\boldsymbol {\\theta} _ {t}, \\hat {\\boldsymbol {\\theta}} _ {0}\\right) + a \\Sigma_ {t} \\nabla \\mathcal {J} \\left(\\boldsymbol {\\theta} _ {t}\\right), \\Sigma_ {t}\\right), \\tag {9}", + "image_path": "507608b312e148b6147830856d75ec5edb693f582c8243c26c98f4f68ac4295a.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 418, + 545, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 418, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 306, + 418, + 545, + 430 + ], + "type": "text", + "content": "where the guidance is modulated by " + }, + { + "bbox": [ + 306, + 418, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\Sigma_{t}" + }, + { + "bbox": [ + 306, + 418, + 545, + 430 + ], + "type": "text", + "content": " and a scale factor " + }, + { + "bbox": [ + 306, + 418, + 545, + 430 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 306, + 418, + 545, + 430 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 437, + 422, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 437, + 422, + 451 + ], + "spans": [ + { + "bbox": [ + 306, + 437, + 422, + 451 + ], + "type": "text", + "content": "4.3. Training Objectives" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 456, + 545, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 456, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 305, + 456, + 545, + 507 + ], + "type": "text", + "content": "The diffusion model is trained with " + }, + { + "bbox": [ + 305, + 456, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{simple}}" + }, + { + "bbox": [ + 305, + 456, + 545, + 507 + ], + "type": "text", + "content": " in Eq. (3) for body pose " + }, + { + "bbox": [ + 305, + 456, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}_0" + }, + { + "bbox": [ + 305, + 456, + 545, + 507 + ], + "type": "text", + "content": ", together with the 3D joint loss " + }, + { + "bbox": [ + 305, + 456, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{3D}}" + }, + { + "bbox": [ + 305, + 456, + 545, + 507 + ], + "type": "text", + "content": ", the 2D keypoint re-projection loss " + }, + { + "bbox": [ + 305, + 456, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{2D}}" + }, + { + "bbox": [ + 305, + 456, + 545, + 507 + ], + "type": "text", + "content": " calculated in the full image frame, and the shape loss " + }, + { + "bbox": [ + 305, + 456, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\beta}" + }, + { + "bbox": [ + 305, + 456, + 545, + 507 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 348, + 516, + 503, + 531 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 516, + 503, + 531 + ], + "spans": [ + { + "bbox": [ + 348, + 516, + 503, + 531 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {3 D}} = \\left\\| F K (\\hat {\\boldsymbol {\\theta}} _ {0}, \\hat {\\boldsymbol {\\beta}}) - F K (\\boldsymbol {\\theta} _ {0}, \\boldsymbol {\\beta}) \\right\\| ^ {2},", + "image_path": "6ee1f030feb07c443d0ab0f96f565d18b2f09376387b31082ab021bfb473df66.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 348, + 533, + 545, + 547 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 533, + 545, + 547 + ], + "spans": [ + { + "bbox": [ + 348, + 533, + 545, + 547 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {2 D}} = \\left\\| \\Pi_ {\\mathcal {K}} \\left(J _ {\\mathrm {3 D}} + \\hat {\\gamma}\\right) - J _ {\\mathrm {e s t}} \\right\\| ^ {2}, \\tag {10}", + "image_path": "fd2d7908ab8d98c48e2d9adcbe202a60ed8be46f606462ab313172c110990b46.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 353, + 549, + 424, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 549, + 424, + 563 + ], + "spans": [ + { + "bbox": [ + 353, + 549, + 424, + 563 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\beta} = \\left\\| \\hat {\\boldsymbol {\\beta}} - \\boldsymbol {\\beta} \\right\\| ^ {2}.", + "image_path": "4fe8d0481ee119e947d688926770f614178d3f01a59c872ec1d3832913590578.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 573, + 545, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 573, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 305, + 573, + 545, + 620 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 305, + 573, + 545, + 620 + ], + "type": "inline_equation", + "content": "FK(\\cdot)" + }, + { + "bbox": [ + 305, + 573, + 545, + 620 + ], + "type": "text", + "content": " denotes the SMPL joint regressor to obtain 3D joint coordinates. " + }, + { + "bbox": [ + 305, + 573, + 545, + 620 + ], + "type": "inline_equation", + "content": "J_{\\mathrm{est}}" + }, + { + "bbox": [ + 305, + 573, + 545, + 620 + ], + "type": "text", + "content": " is the 2D body keypoint detections, and " + }, + { + "bbox": [ + 305, + 573, + 545, + 620 + ], + "type": "inline_equation", + "content": "\\Pi_{\\mathcal{K}}" + }, + { + "bbox": [ + 305, + 573, + 545, + 620 + ], + "type": "text", + "content": " denotes the 3D to 2D projection in the full image with camera intrinsics " + }, + { + "bbox": [ + 305, + 573, + 545, + 620 + ], + "type": "inline_equation", + "content": "\\mathcal{K}" + }, + { + "bbox": [ + 305, + 573, + 545, + 620 + ], + "type": "text", + "content": ". The overall loss is defined as:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 339, + 628, + 545, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 628, + 545, + 657 + ], + "spans": [ + { + "bbox": [ + 339, + 628, + 545, + 657 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\text {s i m p l e}} + \\lambda_ {3 \\mathrm {D}} \\mathcal {L} _ {3 \\mathrm {D}} + \\lambda_ {2 \\mathrm {D}} \\mathcal {L} _ {2 \\mathrm {D}} + \\lambda_ {\\beta} \\mathcal {L} _ {\\beta} \\tag {11} \\\\ + \\lambda_ {\\text {c o l l}} \\mathcal {L} _ {\\text {c o l l}} + \\lambda_ {\\text {o r t h}} \\mathcal {L} _ {\\text {o r t h}}, \\\\ \\end{array}", + "image_path": "f246cb4c627d0c40a5f4203a328e4578b7432acac33d081b6a91aa5f32d21ff5.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{orth}}" + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": " is a regularizer to force the generated 6D pose rotation representation to be orthonormal, " + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{coll}}" + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": " is the scene collision loss the same as defined in Eq. (8), and " + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda s" + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": " are the corresponding weight factors for each loss term." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7993" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 105, + 102 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 105, + 102 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 105, + 102 + ], + "type": "text", + "content": "5.1. Dataset" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 110, + 289, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 110, + 289, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 110, + 289, + 278 + ], + "type": "text", + "content": "Most of existing datasets for 3D human pose evaluation are either captured from the third-person view with the full body visible [15, 20, 42, 67], or do not contain the 3D environment [47]. The most relevant dataset is EgoBody [78], a large-scale egocentric dataset capturing 3D human motions during social interactions in 3D scenes. Each sequence involves two people interacting with each other in 3D environments, and one subject wears a head-mounted camera to capture the egocentric images containing the other interactee. Due to the close social interaction distance, the captured egocentric images typically exhibit strong body truncations for the interactee. We use the official train / test splits for training and evaluation, which include 90,120 / 62,140 frames, respectively." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 286, + 160, + 298 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 286, + 160, + 298 + ], + "spans": [ + { + "bbox": [ + 47, + 286, + 160, + 298 + ], + "type": "text", + "content": "5.2. Evaluation Metrics" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 305, + 287, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 305, + 287, + 377 + ], + "spans": [ + { + "bbox": [ + 46, + 305, + 287, + 377 + ], + "type": "text", + "content": "Strong body truncations pose inherent ambiguity for invisible body parts, while the visible body parts are relatively deterministic given the image observations, thus evaluating the accuracy of full body joints together as in [3, 32] is not suitable for such tasks. We propose to evaluate the proposed method from the following aspects." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 378, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 378, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 287, + 544 + ], + "type": "text", + "content": "Accuracy. We employ Mean Per-Joint Position Error (MPJPE) and Vertex-to-Vertex (V2V) errors in " + }, + { + "bbox": [ + 46, + 378, + 287, + 544 + ], + "type": "inline_equation", + "content": "mm" + }, + { + "bbox": [ + 46, + 378, + 287, + 544 + ], + "type": "text", + "content": " to evaluate the accuracy of estimated body pose and shape. For MPJPE, we report different variations: G-MPJPE as the joint error in the global coordinate; MPJPE as the pelvis-aligned joint errors, and PA-MPJPE as the joint errors after Procrustes Alignment [12]. We report mean MPJPE and V2V metrics over " + }, + { + "bbox": [ + 46, + 378, + 287, + 544 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 378, + 287, + 544 + ], + "type": "text", + "content": " samples for visible joints. Nevertheless, such evaluation protocol assumes a single correct ground truth prediction, which does not hold for invisible joints. Instead of the mean error, we report min-of- " + }, + { + "bbox": [ + 46, + 378, + 287, + 544 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 378, + 287, + 544 + ], + "type": "text", + "content": " MPJPE for invisible body parts following [3]. To be specific, among the generated " + }, + { + "bbox": [ + 46, + 378, + 287, + 544 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 378, + 287, + 544 + ], + "type": "text", + "content": " samples for each input image, we select the one with the minimum MPJPE for all evaluated methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": "Physical plausibility. We evaluate the collision and contact scores between the body mesh and the 3D scene. As the clean scene signed distance field (SDF) is not available in EgoBody, we define the collision score as the ratio of the number of scene vertices inside of the body mesh to the number of all scene vertices. Note that the absolute scale of the collision score may vary with different size of the 3D scene, but within the same scene surface, the relative comparison between different methods indicates different collision levels. We use the cropped scene as described in Sec. 4.1 for evaluation (with a fixed size of 20,000 vertices). Following [19], the contact score is defined as 1 if the body contacts with the scene in a distance within a threshold (2 cm), otherwise 0. We report the mean collision score and" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "contact score over all test samples. Note that a model with better physical plausibility should achieve both a lower collision score and a higher contact score." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 108, + 547, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 547, + 205 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 547, + 205 + ], + "type": "text", + "content": "Diversity. Diversity is evaluated for invisible body parts to demonstrate the expressiveness of the methods, by calculating the standard deviation (std) and Average Pairwise Distance (APD) of invisible body joints [19]. A higher diversity is desired, yet there is usually a trade-off between diversity and accuracy/plausibility. An ideal model should predict diverse poses for invisible body parts, with accurate visible body poses and plausible human-scene interactions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 213, + 454, + 224 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 213, + 454, + 224 + ], + "spans": [ + { + "bbox": [ + 305, + 213, + 454, + 224 + ], + "type": "text", + "content": "5.3. Baselines and Our Method" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 232, + 547, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 547, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 547, + 506 + ], + "type": "text", + "content": "As there is no existing work for our task, we compare our method with the following baselines: (1) ProHMR [32], the state-of-the-art method for probabilistic human mesh recovery from a single image based on conditional normalizing flows; (2) ProHMR-scene, in which we enhance the ProHMR framework by incorporating the scene geometry " + }, + { + "bbox": [ + 304, + 232, + 547, + 506 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 232, + 547, + 506 + ], + "type": "text", + "content": " with a global scene feature encoder. The ProHMR framework is trained with 2D and 3D supervisions for the sample drawn from " + }, + { + "bbox": [ + 304, + 232, + 547, + 506 + ], + "type": "inline_equation", + "content": "z = 0" + }, + { + "bbox": [ + 304, + 232, + 547, + 506 + ], + "type": "text", + "content": " (referred as the 'mode'), such that the 'mode' can be used as a predictive model (see [32] for details). Different training weights for the samples drawn from " + }, + { + "bbox": [ + 304, + 232, + 547, + 506 + ], + "type": "inline_equation", + "content": "z \\neq 0" + }, + { + "bbox": [ + 304, + 232, + 547, + 506 + ], + "type": "text", + "content": " yields a trade-off between the accuracy and diversity for the generated multiple hypotheses. Here " + }, + { + "bbox": [ + 304, + 232, + 547, + 506 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 232, + 547, + 506 + ], + "type": "text", + "content": " denotes the latent space of the normalizing flow. To demonstrate this trade-off, we train the ProHMR-scene baseline with different training configurations. For samples drawn from " + }, + { + "bbox": [ + 304, + 232, + 547, + 506 + ], + "type": "inline_equation", + "content": "z \\neq 0" + }, + { + "bbox": [ + 304, + 232, + 547, + 506 + ], + "type": "text", + "content": ", we supervise with: 1) only 2D re-projection loss (the same as in [32]), denoted as -orig; 2) 3D supervision with small weights, denoted as -weak-3D; 3) 3D supervision with large weights, denoted as -strong-3D. Here the 3D supervision refers to the loss on 3D body joints and SMPL parameters. Please refer to Supp. Mat. for details of the baseline models." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 515, + 362, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 362, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 362, + 526 + ], + "type": "text", + "content": "5.4. Results" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "content": "Tab. 1 shows the quantitative results. Compared to the baselines, our method achieves the best G-MPJPE, MPJPE and V2V metrics for visible joints, demonstrating accurate estimations of the global translation, local body pose for visible joints and body shape. For truncated body joints, our method obtains the best min-of-n MPJPE, indicating that our generated results better covers the ground truth distribution for truncated body parts than baselines, thanks to the efficient scene conditioning. Our method also outperforms the baselines with the higher contact ratios and significantly better collision scores. In particular, our collision score decreased " + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "inline_equation", + "content": "45\\%" + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "content": " compared with ProHMR, and " + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "inline_equation", + "content": "37\\%" + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "content": " compared with the best ProHMR-scene model. This indicates that the proposed method can effectively leverage the scene conditions and resolve body-scene inter-penetrations," + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7994" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 128, + 545, + 264 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 118 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 118 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 118 + ], + "type": "text", + "content": "Table 1: Evaluation for accuracy, physical plausibility and diversity on EgoBody. Here -vis and -invis denote visible and invisible joints, respectively. 'coll' and 'contact' refer to the collision and contact scores, respectively. The percentage for the collision score denotes how much improvement the corresponding method has achieved compared with the ProHMR baseline. The best results are in boldface." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 128, + 545, + 264 + ], + "lines": [ + { + "bbox": [ + 49, + 128, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 49, + 128, + 545, + 264 + ], + "type": "table", + "html": "
nMethodG-MPJPE ↓ -visMPJPE ↓ -visPA-MPJPE ↓ -visV2V ↓ -vismin-of-n MPJPE ↓ -inviscoll ↓contact ↑std ↑ -invisAPD ↑ -invis
5ProHMR [32]181.3372.9246.5790.88128.560.00346 (-)0.9426.5332.95
ProHMR-scene-orig133.7273.1348.8791.59117.880.00305 (12%)0.9635.4244.02
Ours128.6265.7047.1782.93107.770.00191 (45%)0.9929.5935.15
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All results are reported for " + }, + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "type": "inline_equation", + "content": "n = 20" + }, + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 112, + 103, + 483, + 174 + ], + "lines": [ + { + "bbox": [ + 112, + 103, + 483, + 174 + ], + "spans": [ + { + "bbox": [ + 112, + 103, + 483, + 174 + ], + "type": "table", + "html": "
MethodMPJPE ↓ -vismin-of-n MPJPE ↓ -inviscoll ↓contact ↑std ↑ -invisAPD ↑ -invis
Ours65.6994.960.001910.9930.2335.14
Ours w/o Jθ65.0997.200.002250.9921.5325.32
Ours w/o Jθ w/o CF64.5898.820.002290.9915.7519.56
Ours w/o Jθ w/o CF w/o Lcoll64.9196.260.003020.9922.9421.79
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Given the same input, our method can generate diverse poses for invisible body parts." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 308, + 288, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 288, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 288, + 344 + ], + "type": "text", + "content": "while achieving better contact relations between the body and the 3D environment. Fig. 3 (left) shows the qualitative results and the comparison with the baseline method." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 349, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 349, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 349, + 287, + 613 + ], + "type": "text", + "content": "From the results among different ProHMR-scene baselines " + }, + { + "bbox": [ + 46, + 349, + 287, + 613 + ], + "type": "inline_equation", + "content": "(n = 20)" + }, + { + "bbox": [ + 46, + 349, + 287, + 613 + ], + "type": "text", + "content": " in Tab. 1, we can clearly see a trade-off between the accuracy and diversity: stronger 3D supervision (ProHMR-scene-strong-3D) has better accuracy for visible body parts (MPJPE-vis), yet lower diversity (std-invis and APD-invis) for invisible joints. The reason behind this is that the ProHMR framework, like many other existing works, condition the generative process of full body pose only on the global image feature. In contrast, our method leverages the joint visibility and the GCN architecture, achieving the best MPJPE for visible joints, diverse poses for invisible joints, and natural human-scene interactions (see Fig. 4), while the baseline with a similar diversity level (ProHMR) and the baseline with the highest diversity (ProHMR-scene-orig) exhibit much higher MPJPE errors and more severe human-scene collisions. There is a very slight increase for PA-MPJPE of our model compared to the ProHMR-scene-strong/weak-3D baselines, while we obtain a much higher diversity for invisible body joints. This reveals that our method achieves flexible per-body-part control to balance between the accuracy and diversity for different body parts." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": "To validate the reconstruction accuracy, the full-body accuracy of the proposed method is also evaluated and compared against existing deterministic baselines on EgoBody dataset. The results show that our method even achieves higher full-body accuracy than deterministic methods, which demonstrates that the proposed model achieves diversity without sacrificing the reconstruction accuracy. In addition, the proposed method is also evaluated on PROX [15]" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 308, + 547, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 547, + 392 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 547, + 392 + ], + "type": "text", + "content": "dataset, a monocular RGB-based third-person view dataset with human-scene interactions, and our method outperforms the baseline methods in terms of pose accuracy, human-scene interaction plausibility and pose diversity. Please refer to Supp. Mat. for detailed results of evaluations on PROX and comparison with deterministic methods on EgoBody." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 404, + 400, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 404, + 400, + 417 + ], + "spans": [ + { + "bbox": [ + 306, + 404, + 400, + 417 + ], + "type": "text", + "content": "5.5. Ablation Study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 424, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 424, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 424, + 545, + 628 + ], + "type": "text", + "content": "To investigate the influences of different training and sampling schemes for the diffusion model, we perform an ablation study and the results are shown in Tab. 2. The scene collision score efficiently resolves the human-scene interpenetrations from two different perspectives: via the collision loss " + }, + { + "bbox": [ + 304, + 424, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{coll}}" + }, + { + "bbox": [ + 304, + 424, + 545, + 628 + ], + "type": "text", + "content": " during training and via the explicit collision score guidance " + }, + { + "bbox": [ + 304, + 424, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_{\\theta}" + }, + { + "bbox": [ + 304, + 424, + 545, + 628 + ], + "type": "text", + "content": " during the diffusion sampling (Eq. (9)). Fig. 3 (right) shows that the collision score guidance " + }, + { + "bbox": [ + 304, + 424, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_{\\theta}" + }, + { + "bbox": [ + 304, + 424, + 545, + 628 + ], + "type": "text", + "content": " improves the human-scene interaction relationships. The classifier-free guidance during the diffusion sampling in Eq. (7) significantly improves the sample diversity, by leveraging the invisible joints sampled from the model trained excluding the image conditions. It is worth mentioning that the collision score guidance " + }, + { + "bbox": [ + 304, + 424, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_{\\theta}" + }, + { + "bbox": [ + 304, + 424, + 545, + 628 + ], + "type": "text", + "content": " also contributes to the sample diversity. This is not surprising as the gradients of " + }, + { + "bbox": [ + 304, + 424, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_{\\theta}" + }, + { + "bbox": [ + 304, + 424, + 545, + 628 + ], + "type": "text", + "content": " can potentially optimize the body pose to different directions given different initial body poses." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "Compared with the trade-off in the ProHMR-based methods where the accuracy sacrifices a lot for diversity (and vice versa), the classifier-free guidance and the collision score guidance in our model only bring marginal changes for the MPJPE of visible body parts, in the trade-off for significantly enhanced physical plausibility, sample diversity and better min-of-n MPJPE for unobserved joints." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 758 + ], + "type": "text", + "content": "7996" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 119, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 119, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 119, + 83 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 88, + 289, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 88, + 289, + 351 + ], + "spans": [ + { + "bbox": [ + 47, + 88, + 289, + 351 + ], + "type": "text", + "content": "This paper introduces a novel scene-conditioned probabilistic approach for human mesh recovery from the egocentric image given the 3D scene geometry. The proposed diffusion model efficiently leverages the scene conditions and joint visibility to achieve per-body-part control and model human-scene interactions. The classifier-free guidance and the collision score guidance enables flexible sampling process with further enhanced diversity and physical plausibility. We demonstrate that our model generates human bodies in realistic interactions with the 3D environment, with diverse poses for invisible body parts while conforming to the image observation. Nevertheless, the current method also has limitations. For example, currently only a single frame is considered as the input. A promising future direction is to further exploit temporal information to reconstruct temporally consistent human motions from the egocentric view. Acknowledgements. This work was supported by Microsoft Mixed Reality & AI Zurich Lab PhD scholarship. Qianli Ma is partially funded by the Max Planck ETH Center for Learning Systems. We sincerely thank Korrawe Karunratanakul, Marko Mihajlovic and Shaofei Wang for the fruitful discussions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 360, + 107, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 360, + 107, + 372 + ], + "spans": [ + { + "bbox": [ + 48, + 360, + 107, + 372 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 380, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 53, + 380, + 285, + 402 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 380, + 285, + 402 + ], + "spans": [ + { + "bbox": [ + 53, + 380, + 285, + 402 + ], + "type": "text", + "content": "[1] Microsoft Hololens2. https://www.microsoft.com/en-us/hololens.2" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 403, + 287, + 445 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 403, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 53, + 403, + 287, + 445 + ], + "type": "text", + "content": "[2] Simon Alexanderson, Rajmund Nagy, Jonas Beskow, and Gustav Eje Henter. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 11477-11487, 2021. 2, 5" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8000" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Probabilistic Modeling of Inter- and Intra-observer Variability in Medical Image Segmentation/bf4cff8f-5588-469f-97d0-102dd2317c9c_content_list.json b/2023/Probabilistic Modeling of Inter- and Intra-observer Variability in Medical Image Segmentation/bf4cff8f-5588-469f-97d0-102dd2317c9c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..b2c8d518289f23fd61c59773e72558db0ee81ed2 --- /dev/null +++ b/2023/Probabilistic Modeling of Inter- and Intra-observer Variability in Medical Image Segmentation/bf4cff8f-5588-469f-97d0-102dd2317c9c_content_list.json @@ -0,0 +1,2119 @@ +[ + { + "type": "text", + "text": "Probabilistic Modeling of Inter- and Intra-observer Variability in Medical Image Segmentation", + "text_level": 1, + "bbox": [ + 78, + 128, + 890, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Arne Schmidt, Pablo Morales-Álvarez, and Rafael Molina \nUniversidad de Granada, Granada, Spain", + "bbox": [ + 254, + 202, + 715, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{arne, pablomorales, rms}@decsai.ugr.es", + "bbox": [ + 310, + 241, + 656, + 255 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Medical image segmentation is a challenging task, particularly due to inter- and intra-observer variability, even between medical experts. In this paper, we propose a novel model, called Probabilistic Inter-Observed and iNtra-Observed variation NetwOrk (Pionono). It captures the labeling behavior of each rater with a multidimensional probability distribution and integrates this information with the feature maps of the image to produce probabilistic segmentation predictions. The model is optimized by variational inference and can be trained end-to-end. It outperforms state-of-the-art models such as STAPLE, Probabilistic U-Net, and models based on confusion matrices. Additionally, Pionono predicts multiple coherent segmentation maps that mimic the rater's expert opinion, which provides additional valuable information for the diagnostic process. Experiments on real-world cancer segmentation datasets demonstrate the high accuracy and efficiency of Pionono, making it a powerful tool for medical image analysis.", + "bbox": [ + 75, + 324, + 473, + 598 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 630, + 209, + 645 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Artificial Intelligence (AI) algorithms have shown remarkable progress in image analysis, holding great promise for faster and more accurate diagnostic procedures [13, 27, 26, 3]. Nevertheless, in medical practice, there exists a high degree of variability among the opinions of different medical experts, even when the same expert assesses the same data at different times. This inter- and intra-observer variability has been reported across various tasks, including MRI-based segmentation of HCC lesions [7], lung cancer segmentation in CT scans [14], and multiple fields in pathology [21, 2, 5, 22]. It leads to uncertainties when applying AI models because in contrast to other classification tasks, there is not a single ground truth.", + "bbox": [ + 75, + 657, + 468, + 853 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Especially in the medical domain, the careful modeling of uncertainties in its different forms has a high priority to minimize the risk of relying on incorrect predictions", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5a7384810ad2d4459a1e1e41c6a024f89c50d42a85de36fd1b94532b0217de56.jpg", + "image_caption": [ + "Figure 1. The proposed Pionono model. The labeling behavior of each rater $r$ is represented by a multivariate Gaussian distribution $q(z|r)$ . The drawn samples $\\tilde{z}_j$ are concatenated with the extracted features $v$ of $f_{\\omega}$ and then fed into the segmentation head $f_{\\theta}$ . The output simulates the inter- and intra-observer variability of annotations and is optimized using the real annotations $s^r$ of each rater. The model is trained end-to-end with a combination of log-likelihood loss (LL) and Kulback Leibler (KL) divergence between posterior and prior, combined in the overall loss $\\mathcal{L}_{\\mathrm{ELBO}}$ ." + ], + "image_footnote": [], + "bbox": [ + 509, + 287, + 875, + 536 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "[17, 26, 15, 13, 10]. In recent years, probabilistic methods, such as Bayesian Neural Networks [8] and sparse Gaussian processes [10, 33] have gained more and more attention, because they are able to account for uncertainties in a sound manner. They showed promising results when modeling uncertainty in the network weights [8], data ambiguities [15] or attention weights [26]. Although inter- and intra-observer variability is often mentioned as a key challenge when applying AI to medical data [21, 16, 28, 18], to the best of our knowledge there is no method that explicitly models these two types of uncertainty for medical image segmentation.", + "bbox": [ + 496, + 700, + 893, + 868 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address this gap, we propose a novel approach called the Probabilistic Inter-Observer and iNtra-Observer varia", + "bbox": [ + 498, + 869, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21097", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tion NetwOrk (Pionono), depicted in Figure 1. This model accurately accounts for inter- and intra-observer variability using probabilistic deep learning. Specifically, each rater's labeling behavior is represented as a probability distribution in latent space, and optimized using the log Evidence Lower BOund (ELBO) in an end-to-end training process. The variance of each rater's distribution models the intra-observer variability, while the differences between the distributions models the inter-observer variability. When two raters exhibit similar labeling behavior, their probability distributions overlap substantially, while different labeling behavior results in a small overlap of distributions.", + "bbox": [ + 75, + 90, + 472, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The approach is validated in extensive experiments of prostate and breast cancer segmentation, using 'gold' labels. They reflect the expert agreement to show that our probabilistic modeling improves the predictive performance and estimates the predictive uncertainty. Furthermore, we also test its capability to model each rater's labeling behavior. As shown in the experiments, it can simulate expert opinions for a given test image in a consistent manner, providing a realistic estimation of \"what expert X would say in this case\". Our contributions can be summarized as follows:", + "bbox": [ + 75, + 272, + 472, + 421 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose Pionono, a probabilistic deep learning model that uses probability distributions in latent space to represent inter- and intra-observer variability. It can be trained with labels of multiple raters.", + "- The model is able to provide accurate segmentation predictions (compared to the expert agreement and different expert opinions), outperforming existing state-of-the-art algorithms such as STAPLE, Probabilistic U-Net and models based on global or local confusion matrices.", + "- Pionono provides uncertainty estimations that indicate areas where the predictions are not conclusive.", + "- The proposed model can provide several coherent segmentation hypotheses, simulating different medical experts." + ], + "bbox": [ + 94, + 422, + 468, + 648 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 662, + 218, + 679 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we review existing methods of probabilistic deep learning and crowdsourcing for medical images and highlight the differences to our model.", + "bbox": [ + 75, + 689, + 468, + 733 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Probabilistic Deep Learning. As already indicated, probabilistic approaches such as Bayesian neural networks [8, 1, 15, 17] and sparse Gaussian processes [10, 33, 26] have shown promising results in a multitude of tasks in the medical image domain, modeling different sources of uncertainties. Often, a general predictive uncertainty is addressed using probabilistic weight parameters [1]. This uncertainty can be bisected into model and data uncertainty which originate from model parameters or data ambiguities, respectively [15]. Other approaches have modeled the uncertainty of missing instance labels in multiple instance", + "bbox": [ + 75, + 734, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/e68094090a3300768aff71da3682e5953b2d6e4e9bc372ef73407b5ed99d21c9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method(i) Prob. (ii) Uncert.Coh. (iii) Segm.Exp. (iv) OpinionScale
STAPLE×××✓
Prob U-Net✓✓×✓
CM global××✓✓
CM pixel××✓×
Pionono✓✓✓✓
", + "bbox": [ + 527, + 88, + 867, + 218 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Table 1. For AI segmentation models to achieve the best possible diagnostic support, they should address four key issues: (i) provide a probabilistic uncertainty estimation, not only a single prediction for a test image; (ii) provide multiple coherent segmentation hypotheses; (iii) simulate different expert opinions for better explainability and decision support; (iv) scale to a higher amount of raters in the case that more data from different hospitals can be integrated.", + "bbox": [ + 496, + 226, + 893, + 339 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "learning [20, 26] or uncertainty of out of distribution samples [17]. The uncertainty in annotations has previously been addressed by the Probabilistic U-Net [13] (Prob U-Net), which encodes the labeling behavior in a latent random variable. The model is trained as a variational autoencoder with an encoder network predicting the latent distribution. This approach models a general variability in annotations but lacks the explicit modeling of inter- and intraobserver variability. Therefore, it is not able to incorporate the rater information during training and cannot simulate expert opinions.", + "bbox": [ + 496, + 367, + 890, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Crowdsourcing. While existing crowdsourcing methods aim to capture inter-observer variability in the training labels, this variability is often not reflected in the test predictions by probabilistic outputs [13]. The intra-observer variability is often not modeled at all, although it is often mentioned as a challenge in literature [21, 16, 28, 2, 7].", + "bbox": [ + 496, + 535, + 890, + 626 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "One way to handle multiple annotations is label fusion. With this method, the annotations of different raters are merged to a single set of labels. The \"Simultaneous Truth and Performance Level Estimation\" (STAPLE) mechanism performs label fusion with a probabilistic estimate of the true labels by weighting each segmentation depending upon the estimated performance level of each rater [32]. A supervised network can then be trained on these fused labels. More dedicated approaches incorporate different rater labels using confusion matrices (CM), for example for classification of image patches with Gaussian processes [18] or image segmentation with global confusion matrices [31] (CM global). In this direction, also pixel-wise confusion matrices were explored for semantic segmentation that are estimated by a dedicated deep neural network [34] (CM pixel). These models have shown promising results, but come with a conceptual problem: They assume that the pixels are statistically independent of each other, although", + "bbox": [ + 496, + 628, + 892, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21098", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "neighboring pixels have a high correlation. Therefore, the output of different segmentation hypotheses is not coherent. Furthermore, the predictions of the mentioned approaches [31, 34] are not modeled by a predictive distribution, but by a deterministic point estimate. While the global confusion matrix approach [31] has a limited expressiveness, the pixel-wise calculation [34] is hard to scale for multiple raters, because for each rater, a complete deep neural network must be trained and stored.", + "bbox": [ + 75, + 90, + 468, + 224 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Pionono unites the advantages of probabilistic and crowdsourcing methods. We summarize a comparison of different characteristics of Pionono and related methods for image segmentation in Table 1.", + "bbox": [ + 75, + 227, + 470, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 76, + 301, + 174, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we outline the background of the proposed method. It is implemented in the Pytorch [23] framework and is publicly available at https://github.com/arneschmidt/pionono_segmentation.", + "bbox": [ + 75, + 327, + 468, + 387 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Definition", + "text_level": 1, + "bbox": [ + 76, + 397, + 261, + 412 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $X = \\{x_{i} \\in \\mathbb{R}^{H \\times W \\times 3}\\}_{i=1,..,N}$ be a set of images, $S^{r} = \\{s_{i}^{r} \\in \\mathbb{R}^{H \\times W \\times C}\\}_{i=1,..,N}$ the corresponding segmentation maps with image dimensions $H \\times W$ and $C$ the number of classes. The segmentation maps are provided by different raters $r \\in R = \\{1,2,..,M\\}$ . Some or all images can be segmented by multiple raters, such that some segmentation maps $s_{i}^{r}$ can be empty. The proposed model does not require any overlap of the sets of annotated images.", + "bbox": [ + 75, + 419, + 468, + 541 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "If there are images available with segmentations assigned by expert agreements (so-called gold labels), the model should be able to predict a gold distribution over outputs $p(S^{\\mathrm{gold}})$ with the mean estimating the segmentation and the variance estimating the uncertainty. In any case, the model should model different segmentation hypotheses for the raters $\\{p(S^r); r = 1,2,\\dots,M\\}$ for diagnostic decision support.", + "bbox": [ + 75, + 542, + 468, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Proposed Model", + "text_level": 1, + "bbox": [ + 76, + 672, + 238, + 688 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "First, we introduce the common segmentation backbone $f_{\\omega}$ with trainable weights $\\omega$ . We use the well-known U-Net architecture [25] with a Resnet34 feature extractor [9]. This model takes an image $x_{i}$ and extracts a feature map $v_{i} \\in \\mathbb{R}^{H \\times W \\times L}$ with $H \\times W$ being the image resolution and $L$ the dimensions of the feature vectors ( $L = 16$ in the case of U-Net). We denote the feature extraction as", + "bbox": [ + 75, + 696, + 468, + 800 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nv _ {i} = f _ {\\omega} \\left(x _ {i}\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 227, + 814, + 468, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Based on these feature vectors, we could perform segmentation with a segmentation head $f_{\\theta}$ :", + "bbox": [ + 75, + 842, + 468, + 872 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ns _ {i} = f _ {\\theta} \\left(v _ {i}\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 228, + 885, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Now we extend this model to incorporate the inter- and intra-observer variation. The segmentation maps are influenced by the rater's experience, assessment, and personal choices. To encode the labeling behavior, we use a random vector $z \\in \\mathbb{R}^D$ . In practice, $D = 8$ are enough dimensions to reflect different labeling behaviors. We define a prior distribution $p(z) = \\mathcal{N}(z|0, \\sigma_{\\mathrm{prior}} * I)$ which encodes a generic labeling behavior without further information about the rater. It is possible to encode prior knowledge in this distribution, but we present a general model and leave this for future work. We set $\\sigma_{\\mathrm{prior}}^2 = 2.0$ , because we observe a realistic variability in the output for this value. In section 4.5 we prove that the model is robust for different settings of hyperparameters $D$ and $\\sigma_{\\mathrm{prior}}^2$ .", + "bbox": [ + 496, + 90, + 890, + 303 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Now, the posterior distribution of $p(z|r)$ that depends on the rater $r$ should be found. We approximate it with one multivariate Gaussian distribution for each rater:", + "bbox": [ + 496, + 303, + 890, + 347 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq (z | r) = \\mathcal {N} \\left(z \\mid \\mu^ {r}, \\Sigma^ {r}\\right) \\forall r = 1,.., M \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 361, + 890, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\{\\mu^r,\\Sigma^r\\}^{r = 1,\\dots ,M}$ are trainable parameters. The variance of each distribution $q(z|r)$ models the intra - observer variability. The differences between the distributions for different raters model the inter - observer variability. To obtain the predictive gold distribution we add another 'rater' $r = M + 1$ represented by an additional gold distribution $q$ which is trained with the available gold segmentations. During prediction, this distribution provides the estimated agreement between experts.", + "bbox": [ + 496, + 388, + 890, + 526 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The segmentation head $f_{\\theta}$ , parametrized by weights $\\theta$ must be adapted to take the random vector $z$ into account. The approximated predictive distribution is then obtained by:", + "bbox": [ + 496, + 527, + 890, + 585 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(s _ {i} \\mid x _ {i}, r, \\omega , \\theta\\right) = \\int f _ {\\theta} \\left(v _ {i}, z\\right) q (z | r) d z. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 587, + 890, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The closed-form calculation is not feasible and therefore we approximate it by Monte Carlo (MC) sampling:", + "bbox": [ + 496, + 625, + 890, + 656 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {s} _ {i, j} | x _ {i}, r = f _ {\\theta} \\left(v _ {i}, \\tilde {z} _ {j}\\right); \\tilde {z} _ {j} \\sim q (z | r) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 667, + 890, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with $j = 1,\\dots,K$ indexing the MC samples. In practice, we concatenate the feature maps $v_{i}$ and the latent vector $\\tilde{z}_j$ which is broadcasted to the image size, leading to a feature map with dimensions $H\\times W\\times (L + D)$ . The segmentation head consists of three layers with 1x1 convolutions and 16 filters in the first two layers and $C$ filters in the last layer.", + "bbox": [ + 496, + 698, + 890, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Training", + "text_level": 1, + "bbox": [ + 500, + 799, + 604, + 815 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "First, all posterior distributions $q(z|r)$ are initialized randomly. Each initial value of the mean vectors $\\mu^r$ is independently drawn from a distribution $\\mathcal{N}(0,\\sigma_{\\mathrm{post}}^2)$ . We set $\\sigma_{\\mathrm{post}}^2 = 8$ , because this initializes the mean vectors sufficiently different for a good optimization. In section 4.5 we", + "bbox": [ + 496, + 823, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21099", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "show, that the model is robust to other settings of this value. The covariance matrices $\\Sigma^r$ are initialized with $\\sigma_{\\mathrm{prior}} * I$ .", + "bbox": [ + 76, + 90, + 467, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To optimize the parameters $\\{\\mu^r,\\Sigma^r\\}^{r = 1,\\dots ,M}$ of the probability distribution $q(z|r)$ , we maximize the ELBO:", + "bbox": [ + 76, + 119, + 467, + 151 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {E L B O} = \\mathbb {E} _ {q} \\log p \\left(S ^ {r} | X, r, \\omega , \\theta\\right) - \\lambda K L (q (Z | r) | p (Z)). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 162, + 467, + 193 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with distribution $q$ as defined in eq. 4. The first term defines a log-likelihood (LL) loss, making the model fit to the annotations of each rater. The second term defines the KL-divergence between the posterior distribution $q(Z|r)$ and the prior $p(Z)$ and works as a regularization of the latent distributions. The factor $\\lambda$ weights the regularization term and is set to 0.0005 to balance the magnitudes of the log-likelihood and the KL (we will check the robustness of this hyperparameter in Section 4.5). While the KL term can be optimized analytically, the log likelihood term must be approximated. We use the reparametrization trick [12] to split each probabilistic sample $\\tilde{z}^r$ into its probabilistic component and deterministic parameters $\\mu^r$ and $\\Sigma^r$ . These parameters can be optimized by backpropagation of gradients, together with the CNN parameters $\\omega$ and $\\theta$ . For numerical stability, we train the covariance matrix parameters by using the lower triangular matrix $L$ of the Cholesky decomposition $\\Sigma^r = L^r L^{r^\\top}$ . The log-likelihood can be optimized with standard methods like the categorical cross-entropy. We found that the general dice loss [30] leads to better results, so all final results are reported with this loss.", + "bbox": [ + 76, + 194, + 467, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We use the Adam optimizer [11] for 100 epochs with a learning rate of 0.0001. The model parameters $\\mu^r, \\Sigma^r$ are optimized with a higher learning rate of $\\nu = 0.02$ , because else the gradient was not strong enough to properly learn the rater distributions. We tested $\\nu = 0.01, 0.02, 0.04$ and include the results in section 4.5. Both learning rates are decreased after 40 epochs by dividing them by 1.1 in each epoch.", + "bbox": [ + 75, + 511, + 467, + 632 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Predicting", + "text_level": 1, + "bbox": [ + 76, + 641, + 192, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For a test image $x^{*}$ , the predictive gold distribution can again be obtained by drawing Monte-Carlo samples", + "bbox": [ + 76, + 664, + 467, + 695 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {s} _ {j} ^ {*} \\mid x ^ {*}, r = f _ {\\theta} \\left(v ^ {*}, \\tilde {z} _ {j}\\right); \\tilde {z} _ {j} \\sim q (z | r = M + 1) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 124, + 705, + 467, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with $j = 1,..,K$ indexing the MC samples and $q(z|r = M + 1)$ representing the gold distribution as described in section 3.2. The mean of these samples provides the segmentation hypothesis that approximates the expert agreements. The variance of the samples indicates uncertainties in the prediction.", + "bbox": [ + 76, + 734, + 467, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Furthermore, the model is able to simulate intraobserver variations of rater $r^\\prime$ by drawing multiple samples of the distribution $\\tilde{z}_j^{\\prime}\\sim q(z|r = r^{\\prime})$ for the final prediction. The inter-observer variations between rater $r^\\prime$ and $r''$ can be simulated by using samples $\\tilde{z}_j^\\prime \\sim q(z|r = r^\\prime)$ and", + "bbox": [ + 75, + 825, + 467, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\tilde{z}_k^{\\prime \\prime}\\sim q(z|r = r^{\\prime \\prime})$ and finally taking the mean of both output distributions.", + "bbox": [ + 498, + 90, + 888, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The model can therefore simulate expert opinions for a given test image. Other AI methods typically aggregate the expertise provided by all annotators to make predictions (e.g., using STAPLE, Prob U-Net). However, in such approaches, the knowledge of highly specialized experts can be diluted or lost among the less experienced annotators' knowledge. In our framework, we provide consistent predictions for each individual expert, thereby preserving their unique expertise and contributions.", + "bbox": [ + 496, + 121, + 890, + 257 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 268, + 630, + 286 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In several experiments we demonstrate that the uncertainty estimation of the model indicates areas of false predictions (4.2), the model is able to capture the inter and intra-observer variations (4.3) and outperforms other related methods (4.4). Additionally, we analyze the robustness to hyperparameters (4.5), required resources (4.6), and limitations (4.7).", + "bbox": [ + 496, + 295, + 890, + 400 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 409, + 601, + 422 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For empirical validation, three public histopathological datasets were used. The first dataset, \"Gleason 2019\" [22] was published as a MICCAI grand challenge for pathology and includes 333 Tissue Micro Arrays (TMA) of prostate cancer, labeled by 6 different pathologists. The TMAs were scanned with a magnification of $40\\mathrm{x}$ and have a size of approximately $4000 \\times 4000$ pixels. Of the 333 images, 244 are publicly available with labels (the test annotations of the challenge are not available). Each pathologist annotated between 61 and 241 TMAs with segmentation masks and the gold labels were obtained using the STAPLE algorithm [32], following the original work of the dataset [22]. We resize all images to $1024 \\times 1024$ pixels and create 4 cross-validation splits.", + "bbox": [ + 496, + 431, + 890, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The second dataset, which we will refer to as \"Arvaniti TMA\" was published in 2018 [4] and includes a total of 886 TMAs of prostate cancer of which 245 images were annotated by two pathologists (while the other images only have annotations of one pathologist and are therefore discarded in our study). The TMAs were scanned with a magnification of $40\\mathrm{x}$ but the scanned area is smaller than for the Gleason19 dataset. The images have a resolution of $3100\\times 3100$ pixels and we resize them to $512\\times 512$ such that the magnification matches the resized images of the Gleason 2019 dataset. Again, we split the dataset into 4 cross-validation splits for the experimental setup.", + "bbox": [ + 496, + 643, + 890, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the classification of prostate cancer, the tissue is segmented in the Gleason Grading (GG) scheme. The classes are 'Non-cancerous' (NC), 'Gleason 3' (G3), 'Gleason 4' (G4), and 'Gleason 5' (G5) depending on the architectural growth patterns of the tumor [28, 29]. To visualize the", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21100", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/61912018b33ebdb7162fe6ce693c60f855d553d0275246542e8b0d61671a20b1.jpg", + "image_caption": [ + "(a) Image" + ], + "image_footnote": [], + "bbox": [ + 145, + 88, + 207, + 135 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b3387f21303821689611c937ae00b6cb9aafe0231321e10b1f11319b3a4b99cf.jpg", + "image_caption": [ + "c)Pred.Gold" + ], + "image_footnote": [], + "bbox": [ + 212, + 88, + 269, + 135 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/bc57e6dc8a16c77bea99cb7a2fb01d9083dbcb5ce5562a86c680ef467f6c3182.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 88, + 336, + 133 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b3a1032b28790090647b6c6eabbec93e1eb2f31749b22a4d18dd47836f428d0e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 344, + 88, + 403, + 133 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2cc72240d957c593e79bdcbe64186d7cbb7c0467789832635778b78d3a3fe4e7.jpg", + "image_caption": [ + "(e) Image" + ], + "image_footnote": [], + "bbox": [ + 145, + 154, + 207, + 200 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/eb2894143429b0e30764f549aa033e0d42e79f63d6d7098d4a69427bbabbfe3d.jpg", + "image_caption": [ + "(f) GT Gold" + ], + "image_footnote": [], + "bbox": [ + 210, + 154, + 267, + 196 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f3272df02ef56f43eb1e9badfeaea3d1c5171913e9541ba7c1cce3fa28325457.jpg", + "image_caption": [ + "(g)Pred.Gold", + "(h) Uncert.", + "Figure 2. Gold prediction and uncertainty of the Pionono model. The first row shows a confident prediction as the uncertainty in 2d is low (white) for almost all the area. Indeed, the segmentation prediction 2c is very accurate, see the ground truth (GT) 2b. The second row shows an example of an uncertain prediction. Some parts of the area classified as G3 (yellow) in $2\\mathrm{g}$ are labeled as G4 in the ground truth 2f. These areas are estimated with a high uncertainty (black) in $2\\mathrm{h}$ , warning that these predictions are unreliable." + ], + "image_footnote": [], + "bbox": [ + 344, + 154, + 401, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "segmentations we use the colors: green for NC, yellow for G3, orange for G4, and red for G5. For the evaluation of algorithms for prostate cancer classification, previous works used the Cohen's kappa coefficient [22, 4, 28] which measures the agreement of two raters or a rater and an AI model. To compare to previously reported results for the two datasets, we use the unweighted Cohen's kappa $\\kappa$ for the Gleason 2019 dataset [22] and the quadratic weighted Cohen's kappa $\\kappa$ for the Arvaniti TMA dataset [4]. The main difference is that the quadratic kappa takes the class order into account and weighs the errors based on the quadratic distance of the predicted and the real class.", + "bbox": [ + 75, + 364, + 468, + 545 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The third dataset contains 151 WSIs for breast cancer segmentation that were sliced into 11,836 patches of $512 \\times 512$ pixels annotated by 25 raters [3, 19]. We will refer to this dataset as \"bc segmentation\". The tissue was segmented into \"tumor\", \"inflammation\", \"necrosis\", \"stroma\", and \"other\". Here, the gold labels were obtained by an actual discussion of experts. We use the predefined train/validation/test splits [19].", + "bbox": [ + 75, + 547, + 468, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For all datasets we use image augmentation with the albumenations library [6] by applying random flip, rotation, shear, zoom, blur, and shifts in brightness, contrast, hue, and saturation. This leads to a broad range of realistic transformations of the image to avoid overfitting.", + "bbox": [ + 75, + 667, + 468, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Uncertainty estimation", + "text_level": 1, + "bbox": [ + 76, + 755, + 290, + 771 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proposed model provides probabilistic predictions that allow an accurate assessment of the predictive uncertainty. Fig. 2 shows the model predictions and uncertainties obtained with the gold distribution as described in section 3.2. For the first image (2a), the prediction of the model (2c) is accurate and matches the real gold annotation (2b) very well. The uncertainty (2d) for this predictions is low (white), which means that there is a low risk of a wrong", + "bbox": [ + 75, + 780, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "prediction. Therefore, the model correctly indicates that this prediction is reliable. For the second image 2e, some areas that are predicted as G3 (yellow) in $(2\\mathrm{g})$ are actually G4 in the ground truth gold prediction (2f). The model's uncertainty estimation indicates that this prediction is not reliable: the misclassified areas are marked with a high uncertainty (dark) in the image (2h). Therefore, the probabilistic output adds valuable information to the diagnostic process. It estimates if a prediction is reliable - or unreliable and should be double-checked.", + "bbox": [ + 496, + 90, + 890, + 241 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Inter- and Intra-observer Variation", + "text_level": 1, + "bbox": [ + 498, + 253, + 805, + 268 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The Pionono model is able to capture the inter- and intraobserver variability. This accurate probabilistic modeling of the annotations does not only improve the predictive results (see section 4.4), but also allows to simulate specific experts at test time. In this section, we empirically show that the model learns the different label behaviors of the raters and is able to reproduce them.", + "bbox": [ + 496, + 279, + 890, + 383 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Fig. 3a we plot the inter-observer variations between the raters. The figure shows that there is indeed a high variability among the raters, with a Cohen's kappa ranging from 0.36 to 0.72. The simulated test predictions by Pionono show a higher agreement with each rater than the average agreement of the other raters, except for rater 2. For two raters (1 and 5), the simulated predictions of Pionono are even more than 15 percentage points higher than the average rater agreement. We also measured the IoU metric, which was 0.574, 0.540, 0.619, 0.649, 0.692, 0.507, for the 6 raters respectively, compared to a mean inter-pathologist IoU of 0.361. The results confirm that most raters are modeled with high accuracy.", + "bbox": [ + 496, + 386, + 890, + 582 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fig. 3b shows the posterior distributions $q(z|r)$ of the proposed model, encoding the labeling behavior of each rater. The following observations confirm, that these learned distributions approximate well the real-world labeling behavior of the raters: (i) The four raters 3, 4, 5 and 6 show a high overlap of the distributions and corresponding to a high labeling agreement shown in Fig. 3a. (ii) The gold distribution (simulating raters agreement) overlaps significantly with the distribution of these four raters. (iii) The distribution of rater 2 is far away from all other distributions. This rater shows a different labeling behavior due to frequent under-segmentation of images, assigning the 'background' class to areas that contain tissue. (iv) Raters 1 and 6 often deviate from the other raters, especially for the differentiation of classes G3 and G4. Their distribution accordingly has a smaller overlap with the gold distribution and the other raters. Fig. 4 shows some visual image examples of Pionono test predictions, simulating each rater $r$ by drawing samples from the corresponding distribution $q(z|r)$ and then taking the mean of the output samples. The examples confirm that the rater differences are modeled well.", + "bbox": [ + 496, + 583, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21101", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/209f76abb9b2215c4e7df52da06042db7c5b2ae800e1eb0934a2accc9034a536.jpg", + "image_caption": [ + "(a) Rater simulation statistic", + "Figure 3. Analyzing the labeling behavior. In Fig. (a) the agreement of each rater with all other raters is depicted, measured by the unweighted Cohen's Kappa of the true labels [22]. The mean agreement of each rater with all other raters is represented by a black dot and the agreement with Piononos test predictions, simulating the corresponding rater, by a star. This confirms that the model accurately models each rater, reaching even a higher agreement than the other rater's average, except for rater 2. Fig. (b) shows the first two dimensions of the posterior distributions $q(z|r)$ with mean and covariance after training. The distributions of raters 3, 4, 5 and 6 overlap significantly with the gold distribution and with each other, indicating a similar labeling behavior. Indeed, these raters show the highest labeling agreement in Fig. (a)." + ], + "image_footnote": [], + "bbox": [ + 89, + 93, + 269, + 239 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c490c3899e2cd256034e3ca5cf4f7038d2436be76401f257b8447b5830ba209d.jpg", + "image_caption": [ + "(b) Latent distributions" + ], + "image_footnote": [], + "bbox": [ + 285, + 93, + 467, + 239 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Next, we analyze the intra-observer variations. As the dataset does not contain multiple annotations of the same rater for the same image, the assessment of this quality is more difficult. Still, certain intra-observer variability can be assessed by observing the general labeling behavior of one annotator. For example, rater 6 tends to over-assign class G5 (red), and rater 2 tends to not segment all image parts that contain tissue. Interestingly, these intra-observer variations are present in the model predictions when multiple samples are drawn from their corresponding distribution. Fig. 5 shows visual examples of the simulated variations of raters 2 and 6.", + "bbox": [ + 75, + 465, + 468, + 645 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Model Comparison", + "text_level": 1, + "bbox": [ + 76, + 656, + 261, + 672 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The proposed model is compared to previously reported results and several state-of-the-art approaches (see section 2) for medical image segmentation with labels from multiple raters. For fair comparison, we use the same backbone architecture1, epochs, learning rate, and optimizer for all experiments. We have tuned the model-specific hyperparameters to obtain the best possible results for each method.", + "bbox": [ + 75, + 680, + 468, + 785 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "First, we perform experiments with the Gleason 2019 dataset with a 4-fold crossvalidation. For comparison with previous works, we report the unweighted Cohen's kappa metric comparing gold predictions with gold ground truth. Additionally, we report the accuracy. As the results in Table 2 show, the proposed Pionono model outperforms the previ", + "bbox": [ + 75, + 786, + 468, + 876 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/47273e0da3316f35882c2690568881eeb50fd0f25945020c95197e57f0fb2a6a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 549, + 87, + 612, + 135 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8d2958a1d16b833f037670522766e60b5be29b48f8e287b1952a963f15824754.jpg", + "image_caption": [ + "(a) Image" + ], + "image_footnote": [], + "bbox": [ + 553, + 152, + 609, + 198 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a2ea98d21792812f59a6d5c3ba3643d733f5662d513454455edcd150f2204a68.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 627, + 152, + 681, + 196 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/83de155e482c4d41cae91fae8d3147d416a89dfcabb822f7173aceb78217bcb5.jpg", + "image_caption": [ + "(c) $\\mathrm{GT}r = 1$" + ], + "image_footnote": [], + "bbox": [ + 553, + 217, + 609, + 260 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/544d4b4f6601ba5c97f60b5b18e44e2d0b2eb7d78c9fd96e455eb80de3df1188.jpg", + "image_caption": [ + "(g) $\\mathrm{GT}r = 2$", + "(1) PR $r = 3$" + ], + "image_footnote": [], + "bbox": [ + 553, + 281, + 609, + 325 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/644c95b8f6ad36d4d7516a2132bf6e85cf0f69c6466fbd5af878c0866fe88054.jpg", + "image_caption": [ + "(d) PR $r = 1$", + "(h) $\\mathrm{PR}r = 2$" + ], + "image_footnote": [], + "bbox": [ + 627, + 217, + 683, + 260 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/017fa9ed416b935895588a0c5263af3c766090f55d78f9a036cfcdd362b3e8e0.jpg", + "image_caption": [ + "(k) GT $r = 3$" + ], + "image_footnote": [], + "bbox": [ + 553, + 343, + 607, + 387 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ba23e90d6e71986a9c29f76965b401ae001eb082ef398ab67bd0ea9eca98491f.jpg", + "image_caption": [ + "(o) $\\mathrm{GT}r = 4$" + ], + "image_footnote": [], + "bbox": [ + 553, + 407, + 609, + 450 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3ac9df8382fb4d56b0e3e6378e9cb56ba5a52ccfeaca541c1ead7fd78ac71ea5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 627, + 407, + 681, + 450 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/579859d02a5b58ed54d3ad3987a73394807304263e14bc6469d7943aa796c4db.jpg", + "image_caption": [ + "(s) GT $r = 5$", + "(w) GT $r = 6$", + "Figure 4. Inter-observer variations estimated by Pionono. For two test images we depict the ground truth (GT) segmentations of all raters and the predicted segmentations (PR), simulating each rater. The proposed model is able to simulate certain labeling behavior like the tendency of assigning class G5 (red) for raters 2 and 6 (see g and w) where other raters assigned G4 (orange). Furthermore, the model captures the under-segmentation by rater 2 (see i)." + ], + "image_footnote": [], + "bbox": [ + 553, + 470, + 609, + 515 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(t) PR $r = 5$", + "bbox": [ + 627, + 460, + 684, + 468 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a8b47d5bfb4ba084638aff0034c17c7aab6a075b8171d486e0fd59f04c06d3a6.jpg", + "image_caption": [ + "(t) PR $r = 5$", + "(x) PR $r = 6$" + ], + "image_footnote": [], + "bbox": [ + 627, + 470, + 683, + 515 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8e422444dd6baf427d77e1f7b78190a208235d3be2ac3c2de3976d4477193480.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 89, + 767, + 133 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e25304abb570c7a7eb0721b9e075f32bd14f49268fb243c93df9ec5c4fd144e6.jpg", + "image_caption": [ + "(b) Image" + ], + "image_footnote": [], + "bbox": [ + 710, + 154, + 764, + 194 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8f3c01fb048a7fa451b4e7d10fc4db8faa882900a9d0cae6a36ed7f9c2e86ae1.jpg", + "image_caption": [ + "e) GT $r = 1$" + ], + "image_footnote": [], + "bbox": [ + 710, + 217, + 766, + 257 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(f) $\\mathrm{PR}r = 1$", + "bbox": [ + 785, + 205, + 839, + 214 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c3f1c2175fd031237def2dbd5e2b5fccc5219a643ec92ac8a670e673d8baa831.jpg", + "image_caption": [ + "(f) $\\mathrm{PR}r = 1$" + ], + "image_footnote": [], + "bbox": [ + 785, + 217, + 839, + 258 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/45e1b59a531abfcbb35ac7f67212552034fdbc84d91eea90f1d98f0915e6192a.jpg", + "image_caption": [ + "(i) $\\mathrm{GT}r = 2$" + ], + "image_footnote": [], + "bbox": [ + 710, + 282, + 766, + 323 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9b7d943b68770361a1ef35c0c99d1d7244f12976164145740afe8f4f05ac012e.jpg", + "image_caption": [ + "j) PR $r = 2$" + ], + "image_footnote": [], + "bbox": [ + 784, + 282, + 839, + 321 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2e076d2ed7ee694b8d0b4aa797e27f4c457b561e0549432c1711952c7c830206.jpg", + "image_caption": [ + "(m) $\\mathrm{GTr} = 3$" + ], + "image_footnote": [], + "bbox": [ + 712, + 345, + 764, + 383 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/57bb75da1f09cbf260651434cd1bfd29709ec8ecbd71b8aa941a2cbbf0d5eee9.jpg", + "image_caption": [ + "n) PR $r = 3$" + ], + "image_footnote": [], + "bbox": [ + 784, + 345, + 839, + 385 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4d6858bcad3ebc44e1baec17d35f7bd32506386f07ed7de180ad00c27d1f6e2f.jpg", + "image_caption": [ + "(q) GT $r = 4$" + ], + "image_footnote": [], + "bbox": [ + 710, + 409, + 766, + 449 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2c11064145ca86f09d3dc10d0a0242db17c161826fa8e212419dd1b0fedc0771.jpg", + "image_caption": [ + "(r) PR $r = 4$" + ], + "image_footnote": [], + "bbox": [ + 785, + 409, + 839, + 449 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/56e888573e9b6c21a028b894138c14514dce27af9b6593b619a4374faddb51d3.jpg", + "image_caption": [ + "(u) GT $r = 5$", + "(y) GT $r = 6$" + ], + "image_footnote": [], + "bbox": [ + 710, + 474, + 764, + 515 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/be2ed15e726e79569c37577f82868f9a7c472a3132c35f3d4524ee6525e95e2b.jpg", + "image_caption": [ + "v) PR $r = 5$", + "z) PR $r = 6$" + ], + "image_footnote": [], + "bbox": [ + 785, + 474, + 839, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ously reported results [22, 24], including the winner of the Gleason 2019 challenge [24], by a large margin of over 20 percentage points. This accounts for the exact modeling of the raters by Pionono, but also for the different choices of backbone architecture and other training details. Compared to other state-of-the-art methods with the same architecture and training details, Pionono still shows a considerably better performance.", + "bbox": [ + 496, + 657, + 890, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Next, we compare the generalization capabilities of the models by using the Arvaniti TMA dataset as an external test set, as reported in Table 3. This means, that the models are trained with all images from Gleason 2019 and tested with all images from Arvaniti TMA. As the Arvaniti TMA dataset does not contain gold labels, the model's gold predictions are compared to both raters independently, as previously done by Arvaniti et al. [4]. We observe that the model", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "1Only the model CM pixel uses ResNet18 to fit on the GPU.", + "bbox": [ + 94, + 886, + 413, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21102", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/de5a03e294abf5351e600fa766c0baba7551027f1c23c2c24b0d798ecf0048cb.jpg", + "image_caption": [ + "(a) Image" + ], + "image_footnote": [], + "bbox": [ + 127, + 87, + 189, + 135 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4d4b57ce4f762d03817e80a8e35e65ebbaa225c39ca8f0b1aa224780e5f1a221.jpg", + "image_caption": [ + "(b) PR $r = 6$" + ], + "image_footnote": [], + "bbox": [ + 204, + 88, + 256, + 132 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/03d291c31fee1b51a4576a1f1fc94f3842040f5d99ed6c880f3c861e3eb7174f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 204, + 154, + 256, + 194 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ac6e77b9e71e01cecf65e526f4c18c11712ca5ba129bce1266efa279bf7239bc.jpg", + "image_caption": [ + "(e) $\\mathrm{GT}r = 6$", + "(f) PR $r = 6$" + ], + "image_footnote": [], + "bbox": [ + 204, + 215, + 256, + 258 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c999c839c40adb883e0a1cdbed01777037a387a9945f73f4b9fffd6342fa7dd0.jpg", + "image_caption": [ + "(i) PR $r = 6$" + ], + "image_footnote": [], + "bbox": [ + 204, + 280, + 256, + 321 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/88bb68cd2b610ff8e12775115afddc6649b5092754465a9091bcd02c08649da6.jpg", + "image_caption": [ + "(k) PR $r = 6$", + "(m) PR $r = 6$", + "Figure 5. Intra-observer variations estimated by the Pionono model. For two example images we depict the true annotation (GT) of two different raters ( $r = 2$ and $r = 6$ ). On the right sides we show different coherent segmentation predictions (PR) for each rater estimated by our model. The differences in each column reflect possible intra-observer variations. The first example (a) shows that rater 6 might show some variations in the assigned classes. While the segmentation prediction (b) is composed by classes G3 (yellow) and G4 (orange), the segmentation sample (f) only consists of G5 (red). Indeed, this rater often assigns class G5 (red) in areas where other raters assign G4 (see Fig. 4) such that this is a plausible hypothesis. In the second example (c) we see variations due to the under-segmentation of rater 2 in some images. Our model captures this behavior and provides hypothesis of more (d) or less (j) segmentation of class G3 (yellow)." + ], + "image_footnote": [], + "bbox": [ + 204, + 344, + 256, + 385 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b2053efe55d8103ec4a9d289f178e3e63a4edfab7dd975d7752fcbf5d08598ab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 88, + 346, + 133 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2ef7993aa4dcf769db6a43939c5ef37bc2cf22101abd15b7debb0ba8a12f4540.jpg", + "image_caption": [ + "(c) Image", + "(g) $\\mathrm{GT}r = 2$" + ], + "image_footnote": [], + "bbox": [ + 289, + 152, + 344, + 194 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e1213dc2feb68217e88ca75f48dda837438be480327d07c1108b988ab17cc418.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 364, + 90, + 419, + 132 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/98cc3cdea572d4fe0e2a94f69a032cd7af4692bbe6f805c642872660f8b5d678.jpg", + "image_caption": [ + "(d) PR $r = 2$" + ], + "image_footnote": [], + "bbox": [ + 364, + 152, + 418, + 194 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5df5434fb20d3d636c070deeae111a074e31d738aa87de85c19888225a11d8d2.jpg", + "image_caption": [ + "(h) PR $r = 2$" + ], + "image_footnote": [], + "bbox": [ + 370, + 215, + 415, + 256 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8a5fa3318798f86c7805c02f8c54c354b8fc39ccf8a6b260696a190faf0269e7.jpg", + "image_caption": [ + "(j) PR $r = 2$" + ], + "image_footnote": [], + "bbox": [ + 369, + 281, + 421, + 321 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b64c5f1edfff8145a28f0ef4f4a196a5802a522fe621492d14be5589f4ad85a3.jpg", + "image_caption": [ + "(1) PR $r = 2$", + "(n) PR $r = 2$" + ], + "image_footnote": [], + "bbox": [ + 369, + 344, + 421, + 385 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "generalizes better than all other methods, achieving a higher agreement in terms of Cohen's quadratic kappa with both raters. In terms of accuracy, only 'CM global' outperforms Pionono by a small margin.", + "bbox": [ + 75, + 640, + 468, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In the third experiment, we use the Arvaniti TMA dataset for training and testing with the two rater annotations. Again, the proposed model is able to outperform previously reported results as well as other state-of-the-art methods in terms of quadratic Cohen's kappa. In terms of accuracy, only the \"Prob U-Net\" model obtains a better result for rater 1, while Pionono reaches the best accuracy for rater 2.", + "bbox": [ + 75, + 702, + 468, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To validate the model on a different kind of data, we performed the fourth experiment on the \"bc segmentation\" dataset [3]. The results are reported in Table 5 and confirm the strong performance of the proposed Pionono model.", + "bbox": [ + 75, + 809, + 468, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The results support our hypothesis that explicitly modeling the inter- and intra-observer variations improves the", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f1125986204767786bcd6037b5115e2d40e4a2cc4b3237bb47afcaf50be0e858.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodUnweighted κAccuracy
Nir et al. [22]0.51N.A.
Qiu et al. [24]0.524N.A.
STAPLE0.75 ± 0.0060.834 ± 0.005
Prob U-Net0.741 ± 0.0020.83 ± 0.001
CM global0.721 ± 0.0180.814 ± 0.012
CM pixel0.692 ± 0.0190.791 ± 0.012
Pionono0.758 ± 0.0110.84 ± 0.007
", + "bbox": [ + 534, + 88, + 857, + 222 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/bfc5fd54c9b0f0309f6331ab3d966bea50308d50161d2fbee34f39c243d18e62.jpg", + "table_caption": [ + "Table 2. Cohens Kappa Comparison for the 4-fold crossvalidation experiment of the Gleason 2019 dataset, reported by mean and standard error." + ], + "table_footnote": [], + "table_body": "
Rater 1 MethodQuadratic κAccuracy
STAPLE0.629 ± 0.0020.718 ± 0.001
Prob U-Net0.629 ± 0.0050.73 ± 0.003
CM global0.624 ± 0.0030.728 ± 0.002
CM pixel0.618 ± 0.0070.72 ± 0.004
Pionono0.641 ± 0.0060.736 ± 0.004
Rater 2 MethodQuadratic κAccuracy
STAPLE0.563 ± 0.0020.621 ± 0.002
Prob U-Net0.56 ± 0.0030.626 ± 0.006
CM global0.557 ± 0.0030.638 ± 0.006
CM pixel0.551 ± 0.0060.626 ± 0.008
Pionono0.569 ± 0.0050.633 ± 0.005
", + "bbox": [ + 522, + 284, + 867, + 478 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/45eaccad08ea31dd524160401d6ca8a2c0b0033f21cd2b052c7cb7ce236b58b4.jpg", + "table_caption": [ + "Table 3. Cohens Kappa Comparison with the two raters of the Arvaniti TMA dataset trained on the Gleason 2019 dataset, reported by mean and standard error." + ], + "table_footnote": [], + "table_body": "
Rater 1 MethodQuadratic κAccuracy
Arvaniti et al. [4]0.55N.A.
Silva-R. et al. [28]0.536N.A.
supervised0.658 ± 0.0250.734 ± 0.008
Prob U-Net0.697 ± 0.0080.762 ± 0.004
CM global0.677 ± 0.0280.745 ± 0.011
CM pixel0.647 ± 0.0160.731 ± 0.012
Pionono0.716 ± 0.0110.751 ± 0.02
Rater 2 MethodQuadratic κAccuracy
Arvaniti0.49N.A.
supervised0.521 ± 0.0140.678 ± 0.014
Prob U-Net0.534 ± 0.0020.68 ± 0.005
CM global0.533 ± 0.0220.676 ± 0.011
CM pixel0.508 ± 0.0130.663 ± 0.008
Pionono0.548 ± 0.0080.697 ± 0.012
", + "bbox": [ + 519, + 542, + 874, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Cohens Kappa Comparison with the two raters of the Arvaniti TMA dataset trained and validated by 4-fold crossvalidation of the Arvaniti data, reported by mean and standard error.", + "bbox": [ + 498, + 803, + 890, + 844 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "model's performance. Pionono takes the different labeling behavior into account during training which leads to accu", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21103", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/985d98ecbf472cccddd6f7d568fda46044218130ea1d9a276696b1d6b6f379a5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodUnweighted κAccuracy
STAPLE0.647 ± 0.0030.755 ± 0.002
Prob U-Net0.685 ± 0.0230.734 ± 0.004
CM global0.654 ± 0.0050.761 ± 0.004
CM pixel0.689 ± 0.0100.784 ± 0.007
Pionono0.711 ± 0.0020.799 ± 0.001
", + "bbox": [ + 117, + 88, + 431, + 186 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "rate predictions.", + "bbox": [ + 76, + 257, + 187, + 272 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Robustness to Hyperparameter Settings", + "text_level": 1, + "bbox": [ + 76, + 289, + 418, + 306 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To measure the sensitivity of the model regarding different hyperparameters, we performed studies on the 4-fold cross-validation experiment of the Gleason 19 dataset. Table 6 shows that the model is robust to variations of all analyzed hyperparameters. We observe minor performance drops for different values of the regularization factor $\\lambda$ and the initialization variance $\\sigma_{\\mathrm{post}}^2$ . In both cases, wrong choices of the hyperparameters can hinder the correct optimization of the latent distributions. Furthermore, we tested different backbone architectures, indicating a limited performance with a VGG16 backbone. Overall the performance drops are minor and for all other settings, the model shows highly accurate results of $\\kappa >0.75$ .", + "bbox": [ + 75, + 315, + 468, + 512 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Required Resources", + "text_level": 1, + "bbox": [ + 76, + 527, + 266, + 544 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For the Gleason 2019 dataset with images of $1024 \\times 1024$ , the model can be trained with a batch size of 3 on a single NVIDIA GeForce RTX 3090 with 24Gb memory. The training takes less than 1.5h in total and test predictions less than 0.2s per image. The trained model occupies less than 350Mb when saved to the disk. As each additional annotator adds only one additional vector $\\mu^r \\in \\mathbb{R}^8$ and one covariance matrix $\\Sigma^r \\in \\mathbb{R}^{8 \\times 8}$ , it is scalable to a large number of annotators. The model's quick runtime and excellent scalability make it easily applicable in clinical practice.", + "bbox": [ + 75, + 554, + 468, + 705 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.7. Limitations", + "text_level": 1, + "bbox": [ + 76, + 723, + 202, + 738 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As semantic segmentation itself is a challenging task, some details of the annotator segmentations are not captured well by the model, such as the variations of class NC (green) in the GT of Fig. 4d - 4x or class G4 (orange) in the GT of Fig. 4f - 4z. Here, the model tends to predict similar shapes for the raters. A possible solution is to use more layers in the segmentation head $f_{\\theta}$ with a wider kernel (e.g. $5 \\times 5$ convolutions). This would increase the complexity of the model and might enable it to capture the different labeling behavior in even more detail.", + "bbox": [ + 75, + 750, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5b3cc2160389b54e5f4b5be5b64e862a12e8467f4e8db6520732e099e4681af2.jpg", + "table_caption": [ + "Table 5. Results for the breast cancer segmentation of WSIs, reported as mean and standard error of 4 runs." + ], + "table_footnote": [], + "table_body": "
Hyperp.ValueUnweighted κAccuracy
D40.752 ± 0.0050.836 ± 0.003
80.758 ± 0.0110.84 ± 0.007
160.752 ± 0.0060.836 ± 0.004
σ2prior10.758 ± 0.0070.839 ± 0.004
20.758 ± 0.0110.84 ± 0.007
40.757 ± 0.0070.839 ± 0.004
σ2post40.757 ± 0.0070.839 ± 0.004
80.758 ± 0.0110.84 ± 0.007
160.745 ± 0.0090.83 ± 0.005
λ0.00010.744 ± 0.0030.829 ± 0.003
0.00050.758 ± 0.0110.84 ± 0.007
0.0010.745 ± 0.0080.837 ± 0.005
ν0.010.757 ± 0.0040.839 ± 0.002
0.020.758 ± 0.0110.84 ± 0.007
0.040.753 ± 0.010.836 ± 0.005
BackboneVGG160.734 ± 0.010.823 ± 0.005
Resnet340.758 ± 0.0110.84 ± 0.007
Eff.netB20.754 ± 0.010.836 ± 0.004
", + "bbox": [ + 509, + 88, + 883, + 398 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Study of hyperparameter robustness using the Gleason 2019 dataset. The default hyperparameter value is marked with bold letters. While varying one hyperparameter, all other values are set to the default value. We observe consistent and robust performance across all settings of tested hyperparameters.", + "bbox": [ + 496, + 409, + 890, + 479 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 503, + 625, + 518 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work we present \"Pionono\", a method for medical image segmentation that models the inter- and intraobserver variability explicitly with a probabilistic approximation. This is especially relevant for tasks where the labeling behavior of medical experts is known to vary widely, such as in the case of prostate cancer segmentation. Our experiments on real-world cancer segmentation data demonstrate that Pionono outperforms state-of-the-art models such as STAPLE, Probabilistic U-Net, and models based on confusion matrices. Apart from the improved predictive performance, it provides a probabilistic uncertainty estimation and the simulation of expert opinions for a given test image. This makes it a powerful tool for medical image analysis and has the potential to improve the diagnostic process considerably.", + "bbox": [ + 496, + 527, + 890, + 755 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 768, + 687, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was funded by the European Union's H2020 research and innovation programme (Marie Skłodowska Curie grant agreement No 860627, CLARIFY Project), the Spanish Ministry of Science and Innovation (project PID2019-105142RB-C22), and FEDER/Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento y Universidades (project P20_00286).", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21104", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Abdullah A Abdullah, Masoud M Hassan, and Yaseen T Mustafa. 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In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 11244-11253, 2019. 2, 3", + "[32] S.K. Warfield, K.H. Zou, and W.M. Wells. Simultaneous truth and performance level estimation (STAPLE): An algorithm for the validation of image segmentation. 23(7):903-921, 2004. 2, 4", + "[33] Yunan Wu, Arne Schmidt, Enrique Hernández-Sánchez, Rafael Molina, and Aggelos K. Katsaggelos. Combining attention-based multiple instance learning and gaussian processes for CT hemorrhage detection. 12902:582-591. 1, 2", + "[34] Le Zhang, Ryutaro Tanno, Mou-Cheng Xu, Chen Jin, Joseph Jacob, Olga Ciccarelli, Frederik Barkhof, and Daniel C." + ], + "bbox": [ + 78, + 90, + 468, + 900 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Alexander. Disentangling human error from the ground truth in segmentation of medical images. In International Conference on Neural Information Processing Systems (NeurIPS), 2020. 2, 3", + "bbox": [ + 532, + 90, + 890, + 146 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "21106", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Probabilistic Modeling of Inter- and Intra-observer Variability in Medical Image Segmentation/bf4cff8f-5588-469f-97d0-102dd2317c9c_model.json b/2023/Probabilistic Modeling of Inter- and Intra-observer Variability in Medical Image Segmentation/bf4cff8f-5588-469f-97d0-102dd2317c9c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..cceaf7dfbee8d234ecc8ea4059eb7223bd1630c0 --- /dev/null +++ b/2023/Probabilistic Modeling of Inter- and Intra-observer Variability in Medical Image Segmentation/bf4cff8f-5588-469f-97d0-102dd2317c9c_model.json @@ -0,0 +1,2904 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.13, + 0.892, + 0.177 + ], + "angle": 0, + "content": "Probabilistic Modeling of Inter- and Intra-observer Variability in Medical Image Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.255, + 0.203, + 0.717, + 0.239 + ], + "angle": 0, + "content": "Arne Schmidt, Pablo Morales-Álvarez, and Rafael Molina \nUniversidad de Granada, Granada, Spain" + }, + { + "type": "text", + "bbox": [ + 0.312, + 0.242, + 0.658, + 0.256 + ], + "angle": 0, + "content": "{arne, pablomorales, rms}@decsai.ugr.es" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.325, + 0.474, + 0.599 + ], + "angle": 0, + "content": "Medical image segmentation is a challenging task, particularly due to inter- and intra-observer variability, even between medical experts. In this paper, we propose a novel model, called Probabilistic Inter-Observed and iNtra-Observed variation NetwOrk (Pionono). It captures the labeling behavior of each rater with a multidimensional probability distribution and integrates this information with the feature maps of the image to produce probabilistic segmentation predictions. The model is optimized by variational inference and can be trained end-to-end. It outperforms state-of-the-art models such as STAPLE, Probabilistic U-Net, and models based on confusion matrices. Additionally, Pionono predicts multiple coherent segmentation maps that mimic the rater's expert opinion, which provides additional valuable information for the diagnostic process. Experiments on real-world cancer segmentation datasets demonstrate the high accuracy and efficiency of Pionono, making it a powerful tool for medical image analysis." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.631, + 0.21, + 0.646 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.47, + 0.854 + ], + "angle": 0, + "content": "Artificial Intelligence (AI) algorithms have shown remarkable progress in image analysis, holding great promise for faster and more accurate diagnostic procedures [13, 27, 26, 3]. Nevertheless, in medical practice, there exists a high degree of variability among the opinions of different medical experts, even when the same expert assesses the same data at different times. This inter- and intra-observer variability has been reported across various tasks, including MRI-based segmentation of HCC lesions [7], lung cancer segmentation in CT scans [14], and multiple fields in pathology [21, 2, 5, 22]. It leads to uncertainties when applying AI models because in contrast to other classification tasks, there is not a single ground truth." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Especially in the medical domain, the careful modeling of uncertainties in its different forms has a high priority to minimize the risk of relying on incorrect predictions" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.289, + 0.877, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.549, + 0.895, + 0.677 + ], + "angle": 0, + "content": "Figure 1. The proposed Pionono model. The labeling behavior of each rater \\(r\\) is represented by a multivariate Gaussian distribution \\(q(z|r)\\). The drawn samples \\(\\tilde{z}_j\\) are concatenated with the extracted features \\(v\\) of \\(f_{\\omega}\\) and then fed into the segmentation head \\(f_{\\theta}\\). The output simulates the inter- and intra-observer variability of annotations and is optimized using the real annotations \\(s^r\\) of each rater. The model is trained end-to-end with a combination of log-likelihood loss (LL) and Kulback Leibler (KL) divergence between posterior and prior, combined in the overall loss \\(\\mathcal{L}_{\\mathrm{ELBO}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.702, + 0.895, + 0.869 + ], + "angle": 0, + "content": "[17, 26, 15, 13, 10]. In recent years, probabilistic methods, such as Bayesian Neural Networks [8] and sparse Gaussian processes [10, 33] have gained more and more attention, because they are able to account for uncertainties in a sound manner. They showed promising results when modeling uncertainty in the network weights [8], data ambiguities [15] or attention weights [26]. Although inter- and intra-observer variability is often mentioned as a key challenge when applying AI to medical data [21, 16, 28, 18], to the best of our knowledge there is no method that explicitly models these two types of uncertainty for medical image segmentation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.895, + 0.901 + ], + "angle": 0, + "content": "To address this gap, we propose a novel approach called the Probabilistic Inter-Observer and iNtra-Observer varia" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21097" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.272 + ], + "angle": 0, + "content": "tion NetwOrk (Pionono), depicted in Figure 1. This model accurately accounts for inter- and intra-observer variability using probabilistic deep learning. Specifically, each rater's labeling behavior is represented as a probability distribution in latent space, and optimized using the log Evidence Lower BOund (ELBO) in an end-to-end training process. The variance of each rater's distribution models the intra-observer variability, while the differences between the distributions models the inter-observer variability. When two raters exhibit similar labeling behavior, their probability distributions overlap substantially, while different labeling behavior results in a small overlap of distributions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.473, + 0.422 + ], + "angle": 0, + "content": "The approach is validated in extensive experiments of prostate and breast cancer segmentation, using 'gold' labels. They reflect the expert agreement to show that our probabilistic modeling improves the predictive performance and estimates the predictive uncertainty. Furthermore, we also test its capability to model each rater's labeling behavior. As shown in the experiments, it can simulate expert opinions for a given test image in a consistent manner, providing a realistic estimation of \"what expert X would say in this case\". Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.424, + 0.47, + 0.483 + ], + "angle": 0, + "content": "- We propose Pionono, a probabilistic deep learning model that uses probability distributions in latent space to represent inter- and intra-observer variability. It can be trained with labels of multiple raters." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.484, + 0.47, + 0.572 + ], + "angle": 0, + "content": "- The model is able to provide accurate segmentation predictions (compared to the expert agreement and different expert opinions), outperforming existing state-of-the-art algorithms such as STAPLE, Probabilistic U-Net and models based on global or local confusion matrices." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.575, + 0.469, + 0.604 + ], + "angle": 0, + "content": "- Pionono provides uncertainty estimations that indicate areas where the predictions are not conclusive." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.606, + 0.469, + 0.65 + ], + "angle": 0, + "content": "- The proposed model can provide several coherent segmentation hypotheses, simulating different medical experts." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.424, + 0.47, + 0.65 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.664, + 0.22, + 0.68 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.47, + 0.734 + ], + "angle": 0, + "content": "In this section, we review existing methods of probabilistic deep learning and crowdsourcing for medical images and highlight the differences to our model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Probabilistic Deep Learning. As already indicated, probabilistic approaches such as Bayesian neural networks [8, 1, 15, 17] and sparse Gaussian processes [10, 33, 26] have shown promising results in a multitude of tasks in the medical image domain, modeling different sources of uncertainties. Often, a general predictive uncertainty is addressed using probabilistic weight parameters [1]. This uncertainty can be bisected into model and data uncertainty which originate from model parameters or data ambiguities, respectively [15]. Other approaches have modeled the uncertainty of missing instance labels in multiple instance" + }, + { + "type": "table", + "bbox": [ + 0.529, + 0.089, + 0.868, + 0.219 + ], + "angle": 0, + "content": "
Method(i) Prob. (ii) Uncert.Coh. (iii) Segm.Exp. (iv) OpinionScale
STAPLE×××✓
Prob U-Net✓✓×✓
CM global××✓✓
CM pixel××✓×
Pionono✓✓✓✓
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.227, + 0.895, + 0.34 + ], + "angle": 0, + "content": "Table 1. For AI segmentation models to achieve the best possible diagnostic support, they should address four key issues: (i) provide a probabilistic uncertainty estimation, not only a single prediction for a test image; (ii) provide multiple coherent segmentation hypotheses; (iii) simulate different expert opinions for better explainability and decision support; (iv) scale to a higher amount of raters in the case that more data from different hospitals can be integrated." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.368, + 0.892, + 0.534 + ], + "angle": 0, + "content": "learning [20, 26] or uncertainty of out of distribution samples [17]. The uncertainty in annotations has previously been addressed by the Probabilistic U-Net [13] (Prob U-Net), which encodes the labeling behavior in a latent random variable. The model is trained as a variational autoencoder with an encoder network predicting the latent distribution. This approach models a general variability in annotations but lacks the explicit modeling of inter- and intraobserver variability. Therefore, it is not able to incorporate the rater information during training and cannot simulate expert opinions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.536, + 0.892, + 0.627 + ], + "angle": 0, + "content": "Crowdsourcing. While existing crowdsourcing methods aim to capture inter-observer variability in the training labels, this variability is often not reflected in the test predictions by probabilistic outputs [13]. The intra-observer variability is often not modeled at all, although it is often mentioned as a challenge in literature [21, 16, 28, 2, 7]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.893, + 0.902 + ], + "angle": 0, + "content": "One way to handle multiple annotations is label fusion. With this method, the annotations of different raters are merged to a single set of labels. The \"Simultaneous Truth and Performance Level Estimation\" (STAPLE) mechanism performs label fusion with a probabilistic estimate of the true labels by weighting each segmentation depending upon the estimated performance level of each rater [32]. A supervised network can then be trained on these fused labels. More dedicated approaches incorporate different rater labels using confusion matrices (CM), for example for classification of image patches with Gaussian processes [18] or image segmentation with global confusion matrices [31] (CM global). In this direction, also pixel-wise confusion matrices were explored for semantic segmentation that are estimated by a dedicated deep neural network [34] (CM pixel). These models have shown promising results, but come with a conceptual problem: They assume that the pixels are statistically independent of each other, although" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21098" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.226 + ], + "angle": 0, + "content": "neighboring pixels have a high correlation. Therefore, the output of different segmentation hypotheses is not coherent. Furthermore, the predictions of the mentioned approaches [31, 34] are not modeled by a predictive distribution, but by a deterministic point estimate. While the global confusion matrix approach [31] has a limited expressiveness, the pixel-wise calculation [34] is hard to scale for multiple raters, because for each rater, a complete deep neural network must be trained and stored." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.471, + 0.288 + ], + "angle": 0, + "content": "Pionono unites the advantages of probabilistic and crowdsourcing methods. We summarize a comparison of different characteristics of Pionono and related methods for image segmentation in Table 1." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.302, + 0.176, + 0.318 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.328, + 0.469, + 0.388 + ], + "angle": 0, + "content": "In this section, we outline the background of the proposed method. It is implemented in the Pytorch [23] framework and is publicly available at https://github.com/arneschmidt/pionono_segmentation." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.398, + 0.262, + 0.413 + ], + "angle": 0, + "content": "3.1. Problem Definition" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.42, + 0.469, + 0.542 + ], + "angle": 0, + "content": "Let \\( X = \\{x_{i} \\in \\mathbb{R}^{H \\times W \\times 3}\\}_{i=1,..,N} \\) be a set of images, \\( S^{r} = \\{s_{i}^{r} \\in \\mathbb{R}^{H \\times W \\times C}\\}_{i=1,..,N} \\) the corresponding segmentation maps with image dimensions \\( H \\times W \\) and \\( C \\) the number of classes. The segmentation maps are provided by different raters \\( r \\in R = \\{1,2,..,M\\} \\). Some or all images can be segmented by multiple raters, such that some segmentation maps \\( s_{i}^{r} \\) can be empty. The proposed model does not require any overlap of the sets of annotated images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.543, + 0.47, + 0.663 + ], + "angle": 0, + "content": "If there are images available with segmentations assigned by expert agreements (so-called gold labels), the model should be able to predict a gold distribution over outputs \\( p(S^{\\mathrm{gold}}) \\) with the mean estimating the segmentation and the variance estimating the uncertainty. In any case, the model should model different segmentation hypotheses for the raters \\( \\{p(S^r); r = 1,2,\\dots,M\\} \\) for diagnostic decision support." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.673, + 0.24, + 0.689 + ], + "angle": 0, + "content": "3.2. Proposed Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.697, + 0.469, + 0.801 + ], + "angle": 0, + "content": "First, we introduce the common segmentation backbone \\( f_{\\omega} \\) with trainable weights \\( \\omega \\). We use the well-known U-Net architecture [25] with a Resnet34 feature extractor [9]. This model takes an image \\( x_{i} \\) and extracts a feature map \\( v_{i} \\in \\mathbb{R}^{H \\times W \\times L} \\) with \\( H \\times W \\) being the image resolution and \\( L \\) the dimensions of the feature vectors (\\( L = 16 \\) in the case of U-Net). We denote the feature extraction as" + }, + { + "type": "equation", + "bbox": [ + 0.228, + 0.815, + 0.469, + 0.831 + ], + "angle": 0, + "content": "\\[\nv _ {i} = f _ {\\omega} \\left(x _ {i}\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.843, + 0.469, + 0.873 + ], + "angle": 0, + "content": "Based on these feature vectors, we could perform segmentation with a segmentation head \\( f_{\\theta} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.23, + 0.886, + 0.469, + 0.902 + ], + "angle": 0, + "content": "\\[\ns _ {i} = f _ {\\theta} \\left(v _ {i}\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.304 + ], + "angle": 0, + "content": "Now we extend this model to incorporate the inter- and intra-observer variation. The segmentation maps are influenced by the rater's experience, assessment, and personal choices. To encode the labeling behavior, we use a random vector \\( z \\in \\mathbb{R}^D \\). In practice, \\( D = 8 \\) are enough dimensions to reflect different labeling behaviors. We define a prior distribution \\( p(z) = \\mathcal{N}(z|0, \\sigma_{\\mathrm{prior}} * I) \\) which encodes a generic labeling behavior without further information about the rater. It is possible to encode prior knowledge in this distribution, but we present a general model and leave this for future work. We set \\( \\sigma_{\\mathrm{prior}}^2 = 2.0 \\), because we observe a realistic variability in the output for this value. In section 4.5 we prove that the model is robust for different settings of hyperparameters \\( D \\) and \\( \\sigma_{\\mathrm{prior}}^2 \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.304, + 0.892, + 0.348 + ], + "angle": 0, + "content": "Now, the posterior distribution of \\( p(z|r) \\) that depends on the rater \\( r \\) should be found. We approximate it with one multivariate Gaussian distribution for each rater:" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.362, + 0.892, + 0.379 + ], + "angle": 0, + "content": "\\[\nq (z | r) = \\mathcal {N} \\left(z \\mid \\mu^ {r}, \\Sigma^ {r}\\right) \\forall r = 1,.., M \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.39, + 0.892, + 0.527 + ], + "angle": 0, + "content": "where \\(\\{\\mu^r,\\Sigma^r\\}^{r = 1,\\dots ,M}\\) are trainable parameters. The variance of each distribution \\(q(z|r)\\) models the intra - observer variability. The differences between the distributions for different raters model the inter - observer variability. To obtain the predictive gold distribution we add another 'rater' \\(r = M + 1\\) represented by an additional gold distribution \\(q\\) which is trained with the available gold segmentations. During prediction, this distribution provides the estimated agreement between experts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.528, + 0.892, + 0.587 + ], + "angle": 0, + "content": "The segmentation head \\( f_{\\theta} \\), parametrized by weights \\( \\theta \\) must be adapted to take the random vector \\( z \\) into account. The approximated predictive distribution is then obtained by:" + }, + { + "type": "equation", + "bbox": [ + 0.562, + 0.588, + 0.892, + 0.62 + ], + "angle": 0, + "content": "\\[\nq \\left(s _ {i} \\mid x _ {i}, r, \\omega , \\theta\\right) = \\int f _ {\\theta} \\left(v _ {i}, z\\right) q (z | r) d z. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.892, + 0.657 + ], + "angle": 0, + "content": "The closed-form calculation is not feasible and therefore we approximate it by Monte Carlo (MC) sampling:" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.669, + 0.892, + 0.687 + ], + "angle": 0, + "content": "\\[\n\\tilde {s} _ {i, j} | x _ {i}, r = f _ {\\theta} \\left(v _ {i}, \\tilde {z} _ {j}\\right); \\tilde {z} _ {j} \\sim q (z | r) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.699, + 0.892, + 0.789 + ], + "angle": 0, + "content": "with \\( j = 1,\\dots,K \\) indexing the MC samples. In practice, we concatenate the feature maps \\( v_{i} \\) and the latent vector \\( \\tilde{z}_j \\) which is broadcasted to the image size, leading to a feature map with dimensions \\( H\\times W\\times (L + D) \\). The segmentation head consists of three layers with 1x1 convolutions and 16 filters in the first two layers and \\( C \\) filters in the last layer." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.8, + 0.605, + 0.816 + ], + "angle": 0, + "content": "3.3. Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.824, + 0.892, + 0.901 + ], + "angle": 0, + "content": "First, all posterior distributions \\( q(z|r) \\) are initialized randomly. Each initial value of the mean vectors \\( \\mu^r \\) is independently drawn from a distribution \\( \\mathcal{N}(0,\\sigma_{\\mathrm{post}}^2) \\). We set \\( \\sigma_{\\mathrm{post}}^2 = 8 \\), because this initializes the mean vectors sufficiently different for a good optimization. In section 4.5 we" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21099" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.468, + 0.121 + ], + "angle": 0, + "content": "show, that the model is robust to other settings of this value. The covariance matrices \\(\\Sigma^r\\) are initialized with \\(\\sigma_{\\mathrm{prior}} * I\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.121, + 0.468, + 0.152 + ], + "angle": 0, + "content": "To optimize the parameters \\(\\{\\mu^r,\\Sigma^r\\}^{r = 1,\\dots ,M}\\) of the probability distribution \\(q(z|r)\\), we maximize the ELBO:" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.163, + 0.468, + 0.194 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {E L B O} = \\mathbb {E} _ {q} \\log p \\left(S ^ {r} | X, r, \\omega , \\theta\\right) - \\lambda K L (q (Z | r) | p (Z)). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.195, + 0.468, + 0.51 + ], + "angle": 0, + "content": "with distribution \\( q \\) as defined in eq. 4. The first term defines a log-likelihood (LL) loss, making the model fit to the annotations of each rater. The second term defines the KL-divergence between the posterior distribution \\( q(Z|r) \\) and the prior \\( p(Z) \\) and works as a regularization of the latent distributions. The factor \\( \\lambda \\) weights the regularization term and is set to 0.0005 to balance the magnitudes of the log-likelihood and the KL (we will check the robustness of this hyperparameter in Section 4.5). While the KL term can be optimized analytically, the log likelihood term must be approximated. We use the reparametrization trick [12] to split each probabilistic sample \\( \\tilde{z}^r \\) into its probabilistic component and deterministic parameters \\( \\mu^r \\) and \\( \\Sigma^r \\). These parameters can be optimized by backpropagation of gradients, together with the CNN parameters \\( \\omega \\) and \\( \\theta \\). For numerical stability, we train the covariance matrix parameters by using the lower triangular matrix \\( L \\) of the Cholesky decomposition \\( \\Sigma^r = L^r L^{r^\\top} \\). The log-likelihood can be optimized with standard methods like the categorical cross-entropy. We found that the general dice loss [30] leads to better results, so all final results are reported with this loss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.468, + 0.633 + ], + "angle": 0, + "content": "We use the Adam optimizer [11] for 100 epochs with a learning rate of 0.0001. The model parameters \\(\\mu^r, \\Sigma^r\\) are optimized with a higher learning rate of \\(\\nu = 0.02\\), because else the gradient was not strong enough to properly learn the rater distributions. We tested \\(\\nu = 0.01, 0.02, 0.04\\) and include the results in section 4.5. Both learning rates are decreased after 40 epochs by dividing them by 1.1 in each epoch." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.642, + 0.194, + 0.658 + ], + "angle": 0, + "content": "3.4. Predicting" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.665, + 0.468, + 0.696 + ], + "angle": 0, + "content": "For a test image \\( x^{*} \\), the predictive gold distribution can again be obtained by drawing Monte-Carlo samples" + }, + { + "type": "equation", + "bbox": [ + 0.125, + 0.707, + 0.468, + 0.725 + ], + "angle": 0, + "content": "\\[\n\\tilde {s} _ {j} ^ {*} \\mid x ^ {*}, r = f _ {\\theta} \\left(v ^ {*}, \\tilde {z} _ {j}\\right); \\tilde {z} _ {j} \\sim q (z | r = M + 1) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.735, + 0.468, + 0.825 + ], + "angle": 0, + "content": "with \\( j = 1,..,K \\) indexing the MC samples and \\( q(z|r = M + 1) \\) representing the gold distribution as described in section 3.2. The mean of these samples provides the segmentation hypothesis that approximates the expert agreements. The variance of the samples indicates uncertainties in the prediction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.468, + 0.903 + ], + "angle": 0, + "content": "Furthermore, the model is able to simulate intraobserver variations of rater \\(r^\\prime\\) by drawing multiple samples of the distribution \\(\\tilde{z}_j^{\\prime}\\sim q(z|r = r^{\\prime})\\) for the final prediction. The inter-observer variations between rater \\(r^\\prime\\) and \\(r''\\) can be simulated by using samples \\(\\tilde{z}_j^\\prime \\sim q(z|r = r^\\prime)\\) and" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.89, + 0.121 + ], + "angle": 0, + "content": "\\(\\tilde{z}_k^{\\prime \\prime}\\sim q(z|r = r^{\\prime \\prime})\\) and finally taking the mean of both output distributions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.122, + 0.892, + 0.258 + ], + "angle": 0, + "content": "The model can therefore simulate expert opinions for a given test image. Other AI methods typically aggregate the expertise provided by all annotators to make predictions (e.g., using STAPLE, Prob U-Net). However, in such approaches, the knowledge of highly specialized experts can be diluted or lost among the less experienced annotators' knowledge. In our framework, we provide consistent predictions for each individual expert, thereby preserving their unique expertise and contributions." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.27, + 0.632, + 0.287 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.296, + 0.892, + 0.401 + ], + "angle": 0, + "content": "In several experiments we demonstrate that the uncertainty estimation of the model indicates areas of false predictions (4.2), the model is able to capture the inter and intra-observer variations (4.3) and outperforms other related methods (4.4). Additionally, we analyze the robustness to hyperparameters (4.5), required resources (4.6), and limitations (4.7)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.41, + 0.602, + 0.424 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.433, + 0.892, + 0.644 + ], + "angle": 0, + "content": "For empirical validation, three public histopathological datasets were used. The first dataset, \"Gleason 2019\" [22] was published as a MICCAI grand challenge for pathology and includes 333 Tissue Micro Arrays (TMA) of prostate cancer, labeled by 6 different pathologists. The TMAs were scanned with a magnification of \\(40\\mathrm{x}\\) and have a size of approximately \\(4000 \\times 4000\\) pixels. Of the 333 images, 244 are publicly available with labels (the test annotations of the challenge are not available). Each pathologist annotated between 61 and 241 TMAs with segmentation masks and the gold labels were obtained using the STAPLE algorithm [32], following the original work of the dataset [22]. We resize all images to \\(1024 \\times 1024\\) pixels and create 4 cross-validation splits." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.892, + 0.825 + ], + "angle": 0, + "content": "The second dataset, which we will refer to as \"Arvaniti TMA\" was published in 2018 [4] and includes a total of 886 TMAs of prostate cancer of which 245 images were annotated by two pathologists (while the other images only have annotations of one pathologist and are therefore discarded in our study). The TMAs were scanned with a magnification of \\(40\\mathrm{x}\\) but the scanned area is smaller than for the Gleason19 dataset. The images have a resolution of \\(3100\\times 3100\\) pixels and we resize them to \\(512\\times 512\\) such that the magnification matches the resized images of the Gleason 2019 dataset. Again, we split the dataset into 4 cross-validation splits for the experimental setup." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "For the classification of prostate cancer, the tissue is segmented in the Gleason Grading (GG) scheme. The classes are 'Non-cancerous' (NC), 'Gleason 3' (G3), 'Gleason 4' (G4), and 'Gleason 5' (G5) depending on the architectural growth patterns of the tumor [28, 29]. To visualize the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21100" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.147, + 0.089, + 0.208, + 0.136 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.151, + 0.142, + 0.2, + 0.152 + ], + "angle": 0, + "content": "(a) Image" + }, + { + "type": "image", + "bbox": [ + 0.214, + 0.089, + 0.27, + 0.136 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.278, + 0.089, + 0.337, + 0.135 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.345, + 0.089, + 0.404, + 0.135 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.147, + 0.155, + 0.208, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.155, + 0.269, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.279, + 0.142, + 0.342, + 0.151 + ], + "angle": 0, + "content": "c)Pred.Gold" + }, + { + "type": "image", + "bbox": [ + 0.345, + 0.155, + 0.403, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.151, + 0.205, + 0.198, + 0.216 + ], + "angle": 0, + "content": "(e) Image" + }, + { + "type": "image_caption", + "bbox": [ + 0.212, + 0.205, + 0.27, + 0.216 + ], + "angle": 0, + "content": "(f) GT Gold" + }, + { + "type": "image_caption", + "bbox": [ + 0.275, + 0.205, + 0.341, + 0.216 + ], + "angle": 0, + "content": "(g)Pred.Gold" + }, + { + "type": "image_caption", + "bbox": [ + 0.347, + 0.205, + 0.399, + 0.216 + ], + "angle": 0, + "content": "(h) Uncert." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.227, + 0.47, + 0.339 + ], + "angle": 0, + "content": "Figure 2. Gold prediction and uncertainty of the Pionono model. The first row shows a confident prediction as the uncertainty in 2d is low (white) for almost all the area. Indeed, the segmentation prediction 2c is very accurate, see the ground truth (GT) 2b. The second row shows an example of an uncertain prediction. Some parts of the area classified as G3 (yellow) in \\(2\\mathrm{g}\\) are labeled as G4 in the ground truth 2f. These areas are estimated with a high uncertainty (black) in \\(2\\mathrm{h}\\), warning that these predictions are unreliable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.469, + 0.546 + ], + "angle": 0, + "content": "segmentations we use the colors: green for NC, yellow for G3, orange for G4, and red for G5. For the evaluation of algorithms for prostate cancer classification, previous works used the Cohen's kappa coefficient [22, 4, 28] which measures the agreement of two raters or a rater and an AI model. To compare to previously reported results for the two datasets, we use the unweighted Cohen's kappa \\(\\kappa\\) for the Gleason 2019 dataset [22] and the quadratic weighted Cohen's kappa \\(\\kappa\\) for the Arvaniti TMA dataset [4]. The main difference is that the quadratic kappa takes the class order into account and weighs the errors based on the quadratic distance of the predicted and the real class." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.548, + 0.47, + 0.668 + ], + "angle": 0, + "content": "The third dataset contains 151 WSIs for breast cancer segmentation that were sliced into 11,836 patches of \\(512 \\times 512\\) pixels annotated by 25 raters [3, 19]. We will refer to this dataset as \"bc segmentation\". The tissue was segmented into \"tumor\", \"inflammation\", \"necrosis\", \"stroma\", and \"other\". Here, the gold labels were obtained by an actual discussion of experts. We use the predefined train/validation/test splits [19]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.669, + 0.469, + 0.745 + ], + "angle": 0, + "content": "For all datasets we use image augmentation with the albumenations library [6] by applying random flip, rotation, shear, zoom, blur, and shifts in brightness, contrast, hue, and saturation. This leads to a broad range of realistic transformations of the image to avoid overfitting." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.756, + 0.291, + 0.772 + ], + "angle": 0, + "content": "4.2. Uncertainty estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The proposed model provides probabilistic predictions that allow an accurate assessment of the predictive uncertainty. Fig. 2 shows the model predictions and uncertainties obtained with the gold distribution as described in section 3.2. For the first image (2a), the prediction of the model (2c) is accurate and matches the real gold annotation (2b) very well. The uncertainty (2d) for this predictions is low (white), which means that there is a low risk of a wrong" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.242 + ], + "angle": 0, + "content": "prediction. Therefore, the model correctly indicates that this prediction is reliable. For the second image 2e, some areas that are predicted as G3 (yellow) in \\((2\\mathrm{g})\\) are actually G4 in the ground truth gold prediction (2f). The model's uncertainty estimation indicates that this prediction is not reliable: the misclassified areas are marked with a high uncertainty (dark) in the image (2h). Therefore, the probabilistic output adds valuable information to the diagnostic process. It estimates if a prediction is reliable - or unreliable and should be double-checked." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.255, + 0.807, + 0.27 + ], + "angle": 0, + "content": "4.3. Inter- and Intra-observer Variation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.28, + 0.892, + 0.385 + ], + "angle": 0, + "content": "The Pionono model is able to capture the inter- and intraobserver variability. This accurate probabilistic modeling of the annotations does not only improve the predictive results (see section 4.4), but also allows to simulate specific experts at test time. In this section, we empirically show that the model learns the different label behaviors of the raters and is able to reproduce them." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.892, + 0.583 + ], + "angle": 0, + "content": "In Fig. 3a we plot the inter-observer variations between the raters. The figure shows that there is indeed a high variability among the raters, with a Cohen's kappa ranging from 0.36 to 0.72. The simulated test predictions by Pionono show a higher agreement with each rater than the average agreement of the other raters, except for rater 2. For two raters (1 and 5), the simulated predictions of Pionono are even more than 15 percentage points higher than the average rater agreement. We also measured the IoU metric, which was 0.574, 0.540, 0.619, 0.649, 0.692, 0.507, for the 6 raters respectively, compared to a mean inter-pathologist IoU of 0.361. The results confirm that most raters are modeled with high accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Fig. 3b shows the posterior distributions \\( q(z|r) \\) of the proposed model, encoding the labeling behavior of each rater. The following observations confirm, that these learned distributions approximate well the real-world labeling behavior of the raters: (i) The four raters 3, 4, 5 and 6 show a high overlap of the distributions and corresponding to a high labeling agreement shown in Fig. 3a. (ii) The gold distribution (simulating raters agreement) overlaps significantly with the distribution of these four raters. (iii) The distribution of rater 2 is far away from all other distributions. This rater shows a different labeling behavior due to frequent under-segmentation of images, assigning the 'background' class to areas that contain tissue. (iv) Raters 1 and 6 often deviate from the other raters, especially for the differentiation of classes G3 and G4. Their distribution accordingly has a smaller overlap with the gold distribution and the other raters. Fig. 4 shows some visual image examples of Pionono test predictions, simulating each rater \\( r \\) by drawing samples from the corresponding distribution \\( q(z|r) \\) and then taking the mean of the output samples. The examples confirm that the rater differences are modeled well." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21101" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.09, + 0.094, + 0.27, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.243, + 0.246, + 0.254 + ], + "angle": 0, + "content": "(a) Rater simulation statistic" + }, + { + "type": "image", + "bbox": [ + 0.286, + 0.094, + 0.468, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.323, + 0.244, + 0.431, + 0.254 + ], + "angle": 0, + "content": "(b) Latent distributions" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.26, + 0.47, + 0.44 + ], + "angle": 0, + "content": "Figure 3. Analyzing the labeling behavior. In Fig. (a) the agreement of each rater with all other raters is depicted, measured by the unweighted Cohen's Kappa of the true labels [22]. The mean agreement of each rater with all other raters is represented by a black dot and the agreement with Piononos test predictions, simulating the corresponding rater, by a star. This confirms that the model accurately models each rater, reaching even a higher agreement than the other rater's average, except for rater 2. Fig. (b) shows the first two dimensions of the posterior distributions \\( q(z|r) \\) with mean and covariance after training. The distributions of raters 3, 4, 5 and 6 overlap significantly with the gold distribution and with each other, indicating a similar labeling behavior. Indeed, these raters show the highest labeling agreement in Fig. (a)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.469, + 0.646 + ], + "angle": 0, + "content": "Next, we analyze the intra-observer variations. As the dataset does not contain multiple annotations of the same rater for the same image, the assessment of this quality is more difficult. Still, certain intra-observer variability can be assessed by observing the general labeling behavior of one annotator. For example, rater 6 tends to over-assign class G5 (red), and rater 2 tends to not segment all image parts that contain tissue. Interestingly, these intra-observer variations are present in the model predictions when multiple samples are drawn from their corresponding distribution. Fig. 5 shows visual examples of the simulated variations of raters 2 and 6." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.657, + 0.262, + 0.673 + ], + "angle": 0, + "content": "4.4. Model Comparison" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.681, + 0.469, + 0.786 + ], + "angle": 0, + "content": "The proposed model is compared to previously reported results and several state-of-the-art approaches (see section 2) for medical image segmentation with labels from multiple raters. For fair comparison, we use the same backbone architecture1, epochs, learning rate, and optimizer for all experiments. We have tuned the model-specific hyperparameters to obtain the best possible results for each method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.787, + 0.469, + 0.877 + ], + "angle": 0, + "content": "First, we perform experiments with the Gleason 2019 dataset with a 4-fold crossvalidation. For comparison with previous works, we report the unweighted Cohen's kappa metric comparing gold predictions with gold ground truth. Additionally, we report the accuracy. As the results in Table 2 show, the proposed Pionono model outperforms the previ" + }, + { + "type": "image", + "bbox": [ + 0.55, + 0.088, + 0.613, + 0.136 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.555, + 0.142, + 0.602, + 0.153 + ], + "angle": 0, + "content": "(a) Image" + }, + { + "type": "image", + "bbox": [ + 0.555, + 0.154, + 0.61, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.629, + 0.153, + 0.683, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.549, + 0.205, + 0.614, + 0.216 + ], + "angle": 0, + "content": "(c) \\(\\mathrm{GT}r = 1\\)" + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.218, + 0.611, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.625, + 0.206, + 0.687, + 0.215 + ], + "angle": 0, + "content": "(d) PR \\(r = 1\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.552, + 0.268, + 0.615, + 0.28 + ], + "angle": 0, + "content": "(g) \\(\\mathrm{GT}r = 2\\)" + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.282, + 0.611, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.629, + 0.218, + 0.684, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.625, + 0.268, + 0.686, + 0.279 + ], + "angle": 0, + "content": "(h) \\(\\mathrm{PR}r = 2\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.55, + 0.332, + 0.615, + 0.342 + ], + "angle": 0, + "content": "(k) GT \\(r = 3\\)" + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.344, + 0.608, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.626, + 0.332, + 0.687, + 0.342 + ], + "angle": 0, + "content": "(1) PR \\(r = 3\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.55, + 0.397, + 0.614, + 0.407 + ], + "angle": 0, + "content": "(o) \\(\\mathrm{GT}r = 4\\)" + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.408, + 0.611, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.628, + 0.408, + 0.683, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.55, + 0.46, + 0.614, + 0.469 + ], + "angle": 0, + "content": "(s) GT \\(r = 5\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.626, + 0.46, + 0.686, + 0.469 + ], + "angle": 0, + "content": "(t) PR \\(r = 5\\)" + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.472, + 0.61, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.548, + 0.524, + 0.614, + 0.533 + ], + "angle": 0, + "content": "(w) GT \\( r = 6 \\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.629, + 0.461, + 0.685, + 0.469 + ], + "angle": 0, + "content": "(t) PR \\(r = 5\\)" + }, + { + "type": "image", + "bbox": [ + 0.629, + 0.472, + 0.684, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.624, + 0.524, + 0.688, + 0.533 + ], + "angle": 0, + "content": "(x) PR \\(r = 6\\)" + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.09, + 0.769, + 0.135 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.713, + 0.142, + 0.76, + 0.152 + ], + "angle": 0, + "content": "(b) Image" + }, + { + "type": "image", + "bbox": [ + 0.712, + 0.155, + 0.766, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.783, + 0.206, + 0.842, + 0.215 + ], + "angle": 0, + "content": "(f) \\(\\mathrm{PR}r = 1\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.713, + 0.206, + 0.77, + 0.215 + ], + "angle": 0, + "content": "e) GT \\(r = 1\\)" + }, + { + "type": "image", + "bbox": [ + 0.712, + 0.218, + 0.767, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.786, + 0.206, + 0.841, + 0.215 + ], + "angle": 0, + "content": "(f) \\(\\mathrm{PR}r = 1\\)" + }, + { + "type": "image", + "bbox": [ + 0.786, + 0.218, + 0.841, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.707, + 0.268, + 0.771, + 0.279 + ], + "angle": 0, + "content": "(i) \\(\\mathrm{GT}r = 2\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.786, + 0.268, + 0.843, + 0.279 + ], + "angle": 0, + "content": "j) PR \\(r = 2\\)" + }, + { + "type": "image", + "bbox": [ + 0.712, + 0.283, + 0.767, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.785, + 0.284, + 0.841, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.706, + 0.333, + 0.772, + 0.342 + ], + "angle": 0, + "content": "(m) \\(\\mathrm{GTr} = 3\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.785, + 0.333, + 0.844, + 0.342 + ], + "angle": 0, + "content": "n) PR \\(r = 3\\)" + }, + { + "type": "image", + "bbox": [ + 0.713, + 0.346, + 0.766, + 0.385 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.785, + 0.347, + 0.841, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.705, + 0.397, + 0.771, + 0.407 + ], + "angle": 0, + "content": "(q) GT \\(r = 4\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.785, + 0.397, + 0.843, + 0.406 + ], + "angle": 0, + "content": "(r) PR \\(r = 4\\)" + }, + { + "type": "image", + "bbox": [ + 0.711, + 0.41, + 0.767, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.786, + 0.41, + 0.841, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.706, + 0.46, + 0.771, + 0.469 + ], + "angle": 0, + "content": "(u) GT \\(r = 5\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.786, + 0.46, + 0.843, + 0.469 + ], + "angle": 0, + "content": "v) PR \\(r = 5\\)" + }, + { + "type": "image", + "bbox": [ + 0.712, + 0.475, + 0.766, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.786, + 0.475, + 0.841, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.706, + 0.524, + 0.771, + 0.533 + ], + "angle": 0, + "content": "(y) GT \\(r = 6\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.786, + 0.524, + 0.844, + 0.533 + ], + "angle": 0, + "content": "z) PR \\(r = 6\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.534, + 0.892, + 0.63 + ], + "angle": 0, + "content": "Figure 4. Inter-observer variations estimated by Pionono. For two test images we depict the ground truth (GT) segmentations of all raters and the predicted segmentations (PR), simulating each rater. The proposed model is able to simulate certain labeling behavior like the tendency of assigning class G5 (red) for raters 2 and 6 (see g and w) where other raters assigned G4 (orange). Furthermore, the model captures the under-segmentation by rater 2 (see i)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.779 + ], + "angle": 0, + "content": "ously reported results [22, 24], including the winner of the Gleason 2019 challenge [24], by a large margin of over 20 percentage points. This accounts for the exact modeling of the raters by Pionono, but also for the different choices of backbone architecture and other training details. Compared to other state-of-the-art methods with the same architecture and training details, Pionono still shows a considerably better performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Next, we compare the generalization capabilities of the models by using the Arvaniti TMA dataset as an external test set, as reported in Table 3. This means, that the models are trained with all images from Gleason 2019 and tested with all images from Arvaniti TMA. As the Arvaniti TMA dataset does not contain gold labels, the model's gold predictions are compared to both raters independently, as previously done by Arvaniti et al. [4]. We observe that the model" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.414, + 0.9 + ], + "angle": 0, + "content": "1Only the model CM pixel uses ResNet18 to fit on the GPU." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21102" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.129, + 0.088, + 0.191, + 0.136 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.135, + 0.143, + 0.182, + 0.151 + ], + "angle": 0, + "content": "(a) Image" + }, + { + "type": "image", + "bbox": [ + 0.205, + 0.089, + 0.257, + 0.133 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.2, + 0.142, + 0.266, + 0.151 + ], + "angle": 0, + "content": "(b) PR \\(r = 6\\)" + }, + { + "type": "image", + "bbox": [ + 0.205, + 0.155, + 0.258, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.126, + 0.205, + 0.192, + 0.215 + ], + "angle": 0, + "content": "(e) \\(\\mathrm{GT}r = 6\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.202, + 0.205, + 0.265, + 0.215 + ], + "angle": 0, + "content": "(f) PR \\(r = 6\\)" + }, + { + "type": "image", + "bbox": [ + 0.205, + 0.217, + 0.258, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.201, + 0.268, + 0.265, + 0.279 + ], + "angle": 0, + "content": "(i) PR \\(r = 6\\)" + }, + { + "type": "image", + "bbox": [ + 0.205, + 0.281, + 0.258, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.2, + 0.333, + 0.266, + 0.343 + ], + "angle": 0, + "content": "(k) PR \\(r = 6\\)" + }, + { + "type": "image", + "bbox": [ + 0.205, + 0.345, + 0.258, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.199, + 0.396, + 0.267, + 0.406 + ], + "angle": 0, + "content": "(m) PR \\(r = 6\\)" + }, + { + "type": "image", + "bbox": [ + 0.286, + 0.089, + 0.348, + 0.135 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.292, + 0.142, + 0.339, + 0.151 + ], + "angle": 0, + "content": "(c) Image" + }, + { + "type": "image", + "bbox": [ + 0.29, + 0.154, + 0.345, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.282, + 0.205, + 0.349, + 0.215 + ], + "angle": 0, + "content": "(g) \\(\\mathrm{GT}r = 2\\)" + }, + { + "type": "image", + "bbox": [ + 0.365, + 0.091, + 0.421, + 0.133 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.357, + 0.142, + 0.422, + 0.151 + ], + "angle": 0, + "content": "(d) PR \\(r = 2\\)" + }, + { + "type": "image", + "bbox": [ + 0.365, + 0.154, + 0.419, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.358, + 0.205, + 0.422, + 0.215 + ], + "angle": 0, + "content": "(h) PR \\(r = 2\\)" + }, + { + "type": "image", + "bbox": [ + 0.371, + 0.217, + 0.416, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.362, + 0.268, + 0.424, + 0.279 + ], + "angle": 0, + "content": "(j) PR \\(r = 2\\)" + }, + { + "type": "image", + "bbox": [ + 0.37, + 0.282, + 0.423, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.361, + 0.333, + 0.424, + 0.342 + ], + "angle": 0, + "content": "(1) PR \\(r = 2\\)" + }, + { + "type": "image", + "bbox": [ + 0.37, + 0.345, + 0.422, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.36, + 0.396, + 0.426, + 0.406 + ], + "angle": 0, + "content": "(n) PR \\(r = 2\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.407, + 0.47, + 0.614 + ], + "angle": 0, + "content": "Figure 5. Intra-observer variations estimated by the Pionono model. For two example images we depict the true annotation (GT) of two different raters (\\(r = 2\\) and \\(r = 6\\)). On the right sides we show different coherent segmentation predictions (PR) for each rater estimated by our model. The differences in each column reflect possible intra-observer variations. The first example (a) shows that rater 6 might show some variations in the assigned classes. While the segmentation prediction (b) is composed by classes G3 (yellow) and G4 (orange), the segmentation sample (f) only consists of G5 (red). Indeed, this rater often assigns class G5 (red) in areas where other raters assign G4 (see Fig. 4) such that this is a plausible hypothesis. In the second example (c) we see variations due to the under-segmentation of rater 2 in some images. Our model captures this behavior and provides hypothesis of more (d) or less (j) segmentation of class G3 (yellow)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.641, + 0.469, + 0.701 + ], + "angle": 0, + "content": "generalizes better than all other methods, achieving a higher agreement in terms of Cohen's quadratic kappa with both raters. In terms of accuracy, only 'CM global' outperforms Pionono by a small margin." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.469, + 0.808 + ], + "angle": 0, + "content": "In the third experiment, we use the Arvaniti TMA dataset for training and testing with the two rater annotations. Again, the proposed model is able to outperform previously reported results as well as other state-of-the-art methods in terms of quadratic Cohen's kappa. In terms of accuracy, only the \"Prob U-Net\" model obtains a better result for rater 1, while Pionono reaches the best accuracy for rater 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.87 + ], + "angle": 0, + "content": "To validate the model on a different kind of data, we performed the fourth experiment on the \"bc segmentation\" dataset [3]. The results are reported in Table 5 and confirm the strong performance of the proposed Pionono model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The results support our hypothesis that explicitly modeling the inter- and intra-observer variations improves the" + }, + { + "type": "table", + "bbox": [ + 0.535, + 0.089, + 0.859, + 0.223 + ], + "angle": 0, + "content": "
MethodUnweighted κAccuracy
Nir et al. [22]0.51N.A.
Qiu et al. [24]0.524N.A.
STAPLE0.75 ± 0.0060.834 ± 0.005
Prob U-Net0.741 ± 0.0020.83 ± 0.001
CM global0.721 ± 0.0180.814 ± 0.012
CM pixel0.692 ± 0.0190.791 ± 0.012
Pionono0.758 ± 0.0110.84 ± 0.007
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.233, + 0.892, + 0.273 + ], + "angle": 0, + "content": "Table 2. Cohens Kappa Comparison for the 4-fold crossvalidation experiment of the Gleason 2019 dataset, reported by mean and standard error." + }, + { + "type": "table", + "bbox": [ + 0.524, + 0.285, + 0.869, + 0.479 + ], + "angle": 0, + "content": "
Rater 1 MethodQuadratic κAccuracy
STAPLE0.629 ± 0.0020.718 ± 0.001
Prob U-Net0.629 ± 0.0050.73 ± 0.003
CM global0.624 ± 0.0030.728 ± 0.002
CM pixel0.618 ± 0.0070.72 ± 0.004
Pionono0.641 ± 0.0060.736 ± 0.004
Rater 2 MethodQuadratic κAccuracy
STAPLE0.563 ± 0.0020.621 ± 0.002
Prob U-Net0.56 ± 0.0030.626 ± 0.006
CM global0.557 ± 0.0030.638 ± 0.006
CM pixel0.551 ± 0.0060.626 ± 0.008
Pionono0.569 ± 0.0050.633 ± 0.005
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.49, + 0.892, + 0.532 + ], + "angle": 0, + "content": "Table 3. Cohens Kappa Comparison with the two raters of the Arvaniti TMA dataset trained on the Gleason 2019 dataset, reported by mean and standard error." + }, + { + "type": "table", + "bbox": [ + 0.52, + 0.544, + 0.875, + 0.793 + ], + "angle": 0, + "content": "
Rater 1 MethodQuadratic κAccuracy
Arvaniti et al. [4]0.55N.A.
Silva-R. et al. [28]0.536N.A.
supervised0.658 ± 0.0250.734 ± 0.008
Prob U-Net0.697 ± 0.0080.762 ± 0.004
CM global0.677 ± 0.0280.745 ± 0.011
CM pixel0.647 ± 0.0160.731 ± 0.012
Pionono0.716 ± 0.0110.751 ± 0.02
Rater 2 MethodQuadratic κAccuracy
Arvaniti0.49N.A.
supervised0.521 ± 0.0140.678 ± 0.014
Prob U-Net0.534 ± 0.0020.68 ± 0.005
CM global0.533 ± 0.0220.676 ± 0.011
CM pixel0.508 ± 0.0130.663 ± 0.008
Pionono0.548 ± 0.0080.697 ± 0.012
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.804, + 0.892, + 0.845 + ], + "angle": 0, + "content": "Table 4. Cohens Kappa Comparison with the two raters of the Arvaniti TMA dataset trained and validated by 4-fold crossvalidation of the Arvaniti data, reported by mean and standard error." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "model's performance. Pionono takes the different labeling behavior into account during training which leads to accu" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21103" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.118, + 0.089, + 0.432, + 0.188 + ], + "angle": 0, + "content": "
MethodUnweighted κAccuracy
STAPLE0.647 ± 0.0030.755 ± 0.002
Prob U-Net0.685 ± 0.0230.734 ± 0.004
CM global0.654 ± 0.0050.761 ± 0.004
CM pixel0.689 ± 0.0100.784 ± 0.007
Pionono0.711 ± 0.0020.799 ± 0.001
" + }, + { + "type": "table_caption", + "bbox": [ + 0.094, + 0.198, + 0.452, + 0.227 + ], + "angle": 0, + "content": "Table 5. Results for the breast cancer segmentation of WSIs, reported as mean and standard error of 4 runs." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.258, + 0.188, + 0.273 + ], + "angle": 0, + "content": "rate predictions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.29, + 0.419, + 0.307 + ], + "angle": 0, + "content": "4.5. Robustness to Hyperparameter Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.316, + 0.47, + 0.513 + ], + "angle": 0, + "content": "To measure the sensitivity of the model regarding different hyperparameters, we performed studies on the 4-fold cross-validation experiment of the Gleason 19 dataset. Table 6 shows that the model is robust to variations of all analyzed hyperparameters. We observe minor performance drops for different values of the regularization factor \\(\\lambda\\) and the initialization variance \\(\\sigma_{\\mathrm{post}}^2\\). In both cases, wrong choices of the hyperparameters can hinder the correct optimization of the latent distributions. Furthermore, we tested different backbone architectures, indicating a limited performance with a VGG16 backbone. Overall the performance drops are minor and for all other settings, the model shows highly accurate results of \\(\\kappa >0.75\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.529, + 0.267, + 0.545 + ], + "angle": 0, + "content": "4.6. Required Resources" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.555, + 0.47, + 0.707 + ], + "angle": 0, + "content": "For the Gleason 2019 dataset with images of \\(1024 \\times 1024\\), the model can be trained with a batch size of 3 on a single NVIDIA GeForce RTX 3090 with 24Gb memory. The training takes less than 1.5h in total and test predictions less than 0.2s per image. The trained model occupies less than 350Mb when saved to the disk. As each additional annotator adds only one additional vector \\(\\mu^r \\in \\mathbb{R}^8\\) and one covariance matrix \\(\\Sigma^r \\in \\mathbb{R}^{8 \\times 8}\\), it is scalable to a large number of annotators. The model's quick runtime and excellent scalability make it easily applicable in clinical practice." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.724, + 0.204, + 0.739 + ], + "angle": 0, + "content": "4.7. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.901 + ], + "angle": 0, + "content": "As semantic segmentation itself is a challenging task, some details of the annotator segmentations are not captured well by the model, such as the variations of class NC (green) in the GT of Fig. 4d - 4x or class G4 (orange) in the GT of Fig. 4f - 4z. Here, the model tends to predict similar shapes for the raters. A possible solution is to use more layers in the segmentation head \\( f_{\\theta} \\) with a wider kernel (e.g. \\( 5 \\times 5 \\) convolutions). This would increase the complexity of the model and might enable it to capture the different labeling behavior in even more detail." + }, + { + "type": "table", + "bbox": [ + 0.511, + 0.089, + 0.885, + 0.4 + ], + "angle": 0, + "content": "
Hyperp.ValueUnweighted κAccuracy
D40.752 ± 0.0050.836 ± 0.003
80.758 ± 0.0110.84 ± 0.007
160.752 ± 0.0060.836 ± 0.004
σ2prior10.758 ± 0.0070.839 ± 0.004
20.758 ± 0.0110.84 ± 0.007
40.757 ± 0.0070.839 ± 0.004
σ2post40.757 ± 0.0070.839 ± 0.004
80.758 ± 0.0110.84 ± 0.007
160.745 ± 0.0090.83 ± 0.005
λ0.00010.744 ± 0.0030.829 ± 0.003
0.00050.758 ± 0.0110.84 ± 0.007
0.0010.745 ± 0.0080.837 ± 0.005
ν0.010.757 ± 0.0040.839 ± 0.002
0.020.758 ± 0.0110.84 ± 0.007
0.040.753 ± 0.010.836 ± 0.005
BackboneVGG160.734 ± 0.010.823 ± 0.005
Resnet340.758 ± 0.0110.84 ± 0.007
Eff.netB20.754 ± 0.010.836 ± 0.004
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.41, + 0.892, + 0.48 + ], + "angle": 0, + "content": "Table 6. Study of hyperparameter robustness using the Gleason 2019 dataset. The default hyperparameter value is marked with bold letters. While varying one hyperparameter, all other values are set to the default value. We observe consistent and robust performance across all settings of tested hyperparameters." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.504, + 0.627, + 0.519 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.892, + 0.756 + ], + "angle": 0, + "content": "In this work we present \"Pionono\", a method for medical image segmentation that models the inter- and intraobserver variability explicitly with a probabilistic approximation. This is especially relevant for tasks where the labeling behavior of medical experts is known to vary widely, such as in the case of prostate cancer segmentation. Our experiments on real-world cancer segmentation data demonstrate that Pionono outperforms state-of-the-art models such as STAPLE, Probabilistic U-Net, and models based on confusion matrices. Apart from the improved predictive performance, it provides a probabilistic uncertainty estimation and the simulation of expert opinions for a given test image. This makes it a powerful tool for medical image analysis and has the potential to improve the diagnostic process considerably." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.77, + 0.688, + 0.788 + ], + "angle": 0, + "content": "6. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was funded by the European Union's H2020 research and innovation programme (Marie Skłodowska Curie grant agreement No 860627, CLARIFY Project), the Spanish Ministry of Science and Innovation (project PID2019-105142RB-C22), and FEDER/Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento y Universidades (project P20_00286)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21104" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.158 + ], + "angle": 0, + "content": "[1] Abdullah A Abdullah, Masoud M Hassan, and Yaseen T Mustafa. 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In this paper, we propose a novel model, called Probabilistic Inter-Observed and iNtra-Observed variation NetwOrk (Pionono). It captures the labeling behavior of each rater with a multidimensional probability distribution and integrates this information with the feature maps of the image to produce probabilistic segmentation predictions. The model is optimized by variational inference and can be trained end-to-end. It outperforms state-of-the-art models such as STAPLE, Probabilistic U-Net, and models based on confusion matrices. Additionally, Pionono predicts multiple coherent segmentation maps that mimic the rater's expert opinion, which provides additional valuable information for the diagnostic process. Experiments on real-world cancer segmentation datasets demonstrate the high accuracy and efficiency of Pionono, making it a powerful tool for medical image analysis. + +# 1. Introduction + +Artificial Intelligence (AI) algorithms have shown remarkable progress in image analysis, holding great promise for faster and more accurate diagnostic procedures [13, 27, 26, 3]. Nevertheless, in medical practice, there exists a high degree of variability among the opinions of different medical experts, even when the same expert assesses the same data at different times. This inter- and intra-observer variability has been reported across various tasks, including MRI-based segmentation of HCC lesions [7], lung cancer segmentation in CT scans [14], and multiple fields in pathology [21, 2, 5, 22]. It leads to uncertainties when applying AI models because in contrast to other classification tasks, there is not a single ground truth. + +Especially in the medical domain, the careful modeling of uncertainties in its different forms has a high priority to minimize the risk of relying on incorrect predictions + +![](images/5a7384810ad2d4459a1e1e41c6a024f89c50d42a85de36fd1b94532b0217de56.jpg) +Figure 1. The proposed Pionono model. The labeling behavior of each rater $r$ is represented by a multivariate Gaussian distribution $q(z|r)$ . The drawn samples $\tilde{z}_j$ are concatenated with the extracted features $v$ of $f_{\omega}$ and then fed into the segmentation head $f_{\theta}$ . The output simulates the inter- and intra-observer variability of annotations and is optimized using the real annotations $s^r$ of each rater. The model is trained end-to-end with a combination of log-likelihood loss (LL) and Kulback Leibler (KL) divergence between posterior and prior, combined in the overall loss $\mathcal{L}_{\mathrm{ELBO}}$ . + +[17, 26, 15, 13, 10]. In recent years, probabilistic methods, such as Bayesian Neural Networks [8] and sparse Gaussian processes [10, 33] have gained more and more attention, because they are able to account for uncertainties in a sound manner. They showed promising results when modeling uncertainty in the network weights [8], data ambiguities [15] or attention weights [26]. Although inter- and intra-observer variability is often mentioned as a key challenge when applying AI to medical data [21, 16, 28, 18], to the best of our knowledge there is no method that explicitly models these two types of uncertainty for medical image segmentation. + +To address this gap, we propose a novel approach called the Probabilistic Inter-Observer and iNtra-Observer varia + +tion NetwOrk (Pionono), depicted in Figure 1. This model accurately accounts for inter- and intra-observer variability using probabilistic deep learning. Specifically, each rater's labeling behavior is represented as a probability distribution in latent space, and optimized using the log Evidence Lower BOund (ELBO) in an end-to-end training process. The variance of each rater's distribution models the intra-observer variability, while the differences between the distributions models the inter-observer variability. When two raters exhibit similar labeling behavior, their probability distributions overlap substantially, while different labeling behavior results in a small overlap of distributions. + +The approach is validated in extensive experiments of prostate and breast cancer segmentation, using 'gold' labels. They reflect the expert agreement to show that our probabilistic modeling improves the predictive performance and estimates the predictive uncertainty. Furthermore, we also test its capability to model each rater's labeling behavior. As shown in the experiments, it can simulate expert opinions for a given test image in a consistent manner, providing a realistic estimation of "what expert X would say in this case". Our contributions can be summarized as follows: + +- We propose Pionono, a probabilistic deep learning model that uses probability distributions in latent space to represent inter- and intra-observer variability. It can be trained with labels of multiple raters. +- The model is able to provide accurate segmentation predictions (compared to the expert agreement and different expert opinions), outperforming existing state-of-the-art algorithms such as STAPLE, Probabilistic U-Net and models based on global or local confusion matrices. +- Pionono provides uncertainty estimations that indicate areas where the predictions are not conclusive. +- The proposed model can provide several coherent segmentation hypotheses, simulating different medical experts. + +# 2. Related Work + +In this section, we review existing methods of probabilistic deep learning and crowdsourcing for medical images and highlight the differences to our model. + +Probabilistic Deep Learning. As already indicated, probabilistic approaches such as Bayesian neural networks [8, 1, 15, 17] and sparse Gaussian processes [10, 33, 26] have shown promising results in a multitude of tasks in the medical image domain, modeling different sources of uncertainties. Often, a general predictive uncertainty is addressed using probabilistic weight parameters [1]. This uncertainty can be bisected into model and data uncertainty which originate from model parameters or data ambiguities, respectively [15]. Other approaches have modeled the uncertainty of missing instance labels in multiple instance + +
Method(i) Prob. (ii) Uncert.Coh. (iii) Segm.Exp. (iv) OpinionScale
STAPLE×××✓
Prob U-Net✓✓×✓
CM global××✓✓
CM pixel××✓×
Pionono✓✓✓✓
+ +Table 1. For AI segmentation models to achieve the best possible diagnostic support, they should address four key issues: (i) provide a probabilistic uncertainty estimation, not only a single prediction for a test image; (ii) provide multiple coherent segmentation hypotheses; (iii) simulate different expert opinions for better explainability and decision support; (iv) scale to a higher amount of raters in the case that more data from different hospitals can be integrated. + +learning [20, 26] or uncertainty of out of distribution samples [17]. The uncertainty in annotations has previously been addressed by the Probabilistic U-Net [13] (Prob U-Net), which encodes the labeling behavior in a latent random variable. The model is trained as a variational autoencoder with an encoder network predicting the latent distribution. This approach models a general variability in annotations but lacks the explicit modeling of inter- and intraobserver variability. Therefore, it is not able to incorporate the rater information during training and cannot simulate expert opinions. + +Crowdsourcing. While existing crowdsourcing methods aim to capture inter-observer variability in the training labels, this variability is often not reflected in the test predictions by probabilistic outputs [13]. The intra-observer variability is often not modeled at all, although it is often mentioned as a challenge in literature [21, 16, 28, 2, 7]. + +One way to handle multiple annotations is label fusion. With this method, the annotations of different raters are merged to a single set of labels. The "Simultaneous Truth and Performance Level Estimation" (STAPLE) mechanism performs label fusion with a probabilistic estimate of the true labels by weighting each segmentation depending upon the estimated performance level of each rater [32]. A supervised network can then be trained on these fused labels. More dedicated approaches incorporate different rater labels using confusion matrices (CM), for example for classification of image patches with Gaussian processes [18] or image segmentation with global confusion matrices [31] (CM global). In this direction, also pixel-wise confusion matrices were explored for semantic segmentation that are estimated by a dedicated deep neural network [34] (CM pixel). These models have shown promising results, but come with a conceptual problem: They assume that the pixels are statistically independent of each other, although + +neighboring pixels have a high correlation. Therefore, the output of different segmentation hypotheses is not coherent. Furthermore, the predictions of the mentioned approaches [31, 34] are not modeled by a predictive distribution, but by a deterministic point estimate. While the global confusion matrix approach [31] has a limited expressiveness, the pixel-wise calculation [34] is hard to scale for multiple raters, because for each rater, a complete deep neural network must be trained and stored. + +Pionono unites the advantages of probabilistic and crowdsourcing methods. We summarize a comparison of different characteristics of Pionono and related methods for image segmentation in Table 1. + +# 3. Methods + +In this section, we outline the background of the proposed method. It is implemented in the Pytorch [23] framework and is publicly available at https://github.com/arneschmidt/pionono_segmentation. + +# 3.1. Problem Definition + +Let $X = \{x_{i} \in \mathbb{R}^{H \times W \times 3}\}_{i=1,..,N}$ be a set of images, $S^{r} = \{s_{i}^{r} \in \mathbb{R}^{H \times W \times C}\}_{i=1,..,N}$ the corresponding segmentation maps with image dimensions $H \times W$ and $C$ the number of classes. The segmentation maps are provided by different raters $r \in R = \{1,2,..,M\}$ . Some or all images can be segmented by multiple raters, such that some segmentation maps $s_{i}^{r}$ can be empty. The proposed model does not require any overlap of the sets of annotated images. + +If there are images available with segmentations assigned by expert agreements (so-called gold labels), the model should be able to predict a gold distribution over outputs $p(S^{\mathrm{gold}})$ with the mean estimating the segmentation and the variance estimating the uncertainty. In any case, the model should model different segmentation hypotheses for the raters $\{p(S^r); r = 1,2,\dots,M\}$ for diagnostic decision support. + +# 3.2. Proposed Model + +First, we introduce the common segmentation backbone $f_{\omega}$ with trainable weights $\omega$ . We use the well-known U-Net architecture [25] with a Resnet34 feature extractor [9]. This model takes an image $x_{i}$ and extracts a feature map $v_{i} \in \mathbb{R}^{H \times W \times L}$ with $H \times W$ being the image resolution and $L$ the dimensions of the feature vectors ( $L = 16$ in the case of U-Net). We denote the feature extraction as + +$$ +v _ {i} = f _ {\omega} \left(x _ {i}\right). \tag {1} +$$ + +Based on these feature vectors, we could perform segmentation with a segmentation head $f_{\theta}$ : + +$$ +s _ {i} = f _ {\theta} \left(v _ {i}\right). \tag {2} +$$ + +Now we extend this model to incorporate the inter- and intra-observer variation. The segmentation maps are influenced by the rater's experience, assessment, and personal choices. To encode the labeling behavior, we use a random vector $z \in \mathbb{R}^D$ . In practice, $D = 8$ are enough dimensions to reflect different labeling behaviors. We define a prior distribution $p(z) = \mathcal{N}(z|0, \sigma_{\mathrm{prior}} * I)$ which encodes a generic labeling behavior without further information about the rater. It is possible to encode prior knowledge in this distribution, but we present a general model and leave this for future work. We set $\sigma_{\mathrm{prior}}^2 = 2.0$ , because we observe a realistic variability in the output for this value. In section 4.5 we prove that the model is robust for different settings of hyperparameters $D$ and $\sigma_{\mathrm{prior}}^2$ . + +Now, the posterior distribution of $p(z|r)$ that depends on the rater $r$ should be found. We approximate it with one multivariate Gaussian distribution for each rater: + +$$ +q (z | r) = \mathcal {N} \left(z \mid \mu^ {r}, \Sigma^ {r}\right) \forall r = 1,.., M \tag {3} +$$ + +where $\{\mu^r,\Sigma^r\}^{r = 1,\dots ,M}$ are trainable parameters. The variance of each distribution $q(z|r)$ models the intra - observer variability. The differences between the distributions for different raters model the inter - observer variability. To obtain the predictive gold distribution we add another 'rater' $r = M + 1$ represented by an additional gold distribution $q$ which is trained with the available gold segmentations. During prediction, this distribution provides the estimated agreement between experts. + +The segmentation head $f_{\theta}$ , parametrized by weights $\theta$ must be adapted to take the random vector $z$ into account. The approximated predictive distribution is then obtained by: + +$$ +q \left(s _ {i} \mid x _ {i}, r, \omega , \theta\right) = \int f _ {\theta} \left(v _ {i}, z\right) q (z | r) d z. \tag {4} +$$ + +The closed-form calculation is not feasible and therefore we approximate it by Monte Carlo (MC) sampling: + +$$ +\tilde {s} _ {i, j} | x _ {i}, r = f _ {\theta} \left(v _ {i}, \tilde {z} _ {j}\right); \tilde {z} _ {j} \sim q (z | r) \tag {5} +$$ + +with $j = 1,\dots,K$ indexing the MC samples. In practice, we concatenate the feature maps $v_{i}$ and the latent vector $\tilde{z}_j$ which is broadcasted to the image size, leading to a feature map with dimensions $H\times W\times (L + D)$ . The segmentation head consists of three layers with 1x1 convolutions and 16 filters in the first two layers and $C$ filters in the last layer. + +# 3.3. Training + +First, all posterior distributions $q(z|r)$ are initialized randomly. Each initial value of the mean vectors $\mu^r$ is independently drawn from a distribution $\mathcal{N}(0,\sigma_{\mathrm{post}}^2)$ . We set $\sigma_{\mathrm{post}}^2 = 8$ , because this initializes the mean vectors sufficiently different for a good optimization. In section 4.5 we + +show, that the model is robust to other settings of this value. The covariance matrices $\Sigma^r$ are initialized with $\sigma_{\mathrm{prior}} * I$ . + +To optimize the parameters $\{\mu^r,\Sigma^r\}^{r = 1,\dots ,M}$ of the probability distribution $q(z|r)$ , we maximize the ELBO: + +$$ +\mathcal {L} _ {E L B O} = \mathbb {E} _ {q} \log p \left(S ^ {r} | X, r, \omega , \theta\right) - \lambda K L (q (Z | r) | p (Z)). \tag {6} +$$ + +with distribution $q$ as defined in eq. 4. The first term defines a log-likelihood (LL) loss, making the model fit to the annotations of each rater. The second term defines the KL-divergence between the posterior distribution $q(Z|r)$ and the prior $p(Z)$ and works as a regularization of the latent distributions. The factor $\lambda$ weights the regularization term and is set to 0.0005 to balance the magnitudes of the log-likelihood and the KL (we will check the robustness of this hyperparameter in Section 4.5). While the KL term can be optimized analytically, the log likelihood term must be approximated. We use the reparametrization trick [12] to split each probabilistic sample $\tilde{z}^r$ into its probabilistic component and deterministic parameters $\mu^r$ and $\Sigma^r$ . These parameters can be optimized by backpropagation of gradients, together with the CNN parameters $\omega$ and $\theta$ . For numerical stability, we train the covariance matrix parameters by using the lower triangular matrix $L$ of the Cholesky decomposition $\Sigma^r = L^r L^{r^\top}$ . The log-likelihood can be optimized with standard methods like the categorical cross-entropy. We found that the general dice loss [30] leads to better results, so all final results are reported with this loss. + +We use the Adam optimizer [11] for 100 epochs with a learning rate of 0.0001. The model parameters $\mu^r, \Sigma^r$ are optimized with a higher learning rate of $\nu = 0.02$ , because else the gradient was not strong enough to properly learn the rater distributions. We tested $\nu = 0.01, 0.02, 0.04$ and include the results in section 4.5. Both learning rates are decreased after 40 epochs by dividing them by 1.1 in each epoch. + +# 3.4. Predicting + +For a test image $x^{*}$ , the predictive gold distribution can again be obtained by drawing Monte-Carlo samples + +$$ +\tilde {s} _ {j} ^ {*} \mid x ^ {*}, r = f _ {\theta} \left(v ^ {*}, \tilde {z} _ {j}\right); \tilde {z} _ {j} \sim q (z | r = M + 1) \tag {7} +$$ + +with $j = 1,..,K$ indexing the MC samples and $q(z|r = M + 1)$ representing the gold distribution as described in section 3.2. The mean of these samples provides the segmentation hypothesis that approximates the expert agreements. The variance of the samples indicates uncertainties in the prediction. + +Furthermore, the model is able to simulate intraobserver variations of rater $r^\prime$ by drawing multiple samples of the distribution $\tilde{z}_j^{\prime}\sim q(z|r = r^{\prime})$ for the final prediction. The inter-observer variations between rater $r^\prime$ and $r''$ can be simulated by using samples $\tilde{z}_j^\prime \sim q(z|r = r^\prime)$ and + +$\tilde{z}_k^{\prime \prime}\sim q(z|r = r^{\prime \prime})$ and finally taking the mean of both output distributions. + +The model can therefore simulate expert opinions for a given test image. Other AI methods typically aggregate the expertise provided by all annotators to make predictions (e.g., using STAPLE, Prob U-Net). However, in such approaches, the knowledge of highly specialized experts can be diluted or lost among the less experienced annotators' knowledge. In our framework, we provide consistent predictions for each individual expert, thereby preserving their unique expertise and contributions. + +# 4. Experiments + +In several experiments we demonstrate that the uncertainty estimation of the model indicates areas of false predictions (4.2), the model is able to capture the inter and intra-observer variations (4.3) and outperforms other related methods (4.4). Additionally, we analyze the robustness to hyperparameters (4.5), required resources (4.6), and limitations (4.7). + +# 4.1. Datasets + +For empirical validation, three public histopathological datasets were used. The first dataset, "Gleason 2019" [22] was published as a MICCAI grand challenge for pathology and includes 333 Tissue Micro Arrays (TMA) of prostate cancer, labeled by 6 different pathologists. The TMAs were scanned with a magnification of $40\mathrm{x}$ and have a size of approximately $4000 \times 4000$ pixels. Of the 333 images, 244 are publicly available with labels (the test annotations of the challenge are not available). Each pathologist annotated between 61 and 241 TMAs with segmentation masks and the gold labels were obtained using the STAPLE algorithm [32], following the original work of the dataset [22]. We resize all images to $1024 \times 1024$ pixels and create 4 cross-validation splits. + +The second dataset, which we will refer to as "Arvaniti TMA" was published in 2018 [4] and includes a total of 886 TMAs of prostate cancer of which 245 images were annotated by two pathologists (while the other images only have annotations of one pathologist and are therefore discarded in our study). The TMAs were scanned with a magnification of $40\mathrm{x}$ but the scanned area is smaller than for the Gleason19 dataset. The images have a resolution of $3100\times 3100$ pixels and we resize them to $512\times 512$ such that the magnification matches the resized images of the Gleason 2019 dataset. Again, we split the dataset into 4 cross-validation splits for the experimental setup. + +For the classification of prostate cancer, the tissue is segmented in the Gleason Grading (GG) scheme. The classes are 'Non-cancerous' (NC), 'Gleason 3' (G3), 'Gleason 4' (G4), and 'Gleason 5' (G5) depending on the architectural growth patterns of the tumor [28, 29]. To visualize the + +![](images/61912018b33ebdb7162fe6ce693c60f855d553d0275246542e8b0d61671a20b1.jpg) +(a) Image + +![](images/b3387f21303821689611c937ae00b6cb9aafe0231321e10b1f11319b3a4b99cf.jpg) +c)Pred.Gold + +![](images/bc57e6dc8a16c77bea99cb7a2fb01d9083dbcb5ce5562a86c680ef467f6c3182.jpg) + +![](images/b3a1032b28790090647b6c6eabbec93e1eb2f31749b22a4d18dd47836f428d0e.jpg) + +![](images/2cc72240d957c593e79bdcbe64186d7cbb7c0467789832635778b78d3a3fe4e7.jpg) +(e) Image + +![](images/eb2894143429b0e30764f549aa033e0d42e79f63d6d7098d4a69427bbabbfe3d.jpg) +(f) GT Gold + +![](images/f3272df02ef56f43eb1e9badfeaea3d1c5171913e9541ba7c1cce3fa28325457.jpg) +(g)Pred.Gold +(h) Uncert. +Figure 2. Gold prediction and uncertainty of the Pionono model. The first row shows a confident prediction as the uncertainty in 2d is low (white) for almost all the area. Indeed, the segmentation prediction 2c is very accurate, see the ground truth (GT) 2b. The second row shows an example of an uncertain prediction. Some parts of the area classified as G3 (yellow) in $2\mathrm{g}$ are labeled as G4 in the ground truth 2f. These areas are estimated with a high uncertainty (black) in $2\mathrm{h}$ , warning that these predictions are unreliable. + +segmentations we use the colors: green for NC, yellow for G3, orange for G4, and red for G5. For the evaluation of algorithms for prostate cancer classification, previous works used the Cohen's kappa coefficient [22, 4, 28] which measures the agreement of two raters or a rater and an AI model. To compare to previously reported results for the two datasets, we use the unweighted Cohen's kappa $\kappa$ for the Gleason 2019 dataset [22] and the quadratic weighted Cohen's kappa $\kappa$ for the Arvaniti TMA dataset [4]. The main difference is that the quadratic kappa takes the class order into account and weighs the errors based on the quadratic distance of the predicted and the real class. + +The third dataset contains 151 WSIs for breast cancer segmentation that were sliced into 11,836 patches of $512 \times 512$ pixels annotated by 25 raters [3, 19]. We will refer to this dataset as "bc segmentation". The tissue was segmented into "tumor", "inflammation", "necrosis", "stroma", and "other". Here, the gold labels were obtained by an actual discussion of experts. We use the predefined train/validation/test splits [19]. + +For all datasets we use image augmentation with the albumenations library [6] by applying random flip, rotation, shear, zoom, blur, and shifts in brightness, contrast, hue, and saturation. This leads to a broad range of realistic transformations of the image to avoid overfitting. + +# 4.2. Uncertainty estimation + +The proposed model provides probabilistic predictions that allow an accurate assessment of the predictive uncertainty. Fig. 2 shows the model predictions and uncertainties obtained with the gold distribution as described in section 3.2. For the first image (2a), the prediction of the model (2c) is accurate and matches the real gold annotation (2b) very well. The uncertainty (2d) for this predictions is low (white), which means that there is a low risk of a wrong + +prediction. Therefore, the model correctly indicates that this prediction is reliable. For the second image 2e, some areas that are predicted as G3 (yellow) in $(2\mathrm{g})$ are actually G4 in the ground truth gold prediction (2f). The model's uncertainty estimation indicates that this prediction is not reliable: the misclassified areas are marked with a high uncertainty (dark) in the image (2h). Therefore, the probabilistic output adds valuable information to the diagnostic process. It estimates if a prediction is reliable - or unreliable and should be double-checked. + +# 4.3. Inter- and Intra-observer Variation + +The Pionono model is able to capture the inter- and intraobserver variability. This accurate probabilistic modeling of the annotations does not only improve the predictive results (see section 4.4), but also allows to simulate specific experts at test time. In this section, we empirically show that the model learns the different label behaviors of the raters and is able to reproduce them. + +In Fig. 3a we plot the inter-observer variations between the raters. The figure shows that there is indeed a high variability among the raters, with a Cohen's kappa ranging from 0.36 to 0.72. The simulated test predictions by Pionono show a higher agreement with each rater than the average agreement of the other raters, except for rater 2. For two raters (1 and 5), the simulated predictions of Pionono are even more than 15 percentage points higher than the average rater agreement. We also measured the IoU metric, which was 0.574, 0.540, 0.619, 0.649, 0.692, 0.507, for the 6 raters respectively, compared to a mean inter-pathologist IoU of 0.361. The results confirm that most raters are modeled with high accuracy. + +Fig. 3b shows the posterior distributions $q(z|r)$ of the proposed model, encoding the labeling behavior of each rater. The following observations confirm, that these learned distributions approximate well the real-world labeling behavior of the raters: (i) The four raters 3, 4, 5 and 6 show a high overlap of the distributions and corresponding to a high labeling agreement shown in Fig. 3a. (ii) The gold distribution (simulating raters agreement) overlaps significantly with the distribution of these four raters. (iii) The distribution of rater 2 is far away from all other distributions. This rater shows a different labeling behavior due to frequent under-segmentation of images, assigning the 'background' class to areas that contain tissue. (iv) Raters 1 and 6 often deviate from the other raters, especially for the differentiation of classes G3 and G4. Their distribution accordingly has a smaller overlap with the gold distribution and the other raters. Fig. 4 shows some visual image examples of Pionono test predictions, simulating each rater $r$ by drawing samples from the corresponding distribution $q(z|r)$ and then taking the mean of the output samples. The examples confirm that the rater differences are modeled well. + +![](images/209f76abb9b2215c4e7df52da06042db7c5b2ae800e1eb0934a2accc9034a536.jpg) +(a) Rater simulation statistic +Figure 3. Analyzing the labeling behavior. In Fig. (a) the agreement of each rater with all other raters is depicted, measured by the unweighted Cohen's Kappa of the true labels [22]. The mean agreement of each rater with all other raters is represented by a black dot and the agreement with Piononos test predictions, simulating the corresponding rater, by a star. This confirms that the model accurately models each rater, reaching even a higher agreement than the other rater's average, except for rater 2. Fig. (b) shows the first two dimensions of the posterior distributions $q(z|r)$ with mean and covariance after training. The distributions of raters 3, 4, 5 and 6 overlap significantly with the gold distribution and with each other, indicating a similar labeling behavior. Indeed, these raters show the highest labeling agreement in Fig. (a). + +![](images/c490c3899e2cd256034e3ca5cf4f7038d2436be76401f257b8447b5830ba209d.jpg) +(b) Latent distributions + +Next, we analyze the intra-observer variations. As the dataset does not contain multiple annotations of the same rater for the same image, the assessment of this quality is more difficult. Still, certain intra-observer variability can be assessed by observing the general labeling behavior of one annotator. For example, rater 6 tends to over-assign class G5 (red), and rater 2 tends to not segment all image parts that contain tissue. Interestingly, these intra-observer variations are present in the model predictions when multiple samples are drawn from their corresponding distribution. Fig. 5 shows visual examples of the simulated variations of raters 2 and 6. + +# 4.4. Model Comparison + +The proposed model is compared to previously reported results and several state-of-the-art approaches (see section 2) for medical image segmentation with labels from multiple raters. For fair comparison, we use the same backbone architecture1, epochs, learning rate, and optimizer for all experiments. We have tuned the model-specific hyperparameters to obtain the best possible results for each method. + +First, we perform experiments with the Gleason 2019 dataset with a 4-fold crossvalidation. For comparison with previous works, we report the unweighted Cohen's kappa metric comparing gold predictions with gold ground truth. Additionally, we report the accuracy. As the results in Table 2 show, the proposed Pionono model outperforms the previ + +![](images/47273e0da3316f35882c2690568881eeb50fd0f25945020c95197e57f0fb2a6a.jpg) + +![](images/8d2958a1d16b833f037670522766e60b5be29b48f8e287b1952a963f15824754.jpg) +(a) Image + +![](images/a2ea98d21792812f59a6d5c3ba3643d733f5662d513454455edcd150f2204a68.jpg) + +![](images/83de155e482c4d41cae91fae8d3147d416a89dfcabb822f7173aceb78217bcb5.jpg) +(c) $\mathrm{GT}r = 1$ + +![](images/544d4b4f6601ba5c97f60b5b18e44e2d0b2eb7d78c9fd96e455eb80de3df1188.jpg) +(g) $\mathrm{GT}r = 2$ +(1) PR $r = 3$ + +![](images/644c95b8f6ad36d4d7516a2132bf6e85cf0f69c6466fbd5af878c0866fe88054.jpg) +(d) PR $r = 1$ +(h) $\mathrm{PR}r = 2$ + +![](images/017fa9ed416b935895588a0c5263af3c766090f55d78f9a036cfcdd362b3e8e0.jpg) +(k) GT $r = 3$ + +![](images/ba23e90d6e71986a9c29f76965b401ae001eb082ef398ab67bd0ea9eca98491f.jpg) +(o) $\mathrm{GT}r = 4$ + +![](images/3ac9df8382fb4d56b0e3e6378e9cb56ba5a52ccfeaca541c1ead7fd78ac71ea5.jpg) + +![](images/579859d02a5b58ed54d3ad3987a73394807304263e14bc6469d7943aa796c4db.jpg) +(s) GT $r = 5$ +(w) GT $r = 6$ +Figure 4. Inter-observer variations estimated by Pionono. For two test images we depict the ground truth (GT) segmentations of all raters and the predicted segmentations (PR), simulating each rater. The proposed model is able to simulate certain labeling behavior like the tendency of assigning class G5 (red) for raters 2 and 6 (see g and w) where other raters assigned G4 (orange). Furthermore, the model captures the under-segmentation by rater 2 (see i). + +(t) PR $r = 5$ + +![](images/a8b47d5bfb4ba084638aff0034c17c7aab6a075b8171d486e0fd59f04c06d3a6.jpg) +(t) PR $r = 5$ +(x) PR $r = 6$ + +![](images/8e422444dd6baf427d77e1f7b78190a208235d3be2ac3c2de3976d4477193480.jpg) + +![](images/e25304abb570c7a7eb0721b9e075f32bd14f49268fb243c93df9ec5c4fd144e6.jpg) +(b) Image + +![](images/8f3c01fb048a7fa451b4e7d10fc4db8faa882900a9d0cae6a36ed7f9c2e86ae1.jpg) +e) GT $r = 1$ + +(f) $\mathrm{PR}r = 1$ + +![](images/c3f1c2175fd031237def2dbd5e2b5fccc5219a643ec92ac8a670e673d8baa831.jpg) +(f) $\mathrm{PR}r = 1$ + +![](images/45e1b59a531abfcbb35ac7f67212552034fdbc84d91eea90f1d98f0915e6192a.jpg) +(i) $\mathrm{GT}r = 2$ + +![](images/9b7d943b68770361a1ef35c0c99d1d7244f12976164145740afe8f4f05ac012e.jpg) +j) PR $r = 2$ + +![](images/2e076d2ed7ee694b8d0b4aa797e27f4c457b561e0549432c1711952c7c830206.jpg) +(m) $\mathrm{GTr} = 3$ + +![](images/57bb75da1f09cbf260651434cd1bfd29709ec8ecbd71b8aa941a2cbbf0d5eee9.jpg) +n) PR $r = 3$ + +![](images/4d6858bcad3ebc44e1baec17d35f7bd32506386f07ed7de180ad00c27d1f6e2f.jpg) +(q) GT $r = 4$ + +![](images/2c11064145ca86f09d3dc10d0a0242db17c161826fa8e212419dd1b0fedc0771.jpg) +(r) PR $r = 4$ + +![](images/56e888573e9b6c21a028b894138c14514dce27af9b6593b619a4374faddb51d3.jpg) +(u) GT $r = 5$ +(y) GT $r = 6$ + +![](images/be2ed15e726e79569c37577f82868f9a7c472a3132c35f3d4524ee6525e95e2b.jpg) +v) PR $r = 5$ +z) PR $r = 6$ + +ously reported results [22, 24], including the winner of the Gleason 2019 challenge [24], by a large margin of over 20 percentage points. This accounts for the exact modeling of the raters by Pionono, but also for the different choices of backbone architecture and other training details. Compared to other state-of-the-art methods with the same architecture and training details, Pionono still shows a considerably better performance. + +Next, we compare the generalization capabilities of the models by using the Arvaniti TMA dataset as an external test set, as reported in Table 3. This means, that the models are trained with all images from Gleason 2019 and tested with all images from Arvaniti TMA. As the Arvaniti TMA dataset does not contain gold labels, the model's gold predictions are compared to both raters independently, as previously done by Arvaniti et al. [4]. We observe that the model + +![](images/de5a03e294abf5351e600fa766c0baba7551027f1c23c2c24b0d798ecf0048cb.jpg) +(a) Image + +![](images/4d4b57ce4f762d03817e80a8e35e65ebbaa225c39ca8f0b1aa224780e5f1a221.jpg) +(b) PR $r = 6$ + +![](images/03d291c31fee1b51a4576a1f1fc94f3842040f5d99ed6c880f3c861e3eb7174f.jpg) + +![](images/ac6e77b9e71e01cecf65e526f4c18c11712ca5ba129bce1266efa279bf7239bc.jpg) +(e) $\mathrm{GT}r = 6$ +(f) PR $r = 6$ + +![](images/c999c839c40adb883e0a1cdbed01777037a387a9945f73f4b9fffd6342fa7dd0.jpg) +(i) PR $r = 6$ + +![](images/88bb68cd2b610ff8e12775115afddc6649b5092754465a9091bcd02c08649da6.jpg) +(k) PR $r = 6$ +(m) PR $r = 6$ +Figure 5. Intra-observer variations estimated by the Pionono model. For two example images we depict the true annotation (GT) of two different raters ( $r = 2$ and $r = 6$ ). On the right sides we show different coherent segmentation predictions (PR) for each rater estimated by our model. The differences in each column reflect possible intra-observer variations. The first example (a) shows that rater 6 might show some variations in the assigned classes. While the segmentation prediction (b) is composed by classes G3 (yellow) and G4 (orange), the segmentation sample (f) only consists of G5 (red). Indeed, this rater often assigns class G5 (red) in areas where other raters assign G4 (see Fig. 4) such that this is a plausible hypothesis. In the second example (c) we see variations due to the under-segmentation of rater 2 in some images. Our model captures this behavior and provides hypothesis of more (d) or less (j) segmentation of class G3 (yellow). + +![](images/b2053efe55d8103ec4a9d289f178e3e63a4edfab7dd975d7752fcbf5d08598ab.jpg) + +![](images/2ef7993aa4dcf769db6a43939c5ef37bc2cf22101abd15b7debb0ba8a12f4540.jpg) +(c) Image +(g) $\mathrm{GT}r = 2$ + +![](images/e1213dc2feb68217e88ca75f48dda837438be480327d07c1108b988ab17cc418.jpg) + +![](images/98cc3cdea572d4fe0e2a94f69a032cd7af4692bbe6f805c642872660f8b5d678.jpg) +(d) PR $r = 2$ + +![](images/5df5434fb20d3d636c070deeae111a074e31d738aa87de85c19888225a11d8d2.jpg) +(h) PR $r = 2$ + +![](images/8a5fa3318798f86c7805c02f8c54c354b8fc39ccf8a6b260696a190faf0269e7.jpg) +(j) PR $r = 2$ + +![](images/b64c5f1edfff8145a28f0ef4f4a196a5802a522fe621492d14be5589f4ad85a3.jpg) +(1) PR $r = 2$ +(n) PR $r = 2$ + +generalizes better than all other methods, achieving a higher agreement in terms of Cohen's quadratic kappa with both raters. In terms of accuracy, only 'CM global' outperforms Pionono by a small margin. + +In the third experiment, we use the Arvaniti TMA dataset for training and testing with the two rater annotations. Again, the proposed model is able to outperform previously reported results as well as other state-of-the-art methods in terms of quadratic Cohen's kappa. In terms of accuracy, only the "Prob U-Net" model obtains a better result for rater 1, while Pionono reaches the best accuracy for rater 2. + +To validate the model on a different kind of data, we performed the fourth experiment on the "bc segmentation" dataset [3]. The results are reported in Table 5 and confirm the strong performance of the proposed Pionono model. + +The results support our hypothesis that explicitly modeling the inter- and intra-observer variations improves the + +
MethodUnweighted κAccuracy
Nir et al. [22]0.51N.A.
Qiu et al. [24]0.524N.A.
STAPLE0.75 ± 0.0060.834 ± 0.005
Prob U-Net0.741 ± 0.0020.83 ± 0.001
CM global0.721 ± 0.0180.814 ± 0.012
CM pixel0.692 ± 0.0190.791 ± 0.012
Pionono0.758 ± 0.0110.84 ± 0.007
+ +Table 2. Cohens Kappa Comparison for the 4-fold crossvalidation experiment of the Gleason 2019 dataset, reported by mean and standard error. + +
Rater 1 MethodQuadratic κAccuracy
STAPLE0.629 ± 0.0020.718 ± 0.001
Prob U-Net0.629 ± 0.0050.73 ± 0.003
CM global0.624 ± 0.0030.728 ± 0.002
CM pixel0.618 ± 0.0070.72 ± 0.004
Pionono0.641 ± 0.0060.736 ± 0.004
Rater 2 MethodQuadratic κAccuracy
STAPLE0.563 ± 0.0020.621 ± 0.002
Prob U-Net0.56 ± 0.0030.626 ± 0.006
CM global0.557 ± 0.0030.638 ± 0.006
CM pixel0.551 ± 0.0060.626 ± 0.008
Pionono0.569 ± 0.0050.633 ± 0.005
+ +Table 3. Cohens Kappa Comparison with the two raters of the Arvaniti TMA dataset trained on the Gleason 2019 dataset, reported by mean and standard error. + +
Rater 1 MethodQuadratic κAccuracy
Arvaniti et al. [4]0.55N.A.
Silva-R. et al. [28]0.536N.A.
supervised0.658 ± 0.0250.734 ± 0.008
Prob U-Net0.697 ± 0.0080.762 ± 0.004
CM global0.677 ± 0.0280.745 ± 0.011
CM pixel0.647 ± 0.0160.731 ± 0.012
Pionono0.716 ± 0.0110.751 ± 0.02
Rater 2 MethodQuadratic κAccuracy
Arvaniti0.49N.A.
supervised0.521 ± 0.0140.678 ± 0.014
Prob U-Net0.534 ± 0.0020.68 ± 0.005
CM global0.533 ± 0.0220.676 ± 0.011
CM pixel0.508 ± 0.0130.663 ± 0.008
Pionono0.548 ± 0.0080.697 ± 0.012
+ +Table 4. Cohens Kappa Comparison with the two raters of the Arvaniti TMA dataset trained and validated by 4-fold crossvalidation of the Arvaniti data, reported by mean and standard error. + +model's performance. Pionono takes the different labeling behavior into account during training which leads to accu + +
MethodUnweighted κAccuracy
STAPLE0.647 ± 0.0030.755 ± 0.002
Prob U-Net0.685 ± 0.0230.734 ± 0.004
CM global0.654 ± 0.0050.761 ± 0.004
CM pixel0.689 ± 0.0100.784 ± 0.007
Pionono0.711 ± 0.0020.799 ± 0.001
+ +rate predictions. + +# 4.5. Robustness to Hyperparameter Settings + +To measure the sensitivity of the model regarding different hyperparameters, we performed studies on the 4-fold cross-validation experiment of the Gleason 19 dataset. Table 6 shows that the model is robust to variations of all analyzed hyperparameters. We observe minor performance drops for different values of the regularization factor $\lambda$ and the initialization variance $\sigma_{\mathrm{post}}^2$ . In both cases, wrong choices of the hyperparameters can hinder the correct optimization of the latent distributions. Furthermore, we tested different backbone architectures, indicating a limited performance with a VGG16 backbone. Overall the performance drops are minor and for all other settings, the model shows highly accurate results of $\kappa >0.75$ . + +# 4.6. Required Resources + +For the Gleason 2019 dataset with images of $1024 \times 1024$ , the model can be trained with a batch size of 3 on a single NVIDIA GeForce RTX 3090 with 24Gb memory. The training takes less than 1.5h in total and test predictions less than 0.2s per image. The trained model occupies less than 350Mb when saved to the disk. As each additional annotator adds only one additional vector $\mu^r \in \mathbb{R}^8$ and one covariance matrix $\Sigma^r \in \mathbb{R}^{8 \times 8}$ , it is scalable to a large number of annotators. The model's quick runtime and excellent scalability make it easily applicable in clinical practice. + +# 4.7. Limitations + +As semantic segmentation itself is a challenging task, some details of the annotator segmentations are not captured well by the model, such as the variations of class NC (green) in the GT of Fig. 4d - 4x or class G4 (orange) in the GT of Fig. 4f - 4z. Here, the model tends to predict similar shapes for the raters. A possible solution is to use more layers in the segmentation head $f_{\theta}$ with a wider kernel (e.g. $5 \times 5$ convolutions). This would increase the complexity of the model and might enable it to capture the different labeling behavior in even more detail. + +Table 5. Results for the breast cancer segmentation of WSIs, reported as mean and standard error of 4 runs. + +
Hyperp.ValueUnweighted κAccuracy
D40.752 ± 0.0050.836 ± 0.003
80.758 ± 0.0110.84 ± 0.007
160.752 ± 0.0060.836 ± 0.004
σ2prior10.758 ± 0.0070.839 ± 0.004
20.758 ± 0.0110.84 ± 0.007
40.757 ± 0.0070.839 ± 0.004
σ2post40.757 ± 0.0070.839 ± 0.004
80.758 ± 0.0110.84 ± 0.007
160.745 ± 0.0090.83 ± 0.005
λ0.00010.744 ± 0.0030.829 ± 0.003
0.00050.758 ± 0.0110.84 ± 0.007
0.0010.745 ± 0.0080.837 ± 0.005
ν0.010.757 ± 0.0040.839 ± 0.002
0.020.758 ± 0.0110.84 ± 0.007
0.040.753 ± 0.010.836 ± 0.005
BackboneVGG160.734 ± 0.010.823 ± 0.005
Resnet340.758 ± 0.0110.84 ± 0.007
Eff.netB20.754 ± 0.010.836 ± 0.004
+ +Table 6. Study of hyperparameter robustness using the Gleason 2019 dataset. The default hyperparameter value is marked with bold letters. While varying one hyperparameter, all other values are set to the default value. We observe consistent and robust performance across all settings of tested hyperparameters. + +# 5. Conclusions + +In this work we present "Pionono", a method for medical image segmentation that models the inter- and intraobserver variability explicitly with a probabilistic approximation. This is especially relevant for tasks where the labeling behavior of medical experts is known to vary widely, such as in the case of prostate cancer segmentation. Our experiments on real-world cancer segmentation data demonstrate that Pionono outperforms state-of-the-art models such as STAPLE, Probabilistic U-Net, and models based on confusion matrices. Apart from the improved predictive performance, it provides a probabilistic uncertainty estimation and the simulation of expert opinions for a given test image. This makes it a powerful tool for medical image analysis and has the potential to improve the diagnostic process considerably. + +# 6. Acknowledgements + +This work was funded by the European Union's H2020 research and innovation programme (Marie Skłodowska Curie grant agreement No 860627, CLARIFY Project), the Spanish Ministry of Science and Innovation (project PID2019-105142RB-C22), and FEDER/Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento y Universidades (project P20_00286). + +# References + +[1] Abdullah A Abdullah, Masoud M Hassan, and Yaseen T Mustafa. A review on bayesian deep learning in healthcare: Applications and challenges. 2022. 2 +[2] Felicia D. Allard, Jeffrey D. Goldsmith, Gamze Ayata, Tracy L. Challies, Robert M. Najarian, Imad A. Nasser, Helen Wang, and Eric U. Yee. 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In this paper, we propose a novel model, called Probabilistic Inter-Observed and iNtra-Observed variation NetwOrk (Pionono). It captures the labeling behavior of each rater with a multidimensional probability distribution and integrates this information with the feature maps of the image to produce probabilistic segmentation predictions. The model is optimized by variational inference and can be trained end-to-end. It outperforms state-of-the-art models such as STAPLE, Probabilistic U-Net, and models based on confusion matrices. Additionally, Pionono predicts multiple coherent segmentation maps that mimic the rater's expert opinion, which provides additional valuable information for the diagnostic process. Experiments on real-world cancer segmentation datasets demonstrate the high accuracy and efficiency of Pionono, making it a powerful tool for medical image analysis." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 499, + 128, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 499, + 128, + 511 + ], + "spans": [ + { + "bbox": [ + 47, + 499, + 128, + 511 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 521, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 676 + ], + "type": "text", + "content": "Artificial Intelligence (AI) algorithms have shown remarkable progress in image analysis, holding great promise for faster and more accurate diagnostic procedures [13, 27, 26, 3]. Nevertheless, in medical practice, there exists a high degree of variability among the opinions of different medical experts, even when the same expert assesses the same data at different times. This inter- and intra-observer variability has been reported across various tasks, including MRI-based segmentation of HCC lesions [7], lung cancer segmentation in CT scans [14], and multiple fields in pathology [21, 2, 5, 22]. It leads to uncertainties when applying AI models because in contrast to other classification tasks, there is not a single ground truth." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "Especially in the medical domain, the careful modeling of uncertainties in its different forms has a high priority to minimize the risk of relying on incorrect predictions" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 312, + 228, + 536, + 425 + ], + "blocks": [ + { + "bbox": [ + 312, + 228, + 536, + 425 + ], + "lines": [ + { + "bbox": [ + 312, + 228, + 536, + 425 + ], + "spans": [ + { + "bbox": [ + 312, + 228, + 536, + 425 + ], + "type": "image", + "image_path": "5a7384810ad2d4459a1e1e41c6a024f89c50d42a85de36fd1b94532b0217de56.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "lines": [ + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "type": "text", + "content": "Figure 1. The proposed Pionono model. The labeling behavior of each rater " + }, + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "type": "text", + "content": " is represented by a multivariate Gaussian distribution " + }, + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "type": "inline_equation", + "content": "q(z|r)" + }, + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "type": "text", + "content": ". The drawn samples " + }, + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "type": "inline_equation", + "content": "\\tilde{z}_j" + }, + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "type": "text", + "content": " are concatenated with the extracted features " + }, + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "type": "inline_equation", + "content": "f_{\\omega}" + }, + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "type": "text", + "content": " and then fed into the segmentation head " + }, + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "type": "text", + "content": ". The output simulates the inter- and intra-observer variability of annotations and is optimized using the real annotations " + }, + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "type": "inline_equation", + "content": "s^r" + }, + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "type": "text", + "content": " of each rater. The model is trained end-to-end with a combination of log-likelihood loss (LL) and Kulback Leibler (KL) divergence between posterior and prior, combined in the overall loss " + }, + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ELBO}}" + }, + { + "bbox": [ + 304, + 434, + 547, + 536 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 555, + 547, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 547, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 547, + 688 + ], + "type": "text", + "content": "[17, 26, 15, 13, 10]. In recent years, probabilistic methods, such as Bayesian Neural Networks [8] and sparse Gaussian processes [10, 33] have gained more and more attention, because they are able to account for uncertainties in a sound manner. They showed promising results when modeling uncertainty in the network weights [8], data ambiguities [15] or attention weights [26]. Although inter- and intra-observer variability is often mentioned as a key challenge when applying AI to medical data [21, 16, 28, 18], to the best of our knowledge there is no method that explicitly models these two types of uncertainty for medical image segmentation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "content": "To address this gap, we propose a novel approach called the Probabilistic Inter-Observer and iNtra-Observer varia" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21097" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": "tion NetwOrk (Pionono), depicted in Figure 1. This model accurately accounts for inter- and intra-observer variability using probabilistic deep learning. Specifically, each rater's labeling behavior is represented as a probability distribution in latent space, and optimized using the log Evidence Lower BOund (ELBO) in an end-to-end training process. The variance of each rater's distribution models the intra-observer variability, while the differences between the distributions models the inter-observer variability. When two raters exhibit similar labeling behavior, their probability distributions overlap substantially, while different labeling behavior results in a small overlap of distributions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 216, + 289, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 289, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 289, + 334 + ], + "type": "text", + "content": "The approach is validated in extensive experiments of prostate and breast cancer segmentation, using 'gold' labels. They reflect the expert agreement to show that our probabilistic modeling improves the predictive performance and estimates the predictive uncertainty. Furthermore, we also test its capability to model each rater's labeling behavior. As shown in the experiments, it can simulate expert opinions for a given test image in a consistent manner, providing a realistic estimation of \"what expert X would say in this case\". Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 335, + 287, + 514 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 58, + 335, + 287, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 335, + 287, + 382 + ], + "spans": [ + { + "bbox": [ + 58, + 335, + 287, + 382 + ], + "type": "text", + "content": "- We propose Pionono, a probabilistic deep learning model that uses probability distributions in latent space to represent inter- and intra-observer variability. It can be trained with labels of multiple raters." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 383, + 287, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 383, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 58, + 383, + 287, + 453 + ], + "type": "text", + "content": "- The model is able to provide accurate segmentation predictions (compared to the expert agreement and different expert opinions), outperforming existing state-of-the-art algorithms such as STAPLE, Probabilistic U-Net and models based on global or local confusion matrices." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 455, + 287, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 455, + 287, + 478 + ], + "spans": [ + { + "bbox": [ + 58, + 455, + 287, + 478 + ], + "type": "text", + "content": "- Pionono provides uncertainty estimations that indicate areas where the predictions are not conclusive." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 479, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 479, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 58, + 479, + 287, + 514 + ], + "type": "text", + "content": "- The proposed model can provide several coherent segmentation hypotheses, simulating different medical experts." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 525, + 134, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 134, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 134, + 538 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 546, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 287, + 581 + ], + "type": "text", + "content": "In this section, we review existing methods of probabilistic deep learning and crowdsourcing for medical images and highlight the differences to our model." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": "Probabilistic Deep Learning. As already indicated, probabilistic approaches such as Bayesian neural networks [8, 1, 15, 17] and sparse Gaussian processes [10, 33, 26] have shown promising results in a multitude of tasks in the medical image domain, modeling different sources of uncertainties. Often, a general predictive uncertainty is addressed using probabilistic weight parameters [1]. This uncertainty can be bisected into model and data uncertainty which originate from model parameters or data ambiguities, respectively [15]. Other approaches have modeled the uncertainty of missing instance labels in multiple instance" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 323, + 70, + 531, + 173 + ], + "blocks": [ + { + "bbox": [ + 323, + 70, + 531, + 173 + ], + "lines": [ + { + "bbox": [ + 323, + 70, + 531, + 173 + ], + "spans": [ + { + "bbox": [ + 323, + 70, + 531, + 173 + ], + "type": "table", + "html": "
Method(i) Prob. (ii) Uncert.Coh. (iii) Segm.Exp. (iv) OpinionScale
STAPLE×××✓
Prob U-Net✓✓×✓
CM global××✓✓
CM pixel××✓×
Pionono✓✓✓✓
", + "image_path": "e68094090a3300768aff71da3682e5953b2d6e4e9bc372ef73407b5ed99d21c9.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 179, + 547, + 269 + ], + "lines": [ + { + "bbox": [ + 304, + 179, + 547, + 269 + ], + "spans": [ + { + "bbox": [ + 304, + 179, + 547, + 269 + ], + "type": "text", + "content": "Table 1. For AI segmentation models to achieve the best possible diagnostic support, they should address four key issues: (i) provide a probabilistic uncertainty estimation, not only a single prediction for a test image; (ii) provide multiple coherent segmentation hypotheses; (iii) simulate different expert opinions for better explainability and decision support; (iv) scale to a higher amount of raters in the case that more data from different hospitals can be integrated." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 291, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 291, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 291, + 545, + 422 + ], + "type": "text", + "content": "learning [20, 26] or uncertainty of out of distribution samples [17]. The uncertainty in annotations has previously been addressed by the Probabilistic U-Net [13] (Prob U-Net), which encodes the labeling behavior in a latent random variable. The model is trained as a variational autoencoder with an encoder network predicting the latent distribution. This approach models a general variability in annotations but lacks the explicit modeling of inter- and intraobserver variability. Therefore, it is not able to incorporate the rater information during training and cannot simulate expert opinions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 424, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 424, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 424, + 545, + 496 + ], + "type": "text", + "content": "Crowdsourcing. While existing crowdsourcing methods aim to capture inter-observer variability in the training labels, this variability is often not reflected in the test predictions by probabilistic outputs [13]. The intra-observer variability is often not modeled at all, although it is often mentioned as a challenge in literature [21, 16, 28, 2, 7]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "content": "One way to handle multiple annotations is label fusion. With this method, the annotations of different raters are merged to a single set of labels. The \"Simultaneous Truth and Performance Level Estimation\" (STAPLE) mechanism performs label fusion with a probabilistic estimate of the true labels by weighting each segmentation depending upon the estimated performance level of each rater [32]. A supervised network can then be trained on these fused labels. More dedicated approaches incorporate different rater labels using confusion matrices (CM), for example for classification of image patches with Gaussian processes [18] or image segmentation with global confusion matrices [31] (CM global). In this direction, also pixel-wise confusion matrices were explored for semantic segmentation that are estimated by a dedicated deep neural network [34] (CM pixel). These models have shown promising results, but come with a conceptual problem: They assume that the pixels are statistically independent of each other, although" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21098" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 178 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 178 + ], + "type": "text", + "content": "neighboring pixels have a high correlation. Therefore, the output of different segmentation hypotheses is not coherent. Furthermore, the predictions of the mentioned approaches [31, 34] are not modeled by a predictive distribution, but by a deterministic point estimate. While the global confusion matrix approach [31] has a limited expressiveness, the pixel-wise calculation [34] is hard to scale for multiple raters, because for each rater, a complete deep neural network must be trained and stored." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 288, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 288, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 288, + 228 + ], + "type": "text", + "content": "Pionono unites the advantages of probabilistic and crowdsourcing methods. We summarize a comparison of different characteristics of Pionono and related methods for image segmentation in Table 1." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 239, + 107, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 107, + 251 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 107, + 251 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 259, + 287, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 259, + 287, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 287, + 307 + ], + "type": "text", + "content": "In this section, we outline the background of the proposed method. It is implemented in the Pytorch [23] framework and is publicly available at https://github.com/arneschmidt/pionono_segmentation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 315, + 160, + 327 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 315, + 160, + 327 + ], + "spans": [ + { + "bbox": [ + 47, + 315, + 160, + 327 + ], + "type": "text", + "content": "3.1. Problem Definition" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 332, + 287, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 332, + 287, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 332, + 287, + 429 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 46, + 332, + 287, + 429 + ], + "type": "inline_equation", + "content": "X = \\{x_{i} \\in \\mathbb{R}^{H \\times W \\times 3}\\}_{i=1,..,N}" + }, + { + "bbox": [ + 46, + 332, + 287, + 429 + ], + "type": "text", + "content": " be a set of images, " + }, + { + "bbox": [ + 46, + 332, + 287, + 429 + ], + "type": "inline_equation", + "content": "S^{r} = \\{s_{i}^{r} \\in \\mathbb{R}^{H \\times W \\times C}\\}_{i=1,..,N}" + }, + { + "bbox": [ + 46, + 332, + 287, + 429 + ], + "type": "text", + "content": " the corresponding segmentation maps with image dimensions " + }, + { + "bbox": [ + 46, + 332, + 287, + 429 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 46, + 332, + 287, + 429 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 332, + 287, + 429 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 332, + 287, + 429 + ], + "type": "text", + "content": " the number of classes. The segmentation maps are provided by different raters " + }, + { + "bbox": [ + 46, + 332, + 287, + 429 + ], + "type": "inline_equation", + "content": "r \\in R = \\{1,2,..,M\\}" + }, + { + "bbox": [ + 46, + 332, + 287, + 429 + ], + "type": "text", + "content": ". Some or all images can be segmented by multiple raters, such that some segmentation maps " + }, + { + "bbox": [ + 46, + 332, + 287, + 429 + ], + "type": "inline_equation", + "content": "s_{i}^{r}" + }, + { + "bbox": [ + 46, + 332, + 287, + 429 + ], + "type": "text", + "content": " can be empty. The proposed model does not require any overlap of the sets of annotated images." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 430, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 287, + 525 + ], + "type": "text", + "content": "If there are images available with segmentations assigned by expert agreements (so-called gold labels), the model should be able to predict a gold distribution over outputs " + }, + { + "bbox": [ + 46, + 430, + 287, + 525 + ], + "type": "inline_equation", + "content": "p(S^{\\mathrm{gold}})" + }, + { + "bbox": [ + 46, + 430, + 287, + 525 + ], + "type": "text", + "content": " with the mean estimating the segmentation and the variance estimating the uncertainty. In any case, the model should model different segmentation hypotheses for the raters " + }, + { + "bbox": [ + 46, + 430, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\{p(S^r); r = 1,2,\\dots,M\\}" + }, + { + "bbox": [ + 46, + 430, + 287, + 525 + ], + "type": "text", + "content": " for diagnostic decision support." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 533, + 146, + 545 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 146, + 545 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 146, + 545 + ], + "type": "text", + "content": "3.2. Proposed Model" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 552, + 287, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 287, + 634 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 287, + 634 + ], + "type": "text", + "content": "First, we introduce the common segmentation backbone " + }, + { + "bbox": [ + 46, + 552, + 287, + 634 + ], + "type": "inline_equation", + "content": "f_{\\omega}" + }, + { + "bbox": [ + 46, + 552, + 287, + 634 + ], + "type": "text", + "content": " with trainable weights " + }, + { + "bbox": [ + 46, + 552, + 287, + 634 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 552, + 287, + 634 + ], + "type": "text", + "content": ". We use the well-known U-Net architecture [25] with a Resnet34 feature extractor [9]. This model takes an image " + }, + { + "bbox": [ + 46, + 552, + 287, + 634 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 46, + 552, + 287, + 634 + ], + "type": "text", + "content": " and extracts a feature map " + }, + { + "bbox": [ + 46, + 552, + 287, + 634 + ], + "type": "inline_equation", + "content": "v_{i} \\in \\mathbb{R}^{H \\times W \\times L}" + }, + { + "bbox": [ + 46, + 552, + 287, + 634 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 552, + 287, + 634 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 46, + 552, + 287, + 634 + ], + "type": "text", + "content": " being the image resolution and " + }, + { + "bbox": [ + 46, + 552, + 287, + 634 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 552, + 287, + 634 + ], + "type": "text", + "content": " the dimensions of the feature vectors (" + }, + { + "bbox": [ + 46, + 552, + 287, + 634 + ], + "type": "inline_equation", + "content": "L = 16" + }, + { + "bbox": [ + 46, + 552, + 287, + 634 + ], + "type": "text", + "content": " in the case of U-Net). We denote the feature extraction as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 139, + 645, + 287, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 645, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 139, + 645, + 287, + 658 + ], + "type": "interline_equation", + "content": "v _ {i} = f _ {\\omega} \\left(x _ {i}\\right). \\tag {1}", + "image_path": "818ec55f788259c2a873e77fd7af2b915d66268ce6dcda93a4e1030317f89056.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 667, + 287, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 667, + 287, + 691 + ], + "spans": [ + { + "bbox": [ + 46, + 667, + 287, + 691 + ], + "type": "text", + "content": "Based on these feature vectors, we could perform segmentation with a segmentation head " + }, + { + "bbox": [ + 46, + 667, + 287, + 691 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 667, + 287, + 691 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 140, + 701, + 287, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 140, + 701, + 287, + 714 + ], + "type": "interline_equation", + "content": "s _ {i} = f _ {\\theta} \\left(v _ {i}\\right). \\tag {2}", + "image_path": "d2ea8e5ce4d2d90e11067e79fb72c5c4f520c0e0abed817d0113d2f316d61626.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "text", + "content": "Now we extend this model to incorporate the inter- and intra-observer variation. The segmentation maps are influenced by the rater's experience, assessment, and personal choices. To encode the labeling behavior, we use a random vector " + }, + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "inline_equation", + "content": "z \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "text", + "content": ". In practice, " + }, + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "inline_equation", + "content": "D = 8" + }, + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "text", + "content": " are enough dimensions to reflect different labeling behaviors. We define a prior distribution " + }, + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "inline_equation", + "content": "p(z) = \\mathcal{N}(z|0, \\sigma_{\\mathrm{prior}} * I)" + }, + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "text", + "content": " which encodes a generic labeling behavior without further information about the rater. It is possible to encode prior knowledge in this distribution, but we present a general model and leave this for future work. We set " + }, + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{prior}}^2 = 2.0" + }, + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "text", + "content": ", because we observe a realistic variability in the output for this value. In section 4.5 we prove that the model is robust for different settings of hyperparameters " + }, + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{prior}}^2" + }, + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 240, + 545, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 240, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 304, + 240, + 545, + 275 + ], + "type": "text", + "content": "Now, the posterior distribution of " + }, + { + "bbox": [ + 304, + 240, + 545, + 275 + ], + "type": "inline_equation", + "content": "p(z|r)" + }, + { + "bbox": [ + 304, + 240, + 545, + 275 + ], + "type": "text", + "content": " that depends on the rater " + }, + { + "bbox": [ + 304, + 240, + 545, + 275 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 240, + 545, + 275 + ], + "type": "text", + "content": " should be found. We approximate it with one multivariate Gaussian distribution for each rater:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 350, + 286, + 545, + 300 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 286, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 350, + 286, + 545, + 300 + ], + "type": "interline_equation", + "content": "q (z | r) = \\mathcal {N} \\left(z \\mid \\mu^ {r}, \\Sigma^ {r}\\right) \\forall r = 1,.., M \\tag {3}", + "image_path": "b3572a736ef7c16f23f6845b64d476847c0be7bc73ff5defa8ecc9b5bcb63c11.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 308, + 545, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 545, + 417 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 308, + 545, + 417 + ], + "type": "inline_equation", + "content": "\\{\\mu^r,\\Sigma^r\\}^{r = 1,\\dots ,M}" + }, + { + "bbox": [ + 304, + 308, + 545, + 417 + ], + "type": "text", + "content": " are trainable parameters. The variance of each distribution " + }, + { + "bbox": [ + 304, + 308, + 545, + 417 + ], + "type": "inline_equation", + "content": "q(z|r)" + }, + { + "bbox": [ + 304, + 308, + 545, + 417 + ], + "type": "text", + "content": " models the intra - observer variability. The differences between the distributions for different raters model the inter - observer variability. To obtain the predictive gold distribution we add another 'rater' " + }, + { + "bbox": [ + 304, + 308, + 545, + 417 + ], + "type": "inline_equation", + "content": "r = M + 1" + }, + { + "bbox": [ + 304, + 308, + 545, + 417 + ], + "type": "text", + "content": " represented by an additional gold distribution " + }, + { + "bbox": [ + 304, + 308, + 545, + 417 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 308, + 545, + 417 + ], + "type": "text", + "content": " which is trained with the available gold segmentations. During prediction, this distribution provides the estimated agreement between experts." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 418, + 545, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 464 + ], + "type": "text", + "content": "The segmentation head " + }, + { + "bbox": [ + 304, + 418, + 545, + 464 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 418, + 545, + 464 + ], + "type": "text", + "content": ", parametrized by weights " + }, + { + "bbox": [ + 304, + 418, + 545, + 464 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 418, + 545, + 464 + ], + "type": "text", + "content": " must be adapted to take the random vector " + }, + { + "bbox": [ + 304, + 418, + 545, + 464 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 418, + 545, + 464 + ], + "type": "text", + "content": " into account. The approximated predictive distribution is then obtained by:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 343, + 465, + 545, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 465, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 343, + 465, + 545, + 491 + ], + "type": "interline_equation", + "content": "q \\left(s _ {i} \\mid x _ {i}, r, \\omega , \\theta\\right) = \\int f _ {\\theta} \\left(v _ {i}, z\\right) q (z | r) d z. \\tag {4}", + "image_path": "d696fd3f8c72fa70bbd53d33243c18df2e2ec738eecf9aef43b9f6f7ab521665.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 495, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 520 + ], + "type": "text", + "content": "The closed-form calculation is not feasible and therefore we approximate it by Monte Carlo (MC) sampling:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 353, + 529, + 545, + 544 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 529, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 353, + 529, + 545, + 544 + ], + "type": "interline_equation", + "content": "\\tilde {s} _ {i, j} | x _ {i}, r = f _ {\\theta} \\left(v _ {i}, \\tilde {z} _ {j}\\right); \\tilde {z} _ {j} \\sim q (z | r) \\tag {5}", + "image_path": "efeb12968b709429d2b2201fb0df7ae22579ce3fc3119e8223d0caa1b40596e6.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 553, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 553, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 553, + 545, + 624 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 304, + 553, + 545, + 624 + ], + "type": "inline_equation", + "content": "j = 1,\\dots,K" + }, + { + "bbox": [ + 304, + 553, + 545, + 624 + ], + "type": "text", + "content": " indexing the MC samples. In practice, we concatenate the feature maps " + }, + { + "bbox": [ + 304, + 553, + 545, + 624 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 304, + 553, + 545, + 624 + ], + "type": "text", + "content": " and the latent vector " + }, + { + "bbox": [ + 304, + 553, + 545, + 624 + ], + "type": "inline_equation", + "content": "\\tilde{z}_j" + }, + { + "bbox": [ + 304, + 553, + 545, + 624 + ], + "type": "text", + "content": " which is broadcasted to the image size, leading to a feature map with dimensions " + }, + { + "bbox": [ + 304, + 553, + 545, + 624 + ], + "type": "inline_equation", + "content": "H\\times W\\times (L + D)" + }, + { + "bbox": [ + 304, + 553, + 545, + 624 + ], + "type": "text", + "content": ". The segmentation head consists of three layers with 1x1 convolutions and 16 filters in the first two layers and " + }, + { + "bbox": [ + 304, + 553, + 545, + 624 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 553, + 545, + 624 + ], + "type": "text", + "content": " filters in the last layer." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 633, + 370, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 633, + 370, + 646 + ], + "spans": [ + { + "bbox": [ + 306, + 633, + 370, + 646 + ], + "type": "text", + "content": "3.3. Training" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 652, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 652, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 652, + 545, + 713 + ], + "type": "text", + "content": "First, all posterior distributions " + }, + { + "bbox": [ + 304, + 652, + 545, + 713 + ], + "type": "inline_equation", + "content": "q(z|r)" + }, + { + "bbox": [ + 304, + 652, + 545, + 713 + ], + "type": "text", + "content": " are initialized randomly. Each initial value of the mean vectors " + }, + { + "bbox": [ + 304, + 652, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mu^r" + }, + { + "bbox": [ + 304, + 652, + 545, + 713 + ], + "type": "text", + "content": " is independently drawn from a distribution " + }, + { + "bbox": [ + 304, + 652, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,\\sigma_{\\mathrm{post}}^2)" + }, + { + "bbox": [ + 304, + 652, + 545, + 713 + ], + "type": "text", + "content": ". We set " + }, + { + "bbox": [ + 304, + 652, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{post}}^2 = 8" + }, + { + "bbox": [ + 304, + 652, + 545, + 713 + ], + "type": "text", + "content": ", because this initializes the mean vectors sufficiently different for a good optimization. In section 4.5 we" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21099" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "content": "show, that the model is robust to other settings of this value. The covariance matrices " + }, + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "inline_equation", + "content": "\\Sigma^r" + }, + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "content": " are initialized with " + }, + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{prior}} * I" + }, + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 95, + 286, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 95, + 286, + 120 + ], + "spans": [ + { + "bbox": [ + 47, + 95, + 286, + 120 + ], + "type": "text", + "content": "To optimize the parameters " + }, + { + "bbox": [ + 47, + 95, + 286, + 120 + ], + "type": "inline_equation", + "content": "\\{\\mu^r,\\Sigma^r\\}^{r = 1,\\dots ,M}" + }, + { + "bbox": [ + 47, + 95, + 286, + 120 + ], + "type": "text", + "content": " of the probability distribution " + }, + { + "bbox": [ + 47, + 95, + 286, + 120 + ], + "type": "inline_equation", + "content": "q(z|r)" + }, + { + "bbox": [ + 47, + 95, + 286, + 120 + ], + "type": "text", + "content": ", we maximize the ELBO:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 51, + 129, + 286, + 153 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 129, + 286, + 153 + ], + "spans": [ + { + "bbox": [ + 51, + 129, + 286, + 153 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {E L B O} = \\mathbb {E} _ {q} \\log p \\left(S ^ {r} | X, r, \\omega , \\theta\\right) - \\lambda K L (q (Z | r) | p (Z)). \\tag {6}", + "image_path": "b20588b40ed4f46f903ebf918c7c4c407cf62932146df549f1d064d7a3d67a2a.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "text", + "content": "with distribution " + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "text", + "content": " as defined in eq. 4. The first term defines a log-likelihood (LL) loss, making the model fit to the annotations of each rater. The second term defines the KL-divergence between the posterior distribution " + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "inline_equation", + "content": "q(Z|r)" + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "text", + "content": " and the prior " + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "inline_equation", + "content": "p(Z)" + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "text", + "content": " and works as a regularization of the latent distributions. The factor " + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "text", + "content": " weights the regularization term and is set to 0.0005 to balance the magnitudes of the log-likelihood and the KL (we will check the robustness of this hyperparameter in Section 4.5). While the KL term can be optimized analytically, the log likelihood term must be approximated. We use the reparametrization trick [12] to split each probabilistic sample " + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "inline_equation", + "content": "\\tilde{z}^r" + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "text", + "content": " into its probabilistic component and deterministic parameters " + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "inline_equation", + "content": "\\mu^r" + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "inline_equation", + "content": "\\Sigma^r" + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "text", + "content": ". These parameters can be optimized by backpropagation of gradients, together with the CNN parameters " + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "text", + "content": ". For numerical stability, we train the covariance matrix parameters by using the lower triangular matrix " + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "text", + "content": " of the Cholesky decomposition " + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "inline_equation", + "content": "\\Sigma^r = L^r L^{r^\\top}" + }, + { + "bbox": [ + 47, + 154, + 286, + 403 + ], + "type": "text", + "content": ". The log-likelihood can be optimized with standard methods like the categorical cross-entropy. We found that the general dice loss [30] leads to better results, so all final results are reported with this loss." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 405, + 286, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 286, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 286, + 501 + ], + "type": "text", + "content": "We use the Adam optimizer [11] for 100 epochs with a learning rate of 0.0001. The model parameters " + }, + { + "bbox": [ + 46, + 405, + 286, + 501 + ], + "type": "inline_equation", + "content": "\\mu^r, \\Sigma^r" + }, + { + "bbox": [ + 46, + 405, + 286, + 501 + ], + "type": "text", + "content": " are optimized with a higher learning rate of " + }, + { + "bbox": [ + 46, + 405, + 286, + 501 + ], + "type": "inline_equation", + "content": "\\nu = 0.02" + }, + { + "bbox": [ + 46, + 405, + 286, + 501 + ], + "type": "text", + "content": ", because else the gradient was not strong enough to properly learn the rater distributions. We tested " + }, + { + "bbox": [ + 46, + 405, + 286, + 501 + ], + "type": "inline_equation", + "content": "\\nu = 0.01, 0.02, 0.04" + }, + { + "bbox": [ + 46, + 405, + 286, + 501 + ], + "type": "text", + "content": " and include the results in section 4.5. Both learning rates are decreased after 40 epochs by dividing them by 1.1 in each epoch." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 508, + 118, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 508, + 118, + 521 + ], + "spans": [ + { + "bbox": [ + 47, + 508, + 118, + 521 + ], + "type": "text", + "content": "3.4. Predicting" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 526, + 286, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 526, + 286, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 526, + 286, + 551 + ], + "type": "text", + "content": "For a test image " + }, + { + "bbox": [ + 47, + 526, + 286, + 551 + ], + "type": "inline_equation", + "content": "x^{*}" + }, + { + "bbox": [ + 47, + 526, + 286, + 551 + ], + "type": "text", + "content": ", the predictive gold distribution can again be obtained by drawing Monte-Carlo samples" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 76, + 559, + 286, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 559, + 286, + 574 + ], + "spans": [ + { + "bbox": [ + 76, + 559, + 286, + 574 + ], + "type": "interline_equation", + "content": "\\tilde {s} _ {j} ^ {*} \\mid x ^ {*}, r = f _ {\\theta} \\left(v ^ {*}, \\tilde {z} _ {j}\\right); \\tilde {z} _ {j} \\sim q (z | r = M + 1) \\tag {7}", + "image_path": "ba9a5a078c27cced77d89492cccae2f016b1f0c3a746c7638ca147f23144b5f8.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 582, + 286, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 286, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 286, + 653 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 47, + 582, + 286, + 653 + ], + "type": "inline_equation", + "content": "j = 1,..,K" + }, + { + "bbox": [ + 47, + 582, + 286, + 653 + ], + "type": "text", + "content": " indexing the MC samples and " + }, + { + "bbox": [ + 47, + 582, + 286, + 653 + ], + "type": "inline_equation", + "content": "q(z|r = M + 1)" + }, + { + "bbox": [ + 47, + 582, + 286, + 653 + ], + "type": "text", + "content": " representing the gold distribution as described in section 3.2. The mean of these samples provides the segmentation hypothesis that approximates the expert agreements. The variance of the samples indicates uncertainties in the prediction." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 654, + 286, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 286, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 286, + 715 + ], + "type": "text", + "content": "Furthermore, the model is able to simulate intraobserver variations of rater " + }, + { + "bbox": [ + 46, + 654, + 286, + 715 + ], + "type": "inline_equation", + "content": "r^\\prime" + }, + { + "bbox": [ + 46, + 654, + 286, + 715 + ], + "type": "text", + "content": " by drawing multiple samples of the distribution " + }, + { + "bbox": [ + 46, + 654, + 286, + 715 + ], + "type": "inline_equation", + "content": "\\tilde{z}_j^{\\prime}\\sim q(z|r = r^{\\prime})" + }, + { + "bbox": [ + 46, + 654, + 286, + 715 + ], + "type": "text", + "content": " for the final prediction. The inter-observer variations between rater " + }, + { + "bbox": [ + 46, + 654, + 286, + 715 + ], + "type": "inline_equation", + "content": "r^\\prime" + }, + { + "bbox": [ + 46, + 654, + 286, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 654, + 286, + 715 + ], + "type": "inline_equation", + "content": "r''" + }, + { + "bbox": [ + 46, + 654, + 286, + 715 + ], + "type": "text", + "content": " can be simulated by using samples " + }, + { + "bbox": [ + 46, + 654, + 286, + 715 + ], + "type": "inline_equation", + "content": "\\tilde{z}_j^\\prime \\sim q(z|r = r^\\prime)" + }, + { + "bbox": [ + 46, + 654, + 286, + 715 + ], + "type": "text", + "content": " and" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 544, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 544, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 544, + 95 + ], + "type": "inline_equation", + "content": "\\tilde{z}_k^{\\prime \\prime}\\sim q(z|r = r^{\\prime \\prime})" + }, + { + "bbox": [ + 305, + 72, + 544, + 95 + ], + "type": "text", + "content": " and finally taking the mean of both output distributions." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 96, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 96, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 96, + 545, + 204 + ], + "type": "text", + "content": "The model can therefore simulate expert opinions for a given test image. Other AI methods typically aggregate the expertise provided by all annotators to make predictions (e.g., using STAPLE, Prob U-Net). However, in such approaches, the knowledge of highly specialized experts can be diluted or lost among the less experienced annotators' knowledge. In our framework, we provide consistent predictions for each individual expert, thereby preserving their unique expertise and contributions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 213, + 386, + 227 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 213, + 386, + 227 + ], + "spans": [ + { + "bbox": [ + 305, + 213, + 386, + 227 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 234, + 545, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 234, + 545, + 317 + ], + "spans": [ + { + "bbox": [ + 304, + 234, + 545, + 317 + ], + "type": "text", + "content": "In several experiments we demonstrate that the uncertainty estimation of the model indicates areas of false predictions (4.2), the model is able to capture the inter and intra-observer variations (4.3) and outperforms other related methods (4.4). Additionally, we analyze the robustness to hyperparameters (4.5), required resources (4.6), and limitations (4.7)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 324, + 368, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 324, + 368, + 335 + ], + "spans": [ + { + "bbox": [ + 306, + 324, + 368, + 335 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 342, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 545, + 510 + ], + "type": "text", + "content": "For empirical validation, three public histopathological datasets were used. The first dataset, \"Gleason 2019\" [22] was published as a MICCAI grand challenge for pathology and includes 333 Tissue Micro Arrays (TMA) of prostate cancer, labeled by 6 different pathologists. The TMAs were scanned with a magnification of " + }, + { + "bbox": [ + 304, + 342, + 545, + 510 + ], + "type": "inline_equation", + "content": "40\\mathrm{x}" + }, + { + "bbox": [ + 304, + 342, + 545, + 510 + ], + "type": "text", + "content": " and have a size of approximately " + }, + { + "bbox": [ + 304, + 342, + 545, + 510 + ], + "type": "inline_equation", + "content": "4000 \\times 4000" + }, + { + "bbox": [ + 304, + 342, + 545, + 510 + ], + "type": "text", + "content": " pixels. Of the 333 images, 244 are publicly available with labels (the test annotations of the challenge are not available). Each pathologist annotated between 61 and 241 TMAs with segmentation masks and the gold labels were obtained using the STAPLE algorithm [32], following the original work of the dataset [22]. We resize all images to " + }, + { + "bbox": [ + 304, + 342, + 545, + 510 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 304, + 342, + 545, + 510 + ], + "type": "text", + "content": " pixels and create 4 cross-validation splits." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 510, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 653 + ], + "type": "text", + "content": "The second dataset, which we will refer to as \"Arvaniti TMA\" was published in 2018 [4] and includes a total of 886 TMAs of prostate cancer of which 245 images were annotated by two pathologists (while the other images only have annotations of one pathologist and are therefore discarded in our study). The TMAs were scanned with a magnification of " + }, + { + "bbox": [ + 304, + 510, + 545, + 653 + ], + "type": "inline_equation", + "content": "40\\mathrm{x}" + }, + { + "bbox": [ + 304, + 510, + 545, + 653 + ], + "type": "text", + "content": " but the scanned area is smaller than for the Gleason19 dataset. The images have a resolution of " + }, + { + "bbox": [ + 304, + 510, + 545, + 653 + ], + "type": "inline_equation", + "content": "3100\\times 3100" + }, + { + "bbox": [ + 304, + 510, + 545, + 653 + ], + "type": "text", + "content": " pixels and we resize them to " + }, + { + "bbox": [ + 304, + 510, + 545, + 653 + ], + "type": "inline_equation", + "content": "512\\times 512" + }, + { + "bbox": [ + 304, + 510, + 545, + 653 + ], + "type": "text", + "content": " such that the magnification matches the resized images of the Gleason 2019 dataset. Again, we split the dataset into 4 cross-validation splits for the experimental setup." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "For the classification of prostate cancer, the tissue is segmented in the Gleason Grading (GG) scheme. The classes are 'Non-cancerous' (NC), 'Gleason 3' (G3), 'Gleason 4' (G4), and 'Gleason 5' (G5) depending on the architectural growth patterns of the tumor [28, 29]. 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"image_caption" + }, + { + "bbox": [ + 212, + 162, + 244, + 171 + ], + "lines": [ + { + "bbox": [ + 212, + 162, + 244, + 171 + ], + "spans": [ + { + "bbox": [ + 212, + 162, + 244, + 171 + ], + "type": "text", + "content": "(h) Uncert." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 179, + 287, + 268 + ], + "lines": [ + { + "bbox": [ + 46, + 179, + 287, + 268 + ], + "spans": [ + { + "bbox": [ + 46, + 179, + 287, + 268 + ], + "type": "text", + "content": "Figure 2. Gold prediction and uncertainty of the Pionono model. The first row shows a confident prediction as the uncertainty in 2d is low (white) for almost all the area. Indeed, the segmentation prediction 2c is very accurate, see the ground truth (GT) 2b. The second row shows an example of an uncertain prediction. Some parts of the area classified as G3 (yellow) in " + }, + { + "bbox": [ + 46, + 179, + 287, + 268 + ], + "type": "inline_equation", + "content": "2\\mathrm{g}" + }, + { + "bbox": [ + 46, + 179, + 287, + 268 + ], + "type": "text", + "content": " are labeled as G4 in the ground truth 2f. These areas are estimated with a high uncertainty (black) in " + }, + { + "bbox": [ + 46, + 179, + 287, + 268 + ], + "type": "inline_equation", + "content": "2\\mathrm{h}" + }, + { + "bbox": [ + 46, + 179, + 287, + 268 + ], + "type": "text", + "content": ", warning that these predictions are unreliable." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 289, + 287, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 432 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 432 + ], + "type": "text", + "content": "segmentations we use the colors: green for NC, yellow for G3, orange for G4, and red for G5. For the evaluation of algorithms for prostate cancer classification, previous works used the Cohen's kappa coefficient [22, 4, 28] which measures the agreement of two raters or a rater and an AI model. To compare to previously reported results for the two datasets, we use the unweighted Cohen's kappa " + }, + { + "bbox": [ + 46, + 289, + 287, + 432 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 289, + 287, + 432 + ], + "type": "text", + "content": " for the Gleason 2019 dataset [22] and the quadratic weighted Cohen's kappa " + }, + { + "bbox": [ + 46, + 289, + 287, + 432 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 289, + 287, + 432 + ], + "type": "text", + "content": " for the Arvaniti TMA dataset [4]. The main difference is that the quadratic kappa takes the class order into account and weighs the errors based on the quadratic distance of the predicted and the real class." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 434, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 529 + ], + "type": "text", + "content": "The third dataset contains 151 WSIs for breast cancer segmentation that were sliced into 11,836 patches of " + }, + { + "bbox": [ + 46, + 434, + 287, + 529 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 434, + 287, + 529 + ], + "type": "text", + "content": " pixels annotated by 25 raters [3, 19]. We will refer to this dataset as \"bc segmentation\". The tissue was segmented into \"tumor\", \"inflammation\", \"necrosis\", \"stroma\", and \"other\". Here, the gold labels were obtained by an actual discussion of experts. We use the predefined train/validation/test splits [19]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 529, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 590 + ], + "type": "text", + "content": "For all datasets we use image augmentation with the albumenations library [6] by applying random flip, rotation, shear, zoom, blur, and shifts in brightness, contrast, hue, and saturation. This leads to a broad range of realistic transformations of the image to avoid overfitting." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 598, + 178, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 598, + 178, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 598, + 178, + 611 + ], + "type": "text", + "content": "4.2. Uncertainty estimation" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": "The proposed model provides probabilistic predictions that allow an accurate assessment of the predictive uncertainty. Fig. 2 shows the model predictions and uncertainties obtained with the gold distribution as described in section 3.2. For the first image (2a), the prediction of the model (2c) is accurate and matches the real gold annotation (2b) very well. The uncertainty (2d) for this predictions is low (white), which means that there is a low risk of a wrong" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": "prediction. Therefore, the model correctly indicates that this prediction is reliable. For the second image 2e, some areas that are predicted as G3 (yellow) in " + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "inline_equation", + "content": "(2\\mathrm{g})" + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": " are actually G4 in the ground truth gold prediction (2f). The model's uncertainty estimation indicates that this prediction is not reliable: the misclassified areas are marked with a high uncertainty (dark) in the image (2h). Therefore, the probabilistic output adds valuable information to the diagnostic process. It estimates if a prediction is reliable - or unreliable and should be double-checked." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 201, + 493, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 201, + 493, + 213 + ], + "spans": [ + { + "bbox": [ + 305, + 201, + 493, + 213 + ], + "type": "text", + "content": "4.3. Inter- and Intra-observer Variation" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 221, + 545, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 221, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 221, + 545, + 304 + ], + "type": "text", + "content": "The Pionono model is able to capture the inter- and intraobserver variability. This accurate probabilistic modeling of the annotations does not only improve the predictive results (see section 4.4), but also allows to simulate specific experts at test time. In this section, we empirically show that the model learns the different label behaviors of the raters and is able to reproduce them." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 306, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 545, + 461 + ], + "type": "text", + "content": "In Fig. 3a we plot the inter-observer variations between the raters. The figure shows that there is indeed a high variability among the raters, with a Cohen's kappa ranging from 0.36 to 0.72. The simulated test predictions by Pionono show a higher agreement with each rater than the average agreement of the other raters, except for rater 2. For two raters (1 and 5), the simulated predictions of Pionono are even more than 15 percentage points higher than the average rater agreement. We also measured the IoU metric, which was 0.574, 0.540, 0.619, 0.649, 0.692, 0.507, for the 6 raters respectively, compared to a mean inter-pathologist IoU of 0.361. The results confirm that most raters are modeled with high accuracy." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "text", + "content": "Fig. 3b shows the posterior distributions " + }, + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "inline_equation", + "content": "q(z|r)" + }, + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "text", + "content": " of the proposed model, encoding the labeling behavior of each rater. The following observations confirm, that these learned distributions approximate well the real-world labeling behavior of the raters: (i) The four raters 3, 4, 5 and 6 show a high overlap of the distributions and corresponding to a high labeling agreement shown in Fig. 3a. (ii) The gold distribution (simulating raters agreement) overlaps significantly with the distribution of these four raters. (iii) The distribution of rater 2 is far away from all other distributions. This rater shows a different labeling behavior due to frequent under-segmentation of images, assigning the 'background' class to areas that contain tissue. (iv) Raters 1 and 6 often deviate from the other raters, especially for the differentiation of classes G3 and G4. Their distribution accordingly has a smaller overlap with the gold distribution and the other raters. Fig. 4 shows some visual image examples of Pionono test predictions, simulating each rater " + }, + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "text", + "content": " by drawing samples from the corresponding distribution " + }, + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "inline_equation", + "content": "q(z|r)" + }, + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "text", + "content": " and then taking the mean of the output samples. The examples confirm that the rater differences are modeled well." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21101" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 74, + 165, + 190 + ], + "blocks": [ + { + "bbox": [ + 55, + 74, + 165, + 190 + ], + "lines": [ + { + "bbox": [ + 55, + 74, + 165, + 190 + ], + "spans": [ + { + "bbox": [ + 55, + 74, + 165, + 190 + ], + "type": "image", + "image_path": "209f76abb9b2215c4e7df52da06042db7c5b2ae800e1eb0934a2accc9034a536.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 69, + 192, + 150, + 201 + ], + "lines": [ + { + "bbox": [ + 69, + 192, + 150, + 201 + ], + "spans": [ + { + "bbox": [ + 69, + 192, + 150, + 201 + ], + "type": "text", + "content": "(a) Rater simulation statistic" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 205, + 287, + 348 + ], + "lines": [ + { + "bbox": [ + 46, + 205, + 287, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 287, + 348 + ], + "type": "text", + "content": "Figure 3. Analyzing the labeling behavior. In Fig. (a) the agreement of each rater with all other raters is depicted, measured by the unweighted Cohen's Kappa of the true labels [22]. The mean agreement of each rater with all other raters is represented by a black dot and the agreement with Piononos test predictions, simulating the corresponding rater, by a star. This confirms that the model accurately models each rater, reaching even a higher agreement than the other rater's average, except for rater 2. Fig. (b) shows the first two dimensions of the posterior distributions " + }, + { + "bbox": [ + 46, + 205, + 287, + 348 + ], + "type": "inline_equation", + "content": "q(z|r)" + }, + { + "bbox": [ + 46, + 205, + 287, + 348 + ], + "type": "text", + "content": " with mean and covariance after training. The distributions of raters 3, 4, 5 and 6 overlap significantly with the gold distribution and with each other, indicating a similar labeling behavior. Indeed, these raters show the highest labeling agreement in Fig. (a)." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 175, + 74, + 286, + 190 + ], + "blocks": [ + { + "bbox": [ + 175, + 74, + 286, + 190 + ], + "lines": [ + { + "bbox": [ + 175, + 74, + 286, + 190 + ], + "spans": [ + { + "bbox": [ + 175, + 74, + 286, + 190 + ], + "type": "image", + "image_path": "c490c3899e2cd256034e3ca5cf4f7038d2436be76401f257b8447b5830ba209d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 197, + 193, + 263, + 201 + ], + "lines": [ + { + "bbox": [ + 197, + 193, + 263, + 201 + ], + "spans": [ + { + "bbox": [ + 197, + 193, + 263, + 201 + ], + "type": "text", + "content": "(b) Latent distributions" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 369, + 287, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 287, + 511 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 287, + 511 + ], + "type": "text", + "content": "Next, we analyze the intra-observer variations. As the dataset does not contain multiple annotations of the same rater for the same image, the assessment of this quality is more difficult. Still, certain intra-observer variability can be assessed by observing the general labeling behavior of one annotator. For example, rater 6 tends to over-assign class G5 (red), and rater 2 tends to not segment all image parts that contain tissue. Interestingly, these intra-observer variations are present in the model predictions when multiple samples are drawn from their corresponding distribution. Fig. 5 shows visual examples of the simulated variations of raters 2 and 6." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 520, + 160, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 520, + 160, + 533 + ], + "spans": [ + { + "bbox": [ + 47, + 520, + 160, + 533 + ], + "type": "text", + "content": "4.4. Model Comparison" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 539, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 539, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 539, + 287, + 622 + ], + "type": "text", + "content": "The proposed model is compared to previously reported results and several state-of-the-art approaches (see section 2) for medical image segmentation with labels from multiple raters. For fair comparison, we use the same backbone architecture1, epochs, learning rate, and optimizer for all experiments. We have tuned the model-specific hyperparameters to obtain the best possible results for each method." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 623, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 623, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 623, + 287, + 694 + ], + "type": "text", + "content": "First, we perform experiments with the Gleason 2019 dataset with a 4-fold crossvalidation. For comparison with previous works, we report the unweighted Cohen's kappa metric comparing gold predictions with gold ground truth. Additionally, we report the accuracy. As the results in Table 2 show, the proposed Pionono model outperforms the previ" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 336, + 69, + 375, + 107 + ], + "blocks": [ + { + "bbox": [ + 336, + 69, + 375, + 107 + ], + "lines": [ + { + "bbox": [ + 336, + 69, + 375, + 107 + ], + "spans": [ + { + "bbox": [ + 336, + 69, + 375, + 107 + ], + "type": "image", + "image_path": "47273e0da3316f35882c2690568881eeb50fd0f25945020c95197e57f0fb2a6a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 339, + 121, + 373, + 157 + ], + "blocks": [ + { + "bbox": [ + 339, + 112, + 368, + 121 + ], + "lines": [ + { + "bbox": [ + 339, + 112, + 368, + 121 + ], + "spans": [ + { + "bbox": [ + 339, + 112, + 368, + 121 + ], + "type": "text", + "content": "(a) Image" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 339, + 121, + 373, + 157 + ], + "lines": [ + { 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Inter-observer variations estimated by Pionono. For two test images we depict the ground truth (GT) segmentations of all raters and the predicted segmentations (PR), simulating each rater. The proposed model is able to simulate certain labeling behavior like the tendency of assigning class G5 (red) for raters 2 and 6 (see g and w) where other raters assigned G4 (orange). 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over 20 percentage points. This accounts for the exact modeling of the raters by Pionono, but also for the different choices of backbone architecture and other training details. Compared to other state-of-the-art methods with the same architecture and training details, Pionono still shows a considerably better performance." + } + ] + } + ], + "index": 60 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Next, we compare the generalization capabilities of the models by using the Arvaniti TMA dataset as an external test set, as reported in Table 3. This means, that the models are trained with all images from Gleason 2019 and tested with all images from Arvaniti TMA. As the Arvaniti TMA dataset does not contain gold labels, the model's gold predictions are compared to both raters independently, as previously done by Arvaniti et al. [4]. We observe that the model" + } + ] + } + ], + "index": 61 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 253, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 253, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 253, + 712 + ], + "type": "text", + "content": "1Only the model CM pixel uses ResNet18 to fit on the GPU." + } + ] + } + ], + "index": 62 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21102" + } + ] + } + ], + "index": 63 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 78, + 69, + 116, + 107 + ], + "blocks": [ + { + "bbox": [ + 78, + 69, + 116, + 107 + ], + "lines": [ + { + "bbox": [ + 78, + 69, + 116, + 107 + ], + "spans": [ + { + 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Intra-observer variations estimated by the Pionono model. For two example images we depict the true annotation (GT) of two different raters (" + }, + { + "bbox": [ + 46, + 322, + 287, + 486 + ], + "type": "inline_equation", + "content": "r = 2" + }, + { + "bbox": [ + 46, + 322, + 287, + 486 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 322, + 287, + 486 + ], + "type": "inline_equation", + "content": "r = 6" + }, + { + "bbox": [ + 46, + 322, + 287, + 486 + ], + "type": "text", + "content": "). On the right sides we show different coherent segmentation predictions (PR) for each rater estimated by our model. The differences in each column reflect possible intra-observer variations. The first example (a) shows that rater 6 might show some variations in the assigned classes. While the segmentation prediction (b) is composed by classes G3 (yellow) and G4 (orange), the segmentation sample (f) only consists of G5 (red). Indeed, this rater often assigns class G5 (red) in areas where other raters assign G4 (see Fig. 4) such that this is a plausible hypothesis. In the second example (c) we see variations due to the under-segmentation of rater 2 in some images. Our model captures this behavior and provides hypothesis of more (d) or less (j) segmentation of class G3 (yellow)." + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 175, + 70, + 212, + 106 + ], + "blocks": [ + { + "bbox": [ + 175, + 70, + 212, + 106 + ], + "lines": [ + { + "bbox": [ + 175, + 70, + 212, + 106 + ], + "spans": [ + { + "bbox": [ + 175, + 70, + 212, + 106 + ], + "type": "image", + "image_path": "b2053efe55d8103ec4a9d289f178e3e63a4edfab7dd975d7752fcbf5d08598ab.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 177, + 121, + 211, + 154 + ], + "blocks": [ + { + "bbox": [ + 178, + 112, + 207, + 119 + ], + "lines": [ + { + "bbox": [ + 178, + 112, + 207, + 119 + ], + "spans": [ + { + "bbox": [ + 178, + 112, + 207, + 119 + ], + "type": "text", + "content": "(c) Image" + } + ] + } + ], + "index": 14, + 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= 2" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 507, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 507, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 507, + 287, + 555 + ], + "type": "text", + "content": "generalizes better than all other methods, achieving a higher agreement in terms of Cohen's quadratic kappa with both raters. In terms of accuracy, only 'CM global' outperforms Pionono by a small margin." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 46, + 556, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 287, + 639 + ], + "type": "text", + "content": "In the third experiment, we use the Arvaniti TMA dataset for training and testing with the two rater annotations. Again, the proposed model is able to outperform previously reported results as well as other state-of-the-art methods in terms of quadratic Cohen's kappa. In terms of accuracy, only the \"Prob U-Net\" model obtains a better result for rater 1, while Pionono reaches the best accuracy for rater 2." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 46, + 641, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 689 + ], + "type": "text", + "content": "To validate the model on a different kind of data, we performed the fourth experiment on the \"bc segmentation\" dataset [3]. The results are reported in Table 5 and confirm the strong performance of the proposed Pionono model." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "The results support our hypothesis that explicitly modeling the inter- and intra-observer variations improves the" + } + ] + } + ], + "index": 31 + }, + { + "type": "table", + "bbox": [ + 327, + 70, + 525, + 176 + ], + "blocks": [ + { + "bbox": [ + 327, + 70, + 525, + 176 + ], + "lines": [ + { + "bbox": [ + 327, + 70, + 525, + 176 + ], + "spans": [ + { + "bbox": [ + 327, + 70, + 525, + 176 + ], + "type": "table", + "html": "
MethodUnweighted κAccuracy
Nir et al. [22]0.51N.A.
Qiu et al. [24]0.524N.A.
STAPLE0.75 ± 0.0060.834 ± 0.005
Prob U-Net0.741 ± 0.0020.83 ± 0.001
CM global0.721 ± 0.0180.814 ± 0.012
CM pixel0.692 ± 0.0190.791 ± 0.012
Pionono0.758 ± 0.0110.84 ± 0.007
", + "image_path": "f1125986204767786bcd6037b5115e2d40e4a2cc4b3237bb47afcaf50be0e858.jpg" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "table_body" + } + ], + "index": 32 + }, + { + "type": "table", + "bbox": [ + 320, + 225, + 531, + 379 + ], + "blocks": [ + { + "bbox": [ + 305, + 184, + 545, + 216 + ], + "lines": [ + { + "bbox": [ + 305, + 184, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 305, + 184, + 545, + 216 + ], + "type": "text", + "content": "Table 2. Cohens Kappa Comparison for the 4-fold crossvalidation experiment of the Gleason 2019 dataset, reported by mean and standard error." + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 320, + 225, + 531, + 379 + ], + "lines": [ + { + "bbox": [ + 320, + 225, + 531, + 379 + ], + "spans": [ + { + "bbox": [ + 320, + 225, + 531, + 379 + ], + "type": "table", + "html": "
Rater 1 MethodQuadratic κAccuracy
STAPLE0.629 ± 0.0020.718 ± 0.001
Prob U-Net0.629 ± 0.0050.73 ± 0.003
CM global0.624 ± 0.0030.728 ± 0.002
CM pixel0.618 ± 0.0070.72 ± 0.004
Pionono0.641 ± 0.0060.736 ± 0.004
Rater 2 MethodQuadratic κAccuracy
STAPLE0.563 ± 0.0020.621 ± 0.002
Prob U-Net0.56 ± 0.0030.626 ± 0.006
CM global0.557 ± 0.0030.638 ± 0.006
CM pixel0.551 ± 0.0060.626 ± 0.008
Pionono0.569 ± 0.0050.633 ± 0.005
", + "image_path": "bfc5fd54c9b0f0309f6331ab3d966bea50308d50161d2fbee34f39c243d18e62.jpg" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "table_body" + } + ], + "index": 34 + }, + { + "type": "table", + "bbox": [ + 318, + 430, + 535, + 628 + ], + "blocks": [ + { + "bbox": [ + 305, + 388, + 545, + 421 + ], + "lines": [ + { + "bbox": [ + 305, + 388, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 545, + 421 + ], + "type": "text", + "content": "Table 3. Cohens Kappa Comparison with the two raters of the Arvaniti TMA dataset trained on the Gleason 2019 dataset, reported by mean and standard error." + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 318, + 430, + 535, + 628 + ], + "lines": [ + { + "bbox": [ + 318, + 430, + 535, + 628 + ], + "spans": [ + { + "bbox": [ + 318, + 430, + 535, + 628 + ], + "type": "table", + "html": "
Rater 1 MethodQuadratic κAccuracy
Arvaniti et al. [4]0.55N.A.
Silva-R. et al. [28]0.536N.A.
supervised0.658 ± 0.0250.734 ± 0.008
Prob U-Net0.697 ± 0.0080.762 ± 0.004
CM global0.677 ± 0.0280.745 ± 0.011
CM pixel0.647 ± 0.0160.731 ± 0.012
Pionono0.716 ± 0.0110.751 ± 0.02
Rater 2 MethodQuadratic κAccuracy
Arvaniti0.49N.A.
supervised0.521 ± 0.0140.678 ± 0.014
Prob U-Net0.534 ± 0.0020.68 ± 0.005
CM global0.533 ± 0.0220.676 ± 0.011
CM pixel0.508 ± 0.0130.663 ± 0.008
Pionono0.548 ± 0.0080.697 ± 0.012
", + "image_path": "45eaccad08ea31dd524160401d6ca8a2c0b0033f21cd2b052c7cb7ce236b58b4.jpg" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "table_body" + } + ], + "index": 36 + }, + { + "bbox": [ + 305, + 636, + 545, + 669 + ], + "lines": [ + { + "bbox": [ + 305, + 636, + 545, + 669 + ], + "spans": [ + { + "bbox": [ + 305, + 636, + 545, + 669 + ], + "type": "text", + "content": "Table 4. Cohens Kappa Comparison with the two raters of the Arvaniti TMA dataset trained and validated by 4-fold crossvalidation of the Arvaniti data, reported by mean and standard error." + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "model's performance. Pionono takes the different labeling behavior into account during training which leads to accu" + } + ] + } + ], + "index": 38 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21103" + } + ] + } + ], + "index": 39 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 72, + 70, + 264, + 148 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 264, + 148 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 264, + 148 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 264, + 148 + ], + "type": "table", + "html": "
MethodUnweighted κAccuracy
STAPLE0.647 ± 0.0030.755 ± 0.002
Prob U-Net0.685 ± 0.0230.734 ± 0.004
CM global0.654 ± 0.0050.761 ± 0.004
CM pixel0.689 ± 0.0100.784 ± 0.007
Pionono0.711 ± 0.0020.799 ± 0.001
", + "image_path": "985d98ecbf472cccddd6f7d568fda46044218130ea1d9a276696b1d6b6f379a5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 204, + 115, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 204, + 115, + 216 + ], + "spans": [ + { + "bbox": [ + 47, + 204, + 115, + 216 + ], + "type": "text", + "content": "rate predictions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 229, + 256, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 229, + 256, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 229, + 256, + 243 + ], + "type": "text", + "content": "4.5. Robustness to Hyperparameter Settings" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 250, + 287, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 250, + 287, + 406 + ], + "spans": [ + { + "bbox": [ + 46, + 250, + 287, + 406 + ], + "type": "text", + "content": "To measure the sensitivity of the model regarding different hyperparameters, we performed studies on the 4-fold cross-validation experiment of the Gleason 19 dataset. Table 6 shows that the model is robust to variations of all analyzed hyperparameters. We observe minor performance drops for different values of the regularization factor " + }, + { + "bbox": [ + 46, + 250, + 287, + 406 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 250, + 287, + 406 + ], + "type": "text", + "content": " and the initialization variance " + }, + { + "bbox": [ + 46, + 250, + 287, + 406 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{post}}^2" + }, + { + "bbox": [ + 46, + 250, + 287, + 406 + ], + "type": "text", + "content": ". In both cases, wrong choices of the hyperparameters can hinder the correct optimization of the latent distributions. Furthermore, we tested different backbone architectures, indicating a limited performance with a VGG16 backbone. Overall the performance drops are minor and for all other settings, the model shows highly accurate results of " + }, + { + "bbox": [ + 46, + 250, + 287, + 406 + ], + "type": "inline_equation", + "content": "\\kappa >0.75" + }, + { + "bbox": [ + 46, + 250, + 287, + 406 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 418, + 163, + 431 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 418, + 163, + 431 + ], + "spans": [ + { + "bbox": [ + 47, + 418, + 163, + 431 + ], + "type": "text", + "content": "4.6. Required Resources" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 439, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 439, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 439, + 287, + 559 + ], + "type": "text", + "content": "For the Gleason 2019 dataset with images of " + }, + { + "bbox": [ + 46, + 439, + 287, + 559 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 46, + 439, + 287, + 559 + ], + "type": "text", + "content": ", the model can be trained with a batch size of 3 on a single NVIDIA GeForce RTX 3090 with 24Gb memory. The training takes less than 1.5h in total and test predictions less than 0.2s per image. The trained model occupies less than 350Mb when saved to the disk. As each additional annotator adds only one additional vector " + }, + { + "bbox": [ + 46, + 439, + 287, + 559 + ], + "type": "inline_equation", + "content": "\\mu^r \\in \\mathbb{R}^8" + }, + { + "bbox": [ + 46, + 439, + 287, + 559 + ], + "type": "text", + "content": " and one covariance matrix " + }, + { + "bbox": [ + 46, + 439, + 287, + 559 + ], + "type": "inline_equation", + "content": "\\Sigma^r \\in \\mathbb{R}^{8 \\times 8}" + }, + { + "bbox": [ + 46, + 439, + 287, + 559 + ], + "type": "text", + "content": ", it is scalable to a large number of annotators. The model's quick runtime and excellent scalability make it easily applicable in clinical practice." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 573, + 124, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 573, + 124, + 585 + ], + "spans": [ + { + "bbox": [ + 47, + 573, + 124, + 585 + ], + "type": "text", + "content": "4.7. Limitations" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": "As semantic segmentation itself is a challenging task, some details of the annotator segmentations are not captured well by the model, such as the variations of class NC (green) in the GT of Fig. 4d - 4x or class G4 (orange) in the GT of Fig. 4f - 4z. Here, the model tends to predict similar shapes for the raters. A possible solution is to use more layers in the segmentation head " + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": " with a wider kernel (e.g. " + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "inline_equation", + "content": "5 \\times 5" + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": " convolutions). This would increase the complexity of the model and might enable it to capture the different labeling behavior in even more detail." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 312, + 70, + 541, + 316 + ], + "blocks": [ + { + "bbox": [ + 57, + 156, + 276, + 179 + ], + "lines": [ + { + "bbox": [ + 57, + 156, + 276, + 179 + ], + "spans": [ + { + "bbox": [ + 57, + 156, + 276, + 179 + ], + "type": "text", + "content": "Table 5. Results for the breast cancer segmentation of WSIs, reported as mean and standard error of 4 runs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 312, + 70, + 541, + 316 + ], + "lines": [ + { + "bbox": [ + 312, + 70, + 541, + 316 + ], + "spans": [ + { + "bbox": [ + 312, + 70, + 541, + 316 + ], + "type": "table", + "html": "
Hyperp.ValueUnweighted κAccuracy
D40.752 ± 0.0050.836 ± 0.003
80.758 ± 0.0110.84 ± 0.007
160.752 ± 0.0060.836 ± 0.004
σ2prior10.758 ± 0.0070.839 ± 0.004
20.758 ± 0.0110.84 ± 0.007
40.757 ± 0.0070.839 ± 0.004
σ2post40.757 ± 0.0070.839 ± 0.004
80.758 ± 0.0110.84 ± 0.007
160.745 ± 0.0090.83 ± 0.005
λ0.00010.744 ± 0.0030.829 ± 0.003
0.00050.758 ± 0.0110.84 ± 0.007
0.0010.745 ± 0.0080.837 ± 0.005
ν0.010.757 ± 0.0040.839 ± 0.002
0.020.758 ± 0.0110.84 ± 0.007
0.040.753 ± 0.010.836 ± 0.005
BackboneVGG160.734 ± 0.010.823 ± 0.005
Resnet340.758 ± 0.0110.84 ± 0.007
Eff.netB20.754 ± 0.010.836 ± 0.004
", + "image_path": "5b3cc2160389b54e5f4b5be5b64e862a12e8467f4e8db6520732e099e4681af2.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 324, + 545, + 380 + ], + "lines": [ + { + "bbox": [ + 304, + 324, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 545, + 380 + ], + "type": "text", + "content": "Table 6. Study of hyperparameter robustness using the Gleason 2019 dataset. The default hyperparameter value is marked with bold letters. While varying one hyperparameter, all other values are set to the default value. We observe consistent and robust performance across all settings of tested hyperparameters." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 399, + 383, + 411 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 399, + 383, + 411 + ], + "spans": [ + { + "bbox": [ + 306, + 399, + 383, + 411 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 418, + 545, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 598 + ], + "type": "text", + "content": "In this work we present \"Pionono\", a method for medical image segmentation that models the inter- and intraobserver variability explicitly with a probabilistic approximation. This is especially relevant for tasks where the labeling behavior of medical experts is known to vary widely, such as in the case of prostate cancer segmentation. Our experiments on real-world cancer segmentation data demonstrate that Pionono outperforms state-of-the-art models such as STAPLE, Probabilistic U-Net, and models based on confusion matrices. Apart from the improved predictive performance, it provides a probabilistic uncertainty estimation and the simulation of expert opinions for a given test image. This makes it a powerful tool for medical image analysis and has the potential to improve the diagnostic process considerably." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 609, + 421, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 421, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 421, + 624 + ], + "type": "text", + "content": "6. Acknowledgements" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "This work was funded by the European Union's H2020 research and innovation programme (Marie Skłodowska Curie grant agreement No 860627, CLARIFY Project), the Spanish Ministry of Science and Innovation (project PID2019-105142RB-C22), and FEDER/Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento y Universidades (project P20_00286)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21104" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "type": "text", + "content": "[1] Abdullah A Abdullah, Masoud M Hassan, and Yaseen T Mustafa. 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So, recent papers have introduced $k$ -Nearest Neighbor (kNN) based precision-recall metrics to break down the statistical distance into fidelity and diversity. While they provide an intuitive method, we thoroughly analyze these metrics and identify oversimplified assumptions and undesirable properties of kNN that result in unreliable evaluation, such as susceptibility to outliers and insensitivity to distributional changes. Thus, we propose novel metrics, P-precision and P-recall (PP&PR), based on a probabilistic approach that address the problems. Through extensive investigations on toy experiments and state-of-the-art generative models, we show that our PP&PR provide more reliable estimates for comparing fidelity and diversity than the existing metrics. The codes are available at https://github.com/kdst-team/Probabistic_precision_recall.", + "bbox": [ + 75, + 340, + 473, + 598 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 626, + 209, + 642 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Modern state-of-the-art generative models such as Variational Autoencoders (VAEs) [18, 24], Generative Adversarial Networks (GANs) [8, 15, 13, 14], and Score-based Diffusion Models (SDMs) [12, 17, 29, 6, 32, 25, 30] have shown outstanding achievements that surpass human evaluative capabilities. Consequently, reliable evaluation metrics for comparing the performance of generative models are critical for further technological advancement. The widely used Fréchet Inception Distance (FID) evaluation metric [11] has been praised for its robustness and consistency with human perceptual evaluation. However, FID only provides a single score and does not diagnose whether the model lacks fidelity or diversity, two essential aspects for improving generative models. Recent papers [26, 28, 20, 22, 1] have introduced various two-value metrics to measure fidelity", + "bbox": [ + 75, + 651, + 472, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "and diversity, respectively. Especially, $k$ -nearest neighbor ( $k$ NN) based metrics such as Improved Precision and Recall (IP&IR) [20] and Density and Coverage (D&C) [22] have been used to assess fidelity and diversity on various generative models [6, 35, 2, 24, 13, 4, 23]. The pipeline of these metrics [20, 22] starts with estimating distribution support of real and fake distribution by constructing sample-specific hyperspheres around each sample using $k$ NN. Then, they measure the expectation of the likelihood of fake (real) samples with respect to the estimated real (fake) distribution support to represent fidelity (diversity).", + "bbox": [ + 496, + 309, + 895, + 476 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unfortunately, both IP&IR and D&C metrics present certain challenges that compromise their practical reliability. Specifically, IP&IR operate under the assumption of constant-density within the distribution support and overlook the overestimation linked to $k$ NN, leading to an inflated distribution support with constant density. This scenario becomes especially problematic when the distribution houses outliers, resulting in metric overestimation (See Fig. 1a). Density metric [22] attempts to address these limitations by accumulating density over overlapped $k$ NN hyperspheres. Yet, our findings suggest that it still remains unreliable to outliers. Furthermore, it tends to exhibit high variance, due to its extremely wide bound, which further limits the reliability of evaluations. On the other hand, Coverage metric [22] presents an alternative method that measures robust diversity even with the presence of outliers in the fake distribution. However, we show that it suffers from a conceptual limitation that makes it insensitive to changes in fake distribution. An in-depth discussion of these constraints is provided in Sec. 2. In the end, these issues underscore the need for careful revision of $k$ NN-based metrics to provide more reliable evaluations.", + "bbox": [ + 496, + 477, + 895, + 808 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We, therefore, propose a novel set of metrics, P-precision and P-recall (PP&PR), which aim to provide more reliable estimations for the fidelity and diversity of generative models. In particular, we derive our metrics based on a probabilistic approach that relaxes the oversimplified assumptions and undesirable properties of kNN, addressing the limitations of", + "bbox": [ + 496, + 810, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* corresponding author", + "bbox": [ + 94, + 887, + 217, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20099", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4091ae853b43778863d6475bfd47bef549217251e07bb7d586350702c3af826a.jpg", + "image_caption": [ + "(a) I-Precision / Density" + ], + "image_footnote": [], + "bbox": [ + 89, + 88, + 261, + 239 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/eb9b65300a73578ca8bfb995c95e555405ded7513b54cd5692776495a72a387d.jpg", + "image_caption": [ + "(b) P-precision" + ], + "image_footnote": [], + "bbox": [ + 274, + 88, + 436, + 239 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/608c7f901a09e831731686b978e78143613160ae63a1f9d4cf55d77e0361c7af.jpg", + "image_caption": [ + "(c) I-Recall", + "(d) Coverage", + "(e) P-recall", + "Figure 1: Examples of IP&IR, D&C, and PP&PR (better zoom-in). For simplicity, we use $k = 2$ for $k$ -Nearest Neighbor in all metrics. (a), (c): Due to the overestimation of $k$ NN by the outlier and constant-density assumption within hyperspheres, I-precision, I-recall, and Density denote the same values for different $y$ in an overly large space (See $y_1$ , $y_2$ , and $y_3$ in (a)), leading to unreliable-overestimated values. (b), (e): On the other hand, our P-precision and P-recall assign different scores to different $y$ based on a probabilistic approach and address overestimation of $k$ NN (See Sec. 4 for details). (d): This illustrates a case when Coverage exhibits its conceptual limitation. Even if the fake samples have lower relative diversity compared to real samples, they can still be included in multiple hyperspheres of real samples, leading to high Coverage." + ], + "image_footnote": [], + "bbox": [ + 467, + 88, + 883, + 239 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "existing metrics. Through extensive experiments on both toy and real-world datasets, we systematically demonstrate the superiority of our proposed metrics over IP&IR and D&C. To summarize, our contributions are as follows:", + "bbox": [ + 75, + 407, + 470, + 468 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a set of two-value metrics, P-precision and P-recall, that provide reliable fidelity and diversity measures for generative models.", + "- We thoroughly analyze the limitations of existing metrics (IP&IR and D&C), such as vulnerability to outliers and insensitivity to diversity, and introduce a novel method based on the probabilistic approach that remedies the limitations.", + "- Through a series of experiments on toy and real-world datasets with state-of-the-art generative models, we empirically verify the limitations of current metrics and demonstrate the efficacy of our proposed metrics." + ], + "bbox": [ + 96, + 484, + 470, + 705 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 727, + 202, + 744 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Feature embedding for evaluation", + "text_level": 1, + "bbox": [ + 76, + 753, + 372, + 770 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Statistical comparison of high dimensional data in the raw input space $\\mathcal{X}$ is difficult. Therefore, the usual evaluation starts with converting real data $X \\sim P$ and fake data $Y \\sim Q$ into embeddings using a CNN feature $\\Phi(\\Phi(X)$ and $\\Phi(Y))$ [11, 20, 27, 22]. This embedded feature space is believed to have more \"meaningful\" information to compare two samples [7, 33]. For simplicity, we use $X$ and $Y$ in place of $\\Phi(X)$ and $\\Phi(Y)$ for the remainder of the paper.", + "bbox": [ + 75, + 779, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. kNN-based fidelity and diversity measures", + "text_level": 1, + "bbox": [ + 500, + 407, + 857, + 424 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Now, we briefly introduce current $k\\mathrm{NN}$ -based fidelity and diversity measures and discuss their limitations in Sec. 3.", + "bbox": [ + 498, + 431, + 890, + 460 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Improved Precision and Recall (IP&IR). To represent fidelity, Precision is defined as the expected likelihood of a fake sample belonging to the support of the real distribution, which refers to the set of possible real samples whose probability density function is non-zero. Likewise, Recall is defined as the expected likelihood of a real sample belonging to the support of fake distribution to measure diversity.", + "bbox": [ + 498, + 479, + 893, + 584 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\text {P r e c i s i o n} := \\mathbb {E} _ {Y \\sim Q} [ Y \\in \\operatorname {s u p p} (P) ] \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 592, + 893, + 616 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {R e c a l l} := \\mathbb {E} _ {X \\sim P} [ X \\in \\operatorname {s u p p} (Q) ],\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 612, + 816, + 628 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\operatorname{supp}(\\cdot)$ indicates the ground truth support of distribution. Then, IP&IR [20] approximates them using the empirical observations $\\left(\\left\\{x_{i}\\right\\}_{i=1}^{N}\\right.$ and $\\left\\{y_{j}\\right\\}_{j=1}^{M}$ as", + "bbox": [ + 498, + 636, + 893, + 683 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {P r e c i s i o n} \\approx \\mathrm {I} - \\mathrm {P r e c i s i o n}\n$$\n", + "text_format": "latex", + "bbox": [ + 588, + 691, + 746, + 705 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n:= \\frac {1}{M} \\sum_ {j = 1} ^ {M} \\operatorname {B S R} _ {P} \\left(y _ {j}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 656, + 712, + 890, + 762 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {R e c a l l} \\approx \\mathrm {I} - \\mathrm {R e c a l l}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 758, + 727, + 771 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n:= \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathrm {B S R} _ {Q} (x _ {i}).\n$$\n", + "text_format": "latex", + "bbox": [ + 656, + 777, + 800, + 819 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The scoring rule of IP&IR, which we name as Binary Scoring Rule (BSR) for comparison with other scoring rules, is", + "bbox": [ + 498, + 825, + 890, + 856 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {B S R} _ {P} \\left(y _ {j}\\right) = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} y _ {j} \\in \\cup_ {i = 1} ^ {N} B \\left(x _ {i}, \\mathrm {N N D} _ {k} \\left(x _ {i}\\right)\\right) \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 863, + 890, + 904 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20100", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $B(x, r)$ is the hypersphere in $\\mathbb{R}^D$ around $x$ with radius $r$ , and $\\mathrm{NND}_k(x_i)$ denotes the Euclidean distance from $x_i$ to the $k^{th}$ nearest neighbor among $\\{x_i\\}_{i=1}^N$ excluding itself. In other words, $\\mathrm{BSR}_P(y_j)$ assigns a binary score of 1 or 0 to $y_j$ based on whether it falls inside the union of hyperspheres. It is worth noting that BSR employs a deterministic approach that determines the support as the union of $k$ NN hyperspheres without accounting for any uncertainty regarding the true support. This restricts the scoring rule to binary assignments, leading to a constant density within the approximated distribution support.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "I-recall is defined using $\\mathrm{BSR}_Q(x_i)$ , which is defined symmetrically with $\\mathrm{BSR}_P(y_j)$ . It builds hyperspheres around fake samples and tests real samples.", + "bbox": [ + 76, + 257, + 470, + 303 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Density and Coverage (D&C). D&C use different approaches to define fidelity and diversity in comparison to IP&IR. Specifically, Density [22] tackles the issue of constant-density over distribution support in IP&IR by quantifying the degree of overlap between kNN hyperspheres. To this end, Density defines a scoring rule that estimates the density function within distribution support by the superposition of hyperspheres, as opposed to the union in IP&IR. We denote this scoring rule as Density Scoring Rule (DSR).", + "bbox": [ + 75, + 319, + 472, + 455 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {D S R} _ {P} \\left(y _ {j}\\right) = \\frac {1}{k} \\sum_ {i = 1} ^ {N} 1 _ {y _ {j} \\in B \\left(x _ {i}, \\mathrm {N N D} _ {k} \\left(x _ {i}\\right)\\right)} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 460, + 468, + 503 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $k$ is for the $k$ -nearest neighbors. DSR employs a kind of Parzen window density estimation [10] with a uniform kernel whose width is adjusted automatically, except that the integral of the kernel does not sum up to 1. Now, Density is defined as the expectation of DSR over observed samples as", + "bbox": [ + 75, + 507, + 468, + 583 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\text {D e n s i t y} := \\frac {1}{M} \\sum_ {j = 1} ^ {M} \\mathrm {D S R} _ {P} \\left(y _ {j}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 589, + 468, + 631 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For diversity, the authors employ another scoring rule, Coverage Scoring Rule (CSR), which is not symmetric to DSR. It builds $k$ NN hyperspheres around the real samples and counts the real samples whose hyperspheres are occupied by the fake samples. Coverage has demonstrated effectiveness in handling outliers in fake distribution, as the hyperspheres of real samples are not influenced by fake outliers.", + "bbox": [ + 75, + 636, + 470, + 755 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {C S R} _ {Q} \\left(x _ {i}\\right) = 1 _ {\\exists j \\text {s . t .} y _ {j} \\in B \\left(x _ {i}, \\mathrm {N N D} _ {k} \\left(x _ {i}\\right)\\right)}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 761, + 398, + 779 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\text {C o v e r a g e} := \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathrm {C S R} _ {Q} \\left(x _ {i}\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 781, + 468, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Limitations with scoring rules of IP&IR and D&C", + "text_level": 1, + "bbox": [ + 76, + 827, + 468, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Binary scoring rule. BSR can only assign constant density within an approximated distribution support, which can", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "hinder reliable estimates when comparing distributions with complex density functions. Moreover, the use of $k\\mathrm{NN}$ in BSR makes it more susceptible to outliers as it unreliably inflates the size of the hypersphere due to the presence of such outliers. This results in overestimated value as illustrated in Fig. 1a and 1c. Both I-precision and I-recall face similar issues since they symmetrically use BSR.", + "bbox": [ + 496, + 90, + 893, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Density scoring rule. We contend that DSR remains vulnerable to outliers as it accumulates density over the overestimated constant-density hyperspheres. For instance, if there are $s$ outliers, all hyperspheres of outliers can overlap due to the overestimated size of hyperspheres. This causes the overlapped density to accumulate to $s / k$ (note that DSR scales the overlapped density by a factor of $1 / k$ in Eq. 4), resulting in a rapid increase with just a few outliers. We demonstrate this quantitatively with the experiment in Sec. 5. Additionally, reducing the density by a factor of $1 / k$ makes the metric highly dependent on the choice of $k$ , which is not desirable as we demonstrate in Fig. 3.", + "bbox": [ + 496, + 218, + 893, + 398 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Lastly, DSR is bounded within $[0, N / k]$ (e.g., $N / k = 50000 / 5 = 10000$ ), which can result in samples with abnormally high values of DSR, compromising stable evaluations with high standard deviations as demonstrated in Fig. 2c.", + "bbox": [ + 496, + 398, + 893, + 460 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Coverage scoring rule. While CSR can effectively handle outliers in fake distribution, it exhibits a conceptual limitation: a lack of sensitivity to the comparative diversity between fake and real distributions. This arises because CSR doesn't factor in distances between fake samples. Instead, its focus is solely on the count of real sample hyperspheres occupied by fake samples. This leads to a scenario where if real samples are more dispersed compared to fake ones, meaning the fake samples exhibit less relative diversity, the fake samples could still be included in multiple real hyperspheres. This, in turn, can produce a falsely elevated Coverage metric (a conceptual illustration is provided in Fig.1d). Conversely, Coverage can be low if fake samples are more widely distributed compared to real samples. We elucidate this phenomenon quantitatively in Fig. 5b.", + "bbox": [ + 496, + 481, + 893, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 500, + 723, + 589, + 738 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To address the aforementioned limitations, we propose a novel scoring rule based on a probabilistic approach. Our motivation arises from the recognition that accurately estimating the ground truth support is infeasible with empirical observations alone. As a result, it becomes difficult to determine whether a sample belongs to the ground truth support with certainty (0 or 1). Therefore, we adopt a probabilistic perspective and define the probability of a sample belonging to the support, taking into account the uncertainty surrounding the ground truth support. Then, our scoring rule can", + "bbox": [ + 496, + 750, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20101", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "assign lower values to samples that are less likely to belong to the support such as outliers, effectively addressing outlier concerns. We also define the scoring rules for fidelity and diversity symmetrically, similar to IP&IR, to avoid the conceptual limitation of CSR. Although we mainly focus on describing the details of fidelity in the paper, diversity is defined symmetrically.", + "bbox": [ + 75, + 90, + 472, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. P-precision and P-recall (PP&PR)", + "text_level": 1, + "bbox": [ + 76, + 205, + 375, + 222 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given the observations $\\{x_i\\}_{i = 1}^N$ , we assume that there are myriad possible supports of $P$ , denoted as $S_P$ . The collection of these supports is represented by $\\mathbb{S}_P$ . Subsequently, we introduce Probabilistic-Precision that characterizes precision as the probability of $y_{j}$ being an element of support randomly chosen from $\\mathbb{S}_P$ . This is articulated as", + "bbox": [ + 75, + 228, + 473, + 320 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathrm {P} \\text {- p r e c i s i o n} := \\mathbb {E} _ {Y \\sim Q, S _ {P} \\in \\mathbb {S} _ {P}} [ Y \\in S _ {P} ] \\\\ = \\mathbb {E} _ {Y \\sim Q} \\left[ \\mathbb {E} _ {S _ {P} \\in \\mathbb {S} _ {P}} \\left[ Y \\in S _ {P} \\right] \\right] \\tag {7} \\\\ = \\mathbb {E} _ {Y \\sim Q} \\left[ \\Pr \\left(Y \\in S _ {P}\\right) \\right] \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 330, + 468, + 386 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, we approximate it with given observations $\\{y_{j}\\}_{j = 1}^{M}$ as", + "bbox": [ + 76, + 398, + 468, + 417 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {P} \\text { - p r e c i s i o n} \\approx \\frac {1}{M} \\sum_ {j = 1} ^ {M} \\Pr \\left(y _ {j} \\in S _ {P}\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 438, + 468, + 479 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In a similar manner, Probabilistic-recall is approximated as", + "bbox": [ + 76, + 491, + 465, + 506 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Pr \\text {r e c a l l} \\approx \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\Pr \\left(x _ {i} \\in S _ {Q}\\right). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 517, + 468, + 558 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Probabilistic scoring rule", + "text_level": 1, + "bbox": [ + 76, + 569, + 307, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To estimate $\\operatorname*{Pr}(y_j\\in S_P)$ , we first divide $S_{P}$ into subsets around each observation as", + "bbox": [ + 76, + 592, + 468, + 622 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {P} := \\bigcup_ {i = 1} ^ {N} s _ {P} \\left(x _ {i}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 209, + 631, + 468, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{s}_P(x_i)$ , denoted as the subsupport around $x_i$ , represents a subset of $S_P$ that comprises elements for which the nearest reference among $\\{x_i\\}_{i=1}^N$ is $x_i$ . Then, we can further elucidate $\\operatorname*{Pr}(y_j \\in S_P)$ as", + "bbox": [ + 75, + 684, + 470, + 744 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\Pr (y _ {j} \\in S _ {P}) = 1 - \\Pr (y _ {j} \\notin S _ {P}) \\\\ = 1 - \\Pr \\left(y _ {j} \\notin \\cup_ {i = 1} ^ {N} s _ {P} \\left(x _ {i}\\right)\\right) \\\\ = 1 - \\Pr \\left(y _ {j} \\in \\cap_ {i = 1} ^ {N} s _ {P} ^ {C} (x _ {i})\\right) \\\\ = 1 - \\prod_ {i = 1} ^ {N} \\Pr \\left(y _ {j} \\in s _ {P} ^ {\\mathbf {c}} \\left(x _ {i}\\right)\\right) \\tag {11} \\\\ = 1 - \\prod_ {i = 1} ^ {N} \\left(1 - \\Pr \\left(y _ {j} \\in s _ {P} \\left(x _ {i}\\right)\\right)\\right) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 757, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "using Eq. 10 and complement rule, where $s_P^c (\\cdot)$ denotes the complement set of $s_P(\\cdot)$ . The equality in the fourth line of Eq. 11 comes from assuming the independence of events $\\{y_{j}\\in s_{P}^{c}(x_{i})|i = 1,2,\\dots ,N\\}$", + "bbox": [ + 498, + 90, + 890, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Now, we define our new scoring rule termed Probabilistic Scoring Rules (PSR) from the last equation in Eq. 11:", + "bbox": [ + 498, + 152, + 890, + 181 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\operatorname {P S R} _ {P} \\left(y _ {j}\\right) := 1 - \\prod_ {i = 1} ^ {N} \\left(1 - \\Pr \\left(y _ {j} \\in s _ {P} \\left(x _ {i}\\right)\\right)\\right) \\tag {12} \\\\ = \\Pr (y _ {j} \\in S _ {P}) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 531, + 193, + 890, + 253 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In contrast with deterministic methods such as BSR, which make certain assumptions about the definitive shape of subsupport, PSR estimates the probability of $y_{j}$ to belong to the uncertain support by combining the probability to belong to the subsupport around each observation. Utilizing this probabilistic approach allows us to depart from defining the specific subsupport—a task that, in practice, can be ambiguous. Rather, we infer the likelihood of a sample being part of the subsupport based on an intuitive premise: samples in closer proximity to $x_{i}$ are more likely to be an element of the subsupport compared to those further away. Accordingly, we approximate the probability $\\operatorname*{Pr}(y_j\\in s_P(x_i))$ as", + "bbox": [ + 498, + 263, + 893, + 446 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Pr \\left(y _ {j} \\in s _ {P} \\left(x _ {i}\\right)\\right) \\approx \\left\\{ \\begin{array}{l l} 1 - \\frac {d}{R}, & \\text {i f} d \\leq R \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 457, + 890, + 498 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $d$ is $l_{2}$ distance between $x_{i}$ and $y_{j}$ . From Eq. 13, the probability is one when $d = 0$ , given that we know for certain that $x_{i}$ belongs to the subsupport. The probability monotonically decreases with an increase in $d$ until it hits the threshold distance $R$ , where the probability converges to zero. By Eq. 12 and Eq. 13, our proposed PSR can assign varying values to samples based on their likelihood of belonging to the support. Moreover, it is bounded within [0,1] (see supplement for the proof) unlike DSR which has an extremely wide bound. Note that while other distance metrics $d$ or monotonically decreasing functions could serve this purpose, we opted to use $l_{2}$ distance and a linear function since it was sufficiently sensitive based on our empirical results. We leave it for future work.", + "bbox": [ + 498, + 508, + 893, + 717 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It is also important to select $R$ in Eq. 13 since it controls the robustness of the scoring rule. Instead of sample-specific $R(x_{i})$ based on kNN as used in IP&IR and D&C, we propose to use identical $R$ for all samples $x_{i}$ . We set $R$ as a multiple of the average of kNN distances among $\\{x_{i}\\}_{i = 1}^{N}$ , since it can be used as an effective normalization factor in high-dimensional space. This is similar to using a fixed-variance Gaussian kernel for Kernel Density Estimation and offers several advantages over sample-specific kNN: 1) it suppresses the overestimation of kNN by the outlier as shown in Fig. 1b, and 2) makes metric more robust to the choice of $k$ as shown in Fig. 3.", + "bbox": [ + 498, + 719, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20102", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5a04749ac74f1b01197dcc1c74ecba5bf9440cca2418d97e0101d97f969218c4.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 101, + 90, + 356, + 234 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6c3d7d791d7fb109470d8725b9c51e40adb626e83ab9ec6038b54de598ce439d.jpg", + "image_caption": [ + "(b)", + "Figure 2: (a) Behavior of fidelity metrics between two Gaussian distributions $X \\sim N(0, I)$ and $Y \\sim N(u\\mathbf{1}, I)$ as $u$ moves between [-3,3] with outlier $x_o \\sim N(-2, I)$ added to $X$ . (b) Behavior of diversity metrics between two Gaussian distributions $X \\sim N(u\\mathbf{1}, I)$ and $Y \\sim N(0, I)$ as $u$ moves between [-3,3] with outlier $y_o \\sim N(\\mathbf{2}, I)$ added to $Y$ . (c) Estimated bias from the presumed true value between two identical Gaussian distributions for different numbers of datasets $N$ . The line shows the means and the shaded area denotes standard deviations across 50 runs." + ], + "image_footnote": [], + "bbox": [ + 356, + 90, + 612, + 234 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6d96d060210c2802fab0675a167fd015782875d66a6b755d07f165f479257534.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 627, + 90, + 846, + 157 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ed71da9f3fb4a4873100cf32937662a473e6976a8e9817884aeba226d40ff6d1.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 627, + 157, + 844, + 233 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, putting it all together, we propose P-precision as", + "bbox": [ + 96, + 367, + 465, + 383 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {P} \\text { - p r e c i s i o n} = \\frac {1}{M} \\sum_ {j = 1} ^ {M} \\mathrm {P S R} _ {P} \\left(y _ {j}\\right) \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 391, + 470, + 434 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 76, + 443, + 122, + 455 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {P S R} _ {P} \\left(y _ {j}\\right) = 1 - \\prod_ {i = 1} ^ {N} \\left(1 - \\Pr \\left(y _ {j} \\in s _ {P} \\left(x _ {i}\\right)\\right)\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 464, + 423, + 505 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Pr (y _ {j} \\in s _ {P} (x _ {i})) = \\left\\{ \\begin{array}{l l} 1 - \\frac {| | x _ {i} - y _ {j} | | _ {2}}{R}, & \\text {i f} | | x _ {i} - y _ {j} | | _ {2} \\leq R \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right.\n$$\n", + "text_format": "latex", + "bbox": [ + 80, + 513, + 464, + 555 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and", + "bbox": [ + 76, + 559, + 106, + 571 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nR = \\frac {a}{N} \\sum_ {i = 1} ^ {N} \\mathrm {N N D} _ {k} \\left(x _ {i}\\right).\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 569, + 354, + 611 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$a$ is a hyperparameter that controls the magnitude of $R$ , and $k$ is for the $k$ -nearest neighbors. In a similar manner, we propose P-recall as", + "bbox": [ + 75, + 614, + 468, + 660 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP - \\text {r e c a l l} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathrm {P S R} _ {Q} \\left(x _ {i}\\right) \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 669, + 468, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 76, + 719, + 120, + 732 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {P S R} _ {Q} (x _ {i}) = 1 - \\prod_ {j = 1} ^ {M} \\left(1 - \\Pr (x _ {i} \\in s _ {Q} (y _ {j}))\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 739, + 424, + 782 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname * {P r} (x _ {i} \\in s _ {Q} (y _ {j})) = \\left\\{ \\begin{array}{l l} 1 - \\frac {| | x _ {i} - y _ {j} | | _ {2}}{R}, & \\text {i f} | | x _ {i} - y _ {j} | | _ {2} \\leq R \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right.\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 792, + 464, + 833 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and", + "bbox": [ + 76, + 837, + 106, + 849 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nR = \\frac {a}{M} \\sum_ {j = 1} ^ {M} \\mathrm {N N D} _ {k} (y _ {j}).\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 848, + 354, + 891 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/07d53bd6798503751419436e826dc9c3cdd1690d7a7632f967936823a9723355.jpg", + "image_caption": [ + "Figure 3: Ablation over $k$ . We measure each metric for different $k$ between $X \\sim N(0, I)$ and $Y \\sim N(u, I)$ as $u \\in [-3.0, 3.0]$ with outlier $x_{o} \\sim N(-2, I)$ added to $X$ ." + ], + "image_footnote": [], + "bbox": [ + 535, + 387, + 848, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 647, + 633, + 666 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we systematically demonstrate the limitations of current metrics and the improvements of our metrics through toy experiments. We then show the experiments with state-of-the-art generative models, highlighting that our metrics are more reliable for evaluating generative models than IP&IR and D&C. We use the settings described below for the remainder of the experiments unless stated otherwise. We set $k = 4$ and $a = 1.2$ for our metrics in all experiments. For IP&IR and D&C, we follow the recommended value of $k = 3$ and $k = 5$ , respectively. In the toy experiments, we generate Gaussian distributions in $\\mathbb{R}^{64}$ and set $M = N = 10000$ . For the experiments evaluating generative models, we use features extracted from the ImageNet [19] pre-trained Inception model [31] after the second fully connected layer. We compute metrics between", + "bbox": [ + 496, + 674, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20103", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/67150a655c8478e4d0841435cf073066d697a8df598d2d4c5bad7d40a17aa6a2.jpg", + "image_caption": [ + "(a) FFHQ" + ], + "image_footnote": [], + "bbox": [ + 102, + 103, + 637, + 314 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f4a2756ea0e4b64266fc2fb5b29aded249817e10ee65e61939f641a87339c5fd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 645, + 101, + 867, + 205 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/10564ff7fa0598a80d8c26bb02d511d8831f17d9932d52d16cbe3493d2c828cb.jpg", + "image_caption": [ + "(b) CIFAR-10", + "Figure 4: Qualitative examples sorted according to $L$ . We used StyleGAN [15] trained on FFHQ [15] and BigGAN [3] trained on CIFAR-10 [19]. The top two rows are images with the highest $L$ meaning they have high PSR but low DSR. Conversely, the bottom two rows are images with the lowest $L$ , indicating low PSR and high DSR." + ], + "image_footnote": [], + "bbox": [ + 645, + 210, + 867, + 314 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/075c527cbecb2c4c1cf691dc646205707c79478935d80392ab96cbc4a06c2978.jpg", + "image_caption": [ + "(a)", + "Figure 5: Behavior of metrics between $X \\sim N(0, I)$ and $Y \\sim N(0, vI)$ as $v$ changes between [0.2, 1.5]. Because Density goes over 1 (up to nearly 1000), the $y$ -axis for Density is on the right side of the plot for better visualization." + ], + "image_footnote": [], + "bbox": [ + 76, + 425, + 272, + 539 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3b2fd32ae514679643ad1c7d021123c6aac7cd857dad17a67e81e96711e9458f.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 274, + 425, + 467, + 537 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "all available real samples (up to 50K) and 50K generated images following [6].", + "bbox": [ + 75, + 656, + 468, + 688 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Toy experiments", + "text_level": 1, + "bbox": [ + 76, + 699, + 240, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1.1 Robustness to outliers", + "text_level": 1, + "bbox": [ + 76, + 724, + 284, + 738 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Gaussian distribution We first investigate how the metrics behave to outliers through a simple toy experiment with Gaussian distributions, following [22]. We set real $X \\sim N(0, I)$ and fake $Y \\sim N(u\\mathbf{1}, I)$ where $\\mathbf{1}$ is a vector of ones and $I$ is the identity matrix, and measure the metrics between $X$ and $Y$ as $u$ varies in [-3, 3]. To introduce an outlier, we add a sample $x_o \\sim N(-2, I)$ to the set of real samples. A reliable metric should consistently decrease as $u$ moves away from 0, regardless of the outlier. Fig. 2a shows the result for fidelity: I-precision gives overestimated values when", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$u \\leq 0$ due to the enlarged constant-density hypersphere by the outlier. Although Density alleviates the problem by reducing the density inside the hypersphere by $1 / k$ , it does not reflect the change for a wide range of $u$ (See when $u \\leq -1$ ). On the other hand, P-precision denotes reliable estimates even when the fake distribution comes closer to the outlier $(\\mathrm{PP} = 0.006$ when $u = -2)$ , and also shows a robust decrease as $u$ moves away from 0. We observe a similar result on the diversity measures except for Coverage (See Fig. 2b).", + "bbox": [ + 496, + 415, + 893, + 551 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In addition, we perform an ablation over $k$ to investigate whether the improvement of our metric over the outlier is due to a properly chosen $k$ . The same experiment described above is repeated with different $k$ and the metric values are reported in Fig. 3. Our P-precision shows strong consistency over $k$ , due to the employment of identical $R$ for all real samples. However, I-precision continues to suffer from outliers, regardless of the value of $k$ . Moreover, Density exhibits high variation over different values of $k$ as it reduces the density by $1 / k$ , demonstrating that Density needs properly chosen $k$ to achieve adequate robustness to outliers.", + "bbox": [ + 496, + 551, + 895, + 717 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "These results suggest that our metrics are more reliable to estimate fidelity and diversity between distributions, even in the presence of outliers.", + "bbox": [ + 496, + 718, + 893, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1.2 Stability of metrics", + "text_level": 1, + "bbox": [ + 500, + 785, + 687, + 800 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We also test the stability of metrics by measuring the empirical bias of the metric from the presumed true value, which we approximate by averaging across 50 runs with 50K samples, between two identical Gaussian distributions. Fig. 2c shows the bias from the true value with respect to the number of datasets used for estimation, along with the average and", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20104", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "standard deviation across 50 runs. Our PP&PR show a small bias and standard deviation, even for small $N$ , while IP&IR show a large bias. In addition, despite the theoretical value when two distributions are identical [22], Density does not behave nicely: at $N \\leq 10000$ , Density shows quite a large bias and standard deviation due to the extremely wide bound. This demonstrates that our PP&PR provides more reliable estimates than other metrics even for small datasets.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1.3 Reflecting fidelity and diversity", + "text_level": 1, + "bbox": [ + 76, + 237, + 346, + 253 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The main motive of the two-value metric is to capture both fidelity and diversity between two distributions. To assess whether these metrics are capable of reflecting fidelity and diversity, we design a scenario where the two values are at odds. Specifically, we generate samples from $X \\sim N(0, I)$ and $Y \\sim N(0, vI)$ , and vary the value of $v$ from 0.2 to 1.5. As $v$ increases, we expect fidelity to decrease and diversity to increase. As shown in Fig. 5, while Density behaves as expected, Coverage does not; it remains constant at 1 as $v$ increases from 0.2 to 1, despite the increasing relative diversity of fake distribution. We argue that this counter-intuitive behavior is due to the conceptual limitation of Coverage as discussed in Sec. 3. When $v$ increases beyond 1, Coverage becomes 0, as fake samples are no longer included in the hyperspheres of real samples. In contrast, PP&PR and IP&IR nicely reflect the expected behavior.", + "bbox": [ + 75, + 263, + 473, + 505 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Evaluating generative models", + "text_level": 1, + "bbox": [ + 76, + 517, + 339, + 534 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2.1 Comparing scoring rules", + "text_level": 1, + "bbox": [ + 76, + 542, + 305, + 558 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Here, we compare the scoring rules of fidelity metrics to demonstrate how nicely the estimated density reflects the quality of the fake sample. We compare PSR with DSR, as BSR only denotes a binary score. For effective comparison, we focus on cases where two scoring rules have conflicting results. Specifically, we compute $L = \\{\\mathrm{PSR}_P(y_j) - \\mathrm{DSR}_P(y_j) \\mid \\forall j\\}$ using generative models $Q(Y)$ (StyleGAN [15] and BigGAN [3]) trained on real-world datasets $P(X)$ (CIFAR-10 [19] and FFHQ [15]). A high value of $L$ indicates a high PSR but low DSR, while a low value of $L$ indicates the opposite. For a fair comparison, we normalize DSR by its maximum value so that it ranges between 0 and 1. We show images of the highest $L$ and lowest $L$ in Fig. 4 (without cherry-picking). In general, images with a high value of $L$ show more realistic and clear objects, while images with a low $L$ are often distorted with artifacts (See supplement for more examples). Based on the assumption that realistic images should correspond to the high density of real distribution, our results in Fig. 4 qualitatively demonstrate the superiority of PSR over DSR in reflecting the semantic quality of generated images. We also conduct a user study selecting preferences between the", + "bbox": [ + 75, + 568, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/930fdd99476cecf35968a2c708a131ff48390346e37cfcba7bf319f90bc8ca10.jpg", + "image_caption": [ + "$X_{\\text{inlier}}$" + ], + "image_footnote": [], + "bbox": [ + 511, + 88, + 694, + 261 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e8ea4df807e13f5b72fd880a12ab550c603720f65935891f2365d0428abac71c.jpg", + "image_caption": [ + "$X_{outlier}$" + ], + "image_footnote": [], + "bbox": [ + 699, + 88, + 882, + 262 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/83bb99adb8df5df105f66b047d3f85562daf64472e6ae6a2911b91c20a63cdc3.jpg", + "image_caption": [ + "Yinlier" + ], + "image_footnote": [], + "bbox": [ + 511, + 276, + 694, + 452 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8dddcffb3a8d1c580c98bbe24f71a8bc3aefe51e6f372a2099f949283415c5d4.jpg", + "image_caption": [ + "$Y_{outlier}$" + ], + "image_footnote": [], + "bbox": [ + 697, + 276, + 882, + 452 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b484f5bddde6cb6d8ad124a69a6920b1ef1e1ce68b3a96b7fd3ba3a6e62f545e.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 506, + 468, + 697, + 578 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8745474d50b35e3b8b97a1a62ee97b5266c19ea59ad6b798a7cc9efac710a7d6.jpg", + "image_caption": [ + "(b)", + "Figure 6: Behavior of metrics with respect to the number of outliers when evaluating the generative model $Y$ on a real-world dataset $X$ . (a) Fidelity metrics. (b) Diversity metrics." + ], + "image_footnote": [], + "bbox": [ + 699, + 468, + 888, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "highest $L$ and the lowest $L$ and it also shows a similar result to our observation (See supplement).", + "bbox": [ + 498, + 674, + 890, + 705 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2.2 Robustness to outliers", + "text_level": 1, + "bbox": [ + 500, + 724, + 705, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To investigate the efficacy of our proposed metrics in handling outliers with generative models on real-world datasets, we conduct experiments on the state-of-the-art diffusion model (e.g., ADM [6]), which currently has gained attention for its powerful performance, trained on ImageNet [19] dataset $(128^{2}$ resolution). Then, we adopt the outlier selection criterion used in [22] which uses the distance to the $k^{th}$ nearest neighbor. We apply this criterion to select inliers and outliers (at a ratio of 0.95:0.05) for both real and fake samples generated by ADM, resulting in the sets", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20105", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f1dbb1fd9f2817350427ff0a2834d2027913a6ae4b89c90e0f7c8dcdf03f97d0.jpg", + "table_caption": [ + "Table 1: Quantitative result of various generative models on real-world datasets. The reported values are obtained by measuring each metric five times and taking the average. Bolded values indicate the top scores evaluated by the corresponding metric." + ], + "table_footnote": [], + "table_body": "
Model\nImageNet 256x256FID↓PP↑PR↑F1↑IP↑IR↑F1↑D↑C↑F1↑
ADM [6]4.950.5380.7320.6210.6810.6880.6841.520.8761.112
ADM-G [6]4.580.6990.5870.6380.8180.6060.6962.0710.9561.307
BigGAN [3]8.120.7510.4650.5740.8740.4030.5512.4810.9451.368
AFHQv2 512x512
StyleGAN2 [16]4.620.5680.6890.6230.7160.4940.5841.8860.7901.113
StyleGAN3-R [14]4.400.5640.7250.6340.6850.5910.6351.5760.7701.034
StyleGAN3-T [14]4.040.5670.7270.6370.6990.5780.6321.6240.7921.065
LSUN Bedroom 256x256
DDPM [16]4.880.7990.7490.7730.6060.4440.5121.7010.9771.241
ADM [6]1.910.8390.7310.7810.6590.4940.5651.9290.9931.311
StyleGAN2 [16]2.350.8010.7530.7760.5910.5010.5431.7320.9861.257
", + "bbox": [ + 117, + 128, + 848, + 378 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "$X = X_{\\text{inlier}} \\cup X_{\\text{outlier}}$ and $Y = Y_{\\text{inlier}} \\cup Y_{\\text{outlier}}$ . We provide examples of the outliers and inliers in Fig. 6. Note that the inliers tend to exhibit more recognizable objects with clear semantic features compared to the outliers.", + "bbox": [ + 75, + 417, + 468, + 477 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We first observe how fidelity metrics between $X_{\\text{inlier}}$ and $Y$ respond when a portion of $X_{\\text{inlier}}$ is gradually substituted with the subset of $X_{\\text{outlier}}$ . To visualize this, we plot the metric increments compared to the case when no outliers are included in $X_{\\text{inlier}}$ , as shown in Fig. 6a. The results show that I-precision rapidly increases (0.2 increments) when only $5\\%$ of inliers are gradually replaced by outliers, confirming its vulnerability to outliers. Although Density is less affected by outliers initially, it eventually surpasses the increment of I-precision as it accumulates the density over hyperspheres, supporting our claim that Density is still vulnerable to outliers. On the other hand, our P-precision shows the least increment (0.05 increments for $5\\%$ outliers), validating its effectiveness in handling outliers.", + "bbox": [ + 75, + 479, + 470, + 689 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Likewise, we also test the robustness of diversity measures between $X$ and $Y_{\\text{inlier}}$ by gradually replacing a portion of $Y_{\\text{inlier}}$ with the subset of $Y_{\\text{outlier}}$ . In Fig. 6b, we observe that I-recall exhibits a similar vulnerability to outliers as I-precision, while our P-recall is less affected by the presence of outliers. Besides, Coverage demonstrates strong robustness to outliers due to its alternative diversity measure. However, this comes at the cost of losing accuracy, as demonstrated in the experiments in Fig. 5b and 7b.", + "bbox": [ + 75, + 690, + 470, + 828 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2.3 Reflecting fidelity and diversity", + "text_level": 1, + "bbox": [ + 76, + 845, + 348, + 862 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We now verify whether the metrics accurately reflect the change in fidelity and diversity of fake samples generated", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "from generative models. In order to do that, we employ classifier guidance [6] during the image sampling from ADM. This technique uses gradients of a pre-trained classifier to perform conditional sampling from pre-trained unconditional diffusion models. By adjusting the scale of gradients from the classifier, we can explicitly control the balance between fidelity and diversity of generated images. For instance, a larger gradient scale results in the diffusion model sampling more from the modes of the pre-trained classifier, yielding higher fidelity but lower diversity. For more details, please refer to [6]. Therefore, we sample images from ADM, the same model as in Sec. 5.2.2, using gradient scales ranging from 0.5 to 10.0, and measure metrics (IP&IR, D&C and PP&PR) between real and generated samples for each scale. Fig. 7 shows the results; our PP&PR and IP&IR effectively capture the trade-off between fidelity and diversity whereas D&C does not exhibit a clear relationship with the gradient scale. This is due to the conceptual limitation of Coverage in accurately measuring the diversity in generated samples.", + "bbox": [ + 496, + 417, + 893, + 705 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2.4 Image generation benchmark", + "text_level": 1, + "bbox": [ + 500, + 724, + 759, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To evaluate the practical usefulness of our proposed metrics in assessing the state-of-the-art generative models, we present the quantitative results on real-world datasets (LSUN bedroom [34], AFHQ-v2 [5], and ImageNet) for various types of generative models, along with FID. The results, presented in Tab. 1, are obtained by measuring each metric five times and taking their average. For clarity in the presentation, the variance associated with these measurements can be found in the supplementary materials. While FID serves as a holistic reference point for distinguishing superior", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20106", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e9fc54980ec3de93e44e1d77c33c9b0b05e6ad50bc667ec7c9a206e791e3acf6.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 78, + 89, + 272, + 202 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/a0b00d447ec873b68f5a4e284274da6d8e09249a8a79311638d1210e0401152e.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 274, + 88, + 468, + 202 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/c7e42cd0ba050887fece13c8180a23133d576e7360b833d2edd4c303b85df873.jpg", + "image_caption": [ + "Figure 7: Fidelity versus diversity when increasing the gradient scale from 0.5 to 10.0 for sampling diffusion models with classifier guidance [6]. A larger gradient scale tends to result in higher fidelity and lower diversity.", + "Figure 8: Ablation study on PSR: (A): probabilistic estimation for subsupport. (B): identical $R$ ." + ], + "image_footnote": [], + "bbox": [ + 130, + 304, + 411, + 465 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "model performance, our metrics delve deeper, elaborating on aspects of fidelity and diversity. For instance, our metrics explain that the improvement of ADM over StyleGAN [15] on LSUN bedroom in terms of FID is due to an increase in fidelity at the cost of diversity. An analysis between ADM and ADM-G further reveals that the classifier guidance in ADM-G augments fidelity, yet curtails diversity. This demonstrates the usefulness of our metrics in elaborating on the effect of the specific component in models.", + "bbox": [ + 75, + 555, + 468, + 690 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Moreover, to observe whether the metrics harmonize with the widely adopted FID metric, we analyze the consistency between FID and two-value metrics. This is achieved by computing the $\\mathrm{F}_1$ -score [9], which is a harmonic mean of fidelity and diversity. The results demonstrate that $\\mathrm{F}_1$ -scores of our metric mirror the trends set by FID (as underscored by the bold scores for each dataset in Tab. 1).", + "bbox": [ + 75, + 691, + 468, + 797 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Ablation study", + "text_level": 1, + "bbox": [ + 76, + 814, + 225, + 830 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Here, we conduct an ablation study on our proposed scoring rule, PSR, to demonstrate the effectiveness of our approach: (A) probabilistic estimation for subsupport (Eq. 13) and (B) identical $R$ . We repeat the outlier toy experiment", + "bbox": [ + 75, + 840, + 470, + 900 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "with Gaussian distributions in Sec. 5.1.1 with different configurations and the result for fidelity metric is shown in Fig. 8. In both cases where the feature (A) and (B) are individually removed, the metric becomes more susceptible to outlier than the case where both are used $(\\mathrm{(A)} + \\mathrm{(B)})$ but less affected than the case where both are all removed (see when $u\\in [-3, - 1]$ ). This demonstrates that our probabilistic approach for subsupport and addressing overestimation of sample-specific $k_{\\mathrm{NN}}$ both contribute to estimating accurate density and combining them together maximizes it.", + "bbox": [ + 496, + 90, + 893, + 243 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "7. Conclusions and limitations", + "text_level": 1, + "bbox": [ + 498, + 256, + 756, + 272 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we introduced a set of two-value metrics, P-precision and P-recall, based on the probabilistic approach that addresses the limitations of existing metrics (IP&IR and D&C). We have conducted a systematic investigation of the limitations and demonstrated the effectiveness of our proposed metrics by evaluating toy experiments and state-of-the-art generative models. Nevertheless, we recognize there is still room for improvement. While we utilized commonly-used ImageNet embeddings [11, 20, 22] for feature extraction, recent studies such as [1, 21], have proposed domain-agnostic embeddings to enhance the feature quality compared to previous embeddings that rely on dataset-specific statistics. Thus, future research focusing on the quality of feature embedding combined with our method may further enhance the reliability and usefulness of the metric.", + "bbox": [ + 496, + 282, + 893, + 508 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements This work was supported by the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No.2021-0-00456, Development of Ultra-high Speech Quality Technology for remote Multi-speaker Conference System and No.RS-2023-00225630, Development of Artificial Intelligence for Text-based 3D Movie Generation).", + "bbox": [ + 496, + 527, + 893, + 633 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 648, + 596, + 664 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Ahmed Alaa, Boris Van Breugel, Evgeny S Saveliev, and Mihaela van der Schaar. 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The spatially-correlative loss for various image translation tasks. In Conference on Computer Vision and Pattern Recognition, pages 16407-16417, 2021. 1" + ], + "bbox": [ + 78, + 90, + 470, + 204 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "20109", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Probabilistic Precision and Recall Towards Reliable Evaluation of Generative Models/dd6377f8-01ac-488f-b3b2-5ae1ebd477f1_model.json b/2023/Probabilistic Precision and Recall Towards Reliable Evaluation of Generative Models/dd6377f8-01ac-488f-b3b2-5ae1ebd477f1_model.json new file mode 100644 index 0000000000000000000000000000000000000000..6e922b70bcc742d08903129687ff1f641619971c --- /dev/null +++ b/2023/Probabilistic Precision and Recall Towards Reliable Evaluation of Generative Models/dd6377f8-01ac-488f-b3b2-5ae1ebd477f1_model.json @@ -0,0 +1,2488 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.229, + 0.131, + 0.744, + 0.175 + ], + "angle": 0, + "content": "Probabilistic Precision and Recall Towards Reliable Evaluation of Generative Models" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.205, + 0.505, + 0.276 + ], + "angle": 0, + "content": "Dogyun Park \nDepartment of Computer Science, Korea University \nSeoul, South Korea \ngg933@korea.ac.kr" + }, + { + "type": "text", + "bbox": [ + 0.539, + 0.205, + 0.877, + 0.275 + ], + "angle": 0, + "content": "Suhyun Kim* \nKorea Institute of Science and Technology \nSeoul, South Korea \ndr.suhyun.kim@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.341, + 0.474, + 0.599 + ], + "angle": 0, + "content": "Assessing the fidelity and diversity of the generative model is a difficult but important issue for technological advancement. So, recent papers have introduced \\( k \\)-Nearest Neighbor (kNN) based precision-recall metrics to break down the statistical distance into fidelity and diversity. While they provide an intuitive method, we thoroughly analyze these metrics and identify oversimplified assumptions and undesirable properties of kNN that result in unreliable evaluation, such as susceptibility to outliers and insensitivity to distributional changes. Thus, we propose novel metrics, P-precision and P-recall (PP&PR), based on a probabilistic approach that address the problems. Through extensive investigations on toy experiments and state-of-the-art generative models, we show that our PP&PR provide more reliable estimates for comparing fidelity and diversity than the existing metrics. The codes are available at https://github.com/kdst-team/Probabistic_precision_recall." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.627, + 0.21, + 0.643 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.652, + 0.473, + 0.879 + ], + "angle": 0, + "content": "Modern state-of-the-art generative models such as Variational Autoencoders (VAEs) [18, 24], Generative Adversarial Networks (GANs) [8, 15, 13, 14], and Score-based Diffusion Models (SDMs) [12, 17, 29, 6, 32, 25, 30] have shown outstanding achievements that surpass human evaluative capabilities. Consequently, reliable evaluation metrics for comparing the performance of generative models are critical for further technological advancement. The widely used Fréchet Inception Distance (FID) evaluation metric [11] has been praised for its robustness and consistency with human perceptual evaluation. However, FID only provides a single score and does not diagnose whether the model lacks fidelity or diversity, two essential aspects for improving generative models. Recent papers [26, 28, 20, 22, 1] have introduced various two-value metrics to measure fidelity" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.31, + 0.896, + 0.477 + ], + "angle": 0, + "content": "and diversity, respectively. Especially, \\( k \\)-nearest neighbor (\\( k \\)NN) based metrics such as Improved Precision and Recall (IP&IR) [20] and Density and Coverage (D&C) [22] have been used to assess fidelity and diversity on various generative models [6, 35, 2, 24, 13, 4, 23]. The pipeline of these metrics [20, 22] starts with estimating distribution support of real and fake distribution by constructing sample-specific hyperspheres around each sample using \\( k \\) NN. Then, they measure the expectation of the likelihood of fake (real) samples with respect to the estimated real (fake) distribution support to represent fidelity (diversity)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.897, + 0.809 + ], + "angle": 0, + "content": "Unfortunately, both IP&IR and D&C metrics present certain challenges that compromise their practical reliability. Specifically, IP&IR operate under the assumption of constant-density within the distribution support and overlook the overestimation linked to \\( k \\) NN, leading to an inflated distribution support with constant density. This scenario becomes especially problematic when the distribution houses outliers, resulting in metric overestimation (See Fig. 1a). Density metric [22] attempts to address these limitations by accumulating density over overlapped \\( k \\) NN hyperspheres. Yet, our findings suggest that it still remains unreliable to outliers. Furthermore, it tends to exhibit high variance, due to its extremely wide bound, which further limits the reliability of evaluations. On the other hand, Coverage metric [22] presents an alternative method that measures robust diversity even with the presence of outliers in the fake distribution. However, we show that it suffers from a conceptual limitation that makes it insensitive to changes in fake distribution. An in-depth discussion of these constraints is provided in Sec. 2. In the end, these issues underscore the need for careful revision of \\( k \\) NN-based metrics to provide more reliable evaluations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We, therefore, propose a novel set of metrics, P-precision and P-recall (PP&PR), which aim to provide more reliable estimations for the fidelity and diversity of generative models. In particular, we derive our metrics based on a probabilistic approach that relaxes the oversimplified assumptions and undesirable properties of kNN, addressing the limitations of" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.218, + 0.901 + ], + "angle": 0, + "content": "* corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20099" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.09, + 0.089, + 0.262, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.106, + 0.25, + 0.262, + 0.265 + ], + "angle": 0, + "content": "(a) I-Precision / Density" + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.089, + 0.437, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.313, + 0.25, + 0.411, + 0.265 + ], + "angle": 0, + "content": "(b) P-precision" + }, + { + "type": "image", + "bbox": [ + 0.468, + 0.089, + 0.885, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.25, + 0.573, + 0.264 + ], + "angle": 0, + "content": "(c) I-Recall" + }, + { + "type": "image_caption", + "bbox": [ + 0.64, + 0.25, + 0.726, + 0.265 + ], + "angle": 0, + "content": "(d) Coverage" + }, + { + "type": "image_caption", + "bbox": [ + 0.786, + 0.25, + 0.859, + 0.264 + ], + "angle": 0, + "content": "(e) P-recall" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.276, + 0.895, + 0.382 + ], + "angle": 0, + "content": "Figure 1: Examples of IP&IR, D&C, and PP&PR (better zoom-in). For simplicity, we use \\( k = 2 \\) for \\( k \\)-Nearest Neighbor in all metrics. (a), (c): Due to the overestimation of \\( k \\)NN by the outlier and constant-density assumption within hyperspheres, I-precision, I-recall, and Density denote the same values for different \\( y \\) in an overly large space (See \\( y_1 \\), \\( y_2 \\), and \\( y_3 \\) in (a)), leading to unreliable-overestimated values. (b), (e): On the other hand, our P-precision and P-recall assign different scores to different \\( y \\) based on a probabilistic approach and address overestimation of \\( k \\)NN (See Sec. 4 for details). (d): This illustrates a case when Coverage exhibits its conceptual limitation. Even if the fake samples have lower relative diversity compared to real samples, they can still be included in multiple hyperspheres of real samples, leading to high Coverage." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.409, + 0.471, + 0.469 + ], + "angle": 0, + "content": "existing metrics. Through extensive experiments on both toy and real-world datasets, we systematically demonstrate the superiority of our proposed metrics over IP&IR and D&C. To summarize, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.486, + 0.47, + 0.533 + ], + "angle": 0, + "content": "- We propose a set of two-value metrics, P-precision and P-recall, that provide reliable fidelity and diversity measures for generative models." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.551, + 0.472, + 0.626 + ], + "angle": 0, + "content": "- We thoroughly analyze the limitations of existing metrics (IP&IR and D&C), such as vulnerability to outliers and insensitivity to diversity, and introduce a novel method based on the probabilistic approach that remedies the limitations." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.646, + 0.47, + 0.707 + ], + "angle": 0, + "content": "- Through a series of experiments on toy and real-world datasets with state-of-the-art generative models, we empirically verify the limitations of current metrics and demonstrate the efficacy of our proposed metrics." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.486, + 0.472, + 0.707 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.728, + 0.204, + 0.745 + ], + "angle": 0, + "content": "2. Preliminary" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.755, + 0.373, + 0.771 + ], + "angle": 0, + "content": "2.1. Feature embedding for evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Statistical comparison of high dimensional data in the raw input space \\(\\mathcal{X}\\) is difficult. Therefore, the usual evaluation starts with converting real data \\(X \\sim P\\) and fake data \\(Y \\sim Q\\) into embeddings using a CNN feature \\(\\Phi(\\Phi(X)\\) and \\(\\Phi(Y))\\) [11, 20, 27, 22]. This embedded feature space is believed to have more \"meaningful\" information to compare two samples [7, 33]. For simplicity, we use \\(X\\) and \\(Y\\) in place of \\(\\Phi(X)\\) and \\(\\Phi(Y)\\) for the remainder of the paper." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.409, + 0.859, + 0.425 + ], + "angle": 0, + "content": "2.2. kNN-based fidelity and diversity measures" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.432, + 0.892, + 0.462 + ], + "angle": 0, + "content": "Now, we briefly introduce current \\(k\\mathrm{NN}\\)-based fidelity and diversity measures and discuss their limitations in Sec. 3." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.48, + 0.895, + 0.585 + ], + "angle": 0, + "content": "Improved Precision and Recall (IP&IR). To represent fidelity, Precision is defined as the expected likelihood of a fake sample belonging to the support of the real distribution, which refers to the set of possible real samples whose probability density function is non-zero. Likewise, Recall is defined as the expected likelihood of a real sample belonging to the support of fake distribution to measure diversity." + }, + { + "type": "equation", + "bbox": [ + 0.572, + 0.593, + 0.895, + 0.617 + ], + "angle": 0, + "content": "\\[\n\\text {P r e c i s i o n} := \\mathbb {E} _ {Y \\sim Q} [ Y \\in \\operatorname {s u p p} (P) ] \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.613, + 0.818, + 0.629 + ], + "angle": 0, + "content": "\\[\n\\operatorname {R e c a l l} := \\mathbb {E} _ {X \\sim P} [ X \\in \\operatorname {s u p p} (Q) ],\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.637, + 0.894, + 0.684 + ], + "angle": 0, + "content": "where \\(\\operatorname{supp}(\\cdot)\\) indicates the ground truth support of distribution. Then, IP&IR [20] approximates them using the empirical observations \\(\\left(\\left\\{x_{i}\\right\\}_{i=1}^{N}\\right.\\) and \\(\\left\\{y_{j}\\right\\}_{j=1}^{M}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.589, + 0.693, + 0.748, + 0.707 + ], + "angle": 0, + "content": "\\[\n\\mathrm {P r e c i s i o n} \\approx \\mathrm {I} - \\mathrm {P r e c i s i o n}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.658, + 0.713, + 0.892, + 0.763 + ], + "angle": 0, + "content": "\\[\n:= \\frac {1}{M} \\sum_ {j = 1} ^ {M} \\operatorname {B S R} _ {P} \\left(y _ {j}\\right) \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.61, + 0.759, + 0.728, + 0.772 + ], + "angle": 0, + "content": "\\[\n\\mathrm {R e c a l l} \\approx \\mathrm {I} - \\mathrm {R e c a l l}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.658, + 0.779, + 0.802, + 0.82 + ], + "angle": 0, + "content": "\\[\n:= \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathrm {B S R} _ {Q} (x _ {i}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.827, + 0.892, + 0.857 + ], + "angle": 0, + "content": "The scoring rule of IP&IR, which we name as Binary Scoring Rule (BSR) for comparison with other scoring rules, is" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.864, + 0.892, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\operatorname {B S R} _ {P} \\left(y _ {j}\\right) = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} y _ {j} \\in \\cup_ {i = 1} ^ {N} B \\left(x _ {i}, \\mathrm {N N D} _ {k} \\left(x _ {i}\\right)\\right) \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20100" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.258 + ], + "angle": 0, + "content": "where \\( B(x, r) \\) is the hypersphere in \\( \\mathbb{R}^D \\) around \\( x \\) with radius \\( r \\), and \\( \\mathrm{NND}_k(x_i) \\) denotes the Euclidean distance from \\( x_i \\) to the \\( k^{th} \\) nearest neighbor among \\( \\{x_i\\}_{i=1}^N \\) excluding itself. In other words, \\( \\mathrm{BSR}_P(y_j) \\) assigns a binary score of 1 or 0 to \\( y_j \\) based on whether it falls inside the union of hyperspheres. It is worth noting that BSR employs a deterministic approach that determines the support as the union of \\( k \\) NN hyperspheres without accounting for any uncertainty regarding the true support. This restricts the scoring rule to binary assignments, leading to a constant density within the approximated distribution support." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.258, + 0.472, + 0.304 + ], + "angle": 0, + "content": "I-recall is defined using \\(\\mathrm{BSR}_Q(x_i)\\), which is defined symmetrically with \\(\\mathrm{BSR}_P(y_j)\\). It builds hyperspheres around fake samples and tests real samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.473, + 0.457 + ], + "angle": 0, + "content": "Density and Coverage (D&C). D&C use different approaches to define fidelity and diversity in comparison to IP&IR. Specifically, Density [22] tackles the issue of constant-density over distribution support in IP&IR by quantifying the degree of overlap between kNN hyperspheres. To this end, Density defines a scoring rule that estimates the density function within distribution support by the superposition of hyperspheres, as opposed to the union in IP&IR. We denote this scoring rule as Density Scoring Rule (DSR)." + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.462, + 0.47, + 0.504 + ], + "angle": 0, + "content": "\\[\n\\mathrm {D S R} _ {P} \\left(y _ {j}\\right) = \\frac {1}{k} \\sum_ {i = 1} ^ {N} 1 _ {y _ {j} \\in B \\left(x _ {i}, \\mathrm {N N D} _ {k} \\left(x _ {i}\\right)\\right)} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.584 + ], + "angle": 0, + "content": "where \\( k \\) is for the \\( k \\)-nearest neighbors. DSR employs a kind of Parzen window density estimation [10] with a uniform kernel whose width is adjusted automatically, except that the integral of the kernel does not sum up to 1. Now, Density is defined as the expectation of DSR over observed samples as" + }, + { + "type": "equation", + "bbox": [ + 0.171, + 0.59, + 0.47, + 0.632 + ], + "angle": 0, + "content": "\\[\n\\text {D e n s i t y} := \\frac {1}{M} \\sum_ {j = 1} ^ {M} \\mathrm {D S R} _ {P} \\left(y _ {j}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.637, + 0.472, + 0.756 + ], + "angle": 0, + "content": "For diversity, the authors employ another scoring rule, Coverage Scoring Rule (CSR), which is not symmetric to DSR. It builds \\( k \\) NN hyperspheres around the real samples and counts the real samples whose hyperspheres are occupied by the fake samples. Coverage has demonstrated effectiveness in handling outliers in fake distribution, as the hyperspheres of real samples are not influenced by fake outliers." + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.762, + 0.4, + 0.78 + ], + "angle": 0, + "content": "\\[\n\\operatorname {C S R} _ {Q} \\left(x _ {i}\\right) = 1 _ {\\exists j \\text {s . t .} y _ {j} \\in B \\left(x _ {i}, \\mathrm {N N D} _ {k} \\left(x _ {i}\\right)\\right)}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.782, + 0.47, + 0.822 + ], + "angle": 0, + "content": "\\[\n\\text {C o v e r a g e} := \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathrm {C S R} _ {Q} \\left(x _ {i}\\right) \\tag {6}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.828, + 0.47, + 0.861 + ], + "angle": 0, + "content": "3. Limitations with scoring rules of IP&IR and D&C" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Binary scoring rule. BSR can only assign constant density within an approximated distribution support, which can" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.198 + ], + "angle": 0, + "content": "hinder reliable estimates when comparing distributions with complex density functions. Moreover, the use of \\( k\\mathrm{NN} \\) in BSR makes it more susceptible to outliers as it unreliably inflates the size of the hypersphere due to the presence of such outliers. This results in overestimated value as illustrated in Fig. 1a and 1c. Both I-precision and I-recall face similar issues since they symmetrically use BSR." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.219, + 0.895, + 0.4 + ], + "angle": 0, + "content": "Density scoring rule. We contend that DSR remains vulnerable to outliers as it accumulates density over the overestimated constant-density hyperspheres. For instance, if there are \\( s \\) outliers, all hyperspheres of outliers can overlap due to the overestimated size of hyperspheres. This causes the overlapped density to accumulate to \\( s / k \\) (note that DSR scales the overlapped density by a factor of \\( 1 / k \\) in Eq. 4), resulting in a rapid increase with just a few outliers. We demonstrate this quantitatively with the experiment in Sec. 5. Additionally, reducing the density by a factor of \\( 1 / k \\) makes the metric highly dependent on the choice of \\( k \\), which is not desirable as we demonstrate in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.4, + 0.895, + 0.462 + ], + "angle": 0, + "content": "Lastly, DSR is bounded within \\([0, N / k]\\) (e.g., \\(N / k = 50000 / 5 = 10000\\)), which can result in samples with abnormally high values of DSR, compromising stable evaluations with high standard deviations as demonstrated in Fig. 2c." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.482, + 0.895, + 0.71 + ], + "angle": 0, + "content": "Coverage scoring rule. While CSR can effectively handle outliers in fake distribution, it exhibits a conceptual limitation: a lack of sensitivity to the comparative diversity between fake and real distributions. This arises because CSR doesn't factor in distances between fake samples. Instead, its focus is solely on the count of real sample hyperspheres occupied by fake samples. This leads to a scenario where if real samples are more dispersed compared to fake ones, meaning the fake samples exhibit less relative diversity, the fake samples could still be included in multiple real hyperspheres. This, in turn, can produce a falsely elevated Coverage metric (a conceptual illustration is provided in Fig.1d). Conversely, Coverage can be low if fake samples are more widely distributed compared to real samples. We elucidate this phenomenon quantitatively in Fig. 5b." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.724, + 0.591, + 0.739 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.902 + ], + "angle": 0, + "content": "To address the aforementioned limitations, we propose a novel scoring rule based on a probabilistic approach. Our motivation arises from the recognition that accurately estimating the ground truth support is infeasible with empirical observations alone. As a result, it becomes difficult to determine whether a sample belongs to the ground truth support with certainty (0 or 1). Therefore, we adopt a probabilistic perspective and define the probability of a sample belonging to the support, taking into account the uncertainty surrounding the ground truth support. Then, our scoring rule can" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20101" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.198 + ], + "angle": 0, + "content": "assign lower values to samples that are less likely to belong to the support such as outliers, effectively addressing outlier concerns. We also define the scoring rules for fidelity and diversity symmetrically, similar to IP&IR, to avoid the conceptual limitation of CSR. Although we mainly focus on describing the details of fidelity in the paper, diversity is defined symmetrically." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.207, + 0.376, + 0.223 + ], + "angle": 0, + "content": "4.1. P-precision and P-recall (PP&PR)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.229, + 0.474, + 0.321 + ], + "angle": 0, + "content": "Given the observations \\(\\{x_i\\}_{i = 1}^N\\), we assume that there are myriad possible supports of \\(P\\), denoted as \\(S_P\\). The collection of these supports is represented by \\(\\mathbb{S}_P\\). Subsequently, we introduce Probabilistic-Precision that characterizes precision as the probability of \\(y_{j}\\) being an element of support randomly chosen from \\(\\mathbb{S}_P\\). This is articulated as" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.332, + 0.47, + 0.387 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathrm {P} \\text {- p r e c i s i o n} := \\mathbb {E} _ {Y \\sim Q, S _ {P} \\in \\mathbb {S} _ {P}} [ Y \\in S _ {P} ] \\\\ = \\mathbb {E} _ {Y \\sim Q} \\left[ \\mathbb {E} _ {S _ {P} \\in \\mathbb {S} _ {P}} \\left[ Y \\in S _ {P} \\right] \\right] \\tag {7} \\\\ = \\mathbb {E} _ {Y \\sim Q} \\left[ \\Pr \\left(Y \\in S _ {P}\\right) \\right] \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.399, + 0.47, + 0.418 + ], + "angle": 0, + "content": "Then, we approximate it with given observations \\(\\{y_{j}\\}_{j = 1}^{M}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.439, + 0.47, + 0.48 + ], + "angle": 0, + "content": "\\[\n\\mathrm {P} \\text { - p r e c i s i o n} \\approx \\frac {1}{M} \\sum_ {j = 1} ^ {M} \\Pr \\left(y _ {j} \\in S _ {P}\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.492, + 0.466, + 0.507 + ], + "angle": 0, + "content": "In a similar manner, Probabilistic-recall is approximated as" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.518, + 0.47, + 0.559 + ], + "angle": 0, + "content": "\\[\n\\Pr \\text {r e c a l l} \\approx \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\Pr \\left(x _ {i} \\in S _ {Q}\\right). \\tag {9}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.57, + 0.308, + 0.586 + ], + "angle": 0, + "content": "4.2. Probabilistic scoring rule" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.593, + 0.469, + 0.623 + ], + "angle": 0, + "content": "To estimate \\(\\operatorname*{Pr}(y_j\\in S_P)\\), we first divide \\(S_{P}\\) into subsets around each observation as" + }, + { + "type": "equation", + "bbox": [ + 0.21, + 0.632, + 0.47, + 0.673 + ], + "angle": 0, + "content": "\\[\nS _ {P} := \\bigcup_ {i = 1} ^ {N} s _ {P} \\left(x _ {i}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.685, + 0.471, + 0.746 + ], + "angle": 0, + "content": "where \\( \\mathrm{s}_P(x_i) \\), denoted as the subsupport around \\( x_i \\), represents a subset of \\( S_P \\) that comprises elements for which the nearest reference among \\( \\{x_i\\}_{i=1}^N \\) is \\( x_i \\). Then, we can further elucidate \\( \\operatorname*{Pr}(y_j \\in S_P) \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.108, + 0.758, + 0.47, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\Pr (y _ {j} \\in S _ {P}) = 1 - \\Pr (y _ {j} \\notin S _ {P}) \\\\ = 1 - \\Pr \\left(y _ {j} \\notin \\cup_ {i = 1} ^ {N} s _ {P} \\left(x _ {i}\\right)\\right) \\\\ = 1 - \\Pr \\left(y _ {j} \\in \\cap_ {i = 1} ^ {N} s _ {P} ^ {C} (x _ {i})\\right) \\\\ = 1 - \\prod_ {i = 1} ^ {N} \\Pr \\left(y _ {j} \\in s _ {P} ^ {\\mathbf {c}} \\left(x _ {i}\\right)\\right) \\tag {11} \\\\ = 1 - \\prod_ {i = 1} ^ {N} \\left(1 - \\Pr \\left(y _ {j} \\in s _ {P} \\left(x _ {i}\\right)\\right)\\right) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "using Eq. 10 and complement rule, where \\( s_P^c (\\cdot) \\) denotes the complement set of \\( s_P(\\cdot) \\). The equality in the fourth line of Eq. 11 comes from assuming the independence of events \\( \\{y_{j}\\in s_{P}^{c}(x_{i})|i = 1,2,\\dots ,N\\} \\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.153, + 0.892, + 0.183 + ], + "angle": 0, + "content": "Now, we define our new scoring rule termed Probabilistic Scoring Rules (PSR) from the last equation in Eq. 11:" + }, + { + "type": "equation", + "bbox": [ + 0.532, + 0.194, + 0.892, + 0.255 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\operatorname {P S R} _ {P} \\left(y _ {j}\\right) := 1 - \\prod_ {i = 1} ^ {N} \\left(1 - \\Pr \\left(y _ {j} \\in s _ {P} \\left(x _ {i}\\right)\\right)\\right) \\tag {12} \\\\ = \\Pr (y _ {j} \\in S _ {P}) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.265, + 0.895, + 0.448 + ], + "angle": 0, + "content": "In contrast with deterministic methods such as BSR, which make certain assumptions about the definitive shape of subsupport, PSR estimates the probability of \\( y_{j} \\) to belong to the uncertain support by combining the probability to belong to the subsupport around each observation. Utilizing this probabilistic approach allows us to depart from defining the specific subsupport—a task that, in practice, can be ambiguous. Rather, we infer the likelihood of a sample being part of the subsupport based on an intuitive premise: samples in closer proximity to \\( x_{i} \\) are more likely to be an element of the subsupport compared to those further away. Accordingly, we approximate the probability \\( \\operatorname*{Pr}(y_j\\in s_P(x_i)) \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.458, + 0.892, + 0.499 + ], + "angle": 0, + "content": "\\[\n\\Pr \\left(y _ {j} \\in s _ {P} \\left(x _ {i}\\right)\\right) \\approx \\left\\{ \\begin{array}{l l} 1 - \\frac {d}{R}, & \\text {i f} d \\leq R \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.509, + 0.895, + 0.718 + ], + "angle": 0, + "content": "where \\(d\\) is \\(l_{2}\\) distance between \\(x_{i}\\) and \\(y_{j}\\). From Eq. 13, the probability is one when \\(d = 0\\), given that we know for certain that \\(x_{i}\\) belongs to the subsupport. The probability monotonically decreases with an increase in \\(d\\) until it hits the threshold distance \\(R\\), where the probability converges to zero. By Eq. 12 and Eq. 13, our proposed PSR can assign varying values to samples based on their likelihood of belonging to the support. Moreover, it is bounded within [0,1] (see supplement for the proof) unlike DSR which has an extremely wide bound. Note that while other distance metrics \\(d\\) or monotonically decreasing functions could serve this purpose, we opted to use \\(l_{2}\\) distance and a linear function since it was sufficiently sensitive based on our empirical results. We leave it for future work." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "It is also important to select \\( R \\) in Eq. 13 since it controls the robustness of the scoring rule. Instead of sample-specific \\( R(x_{i}) \\) based on kNN as used in IP&IR and D&C, we propose to use identical \\( R \\) for all samples \\( x_{i} \\). We set \\( R \\) as a multiple of the average of kNN distances among \\( \\{x_{i}\\}_{i = 1}^{N} \\), since it can be used as an effective normalization factor in high-dimensional space. This is similar to using a fixed-variance Gaussian kernel for Kernel Density Estimation and offers several advantages over sample-specific kNN: 1) it suppresses the overestimation of kNN by the outlier as shown in Fig. 1b, and 2) makes metric more robust to the choice of \\( k \\) as shown in Fig. 3." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20102" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.091, + 0.357, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.221, + 0.239, + 0.243, + 0.254 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.357, + 0.091, + 0.613, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.475, + 0.239, + 0.499, + 0.254 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.629, + 0.091, + 0.847, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.629, + 0.159, + 0.845, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.731, + 0.239, + 0.752, + 0.254 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.265, + 0.892, + 0.34 + ], + "angle": 0, + "content": "Figure 2: (a) Behavior of fidelity metrics between two Gaussian distributions \\( X \\sim N(0, I) \\) and \\( Y \\sim N(u\\mathbf{1}, I) \\) as \\( u \\) moves between [-3,3] with outlier \\( x_o \\sim N(-2, I) \\) added to \\( X \\). (b) Behavior of diversity metrics between two Gaussian distributions \\( X \\sim N(u\\mathbf{1}, I) \\) and \\( Y \\sim N(0, I) \\) as \\( u \\) moves between [-3,3] with outlier \\( y_o \\sim N(\\mathbf{2}, I) \\) added to \\( Y \\). (c) Estimated bias from the presumed true value between two identical Gaussian distributions for different numbers of datasets \\( N \\). The line shows the means and the shaded area denotes standard deviations across 50 runs." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.368, + 0.466, + 0.384 + ], + "angle": 0, + "content": "Finally, putting it all together, we propose P-precision as" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.392, + 0.471, + 0.435 + ], + "angle": 0, + "content": "\\[\n\\mathrm {P} \\text { - p r e c i s i o n} = \\frac {1}{M} \\sum_ {j = 1} ^ {M} \\mathrm {P S R} _ {P} \\left(y _ {j}\\right) \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.444, + 0.124, + 0.457 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.122, + 0.465, + 0.424, + 0.506 + ], + "angle": 0, + "content": "\\[\n\\operatorname {P S R} _ {P} \\left(y _ {j}\\right) = 1 - \\prod_ {i = 1} ^ {N} \\left(1 - \\Pr \\left(y _ {j} \\in s _ {P} \\left(x _ {i}\\right)\\right)\\right),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.081, + 0.514, + 0.465, + 0.556 + ], + "angle": 0, + "content": "\\[\n\\Pr (y _ {j} \\in s _ {P} (x _ {i})) = \\left\\{ \\begin{array}{l l} 1 - \\frac {| | x _ {i} - y _ {j} | | _ {2}}{R}, & \\text {i f} | | x _ {i} - y _ {j} | | _ {2} \\leq R \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.56, + 0.107, + 0.573 + ], + "angle": 0, + "content": "and" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.57, + 0.355, + 0.612 + ], + "angle": 0, + "content": "\\[\nR = \\frac {a}{N} \\sum_ {i = 1} ^ {N} \\mathrm {N N D} _ {k} \\left(x _ {i}\\right).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.616, + 0.47, + 0.661 + ], + "angle": 0, + "content": "\\(a\\) is a hyperparameter that controls the magnitude of \\(R\\), and \\(k\\) is for the \\(k\\)-nearest neighbors. In a similar manner, we propose P-recall as" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.67, + 0.47, + 0.711 + ], + "angle": 0, + "content": "\\[\nP - \\text {r e c a l l} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathrm {P S R} _ {Q} \\left(x _ {i}\\right) \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.72, + 0.122, + 0.733 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.741, + 0.425, + 0.784 + ], + "angle": 0, + "content": "\\[\n\\mathrm {P S R} _ {Q} (x _ {i}) = 1 - \\prod_ {j = 1} ^ {M} \\left(1 - \\Pr (x _ {i} \\in s _ {Q} (y _ {j}))\\right),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.793, + 0.465, + 0.834 + ], + "angle": 0, + "content": "\\[\n\\operatorname * {P r} (x _ {i} \\in s _ {Q} (y _ {j})) = \\left\\{ \\begin{array}{l l} 1 - \\frac {| | x _ {i} - y _ {j} | | _ {2}}{R}, & \\text {i f} | | x _ {i} - y _ {j} | | _ {2} \\leq R \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.838, + 0.107, + 0.851 + ], + "angle": 0, + "content": "and" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.849, + 0.356, + 0.892 + ], + "angle": 0, + "content": "\\[\nR = \\frac {a}{M} \\sum_ {j = 1} ^ {M} \\mathrm {N N D} _ {k} (y _ {j}).\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.388, + 0.849, + 0.56 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.576, + 0.892, + 0.623 + ], + "angle": 0, + "content": "Figure 3: Ablation over \\( k \\). We measure each metric for different \\( k \\) between \\( X \\sim N(0, I) \\) and \\( Y \\sim N(u, I) \\) as \\( u \\in [-3.0, 3.0] \\) with outlier \\( x_{o} \\sim N(-2, I) \\) added to \\( X \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.648, + 0.634, + 0.667 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.902 + ], + "angle": 0, + "content": "In this section, we systematically demonstrate the limitations of current metrics and the improvements of our metrics through toy experiments. We then show the experiments with state-of-the-art generative models, highlighting that our metrics are more reliable for evaluating generative models than IP&IR and D&C. We use the settings described below for the remainder of the experiments unless stated otherwise. We set \\( k = 4 \\) and \\( a = 1.2 \\) for our metrics in all experiments. For IP&IR and D&C, we follow the recommended value of \\( k = 3 \\) and \\( k = 5 \\), respectively. In the toy experiments, we generate Gaussian distributions in \\( \\mathbb{R}^{64} \\) and set \\( M = N = 10000 \\). For the experiments evaluating generative models, we use features extracted from the ImageNet [19] pre-trained Inception model [31] after the second fully connected layer. We compute metrics between" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "20103" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.103, + 0.104, + 0.638, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.345, + 0.318, + 0.4, + 0.332 + ], + "angle": 0, + "content": "(a) FFHQ" + }, + { + "type": "image", + "bbox": [ + 0.647, + 0.102, + 0.868, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.647, + 0.211, + 0.868, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.719, + 0.318, + 0.796, + 0.331 + ], + "angle": 0, + "content": "(b) CIFAR-10" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.343, + 0.895, + 0.391 + ], + "angle": 0, + "content": "Figure 4: Qualitative examples sorted according to \\( L \\). We used StyleGAN [15] trained on FFHQ [15] and BigGAN [3] trained on CIFAR-10 [19]. The top two rows are images with the highest \\( L \\) meaning they have high PSR but low DSR. Conversely, the bottom two rows are images with the lowest \\( L \\), indicating low PSR and high DSR." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.426, + 0.273, + 0.54 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.17, + 0.544, + 0.188, + 0.555 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.426, + 0.468, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.365, + 0.544, + 0.383, + 0.555 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.567, + 0.472, + 0.63 + ], + "angle": 0, + "content": "Figure 5: Behavior of metrics between \\( X \\sim N(0, I) \\) and \\( Y \\sim N(0, vI) \\) as \\( v \\) changes between [0.2, 1.5]. Because Density goes over 1 (up to nearly 1000), the \\( y \\)-axis for Density is on the right side of the plot for better visualization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.47, + 0.689 + ], + "angle": 0, + "content": "all available real samples (up to 50K) and 50K generated images following [6]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.7, + 0.241, + 0.716 + ], + "angle": 0, + "content": "5.1. Toy experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.725, + 0.285, + 0.739 + ], + "angle": 0, + "content": "5.1.1 Robustness to outliers" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Gaussian distribution We first investigate how the metrics behave to outliers through a simple toy experiment with Gaussian distributions, following [22]. We set real \\( X \\sim N(0, I) \\) and fake \\( Y \\sim N(u\\mathbf{1}, I) \\) where \\( \\mathbf{1} \\) is a vector of ones and \\( I \\) is the identity matrix, and measure the metrics between \\( X \\) and \\( Y \\) as \\( u \\) varies in [-3, 3]. To introduce an outlier, we add a sample \\( x_o \\sim N(-2, I) \\) to the set of real samples. A reliable metric should consistently decrease as \\( u \\) moves away from 0, regardless of the outlier. Fig. 2a shows the result for fidelity: I-precision gives overestimated values when" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.895, + 0.552 + ], + "angle": 0, + "content": "\\(u \\leq 0\\) due to the enlarged constant-density hypersphere by the outlier. Although Density alleviates the problem by reducing the density inside the hypersphere by \\(1 / k\\), it does not reflect the change for a wide range of \\(u\\) (See when \\(u \\leq -1\\)). On the other hand, P-precision denotes reliable estimates even when the fake distribution comes closer to the outlier \\((\\mathrm{PP} = 0.006\\) when \\(u = -2)\\), and also shows a robust decrease as \\(u\\) moves away from 0. We observe a similar result on the diversity measures except for Coverage (See Fig. 2b)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.896, + 0.718 + ], + "angle": 0, + "content": "In addition, we perform an ablation over \\( k \\) to investigate whether the improvement of our metric over the outlier is due to a properly chosen \\( k \\). The same experiment described above is repeated with different \\( k \\) and the metric values are reported in Fig. 3. Our P-precision shows strong consistency over \\( k \\), due to the employment of identical \\( R \\) for all real samples. However, I-precision continues to suffer from outliers, regardless of the value of \\( k \\). Moreover, Density exhibits high variation over different values of \\( k \\) as it reduces the density by \\( 1 / k \\), demonstrating that Density needs properly chosen \\( k \\) to achieve adequate robustness to outliers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.894, + 0.765 + ], + "angle": 0, + "content": "These results suggest that our metrics are more reliable to estimate fidelity and diversity between distributions, even in the presence of outliers." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.786, + 0.688, + 0.801 + ], + "angle": 0, + "content": "5.1.2 Stability of metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We also test the stability of metrics by measuring the empirical bias of the metric from the presumed true value, which we approximate by averaging across 50 runs with 50K samples, between two identical Gaussian distributions. Fig. 2c shows the bias from the true value with respect to the number of datasets used for estimation, along with the average and" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20104" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "standard deviation across 50 runs. Our PP&PR show a small bias and standard deviation, even for small \\( N \\), while IP&IR show a large bias. In addition, despite the theoretical value when two distributions are identical [22], Density does not behave nicely: at \\( N \\leq 10000 \\), Density shows quite a large bias and standard deviation due to the extremely wide bound. This demonstrates that our PP&PR provides more reliable estimates than other metrics even for small datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.238, + 0.348, + 0.254 + ], + "angle": 0, + "content": "5.1.3 Reflecting fidelity and diversity" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.264, + 0.474, + 0.506 + ], + "angle": 0, + "content": "The main motive of the two-value metric is to capture both fidelity and diversity between two distributions. To assess whether these metrics are capable of reflecting fidelity and diversity, we design a scenario where the two values are at odds. Specifically, we generate samples from \\( X \\sim N(0, I) \\) and \\( Y \\sim N(0, vI) \\), and vary the value of \\( v \\) from 0.2 to 1.5. As \\( v \\) increases, we expect fidelity to decrease and diversity to increase. As shown in Fig. 5, while Density behaves as expected, Coverage does not; it remains constant at 1 as \\( v \\) increases from 0.2 to 1, despite the increasing relative diversity of fake distribution. We argue that this counter-intuitive behavior is due to the conceptual limitation of Coverage as discussed in Sec. 3. When \\( v \\) increases beyond 1, Coverage becomes 0, as fake samples are no longer included in the hyperspheres of real samples. In contrast, PP&PR and IP&IR nicely reflect the expected behavior." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.518, + 0.34, + 0.535 + ], + "angle": 0, + "content": "5.2. Evaluating generative models" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.543, + 0.306, + 0.559 + ], + "angle": 0, + "content": "5.2.1 Comparing scoring rules" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Here, we compare the scoring rules of fidelity metrics to demonstrate how nicely the estimated density reflects the quality of the fake sample. We compare PSR with DSR, as BSR only denotes a binary score. For effective comparison, we focus on cases where two scoring rules have conflicting results. Specifically, we compute \\( L = \\{\\mathrm{PSR}_P(y_j) - \\mathrm{DSR}_P(y_j) \\mid \\forall j\\} \\) using generative models \\( Q(Y) \\) (StyleGAN [15] and BigGAN [3]) trained on real-world datasets \\( P(X) \\) (CIFAR-10 [19] and FFHQ [15]). A high value of \\( L \\) indicates a high PSR but low DSR, while a low value of \\( L \\) indicates the opposite. For a fair comparison, we normalize DSR by its maximum value so that it ranges between 0 and 1. We show images of the highest \\( L \\) and lowest \\( L \\) in Fig. 4 (without cherry-picking). In general, images with a high value of \\( L \\) show more realistic and clear objects, while images with a low \\( L \\) are often distorted with artifacts (See supplement for more examples). Based on the assumption that realistic images should correspond to the high density of real distribution, our results in Fig. 4 qualitatively demonstrate the superiority of PSR over DSR in reflecting the semantic quality of generated images. We also conduct a user study selecting preferences between the" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.089, + 0.695, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.581, + 0.264, + 0.619, + 0.275 + ], + "angle": 0, + "content": "\\(X_{\\text{inlier}}\\)" + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.089, + 0.883, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.765, + 0.264, + 0.813, + 0.275 + ], + "angle": 0, + "content": "\\(X_{outlier}\\)" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.277, + 0.696, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.579, + 0.454, + 0.616, + 0.466 + ], + "angle": 0, + "content": "Yinlier" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.277, + 0.883, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.766, + 0.454, + 0.81, + 0.466 + ], + "angle": 0, + "content": "\\(Y_{outlier}\\)" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.469, + 0.699, + 0.579 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.594, + 0.581, + 0.611, + 0.592 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.469, + 0.889, + 0.579 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.786, + 0.581, + 0.802, + 0.591 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.603, + 0.895, + 0.649 + ], + "angle": 0, + "content": "Figure 6: Behavior of metrics with respect to the number of outliers when evaluating the generative model \\( Y \\) on a real-world dataset \\( X \\). (a) Fidelity metrics. (b) Diversity metrics." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.675, + 0.892, + 0.707 + ], + "angle": 0, + "content": "highest \\(L\\) and the lowest \\(L\\) and it also shows a similar result to our observation (See supplement)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.726, + 0.707, + 0.74 + ], + "angle": 0, + "content": "5.2.2 Robustness to outliers" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "To investigate the efficacy of our proposed metrics in handling outliers with generative models on real-world datasets, we conduct experiments on the state-of-the-art diffusion model (e.g., ADM [6]), which currently has gained attention for its powerful performance, trained on ImageNet [19] dataset \\((128^{2}\\) resolution). Then, we adopt the outlier selection criterion used in [22] which uses the distance to the \\(k^{th}\\) nearest neighbor. We apply this criterion to select inliers and outliers (at a ratio of 0.95:0.05) for both real and fake samples generated by ADM, resulting in the sets" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20105" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.09, + 0.894, + 0.121 + ], + "angle": 0, + "content": "Table 1: Quantitative result of various generative models on real-world datasets. The reported values are obtained by measuring each metric five times and taking the average. Bolded values indicate the top scores evaluated by the corresponding metric." + }, + { + "type": "table", + "bbox": [ + 0.119, + 0.13, + 0.849, + 0.379 + ], + "angle": 0, + "content": "
Model\nImageNet 256x256FID↓PP↑PR↑F1↑IP↑IR↑F1↑D↑C↑F1↑
ADM [6]4.950.5380.7320.6210.6810.6880.6841.520.8761.112
ADM-G [6]4.580.6990.5870.6380.8180.6060.6962.0710.9561.307
BigGAN [3]8.120.7510.4650.5740.8740.4030.5512.4810.9451.368
AFHQv2 512x512
StyleGAN2 [16]4.620.5680.6890.6230.7160.4940.5841.8860.7901.113
StyleGAN3-R [14]4.400.5640.7250.6340.6850.5910.6351.5760.7701.034
StyleGAN3-T [14]4.040.5670.7270.6370.6990.5780.6321.6240.7921.065
LSUN Bedroom 256x256
DDPM [16]4.880.7990.7490.7730.6060.4440.5121.7010.9771.241
ADM [6]1.910.8390.7310.7810.6590.4940.5651.9290.9931.311
StyleGAN2 [16]2.350.8010.7530.7760.5910.5010.5431.7320.9861.257
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.47, + 0.478 + ], + "angle": 0, + "content": "\\(X = X_{\\text{inlier}} \\cup X_{\\text{outlier}}\\) and \\(Y = Y_{\\text{inlier}} \\cup Y_{\\text{outlier}}\\). We provide examples of the outliers and inliers in Fig. 6. Note that the inliers tend to exhibit more recognizable objects with clear semantic features compared to the outliers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.48, + 0.471, + 0.69 + ], + "angle": 0, + "content": "We first observe how fidelity metrics between \\( X_{\\text{inlier}} \\) and \\( Y \\) respond when a portion of \\( X_{\\text{inlier}} \\) is gradually substituted with the subset of \\( X_{\\text{outlier}} \\). To visualize this, we plot the metric increments compared to the case when no outliers are included in \\( X_{\\text{inlier}} \\), as shown in Fig. 6a. The results show that I-precision rapidly increases (0.2 increments) when only \\( 5\\% \\) of inliers are gradually replaced by outliers, confirming its vulnerability to outliers. Although Density is less affected by outliers initially, it eventually surpasses the increment of I-precision as it accumulates the density over hyperspheres, supporting our claim that Density is still vulnerable to outliers. On the other hand, our P-precision shows the least increment (0.05 increments for \\( 5\\% \\) outliers), validating its effectiveness in handling outliers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.691, + 0.471, + 0.829 + ], + "angle": 0, + "content": "Likewise, we also test the robustness of diversity measures between \\( X \\) and \\( Y_{\\text{inlier}} \\) by gradually replacing a portion of \\( Y_{\\text{inlier}} \\) with the subset of \\( Y_{\\text{outlier}} \\). In Fig. 6b, we observe that I-recall exhibits a similar vulnerability to outliers as I-precision, while our P-recall is less affected by the presence of outliers. Besides, Coverage demonstrates strong robustness to outliers due to its alternative diversity measure. However, this comes at the cost of losing accuracy, as demonstrated in the experiments in Fig. 5b and 7b." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.349, + 0.863 + ], + "angle": 0, + "content": "5.2.3 Reflecting fidelity and diversity" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We now verify whether the metrics accurately reflect the change in fidelity and diversity of fake samples generated" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.419, + 0.895, + 0.707 + ], + "angle": 0, + "content": "from generative models. In order to do that, we employ classifier guidance [6] during the image sampling from ADM. This technique uses gradients of a pre-trained classifier to perform conditional sampling from pre-trained unconditional diffusion models. By adjusting the scale of gradients from the classifier, we can explicitly control the balance between fidelity and diversity of generated images. For instance, a larger gradient scale results in the diffusion model sampling more from the modes of the pre-trained classifier, yielding higher fidelity but lower diversity. For more details, please refer to [6]. Therefore, we sample images from ADM, the same model as in Sec. 5.2.2, using gradient scales ranging from 0.5 to 10.0, and measure metrics (IP&IR, D&C and PP&PR) between real and generated samples for each scale. Fig. 7 shows the results; our PP&PR and IP&IR effectively capture the trade-off between fidelity and diversity whereas D&C does not exhibit a clear relationship with the gradient scale. This is due to the conceptual limitation of Coverage in accurately measuring the diversity in generated samples." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.726, + 0.761, + 0.74 + ], + "angle": 0, + "content": "5.2.4 Image generation benchmark" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "To evaluate the practical usefulness of our proposed metrics in assessing the state-of-the-art generative models, we present the quantitative results on real-world datasets (LSUN bedroom [34], AFHQ-v2 [5], and ImageNet) for various types of generative models, along with FID. The results, presented in Tab. 1, are obtained by measuring each metric five times and taking their average. For clarity in the presentation, the variance associated with these measurements can be found in the supplementary materials. While FID serves as a holistic reference point for distinguishing superior" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20106" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.079, + 0.09, + 0.273, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.169, + 0.204, + 0.186, + 0.215 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.089, + 0.47, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.364, + 0.204, + 0.381, + 0.215 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.226, + 0.471, + 0.287 + ], + "angle": 0, + "content": "Figure 7: Fidelity versus diversity when increasing the gradient scale from 0.5 to 10.0 for sampling diffusion models with classifier guidance [6]. A larger gradient scale tends to result in higher fidelity and lower diversity." + }, + { + "type": "image", + "bbox": [ + 0.131, + 0.305, + 0.413, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.497, + 0.471, + 0.527 + ], + "angle": 0, + "content": "Figure 8: Ablation study on PSR: (A): probabilistic estimation for subsupport. (B): identical \\( R \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.556, + 0.47, + 0.691 + ], + "angle": 0, + "content": "model performance, our metrics delve deeper, elaborating on aspects of fidelity and diversity. For instance, our metrics explain that the improvement of ADM over StyleGAN [15] on LSUN bedroom in terms of FID is due to an increase in fidelity at the cost of diversity. An analysis between ADM and ADM-G further reveals that the classifier guidance in ADM-G augments fidelity, yet curtails diversity. This demonstrates the usefulness of our metrics in elaborating on the effect of the specific component in models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.692, + 0.47, + 0.799 + ], + "angle": 0, + "content": "Moreover, to observe whether the metrics harmonize with the widely adopted FID metric, we analyze the consistency between FID and two-value metrics. This is achieved by computing the \\( \\mathrm{F}_1 \\)-score [9], which is a harmonic mean of fidelity and diversity. The results demonstrate that \\( \\mathrm{F}_1 \\)-scores of our metric mirror the trends set by FID (as underscored by the bold scores for each dataset in Tab. 1)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.815, + 0.226, + 0.832 + ], + "angle": 0, + "content": "6. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Here, we conduct an ablation study on our proposed scoring rule, PSR, to demonstrate the effectiveness of our approach: (A) probabilistic estimation for subsupport (Eq. 13) and (B) identical \\( R \\). We repeat the outlier toy experiment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.894, + 0.244 + ], + "angle": 0, + "content": "with Gaussian distributions in Sec. 5.1.1 with different configurations and the result for fidelity metric is shown in Fig. 8. In both cases where the feature (A) and (B) are individually removed, the metric becomes more susceptible to outlier than the case where both are used \\((\\mathrm{(A)} + \\mathrm{(B)})\\) but less affected than the case where both are all removed (see when \\(u\\in [-3, - 1]\\)). This demonstrates that our probabilistic approach for subsupport and addressing overestimation of sample-specific \\(k_{\\mathrm{NN}}\\) both contribute to estimating accurate density and combining them together maximizes it." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.257, + 0.757, + 0.273 + ], + "angle": 0, + "content": "7. Conclusions and limitations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.283, + 0.895, + 0.509 + ], + "angle": 0, + "content": "In this paper, we introduced a set of two-value metrics, P-precision and P-recall, based on the probabilistic approach that addresses the limitations of existing metrics (IP&IR and D&C). We have conducted a systematic investigation of the limitations and demonstrated the effectiveness of our proposed metrics by evaluating toy experiments and state-of-the-art generative models. Nevertheless, we recognize there is still room for improvement. While we utilized commonly-used ImageNet embeddings [11, 20, 22] for feature extraction, recent studies such as [1, 21], have proposed domain-agnostic embeddings to enhance the feature quality compared to previous embeddings that rely on dataset-specific statistics. Thus, future research focusing on the quality of feature embedding combined with our method may further enhance the reliability and usefulness of the metric." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.894, + 0.634 + ], + "angle": 0, + "content": "Acknowledgements This work was supported by the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No.2021-0-00456, Development of Ultra-high Speech Quality Technology for remote Multi-speaker Conference System and No.RS-2023-00225630, Development of Artificial Intelligence for Text-based 3D Movie Generation)." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.649, + 0.597, + 0.665 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.674, + 0.892, + 0.743 + ], + "angle": 0, + "content": "[1] Ahmed Alaa, Boris Van Breugel, Evgeny S Saveliev, and Mihaela van der Schaar. 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In Conference on Computer Vision and Pattern Recognition, pages 16407-16417, 2021. 1" + }, + { + "type": "list", + "bbox": [ + 0.079, + 0.092, + 0.471, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20109" + } + ] +] \ No newline at end of file diff --git a/2023/Probabilistic Precision and Recall Towards Reliable Evaluation of Generative Models/dd6377f8-01ac-488f-b3b2-5ae1ebd477f1_origin.pdf b/2023/Probabilistic Precision and Recall Towards Reliable Evaluation of Generative Models/dd6377f8-01ac-488f-b3b2-5ae1ebd477f1_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..598f8b13d39eeebf587e314e5d0536f00df80ba1 --- /dev/null +++ b/2023/Probabilistic Precision and Recall Towards Reliable Evaluation of Generative Models/dd6377f8-01ac-488f-b3b2-5ae1ebd477f1_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0f442056e502c6054ac96995ecc315e5c2121b5830ba516228d1435ce7a5d7ba +size 6416870 diff --git a/2023/Probabilistic Precision and Recall Towards Reliable Evaluation of Generative Models/full.md b/2023/Probabilistic Precision and Recall Towards Reliable Evaluation of Generative Models/full.md new file mode 100644 index 0000000000000000000000000000000000000000..1670848f316d94966c0abf205040c6df2fb66d31 --- /dev/null +++ b/2023/Probabilistic Precision and Recall Towards Reliable Evaluation of Generative Models/full.md @@ -0,0 +1,406 @@ +# Probabilistic Precision and Recall Towards Reliable Evaluation of Generative Models + +Dogyun Park +Department of Computer Science, Korea University +Seoul, South Korea +gg933@korea.ac.kr + +Suhyun Kim* +Korea Institute of Science and Technology +Seoul, South Korea +dr.suhyun.kim@gmail.com + +# Abstract + +Assessing the fidelity and diversity of the generative model is a difficult but important issue for technological advancement. So, recent papers have introduced $k$ -Nearest Neighbor (kNN) based precision-recall metrics to break down the statistical distance into fidelity and diversity. While they provide an intuitive method, we thoroughly analyze these metrics and identify oversimplified assumptions and undesirable properties of kNN that result in unreliable evaluation, such as susceptibility to outliers and insensitivity to distributional changes. Thus, we propose novel metrics, P-precision and P-recall (PP&PR), based on a probabilistic approach that address the problems. Through extensive investigations on toy experiments and state-of-the-art generative models, we show that our PP&PR provide more reliable estimates for comparing fidelity and diversity than the existing metrics. The codes are available at https://github.com/kdst-team/Probabistic_precision_recall. + +# 1. Introduction + +Modern state-of-the-art generative models such as Variational Autoencoders (VAEs) [18, 24], Generative Adversarial Networks (GANs) [8, 15, 13, 14], and Score-based Diffusion Models (SDMs) [12, 17, 29, 6, 32, 25, 30] have shown outstanding achievements that surpass human evaluative capabilities. Consequently, reliable evaluation metrics for comparing the performance of generative models are critical for further technological advancement. The widely used Fréchet Inception Distance (FID) evaluation metric [11] has been praised for its robustness and consistency with human perceptual evaluation. However, FID only provides a single score and does not diagnose whether the model lacks fidelity or diversity, two essential aspects for improving generative models. Recent papers [26, 28, 20, 22, 1] have introduced various two-value metrics to measure fidelity + +and diversity, respectively. Especially, $k$ -nearest neighbor ( $k$ NN) based metrics such as Improved Precision and Recall (IP&IR) [20] and Density and Coverage (D&C) [22] have been used to assess fidelity and diversity on various generative models [6, 35, 2, 24, 13, 4, 23]. The pipeline of these metrics [20, 22] starts with estimating distribution support of real and fake distribution by constructing sample-specific hyperspheres around each sample using $k$ NN. Then, they measure the expectation of the likelihood of fake (real) samples with respect to the estimated real (fake) distribution support to represent fidelity (diversity). + +Unfortunately, both IP&IR and D&C metrics present certain challenges that compromise their practical reliability. Specifically, IP&IR operate under the assumption of constant-density within the distribution support and overlook the overestimation linked to $k$ NN, leading to an inflated distribution support with constant density. This scenario becomes especially problematic when the distribution houses outliers, resulting in metric overestimation (See Fig. 1a). Density metric [22] attempts to address these limitations by accumulating density over overlapped $k$ NN hyperspheres. Yet, our findings suggest that it still remains unreliable to outliers. Furthermore, it tends to exhibit high variance, due to its extremely wide bound, which further limits the reliability of evaluations. On the other hand, Coverage metric [22] presents an alternative method that measures robust diversity even with the presence of outliers in the fake distribution. However, we show that it suffers from a conceptual limitation that makes it insensitive to changes in fake distribution. An in-depth discussion of these constraints is provided in Sec. 2. In the end, these issues underscore the need for careful revision of $k$ NN-based metrics to provide more reliable evaluations. + +We, therefore, propose a novel set of metrics, P-precision and P-recall (PP&PR), which aim to provide more reliable estimations for the fidelity and diversity of generative models. In particular, we derive our metrics based on a probabilistic approach that relaxes the oversimplified assumptions and undesirable properties of kNN, addressing the limitations of + +![](images/4091ae853b43778863d6475bfd47bef549217251e07bb7d586350702c3af826a.jpg) +(a) I-Precision / Density + +![](images/eb9b65300a73578ca8bfb995c95e555405ded7513b54cd5692776495a72a387d.jpg) +(b) P-precision + +![](images/608c7f901a09e831731686b978e78143613160ae63a1f9d4cf55d77e0361c7af.jpg) +(c) I-Recall +(d) Coverage +(e) P-recall +Figure 1: Examples of IP&IR, D&C, and PP&PR (better zoom-in). For simplicity, we use $k = 2$ for $k$ -Nearest Neighbor in all metrics. (a), (c): Due to the overestimation of $k$ NN by the outlier and constant-density assumption within hyperspheres, I-precision, I-recall, and Density denote the same values for different $y$ in an overly large space (See $y_1$ , $y_2$ , and $y_3$ in (a)), leading to unreliable-overestimated values. (b), (e): On the other hand, our P-precision and P-recall assign different scores to different $y$ based on a probabilistic approach and address overestimation of $k$ NN (See Sec. 4 for details). (d): This illustrates a case when Coverage exhibits its conceptual limitation. Even if the fake samples have lower relative diversity compared to real samples, they can still be included in multiple hyperspheres of real samples, leading to high Coverage. + +existing metrics. Through extensive experiments on both toy and real-world datasets, we systematically demonstrate the superiority of our proposed metrics over IP&IR and D&C. To summarize, our contributions are as follows: + +- We propose a set of two-value metrics, P-precision and P-recall, that provide reliable fidelity and diversity measures for generative models. +- We thoroughly analyze the limitations of existing metrics (IP&IR and D&C), such as vulnerability to outliers and insensitivity to diversity, and introduce a novel method based on the probabilistic approach that remedies the limitations. +- Through a series of experiments on toy and real-world datasets with state-of-the-art generative models, we empirically verify the limitations of current metrics and demonstrate the efficacy of our proposed metrics. + +# 2. Preliminary + +# 2.1. Feature embedding for evaluation + +Statistical comparison of high dimensional data in the raw input space $\mathcal{X}$ is difficult. Therefore, the usual evaluation starts with converting real data $X \sim P$ and fake data $Y \sim Q$ into embeddings using a CNN feature $\Phi(\Phi(X)$ and $\Phi(Y))$ [11, 20, 27, 22]. This embedded feature space is believed to have more "meaningful" information to compare two samples [7, 33]. For simplicity, we use $X$ and $Y$ in place of $\Phi(X)$ and $\Phi(Y)$ for the remainder of the paper. + +# 2.2. kNN-based fidelity and diversity measures + +Now, we briefly introduce current $k\mathrm{NN}$ -based fidelity and diversity measures and discuss their limitations in Sec. 3. + +Improved Precision and Recall (IP&IR). To represent fidelity, Precision is defined as the expected likelihood of a fake sample belonging to the support of the real distribution, which refers to the set of possible real samples whose probability density function is non-zero. Likewise, Recall is defined as the expected likelihood of a real sample belonging to the support of fake distribution to measure diversity. + +$$ +\text {P r e c i s i o n} := \mathbb {E} _ {Y \sim Q} [ Y \in \operatorname {s u p p} (P) ] \tag {1} +$$ + +$$ +\operatorname {R e c a l l} := \mathbb {E} _ {X \sim P} [ X \in \operatorname {s u p p} (Q) ], +$$ + +where $\operatorname{supp}(\cdot)$ indicates the ground truth support of distribution. Then, IP&IR [20] approximates them using the empirical observations $\left(\left\{x_{i}\right\}_{i=1}^{N}\right.$ and $\left\{y_{j}\right\}_{j=1}^{M}$ as + +$$ +\mathrm {P r e c i s i o n} \approx \mathrm {I} - \mathrm {P r e c i s i o n} +$$ + +$$ +:= \frac {1}{M} \sum_ {j = 1} ^ {M} \operatorname {B S R} _ {P} \left(y _ {j}\right) \tag {2} +$$ + +$$ +\mathrm {R e c a l l} \approx \mathrm {I} - \mathrm {R e c a l l} +$$ + +$$ +:= \frac {1}{N} \sum_ {i = 1} ^ {N} \mathrm {B S R} _ {Q} (x _ {i}). +$$ + +The scoring rule of IP&IR, which we name as Binary Scoring Rule (BSR) for comparison with other scoring rules, is + +$$ +\operatorname {B S R} _ {P} \left(y _ {j}\right) = \left\{ \begin{array}{l l} 1, & \text {i f} y _ {j} \in \cup_ {i = 1} ^ {N} B \left(x _ {i}, \mathrm {N N D} _ {k} \left(x _ {i}\right)\right) \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {3} +$$ + +where $B(x, r)$ is the hypersphere in $\mathbb{R}^D$ around $x$ with radius $r$ , and $\mathrm{NND}_k(x_i)$ denotes the Euclidean distance from $x_i$ to the $k^{th}$ nearest neighbor among $\{x_i\}_{i=1}^N$ excluding itself. In other words, $\mathrm{BSR}_P(y_j)$ assigns a binary score of 1 or 0 to $y_j$ based on whether it falls inside the union of hyperspheres. It is worth noting that BSR employs a deterministic approach that determines the support as the union of $k$ NN hyperspheres without accounting for any uncertainty regarding the true support. This restricts the scoring rule to binary assignments, leading to a constant density within the approximated distribution support. + +I-recall is defined using $\mathrm{BSR}_Q(x_i)$ , which is defined symmetrically with $\mathrm{BSR}_P(y_j)$ . It builds hyperspheres around fake samples and tests real samples. + +Density and Coverage (D&C). D&C use different approaches to define fidelity and diversity in comparison to IP&IR. Specifically, Density [22] tackles the issue of constant-density over distribution support in IP&IR by quantifying the degree of overlap between kNN hyperspheres. To this end, Density defines a scoring rule that estimates the density function within distribution support by the superposition of hyperspheres, as opposed to the union in IP&IR. We denote this scoring rule as Density Scoring Rule (DSR). + +$$ +\mathrm {D S R} _ {P} \left(y _ {j}\right) = \frac {1}{k} \sum_ {i = 1} ^ {N} 1 _ {y _ {j} \in B \left(x _ {i}, \mathrm {N N D} _ {k} \left(x _ {i}\right)\right)} \tag {4} +$$ + +where $k$ is for the $k$ -nearest neighbors. DSR employs a kind of Parzen window density estimation [10] with a uniform kernel whose width is adjusted automatically, except that the integral of the kernel does not sum up to 1. Now, Density is defined as the expectation of DSR over observed samples as + +$$ +\text {D e n s i t y} := \frac {1}{M} \sum_ {j = 1} ^ {M} \mathrm {D S R} _ {P} \left(y _ {j}\right) \tag {5} +$$ + +For diversity, the authors employ another scoring rule, Coverage Scoring Rule (CSR), which is not symmetric to DSR. It builds $k$ NN hyperspheres around the real samples and counts the real samples whose hyperspheres are occupied by the fake samples. Coverage has demonstrated effectiveness in handling outliers in fake distribution, as the hyperspheres of real samples are not influenced by fake outliers. + +$$ +\operatorname {C S R} _ {Q} \left(x _ {i}\right) = 1 _ {\exists j \text {s . t .} y _ {j} \in B \left(x _ {i}, \mathrm {N N D} _ {k} \left(x _ {i}\right)\right)} +$$ + +$$ +\text {C o v e r a g e} := \frac {1}{N} \sum_ {i = 1} ^ {N} \mathrm {C S R} _ {Q} \left(x _ {i}\right) \tag {6} +$$ + +# 3. Limitations with scoring rules of IP&IR and D&C + +Binary scoring rule. BSR can only assign constant density within an approximated distribution support, which can + +hinder reliable estimates when comparing distributions with complex density functions. Moreover, the use of $k\mathrm{NN}$ in BSR makes it more susceptible to outliers as it unreliably inflates the size of the hypersphere due to the presence of such outliers. This results in overestimated value as illustrated in Fig. 1a and 1c. Both I-precision and I-recall face similar issues since they symmetrically use BSR. + +Density scoring rule. We contend that DSR remains vulnerable to outliers as it accumulates density over the overestimated constant-density hyperspheres. For instance, if there are $s$ outliers, all hyperspheres of outliers can overlap due to the overestimated size of hyperspheres. This causes the overlapped density to accumulate to $s / k$ (note that DSR scales the overlapped density by a factor of $1 / k$ in Eq. 4), resulting in a rapid increase with just a few outliers. We demonstrate this quantitatively with the experiment in Sec. 5. Additionally, reducing the density by a factor of $1 / k$ makes the metric highly dependent on the choice of $k$ , which is not desirable as we demonstrate in Fig. 3. + +Lastly, DSR is bounded within $[0, N / k]$ (e.g., $N / k = 50000 / 5 = 10000$ ), which can result in samples with abnormally high values of DSR, compromising stable evaluations with high standard deviations as demonstrated in Fig. 2c. + +Coverage scoring rule. While CSR can effectively handle outliers in fake distribution, it exhibits a conceptual limitation: a lack of sensitivity to the comparative diversity between fake and real distributions. This arises because CSR doesn't factor in distances between fake samples. Instead, its focus is solely on the count of real sample hyperspheres occupied by fake samples. This leads to a scenario where if real samples are more dispersed compared to fake ones, meaning the fake samples exhibit less relative diversity, the fake samples could still be included in multiple real hyperspheres. This, in turn, can produce a falsely elevated Coverage metric (a conceptual illustration is provided in Fig.1d). Conversely, Coverage can be low if fake samples are more widely distributed compared to real samples. We elucidate this phenomenon quantitatively in Fig. 5b. + +# 4. Method + +To address the aforementioned limitations, we propose a novel scoring rule based on a probabilistic approach. Our motivation arises from the recognition that accurately estimating the ground truth support is infeasible with empirical observations alone. As a result, it becomes difficult to determine whether a sample belongs to the ground truth support with certainty (0 or 1). Therefore, we adopt a probabilistic perspective and define the probability of a sample belonging to the support, taking into account the uncertainty surrounding the ground truth support. Then, our scoring rule can + +assign lower values to samples that are less likely to belong to the support such as outliers, effectively addressing outlier concerns. We also define the scoring rules for fidelity and diversity symmetrically, similar to IP&IR, to avoid the conceptual limitation of CSR. Although we mainly focus on describing the details of fidelity in the paper, diversity is defined symmetrically. + +# 4.1. P-precision and P-recall (PP&PR) + +Given the observations $\{x_i\}_{i = 1}^N$ , we assume that there are myriad possible supports of $P$ , denoted as $S_P$ . The collection of these supports is represented by $\mathbb{S}_P$ . Subsequently, we introduce Probabilistic-Precision that characterizes precision as the probability of $y_{j}$ being an element of support randomly chosen from $\mathbb{S}_P$ . This is articulated as + +$$ +\begin{array}{l} \mathrm {P} \text {- p r e c i s i o n} := \mathbb {E} _ {Y \sim Q, S _ {P} \in \mathbb {S} _ {P}} [ Y \in S _ {P} ] \\ = \mathbb {E} _ {Y \sim Q} \left[ \mathbb {E} _ {S _ {P} \in \mathbb {S} _ {P}} \left[ Y \in S _ {P} \right] \right] \tag {7} \\ = \mathbb {E} _ {Y \sim Q} \left[ \Pr \left(Y \in S _ {P}\right) \right] \\ \end{array} +$$ + +Then, we approximate it with given observations $\{y_{j}\}_{j = 1}^{M}$ as + +$$ +\mathrm {P} \text { - p r e c i s i o n} \approx \frac {1}{M} \sum_ {j = 1} ^ {M} \Pr \left(y _ {j} \in S _ {P}\right). \tag {8} +$$ + +In a similar manner, Probabilistic-recall is approximated as + +$$ +\Pr \text {r e c a l l} \approx \frac {1}{N} \sum_ {i = 1} ^ {N} \Pr \left(x _ {i} \in S _ {Q}\right). \tag {9} +$$ + +# 4.2. Probabilistic scoring rule + +To estimate $\operatorname*{Pr}(y_j\in S_P)$ , we first divide $S_{P}$ into subsets around each observation as + +$$ +S _ {P} := \bigcup_ {i = 1} ^ {N} s _ {P} \left(x _ {i}\right), \tag {10} +$$ + +where $\mathrm{s}_P(x_i)$ , denoted as the subsupport around $x_i$ , represents a subset of $S_P$ that comprises elements for which the nearest reference among $\{x_i\}_{i=1}^N$ is $x_i$ . Then, we can further elucidate $\operatorname*{Pr}(y_j \in S_P)$ as + +$$ +\begin{array}{l} \Pr (y _ {j} \in S _ {P}) = 1 - \Pr (y _ {j} \notin S _ {P}) \\ = 1 - \Pr \left(y _ {j} \notin \cup_ {i = 1} ^ {N} s _ {P} \left(x _ {i}\right)\right) \\ = 1 - \Pr \left(y _ {j} \in \cap_ {i = 1} ^ {N} s _ {P} ^ {C} (x _ {i})\right) \\ = 1 - \prod_ {i = 1} ^ {N} \Pr \left(y _ {j} \in s _ {P} ^ {\mathbf {c}} \left(x _ {i}\right)\right) \tag {11} \\ = 1 - \prod_ {i = 1} ^ {N} \left(1 - \Pr \left(y _ {j} \in s _ {P} \left(x _ {i}\right)\right)\right) \\ \end{array} +$$ + +using Eq. 10 and complement rule, where $s_P^c (\cdot)$ denotes the complement set of $s_P(\cdot)$ . The equality in the fourth line of Eq. 11 comes from assuming the independence of events $\{y_{j}\in s_{P}^{c}(x_{i})|i = 1,2,\dots ,N\}$ + +Now, we define our new scoring rule termed Probabilistic Scoring Rules (PSR) from the last equation in Eq. 11: + +$$ +\begin{array}{l} \operatorname {P S R} _ {P} \left(y _ {j}\right) := 1 - \prod_ {i = 1} ^ {N} \left(1 - \Pr \left(y _ {j} \in s _ {P} \left(x _ {i}\right)\right)\right) \tag {12} \\ = \Pr (y _ {j} \in S _ {P}) \\ \end{array} +$$ + +In contrast with deterministic methods such as BSR, which make certain assumptions about the definitive shape of subsupport, PSR estimates the probability of $y_{j}$ to belong to the uncertain support by combining the probability to belong to the subsupport around each observation. Utilizing this probabilistic approach allows us to depart from defining the specific subsupport—a task that, in practice, can be ambiguous. Rather, we infer the likelihood of a sample being part of the subsupport based on an intuitive premise: samples in closer proximity to $x_{i}$ are more likely to be an element of the subsupport compared to those further away. Accordingly, we approximate the probability $\operatorname*{Pr}(y_j\in s_P(x_i))$ as + +$$ +\Pr \left(y _ {j} \in s _ {P} \left(x _ {i}\right)\right) \approx \left\{ \begin{array}{l l} 1 - \frac {d}{R}, & \text {i f} d \leq R \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {13} +$$ + +where $d$ is $l_{2}$ distance between $x_{i}$ and $y_{j}$ . From Eq. 13, the probability is one when $d = 0$ , given that we know for certain that $x_{i}$ belongs to the subsupport. The probability monotonically decreases with an increase in $d$ until it hits the threshold distance $R$ , where the probability converges to zero. By Eq. 12 and Eq. 13, our proposed PSR can assign varying values to samples based on their likelihood of belonging to the support. Moreover, it is bounded within [0,1] (see supplement for the proof) unlike DSR which has an extremely wide bound. Note that while other distance metrics $d$ or monotonically decreasing functions could serve this purpose, we opted to use $l_{2}$ distance and a linear function since it was sufficiently sensitive based on our empirical results. We leave it for future work. + +It is also important to select $R$ in Eq. 13 since it controls the robustness of the scoring rule. Instead of sample-specific $R(x_{i})$ based on kNN as used in IP&IR and D&C, we propose to use identical $R$ for all samples $x_{i}$ . We set $R$ as a multiple of the average of kNN distances among $\{x_{i}\}_{i = 1}^{N}$ , since it can be used as an effective normalization factor in high-dimensional space. This is similar to using a fixed-variance Gaussian kernel for Kernel Density Estimation and offers several advantages over sample-specific kNN: 1) it suppresses the overestimation of kNN by the outlier as shown in Fig. 1b, and 2) makes metric more robust to the choice of $k$ as shown in Fig. 3. + +![](images/5a04749ac74f1b01197dcc1c74ecba5bf9440cca2418d97e0101d97f969218c4.jpg) +(a) + +![](images/6c3d7d791d7fb109470d8725b9c51e40adb626e83ab9ec6038b54de598ce439d.jpg) +(b) +Figure 2: (a) Behavior of fidelity metrics between two Gaussian distributions $X \sim N(0, I)$ and $Y \sim N(u\mathbf{1}, I)$ as $u$ moves between [-3,3] with outlier $x_o \sim N(-2, I)$ added to $X$ . (b) Behavior of diversity metrics between two Gaussian distributions $X \sim N(u\mathbf{1}, I)$ and $Y \sim N(0, I)$ as $u$ moves between [-3,3] with outlier $y_o \sim N(\mathbf{2}, I)$ added to $Y$ . (c) Estimated bias from the presumed true value between two identical Gaussian distributions for different numbers of datasets $N$ . The line shows the means and the shaded area denotes standard deviations across 50 runs. + +![](images/6d96d060210c2802fab0675a167fd015782875d66a6b755d07f165f479257534.jpg) + +![](images/ed71da9f3fb4a4873100cf32937662a473e6976a8e9817884aeba226d40ff6d1.jpg) +(c) + +Finally, putting it all together, we propose P-precision as + +$$ +\mathrm {P} \text { - p r e c i s i o n} = \frac {1}{M} \sum_ {j = 1} ^ {M} \mathrm {P S R} _ {P} \left(y _ {j}\right) \tag {14} +$$ + +where + +$$ +\operatorname {P S R} _ {P} \left(y _ {j}\right) = 1 - \prod_ {i = 1} ^ {N} \left(1 - \Pr \left(y _ {j} \in s _ {P} \left(x _ {i}\right)\right)\right), +$$ + +$$ +\Pr (y _ {j} \in s _ {P} (x _ {i})) = \left\{ \begin{array}{l l} 1 - \frac {| | x _ {i} - y _ {j} | | _ {2}}{R}, & \text {i f} | | x _ {i} - y _ {j} | | _ {2} \leq R \\ 0, & \text {o t h e r w i s e} \end{array} \right. +$$ + +and + +$$ +R = \frac {a}{N} \sum_ {i = 1} ^ {N} \mathrm {N N D} _ {k} \left(x _ {i}\right). +$$ + +$a$ is a hyperparameter that controls the magnitude of $R$ , and $k$ is for the $k$ -nearest neighbors. In a similar manner, we propose P-recall as + +$$ +P - \text {r e c a l l} = \frac {1}{N} \sum_ {i = 1} ^ {N} \mathrm {P S R} _ {Q} \left(x _ {i}\right) \tag {15} +$$ + +where + +$$ +\mathrm {P S R} _ {Q} (x _ {i}) = 1 - \prod_ {j = 1} ^ {M} \left(1 - \Pr (x _ {i} \in s _ {Q} (y _ {j}))\right), +$$ + +$$ +\operatorname * {P r} (x _ {i} \in s _ {Q} (y _ {j})) = \left\{ \begin{array}{l l} 1 - \frac {| | x _ {i} - y _ {j} | | _ {2}}{R}, & \text {i f} | | x _ {i} - y _ {j} | | _ {2} \leq R \\ 0, & \text {o t h e r w i s e} \end{array} \right. +$$ + +and + +$$ +R = \frac {a}{M} \sum_ {j = 1} ^ {M} \mathrm {N N D} _ {k} (y _ {j}). +$$ + +![](images/07d53bd6798503751419436e826dc9c3cdd1690d7a7632f967936823a9723355.jpg) +Figure 3: Ablation over $k$ . We measure each metric for different $k$ between $X \sim N(0, I)$ and $Y \sim N(u, I)$ as $u \in [-3.0, 3.0]$ with outlier $x_{o} \sim N(-2, I)$ added to $X$ . + +# 5. Experiments + +In this section, we systematically demonstrate the limitations of current metrics and the improvements of our metrics through toy experiments. We then show the experiments with state-of-the-art generative models, highlighting that our metrics are more reliable for evaluating generative models than IP&IR and D&C. We use the settings described below for the remainder of the experiments unless stated otherwise. We set $k = 4$ and $a = 1.2$ for our metrics in all experiments. For IP&IR and D&C, we follow the recommended value of $k = 3$ and $k = 5$ , respectively. In the toy experiments, we generate Gaussian distributions in $\mathbb{R}^{64}$ and set $M = N = 10000$ . For the experiments evaluating generative models, we use features extracted from the ImageNet [19] pre-trained Inception model [31] after the second fully connected layer. We compute metrics between + +![](images/67150a655c8478e4d0841435cf073066d697a8df598d2d4c5bad7d40a17aa6a2.jpg) +(a) FFHQ + +![](images/f4a2756ea0e4b64266fc2fb5b29aded249817e10ee65e61939f641a87339c5fd.jpg) + +![](images/10564ff7fa0598a80d8c26bb02d511d8831f17d9932d52d16cbe3493d2c828cb.jpg) +(b) CIFAR-10 +Figure 4: Qualitative examples sorted according to $L$ . We used StyleGAN [15] trained on FFHQ [15] and BigGAN [3] trained on CIFAR-10 [19]. The top two rows are images with the highest $L$ meaning they have high PSR but low DSR. Conversely, the bottom two rows are images with the lowest $L$ , indicating low PSR and high DSR. + +![](images/075c527cbecb2c4c1cf691dc646205707c79478935d80392ab96cbc4a06c2978.jpg) +(a) +Figure 5: Behavior of metrics between $X \sim N(0, I)$ and $Y \sim N(0, vI)$ as $v$ changes between [0.2, 1.5]. Because Density goes over 1 (up to nearly 1000), the $y$ -axis for Density is on the right side of the plot for better visualization. + +![](images/3b2fd32ae514679643ad1c7d021123c6aac7cd857dad17a67e81e96711e9458f.jpg) +(b) + +all available real samples (up to 50K) and 50K generated images following [6]. + +# 5.1. Toy experiments + +# 5.1.1 Robustness to outliers + +Gaussian distribution We first investigate how the metrics behave to outliers through a simple toy experiment with Gaussian distributions, following [22]. We set real $X \sim N(0, I)$ and fake $Y \sim N(u\mathbf{1}, I)$ where $\mathbf{1}$ is a vector of ones and $I$ is the identity matrix, and measure the metrics between $X$ and $Y$ as $u$ varies in [-3, 3]. To introduce an outlier, we add a sample $x_o \sim N(-2, I)$ to the set of real samples. A reliable metric should consistently decrease as $u$ moves away from 0, regardless of the outlier. Fig. 2a shows the result for fidelity: I-precision gives overestimated values when + +$u \leq 0$ due to the enlarged constant-density hypersphere by the outlier. Although Density alleviates the problem by reducing the density inside the hypersphere by $1 / k$ , it does not reflect the change for a wide range of $u$ (See when $u \leq -1$ ). On the other hand, P-precision denotes reliable estimates even when the fake distribution comes closer to the outlier $(\mathrm{PP} = 0.006$ when $u = -2)$ , and also shows a robust decrease as $u$ moves away from 0. We observe a similar result on the diversity measures except for Coverage (See Fig. 2b). + +In addition, we perform an ablation over $k$ to investigate whether the improvement of our metric over the outlier is due to a properly chosen $k$ . The same experiment described above is repeated with different $k$ and the metric values are reported in Fig. 3. Our P-precision shows strong consistency over $k$ , due to the employment of identical $R$ for all real samples. However, I-precision continues to suffer from outliers, regardless of the value of $k$ . Moreover, Density exhibits high variation over different values of $k$ as it reduces the density by $1 / k$ , demonstrating that Density needs properly chosen $k$ to achieve adequate robustness to outliers. + +These results suggest that our metrics are more reliable to estimate fidelity and diversity between distributions, even in the presence of outliers. + +# 5.1.2 Stability of metrics + +We also test the stability of metrics by measuring the empirical bias of the metric from the presumed true value, which we approximate by averaging across 50 runs with 50K samples, between two identical Gaussian distributions. Fig. 2c shows the bias from the true value with respect to the number of datasets used for estimation, along with the average and + +standard deviation across 50 runs. Our PP&PR show a small bias and standard deviation, even for small $N$ , while IP&IR show a large bias. In addition, despite the theoretical value when two distributions are identical [22], Density does not behave nicely: at $N \leq 10000$ , Density shows quite a large bias and standard deviation due to the extremely wide bound. This demonstrates that our PP&PR provides more reliable estimates than other metrics even for small datasets. + +# 5.1.3 Reflecting fidelity and diversity + +The main motive of the two-value metric is to capture both fidelity and diversity between two distributions. To assess whether these metrics are capable of reflecting fidelity and diversity, we design a scenario where the two values are at odds. Specifically, we generate samples from $X \sim N(0, I)$ and $Y \sim N(0, vI)$ , and vary the value of $v$ from 0.2 to 1.5. As $v$ increases, we expect fidelity to decrease and diversity to increase. As shown in Fig. 5, while Density behaves as expected, Coverage does not; it remains constant at 1 as $v$ increases from 0.2 to 1, despite the increasing relative diversity of fake distribution. We argue that this counter-intuitive behavior is due to the conceptual limitation of Coverage as discussed in Sec. 3. When $v$ increases beyond 1, Coverage becomes 0, as fake samples are no longer included in the hyperspheres of real samples. In contrast, PP&PR and IP&IR nicely reflect the expected behavior. + +# 5.2. Evaluating generative models + +# 5.2.1 Comparing scoring rules + +Here, we compare the scoring rules of fidelity metrics to demonstrate how nicely the estimated density reflects the quality of the fake sample. We compare PSR with DSR, as BSR only denotes a binary score. For effective comparison, we focus on cases where two scoring rules have conflicting results. Specifically, we compute $L = \{\mathrm{PSR}_P(y_j) - \mathrm{DSR}_P(y_j) \mid \forall j\}$ using generative models $Q(Y)$ (StyleGAN [15] and BigGAN [3]) trained on real-world datasets $P(X)$ (CIFAR-10 [19] and FFHQ [15]). A high value of $L$ indicates a high PSR but low DSR, while a low value of $L$ indicates the opposite. For a fair comparison, we normalize DSR by its maximum value so that it ranges between 0 and 1. We show images of the highest $L$ and lowest $L$ in Fig. 4 (without cherry-picking). In general, images with a high value of $L$ show more realistic and clear objects, while images with a low $L$ are often distorted with artifacts (See supplement for more examples). Based on the assumption that realistic images should correspond to the high density of real distribution, our results in Fig. 4 qualitatively demonstrate the superiority of PSR over DSR in reflecting the semantic quality of generated images. We also conduct a user study selecting preferences between the + +![](images/930fdd99476cecf35968a2c708a131ff48390346e37cfcba7bf319f90bc8ca10.jpg) +$X_{\text{inlier}}$ + +![](images/e8ea4df807e13f5b72fd880a12ab550c603720f65935891f2365d0428abac71c.jpg) +$X_{outlier}$ + +![](images/83bb99adb8df5df105f66b047d3f85562daf64472e6ae6a2911b91c20a63cdc3.jpg) +Yinlier + +![](images/8dddcffb3a8d1c580c98bbe24f71a8bc3aefe51e6f372a2099f949283415c5d4.jpg) +$Y_{outlier}$ + +![](images/b484f5bddde6cb6d8ad124a69a6920b1ef1e1ce68b3a96b7fd3ba3a6e62f545e.jpg) +(a) + +![](images/8745474d50b35e3b8b97a1a62ee97b5266c19ea59ad6b798a7cc9efac710a7d6.jpg) +(b) +Figure 6: Behavior of metrics with respect to the number of outliers when evaluating the generative model $Y$ on a real-world dataset $X$ . (a) Fidelity metrics. (b) Diversity metrics. + +highest $L$ and the lowest $L$ and it also shows a similar result to our observation (See supplement). + +# 5.2.2 Robustness to outliers + +To investigate the efficacy of our proposed metrics in handling outliers with generative models on real-world datasets, we conduct experiments on the state-of-the-art diffusion model (e.g., ADM [6]), which currently has gained attention for its powerful performance, trained on ImageNet [19] dataset $(128^{2}$ resolution). Then, we adopt the outlier selection criterion used in [22] which uses the distance to the $k^{th}$ nearest neighbor. We apply this criterion to select inliers and outliers (at a ratio of 0.95:0.05) for both real and fake samples generated by ADM, resulting in the sets + +Table 1: Quantitative result of various generative models on real-world datasets. The reported values are obtained by measuring each metric five times and taking the average. Bolded values indicate the top scores evaluated by the corresponding metric. + +
Model +ImageNet 256x256FID↓PP↑PR↑F1↑IP↑IR↑F1↑D↑C↑F1↑
ADM [6]4.950.5380.7320.6210.6810.6880.6841.520.8761.112
ADM-G [6]4.580.6990.5870.6380.8180.6060.6962.0710.9561.307
BigGAN [3]8.120.7510.4650.5740.8740.4030.5512.4810.9451.368
AFHQv2 512x512
StyleGAN2 [16]4.620.5680.6890.6230.7160.4940.5841.8860.7901.113
StyleGAN3-R [14]4.400.5640.7250.6340.6850.5910.6351.5760.7701.034
StyleGAN3-T [14]4.040.5670.7270.6370.6990.5780.6321.6240.7921.065
LSUN Bedroom 256x256
DDPM [16]4.880.7990.7490.7730.6060.4440.5121.7010.9771.241
ADM [6]1.910.8390.7310.7810.6590.4940.5651.9290.9931.311
StyleGAN2 [16]2.350.8010.7530.7760.5910.5010.5431.7320.9861.257
+ +$X = X_{\text{inlier}} \cup X_{\text{outlier}}$ and $Y = Y_{\text{inlier}} \cup Y_{\text{outlier}}$ . We provide examples of the outliers and inliers in Fig. 6. Note that the inliers tend to exhibit more recognizable objects with clear semantic features compared to the outliers. + +We first observe how fidelity metrics between $X_{\text{inlier}}$ and $Y$ respond when a portion of $X_{\text{inlier}}$ is gradually substituted with the subset of $X_{\text{outlier}}$ . To visualize this, we plot the metric increments compared to the case when no outliers are included in $X_{\text{inlier}}$ , as shown in Fig. 6a. The results show that I-precision rapidly increases (0.2 increments) when only $5\%$ of inliers are gradually replaced by outliers, confirming its vulnerability to outliers. Although Density is less affected by outliers initially, it eventually surpasses the increment of I-precision as it accumulates the density over hyperspheres, supporting our claim that Density is still vulnerable to outliers. On the other hand, our P-precision shows the least increment (0.05 increments for $5\%$ outliers), validating its effectiveness in handling outliers. + +Likewise, we also test the robustness of diversity measures between $X$ and $Y_{\text{inlier}}$ by gradually replacing a portion of $Y_{\text{inlier}}$ with the subset of $Y_{\text{outlier}}$ . In Fig. 6b, we observe that I-recall exhibits a similar vulnerability to outliers as I-precision, while our P-recall is less affected by the presence of outliers. Besides, Coverage demonstrates strong robustness to outliers due to its alternative diversity measure. However, this comes at the cost of losing accuracy, as demonstrated in the experiments in Fig. 5b and 7b. + +# 5.2.3 Reflecting fidelity and diversity + +We now verify whether the metrics accurately reflect the change in fidelity and diversity of fake samples generated + +from generative models. In order to do that, we employ classifier guidance [6] during the image sampling from ADM. This technique uses gradients of a pre-trained classifier to perform conditional sampling from pre-trained unconditional diffusion models. By adjusting the scale of gradients from the classifier, we can explicitly control the balance between fidelity and diversity of generated images. For instance, a larger gradient scale results in the diffusion model sampling more from the modes of the pre-trained classifier, yielding higher fidelity but lower diversity. For more details, please refer to [6]. Therefore, we sample images from ADM, the same model as in Sec. 5.2.2, using gradient scales ranging from 0.5 to 10.0, and measure metrics (IP&IR, D&C and PP&PR) between real and generated samples for each scale. Fig. 7 shows the results; our PP&PR and IP&IR effectively capture the trade-off between fidelity and diversity whereas D&C does not exhibit a clear relationship with the gradient scale. This is due to the conceptual limitation of Coverage in accurately measuring the diversity in generated samples. + +# 5.2.4 Image generation benchmark + +To evaluate the practical usefulness of our proposed metrics in assessing the state-of-the-art generative models, we present the quantitative results on real-world datasets (LSUN bedroom [34], AFHQ-v2 [5], and ImageNet) for various types of generative models, along with FID. The results, presented in Tab. 1, are obtained by measuring each metric five times and taking their average. For clarity in the presentation, the variance associated with these measurements can be found in the supplementary materials. While FID serves as a holistic reference point for distinguishing superior + +![](images/e9fc54980ec3de93e44e1d77c33c9b0b05e6ad50bc667ec7c9a206e791e3acf6.jpg) +(a) + +![](images/a0b00d447ec873b68f5a4e284274da6d8e09249a8a79311638d1210e0401152e.jpg) +(b) + +![](images/c7e42cd0ba050887fece13c8180a23133d576e7360b833d2edd4c303b85df873.jpg) +Figure 7: Fidelity versus diversity when increasing the gradient scale from 0.5 to 10.0 for sampling diffusion models with classifier guidance [6]. A larger gradient scale tends to result in higher fidelity and lower diversity. +Figure 8: Ablation study on PSR: (A): probabilistic estimation for subsupport. (B): identical $R$ . + +model performance, our metrics delve deeper, elaborating on aspects of fidelity and diversity. For instance, our metrics explain that the improvement of ADM over StyleGAN [15] on LSUN bedroom in terms of FID is due to an increase in fidelity at the cost of diversity. An analysis between ADM and ADM-G further reveals that the classifier guidance in ADM-G augments fidelity, yet curtails diversity. This demonstrates the usefulness of our metrics in elaborating on the effect of the specific component in models. + +Moreover, to observe whether the metrics harmonize with the widely adopted FID metric, we analyze the consistency between FID and two-value metrics. This is achieved by computing the $\mathrm{F}_1$ -score [9], which is a harmonic mean of fidelity and diversity. The results demonstrate that $\mathrm{F}_1$ -scores of our metric mirror the trends set by FID (as underscored by the bold scores for each dataset in Tab. 1). + +# 6. Ablation study + +Here, we conduct an ablation study on our proposed scoring rule, PSR, to demonstrate the effectiveness of our approach: (A) probabilistic estimation for subsupport (Eq. 13) and (B) identical $R$ . We repeat the outlier toy experiment + +with Gaussian distributions in Sec. 5.1.1 with different configurations and the result for fidelity metric is shown in Fig. 8. In both cases where the feature (A) and (B) are individually removed, the metric becomes more susceptible to outlier than the case where both are used $(\mathrm{(A)} + \mathrm{(B)})$ but less affected than the case where both are all removed (see when $u\in [-3, - 1]$ ). This demonstrates that our probabilistic approach for subsupport and addressing overestimation of sample-specific $k_{\mathrm{NN}}$ both contribute to estimating accurate density and combining them together maximizes it. + +# 7. Conclusions and limitations + +In this paper, we introduced a set of two-value metrics, P-precision and P-recall, based on the probabilistic approach that addresses the limitations of existing metrics (IP&IR and D&C). We have conducted a systematic investigation of the limitations and demonstrated the effectiveness of our proposed metrics by evaluating toy experiments and state-of-the-art generative models. Nevertheless, we recognize there is still room for improvement. While we utilized commonly-used ImageNet embeddings [11, 20, 22] for feature extraction, recent studies such as [1, 21], have proposed domain-agnostic embeddings to enhance the feature quality compared to previous embeddings that rely on dataset-specific statistics. Thus, future research focusing on the quality of feature embedding combined with our method may further enhance the reliability and usefulness of the metric. + +Acknowledgements This work was supported by the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No.2021-0-00456, Development of Ultra-high Speech Quality Technology for remote Multi-speaker Conference System and No.RS-2023-00225630, Development of Artificial Intelligence for Text-based 3D Movie Generation). + +# References + +[1] Ahmed Alaa, Boris Van Breugel, Evgeny S Saveliev, and Mihaela van der Schaar. How faithful is your synthetic data? sample-level metrics for evaluating and auditing generative models. In International Conference on Machine Learning, pages 290-306. PMLR, 2022. 1, 9 +[2] Ivan Anokhin, Kirill Demochkin, Taras Khakhulin, Gleb Sterkin, Victor Lempitsky, and Denis Korzhenkov. 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In Conference on Computer Vision and Pattern Recognition, pages 16407-16417, 2021. 1 \ No newline at end of file diff --git a/2023/Probabilistic Precision and Recall Towards Reliable Evaluation of Generative Models/images.zip b/2023/Probabilistic Precision and Recall Towards Reliable Evaluation of Generative Models/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..e738a0229425a6523b2f2dde714e752e03d96a16 --- /dev/null +++ b/2023/Probabilistic Precision and Recall Towards Reliable Evaluation of Generative Models/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:03b77ae15aa1110042cf7f3db684296fb4e3d5cb0afec0a226056d7d63ae441a +size 739526 diff --git a/2023/Probabilistic Precision and Recall Towards Reliable Evaluation of Generative Models/layout.json b/2023/Probabilistic Precision and Recall Towards Reliable Evaluation of Generative Models/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..60f8cde8679e07c59f0b4399b60e7a9682e39b6c --- /dev/null +++ b/2023/Probabilistic Precision and Recall Towards Reliable Evaluation of Generative Models/layout.json @@ -0,0 +1,11567 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 140, + 103, + 455, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 103, + 455, + 138 + ], + "spans": [ + { + "bbox": [ + 140, + 103, + 455, + 138 + ], + "type": "text", + "content": "Probabilistic Precision and Recall Towards Reliable Evaluation of Generative Models" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 162, + 309, + 218 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 162, + 309, + 218 + ], + "spans": [ + { + "bbox": [ + 57, + 162, + 309, + 218 + ], + "type": "text", + "content": "Dogyun Park \nDepartment of Computer Science, Korea University \nSeoul, South Korea \ngg933@korea.ac.kr" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 329, + 162, + 536, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 162, + 536, + 217 + ], + "spans": [ + { + "bbox": [ + 329, + 162, + 536, + 217 + ], + "type": "text", + "content": "Suhyun Kim* \nKorea Institute of Science and Technology \nSeoul, South Korea \ndr.suhyun.kim@gmail.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "spans": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 270, + 290, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 290, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 290, + 474 + ], + "type": "text", + "content": "Assessing the fidelity and diversity of the generative model is a difficult but important issue for technological advancement. So, recent papers have introduced " + }, + { + "bbox": [ + 46, + 270, + 290, + 474 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 270, + 290, + 474 + ], + "type": "text", + "content": "-Nearest Neighbor (kNN) based precision-recall metrics to break down the statistical distance into fidelity and diversity. While they provide an intuitive method, we thoroughly analyze these metrics and identify oversimplified assumptions and undesirable properties of kNN that result in unreliable evaluation, such as susceptibility to outliers and insensitivity to distributional changes. Thus, we propose novel metrics, P-precision and P-recall (PP&PR), based on a probabilistic approach that address the problems. Through extensive investigations on toy experiments and state-of-the-art generative models, we show that our PP&PR provide more reliable estimates for comparing fidelity and diversity than the existing metrics. The codes are available at https://github.com/kdst-team/Probabistic_precision_recall." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 496, + 128, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 496, + 128, + 509 + ], + "spans": [ + { + "bbox": [ + 47, + 496, + 128, + 509 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 516, + 289, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 516, + 289, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 516, + 289, + 696 + ], + "type": "text", + "content": "Modern state-of-the-art generative models such as Variational Autoencoders (VAEs) [18, 24], Generative Adversarial Networks (GANs) [8, 15, 13, 14], and Score-based Diffusion Models (SDMs) [12, 17, 29, 6, 32, 25, 30] have shown outstanding achievements that surpass human evaluative capabilities. Consequently, reliable evaluation metrics for comparing the performance of generative models are critical for further technological advancement. The widely used Fréchet Inception Distance (FID) evaluation metric [11] has been praised for its robustness and consistency with human perceptual evaluation. However, FID only provides a single score and does not diagnose whether the model lacks fidelity or diversity, two essential aspects for improving generative models. Recent papers [26, 28, 20, 22, 1] have introduced various two-value metrics to measure fidelity" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 245, + 548, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 245, + 548, + 377 + ], + "spans": [ + { + "bbox": [ + 304, + 245, + 548, + 377 + ], + "type": "text", + "content": "and diversity, respectively. Especially, " + }, + { + "bbox": [ + 304, + 245, + 548, + 377 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 245, + 548, + 377 + ], + "type": "text", + "content": "-nearest neighbor (" + }, + { + "bbox": [ + 304, + 245, + 548, + 377 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 245, + 548, + 377 + ], + "type": "text", + "content": "NN) based metrics such as Improved Precision and Recall (IP&IR) [20] and Density and Coverage (D&C) [22] have been used to assess fidelity and diversity on various generative models [6, 35, 2, 24, 13, 4, 23]. The pipeline of these metrics [20, 22] starts with estimating distribution support of real and fake distribution by constructing sample-specific hyperspheres around each sample using " + }, + { + "bbox": [ + 304, + 245, + 548, + 377 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 245, + 548, + 377 + ], + "type": "text", + "content": " NN. Then, they measure the expectation of the likelihood of fake (real) samples with respect to the estimated real (fake) distribution support to represent fidelity (diversity)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 378, + 548, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 548, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 548, + 640 + ], + "type": "text", + "content": "Unfortunately, both IP&IR and D&C metrics present certain challenges that compromise their practical reliability. Specifically, IP&IR operate under the assumption of constant-density within the distribution support and overlook the overestimation linked to " + }, + { + "bbox": [ + 304, + 378, + 548, + 640 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 378, + 548, + 640 + ], + "type": "text", + "content": " NN, leading to an inflated distribution support with constant density. This scenario becomes especially problematic when the distribution houses outliers, resulting in metric overestimation (See Fig. 1a). Density metric [22] attempts to address these limitations by accumulating density over overlapped " + }, + { + "bbox": [ + 304, + 378, + 548, + 640 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 378, + 548, + 640 + ], + "type": "text", + "content": " NN hyperspheres. Yet, our findings suggest that it still remains unreliable to outliers. Furthermore, it tends to exhibit high variance, due to its extremely wide bound, which further limits the reliability of evaluations. On the other hand, Coverage metric [22] presents an alternative method that measures robust diversity even with the presence of outliers in the fake distribution. However, we show that it suffers from a conceptual limitation that makes it insensitive to changes in fake distribution. An in-depth discussion of these constraints is provided in Sec. 2. In the end, these issues underscore the need for careful revision of " + }, + { + "bbox": [ + 304, + 378, + 548, + 640 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 378, + 548, + 640 + ], + "type": "text", + "content": " NN-based metrics to provide more reliable evaluations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": "We, therefore, propose a novel set of metrics, P-precision and P-recall (PP&PR), which aim to provide more reliable estimations for the fidelity and diversity of generative models. In particular, we derive our metrics based on a probabilistic approach that relaxes the oversimplified assumptions and undesirable properties of kNN, addressing the limitations of" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 133, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 133, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 133, + 713 + ], + "type": "text", + "content": "* corresponding author" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20099" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 70, + 160, + 190 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 160, + 190 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 160, + 190 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 160, + 190 + ], + "type": "image", + "image_path": "4091ae853b43778863d6475bfd47bef549217251e07bb7d586350702c3af826a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 64, + 198, + 160, + 209 + ], + "lines": [ + { + "bbox": [ + 64, + 198, + 160, + 209 + ], + "spans": [ + { + "bbox": [ + 64, + 198, + 160, + 209 + ], + "type": "text", + "content": "(a) I-Precision / Density" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 168, + 70, + 267, + 190 + ], + "blocks": [ + { + "bbox": [ + 168, + 70, + 267, + 190 + ], + "lines": [ + { + "bbox": [ + 168, + 70, + 267, + 190 + ], + "spans": [ + { + "bbox": [ + 168, + 70, + 267, + 190 + ], + "type": "image", + "image_path": "eb9b65300a73578ca8bfb995c95e555405ded7513b54cd5692776495a72a387d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 191, + 198, + 251, + 209 + ], + "lines": [ + { + "bbox": [ + 191, + 198, + 251, + 209 + ], + "spans": [ + { + "bbox": [ + 191, + 198, + 251, + 209 + ], + "type": "text", + "content": "(b) P-precision" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 286, + 70, + 541, + 190 + ], + "blocks": [ + { + "bbox": [ + 286, + 70, + 541, + 190 + ], + "lines": [ + { + "bbox": [ + 286, + 70, + 541, + 190 + ], + "spans": [ + { + "bbox": [ + 286, + 70, + 541, + 190 + ], + "type": "image", + "image_path": "608c7f901a09e831731686b978e78143613160ae63a1f9d4cf55d77e0361c7af.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 198, + 350, + 209 + ], + "lines": [ + { + "bbox": [ + 304, + 198, + 350, + 209 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 350, + 209 + ], + "type": "text", + "content": "(c) I-Recall" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 391, + 198, + 444, + 209 + ], + "lines": [ + { + "bbox": [ + 391, + 198, + 444, + 209 + ], + "spans": [ + { + "bbox": [ + 391, + 198, + 444, + 209 + ], + "type": "text", + "content": "(d) Coverage" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 481, + 198, + 525, + 209 + ], + "lines": [ + { + "bbox": [ + 481, + 198, + 525, + 209 + ], + "spans": [ + { + "bbox": [ + 481, + 198, + 525, + 209 + ], + "type": "text", + "content": "(e) P-recall" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "lines": [ + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "spans": [ + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "text", + "content": "Figure 1: Examples of IP&IR, D&C, and PP&PR (better zoom-in). For simplicity, we use " + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "inline_equation", + "content": "k = 2" + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "text", + "content": "-Nearest Neighbor in all metrics. (a), (c): Due to the overestimation of " + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "text", + "content": "NN by the outlier and constant-density assumption within hyperspheres, I-precision, I-recall, and Density denote the same values for different " + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "text", + "content": " in an overly large space (See " + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "inline_equation", + "content": "y_1" + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "inline_equation", + "content": "y_2" + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "inline_equation", + "content": "y_3" + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "text", + "content": " in (a)), leading to unreliable-overestimated values. (b), (e): On the other hand, our P-precision and P-recall assign different scores to different " + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "text", + "content": " based on a probabilistic approach and address overestimation of " + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 218, + 547, + 302 + ], + "type": "text", + "content": "NN (See Sec. 4 for details). (d): This illustrates a case when Coverage exhibits its conceptual limitation. Even if the fake samples have lower relative diversity compared to real samples, they can still be included in multiple hyperspheres of real samples, leading to high Coverage." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 323, + 288, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 288, + 371 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 288, + 371 + ], + "type": "text", + "content": "existing metrics. Through extensive experiments on both toy and real-world datasets, we systematically demonstrate the superiority of our proposed metrics over IP&IR and D&C. To summarize, our contributions are as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 59, + 384, + 288, + 559 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 59, + 384, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 384, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 59, + 384, + 287, + 422 + ], + "type": "text", + "content": "- We propose a set of two-value metrics, P-precision and P-recall, that provide reliable fidelity and diversity measures for generative models." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 59, + 436, + 288, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 436, + 288, + 495 + ], + "spans": [ + { + "bbox": [ + 59, + 436, + 288, + 495 + ], + "type": "text", + "content": "- We thoroughly analyze the limitations of existing metrics (IP&IR and D&C), such as vulnerability to outliers and insensitivity to diversity, and introduce a novel method based on the probabilistic approach that remedies the limitations." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 59, + 511, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 511, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 59, + 511, + 287, + 559 + ], + "type": "text", + "content": "- Through a series of experiments on toy and real-world datasets with state-of-the-art generative models, we empirically verify the limitations of current metrics and demonstrate the efficacy of our proposed metrics." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 576, + 124, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 576, + 124, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 576, + 124, + 590 + ], + "type": "text", + "content": "2. Preliminary" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 597, + 228, + 610 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 228, + 610 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 228, + 610 + ], + "type": "text", + "content": "2.1. Feature embedding for evaluation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": "Statistical comparison of high dimensional data in the raw input space " + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": " is difficult. Therefore, the usual evaluation starts with converting real data " + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "X \\sim P" + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": " and fake data " + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "Y \\sim Q" + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": " into embeddings using a CNN feature " + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\Phi(\\Phi(X)" + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\Phi(Y))" + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": " [11, 20, 27, 22]. This embedded feature space is believed to have more \"meaningful\" information to compare two samples [7, 33]. For simplicity, we use " + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": " in place of " + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\Phi(X)" + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\Phi(Y)" + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": " for the remainder of the paper." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 323, + 525, + 336 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 323, + 525, + 336 + ], + "spans": [ + { + "bbox": [ + 306, + 323, + 525, + 336 + ], + "type": "text", + "content": "2.2. kNN-based fidelity and diversity measures" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 342, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 342, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 545, + 365 + ], + "type": "text", + "content": "Now, we briefly introduce current " + }, + { + "bbox": [ + 305, + 342, + 545, + 365 + ], + "type": "inline_equation", + "content": "k\\mathrm{NN}" + }, + { + "bbox": [ + 305, + 342, + 545, + 365 + ], + "type": "text", + "content": "-based fidelity and diversity measures and discuss their limitations in Sec. 3." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 380, + 547, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 380, + 547, + 463 + ], + "spans": [ + { + "bbox": [ + 305, + 380, + 547, + 463 + ], + "type": "text", + "content": "Improved Precision and Recall (IP&IR). To represent fidelity, Precision is defined as the expected likelihood of a fake sample belonging to the support of the real distribution, which refers to the set of possible real samples whose probability density function is non-zero. Likewise, Recall is defined as the expected likelihood of a real sample belonging to the support of fake distribution to measure diversity." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 350, + 469, + 547, + 488 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 469, + 547, + 488 + ], + "spans": [ + { + "bbox": [ + 350, + 469, + 547, + 488 + ], + "type": "interline_equation", + "content": "\\text {P r e c i s i o n} := \\mathbb {E} _ {Y \\sim Q} [ Y \\in \\operatorname {s u p p} (P) ] \\tag {1}", + "image_path": "cf76a27d48bbe293ab54ab80208d8c7e6bc925429ebbc5ee56b3413fc4a11e66.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 364, + 485, + 500, + 498 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 485, + 500, + 498 + ], + "spans": [ + { + "bbox": [ + 364, + 485, + 500, + 498 + ], + "type": "interline_equation", + "content": "\\operatorname {R e c a l l} := \\mathbb {E} _ {X \\sim P} [ X \\in \\operatorname {s u p p} (Q) ],", + "image_path": "7d2f6b0a14557710977d9e380f6cc58fd676c9cbb1f13568bdbd27a0864c8597.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 504, + 547, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 504, + 547, + 541 + ], + "spans": [ + { + "bbox": [ + 305, + 504, + 547, + 541 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 504, + 547, + 541 + ], + "type": "inline_equation", + "content": "\\operatorname{supp}(\\cdot)" + }, + { + "bbox": [ + 305, + 504, + 547, + 541 + ], + "type": "text", + "content": " indicates the ground truth support of distribution. Then, IP&IR [20] approximates them using the empirical observations " + }, + { + "bbox": [ + 305, + 504, + 547, + 541 + ], + "type": "inline_equation", + "content": "\\left(\\left\\{x_{i}\\right\\}_{i=1}^{N}\\right." + }, + { + "bbox": [ + 305, + 504, + 547, + 541 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 504, + 547, + 541 + ], + "type": "inline_equation", + "content": "\\left\\{y_{j}\\right\\}_{j=1}^{M}" + }, + { + "bbox": [ + 305, + 504, + 547, + 541 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 360, + 548, + 457, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 360, + 548, + 457, + 559 + ], + "spans": [ + { + "bbox": [ + 360, + 548, + 457, + 559 + ], + "type": "interline_equation", + "content": "\\mathrm {P r e c i s i o n} \\approx \\mathrm {I} - \\mathrm {P r e c i s i o n}", + "image_path": "9a0bdb38cb3f07ec494b2af8bdda9c6752b5aef46f971924503d5fc361ac6fc1.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 402, + 564, + 545, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 402, + 564, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 402, + 564, + 545, + 604 + ], + "type": "interline_equation", + "content": ":= \\frac {1}{M} \\sum_ {j = 1} ^ {M} \\operatorname {B S R} _ {P} \\left(y _ {j}\\right) \\tag {2}", + "image_path": "e12be0737a06fbafe8205810520c3240622eef7656c03721552ad6c076a96a07.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 373, + 601, + 445, + 611 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 601, + 445, + 611 + ], + "spans": [ + { + "bbox": [ + 373, + 601, + 445, + 611 + ], + "type": "interline_equation", + "content": "\\mathrm {R e c a l l} \\approx \\mathrm {I} - \\mathrm {R e c a l l}", + "image_path": "277a1040e91ef68229122ce08c480a9b0ecf1a20299ff8ff1a069f9e300cd64e.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 402, + 616, + 490, + 649 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 402, + 616, + 490, + 649 + ], + "spans": [ + { + "bbox": [ + 402, + 616, + 490, + 649 + ], + "type": "interline_equation", + "content": ":= \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathrm {B S R} _ {Q} (x _ {i}).", + "image_path": "3aef177c012e1d282c40846f98b1d1d072c3bb6e0be8fdf130a52622ca6a0175.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 654, + 545, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 654, + 545, + 678 + ], + "spans": [ + { + "bbox": [ + 305, + 654, + 545, + 678 + ], + "type": "text", + "content": "The scoring rule of IP&IR, which we name as Binary Scoring Rule (BSR) for comparison with other scoring rules, is" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 315, + 684, + 545, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 684, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 315, + 684, + 545, + 716 + ], + "type": "interline_equation", + "content": "\\operatorname {B S R} _ {P} \\left(y _ {j}\\right) = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} y _ {j} \\in \\cup_ {i = 1} ^ {N} B \\left(x _ {i}, \\mathrm {N N D} _ {k} \\left(x _ {i}\\right)\\right) \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}", + "image_path": "40d8f25594c7f5a123ea9d4e8b22353b459be188ae1433526e7ac87ec81e423b.jpg" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20100" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "B(x, r)" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " is the hypersphere in " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^D" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " around " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " with radius " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathrm{NND}_k(x_i)" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " denotes the Euclidean distance from " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " to the " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " nearest neighbor among " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\{x_i\\}_{i=1}^N" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " excluding itself. In other words, " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathrm{BSR}_P(y_j)" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " assigns a binary score of 1 or 0 to " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "y_j" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " based on whether it falls inside the union of hyperspheres. It is worth noting that BSR employs a deterministic approach that determines the support as the union of " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " NN hyperspheres without accounting for any uncertainty regarding the true support. This restricts the scoring rule to binary assignments, leading to a constant density within the approximated distribution support." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 204, + 288, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 204, + 288, + 240 + ], + "spans": [ + { + "bbox": [ + 47, + 204, + 288, + 240 + ], + "type": "text", + "content": "I-recall is defined using " + }, + { + "bbox": [ + 47, + 204, + 288, + 240 + ], + "type": "inline_equation", + "content": "\\mathrm{BSR}_Q(x_i)" + }, + { + "bbox": [ + 47, + 204, + 288, + 240 + ], + "type": "text", + "content": ", which is defined symmetrically with " + }, + { + "bbox": [ + 47, + 204, + 288, + 240 + ], + "type": "inline_equation", + "content": "\\mathrm{BSR}_P(y_j)" + }, + { + "bbox": [ + 47, + 204, + 288, + 240 + ], + "type": "text", + "content": ". It builds hyperspheres around fake samples and tests real samples." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 253, + 289, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 289, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 289, + 361 + ], + "type": "text", + "content": "Density and Coverage (D&C). D&C use different approaches to define fidelity and diversity in comparison to IP&IR. Specifically, Density [22] tackles the issue of constant-density over distribution support in IP&IR by quantifying the degree of overlap between kNN hyperspheres. To this end, Density defines a scoring rule that estimates the density function within distribution support by the superposition of hyperspheres, as opposed to the union in IP&IR. We denote this scoring rule as Density Scoring Rule (DSR)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 86, + 365, + 287, + 399 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 365, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 86, + 365, + 287, + 399 + ], + "type": "interline_equation", + "content": "\\mathrm {D S R} _ {P} \\left(y _ {j}\\right) = \\frac {1}{k} \\sum_ {i = 1} ^ {N} 1 _ {y _ {j} \\in B \\left(x _ {i}, \\mathrm {N N D} _ {k} \\left(x _ {i}\\right)\\right)} \\tag {4}", + "image_path": "4ee06b4214762af6984fb6bb0caf51899b541b21f85fe8fc65db21590b4e9987.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 402, + 287, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 462 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 402, + 287, + 462 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 402, + 287, + 462 + ], + "type": "text", + "content": " is for the " + }, + { + "bbox": [ + 46, + 402, + 287, + 462 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 402, + 287, + 462 + ], + "type": "text", + "content": "-nearest neighbors. DSR employs a kind of Parzen window density estimation [10] with a uniform kernel whose width is adjusted automatically, except that the integral of the kernel does not sum up to 1. Now, Density is defined as the expectation of DSR over observed samples as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 467, + 287, + 500 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 467, + 287, + 500 + ], + "spans": [ + { + "bbox": [ + 104, + 467, + 287, + 500 + ], + "type": "interline_equation", + "content": "\\text {D e n s i t y} := \\frac {1}{M} \\sum_ {j = 1} ^ {M} \\mathrm {D S R} _ {P} \\left(y _ {j}\\right) \\tag {5}", + "image_path": "7d2bb23cf7682d3ab2be394274da1a2ffb0ecaa88dc1375e16837b285a01cb0e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 504, + 288, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 504, + 288, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 504, + 288, + 598 + ], + "type": "text", + "content": "For diversity, the authors employ another scoring rule, Coverage Scoring Rule (CSR), which is not symmetric to DSR. It builds " + }, + { + "bbox": [ + 46, + 504, + 288, + 598 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 504, + 288, + 598 + ], + "type": "text", + "content": " NN hyperspheres around the real samples and counts the real samples whose hyperspheres are occupied by the fake samples. Coverage has demonstrated effectiveness in handling outliers in fake distribution, as the hyperspheres of real samples are not influenced by fake outliers." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 89, + 603, + 244, + 617 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 603, + 244, + 617 + ], + "spans": [ + { + "bbox": [ + 89, + 603, + 244, + 617 + ], + "type": "interline_equation", + "content": "\\operatorname {C S R} _ {Q} \\left(x _ {i}\\right) = 1 _ {\\exists j \\text {s . t .} y _ {j} \\in B \\left(x _ {i}, \\mathrm {N N D} _ {k} \\left(x _ {i}\\right)\\right)}", + "image_path": "7460a5275da43b126c8aed4fa84f53ca5145f57d4a26c4afab0a686962cffd63.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 91, + 619, + 287, + 651 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 619, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 91, + 619, + 287, + 651 + ], + "type": "interline_equation", + "content": "\\text {C o v e r a g e} := \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathrm {C S R} _ {Q} \\left(x _ {i}\\right) \\tag {6}", + "image_path": "8d2fe37332a98b522f4a4f6d3592ae82d2e5eb121d41a9520d05c410ba57d1aa.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 655, + 287, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 655, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 655, + 287, + 681 + ], + "type": "text", + "content": "3. Limitations with scoring rules of IP&IR and D&C" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "Binary scoring rule. BSR can only assign constant density within an approximated distribution support, which can" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "text", + "content": "hinder reliable estimates when comparing distributions with complex density functions. Moreover, the use of " + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "inline_equation", + "content": "k\\mathrm{NN}" + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "text", + "content": " in BSR makes it more susceptible to outliers as it unreliably inflates the size of the hypersphere due to the presence of such outliers. This results in overestimated value as illustrated in Fig. 1a and 1c. Both I-precision and I-recall face similar issues since they symmetrically use BSR." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 173, + 547, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 173, + 547, + 316 + ], + "spans": [ + { + "bbox": [ + 304, + 173, + 547, + 316 + ], + "type": "text", + "content": "Density scoring rule. We contend that DSR remains vulnerable to outliers as it accumulates density over the overestimated constant-density hyperspheres. For instance, if there are " + }, + { + "bbox": [ + 304, + 173, + 547, + 316 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 173, + 547, + 316 + ], + "type": "text", + "content": " outliers, all hyperspheres of outliers can overlap due to the overestimated size of hyperspheres. This causes the overlapped density to accumulate to " + }, + { + "bbox": [ + 304, + 173, + 547, + 316 + ], + "type": "inline_equation", + "content": "s / k" + }, + { + "bbox": [ + 304, + 173, + 547, + 316 + ], + "type": "text", + "content": " (note that DSR scales the overlapped density by a factor of " + }, + { + "bbox": [ + 304, + 173, + 547, + 316 + ], + "type": "inline_equation", + "content": "1 / k" + }, + { + "bbox": [ + 304, + 173, + 547, + 316 + ], + "type": "text", + "content": " in Eq. 4), resulting in a rapid increase with just a few outliers. We demonstrate this quantitatively with the experiment in Sec. 5. Additionally, reducing the density by a factor of " + }, + { + "bbox": [ + 304, + 173, + 547, + 316 + ], + "type": "inline_equation", + "content": "1 / k" + }, + { + "bbox": [ + 304, + 173, + 547, + 316 + ], + "type": "text", + "content": " makes the metric highly dependent on the choice of " + }, + { + "bbox": [ + 304, + 173, + 547, + 316 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 173, + 547, + 316 + ], + "type": "text", + "content": ", which is not desirable as we demonstrate in Fig. 3." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 316, + 547, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 547, + 365 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 547, + 365 + ], + "type": "text", + "content": "Lastly, DSR is bounded within " + }, + { + "bbox": [ + 304, + 316, + 547, + 365 + ], + "type": "inline_equation", + "content": "[0, N / k]" + }, + { + "bbox": [ + 304, + 316, + 547, + 365 + ], + "type": "text", + "content": " (e.g., " + }, + { + "bbox": [ + 304, + 316, + 547, + 365 + ], + "type": "inline_equation", + "content": "N / k = 50000 / 5 = 10000" + }, + { + "bbox": [ + 304, + 316, + 547, + 365 + ], + "type": "text", + "content": "), which can result in samples with abnormally high values of DSR, compromising stable evaluations with high standard deviations as demonstrated in Fig. 2c." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 381, + 547, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 381, + 547, + 562 + ], + "spans": [ + { + "bbox": [ + 304, + 381, + 547, + 562 + ], + "type": "text", + "content": "Coverage scoring rule. While CSR can effectively handle outliers in fake distribution, it exhibits a conceptual limitation: a lack of sensitivity to the comparative diversity between fake and real distributions. This arises because CSR doesn't factor in distances between fake samples. Instead, its focus is solely on the count of real sample hyperspheres occupied by fake samples. This leads to a scenario where if real samples are more dispersed compared to fake ones, meaning the fake samples exhibit less relative diversity, the fake samples could still be included in multiple real hyperspheres. This, in turn, can produce a falsely elevated Coverage metric (a conceptual illustration is provided in Fig.1d). Conversely, Coverage can be low if fake samples are more widely distributed compared to real samples. We elucidate this phenomenon quantitatively in Fig. 5b." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 573, + 361, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 573, + 361, + 585 + ], + "spans": [ + { + "bbox": [ + 306, + 573, + 361, + 585 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": "To address the aforementioned limitations, we propose a novel scoring rule based on a probabilistic approach. Our motivation arises from the recognition that accurately estimating the ground truth support is infeasible with empirical observations alone. As a result, it becomes difficult to determine whether a sample belongs to the ground truth support with certainty (0 or 1). Therefore, we adopt a probabilistic perspective and define the probability of a sample belonging to the support, taking into account the uncertainty surrounding the ground truth support. Then, our scoring rule can" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20101" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": "assign lower values to samples that are less likely to belong to the support such as outliers, effectively addressing outlier concerns. We also define the scoring rules for fidelity and diversity symmetrically, similar to IP&IR, to avoid the conceptual limitation of CSR. Although we mainly focus on describing the details of fidelity in the paper, diversity is defined symmetrically." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 163, + 230, + 176 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 163, + 230, + 176 + ], + "spans": [ + { + "bbox": [ + 47, + 163, + 230, + 176 + ], + "type": "text", + "content": "4.1. P-precision and P-recall (PP&PR)" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 181, + 290, + 254 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 181, + 290, + 254 + ], + "spans": [ + { + "bbox": [ + 46, + 181, + 290, + 254 + ], + "type": "text", + "content": "Given the observations " + }, + { + "bbox": [ + 46, + 181, + 290, + 254 + ], + "type": "inline_equation", + "content": "\\{x_i\\}_{i = 1}^N" + }, + { + "bbox": [ + 46, + 181, + 290, + 254 + ], + "type": "text", + "content": ", we assume that there are myriad possible supports of " + }, + { + "bbox": [ + 46, + 181, + 290, + 254 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 181, + 290, + 254 + ], + "type": "text", + "content": ", denoted as " + }, + { + "bbox": [ + 46, + 181, + 290, + 254 + ], + "type": "inline_equation", + "content": "S_P" + }, + { + "bbox": [ + 46, + 181, + 290, + 254 + ], + "type": "text", + "content": ". The collection of these supports is represented by " + }, + { + "bbox": [ + 46, + 181, + 290, + 254 + ], + "type": "inline_equation", + "content": "\\mathbb{S}_P" + }, + { + "bbox": [ + 46, + 181, + 290, + 254 + ], + "type": "text", + "content": ". Subsequently, we introduce Probabilistic-Precision that characterizes precision as the probability of " + }, + { + "bbox": [ + 46, + 181, + 290, + 254 + ], + "type": "inline_equation", + "content": "y_{j}" + }, + { + "bbox": [ + 46, + 181, + 290, + 254 + ], + "type": "text", + "content": " being an element of support randomly chosen from " + }, + { + "bbox": [ + 46, + 181, + 290, + 254 + ], + "type": "inline_equation", + "content": "\\mathbb{S}_P" + }, + { + "bbox": [ + 46, + 181, + 290, + 254 + ], + "type": "text", + "content": ". This is articulated as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 83, + 262, + 287, + 306 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 262, + 287, + 306 + ], + "spans": [ + { + "bbox": [ + 83, + 262, + 287, + 306 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathrm {P} \\text {- p r e c i s i o n} := \\mathbb {E} _ {Y \\sim Q, S _ {P} \\in \\mathbb {S} _ {P}} [ Y \\in S _ {P} ] \\\\ = \\mathbb {E} _ {Y \\sim Q} \\left[ \\mathbb {E} _ {S _ {P} \\in \\mathbb {S} _ {P}} \\left[ Y \\in S _ {P} \\right] \\right] \\tag {7} \\\\ = \\mathbb {E} _ {Y \\sim Q} \\left[ \\Pr \\left(Y \\in S _ {P}\\right) \\right] \\\\ \\end{array}", + "image_path": "c9786c154917844c675deb8d49a49265a7a28e00cebd60891f18a9f4465f3d3b.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 316, + 287, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 287, + 331 + ], + "type": "text", + "content": "Then, we approximate it with given observations " + }, + { + "bbox": [ + 47, + 316, + 287, + 331 + ], + "type": "inline_equation", + "content": "\\{y_{j}\\}_{j = 1}^{M}" + }, + { + "bbox": [ + 47, + 316, + 287, + 331 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 93, + 347, + 287, + 380 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 347, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 93, + 347, + 287, + 380 + ], + "type": "interline_equation", + "content": "\\mathrm {P} \\text { - p r e c i s i o n} \\approx \\frac {1}{M} \\sum_ {j = 1} ^ {M} \\Pr \\left(y _ {j} \\in S _ {P}\\right). \\tag {8}", + "image_path": "3f76944913a028d61ce4cbd8bc845accfb07062c32eaf246492658aa5117cc09.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 389, + 285, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 389, + 285, + 401 + ], + "spans": [ + { + "bbox": [ + 47, + 389, + 285, + 401 + ], + "type": "text", + "content": "In a similar manner, Probabilistic-recall is approximated as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 101, + 410, + 287, + 442 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 410, + 287, + 442 + ], + "spans": [ + { + "bbox": [ + 101, + 410, + 287, + 442 + ], + "type": "interline_equation", + "content": "\\Pr \\text {r e c a l l} \\approx \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\Pr \\left(x _ {i} \\in S _ {Q}\\right). \\tag {9}", + "image_path": "885301a96c2f53ef48c3889eb82fcff9daa99ce3582dc6e4d18d5bde91ffcdbd.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 451, + 188, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 451, + 188, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 451, + 188, + 464 + ], + "type": "text", + "content": "4.2. Probabilistic scoring rule" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 469, + 287, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 469, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 47, + 469, + 287, + 493 + ], + "type": "text", + "content": "To estimate " + }, + { + "bbox": [ + 47, + 469, + 287, + 493 + ], + "type": "inline_equation", + "content": "\\operatorname*{Pr}(y_j\\in S_P)" + }, + { + "bbox": [ + 47, + 469, + 287, + 493 + ], + "type": "text", + "content": ", we first divide " + }, + { + "bbox": [ + 47, + 469, + 287, + 493 + ], + "type": "inline_equation", + "content": "S_{P}" + }, + { + "bbox": [ + 47, + 469, + 287, + 493 + ], + "type": "text", + "content": " into subsets around each observation as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 128, + 500, + 287, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 128, + 500, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 128, + 500, + 287, + 533 + ], + "type": "interline_equation", + "content": "S _ {P} := \\bigcup_ {i = 1} ^ {N} s _ {P} \\left(x _ {i}\\right), \\tag {10}", + "image_path": "5e0206829c2e0f2d8c2aee698baf5c97fa66cbf1ed998af157a469c0146b18aa.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 542, + 288, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 542, + 288, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 542, + 288, + 590 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 542, + 288, + 590 + ], + "type": "inline_equation", + "content": "\\mathrm{s}_P(x_i)" + }, + { + "bbox": [ + 46, + 542, + 288, + 590 + ], + "type": "text", + "content": ", denoted as the subsupport around " + }, + { + "bbox": [ + 46, + 542, + 288, + 590 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 46, + 542, + 288, + 590 + ], + "type": "text", + "content": ", represents a subset of " + }, + { + "bbox": [ + 46, + 542, + 288, + 590 + ], + "type": "inline_equation", + "content": "S_P" + }, + { + "bbox": [ + 46, + 542, + 288, + 590 + ], + "type": "text", + "content": " that comprises elements for which the nearest reference among " + }, + { + "bbox": [ + 46, + 542, + 288, + 590 + ], + "type": "inline_equation", + "content": "\\{x_i\\}_{i=1}^N" + }, + { + "bbox": [ + 46, + 542, + 288, + 590 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 46, + 542, + 288, + 590 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 46, + 542, + 288, + 590 + ], + "type": "text", + "content": ". Then, we can further elucidate " + }, + { + "bbox": [ + 46, + 542, + 288, + 590 + ], + "type": "inline_equation", + "content": "\\operatorname*{Pr}(y_j \\in S_P)" + }, + { + "bbox": [ + 46, + 542, + 288, + 590 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 66, + 600, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 600, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 66, + 600, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\Pr (y _ {j} \\in S _ {P}) = 1 - \\Pr (y _ {j} \\notin S _ {P}) \\\\ = 1 - \\Pr \\left(y _ {j} \\notin \\cup_ {i = 1} ^ {N} s _ {P} \\left(x _ {i}\\right)\\right) \\\\ = 1 - \\Pr \\left(y _ {j} \\in \\cap_ {i = 1} ^ {N} s _ {P} ^ {C} (x _ {i})\\right) \\\\ = 1 - \\prod_ {i = 1} ^ {N} \\Pr \\left(y _ {j} \\in s _ {P} ^ {\\mathbf {c}} \\left(x _ {i}\\right)\\right) \\tag {11} \\\\ = 1 - \\prod_ {i = 1} ^ {N} \\left(1 - \\Pr \\left(y _ {j} \\in s _ {P} \\left(x _ {i}\\right)\\right)\\right) \\\\ \\end{array}", + "image_path": "7ad9d925d5020c0d5e775e320f351bd21e01b93f622066fb9168b69df65232a5.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": "using Eq. 10 and complement rule, where " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "s_P^c (\\cdot)" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": " denotes the complement set of " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "s_P(\\cdot)" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": ". The equality in the fourth line of Eq. 11 comes from assuming the independence of events " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\{y_{j}\\in s_{P}^{c}(x_{i})|i = 1,2,\\dots ,N\\}" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 121, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 121, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 305, + 121, + 545, + 144 + ], + "type": "text", + "content": "Now, we define our new scoring rule termed Probabilistic Scoring Rules (PSR) from the last equation in Eq. 11:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 325, + 153, + 545, + 201 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 153, + 545, + 201 + ], + "spans": [ + { + "bbox": [ + 325, + 153, + 545, + 201 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\operatorname {P S R} _ {P} \\left(y _ {j}\\right) := 1 - \\prod_ {i = 1} ^ {N} \\left(1 - \\Pr \\left(y _ {j} \\in s _ {P} \\left(x _ {i}\\right)\\right)\\right) \\tag {12} \\\\ = \\Pr (y _ {j} \\in S _ {P}) \\\\ \\end{array}", + "image_path": "d743358ab8baee39e36ca39acbfe4d7ba066c18b9b92ff15f4cee133c2957d04.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 209, + 547, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 209, + 547, + 354 + ], + "spans": [ + { + "bbox": [ + 305, + 209, + 547, + 354 + ], + "type": "text", + "content": "In contrast with deterministic methods such as BSR, which make certain assumptions about the definitive shape of subsupport, PSR estimates the probability of " + }, + { + "bbox": [ + 305, + 209, + 547, + 354 + ], + "type": "inline_equation", + "content": "y_{j}" + }, + { + "bbox": [ + 305, + 209, + 547, + 354 + ], + "type": "text", + "content": " to belong to the uncertain support by combining the probability to belong to the subsupport around each observation. Utilizing this probabilistic approach allows us to depart from defining the specific subsupport—a task that, in practice, can be ambiguous. Rather, we infer the likelihood of a sample being part of the subsupport based on an intuitive premise: samples in closer proximity to " + }, + { + "bbox": [ + 305, + 209, + 547, + 354 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 305, + 209, + 547, + 354 + ], + "type": "text", + "content": " are more likely to be an element of the subsupport compared to those further away. Accordingly, we approximate the probability " + }, + { + "bbox": [ + 305, + 209, + 547, + 354 + ], + "type": "inline_equation", + "content": "\\operatorname*{Pr}(y_j\\in s_P(x_i))" + }, + { + "bbox": [ + 305, + 209, + 547, + 354 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 340, + 362, + 545, + 395 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 362, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 340, + 362, + 545, + 395 + ], + "type": "interline_equation", + "content": "\\Pr \\left(y _ {j} \\in s _ {P} \\left(x _ {i}\\right)\\right) \\approx \\left\\{ \\begin{array}{l l} 1 - \\frac {d}{R}, & \\text {i f} d \\leq R \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {13}", + "image_path": "8fffbd5233f10b3ba1bcd8ef18b06680e27c0f7ca4bec4507f78d31fa362349a.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "spans": [ + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "text", + "content": " distance between " + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "inline_equation", + "content": "y_{j}" + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "text", + "content": ". From Eq. 13, the probability is one when " + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "inline_equation", + "content": "d = 0" + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "text", + "content": ", given that we know for certain that " + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "text", + "content": " belongs to the subsupport. The probability monotonically decreases with an increase in " + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "text", + "content": " until it hits the threshold distance " + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "text", + "content": ", where the probability converges to zero. By Eq. 12 and Eq. 13, our proposed PSR can assign varying values to samples based on their likelihood of belonging to the support. Moreover, it is bounded within [0,1] (see supplement for the proof) unlike DSR which has an extremely wide bound. Note that while other distance metrics " + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "text", + "content": " or monotonically decreasing functions could serve this purpose, we opted to use " + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 305, + 403, + 547, + 568 + ], + "type": "text", + "content": " distance and a linear function since it was sufficiently sensitive based on our empirical results. We leave it for future work." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 570, + 547, + 713 + ], + "type": "text", + "content": "It is also important to select " + }, + { + "bbox": [ + 305, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 305, + 570, + 547, + 713 + ], + "type": "text", + "content": " in Eq. 13 since it controls the robustness of the scoring rule. Instead of sample-specific " + }, + { + "bbox": [ + 305, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "R(x_{i})" + }, + { + "bbox": [ + 305, + 570, + 547, + 713 + ], + "type": "text", + "content": " based on kNN as used in IP&IR and D&C, we propose to use identical " + }, + { + "bbox": [ + 305, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 305, + 570, + 547, + 713 + ], + "type": "text", + "content": " for all samples " + }, + { + "bbox": [ + 305, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 305, + 570, + 547, + 713 + ], + "type": "text", + "content": ". We set " + }, + { + "bbox": [ + 305, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 305, + 570, + 547, + 713 + ], + "type": "text", + "content": " as a multiple of the average of kNN distances among " + }, + { + "bbox": [ + 305, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\{x_{i}\\}_{i = 1}^{N}" + }, + { + "bbox": [ + 305, + 570, + 547, + 713 + ], + "type": "text", + "content": ", since it can be used as an effective normalization factor in high-dimensional space. This is similar to using a fixed-variance Gaussian kernel for Kernel Density Estimation and offers several advantages over sample-specific kNN: 1) it suppresses the overestimation of kNN by the outlier as shown in Fig. 1b, and 2) makes metric more robust to the choice of " + }, + { + "bbox": [ + 305, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 570, + 547, + 713 + ], + "type": "text", + "content": " as shown in Fig. 3." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20102" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 72, + 218, + 186 + ], + "blocks": [ + { + "bbox": [ + 62, + 72, + 218, + 186 + ], + "lines": [ + { + "bbox": [ + 62, + 72, + 218, + 186 + ], + "spans": [ + { + "bbox": [ + 62, + 72, + 218, + 186 + ], + "type": "image", + "image_path": "5a04749ac74f1b01197dcc1c74ecba5bf9440cca2418d97e0101d97f969218c4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 135, + 189, + 148, + 201 + ], + "lines": [ + { + "bbox": [ + 135, + 189, + 148, + 201 + ], + "spans": [ + { + "bbox": [ + 135, + 189, + 148, + 201 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 218, + 72, + 375, + 186 + ], + "blocks": [ + { + "bbox": [ + 218, + 72, + 375, + 186 + ], + "lines": [ + { + "bbox": [ + 218, + 72, + 375, + 186 + ], + "spans": [ + { + "bbox": [ + 218, + 72, + 375, + 186 + ], + "type": "image", + "image_path": "6c3d7d791d7fb109470d8725b9c51e40adb626e83ab9ec6038b54de598ce439d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 290, + 189, + 305, + 201 + ], + "lines": [ + { + "bbox": [ + 290, + 189, + 305, + 201 + ], + "spans": [ + { + "bbox": [ + 290, + 189, + 305, + 201 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 209, + 545, + 269 + ], + "lines": [ + { + "bbox": [ + 46, + 209, + 545, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 545, + 269 + ], + "type": "text", + "content": "Figure 2: (a) Behavior of fidelity metrics between two Gaussian distributions " + }, + { + "bbox": [ + 46, + 209, + 545, + 269 + ], + "type": "inline_equation", + "content": "X \\sim N(0, I)" + }, + { + "bbox": [ + 46, + 209, + 545, + 269 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 209, + 545, + 269 + ], + "type": "inline_equation", + "content": "Y \\sim N(u\\mathbf{1}, I)" + }, + { + "bbox": [ + 46, + 209, + 545, + 269 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 209, + 545, + 269 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 209, + 545, + 269 + ], + "type": "text", + "content": " moves between [-3,3] with outlier " + }, + { + "bbox": [ + 46, + 209, + 545, + 269 + ], + "type": "inline_equation", + "content": "x_o \\sim N(-2, I)" + }, + { + "bbox": [ + 46, + 209, + 545, + 269 + ], + "type": "text", + "content": " added to " + }, + { + "bbox": [ + 46, + 209, + 545, + 269 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 209, + 545, + 269 + ], + "type": "text", + "content": ". 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The line shows the means and the shaded area denotes standard deviations across 50 runs." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 384, + 72, + 518, + 125 + ], + "blocks": [ + { + "bbox": [ + 384, + 72, + 518, + 125 + ], + "lines": [ + { + "bbox": [ + 384, + 72, + 518, + 125 + ], + "spans": [ + { + "bbox": [ + 384, + 72, + 518, + 125 + ], + "type": "image", + "image_path": "6d96d060210c2802fab0675a167fd015782875d66a6b755d07f165f479257534.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 384, + 125, + 517, + 185 + ], + "blocks": [ + { + "bbox": [ + 384, + 125, + 517, + 185 + ], + "lines": [ + { + "bbox": [ + 384, + 125, + 517, + 185 + ], + "spans": [ + { + "bbox": [ + 384, + 125, + 517, + 185 + ], + "type": "image", + "image_path": "ed71da9f3fb4a4873100cf32937662a473e6976a8e9817884aeba226d40ff6d1.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 447, + 189, + 460, + 201 + ], + "lines": [ + { + "bbox": [ + 447, + 189, + 460, + 201 + ], + "spans": [ + { + "bbox": [ + 447, + 189, + 460, + 201 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 291, + 285, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 291, + 285, + 304 + ], + "spans": [ + { + "bbox": [ + 59, + 291, + 285, + 304 + ], + "type": "text", + "content": "Finally, putting it all together, we propose P-precision as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 99, + 310, + 288, + 344 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 310, + 288, + 344 + ], + "spans": [ + { + "bbox": [ + 99, + 310, + 288, + 344 + ], + "type": "interline_equation", + "content": "\\mathrm {P} \\text { - p r e c i s i o n} = \\frac {1}{M} \\sum_ {j = 1} ^ {M} \\mathrm {P S R} _ {P} \\left(y _ {j}\\right) \\tag {14}", + "image_path": "f5945b78e16b322df87df7c94f231313e63ff1a81e10ea14cc09defc43ef5cd3.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 351, + 75, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 351, + 75, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 351, + 75, + 361 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 74, + 368, + 259, + 400 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 368, + 259, + 400 + ], + "spans": [ + { + "bbox": [ + 74, + 368, + 259, + 400 + ], + "type": "interline_equation", + "content": "\\operatorname {P S R} _ {P} \\left(y _ {j}\\right) = 1 - \\prod_ {i = 1} ^ {N} \\left(1 - \\Pr \\left(y _ {j} \\in s _ {P} \\left(x _ {i}\\right)\\right)\\right),", + "image_path": "65cdc5fd7f692c920795b7edceaeb0c9c6ef6a12c3061305724d9ecf40e3791b.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 49, + 407, + 284, + 440 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 407, + 284, + 440 + ], + "spans": [ + { + "bbox": [ + 49, + 407, + 284, + 440 + ], + "type": "interline_equation", + "content": "\\Pr (y _ {j} \\in s _ {P} (x _ {i})) = \\left\\{ \\begin{array}{l l} 1 - \\frac {| | x _ {i} - y _ {j} | | _ {2}}{R}, & \\text {i f} | | x _ {i} - y _ {j} | | _ {2} \\leq R \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right.", + "image_path": "a8b360603284240195297caeeace3e6070ce58a81b3a000f22560e5922d77000.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 443, + 65, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 443, + 65, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 443, + 65, + 453 + ], + "type": "text", + "content": "and" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 117, + 451, + 217, + 484 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 451, + 217, + 484 + ], + "spans": [ + { + "bbox": [ + 117, + 451, + 217, + 484 + ], + "type": "interline_equation", + "content": "R = \\frac {a}{N} \\sum_ {i = 1} ^ {N} \\mathrm {N N D} _ {k} \\left(x _ {i}\\right).", + "image_path": "235855defb49359a51aefccb16a541546d23767b193f17ca84a98a18eff536a2.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 487, + 287, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 287, + 523 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 287, + 523 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 46, + 487, + 287, + 523 + ], + "type": "text", + "content": " is a hyperparameter that controls the magnitude of " + }, + { + "bbox": [ + 46, + 487, + 287, + 523 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 487, + 287, + 523 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 487, + 287, + 523 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 487, + 287, + 523 + ], + "type": "text", + "content": " is for the " + }, + { + "bbox": [ + 46, + 487, + 287, + 523 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 487, + 287, + 523 + ], + "type": "text", + "content": "-nearest neighbors. In a similar manner, we propose P-recall as" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 107, + 530, + 287, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 530, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 107, + 530, + 287, + 563 + ], + "type": "interline_equation", + "content": "P - \\text {r e c a l l} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathrm {P S R} _ {Q} \\left(x _ {i}\\right) \\tag {15}", + "image_path": "c024ead26503ab883ba8bf4f97a3912853383dd8fbc9a6301142848041e503b0.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 570, + 74, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 74, + 580 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 74, + 580 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 73, + 586, + 260, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 586, + 260, + 620 + ], + "spans": [ + { + "bbox": [ + 73, + 586, + 260, + 620 + ], + "type": "interline_equation", + "content": "\\mathrm {P S R} _ {Q} (x _ {i}) = 1 - \\prod_ {j = 1} ^ {M} \\left(1 - \\Pr (x _ {i} \\in s _ {Q} (y _ {j}))\\right),", + "image_path": "90f94ba90510e5d3099f379be5d279d8be44dc99a4186c0b7fa11176e14b3cbf.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 48, + 628, + 284, + 660 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 628, + 284, + 660 + ], + "spans": [ + { + "bbox": [ + 48, + 628, + 284, + 660 + ], + "type": "interline_equation", + "content": "\\operatorname * {P r} (x _ {i} \\in s _ {Q} (y _ {j})) = \\left\\{ \\begin{array}{l l} 1 - \\frac {| | x _ {i} - y _ {j} | | _ {2}}{R}, & \\text {i f} | | x _ {i} - y _ {j} | | _ {2} \\leq R \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right.", + "image_path": "0d4e3ab8638325e9f7eef6160a83d2bd643895ede2c526feba9c4d413f378fd3.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 47, + 663, + 65, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 663, + 65, + 673 + ], + "spans": [ + { + "bbox": [ + 47, + 663, + 65, + 673 + ], + "type": "text", + "content": "and" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 116, + 672, + 217, + 706 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 672, + 217, + 706 + ], + "spans": [ + { + "bbox": [ + 116, + 672, + 217, + 706 + ], + "type": "interline_equation", + "content": "R = \\frac {a}{M} \\sum_ {j = 1} ^ {M} \\mathrm {N N D} _ {k} (y _ {j}).", + "image_path": "cb0243b0568fe58cf6618ccd15ba24ffb80118d76762804d50902bdf5d8ca378.jpg" + } + ] + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 328, + 307, + 519, + 443 + ], + "blocks": [ + { + "bbox": [ + 328, + 307, + 519, + 443 + ], + "lines": [ + { + "bbox": [ + 328, + 307, + 519, + 443 + ], + "spans": [ + { + "bbox": [ + 328, + 307, + 519, + 443 + ], + "type": "image", + "image_path": "07d53bd6798503751419436e826dc9c3cdd1690d7a7632f967936823a9723355.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 456, + 545, + 493 + ], + "lines": [ + { + "bbox": [ + 305, + 456, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 305, + 456, + 545, + 493 + ], + "type": "text", + "content": "Figure 3: Ablation over " + }, + { + "bbox": [ + 305, + 456, + 545, + 493 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 456, + 545, + 493 + ], + "type": "text", + "content": ". We measure each metric for different " + }, + { + "bbox": [ + 305, + 456, + 545, + 493 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 456, + 545, + 493 + ], + "type": "text", + "content": " between " + }, + { + "bbox": [ + 305, + 456, + 545, + 493 + ], + "type": "inline_equation", + "content": "X \\sim N(0, I)" + }, + { + "bbox": [ + 305, + 456, + 545, + 493 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 456, + 545, + 493 + ], + "type": "inline_equation", + "content": "Y \\sim N(u, I)" + }, + { + "bbox": [ + 305, + 456, + 545, + 493 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 305, + 456, + 545, + 493 + ], + "type": "inline_equation", + "content": "u \\in [-3.0, 3.0]" + }, + { + "bbox": [ + 305, + 456, + 545, + 493 + ], + "type": "text", + "content": " with outlier " + }, + { + "bbox": [ + 305, + 456, + 545, + 493 + ], + "type": "inline_equation", + "content": "x_{o} \\sim N(-2, I)" + }, + { + "bbox": [ + 305, + 456, + 545, + 493 + ], + "type": "text", + "content": " added to " + }, + { + "bbox": [ + 305, + 456, + 545, + 493 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 305, + 456, + 545, + 493 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 513, + 388, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 513, + 388, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 513, + 388, + 528 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": "In this section, we systematically demonstrate the limitations of current metrics and the improvements of our metrics through toy experiments. We then show the experiments with state-of-the-art generative models, highlighting that our metrics are more reliable for evaluating generative models than IP&IR and D&C. We use the settings described below for the remainder of the experiments unless stated otherwise. We set " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "k = 4" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "a = 1.2" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " for our metrics in all experiments. For IP&IR and D&C, we follow the recommended value of " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "k = 3" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "k = 5" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": ", respectively. In the toy experiments, we generate Gaussian distributions in " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{64}" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": " and set " + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "inline_equation", + "content": "M = N = 10000" + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": ". For the experiments evaluating generative models, we use features extracted from the ImageNet [19] pre-trained Inception model [31] after the second fully connected layer. We compute metrics between" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "20103" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 82, + 390, + 249 + ], + "blocks": [ + { + "bbox": [ + 63, + 82, + 390, + 249 + ], + "lines": [ + { + "bbox": [ + 63, + 82, + 390, + 249 + ], + "spans": [ + { + "bbox": [ + 63, + 82, + 390, + 249 + ], + "type": "image", + "image_path": "67150a655c8478e4d0841435cf073066d697a8df598d2d4c5bad7d40a17aa6a2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 211, + 251, + 244, + 262 + ], + "lines": [ + { + "bbox": [ + 211, + 251, + 244, + 262 + ], + "spans": [ + { + "bbox": [ + 211, + 251, + 244, + 262 + ], + "type": "text", + "content": "(a) FFHQ" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 395, + 80, + 531, + 163 + ], + "blocks": [ + { + "bbox": [ + 395, + 80, + 531, + 163 + ], + "lines": [ + { + "bbox": [ + 395, + 80, + 531, + 163 + ], + "spans": [ + { + "bbox": [ + 395, + 80, + 531, + 163 + ], + "type": "image", + "image_path": "f4a2756ea0e4b64266fc2fb5b29aded249817e10ee65e61939f641a87339c5fd.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 395, + 167, + 531, + 249 + ], + "blocks": [ + { + "bbox": [ + 395, + 167, + 531, + 249 + ], + "lines": [ + { + "bbox": [ + 395, + 167, + 531, + 249 + ], + "spans": [ + { + "bbox": [ + 395, + 167, + 531, + 249 + ], + "type": "image", + "image_path": "10564ff7fa0598a80d8c26bb02d511d8831f17d9932d52d16cbe3493d2c828cb.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 440, + 251, + 487, + 262 + ], + "lines": [ + { + "bbox": [ + 440, + 251, + 487, + 262 + ], + "spans": [ + { + "bbox": [ + 440, + 251, + 487, + 262 + ], + "type": "text", + "content": "(b) CIFAR-10" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 271, + 547, + 309 + ], + "lines": [ + { + "bbox": [ + 46, + 271, + 547, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 271, + 547, + 309 + ], + "type": "text", + "content": "Figure 4: Qualitative examples sorted according to " + }, + { + "bbox": [ + 46, + 271, + 547, + 309 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 271, + 547, + 309 + ], + "type": "text", + "content": ". We used StyleGAN [15] trained on FFHQ [15] and BigGAN [3] trained on CIFAR-10 [19]. The top two rows are images with the highest " + }, + { + "bbox": [ + 46, + 271, + 547, + 309 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 271, + 547, + 309 + ], + "type": "text", + "content": " meaning they have high PSR but low DSR. Conversely, the bottom two rows are images with the lowest " + }, + { + "bbox": [ + 46, + 271, + 547, + 309 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 271, + 547, + 309 + ], + "type": "text", + "content": ", indicating low PSR and high DSR." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 47, + 337, + 167, + 427 + ], + "blocks": [ + { + "bbox": [ + 47, + 337, + 167, + 427 + ], + "lines": [ + { + "bbox": [ + 47, + 337, + 167, + 427 + ], + "spans": [ + { + "bbox": [ + 47, + 337, + 167, + 427 + ], + "type": "image", + "image_path": "075c527cbecb2c4c1cf691dc646205707c79478935d80392ab96cbc4a06c2978.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 430, + 115, + 439 + ], + "lines": [ + { + "bbox": [ + 104, + 430, + 115, + 439 + ], + "spans": [ + { + "bbox": [ + 104, + 430, + 115, + 439 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 449, + 288, + 498 + ], + "lines": [ + { + "bbox": [ + 46, + 449, + 288, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 288, + 498 + ], + "type": "text", + "content": "Figure 5: Behavior of metrics between " + }, + { + "bbox": [ + 46, + 449, + 288, + 498 + ], + "type": "inline_equation", + "content": "X \\sim N(0, I)" + }, + { + "bbox": [ + 46, + 449, + 288, + 498 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 449, + 288, + 498 + ], + "type": "inline_equation", + "content": "Y \\sim N(0, vI)" + }, + { + "bbox": [ + 46, + 449, + 288, + 498 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 449, + 288, + 498 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 449, + 288, + 498 + ], + "type": "text", + "content": " changes between [0.2, 1.5]. Because Density goes over 1 (up to nearly 1000), the " + }, + { + "bbox": [ + 46, + 449, + 288, + 498 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 449, + 288, + 498 + ], + "type": "text", + "content": "-axis for Density is on the right side of the plot for better visualization." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 168, + 337, + 286, + 426 + ], + "blocks": [ + { + "bbox": [ + 168, + 337, + 286, + 426 + ], + "lines": [ + { + "bbox": [ + 168, + 337, + 286, + 426 + ], + "spans": [ + { + "bbox": [ + 168, + 337, + 286, + 426 + ], + "type": "image", + "image_path": "3b2fd32ae514679643ad1c7d021123c6aac7cd857dad17a67e81e96711e9458f.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 223, + 430, + 234, + 439 + ], + "lines": [ + { + "bbox": [ + 223, + 430, + 234, + 439 + ], + "spans": [ + { + "bbox": [ + 223, + 430, + 234, + 439 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 520, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 287, + 545 + ], + "type": "text", + "content": "all available real samples (up to 50K) and 50K generated images following [6]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 554, + 147, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 554, + 147, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 554, + 147, + 567 + ], + "type": "text", + "content": "5.1. Toy experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 574, + 174, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 174, + 585 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 174, + 585 + ], + "type": "text", + "content": "5.1.1 Robustness to outliers" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "Gaussian distribution We first investigate how the metrics behave to outliers through a simple toy experiment with Gaussian distributions, following [22]. We set real " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "X \\sim N(0, I)" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " and fake " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "Y \\sim N(u\\mathbf{1}, I)" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{1}" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " is a vector of ones and " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " is the identity matrix, and measure the metrics between " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " varies in [-3, 3]. To introduce an outlier, we add a sample " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "x_o \\sim N(-2, I)" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " to the set of real samples. A reliable metric should consistently decrease as " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " moves away from 0, regardless of the outlier. Fig. 2a shows the result for fidelity: I-precision gives overestimated values when" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "inline_equation", + "content": "u \\leq 0" + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "text", + "content": " due to the enlarged constant-density hypersphere by the outlier. Although Density alleviates the problem by reducing the density inside the hypersphere by " + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "inline_equation", + "content": "1 / k" + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "text", + "content": ", it does not reflect the change for a wide range of " + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "text", + "content": " (See when " + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "inline_equation", + "content": "u \\leq -1" + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "text", + "content": "). On the other hand, P-precision denotes reliable estimates even when the fake distribution comes closer to the outlier " + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "inline_equation", + "content": "(\\mathrm{PP} = 0.006" + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "text", + "content": " when " + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "inline_equation", + "content": "u = -2)" + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "text", + "content": ", and also shows a robust decrease as " + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "text", + "content": " moves away from 0. We observe a similar result on the diversity measures except for Coverage (See Fig. 2b)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "text", + "content": "In addition, we perform an ablation over " + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "text", + "content": " to investigate whether the improvement of our metric over the outlier is due to a properly chosen " + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "text", + "content": ". The same experiment described above is repeated with different " + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "text", + "content": " and the metric values are reported in Fig. 3. Our P-precision shows strong consistency over " + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "text", + "content": ", due to the employment of identical " + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "text", + "content": " for all real samples. However, I-precision continues to suffer from outliers, regardless of the value of " + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "text", + "content": ". Moreover, Density exhibits high variation over different values of " + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "text", + "content": " as it reduces the density by " + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "inline_equation", + "content": "1 / k" + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "text", + "content": ", demonstrating that Density needs properly chosen " + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 437, + 548, + 568 + ], + "type": "text", + "content": " to achieve adequate robustness to outliers." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 569, + 547, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 547, + 605 + ], + "type": "text", + "content": "These results suggest that our metrics are more reliable to estimate fidelity and diversity between distributions, even in the presence of outliers." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 622, + 421, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 622, + 421, + 634 + ], + "spans": [ + { + "bbox": [ + 306, + 622, + 421, + 634 + ], + "type": "text", + "content": "5.1.2 Stability of metrics" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "We also test the stability of metrics by measuring the empirical bias of the metric from the presumed true value, which we approximate by averaging across 50 runs with 50K samples, between two identical Gaussian distributions. Fig. 2c shows the bias from the true value with respect to the number of datasets used for estimation, along with the average and" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20104" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "standard deviation across 50 runs. Our PP&PR show a small bias and standard deviation, even for small " + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": ", while IP&IR show a large bias. In addition, despite the theoretical value when two distributions are identical [22], Density does not behave nicely: at " + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "N \\leq 10000" + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": ", Density shows quite a large bias and standard deviation due to the extremely wide bound. This demonstrates that our PP&PR provides more reliable estimates than other metrics even for small datasets." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 188, + 212, + 201 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 188, + 212, + 201 + ], + "spans": [ + { + "bbox": [ + 47, + 188, + 212, + 201 + ], + "type": "text", + "content": "5.1.3 Reflecting fidelity and diversity" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 209, + 290, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 209, + 290, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 290, + 400 + ], + "type": "text", + "content": "The main motive of the two-value metric is to capture both fidelity and diversity between two distributions. To assess whether these metrics are capable of reflecting fidelity and diversity, we design a scenario where the two values are at odds. Specifically, we generate samples from " + }, + { + "bbox": [ + 46, + 209, + 290, + 400 + ], + "type": "inline_equation", + "content": "X \\sim N(0, I)" + }, + { + "bbox": [ + 46, + 209, + 290, + 400 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 209, + 290, + 400 + ], + "type": "inline_equation", + "content": "Y \\sim N(0, vI)" + }, + { + "bbox": [ + 46, + 209, + 290, + 400 + ], + "type": "text", + "content": ", and vary the value of " + }, + { + "bbox": [ + 46, + 209, + 290, + 400 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 209, + 290, + 400 + ], + "type": "text", + "content": " from 0.2 to 1.5. As " + }, + { + "bbox": [ + 46, + 209, + 290, + 400 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 209, + 290, + 400 + ], + "type": "text", + "content": " increases, we expect fidelity to decrease and diversity to increase. As shown in Fig. 5, while Density behaves as expected, Coverage does not; it remains constant at 1 as " + }, + { + "bbox": [ + 46, + 209, + 290, + 400 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 209, + 290, + 400 + ], + "type": "text", + "content": " increases from 0.2 to 1, despite the increasing relative diversity of fake distribution. We argue that this counter-intuitive behavior is due to the conceptual limitation of Coverage as discussed in Sec. 3. When " + }, + { + "bbox": [ + 46, + 209, + 290, + 400 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 209, + 290, + 400 + ], + "type": "text", + "content": " increases beyond 1, Coverage becomes 0, as fake samples are no longer included in the hyperspheres of real samples. In contrast, PP&PR and IP&IR nicely reflect the expected behavior." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 410, + 208, + 423 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 410, + 208, + 423 + ], + "spans": [ + { + "bbox": [ + 47, + 410, + 208, + 423 + ], + "type": "text", + "content": "5.2. Evaluating generative models" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 430, + 187, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 187, + 442 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 187, + 442 + ], + "type": "text", + "content": "5.2.1 Comparing scoring rules" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": "Here, we compare the scoring rules of fidelity metrics to demonstrate how nicely the estimated density reflects the quality of the fake sample. We compare PSR with DSR, as BSR only denotes a binary score. For effective comparison, we focus on cases where two scoring rules have conflicting results. Specifically, we compute " + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "inline_equation", + "content": "L = \\{\\mathrm{PSR}_P(y_j) - \\mathrm{DSR}_P(y_j) \\mid \\forall j\\}" + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": " using generative models " + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "inline_equation", + "content": "Q(Y)" + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": " (StyleGAN [15] and BigGAN [3]) trained on real-world datasets " + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "inline_equation", + "content": "P(X)" + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": " (CIFAR-10 [19] and FFHQ [15]). A high value of " + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": " indicates a high PSR but low DSR, while a low value of " + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": " indicates the opposite. For a fair comparison, we normalize DSR by its maximum value so that it ranges between 0 and 1. We show images of the highest " + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": " and lowest " + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": " in Fig. 4 (without cherry-picking). In general, images with a high value of " + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": " show more realistic and clear objects, while images with a low " + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": " are often distorted with artifacts (See supplement for more examples). Based on the assumption that realistic images should correspond to the high density of real distribution, our results in Fig. 4 qualitatively demonstrate the superiority of PSR over DSR in reflecting the semantic quality of generated images. We also conduct a user study selecting preferences between the" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 313, + 70, + 425, + 207 + ], + "blocks": [ + { + "bbox": [ + 313, + 70, + 425, + 207 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 425, + 207 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 425, + 207 + ], + "type": "image", + "image_path": "930fdd99476cecf35968a2c708a131ff48390346e37cfcba7bf319f90bc8ca10.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 355, + 209, + 378, + 217 + ], + "lines": [ + { + "bbox": [ + 355, + 209, + 378, + 217 + ], + "spans": [ + { + "bbox": [ + 355, + 209, + 378, + 217 + ], + "type": "inline_equation", + "content": "X_{\\text{inlier}}" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 428, + 70, + 540, + 208 + ], + "blocks": [ + { + "bbox": [ + 428, + 70, + 540, + 208 + ], + "lines": [ + { 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"Y_{outlier}" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 310, + 371, + 427, + 458 + ], + "blocks": [ + { + "bbox": [ + 310, + 371, + 427, + 458 + ], + "lines": [ + { + "bbox": [ + 310, + 371, + 427, + 458 + ], + "spans": [ + { + "bbox": [ + 310, + 371, + 427, + 458 + ], + "type": "image", + "image_path": "b484f5bddde6cb6d8ad124a69a6920b1ef1e1ce68b3a96b7fd3ba3a6e62f545e.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 363, + 460, + 373, + 468 + ], + "lines": [ + { + "bbox": [ + 363, + 460, + 373, + 468 + ], + "spans": [ + { + "bbox": [ + 363, + 460, + 373, + 468 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 428, + 371, + 544, + 458 + ], + "blocks": [ + { + "bbox": [ + 428, + 371, + 544, + 458 + ], + "lines": [ + { + 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305, + 477, + 547, + 514 + ], + "type": "text", + "content": " on a real-world dataset " + }, + { + "bbox": [ + 305, + 477, + 547, + 514 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 305, + 477, + 547, + 514 + ], + "type": "text", + "content": ". (a) Fidelity metrics. (b) Diversity metrics." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 534, + 545, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 534, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 305, + 534, + 545, + 559 + ], + "type": "text", + "content": "highest " + }, + { + "bbox": [ + 305, + 534, + 545, + 559 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 305, + 534, + 545, + 559 + ], + "type": "text", + "content": " and the lowest " + }, + { + "bbox": [ + 305, + 534, + 545, + 559 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 305, + 534, + 545, + 559 + ], + "type": "text", + "content": " and it also shows a similar result to our observation (See supplement)." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 574, + 432, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 432, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 432, + 586 + ], + "type": "text", + "content": "5.2.2 Robustness to outliers" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "To investigate the efficacy of our proposed metrics in handling outliers with generative models on real-world datasets, we conduct experiments on the state-of-the-art diffusion model (e.g., ADM [6]), which currently has gained attention for its powerful performance, trained on ImageNet [19] dataset " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "(128^{2}" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " resolution). Then, we adopt the outlier selection criterion used in [22] which uses the distance to the " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " nearest neighbor. We apply this criterion to select inliers and outliers (at a ratio of 0.95:0.05) for both real and fake samples generated by ADM, resulting in the sets" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20105" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 72, + 102, + 519, + 300 + ], + "blocks": [ + { + "bbox": [ + 46, + 71, + 547, + 95 + ], + "lines": [ + { + "bbox": [ + 46, + 71, + 547, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 71, + 547, + 95 + ], + "type": "text", + "content": "Table 1: Quantitative result of various generative models on real-world datasets. The reported values are obtained by measuring each metric five times and taking the average. Bolded values indicate the top scores evaluated by the corresponding metric." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 72, + 102, + 519, + 300 + ], + "lines": [ + { + "bbox": [ + 72, + 102, + 519, + 300 + ], + "spans": [ + { + "bbox": [ + 72, + 102, + 519, + 300 + ], + "type": "table", + "html": "
Model\nImageNet 256x256FID↓PP↑PR↑F1↑IP↑IR↑F1↑D↑C↑F1↑
ADM [6]4.950.5380.7320.6210.6810.6880.6841.520.8761.112
ADM-G [6]4.580.6990.5870.6380.8180.6060.6962.0710.9561.307
BigGAN [3]8.120.7510.4650.5740.8740.4030.5512.4810.9451.368
AFHQv2 512x512
StyleGAN2 [16]4.620.5680.6890.6230.7160.4940.5841.8860.7901.113
StyleGAN3-R [14]4.400.5640.7250.6340.6850.5910.6351.5760.7701.034
StyleGAN3-T [14]4.040.5670.7270.6370.6990.5780.6321.6240.7921.065
LSUN Bedroom 256x256
DDPM [16]4.880.7990.7490.7730.6060.4440.5121.7010.9771.241
ADM [6]1.910.8390.7310.7810.6590.4940.5651.9290.9931.311
StyleGAN2 [16]2.350.8010.7530.7760.5910.5010.5431.7320.9861.257
", + "image_path": "f1dbb1fd9f2817350427ff0a2834d2027913a6ae4b89c90e0f7c8dcdf03f97d0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 331, + 287, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 378 + ], + "type": "inline_equation", + "content": "X = X_{\\text{inlier}} \\cup X_{\\text{outlier}}" + }, + { + "bbox": [ + 46, + 331, + 287, + 378 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 331, + 287, + 378 + ], + "type": "inline_equation", + "content": "Y = Y_{\\text{inlier}} \\cup Y_{\\text{outlier}}" + }, + { + "bbox": [ + 46, + 331, + 287, + 378 + ], + "type": "text", + "content": ". We provide examples of the outliers and inliers in Fig. 6. Note that the inliers tend to exhibit more recognizable objects with clear semantic features compared to the outliers." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 380, + 288, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 288, + 546 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 288, + 546 + ], + "type": "text", + "content": "We first observe how fidelity metrics between " + }, + { + "bbox": [ + 46, + 380, + 288, + 546 + ], + "type": "inline_equation", + "content": "X_{\\text{inlier}}" + }, + { + "bbox": [ + 46, + 380, + 288, + 546 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 380, + 288, + 546 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 46, + 380, + 288, + 546 + ], + "type": "text", + "content": " respond when a portion of " + }, + { + "bbox": [ + 46, + 380, + 288, + 546 + ], + "type": "inline_equation", + "content": "X_{\\text{inlier}}" + }, + { + "bbox": [ + 46, + 380, + 288, + 546 + ], + "type": "text", + "content": " is gradually substituted with the subset of " + }, + { + "bbox": [ + 46, + 380, + 288, + 546 + ], + "type": "inline_equation", + "content": "X_{\\text{outlier}}" + }, + { + "bbox": [ + 46, + 380, + 288, + 546 + ], + "type": "text", + "content": ". To visualize this, we plot the metric increments compared to the case when no outliers are included in " + }, + { + "bbox": [ + 46, + 380, + 288, + 546 + ], + "type": "inline_equation", + "content": "X_{\\text{inlier}}" + }, + { + "bbox": [ + 46, + 380, + 288, + 546 + ], + "type": "text", + "content": ", as shown in Fig. 6a. The results show that I-precision rapidly increases (0.2 increments) when only " + }, + { + "bbox": [ + 46, + 380, + 288, + 546 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 380, + 288, + 546 + ], + "type": "text", + "content": " of inliers are gradually replaced by outliers, confirming its vulnerability to outliers. Although Density is less affected by outliers initially, it eventually surpasses the increment of I-precision as it accumulates the density over hyperspheres, supporting our claim that Density is still vulnerable to outliers. On the other hand, our P-precision shows the least increment (0.05 increments for " + }, + { + "bbox": [ + 46, + 380, + 288, + 546 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 380, + 288, + 546 + ], + "type": "text", + "content": " outliers), validating its effectiveness in handling outliers." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 547, + 288, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 547, + 288, + 656 + ], + "spans": [ + { + "bbox": [ + 46, + 547, + 288, + 656 + ], + "type": "text", + "content": "Likewise, we also test the robustness of diversity measures between " + }, + { + "bbox": [ + 46, + 547, + 288, + 656 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 547, + 288, + 656 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 547, + 288, + 656 + ], + "type": "inline_equation", + "content": "Y_{\\text{inlier}}" + }, + { + "bbox": [ + 46, + 547, + 288, + 656 + ], + "type": "text", + "content": " by gradually replacing a portion of " + }, + { + "bbox": [ + 46, + 547, + 288, + 656 + ], + "type": "inline_equation", + "content": "Y_{\\text{inlier}}" + }, + { + "bbox": [ + 46, + 547, + 288, + 656 + ], + "type": "text", + "content": " with the subset of " + }, + { + "bbox": [ + 46, + 547, + 288, + 656 + ], + "type": "inline_equation", + "content": "Y_{\\text{outlier}}" + }, + { + "bbox": [ + 46, + 547, + 288, + 656 + ], + "type": "text", + "content": ". In Fig. 6b, we observe that I-recall exhibits a similar vulnerability to outliers as I-precision, while our P-recall is less affected by the presence of outliers. Besides, Coverage demonstrates strong robustness to outliers due to its alternative diversity measure. However, this comes at the cost of losing accuracy, as demonstrated in the experiments in Fig. 5b and 7b." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 670, + 213, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 213, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 213, + 683 + ], + "type": "text", + "content": "5.2.3 Reflecting fidelity and diversity" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "We now verify whether the metrics accurately reflect the change in fidelity and diversity of fake samples generated" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 331, + 547, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 547, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 547, + 559 + ], + "type": "text", + "content": "from generative models. In order to do that, we employ classifier guidance [6] during the image sampling from ADM. This technique uses gradients of a pre-trained classifier to perform conditional sampling from pre-trained unconditional diffusion models. By adjusting the scale of gradients from the classifier, we can explicitly control the balance between fidelity and diversity of generated images. For instance, a larger gradient scale results in the diffusion model sampling more from the modes of the pre-trained classifier, yielding higher fidelity but lower diversity. For more details, please refer to [6]. Therefore, we sample images from ADM, the same model as in Sec. 5.2.2, using gradient scales ranging from 0.5 to 10.0, and measure metrics (IP&IR, D&C and PP&PR) between real and generated samples for each scale. Fig. 7 shows the results; our PP&PR and IP&IR effectively capture the trade-off between fidelity and diversity whereas D&C does not exhibit a clear relationship with the gradient scale. This is due to the conceptual limitation of Coverage in accurately measuring the diversity in generated samples." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 574, + 465, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 465, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 465, + 586 + ], + "type": "text", + "content": "5.2.4 Image generation benchmark" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "To evaluate the practical usefulness of our proposed metrics in assessing the state-of-the-art generative models, we present the quantitative results on real-world datasets (LSUN bedroom [34], AFHQ-v2 [5], and ImageNet) for various types of generative models, along with FID. The results, presented in Tab. 1, are obtained by measuring each metric five times and taking their average. For clarity in the presentation, the variance associated with these measurements can be found in the supplementary materials. While FID serves as a holistic reference point for distinguishing superior" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20106" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 71, + 167, + 160 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 167, + 160 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 167, + 160 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 167, + 160 + ], + "type": "image", + "image_path": "e9fc54980ec3de93e44e1d77c33c9b0b05e6ad50bc667ec7c9a206e791e3acf6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 103, + 161, + 113, + 170 + ], + "lines": [ + { + "bbox": [ + 103, + 161, + 113, + 170 + ], + "spans": [ + { + "bbox": [ + 103, + 161, + 113, + 170 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 168, + 70, + 287, + 160 + ], + "blocks": [ + { + "bbox": [ + 168, + 70, + 287, + 160 + ], + "lines": [ + { + "bbox": [ + 168, + 70, + 287, + 160 + ], + "spans": [ + { + "bbox": [ + 168, + 70, + 287, + 160 + ], + "type": "image", + "image_path": "a0b00d447ec873b68f5a4e284274da6d8e09249a8a79311638d1210e0401152e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 222, + 161, + 233, + 170 + ], + "lines": [ + { + "bbox": [ + 222, + 161, + 233, + 170 + ], + "spans": [ + { + "bbox": [ + 222, + 161, + 233, + 170 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 80, + 241, + 252, + 369 + ], + "blocks": [ + { + "bbox": [ + 46, + 178, + 288, + 227 + ], + "lines": [ + { + "bbox": [ + 46, + 178, + 288, + 227 + ], + "spans": [ + { + "bbox": [ + 46, + 178, + 288, + 227 + ], + "type": "text", + "content": "Figure 7: Fidelity versus diversity when increasing the gradient scale from 0.5 to 10.0 for sampling diffusion models with classifier guidance [6]. A larger gradient scale tends to result in higher fidelity and lower diversity." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 80, + 241, + 252, + 369 + ], + "lines": [ + { + "bbox": [ + 80, + 241, + 252, + 369 + ], + "spans": [ + { + "bbox": [ + 80, + 241, + 252, + 369 + ], + "type": "image", + "image_path": "c7e42cd0ba050887fece13c8180a23133d576e7360b833d2edd4c303b85df873.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 393, + 288, + 417 + ], + "lines": [ + { + "bbox": [ + 46, + 393, + 288, + 417 + ], + "spans": [ + { + "bbox": [ + 46, + 393, + 288, + 417 + ], + "type": "text", + "content": "Figure 8: Ablation study on PSR: (A): probabilistic estimation for subsupport. (B): identical " + }, + { + "bbox": [ + 46, + 393, + 288, + 417 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 393, + 288, + 417 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 440, + 287, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 440, + 287, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 440, + 287, + 547 + ], + "type": "text", + "content": "model performance, our metrics delve deeper, elaborating on aspects of fidelity and diversity. For instance, our metrics explain that the improvement of ADM over StyleGAN [15] on LSUN bedroom in terms of FID is due to an increase in fidelity at the cost of diversity. An analysis between ADM and ADM-G further reveals that the classifier guidance in ADM-G augments fidelity, yet curtails diversity. This demonstrates the usefulness of our metrics in elaborating on the effect of the specific component in models." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 548, + 287, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 548, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 287, + 632 + ], + "type": "text", + "content": "Moreover, to observe whether the metrics harmonize with the widely adopted FID metric, we analyze the consistency between FID and two-value metrics. This is achieved by computing the " + }, + { + "bbox": [ + 46, + 548, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\mathrm{F}_1" + }, + { + "bbox": [ + 46, + 548, + 287, + 632 + ], + "type": "text", + "content": "-score [9], which is a harmonic mean of fidelity and diversity. The results demonstrate that " + }, + { + "bbox": [ + 46, + 548, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\mathrm{F}_1" + }, + { + "bbox": [ + 46, + 548, + 287, + 632 + ], + "type": "text", + "content": "-scores of our metric mirror the trends set by FID (as underscored by the bold scores for each dataset in Tab. 1)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 645, + 138, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 138, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 138, + 658 + ], + "type": "text", + "content": "6. Ablation study" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 666, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 288, + 713 + ], + "type": "text", + "content": "Here, we conduct an ablation study on our proposed scoring rule, PSR, to demonstrate the effectiveness of our approach: (A) probabilistic estimation for subsupport (Eq. 13) and (B) identical " + }, + { + "bbox": [ + 46, + 666, + 288, + 713 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 666, + 288, + 713 + ], + "type": "text", + "content": ". We repeat the outlier toy experiment" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "content": "with Gaussian distributions in Sec. 5.1.1 with different configurations and the result for fidelity metric is shown in Fig. 8. In both cases where the feature (A) and (B) are individually removed, the metric becomes more susceptible to outlier than the case where both are used " + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "inline_equation", + "content": "(\\mathrm{(A)} + \\mathrm{(B)})" + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "content": " but less affected than the case where both are all removed (see when " + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "inline_equation", + "content": "u\\in [-3, - 1]" + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "content": "). This demonstrates that our probabilistic approach for subsupport and addressing overestimation of sample-specific " + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "inline_equation", + "content": "k_{\\mathrm{NN}}" + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "content": " both contribute to estimating accurate density and combining them together maximizes it." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 203, + 463, + 216 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 203, + 463, + 216 + ], + "spans": [ + { + "bbox": [ + 305, + 203, + 463, + 216 + ], + "type": "text", + "content": "7. Conclusions and limitations" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 224, + 547, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 547, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 547, + 403 + ], + "type": "text", + "content": "In this paper, we introduced a set of two-value metrics, P-precision and P-recall, based on the probabilistic approach that addresses the limitations of existing metrics (IP&IR and D&C). We have conducted a systematic investigation of the limitations and demonstrated the effectiveness of our proposed metrics by evaluating toy experiments and state-of-the-art generative models. Nevertheless, we recognize there is still room for improvement. While we utilized commonly-used ImageNet embeddings [11, 20, 22] for feature extraction, recent studies such as [1, 21], have proposed domain-agnostic embeddings to enhance the feature quality compared to previous embeddings that rely on dataset-specific statistics. Thus, future research focusing on the quality of feature embedding combined with our method may further enhance the reliability and usefulness of the metric." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 418, + 547, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 547, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 547, + 502 + ], + "type": "text", + "content": "Acknowledgements This work was supported by the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No.2021-0-00456, Development of Ultra-high Speech Quality Technology for remote Multi-speaker Conference System and No.RS-2023-00225630, Development of Artificial Intelligence for Text-based 3D Movie Generation)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 514, + 365, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 365, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 365, + 526 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 310, + 533, + 547, + 714 + ], + "type": "list", + "angle": 0, + "index": 20, + "blocks": [ + { + "bbox": [ + 310, + 533, + 545, + 588 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 533, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 310, + 533, + 545, + 588 + ], + "type": "text", + "content": "[1] Ahmed Alaa, Boris Van Breugel, Evgeny S Saveliev, and Mihaela van der Schaar. 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In Conference on Computer Vision and Pattern Recognition, pages 16407-16417, 2021. 1" + } + ] + } + ], + "index": 1 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "20109" + } + ] + } + ], + "index": 3 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Probabilistic Triangulation for Uncalibrated Multi-View 3D Human Pose Estimation/b6b4e04e-10fb-49dc-be18-fbc2e2b53da9_content_list.json b/2023/Probabilistic Triangulation for Uncalibrated Multi-View 3D Human Pose Estimation/b6b4e04e-10fb-49dc-be18-fbc2e2b53da9_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ec7d1a8bf14f78c2039320c2926339c305bd841e --- /dev/null +++ b/2023/Probabilistic Triangulation for Uncalibrated Multi-View 3D Human Pose Estimation/b6b4e04e-10fb-49dc-be18-fbc2e2b53da9_content_list.json @@ -0,0 +1,1813 @@ +[ + { + "type": "text", + "text": "Probabilistic Triangulation for Uncalibrated Multi-View 3D Human Pose Estimation", + "text_level": 1, + "bbox": [ + 117, + 128, + 852, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Boyuan Jiang $^{1,2}$ , Lei Hu $^{1,2}$ Shihong Xia $^{1,2*}$ $^{1}$ Institute of Computing Technology, Chinese Academy of Sciences; $^{2}$ University of Chinese Academy of Sciences {jiangboyuan20s, hulei19z, xsh}@ict.ac.cn", + "bbox": [ + 215, + 202, + 754, + 276 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3D human pose estimation has been a long-standing challenge in computer vision and graphics, where multiview methods have significantly progressed but are limited by the tedious calibration processes. Existing multi-view methods are restricted to fixed camera pose and therefore lack generalization ability. This paper presents a novel Probabilistic Triangulation module that can be embedded in a calibrated 3D human pose estimation method, generalizing it to uncalibration scenes. The key idea is to use a probability distribution to model the camera pose and iteratively update the distribution from 2D features instead of using camera pose. Specifically, We maintain a camera pose distribution and then iteratively update this distribution by computing the posterior probability of the camera pose through Monte Carlo sampling. This way, the gradients can be directly back-propagated from the 3D pose estimation to the 2D heatmap, enabling end-to-end training. Extensive experiments on Human3.6M and CMU Panoptic demonstrate that our method outperforms other uncalibration methods and achieves comparable results with state-of-the-art calibration methods. Thus, our method achieves a trade-off between estimation accuracy and generalizability. Our code is in https://github.com/bymaths/probabilistic_triangulation", + "bbox": [ + 75, + 340, + 472, + 704 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 731, + 209, + 748 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3D human pose estimation is a fundamental tool in many downstream applications of computer vision and computer graphics, such as motion recognition[13], human-computer interaction[23], movie game animation[4], virtual reality[24], etc. The development of these fields requires a more accurate, convenient, and robust 3D human pose estimation algorithm.", + "bbox": [ + 75, + 756, + 468, + 862 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, RGB-based pose estimation has become the", + "bbox": [ + 94, + 862, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "trend because of its convenience, wide application scenarios, and low cost[27]. These methods can be divided into two categories: single-view and multi-view methods. Although single-view methods[39, 37, 11, 38, 25] have more widespread application scenarios, the lack of depth information makes single-view estimation of 3D human pose an ill-posed problem, especially when dealing with occlusions and multi-person scenes[21]. Multi-view methods[18, 16, 36, 33, 2, 14, 31, 20] can achieve more accurate results than single view-based methods because multi-view cameras can restore the depth information as well as the occluded parts.", + "bbox": [ + 496, + 310, + 893, + 491 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, the multi-view approach faces several issues when applied in practice. First, multi-view methods require synchronized and calibrated cameras, which complicates the process. Second, existing datasets for multi-view human pose estimation lack the diversity of camera external parameters. This results in the trained model cannot generalize well to unseen camera parameters, thus requiring re-annotation and re-training once the camera configurations change.", + "bbox": [ + 496, + 492, + 893, + 628 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To alleviate the above issues, we propose Probabilistic Triangulation module for uncalibrated 3D human pose estimation. Our module enables the network to get rid of camera pose parameters during the training process, which results in better generalization performance to be applied to wild scenes. The main idea is to use a probability distribution to model the camera pose, making the whole process differentiable. Specifically, we transform the uncalibrated 3D human pose estimation into a nonlinear optimization problem based on the reprojection error. The camera pose distribution is estimated from the 2D pose features, and then the posterior probability of the camera pose is computed by Monte Carlo sampling to iteratively update this distribution.", + "bbox": [ + 496, + 628, + 895, + 824 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We conducted extensive experiments on two benchmark datasets (Human3.6M[17] and CMU Panoptic[19, 29, 35]) to demonstrate that our method outperforms other uncalibrated methods and achieves comparable results with the state-of-the-art calibration methods, which indicates that", + "bbox": [ + 496, + 825, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 94, + 886, + 220, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14850", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "our method improves the generalized ability to camera parameters in multi-view human pose estimation while maintaining high accuracy.", + "bbox": [ + 76, + 90, + 468, + 135 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are mainly three-fold.", + "bbox": [ + 96, + 137, + 442, + 151 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose Probabilistic Triangulation that can generalize the calibrated 3D human pose estimation algorithm to uncalibrated scenes to estimate 3D human pose in the absence of camera pose.", + "- We propose an approximation method for camera pose distribution and an updated distribution method based on Monte Carlo sampling. It is used to model the camera pose of uncalibrated scenes with accuracy and robustness beyond classical algorithms.", + "- We conducted extensive experiments on two benchmark datasets (Human3.6M and CMU Panoptic) to demonstrate the accuracy, generalization capability, and applicability of Probabilistic Triangulation to wild scenes." + ], + "bbox": [ + 96, + 162, + 467, + 397 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 76, + 412, + 215, + 428 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Calibrated 3D pose estimation", + "text_level": 1, + "bbox": [ + 76, + 438, + 344, + 454 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D human pose estimation is a vital problem in computer vision and graphics, where the single view-based method has been a research spotlight due to the convenience and comprehensive application scenarios of a monocular camera. To alleviate the ambiguity problem caused by occlusion and the lack of depth information, many single view-based works[37, 11, 38, 25, 3] have tried to introduce the temporal information or body-related prior during training.", + "bbox": [ + 76, + 462, + 467, + 583 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-view images retain more information compared to single-view ones. The association of information between different views eliminates most of the ambiguity. So it is easier to achieve high-accuracy 3D human pose estimation in multi-view settings. Fusing the information of different views is the core problem of multi-view human pose estimation. Existing multi-view methods include two processes, 2D pose estimation and 3D pose reconstruction. The former consists of a pre-trained 2D pose estimator[10, 6], and multi-view information fusion occurs in the 3D pose reconstruction. Multi-view methods are divided into two categories according to the different ways of representing human pose. The first is the point-based method[26, 5, 12], which uses the spatial coordinates of the joint points as the human pose representation. This representation makes it easier to introduce temporal and body information explicitly. The second is the heatmap-based method, which uses the heatmap as the human pose representation[16, 36, 18], and learnable triangulation represents this method[18, 33]. The point representation is more concise and explicit but loses information, while the heatmap representation retains", + "bbox": [ + 76, + 584, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "more information but is not easily bounded explicitly. Our proposed Probabilistic Triangulation is applicable in both representations.", + "bbox": [ + 498, + 90, + 890, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Uncalibrated 3D pose estimation", + "text_level": 1, + "bbox": [ + 500, + 147, + 785, + 162 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Uncalibrated 3D pose estimation is a relatively new field[31, 2, 14, 20]. Takahashi's work[31] is a point-based method that establishes explicit constraints based on reprojection errors and the human body prior to transform the problem into an optimization problem and iteratively solve for the optimal solution. Lee's work[20] is also a point-based method, estimating the camera pose using the 3D pose estimated from different views. FLEX[14] estimates a time-invariant bone length while estimating joint rotations frame by frame and reconstructing 3D pose by forward kinematics. In this approach, the bone length is a link to fuse the multi-view information, and the rotation estimated for each view implicitly constrains the camera pose. However, this method cannot accurately estimate the camera pose due to the lack of transformation of the global coordinate system. Therefore, the output 3D pose is camera dependent. Bartol et al. [2] use a scoring network to evaluate the weight of the current proposal's camera pose or 3D human pose, and the final weighting is used to obtain a definite result. This method does not directly estimate the 3D human pose for uncalibrated scenes, but it can estimate the camera pose before and use other calibration methods to estimate the 3D human pose. This method does not directly estimate the 3D human pose for uncalibrated scenes, but it can estimate the camera pose before using other calibration methods to estimate the 3D human pose. Because the experiments for 3D human pose estimation in this work are for calibrated scenes, they are placed in the calibration method in the comparison experiments later in the paper.", + "bbox": [ + 496, + 170, + 890, + 608 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Current methods are limited to point-based representation. The heatmap-based representation retains more information than the point-based representation. This is because the accuracy of existing 2D human pose estimators is not sufficient for direct calibration. Small errors in points can be rapidly amplified by the camera pose estimation process, making the method ineffective. Our proposed camera pose distribution can effectively increase the robustness of the camera estimation process and support heatmap-based representation.", + "bbox": [ + 496, + 609, + 890, + 758 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Probabilistic camera pose estimation", + "text_level": 1, + "bbox": [ + 500, + 771, + 816, + 787 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Camera pose estimation is a fundamental problem in computer vision[15]. PNP methods solve the case of known 3D-2D point pairs, while triangulation solves the case of known 2D-2D point pairs. Bundle adjustment transforms the camera matching problem into an optimization problem starting from reprojection errors[1]. However, matching feature points and solving them using classical meth", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14851", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/2d4721dfbcf920343409bb46edbf0c2925505c4db7b6d17c2e27a478b1553189.jpg", + "image_caption": [ + "Figure 1: Probabilistic Triangulation for uncalibrated 3D human pose estimation pipeline. The inputs to the network are images from different views at the same moment. The 2D human pose heatmaps are estimated from the images and used to initialize the camera pose distribution. Then, Monte Carlo sampling is performed iteratively and each sampled camera parameter is computed by reprojection to obtain an explicit approximation of the 3D heatmap. The 3D heatmap calculates the weights of the sampled camera parameters. These weights are then used to update the pose distribution of the cameras. The weighted 3D heat map is used as input for the subsequent 3D pose reconstruction, for estimating the 3D human pose." + ], + "image_footnote": [], + "bbox": [ + 94, + 88, + 877, + 402 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ods does not apply to all scenarios. In the field of object and camera pose estimation, many works try to improve the network architecture that allows an end-to-end approach for pose estimation[8, 7]. The work EPro-PnP by Chen et al[9]. proposes a probabilistic PnP layer that allows the gradient back-propagated through the pose.", + "bbox": [ + 75, + 531, + 468, + 621 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by EPro-PnP, we use probability distributions to model camera pose. Compared with the camera pose represented by a single variable, the camera pose represented by the distribution has more robust performance and effectively mitigates the effect of 2D human pose detection errors.", + "bbox": [ + 75, + 621, + 468, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 723, + 168, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paragraph, we will review the multi-view uncalibrated 3D human pose estimation problem and introduce our Probabilistic Triangulation module. The overall pipeline is shown in Figure 1.", + "bbox": [ + 75, + 750, + 468, + 810 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Uncalibrated 3D human pose estimation", + "text_level": 1, + "bbox": [ + 76, + 816, + 421, + 833 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given that the images $I \\in \\mathbb{R}^{K \\times H \\times W}$ from $K$ views at a specific moment, our goal is to estimate the 3D pose $X^{3D}$ of the target human from it. Given the camera pose $y = \\{y_{k} \\in SE(3) | k = 1 \\dots K\\}$ , the optimal $X^{3D}$ will", + "bbox": [ + 76, + 838, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "make the reprojection error $(3\\mathrm{D}\\rightarrow 2D)$ small enough and fits the prior distribution of the human pose learned in the dataset. Therefore, the estimation algorithm is often divided into two parts, 2D pose estimation, and 3D pose reconstruction. In 2D pose estimation, a neural network $M_{1}$ is employed to estimate the 2D pose $X^{2D} = M_1(I)$ from each view. In the 3D pose reconstruction, the $X^{2D}$ of different views are fused using a triangulation or a learnable triangulation method $M_{2}$ to obtain $X^{3D} = M_2(X^{2D},y)$ .", + "bbox": [ + 496, + 531, + 890, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Based on the reprojection error, the calibrated 3D human pose estimation is to solve an optimization problem:", + "bbox": [ + 496, + 667, + 890, + 698 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {X ^ {3 D}} E \\left[ \\operatorname {p r o j} \\left(X ^ {3 D}, y\\right) - X ^ {2 D} \\right] \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 710, + 890, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $proj(\\cdot)$ denotes the projection function. The neural network-based algorithm replaces $X^{3D}$ in it with $M_2(X^{2D},y)$ , transforming the original optimization problem into solving for the optimal $M_2(\\cdot)$ network parameters.", + "bbox": [ + 496, + 744, + 890, + 805 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "When the camera pose $y$ is an unknown parameter, $y$ also becomes a variable to be optimized. Uncalibrated 3D human pose estimation can be similarly transformed into an optimization problem:", + "bbox": [ + 496, + 805, + 890, + 866 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {X _ {3 D}, y} \\quad E [ \\operatorname {p r o j} \\left(X ^ {3 D}, y\\right) - X ^ {2 D} ] \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 877, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14852", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b00c0637f0c63bc32b4deeb1e9bfba504edc7bdb7f7af0ef8509f5d480908de2.jpg", + "image_caption": [ + "(a) Implicit continuous." + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 318, + 224 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/64ae607bc9b9ade50c4041c3be64a868127259360cadad7b0c4fd48832b3cf09.jpg", + "image_caption": [ + "(b) Implicitly discrete." + ], + "image_footnote": [], + "bbox": [ + 344, + 85, + 588, + 224 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f26170b4583059fff5d6e472ae42b410a6cc5bc7d8abb97a52aa86292df22b4a.jpg", + "image_caption": [ + "(c) Explicit discrete approximation.", + "Figure 2: 3D heatmap under different definitions" + ], + "image_footnote": [], + "bbox": [ + 617, + 85, + 859, + 224 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This problem is tough to solve and exists multiple solutions. There are three main reasons for this:", + "bbox": [ + 76, + 297, + 467, + 327 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. If an iterative method is used to optimize $y$ and $X^{3D}$ alternately, the results tend to fall into local optimum.", + "2. If a neural network is used to regress $y$ and then solve for $X^{3D}$ , it will be constrained by the lack of diversity in the existing data set $y$ to train.", + "3. If the neural network is used to regress $X^{3D}$ directly from the monocular view and then to solve $y$ , it will introduce the ill-conditioned problem of monocular scale ambiguity." + ], + "bbox": [ + 88, + 333, + 468, + 486 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In summary, we have to extract more information from the only known quantity $X_{2D}$ to obtain a relatively accurate estimate of $y$ , i.e., a valid estimate $p(y|X^{2D})$ .", + "bbox": [ + 76, + 492, + 468, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We use camera pose distribution approximation and Monte Carlo sampling to solve this problem. (see Probabilistic Triangulation part of Figure 1) Specifically, we maintain a proposal distribution $q(y)$ for approximating the posterior distribution $p(y|X^{2D})$ of camera poses during one inference. Monte Carlo sampling is continuously performed on $q(y)$ , and the weights are calculated from the sampled points, and then $q(y)$ is updated according to the weights. After several iterations, the results generated from the sampled points are weighted and averaged as the input to the 3D pose reconstruction network. We refer to this process as Probabilistic Triangulation. Figure 1 shows the pipeline of uncalibrated 3D human pose estimation after adding Probabilistic Triangulation.", + "bbox": [ + 75, + 537, + 468, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The Probabilistic Triangulation can be flexibly embedded into any kind of calibrated 3D human pose estimation, reducing its dependence on camera pose for realistic scenarios. The differentiable computational process makes it possible to connect the 2D pose estimation and 3D pose reconstruction parts, allowing end-to-end training.", + "bbox": [ + 75, + 750, + 468, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Probabilistic Triangulation", + "text_level": 1, + "bbox": [ + 76, + 847, + 320, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We detail the Probabilistic Triangulation using the pipeline in Figure 1 as an example. In subsequent repre", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "sentations, $y$ is used to denote the camera pose and $y_{gt}$ the ground truth of the camera pose. The 2D human pose is represented as $X^{2D} = \\{x_i^{2D}\\in \\mathbb{R}^{K\\times H'\\times W'}|i = 1\\ldots N\\}$ , and the 3D human pose is represented as $X^{3D} = \\{x_i^{3D}\\in \\mathbb{R}^{K\\times L_1\\times L_2\\times L_3}|i = 1\\ldots N\\}$ , where $H^{\\prime}$ and $W^{\\prime}$ denote the height and width of the 2D heatmap, and $L_{1},L_{2},L_{3}$ denote the length, width, and height of the 3D heatmap.", + "bbox": [ + 498, + 297, + 890, + 404 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Camera pose distribution approximation In order to solve the optimization problem 2 with multiple solutions, we first normalized the multi-view camera pose to limit the range of solutions. Specifically, through an affine transformation of the whole coordinate system, the rotation matrix of the first view is changed into a unit matrix, the translation vector becomes a zero vector, and the translation vector of the second view has a modulus of one. The above affine changes can guarantee the uniqueness of the solution.", + "bbox": [ + 496, + 407, + 890, + 545 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Each camera pose is represented as a 7-dimensional vector, where 3D rotations are represented using unit quaternions and 3D translations are represented using 3D vectors. To better express the camera distribution, the angular central Gaussian distribution is introduced to represent the 3D rotation [34], and the multivariate t-distribution is introduced to represent the 3D translation. The $p(y|X^{2D})$ is calculated for each sampling point $y$ to obtain the covariance matrix of the angular central Gaussian distribution, and the mean and covariance matrix of the multivariate t-distribution, which in turn updates the parameters. The initial parameters of the distributions are first estimated based on the 2D human pose using the eight-point method. Then, a portion is sampled around the initial value and another portion is sampled around the entire camera domain. The distribution is initialized by the sampling result. Since the input of a single frame may cause a large error in the eight-point method, and initializing the distribution in this way increases the robustness of the algorithm.", + "bbox": [ + 496, + 547, + 890, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Monte Carlo sampling We assume that the 2D heatmap is the marginal distribution of the 3D heatmap along the projection direction, and the problem can be transformed into an optimization problem based on the reprojection error:", + "bbox": [ + 496, + 839, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14853", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {y, X ^ {3 D}} \\quad \\sum_ {i} ^ {N} \\int_ {\\sigma_ {i}} \\left\\| x _ {i} ^ {2 D} \\left(\\sigma_ {i}\\right) - \\int_ {p r o j \\left(z, y _ {i}\\right) = \\sigma_ {i}} x ^ {3 D} (z) \\mathrm {d} z \\right\\| _ {2} \\mathrm {d} \\sigma_ {i} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 116, + 485, + 170 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $z$ denotes the body element in 3D space, $\\sigma_{i}$ denotes the area element of the $i$ th camera plane, and $proj(\\cdot)$ denotes the projection function. A more general heatmap representation is adopted here, where $x^{3D}$ and $x^{2D}$ are considered as the probability density functions of the heatmap distribution. In practice, the heatmap is often stored in a discrete way, and the integrals need to be discretized as well. However, it is difficult to establish the constraints between $y$ and $X^{3D}$ explicitly, making the above optimization problem difficult to solve.", + "bbox": [ + 76, + 171, + 468, + 320 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Therefore, we use an approximate 3D heatmap explicitly defined as:", + "bbox": [ + 76, + 323, + 468, + 353 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nx ^ {3 D} (z) = \\frac {1}{N} \\sum_ {\\substack {i \\\\ p r o j (z, y _ {i}) = \\sigma_ {i}}} ^ {N} x _ {i} ^ {2 D} (\\sigma_ {i}) \\tag{4}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 369, + 468, + 419 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nx _ {i} ^ {2 D} (\\sigma_ {i}) = \\max _ {p r o j (z, y _ {i}) = \\sigma_ {i}} x ^ {3 D} (z)\n$$\n", + "text_format": "latex", + "bbox": [ + 178, + 421, + 388, + 448 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This definition is similar to the volume of the learnable triangulation, with the advantage that $X^{3D}$ can be computed explicitly and differentiably from $y$ and $X^{2D}$ . It also has some physical meaning as far as the location of the extreme points taken is similar to the original representation. The visualization of the 3D heatmap under different definitions is shown in Figure 2.", + "bbox": [ + 76, + 457, + 468, + 563 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The generated $X^{3D}$ retains the information of the heatmap and can be used as input for subsequent networks. Thus, the problem is simplified to:", + "bbox": [ + 76, + 564, + 468, + 609 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {y} \\sum_ {i} ^ {N} \\| \\underbrace {\\sum_ {z} \\left(x ^ {3 D} (z) x _ {i} ^ {2 D} \\left(\\sigma_ {i}\\right)\\right) ^ {2} \\left(x _ {i} ^ {2 D} \\left(\\sigma_ {i}\\right) - x ^ {3 D} (z)\\right)} _ {f _ {i} (y)} \\| _ {2} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 637, + 468, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The reprojection error is employed as the negative logarithm of the likelihood function $p(X_{2D}|y)$ .", + "bbox": [ + 76, + 713, + 467, + 743 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np \\left(X ^ {2 D} | y\\right) = \\exp - \\sum_ {i} ^ {N} \\| f _ {i} (y) \\| _ {2} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 160, + 758, + 468, + 799 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Suppose that the camera pose $p(y)$ is subject to a uniform distribution, $p(y|X^{2D})$ can be calculated by Bayesian formula:", + "bbox": [ + 76, + 810, + 468, + 854 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np (y | X ^ {2 D}) = \\frac {p \\left(X ^ {2 D} \\mid y\\right)}{E \\left[ p \\left(X ^ {2 D} \\mid y\\right) \\right]} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 869, + 468, + 905 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The calculation of denominator expectation can be estimated by Monte Carlo sampling approximation. The specific calculation formula is as follows.", + "bbox": [ + 498, + 90, + 890, + 135 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nE \\left[ p \\left(X ^ {2 D} | y\\right) \\right] \\approx \\frac {1}{M} \\sum_ {j} ^ {M} q \\left(y _ {j}\\right) p \\left(X ^ {2 D} | y\\right), y _ {j} \\sim q (y) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 159, + 890, + 202 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $M$ denotes the total number of samples. Then, $q(y)$ is updated using the computed $p(y|X^{2D})$ .", + "bbox": [ + 498, + 213, + 890, + 243 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, the normalized $q(y)$ is used as the weight and the $X^{3D}$ generated by all sampled points $y$ is weighted and averaged as the input to the subsequent 3D pose reconstruction network.", + "bbox": [ + 498, + 243, + 890, + 301 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nX ^ {3 D} = \\frac {\\sum_ {j} q \\left(y _ {j}\\right) X _ {j} ^ {3 D}}{\\sum_ {j} q \\left(y _ {j}\\right)} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 314, + 890, + 353 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Training Loss", + "text_level": 1, + "bbox": [ + 500, + 367, + 642, + 383 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The entire training process includes two loss terms: $\\mathcal{L}_{3d}$ and $\\mathcal{L}_{cam}$ .", + "bbox": [ + 498, + 390, + 890, + 420 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We measure the difference between the true distribution of camera pose $z(y)$ and the posterior distribution $p(y|X^{2D})$ using KL divergence.", + "bbox": [ + 498, + 421, + 890, + 465 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {c a m} = D _ {K L} (z (y) \\| p (y | X ^ {2 D})) \\\\ = - \\frac {1}{2} \\sum_ {i} ^ {N} \\| f _ {i} \\left(y _ {g t}\\right) \\| _ {2} + \\log E [ p \\left(X ^ {2 D} | y\\right) ] \\tag {10} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 488, + 890, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the expectation of the second half is also obtained by the calculation of the equation 8.", + "bbox": [ + 498, + 561, + 888, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The 3D human pose estimation loss is the same as previous works[18], which encourages the predicted 3d poses to be close to the ground truth. The formula can be summarized as follow:", + "bbox": [ + 498, + 590, + 890, + 650 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {3 d} = \\left\\| \\operatorname {s o f t a r g m a x} \\left(X ^ {3 D}\\right) - X _ {g t} \\right\\| _ {1} - \\beta \\cdot \\log \\left(X ^ {3 D} \\left(X _ {g t}\\right)\\right) \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 661, + 888, + 693 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In end-to-end training, we simultaneously optimize these two loss terms to train the networks, and the total loss function can be written as:", + "bbox": [ + 498, + 694, + 890, + 738 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\mathcal {L} _ {\\text {c a m}} + \\lambda_ {2} \\mathcal {L} _ {3 d} \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 751, + 890, + 767 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the $\\lambda_{1} = 1$ and $\\lambda_{2} = 0.1$ in our experiment setting.", + "bbox": [ + 500, + 777, + 880, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 806, + 632, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Dataset & Metrics", + "text_level": 1, + "bbox": [ + 500, + 830, + 684, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conducted experiments on two of the most commonly used 3D human pose datasets available today, Human3.6M[17] and CMU Panoptic[19, 29, 35]. We used", + "bbox": [ + 500, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14854", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/a5d7f978afb05b2ee9c383504741207e84db4b1e1a2df252a943b112a5810b26.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodDir.Disc.EatGreetPhonePhotoPosePurch.SitSitD.SmokeWaitWalkD.WalkWalkT.Mean
Calibration method
Remelli et al.[28]27.332.125.026.529.335.428.831.636.431.731.229.926.933.730.430.2
Bartol et al.[2]27.528.429.327.530.128.127.930.832.932.530.829.428.530.530.129.1
He et al. [16]25.727.723.724.826.931.424.926.528.831.728.226.423.628.323.526.9
Qiu et al. [26]24.026.723.224.324.822.824.128.632.126.931.025.625.028.024.426.2
Ma et al. [22]24.426.423.421.125.223.224.733.829.826.426.824.223.226.123.325.8
Iskakov et al.[18]19.920.018.918.520.519.418.422.122.528.721.220.819.722.120.220.8
Uncalibration method
Gordon et al.[14]22.023.624.926.730.635.725.132.929.532.532.626.534.726.027.730.2
Ours method24.025.426.630.432.120.120.536.540.129.527.427.620.824.122.027.8
", + "bbox": [ + 91, + 88, + 879, + 282 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4c37961fd87bd9ad61d28fa6e0675f339c20b0f4479a7cf055c2e1f44460dafd.jpg", + "table_caption": [ + "Table 1: Results of the evaluation on the Human3.6M dataset. The table shows the MPJPE in millimeters for the published state-of-the-art calibrated and uncalibrated methods." + ], + "table_footnote": [], + "table_body": "
MethodMPJPE,mm
Calibrated method
Iskakov et al. Algebraic[18]21.3
Iskakov et al. Volumetric[18]13.7
Uncalibrated method
Bartol et al. [2]25.4
Our method24.2
", + "bbox": [ + 140, + 345, + 406, + 486 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2: Results of the MPJPE on the CMU Panoptic dataset ( using four cameras).", + "bbox": [ + 75, + 496, + 468, + 527 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the 17-joint MPJPE (Mean Per Joint Position Error) as a metric to evaluate our method. In training, we normalize the ground truth according to the method in section3.2 to ensure the uniqueness in the camera pose solution. In validation, the estimated 3D human pose is denormalized to the original coordinate system to ensure the correctness of the MPJPE calculation.", + "bbox": [ + 75, + 573, + 468, + 679 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation details", + "text_level": 1, + "bbox": [ + 76, + 717, + 290, + 732 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We added the Probabilistic Triangulation based on the work learnable triangulation by Iskakov et al.[18] to realize uncalibrated 3D human pose estimation. The same experimental parameter settings as the learnable triangulation method were used. As with learnable triangulation, our method uses predictions from the algebraic triangulation. Our method can also be fine-tuned and be trained in an end-to-end manner. $q(y)$ is initialized using a uniform distribution. The number of iterations is four, and the number of Monte Carlo samples is 256.", + "bbox": [ + 75, + 750, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparisons with State-of-the-art", + "text_level": 1, + "bbox": [ + 498, + 349, + 799, + 366 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compared the existing state-of-the-art calibrated and uncalibrated 3D pose estimation algorithms. The evaluation results on the Human3.6M dataset and the CMU Panoptic dataset are shown in Table 1 and Table 2, respectively. The experimental results show that the MPJPE of our method has outperformed the state-of-the-art uncalibrated approaches and achieved comparable performance to calibrated methods. It is worth noting that our method achieves better results in most scenarios of uncalibrated setting (see Table 1), but the results are poor in the Purch. and Sit. sub-datasets. This is because there are more occlusions in these two subsets, resulting in the 2D joint estimation being inaccurate, which further affects the estimation of the camera parameter distribution. Therefore, the final accumulated error affects the 3D human pose estimation performance. Inferring the camera parameters from the features of the detected human inevitably leads to estimation results depending on the capability of the human feature detector. However, our method still outperforms existing uncalibrated methods in terms of overall MPJPE for both datasets.", + "bbox": [ + 496, + 375, + 890, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Evaluation on Camera Pose Estimation", + "text_level": 1, + "bbox": [ + 498, + 709, + 836, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate the capability of our camera pose estimation, we have conducted comparisons with some classical camera parameter estimation algorithms on the Human3.6M dataset. Due to the large parallax between different camera views, we choose 2D human keypoints estimated from 20 consecutive frames as image feature points to solve the camera pose parameters. We compare our camera estimation with Bundle Adjustment[32] and RANSAC 8-point algorithm[30]. Bundle Adjustment choose to minimize the reprojection error using the LM algorithm to find the camera parameters and the RANSAC 8-point algorithm uses the", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14855", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4eeb0c04e06036b306911c2bc47d094c672a337517cf6a0d4b18276a6c8b71b2.jpg", + "image_caption": [ + "(a) Bundle Adjustment." + ], + "image_footnote": [], + "bbox": [ + 122, + 95, + 310, + 422 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f67cb64b06dc89e4de3ffa114bb5b52378c276cca547ebdba5c48903dc130966.jpg", + "image_caption": [ + "(b) RANSAC 8-point algorithm." + ], + "image_footnote": [], + "bbox": [ + 388, + 95, + 581, + 422 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9574540b4dc48dbbcbaad0aeb0e664f774c628fb463d4a166f96a3b9844f9f22.jpg", + "image_caption": [ + "(c) Ours method.", + "Figure 3: Visualization of the camera pose parameters and 3D human pose obtained by different algorithms. The quadrilateral cone indicates the camera pose parameters, the gray part indicates the ground truth, and the colored part indicates the prediction results of different algorithms." + ], + "image_footnote": [], + "bbox": [ + 663, + 90, + 851, + 422 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "8-point method to find the fundamental matrix after screening out the outliers by RANSAC, and then uses the eigenvalue decomposition to find the camera pose. We provide some visualization examples in Figure 3. From the Figure 3, we can see that Bundle Adjustment often falls into the local optimal solution, resulting in poor camera poses. The RANSAC 8-point algorithm can remove outliers, but the estimation of the camera pose is sensitive to 2D human pose estimation, which will lead to accumulated errors when reconstructing 3D human poses. The 3D human and camera pose estimation results are more robust and accurate when introducing our Probabilistic Triangulation (see (c) of Figure 3)", + "bbox": [ + 75, + 526, + 468, + 720 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3 shows more detailed results of camera pose evaluation, using the same experimental setup as [2]. Among the evaluation metrics used: 1. 3D estimation error $(\\mathrm{mm})$ $E_{3D} = E[\\| x^{\\hat{3} D} - x^{3D}\\| _2]$ ; 2. Projection 2D error $(\\mathrm{mm})E_{2D} = E[\\| x^{\\hat{2} D} - x^{2D}\\| _2]$ ; 3. Camera rotation error $E_{R} = E[\\| \\hat{q} -q\\|_{2}]$ ; 4. Camera translation error (mm) $E_{t} = E[\\| \\hat{t} -t\\|_{2}]$", + "bbox": [ + 75, + 723, + 470, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Cross-dataset experiments", + "text_level": 1, + "bbox": [ + 76, + 845, + 316, + 862 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To test the generalization ability of Probabilistic Triangulation across datasets, we segment CMU Panoptic and", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/630f27edb79e2de9c9dc6aa9b5fe49dfe1f65dfd32cd6b6cdf3e433d91630720.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
methodsE3D↓E2D↓ER↓Et↓
BA736.82130.180.02546.87
RANSAC 8-point97.5050.140.0125.30
Our methods27.805.980.00432.71
", + "bbox": [ + 531, + 523, + 862, + 601 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3: Quantitative experiments on camera pose estimation on the Human3.6M dataset.", + "bbox": [ + 498, + 611, + 890, + 642 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Human36M into five sub-datasets in the same way as Bartol et al.[2]. Cross-dataset experiments are conducted between these sub-datasets two by two. It was found that there was no significant loss of accuracy between the CMU Panoptic sub-datasets even after segmentation (this is because the distribution between the sub-datasets of the CMU Panoptic dataset is very similar). However, the results trained from the CMU dataset have a significant loss of accuracy on Human3.6M. Table 4 shows the generalization ability of Probabilistic Triangulation and Bartol et al.[2] from the CMU dataset to the Human3.6M dataset. Probabilistic Triangulation exhibits stronger generalization.", + "bbox": [ + 496, + 652, + 890, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.6. Ablation study on the number of cameras", + "text_level": 1, + "bbox": [ + 500, + 845, + 854, + 862 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We show the results of the ablation study in Table 5. After training on 4-view data, our method generalizes well to", + "bbox": [ + 500, + 869, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14856", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6a7c6440ef52c0eac8a6b2ee2e35944284272fc00c517272c6e739b9fca8cb53.jpg", + "image_caption": [ + "Figure 4: Visualization of the sampled points in four iterations after dimensionality reduction using t-SNE. From left to right corresponds to the sampled values after four iterations. The value of the sampled point is the logarithmic sampling loss, and the smaller the value means that the sampled point is closer to the true value." + ], + "image_footnote": [], + "bbox": [ + 94, + 95, + 272, + 242 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/93458b7ef489592e1fbe64deeff7c648ffdf0c5d9f6107673354f00731f0ccb6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 279, + 95, + 457, + 242 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3a65ad2328f2ecc83327c8dea7f954af1a74e2067d71594a5ebf653d98b56eb6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 464, + 95, + 643, + 242 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bb4193fee109018510e72c48ea05462f149af2e3d0b4f7254b0956092f692bc6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 651, + 94, + 828, + 242 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1c6968438308a59bf00d04346626165ad5f3f2865e135d0ba5c52138d1025bce.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 836, + 92, + 875, + 236 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/cb5f27a1de344104b9077bfe700f3d1978f271c5eb43a4f6ddd8e42677c1a3b3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodTrainSelf-TestH36M-Testdiff
Bartol et al.[2]CMU125.833.530%
CMU226.033.428%
CMU325.031.024%
CMU425.132.528%
Ours methodCMU124.630.825%
CMU223.729.123%
CMU324.129.221%
CMU424.931.125%
", + "bbox": [ + 78, + 325, + 478, + 483 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "3-view and 2-view because the network has seen rich information during training. There is some performance degradation when the model is trained on 2-view and tested on 3-view and 4-view as shown in Table 5.", + "bbox": [ + 75, + 643, + 468, + 705 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/37058f5ab3dd1f6840c58c58e92bd8c8d6fe20c35aa44fead40edcc12697446a.jpg", + "table_caption": [ + "Table 4: Experiments on generalization ability between datasets (MPJPE in mm). The CMU Panoptic dataset was split into four sub-datasets with different number of cameras and different spatial distributions of cameras. The models were trained on the four datasets separately, and the results were evaluated on their own test set and the Human3.6M test set. The last column represents the cross-data accuracy decline rate." + ], + "table_footnote": [], + "table_body": "
2-view3-view4-view
Training on 2-view29.542.439.2
Training on 4-view32.629.327.8
", + "bbox": [ + 125, + 714, + 421, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5: Ablation study on Human3.6M for camera numbers (MPJPE, mm).", + "bbox": [ + 75, + 787, + 470, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.7. Ablation study on each module", + "text_level": 1, + "bbox": [ + 76, + 830, + 352, + 848 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In order to demonstrate the irreplaceable role that probabilistic triangularization plays in camera pose estimation and 3D human reconstruction in uncalibrated 3D human", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "pose estimation. We design two ablation experiments to remove the influence of the rest of the network on the results and to demonstrate the role of Probabilistic Triangulation better.", + "bbox": [ + 496, + 328, + 890, + 388 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "First, we use 2D heatmaps ground truth as the input of Probabilistic Triangulation to eliminate the effect of 2D backbone on the results. Also, the upper bound of our method is shown (see Table 6 middle). The table shows that our method achieves comparable results to the calibration method [18] when given the 2D ground truth.", + "bbox": [ + 496, + 390, + 890, + 481 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The 3D error still cannot reach zero under the condition of using 2D ground truth because there is a theoretical upper limit to the accuracy of the voxel structure. However, the 2D human pose estimator error cannot be avoided, and the better robustness of the voxel structure to error is the reason it was chosen.", + "bbox": [ + 496, + 482, + 890, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In addition, we demonstrate the necessity of introducing the camera pose estimation module by comparing it with Iskaov et al. (V2V network and triangulation). We rotated the world coordinate system $(0^{\\circ}$ to $180^{\\circ}$ randomly around the vertical axis and $0^{\\circ}$ to $45^{\\circ}$ randomly around the pitch) to change the values of the camera's external parameters, resulting in a new test set called \"Test*\" in Table 6. We can find that only using a V2V network and triangulation will make the network overfit the camera poses, resulting in performance degradation. Our method does not require the input of camera poses, so changes in the world coordinate system do not affect our method's final pose estimation results. It demonstrates that our camera estimation module, i.e., the main contribution, is necessary and reasonable.", + "bbox": [ + 496, + 575, + 890, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.8. Visualization of Sampling Process", + "text_level": 1, + "bbox": [ + 500, + 800, + 795, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In order to visualize the sampling process in the Probabilistic Triangulation, the 256 sampling points of each iteration are embedded by t-SNE and plotted in Figure 4. From the figure, as the iteration proceeds, the approximation of the camera distribution becomes more and more ac", + "bbox": [ + 496, + 825, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14857", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d17212e0d2d9c0e6a8046d2ff7e1521f638ba34594eb828e27b81370cf230b51.jpg", + "table_caption": [], + "table_footnote": [ + "Table 6: Pose estimation results (MPJPE, mm) on different 2D and test settings. The middle two columns show the results of 3D pose estimation using the 2D estimator and 2D GT, respectively. The rightmost column shows the estimation results on the Test* set." + ], + "table_body": "
Baseline2D GTTest*
Iskakov et al.20.816.325.12
Our methods27.818.527.8
", + "bbox": [ + 102, + 88, + 442, + 150 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "curate, the sampled points are closer to the ground truth, and the sampling loss keeps decreasing. At the same time, the whole camera pose space is not smooth, and there are many local optimums and pseudo-solutions. The 2D human pose estimator generates noise, making the classical camera pose estimation more likely to fall into local optimal solutions. Distributed representation of camera pose (Probabilistic Triangulation) can alleviate this problem.", + "bbox": [ + 75, + 248, + 467, + 369 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Furthermore, from Figure 4, the sampling points are concentrated around a few extreme points as the iteration parameters increase. This is because an incremental solution exists to the camera pose estimation, so there are multiple extreme points. However, only one of them has real physical significance, whereas, in the projection process, these extreme points produce the same projection result. The distribution also tends to converge to a single extreme point if an initial value is used to initialize the camera pose distribution, and the sampling points of the distribution are spread out to appear near multiple extreme points if a uniform distribution is used to initialize the distribution.", + "bbox": [ + 75, + 369, + 467, + 550 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.9. Generalize to Wide Scenes", + "text_level": 1, + "bbox": [ + 76, + 561, + 316, + 578 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "To demonstrate the generalization of our Probabilistic Triangulation in the wild scenes, we use a model trained from the CMU Panoptic dataset and test it on the natural scenes. Two iPhones with a $26\\mathrm{mm}$ primary camera were used for the shooting, and the intrinsic parameters were read using the swift function. The results are shown in Figure 5. Our method remains in effect even when the camera space location and the number of cameras change.", + "bbox": [ + 75, + 585, + 467, + 708 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusions and limitations", + "text_level": 1, + "bbox": [ + 76, + 723, + 333, + 739 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We propose a novel Probabilistic Triangulation module for multi-view 3D human pose estimation, which enables the existing calibrated methods to reduce the dependence on calibration and can be applied to uncalibrated wild scenes. Extensive experiments demonstrate that the 3D human pose estimation based on our Probabilistic Triangulation can achieve state-of-the-art performance when compared to uncalibrated methods. And the employment of camera pose distribution and Monte Carlo sampling alleviates the problem of easy access to local optimums and pseudo-solutions", + "bbox": [ + 75, + 750, + 467, + 900 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/43d1281dd326e15e6f0b7bc8d1d8c5ef2a3d484f0d0e8c672ab4eb0e5052d232.jpg", + "image_caption": [ + "Figure 5: Our method demonstrates the results in a non-calibrated wild scene. The first and second columns represent the two iPhone camera views, and the third column shows the estimated camera pose and 3D human pose." + ], + "image_footnote": [], + "bbox": [ + 532, + 93, + 859, + 338 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "in camera pose estimation. Since our Probabilistic Triangulation does not take the camera pose parameters as input, it is possible to build the multi-view 3D human pose estimation system in wild scenes and achieve a high-accurate capture. In the wild scenes, the Probabilistic Triangulation is not affected by the spatial location changes and the number of cameras. It can be directly applied to uncalibrated scenes after training with calibrated data.", + "bbox": [ + 496, + 440, + 890, + 561 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The main limitation of our method is that it can only be applied to single-person scenes. Extending to multi-person scenarios requires taking into account the cross-view matching problem, which is difficult to solve in the absence of a camera pose. In addition, although the Probabilistic Triangulation does not require the camera pose as input during validation, the ground truth of the 3D human pose and the camera pose are used in the training process, and these data need to be obtained from the dataset of the calibration scene. In fact, the ground truth of camera pose is not directly involved in the training, but indirectly guides the 2D pose estimation network learning through cross-view information. The ground truth of the 3D human pose influences the 2D pose estimation network and enables the 3D pose reconstruction network to learn the human prior and integrate the information generated by previous sampling.", + "bbox": [ + 496, + 561, + 890, + 818 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements This work was supported by National Key Research and Development Program of China (NO. 2022YFB3303202).", + "bbox": [ + 496, + 847, + 890, + 893 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "14858", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sameer Agarwal and Keir Mierle. Others, \"ceres solver\". Available: http://ceres-solver.org, 2015.", + "[2] Kristijan Bartol, David Bojanic, Tomislav Petkovic, and Tomislav Pribanic. 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Advances in Neural Information Processing Systems, 34:13153-13164, 2021.", + "[37] Jinlu Zhang, Zhigang Tu, Jianyu Yang, Yujin Chen, and Jun-song Yuan. Mixste: Seq2seq mixed spatio-temporal encoder for 3d human pose estimation in video. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13232-13242, 2022.", + "[38] Ce Zheng, Sijie Zhu, Matias Mendieta, Taojiannan Yang, Chen Chen, and Zhengming Ding. 3d human pose estimation with spatial and temporal transformers. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 11656-11665, 2021.", + "[39] Wentao Zhu, Xiaoxuan Ma, Zhaoyang Liu, Libin Liu, Wayne Wu, and Yizhou Wang. Motionbert: Unified pretraining for" + ], + "bbox": [ + 78, + 90, + 468, + 900 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "human motion analysis. arXiv preprint arXiv:2210.06551, 2022.", + "bbox": [ + 532, + 90, + 890, + 118 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "14860", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Probabilistic Triangulation for Uncalibrated Multi-View 3D Human Pose Estimation/b6b4e04e-10fb-49dc-be18-fbc2e2b53da9_model.json b/2023/Probabilistic Triangulation for Uncalibrated Multi-View 3D Human Pose Estimation/b6b4e04e-10fb-49dc-be18-fbc2e2b53da9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..1629fa29b74cdf1954435d569afd88b1f892be3c --- /dev/null +++ b/2023/Probabilistic Triangulation for Uncalibrated Multi-View 3D Human Pose Estimation/b6b4e04e-10fb-49dc-be18-fbc2e2b53da9_model.json @@ -0,0 +1,2323 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.119, + 0.13, + 0.853, + 0.175 + ], + "angle": 0, + "content": "Probabilistic Triangulation for Uncalibrated Multi-View 3D Human Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.216, + 0.203, + 0.756, + 0.277 + ], + "angle": 0, + "content": "Boyuan Jiang\\(^{1,2}\\), Lei Hu\\(^{1,2}\\) Shihong Xia\\(^{1,2*}\\) \n\\(^{1}\\)Institute of Computing Technology, Chinese Academy of Sciences; \\(^{2}\\)University of Chinese Academy of Sciences {jiangboyuan20s, hulei19z, xsh}@ict.ac.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.473, + 0.705 + ], + "angle": 0, + "content": "3D human pose estimation has been a long-standing challenge in computer vision and graphics, where multiview methods have significantly progressed but are limited by the tedious calibration processes. Existing multi-view methods are restricted to fixed camera pose and therefore lack generalization ability. This paper presents a novel Probabilistic Triangulation module that can be embedded in a calibrated 3D human pose estimation method, generalizing it to uncalibration scenes. The key idea is to use a probability distribution to model the camera pose and iteratively update the distribution from 2D features instead of using camera pose. Specifically, We maintain a camera pose distribution and then iteratively update this distribution by computing the posterior probability of the camera pose through Monte Carlo sampling. This way, the gradients can be directly back-propagated from the 3D pose estimation to the 2D heatmap, enabling end-to-end training. Extensive experiments on Human3.6M and CMU Panoptic demonstrate that our method outperforms other uncalibration methods and achieves comparable results with state-of-the-art calibration methods. Thus, our method achieves a trade-off between estimation accuracy and generalizability. Our code is in https://github.com/bymaths/probabilistic_triangulation" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.732, + 0.21, + 0.749 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.757, + 0.47, + 0.863 + ], + "angle": 0, + "content": "3D human pose estimation is a fundamental tool in many downstream applications of computer vision and computer graphics, such as motion recognition[13], human-computer interaction[23], movie game animation[4], virtual reality[24], etc. The development of these fields requires a more accurate, convenient, and robust 3D human pose estimation algorithm." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.863, + 0.469, + 0.879 + ], + "angle": 0, + "content": "Recently, RGB-based pose estimation has become the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.311, + 0.895, + 0.492 + ], + "angle": 0, + "content": "trend because of its convenience, wide application scenarios, and low cost[27]. These methods can be divided into two categories: single-view and multi-view methods. Although single-view methods[39, 37, 11, 38, 25] have more widespread application scenarios, the lack of depth information makes single-view estimation of 3D human pose an ill-posed problem, especially when dealing with occlusions and multi-person scenes[21]. Multi-view methods[18, 16, 36, 33, 2, 14, 31, 20] can achieve more accurate results than single view-based methods because multi-view cameras can restore the depth information as well as the occluded parts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.895, + 0.629 + ], + "angle": 0, + "content": "However, the multi-view approach faces several issues when applied in practice. First, multi-view methods require synchronized and calibrated cameras, which complicates the process. Second, existing datasets for multi-view human pose estimation lack the diversity of camera external parameters. This results in the trained model cannot generalize well to unseen camera parameters, thus requiring re-annotation and re-training once the camera configurations change." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.896, + 0.825 + ], + "angle": 0, + "content": "To alleviate the above issues, we propose Probabilistic Triangulation module for uncalibrated 3D human pose estimation. Our module enables the network to get rid of camera pose parameters during the training process, which results in better generalization performance to be applied to wild scenes. The main idea is to use a probability distribution to model the camera pose, making the whole process differentiable. Specifically, we transform the uncalibrated 3D human pose estimation into a nonlinear optimization problem based on the reprojection error. The camera pose distribution is estimated from the 2D pose features, and then the posterior probability of the camera pose is computed by Monte Carlo sampling to iteratively update this distribution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.901 + ], + "angle": 0, + "content": "We conducted extensive experiments on two benchmark datasets (Human3.6M[17] and CMU Panoptic[19, 29, 35]) to demonstrate that our method outperforms other uncalibrated methods and achieves comparable results with the state-of-the-art calibration methods, which indicates that" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "14850" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.136 + ], + "angle": 0, + "content": "our method improves the generalized ability to camera parameters in multi-view human pose estimation while maintaining high accuracy." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.138, + 0.444, + 0.152 + ], + "angle": 0, + "content": "In summary, our contributions are mainly three-fold." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.164, + 0.468, + 0.224 + ], + "angle": 0, + "content": "- We propose Probabilistic Triangulation that can generalize the calibrated 3D human pose estimation algorithm to uncalibrated scenes to estimate 3D human pose in the absence of camera pose." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.236, + 0.468, + 0.311 + ], + "angle": 0, + "content": "- We propose an approximation method for camera pose distribution and an updated distribution method based on Monte Carlo sampling. It is used to model the camera pose of uncalibrated scenes with accuracy and robustness beyond classical algorithms." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.324, + 0.468, + 0.398 + ], + "angle": 0, + "content": "- We conducted extensive experiments on two benchmark datasets (Human3.6M and CMU Panoptic) to demonstrate the accuracy, generalization capability, and applicability of Probabilistic Triangulation to wild scenes." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.164, + 0.468, + 0.398 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.414, + 0.216, + 0.429 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.439, + 0.345, + 0.455 + ], + "angle": 0, + "content": "2.1. Calibrated 3D pose estimation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.463, + 0.468, + 0.584 + ], + "angle": 0, + "content": "3D human pose estimation is a vital problem in computer vision and graphics, where the single view-based method has been a research spotlight due to the convenience and comprehensive application scenarios of a monocular camera. To alleviate the ambiguity problem caused by occlusion and the lack of depth information, many single view-based works[37, 11, 38, 25, 3] have tried to introduce the temporal information or body-related prior during training." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.585, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Multi-view images retain more information compared to single-view ones. The association of information between different views eliminates most of the ambiguity. So it is easier to achieve high-accuracy 3D human pose estimation in multi-view settings. Fusing the information of different views is the core problem of multi-view human pose estimation. Existing multi-view methods include two processes, 2D pose estimation and 3D pose reconstruction. The former consists of a pre-trained 2D pose estimator[10, 6], and multi-view information fusion occurs in the 3D pose reconstruction. Multi-view methods are divided into two categories according to the different ways of representing human pose. The first is the point-based method[26, 5, 12], which uses the spatial coordinates of the joint points as the human pose representation. This representation makes it easier to introduce temporal and body information explicitly. The second is the heatmap-based method, which uses the heatmap as the human pose representation[16, 36, 18], and learnable triangulation represents this method[18, 33]. The point representation is more concise and explicit but loses information, while the heatmap representation retains" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "more information but is not easily bounded explicitly. Our proposed Probabilistic Triangulation is applicable in both representations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.148, + 0.787, + 0.164 + ], + "angle": 0, + "content": "2.2. Uncalibrated 3D pose estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.171, + 0.892, + 0.609 + ], + "angle": 0, + "content": "Uncalibrated 3D pose estimation is a relatively new field[31, 2, 14, 20]. Takahashi's work[31] is a point-based method that establishes explicit constraints based on reprojection errors and the human body prior to transform the problem into an optimization problem and iteratively solve for the optimal solution. Lee's work[20] is also a point-based method, estimating the camera pose using the 3D pose estimated from different views. FLEX[14] estimates a time-invariant bone length while estimating joint rotations frame by frame and reconstructing 3D pose by forward kinematics. In this approach, the bone length is a link to fuse the multi-view information, and the rotation estimated for each view implicitly constrains the camera pose. However, this method cannot accurately estimate the camera pose due to the lack of transformation of the global coordinate system. Therefore, the output 3D pose is camera dependent. Bartol et al. [2] use a scoring network to evaluate the weight of the current proposal's camera pose or 3D human pose, and the final weighting is used to obtain a definite result. This method does not directly estimate the 3D human pose for uncalibrated scenes, but it can estimate the camera pose before and use other calibration methods to estimate the 3D human pose. This method does not directly estimate the 3D human pose for uncalibrated scenes, but it can estimate the camera pose before using other calibration methods to estimate the 3D human pose. Because the experiments for 3D human pose estimation in this work are for calibrated scenes, they are placed in the calibration method in the comparison experiments later in the paper." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.61, + 0.892, + 0.76 + ], + "angle": 0, + "content": "Current methods are limited to point-based representation. The heatmap-based representation retains more information than the point-based representation. This is because the accuracy of existing 2D human pose estimators is not sufficient for direct calibration. Small errors in points can be rapidly amplified by the camera pose estimation process, making the method ineffective. Our proposed camera pose distribution can effectively increase the robustness of the camera estimation process and support heatmap-based representation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.818, + 0.788 + ], + "angle": 0, + "content": "2.3. Probabilistic camera pose estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Camera pose estimation is a fundamental problem in computer vision[15]. PNP methods solve the case of known 3D-2D point pairs, while triangulation solves the case of known 2D-2D point pairs. Bundle adjustment transforms the camera matching problem into an optimization problem starting from reprojection errors[1]. However, matching feature points and solving them using classical meth" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14851" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.096, + 0.089, + 0.878, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.414, + 0.896, + 0.507 + ], + "angle": 0, + "content": "Figure 1: Probabilistic Triangulation for uncalibrated 3D human pose estimation pipeline. The inputs to the network are images from different views at the same moment. The 2D human pose heatmaps are estimated from the images and used to initialize the camera pose distribution. Then, Monte Carlo sampling is performed iteratively and each sampled camera parameter is computed by reprojection to obtain an explicit approximation of the 3D heatmap. The 3D heatmap calculates the weights of the sampled camera parameters. These weights are then used to update the pose distribution of the cameras. The weighted 3D heat map is used as input for the subsequent 3D pose reconstruction, for estimating the 3D human pose." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.532, + 0.47, + 0.622 + ], + "angle": 0, + "content": "ods does not apply to all scenarios. In the field of object and camera pose estimation, many works try to improve the network architecture that allows an end-to-end approach for pose estimation[8, 7]. The work EPro-PnP by Chen et al[9]. proposes a probabilistic PnP layer that allows the gradient back-propagated through the pose." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.622, + 0.47, + 0.711 + ], + "angle": 0, + "content": "Inspired by EPro-PnP, we use probability distributions to model camera pose. Compared with the camera pose represented by a single variable, the camera pose represented by the distribution has more robust performance and effectively mitigates the effect of 2D human pose detection errors." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.724, + 0.169, + 0.74 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.811 + ], + "angle": 0, + "content": "In this paragraph, we will review the multi-view uncalibrated 3D human pose estimation problem and introduce our Probabilistic Triangulation module. The overall pipeline is shown in Figure 1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.818, + 0.423, + 0.834 + ], + "angle": 0, + "content": "3.1. Uncalibrated 3D human pose estimation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.839, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Given that the images \\( I \\in \\mathbb{R}^{K \\times H \\times W} \\) from \\( K \\) views at a specific moment, our goal is to estimate the 3D pose \\( X^{3D} \\) of the target human from it. Given the camera pose \\( y = \\{y_{k} \\in SE(3) | k = 1 \\dots K\\} \\), the optimal \\( X^{3D} \\) will" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.532, + 0.892, + 0.668 + ], + "angle": 0, + "content": "make the reprojection error \\((3\\mathrm{D}\\rightarrow 2D)\\) small enough and fits the prior distribution of the human pose learned in the dataset. Therefore, the estimation algorithm is often divided into two parts, 2D pose estimation, and 3D pose reconstruction. In 2D pose estimation, a neural network \\(M_{1}\\) is employed to estimate the 2D pose \\(X^{2D} = M_1(I)\\) from each view. In the 3D pose reconstruction, the \\(X^{2D}\\) of different views are fused using a triangulation or a learnable triangulation method \\(M_{2}\\) to obtain \\(X^{3D} = M_2(X^{2D},y)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.668, + 0.892, + 0.699 + ], + "angle": 0, + "content": "Based on the reprojection error, the calibrated 3D human pose estimation is to solve an optimization problem:" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.712, + 0.892, + 0.736 + ], + "angle": 0, + "content": "\\[\n\\min _ {X ^ {3 D}} E \\left[ \\operatorname {p r o j} \\left(X ^ {3 D}, y\\right) - X ^ {2 D} \\right] \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.745, + 0.892, + 0.806 + ], + "angle": 0, + "content": "where \\( proj(\\cdot) \\) denotes the projection function. The neural network-based algorithm replaces \\( X^{3D} \\) in it with \\( M_2(X^{2D},y) \\), transforming the original optimization problem into solving for the optimal \\( M_2(\\cdot) \\) network parameters." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.806, + 0.892, + 0.867 + ], + "angle": 0, + "content": "When the camera pose \\( y \\) is an unknown parameter, \\( y \\) also becomes a variable to be optimized. Uncalibrated 3D human pose estimation can be similarly transformed into an optimization problem:" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.878, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\min _ {X _ {3 D}, y} \\quad E [ \\operatorname {p r o j} \\left(X ^ {3 D}, y\\right) - X ^ {2 D} ] \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "14852" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.086, + 0.319, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.143, + 0.231, + 0.285, + 0.245 + ], + "angle": 0, + "content": "(a) Implicit continuous." + }, + { + "type": "image", + "bbox": [ + 0.346, + 0.087, + 0.589, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.418, + 0.231, + 0.553, + 0.245 + ], + "angle": 0, + "content": "(b) Implicitly discrete." + }, + { + "type": "image", + "bbox": [ + 0.618, + 0.087, + 0.861, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.651, + 0.231, + 0.861, + 0.245 + ], + "angle": 0, + "content": "(c) Explicit discrete approximation." + }, + { + "type": "image_caption", + "bbox": [ + 0.323, + 0.257, + 0.645, + 0.273 + ], + "angle": 0, + "content": "Figure 2: 3D heatmap under different definitions" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.299, + 0.468, + 0.328 + ], + "angle": 0, + "content": "This problem is tough to solve and exists multiple solutions. There are three main reasons for this:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.334, + 0.468, + 0.367 + ], + "angle": 0, + "content": "1. If an iterative method is used to optimize \\( y \\) and \\( X^{3D} \\) alternately, the results tend to fall into local optimum." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.374, + 0.469, + 0.419 + ], + "angle": 0, + "content": "2. If a neural network is used to regress \\( y \\) and then solve for \\( X^{3D} \\), it will be constrained by the lack of diversity in the existing data set \\( y \\) to train." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.426, + 0.469, + 0.487 + ], + "angle": 0, + "content": "3. If the neural network is used to regress \\( X^{3D} \\) directly from the monocular view and then to solve \\( y \\), it will introduce the ill-conditioned problem of monocular scale ambiguity." + }, + { + "type": "list", + "bbox": [ + 0.089, + 0.334, + 0.469, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.493, + 0.469, + 0.539 + ], + "angle": 0, + "content": "In summary, we have to extract more information from the only known quantity \\( X_{2D} \\) to obtain a relatively accurate estimate of \\( y \\), i.e., a valid estimate \\( p(y|X^{2D}) \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.469, + 0.75 + ], + "angle": 0, + "content": "We use camera pose distribution approximation and Monte Carlo sampling to solve this problem. (see Probabilistic Triangulation part of Figure 1) Specifically, we maintain a proposal distribution \\( q(y) \\) for approximating the posterior distribution \\( p(y|X^{2D}) \\) of camera poses during one inference. Monte Carlo sampling is continuously performed on \\( q(y) \\), and the weights are calculated from the sampled points, and then \\( q(y) \\) is updated according to the weights. After several iterations, the results generated from the sampled points are weighted and averaged as the input to the 3D pose reconstruction network. We refer to this process as Probabilistic Triangulation. Figure 1 shows the pipeline of uncalibrated 3D human pose estimation after adding Probabilistic Triangulation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.469, + 0.84 + ], + "angle": 0, + "content": "The Probabilistic Triangulation can be flexibly embedded into any kind of calibrated 3D human pose estimation, reducing its dependence on camera pose for realistic scenarios. The differentiable computational process makes it possible to connect the 2D pose estimation and 3D pose reconstruction parts, allowing end-to-end training." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.848, + 0.321, + 0.864 + ], + "angle": 0, + "content": "3.2. Probabilistic Triangulation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "We detail the Probabilistic Triangulation using the pipeline in Figure 1 as an example. In subsequent repre" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.299, + 0.892, + 0.405 + ], + "angle": 0, + "content": "sentations, \\(y\\) is used to denote the camera pose and \\(y_{gt}\\) the ground truth of the camera pose. The 2D human pose is represented as \\(X^{2D} = \\{x_i^{2D}\\in \\mathbb{R}^{K\\times H'\\times W'}|i = 1\\ldots N\\}\\), and the 3D human pose is represented as \\(X^{3D} = \\{x_i^{3D}\\in \\mathbb{R}^{K\\times L_1\\times L_2\\times L_3}|i = 1\\ldots N\\}\\), where \\(H^{\\prime}\\) and \\(W^{\\prime}\\) denote the height and width of the 2D heatmap, and \\(L_{1},L_{2},L_{3}\\) denote the length, width, and height of the 3D heatmap." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.409, + 0.892, + 0.546 + ], + "angle": 0, + "content": "Camera pose distribution approximation In order to solve the optimization problem 2 with multiple solutions, we first normalized the multi-view camera pose to limit the range of solutions. Specifically, through an affine transformation of the whole coordinate system, the rotation matrix of the first view is changed into a unit matrix, the translation vector becomes a zero vector, and the translation vector of the second view has a modulus of one. The above affine changes can guarantee the uniqueness of the solution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.549, + 0.892, + 0.837 + ], + "angle": 0, + "content": "Each camera pose is represented as a 7-dimensional vector, where 3D rotations are represented using unit quaternions and 3D translations are represented using 3D vectors. To better express the camera distribution, the angular central Gaussian distribution is introduced to represent the 3D rotation [34], and the multivariate t-distribution is introduced to represent the 3D translation. The \\( p(y|X^{2D}) \\) is calculated for each sampling point \\( y \\) to obtain the covariance matrix of the angular central Gaussian distribution, and the mean and covariance matrix of the multivariate t-distribution, which in turn updates the parameters. The initial parameters of the distributions are first estimated based on the 2D human pose using the eight-point method. Then, a portion is sampled around the initial value and another portion is sampled around the entire camera domain. The distribution is initialized by the sampling result. Since the input of a single frame may cause a large error in the eight-point method, and initializing the distribution in this way increases the robustness of the algorithm." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Monte Carlo sampling We assume that the 2D heatmap is the marginal distribution of the 3D heatmap along the projection direction, and the problem can be transformed into an optimization problem based on the reprojection error:" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14853" + } + ], + [ + { + "type": "equation", + "bbox": [ + 0.08, + 0.117, + 0.486, + 0.171 + ], + "angle": 0, + "content": "\\[\n\\min _ {y, X ^ {3 D}} \\quad \\sum_ {i} ^ {N} \\int_ {\\sigma_ {i}} \\left\\| x _ {i} ^ {2 D} \\left(\\sigma_ {i}\\right) - \\int_ {p r o j \\left(z, y _ {i}\\right) = \\sigma_ {i}} x ^ {3 D} (z) \\mathrm {d} z \\right\\| _ {2} \\mathrm {d} \\sigma_ {i} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.172, + 0.469, + 0.321 + ], + "angle": 0, + "content": "where \\(z\\) denotes the body element in 3D space, \\(\\sigma_{i}\\) denotes the area element of the \\(i\\)th camera plane, and \\(proj(\\cdot)\\) denotes the projection function. A more general heatmap representation is adopted here, where \\(x^{3D}\\) and \\(x^{2D}\\) are considered as the probability density functions of the heatmap distribution. In practice, the heatmap is often stored in a discrete way, and the integrals need to be discretized as well. However, it is difficult to establish the constraints between \\(y\\) and \\(X^{3D}\\) explicitly, making the above optimization problem difficult to solve." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.324, + 0.469, + 0.354 + ], + "angle": 0, + "content": "Therefore, we use an approximate 3D heatmap explicitly defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.37, + 0.47, + 0.42 + ], + "angle": 0, + "content": "\\[\nx ^ {3 D} (z) = \\frac {1}{N} \\sum_ {\\substack {i \\\\ p r o j (z, y _ {i}) = \\sigma_ {i}}} ^ {N} x _ {i} ^ {2 D} (\\sigma_ {i}) \\tag{4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.179, + 0.422, + 0.39, + 0.449 + ], + "angle": 0, + "content": "\\[\nx _ {i} ^ {2 D} (\\sigma_ {i}) = \\max _ {p r o j (z, y _ {i}) = \\sigma_ {i}} x ^ {3 D} (z)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.458, + 0.469, + 0.564 + ], + "angle": 0, + "content": "This definition is similar to the volume of the learnable triangulation, with the advantage that \\( X^{3D} \\) can be computed explicitly and differentiably from \\( y \\) and \\( X^{2D} \\). It also has some physical meaning as far as the location of the extreme points taken is similar to the original representation. The visualization of the 3D heatmap under different definitions is shown in Figure 2." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.565, + 0.469, + 0.611 + ], + "angle": 0, + "content": "The generated \\( X^{3D} \\) retains the information of the heatmap and can be used as input for subsequent networks. Thus, the problem is simplified to:" + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.638, + 0.469, + 0.712 + ], + "angle": 0, + "content": "\\[\n\\min _ {y} \\sum_ {i} ^ {N} \\| \\underbrace {\\sum_ {z} \\left(x ^ {3 D} (z) x _ {i} ^ {2 D} \\left(\\sigma_ {i}\\right)\\right) ^ {2} \\left(x _ {i} ^ {2 D} \\left(\\sigma_ {i}\\right) - x ^ {3 D} (z)\\right)} _ {f _ {i} (y)} \\| _ {2} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.714, + 0.468, + 0.744 + ], + "angle": 0, + "content": "The reprojection error is employed as the negative logarithm of the likelihood function \\( p(X_{2D}|y) \\)." + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.759, + 0.469, + 0.8 + ], + "angle": 0, + "content": "\\[\np \\left(X ^ {2 D} | y\\right) = \\exp - \\sum_ {i} ^ {N} \\| f _ {i} (y) \\| _ {2} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.811, + 0.469, + 0.855 + ], + "angle": 0, + "content": "Suppose that the camera pose \\( p(y) \\) is subject to a uniform distribution, \\( p(y|X^{2D}) \\) can be calculated by Bayesian formula:" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.87, + 0.469, + 0.906 + ], + "angle": 0, + "content": "\\[\np (y | X ^ {2 D}) = \\frac {p \\left(X ^ {2 D} \\mid y\\right)}{E \\left[ p \\left(X ^ {2 D} \\mid y\\right) \\right]} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "The calculation of denominator expectation can be estimated by Monte Carlo sampling approximation. The specific calculation formula is as follows." + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.16, + 0.892, + 0.203 + ], + "angle": 0, + "content": "\\[\nE \\left[ p \\left(X ^ {2 D} | y\\right) \\right] \\approx \\frac {1}{M} \\sum_ {j} ^ {M} q \\left(y _ {j}\\right) p \\left(X ^ {2 D} | y\\right), y _ {j} \\sim q (y) \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.214, + 0.891, + 0.244 + ], + "angle": 0, + "content": "where \\(M\\) denotes the total number of samples. Then, \\(q(y)\\) is updated using the computed \\(p(y|X^{2D})\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.244, + 0.892, + 0.303 + ], + "angle": 0, + "content": "Finally, the normalized \\( q(y) \\) is used as the weight and the \\( X^{3D} \\) generated by all sampled points \\( y \\) is weighted and averaged as the input to the subsequent 3D pose reconstruction network." + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.315, + 0.891, + 0.354 + ], + "angle": 0, + "content": "\\[\nX ^ {3 D} = \\frac {\\sum_ {j} q \\left(y _ {j}\\right) X _ {j} ^ {3 D}}{\\sum_ {j} q \\left(y _ {j}\\right)} \\tag {9}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.368, + 0.643, + 0.384 + ], + "angle": 0, + "content": "3.3. Training Loss" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.391, + 0.891, + 0.421 + ], + "angle": 0, + "content": "The entire training process includes two loss terms: \\(\\mathcal{L}_{3d}\\) and \\(\\mathcal{L}_{cam}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.422, + 0.892, + 0.467 + ], + "angle": 0, + "content": "We measure the difference between the true distribution of camera pose \\( z(y) \\) and the posterior distribution \\( p(y|X^{2D}) \\) using KL divergence." + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.489, + 0.891, + 0.552 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {c a m} = D _ {K L} (z (y) \\| p (y | X ^ {2 D})) \\\\ = - \\frac {1}{2} \\sum_ {i} ^ {N} \\| f _ {i} \\left(y _ {g t}\\right) \\| _ {2} + \\log E [ p \\left(X ^ {2 D} | y\\right) ] \\tag {10} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.562, + 0.89, + 0.592 + ], + "angle": 0, + "content": "where the expectation of the second half is also obtained by the calculation of the equation 8." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.592, + 0.891, + 0.651 + ], + "angle": 0, + "content": "The 3D human pose estimation loss is the same as previous works[18], which encourages the predicted 3d poses to be close to the ground truth. The formula can be summarized as follow:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.662, + 0.89, + 0.694 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {3 d} = \\left\\| \\operatorname {s o f t a r g m a x} \\left(X ^ {3 D}\\right) - X _ {g t} \\right\\| _ {1} - \\beta \\cdot \\log \\left(X ^ {3 D} \\left(X _ {g t}\\right)\\right) \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.695, + 0.891, + 0.739 + ], + "angle": 0, + "content": "In end-to-end training, we simultaneously optimize these two loss terms to train the networks, and the total loss function can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.752, + 0.891, + 0.768 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\mathcal {L} _ {\\text {c a m}} + \\lambda_ {2} \\mathcal {L} _ {3 d} \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.779, + 0.881, + 0.795 + ], + "angle": 0, + "content": "where the \\(\\lambda_{1} = 1\\) and \\(\\lambda_{2} = 0.1\\) in our experiment setting." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.808, + 0.633, + 0.825 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.686, + 0.847 + ], + "angle": 0, + "content": "4.1. Dataset & Metrics" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We conducted experiments on two of the most commonly used 3D human pose datasets available today, Human3.6M[17] and CMU Panoptic[19, 29, 35]. We used" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14854" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.089, + 0.88, + 0.284 + ], + "angle": 0, + "content": "
MethodDir.Disc.EatGreetPhonePhotoPosePurch.SitSitD.SmokeWaitWalkD.WalkWalkT.Mean
Calibration method
Remelli et al.[28]27.332.125.026.529.335.428.831.636.431.731.229.926.933.730.430.2
Bartol et al.[2]27.528.429.327.530.128.127.930.832.932.530.829.428.530.530.129.1
He et al. [16]25.727.723.724.826.931.424.926.528.831.728.226.423.628.323.526.9
Qiu et al. [26]24.026.723.224.324.822.824.128.632.126.931.025.625.028.024.426.2
Ma et al. [22]24.426.423.421.125.223.224.733.829.826.426.824.223.226.123.325.8
Iskakov et al.[18]19.920.018.918.520.519.418.422.122.528.721.220.819.722.120.220.8
Uncalibration method
Gordon et al.[14]22.023.624.926.730.635.725.132.929.532.532.626.534.726.027.730.2
Ours method24.025.426.630.432.120.120.536.540.129.527.427.620.824.122.027.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.293, + 0.893, + 0.325 + ], + "angle": 0, + "content": "Table 1: Results of the evaluation on the Human3.6M dataset. The table shows the MPJPE in millimeters for the published state-of-the-art calibrated and uncalibrated methods." + }, + { + "type": "table", + "bbox": [ + 0.141, + 0.347, + 0.408, + 0.487 + ], + "angle": 0, + "content": "
MethodMPJPE,mm
Calibrated method
Iskakov et al. Algebraic[18]21.3
Iskakov et al. Volumetric[18]13.7
Uncalibrated method
Bartol et al. [2]25.4
Our method24.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.497, + 0.47, + 0.529 + ], + "angle": 0, + "content": "Table 2: Results of the MPJPE on the CMU Panoptic dataset ( using four cameras)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.574, + 0.47, + 0.68 + ], + "angle": 0, + "content": "the 17-joint MPJPE (Mean Per Joint Position Error) as a metric to evaluate our method. In training, we normalize the ground truth according to the method in section3.2 to ensure the uniqueness in the camera pose solution. In validation, the estimated 3D human pose is denormalized to the original coordinate system to ensure the correctness of the MPJPE calculation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.718, + 0.292, + 0.733 + ], + "angle": 0, + "content": "4.2. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We added the Probabilistic Triangulation based on the work learnable triangulation by Iskakov et al.[18] to realize uncalibrated 3D human pose estimation. The same experimental parameter settings as the learnable triangulation method were used. As with learnable triangulation, our method uses predictions from the algebraic triangulation. Our method can also be fine-tuned and be trained in an end-to-end manner. \\( q(y) \\) is initialized using a uniform distribution. The number of iterations is four, and the number of Monte Carlo samples is 256." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.35, + 0.8, + 0.367 + ], + "angle": 0, + "content": "4.3. Comparisons with State-of-the-art" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.376, + 0.892, + 0.692 + ], + "angle": 0, + "content": "We compared the existing state-of-the-art calibrated and uncalibrated 3D pose estimation algorithms. The evaluation results on the Human3.6M dataset and the CMU Panoptic dataset are shown in Table 1 and Table 2, respectively. The experimental results show that the MPJPE of our method has outperformed the state-of-the-art uncalibrated approaches and achieved comparable performance to calibrated methods. It is worth noting that our method achieves better results in most scenarios of uncalibrated setting (see Table 1), but the results are poor in the Purch. and Sit. sub-datasets. This is because there are more occlusions in these two subsets, resulting in the 2D joint estimation being inaccurate, which further affects the estimation of the camera parameter distribution. Therefore, the final accumulated error affects the 3D human pose estimation performance. Inferring the camera parameters from the features of the detected human inevitably leads to estimation results depending on the capability of the human feature detector. However, our method still outperforms existing uncalibrated methods in terms of overall MPJPE for both datasets." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.71, + 0.838, + 0.725 + ], + "angle": 0, + "content": "4.4. Evaluation on Camera Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To evaluate the capability of our camera pose estimation, we have conducted comparisons with some classical camera parameter estimation algorithms on the Human3.6M dataset. Due to the large parallax between different camera views, we choose 2D human keypoints estimated from 20 consecutive frames as image feature points to solve the camera pose parameters. We compare our camera estimation with Bundle Adjustment[32] and RANSAC 8-point algorithm[30]. Bundle Adjustment choose to minimize the reprojection error using the LM algorithm to find the camera parameters and the RANSAC 8-point algorithm uses the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14855" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.096, + 0.312, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.143, + 0.429, + 0.285, + 0.442 + ], + "angle": 0, + "content": "(a) Bundle Adjustment." + }, + { + "type": "image", + "bbox": [ + 0.389, + 0.096, + 0.583, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.389, + 0.428, + 0.581, + 0.442 + ], + "angle": 0, + "content": "(b) RANSAC 8-point algorithm." + }, + { + "type": "image", + "bbox": [ + 0.664, + 0.091, + 0.852, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.705, + 0.428, + 0.807, + 0.441 + ], + "angle": 0, + "content": "(c) Ours method." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.454, + 0.894, + 0.501 + ], + "angle": 0, + "content": "Figure 3: Visualization of the camera pose parameters and 3D human pose obtained by different algorithms. The quadrilateral cone indicates the camera pose parameters, the gray part indicates the ground truth, and the colored part indicates the prediction results of different algorithms." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.527, + 0.47, + 0.722 + ], + "angle": 0, + "content": "8-point method to find the fundamental matrix after screening out the outliers by RANSAC, and then uses the eigenvalue decomposition to find the camera pose. We provide some visualization examples in Figure 3. From the Figure 3, we can see that Bundle Adjustment often falls into the local optimal solution, resulting in poor camera poses. The RANSAC 8-point algorithm can remove outliers, but the estimation of the camera pose is sensitive to 2D human pose estimation, which will lead to accumulated errors when reconstructing 3D human poses. The 3D human and camera pose estimation results are more robust and accurate when introducing our Probabilistic Triangulation (see (c) of Figure 3)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.724, + 0.471, + 0.837 + ], + "angle": 0, + "content": "Table 3 shows more detailed results of camera pose evaluation, using the same experimental setup as [2]. Among the evaluation metrics used: 1. 3D estimation error \\((\\mathrm{mm})\\) \\(E_{3D} = E[\\| x^{\\hat{3} D} - x^{3D}\\| _2]\\) ; 2. Projection 2D error \\((\\mathrm{mm})E_{2D} = E[\\| x^{\\hat{2} D} - x^{2D}\\| _2]\\) ; 3. Camera rotation error \\(E_{R} = E[\\| \\hat{q} -q\\|_{2}]\\) ; 4. Camera translation error (mm) \\(E_{t} = E[\\| \\hat{t} -t\\|_{2}]\\)" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.317, + 0.863 + ], + "angle": 0, + "content": "4.5. Cross-dataset experiments" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To test the generalization ability of Probabilistic Triangulation across datasets, we segment CMU Panoptic and" + }, + { + "type": "table", + "bbox": [ + 0.532, + 0.524, + 0.864, + 0.602 + ], + "angle": 0, + "content": "
methodsE3D↓E2D↓ER↓Et↓
BA736.82130.180.02546.87
RANSAC 8-point97.5050.140.0125.30
Our methods27.805.980.00432.71
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.612, + 0.892, + 0.643 + ], + "angle": 0, + "content": "Table 3: Quantitative experiments on camera pose estimation on the Human3.6M dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.654, + 0.892, + 0.837 + ], + "angle": 0, + "content": "Human36M into five sub-datasets in the same way as Bartol et al.[2]. Cross-dataset experiments are conducted between these sub-datasets two by two. It was found that there was no significant loss of accuracy between the CMU Panoptic sub-datasets even after segmentation (this is because the distribution between the sub-datasets of the CMU Panoptic dataset is very similar). However, the results trained from the CMU dataset have a significant loss of accuracy on Human3.6M. Table 4 shows the generalization ability of Probabilistic Triangulation and Bartol et al.[2] from the CMU dataset to the Human3.6M dataset. Probabilistic Triangulation exhibits stronger generalization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.855, + 0.863 + ], + "angle": 0, + "content": "4.6. Ablation study on the number of cameras" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.894, + 0.902 + ], + "angle": 0, + "content": "We show the results of the ablation study in Table 5. After training on 4-view data, our method generalizes well to" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14856" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.096, + 0.096, + 0.273, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.28, + 0.097, + 0.458, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.465, + 0.096, + 0.644, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.652, + 0.095, + 0.829, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.837, + 0.093, + 0.877, + 0.237 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.257, + 0.895, + 0.304 + ], + "angle": 0, + "content": "Figure 4: Visualization of the sampled points in four iterations after dimensionality reduction using t-SNE. From left to right corresponds to the sampled values after four iterations. The value of the sampled point is the logarithmic sampling loss, and the smaller the value means that the sampled point is closer to the true value." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.327, + 0.48, + 0.484 + ], + "angle": 0, + "content": "
MethodTrainSelf-TestH36M-Testdiff
Bartol et al.[2]CMU125.833.530%
CMU226.033.428%
CMU325.031.024%
CMU425.132.528%
Ours methodCMU124.630.825%
CMU223.729.123%
CMU324.129.221%
CMU424.931.125%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.496, + 0.471, + 0.618 + ], + "angle": 0, + "content": "Table 4: Experiments on generalization ability between datasets (MPJPE in mm). The CMU Panoptic dataset was split into four sub-datasets with different number of cameras and different spatial distributions of cameras. The models were trained on the four datasets separately, and the results were evaluated on their own test set and the Human3.6M test set. The last column represents the cross-data accuracy decline rate." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.47, + 0.706 + ], + "angle": 0, + "content": "3-view and 2-view because the network has seen rich information during training. There is some performance degradation when the model is trained on 2-view and tested on 3-view and 4-view as shown in Table 5." + }, + { + "type": "table", + "bbox": [ + 0.127, + 0.715, + 0.422, + 0.778 + ], + "angle": 0, + "content": "
2-view3-view4-view
Training on 2-view29.542.439.2
Training on 4-view32.629.327.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.788, + 0.471, + 0.818 + ], + "angle": 0, + "content": "Table 5: Ablation study on Human3.6M for camera numbers (MPJPE, mm)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.353, + 0.849 + ], + "angle": 0, + "content": "4.7. Ablation study on each module" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "In order to demonstrate the irreplaceable role that probabilistic triangularization plays in camera pose estimation and 3D human reconstruction in uncalibrated 3D human" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.329, + 0.892, + 0.389 + ], + "angle": 0, + "content": "pose estimation. We design two ablation experiments to remove the influence of the rest of the network on the results and to demonstrate the role of Probabilistic Triangulation better." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.391, + 0.892, + 0.482 + ], + "angle": 0, + "content": "First, we use 2D heatmaps ground truth as the input of Probabilistic Triangulation to eliminate the effect of 2D backbone on the results. Also, the upper bound of our method is shown (see Table 6 middle). The table shows that our method achieves comparable results to the calibration method [18] when given the 2D ground truth." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.483, + 0.892, + 0.572 + ], + "angle": 0, + "content": "The 3D error still cannot reach zero under the condition of using 2D ground truth because there is a theoretical upper limit to the accuracy of the voxel structure. However, the 2D human pose estimator error cannot be avoided, and the better robustness of the voxel structure to error is the reason it was chosen." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.576, + 0.892, + 0.788 + ], + "angle": 0, + "content": "In addition, we demonstrate the necessity of introducing the camera pose estimation module by comparing it with Iskaov et al. (V2V network and triangulation). We rotated the world coordinate system \\((0^{\\circ}\\) to \\(180^{\\circ}\\) randomly around the vertical axis and \\(0^{\\circ}\\) to \\(45^{\\circ}\\) randomly around the pitch) to change the values of the camera's external parameters, resulting in a new test set called \"Test*\" in Table 6. We can find that only using a V2V network and triangulation will make the network overfit the camera poses, resulting in performance degradation. Our method does not require the input of camera poses, so changes in the world coordinate system do not affect our method's final pose estimation results. It demonstrates that our camera estimation module, i.e., the main contribution, is necessary and reasonable." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.801, + 0.796, + 0.817 + ], + "angle": 0, + "content": "4.8. Visualization of Sampling Process" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.9 + ], + "angle": 0, + "content": "In order to visualize the sampling process in the Probabilistic Triangulation, the 256 sampling points of each iteration are embedded by t-SNE and plotted in Figure 4. From the figure, as the iteration proceeds, the approximation of the camera distribution becomes more and more ac" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14857" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.104, + 0.089, + 0.444, + 0.151 + ], + "angle": 0, + "content": "
Baseline2D GTTest*
Iskakov et al.20.816.325.12
Our methods27.818.527.8
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.161, + 0.47, + 0.236 + ], + "angle": 0, + "content": "Table 6: Pose estimation results (MPJPE, mm) on different 2D and test settings. The middle two columns show the results of 3D pose estimation using the 2D estimator and 2D GT, respectively. The rightmost column shows the estimation results on the Test* set." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.249, + 0.468, + 0.37 + ], + "angle": 0, + "content": "curate, the sampled points are closer to the ground truth, and the sampling loss keeps decreasing. At the same time, the whole camera pose space is not smooth, and there are many local optimums and pseudo-solutions. The 2D human pose estimator generates noise, making the classical camera pose estimation more likely to fall into local optimal solutions. Distributed representation of camera pose (Probabilistic Triangulation) can alleviate this problem." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.371, + 0.468, + 0.551 + ], + "angle": 0, + "content": "Furthermore, from Figure 4, the sampling points are concentrated around a few extreme points as the iteration parameters increase. This is because an incremental solution exists to the camera pose estimation, so there are multiple extreme points. However, only one of them has real physical significance, whereas, in the projection process, these extreme points produce the same projection result. The distribution also tends to converge to a single extreme point if an initial value is used to initialize the camera pose distribution, and the sampling points of the distribution are spread out to appear near multiple extreme points if a uniform distribution is used to initialize the distribution." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.563, + 0.317, + 0.579 + ], + "angle": 0, + "content": "4.9. Generalize to Wide Scenes" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.587, + 0.468, + 0.709 + ], + "angle": 0, + "content": "To demonstrate the generalization of our Probabilistic Triangulation in the wild scenes, we use a model trained from the CMU Panoptic dataset and test it on the natural scenes. Two iPhones with a \\(26\\mathrm{mm}\\) primary camera were used for the shooting, and the intrinsic parameters were read using the swift function. The results are shown in Figure 5. Our method remains in effect even when the camera space location and the number of cameras change." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.724, + 0.334, + 0.74 + ], + "angle": 0, + "content": "5. Conclusions and limitations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We propose a novel Probabilistic Triangulation module for multi-view 3D human pose estimation, which enables the existing calibrated methods to reduce the dependence on calibration and can be applied to uncalibrated wild scenes. Extensive experiments demonstrate that the 3D human pose estimation based on our Probabilistic Triangulation can achieve state-of-the-art performance when compared to uncalibrated methods. And the employment of camera pose distribution and Monte Carlo sampling alleviates the problem of easy access to local optimums and pseudo-solutions" + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.094, + 0.861, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.354, + 0.892, + 0.415 + ], + "angle": 0, + "content": "Figure 5: Our method demonstrates the results in a non-calibrated wild scene. The first and second columns represent the two iPhone camera views, and the third column shows the estimated camera pose and 3D human pose." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.441, + 0.892, + 0.562 + ], + "angle": 0, + "content": "in camera pose estimation. Since our Probabilistic Triangulation does not take the camera pose parameters as input, it is possible to build the multi-view 3D human pose estimation system in wild scenes and achieve a high-accurate capture. In the wild scenes, the Probabilistic Triangulation is not affected by the spatial location changes and the number of cameras. It can be directly applied to uncalibrated scenes after training with calibrated data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.562, + 0.892, + 0.819 + ], + "angle": 0, + "content": "The main limitation of our method is that it can only be applied to single-person scenes. Extending to multi-person scenarios requires taking into account the cross-view matching problem, which is difficult to solve in the absence of a camera pose. In addition, although the Probabilistic Triangulation does not require the camera pose as input during validation, the ground truth of the 3D human pose and the camera pose are used in the training process, and these data need to be obtained from the dataset of the calibration scene. In fact, the ground truth of camera pose is not directly involved in the training, but indirectly guides the 2D pose estimation network learning through cross-view information. The ground truth of the 3D human pose influences the 2D pose estimation network and enables the 3D pose reconstruction network to learn the human prior and integrate the information generated by previous sampling." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.848, + 0.891, + 0.894 + ], + "angle": 0, + "content": "Acknowledgements This work was supported by National Key Research and Development Program of China (NO. 2022YFB3303202)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14858" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.468, + 0.143 + ], + "angle": 0, + "content": "[1] Sameer Agarwal and Keir Mierle. Others, \"ceres solver\". 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Advances in Neural Information Processing Systems, 34:13153-13164, 2021." + }, + { + "type": "ref_text", + "bbox": [ + 0.08, + 0.732, + 0.47, + 0.8 + ], + "angle": 0, + "content": "[37] Jinlu Zhang, Zhigang Tu, Jianyu Yang, Yujin Chen, and Jun-song Yuan. Mixste: Seq2seq mixed spatio-temporal encoder for 3d human pose estimation in video. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13232-13242, 2022." + }, + { + "type": "ref_text", + "bbox": [ + 0.08, + 0.803, + 0.47, + 0.871 + ], + "angle": 0, + "content": "[38] Ce Zheng, Sijie Zhu, Matias Mendieta, Taojiannan Yang, Chen Chen, and Zhengming Ding. 3d human pose estimation with spatial and temporal transformers. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 11656-11665, 2021." + }, + { + "type": "ref_text", + "bbox": [ + 0.08, + 0.874, + 0.47, + 0.901 + ], + "angle": 0, + "content": "[39] Wentao Zhu, Xiaoxuan Ma, Zhaoyang Liu, Libin Liu, Wayne Wu, and Yizhou Wang. Motionbert: Unified pretraining for" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.092, + 0.892, + 0.119 + ], + "angle": 0, + "content": "human motion analysis. arXiv preprint arXiv:2210.06551, 2022." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14860" + } + ] +] \ No newline at end of file diff --git a/2023/Probabilistic Triangulation for Uncalibrated Multi-View 3D Human Pose Estimation/b6b4e04e-10fb-49dc-be18-fbc2e2b53da9_origin.pdf b/2023/Probabilistic Triangulation for Uncalibrated Multi-View 3D Human Pose Estimation/b6b4e04e-10fb-49dc-be18-fbc2e2b53da9_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..468483d9eeae344aaae489a17c9893ceff3641aa --- /dev/null +++ b/2023/Probabilistic Triangulation for Uncalibrated Multi-View 3D Human Pose Estimation/b6b4e04e-10fb-49dc-be18-fbc2e2b53da9_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:70b442dac1c15b7ab493a5917cce4e39b430a3cf6829893d30d606e1daac745d +size 4541774 diff --git a/2023/Probabilistic Triangulation for Uncalibrated Multi-View 3D Human Pose Estimation/full.md b/2023/Probabilistic Triangulation for Uncalibrated Multi-View 3D Human Pose Estimation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..9c5d99870667ad2d839f1ce780d05f582c0c3a06 --- /dev/null +++ b/2023/Probabilistic Triangulation for Uncalibrated Multi-View 3D Human Pose Estimation/full.md @@ -0,0 +1,354 @@ +# Probabilistic Triangulation for Uncalibrated Multi-View 3D Human Pose Estimation + +Boyuan Jiang $^{1,2}$ , Lei Hu $^{1,2}$ Shihong Xia $^{1,2*}$ $^{1}$ Institute of Computing Technology, Chinese Academy of Sciences; $^{2}$ University of Chinese Academy of Sciences {jiangboyuan20s, hulei19z, xsh}@ict.ac.cn + +# Abstract + +3D human pose estimation has been a long-standing challenge in computer vision and graphics, where multiview methods have significantly progressed but are limited by the tedious calibration processes. Existing multi-view methods are restricted to fixed camera pose and therefore lack generalization ability. This paper presents a novel Probabilistic Triangulation module that can be embedded in a calibrated 3D human pose estimation method, generalizing it to uncalibration scenes. The key idea is to use a probability distribution to model the camera pose and iteratively update the distribution from 2D features instead of using camera pose. Specifically, We maintain a camera pose distribution and then iteratively update this distribution by computing the posterior probability of the camera pose through Monte Carlo sampling. This way, the gradients can be directly back-propagated from the 3D pose estimation to the 2D heatmap, enabling end-to-end training. Extensive experiments on Human3.6M and CMU Panoptic demonstrate that our method outperforms other uncalibration methods and achieves comparable results with state-of-the-art calibration methods. Thus, our method achieves a trade-off between estimation accuracy and generalizability. Our code is in https://github.com/bymaths/probabilistic_triangulation + +# 1. Introduction + +3D human pose estimation is a fundamental tool in many downstream applications of computer vision and computer graphics, such as motion recognition[13], human-computer interaction[23], movie game animation[4], virtual reality[24], etc. The development of these fields requires a more accurate, convenient, and robust 3D human pose estimation algorithm. + +Recently, RGB-based pose estimation has become the + +trend because of its convenience, wide application scenarios, and low cost[27]. These methods can be divided into two categories: single-view and multi-view methods. Although single-view methods[39, 37, 11, 38, 25] have more widespread application scenarios, the lack of depth information makes single-view estimation of 3D human pose an ill-posed problem, especially when dealing with occlusions and multi-person scenes[21]. Multi-view methods[18, 16, 36, 33, 2, 14, 31, 20] can achieve more accurate results than single view-based methods because multi-view cameras can restore the depth information as well as the occluded parts. + +However, the multi-view approach faces several issues when applied in practice. First, multi-view methods require synchronized and calibrated cameras, which complicates the process. Second, existing datasets for multi-view human pose estimation lack the diversity of camera external parameters. This results in the trained model cannot generalize well to unseen camera parameters, thus requiring re-annotation and re-training once the camera configurations change. + +To alleviate the above issues, we propose Probabilistic Triangulation module for uncalibrated 3D human pose estimation. Our module enables the network to get rid of camera pose parameters during the training process, which results in better generalization performance to be applied to wild scenes. The main idea is to use a probability distribution to model the camera pose, making the whole process differentiable. Specifically, we transform the uncalibrated 3D human pose estimation into a nonlinear optimization problem based on the reprojection error. The camera pose distribution is estimated from the 2D pose features, and then the posterior probability of the camera pose is computed by Monte Carlo sampling to iteratively update this distribution. + +We conducted extensive experiments on two benchmark datasets (Human3.6M[17] and CMU Panoptic[19, 29, 35]) to demonstrate that our method outperforms other uncalibrated methods and achieves comparable results with the state-of-the-art calibration methods, which indicates that + +our method improves the generalized ability to camera parameters in multi-view human pose estimation while maintaining high accuracy. + +In summary, our contributions are mainly three-fold. + +- We propose Probabilistic Triangulation that can generalize the calibrated 3D human pose estimation algorithm to uncalibrated scenes to estimate 3D human pose in the absence of camera pose. +- We propose an approximation method for camera pose distribution and an updated distribution method based on Monte Carlo sampling. It is used to model the camera pose of uncalibrated scenes with accuracy and robustness beyond classical algorithms. +- We conducted extensive experiments on two benchmark datasets (Human3.6M and CMU Panoptic) to demonstrate the accuracy, generalization capability, and applicability of Probabilistic Triangulation to wild scenes. + +# 2. Related work + +# 2.1. Calibrated 3D pose estimation + +3D human pose estimation is a vital problem in computer vision and graphics, where the single view-based method has been a research spotlight due to the convenience and comprehensive application scenarios of a monocular camera. To alleviate the ambiguity problem caused by occlusion and the lack of depth information, many single view-based works[37, 11, 38, 25, 3] have tried to introduce the temporal information or body-related prior during training. + +Multi-view images retain more information compared to single-view ones. The association of information between different views eliminates most of the ambiguity. So it is easier to achieve high-accuracy 3D human pose estimation in multi-view settings. Fusing the information of different views is the core problem of multi-view human pose estimation. Existing multi-view methods include two processes, 2D pose estimation and 3D pose reconstruction. The former consists of a pre-trained 2D pose estimator[10, 6], and multi-view information fusion occurs in the 3D pose reconstruction. Multi-view methods are divided into two categories according to the different ways of representing human pose. The first is the point-based method[26, 5, 12], which uses the spatial coordinates of the joint points as the human pose representation. This representation makes it easier to introduce temporal and body information explicitly. The second is the heatmap-based method, which uses the heatmap as the human pose representation[16, 36, 18], and learnable triangulation represents this method[18, 33]. The point representation is more concise and explicit but loses information, while the heatmap representation retains + +more information but is not easily bounded explicitly. Our proposed Probabilistic Triangulation is applicable in both representations. + +# 2.2. Uncalibrated 3D pose estimation + +Uncalibrated 3D pose estimation is a relatively new field[31, 2, 14, 20]. Takahashi's work[31] is a point-based method that establishes explicit constraints based on reprojection errors and the human body prior to transform the problem into an optimization problem and iteratively solve for the optimal solution. Lee's work[20] is also a point-based method, estimating the camera pose using the 3D pose estimated from different views. FLEX[14] estimates a time-invariant bone length while estimating joint rotations frame by frame and reconstructing 3D pose by forward kinematics. In this approach, the bone length is a link to fuse the multi-view information, and the rotation estimated for each view implicitly constrains the camera pose. However, this method cannot accurately estimate the camera pose due to the lack of transformation of the global coordinate system. Therefore, the output 3D pose is camera dependent. Bartol et al. [2] use a scoring network to evaluate the weight of the current proposal's camera pose or 3D human pose, and the final weighting is used to obtain a definite result. This method does not directly estimate the 3D human pose for uncalibrated scenes, but it can estimate the camera pose before and use other calibration methods to estimate the 3D human pose. This method does not directly estimate the 3D human pose for uncalibrated scenes, but it can estimate the camera pose before using other calibration methods to estimate the 3D human pose. Because the experiments for 3D human pose estimation in this work are for calibrated scenes, they are placed in the calibration method in the comparison experiments later in the paper. + +Current methods are limited to point-based representation. The heatmap-based representation retains more information than the point-based representation. This is because the accuracy of existing 2D human pose estimators is not sufficient for direct calibration. Small errors in points can be rapidly amplified by the camera pose estimation process, making the method ineffective. Our proposed camera pose distribution can effectively increase the robustness of the camera estimation process and support heatmap-based representation. + +# 2.3. Probabilistic camera pose estimation + +Camera pose estimation is a fundamental problem in computer vision[15]. PNP methods solve the case of known 3D-2D point pairs, while triangulation solves the case of known 2D-2D point pairs. Bundle adjustment transforms the camera matching problem into an optimization problem starting from reprojection errors[1]. However, matching feature points and solving them using classical meth + +![](images/2d4721dfbcf920343409bb46edbf0c2925505c4db7b6d17c2e27a478b1553189.jpg) +Figure 1: Probabilistic Triangulation for uncalibrated 3D human pose estimation pipeline. The inputs to the network are images from different views at the same moment. The 2D human pose heatmaps are estimated from the images and used to initialize the camera pose distribution. Then, Monte Carlo sampling is performed iteratively and each sampled camera parameter is computed by reprojection to obtain an explicit approximation of the 3D heatmap. The 3D heatmap calculates the weights of the sampled camera parameters. These weights are then used to update the pose distribution of the cameras. The weighted 3D heat map is used as input for the subsequent 3D pose reconstruction, for estimating the 3D human pose. + +ods does not apply to all scenarios. In the field of object and camera pose estimation, many works try to improve the network architecture that allows an end-to-end approach for pose estimation[8, 7]. The work EPro-PnP by Chen et al[9]. proposes a probabilistic PnP layer that allows the gradient back-propagated through the pose. + +Inspired by EPro-PnP, we use probability distributions to model camera pose. Compared with the camera pose represented by a single variable, the camera pose represented by the distribution has more robust performance and effectively mitigates the effect of 2D human pose detection errors. + +# 3. Method + +In this paragraph, we will review the multi-view uncalibrated 3D human pose estimation problem and introduce our Probabilistic Triangulation module. The overall pipeline is shown in Figure 1. + +# 3.1. Uncalibrated 3D human pose estimation + +Given that the images $I \in \mathbb{R}^{K \times H \times W}$ from $K$ views at a specific moment, our goal is to estimate the 3D pose $X^{3D}$ of the target human from it. Given the camera pose $y = \{y_{k} \in SE(3) | k = 1 \dots K\}$ , the optimal $X^{3D}$ will + +make the reprojection error $(3\mathrm{D}\rightarrow 2D)$ small enough and fits the prior distribution of the human pose learned in the dataset. Therefore, the estimation algorithm is often divided into two parts, 2D pose estimation, and 3D pose reconstruction. In 2D pose estimation, a neural network $M_{1}$ is employed to estimate the 2D pose $X^{2D} = M_1(I)$ from each view. In the 3D pose reconstruction, the $X^{2D}$ of different views are fused using a triangulation or a learnable triangulation method $M_{2}$ to obtain $X^{3D} = M_2(X^{2D},y)$ . + +Based on the reprojection error, the calibrated 3D human pose estimation is to solve an optimization problem: + +$$ +\min _ {X ^ {3 D}} E \left[ \operatorname {p r o j} \left(X ^ {3 D}, y\right) - X ^ {2 D} \right] \tag {1} +$$ + +where $proj(\cdot)$ denotes the projection function. The neural network-based algorithm replaces $X^{3D}$ in it with $M_2(X^{2D},y)$ , transforming the original optimization problem into solving for the optimal $M_2(\cdot)$ network parameters. + +When the camera pose $y$ is an unknown parameter, $y$ also becomes a variable to be optimized. Uncalibrated 3D human pose estimation can be similarly transformed into an optimization problem: + +$$ +\min _ {X _ {3 D}, y} \quad E [ \operatorname {p r o j} \left(X ^ {3 D}, y\right) - X ^ {2 D} ] \tag {2} +$$ + +![](images/b00c0637f0c63bc32b4deeb1e9bfba504edc7bdb7f7af0ef8509f5d480908de2.jpg) +(a) Implicit continuous. + +![](images/64ae607bc9b9ade50c4041c3be64a868127259360cadad7b0c4fd48832b3cf09.jpg) +(b) Implicitly discrete. + +![](images/f26170b4583059fff5d6e472ae42b410a6cc5bc7d8abb97a52aa86292df22b4a.jpg) +(c) Explicit discrete approximation. +Figure 2: 3D heatmap under different definitions + +This problem is tough to solve and exists multiple solutions. There are three main reasons for this: + +1. If an iterative method is used to optimize $y$ and $X^{3D}$ alternately, the results tend to fall into local optimum. +2. If a neural network is used to regress $y$ and then solve for $X^{3D}$ , it will be constrained by the lack of diversity in the existing data set $y$ to train. +3. If the neural network is used to regress $X^{3D}$ directly from the monocular view and then to solve $y$ , it will introduce the ill-conditioned problem of monocular scale ambiguity. + +In summary, we have to extract more information from the only known quantity $X_{2D}$ to obtain a relatively accurate estimate of $y$ , i.e., a valid estimate $p(y|X^{2D})$ . + +We use camera pose distribution approximation and Monte Carlo sampling to solve this problem. (see Probabilistic Triangulation part of Figure 1) Specifically, we maintain a proposal distribution $q(y)$ for approximating the posterior distribution $p(y|X^{2D})$ of camera poses during one inference. Monte Carlo sampling is continuously performed on $q(y)$ , and the weights are calculated from the sampled points, and then $q(y)$ is updated according to the weights. After several iterations, the results generated from the sampled points are weighted and averaged as the input to the 3D pose reconstruction network. We refer to this process as Probabilistic Triangulation. Figure 1 shows the pipeline of uncalibrated 3D human pose estimation after adding Probabilistic Triangulation. + +The Probabilistic Triangulation can be flexibly embedded into any kind of calibrated 3D human pose estimation, reducing its dependence on camera pose for realistic scenarios. The differentiable computational process makes it possible to connect the 2D pose estimation and 3D pose reconstruction parts, allowing end-to-end training. + +# 3.2. Probabilistic Triangulation + +We detail the Probabilistic Triangulation using the pipeline in Figure 1 as an example. In subsequent repre + +sentations, $y$ is used to denote the camera pose and $y_{gt}$ the ground truth of the camera pose. The 2D human pose is represented as $X^{2D} = \{x_i^{2D}\in \mathbb{R}^{K\times H'\times W'}|i = 1\ldots N\}$ , and the 3D human pose is represented as $X^{3D} = \{x_i^{3D}\in \mathbb{R}^{K\times L_1\times L_2\times L_3}|i = 1\ldots N\}$ , where $H^{\prime}$ and $W^{\prime}$ denote the height and width of the 2D heatmap, and $L_{1},L_{2},L_{3}$ denote the length, width, and height of the 3D heatmap. + +Camera pose distribution approximation In order to solve the optimization problem 2 with multiple solutions, we first normalized the multi-view camera pose to limit the range of solutions. Specifically, through an affine transformation of the whole coordinate system, the rotation matrix of the first view is changed into a unit matrix, the translation vector becomes a zero vector, and the translation vector of the second view has a modulus of one. The above affine changes can guarantee the uniqueness of the solution. + +Each camera pose is represented as a 7-dimensional vector, where 3D rotations are represented using unit quaternions and 3D translations are represented using 3D vectors. To better express the camera distribution, the angular central Gaussian distribution is introduced to represent the 3D rotation [34], and the multivariate t-distribution is introduced to represent the 3D translation. The $p(y|X^{2D})$ is calculated for each sampling point $y$ to obtain the covariance matrix of the angular central Gaussian distribution, and the mean and covariance matrix of the multivariate t-distribution, which in turn updates the parameters. The initial parameters of the distributions are first estimated based on the 2D human pose using the eight-point method. Then, a portion is sampled around the initial value and another portion is sampled around the entire camera domain. The distribution is initialized by the sampling result. Since the input of a single frame may cause a large error in the eight-point method, and initializing the distribution in this way increases the robustness of the algorithm. + +Monte Carlo sampling We assume that the 2D heatmap is the marginal distribution of the 3D heatmap along the projection direction, and the problem can be transformed into an optimization problem based on the reprojection error: + +$$ +\min _ {y, X ^ {3 D}} \quad \sum_ {i} ^ {N} \int_ {\sigma_ {i}} \left\| x _ {i} ^ {2 D} \left(\sigma_ {i}\right) - \int_ {p r o j \left(z, y _ {i}\right) = \sigma_ {i}} x ^ {3 D} (z) \mathrm {d} z \right\| _ {2} \mathrm {d} \sigma_ {i} \tag {3} +$$ + +where $z$ denotes the body element in 3D space, $\sigma_{i}$ denotes the area element of the $i$ th camera plane, and $proj(\cdot)$ denotes the projection function. A more general heatmap representation is adopted here, where $x^{3D}$ and $x^{2D}$ are considered as the probability density functions of the heatmap distribution. In practice, the heatmap is often stored in a discrete way, and the integrals need to be discretized as well. However, it is difficult to establish the constraints between $y$ and $X^{3D}$ explicitly, making the above optimization problem difficult to solve. + +Therefore, we use an approximate 3D heatmap explicitly defined as: + +$$ +x ^ {3 D} (z) = \frac {1}{N} \sum_ {\substack {i \\ p r o j (z, y _ {i}) = \sigma_ {i}}} ^ {N} x _ {i} ^ {2 D} (\sigma_ {i}) \tag{4} +$$ + +$$ +x _ {i} ^ {2 D} (\sigma_ {i}) = \max _ {p r o j (z, y _ {i}) = \sigma_ {i}} x ^ {3 D} (z) +$$ + +This definition is similar to the volume of the learnable triangulation, with the advantage that $X^{3D}$ can be computed explicitly and differentiably from $y$ and $X^{2D}$ . It also has some physical meaning as far as the location of the extreme points taken is similar to the original representation. The visualization of the 3D heatmap under different definitions is shown in Figure 2. + +The generated $X^{3D}$ retains the information of the heatmap and can be used as input for subsequent networks. Thus, the problem is simplified to: + +$$ +\min _ {y} \sum_ {i} ^ {N} \| \underbrace {\sum_ {z} \left(x ^ {3 D} (z) x _ {i} ^ {2 D} \left(\sigma_ {i}\right)\right) ^ {2} \left(x _ {i} ^ {2 D} \left(\sigma_ {i}\right) - x ^ {3 D} (z)\right)} _ {f _ {i} (y)} \| _ {2} \tag {5} +$$ + +The reprojection error is employed as the negative logarithm of the likelihood function $p(X_{2D}|y)$ . + +$$ +p \left(X ^ {2 D} | y\right) = \exp - \sum_ {i} ^ {N} \| f _ {i} (y) \| _ {2} \tag {6} +$$ + +Suppose that the camera pose $p(y)$ is subject to a uniform distribution, $p(y|X^{2D})$ can be calculated by Bayesian formula: + +$$ +p (y | X ^ {2 D}) = \frac {p \left(X ^ {2 D} \mid y\right)}{E \left[ p \left(X ^ {2 D} \mid y\right) \right]} \tag {7} +$$ + +The calculation of denominator expectation can be estimated by Monte Carlo sampling approximation. The specific calculation formula is as follows. + +$$ +E \left[ p \left(X ^ {2 D} | y\right) \right] \approx \frac {1}{M} \sum_ {j} ^ {M} q \left(y _ {j}\right) p \left(X ^ {2 D} | y\right), y _ {j} \sim q (y) \tag {8} +$$ + +where $M$ denotes the total number of samples. Then, $q(y)$ is updated using the computed $p(y|X^{2D})$ . + +Finally, the normalized $q(y)$ is used as the weight and the $X^{3D}$ generated by all sampled points $y$ is weighted and averaged as the input to the subsequent 3D pose reconstruction network. + +$$ +X ^ {3 D} = \frac {\sum_ {j} q \left(y _ {j}\right) X _ {j} ^ {3 D}}{\sum_ {j} q \left(y _ {j}\right)} \tag {9} +$$ + +# 3.3. Training Loss + +The entire training process includes two loss terms: $\mathcal{L}_{3d}$ and $\mathcal{L}_{cam}$ . + +We measure the difference between the true distribution of camera pose $z(y)$ and the posterior distribution $p(y|X^{2D})$ using KL divergence. + +$$ +\begin{array}{l} \mathcal {L} _ {c a m} = D _ {K L} (z (y) \| p (y | X ^ {2 D})) \\ = - \frac {1}{2} \sum_ {i} ^ {N} \| f _ {i} \left(y _ {g t}\right) \| _ {2} + \log E [ p \left(X ^ {2 D} | y\right) ] \tag {10} \\ \end{array} +$$ + +where the expectation of the second half is also obtained by the calculation of the equation 8. + +The 3D human pose estimation loss is the same as previous works[18], which encourages the predicted 3d poses to be close to the ground truth. The formula can be summarized as follow: + +$$ +\mathcal {L} _ {3 d} = \left\| \operatorname {s o f t a r g m a x} \left(X ^ {3 D}\right) - X _ {g t} \right\| _ {1} - \beta \cdot \log \left(X ^ {3 D} \left(X _ {g t}\right)\right) \tag {11} +$$ + +In end-to-end training, we simultaneously optimize these two loss terms to train the networks, and the total loss function can be written as: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \lambda_ {1} \mathcal {L} _ {\text {c a m}} + \lambda_ {2} \mathcal {L} _ {3 d} \tag {12} +$$ + +where the $\lambda_{1} = 1$ and $\lambda_{2} = 0.1$ in our experiment setting. + +# 4. Experiments + +# 4.1. Dataset & Metrics + +We conducted experiments on two of the most commonly used 3D human pose datasets available today, Human3.6M[17] and CMU Panoptic[19, 29, 35]. We used + +
MethodDir.Disc.EatGreetPhonePhotoPosePurch.SitSitD.SmokeWaitWalkD.WalkWalkT.Mean
Calibration method
Remelli et al.[28]27.332.125.026.529.335.428.831.636.431.731.229.926.933.730.430.2
Bartol et al.[2]27.528.429.327.530.128.127.930.832.932.530.829.428.530.530.129.1
He et al. [16]25.727.723.724.826.931.424.926.528.831.728.226.423.628.323.526.9
Qiu et al. [26]24.026.723.224.324.822.824.128.632.126.931.025.625.028.024.426.2
Ma et al. [22]24.426.423.421.125.223.224.733.829.826.426.824.223.226.123.325.8
Iskakov et al.[18]19.920.018.918.520.519.418.422.122.528.721.220.819.722.120.220.8
Uncalibration method
Gordon et al.[14]22.023.624.926.730.635.725.132.929.532.532.626.534.726.027.730.2
Ours method24.025.426.630.432.120.120.536.540.129.527.427.620.824.122.027.8
+ +Table 1: Results of the evaluation on the Human3.6M dataset. The table shows the MPJPE in millimeters for the published state-of-the-art calibrated and uncalibrated methods. + +
MethodMPJPE,mm
Calibrated method
Iskakov et al. Algebraic[18]21.3
Iskakov et al. Volumetric[18]13.7
Uncalibrated method
Bartol et al. [2]25.4
Our method24.2
+ +Table 2: Results of the MPJPE on the CMU Panoptic dataset ( using four cameras). + +the 17-joint MPJPE (Mean Per Joint Position Error) as a metric to evaluate our method. In training, we normalize the ground truth according to the method in section3.2 to ensure the uniqueness in the camera pose solution. In validation, the estimated 3D human pose is denormalized to the original coordinate system to ensure the correctness of the MPJPE calculation. + +# 4.2. Implementation details + +We added the Probabilistic Triangulation based on the work learnable triangulation by Iskakov et al.[18] to realize uncalibrated 3D human pose estimation. The same experimental parameter settings as the learnable triangulation method were used. As with learnable triangulation, our method uses predictions from the algebraic triangulation. Our method can also be fine-tuned and be trained in an end-to-end manner. $q(y)$ is initialized using a uniform distribution. The number of iterations is four, and the number of Monte Carlo samples is 256. + +# 4.3. Comparisons with State-of-the-art + +We compared the existing state-of-the-art calibrated and uncalibrated 3D pose estimation algorithms. The evaluation results on the Human3.6M dataset and the CMU Panoptic dataset are shown in Table 1 and Table 2, respectively. The experimental results show that the MPJPE of our method has outperformed the state-of-the-art uncalibrated approaches and achieved comparable performance to calibrated methods. It is worth noting that our method achieves better results in most scenarios of uncalibrated setting (see Table 1), but the results are poor in the Purch. and Sit. sub-datasets. This is because there are more occlusions in these two subsets, resulting in the 2D joint estimation being inaccurate, which further affects the estimation of the camera parameter distribution. Therefore, the final accumulated error affects the 3D human pose estimation performance. Inferring the camera parameters from the features of the detected human inevitably leads to estimation results depending on the capability of the human feature detector. However, our method still outperforms existing uncalibrated methods in terms of overall MPJPE for both datasets. + +# 4.4. Evaluation on Camera Pose Estimation + +To evaluate the capability of our camera pose estimation, we have conducted comparisons with some classical camera parameter estimation algorithms on the Human3.6M dataset. Due to the large parallax between different camera views, we choose 2D human keypoints estimated from 20 consecutive frames as image feature points to solve the camera pose parameters. We compare our camera estimation with Bundle Adjustment[32] and RANSAC 8-point algorithm[30]. Bundle Adjustment choose to minimize the reprojection error using the LM algorithm to find the camera parameters and the RANSAC 8-point algorithm uses the + +![](images/4eeb0c04e06036b306911c2bc47d094c672a337517cf6a0d4b18276a6c8b71b2.jpg) +(a) Bundle Adjustment. + +![](images/f67cb64b06dc89e4de3ffa114bb5b52378c276cca547ebdba5c48903dc130966.jpg) +(b) RANSAC 8-point algorithm. + +![](images/9574540b4dc48dbbcbaad0aeb0e664f774c628fb463d4a166f96a3b9844f9f22.jpg) +(c) Ours method. +Figure 3: Visualization of the camera pose parameters and 3D human pose obtained by different algorithms. The quadrilateral cone indicates the camera pose parameters, the gray part indicates the ground truth, and the colored part indicates the prediction results of different algorithms. + +8-point method to find the fundamental matrix after screening out the outliers by RANSAC, and then uses the eigenvalue decomposition to find the camera pose. We provide some visualization examples in Figure 3. From the Figure 3, we can see that Bundle Adjustment often falls into the local optimal solution, resulting in poor camera poses. The RANSAC 8-point algorithm can remove outliers, but the estimation of the camera pose is sensitive to 2D human pose estimation, which will lead to accumulated errors when reconstructing 3D human poses. The 3D human and camera pose estimation results are more robust and accurate when introducing our Probabilistic Triangulation (see (c) of Figure 3) + +Table 3 shows more detailed results of camera pose evaluation, using the same experimental setup as [2]. Among the evaluation metrics used: 1. 3D estimation error $(\mathrm{mm})$ $E_{3D} = E[\| x^{\hat{3} D} - x^{3D}\| _2]$ ; 2. Projection 2D error $(\mathrm{mm})E_{2D} = E[\| x^{\hat{2} D} - x^{2D}\| _2]$ ; 3. Camera rotation error $E_{R} = E[\| \hat{q} -q\|_{2}]$ ; 4. Camera translation error (mm) $E_{t} = E[\| \hat{t} -t\|_{2}]$ + +# 4.5. Cross-dataset experiments + +To test the generalization ability of Probabilistic Triangulation across datasets, we segment CMU Panoptic and + +
methodsE3D↓E2D↓ER↓Et↓
BA736.82130.180.02546.87
RANSAC 8-point97.5050.140.0125.30
Our methods27.805.980.00432.71
+ +Table 3: Quantitative experiments on camera pose estimation on the Human3.6M dataset. + +Human36M into five sub-datasets in the same way as Bartol et al.[2]. Cross-dataset experiments are conducted between these sub-datasets two by two. It was found that there was no significant loss of accuracy between the CMU Panoptic sub-datasets even after segmentation (this is because the distribution between the sub-datasets of the CMU Panoptic dataset is very similar). However, the results trained from the CMU dataset have a significant loss of accuracy on Human3.6M. Table 4 shows the generalization ability of Probabilistic Triangulation and Bartol et al.[2] from the CMU dataset to the Human3.6M dataset. Probabilistic Triangulation exhibits stronger generalization. + +# 4.6. Ablation study on the number of cameras + +We show the results of the ablation study in Table 5. After training on 4-view data, our method generalizes well to + +![](images/6a7c6440ef52c0eac8a6b2ee2e35944284272fc00c517272c6e739b9fca8cb53.jpg) +Figure 4: Visualization of the sampled points in four iterations after dimensionality reduction using t-SNE. From left to right corresponds to the sampled values after four iterations. The value of the sampled point is the logarithmic sampling loss, and the smaller the value means that the sampled point is closer to the true value. + +![](images/93458b7ef489592e1fbe64deeff7c648ffdf0c5d9f6107673354f00731f0ccb6.jpg) + +![](images/3a65ad2328f2ecc83327c8dea7f954af1a74e2067d71594a5ebf653d98b56eb6.jpg) + +![](images/bb4193fee109018510e72c48ea05462f149af2e3d0b4f7254b0956092f692bc6.jpg) + +![](images/1c6968438308a59bf00d04346626165ad5f3f2865e135d0ba5c52138d1025bce.jpg) + +
MethodTrainSelf-TestH36M-Testdiff
Bartol et al.[2]CMU125.833.530%
CMU226.033.428%
CMU325.031.024%
CMU425.132.528%
Ours methodCMU124.630.825%
CMU223.729.123%
CMU324.129.221%
CMU424.931.125%
+ +3-view and 2-view because the network has seen rich information during training. There is some performance degradation when the model is trained on 2-view and tested on 3-view and 4-view as shown in Table 5. + +Table 4: Experiments on generalization ability between datasets (MPJPE in mm). The CMU Panoptic dataset was split into four sub-datasets with different number of cameras and different spatial distributions of cameras. The models were trained on the four datasets separately, and the results were evaluated on their own test set and the Human3.6M test set. The last column represents the cross-data accuracy decline rate. + +
2-view3-view4-view
Training on 2-view29.542.439.2
Training on 4-view32.629.327.8
+ +Table 5: Ablation study on Human3.6M for camera numbers (MPJPE, mm). + +# 4.7. Ablation study on each module + +In order to demonstrate the irreplaceable role that probabilistic triangularization plays in camera pose estimation and 3D human reconstruction in uncalibrated 3D human + +pose estimation. We design two ablation experiments to remove the influence of the rest of the network on the results and to demonstrate the role of Probabilistic Triangulation better. + +First, we use 2D heatmaps ground truth as the input of Probabilistic Triangulation to eliminate the effect of 2D backbone on the results. Also, the upper bound of our method is shown (see Table 6 middle). The table shows that our method achieves comparable results to the calibration method [18] when given the 2D ground truth. + +The 3D error still cannot reach zero under the condition of using 2D ground truth because there is a theoretical upper limit to the accuracy of the voxel structure. However, the 2D human pose estimator error cannot be avoided, and the better robustness of the voxel structure to error is the reason it was chosen. + +In addition, we demonstrate the necessity of introducing the camera pose estimation module by comparing it with Iskaov et al. (V2V network and triangulation). We rotated the world coordinate system $(0^{\circ}$ to $180^{\circ}$ randomly around the vertical axis and $0^{\circ}$ to $45^{\circ}$ randomly around the pitch) to change the values of the camera's external parameters, resulting in a new test set called "Test*" in Table 6. We can find that only using a V2V network and triangulation will make the network overfit the camera poses, resulting in performance degradation. Our method does not require the input of camera poses, so changes in the world coordinate system do not affect our method's final pose estimation results. It demonstrates that our camera estimation module, i.e., the main contribution, is necessary and reasonable. + +# 4.8. Visualization of Sampling Process + +In order to visualize the sampling process in the Probabilistic Triangulation, the 256 sampling points of each iteration are embedded by t-SNE and plotted in Figure 4. From the figure, as the iteration proceeds, the approximation of the camera distribution becomes more and more ac + +
Baseline2D GTTest*
Iskakov et al.20.816.325.12
Our methods27.818.527.8
+ +Table 6: Pose estimation results (MPJPE, mm) on different 2D and test settings. The middle two columns show the results of 3D pose estimation using the 2D estimator and 2D GT, respectively. The rightmost column shows the estimation results on the Test* set. + +curate, the sampled points are closer to the ground truth, and the sampling loss keeps decreasing. At the same time, the whole camera pose space is not smooth, and there are many local optimums and pseudo-solutions. The 2D human pose estimator generates noise, making the classical camera pose estimation more likely to fall into local optimal solutions. Distributed representation of camera pose (Probabilistic Triangulation) can alleviate this problem. + +Furthermore, from Figure 4, the sampling points are concentrated around a few extreme points as the iteration parameters increase. This is because an incremental solution exists to the camera pose estimation, so there are multiple extreme points. However, only one of them has real physical significance, whereas, in the projection process, these extreme points produce the same projection result. The distribution also tends to converge to a single extreme point if an initial value is used to initialize the camera pose distribution, and the sampling points of the distribution are spread out to appear near multiple extreme points if a uniform distribution is used to initialize the distribution. + +# 4.9. Generalize to Wide Scenes + +To demonstrate the generalization of our Probabilistic Triangulation in the wild scenes, we use a model trained from the CMU Panoptic dataset and test it on the natural scenes. Two iPhones with a $26\mathrm{mm}$ primary camera were used for the shooting, and the intrinsic parameters were read using the swift function. The results are shown in Figure 5. Our method remains in effect even when the camera space location and the number of cameras change. + +# 5. Conclusions and limitations + +We propose a novel Probabilistic Triangulation module for multi-view 3D human pose estimation, which enables the existing calibrated methods to reduce the dependence on calibration and can be applied to uncalibrated wild scenes. Extensive experiments demonstrate that the 3D human pose estimation based on our Probabilistic Triangulation can achieve state-of-the-art performance when compared to uncalibrated methods. And the employment of camera pose distribution and Monte Carlo sampling alleviates the problem of easy access to local optimums and pseudo-solutions + +![](images/43d1281dd326e15e6f0b7bc8d1d8c5ef2a3d484f0d0e8c672ab4eb0e5052d232.jpg) +Figure 5: Our method demonstrates the results in a non-calibrated wild scene. The first and second columns represent the two iPhone camera views, and the third column shows the estimated camera pose and 3D human pose. + +in camera pose estimation. Since our Probabilistic Triangulation does not take the camera pose parameters as input, it is possible to build the multi-view 3D human pose estimation system in wild scenes and achieve a high-accurate capture. In the wild scenes, the Probabilistic Triangulation is not affected by the spatial location changes and the number of cameras. It can be directly applied to uncalibrated scenes after training with calibrated data. + +The main limitation of our method is that it can only be applied to single-person scenes. Extending to multi-person scenarios requires taking into account the cross-view matching problem, which is difficult to solve in the absence of a camera pose. In addition, although the Probabilistic Triangulation does not require the camera pose as input during validation, the ground truth of the 3D human pose and the camera pose are used in the training process, and these data need to be obtained from the dataset of the calibration scene. In fact, the ground truth of camera pose is not directly involved in the training, but indirectly guides the 2D pose estimation network learning through cross-view information. The ground truth of the 3D human pose influences the 2D pose estimation network and enables the 3D pose reconstruction network to learn the human prior and integrate the information generated by previous sampling. + +Acknowledgements This work was supported by National Key Research and Development Program of China (NO. 2022YFB3303202). + +# References + +[1] Sameer Agarwal and Keir Mierle. Others, "ceres solver". Available: http://ceres-solver.org, 2015. +[2] Kristijan Bartol, David Bojanic, Tomislav Petkovic, and Tomislav Pribanic. Generalizable human pose triangulation. 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Existing multi-view methods are restricted to fixed camera pose and therefore lack generalization ability. This paper presents a novel Probabilistic Triangulation module that can be embedded in a calibrated 3D human pose estimation method, generalizing it to uncalibration scenes. The key idea is to use a probability distribution to model the camera pose and iteratively update the distribution from 2D features instead of using camera pose. Specifically, We maintain a camera pose distribution and then iteratively update this distribution by computing the posterior probability of the camera pose through Monte Carlo sampling. This way, the gradients can be directly back-propagated from the 3D pose estimation to the 2D heatmap, enabling end-to-end training. Extensive experiments on Human3.6M and CMU Panoptic demonstrate that our method outperforms other uncalibration methods and achieves comparable results with state-of-the-art calibration methods. Thus, our method achieves a trade-off between estimation accuracy and generalizability. Our code is in https://github.com/bymaths/probabilistic_triangulation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 579, + 128, + 593 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 579, + 128, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 579, + 128, + 593 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 599, + 287, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 599, + 287, + 683 + ], + "spans": [ + { + "bbox": [ + 46, + 599, + 287, + 683 + ], + "type": "text", + "content": "3D human pose estimation is a fundamental tool in many downstream applications of computer vision and computer graphics, such as motion recognition[13], human-computer interaction[23], movie game animation[4], virtual reality[24], etc. The development of these fields requires a more accurate, convenient, and robust 3D human pose estimation algorithm." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 58, + 683, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 683, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 58, + 683, + 287, + 696 + ], + "type": "text", + "content": "Recently, RGB-based pose estimation has become the" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 246, + 547, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 246, + 547, + 389 + ], + "spans": [ + { + "bbox": [ + 304, + 246, + 547, + 389 + ], + "type": "text", + "content": "trend because of its convenience, wide application scenarios, and low cost[27]. These methods can be divided into two categories: single-view and multi-view methods. Although single-view methods[39, 37, 11, 38, 25] have more widespread application scenarios, the lack of depth information makes single-view estimation of 3D human pose an ill-posed problem, especially when dealing with occlusions and multi-person scenes[21]. Multi-view methods[18, 16, 36, 33, 2, 14, 31, 20] can achieve more accurate results than single view-based methods because multi-view cameras can restore the depth information as well as the occluded parts." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 390, + 547, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 547, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 547, + 498 + ], + "type": "text", + "content": "However, the multi-view approach faces several issues when applied in practice. First, multi-view methods require synchronized and calibrated cameras, which complicates the process. Second, existing datasets for multi-view human pose estimation lack the diversity of camera external parameters. This results in the trained model cannot generalize well to unseen camera parameters, thus requiring re-annotation and re-training once the camera configurations change." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 498, + 548, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 548, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 548, + 653 + ], + "type": "text", + "content": "To alleviate the above issues, we propose Probabilistic Triangulation module for uncalibrated 3D human pose estimation. Our module enables the network to get rid of camera pose parameters during the training process, which results in better generalization performance to be applied to wild scenes. The main idea is to use a probability distribution to model the camera pose, making the whole process differentiable. Specifically, we transform the uncalibrated 3D human pose estimation into a nonlinear optimization problem based on the reprojection error. The camera pose distribution is estimated from the 2D pose features, and then the posterior probability of the camera pose is computed by Monte Carlo sampling to iteratively update this distribution." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": "We conducted extensive experiments on two benchmark datasets (Human3.6M[17] and CMU Panoptic[19, 29, 35]) to demonstrate that our method outperforms other uncalibrated methods and achieves comparable results with the state-of-the-art calibration methods, which indicates that" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 713 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "14850" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": "our method improves the generalized ability to camera parameters in multi-view human pose estimation while maintaining high accuracy." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 109, + 271, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 109, + 271, + 120 + ], + "spans": [ + { + "bbox": [ + 59, + 109, + 271, + 120 + ], + "type": "text", + "content": "In summary, our contributions are mainly three-fold." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 129, + 286, + 315 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 59, + 129, + 286, + 177 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 129, + 286, + 177 + ], + "spans": [ + { + "bbox": [ + 59, + 129, + 286, + 177 + ], + "type": "text", + "content": "- We propose Probabilistic Triangulation that can generalize the calibrated 3D human pose estimation algorithm to uncalibrated scenes to estimate 3D human pose in the absence of camera pose." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 186, + 286, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 186, + 286, + 246 + ], + "spans": [ + { + "bbox": [ + 59, + 186, + 286, + 246 + ], + "type": "text", + "content": "- We propose an approximation method for camera pose distribution and an updated distribution method based on Monte Carlo sampling. It is used to model the camera pose of uncalibrated scenes with accuracy and robustness beyond classical algorithms." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 256, + 286, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 256, + 286, + 315 + ], + "spans": [ + { + "bbox": [ + 59, + 256, + 286, + 315 + ], + "type": "text", + "content": "- We conducted extensive experiments on two benchmark datasets (Human3.6M and CMU Panoptic) to demonstrate the accuracy, generalization capability, and applicability of Probabilistic Triangulation to wild scenes." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 327, + 132, + 339 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 327, + 132, + 339 + ], + "spans": [ + { + "bbox": [ + 47, + 327, + 132, + 339 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 347, + 211, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 347, + 211, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 347, + 211, + 360 + ], + "type": "text", + "content": "2.1. Calibrated 3D pose estimation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 366, + 286, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 366, + 286, + 462 + ], + "spans": [ + { + "bbox": [ + 47, + 366, + 286, + 462 + ], + "type": "text", + "content": "3D human pose estimation is a vital problem in computer vision and graphics, where the single view-based method has been a research spotlight due to the convenience and comprehensive application scenarios of a monocular camera. To alleviate the ambiguity problem caused by occlusion and the lack of depth information, many single view-based works[37, 11, 38, 25, 3] have tried to introduce the temporal information or body-related prior during training." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 463, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 463, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 463, + 286, + 713 + ], + "type": "text", + "content": "Multi-view images retain more information compared to single-view ones. The association of information between different views eliminates most of the ambiguity. So it is easier to achieve high-accuracy 3D human pose estimation in multi-view settings. Fusing the information of different views is the core problem of multi-view human pose estimation. Existing multi-view methods include two processes, 2D pose estimation and 3D pose reconstruction. The former consists of a pre-trained 2D pose estimator[10, 6], and multi-view information fusion occurs in the 3D pose reconstruction. Multi-view methods are divided into two categories according to the different ways of representing human pose. The first is the point-based method[26, 5, 12], which uses the spatial coordinates of the joint points as the human pose representation. This representation makes it easier to introduce temporal and body information explicitly. The second is the heatmap-based method, which uses the heatmap as the human pose representation[16, 36, 18], and learnable triangulation represents this method[18, 33]. The point representation is more concise and explicit but loses information, while the heatmap representation retains" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": "more information but is not easily bounded explicitly. Our proposed Probabilistic Triangulation is applicable in both representations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 117, + 481, + 129 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 117, + 481, + 129 + ], + "spans": [ + { + "bbox": [ + 306, + 117, + 481, + 129 + ], + "type": "text", + "content": "2.2. Uncalibrated 3D pose estimation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 135, + 545, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 135, + 545, + 482 + ], + "spans": [ + { + "bbox": [ + 304, + 135, + 545, + 482 + ], + "type": "text", + "content": "Uncalibrated 3D pose estimation is a relatively new field[31, 2, 14, 20]. Takahashi's work[31] is a point-based method that establishes explicit constraints based on reprojection errors and the human body prior to transform the problem into an optimization problem and iteratively solve for the optimal solution. Lee's work[20] is also a point-based method, estimating the camera pose using the 3D pose estimated from different views. FLEX[14] estimates a time-invariant bone length while estimating joint rotations frame by frame and reconstructing 3D pose by forward kinematics. In this approach, the bone length is a link to fuse the multi-view information, and the rotation estimated for each view implicitly constrains the camera pose. However, this method cannot accurately estimate the camera pose due to the lack of transformation of the global coordinate system. Therefore, the output 3D pose is camera dependent. Bartol et al. [2] use a scoring network to evaluate the weight of the current proposal's camera pose or 3D human pose, and the final weighting is used to obtain a definite result. This method does not directly estimate the 3D human pose for uncalibrated scenes, but it can estimate the camera pose before and use other calibration methods to estimate the 3D human pose. This method does not directly estimate the 3D human pose for uncalibrated scenes, but it can estimate the camera pose before using other calibration methods to estimate the 3D human pose. Because the experiments for 3D human pose estimation in this work are for calibrated scenes, they are placed in the calibration method in the comparison experiments later in the paper." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 483, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 601 + ], + "type": "text", + "content": "Current methods are limited to point-based representation. The heatmap-based representation retains more information than the point-based representation. This is because the accuracy of existing 2D human pose estimators is not sufficient for direct calibration. Small errors in points can be rapidly amplified by the camera pose estimation process, making the method ineffective. Our proposed camera pose distribution can effectively increase the robustness of the camera estimation process and support heatmap-based representation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 611, + 500, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 500, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 500, + 624 + ], + "type": "text", + "content": "2.3. Probabilistic camera pose estimation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Camera pose estimation is a fundamental problem in computer vision[15]. PNP methods solve the case of known 3D-2D point pairs, while triangulation solves the case of known 2D-2D point pairs. Bundle adjustment transforms the camera matching problem into an optimization problem starting from reprojection errors[1]. However, matching feature points and solving them using classical meth" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "14851" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 70, + 537, + 319 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 537, + 319 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 537, + 319 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 537, + 319 + ], + "type": "image", + "image_path": "2d4721dfbcf920343409bb46edbf0c2925505c4db7b6d17c2e27a478b1553189.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 327, + 548, + 401 + ], + "lines": [ + { + "bbox": [ + 46, + 327, + 548, + 401 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 548, + 401 + ], + "type": "text", + "content": "Figure 1: Probabilistic Triangulation for uncalibrated 3D human pose estimation pipeline. The inputs to the network are images from different views at the same moment. The 2D human pose heatmaps are estimated from the images and used to initialize the camera pose distribution. Then, Monte Carlo sampling is performed iteratively and each sampled camera parameter is computed by reprojection to obtain an explicit approximation of the 3D heatmap. The 3D heatmap calculates the weights of the sampled camera parameters. These weights are then used to update the pose distribution of the cameras. The weighted 3D heat map is used as input for the subsequent 3D pose reconstruction, for estimating the 3D human pose." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 421, + 287, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 421, + 287, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 421, + 287, + 492 + ], + "type": "text", + "content": "ods does not apply to all scenarios. In the field of object and camera pose estimation, many works try to improve the network architecture that allows an end-to-end approach for pose estimation[8, 7]. The work EPro-PnP by Chen et al[9]. proposes a probabilistic PnP layer that allows the gradient back-propagated through the pose." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 492, + 287, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 492, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 492, + 287, + 563 + ], + "type": "text", + "content": "Inspired by EPro-PnP, we use probability distributions to model camera pose. Compared with the camera pose represented by a single variable, the camera pose represented by the distribution has more robust performance and effectively mitigates the effect of 2D human pose detection errors." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 573, + 103, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 573, + 103, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 573, + 103, + 586 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 287, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 642 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 642 + ], + "type": "text", + "content": "In this paragraph, we will review the multi-view uncalibrated 3D human pose estimation problem and introduce our Probabilistic Triangulation module. The overall pipeline is shown in Figure 1." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 647, + 258, + 660 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 258, + 660 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 258, + 660 + ], + "type": "text", + "content": "3.1. Uncalibrated 3D human pose estimation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 664, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 664, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 664, + 288, + 715 + ], + "type": "text", + "content": "Given that the images " + }, + { + "bbox": [ + 47, + 664, + 288, + 715 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{K \\times H \\times W}" + }, + { + "bbox": [ + 47, + 664, + 288, + 715 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 47, + 664, + 288, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 664, + 288, + 715 + ], + "type": "text", + "content": " views at a specific moment, our goal is to estimate the 3D pose " + }, + { + "bbox": [ + 47, + 664, + 288, + 715 + ], + "type": "inline_equation", + "content": "X^{3D}" + }, + { + "bbox": [ + 47, + 664, + 288, + 715 + ], + "type": "text", + "content": " of the target human from it. Given the camera pose " + }, + { + "bbox": [ + 47, + 664, + 288, + 715 + ], + "type": "inline_equation", + "content": "y = \\{y_{k} \\in SE(3) | k = 1 \\dots K\\}" + }, + { + "bbox": [ + 47, + 664, + 288, + 715 + ], + "type": "text", + "content": ", the optimal " + }, + { + "bbox": [ + 47, + 664, + 288, + 715 + ], + "type": "inline_equation", + "content": "X^{3D}" + }, + { + "bbox": [ + 47, + 664, + 288, + 715 + ], + "type": "text", + "content": " will" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "type": "text", + "content": "make the reprojection error " + }, + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "type": "inline_equation", + "content": "(3\\mathrm{D}\\rightarrow 2D)" + }, + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "type": "text", + "content": " small enough and fits the prior distribution of the human pose learned in the dataset. Therefore, the estimation algorithm is often divided into two parts, 2D pose estimation, and 3D pose reconstruction. In 2D pose estimation, a neural network " + }, + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "type": "inline_equation", + "content": "M_{1}" + }, + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "type": "text", + "content": " is employed to estimate the 2D pose " + }, + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "type": "inline_equation", + "content": "X^{2D} = M_1(I)" + }, + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "type": "text", + "content": " from each view. In the 3D pose reconstruction, the " + }, + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "type": "inline_equation", + "content": "X^{2D}" + }, + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "type": "text", + "content": " of different views are fused using a triangulation or a learnable triangulation method " + }, + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "type": "inline_equation", + "content": "M_{2}" + }, + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "type": "text", + "content": " to obtain " + }, + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "type": "inline_equation", + "content": "X^{3D} = M_2(X^{2D},y)" + }, + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 529, + 545, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 545, + 553 + ], + "type": "text", + "content": "Based on the reprojection error, the calibrated 3D human pose estimation is to solve an optimization problem:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 351, + 563, + 545, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 563, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 351, + 563, + 545, + 582 + ], + "type": "interline_equation", + "content": "\\min _ {X ^ {3 D}} E \\left[ \\operatorname {p r o j} \\left(X ^ {3 D}, y\\right) - X ^ {2 D} \\right] \\tag {1}", + "image_path": "bf68ef9f373603d516d45bc1827841bd17f6b276d870aa88a107f96fcb4f332e.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "spans": [ + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "type": "inline_equation", + "content": "proj(\\cdot)" + }, + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "type": "text", + "content": " denotes the projection function. The neural network-based algorithm replaces " + }, + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "type": "inline_equation", + "content": "X^{3D}" + }, + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "type": "text", + "content": " in it with " + }, + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "type": "inline_equation", + "content": "M_2(X^{2D},y)" + }, + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "type": "text", + "content": ", transforming the original optimization problem into solving for the optimal " + }, + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "type": "inline_equation", + "content": "M_2(\\cdot)" + }, + { + "bbox": [ + 304, + 590, + 545, + 638 + ], + "type": "text", + "content": " network parameters." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 638, + 545, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 638, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 638, + 545, + 686 + ], + "type": "text", + "content": "When the camera pose " + }, + { + "bbox": [ + 304, + 638, + 545, + 686 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 638, + 545, + 686 + ], + "type": "text", + "content": " is an unknown parameter, " + }, + { + "bbox": [ + 304, + 638, + 545, + 686 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 638, + 545, + 686 + ], + "type": "text", + "content": " also becomes a variable to be optimized. Uncalibrated 3D human pose estimation can be similarly transformed into an optimization problem:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 354, + 695, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 695, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 354, + 695, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\min _ {X _ {3 D}, y} \\quad E [ \\operatorname {p r o j} \\left(X ^ {3 D}, y\\right) - X ^ {2 D} ] \\tag {2}", + "image_path": "db29a1812bffdce6134239e8a0c7e55f6d563e346f2e610efa9bb14283f86067.jpg" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "14852" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 195, + 178 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 195, + 178 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 195, + 178 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 195, + 178 + ], + "type": "image", + "image_path": "b00c0637f0c63bc32b4deeb1e9bfba504edc7bdb7f7af0ef8509f5d480908de2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 87, + 182, + 174, + 194 + ], + "lines": [ + { + "bbox": [ + 87, + 182, + 174, + 194 + ], + "spans": [ + { + "bbox": [ + 87, + 182, + 174, + 194 + ], + "type": "text", + "content": "(a) Implicit continuous." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 211, + 68, + 360, + 178 + ], + "blocks": [ + { + "bbox": [ + 211, + 68, + 360, + 178 + ], + "lines": [ + { + "bbox": [ + 211, + 68, + 360, + 178 + ], + "spans": [ + { + "bbox": [ + 211, + 68, + 360, + 178 + ], + "type": "image", + "image_path": "64ae607bc9b9ade50c4041c3be64a868127259360cadad7b0c4fd48832b3cf09.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 255, + 182, + 338, + 194 + ], + "lines": [ + { + "bbox": [ + 255, + 182, + 338, + 194 + ], + "spans": [ + { + "bbox": [ + 255, + 182, + 338, + 194 + ], + "type": "text", + "content": "(b) Implicitly discrete." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 378, + 68, + 526, + 178 + ], + "blocks": [ + { + "bbox": [ + 378, + 68, + 526, + 178 + ], + "lines": [ + { + "bbox": [ + 378, + 68, + 526, + 178 + ], + "spans": [ + { + "bbox": [ + 378, + 68, + 526, + 178 + ], + "type": "image", + "image_path": "f26170b4583059fff5d6e472ae42b410a6cc5bc7d8abb97a52aa86292df22b4a.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 398, + 182, + 526, + 194 + ], + "lines": [ + { + "bbox": [ + 398, + 182, + 526, + 194 + ], + "spans": [ + { + "bbox": [ + 398, + 182, + 526, + 194 + ], + "type": "text", + "content": "(c) Explicit discrete approximation." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 197, + 203, + 394, + 216 + ], + "lines": [ + { + "bbox": [ + 197, + 203, + 394, + 216 + ], + "spans": [ + { + "bbox": [ + 197, + 203, + 394, + 216 + ], + "type": "text", + "content": "Figure 2: 3D heatmap under different definitions" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 236, + 286, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 236, + 286, + 259 + ], + "spans": [ + { + "bbox": [ + 47, + 236, + 286, + 259 + ], + "type": "text", + "content": "This problem is tough to solve and exists multiple solutions. There are three main reasons for this:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 54, + 264, + 287, + 385 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 55, + 264, + 286, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 264, + 286, + 290 + ], + "spans": [ + { + "bbox": [ + 55, + 264, + 286, + 290 + ], + "type": "text", + "content": "1. If an iterative method is used to optimize " + }, + { + "bbox": [ + 55, + 264, + 286, + 290 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 264, + 286, + 290 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 264, + 286, + 290 + ], + "type": "inline_equation", + "content": "X^{3D}" + }, + { + "bbox": [ + 55, + 264, + 286, + 290 + ], + "type": "text", + "content": " alternately, the results tend to fall into local optimum." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 54, + 296, + 287, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 296, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 54, + 296, + 287, + 331 + ], + "type": "text", + "content": "2. If a neural network is used to regress " + }, + { + "bbox": [ + 54, + 296, + 287, + 331 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 54, + 296, + 287, + 331 + ], + "type": "text", + "content": " and then solve for " + }, + { + "bbox": [ + 54, + 296, + 287, + 331 + ], + "type": "inline_equation", + "content": "X^{3D}" + }, + { + "bbox": [ + 54, + 296, + 287, + 331 + ], + "type": "text", + "content": ", it will be constrained by the lack of diversity in the existing data set " + }, + { + "bbox": [ + 54, + 296, + 287, + 331 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 54, + 296, + 287, + 331 + ], + "type": "text", + "content": " to train." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 54, + 337, + 287, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 337, + 287, + 385 + ], + "spans": [ + { + "bbox": [ + 54, + 337, + 287, + 385 + ], + "type": "text", + "content": "3. If the neural network is used to regress " + }, + { + "bbox": [ + 54, + 337, + 287, + 385 + ], + "type": "inline_equation", + "content": "X^{3D}" + }, + { + "bbox": [ + 54, + 337, + 287, + 385 + ], + "type": "text", + "content": " directly from the monocular view and then to solve " + }, + { + "bbox": [ + 54, + 337, + 287, + 385 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 54, + 337, + 287, + 385 + ], + "type": "text", + "content": ", it will introduce the ill-conditioned problem of monocular scale ambiguity." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "text", + "content": "In summary, we have to extract more information from the only known quantity " + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "inline_equation", + "content": "X_{2D}" + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "text", + "content": " to obtain a relatively accurate estimate of " + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "text", + "content": ", i.e., a valid estimate " + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "inline_equation", + "content": "p(y|X^{2D})" + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "text", + "content": "We use camera pose distribution approximation and Monte Carlo sampling to solve this problem. (see Probabilistic Triangulation part of Figure 1) Specifically, we maintain a proposal distribution " + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "inline_equation", + "content": "q(y)" + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "text", + "content": " for approximating the posterior distribution " + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "inline_equation", + "content": "p(y|X^{2D})" + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "text", + "content": " of camera poses during one inference. Monte Carlo sampling is continuously performed on " + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "inline_equation", + "content": "q(y)" + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "text", + "content": ", and the weights are calculated from the sampled points, and then " + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "inline_equation", + "content": "q(y)" + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "text", + "content": " is updated according to the weights. After several iterations, the results generated from the sampled points are weighted and averaged as the input to the 3D pose reconstruction network. We refer to this process as Probabilistic Triangulation. Figure 1 shows the pipeline of uncalibrated 3D human pose estimation after adding Probabilistic Triangulation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 594, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 665 + ], + "type": "text", + "content": "The Probabilistic Triangulation can be flexibly embedded into any kind of calibrated 3D human pose estimation, reducing its dependence on camera pose for realistic scenarios. The differentiable computational process makes it possible to connect the 2D pose estimation and 3D pose reconstruction parts, allowing end-to-end training." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 671, + 196, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 196, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 196, + 684 + ], + "type": "text", + "content": "3.2. Probabilistic Triangulation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "We detail the Probabilistic Triangulation using the pipeline in Figure 1 as an example. In subsequent repre" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 236, + 545, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 236, + 545, + 320 + ], + "spans": [ + { + "bbox": [ + 305, + 236, + 545, + 320 + ], + "type": "text", + "content": "sentations, " + }, + { + "bbox": [ + 305, + 236, + 545, + 320 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 236, + 545, + 320 + ], + "type": "text", + "content": " is used to denote the camera pose and " + }, + { + "bbox": [ + 305, + 236, + 545, + 320 + ], + "type": "inline_equation", + "content": "y_{gt}" + }, + { + "bbox": [ + 305, + 236, + 545, + 320 + ], + "type": "text", + "content": " the ground truth of the camera pose. The 2D human pose is represented as " + }, + { + "bbox": [ + 305, + 236, + 545, + 320 + ], + "type": "inline_equation", + "content": "X^{2D} = \\{x_i^{2D}\\in \\mathbb{R}^{K\\times H'\\times W'}|i = 1\\ldots N\\}" + }, + { + "bbox": [ + 305, + 236, + 545, + 320 + ], + "type": "text", + "content": ", and the 3D human pose is represented as " + }, + { + "bbox": [ + 305, + 236, + 545, + 320 + ], + "type": "inline_equation", + "content": "X^{3D} = \\{x_i^{3D}\\in \\mathbb{R}^{K\\times L_1\\times L_2\\times L_3}|i = 1\\ldots N\\}" + }, + { + "bbox": [ + 305, + 236, + 545, + 320 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 236, + 545, + 320 + ], + "type": "inline_equation", + "content": "H^{\\prime}" + }, + { + "bbox": [ + 305, + 236, + 545, + 320 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 236, + 545, + 320 + ], + "type": "inline_equation", + "content": "W^{\\prime}" + }, + { + "bbox": [ + 305, + 236, + 545, + 320 + ], + "type": "text", + "content": " denote the height and width of the 2D heatmap, and " + }, + { + "bbox": [ + 305, + 236, + 545, + 320 + ], + "type": "inline_equation", + "content": "L_{1},L_{2},L_{3}" + }, + { + "bbox": [ + 305, + 236, + 545, + 320 + ], + "type": "text", + "content": " denote the length, width, and height of the 3D heatmap." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 323, + 545, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 323, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 545, + 432 + ], + "type": "text", + "content": "Camera pose distribution approximation In order to solve the optimization problem 2 with multiple solutions, we first normalized the multi-view camera pose to limit the range of solutions. Specifically, through an affine transformation of the whole coordinate system, the rotation matrix of the first view is changed into a unit matrix, the translation vector becomes a zero vector, and the translation vector of the second view has a modulus of one. The above affine changes can guarantee the uniqueness of the solution." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 434, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 662 + ], + "type": "text", + "content": "Each camera pose is represented as a 7-dimensional vector, where 3D rotations are represented using unit quaternions and 3D translations are represented using 3D vectors. To better express the camera distribution, the angular central Gaussian distribution is introduced to represent the 3D rotation [34], and the multivariate t-distribution is introduced to represent the 3D translation. The " + }, + { + "bbox": [ + 304, + 434, + 545, + 662 + ], + "type": "inline_equation", + "content": "p(y|X^{2D})" + }, + { + "bbox": [ + 304, + 434, + 545, + 662 + ], + "type": "text", + "content": " is calculated for each sampling point " + }, + { + "bbox": [ + 304, + 434, + 545, + 662 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 434, + 545, + 662 + ], + "type": "text", + "content": " to obtain the covariance matrix of the angular central Gaussian distribution, and the mean and covariance matrix of the multivariate t-distribution, which in turn updates the parameters. The initial parameters of the distributions are first estimated based on the 2D human pose using the eight-point method. Then, a portion is sampled around the initial value and another portion is sampled around the entire camera domain. The distribution is initialized by the sampling result. Since the input of a single frame may cause a large error in the eight-point method, and initializing the distribution in this way increases the robustness of the algorithm." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "content": "Monte Carlo sampling We assume that the 2D heatmap is the marginal distribution of the 3D heatmap along the projection direction, and the problem can be transformed into an optimization problem based on the reprojection error:" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14853" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 92, + 297, + 135 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 92, + 297, + 135 + ], + "spans": [ + { + "bbox": [ + 48, + 92, + 297, + 135 + ], + "type": "interline_equation", + "content": "\\min _ {y, X ^ {3 D}} \\quad \\sum_ {i} ^ {N} \\int_ {\\sigma_ {i}} \\left\\| x _ {i} ^ {2 D} \\left(\\sigma_ {i}\\right) - \\int_ {p r o j \\left(z, y _ {i}\\right) = \\sigma_ {i}} x ^ {3 D} (z) \\mathrm {d} z \\right\\| _ {2} \\mathrm {d} \\sigma_ {i} \\tag {3}", + "image_path": "8474c235a3c34c0f7b0185e40b46a9ad91f8b0cb25b6907e951f2869bb505b07.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "spans": [ + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "type": "text", + "content": " denotes the body element in 3D space, " + }, + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "type": "inline_equation", + "content": "\\sigma_{i}" + }, + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "type": "text", + "content": " denotes the area element of the " + }, + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "type": "text", + "content": "th camera plane, and " + }, + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "type": "inline_equation", + "content": "proj(\\cdot)" + }, + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "type": "text", + "content": " denotes the projection function. A more general heatmap representation is adopted here, where " + }, + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "type": "inline_equation", + "content": "x^{3D}" + }, + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "type": "inline_equation", + "content": "x^{2D}" + }, + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "type": "text", + "content": " are considered as the probability density functions of the heatmap distribution. In practice, the heatmap is often stored in a discrete way, and the integrals need to be discretized as well. However, it is difficult to establish the constraints between " + }, + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "type": "inline_equation", + "content": "X^{3D}" + }, + { + "bbox": [ + 47, + 136, + 287, + 254 + ], + "type": "text", + "content": " explicitly, making the above optimization problem difficult to solve." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 256, + 287, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 256, + 287, + 280 + ], + "spans": [ + { + "bbox": [ + 47, + 256, + 287, + 280 + ], + "type": "text", + "content": "Therefore, we use an approximate 3D heatmap explicitly defined as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 94, + 293, + 287, + 332 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 293, + 287, + 332 + ], + "spans": [ + { + "bbox": [ + 94, + 293, + 287, + 332 + ], + "type": "interline_equation", + "content": "x ^ {3 D} (z) = \\frac {1}{N} \\sum_ {\\substack {i \\\\ p r o j (z, y _ {i}) = \\sigma_ {i}}} ^ {N} x _ {i} ^ {2 D} (\\sigma_ {i}) \\tag{4}", + "image_path": "e94aee99a9a6d2ce71ad6251dcce0c18bb6da9f6f10aa25659c37a2896889428.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 109, + 334, + 238, + 355 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 334, + 238, + 355 + ], + "spans": [ + { + "bbox": [ + 109, + 334, + 238, + 355 + ], + "type": "interline_equation", + "content": "x _ {i} ^ {2 D} (\\sigma_ {i}) = \\max _ {p r o j (z, y _ {i}) = \\sigma_ {i}} x ^ {3 D} (z)", + "image_path": "f465d0d1d984ae5122e6786875dbef75cc7b70e5d011fb0968f38dc1449829fd.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 362, + 287, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 362, + 287, + 446 + ], + "spans": [ + { + "bbox": [ + 47, + 362, + 287, + 446 + ], + "type": "text", + "content": "This definition is similar to the volume of the learnable triangulation, with the advantage that " + }, + { + "bbox": [ + 47, + 362, + 287, + 446 + ], + "type": "inline_equation", + "content": "X^{3D}" + }, + { + "bbox": [ + 47, + 362, + 287, + 446 + ], + "type": "text", + "content": " can be computed explicitly and differentiably from " + }, + { + "bbox": [ + 47, + 362, + 287, + 446 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 47, + 362, + 287, + 446 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 362, + 287, + 446 + ], + "type": "inline_equation", + "content": "X^{2D}" + }, + { + "bbox": [ + 47, + 362, + 287, + 446 + ], + "type": "text", + "content": ". It also has some physical meaning as far as the location of the extreme points taken is similar to the original representation. The visualization of the 3D heatmap under different definitions is shown in Figure 2." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 447, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 447, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 47, + 447, + 287, + 483 + ], + "type": "text", + "content": "The generated " + }, + { + "bbox": [ + 47, + 447, + 287, + 483 + ], + "type": "inline_equation", + "content": "X^{3D}" + }, + { + "bbox": [ + 47, + 447, + 287, + 483 + ], + "type": "text", + "content": " retains the information of the heatmap and can be used as input for subsequent networks. Thus, the problem is simplified to:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 48, + 505, + 287, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 505, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 48, + 505, + 287, + 563 + ], + "type": "interline_equation", + "content": "\\min _ {y} \\sum_ {i} ^ {N} \\| \\underbrace {\\sum_ {z} \\left(x ^ {3 D} (z) x _ {i} ^ {2 D} \\left(\\sigma_ {i}\\right)\\right) ^ {2} \\left(x _ {i} ^ {2 D} \\left(\\sigma_ {i}\\right) - x ^ {3 D} (z)\\right)} _ {f _ {i} (y)} \\| _ {2} \\tag {5}", + "image_path": "74836e5c9bf8c62082dd0d2b6e66b818de9df8b4fabb6c85981dc9ab2242f0ec.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 565, + 286, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 565, + 286, + 589 + ], + "spans": [ + { + "bbox": [ + 47, + 565, + 286, + 589 + ], + "type": "text", + "content": "The reprojection error is employed as the negative logarithm of the likelihood function " + }, + { + "bbox": [ + 47, + 565, + 286, + 589 + ], + "type": "inline_equation", + "content": "p(X_{2D}|y)" + }, + { + "bbox": [ + 47, + 565, + 286, + 589 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 98, + 601, + 287, + 633 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 601, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 98, + 601, + 287, + 633 + ], + "type": "interline_equation", + "content": "p \\left(X ^ {2 D} | y\\right) = \\exp - \\sum_ {i} ^ {N} \\| f _ {i} (y) \\| _ {2} \\tag {6}", + "image_path": "3405f55ed31728cde2014aaafa03ace5262a4e2f95be0f3415f772331c803b20.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 642, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 287, + 677 + ], + "type": "text", + "content": "Suppose that the camera pose " + }, + { + "bbox": [ + 47, + 642, + 287, + 677 + ], + "type": "inline_equation", + "content": "p(y)" + }, + { + "bbox": [ + 47, + 642, + 287, + 677 + ], + "type": "text", + "content": " is subject to a uniform distribution, " + }, + { + "bbox": [ + 47, + 642, + 287, + 677 + ], + "type": "inline_equation", + "content": "p(y|X^{2D})" + }, + { + "bbox": [ + 47, + 642, + 287, + 677 + ], + "type": "text", + "content": " can be calculated by Bayesian formula:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 108, + 689, + 287, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 689, + 287, + 717 + ], + "spans": [ + { + "bbox": [ + 108, + 689, + 287, + 717 + ], + "type": "interline_equation", + "content": "p (y | X ^ {2 D}) = \\frac {p \\left(X ^ {2 D} \\mid y\\right)}{E \\left[ p \\left(X ^ {2 D} \\mid y\\right) \\right]} \\tag {7}", + "image_path": "3f564da1787bd86fa08357b8ce907f379b1b7c1bad309a5080faf29f5fa061d0.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": "The calculation of denominator expectation can be estimated by Monte Carlo sampling approximation. The specific calculation formula is as follows." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 126, + 545, + 160 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 126, + 545, + 160 + ], + "spans": [ + { + "bbox": [ + 313, + 126, + 545, + 160 + ], + "type": "interline_equation", + "content": "E \\left[ p \\left(X ^ {2 D} | y\\right) \\right] \\approx \\frac {1}{M} \\sum_ {j} ^ {M} q \\left(y _ {j}\\right) p \\left(X ^ {2 D} | y\\right), y _ {j} \\sim q (y) \\tag {8}", + "image_path": "cb894962eba0122ccba728d31068570b2216726bb2ff79f6ad35c9829a80927c.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 169, + 545, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 169, + 545, + 193 + ], + "spans": [ + { + "bbox": [ + 305, + 169, + 545, + 193 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 169, + 545, + 193 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 169, + 545, + 193 + ], + "type": "text", + "content": " denotes the total number of samples. Then, " + }, + { + "bbox": [ + 305, + 169, + 545, + 193 + ], + "type": "inline_equation", + "content": "q(y)" + }, + { + "bbox": [ + 305, + 169, + 545, + 193 + ], + "type": "text", + "content": " is updated using the computed " + }, + { + "bbox": [ + 305, + 169, + 545, + 193 + ], + "type": "inline_equation", + "content": "p(y|X^{2D})" + }, + { + "bbox": [ + 305, + 169, + 545, + 193 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 193, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 193, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 305, + 193, + 545, + 239 + ], + "type": "text", + "content": "Finally, the normalized " + }, + { + "bbox": [ + 305, + 193, + 545, + 239 + ], + "type": "inline_equation", + "content": "q(y)" + }, + { + "bbox": [ + 305, + 193, + 545, + 239 + ], + "type": "text", + "content": " is used as the weight and the " + }, + { + "bbox": [ + 305, + 193, + 545, + 239 + ], + "type": "inline_equation", + "content": "X^{3D}" + }, + { + "bbox": [ + 305, + 193, + 545, + 239 + ], + "type": "text", + "content": " generated by all sampled points " + }, + { + "bbox": [ + 305, + 193, + 545, + 239 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 193, + 545, + 239 + ], + "type": "text", + "content": " is weighted and averaged as the input to the subsequent 3D pose reconstruction network." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 376, + 249, + 545, + 280 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 249, + 545, + 280 + ], + "spans": [ + { + "bbox": [ + 376, + 249, + 545, + 280 + ], + "type": "interline_equation", + "content": "X ^ {3 D} = \\frac {\\sum_ {j} q \\left(y _ {j}\\right) X _ {j} ^ {3 D}}{\\sum_ {j} q \\left(y _ {j}\\right)} \\tag {9}", + "image_path": "1601a6903e51a7204ccc0a80d895769a6cf2195b5770ed31ca5a55ebf438ce22.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 291, + 393, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 291, + 393, + 304 + ], + "spans": [ + { + "bbox": [ + 306, + 291, + 393, + 304 + ], + "type": "text", + "content": "3.3. Training Loss" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 309, + 545, + 333 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 309, + 545, + 333 + ], + "spans": [ + { + "bbox": [ + 305, + 309, + 545, + 333 + ], + "type": "text", + "content": "The entire training process includes two loss terms: " + }, + { + "bbox": [ + 305, + 309, + 545, + 333 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{3d}" + }, + { + "bbox": [ + 305, + 309, + 545, + 333 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 309, + 545, + 333 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cam}" + }, + { + "bbox": [ + 305, + 309, + 545, + 333 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 334, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 334, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 305, + 334, + 545, + 369 + ], + "type": "text", + "content": "We measure the difference between the true distribution of camera pose " + }, + { + "bbox": [ + 305, + 334, + 545, + 369 + ], + "type": "inline_equation", + "content": "z(y)" + }, + { + "bbox": [ + 305, + 334, + 545, + 369 + ], + "type": "text", + "content": " and the posterior distribution " + }, + { + "bbox": [ + 305, + 334, + 545, + 369 + ], + "type": "inline_equation", + "content": "p(y|X^{2D})" + }, + { + "bbox": [ + 305, + 334, + 545, + 369 + ], + "type": "text", + "content": " using KL divergence." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 321, + 387, + 545, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 387, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 321, + 387, + 545, + 437 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {c a m} = D _ {K L} (z (y) \\| p (y | X ^ {2 D})) \\\\ = - \\frac {1}{2} \\sum_ {i} ^ {N} \\| f _ {i} \\left(y _ {g t}\\right) \\| _ {2} + \\log E [ p \\left(X ^ {2 D} | y\\right) ] \\tag {10} \\\\ \\end{array}", + "image_path": "e432a18f8f765ea316252ec1ea8f4f3d69ef6b2bb33b20c8186b75ca7a3b8b32.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 445, + 544, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 445, + 544, + 468 + ], + "spans": [ + { + "bbox": [ + 305, + 445, + 544, + 468 + ], + "type": "text", + "content": "where the expectation of the second half is also obtained by the calculation of the equation 8." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 468, + 545, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 468, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 305, + 468, + 545, + 515 + ], + "type": "text", + "content": "The 3D human pose estimation loss is the same as previous works[18], which encourages the predicted 3d poses to be close to the ground truth. The formula can be summarized as follow:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 524, + 544, + 549 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 524, + 544, + 549 + ], + "spans": [ + { + "bbox": [ + 306, + 524, + 544, + 549 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {3 d} = \\left\\| \\operatorname {s o f t a r g m a x} \\left(X ^ {3 D}\\right) - X _ {g t} \\right\\| _ {1} - \\beta \\cdot \\log \\left(X ^ {3 D} \\left(X _ {g t}\\right)\\right) \\tag {11}", + "image_path": "8cc500a4566553412573fc25c1691b50d5698de3502f1027cd7545b1c0221235.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 550, + 545, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 550, + 545, + 585 + ], + "spans": [ + { + "bbox": [ + 305, + 550, + 545, + 585 + ], + "type": "text", + "content": "In end-to-end training, we simultaneously optimize these two loss terms to train the networks, and the total loss function can be written as:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 370, + 595, + 545, + 608 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 595, + 545, + 608 + ], + "spans": [ + { + "bbox": [ + 370, + 595, + 545, + 608 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\mathcal {L} _ {\\text {c a m}} + \\lambda_ {2} \\mathcal {L} _ {3 d} \\tag {12}", + "image_path": "c9fe44e5d26bc9a7a4e9f9fc0c5dd51cec689c1aa54a240ff8dc46ad62041d82.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 616, + 539, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 616, + 539, + 629 + ], + "spans": [ + { + "bbox": [ + 306, + 616, + 539, + 629 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 306, + 616, + 539, + 629 + ], + "type": "inline_equation", + "content": "\\lambda_{1} = 1" + }, + { + "bbox": [ + 306, + 616, + 539, + 629 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 616, + 539, + 629 + ], + "type": "inline_equation", + "content": "\\lambda_{2} = 0.1" + }, + { + "bbox": [ + 306, + 616, + 539, + 629 + ], + "type": "text", + "content": " in our experiment setting." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 639, + 387, + 653 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 639, + 387, + 653 + ], + "spans": [ + { + "bbox": [ + 306, + 639, + 387, + 653 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 658, + 419, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 419, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 419, + 670 + ], + "type": "text", + "content": "4.1. Dataset & Metrics" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": "We conducted experiments on two of the most commonly used 3D human pose datasets available today, Human3.6M[17] and CMU Panoptic[19, 29, 35]. We used" + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14854" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 538, + 224 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 538, + 224 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 538, + 224 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 538, + 224 + ], + "type": "table", + "html": "
MethodDir.Disc.EatGreetPhonePhotoPosePurch.SitSitD.SmokeWaitWalkD.WalkWalkT.Mean
Calibration method
Remelli et al.[28]27.332.125.026.529.335.428.831.636.431.731.229.926.933.730.430.2
Bartol et al.[2]27.528.429.327.530.128.127.930.832.932.530.829.428.530.530.129.1
He et al. [16]25.727.723.724.826.931.424.926.528.831.728.226.423.628.323.526.9
Qiu et al. [26]24.026.723.224.324.822.824.128.632.126.931.025.625.028.024.426.2
Ma et al. [22]24.426.423.421.125.223.224.733.829.826.426.824.223.226.123.325.8
Iskakov et al.[18]19.920.018.918.520.519.418.422.122.528.721.220.819.722.120.220.8
Uncalibration method
Gordon et al.[14]22.023.624.926.730.635.725.132.929.532.532.626.534.726.027.730.2
Ours method24.025.426.630.432.120.120.536.540.129.527.427.620.824.122.027.8
", + "image_path": "a5d7f978afb05b2ee9c383504741207e84db4b1e1a2df252a943b112a5810b26.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 86, + 274, + 249, + 385 + ], + "blocks": [ + { + "bbox": [ + 46, + 232, + 546, + 257 + ], + "lines": [ + { + "bbox": [ + 46, + 232, + 546, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 232, + 546, + 257 + ], + "type": "text", + "content": "Table 1: Results of the evaluation on the Human3.6M dataset. The table shows the MPJPE in millimeters for the published state-of-the-art calibrated and uncalibrated methods." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 86, + 274, + 249, + 385 + ], + "lines": [ + { + "bbox": [ + 86, + 274, + 249, + 385 + ], + "spans": [ + { + "bbox": [ + 86, + 274, + 249, + 385 + ], + "type": "table", + "html": "
MethodMPJPE,mm
Calibrated method
Iskakov et al. Algebraic[18]21.3
Iskakov et al. Volumetric[18]13.7
Uncalibrated method
Bartol et al. [2]25.4
Our method24.2
", + "image_path": "4c37961fd87bd9ad61d28fa6e0675f339c20b0f4479a7cf055c2e1f44460dafd.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 393, + 287, + 418 + ], + "lines": [ + { + "bbox": [ + 46, + 393, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 393, + 287, + 418 + ], + "type": "text", + "content": "Table 2: Results of the MPJPE on the CMU Panoptic dataset ( using four cameras)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 454, + 287, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 454, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 46, + 454, + 287, + 538 + ], + "type": "text", + "content": "the 17-joint MPJPE (Mean Per Joint Position Error) as a metric to evaluate our method. In training, we normalize the ground truth according to the method in section3.2 to ensure the uniqueness in the camera pose solution. In validation, the estimated 3D human pose is denormalized to the original coordinate system to ensure the correctness of the MPJPE calculation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 568, + 178, + 580 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 568, + 178, + 580 + ], + "spans": [ + { + "bbox": [ + 47, + 568, + 178, + 580 + ], + "type": "text", + "content": "4.2. Implementation details" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": "We added the Probabilistic Triangulation based on the work learnable triangulation by Iskakov et al.[18] to realize uncalibrated 3D human pose estimation. The same experimental parameter settings as the learnable triangulation method were used. As with learnable triangulation, our method uses predictions from the algebraic triangulation. Our method can also be fine-tuned and be trained in an end-to-end manner. " + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "inline_equation", + "content": "q(y)" + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": " is initialized using a uniform distribution. The number of iterations is four, and the number of Monte Carlo samples is 256." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 277, + 489, + 290 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 277, + 489, + 290 + ], + "spans": [ + { + "bbox": [ + 305, + 277, + 489, + 290 + ], + "type": "text", + "content": "4.3. Comparisons with State-of-the-art" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 297, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 545, + 548 + ], + "type": "text", + "content": "We compared the existing state-of-the-art calibrated and uncalibrated 3D pose estimation algorithms. The evaluation results on the Human3.6M dataset and the CMU Panoptic dataset are shown in Table 1 and Table 2, respectively. The experimental results show that the MPJPE of our method has outperformed the state-of-the-art uncalibrated approaches and achieved comparable performance to calibrated methods. It is worth noting that our method achieves better results in most scenarios of uncalibrated setting (see Table 1), but the results are poor in the Purch. and Sit. sub-datasets. This is because there are more occlusions in these two subsets, resulting in the 2D joint estimation being inaccurate, which further affects the estimation of the camera parameter distribution. Therefore, the final accumulated error affects the 3D human pose estimation performance. Inferring the camera parameters from the features of the detected human inevitably leads to estimation results depending on the capability of the human feature detector. However, our method still outperforms existing uncalibrated methods in terms of overall MPJPE for both datasets." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 562, + 512, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 562, + 512, + 574 + ], + "spans": [ + { + "bbox": [ + 305, + 562, + 512, + 574 + ], + "type": "text", + "content": "4.4. Evaluation on Camera Pose Estimation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "To evaluate the capability of our camera pose estimation, we have conducted comparisons with some classical camera parameter estimation algorithms on the Human3.6M dataset. Due to the large parallax between different camera views, we choose 2D human keypoints estimated from 20 consecutive frames as image feature points to solve the camera pose parameters. We compare our camera estimation with Bundle Adjustment[32] and RANSAC 8-point algorithm[30]. Bundle Adjustment choose to minimize the reprojection error using the LM algorithm to find the camera parameters and the RANSAC 8-point algorithm uses the" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14855" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 76, + 190, + 335 + ], + "blocks": [ + { + "bbox": [ + 75, + 76, + 190, + 335 + ], + "lines": [ + { + "bbox": [ + 75, + 76, + 190, + 335 + ], + "spans": [ + { + "bbox": [ + 75, + 76, + 190, + 335 + ], + "type": "image", + "image_path": "4eeb0c04e06036b306911c2bc47d094c672a337517cf6a0d4b18276a6c8b71b2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 87, + 339, + 174, + 350 + ], + "lines": [ + { + "bbox": [ + 87, + 339, + 174, + 350 + ], + "spans": [ + { + "bbox": [ + 87, + 339, + 174, + 350 + ], + "type": "text", + "content": "(a) Bundle Adjustment." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 238, + 76, + 356, + 335 + ], + "blocks": [ + { + "bbox": [ + 238, + 76, + 356, + 335 + ], + "lines": [ + { + "bbox": [ + 238, + 76, + 356, + 335 + ], + "spans": [ + { + "bbox": [ + 238, + 76, + 356, + 335 + ], + "type": "image", + "image_path": "f67cb64b06dc89e4de3ffa114bb5b52378c276cca547ebdba5c48903dc130966.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 238, + 338, + 355, + 350 + ], + "lines": [ + { + "bbox": [ + 238, + 338, + 355, + 350 + ], + "spans": [ + { + "bbox": [ + 238, + 338, + 355, + 350 + ], + "type": "text", + "content": "(b) RANSAC 8-point algorithm." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 406, + 72, + 521, + 335 + ], + "blocks": [ + { + "bbox": [ + 406, + 72, + 521, + 335 + ], + "lines": [ + { + "bbox": [ + 406, + 72, + 521, + 335 + ], + "spans": [ + { + "bbox": [ + 406, + 72, + 521, + 335 + ], + "type": "image", + "image_path": "9574540b4dc48dbbcbaad0aeb0e664f774c628fb463d4a166f96a3b9844f9f22.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 431, + 338, + 493, + 349 + ], + "lines": [ + { + "bbox": [ + 431, + 338, + 493, + 349 + ], + "spans": [ + { + "bbox": [ + 431, + 338, + 493, + 349 + ], + "type": "text", + "content": "(c) Ours method." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 359, + 547, + 396 + ], + "lines": [ + { + "bbox": [ + 46, + 359, + 547, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 359, + 547, + 396 + ], + "type": "text", + "content": "Figure 3: Visualization of the camera pose parameters and 3D human pose obtained by different algorithms. The quadrilateral cone indicates the camera pose parameters, the gray part indicates the ground truth, and the colored part indicates the prediction results of different algorithms." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 417, + 287, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 417, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 417, + 287, + 571 + ], + "type": "text", + "content": "8-point method to find the fundamental matrix after screening out the outliers by RANSAC, and then uses the eigenvalue decomposition to find the camera pose. We provide some visualization examples in Figure 3. From the Figure 3, we can see that Bundle Adjustment often falls into the local optimal solution, resulting in poor camera poses. The RANSAC 8-point algorithm can remove outliers, but the estimation of the camera pose is sensitive to 2D human pose estimation, which will lead to accumulated errors when reconstructing 3D human poses. The 3D human and camera pose estimation results are more robust and accurate when introducing our Probabilistic Triangulation (see (c) of Figure 3)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 573, + 288, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 573, + 288, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 573, + 288, + 662 + ], + "type": "text", + "content": "Table 3 shows more detailed results of camera pose evaluation, using the same experimental setup as [2]. Among the evaluation metrics used: 1. 3D estimation error " + }, + { + "bbox": [ + 46, + 573, + 288, + 662 + ], + "type": "inline_equation", + "content": "(\\mathrm{mm})" + }, + { + "bbox": [ + 46, + 573, + 288, + 662 + ], + "type": "inline_equation", + "content": "E_{3D} = E[\\| x^{\\hat{3} D} - x^{3D}\\| _2]" + }, + { + "bbox": [ + 46, + 573, + 288, + 662 + ], + "type": "text", + "content": " ; 2. Projection 2D error " + }, + { + "bbox": [ + 46, + 573, + 288, + 662 + ], + "type": "inline_equation", + "content": "(\\mathrm{mm})E_{2D} = E[\\| x^{\\hat{2} D} - x^{2D}\\| _2]" + }, + { + "bbox": [ + 46, + 573, + 288, + 662 + ], + "type": "text", + "content": " ; 3. Camera rotation error " + }, + { + "bbox": [ + 46, + 573, + 288, + 662 + ], + "type": "inline_equation", + "content": "E_{R} = E[\\| \\hat{q} -q\\|_{2}]" + }, + { + "bbox": [ + 46, + 573, + 288, + 662 + ], + "type": "text", + "content": " ; 4. Camera translation error (mm) " + }, + { + "bbox": [ + 46, + 573, + 288, + 662 + ], + "type": "inline_equation", + "content": "E_{t} = E[\\| \\hat{t} -t\\|_{2}]" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 670, + 194, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 194, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 194, + 683 + ], + "type": "text", + "content": "4.5. Cross-dataset experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "To test the generalization ability of Probabilistic Triangulation across datasets, we segment CMU Panoptic and" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 325, + 415, + 528, + 476 + ], + "blocks": [ + { + "bbox": [ + 325, + 415, + 528, + 476 + ], + "lines": [ + { + "bbox": [ + 325, + 415, + 528, + 476 + ], + "spans": [ + { + "bbox": [ + 325, + 415, + 528, + 476 + ], + "type": "table", + "html": "
methodsE3D↓E2D↓ER↓Et↓
BA736.82130.180.02546.87
RANSAC 8-point97.5050.140.0125.30
Our methods27.805.980.00432.71
", + "image_path": "630f27edb79e2de9c9dc6aa9b5fe49dfe1f65dfd32cd6b6cdf3e433d91630720.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 484, + 545, + 509 + ], + "lines": [ + { + "bbox": [ + 305, + 484, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 305, + 484, + 545, + 509 + ], + "type": "text", + "content": "Table 3: Quantitative experiments on camera pose estimation on the Human3.6M dataset." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 517, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 545, + 662 + ], + "type": "text", + "content": "Human36M into five sub-datasets in the same way as Bartol et al.[2]. Cross-dataset experiments are conducted between these sub-datasets two by two. It was found that there was no significant loss of accuracy between the CMU Panoptic sub-datasets even after segmentation (this is because the distribution between the sub-datasets of the CMU Panoptic dataset is very similar). However, the results trained from the CMU dataset have a significant loss of accuracy on Human3.6M. Table 4 shows the generalization ability of Probabilistic Triangulation and Bartol et al.[2] from the CMU dataset to the Human3.6M dataset. Probabilistic Triangulation exhibits stronger generalization." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 670, + 523, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 523, + 683 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 523, + 683 + ], + "type": "text", + "content": "4.6. Ablation study on the number of cameras" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "content": "We show the results of the ablation study in Table 5. 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MethodTrainSelf-TestH36M-Testdiff
Bartol et al.[2]CMU125.833.530%
CMU226.033.428%
CMU325.031.024%
CMU425.132.528%
Ours methodCMU124.630.825%
CMU223.729.123%
CMU324.129.221%
CMU424.931.125%
", + "image_path": "cb5f27a1de344104b9077bfe700f3d1978f271c5eb43a4f6ddd8e42677c1a3b3.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 510, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 559 + ], + "type": "text", + "content": "3-view and 2-view because the network has seen rich information during training. There is some performance degradation when the model is trained on 2-view and tested on 3-view and 4-view as shown in Table 5." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 77, + 566, + 258, + 616 + ], + "blocks": [ + { + "bbox": [ + 46, + 392, + 288, + 489 + ], + "lines": [ + { + "bbox": [ + 46, + 392, + 288, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 288, + 489 + ], + "type": "text", + "content": "Table 4: Experiments on generalization ability between datasets (MPJPE in mm). The CMU Panoptic dataset was split into four sub-datasets with different number of cameras and different spatial distributions of cameras. The models were trained on the four datasets separately, and the results were evaluated on their own test set and the Human3.6M test set. The last column represents the cross-data accuracy decline rate." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 77, + 566, + 258, + 616 + ], + "lines": [ + { + "bbox": [ + 77, + 566, + 258, + 616 + ], + "spans": [ + { + "bbox": [ + 77, + 566, + 258, + 616 + ], + "type": "table", + "html": "
2-view3-view4-view
Training on 2-view29.542.439.2
Training on 4-view32.629.327.8
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Ablation study on each module" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "In order to demonstrate the irreplaceable role that probabilistic triangularization plays in camera pose estimation and 3D human reconstruction in uncalibrated 3D human" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 260, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 260, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 260, + 545, + 308 + ], + "type": "text", + "content": "pose estimation. We design two ablation experiments to remove the influence of the rest of the network on the results and to demonstrate the role of Probabilistic Triangulation better." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 309, + 545, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 309, + 545, + 381 + ], + "spans": [ + { + "bbox": [ + 304, + 309, + 545, + 381 + ], + "type": "text", + "content": "First, we use 2D heatmaps ground truth as the input of Probabilistic Triangulation to eliminate the effect of 2D backbone on the results. Also, the upper bound of our method is shown (see Table 6 middle). The table shows that our method achieves comparable results to the calibration method [18] when given the 2D ground truth." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 382, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 382, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 382, + 545, + 453 + ], + "type": "text", + "content": "The 3D error still cannot reach zero under the condition of using 2D ground truth because there is a theoretical upper limit to the accuracy of the voxel structure. However, the 2D human pose estimator error cannot be avoided, and the better robustness of the voxel structure to error is the reason it was chosen." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "text", + "content": "In addition, we demonstrate the necessity of introducing the camera pose estimation module by comparing it with Iskaov et al. (V2V network and triangulation). We rotated the world coordinate system " + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "inline_equation", + "content": "(0^{\\circ}" + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "inline_equation", + "content": "180^{\\circ}" + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "text", + "content": " randomly around the vertical axis and " + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "inline_equation", + "content": "0^{\\circ}" + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "inline_equation", + "content": "45^{\\circ}" + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "text", + "content": " randomly around the pitch) to change the values of the camera's external parameters, resulting in a new test set called \"Test*\" in Table 6. We can find that only using a V2V network and triangulation will make the network overfit the camera poses, resulting in performance degradation. Our method does not require the input of camera poses, so changes in the world coordinate system do not affect our method's final pose estimation results. It demonstrates that our camera estimation module, i.e., the main contribution, is necessary and reasonable." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 634, + 487, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 634, + 487, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 634, + 487, + 647 + ], + "type": "text", + "content": "4.8. Visualization of Sampling Process" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "content": "In order to visualize the sampling process in the Probabilistic Triangulation, the 256 sampling points of each iteration are embedded by t-SNE and plotted in Figure 4. From the figure, as the iteration proceeds, the approximation of the camera distribution becomes more and more ac" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14857" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 63, + 70, + 271, + 119 + ], + "blocks": [ + { + "bbox": [ + 63, + 70, + 271, + 119 + ], + "lines": [ + { + "bbox": [ + 63, + 70, + 271, + 119 + ], + "spans": [ + { + "bbox": [ + 63, + 70, + 271, + 119 + ], + "type": "table", + "html": "
Baseline2D GTTest*
Iskakov et al.20.816.325.12
Our methods27.818.527.8
", + "image_path": "d17212e0d2d9c0e6a8046d2ff7e1521f638ba34594eb828e27b81370cf230b51.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 127, + 287, + 186 + ], + "lines": [ + { + "bbox": [ + 46, + 127, + 287, + 186 + ], + "spans": [ + { + "bbox": [ + 46, + 127, + 287, + 186 + ], + "type": "text", + "content": "Table 6: Pose estimation results (MPJPE, mm) on different 2D and test settings. The middle two columns show the results of 3D pose estimation using the 2D estimator and 2D GT, respectively. The rightmost column shows the estimation results on the Test* set." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 197, + 286, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 197, + 286, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 197, + 286, + 293 + ], + "type": "text", + "content": "curate, the sampled points are closer to the ground truth, and the sampling loss keeps decreasing. At the same time, the whole camera pose space is not smooth, and there are many local optimums and pseudo-solutions. The 2D human pose estimator generates noise, making the classical camera pose estimation more likely to fall into local optimal solutions. Distributed representation of camera pose (Probabilistic Triangulation) can alleviate this problem." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 293, + 286, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 286, + 436 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 286, + 436 + ], + "type": "text", + "content": "Furthermore, from Figure 4, the sampling points are concentrated around a few extreme points as the iteration parameters increase. This is because an incremental solution exists to the camera pose estimation, so there are multiple extreme points. However, only one of them has real physical significance, whereas, in the projection process, these extreme points produce the same projection result. The distribution also tends to converge to a single extreme point if an initial value is used to initialize the camera pose distribution, and the sampling points of the distribution are spread out to appear near multiple extreme points if a uniform distribution is used to initialize the distribution." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 445, + 194, + 458 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 445, + 194, + 458 + ], + "spans": [ + { + "bbox": [ + 47, + 445, + 194, + 458 + ], + "type": "text", + "content": "4.9. Generalize to Wide Scenes" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 464, + 286, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 286, + 561 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 286, + 561 + ], + "type": "text", + "content": "To demonstrate the generalization of our Probabilistic Triangulation in the wild scenes, we use a model trained from the CMU Panoptic dataset and test it on the natural scenes. Two iPhones with a " + }, + { + "bbox": [ + 46, + 464, + 286, + 561 + ], + "type": "inline_equation", + "content": "26\\mathrm{mm}" + }, + { + "bbox": [ + 46, + 464, + 286, + 561 + ], + "type": "text", + "content": " primary camera were used for the shooting, and the intrinsic parameters were read using the swift function. The results are shown in Figure 5. Our method remains in effect even when the camera space location and the number of cameras change." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 573, + 204, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 573, + 204, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 573, + 204, + 586 + ], + "type": "text", + "content": "5. Conclusions and limitations" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": "We propose a novel Probabilistic Triangulation module for multi-view 3D human pose estimation, which enables the existing calibrated methods to reduce the dependence on calibration and can be applied to uncalibrated wild scenes. Extensive experiments demonstrate that the 3D human pose estimation based on our Probabilistic Triangulation can achieve state-of-the-art performance when compared to uncalibrated methods. And the employment of camera pose distribution and Monte Carlo sampling alleviates the problem of easy access to local optimums and pseudo-solutions" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 326, + 74, + 526, + 268 + ], + "blocks": [ + { + "bbox": [ + 326, + 74, + 526, + 268 + ], + "lines": [ + { + "bbox": [ + 326, + 74, + 526, + 268 + ], + "spans": [ + { + "bbox": [ + 326, + 74, + 526, + 268 + ], + "type": "image", + "image_path": "43d1281dd326e15e6f0b7bc8d1d8c5ef2a3d484f0d0e8c672ab4eb0e5052d232.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 280, + 545, + 328 + ], + "lines": [ + { + "bbox": [ + 305, + 280, + 545, + 328 + ], + "spans": [ + { + "bbox": [ + 305, + 280, + 545, + 328 + ], + "type": "text", + "content": "Figure 5: Our method demonstrates the results in a non-calibrated wild scene. The first and second columns represent the two iPhone camera views, and the third column shows the estimated camera pose and 3D human pose." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 349, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 349, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 349, + 545, + 445 + ], + "type": "text", + "content": "in camera pose estimation. Since our Probabilistic Triangulation does not take the camera pose parameters as input, it is possible to build the multi-view 3D human pose estimation system in wild scenes and achieve a high-accurate capture. In the wild scenes, the Probabilistic Triangulation is not affected by the spatial location changes and the number of cameras. It can be directly applied to uncalibrated scenes after training with calibrated data." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 445, + 545, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 648 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 648 + ], + "type": "text", + "content": "The main limitation of our method is that it can only be applied to single-person scenes. Extending to multi-person scenarios requires taking into account the cross-view matching problem, which is difficult to solve in the absence of a camera pose. In addition, although the Probabilistic Triangulation does not require the camera pose as input during validation, the ground truth of the 3D human pose and the camera pose are used in the training process, and these data need to be obtained from the dataset of the calibration scene. In fact, the ground truth of camera pose is not directly involved in the training, but indirectly guides the 2D pose estimation network learning through cross-view information. The ground truth of the 3D human pose influences the 2D pose estimation network and enables the 3D pose reconstruction network to learn the human prior and integrate the information generated by previous sampling." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 671, + 545, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 671, + 545, + 708 + ], + "spans": [ + { + "bbox": [ + 304, + 671, + 545, + 708 + ], + "type": "text", + "content": "Acknowledgements This work was supported by National Key Research and Development Program of China (NO. 2022YFB3303202)." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14858" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 113 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 113 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 113 + ], + "type": "text", + "content": "[1] Sameer Agarwal and Keir Mierle. 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Motionbert: Unified pretraining for" + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "ref_text" + }, + { + "bbox": [ + 326, + 72, + 545, + 94 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 72, + 545, + 94 + ], + "spans": [ + { + "bbox": [ + 326, + 72, + 545, + 94 + ], + "type": "text", + "content": "human motion analysis. arXiv preprint arXiv:2210.06551, 2022." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "14860" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Progressive Spatio-Temporal Prototype Matching for Text-Video Retrieval/480eca60-b42e-4764-a2ee-88684bf2c389_content_list.json b/2023/Progressive Spatio-Temporal Prototype Matching for Text-Video Retrieval/480eca60-b42e-4764-a2ee-88684bf2c389_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..c1d278ae3910f43cb8d96ed29f89d143543b851d --- /dev/null +++ b/2023/Progressive Spatio-Temporal Prototype Matching for Text-Video Retrieval/480eca60-b42e-4764-a2ee-88684bf2c389_content_list.json @@ -0,0 +1,1581 @@ +[ + { + "type": "text", + "text": "Progressive Spatio-Temporal Prototype Matching for Text-Video Retrieval", + "text_level": 1, + "bbox": [ + 109, + 130, + 859, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Pandeng Li $^{1*}$ , Chen-Wei Xie $^{2}$ , Liming Zhao $^{2}$ , Hongtao Xie $^{1\\dagger}$ , Jiannan Ge $^{1}$ , Yun Zheng $^{2}$ , Deli Zhao $^{2}$ , Yongdong Zhang $^{1}$", + "bbox": [ + 192, + 179, + 774, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 University of Science and Technology of China, 2DAMO Academy, Alibaba Group", + "bbox": [ + 148, + 215, + 818, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{lpd, gejn}@mail.ustc.edu.cn, {htxie, zhyd73}@ustc.edu.cn", + "bbox": [ + 233, + 236, + 735, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{eniac.xcw, lingchen.zlm, zhengyun.zy}@alibaba-inc.com, zhaodeli@gmail.com", + "bbox": [ + 156, + 253, + 810, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 304, + 313, + 319 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The performance of text-video retrieval has been significantly improved by vision-language cross-modal learning schemes. The typical solution is to directly align the global video-level and sentence-level features during learning, which would ignore the intrinsic video-text relations, i.e., a text description only corresponds to a spatio-temporal part of videos. Hence, the matching process should consider both fine-grained spatial content and various temporal semantic events. To this end, we propose a text-video learning framework with progressive spatio-temporal prototype matching. Specifically, the matching process is decomposed into two complementary phases: object-phrase prototype matching and event-sentence prototype matching. In the object-phrase prototype matching phase, the spatial prototype generation mechanism predicts key patches or words, which are aggregated into object or phrase prototypes. Importantly, optimizing the local alignment between object-phrase prototypes helps the model perceive spatial details. In the event-sentence prototype matching phase, we design a temporal prototype generation mechanism to associate intra-frame objects and interact inter-frame temporal relations. Such progressively generated event prototypes can reveal semantic diversity in videos for dynamic matching. Validated by comprehensive experiments, our method consistently outperforms the state-of-the-art methods on four video retrieval benchmark.", + "bbox": [ + 75, + 335, + 473, + 729 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 751, + 209, + 767 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Understanding multimodal information [13, 37, 40, 76, 6, 79, 41, 12, 53, 54] is an essential way for humans to perceive the world. As a fundamental task in multimodal learning [25, 62, 60], Text-Video Retrieval (TVR) [22, 70, 68, 24] has garnered huge interest with the rapid devel", + "bbox": [ + 75, + 776, + 468, + 853 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0e7b72f3e44ac5c2bd3d79c230398ca43bfa0c035dd92a05235dea96722212c1.jpg", + "image_caption": [ + "(1) Adaptive event matching w/o object-phrase prototypes" + ], + "image_footnote": [], + "bbox": [ + 506, + 325, + 885, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/29070ad6abfd347d64546d3d5c3d95239bf7930b3e5f3f3bf929d1ea2b6216e5.jpg", + "image_caption": [ + "(2) Our object-phrase prototype matching", + "Figure 1. Visualization of event and object prototypes learned by 1) adaptive event matching w/o object-phrase prototypes and 2) object-phrase prototype matching. Object prototypes can focus on local patches (e.g., tail) and complement event-level matching." + ], + "image_footnote": [], + "bbox": [ + 570, + 477, + 823, + 585 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "opment of short video platforms. TVR [45, 21] aims to search semantically relevant videos based on user-entered text queries. Unfortunately, the inherent modality gap phenomenon [42, 61, 38, 3, 67] increases the difficulty of associating multimodal data. Towards such a concern, pioneering works [47, 65, 73] usually exploit multiple unimodal pre-trained models to extract features, and then use metric learning strategies [14] to strengthen the modality alignment in the joint space. However, there are large differences in the initial distributions of multiple unimodal offline features, which inevitably brings the feature fusion challenge to affect the retrieval results.", + "bbox": [ + 496, + 672, + 892, + 853 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, encouraged by the success of vision-language pre-training [50, 66, 34, 27, 72, 35, 4], a series of canonical works [51, 20, 44, 16] are proposed by transferring knowl-", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Interns at DAMO Academy, Alibaba Group", + "bbox": [ + 94, + 862, + 334, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author", + "bbox": [ + 96, + 875, + 220, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{1}$ Code is available at https://github.com/IMCCretrieval/ProST.", + "bbox": [ + 94, + 887, + 424, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4100", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7a112fc02f46f7ae64523cdefe5521e51dbafb6446885a2624cf796c1c58eefb.jpg", + "image_caption": [ + "Figure 2. The progressive prototype generation process: 1) focus on patch-level spatial details; 2) aggregate intra-frame object prototypes; 3) interact inter-frame relations temporally as event prototypes, corresponding to multiple semantics." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 472, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "edge from cross-modal pre-trained models (e.g., CLIP [57]) to the TVR task. Among them, some methods [51, 1, 28] learn to encode text or video data as a single embedding and perform global alignment between the sentence and the whole video. Subsequent approaches [48, 78] employ frame-level or segment-level matching by taking into account the different importance of video content. These methods try to encode the video into a single semantic content described by corresponding text, establishing one-to-one relations. However, videos contain rich visual elements [39] and a text description may only correspond to a spatio-temporal part of the video, dynamic and fine-grained matching is needed beyond the global video-level or frame-level matching. Specifically, feature encoding should characterize different semantic information to support dynamic partial alignment during the matching process. Recently, Lin et al. [43] attempt to address the dynamic matching problem by temporally segmenting videos into multiple semantic events, so that different text descriptions can adaptively match event prototypes. Nevertheless, various event prototypes are still inadequate to model the relations between fine-grained objects and content words, lacking the perception of local details. As shown in Fig. 1(1), the correct video corresponding to the text should focus on \"tail\", but the event prototype corresponding to the maximum similarity may suffer from scene bias [8, 63] and ignore this small object. Based on the above observation, an effective event-sentence matching process needs to emphasize fine-grained local spatial matching. This also suggests that the generation of event prototypes should be bootstrapped from the semantic combination of important objects. Therefore, we should construct event prototypes progressively, i.e., explicitly preserve the local information learned in the spatial", + "bbox": [ + 75, + 401, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "matching stage, and then perform temporal aggregation.", + "bbox": [ + 498, + 90, + 870, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we propose a novel Progressive Spatio-Temporal Prototype Matching (ProST) framework, which decomposes the matching process into complementary object-phrase and event-sentence prototype alignments. In the object-phrase prototype matching phase, a spatial prototype generation mechanism is first developed to focus on key image patches or word tokens. To prevent massive video redundancy, we use sparse weights to filter irrelevant background interference and aggregate important patch or word tokens into object or phrase prototypes. As shown in Fig. 1(2), optimal local responses can be found by the maximum similarity between object and phrase prototypes to help the model perceive spatial details.", + "bbox": [ + 496, + 107, + 890, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the event-sentence prototype matching phase, a temporal prototype generation mechanism is designed to decode various event prototypes for dynamic semantic alignment. Specifically, since the spatial details should not be ignored in the event generation process, we send object prototypes to the frame and event decoder for progressive prototype learning. Multiple different event prototypes are generated to reveal the semantic diversity in videos and support dynamic matching. Finally, as shown in Fig. 2, different text sentences can match the most appropriate event prototype learned from the video. Overall, ProST encodes the rich video content by generating object-level, frame-level and event-level prototypes in a progressive manner, and constructs dynamic and fine-grained spatio-temporal matching strategies. ProST not only strengthens the interaction of local spatial content, but also considers the intrinsic relations where video and text are only partially aligned.", + "bbox": [ + 496, + 303, + 892, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions of this paper are threefold: 1) we propose a novel framework, ProST, to decompose the matching process into complementary object-phrase and event-sentence prototype alignments; 2) two prototype generation mechanisms are developed to learn sparse spatial and dynamic temporal information respectively, which can fully explore fine-grained local details and video semantic diversity; 3) extensive experiments demonstrate that ProST outperforms state-of-the-art methods on MSRVTT, DiDeMo, VATEX and LSMDC datasets.", + "bbox": [ + 496, + 560, + 890, + 709 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 724, + 640, + 739 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text-video retrieval. Existing works can be divided into two categories: offline feature based [47, 11, 77, 26] and end-to-end training [1, 51, 48, 43, 31, 29, 30, 28] methods.", + "bbox": [ + 496, + 750, + 890, + 794 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Early methods [69, 11] extract video-text features offline, and then perform embedding alignment in a common space. To enhance representation quality, CE [47], MMT [17] and HiT [46] employ multiple unimodal experts (OCR, speech, etc.) to enrich video features. Teach-Text [10] adopts multiple text encoders to gather text information and obtain more credible alignments. Besides,", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4101", + "bbox": [ + 480, + 944, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "HGR [5] and T2vlad [65] build semantic graphs or shared centers to explore global-local relations. However, these methods employ additional analysis tools or experts to preprocess data, which increases the complexity and limits flexibility. Unlike the global-local alignment explored on multiple experts [65, 46], we consider finer-grained patch-level visual content without requiring additional experts.", + "bbox": [ + 75, + 90, + 470, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Current mainstream works benefit from large-scale vision-language pre-training [57, 19]. ClipBERT [33] and Frozen [1] first propose efficient end-to-end pre-training schemes. MCQ [18] builds cross-modal associations by predicting verb or noun features. Recently, CLIP4clip [51] uses CLIP [57] as the backbone network, significantly improving TVR performance and inspiring a series of works [48, 15, 20, 78, 28]. Centerclip [78] conducts segment-level clustering, which reduces token redundancy and computational overhead. TS2Net [48] designs the token shift module to realize the perception of local movement between frames. Xpool [20] uses text as a condition to guide the aggregation of video tokens. But the limitation is that the video encoding process must involve both modal data.", + "bbox": [ + 75, + 199, + 468, + 411 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Adaptive cross-modal retrieval. Recently, the correspondence ambiguity problem (i.e., a text may only correspond to a part of the video or image) has raised concerns in the cross-modal retrieval community [9, 59, 43]. In text-image retrieval, PVSE [59] employs the self-attention mechanism to explore different local parts of instances and generates $K$ candidate features for adaptive matching. PCME [9] samples the text-image probabilistic embeddings multiple times from the learned Gaussian distribution to explore one-to-many multiplicity relationships. In text-video retrieval, TVMM [43] utilizes fully connected layers to directly aggregate all tokens into multiple event prototypes for text-adaptive event matching. However, fine-grained object-level information is not well exploited in the event matching process of TVMM, while the proposed progressive spatiotemporal matching framework could simultaneously consider local spatial details and dynamic temporal relations.", + "bbox": [ + 75, + 412, + 470, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 691, + 168, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a dataset consisting of $n$ videos $\\mathcal{V} = \\{\\pmb{v}_i\\}_{i=1}^n$ and their corresponding $m$ captions $\\mathcal{T} = \\{\\pmb{t}_i\\}_{i=1}^m$ , Text-Video Retrieval (TVR) aims to learn a function $s(\\pmb{t}_i, \\pmb{v}_i)$ to effectively measure the similarity between modalities. For a text query $\\pmb{t}_i$ , we can rank all videos in the dataset according to the similarity scores. Ideally, the cross-modal similarity (e.g., cosine similarity) between paired cross-modal instances should be greater than that of unpaired instances: $s(\\pmb{t}_i, \\pmb{v}_i) > s(\\pmb{t}_i, \\pmb{v}_j)$ . This requires the model to learn powerful text encoding network $\\pmb{f}_t : \\mathcal{T} \\to \\mathcal{Y}$ and video encoding network $\\pmb{f}_v : \\mathcal{V} \\to \\mathcal{X}$ , which generate high-quality features and ultimately enable efficient matching.", + "bbox": [ + 75, + 719, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Framework", + "text_level": 1, + "bbox": [ + 500, + 90, + 627, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fig. 3 sheds light on our end-to-end trainable architecture, which consists of a backbone network and two prototype matching schemes. For a fair comparison with recent methods [48, 51, 20], we adopt CLIP [57] as the backbone network, which exhibits strong performance in downstream tasks. Given an input video $\\mathbf{v}_i$ , we uniformly select $L$ frames as keyframes to extract sequential features $\\mathbf{X}_i = \\{\\mathbf{x}_C^l, \\mathbf{x}_{T_1}^l, \\dots, \\mathbf{x}_{T_K}^l\\}_{l=1}^L \\in \\mathbb{R}^{L \\times (K+1) \\times D}$ , where $\\mathbf{x}_C^l$ is the global frame token feature ([CLS]) and $K$ is the patch number. For each query text $t_i$ , we add the [SOT] and [EOT] tokens to indicate the start and the end of the text. The output text token features can be defined as $\\mathbf{Y}_i = \\{\\mathbf{y}_S, \\mathbf{y}_{T_1}, \\dots, \\mathbf{y}_{T_M}, \\mathbf{y}_E\\} \\in \\mathbb{R}^{(M+2) \\times D}$ , where $\\mathbf{y}_E$ is the global text token feature([EOT]), $M$ and $D$ are the number of words and dimensions, respectively.", + "bbox": [ + 496, + 112, + 890, + 340 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Apart from the backbone network, we decompose the matching process into two spatio-temporal complementary parts: 1) Object-Phrase Prototype Matching (Sec. 3.2) aligns the visual object prototypes and text phrase prototypes generated by Spatial Prototype Generation (SPG) to emphasize fine-grained spatial information; 2) Event-Sentence Prototype Matching (Sec. 3.3) exploits event prototypes progressively generated by Temporal Prototype Generation (TPG) to learn dynamic semantic alignment, which explores intrinsic one-to-many video-text relations. The object-phrase and event-sentence prototype matching schemes determine the final cross-modal similarity.", + "bbox": [ + 496, + 340, + 890, + 523 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Object-Phrase Prototype Matching", + "text_level": 1, + "bbox": [ + 500, + 530, + 805, + 546 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The text of the video caption subjectively describes a certain event composed of different objects, actions and temporal activities across the video sequence. This results in pairs of video and text that are often partially matched. To solve this problem [9, 59], existing method [43] learns a single patch-event projection to aggregate multiple event prototypes for text-adaptive matching. However, these prototypes are still inadequate to perceive the local details. Our intuition is that decoupling the spatio-temporal modeling process in a divide-and-conquer manner is more beneficial than a single projection. Therefore, we conduct progressive spatio-temporal prototype matching for text-video retrieval. In this section, we illustrate how to model spatial matching. We first perform patch-object and word-phrase spatial prototype aggregation to reveal key local details, and then introduce the fine-grained prototype alignment.", + "bbox": [ + 496, + 553, + 890, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Spatial prototype generation. For videos, we aggregate the patch tokens into object prototypes to represent fine-grained spatial information, such as object instance, object part, and action region. In the prototype generation process, not all patch tokens are aggregated. Although the patch tokens contain important spatial information, they also bring redundancy. For example, some background to", + "bbox": [ + 496, + 795, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4102", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4c442d68a00fd58715e4583d1045146bfab56c1ee0fef0bd806988fdedc0bb3d.jpg", + "image_caption": [ + "Figure 3. Our ProST framework. We decompose the matching process into two spatio-temporal complementary parts: 1) Object-Phrase Prototype Matching aligns the visual object prototypes and text phrase prototypes generated by Spatial Prototype Generation (SPG) to emphasize fine-grained spatial information; 2) Event-Sentence Prototype Matching exploits event prototypes progressively generated by Temporal Prototype Generation (TPG) to learn dynamic semantic alignment, which explores intrinsic one-to-many video-text relations." + ], + "image_footnote": [], + "bbox": [ + 119, + 89, + 848, + 239 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6b48532e4ccd86f98e7a9669041c458a0ba365ab69aac3d2456d7cb580c92847.jpg", + "image_caption": [ + "Figure 4. Details of the Spatial Prototype Generation (SPG) and Temporal Prototype Generation (TPG) mechanisms." + ], + "image_footnote": [], + "bbox": [ + 102, + 313, + 869, + 429 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "kens may interfere with cross-modal alignment. Hence, we hope to filter out retrieval-superfluous information and generate object-level prototypes in a sparse aggregation manner. For simplicity, two Fully Connected (FC) layers and ReLU functions are used to predict sparse weights $\\pmb{W}_{o}^{l} \\in \\mathbb{R}^{(K + 1)\\times N_{o}}$ , where $N_{o}$ is the number of object prototypes. This way prevents object prototypes from being affected by redundant patches. For each frame $\\pmb{X}^{l} \\in \\mathbb{R}^{(K + 1)\\times D}$ , SPG can be defined as:", + "bbox": [ + 75, + 474, + 472, + 609 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {P} _ {o} ^ {l} = \\boldsymbol {W} _ {o} ^ {l ^ {T}} \\cdot \\boldsymbol {X} ^ {l} \\in \\mathbb {R} ^ {N _ {o} \\times D}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 178, + 614, + 468, + 636 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Ideally, each object prototype can adaptively aggregate the corresponding object-related or action-related patches.", + "bbox": [ + 75, + 643, + 468, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For text, we draw on the SPG mechanism and design a similar network structure to aggregate word tokens, which generates phrase prototypes $P_{p} \\in \\mathbb{R}^{N_{p} \\times D}$ . In this way, we explore spatially important information based on fine-grained patch tokens and word tokens. Then, the prototypes are optimized by spatial object-phrase prototype matching.", + "bbox": [ + 75, + 674, + 470, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Object-phrase matching. Different from the existing text-image token-wise interaction [74], we propose a text-video prototype-wise interaction designed from a spatial perspective. Specifically, we first compute the maximum similarity of object-phrase prototypes within each frame. This associates the most similar phrase prototypes to each object prototype, reflecting cross-modal fine-grained matching. Then, for the multi-frame object similarity matrix, we find the largest similarity score across the frame sequences, which", + "bbox": [ + 75, + 763, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "gives a more confident probability of object-phrase matching. Finally, the object-phrase matching scores are summed to obtain the final similarity $s_{op}$ . The prototype-wise interaction process is defined as:", + "bbox": [ + 496, + 474, + 892, + 535 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ns _ {o p} = \\frac {1}{N _ {o}} \\sum_ {j = 1} ^ {N _ {o}} \\max _ {l = 1} ^ {L} \\max _ {i = 1} ^ {N _ {p}} \\left[ \\boldsymbol {P} _ {p} \\cdot \\boldsymbol {P} _ {o} ^ {l ^ {T}} \\right] _ {i j}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 544, + 890, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $N_{o}, N_{p}$ and $L$ are the number of object prototypes, phrase prototypes and frames, respectively.", + "bbox": [ + 496, + 595, + 890, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Event-Sentence Prototype Matching", + "text_level": 1, + "bbox": [ + 500, + 635, + 815, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we illustrate how to model dynamic temporal matching. We first perform progressive object-event prototype aggregation to reveal the video semantic diversity, and then introduce dynamic prototype matching.", + "bbox": [ + 496, + 659, + 890, + 719 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Temporal prototype generation. A naive solution to obtain video-level features based on global frame features is by mean pooling [51, 65, 5], or by adding temporal encoder layers [11]. However, this leads to two issues: 1) failure to perceive local details [43, 78, 48] and ignoring important objects will exacerbate the bias of video feature learning; 2) these strategies generate a single video-level feature, which can only quantify one-to-one relations. Therefore, we investigate how to incorporate key fine-grained objects and dynamic temporal changes into diverse event prototypes.", + "bbox": [ + 496, + 719, + 892, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The core idea is to progressively aggregate spatial object prototypes into frame prototypes and then perform inter", + "bbox": [ + 496, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4103", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "frame interaction to generate various event prototypes. In Fig. 4, a frame decoder is first designed to incorporate all object prototypes $P_{o} \\in \\mathbb{R}^{(L \\times N_{o}) \\times D}$ into frame-level prototypes $P_{f} \\in \\mathbb{R}^{L \\times D}$ , which implies fine-grained inter-object spatial relations. To learn frame-level object relations, we define the masked attention as:", + "bbox": [ + 75, + 90, + 472, + 181 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {P} _ {f} = \\operatorname {s o f t m a x} \\left(\\boldsymbol {M} _ {f} + \\boldsymbol {Q} _ {f} \\boldsymbol {K} _ {o} ^ {\\mathrm {T}}\\right) \\boldsymbol {V} _ {o} + \\boldsymbol {Q} _ {f}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 191, + 468, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $Q_{f}\\in \\mathbb{R}^{L\\times D}$ refers to frame queries (i.e., a set of randomly initialized learnable tokens), $K_{o}$ and $V_{o}$ are the features after the linear transformation of object prototypes $P_{o}$ . The attention mask $M_{f}\\in \\mathbb{R}^{L\\times (L\\times N_{o})}$ is:", + "bbox": [ + 76, + 218, + 468, + 281 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {M} _ {f} (i, j) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} i \\cdot N _ {o} \\leq j < (i + 1) \\cdot N _ {o} \\\\ - \\infty & \\text {o t h e r w i s e} \\end{array} . \\right. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 290, + 468, + 330 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspired by [9], we add frame prototype $\\pmb{p}_f^l$ and original global feature $\\pmb{x}_C^l$ of corresponding frames to enhance the robustness of the model:", + "bbox": [ + 76, + 340, + 468, + 388 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {p} _ {f} ^ {l} = \\left(\\boldsymbol {p} _ {f} ^ {l} + \\boldsymbol {x} _ {C} ^ {l}\\right) / 2. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 398, + 468, + 419 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Next, a dynamic event decoder is developed to learn the inter-frame relations in $P_{f}$ , which can obtain different event prototypes $P_{e} \\in \\mathbb{R}^{N_{e} \\times D}$ to illustrate the rich information of videos. Our dynamic attention is formulated as:", + "bbox": [ + 76, + 428, + 468, + 488 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {P} _ {e} = \\operatorname {s o f t m a x} \\left(\\boldsymbol {Q} _ {e} \\boldsymbol {K} _ {f} ^ {\\mathrm {T}}\\right) \\boldsymbol {V} _ {f} + \\boldsymbol {Q} _ {e}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 497, + 468, + 517 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $Q_{e} \\in \\mathbb{R}^{N_{e} \\times D}$ refers to event queries, $K_{f}$ and $V_{f}$ are the linear transformation features of frame prototypes $P_{f}$ . During training, each event query learns how to adaptively focus on video frame prototypes, while multiple queries implicitly guarantee a certain event diversity.", + "bbox": [ + 76, + 526, + 468, + 602 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Differently, since the same video often corresponds to multiple text semantic descriptions, we directly use the global text representation $\\pmb{y}_E$ as a sentence prototype to align with the event prototypes $\\pmb{P}_e$ .", + "bbox": [ + 76, + 603, + 468, + 662 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Event-sentence matching. Similar to [43], this event-sentence prototype matching process can be expressed as:", + "bbox": [ + 76, + 662, + 468, + 694 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ns _ {e s} = \\max _ {i = 1} ^ {N _ {e}} \\left\\langle \\boldsymbol {y} _ {E}, \\boldsymbol {P} _ {e _ {i}} \\right\\rangle . \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 705, + 468, + 731 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We look for the closest event prototype to the text representation for dynamic matching.", + "bbox": [ + 76, + 734, + 468, + 766 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training and Inference", + "text_level": 1, + "bbox": [ + 76, + 773, + 290, + 791 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The InfoNCE loss [55, 75] is employed to optimize the prototype matching within a batch. We treat text-video pairs as positive examples, while considering all other pairwise combinations in the batch as negative examples:", + "bbox": [ + 76, + 797, + 468, + 859 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {t v c} = \\left(\\mathcal {L} _ {t 2 v} \\left(\\boldsymbol {S} _ {o p}\\right) + \\mathcal {L} _ {v 2 t} \\left(\\boldsymbol {S} _ {o p}\\right) + \\mathcal {L} _ {t 2 v} \\left(\\boldsymbol {S} _ {e s}\\right) + \\mathcal {L} _ {v 2 t} \\left(\\boldsymbol {S} _ {e s}\\right)\\right) / 4, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 869, + 475, + 900 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {t 2 v} (\\boldsymbol {S}) = - \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(\\boldsymbol {S} ^ {i i} / \\sigma\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\boldsymbol {S} ^ {i j} / \\sigma\\right)}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 102, + 890, + 143 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {v 2 t} (\\boldsymbol {S}) = - \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(\\boldsymbol {S} ^ {i i} / \\sigma\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\boldsymbol {S} ^ {j i} / \\sigma\\right)}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 151, + 890, + 191 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the $\\sigma$ is a learnable temperature parameter, $S_{op}$ and $S_{es}$ are object-phrase and event-sentence prototype matching similarity matrices in a batch of size $B$ .", + "bbox": [ + 500, + 196, + 890, + 241 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During the inference stage, we directly weight the spatiotemporal matching scores for the final similarity matching: $s = s_{es} + \\beta s_{op}$ , where $\\beta$ is the spatial matching factor.", + "bbox": [ + 500, + 242, + 890, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 300, + 632, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We carry out experiments on the standard text-video retrieval datasets of MSRVTT [71], DiDeMo [23], VATEX [64] and LSMDC [58]. Standard metrics in information retrieval [48, 17] are adopted to measure the retrieval performance, including Recall@1/5/10 (R@1/5/10), Median Rank (MdR), and Mean Rank (MnR).", + "bbox": [ + 498, + 324, + 890, + 416 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 500, + 424, + 705, + 440 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. (1) MSRVTT [71] consists of 10k videos and 200k human-labeled descriptions, where many videos have diverse captions. To thoroughly compare the existing methods, we follow [20] to train on 7k or 9k train+val videos and test on a test set of 1k text-video pairs. (2) DiDeMo [23] contains 10K Flickr videos and 40K captions. Following [43], all caption descriptions of a video are concatenated as a query to evaluate all methods. (3) VATEX [64] is comprised of 34,991 video clips. According to [5], we select 25,991, 1, 500 and 1, 500 videos as the training, validation and test sets. (4) LSMDC [58] consists of 118,081 movie clips each paired with a single caption description. We choose 101, 079, 7, 408 and 1, 000 videos as the training, validation and test sets.", + "bbox": [ + 498, + 446, + 890, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. We initialize the backbone with the pre-trained model CLIP (ViT-B/32) [57] following [48]. Our decoders consist of two transformer layers with a single attention head. To reduce the computing overhead, all videos are resized to $224 \\times 224$ with random cropping and flipping, and the frame rate is 3. We set the max text length as 32 and video frame number as 12 except for DiDeMo (set to 64 and 64) as its videos are longer. We optimize the model for 5 epochs on 4 NVIDIA Tesla A100 GPUs, employ Adam optimizer [32] with 0.2 weight decay and fix the batch size as 128. The learning rate is set to 1e-7 for CLIP-initialized weights and 1e-4 for all other parameters. Following [57], we decay the learning rate using a warmup cosine schedule [49]. The spatial matching factor $\\beta$ is 1.5. By default, the prototype number $N_{o}$ , $N_{p}$ , and $N_{e}$ are 12, 28 and 3. The dimension of prototypes is 512.", + "bbox": [ + 498, + 659, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4104", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/46b496ab4fa227bd7fb6bad82f98e2c8af4a7e227954fd1327ca7a0dc646e0b7.jpg", + "table_caption": [ + "Table 1. Retrieval results on MSRVTT-9k. We reproduce TVMM* [43] using the same backbone network CLIP (ViT-B/32) [57]. All results in this table do not use additional post-processing techniques [2, 7]." + ], + "table_footnote": [], + "table_body": "
MethodReferenceText → VideoVideo → Text
R@1↑R@5↑R@10↑MdR↓MnR↓R@1↑R@5↑R@10↑MdR↓MnR↓
CE [47]BMVC1920.650.364.05.3-20.948.862.46.0-
MMT [17]ECCV2026.657.169.64.024.027.057.569.73.721.3
T2vlad [65]CVPR2129.559.070.14.0-31.860.071.13.0-
HiT [46]ICCV2127.759.272.02.9-28.860.372.33.0-
TeachText [10]ICCV2129.661.674.23.0-32.162.775.03.0-
ClipBERT [33]CVPR2122.046.859.96.0------
SupportSet [56]ICLR2130.158.569.33.0-28.558.671.63.0-
Frozen [1]ICCV2131.059.570.53.0------
BridgeFormer [18]CVPR2237.664.875.1-------
TVMM [43]NeurIPS2236.264.275.73.0-34.863.873.73.0-
CLIP4Clip [51]NeurCom2244.571.481.62.015.342.770.980.62.011.6
CenterCLIP [78]SIGIR2244.271.682.12.015.142.871.782.22.010.9
X-Pool [20]CVPR2246.972.882.22.014.3-----
TVMM* [43]NeurIPS2245.871.781.92.014.844.071.982.32.010.6
TS2-Net [48]ECCV2247.074.283.32.013.644.373.983.02.09.2
ProSTProposed48.274.683.42.012.446.374.283.22.08.7
ProST (ViT-B/16)Proposed49.575.084.02.011.748.075.985.22.08.3
", + "bbox": [ + 83, + 116, + 885, + 351 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c1dc12b7c4aa805eddaef1570f56a974322c91c8bdb544e8cd028f001ef8e954.jpg", + "table_caption": [ + "Table 2. Text-to-Video retrieval results on MSRVTT-7k." + ], + "table_footnote": [], + "table_body": "
MethodText → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
HowTo100M [52]14.940.252.89.0-
HERO [36]16.843.457.7--
ClipBERT [33]22.046.859.96.0-
CLIP4Clip [51]42.171.981.42.015.7
X-Pool [20]43.972.582.32.014.6
TS2-Net [48]43.172.282.12.014.2
ProST44.572.382.42.013.8
ProST (ViT-B/16)46.973.382.92.013.0
", + "bbox": [ + 83, + 386, + 462, + 502 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f92fed91bf7cb996973ee6d2b252bf2e34949dc6489f2f4777cfb67c1e2a4c46.jpg", + "table_caption": [ + "Table 3. Text-to-Video retrieval results on the DiDeMo dataset." + ], + "table_footnote": [], + "table_body": "
MethodText → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
CE [47]16.141.182.78.3-
ClipBERT [33]20.448.060.86.0-
Frozen [1]31.059.872.43.0-
MCQ [18]37.062.273.93.0-
TVMM [43]36.564.975.43.0-
CLIP4Clip [51]42.868.579.22.018.9
TS2-Net [48]41.871.682.02.014.8
ProST44.972.782.72.013.7
ProST (ViT-B/16)47.575.584.42.012.3
", + "bbox": [ + 81, + 529, + 460, + 655 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 76, + 680, + 441, + 696 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate the relative benefits of ProST, we compare its performance with recent works [48, 20, 78, 51] from the literature. The results on the 9k and 7k splits of MSRVTT are shown in Tab. 1 and Tab. 2 respectively. We consistently achieve the best results for text-to-video retrieval and video-to-text retrieval across all splits and all metrics. Specifically, TS2-Net [48] integrates important patches into frame features for frame-level matching, which achieves the second best performance. Notably, for text-to-video retrieval, ProST outperforms TS2-Net [48] with $1.2\\%$ and $1.4\\%$ R@1 gains on the 9k split (47.0% vs. 48.2%) and the 7k split (43.1% vs. 44.5%). A $2.0\\%$ improvement on R@1 (9k split) is also obtained compared to TS2-Net for video-to", + "bbox": [ + 75, + 703, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/51fe0e78b8b5c4c32fca7f0290e5728259af9e673fc14980441643384492c6ac.jpg", + "table_caption": [ + "Table 4. Text-to-Video retrieval results on the VATEX dataset." + ], + "table_footnote": [], + "table_body": "
MethodText → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
HGR [5]35.173.583.52.0-
CLIP [57]39.772.382.22.012.8
CLIP4Clip [51]55.989.295.01.03.9
QB-Norm [2]58.888.393.81.0-
CLIP2Video [15]57.390.095.51.03.6
TS2-Net [48]59.190.095.21.03.5
ProST60.690.595.41.03.4
ProST (ViT-B/16)64.092.296.31.03.1
", + "bbox": [ + 504, + 386, + 883, + 502 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/141462b676c230d4a0bddb6a563ba33451746db677789388314cb5974d53952c.jpg", + "table_caption": [ + "Table 5. Text-to-Video retrieval results on the LSMDC dataset." + ], + "table_footnote": [], + "table_body": "
MethodText → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
Frozen [1]15.030.839.820.0-
TVMM [43]17.837.145.913.5-
CLIP4Clip [51]21.641.849.811.061.0
X-Pool [20]24.042.951.59.055.1
QB-Norm [2]22.440.149.511.0-
TS2-Net [48]23.042.150.49.057.0
ProST24.142.551.69.054.6
ProST (ViT-B/16)26.346.155.28.051.4
", + "bbox": [ + 504, + 529, + 883, + 645 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "text retrieval (44.3% vs. 46.3%). Furthermore, we reproduce TVMM [43] based on CLIP (ViT-B/32), which has 2.4% (45.8% vs. 48.2%) and 2.3% (44.0% vs. 46.3%) lower R@1 than ProST on the 9k split. The results demonstrate the effectiveness of ProST, which mines the spatial object details and temporal event diversity of videos, improving the model discrimination. Besides, ProST achieves a low MnR metric of 12.4 (text-to-video) on the 9k split, demonstrating the model robustness to erroneous results.", + "bbox": [ + 496, + 672, + 890, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Tab. 3, 4 and 5, we examine the performance of ProST on the DiDeMo, VATEX and LSMDC datasets respectively. Compared with TS2-Net [48], ProST achieves a substantial boost of $3.1\\%$ , $1.5\\%$ and $1.1\\%$ on the R@1 metric for DiDeMo, VATEX and LSMDC, respectively. ProST outperforms state-of-the-art methods by a large margin with the", + "bbox": [ + 496, + 809, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4105", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7b96d93f03880bd42dea821c5d0e428f080f8dc7fbb57677b2cdb4043f13ab8d.jpg", + "table_caption": [ + "Table 6. The ablation study on MSRVTT-9k to investigate the effectiveness of Object-Phrase Prototype Matching (OPPM) and EventSentence Prototype Matching (ESPM). MdR results are not shown, as MdR=2.0 for all variants. Definition of important symbols: $\\checkmark$ indicates default settings; $\\odot$ TPG or $\\odot$ SPG means replace with TPG or SPG to generate prototypes; P-P or O-W refers the alignment of patch-phrase or object-word; -F, -M or -R refers to removing frame decoder, attention mask or residual structure in Eq. 5; F-W or $\\bar{\\mathbb{F}}$ -S means directly aligning frame global tokens and word tokens or aligning the mean of frame global tokens and text global token." + ], + "table_footnote": [], + "table_body": "
IDOPPMESPMText → VideoVideo → Text
SPGMatchingTPGMatchingR@1↑R@5↑R@10↑MnRR@1↑R@5↑R@10↑MnR
1✓✓45.672.281.114.344.971.682.310.0
2○SPG✓45.871.781.914.844.071.982.310.6
3✓✓45.972.882.413.245.173.382.79.8
4○TPG✓✓✓46.373.381.813.545.073.182.49.8
5✓✓○SPG✓47.773.683.012.645.974.083.09.0
6✓P-P✓✓46.072.581.614.943.172.482.110.8
7✓O-W✓✓47.173.382.212.845.773.382.69.6
8✓✓-F✓46.472.881.713.544.572.582.010.2
9✓✓-M✓47.873.882.912.646.073.782.89.0
10✓✓-R✓46.672.982.414.045.372.181.810.1
11F-W✓✓47.373.582.812.645.973.783.19.0
12✓✓F-S46.572.682.313.445.173.482.59.8
Ours✓✓✓✓48.274.683.412.446.374.283.28.7
", + "bbox": [ + 86, + 157, + 877, + 373 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b6251a47d69fc0178c4ce40f529d9e36aa662fad81be233c440c13a97998c78a.jpg", + "table_caption": [ + "Table 7. The ablation study on MSRVTT-9k to investigate the configuration of the number of prototypes." + ], + "table_footnote": [], + "table_body": "
{No, Np, Ne}Text → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
{6, 14, 3}45.673.281.62.014.3
{6, 28, 3}46.773.482.22.013.4
{12, 14, 3}47.073.783.02.012.9
{24, 32, 3}46.073.382.02.013.8
{12, 28, 1}46.373.082.12.013.5
{12, 28, 2}47.474.083.12.012.7
{12, 28, 4}47.674.383.22.012.5
{12, 28, 3}48.274.683.42.012.4
", + "bbox": [ + 81, + 421, + 467, + 547 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2ed5fcb075312643981cafe1e97d366acca2c3f6774477fc0ecd1b7dd0e58c78.jpg", + "image_caption": [ + "Figure 5. The R@1 results at different spatial matching factors $\\beta$ ." + ], + "image_footnote": [], + "bbox": [ + 81, + 563, + 464, + 654 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "CLIP (ViT-B/16) backbone. These results suggest the versatility and generalization of ProST, which can effectively process videos from different domains (e.g., movies). We owe the advantage of ProST over these works to the full use of dynamic spatio-temporal prototype matching.", + "bbox": [ + 75, + 696, + 467, + 773 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 785, + 230, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis of progressive spatio-temporal prototype matching. In Tab. 6, we compare ProST with 12 variants, which proves that each module contributes to final results.", + "bbox": [ + 75, + 809, + 467, + 854 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We elaborate on some important observations. First, we show the results relying only on Object-Phrase Prototype Matching (OPPM) or Event-Sentence Prototype Match", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ing (ESPM). To implement our model without OPPM, all tokens are fed directly into the frame decoder and event decoder (TPG) to get multiple event prototypes. When only ESPM is used, there is a $2.6\\%$ decrease in $\\mathbb{R}@\\mathbb{1}$ . This confirms the complementary role of fine-grained spatial details for ESPM. Next, we replace TPG with SPG and find that there is a certain suppression effect on noise. However, both of the above variants perform poorly due to the lack of progressive prototype generation and matching. When we only train model with OPPM, the model still underperforms. This may be due to the lack of temporal understanding and the inability to resolve correspondence ambiguity.", + "bbox": [ + 496, + 397, + 890, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Second, $\\mathbb{O}$ TPG, P-P and O-W prove that there is indeed redundancy in the original video tokens. The sparse weights in SPG can alleviate this problem. However, FC layers in SPG cannot interact with intra-frame and inter-frame information, making it difficult to generate better event prototypes. This may be the reason for the drop in $\\mathbb{O}$ SPG. Third, P-P and O-W also confirm the benefits of prototype matching. Raw patches or words without aggregation strategies may worsen the cross-modal alignment.", + "bbox": [ + 496, + 580, + 890, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fourth, the results for -F, -M and -R also decreased. Because intra-frame local object relations and global frame features jointly complement comprehensive frame-level spatial information, which is helpful for subsequent temporal learning. Fifth, from F-W and $\\overline{\\mathbf{F}}$ -S, we can see the importance of prototype design mode. Directly using global frame features ([CLS] tokens) in ProST-S for frame-word alignments lacks object details. In $\\overline{\\mathbf{F}}$ -S, the mean value of frame global features mixes all information equally, making it difficult to characterize dynamic and changeable videos.", + "bbox": [ + 496, + 717, + 890, + 868 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis of prototype configuration. We conduct experiments on various prototype configurations in Tab. 7. Im", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4106", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4dd685fda007b8295aa3ccaab445c98cc379e836c6806b8f6cfe9bc68e3ce92c.jpg", + "image_caption": [ + "Figure 6. Visualization of the object and event prototypes. We sample 12 frames in the video and object prototypes are shown as highlighted response regions in the frame. Then, we show cross-attention event weights of Eq. 6 in a line graph. Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 83, + 87, + 890, + 301 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "proper configuration of spatial prototypes leads to performance degradation, possibly because too many prototypes may introduce local noise, while few prototypes are not enough to express semantics. Furthermore, the best result is obtained when the number of event prototypes is 3, which may be related to the degree of semantic divergence of texts.", + "bbox": [ + 75, + 357, + 468, + 446 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Hyperparameter analysis. As shown in Fig. 5, we investigate the spatial matching factor $\\beta$ and present results for text-video (T2V) and video-text retrieval (V2T). As $\\beta$ grows, the performance increases at first and reaches the best results, then decreases as a whole. A small $\\beta$ may not fully exploit the underlying fine-grained spatial information, while a large $\\beta$ may overemphasize local matching and destroy the overall dynamic semantic understanding.", + "bbox": [ + 75, + 448, + 470, + 568 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Qualitative Results", + "text_level": 1, + "bbox": [ + 76, + 575, + 261, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization of prototypes. In Fig. 6, we first present object prototypes in video frames. Many redundant patches are removed by prototypes, and the spatially highlighted object part and the phrase can be well locally corresponded. Then, we compute cross-attention for 3 event queries and 12 video frames according to Eq. 6, whose weights are shown in a line graph. The weights of different event prototypes on different frames are quite different, which proves that our model can learn temporal relations and event prototypes can express diverse semantics. For example, event prototype 1 has larger weights on the first three frames, which indicates that it may correspond to the semantics contained in text 1. Similarly, event prototype 2 or 3 corresponds to text 2 or 3.", + "bbox": [ + 75, + 598, + 468, + 794 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Retrieval results. Top-3 TVR results are illustrated in Fig. 7. Specifically, for query 97, although the top-2 recalled videos are women in the same dress, the difference is that the correct video discusses the cushion seat, while the incorrect video does not. This proves that object-phrase prototype matching provides fine-grained spatial knowledge (i.e., objects). For query 353, ProST pays attention to", + "bbox": [ + 75, + 795, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/34a3909e2a8762b93ab62929c285012e198bdf76e9c6df391094d9336cb27f94.jpg", + "image_caption": [ + "Figure 7. Top-3 TVR results on MSRVTT-9k. Left: the ranked videos by our ProST. Right: the ranked videos with only event-sentence prototype matching. Red: correct videos." + ], + "image_footnote": [], + "bbox": [ + 503, + 354, + 888, + 642 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "both the brief human speech at the beginning of the video and the subsequent earth display. However, using only event prototypes will result in a matching error. This shows that ProST can make a trade-off between the spatio-temporal matching relations to achieve better discrimination.", + "bbox": [ + 498, + 717, + 890, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 811, + 617, + 828 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have proposed a novel text-video retrieval framework, ProST, to decompose the matching process into complementary object-phrase and event-sentence prototype alignments. In the object-phrase prototype matching stage,", + "bbox": [ + 498, + 839, + 890, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4107", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "we design the spatial prototype generation mechanism to focus on important video content and strengthen the fine-grained spatial alignment. In the event-sentence prototype matching phase, we use the temporal prototype generation mechanism to progressively generate diverse event prototypes and learn dynamic one-to-many relations. In this paper, we hope not only to provide insights into the importance of complementary spatio-temporal matching but also to facilitate future work that advances text-video retrieval by solving design flaws rather than mostly trial and error.", + "bbox": [ + 75, + 90, + 472, + 242 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgment. This work is supported by the National Key Research and Development Program of China (2022YFB3104700), the National Nature Science Foundation of China (62121002, 62022076, U1936210, 62102384).", + "bbox": [ + 75, + 242, + 472, + 316 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 332, + 174, + 348 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. Frozen in time: A joint video and image encoder for end-to-end retrieval. In ICCV, 2021. 2, 3, 6", + "[2] Simion-Vlad Bogolin, Ioana Croitoru, Hailin Jin, Yang Liu, and Samuel Albanie. Cross modal retrieval with querybank normalisation. In CVPR, 2022. 6", + "[3] Soravit Changpinyo, Jordi Pont-Tuset, Vittorio Ferrari, and Radu Soricut. Telling the what while pointing to the where: Multimodal queries for image retrieval. 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Tps++: Attention-enhanced thin-plate spline for scene text recognition. *IJCAI*, 2023. 1", + "bbox": [ + 501, + 90, + 890, + 133 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "4110", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Progressive Spatio-Temporal Prototype Matching for Text-Video Retrieval/480eca60-b42e-4764-a2ee-88684bf2c389_model.json b/2023/Progressive Spatio-Temporal Prototype Matching for Text-Video Retrieval/480eca60-b42e-4764-a2ee-88684bf2c389_model.json new file mode 100644 index 0000000000000000000000000000000000000000..acf51c3ab618f1b998dd9d965cd43eb9e37710bd --- /dev/null +++ b/2023/Progressive Spatio-Temporal Prototype Matching for Text-Video Retrieval/480eca60-b42e-4764-a2ee-88684bf2c389_model.json @@ -0,0 +1,2466 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.111, + 0.131, + 0.861, + 0.154 + ], + "angle": 0, + "content": "Progressive Spatio-Temporal Prototype Matching for Text-Video Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.18, + 0.775, + 0.218 + ], + "angle": 0, + "content": "Pandeng Li\\(^{1*}\\), Chen-Wei Xie\\(^{2}\\), Liming Zhao\\(^{2}\\), Hongtao Xie\\(^{1\\dagger}\\), Jiannan Ge\\(^{1}\\), Yun Zheng\\(^{2}\\), Deli Zhao\\(^{2}\\), Yongdong Zhang\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.15, + 0.217, + 0.82, + 0.235 + ], + "angle": 0, + "content": "1 University of Science and Technology of China, 2DAMO Academy, Alibaba Group" + }, + { + "type": "text", + "bbox": [ + 0.235, + 0.237, + 0.736, + 0.252 + ], + "angle": 0, + "content": "{lpd, gejn}@mail.ustc.edu.cn, {htxie, zhyd73}@ustc.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.158, + 0.255, + 0.812, + 0.27 + ], + "angle": 0, + "content": "{eniac.xcw, lingchen.zlm, zhengyun.zy}@alibaba-inc.com, zhaodeli@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.314, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.474, + 0.73 + ], + "angle": 0, + "content": "The performance of text-video retrieval has been significantly improved by vision-language cross-modal learning schemes. The typical solution is to directly align the global video-level and sentence-level features during learning, which would ignore the intrinsic video-text relations, i.e., a text description only corresponds to a spatio-temporal part of videos. Hence, the matching process should consider both fine-grained spatial content and various temporal semantic events. To this end, we propose a text-video learning framework with progressive spatio-temporal prototype matching. Specifically, the matching process is decomposed into two complementary phases: object-phrase prototype matching and event-sentence prototype matching. In the object-phrase prototype matching phase, the spatial prototype generation mechanism predicts key patches or words, which are aggregated into object or phrase prototypes. Importantly, optimizing the local alignment between object-phrase prototypes helps the model perceive spatial details. In the event-sentence prototype matching phase, we design a temporal prototype generation mechanism to associate intra-frame objects and interact inter-frame temporal relations. Such progressively generated event prototypes can reveal semantic diversity in videos for dynamic matching. Validated by comprehensive experiments, our method consistently outperforms the state-of-the-art methods on four video retrieval benchmark." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.752, + 0.21, + 0.768 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.777, + 0.47, + 0.854 + ], + "angle": 0, + "content": "Understanding multimodal information [13, 37, 40, 76, 6, 79, 41, 12, 53, 54] is an essential way for humans to perceive the world. As a fundamental task in multimodal learning [25, 62, 60], Text-Video Retrieval (TVR) [22, 70, 68, 24] has garnered huge interest with the rapid devel" + }, + { + "type": "image_caption", + "bbox": [ + 0.51, + 0.309, + 0.88, + 0.325 + ], + "angle": 0, + "content": "(1) Adaptive event matching w/o object-phrase prototypes" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.327, + 0.887, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.46, + 0.78, + 0.475 + ], + "angle": 0, + "content": "(2) Our object-phrase prototype matching" + }, + { + "type": "image", + "bbox": [ + 0.571, + 0.478, + 0.825, + 0.587 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.593, + 0.895, + 0.651 + ], + "angle": 0, + "content": "Figure 1. Visualization of event and object prototypes learned by 1) adaptive event matching w/o object-phrase prototypes and 2) object-phrase prototype matching. Object prototypes can focus on local patches (e.g., tail) and complement event-level matching." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.893, + 0.854 + ], + "angle": 0, + "content": "opment of short video platforms. TVR [45, 21] aims to search semantically relevant videos based on user-entered text queries. Unfortunately, the inherent modality gap phenomenon [42, 61, 38, 3, 67] increases the difficulty of associating multimodal data. Towards such a concern, pioneering works [47, 65, 73] usually exploit multiple unimodal pre-trained models to extract features, and then use metric learning strategies [14] to strengthen the modality alignment in the joint space. However, there are large differences in the initial distributions of multiple unimodal offline features, which inevitably brings the feature fusion challenge to affect the retrieval results." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Recently, encouraged by the success of vision-language pre-training [50, 66, 34, 27, 72, 35, 4], a series of canonical works [51, 20, 44, 16] are proposed by transferring knowl-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.863, + 0.336, + 0.876 + ], + "angle": 0, + "content": "*Interns at DAMO Academy, Alibaba Group" + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.876, + 0.221, + 0.888 + ], + "angle": 0, + "content": "† Corresponding author" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.425, + 0.9 + ], + "angle": 0, + "content": "\\(^{1}\\)Code is available at https://github.com/IMCCretrieval/ProST." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.863, + 0.425, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "4100" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.473, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.32, + 0.471, + 0.378 + ], + "angle": 0, + "content": "Figure 2. The progressive prototype generation process: 1) focus on patch-level spatial details; 2) aggregate intra-frame object prototypes; 3) interact inter-frame relations temporally as event prototypes, corresponding to multiple semantics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.402, + 0.473, + 0.904 + ], + "angle": 0, + "content": "edge from cross-modal pre-trained models (e.g., CLIP [57]) to the TVR task. Among them, some methods [51, 1, 28] learn to encode text or video data as a single embedding and perform global alignment between the sentence and the whole video. Subsequent approaches [48, 78] employ frame-level or segment-level matching by taking into account the different importance of video content. These methods try to encode the video into a single semantic content described by corresponding text, establishing one-to-one relations. However, videos contain rich visual elements [39] and a text description may only correspond to a spatio-temporal part of the video, dynamic and fine-grained matching is needed beyond the global video-level or frame-level matching. Specifically, feature encoding should characterize different semantic information to support dynamic partial alignment during the matching process. Recently, Lin et al. [43] attempt to address the dynamic matching problem by temporally segmenting videos into multiple semantic events, so that different text descriptions can adaptively match event prototypes. Nevertheless, various event prototypes are still inadequate to model the relations between fine-grained objects and content words, lacking the perception of local details. As shown in Fig. 1(1), the correct video corresponding to the text should focus on \"tail\", but the event prototype corresponding to the maximum similarity may suffer from scene bias [8, 63] and ignore this small object. Based on the above observation, an effective event-sentence matching process needs to emphasize fine-grained local spatial matching. This also suggests that the generation of event prototypes should be bootstrapped from the semantic combination of important objects. Therefore, we should construct event prototypes progressively, i.e., explicitly preserve the local information learned in the spatial" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.871, + 0.107 + ], + "angle": 0, + "content": "matching stage, and then perform temporal aggregation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.108, + 0.892, + 0.303 + ], + "angle": 0, + "content": "To this end, we propose a novel Progressive Spatio-Temporal Prototype Matching (ProST) framework, which decomposes the matching process into complementary object-phrase and event-sentence prototype alignments. In the object-phrase prototype matching phase, a spatial prototype generation mechanism is first developed to focus on key image patches or word tokens. To prevent massive video redundancy, we use sparse weights to filter irrelevant background interference and aggregate important patch or word tokens into object or phrase prototypes. As shown in Fig. 1(2), optimal local responses can be found by the maximum similarity between object and phrase prototypes to help the model perceive spatial details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.304, + 0.893, + 0.56 + ], + "angle": 0, + "content": "In the event-sentence prototype matching phase, a temporal prototype generation mechanism is designed to decode various event prototypes for dynamic semantic alignment. Specifically, since the spatial details should not be ignored in the event generation process, we send object prototypes to the frame and event decoder for progressive prototype learning. Multiple different event prototypes are generated to reveal the semantic diversity in videos and support dynamic matching. Finally, as shown in Fig. 2, different text sentences can match the most appropriate event prototype learned from the video. Overall, ProST encodes the rich video content by generating object-level, frame-level and event-level prototypes in a progressive manner, and constructs dynamic and fine-grained spatio-temporal matching strategies. ProST not only strengthens the interaction of local spatial content, but also considers the intrinsic relations where video and text are only partially aligned." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.71 + ], + "angle": 0, + "content": "The contributions of this paper are threefold: 1) we propose a novel framework, ProST, to decompose the matching process into complementary object-phrase and event-sentence prototype alignments; 2) two prototype generation mechanisms are developed to learn sparse spatial and dynamic temporal information respectively, which can fully explore fine-grained local details and video semantic diversity; 3) extensive experiments demonstrate that ProST outperforms state-of-the-art methods on MSRVTT, DiDeMo, VATEX and LSMDC datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.725, + 0.642, + 0.74 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.795 + ], + "angle": 0, + "content": "Text-video retrieval. Existing works can be divided into two categories: offline feature based [47, 11, 77, 26] and end-to-end training [1, 51, 48, 43, 31, 29, 30, 28] methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Early methods [69, 11] extract video-text features offline, and then perform embedding alignment in a common space. To enhance representation quality, CE [47], MMT [17] and HiT [46] employ multiple unimodal experts (OCR, speech, etc.) to enrich video features. Teach-Text [10] adopts multiple text encoders to gather text information and obtain more credible alignments. Besides," + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "4101" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.471, + 0.198 + ], + "angle": 0, + "content": "HGR [5] and T2vlad [65] build semantic graphs or shared centers to explore global-local relations. However, these methods employ additional analysis tools or experts to preprocess data, which increases the complexity and limits flexibility. Unlike the global-local alignment explored on multiple experts [65, 46], we consider finer-grained patch-level visual content without requiring additional experts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.2, + 0.47, + 0.412 + ], + "angle": 0, + "content": "Current mainstream works benefit from large-scale vision-language pre-training [57, 19]. ClipBERT [33] and Frozen [1] first propose efficient end-to-end pre-training schemes. MCQ [18] builds cross-modal associations by predicting verb or noun features. Recently, CLIP4clip [51] uses CLIP [57] as the backbone network, significantly improving TVR performance and inspiring a series of works [48, 15, 20, 78, 28]. Centerclip [78] conducts segment-level clustering, which reduces token redundancy and computational overhead. TS2Net [48] designs the token shift module to realize the perception of local movement between frames. Xpool [20] uses text as a condition to guide the aggregation of video tokens. But the limitation is that the video encoding process must involve both modal data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.413, + 0.471, + 0.673 + ], + "angle": 0, + "content": "Adaptive cross-modal retrieval. Recently, the correspondence ambiguity problem (i.e., a text may only correspond to a part of the video or image) has raised concerns in the cross-modal retrieval community [9, 59, 43]. In text-image retrieval, PVSE [59] employs the self-attention mechanism to explore different local parts of instances and generates \\( K \\) candidate features for adaptive matching. PCME [9] samples the text-image probabilistic embeddings multiple times from the learned Gaussian distribution to explore one-to-many multiplicity relationships. In text-video retrieval, TVMM [43] utilizes fully connected layers to directly aggregate all tokens into multiple event prototypes for text-adaptive event matching. However, fine-grained object-level information is not well exploited in the event matching process of TVMM, while the proposed progressive spatiotemporal matching framework could simultaneously consider local spatial details and dynamic temporal relations." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.692, + 0.169, + 0.707 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Given a dataset consisting of \\( n \\) videos \\( \\mathcal{V} = \\{\\pmb{v}_i\\}_{i=1}^n \\) and their corresponding \\( m \\) captions \\( \\mathcal{T} = \\{\\pmb{t}_i\\}_{i=1}^m \\), Text-Video Retrieval (TVR) aims to learn a function \\( s(\\pmb{t}_i, \\pmb{v}_i) \\) to effectively measure the similarity between modalities. For a text query \\( \\pmb{t}_i \\), we can rank all videos in the dataset according to the similarity scores. Ideally, the cross-modal similarity (e.g., cosine similarity) between paired cross-modal instances should be greater than that of unpaired instances: \\( s(\\pmb{t}_i, \\pmb{v}_i) > s(\\pmb{t}_i, \\pmb{v}_j) \\). This requires the model to learn powerful text encoding network \\( \\pmb{f}_t : \\mathcal{T} \\to \\mathcal{Y} \\) and video encoding network \\( \\pmb{f}_v : \\mathcal{V} \\to \\mathcal{X} \\), which generate high-quality features and ultimately enable efficient matching." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.628, + 0.105 + ], + "angle": 0, + "content": "3.1. Framework" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.113, + 0.892, + 0.342 + ], + "angle": 0, + "content": "Fig. 3 sheds light on our end-to-end trainable architecture, which consists of a backbone network and two prototype matching schemes. For a fair comparison with recent methods [48, 51, 20], we adopt CLIP [57] as the backbone network, which exhibits strong performance in downstream tasks. Given an input video \\( \\mathbf{v}_i \\), we uniformly select \\( L \\) frames as keyframes to extract sequential features \\( \\mathbf{X}_i = \\{\\mathbf{x}_C^l, \\mathbf{x}_{T_1}^l, \\dots, \\mathbf{x}_{T_K}^l\\}_{l=1}^L \\in \\mathbb{R}^{L \\times (K+1) \\times D} \\), where \\( \\mathbf{x}_C^l \\) is the global frame token feature ([CLS]) and \\( K \\) is the patch number. For each query text \\( t_i \\), we add the [SOT] and [EOT] tokens to indicate the start and the end of the text. The output text token features can be defined as \\( \\mathbf{Y}_i = \\{\\mathbf{y}_S, \\mathbf{y}_{T_1}, \\dots, \\mathbf{y}_{T_M}, \\mathbf{y}_E\\} \\in \\mathbb{R}^{(M+2) \\times D} \\), where \\( \\mathbf{y}_E \\) is the global text token feature([EOT]), \\( M \\) and \\( D \\) are the number of words and dimensions, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.342, + 0.892, + 0.524 + ], + "angle": 0, + "content": "Apart from the backbone network, we decompose the matching process into two spatio-temporal complementary parts: 1) Object-Phrase Prototype Matching (Sec. 3.2) aligns the visual object prototypes and text phrase prototypes generated by Spatial Prototype Generation (SPG) to emphasize fine-grained spatial information; 2) Event-Sentence Prototype Matching (Sec. 3.3) exploits event prototypes progressively generated by Temporal Prototype Generation (TPG) to learn dynamic semantic alignment, which explores intrinsic one-to-many video-text relations. The object-phrase and event-sentence prototype matching schemes determine the final cross-modal similarity." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.531, + 0.807, + 0.547 + ], + "angle": 0, + "content": "3.2. Object-Phrase Prototype Matching" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.795 + ], + "angle": 0, + "content": "The text of the video caption subjectively describes a certain event composed of different objects, actions and temporal activities across the video sequence. This results in pairs of video and text that are often partially matched. To solve this problem [9, 59], existing method [43] learns a single patch-event projection to aggregate multiple event prototypes for text-adaptive matching. However, these prototypes are still inadequate to perceive the local details. Our intuition is that decoupling the spatio-temporal modeling process in a divide-and-conquer manner is more beneficial than a single projection. Therefore, we conduct progressive spatio-temporal prototype matching for text-video retrieval. In this section, we illustrate how to model spatial matching. We first perform patch-object and word-phrase spatial prototype aggregation to reveal key local details, and then introduce the fine-grained prototype alignment." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Spatial prototype generation. For videos, we aggregate the patch tokens into object prototypes to represent fine-grained spatial information, such as object instance, object part, and action region. In the prototype generation process, not all patch tokens are aggregated. Although the patch tokens contain important spatial information, they also bring redundancy. For example, some background to" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4102" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.09, + 0.849, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.245, + 0.895, + 0.304 + ], + "angle": 0, + "content": "Figure 3. Our ProST framework. We decompose the matching process into two spatio-temporal complementary parts: 1) Object-Phrase Prototype Matching aligns the visual object prototypes and text phrase prototypes generated by Spatial Prototype Generation (SPG) to emphasize fine-grained spatial information; 2) Event-Sentence Prototype Matching exploits event prototypes progressively generated by Temporal Prototype Generation (TPG) to learn dynamic semantic alignment, which explores intrinsic one-to-many video-text relations." + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.314, + 0.87, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.136, + 0.435, + 0.828, + 0.451 + ], + "angle": 0, + "content": "Figure 4. Details of the Spatial Prototype Generation (SPG) and Temporal Prototype Generation (TPG) mechanisms." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.475, + 0.473, + 0.61 + ], + "angle": 0, + "content": "kens may interfere with cross-modal alignment. Hence, we hope to filter out retrieval-superfluous information and generate object-level prototypes in a sparse aggregation manner. For simplicity, two Fully Connected (FC) layers and ReLU functions are used to predict sparse weights \\( \\pmb{W}_{o}^{l} \\in \\mathbb{R}^{(K + 1)\\times N_{o}} \\), where \\( N_{o} \\) is the number of object prototypes. This way prevents object prototypes from being affected by redundant patches. For each frame \\( \\pmb{X}^{l} \\in \\mathbb{R}^{(K + 1)\\times D} \\), SPG can be defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.179, + 0.616, + 0.47, + 0.637 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {P} _ {o} ^ {l} = \\boldsymbol {W} _ {o} ^ {l ^ {T}} \\cdot \\boldsymbol {X} ^ {l} \\in \\mathbb {R} ^ {N _ {o} \\times D}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.47, + 0.674 + ], + "angle": 0, + "content": "Ideally, each object prototype can adaptively aggregate the corresponding object-related or action-related patches." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.471, + 0.765 + ], + "angle": 0, + "content": "For text, we draw on the SPG mechanism and design a similar network structure to aggregate word tokens, which generates phrase prototypes \\( P_{p} \\in \\mathbb{R}^{N_{p} \\times D} \\). In this way, we explore spatially important information based on fine-grained patch tokens and word tokens. Then, the prototypes are optimized by spatial object-phrase prototype matching." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Object-phrase matching. Different from the existing text-image token-wise interaction [74], we propose a text-video prototype-wise interaction designed from a spatial perspective. Specifically, we first compute the maximum similarity of object-phrase prototypes within each frame. This associates the most similar phrase prototypes to each object prototype, reflecting cross-modal fine-grained matching. Then, for the multi-frame object similarity matrix, we find the largest similarity score across the frame sequences, which" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.893, + 0.536 + ], + "angle": 0, + "content": "gives a more confident probability of object-phrase matching. Finally, the object-phrase matching scores are summed to obtain the final similarity \\( s_{op} \\). The prototype-wise interaction process is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.545, + 0.892, + 0.587 + ], + "angle": 0, + "content": "\\[\ns _ {o p} = \\frac {1}{N _ {o}} \\sum_ {j = 1} ^ {N _ {o}} \\max _ {l = 1} ^ {L} \\max _ {i = 1} ^ {N _ {p}} \\left[ \\boldsymbol {P} _ {p} \\cdot \\boldsymbol {P} _ {o} ^ {l ^ {T}} \\right] _ {i j}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.597, + 0.892, + 0.629 + ], + "angle": 0, + "content": "where \\(N_{o}, N_{p}\\) and \\(L\\) are the number of object prototypes, phrase prototypes and frames, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.636, + 0.816, + 0.654 + ], + "angle": 0, + "content": "3.3. Event-Sentence Prototype Matching" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.72 + ], + "angle": 0, + "content": "In this section, we illustrate how to model dynamic temporal matching. We first perform progressive object-event prototype aggregation to reveal the video semantic diversity, and then introduce dynamic prototype matching." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.871 + ], + "angle": 0, + "content": "Temporal prototype generation. A naive solution to obtain video-level features based on global frame features is by mean pooling [51, 65, 5], or by adding temporal encoder layers [11]. However, this leads to two issues: 1) failure to perceive local details [43, 78, 48] and ignoring important objects will exacerbate the bias of video feature learning; 2) these strategies generate a single video-level feature, which can only quantify one-to-one relations. Therefore, we investigate how to incorporate key fine-grained objects and dynamic temporal changes into diverse event prototypes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "The core idea is to progressively aggregate spatial object prototypes into frame prototypes and then perform inter" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4103" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.182 + ], + "angle": 0, + "content": "frame interaction to generate various event prototypes. In Fig. 4, a frame decoder is first designed to incorporate all object prototypes \\( P_{o} \\in \\mathbb{R}^{(L \\times N_{o}) \\times D} \\) into frame-level prototypes \\( P_{f} \\in \\mathbb{R}^{L \\times D} \\), which implies fine-grained inter-object spatial relations. To learn frame-level object relations, we define the masked attention as:" + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.192, + 0.47, + 0.211 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {P} _ {f} = \\operatorname {s o f t m a x} \\left(\\boldsymbol {M} _ {f} + \\boldsymbol {Q} _ {f} \\boldsymbol {K} _ {o} ^ {\\mathrm {T}}\\right) \\boldsymbol {V} _ {o} + \\boldsymbol {Q} _ {f}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.219, + 0.47, + 0.282 + ], + "angle": 0, + "content": "where \\(Q_{f}\\in \\mathbb{R}^{L\\times D}\\) refers to frame queries (i.e., a set of randomly initialized learnable tokens), \\(K_{o}\\) and \\(V_{o}\\) are the features after the linear transformation of object prototypes \\(P_{o}\\). The attention mask \\(M_{f}\\in \\mathbb{R}^{L\\times (L\\times N_{o})}\\) is:" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.291, + 0.47, + 0.332 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {M} _ {f} (i, j) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} i \\cdot N _ {o} \\leq j < (i + 1) \\cdot N _ {o} \\\\ - \\infty & \\text {o t h e r w i s e} \\end{array} . \\right. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.342, + 0.47, + 0.39 + ], + "angle": 0, + "content": "Inspired by [9], we add frame prototype \\( \\pmb{p}_f^l \\) and original global feature \\( \\pmb{x}_C^l \\) of corresponding frames to enhance the robustness of the model:" + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.399, + 0.47, + 0.42 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {p} _ {f} ^ {l} = \\left(\\boldsymbol {p} _ {f} ^ {l} + \\boldsymbol {x} _ {C} ^ {l}\\right) / 2. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.429, + 0.47, + 0.489 + ], + "angle": 0, + "content": "Next, a dynamic event decoder is developed to learn the inter-frame relations in \\( P_{f} \\), which can obtain different event prototypes \\( P_{e} \\in \\mathbb{R}^{N_{e} \\times D} \\) to illustrate the rich information of videos. Our dynamic attention is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.498, + 0.469, + 0.518 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {P} _ {e} = \\operatorname {s o f t m a x} \\left(\\boldsymbol {Q} _ {e} \\boldsymbol {K} _ {f} ^ {\\mathrm {T}}\\right) \\boldsymbol {V} _ {f} + \\boldsymbol {Q} _ {e}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.527, + 0.469, + 0.603 + ], + "angle": 0, + "content": "where \\( Q_{e} \\in \\mathbb{R}^{N_{e} \\times D} \\) refers to event queries, \\( K_{f} \\) and \\( V_{f} \\) are the linear transformation features of frame prototypes \\( P_{f} \\). During training, each event query learns how to adaptively focus on video frame prototypes, while multiple queries implicitly guarantee a certain event diversity." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.604, + 0.469, + 0.664 + ], + "angle": 0, + "content": "Differently, since the same video often corresponds to multiple text semantic descriptions, we directly use the global text representation \\( \\pmb{y}_E \\) as a sentence prototype to align with the event prototypes \\( \\pmb{P}_e \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.664, + 0.469, + 0.695 + ], + "angle": 0, + "content": "Event-sentence matching. Similar to [43], this event-sentence prototype matching process can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.706, + 0.469, + 0.732 + ], + "angle": 0, + "content": "\\[\ns _ {e s} = \\max _ {i = 1} ^ {N _ {e}} \\left\\langle \\boldsymbol {y} _ {E}, \\boldsymbol {P} _ {e _ {i}} \\right\\rangle . \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.736, + 0.469, + 0.767 + ], + "angle": 0, + "content": "We look for the closest event prototype to the text representation for dynamic matching." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.775, + 0.292, + 0.792 + ], + "angle": 0, + "content": "3.4. Training and Inference" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.799, + 0.47, + 0.86 + ], + "angle": 0, + "content": "The InfoNCE loss [55, 75] is employed to optimize the prototype matching within a batch. We treat text-video pairs as positive examples, while considering all other pairwise combinations in the batch as negative examples:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.87, + 0.477, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {t v c} = \\left(\\mathcal {L} _ {t 2 v} \\left(\\boldsymbol {S} _ {o p}\\right) + \\mathcal {L} _ {v 2 t} \\left(\\boldsymbol {S} _ {o p}\\right) + \\mathcal {L} _ {t 2 v} \\left(\\boldsymbol {S} _ {e s}\\right) + \\mathcal {L} _ {v 2 t} \\left(\\boldsymbol {S} _ {e s}\\right)\\right) / 4, \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.103, + 0.892, + 0.145 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {t 2 v} (\\boldsymbol {S}) = - \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(\\boldsymbol {S} ^ {i i} / \\sigma\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\boldsymbol {S} ^ {i j} / \\sigma\\right)}, \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.534, + 0.152, + 0.892, + 0.193 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {v 2 t} (\\boldsymbol {S}) = - \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(\\boldsymbol {S} ^ {i i} / \\sigma\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\boldsymbol {S} ^ {j i} / \\sigma\\right)}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.197, + 0.892, + 0.242 + ], + "angle": 0, + "content": "where the \\(\\sigma\\) is a learnable temperature parameter, \\(S_{op}\\) and \\(S_{es}\\) are object-phrase and event-sentence prototype matching similarity matrices in a batch of size \\(B\\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.243, + 0.892, + 0.289 + ], + "angle": 0, + "content": "During the inference stage, we directly weight the spatiotemporal matching scores for the final similarity matching: \\( s = s_{es} + \\beta s_{op} \\), where \\( \\beta \\) is the spatial matching factor." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.301, + 0.633, + 0.317 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.325, + 0.892, + 0.417 + ], + "angle": 0, + "content": "We carry out experiments on the standard text-video retrieval datasets of MSRVTT [71], DiDeMo [23], VATEX [64] and LSMDC [58]. Standard metrics in information retrieval [48, 17] are adopted to measure the retrieval performance, including Recall@1/5/10 (R@1/5/10), Median Rank (MdR), and Mean Rank (MnR)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.425, + 0.707, + 0.441 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.448, + 0.892, + 0.659 + ], + "angle": 0, + "content": "Datasets. (1) MSRVTT [71] consists of 10k videos and 200k human-labeled descriptions, where many videos have diverse captions. To thoroughly compare the existing methods, we follow [20] to train on 7k or 9k train+val videos and test on a test set of 1k text-video pairs. (2) DiDeMo [23] contains 10K Flickr videos and 40K captions. Following [43], all caption descriptions of a video are concatenated as a query to evaluate all methods. (3) VATEX [64] is comprised of 34,991 video clips. According to [5], we select 25,991, 1, 500 and 1, 500 videos as the training, validation and test sets. (4) LSMDC [58] consists of 118,081 movie clips each paired with a single caption description. We choose 101, 079, 7, 408 and 1, 000 videos as the training, validation and test sets." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Implementation details. We initialize the backbone with the pre-trained model CLIP (ViT-B/32) [57] following [48]. Our decoders consist of two transformer layers with a single attention head. To reduce the computing overhead, all videos are resized to \\(224 \\times 224\\) with random cropping and flipping, and the frame rate is 3. We set the max text length as 32 and video frame number as 12 except for DiDeMo (set to 64 and 64) as its videos are longer. We optimize the model for 5 epochs on 4 NVIDIA Tesla A100 GPUs, employ Adam optimizer [32] with 0.2 weight decay and fix the batch size as 128. The learning rate is set to 1e-7 for CLIP-initialized weights and 1e-4 for all other parameters. Following [57], we decay the learning rate using a warmup cosine schedule [49]. The spatial matching factor \\(\\beta\\) is 1.5. By default, the prototype number \\(N_{o}\\), \\(N_{p}\\), and \\(N_{e}\\) are 12, 28 and 3. The dimension of prototypes is 512." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4104" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.892, + 0.117 + ], + "angle": 0, + "content": "Table 1. Retrieval results on MSRVTT-9k. We reproduce TVMM* [43] using the same backbone network CLIP (ViT-B/32) [57]. All results in this table do not use additional post-processing techniques [2, 7]." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.117, + 0.887, + 0.352 + ], + "angle": 0, + "content": "
MethodReferenceText → VideoVideo → Text
R@1↑R@5↑R@10↑MdR↓MnR↓R@1↑R@5↑R@10↑MdR↓MnR↓
CE [47]BMVC1920.650.364.05.3-20.948.862.46.0-
MMT [17]ECCV2026.657.169.64.024.027.057.569.73.721.3
T2vlad [65]CVPR2129.559.070.14.0-31.860.071.13.0-
HiT [46]ICCV2127.759.272.02.9-28.860.372.33.0-
TeachText [10]ICCV2129.661.674.23.0-32.162.775.03.0-
ClipBERT [33]CVPR2122.046.859.96.0------
SupportSet [56]ICLR2130.158.569.33.0-28.558.671.63.0-
Frozen [1]ICCV2131.059.570.53.0------
BridgeFormer [18]CVPR2237.664.875.1-------
TVMM [43]NeurIPS2236.264.275.73.0-34.863.873.73.0-
CLIP4Clip [51]NeurCom2244.571.481.62.015.342.770.980.62.011.6
CenterCLIP [78]SIGIR2244.271.682.12.015.142.871.782.22.010.9
X-Pool [20]CVPR2246.972.882.22.014.3-----
TVMM* [43]NeurIPS2245.871.781.92.014.844.071.982.32.010.6
TS2-Net [48]ECCV2247.074.283.32.013.644.373.983.02.09.2
ProSTProposed48.274.683.42.012.446.374.283.22.08.7
ProST (ViT-B/16)Proposed49.575.084.02.011.748.075.985.22.08.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.103, + 0.375, + 0.438, + 0.387 + ], + "angle": 0, + "content": "Table 2. Text-to-Video retrieval results on MSRVTT-7k." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.387, + 0.464, + 0.503 + ], + "angle": 0, + "content": "
MethodText → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
HowTo100M [52]14.940.252.89.0-
HERO [36]16.843.457.7--
ClipBERT [33]22.046.859.96.0-
CLIP4Clip [51]42.171.981.42.015.7
X-Pool [20]43.972.582.32.014.6
TS2-Net [48]43.172.282.12.014.2
ProST44.572.382.42.013.8
ProST (ViT-B/16)46.973.382.92.013.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.081, + 0.518, + 0.456, + 0.529 + ], + "angle": 0, + "content": "Table 3. Text-to-Video retrieval results on the DiDeMo dataset." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.53, + 0.461, + 0.656 + ], + "angle": 0, + "content": "
MethodText → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
CE [47]16.141.182.78.3-
ClipBERT [33]20.448.060.86.0-
Frozen [1]31.059.872.43.0-
MCQ [18]37.062.273.93.0-
TVMM [43]36.564.975.43.0-
CLIP4Clip [51]42.868.579.22.018.9
TS2-Net [48]41.871.682.02.014.8
ProST44.972.782.72.013.7
ProST (ViT-B/16)47.575.584.42.012.3
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.681, + 0.442, + 0.697 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.901 + ], + "angle": 0, + "content": "To evaluate the relative benefits of ProST, we compare its performance with recent works [48, 20, 78, 51] from the literature. The results on the 9k and 7k splits of MSRVTT are shown in Tab. 1 and Tab. 2 respectively. We consistently achieve the best results for text-to-video retrieval and video-to-text retrieval across all splits and all metrics. Specifically, TS2-Net [48] integrates important patches into frame features for frame-level matching, which achieves the second best performance. Notably, for text-to-video retrieval, ProST outperforms TS2-Net [48] with \\(1.2\\%\\) and \\(1.4\\%\\) R@1 gains on the 9k split (47.0% vs. 48.2%) and the 7k split (43.1% vs. 44.5%). A \\(2.0\\%\\) improvement on R@1 (9k split) is also obtained compared to TS2-Net for video-to" + }, + { + "type": "table_caption", + "bbox": [ + 0.501, + 0.375, + 0.874, + 0.387 + ], + "angle": 0, + "content": "Table 4. Text-to-Video retrieval results on the VATEX dataset." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.387, + 0.884, + 0.503 + ], + "angle": 0, + "content": "
MethodText → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
HGR [5]35.173.583.52.0-
CLIP [57]39.772.382.22.012.8
CLIP4Clip [51]55.989.295.01.03.9
QB-Norm [2]58.888.393.81.0-
CLIP2Video [15]57.390.095.51.03.6
TS2-Net [48]59.190.095.21.03.5
ProST60.690.595.41.03.4
ProST (ViT-B/16)64.092.296.31.03.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.501, + 0.518, + 0.877, + 0.53 + ], + "angle": 0, + "content": "Table 5. Text-to-Video retrieval results on the LSMDC dataset." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.53, + 0.884, + 0.646 + ], + "angle": 0, + "content": "
MethodText → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
Frozen [1]15.030.839.820.0-
TVMM [43]17.837.145.913.5-
CLIP4Clip [51]21.641.849.811.061.0
X-Pool [20]24.042.951.59.055.1
QB-Norm [2]22.440.149.511.0-
TS2-Net [48]23.042.150.49.057.0
ProST24.142.551.69.054.6
ProST (ViT-B/16)26.346.155.28.051.4
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.809 + ], + "angle": 0, + "content": "text retrieval (44.3% vs. 46.3%). Furthermore, we reproduce TVMM [43] based on CLIP (ViT-B/32), which has 2.4% (45.8% vs. 48.2%) and 2.3% (44.0% vs. 46.3%) lower R@1 than ProST on the 9k split. The results demonstrate the effectiveness of ProST, which mines the spatial object details and temporal event diversity of videos, improving the model discrimination. Besides, ProST achieves a low MnR metric of 12.4 (text-to-video) on the 9k split, demonstrating the model robustness to erroneous results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.893, + 0.901 + ], + "angle": 0, + "content": "In Tab. 3, 4 and 5, we examine the performance of ProST on the DiDeMo, VATEX and LSMDC datasets respectively. Compared with TS2-Net [48], ProST achieves a substantial boost of \\(3.1\\%\\), \\(1.5\\%\\) and \\(1.1\\%\\) on the R@1 metric for DiDeMo, VATEX and LSMDC, respectively. ProST outperforms state-of-the-art methods by a large margin with the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4105" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.087, + 0.892, + 0.156 + ], + "angle": 0, + "content": "Table 6. The ablation study on MSRVTT-9k to investigate the effectiveness of Object-Phrase Prototype Matching (OPPM) and EventSentence Prototype Matching (ESPM). MdR results are not shown, as MdR=2.0 for all variants. Definition of important symbols: \\(\\checkmark\\) indicates default settings; \\(\\odot\\)TPG or \\(\\odot\\)SPG means replace with TPG or SPG to generate prototypes; P-P or O-W refers the alignment of patch-phrase or object-word; -F, -M or -R refers to removing frame decoder, attention mask or residual structure in Eq. 5; F-W or \\(\\bar{\\mathbb{F}}\\)-S means directly aligning frame global tokens and word tokens or aligning the mean of frame global tokens and text global token." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.158, + 0.879, + 0.374 + ], + "angle": 0, + "content": "
IDOPPMESPMText → VideoVideo → Text
SPGMatchingTPGMatchingR@1↑R@5↑R@10↑MnRR@1↑R@5↑R@10↑MnR
1✓✓45.672.281.114.344.971.682.310.0
2○SPG✓45.871.781.914.844.071.982.310.6
3✓✓45.972.882.413.245.173.382.79.8
4○TPG✓✓✓46.373.381.813.545.073.182.49.8
5✓✓○SPG✓47.773.683.012.645.974.083.09.0
6✓P-P✓✓46.072.581.614.943.172.482.110.8
7✓O-W✓✓47.173.382.212.845.773.382.69.6
8✓✓-F✓46.472.881.713.544.572.582.010.2
9✓✓-M✓47.873.882.912.646.073.782.89.0
10✓✓-R✓46.672.982.414.045.372.181.810.1
11F-W✓✓47.373.582.812.645.973.783.19.0
12✓✓F-S46.572.682.313.445.173.482.59.8
Ours✓✓✓✓48.274.683.412.446.374.283.28.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.394, + 0.468, + 0.422 + ], + "angle": 0, + "content": "Table 7. The ablation study on MSRVTT-9k to investigate the configuration of the number of prototypes." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.422, + 0.468, + 0.548 + ], + "angle": 0, + "content": "
{No, Np, Ne}Text → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
{6, 14, 3}45.673.281.62.014.3
{6, 28, 3}46.773.482.22.013.4
{12, 14, 3}47.073.783.02.012.9
{24, 32, 3}46.073.382.02.013.8
{12, 28, 1}46.373.082.12.013.5
{12, 28, 2}47.474.083.12.012.7
{12, 28, 4}47.674.383.22.012.5
{12, 28, 3}48.274.683.42.012.4
" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.564, + 0.465, + 0.655 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.658, + 0.466, + 0.673 + ], + "angle": 0, + "content": "Figure 5. The R@1 results at different spatial matching factors \\(\\beta\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.698, + 0.468, + 0.775 + ], + "angle": 0, + "content": "CLIP (ViT-B/16) backbone. These results suggest the versatility and generalization of ProST, which can effectively process videos from different domains (e.g., movies). We owe the advantage of ProST over these works to the full use of dynamic spatio-temporal prototype matching." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.786, + 0.231, + 0.803 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.468, + 0.855 + ], + "angle": 0, + "content": "Analysis of progressive spatio-temporal prototype matching. In Tab. 6, we compare ProST with 12 variants, which proves that each module contributes to final results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We elaborate on some important observations. First, we show the results relying only on Object-Phrase Prototype Matching (OPPM) or Event-Sentence Prototype Match" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.398, + 0.892, + 0.579 + ], + "angle": 0, + "content": "ing (ESPM). To implement our model without OPPM, all tokens are fed directly into the frame decoder and event decoder (TPG) to get multiple event prototypes. When only ESPM is used, there is a \\(2.6\\%\\) decrease in \\(\\mathbb{R}@\\mathbb{1}\\). This confirms the complementary role of fine-grained spatial details for ESPM. Next, we replace TPG with SPG and find that there is a certain suppression effect on noise. However, both of the above variants perform poorly due to the lack of progressive prototype generation and matching. When we only train model with OPPM, the model still underperforms. This may be due to the lack of temporal understanding and the inability to resolve correspondence ambiguity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.892, + 0.717 + ], + "angle": 0, + "content": "Second, \\(\\mathbb{O}\\) TPG, P-P and O-W prove that there is indeed redundancy in the original video tokens. The sparse weights in SPG can alleviate this problem. However, FC layers in SPG cannot interact with intra-frame and inter-frame information, making it difficult to generate better event prototypes. This may be the reason for the drop in \\(\\mathbb{O}\\) SPG. Third, P-P and O-W also confirm the benefits of prototype matching. Raw patches or words without aggregation strategies may worsen the cross-modal alignment." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.718, + 0.892, + 0.869 + ], + "angle": 0, + "content": "Fourth, the results for -F, -M and -R also decreased. Because intra-frame local object relations and global frame features jointly complement comprehensive frame-level spatial information, which is helpful for subsequent temporal learning. Fifth, from F-W and \\(\\overline{\\mathbf{F}}\\)-S, we can see the importance of prototype design mode. Directly using global frame features ([CLS] tokens) in ProST-S for frame-word alignments lacks object details. In \\(\\overline{\\mathbf{F}}\\)-S, the mean value of frame global features mixes all information equally, making it difficult to characterize dynamic and changeable videos." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Analysis of prototype configuration. We conduct experiments on various prototype configurations in Tab. 7. Im" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4106" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.088, + 0.891, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.304, + 0.893, + 0.334 + ], + "angle": 0, + "content": "Figure 6. Visualization of the object and event prototypes. We sample 12 frames in the video and object prototypes are shown as highlighted response regions in the frame. Then, we show cross-attention event weights of Eq. 6 in a line graph. Best viewed in color." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.358, + 0.47, + 0.447 + ], + "angle": 0, + "content": "proper configuration of spatial prototypes leads to performance degradation, possibly because too many prototypes may introduce local noise, while few prototypes are not enough to express semantics. Furthermore, the best result is obtained when the number of event prototypes is 3, which may be related to the degree of semantic divergence of texts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.449, + 0.471, + 0.569 + ], + "angle": 0, + "content": "Hyperparameter analysis. As shown in Fig. 5, we investigate the spatial matching factor \\(\\beta\\) and present results for text-video (T2V) and video-text retrieval (V2T). As \\(\\beta\\) grows, the performance increases at first and reaches the best results, then decreases as a whole. A small \\(\\beta\\) may not fully exploit the underlying fine-grained spatial information, while a large \\(\\beta\\) may overemphasize local matching and destroy the overall dynamic semantic understanding." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.576, + 0.262, + 0.591 + ], + "angle": 0, + "content": "4.4. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.795 + ], + "angle": 0, + "content": "Visualization of prototypes. In Fig. 6, we first present object prototypes in video frames. Many redundant patches are removed by prototypes, and the spatially highlighted object part and the phrase can be well locally corresponded. Then, we compute cross-attention for 3 event queries and 12 video frames according to Eq. 6, whose weights are shown in a line graph. The weights of different event prototypes on different frames are quite different, which proves that our model can learn temporal relations and event prototypes can express diverse semantics. For example, event prototype 1 has larger weights on the first three frames, which indicates that it may correspond to the semantics contained in text 1. Similarly, event prototype 2 or 3 corresponds to text 2 or 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Retrieval results. Top-3 TVR results are illustrated in Fig. 7. Specifically, for query 97, although the top-2 recalled videos are women in the same dress, the difference is that the correct video discusses the cushion seat, while the incorrect video does not. This proves that object-phrase prototype matching provides fine-grained spatial knowledge (i.e., objects). For query 353, ProST pays attention to" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.355, + 0.889, + 0.643 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.647, + 0.892, + 0.689 + ], + "angle": 0, + "content": "Figure 7. Top-3 TVR results on MSRVTT-9k. Left: the ranked videos by our ProST. Right: the ranked videos with only event-sentence prototype matching. Red: correct videos." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.718, + 0.892, + 0.793 + ], + "angle": 0, + "content": "both the brief human speech at the beginning of the video and the subsequent earth display. However, using only event prototypes will result in a matching error. This shows that ProST can make a trade-off between the spatio-temporal matching relations to achieve better discrimination." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.813, + 0.619, + 0.829 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.902 + ], + "angle": 0, + "content": "We have proposed a novel text-video retrieval framework, ProST, to decompose the matching process into complementary object-phrase and event-sentence prototype alignments. In the object-phrase prototype matching stage," + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4107" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.243 + ], + "angle": 0, + "content": "we design the spatial prototype generation mechanism to focus on important video content and strengthen the fine-grained spatial alignment. In the event-sentence prototype matching phase, we use the temporal prototype generation mechanism to progressively generate diverse event prototypes and learn dynamic one-to-many relations. In this paper, we hope not only to provide insights into the importance of complementary spatio-temporal matching but also to facilitate future work that advances text-video retrieval by solving design flaws rather than mostly trial and error." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.473, + 0.318 + ], + "angle": 0, + "content": "Acknowledgment. This work is supported by the National Key Research and Development Program of China (2022YFB3104700), the National Nature Science Foundation of China (62121002, 62022076, U1936210, 62102384)." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.333, + 0.175, + 0.349 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.358, + 0.47, + 0.4 + ], + "angle": 0, + "content": "[1] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. Frozen in time: A joint video and image encoder for end-to-end retrieval. In ICCV, 2021. 2, 3, 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.402, + 0.472, + 0.442 + ], + "angle": 0, + "content": "[2] Simion-Vlad Bogolin, Ioana Croitoru, Hailin Jin, Yang Liu, and Samuel Albanie. Cross modal retrieval with querybank normalisation. 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Tps++: Attention-enhanced thin-plate spline for scene text recognition. *IJCAI*, 2023. 1" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4110" + } + ] +] \ No newline at end of file diff --git a/2023/Progressive Spatio-Temporal Prototype Matching for Text-Video Retrieval/480eca60-b42e-4764-a2ee-88684bf2c389_origin.pdf b/2023/Progressive Spatio-Temporal Prototype Matching for Text-Video Retrieval/480eca60-b42e-4764-a2ee-88684bf2c389_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ecac8f3ba17a936870c8e699d1639814c155dbe5 --- /dev/null +++ b/2023/Progressive Spatio-Temporal Prototype Matching for Text-Video Retrieval/480eca60-b42e-4764-a2ee-88684bf2c389_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8c235362101f0c351086acf39ebefc5fefbe951ffaec7247f7815af8686e9e30 +size 2639713 diff --git a/2023/Progressive Spatio-Temporal Prototype Matching for Text-Video Retrieval/full.md b/2023/Progressive Spatio-Temporal Prototype Matching for Text-Video Retrieval/full.md new file mode 100644 index 0000000000000000000000000000000000000000..69e3c7eecaba8d943ccba5b441eb69f1429a7eb4 --- /dev/null +++ b/2023/Progressive Spatio-Temporal Prototype Matching for Text-Video Retrieval/full.md @@ -0,0 +1,337 @@ +# Progressive Spatio-Temporal Prototype Matching for Text-Video Retrieval + +Pandeng Li $^{1*}$ , Chen-Wei Xie $^{2}$ , Liming Zhao $^{2}$ , Hongtao Xie $^{1\dagger}$ , Jiannan Ge $^{1}$ , Yun Zheng $^{2}$ , Deli Zhao $^{2}$ , Yongdong Zhang $^{1}$ + +1 University of Science and Technology of China, 2DAMO Academy, Alibaba Group + +{lpd, gejn}@mail.ustc.edu.cn, {htxie, zhyd73}@ustc.edu.cn + +{eniac.xcw, lingchen.zlm, zhengyun.zy}@alibaba-inc.com, zhaodeli@gmail.com + +# Abstract + +The performance of text-video retrieval has been significantly improved by vision-language cross-modal learning schemes. The typical solution is to directly align the global video-level and sentence-level features during learning, which would ignore the intrinsic video-text relations, i.e., a text description only corresponds to a spatio-temporal part of videos. Hence, the matching process should consider both fine-grained spatial content and various temporal semantic events. To this end, we propose a text-video learning framework with progressive spatio-temporal prototype matching. Specifically, the matching process is decomposed into two complementary phases: object-phrase prototype matching and event-sentence prototype matching. In the object-phrase prototype matching phase, the spatial prototype generation mechanism predicts key patches or words, which are aggregated into object or phrase prototypes. Importantly, optimizing the local alignment between object-phrase prototypes helps the model perceive spatial details. In the event-sentence prototype matching phase, we design a temporal prototype generation mechanism to associate intra-frame objects and interact inter-frame temporal relations. Such progressively generated event prototypes can reveal semantic diversity in videos for dynamic matching. Validated by comprehensive experiments, our method consistently outperforms the state-of-the-art methods on four video retrieval benchmark. + +# 1. Introduction + +Understanding multimodal information [13, 37, 40, 76, 6, 79, 41, 12, 53, 54] is an essential way for humans to perceive the world. As a fundamental task in multimodal learning [25, 62, 60], Text-Video Retrieval (TVR) [22, 70, 68, 24] has garnered huge interest with the rapid devel + +![](images/0e7b72f3e44ac5c2bd3d79c230398ca43bfa0c035dd92a05235dea96722212c1.jpg) +(1) Adaptive event matching w/o object-phrase prototypes + +![](images/29070ad6abfd347d64546d3d5c3d95239bf7930b3e5f3f3bf929d1ea2b6216e5.jpg) +(2) Our object-phrase prototype matching +Figure 1. Visualization of event and object prototypes learned by 1) adaptive event matching w/o object-phrase prototypes and 2) object-phrase prototype matching. Object prototypes can focus on local patches (e.g., tail) and complement event-level matching. + +opment of short video platforms. TVR [45, 21] aims to search semantically relevant videos based on user-entered text queries. Unfortunately, the inherent modality gap phenomenon [42, 61, 38, 3, 67] increases the difficulty of associating multimodal data. Towards such a concern, pioneering works [47, 65, 73] usually exploit multiple unimodal pre-trained models to extract features, and then use metric learning strategies [14] to strengthen the modality alignment in the joint space. However, there are large differences in the initial distributions of multiple unimodal offline features, which inevitably brings the feature fusion challenge to affect the retrieval results. + +Recently, encouraged by the success of vision-language pre-training [50, 66, 34, 27, 72, 35, 4], a series of canonical works [51, 20, 44, 16] are proposed by transferring knowl- + +![](images/7a112fc02f46f7ae64523cdefe5521e51dbafb6446885a2624cf796c1c58eefb.jpg) +Figure 2. The progressive prototype generation process: 1) focus on patch-level spatial details; 2) aggregate intra-frame object prototypes; 3) interact inter-frame relations temporally as event prototypes, corresponding to multiple semantics. + +edge from cross-modal pre-trained models (e.g., CLIP [57]) to the TVR task. Among them, some methods [51, 1, 28] learn to encode text or video data as a single embedding and perform global alignment between the sentence and the whole video. Subsequent approaches [48, 78] employ frame-level or segment-level matching by taking into account the different importance of video content. These methods try to encode the video into a single semantic content described by corresponding text, establishing one-to-one relations. However, videos contain rich visual elements [39] and a text description may only correspond to a spatio-temporal part of the video, dynamic and fine-grained matching is needed beyond the global video-level or frame-level matching. Specifically, feature encoding should characterize different semantic information to support dynamic partial alignment during the matching process. Recently, Lin et al. [43] attempt to address the dynamic matching problem by temporally segmenting videos into multiple semantic events, so that different text descriptions can adaptively match event prototypes. Nevertheless, various event prototypes are still inadequate to model the relations between fine-grained objects and content words, lacking the perception of local details. As shown in Fig. 1(1), the correct video corresponding to the text should focus on "tail", but the event prototype corresponding to the maximum similarity may suffer from scene bias [8, 63] and ignore this small object. Based on the above observation, an effective event-sentence matching process needs to emphasize fine-grained local spatial matching. This also suggests that the generation of event prototypes should be bootstrapped from the semantic combination of important objects. Therefore, we should construct event prototypes progressively, i.e., explicitly preserve the local information learned in the spatial + +matching stage, and then perform temporal aggregation. + +To this end, we propose a novel Progressive Spatio-Temporal Prototype Matching (ProST) framework, which decomposes the matching process into complementary object-phrase and event-sentence prototype alignments. In the object-phrase prototype matching phase, a spatial prototype generation mechanism is first developed to focus on key image patches or word tokens. To prevent massive video redundancy, we use sparse weights to filter irrelevant background interference and aggregate important patch or word tokens into object or phrase prototypes. As shown in Fig. 1(2), optimal local responses can be found by the maximum similarity between object and phrase prototypes to help the model perceive spatial details. + +In the event-sentence prototype matching phase, a temporal prototype generation mechanism is designed to decode various event prototypes for dynamic semantic alignment. Specifically, since the spatial details should not be ignored in the event generation process, we send object prototypes to the frame and event decoder for progressive prototype learning. Multiple different event prototypes are generated to reveal the semantic diversity in videos and support dynamic matching. Finally, as shown in Fig. 2, different text sentences can match the most appropriate event prototype learned from the video. Overall, ProST encodes the rich video content by generating object-level, frame-level and event-level prototypes in a progressive manner, and constructs dynamic and fine-grained spatio-temporal matching strategies. ProST not only strengthens the interaction of local spatial content, but also considers the intrinsic relations where video and text are only partially aligned. + +The contributions of this paper are threefold: 1) we propose a novel framework, ProST, to decompose the matching process into complementary object-phrase and event-sentence prototype alignments; 2) two prototype generation mechanisms are developed to learn sparse spatial and dynamic temporal information respectively, which can fully explore fine-grained local details and video semantic diversity; 3) extensive experiments demonstrate that ProST outperforms state-of-the-art methods on MSRVTT, DiDeMo, VATEX and LSMDC datasets. + +# 2. Related Work + +Text-video retrieval. Existing works can be divided into two categories: offline feature based [47, 11, 77, 26] and end-to-end training [1, 51, 48, 43, 31, 29, 30, 28] methods. + +Early methods [69, 11] extract video-text features offline, and then perform embedding alignment in a common space. To enhance representation quality, CE [47], MMT [17] and HiT [46] employ multiple unimodal experts (OCR, speech, etc.) to enrich video features. Teach-Text [10] adopts multiple text encoders to gather text information and obtain more credible alignments. Besides, + +HGR [5] and T2vlad [65] build semantic graphs or shared centers to explore global-local relations. However, these methods employ additional analysis tools or experts to preprocess data, which increases the complexity and limits flexibility. Unlike the global-local alignment explored on multiple experts [65, 46], we consider finer-grained patch-level visual content without requiring additional experts. + +Current mainstream works benefit from large-scale vision-language pre-training [57, 19]. ClipBERT [33] and Frozen [1] first propose efficient end-to-end pre-training schemes. MCQ [18] builds cross-modal associations by predicting verb or noun features. Recently, CLIP4clip [51] uses CLIP [57] as the backbone network, significantly improving TVR performance and inspiring a series of works [48, 15, 20, 78, 28]. Centerclip [78] conducts segment-level clustering, which reduces token redundancy and computational overhead. TS2Net [48] designs the token shift module to realize the perception of local movement between frames. Xpool [20] uses text as a condition to guide the aggregation of video tokens. But the limitation is that the video encoding process must involve both modal data. + +Adaptive cross-modal retrieval. Recently, the correspondence ambiguity problem (i.e., a text may only correspond to a part of the video or image) has raised concerns in the cross-modal retrieval community [9, 59, 43]. In text-image retrieval, PVSE [59] employs the self-attention mechanism to explore different local parts of instances and generates $K$ candidate features for adaptive matching. PCME [9] samples the text-image probabilistic embeddings multiple times from the learned Gaussian distribution to explore one-to-many multiplicity relationships. In text-video retrieval, TVMM [43] utilizes fully connected layers to directly aggregate all tokens into multiple event prototypes for text-adaptive event matching. However, fine-grained object-level information is not well exploited in the event matching process of TVMM, while the proposed progressive spatiotemporal matching framework could simultaneously consider local spatial details and dynamic temporal relations. + +# 3. Method + +Given a dataset consisting of $n$ videos $\mathcal{V} = \{\pmb{v}_i\}_{i=1}^n$ and their corresponding $m$ captions $\mathcal{T} = \{\pmb{t}_i\}_{i=1}^m$ , Text-Video Retrieval (TVR) aims to learn a function $s(\pmb{t}_i, \pmb{v}_i)$ to effectively measure the similarity between modalities. For a text query $\pmb{t}_i$ , we can rank all videos in the dataset according to the similarity scores. Ideally, the cross-modal similarity (e.g., cosine similarity) between paired cross-modal instances should be greater than that of unpaired instances: $s(\pmb{t}_i, \pmb{v}_i) > s(\pmb{t}_i, \pmb{v}_j)$ . This requires the model to learn powerful text encoding network $\pmb{f}_t : \mathcal{T} \to \mathcal{Y}$ and video encoding network $\pmb{f}_v : \mathcal{V} \to \mathcal{X}$ , which generate high-quality features and ultimately enable efficient matching. + +# 3.1. Framework + +Fig. 3 sheds light on our end-to-end trainable architecture, which consists of a backbone network and two prototype matching schemes. For a fair comparison with recent methods [48, 51, 20], we adopt CLIP [57] as the backbone network, which exhibits strong performance in downstream tasks. Given an input video $\mathbf{v}_i$ , we uniformly select $L$ frames as keyframes to extract sequential features $\mathbf{X}_i = \{\mathbf{x}_C^l, \mathbf{x}_{T_1}^l, \dots, \mathbf{x}_{T_K}^l\}_{l=1}^L \in \mathbb{R}^{L \times (K+1) \times D}$ , where $\mathbf{x}_C^l$ is the global frame token feature ([CLS]) and $K$ is the patch number. For each query text $t_i$ , we add the [SOT] and [EOT] tokens to indicate the start and the end of the text. The output text token features can be defined as $\mathbf{Y}_i = \{\mathbf{y}_S, \mathbf{y}_{T_1}, \dots, \mathbf{y}_{T_M}, \mathbf{y}_E\} \in \mathbb{R}^{(M+2) \times D}$ , where $\mathbf{y}_E$ is the global text token feature([EOT]), $M$ and $D$ are the number of words and dimensions, respectively. + +Apart from the backbone network, we decompose the matching process into two spatio-temporal complementary parts: 1) Object-Phrase Prototype Matching (Sec. 3.2) aligns the visual object prototypes and text phrase prototypes generated by Spatial Prototype Generation (SPG) to emphasize fine-grained spatial information; 2) Event-Sentence Prototype Matching (Sec. 3.3) exploits event prototypes progressively generated by Temporal Prototype Generation (TPG) to learn dynamic semantic alignment, which explores intrinsic one-to-many video-text relations. The object-phrase and event-sentence prototype matching schemes determine the final cross-modal similarity. + +# 3.2. Object-Phrase Prototype Matching + +The text of the video caption subjectively describes a certain event composed of different objects, actions and temporal activities across the video sequence. This results in pairs of video and text that are often partially matched. To solve this problem [9, 59], existing method [43] learns a single patch-event projection to aggregate multiple event prototypes for text-adaptive matching. However, these prototypes are still inadequate to perceive the local details. Our intuition is that decoupling the spatio-temporal modeling process in a divide-and-conquer manner is more beneficial than a single projection. Therefore, we conduct progressive spatio-temporal prototype matching for text-video retrieval. In this section, we illustrate how to model spatial matching. We first perform patch-object and word-phrase spatial prototype aggregation to reveal key local details, and then introduce the fine-grained prototype alignment. + +Spatial prototype generation. For videos, we aggregate the patch tokens into object prototypes to represent fine-grained spatial information, such as object instance, object part, and action region. In the prototype generation process, not all patch tokens are aggregated. Although the patch tokens contain important spatial information, they also bring redundancy. For example, some background to + +![](images/4c442d68a00fd58715e4583d1045146bfab56c1ee0fef0bd806988fdedc0bb3d.jpg) +Figure 3. Our ProST framework. We decompose the matching process into two spatio-temporal complementary parts: 1) Object-Phrase Prototype Matching aligns the visual object prototypes and text phrase prototypes generated by Spatial Prototype Generation (SPG) to emphasize fine-grained spatial information; 2) Event-Sentence Prototype Matching exploits event prototypes progressively generated by Temporal Prototype Generation (TPG) to learn dynamic semantic alignment, which explores intrinsic one-to-many video-text relations. + +![](images/6b48532e4ccd86f98e7a9669041c458a0ba365ab69aac3d2456d7cb580c92847.jpg) +Figure 4. Details of the Spatial Prototype Generation (SPG) and Temporal Prototype Generation (TPG) mechanisms. + +kens may interfere with cross-modal alignment. Hence, we hope to filter out retrieval-superfluous information and generate object-level prototypes in a sparse aggregation manner. For simplicity, two Fully Connected (FC) layers and ReLU functions are used to predict sparse weights $\pmb{W}_{o}^{l} \in \mathbb{R}^{(K + 1)\times N_{o}}$ , where $N_{o}$ is the number of object prototypes. This way prevents object prototypes from being affected by redundant patches. For each frame $\pmb{X}^{l} \in \mathbb{R}^{(K + 1)\times D}$ , SPG can be defined as: + +$$ +\boldsymbol {P} _ {o} ^ {l} = \boldsymbol {W} _ {o} ^ {l ^ {T}} \cdot \boldsymbol {X} ^ {l} \in \mathbb {R} ^ {N _ {o} \times D}. \tag {1} +$$ + +Ideally, each object prototype can adaptively aggregate the corresponding object-related or action-related patches. + +For text, we draw on the SPG mechanism and design a similar network structure to aggregate word tokens, which generates phrase prototypes $P_{p} \in \mathbb{R}^{N_{p} \times D}$ . In this way, we explore spatially important information based on fine-grained patch tokens and word tokens. Then, the prototypes are optimized by spatial object-phrase prototype matching. + +Object-phrase matching. Different from the existing text-image token-wise interaction [74], we propose a text-video prototype-wise interaction designed from a spatial perspective. Specifically, we first compute the maximum similarity of object-phrase prototypes within each frame. This associates the most similar phrase prototypes to each object prototype, reflecting cross-modal fine-grained matching. Then, for the multi-frame object similarity matrix, we find the largest similarity score across the frame sequences, which + +gives a more confident probability of object-phrase matching. Finally, the object-phrase matching scores are summed to obtain the final similarity $s_{op}$ . The prototype-wise interaction process is defined as: + +$$ +s _ {o p} = \frac {1}{N _ {o}} \sum_ {j = 1} ^ {N _ {o}} \max _ {l = 1} ^ {L} \max _ {i = 1} ^ {N _ {p}} \left[ \boldsymbol {P} _ {p} \cdot \boldsymbol {P} _ {o} ^ {l ^ {T}} \right] _ {i j}, \tag {2} +$$ + +where $N_{o}, N_{p}$ and $L$ are the number of object prototypes, phrase prototypes and frames, respectively. + +# 3.3. Event-Sentence Prototype Matching + +In this section, we illustrate how to model dynamic temporal matching. We first perform progressive object-event prototype aggregation to reveal the video semantic diversity, and then introduce dynamic prototype matching. + +Temporal prototype generation. A naive solution to obtain video-level features based on global frame features is by mean pooling [51, 65, 5], or by adding temporal encoder layers [11]. However, this leads to two issues: 1) failure to perceive local details [43, 78, 48] and ignoring important objects will exacerbate the bias of video feature learning; 2) these strategies generate a single video-level feature, which can only quantify one-to-one relations. Therefore, we investigate how to incorporate key fine-grained objects and dynamic temporal changes into diverse event prototypes. + +The core idea is to progressively aggregate spatial object prototypes into frame prototypes and then perform inter + +frame interaction to generate various event prototypes. In Fig. 4, a frame decoder is first designed to incorporate all object prototypes $P_{o} \in \mathbb{R}^{(L \times N_{o}) \times D}$ into frame-level prototypes $P_{f} \in \mathbb{R}^{L \times D}$ , which implies fine-grained inter-object spatial relations. To learn frame-level object relations, we define the masked attention as: + +$$ +\boldsymbol {P} _ {f} = \operatorname {s o f t m a x} \left(\boldsymbol {M} _ {f} + \boldsymbol {Q} _ {f} \boldsymbol {K} _ {o} ^ {\mathrm {T}}\right) \boldsymbol {V} _ {o} + \boldsymbol {Q} _ {f}, \tag {3} +$$ + +where $Q_{f}\in \mathbb{R}^{L\times D}$ refers to frame queries (i.e., a set of randomly initialized learnable tokens), $K_{o}$ and $V_{o}$ are the features after the linear transformation of object prototypes $P_{o}$ . The attention mask $M_{f}\in \mathbb{R}^{L\times (L\times N_{o})}$ is: + +$$ +\boldsymbol {M} _ {f} (i, j) = \left\{ \begin{array}{l l} 0 & \text {i f} i \cdot N _ {o} \leq j < (i + 1) \cdot N _ {o} \\ - \infty & \text {o t h e r w i s e} \end{array} . \right. \tag {4} +$$ + +Inspired by [9], we add frame prototype $\pmb{p}_f^l$ and original global feature $\pmb{x}_C^l$ of corresponding frames to enhance the robustness of the model: + +$$ +\boldsymbol {p} _ {f} ^ {l} = \left(\boldsymbol {p} _ {f} ^ {l} + \boldsymbol {x} _ {C} ^ {l}\right) / 2. \tag {5} +$$ + +Next, a dynamic event decoder is developed to learn the inter-frame relations in $P_{f}$ , which can obtain different event prototypes $P_{e} \in \mathbb{R}^{N_{e} \times D}$ to illustrate the rich information of videos. Our dynamic attention is formulated as: + +$$ +\boldsymbol {P} _ {e} = \operatorname {s o f t m a x} \left(\boldsymbol {Q} _ {e} \boldsymbol {K} _ {f} ^ {\mathrm {T}}\right) \boldsymbol {V} _ {f} + \boldsymbol {Q} _ {e}, \tag {6} +$$ + +where $Q_{e} \in \mathbb{R}^{N_{e} \times D}$ refers to event queries, $K_{f}$ and $V_{f}$ are the linear transformation features of frame prototypes $P_{f}$ . During training, each event query learns how to adaptively focus on video frame prototypes, while multiple queries implicitly guarantee a certain event diversity. + +Differently, since the same video often corresponds to multiple text semantic descriptions, we directly use the global text representation $\pmb{y}_E$ as a sentence prototype to align with the event prototypes $\pmb{P}_e$ . + +Event-sentence matching. Similar to [43], this event-sentence prototype matching process can be expressed as: + +$$ +s _ {e s} = \max _ {i = 1} ^ {N _ {e}} \left\langle \boldsymbol {y} _ {E}, \boldsymbol {P} _ {e _ {i}} \right\rangle . \tag {7} +$$ + +We look for the closest event prototype to the text representation for dynamic matching. + +# 3.4. Training and Inference + +The InfoNCE loss [55, 75] is employed to optimize the prototype matching within a batch. We treat text-video pairs as positive examples, while considering all other pairwise combinations in the batch as negative examples: + +$$ +\mathcal {L} _ {t v c} = \left(\mathcal {L} _ {t 2 v} \left(\boldsymbol {S} _ {o p}\right) + \mathcal {L} _ {v 2 t} \left(\boldsymbol {S} _ {o p}\right) + \mathcal {L} _ {t 2 v} \left(\boldsymbol {S} _ {e s}\right) + \mathcal {L} _ {v 2 t} \left(\boldsymbol {S} _ {e s}\right)\right) / 4, \tag {8} +$$ + +$$ +\mathcal {L} _ {t 2 v} (\boldsymbol {S}) = - \frac {1}{B} \sum_ {i = 1} ^ {B} \log \frac {\exp \left(\boldsymbol {S} ^ {i i} / \sigma\right)}{\sum_ {j = 1} ^ {B} \exp \left(\boldsymbol {S} ^ {i j} / \sigma\right)}, \tag {9} +$$ + +$$ +\mathcal {L} _ {v 2 t} (\boldsymbol {S}) = - \frac {1}{B} \sum_ {i = 1} ^ {B} \log \frac {\exp \left(\boldsymbol {S} ^ {i i} / \sigma\right)}{\sum_ {j = 1} ^ {B} \exp \left(\boldsymbol {S} ^ {j i} / \sigma\right)}, \tag {10} +$$ + +where the $\sigma$ is a learnable temperature parameter, $S_{op}$ and $S_{es}$ are object-phrase and event-sentence prototype matching similarity matrices in a batch of size $B$ . + +During the inference stage, we directly weight the spatiotemporal matching scores for the final similarity matching: $s = s_{es} + \beta s_{op}$ , where $\beta$ is the spatial matching factor. + +# 4. Experiments + +We carry out experiments on the standard text-video retrieval datasets of MSRVTT [71], DiDeMo [23], VATEX [64] and LSMDC [58]. Standard metrics in information retrieval [48, 17] are adopted to measure the retrieval performance, including Recall@1/5/10 (R@1/5/10), Median Rank (MdR), and Mean Rank (MnR). + +# 4.1. Experimental Settings + +Datasets. (1) MSRVTT [71] consists of 10k videos and 200k human-labeled descriptions, where many videos have diverse captions. To thoroughly compare the existing methods, we follow [20] to train on 7k or 9k train+val videos and test on a test set of 1k text-video pairs. (2) DiDeMo [23] contains 10K Flickr videos and 40K captions. Following [43], all caption descriptions of a video are concatenated as a query to evaluate all methods. (3) VATEX [64] is comprised of 34,991 video clips. According to [5], we select 25,991, 1, 500 and 1, 500 videos as the training, validation and test sets. (4) LSMDC [58] consists of 118,081 movie clips each paired with a single caption description. We choose 101, 079, 7, 408 and 1, 000 videos as the training, validation and test sets. + +Implementation details. We initialize the backbone with the pre-trained model CLIP (ViT-B/32) [57] following [48]. Our decoders consist of two transformer layers with a single attention head. To reduce the computing overhead, all videos are resized to $224 \times 224$ with random cropping and flipping, and the frame rate is 3. We set the max text length as 32 and video frame number as 12 except for DiDeMo (set to 64 and 64) as its videos are longer. We optimize the model for 5 epochs on 4 NVIDIA Tesla A100 GPUs, employ Adam optimizer [32] with 0.2 weight decay and fix the batch size as 128. The learning rate is set to 1e-7 for CLIP-initialized weights and 1e-4 for all other parameters. Following [57], we decay the learning rate using a warmup cosine schedule [49]. The spatial matching factor $\beta$ is 1.5. By default, the prototype number $N_{o}$ , $N_{p}$ , and $N_{e}$ are 12, 28 and 3. The dimension of prototypes is 512. + +Table 1. Retrieval results on MSRVTT-9k. We reproduce TVMM* [43] using the same backbone network CLIP (ViT-B/32) [57]. All results in this table do not use additional post-processing techniques [2, 7]. + +
MethodReferenceText → VideoVideo → Text
R@1↑R@5↑R@10↑MdR↓MnR↓R@1↑R@5↑R@10↑MdR↓MnR↓
CE [47]BMVC1920.650.364.05.3-20.948.862.46.0-
MMT [17]ECCV2026.657.169.64.024.027.057.569.73.721.3
T2vlad [65]CVPR2129.559.070.14.0-31.860.071.13.0-
HiT [46]ICCV2127.759.272.02.9-28.860.372.33.0-
TeachText [10]ICCV2129.661.674.23.0-32.162.775.03.0-
ClipBERT [33]CVPR2122.046.859.96.0------
SupportSet [56]ICLR2130.158.569.33.0-28.558.671.63.0-
Frozen [1]ICCV2131.059.570.53.0------
BridgeFormer [18]CVPR2237.664.875.1-------
TVMM [43]NeurIPS2236.264.275.73.0-34.863.873.73.0-
CLIP4Clip [51]NeurCom2244.571.481.62.015.342.770.980.62.011.6
CenterCLIP [78]SIGIR2244.271.682.12.015.142.871.782.22.010.9
X-Pool [20]CVPR2246.972.882.22.014.3-----
TVMM* [43]NeurIPS2245.871.781.92.014.844.071.982.32.010.6
TS2-Net [48]ECCV2247.074.283.32.013.644.373.983.02.09.2
ProSTProposed48.274.683.42.012.446.374.283.22.08.7
ProST (ViT-B/16)Proposed49.575.084.02.011.748.075.985.22.08.3
+ +Table 2. Text-to-Video retrieval results on MSRVTT-7k. + +
MethodText → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
HowTo100M [52]14.940.252.89.0-
HERO [36]16.843.457.7--
ClipBERT [33]22.046.859.96.0-
CLIP4Clip [51]42.171.981.42.015.7
X-Pool [20]43.972.582.32.014.6
TS2-Net [48]43.172.282.12.014.2
ProST44.572.382.42.013.8
ProST (ViT-B/16)46.973.382.92.013.0
+ +Table 3. Text-to-Video retrieval results on the DiDeMo dataset. + +
MethodText → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
CE [47]16.141.182.78.3-
ClipBERT [33]20.448.060.86.0-
Frozen [1]31.059.872.43.0-
MCQ [18]37.062.273.93.0-
TVMM [43]36.564.975.43.0-
CLIP4Clip [51]42.868.579.22.018.9
TS2-Net [48]41.871.682.02.014.8
ProST44.972.782.72.013.7
ProST (ViT-B/16)47.575.584.42.012.3
+ +# 4.2. Comparison with State-of-the-art Methods + +To evaluate the relative benefits of ProST, we compare its performance with recent works [48, 20, 78, 51] from the literature. The results on the 9k and 7k splits of MSRVTT are shown in Tab. 1 and Tab. 2 respectively. We consistently achieve the best results for text-to-video retrieval and video-to-text retrieval across all splits and all metrics. Specifically, TS2-Net [48] integrates important patches into frame features for frame-level matching, which achieves the second best performance. Notably, for text-to-video retrieval, ProST outperforms TS2-Net [48] with $1.2\%$ and $1.4\%$ R@1 gains on the 9k split (47.0% vs. 48.2%) and the 7k split (43.1% vs. 44.5%). A $2.0\%$ improvement on R@1 (9k split) is also obtained compared to TS2-Net for video-to + +Table 4. Text-to-Video retrieval results on the VATEX dataset. + +
MethodText → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
HGR [5]35.173.583.52.0-
CLIP [57]39.772.382.22.012.8
CLIP4Clip [51]55.989.295.01.03.9
QB-Norm [2]58.888.393.81.0-
CLIP2Video [15]57.390.095.51.03.6
TS2-Net [48]59.190.095.21.03.5
ProST60.690.595.41.03.4
ProST (ViT-B/16)64.092.296.31.03.1
+ +Table 5. Text-to-Video retrieval results on the LSMDC dataset. + +
MethodText → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
Frozen [1]15.030.839.820.0-
TVMM [43]17.837.145.913.5-
CLIP4Clip [51]21.641.849.811.061.0
X-Pool [20]24.042.951.59.055.1
QB-Norm [2]22.440.149.511.0-
TS2-Net [48]23.042.150.49.057.0
ProST24.142.551.69.054.6
ProST (ViT-B/16)26.346.155.28.051.4
+ +text retrieval (44.3% vs. 46.3%). Furthermore, we reproduce TVMM [43] based on CLIP (ViT-B/32), which has 2.4% (45.8% vs. 48.2%) and 2.3% (44.0% vs. 46.3%) lower R@1 than ProST on the 9k split. The results demonstrate the effectiveness of ProST, which mines the spatial object details and temporal event diversity of videos, improving the model discrimination. Besides, ProST achieves a low MnR metric of 12.4 (text-to-video) on the 9k split, demonstrating the model robustness to erroneous results. + +In Tab. 3, 4 and 5, we examine the performance of ProST on the DiDeMo, VATEX and LSMDC datasets respectively. Compared with TS2-Net [48], ProST achieves a substantial boost of $3.1\%$ , $1.5\%$ and $1.1\%$ on the R@1 metric for DiDeMo, VATEX and LSMDC, respectively. ProST outperforms state-of-the-art methods by a large margin with the + +Table 6. The ablation study on MSRVTT-9k to investigate the effectiveness of Object-Phrase Prototype Matching (OPPM) and EventSentence Prototype Matching (ESPM). MdR results are not shown, as MdR=2.0 for all variants. Definition of important symbols: $\checkmark$ indicates default settings; $\odot$ TPG or $\odot$ SPG means replace with TPG or SPG to generate prototypes; P-P or O-W refers the alignment of patch-phrase or object-word; -F, -M or -R refers to removing frame decoder, attention mask or residual structure in Eq. 5; F-W or $\bar{\mathbb{F}}$ -S means directly aligning frame global tokens and word tokens or aligning the mean of frame global tokens and text global token. + +
IDOPPMESPMText → VideoVideo → Text
SPGMatchingTPGMatchingR@1↑R@5↑R@10↑MnRR@1↑R@5↑R@10↑MnR
1✓✓45.672.281.114.344.971.682.310.0
2○SPG✓45.871.781.914.844.071.982.310.6
3✓✓45.972.882.413.245.173.382.79.8
4○TPG✓✓✓46.373.381.813.545.073.182.49.8
5✓✓○SPG✓47.773.683.012.645.974.083.09.0
6✓P-P✓✓46.072.581.614.943.172.482.110.8
7✓O-W✓✓47.173.382.212.845.773.382.69.6
8✓✓-F✓46.472.881.713.544.572.582.010.2
9✓✓-M✓47.873.882.912.646.073.782.89.0
10✓✓-R✓46.672.982.414.045.372.181.810.1
11F-W✓✓47.373.582.812.645.973.783.19.0
12✓✓F-S46.572.682.313.445.173.482.59.8
Ours✓✓✓✓48.274.683.412.446.374.283.28.7
+ +Table 7. The ablation study on MSRVTT-9k to investigate the configuration of the number of prototypes. + +
{No, Np, Ne}Text → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
{6, 14, 3}45.673.281.62.014.3
{6, 28, 3}46.773.482.22.013.4
{12, 14, 3}47.073.783.02.012.9
{24, 32, 3}46.073.382.02.013.8
{12, 28, 1}46.373.082.12.013.5
{12, 28, 2}47.474.083.12.012.7
{12, 28, 4}47.674.383.22.012.5
{12, 28, 3}48.274.683.42.012.4
+ +![](images/2ed5fcb075312643981cafe1e97d366acca2c3f6774477fc0ecd1b7dd0e58c78.jpg) +Figure 5. The R@1 results at different spatial matching factors $\beta$ . + +CLIP (ViT-B/16) backbone. These results suggest the versatility and generalization of ProST, which can effectively process videos from different domains (e.g., movies). We owe the advantage of ProST over these works to the full use of dynamic spatio-temporal prototype matching. + +# 4.3. Ablation Study + +Analysis of progressive spatio-temporal prototype matching. In Tab. 6, we compare ProST with 12 variants, which proves that each module contributes to final results. + +We elaborate on some important observations. First, we show the results relying only on Object-Phrase Prototype Matching (OPPM) or Event-Sentence Prototype Match + +ing (ESPM). To implement our model without OPPM, all tokens are fed directly into the frame decoder and event decoder (TPG) to get multiple event prototypes. When only ESPM is used, there is a $2.6\%$ decrease in $\mathbb{R}@\mathbb{1}$ . This confirms the complementary role of fine-grained spatial details for ESPM. Next, we replace TPG with SPG and find that there is a certain suppression effect on noise. However, both of the above variants perform poorly due to the lack of progressive prototype generation and matching. When we only train model with OPPM, the model still underperforms. This may be due to the lack of temporal understanding and the inability to resolve correspondence ambiguity. + +Second, $\mathbb{O}$ TPG, P-P and O-W prove that there is indeed redundancy in the original video tokens. The sparse weights in SPG can alleviate this problem. However, FC layers in SPG cannot interact with intra-frame and inter-frame information, making it difficult to generate better event prototypes. This may be the reason for the drop in $\mathbb{O}$ SPG. Third, P-P and O-W also confirm the benefits of prototype matching. Raw patches or words without aggregation strategies may worsen the cross-modal alignment. + +Fourth, the results for -F, -M and -R also decreased. Because intra-frame local object relations and global frame features jointly complement comprehensive frame-level spatial information, which is helpful for subsequent temporal learning. Fifth, from F-W and $\overline{\mathbf{F}}$ -S, we can see the importance of prototype design mode. Directly using global frame features ([CLS] tokens) in ProST-S for frame-word alignments lacks object details. In $\overline{\mathbf{F}}$ -S, the mean value of frame global features mixes all information equally, making it difficult to characterize dynamic and changeable videos. + +Analysis of prototype configuration. We conduct experiments on various prototype configurations in Tab. 7. Im + +![](images/4dd685fda007b8295aa3ccaab445c98cc379e836c6806b8f6cfe9bc68e3ce92c.jpg) +Figure 6. Visualization of the object and event prototypes. We sample 12 frames in the video and object prototypes are shown as highlighted response regions in the frame. Then, we show cross-attention event weights of Eq. 6 in a line graph. Best viewed in color. + +proper configuration of spatial prototypes leads to performance degradation, possibly because too many prototypes may introduce local noise, while few prototypes are not enough to express semantics. Furthermore, the best result is obtained when the number of event prototypes is 3, which may be related to the degree of semantic divergence of texts. + +Hyperparameter analysis. As shown in Fig. 5, we investigate the spatial matching factor $\beta$ and present results for text-video (T2V) and video-text retrieval (V2T). As $\beta$ grows, the performance increases at first and reaches the best results, then decreases as a whole. A small $\beta$ may not fully exploit the underlying fine-grained spatial information, while a large $\beta$ may overemphasize local matching and destroy the overall dynamic semantic understanding. + +# 4.4. Qualitative Results + +Visualization of prototypes. In Fig. 6, we first present object prototypes in video frames. Many redundant patches are removed by prototypes, and the spatially highlighted object part and the phrase can be well locally corresponded. Then, we compute cross-attention for 3 event queries and 12 video frames according to Eq. 6, whose weights are shown in a line graph. The weights of different event prototypes on different frames are quite different, which proves that our model can learn temporal relations and event prototypes can express diverse semantics. For example, event prototype 1 has larger weights on the first three frames, which indicates that it may correspond to the semantics contained in text 1. Similarly, event prototype 2 or 3 corresponds to text 2 or 3. + +Retrieval results. Top-3 TVR results are illustrated in Fig. 7. Specifically, for query 97, although the top-2 recalled videos are women in the same dress, the difference is that the correct video discusses the cushion seat, while the incorrect video does not. This proves that object-phrase prototype matching provides fine-grained spatial knowledge (i.e., objects). For query 353, ProST pays attention to + +![](images/34a3909e2a8762b93ab62929c285012e198bdf76e9c6df391094d9336cb27f94.jpg) +Figure 7. Top-3 TVR results on MSRVTT-9k. Left: the ranked videos by our ProST. Right: the ranked videos with only event-sentence prototype matching. Red: correct videos. + +both the brief human speech at the beginning of the video and the subsequent earth display. However, using only event prototypes will result in a matching error. This shows that ProST can make a trade-off between the spatio-temporal matching relations to achieve better discrimination. + +# 5. Conclusion + +We have proposed a novel text-video retrieval framework, ProST, to decompose the matching process into complementary object-phrase and event-sentence prototype alignments. In the object-phrase prototype matching stage, + +we design the spatial prototype generation mechanism to focus on important video content and strengthen the fine-grained spatial alignment. In the event-sentence prototype matching phase, we use the temporal prototype generation mechanism to progressively generate diverse event prototypes and learn dynamic one-to-many relations. In this paper, we hope not only to provide insights into the importance of complementary spatio-temporal matching but also to facilitate future work that advances text-video retrieval by solving design flaws rather than mostly trial and error. + +Acknowledgment. This work is supported by the National Key Research and Development Program of China (2022YFB3104700), the National Nature Science Foundation of China (62121002, 62022076, U1936210, 62102384). + +# References + +[1] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. Frozen in time: A joint video and image encoder for end-to-end retrieval. In ICCV, 2021. 2, 3, 6 +[2] Simion-Vlad Bogolin, Ioana Croitoru, Hailin Jin, Yang Liu, and Samuel Albanie. Cross modal retrieval with querybank normalisation. In CVPR, 2022. 6 +[3] Soravit Changpinyo, Jordi Pont-Tuset, Vittorio Ferrari, and Radu Soricut. Telling the what while pointing to the where: Multimodal queries for image retrieval. In ICCV, 2021. 1 +[4] Sihan Chen, Xingjian He, Longteng Guo, Xinxin Zhu, Weining Wang, Jinhui Tang, and Jing Liu. VALOR: vision-audiolanguage omni-perception pretraining model and dataset. arXiv preprint arXiv:2304.08345, 2023. 1 +[5] Shizhe Chen, Yida Zhao, Qin Jin, and Qi Wu. 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The typical solution is to directly align the global video-level and sentence-level features during learning, which would ignore the intrinsic video-text relations, i.e., a text description only corresponds to a spatio-temporal part of videos. Hence, the matching process should consider both fine-grained spatial content and various temporal semantic events. To this end, we propose a text-video learning framework with progressive spatio-temporal prototype matching. Specifically, the matching process is decomposed into two complementary phases: object-phrase prototype matching and event-sentence prototype matching. In the object-phrase prototype matching phase, the spatial prototype generation mechanism predicts key patches or words, which are aggregated into object or phrase prototypes. Importantly, optimizing the local alignment between object-phrase prototypes helps the model perceive spatial details. In the event-sentence prototype matching phase, we design a temporal prototype generation mechanism to associate intra-frame objects and interact inter-frame temporal relations. Such progressively generated event prototypes can reveal semantic diversity in videos for dynamic matching. Validated by comprehensive experiments, our method consistently outperforms the state-of-the-art methods on four video retrieval benchmark." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 595, + 128, + 608 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 595, + 128, + 608 + ], + "spans": [ + { + "bbox": [ + 47, + 595, + 128, + 608 + ], + "type": "text", + "content": "1. 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Visualization of event and object prototypes learned by 1) adaptive event matching w/o object-phrase prototypes and 2) object-phrase prototype matching. Object prototypes can focus on local patches (e.g., tail) and complement event-level matching." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 533, + 546, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 546, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 546, + 676 + ], + "type": "text", + "content": "opment of short video platforms. TVR [45, 21] aims to search semantically relevant videos based on user-entered text queries. Unfortunately, the inherent modality gap phenomenon [42, 61, 38, 3, 67] increases the difficulty of associating multimodal data. Towards such a concern, pioneering works [47, 65, 73] usually exploit multiple unimodal pre-trained models to extract features, and then use metric learning strategies [14] to strengthen the modality alignment in the joint space. However, there are large differences in the initial distributions of multiple unimodal offline features, which inevitably brings the feature fusion challenge to affect the retrieval results." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "Recently, encouraged by the success of vision-language pre-training [50, 66, 34, 27, 72, 35, 4], a series of canonical works [51, 20, 44, 16] are proposed by transferring knowl-" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 683, + 205, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 683, + 205, + 693 + ], + "spans": [ + { + "bbox": [ + 58, + 683, + 205, + 693 + ], + "type": "text", + "content": "*Interns at DAMO Academy, Alibaba Group" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 59, + 693, + 135, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 693, + 135, + 703 + ], + "spans": [ + { + "bbox": [ + 59, + 693, + 135, + 703 + ], + "type": "text", + "content": "† Corresponding author" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 58, + 703, + 260, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 260, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 260, + 712 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 58, + 703, + 260, + 712 + ], + "type": "text", + "content": "Code is available at https://github.com/IMCCretrieval/ProST." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "4100" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 289, + 251 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 289, + 251 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 289, + 251 + ], + "type": "image", + "image_path": "7a112fc02f46f7ae64523cdefe5521e51dbafb6446885a2624cf796c1c58eefb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 253, + 288, + 299 + ], + "lines": [ + { + "bbox": [ + 46, + 253, + 288, + 299 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 288, + 299 + ], + "type": "text", + "content": "Figure 2. The progressive prototype generation process: 1) focus on patch-level spatial details; 2) aggregate intra-frame object prototypes; 3) interact inter-frame relations temporally as event prototypes, corresponding to multiple semantics." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 318, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 318, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 318, + 289, + 715 + ], + "type": "text", + "content": "edge from cross-modal pre-trained models (e.g., CLIP [57]) to the TVR task. Among them, some methods [51, 1, 28] learn to encode text or video data as a single embedding and perform global alignment between the sentence and the whole video. Subsequent approaches [48, 78] employ frame-level or segment-level matching by taking into account the different importance of video content. These methods try to encode the video into a single semantic content described by corresponding text, establishing one-to-one relations. However, videos contain rich visual elements [39] and a text description may only correspond to a spatio-temporal part of the video, dynamic and fine-grained matching is needed beyond the global video-level or frame-level matching. Specifically, feature encoding should characterize different semantic information to support dynamic partial alignment during the matching process. Recently, Lin et al. [43] attempt to address the dynamic matching problem by temporally segmenting videos into multiple semantic events, so that different text descriptions can adaptively match event prototypes. Nevertheless, various event prototypes are still inadequate to model the relations between fine-grained objects and content words, lacking the perception of local details. As shown in Fig. 1(1), the correct video corresponding to the text should focus on \"tail\", but the event prototype corresponding to the maximum similarity may suffer from scene bias [8, 63] and ignore this small object. Based on the above observation, an effective event-sentence matching process needs to emphasize fine-grained local spatial matching. This also suggests that the generation of event prototypes should be bootstrapped from the semantic combination of important objects. Therefore, we should construct event prototypes progressively, i.e., explicitly preserve the local information learned in the spatial" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 305, + 72, + 533, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 533, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 533, + 84 + ], + "type": "text", + "content": "matching stage, and then perform temporal aggregation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 85, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 85, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 85, + 545, + 239 + ], + "type": "text", + "content": "To this end, we propose a novel Progressive Spatio-Temporal Prototype Matching (ProST) framework, which decomposes the matching process into complementary object-phrase and event-sentence prototype alignments. In the object-phrase prototype matching phase, a spatial prototype generation mechanism is first developed to focus on key image patches or word tokens. To prevent massive video redundancy, we use sparse weights to filter irrelevant background interference and aggregate important patch or word tokens into object or phrase prototypes. As shown in Fig. 1(2), optimal local responses can be found by the maximum similarity between object and phrase prototypes to help the model perceive spatial details." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 240, + 546, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 240, + 546, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 240, + 546, + 443 + ], + "type": "text", + "content": "In the event-sentence prototype matching phase, a temporal prototype generation mechanism is designed to decode various event prototypes for dynamic semantic alignment. Specifically, since the spatial details should not be ignored in the event generation process, we send object prototypes to the frame and event decoder for progressive prototype learning. Multiple different event prototypes are generated to reveal the semantic diversity in videos and support dynamic matching. Finally, as shown in Fig. 2, different text sentences can match the most appropriate event prototype learned from the video. Overall, ProST encodes the rich video content by generating object-level, frame-level and event-level prototypes in a progressive manner, and constructs dynamic and fine-grained spatio-temporal matching strategies. ProST not only strengthens the interaction of local spatial content, but also considers the intrinsic relations where video and text are only partially aligned." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 444, + 545, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 545, + 562 + ], + "type": "text", + "content": "The contributions of this paper are threefold: 1) we propose a novel framework, ProST, to decompose the matching process into complementary object-phrase and event-sentence prototype alignments; 2) two prototype generation mechanisms are developed to learn sparse spatial and dynamic temporal information respectively, which can fully explore fine-grained local details and video semantic diversity; 3) extensive experiments demonstrate that ProST outperforms state-of-the-art methods on MSRVTT, DiDeMo, VATEX and LSMDC datasets." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 574, + 392, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 392, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 392, + 586 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 594, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 629 + ], + "type": "text", + "content": "Text-video retrieval. Existing works can be divided into two categories: offline feature based [47, 11, 77, 26] and end-to-end training [1, 51, 48, 43, 31, 29, 30, 28] methods." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Early methods [69, 11] extract video-text features offline, and then perform embedding alignment in a common space. To enhance representation quality, CE [47], MMT [17] and HiT [46] employ multiple unimodal experts (OCR, speech, etc.) to enrich video features. Teach-Text [10] adopts multiple text encoders to gather text information and obtain more credible alignments. Besides," + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "text", + "content": "4101" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "content": "HGR [5] and T2vlad [65] build semantic graphs or shared centers to explore global-local relations. However, these methods employ additional analysis tools or experts to preprocess data, which increases the complexity and limits flexibility. Unlike the global-local alignment explored on multiple experts [65, 46], we consider finer-grained patch-level visual content without requiring additional experts." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 158, + 287, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 158, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 158, + 287, + 326 + ], + "type": "text", + "content": "Current mainstream works benefit from large-scale vision-language pre-training [57, 19]. ClipBERT [33] and Frozen [1] first propose efficient end-to-end pre-training schemes. MCQ [18] builds cross-modal associations by predicting verb or noun features. Recently, CLIP4clip [51] uses CLIP [57] as the backbone network, significantly improving TVR performance and inspiring a series of works [48, 15, 20, 78, 28]. Centerclip [78] conducts segment-level clustering, which reduces token redundancy and computational overhead. TS2Net [48] designs the token shift module to realize the perception of local movement between frames. Xpool [20] uses text as a condition to guide the aggregation of video tokens. But the limitation is that the video encoding process must involve both modal data." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 327, + 288, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 288, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 288, + 533 + ], + "type": "text", + "content": "Adaptive cross-modal retrieval. Recently, the correspondence ambiguity problem (i.e., a text may only correspond to a part of the video or image) has raised concerns in the cross-modal retrieval community [9, 59, 43]. In text-image retrieval, PVSE [59] employs the self-attention mechanism to explore different local parts of instances and generates " + }, + { + "bbox": [ + 46, + 327, + 288, + 533 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 327, + 288, + 533 + ], + "type": "text", + "content": " candidate features for adaptive matching. PCME [9] samples the text-image probabilistic embeddings multiple times from the learned Gaussian distribution to explore one-to-many multiplicity relationships. In text-video retrieval, TVMM [43] utilizes fully connected layers to directly aggregate all tokens into multiple event prototypes for text-adaptive event matching. However, fine-grained object-level information is not well exploited in the event matching process of TVMM, while the proposed progressive spatiotemporal matching framework could simultaneously consider local spatial details and dynamic temporal relations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 548, + 103, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 103, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 103, + 559 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "text", + "content": "Given a dataset consisting of " + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "text", + "content": " videos " + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = \\{\\pmb{v}_i\\}_{i=1}^n" + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "text", + "content": " and their corresponding " + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "text", + "content": " captions " + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{T} = \\{\\pmb{t}_i\\}_{i=1}^m" + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "text", + "content": ", Text-Video Retrieval (TVR) aims to learn a function " + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "inline_equation", + "content": "s(\\pmb{t}_i, \\pmb{v}_i)" + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "text", + "content": " to effectively measure the similarity between modalities. For a text query " + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{t}_i" + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "text", + "content": ", we can rank all videos in the dataset according to the similarity scores. Ideally, the cross-modal similarity (e.g., cosine similarity) between paired cross-modal instances should be greater than that of unpaired instances: " + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "inline_equation", + "content": "s(\\pmb{t}_i, \\pmb{v}_i) > s(\\pmb{t}_i, \\pmb{v}_j)" + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "text", + "content": ". This requires the model to learn powerful text encoding network " + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{f}_t : \\mathcal{T} \\to \\mathcal{Y}" + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "text", + "content": " and video encoding network " + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{f}_v : \\mathcal{V} \\to \\mathcal{X}" + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "text", + "content": ", which generate high-quality features and ultimately enable efficient matching." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 72, + 384, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 384, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 384, + 83 + ], + "type": "text", + "content": "3.1. Framework" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "text", + "content": "Fig. 3 sheds light on our end-to-end trainable architecture, which consists of a backbone network and two prototype matching schemes. For a fair comparison with recent methods [48, 51, 20], we adopt CLIP [57] as the backbone network, which exhibits strong performance in downstream tasks. Given an input video " + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "text", + "content": ", we uniformly select " + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "text", + "content": " frames as keyframes to extract sequential features " + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_i = \\{\\mathbf{x}_C^l, \\mathbf{x}_{T_1}^l, \\dots, \\mathbf{x}_{T_K}^l\\}_{l=1}^L \\in \\mathbb{R}^{L \\times (K+1) \\times D}" + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_C^l" + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "text", + "content": " is the global frame token feature ([CLS]) and " + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "text", + "content": " is the patch number. For each query text " + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "text", + "content": ", we add the [SOT] and [EOT] tokens to indicate the start and the end of the text. The output text token features can be defined as " + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}_i = \\{\\mathbf{y}_S, \\mathbf{y}_{T_1}, \\dots, \\mathbf{y}_{T_M}, \\mathbf{y}_E\\} \\in \\mathbb{R}^{(M+2) \\times D}" + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_E" + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "text", + "content": " is the global text token feature([EOT]), " + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 89, + 545, + 270 + ], + "type": "text", + "content": " are the number of words and dimensions, respectively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 270, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 545, + 415 + ], + "type": "text", + "content": "Apart from the backbone network, we decompose the matching process into two spatio-temporal complementary parts: 1) Object-Phrase Prototype Matching (Sec. 3.2) aligns the visual object prototypes and text phrase prototypes generated by Spatial Prototype Generation (SPG) to emphasize fine-grained spatial information; 2) Event-Sentence Prototype Matching (Sec. 3.3) exploits event prototypes progressively generated by Temporal Prototype Generation (TPG) to learn dynamic semantic alignment, which explores intrinsic one-to-many video-text relations. The object-phrase and event-sentence prototype matching schemes determine the final cross-modal similarity." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 420, + 493, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 420, + 493, + 433 + ], + "spans": [ + { + "bbox": [ + 306, + 420, + 493, + 433 + ], + "type": "text", + "content": "3.2. Object-Phrase Prototype Matching" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 438, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 629 + ], + "type": "text", + "content": "The text of the video caption subjectively describes a certain event composed of different objects, actions and temporal activities across the video sequence. This results in pairs of video and text that are often partially matched. To solve this problem [9, 59], existing method [43] learns a single patch-event projection to aggregate multiple event prototypes for text-adaptive matching. However, these prototypes are still inadequate to perceive the local details. Our intuition is that decoupling the spatio-temporal modeling process in a divide-and-conquer manner is more beneficial than a single projection. Therefore, we conduct progressive spatio-temporal prototype matching for text-video retrieval. In this section, we illustrate how to model spatial matching. We first perform patch-object and word-phrase spatial prototype aggregation to reveal key local details, and then introduce the fine-grained prototype alignment." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "type": "text", + "content": "Spatial prototype generation. For videos, we aggregate the patch tokens into object prototypes to represent fine-grained spatial information, such as object instance, object part, and action region. In the prototype generation process, not all patch tokens are aggregated. Although the patch tokens contain important spatial information, they also bring redundancy. For example, some background to" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4102" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 73, + 71, + 519, + 190 + ], + "blocks": [ + { + "bbox": [ + 73, + 71, + 519, + 190 + ], + "lines": [ + { + "bbox": [ + 73, + 71, + 519, + 190 + ], + "spans": [ + { + "bbox": [ + 73, + 71, + 519, + 190 + ], + "type": "image", + "image_path": "4c442d68a00fd58715e4583d1045146bfab56c1ee0fef0bd806988fdedc0bb3d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 194, + 547, + 240 + ], + "lines": [ + { + "bbox": [ + 46, + 194, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 547, + 240 + ], + "type": "text", + "content": "Figure 3. Our ProST framework. We decompose the matching process into two spatio-temporal complementary parts: 1) Object-Phrase Prototype Matching aligns the visual object prototypes and text phrase prototypes generated by Spatial Prototype Generation (SPG) to emphasize fine-grained spatial information; 2) Event-Sentence Prototype Matching exploits event prototypes progressively generated by Temporal Prototype Generation (TPG) to learn dynamic semantic alignment, which explores intrinsic one-to-many video-text relations." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 63, + 248, + 532, + 340 + ], + "blocks": [ + { + "bbox": [ + 63, + 248, + 532, + 340 + ], + "lines": [ + { + "bbox": [ + 63, + 248, + 532, + 340 + ], + "spans": [ + { + "bbox": [ + 63, + 248, + 532, + 340 + ], + "type": "image", + "image_path": "6b48532e4ccd86f98e7a9669041c458a0ba365ab69aac3d2456d7cb580c92847.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 83, + 344, + 506, + 357 + ], + "lines": [ + { + "bbox": [ + 83, + 344, + 506, + 357 + ], + "spans": [ + { + "bbox": [ + 83, + 344, + 506, + 357 + ], + "type": "text", + "content": "Figure 4. Details of the Spatial Prototype Generation (SPG) and Temporal Prototype Generation (TPG) mechanisms." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 376, + 289, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 289, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 289, + 483 + ], + "type": "text", + "content": "kens may interfere with cross-modal alignment. Hence, we hope to filter out retrieval-superfluous information and generate object-level prototypes in a sparse aggregation manner. For simplicity, two Fully Connected (FC) layers and ReLU functions are used to predict sparse weights " + }, + { + "bbox": [ + 46, + 376, + 289, + 483 + ], + "type": "inline_equation", + "content": "\\pmb{W}_{o}^{l} \\in \\mathbb{R}^{(K + 1)\\times N_{o}}" + }, + { + "bbox": [ + 46, + 376, + 289, + 483 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 376, + 289, + 483 + ], + "type": "inline_equation", + "content": "N_{o}" + }, + { + "bbox": [ + 46, + 376, + 289, + 483 + ], + "type": "text", + "content": " is the number of object prototypes. This way prevents object prototypes from being affected by redundant patches. For each frame " + }, + { + "bbox": [ + 46, + 376, + 289, + 483 + ], + "type": "inline_equation", + "content": "\\pmb{X}^{l} \\in \\mathbb{R}^{(K + 1)\\times D}" + }, + { + "bbox": [ + 46, + 376, + 289, + 483 + ], + "type": "text", + "content": ", SPG can be defined as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 109, + 487, + 287, + 504 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 487, + 287, + 504 + ], + "spans": [ + { + "bbox": [ + 109, + 487, + 287, + 504 + ], + "type": "interline_equation", + "content": "\\boldsymbol {P} _ {o} ^ {l} = \\boldsymbol {W} _ {o} ^ {l ^ {T}} \\cdot \\boldsymbol {X} ^ {l} \\in \\mathbb {R} ^ {N _ {o} \\times D}. \\tag {1}", + "image_path": "3dc66ee6fd7f95b1e681a30ae3290a6b06c6e9672dddff902d3e1a609e9974bb.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 510, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 533 + ], + "type": "text", + "content": "Ideally, each object prototype can adaptively aggregate the corresponding object-related or action-related patches." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 534, + 288, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 288, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 288, + 605 + ], + "type": "text", + "content": "For text, we draw on the SPG mechanism and design a similar network structure to aggregate word tokens, which generates phrase prototypes " + }, + { + "bbox": [ + 46, + 534, + 288, + 605 + ], + "type": "inline_equation", + "content": "P_{p} \\in \\mathbb{R}^{N_{p} \\times D}" + }, + { + "bbox": [ + 46, + 534, + 288, + 605 + ], + "type": "text", + "content": ". In this way, we explore spatially important information based on fine-grained patch tokens and word tokens. Then, the prototypes are optimized by spatial object-phrase prototype matching." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": "Object-phrase matching. Different from the existing text-image token-wise interaction [74], we propose a text-video prototype-wise interaction designed from a spatial perspective. Specifically, we first compute the maximum similarity of object-phrase prototypes within each frame. This associates the most similar phrase prototypes to each object prototype, reflecting cross-modal fine-grained matching. Then, for the multi-frame object similarity matrix, we find the largest similarity score across the frame sequences, which" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 376, + 546, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 546, + 424 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 546, + 424 + ], + "type": "text", + "content": "gives a more confident probability of object-phrase matching. Finally, the object-phrase matching scores are summed to obtain the final similarity " + }, + { + "bbox": [ + 304, + 376, + 546, + 424 + ], + "type": "inline_equation", + "content": "s_{op}" + }, + { + "bbox": [ + 304, + 376, + 546, + 424 + ], + "type": "text", + "content": ". The prototype-wise interaction process is defined as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 349, + 431, + 545, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 431, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 349, + 431, + 545, + 464 + ], + "type": "interline_equation", + "content": "s _ {o p} = \\frac {1}{N _ {o}} \\sum_ {j = 1} ^ {N _ {o}} \\max _ {l = 1} ^ {L} \\max _ {i = 1} ^ {N _ {p}} \\left[ \\boldsymbol {P} _ {p} \\cdot \\boldsymbol {P} _ {o} ^ {l ^ {T}} \\right] _ {i j}, \\tag {2}", + "image_path": "0d139986f66ffe217cda14b4e798edd69aed432af97176f046326310a774b37d.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 472, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 545, + 498 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 472, + 545, + 498 + ], + "type": "inline_equation", + "content": "N_{o}, N_{p}" + }, + { + "bbox": [ + 304, + 472, + 545, + 498 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 472, + 545, + 498 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 472, + 545, + 498 + ], + "type": "text", + "content": " are the number of object prototypes, phrase prototypes and frames, respectively." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 503, + 499, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 503, + 499, + 517 + ], + "spans": [ + { + "bbox": [ + 306, + 503, + 499, + 517 + ], + "type": "text", + "content": "3.3. Event-Sentence Prototype Matching" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 522, + 545, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 570 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 570 + ], + "type": "text", + "content": "In this section, we illustrate how to model dynamic temporal matching. We first perform progressive object-event prototype aggregation to reveal the video semantic diversity, and then introduce dynamic prototype matching." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 570, + 546, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 689 + ], + "type": "text", + "content": "Temporal prototype generation. A naive solution to obtain video-level features based on global frame features is by mean pooling [51, 65, 5], or by adding temporal encoder layers [11]. However, this leads to two issues: 1) failure to perceive local details [43, 78, 48] and ignoring important objects will exacerbate the bias of video feature learning; 2) these strategies generate a single video-level feature, which can only quantify one-to-one relations. Therefore, we investigate how to incorporate key fine-grained objects and dynamic temporal changes into diverse event prototypes." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "The core idea is to progressively aggregate spatial object prototypes into frame prototypes and then perform inter" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4103" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "type": "text", + "content": "frame interaction to generate various event prototypes. In Fig. 4, a frame decoder is first designed to incorporate all object prototypes " + }, + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "type": "inline_equation", + "content": "P_{o} \\in \\mathbb{R}^{(L \\times N_{o}) \\times D}" + }, + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "type": "text", + "content": " into frame-level prototypes " + }, + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "type": "inline_equation", + "content": "P_{f} \\in \\mathbb{R}^{L \\times D}" + }, + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "type": "text", + "content": ", which implies fine-grained inter-object spatial relations. To learn frame-level object relations, we define the masked attention as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 80, + 152, + 287, + 167 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 152, + 287, + 167 + ], + "spans": [ + { + "bbox": [ + 80, + 152, + 287, + 167 + ], + "type": "interline_equation", + "content": "\\boldsymbol {P} _ {f} = \\operatorname {s o f t m a x} \\left(\\boldsymbol {M} _ {f} + \\boldsymbol {Q} _ {f} \\boldsymbol {K} _ {o} ^ {\\mathrm {T}}\\right) \\boldsymbol {V} _ {o} + \\boldsymbol {Q} _ {f}, \\tag {3}", + "image_path": "0f872d71fdd07fd7edfa7c29cc4f62eca0aca1435aa0ac2fedb6157a5092c472.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 173, + 287, + 223 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 173, + 287, + 223 + ], + "spans": [ + { + "bbox": [ + 47, + 173, + 287, + 223 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 173, + 287, + 223 + ], + "type": "inline_equation", + "content": "Q_{f}\\in \\mathbb{R}^{L\\times D}" + }, + { + "bbox": [ + 47, + 173, + 287, + 223 + ], + "type": "text", + "content": " refers to frame queries (i.e., a set of randomly initialized learnable tokens), " + }, + { + "bbox": [ + 47, + 173, + 287, + 223 + ], + "type": "inline_equation", + "content": "K_{o}" + }, + { + "bbox": [ + 47, + 173, + 287, + 223 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 173, + 287, + 223 + ], + "type": "inline_equation", + "content": "V_{o}" + }, + { + "bbox": [ + 47, + 173, + 287, + 223 + ], + "type": "text", + "content": " are the features after the linear transformation of object prototypes " + }, + { + "bbox": [ + 47, + 173, + 287, + 223 + ], + "type": "inline_equation", + "content": "P_{o}" + }, + { + "bbox": [ + 47, + 173, + 287, + 223 + ], + "type": "text", + "content": ". The attention mask " + }, + { + "bbox": [ + 47, + 173, + 287, + 223 + ], + "type": "inline_equation", + "content": "M_{f}\\in \\mathbb{R}^{L\\times (L\\times N_{o})}" + }, + { + "bbox": [ + 47, + 173, + 287, + 223 + ], + "type": "text", + "content": " is:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 230, + 287, + 262 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 230, + 287, + 262 + ], + "spans": [ + { + "bbox": [ + 56, + 230, + 287, + 262 + ], + "type": "interline_equation", + "content": "\\boldsymbol {M} _ {f} (i, j) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} i \\cdot N _ {o} \\leq j < (i + 1) \\cdot N _ {o} \\\\ - \\infty & \\text {o t h e r w i s e} \\end{array} . \\right. \\tag {4}", + "image_path": "4e375d5204419633b58226eb6fbe7df0c9a0e042060b13b5ed68074b00117f32.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 270, + 287, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 270, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 47, + 270, + 287, + 308 + ], + "type": "text", + "content": "Inspired by [9], we add frame prototype " + }, + { + "bbox": [ + 47, + 270, + 287, + 308 + ], + "type": "inline_equation", + "content": "\\pmb{p}_f^l" + }, + { + "bbox": [ + 47, + 270, + 287, + 308 + ], + "type": "text", + "content": " and original global feature " + }, + { + "bbox": [ + 47, + 270, + 287, + 308 + ], + "type": "inline_equation", + "content": "\\pmb{x}_C^l" + }, + { + "bbox": [ + 47, + 270, + 287, + 308 + ], + "type": "text", + "content": " of corresponding frames to enhance the robustness of the model:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 123, + 316, + 287, + 332 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 316, + 287, + 332 + ], + "spans": [ + { + "bbox": [ + 123, + 316, + 287, + 332 + ], + "type": "interline_equation", + "content": "\\boldsymbol {p} _ {f} ^ {l} = \\left(\\boldsymbol {p} _ {f} ^ {l} + \\boldsymbol {x} _ {C} ^ {l}\\right) / 2. \\tag {5}", + "image_path": "72ca161448854ff2b34dd06bd46a6c0bb829179f731e8bb13240702c854c3de8.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 339, + 287, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 339, + 287, + 387 + ], + "spans": [ + { + "bbox": [ + 47, + 339, + 287, + 387 + ], + "type": "text", + "content": "Next, a dynamic event decoder is developed to learn the inter-frame relations in " + }, + { + "bbox": [ + 47, + 339, + 287, + 387 + ], + "type": "inline_equation", + "content": "P_{f}" + }, + { + "bbox": [ + 47, + 339, + 287, + 387 + ], + "type": "text", + "content": ", which can obtain different event prototypes " + }, + { + "bbox": [ + 47, + 339, + 287, + 387 + ], + "type": "inline_equation", + "content": "P_{e} \\in \\mathbb{R}^{N_{e} \\times D}" + }, + { + "bbox": [ + 47, + 339, + 287, + 387 + ], + "type": "text", + "content": " to illustrate the rich information of videos. Our dynamic attention is formulated as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 94, + 394, + 287, + 410 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 394, + 287, + 410 + ], + "spans": [ + { + "bbox": [ + 94, + 394, + 287, + 410 + ], + "type": "interline_equation", + "content": "\\boldsymbol {P} _ {e} = \\operatorname {s o f t m a x} \\left(\\boldsymbol {Q} _ {e} \\boldsymbol {K} _ {f} ^ {\\mathrm {T}}\\right) \\boldsymbol {V} _ {f} + \\boldsymbol {Q} _ {e}, \\tag {6}", + "image_path": "f53dba08d2eaf959e239b5125524bad300eda1ca30f0585e165b2d7cdb46de18.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 417, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 417, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 47, + 417, + 287, + 477 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 417, + 287, + 477 + ], + "type": "inline_equation", + "content": "Q_{e} \\in \\mathbb{R}^{N_{e} \\times D}" + }, + { + "bbox": [ + 47, + 417, + 287, + 477 + ], + "type": "text", + "content": " refers to event queries, " + }, + { + "bbox": [ + 47, + 417, + 287, + 477 + ], + "type": "inline_equation", + "content": "K_{f}" + }, + { + "bbox": [ + 47, + 417, + 287, + 477 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 417, + 287, + 477 + ], + "type": "inline_equation", + "content": "V_{f}" + }, + { + "bbox": [ + 47, + 417, + 287, + 477 + ], + "type": "text", + "content": " are the linear transformation features of frame prototypes " + }, + { + "bbox": [ + 47, + 417, + 287, + 477 + ], + "type": "inline_equation", + "content": "P_{f}" + }, + { + "bbox": [ + 47, + 417, + 287, + 477 + ], + "type": "text", + "content": ". During training, each event query learns how to adaptively focus on video frame prototypes, while multiple queries implicitly guarantee a certain event diversity." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 478, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 478, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 478, + 287, + 525 + ], + "type": "text", + "content": "Differently, since the same video often corresponds to multiple text semantic descriptions, we directly use the global text representation " + }, + { + "bbox": [ + 47, + 478, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\pmb{y}_E" + }, + { + "bbox": [ + 47, + 478, + 287, + 525 + ], + "type": "text", + "content": " as a sentence prototype to align with the event prototypes " + }, + { + "bbox": [ + 47, + 478, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\pmb{P}_e" + }, + { + "bbox": [ + 47, + 478, + 287, + 525 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 525, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 287, + 550 + ], + "type": "text", + "content": "Event-sentence matching. Similar to [43], this event-sentence prototype matching process can be expressed as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 119, + 559, + 287, + 579 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 559, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 119, + 559, + 287, + 579 + ], + "type": "interline_equation", + "content": "s _ {e s} = \\max _ {i = 1} ^ {N _ {e}} \\left\\langle \\boldsymbol {y} _ {E}, \\boldsymbol {P} _ {e _ {i}} \\right\\rangle . \\tag {7}", + "image_path": "8c0d5737bd94ad21711b3e3e89589b9f44f4ba250671e0fa2001861979420453.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 582, + 287, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 287, + 607 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 287, + 607 + ], + "type": "text", + "content": "We look for the closest event prototype to the text representation for dynamic matching." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 613, + 178, + 627 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 178, + 627 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 178, + 627 + ], + "type": "text", + "content": "3.4. Training and Inference" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 632, + 287, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 632, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 632, + 287, + 681 + ], + "type": "text", + "content": "The InfoNCE loss [55, 75] is employed to optimize the prototype matching within a batch. We treat text-video pairs as positive examples, while considering all other pairwise combinations in the batch as negative examples:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 689, + 291, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 291, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 291, + 713 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {t v c} = \\left(\\mathcal {L} _ {t 2 v} \\left(\\boldsymbol {S} _ {o p}\\right) + \\mathcal {L} _ {v 2 t} \\left(\\boldsymbol {S} _ {o p}\\right) + \\mathcal {L} _ {t 2 v} \\left(\\boldsymbol {S} _ {e s}\\right) + \\mathcal {L} _ {v 2 t} \\left(\\boldsymbol {S} _ {e s}\\right)\\right) / 4, \\tag {8}", + "image_path": "a7f70aabba36454b48dce742db942c763c70617be0a96be3f29ca2298bab05aa.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 334, + 81, + 545, + 114 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 81, + 545, + 114 + ], + "spans": [ + { + "bbox": [ + 334, + 81, + 545, + 114 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {t 2 v} (\\boldsymbol {S}) = - \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(\\boldsymbol {S} ^ {i i} / \\sigma\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\boldsymbol {S} ^ {i j} / \\sigma\\right)}, \\tag {9}", + "image_path": "abd63fa3af34214d6dbbff10a835cc0ac45c5340d577599c6d3530c8ece3da70.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 326, + 120, + 545, + 152 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 120, + 545, + 152 + ], + "spans": [ + { + "bbox": [ + 326, + 120, + 545, + 152 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {v 2 t} (\\boldsymbol {S}) = - \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(\\boldsymbol {S} ^ {i i} / \\sigma\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(\\boldsymbol {S} ^ {j i} / \\sigma\\right)}, \\tag {10}", + "image_path": "395c4a7c52fb104e11216dd01beddafe053d39feb5ee46cdcd5652f4e193d97f.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 156, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 156, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 306, + 156, + 545, + 191 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 306, + 156, + 545, + 191 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 306, + 156, + 545, + 191 + ], + "type": "text", + "content": " is a learnable temperature parameter, " + }, + { + "bbox": [ + 306, + 156, + 545, + 191 + ], + "type": "inline_equation", + "content": "S_{op}" + }, + { + "bbox": [ + 306, + 156, + 545, + 191 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 156, + 545, + 191 + ], + "type": "inline_equation", + "content": "S_{es}" + }, + { + "bbox": [ + 306, + 156, + 545, + 191 + ], + "type": "text", + "content": " are object-phrase and event-sentence prototype matching similarity matrices in a batch of size " + }, + { + "bbox": [ + 306, + 156, + 545, + 191 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 306, + 156, + 545, + 191 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 192, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 192, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 306, + 192, + 545, + 228 + ], + "type": "text", + "content": "During the inference stage, we directly weight the spatiotemporal matching scores for the final similarity matching: " + }, + { + "bbox": [ + 306, + 192, + 545, + 228 + ], + "type": "inline_equation", + "content": "s = s_{es} + \\beta s_{op}" + }, + { + "bbox": [ + 306, + 192, + 545, + 228 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 306, + 192, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 306, + 192, + 545, + 228 + ], + "type": "text", + "content": " is the spatial matching factor." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 238, + 387, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 238, + 387, + 251 + ], + "spans": [ + { + "bbox": [ + 306, + 238, + 387, + 251 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 257, + 545, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 257, + 545, + 330 + ], + "spans": [ + { + "bbox": [ + 305, + 257, + 545, + 330 + ], + "type": "text", + "content": "We carry out experiments on the standard text-video retrieval datasets of MSRVTT [71], DiDeMo [23], VATEX [64] and LSMDC [58]. Standard metrics in information retrieval [48, 17] are adopted to measure the retrieval performance, including Recall@1/5/10 (R@1/5/10), Median Rank (MdR), and Mean Rank (MnR)." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 336, + 432, + 349 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 336, + 432, + 349 + ], + "spans": [ + { + "bbox": [ + 306, + 336, + 432, + 349 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 354, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 354, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 305, + 354, + 545, + 521 + ], + "type": "text", + "content": "Datasets. (1) MSRVTT [71] consists of 10k videos and 200k human-labeled descriptions, where many videos have diverse captions. To thoroughly compare the existing methods, we follow [20] to train on 7k or 9k train+val videos and test on a test set of 1k text-video pairs. (2) DiDeMo [23] contains 10K Flickr videos and 40K captions. Following [43], all caption descriptions of a video are concatenated as a query to evaluate all methods. (3) VATEX [64] is comprised of 34,991 video clips. According to [5], we select 25,991, 1, 500 and 1, 500 videos as the training, validation and test sets. (4) LSMDC [58] consists of 118,081 movie clips each paired with a single caption description. We choose 101, 079, 7, 408 and 1, 000 videos as the training, validation and test sets." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": "Implementation details. We initialize the backbone with the pre-trained model CLIP (ViT-B/32) [57] following [48]. Our decoders consist of two transformer layers with a single attention head. To reduce the computing overhead, all videos are resized to " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": " with random cropping and flipping, and the frame rate is 3. We set the max text length as 32 and video frame number as 12 except for DiDeMo (set to 64 and 64) as its videos are longer. We optimize the model for 5 epochs on 4 NVIDIA Tesla A100 GPUs, employ Adam optimizer [32] with 0.2 weight decay and fix the batch size as 128. The learning rate is set to 1e-7 for CLIP-initialized weights and 1e-4 for all other parameters. Following [57], we decay the learning rate using a warmup cosine schedule [49]. The spatial matching factor " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": " is 1.5. By default, the prototype number " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "N_{o}" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "N_{e}" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": " are 12, 28 and 3. The dimension of prototypes is 512." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4104" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 92, + 542, + 278 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 545, + 92 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 545, + 92 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 545, + 92 + ], + "type": "text", + "content": "Table 1. Retrieval results on MSRVTT-9k. We reproduce TVMM* [43] using the same backbone network CLIP (ViT-B/32) [57]. All results in this table do not use additional post-processing techniques [2, 7]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 92, + 542, + 278 + ], + "lines": [ + { + "bbox": [ + 51, + 92, + 542, + 278 + ], + "spans": [ + { + "bbox": [ + 51, + 92, + 542, + 278 + ], + "type": "table", + "html": "
MethodReferenceText → VideoVideo → Text
R@1↑R@5↑R@10↑MdR↓MnR↓R@1↑R@5↑R@10↑MdR↓MnR↓
CE [47]BMVC1920.650.364.05.3-20.948.862.46.0-
MMT [17]ECCV2026.657.169.64.024.027.057.569.73.721.3
T2vlad [65]CVPR2129.559.070.14.0-31.860.071.13.0-
HiT [46]ICCV2127.759.272.02.9-28.860.372.33.0-
TeachText [10]ICCV2129.661.674.23.0-32.162.775.03.0-
ClipBERT [33]CVPR2122.046.859.96.0------
SupportSet [56]ICLR2130.158.569.33.0-28.558.671.63.0-
Frozen [1]ICCV2131.059.570.53.0------
BridgeFormer [18]CVPR2237.664.875.1-------
TVMM [43]NeurIPS2236.264.275.73.0-34.863.873.73.0-
CLIP4Clip [51]NeurCom2244.571.481.62.015.342.770.980.62.011.6
CenterCLIP [78]SIGIR2244.271.682.12.015.142.871.782.22.010.9
X-Pool [20]CVPR2246.972.882.22.014.3-----
TVMM* [43]NeurIPS2245.871.781.92.014.844.071.982.32.010.6
TS2-Net [48]ECCV2247.074.283.32.013.644.373.983.02.09.2
ProSTProposed48.274.683.42.012.446.374.283.22.08.7
ProST (ViT-B/16)Proposed49.575.084.02.011.748.075.985.22.08.3
", + "image_path": "46b496ab4fa227bd7fb6bad82f98e2c8af4a7e227954fd1327ca7a0dc646e0b7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 51, + 306, + 283, + 398 + ], + "blocks": [ + { + "bbox": [ + 63, + 297, + 268, + 306 + ], + "lines": [ + { + "bbox": [ + 63, + 297, + 268, + 306 + ], + "spans": [ + { + "bbox": [ + 63, + 297, + 268, + 306 + ], + "type": "text", + "content": "Table 2. Text-to-Video retrieval results on MSRVTT-7k." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 306, + 283, + 398 + ], + "lines": [ + { + "bbox": [ + 51, + 306, + 283, + 398 + ], + "spans": [ + { + "bbox": [ + 51, + 306, + 283, + 398 + ], + "type": "table", + "html": "
MethodText → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
HowTo100M [52]14.940.252.89.0-
HERO [36]16.843.457.7--
ClipBERT [33]22.046.859.96.0-
CLIP4Clip [51]42.171.981.42.015.7
X-Pool [20]43.972.582.32.014.6
TS2-Net [48]43.172.282.12.014.2
ProST44.572.382.42.013.8
ProST (ViT-B/16)46.973.382.92.013.0
", + "image_path": "c1dc12b7c4aa805eddaef1570f56a974322c91c8bdb544e8cd028f001ef8e954.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 50, + 419, + 282, + 519 + ], + "blocks": [ + { + "bbox": [ + 49, + 410, + 279, + 418 + ], + "lines": [ + { + "bbox": [ + 49, + 410, + 279, + 418 + ], + "spans": [ + { + "bbox": [ + 49, + 410, + 279, + 418 + ], + "type": "text", + "content": "Table 3. Text-to-Video retrieval results on the DiDeMo dataset." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 419, + 282, + 519 + ], + "lines": [ + { + "bbox": [ + 50, + 419, + 282, + 519 + ], + "spans": [ + { + "bbox": [ + 50, + 419, + 282, + 519 + ], + "type": "table", + "html": "
MethodText → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
CE [47]16.141.182.78.3-
ClipBERT [33]20.448.060.86.0-
Frozen [1]31.059.872.43.0-
MCQ [18]37.062.273.93.0-
TVMM [43]36.564.975.43.0-
CLIP4Clip [51]42.868.579.22.018.9
TS2-Net [48]41.871.682.02.014.8
ProST44.972.782.72.013.7
ProST (ViT-B/16)47.575.584.42.012.3
", + "image_path": "f92fed91bf7cb996973ee6d2b252bf2e34949dc6489f2f4777cfb67c1e2a4c46.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 539, + 270, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 539, + 270, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 539, + 270, + 552 + ], + "type": "text", + "content": "4.2. Comparison with State-of-the-art Methods" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 557, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 713 + ], + "type": "text", + "content": "To evaluate the relative benefits of ProST, we compare its performance with recent works [48, 20, 78, 51] from the literature. The results on the 9k and 7k splits of MSRVTT are shown in Tab. 1 and Tab. 2 respectively. We consistently achieve the best results for text-to-video retrieval and video-to-text retrieval across all splits and all metrics. Specifically, TS2-Net [48] integrates important patches into frame features for frame-level matching, which achieves the second best performance. Notably, for text-to-video retrieval, ProST outperforms TS2-Net [48] with " + }, + { + "bbox": [ + 46, + 557, + 287, + 713 + ], + "type": "inline_equation", + "content": "1.2\\%" + }, + { + "bbox": [ + 46, + 557, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 557, + 287, + 713 + ], + "type": "inline_equation", + "content": "1.4\\%" + }, + { + "bbox": [ + 46, + 557, + 287, + 713 + ], + "type": "text", + "content": " R@1 gains on the 9k split (47.0% vs. 48.2%) and the 7k split (43.1% vs. 44.5%). A " + }, + { + "bbox": [ + 46, + 557, + 287, + 713 + ], + "type": "inline_equation", + "content": "2.0\\%" + }, + { + "bbox": [ + 46, + 557, + 287, + 713 + ], + "type": "text", + "content": " improvement on R@1 (9k split) is also obtained compared to TS2-Net for video-to" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 309, + 306, + 541, + 398 + ], + "blocks": [ + { + "bbox": [ + 306, + 297, + 534, + 306 + ], + "lines": [ + { + "bbox": [ + 306, + 297, + 534, + 306 + ], + "spans": [ + { + "bbox": [ + 306, + 297, + 534, + 306 + ], + "type": "text", + "content": "Table 4. Text-to-Video retrieval results on the VATEX dataset." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 306, + 541, + 398 + ], + "lines": [ + { + "bbox": [ + 309, + 306, + 541, + 398 + ], + "spans": [ + { + "bbox": [ + 309, + 306, + 541, + 398 + ], + "type": "table", + "html": "
MethodText → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
HGR [5]35.173.583.52.0-
CLIP [57]39.772.382.22.012.8
CLIP4Clip [51]55.989.295.01.03.9
QB-Norm [2]58.888.393.81.0-
CLIP2Video [15]57.390.095.51.03.6
TS2-Net [48]59.190.095.21.03.5
ProST60.690.595.41.03.4
ProST (ViT-B/16)64.092.296.31.03.1
", + "image_path": "51fe0e78b8b5c4c32fca7f0290e5728259af9e673fc14980441643384492c6ac.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 309, + 419, + 541, + 511 + ], + "blocks": [ + { + "bbox": [ + 306, + 410, + 536, + 419 + ], + "lines": [ + { + "bbox": [ + 306, + 410, + 536, + 419 + ], + "spans": [ + { + "bbox": [ + 306, + 410, + 536, + 419 + ], + "type": "text", + "content": "Table 5. Text-to-Video retrieval results on the LSMDC dataset." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 419, + 541, + 511 + ], + "lines": [ + { + "bbox": [ + 309, + 419, + 541, + 511 + ], + "spans": [ + { + "bbox": [ + 309, + 419, + 541, + 511 + ], + "type": "table", + "html": "
MethodText → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
Frozen [1]15.030.839.820.0-
TVMM [43]17.837.145.913.5-
CLIP4Clip [51]21.641.849.811.061.0
X-Pool [20]24.042.951.59.055.1
QB-Norm [2]22.440.149.511.0-
TS2-Net [48]23.042.150.49.057.0
ProST24.142.551.69.054.6
ProST (ViT-B/16)26.346.155.28.051.4
", + "image_path": "141462b676c230d4a0bddb6a563ba33451746db677789388314cb5974d53952c.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "content": "text retrieval (44.3% vs. 46.3%). Furthermore, we reproduce TVMM [43] based on CLIP (ViT-B/32), which has 2.4% (45.8% vs. 48.2%) and 2.3% (44.0% vs. 46.3%) lower R@1 than ProST on the 9k split. The results demonstrate the effectiveness of ProST, which mines the spatial object details and temporal event diversity of videos, improving the model discrimination. Besides, ProST achieves a low MnR metric of 12.4 (text-to-video) on the 9k split, demonstrating the model robustness to erroneous results." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 641, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 546, + 713 + ], + "type": "text", + "content": "In Tab. 3, 4 and 5, we examine the performance of ProST on the DiDeMo, VATEX and LSMDC datasets respectively. Compared with TS2-Net [48], ProST achieves a substantial boost of " + }, + { + "bbox": [ + 304, + 641, + 546, + 713 + ], + "type": "inline_equation", + "content": "3.1\\%" + }, + { + "bbox": [ + 304, + 641, + 546, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 641, + 546, + 713 + ], + "type": "inline_equation", + "content": "1.5\\%" + }, + { + "bbox": [ + 304, + 641, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 641, + 546, + 713 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 304, + 641, + 546, + 713 + ], + "type": "text", + "content": " on the R@1 metric for DiDeMo, VATEX and LSMDC, respectively. ProST outperforms state-of-the-art methods by a large margin with the" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4105" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 125, + 537, + 296 + ], + "blocks": [ + { + "bbox": [ + 46, + 68, + 545, + 123 + ], + "lines": [ + { + "bbox": [ + 46, + 68, + 545, + 123 + ], + "spans": [ + { + "bbox": [ + 46, + 68, + 545, + 123 + ], + "type": "text", + "content": "Table 6. The ablation study on MSRVTT-9k to investigate the effectiveness of Object-Phrase Prototype Matching (OPPM) and EventSentence Prototype Matching (ESPM). MdR results are not shown, as MdR=2.0 for all variants. Definition of important symbols: " + }, + { + "bbox": [ + 46, + 68, + 545, + 123 + ], + "type": "inline_equation", + "content": "\\checkmark" + }, + { + "bbox": [ + 46, + 68, + 545, + 123 + ], + "type": "text", + "content": " indicates default settings; " + }, + { + "bbox": [ + 46, + 68, + 545, + 123 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 68, + 545, + 123 + ], + "type": "text", + "content": "TPG or " + }, + { + "bbox": [ + 46, + 68, + 545, + 123 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 68, + 545, + 123 + ], + "type": "text", + "content": "SPG means replace with TPG or SPG to generate prototypes; P-P or O-W refers the alignment of patch-phrase or object-word; -F, -M or -R refers to removing frame decoder, attention mask or residual structure in Eq. 5; F-W or " + }, + { + "bbox": [ + 46, + 68, + 545, + 123 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbb{F}}" + }, + { + "bbox": [ + 46, + 68, + 545, + 123 + ], + "type": "text", + "content": "-S means directly aligning frame global tokens and word tokens or aligning the mean of frame global tokens and text global token." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 125, + 537, + 296 + ], + "lines": [ + { + "bbox": [ + 53, + 125, + 537, + 296 + ], + "spans": [ + { + "bbox": [ + 53, + 125, + 537, + 296 + ], + "type": "table", + "html": "
IDOPPMESPMText → VideoVideo → Text
SPGMatchingTPGMatchingR@1↑R@5↑R@10↑MnRR@1↑R@5↑R@10↑MnR
1✓✓45.672.281.114.344.971.682.310.0
2○SPG✓45.871.781.914.844.071.982.310.6
3✓✓45.972.882.413.245.173.382.79.8
4○TPG✓✓✓46.373.381.813.545.073.182.49.8
5✓✓○SPG✓47.773.683.012.645.974.083.09.0
6✓P-P✓✓46.072.581.614.943.172.482.110.8
7✓O-W✓✓47.173.382.212.845.773.382.69.6
8✓✓-F✓46.472.881.713.544.572.582.010.2
9✓✓-M✓47.873.882.912.646.073.782.89.0
10✓✓-R✓46.672.982.414.045.372.181.810.1
11F-W✓✓47.373.582.812.645.973.783.19.0
12✓✓F-S46.572.682.313.445.173.482.59.8
Ours✓✓✓✓48.274.683.412.446.374.283.28.7
", + "image_path": "7b96d93f03880bd42dea821c5d0e428f080f8dc7fbb57677b2cdb4043f13ab8d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 334, + 286, + 434 + ], + "blocks": [ + { + "bbox": [ + 47, + 312, + 286, + 334 + ], + "lines": [ + { + "bbox": [ + 47, + 312, + 286, + 334 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 286, + 334 + ], + "type": "text", + "content": "Table 7. The ablation study on MSRVTT-9k to investigate the configuration of the number of prototypes." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 334, + 286, + 434 + ], + "lines": [ + { + "bbox": [ + 50, + 334, + 286, + 434 + ], + "spans": [ + { + "bbox": [ + 50, + 334, + 286, + 434 + ], + "type": "table", + "html": "
{No, Np, Ne}Text → Video
R@1↑R@5↑R@10↑MdR ↓MnR ↓
{6, 14, 3}45.673.281.62.014.3
{6, 28, 3}46.773.482.22.013.4
{12, 14, 3}47.073.783.02.012.9
{24, 32, 3}46.073.382.02.013.8
{12, 28, 1}46.373.082.12.013.5
{12, 28, 2}47.474.083.12.012.7
{12, 28, 4}47.674.383.22.012.5
{12, 28, 3}48.274.683.42.012.4
", + "image_path": "b6251a47d69fc0178c4ce40f529d9e36aa662fad81be233c440c13a97998c78a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 50, + 446, + 284, + 518 + ], + "blocks": [ + { + "bbox": [ + 50, + 446, + 284, + 518 + ], + "lines": [ + { + "bbox": [ + 50, + 446, + 284, + 518 + ], + "spans": [ + { + "bbox": [ + 50, + 446, + 284, + 518 + ], + "type": "image", + "image_path": "2ed5fcb075312643981cafe1e97d366acca2c3f6774477fc0ecd1b7dd0e58c78.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 521, + 285, + 533 + ], + "lines": [ + { + "bbox": [ + 47, + 521, + 285, + 533 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 285, + 533 + ], + "type": "text", + "content": "Figure 5. The R@1 results at different spatial matching factors " + }, + { + "bbox": [ + 47, + 521, + 285, + 533 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 521, + 285, + 533 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 552, + 286, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 286, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 286, + 613 + ], + "type": "text", + "content": "CLIP (ViT-B/16) backbone. These results suggest the versatility and generalization of ProST, which can effectively process videos from different domains (e.g., movies). We owe the advantage of ProST over these works to the full use of dynamic spatio-temporal prototype matching." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 622, + 141, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 622, + 141, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 622, + 141, + 635 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 641, + 286, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 286, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 286, + 677 + ], + "type": "text", + "content": "Analysis of progressive spatio-temporal prototype matching. In Tab. 6, we compare ProST with 12 variants, which proves that each module contributes to final results." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "We elaborate on some important observations. First, we show the results relying only on Object-Phrase Prototype Matching (OPPM) or Event-Sentence Prototype Match" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 315, + 545, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 315, + 545, + 458 + ], + "spans": [ + { + "bbox": [ + 304, + 315, + 545, + 458 + ], + "type": "text", + "content": "ing (ESPM). To implement our model without OPPM, all tokens are fed directly into the frame decoder and event decoder (TPG) to get multiple event prototypes. When only ESPM is used, there is a " + }, + { + "bbox": [ + 304, + 315, + 545, + 458 + ], + "type": "inline_equation", + "content": "2.6\\%" + }, + { + "bbox": [ + 304, + 315, + 545, + 458 + ], + "type": "text", + "content": " decrease in " + }, + { + "bbox": [ + 304, + 315, + 545, + 458 + ], + "type": "inline_equation", + "content": "\\mathbb{R}@\\mathbb{1}" + }, + { + "bbox": [ + 304, + 315, + 545, + 458 + ], + "type": "text", + "content": ". This confirms the complementary role of fine-grained spatial details for ESPM. Next, we replace TPG with SPG and find that there is a certain suppression effect on noise. However, both of the above variants perform poorly due to the lack of progressive prototype generation and matching. When we only train model with OPPM, the model still underperforms. This may be due to the lack of temporal understanding and the inability to resolve correspondence ambiguity." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 460, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 567 + ], + "type": "text", + "content": "Second, " + }, + { + "bbox": [ + 304, + 460, + 545, + 567 + ], + "type": "inline_equation", + "content": "\\mathbb{O}" + }, + { + "bbox": [ + 304, + 460, + 545, + 567 + ], + "type": "text", + "content": " TPG, P-P and O-W prove that there is indeed redundancy in the original video tokens. The sparse weights in SPG can alleviate this problem. However, FC layers in SPG cannot interact with intra-frame and inter-frame information, making it difficult to generate better event prototypes. This may be the reason for the drop in " + }, + { + "bbox": [ + 304, + 460, + 545, + 567 + ], + "type": "inline_equation", + "content": "\\mathbb{O}" + }, + { + "bbox": [ + 304, + 460, + 545, + 567 + ], + "type": "text", + "content": " SPG. Third, P-P and O-W also confirm the benefits of prototype matching. Raw patches or words without aggregation strategies may worsen the cross-modal alignment." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 568, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 568, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 568, + 545, + 688 + ], + "type": "text", + "content": "Fourth, the results for -F, -M and -R also decreased. Because intra-frame local object relations and global frame features jointly complement comprehensive frame-level spatial information, which is helpful for subsequent temporal learning. Fifth, from F-W and " + }, + { + "bbox": [ + 304, + 568, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{F}}" + }, + { + "bbox": [ + 304, + 568, + 545, + 688 + ], + "type": "text", + "content": "-S, we can see the importance of prototype design mode. Directly using global frame features ([CLS] tokens) in ProST-S for frame-word alignments lacks object details. In " + }, + { + "bbox": [ + 304, + 568, + 545, + 688 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{F}}" + }, + { + "bbox": [ + 304, + 568, + 545, + 688 + ], + "type": "text", + "content": "-S, the mean value of frame global features mixes all information equally, making it difficult to characterize dynamic and changeable videos." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Analysis of prototype configuration. We conduct experiments on various prototype configurations in Tab. 7. Im" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4106" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 69, + 545, + 239 + ], + "blocks": [ + { + "bbox": [ + 51, + 69, + 545, + 239 + ], + "lines": [ + { + "bbox": [ + 51, + 69, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 51, + 69, + 545, + 239 + ], + "type": "image", + "image_path": "4dd685fda007b8295aa3ccaab445c98cc379e836c6806b8f6cfe9bc68e3ce92c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 240, + 546, + 264 + ], + "lines": [ + { + "bbox": [ + 46, + 240, + 546, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 546, + 264 + ], + "type": "text", + "content": "Figure 6. Visualization of the object and event prototypes. We sample 12 frames in the video and object prototypes are shown as highlighted response regions in the frame. Then, we show cross-attention event weights of Eq. 6 in a line graph. Best viewed in color." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 283, + 287, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 283, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 283, + 287, + 354 + ], + "type": "text", + "content": "proper configuration of spatial prototypes leads to performance degradation, possibly because too many prototypes may introduce local noise, while few prototypes are not enough to express semantics. Furthermore, the best result is obtained when the number of event prototypes is 3, which may be related to the degree of semantic divergence of texts." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 355, + 288, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 355, + 288, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 355, + 288, + 450 + ], + "type": "text", + "content": "Hyperparameter analysis. As shown in Fig. 5, we investigate the spatial matching factor " + }, + { + "bbox": [ + 46, + 355, + 288, + 450 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 355, + 288, + 450 + ], + "type": "text", + "content": " and present results for text-video (T2V) and video-text retrieval (V2T). As " + }, + { + "bbox": [ + 46, + 355, + 288, + 450 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 355, + 288, + 450 + ], + "type": "text", + "content": " grows, the performance increases at first and reaches the best results, then decreases as a whole. A small " + }, + { + "bbox": [ + 46, + 355, + 288, + 450 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 355, + 288, + 450 + ], + "type": "text", + "content": " may not fully exploit the underlying fine-grained spatial information, while a large " + }, + { + "bbox": [ + 46, + 355, + 288, + 450 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 355, + 288, + 450 + ], + "type": "text", + "content": " may overemphasize local matching and destroy the overall dynamic semantic understanding." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 456, + 160, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 160, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 160, + 468 + ], + "type": "text", + "content": "4.4. Qualitative Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 474, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 629 + ], + "type": "text", + "content": "Visualization of prototypes. In Fig. 6, we first present object prototypes in video frames. Many redundant patches are removed by prototypes, and the spatially highlighted object part and the phrase can be well locally corresponded. Then, we compute cross-attention for 3 event queries and 12 video frames according to Eq. 6, whose weights are shown in a line graph. The weights of different event prototypes on different frames are quite different, which proves that our model can learn temporal relations and event prototypes can express diverse semantics. For example, event prototype 1 has larger weights on the first three frames, which indicates that it may correspond to the semantics contained in text 1. Similarly, event prototype 2 or 3 corresponds to text 2 or 3." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "content": "Retrieval results. Top-3 TVR results are illustrated in Fig. 7. Specifically, for query 97, although the top-2 recalled videos are women in the same dress, the difference is that the correct video discusses the cushion seat, while the incorrect video does not. This proves that object-phrase prototype matching provides fine-grained spatial knowledge (i.e., objects). For query 353, ProST pays attention to" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 308, + 281, + 544, + 509 + ], + "blocks": [ + { + "bbox": [ + 308, + 281, + 544, + 509 + ], + "lines": [ + { + "bbox": [ + 308, + 281, + 544, + 509 + ], + "spans": [ + { + "bbox": [ + 308, + 281, + 544, + 509 + ], + "type": "image", + "image_path": "34a3909e2a8762b93ab62929c285012e198bdf76e9c6df391094d9336cb27f94.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 512, + 545, + 545 + ], + "lines": [ + { + "bbox": [ + 305, + 512, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 305, + 512, + 545, + 545 + ], + "type": "text", + "content": "Figure 7. Top-3 TVR results on MSRVTT-9k. Left: the ranked videos by our ProST. Right: the ranked videos with only event-sentence prototype matching. Red: correct videos." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 568, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 568, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 305, + 568, + 545, + 628 + ], + "type": "text", + "content": "both the brief human speech at the beginning of the video and the subsequent earth display. However, using only event prototypes will result in a matching error. This shows that ProST can make a trade-off between the spatio-temporal matching relations to achieve better discrimination." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 643, + 378, + 656 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 643, + 378, + 656 + ], + "spans": [ + { + "bbox": [ + 306, + 643, + 378, + 656 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 665, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 714 + ], + "type": "text", + "content": "We have proposed a novel text-video retrieval framework, ProST, to decompose the matching process into complementary object-phrase and event-sentence prototype alignments. In the object-phrase prototype matching stage," + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4107" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": "we design the spatial prototype generation mechanism to focus on important video content and strengthen the fine-grained spatial alignment. In the event-sentence prototype matching phase, we use the temporal prototype generation mechanism to progressively generate diverse event prototypes and learn dynamic one-to-many relations. In this paper, we hope not only to provide insights into the importance of complementary spatio-temporal matching but also to facilitate future work that advances text-video retrieval by solving design flaws rather than mostly trial and error." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 192, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 289, + 251 + ], + "type": "text", + "content": "Acknowledgment. This work is supported by the National Key Research and Development Program of China (2022YFB3104700), the National Nature Science Foundation of China (62121002, 62022076, U1936210, 62102384)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 263, + 107, + 276 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 263, + 107, + 276 + ], + "spans": [ + { + "bbox": [ + 48, + 263, + 107, + 276 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 283, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 283, + 287, + 316 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 283, + 287, + 316 + ], + "spans": [ + { + "bbox": [ + 53, + 283, + 287, + 316 + ], + "type": "text", + "content": "[1] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. Frozen in time: A joint video and image encoder for end-to-end retrieval. 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Tps++: Attention-enhanced thin-plate spline for scene text recognition. *IJCAI*, 2023. 1" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "4110" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Prompt Switch_ Efficient CLIP Adaptation for Text-Video Retrieval/408eb595-fd0b-42c6-8600-a2efb5916c5c_content_list.json b/2023/Prompt Switch_ Efficient CLIP Adaptation for Text-Video Retrieval/408eb595-fd0b-42c6-8600-a2efb5916c5c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..360c38aba411bdd2fe612af1af37d667d7f8fd84 --- /dev/null +++ b/2023/Prompt Switch_ Efficient CLIP Adaptation for Text-Video Retrieval/408eb595-fd0b-42c6-8600-a2efb5916c5c_content_list.json @@ -0,0 +1,1383 @@ +[ + { + "type": "text", + "text": "Prompt Switch: Efficient CLIP Adaptation for Text-Video Retrieval", + "text_level": 1, + "bbox": [ + 142, + 161, + 826, + 181 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chaorui Deng $^{1,\\ast}$ , Qi Chen $^{1,\\ast}$ , Pengda Qin $^{2}$ , Da Chen $^{3}$ , Qi Wu $^{1,\\dagger}$ $^{1}$ Australia Institute of Machine Learning, University of Adelaide \nAlibaba Group, $^{3}$ Department of Computer Science, University of Bath", + "bbox": [ + 220, + 206, + 766, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 288, + 312, + 302 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In text-video retrieval, recent works have benefited from the powerful learning capabilities of pre-trained text-image foundation models (e.g., CLIP) by adapting them to the video domain. A critical problem for them is how to effectively capture the rich semantics inside the video using the image encoder of CLIP. To tackle this, state-of-the-art methods adopt complex cross-modal modeling techniques to fuse the text information into video frame representations, which, however, incurs severe efficiency issues in large-scale retrieval systems as the video representations must be recomputed online for every text query. In this paper, we discard this problematic cross-modal fusion process and aim to learn semantically-enhanced representations purely from the video, so that the video representations can be computed offline and reused for different texts. Concretely, we first introduce a spatial-temporal \"Prompt Cube\" into the CLIP image encoder and iteratively switch it within the encoder layers to efficiently incorporate the global video semantics into frame representations. We then propose to apply an auxiliary video captioning objective to train the frame representations, which facilitates the learning of detailed video semantics by providing fine-grained guidance in the semantic space. With a naive temporal fusion strategy (i.e., mean-pooling) on the enhanced frame representations, we obtain state-of-the-art performances on three benchmark datasets, i.e., MSR-VTT, MSVD, and LSMDC.", + "bbox": [ + 75, + 317, + 472, + 690 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 77, + 714, + 208, + 730 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Text-video retrieval [1, 6, 30, 42] is a fundamental task in the area of video-language understanding that seeks to find the most relevant video from a large set of candidates to match a text query. With the rapid growth of video data, text-video retrieval has become increasingly important for various applications, including video recommendation [36, 43], video search [20, 45], and video summa", + "bbox": [ + 75, + 738, + 468, + 836 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3e23a35dbe4e05e843156b477ea34fc6d67a3b12eb6f487eb9c86f1d9b6d889b.jpg", + "image_caption": [ + "Figure 1: The performance (i.e., R@1), retrieval time, and memory usage during retrieval for baseline models and ours on the MSRVTT dataset. The center of the bubble indicates the value of R@1. The diameter of the bubble or star is proportional to the memory usage (GB) while the horizontal axis indicates the inference time (s)." + ], + "image_footnote": [], + "bbox": [ + 507, + 286, + 878, + 445 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "rization [7, 29, 31, 33, 37, 47]. Due to the high cost of constructing text-video datasets, one promising approach for this task is to leverage pre-trained text-image foundation models and transfer their powerful representation capabilities to the video domain. Specifically, the CLIP [34] model, which is trained using a text-image alignment objective, is particularly suitable for text-video retrieval and has been frequently studied recently [27, 46, 16]. It has two transformer encoders [38, 9] to process images and texts, respectively. A vector representation is extracted from the input of each modality with the corresponding encoder and is optimized to be close to its paired representation and away from the unpaired ones.", + "bbox": [ + 497, + 561, + 892, + 741 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Adapting CLIP to the video domain is non-trivial and requires careful consideration of both efficiency and effectiveness. In CLIP4Clip [27], the authors directly mean-pool the frame representations extracted by the CLIP image encoder to get the video representation and use it to calculate the cosine similarity with the text representations during retrieval. However, the mean-pooling of frame representations may lose some essential semantic details of the video and hamper the retrieval performance. Thus, more advanced meth", + "bbox": [ + 497, + 741, + 892, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 129, + 49, + 200, + 85 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 253, + 48, + 789, + 86 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Co-first author. †Corresponds to qi.wu01@adelaide.edu.au. Code: https://github.com/bladewaltz1/PromptSwitch.", + "bbox": [ + 75, + 842, + 468, + 866 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15648", + "bbox": [ + 465, + 885, + 505, + 897 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ods, such as [14, 16, 18, 24, 28], generate the video representation by applying various cross-modal temporal fusion approaches on the frame representations, using text queries as the condition. While achieving state-of-the-art results, these methods encounter severe efficiency issues in practice, as the text-conditioned fusion of each video has to be performed on-the-fly for every incoming text query. Even with a lightweight fusion module (compared to the CLIP backbone), its computation cost grows geometrically as the number of videos and texts increases.", + "bbox": [ + 75, + 125, + 472, + 264 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Formally, given a query set of $N_{t}$ texts with an average length of $N_{w}$ words and a candidate set of $N_{v}$ videos where each video contains $N_{f}$ frames. Then, the space and time complexities are $\\mathcal{O}(N_vN_tN_f)$ for the text-conditioned fusion in X-Pool [16] and TS2-Net [24], and $\\mathcal{O}(N_vN_tN_fN_w)$ for that of X-CLIP [28]. While for CLIP4Clip, the complexity is $\\mathcal{O}(N_vN_t)$ as it only requires a simple dot-product between the text and mean-pooled frame representations, although its performance is inferior to X-Pool and X-CLIP. To better reveal this gap, we show an example in Figure 1 about the real-world efficiency of several methods while omitting the backbone computation. Here, we set $N_{v} = 16384$ , $N_{t} = 512$ , $N_{f} = 12$ , and $N_{w} = 10$ . From the figure, with large $N_{t}$ and $N_{v}$ , the latency and memory consumption for text-conditioned temporal fusion methods [16, 24, 28] are orders of magnitude higher than text-agnostic temporal fusion (i.e., mean-pooling) [27, 57], and can rapidly become enormous in large-scale scenarios.", + "bbox": [ + 75, + 264, + 472, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "On the other hand, the backbone computation of CLIP is much less of a burden in real-world retrieval systems, as the frame representations of the video can be pre-computed offline and reused for different text queries. Therefore, a more practical CLIP-based text-video retrieval method should focus on improving the backbone representation ability while keeping the cross-modal interaction as simple as possible. Motivated by this, we propose a simple and efficient adaptation method for CLIP to facilitate its ability to capture both the global and detailed semantics of videos.", + "bbox": [ + 75, + 511, + 472, + 650 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Concretely, we first feed a tiny ( $\\sim 0.1\\mathrm{M}$ ) \"Prompt Cube\" into the image encoder of CLIP, which is a 3D tensor spanning over the spatial, temporal, and channel axis, as shown in the right of Figure 2. $^{1}$ It is designed to have the same temporal and spatial sizes and is concatenated with the patch tokens alongside the spatial axis. To propagate temporal semantics among different frames, we switch the spatial and temporal dimensions of the prompt cube before each self-attention layer, so that the prompt cube builds up a peer-to-peer connection between every two-frame pair. In this way, our modified CLIP model enjoys an improved global semantic modeling ability thanks to the comprehensive spatial-temporal modeling between the prompt cube and the patch tokens of all frames, while only bringing neg-", + "bbox": [ + 75, + 650, + 472, + 845 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ligible extra parameters and computations. This also allows the prompt cube to serve as a compact summarization of the whole video, and further enables us to design a CLIP-guided Prompt Aggregation approach and obtain the frame representations from the prompt cube. Then, we use naive mean-pooling instead of cross-modal fusion on these frame representations to get the final video representation.", + "bbox": [ + 499, + 125, + 890, + 223 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Moreover, since we will not use any fine-grained cross-modal interaction modules in our model, we adopt an Auxiliary Video Captioning objective as an alternative to provide fine-grained guidance in the semantic space when learning video representations. Specifically, we introduce a light captioning head on top of our modified CLIP image encoder during training, which takes the frame representations aggregated from the prompt cube as input and generates the paired text of the input video. This auxiliary objective plays a critical role because CLIP's original contrastive learning objective is relatively easy to fit due to the lack of in-batch negatives during training (which is generally the case in text-video retrieval). During inference, the light captioning branch is removed, thus it incurs no extra computation and memory consumption.", + "bbox": [ + 497, + 223, + 892, + 429 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We verify the effectiveness of the proposed method on three text-video retrieval benchmarks, i.e. MSR-VTT [50], MSVD [4], and LSMDC [35], where our method consistently achieves state-of-the-art performance while being significantly more efficient than the previous state of the arts. We also provide extensive performance analyses to show the superiority of our proposed method.", + "bbox": [ + 497, + 429, + 892, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 536, + 640, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text-video retrieval is one of the fundamental tasks in video-language modeling and has lots of applications in the industry. Here, we broadly classify the previous works into three categories and briefly review them below.", + "bbox": [ + 497, + 560, + 890, + 616 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Off-the-Shelf Single-Modal Representations An early trend in text-video retrieval is to use the off-the-shelf video (e.g., I3D [3]) and text representations (e.g., GloVe [32]) and design sophisticated feature encoding methods or multi-modal fusion mechanisms on them to improve the retrieval performance [6, 8, 19, 54, 55]. For example, in [6], a hierarchical graph reasoning approach is proposed to decompose video-text matching into global-to-local levels and disentangle texts into a hierarchical semantic graph with three levels of events, actions, and entities. Yu et al. [54] propose a joint sequence fusion model for the sequential interaction of videos and texts. Dong et al. [8] leverages multi-level single-modal features that represent the rich content of both video and text in a coarse-to-fine fashion. However, their performances are limited due to the mismatched training objectives between the pre-computed representations and the text-video retrieval task.", + "bbox": [ + 497, + 631, + 894, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1The channel axis is omitted for simplicity.", + "bbox": [ + 95, + 853, + 326, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15649", + "bbox": [ + 465, + 885, + 505, + 897 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/127eb9451882f31302958f9ba1fd2195f633da5a7738114f2eace6b9cd94019c.jpg", + "image_caption": [ + "Figure 2: Overall architecture. For a video clip with $N_{f}$ frames, we accompany it with $N_{f} \\times N_{f}$ prompt tokens, resulting in a 3D prompt cube. We show the Prompt Switch operation on the right. For simplicity, we omit the feed-forward network and shot-cut connections in the ViT layer. We provide more details for Prompt Aggregation in Figure 4. $\\otimes$ is cosine similarity." + ], + "image_footnote": [], + "bbox": [ + 100, + 125, + 868, + 352 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Video-Language Pre-training To reduce the gap between pre-training and downstream tasks, large-scale pretrained video-language representations have been proposed, such as [1, 13, 15, 21, 26, 40, 48, 49, 51]. Most of these models are pre-trained on the large-scale video-text datasets, e.g., HowTo100M [30] and WebVid-2M [1], which boosts promising cross-modal video understanding [22, 23, 26]. One line of works [1, 13, 49] uses two independent encoders for video and text and then projects them into a common latent space. These methods often adopt a contrastive loss to distinguish the paired video-text data. For example, Bain et al. [1] design an end-to-end trainable model, aiming to take advantage of both large-scale image and video captioning datasets. Gabeur et al. [13] propose a multi-modal transformer that can extract features at different moments and from different modalities (e.g., audio or speech) in a video. The other line of works [21, 26, 48] employs a single cross-modal encoder, which concatenates the video and text sequences as inputs and models them jointly in the transformer, followed by a binary classifier predicting whether these videos and texts are aligned. Despite they can build fine-grained associations between video-text tokens, they need to input each video-text candidate pair into the model for matching score calculation during inference and thus hampers efficiency. Besides, although the idea of video-language pre-training is promising, due to the high cost of collecting wild videos, its scale is generally much smaller than image-language pre-training, leading to an unsatisfactory generalization ability. Thus, like [16, 27], we seek to boost from the image-language pre-training model (e.g., CLIP [34]) for text-video retrieval.", + "bbox": [ + 75, + 428, + 472, + 858 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "CLIP-based Adaptation. Recently, due to the great advantage of CLIP [34] for vision-and-language representation learning, many works [11, 14, 17, 18, 28, 41, 52, 56] seek to transfer the knowledge of CLIP to text-video retrieval tasks. Roughly, the existing works transfer CLIP from views of feature aggregation [12, 16, 27, 28, 57], representation alignment [12, 28, 41], and post pretraining [46, 52]. Specifically, X-Pool [16] designs a cross-modal attention model, seeking to enable the model to only focus on the relevant video frames conditioned on a given text. TS2-Net [24] adapts CLIP by introducing a token shift module and a token selection module, which capture the temporal information and remove unimportant tokens, respectively. X-CLIP [28] calculates both the coarse- and fine-grained similarity for higher retrieval accuracy. While these methods can be effective, their retrieval efficiency is low due to the coupling of video and text in the cross-modal fusion process. A more ideal way should focus on improving the representation ability of the backbone while maintaining the cross-modal interaction as efficiently as possible. We follow this principle in our method.", + "bbox": [ + 497, + 428, + 892, + 719 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 499, + 731, + 591, + 745 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The overview of our method is shown in Figure 2. It is based on a pre-trained CLIP with a ViT [10]-based image encoder. Given an input video, we first split each video frame into fix-sized non-overlapping patches and linearly project them into 1D patch embeddings. Following CLIP, a [CLS] embedding is concatenated to the embedding sequence of each frame, which is pre-trained to capture the local semantics within the sequence. Then, in the ViT en", + "bbox": [ + 497, + 755, + 894, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15650", + "bbox": [ + 465, + 885, + 505, + 897 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "coder, our proposed \"Prompt Cube\" bridges the global semantic information from the patch embeddings of all frames through a Prompt Switch operation. After that, we feed the output [CLS] embeddings of the video frames and the final prompt cube into a Prompt Aggregation module, where the prompt cube is aggregated into 1D vectors according to the [CLS] embeddings, and is further enhanced with fine-grained semantics through an Auxiliary Captioning Objective. To ensure an efficient measurement of the text-video similarity, we avoid using cross-modal fusion modules and directly average these aggregated vectors into the final video representation. A simple dot product operation is used to compute the similarity. More details are in the following.", + "bbox": [ + 75, + 125, + 472, + 319 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Prompt Cube for Bridging Global Semantics", + "text_level": 1, + "bbox": [ + 75, + 328, + 455, + 344 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At the core of our method is the proposed Prompt Cube. It is designed to capture the rich temporal semantics of the whole video while bringing negligible modifications and computations to the CLIP image encoder. Formally, given an input video clip with $N_{f}$ frames, we first obtain its patch embeddings $V \\in \\mathbb{R}^{N_f \\times L \\times D}$ , where $L$ indicates the size of the spatial dimension, i.e., the number of patches divided from a video frame plus one [CLS] embedding. $D$ is the embedding size. Then, our prompt cube is constructed as a 3D tensor $P \\in \\mathbb{R}^{N_f \\times N_f \\times D}$ . At the start of the ViT layer, we concatenate $V$ and $P$ alongside the spatial dimension, denoted by $[V; P] \\in \\mathbb{R}^{N_f \\times (L + N_f) \\times D}$ , and then process them jointly. The first two dimensions of $P$ (corresponding to the temporal and spatial axis, respectively) have the same size, thus they can be transposed flexibly without altering the shape of $P$ . This allows us to further propose an efficient Prompt Switch operation to exchange the local spatial semantics of each frame and the global temporal semantics from the whole video through the prompt cube.", + "bbox": [ + 75, + 351, + 472, + 615 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Prompt Switch The proposed Prompt Switch operation can be defined in a one-line formula:", + "bbox": [ + 75, + 633, + 468, + 661 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {T} := [ V; P ] \\rightarrow [ V; P ^ {\\top} ]. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 672, + 468, + 690 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "See the right of Figure 2, we apply this operation before every self-attention layer of the ViT encoder. Then, self-attention is performed over the spatial dimension of $[V;P]$ , where the $i$ -th row of the prompt cube (denoted by $\\pmb{p}_i \\in \\mathbb{R}^{1 \\times N_f \\times D}$ ) and the patch embeddings of the $i$ -th frame (denoted by $\\pmb{v}_i \\in \\mathbb{R}^{1 \\times L \\times D}$ ) acquire information from each other. In this way, for two consecutive ViT layers in the encoder, each element in the prompt cube (denoted by $\\pmb{p}_{i,j} \\in \\mathbb{R}^D$ ) is first attached to the $i$ -th frame and communicates with $\\pmb{v}_i$ , and then switch to the $j$ -th frame and communicates with $\\pmb{v}_j$ . By repeatedly performing this operation, the whole prompt cube builds up a peer-to-peer", + "bbox": [ + 75, + 700, + 472, + 866 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c7b333532b12e1a77b81ac4444b6cdcb265642215398379925589530101c858e.jpg", + "image_caption": [ + "Figure 3: Video Proxy adopts a shared \"prompt\" to exchange information among all frames (b). Differently, our Prompt Switch method builds up a peer-to-peer connection between every two-frame pair (a) to obtain more comprehensive spatial-temporal modeling. This improves the representation ability of CLIP on video data. Besides, our method may also ease the learning problem as each element in the prompt cube only needs to handle the information of two frames instead of the whole video, thus improving the optimization ability of CLIP on video data." + ], + "image_footnote": [], + "bbox": [ + 512, + 123, + 702, + 254 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/82fd31b840db1242d32a310659d91d786bd89a580aca215f3e708ea064f5f92b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 717, + 123, + 880, + 254 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "connection between every two-frame pair in the video clip, enabling comprehensive temporal modeling.", + "bbox": [ + 497, + 429, + 890, + 456 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Some previous text-video retrieval methods have also attempted to introduce temporal adaptation to the backbone of the CLIP ViT encoder, such as Token Shift [24] and Video Proxy [52]. Specifically, the Token Shift method shifts token embeddings from adjacent frames to the current frame, which fails to model the temporal semantics from a global perspective. Moreover, it damages the spatial modeling ability of the original CLIP as the information contained in the shifted tokens is no longer accessible in the current frame. In Video Proxy, the information from all video frames is exchanged using several proxy embeddings, which lack peer-to-peer connections within the frames and thus can be inferior in the temporal modeling capacity. We illustrate the importance of building peer-to-peer connections in Figure 3. Besides, a naive full-attention approach has also been investigated where no adaptation is applied to the CLIP model except allowing its self-attention layers to attend to the patch tokens from the whole video. However, this approach is neither effective due to the domain gap between the input data (video) and the pre-training data (image), nor efficient since the computation complexity of the self-attention layers grows quadratically w.r.t. the number of attended patch tokens. We show the superiority of our proposed prompt cube to these previous methods in Section 4.1.", + "bbox": [ + 497, + 458, + 892, + 802 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Prompt Aggregation As the prompt cube acquires the global semantics through a comprehensive interaction with all patch embeddings, it can serve as a compact summariza", + "bbox": [ + 497, + 825, + 890, + 866 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15651", + "bbox": [ + 465, + 887, + 504, + 897 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tion of the video. Therefore, we propose to obtain the final video representation from the prompt cube, instead of the [CLS] embedding as the original CLIP. To achieve this, we design a CLIP-guided Prompt Aggregation module, which aggregates the output prompt cube into 1D vectors according to the final [CLS] embeddings of the video frames. It is a lightweight multi-head attention (MHA) layer placed before the last layer normalization (LN) layer of the ViT encoder. The [CLS] embedding of the $i$ -th frame (denoted by $\\pmb{c}_i \\in \\mathbb{R}^{1 \\times D}$ ) is used as the \"query\" while the \"key\" and \"value\" are both the prompt cube flattened over the temporal and spatial dimensions, denoted by $\\hat{\\pmb{P}} \\in \\mathbb{R}^{N_f^2 \\times D}$ . Let $\\bar{p}_i \\in \\mathbb{R}^{1 \\times D}$ be the aggregated prompt vector for the $i$ -th frame, we have", + "bbox": [ + 75, + 125, + 472, + 321 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {p} _ {i} := \\mathrm {L N} \\left(\\boldsymbol {c} _ {i} + \\operatorname {M H A} \\left(\\boldsymbol {c} _ {i}, \\hat {\\boldsymbol {P}}, \\hat {\\boldsymbol {P}}\\right)\\right), \\quad \\forall i \\in [ 1, N _ {f} ], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 95, + 332, + 468, + 350 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where LN denotes the last layer normalization layer of the CLIP ViT encoder. Notably, the last linear projection weight in the MHA layer is initialized as a 0 tensor to ensure that $\\bar{p}_i$ is optimized from the original output of the CLIP image encoder. The final video representation is the naive mean-pooling of the normalized prompt vectors, i.e.,", + "bbox": [ + 75, + 359, + 468, + 444 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {x} := \\frac {1}{N _ {f}} \\sum_ {i = 1} ^ {N _ {f}} \\frac {\\bar {\\boldsymbol {p}} _ {i}}{\\| \\bar {\\boldsymbol {p}} _ {i} \\|}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 203, + 453, + 468, + 492 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We provide a detailed illustration for the Prompt Aggregation module on the left of Figure 4. To enhance the learning of temporal information for the prompt cube, inspired by [58], we adopt a frame sampling strategy where we randomly sample $k < N_f$ prompt vectors for the final mean-pooling operation in Eq. (3) during training.", + "bbox": [ + 75, + 501, + 468, + 586 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Learning Detailed Semantics via Captioning", + "text_level": 1, + "bbox": [ + 77, + 593, + 452, + 608 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As we have discussed in Section 1, the key criterion in the design of our model architecture is to ensure the model contains no extra cross-modal interaction procedure during inference except computing the cosine similarity between text and video representations. While this ensures the efficiency of the similarity measurement in large-scale production systems, it also prevents the video representation from utilizing the fine-grained semantic information from the text query. To aid this, inspired by [5, 53], we propose to learn our video representation with an Auxiliary Captioning objective, which alternatively provides fine-grained guidance in the semantic space during training.", + "bbox": [ + 75, + 614, + 468, + 781 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Auxiliary Captioning Head As shown on the right of Figure 4, the Auxiliary Captioning Head, denoted by $\\mathcal{H}$ , is a stack of $M$ transformer decoders. We first shift the text token by one step to the right, and feed it into a Masked MHA layer, where each text token only attends to its preceding", + "bbox": [ + 75, + 796, + 470, + 866 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6809609bbbe0a770b989fc954f692f79003a451ced44a72e0eb8ffc339bf69d9.jpg", + "image_caption": [ + "Figure 4: Detailed architecture of Prompt Aggregation (left) and Auxiliary Captioning Head (right)." + ], + "image_footnote": [], + "bbox": [ + 527, + 123, + 867, + 361 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "tokens. Then, another MHA layer is used, where the text tokens attend to the aggregated prompt vectors $\\{\\overline{p_i}\\}_{i = 1}^{N_f}$ . The model is trained via the autoregressive Teacher Forcing [44] scheme, i.e., the prediction in each step should maximize the likelihood of the token in the next step:", + "bbox": [ + 497, + 421, + 892, + 492 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c a p} = \\sum_ {l = 1} ^ {N _ {w}} - \\log p \\left(w _ {l} \\mid w _ {< l}, \\left\\{\\bar {\\boldsymbol {p}} _ {i} \\right\\} _ {i = 1} ^ {N _ {f}}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 564, + 500, + 890, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $w_{l}$ indicates the $l$ -th token in the text, and $w_{MethodR@1↑R@5↑R@10↑MnR↓baseline CLIP43.170.980.416.0+ Prompt Switch44.8 (+1.7)71.980.915.2+ Temporal Transformer44.271.481.115.6+ Prompt Aggregation45.4 (+0.6)71.981.114.9+ Captioning Loss46.1 (+0.7)72.881.814.4", + "bbox": [ + 80, + 122, + 468, + 201 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ae3fdd674becad28837e254de30ec67c7a4af165a823297178ab9484bf148522.jpg", + "table_caption": [ + "Table 1: Performance analysis of our model components for text-video retrieval on MSRVTT 1K-A test set. Both Prompt Aggregation and Temporal Transformer are applied on top of our Prompt Switch. The Captioning Loss is applied only on top of the Prompt Aggregation." + ], + "table_footnote": [], + "table_body": "
MethodR@1↑R@5↑R@10↑MnR↓
Temporal Transformer44.271.481.115.6
Token Shift [24]43.270.779.815.9
Video Proxy [52]45.271.081.515.3
Full Attention43.871.480.916.4
Prompt Switch & Aggregation45.471.981.114.9
", + "bbox": [ + 80, + 292, + 468, + 375 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tion (obtained by Eq. (3) and text representation of the $i$ -th video-text pair in the mini-batch. The final loss function is", + "bbox": [ + 75, + 435, + 468, + 463 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {c o n}} + \\lambda \\mathcal {L} _ {\\text {c a p}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 203, + 472, + 468, + 488 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda$ is the weighting hyper-parameter.", + "bbox": [ + 77, + 496, + 357, + 511 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 77, + 522, + 201, + 538 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset and Metrics We evaluate the effectiveness of our method on three widely used text-video retrieval datasets, including MSR-VTT [50], MSVD [4] and LSMDC [35]. MSR-VTT [50] consists of 10,000 videos with 200K descriptions. We follow the setting in previous works [13, 54], training our models with 9,000 videos and evaluating them on the 1K-A test set. MSVD [4] contains 1,970 videos with about 120K captions, where the train, validation, and test splits contain 1, 200, 100 and 670 videos, respectively. LSMDC [35] has 118,081 video-caption pairs, where 109, 673 videos are used for training, 7, 408 videos for validation, and 1, 000 videos for testing. Following [16, 24, 27], we report the results of Recall@ $K$ ( $R@K$ , $K = 1, 5, 10$ ) and Mean Rank (MnR) for quantitative evaluation. Besides, we sum the value of $R@1$ , $R@5$ , and $R@10$ for both text-video and video-text retrieval tasks as an overall evaluation metric, named Meta Sum.", + "bbox": [ + 75, + 545, + 468, + 780 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details Following previous work [16, 27], both the text and video encoders are initialized with the pre-trained CLIP (ViT-B/32) [34]. The prompt cube is randomly initialized from a Gaussian distribution with a zero mean and 0.02 std. During training, we uniformly sample", + "bbox": [ + 75, + 796, + 468, + 866 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3128bf43d78d0f4a29a122a3017c1a0f628391a2a6a0180daf2fae4fa1ea58de.jpg", + "table_caption": [ + "Table 2: Comparisons with other temporal modeling methods for text-video retrieval on MSRVTT 1K-A test set." + ], + "table_footnote": [], + "table_body": "
MethodR@1↑R@5↑R@10↑Mem. / Time
Text ⇒ Video
TS2-Net* [24]46.573.683.30.3G / 0.2s
X-Pool [16]46.972.882.23.9G / 3.9s
ours (mean pool)46.172.881.82.0M / 8.1ms
ours (attention pool)46.472.982.40.2G / 0.2s
ours (top-3 pool)46.773.482.00.3G / 0.3s
ours (X-Pool [16])47.873.982.23.9G / 3.9s
Video ⇒ Text
TS2-Net* [24]44.573.883.20.3G / 0.2s
X-Pool [16]44.473.384.03.9G / 3.9s
ours (mean pool)44.873.782.42.0M / 8.1ms
ours (attention pool)45.473.983.20.2G / 0.2s
ours (top-3 pool)45.273.683.70.3G / 0.3s
ours (X-Pool [16])46.074.384.83.9G / 3.9s
", + "bbox": [ + 504, + 122, + 890, + 331 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3: Performance and complexity comparisons with different temporal fusion methods on MSRVTT 1K-A test set. * denotes the results reproduced by official code & setting.", + "bbox": [ + 499, + 340, + 890, + 382 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6 frames from each video and resize all video frames into $224 \\times 224$ . Therefore, the size of the spatial and temporal dimensions of the prompt cube is set to 6 by default. While for the testing, 12 frames are used as in previous works, so we split them into two 6-frame chunks through interval sampling to make the temporal dimension compatible with the prompt cube. The Prompt Aggregation is applied on the prompt cubes of all chunks. The number of decoder layers in the captioning head is 3. The hyper-parameter $k$ used for frame sampling in Eq. (3) is set to 3. We set the hyperparameter $\\lambda = 0.5$ in Eq. (6). The training epochs are 10 for all the datasets with a batch size of 128. We use AdamW optimizer [25] with a learning rate of 3e-5 and adopt a cosine decay strategy for the learning rate.", + "bbox": [ + 497, + 407, + 890, + 600 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Performance Analysis", + "text_level": 1, + "bbox": [ + 499, + 610, + 705, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first thoroughly analyze the model designs and critical components of our proposed method and then verify their effectiveness. The experiments are conducted on the MSRVTT dataset and evaluated on the 1K-A test set.", + "bbox": [ + 497, + 631, + 890, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Model Components As shown in Table 1, we conduct an ablation study on the Prompt Switch, Prompt Aggregation, and Auxiliary Captioning Objective by introducing them gradually into the model for text-video retrieval. The baseline CLIP model directly uses the mean-pooled [CLS] embeddings of the video frames as the final video representation, and is trained using only contrastive loss. Specifically, when incorporating the Prompt Switch mechanism, the result of R@1 increases significantly (i.e., from 43.1 to 44.8) compared with the baseline CLIP, which demonstrates the effectiveness of the proposed Prompt Switch. With the help of Prompt Aggregation, it further improves 0.6 and", + "bbox": [ + 497, + 700, + 890, + 866 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15653", + "bbox": [ + 465, + 887, + 504, + 897 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8679c8ea42c4afd031d57140cd50b08968d3d040365c17c503f7a7310f52fcf6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsText ⇒ VideoVideo ⇒ TextMeta Sum ↑
R@1 ↑R@5 ↑R@10 ↑MnR ↓R@1R@5 ↑R@10 ↑MnR ↓
cross-modal temporal fusion
CLIP2TV [14]46.172.582.915.243.973.082.811.1401.2
CLIP2Video [12]45.672.681.714.643.372.382.110.2397.6
TS2-Net* [24]46.573.683.313.944.573.883.29.2404.9
EMCL [18]46.873.183.1-46.573.583.5-406.5
X-CLIP [28]46.173.083.113.246.873.384.09.1406.3
DRL [41]47.474.683.8-45.373.983.3-408.3
X-Pool [16]46.972.882.214.344.473.384.09.0403.6
ours (X-Pool)47.873.982.214.146.074.384.88.5409.0
text-agnostic temporal pooling
CLIP4Clip† (seqTransf) [27]44.571.481.615.342.770.980.611.6391.7
CenterCLIP† (spectral) [57]44.271.682.115.142.871.782.211.1394.6
X-CLIP (mean pool) [28]43.070.781.616.343.070.281.211.5389.7
TS2-Net* (mean pool) [24]44.472.182.214.643.770.880.411.6393.6
ours (mean pool)46.172.881.814.444.873.782.49.9401.6
", + "bbox": [ + 122, + 123, + 852, + 344 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/79521b792fa9775aecee81242493bf235f6611fe8e8011ee5a3e715c4ba00145.jpg", + "table_caption": [ + "Table 4: Comparisons with state-of-the-arts on MSRVTT. † both CLIP4Clip and CenterCLIP have multiple versions in their papers, here we choose the versions with the highest Meta Sum. * denotes the results reproduced by official code & setting." + ], + "table_footnote": [], + "table_body": "
MethodsText ⇒ VideoVideo ⇒ TextMeta Sum ↑
R@1↑R@5↑R@10↑MnR ↓R@1R@5↑R@10↑MnR ↓
cross-modal temporal fusion
CLIP2TV [14]47.076.585.110.1-----
CLIP2Video [12]47.076.885.99.658.785.691.64.3445.6
X-CLIP [28]47.177.8-9.560.987.8-4.7-
X-Pool [16]47.277.486.09.366.490.094.23.3461.2
text-agnostic temporal pooling
CLIP4Clip† (seqTransf) [27]45.275.584.310.362.087.392.64.3446.9
CenterCLIP† (spectral) [57]47.476.585.29.762.788.192.84.1452.7
ours (mean pool)47.176.986.19.568.591.895.62.8466.0
", + "bbox": [ + 122, + 394, + 852, + 543 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5: Comparisons with state-of-the-arts on MSVD. † both CLIP4Clip and CenterCLIP have multiple versions in their papers, here we choose the versions with the highest Meta Sum values.", + "bbox": [ + 75, + 553, + 892, + 583 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "achieves 45.4 in R@1. Our final model containing the Auxiliary Captioning Loss further improves the performance in R@1, R@5, R@10, and MnR by a large margin. These results demonstrate that all the proposed components contribute clearly to the final performance. Besides, we also compare the performance of an alternative temporal aggregation method to Prompt Aggregation termed Temporal Transformer, which adopts an additional transformer layer on the [CLS] embeddings of all video frames and averages the output. From Table 1, Prompt Aggregation is better than Temporal Transformer on all metrics.", + "bbox": [ + 75, + 606, + 470, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison on Temporal Modeling Methods To investigate the effectiveness of our temporal modeling method, i.e., Prompt Switch + Prompt Aggregation, we compare it with other four temporal modeling methods, including the Temporal Transformer, Full Attention (attention over patch tokens from all video frames), Token Shift [24], and Video Proxy [52]. All methods are implemented on the baseline", + "bbox": [ + 75, + 769, + 470, + 866 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "CLIP model without extra components like the Token Selection Transformer in [24], and are trained using our default setting. From Table 2, our Prompt Switch & Aggregation approach outperforms all the baselines on R@1, R@5, and MnR while achieving the second-best result on R@10, which demonstrates its superiority in learning global video semantics across frames.", + "bbox": [ + 497, + 606, + 890, + 703 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Cross-Modal Temporal Fusion vs. Naive Mean Pooling While our method is able to achieve significantly better performance than the baseline CLIP using the mean-pooling setting, we further investigate whether it is compatible with the advanced cross-modal temporal fusion methods, namely, attention pooling, top-3 pooling, and X-Pool [16]. We simply replace the final mean-pooling in Eq. (3) with these cross-modal approaches and show the performance in Table 3. From the table, when adopting these cross-modal fusion methods, our models obtain clearly boosted performance, especially for X-Pool, which obtains the best per", + "bbox": [ + 497, + 713, + 892, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15654", + "bbox": [ + 465, + 885, + 505, + 897 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9f79d2185ea2b0da79b28541a4c4867ac60be8694f16970f74906990ad413e42.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsText ⇒ VideoVideo ⇒ TextMeta Sum ↑
R@1↑R@5↑R@10↑MnR↓R@1↑R@5↑R@10↑MnR↓
cross-modal temporal fusion
X-Pool [16]25.243.753.553.222.742.651.247.4238.9
TS2-Net [24]23.442.350.956.9-----
EMCL [18]23.942.450.9-22.240.649.2-229.2
X-CLIP [28]23.343.0-56.022.542.2-50.7-
text-agnostic temporal pooling
CLIP4Clip† (seqLSTM) [27]21.641.849.858.020.940.749.153.9223.9
CenterCLIP† (k-medoids++) [57]21.941.150.755.621.141.250.248.7226.2
ours (mean pool)23.141.750.556.822.040.850.351.0228.4
", + "bbox": [ + 122, + 123, + 850, + 271 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6: Comparisons with state-of-the-arts on LSMDC. † both CLIP4Clip and CenterCLIP have multiple versions in their papers and here we choose the versions with the highest Meta Sum values.", + "bbox": [ + 75, + 280, + 892, + 309 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "formance for both text-video and video-text retrieval and outperforms the original X-Pool by a large margin. Moreover, even compared with the state-of-the-art cross-modal fusion methods, our model with naive mean-pooling is still competitive for both text-video and video-text retrieval.", + "bbox": [ + 75, + 330, + 468, + 399 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We further measure the memory usage and latency of the compared methods during inference on the test set. To make the experiment setting close to real-world scenarios and for fair comparisons, we use the same pre-computed frame and text representations while only monitoring space and time consumption for the ranking procedure. As shown in the last column of Table 3, our model with mean-pooling is orders of magnitude more efficient than those baseline models with cross-modal temporal fusion. This conclusion is generalizable to other datasets, i.e., the same model will always have the same ranking efficiency if using the same inference and evaluation settings. This reveals the importance of using text-agnostic temporal fusion (e.g., mean-pooling) for real-world text-video retrieval.", + "bbox": [ + 75, + 400, + 470, + 593 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2. Comparison with the State-of-the-arts", + "text_level": 1, + "bbox": [ + 75, + 608, + 405, + 624 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this section, we compare our proposed method with state-of-the-art methods on MSRVTT, MSVD, and LSMDC dataset. To better reveal the performance gap among the compared methods, we do not consider post-processing techniques like QB-NORM [2]. The results of both text-video and video-text retrieval tasks are presented in Tables 4, 5 and 6. From the tables, when compared under the text-agnostic temporal fusion setting, our model outperforms the baseline models on most of the evaluation metrics, especially for Meta Sum, where it achieves the best performance on all three datasets. Specifically, on MSRVTT, the Meta Sum of our model is 7 points better than the second-best model; on MSVD, our method outperforms CenterCLIP [57] by 13.3; On LSMDC, our model consistently achieves the highest Meta Sum. Moreover, when compared with methods using cross-modal temporal fusion, our model with mean-pooling is still competitive in terms", + "bbox": [ + 75, + 631, + 468, + 866 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bba94add5c4feb1523c564bcda6f66d308f15b2303ac2325415acbb896eaee01.jpg", + "image_caption": [ + "(a) $\\mathbb{R}@\\mathbb{1}$ performance with different number of decoder layers" + ], + "image_footnote": [], + "bbox": [ + 500, + 327, + 690, + 382 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/eb1db2f7a06406b2d802c8b0c630a43d85113cc35b8e10a1a6c3d6c5bf540f91.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 327, + 890, + 382 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/22449661e7bd53de1d4938b4c9f0dff45b3e39cdb6a44398c9bde623da1eccee.jpg", + "image_caption": [ + "(b) R@1 performance with different number of subsampling frames" + ], + "image_footnote": [], + "bbox": [ + 500, + 409, + 692, + 469 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/211ec0cc2ba3c007d8c7077e33123532c4bd3b9bdaadf33aa8aa3fb0d4ae5549.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 409, + 890, + 469 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2fdee8c2a3e805f602de70b86f014e8d74496978767905df18eff5e154612b9b.jpg", + "image_caption": [ + "(c) $\\mathrm{R}@\\mathrm{l}$ performance with different value of hyper-parameter $\\lambda$" + ], + "image_footnote": [], + "bbox": [ + 500, + 496, + 690, + 553 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6896488aea93575cc41f73f9f6db5f21f215eaed94fe859e62e3f13e8a0cb343.jpg", + "image_caption": [ + "Figure 5: We show the effects of (a) the number of captioning decoder layers; (b) the number of subsampling frames $k$ in training; (c) the values of hyper-parameter $\\lambda$ in Eq. (6)." + ], + "image_footnote": [], + "bbox": [ + 700, + 496, + 889, + 553 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of Meta Sum, while being much more efficient in practice (refer to Figure 1 and Table 3 for detailed discussions). Specifically, on MSRVTT, it outperforms CLIP2TV [14] and CLIP2Video [12]; on MSVD, it surpasses all compared baselines and improves over the second-best model (X-Pool [16]) by 4.8; on LSMDC, it is still comparable with EMCL [18]. These results show that our proposed method has a better trade-off between performance and efficiency, and is more suitable for large-scale production systems.", + "bbox": [ + 497, + 649, + 890, + 776 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Further Discussions", + "text_level": 1, + "bbox": [ + 499, + 788, + 690, + 802 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Number of Decoder Layers Generally, more layers in the captioning decoder would improve its capacity for learning fine-grained knowledge, which, however, also makes it easier to over-fit. To find a better trade-off, we study the", + "bbox": [ + 497, + 809, + 892, + 866 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15655", + "bbox": [ + 465, + 887, + 504, + 897 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "effect of the number of layers. As shown in Figure 5(a), the performance of our model improves and reaches the peak with 3 layers of decoder for both text-video and video-text retrieval tasks. Thus, we set the number of decoder layers to 3 for all the experiments.", + "bbox": [ + 75, + 125, + 468, + 195 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Number of Subsampling Frames In practice, we set the number of training frames as 6 and validation frames as 12. Then, we randomly sample $k$ frames before mean-pooling for training while using all 12 frames for evaluation. Notably, if $k = 6$ , that means we average all the training frames in the mean-pooling operation. In Figure 5(b), we observe that the performance improves when reducing the value of $k$ and achieves the peak when $k = 3$ , which demonstrates its effectiveness. While further decreasing the value of $k$ , the mean-pooling operation may lose a great deal of semantics derived from frames, which causes performance degradation. Therefore, we set $k = 3$ for all the experiments.", + "bbox": [ + 75, + 217, + 468, + 383 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Hyper-parameter $\\lambda$ in Eq. (6) From Figure 5(c), in the case of a small $\\lambda$ (e.g., $\\lambda = 0.3$ ), the model can only achieve suboptimal performance due to insufficient exploitation of the detailed semantics. When increasing the value of $\\lambda$ , the performance of our model peaks at the $\\lambda = 0.5$ and degrades thereafter. Considering the trade-off between typical contrastive loss and captioning loss, we choose the weighting parameter $\\lambda$ as 0.5 for all the datasets.", + "bbox": [ + 75, + 404, + 468, + 515 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 75, + 530, + 194, + 545 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we tackle the task of text-video retrieval, where we aim to learn semantically-enhanced representations purely from the video, allowing for offline computation and reuse for different text queries. Our method introduces a new Prompt Cube into the CLIP image encoder, which is iteratively transposed within the encoder layers to incorporate global video semantics into frame representations. We also adopt an auxiliary video captioning objective to optimize the frame representations, providing detailed guidance in the semantic space. With mean pooling fusion on the enhanced frame representations, the proposed model achieves SoTA performance on three benchmark datasets. Comprehensive experiments verify the effectiveness of all critical components of our proposed method.", + "bbox": [ + 75, + 555, + 468, + 749 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 763, + 171, + 777 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. Frozen in time: A joint video and image encoder for end-to-end retrieval. In ICCV, pages 1728-1738, 2021.", + "[2] Simion-Vlad Bogolin, Ioana Croitoru, Hailin Jin, Yang Liu, and Samuel Albanie. Cross modal retrieval with querybank normalisation. In CVPR, pages 5194-5205, 2022." + ], + "bbox": [ + 84, + 786, + 468, + 866 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[3] Joao Carreira and Andrew Zisserman. Quo vadis, action recognition? a new model and the kinetics dataset. 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In ICCV, pages 408-417, 2017." + ], + "bbox": [ + 78, + 125, + 468, + 618 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "15658", + "bbox": [ + 465, + 885, + 504, + 897 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Prompt Switch_ Efficient CLIP Adaptation for Text-Video Retrieval/408eb595-fd0b-42c6-8600-a2efb5916c5c_model.json b/2023/Prompt Switch_ Efficient CLIP Adaptation for Text-Video Retrieval/408eb595-fd0b-42c6-8600-a2efb5916c5c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..4efe53475cb19b17212c8822cecd09b8ab0a675a --- /dev/null +++ b/2023/Prompt Switch_ Efficient CLIP Adaptation for Text-Video Retrieval/408eb595-fd0b-42c6-8600-a2efb5916c5c_model.json @@ -0,0 +1,2015 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.13, + 0.051, + 0.201, + 0.086 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.254, + 0.049, + 0.79, + 0.087 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.143, + 0.162, + 0.828, + 0.182 + ], + "angle": 0, + "content": "Prompt Switch: Efficient CLIP Adaptation for Text-Video Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.221, + 0.207, + 0.768, + 0.258 + ], + "angle": 0, + "content": "Chaorui Deng\\(^{1,\\ast}\\), Qi Chen\\(^{1,\\ast}\\), Pengda Qin\\(^{2}\\), Da Chen\\(^{3}\\), Qi Wu\\(^{1,\\dagger}\\) \n\\(^{1}\\)Australia Institute of Machine Learning, University of Adelaide \nAlibaba Group, \\(^{3}\\)Department of Computer Science, University of Bath" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.289, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.473, + 0.691 + ], + "angle": 0, + "content": "In text-video retrieval, recent works have benefited from the powerful learning capabilities of pre-trained text-image foundation models (e.g., CLIP) by adapting them to the video domain. A critical problem for them is how to effectively capture the rich semantics inside the video using the image encoder of CLIP. To tackle this, state-of-the-art methods adopt complex cross-modal modeling techniques to fuse the text information into video frame representations, which, however, incurs severe efficiency issues in large-scale retrieval systems as the video representations must be recomputed online for every text query. In this paper, we discard this problematic cross-modal fusion process and aim to learn semantically-enhanced representations purely from the video, so that the video representations can be computed offline and reused for different texts. Concretely, we first introduce a spatial-temporal \"Prompt Cube\" into the CLIP image encoder and iteratively switch it within the encoder layers to efficiently incorporate the global video semantics into frame representations. We then propose to apply an auxiliary video captioning objective to train the frame representations, which facilitates the learning of detailed video semantics by providing fine-grained guidance in the semantic space. With a naive temporal fusion strategy (i.e., mean-pooling) on the enhanced frame representations, we obtain state-of-the-art performances on three benchmark datasets, i.e., MSR-VTT, MSVD, and LSMDC." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.716, + 0.21, + 0.731 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.739, + 0.47, + 0.837 + ], + "angle": 0, + "content": "Text-video retrieval [1, 6, 30, 42] is a fundamental task in the area of video-language understanding that seeks to find the most relevant video from a large set of candidates to match a text query. With the rapid growth of video data, text-video retrieval has become increasingly important for various applications, including video recommendation [36, 43], video search [20, 45], and video summa" + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.287, + 0.88, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.455, + 0.893, + 0.538 + ], + "angle": 0, + "content": "Figure 1: The performance (i.e., R@1), retrieval time, and memory usage during retrieval for baseline models and ours on the MSRVTT dataset. The center of the bubble indicates the value of R@1. The diameter of the bubble or star is proportional to the memory usage (GB) while the horizontal axis indicates the inference time (s)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.562, + 0.893, + 0.742 + ], + "angle": 0, + "content": "rization [7, 29, 31, 33, 37, 47]. Due to the high cost of constructing text-video datasets, one promising approach for this task is to leverage pre-trained text-image foundation models and transfer their powerful representation capabilities to the video domain. Specifically, the CLIP [34] model, which is trained using a text-image alignment objective, is particularly suitable for text-video retrieval and has been frequently studied recently [27, 46, 16]. It has two transformer encoders [38, 9] to process images and texts, respectively. A vector representation is extracted from the input of each modality with the corresponding encoder and is optimized to be close to its paired representation and away from the unpaired ones." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.742, + 0.894, + 0.868 + ], + "angle": 0, + "content": "Adapting CLIP to the video domain is non-trivial and requires careful consideration of both efficiency and effectiveness. In CLIP4Clip [27], the authors directly mean-pool the frame representations extracted by the CLIP image encoder to get the video representation and use it to calculate the cosine similarity with the text representations during retrieval. However, the mean-pooling of frame representations may lose some essential semantic details of the video and hamper the retrieval performance. Thus, more advanced meth" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.843, + 0.47, + 0.867 + ], + "angle": 0, + "content": "*Co-first author. †Corresponds to qi.wu01@adelaide.edu.au. Code: https://github.com/bladewaltz1/PromptSwitch." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.887, + 0.506, + 0.898 + ], + "angle": 0, + "content": "15648" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.126, + 0.473, + 0.265 + ], + "angle": 0, + "content": "ods, such as [14, 16, 18, 24, 28], generate the video representation by applying various cross-modal temporal fusion approaches on the frame representations, using text queries as the condition. While achieving state-of-the-art results, these methods encounter severe efficiency issues in practice, as the text-conditioned fusion of each video has to be performed on-the-fly for every incoming text query. Even with a lightweight fusion module (compared to the CLIP backbone), its computation cost grows geometrically as the number of videos and texts increases." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.266, + 0.473, + 0.514 + ], + "angle": 0, + "content": "Formally, given a query set of \\(N_{t}\\) texts with an average length of \\(N_{w}\\) words and a candidate set of \\(N_{v}\\) videos where each video contains \\(N_{f}\\) frames. Then, the space and time complexities are \\(\\mathcal{O}(N_vN_tN_f)\\) for the text-conditioned fusion in X-Pool [16] and TS2-Net [24], and \\(\\mathcal{O}(N_vN_tN_fN_w)\\) for that of X-CLIP [28]. While for CLIP4Clip, the complexity is \\(\\mathcal{O}(N_vN_t)\\) as it only requires a simple dot-product between the text and mean-pooled frame representations, although its performance is inferior to X-Pool and X-CLIP. To better reveal this gap, we show an example in Figure 1 about the real-world efficiency of several methods while omitting the backbone computation. Here, we set \\(N_{v} = 16384\\), \\(N_{t} = 512\\), \\(N_{f} = 12\\), and \\(N_{w} = 10\\). From the figure, with large \\(N_{t}\\) and \\(N_{v}\\), the latency and memory consumption for text-conditioned temporal fusion methods [16, 24, 28] are orders of magnitude higher than text-agnostic temporal fusion (i.e., mean-pooling) [27, 57], and can rapidly become enormous in large-scale scenarios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.513, + 0.473, + 0.652 + ], + "angle": 0, + "content": "On the other hand, the backbone computation of CLIP is much less of a burden in real-world retrieval systems, as the frame representations of the video can be pre-computed offline and reused for different text queries. Therefore, a more practical CLIP-based text-video retrieval method should focus on improving the backbone representation ability while keeping the cross-modal interaction as simple as possible. Motivated by this, we propose a simple and efficient adaptation method for CLIP to facilitate its ability to capture both the global and detailed semantics of videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.652, + 0.473, + 0.846 + ], + "angle": 0, + "content": "Concretely, we first feed a tiny (\\(\\sim 0.1\\mathrm{M}\\)) \"Prompt Cube\" into the image encoder of CLIP, which is a 3D tensor spanning over the spatial, temporal, and channel axis, as shown in the right of Figure 2.\\(^{1}\\) It is designed to have the same temporal and spatial sizes and is concatenated with the patch tokens alongside the spatial axis. To propagate temporal semantics among different frames, we switch the spatial and temporal dimensions of the prompt cube before each self-attention layer, so that the prompt cube builds up a peer-to-peer connection between every two-frame pair. In this way, our modified CLIP model enjoys an improved global semantic modeling ability thanks to the comprehensive spatial-temporal modeling between the prompt cube and the patch tokens of all frames, while only bringing neg-" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.126, + 0.892, + 0.224 + ], + "angle": 0, + "content": "ligible extra parameters and computations. This also allows the prompt cube to serve as a compact summarization of the whole video, and further enables us to design a CLIP-guided Prompt Aggregation approach and obtain the frame representations from the prompt cube. Then, we use naive mean-pooling instead of cross-modal fusion on these frame representations to get the final video representation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.224, + 0.893, + 0.431 + ], + "angle": 0, + "content": "Moreover, since we will not use any fine-grained cross-modal interaction modules in our model, we adopt an Auxiliary Video Captioning objective as an alternative to provide fine-grained guidance in the semantic space when learning video representations. Specifically, we introduce a light captioning head on top of our modified CLIP image encoder during training, which takes the frame representations aggregated from the prompt cube as input and generates the paired text of the input video. This auxiliary objective plays a critical role because CLIP's original contrastive learning objective is relatively easy to fit due to the lack of in-batch negatives during training (which is generally the case in text-video retrieval). During inference, the light captioning branch is removed, thus it incurs no extra computation and memory consumption." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.431, + 0.894, + 0.528 + ], + "angle": 0, + "content": "We verify the effectiveness of the proposed method on three text-video retrieval benchmarks, i.e. MSR-VTT [50], MSVD [4], and LSMDC [35], where our method consistently achieves state-of-the-art performance while being significantly more efficient than the previous state of the arts. We also provide extensive performance analyses to show the superiority of our proposed method." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.538, + 0.642, + 0.552 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.617 + ], + "angle": 0, + "content": "Text-video retrieval is one of the fundamental tasks in video-language modeling and has lots of applications in the industry. Here, we broadly classify the previous works into three categories and briefly review them below." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.632, + 0.895, + 0.868 + ], + "angle": 0, + "content": "Off-the-Shelf Single-Modal Representations An early trend in text-video retrieval is to use the off-the-shelf video (e.g., I3D [3]) and text representations (e.g., GloVe [32]) and design sophisticated feature encoding methods or multi-modal fusion mechanisms on them to improve the retrieval performance [6, 8, 19, 54, 55]. For example, in [6], a hierarchical graph reasoning approach is proposed to decompose video-text matching into global-to-local levels and disentangle texts into a hierarchical semantic graph with three levels of events, actions, and entities. Yu et al. [54] propose a joint sequence fusion model for the sequential interaction of videos and texts. Dong et al. [8] leverages multi-level single-modal features that represent the rich content of both video and text in a coarse-to-fine fashion. However, their performances are limited due to the mismatched training objectives between the pre-computed representations and the text-video retrieval task." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.854, + 0.327, + 0.867 + ], + "angle": 0, + "content": "1The channel axis is omitted for simplicity." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.887, + 0.506, + 0.898 + ], + "angle": 0, + "content": "15649" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.127, + 0.87, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.363, + 0.893, + 0.406 + ], + "angle": 0, + "content": "Figure 2: Overall architecture. For a video clip with \\( N_{f} \\) frames, we accompany it with \\( N_{f} \\times N_{f} \\) prompt tokens, resulting in a 3D prompt cube. We show the Prompt Switch operation on the right. For simplicity, we omit the feed-forward network and shot-cut connections in the ViT layer. We provide more details for Prompt Aggregation in Figure 4. \\( \\otimes \\) is cosine similarity." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.429, + 0.473, + 0.859 + ], + "angle": 0, + "content": "Video-Language Pre-training To reduce the gap between pre-training and downstream tasks, large-scale pretrained video-language representations have been proposed, such as [1, 13, 15, 21, 26, 40, 48, 49, 51]. Most of these models are pre-trained on the large-scale video-text datasets, e.g., HowTo100M [30] and WebVid-2M [1], which boosts promising cross-modal video understanding [22, 23, 26]. One line of works [1, 13, 49] uses two independent encoders for video and text and then projects them into a common latent space. These methods often adopt a contrastive loss to distinguish the paired video-text data. For example, Bain et al. [1] design an end-to-end trainable model, aiming to take advantage of both large-scale image and video captioning datasets. Gabeur et al. [13] propose a multi-modal transformer that can extract features at different moments and from different modalities (e.g., audio or speech) in a video. The other line of works [21, 26, 48] employs a single cross-modal encoder, which concatenates the video and text sequences as inputs and models them jointly in the transformer, followed by a binary classifier predicting whether these videos and texts are aligned. Despite they can build fine-grained associations between video-text tokens, they need to input each video-text candidate pair into the model for matching score calculation during inference and thus hampers efficiency. Besides, although the idea of video-language pre-training is promising, due to the high cost of collecting wild videos, its scale is generally much smaller than image-language pre-training, leading to an unsatisfactory generalization ability. Thus, like [16, 27], we seek to boost from the image-language pre-training model (e.g., CLIP [34]) for text-video retrieval." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.893, + 0.72 + ], + "angle": 0, + "content": "CLIP-based Adaptation. Recently, due to the great advantage of CLIP [34] for vision-and-language representation learning, many works [11, 14, 17, 18, 28, 41, 52, 56] seek to transfer the knowledge of CLIP to text-video retrieval tasks. Roughly, the existing works transfer CLIP from views of feature aggregation [12, 16, 27, 28, 57], representation alignment [12, 28, 41], and post pretraining [46, 52]. Specifically, X-Pool [16] designs a cross-modal attention model, seeking to enable the model to only focus on the relevant video frames conditioned on a given text. TS2-Net [24] adapts CLIP by introducing a token shift module and a token selection module, which capture the temporal information and remove unimportant tokens, respectively. X-CLIP [28] calculates both the coarse- and fine-grained similarity for higher retrieval accuracy. While these methods can be effective, their retrieval efficiency is low due to the coupling of video and text in the cross-modal fusion process. A more ideal way should focus on improving the representation ability of the backbone while maintaining the cross-modal interaction as efficiently as possible. We follow this principle in our method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.732, + 0.593, + 0.747 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.756, + 0.895, + 0.868 + ], + "angle": 0, + "content": "The overview of our method is shown in Figure 2. It is based on a pre-trained CLIP with a ViT [10]-based image encoder. Given an input video, we first split each video frame into fix-sized non-overlapping patches and linearly project them into 1D patch embeddings. Following CLIP, a [CLS] embedding is concatenated to the embedding sequence of each frame, which is pre-trained to capture the local semantics within the sequence. Then, in the ViT en" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.887, + 0.506, + 0.898 + ], + "angle": 0, + "content": "15650" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.126, + 0.473, + 0.32 + ], + "angle": 0, + "content": "coder, our proposed \"Prompt Cube\" bridges the global semantic information from the patch embeddings of all frames through a Prompt Switch operation. After that, we feed the output [CLS] embeddings of the video frames and the final prompt cube into a Prompt Aggregation module, where the prompt cube is aggregated into 1D vectors according to the [CLS] embeddings, and is further enhanced with fine-grained semantics through an Auxiliary Captioning Objective. To ensure an efficient measurement of the text-video similarity, we avoid using cross-modal fusion modules and directly average these aggregated vectors into the final video representation. A simple dot product operation is used to compute the similarity. More details are in the following." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.33, + 0.457, + 0.345 + ], + "angle": 0, + "content": "3.1. Prompt Cube for Bridging Global Semantics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.352, + 0.473, + 0.616 + ], + "angle": 0, + "content": "At the core of our method is the proposed Prompt Cube. It is designed to capture the rich temporal semantics of the whole video while bringing negligible modifications and computations to the CLIP image encoder. Formally, given an input video clip with \\( N_{f} \\) frames, we first obtain its patch embeddings \\( V \\in \\mathbb{R}^{N_f \\times L \\times D} \\), where \\( L \\) indicates the size of the spatial dimension, i.e., the number of patches divided from a video frame plus one [CLS] embedding. \\( D \\) is the embedding size. Then, our prompt cube is constructed as a 3D tensor \\( P \\in \\mathbb{R}^{N_f \\times N_f \\times D} \\). At the start of the ViT layer, we concatenate \\( V \\) and \\( P \\) alongside the spatial dimension, denoted by \\( [V; P] \\in \\mathbb{R}^{N_f \\times (L + N_f) \\times D} \\), and then process them jointly. The first two dimensions of \\( P \\) (corresponding to the temporal and spatial axis, respectively) have the same size, thus they can be transposed flexibly without altering the shape of \\( P \\). This allows us to further propose an efficient Prompt Switch operation to exchange the local spatial semantics of each frame and the global temporal semantics from the whole video through the prompt cube." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.634, + 0.47, + 0.662 + ], + "angle": 0, + "content": "Prompt Switch The proposed Prompt Switch operation can be defined in a one-line formula:" + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.673, + 0.47, + 0.691 + ], + "angle": 0, + "content": "\\[\n\\mathcal {T} := [ V; P ] \\rightarrow [ V; P ^ {\\top} ]. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.701, + 0.473, + 0.868 + ], + "angle": 0, + "content": "See the right of Figure 2, we apply this operation before every self-attention layer of the ViT encoder. Then, self-attention is performed over the spatial dimension of \\([V;P]\\), where the \\(i\\)-th row of the prompt cube (denoted by \\(\\pmb{p}_i \\in \\mathbb{R}^{1 \\times N_f \\times D}\\)) and the patch embeddings of the \\(i\\)-th frame (denoted by \\(\\pmb{v}_i \\in \\mathbb{R}^{1 \\times L \\times D}\\)) acquire information from each other. In this way, for two consecutive ViT layers in the encoder, each element in the prompt cube (denoted by \\(\\pmb{p}_{i,j} \\in \\mathbb{R}^D\\)) is first attached to the \\(i\\)-th frame and communicates with \\(\\pmb{v}_i\\), and then switch to the \\(j\\)-th frame and communicates with \\(\\pmb{v}_j\\). By repeatedly performing this operation, the whole prompt cube builds up a peer-to-peer" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.124, + 0.703, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.718, + 0.124, + 0.882, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.265, + 0.893, + 0.404 + ], + "angle": 0, + "content": "Figure 3: Video Proxy adopts a shared \"prompt\" to exchange information among all frames (b). Differently, our Prompt Switch method builds up a peer-to-peer connection between every two-frame pair (a) to obtain more comprehensive spatial-temporal modeling. This improves the representation ability of CLIP on video data. Besides, our method may also ease the learning problem as each element in the prompt cube only needs to handle the information of two frames instead of the whole video, thus improving the optimization ability of CLIP on video data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.43, + 0.892, + 0.457 + ], + "angle": 0, + "content": "connection between every two-frame pair in the video clip, enabling comprehensive temporal modeling." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.893, + 0.803 + ], + "angle": 0, + "content": "Some previous text-video retrieval methods have also attempted to introduce temporal adaptation to the backbone of the CLIP ViT encoder, such as Token Shift [24] and Video Proxy [52]. Specifically, the Token Shift method shifts token embeddings from adjacent frames to the current frame, which fails to model the temporal semantics from a global perspective. Moreover, it damages the spatial modeling ability of the original CLIP as the information contained in the shifted tokens is no longer accessible in the current frame. In Video Proxy, the information from all video frames is exchanged using several proxy embeddings, which lack peer-to-peer connections within the frames and thus can be inferior in the temporal modeling capacity. We illustrate the importance of building peer-to-peer connections in Figure 3. Besides, a naive full-attention approach has also been investigated where no adaptation is applied to the CLIP model except allowing its self-attention layers to attend to the patch tokens from the whole video. However, this approach is neither effective due to the domain gap between the input data (video) and the pre-training data (image), nor efficient since the computation complexity of the self-attention layers grows quadratically w.r.t. the number of attended patch tokens. We show the superiority of our proposed prompt cube to these previous methods in Section 4.1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Prompt Aggregation As the prompt cube acquires the global semantics through a comprehensive interaction with all patch embeddings, it can serve as a compact summariza" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.505, + 0.898 + ], + "angle": 0, + "content": "15651" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.126, + 0.473, + 0.322 + ], + "angle": 0, + "content": "tion of the video. Therefore, we propose to obtain the final video representation from the prompt cube, instead of the [CLS] embedding as the original CLIP. To achieve this, we design a CLIP-guided Prompt Aggregation module, which aggregates the output prompt cube into 1D vectors according to the final [CLS] embeddings of the video frames. It is a lightweight multi-head attention (MHA) layer placed before the last layer normalization (LN) layer of the ViT encoder. The [CLS] embedding of the \\(i\\)-th frame (denoted by \\(\\pmb{c}_i \\in \\mathbb{R}^{1 \\times D}\\)) is used as the \"query\" while the \"key\" and \"value\" are both the prompt cube flattened over the temporal and spatial dimensions, denoted by \\(\\hat{\\pmb{P}} \\in \\mathbb{R}^{N_f^2 \\times D}\\). Let \\(\\bar{p}_i \\in \\mathbb{R}^{1 \\times D}\\) be the aggregated prompt vector for the \\(i\\)-th frame, we have" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.333, + 0.47, + 0.351 + ], + "angle": 0, + "content": "\\[\n\\bar {p} _ {i} := \\mathrm {L N} \\left(\\boldsymbol {c} _ {i} + \\operatorname {M H A} \\left(\\boldsymbol {c} _ {i}, \\hat {\\boldsymbol {P}}, \\hat {\\boldsymbol {P}}\\right)\\right), \\quad \\forall i \\in [ 1, N _ {f} ], \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.361, + 0.47, + 0.445 + ], + "angle": 0, + "content": "where LN denotes the last layer normalization layer of the CLIP ViT encoder. Notably, the last linear projection weight in the MHA layer is initialized as a 0 tensor to ensure that \\(\\bar{p}_i\\) is optimized from the original output of the CLIP image encoder. The final video representation is the naive mean-pooling of the normalized prompt vectors, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.204, + 0.454, + 0.47, + 0.494 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {x} := \\frac {1}{N _ {f}} \\sum_ {i = 1} ^ {N _ {f}} \\frac {\\bar {\\boldsymbol {p}} _ {i}}{\\| \\bar {\\boldsymbol {p}} _ {i} \\|}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.502, + 0.47, + 0.587 + ], + "angle": 0, + "content": "We provide a detailed illustration for the Prompt Aggregation module on the left of Figure 4. To enhance the learning of temporal information for the prompt cube, inspired by [58], we adopt a frame sampling strategy where we randomly sample \\( k < N_f \\) prompt vectors for the final mean-pooling operation in Eq. (3) during training." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.594, + 0.453, + 0.609 + ], + "angle": 0, + "content": "3.2. Learning Detailed Semantics via Captioning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.615, + 0.47, + 0.782 + ], + "angle": 0, + "content": "As we have discussed in Section 1, the key criterion in the design of our model architecture is to ensure the model contains no extra cross-modal interaction procedure during inference except computing the cosine similarity between text and video representations. While this ensures the efficiency of the similarity measurement in large-scale production systems, it also prevents the video representation from utilizing the fine-grained semantic information from the text query. To aid this, inspired by [5, 53], we propose to learn our video representation with an Auxiliary Captioning objective, which alternatively provides fine-grained guidance in the semantic space during training." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.797, + 0.471, + 0.868 + ], + "angle": 0, + "content": "Auxiliary Captioning Head As shown on the right of Figure 4, the Auxiliary Captioning Head, denoted by \\(\\mathcal{H}\\), is a stack of \\(M\\) transformer decoders. We first shift the text token by one step to the right, and feed it into a Masked MHA layer, where each text token only attends to its preceding" + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.124, + 0.868, + 0.362 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.371, + 0.892, + 0.4 + ], + "angle": 0, + "content": "Figure 4: Detailed architecture of Prompt Aggregation (left) and Auxiliary Captioning Head (right)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.422, + 0.893, + 0.493 + ], + "angle": 0, + "content": "tokens. Then, another MHA layer is used, where the text tokens attend to the aggregated prompt vectors \\(\\{\\overline{p_i}\\}_{i = 1}^{N_f}\\). The model is trained via the autoregressive Teacher Forcing [44] scheme, i.e., the prediction in each step should maximize the likelihood of the token in the next step:" + }, + { + "type": "equation", + "bbox": [ + 0.566, + 0.501, + 0.892, + 0.54 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c a p} = \\sum_ {l = 1} ^ {N _ {w}} - \\log p \\left(w _ {l} \\mid w _ {< l}, \\left\\{\\bar {\\boldsymbol {p}} _ {i} \\right\\} _ {i = 1} ^ {N _ {f}}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.547, + 0.892, + 0.659 + ], + "angle": 0, + "content": "where \\( w_{l} \\) indicates the \\( l \\)-th token in the text, and \\( w_{MethodR@1↑R@5↑R@10↑MnR↓baseline CLIP43.170.980.416.0+ Prompt Switch44.8 (+1.7)71.980.915.2+ Temporal Transformer44.271.481.115.6+ Prompt Aggregation45.4 (+0.6)71.981.114.9+ Captioning Loss46.1 (+0.7)72.881.814.4" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.212, + 0.47, + 0.282 + ], + "angle": 0, + "content": "Table 1: Performance analysis of our model components for text-video retrieval on MSRVTT 1K-A test set. Both Prompt Aggregation and Temporal Transformer are applied on top of our Prompt Switch. The Captioning Loss is applied only on top of the Prompt Aggregation." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.293, + 0.469, + 0.376 + ], + "angle": 0, + "content": "
MethodR@1↑R@5↑R@10↑MnR↓
Temporal Transformer44.271.481.115.6
Token Shift [24]43.270.779.815.9
Video Proxy [52]45.271.081.515.3
Full Attention43.871.480.916.4
Prompt Switch & Aggregation45.471.981.114.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.385, + 0.469, + 0.412 + ], + "angle": 0, + "content": "Table 2: Comparisons with other temporal modeling methods for text-video retrieval on MSRVTT 1K-A test set." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.436, + 0.469, + 0.464 + ], + "angle": 0, + "content": "tion (obtained by Eq. (3) and text representation of the \\(i\\)-th video-text pair in the mini-batch. The final loss function is" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.473, + 0.469, + 0.489 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {c o n}} + \\lambda \\mathcal {L} _ {\\text {c a p}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.497, + 0.358, + 0.512 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is the weighting hyper-parameter." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.523, + 0.203, + 0.539 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.546, + 0.47, + 0.781 + ], + "angle": 0, + "content": "Dataset and Metrics We evaluate the effectiveness of our method on three widely used text-video retrieval datasets, including MSR-VTT [50], MSVD [4] and LSMDC [35]. MSR-VTT [50] consists of 10,000 videos with 200K descriptions. We follow the setting in previous works [13, 54], training our models with 9,000 videos and evaluating them on the 1K-A test set. MSVD [4] contains 1,970 videos with about 120K captions, where the train, validation, and test splits contain 1, 200, 100 and 670 videos, respectively. LSMDC [35] has 118,081 video-caption pairs, where 109, 673 videos are used for training, 7, 408 videos for validation, and 1, 000 videos for testing. Following [16, 24, 27], we report the results of Recall@ \\( K \\) (\\( R@K \\), \\( K = 1, 5, 10 \\)) and Mean Rank (MnR) for quantitative evaluation. Besides, we sum the value of \\( R@1 \\), \\( R@5 \\), and \\( R@10 \\) for both text-video and video-text retrieval tasks as an overall evaluation metric, named Meta Sum." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.797, + 0.469, + 0.867 + ], + "angle": 0, + "content": "Implementation Details Following previous work [16, 27], both the text and video encoders are initialized with the pre-trained CLIP (ViT-B/32) [34]. The prompt cube is randomly initialized from a Gaussian distribution with a zero mean and 0.02 std. During training, we uniformly sample" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.123, + 0.892, + 0.332 + ], + "angle": 0, + "content": "
MethodR@1↑R@5↑R@10↑Mem. / Time
Text ⇒ Video
TS2-Net* [24]46.573.683.30.3G / 0.2s
X-Pool [16]46.972.882.23.9G / 3.9s
ours (mean pool)46.172.881.82.0M / 8.1ms
ours (attention pool)46.472.982.40.2G / 0.2s
ours (top-3 pool)46.773.482.00.3G / 0.3s
ours (X-Pool [16])47.873.982.23.9G / 3.9s
Video ⇒ Text
TS2-Net* [24]44.573.883.20.3G / 0.2s
X-Pool [16]44.473.384.03.9G / 3.9s
ours (mean pool)44.873.782.42.0M / 8.1ms
ours (attention pool)45.473.983.20.2G / 0.2s
ours (top-3 pool)45.273.683.70.3G / 0.3s
ours (X-Pool [16])46.074.384.83.9G / 3.9s
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.341, + 0.892, + 0.383 + ], + "angle": 0, + "content": "Table 3: Performance and complexity comparisons with different temporal fusion methods on MSRVTT 1K-A test set. * denotes the results reproduced by official code & setting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.408, + 0.892, + 0.602 + ], + "angle": 0, + "content": "6 frames from each video and resize all video frames into \\(224 \\times 224\\). Therefore, the size of the spatial and temporal dimensions of the prompt cube is set to 6 by default. While for the testing, 12 frames are used as in previous works, so we split them into two 6-frame chunks through interval sampling to make the temporal dimension compatible with the prompt cube. The Prompt Aggregation is applied on the prompt cubes of all chunks. The number of decoder layers in the captioning head is 3. The hyper-parameter \\(k\\) used for frame sampling in Eq. (3) is set to 3. We set the hyperparameter \\(\\lambda = 0.5\\) in Eq. (6). The training epochs are 10 for all the datasets with a batch size of 128. We use AdamW optimizer [25] with a learning rate of 3e-5 and adopt a cosine decay strategy for the learning rate." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.611, + 0.706, + 0.626 + ], + "angle": 0, + "content": "4.1. Performance Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.633, + 0.892, + 0.687 + ], + "angle": 0, + "content": "We first thoroughly analyze the model designs and critical components of our proposed method and then verify their effectiveness. The experiments are conducted on the MSRVTT dataset and evaluated on the 1K-A test set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.701, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Model Components As shown in Table 1, we conduct an ablation study on the Prompt Switch, Prompt Aggregation, and Auxiliary Captioning Objective by introducing them gradually into the model for text-video retrieval. The baseline CLIP model directly uses the mean-pooled [CLS] embeddings of the video frames as the final video representation, and is trained using only contrastive loss. Specifically, when incorporating the Prompt Switch mechanism, the result of R@1 increases significantly (i.e., from 43.1 to 44.8) compared with the baseline CLIP, which demonstrates the effectiveness of the proposed Prompt Switch. With the help of Prompt Aggregation, it further improves 0.6 and" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.505, + 0.898 + ], + "angle": 0, + "content": "15653" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.123, + 0.124, + 0.853, + 0.345 + ], + "angle": 0, + "content": "
MethodsText ⇒ VideoVideo ⇒ TextMeta Sum ↑
R@1 ↑R@5 ↑R@10 ↑MnR ↓R@1R@5 ↑R@10 ↑MnR ↓
cross-modal temporal fusion
CLIP2TV [14]46.172.582.915.243.973.082.811.1401.2
CLIP2Video [12]45.672.681.714.643.372.382.110.2397.6
TS2-Net* [24]46.573.683.313.944.573.883.29.2404.9
EMCL [18]46.873.183.1-46.573.583.5-406.5
X-CLIP [28]46.173.083.113.246.873.384.09.1406.3
DRL [41]47.474.683.8-45.373.983.3-408.3
X-Pool [16]46.972.882.214.344.473.384.09.0403.6
ours (X-Pool)47.873.982.214.146.074.384.88.5409.0
text-agnostic temporal pooling
CLIP4Clip† (seqTransf) [27]44.571.481.615.342.770.980.611.6391.7
CenterCLIP† (spectral) [57]44.271.682.115.142.871.782.211.1394.6
X-CLIP (mean pool) [28]43.070.781.616.343.070.281.211.5389.7
TS2-Net* (mean pool) [24]44.472.182.214.643.770.880.411.6393.6
ours (mean pool)46.172.881.814.444.873.782.49.9401.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.354, + 0.893, + 0.385 + ], + "angle": 0, + "content": "Table 4: Comparisons with state-of-the-arts on MSRVTT. † both CLIP4Clip and CenterCLIP have multiple versions in their papers, here we choose the versions with the highest Meta Sum. * denotes the results reproduced by official code & setting." + }, + { + "type": "table", + "bbox": [ + 0.123, + 0.395, + 0.853, + 0.545 + ], + "angle": 0, + "content": "
MethodsText ⇒ VideoVideo ⇒ TextMeta Sum ↑
R@1↑R@5↑R@10↑MnR ↓R@1R@5↑R@10↑MnR ↓
cross-modal temporal fusion
CLIP2TV [14]47.076.585.110.1-----
CLIP2Video [12]47.076.885.99.658.785.691.64.3445.6
X-CLIP [28]47.177.8-9.560.987.8-4.7-
X-Pool [16]47.277.486.09.366.490.094.23.3461.2
text-agnostic temporal pooling
CLIP4Clip† (seqTransf) [27]45.275.584.310.362.087.392.64.3446.9
CenterCLIP† (spectral) [57]47.476.585.29.762.788.192.84.1452.7
ours (mean pool)47.176.986.19.568.591.895.62.8466.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.554, + 0.893, + 0.584 + ], + "angle": 0, + "content": "Table 5: Comparisons with state-of-the-arts on MSVD. † both CLIP4Clip and CenterCLIP have multiple versions in their papers, here we choose the versions with the highest Meta Sum values." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.607, + 0.471, + 0.76 + ], + "angle": 0, + "content": "achieves 45.4 in R@1. Our final model containing the Auxiliary Captioning Loss further improves the performance in R@1, R@5, R@10, and MnR by a large margin. These results demonstrate that all the proposed components contribute clearly to the final performance. Besides, we also compare the performance of an alternative temporal aggregation method to Prompt Aggregation termed Temporal Transformer, which adopts an additional transformer layer on the [CLS] embeddings of all video frames and averages the output. From Table 1, Prompt Aggregation is better than Temporal Transformer on all metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.77, + 0.471, + 0.868 + ], + "angle": 0, + "content": "Comparison on Temporal Modeling Methods To investigate the effectiveness of our temporal modeling method, i.e., Prompt Switch + Prompt Aggregation, we compare it with other four temporal modeling methods, including the Temporal Transformer, Full Attention (attention over patch tokens from all video frames), Token Shift [24], and Video Proxy [52]. All methods are implemented on the baseline" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.607, + 0.892, + 0.704 + ], + "angle": 0, + "content": "CLIP model without extra components like the Token Selection Transformer in [24], and are trained using our default setting. From Table 2, our Prompt Switch & Aggregation approach outperforms all the baselines on R@1, R@5, and MnR while achieving the second-best result on R@10, which demonstrates its superiority in learning global video semantics across frames." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.714, + 0.893, + 0.868 + ], + "angle": 0, + "content": "Cross-Modal Temporal Fusion vs. Naive Mean Pooling While our method is able to achieve significantly better performance than the baseline CLIP using the mean-pooling setting, we further investigate whether it is compatible with the advanced cross-modal temporal fusion methods, namely, attention pooling, top-3 pooling, and X-Pool [16]. We simply replace the final mean-pooling in Eq. (3) with these cross-modal approaches and show the performance in Table 3. From the table, when adopting these cross-modal fusion methods, our models obtain clearly boosted performance, especially for X-Pool, which obtains the best per" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.887, + 0.506, + 0.898 + ], + "angle": 0, + "content": "15654" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.123, + 0.124, + 0.852, + 0.273 + ], + "angle": 0, + "content": "
MethodsText ⇒ VideoVideo ⇒ TextMeta Sum ↑
R@1↑R@5↑R@10↑MnR↓R@1↑R@5↑R@10↑MnR↓
cross-modal temporal fusion
X-Pool [16]25.243.753.553.222.742.651.247.4238.9
TS2-Net [24]23.442.350.956.9-----
EMCL [18]23.942.450.9-22.240.649.2-229.2
X-CLIP [28]23.343.0-56.022.542.2-50.7-
text-agnostic temporal pooling
CLIP4Clip† (seqLSTM) [27]21.641.849.858.020.940.749.153.9223.9
CenterCLIP† (k-medoids++) [57]21.941.150.755.621.141.250.248.7226.2
ours (mean pool)23.141.750.556.822.040.850.351.0228.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.281, + 0.893, + 0.311 + ], + "angle": 0, + "content": "Table 6: Comparisons with state-of-the-arts on LSMDC. † both CLIP4Clip and CenterCLIP have multiple versions in their papers and here we choose the versions with the highest Meta Sum values." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.331, + 0.47, + 0.4 + ], + "angle": 0, + "content": "formance for both text-video and video-text retrieval and outperforms the original X-Pool by a large margin. Moreover, even compared with the state-of-the-art cross-modal fusion methods, our model with naive mean-pooling is still competitive for both text-video and video-text retrieval." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.401, + 0.471, + 0.595 + ], + "angle": 0, + "content": "We further measure the memory usage and latency of the compared methods during inference on the test set. To make the experiment setting close to real-world scenarios and for fair comparisons, we use the same pre-computed frame and text representations while only monitoring space and time consumption for the ranking procedure. As shown in the last column of Table 3, our model with mean-pooling is orders of magnitude more efficient than those baseline models with cross-modal temporal fusion. This conclusion is generalizable to other datasets, i.e., the same model will always have the same ranking efficiency if using the same inference and evaluation settings. This reveals the importance of using text-agnostic temporal fusion (e.g., mean-pooling) for real-world text-video retrieval." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.609, + 0.406, + 0.625 + ], + "angle": 0, + "content": "4.2. Comparison with the State-of-the-arts" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.632, + 0.47, + 0.868 + ], + "angle": 0, + "content": "In this section, we compare our proposed method with state-of-the-art methods on MSRVTT, MSVD, and LSMDC dataset. To better reveal the performance gap among the compared methods, we do not consider post-processing techniques like QB-NORM [2]. The results of both text-video and video-text retrieval tasks are presented in Tables 4, 5 and 6. From the tables, when compared under the text-agnostic temporal fusion setting, our model outperforms the baseline models on most of the evaluation metrics, especially for Meta Sum, where it achieves the best performance on all three datasets. Specifically, on MSRVTT, the Meta Sum of our model is 7 points better than the second-best model; on MSVD, our method outperforms CenterCLIP [57] by 13.3; On LSMDC, our model consistently achieves the highest Meta Sum. Moreover, when compared with methods using cross-modal temporal fusion, our model with mean-pooling is still competitive in terms" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.328, + 0.691, + 0.383 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.328, + 0.892, + 0.383 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.532, + 0.387, + 0.861, + 0.398 + ], + "angle": 0, + "content": "(a) \\(\\mathbb{R}@\\mathbb{1}\\) performance with different number of decoder layers" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.41, + 0.693, + 0.47 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.41, + 0.891, + 0.47 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.518, + 0.474, + 0.875, + 0.485 + ], + "angle": 0, + "content": "(b) R@1 performance with different number of subsampling frames" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.497, + 0.692, + 0.554 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.701, + 0.497, + 0.89, + 0.554 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.527, + 0.558, + 0.865, + 0.57 + ], + "angle": 0, + "content": "(c) \\( \\mathrm{R}@\\mathrm{l} \\) performance with different value of hyper-parameter \\( \\lambda \\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.58, + 0.892, + 0.623 + ], + "angle": 0, + "content": "Figure 5: We show the effects of (a) the number of captioning decoder layers; (b) the number of subsampling frames \\( k \\) in training; (c) the values of hyper-parameter \\( \\lambda \\) in Eq. (6)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.65, + 0.892, + 0.777 + ], + "angle": 0, + "content": "of Meta Sum, while being much more efficient in practice (refer to Figure 1 and Table 3 for detailed discussions). Specifically, on MSRVTT, it outperforms CLIP2TV [14] and CLIP2Video [12]; on MSVD, it surpasses all compared baselines and improves over the second-best model (X-Pool [16]) by 4.8; on LSMDC, it is still comparable with EMCL [18]. These results show that our proposed method has a better trade-off between performance and efficiency, and is more suitable for large-scale production systems." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.789, + 0.691, + 0.803 + ], + "angle": 0, + "content": "4.3. Further Discussions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.893, + 0.868 + ], + "angle": 0, + "content": "Number of Decoder Layers Generally, more layers in the captioning decoder would improve its capacity for learning fine-grained knowledge, which, however, also makes it easier to over-fit. To find a better trade-off, we study the" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.505, + 0.898 + ], + "angle": 0, + "content": "15655" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.126, + 0.47, + 0.196 + ], + "angle": 0, + "content": "effect of the number of layers. As shown in Figure 5(a), the performance of our model improves and reaches the peak with 3 layers of decoder for both text-video and video-text retrieval tasks. Thus, we set the number of decoder layers to 3 for all the experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.218, + 0.47, + 0.384 + ], + "angle": 0, + "content": "Number of Subsampling Frames In practice, we set the number of training frames as 6 and validation frames as 12. Then, we randomly sample \\( k \\) frames before mean-pooling for training while using all 12 frames for evaluation. Notably, if \\( k = 6 \\), that means we average all the training frames in the mean-pooling operation. In Figure 5(b), we observe that the performance improves when reducing the value of \\( k \\) and achieves the peak when \\( k = 3 \\), which demonstrates its effectiveness. While further decreasing the value of \\( k \\), the mean-pooling operation may lose a great deal of semantics derived from frames, which causes performance degradation. Therefore, we set \\( k = 3 \\) for all the experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.405, + 0.47, + 0.516 + ], + "angle": 0, + "content": "Hyper-parameter \\(\\lambda\\) in Eq. (6) From Figure 5(c), in the case of a small \\(\\lambda\\) (e.g., \\(\\lambda = 0.3\\)), the model can only achieve suboptimal performance due to insufficient exploitation of the detailed semantics. When increasing the value of \\(\\lambda\\), the performance of our model peaks at the \\(\\lambda = 0.5\\) and degrades thereafter. Considering the trade-off between typical contrastive loss and captioning loss, we choose the weighting parameter \\(\\lambda\\) as 0.5 for all the datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.532, + 0.196, + 0.546 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.556, + 0.469, + 0.75 + ], + "angle": 0, + "content": "In this paper, we tackle the task of text-video retrieval, where we aim to learn semantically-enhanced representations purely from the video, allowing for offline computation and reuse for different text queries. Our method introduces a new Prompt Cube into the CLIP image encoder, which is iteratively transposed within the encoder layers to incorporate global video semantics into frame representations. We also adopt an auxiliary video captioning objective to optimize the frame representations, providing detailed guidance in the semantic space. With mean pooling fusion on the enhanced frame representations, the proposed model achieves SoTA performance on three benchmark datasets. Comprehensive experiments verify the effectiveness of all critical components of our proposed method." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.764, + 0.173, + 0.779 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.085, + 0.787, + 0.469, + 0.826 + ], + "angle": 0, + "content": "[1] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. Frozen in time: A joint video and image encoder for end-to-end retrieval. In ICCV, pages 1728-1738, 2021." + }, + { + "type": "ref_text", + "bbox": [ + 0.086, + 0.827, + 0.469, + 0.867 + ], + "angle": 0, + "content": "[2] Simion-Vlad Bogolin, Ioana Croitoru, Hailin Jin, Yang Liu, and Samuel Albanie. Cross modal retrieval with querybank normalisation. 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A critical problem for them is how to effectively capture the rich semantics inside the video using the image encoder of CLIP. To tackle this, state-of-the-art methods adopt complex cross-modal modeling techniques to fuse the text information into video frame representations, which, however, incurs severe efficiency issues in large-scale retrieval systems as the video representations must be recomputed online for every text query. In this paper, we discard this problematic cross-modal fusion process and aim to learn semantically-enhanced representations purely from the video, so that the video representations can be computed offline and reused for different texts. Concretely, we first introduce a spatial-temporal "Prompt Cube" into the CLIP image encoder and iteratively switch it within the encoder layers to efficiently incorporate the global video semantics into frame representations. We then propose to apply an auxiliary video captioning objective to train the frame representations, which facilitates the learning of detailed video semantics by providing fine-grained guidance in the semantic space. With a naive temporal fusion strategy (i.e., mean-pooling) on the enhanced frame representations, we obtain state-of-the-art performances on three benchmark datasets, i.e., MSR-VTT, MSVD, and LSMDC. + +# 1. Introduction + +Text-video retrieval [1, 6, 30, 42] is a fundamental task in the area of video-language understanding that seeks to find the most relevant video from a large set of candidates to match a text query. With the rapid growth of video data, text-video retrieval has become increasingly important for various applications, including video recommendation [36, 43], video search [20, 45], and video summa + +![](images/3e23a35dbe4e05e843156b477ea34fc6d67a3b12eb6f487eb9c86f1d9b6d889b.jpg) +Figure 1: The performance (i.e., R@1), retrieval time, and memory usage during retrieval for baseline models and ours on the MSRVTT dataset. The center of the bubble indicates the value of R@1. The diameter of the bubble or star is proportional to the memory usage (GB) while the horizontal axis indicates the inference time (s). + +rization [7, 29, 31, 33, 37, 47]. Due to the high cost of constructing text-video datasets, one promising approach for this task is to leverage pre-trained text-image foundation models and transfer their powerful representation capabilities to the video domain. Specifically, the CLIP [34] model, which is trained using a text-image alignment objective, is particularly suitable for text-video retrieval and has been frequently studied recently [27, 46, 16]. It has two transformer encoders [38, 9] to process images and texts, respectively. A vector representation is extracted from the input of each modality with the corresponding encoder and is optimized to be close to its paired representation and away from the unpaired ones. + +Adapting CLIP to the video domain is non-trivial and requires careful consideration of both efficiency and effectiveness. In CLIP4Clip [27], the authors directly mean-pool the frame representations extracted by the CLIP image encoder to get the video representation and use it to calculate the cosine similarity with the text representations during retrieval. However, the mean-pooling of frame representations may lose some essential semantic details of the video and hamper the retrieval performance. Thus, more advanced meth + +ods, such as [14, 16, 18, 24, 28], generate the video representation by applying various cross-modal temporal fusion approaches on the frame representations, using text queries as the condition. While achieving state-of-the-art results, these methods encounter severe efficiency issues in practice, as the text-conditioned fusion of each video has to be performed on-the-fly for every incoming text query. Even with a lightweight fusion module (compared to the CLIP backbone), its computation cost grows geometrically as the number of videos and texts increases. + +Formally, given a query set of $N_{t}$ texts with an average length of $N_{w}$ words and a candidate set of $N_{v}$ videos where each video contains $N_{f}$ frames. Then, the space and time complexities are $\mathcal{O}(N_vN_tN_f)$ for the text-conditioned fusion in X-Pool [16] and TS2-Net [24], and $\mathcal{O}(N_vN_tN_fN_w)$ for that of X-CLIP [28]. While for CLIP4Clip, the complexity is $\mathcal{O}(N_vN_t)$ as it only requires a simple dot-product between the text and mean-pooled frame representations, although its performance is inferior to X-Pool and X-CLIP. To better reveal this gap, we show an example in Figure 1 about the real-world efficiency of several methods while omitting the backbone computation. Here, we set $N_{v} = 16384$ , $N_{t} = 512$ , $N_{f} = 12$ , and $N_{w} = 10$ . From the figure, with large $N_{t}$ and $N_{v}$ , the latency and memory consumption for text-conditioned temporal fusion methods [16, 24, 28] are orders of magnitude higher than text-agnostic temporal fusion (i.e., mean-pooling) [27, 57], and can rapidly become enormous in large-scale scenarios. + +On the other hand, the backbone computation of CLIP is much less of a burden in real-world retrieval systems, as the frame representations of the video can be pre-computed offline and reused for different text queries. Therefore, a more practical CLIP-based text-video retrieval method should focus on improving the backbone representation ability while keeping the cross-modal interaction as simple as possible. Motivated by this, we propose a simple and efficient adaptation method for CLIP to facilitate its ability to capture both the global and detailed semantics of videos. + +Concretely, we first feed a tiny ( $\sim 0.1\mathrm{M}$ ) "Prompt Cube" into the image encoder of CLIP, which is a 3D tensor spanning over the spatial, temporal, and channel axis, as shown in the right of Figure 2. $^{1}$ It is designed to have the same temporal and spatial sizes and is concatenated with the patch tokens alongside the spatial axis. To propagate temporal semantics among different frames, we switch the spatial and temporal dimensions of the prompt cube before each self-attention layer, so that the prompt cube builds up a peer-to-peer connection between every two-frame pair. In this way, our modified CLIP model enjoys an improved global semantic modeling ability thanks to the comprehensive spatial-temporal modeling between the prompt cube and the patch tokens of all frames, while only bringing neg- + +ligible extra parameters and computations. This also allows the prompt cube to serve as a compact summarization of the whole video, and further enables us to design a CLIP-guided Prompt Aggregation approach and obtain the frame representations from the prompt cube. Then, we use naive mean-pooling instead of cross-modal fusion on these frame representations to get the final video representation. + +Moreover, since we will not use any fine-grained cross-modal interaction modules in our model, we adopt an Auxiliary Video Captioning objective as an alternative to provide fine-grained guidance in the semantic space when learning video representations. Specifically, we introduce a light captioning head on top of our modified CLIP image encoder during training, which takes the frame representations aggregated from the prompt cube as input and generates the paired text of the input video. This auxiliary objective plays a critical role because CLIP's original contrastive learning objective is relatively easy to fit due to the lack of in-batch negatives during training (which is generally the case in text-video retrieval). During inference, the light captioning branch is removed, thus it incurs no extra computation and memory consumption. + +We verify the effectiveness of the proposed method on three text-video retrieval benchmarks, i.e. MSR-VTT [50], MSVD [4], and LSMDC [35], where our method consistently achieves state-of-the-art performance while being significantly more efficient than the previous state of the arts. We also provide extensive performance analyses to show the superiority of our proposed method. + +# 2. Related Work + +Text-video retrieval is one of the fundamental tasks in video-language modeling and has lots of applications in the industry. Here, we broadly classify the previous works into three categories and briefly review them below. + +Off-the-Shelf Single-Modal Representations An early trend in text-video retrieval is to use the off-the-shelf video (e.g., I3D [3]) and text representations (e.g., GloVe [32]) and design sophisticated feature encoding methods or multi-modal fusion mechanisms on them to improve the retrieval performance [6, 8, 19, 54, 55]. For example, in [6], a hierarchical graph reasoning approach is proposed to decompose video-text matching into global-to-local levels and disentangle texts into a hierarchical semantic graph with three levels of events, actions, and entities. Yu et al. [54] propose a joint sequence fusion model for the sequential interaction of videos and texts. Dong et al. [8] leverages multi-level single-modal features that represent the rich content of both video and text in a coarse-to-fine fashion. However, their performances are limited due to the mismatched training objectives between the pre-computed representations and the text-video retrieval task. + +![](images/127eb9451882f31302958f9ba1fd2195f633da5a7738114f2eace6b9cd94019c.jpg) +Figure 2: Overall architecture. For a video clip with $N_{f}$ frames, we accompany it with $N_{f} \times N_{f}$ prompt tokens, resulting in a 3D prompt cube. We show the Prompt Switch operation on the right. For simplicity, we omit the feed-forward network and shot-cut connections in the ViT layer. We provide more details for Prompt Aggregation in Figure 4. $\otimes$ is cosine similarity. + +Video-Language Pre-training To reduce the gap between pre-training and downstream tasks, large-scale pretrained video-language representations have been proposed, such as [1, 13, 15, 21, 26, 40, 48, 49, 51]. Most of these models are pre-trained on the large-scale video-text datasets, e.g., HowTo100M [30] and WebVid-2M [1], which boosts promising cross-modal video understanding [22, 23, 26]. One line of works [1, 13, 49] uses two independent encoders for video and text and then projects them into a common latent space. These methods often adopt a contrastive loss to distinguish the paired video-text data. For example, Bain et al. [1] design an end-to-end trainable model, aiming to take advantage of both large-scale image and video captioning datasets. Gabeur et al. [13] propose a multi-modal transformer that can extract features at different moments and from different modalities (e.g., audio or speech) in a video. The other line of works [21, 26, 48] employs a single cross-modal encoder, which concatenates the video and text sequences as inputs and models them jointly in the transformer, followed by a binary classifier predicting whether these videos and texts are aligned. Despite they can build fine-grained associations between video-text tokens, they need to input each video-text candidate pair into the model for matching score calculation during inference and thus hampers efficiency. Besides, although the idea of video-language pre-training is promising, due to the high cost of collecting wild videos, its scale is generally much smaller than image-language pre-training, leading to an unsatisfactory generalization ability. Thus, like [16, 27], we seek to boost from the image-language pre-training model (e.g., CLIP [34]) for text-video retrieval. + +CLIP-based Adaptation. Recently, due to the great advantage of CLIP [34] for vision-and-language representation learning, many works [11, 14, 17, 18, 28, 41, 52, 56] seek to transfer the knowledge of CLIP to text-video retrieval tasks. Roughly, the existing works transfer CLIP from views of feature aggregation [12, 16, 27, 28, 57], representation alignment [12, 28, 41], and post pretraining [46, 52]. Specifically, X-Pool [16] designs a cross-modal attention model, seeking to enable the model to only focus on the relevant video frames conditioned on a given text. TS2-Net [24] adapts CLIP by introducing a token shift module and a token selection module, which capture the temporal information and remove unimportant tokens, respectively. X-CLIP [28] calculates both the coarse- and fine-grained similarity for higher retrieval accuracy. While these methods can be effective, their retrieval efficiency is low due to the coupling of video and text in the cross-modal fusion process. A more ideal way should focus on improving the representation ability of the backbone while maintaining the cross-modal interaction as efficiently as possible. We follow this principle in our method. + +# 3. Method + +The overview of our method is shown in Figure 2. It is based on a pre-trained CLIP with a ViT [10]-based image encoder. Given an input video, we first split each video frame into fix-sized non-overlapping patches and linearly project them into 1D patch embeddings. Following CLIP, a [CLS] embedding is concatenated to the embedding sequence of each frame, which is pre-trained to capture the local semantics within the sequence. Then, in the ViT en + +coder, our proposed "Prompt Cube" bridges the global semantic information from the patch embeddings of all frames through a Prompt Switch operation. After that, we feed the output [CLS] embeddings of the video frames and the final prompt cube into a Prompt Aggregation module, where the prompt cube is aggregated into 1D vectors according to the [CLS] embeddings, and is further enhanced with fine-grained semantics through an Auxiliary Captioning Objective. To ensure an efficient measurement of the text-video similarity, we avoid using cross-modal fusion modules and directly average these aggregated vectors into the final video representation. A simple dot product operation is used to compute the similarity. More details are in the following. + +# 3.1. Prompt Cube for Bridging Global Semantics + +At the core of our method is the proposed Prompt Cube. It is designed to capture the rich temporal semantics of the whole video while bringing negligible modifications and computations to the CLIP image encoder. Formally, given an input video clip with $N_{f}$ frames, we first obtain its patch embeddings $V \in \mathbb{R}^{N_f \times L \times D}$ , where $L$ indicates the size of the spatial dimension, i.e., the number of patches divided from a video frame plus one [CLS] embedding. $D$ is the embedding size. Then, our prompt cube is constructed as a 3D tensor $P \in \mathbb{R}^{N_f \times N_f \times D}$ . At the start of the ViT layer, we concatenate $V$ and $P$ alongside the spatial dimension, denoted by $[V; P] \in \mathbb{R}^{N_f \times (L + N_f) \times D}$ , and then process them jointly. The first two dimensions of $P$ (corresponding to the temporal and spatial axis, respectively) have the same size, thus they can be transposed flexibly without altering the shape of $P$ . This allows us to further propose an efficient Prompt Switch operation to exchange the local spatial semantics of each frame and the global temporal semantics from the whole video through the prompt cube. + +Prompt Switch The proposed Prompt Switch operation can be defined in a one-line formula: + +$$ +\mathcal {T} := [ V; P ] \rightarrow [ V; P ^ {\top} ]. \tag {1} +$$ + +See the right of Figure 2, we apply this operation before every self-attention layer of the ViT encoder. Then, self-attention is performed over the spatial dimension of $[V;P]$ , where the $i$ -th row of the prompt cube (denoted by $\pmb{p}_i \in \mathbb{R}^{1 \times N_f \times D}$ ) and the patch embeddings of the $i$ -th frame (denoted by $\pmb{v}_i \in \mathbb{R}^{1 \times L \times D}$ ) acquire information from each other. In this way, for two consecutive ViT layers in the encoder, each element in the prompt cube (denoted by $\pmb{p}_{i,j} \in \mathbb{R}^D$ ) is first attached to the $i$ -th frame and communicates with $\pmb{v}_i$ , and then switch to the $j$ -th frame and communicates with $\pmb{v}_j$ . By repeatedly performing this operation, the whole prompt cube builds up a peer-to-peer + +![](images/c7b333532b12e1a77b81ac4444b6cdcb265642215398379925589530101c858e.jpg) +Figure 3: Video Proxy adopts a shared "prompt" to exchange information among all frames (b). Differently, our Prompt Switch method builds up a peer-to-peer connection between every two-frame pair (a) to obtain more comprehensive spatial-temporal modeling. This improves the representation ability of CLIP on video data. Besides, our method may also ease the learning problem as each element in the prompt cube only needs to handle the information of two frames instead of the whole video, thus improving the optimization ability of CLIP on video data. + +![](images/82fd31b840db1242d32a310659d91d786bd89a580aca215f3e708ea064f5f92b.jpg) + +connection between every two-frame pair in the video clip, enabling comprehensive temporal modeling. + +Some previous text-video retrieval methods have also attempted to introduce temporal adaptation to the backbone of the CLIP ViT encoder, such as Token Shift [24] and Video Proxy [52]. Specifically, the Token Shift method shifts token embeddings from adjacent frames to the current frame, which fails to model the temporal semantics from a global perspective. Moreover, it damages the spatial modeling ability of the original CLIP as the information contained in the shifted tokens is no longer accessible in the current frame. In Video Proxy, the information from all video frames is exchanged using several proxy embeddings, which lack peer-to-peer connections within the frames and thus can be inferior in the temporal modeling capacity. We illustrate the importance of building peer-to-peer connections in Figure 3. Besides, a naive full-attention approach has also been investigated where no adaptation is applied to the CLIP model except allowing its self-attention layers to attend to the patch tokens from the whole video. However, this approach is neither effective due to the domain gap between the input data (video) and the pre-training data (image), nor efficient since the computation complexity of the self-attention layers grows quadratically w.r.t. the number of attended patch tokens. We show the superiority of our proposed prompt cube to these previous methods in Section 4.1. + +Prompt Aggregation As the prompt cube acquires the global semantics through a comprehensive interaction with all patch embeddings, it can serve as a compact summariza + +tion of the video. Therefore, we propose to obtain the final video representation from the prompt cube, instead of the [CLS] embedding as the original CLIP. To achieve this, we design a CLIP-guided Prompt Aggregation module, which aggregates the output prompt cube into 1D vectors according to the final [CLS] embeddings of the video frames. It is a lightweight multi-head attention (MHA) layer placed before the last layer normalization (LN) layer of the ViT encoder. The [CLS] embedding of the $i$ -th frame (denoted by $\pmb{c}_i \in \mathbb{R}^{1 \times D}$ ) is used as the "query" while the "key" and "value" are both the prompt cube flattened over the temporal and spatial dimensions, denoted by $\hat{\pmb{P}} \in \mathbb{R}^{N_f^2 \times D}$ . Let $\bar{p}_i \in \mathbb{R}^{1 \times D}$ be the aggregated prompt vector for the $i$ -th frame, we have + +$$ +\bar {p} _ {i} := \mathrm {L N} \left(\boldsymbol {c} _ {i} + \operatorname {M H A} \left(\boldsymbol {c} _ {i}, \hat {\boldsymbol {P}}, \hat {\boldsymbol {P}}\right)\right), \quad \forall i \in [ 1, N _ {f} ], \tag {2} +$$ + +where LN denotes the last layer normalization layer of the CLIP ViT encoder. Notably, the last linear projection weight in the MHA layer is initialized as a 0 tensor to ensure that $\bar{p}_i$ is optimized from the original output of the CLIP image encoder. The final video representation is the naive mean-pooling of the normalized prompt vectors, i.e., + +$$ +\boldsymbol {x} := \frac {1}{N _ {f}} \sum_ {i = 1} ^ {N _ {f}} \frac {\bar {\boldsymbol {p}} _ {i}}{\| \bar {\boldsymbol {p}} _ {i} \|}. \tag {3} +$$ + +We provide a detailed illustration for the Prompt Aggregation module on the left of Figure 4. To enhance the learning of temporal information for the prompt cube, inspired by [58], we adopt a frame sampling strategy where we randomly sample $k < N_f$ prompt vectors for the final mean-pooling operation in Eq. (3) during training. + +# 3.2. Learning Detailed Semantics via Captioning + +As we have discussed in Section 1, the key criterion in the design of our model architecture is to ensure the model contains no extra cross-modal interaction procedure during inference except computing the cosine similarity between text and video representations. While this ensures the efficiency of the similarity measurement in large-scale production systems, it also prevents the video representation from utilizing the fine-grained semantic information from the text query. To aid this, inspired by [5, 53], we propose to learn our video representation with an Auxiliary Captioning objective, which alternatively provides fine-grained guidance in the semantic space during training. + +Auxiliary Captioning Head As shown on the right of Figure 4, the Auxiliary Captioning Head, denoted by $\mathcal{H}$ , is a stack of $M$ transformer decoders. We first shift the text token by one step to the right, and feed it into a Masked MHA layer, where each text token only attends to its preceding + +![](images/6809609bbbe0a770b989fc954f692f79003a451ced44a72e0eb8ffc339bf69d9.jpg) +Figure 4: Detailed architecture of Prompt Aggregation (left) and Auxiliary Captioning Head (right). + +tokens. Then, another MHA layer is used, where the text tokens attend to the aggregated prompt vectors $\{\overline{p_i}\}_{i = 1}^{N_f}$ . The model is trained via the autoregressive Teacher Forcing [44] scheme, i.e., the prediction in each step should maximize the likelihood of the token in the next step: + +$$ +\mathcal {L} _ {c a p} = \sum_ {l = 1} ^ {N _ {w}} - \log p \left(w _ {l} \mid w _ {< l}, \left\{\bar {\boldsymbol {p}} _ {i} \right\} _ {i = 1} ^ {N _ {f}}\right), \tag {4} +$$ + +where $w_{l}$ indicates the $l$ -th token in the text, and $w_{MethodR@1↑R@5↑R@10↑MnR↓baseline CLIP43.170.980.416.0+ Prompt Switch44.8 (+1.7)71.980.915.2+ Temporal Transformer44.271.481.115.6+ Prompt Aggregation45.4 (+0.6)71.981.114.9+ Captioning Loss46.1 (+0.7)72.881.814.4 + +Table 1: Performance analysis of our model components for text-video retrieval on MSRVTT 1K-A test set. Both Prompt Aggregation and Temporal Transformer are applied on top of our Prompt Switch. The Captioning Loss is applied only on top of the Prompt Aggregation. + +
MethodR@1↑R@5↑R@10↑MnR↓
Temporal Transformer44.271.481.115.6
Token Shift [24]43.270.779.815.9
Video Proxy [52]45.271.081.515.3
Full Attention43.871.480.916.4
Prompt Switch & Aggregation45.471.981.114.9
+ +tion (obtained by Eq. (3) and text representation of the $i$ -th video-text pair in the mini-batch. The final loss function is + +$$ +\mathcal {L} = \mathcal {L} _ {\text {c o n}} + \lambda \mathcal {L} _ {\text {c a p}}, \tag {6} +$$ + +where $\lambda$ is the weighting hyper-parameter. + +# 4. Experiment + +Dataset and Metrics We evaluate the effectiveness of our method on three widely used text-video retrieval datasets, including MSR-VTT [50], MSVD [4] and LSMDC [35]. MSR-VTT [50] consists of 10,000 videos with 200K descriptions. We follow the setting in previous works [13, 54], training our models with 9,000 videos and evaluating them on the 1K-A test set. MSVD [4] contains 1,970 videos with about 120K captions, where the train, validation, and test splits contain 1, 200, 100 and 670 videos, respectively. LSMDC [35] has 118,081 video-caption pairs, where 109, 673 videos are used for training, 7, 408 videos for validation, and 1, 000 videos for testing. Following [16, 24, 27], we report the results of Recall@ $K$ ( $R@K$ , $K = 1, 5, 10$ ) and Mean Rank (MnR) for quantitative evaluation. Besides, we sum the value of $R@1$ , $R@5$ , and $R@10$ for both text-video and video-text retrieval tasks as an overall evaluation metric, named Meta Sum. + +Implementation Details Following previous work [16, 27], both the text and video encoders are initialized with the pre-trained CLIP (ViT-B/32) [34]. The prompt cube is randomly initialized from a Gaussian distribution with a zero mean and 0.02 std. During training, we uniformly sample + +Table 2: Comparisons with other temporal modeling methods for text-video retrieval on MSRVTT 1K-A test set. + +
MethodR@1↑R@5↑R@10↑Mem. / Time
Text ⇒ Video
TS2-Net* [24]46.573.683.30.3G / 0.2s
X-Pool [16]46.972.882.23.9G / 3.9s
ours (mean pool)46.172.881.82.0M / 8.1ms
ours (attention pool)46.472.982.40.2G / 0.2s
ours (top-3 pool)46.773.482.00.3G / 0.3s
ours (X-Pool [16])47.873.982.23.9G / 3.9s
Video ⇒ Text
TS2-Net* [24]44.573.883.20.3G / 0.2s
X-Pool [16]44.473.384.03.9G / 3.9s
ours (mean pool)44.873.782.42.0M / 8.1ms
ours (attention pool)45.473.983.20.2G / 0.2s
ours (top-3 pool)45.273.683.70.3G / 0.3s
ours (X-Pool [16])46.074.384.83.9G / 3.9s
+ +Table 3: Performance and complexity comparisons with different temporal fusion methods on MSRVTT 1K-A test set. * denotes the results reproduced by official code & setting. + +6 frames from each video and resize all video frames into $224 \times 224$ . Therefore, the size of the spatial and temporal dimensions of the prompt cube is set to 6 by default. While for the testing, 12 frames are used as in previous works, so we split them into two 6-frame chunks through interval sampling to make the temporal dimension compatible with the prompt cube. The Prompt Aggregation is applied on the prompt cubes of all chunks. The number of decoder layers in the captioning head is 3. The hyper-parameter $k$ used for frame sampling in Eq. (3) is set to 3. We set the hyperparameter $\lambda = 0.5$ in Eq. (6). The training epochs are 10 for all the datasets with a batch size of 128. We use AdamW optimizer [25] with a learning rate of 3e-5 and adopt a cosine decay strategy for the learning rate. + +# 4.1. Performance Analysis + +We first thoroughly analyze the model designs and critical components of our proposed method and then verify their effectiveness. The experiments are conducted on the MSRVTT dataset and evaluated on the 1K-A test set. + +Model Components As shown in Table 1, we conduct an ablation study on the Prompt Switch, Prompt Aggregation, and Auxiliary Captioning Objective by introducing them gradually into the model for text-video retrieval. The baseline CLIP model directly uses the mean-pooled [CLS] embeddings of the video frames as the final video representation, and is trained using only contrastive loss. Specifically, when incorporating the Prompt Switch mechanism, the result of R@1 increases significantly (i.e., from 43.1 to 44.8) compared with the baseline CLIP, which demonstrates the effectiveness of the proposed Prompt Switch. With the help of Prompt Aggregation, it further improves 0.6 and + +
MethodsText ⇒ VideoVideo ⇒ TextMeta Sum ↑
R@1 ↑R@5 ↑R@10 ↑MnR ↓R@1R@5 ↑R@10 ↑MnR ↓
cross-modal temporal fusion
CLIP2TV [14]46.172.582.915.243.973.082.811.1401.2
CLIP2Video [12]45.672.681.714.643.372.382.110.2397.6
TS2-Net* [24]46.573.683.313.944.573.883.29.2404.9
EMCL [18]46.873.183.1-46.573.583.5-406.5
X-CLIP [28]46.173.083.113.246.873.384.09.1406.3
DRL [41]47.474.683.8-45.373.983.3-408.3
X-Pool [16]46.972.882.214.344.473.384.09.0403.6
ours (X-Pool)47.873.982.214.146.074.384.88.5409.0
text-agnostic temporal pooling
CLIP4Clip† (seqTransf) [27]44.571.481.615.342.770.980.611.6391.7
CenterCLIP† (spectral) [57]44.271.682.115.142.871.782.211.1394.6
X-CLIP (mean pool) [28]43.070.781.616.343.070.281.211.5389.7
TS2-Net* (mean pool) [24]44.472.182.214.643.770.880.411.6393.6
ours (mean pool)46.172.881.814.444.873.782.49.9401.6
+ +Table 4: Comparisons with state-of-the-arts on MSRVTT. † both CLIP4Clip and CenterCLIP have multiple versions in their papers, here we choose the versions with the highest Meta Sum. * denotes the results reproduced by official code & setting. + +
MethodsText ⇒ VideoVideo ⇒ TextMeta Sum ↑
R@1↑R@5↑R@10↑MnR ↓R@1R@5↑R@10↑MnR ↓
cross-modal temporal fusion
CLIP2TV [14]47.076.585.110.1-----
CLIP2Video [12]47.076.885.99.658.785.691.64.3445.6
X-CLIP [28]47.177.8-9.560.987.8-4.7-
X-Pool [16]47.277.486.09.366.490.094.23.3461.2
text-agnostic temporal pooling
CLIP4Clip† (seqTransf) [27]45.275.584.310.362.087.392.64.3446.9
CenterCLIP† (spectral) [57]47.476.585.29.762.788.192.84.1452.7
ours (mean pool)47.176.986.19.568.591.895.62.8466.0
+ +Table 5: Comparisons with state-of-the-arts on MSVD. † both CLIP4Clip and CenterCLIP have multiple versions in their papers, here we choose the versions with the highest Meta Sum values. + +achieves 45.4 in R@1. Our final model containing the Auxiliary Captioning Loss further improves the performance in R@1, R@5, R@10, and MnR by a large margin. These results demonstrate that all the proposed components contribute clearly to the final performance. Besides, we also compare the performance of an alternative temporal aggregation method to Prompt Aggregation termed Temporal Transformer, which adopts an additional transformer layer on the [CLS] embeddings of all video frames and averages the output. From Table 1, Prompt Aggregation is better than Temporal Transformer on all metrics. + +Comparison on Temporal Modeling Methods To investigate the effectiveness of our temporal modeling method, i.e., Prompt Switch + Prompt Aggregation, we compare it with other four temporal modeling methods, including the Temporal Transformer, Full Attention (attention over patch tokens from all video frames), Token Shift [24], and Video Proxy [52]. All methods are implemented on the baseline + +CLIP model without extra components like the Token Selection Transformer in [24], and are trained using our default setting. From Table 2, our Prompt Switch & Aggregation approach outperforms all the baselines on R@1, R@5, and MnR while achieving the second-best result on R@10, which demonstrates its superiority in learning global video semantics across frames. + +Cross-Modal Temporal Fusion vs. Naive Mean Pooling While our method is able to achieve significantly better performance than the baseline CLIP using the mean-pooling setting, we further investigate whether it is compatible with the advanced cross-modal temporal fusion methods, namely, attention pooling, top-3 pooling, and X-Pool [16]. We simply replace the final mean-pooling in Eq. (3) with these cross-modal approaches and show the performance in Table 3. From the table, when adopting these cross-modal fusion methods, our models obtain clearly boosted performance, especially for X-Pool, which obtains the best per + +
MethodsText ⇒ VideoVideo ⇒ TextMeta Sum ↑
R@1↑R@5↑R@10↑MnR↓R@1↑R@5↑R@10↑MnR↓
cross-modal temporal fusion
X-Pool [16]25.243.753.553.222.742.651.247.4238.9
TS2-Net [24]23.442.350.956.9-----
EMCL [18]23.942.450.9-22.240.649.2-229.2
X-CLIP [28]23.343.0-56.022.542.2-50.7-
text-agnostic temporal pooling
CLIP4Clip† (seqLSTM) [27]21.641.849.858.020.940.749.153.9223.9
CenterCLIP† (k-medoids++) [57]21.941.150.755.621.141.250.248.7226.2
ours (mean pool)23.141.750.556.822.040.850.351.0228.4
+ +Table 6: Comparisons with state-of-the-arts on LSMDC. † both CLIP4Clip and CenterCLIP have multiple versions in their papers and here we choose the versions with the highest Meta Sum values. + +formance for both text-video and video-text retrieval and outperforms the original X-Pool by a large margin. Moreover, even compared with the state-of-the-art cross-modal fusion methods, our model with naive mean-pooling is still competitive for both text-video and video-text retrieval. + +We further measure the memory usage and latency of the compared methods during inference on the test set. To make the experiment setting close to real-world scenarios and for fair comparisons, we use the same pre-computed frame and text representations while only monitoring space and time consumption for the ranking procedure. As shown in the last column of Table 3, our model with mean-pooling is orders of magnitude more efficient than those baseline models with cross-modal temporal fusion. This conclusion is generalizable to other datasets, i.e., the same model will always have the same ranking efficiency if using the same inference and evaluation settings. This reveals the importance of using text-agnostic temporal fusion (e.g., mean-pooling) for real-world text-video retrieval. + +# 4.2. Comparison with the State-of-the-arts + +In this section, we compare our proposed method with state-of-the-art methods on MSRVTT, MSVD, and LSMDC dataset. To better reveal the performance gap among the compared methods, we do not consider post-processing techniques like QB-NORM [2]. The results of both text-video and video-text retrieval tasks are presented in Tables 4, 5 and 6. From the tables, when compared under the text-agnostic temporal fusion setting, our model outperforms the baseline models on most of the evaluation metrics, especially for Meta Sum, where it achieves the best performance on all three datasets. Specifically, on MSRVTT, the Meta Sum of our model is 7 points better than the second-best model; on MSVD, our method outperforms CenterCLIP [57] by 13.3; On LSMDC, our model consistently achieves the highest Meta Sum. Moreover, when compared with methods using cross-modal temporal fusion, our model with mean-pooling is still competitive in terms + +![](images/bba94add5c4feb1523c564bcda6f66d308f15b2303ac2325415acbb896eaee01.jpg) +(a) $\mathbb{R}@\mathbb{1}$ performance with different number of decoder layers + +![](images/eb1db2f7a06406b2d802c8b0c630a43d85113cc35b8e10a1a6c3d6c5bf540f91.jpg) + +![](images/22449661e7bd53de1d4938b4c9f0dff45b3e39cdb6a44398c9bde623da1eccee.jpg) +(b) R@1 performance with different number of subsampling frames + +![](images/211ec0cc2ba3c007d8c7077e33123532c4bd3b9bdaadf33aa8aa3fb0d4ae5549.jpg) + +![](images/2fdee8c2a3e805f602de70b86f014e8d74496978767905df18eff5e154612b9b.jpg) +(c) $\mathrm{R}@\mathrm{l}$ performance with different value of hyper-parameter $\lambda$ + +![](images/6896488aea93575cc41f73f9f6db5f21f215eaed94fe859e62e3f13e8a0cb343.jpg) +Figure 5: We show the effects of (a) the number of captioning decoder layers; (b) the number of subsampling frames $k$ in training; (c) the values of hyper-parameter $\lambda$ in Eq. (6). + +of Meta Sum, while being much more efficient in practice (refer to Figure 1 and Table 3 for detailed discussions). Specifically, on MSRVTT, it outperforms CLIP2TV [14] and CLIP2Video [12]; on MSVD, it surpasses all compared baselines and improves over the second-best model (X-Pool [16]) by 4.8; on LSMDC, it is still comparable with EMCL [18]. These results show that our proposed method has a better trade-off between performance and efficiency, and is more suitable for large-scale production systems. + +# 4.3. Further Discussions + +Number of Decoder Layers Generally, more layers in the captioning decoder would improve its capacity for learning fine-grained knowledge, which, however, also makes it easier to over-fit. To find a better trade-off, we study the + +effect of the number of layers. As shown in Figure 5(a), the performance of our model improves and reaches the peak with 3 layers of decoder for both text-video and video-text retrieval tasks. Thus, we set the number of decoder layers to 3 for all the experiments. + +Number of Subsampling Frames In practice, we set the number of training frames as 6 and validation frames as 12. Then, we randomly sample $k$ frames before mean-pooling for training while using all 12 frames for evaluation. Notably, if $k = 6$ , that means we average all the training frames in the mean-pooling operation. In Figure 5(b), we observe that the performance improves when reducing the value of $k$ and achieves the peak when $k = 3$ , which demonstrates its effectiveness. While further decreasing the value of $k$ , the mean-pooling operation may lose a great deal of semantics derived from frames, which causes performance degradation. Therefore, we set $k = 3$ for all the experiments. + +Hyper-parameter $\lambda$ in Eq. (6) From Figure 5(c), in the case of a small $\lambda$ (e.g., $\lambda = 0.3$ ), the model can only achieve suboptimal performance due to insufficient exploitation of the detailed semantics. When increasing the value of $\lambda$ , the performance of our model peaks at the $\lambda = 0.5$ and degrades thereafter. Considering the trade-off between typical contrastive loss and captioning loss, we choose the weighting parameter $\lambda$ as 0.5 for all the datasets. + +# 5. Conclusion + +In this paper, we tackle the task of text-video retrieval, where we aim to learn semantically-enhanced representations purely from the video, allowing for offline computation and reuse for different text queries. Our method introduces a new Prompt Cube into the CLIP image encoder, which is iteratively transposed within the encoder layers to incorporate global video semantics into frame representations. We also adopt an auxiliary video captioning objective to optimize the frame representations, providing detailed guidance in the semantic space. With mean pooling fusion on the enhanced frame representations, the proposed model achieves SoTA performance on three benchmark datasets. Comprehensive experiments verify the effectiveness of all critical components of our proposed method. + +# References + +[1] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. Frozen in time: A joint video and image encoder for end-to-end retrieval. In ICCV, pages 1728-1738, 2021. +[2] Simion-Vlad Bogolin, Ioana Croitoru, Hailin Jin, Yang Liu, and Samuel Albanie. Cross modal retrieval with querybank normalisation. In CVPR, pages 5194-5205, 2022. + +[3] Joao Carreira and Andrew Zisserman. Quo vadis, action recognition? a new model and the kinetics dataset. In CVPR, pages 6299-6308, 2017. +[4] David Chen and William B Dolan. Collecting highly parallel data for paraphrase evaluation. 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In ICCV, pages 408-417, 2017. \ No newline at end of file diff --git a/2023/Prompt Switch_ Efficient CLIP Adaptation for Text-Video Retrieval/images.zip b/2023/Prompt Switch_ Efficient CLIP Adaptation for Text-Video Retrieval/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..2c1d8e46718e9e3a3ae90448b14ad97a84e7e048 --- /dev/null +++ b/2023/Prompt Switch_ Efficient CLIP Adaptation for Text-Video Retrieval/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d944ecf8ba1df9838cc5b1f345594926e49dbb5e55787b1fda339390e6fcb0b1 +size 531622 diff --git a/2023/Prompt Switch_ Efficient CLIP Adaptation for Text-Video Retrieval/layout.json b/2023/Prompt Switch_ Efficient CLIP Adaptation for Text-Video Retrieval/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..7f8899df1306a4236df4f1541a90669bac738f9b --- /dev/null +++ b/2023/Prompt Switch_ Efficient CLIP Adaptation for Text-Video Retrieval/layout.json @@ -0,0 +1,8061 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 85, + 136, + 492, + 153 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 136, + 492, + 153 + ], + "spans": [ + { + "bbox": [ + 85, + 136, + 492, + 153 + ], + "type": "text", + "content": "Prompt Switch: Efficient CLIP Adaptation for Text-Video Retrieval" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 131, + 174, + 456, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 131, + 174, + 456, + 217 + ], + "spans": [ + { + "bbox": [ + 131, + 174, + 456, + 217 + ], + "type": "text", + "content": "Chaorui Deng" + }, + { + "bbox": [ + 131, + 174, + 456, + 217 + ], + "type": "inline_equation", + "content": "^{1,\\ast}" + }, + { + "bbox": [ + 131, + 174, + 456, + 217 + ], + "type": "text", + "content": ", Qi Chen" + }, + { + "bbox": [ + 131, + 174, + 456, + 217 + ], + "type": "inline_equation", + "content": "^{1,\\ast}" + }, + { + "bbox": [ + 131, + 174, + 456, + 217 + ], + "type": "text", + "content": ", Pengda Qin" + }, + { + "bbox": [ + 131, + 174, + 456, + 217 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 131, + 174, + 456, + 217 + ], + "type": "text", + "content": ", Da Chen" + }, + { + "bbox": [ + 131, + 174, + 456, + 217 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 131, + 174, + 456, + 217 + ], + "type": "text", + "content": ", Qi Wu" + }, + { + "bbox": [ + 131, + 174, + 456, + 217 + ], + "type": "inline_equation", + "content": "^{1,\\dagger}" + }, + { + "bbox": [ + 131, + 174, + 456, + 217 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 131, + 174, + 456, + 217 + ], + "type": "text", + "content": "Australia Institute of Machine Learning, University of Adelaide \nAlibaba Group, " + }, + { + "bbox": [ + 131, + 174, + 456, + 217 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 131, + 174, + 456, + 217 + ], + "type": "text", + "content": "Department of Computer Science, University of Bath" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 139, + 243, + 186, + 255 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 243, + 186, + 255 + ], + "spans": [ + { + "bbox": [ + 139, + 243, + 186, + 255 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 267, + 281, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 267, + 281, + 581 + ], + "spans": [ + { + "bbox": [ + 45, + 267, + 281, + 581 + ], + "type": "text", + "content": "In text-video retrieval, recent works have benefited from the powerful learning capabilities of pre-trained text-image foundation models (e.g., CLIP) by adapting them to the video domain. A critical problem for them is how to effectively capture the rich semantics inside the video using the image encoder of CLIP. To tackle this, state-of-the-art methods adopt complex cross-modal modeling techniques to fuse the text information into video frame representations, which, however, incurs severe efficiency issues in large-scale retrieval systems as the video representations must be recomputed online for every text query. In this paper, we discard this problematic cross-modal fusion process and aim to learn semantically-enhanced representations purely from the video, so that the video representations can be computed offline and reused for different texts. Concretely, we first introduce a spatial-temporal \"Prompt Cube\" into the CLIP image encoder and iteratively switch it within the encoder layers to efficiently incorporate the global video semantics into frame representations. We then propose to apply an auxiliary video captioning objective to train the frame representations, which facilitates the learning of detailed video semantics by providing fine-grained guidance in the semantic space. With a naive temporal fusion strategy (i.e., mean-pooling) on the enhanced frame representations, we obtain state-of-the-art performances on three benchmark datasets, i.e., MSR-VTT, MSVD, and LSMDC." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 602, + 124, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 602, + 124, + 615 + ], + "spans": [ + { + "bbox": [ + 46, + 602, + 124, + 615 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 622, + 279, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 622, + 279, + 704 + ], + "spans": [ + { + "bbox": [ + 45, + 622, + 279, + 704 + ], + "type": "text", + "content": "Text-video retrieval [1, 6, 30, 42] is a fundamental task in the area of video-language understanding that seeks to find the most relevant video from a large set of candidates to match a text query. With the rapid growth of video data, text-video retrieval has become increasingly important for various applications, including video recommendation [36, 43], video search [20, 45], and video summa" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 302, + 241, + 523, + 375 + ], + "blocks": [ + { + "bbox": [ + 302, + 241, + 523, + 375 + ], + "lines": [ + { + "bbox": [ + 302, + 241, + 523, + 375 + ], + "spans": [ + { + "bbox": [ + 302, + 241, + 523, + 375 + ], + "type": "image", + "image_path": "3e23a35dbe4e05e843156b477ea34fc6d67a3b12eb6f487eb9c86f1d9b6d889b.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 383, + 531, + 452 + ], + "lines": [ + { + "bbox": [ + 296, + 383, + 531, + 452 + ], + "spans": [ + { + "bbox": [ + 296, + 383, + 531, + 452 + ], + "type": "text", + "content": "Figure 1: The performance (i.e., R@1), retrieval time, and memory usage during retrieval for baseline models and ours on the MSRVTT dataset. The center of the bubble indicates the value of R@1. The diameter of the bubble or star is proportional to the memory usage (GB) while the horizontal axis indicates the inference time (s)." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 473, + 531, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 473, + 531, + 624 + ], + "spans": [ + { + "bbox": [ + 296, + 473, + 531, + 624 + ], + "type": "text", + "content": "rization [7, 29, 31, 33, 37, 47]. Due to the high cost of constructing text-video datasets, one promising approach for this task is to leverage pre-trained text-image foundation models and transfer their powerful representation capabilities to the video domain. Specifically, the CLIP [34] model, which is trained using a text-image alignment objective, is particularly suitable for text-video retrieval and has been frequently studied recently [27, 46, 16]. It has two transformer encoders [38, 9] to process images and texts, respectively. A vector representation is extracted from the input of each modality with the corresponding encoder and is optimized to be close to its paired representation and away from the unpaired ones." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 624, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 624, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 624, + 531, + 730 + ], + "type": "text", + "content": "Adapting CLIP to the video domain is non-trivial and requires careful consideration of both efficiency and effectiveness. In CLIP4Clip [27], the authors directly mean-pool the frame representations extracted by the CLIP image encoder to get the video representation and use it to calculate the cosine similarity with the text representations during retrieval. However, the mean-pooling of frame representations may lose some essential semantic details of the video and hamper the retrieval performance. Thus, more advanced meth" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "spans": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 151, + 41, + 470, + 73 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 41, + 470, + 73 + ], + "spans": [ + { + "bbox": [ + 151, + 41, + 470, + 73 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 709, + 279, + 730 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 709, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 709, + 279, + 730 + ], + "type": "text", + "content": "*Co-first author. †Corresponds to qi.wu01@adelaide.edu.au. Code: https://github.com/bladewaltz1/PromptSwitch." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "type": "text", + "content": "15648" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "type": "text", + "content": "ods, such as [14, 16, 18, 24, 28], generate the video representation by applying various cross-modal temporal fusion approaches on the frame representations, using text queries as the condition. While achieving state-of-the-art results, these methods encounter severe efficiency issues in practice, as the text-conditioned fusion of each video has to be performed on-the-fly for every incoming text query. Even with a lightweight fusion module (compared to the CLIP backbone), its computation cost grows geometrically as the number of videos and texts increases." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "spans": [ + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "text", + "content": "Formally, given a query set of " + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "inline_equation", + "content": "N_{t}" + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "text", + "content": " texts with an average length of " + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "inline_equation", + "content": "N_{w}" + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "text", + "content": " words and a candidate set of " + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "inline_equation", + "content": "N_{v}" + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "text", + "content": " videos where each video contains " + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "inline_equation", + "content": "N_{f}" + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "text", + "content": " frames. Then, the space and time complexities are " + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(N_vN_tN_f)" + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "text", + "content": " for the text-conditioned fusion in X-Pool [16] and TS2-Net [24], and " + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(N_vN_tN_fN_w)" + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "text", + "content": " for that of X-CLIP [28]. While for CLIP4Clip, the complexity is " + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(N_vN_t)" + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "text", + "content": " as it only requires a simple dot-product between the text and mean-pooled frame representations, although its performance is inferior to X-Pool and X-CLIP. To better reveal this gap, we show an example in Figure 1 about the real-world efficiency of several methods while omitting the backbone computation. Here, we set " + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "inline_equation", + "content": "N_{v} = 16384" + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "inline_equation", + "content": "N_{t} = 512" + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "inline_equation", + "content": "N_{f} = 12" + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "inline_equation", + "content": "N_{w} = 10" + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "text", + "content": ". From the figure, with large " + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "inline_equation", + "content": "N_{t}" + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "inline_equation", + "content": "N_{v}" + }, + { + "bbox": [ + 45, + 223, + 281, + 432 + ], + "type": "text", + "content": ", the latency and memory consumption for text-conditioned temporal fusion methods [16, 24, 28] are orders of magnitude higher than text-agnostic temporal fusion (i.e., mean-pooling) [27, 57], and can rapidly become enormous in large-scale scenarios." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 431, + 281, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 431, + 281, + 548 + ], + "spans": [ + { + "bbox": [ + 45, + 431, + 281, + 548 + ], + "type": "text", + "content": "On the other hand, the backbone computation of CLIP is much less of a burden in real-world retrieval systems, as the frame representations of the video can be pre-computed offline and reused for different text queries. Therefore, a more practical CLIP-based text-video retrieval method should focus on improving the backbone representation ability while keeping the cross-modal interaction as simple as possible. Motivated by this, we propose a simple and efficient adaptation method for CLIP to facilitate its ability to capture both the global and detailed semantics of videos." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 548, + 281, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 548, + 281, + 712 + ], + "spans": [ + { + "bbox": [ + 45, + 548, + 281, + 712 + ], + "type": "text", + "content": "Concretely, we first feed a tiny (" + }, + { + "bbox": [ + 45, + 548, + 281, + 712 + ], + "type": "inline_equation", + "content": "\\sim 0.1\\mathrm{M}" + }, + { + "bbox": [ + 45, + 548, + 281, + 712 + ], + "type": "text", + "content": ") \"Prompt Cube\" into the image encoder of CLIP, which is a 3D tensor spanning over the spatial, temporal, and channel axis, as shown in the right of Figure 2." + }, + { + "bbox": [ + 45, + 548, + 281, + 712 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 45, + 548, + 281, + 712 + ], + "type": "text", + "content": " It is designed to have the same temporal and spatial sizes and is concatenated with the patch tokens alongside the spatial axis. To propagate temporal semantics among different frames, we switch the spatial and temporal dimensions of the prompt cube before each self-attention layer, so that the prompt cube builds up a peer-to-peer connection between every two-frame pair. In this way, our modified CLIP model enjoys an improved global semantic modeling ability thanks to the comprehensive spatial-temporal modeling between the prompt cube and the patch tokens of all frames, while only bringing neg-" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 297, + 106, + 530, + 188 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 106, + 530, + 188 + ], + "spans": [ + { + "bbox": [ + 297, + 106, + 530, + 188 + ], + "type": "text", + "content": "ligible extra parameters and computations. This also allows the prompt cube to serve as a compact summarization of the whole video, and further enables us to design a CLIP-guided Prompt Aggregation approach and obtain the frame representations from the prompt cube. Then, we use naive mean-pooling instead of cross-modal fusion on these frame representations to get the final video representation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 296, + 188, + 531, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 188, + 531, + 362 + ], + "spans": [ + { + "bbox": [ + 296, + 188, + 531, + 362 + ], + "type": "text", + "content": "Moreover, since we will not use any fine-grained cross-modal interaction modules in our model, we adopt an Auxiliary Video Captioning objective as an alternative to provide fine-grained guidance in the semantic space when learning video representations. Specifically, we introduce a light captioning head on top of our modified CLIP image encoder during training, which takes the frame representations aggregated from the prompt cube as input and generates the paired text of the input video. This auxiliary objective plays a critical role because CLIP's original contrastive learning objective is relatively easy to fit due to the lack of in-batch negatives during training (which is generally the case in text-video retrieval). During inference, the light captioning branch is removed, thus it incurs no extra computation and memory consumption." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 296, + 362, + 531, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 362, + 531, + 444 + ], + "spans": [ + { + "bbox": [ + 296, + 362, + 531, + 444 + ], + "type": "text", + "content": "We verify the effectiveness of the proposed method on three text-video retrieval benchmarks, i.e. MSR-VTT [50], MSVD [4], and LSMDC [35], where our method consistently achieves state-of-the-art performance while being significantly more efficient than the previous state of the arts. We also provide extensive performance analyses to show the superiority of our proposed method." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 298, + 452, + 381, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 452, + 381, + 464 + ], + "spans": [ + { + "bbox": [ + 298, + 452, + 381, + 464 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 472, + 530, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 472, + 530, + 519 + ], + "spans": [ + { + "bbox": [ + 296, + 472, + 530, + 519 + ], + "type": "text", + "content": "Text-video retrieval is one of the fundamental tasks in video-language modeling and has lots of applications in the industry. Here, we broadly classify the previous works into three categories and briefly review them below." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 532, + 532, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 532, + 532, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 532, + 532, + 730 + ], + "type": "text", + "content": "Off-the-Shelf Single-Modal Representations An early trend in text-video retrieval is to use the off-the-shelf video (e.g., I3D [3]) and text representations (e.g., GloVe [32]) and design sophisticated feature encoding methods or multi-modal fusion mechanisms on them to improve the retrieval performance [6, 8, 19, 54, 55]. For example, in [6], a hierarchical graph reasoning approach is proposed to decompose video-text matching into global-to-local levels and disentangle texts into a hierarchical semantic graph with three levels of events, actions, and entities. Yu et al. [54] propose a joint sequence fusion model for the sequential interaction of videos and texts. Dong et al. [8] leverages multi-level single-modal features that represent the rich content of both video and text in a coarse-to-fine fashion. However, their performances are limited due to the mismatched training objectives between the pre-computed representations and the text-video retrieval task." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 719, + 194, + 730 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 719, + 194, + 730 + ], + "spans": [ + { + "bbox": [ + 57, + 719, + 194, + 730 + ], + "type": "text", + "content": "1The channel axis is omitted for simplicity." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "type": "text", + "content": "15649" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 106, + 517, + 297 + ], + "blocks": [ + { + "bbox": [ + 60, + 106, + 517, + 297 + ], + "lines": [ + { + "bbox": [ + 60, + 106, + 517, + 297 + ], + "spans": [ + { + "bbox": [ + 60, + 106, + 517, + 297 + ], + "type": "image", + "image_path": "127eb9451882f31302958f9ba1fd2195f633da5a7738114f2eace6b9cd94019c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 305, + 531, + 341 + ], + "lines": [ + { + "bbox": [ + 45, + 305, + 531, + 341 + ], + "spans": [ + { + "bbox": [ + 45, + 305, + 531, + 341 + ], + "type": "text", + "content": "Figure 2: Overall architecture. For a video clip with " + }, + { + "bbox": [ + 45, + 305, + 531, + 341 + ], + "type": "inline_equation", + "content": "N_{f}" + }, + { + "bbox": [ + 45, + 305, + 531, + 341 + ], + "type": "text", + "content": " frames, we accompany it with " + }, + { + "bbox": [ + 45, + 305, + 531, + 341 + ], + "type": "inline_equation", + "content": "N_{f} \\times N_{f}" + }, + { + "bbox": [ + 45, + 305, + 531, + 341 + ], + "type": "text", + "content": " prompt tokens, resulting in a 3D prompt cube. We show the Prompt Switch operation on the right. For simplicity, we omit the feed-forward network and shot-cut connections in the ViT layer. We provide more details for Prompt Aggregation in Figure 4. " + }, + { + "bbox": [ + 45, + 305, + 531, + 341 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 45, + 305, + 531, + 341 + ], + "type": "text", + "content": " is cosine similarity." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 361, + 281, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 361, + 281, + 723 + ], + "spans": [ + { + "bbox": [ + 45, + 361, + 281, + 723 + ], + "type": "text", + "content": "Video-Language Pre-training To reduce the gap between pre-training and downstream tasks, large-scale pretrained video-language representations have been proposed, such as [1, 13, 15, 21, 26, 40, 48, 49, 51]. Most of these models are pre-trained on the large-scale video-text datasets, e.g., HowTo100M [30] and WebVid-2M [1], which boosts promising cross-modal video understanding [22, 23, 26]. One line of works [1, 13, 49] uses two independent encoders for video and text and then projects them into a common latent space. These methods often adopt a contrastive loss to distinguish the paired video-text data. For example, Bain et al. [1] design an end-to-end trainable model, aiming to take advantage of both large-scale image and video captioning datasets. Gabeur et al. [13] propose a multi-modal transformer that can extract features at different moments and from different modalities (e.g., audio or speech) in a video. The other line of works [21, 26, 48] employs a single cross-modal encoder, which concatenates the video and text sequences as inputs and models them jointly in the transformer, followed by a binary classifier predicting whether these videos and texts are aligned. Despite they can build fine-grained associations between video-text tokens, they need to input each video-text candidate pair into the model for matching score calculation during inference and thus hampers efficiency. Besides, although the idea of video-language pre-training is promising, due to the high cost of collecting wild videos, its scale is generally much smaller than image-language pre-training, leading to an unsatisfactory generalization ability. Thus, like [16, 27], we seek to boost from the image-language pre-training model (e.g., CLIP [34]) for text-video retrieval." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 296, + 361, + 531, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 361, + 531, + 606 + ], + "spans": [ + { + "bbox": [ + 296, + 361, + 531, + 606 + ], + "type": "text", + "content": "CLIP-based Adaptation. Recently, due to the great advantage of CLIP [34] for vision-and-language representation learning, many works [11, 14, 17, 18, 28, 41, 52, 56] seek to transfer the knowledge of CLIP to text-video retrieval tasks. Roughly, the existing works transfer CLIP from views of feature aggregation [12, 16, 27, 28, 57], representation alignment [12, 28, 41], and post pretraining [46, 52]. Specifically, X-Pool [16] designs a cross-modal attention model, seeking to enable the model to only focus on the relevant video frames conditioned on a given text. TS2-Net [24] adapts CLIP by introducing a token shift module and a token selection module, which capture the temporal information and remove unimportant tokens, respectively. X-CLIP [28] calculates both the coarse- and fine-grained similarity for higher retrieval accuracy. While these methods can be effective, their retrieval efficiency is low due to the coupling of video and text in the cross-modal fusion process. A more ideal way should focus on improving the representation ability of the backbone while maintaining the cross-modal interaction as efficiently as possible. We follow this principle in our method." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 297, + 616, + 352, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 616, + 352, + 628 + ], + "spans": [ + { + "bbox": [ + 297, + 616, + 352, + 628 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 296, + 636, + 532, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 636, + 532, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 636, + 532, + 730 + ], + "type": "text", + "content": "The overview of our method is shown in Figure 2. It is based on a pre-trained CLIP with a ViT [10]-based image encoder. Given an input video, we first split each video frame into fix-sized non-overlapping patches and linearly project them into 1D patch embeddings. Following CLIP, a [CLS] embedding is concatenated to the embedding sequence of each frame, which is pre-trained to capture the local semantics within the sequence. Then, in the ViT en" + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "type": "text", + "content": "15650" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 281, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 281, + 269 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 281, + 269 + ], + "type": "text", + "content": "coder, our proposed \"Prompt Cube\" bridges the global semantic information from the patch embeddings of all frames through a Prompt Switch operation. After that, we feed the output [CLS] embeddings of the video frames and the final prompt cube into a Prompt Aggregation module, where the prompt cube is aggregated into 1D vectors according to the [CLS] embeddings, and is further enhanced with fine-grained semantics through an Auxiliary Captioning Objective. To ensure an efficient measurement of the text-video similarity, we avoid using cross-modal fusion modules and directly average these aggregated vectors into the final video representation. A simple dot product operation is used to compute the similarity. More details are in the following." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 277, + 271, + 290 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 277, + 271, + 290 + ], + "spans": [ + { + "bbox": [ + 45, + 277, + 271, + 290 + ], + "type": "text", + "content": "3.1. Prompt Cube for Bridging Global Semantics" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "spans": [ + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "text", + "content": "At the core of our method is the proposed Prompt Cube. It is designed to capture the rich temporal semantics of the whole video while bringing negligible modifications and computations to the CLIP image encoder. Formally, given an input video clip with " + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "inline_equation", + "content": "N_{f}" + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "text", + "content": " frames, we first obtain its patch embeddings " + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "inline_equation", + "content": "V \\in \\mathbb{R}^{N_f \\times L \\times D}" + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "text", + "content": " indicates the size of the spatial dimension, i.e., the number of patches divided from a video frame plus one [CLS] embedding. " + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "text", + "content": " is the embedding size. Then, our prompt cube is constructed as a 3D tensor " + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "inline_equation", + "content": "P \\in \\mathbb{R}^{N_f \\times N_f \\times D}" + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "text", + "content": ". At the start of the ViT layer, we concatenate " + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "text", + "content": " alongside the spatial dimension, denoted by " + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "inline_equation", + "content": "[V; P] \\in \\mathbb{R}^{N_f \\times (L + N_f) \\times D}" + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "text", + "content": ", and then process them jointly. The first two dimensions of " + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "text", + "content": " (corresponding to the temporal and spatial axis, respectively) have the same size, thus they can be transposed flexibly without altering the shape of " + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 45, + 296, + 281, + 518 + ], + "type": "text", + "content": ". This allows us to further propose an efficient Prompt Switch operation to exchange the local spatial semantics of each frame and the global temporal semantics from the whole video through the prompt cube." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 533, + 279, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 533, + 279, + 557 + ], + "spans": [ + { + "bbox": [ + 45, + 533, + 279, + 557 + ], + "type": "text", + "content": "Prompt Switch The proposed Prompt Switch operation can be defined in a one-line formula:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 109, + 566, + 279, + 581 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 566, + 279, + 581 + ], + "spans": [ + { + "bbox": [ + 109, + 566, + 279, + 581 + ], + "type": "interline_equation", + "content": "\\mathcal {T} := [ V; P ] \\rightarrow [ V; P ^ {\\top} ]. \\tag {1}", + "image_path": "dc5019750bdbb6e244c738ee206187134483a7fed16b579db2b9d7e383ada056.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": "See the right of Figure 2, we apply this operation before every self-attention layer of the ViT encoder. Then, self-attention is performed over the spatial dimension of " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "[V;P]" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": ", where the " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": "-th row of the prompt cube (denoted by " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "\\pmb{p}_i \\in \\mathbb{R}^{1 \\times N_f \\times D}" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": ") and the patch embeddings of the " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": "-th frame (denoted by " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "\\pmb{v}_i \\in \\mathbb{R}^{1 \\times L \\times D}" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": ") acquire information from each other. In this way, for two consecutive ViT layers in the encoder, each element in the prompt cube (denoted by " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "\\pmb{p}_{i,j} \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": ") is first attached to the " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": "-th frame and communicates with " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "\\pmb{v}_i" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": ", and then switch to the " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": "-th frame and communicates with " + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "inline_equation", + "content": "\\pmb{v}_j" + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": ". By repeatedly performing this operation, the whole prompt cube builds up a peer-to-peer" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 305, + 104, + 418, + 214 + ], + "blocks": [ + { + "bbox": [ + 305, + 104, + 418, + 214 + ], + "lines": [ + { + "bbox": [ + 305, + 104, + 418, + 214 + ], + "spans": [ + { + "bbox": [ + 305, + 104, + 418, + 214 + ], + "type": "image", + "image_path": "c7b333532b12e1a77b81ac4444b6cdcb265642215398379925589530101c858e.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 223, + 531, + 340 + ], + "lines": [ + { + "bbox": [ + 296, + 223, + 531, + 340 + ], + "spans": [ + { + "bbox": [ + 296, + 223, + 531, + 340 + ], + "type": "text", + "content": "Figure 3: Video Proxy adopts a shared \"prompt\" to exchange information among all frames (b). Differently, our Prompt Switch method builds up a peer-to-peer connection between every two-frame pair (a) to obtain more comprehensive spatial-temporal modeling. This improves the representation ability of CLIP on video data. Besides, our method may also ease the learning problem as each element in the prompt cube only needs to handle the information of two frames instead of the whole video, thus improving the optimization ability of CLIP on video data." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 427, + 104, + 524, + 214 + ], + "blocks": [ + { + "bbox": [ + 427, + 104, + 524, + 214 + ], + "lines": [ + { + "bbox": [ + 427, + 104, + 524, + 214 + ], + "spans": [ + { + "bbox": [ + 427, + 104, + 524, + 214 + ], + "type": "image", + "image_path": "82fd31b840db1242d32a310659d91d786bd89a580aca215f3e708ea064f5f92b.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 362, + 530, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 362, + 530, + 384 + ], + "spans": [ + { + "bbox": [ + 296, + 362, + 530, + 384 + ], + "type": "text", + "content": "connection between every two-frame pair in the video clip, enabling comprehensive temporal modeling." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 386, + 531, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 386, + 531, + 676 + ], + "spans": [ + { + "bbox": [ + 296, + 386, + 531, + 676 + ], + "type": "text", + "content": "Some previous text-video retrieval methods have also attempted to introduce temporal adaptation to the backbone of the CLIP ViT encoder, such as Token Shift [24] and Video Proxy [52]. Specifically, the Token Shift method shifts token embeddings from adjacent frames to the current frame, which fails to model the temporal semantics from a global perspective. Moreover, it damages the spatial modeling ability of the original CLIP as the information contained in the shifted tokens is no longer accessible in the current frame. In Video Proxy, the information from all video frames is exchanged using several proxy embeddings, which lack peer-to-peer connections within the frames and thus can be inferior in the temporal modeling capacity. We illustrate the importance of building peer-to-peer connections in Figure 3. Besides, a naive full-attention approach has also been investigated where no adaptation is applied to the CLIP model except allowing its self-attention layers to attend to the patch tokens from the whole video. However, this approach is neither effective due to the domain gap between the input data (video) and the pre-training data (image), nor efficient since the computation complexity of the self-attention layers grows quadratically w.r.t. the number of attended patch tokens. We show the superiority of our proposed prompt cube to these previous methods in Section 4.1." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 695, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 695, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 695, + 530, + 730 + ], + "type": "text", + "content": "Prompt Aggregation As the prompt cube acquires the global semantics through a comprehensive interaction with all patch embeddings, it can serve as a compact summariza" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "text", + "content": "15651" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 281, + 271 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 281, + 271 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 281, + 271 + ], + "type": "text", + "content": "tion of the video. Therefore, we propose to obtain the final video representation from the prompt cube, instead of the [CLS] embedding as the original CLIP. To achieve this, we design a CLIP-guided Prompt Aggregation module, which aggregates the output prompt cube into 1D vectors according to the final [CLS] embeddings of the video frames. It is a lightweight multi-head attention (MHA) layer placed before the last layer normalization (LN) layer of the ViT encoder. The [CLS] embedding of the " + }, + { + "bbox": [ + 45, + 106, + 281, + 271 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 106, + 281, + 271 + ], + "type": "text", + "content": "-th frame (denoted by " + }, + { + "bbox": [ + 45, + 106, + 281, + 271 + ], + "type": "inline_equation", + "content": "\\pmb{c}_i \\in \\mathbb{R}^{1 \\times D}" + }, + { + "bbox": [ + 45, + 106, + 281, + 271 + ], + "type": "text", + "content": ") is used as the \"query\" while the \"key\" and \"value\" are both the prompt cube flattened over the temporal and spatial dimensions, denoted by " + }, + { + "bbox": [ + 45, + 106, + 281, + 271 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{P}} \\in \\mathbb{R}^{N_f^2 \\times D}" + }, + { + "bbox": [ + 45, + 106, + 281, + 271 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 45, + 106, + 281, + 271 + ], + "type": "inline_equation", + "content": "\\bar{p}_i \\in \\mathbb{R}^{1 \\times D}" + }, + { + "bbox": [ + 45, + 106, + 281, + 271 + ], + "type": "text", + "content": " be the aggregated prompt vector for the " + }, + { + "bbox": [ + 45, + 106, + 281, + 271 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 106, + 281, + 271 + ], + "type": "text", + "content": "-th frame, we have" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 280, + 279, + 295 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 280, + 279, + 295 + ], + "spans": [ + { + "bbox": [ + 57, + 280, + 279, + 295 + ], + "type": "interline_equation", + "content": "\\bar {p} _ {i} := \\mathrm {L N} \\left(\\boldsymbol {c} _ {i} + \\operatorname {M H A} \\left(\\boldsymbol {c} _ {i}, \\hat {\\boldsymbol {P}}, \\hat {\\boldsymbol {P}}\\right)\\right), \\quad \\forall i \\in [ 1, N _ {f} ], \\tag {2}", + "image_path": "4cee2eea7ad58112579d21534649f579cc54a79771a59a5c0b85ecab8cae1215.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 303, + 279, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 303, + 279, + 374 + ], + "spans": [ + { + "bbox": [ + 45, + 303, + 279, + 374 + ], + "type": "text", + "content": "where LN denotes the last layer normalization layer of the CLIP ViT encoder. Notably, the last linear projection weight in the MHA layer is initialized as a 0 tensor to ensure that " + }, + { + "bbox": [ + 45, + 303, + 279, + 374 + ], + "type": "inline_equation", + "content": "\\bar{p}_i" + }, + { + "bbox": [ + 45, + 303, + 279, + 374 + ], + "type": "text", + "content": " is optimized from the original output of the CLIP image encoder. The final video representation is the naive mean-pooling of the normalized prompt vectors, i.e.," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 121, + 382, + 279, + 415 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 382, + 279, + 415 + ], + "spans": [ + { + "bbox": [ + 121, + 382, + 279, + 415 + ], + "type": "interline_equation", + "content": "\\boldsymbol {x} := \\frac {1}{N _ {f}} \\sum_ {i = 1} ^ {N _ {f}} \\frac {\\bar {\\boldsymbol {p}} _ {i}}{\\| \\bar {\\boldsymbol {p}} _ {i} \\|}. \\tag {3}", + "image_path": "e870640aedd839bb8e8b346f26fc72e3a17308dcb0530d200d5aec5e4eb4c5ba.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 422, + 279, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 422, + 279, + 494 + ], + "spans": [ + { + "bbox": [ + 45, + 422, + 279, + 494 + ], + "type": "text", + "content": "We provide a detailed illustration for the Prompt Aggregation module on the left of Figure 4. To enhance the learning of temporal information for the prompt cube, inspired by [58], we adopt a frame sampling strategy where we randomly sample " + }, + { + "bbox": [ + 45, + 422, + 279, + 494 + ], + "type": "inline_equation", + "content": "k < N_f" + }, + { + "bbox": [ + 45, + 422, + 279, + 494 + ], + "type": "text", + "content": " prompt vectors for the final mean-pooling operation in Eq. (3) during training." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 500, + 269, + 512 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 500, + 269, + 512 + ], + "spans": [ + { + "bbox": [ + 46, + 500, + 269, + 512 + ], + "type": "text", + "content": "3.2. Learning Detailed Semantics via Captioning" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 517, + 279, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 517, + 279, + 658 + ], + "spans": [ + { + "bbox": [ + 45, + 517, + 279, + 658 + ], + "type": "text", + "content": "As we have discussed in Section 1, the key criterion in the design of our model architecture is to ensure the model contains no extra cross-modal interaction procedure during inference except computing the cosine similarity between text and video representations. While this ensures the efficiency of the similarity measurement in large-scale production systems, it also prevents the video representation from utilizing the fine-grained semantic information from the text query. To aid this, inspired by [5, 53], we propose to learn our video representation with an Auxiliary Captioning objective, which alternatively provides fine-grained guidance in the semantic space during training." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "type": "text", + "content": "Auxiliary Captioning Head As shown on the right of Figure 4, the Auxiliary Captioning Head, denoted by " + }, + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "type": "text", + "content": ", is a stack of " + }, + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "type": "text", + "content": " transformer decoders. We first shift the text token by one step to the right, and feed it into a Masked MHA layer, where each text token only attends to its preceding" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 314, + 104, + 516, + 304 + ], + "blocks": [ + { + "bbox": [ + 314, + 104, + 516, + 304 + ], + "lines": [ + { + "bbox": [ + 314, + 104, + 516, + 304 + ], + "spans": [ + { + "bbox": [ + 314, + 104, + 516, + 304 + ], + "type": "image", + "image_path": "6809609bbbe0a770b989fc954f692f79003a451ced44a72e0eb8ffc339bf69d9.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 312, + 530, + 336 + ], + "lines": [ + { + "bbox": [ + 296, + 312, + 530, + 336 + ], + "spans": [ + { + "bbox": [ + 296, + 312, + 530, + 336 + ], + "type": "text", + "content": "Figure 4: Detailed architecture of Prompt Aggregation (left) and Auxiliary Captioning Head (right)." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 355, + 531, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 355, + 531, + 415 + ], + "spans": [ + { + "bbox": [ + 296, + 355, + 531, + 415 + ], + "type": "text", + "content": "tokens. Then, another MHA layer is used, where the text tokens attend to the aggregated prompt vectors " + }, + { + "bbox": [ + 296, + 355, + 531, + 415 + ], + "type": "inline_equation", + "content": "\\{\\overline{p_i}\\}_{i = 1}^{N_f}" + }, + { + "bbox": [ + 296, + 355, + 531, + 415 + ], + "type": "text", + "content": ". The model is trained via the autoregressive Teacher Forcing [44] scheme, i.e., the prediction in each step should maximize the likelihood of the token in the next step:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 336, + 421, + 530, + 454 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 421, + 530, + 454 + ], + "spans": [ + { + "bbox": [ + 336, + 421, + 530, + 454 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c a p} = \\sum_ {l = 1} ^ {N _ {w}} - \\log p \\left(w _ {l} \\mid w _ {< l}, \\left\\{\\bar {\\boldsymbol {p}} _ {i} \\right\\} _ {i = 1} ^ {N _ {f}}\\right), \\tag {4}", + "image_path": "659088d6ad1dca8e070aa78d010c0dad424e476076b6c633962c47429486b0a1.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 460, + 530, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 460, + 530, + 554 + ], + "spans": [ + { + "bbox": [ + 296, + 460, + 530, + 554 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 460, + 530, + 554 + ], + "type": "inline_equation", + "content": "w_{l}" + }, + { + "bbox": [ + 296, + 460, + 530, + 554 + ], + "type": "text", + "content": " indicates the " + }, + { + "bbox": [ + 296, + 460, + 530, + 554 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 296, + 460, + 530, + 554 + ], + "type": "text", + "content": "-th token in the text, and " + }, + { + "bbox": [ + 296, + 460, + 530, + 554 + ], + "type": "inline_equation", + "content": "w_{MethodR@1↑R@5↑R@10↑MnR↓baseline CLIP43.170.980.416.0+ Prompt Switch44.8 (+1.7)71.980.915.2+ Temporal Transformer44.271.481.115.6+ Prompt Aggregation45.4 (+0.6)71.981.114.9+ Captioning Loss46.1 (+0.7)72.881.814.4", + "image_path": "b685670d84649090a1bd0cc17c8d68aa837e033716dcde5f237c700943159233.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 246, + 279, + 316 + ], + "blocks": [ + { + "bbox": [ + 45, + 178, + 279, + 237 + ], + "lines": [ + { + "bbox": [ + 45, + 178, + 279, + 237 + ], + "spans": [ + { + "bbox": [ + 45, + 178, + 279, + 237 + ], + "type": "text", + "content": "Table 1: Performance analysis of our model components for text-video retrieval on MSRVTT 1K-A test set. Both Prompt Aggregation and Temporal Transformer are applied on top of our Prompt Switch. The Captioning Loss is applied only on top of the Prompt Aggregation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 246, + 279, + 316 + ], + "lines": [ + { + "bbox": [ + 48, + 246, + 279, + 316 + ], + "spans": [ + { + "bbox": [ + 48, + 246, + 279, + 316 + ], + "type": "table", + "html": "
MethodR@1↑R@5↑R@10↑MnR↓
Temporal Transformer44.271.481.115.6
Token Shift [24]43.270.779.815.9
Video Proxy [52]45.271.081.515.3
Full Attention43.871.480.916.4
Prompt Switch & Aggregation45.471.981.114.9
", + "image_path": "ae3fdd674becad28837e254de30ec67c7a4af165a823297178ab9484bf148522.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 367, + 279, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 367, + 279, + 390 + ], + "spans": [ + { + "bbox": [ + 45, + 367, + 279, + 390 + ], + "type": "text", + "content": "tion (obtained by Eq. (3) and text representation of the " + }, + { + "bbox": [ + 45, + 367, + 279, + 390 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 367, + 279, + 390 + ], + "type": "text", + "content": "-th video-text pair in the mini-batch. The final loss function is" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 121, + 398, + 279, + 411 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 398, + 279, + 411 + ], + "spans": [ + { + "bbox": [ + 121, + 398, + 279, + 411 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {c o n}} + \\lambda \\mathcal {L} _ {\\text {c a p}}, \\tag {6}", + "image_path": "e9e9e5d42ee4665fe462fa5fd7182d6a9730b72b6890e5ea2761eb12b139bb59.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 418, + 213, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 213, + 431 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 213, + 431 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 418, + 213, + 431 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 418, + 213, + 431 + ], + "type": "text", + "content": " is the weighting hyper-parameter." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 440, + 120, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 440, + 120, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 440, + 120, + 453 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 459, + 279, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 459, + 279, + 657 + ], + "spans": [ + { + "bbox": [ + 45, + 459, + 279, + 657 + ], + "type": "text", + "content": "Dataset and Metrics We evaluate the effectiveness of our method on three widely used text-video retrieval datasets, including MSR-VTT [50], MSVD [4] and LSMDC [35]. MSR-VTT [50] consists of 10,000 videos with 200K descriptions. We follow the setting in previous works [13, 54], training our models with 9,000 videos and evaluating them on the 1K-A test set. MSVD [4] contains 1,970 videos with about 120K captions, where the train, validation, and test splits contain 1, 200, 100 and 670 videos, respectively. LSMDC [35] has 118,081 video-caption pairs, where 109, 673 videos are used for training, 7, 408 videos for validation, and 1, 000 videos for testing. Following [16, 24, 27], we report the results of Recall@ " + }, + { + "bbox": [ + 45, + 459, + 279, + 657 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 459, + 279, + 657 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 45, + 459, + 279, + 657 + ], + "type": "inline_equation", + "content": "R@K" + }, + { + "bbox": [ + 45, + 459, + 279, + 657 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 459, + 279, + 657 + ], + "type": "inline_equation", + "content": "K = 1, 5, 10" + }, + { + "bbox": [ + 45, + 459, + 279, + 657 + ], + "type": "text", + "content": ") and Mean Rank (MnR) for quantitative evaluation. Besides, we sum the value of " + }, + { + "bbox": [ + 45, + 459, + 279, + 657 + ], + "type": "inline_equation", + "content": "R@1" + }, + { + "bbox": [ + 45, + 459, + 279, + 657 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 459, + 279, + 657 + ], + "type": "inline_equation", + "content": "R@5" + }, + { + "bbox": [ + 45, + 459, + 279, + 657 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 45, + 459, + 279, + 657 + ], + "type": "inline_equation", + "content": "R@10" + }, + { + "bbox": [ + 45, + 459, + 279, + 657 + ], + "type": "text", + "content": " for both text-video and video-text retrieval tasks as an overall evaluation metric, named Meta Sum." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "content": "Implementation Details Following previous work [16, 27], both the text and video encoders are initialized with the pre-trained CLIP (ViT-B/32) [34]. The prompt cube is randomly initialized from a Gaussian distribution with a zero mean and 0.02 std. During training, we uniformly sample" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 300, + 103, + 530, + 279 + ], + "blocks": [ + { + "bbox": [ + 45, + 324, + 279, + 346 + ], + "lines": [ + { + "bbox": [ + 45, + 324, + 279, + 346 + ], + "spans": [ + { + "bbox": [ + 45, + 324, + 279, + 346 + ], + "type": "text", + "content": "Table 2: Comparisons with other temporal modeling methods for text-video retrieval on MSRVTT 1K-A test set." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 300, + 103, + 530, + 279 + ], + "lines": [ + { + "bbox": [ + 300, + 103, + 530, + 279 + ], + "spans": [ + { + "bbox": [ + 300, + 103, + 530, + 279 + ], + "type": "table", + "html": "
MethodR@1↑R@5↑R@10↑Mem. / Time
Text ⇒ Video
TS2-Net* [24]46.573.683.30.3G / 0.2s
X-Pool [16]46.972.882.23.9G / 3.9s
ours (mean pool)46.172.881.82.0M / 8.1ms
ours (attention pool)46.472.982.40.2G / 0.2s
ours (top-3 pool)46.773.482.00.3G / 0.3s
ours (X-Pool [16])47.873.982.23.9G / 3.9s
Video ⇒ Text
TS2-Net* [24]44.573.883.20.3G / 0.2s
X-Pool [16]44.473.384.03.9G / 3.9s
ours (mean pool)44.873.782.42.0M / 8.1ms
ours (attention pool)45.473.983.20.2G / 0.2s
ours (top-3 pool)45.273.683.70.3G / 0.3s
ours (X-Pool [16])46.074.384.83.9G / 3.9s
", + "image_path": "3128bf43d78d0f4a29a122a3017c1a0f628391a2a6a0180daf2fae4fa1ea58de.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 297, + 287, + 530, + 322 + ], + "lines": [ + { + "bbox": [ + 297, + 287, + 530, + 322 + ], + "spans": [ + { + "bbox": [ + 297, + 287, + 530, + 322 + ], + "type": "text", + "content": "Table 3: Performance and complexity comparisons with different temporal fusion methods on MSRVTT 1K-A test set. * denotes the results reproduced by official code & setting." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 296, + 343, + 530, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 343, + 530, + 506 + ], + "spans": [ + { + "bbox": [ + 296, + 343, + 530, + 506 + ], + "type": "text", + "content": "6 frames from each video and resize all video frames into " + }, + { + "bbox": [ + 296, + 343, + 530, + 506 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 296, + 343, + 530, + 506 + ], + "type": "text", + "content": ". Therefore, the size of the spatial and temporal dimensions of the prompt cube is set to 6 by default. While for the testing, 12 frames are used as in previous works, so we split them into two 6-frame chunks through interval sampling to make the temporal dimension compatible with the prompt cube. The Prompt Aggregation is applied on the prompt cubes of all chunks. The number of decoder layers in the captioning head is 3. The hyper-parameter " + }, + { + "bbox": [ + 296, + 343, + 530, + 506 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 296, + 343, + 530, + 506 + ], + "type": "text", + "content": " used for frame sampling in Eq. (3) is set to 3. We set the hyperparameter " + }, + { + "bbox": [ + 296, + 343, + 530, + 506 + ], + "type": "inline_equation", + "content": "\\lambda = 0.5" + }, + { + "bbox": [ + 296, + 343, + 530, + 506 + ], + "type": "text", + "content": " in Eq. (6). The training epochs are 10 for all the datasets with a batch size of 128. We use AdamW optimizer [25] with a learning rate of 3e-5 and adopt a cosine decay strategy for the learning rate." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 297, + 514, + 420, + 527 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 514, + 420, + 527 + ], + "spans": [ + { + "bbox": [ + 297, + 514, + 420, + 527 + ], + "type": "text", + "content": "4.1. Performance Analysis" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 532, + 530, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 532, + 530, + 578 + ], + "spans": [ + { + "bbox": [ + 296, + 532, + 530, + 578 + ], + "type": "text", + "content": "We first thoroughly analyze the model designs and critical components of our proposed method and then verify their effectiveness. The experiments are conducted on the MSRVTT dataset and evaluated on the 1K-A test set." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "text", + "content": "Model Components As shown in Table 1, we conduct an ablation study on the Prompt Switch, Prompt Aggregation, and Auxiliary Captioning Objective by introducing them gradually into the model for text-video retrieval. The baseline CLIP model directly uses the mean-pooled [CLS] embeddings of the video frames as the final video representation, and is trained using only contrastive loss. Specifically, when incorporating the Prompt Switch mechanism, the result of R@1 increases significantly (i.e., from 43.1 to 44.8) compared with the baseline CLIP, which demonstrates the effectiveness of the proposed Prompt Switch. With the help of Prompt Aggregation, it further improves 0.6 and" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "text", + "content": "15653" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 104, + 507, + 290 + ], + "blocks": [ + { + "bbox": [ + 73, + 104, + 507, + 290 + ], + "lines": [ + { + "bbox": [ + 73, + 104, + 507, + 290 + ], + "spans": [ + { + "bbox": [ + 73, + 104, + 507, + 290 + ], + "type": "table", + "html": "
MethodsText ⇒ VideoVideo ⇒ TextMeta Sum ↑
R@1 ↑R@5 ↑R@10 ↑MnR ↓R@1R@5 ↑R@10 ↑MnR ↓
cross-modal temporal fusion
CLIP2TV [14]46.172.582.915.243.973.082.811.1401.2
CLIP2Video [12]45.672.681.714.643.372.382.110.2397.6
TS2-Net* [24]46.573.683.313.944.573.883.29.2404.9
EMCL [18]46.873.183.1-46.573.583.5-406.5
X-CLIP [28]46.173.083.113.246.873.384.09.1406.3
DRL [41]47.474.683.8-45.373.983.3-408.3
X-Pool [16]46.972.882.214.344.473.384.09.0403.6
ours (X-Pool)47.873.982.214.146.074.384.88.5409.0
text-agnostic temporal pooling
CLIP4Clip† (seqTransf) [27]44.571.481.615.342.770.980.611.6391.7
CenterCLIP† (spectral) [57]44.271.682.115.142.871.782.211.1394.6
X-CLIP (mean pool) [28]43.070.781.616.343.070.281.211.5389.7
TS2-Net* (mean pool) [24]44.472.182.214.643.770.880.411.6393.6
ours (mean pool)46.172.881.814.444.873.782.49.9401.6
", + "image_path": "8679c8ea42c4afd031d57140cd50b08968d3d040365c17c503f7a7310f52fcf6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 73, + 332, + 507, + 458 + ], + "blocks": [ + { + "bbox": [ + 45, + 298, + 531, + 324 + ], + "lines": [ + { + "bbox": [ + 45, + 298, + 531, + 324 + ], + "spans": [ + { + "bbox": [ + 45, + 298, + 531, + 324 + ], + "type": "text", + "content": "Table 4: Comparisons with state-of-the-arts on MSRVTT. † both CLIP4Clip and CenterCLIP have multiple versions in their papers, here we choose the versions with the highest Meta Sum. * denotes the results reproduced by official code & setting." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 73, + 332, + 507, + 458 + ], + "lines": [ + { + "bbox": [ + 73, + 332, + 507, + 458 + ], + "spans": [ + { + "bbox": [ + 73, + 332, + 507, + 458 + ], + "type": "table", + "html": "
MethodsText ⇒ VideoVideo ⇒ TextMeta Sum ↑
R@1↑R@5↑R@10↑MnR ↓R@1R@5↑R@10↑MnR ↓
cross-modal temporal fusion
CLIP2TV [14]47.076.585.110.1-----
CLIP2Video [12]47.076.885.99.658.785.691.64.3445.6
X-CLIP [28]47.177.8-9.560.987.8-4.7-
X-Pool [16]47.277.486.09.366.490.094.23.3461.2
text-agnostic temporal pooling
CLIP4Clip† (seqTransf) [27]45.275.584.310.362.087.392.64.3446.9
CenterCLIP† (spectral) [57]47.476.585.29.762.788.192.84.1452.7
ours (mean pool)47.176.986.19.568.591.895.62.8466.0
", + "image_path": "79521b792fa9775aecee81242493bf235f6611fe8e8011ee5a3e715c4ba00145.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 466, + 531, + 491 + ], + "lines": [ + { + "bbox": [ + 45, + 466, + 531, + 491 + ], + "spans": [ + { + "bbox": [ + 45, + 466, + 531, + 491 + ], + "type": "text", + "content": "Table 5: Comparisons with state-of-the-arts on MSVD. † both CLIP4Clip and CenterCLIP have multiple versions in their papers, here we choose the versions with the highest Meta Sum values." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 45, + 511, + 280, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 511, + 280, + 639 + ], + "spans": [ + { + "bbox": [ + 45, + 511, + 280, + 639 + ], + "type": "text", + "content": "achieves 45.4 in R@1. Our final model containing the Auxiliary Captioning Loss further improves the performance in R@1, R@5, R@10, and MnR by a large margin. These results demonstrate that all the proposed components contribute clearly to the final performance. Besides, we also compare the performance of an alternative temporal aggregation method to Prompt Aggregation termed Temporal Transformer, which adopts an additional transformer layer on the [CLS] embeddings of all video frames and averages the output. From Table 1, Prompt Aggregation is better than Temporal Transformer on all metrics." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 648, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 648, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 648, + 280, + 730 + ], + "type": "text", + "content": "Comparison on Temporal Modeling Methods To investigate the effectiveness of our temporal modeling method, i.e., Prompt Switch + Prompt Aggregation, we compare it with other four temporal modeling methods, including the Temporal Transformer, Full Attention (attention over patch tokens from all video frames), Token Shift [24], and Video Proxy [52]. All methods are implemented on the baseline" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 296, + 511, + 530, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 511, + 530, + 592 + ], + "spans": [ + { + "bbox": [ + 296, + 511, + 530, + 592 + ], + "type": "text", + "content": "CLIP model without extra components like the Token Selection Transformer in [24], and are trained using our default setting. From Table 2, our Prompt Switch & Aggregation approach outperforms all the baselines on R@1, R@5, and MnR while achieving the second-best result on R@10, which demonstrates its superiority in learning global video semantics across frames." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 601, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 601, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 601, + 531, + 730 + ], + "type": "text", + "content": "Cross-Modal Temporal Fusion vs. Naive Mean Pooling While our method is able to achieve significantly better performance than the baseline CLIP using the mean-pooling setting, we further investigate whether it is compatible with the advanced cross-modal temporal fusion methods, namely, attention pooling, top-3 pooling, and X-Pool [16]. We simply replace the final mean-pooling in Eq. (3) with these cross-modal approaches and show the performance in Table 3. From the table, when adopting these cross-modal fusion methods, our models obtain clearly boosted performance, especially for X-Pool, which obtains the best per" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "type": "text", + "content": "15654" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 104, + 506, + 229 + ], + "blocks": [ + { + "bbox": [ + 73, + 104, + 506, + 229 + ], + "lines": [ + { + "bbox": [ + 73, + 104, + 506, + 229 + ], + "spans": [ + { + "bbox": [ + 73, + 104, + 506, + 229 + ], + "type": "table", + "html": "
MethodsText ⇒ VideoVideo ⇒ TextMeta Sum ↑
R@1↑R@5↑R@10↑MnR↓R@1↑R@5↑R@10↑MnR↓
cross-modal temporal fusion
X-Pool [16]25.243.753.553.222.742.651.247.4238.9
TS2-Net [24]23.442.350.956.9-----
EMCL [18]23.942.450.9-22.240.649.2-229.2
X-CLIP [28]23.343.0-56.022.542.2-50.7-
text-agnostic temporal pooling
CLIP4Clip† (seqLSTM) [27]21.641.849.858.020.940.749.153.9223.9
CenterCLIP† (k-medoids++) [57]21.941.150.755.621.141.250.248.7226.2
ours (mean pool)23.141.750.556.822.040.850.351.0228.4
", + "image_path": "9f79d2185ea2b0da79b28541a4c4867ac60be8694f16970f74906990ad413e42.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 236, + 531, + 261 + ], + "lines": [ + { + "bbox": [ + 45, + 236, + 531, + 261 + ], + "spans": [ + { + "bbox": [ + 45, + 236, + 531, + 261 + ], + "type": "text", + "content": "Table 6: Comparisons with state-of-the-arts on LSMDC. † both CLIP4Clip and CenterCLIP have multiple versions in their papers and here we choose the versions with the highest Meta Sum values." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 45, + 278, + 279, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 278, + 279, + 336 + ], + "spans": [ + { + "bbox": [ + 45, + 278, + 279, + 336 + ], + "type": "text", + "content": "formance for both text-video and video-text retrieval and outperforms the original X-Pool by a large margin. Moreover, even compared with the state-of-the-art cross-modal fusion methods, our model with naive mean-pooling is still competitive for both text-video and video-text retrieval." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 337, + 280, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 337, + 280, + 500 + ], + "spans": [ + { + "bbox": [ + 45, + 337, + 280, + 500 + ], + "type": "text", + "content": "We further measure the memory usage and latency of the compared methods during inference on the test set. To make the experiment setting close to real-world scenarios and for fair comparisons, we use the same pre-computed frame and text representations while only monitoring space and time consumption for the ranking procedure. As shown in the last column of Table 3, our model with mean-pooling is orders of magnitude more efficient than those baseline models with cross-modal temporal fusion. This conclusion is generalizable to other datasets, i.e., the same model will always have the same ranking efficiency if using the same inference and evaluation settings. This reveals the importance of using text-agnostic temporal fusion (e.g., mean-pooling) for real-world text-video retrieval." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 512, + 241, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 512, + 241, + 526 + ], + "spans": [ + { + "bbox": [ + 45, + 512, + 241, + 526 + ], + "type": "text", + "content": "4.2. Comparison with the State-of-the-arts" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 532, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 532, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 532, + 279, + 730 + ], + "type": "text", + "content": "In this section, we compare our proposed method with state-of-the-art methods on MSRVTT, MSVD, and LSMDC dataset. To better reveal the performance gap among the compared methods, we do not consider post-processing techniques like QB-NORM [2]. The results of both text-video and video-text retrieval tasks are presented in Tables 4, 5 and 6. From the tables, when compared under the text-agnostic temporal fusion setting, our model outperforms the baseline models on most of the evaluation metrics, especially for Meta Sum, where it achieves the best performance on all three datasets. Specifically, on MSRVTT, the Meta Sum of our model is 7 points better than the second-best model; on MSVD, our method outperforms CenterCLIP [57] by 13.3; On LSMDC, our model consistently achieves the highest Meta Sum. Moreover, when compared with methods using cross-modal temporal fusion, our model with mean-pooling is still competitive in terms" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 298, + 276, + 411, + 322 + ], + "blocks": [ + { + "bbox": [ + 298, + 276, + 411, + 322 + ], + "lines": [ + { + "bbox": [ + 298, + 276, + 411, + 322 + ], + "spans": [ + { + "bbox": [ + 298, + 276, + 411, + 322 + ], + "type": "image", + "image_path": "bba94add5c4feb1523c564bcda6f66d308f15b2303ac2325415acbb896eaee01.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 316, + 325, + 512, + 335 + ], + "lines": [ + { + "bbox": [ + 316, + 325, + 512, + 335 + ], + "spans": [ + { + "bbox": [ + 316, + 325, + 512, + 335 + ], + "type": "text", + "content": "(a) " + }, + { + "bbox": [ + 316, + 325, + 512, + 335 + ], + "type": "inline_equation", + "content": "\\mathbb{R}@\\mathbb{1}" + }, + { + "bbox": [ + 316, + 325, + 512, + 335 + ], + "type": "text", + "content": " performance with different number of decoder layers" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 418, + 276, + 530, + 322 + ], + "blocks": [ + { + "bbox": [ + 418, + 276, + 530, + 322 + ], + "lines": [ + { + "bbox": [ + 418, + 276, + 530, + 322 + ], + "spans": [ + { + "bbox": [ + 418, + 276, + 530, + 322 + ], + "type": "image", + "image_path": "eb1db2f7a06406b2d802c8b0c630a43d85113cc35b8e10a1a6c3d6c5bf540f91.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 298, + 345, + 412, + 395 + ], + "blocks": [ + { + "bbox": [ + 298, + 345, + 412, + 395 + ], + "lines": [ + { + "bbox": [ + 298, + 345, + 412, + 395 + ], + "spans": [ + { + "bbox": [ + 298, + 345, + 412, + 395 + ], + "type": "image", + "image_path": "22449661e7bd53de1d4938b4c9f0dff45b3e39cdb6a44398c9bde623da1eccee.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 308, + 399, + 520, + 408 + ], + "lines": [ + { + "bbox": [ + 308, + 399, + 520, + 408 + ], + "spans": [ + { + "bbox": [ + 308, + 399, + 520, + 408 + ], + "type": "text", + "content": "(b) R@1 performance with different number of subsampling frames" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 416, + 345, + 530, + 395 + ], + "blocks": [ + { + "bbox": [ + 416, + 345, + 530, + 395 + ], + "lines": [ + { + "bbox": [ + 416, + 345, + 530, + 395 + ], + "spans": [ + { + "bbox": [ + 416, + 345, + 530, + 395 + ], + "type": "image", + "image_path": "211ec0cc2ba3c007d8c7077e33123532c4bd3b9bdaadf33aa8aa3fb0d4ae5549.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 298, + 418, + 411, + 466 + ], + "blocks": [ + { + "bbox": [ + 298, + 418, + 411, + 466 + ], + "lines": [ + { + "bbox": [ + 298, + 418, + 411, + 466 + ], + "spans": [ + { + "bbox": [ + 298, + 418, + 411, + 466 + ], + "type": "image", + "image_path": "2fdee8c2a3e805f602de70b86f014e8d74496978767905df18eff5e154612b9b.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 469, + 514, + 479 + ], + "lines": [ + { + "bbox": [ + 313, + 469, + 514, + 479 + ], + "spans": [ + { + "bbox": [ + 313, + 469, + 514, + 479 + ], + "type": "text", + "content": "(c) " + }, + { + "bbox": [ + 313, + 469, + 514, + 479 + ], + "type": "inline_equation", + "content": "\\mathrm{R}@\\mathrm{l}" + }, + { + "bbox": [ + 313, + 469, + 514, + 479 + ], + "type": "text", + "content": " performance with different value of hyper-parameter " + }, + { + "bbox": [ + 313, + 469, + 514, + 479 + ], + "type": "inline_equation", + "content": "\\lambda" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 417, + 418, + 529, + 466 + ], + "blocks": [ + { + "bbox": [ + 417, + 418, + 529, + 466 + ], + "lines": [ + { + "bbox": [ + 417, + 418, + 529, + 466 + ], + "spans": [ + { + "bbox": [ + 417, + 418, + 529, + 466 + ], + "type": "image", + "image_path": "6896488aea93575cc41f73f9f6db5f21f215eaed94fe859e62e3f13e8a0cb343.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 297, + 488, + 530, + 524 + ], + "lines": [ + { + "bbox": [ + 297, + 488, + 530, + 524 + ], + "spans": [ + { + "bbox": [ + 297, + 488, + 530, + 524 + ], + "type": "text", + "content": "Figure 5: We show the effects of (a) the number of captioning decoder layers; (b) the number of subsampling frames " + }, + { + "bbox": [ + 297, + 488, + 530, + 524 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 297, + 488, + 530, + 524 + ], + "type": "text", + "content": " in training; (c) the values of hyper-parameter " + }, + { + "bbox": [ + 297, + 488, + 530, + 524 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 297, + 488, + 530, + 524 + ], + "type": "text", + "content": " in Eq. (6)." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 547, + 530, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 547, + 530, + 654 + ], + "spans": [ + { + "bbox": [ + 296, + 547, + 530, + 654 + ], + "type": "text", + "content": "of Meta Sum, while being much more efficient in practice (refer to Figure 1 and Table 3 for detailed discussions). Specifically, on MSRVTT, it outperforms CLIP2TV [14] and CLIP2Video [12]; on MSVD, it surpasses all compared baselines and improves over the second-best model (X-Pool [16]) by 4.8; on LSMDC, it is still comparable with EMCL [18]. These results show that our proposed method has a better trade-off between performance and efficiency, and is more suitable for large-scale production systems." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 297, + 664, + 411, + 676 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 664, + 411, + 676 + ], + "spans": [ + { + "bbox": [ + 297, + 664, + 411, + 676 + ], + "type": "text", + "content": "4.3. Further Discussions" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 682, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 682, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 682, + 531, + 730 + ], + "type": "text", + "content": "Number of Decoder Layers Generally, more layers in the captioning decoder would improve its capacity for learning fine-grained knowledge, which, however, also makes it easier to over-fit. To find a better trade-off, we study the" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "text", + "content": "15655" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 279, + 165 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 279, + 165 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 279, + 165 + ], + "type": "text", + "content": "effect of the number of layers. As shown in Figure 5(a), the performance of our model improves and reaches the peak with 3 layers of decoder for both text-video and video-text retrieval tasks. Thus, we set the number of decoder layers to 3 for all the experiments." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 183, + 279, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 183, + 279, + 323 + ], + "spans": [ + { + "bbox": [ + 45, + 183, + 279, + 323 + ], + "type": "text", + "content": "Number of Subsampling Frames In practice, we set the number of training frames as 6 and validation frames as 12. Then, we randomly sample " + }, + { + "bbox": [ + 45, + 183, + 279, + 323 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 45, + 183, + 279, + 323 + ], + "type": "text", + "content": " frames before mean-pooling for training while using all 12 frames for evaluation. Notably, if " + }, + { + "bbox": [ + 45, + 183, + 279, + 323 + ], + "type": "inline_equation", + "content": "k = 6" + }, + { + "bbox": [ + 45, + 183, + 279, + 323 + ], + "type": "text", + "content": ", that means we average all the training frames in the mean-pooling operation. In Figure 5(b), we observe that the performance improves when reducing the value of " + }, + { + "bbox": [ + 45, + 183, + 279, + 323 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 45, + 183, + 279, + 323 + ], + "type": "text", + "content": " and achieves the peak when " + }, + { + "bbox": [ + 45, + 183, + 279, + 323 + ], + "type": "inline_equation", + "content": "k = 3" + }, + { + "bbox": [ + 45, + 183, + 279, + 323 + ], + "type": "text", + "content": ", which demonstrates its effectiveness. While further decreasing the value of " + }, + { + "bbox": [ + 45, + 183, + 279, + 323 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 45, + 183, + 279, + 323 + ], + "type": "text", + "content": ", the mean-pooling operation may lose a great deal of semantics derived from frames, which causes performance degradation. Therefore, we set " + }, + { + "bbox": [ + 45, + 183, + 279, + 323 + ], + "type": "inline_equation", + "content": "k = 3" + }, + { + "bbox": [ + 45, + 183, + 279, + 323 + ], + "type": "text", + "content": " for all the experiments." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 341, + 279, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 341, + 279, + 434 + ], + "spans": [ + { + "bbox": [ + 45, + 341, + 279, + 434 + ], + "type": "text", + "content": "Hyper-parameter " + }, + { + "bbox": [ + 45, + 341, + 279, + 434 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 45, + 341, + 279, + 434 + ], + "type": "text", + "content": " in Eq. (6) From Figure 5(c), in the case of a small " + }, + { + "bbox": [ + 45, + 341, + 279, + 434 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 45, + 341, + 279, + 434 + ], + "type": "text", + "content": " (e.g., " + }, + { + "bbox": [ + 45, + 341, + 279, + 434 + ], + "type": "inline_equation", + "content": "\\lambda = 0.3" + }, + { + "bbox": [ + 45, + 341, + 279, + 434 + ], + "type": "text", + "content": "), the model can only achieve suboptimal performance due to insufficient exploitation of the detailed semantics. When increasing the value of " + }, + { + "bbox": [ + 45, + 341, + 279, + 434 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 45, + 341, + 279, + 434 + ], + "type": "text", + "content": ", the performance of our model peaks at the " + }, + { + "bbox": [ + 45, + 341, + 279, + 434 + ], + "type": "inline_equation", + "content": "\\lambda = 0.5" + }, + { + "bbox": [ + 45, + 341, + 279, + 434 + ], + "type": "text", + "content": " and degrades thereafter. Considering the trade-off between typical contrastive loss and captioning loss, we choose the weighting parameter " + }, + { + "bbox": [ + 45, + 341, + 279, + 434 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 45, + 341, + 279, + 434 + ], + "type": "text", + "content": " as 0.5 for all the datasets." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 447, + 116, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 447, + 116, + 459 + ], + "spans": [ + { + "bbox": [ + 45, + 447, + 116, + 459 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 468, + 279, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 468, + 279, + 631 + ], + "spans": [ + { + "bbox": [ + 45, + 468, + 279, + 631 + ], + "type": "text", + "content": "In this paper, we tackle the task of text-video retrieval, where we aim to learn semantically-enhanced representations purely from the video, allowing for offline computation and reuse for different text queries. Our method introduces a new Prompt Cube into the CLIP image encoder, which is iteratively transposed within the encoder layers to incorporate global video semantics into frame representations. We also adopt an auxiliary video captioning objective to optimize the frame representations, providing detailed guidance in the semantic space. With mean pooling fusion on the enhanced frame representations, the proposed model achieves SoTA performance on three benchmark datasets. Comprehensive experiments verify the effectiveness of all critical components of our proposed method." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 643, + 102, + 655 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 643, + 102, + 655 + ], + "spans": [ + { + "bbox": [ + 47, + 643, + 102, + 655 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 50, + 662, + 279, + 730 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 50, + 662, + 279, + 695 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 662, + 279, + 695 + ], + "spans": [ + { + "bbox": [ + 50, + 662, + 279, + 695 + ], + "type": "text", + "content": "[1] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. Frozen in time: A joint video and image encoder for end-to-end retrieval. 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In ICCV, pages 408-417, 2017." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 746, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 746, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 746, + 300, + 756 + ], + "type": "text", + "content": "15658" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models/f6450b64-da9d-48f8-bcd6-4de4863bfc2b_content_list.json b/2023/Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models/f6450b64-da9d-48f8-bcd6-4de4863bfc2b_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..eec48d37083ae75c41a5310cceaa5ea0e66b82d8 --- /dev/null +++ b/2023/Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models/f6450b64-da9d-48f8-bcd6-4de4863bfc2b_content_list.json @@ -0,0 +1,1602 @@ +[ + { + "type": "text", + "text": "Prompt Tuning Inversion for Text-Driven Image Editing Using Diffusion Models", + "text_level": 1, + "bbox": [ + 81, + 130, + 888, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Wenkai Dong $^{1}$ Song Xue $^{1}$ Xiaoyue Duan $^{1,2*}$ Shumin Han $^{1\\dagger}$ $^{1}$ Baidu VIS, $^{2}$ Beihang University", + "bbox": [ + 227, + 179, + 746, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{dongwenkai, xuesong06, duanxiaoyue, hanshumin}@baidu.com", + "bbox": [ + 233, + 219, + 736, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently large-scale language-image models (e.g., text-guided diffusion models) have considerably improved the image generation capabilities to generate photorealistic images in various domains. Based on this success, current image editing methods use texts to achieve intuitive and versatile modification of images. To edit a real image using diffusion models, one must first invert the image to a noisy latent from which an edited image is sampled with a target text prompt. However, most methods lack one of the following: user-friendliness (e.g., additional masks or precise descriptions of the input image are required), generalization to larger domains, or high fidelity to the input image. In this paper, we design an accurate and quick inversion technique, Prompt Tuning Inversion, for text-driven image editing. Specifically, our proposed editing method consists of a reconstruction stage and an editing stage. In the first stage, we encode the information of the input image into a learnable conditional embedding via Prompt Tuning Inversion. In the second stage, we apply classifier-free guidance to sample the edited image, where the conditional embedding is calculated by linearly interpolating between the target embedding and the optimized one obtained in the first stage. This technique ensures a superior trade-off between editability and high fidelity to the input image of our method. For example, we can change the color of a specific object while preserving its original shape and background under the guidance of only a target text prompt. Extensive experiments on ImageNet demonstrate the superior editing performance of our method compared to the state-of-the-art baselines.", + "bbox": [ + 76, + 300, + 473, + 753 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 781, + 209, + 796 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Text-based image editing, a long-standing problem in image processing, aims to modify an input image to align its visual content with the target text prompts. It has drawn increasing attention in recent years and many meth", + "bbox": [ + 75, + 806, + 468, + 867 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ec9946c23ea0759f221389fe38474c4b169db3f781a45b4f968432bebcfd902b.jpg", + "image_caption": [ + "Input image" + ], + "image_footnote": [], + "bbox": [ + 527, + 271, + 640, + 358 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6ad35496e83e3be457961aff002c8b50c07a7b5be06ca35e94876b0d5aae6984.jpg", + "image_caption": [ + "DDIM Inversion" + ], + "image_footnote": [], + "bbox": [ + 640, + 271, + 751, + 358 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/eaf0eb36aeee9da29fe5acd45e32e853ff696bd10499024ce978583d86c69a4a.jpg", + "image_caption": [ + "DDIM-Edit" + ], + "image_footnote": [], + "bbox": [ + 753, + 271, + 864, + 358 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3799b4b5e70aee63b720e72ad8ad0f4b5dcbfaaf630050bd1299bd0c7f1a079a.jpg", + "image_caption": [ + "DiffEdit", + "Figure 1. Illustration of different methods in editing the color of the car. Methods based on the original DDIM inversion (i.e., DDIM-Edit, DiffEdit and DiffEdit w/o src) cannot preserve the shape of the car. In contrast, our method successfully changes the color while preserving the structural information. The target text is \"a yellow car\". The source text is \"a red car\" for DiffEdit." + ], + "image_footnote": [], + "bbox": [ + 527, + 368, + 640, + 454 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c4226ed19c5dbf37eae79b6d1657a438d1fd354e8a37a8576b34b48aa05238b4.jpg", + "image_caption": [ + "DiffEdit w/o src" + ], + "image_footnote": [], + "bbox": [ + 640, + 368, + 751, + 454 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5a8cd4165c7a34893361c2a33e85882307b8e0fa6a606963eb1b33fa89db920d.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 753, + 368, + 864, + 454 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ods built upon text-to-image generation have been developed. In past years, GAN-based image editing methods [30, 31, 52, 53] achieve impressive results due to the powerful generation abilities of GANs [37, 23, 33, 60]. However, these methods only work well in domains where the models are trained. More recently, diffusion models such as DDPM [18] and score-based generative models [48] have demonstrated competitive or even better capability of generating images compared to VAE-, GAN-, flow- and autoregressive-based models [36, 14, 38, 12]. Especially, large-scale language-image models (LLIMs), such as Imagegen [43], DALL-E2 [35] and Stable Diffusion [41], have attracted unprecedented attention from the research community and public society. With the help of large-scale pretrained language models [34, 10], LLIMs can generate high-fidelity images well aligned with the provided text prompts without further fine-tuning. To fully leverage the generation and generalization capabilities of LLIMs, we aim to develop a text-driven image editing method based on open-sourced LLIMs, e.g., Stable Diffusion [41].", + "bbox": [ + 496, + 580, + 893, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Editability and fidelity are two essential requirements", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*This work was done when Xiaoyue Duan was an intern at Baidu VIS.", + "bbox": [ + 94, + 875, + 467, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author", + "bbox": [ + 96, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7430", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "of image editing tasks. The former requires that the edited images are supposed to contain visual contents well aligned with the corresponding textual contents provided in the target prompts, while the latter expects that areas other than the edited parts should stay as close to those of the input image as possible. For example, when modifying the color of a specific object, its other attributes (e.g., size and shape) are expected to be preserved. As shown in Fig. 1, given an image of a red car and the target text prompt (\"a yellow car\"), the desired edited image should contain a yellow car while keeping the background as well as the car's size and shape unchanged. To achieve this editing, the simplest way is to first invert the image to a noisy latent via the reversed deterministic DDIM sampling process [46], and then obtain the edited image via the deterministic DDIM sampling process with the guidance of the target prompt embedding. We refer to this approach as \"DDIM-Edit\" in our paper. Although this approach successfully turns the color of the car to yellow (see \"DDIM-Edit\" in Fig. 1), the background and the shape of the car change drastically, which obviously fails to meet the requirement of high fidelity. The reason lies in that the deterministic DDIM sampling process cannot be reversed perfectly in practice. A slight error is amplified by a large classifier-free guidance scale, and is accumulated in each sampling step, which consequently results in a significantly different image.", + "bbox": [ + 76, + 90, + 472, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To improve fidelity, some methods consider the image editing tasks as inpainting tasks, which require users to explicitly provide masks of the inpainting regions [3, 25]. With the mask prior, the background can remain the same, but masking out image contents also removes important structural information that is helpful in the editing process, leading to unsatisfactory editing results. Moreover, asking users to provide masks is cumbersome and not suitable for quick and intuitive text-driven image editing. As a solution, DiffEdit [7] presents an algorithm that can automatically generate a mask given a target text prompt to locate the region to be edited. However, the editability of DiffEdit largely depends on DDIM-Edit, which may fail to preserve the structural information of the edited object, e.g., the shape of the car (see \"DiffEdit\" in Fig. 1). Moreover, to generate an accurate mask, DiffEdit requires a precise text description of the input image (referred to as \"source text\"), hampering the editing efficiency. Without the source text (see \"DiffEdit w/o src\" in Fig. 1), the automatically generated mask cannot locate the body of the car accurately, further decreasing editability.", + "bbox": [ + 76, + 488, + 472, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we aim to propose an image editing method to mitigate all the above problems, i.e., the method should be user-friendly, generalizable to various domains, and generate edited images with high fidelity. Specifically, for a quick and intuitive text-based method, users only need to provide an input image and the corresponding target text", + "bbox": [ + 76, + 810, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "prompts, without the need for a mask or a source text describing the input image. Secondly, the method should be able to operate on real images from various domains. Thirdly, the objects should be precisely edited with the background preserved. In some cases, only certain attributes of the objects should be modified, while other attributes are supposed to be left untouched.", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To achieve these merits, we believe that image editing needs a new inversion method based on diffusion models to reconstruct the input image. Inspired by the classifier-free guidance [20] and textual-inversion methods [27], we propose a Prompt Tuning Inversion method to encode the information of the input image into a conditional embedding. More specifically, we first apply DDIM inversion to the input image latent to obtain a sequence of noisy ones. These noisy latents can be taken as a prior trajectory for reconstructing the original image. Then, we introduce a learnable embedding in the sampling process. The diffusion model reconstructs the input image step by step along the trajectory conditioned on this embedding while optimizing it at the same time. In this way, the contents of the input image are learned in the embedding. Finally, we obtain a new conditional embedding by linearly interpolating between the optimized embedding and the target embedding, resulting in a representation that combines both the structural information of the input image and the visual content of the target text.", + "bbox": [ + 496, + 199, + 892, + 501 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Overall, our proposed method consists of two stages. In the first stage, we encode the information of the input image into a learnable conditional embedding via prompt tuning in the reconstruction process. In the second stage, a new conditional embedding is computed by linearly interpolating between the target embedding and the optimized one obtained in the first stage, which boosts a trade-off between editability and fidelity. The classifier-free guidance is then applied to sample the edited image. In sum, our contributions are as follows:", + "bbox": [ + 496, + 505, + 893, + 655 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a user-friendly text-driven image editing method which requires only an input image and a target text for editing, without any need for user-provided masks or source descriptions of the input images.", + "- We propose a Prompt Tuning Inversion method for diffusion models which can quickly and accurately reconstruct the original image, providing a strong basis for sampling edited images with high fidelity to the inputs.", + "- We compare against the state-of-the-art methods both qualitatively and quantitatively, and show that our method outperforms these works in terms of the trade-off between editability and fidelity." + ], + "bbox": [ + 517, + 674, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7431", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 76, + 89, + 215, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Text-to-image synthesis. Text-guided synthesis has been widely adopted for image generation [12, 54, 4, 41]. Works based on generative adversarial networks (GANs) [37, 23, 33, 60] have been proposed for text-to-image synthesis. CLIP-based methods [8, 54] have also been proposed to utilize the language-image priors from a pre-trained CLIP [34] model to generate images from texts. Recently, works [11, 18, 19, 29] based on the Diffusion Probabilistic Models (DPM) [45] have achieved state-of-the-art results in text-to-image synthesis. Among these works, Latent Diffusion Model (LDM) [41] trains DPM in the latent space using a powerful pre-trained auto-encoder, and introduces a cross-attention layer into the model architecture, thus turning the diffusion model into a powerful and flexible generator with greatly improved visual fidelity. Our work of image editing is based on LDM [41] thanks to its powerful image generation capability.", + "bbox": [ + 75, + 114, + 472, + 372 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image editing. Image editing with generative adversarial networks (GANs) has been studied extensively [30, 31, 52, 53]. Some other techniques also leverage the image-text alignment capability of CLIP [34] and transfer it to the framework of GANs [2, 49, 55]. More recently, the development of diffusion models [18, 45, 47] provides a more flexible design space than GANs for the editing task, while following a simpler training setup (e.g., SDEdit [26] and ILVR [6]). Textual Inversion [13] and Dream-Booth [42] demonstrate the capability to generate diverse images with unique object characteristics by fine-tuning the diffusion model with multiple images. Imagic [21] and UniTune [51], which are based on the powerful Imagen model [43], also show impressive editing performance. However, the above methods require restrictive fine-tuning of the pre-trained model, and thus may not fully leverage the generalization ability of the pre-trained model due to overfitting or language drift. Other methods [3, 28] require a user-provided mask to guide the diffusion process, making it hard for them to be interactive. To achieve text-only interactive editing, some optimization-free methods have been proposed recently (e.g., Prompt-to-Prompt [16] and DiffEdit [7]) to automatically infers a mask before editing.", + "bbox": [ + 75, + 372, + 472, + 718 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inversion. In the GAN literature, the inversion process requires one to find a corresponding latent representation of the given image [59, 56]. This process has been extensively studied for GANs [1, 61, 15, 39, 32, 50]. For diffusion models, the inversion requires to find a noise map and a conditional vector corresponding to a generated image but simply adding noise and denoising it may arouse the problem that the image content can be changed drastically. Works [6, 11, 35] have been proposed to improve the inversion process. However, it is still challenging for these methods to generate new instances of a given example while maintaining fidelity. Textual Inversion [13] and Dream-", + "bbox": [ + 75, + 719, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Booth [42] propose to learn concepts from images through textual inversion by either directly optimizing the embedding of the textual concept or fine-tuning the diffusion models, which can be computationally inefficient. Null-Text Inversion [27] modifies the unconditional textual embedding that is used for classifier-free guidance instead of the input text embedding, which enables applying prompt-based editing without the cumbersome tuning of the model parameters. Different from these methods, our method encodes the information of the input image into a learnable conditional embedding, which provides a helpful prior in sampling edited image with high fidelity to the input image.", + "bbox": [ + 496, + 90, + 893, + 273 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 498, + 284, + 635, + 301 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a real or synthesized image $\\mathcal{I}$ , we aim to edit $\\mathcal{I}$ to get an edited image $\\mathcal{I}^*$ with the guidance of text. Different from existing methods which require source prompts provided by users or produced by an off-the-shelf image captioning model, our proposed editing process is guided by only target or edited prompt $\\mathcal{P}^*$ . An overview of our method is provided in Fig. 2, which consists of two stages. In the first stage, we encode the information of the input image into a learnable conditional embedding via prompt tuning in the reconstruction process. A new conditional embedding is then computed in the second stage by linearly interpolating between the target embedding and the optimized one from the first stage, thus achieving effective editing while maintaining high fidelity. Conditioned on this interpolated embedding, the classifier-free guidance is adopted to sample the final edited image.", + "bbox": [ + 496, + 309, + 893, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Background and preliminaries", + "text_level": 1, + "bbox": [ + 498, + 559, + 772, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models. Diffusion probabilistic models are designed to learn a data distribution by gradually denoising normally distributed noise, which corresponds to learning to reverse a fixed forward diffusion process:", + "bbox": [ + 496, + 582, + 893, + 643 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(x _ {t} \\mid x _ {t - 1}\\right) := \\mathcal {N} \\left(x _ {t}; \\sqrt {\\alpha_ {t}} x _ {t - 1}, (1 - \\alpha_ {t}) \\mathbf {I}\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 651, + 890, + 670 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the forward process, normally distributed noise is gradually added to the sample $x_{t - 1}$ to obtain a more noisy variant $x_{t}$ . The noise is dependent on a variance schedule $\\alpha_{t}$ where $t\\in 1,\\dots,T$ , with $T$ being the total number of steps, $x_0$ the original image, and $x_{T}$ approximately the standard Gaussian noise. The reverse process is defined with parameters $\\theta$ :", + "bbox": [ + 496, + 676, + 893, + 781 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right) := \\mathcal {N} \\left(x _ {t - 1}; \\mu_ {\\theta} \\left(x _ {t}, t\\right), \\Sigma_ {\\theta}\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 791, + 890, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Using a fixed variance $\\Sigma_{\\theta}$ , only the mean value $\\mu_{\\theta}(x_t,t)$ needs to be learned. With the parameterization trick, the network $\\epsilon_{\\theta}$ is trained to predict the noise $\\epsilon$ , resulting in a loss, where $c$ represents the conditional embedding:", + "bbox": [ + 496, + 815, + 893, + 878 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {t, x _ {0}, \\epsilon} [ \\| \\epsilon - \\epsilon_ {\\theta} (x _ {t}, t, c) \\| ^ {2} ]. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 883, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7432", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/937569000531e3da916ea9434e390e0b08a233bfa4442e7e8887dc5966611402.jpg", + "image_caption": [ + "Figure 2. An overview of our proposed image editing method. **Stage 1:** we first apply DDIM inversion to the input image embedding to obtain a diffusion trajectory $\\{z_t^*\\}_{t=0}^T$ . Then we reconstruct the input image along with the reversed trajectory by optimizing the learnable conditional embedding $c_t$ . **Stage 2:** we perform classifier-free guidance sampling conditioned on a linear interpolation between target embedding $c^*$ and $c_t$ at each diffusion step. $\\bigoplus$ denotes element-wise weighted addition. Red dashes indicate the gradient flow in PTI." + ], + "image_footnote": [], + "bbox": [ + 181, + 87, + 795, + 339 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this work, we employ the deterministic DDIM sampling [46]:", + "bbox": [ + 76, + 421, + 470, + 454 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t - 1} = \\sqrt {\\alpha_ {t - 1}} f _ {\\theta} (x _ {t}, t) + \\sqrt {1 - \\alpha_ {t - 1}} \\epsilon_ {\\theta} (x _ {t}, t), \\qquad (4)\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 463, + 468, + 482 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $f_{\\theta}$ is the prediction of $x_0$ given $x_t$ at step $t$ . Given a noisy image $x_T$ , the noise is gradually removed to generate an image $x_0$ by applying Eq. 4 for $T$ steps.", + "bbox": [ + 76, + 492, + 468, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Latent diffusion. Instead of operating in the image pixel space, Latent Diffusion Models [41] (LDMs) utilize an autoencoder to learn a latent space which is perceptually equivalent to the pixel space. First, an encoder $ENC$ is adopted to map a given image $x_0$ into a latent embedding $z_0$ . Then a decoder $DEC$ is designed to reconstruct the input image given $z_0$ , i.e., $DEC(ENC(x_0)) \\approx x_0$ . The encoder downsamples the original images by a factor of 4 or 8. In this way, the diffusion model operates on a much smaller representation with lower time complexity and memory burden. Thus, for our method, we apply one of the state-of-the-art LDMs, Stable Diffusion [41]. In the forward and reverse process described above, we only need to replace the image $x_t$ with its latent embedding $z_t$ at each step.", + "bbox": [ + 75, + 537, + 468, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Classifier-free guidance. Our editing method is built upon text-guided diffusion models. In Stable Diffusion, the text $\\mathcal{P}$ is fed into a pre-trained CLIP [34] text encoder $\\tau_{\\theta}$ to obtain its corresponding embedding and the underlying UNet model is augmented with the cross attention mechanism, which is effective for generating visual contents conditioned on the text $\\mathcal{P}$ . One of the key challenges in this kind of generation models is the amplification of the effect induced by the conditional text. To this end, the classifier-free guidance technique is proposed, where the prediction for each step is", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "a combination of conditional and unconditional predictions. Formally, let $c = \\tau_{\\theta}(\\mathcal{P})$ be the conditional embedding vector and $\\varnothing = \\tau_{\\theta}(\\varnothing)$ be the unconditional one, the classifier-free guidance prediction is calculated by:", + "bbox": [ + 498, + 421, + 890, + 484 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\epsilon} _ {t} = \\epsilon_ {\\theta} \\left(z _ {t}, t, \\varnothing\\right) + \\omega \\cdot \\left(\\epsilon_ {\\theta} \\left(z _ {t}, t, c\\right) - \\epsilon_ {\\theta} \\left(z _ {t}, t, \\varnothing\\right)\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 494, + 890, + 511 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\omega$ is the guidance scale parameter.", + "bbox": [ + 500, + 523, + 769, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Problems of DDIM inversion", + "text_level": 1, + "bbox": [ + 500, + 547, + 756, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given an input image $\\mathcal{I}$ and a target prompt $\\mathcal{P}^*$ , we aim to edit $\\mathcal{I}$ to make its visual content consistent with textual content in $\\mathcal{P}^*$ , while preserving a maximal amount of details from $\\mathcal{I}$ . The above two aspects are referred to asEditability and input image fidelity, respectively.", + "bbox": [ + 496, + 570, + 890, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To achieve effective editing while maintaining high fidelity, we first need to inverse the input image into an appropriate noise map, based on which the edited image can be sampled. Eqs. 1 and 2 show a naive way to add noise to the input image and then denoise it through the diffusion network, respectively. However, as the sampling process is stochastic, the samples generated from the same latent can be different every time. Even if the sampling process becomes deterministic, the random noise in the forward process still makes the generated image content change significantly. To address this issue, DiffusionCLIP [22] reverses the deterministic DDIM sampling process in Eq. 4 based on the assumption that the ordinary differential equation (ODE) process can be reversed within the limit of small steps:", + "bbox": [ + 496, + 647, + 892, + 872 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nz _ {t + 1} = \\sqrt {\\alpha_ {t + 1}} f _ {\\theta} \\left(z _ {t}, t\\right) + \\sqrt {1 - \\alpha_ {t + 1}} \\epsilon_ {\\theta} \\left(z _ {t}, t\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 883, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7433", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5c7411c6a54a2f60320f575a5bb1deeda7b4770c79a1c00e6b70fce12c39b8fd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 90, + 181, + 162 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/68c69a50553b254fa4ef16610e28b5767436b0281aa6ed38bad8fd50887a12c9.jpg", + "image_caption": [ + "CFG $(\\omega = 0.0)$" + ], + "image_footnote": [], + "bbox": [ + 181, + 90, + 272, + 162 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/692145787054f0c4979c47c842c11b8a6f796d1ef1804474566c289e5e182813.jpg", + "image_caption": [ + "CFG $(\\omega = 1.0)$" + ], + "image_footnote": [], + "bbox": [ + 274, + 90, + 364, + 162 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8371103b6d97dc5944802e8c3c97918322aafca63676da40784be39b114bf59e.jpg", + "image_caption": [ + "CFG $(\\omega = 2.5)$" + ], + "image_footnote": [], + "bbox": [ + 367, + 90, + 457, + 162 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/62e2025b4d3460da294c929527e302725a4b4549e3d65d04e120b3d5043b05d3.jpg", + "image_caption": [ + "Input image", + "PTI (ours)", + "Figure 3. Reconstruction quality of our Prompt Tuning Inversion, and DDIM inversion with different classifier-free guidance (CFG) scales $\\omega$ in the sampling process. $\\omega = 0$ in the forward process for all methods." + ], + "image_footnote": [], + "bbox": [ + 86, + 172, + 179, + 244 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4a686a4c4ed117e2f3545825ac178c4819a9f013ad07d375765d9519b2aec22c.jpg", + "image_caption": [ + "CFG $(\\omega = 5.0)$" + ], + "image_footnote": [], + "bbox": [ + 181, + 172, + 272, + 244 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/33fff96fc7010df38375a6aa71e1138788c789b7fe1cbaec2261ace48d787b3a.jpg", + "image_caption": [ + "CFG $(\\omega = 7.5)$" + ], + "image_footnote": [], + "bbox": [ + 274, + 172, + 364, + 244 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/bfab0eff8fa91c0cd4001cb2e260ab7bcd95cf124c27af9276c033347efdce90.jpg", + "image_caption": [ + "CFG $(\\omega = 10.0)$" + ], + "image_footnote": [], + "bbox": [ + 367, + 172, + 457, + 244 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/2172c4fbcbc416d7b11604c9a73e96cfb1538bc3259717546670a9101db83568.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Reconstruction quality by measuring the PSNR score of DDIM inversion with different classifier-guidance scales $\\omega$ . $\\omega_{\\mathrm{enc}}$ and $\\omega_{\\mathrm{dec}}$ denote the guidance scale used in the DDIM forward and sampling processes, respectively." + ], + "table_body": "
ωdec\nωenc0.01.02.55.07.5
0.021.3619.7917.0414.8813.64
1.017.1621.9418.2215.4714.02
2.514.5115.7318.1315.7414.24
5.011.3011.4811.7012.1212.06
", + "bbox": [ + 102, + 333, + 439, + 417 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $z_{t}$ is the latent embedding of $x_{t}$ .", + "bbox": [ + 76, + 506, + 334, + 520 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To investigate the reconstruction performance of DDIM, we first invert the latent embedding of the input image into noise maps via Eq. 6 and then use the deterministic DDIM sampling process in Eq. 4 to reconstruct the input. Note that both processes are performed with unconditional diffusion models, i.e., the classifier-free guidance scale in Eq. 5 is set to $\\omega = 0$ for both forward and reverse sampling processes. Although a slight error is incorporated in every step as ODE process cannot be reversed perfectly in practice, the accumulated error is negligible, and DDIM inversion can nearly reconstruct the original image (see \"CFG ( $\\omega = 0.0$ )\" in Fig. 3). However, to generate an image well aligned with the conditional text prompt using Stable Diffusion, a large guidance scale $\\omega > 1$ is necessary for the sampling process in Eq. 4. This arouses the problem that when enlarging $\\omega$ , the generated images are far from the original ones as shown in Fig. 3. We believe that when $\\omega$ of the sampling process is different from that of the forward process, the accumulated error would be amplified, leading to unsatisfactory reconstruction quality. This can be illustrated in Table 1, i.e., the best reconstruction quality in each line is obtained when $\\omega$ used in the DDIM sampling process is the same as that used in the forward process. Even if $\\omega$ used in the forward and sampling processes are kept the same, PSNR still decreases with $\\omega$ increasing (see the numbers in bold in Ta", + "bbox": [ + 75, + 523, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ble 1). The above analysis demonstrates that it is hard for DDIM inversion to achieve a satisfactory trade-off between editability (which requires larger $\\omega$ ) and fidelity (which requires smaller $\\omega$ ). To address this issue, we propose a new inversion technique, i.e., Prompt Tuning Inversion.", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Prompt tuning for inversion", + "text_level": 1, + "bbox": [ + 500, + 174, + 750, + 190 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To successfully invert real images into the model's domain, recent works optimize the textual encoding, the network's parameters, or both. Motivated by Pivotal Inversion [40], we replace the conditional embedding of the text prompt with an optimized one, referred to as Prompt Tuning in this work. Namely, for each input image, we optimize only the conditional embedding $c$ so that it encodes important information of the input image which helps the reconstruction. The parameters of the diffusion network and the text encoder $\\tau_{\\theta}$ are frozen during prompt tuning.", + "bbox": [ + 496, + 198, + 890, + 348 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first initialize $z_0^* = z_0 = ENC(x_0)$ , and adopt DDIM inversion with $\\omega = 0$ to obtain a trajectory of noisy latent codes $\\{z_t^*\\}_{t=1}^T$ . Then we initialize $\\tilde{z}_T = z_T^*$ and perform the following optimization to the conditional embedding $c$ with $\\omega > 1$ for the timestamps $t = T, \\dots, 1$ , each for $N$ iterations:", + "bbox": [ + 496, + 349, + 890, + 424 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nc _ {t} = \\underset {c _ {t}} {\\arg \\min } \\left\\| z _ {t - 1} ^ {*} - z _ {t - 1} \\left(\\tilde {z} _ {t}, t, c _ {t}\\right) \\right\\| ^ {2}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 431, + 890, + 458 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For brevity, $z_{t-1}(\\tilde{z}_t, t, c_t)$ denotes applying a DDIM sampling step using $\\tilde{z}_t$ and the conditional embedding $c_t$ at the timestep $t$ . At the end of each timestep, we update", + "bbox": [ + 496, + 467, + 890, + 513 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {z} _ {t - 1} = z _ {t - 1} \\left(\\tilde {z} _ {t}, t, c _ {t}\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 619, + 522, + 890, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we can reconstruct the input image by using the noise latent $\\tilde{z}_T = z_T^*$ and the optimized conditional embeddings $\\{c_t\\}_{t=1}^T$ . In the next subsection, we will introduce the approach to editing images with the target text prompt and the conditional embeddings.", + "bbox": [ + 496, + 547, + 890, + 622 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Prompt tuning for editing", + "text_level": 1, + "bbox": [ + 500, + 631, + 733, + 647 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since the sequence of the conditional embeddings $\\{c_t\\}_{t=1}^T$ is optimized to fully reconstruct the input image, we believe that these optimized conditional embeddings have contained the most information of the original image, and thus ensure high fidelity. To achieve the desired modification, these optimized embeddings are adopted to perform the editing by advancing in the direction of the target text embedding $c^* = \\tau_\\theta(\\mathcal{P}^*)$ to ensure good editability also. More formally, in the second stage, we simply interpolate between the target embedding $c^*$ and the optimized $c_t$ linearly at each timestamp. For a given hyper-parameter $\\eta \\in (0,1]$ , we obtain", + "bbox": [ + 496, + 654, + 890, + 835 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nc _ {t} = \\eta \\cdot c ^ {*} + (1 - \\eta) \\cdot c _ {t}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 845, + 890, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the first term ensures the effective editability corresponding to the semantic contents in the target text, while", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7434", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the second term guarantees a good reconstruction of the original image. The algorithm is presented in Lines 14-21 in Algorithm 1. Note that when $\\eta = 0$ or $\\eta = 1$ , the output of our editing method is the reconstructed original image, or the output of the baseline DDIM-Edit, respectively.", + "bbox": [ + 75, + 90, + 472, + 167 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Intuitively, our editing method is to find an intermediate representation between the original image and the output of DDIM-Edit. For a desired modification, the intermediate representation is supposed to contain both the structural information of the source image and the semantic contents of the target text prompt. Eq. 9 is only one way to achieve this, which we refer to as condition interpolation. We also test a different interpolation method (referred to as latent interpolation), where we linearly interpolate between the noisy latent $z_{t}$ and $z_{t}^{*}$ at each timestamp:", + "bbox": [ + 75, + 172, + 472, + 325 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nz _ {t} ^ {e d t} = \\eta \\cdot z _ {t} + (1 - \\eta) \\cdot z _ {t} ^ {*}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 178, + 348, + 468, + 367 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $z_{t}^{*}$ is the noisy latent calculated by DDIM inversion via Eq. 6, and $z_{t}$ is the latent obtained in the vanilla DDIM sampling process conditioned on the target embedding. Although this approach is more simple since the process of prompt tuning is no longer needed, we observe that this interpolation method may lead to cluttered images. This is because the interpolation of latent embeddings mixes the source object and the edited object spatially, rather than semantically (as condition interpolation does), leading to cluttered contents in images.", + "bbox": [ + 75, + 390, + 472, + 541 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.5. Discussion", + "text_level": 1, + "bbox": [ + 76, + 570, + 194, + 585 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our proposed image editing method shares similar motivations with existing works [21, 51, 27, 16], all of which aim to modify an image in a text-driven and mask-free manner. However, our approach differs from them significantly in the following aspects:", + "bbox": [ + 75, + 599, + 468, + 676 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1) Imagic [21] and UniTune [51] finetune the diffusion models for hundreds of steps to maintain high fidelity to the input image. In contrast, we only need to optimize the conditional embedding, which greatly reduces computational budgets.", + "2) Our proposed Prompt Tuning Inversion is inspired by the Null-Text Inversion method [27]. However, Null-Text Inversion chooses to optimize the unconditional embedding while we optimize the conditional one. Moreover, the editing process of Null-Text Inversion is achieved by the cross-attention map control in Prompt-to-Prompt [16], which requires an additional description of the input image. Compared to theirs, our method only needs the target text prompt and is thus more user-friendly." + ], + "bbox": [ + 75, + 681, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: Prompt Tuning Inversion for Editing" + ], + "code_body": "Input: An input image $\\mathcal{I}$ and a target prompt embedding $c^{*} = \\tau_{\\theta}(\\mathcal{P}^{*})$ \nOutput: Edited image $\\mathcal{I}^*$ \n1 // DDIM Inversion \n2 Set guidance scale $\\omega = 0,z_0^* = ENC(\\mathcal{I})$ . \n3 Compute the intermediate trajectory $\\{z_t^*\\}_{t = 0}^T$ using DDIM inversion over $\\mathcal{I}$ without conditional guidance via Eq. 6; \n4// Prompt Tuning \n5 Set guidance scale $\\omega >1,\\eta \\in (0,1]$ . \n6 Initialize $\\tilde{z}_T\\gets z_T^*,c_T\\gets c^*$ . \n7 for $t = T,T - 1,\\dots ,1$ do \n8 for $j = 0,\\ldots ,N - 1$ do \n9 $|c_{t}\\gets c_{t} - \\beta \\nabla_{c}||z_{t - 1}^{*} - z_{t - 1}(\\tilde{z}_{t},t,c_{t})||_{2}^{2};$ \n10 end \n11 $\\tilde{z}_{t - 1}\\gets z_{t - 1}(\\tilde{z}_{t},t,c_{t}),c_{t - 1}\\gets c_{t}$ \n12 end \n13 // Editing \n14 Set $z_{T}^{edt}\\gets z_{T}^{*}$ . \n15 for $t = T,T - 1,\\ldots ,1$ do \n16 $c_{t} = (1 - \\eta)\\cdot c_{t} + \\eta \\cdot c^{*};$ \n17 $z_{t - 1}^{edt} = z_{t - 1}(z_{t}^{edt},t,c_{t});$ \n18 end \n19 $\\mathcal{I}^* = DEC(z_0^{edt})$ \n20 return $\\mathcal{I}^*$", + "bbox": [ + 500, + 111, + 890, + 502 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 532, + 633, + 549 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Setup", + "text_level": 1, + "bbox": [ + 500, + 558, + 581, + 574 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. In our experiments, we adopt the text-conditional Latent Diffusion Model [41] (known as Stable Diffusion) with 890M parameters trained on LAION-5B [44] at $512 \\times 512$ resolution. For the DDIM schedule, we adopt 50 steps and retain the original hyperparameter choices of Stable Diffusion. The encoding ratio parameter is set to 0.8. The number of iterations to optimize $c$ per diffusion step is set to $N = 1$ . The hyper-parameters $\\beta$ and $\\eta$ in Algorithm 1 are set to 0.1 and 0.9, respectively, unless specified. These allow editing an image in $\\sim 1$ minute on a single Tesla V100 GPU. For better performance, we adopt attention maps to localize the edited regions (referred to as local blending), and re-weight the attention maps as in [16].", + "bbox": [ + 496, + 582, + 890, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation and datasets. In semantic image editing, the visual content of the edited image is supposed to align well with the target text prompt (editability) while staying close to the input image in terms of the unedited parts (fidelity). For a given method, better editability usually comes at the cost of decreased fidelity to the input image, and vice versa. This forms a trade-off curve between the two objectives.", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7435", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/078554bf6836db688f4f76d7be8f798ed3057c994f750b7709ba9a4d0c379c2f.jpg", + "image_caption": [ + "Figure 4. Comparison with DiffEdit and DDIM-Edit on ImageNet. For all methods, we set the DDIM encoding ratio to 0.8, and only vary the mask threshold to draw the trade-off curve." + ], + "image_footnote": [], + "bbox": [ + 119, + 93, + 428, + 258 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Following DiffEdit [7], we evaluate different editing methods by comparing their trade-off curves on ImageNet [9]. Specifically, given an image of one class from ImageNet, we aim to edit it to another class of ImageNet as instructed by the target text prompt. The editability and fidelity are measured using the LPIPS perceptual distance [58] and CS-FID, which is a class-conditional FID metric [17], respectively. The former measures the distance with the input image while the latter measures both image realism and consistency w.r.t. the target class. For both metrics, lower values indicate better editing performance.", + "bbox": [ + 75, + 335, + 468, + 503 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Comparison with other methods on ImageNet", + "text_level": 1, + "bbox": [ + 76, + 512, + 465, + 529 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our method with DiffEdit and our baseline DDIM-Edit, since they both share the same DDIM forward process and a similar sampling process. Besides, they load the same publicly available pre-trained weights for a fair comparison. To leverage the generalization capability of large-scale language-image models, we adopt the text-conditional Stable Diffusion model \"sd-v1-4\" instead of the class-conditional model trained on ImageNet as the pre-trained model.", + "bbox": [ + 75, + 536, + 468, + 671 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As pointed out by DiffEdit [7], different editing methods often have hyper-parameters which control editability, e.g., the mask threshold, or the encoding ratio. A lower mask threshold or higher encoding ratio leads to stronger editing. In our proposed method, we can also control the editing strength by varying the conditional interpolation ratio $\\eta$ introduced in Eq. 9. In our evaluation, we fix the DDIM encoding ratio and draw the trade-off curve by varying the mask threshold for all methods1. The results are presented in Fig. 4, where \"DDIM-Global\" denotes that the images are edited via \"DDIM-Edit\" but without using any masks, i.e., the editing is performed globally. This can", + "bbox": [ + 75, + 671, + 470, + 854 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c72a62424e3ab6a466d8fcd8d0e367887d26175c1bd481d3348b5003337f76af.jpg", + "image_caption": [ + "Figure 5. Editing examples on ImageNet by our method and other methods. DDIM-G/DDIM-L indicates the baseline method DDIM-Edit with/without the local blend trick." + ], + "image_footnote": [], + "bbox": [ + 519, + 97, + 862, + 404 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "be regarded as a lower bound of fidelity for all methods. As the mask threshold increases, LPIPS decreases since fewer parts of the image are edited. Compared to DiffEdit, our baseline method DDIM-Edit achieves a better trade-off. Note that the only difference between the two methods is the approach to generating masks. The comparison shows that inferring editing masks using cross-attention maps, as adopted by DDIM-Edit, is more appropriate. Based on DDIM-Edit, our method can further improve the fidelity to the input images while maintaining editability. The best CSFID-LPIPS trade-off of our method demonstrates its superiority over DiffEdit and the baseline.", + "bbox": [ + 496, + 473, + 890, + 654 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also present qualitative examples of these methods. As shown in Fig. 5, without automatically generated masks, \"DDIM-G\" tends to modify images globally. For simple cases (e.g., example (d)), image editing methods with the original DDIM inversion works well. However, for complex cases, we observe undesired and unreasonable edits to the objects. In contrast, with the help of the learnable conditional embedding, our method achieves realistic editing while successfully preserving the original details.", + "bbox": [ + 496, + 655, + 890, + 791 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation study", + "text_level": 1, + "bbox": [ + 500, + 801, + 650, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison to existing inversion methods. We randomly select 128 images and their corresponding captions from the COCO validation set [24]. We then apply the following reconstruction methods to each image-caption pair: (1) AE denotes the variational auto-encoder with a slight KL-", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "1As there was no official implementation of DiffEdit available at the time of writing, we adopted the unofficial implementation for inferring editing masks from https://github.com/LuChengTHU/dpm-solver.", + "bbox": [ + 75, + 862, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7436", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/476feed1c294a2bdb79584779bdc2e67ffbd46237d7915e28768d9c9cd9edd4b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodAEDDIMNTIPTI (ours)
PSNR26.2213.6424.4525.71
SSIM0.85640.46410.82700.8501
", + "bbox": [ + 109, + 88, + 433, + 132 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/bf844a8d3d796463ca11261a0fef0300d7cf019bb493d3f28893b1d0f206b374.jpg", + "table_caption": [ + "Table 2. Reconstruction quality of different methods measured by PSNR and SSIM. For both metrics, higher values indicate better quality." + ], + "table_footnote": [], + "table_body": "
iters12345
learning rate β = 0.01
NTI17.0520.1222.2523.6124.45
PTI19.3623.2024.8625.4725.71
learning rate β = 0.1
NTI23.0824.7425.6225.8225.91
PTI24.7425.2325.7825.9025.97
", + "bbox": [ + 107, + 195, + 433, + 301 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. PSNR scores under different optimizing settings.", + "bbox": [ + 101, + 303, + 442, + 316 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "penalty used in Stable Diffusion. An image is first encoded by the encoder of AE. Afterwards, the decoder directly reconstructs the image from the latent. Therefore, we consider AE as an upper bound of reconstruction quality. (2) DDIM denotes the DDIM inversion method, which is a baseline inversion method. As analyzed in Sec. 3.2, it usually outputs a low-quality reconstruction result under a large classifier-free guidance scale $\\omega$ . (3) NTI denotes the Null-Text Inversion method [27], which is our main point of comparison. Different from our method, it optimizes the unconditional embedding. (4) PTI denotes our proposed Prompt Tuning Inversion method. We introduce a learnable conditional embedding and the optimizing details are presented in Algorithm 1.", + "bbox": [ + 75, + 349, + 468, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The experimental results are provided in Table 2. For the diffusion-based inversion methods, we apply the diffusion model in an unconditional manner (i.e., the classifier guidance scale $\\omega = 0$ ) for the DDIM forward process. For the sampling process, we set $\\omega = 7.5$ . As shown in Table 2, DDIM inversion fails to reconstruct the original images since $\\omega$ in the sampling process is different from that in the forward process, leading to a low PSNR score (13.64). For NTI and PTI, we set the number of iterations $N$ to 5 and the learning rate $\\beta$ to 0.01. We observe that both methods can reconstruct the images but the reconstruction quality of our method is better (25.71 vs. 24.45). To further demonstrate the effectiveness of our method, we vary $N$ from 1 to 5 and increase the learning rate $\\beta$ from 0.01 to 0.1. The experimental results in Table 3 show that the reconstruction quality of PTI is always better than NTI under all settings, demonstrating that our method converges faster.", + "bbox": [ + 75, + 564, + 468, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Influence of the hyper-parameter $\\eta$ . We also perform ablation on the hyper-parameter $\\eta$ and the results are presented in Fig. 6. By adjusting $\\eta$ , we can achieve a good trade-off between fidelity and editability. More quantitative analyses are presented in supplementary materials.", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7370967ba997d267657f4937f72ce74ffa8670288faef971c02451683d9504e2.jpg", + "image_caption": [ + "Figure 6. Qualitative examples for the effect of $\\eta$ ." + ], + "image_footnote": [], + "bbox": [ + 503, + 88, + 895, + 226 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/07cab73b5cd3ba16b3fd693e060674fc3063c2f6cf1041f14f13724892aa9376.jpg", + "image_caption": [ + "Figure 7. A failure example on ImageNet: when multiple objects exist, only one of them is edited successfully." + ], + "image_footnote": [], + "bbox": [ + 503, + 263, + 893, + 356 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and future work", + "text_level": 1, + "bbox": [ + 500, + 405, + 759, + 421 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose an intuitive and user-friendly text-based image editing method, which benefits from the superior generation and generalization capacities of large-scale image language diffusion models (e.g., Stable Diffusion). The key idea of our method is that important structural information of the input image can be encoded into conditional embeddings, which can guide the diffusion model to reconstruct the original image via the sampling process. Based on this, our method consists of two stages. In the first reconstruction stage, we propose a novel Prompt Tuning Inversion method which encodes image information to learnable conditional embeddings quickly and accurately. In the second editing stage, we introduce an interpolation which linearly combines the target text embedding with the optimized embedding obtained in the first stage. In this way, the new conditional embedding contains both information from the input image and the target text prompt, resulting in an edited image with an appropriate trade-off between editability and fidelity.", + "bbox": [ + 496, + 431, + 890, + 718 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "While our method works well in most scenarios, it still faces some limitations. As shown in Fig. 7, there are multiple objects in the input images. However, neither DiffEdit nor our method changes all \"gooses\" to \"black storks\". This limitation can possibly be mitigated by operating the attention maps more precisely [5] or adding different modes of conditional control [57], providing a research direction for image editing. Besides, the proposed method still requires running inversion every time given a new text since initialization is based on the target text, and not using attention is not always an advantage. 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Improved stylegan embedding: Where are the good latents? arXiv preprint arXiv:2012.09036, 2020. 3" + ], + "bbox": [ + 78, + 90, + 468, + 599 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "7440", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models/f6450b64-da9d-48f8-bcd6-4de4863bfc2b_model.json b/2023/Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models/f6450b64-da9d-48f8-bcd6-4de4863bfc2b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b60f1170a157c9cf833030e8d8fd58af299a44d2 --- /dev/null +++ b/2023/Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models/f6450b64-da9d-48f8-bcd6-4de4863bfc2b_model.json @@ -0,0 +1,2455 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.082, + 0.131, + 0.89, + 0.153 + ], + "angle": 0, + "content": "Prompt Tuning Inversion for Text-Driven Image Editing Using Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.228, + 0.18, + 0.748, + 0.218 + ], + "angle": 0, + "content": "Wenkai Dong\\(^{1}\\) Song Xue\\(^{1}\\) Xiaoyue Duan\\(^{1,2*}\\) Shumin Han\\(^{1\\dagger}\\) \n\\(^{1}\\)Baidu VIS, \\(^{2}\\)Beihang University" + }, + { + "type": "text", + "bbox": [ + 0.234, + 0.22, + 0.737, + 0.234 + ], + "angle": 0, + "content": "{dongwenkai, xuesong06, duanxiaoyue, hanshumin}@baidu.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.301, + 0.474, + 0.755 + ], + "angle": 0, + "content": "Recently large-scale language-image models (e.g., text-guided diffusion models) have considerably improved the image generation capabilities to generate photorealistic images in various domains. Based on this success, current image editing methods use texts to achieve intuitive and versatile modification of images. To edit a real image using diffusion models, one must first invert the image to a noisy latent from which an edited image is sampled with a target text prompt. However, most methods lack one of the following: user-friendliness (e.g., additional masks or precise descriptions of the input image are required), generalization to larger domains, or high fidelity to the input image. In this paper, we design an accurate and quick inversion technique, Prompt Tuning Inversion, for text-driven image editing. Specifically, our proposed editing method consists of a reconstruction stage and an editing stage. In the first stage, we encode the information of the input image into a learnable conditional embedding via Prompt Tuning Inversion. In the second stage, we apply classifier-free guidance to sample the edited image, where the conditional embedding is calculated by linearly interpolating between the target embedding and the optimized one obtained in the first stage. This technique ensures a superior trade-off between editability and high fidelity to the input image of our method. For example, we can change the color of a specific object while preserving its original shape and background under the guidance of only a target text prompt. Extensive experiments on ImageNet demonstrate the superior editing performance of our method compared to the state-of-the-art baselines." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.782, + 0.21, + 0.797 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.807, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Text-based image editing, a long-standing problem in image processing, aims to modify an input image to align its visual content with the target text prompts. It has drawn increasing attention in recent years and many meth" + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.272, + 0.642, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.555, + 0.359, + 0.614, + 0.368 + ], + "angle": 0, + "content": "Input image" + }, + { + "type": "image", + "bbox": [ + 0.642, + 0.272, + 0.753, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.656, + 0.359, + 0.738, + 0.368 + ], + "angle": 0, + "content": "DDIM Inversion" + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.272, + 0.866, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.78, + 0.359, + 0.839, + 0.368 + ], + "angle": 0, + "content": "DDIM-Edit" + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.369, + 0.641, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.564, + 0.455, + 0.606, + 0.464 + ], + "angle": 0, + "content": "DiffEdit" + }, + { + "type": "image", + "bbox": [ + 0.642, + 0.369, + 0.753, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.657, + 0.455, + 0.736, + 0.464 + ], + "angle": 0, + "content": "DiffEdit w/o src" + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.369, + 0.866, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.793, + 0.455, + 0.822, + 0.464 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.47, + 0.895, + 0.553 + ], + "angle": 0, + "content": "Figure 1. Illustration of different methods in editing the color of the car. Methods based on the original DDIM inversion (i.e., DDIM-Edit, DiffEdit and DiffEdit w/o src) cannot preserve the shape of the car. In contrast, our method successfully changes the color while preserving the structural information. The target text is \"a yellow car\". The source text is \"a red car\" for DiffEdit." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.895, + 0.884 + ], + "angle": 0, + "content": "ods built upon text-to-image generation have been developed. In past years, GAN-based image editing methods [30, 31, 52, 53] achieve impressive results due to the powerful generation abilities of GANs [37, 23, 33, 60]. However, these methods only work well in domains where the models are trained. More recently, diffusion models such as DDPM [18] and score-based generative models [48] have demonstrated competitive or even better capability of generating images compared to VAE-, GAN-, flow- and autoregressive-based models [36, 14, 38, 12]. Especially, large-scale language-image models (LLIMs), such as Imagegen [43], DALL-E2 [35] and Stable Diffusion [41], have attracted unprecedented attention from the research community and public society. With the help of large-scale pretrained language models [34, 10], LLIMs can generate high-fidelity images well aligned with the provided text prompts without further fine-tuning. To fully leverage the generation and generalization capabilities of LLIMs, we aim to develop a text-driven image editing method based on open-sourced LLIMs, e.g., Stable Diffusion [41]." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Editability and fidelity are two essential requirements" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.875, + 0.468, + 0.888 + ], + "angle": 0, + "content": "*This work was done when Xiaoyue Duan was an intern at Baidu VIS." + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.221, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author" + }, + { + "type": "list", + "bbox": [ + 0.095, + 0.875, + 0.468, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7430" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.485 + ], + "angle": 0, + "content": "of image editing tasks. The former requires that the edited images are supposed to contain visual contents well aligned with the corresponding textual contents provided in the target prompts, while the latter expects that areas other than the edited parts should stay as close to those of the input image as possible. For example, when modifying the color of a specific object, its other attributes (e.g., size and shape) are expected to be preserved. As shown in Fig. 1, given an image of a red car and the target text prompt (\"a yellow car\"), the desired edited image should contain a yellow car while keeping the background as well as the car's size and shape unchanged. To achieve this editing, the simplest way is to first invert the image to a noisy latent via the reversed deterministic DDIM sampling process [46], and then obtain the edited image via the deterministic DDIM sampling process with the guidance of the target prompt embedding. We refer to this approach as \"DDIM-Edit\" in our paper. Although this approach successfully turns the color of the car to yellow (see \"DDIM-Edit\" in Fig. 1), the background and the shape of the car change drastically, which obviously fails to meet the requirement of high fidelity. The reason lies in that the deterministic DDIM sampling process cannot be reversed perfectly in practice. A slight error is amplified by a large classifier-free guidance scale, and is accumulated in each sampling step, which consequently results in a significantly different image." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.489, + 0.473, + 0.807 + ], + "angle": 0, + "content": "To improve fidelity, some methods consider the image editing tasks as inpainting tasks, which require users to explicitly provide masks of the inpainting regions [3, 25]. With the mask prior, the background can remain the same, but masking out image contents also removes important structural information that is helpful in the editing process, leading to unsatisfactory editing results. Moreover, asking users to provide masks is cumbersome and not suitable for quick and intuitive text-driven image editing. As a solution, DiffEdit [7] presents an algorithm that can automatically generate a mask given a target text prompt to locate the region to be edited. However, the editability of DiffEdit largely depends on DDIM-Edit, which may fail to preserve the structural information of the edited object, e.g., the shape of the car (see \"DiffEdit\" in Fig. 1). Moreover, to generate an accurate mask, DiffEdit requires a precise text description of the input image (referred to as \"source text\"), hampering the editing efficiency. Without the source text (see \"DiffEdit w/o src\" in Fig. 1), the automatically generated mask cannot locate the body of the car accurately, further decreasing editability." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.811, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In this work, we aim to propose an image editing method to mitigate all the above problems, i.e., the method should be user-friendly, generalizable to various domains, and generate edited images with high fidelity. Specifically, for a quick and intuitive text-based method, users only need to provide an input image and the corresponding target text" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "prompts, without the need for a mask or a source text describing the input image. Secondly, the method should be able to operate on real images from various domains. Thirdly, the objects should be precisely edited with the background preserved. In some cases, only certain attributes of the objects should be modified, while other attributes are supposed to be left untouched." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.2, + 0.893, + 0.502 + ], + "angle": 0, + "content": "To achieve these merits, we believe that image editing needs a new inversion method based on diffusion models to reconstruct the input image. Inspired by the classifier-free guidance [20] and textual-inversion methods [27], we propose a Prompt Tuning Inversion method to encode the information of the input image into a conditional embedding. More specifically, we first apply DDIM inversion to the input image latent to obtain a sequence of noisy ones. These noisy latents can be taken as a prior trajectory for reconstructing the original image. Then, we introduce a learnable embedding in the sampling process. The diffusion model reconstructs the input image step by step along the trajectory conditioned on this embedding while optimizing it at the same time. In this way, the contents of the input image are learned in the embedding. Finally, we obtain a new conditional embedding by linearly interpolating between the optimized embedding and the target embedding, resulting in a representation that combines both the structural information of the input image and the visual content of the target text." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.895, + 0.656 + ], + "angle": 0, + "content": "Overall, our proposed method consists of two stages. In the first stage, we encode the information of the input image into a learnable conditional embedding via prompt tuning in the reconstruction process. In the second stage, a new conditional embedding is computed by linearly interpolating between the target embedding and the optimized one obtained in the first stage, which boosts a trade-off between editability and fidelity. The classifier-free guidance is then applied to sample the edited image. In sum, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.675, + 0.892, + 0.737 + ], + "angle": 0, + "content": "- We propose a user-friendly text-driven image editing method which requires only an input image and a target text for editing, without any need for user-provided masks or source descriptions of the input images." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.758, + 0.892, + 0.819 + ], + "angle": 0, + "content": "- We propose a Prompt Tuning Inversion method for diffusion models which can quickly and accurately reconstruct the original image, providing a strong basis for sampling edited images with high fidelity to the inputs." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "- We compare against the state-of-the-art methods both qualitatively and quantitatively, and show that our method outperforms these works in terms of the trade-off between editability and fidelity." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "7431" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.216, + 0.106 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.473, + 0.373 + ], + "angle": 0, + "content": "Text-to-image synthesis. Text-guided synthesis has been widely adopted for image generation [12, 54, 4, 41]. Works based on generative adversarial networks (GANs) [37, 23, 33, 60] have been proposed for text-to-image synthesis. CLIP-based methods [8, 54] have also been proposed to utilize the language-image priors from a pre-trained CLIP [34] model to generate images from texts. Recently, works [11, 18, 19, 29] based on the Diffusion Probabilistic Models (DPM) [45] have achieved state-of-the-art results in text-to-image synthesis. Among these works, Latent Diffusion Model (LDM) [41] trains DPM in the latent space using a powerful pre-trained auto-encoder, and introduces a cross-attention layer into the model architecture, thus turning the diffusion model into a powerful and flexible generator with greatly improved visual fidelity. Our work of image editing is based on LDM [41] thanks to its powerful image generation capability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.373, + 0.473, + 0.719 + ], + "angle": 0, + "content": "Image editing. Image editing with generative adversarial networks (GANs) has been studied extensively [30, 31, 52, 53]. Some other techniques also leverage the image-text alignment capability of CLIP [34] and transfer it to the framework of GANs [2, 49, 55]. More recently, the development of diffusion models [18, 45, 47] provides a more flexible design space than GANs for the editing task, while following a simpler training setup (e.g., SDEdit [26] and ILVR [6]). Textual Inversion [13] and Dream-Booth [42] demonstrate the capability to generate diverse images with unique object characteristics by fine-tuning the diffusion model with multiple images. Imagic [21] and UniTune [51], which are based on the powerful Imagen model [43], also show impressive editing performance. However, the above methods require restrictive fine-tuning of the pre-trained model, and thus may not fully leverage the generalization ability of the pre-trained model due to overfitting or language drift. Other methods [3, 28] require a user-provided mask to guide the diffusion process, making it hard for them to be interactive. To achieve text-only interactive editing, some optimization-free methods have been proposed recently (e.g., Prompt-to-Prompt [16] and DiffEdit [7]) to automatically infers a mask before editing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Inversion. In the GAN literature, the inversion process requires one to find a corresponding latent representation of the given image [59, 56]. This process has been extensively studied for GANs [1, 61, 15, 39, 32, 50]. For diffusion models, the inversion requires to find a noise map and a conditional vector corresponding to a generated image but simply adding noise and denoising it may arouse the problem that the image content can be changed drastically. Works [6, 11, 35] have been proposed to improve the inversion process. However, it is still challenging for these methods to generate new instances of a given example while maintaining fidelity. Textual Inversion [13] and Dream-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.275 + ], + "angle": 0, + "content": "Booth [42] propose to learn concepts from images through textual inversion by either directly optimizing the embedding of the textual concept or fine-tuning the diffusion models, which can be computationally inefficient. Null-Text Inversion [27] modifies the unconditional textual embedding that is used for classifier-free guidance instead of the input text embedding, which enables applying prompt-based editing without the cumbersome tuning of the model parameters. Different from these methods, our method encodes the information of the input image into a learnable conditional embedding, which provides a helpful prior in sampling edited image with high fidelity to the input image." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.285, + 0.637, + 0.303 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.31, + 0.895, + 0.553 + ], + "angle": 0, + "content": "Given a real or synthesized image \\(\\mathcal{I}\\), we aim to edit \\(\\mathcal{I}\\) to get an edited image \\(\\mathcal{I}^*\\) with the guidance of text. Different from existing methods which require source prompts provided by users or produced by an off-the-shelf image captioning model, our proposed editing process is guided by only target or edited prompt \\(\\mathcal{P}^*\\). An overview of our method is provided in Fig. 2, which consists of two stages. In the first stage, we encode the information of the input image into a learnable conditional embedding via prompt tuning in the reconstruction process. A new conditional embedding is then computed in the second stage by linearly interpolating between the target embedding and the optimized one from the first stage, thus achieving effective editing while maintaining high fidelity. Conditioned on this interpolated embedding, the classifier-free guidance is adopted to sample the final edited image." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.56, + 0.774, + 0.577 + ], + "angle": 0, + "content": "3.1. Background and preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.894, + 0.645 + ], + "angle": 0, + "content": "Diffusion models. Diffusion probabilistic models are designed to learn a data distribution by gradually denoising normally distributed noise, which corresponds to learning to reverse a fixed forward diffusion process:" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.652, + 0.892, + 0.671 + ], + "angle": 0, + "content": "\\[\nq \\left(x _ {t} \\mid x _ {t - 1}\\right) := \\mathcal {N} \\left(x _ {t}; \\sqrt {\\alpha_ {t}} x _ {t - 1}, (1 - \\alpha_ {t}) \\mathbf {I}\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.677, + 0.895, + 0.782 + ], + "angle": 0, + "content": "In the forward process, normally distributed noise is gradually added to the sample \\( x_{t - 1} \\) to obtain a more noisy variant \\( x_{t} \\). The noise is dependent on a variance schedule \\( \\alpha_{t} \\) where \\( t\\in 1,\\dots,T \\), with \\( T \\) being the total number of steps, \\( x_0 \\) the original image, and \\( x_{T} \\) approximately the standard Gaussian noise. The reverse process is defined with parameters \\( \\theta \\):" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.792, + 0.892, + 0.809 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right) := \\mathcal {N} \\left(x _ {t - 1}; \\mu_ {\\theta} \\left(x _ {t}, t\\right), \\Sigma_ {\\theta}\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.816, + 0.894, + 0.879 + ], + "angle": 0, + "content": "Using a fixed variance \\(\\Sigma_{\\theta}\\), only the mean value \\(\\mu_{\\theta}(x_t,t)\\) needs to be learned. With the parameterization trick, the network \\(\\epsilon_{\\theta}\\) is trained to predict the noise \\(\\epsilon\\), resulting in a loss, where \\(c\\) represents the conditional embedding:" + }, + { + "type": "equation", + "bbox": [ + 0.603, + 0.884, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {t, x _ {0}, \\epsilon} [ \\| \\epsilon - \\epsilon_ {\\theta} (x _ {t}, t, c) \\| ^ {2} ]. \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "7432" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.182, + 0.088, + 0.797, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.342, + 0.895, + 0.399 + ], + "angle": 0, + "content": "Figure 2. An overview of our proposed image editing method. **Stage 1:** we first apply DDIM inversion to the input image embedding to obtain a diffusion trajectory \\(\\{z_t^*\\}_{t=0}^T\\). Then we reconstruct the input image along with the reversed trajectory by optimizing the learnable conditional embedding \\(c_t\\). **Stage 2:** we perform classifier-free guidance sampling conditioned on a linear interpolation between target embedding \\(c^*\\) and \\(c_t\\) at each diffusion step. \\(\\bigoplus\\) denotes element-wise weighted addition. Red dashes indicate the gradient flow in PTI." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.422, + 0.471, + 0.455 + ], + "angle": 0, + "content": "In this work, we employ the deterministic DDIM sampling [46]:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.464, + 0.47, + 0.483 + ], + "angle": 0, + "content": "\\[\nx _ {t - 1} = \\sqrt {\\alpha_ {t - 1}} f _ {\\theta} (x _ {t}, t) + \\sqrt {1 - \\alpha_ {t - 1}} \\epsilon_ {\\theta} (x _ {t}, t), \\qquad (4)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.493, + 0.47, + 0.539 + ], + "angle": 0, + "content": "where \\( f_{\\theta} \\) is the prediction of \\( x_0 \\) given \\( x_t \\) at step \\( t \\). Given a noisy image \\( x_T \\), the noise is gradually removed to generate an image \\( x_0 \\) by applying Eq. 4 for \\( T \\) steps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.47, + 0.75 + ], + "angle": 0, + "content": "Latent diffusion. Instead of operating in the image pixel space, Latent Diffusion Models [41] (LDMs) utilize an autoencoder to learn a latent space which is perceptually equivalent to the pixel space. First, an encoder \\(ENC\\) is adopted to map a given image \\(x_0\\) into a latent embedding \\(z_0\\). Then a decoder \\(DEC\\) is designed to reconstruct the input image given \\(z_0\\), i.e., \\(DEC(ENC(x_0)) \\approx x_0\\). The encoder downsamples the original images by a factor of 4 or 8. In this way, the diffusion model operates on a much smaller representation with lower time complexity and memory burden. Thus, for our method, we apply one of the state-of-the-art LDMs, Stable Diffusion [41]. In the forward and reverse process described above, we only need to replace the image \\(x_t\\) with its latent embedding \\(z_t\\) at each step." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Classifier-free guidance. Our editing method is built upon text-guided diffusion models. In Stable Diffusion, the text \\(\\mathcal{P}\\) is fed into a pre-trained CLIP [34] text encoder \\(\\tau_{\\theta}\\) to obtain its corresponding embedding and the underlying UNet model is augmented with the cross attention mechanism, which is effective for generating visual contents conditioned on the text \\(\\mathcal{P}\\). One of the key challenges in this kind of generation models is the amplification of the effect induced by the conditional text. To this end, the classifier-free guidance technique is proposed, where the prediction for each step is" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.422, + 0.892, + 0.485 + ], + "angle": 0, + "content": "a combination of conditional and unconditional predictions. Formally, let \\( c = \\tau_{\\theta}(\\mathcal{P}) \\) be the conditional embedding vector and \\( \\varnothing = \\tau_{\\theta}(\\varnothing) \\) be the unconditional one, the classifier-free guidance prediction is calculated by:" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.495, + 0.892, + 0.512 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\epsilon} _ {t} = \\epsilon_ {\\theta} \\left(z _ {t}, t, \\varnothing\\right) + \\omega \\cdot \\left(\\epsilon_ {\\theta} \\left(z _ {t}, t, c\\right) - \\epsilon_ {\\theta} \\left(z _ {t}, t, \\varnothing\\right)\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.524, + 0.771, + 0.539 + ], + "angle": 0, + "content": "where \\(\\omega\\) is the guidance scale parameter." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.548, + 0.757, + 0.563 + ], + "angle": 0, + "content": "3.2. Problems of DDIM inversion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.571, + 0.892, + 0.648 + ], + "angle": 0, + "content": "Given an input image \\(\\mathcal{I}\\) and a target prompt \\(\\mathcal{P}^*\\), we aim to edit \\(\\mathcal{I}\\) to make its visual content consistent with textual content in \\(\\mathcal{P}^*\\), while preserving a maximal amount of details from \\(\\mathcal{I}\\). The above two aspects are referred to asEditability and input image fidelity, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.648, + 0.893, + 0.873 + ], + "angle": 0, + "content": "To achieve effective editing while maintaining high fidelity, we first need to inverse the input image into an appropriate noise map, based on which the edited image can be sampled. Eqs. 1 and 2 show a naive way to add noise to the input image and then denoise it through the diffusion network, respectively. However, as the sampling process is stochastic, the samples generated from the same latent can be different every time. Even if the sampling process becomes deterministic, the random noise in the forward process still makes the generated image content change significantly. To address this issue, DiffusionCLIP [22] reverses the deterministic DDIM sampling process in Eq. 4 based on the assumption that the ordinary differential equation (ODE) process can be reversed within the limit of small steps:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.885, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\nz _ {t + 1} = \\sqrt {\\alpha_ {t + 1}} f _ {\\theta} \\left(z _ {t}, t\\right) + \\sqrt {1 - \\alpha_ {t + 1}} \\epsilon_ {\\theta} \\left(z _ {t}, t\\right), \\tag {6}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7433" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.091, + 0.182, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.109, + 0.165, + 0.16, + 0.174 + ], + "angle": 0, + "content": "Input image" + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.092, + 0.274, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.199, + 0.164, + 0.264, + 0.173 + ], + "angle": 0, + "content": "CFG \\((\\omega = 0.0)\\)" + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.092, + 0.366, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.287, + 0.164, + 0.352, + 0.173 + ], + "angle": 0, + "content": "CFG \\((\\omega = 1.0)\\)" + }, + { + "type": "image", + "bbox": [ + 0.368, + 0.092, + 0.458, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.38, + 0.164, + 0.445, + 0.173 + ], + "angle": 0, + "content": "CFG \\((\\omega = 2.5)\\)" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.174, + 0.181, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.245, + 0.157, + 0.255 + ], + "angle": 0, + "content": "PTI (ours)" + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.174, + 0.274, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.199, + 0.245, + 0.264, + 0.255 + ], + "angle": 0, + "content": "CFG \\((\\omega = 5.0)\\)" + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.174, + 0.365, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.287, + 0.245, + 0.352, + 0.255 + ], + "angle": 0, + "content": "CFG \\((\\omega = 7.5)\\)" + }, + { + "type": "image", + "bbox": [ + 0.368, + 0.174, + 0.459, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.38, + 0.245, + 0.451, + 0.255 + ], + "angle": 0, + "content": "CFG \\((\\omega = 10.0)\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.265, + 0.47, + 0.32 + ], + "angle": 0, + "content": "Figure 3. Reconstruction quality of our Prompt Tuning Inversion, and DDIM inversion with different classifier-free guidance (CFG) scales \\(\\omega\\) in the sampling process. \\(\\omega = 0\\) in the forward process for all methods." + }, + { + "type": "table", + "bbox": [ + 0.103, + 0.334, + 0.441, + 0.419 + ], + "angle": 0, + "content": "
ωdec\nωenc0.01.02.55.07.5
0.021.3619.7917.0414.8813.64
1.017.1621.9418.2215.4714.02
2.514.5115.7318.1315.7414.24
5.011.3011.4811.7012.1212.06
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.421, + 0.472, + 0.477 + ], + "angle": 0, + "content": "Table 1. Reconstruction quality by measuring the PSNR score of DDIM inversion with different classifier-guidance scales \\(\\omega\\). \\(\\omega_{\\mathrm{enc}}\\) and \\(\\omega_{\\mathrm{dec}}\\) denote the guidance scale used in the DDIM forward and sampling processes, respectively." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.507, + 0.336, + 0.521 + ], + "angle": 0, + "content": "where \\( z_{t} \\) is the latent embedding of \\( x_{t} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.47, + 0.901 + ], + "angle": 0, + "content": "To investigate the reconstruction performance of DDIM, we first invert the latent embedding of the input image into noise maps via Eq. 6 and then use the deterministic DDIM sampling process in Eq. 4 to reconstruct the input. Note that both processes are performed with unconditional diffusion models, i.e., the classifier-free guidance scale in Eq. 5 is set to \\(\\omega = 0\\) for both forward and reverse sampling processes. Although a slight error is incorporated in every step as ODE process cannot be reversed perfectly in practice, the accumulated error is negligible, and DDIM inversion can nearly reconstruct the original image (see \"CFG (\\(\\omega = 0.0\\))\" in Fig. 3). However, to generate an image well aligned with the conditional text prompt using Stable Diffusion, a large guidance scale \\(\\omega > 1\\) is necessary for the sampling process in Eq. 4. This arouses the problem that when enlarging \\(\\omega\\), the generated images are far from the original ones as shown in Fig. 3. We believe that when \\(\\omega\\) of the sampling process is different from that of the forward process, the accumulated error would be amplified, leading to unsatisfactory reconstruction quality. This can be illustrated in Table 1, i.e., the best reconstruction quality in each line is obtained when \\(\\omega\\) used in the DDIM sampling process is the same as that used in the forward process. Even if \\(\\omega\\) used in the forward and sampling processes are kept the same, PSNR still decreases with \\(\\omega\\) increasing (see the numbers in bold in Ta" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "ble 1). The above analysis demonstrates that it is hard for DDIM inversion to achieve a satisfactory trade-off between editability (which requires larger \\(\\omega\\)) and fidelity (which requires smaller \\(\\omega\\)). To address this issue, we propose a new inversion technique, i.e., Prompt Tuning Inversion." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.175, + 0.75, + 0.191 + ], + "angle": 0, + "content": "3.3. Prompt tuning for inversion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.199, + 0.892, + 0.349 + ], + "angle": 0, + "content": "To successfully invert real images into the model's domain, recent works optimize the textual encoding, the network's parameters, or both. Motivated by Pivotal Inversion [40], we replace the conditional embedding of the text prompt with an optimized one, referred to as Prompt Tuning in this work. Namely, for each input image, we optimize only the conditional embedding \\( c \\) so that it encodes important information of the input image which helps the reconstruction. The parameters of the diffusion network and the text encoder \\( \\tau_{\\theta} \\) are frozen during prompt tuning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.35, + 0.892, + 0.425 + ], + "angle": 0, + "content": "We first initialize \\( z_0^* = z_0 = ENC(x_0) \\), and adopt DDIM inversion with \\( \\omega = 0 \\) to obtain a trajectory of noisy latent codes \\( \\{z_t^*\\}_{t=1}^T \\). Then we initialize \\( \\tilde{z}_T = z_T^* \\) and perform the following optimization to the conditional embedding \\( c \\) with \\( \\omega > 1 \\) for the timestamps \\( t = T, \\dots, 1 \\), each for \\( N \\) iterations:" + }, + { + "type": "equation", + "bbox": [ + 0.562, + 0.433, + 0.892, + 0.459 + ], + "angle": 0, + "content": "\\[\nc _ {t} = \\underset {c _ {t}} {\\arg \\min } \\left\\| z _ {t - 1} ^ {*} - z _ {t - 1} \\left(\\tilde {z} _ {t}, t, c _ {t}\\right) \\right\\| ^ {2}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.468, + 0.892, + 0.514 + ], + "angle": 0, + "content": "For brevity, \\( z_{t-1}(\\tilde{z}_t, t, c_t) \\) denotes applying a DDIM sampling step using \\( \\tilde{z}_t \\) and the conditional embedding \\( c_t \\) at the timestep \\( t \\). At the end of each timestep, we update" + }, + { + "type": "equation", + "bbox": [ + 0.62, + 0.523, + 0.892, + 0.54 + ], + "angle": 0, + "content": "\\[\n\\tilde {z} _ {t - 1} = z _ {t - 1} \\left(\\tilde {z} _ {t}, t, c _ {t}\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.892, + 0.623 + ], + "angle": 0, + "content": "Finally, we can reconstruct the input image by using the noise latent \\(\\tilde{z}_T = z_T^*\\) and the optimized conditional embeddings \\(\\{c_t\\}_{t=1}^T\\). In the next subsection, we will introduce the approach to editing images with the target text prompt and the conditional embeddings." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.632, + 0.734, + 0.648 + ], + "angle": 0, + "content": "3.4. Prompt tuning for editing" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.892, + 0.836 + ], + "angle": 0, + "content": "Since the sequence of the conditional embeddings \\(\\{c_t\\}_{t=1}^T\\) is optimized to fully reconstruct the input image, we believe that these optimized conditional embeddings have contained the most information of the original image, and thus ensure high fidelity. To achieve the desired modification, these optimized embeddings are adopted to perform the editing by advancing in the direction of the target text embedding \\(c^* = \\tau_\\theta(\\mathcal{P}^*)\\) to ensure good editability also. More formally, in the second stage, we simply interpolate between the target embedding \\(c^*\\) and the optimized \\(c_t\\) linearly at each timestamp. For a given hyper-parameter \\(\\eta \\in (0,1]\\), we obtain" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.846, + 0.892, + 0.862 + ], + "angle": 0, + "content": "\\[\nc _ {t} = \\eta \\cdot c ^ {*} + (1 - \\eta) \\cdot c _ {t}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where the first term ensures the effective editability corresponding to the semantic contents in the target text, while" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7434" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.168 + ], + "angle": 0, + "content": "the second term guarantees a good reconstruction of the original image. The algorithm is presented in Lines 14-21 in Algorithm 1. Note that when \\(\\eta = 0\\) or \\(\\eta = 1\\), the output of our editing method is the reconstructed original image, or the output of the baseline DDIM-Edit, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.173, + 0.473, + 0.326 + ], + "angle": 0, + "content": "Intuitively, our editing method is to find an intermediate representation between the original image and the output of DDIM-Edit. For a desired modification, the intermediate representation is supposed to contain both the structural information of the source image and the semantic contents of the target text prompt. Eq. 9 is only one way to achieve this, which we refer to as condition interpolation. We also test a different interpolation method (referred to as latent interpolation), where we linearly interpolate between the noisy latent \\( z_{t} \\) and \\( z_{t}^{*} \\) at each timestamp:" + }, + { + "type": "equation", + "bbox": [ + 0.179, + 0.349, + 0.47, + 0.368 + ], + "angle": 0, + "content": "\\[\nz _ {t} ^ {e d t} = \\eta \\cdot z _ {t} + (1 - \\eta) \\cdot z _ {t} ^ {*}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.391, + 0.473, + 0.542 + ], + "angle": 0, + "content": "where \\( z_{t}^{*} \\) is the noisy latent calculated by DDIM inversion via Eq. 6, and \\( z_{t} \\) is the latent obtained in the vanilla DDIM sampling process conditioned on the target embedding. Although this approach is more simple since the process of prompt tuning is no longer needed, we observe that this interpolation method may lead to cluttered images. This is because the interpolation of latent embeddings mixes the source object and the edited object spatially, rather than semantically (as condition interpolation does), leading to cluttered contents in images." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.571, + 0.195, + 0.587 + ], + "angle": 0, + "content": "3.5. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.601, + 0.47, + 0.678 + ], + "angle": 0, + "content": "Our proposed image editing method shares similar motivations with existing works [21, 51, 27, 16], all of which aim to modify an image in a text-driven and mask-free manner. However, our approach differs from them significantly in the following aspects:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.683, + 0.47, + 0.759 + ], + "angle": 0, + "content": "1) Imagic [21] and UniTune [51] finetune the diffusion models for hundreds of steps to maintain high fidelity to the input image. In contrast, we only need to optimize the conditional embedding, which greatly reduces computational budgets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.902 + ], + "angle": 0, + "content": "2) Our proposed Prompt Tuning Inversion is inspired by the Null-Text Inversion method [27]. However, Null-Text Inversion chooses to optimize the unconditional embedding while we optimize the conditional one. Moreover, the editing process of Null-Text Inversion is achieved by the cross-attention map control in Prompt-to-Prompt [16], which requires an additional description of the input image. Compared to theirs, our method only needs the target text prompt and is thus more user-friendly." + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.683, + 0.471, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "code_caption", + "bbox": [ + 0.51, + 0.095, + 0.848, + 0.111 + ], + "angle": 0, + "content": "Algorithm 1: Prompt Tuning Inversion for Editing" + }, + { + "type": "algorithm", + "bbox": [ + 0.501, + 0.112, + 0.892, + 0.503 + ], + "angle": 0, + "content": "Input: An input image \\(\\mathcal{I}\\) and a target prompt embedding \\(c^{*} = \\tau_{\\theta}(\\mathcal{P}^{*})\\) \nOutput: Edited image \\(\\mathcal{I}^*\\) \n1 // DDIM Inversion \n2 Set guidance scale \\(\\omega = 0,z_0^* = ENC(\\mathcal{I})\\) . \n3 Compute the intermediate trajectory \\(\\{z_t^*\\}_{t = 0}^T\\) using DDIM inversion over \\(\\mathcal{I}\\) without conditional guidance via Eq. 6; \n4// Prompt Tuning \n5 Set guidance scale \\(\\omega >1,\\eta \\in (0,1]\\) . \n6 Initialize \\(\\tilde{z}_T\\gets z_T^*,c_T\\gets c^*\\) . \n7 for \\(t = T,T - 1,\\dots ,1\\) do \n8 for \\(j = 0,\\ldots ,N - 1\\) do \n9 \\(|c_{t}\\gets c_{t} - \\beta \\nabla_{c}||z_{t - 1}^{*} - z_{t - 1}(\\tilde{z}_{t},t,c_{t})||_{2}^{2};\\) \n10 end \n11 \\(\\tilde{z}_{t - 1}\\gets z_{t - 1}(\\tilde{z}_{t},t,c_{t}),c_{t - 1}\\gets c_{t}\\) \n12 end \n13 // Editing \n14 Set \\(z_{T}^{edt}\\gets z_{T}^{*}\\) . \n15 for \\(t = T,T - 1,\\ldots ,1\\) do \n16 \\(c_{t} = (1 - \\eta)\\cdot c_{t} + \\eta \\cdot c^{*};\\) \n17 \\(z_{t - 1}^{edt} = z_{t - 1}(z_{t}^{edt},t,c_{t});\\) \n18 end \n19 \\(\\mathcal{I}^* = DEC(z_0^{edt})\\) \n20 return \\(\\mathcal{I}^*\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.533, + 0.634, + 0.55 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.559, + 0.583, + 0.575 + ], + "angle": 0, + "content": "4.1. Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.793 + ], + "angle": 0, + "content": "Implementation details. In our experiments, we adopt the text-conditional Latent Diffusion Model [41] (known as Stable Diffusion) with 890M parameters trained on LAION-5B [44] at \\(512 \\times 512\\) resolution. For the DDIM schedule, we adopt 50 steps and retain the original hyperparameter choices of Stable Diffusion. The encoding ratio parameter is set to 0.8. The number of iterations to optimize \\(c\\) per diffusion step is set to \\(N = 1\\). The hyper-parameters \\(\\beta\\) and \\(\\eta\\) in Algorithm 1 are set to 0.1 and 0.9, respectively, unless specified. These allow editing an image in \\(\\sim 1\\) minute on a single Tesla V100 GPU. For better performance, we adopt attention maps to localize the edited regions (referred to as local blending), and re-weight the attention maps as in [16]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Evaluation and datasets. In semantic image editing, the visual content of the edited image is supposed to align well with the target text prompt (editability) while staying close to the input image in terms of the unedited parts (fidelity). For a given method, better editability usually comes at the cost of decreased fidelity to the input image, and vice versa. This forms a trade-off curve between the two objectives." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7435" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.094, + 0.429, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.269, + 0.47, + 0.312 + ], + "angle": 0, + "content": "Figure 4. Comparison with DiffEdit and DDIM-Edit on ImageNet. For all methods, we set the DDIM encoding ratio to 0.8, and only vary the mask threshold to draw the trade-off curve." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.47, + 0.504 + ], + "angle": 0, + "content": "Following DiffEdit [7], we evaluate different editing methods by comparing their trade-off curves on ImageNet [9]. Specifically, given an image of one class from ImageNet, we aim to edit it to another class of ImageNet as instructed by the target text prompt. The editability and fidelity are measured using the LPIPS perceptual distance [58] and CS-FID, which is a class-conditional FID metric [17], respectively. The former measures the distance with the input image while the latter measures both image realism and consistency w.r.t. the target class. For both metrics, lower values indicate better editing performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.513, + 0.466, + 0.53 + ], + "angle": 0, + "content": "4.2. Comparison with other methods on ImageNet" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.47, + 0.672 + ], + "angle": 0, + "content": "We compare our method with DiffEdit and our baseline DDIM-Edit, since they both share the same DDIM forward process and a similar sampling process. Besides, they load the same publicly available pre-trained weights for a fair comparison. To leverage the generalization capability of large-scale language-image models, we adopt the text-conditional Stable Diffusion model \"sd-v1-4\" instead of the class-conditional model trained on ImageNet as the pre-trained model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.471, + 0.855 + ], + "angle": 0, + "content": "As pointed out by DiffEdit [7], different editing methods often have hyper-parameters which control editability, e.g., the mask threshold, or the encoding ratio. A lower mask threshold or higher encoding ratio leads to stronger editing. In our proposed method, we can also control the editing strength by varying the conditional interpolation ratio \\(\\eta\\) introduced in Eq. 9. In our evaluation, we fix the DDIM encoding ratio and draw the trade-off curve by varying the mask threshold for all methods1. The results are presented in Fig. 4, where \"DDIM-Global\" denotes that the images are edited via \"DDIM-Edit\" but without using any masks, i.e., the editing is performed globally. This can" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.098, + 0.864, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.409, + 0.895, + 0.451 + ], + "angle": 0, + "content": "Figure 5. Editing examples on ImageNet by our method and other methods. DDIM-G/DDIM-L indicates the baseline method DDIM-Edit with/without the local blend trick." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.892, + 0.655 + ], + "angle": 0, + "content": "be regarded as a lower bound of fidelity for all methods. As the mask threshold increases, LPIPS decreases since fewer parts of the image are edited. Compared to DiffEdit, our baseline method DDIM-Edit achieves a better trade-off. Note that the only difference between the two methods is the approach to generating masks. The comparison shows that inferring editing masks using cross-attention maps, as adopted by DDIM-Edit, is more appropriate. Based on DDIM-Edit, our method can further improve the fidelity to the input images while maintaining editability. The best CSFID-LPIPS trade-off of our method demonstrates its superiority over DiffEdit and the baseline." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.892, + 0.792 + ], + "angle": 0, + "content": "We also present qualitative examples of these methods. As shown in Fig. 5, without automatically generated masks, \"DDIM-G\" tends to modify images globally. For simple cases (e.g., example (d)), image editing methods with the original DDIM inversion works well. However, for complex cases, we observe undesired and unreasonable edits to the objects. In contrast, with the help of the learnable conditional embedding, our method achieves realistic editing while successfully preserving the original details." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.651, + 0.818 + ], + "angle": 0, + "content": "4.3. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Comparison to existing inversion methods. We randomly select 128 images and their corresponding captions from the COCO validation set [24]. We then apply the following reconstruction methods to each image-caption pair: (1) AE denotes the variational auto-encoder with a slight KL-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.863, + 0.47, + 0.901 + ], + "angle": 0, + "content": "1As there was no official implementation of DiffEdit available at the time of writing, we adopted the unofficial implementation for inferring editing masks from https://github.com/LuChengTHU/dpm-solver." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "7436" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.11, + 0.089, + 0.434, + 0.133 + ], + "angle": 0, + "content": "
MethodAEDDIMNTIPTI (ours)
PSNR26.2213.6424.4525.71
SSIM0.85640.46410.82700.8501
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.135, + 0.47, + 0.178 + ], + "angle": 0, + "content": "Table 2. Reconstruction quality of different methods measured by PSNR and SSIM. For both metrics, higher values indicate better quality." + }, + { + "type": "table", + "bbox": [ + 0.109, + 0.196, + 0.434, + 0.302 + ], + "angle": 0, + "content": "
iters12345
learning rate β = 0.01
NTI17.0520.1222.2523.6124.45
PTI19.3623.2024.8625.4725.71
learning rate β = 0.1
NTI23.0824.7425.6225.8225.91
PTI24.7425.2325.7825.9025.97
" + }, + { + "type": "table_caption", + "bbox": [ + 0.102, + 0.304, + 0.443, + 0.318 + ], + "angle": 0, + "content": "Table 3. PSNR scores under different optimizing settings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.47, + 0.562 + ], + "angle": 0, + "content": "penalty used in Stable Diffusion. An image is first encoded by the encoder of AE. Afterwards, the decoder directly reconstructs the image from the latent. Therefore, we consider AE as an upper bound of reconstruction quality. (2) DDIM denotes the DDIM inversion method, which is a baseline inversion method. As analyzed in Sec. 3.2, it usually outputs a low-quality reconstruction result under a large classifier-free guidance scale \\(\\omega\\). (3) NTI denotes the Null-Text Inversion method [27], which is our main point of comparison. Different from our method, it optimizes the unconditional embedding. (4) PTI denotes our proposed Prompt Tuning Inversion method. We introduce a learnable conditional embedding and the optimizing details are presented in Algorithm 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.47, + 0.822 + ], + "angle": 0, + "content": "The experimental results are provided in Table 2. For the diffusion-based inversion methods, we apply the diffusion model in an unconditional manner (i.e., the classifier guidance scale \\(\\omega = 0\\)) for the DDIM forward process. For the sampling process, we set \\(\\omega = 7.5\\). As shown in Table 2, DDIM inversion fails to reconstruct the original images since \\(\\omega\\) in the sampling process is different from that in the forward process, leading to a low PSNR score (13.64). For NTI and PTI, we set the number of iterations \\(N\\) to 5 and the learning rate \\(\\beta\\) to 0.01. We observe that both methods can reconstruct the images but the reconstruction quality of our method is better (25.71 vs. 24.45). To further demonstrate the effectiveness of our method, we vary \\(N\\) from 1 to 5 and increase the learning rate \\(\\beta\\) from 0.01 to 0.1. The experimental results in Table 3 show that the reconstruction quality of PTI is always better than NTI under all settings, demonstrating that our method converges faster." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.903 + ], + "angle": 0, + "content": "Influence of the hyper-parameter \\(\\eta\\). We also perform ablation on the hyper-parameter \\(\\eta\\) and the results are presented in Fig. 6. By adjusting \\(\\eta\\), we can achieve a good trade-off between fidelity and editability. More quantitative analyses are presented in supplementary materials." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.089, + 0.896, + 0.227 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.548, + 0.231, + 0.843, + 0.245 + ], + "angle": 0, + "content": "Figure 6. Qualitative examples for the effect of \\(\\eta\\)." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.264, + 0.895, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.362, + 0.892, + 0.391 + ], + "angle": 0, + "content": "Figure 7. A failure example on ImageNet: when multiple objects exist, only one of them is edited successfully." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.406, + 0.76, + 0.422 + ], + "angle": 0, + "content": "5. Conclusion and future work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.432, + 0.892, + 0.719 + ], + "angle": 0, + "content": "We propose an intuitive and user-friendly text-based image editing method, which benefits from the superior generation and generalization capacities of large-scale image language diffusion models (e.g., Stable Diffusion). The key idea of our method is that important structural information of the input image can be encoded into conditional embeddings, which can guide the diffusion model to reconstruct the original image via the sampling process. Based on this, our method consists of two stages. In the first reconstruction stage, we propose a novel Prompt Tuning Inversion method which encodes image information to learnable conditional embeddings quickly and accurately. In the second editing stage, we introduce an interpolation which linearly combines the target text embedding with the optimized embedding obtained in the first stage. In this way, the new conditional embedding contains both information from the input image and the target text prompt, resulting in an edited image with an appropriate trade-off between editability and fidelity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.9 + ], + "angle": 0, + "content": "While our method works well in most scenarios, it still faces some limitations. As shown in Fig. 7, there are multiple objects in the input images. However, neither DiffEdit nor our method changes all \"gooses\" to \"black storks\". This limitation can possibly be mitigated by operating the attention maps more precisely [5] or adding different modes of conditional control [57], providing a research direction for image editing. Besides, the proposed method still requires running inversion every time given a new text since initialization is based on the target text, and not using attention is not always an advantage. We leave these options for future work." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7437" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 4432-4441, 2019. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.173, + 0.472, + 0.228 + ], + "angle": 0, + "content": "[2] Rameen Abdal, Peihao Zhu, John Femiani, Niloy Mitra, and Peter Wonka. Clip2stylegan: Unsupervised extraction of stylegan edit directions. 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Improved stylegan embedding: Where are the good latents? arXiv preprint arXiv:2012.09036, 2020. 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.601 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.956 + ], + "angle": 0, + "content": "7440" + } + ] +] \ No newline at end of file diff --git a/2023/Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models/f6450b64-da9d-48f8-bcd6-4de4863bfc2b_origin.pdf b/2023/Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models/f6450b64-da9d-48f8-bcd6-4de4863bfc2b_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..15052e5998e5d5c3c4777545a5167a0b10db92c6 --- /dev/null +++ b/2023/Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models/f6450b64-da9d-48f8-bcd6-4de4863bfc2b_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2785018897f5b06657add0f21284f0c2aef7fd28eccdc2c6b014f03bf942e71d +size 3717784 diff --git a/2023/Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models/full.md b/2023/Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d4d80a4770afc7b73fe7833ed47c6adc385edda6 --- /dev/null +++ b/2023/Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models/full.md @@ -0,0 +1,351 @@ +# Prompt Tuning Inversion for Text-Driven Image Editing Using Diffusion Models + +Wenkai Dong $^{1}$ Song Xue $^{1}$ Xiaoyue Duan $^{1,2*}$ Shumin Han $^{1\dagger}$ $^{1}$ Baidu VIS, $^{2}$ Beihang University + +{dongwenkai, xuesong06, duanxiaoyue, hanshumin}@baidu.com + +# Abstract + +Recently large-scale language-image models (e.g., text-guided diffusion models) have considerably improved the image generation capabilities to generate photorealistic images in various domains. Based on this success, current image editing methods use texts to achieve intuitive and versatile modification of images. To edit a real image using diffusion models, one must first invert the image to a noisy latent from which an edited image is sampled with a target text prompt. However, most methods lack one of the following: user-friendliness (e.g., additional masks or precise descriptions of the input image are required), generalization to larger domains, or high fidelity to the input image. In this paper, we design an accurate and quick inversion technique, Prompt Tuning Inversion, for text-driven image editing. Specifically, our proposed editing method consists of a reconstruction stage and an editing stage. In the first stage, we encode the information of the input image into a learnable conditional embedding via Prompt Tuning Inversion. In the second stage, we apply classifier-free guidance to sample the edited image, where the conditional embedding is calculated by linearly interpolating between the target embedding and the optimized one obtained in the first stage. This technique ensures a superior trade-off between editability and high fidelity to the input image of our method. For example, we can change the color of a specific object while preserving its original shape and background under the guidance of only a target text prompt. Extensive experiments on ImageNet demonstrate the superior editing performance of our method compared to the state-of-the-art baselines. + +# 1. Introduction + +Text-based image editing, a long-standing problem in image processing, aims to modify an input image to align its visual content with the target text prompts. It has drawn increasing attention in recent years and many meth + +![](images/ec9946c23ea0759f221389fe38474c4b169db3f781a45b4f968432bebcfd902b.jpg) +Input image + +![](images/6ad35496e83e3be457961aff002c8b50c07a7b5be06ca35e94876b0d5aae6984.jpg) +DDIM Inversion + +![](images/eaf0eb36aeee9da29fe5acd45e32e853ff696bd10499024ce978583d86c69a4a.jpg) +DDIM-Edit + +![](images/3799b4b5e70aee63b720e72ad8ad0f4b5dcbfaaf630050bd1299bd0c7f1a079a.jpg) +DiffEdit +Figure 1. Illustration of different methods in editing the color of the car. Methods based on the original DDIM inversion (i.e., DDIM-Edit, DiffEdit and DiffEdit w/o src) cannot preserve the shape of the car. In contrast, our method successfully changes the color while preserving the structural information. The target text is "a yellow car". The source text is "a red car" for DiffEdit. + +![](images/c4226ed19c5dbf37eae79b6d1657a438d1fd354e8a37a8576b34b48aa05238b4.jpg) +DiffEdit w/o src + +![](images/5a8cd4165c7a34893361c2a33e85882307b8e0fa6a606963eb1b33fa89db920d.jpg) +Ours + +ods built upon text-to-image generation have been developed. In past years, GAN-based image editing methods [30, 31, 52, 53] achieve impressive results due to the powerful generation abilities of GANs [37, 23, 33, 60]. However, these methods only work well in domains where the models are trained. More recently, diffusion models such as DDPM [18] and score-based generative models [48] have demonstrated competitive or even better capability of generating images compared to VAE-, GAN-, flow- and autoregressive-based models [36, 14, 38, 12]. Especially, large-scale language-image models (LLIMs), such as Imagegen [43], DALL-E2 [35] and Stable Diffusion [41], have attracted unprecedented attention from the research community and public society. With the help of large-scale pretrained language models [34, 10], LLIMs can generate high-fidelity images well aligned with the provided text prompts without further fine-tuning. To fully leverage the generation and generalization capabilities of LLIMs, we aim to develop a text-driven image editing method based on open-sourced LLIMs, e.g., Stable Diffusion [41]. + +Editability and fidelity are two essential requirements + +of image editing tasks. The former requires that the edited images are supposed to contain visual contents well aligned with the corresponding textual contents provided in the target prompts, while the latter expects that areas other than the edited parts should stay as close to those of the input image as possible. For example, when modifying the color of a specific object, its other attributes (e.g., size and shape) are expected to be preserved. As shown in Fig. 1, given an image of a red car and the target text prompt ("a yellow car"), the desired edited image should contain a yellow car while keeping the background as well as the car's size and shape unchanged. To achieve this editing, the simplest way is to first invert the image to a noisy latent via the reversed deterministic DDIM sampling process [46], and then obtain the edited image via the deterministic DDIM sampling process with the guidance of the target prompt embedding. We refer to this approach as "DDIM-Edit" in our paper. Although this approach successfully turns the color of the car to yellow (see "DDIM-Edit" in Fig. 1), the background and the shape of the car change drastically, which obviously fails to meet the requirement of high fidelity. The reason lies in that the deterministic DDIM sampling process cannot be reversed perfectly in practice. A slight error is amplified by a large classifier-free guidance scale, and is accumulated in each sampling step, which consequently results in a significantly different image. + +To improve fidelity, some methods consider the image editing tasks as inpainting tasks, which require users to explicitly provide masks of the inpainting regions [3, 25]. With the mask prior, the background can remain the same, but masking out image contents also removes important structural information that is helpful in the editing process, leading to unsatisfactory editing results. Moreover, asking users to provide masks is cumbersome and not suitable for quick and intuitive text-driven image editing. As a solution, DiffEdit [7] presents an algorithm that can automatically generate a mask given a target text prompt to locate the region to be edited. However, the editability of DiffEdit largely depends on DDIM-Edit, which may fail to preserve the structural information of the edited object, e.g., the shape of the car (see "DiffEdit" in Fig. 1). Moreover, to generate an accurate mask, DiffEdit requires a precise text description of the input image (referred to as "source text"), hampering the editing efficiency. Without the source text (see "DiffEdit w/o src" in Fig. 1), the automatically generated mask cannot locate the body of the car accurately, further decreasing editability. + +In this work, we aim to propose an image editing method to mitigate all the above problems, i.e., the method should be user-friendly, generalizable to various domains, and generate edited images with high fidelity. Specifically, for a quick and intuitive text-based method, users only need to provide an input image and the corresponding target text + +prompts, without the need for a mask or a source text describing the input image. Secondly, the method should be able to operate on real images from various domains. Thirdly, the objects should be precisely edited with the background preserved. In some cases, only certain attributes of the objects should be modified, while other attributes are supposed to be left untouched. + +To achieve these merits, we believe that image editing needs a new inversion method based on diffusion models to reconstruct the input image. Inspired by the classifier-free guidance [20] and textual-inversion methods [27], we propose a Prompt Tuning Inversion method to encode the information of the input image into a conditional embedding. More specifically, we first apply DDIM inversion to the input image latent to obtain a sequence of noisy ones. These noisy latents can be taken as a prior trajectory for reconstructing the original image. Then, we introduce a learnable embedding in the sampling process. The diffusion model reconstructs the input image step by step along the trajectory conditioned on this embedding while optimizing it at the same time. In this way, the contents of the input image are learned in the embedding. Finally, we obtain a new conditional embedding by linearly interpolating between the optimized embedding and the target embedding, resulting in a representation that combines both the structural information of the input image and the visual content of the target text. + +Overall, our proposed method consists of two stages. In the first stage, we encode the information of the input image into a learnable conditional embedding via prompt tuning in the reconstruction process. In the second stage, a new conditional embedding is computed by linearly interpolating between the target embedding and the optimized one obtained in the first stage, which boosts a trade-off between editability and fidelity. The classifier-free guidance is then applied to sample the edited image. In sum, our contributions are as follows: + +- We propose a user-friendly text-driven image editing method which requires only an input image and a target text for editing, without any need for user-provided masks or source descriptions of the input images. +- We propose a Prompt Tuning Inversion method for diffusion models which can quickly and accurately reconstruct the original image, providing a strong basis for sampling edited images with high fidelity to the inputs. +- We compare against the state-of-the-art methods both qualitatively and quantitatively, and show that our method outperforms these works in terms of the trade-off between editability and fidelity. + +# 2. Related work + +Text-to-image synthesis. Text-guided synthesis has been widely adopted for image generation [12, 54, 4, 41]. Works based on generative adversarial networks (GANs) [37, 23, 33, 60] have been proposed for text-to-image synthesis. CLIP-based methods [8, 54] have also been proposed to utilize the language-image priors from a pre-trained CLIP [34] model to generate images from texts. Recently, works [11, 18, 19, 29] based on the Diffusion Probabilistic Models (DPM) [45] have achieved state-of-the-art results in text-to-image synthesis. Among these works, Latent Diffusion Model (LDM) [41] trains DPM in the latent space using a powerful pre-trained auto-encoder, and introduces a cross-attention layer into the model architecture, thus turning the diffusion model into a powerful and flexible generator with greatly improved visual fidelity. Our work of image editing is based on LDM [41] thanks to its powerful image generation capability. + +Image editing. Image editing with generative adversarial networks (GANs) has been studied extensively [30, 31, 52, 53]. Some other techniques also leverage the image-text alignment capability of CLIP [34] and transfer it to the framework of GANs [2, 49, 55]. More recently, the development of diffusion models [18, 45, 47] provides a more flexible design space than GANs for the editing task, while following a simpler training setup (e.g., SDEdit [26] and ILVR [6]). Textual Inversion [13] and Dream-Booth [42] demonstrate the capability to generate diverse images with unique object characteristics by fine-tuning the diffusion model with multiple images. Imagic [21] and UniTune [51], which are based on the powerful Imagen model [43], also show impressive editing performance. However, the above methods require restrictive fine-tuning of the pre-trained model, and thus may not fully leverage the generalization ability of the pre-trained model due to overfitting or language drift. Other methods [3, 28] require a user-provided mask to guide the diffusion process, making it hard for them to be interactive. To achieve text-only interactive editing, some optimization-free methods have been proposed recently (e.g., Prompt-to-Prompt [16] and DiffEdit [7]) to automatically infers a mask before editing. + +Inversion. In the GAN literature, the inversion process requires one to find a corresponding latent representation of the given image [59, 56]. This process has been extensively studied for GANs [1, 61, 15, 39, 32, 50]. For diffusion models, the inversion requires to find a noise map and a conditional vector corresponding to a generated image but simply adding noise and denoising it may arouse the problem that the image content can be changed drastically. Works [6, 11, 35] have been proposed to improve the inversion process. However, it is still challenging for these methods to generate new instances of a given example while maintaining fidelity. Textual Inversion [13] and Dream- + +Booth [42] propose to learn concepts from images through textual inversion by either directly optimizing the embedding of the textual concept or fine-tuning the diffusion models, which can be computationally inefficient. Null-Text Inversion [27] modifies the unconditional textual embedding that is used for classifier-free guidance instead of the input text embedding, which enables applying prompt-based editing without the cumbersome tuning of the model parameters. Different from these methods, our method encodes the information of the input image into a learnable conditional embedding, which provides a helpful prior in sampling edited image with high fidelity to the input image. + +# 3. Methodology + +Given a real or synthesized image $\mathcal{I}$ , we aim to edit $\mathcal{I}$ to get an edited image $\mathcal{I}^*$ with the guidance of text. Different from existing methods which require source prompts provided by users or produced by an off-the-shelf image captioning model, our proposed editing process is guided by only target or edited prompt $\mathcal{P}^*$ . An overview of our method is provided in Fig. 2, which consists of two stages. In the first stage, we encode the information of the input image into a learnable conditional embedding via prompt tuning in the reconstruction process. A new conditional embedding is then computed in the second stage by linearly interpolating between the target embedding and the optimized one from the first stage, thus achieving effective editing while maintaining high fidelity. Conditioned on this interpolated embedding, the classifier-free guidance is adopted to sample the final edited image. + +# 3.1. Background and preliminaries + +Diffusion models. Diffusion probabilistic models are designed to learn a data distribution by gradually denoising normally distributed noise, which corresponds to learning to reverse a fixed forward diffusion process: + +$$ +q \left(x _ {t} \mid x _ {t - 1}\right) := \mathcal {N} \left(x _ {t}; \sqrt {\alpha_ {t}} x _ {t - 1}, (1 - \alpha_ {t}) \mathbf {I}\right). \tag {1} +$$ + +In the forward process, normally distributed noise is gradually added to the sample $x_{t - 1}$ to obtain a more noisy variant $x_{t}$ . The noise is dependent on a variance schedule $\alpha_{t}$ where $t\in 1,\dots,T$ , with $T$ being the total number of steps, $x_0$ the original image, and $x_{T}$ approximately the standard Gaussian noise. The reverse process is defined with parameters $\theta$ : + +$$ +p _ {\theta} \left(x _ {t - 1} \mid x _ {t}\right) := \mathcal {N} \left(x _ {t - 1}; \mu_ {\theta} \left(x _ {t}, t\right), \Sigma_ {\theta}\right). \tag {2} +$$ + +Using a fixed variance $\Sigma_{\theta}$ , only the mean value $\mu_{\theta}(x_t,t)$ needs to be learned. With the parameterization trick, the network $\epsilon_{\theta}$ is trained to predict the noise $\epsilon$ , resulting in a loss, where $c$ represents the conditional embedding: + +$$ +\mathbb {E} _ {t, x _ {0}, \epsilon} [ \| \epsilon - \epsilon_ {\theta} (x _ {t}, t, c) \| ^ {2} ]. \tag {3} +$$ + +![](images/937569000531e3da916ea9434e390e0b08a233bfa4442e7e8887dc5966611402.jpg) +Figure 2. An overview of our proposed image editing method. **Stage 1:** we first apply DDIM inversion to the input image embedding to obtain a diffusion trajectory $\{z_t^*\}_{t=0}^T$ . Then we reconstruct the input image along with the reversed trajectory by optimizing the learnable conditional embedding $c_t$ . **Stage 2:** we perform classifier-free guidance sampling conditioned on a linear interpolation between target embedding $c^*$ and $c_t$ at each diffusion step. $\bigoplus$ denotes element-wise weighted addition. Red dashes indicate the gradient flow in PTI. + +In this work, we employ the deterministic DDIM sampling [46]: + +$$ +x _ {t - 1} = \sqrt {\alpha_ {t - 1}} f _ {\theta} (x _ {t}, t) + \sqrt {1 - \alpha_ {t - 1}} \epsilon_ {\theta} (x _ {t}, t), \qquad (4) +$$ + +where $f_{\theta}$ is the prediction of $x_0$ given $x_t$ at step $t$ . Given a noisy image $x_T$ , the noise is gradually removed to generate an image $x_0$ by applying Eq. 4 for $T$ steps. + +Latent diffusion. Instead of operating in the image pixel space, Latent Diffusion Models [41] (LDMs) utilize an autoencoder to learn a latent space which is perceptually equivalent to the pixel space. First, an encoder $ENC$ is adopted to map a given image $x_0$ into a latent embedding $z_0$ . Then a decoder $DEC$ is designed to reconstruct the input image given $z_0$ , i.e., $DEC(ENC(x_0)) \approx x_0$ . The encoder downsamples the original images by a factor of 4 or 8. In this way, the diffusion model operates on a much smaller representation with lower time complexity and memory burden. Thus, for our method, we apply one of the state-of-the-art LDMs, Stable Diffusion [41]. In the forward and reverse process described above, we only need to replace the image $x_t$ with its latent embedding $z_t$ at each step. + +Classifier-free guidance. Our editing method is built upon text-guided diffusion models. In Stable Diffusion, the text $\mathcal{P}$ is fed into a pre-trained CLIP [34] text encoder $\tau_{\theta}$ to obtain its corresponding embedding and the underlying UNet model is augmented with the cross attention mechanism, which is effective for generating visual contents conditioned on the text $\mathcal{P}$ . One of the key challenges in this kind of generation models is the amplification of the effect induced by the conditional text. To this end, the classifier-free guidance technique is proposed, where the prediction for each step is + +a combination of conditional and unconditional predictions. Formally, let $c = \tau_{\theta}(\mathcal{P})$ be the conditional embedding vector and $\varnothing = \tau_{\theta}(\varnothing)$ be the unconditional one, the classifier-free guidance prediction is calculated by: + +$$ +\tilde {\epsilon} _ {t} = \epsilon_ {\theta} \left(z _ {t}, t, \varnothing\right) + \omega \cdot \left(\epsilon_ {\theta} \left(z _ {t}, t, c\right) - \epsilon_ {\theta} \left(z _ {t}, t, \varnothing\right)\right), \tag {5} +$$ + +where $\omega$ is the guidance scale parameter. + +# 3.2. Problems of DDIM inversion + +Given an input image $\mathcal{I}$ and a target prompt $\mathcal{P}^*$ , we aim to edit $\mathcal{I}$ to make its visual content consistent with textual content in $\mathcal{P}^*$ , while preserving a maximal amount of details from $\mathcal{I}$ . The above two aspects are referred to asEditability and input image fidelity, respectively. + +To achieve effective editing while maintaining high fidelity, we first need to inverse the input image into an appropriate noise map, based on which the edited image can be sampled. Eqs. 1 and 2 show a naive way to add noise to the input image and then denoise it through the diffusion network, respectively. However, as the sampling process is stochastic, the samples generated from the same latent can be different every time. Even if the sampling process becomes deterministic, the random noise in the forward process still makes the generated image content change significantly. To address this issue, DiffusionCLIP [22] reverses the deterministic DDIM sampling process in Eq. 4 based on the assumption that the ordinary differential equation (ODE) process can be reversed within the limit of small steps: + +$$ +z _ {t + 1} = \sqrt {\alpha_ {t + 1}} f _ {\theta} \left(z _ {t}, t\right) + \sqrt {1 - \alpha_ {t + 1}} \epsilon_ {\theta} \left(z _ {t}, t\right), \tag {6} +$$ + +![](images/5c7411c6a54a2f60320f575a5bb1deeda7b4770c79a1c00e6b70fce12c39b8fd.jpg) + +![](images/68c69a50553b254fa4ef16610e28b5767436b0281aa6ed38bad8fd50887a12c9.jpg) +CFG $(\omega = 0.0)$ + +![](images/692145787054f0c4979c47c842c11b8a6f796d1ef1804474566c289e5e182813.jpg) +CFG $(\omega = 1.0)$ + +![](images/8371103b6d97dc5944802e8c3c97918322aafca63676da40784be39b114bf59e.jpg) +CFG $(\omega = 2.5)$ + +![](images/62e2025b4d3460da294c929527e302725a4b4549e3d65d04e120b3d5043b05d3.jpg) +Input image +PTI (ours) +Figure 3. Reconstruction quality of our Prompt Tuning Inversion, and DDIM inversion with different classifier-free guidance (CFG) scales $\omega$ in the sampling process. $\omega = 0$ in the forward process for all methods. + +![](images/4a686a4c4ed117e2f3545825ac178c4819a9f013ad07d375765d9519b2aec22c.jpg) +CFG $(\omega = 5.0)$ + +![](images/33fff96fc7010df38375a6aa71e1138788c789b7fe1cbaec2261ace48d787b3a.jpg) +CFG $(\omega = 7.5)$ + +![](images/bfab0eff8fa91c0cd4001cb2e260ab7bcd95cf124c27af9276c033347efdce90.jpg) +CFG $(\omega = 10.0)$ + +
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2.514.5115.7318.1315.7414.24
5.011.3011.4811.7012.1212.06
+ +Table 1. Reconstruction quality by measuring the PSNR score of DDIM inversion with different classifier-guidance scales $\omega$ . $\omega_{\mathrm{enc}}$ and $\omega_{\mathrm{dec}}$ denote the guidance scale used in the DDIM forward and sampling processes, respectively. + +where $z_{t}$ is the latent embedding of $x_{t}$ . + +To investigate the reconstruction performance of DDIM, we first invert the latent embedding of the input image into noise maps via Eq. 6 and then use the deterministic DDIM sampling process in Eq. 4 to reconstruct the input. Note that both processes are performed with unconditional diffusion models, i.e., the classifier-free guidance scale in Eq. 5 is set to $\omega = 0$ for both forward and reverse sampling processes. Although a slight error is incorporated in every step as ODE process cannot be reversed perfectly in practice, the accumulated error is negligible, and DDIM inversion can nearly reconstruct the original image (see "CFG ( $\omega = 0.0$ )" in Fig. 3). However, to generate an image well aligned with the conditional text prompt using Stable Diffusion, a large guidance scale $\omega > 1$ is necessary for the sampling process in Eq. 4. This arouses the problem that when enlarging $\omega$ , the generated images are far from the original ones as shown in Fig. 3. We believe that when $\omega$ of the sampling process is different from that of the forward process, the accumulated error would be amplified, leading to unsatisfactory reconstruction quality. This can be illustrated in Table 1, i.e., the best reconstruction quality in each line is obtained when $\omega$ used in the DDIM sampling process is the same as that used in the forward process. Even if $\omega$ used in the forward and sampling processes are kept the same, PSNR still decreases with $\omega$ increasing (see the numbers in bold in Ta + +ble 1). The above analysis demonstrates that it is hard for DDIM inversion to achieve a satisfactory trade-off between editability (which requires larger $\omega$ ) and fidelity (which requires smaller $\omega$ ). To address this issue, we propose a new inversion technique, i.e., Prompt Tuning Inversion. + +# 3.3. Prompt tuning for inversion + +To successfully invert real images into the model's domain, recent works optimize the textual encoding, the network's parameters, or both. Motivated by Pivotal Inversion [40], we replace the conditional embedding of the text prompt with an optimized one, referred to as Prompt Tuning in this work. Namely, for each input image, we optimize only the conditional embedding $c$ so that it encodes important information of the input image which helps the reconstruction. The parameters of the diffusion network and the text encoder $\tau_{\theta}$ are frozen during prompt tuning. + +We first initialize $z_0^* = z_0 = ENC(x_0)$ , and adopt DDIM inversion with $\omega = 0$ to obtain a trajectory of noisy latent codes $\{z_t^*\}_{t=1}^T$ . Then we initialize $\tilde{z}_T = z_T^*$ and perform the following optimization to the conditional embedding $c$ with $\omega > 1$ for the timestamps $t = T, \dots, 1$ , each for $N$ iterations: + +$$ +c _ {t} = \underset {c _ {t}} {\arg \min } \left\| z _ {t - 1} ^ {*} - z _ {t - 1} \left(\tilde {z} _ {t}, t, c _ {t}\right) \right\| ^ {2}. \tag {7} +$$ + +For brevity, $z_{t-1}(\tilde{z}_t, t, c_t)$ denotes applying a DDIM sampling step using $\tilde{z}_t$ and the conditional embedding $c_t$ at the timestep $t$ . At the end of each timestep, we update + +$$ +\tilde {z} _ {t - 1} = z _ {t - 1} \left(\tilde {z} _ {t}, t, c _ {t}\right). \tag {8} +$$ + +Finally, we can reconstruct the input image by using the noise latent $\tilde{z}_T = z_T^*$ and the optimized conditional embeddings $\{c_t\}_{t=1}^T$ . In the next subsection, we will introduce the approach to editing images with the target text prompt and the conditional embeddings. + +# 3.4. Prompt tuning for editing + +Since the sequence of the conditional embeddings $\{c_t\}_{t=1}^T$ is optimized to fully reconstruct the input image, we believe that these optimized conditional embeddings have contained the most information of the original image, and thus ensure high fidelity. To achieve the desired modification, these optimized embeddings are adopted to perform the editing by advancing in the direction of the target text embedding $c^* = \tau_\theta(\mathcal{P}^*)$ to ensure good editability also. More formally, in the second stage, we simply interpolate between the target embedding $c^*$ and the optimized $c_t$ linearly at each timestamp. For a given hyper-parameter $\eta \in (0,1]$ , we obtain + +$$ +c _ {t} = \eta \cdot c ^ {*} + (1 - \eta) \cdot c _ {t}, \tag {9} +$$ + +where the first term ensures the effective editability corresponding to the semantic contents in the target text, while + +the second term guarantees a good reconstruction of the original image. The algorithm is presented in Lines 14-21 in Algorithm 1. Note that when $\eta = 0$ or $\eta = 1$ , the output of our editing method is the reconstructed original image, or the output of the baseline DDIM-Edit, respectively. + +Intuitively, our editing method is to find an intermediate representation between the original image and the output of DDIM-Edit. For a desired modification, the intermediate representation is supposed to contain both the structural information of the source image and the semantic contents of the target text prompt. Eq. 9 is only one way to achieve this, which we refer to as condition interpolation. We also test a different interpolation method (referred to as latent interpolation), where we linearly interpolate between the noisy latent $z_{t}$ and $z_{t}^{*}$ at each timestamp: + +$$ +z _ {t} ^ {e d t} = \eta \cdot z _ {t} + (1 - \eta) \cdot z _ {t} ^ {*}, \tag {10} +$$ + +where $z_{t}^{*}$ is the noisy latent calculated by DDIM inversion via Eq. 6, and $z_{t}$ is the latent obtained in the vanilla DDIM sampling process conditioned on the target embedding. Although this approach is more simple since the process of prompt tuning is no longer needed, we observe that this interpolation method may lead to cluttered images. This is because the interpolation of latent embeddings mixes the source object and the edited object spatially, rather than semantically (as condition interpolation does), leading to cluttered contents in images. + +# 3.5. Discussion + +Our proposed image editing method shares similar motivations with existing works [21, 51, 27, 16], all of which aim to modify an image in a text-driven and mask-free manner. However, our approach differs from them significantly in the following aspects: + +1) Imagic [21] and UniTune [51] finetune the diffusion models for hundreds of steps to maintain high fidelity to the input image. In contrast, we only need to optimize the conditional embedding, which greatly reduces computational budgets. +2) Our proposed Prompt Tuning Inversion is inspired by the Null-Text Inversion method [27]. However, Null-Text Inversion chooses to optimize the unconditional embedding while we optimize the conditional one. Moreover, the editing process of Null-Text Inversion is achieved by the cross-attention map control in Prompt-to-Prompt [16], which requires an additional description of the input image. Compared to theirs, our method only needs the target text prompt and is thus more user-friendly. + +Algorithm 1: Prompt Tuning Inversion for Editing +Input: An input image $\mathcal{I}$ and a target prompt embedding $c^{*} = \tau_{\theta}(\mathcal{P}^{*})$ +Output: Edited image $\mathcal{I}^*$ +1 // DDIM Inversion +2 Set guidance scale $\omega = 0,z_0^* = ENC(\mathcal{I})$ . +3 Compute the intermediate trajectory $\{z_t^*\}_{t = 0}^T$ using DDIM inversion over $\mathcal{I}$ without conditional guidance via Eq. 6; +4// Prompt Tuning +5 Set guidance scale $\omega >1,\eta \in (0,1]$ . +6 Initialize $\tilde{z}_T\gets z_T^*,c_T\gets c^*$ . +7 for $t = T,T - 1,\dots ,1$ do +8 for $j = 0,\ldots ,N - 1$ do +9 $|c_{t}\gets c_{t} - \beta \nabla_{c}||z_{t - 1}^{*} - z_{t - 1}(\tilde{z}_{t},t,c_{t})||_{2}^{2};$ +10 end +11 $\tilde{z}_{t - 1}\gets z_{t - 1}(\tilde{z}_{t},t,c_{t}),c_{t - 1}\gets c_{t}$ +12 end +13 // Editing +14 Set $z_{T}^{edt}\gets z_{T}^{*}$ . +15 for $t = T,T - 1,\ldots ,1$ do +16 $c_{t} = (1 - \eta)\cdot c_{t} + \eta \cdot c^{*};$ +17 $z_{t - 1}^{edt} = z_{t - 1}(z_{t}^{edt},t,c_{t});$ +18 end +19 $\mathcal{I}^* = DEC(z_0^{edt})$ +20 return $\mathcal{I}^*$ + +# 4. Experiments + +# 4.1. Setup + +Implementation details. In our experiments, we adopt the text-conditional Latent Diffusion Model [41] (known as Stable Diffusion) with 890M parameters trained on LAION-5B [44] at $512 \times 512$ resolution. For the DDIM schedule, we adopt 50 steps and retain the original hyperparameter choices of Stable Diffusion. The encoding ratio parameter is set to 0.8. The number of iterations to optimize $c$ per diffusion step is set to $N = 1$ . The hyper-parameters $\beta$ and $\eta$ in Algorithm 1 are set to 0.1 and 0.9, respectively, unless specified. These allow editing an image in $\sim 1$ minute on a single Tesla V100 GPU. For better performance, we adopt attention maps to localize the edited regions (referred to as local blending), and re-weight the attention maps as in [16]. + +Evaluation and datasets. In semantic image editing, the visual content of the edited image is supposed to align well with the target text prompt (editability) while staying close to the input image in terms of the unedited parts (fidelity). For a given method, better editability usually comes at the cost of decreased fidelity to the input image, and vice versa. This forms a trade-off curve between the two objectives. + +![](images/078554bf6836db688f4f76d7be8f798ed3057c994f750b7709ba9a4d0c379c2f.jpg) +Figure 4. Comparison with DiffEdit and DDIM-Edit on ImageNet. For all methods, we set the DDIM encoding ratio to 0.8, and only vary the mask threshold to draw the trade-off curve. + +Following DiffEdit [7], we evaluate different editing methods by comparing their trade-off curves on ImageNet [9]. Specifically, given an image of one class from ImageNet, we aim to edit it to another class of ImageNet as instructed by the target text prompt. The editability and fidelity are measured using the LPIPS perceptual distance [58] and CS-FID, which is a class-conditional FID metric [17], respectively. The former measures the distance with the input image while the latter measures both image realism and consistency w.r.t. the target class. For both metrics, lower values indicate better editing performance. + +# 4.2. Comparison with other methods on ImageNet + +We compare our method with DiffEdit and our baseline DDIM-Edit, since they both share the same DDIM forward process and a similar sampling process. Besides, they load the same publicly available pre-trained weights for a fair comparison. To leverage the generalization capability of large-scale language-image models, we adopt the text-conditional Stable Diffusion model "sd-v1-4" instead of the class-conditional model trained on ImageNet as the pre-trained model. + +As pointed out by DiffEdit [7], different editing methods often have hyper-parameters which control editability, e.g., the mask threshold, or the encoding ratio. A lower mask threshold or higher encoding ratio leads to stronger editing. In our proposed method, we can also control the editing strength by varying the conditional interpolation ratio $\eta$ introduced in Eq. 9. In our evaluation, we fix the DDIM encoding ratio and draw the trade-off curve by varying the mask threshold for all methods1. The results are presented in Fig. 4, where "DDIM-Global" denotes that the images are edited via "DDIM-Edit" but without using any masks, i.e., the editing is performed globally. This can + +![](images/c72a62424e3ab6a466d8fcd8d0e367887d26175c1bd481d3348b5003337f76af.jpg) +Figure 5. Editing examples on ImageNet by our method and other methods. DDIM-G/DDIM-L indicates the baseline method DDIM-Edit with/without the local blend trick. + +be regarded as a lower bound of fidelity for all methods. As the mask threshold increases, LPIPS decreases since fewer parts of the image are edited. Compared to DiffEdit, our baseline method DDIM-Edit achieves a better trade-off. Note that the only difference between the two methods is the approach to generating masks. The comparison shows that inferring editing masks using cross-attention maps, as adopted by DDIM-Edit, is more appropriate. Based on DDIM-Edit, our method can further improve the fidelity to the input images while maintaining editability. The best CSFID-LPIPS trade-off of our method demonstrates its superiority over DiffEdit and the baseline. + +We also present qualitative examples of these methods. As shown in Fig. 5, without automatically generated masks, "DDIM-G" tends to modify images globally. For simple cases (e.g., example (d)), image editing methods with the original DDIM inversion works well. However, for complex cases, we observe undesired and unreasonable edits to the objects. In contrast, with the help of the learnable conditional embedding, our method achieves realistic editing while successfully preserving the original details. + +# 4.3. Ablation study + +Comparison to existing inversion methods. We randomly select 128 images and their corresponding captions from the COCO validation set [24]. We then apply the following reconstruction methods to each image-caption pair: (1) AE denotes the variational auto-encoder with a slight KL- + +
MethodAEDDIMNTIPTI (ours)
PSNR26.2213.6424.4525.71
SSIM0.85640.46410.82700.8501
+ +Table 2. Reconstruction quality of different methods measured by PSNR and SSIM. For both metrics, higher values indicate better quality. + +
iters12345
learning rate β = 0.01
NTI17.0520.1222.2523.6124.45
PTI19.3623.2024.8625.4725.71
learning rate β = 0.1
NTI23.0824.7425.6225.8225.91
PTI24.7425.2325.7825.9025.97
+ +Table 3. PSNR scores under different optimizing settings. + +penalty used in Stable Diffusion. An image is first encoded by the encoder of AE. Afterwards, the decoder directly reconstructs the image from the latent. Therefore, we consider AE as an upper bound of reconstruction quality. (2) DDIM denotes the DDIM inversion method, which is a baseline inversion method. As analyzed in Sec. 3.2, it usually outputs a low-quality reconstruction result under a large classifier-free guidance scale $\omega$ . (3) NTI denotes the Null-Text Inversion method [27], which is our main point of comparison. Different from our method, it optimizes the unconditional embedding. (4) PTI denotes our proposed Prompt Tuning Inversion method. We introduce a learnable conditional embedding and the optimizing details are presented in Algorithm 1. + +The experimental results are provided in Table 2. For the diffusion-based inversion methods, we apply the diffusion model in an unconditional manner (i.e., the classifier guidance scale $\omega = 0$ ) for the DDIM forward process. For the sampling process, we set $\omega = 7.5$ . As shown in Table 2, DDIM inversion fails to reconstruct the original images since $\omega$ in the sampling process is different from that in the forward process, leading to a low PSNR score (13.64). For NTI and PTI, we set the number of iterations $N$ to 5 and the learning rate $\beta$ to 0.01. We observe that both methods can reconstruct the images but the reconstruction quality of our method is better (25.71 vs. 24.45). To further demonstrate the effectiveness of our method, we vary $N$ from 1 to 5 and increase the learning rate $\beta$ from 0.01 to 0.1. The experimental results in Table 3 show that the reconstruction quality of PTI is always better than NTI under all settings, demonstrating that our method converges faster. + +Influence of the hyper-parameter $\eta$ . We also perform ablation on the hyper-parameter $\eta$ and the results are presented in Fig. 6. By adjusting $\eta$ , we can achieve a good trade-off between fidelity and editability. More quantitative analyses are presented in supplementary materials. + +![](images/7370967ba997d267657f4937f72ce74ffa8670288faef971c02451683d9504e2.jpg) +Figure 6. Qualitative examples for the effect of $\eta$ . + +![](images/07cab73b5cd3ba16b3fd693e060674fc3063c2f6cf1041f14f13724892aa9376.jpg) +Figure 7. A failure example on ImageNet: when multiple objects exist, only one of them is edited successfully. + +# 5. Conclusion and future work + +We propose an intuitive and user-friendly text-based image editing method, which benefits from the superior generation and generalization capacities of large-scale image language diffusion models (e.g., Stable Diffusion). The key idea of our method is that important structural information of the input image can be encoded into conditional embeddings, which can guide the diffusion model to reconstruct the original image via the sampling process. Based on this, our method consists of two stages. In the first reconstruction stage, we propose a novel Prompt Tuning Inversion method which encodes image information to learnable conditional embeddings quickly and accurately. In the second editing stage, we introduce an interpolation which linearly combines the target text embedding with the optimized embedding obtained in the first stage. In this way, the new conditional embedding contains both information from the input image and the target text prompt, resulting in an edited image with an appropriate trade-off between editability and fidelity. + +While our method works well in most scenarios, it still faces some limitations. As shown in Fig. 7, there are multiple objects in the input images. However, neither DiffEdit nor our method changes all "gooses" to "black storks". This limitation can possibly be mitigated by operating the attention maps more precisely [5] or adding different modes of conditional control [57], providing a research direction for image editing. Besides, the proposed method still requires running inversion every time given a new text since initialization is based on the target text, and not using attention is not always an advantage. We leave these options for future work. + +# References + +[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. 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Improved stylegan embedding: Where are the good latents? arXiv preprint arXiv:2012.09036, 2020. 3 \ No newline at end of file diff --git a/2023/Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models/images.zip b/2023/Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..377e2ee66082a35182acb00971d483fd237dd313 --- /dev/null +++ b/2023/Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:bac29069ed78366f29f177a21924d0ed853c68484e36db318b8921eb32b579e1 +size 414812 diff --git a/2023/Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models/layout.json b/2023/Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..66da4ac4f549c47c4efa0b97d73e93eab813ea2e --- /dev/null +++ b/2023/Prompt Tuning Inversion for Text-driven Image Editing Using Diffusion Models/layout.json @@ -0,0 +1,10284 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 50, + 103, + 544, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 103, + 544, + 121 + ], + "spans": [ + { + "bbox": [ + 50, + 103, + 544, + 121 + ], + "type": "text", + "content": "Prompt Tuning Inversion for Text-Driven Image Editing Using Diffusion Models" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 139, + 142, + 457, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 142, + 457, + 172 + ], + "spans": [ + { + "bbox": [ + 139, + 142, + 457, + 172 + ], + "type": "text", + "content": "Wenkai Dong" + }, + { + "bbox": [ + 139, + 142, + 457, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 139, + 142, + 457, + 172 + ], + "type": "text", + "content": " Song Xue" + }, + { + "bbox": [ + 139, + 142, + 457, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 139, + 142, + 457, + 172 + ], + "type": "text", + "content": " Xiaoyue Duan" + }, + { + "bbox": [ + 139, + 142, + 457, + 172 + ], + "type": "inline_equation", + "content": "^{1,2*}" + }, + { + "bbox": [ + 139, + 142, + 457, + 172 + ], + "type": "text", + "content": " Shumin Han" + }, + { + "bbox": [ + 139, + 142, + 457, + 172 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + }, + { + "bbox": [ + 139, + 142, + 457, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 139, + 142, + 457, + 172 + ], + "type": "text", + "content": "Baidu VIS, " + }, + { + "bbox": [ + 139, + 142, + 457, + 172 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 139, + 142, + 457, + 172 + ], + "type": "text", + "content": "Beihang University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 174, + 451, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 174, + 451, + 185 + ], + "spans": [ + { + "bbox": [ + 143, + 174, + 451, + 185 + ], + "type": "text", + "content": "{dongwenkai, xuesong06, duanxiaoyue, hanshumin}@baidu.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 238, + 290, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 238, + 290, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 238, + 290, + 597 + ], + "type": "text", + "content": "Recently large-scale language-image models (e.g., text-guided diffusion models) have considerably improved the image generation capabilities to generate photorealistic images in various domains. Based on this success, current image editing methods use texts to achieve intuitive and versatile modification of images. To edit a real image using diffusion models, one must first invert the image to a noisy latent from which an edited image is sampled with a target text prompt. However, most methods lack one of the following: user-friendliness (e.g., additional masks or precise descriptions of the input image are required), generalization to larger domains, or high fidelity to the input image. In this paper, we design an accurate and quick inversion technique, Prompt Tuning Inversion, for text-driven image editing. Specifically, our proposed editing method consists of a reconstruction stage and an editing stage. In the first stage, we encode the information of the input image into a learnable conditional embedding via Prompt Tuning Inversion. In the second stage, we apply classifier-free guidance to sample the edited image, where the conditional embedding is calculated by linearly interpolating between the target embedding and the optimized one obtained in the first stage. This technique ensures a superior trade-off between editability and high fidelity to the input image of our method. For example, we can change the color of a specific object while preserving its original shape and background under the guidance of only a target text prompt. Extensive experiments on ImageNet demonstrate the superior editing performance of our method compared to the state-of-the-art baselines." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 619, + 128, + 631 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 619, + 128, + 631 + ], + "spans": [ + { + "bbox": [ + 47, + 619, + 128, + 631 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 639, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 639, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 639, + 287, + 687 + ], + "type": "text", + "content": "Text-based image editing, a long-standing problem in image processing, aims to modify an input image to align its visual content with the target text prompts. 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Illustration of different methods in editing the color of the car. Methods based on the original DDIM inversion (i.e., DDIM-Edit, DiffEdit and DiffEdit w/o src) cannot preserve the shape of the car. In contrast, our method successfully changes the color while preserving the structural information. The target text is \"a yellow car\". The source text is \"a red car\" for DiffEdit." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 392, + 292, + 460, + 360 + ], + "blocks": [ + { + "bbox": [ + 392, + 292, + 460, + 360 + ], + "lines": [ + { + "bbox": [ + 392, + 292, + 460, + 360 + ], + "spans": [ + { + "bbox": [ + 392, + 292, + 460, + 360 + ], + "type": "image", + "image_path": "c4226ed19c5dbf37eae79b6d1657a438d1fd354e8a37a8576b34b48aa05238b4.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 402, + 360, + 450, + 367 + ], + "lines": [ + { + "bbox": [ + 402, + 360, + 450, + 367 + ], + "spans": [ + { + "bbox": [ + 402, + 360, + 450, + 367 + ], + "type": "text", + "content": "DiffEdit w/o src" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 461, + 292, + 529, + 360 + ], + "blocks": [ + { + "bbox": [ + 461, + 292, + 529, + 360 + ], + "lines": [ + { + "bbox": [ + 461, + 292, + 529, + 360 + ], + "spans": [ + { + "bbox": [ + 461, + 292, + 529, + 360 + ], + "type": "image", + "image_path": "5a8cd4165c7a34893361c2a33e85882307b8e0fa6a606963eb1b33fa89db920d.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 485, + 360, + 503, + 367 + ], + "lines": [ + { + "bbox": [ + 485, + 360, + 503, + 367 + ], + "spans": [ + { + "bbox": [ + 485, + 360, + 503, + 367 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 460, + 547, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 547, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 547, + 700 + ], + "type": "text", + "content": "ods built upon text-to-image generation have been developed. In past years, GAN-based image editing methods [30, 31, 52, 53] achieve impressive results due to the powerful generation abilities of GANs [37, 23, 33, 60]. However, these methods only work well in domains where the models are trained. More recently, diffusion models such as DDPM [18] and score-based generative models [48] have demonstrated competitive or even better capability of generating images compared to VAE-, GAN-, flow- and autoregressive-based models [36, 14, 38, 12]. Especially, large-scale language-image models (LLIMs), such as Imagegen [43], DALL-E2 [35] and Stable Diffusion [41], have attracted unprecedented attention from the research community and public society. With the help of large-scale pretrained language models [34, 10], LLIMs can generate high-fidelity images well aligned with the provided text prompts without further fine-tuning. To fully leverage the generation and generalization capabilities of LLIMs, we aim to develop a text-driven image editing method based on open-sourced LLIMs, e.g., Stable Diffusion [41]." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "Editability and fidelity are two essential requirements" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 286, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 286, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 286, + 703 + ], + "type": "text", + "content": "*This work was done when Xiaoyue Duan was an intern at Baidu VIS." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "text", + "content": "† Corresponding author" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7430" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "content": "of image editing tasks. The former requires that the edited images are supposed to contain visual contents well aligned with the corresponding textual contents provided in the target prompts, while the latter expects that areas other than the edited parts should stay as close to those of the input image as possible. For example, when modifying the color of a specific object, its other attributes (e.g., size and shape) are expected to be preserved. As shown in Fig. 1, given an image of a red car and the target text prompt (\"a yellow car\"), the desired edited image should contain a yellow car while keeping the background as well as the car's size and shape unchanged. To achieve this editing, the simplest way is to first invert the image to a noisy latent via the reversed deterministic DDIM sampling process [46], and then obtain the edited image via the deterministic DDIM sampling process with the guidance of the target prompt embedding. We refer to this approach as \"DDIM-Edit\" in our paper. Although this approach successfully turns the color of the car to yellow (see \"DDIM-Edit\" in Fig. 1), the background and the shape of the car change drastically, which obviously fails to meet the requirement of high fidelity. The reason lies in that the deterministic DDIM sampling process cannot be reversed perfectly in practice. A slight error is amplified by a large classifier-free guidance scale, and is accumulated in each sampling step, which consequently results in a significantly different image." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 387, + 289, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 387, + 289, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 387, + 289, + 639 + ], + "type": "text", + "content": "To improve fidelity, some methods consider the image editing tasks as inpainting tasks, which require users to explicitly provide masks of the inpainting regions [3, 25]. With the mask prior, the background can remain the same, but masking out image contents also removes important structural information that is helpful in the editing process, leading to unsatisfactory editing results. Moreover, asking users to provide masks is cumbersome and not suitable for quick and intuitive text-driven image editing. As a solution, DiffEdit [7] presents an algorithm that can automatically generate a mask given a target text prompt to locate the region to be edited. However, the editability of DiffEdit largely depends on DDIM-Edit, which may fail to preserve the structural information of the edited object, e.g., the shape of the car (see \"DiffEdit\" in Fig. 1). Moreover, to generate an accurate mask, DiffEdit requires a precise text description of the input image (referred to as \"source text\"), hampering the editing efficiency. Without the source text (see \"DiffEdit w/o src\" in Fig. 1), the automatically generated mask cannot locate the body of the car accurately, further decreasing editability." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 642, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 289, + 715 + ], + "type": "text", + "content": "In this work, we aim to propose an image editing method to mitigate all the above problems, i.e., the method should be user-friendly, generalizable to various domains, and generate edited images with high fidelity. Specifically, for a quick and intuitive text-based method, users only need to provide an input image and the corresponding target text" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "prompts, without the need for a mask or a source text describing the input image. Secondly, the method should be able to operate on real images from various domains. Thirdly, the objects should be precisely edited with the background preserved. In some cases, only certain attributes of the objects should be modified, while other attributes are supposed to be left untouched." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 158, + 546, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 158, + 546, + 397 + ], + "spans": [ + { + "bbox": [ + 304, + 158, + 546, + 397 + ], + "type": "text", + "content": "To achieve these merits, we believe that image editing needs a new inversion method based on diffusion models to reconstruct the input image. Inspired by the classifier-free guidance [20] and textual-inversion methods [27], we propose a Prompt Tuning Inversion method to encode the information of the input image into a conditional embedding. More specifically, we first apply DDIM inversion to the input image latent to obtain a sequence of noisy ones. These noisy latents can be taken as a prior trajectory for reconstructing the original image. Then, we introduce a learnable embedding in the sampling process. The diffusion model reconstructs the input image step by step along the trajectory conditioned on this embedding while optimizing it at the same time. In this way, the contents of the input image are learned in the embedding. Finally, we obtain a new conditional embedding by linearly interpolating between the optimized embedding and the target embedding, resulting in a representation that combines both the structural information of the input image and the visual content of the target text." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 400, + 547, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 547, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 547, + 519 + ], + "type": "text", + "content": "Overall, our proposed method consists of two stages. In the first stage, we encode the information of the input image into a learnable conditional embedding via prompt tuning in the reconstruction process. In the second stage, a new conditional embedding is computed by linearly interpolating between the target embedding and the optimized one obtained in the first stage, which boosts a trade-off between editability and fidelity. The classifier-free guidance is then applied to sample the edited image. In sum, our contributions are as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 534, + 545, + 713 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 317, + 534, + 545, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 534, + 545, + 583 + ], + "spans": [ + { + "bbox": [ + 317, + 534, + 545, + 583 + ], + "type": "text", + "content": "- We propose a user-friendly text-driven image editing method which requires only an input image and a target text for editing, without any need for user-provided masks or source descriptions of the input images." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 600, + 545, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 600, + 545, + 648 + ], + "spans": [ + { + "bbox": [ + 317, + 600, + 545, + 648 + ], + "type": "text", + "content": "- We propose a Prompt Tuning Inversion method for diffusion models which can quickly and accurately reconstruct the original image, providing a strong basis for sampling edited images with high fidelity to the inputs." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 665, + 545, + 713 + ], + "type": "text", + "content": "- We compare against the state-of-the-art methods both qualitatively and quantitatively, and show that our method outperforms these works in terms of the trade-off between editability and fidelity." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "7431" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 132, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 132, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 132, + 83 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 289, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 289, + 295 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 289, + 295 + ], + "type": "text", + "content": "Text-to-image synthesis. Text-guided synthesis has been widely adopted for image generation [12, 54, 4, 41]. Works based on generative adversarial networks (GANs) [37, 23, 33, 60] have been proposed for text-to-image synthesis. CLIP-based methods [8, 54] have also been proposed to utilize the language-image priors from a pre-trained CLIP [34] model to generate images from texts. Recently, works [11, 18, 19, 29] based on the Diffusion Probabilistic Models (DPM) [45] have achieved state-of-the-art results in text-to-image synthesis. Among these works, Latent Diffusion Model (LDM) [41] trains DPM in the latent space using a powerful pre-trained auto-encoder, and introduces a cross-attention layer into the model architecture, thus turning the diffusion model into a powerful and flexible generator with greatly improved visual fidelity. Our work of image editing is based on LDM [41] thanks to its powerful image generation capability." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 295, + 289, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 295, + 289, + 569 + ], + "spans": [ + { + "bbox": [ + 46, + 295, + 289, + 569 + ], + "type": "text", + "content": "Image editing. Image editing with generative adversarial networks (GANs) has been studied extensively [30, 31, 52, 53]. Some other techniques also leverage the image-text alignment capability of CLIP [34] and transfer it to the framework of GANs [2, 49, 55]. More recently, the development of diffusion models [18, 45, 47] provides a more flexible design space than GANs for the editing task, while following a simpler training setup (e.g., SDEdit [26] and ILVR [6]). Textual Inversion [13] and Dream-Booth [42] demonstrate the capability to generate diverse images with unique object characteristics by fine-tuning the diffusion model with multiple images. Imagic [21] and UniTune [51], which are based on the powerful Imagen model [43], also show impressive editing performance. However, the above methods require restrictive fine-tuning of the pre-trained model, and thus may not fully leverage the generalization ability of the pre-trained model due to overfitting or language drift. Other methods [3, 28] require a user-provided mask to guide the diffusion process, making it hard for them to be interactive. To achieve text-only interactive editing, some optimization-free methods have been proposed recently (e.g., Prompt-to-Prompt [16] and DiffEdit [7]) to automatically infers a mask before editing." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": "Inversion. In the GAN literature, the inversion process requires one to find a corresponding latent representation of the given image [59, 56]. This process has been extensively studied for GANs [1, 61, 15, 39, 32, 50]. For diffusion models, the inversion requires to find a noise map and a conditional vector corresponding to a generated image but simply adding noise and denoising it may arouse the problem that the image content can be changed drastically. Works [6, 11, 35] have been proposed to improve the inversion process. However, it is still challenging for these methods to generate new instances of a given example while maintaining fidelity. Textual Inversion [13] and Dream-" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "text", + "content": "Booth [42] propose to learn concepts from images through textual inversion by either directly optimizing the embedding of the textual concept or fine-tuning the diffusion models, which can be computationally inefficient. Null-Text Inversion [27] modifies the unconditional textual embedding that is used for classifier-free guidance instead of the input text embedding, which enables applying prompt-based editing without the cumbersome tuning of the model parameters. Different from these methods, our method encodes the information of the input image into a learnable conditional embedding, which provides a helpful prior in sampling edited image with high fidelity to the input image." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 225, + 389, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 225, + 389, + 239 + ], + "spans": [ + { + "bbox": [ + 305, + 225, + 389, + 239 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 245, + 547, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 245, + 547, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 245, + 547, + 437 + ], + "type": "text", + "content": "Given a real or synthesized image " + }, + { + "bbox": [ + 304, + 245, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 245, + 547, + 437 + ], + "type": "text", + "content": ", we aim to edit " + }, + { + "bbox": [ + 304, + 245, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 245, + 547, + 437 + ], + "type": "text", + "content": " to get an edited image " + }, + { + "bbox": [ + 304, + 245, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^*" + }, + { + "bbox": [ + 304, + 245, + 547, + 437 + ], + "type": "text", + "content": " with the guidance of text. Different from existing methods which require source prompts provided by users or produced by an off-the-shelf image captioning model, our proposed editing process is guided by only target or edited prompt " + }, + { + "bbox": [ + 304, + 245, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^*" + }, + { + "bbox": [ + 304, + 245, + 547, + 437 + ], + "type": "text", + "content": ". An overview of our method is provided in Fig. 2, which consists of two stages. In the first stage, we encode the information of the input image into a learnable conditional embedding via prompt tuning in the reconstruction process. A new conditional embedding is then computed in the second stage by linearly interpolating between the target embedding and the optimized one from the first stage, thus achieving effective editing while maintaining high fidelity. Conditioned on this interpolated embedding, the classifier-free guidance is adopted to sample the final edited image." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 443, + 473, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 443, + 473, + 456 + ], + "spans": [ + { + "bbox": [ + 305, + 443, + 473, + 456 + ], + "type": "text", + "content": "3.1. Background and preliminaries" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 461, + 547, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 547, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 547, + 510 + ], + "type": "text", + "content": "Diffusion models. Diffusion probabilistic models are designed to learn a data distribution by gradually denoising normally distributed noise, which corresponds to learning to reverse a fixed forward diffusion process:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 336, + 516, + 545, + 531 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 516, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 336, + 516, + 545, + 531 + ], + "type": "interline_equation", + "content": "q \\left(x _ {t} \\mid x _ {t - 1}\\right) := \\mathcal {N} \\left(x _ {t}; \\sqrt {\\alpha_ {t}} x _ {t - 1}, (1 - \\alpha_ {t}) \\mathbf {I}\\right). \\tag {1}", + "image_path": "4b65743eba6afa318af42eefe72281eb06c14b62f377d8bcb68a5d63d98b39c0.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "spans": [ + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "type": "text", + "content": "In the forward process, normally distributed noise is gradually added to the sample " + }, + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "type": "inline_equation", + "content": "x_{t - 1}" + }, + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "type": "text", + "content": " to obtain a more noisy variant " + }, + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "type": "text", + "content": ". The noise is dependent on a variance schedule " + }, + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "type": "inline_equation", + "content": "t\\in 1,\\dots,T" + }, + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "type": "text", + "content": " being the total number of steps, " + }, + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "type": "text", + "content": " the original image, and " + }, + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "type": "inline_equation", + "content": "x_{T}" + }, + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "type": "text", + "content": " approximately the standard Gaussian noise. The reverse process is defined with parameters " + }, + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 536, + 547, + 619 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 343, + 627, + 545, + 640 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 627, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 343, + 627, + 545, + 640 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right) := \\mathcal {N} \\left(x _ {t - 1}; \\mu_ {\\theta} \\left(x _ {t}, t\\right), \\Sigma_ {\\theta}\\right). \\tag {2}", + "image_path": "8bd8a8f12b52c776c145e8fcabb8c6bca020a4057e01ef380059b208818372dd.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 646, + 547, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 646, + 547, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 646, + 547, + 696 + ], + "type": "text", + "content": "Using a fixed variance " + }, + { + "bbox": [ + 304, + 646, + 547, + 696 + ], + "type": "inline_equation", + "content": "\\Sigma_{\\theta}" + }, + { + "bbox": [ + 304, + 646, + 547, + 696 + ], + "type": "text", + "content": ", only the mean value " + }, + { + "bbox": [ + 304, + 646, + 547, + 696 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta}(x_t,t)" + }, + { + "bbox": [ + 304, + 646, + 547, + 696 + ], + "type": "text", + "content": " needs to be learned. With the parameterization trick, the network " + }, + { + "bbox": [ + 304, + 646, + 547, + 696 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 304, + 646, + 547, + 696 + ], + "type": "text", + "content": " is trained to predict the noise " + }, + { + "bbox": [ + 304, + 646, + 547, + 696 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 646, + 547, + 696 + ], + "type": "text", + "content": ", resulting in a loss, where " + }, + { + "bbox": [ + 304, + 646, + 547, + 696 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 646, + 547, + 696 + ], + "type": "text", + "content": " represents the conditional embedding:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 369, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 369, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {t, x _ {0}, \\epsilon} [ \\| \\epsilon - \\epsilon_ {\\theta} (x _ {t}, t, c) \\| ^ {2} ]. \\tag {3}", + "image_path": "abc2f31bde15da42ec5a743cc0a62befc9350cf28a85c1040989ddfc788b989f.jpg" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "7432" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 111, + 69, + 487, + 269 + ], + "blocks": [ + { + "bbox": [ + 111, + 69, + 487, + 269 + ], + "lines": [ + { + "bbox": [ + 111, + 69, + 487, + 269 + ], + "spans": [ + { + "bbox": [ + 111, + 69, + 487, + 269 + ], + "type": "image", + "image_path": "937569000531e3da916ea9434e390e0b08a233bfa4442e7e8887dc5966611402.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 270, + 547, + 316 + ], + "lines": [ + { + "bbox": [ + 46, + 270, + 547, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 547, + 316 + ], + "type": "text", + "content": "Figure 2. An overview of our proposed image editing method. **Stage 1:** we first apply DDIM inversion to the input image embedding to obtain a diffusion trajectory " + }, + { + "bbox": [ + 46, + 270, + 547, + 316 + ], + "type": "inline_equation", + "content": "\\{z_t^*\\}_{t=0}^T" + }, + { + "bbox": [ + 46, + 270, + 547, + 316 + ], + "type": "text", + "content": ". Then we reconstruct the input image along with the reversed trajectory by optimizing the learnable conditional embedding " + }, + { + "bbox": [ + 46, + 270, + 547, + 316 + ], + "type": "inline_equation", + "content": "c_t" + }, + { + "bbox": [ + 46, + 270, + 547, + 316 + ], + "type": "text", + "content": ". **Stage 2:** we perform classifier-free guidance sampling conditioned on a linear interpolation between target embedding " + }, + { + "bbox": [ + 46, + 270, + 547, + 316 + ], + "type": "inline_equation", + "content": "c^*" + }, + { + "bbox": [ + 46, + 270, + 547, + 316 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 270, + 547, + 316 + ], + "type": "inline_equation", + "content": "c_t" + }, + { + "bbox": [ + 46, + 270, + 547, + 316 + ], + "type": "text", + "content": " at each diffusion step. " + }, + { + "bbox": [ + 46, + 270, + 547, + 316 + ], + "type": "inline_equation", + "content": "\\bigoplus" + }, + { + "bbox": [ + 46, + 270, + 547, + 316 + ], + "type": "text", + "content": " denotes element-wise weighted addition. Red dashes indicate the gradient flow in PTI." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 334, + 288, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 334, + 288, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 334, + 288, + 360 + ], + "type": "text", + "content": "In this work, we employ the deterministic DDIM sampling [46]:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 63, + 367, + 287, + 382 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 367, + 287, + 382 + ], + "spans": [ + { + "bbox": [ + 63, + 367, + 287, + 382 + ], + "type": "interline_equation", + "content": "x _ {t - 1} = \\sqrt {\\alpha_ {t - 1}} f _ {\\theta} (x _ {t}, t) + \\sqrt {1 - \\alpha_ {t - 1}} \\epsilon_ {\\theta} (x _ {t}, t), \\qquad (4)", + "image_path": "c08a0c9f1d0f6e6a714def767eed097a3fd2d51241db8a13c5027fbc0ea11287.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "text", + "content": " is the prediction of " + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "inline_equation", + "content": "x_t" + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "text", + "content": " at step " + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "text", + "content": ". Given a noisy image " + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "inline_equation", + "content": "x_T" + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "text", + "content": ", the noise is gradually removed to generate an image " + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "text", + "content": " by applying Eq. 4 for " + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 390, + 287, + 426 + ], + "type": "text", + "content": " steps." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "text", + "content": "Latent diffusion. Instead of operating in the image pixel space, Latent Diffusion Models [41] (LDMs) utilize an autoencoder to learn a latent space which is perceptually equivalent to the pixel space. First, an encoder " + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "inline_equation", + "content": "ENC" + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "text", + "content": " is adopted to map a given image " + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "text", + "content": " into a latent embedding " + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "inline_equation", + "content": "z_0" + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "text", + "content": ". 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In the forward and reverse process described above, we only need to replace the image " + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "inline_equation", + "content": "x_t" + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "text", + "content": " with its latent embedding " + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "inline_equation", + "content": "z_t" + }, + { + "bbox": [ + 46, + 426, + 287, + 594 + ], + "type": "text", + "content": " at each step." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "Classifier-free guidance. Our editing method is built upon text-guided diffusion models. In Stable Diffusion, the text " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " is fed into a pre-trained CLIP [34] text encoder " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\tau_{\\theta}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " to obtain its corresponding embedding and the underlying UNet model is augmented with the cross attention mechanism, which is effective for generating visual contents conditioned on the text " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": ". One of the key challenges in this kind of generation models is the amplification of the effect induced by the conditional text. To this end, the classifier-free guidance technique is proposed, where the prediction for each step is" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 334, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 334, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 305, + 334, + 545, + 384 + ], + "type": "text", + "content": "a combination of conditional and unconditional predictions. 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Problems of DDIM inversion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 452, + 545, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 452, + 545, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 452, + 545, + 513 + ], + "type": "text", + "content": "Given an input image " + }, + { + "bbox": [ + 304, + 452, + 545, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 452, + 545, + 513 + ], + "type": "text", + "content": " and a target prompt " + }, + { + "bbox": [ + 304, + 452, + 545, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^*" + }, + { + "bbox": [ + 304, + 452, + 545, + 513 + ], + "type": "text", + "content": ", we aim to edit " + }, + { + "bbox": [ + 304, + 452, + 545, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 452, + 545, + 513 + ], + "type": "text", + "content": " to make its visual content consistent with textual content in " + }, + { + "bbox": [ + 304, + 452, + 545, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^*" + }, + { + "bbox": [ + 304, + 452, + 545, + 513 + ], + "type": "text", + "content": ", while preserving a maximal amount of details from " + }, + { + "bbox": [ + 304, + 452, + 545, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 452, + 545, + 513 + ], + "type": "text", + "content": ". 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", + "image_path": "2172c4fbcbc416d7b11604c9a73e96cfb1538bc3259717546670a9101db83568.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 333, + 288, + 377 + ], + "lines": [ + { + "bbox": [ + 46, + 333, + 288, + 377 + ], + "spans": [ + { + "bbox": [ + 46, + 333, + 288, + 377 + ], + "type": "text", + "content": "Table 1. Reconstruction quality by measuring the PSNR score of DDIM inversion with different classifier-guidance scales " + }, + { + "bbox": [ + 46, + 333, + 288, + 377 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 333, + 288, + 377 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 333, + 288, + 377 + ], + "type": "inline_equation", + "content": "\\omega_{\\mathrm{enc}}" + }, + { + "bbox": [ + 46, + 333, + 288, + 377 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 333, + 288, + 377 + ], + "type": "inline_equation", + "content": "\\omega_{\\mathrm{dec}}" + }, + { + "bbox": [ + 46, + 333, + 288, + 377 + ], + "type": "text", + "content": " denote the guidance scale used in the DDIM forward and sampling processes, respectively." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 401, + 205, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 401, + 205, + 412 + ], + "spans": [ + { + "bbox": [ + 47, + 401, + 205, + 412 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 401, + 205, + 412 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 47, + 401, + 205, + 412 + ], + "type": "text", + "content": " is the latent embedding of " + }, + { + "bbox": [ + 47, + 401, + 205, + 412 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 47, + 401, + 205, + 412 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "type": "text", + "content": "To investigate the reconstruction performance of DDIM, we first invert the latent embedding of the input image into noise maps via Eq. 6 and then use the deterministic DDIM sampling process in Eq. 4 to reconstruct the input. Note that both processes are performed with unconditional diffusion models, i.e., the classifier-free guidance scale in Eq. 5 is set to " + }, + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\omega = 0" + }, + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "type": "text", + "content": " for both forward and reverse sampling processes. Although a slight error is incorporated in every step as ODE process cannot be reversed perfectly in practice, the accumulated error is negligible, and DDIM inversion can nearly reconstruct the original image (see \"CFG (" + }, + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\omega = 0.0" + }, + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "type": "text", + "content": ")\" in Fig. 3). However, to generate an image well aligned with the conditional text prompt using Stable Diffusion, a large guidance scale " + }, + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\omega > 1" + }, + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "type": "text", + "content": " is necessary for the sampling process in Eq. 4. This arouses the problem that when enlarging " + }, + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "type": "text", + "content": ", the generated images are far from the original ones as shown in Fig. 3. We believe that when " + }, + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "type": "text", + "content": " of the sampling process is different from that of the forward process, the accumulated error would be amplified, leading to unsatisfactory reconstruction quality. This can be illustrated in Table 1, i.e., the best reconstruction quality in each line is obtained when " + }, + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "type": "text", + "content": " used in the DDIM sampling process is the same as that used in the forward process. Even if " + }, + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "type": "text", + "content": " used in the forward and sampling processes are kept the same, PSNR still decreases with " + }, + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 415, + 287, + 713 + ], + "type": "text", + "content": " increasing (see the numbers in bold in Ta" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "ble 1). The above analysis demonstrates that it is hard for DDIM inversion to achieve a satisfactory trade-off between editability (which requires larger " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": ") and fidelity (which requires smaller " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "). To address this issue, we propose a new inversion technique, i.e., Prompt Tuning Inversion." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 138, + 459, + 151 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 138, + 459, + 151 + ], + "spans": [ + { + "bbox": [ + 306, + 138, + 459, + 151 + ], + "type": "text", + "content": "3.3. Prompt tuning for inversion" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 157, + 545, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 157, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 157, + 545, + 276 + ], + "type": "text", + "content": "To successfully invert real images into the model's domain, recent works optimize the textual encoding, the network's parameters, or both. Motivated by Pivotal Inversion [40], we replace the conditional embedding of the text prompt with an optimized one, referred to as Prompt Tuning in this work. Namely, for each input image, we optimize only the conditional embedding " + }, + { + "bbox": [ + 304, + 157, + 545, + 276 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 157, + 545, + 276 + ], + "type": "text", + "content": " so that it encodes important information of the input image which helps the reconstruction. The parameters of the diffusion network and the text encoder " + }, + { + "bbox": [ + 304, + 157, + 545, + 276 + ], + "type": "inline_equation", + "content": "\\tau_{\\theta}" + }, + { + "bbox": [ + 304, + 157, + 545, + 276 + ], + "type": "text", + "content": " are frozen during prompt tuning." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "type": "text", + "content": "We first initialize " + }, + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "type": "inline_equation", + "content": "z_0^* = z_0 = ENC(x_0)" + }, + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "type": "text", + "content": ", and adopt DDIM inversion with " + }, + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "type": "inline_equation", + "content": "\\omega = 0" + }, + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "type": "text", + "content": " to obtain a trajectory of noisy latent codes " + }, + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "type": "inline_equation", + "content": "\\{z_t^*\\}_{t=1}^T" + }, + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "type": "text", + "content": ". Then we initialize " + }, + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "type": "inline_equation", + "content": "\\tilde{z}_T = z_T^*" + }, + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "type": "text", + "content": " and perform the following optimization to the conditional embedding " + }, + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "type": "inline_equation", + "content": "\\omega > 1" + }, + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "type": "text", + "content": " for the timestamps " + }, + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "type": "inline_equation", + "content": "t = T, \\dots, 1" + }, + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "type": "text", + "content": ", each for " + }, + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 277, + 545, + 336 + ], + "type": "text", + "content": " iterations:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 343, + 342, + 545, + 363 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 342, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 343, + 342, + 545, + 363 + ], + "type": "interline_equation", + "content": "c _ {t} = \\underset {c _ {t}} {\\arg \\min } \\left\\| z _ {t - 1} ^ {*} - z _ {t - 1} \\left(\\tilde {z} _ {t}, t, c _ {t}\\right) \\right\\| ^ {2}. \\tag {7}", + "image_path": "f64acca269afa76b1db189abc1930446ddba853939320a6fb221dabe3eece973.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "type": "text", + "content": "For brevity, " + }, + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "type": "inline_equation", + "content": "z_{t-1}(\\tilde{z}_t, t, c_t)" + }, + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "type": "text", + "content": " denotes applying a DDIM sampling step using " + }, + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\tilde{z}_t" + }, + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "type": "text", + "content": " and the conditional embedding " + }, + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "type": "inline_equation", + "content": "c_t" + }, + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "type": "text", + "content": " at the timestep " + }, + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 370, + 545, + 407 + ], + "type": "text", + "content": ". At the end of each timestep, we update" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 379, + 414, + 545, + 427 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 379, + 414, + 545, + 427 + ], + "spans": [ + { + "bbox": [ + 379, + 414, + 545, + 427 + ], + "type": "interline_equation", + "content": "\\tilde {z} _ {t - 1} = z _ {t - 1} \\left(\\tilde {z} _ {t}, t, c _ {t}\\right). \\tag {8}", + "image_path": "04853d0366acffee531aa86b04a1f9e9894aa89d03583d1a3340e98c8557a008.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "type": "text", + "content": "Finally, we can reconstruct the input image by using the noise latent " + }, + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "type": "inline_equation", + "content": "\\tilde{z}_T = z_T^*" + }, + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "type": "text", + "content": " and the optimized conditional embeddings " + }, + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "type": "inline_equation", + "content": "\\{c_t\\}_{t=1}^T" + }, + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "type": "text", + "content": ". In the next subsection, we will introduce the approach to editing images with the target text prompt and the conditional embeddings." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 500, + 449, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 500, + 449, + 513 + ], + "spans": [ + { + "bbox": [ + 306, + 500, + 449, + 513 + ], + "type": "text", + "content": "3.4. Prompt tuning for editing" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 518, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 518, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 518, + 545, + 662 + ], + "type": "text", + "content": "Since the sequence of the conditional embeddings " + }, + { + "bbox": [ + 304, + 518, + 545, + 662 + ], + "type": "inline_equation", + "content": "\\{c_t\\}_{t=1}^T" + }, + { + "bbox": [ + 304, + 518, + 545, + 662 + ], + "type": "text", + "content": " is optimized to fully reconstruct the input image, we believe that these optimized conditional embeddings have contained the most information of the original image, and thus ensure high fidelity. To achieve the desired modification, these optimized embeddings are adopted to perform the editing by advancing in the direction of the target text embedding " + }, + { + "bbox": [ + 304, + 518, + 545, + 662 + ], + "type": "inline_equation", + "content": "c^* = \\tau_\\theta(\\mathcal{P}^*)" + }, + { + "bbox": [ + 304, + 518, + 545, + 662 + ], + "type": "text", + "content": " to ensure good editability also. More formally, in the second stage, we simply interpolate between the target embedding " + }, + { + "bbox": [ + 304, + 518, + 545, + 662 + ], + "type": "inline_equation", + "content": "c^*" + }, + { + "bbox": [ + 304, + 518, + 545, + 662 + ], + "type": "text", + "content": " and the optimized " + }, + { + "bbox": [ + 304, + 518, + 545, + 662 + ], + "type": "inline_equation", + "content": "c_t" + }, + { + "bbox": [ + 304, + 518, + 545, + 662 + ], + "type": "text", + "content": " linearly at each timestamp. For a given hyper-parameter " + }, + { + "bbox": [ + 304, + 518, + 545, + 662 + ], + "type": "inline_equation", + "content": "\\eta \\in (0,1]" + }, + { + "bbox": [ + 304, + 518, + 545, + 662 + ], + "type": "text", + "content": ", we obtain" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 372, + 670, + 545, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 670, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 372, + 670, + 545, + 682 + ], + "type": "interline_equation", + "content": "c _ {t} = \\eta \\cdot c ^ {*} + (1 - \\eta) \\cdot c _ {t}, \\tag {9}", + "image_path": "23d51ae912010d8a25fde6a2cac684aa15d5b830c31ce948246abf8071a80306.jpg" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "where the first term ensures the effective editability corresponding to the semantic contents in the target text, while" + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7434" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "content": "the second term guarantees a good reconstruction of the original image. The algorithm is presented in Lines 14-21 in Algorithm 1. Note that when " + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "inline_equation", + "content": "\\eta = 0" + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "inline_equation", + "content": "\\eta = 1" + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "content": ", the output of our editing method is the reconstructed original image, or the output of the baseline DDIM-Edit, respectively." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 137, + 289, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 137, + 289, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 137, + 289, + 258 + ], + "type": "text", + "content": "Intuitively, our editing method is to find an intermediate representation between the original image and the output of DDIM-Edit. For a desired modification, the intermediate representation is supposed to contain both the structural information of the source image and the semantic contents of the target text prompt. Eq. 9 is only one way to achieve this, which we refer to as condition interpolation. We also test a different interpolation method (referred to as latent interpolation), where we linearly interpolate between the noisy latent " + }, + { + "bbox": [ + 46, + 137, + 289, + 258 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 46, + 137, + 289, + 258 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 137, + 289, + 258 + ], + "type": "inline_equation", + "content": "z_{t}^{*}" + }, + { + "bbox": [ + 46, + 137, + 289, + 258 + ], + "type": "text", + "content": " at each timestamp:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 109, + 276, + 287, + 291 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 276, + 287, + 291 + ], + "spans": [ + { + "bbox": [ + 109, + 276, + 287, + 291 + ], + "type": "interline_equation", + "content": "z _ {t} ^ {e d t} = \\eta \\cdot z _ {t} + (1 - \\eta) \\cdot z _ {t} ^ {*}, \\tag {10}", + "image_path": "d0c4a52663d16fa323156e5e631fe9a102a0d7aecd86e8cd509e51e31bcf58ea.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 309, + 289, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 309, + 289, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 309, + 289, + 429 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 309, + 289, + 429 + ], + "type": "inline_equation", + "content": "z_{t}^{*}" + }, + { + "bbox": [ + 46, + 309, + 289, + 429 + ], + "type": "text", + "content": " is the noisy latent calculated by DDIM inversion via Eq. 6, and " + }, + { + "bbox": [ + 46, + 309, + 289, + 429 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 46, + 309, + 289, + 429 + ], + "type": "text", + "content": " is the latent obtained in the vanilla DDIM sampling process conditioned on the target embedding. Although this approach is more simple since the process of prompt tuning is no longer needed, we observe that this interpolation method may lead to cluttered images. This is because the interpolation of latent embeddings mixes the source object and the edited object spatially, rather than semantically (as condition interpolation does), leading to cluttered contents in images." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 452, + 119, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 452, + 119, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 452, + 119, + 464 + ], + "type": "text", + "content": "3.5. Discussion" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 475, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 287, + 536 + ], + "type": "text", + "content": "Our proposed image editing method shares similar motivations with existing works [21, 51, 27, 16], all of which aim to modify an image in a text-driven and mask-free manner. However, our approach differs from them significantly in the following aspects:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 540, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 46, + 540, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 287, + 601 + ], + "type": "text", + "content": "1) Imagic [21] and UniTune [51] finetune the diffusion models for hundreds of steps to maintain high fidelity to the input image. In contrast, we only need to optimize the conditional embedding, which greatly reduces computational budgets." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": "2) Our proposed Prompt Tuning Inversion is inspired by the Null-Text Inversion method [27]. However, Null-Text Inversion chooses to optimize the unconditional embedding while we optimize the conditional one. Moreover, the editing process of Null-Text Inversion is achieved by the cross-attention map control in Prompt-to-Prompt [16], which requires an additional description of the input image. Compared to theirs, our method only needs the target text prompt and is thus more user-friendly." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "type": "code", + "bbox": [ + 306, + 88, + 545, + 398 + ], + "blocks": [ + { + "bbox": [ + 312, + 75, + 518, + 87 + ], + "lines": [ + { + "bbox": [ + 312, + 75, + 518, + 87 + ], + "spans": [ + { + "bbox": [ + 312, + 75, + 518, + 87 + ], + "type": "text", + "content": "Algorithm 1: Prompt Tuning Inversion for Editing" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "lines": [ + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "spans": [ + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "text", + "content": "Input: An input image " + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "text", + "content": " and a target prompt embedding " + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "inline_equation", + "content": "c^{*} = \\tau_{\\theta}(\\mathcal{P}^{*})" + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "text", + "content": " \nOutput: Edited image " + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^*" + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "text", + "content": " \n1 // DDIM Inversion \n2 Set guidance scale " + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "inline_equation", + "content": "\\omega = 0,z_0^* = ENC(\\mathcal{I})" + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "text", + "content": " . \n3 Compute the intermediate trajectory " + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "inline_equation", + "content": "\\{z_t^*\\}_{t = 0}^T" + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "text", + "content": " using DDIM inversion over " + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "text", + "content": " without conditional guidance via Eq. 6; \n4// Prompt Tuning \n5 Set guidance scale " + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "inline_equation", + "content": "\\omega >1,\\eta \\in (0,1]" + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "text", + "content": " . \n6 Initialize " + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "inline_equation", + "content": "\\tilde{z}_T\\gets z_T^*,c_T\\gets c^*" + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "text", + "content": " . \n7 for " + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "inline_equation", + "content": "t = T,T - 1,\\dots ,1" + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "text", + "content": " do \n8 for " + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "inline_equation", + "content": "j = 0,\\ldots ,N - 1" + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "text", + "content": " do \n9 " + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "inline_equation", + "content": "|c_{t}\\gets c_{t} - \\beta \\nabla_{c}||z_{t - 1}^{*} - z_{t - 1}(\\tilde{z}_{t},t,c_{t})||_{2}^{2};" + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "text", + "content": " \n10 end \n11 " + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "inline_equation", + "content": "\\tilde{z}_{t - 1}\\gets z_{t - 1}(\\tilde{z}_{t},t,c_{t}),c_{t - 1}\\gets c_{t}" + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "text", + "content": " \n12 end \n13 // Editing \n14 Set " + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "inline_equation", + "content": "z_{T}^{edt}\\gets z_{T}^{*}" + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "text", + "content": " . \n15 for " + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "inline_equation", + "content": "t = T,T - 1,\\ldots ,1" + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "text", + "content": " do \n16 " + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "inline_equation", + "content": "c_{t} = (1 - \\eta)\\cdot c_{t} + \\eta \\cdot c^{*};" + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "text", + "content": " \n17 " + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "inline_equation", + "content": "z_{t - 1}^{edt} = z_{t - 1}(z_{t}^{edt},t,c_{t});" + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "text", + "content": " \n18 end \n19 " + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^* = DEC(z_0^{edt})" + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "text", + "content": " \n20 return " + }, + { + "bbox": [ + 306, + 88, + 545, + 398 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^*" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "code_body" + } + ], + "index": 10, + "sub_type": "algorithm" + }, + { + "bbox": [ + 306, + 422, + 388, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 422, + 388, + 435 + ], + "spans": [ + { + "bbox": [ + 306, + 422, + 388, + 435 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 442, + 356, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 442, + 356, + 455 + ], + "spans": [ + { + "bbox": [ + 306, + 442, + 356, + 455 + ], + "type": "text", + "content": "4.1. Setup" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "text", + "content": "Implementation details. In our experiments, we adopt the text-conditional Latent Diffusion Model [41] (known as Stable Diffusion) with 890M parameters trained on LAION-5B [44] at " + }, + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "text", + "content": " resolution. For the DDIM schedule, we adopt 50 steps and retain the original hyperparameter choices of Stable Diffusion. The encoding ratio parameter is set to 0.8. The number of iterations to optimize " + }, + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "text", + "content": " per diffusion step is set to " + }, + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "inline_equation", + "content": "N = 1" + }, + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "text", + "content": ". The hyper-parameters " + }, + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "text", + "content": " in Algorithm 1 are set to 0.1 and 0.9, respectively, unless specified. These allow editing an image in " + }, + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\sim 1" + }, + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "text", + "content": " minute on a single Tesla V100 GPU. For better performance, we adopt attention maps to localize the edited regions (referred to as local blending), and re-weight the attention maps as in [16]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Evaluation and datasets. In semantic image editing, the visual content of the edited image is supposed to align well with the target text prompt (editability) while staying close to the input image in terms of the unedited parts (fidelity). For a given method, better editability usually comes at the cost of decreased fidelity to the input image, and vice versa. This forms a trade-off curve between the two objectives." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7435" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 73, + 74, + 262, + 205 + ], + "blocks": [ + { + "bbox": [ + 73, + 74, + 262, + 205 + ], + "lines": [ + { + "bbox": [ + 73, + 74, + 262, + 205 + ], + "spans": [ + { + "bbox": [ + 73, + 74, + 262, + 205 + ], + "type": "image", + "image_path": "078554bf6836db688f4f76d7be8f798ed3057c994f750b7709ba9a4d0c379c2f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 213, + 287, + 247 + ], + "lines": [ + { + "bbox": [ + 46, + 213, + 287, + 247 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 287, + 247 + ], + "type": "text", + "content": "Figure 4. Comparison with DiffEdit and DDIM-Edit on ImageNet. For all methods, we set the DDIM encoding ratio to 0.8, and only vary the mask threshold to draw the trade-off curve." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 266, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 287, + 399 + ], + "type": "text", + "content": "Following DiffEdit [7], we evaluate different editing methods by comparing their trade-off curves on ImageNet [9]. Specifically, given an image of one class from ImageNet, we aim to edit it to another class of ImageNet as instructed by the target text prompt. The editability and fidelity are measured using the LPIPS perceptual distance [58] and CS-FID, which is a class-conditional FID metric [17], respectively. The former measures the distance with the input image while the latter measures both image realism and consistency w.r.t. the target class. For both metrics, lower values indicate better editing performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 406, + 285, + 419 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 406, + 285, + 419 + ], + "spans": [ + { + "bbox": [ + 47, + 406, + 285, + 419 + ], + "type": "text", + "content": "4.2. Comparison with other methods on ImageNet" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 425, + 287, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 287, + 532 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 287, + 532 + ], + "type": "text", + "content": "We compare our method with DiffEdit and our baseline DDIM-Edit, since they both share the same DDIM forward process and a similar sampling process. Besides, they load the same publicly available pre-trained weights for a fair comparison. To leverage the generalization capability of large-scale language-image models, we adopt the text-conditional Stable Diffusion model \"sd-v1-4\" instead of the class-conditional model trained on ImageNet as the pre-trained model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 532, + 288, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 532, + 288, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 532, + 288, + 677 + ], + "type": "text", + "content": "As pointed out by DiffEdit [7], different editing methods often have hyper-parameters which control editability, e.g., the mask threshold, or the encoding ratio. A lower mask threshold or higher encoding ratio leads to stronger editing. In our proposed method, we can also control the editing strength by varying the conditional interpolation ratio " + }, + { + "bbox": [ + 46, + 532, + 288, + 677 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 532, + 288, + 677 + ], + "type": "text", + "content": " introduced in Eq. 9. In our evaluation, we fix the DDIM encoding ratio and draw the trade-off curve by varying the mask threshold for all methods1. The results are presented in Fig. 4, where \"DDIM-Global\" denotes that the images are edited via \"DDIM-Edit\" but without using any masks, i.e., the editing is performed globally. This can" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 318, + 77, + 528, + 320 + ], + "blocks": [ + { + "bbox": [ + 318, + 77, + 528, + 320 + ], + "lines": [ + { + "bbox": [ + 318, + 77, + 528, + 320 + ], + "spans": [ + { + "bbox": [ + 318, + 77, + 528, + 320 + ], + "type": "image", + "image_path": "c72a62424e3ab6a466d8fcd8d0e367887d26175c1bd481d3348b5003337f76af.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 323, + 547, + 357 + ], + "lines": [ + { + "bbox": [ + 305, + 323, + 547, + 357 + ], + "spans": [ + { + "bbox": [ + 305, + 323, + 547, + 357 + ], + "type": "text", + "content": "Figure 5. Editing examples on ImageNet by our method and other methods. DDIM-G/DDIM-L indicates the baseline method DDIM-Edit with/without the local blend trick." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 375, + 545, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 545, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 545, + 518 + ], + "type": "text", + "content": "be regarded as a lower bound of fidelity for all methods. As the mask threshold increases, LPIPS decreases since fewer parts of the image are edited. Compared to DiffEdit, our baseline method DDIM-Edit achieves a better trade-off. Note that the only difference between the two methods is the approach to generating masks. The comparison shows that inferring editing masks using cross-attention maps, as adopted by DDIM-Edit, is more appropriate. Based on DDIM-Edit, our method can further improve the fidelity to the input images while maintaining editability. The best CSFID-LPIPS trade-off of our method demonstrates its superiority over DiffEdit and the baseline." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 519, + 545, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 519, + 545, + 627 + ], + "spans": [ + { + "bbox": [ + 304, + 519, + 545, + 627 + ], + "type": "text", + "content": "We also present qualitative examples of these methods. As shown in Fig. 5, without automatically generated masks, \"DDIM-G\" tends to modify images globally. For simple cases (e.g., example (d)), image editing methods with the original DDIM inversion works well. However, for complex cases, we observe undesired and unreasonable edits to the objects. In contrast, with the help of the learnable conditional embedding, our method achieves realistic editing while successfully preserving the original details." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 635, + 398, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 398, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 398, + 647 + ], + "type": "text", + "content": "4.3. Ablation study" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "Comparison to existing inversion methods. We randomly select 128 images and their corresponding captions from the COCO validation set [24]. We then apply the following reconstruction methods to each image-caption pair: (1) AE denotes the variational auto-encoder with a slight KL-" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "text", + "content": "1As there was no official implementation of DiffEdit available at the time of writing, we adopted the unofficial implementation for inferring editing masks from https://github.com/LuChengTHU/dpm-solver." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7436" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 70, + 265, + 105 + ], + "blocks": [ + { + "bbox": [ + 67, + 70, + 265, + 105 + ], + "lines": [ + { + "bbox": [ + 67, + 70, + 265, + 105 + ], + "spans": [ + { + "bbox": [ + 67, + 70, + 265, + 105 + ], + "type": "table", + "html": "
MethodAEDDIMNTIPTI (ours)
PSNR26.2213.6424.4525.71
SSIM0.85640.46410.82700.8501
", + "image_path": "476feed1c294a2bdb79584779bdc2e67ffbd46237d7915e28768d9c9cd9edd4b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 66, + 155, + 265, + 239 + ], + "blocks": [ + { + "bbox": [ + 47, + 106, + 287, + 140 + ], + "lines": [ + { + "bbox": [ + 47, + 106, + 287, + 140 + ], + "spans": [ + { + "bbox": [ + 47, + 106, + 287, + 140 + ], + "type": "text", + "content": "Table 2. Reconstruction quality of different methods measured by PSNR and SSIM. For both metrics, higher values indicate better quality." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 155, + 265, + 239 + ], + "lines": [ + { + "bbox": [ + 66, + 155, + 265, + 239 + ], + "spans": [ + { + "bbox": [ + 66, + 155, + 265, + 239 + ], + "type": "table", + "html": "
iters12345
learning rate β = 0.01
NTI17.0520.1222.2523.6124.45
PTI19.3623.2024.8625.4725.71
learning rate β = 0.1
NTI23.0824.7425.6225.8225.91
PTI24.7425.2325.7825.9025.97
", + "image_path": "bf844a8d3d796463ca11261a0fef0300d7cf019bb493d3f28893b1d0f206b374.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 62, + 240, + 271, + 251 + ], + "lines": [ + { + "bbox": [ + 62, + 240, + 271, + 251 + ], + "spans": [ + { + "bbox": [ + 62, + 240, + 271, + 251 + ], + "type": "text", + "content": "Table 3. PSNR scores under different optimizing settings." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 277, + 287, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 287, + 445 + ], + "type": "text", + "content": "penalty used in Stable Diffusion. An image is first encoded by the encoder of AE. Afterwards, the decoder directly reconstructs the image from the latent. Therefore, we consider AE as an upper bound of reconstruction quality. (2) DDIM denotes the DDIM inversion method, which is a baseline inversion method. As analyzed in Sec. 3.2, it usually outputs a low-quality reconstruction result under a large classifier-free guidance scale " + }, + { + "bbox": [ + 46, + 277, + 287, + 445 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 277, + 287, + 445 + ], + "type": "text", + "content": ". (3) NTI denotes the Null-Text Inversion method [27], which is our main point of comparison. Different from our method, it optimizes the unconditional embedding. (4) PTI denotes our proposed Prompt Tuning Inversion method. We introduce a learnable conditional embedding and the optimizing details are presented in Algorithm 1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "type": "text", + "content": "The experimental results are provided in Table 2. For the diffusion-based inversion methods, we apply the diffusion model in an unconditional manner (i.e., the classifier guidance scale " + }, + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\omega = 0" + }, + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "type": "text", + "content": ") for the DDIM forward process. For the sampling process, we set " + }, + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\omega = 7.5" + }, + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "type": "text", + "content": ". As shown in Table 2, DDIM inversion fails to reconstruct the original images since " + }, + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "type": "text", + "content": " in the sampling process is different from that in the forward process, leading to a low PSNR score (13.64). For NTI and PTI, we set the number of iterations " + }, + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "type": "text", + "content": " to 5 and the learning rate " + }, + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "type": "text", + "content": " to 0.01. We observe that both methods can reconstruct the images but the reconstruction quality of our method is better (25.71 vs. 24.45). To further demonstrate the effectiveness of our method, we vary " + }, + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "type": "text", + "content": " from 1 to 5 and increase the learning rate " + }, + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "type": "text", + "content": " from 0.01 to 0.1. The experimental results in Table 3 show that the reconstruction quality of PTI is always better than NTI under all settings, demonstrating that our method converges faster." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Influence of the hyper-parameter " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": ". We also perform ablation on the hyper-parameter " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": " and the results are presented in Fig. 6. By adjusting " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": ", we can achieve a good trade-off between fidelity and editability. More quantitative analyses are presented in supplementary materials." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 308, + 70, + 548, + 179 + ], + "blocks": [ + { + "bbox": [ + 308, + 70, + 548, + 179 + ], + "lines": [ + { + "bbox": [ + 308, + 70, + 548, + 179 + ], + "spans": [ + { + "bbox": [ + 308, + 70, + 548, + 179 + ], + "type": "image", + "image_path": "7370967ba997d267657f4937f72ce74ffa8670288faef971c02451683d9504e2.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 335, + 182, + 515, + 194 + ], + "lines": [ + { + "bbox": [ + 335, + 182, + 515, + 194 + ], + "spans": [ + { + "bbox": [ + 335, + 182, + 515, + 194 + ], + "type": "text", + "content": "Figure 6. Qualitative examples for the effect of " + }, + { + "bbox": [ + 335, + 182, + 515, + 194 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 335, + 182, + 515, + 194 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 308, + 209, + 547, + 282 + ], + "blocks": [ + { + "bbox": [ + 308, + 209, + 547, + 282 + ], + "lines": [ + { + "bbox": [ + 308, + 209, + 547, + 282 + ], + "spans": [ + { + "bbox": [ + 308, + 209, + 547, + 282 + ], + "type": "image", + "image_path": "07cab73b5cd3ba16b3fd693e060674fc3063c2f6cf1041f14f13724892aa9376.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 286, + 545, + 309 + ], + "lines": [ + { + "bbox": [ + 305, + 286, + 545, + 309 + ], + "spans": [ + { + "bbox": [ + 305, + 286, + 545, + 309 + ], + "type": "text", + "content": "Figure 7. A failure example on ImageNet: when multiple objects exist, only one of them is edited successfully." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 321, + 465, + 334 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 321, + 465, + 334 + ], + "spans": [ + { + "bbox": [ + 306, + 321, + 465, + 334 + ], + "type": "text", + "content": "5. Conclusion and future work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 342, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 545, + 569 + ], + "type": "text", + "content": "We propose an intuitive and user-friendly text-based image editing method, which benefits from the superior generation and generalization capacities of large-scale image language diffusion models (e.g., Stable Diffusion). The key idea of our method is that important structural information of the input image can be encoded into conditional embeddings, which can guide the diffusion model to reconstruct the original image via the sampling process. Based on this, our method consists of two stages. In the first reconstruction stage, we propose a novel Prompt Tuning Inversion method which encodes image information to learnable conditional embeddings quickly and accurately. In the second editing stage, we introduce an interpolation which linearly combines the target text embedding with the optimized embedding obtained in the first stage. In this way, the new conditional embedding contains both information from the input image and the target text prompt, resulting in an edited image with an appropriate trade-off between editability and fidelity." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 570, + 546, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 712 + ], + "type": "text", + "content": "While our method works well in most scenarios, it still faces some limitations. As shown in Fig. 7, there are multiple objects in the input images. However, neither DiffEdit nor our method changes all \"gooses\" to \"black storks\". This limitation can possibly be mitigated by operating the attention maps more precisely [5] or adding different modes of conditional control [57], providing a research direction for image editing. Besides, the proposed method still requires running inversion every time given a new text since initialization is based on the target text, and not using attention is not always an advantage. 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Improved stylegan embedding: Where are the good latents? arXiv preprint arXiv:2012.09036, 2020. 3" + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "7440" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Prompt-aligned Gradient for Prompt Tuning/7786570f-2ec2-4f85-a04c-e553c7832bc6_content_list.json b/2023/Prompt-aligned Gradient for Prompt Tuning/7786570f-2ec2-4f85-a04c-e553c7832bc6_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..4dc6c26921e3bbf13431be314c4a3c41bae79d8b --- /dev/null +++ b/2023/Prompt-aligned Gradient for Prompt Tuning/7786570f-2ec2-4f85-a04c-e553c7832bc6_content_list.json @@ -0,0 +1,1798 @@ +[ + { + "type": "text", + "text": "Prompt-aligned Gradient for Prompt Tuning", + "text_level": 1, + "bbox": [ + 258, + 130, + 712, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Beier Zhu1 Yulei Niu2 Yucheng Han1 Yue Wu3 Hanwang Zhang1*", + "bbox": [ + 184, + 179, + 785, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Nanyang Technological University $^{2}$ Columbia University $^{3}$ Damo Academy, Alibaba Group", + "bbox": [ + 184, + 200, + 785, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "beier002@e.ntu.edu.sg, yn.yuleiniu@gmail.com yucheng002@e.ntu.edu.sg", + "bbox": [ + 183, + 218, + 785, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "matthew.wy@alibaba-inc.com hanwangzhang@ntu.edu.sg", + "bbox": [ + 254, + 237, + 712, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Thanks to the large pre-trained vision-language models (VLMs) like CLIP [37], we can craft a zero-shot classifier by discrete prompt design, e.g., the confidence score of an image being \"[CLASS]\" can be obtained by using the VLM provided similarity between the image and the prompt sentence \"a photo of a [CLASS]\". Furthermore, prompting shows great potential for fast adaptation of VLMs to downstream tasks if we fine-tune the soft prompts with few samples. However, we find a common failure that improper fine-tuning or learning with extremely few-shot samples may even under-perform the zero-shot prediction. Existing methods still address this problem by using traditional anti-overfitting techniques such as early stopping and data augmentation, which lack a principled solution specific to prompting. In this paper, we present Prompt-aligned Gradient, dubbed ProGrad to prevent prompt tuning from forgetting the general knowledge learned from VLMs. In particular, ProGrad only updates the prompt whose gradient is aligned (or non-conflicting) to the general knowledge, which is represented as the optimization direction offered by the pre-defined prompt predictions. Extensive experiments under the few-shot learning, domain generalization, baseto-new generalization and cross-dataset transfer settings demonstrate the stronger few-shot generalization ability of ProGrad over state-of-the-art prompt tuning methods.", + "bbox": [ + 75, + 318, + 473, + 698 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 727, + 209, + 742 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "After seeing and reading countless image-text association pairs, large and deep vision-language models (VLM) [37, 18] can memorize the general knowledge (a.k.a. encyclopedic knowledge) about what visual patterns correspond to what textual sequence and vice versa. Thanks to the powerful language modeling of VLMs, we can establish a communication channel in human-readable natural language, i.e., prompt [25, 51, 19], to query the general knowledge.", + "bbox": [ + 75, + 753, + 470, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Prompting bridges the interface gap between the pre-trained and downstream tasks (e.g., regression vs. classification) without the need for additional fine-tuning adaptation. For example, we can craft a concrete prompt—\"a photo of a [CLASS]\"—for zero-shot image classification: by using the popular vision-language model CLIP [37], we input the image to the vision end and the prompt sentence to the language end, then obtain a vision-language similarity as the confidence score of classifying the image as \"[CLASS]\".", + "bbox": [ + 500, + 287, + 893, + 425 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In practice, the prompt-based zero-shot image classification is not accurate because the hand-crafted prompt may not be the most machine-favorable (e.g., \"this is a picture of\" could be more grammatically prevailing in VLM training), or not specific to the downstream domain (e.g., \"a photo of a person doing\" is better in action recognition) [37]. Recently, prompt tuning or prefix tuning [23, 26, 54, 55] has been proposed to replace the handcrafted prompt with a set of tunable word embedding vectors, which do not have to be translatable back to human-readable words. Yet, prompt tuning is still as tricky as conventional fine-tuning: as the training continues, the generalization ability may decrease and even under-perform the zero-shot baseline. As shown in Figure 1(a&b), the prompt tuning method CoOp [54] achieves the best results via early stopping, and its accuracies heavily drop by at most $4\\%$ when the training continues. Besides, Figure 1(c&d) show that CoOp underperforms zero-shot CLIP without augmentation or enough samples from downstream tasks. To the best of our knowledge, existing methods still rely on the conventional anti-overfitting techniques such as early stopping and data augmentation [54, 55, 11, 36], which lacks a principled solution to the nature of improper prompt tuning. Furthermore, the Grad-CAM visualization results indicate that the fine-tuned prompt misleads the VLM to forget the general knowledge that the classification should at least focus on the foreground object but not the background. Comparing CoOp (Figure 2(b)) with zero-shot CLIP (Figure 2(c)), we find that the CoOp model distracts its attention to the background, while CLIP mainly focuses on the foreground object. These results demonstrate the over-fitting risk of existing prompt", + "bbox": [ + 496, + 431, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15659", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6dec5c597949dd7a192e765da9f21fc01ef71921e0cfd522cbd56e2d21d99d93.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 282, + 213 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/49900bff427d46d74be1ce14c0d844163eb1b7b8e1abe16330744ef01658ef0f.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 282, + 88, + 483, + 213 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7acf57b79896358ce050094d546b46b4a2793682a02e39ab5e253e2fd1e79c41.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 486, + 89, + 687, + 213 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/2bdc7a1dff0e53c8194a3b7a4f6c6e4371d0e5a1247734bb84db3a41d4851847.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 687, + 89, + 888, + 213 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5f0567276f17fb59eabfc055f5bf605d123755a6635b983e706ce691dcfa1f07.jpg", + "image_caption": [ + "Figure 1: Comparison of Zero-shot CLIP, CoOp, and our ProGrad on Stanford Cars and OxfordPets datasets. (a)&(b): Given 1 shot training sample, CoOp's performance severely drops and under-performs zero-shot CLIP by large margins when the training continues. (c)&(d): CoOp may fail to improve CLIP without data augmentation or plenty of samples.", + "Figure 2: Comparisons of Grad-CAM [43] visualization for prompt tuning methods using different gradient strategies on Stanford Cars Datasets." + ], + "image_footnote": [], + "bbox": [ + 81, + 299, + 890, + 554 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tuning strategies, especially when the number of training samples is extremely limited (e.g., 1 or 2).", + "bbox": [ + 75, + 622, + 468, + 652 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we present a novel prompt tuning method called Prompt-aligned Gradient (ProGrad) to overcome the improperly biased tuning for CLIP. The principle of ProGrad is to regularize each tuning step not to conflict with the general knowledge offered by the original prompt, e.g., the zero-shot CLIP predictions. Specifically, we measure the general knowledge direction $G_{\\mathrm{g}}$ using the gradient of Kullback-Leibler (KL) divergence between the predictions of the zero-shot prompted CLIP and the few-shot fine-tuned model, which we name as general direction. Similarly, we compute the domain-specific knowledge direction $G_{\\mathrm{d}}$ using the gradient of cross-entropy between the ground-truth and the few-shot fine-tuned model, dubbed domain-specific direction. We decompose the domain-specific direction $G_{\\mathrm{d}}$ into: 1) a vector $G_{\\perp}$ orthogonal to the general direction, which denotes the non-conflicting domain-specific knowl", + "bbox": [ + 75, + 657, + 472, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "edge; and 2) a vector $G_{\\parallel}$ parallel to the general direction, which denotes the general knowledge. Note that the first gradient component does NOT override the general direction as any two orthogonal vectors can be transformed into two nonconflicting base vectors. For the second component, it must be one of the two directions: 1) the same of the general direction, which indicates that the update is aligned to the general knowledge, and 2) the opposite of general direction, indicating a conflicting update that should be discarded to avoid forgetting. Overall, in each iteration, ProGrad only updates the parameters in the prompt-aligned direction that has an acute angle to the general direction. Compared to CoOp and CLIP, both $G_{g}$ and $G_{\\perp}$ (Figure 2(d&e)) help to regularize the model to focus on the foreground, and ProGrad (Figure 2(f)) further improves the visual response.", + "bbox": [ + 496, + 622, + 893, + 849 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Following CLIP, CoOp and CoCoOp [55], we evaluate ProGrad under the few-shot learning, domain generalization, base-to-new generalization and cross-dataset transfer", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15660", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "settings over 15 image classification benchmarks, covering generic object classification, fine-grained image recognition, action classification. In summary, our ProGrad achieves: 1) clear improvement compared to CoOp over all of the 11 datasets; 2) clear improvement on the harmonic mean of base and new classes accuracies on all 11 datasets compared to CoOp and CoCoOp, and 3) clear improvement on both the source and target datasets of the domain generalization.", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 224, + 218, + 242 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "VLMs Adaptation. VLM can be adapted for various downstream tasks, e.g., visual question answering [21, 48], visual grounding [51], image retrieval [28] and semantic segmentation [39]. We focus on image classification task. Conventional \"pre-train then fine-tune\" paradigm that plugs in a classifier to the visual backbone and trained on downstream data has been widely-adopted, e.g., Linear Probe [37]. CLIP-Adapter [10] add feature adapters to boost fine-tuning results. Recently, NLP community has introduced a \"prompt-based learning\" paradigm that fine-tunes the prompt using a \"fill-in-the-blank\" cloze test to maximize the ground-truth token [23, 26]. The prompt-based learning has recently been applied in CV community [54, 29, 7, 46, 4, 20, 56]: CoOp [54] uses a continuous prompt optimization from downstream data instead of hand-craft design. CoCoOp [55] further extends CoOp by learning image conditional prompt to improve generalization. ProDA [29] learns a prompt distribution over the output embedding space. VPT [7] introduces variational prompt tuning by combining a base learned prompt with a residual vector sampled from a instance-specific underlying distribution. TPT [46] proposes a test-time prompt tuning, which does not require training data and optimizes the prompt to achieve consistent predictions across different augmented views. Our ProGrad follows the line of prompt-based learning to improve few-shot generalization ability by aligning the gradient to general direction, without model structure modification or tuning the pre-trained parameters.", + "bbox": [ + 75, + 250, + 472, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Knowledge Transfer. Forgetting mitigation is widely used in incremental learning [27, 40, 35, 42, 17] through knowledge distillation or memory replay. However, prompt-based learning differs fundamentally from incremental learning in that it does not have access to pre-trained data, which is required for incremental learning to store old data from memory storage. For example, OGD [8] projects gradients from new classes to the orthogonal direction of previous task gradients, but the requirement to store old task gradients is not possible for prompt tuning since we lack access to the pre-training process. Moreover, OGD modifies gradients of downstream tasks in non-conflicting scenarios, potentially leading to sub-optimal performance. Another related field that leverages gradient matching to transfer knowledge is domain generalization [45, 38] and multi-task learning [44, 52].", + "bbox": [ + 75, + 674, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, these methods are not directly applicable in prompt tuning whose transfer direction is only from general to downstream. In Appendix, we will show how their methods fail in several ablative studies.", + "bbox": [ + 496, + 90, + 893, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 498, + 165, + 635, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we introduce the preliminary concepts of prompt-based zero-shot inference, prompt-based learning, and present our proposed Prompt-aligned Gradient solution to align the domain knowledge with general knowledge for few-shot generalization.", + "bbox": [ + 496, + 190, + 893, + 267 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 498, + 275, + 640, + 291 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Contrastive language-image pre-training (CLIP) [37] adopts a contrastive language-image pre-training paradigm on tremendous pairs of images with natural language descriptions. For contrastive learning, the associated image and sentences are taken as the positive samples, while the non-associated pairs are regarded as negative samples. The contrastive objective maximizes the similarity of positive pairs while minimize the similarity of negative pairs.", + "bbox": [ + 496, + 297, + 893, + 419 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Zero-shot transfer inference adapts the pre-trained CLIP model to downstream tasks without fine-tuning the model. Taking image classification as an example, zero-shot transfer is enabled by formulating the classification task as an image-text matching problem, where the text is obtained by extending the \"[CLASS]\" name using a template like \"a photo of a [CLASS]\". CLIP [37] finds that such a simple template narrows the distribution gap to pre-training text inputs. The image-class matching score is measured based on the cosine similarity $< \\pmb{w}_i$ , $f >$ between the image feature $\\pmb{f}$ and the class-extended text feature $\\pmb{w}_i$ for $i$ -th class. The image feature $\\pmb{f}$ for image $\\pmb{x}$ is extracted by the image encoder, while the text feature $\\pmb{w}_i$ for $i$ -th class is obtained by feeding the prompt description into the text encoder. The probability for $i$ -th class is obtained as", + "bbox": [ + 496, + 419, + 895, + 647 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\mathrm {z s}} (\\boldsymbol {w} _ {i} | \\boldsymbol {x}) = \\frac {\\exp \\left(< \\boldsymbol {w} _ {i} , \\boldsymbol {f} > / \\tau\\right)}{\\sum_ {j = 1} ^ {K} \\exp \\left(< \\boldsymbol {w} _ {j} , \\boldsymbol {f} > / \\tau\\right)}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 656, + 893, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $K$ denotes the number of classes, and $\\tau$ is a temperature learned by CLIP.", + "bbox": [ + 496, + 704, + 893, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Prompt-based learning further strengths the transferring ability of the CLIP model and avoids prompt engineering by automatically learning the prompt given few samples from the downstream task. Different from the zero-shot transfer that used a fixed hand-craft prompt, CoOp [54] constructs and fine-tunes a set of $M$ continuous context vectors $\\pmb{v} = \\{\\pmb{v}_1,\\pmb{v}_2,\\dots,\\pmb{v}_M\\}$ as the turnable prompt. Specifically, the prompt $\\pmb{t}_i = \\{\\pmb{v}_1,\\pmb{v}_2,\\dots,\\pmb{v}_M,\\pmb{c}_i\\}$ combines the learnable context vectors $\\pmb{v}$ and the class token embedding $\\pmb{c}_i$ , and is fed to the text encoder $g(\\cdot)$ . CoOp optimizes the static context vectors $\\pmb{v}$ by minimizing the negative log-likelihood", + "bbox": [ + 496, + 734, + 895, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15661", + "bbox": [ + 480, + 944, + 517, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "of the ground-truth token:", + "bbox": [ + 76, + 90, + 251, + 104 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {c e}} (\\boldsymbol {v}) = - \\sum_ {i} \\boldsymbol {y} _ {i} \\log p (\\boldsymbol {t} _ {i} | \\boldsymbol {x}),\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 113, + 346, + 143 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np \\left(\\boldsymbol {t} _ {i} \\mid \\boldsymbol {x}\\right) = \\frac {\\exp \\left(< g \\left(\\boldsymbol {t} _ {i}\\right) , \\boldsymbol {f} > / \\tau\\right)}{\\sum_ {j = 1} ^ {K} \\exp \\left(< g \\left(\\boldsymbol {t} _ {j}\\right) , \\boldsymbol {f} > / \\tau\\right)}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 143, + 468, + 185 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{y}$ denotes the one-hot ground-truth annotation and $K$ denotes the number of classes.", + "bbox": [ + 76, + 191, + 468, + 220 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Prompt-aligned Gradient", + "text_level": 1, + "bbox": [ + 76, + 228, + 308, + 244 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "CoOp faced a challenge that the transfer performance drops when the number of annotations is very limited (e.g., one per class), even underperforms the zero-shot transfer. Also, CoOp heavily relies on anti-overfitting techniques such as early stopping and data augmentation. To overcome the over-fitting challenge, we propose an effective and efficient fine-tuning paradigm ProGrad to align the few-shot downstream knowledge with the large-scale general knowledge.", + "bbox": [ + 75, + 252, + 470, + 372 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Motivated by the success of knowledge distillation [34, 16] in knowledge transfer, we leverage the zero-shot CLIP predictions as the general knowledge, and compare the finetuned predictions with the general knowledge to regularize the gradient direction. Specifically, we obtain the domain-specific direction by calculating the cross-entropy $\\mathcal{L}_{\\mathrm{ce}}(\\boldsymbol{v})$ between the model prediction $p(\\boldsymbol{t}_i|\\boldsymbol{x})$ and the ground-truth $\\boldsymbol{y}$ according to Eq. (2), and the general knowledge direction based on the Kullback-Leibler (KL) divergence between $p(\\boldsymbol{t}_i|\\boldsymbol{x})$ and the zero-shot CLIP prediction $p_{\\mathrm{zs}}(\\boldsymbol{w}_i|\\boldsymbol{x})$ :", + "bbox": [ + 75, + 373, + 470, + 525 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {k l}} (\\boldsymbol {v}) = - \\sum_ {i} p _ {\\mathrm {z s}} \\left(\\boldsymbol {w} _ {i} | \\boldsymbol {x}\\right) \\log \\frac {p \\left(\\boldsymbol {t} _ {i} \\mid \\boldsymbol {x}\\right)}{p _ {\\mathrm {z s}} \\left(\\boldsymbol {w} _ {i} \\mid \\boldsymbol {x}\\right)}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 531, + 468, + 568 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We denote the gradients of $\\mathcal{L}_{\\mathrm{kl}}(\\pmb{v})$ and $\\mathcal{L}_{\\mathrm{ce}}(\\pmb{v})$ as $G_{\\mathrm{g}} = \\nabla_{\\pmb{v}}\\mathcal{L}_{\\mathrm{kl}}(\\pmb{v})$ and $G_{\\mathrm{d}} = \\nabla_{\\pmb{v}}\\mathcal{L}_{\\mathrm{ce}}(\\pmb{v})$ , respectively. The relations between $G_{\\mathrm{g}}$ and $G_{\\mathrm{d}}$ are two-fold. (1) Their angle is smaller than $90^{\\circ}$ (Figure 3(a)), which indicates that the optimization direction of few-shot downstream knowledge does not conflict with general knowledge. In this case, we safely set the updated gradient direction $G_{\\mathrm{prograd}}$ as $G_{\\mathrm{d}}$ . (2) Their angle is larger than $90^{\\circ}$ (Figure 3(b)), which indicates that the few-shot downstream knowledge conflicts with general knowledge. In other words, optimizing the context vectors following $G_{\\mathrm{d}}$ will lead to the forgetting of the pre-trained general knowledge. In this case, we project the $G_{\\mathrm{d}}$ to the orthogonal direction of $G_{\\mathrm{g}}$ to optimize the model for classification, which avoids increasing the KL loss. Our ProGrad strategy is mathematically formulated as:", + "bbox": [ + 75, + 574, + 470, + 801 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {G} _ {\\text {p r o g r a d}} = \\left\\{ \\begin{array}{l l} \\boldsymbol {G} _ {\\mathrm {d}}, & \\text {i f} \\boldsymbol {G} _ {\\mathrm {d}} \\cdot \\boldsymbol {G} _ {\\mathrm {g}} \\geq 0 \\\\ \\boldsymbol {G} _ {\\mathrm {d}} - \\lambda \\cdot \\frac {\\boldsymbol {G} _ {\\mathrm {d}} \\cdot \\boldsymbol {G} _ {\\mathrm {g}}}{\\| \\boldsymbol {G} _ {\\mathrm {g}} \\| ^ {2}} \\boldsymbol {G} _ {\\mathrm {g}}, & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 809, + 468, + 849 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fig 3(c) illustrates the pipeline of our ProGrad. Instead of updating the context vectors using $G_{\\mathrm{d}}$ in CoOp [54], we optimize the context vectors using $G_{\\mathrm{prograd}}$ , which prevent the", + "bbox": [ + 75, + 854, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "gradient direction from overfitting to few-shot downstream samples. We further introduce $\\lambda$ in Eq. (4) to generalize the formulation, which can flexibly control the strength of general knowledge guidance in applications. In particular, $\\lambda = 1$ denotes projecting $G_{\\mathrm{d}}$ to the orthogonal direction of $G_{\\mathrm{g}}$ (Figure 3(b)), while setting $\\lambda = 0$ makes ProGrad degenerate to CoOp, i.e., CoOp is a special case of our strategy. We include the detailed analysis of $\\lambda$ in Appendix.", + "bbox": [ + 496, + 90, + 893, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Generalization Error Analysis. We further theoretically analyze the generalization error of our ProGrad. Here, we provide a sketch proof and include the detailed justification in Appendix. Our ProGrad keeps the optimal value $\\mathcal{L}_{\\mathrm{kl}}$ of the pre-trained domain when optimizing the empirical risk on the downstream domain. The model $\\hat{f}_{\\mathrm{prograd}}$ learned by such update rule can be viewed as optimizing the empirical risk on pre-trained and downstream domains [52]:", + "bbox": [ + 496, + 212, + 893, + 334 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {f} _ {\\text {p r o g r a d}} = \\underset {f \\in \\mathcal {F}} {\\operatorname {a r g m i n}} \\hat {\\mathcal {R}} _ {(d + p)} (f) = \\underset {f \\in \\mathcal {F}} {\\operatorname {a r g m i n}} \\hat {\\mathcal {R}} _ {d} (f) + \\hat {\\mathcal {R}} _ {p} (f), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 345, + 890, + 387 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{F}$ is the function class, and $\\mathcal{R}(\\cdot)$ and $\\hat{\\mathcal{R}} (\\cdot)$ denote the expected risk and empirical risk. We bound the generalization error of ProGrad by virtue of Rademacher Complexity [1] and the Theorem 6.2 in [53]. The detailed proof is in Appendix.", + "bbox": [ + 496, + 387, + 893, + 463 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 1 Let $\\mathbf{X}_1^{N_d} = \\{\\mathbf{x}_n^{(d)}\\}_{n=1}^{N_d}$ and $\\mathbf{X}_1^{N_p} = \\{\\mathbf{x}_n^{(p)}\\}_{n=1}^{N_p}$ be two sets of i.i.d. samples drawn from the downstream domain $\\mathcal{D}_d$ and the pre-trained domain $\\mathcal{D}_p$ . Then for any $\\epsilon > 0$ , we have with probability at least $1 - \\epsilon$ ,", + "bbox": [ + 496, + 479, + 893, + 544 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {R} _ {d} (\\hat {f} _ {\\text {p r o g r a d}}) \\leq \\hat {\\mathcal {R}} _ {(d + p)} (\\hat {f} _ {\\text {p r o g r a d}}) + \\frac {1}{2} \\gamma_ {\\mathcal {F}} (D, P) \\\\ + \\Re_ {p} (\\mathcal {F}) + \\Re_ {d} (\\mathcal {F}) + \\frac {3}{2} \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2 N _ {d}}} \\\\ + \\frac {3}{2} \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2 N _ {p}}} + \\frac {1}{2} \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2} \\left(\\frac {1}{N _ {d}} + \\frac {1}{N _ {p}}\\right)}, \\tag {6} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 501, + 556, + 890, + 684 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\gamma_{\\mathcal{F}}(D,P)$ is the integral probability metric [31] that measures the difference between the distribution of pretrained domain and the downstream domain, $\\Re_d(\\mathcal{F})$ and $\\Re_p(\\mathcal{F})$ are the Rademacher complexity of $\\mathcal{F}$ .", + "bbox": [ + 496, + 685, + 893, + 746 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that the bound of $\\Re (\\mathcal{F})$ is inversely proportional to the number of training samples. Theorem 1 shows that the generalization error $\\mathcal{R}_d(\\hat{f}_{\\mathrm{prog}})$ is bounded by the empirical training risk $\\hat{\\mathcal{R}}_{(d + p)}(\\hat{f}_{\\mathrm{prog}})$ , the two domain gap $\\gamma_{\\mathcal{F}}(D,P)$ and the estimation error. The empirical training risk can be minimized to arbitrary small value when using deep models with high capacity. The estimation error that related to $N_{p}$ asymptotically tends to 0 as the sample size $N_{p}$ tends to infinity. Thanks to the large amount of pretrained samples", + "bbox": [ + 496, + 762, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15662", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4a9d9d174858b5007de3dff35e3714c3794aad053edb42b08f18ca05a1e04eb5.jpg", + "image_caption": [ + "Figure 3: (a) If $G_{\\mathrm{d}}$ is aligned with $G_{\\mathrm{g}}$ , we set $G_{\\mathrm{prograd}}$ as $G_{\\mathrm{d}}$ . (b) If $G_{\\mathrm{d}}$ conflicts with $G_{\\mathrm{g}}$ (i.e., their angle is larger than $90^{\\circ}$ ), we set $G_{\\mathrm{prograd}}$ as the projection of $G_{\\mathrm{d}}$ on the orthogonal direction of $G_{\\mathrm{g}}$ . (c) Training pipeline of our ProGrad. Only the context vectors are learnable." + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 251, + 352 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3f13c3f2054dca0fcd4976ab1768e0141c95e4b07b77440e9bb914c103f306fb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 261, + 89, + 890, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$N_{p}$ , we can approximate the generalization error bound as", + "bbox": [ + 76, + 434, + 460, + 450 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {R} _ {d} (\\hat {f} _ {\\text {p r o g r a d}}) \\leq \\frac {1}{2} \\gamma_ {\\mathcal {F}} (S, P) + \\Re_ {d} (\\mathcal {F}) \\\\ + \\frac {3}{2} \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2 N _ {d}}} + \\frac {1}{2} \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2} \\frac {1}{N _ {d}}}. \\tag {7} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 457, + 468, + 530 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similarly, we have the generalization error for CoOp $\\hat{f}_{\\mathrm{coop}}$ as", + "bbox": [ + 75, + 539, + 468, + 570 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {R} _ {d} \\left(\\hat {f} _ {\\text {c o o p}}\\right) \\leq 2 \\Re_ {d} (\\mathcal {F}) + 3 \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2 N _ {d}}} + \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2} \\frac {1}{N _ {d}}}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 575, + 468, + 616 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Under the assumption that the gap between pre-trained and downstream domains $\\gamma (P,D)$ is small, the estimation error bound of $\\mathcal{R}_d(\\hat{f}_{\\mathrm{coop}})$ is at least two times greater than $\\mathcal{R}_d(\\hat{f}_{\\mathrm{prograd}})$ . Considering that $N_{d}$ is typically very small in few-shot setting, our ProGrad model $\\hat{f}_{\\mathrm{prograd}}$ achieves a much lower error bound than conventional fine-tuning model like CoOp $\\hat{f}_{\\mathrm{coop}}$ .", + "bbox": [ + 75, + 623, + 472, + 736 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 746, + 209, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 771, + 397, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We validate the effectiveness of ProGrad on four settings: (1) few-shot classification, (2) domain generalization, (3) base-to-new generalization, (4) cross-dataset transfer.", + "bbox": [ + 75, + 794, + 472, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. For few-shot learning, base-to-new generalization and cross-dataset transfer, we use 11 datasets, i.e., ImageNet [6] and Caltech101 [9] for generic object classification, OxfordPets [33], StanfordCars [22], Flowers102 [32],", + "bbox": [ + 75, + 840, + 472, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Food101 [2] and FGVCAircraft [30] for fine-grained image recognition, EuroSAT [13] for satellite image classification, UCF101 [47] for action classification, DTD [5] for texture classification, and SUN397 [50] for scene recognition. For domain generalization, we use ImageNet as the source dataset and select ImageNet-V2 [41], ImageNet-Sketch [49], ImageNet-A [15], ImageNet-R [14] as the target datasets.", + "bbox": [ + 496, + 434, + 895, + 541 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training Details. For few-shot learning, following CoOp and CLIP, all models are trained with $\\{1,2,4,8,16\\}$ shots respectively then evaluated on the full test split. For domain generalization and base-to-new generalization, we evaluate 4-shot performance, which justifies the robustness under low-shots condition. All results of learning-based models are averaged over three random seeds. The standard deviation values can be found in the Appendix. Unless otherwise stated, we adhere to CoOp to use ResNet-50 [12] as the backbone of image encoder. Following [54] and [55], the length of context tokens $M$ is set to 16 for few-shot classification and $M = 4$ for the other three settings. $\\lambda$ is set to 1 by default, except that $\\lambda$ is set to 0.8 for 16 shots. We adopt the training settings from CoOp, e.g., training epochs, training schedule and the data augmentation settings, and refer readers to Appendix for further details", + "bbox": [ + 496, + 554, + 893, + 797 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. We compare ProGrad against 4 methods: (1) Zero-shot CLIP (2) Linear probe (3) CoOp and (4) CoCoOp. Although our method can beat some other fine-tune methods, e.g., CLIP-Adapter [10], we focus on single prompt-based learning methods. The results of other fine-tuning methods are in Appendix.", + "bbox": [ + 496, + 809, + 895, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15663", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b5d3d5921271b796dc926f68d83dfaca50c28d4ad30c1f9ba1899ac5cd2e72dd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 88, + 289, + 255 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6120cf81065e0eb16ef80b94e3acdde0f628e240ae61eae17145e59b49710f0b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 88, + 488, + 255 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cada85245cfa05915b3d46c3c20e5e379282c5d3164ea16a311ca9c628dd724e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 490, + 88, + 689, + 255 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b20f5abee9f8a48f19d80f13dff4447e36010f27138b88c966366a287e74c57f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 689, + 88, + 890, + 255 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/956d65616edd43d4da0db29e9c5c448130cea5da1b459097c2938720eaeb47ee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 256, + 289, + 421 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6641f3ed6c4a1b1d06a8f27b37b51d9f71f833dce4c73b8a41040786c2c2c66e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 256, + 488, + 421 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3a333e3a041cb6415b98de464edbcfb8f793dd0374c23239a91d4e61d8eb49ed.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 490, + 256, + 689, + 421 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/35cee9e09a99db379fe28df7f3586aeedbe39462f51bfa4252708b2724937038.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 689, + 256, + 890, + 421 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d9ab04434a8cb151add0dfb9020b2f4cc6a0e44398f5c146722e200da979db08.jpg", + "image_caption": [ + "Figure 4: Accuracy $(\\%)$ of few-shot learning on 11 datasets. The context length $M$ is set to 16. Standard deviations are reported in Appendix." + ], + "image_footnote": [], + "bbox": [ + 86, + 422, + 289, + 589 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3f4efe6b775d1f262c722826559b5a76743108e5c739bc76929cb28c911a5048.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 422, + 488, + 589 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e0fa688a17f6aa88d6e15a8c971993b680ab79b6f75c714ae287f30da93b0a1f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 490, + 422, + 689, + 589 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a0f62df0fe0b44ba24519a789c694b7d2d5f05b3252f8929d0d9add3ca213f53.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 689, + 422, + 890, + 589 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Few-Shot Classification", + "text_level": 1, + "bbox": [ + 75, + 657, + 294, + 674 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Setup. We compare with two zero-shot CLIP models, i.e., CLIP and $\\mathrm{CLIP}++$ stand for using single prompt and prompt ensembling respectively (Please refer to Appendix for the prompts templates). ProGrad and ProGrad++ stand for using single prompt and prompt ensembling as general knowledge to implement ProGrad respectively. Note that we only use the hand-crafted prompt ensembling to generate $G_{\\mathrm{g}}$ , which provides a more accurate general direction. Therefore, ProGrad++ still optimizes a single prompt with 16 learnable tokens, which is identical to the size of CoOp.", + "bbox": [ + 75, + 685, + 470, + 835 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1 provides averaged accuracy over 11 datasets, and Figure 4 illustrates the detailed comparisons. Overall, ProGrad clearly outperforms over baselines on average performance. Specifically, ProGrad outperforms CoOp", + "bbox": [ + 75, + 839, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/43b52bf3bde59253ec1a0c3e0d1ca66a10b325d0945446703a1cdec95a1355a3.jpg", + "table_caption": [ + "Table 1: Averaged accuracy $(\\%)$ of few-shot learning on 11 datasets. $M = 16$" + ], + "table_footnote": [], + "table_body": "
#shots0124816
CLIP58.77-----
CLIP++59.38-----
LP-37.3248.0257.2764.8870.57
CoOp-59.4662.3766.7970.0473.49
ProGrad-62.6164.9068.4571.4174.28
ProGrad++-63.0665.2868.7171.8075.03
", + "bbox": [ + 522, + 698, + 874, + 813 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "by $9.5\\%$ , $6.9\\%$ and $5.1\\%$ on FGVCAircraft, EuroSAT and Flowers102 given 1 shot, and the average improvement is $3.2\\%$ . These results demonstrate the anti-overfitting ability of our ProGrad when the training samples are extremely", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15664", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/dc40bca0899109bf3ff168f0db238c8e67e0b34f8a2c94aeaf68775b24dfb264.jpg", + "table_caption": [ + "Table 2: Evaluation on robustness to distribution shift with different visual backbones. Standard deviations are reported in Appendix.", + "(a) ResNet50" + ], + "table_footnote": [], + "table_body": "
SourceTarget
ImageNet-V2-Sketch-A-R
CLIP58.1851.3433.3221.6556.00
LP41.2933.6513.0911.1826.82
CoOp61.3453.8132.8322.0854.62
CoCoOp61.0453.7132.3022.0753.60
ProGrad62.1754.7034.4023.0556.77
", + "bbox": [ + 102, + 167, + 447, + 286 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/29ba95b4abb239077b3e65768bc64cd69849365c70d131de9956db042013b0f9.jpg", + "table_caption": [ + "(b) ResNet101" + ], + "table_footnote": [], + "table_body": "
SourceTarget
ImageNet-V2-Sketch-A-R
CLIP61.2454.8238.6628.0364.34
LP47.0138.4619.0916.3339.43
CoOp63.9956.9939.4029.5064.04
CoCoOp63.5956.9839.1629.0964.14
ProGrad64.9857.8640.5330.1365.61
", + "bbox": [ + 102, + 308, + 447, + 426 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f43283c622165e2b0719c179379f870441899562c11ccf2c86f9b671486e6bd3.jpg", + "table_caption": [ + "(c) ViT-B/32" + ], + "table_footnote": [], + "table_body": "
SourceTarget
ImageNet-V2-Sketch-A-R
CLIP62.0054.7540.8229.5966.01
LP46.7739.1220.3216.3239.48
CoOp64.7456.5940.0331.1064.54
CoCoOp64.6356.5940.7430.2764.12
ProGrad65.3657.4241.7331.8966.53
", + "bbox": [ + 102, + 449, + 447, + 566 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5186b4b6550a552761bcb391f3568feb5273dafde08a7241cd377b4384220987.jpg", + "table_caption": [ + "(d) ViT-B/16" + ], + "table_footnote": [], + "table_body": "
SourceTarget
ImageNet-V2-Sketch-A-R
CLIP66.7360.8446.1347.8074.01
LP54.7045.5728.2022.4744.12
CoOp69.8662.8346.9048.9874.55
CoCoOp70.1363.0546.4849.3673.80
ProGrad70.4563.3548.1749.4575.21
", + "bbox": [ + 102, + 588, + 447, + 709 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "limited. Furthermore, leveraging prompt ensembling can further explore the potential of ProGrad. From Table 1, with more accurate general knowledge offered by prompt ensembling, $\\mathrm{CLIP}++$ improves the zero-shot CLIP from $58.77\\%$ to $59.38\\%$ ; ProGrad++ increases the accuracy of ProGrad from $74.28\\%$ to $75.03\\%$ at 16 shots.", + "bbox": [ + 75, + 732, + 470, + 823 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Domain Generalization", + "text_level": 1, + "bbox": [ + 76, + 830, + 292, + 847 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We train our ProGrad on the source dataset (ImageNet) for three different random seeds, and assess it on ImageNet-V2, ImageNet-Sketch, ImageNet-A, and ImageNet-R. This", + "bbox": [ + 75, + 854, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "setting evaluates the generalizability on a target domain which differs from the source domain. Fine-tuning on limited data from a specific domain may mislead the model to learn spurious correlations or in-distribution patterns, resulting in biased models with poor performance in unseen domains. In contrast, zero-shot CLIP avoids exploiting such spurious correlations or patterns, as it is not learned on that distribution. By leveraging knowledge from the pre-trained domain to regularize fine-tuning on a specific distribution, our ProGrad method is expected to be robust to distribution shifts. As shown in Table 2, despite the exposure to the source dataset, ProGrad clearly outperforms other methods on all target datasets as well as the source dataset with ResNet-based and ViT-based backbones.", + "bbox": [ + 496, + 90, + 893, + 303 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Base-to-New Generalization", + "text_level": 1, + "bbox": [ + 500, + 311, + 751, + 327 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We follow CoCoOp [55] to evaluate the generalization performance from seen classes to unseen classes. All the classes are equally divided into two groups, i.e., base classes and new classes, and all methods are only trained on base classes and tested on both base classes and new classes.", + "bbox": [ + 496, + 335, + 681, + 500 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/82308c7a7c067fd24d2cebbaaa5e8958c5ccd068a1ad1417ba48f43a3cb61ac4.jpg", + "table_caption": [ + "Table 3: Averaged accuracy $(\\%)$ over 11 datasets for base-to-new generalization." + ], + "table_footnote": [], + "table_body": "
BaseNewH.
CLIP61.7265.9163.64
CoOp71.9661.2665.58
CoCoOp72.2360.7765.35
ProGrad73.2965.9669.06
", + "bbox": [ + 686, + 401, + 890, + 487 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The harmonic mean of base classes and new classes accuracies is reported to evaluate the trade-off. As illustrated in Table 3, ProGrad yields the highest average performance across all metrics, whereas CoOp and CoCoOp exhibit poor performance for new classes, consistently underperforming zero-shot CLIP. These results highlight that ProGrad's superior generalizability to both base and new classes. The detailed results of 11 datasets are in Appendix.", + "bbox": [ + 496, + 502, + 893, + 623 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Cross-Dataset Transfer", + "text_level": 1, + "bbox": [ + 500, + 632, + 715, + 647 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "All models are trained on ImageNet as source dataset and evaluated on the rest 10 target datasets. The goal of this setting is to demonstrate the potential to transfer beyond a single dataset. The results are presented in Table 4. As shown, our ProGrad not only achieves the highest performance on source datasets but also outperforms other baselines 9 out of 10 target datasets.", + "bbox": [ + 496, + 655, + 893, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.6. Further Analysis", + "text_level": 1, + "bbox": [ + 500, + 771, + 666, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with Learning without Forgetting (LwF). ProGrad employs the gradient direction of knowledge distillation loss as a form of regularization. To determine whether our approach is equivalent to conventional knowledge distillation, we compared its performance against a simple knowledge distillation method, i.e., $\\mathcal{L}_{\\mathrm{total}} = \\mathcal{L}_{\\mathrm{ce}} + \\alpha \\cdot \\mathcal{L}_{\\mathrm{kd}}$ which is identical to the implementation of Learning without", + "bbox": [ + 496, + 794, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15665", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9b381fa6536708e3682e46a66aa725a509e61720884288d1dadefe16eed03458.jpg", + "table_caption": [ + "Table 4: Comparison of prompt learning methods in the cross-dataset transfer setting. Prompts are learned from 4-shots ImageNet." + ], + "table_footnote": [], + "table_body": "
SourceTarget
ImageNetCaltech101OxfordPetsStanfordCarsFlowers102Food101FGVCAircraftSUN397DTDEuroSATUCF101Average
CoOp61.3484.4885.9954.1660.1075.4814.0957.4835.3226.7257.5655.70
CoCoOp61.0484.7386.4252.3461.2473.7913.7455.9436.6023.4657.9755.21
ProGrad62.1788.3086.4355.6162.6976.7615.7660.1639.4824.8758.7057.36
", + "bbox": [ + 143, + 130, + 831, + 282 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/353b0cf8762daa5f41a7620d003d4690ea0206ba56427836733b496c88d2bfed.jpg", + "table_caption": [ + "Table 5: Comparison with LwF (knowledge distillation). Average accuracy $(\\%)$ over 11 datasets." + ], + "table_footnote": [], + "table_body": "
#shots124816
CoOp59.4662.3766.7970.0473.49
LwF(KD), α = 0.2561.0963.0167.7470.9073.39
LwF(KD), α = 0.561.1363.3667.1470.3472.68
LwF(KD), α = 161.5264.0766.5270.0172.01
LwF(KD), α = 260.9862.6664.9267.7868.98
LwF(KD), α = 459.5861.7662.9265.0165.42
ProGrad62.6164.9068.4571.4174.28
", + "bbox": [ + 88, + 344, + 439, + 474 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9c9c5aa36d3a8dd90a4c9150b82ebc674918a5368b355aca7d6ddb68e4ea232b.jpg", + "table_caption": [ + "Table 6: Applying ProGrad to cosine classifier. Average accuracy $(\\%)$ over 11 datasets." + ], + "table_footnote": [], + "table_body": "
#shots124816
Cosine30.5043.7453.3361.2665.00
+ProGrad32.2946.1455.1862.0566.47
", + "bbox": [ + 122, + 521, + 424, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Forgetting (LwF)[24]. We repeated few-shot experiments on 11 datasets using a range of $\\alpha$ values and report the average results in Table 5. The results demonstrate that ProGrad outperforms KD for various few-shot settings. Although KD (LwF) with small $\\alpha \\leq 1$ improves the performance of CoOp in low-shot scenarios (e.g., 1, 2, and 4 shots), its performance drops when the shots is large (i.e., 8 and 16 shots). These findings suggest that ProGrad operates differently from KD (LwF) and is more robust to the sample number.", + "bbox": [ + 75, + 609, + 468, + 747 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Failure cases. We analyze cases where ProGrad models fail while CoOp succeeds. In specific, we count the percentage of the failure cases that zero-shot CLIP models also fails in Figure 5. We found that a high proportion of the failure cases are also mis-classified by zero-shot CLIP model (red bar in Figure 5), implying that the imprecision of zero-shot general knowledge represented by $G_{\\mathrm{g}}$ is detrimental to model generalization. As sample size increases, $G_{\\mathrm{d}}$ represents downstream knowledge more accurately and with less bias. As expected, the red bar becomes larger.", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/63454d01965cad8fc6a717945be98073ff7b9a18c3af9520015941182c3a7a3a.jpg", + "image_caption": [ + "Figure 5: Distribution of samples that are mis-classified by ProGrad but correctly classified by CoOp." + ], + "image_footnote": [], + "bbox": [ + 501, + 303, + 691, + 412 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/52e978cdbc767b9bbb8d2a5fd0e31a605c03ca7ba118044cef7984c1ebb2170e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 303, + 888, + 411 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/73bbac49f50b2c0427e25a8e788ef1f15bfe157d0e826078ba27cad1c6fcab64.jpg", + "image_caption": [ + "(a) 1 shot", + "Figure 6: Angles between $G_{\\mathrm{d}}$ and $G_{\\mathrm{g}}$ during training on StanfordCars and Caltech101." + ], + "image_footnote": [], + "bbox": [ + 501, + 472, + 696, + 585 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/20a2bac3bcfdfed7760c2bf3b9c67093e28704328238171af2435b2558582d66.jpg", + "image_caption": [ + "(b) 2 shots" + ], + "image_footnote": [], + "bbox": [ + 696, + 472, + 890, + 585 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conflict of knowledge. ProGrad requires the updated gradient direction be acute to the general knowledge gradient directions. We explore how this constraint helps to defuse the conflicts of domain-specific and general knowledge by visualizing the angle between their representative gradients during training (angle between $G_{\\mathrm{d}}$ and $G_{\\mathrm{g}}$ ). As depicted in Figure 6, without $G_{\\mathrm{prograd}}$ , the angle between $G_{\\mathrm{d}}$ and $G_{\\mathrm{g}}$ converges to 90 degrees due to the fact that \"all high-dimensional random vectors are almost always orthogonal to each other\" [3]. Intuitively, without any constraint, the optimization direction $G_{\\mathrm{d}}$ is independent of the general direction, and the average angle would be orthogonal. In contrast, utilizing $G_{\\mathrm{prograd}}$ results in the convergence of the angle to an obtuse angle. The reason is that $G_{\\mathrm{prograd}}$ intervenes the model to learn the downstream knowledge aligned with the", + "bbox": [ + 496, + 672, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15666", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "general knowledge and leads to the insufficient learning of downstream knowledge that is incompatible with the general knowledge. As training stabilizes, $G_{\\mathrm{d}}$ struggles to learn the conflicting knowledge, reflecting an obtuse angle to the $G_{\\mathrm{g}}$ . Thanks to ProGrad, we discard such conflicting knowledge to avoid forgetting.", + "bbox": [ + 75, + 90, + 472, + 181 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Upper Bound of Performance.", + "text_level": 1, + "bbox": [ + 76, + 181, + 292, + 196 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "As the general gradient direction $G_{g}$ is the key for improvement, we are interested in the upper-bound of performance if we can find an oracle general direction $G_{g}^{\\mathrm{full}}$ instead of the one offered by hand-crafted prompt. To achieve this, we first optimize a prompt with plain cross-entropy loss on the full dataset to create $G_{g}^{\\mathrm{full}}$ and then use such gradient to implement ProGrad. The averaged performance over 11 datasets, as", + "bbox": [ + 75, + 196, + 276, + 421 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/e46f47daff40a8aa0851481e88970e09ad22c40ea5254731bbae88cd64460c26.jpg", + "image_caption": [ + "Figure 7: The upper bound of performance (averaged accuracy) of GradPrad." + ], + "image_footnote": [], + "bbox": [ + 279, + 204, + 467, + 356 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "shown in Figure 7, indicate a more accurate regularization direction $G_{g}^{\\mathrm{full}}$ elicits a stronger ProGrad model. The detailed results of 11 datasets are in Appendix.", + "bbox": [ + 75, + 422, + 470, + 468 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Applying ProGrad to conventional fine-tuning. We are also interested in the effectiveness of ProGrad for the conventional \"pre-train then fine-tune\" paradigm. Specifically, we plug in an additional cosine classifier on top of the visual backbone and compare the averaged performance over 11 datasets of few-shot classification. Table 6 shows that conventional fine-tuning can benefit from our ProGrad. The implementation details and the result of each dataset are provided in Appendix.", + "bbox": [ + 75, + 468, + 470, + 604 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Effect of hyper-parameter $\\lambda$ . We further analyze the effect of the hyper-parameter $\\lambda$ described in Eq. (4) in the main paper. Results are shown in Table 7. As discussed in Section 3.2 in the main paper, a smaller $\\lambda$ weakens the general knowledge regularization, which results in a inferior performance under low-shot setting for most datasets. However, for DTD in Table 7, using a smaller $\\lambda = 0.9$ to reduce the general knowledge regularization can improve the 16 shots results. One possible reason is that texture images of DTD has large gap with the CLIP pre-trained images that collected from the Internet, stronger regularization from pre-trained knowledge might be detrimental to the fine-tune performance if downstream data is sufficient.", + "bbox": [ + 75, + 604, + 470, + 800 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 814, + 194, + 830 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we pointed out the over-fitting issues of existing prompt tuning methods for few-shot generalization, which heavily relies on early stopping and data augmentation. We proposed a prompt tuning method ProGrad that", + "bbox": [ + 75, + 839, + 472, + 901 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/c664055f57324730d86bdff5d5e0d81aa4b13e13c8825132fda2417c76635b79.jpg", + "table_caption": [ + "Table 7: Accuracy $(\\%)$ of 1, 2, 4, 8, and 16 shots training with different $\\lambda$ on DTD and OxfordPets.", + "(a) OxfordPets." + ], + "table_footnote": [], + "table_body": "
λ1 shot2 shots4 shots8 shots16 shots
086.0182.2186.6385.1587.06
0.287.1283.1684.8784.0086.15
0.488.0983.5685.5084.0486.67
0.787.7484.7086.9386.3087.90
0.988.2686.4787.5287.3888.52
1.088.3686.8988.0487.9189.00
", + "bbox": [ + 560, + 152, + 849, + 265 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/2824ffeca2bfdf5fb8732c1b96c142efdcf3af2f68b927b2eac01e94856f07fc.jpg", + "table_caption": [ + "(b) DTD." + ], + "table_footnote": [], + "table_body": "
λ1 shot2 shots4 shots8 shots16 shots
044.3346.2254.0859.9962.89
0.243.8045.2154.0260.1463.61
0.444.1747.4454.3259.6563.16
0.744.9347.7754.9259.2863.10
0.945.7848.4655.4460.4664.28
1.046.1449.7854.4357.9861.15
", + "bbox": [ + 560, + 287, + 849, + 400 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "regularize each tuning step not to conflict with the general knowledge of the hand-crafted prompt. Experiments on few-shot classification, base-to-new generalization, domain generalization and cross-dataset transfer over 11 datasets demonstrate the effectiveness and efficiency of our ProGrad. In the future, we will explore how to apply ProGrad on other tasks like object detection and segmentation.", + "bbox": [ + 496, + 429, + 893, + 536 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 553, + 658, + 570 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-PhD-2021-01-002). The authors would like to thank the reviewers for their comments that help improve the manuscript.", + "bbox": [ + 496, + 579, + 893, + 656 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 672, + 596, + 686 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Peter L Bartlett and Shahar Mendelson. Rademacher and gaussian complexities: Risk bounds and structural results. Journal of Machine Learning Research, 3(Nov):463-482, 2002. 4", + "[2] Lukas Bossard, Matthieu Guillaumin, and Luc Van Gool. Food-101-mining discriminative components with random forests. In ECCV, 2014. 5", + "[3] Tony Cai, Jianqing Fan, and Tiefeng Jiang. Distributions of angles in random packing on spheres. Journal of Machine Learning Research, 14(21):1837-1864, 2013. 8", + "[4] Guangyi Chen, Weiran Yao, Xiangchen Song, Xinyue Li, Yongming Rao, and Kun Zhang. 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AAAI, 2023. 3" + ], + "bbox": [ + 501, + 92, + 892, + 176 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "15669", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Prompt-aligned Gradient for Prompt Tuning/7786570f-2ec2-4f85-a04c-e553c7832bc6_model.json b/2023/Prompt-aligned Gradient for Prompt Tuning/7786570f-2ec2-4f85-a04c-e553c7832bc6_model.json new file mode 100644 index 0000000000000000000000000000000000000000..556c30894f00ee5a178e1841a668b14129e0d03b --- /dev/null +++ b/2023/Prompt-aligned Gradient for Prompt Tuning/7786570f-2ec2-4f85-a04c-e553c7832bc6_model.json @@ -0,0 +1,2510 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.259, + 0.131, + 0.713, + 0.154 + ], + "angle": 0, + "content": "Prompt-aligned Gradient for Prompt Tuning" + }, + { + "type": "text", + "bbox": [ + 0.186, + 0.18, + 0.787, + 0.2 + ], + "angle": 0, + "content": "Beier Zhu1 Yulei Niu2 Yucheng Han1 Yue Wu3 Hanwang Zhang1*" + }, + { + "type": "text", + "bbox": [ + 0.185, + 0.201, + 0.786, + 0.217 + ], + "angle": 0, + "content": "\\(^{1}\\)Nanyang Technological University \\(^{2}\\)Columbia University \\(^{3}\\)Damo Academy, Alibaba Group" + }, + { + "type": "text", + "bbox": [ + 0.184, + 0.219, + 0.786, + 0.234 + ], + "angle": 0, + "content": "beier002@e.ntu.edu.sg, yn.yuleiniu@gmail.com yucheng002@e.ntu.edu.sg" + }, + { + "type": "text", + "bbox": [ + 0.255, + 0.238, + 0.714, + 0.251 + ], + "angle": 0, + "content": "matthew.wy@alibaba-inc.com hanwangzhang@ntu.edu.sg" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.474, + 0.699 + ], + "angle": 0, + "content": "Thanks to the large pre-trained vision-language models (VLMs) like CLIP [37], we can craft a zero-shot classifier by discrete prompt design, e.g., the confidence score of an image being \"[CLASS]\" can be obtained by using the VLM provided similarity between the image and the prompt sentence \"a photo of a [CLASS]\". Furthermore, prompting shows great potential for fast adaptation of VLMs to downstream tasks if we fine-tune the soft prompts with few samples. However, we find a common failure that improper fine-tuning or learning with extremely few-shot samples may even under-perform the zero-shot prediction. Existing methods still address this problem by using traditional anti-overfitting techniques such as early stopping and data augmentation, which lack a principled solution specific to prompting. In this paper, we present Prompt-aligned Gradient, dubbed ProGrad to prevent prompt tuning from forgetting the general knowledge learned from VLMs. In particular, ProGrad only updates the prompt whose gradient is aligned (or non-conflicting) to the general knowledge, which is represented as the optimization direction offered by the pre-defined prompt predictions. Extensive experiments under the few-shot learning, domain generalization, baseto-new generalization and cross-dataset transfer settings demonstrate the stronger few-shot generalization ability of ProGrad over state-of-the-art prompt tuning methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.728, + 0.21, + 0.743 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.755, + 0.472, + 0.876 + ], + "angle": 0, + "content": "After seeing and reading countless image-text association pairs, large and deep vision-language models (VLM) [37, 18] can memorize the general knowledge (a.k.a. encyclopedic knowledge) about what visual patterns correspond to what textual sequence and vice versa. Thanks to the powerful language modeling of VLMs, we can establish a communication channel in human-readable natural language, i.e., prompt [25, 51, 19], to query the general knowledge." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.288, + 0.895, + 0.426 + ], + "angle": 0, + "content": "Prompting bridges the interface gap between the pre-trained and downstream tasks (e.g., regression vs. classification) without the need for additional fine-tuning adaptation. For example, we can craft a concrete prompt—\"a photo of a [CLASS]\"—for zero-shot image classification: by using the popular vision-language model CLIP [37], we input the image to the vision end and the prompt sentence to the language end, then obtain a vision-language similarity as the confidence score of classifying the image as \"[CLASS]\"." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.433, + 0.897, + 0.903 + ], + "angle": 0, + "content": "In practice, the prompt-based zero-shot image classification is not accurate because the hand-crafted prompt may not be the most machine-favorable (e.g., \"this is a picture of\" could be more grammatically prevailing in VLM training), or not specific to the downstream domain (e.g., \"a photo of a person doing\" is better in action recognition) [37]. Recently, prompt tuning or prefix tuning [23, 26, 54, 55] has been proposed to replace the handcrafted prompt with a set of tunable word embedding vectors, which do not have to be translatable back to human-readable words. Yet, prompt tuning is still as tricky as conventional fine-tuning: as the training continues, the generalization ability may decrease and even under-perform the zero-shot baseline. As shown in Figure 1(a&b), the prompt tuning method CoOp [54] achieves the best results via early stopping, and its accuracies heavily drop by at most \\(4\\%\\) when the training continues. Besides, Figure 1(c&d) show that CoOp underperforms zero-shot CLIP without augmentation or enough samples from downstream tasks. To the best of our knowledge, existing methods still rely on the conventional anti-overfitting techniques such as early stopping and data augmentation [54, 55, 11, 36], which lacks a principled solution to the nature of improper prompt tuning. Furthermore, the Grad-CAM visualization results indicate that the fine-tuned prompt misleads the VLM to forget the general knowledge that the classification should at least focus on the foreground object but not the background. Comparing CoOp (Figure 2(b)) with zero-shot CLIP (Figure 2(c)), we find that the CoOp model distracts its attention to the background, while CLIP mainly focuses on the foreground object. These results demonstrate the over-fitting risk of existing prompt" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15659" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.283, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.185, + 0.216, + 0.202, + 0.228 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.089, + 0.485, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.389, + 0.216, + 0.406, + 0.228 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.09, + 0.688, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.591, + 0.216, + 0.607, + 0.228 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.688, + 0.09, + 0.89, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.216, + 0.808, + 0.228 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.239, + 0.893, + 0.286 + ], + "angle": 0, + "content": "Figure 1: Comparison of Zero-shot CLIP, CoOp, and our ProGrad on Stanford Cars and OxfordPets datasets. (a)&(b): Given 1 shot training sample, CoOp's performance severely drops and under-performs zero-shot CLIP by large margins when the training continues. (c)&(d): CoOp may fail to improve CLIP without data augmentation or plenty of samples." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.3, + 0.891, + 0.555 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.565, + 0.893, + 0.595 + ], + "angle": 0, + "content": "Figure 2: Comparisons of Grad-CAM [43] visualization for prompt tuning methods using different gradient strategies on Stanford Cars Datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.623, + 0.47, + 0.654 + ], + "angle": 0, + "content": "tuning strategies, especially when the number of training samples is extremely limited (e.g., 1 or 2)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.473, + 0.902 + ], + "angle": 0, + "content": "To this end, we present a novel prompt tuning method called Prompt-aligned Gradient (ProGrad) to overcome the improperly biased tuning for CLIP. The principle of ProGrad is to regularize each tuning step not to conflict with the general knowledge offered by the original prompt, e.g., the zero-shot CLIP predictions. Specifically, we measure the general knowledge direction \\( G_{\\mathrm{g}} \\) using the gradient of Kullback-Leibler (KL) divergence between the predictions of the zero-shot prompted CLIP and the few-shot fine-tuned model, which we name as general direction. Similarly, we compute the domain-specific knowledge direction \\( G_{\\mathrm{d}} \\) using the gradient of cross-entropy between the ground-truth and the few-shot fine-tuned model, dubbed domain-specific direction. We decompose the domain-specific direction \\( G_{\\mathrm{d}} \\) into: 1) a vector \\( G_{\\perp} \\) orthogonal to the general direction, which denotes the non-conflicting domain-specific knowl" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.623, + 0.895, + 0.85 + ], + "angle": 0, + "content": "edge; and 2) a vector \\( G_{\\parallel} \\) parallel to the general direction, which denotes the general knowledge. Note that the first gradient component does NOT override the general direction as any two orthogonal vectors can be transformed into two nonconflicting base vectors. For the second component, it must be one of the two directions: 1) the same of the general direction, which indicates that the update is aligned to the general knowledge, and 2) the opposite of general direction, indicating a conflicting update that should be discarded to avoid forgetting. Overall, in each iteration, ProGrad only updates the parameters in the prompt-aligned direction that has an acute angle to the general direction. Compared to CoOp and CLIP, both \\( G_{g} \\) and \\( G_{\\perp} \\) (Figure 2(d&e)) help to regularize the model to focus on the foreground, and ProGrad (Figure 2(f)) further improves the visual response." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Following CLIP, CoOp and CoCoOp [55], we evaluate ProGrad under the few-shot learning, domain generalization, base-to-new generalization and cross-dataset transfer" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15660" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "settings over 15 image classification benchmarks, covering generic object classification, fine-grained image recognition, action classification. In summary, our ProGrad achieves: 1) clear improvement compared to CoOp over all of the 11 datasets; 2) clear improvement on the harmonic mean of base and new classes accuracies on all 11 datasets compared to CoOp and CoCoOp, and 3) clear improvement on both the source and target datasets of the domain generalization." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.226, + 0.22, + 0.243 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.251, + 0.473, + 0.674 + ], + "angle": 0, + "content": "VLMs Adaptation. VLM can be adapted for various downstream tasks, e.g., visual question answering [21, 48], visual grounding [51], image retrieval [28] and semantic segmentation [39]. We focus on image classification task. Conventional \"pre-train then fine-tune\" paradigm that plugs in a classifier to the visual backbone and trained on downstream data has been widely-adopted, e.g., Linear Probe [37]. CLIP-Adapter [10] add feature adapters to boost fine-tuning results. Recently, NLP community has introduced a \"prompt-based learning\" paradigm that fine-tunes the prompt using a \"fill-in-the-blank\" cloze test to maximize the ground-truth token [23, 26]. The prompt-based learning has recently been applied in CV community [54, 29, 7, 46, 4, 20, 56]: CoOp [54] uses a continuous prompt optimization from downstream data instead of hand-craft design. CoCoOp [55] further extends CoOp by learning image conditional prompt to improve generalization. ProDA [29] learns a prompt distribution over the output embedding space. VPT [7] introduces variational prompt tuning by combining a base learned prompt with a residual vector sampled from a instance-specific underlying distribution. TPT [46] proposes a test-time prompt tuning, which does not require training data and optimizes the prompt to achieve consistent predictions across different augmented views. Our ProGrad follows the line of prompt-based learning to improve few-shot generalization ability by aligning the gradient to general direction, without model structure modification or tuning the pre-trained parameters." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Knowledge Transfer. Forgetting mitigation is widely used in incremental learning [27, 40, 35, 42, 17] through knowledge distillation or memory replay. However, prompt-based learning differs fundamentally from incremental learning in that it does not have access to pre-trained data, which is required for incremental learning to store old data from memory storage. For example, OGD [8] projects gradients from new classes to the orthogonal direction of previous task gradients, but the requirement to store old task gradients is not possible for prompt tuning since we lack access to the pre-training process. Moreover, OGD modifies gradients of downstream tasks in non-conflicting scenarios, potentially leading to sub-optimal performance. Another related field that leverages gradient matching to transfer knowledge is domain generalization [45, 38] and multi-task learning [44, 52]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.152 + ], + "angle": 0, + "content": "However, these methods are not directly applicable in prompt tuning whose transfer direction is only from general to downstream. In Appendix, we will show how their methods fail in several ablative studies." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.166, + 0.637, + 0.183 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.191, + 0.895, + 0.268 + ], + "angle": 0, + "content": "In this section, we introduce the preliminary concepts of prompt-based zero-shot inference, prompt-based learning, and present our proposed Prompt-aligned Gradient solution to align the domain knowledge with general knowledge for few-shot generalization." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.276, + 0.642, + 0.292 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.299, + 0.895, + 0.42 + ], + "angle": 0, + "content": "Contrastive language-image pre-training (CLIP) [37] adopts a contrastive language-image pre-training paradigm on tremendous pairs of images with natural language descriptions. For contrastive learning, the associated image and sentences are taken as the positive samples, while the non-associated pairs are regarded as negative samples. The contrastive objective maximizes the similarity of positive pairs while minimize the similarity of negative pairs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.42, + 0.897, + 0.648 + ], + "angle": 0, + "content": "Zero-shot transfer inference adapts the pre-trained CLIP model to downstream tasks without fine-tuning the model. Taking image classification as an example, zero-shot transfer is enabled by formulating the classification task as an image-text matching problem, where the text is obtained by extending the \"[CLASS]\" name using a template like \"a photo of a [CLASS]\". CLIP [37] finds that such a simple template narrows the distribution gap to pre-training text inputs. The image-class matching score is measured based on the cosine similarity \\(< \\pmb{w}_i\\), \\(f >\\) between the image feature \\(\\pmb{f}\\) and the class-extended text feature \\(\\pmb{w}_i\\) for \\(i\\)-th class. The image feature \\(\\pmb{f}\\) for image \\(\\pmb{x}\\) is extracted by the image encoder, while the text feature \\(\\pmb{w}_i\\) for \\(i\\)-th class is obtained by feeding the prompt description into the text encoder. The probability for \\(i\\)-th class is obtained as" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.657, + 0.895, + 0.697 + ], + "angle": 0, + "content": "\\[\np _ {\\mathrm {z s}} (\\boldsymbol {w} _ {i} | \\boldsymbol {x}) = \\frac {\\exp \\left(< \\boldsymbol {w} _ {i} , \\boldsymbol {f} > / \\tau\\right)}{\\sum_ {j = 1} ^ {K} \\exp \\left(< \\boldsymbol {w} _ {j} , \\boldsymbol {f} > / \\tau\\right)}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.734 + ], + "angle": 0, + "content": "where \\(K\\) denotes the number of classes, and \\(\\tau\\) is a temperature learned by CLIP." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Prompt-based learning further strengths the transferring ability of the CLIP model and avoids prompt engineering by automatically learning the prompt given few samples from the downstream task. Different from the zero-shot transfer that used a fixed hand-craft prompt, CoOp [54] constructs and fine-tunes a set of \\(M\\) continuous context vectors \\(\\pmb{v} = \\{\\pmb{v}_1,\\pmb{v}_2,\\dots,\\pmb{v}_M\\}\\) as the turnable prompt. Specifically, the prompt \\(\\pmb{t}_i = \\{\\pmb{v}_1,\\pmb{v}_2,\\dots,\\pmb{v}_M,\\pmb{c}_i\\}\\) combines the learnable context vectors \\(\\pmb{v}\\) and the class token embedding \\(\\pmb{c}_i\\), and is fed to the text encoder \\(g(\\cdot)\\). CoOp optimizes the static context vectors \\(\\pmb{v}\\) by minimizing the negative log-likelihood" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "15661" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.252, + 0.106 + ], + "angle": 0, + "content": "of the ground-truth token:" + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.114, + 0.347, + 0.144 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {c e}} (\\boldsymbol {v}) = - \\sum_ {i} \\boldsymbol {y} _ {i} \\log p (\\boldsymbol {t} _ {i} | \\boldsymbol {x}),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.144, + 0.47, + 0.186 + ], + "angle": 0, + "content": "\\[\np \\left(\\boldsymbol {t} _ {i} \\mid \\boldsymbol {x}\\right) = \\frac {\\exp \\left(< g \\left(\\boldsymbol {t} _ {i}\\right) , \\boldsymbol {f} > / \\tau\\right)}{\\sum_ {j = 1} ^ {K} \\exp \\left(< g \\left(\\boldsymbol {t} _ {j}\\right) , \\boldsymbol {f} > / \\tau\\right)}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.192, + 0.47, + 0.221 + ], + "angle": 0, + "content": "where \\( \\mathbf{y} \\) denotes the one-hot ground-truth annotation and \\( K \\) denotes the number of classes." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.229, + 0.31, + 0.245 + ], + "angle": 0, + "content": "3.2. Prompt-aligned Gradient" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.253, + 0.471, + 0.373 + ], + "angle": 0, + "content": "CoOp faced a challenge that the transfer performance drops when the number of annotations is very limited (e.g., one per class), even underperforms the zero-shot transfer. Also, CoOp heavily relies on anti-overfitting techniques such as early stopping and data augmentation. To overcome the over-fitting challenge, we propose an effective and efficient fine-tuning paradigm ProGrad to align the few-shot downstream knowledge with the large-scale general knowledge." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.374, + 0.472, + 0.526 + ], + "angle": 0, + "content": "Motivated by the success of knowledge distillation [34, 16] in knowledge transfer, we leverage the zero-shot CLIP predictions as the general knowledge, and compare the finetuned predictions with the general knowledge to regularize the gradient direction. Specifically, we obtain the domain-specific direction by calculating the cross-entropy \\(\\mathcal{L}_{\\mathrm{ce}}(\\boldsymbol{v})\\) between the model prediction \\(p(\\boldsymbol{t}_i|\\boldsymbol{x})\\) and the ground-truth \\(\\boldsymbol{y}\\) according to Eq. (2), and the general knowledge direction based on the Kullback-Leibler (KL) divergence between \\(p(\\boldsymbol{t}_i|\\boldsymbol{x})\\) and the zero-shot CLIP prediction \\(p_{\\mathrm{zs}}(\\boldsymbol{w}_i|\\boldsymbol{x})\\):" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.532, + 0.47, + 0.569 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {k l}} (\\boldsymbol {v}) = - \\sum_ {i} p _ {\\mathrm {z s}} \\left(\\boldsymbol {w} _ {i} | \\boldsymbol {x}\\right) \\log \\frac {p \\left(\\boldsymbol {t} _ {i} \\mid \\boldsymbol {x}\\right)}{p _ {\\mathrm {z s}} \\left(\\boldsymbol {w} _ {i} \\mid \\boldsymbol {x}\\right)}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.575, + 0.472, + 0.803 + ], + "angle": 0, + "content": "We denote the gradients of \\(\\mathcal{L}_{\\mathrm{kl}}(\\pmb{v})\\) and \\(\\mathcal{L}_{\\mathrm{ce}}(\\pmb{v})\\) as \\(G_{\\mathrm{g}} = \\nabla_{\\pmb{v}}\\mathcal{L}_{\\mathrm{kl}}(\\pmb{v})\\) and \\(G_{\\mathrm{d}} = \\nabla_{\\pmb{v}}\\mathcal{L}_{\\mathrm{ce}}(\\pmb{v})\\), respectively. The relations between \\(G_{\\mathrm{g}}\\) and \\(G_{\\mathrm{d}}\\) are two-fold. (1) Their angle is smaller than \\(90^{\\circ}\\) (Figure 3(a)), which indicates that the optimization direction of few-shot downstream knowledge does not conflict with general knowledge. In this case, we safely set the updated gradient direction \\(G_{\\mathrm{prograd}}\\) as \\(G_{\\mathrm{d}}\\). (2) Their angle is larger than \\(90^{\\circ}\\) (Figure 3(b)), which indicates that the few-shot downstream knowledge conflicts with general knowledge. In other words, optimizing the context vectors following \\(G_{\\mathrm{d}}\\) will lead to the forgetting of the pre-trained general knowledge. In this case, we project the \\(G_{\\mathrm{d}}\\) to the orthogonal direction of \\(G_{\\mathrm{g}}\\) to optimize the model for classification, which avoids increasing the KL loss. Our ProGrad strategy is mathematically formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.81, + 0.47, + 0.85 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {G} _ {\\text {p r o g r a d}} = \\left\\{ \\begin{array}{l l} \\boldsymbol {G} _ {\\mathrm {d}}, & \\text {i f} \\boldsymbol {G} _ {\\mathrm {d}} \\cdot \\boldsymbol {G} _ {\\mathrm {g}} \\geq 0 \\\\ \\boldsymbol {G} _ {\\mathrm {d}} - \\lambda \\cdot \\frac {\\boldsymbol {G} _ {\\mathrm {d}} \\cdot \\boldsymbol {G} _ {\\mathrm {g}}}{\\| \\boldsymbol {G} _ {\\mathrm {g}} \\| ^ {2}} \\boldsymbol {G} _ {\\mathrm {g}}, & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Fig 3(c) illustrates the pipeline of our ProGrad. Instead of updating the context vectors using \\( G_{\\mathrm{d}} \\) in CoOp [54], we optimize the context vectors using \\( G_{\\mathrm{prograd}} \\), which prevent the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.213 + ], + "angle": 0, + "content": "gradient direction from overfitting to few-shot downstream samples. We further introduce \\(\\lambda\\) in Eq. (4) to generalize the formulation, which can flexibly control the strength of general knowledge guidance in applications. In particular, \\(\\lambda = 1\\) denotes projecting \\(G_{\\mathrm{d}}\\) to the orthogonal direction of \\(G_{\\mathrm{g}}\\) (Figure 3(b)), while setting \\(\\lambda = 0\\) makes ProGrad degenerate to CoOp, i.e., CoOp is a special case of our strategy. We include the detailed analysis of \\(\\lambda\\) in Appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.213, + 0.895, + 0.335 + ], + "angle": 0, + "content": "Generalization Error Analysis. We further theoretically analyze the generalization error of our ProGrad. Here, we provide a sketch proof and include the detailed justification in Appendix. Our ProGrad keeps the optimal value \\(\\mathcal{L}_{\\mathrm{kl}}\\) of the pre-trained domain when optimizing the empirical risk on the downstream domain. The model \\(\\hat{f}_{\\mathrm{prograd}}\\) learned by such update rule can be viewed as optimizing the empirical risk on pre-trained and downstream domains [52]:" + }, + { + "type": "equation", + "bbox": [ + 0.505, + 0.347, + 0.892, + 0.388 + ], + "angle": 0, + "content": "\\[\n\\hat {f} _ {\\text {p r o g r a d}} = \\underset {f \\in \\mathcal {F}} {\\operatorname {a r g m i n}} \\hat {\\mathcal {R}} _ {(d + p)} (f) = \\underset {f \\in \\mathcal {F}} {\\operatorname {a r g m i n}} \\hat {\\mathcal {R}} _ {d} (f) + \\hat {\\mathcal {R}} _ {p} (f), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.388, + 0.895, + 0.464 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}\\) is the function class, and \\(\\mathcal{R}(\\cdot)\\) and \\(\\hat{\\mathcal{R}} (\\cdot)\\) denote the expected risk and empirical risk. We bound the generalization error of ProGrad by virtue of Rademacher Complexity [1] and the Theorem 6.2 in [53]. The detailed proof is in Appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.48, + 0.894, + 0.545 + ], + "angle": 0, + "content": "Theorem 1 Let \\(\\mathbf{X}_1^{N_d} = \\{\\mathbf{x}_n^{(d)}\\}_{n=1}^{N_d}\\) and \\(\\mathbf{X}_1^{N_p} = \\{\\mathbf{x}_n^{(p)}\\}_{n=1}^{N_p}\\) be two sets of i.i.d. samples drawn from the downstream domain \\(\\mathcal{D}_d\\) and the pre-trained domain \\(\\mathcal{D}_p\\). Then for any \\(\\epsilon > 0\\), we have with probability at least \\(1 - \\epsilon\\)," + }, + { + "type": "equation", + "bbox": [ + 0.502, + 0.558, + 0.892, + 0.685 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {R} _ {d} (\\hat {f} _ {\\text {p r o g r a d}}) \\leq \\hat {\\mathcal {R}} _ {(d + p)} (\\hat {f} _ {\\text {p r o g r a d}}) + \\frac {1}{2} \\gamma_ {\\mathcal {F}} (D, P) \\\\ + \\Re_ {p} (\\mathcal {F}) + \\Re_ {d} (\\mathcal {F}) + \\frac {3}{2} \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2 N _ {d}}} \\\\ + \\frac {3}{2} \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2 N _ {p}}} + \\frac {1}{2} \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2} \\left(\\frac {1}{N _ {d}} + \\frac {1}{N _ {p}}\\right)}, \\tag {6} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.686, + 0.895, + 0.747 + ], + "angle": 0, + "content": "where \\(\\gamma_{\\mathcal{F}}(D,P)\\) is the integral probability metric [31] that measures the difference between the distribution of pretrained domain and the downstream domain, \\(\\Re_d(\\mathcal{F})\\) and \\(\\Re_p(\\mathcal{F})\\) are the Rademacher complexity of \\(\\mathcal{F}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Note that the bound of \\(\\Re (\\mathcal{F})\\) is inversely proportional to the number of training samples. Theorem 1 shows that the generalization error \\(\\mathcal{R}_d(\\hat{f}_{\\mathrm{prog}})\\) is bounded by the empirical training risk \\(\\hat{\\mathcal{R}}_{(d + p)}(\\hat{f}_{\\mathrm{prog}})\\), the two domain gap \\(\\gamma_{\\mathcal{F}}(D,P)\\) and the estimation error. The empirical training risk can be minimized to arbitrary small value when using deep models with high capacity. The estimation error that related to \\(N_{p}\\) asymptotically tends to 0 as the sample size \\(N_{p}\\) tends to infinity. Thanks to the large amount of pretrained samples" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15662" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.253, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.263, + 0.09, + 0.891, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.362, + 0.897, + 0.409 + ], + "angle": 0, + "content": "Figure 3: (a) If \\( G_{\\mathrm{d}} \\) is aligned with \\( G_{\\mathrm{g}} \\), we set \\( G_{\\mathrm{prograd}} \\) as \\( G_{\\mathrm{d}} \\). (b) If \\( G_{\\mathrm{d}} \\) conflicts with \\( G_{\\mathrm{g}} \\) (i.e., their angle is larger than \\( 90^{\\circ} \\)), we set \\( G_{\\mathrm{prograd}} \\) as the projection of \\( G_{\\mathrm{d}} \\) on the orthogonal direction of \\( G_{\\mathrm{g}} \\). (c) Training pipeline of our ProGrad. Only the context vectors are learnable." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.435, + 0.462, + 0.452 + ], + "angle": 0, + "content": "\\(N_{p}\\), we can approximate the generalization error bound as" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.458, + 0.47, + 0.531 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {R} _ {d} (\\hat {f} _ {\\text {p r o g r a d}}) \\leq \\frac {1}{2} \\gamma_ {\\mathcal {F}} (S, P) + \\Re_ {d} (\\mathcal {F}) \\\\ + \\frac {3}{2} \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2 N _ {d}}} + \\frac {1}{2} \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2} \\frac {1}{N _ {d}}}. \\tag {7} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.54, + 0.469, + 0.571 + ], + "angle": 0, + "content": "Similarly, we have the generalization error for CoOp \\(\\hat{f}_{\\mathrm{coop}}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.576, + 0.47, + 0.617 + ], + "angle": 0, + "content": "\\[\n\\mathcal {R} _ {d} \\left(\\hat {f} _ {\\text {c o o p}}\\right) \\leq 2 \\Re_ {d} (\\mathcal {F}) + 3 \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2 N _ {d}}} + \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2} \\frac {1}{N _ {d}}}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.473, + 0.737 + ], + "angle": 0, + "content": "Under the assumption that the gap between pre-trained and downstream domains \\(\\gamma (P,D)\\) is small, the estimation error bound of \\(\\mathcal{R}_d(\\hat{f}_{\\mathrm{coop}})\\) is at least two times greater than \\(\\mathcal{R}_d(\\hat{f}_{\\mathrm{prograd}})\\). Considering that \\(N_{d}\\) is typically very small in few-shot setting, our ProGrad model \\(\\hat{f}_{\\mathrm{prograd}}\\) achieves a much lower error bound than conventional fine-tuning model like CoOp \\(\\hat{f}_{\\mathrm{coop}}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.747, + 0.21, + 0.765 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.772, + 0.398, + 0.789 + ], + "angle": 0, + "content": "4.1. Datasets and Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.473, + 0.841 + ], + "angle": 0, + "content": "We validate the effectiveness of ProGrad on four settings: (1) few-shot classification, (2) domain generalization, (3) base-to-new generalization, (4) cross-dataset transfer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Datasets. For few-shot learning, base-to-new generalization and cross-dataset transfer, we use 11 datasets, i.e., ImageNet [6] and Caltech101 [9] for generic object classification, OxfordPets [33], StanfordCars [22], Flowers102 [32]," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.435, + 0.896, + 0.542 + ], + "angle": 0, + "content": "Food101 [2] and FGVCAircraft [30] for fine-grained image recognition, EuroSAT [13] for satellite image classification, UCF101 [47] for action classification, DTD [5] for texture classification, and SUN397 [50] for scene recognition. For domain generalization, we use ImageNet as the source dataset and select ImageNet-V2 [41], ImageNet-Sketch [49], ImageNet-A [15], ImageNet-R [14] as the target datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.555, + 0.895, + 0.798 + ], + "angle": 0, + "content": "Training Details. For few-shot learning, following CoOp and CLIP, all models are trained with \\(\\{1,2,4,8,16\\}\\) shots respectively then evaluated on the full test split. For domain generalization and base-to-new generalization, we evaluate 4-shot performance, which justifies the robustness under low-shots condition. All results of learning-based models are averaged over three random seeds. The standard deviation values can be found in the Appendix. Unless otherwise stated, we adhere to CoOp to use ResNet-50 [12] as the backbone of image encoder. Following [54] and [55], the length of context tokens \\(M\\) is set to 16 for few-shot classification and \\(M = 4\\) for the other three settings. \\(\\lambda\\) is set to 1 by default, except that \\(\\lambda\\) is set to 0.8 for 16 shots. We adopt the training settings from CoOp, e.g., training epochs, training schedule and the data augmentation settings, and refer readers to Appendix for further details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Baselines. We compare ProGrad against 4 methods: (1) Zero-shot CLIP (2) Linear probe (3) CoOp and (4) CoCoOp. Although our method can beat some other fine-tune methods, e.g., CLIP-Adapter [10], we focus on single prompt-based learning methods. The results of other fine-tuning methods are in Appendix." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15663" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.29, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.089, + 0.49, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.089, + 0.691, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.691, + 0.089, + 0.892, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.257, + 0.29, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.257, + 0.49, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.257, + 0.69, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.691, + 0.257, + 0.891, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.423, + 0.29, + 0.59 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.423, + 0.49, + 0.59 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.423, + 0.69, + 0.59 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.691, + 0.423, + 0.891, + 0.59 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.602, + 0.894, + 0.634 + ], + "angle": 0, + "content": "Figure 4: Accuracy \\((\\%)\\) of few-shot learning on 11 datasets. The context length \\(M\\) is set to 16. Standard deviations are reported in Appendix." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.659, + 0.295, + 0.675 + ], + "angle": 0, + "content": "4.2. Few-Shot Classification" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.686, + 0.471, + 0.837 + ], + "angle": 0, + "content": "Setup. We compare with two zero-shot CLIP models, i.e., CLIP and \\(\\mathrm{CLIP}++\\) stand for using single prompt and prompt ensembling respectively (Please refer to Appendix for the prompts templates). ProGrad and ProGrad++ stand for using single prompt and prompt ensembling as general knowledge to implement ProGrad respectively. Note that we only use the hand-crafted prompt ensembling to generate \\(G_{\\mathrm{g}}\\), which provides a more accurate general direction. Therefore, ProGrad++ still optimizes a single prompt with 16 learnable tokens, which is identical to the size of CoOp." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Table 1 provides averaged accuracy over 11 datasets, and Figure 4 illustrates the detailed comparisons. Overall, ProGrad clearly outperforms over baselines on average performance. Specifically, ProGrad outperforms CoOp" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.658, + 0.892, + 0.687 + ], + "angle": 0, + "content": "Table 1: Averaged accuracy \\((\\%)\\) of few-shot learning on 11 datasets. \\(M = 16\\)" + }, + { + "type": "table", + "bbox": [ + 0.524, + 0.699, + 0.875, + 0.814 + ], + "angle": 0, + "content": "
#shots0124816
CLIP58.77-----
CLIP++59.38-----
LP-37.3248.0257.2764.8870.57
CoOp-59.4662.3766.7970.0473.49
ProGrad-62.6164.9068.4571.4174.28
ProGrad++-63.0665.2868.7171.8075.03
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.903 + ], + "angle": 0, + "content": "by \\(9.5\\%\\), \\(6.9\\%\\) and \\(5.1\\%\\) on FGVCAircraft, EuroSAT and Flowers102 given 1 shot, and the average improvement is \\(3.2\\%\\). These results demonstrate the anti-overfitting ability of our ProGrad when the training samples are extremely" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15664" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.471, + 0.135 + ], + "angle": 0, + "content": "Table 2: Evaluation on robustness to distribution shift with different visual backbones. Standard deviations are reported in Appendix." + }, + { + "type": "table_caption", + "bbox": [ + 0.234, + 0.148, + 0.315, + 0.162 + ], + "angle": 0, + "content": "(a) ResNet50" + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.168, + 0.449, + 0.287 + ], + "angle": 0, + "content": "
SourceTarget
ImageNet-V2-Sketch-A-R
CLIP58.1851.3433.3221.6556.00
LP41.2933.6513.0911.1826.82
CoOp61.3453.8132.8322.0854.62
CoCoOp61.0453.7132.3022.0753.60
ProGrad62.1754.7034.4023.0556.77
" + }, + { + "type": "table_caption", + "bbox": [ + 0.229, + 0.289, + 0.318, + 0.301 + ], + "angle": 0, + "content": "(b) ResNet101" + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.309, + 0.449, + 0.428 + ], + "angle": 0, + "content": "
SourceTarget
ImageNet-V2-Sketch-A-R
CLIP61.2454.8238.6628.0364.34
LP47.0138.4619.0916.3339.43
CoOp63.9956.9939.4029.5064.04
CoCoOp63.5956.9839.1629.0964.14
ProGrad64.9857.8640.5330.1365.61
" + }, + { + "type": "table_caption", + "bbox": [ + 0.235, + 0.429, + 0.313, + 0.442 + ], + "angle": 0, + "content": "(c) ViT-B/32" + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.45, + 0.449, + 0.567 + ], + "angle": 0, + "content": "
SourceTarget
ImageNet-V2-Sketch-A-R
CLIP62.0054.7540.8229.5966.01
LP46.7739.1220.3216.3239.48
CoOp64.7456.5940.0331.1064.54
CoCoOp64.6356.5940.7430.2764.12
ProGrad65.3657.4241.7331.8966.53
" + }, + { + "type": "table_caption", + "bbox": [ + 0.235, + 0.569, + 0.313, + 0.582 + ], + "angle": 0, + "content": "(d) ViT-B/16" + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.589, + 0.449, + 0.71 + ], + "angle": 0, + "content": "
SourceTarget
ImageNet-V2-Sketch-A-R
CLIP66.7360.8446.1347.8074.01
LP54.7045.5728.2022.4744.12
CoOp69.8662.8346.9048.9874.55
CoCoOp70.1363.0546.4849.3673.80
ProGrad70.4563.3548.1749.4575.21
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.471, + 0.824 + ], + "angle": 0, + "content": "limited. Furthermore, leveraging prompt ensembling can further explore the potential of ProGrad. From Table 1, with more accurate general knowledge offered by prompt ensembling, \\(\\mathrm{CLIP}++\\) improves the zero-shot CLIP from \\(58.77\\%\\) to \\(59.38\\%\\); ProGrad++ increases the accuracy of ProGrad from \\(74.28\\%\\) to \\(75.03\\%\\) at 16 shots." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.294, + 0.848 + ], + "angle": 0, + "content": "4.3. Domain Generalization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We train our ProGrad on the source dataset (ImageNet) for three different random seeds, and assess it on ImageNet-V2, ImageNet-Sketch, ImageNet-A, and ImageNet-R. This" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.304 + ], + "angle": 0, + "content": "setting evaluates the generalizability on a target domain which differs from the source domain. Fine-tuning on limited data from a specific domain may mislead the model to learn spurious correlations or in-distribution patterns, resulting in biased models with poor performance in unseen domains. In contrast, zero-shot CLIP avoids exploiting such spurious correlations or patterns, as it is not learned on that distribution. By leveraging knowledge from the pre-trained domain to regularize fine-tuning on a specific distribution, our ProGrad method is expected to be robust to distribution shifts. As shown in Table 2, despite the exposure to the source dataset, ProGrad clearly outperforms other methods on all target datasets as well as the source dataset with ResNet-based and ViT-based backbones." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.313, + 0.753, + 0.328 + ], + "angle": 0, + "content": "4.4. Base-to-New Generalization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.336, + 0.682, + 0.501 + ], + "angle": 0, + "content": "We follow CoCoOp [55] to evaluate the generalization performance from seen classes to unseen classes. All the classes are equally divided into two groups, i.e., base classes and new classes, and all methods are only trained on base classes and tested on both base classes and new classes." + }, + { + "type": "table_caption", + "bbox": [ + 0.686, + 0.345, + 0.894, + 0.391 + ], + "angle": 0, + "content": "Table 3: Averaged accuracy \\((\\%)\\) over 11 datasets for base-to-new generalization." + }, + { + "type": "table", + "bbox": [ + 0.687, + 0.402, + 0.892, + 0.488 + ], + "angle": 0, + "content": "
BaseNewH.
CLIP61.7265.9163.64
CoOp71.9661.2665.58
CoCoOp72.2360.7765.35
ProGrad73.2965.9669.06
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.503, + 0.895, + 0.624 + ], + "angle": 0, + "content": "The harmonic mean of base classes and new classes accuracies is reported to evaluate the trade-off. As illustrated in Table 3, ProGrad yields the highest average performance across all metrics, whereas CoOp and CoCoOp exhibit poor performance for new classes, consistently underperforming zero-shot CLIP. These results highlight that ProGrad's superior generalizability to both base and new classes. The detailed results of 11 datasets are in Appendix." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.633, + 0.716, + 0.648 + ], + "angle": 0, + "content": "4.5. Cross-Dataset Transfer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.894, + 0.763 + ], + "angle": 0, + "content": "All models are trained on ImageNet as source dataset and evaluated on the rest 10 target datasets. The goal of this setting is to demonstrate the potential to transfer beyond a single dataset. The results are presented in Table 4. As shown, our ProGrad not only achieves the highest performance on source datasets but also outperforms other baselines 9 out of 10 target datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.667, + 0.789 + ], + "angle": 0, + "content": "4.6. Further Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Comparison with Learning without Forgetting (LwF). ProGrad employs the gradient direction of knowledge distillation loss as a form of regularization. To determine whether our approach is equivalent to conventional knowledge distillation, we compared its performance against a simple knowledge distillation method, i.e., \\(\\mathcal{L}_{\\mathrm{total}} = \\mathcal{L}_{\\mathrm{ce}} + \\alpha \\cdot \\mathcal{L}_{\\mathrm{kd}}\\) which is identical to the implementation of Learning without" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15665" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.121 + ], + "angle": 0, + "content": "Table 4: Comparison of prompt learning methods in the cross-dataset transfer setting. Prompts are learned from 4-shots ImageNet." + }, + { + "type": "table", + "bbox": [ + 0.145, + 0.131, + 0.832, + 0.283 + ], + "angle": 0, + "content": "
SourceTarget
ImageNetCaltech101OxfordPetsStanfordCarsFlowers102Food101FGVCAircraftSUN397DTDEuroSATUCF101Average
CoOp61.3484.4885.9954.1660.1075.4814.0957.4835.3226.7257.5655.70
CoCoOp61.0484.7386.4252.3461.2473.7913.7455.9436.6023.4657.9755.21
ProGrad62.1788.3086.4355.6162.6976.7615.7660.1639.4824.8758.7057.36
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.304, + 0.471, + 0.334 + ], + "angle": 0, + "content": "Table 5: Comparison with LwF (knowledge distillation). Average accuracy \\((\\%)\\) over 11 datasets." + }, + { + "type": "table", + "bbox": [ + 0.089, + 0.345, + 0.441, + 0.475 + ], + "angle": 0, + "content": "
#shots124816
CoOp59.4662.3766.7970.0473.49
LwF(KD), α = 0.2561.0963.0167.7470.9073.39
LwF(KD), α = 0.561.1363.3667.1470.3472.68
LwF(KD), α = 161.5264.0766.5270.0172.01
LwF(KD), α = 260.9862.6664.9267.7868.98
LwF(KD), α = 459.5861.7662.9265.0165.42
ProGrad62.6164.9068.4571.4174.28
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.481, + 0.47, + 0.511 + ], + "angle": 0, + "content": "Table 6: Applying ProGrad to cosine classifier. Average accuracy \\((\\%)\\) over 11 datasets." + }, + { + "type": "table", + "bbox": [ + 0.124, + 0.522, + 0.426, + 0.582 + ], + "angle": 0, + "content": "
#shots124816
Cosine30.5043.7453.3361.2665.00
+ProGrad32.2946.1455.1862.0566.47
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.611, + 0.47, + 0.748 + ], + "angle": 0, + "content": "Forgetting (LwF)[24]. We repeated few-shot experiments on 11 datasets using a range of \\(\\alpha\\) values and report the average results in Table 5. The results demonstrate that ProGrad outperforms KD for various few-shot settings. Although KD (LwF) with small \\(\\alpha \\leq 1\\) improves the performance of CoOp in low-shot scenarios (e.g., 1, 2, and 4 shots), its performance drops when the shots is large (i.e., 8 and 16 shots). These findings suggest that ProGrad operates differently from KD (LwF) and is more robust to the sample number." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Failure cases. We analyze cases where ProGrad models fail while CoOp succeeds. In specific, we count the percentage of the failure cases that zero-shot CLIP models also fails in Figure 5. We found that a high proportion of the failure cases are also mis-classified by zero-shot CLIP model (red bar in Figure 5), implying that the imprecision of zero-shot general knowledge represented by \\( G_{\\mathrm{g}} \\) is detrimental to model generalization. As sample size increases, \\( G_{\\mathrm{d}} \\) represents downstream knowledge more accurately and with less bias. As expected, the red bar becomes larger." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.304, + 0.692, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.304, + 0.889, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.422, + 0.893, + 0.454 + ], + "angle": 0, + "content": "Figure 5: Distribution of samples that are mis-classified by ProGrad but correctly classified by CoOp." + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.473, + 0.697, + 0.586 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.582, + 0.587, + 0.638, + 0.599 + ], + "angle": 0, + "content": "(a) 1 shot" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.473, + 0.892, + 0.586 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.773, + 0.587, + 0.834, + 0.598 + ], + "angle": 0, + "content": "(b) 2 shots" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.611, + 0.892, + 0.641 + ], + "angle": 0, + "content": "Figure 6: Angles between \\( G_{\\mathrm{d}} \\) and \\( G_{\\mathrm{g}} \\) during training on StanfordCars and Caltech101." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Conflict of knowledge. ProGrad requires the updated gradient direction be acute to the general knowledge gradient directions. We explore how this constraint helps to defuse the conflicts of domain-specific and general knowledge by visualizing the angle between their representative gradients during training (angle between \\( G_{\\mathrm{d}} \\) and \\( G_{\\mathrm{g}} \\)). As depicted in Figure 6, without \\( G_{\\mathrm{prograd}} \\), the angle between \\( G_{\\mathrm{d}} \\) and \\( G_{\\mathrm{g}} \\) converges to 90 degrees due to the fact that \"all high-dimensional random vectors are almost always orthogonal to each other\" [3]. Intuitively, without any constraint, the optimization direction \\( G_{\\mathrm{d}} \\) is independent of the general direction, and the average angle would be orthogonal. In contrast, utilizing \\( G_{\\mathrm{prograd}} \\) results in the convergence of the angle to an obtuse angle. The reason is that \\( G_{\\mathrm{prograd}} \\) intervenes the model to learn the downstream knowledge aligned with the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15666" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.182 + ], + "angle": 0, + "content": "general knowledge and leads to the insufficient learning of downstream knowledge that is incompatible with the general knowledge. As training stabilizes, \\( G_{\\mathrm{d}} \\) struggles to learn the conflicting knowledge, reflecting an obtuse angle to the \\( G_{\\mathrm{g}} \\). Thanks to ProGrad, we discard such conflicting knowledge to avoid forgetting." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.183, + 0.293, + 0.197 + ], + "angle": 0, + "content": "Upper Bound of Performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.198, + 0.277, + 0.422 + ], + "angle": 0, + "content": "As the general gradient direction \\( G_{g} \\) is the key for improvement, we are interested in the upper-bound of performance if we can find an oracle general direction \\( G_{g}^{\\mathrm{full}} \\) instead of the one offered by hand-crafted prompt. To achieve this, we first optimize a prompt with plain cross-entropy loss on the full dataset to create \\( G_{g}^{\\mathrm{full}} \\) and then use such gradient to implement ProGrad. The averaged performance over 11 datasets, as" + }, + { + "type": "image", + "bbox": [ + 0.281, + 0.205, + 0.468, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.278, + 0.368, + 0.472, + 0.414 + ], + "angle": 0, + "content": "Figure 7: The upper bound of performance (averaged accuracy) of GradPrad." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.472, + 0.469 + ], + "angle": 0, + "content": "shown in Figure 7, indicate a more accurate regularization direction \\( G_{g}^{\\mathrm{full}} \\) elicits a stronger ProGrad model. The detailed results of 11 datasets are in Appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.469, + 0.472, + 0.605 + ], + "angle": 0, + "content": "Applying ProGrad to conventional fine-tuning. We are also interested in the effectiveness of ProGrad for the conventional \"pre-train then fine-tune\" paradigm. Specifically, we plug in an additional cosine classifier on top of the visual backbone and compare the averaged performance over 11 datasets of few-shot classification. Table 6 shows that conventional fine-tuning can benefit from our ProGrad. The implementation details and the result of each dataset are provided in Appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.605, + 0.472, + 0.801 + ], + "angle": 0, + "content": "Effect of hyper-parameter \\(\\lambda\\). We further analyze the effect of the hyper-parameter \\(\\lambda\\) described in Eq. (4) in the main paper. Results are shown in Table 7. As discussed in Section 3.2 in the main paper, a smaller \\(\\lambda\\) weakens the general knowledge regularization, which results in a inferior performance under low-shot setting for most datasets. However, for DTD in Table 7, using a smaller \\(\\lambda = 0.9\\) to reduce the general knowledge regularization can improve the 16 shots results. One possible reason is that texture images of DTD has large gap with the CLIP pre-trained images that collected from the Internet, stronger regularization from pre-trained knowledge might be detrimental to the fine-tune performance if downstream data is sufficient." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.815, + 0.196, + 0.831 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.473, + 0.902 + ], + "angle": 0, + "content": "In this paper, we pointed out the over-fitting issues of existing prompt tuning methods for few-shot generalization, which heavily relies on early stopping and data augmentation. We proposed a prompt tuning method ProGrad that" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.119 + ], + "angle": 0, + "content": "Table 7: Accuracy \\((\\%)\\) of 1, 2, 4, 8, and 16 shots training with different \\(\\lambda\\) on DTD and OxfordPets." + }, + { + "type": "table_caption", + "bbox": [ + 0.657, + 0.133, + 0.755, + 0.146 + ], + "angle": 0, + "content": "(a) OxfordPets." + }, + { + "type": "table", + "bbox": [ + 0.562, + 0.153, + 0.85, + 0.266 + ], + "angle": 0, + "content": "
λ1 shot2 shots4 shots8 shots16 shots
086.0182.2186.6385.1587.06
0.287.1283.1684.8784.0086.15
0.488.0983.5685.5084.0486.67
0.787.7484.7086.9386.3087.90
0.988.2686.4787.5287.3888.52
1.088.3686.8988.0487.9189.00
" + }, + { + "type": "table_caption", + "bbox": [ + 0.677, + 0.267, + 0.735, + 0.28 + ], + "angle": 0, + "content": "(b) DTD." + }, + { + "type": "table", + "bbox": [ + 0.562, + 0.288, + 0.851, + 0.401 + ], + "angle": 0, + "content": "
λ1 shot2 shots4 shots8 shots16 shots
044.3346.2254.0859.9962.89
0.243.8045.2154.0260.1463.61
0.444.1747.4454.3259.6563.16
0.744.9347.7754.9259.2863.10
0.945.7848.4655.4460.4664.28
1.046.1449.7854.4357.9861.15
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.43, + 0.895, + 0.537 + ], + "angle": 0, + "content": "regularize each tuning step not to conflict with the general knowledge of the hand-crafted prompt. Experiments on few-shot classification, base-to-new generalization, domain generalization and cross-dataset transfer over 11 datasets demonstrate the effectiveness and efficiency of our ProGrad. In the future, we will explore how to apply ProGrad on other tasks like object detection and segmentation." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.554, + 0.66, + 0.571 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.895, + 0.657 + ], + "angle": 0, + "content": "This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-PhD-2021-01-002). 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AAAI, 2023. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.893, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15669" + } + ] +] \ No newline at end of file diff --git a/2023/Prompt-aligned Gradient for Prompt Tuning/7786570f-2ec2-4f85-a04c-e553c7832bc6_origin.pdf b/2023/Prompt-aligned Gradient for Prompt Tuning/7786570f-2ec2-4f85-a04c-e553c7832bc6_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..6ed824089d2339d9b1b3d8de2ec5902496bdc03d --- /dev/null +++ b/2023/Prompt-aligned Gradient for Prompt Tuning/7786570f-2ec2-4f85-a04c-e553c7832bc6_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:91314ae3a0a586f45cfdfb1526333d95854ab484795feb8187b29808faeccff9 +size 4397894 diff --git a/2023/Prompt-aligned Gradient for Prompt Tuning/full.md b/2023/Prompt-aligned Gradient for Prompt Tuning/full.md new file mode 100644 index 0000000000000000000000000000000000000000..14917cc697a92fdfdc150866874f12940069d82c --- /dev/null +++ b/2023/Prompt-aligned Gradient for Prompt Tuning/full.md @@ -0,0 +1,364 @@ +# Prompt-aligned Gradient for Prompt Tuning + +Beier Zhu1 Yulei Niu2 Yucheng Han1 Yue Wu3 Hanwang Zhang1* + +$^{1}$ Nanyang Technological University $^{2}$ Columbia University $^{3}$ Damo Academy, Alibaba Group + +beier002@e.ntu.edu.sg, yn.yuleiniu@gmail.com yucheng002@e.ntu.edu.sg + +matthew.wy@alibaba-inc.com hanwangzhang@ntu.edu.sg + +# Abstract + +Thanks to the large pre-trained vision-language models (VLMs) like CLIP [37], we can craft a zero-shot classifier by discrete prompt design, e.g., the confidence score of an image being "[CLASS]" can be obtained by using the VLM provided similarity between the image and the prompt sentence "a photo of a [CLASS]". Furthermore, prompting shows great potential for fast adaptation of VLMs to downstream tasks if we fine-tune the soft prompts with few samples. However, we find a common failure that improper fine-tuning or learning with extremely few-shot samples may even under-perform the zero-shot prediction. Existing methods still address this problem by using traditional anti-overfitting techniques such as early stopping and data augmentation, which lack a principled solution specific to prompting. In this paper, we present Prompt-aligned Gradient, dubbed ProGrad to prevent prompt tuning from forgetting the general knowledge learned from VLMs. In particular, ProGrad only updates the prompt whose gradient is aligned (or non-conflicting) to the general knowledge, which is represented as the optimization direction offered by the pre-defined prompt predictions. Extensive experiments under the few-shot learning, domain generalization, baseto-new generalization and cross-dataset transfer settings demonstrate the stronger few-shot generalization ability of ProGrad over state-of-the-art prompt tuning methods. + +# 1. Introduction + +After seeing and reading countless image-text association pairs, large and deep vision-language models (VLM) [37, 18] can memorize the general knowledge (a.k.a. encyclopedic knowledge) about what visual patterns correspond to what textual sequence and vice versa. Thanks to the powerful language modeling of VLMs, we can establish a communication channel in human-readable natural language, i.e., prompt [25, 51, 19], to query the general knowledge. + +Prompting bridges the interface gap between the pre-trained and downstream tasks (e.g., regression vs. classification) without the need for additional fine-tuning adaptation. For example, we can craft a concrete prompt—"a photo of a [CLASS]"—for zero-shot image classification: by using the popular vision-language model CLIP [37], we input the image to the vision end and the prompt sentence to the language end, then obtain a vision-language similarity as the confidence score of classifying the image as "[CLASS]". + +In practice, the prompt-based zero-shot image classification is not accurate because the hand-crafted prompt may not be the most machine-favorable (e.g., "this is a picture of" could be more grammatically prevailing in VLM training), or not specific to the downstream domain (e.g., "a photo of a person doing" is better in action recognition) [37]. Recently, prompt tuning or prefix tuning [23, 26, 54, 55] has been proposed to replace the handcrafted prompt with a set of tunable word embedding vectors, which do not have to be translatable back to human-readable words. Yet, prompt tuning is still as tricky as conventional fine-tuning: as the training continues, the generalization ability may decrease and even under-perform the zero-shot baseline. As shown in Figure 1(a&b), the prompt tuning method CoOp [54] achieves the best results via early stopping, and its accuracies heavily drop by at most $4\%$ when the training continues. Besides, Figure 1(c&d) show that CoOp underperforms zero-shot CLIP without augmentation or enough samples from downstream tasks. To the best of our knowledge, existing methods still rely on the conventional anti-overfitting techniques such as early stopping and data augmentation [54, 55, 11, 36], which lacks a principled solution to the nature of improper prompt tuning. Furthermore, the Grad-CAM visualization results indicate that the fine-tuned prompt misleads the VLM to forget the general knowledge that the classification should at least focus on the foreground object but not the background. Comparing CoOp (Figure 2(b)) with zero-shot CLIP (Figure 2(c)), we find that the CoOp model distracts its attention to the background, while CLIP mainly focuses on the foreground object. These results demonstrate the over-fitting risk of existing prompt + +![](images/6dec5c597949dd7a192e765da9f21fc01ef71921e0cfd522cbd56e2d21d99d93.jpg) +(a) + +![](images/49900bff427d46d74be1ce14c0d844163eb1b7b8e1abe16330744ef01658ef0f.jpg) +(b) + +![](images/7acf57b79896358ce050094d546b46b4a2793682a02e39ab5e253e2fd1e79c41.jpg) +(c) + +![](images/2bdc7a1dff0e53c8194a3b7a4f6c6e4371d0e5a1247734bb84db3a41d4851847.jpg) +(d) + +![](images/5f0567276f17fb59eabfc055f5bf605d123755a6635b983e706ce691dcfa1f07.jpg) +Figure 1: Comparison of Zero-shot CLIP, CoOp, and our ProGrad on Stanford Cars and OxfordPets datasets. (a)&(b): Given 1 shot training sample, CoOp's performance severely drops and under-performs zero-shot CLIP by large margins when the training continues. (c)&(d): CoOp may fail to improve CLIP without data augmentation or plenty of samples. +Figure 2: Comparisons of Grad-CAM [43] visualization for prompt tuning methods using different gradient strategies on Stanford Cars Datasets. + +tuning strategies, especially when the number of training samples is extremely limited (e.g., 1 or 2). + +To this end, we present a novel prompt tuning method called Prompt-aligned Gradient (ProGrad) to overcome the improperly biased tuning for CLIP. The principle of ProGrad is to regularize each tuning step not to conflict with the general knowledge offered by the original prompt, e.g., the zero-shot CLIP predictions. Specifically, we measure the general knowledge direction $G_{\mathrm{g}}$ using the gradient of Kullback-Leibler (KL) divergence between the predictions of the zero-shot prompted CLIP and the few-shot fine-tuned model, which we name as general direction. Similarly, we compute the domain-specific knowledge direction $G_{\mathrm{d}}$ using the gradient of cross-entropy between the ground-truth and the few-shot fine-tuned model, dubbed domain-specific direction. We decompose the domain-specific direction $G_{\mathrm{d}}$ into: 1) a vector $G_{\perp}$ orthogonal to the general direction, which denotes the non-conflicting domain-specific knowl + +edge; and 2) a vector $G_{\parallel}$ parallel to the general direction, which denotes the general knowledge. Note that the first gradient component does NOT override the general direction as any two orthogonal vectors can be transformed into two nonconflicting base vectors. For the second component, it must be one of the two directions: 1) the same of the general direction, which indicates that the update is aligned to the general knowledge, and 2) the opposite of general direction, indicating a conflicting update that should be discarded to avoid forgetting. Overall, in each iteration, ProGrad only updates the parameters in the prompt-aligned direction that has an acute angle to the general direction. Compared to CoOp and CLIP, both $G_{g}$ and $G_{\perp}$ (Figure 2(d&e)) help to regularize the model to focus on the foreground, and ProGrad (Figure 2(f)) further improves the visual response. + +Following CLIP, CoOp and CoCoOp [55], we evaluate ProGrad under the few-shot learning, domain generalization, base-to-new generalization and cross-dataset transfer + +settings over 15 image classification benchmarks, covering generic object classification, fine-grained image recognition, action classification. In summary, our ProGrad achieves: 1) clear improvement compared to CoOp over all of the 11 datasets; 2) clear improvement on the harmonic mean of base and new classes accuracies on all 11 datasets compared to CoOp and CoCoOp, and 3) clear improvement on both the source and target datasets of the domain generalization. + +# 2. Related Work + +VLMs Adaptation. VLM can be adapted for various downstream tasks, e.g., visual question answering [21, 48], visual grounding [51], image retrieval [28] and semantic segmentation [39]. We focus on image classification task. Conventional "pre-train then fine-tune" paradigm that plugs in a classifier to the visual backbone and trained on downstream data has been widely-adopted, e.g., Linear Probe [37]. CLIP-Adapter [10] add feature adapters to boost fine-tuning results. Recently, NLP community has introduced a "prompt-based learning" paradigm that fine-tunes the prompt using a "fill-in-the-blank" cloze test to maximize the ground-truth token [23, 26]. The prompt-based learning has recently been applied in CV community [54, 29, 7, 46, 4, 20, 56]: CoOp [54] uses a continuous prompt optimization from downstream data instead of hand-craft design. CoCoOp [55] further extends CoOp by learning image conditional prompt to improve generalization. ProDA [29] learns a prompt distribution over the output embedding space. VPT [7] introduces variational prompt tuning by combining a base learned prompt with a residual vector sampled from a instance-specific underlying distribution. TPT [46] proposes a test-time prompt tuning, which does not require training data and optimizes the prompt to achieve consistent predictions across different augmented views. Our ProGrad follows the line of prompt-based learning to improve few-shot generalization ability by aligning the gradient to general direction, without model structure modification or tuning the pre-trained parameters. + +Knowledge Transfer. Forgetting mitigation is widely used in incremental learning [27, 40, 35, 42, 17] through knowledge distillation or memory replay. However, prompt-based learning differs fundamentally from incremental learning in that it does not have access to pre-trained data, which is required for incremental learning to store old data from memory storage. For example, OGD [8] projects gradients from new classes to the orthogonal direction of previous task gradients, but the requirement to store old task gradients is not possible for prompt tuning since we lack access to the pre-training process. Moreover, OGD modifies gradients of downstream tasks in non-conflicting scenarios, potentially leading to sub-optimal performance. Another related field that leverages gradient matching to transfer knowledge is domain generalization [45, 38] and multi-task learning [44, 52]. + +However, these methods are not directly applicable in prompt tuning whose transfer direction is only from general to downstream. In Appendix, we will show how their methods fail in several ablative studies. + +# 3. Methodology + +In this section, we introduce the preliminary concepts of prompt-based zero-shot inference, prompt-based learning, and present our proposed Prompt-aligned Gradient solution to align the domain knowledge with general knowledge for few-shot generalization. + +# 3.1. Preliminaries + +Contrastive language-image pre-training (CLIP) [37] adopts a contrastive language-image pre-training paradigm on tremendous pairs of images with natural language descriptions. For contrastive learning, the associated image and sentences are taken as the positive samples, while the non-associated pairs are regarded as negative samples. The contrastive objective maximizes the similarity of positive pairs while minimize the similarity of negative pairs. + +Zero-shot transfer inference adapts the pre-trained CLIP model to downstream tasks without fine-tuning the model. Taking image classification as an example, zero-shot transfer is enabled by formulating the classification task as an image-text matching problem, where the text is obtained by extending the "[CLASS]" name using a template like "a photo of a [CLASS]". CLIP [37] finds that such a simple template narrows the distribution gap to pre-training text inputs. The image-class matching score is measured based on the cosine similarity $< \pmb{w}_i$ , $f >$ between the image feature $\pmb{f}$ and the class-extended text feature $\pmb{w}_i$ for $i$ -th class. The image feature $\pmb{f}$ for image $\pmb{x}$ is extracted by the image encoder, while the text feature $\pmb{w}_i$ for $i$ -th class is obtained by feeding the prompt description into the text encoder. The probability for $i$ -th class is obtained as + +$$ +p _ {\mathrm {z s}} (\boldsymbol {w} _ {i} | \boldsymbol {x}) = \frac {\exp \left(< \boldsymbol {w} _ {i} , \boldsymbol {f} > / \tau\right)}{\sum_ {j = 1} ^ {K} \exp \left(< \boldsymbol {w} _ {j} , \boldsymbol {f} > / \tau\right)}, \tag {1} +$$ + +where $K$ denotes the number of classes, and $\tau$ is a temperature learned by CLIP. + +Prompt-based learning further strengths the transferring ability of the CLIP model and avoids prompt engineering by automatically learning the prompt given few samples from the downstream task. Different from the zero-shot transfer that used a fixed hand-craft prompt, CoOp [54] constructs and fine-tunes a set of $M$ continuous context vectors $\pmb{v} = \{\pmb{v}_1,\pmb{v}_2,\dots,\pmb{v}_M\}$ as the turnable prompt. Specifically, the prompt $\pmb{t}_i = \{\pmb{v}_1,\pmb{v}_2,\dots,\pmb{v}_M,\pmb{c}_i\}$ combines the learnable context vectors $\pmb{v}$ and the class token embedding $\pmb{c}_i$ , and is fed to the text encoder $g(\cdot)$ . CoOp optimizes the static context vectors $\pmb{v}$ by minimizing the negative log-likelihood + +of the ground-truth token: + +$$ +\mathcal {L} _ {\mathrm {c e}} (\boldsymbol {v}) = - \sum_ {i} \boldsymbol {y} _ {i} \log p (\boldsymbol {t} _ {i} | \boldsymbol {x}), +$$ + +$$ +p \left(\boldsymbol {t} _ {i} \mid \boldsymbol {x}\right) = \frac {\exp \left(< g \left(\boldsymbol {t} _ {i}\right) , \boldsymbol {f} > / \tau\right)}{\sum_ {j = 1} ^ {K} \exp \left(< g \left(\boldsymbol {t} _ {j}\right) , \boldsymbol {f} > / \tau\right)}, \tag {2} +$$ + +where $\mathbf{y}$ denotes the one-hot ground-truth annotation and $K$ denotes the number of classes. + +# 3.2. Prompt-aligned Gradient + +CoOp faced a challenge that the transfer performance drops when the number of annotations is very limited (e.g., one per class), even underperforms the zero-shot transfer. Also, CoOp heavily relies on anti-overfitting techniques such as early stopping and data augmentation. To overcome the over-fitting challenge, we propose an effective and efficient fine-tuning paradigm ProGrad to align the few-shot downstream knowledge with the large-scale general knowledge. + +Motivated by the success of knowledge distillation [34, 16] in knowledge transfer, we leverage the zero-shot CLIP predictions as the general knowledge, and compare the finetuned predictions with the general knowledge to regularize the gradient direction. Specifically, we obtain the domain-specific direction by calculating the cross-entropy $\mathcal{L}_{\mathrm{ce}}(\boldsymbol{v})$ between the model prediction $p(\boldsymbol{t}_i|\boldsymbol{x})$ and the ground-truth $\boldsymbol{y}$ according to Eq. (2), and the general knowledge direction based on the Kullback-Leibler (KL) divergence between $p(\boldsymbol{t}_i|\boldsymbol{x})$ and the zero-shot CLIP prediction $p_{\mathrm{zs}}(\boldsymbol{w}_i|\boldsymbol{x})$ : + +$$ +\mathcal {L} _ {\mathrm {k l}} (\boldsymbol {v}) = - \sum_ {i} p _ {\mathrm {z s}} \left(\boldsymbol {w} _ {i} | \boldsymbol {x}\right) \log \frac {p \left(\boldsymbol {t} _ {i} \mid \boldsymbol {x}\right)}{p _ {\mathrm {z s}} \left(\boldsymbol {w} _ {i} \mid \boldsymbol {x}\right)}. \tag {3} +$$ + +We denote the gradients of $\mathcal{L}_{\mathrm{kl}}(\pmb{v})$ and $\mathcal{L}_{\mathrm{ce}}(\pmb{v})$ as $G_{\mathrm{g}} = \nabla_{\pmb{v}}\mathcal{L}_{\mathrm{kl}}(\pmb{v})$ and $G_{\mathrm{d}} = \nabla_{\pmb{v}}\mathcal{L}_{\mathrm{ce}}(\pmb{v})$ , respectively. The relations between $G_{\mathrm{g}}$ and $G_{\mathrm{d}}$ are two-fold. (1) Their angle is smaller than $90^{\circ}$ (Figure 3(a)), which indicates that the optimization direction of few-shot downstream knowledge does not conflict with general knowledge. In this case, we safely set the updated gradient direction $G_{\mathrm{prograd}}$ as $G_{\mathrm{d}}$ . (2) Their angle is larger than $90^{\circ}$ (Figure 3(b)), which indicates that the few-shot downstream knowledge conflicts with general knowledge. In other words, optimizing the context vectors following $G_{\mathrm{d}}$ will lead to the forgetting of the pre-trained general knowledge. In this case, we project the $G_{\mathrm{d}}$ to the orthogonal direction of $G_{\mathrm{g}}$ to optimize the model for classification, which avoids increasing the KL loss. Our ProGrad strategy is mathematically formulated as: + +$$ +\boldsymbol {G} _ {\text {p r o g r a d}} = \left\{ \begin{array}{l l} \boldsymbol {G} _ {\mathrm {d}}, & \text {i f} \boldsymbol {G} _ {\mathrm {d}} \cdot \boldsymbol {G} _ {\mathrm {g}} \geq 0 \\ \boldsymbol {G} _ {\mathrm {d}} - \lambda \cdot \frac {\boldsymbol {G} _ {\mathrm {d}} \cdot \boldsymbol {G} _ {\mathrm {g}}}{\| \boldsymbol {G} _ {\mathrm {g}} \| ^ {2}} \boldsymbol {G} _ {\mathrm {g}}, & \text {o t h e r w i s e .} \end{array} \right. \tag {4} +$$ + +Fig 3(c) illustrates the pipeline of our ProGrad. Instead of updating the context vectors using $G_{\mathrm{d}}$ in CoOp [54], we optimize the context vectors using $G_{\mathrm{prograd}}$ , which prevent the + +gradient direction from overfitting to few-shot downstream samples. We further introduce $\lambda$ in Eq. (4) to generalize the formulation, which can flexibly control the strength of general knowledge guidance in applications. In particular, $\lambda = 1$ denotes projecting $G_{\mathrm{d}}$ to the orthogonal direction of $G_{\mathrm{g}}$ (Figure 3(b)), while setting $\lambda = 0$ makes ProGrad degenerate to CoOp, i.e., CoOp is a special case of our strategy. We include the detailed analysis of $\lambda$ in Appendix. + +Generalization Error Analysis. We further theoretically analyze the generalization error of our ProGrad. Here, we provide a sketch proof and include the detailed justification in Appendix. Our ProGrad keeps the optimal value $\mathcal{L}_{\mathrm{kl}}$ of the pre-trained domain when optimizing the empirical risk on the downstream domain. The model $\hat{f}_{\mathrm{prograd}}$ learned by such update rule can be viewed as optimizing the empirical risk on pre-trained and downstream domains [52]: + +$$ +\hat {f} _ {\text {p r o g r a d}} = \underset {f \in \mathcal {F}} {\operatorname {a r g m i n}} \hat {\mathcal {R}} _ {(d + p)} (f) = \underset {f \in \mathcal {F}} {\operatorname {a r g m i n}} \hat {\mathcal {R}} _ {d} (f) + \hat {\mathcal {R}} _ {p} (f), \tag {5} +$$ + +where $\mathcal{F}$ is the function class, and $\mathcal{R}(\cdot)$ and $\hat{\mathcal{R}} (\cdot)$ denote the expected risk and empirical risk. We bound the generalization error of ProGrad by virtue of Rademacher Complexity [1] and the Theorem 6.2 in [53]. The detailed proof is in Appendix. + +Theorem 1 Let $\mathbf{X}_1^{N_d} = \{\mathbf{x}_n^{(d)}\}_{n=1}^{N_d}$ and $\mathbf{X}_1^{N_p} = \{\mathbf{x}_n^{(p)}\}_{n=1}^{N_p}$ be two sets of i.i.d. samples drawn from the downstream domain $\mathcal{D}_d$ and the pre-trained domain $\mathcal{D}_p$ . Then for any $\epsilon > 0$ , we have with probability at least $1 - \epsilon$ , + +$$ +\begin{array}{l} \mathcal {R} _ {d} (\hat {f} _ {\text {p r o g r a d}}) \leq \hat {\mathcal {R}} _ {(d + p)} (\hat {f} _ {\text {p r o g r a d}}) + \frac {1}{2} \gamma_ {\mathcal {F}} (D, P) \\ + \Re_ {p} (\mathcal {F}) + \Re_ {d} (\mathcal {F}) + \frac {3}{2} \sqrt {\frac {\ln (4 / \epsilon)}{2 N _ {d}}} \\ + \frac {3}{2} \sqrt {\frac {\ln (4 / \epsilon)}{2 N _ {p}}} + \frac {1}{2} \sqrt {\frac {\ln (4 / \epsilon)}{2} \left(\frac {1}{N _ {d}} + \frac {1}{N _ {p}}\right)}, \tag {6} \\ \end{array} +$$ + +where $\gamma_{\mathcal{F}}(D,P)$ is the integral probability metric [31] that measures the difference between the distribution of pretrained domain and the downstream domain, $\Re_d(\mathcal{F})$ and $\Re_p(\mathcal{F})$ are the Rademacher complexity of $\mathcal{F}$ . + +Note that the bound of $\Re (\mathcal{F})$ is inversely proportional to the number of training samples. Theorem 1 shows that the generalization error $\mathcal{R}_d(\hat{f}_{\mathrm{prog}})$ is bounded by the empirical training risk $\hat{\mathcal{R}}_{(d + p)}(\hat{f}_{\mathrm{prog}})$ , the two domain gap $\gamma_{\mathcal{F}}(D,P)$ and the estimation error. The empirical training risk can be minimized to arbitrary small value when using deep models with high capacity. The estimation error that related to $N_{p}$ asymptotically tends to 0 as the sample size $N_{p}$ tends to infinity. Thanks to the large amount of pretrained samples + +![](images/4a9d9d174858b5007de3dff35e3714c3794aad053edb42b08f18ca05a1e04eb5.jpg) +Figure 3: (a) If $G_{\mathrm{d}}$ is aligned with $G_{\mathrm{g}}$ , we set $G_{\mathrm{prograd}}$ as $G_{\mathrm{d}}$ . (b) If $G_{\mathrm{d}}$ conflicts with $G_{\mathrm{g}}$ (i.e., their angle is larger than $90^{\circ}$ ), we set $G_{\mathrm{prograd}}$ as the projection of $G_{\mathrm{d}}$ on the orthogonal direction of $G_{\mathrm{g}}$ . (c) Training pipeline of our ProGrad. Only the context vectors are learnable. + +![](images/3f13c3f2054dca0fcd4976ab1768e0141c95e4b07b77440e9bb914c103f306fb.jpg) + +$N_{p}$ , we can approximate the generalization error bound as + +$$ +\begin{array}{l} \mathcal {R} _ {d} (\hat {f} _ {\text {p r o g r a d}}) \leq \frac {1}{2} \gamma_ {\mathcal {F}} (S, P) + \Re_ {d} (\mathcal {F}) \\ + \frac {3}{2} \sqrt {\frac {\ln (4 / \epsilon)}{2 N _ {d}}} + \frac {1}{2} \sqrt {\frac {\ln (4 / \epsilon)}{2} \frac {1}{N _ {d}}}. \tag {7} \\ \end{array} +$$ + +Similarly, we have the generalization error for CoOp $\hat{f}_{\mathrm{coop}}$ as + +$$ +\mathcal {R} _ {d} \left(\hat {f} _ {\text {c o o p}}\right) \leq 2 \Re_ {d} (\mathcal {F}) + 3 \sqrt {\frac {\ln (4 / \epsilon)}{2 N _ {d}}} + \sqrt {\frac {\ln (4 / \epsilon)}{2} \frac {1}{N _ {d}}}. \tag {8} +$$ + +Under the assumption that the gap between pre-trained and downstream domains $\gamma (P,D)$ is small, the estimation error bound of $\mathcal{R}_d(\hat{f}_{\mathrm{coop}})$ is at least two times greater than $\mathcal{R}_d(\hat{f}_{\mathrm{prograd}})$ . Considering that $N_{d}$ is typically very small in few-shot setting, our ProGrad model $\hat{f}_{\mathrm{prograd}}$ achieves a much lower error bound than conventional fine-tuning model like CoOp $\hat{f}_{\mathrm{coop}}$ . + +# 4. Experiments + +# 4.1. Datasets and Implementation Details + +We validate the effectiveness of ProGrad on four settings: (1) few-shot classification, (2) domain generalization, (3) base-to-new generalization, (4) cross-dataset transfer. + +Datasets. For few-shot learning, base-to-new generalization and cross-dataset transfer, we use 11 datasets, i.e., ImageNet [6] and Caltech101 [9] for generic object classification, OxfordPets [33], StanfordCars [22], Flowers102 [32], + +Food101 [2] and FGVCAircraft [30] for fine-grained image recognition, EuroSAT [13] for satellite image classification, UCF101 [47] for action classification, DTD [5] for texture classification, and SUN397 [50] for scene recognition. For domain generalization, we use ImageNet as the source dataset and select ImageNet-V2 [41], ImageNet-Sketch [49], ImageNet-A [15], ImageNet-R [14] as the target datasets. + +Training Details. For few-shot learning, following CoOp and CLIP, all models are trained with $\{1,2,4,8,16\}$ shots respectively then evaluated on the full test split. For domain generalization and base-to-new generalization, we evaluate 4-shot performance, which justifies the robustness under low-shots condition. All results of learning-based models are averaged over three random seeds. The standard deviation values can be found in the Appendix. Unless otherwise stated, we adhere to CoOp to use ResNet-50 [12] as the backbone of image encoder. Following [54] and [55], the length of context tokens $M$ is set to 16 for few-shot classification and $M = 4$ for the other three settings. $\lambda$ is set to 1 by default, except that $\lambda$ is set to 0.8 for 16 shots. We adopt the training settings from CoOp, e.g., training epochs, training schedule and the data augmentation settings, and refer readers to Appendix for further details + +Baselines. We compare ProGrad against 4 methods: (1) Zero-shot CLIP (2) Linear probe (3) CoOp and (4) CoCoOp. Although our method can beat some other fine-tune methods, e.g., CLIP-Adapter [10], we focus on single prompt-based learning methods. The results of other fine-tuning methods are in Appendix. + +![](images/b5d3d5921271b796dc926f68d83dfaca50c28d4ad30c1f9ba1899ac5cd2e72dd.jpg) + +![](images/6120cf81065e0eb16ef80b94e3acdde0f628e240ae61eae17145e59b49710f0b.jpg) + +![](images/cada85245cfa05915b3d46c3c20e5e379282c5d3164ea16a311ca9c628dd724e.jpg) + +![](images/b20f5abee9f8a48f19d80f13dff4447e36010f27138b88c966366a287e74c57f.jpg) + +![](images/956d65616edd43d4da0db29e9c5c448130cea5da1b459097c2938720eaeb47ee.jpg) + +![](images/6641f3ed6c4a1b1d06a8f27b37b51d9f71f833dce4c73b8a41040786c2c2c66e.jpg) + +![](images/3a333e3a041cb6415b98de464edbcfb8f793dd0374c23239a91d4e61d8eb49ed.jpg) + +![](images/35cee9e09a99db379fe28df7f3586aeedbe39462f51bfa4252708b2724937038.jpg) + +![](images/d9ab04434a8cb151add0dfb9020b2f4cc6a0e44398f5c146722e200da979db08.jpg) +Figure 4: Accuracy $(\%)$ of few-shot learning on 11 datasets. The context length $M$ is set to 16. Standard deviations are reported in Appendix. + +![](images/3f4efe6b775d1f262c722826559b5a76743108e5c739bc76929cb28c911a5048.jpg) + +![](images/e0fa688a17f6aa88d6e15a8c971993b680ab79b6f75c714ae287f30da93b0a1f.jpg) + +![](images/a0f62df0fe0b44ba24519a789c694b7d2d5f05b3252f8929d0d9add3ca213f53.jpg) + +# 4.2. Few-Shot Classification + +Setup. We compare with two zero-shot CLIP models, i.e., CLIP and $\mathrm{CLIP}++$ stand for using single prompt and prompt ensembling respectively (Please refer to Appendix for the prompts templates). ProGrad and ProGrad++ stand for using single prompt and prompt ensembling as general knowledge to implement ProGrad respectively. Note that we only use the hand-crafted prompt ensembling to generate $G_{\mathrm{g}}$ , which provides a more accurate general direction. Therefore, ProGrad++ still optimizes a single prompt with 16 learnable tokens, which is identical to the size of CoOp. + +Table 1 provides averaged accuracy over 11 datasets, and Figure 4 illustrates the detailed comparisons. Overall, ProGrad clearly outperforms over baselines on average performance. Specifically, ProGrad outperforms CoOp + +Table 1: Averaged accuracy $(\%)$ of few-shot learning on 11 datasets. $M = 16$ + +
#shots0124816
CLIP58.77-----
CLIP++59.38-----
LP-37.3248.0257.2764.8870.57
CoOp-59.4662.3766.7970.0473.49
ProGrad-62.6164.9068.4571.4174.28
ProGrad++-63.0665.2868.7171.8075.03
+ +by $9.5\%$ , $6.9\%$ and $5.1\%$ on FGVCAircraft, EuroSAT and Flowers102 given 1 shot, and the average improvement is $3.2\%$ . These results demonstrate the anti-overfitting ability of our ProGrad when the training samples are extremely + +Table 2: Evaluation on robustness to distribution shift with different visual backbones. Standard deviations are reported in Appendix. +(a) ResNet50 + +
SourceTarget
ImageNet-V2-Sketch-A-R
CLIP58.1851.3433.3221.6556.00
LP41.2933.6513.0911.1826.82
CoOp61.3453.8132.8322.0854.62
CoCoOp61.0453.7132.3022.0753.60
ProGrad62.1754.7034.4023.0556.77
+ +(b) ResNet101 + +
SourceTarget
ImageNet-V2-Sketch-A-R
CLIP61.2454.8238.6628.0364.34
LP47.0138.4619.0916.3339.43
CoOp63.9956.9939.4029.5064.04
CoCoOp63.5956.9839.1629.0964.14
ProGrad64.9857.8640.5330.1365.61
+ +(c) ViT-B/32 + +
SourceTarget
ImageNet-V2-Sketch-A-R
CLIP62.0054.7540.8229.5966.01
LP46.7739.1220.3216.3239.48
CoOp64.7456.5940.0331.1064.54
CoCoOp64.6356.5940.7430.2764.12
ProGrad65.3657.4241.7331.8966.53
+ +(d) ViT-B/16 + +
SourceTarget
ImageNet-V2-Sketch-A-R
CLIP66.7360.8446.1347.8074.01
LP54.7045.5728.2022.4744.12
CoOp69.8662.8346.9048.9874.55
CoCoOp70.1363.0546.4849.3673.80
ProGrad70.4563.3548.1749.4575.21
+ +limited. Furthermore, leveraging prompt ensembling can further explore the potential of ProGrad. From Table 1, with more accurate general knowledge offered by prompt ensembling, $\mathrm{CLIP}++$ improves the zero-shot CLIP from $58.77\%$ to $59.38\%$ ; ProGrad++ increases the accuracy of ProGrad from $74.28\%$ to $75.03\%$ at 16 shots. + +# 4.3. Domain Generalization + +We train our ProGrad on the source dataset (ImageNet) for three different random seeds, and assess it on ImageNet-V2, ImageNet-Sketch, ImageNet-A, and ImageNet-R. This + +setting evaluates the generalizability on a target domain which differs from the source domain. Fine-tuning on limited data from a specific domain may mislead the model to learn spurious correlations or in-distribution patterns, resulting in biased models with poor performance in unseen domains. In contrast, zero-shot CLIP avoids exploiting such spurious correlations or patterns, as it is not learned on that distribution. By leveraging knowledge from the pre-trained domain to regularize fine-tuning on a specific distribution, our ProGrad method is expected to be robust to distribution shifts. As shown in Table 2, despite the exposure to the source dataset, ProGrad clearly outperforms other methods on all target datasets as well as the source dataset with ResNet-based and ViT-based backbones. + +# 4.4. Base-to-New Generalization + +We follow CoCoOp [55] to evaluate the generalization performance from seen classes to unseen classes. All the classes are equally divided into two groups, i.e., base classes and new classes, and all methods are only trained on base classes and tested on both base classes and new classes. + +Table 3: Averaged accuracy $(\%)$ over 11 datasets for base-to-new generalization. + +
BaseNewH.
CLIP61.7265.9163.64
CoOp71.9661.2665.58
CoCoOp72.2360.7765.35
ProGrad73.2965.9669.06
+ +The harmonic mean of base classes and new classes accuracies is reported to evaluate the trade-off. As illustrated in Table 3, ProGrad yields the highest average performance across all metrics, whereas CoOp and CoCoOp exhibit poor performance for new classes, consistently underperforming zero-shot CLIP. These results highlight that ProGrad's superior generalizability to both base and new classes. The detailed results of 11 datasets are in Appendix. + +# 4.5. Cross-Dataset Transfer + +All models are trained on ImageNet as source dataset and evaluated on the rest 10 target datasets. The goal of this setting is to demonstrate the potential to transfer beyond a single dataset. The results are presented in Table 4. As shown, our ProGrad not only achieves the highest performance on source datasets but also outperforms other baselines 9 out of 10 target datasets. + +# 4.6. Further Analysis + +Comparison with Learning without Forgetting (LwF). ProGrad employs the gradient direction of knowledge distillation loss as a form of regularization. To determine whether our approach is equivalent to conventional knowledge distillation, we compared its performance against a simple knowledge distillation method, i.e., $\mathcal{L}_{\mathrm{total}} = \mathcal{L}_{\mathrm{ce}} + \alpha \cdot \mathcal{L}_{\mathrm{kd}}$ which is identical to the implementation of Learning without + +Table 4: Comparison of prompt learning methods in the cross-dataset transfer setting. Prompts are learned from 4-shots ImageNet. + +
SourceTarget
ImageNetCaltech101OxfordPetsStanfordCarsFlowers102Food101FGVCAircraftSUN397DTDEuroSATUCF101Average
CoOp61.3484.4885.9954.1660.1075.4814.0957.4835.3226.7257.5655.70
CoCoOp61.0484.7386.4252.3461.2473.7913.7455.9436.6023.4657.9755.21
ProGrad62.1788.3086.4355.6162.6976.7615.7660.1639.4824.8758.7057.36
+ +Table 5: Comparison with LwF (knowledge distillation). Average accuracy $(\%)$ over 11 datasets. + +
#shots124816
CoOp59.4662.3766.7970.0473.49
LwF(KD), α = 0.2561.0963.0167.7470.9073.39
LwF(KD), α = 0.561.1363.3667.1470.3472.68
LwF(KD), α = 161.5264.0766.5270.0172.01
LwF(KD), α = 260.9862.6664.9267.7868.98
LwF(KD), α = 459.5861.7662.9265.0165.42
ProGrad62.6164.9068.4571.4174.28
+ +Table 6: Applying ProGrad to cosine classifier. Average accuracy $(\%)$ over 11 datasets. + +
#shots124816
Cosine30.5043.7453.3361.2665.00
+ProGrad32.2946.1455.1862.0566.47
+ +Forgetting (LwF)[24]. We repeated few-shot experiments on 11 datasets using a range of $\alpha$ values and report the average results in Table 5. The results demonstrate that ProGrad outperforms KD for various few-shot settings. Although KD (LwF) with small $\alpha \leq 1$ improves the performance of CoOp in low-shot scenarios (e.g., 1, 2, and 4 shots), its performance drops when the shots is large (i.e., 8 and 16 shots). These findings suggest that ProGrad operates differently from KD (LwF) and is more robust to the sample number. + +Failure cases. We analyze cases where ProGrad models fail while CoOp succeeds. In specific, we count the percentage of the failure cases that zero-shot CLIP models also fails in Figure 5. We found that a high proportion of the failure cases are also mis-classified by zero-shot CLIP model (red bar in Figure 5), implying that the imprecision of zero-shot general knowledge represented by $G_{\mathrm{g}}$ is detrimental to model generalization. As sample size increases, $G_{\mathrm{d}}$ represents downstream knowledge more accurately and with less bias. As expected, the red bar becomes larger. + +![](images/63454d01965cad8fc6a717945be98073ff7b9a18c3af9520015941182c3a7a3a.jpg) +Figure 5: Distribution of samples that are mis-classified by ProGrad but correctly classified by CoOp. + +![](images/52e978cdbc767b9bbb8d2a5fd0e31a605c03ca7ba118044cef7984c1ebb2170e.jpg) + +![](images/73bbac49f50b2c0427e25a8e788ef1f15bfe157d0e826078ba27cad1c6fcab64.jpg) +(a) 1 shot +Figure 6: Angles between $G_{\mathrm{d}}$ and $G_{\mathrm{g}}$ during training on StanfordCars and Caltech101. + +![](images/20a2bac3bcfdfed7760c2bf3b9c67093e28704328238171af2435b2558582d66.jpg) +(b) 2 shots + +Conflict of knowledge. ProGrad requires the updated gradient direction be acute to the general knowledge gradient directions. We explore how this constraint helps to defuse the conflicts of domain-specific and general knowledge by visualizing the angle between their representative gradients during training (angle between $G_{\mathrm{d}}$ and $G_{\mathrm{g}}$ ). As depicted in Figure 6, without $G_{\mathrm{prograd}}$ , the angle between $G_{\mathrm{d}}$ and $G_{\mathrm{g}}$ converges to 90 degrees due to the fact that "all high-dimensional random vectors are almost always orthogonal to each other" [3]. Intuitively, without any constraint, the optimization direction $G_{\mathrm{d}}$ is independent of the general direction, and the average angle would be orthogonal. In contrast, utilizing $G_{\mathrm{prograd}}$ results in the convergence of the angle to an obtuse angle. The reason is that $G_{\mathrm{prograd}}$ intervenes the model to learn the downstream knowledge aligned with the + +general knowledge and leads to the insufficient learning of downstream knowledge that is incompatible with the general knowledge. As training stabilizes, $G_{\mathrm{d}}$ struggles to learn the conflicting knowledge, reflecting an obtuse angle to the $G_{\mathrm{g}}$ . Thanks to ProGrad, we discard such conflicting knowledge to avoid forgetting. + +# Upper Bound of Performance. + +As the general gradient direction $G_{g}$ is the key for improvement, we are interested in the upper-bound of performance if we can find an oracle general direction $G_{g}^{\mathrm{full}}$ instead of the one offered by hand-crafted prompt. To achieve this, we first optimize a prompt with plain cross-entropy loss on the full dataset to create $G_{g}^{\mathrm{full}}$ and then use such gradient to implement ProGrad. The averaged performance over 11 datasets, as + +![](images/e46f47daff40a8aa0851481e88970e09ad22c40ea5254731bbae88cd64460c26.jpg) +Figure 7: The upper bound of performance (averaged accuracy) of GradPrad. + +shown in Figure 7, indicate a more accurate regularization direction $G_{g}^{\mathrm{full}}$ elicits a stronger ProGrad model. The detailed results of 11 datasets are in Appendix. + +Applying ProGrad to conventional fine-tuning. We are also interested in the effectiveness of ProGrad for the conventional "pre-train then fine-tune" paradigm. Specifically, we plug in an additional cosine classifier on top of the visual backbone and compare the averaged performance over 11 datasets of few-shot classification. Table 6 shows that conventional fine-tuning can benefit from our ProGrad. The implementation details and the result of each dataset are provided in Appendix. + +Effect of hyper-parameter $\lambda$ . We further analyze the effect of the hyper-parameter $\lambda$ described in Eq. (4) in the main paper. Results are shown in Table 7. As discussed in Section 3.2 in the main paper, a smaller $\lambda$ weakens the general knowledge regularization, which results in a inferior performance under low-shot setting for most datasets. However, for DTD in Table 7, using a smaller $\lambda = 0.9$ to reduce the general knowledge regularization can improve the 16 shots results. One possible reason is that texture images of DTD has large gap with the CLIP pre-trained images that collected from the Internet, stronger regularization from pre-trained knowledge might be detrimental to the fine-tune performance if downstream data is sufficient. + +# 5. Conclusion + +In this paper, we pointed out the over-fitting issues of existing prompt tuning methods for few-shot generalization, which heavily relies on early stopping and data augmentation. We proposed a prompt tuning method ProGrad that + +Table 7: Accuracy $(\%)$ of 1, 2, 4, 8, and 16 shots training with different $\lambda$ on DTD and OxfordPets. +(a) OxfordPets. + +
λ1 shot2 shots4 shots8 shots16 shots
086.0182.2186.6385.1587.06
0.287.1283.1684.8784.0086.15
0.488.0983.5685.5084.0486.67
0.787.7484.7086.9386.3087.90
0.988.2686.4787.5287.3888.52
1.088.3686.8988.0487.9189.00
+ +(b) DTD. + +
λ1 shot2 shots4 shots8 shots16 shots
044.3346.2254.0859.9962.89
0.243.8045.2154.0260.1463.61
0.444.1747.4454.3259.6563.16
0.744.9347.7754.9259.2863.10
0.945.7848.4655.4460.4664.28
1.046.1449.7854.4357.9861.15
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Sun database: Large-scale scene recognition from abbey to zoo. In CVPR, 2010. 5 +[51] Yuan Yao, Ao Zhang, Zhengyan Zhang, Zhiyuan Liu, TatSeng Chua, and Maosong Sun. Cpt: Colorful prompt tuning for pre-trained vision-language models. arXiv preprint arXiv:2109.11797, 2021. 1, 3 +[52] Tianhe Yu, Saurabh Kumar, Abhishek Gupta, Sergey Levine, Karol Hausman, and Chelsea Finn. Gradient surgery for multi-task learning. NeurIPS, 2020. 3, 4 +[53] Chao Zhang, Lei Zhang, and Jieping Ye. Generalization bounds for domain adaptation. NeurIPS, 2012. 4 +[54] Kaiyang Zhou, Jingkang Yang, Chen Change Loy, and Ziwei Liu. Learning to prompt for vision-language models. arXiv preprint arXiv:2109.01134, 2021. 1, 3, 4, 5 + +[55] Kaiyang Zhou, Jingkang Yang, Chen Change Loy, and Ziwei Liu. Conditional prompt learning for vision-language models. In CVPR, 2022. 1, 2, 3, 5, 7 +[56] Beier Zhu, Yulei Niu, Saeil Lee, Minhoe Hur, and Hanwang Zhang. Debiased fine-tuning for vision-language models by prompt regularization. AAAI, 2023. 3 \ No newline at end of file diff --git a/2023/Prompt-aligned Gradient for Prompt Tuning/images.zip b/2023/Prompt-aligned Gradient for Prompt Tuning/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..28c0ee66972ebebb86dc3c415f5299bc944f922a --- /dev/null +++ b/2023/Prompt-aligned Gradient for Prompt Tuning/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:82e6217783b86bb7f1b7a444ef49332d68796a9c654ff28be02c0604d0675b68 +size 877156 diff --git a/2023/Prompt-aligned Gradient for Prompt Tuning/layout.json b/2023/Prompt-aligned Gradient for Prompt Tuning/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..d9f6ad2e66c0105ecc342d152d3ad8bccd069703 --- /dev/null +++ b/2023/Prompt-aligned Gradient for Prompt Tuning/layout.json @@ -0,0 +1,10840 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 158, + 103, + 436, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 158, + 103, + 436, + 121 + ], + "spans": [ + { + "bbox": [ + 158, + 103, + 436, + 121 + ], + "type": "text", + "content": "Prompt-aligned Gradient for Prompt Tuning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 113, + 142, + 481, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 142, + 481, + 158 + ], + "spans": [ + { + "bbox": [ + 113, + 142, + 481, + 158 + ], + "type": "text", + "content": "Beier Zhu1 Yulei Niu2 Yucheng Han1 Yue Wu3 Hanwang Zhang1*" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 113, + 159, + 481, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 159, + 481, + 171 + ], + "spans": [ + { + "bbox": [ + 113, + 159, + 481, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 113, + 159, + 481, + 171 + ], + "type": "text", + "content": "Nanyang Technological University " + }, + { + "bbox": [ + 113, + 159, + 481, + 171 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 113, + 159, + 481, + 171 + ], + "type": "text", + "content": "Columbia University " + }, + { + "bbox": [ + 113, + 159, + 481, + 171 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 113, + 159, + 481, + 171 + ], + "type": "text", + "content": "Damo Academy, Alibaba Group" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 112, + 173, + 481, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 173, + 481, + 185 + ], + "spans": [ + { + "bbox": [ + 112, + 173, + 481, + 185 + ], + "type": "text", + "content": "beier002@e.ntu.edu.sg, yn.yuleiniu@gmail.com yucheng002@e.ntu.edu.sg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 156, + 188, + 436, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 156, + 188, + 436, + 198 + ], + "spans": [ + { + "bbox": [ + 156, + 188, + 436, + 198 + ], + "type": "text", + "content": "matthew.wy@alibaba-inc.com hanwangzhang@ntu.edu.sg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 252, + 290, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 290, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 290, + 553 + ], + "type": "text", + "content": "Thanks to the large pre-trained vision-language models (VLMs) like CLIP [37], we can craft a zero-shot classifier by discrete prompt design, e.g., the confidence score of an image being \"[CLASS]\" can be obtained by using the VLM provided similarity between the image and the prompt sentence \"a photo of a [CLASS]\". Furthermore, prompting shows great potential for fast adaptation of VLMs to downstream tasks if we fine-tune the soft prompts with few samples. However, we find a common failure that improper fine-tuning or learning with extremely few-shot samples may even under-perform the zero-shot prediction. Existing methods still address this problem by using traditional anti-overfitting techniques such as early stopping and data augmentation, which lack a principled solution specific to prompting. In this paper, we present Prompt-aligned Gradient, dubbed ProGrad to prevent prompt tuning from forgetting the general knowledge learned from VLMs. In particular, ProGrad only updates the prompt whose gradient is aligned (or non-conflicting) to the general knowledge, which is represented as the optimization direction offered by the pre-defined prompt predictions. Extensive experiments under the few-shot learning, domain generalization, baseto-new generalization and cross-dataset transfer settings demonstrate the stronger few-shot generalization ability of ProGrad over state-of-the-art prompt tuning methods." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 576, + 128, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 576, + 128, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 576, + 128, + 588 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 597, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 288, + 693 + ], + "type": "text", + "content": "After seeing and reading countless image-text association pairs, large and deep vision-language models (VLM) [37, 18] can memorize the general knowledge (a.k.a. encyclopedic knowledge) about what visual patterns correspond to what textual sequence and vice versa. Thanks to the powerful language modeling of VLMs, we can establish a communication channel in human-readable natural language, i.e., prompt [25, 51, 19], to query the general knowledge." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 228, + 547, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 228, + 547, + 337 + ], + "spans": [ + { + "bbox": [ + 306, + 228, + 547, + 337 + ], + "type": "text", + "content": "Prompting bridges the interface gap between the pre-trained and downstream tasks (e.g., regression vs. classification) without the need for additional fine-tuning adaptation. For example, we can craft a concrete prompt—\"a photo of a [CLASS]\"—for zero-shot image classification: by using the popular vision-language model CLIP [37], we input the image to the vision end and the prompt sentence to the language end, then obtain a vision-language similarity as the confidence score of classifying the image as \"[CLASS]\"." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 342, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 548, + 715 + ], + "type": "text", + "content": "In practice, the prompt-based zero-shot image classification is not accurate because the hand-crafted prompt may not be the most machine-favorable (e.g., \"this is a picture of\" could be more grammatically prevailing in VLM training), or not specific to the downstream domain (e.g., \"a photo of a person doing\" is better in action recognition) [37]. Recently, prompt tuning or prefix tuning [23, 26, 54, 55] has been proposed to replace the handcrafted prompt with a set of tunable word embedding vectors, which do not have to be translatable back to human-readable words. Yet, prompt tuning is still as tricky as conventional fine-tuning: as the training continues, the generalization ability may decrease and even under-perform the zero-shot baseline. As shown in Figure 1(a&b), the prompt tuning method CoOp [54] achieves the best results via early stopping, and its accuracies heavily drop by at most " + }, + { + "bbox": [ + 304, + 342, + 548, + 715 + ], + "type": "inline_equation", + "content": "4\\%" + }, + { + "bbox": [ + 304, + 342, + 548, + 715 + ], + "type": "text", + "content": " when the training continues. Besides, Figure 1(c&d) show that CoOp underperforms zero-shot CLIP without augmentation or enough samples from downstream tasks. To the best of our knowledge, existing methods still rely on the conventional anti-overfitting techniques such as early stopping and data augmentation [54, 55, 11, 36], which lacks a principled solution to the nature of improper prompt tuning. Furthermore, the Grad-CAM visualization results indicate that the fine-tuned prompt misleads the VLM to forget the general knowledge that the classification should at least focus on the foreground object but not the background. Comparing CoOp (Figure 2(b)) with zero-shot CLIP (Figure 2(c)), we find that the CoOp model distracts its attention to the background, while CLIP mainly focuses on the foreground object. These results demonstrate the over-fitting risk of existing prompt" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15659" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 173, + 169 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 173, + 169 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 173, + 169 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 173, + 169 + ], + "type": "image", + "image_path": "6dec5c597949dd7a192e765da9f21fc01ef71921e0cfd522cbd56e2d21d99d93.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 113, + 171, + 123, + 180 + ], + "lines": [ + { + "bbox": [ + 113, + 171, + 123, + 180 + ], + "spans": [ + { + "bbox": [ + 113, + 171, + 123, + 180 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 173, + 70, + 296, + 169 + ], + "blocks": [ + { + "bbox": [ + 173, + 70, + 296, + 169 + ], + "lines": [ + { + "bbox": [ + 173, + 70, + 296, + 169 + ], + "spans": [ + { + "bbox": [ + 173, + 70, + 296, + 169 + ], + "type": "image", + "image_path": "49900bff427d46d74be1ce14c0d844163eb1b7b8e1abe16330744ef01658ef0f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 238, + 171, + 248, + 180 + ], + "lines": [ + { + "bbox": [ + 238, + 171, + 248, + 180 + ], + "spans": [ + { + "bbox": [ + 238, + 171, + 248, + 180 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 298, + 71, + 421, + 169 + ], + "blocks": [ + { + "bbox": [ + 298, + 71, + 421, + 169 + ], + "lines": [ + { + "bbox": [ + 298, + 71, + 421, + 169 + ], + "spans": [ + { + "bbox": [ + 298, + 71, + 421, + 169 + ], + "type": "image", + "image_path": "7acf57b79896358ce050094d546b46b4a2793682a02e39ab5e253e2fd1e79c41.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 361, + 171, + 371, + 180 + ], + "lines": [ + { + "bbox": [ + 361, + 171, + 371, + 180 + ], + "spans": [ + { + "bbox": [ + 361, + 171, + 371, + 180 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 421, + 71, + 544, + 169 + ], + "blocks": [ + { + "bbox": [ + 421, + 71, + 544, + 169 + ], + "lines": [ + { + "bbox": [ + 421, + 71, + 544, + 169 + ], + "spans": [ + { + "bbox": [ + 421, + 71, + 544, + 169 + ], + "type": "image", + "image_path": "2bdc7a1dff0e53c8194a3b7a4f6c6e4371d0e5a1247734bb84db3a41d4851847.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 484, + 171, + 494, + 180 + ], + "lines": [ + { + "bbox": [ + 484, + 171, + 494, + 180 + ], + "spans": [ + { + "bbox": [ + 484, + 171, + 494, + 180 + ], + "type": "text", + "content": "(d)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 50, + 237, + 545, + 439 + ], + "blocks": [ + { + "bbox": [ + 46, + 189, + 546, + 226 + ], + "lines": [ + { + "bbox": [ + 46, + 189, + 546, + 226 + ], + "spans": [ + { + "bbox": [ + 46, + 189, + 546, + 226 + ], + "type": "text", + "content": "Figure 1: Comparison of Zero-shot CLIP, CoOp, and our ProGrad on Stanford Cars and OxfordPets datasets. (a)&(b): Given 1 shot training sample, CoOp's performance severely drops and under-performs zero-shot CLIP by large margins when the training continues. (c)&(d): CoOp may fail to improve CLIP without data augmentation or plenty of samples." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 237, + 545, + 439 + ], + "lines": [ + { + "bbox": [ + 50, + 237, + 545, + 439 + ], + "spans": [ + { + "bbox": [ + 50, + 237, + 545, + 439 + ], + "type": "image", + "image_path": "5f0567276f17fb59eabfc055f5bf605d123755a6635b983e706ce691dcfa1f07.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 447, + 546, + 471 + ], + "lines": [ + { + "bbox": [ + 46, + 447, + 546, + 471 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 546, + 471 + ], + "type": "text", + "content": "Figure 2: Comparisons of Grad-CAM [43] visualization for prompt tuning methods using different gradient strategies on Stanford Cars Datasets." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 493, + 287, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 493, + 287, + 517 + ], + "spans": [ + { + "bbox": [ + 46, + 493, + 287, + 517 + ], + "type": "text", + "content": "tuning strategies, especially when the number of training samples is extremely limited (e.g., 1 or 2)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "content": "To this end, we present a novel prompt tuning method called Prompt-aligned Gradient (ProGrad) to overcome the improperly biased tuning for CLIP. The principle of ProGrad is to regularize each tuning step not to conflict with the general knowledge offered by the original prompt, e.g., the zero-shot CLIP predictions. Specifically, we measure the general knowledge direction " + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{g}}" + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "content": " using the gradient of Kullback-Leibler (KL) divergence between the predictions of the zero-shot prompted CLIP and the few-shot fine-tuned model, which we name as general direction. Similarly, we compute the domain-specific knowledge direction " + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "content": " using the gradient of cross-entropy between the ground-truth and the few-shot fine-tuned model, dubbed domain-specific direction. We decompose the domain-specific direction " + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "content": " into: 1) a vector " + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "inline_equation", + "content": "G_{\\perp}" + }, + { + "bbox": [ + 46, + 521, + 289, + 714 + ], + "type": "text", + "content": " orthogonal to the general direction, which denotes the non-conflicting domain-specific knowl" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 493, + 547, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 493, + 547, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 493, + 547, + 673 + ], + "type": "text", + "content": "edge; and 2) a vector " + }, + { + "bbox": [ + 304, + 493, + 547, + 673 + ], + "type": "inline_equation", + "content": "G_{\\parallel}" + }, + { + "bbox": [ + 304, + 493, + 547, + 673 + ], + "type": "text", + "content": " parallel to the general direction, which denotes the general knowledge. Note that the first gradient component does NOT override the general direction as any two orthogonal vectors can be transformed into two nonconflicting base vectors. For the second component, it must be one of the two directions: 1) the same of the general direction, which indicates that the update is aligned to the general knowledge, and 2) the opposite of general direction, indicating a conflicting update that should be discarded to avoid forgetting. Overall, in each iteration, ProGrad only updates the parameters in the prompt-aligned direction that has an acute angle to the general direction. Compared to CoOp and CLIP, both " + }, + { + "bbox": [ + 304, + 493, + 547, + 673 + ], + "type": "inline_equation", + "content": "G_{g}" + }, + { + "bbox": [ + 304, + 493, + 547, + 673 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 493, + 547, + 673 + ], + "type": "inline_equation", + "content": "G_{\\perp}" + }, + { + "bbox": [ + 304, + 493, + 547, + 673 + ], + "type": "text", + "content": " (Figure 2(d&e)) help to regularize the model to focus on the foreground, and ProGrad (Figure 2(f)) further improves the visual response." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "Following CLIP, CoOp and CoCoOp [55], we evaluate ProGrad under the few-shot learning, domain generalization, base-to-new generalization and cross-dataset transfer" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15660" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "settings over 15 image classification benchmarks, covering generic object classification, fine-grained image recognition, action classification. In summary, our ProGrad achieves: 1) clear improvement compared to CoOp over all of the 11 datasets; 2) clear improvement on the harmonic mean of base and new classes accuracies on all 11 datasets compared to CoOp and CoCoOp, and 3) clear improvement on both the source and target datasets of the domain generalization." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 178, + 134, + 192 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 178, + 134, + 192 + ], + "spans": [ + { + "bbox": [ + 47, + 178, + 134, + 192 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 198, + 289, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 198, + 289, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 289, + 533 + ], + "type": "text", + "content": "VLMs Adaptation. VLM can be adapted for various downstream tasks, e.g., visual question answering [21, 48], visual grounding [51], image retrieval [28] and semantic segmentation [39]. We focus on image classification task. Conventional \"pre-train then fine-tune\" paradigm that plugs in a classifier to the visual backbone and trained on downstream data has been widely-adopted, e.g., Linear Probe [37]. CLIP-Adapter [10] add feature adapters to boost fine-tuning results. Recently, NLP community has introduced a \"prompt-based learning\" paradigm that fine-tunes the prompt using a \"fill-in-the-blank\" cloze test to maximize the ground-truth token [23, 26]. The prompt-based learning has recently been applied in CV community [54, 29, 7, 46, 4, 20, 56]: CoOp [54] uses a continuous prompt optimization from downstream data instead of hand-craft design. CoCoOp [55] further extends CoOp by learning image conditional prompt to improve generalization. ProDA [29] learns a prompt distribution over the output embedding space. VPT [7] introduces variational prompt tuning by combining a base learned prompt with a residual vector sampled from a instance-specific underlying distribution. TPT [46] proposes a test-time prompt tuning, which does not require training data and optimizes the prompt to achieve consistent predictions across different augmented views. Our ProGrad follows the line of prompt-based learning to improve few-shot generalization ability by aligning the gradient to general direction, without model structure modification or tuning the pre-trained parameters." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "content": "Knowledge Transfer. Forgetting mitigation is widely used in incremental learning [27, 40, 35, 42, 17] through knowledge distillation or memory replay. However, prompt-based learning differs fundamentally from incremental learning in that it does not have access to pre-trained data, which is required for incremental learning to store old data from memory storage. For example, OGD [8] projects gradients from new classes to the orthogonal direction of previous task gradients, but the requirement to store old task gradients is not possible for prompt tuning since we lack access to the pre-training process. Moreover, OGD modifies gradients of downstream tasks in non-conflicting scenarios, potentially leading to sub-optimal performance. Another related field that leverages gradient matching to transfer knowledge is domain generalization [45, 38] and multi-task learning [44, 52]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "text", + "content": "However, these methods are not directly applicable in prompt tuning whose transfer direction is only from general to downstream. In Appendix, we will show how their methods fail in several ablative studies." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 131, + 389, + 144 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 131, + 389, + 144 + ], + "spans": [ + { + "bbox": [ + 305, + 131, + 389, + 144 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 151, + 547, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 151, + 547, + 212 + ], + "spans": [ + { + "bbox": [ + 304, + 151, + 547, + 212 + ], + "type": "text", + "content": "In this section, we introduce the preliminary concepts of prompt-based zero-shot inference, prompt-based learning, and present our proposed Prompt-aligned Gradient solution to align the domain knowledge with general knowledge for few-shot generalization." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 218, + 392, + 231 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 218, + 392, + 231 + ], + "spans": [ + { + "bbox": [ + 305, + 218, + 392, + 231 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 236, + 547, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 236, + 547, + 332 + ], + "spans": [ + { + "bbox": [ + 304, + 236, + 547, + 332 + ], + "type": "text", + "content": "Contrastive language-image pre-training (CLIP) [37] adopts a contrastive language-image pre-training paradigm on tremendous pairs of images with natural language descriptions. For contrastive learning, the associated image and sentences are taken as the positive samples, while the non-associated pairs are regarded as negative samples. The contrastive objective maximizes the similarity of positive pairs while minimize the similarity of negative pairs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "text", + "content": "Zero-shot transfer inference adapts the pre-trained CLIP model to downstream tasks without fine-tuning the model. Taking image classification as an example, zero-shot transfer is enabled by formulating the classification task as an image-text matching problem, where the text is obtained by extending the \"[CLASS]\" name using a template like \"a photo of a [CLASS]\". CLIP [37] finds that such a simple template narrows the distribution gap to pre-training text inputs. The image-class matching score is measured based on the cosine similarity " + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "inline_equation", + "content": "< \\pmb{w}_i" + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "inline_equation", + "content": "f >" + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "text", + "content": " between the image feature " + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "text", + "content": " and the class-extended text feature " + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "inline_equation", + "content": "\\pmb{w}_i" + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "text", + "content": "-th class. The image feature " + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "text", + "content": " for image " + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "text", + "content": " is extracted by the image encoder, while the text feature " + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "inline_equation", + "content": "\\pmb{w}_i" + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "text", + "content": "-th class is obtained by feeding the prompt description into the text encoder. The probability for " + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 332, + 548, + 513 + ], + "type": "text", + "content": "-th class is obtained as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 340, + 520, + 547, + 552 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 520, + 547, + 552 + ], + "spans": [ + { + "bbox": [ + 340, + 520, + 547, + 552 + ], + "type": "interline_equation", + "content": "p _ {\\mathrm {z s}} (\\boldsymbol {w} _ {i} | \\boldsymbol {x}) = \\frac {\\exp \\left(< \\boldsymbol {w} _ {i} , \\boldsymbol {f} > / \\tau\\right)}{\\sum_ {j = 1} ^ {K} \\exp \\left(< \\boldsymbol {w} _ {j} , \\boldsymbol {f} > / \\tau\\right)}, \\tag {1}", + "image_path": "6e742b42317999fd23d7144abf1759c5ff6c60b713572c5dc94b6cf0ac48d4f6.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 558, + 547, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 581 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 558, + 547, + 581 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 558, + 547, + 581 + ], + "type": "text", + "content": " denotes the number of classes, and " + }, + { + "bbox": [ + 304, + 558, + 547, + 581 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 558, + 547, + 581 + ], + "type": "text", + "content": " is a temperature learned by CLIP." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": "Prompt-based learning further strengths the transferring ability of the CLIP model and avoids prompt engineering by automatically learning the prompt given few samples from the downstream task. Different from the zero-shot transfer that used a fixed hand-craft prompt, CoOp [54] constructs and fine-tunes a set of " + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": " continuous context vectors " + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{v} = \\{\\pmb{v}_1,\\pmb{v}_2,\\dots,\\pmb{v}_M\\}" + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": " as the turnable prompt. Specifically, the prompt " + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{t}_i = \\{\\pmb{v}_1,\\pmb{v}_2,\\dots,\\pmb{v}_M,\\pmb{c}_i\\}" + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": " combines the learnable context vectors " + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{v}" + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": " and the class token embedding " + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{c}_i" + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": ", and is fed to the text encoder " + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": ". CoOp optimizes the static context vectors " + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{v}" + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": " by minimizing the negative log-likelihood" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "type": "text", + "content": "15661" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 154, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 154, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 154, + 83 + ], + "type": "text", + "content": "of the ground-truth token:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 85, + 90, + 212, + 114 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 90, + 212, + 114 + ], + "spans": [ + { + "bbox": [ + 85, + 90, + 212, + 114 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {c e}} (\\boldsymbol {v}) = - \\sum_ {i} \\boldsymbol {y} _ {i} \\log p (\\boldsymbol {t} _ {i} | \\boldsymbol {x}),", + "image_path": "fa58f2c2ee65c87f35e901dbfa6d620df46364d3821ec846f9fb08d070be3699.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 83, + 114, + 287, + 147 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 114, + 287, + 147 + ], + "spans": [ + { + "bbox": [ + 83, + 114, + 287, + 147 + ], + "type": "interline_equation", + "content": "p \\left(\\boldsymbol {t} _ {i} \\mid \\boldsymbol {x}\\right) = \\frac {\\exp \\left(< g \\left(\\boldsymbol {t} _ {i}\\right) , \\boldsymbol {f} > / \\tau\\right)}{\\sum_ {j = 1} ^ {K} \\exp \\left(< g \\left(\\boldsymbol {t} _ {j}\\right) , \\boldsymbol {f} > / \\tau\\right)}, \\tag {2}", + "image_path": "92526d5b3d6622eb466c54b25efd345aba3bc9eb2144bf39754b0d7c01baaec4.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 152, + 287, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 152, + 287, + 175 + ], + "spans": [ + { + "bbox": [ + 47, + 152, + 287, + 175 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 152, + 287, + 175 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 47, + 152, + 287, + 175 + ], + "type": "text", + "content": " denotes the one-hot ground-truth annotation and " + }, + { + "bbox": [ + 47, + 152, + 287, + 175 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 152, + 287, + 175 + ], + "type": "text", + "content": " denotes the number of classes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 181, + 189, + 194 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 181, + 189, + 194 + ], + "spans": [ + { + "bbox": [ + 47, + 181, + 189, + 194 + ], + "type": "text", + "content": "3.2. Prompt-aligned Gradient" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 200, + 288, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 200, + 288, + 295 + ], + "spans": [ + { + "bbox": [ + 46, + 200, + 288, + 295 + ], + "type": "text", + "content": "CoOp faced a challenge that the transfer performance drops when the number of annotations is very limited (e.g., one per class), even underperforms the zero-shot transfer. Also, CoOp heavily relies on anti-overfitting techniques such as early stopping and data augmentation. To overcome the over-fitting challenge, we propose an effective and efficient fine-tuning paradigm ProGrad to align the few-shot downstream knowledge with the large-scale general knowledge." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 296, + 288, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 296, + 288, + 416 + ], + "spans": [ + { + "bbox": [ + 46, + 296, + 288, + 416 + ], + "type": "text", + "content": "Motivated by the success of knowledge distillation [34, 16] in knowledge transfer, we leverage the zero-shot CLIP predictions as the general knowledge, and compare the finetuned predictions with the general knowledge to regularize the gradient direction. Specifically, we obtain the domain-specific direction by calculating the cross-entropy " + }, + { + "bbox": [ + 46, + 296, + 288, + 416 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ce}}(\\boldsymbol{v})" + }, + { + "bbox": [ + 46, + 296, + 288, + 416 + ], + "type": "text", + "content": " between the model prediction " + }, + { + "bbox": [ + 46, + 296, + 288, + 416 + ], + "type": "inline_equation", + "content": "p(\\boldsymbol{t}_i|\\boldsymbol{x})" + }, + { + "bbox": [ + 46, + 296, + 288, + 416 + ], + "type": "text", + "content": " and the ground-truth " + }, + { + "bbox": [ + 46, + 296, + 288, + 416 + ], + "type": "inline_equation", + "content": "\\boldsymbol{y}" + }, + { + "bbox": [ + 46, + 296, + 288, + 416 + ], + "type": "text", + "content": " according to Eq. (2), and the general knowledge direction based on the Kullback-Leibler (KL) divergence between " + }, + { + "bbox": [ + 46, + 296, + 288, + 416 + ], + "type": "inline_equation", + "content": "p(\\boldsymbol{t}_i|\\boldsymbol{x})" + }, + { + "bbox": [ + 46, + 296, + 288, + 416 + ], + "type": "text", + "content": " and the zero-shot CLIP prediction " + }, + { + "bbox": [ + 46, + 296, + 288, + 416 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{zs}}(\\boldsymbol{w}_i|\\boldsymbol{x})" + }, + { + "bbox": [ + 46, + 296, + 288, + 416 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 82, + 421, + 287, + 450 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 421, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 82, + 421, + 287, + 450 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {k l}} (\\boldsymbol {v}) = - \\sum_ {i} p _ {\\mathrm {z s}} \\left(\\boldsymbol {w} _ {i} | \\boldsymbol {x}\\right) \\log \\frac {p \\left(\\boldsymbol {t} _ {i} \\mid \\boldsymbol {x}\\right)}{p _ {\\mathrm {z s}} \\left(\\boldsymbol {w} _ {i} \\mid \\boldsymbol {x}\\right)}. \\tag {3}", + "image_path": "517d8ecb9f4318f2daeeb8dc375263a6bbe8bf2be75ec600c4aed4fbae65e0f5.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "text", + "content": "We denote the gradients of " + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{kl}}(\\pmb{v})" + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ce}}(\\pmb{v})" + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{g}} = \\nabla_{\\pmb{v}}\\mathcal{L}_{\\mathrm{kl}}(\\pmb{v})" + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}} = \\nabla_{\\pmb{v}}\\mathcal{L}_{\\mathrm{ce}}(\\pmb{v})" + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "text", + "content": ", respectively. The relations between " + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{g}}" + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "text", + "content": " are two-fold. (1) Their angle is smaller than " + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "text", + "content": " (Figure 3(a)), which indicates that the optimization direction of few-shot downstream knowledge does not conflict with general knowledge. In this case, we safely set the updated gradient direction " + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{prograd}}" + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "text", + "content": ". (2) Their angle is larger than " + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "text", + "content": " (Figure 3(b)), which indicates that the few-shot downstream knowledge conflicts with general knowledge. In other words, optimizing the context vectors following " + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "text", + "content": " will lead to the forgetting of the pre-trained general knowledge. In this case, we project the " + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "text", + "content": " to the orthogonal direction of " + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{g}}" + }, + { + "bbox": [ + 46, + 455, + 288, + 635 + ], + "type": "text", + "content": " to optimize the model for classification, which avoids increasing the KL loss. Our ProGrad strategy is mathematically formulated as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 53, + 641, + 287, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 641, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 53, + 641, + 287, + 673 + ], + "type": "interline_equation", + "content": "\\boldsymbol {G} _ {\\text {p r o g r a d}} = \\left\\{ \\begin{array}{l l} \\boldsymbol {G} _ {\\mathrm {d}}, & \\text {i f} \\boldsymbol {G} _ {\\mathrm {d}} \\cdot \\boldsymbol {G} _ {\\mathrm {g}} \\geq 0 \\\\ \\boldsymbol {G} _ {\\mathrm {d}} - \\lambda \\cdot \\frac {\\boldsymbol {G} _ {\\mathrm {d}} \\cdot \\boldsymbol {G} _ {\\mathrm {g}}}{\\| \\boldsymbol {G} _ {\\mathrm {g}} \\| ^ {2}} \\boldsymbol {G} _ {\\mathrm {g}}, & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {4}", + "image_path": "108681ec38a9c9941f8253268813f178c1bb485628e27642aaed652cea8efb65.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": "Fig 3(c) illustrates the pipeline of our ProGrad. Instead of updating the context vectors using " + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": " in CoOp [54], we optimize the context vectors using " + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{prograd}}" + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": ", which prevent the" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": "gradient direction from overfitting to few-shot downstream samples. We further introduce " + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": " in Eq. (4) to generalize the formulation, which can flexibly control the strength of general knowledge guidance in applications. In particular, " + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "inline_equation", + "content": "\\lambda = 1" + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": " denotes projecting " + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}}" + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": " to the orthogonal direction of " + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{g}}" + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": " (Figure 3(b)), while setting " + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "inline_equation", + "content": "\\lambda = 0" + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": " makes ProGrad degenerate to CoOp, i.e., CoOp is a special case of our strategy. We include the detailed analysis of " + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": " in Appendix." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 168, + 547, + 265 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 547, + 265 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 547, + 265 + ], + "type": "text", + "content": "Generalization Error Analysis. We further theoretically analyze the generalization error of our ProGrad. Here, we provide a sketch proof and include the detailed justification in Appendix. Our ProGrad keeps the optimal value " + }, + { + "bbox": [ + 304, + 168, + 547, + 265 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{kl}}" + }, + { + "bbox": [ + 304, + 168, + 547, + 265 + ], + "type": "text", + "content": " of the pre-trained domain when optimizing the empirical risk on the downstream domain. The model " + }, + { + "bbox": [ + 304, + 168, + 547, + 265 + ], + "type": "inline_equation", + "content": "\\hat{f}_{\\mathrm{prograd}}" + }, + { + "bbox": [ + 304, + 168, + 547, + 265 + ], + "type": "text", + "content": " learned by such update rule can be viewed as optimizing the empirical risk on pre-trained and downstream domains [52]:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 309, + 274, + 545, + 307 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 274, + 545, + 307 + ], + "spans": [ + { + "bbox": [ + 309, + 274, + 545, + 307 + ], + "type": "interline_equation", + "content": "\\hat {f} _ {\\text {p r o g r a d}} = \\underset {f \\in \\mathcal {F}} {\\operatorname {a r g m i n}} \\hat {\\mathcal {R}} _ {(d + p)} (f) = \\underset {f \\in \\mathcal {F}} {\\operatorname {a r g m i n}} \\hat {\\mathcal {R}} _ {d} (f) + \\hat {\\mathcal {R}} _ {p} (f), \\tag {5}", + "image_path": "d23f9671b33a2e621c5dc61552077c113fdab849b177b737ec4818cee0d603b4.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 307, + 547, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 307, + 547, + 367 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 547, + 367 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 307, + 547, + 367 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 304, + 307, + 547, + 367 + ], + "type": "text", + "content": " is the function class, and " + }, + { + "bbox": [ + 304, + 307, + 547, + 367 + ], + "type": "inline_equation", + "content": "\\mathcal{R}(\\cdot)" + }, + { + "bbox": [ + 304, + 307, + 547, + 367 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 307, + 547, + 367 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{R}} (\\cdot)" + }, + { + "bbox": [ + 304, + 307, + 547, + 367 + ], + "type": "text", + "content": " denote the expected risk and empirical risk. We bound the generalization error of ProGrad by virtue of Rademacher Complexity [1] and the Theorem 6.2 in [53]. The detailed proof is in Appendix." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 380, + 547, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 547, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 547, + 431 + ], + "type": "text", + "content": "Theorem 1 Let " + }, + { + "bbox": [ + 304, + 380, + 547, + 431 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_1^{N_d} = \\{\\mathbf{x}_n^{(d)}\\}_{n=1}^{N_d}" + }, + { + "bbox": [ + 304, + 380, + 547, + 431 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 380, + 547, + 431 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_1^{N_p} = \\{\\mathbf{x}_n^{(p)}\\}_{n=1}^{N_p}" + }, + { + "bbox": [ + 304, + 380, + 547, + 431 + ], + "type": "text", + "content": " be two sets of i.i.d. samples drawn from the downstream domain " + }, + { + "bbox": [ + 304, + 380, + 547, + 431 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_d" + }, + { + "bbox": [ + 304, + 380, + 547, + 431 + ], + "type": "text", + "content": " and the pre-trained domain " + }, + { + "bbox": [ + 304, + 380, + 547, + 431 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_p" + }, + { + "bbox": [ + 304, + 380, + 547, + 431 + ], + "type": "text", + "content": ". Then for any " + }, + { + "bbox": [ + 304, + 380, + 547, + 431 + ], + "type": "inline_equation", + "content": "\\epsilon > 0" + }, + { + "bbox": [ + 304, + 380, + 547, + 431 + ], + "type": "text", + "content": ", we have with probability at least " + }, + { + "bbox": [ + 304, + 380, + 547, + 431 + ], + "type": "inline_equation", + "content": "1 - \\epsilon" + }, + { + "bbox": [ + 304, + 380, + 547, + 431 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 307, + 441, + 545, + 542 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 441, + 545, + 542 + ], + "spans": [ + { + "bbox": [ + 307, + 441, + 545, + 542 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {R} _ {d} (\\hat {f} _ {\\text {p r o g r a d}}) \\leq \\hat {\\mathcal {R}} _ {(d + p)} (\\hat {f} _ {\\text {p r o g r a d}}) + \\frac {1}{2} \\gamma_ {\\mathcal {F}} (D, P) \\\\ + \\Re_ {p} (\\mathcal {F}) + \\Re_ {d} (\\mathcal {F}) + \\frac {3}{2} \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2 N _ {d}}} \\\\ + \\frac {3}{2} \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2 N _ {p}}} + \\frac {1}{2} \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2} \\left(\\frac {1}{N _ {d}} + \\frac {1}{N _ {p}}\\right)}, \\tag {6} \\\\ \\end{array}", + "image_path": "e959a001dba813744d53e93ae7fbb0eebd353070a54548ff636a3c3ffaa8d72e.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 543, + 547, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 543, + 547, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 543, + 547, + 591 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 543, + 547, + 591 + ], + "type": "inline_equation", + "content": "\\gamma_{\\mathcal{F}}(D,P)" + }, + { + "bbox": [ + 304, + 543, + 547, + 591 + ], + "type": "text", + "content": " is the integral probability metric [31] that measures the difference between the distribution of pretrained domain and the downstream domain, " + }, + { + "bbox": [ + 304, + 543, + 547, + 591 + ], + "type": "inline_equation", + "content": "\\Re_d(\\mathcal{F})" + }, + { + "bbox": [ + 304, + 543, + 547, + 591 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 543, + 547, + 591 + ], + "type": "inline_equation", + "content": "\\Re_p(\\mathcal{F})" + }, + { + "bbox": [ + 304, + 543, + 547, + 591 + ], + "type": "text", + "content": " are the Rademacher complexity of " + }, + { + "bbox": [ + 304, + 543, + 547, + 591 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 304, + 543, + 547, + 591 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 604, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 547, + 714 + ], + "type": "text", + "content": "Note that the bound of " + }, + { + "bbox": [ + 304, + 604, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\Re (\\mathcal{F})" + }, + { + "bbox": [ + 304, + 604, + 547, + 714 + ], + "type": "text", + "content": " is inversely proportional to the number of training samples. Theorem 1 shows that the generalization error " + }, + { + "bbox": [ + 304, + 604, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_d(\\hat{f}_{\\mathrm{prog}})" + }, + { + "bbox": [ + 304, + 604, + 547, + 714 + ], + "type": "text", + "content": " is bounded by the empirical training risk " + }, + { + "bbox": [ + 304, + 604, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{R}}_{(d + p)}(\\hat{f}_{\\mathrm{prog}})" + }, + { + "bbox": [ + 304, + 604, + 547, + 714 + ], + "type": "text", + "content": ", the two domain gap " + }, + { + "bbox": [ + 304, + 604, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\gamma_{\\mathcal{F}}(D,P)" + }, + { + "bbox": [ + 304, + 604, + 547, + 714 + ], + "type": "text", + "content": " and the estimation error. The empirical training risk can be minimized to arbitrary small value when using deep models with high capacity. The estimation error that related to " + }, + { + "bbox": [ + 304, + 604, + 547, + 714 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 304, + 604, + 547, + 714 + ], + "type": "text", + "content": " asymptotically tends to 0 as the sample size " + }, + { + "bbox": [ + 304, + 604, + 547, + 714 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 304, + 604, + 547, + 714 + ], + "type": "text", + "content": " tends to infinity. Thanks to the large amount of pretrained samples" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15662" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 154, + 279 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 154, + 279 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 154, + 279 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 154, + 279 + ], + "type": "image", + "image_path": "4a9d9d174858b5007de3dff35e3714c3794aad053edb42b08f18ca05a1e04eb5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "lines": [ + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "text", + "content": "Figure 3: (a) If " + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "text", + "content": " is aligned with " + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{g}}" + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "text", + "content": ", we set " + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{prograd}}" + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "text", + "content": ". (b) If " + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "text", + "content": " conflicts with " + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{g}}" + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "text", + "content": " (i.e., their angle is larger than " + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "text", + "content": "), we set " + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{prograd}}" + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "text", + "content": " as the projection of " + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "text", + "content": " on the orthogonal direction of " + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{g}}" + }, + { + "bbox": [ + 46, + 286, + 548, + 323 + ], + "type": "text", + "content": ". (c) Training pipeline of our ProGrad. Only the context vectors are learnable." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 160, + 71, + 545, + 281 + ], + "blocks": [ + { + "bbox": [ + 160, + 71, + 545, + 281 + ], + "lines": [ + { + "bbox": [ + 160, + 71, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 160, + 71, + 545, + 281 + ], + "type": "image", + "image_path": "3f13c3f2054dca0fcd4976ab1768e0141c95e4b07b77440e9bb914c103f306fb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 344, + 282, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 344, + 282, + 357 + ], + "spans": [ + { + "bbox": [ + 47, + 344, + 282, + 357 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 47, + 344, + 282, + 357 + ], + "type": "text", + "content": ", we can approximate the generalization error bound as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 69, + 362, + 287, + 420 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 362, + 287, + 420 + ], + "spans": [ + { + "bbox": [ + 69, + 362, + 287, + 420 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {R} _ {d} (\\hat {f} _ {\\text {p r o g r a d}}) \\leq \\frac {1}{2} \\gamma_ {\\mathcal {F}} (S, P) + \\Re_ {d} (\\mathcal {F}) \\\\ + \\frac {3}{2} \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2 N _ {d}}} + \\frac {1}{2} \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2} \\frac {1}{N _ {d}}}. \\tag {7} \\\\ \\end{array}", + "image_path": "d763acf2132ce64421fcf76f6653ac8cafd8c25abde4d19d7512eb249e9ba17c.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 427, + 287, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 427, + 287, + 452 + ], + "spans": [ + { + "bbox": [ + 46, + 427, + 287, + 452 + ], + "type": "text", + "content": "Similarly, we have the generalization error for CoOp " + }, + { + "bbox": [ + 46, + 427, + 287, + 452 + ], + "type": "inline_equation", + "content": "\\hat{f}_{\\mathrm{coop}}" + }, + { + "bbox": [ + 46, + 427, + 287, + 452 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 456, + 287, + 488 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 456, + 287, + 488 + ], + "spans": [ + { + "bbox": [ + 52, + 456, + 287, + 488 + ], + "type": "interline_equation", + "content": "\\mathcal {R} _ {d} \\left(\\hat {f} _ {\\text {c o o p}}\\right) \\leq 2 \\Re_ {d} (\\mathcal {F}) + 3 \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2 N _ {d}}} + \\sqrt {\\frac {\\ln (4 / \\epsilon)}{2} \\frac {1}{N _ {d}}}. \\tag {8}", + "image_path": "acc2d2403eb0561b974a300106afae41c3ec9b7f8f0afb87765d5a7ef8d4cd71.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 494, + 289, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 289, + 583 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 289, + 583 + ], + "type": "text", + "content": "Under the assumption that the gap between pre-trained and downstream domains " + }, + { + "bbox": [ + 46, + 494, + 289, + 583 + ], + "type": "inline_equation", + "content": "\\gamma (P,D)" + }, + { + "bbox": [ + 46, + 494, + 289, + 583 + ], + "type": "text", + "content": " is small, the estimation error bound of " + }, + { + "bbox": [ + 46, + 494, + 289, + 583 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_d(\\hat{f}_{\\mathrm{coop}})" + }, + { + "bbox": [ + 46, + 494, + 289, + 583 + ], + "type": "text", + "content": " is at least two times greater than " + }, + { + "bbox": [ + 46, + 494, + 289, + 583 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_d(\\hat{f}_{\\mathrm{prograd}})" + }, + { + "bbox": [ + 46, + 494, + 289, + 583 + ], + "type": "text", + "content": ". Considering that " + }, + { + "bbox": [ + 46, + 494, + 289, + 583 + ], + "type": "inline_equation", + "content": "N_{d}" + }, + { + "bbox": [ + 46, + 494, + 289, + 583 + ], + "type": "text", + "content": " is typically very small in few-shot setting, our ProGrad model " + }, + { + "bbox": [ + 46, + 494, + 289, + 583 + ], + "type": "inline_equation", + "content": "\\hat{f}_{\\mathrm{prograd}}" + }, + { + "bbox": [ + 46, + 494, + 289, + 583 + ], + "type": "text", + "content": " achieves a much lower error bound than conventional fine-tuning model like CoOp " + }, + { + "bbox": [ + 46, + 494, + 289, + 583 + ], + "type": "inline_equation", + "content": "\\hat{f}_{\\mathrm{coop}}" + }, + { + "bbox": [ + 46, + 494, + 289, + 583 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 591, + 128, + 605 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 591, + 128, + 605 + ], + "spans": [ + { + "bbox": [ + 47, + 591, + 128, + 605 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 611, + 243, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 243, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 243, + 624 + ], + "type": "text", + "content": "4.1. Datasets and Implementation Details" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 629, + 289, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 289, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 289, + 666 + ], + "type": "text", + "content": "We validate the effectiveness of ProGrad on four settings: (1) few-shot classification, (2) domain generalization, (3) base-to-new generalization, (4) cross-dataset transfer." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 666, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 289, + 714 + ], + "type": "text", + "content": "Datasets. For few-shot learning, base-to-new generalization and cross-dataset transfer, we use 11 datasets, i.e., ImageNet [6] and Caltech101 [9] for generic object classification, OxfordPets [33], StanfordCars [22], Flowers102 [32]," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 344, + 548, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 344, + 548, + 429 + ], + "spans": [ + { + "bbox": [ + 304, + 344, + 548, + 429 + ], + "type": "text", + "content": "Food101 [2] and FGVCAircraft [30] for fine-grained image recognition, EuroSAT [13] for satellite image classification, UCF101 [47] for action classification, DTD [5] for texture classification, and SUN397 [50] for scene recognition. For domain generalization, we use ImageNet as the source dataset and select ImageNet-V2 [41], ImageNet-Sketch [49], ImageNet-A [15], ImageNet-R [14] as the target datasets." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 439, + 547, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 439, + 547, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 439, + 547, + 632 + ], + "type": "text", + "content": "Training Details. For few-shot learning, following CoOp and CLIP, all models are trained with " + }, + { + "bbox": [ + 304, + 439, + 547, + 632 + ], + "type": "inline_equation", + "content": "\\{1,2,4,8,16\\}" + }, + { + "bbox": [ + 304, + 439, + 547, + 632 + ], + "type": "text", + "content": " shots respectively then evaluated on the full test split. For domain generalization and base-to-new generalization, we evaluate 4-shot performance, which justifies the robustness under low-shots condition. All results of learning-based models are averaged over three random seeds. The standard deviation values can be found in the Appendix. Unless otherwise stated, we adhere to CoOp to use ResNet-50 [12] as the backbone of image encoder. Following [54] and [55], the length of context tokens " + }, + { + "bbox": [ + 304, + 439, + 547, + 632 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 439, + 547, + 632 + ], + "type": "text", + "content": " is set to 16 for few-shot classification and " + }, + { + "bbox": [ + 304, + 439, + 547, + 632 + ], + "type": "inline_equation", + "content": "M = 4" + }, + { + "bbox": [ + 304, + 439, + 547, + 632 + ], + "type": "text", + "content": " for the other three settings. " + }, + { + "bbox": [ + 304, + 439, + 547, + 632 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 439, + 547, + 632 + ], + "type": "text", + "content": " is set to 1 by default, except that " + }, + { + "bbox": [ + 304, + 439, + 547, + 632 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 439, + 547, + 632 + ], + "type": "text", + "content": " is set to 0.8 for 16 shots. We adopt the training settings from CoOp, e.g., training epochs, training schedule and the data augmentation settings, and refer readers to Appendix for further details" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 641, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 548, + 715 + ], + "type": "text", + "content": "Baselines. We compare ProGrad against 4 methods: (1) Zero-shot CLIP (2) Linear probe (3) CoOp and (4) CoCoOp. Although our method can beat some other fine-tune methods, e.g., CLIP-Adapter [10], we focus on single prompt-based learning methods. The results of other fine-tuning methods are in Appendix." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15663" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 177, + 202 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 177, + 202 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 177, + 202 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 177, + 202 + ], + "type": "image", + "image_path": "b5d3d5921271b796dc926f68d83dfaca50c28d4ad30c1f9ba1899ac5cd2e72dd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 178, + 70, + 299, + 202 + ], + "blocks": [ + { + "bbox": [ + 178, + 70, + 299, + 202 + ], + "lines": [ + { + "bbox": [ + 178, + 70, + 299, + 202 + ], + "spans": [ + { + "bbox": [ + 178, + 70, + 299, + 202 + ], + "type": "image", + "image_path": "6120cf81065e0eb16ef80b94e3acdde0f628e240ae61eae17145e59b49710f0b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 300, + 70, + 422, + 202 + ], + "blocks": [ + { + "bbox": [ + 300, + 70, + 422, + 202 + ], + "lines": [ + { + "bbox": [ + 300, + 70, + 422, + 202 + ], + "spans": [ + { + "bbox": [ + 300, + 70, + 422, + 202 + ], + "type": "image", + "image_path": "cada85245cfa05915b3d46c3c20e5e379282c5d3164ea16a311ca9c628dd724e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 422, + 70, + 545, + 202 + ], + "blocks": [ + { + "bbox": [ + 422, + 70, + 545, + 202 + ], + "lines": [ + { + "bbox": [ + 422, + 70, + 545, + 202 + ], + "spans": [ + { + "bbox": [ + 422, + 70, + 545, + 202 + ], + "type": "image", + "image_path": "b20f5abee9f8a48f19d80f13dff4447e36010f27138b88c966366a287e74c57f.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 49, + 203, + 177, + 334 + ], + "blocks": [ + { + "bbox": [ + 49, + 203, + 177, + 334 + ], + "lines": [ + { + "bbox": [ + 49, + 203, + 177, + 334 + ], + "spans": [ + { + "bbox": [ + 49, + 203, + 177, + 334 + ], + "type": "image", + "image_path": "956d65616edd43d4da0db29e9c5c448130cea5da1b459097c2938720eaeb47ee.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 178, + 203, + 299, + 334 + ], + "blocks": [ + { + "bbox": [ + 178, + 203, + 299, + 334 + ], + "lines": [ + { + "bbox": [ + 178, + 203, + 299, + 334 + ], + "spans": [ + { + "bbox": [ + 178, + 203, + 299, + 334 + ], + "type": "image", + "image_path": "6641f3ed6c4a1b1d06a8f27b37b51d9f71f833dce4c73b8a41040786c2c2c66e.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 300, + 203, + 422, + 334 + ], + "blocks": [ + { + "bbox": [ + 300, + 203, + 422, + 334 + ], + "lines": [ + { + "bbox": [ + 300, + 203, + 422, + 334 + ], + "spans": [ + { + "bbox": [ + 300, + 203, + 422, + 334 + ], + "type": "image", + "image_path": "3a333e3a041cb6415b98de464edbcfb8f793dd0374c23239a91d4e61d8eb49ed.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 422, + 203, + 545, + 334 + ], + "blocks": [ + { + "bbox": [ + 422, + 203, + 545, + 334 + ], + "lines": [ + { + "bbox": [ + 422, + 203, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 422, + 203, + 545, + 334 + ], + "type": "image", + "image_path": "35cee9e09a99db379fe28df7f3586aeedbe39462f51bfa4252708b2724937038.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 53, + 335, + 177, + 467 + ], + "blocks": [ + { + "bbox": [ + 53, + 335, + 177, + 467 + ], + "lines": [ + { + "bbox": [ + 53, + 335, + 177, + 467 + ], + "spans": [ + { + "bbox": [ + 53, + 335, + 177, + 467 + ], + "type": "image", + "image_path": "d9ab04434a8cb151add0dfb9020b2f4cc6a0e44398f5c146722e200da979db08.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 476, + 547, + 502 + ], + "lines": [ + { + "bbox": [ + 45, + 476, + 547, + 502 + ], + "spans": [ + { + "bbox": [ + 45, + 476, + 547, + 502 + ], + "type": "text", + "content": "Figure 4: Accuracy " + }, + { + "bbox": [ + 45, + 476, + 547, + 502 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 45, + 476, + 547, + 502 + ], + "type": "text", + "content": " of few-shot learning on 11 datasets. 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CLIP66.7360.8446.1347.8074.01
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Domain Generalization" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "content": "We train our ProGrad on the source dataset (ImageNet) for three different random seeds, and assess it on ImageNet-V2, ImageNet-Sketch, ImageNet-A, and ImageNet-R. This" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": "setting evaluates the generalizability on a target domain which differs from the source domain. Fine-tuning on limited data from a specific domain may mislead the model to learn spurious correlations or in-distribution patterns, resulting in biased models with poor performance in unseen domains. In contrast, zero-shot CLIP avoids exploiting such spurious correlations or patterns, as it is not learned on that distribution. By leveraging knowledge from the pre-trained domain to regularize fine-tuning on a specific distribution, our ProGrad method is expected to be robust to distribution shifts. As shown in Table 2, despite the exposure to the source dataset, ProGrad clearly outperforms other methods on all target datasets as well as the source dataset with ResNet-based and ViT-based backbones." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 247, + 460, + 259 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 247, + 460, + 259 + ], + "spans": [ + { + "bbox": [ + 306, + 247, + 460, + 259 + ], + "type": "text", + "content": "4.4. Base-to-New Generalization" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 266, + 417, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 417, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 417, + 396 + ], + "type": "text", + "content": "We follow CoCoOp [55] to evaluate the generalization performance from seen classes to unseen classes. All the classes are equally divided into two groups, i.e., base classes and new classes, and all methods are only trained on base classes and tested on both base classes and new classes." + } + ] + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 420, + 318, + 545, + 386 + ], + "blocks": [ + { + "bbox": [ + 419, + 273, + 547, + 309 + ], + "lines": [ + { + "bbox": [ + 419, + 273, + 547, + 309 + ], + "spans": [ + { + "bbox": [ + 419, + 273, + 547, + 309 + ], + "type": "text", + "content": "Table 3: Averaged accuracy " + }, + { + "bbox": [ + 419, + 273, + 547, + 309 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 419, + 273, + 547, + 309 + ], + "type": "text", + "content": " over 11 datasets for base-to-new generalization." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 420, + 318, + 545, + 386 + ], + "lines": [ + { + "bbox": [ + 420, + 318, + 545, + 386 + ], + "spans": [ + { + "bbox": [ + 420, + 318, + 545, + 386 + ], + "type": "table", + "html": "
BaseNewH.
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CoOp71.9661.2665.58
CoCoOp72.2360.7765.35
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SourceTarget
ImageNetCaltech101OxfordPetsStanfordCarsFlowers102Food101FGVCAircraftSUN397DTDEuroSATUCF101Average
CoOp61.3484.4885.9954.1660.1075.4814.0957.4835.3226.7257.5655.70
CoCoOp61.0484.7386.4252.3461.2473.7913.7455.9436.6023.4657.9755.21
ProGrad62.1788.3086.4355.6162.6976.7615.7660.1639.4824.8758.7057.36
", + "image_path": "9b381fa6536708e3682e46a66aa725a509e61720884288d1dadefe16eed03458.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 54, + 273, + 269, + 376 + ], + "blocks": [ + { + "bbox": [ + 46, + 240, + 288, + 264 + ], + "lines": [ + { + "bbox": [ + 46, + 240, + 288, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 288, + 264 + ], + "type": "text", + "content": "Table 5: Comparison with LwF (knowledge distillation). Average accuracy " + }, + { + "bbox": [ + 46, + 240, + 288, + 264 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 240, + 288, + 264 + ], + "type": "text", + "content": " over 11 datasets." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 54, + 273, + 269, + 376 + ], + "lines": [ + { + "bbox": [ + 54, + 273, + 269, + 376 + ], + "spans": [ + { + "bbox": [ + 54, + 273, + 269, + 376 + ], + "type": "table", + "html": "
#shots124816
CoOp59.4662.3766.7970.0473.49
LwF(KD), α = 0.2561.0963.0167.7470.9073.39
LwF(KD), α = 0.561.1363.3667.1470.3472.68
LwF(KD), α = 161.5264.0766.5270.0172.01
LwF(KD), α = 260.9862.6664.9267.7868.98
LwF(KD), α = 459.5861.7662.9265.0165.42
ProGrad62.6164.9068.4571.4174.28
", + "image_path": "353b0cf8762daa5f41a7620d003d4690ea0206ba56427836733b496c88d2bfed.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 75, + 413, + 260, + 460 + ], + "blocks": [ + { + "bbox": [ + 46, + 380, + 287, + 404 + ], + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 404 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 404 + ], + "type": "text", + "content": "Table 6: Applying ProGrad to cosine classifier. Average accuracy " + }, + { + "bbox": [ + 46, + 380, + 287, + 404 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 380, + 287, + 404 + ], + "type": "text", + "content": " over 11 datasets." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 75, + 413, + 260, + 460 + ], + "lines": [ + { + "bbox": [ + 75, + 413, + 260, + 460 + ], + "spans": [ + { + "bbox": [ + 75, + 413, + 260, + 460 + ], + "type": "table", + "html": "
#shots124816
Cosine30.5043.7453.3361.2665.00
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", + "image_path": "9c9c5aa36d3a8dd90a4c9150b82ebc674918a5368b355aca7d6ddb68e4ea232b.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 483, + 287, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 287, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 287, + 592 + ], + "type": "text", + "content": "Forgetting (LwF)[24]. We repeated few-shot experiments on 11 datasets using a range of " + }, + { + "bbox": [ + 46, + 483, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 483, + 287, + 592 + ], + "type": "text", + "content": " values and report the average results in Table 5. The results demonstrate that ProGrad outperforms KD for various few-shot settings. Although KD (LwF) with small " + }, + { + "bbox": [ + 46, + 483, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\alpha \\leq 1" + }, + { + "bbox": [ + 46, + 483, + 287, + 592 + ], + "type": "text", + "content": " improves the performance of CoOp in low-shot scenarios (e.g., 1, 2, and 4 shots), its performance drops when the shots is large (i.e., 8 and 16 shots). These findings suggest that ProGrad operates differently from KD (LwF) and is more robust to the sample number." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "Failure cases. We analyze cases where ProGrad models fail while CoOp succeeds. In specific, we count the percentage of the failure cases that zero-shot CLIP models also fails in Figure 5. We found that a high proportion of the failure cases are also mis-classified by zero-shot CLIP model (red bar in Figure 5), implying that the imprecision of zero-shot general knowledge represented by " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{g}}" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": " is detrimental to model generalization. As sample size increases, " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": " represents downstream knowledge more accurately and with less bias. As expected, the red bar becomes larger." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 240, + 423, + 327 + ], + "blocks": [ + { + "bbox": [ + 307, + 240, + 423, + 327 + ], + "lines": [ + { + "bbox": [ + 307, + 240, + 423, + 327 + ], + "spans": [ + { + "bbox": [ + 307, + 240, + 423, + 327 + ], + "type": "image", + "image_path": "63454d01965cad8fc6a717945be98073ff7b9a18c3af9520015941182c3a7a3a.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 334, + 546, + 359 + ], + "lines": [ + { + "bbox": [ + 305, + 334, + 546, + 359 + ], + "spans": [ + { + "bbox": [ + 305, + 334, + 546, + 359 + ], + "type": "text", + "content": "Figure 5: Distribution of samples that are mis-classified by ProGrad but correctly classified by CoOp." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 426, + 240, + 544, + 326 + ], + "blocks": [ + { + "bbox": [ + 426, + 240, + 544, + 326 + ], + "lines": [ + { + "bbox": [ + 426, + 240, + 544, + 326 + ], + "spans": [ + { + "bbox": [ + 426, + 240, + 544, + 326 + ], + "type": "image", + "image_path": "52e978cdbc767b9bbb8d2a5fd0e31a605c03ca7ba118044cef7984c1ebb2170e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 374, + 426, + 464 + ], + "blocks": [ + { + "bbox": [ + 307, + 374, + 426, + 464 + ], + "lines": [ + { + "bbox": [ + 307, + 374, + 426, + 464 + ], + "spans": [ + { + "bbox": [ + 307, + 374, + 426, + 464 + ], + "type": "image", + "image_path": "73bbac49f50b2c0427e25a8e788ef1f15bfe157d0e826078ba27cad1c6fcab64.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 356, + 464, + 390, + 474 + ], + "lines": [ + { + "bbox": [ + 356, + 464, + 390, + 474 + ], + "spans": [ + { + "bbox": [ + 356, + 464, + 390, + 474 + ], + "type": "text", + "content": "(a) 1 shot" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 483, + 545, + 507 + ], + "lines": [ + { + "bbox": [ + 306, + 483, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 306, + 483, + 545, + 507 + ], + "type": "text", + "content": "Figure 6: Angles between " + }, + { + "bbox": [ + 306, + 483, + 545, + 507 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}}" + }, + { + "bbox": [ + 306, + 483, + 545, + 507 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 483, + 545, + 507 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{g}}" + }, + { + "bbox": [ + 306, + 483, + 545, + 507 + ], + "type": "text", + "content": " during training on StanfordCars and Caltech101." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 426, + 374, + 545, + 464 + ], + "blocks": [ + { + "bbox": [ + 426, + 374, + 545, + 464 + ], + "lines": [ + { + "bbox": [ + 426, + 374, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 426, + 374, + 545, + 464 + ], + "type": "image", + "image_path": "20a2bac3bcfdfed7760c2bf3b9c67093e28704328238171af2435b2558582d66.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 473, + 464, + 510, + 473 + ], + "lines": [ + { + "bbox": [ + 473, + 464, + 510, + 473 + ], + "spans": [ + { + "bbox": [ + 473, + 464, + 510, + 473 + ], + "type": "text", + "content": "(b) 2 shots" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "text", + "content": "Conflict of knowledge. ProGrad requires the updated gradient direction be acute to the general knowledge gradient directions. We explore how this constraint helps to defuse the conflicts of domain-specific and general knowledge by visualizing the angle between their representative gradients during training (angle between " + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}}" + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{g}}" + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "text", + "content": "). As depicted in Figure 6, without " + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{prograd}}" + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "text", + "content": ", the angle between " + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}}" + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{g}}" + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "text", + "content": " converges to 90 degrees due to the fact that \"all high-dimensional random vectors are almost always orthogonal to each other\" [3]. Intuitively, without any constraint, the optimization direction " + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}}" + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "text", + "content": " is independent of the general direction, and the average angle would be orthogonal. In contrast, utilizing " + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{prograd}}" + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "text", + "content": " results in the convergence of the angle to an obtuse angle. The reason is that " + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{prograd}}" + }, + { + "bbox": [ + 304, + 533, + 547, + 715 + ], + "type": "text", + "content": " intervenes the model to learn the downstream knowledge aligned with the" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15666" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "type": "text", + "content": "general knowledge and leads to the insufficient learning of downstream knowledge that is incompatible with the general knowledge. As training stabilizes, " + }, + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "type": "text", + "content": " struggles to learn the conflicting knowledge, reflecting an obtuse angle to the " + }, + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{g}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "type": "text", + "content": ". Thanks to ProGrad, we discard such conflicting knowledge to avoid forgetting." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 144, + 179, + 156 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 144, + 179, + 156 + ], + "spans": [ + { + "bbox": [ + 47, + 144, + 179, + 156 + ], + "type": "text", + "content": "Upper Bound of Performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 156, + 169, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 156, + 169, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 169, + 334 + ], + "type": "text", + "content": "As the general gradient direction " + }, + { + "bbox": [ + 46, + 156, + 169, + 334 + ], + "type": "inline_equation", + "content": "G_{g}" + }, + { + "bbox": [ + 46, + 156, + 169, + 334 + ], + "type": "text", + "content": " is the key for improvement, we are interested in the upper-bound of performance if we can find an oracle general direction " + }, + { + "bbox": [ + 46, + 156, + 169, + 334 + ], + "type": "inline_equation", + "content": "G_{g}^{\\mathrm{full}}" + }, + { + "bbox": [ + 46, + 156, + 169, + 334 + ], + "type": "text", + "content": " instead of the one offered by hand-crafted prompt. To achieve this, we first optimize a prompt with plain cross-entropy loss on the full dataset to create " + }, + { + "bbox": [ + 46, + 156, + 169, + 334 + ], + "type": "inline_equation", + "content": "G_{g}^{\\mathrm{full}}" + }, + { + "bbox": [ + 46, + 156, + 169, + 334 + ], + "type": "text", + "content": " and then use such gradient to implement ProGrad. The averaged performance over 11 datasets, as" + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 171, + 162, + 286, + 282 + ], + "blocks": [ + { + "bbox": [ + 171, + 162, + 286, + 282 + ], + "lines": [ + { + "bbox": [ + 171, + 162, + 286, + 282 + ], + "spans": [ + { + "bbox": [ + 171, + 162, + 286, + 282 + ], + "type": "image", + "image_path": "e46f47daff40a8aa0851481e88970e09ad22c40ea5254731bbae88cd64460c26.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 170, + 291, + 288, + 327 + ], + "lines": [ + { + "bbox": [ + 170, + 291, + 288, + 327 + ], + "spans": [ + { + "bbox": [ + 170, + 291, + 288, + 327 + ], + "type": "text", + "content": "Figure 7: The upper bound of performance (averaged accuracy) of GradPrad." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 335, + 288, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 288, + 371 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 288, + 371 + ], + "type": "text", + "content": "shown in Figure 7, indicate a more accurate regularization direction " + }, + { + "bbox": [ + 46, + 335, + 288, + 371 + ], + "type": "inline_equation", + "content": "G_{g}^{\\mathrm{full}}" + }, + { + "bbox": [ + 46, + 335, + 288, + 371 + ], + "type": "text", + "content": " elicits a stronger ProGrad model. The detailed results of 11 datasets are in Appendix." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 371, + 288, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 371, + 288, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 288, + 479 + ], + "type": "text", + "content": "Applying ProGrad to conventional fine-tuning. We are also interested in the effectiveness of ProGrad for the conventional \"pre-train then fine-tune\" paradigm. Specifically, we plug in an additional cosine classifier on top of the visual backbone and compare the averaged performance over 11 datasets of few-shot classification. Table 6 shows that conventional fine-tuning can benefit from our ProGrad. The implementation details and the result of each dataset are provided in Appendix." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 479, + 288, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 288, + 634 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 288, + 634 + ], + "type": "text", + "content": "Effect of hyper-parameter " + }, + { + "bbox": [ + 46, + 479, + 288, + 634 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 479, + 288, + 634 + ], + "type": "text", + "content": ". We further analyze the effect of the hyper-parameter " + }, + { + "bbox": [ + 46, + 479, + 288, + 634 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 479, + 288, + 634 + ], + "type": "text", + "content": " described in Eq. (4) in the main paper. Results are shown in Table 7. As discussed in Section 3.2 in the main paper, a smaller " + }, + { + "bbox": [ + 46, + 479, + 288, + 634 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 479, + 288, + 634 + ], + "type": "text", + "content": " weakens the general knowledge regularization, which results in a inferior performance under low-shot setting for most datasets. However, for DTD in Table 7, using a smaller " + }, + { + "bbox": [ + 46, + 479, + 288, + 634 + ], + "type": "inline_equation", + "content": "\\lambda = 0.9" + }, + { + "bbox": [ + 46, + 479, + 288, + 634 + ], + "type": "text", + "content": " to reduce the general knowledge regularization can improve the 16 shots results. One possible reason is that texture images of DTD has large gap with the CLIP pre-trained images that collected from the Internet, stronger regularization from pre-trained knowledge might be detrimental to the fine-tune performance if downstream data is sufficient." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 645, + 119, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 119, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 119, + 658 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 289, + 714 + ], + "type": "text", + "content": "In this paper, we pointed out the over-fitting issues of existing prompt tuning methods for few-shot generalization, which heavily relies on early stopping and data augmentation. We proposed a prompt tuning method ProGrad that" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 343, + 121, + 520, + 210 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "type": "text", + "content": "Table 7: Accuracy " + }, + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "type": "text", + "content": " of 1, 2, 4, 8, and 16 shots training with different " + }, + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "type": "text", + "content": " on DTD and OxfordPets." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 402, + 105, + 462, + 115 + ], + "lines": [ + { + "bbox": [ + 402, + 105, + 462, + 115 + ], + "spans": [ + { + "bbox": [ + 402, + 105, + 462, + 115 + ], + "type": "text", + "content": "(a) OxfordPets." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 343, + 121, + 520, + 210 + ], + "lines": [ + { + "bbox": [ + 343, + 121, + 520, + 210 + ], + "spans": [ + { + "bbox": [ + 343, + 121, + 520, + 210 + ], + "type": "table", + "html": "
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", + "image_path": "2824ffeca2bfdf5fb8732c1b96c142efdcf3af2f68b927b2eac01e94856f07fc.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 340, + 547, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 340, + 547, + 425 + ], + "spans": [ + { + "bbox": [ + 304, + 340, + 547, + 425 + ], + "type": "text", + "content": "regularize each tuning step not to conflict with the general knowledge of the hand-crafted prompt. Experiments on few-shot classification, base-to-new generalization, domain generalization and cross-dataset transfer over 11 datasets demonstrate the effectiveness and efficiency of our ProGrad. In the future, we will explore how to apply ProGrad on other tasks like object detection and segmentation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 438, + 403, + 452 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 438, + 403, + 452 + ], + "spans": [ + { + "bbox": [ + 306, + 438, + 403, + 452 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 459, + 547, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 547, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 547, + 520 + ], + "type": "text", + "content": "This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-PhD-2021-01-002). 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AAAI, 2023. 3" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15669" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/PromptCap_ Prompt-Guided Image Captioning for VQA with GPT-3/4ffd89d6-8734-4748-beec-1543acfdd6d0_content_list.json b/2023/PromptCap_ Prompt-Guided Image Captioning for VQA with GPT-3/4ffd89d6-8734-4748-beec-1543acfdd6d0_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9f9fa61809497eec98f3ad120bbeffd355de7d34 --- /dev/null +++ b/2023/PromptCap_ Prompt-Guided Image Captioning for VQA with GPT-3/4ffd89d6-8734-4748-beec-1543acfdd6d0_content_list.json @@ -0,0 +1,1703 @@ +[ + { + "type": "text", + "text": "PROMPTCAP: Prompt-Guided Image Captioning for VQA with GPT-3", + "text_level": 1, + "bbox": [ + 127, + 130, + 843, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yushi Hu $^{1*}$ Hang Hua $^{2*}$ Zhengyuan Yang $^{3}$ Weijia Shi $^{1}$ Noah A. Smith $^{1,4}$ Jiebo Luo $^{2}$ $^{1}$ University of Washington $^{2}$ University of Rochester $^{3}$ Microsoft $^{4}$ Allen Institute for AI \nhttps://yushi-hu.github.io/promptcap_demo/", + "bbox": [ + 233, + 178, + 733, + 272 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 304, + 312, + 319 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Knowledge-based visual question answering (VQA) involves questions that require world knowledge beyond the image to yield the correct answer. Large language models (LMs) like GPT-3 are particularly helpful for this task because of their strong knowledge retrieval and reasoning capabilities. To enable LM to understand images, prior work uses a captioning model to convert images into text. However, when summarizing an image in a single caption sentence, which visual entities to describe are often underspecified. Generic image captions often miss visual details essential for the LM to answer visual questions correctly. To address this challenge, we propose PROMPTCAP (Prompt-guided image Captioning), a captioning model designed to serve as a better connector between images and black-box LMs. Different from generic captions, PROMPTCAP takes a natural-language prompt to control the visual entities to describe in the generated caption. The prompt contains a question that the caption should aid in answering. To avoid extra annotation, PROMPTCAP is trained by examples synthesized with GPT-3 and existing datasets. We demonstrate PROMPTCAP's effectiveness on an existing pipeline in which GPT-3 is prompted with image captions to carry out VQA. PROMPTCAP outperforms generic captions by a large margin and achieves state-of-the-art accuracy on knowledge-based VQA tasks (60.4% on OK-VQA and 59.6% on A-OKVQA). Zeroshot results on WebQA show that PROMPTCAP generalizes well to unseen domains.1", + "bbox": [ + 75, + 335, + 473, + 743 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 773, + 209, + 787 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Knowledge-based visual question answering (VQA) [37] extends traditional VQA tasks [3] with questions that require", + "bbox": [ + 75, + 797, + 468, + 829 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "*Equal contribution. Correspondance to , \n1All codes, data, and demos are available on the project page. HF checkpoint: https://huggingface.co/tifa-benchmark/promptcap-coco-vqa", + "bbox": [ + 73, + 838, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/50ec01164af43b0de5d2b01716d6ccd2b3fb1404309cf269baedf60abc8aa1e6.jpg", + "image_caption": [], + "image_footnote": [ + "v.s. COCO caption: A traffic light on a pole on a city street.", + "Figure 1. Illustration of VQA with PROMPTCAP and ChatGPT. PROMPTCAP is designed to work with black-box language models (e.g., GPT-3, ChatGPT) by describing question-related visual information in the text. Different from generic captions, PROMPTCAP customizes the caption according to the input question prompt, which helps ChatGPT understand the image and give correct answers to the user. In contrast, ChatGPT cannot infer the answers from the vanilla human-written caption from MSCOCO." + ], + "bbox": [ + 516, + 303, + 879, + 571 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "broad knowledge and commonsense reasoning to yield the correct answer. Existing systems on knowledge-based VQA retrieve external knowledge from various sources, including knowledge graphs [13, 36, 63], Wikipedia [36, 63, 12, 15, 29], and web search [35, 63]. Recent work [67] finds that modern language models (LMs) like GPT-3 [5] are particularly useful for this task because of their striking knowledge retrieval and reasoning abilities. The current state-of-the-art methods [67, 15, 29, 1] all make use of recent large language models (GPT-3 or Chinchilla).", + "bbox": [ + 496, + 715, + 893, + 866 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "One key challenge is to allow LMs to understand images. Many top-performing LMs (e.g., GPT-3, ChatGPT) are only", + "bbox": [ + 500, + 869, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2963", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "accessible via APIs, making it impossible to access their internal representations or conduct fine-tuning [49]. A popular solution is to project images into texts that black-box LMs can process, via a generic image captioning model [7] or an image tagger [67]. This framework has been successful on multiple tasks, including VQA [67, 15, 29], image paragraph captioning [65], and video-language tasks [70, 60]. Despite promising results, converting visual inputs into a generic, finite text description risks excluding information necessary for the task. As discussed in PICa [67], when used for VQA tasks, the generic caption might miss the detailed visual information needed to answer the question, such as missing the \"McDonald's\" in Figure 1.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the above challenges, we introduce PROMPTCAP, a question-aware captioning model designed to serve as a better connector between images and a black-box LM. PROMPTCAP is illustrated in Figure 2. PROMPTCAP takes an extra natural language prompt as input to control the visual content to describe. The prompt contains the question that the generated caption should help to answer. LMs can better answer visual questions by using PROMPTCAP as their \"visual front-end\". For example, in Figure 1, when asked \"what is the time of the day?\", PROMPTCAP includes \"in the evening\" in its image description; when asked \"what kind of food does the restaurant on the sign serve?\", PROMPTCAP includes \"McDonald's\" in its description. Such visual information is critical for ChatGPT to reply to the user with the correct answers. In contrast, the generic COCO [28] caption often contains no information about the time or the sign, making ChatGPT unable to answer the questions.", + "bbox": [ + 75, + 289, + 472, + 547 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "One major technical challenge is PROMPTCAP training. The pipeline of \"PROMPTCAP + black-box LM\" cannot be end-to-end fine-tuned on VQA tasks because the LM parameters are not exposed through the API. Also, there are no training data for question-aware captions. To avoid extra annotation, we propose a pipeline to synthesize and filter training samples with GPT-3. Specifically, we view existing VQA datasets as pairs of question and question-related visual details. Given a question-answer pair, we rewrite the corresponding image's generic caption into a customized caption that helps answer the question. Following 20 human-annotated examples, GPT-3 synthesizes a large number of question-aware captions via few-shot in-context learning [5]. To ensure the sample quality, we filter the generated captions by performing QA with GPT-3, checking if the answer can be inferred given the question and the synthesized caption. Notice that GPT-3 is frozen in the whole pipeline. Its strong few-shot learning ability makes this pipeline possible.", + "bbox": [ + 75, + 549, + 472, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We demonstrate the effectiveness of PROMPTCAP on knowledge-based VQA tasks with the pipeline in PICa [67]. Details of the pipeline are illustrated in §4. The images are converted into texts via PROMPTCAP, allowing GPT-3 to perform VQA via in-context learning. This pipeline, despite", + "bbox": [ + 75, + 824, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/bfc6284309143059a3d41501f08deea082faf709896804f9e8d62775641f6bee.jpg", + "image_caption": [ + "Figure 2. Overview of PROMPTCAP training. PROMPTCAP takes two inputs, including an image and a natural language prompt. The model is trained to generate a caption that helps downstream LMs to answer the question. During training, we use GPT-3 to synthesize VQA samples into captioning examples. The original caption is rewritten into a caption that helps answer the question. PROMPTCAP is trained to generate this synthesized caption given the image and the prompt." + ], + "image_footnote": [], + "bbox": [ + 501, + 87, + 895, + 277 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "its simplicity, achieves state-of-the-art results on knowledge-based VQA tasks (60.4% on OK-VQA [38] and 59.6% on A-OKVQA [46]). We also conduct extensive ablation studies on the contribution of each component, showing that PROMPTCAP gives a consistent performance gain (3.8% on OK-VQA, 5.3% on A-OKVQA, and 9.2% on VQAv2) over a generic captioning model that shares the same architecture and training data. Finally, we investigate PROMPTCAP's generalization ability on WebQA [6], showing that PROMPTCAP, without any training on the compositional questions in WebQA, outperforms the generic caption approach and all supervised baselines.", + "bbox": [ + 496, + 417, + 893, + 598 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are as follows:", + "bbox": [ + 517, + 599, + 821, + 613 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose PROMPTCAP, a novel question-aware captioning model that uses natural language prompt to control the visual content to be described. (§3)", + "- To the best of our knowledge, we are the first to propose a pipeline to synthesize and filter training samples for vision-language tasks via GPT-3 (§3.1).", + "- PROMPTCAP helps GPT-3 in-context learning (\\$4) achieve state-of-the-art results on OK-VQA and A-OKVQA, substantially outperforming generic captions on various VQA tasks. (\\$5)." + ], + "bbox": [ + 517, + 627, + 893, + 800 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 814, + 640, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Knowledge-Based VQA Knowledge-based VQA [38, 46] requires systems to leverage external knowledge beyond image content to answer the question. Prior works [13, 36, 63, 72, 40, 41, 17, 18, 12] investigate leveraging knowledge", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2964", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "from various external knowledge resources, e.g., Wikipedia [56], ConceptNet [50], and ASER [71], to improve the performance of the VQA models. Inspired by PICa [67], recent works [15, 29] use GPT-3 as an implicit knowledge base and achieve state-of-the-art results. We identify the critical problem: generic captions used to prompt GPT-3 often miss critical visual details for VQA. We address this challenge with PROMPTCAP.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Vision-Language Models Vision-language models have recently shown striking success on various multimodal tasks [51, 33, 9, 27, 61, 22, 43, 66, 57, 58, 34, 68, 8, 26]. These works first pretrain multimodal models on large-scale image-text datasets and then finetune the models for particular tasks. The works most related to ours are Frozen [54], Flamingo [1], and BLIP-2 [26], which keeps the LMs frozen and tune a visual encoder for the LM. However, such techniques require access to internal LM parameters and are thus difficult to be applied to black-box LMs like GPT-3.", + "bbox": [ + 75, + 220, + 473, + 371 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Prompting for Language Models Prompting allows a pre-trained model to adapt to different tasks via different prompts without modifying any parameters. LLMs like GPT-3 [5] have shown strong zero-shot and few-shot ability via prompting. Prompting has been successful for a variety of natural language tasks [32], including but not limited to classification tasks [39, 48], semantic parsing [64], knowledge generation [49, 30], and dialogue systems [24, 16]. The most closely-related works to ours are the instruction-finetuned language models [45, 62, 59].", + "bbox": [ + 75, + 380, + 470, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. PROMPTCAP", + "text_level": 1, + "bbox": [ + 76, + 542, + 215, + 558 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We introduce PROMPTCAP, an image captioning model that utilizes a natural language prompt as an input condition. The overview of PROMPTCAP training is in Figure 2. Given an image $I$ , and a natural language prompt $P$ , PROMPTCAP generates a prompt-guided caption $C$ . $P$ contains instructions about the image contents of interest to the user. For VQA, an example prompt could be \"Please describe this image according to the following question: what type plane is this?. The prompt-guided caption $C$ should (1) cover the visual details required by the instruction in the prompt, (2) describe the main objects as general captions do, and (3) use auxiliary information in the prompt if necessary. For instance, assuming the prompt contains a VQA question, $C$ may directly describe the asked visual contents (e.g., for questions about visual details), or provide information that helps downstream models to infer the answer (e.g., for questions that need external knowledge to solve).", + "bbox": [ + 75, + 568, + 470, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given the above design, the major technical challenge is PROMPTCAP training. PROMPTCAP is designed to work with black-box LMs, which cannot be end-to-end fine-tuned on VQA tasks because the LM parameters are not accessible. Besides, there are no training data for question-aware", + "bbox": [ + 75, + 825, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/20c81328417e3cfe2ceb49ecd585084ac011578342b015f1781174aa0b6000b5.jpg", + "image_caption": [ + "Figure 3. Training example synthesis with GPT-3 in-context learning. The \"Original Contexts\" are ground-truth image captions. The question-answer pairs come from existing VQA datasets. GPT-3 generalizes (without parameter updates) from the human-written examples to produce the question-aware caption given the caption, question, and answer. The images are shown for clarity but are not used in our data synthesis procedure." + ], + "image_footnote": [], + "bbox": [ + 516, + 90, + 880, + 353 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": " captions. To address these challenges, we propose training PROMPTCAP with data synthesized with GPT-3.", + "bbox": [ + 498, + 468, + 890, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Training Data Synthesis", + "text_level": 1, + "bbox": [ + 500, + 517, + 720, + 534 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To avoid annotating question-aware caption examples, we use GPT-3 to generate training examples for PROMPTCAP via in-context learning [5, 44, 16, 10].", + "bbox": [ + 498, + 542, + 890, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1.1 Training Example Generation with GPT-3", + "text_level": 1, + "bbox": [ + 500, + 614, + 846, + 630 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For PROMPTCAP training, we view existing VQA datasets as natural sources of pairs of task and task-related visual details. We synthesize question-aware captions by combining the general image captions and the question-answering pairs using GPT-3 in-context learning. Figure 3 illustrates the GPT-3 prompt we use for training example generation. The prompt contains the task instruction, 20 human-written examples, and the VQA question-image pair that we synthesize the task-aware caption from. Since GPT-3 only accepts text inputs, we represent each image by concatenating the 5 human-written COCO captions [7], as shown in the \"Original Context\". The human-written examples follow the three principles of prompt-guided captions described in Section 3. The commonsense reasoning ability of GPT-3 allows the model to understand the image to some extent via the COCO captions and synthesize new examples by following the human-written examples.", + "bbox": [ + 496, + 643, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2965", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1.2 Training Example Filtering", + "text_level": 1, + "bbox": [ + 76, + 90, + 323, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To ensure the quality of the generated captions, we sample 5 candidate captions from GPT-3 for each question-answer pair. We devise a pipeline to filter out the best candidate caption as the training example for PROMPTCAP. The idea is that a text-only QA system should correctly answer the question given a high-quality prompt-guided caption as the context. For each candidate caption, we use the GPT-3 in-context learning VQA system in §4 to predict an answer, and score the candidate captions by comparing this answer with the ground-truth answers.", + "bbox": [ + 75, + 114, + 470, + 267 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Soft VQA Accuracy We find that in the open-ended generation setting, the VQA accuracy [14] incorrectly punishes answers with a slight difference in surface form. For example, the answer \"coins\" gets 0 when the ground truth is \"coin\". To address this problem, we devise a new soft VQA accuracy for example filtering. Suppose the predicted answer is $a$ and the human-written ground truth answers are $[g_1, g_2, \\dots, g_n]$ . The soft accuracy is given by the three lowest-CER ground truth answers:", + "bbox": [ + 75, + 277, + 472, + 414 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA c c _ {s o f t} (a) = \\max _ {x, y, z \\in [ n ]} \\sum_ {i \\in \\{x, y, z \\}} \\frac {\\max [ 0 , 1 - C E R (a , g _ {i}) ]}{3},\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 422, + 465, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where CER is the character error rate, calculated by the character edit distance over the total number of characters of the ground truth. In contrast, the traditional VQA accuracy [14] uses exact match. We sort the candidate captions based on this soft score.", + "bbox": [ + 75, + 474, + 470, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Comparing with COCO ground-truth Multiple candidates may answer the question correctly and get the same soft score. To break ties, we also compute the CIDEr score [55] between the candidate captions and the COCO ground-truth captions. Among the candidates with the highest soft VQA accuracy, the one with the highest CIDEr score is selected as the training example for PROMPTCAP.", + "bbox": [ + 75, + 561, + 470, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. PROMPTCAP Training", + "text_level": 1, + "bbox": [ + 76, + 678, + 274, + 695 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For PROMPTCAP training, we start with the state-of-the-art pre-trained vision-language model OFA [58] and make some modifications to the OFA captioning model. OFA has an encoder-decoder structure. As discussed earlier, our training data are synthesized with VQA data in the form of question-caption pairs. Given a question-caption pair, we first rewrite the question into an instruction prompt via a template. For example, the instruction prompt might be \"describe to answer: What is the clock saying the time is?\" We apply byte-pair encoding (BPE) [47] to the given text sequence, encoding it as subwords. Images are transformed into image patches that share the same subword token set. Let the training samples be $\\mathcal{D} = \\{P_i,I_i,C_i\\}_{i = 1}^{|\\mathcal{D}|}$ ,", + "bbox": [ + 75, + 702, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "in which $P_{i}$ is the text prompt, $I_{i}$ is the image patch, and $C_i$ is the synthesized task-aware caption. The captioning model takes $[P_{i}:I_{i}]$ as input and is trained to generate $C_i = [c_1,c_2,\\dots ,c_{|C_i|}]$ . Here $[:]$ is concatenation. We use negative log-likelihood loss and train the model in an end-to-end manner. The training loss is:", + "bbox": [ + 496, + 90, + 893, + 181 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = - \\sum_ {\\mathcal {D}} \\sum_ {t = 1} ^ {| C _ {i} |} \\log p (c _ {t} \\mid [ P _ {i}: I _ {i} ], c _ {\\leq t - 1}).\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 191, + 836, + 236 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. VQA with PROMPTCAP and GPT-3", + "text_level": 1, + "bbox": [ + 498, + 258, + 825, + 275 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our VQA pipeline is illustrated in Figure 4, which is adopted from PICa [67]. The pipeline consists of two components, PROMPTCAP and GPT-3.", + "bbox": [ + 496, + 282, + 893, + 329 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Step 1: Converting images into texts via PROMPTCAP GPT-3 can perform a new task by simply conditioning on several task training examples as demonstrations. As we have discussed, the major challenge is that GPT-3 does not understand images. To bridge this modality gap, we convert the images in VQA samples to texts using PROMPTCAP (Figure 4a). Notice that different from generic captioning models, PROMPTCAP customizes the image caption according to the question, which enables LMs to understand question-related visual information in the image. As such, we are able to convert VQA samples into question-answering examples that GPT-3 can understand.", + "bbox": [ + 496, + 338, + 893, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Step 2: GPT-3 in-context learning for VQA Having used PROMPTCAP to convert VQA examples into question-answer examples that GPT-3 can understand (Step 1), we use a subset of these examples as the task demonstration for GPT-3. We concatenate the in-context learning examples to form a prompt, as shown in Figure 4b. Each in-context learning example consists of a question (Question: When was the first time this was invented?), a context generated by PROMPTCAP (Context: a train traveling down tracks next to a dirt road), and an answer (Answer: 1804). Then we append the test example to the in-context learning examples, and provide them as inputs to GPT-3. GPT-3 generates predictions based on an open-ended text generation approach, taking into account the information provided in the in-context learning examples and the test example.", + "bbox": [ + 496, + 527, + 895, + 786 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Example retrieval Previous research has shown that the effectiveness of in-context learning examples chosen for GPT-3 can significantly impact its performance [31]. In the few-shot setting where only a few training examples are available, we simply use these examples as in-context learning examples (referred to as \"Random\" in later sections because they are selected at random from our collection). However,", + "bbox": [ + 496, + 794, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2966", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/52698ffdeb7ac290a3c2d13516fce01c0bd7d6f37830821568c5503bbebafeb4.jpg", + "image_caption": [ + "(a) Step 1: Using PromptCap to convert images into texts" + ], + "image_footnote": [], + "bbox": [ + 127, + 107, + 830, + 223 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/656dece4e825f8a086d58d753dd5f7fc5fff7142237eacc22382f5914b2a2afe.jpg", + "image_caption": [ + "(b) Step 2: VQA with PromptCap and in-context learning on GPT-3", + "Figure 4. Our inference pipeline for VQA. (a) Illustration of how we convert a VQA sample into pure text. Given the image and the question, PROMPTCAP describes the question-related visual information in natural language. The VQA sample is turned into a QA sample that GPT-3 can understand. (b) GPT-3 in-context learning for VQA. After converting the VQA examples into text with PROMPTCAP, we carry out VQA by in-context learning on GPT-3. The input consists of the task instruction (not shown in the figure), the in-context examples, and the test instance. GPT-3 takes the input and generates the answer. Notice that the GPT-3 is treated as a black box and is only used for inference. The question-aware captions PROMPTCAP generated are marked red." + ], + "image_footnote": [], + "bbox": [ + 119, + 244, + 849, + 383 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in practice, we often have access to more than small- $n$ examples (i.e., full training data setting). To improve the selection of in-context learning examples, we follow the approach proposed by [67]: we compute the similarity between examples using CLIP [43] by summing up the cosine similarities of the question and image embeddings. The $n$ most similar examples in the training set are then selected as in-context examples (referred to as \"CLIP\" in this paper). By using the most similar in-context examples to the test instance, our approach can improve the quality of the learned representations and boost the performance of GPT-3 on VQA tasks.", + "bbox": [ + 75, + 479, + 470, + 645 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 660, + 209, + 678 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we demonstrate PROMPTCAP's effectiveness on knowledge-based VQA tasks. First, we show that PROMPTCAP captions enable GPT-3 to achieve state-of-the-art performance on OK-VQA [38] and A-OKVQA [46] with in-context learning. Then we conduct ablation experiments on the contribution of each component, showing that PROMPTCAP is giving consistent gains over generic captions. In addition, experiments on WebQA [6] demonstrate that PROMPTCAP generalizes well to unseen domains.", + "bbox": [ + 75, + 686, + 470, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 830, + 266, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets We use three knowledge-based VQA datasets, namely OK-VQA [38], A-OKVQA [46], and WebQA [6]. OK-VQA[38] is a large knowledge-based VQA dataset that", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "contains 14K image-question pairs. Questions are manually filtered to ensure that outside knowledge is required to answer the questions. A-OKVQA[46] is an augmented successor of OK-VQA, containing 25K image-question pairs that require broader commonsense and world knowledge to answer. For both OK-VQA and A-OKVQA, the direct answers are evaluated by the soft accuracy from VQAv2[14]. Besides direct answer evaluation, A-OKVQA also provides multiple-choice evaluation, where the model should choose one correct answer among 4 candidates. WebQA [6] is a multimodal multi-hop reasoning benchmark that requires the model to combine multiple text and image sources to answer a question.", + "bbox": [ + 496, + 479, + 893, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "PROMPTCAP implementation details We adopt the officially released OFA [58] captioning checkpoint \"caption-large-best-clean\" (470M) for model initialization and use the GPT-3 synthesized examples in §3.1 to fine-tune the model. The examples are synthesized from VQAv2 [3, 14]. Notice that this dataset is included in OFA pre-training, so we are not adding additional annotated training data compared with OFA. We use AdamW [23] optimizer with learning rate $\\{2 \\times 10^{-5}, 3 \\times 10^{-5}, 5 \\times 10^{-5}\\}$ , batch size $\\{32, 64, 128\\}$ , and $\\beta_{1} = 0.9$ , $\\beta_{2} = 0.999$ for training.", + "bbox": [ + 496, + 690, + 893, + 842 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In-context learning details We use code-davinci-002 engine (175B) for GPT-3 in all the experiments. Due to the input length limit, we use $n = 32$ most similar examples in", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2967", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/c1843cc71e1d2390adce8dd6e67a5625c7139167756442fdf9bc2da93b9a06ac.jpg", + "table_caption": [ + "Table 1. Results comparison with existing systems on OK-VQA, with the image representation and the knowledge source each method uses. GPT-3 is frozen for all methods. The methods on top require end-to-end finetuning on OK-VQA. The methods below are fully based on in-context learning or zero-shot learning and do not require task-specific finetuning." + ], + "table_footnote": [], + "table_body": "
MethodImage RepresentationKnowledge SourceAccuracy (%)
End-to-End Finetuning
Question only [37]--14.9
MUTAN [38]Feature-26.4
BAN + KG + AUG [25]FeatureWikipedia + ConceptNet26.7
ConceptBERT [13]FeatureConceptNet33.7
KRISP [36]FeatureWikipedia + ConceptNet38.4
Vis-DPR [35]FeatureGoogle Search39.2
MAVEx [63]FeatureWikipedia + ConceptNet + Google Images39.4
TRiG [12]Caption + Tags + OCRWikipedia50.5
KAT (Single) [15]Caption + Tags + FeatureGPT-3 (175B) + Wikidata54.4
KAT (Ensemble) [15]Caption + Tags + FeatureGPT-3 (175B) + Wikidata54.4
REVIVE (Single) [29]Caption + FeatureGPT-3 (175B) + Wikidata56.6
REVIVE (Ensemble) [29]Caption + FeatureGPT-3 (175B) + Wikidata58.0
In-Context Learning & Zero-Shot
BLIP-2 VIT-G FlanT5XXL [26] (zero-shot)FeatureFlanT5-XXL (11B)45.9
PICa-Base [67]Caption + TagsGPT-3 (175B)43.3
PICa-Full [67]Caption + TagsGPT-3 (175B)48.0
Flamingo (80B) [1] (zero-shot)FeatureChinchilla (70B)50.6
Flamingo (80B) [1] (32-shot)FeatureChinchilla (70B)57.8
PromptCap + GPT-3CaptionGPT-3 (175B)60.4
", + "bbox": [ + 76, + 128, + 893, + 444 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/257828fbb48af174930973d402d8c0d6299ef58a17a6559119282710d6d6f154.jpg", + "table_caption": [ + "Table 2. Results comparison with existing systems on A-OKVQA. There are two evaluations, namely multiple-choice and direct-answer. Both are measured by accuracy $(\\%)$ ." + ], + "table_footnote": [], + "table_body": "
MethodMultiple ChoiceDirect Answer
valtestvaltest
ClipCap [46]44.043.818.115.8
Pythia [19]49.040.125.221.9
ViLBERT [33]49.141.530.625.9
LXMERT [53]51.441.630.725.9
KRISP [36]51.942.233.727.1
GPV-2 [20]60.353.748.640.7
PromptCap + GPT-373.273.156.359.6
", + "bbox": [ + 84, + 505, + 460, + 652 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the prompt for GPT-3. The examples are retrieved by CLIP (VIT-L/14) using the method discussed in $\\S 4$ .", + "bbox": [ + 75, + 667, + 468, + 698 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Results on OK-VQA and A-OKVQA", + "text_level": 1, + "bbox": [ + 76, + 709, + 395, + 726 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1 compares PROMPTCAP + GPT-3 with other methods on the OK-VQA validation set. For each method, we also list the way it represents the images, and the knowledge source used. The table is split into two sections. The upper section lists fully supervised methods. These methods require end-to-end finetuning. The methods in the bottom section are based on in-context learning and no task-specific finetuning is done on the models.", + "bbox": [ + 75, + 733, + 468, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We can see that all state-of-the-art systems use GPT-3 (or Chinchilla) as part of their systems. These methods obtain significant performance gains compared with previous", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "methods, showing the importance of the LM in knowledge-based VQA tasks. PICa is the first system that used GPT-3 as the knowledge source. KAT [15] further improves over PICa by introducing Wikidata [56] as the knowledge source, doing ensemble and end-to-end finetuning on multiple components. REVIVE [29] is the current state of the art on OK-VQA. Compared with KAT, it introduces extra object-centric visual features to the ensemble, which brings additional gains over KAT. However, all of the above methods use generic image captions to prompt knowledge from GPT-3. We identify this as a critical bottleneck in using LMs for VQA tasks. PROMPTCAP is designed to address this bottleneck.", + "bbox": [ + 496, + 467, + 893, + 648 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with state of the art Our proposed PROMPT-CAP + GPT-3, despite using no additional knowledge source, no ensemble with visual features, and no end-to-end finetuning, achieves $60.4\\%$ accuracy and outperforms all existing methods on OK-VQA. Table 2 shows similar results on AOKVQA, in which PROMPTCAP + GPT-3 outperforms all prior methods by a large margin on both multiple-choice $(73.1\\%)$ and direct-answer $(59.6\\%)$ evaluations. These results demonstrate PROMPTCAP's effectiveness in connecting LMs with images. Besides, we would like to emphasize that PROMPTCAP could replace the captioning module in the systems KAT and REVIVE have proposed, which might further boost the performance. We expect that PROMPTCAP will help future systems with complementary advances to achieve even better performance on these tasks.", + "bbox": [ + 496, + 674, + 895, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2968", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 90, + 228, + 107 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct extensive ablation studies to quantify the performance benefit of each component in our system, i.e., the captioning model PROMPTCAP, the language model, and the prompting method. We conduct ablation experiments on each component.", + "bbox": [ + 76, + 113, + 470, + 189 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Additional dataset for analysis Besides knowledge-based VQA tasks, we would also like to investigate the performance gain from PROMPTCAP for traditional VQA. Thus, we also include VQAv2 [3] in our ablation studies.", + "bbox": [ + 76, + 198, + 470, + 258 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d46df63e9ea704649cbe6db2d9b6236ee5cc80e571f96e07d31a2ff2b487025b.jpg", + "table_caption": [ + "Table 3. Ablation on the contribution of PROMPTCAP, compared with generic captioning model OFA-Cap. The LM we use is GPT-3." + ], + "table_footnote": [], + "table_body": "
Captioning ModelOK-VQAA-OKVQAVQAv2
OFA-Cap56.651.064.9
PROMPTCAP60.456.374.1
", + "bbox": [ + 89, + 296, + 452, + 353 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3.1 Performance Benefit from PROMPTCAP", + "text_level": 1, + "bbox": [ + 76, + 368, + 410, + 382 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baseline generic captioning model We use the officially released OFA [58] captioning checkpoint \"caption-large-best-clean\" (470M) as the baseline generic captioning model. We refer to it as \"OFA-Cap\". We choose this model because this is the model initialization we use for PROMPTCAP, sharing the same model architecture. Notice that OFA is a large vision-language model pre-trained on 20M image-text pairs and 20 vision-language tasks, including many VQA tasks. We are not using additional annotated data during PROMPT-CAP finetuning.", + "bbox": [ + 75, + 391, + 470, + 542 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "PROMPTCAP captions give consistent gains over generic captions. Table 3 measures the performance benefit from PROMPTCAP on OK-VQA, A-OKVQA, and VQAv2 validation sets. Here we focus on the performance gap between using PROMPTCAP captions and generic OFA captions. We can see that PROMPTCAP gives consistent improvements over generic captions. Specifically, with GPT-3, PROMPTCAP improves over OFA-Cap by $3.8\\%$ , $5.3\\%$ , and $9.2\\%$ absolute accuracy on OK-VQA, A-OKVQA, and VQAv2, respectively.", + "bbox": [ + 75, + 551, + 468, + 703 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/784a9aac89fa3df154f3a09e9ceaaf547703a076e96c75275ffdd5fcc946825a.jpg", + "table_caption": [ + "Table 4. Ablation on the contribution of GPT-3. We measure the performance gain of using GPT-3 as the language model, compared with Flan-T5-XXL (11B). The captioning model we use is PROMPTCAP." + ], + "table_footnote": [], + "table_body": "
Language ModelOK-VQAA-OKVQAVQAv2
Flan-T5-XXL (11B)42.041.570.9
GPT-3 (175B)60.456.374.1
", + "bbox": [ + 84, + 766, + 459, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3.2 Performance Benefit from Language Model", + "text_level": 1, + "bbox": [ + 76, + 845, + 433, + 862 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baseline language model To measure the performance gain from GPT-3, we choose Flan-T5-XXL(11B) [11] as", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the baseline language model. FlanT5-XXL is an instructionfinetuned LM that has shown good in-context learning ability. Notice that for Flan-T5-XXL, because of the input length limit, we use $n = 16$ in-context examples in the input.", + "bbox": [ + 496, + 90, + 893, + 152 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "GPT-3 yields huge gains on knowledge-based VQA, but not on VQAv2. Results in Table 4 quantify the benefit of GPT-3 over Flan-T5-XXL. GPT-3 yields great performance gains on knowledge-based VQA tasks, improving over Flan-T5 by $18.4\\%$ and $14.8\\%$ absolute accuracy on OK-VQA and A-OKVQA, respectively. In comparison, on VQAv2, GPT-3 only gives $3.2\\%$ accuracy gain, which is much smaller than the gain from PROMPTCAP over generic captions. The results indicate that GPT-3's external knowledge is critical for knowledge-based VQA tasks but not for VQAv2. We speculate that this disparity arises from VQAv2's focus on information in the image, without requiring additional knowledge beyond visual information.", + "bbox": [ + 496, + 171, + 893, + 369 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ad57ec870d43245c655a1bcd2478294b426b8922b9a7788065c6126ffb78dfd1.jpg", + "table_caption": [ + "Table 5. Ablation of GPT-3 prompting on OK-VQA. We experiment with different numbers of in-context examples in the input and measure the performance gain from retrieving similar in-context examples compared with random examples." + ], + "table_footnote": [], + "table_body": "
ExamplesCaptionn=1n=4n=16n=32
RandomOFA-Cap42.846.649.750.8
PROMPTCAP46.550.053.155.2
CLIPOFA-Cap44.550.055.356.6
PROMPTCAP48.753.358.460.4
", + "bbox": [ + 508, + 436, + 879, + 527 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3.3 Ablation on GPT-3 Prompting", + "text_level": 1, + "bbox": [ + 498, + 555, + 766, + 570 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As discussed in §4, two factors affect the in-context learning performance: the number of in-context examples, and the example selection strategy. To measure the effects of these two factors, we conduct an ablation study on GPT-3 prompting for OK-VQA in Table 5. We vary the number of examples $n \\in \\{1, 4, 16, 32\\}$ and experiment with random examples and the most similar examples retrieved by CLIP (VIT-L/14) [43]. We can see that for both example selection strategies, the more in-context examples, the better the performance. Also, retrieving most similar examples with CLIP gives substantial performance gain (5.2% absolute accuracy for PROMPTCAP when $n = 32$ ). Both findings agree with the claims in prior work [5, 31, 67].", + "bbox": [ + 496, + 579, + 893, + 776 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Domain Transfer on WebQA", + "text_level": 1, + "bbox": [ + 500, + 786, + 756, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We apply PROMPTCAP to WebQA [6] to evaluate PROMPTCAP's generalization ability on images and tasks from different domains. WebQA images are crawled from the web and are from domains different from the COCO [28] images used in PROMPTCAP's training data synthesized from VQAv2 [14]. Due to the task setting, questions are", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2969", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0bae8e450082eb547aa88072889fe78a8b908eb38d925e0a7457b59fb125e46e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 88, + 279, + 255 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/78890cc4b01b705191ec701e7d411ffae4c7b7c6b6fd98afb440bea439f317fd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 88, + 482, + 256 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2d5340a6a39474a5e54e11ee3ba1cd806e71d77cee1792ddd951aa4200a4d5b7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 88, + 687, + 256 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2655bc5e64208ec69e8073ebc16e462b5074eb674d5128152a1bf63b65483717.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 689, + 88, + 890, + 256 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3fe19f5859804d3acc129cc74c9e67fb7cd2a7c6e9bddebe29124882ce7702a4.jpg", + "image_caption": [ + "Figure 5. Example captions generated by PROMPTCAP and OFA-Cap, and the answers GPT-3 generated the captions. For all these questions, GPT-3 yields the correct answer given PROMPTCAP captions but fails given the generic caption. Questions are from OK-VQA." + ], + "image_footnote": [], + "bbox": [ + 78, + 257, + 482, + 321 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5cc81f5b7b6a07af6ca11e1e461558a2ae6ec543ea75fa49bdd2d44f28908073.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 257, + 687, + 321 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/052d6805ee332afd16f6b4b49264d18e02d35cf7d81e640e0109b8ce3c670834.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 689, + 257, + 890, + 321 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3dc6f2f353d1c8815f4df3a2f47c7f643dd3f463529d241a24dbf7047a283165.jpg", + "image_caption": [ + "Figure 6. Representative failure cases of PROMPTCAP and GPT-3 pipeline on OK-VQA." + ], + "image_footnote": [], + "bbox": [ + 81, + 366, + 279, + 551 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3fda532b6c76d546cbcaf922bb8d12f6e3be16aa9fec3a46216d3654b82fa939.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 366, + 483, + 551 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9a5b927fcc360f4fb4970c929002467af7ce33e3a0bdab3dc1c4c8ae0f878ce9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 366, + 687, + 551 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a1d5331937802f7ec849f7205940a7f424319c8f631f69ebfe9fa5909daaaf92.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 689, + 366, + 890, + 551 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e5a130c66d4f5cf56b95ce52dc1fdeab506e009cb355cc870e988c5936abef5b.jpg", + "table_caption": [ + "Table 6. Results on the WebQA validation set with oracle sources on image queries. The baselines in the upper part are fully supervised, while our methods only use 8-shot in-context learning." + ], + "table_footnote": [], + "table_body": "
MethodFLAccFL*Acc
Fully supervised VLP + VinVL [6]47.649.627.5
VLP + x101fpn [6]46.944.323.8
8-shot in-context learning OFA-Cap + GPT-3 PROMPTCAP + GPT-352.855.433.5
53.057.234.5
", + "bbox": [ + 101, + 619, + 444, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "compositional and much longer than typical VQA questions. We convert the source images into captions and use GPT-3 in-context learning to carry out the task with only 8 random examples. The answers are long-form and measured by two scores: the fluency score measured by BARTScore [69] and the accuracy score that measures if human-annotated keywords are included in the answer. The results in the image-query setting with oracle sources on the validation", + "bbox": [ + 75, + 779, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "set $^2$ are shown on Table 6. Our systems outperform all the official baselines. PROMPTCAP outperforms the generic OFA captions, showing that PROMPTCAP is generalizable to a different domain of questions and images.", + "bbox": [ + 496, + 582, + 890, + 643 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5. Qualitative Analysis", + "text_level": 1, + "bbox": [ + 500, + 651, + 692, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Representative captions generated by PROMPTCAP and OFA are illustrated in Figure 5. The task is to answer the questions in OK-VQA. For all these questions, GPT-3 generates the correct answer when taking PROMPTCAP's caption as input, but fails when taking the generic caption. PROMPTCAP is able to capture visual attributes according to the question, for example, \"brand\" in (b) and \"color\" in (c). In addition, it can focus on particular objects asked in the question, such as the clothing the boy is \"putting on\" in (d). For tasks beyond PROMPTCAP's reasoning ability, GPT-3 infers the answer by the visual details PROMPTCAP gives. For example, GPT-3 infers \"green\" for the \"complimentary", + "bbox": [ + 496, + 674, + 893, + 856 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "2Setting at https://github.com/WebQnA/WebQA/tree/ main/baseline_output_files/Baseline_prediction_ files_on_VAL", + "bbox": [ + 500, + 862, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2970", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "color of red\" in (c) and \"7\" for SUV's seating capacity in (a). We also show some representative failure cases in Figure 6. The majority of failures are as shown in (a) and (b), in which PROMPTCAP fails to provide helpful information, or provides unfactual information. GPT-3 sometimes makes mistakes, as shown in (c) and (d).", + "bbox": [ + 75, + 90, + 472, + 181 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/5f4e1ab4d31bb8c10898e1cfd515a9263d263b981c5ed255de1a919b2953eba3.jpg", + "table_caption": [ + "Table 7. Comparison of captions. \"GPT-3-Syn\" are the question-aware captions synthesized by GPT-3. \"COCO-GT\" are the MSCOCO ground-truth captions. Higher scores imply higher similarities between the captions." + ], + "table_footnote": [], + "table_body": "
CaptionsBMCS
Comparison between “gold captions”
GPT-3-SynCOCO-GT67.144.3182.932.1
Inferenced captions vs. “gold captions”
OFA-CapGPT-3-Syn26.225.3231.040.2
PROMPTCAPGPT-3-Syn33.029.7307.147.3
OFA-CapCOCO-GT44.530.9147.924.6
PROMPTCAPCOCO-GT45.431.6150.125.2
", + "bbox": [ + 80, + 247, + 464, + 382 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5.6. Analysis: How Do Question-Aware Captions Differ from Generic Captions?", + "text_level": 1, + "bbox": [ + 76, + 397, + 468, + 429 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "To further analyze the question-aware captions, we compare different inferred/gold captions in Table 7. The captions are compared by the automatic evaluations used in MSCOCO [7]: BLEU-4 (B) [42], METEOR (M) [4], CIDEr (C) [55], and SPICE (S) [2]. We evaluate the captions on the VQAv2 question-image pairs with images in the Karpathy test split [21] and average the scores over the questions. The upper part of the table compares the \"training targets\" for PROMPTCAP and the generic captioning model OFA-Cap. The lower part compares the captions inferred by each captioning model with these \"gold captions\". We make several observations from the table:", + "bbox": [ + 75, + 436, + 472, + 617 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "GPT-3 synthesized question-aware captions synthesized by GPT-3 are highly similar to the MSCOCO ground truth generic captions. As seen in the upper part of Table 7, the question-aware captions are really similar to the MSCOCO ground-truth captions.", + "bbox": [ + 75, + 619, + 470, + 696 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "PROMPTCAP achieves high CIDEr and SPICE scores using GPT-3 synthesized captions as reference. The second row in the lower part compares the prompt-guided captions generated by PROMPTCAP with the GPT-3 synthesized question-aware captions. We can see that the CIDEr and SPICE scores are really high. One possible reason for the high scores is that synthesized question-aware captions are typically less diverse, shorter, and cover fewer visual entities compared with human-written general captions. Moreover, the image captioning task becomes less ambiguous via the prompt's control, making it easier for PROMPTCAP to learn.", + "bbox": [ + 75, + 699, + 470, + 866 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "PROMPTCAP can also generate high-quality generic captions. The last row shows the quality of the generic captions", + "bbox": [ + 75, + 869, + 472, + 901 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "generated by PROMPTCAP. Users can get generic captions by prompting PROMPTCAP with the question \"what does the image describe?\". All the automatic metrics show that PROMPTCAP achieves SOTA performance on COCO validation set, with even higher scores than the original OFA-Cap model.", + "bbox": [ + 496, + 90, + 893, + 181 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Limitations and Broader Impact", + "text_level": 1, + "bbox": [ + 498, + 193, + 797, + 210 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "One limitation is that the current PROMPTCAP only focuses on knowledge-based VQA tasks. PROMPTCAP can be extended to other vision-language tasks beyond VQA. Figure 7 shows an example of solving NLVR2 [52] via a series of vision and reasoning steps between PROMPTCAP and ChatGPT. Future work may scale up PROMPTCAP training with more diverse tasks and instructions, and explore broader applications of PROMPTCAP beyond VQA.", + "bbox": [ + 496, + 218, + 893, + 339 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Another limitation is that images contain information that cannot be abstracted as text. While PROMPTCAP has demonstrated promising results in bridging the gap between LMs and images, it is important to recognize its limitations and use it in conjunction with other methods to ensure a comprehensive understanding of visual data.", + "bbox": [ + 496, + 339, + 893, + 429 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/5400caa03ef293aa5fe96b90b925fbc4dfb8b01ca63a8055be908206e9b8fb5e.jpg", + "image_caption": [ + "Figure 7. Demo of solving the NLVR2 task with off-the-shelf PROMPTCAP and ChatGPT via an interpretable reasoning process." + ], + "image_footnote": [], + "bbox": [ + 514, + 440, + 879, + 647 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 694, + 617, + 709 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We present PROMPTCAP, a novel question-aware captioning model that can be controlled via a natural language prompt. To train this captioning model with no extra annotation, we devise an efficient pipeline for synthesizing and filtering training examples via GPT-3. We demonstrate the effectiveness of PROMPTCAP on knowledge-based VQA tasks. Our system achieves state-of-the-art performance on OKVQA and A-OKVQA. Ablations show that PROMPTCAP is giving consistent gains over generic captions. Furthermore, we investigate PROMPTCAP's generalization ability on WebQA. PROMPTCAP works as a simple and general module for converting question-related visual information into text.", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "2971", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, Roman Ring, Eliza Rutherford, Serkan Cabi, Tengda Han, Zhitao Gong, Sina Samangooei, Marianne Monteiro, Jacob Menick, Sebastian Borgeaud, Andrew Brock, Aida Nematzadeh, Sahand Sharifzadeh, Mikolaj Binkowski, Ricardo Barreira, Oriol Vinyals, Andrew Zisserman, and Karen Simonyan. 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Mucko: multi-layer cross-modal knowledge reasoning for fact-based visual question answering. arXiv preprint arXiv:2006.09073, 2020. 2" + ], + "bbox": [ + 78, + 90, + 470, + 373 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "2975", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 12 + } +] \ No newline at end of file diff --git a/2023/PromptCap_ Prompt-Guided Image Captioning for VQA with GPT-3/4ffd89d6-8734-4748-beec-1543acfdd6d0_model.json b/2023/PromptCap_ Prompt-Guided Image Captioning for VQA with GPT-3/4ffd89d6-8734-4748-beec-1543acfdd6d0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..03871a9eb727899532f1ed35fa7c04835c7602a3 --- /dev/null +++ b/2023/PromptCap_ Prompt-Guided Image Captioning for VQA with GPT-3/4ffd89d6-8734-4748-beec-1543acfdd6d0_model.json @@ -0,0 +1,2558 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.128, + 0.131, + 0.844, + 0.154 + ], + "angle": 0, + "content": "PROMPTCAP: Prompt-Guided Image Captioning for VQA with GPT-3" + }, + { + "type": "text", + "bbox": [ + 0.235, + 0.179, + 0.734, + 0.273 + ], + "angle": 0, + "content": "Yushi Hu\\(^{1*}\\) Hang Hua\\(^{2*}\\) Zhengyuan Yang\\(^{3}\\) Weijia Shi\\(^{1}\\) Noah A. Smith\\(^{1,4}\\) Jiebo Luo\\(^{2}\\) \n\\(^{1}\\)University of Washington \\(^{2}\\)University of Rochester \\(^{3}\\)Microsoft \\(^{4}\\)Allen Institute for AI \nhttps://yushi-hu.github.io/promptcap_demo/" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.313, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.474, + 0.744 + ], + "angle": 0, + "content": "Knowledge-based visual question answering (VQA) involves questions that require world knowledge beyond the image to yield the correct answer. Large language models (LMs) like GPT-3 are particularly helpful for this task because of their strong knowledge retrieval and reasoning capabilities. To enable LM to understand images, prior work uses a captioning model to convert images into text. However, when summarizing an image in a single caption sentence, which visual entities to describe are often underspecified. Generic image captions often miss visual details essential for the LM to answer visual questions correctly. To address this challenge, we propose PROMPTCAP (Prompt-guided image Captioning), a captioning model designed to serve as a better connector between images and black-box LMs. Different from generic captions, PROMPTCAP takes a natural-language prompt to control the visual entities to describe in the generated caption. The prompt contains a question that the caption should aid in answering. To avoid extra annotation, PROMPTCAP is trained by examples synthesized with GPT-3 and existing datasets. We demonstrate PROMPTCAP's effectiveness on an existing pipeline in which GPT-3 is prompted with image captions to carry out VQA. PROMPTCAP outperforms generic captions by a large margin and achieves state-of-the-art accuracy on knowledge-based VQA tasks (60.4% on OK-VQA and 59.6% on A-OKVQA). Zeroshot results on WebQA show that PROMPTCAP generalizes well to unseen domains.1" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.774, + 0.21, + 0.789 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.799, + 0.47, + 0.83 + ], + "angle": 0, + "content": "Knowledge-based visual question answering (VQA) [37] extends traditional VQA tasks [3] with questions that require" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.839, + 0.472, + 0.902 + ], + "angle": 0, + "content": "*Equal contribution. Correspondance to , \n1All codes, data, and demos are available on the project page. HF checkpoint: https://huggingface.co/tifa-benchmark/promptcap-coco-vqa" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.304, + 0.88, + 0.573 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.55, + 0.575, + 0.851, + 0.588 + ], + "angle": 0, + "content": "v.s. COCO caption: A traffic light on a pole on a city street." + }, + { + "type": "image_footnote", + "bbox": [ + 0.499, + 0.591, + 0.896, + 0.703 + ], + "angle": 0, + "content": "Figure 1. Illustration of VQA with PROMPTCAP and ChatGPT. PROMPTCAP is designed to work with black-box language models (e.g., GPT-3, ChatGPT) by describing question-related visual information in the text. Different from generic captions, PROMPTCAP customizes the caption according to the input question prompt, which helps ChatGPT understand the image and give correct answers to the user. In contrast, ChatGPT cannot infer the answers from the vanilla human-written caption from MSCOCO." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.716, + 0.895, + 0.867 + ], + "angle": 0, + "content": "broad knowledge and commonsense reasoning to yield the correct answer. Existing systems on knowledge-based VQA retrieve external knowledge from various sources, including knowledge graphs [13, 36, 63], Wikipedia [36, 63, 12, 15, 29], and web search [35, 63]. Recent work [67] finds that modern language models (LMs) like GPT-3 [5] are particularly useful for this task because of their striking knowledge retrieval and reasoning abilities. The current state-of-the-art methods [67, 15, 29, 1] all make use of recent large language models (GPT-3 or Chinchilla)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.895, + 0.902 + ], + "angle": 0, + "content": "One key challenge is to allow LMs to understand images. Many top-performing LMs (e.g., GPT-3, ChatGPT) are only" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2963" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "accessible via APIs, making it impossible to access their internal representations or conduct fine-tuning [49]. A popular solution is to project images into texts that black-box LMs can process, via a generic image captioning model [7] or an image tagger [67]. This framework has been successful on multiple tasks, including VQA [67, 15, 29], image paragraph captioning [65], and video-language tasks [70, 60]. Despite promising results, converting visual inputs into a generic, finite text description risks excluding information necessary for the task. As discussed in PICa [67], when used for VQA tasks, the generic caption might miss the detailed visual information needed to answer the question, such as missing the \"McDonald's\" in Figure 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.29, + 0.473, + 0.548 + ], + "angle": 0, + "content": "To address the above challenges, we introduce PROMPTCAP, a question-aware captioning model designed to serve as a better connector between images and a black-box LM. PROMPTCAP is illustrated in Figure 2. PROMPTCAP takes an extra natural language prompt as input to control the visual content to describe. The prompt contains the question that the generated caption should help to answer. LMs can better answer visual questions by using PROMPTCAP as their \"visual front-end\". For example, in Figure 1, when asked \"what is the time of the day?\", PROMPTCAP includes \"in the evening\" in its image description; when asked \"what kind of food does the restaurant on the sign serve?\", PROMPTCAP includes \"McDonald's\" in its description. Such visual information is critical for ChatGPT to reply to the user with the correct answers. In contrast, the generic COCO [28] caption often contains no information about the time or the sign, making ChatGPT unable to answer the questions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.473, + 0.822 + ], + "angle": 0, + "content": "One major technical challenge is PROMPTCAP training. The pipeline of \"PROMPTCAP + black-box LM\" cannot be end-to-end fine-tuned on VQA tasks because the LM parameters are not exposed through the API. Also, there are no training data for question-aware captions. To avoid extra annotation, we propose a pipeline to synthesize and filter training samples with GPT-3. Specifically, we view existing VQA datasets as pairs of question and question-related visual details. Given a question-answer pair, we rewrite the corresponding image's generic caption into a customized caption that helps answer the question. Following 20 human-annotated examples, GPT-3 synthesizes a large number of question-aware captions via few-shot in-context learning [5]. To ensure the sample quality, we filter the generated captions by performing QA with GPT-3, checking if the answer can be inferred given the question and the synthesized caption. Notice that GPT-3 is frozen in the whole pipeline. Its strong few-shot learning ability makes this pipeline possible." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We demonstrate the effectiveness of PROMPTCAP on knowledge-based VQA tasks with the pipeline in PICa [67]. Details of the pipeline are illustrated in §4. The images are converted into texts via PROMPTCAP, allowing GPT-3 to perform VQA via in-context learning. This pipeline, despite" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.088, + 0.896, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.282, + 0.896, + 0.394 + ], + "angle": 0, + "content": "Figure 2. Overview of PROMPTCAP training. PROMPTCAP takes two inputs, including an image and a natural language prompt. The model is trained to generate a caption that helps downstream LMs to answer the question. During training, we use GPT-3 to synthesize VQA samples into captioning examples. The original caption is rewritten into a caption that helps answer the question. PROMPTCAP is trained to generate this synthesized caption given the image and the prompt." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.418, + 0.895, + 0.599 + ], + "angle": 0, + "content": "its simplicity, achieves state-of-the-art results on knowledge-based VQA tasks (60.4% on OK-VQA [38] and 59.6% on A-OKVQA [46]). We also conduct extensive ablation studies on the contribution of each component, showing that PROMPTCAP gives a consistent performance gain (3.8% on OK-VQA, 5.3% on A-OKVQA, and 9.2% on VQAv2) over a generic captioning model that shares the same architecture and training data. Finally, we investigate PROMPTCAP's generalization ability on WebQA [6], showing that PROMPTCAP, without any training on the compositional questions in WebQA, outperforms the generic caption approach and all supervised baselines." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.6, + 0.822, + 0.614 + ], + "angle": 0, + "content": "In summary, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.628, + 0.894, + 0.673 + ], + "angle": 0, + "content": "- We propose PROMPTCAP, a novel question-aware captioning model that uses natural language prompt to control the visual content to be described. (§3)" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.684, + 0.894, + 0.73 + ], + "angle": 0, + "content": "- To the best of our knowledge, we are the first to propose a pipeline to synthesize and filter training samples for vision-language tasks via GPT-3 (§3.1)." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.74, + 0.894, + 0.801 + ], + "angle": 0, + "content": "- PROMPTCAP helps GPT-3 in-context learning (\\$4) achieve state-of-the-art results on OK-VQA and A-OKVQA, substantially outperforming generic captions on various VQA tasks. (\\$5)." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.628, + 0.894, + 0.801 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.815, + 0.642, + 0.831 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Knowledge-Based VQA Knowledge-based VQA [38, 46] requires systems to leverage external knowledge beyond image content to answer the question. Prior works [13, 36, 63, 72, 40, 41, 17, 18, 12] investigate leveraging knowledge" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2964" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "from various external knowledge resources, e.g., Wikipedia [56], ConceptNet [50], and ASER [71], to improve the performance of the VQA models. Inspired by PICa [67], recent works [15, 29] use GPT-3 as an implicit knowledge base and achieve state-of-the-art results. We identify the critical problem: generic captions used to prompt GPT-3 often miss critical visual details for VQA. We address this challenge with PROMPTCAP." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.221, + 0.474, + 0.372 + ], + "angle": 0, + "content": "Vision-Language Models Vision-language models have recently shown striking success on various multimodal tasks [51, 33, 9, 27, 61, 22, 43, 66, 57, 58, 34, 68, 8, 26]. These works first pretrain multimodal models on large-scale image-text datasets and then finetune the models for particular tasks. The works most related to ours are Frozen [54], Flamingo [1], and BLIP-2 [26], which keeps the LMs frozen and tune a visual encoder for the LM. However, such techniques require access to internal LM parameters and are thus difficult to be applied to black-box LMs like GPT-3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.472, + 0.533 + ], + "angle": 0, + "content": "Prompting for Language Models Prompting allows a pre-trained model to adapt to different tasks via different prompts without modifying any parameters. LLMs like GPT-3 [5] have shown strong zero-shot and few-shot ability via prompting. Prompting has been successful for a variety of natural language tasks [32], including but not limited to classification tasks [39, 48], semantic parsing [64], knowledge generation [49, 30], and dialogue systems [24, 16]. The most closely-related works to ours are the instruction-finetuned language models [45, 62, 59]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.544, + 0.216, + 0.559 + ], + "angle": 0, + "content": "3. PROMPTCAP" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.472, + 0.825 + ], + "angle": 0, + "content": "We introduce PROMPTCAP, an image captioning model that utilizes a natural language prompt as an input condition. The overview of PROMPTCAP training is in Figure 2. Given an image \\( I \\), and a natural language prompt \\( P \\), PROMPTCAP generates a prompt-guided caption \\( C \\). \\( P \\) contains instructions about the image contents of interest to the user. For VQA, an example prompt could be \"Please describe this image according to the following question: what type plane is this?. The prompt-guided caption \\( C \\) should (1) cover the visual details required by the instruction in the prompt, (2) describe the main objects as general captions do, and (3) use auxiliary information in the prompt if necessary. For instance, assuming the prompt contains a VQA question, \\( C \\) may directly describe the asked visual contents (e.g., for questions about visual details), or provide information that helps downstream models to infer the answer (e.g., for questions that need external knowledge to solve)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Given the above design, the major technical challenge is PROMPTCAP training. PROMPTCAP is designed to work with black-box LMs, which cannot be end-to-end fine-tuned on VQA tasks because the LM parameters are not accessible. Besides, there are no training data for question-aware" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.091, + 0.882, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.355, + 0.895, + 0.453 + ], + "angle": 0, + "content": "Figure 3. Training example synthesis with GPT-3 in-context learning. The \"Original Contexts\" are ground-truth image captions. The question-answer pairs come from existing VQA datasets. GPT-3 generalizes (without parameter updates) from the human-written examples to produce the question-aware caption given the caption, question, and answer. The images are shown for clarity but are not used in our data synthesis procedure." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.469, + 0.892, + 0.5 + ], + "angle": 0, + "content": " captions. To address these challenges, we propose training PROMPTCAP with data synthesized with GPT-3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.518, + 0.722, + 0.535 + ], + "angle": 0, + "content": "3.1. Training Data Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.544, + 0.892, + 0.59 + ], + "angle": 0, + "content": "To avoid annotating question-aware caption examples, we use GPT-3 to generate training examples for PROMPTCAP via in-context learning [5, 44, 16, 10]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.615, + 0.848, + 0.631 + ], + "angle": 0, + "content": "3.1.1 Training Example Generation with GPT-3" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.902 + ], + "angle": 0, + "content": "For PROMPTCAP training, we view existing VQA datasets as natural sources of pairs of task and task-related visual details. We synthesize question-aware captions by combining the general image captions and the question-answering pairs using GPT-3 in-context learning. Figure 3 illustrates the GPT-3 prompt we use for training example generation. The prompt contains the task instruction, 20 human-written examples, and the VQA question-image pair that we synthesize the task-aware caption from. Since GPT-3 only accepts text inputs, we represent each image by concatenating the 5 human-written COCO captions [7], as shown in the \"Original Context\". The human-written examples follow the three principles of prompt-guided captions described in Section 3. The commonsense reasoning ability of GPT-3 allows the model to understand the image to some extent via the COCO captions and synthesize new examples by following the human-written examples." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2965" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.092, + 0.325, + 0.108 + ], + "angle": 0, + "content": "3.1.2 Training Example Filtering" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.471, + 0.268 + ], + "angle": 0, + "content": "To ensure the quality of the generated captions, we sample 5 candidate captions from GPT-3 for each question-answer pair. We devise a pipeline to filter out the best candidate caption as the training example for PROMPTCAP. The idea is that a text-only QA system should correctly answer the question given a high-quality prompt-guided caption as the context. For each candidate caption, we use the GPT-3 in-context learning VQA system in §4 to predict an answer, and score the candidate captions by comparing this answer with the ground-truth answers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.278, + 0.473, + 0.415 + ], + "angle": 0, + "content": "Soft VQA Accuracy We find that in the open-ended generation setting, the VQA accuracy [14] incorrectly punishes answers with a slight difference in surface form. For example, the answer \"coins\" gets 0 when the ground truth is \"coin\". To address this problem, we devise a new soft VQA accuracy for example filtering. Suppose the predicted answer is \\( a \\) and the human-written ground truth answers are \\( [g_1, g_2, \\dots, g_n] \\). The soft accuracy is given by the three lowest-CER ground truth answers:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.424, + 0.466, + 0.466 + ], + "angle": 0, + "content": "\\[\nA c c _ {s o f t} (a) = \\max _ {x, y, z \\in [ n ]} \\sum_ {i \\in \\{x, y, z \\}} \\frac {\\max [ 0 , 1 - C E R (a , g _ {i}) ]}{3},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.471, + 0.552 + ], + "angle": 0, + "content": "where CER is the character error rate, calculated by the character edit distance over the total number of characters of the ground truth. In contrast, the traditional VQA accuracy [14] uses exact match. We sort the candidate captions based on this soft score." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.563, + 0.472, + 0.669 + ], + "angle": 0, + "content": "Comparing with COCO ground-truth Multiple candidates may answer the question correctly and get the same soft score. To break ties, we also compute the CIDEr score [55] between the candidate captions and the COCO ground-truth captions. Among the candidates with the highest soft VQA accuracy, the one with the highest CIDEr score is selected as the training example for PROMPTCAP." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.679, + 0.275, + 0.696 + ], + "angle": 0, + "content": "3.2. PROMPTCAP Training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.473, + 0.904 + ], + "angle": 0, + "content": "For PROMPTCAP training, we start with the state-of-the-art pre-trained vision-language model OFA [58] and make some modifications to the OFA captioning model. OFA has an encoder-decoder structure. As discussed earlier, our training data are synthesized with VQA data in the form of question-caption pairs. Given a question-caption pair, we first rewrite the question into an instruction prompt via a template. For example, the instruction prompt might be \"describe to answer: What is the clock saying the time is?\" We apply byte-pair encoding (BPE) [47] to the given text sequence, encoding it as subwords. Images are transformed into image patches that share the same subword token set. Let the training samples be \\(\\mathcal{D} = \\{P_i,I_i,C_i\\}_{i = 1}^{|\\mathcal{D}|}\\)," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.183 + ], + "angle": 0, + "content": "in which \\( P_{i} \\) is the text prompt, \\( I_{i} \\) is the image patch, and \\( C_i \\) is the synthesized task-aware caption. The captioning model takes \\( [P_{i}:I_{i}] \\) as input and is trained to generate \\( C_i = [c_1,c_2,\\dots ,c_{|C_i|}] \\). Here \\( [:] \\) is concatenation. We use negative log-likelihood loss and train the model in an end-to-end manner. The training loss is:" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.193, + 0.838, + 0.237 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = - \\sum_ {\\mathcal {D}} \\sum_ {t = 1} ^ {| C _ {i} |} \\log p (c _ {t} \\mid [ P _ {i}: I _ {i} ], c _ {\\leq t - 1}).\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.259, + 0.826, + 0.276 + ], + "angle": 0, + "content": "4. VQA with PROMPTCAP and GPT-3" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.284, + 0.895, + 0.33 + ], + "angle": 0, + "content": "Our VQA pipeline is illustrated in Figure 4, which is adopted from PICa [67]. The pipeline consists of two components, PROMPTCAP and GPT-3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.895, + 0.52 + ], + "angle": 0, + "content": "Step 1: Converting images into texts via PROMPTCAP GPT-3 can perform a new task by simply conditioning on several task training examples as demonstrations. As we have discussed, the major challenge is that GPT-3 does not understand images. To bridge this modality gap, we convert the images in VQA samples to texts using PROMPTCAP (Figure 4a). Notice that different from generic captioning models, PROMPTCAP customizes the image caption according to the question, which enables LMs to understand question-related visual information in the image. As such, we are able to convert VQA samples into question-answering examples that GPT-3 can understand." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.897, + 0.787 + ], + "angle": 0, + "content": "Step 2: GPT-3 in-context learning for VQA Having used PROMPTCAP to convert VQA examples into question-answer examples that GPT-3 can understand (Step 1), we use a subset of these examples as the task demonstration for GPT-3. We concatenate the in-context learning examples to form a prompt, as shown in Figure 4b. Each in-context learning example consists of a question (Question: When was the first time this was invented?), a context generated by PROMPTCAP (Context: a train traveling down tracks next to a dirt road), and an answer (Answer: 1804). Then we append the test example to the in-context learning examples, and provide them as inputs to GPT-3. GPT-3 generates predictions based on an open-ended text generation approach, taking into account the information provided in the in-context learning examples and the test example." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Example retrieval Previous research has shown that the effectiveness of in-context learning examples chosen for GPT-3 can significantly impact its performance [31]. In the few-shot setting where only a few training examples are available, we simply use these examples as in-context learning examples (referred to as \"Random\" in later sections because they are selected at random from our collection). However," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2966" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.12, + 0.089, + 0.44, + 0.102 + ], + "angle": 0, + "content": "(a) Step 1: Using PromptCap to convert images into texts" + }, + { + "type": "image", + "bbox": [ + 0.129, + 0.108, + 0.831, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.123, + 0.229, + 0.49, + 0.242 + ], + "angle": 0, + "content": "(b) Step 2: VQA with PromptCap and in-context learning on GPT-3" + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.245, + 0.85, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.387, + 0.892, + 0.471 + ], + "angle": 0, + "content": "Figure 4. Our inference pipeline for VQA. (a) Illustration of how we convert a VQA sample into pure text. Given the image and the question, PROMPTCAP describes the question-related visual information in natural language. The VQA sample is turned into a QA sample that GPT-3 can understand. (b) GPT-3 in-context learning for VQA. After converting the VQA examples into text with PROMPTCAP, we carry out VQA by in-context learning on GPT-3. The input consists of the task instruction (not shown in the figure), the in-context examples, and the test instance. GPT-3 takes the input and generates the answer. Notice that the GPT-3 is treated as a black box and is only used for inference. The question-aware captions PROMPTCAP generated are marked red." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.481, + 0.472, + 0.646 + ], + "angle": 0, + "content": "in practice, we often have access to more than small-\\(n\\) examples (i.e., full training data setting). To improve the selection of in-context learning examples, we follow the approach proposed by [67]: we compute the similarity between examples using CLIP [43] by summing up the cosine similarities of the question and image embeddings. The \\(n\\) most similar examples in the training set are then selected as in-context examples (referred to as \"CLIP\" in this paper). By using the most similar in-context examples to the test instance, our approach can improve the quality of the learned representations and boost the performance of GPT-3 on VQA tasks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.661, + 0.21, + 0.679 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.471, + 0.822 + ], + "angle": 0, + "content": "In this section, we demonstrate PROMPTCAP's effectiveness on knowledge-based VQA tasks. First, we show that PROMPTCAP captions enable GPT-3 to achieve state-of-the-art performance on OK-VQA [38] and A-OKVQA [46] with in-context learning. Then we conduct ablation experiments on the contribution of each component, showing that PROMPTCAP is giving consistent gains over generic captions. In addition, experiments on WebQA [6] demonstrate that PROMPTCAP generalizes well to unseen domains." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.267, + 0.849 + ], + "angle": 0, + "content": "5.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Datasets We use three knowledge-based VQA datasets, namely OK-VQA [38], A-OKVQA [46], and WebQA [6]. OK-VQA[38] is a large knowledge-based VQA dataset that" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.481, + 0.895, + 0.678 + ], + "angle": 0, + "content": "contains 14K image-question pairs. Questions are manually filtered to ensure that outside knowledge is required to answer the questions. A-OKVQA[46] is an augmented successor of OK-VQA, containing 25K image-question pairs that require broader commonsense and world knowledge to answer. For both OK-VQA and A-OKVQA, the direct answers are evaluated by the soft accuracy from VQAv2[14]. Besides direct answer evaluation, A-OKVQA also provides multiple-choice evaluation, where the model should choose one correct answer among 4 candidates. WebQA [6] is a multimodal multi-hop reasoning benchmark that requires the model to combine multiple text and image sources to answer a question." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.691, + 0.895, + 0.843 + ], + "angle": 0, + "content": "PROMPTCAP implementation details We adopt the officially released OFA [58] captioning checkpoint \"caption-large-best-clean\" (470M) for model initialization and use the GPT-3 synthesized examples in §3.1 to fine-tune the model. The examples are synthesized from VQAv2 [3, 14]. Notice that this dataset is included in OFA pre-training, so we are not adding additional annotated training data compared with OFA. We use AdamW [23] optimizer with learning rate \\(\\{2 \\times 10^{-5}, 3 \\times 10^{-5}, 5 \\times 10^{-5}\\}\\), batch size \\(\\{32, 64, 128\\}\\), and \\(\\beta_{1} = 0.9\\), \\(\\beta_{2} = 0.999\\) for training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In-context learning details We use code-davinci-002 engine (175B) for GPT-3 in all the experiments. Due to the input length limit, we use \\( n = 32 \\) most similar examples in" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2967" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.088, + 0.894, + 0.129 + ], + "angle": 0, + "content": "Table 1. Results comparison with existing systems on OK-VQA, with the image representation and the knowledge source each method uses. GPT-3 is frozen for all methods. The methods on top require end-to-end finetuning on OK-VQA. The methods below are fully based on in-context learning or zero-shot learning and do not require task-specific finetuning." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.13, + 0.895, + 0.445 + ], + "angle": 0, + "content": "
MethodImage RepresentationKnowledge SourceAccuracy (%)
End-to-End Finetuning
Question only [37]--14.9
MUTAN [38]Feature-26.4
BAN + KG + AUG [25]FeatureWikipedia + ConceptNet26.7
ConceptBERT [13]FeatureConceptNet33.7
KRISP [36]FeatureWikipedia + ConceptNet38.4
Vis-DPR [35]FeatureGoogle Search39.2
MAVEx [63]FeatureWikipedia + ConceptNet + Google Images39.4
TRiG [12]Caption + Tags + OCRWikipedia50.5
KAT (Single) [15]Caption + Tags + FeatureGPT-3 (175B) + Wikidata54.4
KAT (Ensemble) [15]Caption + Tags + FeatureGPT-3 (175B) + Wikidata54.4
REVIVE (Single) [29]Caption + FeatureGPT-3 (175B) + Wikidata56.6
REVIVE (Ensemble) [29]Caption + FeatureGPT-3 (175B) + Wikidata58.0
In-Context Learning & Zero-Shot
BLIP-2 VIT-G FlanT5XXL [26] (zero-shot)FeatureFlanT5-XXL (11B)45.9
PICa-Base [67]Caption + TagsGPT-3 (175B)43.3
PICa-Full [67]Caption + TagsGPT-3 (175B)48.0
Flamingo (80B) [1] (zero-shot)FeatureChinchilla (70B)50.6
Flamingo (80B) [1] (32-shot)FeatureChinchilla (70B)57.8
PromptCap + GPT-3CaptionGPT-3 (175B)60.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.464, + 0.472, + 0.506 + ], + "angle": 0, + "content": "Table 2. Results comparison with existing systems on A-OKVQA. There are two evaluations, namely multiple-choice and direct-answer. Both are measured by accuracy \\((\\%)\\)." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.506, + 0.462, + 0.654 + ], + "angle": 0, + "content": "
MethodMultiple ChoiceDirect Answer
valtestvaltest
ClipCap [46]44.043.818.115.8
Pythia [19]49.040.125.221.9
ViLBERT [33]49.141.530.625.9
LXMERT [53]51.441.630.725.9
KRISP [36]51.942.233.727.1
GPV-2 [20]60.353.748.640.7
PromptCap + GPT-373.273.156.359.6
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.669, + 0.47, + 0.699 + ], + "angle": 0, + "content": "the prompt for GPT-3. The examples are retrieved by CLIP (VIT-L/14) using the method discussed in \\(\\S 4\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.71, + 0.396, + 0.727 + ], + "angle": 0, + "content": "5.2. Results on OK-VQA and A-OKVQA" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.734, + 0.47, + 0.854 + ], + "angle": 0, + "content": "Table 1 compares PROMPTCAP + GPT-3 with other methods on the OK-VQA validation set. For each method, we also list the way it represents the images, and the knowledge source used. The table is split into two sections. The upper section lists fully supervised methods. These methods require end-to-end finetuning. The methods in the bottom section are based on in-context learning and no task-specific finetuning is done on the models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We can see that all state-of-the-art systems use GPT-3 (or Chinchilla) as part of their systems. These methods obtain significant performance gains compared with previous" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.468, + 0.895, + 0.649 + ], + "angle": 0, + "content": "methods, showing the importance of the LM in knowledge-based VQA tasks. PICa is the first system that used GPT-3 as the knowledge source. KAT [15] further improves over PICa by introducing Wikidata [56] as the knowledge source, doing ensemble and end-to-end finetuning on multiple components. REVIVE [29] is the current state of the art on OK-VQA. Compared with KAT, it introduces extra object-centric visual features to the ensemble, which brings additional gains over KAT. However, all of the above methods use generic image captions to prompt knowledge from GPT-3. We identify this as a critical bottleneck in using LMs for VQA tasks. PROMPTCAP is designed to address this bottleneck." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.897, + 0.901 + ], + "angle": 0, + "content": "Comparison with state of the art Our proposed PROMPT-CAP + GPT-3, despite using no additional knowledge source, no ensemble with visual features, and no end-to-end finetuning, achieves \\(60.4\\%\\) accuracy and outperforms all existing methods on OK-VQA. Table 2 shows similar results on AOKVQA, in which PROMPTCAP + GPT-3 outperforms all prior methods by a large margin on both multiple-choice \\((73.1\\%)\\) and direct-answer \\((59.6\\%)\\) evaluations. These results demonstrate PROMPTCAP's effectiveness in connecting LMs with images. Besides, we would like to emphasize that PROMPTCAP could replace the captioning module in the systems KAT and REVIVE have proposed, which might further boost the performance. We expect that PROMPTCAP will help future systems with complementary advances to achieve even better performance on these tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2968" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.23, + 0.108 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.114, + 0.471, + 0.19 + ], + "angle": 0, + "content": "We conduct extensive ablation studies to quantify the performance benefit of each component in our system, i.e., the captioning model PROMPTCAP, the language model, and the prompting method. We conduct ablation experiments on each component." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.199, + 0.472, + 0.26 + ], + "angle": 0, + "content": "Additional dataset for analysis Besides knowledge-based VQA tasks, we would also like to investigate the performance gain from PROMPTCAP for traditional VQA. Thus, we also include VQAv2 [3] in our ablation studies." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.269, + 0.471, + 0.297 + ], + "angle": 0, + "content": "Table 3. Ablation on the contribution of PROMPTCAP, compared with generic captioning model OFA-Cap. The LM we use is GPT-3." + }, + { + "type": "table", + "bbox": [ + 0.091, + 0.297, + 0.454, + 0.354 + ], + "angle": 0, + "content": "
Captioning ModelOK-VQAA-OKVQAVQAv2
OFA-Cap56.651.064.9
PROMPTCAP60.456.374.1
" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.369, + 0.411, + 0.383 + ], + "angle": 0, + "content": "5.3.1 Performance Benefit from PROMPTCAP" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.392, + 0.472, + 0.543 + ], + "angle": 0, + "content": "Baseline generic captioning model We use the officially released OFA [58] captioning checkpoint \"caption-large-best-clean\" (470M) as the baseline generic captioning model. We refer to it as \"OFA-Cap\". We choose this model because this is the model initialization we use for PROMPTCAP, sharing the same model architecture. Notice that OFA is a large vision-language model pre-trained on 20M image-text pairs and 20 vision-language tasks, including many VQA tasks. We are not using additional annotated data during PROMPT-CAP finetuning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.552, + 0.47, + 0.704 + ], + "angle": 0, + "content": "PROMPTCAP captions give consistent gains over generic captions. Table 3 measures the performance benefit from PROMPTCAP on OK-VQA, A-OKVQA, and VQAv2 validation sets. Here we focus on the performance gap between using PROMPTCAP captions and generic OFA captions. We can see that PROMPTCAP gives consistent improvements over generic captions. Specifically, with GPT-3, PROMPTCAP improves over OFA-Cap by \\(3.8\\%\\), \\(5.3\\%\\), and \\(9.2\\%\\) absolute accuracy on OK-VQA, A-OKVQA, and VQAv2, respectively." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.713, + 0.471, + 0.767 + ], + "angle": 0, + "content": "Table 4. Ablation on the contribution of GPT-3. We measure the performance gain of using GPT-3 as the language model, compared with Flan-T5-XXL (11B). The captioning model we use is PROMPTCAP." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.767, + 0.46, + 0.825 + ], + "angle": 0, + "content": "
Language ModelOK-VQAA-OKVQAVQAv2
Flan-T5-XXL (11B)42.041.570.9
GPT-3 (175B)60.456.374.1
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.434, + 0.863 + ], + "angle": 0, + "content": "5.3.2 Performance Benefit from Language Model" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Baseline language model To measure the performance gain from GPT-3, we choose Flan-T5-XXL(11B) [11] as" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.153 + ], + "angle": 0, + "content": "the baseline language model. FlanT5-XXL is an instructionfinetuned LM that has shown good in-context learning ability. Notice that for Flan-T5-XXL, because of the input length limit, we use \\( n = 16 \\) in-context examples in the input." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.172, + 0.895, + 0.37 + ], + "angle": 0, + "content": "GPT-3 yields huge gains on knowledge-based VQA, but not on VQAv2. Results in Table 4 quantify the benefit of GPT-3 over Flan-T5-XXL. GPT-3 yields great performance gains on knowledge-based VQA tasks, improving over Flan-T5 by \\(18.4\\%\\) and \\(14.8\\%\\) absolute accuracy on OK-VQA and A-OKVQA, respectively. In comparison, on VQAv2, GPT-3 only gives \\(3.2\\%\\) accuracy gain, which is much smaller than the gain from PROMPTCAP over generic captions. The results indicate that GPT-3's external knowledge is critical for knowledge-based VQA tasks but not for VQAv2. We speculate that this disparity arises from VQAv2's focus on information in the image, without requiring additional knowledge beyond visual information." + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.38, + 0.895, + 0.436 + ], + "angle": 0, + "content": "Table 5. Ablation of GPT-3 prompting on OK-VQA. We experiment with different numbers of in-context examples in the input and measure the performance gain from retrieving similar in-context examples compared with random examples." + }, + { + "type": "table", + "bbox": [ + 0.509, + 0.437, + 0.88, + 0.528 + ], + "angle": 0, + "content": "
ExamplesCaptionn=1n=4n=16n=32
RandomOFA-Cap42.846.649.750.8
PROMPTCAP46.550.053.155.2
CLIPOFA-Cap44.550.055.356.6
PROMPTCAP48.753.358.460.4
" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.556, + 0.767, + 0.571 + ], + "angle": 0, + "content": "5.3.3 Ablation on GPT-3 Prompting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.895, + 0.777 + ], + "angle": 0, + "content": "As discussed in §4, two factors affect the in-context learning performance: the number of in-context examples, and the example selection strategy. To measure the effects of these two factors, we conduct an ablation study on GPT-3 prompting for OK-VQA in Table 5. We vary the number of examples \\( n \\in \\{1, 4, 16, 32\\} \\) and experiment with random examples and the most similar examples retrieved by CLIP (VIT-L/14) [43]. We can see that for both example selection strategies, the more in-context examples, the better the performance. Also, retrieving most similar examples with CLIP gives substantial performance gain (5.2% absolute accuracy for PROMPTCAP when \\( n = 32 \\)). Both findings agree with the claims in prior work [5, 31, 67]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.757, + 0.803 + ], + "angle": 0, + "content": "5.4. Domain Transfer on WebQA" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.894, + 0.903 + ], + "angle": 0, + "content": "We apply PROMPTCAP to WebQA [6] to evaluate PROMPTCAP's generalization ability on images and tasks from different domains. WebQA images are crawled from the web and are from domains different from the COCO [28] images used in PROMPTCAP's training data synthesized from VQAv2 [14]. Due to the task setting, questions are" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2969" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.28, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.089, + 0.483, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.089, + 0.688, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.69, + 0.089, + 0.891, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.258, + 0.483, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.258, + 0.688, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.69, + 0.258, + 0.891, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.325, + 0.895, + 0.354 + ], + "angle": 0, + "content": "Figure 5. Example captions generated by PROMPTCAP and OFA-Cap, and the answers GPT-3 generated the captions. For all these questions, GPT-3 yields the correct answer given PROMPTCAP captions but fails given the generic caption. Questions are from OK-VQA." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.367, + 0.28, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.367, + 0.485, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.367, + 0.688, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.69, + 0.367, + 0.891, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.219, + 0.558, + 0.746, + 0.573 + ], + "angle": 0, + "content": "Figure 6. Representative failure cases of PROMPTCAP and GPT-3 pipeline on OK-VQA." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.579, + 0.472, + 0.621 + ], + "angle": 0, + "content": "Table 6. Results on the WebQA validation set with oracle sources on image queries. The baselines in the upper part are fully supervised, while our methods only use 8-shot in-context learning." + }, + { + "type": "table", + "bbox": [ + 0.102, + 0.621, + 0.445, + 0.741 + ], + "angle": 0, + "content": "
MethodFLAccFL*Acc
Fully supervised VLP + VinVL [6]47.649.627.5
VLP + x101fpn [6]46.944.323.8
8-shot in-context learning OFA-Cap + GPT-3 PROMPTCAP + GPT-352.855.433.5
53.057.234.5
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.472, + 0.901 + ], + "angle": 0, + "content": "compositional and much longer than typical VQA questions. We convert the source images into captions and use GPT-3 in-context learning to carry out the task with only 8 random examples. The answers are long-form and measured by two scores: the fluency score measured by BARTScore [69] and the accuracy score that measures if human-annotated keywords are included in the answer. The results in the image-query setting with oracle sources on the validation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.645 + ], + "angle": 0, + "content": "set\\(^2\\) are shown on Table 6. Our systems outperform all the official baselines. PROMPTCAP outperforms the generic OFA captions, showing that PROMPTCAP is generalizable to a different domain of questions and images." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.652, + 0.693, + 0.669 + ], + "angle": 0, + "content": "5.5. Qualitative Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.857 + ], + "angle": 0, + "content": "Representative captions generated by PROMPTCAP and OFA are illustrated in Figure 5. The task is to answer the questions in OK-VQA. For all these questions, GPT-3 generates the correct answer when taking PROMPTCAP's caption as input, but fails when taking the generic caption. PROMPTCAP is able to capture visual attributes according to the question, for example, \"brand\" in (b) and \"color\" in (c). In addition, it can focus on particular objects asked in the question, such as the clothing the boy is \"putting on\" in (d). For tasks beyond PROMPTCAP's reasoning ability, GPT-3 infers the answer by the visual details PROMPTCAP gives. For example, GPT-3 infers \"green\" for the \"complimentary" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.863, + 0.894, + 0.901 + ], + "angle": 0, + "content": "2Setting at https://github.com/WebQnA/WebQA/tree/ main/baseline_output_files/Baseline_prediction_ files_on_VAL" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2970" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.182 + ], + "angle": 0, + "content": "color of red\" in (c) and \"7\" for SUV's seating capacity in (a). We also show some representative failure cases in Figure 6. The majority of failures are as shown in (a) and (b), in which PROMPTCAP fails to provide helpful information, or provides unfactual information. GPT-3 sometimes makes mistakes, as shown in (c) and (d)." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.193, + 0.472, + 0.248 + ], + "angle": 0, + "content": "Table 7. Comparison of captions. \"GPT-3-Syn\" are the question-aware captions synthesized by GPT-3. \"COCO-GT\" are the MSCOCO ground-truth captions. Higher scores imply higher similarities between the captions." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.248, + 0.465, + 0.383 + ], + "angle": 0, + "content": "
CaptionsBMCS
Comparison between “gold captions”
GPT-3-SynCOCO-GT67.144.3182.932.1
Inferenced captions vs. “gold captions”
OFA-CapGPT-3-Syn26.225.3231.040.2
PROMPTCAPGPT-3-Syn33.029.7307.147.3
OFA-CapCOCO-GT44.530.9147.924.6
PROMPTCAPCOCO-GT45.431.6150.125.2
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.398, + 0.47, + 0.43 + ], + "angle": 0, + "content": "5.6. Analysis: How Do Question-Aware Captions Differ from Generic Captions?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.437, + 0.473, + 0.618 + ], + "angle": 0, + "content": "To further analyze the question-aware captions, we compare different inferred/gold captions in Table 7. The captions are compared by the automatic evaluations used in MSCOCO [7]: BLEU-4 (B) [42], METEOR (M) [4], CIDEr (C) [55], and SPICE (S) [2]. We evaluate the captions on the VQAv2 question-image pairs with images in the Karpathy test split [21] and average the scores over the questions. The upper part of the table compares the \"training targets\" for PROMPTCAP and the generic captioning model OFA-Cap. The lower part compares the captions inferred by each captioning model with these \"gold captions\". We make several observations from the table:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.621, + 0.471, + 0.698 + ], + "angle": 0, + "content": "GPT-3 synthesized question-aware captions synthesized by GPT-3 are highly similar to the MSCOCO ground truth generic captions. As seen in the upper part of Table 7, the question-aware captions are really similar to the MSCOCO ground-truth captions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.7, + 0.472, + 0.867 + ], + "angle": 0, + "content": "PROMPTCAP achieves high CIDEr and SPICE scores using GPT-3 synthesized captions as reference. The second row in the lower part compares the prompt-guided captions generated by PROMPTCAP with the GPT-3 synthesized question-aware captions. We can see that the CIDEr and SPICE scores are really high. One possible reason for the high scores is that synthesized question-aware captions are typically less diverse, shorter, and cover fewer visual entities compared with human-written general captions. Moreover, the image captioning task becomes less ambiguous via the prompt's control, making it easier for PROMPTCAP to learn." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.473, + 0.902 + ], + "angle": 0, + "content": "PROMPTCAP can also generate high-quality generic captions. The last row shows the quality of the generic captions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.182 + ], + "angle": 0, + "content": "generated by PROMPTCAP. Users can get generic captions by prompting PROMPTCAP with the question \"what does the image describe?\". All the automatic metrics show that PROMPTCAP achieves SOTA performance on COCO validation set, with even higher scores than the original OFA-Cap model." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.194, + 0.799, + 0.212 + ], + "angle": 0, + "content": "6. Limitations and Broader Impact" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.219, + 0.895, + 0.34 + ], + "angle": 0, + "content": "One limitation is that the current PROMPTCAP only focuses on knowledge-based VQA tasks. PROMPTCAP can be extended to other vision-language tasks beyond VQA. Figure 7 shows an example of solving NLVR2 [52] via a series of vision and reasoning steps between PROMPTCAP and ChatGPT. Future work may scale up PROMPTCAP training with more diverse tasks and instructions, and explore broader applications of PROMPTCAP beyond VQA." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.34, + 0.894, + 0.43 + ], + "angle": 0, + "content": "Another limitation is that images contain information that cannot be abstracted as text. While PROMPTCAP has demonstrated promising results in bridging the gap between LMs and images, it is important to recognize its limitations and use it in conjunction with other methods to ensure a comprehensive understanding of visual data." + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.441, + 0.88, + 0.648 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.652, + 0.895, + 0.681 + ], + "angle": 0, + "content": "Figure 7. Demo of solving the NLVR2 task with off-the-shelf PROMPTCAP and ChatGPT via an interpretable reasoning process." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.695, + 0.619, + 0.71 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "We present PROMPTCAP, a novel question-aware captioning model that can be controlled via a natural language prompt. To train this captioning model with no extra annotation, we devise an efficient pipeline for synthesizing and filtering training examples via GPT-3. We demonstrate the effectiveness of PROMPTCAP on knowledge-based VQA tasks. Our system achieves state-of-the-art performance on OKVQA and A-OKVQA. Ablations show that PROMPTCAP is giving consistent gains over generic captions. Furthermore, we investigate PROMPTCAP's generalization ability on WebQA. PROMPTCAP works as a simple and general module for converting question-related visual information into text." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2971" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.241 + ], + "angle": 0, + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, Roman Ring, Eliza Rutherford, Serkan Cabi, Tengda Han, Zhitao Gong, Sina Samangooei, Marianne Monteiro, Jacob Menick, Sebastian Borgeaud, Andrew Brock, Aida Nematzadeh, Sahand Sharifzadeh, Mikolaj Binkowski, Ricardo Barreira, Oriol Vinyals, Andrew Zisserman, and Karen Simonyan. 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Mucko: multi-layer cross-modal knowledge reasoning for fact-based visual question answering. arXiv preprint arXiv:2006.09073, 2020. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.472, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2975" + } + ] +] \ No newline at end of file diff --git a/2023/PromptCap_ Prompt-Guided Image Captioning for VQA with GPT-3/4ffd89d6-8734-4748-beec-1543acfdd6d0_origin.pdf b/2023/PromptCap_ Prompt-Guided Image Captioning for VQA with GPT-3/4ffd89d6-8734-4748-beec-1543acfdd6d0_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0268734ec4af057d16a92498dd19128b2d9d0b6a --- /dev/null +++ b/2023/PromptCap_ Prompt-Guided Image Captioning for VQA with GPT-3/4ffd89d6-8734-4748-beec-1543acfdd6d0_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fa5be3909352dec92973d9c3bac1d97f62d26d0c10d0a5802faba7974f989a55 +size 6435276 diff --git a/2023/PromptCap_ Prompt-Guided Image Captioning for VQA with GPT-3/full.md b/2023/PromptCap_ Prompt-Guided Image Captioning for VQA with GPT-3/full.md new file mode 100644 index 0000000000000000000000000000000000000000..33ccc186a81355019720d555db2275f68b164415 --- /dev/null +++ b/2023/PromptCap_ Prompt-Guided Image Captioning for VQA with GPT-3/full.md @@ -0,0 +1,338 @@ +# PROMPTCAP: Prompt-Guided Image Captioning for VQA with GPT-3 + +Yushi Hu $^{1*}$ Hang Hua $^{2*}$ Zhengyuan Yang $^{3}$ Weijia Shi $^{1}$ Noah A. Smith $^{1,4}$ Jiebo Luo $^{2}$ $^{1}$ University of Washington $^{2}$ University of Rochester $^{3}$ Microsoft $^{4}$ Allen Institute for AI +https://yushi-hu.github.io/promptcap_demo/ + +# Abstract + +Knowledge-based visual question answering (VQA) involves questions that require world knowledge beyond the image to yield the correct answer. Large language models (LMs) like GPT-3 are particularly helpful for this task because of their strong knowledge retrieval and reasoning capabilities. To enable LM to understand images, prior work uses a captioning model to convert images into text. However, when summarizing an image in a single caption sentence, which visual entities to describe are often underspecified. Generic image captions often miss visual details essential for the LM to answer visual questions correctly. To address this challenge, we propose PROMPTCAP (Prompt-guided image Captioning), a captioning model designed to serve as a better connector between images and black-box LMs. Different from generic captions, PROMPTCAP takes a natural-language prompt to control the visual entities to describe in the generated caption. The prompt contains a question that the caption should aid in answering. To avoid extra annotation, PROMPTCAP is trained by examples synthesized with GPT-3 and existing datasets. We demonstrate PROMPTCAP's effectiveness on an existing pipeline in which GPT-3 is prompted with image captions to carry out VQA. PROMPTCAP outperforms generic captions by a large margin and achieves state-of-the-art accuracy on knowledge-based VQA tasks (60.4% on OK-VQA and 59.6% on A-OKVQA). Zeroshot results on WebQA show that PROMPTCAP generalizes well to unseen domains.1 + +# 1. Introduction + +Knowledge-based visual question answering (VQA) [37] extends traditional VQA tasks [3] with questions that require + +*Equal contribution. Correspondance to , +1All codes, data, and demos are available on the project page. HF checkpoint: https://huggingface.co/tifa-benchmark/promptcap-coco-vqa + +![](images/50ec01164af43b0de5d2b01716d6ccd2b3fb1404309cf269baedf60abc8aa1e6.jpg) +v.s. COCO caption: A traffic light on a pole on a city street. +Figure 1. Illustration of VQA with PROMPTCAP and ChatGPT. PROMPTCAP is designed to work with black-box language models (e.g., GPT-3, ChatGPT) by describing question-related visual information in the text. Different from generic captions, PROMPTCAP customizes the caption according to the input question prompt, which helps ChatGPT understand the image and give correct answers to the user. In contrast, ChatGPT cannot infer the answers from the vanilla human-written caption from MSCOCO. + +broad knowledge and commonsense reasoning to yield the correct answer. Existing systems on knowledge-based VQA retrieve external knowledge from various sources, including knowledge graphs [13, 36, 63], Wikipedia [36, 63, 12, 15, 29], and web search [35, 63]. Recent work [67] finds that modern language models (LMs) like GPT-3 [5] are particularly useful for this task because of their striking knowledge retrieval and reasoning abilities. The current state-of-the-art methods [67, 15, 29, 1] all make use of recent large language models (GPT-3 or Chinchilla). + +One key challenge is to allow LMs to understand images. Many top-performing LMs (e.g., GPT-3, ChatGPT) are only + +accessible via APIs, making it impossible to access their internal representations or conduct fine-tuning [49]. A popular solution is to project images into texts that black-box LMs can process, via a generic image captioning model [7] or an image tagger [67]. This framework has been successful on multiple tasks, including VQA [67, 15, 29], image paragraph captioning [65], and video-language tasks [70, 60]. Despite promising results, converting visual inputs into a generic, finite text description risks excluding information necessary for the task. As discussed in PICa [67], when used for VQA tasks, the generic caption might miss the detailed visual information needed to answer the question, such as missing the "McDonald's" in Figure 1. + +To address the above challenges, we introduce PROMPTCAP, a question-aware captioning model designed to serve as a better connector between images and a black-box LM. PROMPTCAP is illustrated in Figure 2. PROMPTCAP takes an extra natural language prompt as input to control the visual content to describe. The prompt contains the question that the generated caption should help to answer. LMs can better answer visual questions by using PROMPTCAP as their "visual front-end". For example, in Figure 1, when asked "what is the time of the day?", PROMPTCAP includes "in the evening" in its image description; when asked "what kind of food does the restaurant on the sign serve?", PROMPTCAP includes "McDonald's" in its description. Such visual information is critical for ChatGPT to reply to the user with the correct answers. In contrast, the generic COCO [28] caption often contains no information about the time or the sign, making ChatGPT unable to answer the questions. + +One major technical challenge is PROMPTCAP training. The pipeline of "PROMPTCAP + black-box LM" cannot be end-to-end fine-tuned on VQA tasks because the LM parameters are not exposed through the API. Also, there are no training data for question-aware captions. To avoid extra annotation, we propose a pipeline to synthesize and filter training samples with GPT-3. Specifically, we view existing VQA datasets as pairs of question and question-related visual details. Given a question-answer pair, we rewrite the corresponding image's generic caption into a customized caption that helps answer the question. Following 20 human-annotated examples, GPT-3 synthesizes a large number of question-aware captions via few-shot in-context learning [5]. To ensure the sample quality, we filter the generated captions by performing QA with GPT-3, checking if the answer can be inferred given the question and the synthesized caption. Notice that GPT-3 is frozen in the whole pipeline. Its strong few-shot learning ability makes this pipeline possible. + +We demonstrate the effectiveness of PROMPTCAP on knowledge-based VQA tasks with the pipeline in PICa [67]. Details of the pipeline are illustrated in §4. The images are converted into texts via PROMPTCAP, allowing GPT-3 to perform VQA via in-context learning. This pipeline, despite + +![](images/bfc6284309143059a3d41501f08deea082faf709896804f9e8d62775641f6bee.jpg) +Figure 2. Overview of PROMPTCAP training. PROMPTCAP takes two inputs, including an image and a natural language prompt. The model is trained to generate a caption that helps downstream LMs to answer the question. During training, we use GPT-3 to synthesize VQA samples into captioning examples. The original caption is rewritten into a caption that helps answer the question. PROMPTCAP is trained to generate this synthesized caption given the image and the prompt. + +its simplicity, achieves state-of-the-art results on knowledge-based VQA tasks (60.4% on OK-VQA [38] and 59.6% on A-OKVQA [46]). We also conduct extensive ablation studies on the contribution of each component, showing that PROMPTCAP gives a consistent performance gain (3.8% on OK-VQA, 5.3% on A-OKVQA, and 9.2% on VQAv2) over a generic captioning model that shares the same architecture and training data. Finally, we investigate PROMPTCAP's generalization ability on WebQA [6], showing that PROMPTCAP, without any training on the compositional questions in WebQA, outperforms the generic caption approach and all supervised baselines. + +In summary, our contributions are as follows: + +- We propose PROMPTCAP, a novel question-aware captioning model that uses natural language prompt to control the visual content to be described. (§3) +- To the best of our knowledge, we are the first to propose a pipeline to synthesize and filter training samples for vision-language tasks via GPT-3 (§3.1). +- PROMPTCAP helps GPT-3 in-context learning (\$4) achieve state-of-the-art results on OK-VQA and A-OKVQA, substantially outperforming generic captions on various VQA tasks. (\$5). + +# 2. Related Work + +Knowledge-Based VQA Knowledge-based VQA [38, 46] requires systems to leverage external knowledge beyond image content to answer the question. Prior works [13, 36, 63, 72, 40, 41, 17, 18, 12] investigate leveraging knowledge + +from various external knowledge resources, e.g., Wikipedia [56], ConceptNet [50], and ASER [71], to improve the performance of the VQA models. Inspired by PICa [67], recent works [15, 29] use GPT-3 as an implicit knowledge base and achieve state-of-the-art results. We identify the critical problem: generic captions used to prompt GPT-3 often miss critical visual details for VQA. We address this challenge with PROMPTCAP. + +Vision-Language Models Vision-language models have recently shown striking success on various multimodal tasks [51, 33, 9, 27, 61, 22, 43, 66, 57, 58, 34, 68, 8, 26]. These works first pretrain multimodal models on large-scale image-text datasets and then finetune the models for particular tasks. The works most related to ours are Frozen [54], Flamingo [1], and BLIP-2 [26], which keeps the LMs frozen and tune a visual encoder for the LM. However, such techniques require access to internal LM parameters and are thus difficult to be applied to black-box LMs like GPT-3. + +Prompting for Language Models Prompting allows a pre-trained model to adapt to different tasks via different prompts without modifying any parameters. LLMs like GPT-3 [5] have shown strong zero-shot and few-shot ability via prompting. Prompting has been successful for a variety of natural language tasks [32], including but not limited to classification tasks [39, 48], semantic parsing [64], knowledge generation [49, 30], and dialogue systems [24, 16]. The most closely-related works to ours are the instruction-finetuned language models [45, 62, 59]. + +# 3. PROMPTCAP + +We introduce PROMPTCAP, an image captioning model that utilizes a natural language prompt as an input condition. The overview of PROMPTCAP training is in Figure 2. Given an image $I$ , and a natural language prompt $P$ , PROMPTCAP generates a prompt-guided caption $C$ . $P$ contains instructions about the image contents of interest to the user. For VQA, an example prompt could be "Please describe this image according to the following question: what type plane is this?. The prompt-guided caption $C$ should (1) cover the visual details required by the instruction in the prompt, (2) describe the main objects as general captions do, and (3) use auxiliary information in the prompt if necessary. For instance, assuming the prompt contains a VQA question, $C$ may directly describe the asked visual contents (e.g., for questions about visual details), or provide information that helps downstream models to infer the answer (e.g., for questions that need external knowledge to solve). + +Given the above design, the major technical challenge is PROMPTCAP training. PROMPTCAP is designed to work with black-box LMs, which cannot be end-to-end fine-tuned on VQA tasks because the LM parameters are not accessible. Besides, there are no training data for question-aware + +![](images/20c81328417e3cfe2ceb49ecd585084ac011578342b015f1781174aa0b6000b5.jpg) +Figure 3. Training example synthesis with GPT-3 in-context learning. The "Original Contexts" are ground-truth image captions. The question-answer pairs come from existing VQA datasets. GPT-3 generalizes (without parameter updates) from the human-written examples to produce the question-aware caption given the caption, question, and answer. The images are shown for clarity but are not used in our data synthesis procedure. + +captions. To address these challenges, we propose training PROMPTCAP with data synthesized with GPT-3. + +# 3.1. Training Data Synthesis + +To avoid annotating question-aware caption examples, we use GPT-3 to generate training examples for PROMPTCAP via in-context learning [5, 44, 16, 10]. + +# 3.1.1 Training Example Generation with GPT-3 + +For PROMPTCAP training, we view existing VQA datasets as natural sources of pairs of task and task-related visual details. We synthesize question-aware captions by combining the general image captions and the question-answering pairs using GPT-3 in-context learning. Figure 3 illustrates the GPT-3 prompt we use for training example generation. The prompt contains the task instruction, 20 human-written examples, and the VQA question-image pair that we synthesize the task-aware caption from. Since GPT-3 only accepts text inputs, we represent each image by concatenating the 5 human-written COCO captions [7], as shown in the "Original Context". The human-written examples follow the three principles of prompt-guided captions described in Section 3. The commonsense reasoning ability of GPT-3 allows the model to understand the image to some extent via the COCO captions and synthesize new examples by following the human-written examples. + +# 3.1.2 Training Example Filtering + +To ensure the quality of the generated captions, we sample 5 candidate captions from GPT-3 for each question-answer pair. We devise a pipeline to filter out the best candidate caption as the training example for PROMPTCAP. The idea is that a text-only QA system should correctly answer the question given a high-quality prompt-guided caption as the context. For each candidate caption, we use the GPT-3 in-context learning VQA system in §4 to predict an answer, and score the candidate captions by comparing this answer with the ground-truth answers. + +Soft VQA Accuracy We find that in the open-ended generation setting, the VQA accuracy [14] incorrectly punishes answers with a slight difference in surface form. For example, the answer "coins" gets 0 when the ground truth is "coin". To address this problem, we devise a new soft VQA accuracy for example filtering. Suppose the predicted answer is $a$ and the human-written ground truth answers are $[g_1, g_2, \dots, g_n]$ . The soft accuracy is given by the three lowest-CER ground truth answers: + +$$ +A c c _ {s o f t} (a) = \max _ {x, y, z \in [ n ]} \sum_ {i \in \{x, y, z \}} \frac {\max [ 0 , 1 - C E R (a , g _ {i}) ]}{3}, +$$ + +where CER is the character error rate, calculated by the character edit distance over the total number of characters of the ground truth. In contrast, the traditional VQA accuracy [14] uses exact match. We sort the candidate captions based on this soft score. + +Comparing with COCO ground-truth Multiple candidates may answer the question correctly and get the same soft score. To break ties, we also compute the CIDEr score [55] between the candidate captions and the COCO ground-truth captions. Among the candidates with the highest soft VQA accuracy, the one with the highest CIDEr score is selected as the training example for PROMPTCAP. + +# 3.2. PROMPTCAP Training + +For PROMPTCAP training, we start with the state-of-the-art pre-trained vision-language model OFA [58] and make some modifications to the OFA captioning model. OFA has an encoder-decoder structure. As discussed earlier, our training data are synthesized with VQA data in the form of question-caption pairs. Given a question-caption pair, we first rewrite the question into an instruction prompt via a template. For example, the instruction prompt might be "describe to answer: What is the clock saying the time is?" We apply byte-pair encoding (BPE) [47] to the given text sequence, encoding it as subwords. Images are transformed into image patches that share the same subword token set. Let the training samples be $\mathcal{D} = \{P_i,I_i,C_i\}_{i = 1}^{|\mathcal{D}|}$ , + +in which $P_{i}$ is the text prompt, $I_{i}$ is the image patch, and $C_i$ is the synthesized task-aware caption. The captioning model takes $[P_{i}:I_{i}]$ as input and is trained to generate $C_i = [c_1,c_2,\dots ,c_{|C_i|}]$ . Here $[:]$ is concatenation. We use negative log-likelihood loss and train the model in an end-to-end manner. The training loss is: + +$$ +\mathcal {L} = - \sum_ {\mathcal {D}} \sum_ {t = 1} ^ {| C _ {i} |} \log p (c _ {t} \mid [ P _ {i}: I _ {i} ], c _ {\leq t - 1}). +$$ + +# 4. VQA with PROMPTCAP and GPT-3 + +Our VQA pipeline is illustrated in Figure 4, which is adopted from PICa [67]. The pipeline consists of two components, PROMPTCAP and GPT-3. + +Step 1: Converting images into texts via PROMPTCAP GPT-3 can perform a new task by simply conditioning on several task training examples as demonstrations. As we have discussed, the major challenge is that GPT-3 does not understand images. To bridge this modality gap, we convert the images in VQA samples to texts using PROMPTCAP (Figure 4a). Notice that different from generic captioning models, PROMPTCAP customizes the image caption according to the question, which enables LMs to understand question-related visual information in the image. As such, we are able to convert VQA samples into question-answering examples that GPT-3 can understand. + +Step 2: GPT-3 in-context learning for VQA Having used PROMPTCAP to convert VQA examples into question-answer examples that GPT-3 can understand (Step 1), we use a subset of these examples as the task demonstration for GPT-3. We concatenate the in-context learning examples to form a prompt, as shown in Figure 4b. Each in-context learning example consists of a question (Question: When was the first time this was invented?), a context generated by PROMPTCAP (Context: a train traveling down tracks next to a dirt road), and an answer (Answer: 1804). Then we append the test example to the in-context learning examples, and provide them as inputs to GPT-3. GPT-3 generates predictions based on an open-ended text generation approach, taking into account the information provided in the in-context learning examples and the test example. + +Example retrieval Previous research has shown that the effectiveness of in-context learning examples chosen for GPT-3 can significantly impact its performance [31]. In the few-shot setting where only a few training examples are available, we simply use these examples as in-context learning examples (referred to as "Random" in later sections because they are selected at random from our collection). However, + +![](images/52698ffdeb7ac290a3c2d13516fce01c0bd7d6f37830821568c5503bbebafeb4.jpg) +(a) Step 1: Using PromptCap to convert images into texts + +![](images/656dece4e825f8a086d58d753dd5f7fc5fff7142237eacc22382f5914b2a2afe.jpg) +(b) Step 2: VQA with PromptCap and in-context learning on GPT-3 +Figure 4. Our inference pipeline for VQA. (a) Illustration of how we convert a VQA sample into pure text. Given the image and the question, PROMPTCAP describes the question-related visual information in natural language. The VQA sample is turned into a QA sample that GPT-3 can understand. (b) GPT-3 in-context learning for VQA. After converting the VQA examples into text with PROMPTCAP, we carry out VQA by in-context learning on GPT-3. The input consists of the task instruction (not shown in the figure), the in-context examples, and the test instance. GPT-3 takes the input and generates the answer. Notice that the GPT-3 is treated as a black box and is only used for inference. The question-aware captions PROMPTCAP generated are marked red. + +in practice, we often have access to more than small- $n$ examples (i.e., full training data setting). To improve the selection of in-context learning examples, we follow the approach proposed by [67]: we compute the similarity between examples using CLIP [43] by summing up the cosine similarities of the question and image embeddings. The $n$ most similar examples in the training set are then selected as in-context examples (referred to as "CLIP" in this paper). By using the most similar in-context examples to the test instance, our approach can improve the quality of the learned representations and boost the performance of GPT-3 on VQA tasks. + +# 5. Experiments + +In this section, we demonstrate PROMPTCAP's effectiveness on knowledge-based VQA tasks. First, we show that PROMPTCAP captions enable GPT-3 to achieve state-of-the-art performance on OK-VQA [38] and A-OKVQA [46] with in-context learning. Then we conduct ablation experiments on the contribution of each component, showing that PROMPTCAP is giving consistent gains over generic captions. In addition, experiments on WebQA [6] demonstrate that PROMPTCAP generalizes well to unseen domains. + +# 5.1. Experimental Setup + +Datasets We use three knowledge-based VQA datasets, namely OK-VQA [38], A-OKVQA [46], and WebQA [6]. OK-VQA[38] is a large knowledge-based VQA dataset that + +contains 14K image-question pairs. Questions are manually filtered to ensure that outside knowledge is required to answer the questions. A-OKVQA[46] is an augmented successor of OK-VQA, containing 25K image-question pairs that require broader commonsense and world knowledge to answer. For both OK-VQA and A-OKVQA, the direct answers are evaluated by the soft accuracy from VQAv2[14]. Besides direct answer evaluation, A-OKVQA also provides multiple-choice evaluation, where the model should choose one correct answer among 4 candidates. WebQA [6] is a multimodal multi-hop reasoning benchmark that requires the model to combine multiple text and image sources to answer a question. + +PROMPTCAP implementation details We adopt the officially released OFA [58] captioning checkpoint "caption-large-best-clean" (470M) for model initialization and use the GPT-3 synthesized examples in §3.1 to fine-tune the model. The examples are synthesized from VQAv2 [3, 14]. Notice that this dataset is included in OFA pre-training, so we are not adding additional annotated training data compared with OFA. We use AdamW [23] optimizer with learning rate $\{2 \times 10^{-5}, 3 \times 10^{-5}, 5 \times 10^{-5}\}$ , batch size $\{32, 64, 128\}$ , and $\beta_{1} = 0.9$ , $\beta_{2} = 0.999$ for training. + +In-context learning details We use code-davinci-002 engine (175B) for GPT-3 in all the experiments. Due to the input length limit, we use $n = 32$ most similar examples in + +Table 1. Results comparison with existing systems on OK-VQA, with the image representation and the knowledge source each method uses. GPT-3 is frozen for all methods. The methods on top require end-to-end finetuning on OK-VQA. The methods below are fully based on in-context learning or zero-shot learning and do not require task-specific finetuning. + +
MethodImage RepresentationKnowledge SourceAccuracy (%)
End-to-End Finetuning
Question only [37]--14.9
MUTAN [38]Feature-26.4
BAN + KG + AUG [25]FeatureWikipedia + ConceptNet26.7
ConceptBERT [13]FeatureConceptNet33.7
KRISP [36]FeatureWikipedia + ConceptNet38.4
Vis-DPR [35]FeatureGoogle Search39.2
MAVEx [63]FeatureWikipedia + ConceptNet + Google Images39.4
TRiG [12]Caption + Tags + OCRWikipedia50.5
KAT (Single) [15]Caption + Tags + FeatureGPT-3 (175B) + Wikidata54.4
KAT (Ensemble) [15]Caption + Tags + FeatureGPT-3 (175B) + Wikidata54.4
REVIVE (Single) [29]Caption + FeatureGPT-3 (175B) + Wikidata56.6
REVIVE (Ensemble) [29]Caption + FeatureGPT-3 (175B) + Wikidata58.0
In-Context Learning & Zero-Shot
BLIP-2 VIT-G FlanT5XXL [26] (zero-shot)FeatureFlanT5-XXL (11B)45.9
PICa-Base [67]Caption + TagsGPT-3 (175B)43.3
PICa-Full [67]Caption + TagsGPT-3 (175B)48.0
Flamingo (80B) [1] (zero-shot)FeatureChinchilla (70B)50.6
Flamingo (80B) [1] (32-shot)FeatureChinchilla (70B)57.8
PromptCap + GPT-3CaptionGPT-3 (175B)60.4
+ +Table 2. Results comparison with existing systems on A-OKVQA. There are two evaluations, namely multiple-choice and direct-answer. Both are measured by accuracy $(\%)$ . + +
MethodMultiple ChoiceDirect Answer
valtestvaltest
ClipCap [46]44.043.818.115.8
Pythia [19]49.040.125.221.9
ViLBERT [33]49.141.530.625.9
LXMERT [53]51.441.630.725.9
KRISP [36]51.942.233.727.1
GPV-2 [20]60.353.748.640.7
PromptCap + GPT-373.273.156.359.6
+ +the prompt for GPT-3. The examples are retrieved by CLIP (VIT-L/14) using the method discussed in $\S 4$ . + +# 5.2. Results on OK-VQA and A-OKVQA + +Table 1 compares PROMPTCAP + GPT-3 with other methods on the OK-VQA validation set. For each method, we also list the way it represents the images, and the knowledge source used. The table is split into two sections. The upper section lists fully supervised methods. These methods require end-to-end finetuning. The methods in the bottom section are based on in-context learning and no task-specific finetuning is done on the models. + +We can see that all state-of-the-art systems use GPT-3 (or Chinchilla) as part of their systems. These methods obtain significant performance gains compared with previous + +methods, showing the importance of the LM in knowledge-based VQA tasks. PICa is the first system that used GPT-3 as the knowledge source. KAT [15] further improves over PICa by introducing Wikidata [56] as the knowledge source, doing ensemble and end-to-end finetuning on multiple components. REVIVE [29] is the current state of the art on OK-VQA. Compared with KAT, it introduces extra object-centric visual features to the ensemble, which brings additional gains over KAT. However, all of the above methods use generic image captions to prompt knowledge from GPT-3. We identify this as a critical bottleneck in using LMs for VQA tasks. PROMPTCAP is designed to address this bottleneck. + +Comparison with state of the art Our proposed PROMPT-CAP + GPT-3, despite using no additional knowledge source, no ensemble with visual features, and no end-to-end finetuning, achieves $60.4\%$ accuracy and outperforms all existing methods on OK-VQA. Table 2 shows similar results on AOKVQA, in which PROMPTCAP + GPT-3 outperforms all prior methods by a large margin on both multiple-choice $(73.1\%)$ and direct-answer $(59.6\%)$ evaluations. These results demonstrate PROMPTCAP's effectiveness in connecting LMs with images. Besides, we would like to emphasize that PROMPTCAP could replace the captioning module in the systems KAT and REVIVE have proposed, which might further boost the performance. We expect that PROMPTCAP will help future systems with complementary advances to achieve even better performance on these tasks. + +# 5.3. Ablation Study + +We conduct extensive ablation studies to quantify the performance benefit of each component in our system, i.e., the captioning model PROMPTCAP, the language model, and the prompting method. We conduct ablation experiments on each component. + +Additional dataset for analysis Besides knowledge-based VQA tasks, we would also like to investigate the performance gain from PROMPTCAP for traditional VQA. Thus, we also include VQAv2 [3] in our ablation studies. + +Table 3. Ablation on the contribution of PROMPTCAP, compared with generic captioning model OFA-Cap. The LM we use is GPT-3. + +
Captioning ModelOK-VQAA-OKVQAVQAv2
OFA-Cap56.651.064.9
PROMPTCAP60.456.374.1
+ +# 5.3.1 Performance Benefit from PROMPTCAP + +Baseline generic captioning model We use the officially released OFA [58] captioning checkpoint "caption-large-best-clean" (470M) as the baseline generic captioning model. We refer to it as "OFA-Cap". We choose this model because this is the model initialization we use for PROMPTCAP, sharing the same model architecture. Notice that OFA is a large vision-language model pre-trained on 20M image-text pairs and 20 vision-language tasks, including many VQA tasks. We are not using additional annotated data during PROMPT-CAP finetuning. + +PROMPTCAP captions give consistent gains over generic captions. Table 3 measures the performance benefit from PROMPTCAP on OK-VQA, A-OKVQA, and VQAv2 validation sets. Here we focus on the performance gap between using PROMPTCAP captions and generic OFA captions. We can see that PROMPTCAP gives consistent improvements over generic captions. Specifically, with GPT-3, PROMPTCAP improves over OFA-Cap by $3.8\%$ , $5.3\%$ , and $9.2\%$ absolute accuracy on OK-VQA, A-OKVQA, and VQAv2, respectively. + +Table 4. Ablation on the contribution of GPT-3. We measure the performance gain of using GPT-3 as the language model, compared with Flan-T5-XXL (11B). The captioning model we use is PROMPTCAP. + +
Language ModelOK-VQAA-OKVQAVQAv2
Flan-T5-XXL (11B)42.041.570.9
GPT-3 (175B)60.456.374.1
+ +# 5.3.2 Performance Benefit from Language Model + +Baseline language model To measure the performance gain from GPT-3, we choose Flan-T5-XXL(11B) [11] as + +the baseline language model. FlanT5-XXL is an instructionfinetuned LM that has shown good in-context learning ability. Notice that for Flan-T5-XXL, because of the input length limit, we use $n = 16$ in-context examples in the input. + +GPT-3 yields huge gains on knowledge-based VQA, but not on VQAv2. Results in Table 4 quantify the benefit of GPT-3 over Flan-T5-XXL. GPT-3 yields great performance gains on knowledge-based VQA tasks, improving over Flan-T5 by $18.4\%$ and $14.8\%$ absolute accuracy on OK-VQA and A-OKVQA, respectively. In comparison, on VQAv2, GPT-3 only gives $3.2\%$ accuracy gain, which is much smaller than the gain from PROMPTCAP over generic captions. The results indicate that GPT-3's external knowledge is critical for knowledge-based VQA tasks but not for VQAv2. We speculate that this disparity arises from VQAv2's focus on information in the image, without requiring additional knowledge beyond visual information. + +Table 5. Ablation of GPT-3 prompting on OK-VQA. We experiment with different numbers of in-context examples in the input and measure the performance gain from retrieving similar in-context examples compared with random examples. + +
ExamplesCaptionn=1n=4n=16n=32
RandomOFA-Cap42.846.649.750.8
PROMPTCAP46.550.053.155.2
CLIPOFA-Cap44.550.055.356.6
PROMPTCAP48.753.358.460.4
+ +# 5.3.3 Ablation on GPT-3 Prompting + +As discussed in §4, two factors affect the in-context learning performance: the number of in-context examples, and the example selection strategy. To measure the effects of these two factors, we conduct an ablation study on GPT-3 prompting for OK-VQA in Table 5. We vary the number of examples $n \in \{1, 4, 16, 32\}$ and experiment with random examples and the most similar examples retrieved by CLIP (VIT-L/14) [43]. We can see that for both example selection strategies, the more in-context examples, the better the performance. Also, retrieving most similar examples with CLIP gives substantial performance gain (5.2% absolute accuracy for PROMPTCAP when $n = 32$ ). Both findings agree with the claims in prior work [5, 31, 67]. + +# 5.4. Domain Transfer on WebQA + +We apply PROMPTCAP to WebQA [6] to evaluate PROMPTCAP's generalization ability on images and tasks from different domains. WebQA images are crawled from the web and are from domains different from the COCO [28] images used in PROMPTCAP's training data synthesized from VQAv2 [14]. Due to the task setting, questions are + +![](images/0bae8e450082eb547aa88072889fe78a8b908eb38d925e0a7457b59fb125e46e.jpg) + +![](images/78890cc4b01b705191ec701e7d411ffae4c7b7c6b6fd98afb440bea439f317fd.jpg) + +![](images/2d5340a6a39474a5e54e11ee3ba1cd806e71d77cee1792ddd951aa4200a4d5b7.jpg) + +![](images/2655bc5e64208ec69e8073ebc16e462b5074eb674d5128152a1bf63b65483717.jpg) + +![](images/3fe19f5859804d3acc129cc74c9e67fb7cd2a7c6e9bddebe29124882ce7702a4.jpg) +Figure 5. Example captions generated by PROMPTCAP and OFA-Cap, and the answers GPT-3 generated the captions. For all these questions, GPT-3 yields the correct answer given PROMPTCAP captions but fails given the generic caption. Questions are from OK-VQA. + +![](images/5cc81f5b7b6a07af6ca11e1e461558a2ae6ec543ea75fa49bdd2d44f28908073.jpg) + +![](images/052d6805ee332afd16f6b4b49264d18e02d35cf7d81e640e0109b8ce3c670834.jpg) + +![](images/3dc6f2f353d1c8815f4df3a2f47c7f643dd3f463529d241a24dbf7047a283165.jpg) +Figure 6. Representative failure cases of PROMPTCAP and GPT-3 pipeline on OK-VQA. + +![](images/3fda532b6c76d546cbcaf922bb8d12f6e3be16aa9fec3a46216d3654b82fa939.jpg) + +![](images/9a5b927fcc360f4fb4970c929002467af7ce33e3a0bdab3dc1c4c8ae0f878ce9.jpg) + +![](images/a1d5331937802f7ec849f7205940a7f424319c8f631f69ebfe9fa5909daaaf92.jpg) + +Table 6. Results on the WebQA validation set with oracle sources on image queries. The baselines in the upper part are fully supervised, while our methods only use 8-shot in-context learning. + +
MethodFLAccFL*Acc
Fully supervised VLP + VinVL [6]47.649.627.5
VLP + x101fpn [6]46.944.323.8
8-shot in-context learning OFA-Cap + GPT-3 PROMPTCAP + GPT-352.855.433.5
53.057.234.5
+ +compositional and much longer than typical VQA questions. We convert the source images into captions and use GPT-3 in-context learning to carry out the task with only 8 random examples. The answers are long-form and measured by two scores: the fluency score measured by BARTScore [69] and the accuracy score that measures if human-annotated keywords are included in the answer. The results in the image-query setting with oracle sources on the validation + +set $^2$ are shown on Table 6. Our systems outperform all the official baselines. PROMPTCAP outperforms the generic OFA captions, showing that PROMPTCAP is generalizable to a different domain of questions and images. + +# 5.5. Qualitative Analysis + +Representative captions generated by PROMPTCAP and OFA are illustrated in Figure 5. The task is to answer the questions in OK-VQA. For all these questions, GPT-3 generates the correct answer when taking PROMPTCAP's caption as input, but fails when taking the generic caption. PROMPTCAP is able to capture visual attributes according to the question, for example, "brand" in (b) and "color" in (c). In addition, it can focus on particular objects asked in the question, such as the clothing the boy is "putting on" in (d). For tasks beyond PROMPTCAP's reasoning ability, GPT-3 infers the answer by the visual details PROMPTCAP gives. For example, GPT-3 infers "green" for the "complimentary + +color of red" in (c) and "7" for SUV's seating capacity in (a). We also show some representative failure cases in Figure 6. The majority of failures are as shown in (a) and (b), in which PROMPTCAP fails to provide helpful information, or provides unfactual information. GPT-3 sometimes makes mistakes, as shown in (c) and (d). + +Table 7. Comparison of captions. "GPT-3-Syn" are the question-aware captions synthesized by GPT-3. "COCO-GT" are the MSCOCO ground-truth captions. Higher scores imply higher similarities between the captions. + +
CaptionsBMCS
Comparison between “gold captions”
GPT-3-SynCOCO-GT67.144.3182.932.1
Inferenced captions vs. “gold captions”
OFA-CapGPT-3-Syn26.225.3231.040.2
PROMPTCAPGPT-3-Syn33.029.7307.147.3
OFA-CapCOCO-GT44.530.9147.924.6
PROMPTCAPCOCO-GT45.431.6150.125.2
+ +# 5.6. Analysis: How Do Question-Aware Captions Differ from Generic Captions? + +To further analyze the question-aware captions, we compare different inferred/gold captions in Table 7. The captions are compared by the automatic evaluations used in MSCOCO [7]: BLEU-4 (B) [42], METEOR (M) [4], CIDEr (C) [55], and SPICE (S) [2]. We evaluate the captions on the VQAv2 question-image pairs with images in the Karpathy test split [21] and average the scores over the questions. The upper part of the table compares the "training targets" for PROMPTCAP and the generic captioning model OFA-Cap. The lower part compares the captions inferred by each captioning model with these "gold captions". We make several observations from the table: + +GPT-3 synthesized question-aware captions synthesized by GPT-3 are highly similar to the MSCOCO ground truth generic captions. As seen in the upper part of Table 7, the question-aware captions are really similar to the MSCOCO ground-truth captions. + +PROMPTCAP achieves high CIDEr and SPICE scores using GPT-3 synthesized captions as reference. The second row in the lower part compares the prompt-guided captions generated by PROMPTCAP with the GPT-3 synthesized question-aware captions. We can see that the CIDEr and SPICE scores are really high. One possible reason for the high scores is that synthesized question-aware captions are typically less diverse, shorter, and cover fewer visual entities compared with human-written general captions. Moreover, the image captioning task becomes less ambiguous via the prompt's control, making it easier for PROMPTCAP to learn. + +PROMPTCAP can also generate high-quality generic captions. The last row shows the quality of the generic captions + +generated by PROMPTCAP. Users can get generic captions by prompting PROMPTCAP with the question "what does the image describe?". All the automatic metrics show that PROMPTCAP achieves SOTA performance on COCO validation set, with even higher scores than the original OFA-Cap model. + +# 6. Limitations and Broader Impact + +One limitation is that the current PROMPTCAP only focuses on knowledge-based VQA tasks. PROMPTCAP can be extended to other vision-language tasks beyond VQA. Figure 7 shows an example of solving NLVR2 [52] via a series of vision and reasoning steps between PROMPTCAP and ChatGPT. Future work may scale up PROMPTCAP training with more diverse tasks and instructions, and explore broader applications of PROMPTCAP beyond VQA. + +Another limitation is that images contain information that cannot be abstracted as text. While PROMPTCAP has demonstrated promising results in bridging the gap between LMs and images, it is important to recognize its limitations and use it in conjunction with other methods to ensure a comprehensive understanding of visual data. + +![](images/5400caa03ef293aa5fe96b90b925fbc4dfb8b01ca63a8055be908206e9b8fb5e.jpg) +Figure 7. Demo of solving the NLVR2 task with off-the-shelf PROMPTCAP and ChatGPT via an interpretable reasoning process. + +# 7. Conclusion + +We present PROMPTCAP, a novel question-aware captioning model that can be controlled via a natural language prompt. To train this captioning model with no extra annotation, we devise an efficient pipeline for synthesizing and filtering training examples via GPT-3. We demonstrate the effectiveness of PROMPTCAP on knowledge-based VQA tasks. Our system achieves state-of-the-art performance on OKVQA and A-OKVQA. Ablations show that PROMPTCAP is giving consistent gains over generic captions. 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Mucko: multi-layer cross-modal knowledge reasoning for fact-based visual question answering. arXiv preprint arXiv:2006.09073, 2020. 2 \ No newline at end of file diff --git a/2023/PromptCap_ Prompt-Guided Image Captioning for VQA with GPT-3/images.zip b/2023/PromptCap_ Prompt-Guided Image Captioning for VQA with GPT-3/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..21eddf0f0b838cff8d11dfa9ce61316430073e34 --- /dev/null +++ b/2023/PromptCap_ Prompt-Guided Image Captioning for VQA with GPT-3/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6b2ecb842cc54bb3f8ba6562499549c96bee51a87095e505142f4beaae27485a +size 761371 diff --git a/2023/PromptCap_ Prompt-Guided Image Captioning for VQA with GPT-3/layout.json b/2023/PromptCap_ Prompt-Guided Image Captioning for VQA with GPT-3/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..700c0f19249e32d9deabd0cad6cf1f0baf4abfa8 --- /dev/null +++ b/2023/PromptCap_ Prompt-Guided Image Captioning for VQA with GPT-3/layout.json @@ -0,0 +1,8834 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 78, + 103, + 516, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 103, + 516, + 121 + ], + "spans": [ + { + "bbox": [ + 78, + 103, + 516, + 121 + ], + "type": "text", + "content": "PROMPTCAP: Prompt-Guided Image Captioning for VQA with GPT-3" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 143, + 141, + 449, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 141, + 449, + 216 + ], + "spans": [ + { + "bbox": [ + 143, + 141, + 449, + 216 + ], + "type": "text", + "content": "Yushi Hu" + }, + { + "bbox": [ + 143, + 141, + 449, + 216 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 143, + 141, + 449, + 216 + ], + "type": "text", + "content": " Hang Hua" + }, + { + "bbox": [ + 143, + 141, + 449, + 216 + ], + "type": "inline_equation", + "content": "^{2*}" + }, + { + "bbox": [ + 143, + 141, + 449, + 216 + ], + "type": "text", + "content": " Zhengyuan Yang" + }, + { + "bbox": [ + 143, + 141, + 449, + 216 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 143, + 141, + 449, + 216 + ], + "type": "text", + "content": " Weijia Shi" + }, + { + "bbox": [ + 143, + 141, + 449, + 216 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 143, + 141, + 449, + 216 + ], + "type": "text", + "content": " Noah A. 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Large language models (LMs) like GPT-3 are particularly helpful for this task because of their strong knowledge retrieval and reasoning capabilities. To enable LM to understand images, prior work uses a captioning model to convert images into text. However, when summarizing an image in a single caption sentence, which visual entities to describe are often underspecified. Generic image captions often miss visual details essential for the LM to answer visual questions correctly. To address this challenge, we propose PROMPTCAP (Prompt-guided image Captioning), a captioning model designed to serve as a better connector between images and black-box LMs. Different from generic captions, PROMPTCAP takes a natural-language prompt to control the visual entities to describe in the generated caption. The prompt contains a question that the caption should aid in answering. To avoid extra annotation, PROMPTCAP is trained by examples synthesized with GPT-3 and existing datasets. We demonstrate PROMPTCAP's effectiveness on an existing pipeline in which GPT-3 is prompted with image captions to carry out VQA. PROMPTCAP outperforms generic captions by a large margin and achieves state-of-the-art accuracy on knowledge-based VQA tasks (60.4% on OK-VQA and 59.6% on A-OKVQA). Zeroshot results on WebQA show that PROMPTCAP generalizes well to unseen domains.1" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 613, + 128, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 128, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 128, + 624 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 632, + 287, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 632, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 46, + 632, + 287, + 657 + ], + "type": "text", + "content": "Knowledge-based visual question answering (VQA) [37] extends traditional VQA tasks [3] with questions that require" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 664, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 664, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 45, + 664, + 288, + 714 + ], + "type": "text", + "content": "*Equal contribution. Correspondance to , \n1All codes, data, and demos are available on the project page. HF checkpoint: https://huggingface.co/tifa-benchmark/promptcap-coco-vqa" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 316, + 240, + 538, + 453 + ], + "blocks": [ + { + "bbox": [ + 316, + 240, + 538, + 453 + ], + "lines": [ + { + "bbox": [ + 316, + 240, + 538, + 453 + ], + "spans": [ + { + "bbox": [ + 316, + 240, + 538, + 453 + ], + "type": "image", + "image_path": "50ec01164af43b0de5d2b01716d6ccd2b3fb1404309cf269baedf60abc8aa1e6.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 336, + 455, + 520, + 465 + ], + "lines": [ + { + "bbox": [ + 336, + 455, + 520, + 465 + ], + "spans": [ + { + "bbox": [ + 336, + 455, + 520, + 465 + ], + "type": "text", + "content": "v.s. COCO caption: A traffic light on a pole on a city street." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 305, + 468, + 548, + 556 + ], + "lines": [ + { + "bbox": [ + 305, + 468, + 548, + 556 + ], + "spans": [ + { + "bbox": [ + 305, + 468, + 548, + 556 + ], + "type": "text", + "content": "Figure 1. Illustration of VQA with PROMPTCAP and ChatGPT. PROMPTCAP is designed to work with black-box language models (e.g., GPT-3, ChatGPT) by describing question-related visual information in the text. Different from generic captions, PROMPTCAP customizes the caption according to the input question prompt, which helps ChatGPT understand the image and give correct answers to the user. In contrast, ChatGPT cannot infer the answers from the vanilla human-written caption from MSCOCO." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 567, + 547, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 547, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 547, + 686 + ], + "type": "text", + "content": "broad knowledge and commonsense reasoning to yield the correct answer. Existing systems on knowledge-based VQA retrieve external knowledge from various sources, including knowledge graphs [13, 36, 63], Wikipedia [36, 63, 12, 15, 29], and web search [35, 63]. Recent work [67] finds that modern language models (LMs) like GPT-3 [5] are particularly useful for this task because of their striking knowledge retrieval and reasoning abilities. The current state-of-the-art methods [67, 15, 29, 1] all make use of recent large language models (GPT-3 or Chinchilla)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "content": "One key challenge is to allow LMs to understand images. Many top-performing LMs (e.g., GPT-3, ChatGPT) are only" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2963" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "accessible via APIs, making it impossible to access their internal representations or conduct fine-tuning [49]. A popular solution is to project images into texts that black-box LMs can process, via a generic image captioning model [7] or an image tagger [67]. This framework has been successful on multiple tasks, including VQA [67, 15, 29], image paragraph captioning [65], and video-language tasks [70, 60]. Despite promising results, converting visual inputs into a generic, finite text description risks excluding information necessary for the task. As discussed in PICa [67], when used for VQA tasks, the generic caption might miss the detailed visual information needed to answer the question, such as missing the \"McDonald's\" in Figure 1." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 229, + 289, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 229, + 289, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 229, + 289, + 434 + ], + "type": "text", + "content": "To address the above challenges, we introduce PROMPTCAP, a question-aware captioning model designed to serve as a better connector between images and a black-box LM. PROMPTCAP is illustrated in Figure 2. PROMPTCAP takes an extra natural language prompt as input to control the visual content to describe. The prompt contains the question that the generated caption should help to answer. LMs can better answer visual questions by using PROMPTCAP as their \"visual front-end\". For example, in Figure 1, when asked \"what is the time of the day?\", PROMPTCAP includes \"in the evening\" in its image description; when asked \"what kind of food does the restaurant on the sign serve?\", PROMPTCAP includes \"McDonald's\" in its description. Such visual information is critical for ChatGPT to reply to the user with the correct answers. In contrast, the generic COCO [28] caption often contains no information about the time or the sign, making ChatGPT unable to answer the questions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 435, + 289, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 289, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 289, + 651 + ], + "type": "text", + "content": "One major technical challenge is PROMPTCAP training. The pipeline of \"PROMPTCAP + black-box LM\" cannot be end-to-end fine-tuned on VQA tasks because the LM parameters are not exposed through the API. Also, there are no training data for question-aware captions. To avoid extra annotation, we propose a pipeline to synthesize and filter training samples with GPT-3. Specifically, we view existing VQA datasets as pairs of question and question-related visual details. Given a question-answer pair, we rewrite the corresponding image's generic caption into a customized caption that helps answer the question. Following 20 human-annotated examples, GPT-3 synthesizes a large number of question-aware captions via few-shot in-context learning [5]. To ensure the sample quality, we filter the generated captions by performing QA with GPT-3, checking if the answer can be inferred given the question and the synthesized caption. Notice that GPT-3 is frozen in the whole pipeline. Its strong few-shot learning ability makes this pipeline possible." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "content": "We demonstrate the effectiveness of PROMPTCAP on knowledge-based VQA tasks with the pipeline in PICa [67]. Details of the pipeline are illustrated in §4. The images are converted into texts via PROMPTCAP, allowing GPT-3 to perform VQA via in-context learning. This pipeline, despite" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 307, + 69, + 548, + 220 + ], + "blocks": [ + { + "bbox": [ + 307, + 69, + 548, + 220 + ], + "lines": [ + { + "bbox": [ + 307, + 69, + 548, + 220 + ], + "spans": [ + { + "bbox": [ + 307, + 69, + 548, + 220 + ], + "type": "image", + "image_path": "bfc6284309143059a3d41501f08deea082faf709896804f9e8d62775641f6bee.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 223, + 548, + 312 + ], + "lines": [ + { + "bbox": [ + 304, + 223, + 548, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 223, + 548, + 312 + ], + "type": "text", + "content": "Figure 2. Overview of PROMPTCAP training. PROMPTCAP takes two inputs, including an image and a natural language prompt. The model is trained to generate a caption that helps downstream LMs to answer the question. During training, we use GPT-3 to synthesize VQA samples into captioning examples. The original caption is rewritten into a caption that helps answer the question. PROMPTCAP is trained to generate this synthesized caption given the image and the prompt." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "text", + "content": "its simplicity, achieves state-of-the-art results on knowledge-based VQA tasks (60.4% on OK-VQA [38] and 59.6% on A-OKVQA [46]). We also conduct extensive ablation studies on the contribution of each component, showing that PROMPTCAP gives a consistent performance gain (3.8% on OK-VQA, 5.3% on A-OKVQA, and 9.2% on VQAv2) over a generic captioning model that shares the same architecture and training data. Finally, we investigate PROMPTCAP's generalization ability on WebQA [6], showing that PROMPTCAP, without any training on the compositional questions in WebQA, outperforms the generic caption approach and all supervised baselines." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 475, + 503, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 475, + 503, + 486 + ], + "spans": [ + { + "bbox": [ + 317, + 475, + 503, + 486 + ], + "type": "text", + "content": "In summary, our contributions are as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 497, + 547, + 634 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 317, + 497, + 547, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 497, + 547, + 533 + ], + "spans": [ + { + "bbox": [ + 317, + 497, + 547, + 533 + ], + "type": "text", + "content": "- We propose PROMPTCAP, a novel question-aware captioning model that uses natural language prompt to control the visual content to be described. (§3)" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 541, + 547, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 541, + 547, + 578 + ], + "spans": [ + { + "bbox": [ + 317, + 541, + 547, + 578 + ], + "type": "text", + "content": "- To the best of our knowledge, we are the first to propose a pipeline to synthesize and filter training samples for vision-language tasks via GPT-3 (§3.1)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 586, + 547, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 586, + 547, + 634 + ], + "spans": [ + { + "bbox": [ + 317, + 586, + 547, + 634 + ], + "type": "text", + "content": "- PROMPTCAP helps GPT-3 in-context learning (\\$4) achieve state-of-the-art results on OK-VQA and A-OKVQA, substantially outperforming generic captions on various VQA tasks. (\\$5)." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 645, + 392, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 645, + 392, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 645, + 392, + 658 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Knowledge-Based VQA Knowledge-based VQA [38, 46] requires systems to leverage external knowledge beyond image content to answer the question. Prior works [13, 36, 63, 72, 40, 41, 17, 18, 12] investigate leveraging knowledge" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2964" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "from various external knowledge resources, e.g., Wikipedia [56], ConceptNet [50], and ASER [71], to improve the performance of the VQA models. Inspired by PICa [67], recent works [15, 29] use GPT-3 as an implicit knowledge base and achieve state-of-the-art results. We identify the critical problem: generic captions used to prompt GPT-3 often miss critical visual details for VQA. We address this challenge with PROMPTCAP." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 175, + 290, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 175, + 290, + 294 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 290, + 294 + ], + "type": "text", + "content": "Vision-Language Models Vision-language models have recently shown striking success on various multimodal tasks [51, 33, 9, 27, 61, 22, 43, 66, 57, 58, 34, 68, 8, 26]. These works first pretrain multimodal models on large-scale image-text datasets and then finetune the models for particular tasks. The works most related to ours are Frozen [54], Flamingo [1], and BLIP-2 [26], which keeps the LMs frozen and tune a visual encoder for the LM. However, such techniques require access to internal LM parameters and are thus difficult to be applied to black-box LMs like GPT-3." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 301, + 288, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 288, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 288, + 422 + ], + "type": "text", + "content": "Prompting for Language Models Prompting allows a pre-trained model to adapt to different tasks via different prompts without modifying any parameters. LLMs like GPT-3 [5] have shown strong zero-shot and few-shot ability via prompting. Prompting has been successful for a variety of natural language tasks [32], including but not limited to classification tasks [39, 48], semantic parsing [64], knowledge generation [49, 30], and dialogue systems [24, 16]. The most closely-related works to ours are the instruction-finetuned language models [45, 62, 59]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 430, + 132, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 132, + 442 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 132, + 442 + ], + "type": "text", + "content": "3. PROMPTCAP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 450, + 288, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 288, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 288, + 653 + ], + "type": "text", + "content": "We introduce PROMPTCAP, an image captioning model that utilizes a natural language prompt as an input condition. The overview of PROMPTCAP training is in Figure 2. Given an image " + }, + { + "bbox": [ + 46, + 450, + 288, + 653 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 450, + 288, + 653 + ], + "type": "text", + "content": ", and a natural language prompt " + }, + { + "bbox": [ + 46, + 450, + 288, + 653 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 450, + 288, + 653 + ], + "type": "text", + "content": ", PROMPTCAP generates a prompt-guided caption " + }, + { + "bbox": [ + 46, + 450, + 288, + 653 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 450, + 288, + 653 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 450, + 288, + 653 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 450, + 288, + 653 + ], + "type": "text", + "content": " contains instructions about the image contents of interest to the user. For VQA, an example prompt could be \"Please describe this image according to the following question: what type plane is this?. The prompt-guided caption " + }, + { + "bbox": [ + 46, + 450, + 288, + 653 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 450, + 288, + 653 + ], + "type": "text", + "content": " should (1) cover the visual details required by the instruction in the prompt, (2) describe the main objects as general captions do, and (3) use auxiliary information in the prompt if necessary. For instance, assuming the prompt contains a VQA question, " + }, + { + "bbox": [ + 46, + 450, + 288, + 653 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 450, + 288, + 653 + ], + "type": "text", + "content": " may directly describe the asked visual contents (e.g., for questions about visual details), or provide information that helps downstream models to infer the answer (e.g., for questions that need external knowledge to solve)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": "Given the above design, the major technical challenge is PROMPTCAP training. PROMPTCAP is designed to work with black-box LMs, which cannot be end-to-end fine-tuned on VQA tasks because the LM parameters are not accessible. Besides, there are no training data for question-aware" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 316, + 72, + 539, + 280 + ], + "blocks": [ + { + "bbox": [ + 316, + 72, + 539, + 280 + ], + "lines": [ + { + "bbox": [ + 316, + 72, + 539, + 280 + ], + "spans": [ + { + "bbox": [ + 316, + 72, + 539, + 280 + ], + "type": "image", + "image_path": "20c81328417e3cfe2ceb49ecd585084ac011578342b015f1781174aa0b6000b5.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 281, + 547, + 358 + ], + "lines": [ + { + "bbox": [ + 304, + 281, + 547, + 358 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 547, + 358 + ], + "type": "text", + "content": "Figure 3. Training example synthesis with GPT-3 in-context learning. The \"Original Contexts\" are ground-truth image captions. The question-answer pairs come from existing VQA datasets. GPT-3 generalizes (without parameter updates) from the human-written examples to produce the question-aware caption given the caption, question, and answer. The images are shown for clarity but are not used in our data synthesis procedure." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 371, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 371, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 305, + 371, + 545, + 396 + ], + "type": "text", + "content": " captions. To address these challenges, we propose training PROMPTCAP with data synthesized with GPT-3." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 410, + 441, + 423 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 410, + 441, + 423 + ], + "spans": [ + { + "bbox": [ + 306, + 410, + 441, + 423 + ], + "type": "text", + "content": "3.1. Training Data Synthesis" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 430, + 545, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 430, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 305, + 430, + 545, + 467 + ], + "type": "text", + "content": "To avoid annotating question-aware caption examples, we use GPT-3 to generate training examples for PROMPTCAP via in-context learning [5, 44, 16, 10]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 487, + 518, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 487, + 518, + 499 + ], + "spans": [ + { + "bbox": [ + 306, + 487, + 518, + 499 + ], + "type": "text", + "content": "3.1.1 Training Example Generation with GPT-3" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "content": "For PROMPTCAP training, we view existing VQA datasets as natural sources of pairs of task and task-related visual details. We synthesize question-aware captions by combining the general image captions and the question-answering pairs using GPT-3 in-context learning. Figure 3 illustrates the GPT-3 prompt we use for training example generation. The prompt contains the task instruction, 20 human-written examples, and the VQA question-image pair that we synthesize the task-aware caption from. Since GPT-3 only accepts text inputs, we represent each image by concatenating the 5 human-written COCO captions [7], as shown in the \"Original Context\". The human-written examples follow the three principles of prompt-guided captions described in Section 3. The commonsense reasoning ability of GPT-3 allows the model to understand the image to some extent via the COCO captions and synthesize new examples by following the human-written examples." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2965" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 198, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 198, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 198, + 85 + ], + "type": "text", + "content": "3.1.2 Training Example Filtering" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 288, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 288, + 212 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 288, + 212 + ], + "type": "text", + "content": "To ensure the quality of the generated captions, we sample 5 candidate captions from GPT-3 for each question-answer pair. We devise a pipeline to filter out the best candidate caption as the training example for PROMPTCAP. The idea is that a text-only QA system should correctly answer the question given a high-quality prompt-guided caption as the context. For each candidate caption, we use the GPT-3 in-context learning VQA system in §4 to predict an answer, and score the candidate captions by comparing this answer with the ground-truth answers." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 220, + 289, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 220, + 289, + 328 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 289, + 328 + ], + "type": "text", + "content": "Soft VQA Accuracy We find that in the open-ended generation setting, the VQA accuracy [14] incorrectly punishes answers with a slight difference in surface form. For example, the answer \"coins\" gets 0 when the ground truth is \"coin\". To address this problem, we devise a new soft VQA accuracy for example filtering. Suppose the predicted answer is " + }, + { + "bbox": [ + 46, + 220, + 289, + 328 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 46, + 220, + 289, + 328 + ], + "type": "text", + "content": " and the human-written ground truth answers are " + }, + { + "bbox": [ + 46, + 220, + 289, + 328 + ], + "type": "inline_equation", + "content": "[g_1, g_2, \\dots, g_n]" + }, + { + "bbox": [ + 46, + 220, + 289, + 328 + ], + "type": "text", + "content": ". The soft accuracy is given by the three lowest-CER ground truth answers:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 52, + 335, + 285, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 335, + 285, + 369 + ], + "spans": [ + { + "bbox": [ + 52, + 335, + 285, + 369 + ], + "type": "interline_equation", + "content": "A c c _ {s o f t} (a) = \\max _ {x, y, z \\in [ n ]} \\sum_ {i \\in \\{x, y, z \\}} \\frac {\\max [ 0 , 1 - C E R (a , g _ {i}) ]}{3},", + "image_path": "4416cc16c0bd26d9c81a629ffea7fbdf3394c9f0eeb4df2a5cb39f7decbb172f.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 376, + 288, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 288, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 288, + 437 + ], + "type": "text", + "content": "where CER is the character error rate, calculated by the character edit distance over the total number of characters of the ground truth. In contrast, the traditional VQA accuracy [14] uses exact match. We sort the candidate captions based on this soft score." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 445, + 288, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 288, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 288, + 529 + ], + "type": "text", + "content": "Comparing with COCO ground-truth Multiple candidates may answer the question correctly and get the same soft score. To break ties, we also compute the CIDEr score [55] between the candidate captions and the COCO ground-truth captions. Among the candidates with the highest soft VQA accuracy, the one with the highest CIDEr score is selected as the training example for PROMPTCAP." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 537, + 168, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 537, + 168, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 537, + 168, + 551 + ], + "type": "text", + "content": "3.2. PROMPTCAP Training" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 556, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 289, + 715 + ], + "type": "text", + "content": "For PROMPTCAP training, we start with the state-of-the-art pre-trained vision-language model OFA [58] and make some modifications to the OFA captioning model. OFA has an encoder-decoder structure. As discussed earlier, our training data are synthesized with VQA data in the form of question-caption pairs. Given a question-caption pair, we first rewrite the question into an instruction prompt via a template. For example, the instruction prompt might be \"describe to answer: What is the clock saying the time is?\" We apply byte-pair encoding (BPE) [47] to the given text sequence, encoding it as subwords. Images are transformed into image patches that share the same subword token set. Let the training samples be " + }, + { + "bbox": [ + 46, + 556, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{P_i,I_i,C_i\\}_{i = 1}^{|\\mathcal{D}|}" + }, + { + "bbox": [ + 46, + 556, + 289, + 715 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "content": " is the text prompt, " + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "content": " is the image patch, and " + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "content": " is the synthesized task-aware caption. The captioning model takes " + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "inline_equation", + "content": "[P_{i}:I_{i}]" + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "content": " as input and is trained to generate " + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "inline_equation", + "content": "C_i = [c_1,c_2,\\dots ,c_{|C_i|}]" + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "content": ". Here " + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "inline_equation", + "content": "[:]" + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "content": " is concatenation. We use negative log-likelihood loss and train the model in an end-to-end manner. The training loss is:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 339, + 152, + 512, + 187 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 152, + 512, + 187 + ], + "spans": [ + { + "bbox": [ + 339, + 152, + 512, + 187 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = - \\sum_ {\\mathcal {D}} \\sum_ {t = 1} ^ {| C _ {i} |} \\log p (c _ {t} \\mid [ P _ {i}: I _ {i} ], c _ {\\leq t - 1}).", + "image_path": "19acccb525b247420316729aab400ca6be2474549c73d599b3bae9d0dc77822c.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 205, + 505, + 218 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 205, + 505, + 218 + ], + "spans": [ + { + "bbox": [ + 305, + 205, + 505, + 218 + ], + "type": "text", + "content": "4. VQA with PROMPTCAP and GPT-3" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 224, + 547, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 547, + 261 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 547, + 261 + ], + "type": "text", + "content": "Our VQA pipeline is illustrated in Figure 4, which is adopted from PICa [67]. The pipeline consists of two components, PROMPTCAP and GPT-3." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 268, + 547, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 268, + 547, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 547, + 411 + ], + "type": "text", + "content": "Step 1: Converting images into texts via PROMPTCAP GPT-3 can perform a new task by simply conditioning on several task training examples as demonstrations. As we have discussed, the major challenge is that GPT-3 does not understand images. To bridge this modality gap, we convert the images in VQA samples to texts using PROMPTCAP (Figure 4a). Notice that different from generic captioning models, PROMPTCAP customizes the image caption according to the question, which enables LMs to understand question-related visual information in the image. As such, we are able to convert VQA samples into question-answering examples that GPT-3 can understand." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 418, + 548, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 548, + 623 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 548, + 623 + ], + "type": "text", + "content": "Step 2: GPT-3 in-context learning for VQA Having used PROMPTCAP to convert VQA examples into question-answer examples that GPT-3 can understand (Step 1), we use a subset of these examples as the task demonstration for GPT-3. We concatenate the in-context learning examples to form a prompt, as shown in Figure 4b. Each in-context learning example consists of a question (Question: When was the first time this was invented?), a context generated by PROMPTCAP (Context: a train traveling down tracks next to a dirt road), and an answer (Answer: 1804). Then we append the test example to the in-context learning examples, and provide them as inputs to GPT-3. GPT-3 generates predictions based on an open-ended text generation approach, taking into account the information provided in the in-context learning examples and the test example." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "content": "Example retrieval Previous research has shown that the effectiveness of in-context learning examples chosen for GPT-3 can significantly impact its performance [31]. In the few-shot setting where only a few training examples are available, we simply use these examples as in-context learning examples (referred to as \"Random\" in later sections because they are selected at random from our collection). However," + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2966" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 78, + 85, + 508, + 177 + ], + "blocks": [ + { + "bbox": [ + 73, + 70, + 269, + 80 + ], + "lines": [ + { + "bbox": [ + 73, + 70, + 269, + 80 + ], + "spans": [ + { + "bbox": [ + 73, + 70, + 269, + 80 + ], + "type": "text", + "content": "(a) Step 1: Using PromptCap to convert images into texts" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 78, + 85, + 508, + 177 + ], + "lines": [ + { + "bbox": [ + 78, + 85, + 508, + 177 + ], + "spans": [ + { + "bbox": [ + 78, + 85, + 508, + 177 + ], + "type": "image", + "image_path": "52698ffdeb7ac290a3c2d13516fce01c0bd7d6f37830821568c5503bbebafeb4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 73, + 194, + 520, + 304 + ], + "blocks": [ + { + "bbox": [ + 75, + 181, + 299, + 191 + ], + "lines": [ + { + "bbox": [ + 75, + 181, + 299, + 191 + ], + "spans": [ + { + "bbox": [ + 75, + 181, + 299, + 191 + ], + "type": "text", + "content": "(b) Step 2: VQA with PromptCap and in-context learning on GPT-3" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 73, + 194, + 520, + 304 + ], + "lines": [ + { + "bbox": [ + 73, + 194, + 520, + 304 + ], + "spans": [ + { + "bbox": [ + 73, + 194, + 520, + 304 + ], + "type": "image", + "image_path": "656dece4e825f8a086d58d753dd5f7fc5fff7142237eacc22382f5914b2a2afe.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 306, + 545, + 373 + ], + "lines": [ + { + "bbox": [ + 46, + 306, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 306, + 545, + 373 + ], + "type": "text", + "content": "Figure 4. Our inference pipeline for VQA. (a) Illustration of how we convert a VQA sample into pure text. Given the image and the question, PROMPTCAP describes the question-related visual information in natural language. The VQA sample is turned into a QA sample that GPT-3 can understand. (b) GPT-3 in-context learning for VQA. After converting the VQA examples into text with PROMPTCAP, we carry out VQA by in-context learning on GPT-3. The input consists of the task instruction (not shown in the figure), the in-context examples, and the test instance. GPT-3 takes the input and generates the answer. Notice that the GPT-3 is treated as a black box and is only used for inference. The question-aware captions PROMPTCAP generated are marked red." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 380, + 288, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 288, + 511 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 288, + 511 + ], + "type": "text", + "content": "in practice, we often have access to more than small-" + }, + { + "bbox": [ + 46, + 380, + 288, + 511 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 380, + 288, + 511 + ], + "type": "text", + "content": " examples (i.e., full training data setting). To improve the selection of in-context learning examples, we follow the approach proposed by [67]: we compute the similarity between examples using CLIP [43] by summing up the cosine similarities of the question and image embeddings. The " + }, + { + "bbox": [ + 46, + 380, + 288, + 511 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 380, + 288, + 511 + ], + "type": "text", + "content": " most similar examples in the training set are then selected as in-context examples (referred to as \"CLIP\" in this paper). By using the most similar in-context examples to the test instance, our approach can improve the quality of the learned representations and boost the performance of GPT-3 on VQA tasks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 523, + 128, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 523, + 128, + 537 + ], + "spans": [ + { + "bbox": [ + 47, + 523, + 128, + 537 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 544, + 288, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 288, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 288, + 651 + ], + "type": "text", + "content": "In this section, we demonstrate PROMPTCAP's effectiveness on knowledge-based VQA tasks. First, we show that PROMPTCAP captions enable GPT-3 to achieve state-of-the-art performance on OK-VQA [38] and A-OKVQA [46] with in-context learning. Then we conduct ablation experiments on the contribution of each component, showing that PROMPTCAP is giving consistent gains over generic captions. In addition, experiments on WebQA [6] demonstrate that PROMPTCAP generalizes well to unseen domains." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 658, + 163, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 163, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 163, + 672 + ], + "type": "text", + "content": "5.1. Experimental Setup" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "Datasets We use three knowledge-based VQA datasets, namely OK-VQA [38], A-OKVQA [46], and WebQA [6]. OK-VQA[38] is a large knowledge-based VQA dataset that" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 380, + 547, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 547, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 547, + 536 + ], + "type": "text", + "content": "contains 14K image-question pairs. Questions are manually filtered to ensure that outside knowledge is required to answer the questions. A-OKVQA[46] is an augmented successor of OK-VQA, containing 25K image-question pairs that require broader commonsense and world knowledge to answer. For both OK-VQA and A-OKVQA, the direct answers are evaluated by the soft accuracy from VQAv2[14]. Besides direct answer evaluation, A-OKVQA also provides multiple-choice evaluation, where the model should choose one correct answer among 4 candidates. WebQA [6] is a multimodal multi-hop reasoning benchmark that requires the model to combine multiple text and image sources to answer a question." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 547, + 547, + 667 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 547, + 547, + 667 + ], + "spans": [ + { + "bbox": [ + 304, + 547, + 547, + 667 + ], + "type": "text", + "content": "PROMPTCAP implementation details We adopt the officially released OFA [58] captioning checkpoint \"caption-large-best-clean\" (470M) for model initialization and use the GPT-3 synthesized examples in §3.1 to fine-tune the model. The examples are synthesized from VQAv2 [3, 14]. Notice that this dataset is included in OFA pre-training, so we are not adding additional annotated training data compared with OFA. We use AdamW [23] optimizer with learning rate " + }, + { + "bbox": [ + 304, + 547, + 547, + 667 + ], + "type": "inline_equation", + "content": "\\{2 \\times 10^{-5}, 3 \\times 10^{-5}, 5 \\times 10^{-5}\\}" + }, + { + "bbox": [ + 304, + 547, + 547, + 667 + ], + "type": "text", + "content": ", batch size " + }, + { + "bbox": [ + 304, + 547, + 547, + 667 + ], + "type": "inline_equation", + "content": "\\{32, 64, 128\\}" + }, + { + "bbox": [ + 304, + 547, + 547, + 667 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 547, + 547, + 667 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 304, + 547, + 547, + 667 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 547, + 547, + 667 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 304, + 547, + 547, + 667 + ], + "type": "text", + "content": " for training." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "In-context learning details We use code-davinci-002 engine (175B) for GPT-3 in all the experiments. Due to the input length limit, we use " + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "n = 32" + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": " most similar examples in" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2967" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 102, + 547, + 352 + ], + "blocks": [ + { + "bbox": [ + 46, + 69, + 547, + 102 + ], + "lines": [ + { + "bbox": [ + 46, + 69, + 547, + 102 + ], + "spans": [ + { + "bbox": [ + 46, + 69, + 547, + 102 + ], + "type": "text", + "content": "Table 1. Results comparison with existing systems on OK-VQA, with the image representation and the knowledge source each method uses. GPT-3 is frozen for all methods. The methods on top require end-to-end finetuning on OK-VQA. The methods below are fully based on in-context learning or zero-shot learning and do not require task-specific finetuning." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 102, + 547, + 352 + ], + "lines": [ + { + "bbox": [ + 47, + 102, + 547, + 352 + ], + "spans": [ + { + "bbox": [ + 47, + 102, + 547, + 352 + ], + "type": "table", + "html": "
MethodImage RepresentationKnowledge SourceAccuracy (%)
End-to-End Finetuning
Question only [37]--14.9
MUTAN [38]Feature-26.4
BAN + KG + AUG [25]FeatureWikipedia + ConceptNet26.7
ConceptBERT [13]FeatureConceptNet33.7
KRISP [36]FeatureWikipedia + ConceptNet38.4
Vis-DPR [35]FeatureGoogle Search39.2
MAVEx [63]FeatureWikipedia + ConceptNet + Google Images39.4
TRiG [12]Caption + Tags + OCRWikipedia50.5
KAT (Single) [15]Caption + Tags + FeatureGPT-3 (175B) + Wikidata54.4
KAT (Ensemble) [15]Caption + Tags + FeatureGPT-3 (175B) + Wikidata54.4
REVIVE (Single) [29]Caption + FeatureGPT-3 (175B) + Wikidata56.6
REVIVE (Ensemble) [29]Caption + FeatureGPT-3 (175B) + Wikidata58.0
In-Context Learning & Zero-Shot
BLIP-2 VIT-G FlanT5XXL [26] (zero-shot)FeatureFlanT5-XXL (11B)45.9
PICa-Base [67]Caption + TagsGPT-3 (175B)43.3
PICa-Full [67]Caption + TagsGPT-3 (175B)48.0
Flamingo (80B) [1] (zero-shot)FeatureChinchilla (70B)50.6
Flamingo (80B) [1] (32-shot)FeatureChinchilla (70B)57.8
PromptCap + GPT-3CaptionGPT-3 (175B)60.4
", + "image_path": "c1843cc71e1d2390adce8dd6e67a5625c7139167756442fdf9bc2da93b9a06ac.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 52, + 400, + 282, + 517 + ], + "blocks": [ + { + "bbox": [ + 46, + 367, + 288, + 400 + ], + "lines": [ + { + "bbox": [ + 46, + 367, + 288, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 367, + 288, + 400 + ], + "type": "text", + "content": "Table 2. Results comparison with existing systems on A-OKVQA. There are two evaluations, namely multiple-choice and direct-answer. Both are measured by accuracy " + }, + { + "bbox": [ + 46, + 367, + 288, + 400 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 367, + 288, + 400 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 400, + 282, + 517 + ], + "lines": [ + { + "bbox": [ + 52, + 400, + 282, + 517 + ], + "spans": [ + { + "bbox": [ + 52, + 400, + 282, + 517 + ], + "type": "table", + "html": "
MethodMultiple ChoiceDirect Answer
valtestvaltest
ClipCap [46]44.043.818.115.8
Pythia [19]49.040.125.221.9
ViLBERT [33]49.141.530.625.9
LXMERT [53]51.441.630.725.9
KRISP [36]51.942.233.727.1
GPV-2 [20]60.353.748.640.7
PromptCap + GPT-373.273.156.359.6
", + "image_path": "257828fbb48af174930973d402d8c0d6299ef58a17a6559119282710d6d6f154.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 529, + 287, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 553 + ], + "type": "text", + "content": "the prompt for GPT-3. The examples are retrieved by CLIP (VIT-L/14) using the method discussed in " + }, + { + "bbox": [ + 46, + 529, + 287, + 553 + ], + "type": "inline_equation", + "content": "\\S 4" + }, + { + "bbox": [ + 46, + 529, + 287, + 553 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 562, + 242, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 242, + 575 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 242, + 575 + ], + "type": "text", + "content": "5.2. Results on OK-VQA and A-OKVQA" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 581, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 581, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 581, + 287, + 676 + ], + "type": "text", + "content": "Table 1 compares PROMPTCAP + GPT-3 with other methods on the OK-VQA validation set. For each method, we also list the way it represents the images, and the knowledge source used. The table is split into two sections. The upper section lists fully supervised methods. These methods require end-to-end finetuning. The methods in the bottom section are based on in-context learning and no task-specific finetuning is done on the models." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "We can see that all state-of-the-art systems use GPT-3 (or Chinchilla) as part of their systems. These methods obtain significant performance gains compared with previous" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 370, + 547, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 370, + 547, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 370, + 547, + 514 + ], + "type": "text", + "content": "methods, showing the importance of the LM in knowledge-based VQA tasks. PICa is the first system that used GPT-3 as the knowledge source. KAT [15] further improves over PICa by introducing Wikidata [56] as the knowledge source, doing ensemble and end-to-end finetuning on multiple components. REVIVE [29] is the current state of the art on OK-VQA. Compared with KAT, it introduces extra object-centric visual features to the ensemble, which brings additional gains over KAT. However, all of the above methods use generic image captions to prompt knowledge from GPT-3. We identify this as a critical bottleneck in using LMs for VQA tasks. PROMPTCAP is designed to address this bottleneck." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 534, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 548, + 713 + ], + "type": "text", + "content": "Comparison with state of the art Our proposed PROMPT-CAP + GPT-3, despite using no additional knowledge source, no ensemble with visual features, and no end-to-end finetuning, achieves " + }, + { + "bbox": [ + 304, + 534, + 548, + 713 + ], + "type": "inline_equation", + "content": "60.4\\%" + }, + { + "bbox": [ + 304, + 534, + 548, + 713 + ], + "type": "text", + "content": " accuracy and outperforms all existing methods on OK-VQA. Table 2 shows similar results on AOKVQA, in which PROMPTCAP + GPT-3 outperforms all prior methods by a large margin on both multiple-choice " + }, + { + "bbox": [ + 304, + 534, + 548, + 713 + ], + "type": "inline_equation", + "content": "(73.1\\%)" + }, + { + "bbox": [ + 304, + 534, + 548, + 713 + ], + "type": "text", + "content": " and direct-answer " + }, + { + "bbox": [ + 304, + 534, + 548, + 713 + ], + "type": "inline_equation", + "content": "(59.6\\%)" + }, + { + "bbox": [ + 304, + 534, + 548, + 713 + ], + "type": "text", + "content": " evaluations. These results demonstrate PROMPTCAP's effectiveness in connecting LMs with images. Besides, we would like to emphasize that PROMPTCAP could replace the captioning module in the systems KAT and REVIVE have proposed, which might further boost the performance. We expect that PROMPTCAP will help future systems with complementary advances to achieve even better performance on these tasks." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2968" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 140, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 140, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 140, + 85 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 90, + 288, + 150 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 90, + 288, + 150 + ], + "spans": [ + { + "bbox": [ + 47, + 90, + 288, + 150 + ], + "type": "text", + "content": "We conduct extensive ablation studies to quantify the performance benefit of each component in our system, i.e., the captioning model PROMPTCAP, the language model, and the prompting method. We conduct ablation experiments on each component." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 157, + 288, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 157, + 288, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 157, + 288, + 205 + ], + "type": "text", + "content": "Additional dataset for analysis Besides knowledge-based VQA tasks, we would also like to investigate the performance gain from PROMPTCAP for traditional VQA. Thus, we also include VQAv2 [3] in our ablation studies." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 55, + 235, + 277, + 280 + ], + "blocks": [ + { + "bbox": [ + 47, + 213, + 288, + 235 + ], + "lines": [ + { + "bbox": [ + 47, + 213, + 288, + 235 + ], + "spans": [ + { + "bbox": [ + 47, + 213, + 288, + 235 + ], + "type": "text", + "content": "Table 3. Ablation on the contribution of PROMPTCAP, compared with generic captioning model OFA-Cap. The LM we use is GPT-3." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 235, + 277, + 280 + ], + "lines": [ + { + "bbox": [ + 55, + 235, + 277, + 280 + ], + "spans": [ + { + "bbox": [ + 55, + 235, + 277, + 280 + ], + "type": "table", + "html": "
Captioning ModelOK-VQAA-OKVQAVQAv2
OFA-Cap56.651.064.9
PROMPTCAP60.456.374.1
", + "image_path": "d46df63e9ea704649cbe6db2d9b6236ee5cc80e571f96e07d31a2ff2b487025b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 292, + 251, + 303 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 292, + 251, + 303 + ], + "spans": [ + { + "bbox": [ + 47, + 292, + 251, + 303 + ], + "type": "text", + "content": "5.3.1 Performance Benefit from PROMPTCAP" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 310, + 288, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 310, + 288, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 288, + 430 + ], + "type": "text", + "content": "Baseline generic captioning model We use the officially released OFA [58] captioning checkpoint \"caption-large-best-clean\" (470M) as the baseline generic captioning model. We refer to it as \"OFA-Cap\". We choose this model because this is the model initialization we use for PROMPTCAP, sharing the same model architecture. Notice that OFA is a large vision-language model pre-trained on 20M image-text pairs and 20 vision-language tasks, including many VQA tasks. We are not using additional annotated data during PROMPT-CAP finetuning." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 437, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 557 + ], + "type": "text", + "content": "PROMPTCAP captions give consistent gains over generic captions. Table 3 measures the performance benefit from PROMPTCAP on OK-VQA, A-OKVQA, and VQAv2 validation sets. Here we focus on the performance gap between using PROMPTCAP captions and generic OFA captions. We can see that PROMPTCAP gives consistent improvements over generic captions. Specifically, with GPT-3, PROMPTCAP improves over OFA-Cap by " + }, + { + "bbox": [ + 46, + 437, + 287, + 557 + ], + "type": "inline_equation", + "content": "3.8\\%" + }, + { + "bbox": [ + 46, + 437, + 287, + 557 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 437, + 287, + 557 + ], + "type": "inline_equation", + "content": "5.3\\%" + }, + { + "bbox": [ + 46, + 437, + 287, + 557 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 437, + 287, + 557 + ], + "type": "inline_equation", + "content": "9.2\\%" + }, + { + "bbox": [ + 46, + 437, + 287, + 557 + ], + "type": "text", + "content": " absolute accuracy on OK-VQA, A-OKVQA, and VQAv2, respectively." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 52, + 607, + 281, + 653 + ], + "blocks": [ + { + "bbox": [ + 47, + 564, + 288, + 607 + ], + "lines": [ + { + "bbox": [ + 47, + 564, + 288, + 607 + ], + "spans": [ + { + "bbox": [ + 47, + 564, + 288, + 607 + ], + "type": "text", + "content": "Table 4. Ablation on the contribution of GPT-3. We measure the performance gain of using GPT-3 as the language model, compared with Flan-T5-XXL (11B). The captioning model we use is PROMPTCAP." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 607, + 281, + 653 + ], + "lines": [ + { + "bbox": [ + 52, + 607, + 281, + 653 + ], + "spans": [ + { + "bbox": [ + 52, + 607, + 281, + 653 + ], + "type": "table", + "html": "
Language ModelOK-VQAA-OKVQAVQAv2
Flan-T5-XXL (11B)42.041.570.9
GPT-3 (175B)60.456.374.1
", + "image_path": "784a9aac89fa3df154f3a09e9ceaaf547703a076e96c75275ffdd5fcc946825a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 670, + 265, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 265, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 265, + 683 + ], + "type": "text", + "content": "5.3.2 Performance Benefit from Language Model" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Baseline language model To measure the performance gain from GPT-3, we choose Flan-T5-XXL(11B) [11] as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 547, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 121 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 121 + ], + "type": "text", + "content": "the baseline language model. FlanT5-XXL is an instructionfinetuned LM that has shown good in-context learning ability. Notice that for Flan-T5-XXL, because of the input length limit, we use " + }, + { + "bbox": [ + 304, + 72, + 547, + 121 + ], + "type": "inline_equation", + "content": "n = 16" + }, + { + "bbox": [ + 304, + 72, + 547, + 121 + ], + "type": "text", + "content": " in-context examples in the input." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 136, + 547, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 136, + 547, + 293 + ], + "spans": [ + { + "bbox": [ + 304, + 136, + 547, + 293 + ], + "type": "text", + "content": "GPT-3 yields huge gains on knowledge-based VQA, but not on VQAv2. Results in Table 4 quantify the benefit of GPT-3 over Flan-T5-XXL. GPT-3 yields great performance gains on knowledge-based VQA tasks, improving over Flan-T5 by " + }, + { + "bbox": [ + 304, + 136, + 547, + 293 + ], + "type": "inline_equation", + "content": "18.4\\%" + }, + { + "bbox": [ + 304, + 136, + 547, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 136, + 547, + 293 + ], + "type": "inline_equation", + "content": "14.8\\%" + }, + { + "bbox": [ + 304, + 136, + 547, + 293 + ], + "type": "text", + "content": " absolute accuracy on OK-VQA and A-OKVQA, respectively. In comparison, on VQAv2, GPT-3 only gives " + }, + { + "bbox": [ + 304, + 136, + 547, + 293 + ], + "type": "inline_equation", + "content": "3.2\\%" + }, + { + "bbox": [ + 304, + 136, + 547, + 293 + ], + "type": "text", + "content": " accuracy gain, which is much smaller than the gain from PROMPTCAP over generic captions. The results indicate that GPT-3's external knowledge is critical for knowledge-based VQA tasks but not for VQAv2. We speculate that this disparity arises from VQAv2's focus on information in the image, without requiring additional knowledge beyond visual information." + } + ] + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 311, + 346, + 538, + 418 + ], + "blocks": [ + { + "bbox": [ + 304, + 300, + 547, + 345 + ], + "lines": [ + { + "bbox": [ + 304, + 300, + 547, + 345 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 547, + 345 + ], + "type": "text", + "content": "Table 5. Ablation of GPT-3 prompting on OK-VQA. We experiment with different numbers of in-context examples in the input and measure the performance gain from retrieving similar in-context examples compared with random examples." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 311, + 346, + 538, + 418 + ], + "lines": [ + { + "bbox": [ + 311, + 346, + 538, + 418 + ], + "spans": [ + { + "bbox": [ + 311, + 346, + 538, + 418 + ], + "type": "table", + "html": "
ExamplesCaptionn=1n=4n=16n=32
RandomOFA-Cap42.846.649.750.8
PROMPTCAP46.550.053.155.2
CLIPOFA-Cap44.550.055.356.6
PROMPTCAP48.753.358.460.4
", + "image_path": "ad57ec870d43245c655a1bcd2478294b426b8922b9a7788065c6126ffb78dfd1.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 440, + 469, + 452 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 440, + 469, + 452 + ], + "spans": [ + { + "bbox": [ + 305, + 440, + 469, + 452 + ], + "type": "text", + "content": "5.3.3 Ablation on GPT-3 Prompting" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 459, + 547, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 547, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 547, + 615 + ], + "type": "text", + "content": "As discussed in §4, two factors affect the in-context learning performance: the number of in-context examples, and the example selection strategy. To measure the effects of these two factors, we conduct an ablation study on GPT-3 prompting for OK-VQA in Table 5. We vary the number of examples " + }, + { + "bbox": [ + 304, + 459, + 547, + 615 + ], + "type": "inline_equation", + "content": "n \\in \\{1, 4, 16, 32\\}" + }, + { + "bbox": [ + 304, + 459, + 547, + 615 + ], + "type": "text", + "content": " and experiment with random examples and the most similar examples retrieved by CLIP (VIT-L/14) [43]. We can see that for both example selection strategies, the more in-context examples, the better the performance. Also, retrieving most similar examples with CLIP gives substantial performance gain (5.2% absolute accuracy for PROMPTCAP when " + }, + { + "bbox": [ + 304, + 459, + 547, + 615 + ], + "type": "inline_equation", + "content": "n = 32" + }, + { + "bbox": [ + 304, + 459, + 547, + 615 + ], + "type": "text", + "content": "). Both findings agree with the claims in prior work [5, 31, 67]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 623, + 463, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 463, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 463, + 635 + ], + "type": "text", + "content": "5.4. Domain Transfer on WebQA" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "We apply PROMPTCAP to WebQA [6] to evaluate PROMPTCAP's generalization ability on images and tasks from different domains. WebQA images are crawled from the web and are from domains different from the COCO [28] images used in PROMPTCAP's training data synthesized from VQAv2 [14]. Due to the task setting, questions are" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2969" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 171, + 202 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 171, + 202 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 171, + 202 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 171, + 202 + ], + "type": "image", + "image_path": "0bae8e450082eb547aa88072889fe78a8b908eb38d925e0a7457b59fb125e46e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 173, + 70, + 295, + 203 + ], + "blocks": [ + { + "bbox": [ + 173, + 70, + 295, + 203 + ], + "lines": [ + { + "bbox": [ + 173, + 70, + 295, + 203 + ], + "spans": [ + { + "bbox": [ + 173, + 70, + 295, + 203 + ], + "type": "image", + "image_path": "78890cc4b01b705191ec701e7d411ffae4c7b7c6b6fd98afb440bea439f317fd.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 296, + 70, + 421, + 203 + ], + "blocks": [ + { + "bbox": [ + 296, + 70, + 421, + 203 + ], + "lines": [ + { + "bbox": [ + 296, + 70, + 421, + 203 + ], + "spans": [ + { + "bbox": [ + 296, + 70, + 421, + 203 + ], + "type": "image", + "image_path": "2d5340a6a39474a5e54e11ee3ba1cd806e71d77cee1792ddd951aa4200a4d5b7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 422, + 70, + 545, + 203 + ], + "blocks": [ + { + "bbox": [ + 422, + 70, + 545, + 203 + ], + "lines": [ + { + "bbox": [ + 422, + 70, + 545, + 203 + ], + "spans": [ + { + "bbox": [ + 422, + 70, + 545, + 203 + ], + "type": "image", + "image_path": "2655bc5e64208ec69e8073ebc16e462b5074eb674d5128152a1bf63b65483717.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 48, + 204, + 295, + 255 + ], + "blocks": [ + { + "bbox": [ + 48, + 204, + 295, + 255 + ], + "lines": [ + { + "bbox": [ + 48, + 204, + 295, + 255 + ], + "spans": [ + { + "bbox": [ + 48, + 204, + 295, + 255 + ], + "type": "image", + "image_path": "3fe19f5859804d3acc129cc74c9e67fb7cd2a7c6e9bddebe29124882ce7702a4.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 257, + 547, + 280 + ], + "lines": [ + { + "bbox": [ + 46, + 257, + 547, + 280 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 547, + 280 + ], + "type": "text", + "content": "Figure 5. Example captions generated by PROMPTCAP and OFA-Cap, and the answers GPT-3 generated the captions. For all these questions, GPT-3 yields the correct answer given PROMPTCAP captions but fails given the generic caption. Questions are from OK-VQA." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 296, + 204, + 421, + 255 + ], + "blocks": [ + { + "bbox": [ + 296, + 204, + 421, + 255 + ], + "lines": [ + { + "bbox": [ + 296, + 204, + 421, + 255 + ], + "spans": [ + { + "bbox": [ + 296, + 204, + 421, + 255 + ], + "type": "image", + "image_path": "5cc81f5b7b6a07af6ca11e1e461558a2ae6ec543ea75fa49bdd2d44f28908073.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 422, + 204, + 545, + 255 + ], + "blocks": [ + { + "bbox": [ + 422, + 204, + 545, + 255 + ], + "lines": [ + { + "bbox": [ + 422, + 204, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 422, + 204, + 545, + 255 + ], + "type": "image", + "image_path": "052d6805ee332afd16f6b4b49264d18e02d35cf7d81e640e0109b8ce3c670834.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 50, + 290, + 171, + 437 + ], + "blocks": [ + { + "bbox": [ + 50, + 290, + 171, + 437 + ], + "lines": [ + { + "bbox": [ + 50, + 290, + 171, + 437 + ], + "spans": [ + { + "bbox": [ + 50, + 290, + 171, + 437 + ], + "type": "image", + "image_path": "3dc6f2f353d1c8815f4df3a2f47c7f643dd3f463529d241a24dbf7047a283165.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 134, + 441, + 456, + 453 + ], + "lines": [ + { + "bbox": [ + 134, + 441, + 456, + 453 + ], + "spans": [ + { + "bbox": [ + 134, + 441, + 456, + 453 + ], + "type": "text", + "content": "Figure 6. Representative failure cases of PROMPTCAP and GPT-3 pipeline on OK-VQA." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 173, + 290, + 296, + 437 + ], + "blocks": [ + { + "bbox": [ + 173, + 290, + 296, + 437 + ], + "lines": [ + { + "bbox": [ + 173, + 290, + 296, + 437 + ], + "spans": [ + { + "bbox": [ + 173, + 290, + 296, + 437 + ], + "type": "image", + "image_path": "3fda532b6c76d546cbcaf922bb8d12f6e3be16aa9fec3a46216d3654b82fa939.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 298, + 290, + 421, + 437 + ], + "blocks": [ + { + "bbox": [ + 298, + 290, + 421, + 437 + ], + "lines": [ + { + "bbox": [ + 298, + 290, + 421, + 437 + ], + "spans": [ + { + "bbox": [ + 298, + 290, + 421, + 437 + ], + "type": "image", + "image_path": "9a5b927fcc360f4fb4970c929002467af7ce33e3a0bdab3dc1c4c8ae0f878ce9.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 422, + 290, + 545, + 437 + ], + "blocks": [ + { + "bbox": [ + 422, + 290, + 545, + 437 + ], + "lines": [ + { + "bbox": [ + 422, + 290, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 422, + 290, + 545, + 437 + ], + "type": "image", + "image_path": "a1d5331937802f7ec849f7205940a7f424319c8f631f69ebfe9fa5909daaaf92.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 62, + 491, + 272, + 586 + ], + "blocks": [ + { + "bbox": [ + 46, + 458, + 288, + 491 + ], + "lines": [ + { + "bbox": [ + 46, + 458, + 288, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 458, + 288, + 491 + ], + "type": "text", + "content": "Table 6. Results on the WebQA validation set with oracle sources on image queries. The baselines in the upper part are fully supervised, while our methods only use 8-shot in-context learning." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 62, + 491, + 272, + 586 + ], + "lines": [ + { + "bbox": [ + 62, + 491, + 272, + 586 + ], + "spans": [ + { + "bbox": [ + 62, + 491, + 272, + 586 + ], + "type": "table", + "html": "
MethodFLAccFL*Acc
Fully supervised VLP + VinVL [6]47.649.627.5
VLP + x101fpn [6]46.944.323.8
8-shot in-context learning OFA-Cap + GPT-3 PROMPTCAP + GPT-352.855.433.5
53.057.234.5
", + "image_path": "e5a130c66d4f5cf56b95ce52dc1fdeab506e009cb355cc870e988c5936abef5b.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "content": "compositional and much longer than typical VQA questions. We convert the source images into captions and use GPT-3 in-context learning to carry out the task with only 8 random examples. The answers are long-form and measured by two scores: the fluency score measured by BARTScore [69] and the accuracy score that measures if human-annotated keywords are included in the answer. The results in the image-query setting with oracle sources on the validation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 461, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 510 + ], + "type": "text", + "content": "set" + }, + { + "bbox": [ + 304, + 461, + 545, + 510 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 461, + 545, + 510 + ], + "type": "text", + "content": " are shown on Table 6. Our systems outperform all the official baselines. PROMPTCAP outperforms the generic OFA captions, showing that PROMPTCAP is generalizable to a different domain of questions and images." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 516, + 424, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 516, + 424, + 529 + ], + "spans": [ + { + "bbox": [ + 306, + 516, + 424, + 529 + ], + "type": "text", + "content": "5.5. Qualitative Analysis" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 534, + 547, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 678 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 678 + ], + "type": "text", + "content": "Representative captions generated by PROMPTCAP and OFA are illustrated in Figure 5. The task is to answer the questions in OK-VQA. For all these questions, GPT-3 generates the correct answer when taking PROMPTCAP's caption as input, but fails when taking the generic caption. PROMPTCAP is able to capture visual attributes according to the question, for example, \"brand\" in (b) and \"color\" in (c). In addition, it can focus on particular objects asked in the question, such as the clothing the boy is \"putting on\" in (d). For tasks beyond PROMPTCAP's reasoning ability, GPT-3 infers the answer by the visual details PROMPTCAP gives. For example, GPT-3 infers \"green\" for the \"complimentary" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 683, + 547, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 683, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 683, + 547, + 713 + ], + "type": "text", + "content": "2Setting at https://github.com/WebQnA/WebQA/tree/ main/baseline_output_files/Baseline_prediction_ files_on_VAL" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2970" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 144 + ], + "type": "text", + "content": "color of red\" in (c) and \"7\" for SUV's seating capacity in (a). We also show some representative failure cases in Figure 6. The majority of failures are as shown in (a) and (b), in which PROMPTCAP fails to provide helpful information, or provides unfactual information. GPT-3 sometimes makes mistakes, as shown in (c) and (d)." + } + ] + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 49, + 196, + 284, + 303 + ], + "blocks": [ + { + "bbox": [ + 46, + 152, + 288, + 196 + ], + "lines": [ + { + "bbox": [ + 46, + 152, + 288, + 196 + ], + "spans": [ + { + "bbox": [ + 46, + 152, + 288, + 196 + ], + "type": "text", + "content": "Table 7. Comparison of captions. \"GPT-3-Syn\" are the question-aware captions synthesized by GPT-3. \"COCO-GT\" are the MSCOCO ground-truth captions. Higher scores imply higher similarities between the captions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 196, + 284, + 303 + ], + "lines": [ + { + "bbox": [ + 49, + 196, + 284, + 303 + ], + "spans": [ + { + "bbox": [ + 49, + 196, + 284, + 303 + ], + "type": "table", + "html": "
CaptionsBMCS
Comparison between “gold captions”
GPT-3-SynCOCO-GT67.144.3182.932.1
Inferenced captions vs. “gold captions”
OFA-CapGPT-3-Syn26.225.3231.040.2
PROMPTCAPGPT-3-Syn33.029.7307.147.3
OFA-CapCOCO-GT44.530.9147.924.6
PROMPTCAPCOCO-GT45.431.6150.125.2
", + "image_path": "5f4e1ab4d31bb8c10898e1cfd515a9263d263b981c5ed255de1a919b2953eba3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 315, + 287, + 340 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 315, + 287, + 340 + ], + "spans": [ + { + "bbox": [ + 47, + 315, + 287, + 340 + ], + "type": "text", + "content": "5.6. Analysis: How Do Question-Aware Captions Differ from Generic Captions?" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 346, + 289, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 289, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 289, + 489 + ], + "type": "text", + "content": "To further analyze the question-aware captions, we compare different inferred/gold captions in Table 7. The captions are compared by the automatic evaluations used in MSCOCO [7]: BLEU-4 (B) [42], METEOR (M) [4], CIDEr (C) [55], and SPICE (S) [2]. We evaluate the captions on the VQAv2 question-image pairs with images in the Karpathy test split [21] and average the scores over the questions. The upper part of the table compares the \"training targets\" for PROMPTCAP and the generic captioning model OFA-Cap. The lower part compares the captions inferred by each captioning model with these \"gold captions\". We make several observations from the table:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 491, + 288, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 288, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 288, + 552 + ], + "type": "text", + "content": "GPT-3 synthesized question-aware captions synthesized by GPT-3 are highly similar to the MSCOCO ground truth generic captions. As seen in the upper part of Table 7, the question-aware captions are really similar to the MSCOCO ground-truth captions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 554, + 288, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 554, + 288, + 686 + ], + "spans": [ + { + "bbox": [ + 46, + 554, + 288, + 686 + ], + "type": "text", + "content": "PROMPTCAP achieves high CIDEr and SPICE scores using GPT-3 synthesized captions as reference. The second row in the lower part compares the prompt-guided captions generated by PROMPTCAP with the GPT-3 synthesized question-aware captions. We can see that the CIDEr and SPICE scores are really high. One possible reason for the high scores is that synthesized question-aware captions are typically less diverse, shorter, and cover fewer visual entities compared with human-written general captions. Moreover, the image captioning task becomes less ambiguous via the prompt's control, making it easier for PROMPTCAP to learn." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 689, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 289, + 714 + ], + "type": "text", + "content": "PROMPTCAP can also generate high-quality generic captions. The last row shows the quality of the generic captions" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "content": "generated by PROMPTCAP. Users can get generic captions by prompting PROMPTCAP with the question \"what does the image describe?\". All the automatic metrics show that PROMPTCAP achieves SOTA performance on COCO validation set, with even higher scores than the original OFA-Cap model." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 153, + 488, + 167 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 153, + 488, + 167 + ], + "spans": [ + { + "bbox": [ + 305, + 153, + 488, + 167 + ], + "type": "text", + "content": "6. Limitations and Broader Impact" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 173, + 547, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 173, + 547, + 269 + ], + "spans": [ + { + "bbox": [ + 304, + 173, + 547, + 269 + ], + "type": "text", + "content": "One limitation is that the current PROMPTCAP only focuses on knowledge-based VQA tasks. PROMPTCAP can be extended to other vision-language tasks beyond VQA. Figure 7 shows an example of solving NLVR2 [52] via a series of vision and reasoning steps between PROMPTCAP and ChatGPT. Future work may scale up PROMPTCAP training with more diverse tasks and instructions, and explore broader applications of PROMPTCAP beyond VQA." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 269, + 547, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 269, + 547, + 340 + ], + "spans": [ + { + "bbox": [ + 304, + 269, + 547, + 340 + ], + "type": "text", + "content": "Another limitation is that images contain information that cannot be abstracted as text. While PROMPTCAP has demonstrated promising results in bridging the gap between LMs and images, it is important to recognize its limitations and use it in conjunction with other methods to ensure a comprehensive understanding of visual data." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 315, + 349, + 538, + 513 + ], + "blocks": [ + { + "bbox": [ + 315, + 349, + 538, + 513 + ], + "lines": [ + { + "bbox": [ + 315, + 349, + 538, + 513 + ], + "spans": [ + { + "bbox": [ + 315, + 349, + 538, + 513 + ], + "type": "image", + "image_path": "5400caa03ef293aa5fe96b90b925fbc4dfb8b01ca63a8055be908206e9b8fb5e.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 516, + 547, + 539 + ], + "lines": [ + { + "bbox": [ + 305, + 516, + 547, + 539 + ], + "spans": [ + { + "bbox": [ + 305, + 516, + 547, + 539 + ], + "type": "text", + "content": "Figure 7. Demo of solving the NLVR2 task with off-the-shelf PROMPTCAP and ChatGPT via an interpretable reasoning process." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 550, + 378, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 550, + 378, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 550, + 378, + 562 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "We present PROMPTCAP, a novel question-aware captioning model that can be controlled via a natural language prompt. To train this captioning model with no extra annotation, we devise an efficient pipeline for synthesizing and filtering training examples via GPT-3. We demonstrate the effectiveness of PROMPTCAP on knowledge-based VQA tasks. Our system achieves state-of-the-art performance on OKVQA and A-OKVQA. Ablations show that PROMPTCAP is giving consistent gains over generic captions. Furthermore, we investigate PROMPTCAP's generalization ability on WebQA. PROMPTCAP works as a simple and general module for converting question-related visual information into text." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "2971" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 190 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 190 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 190 + ], + "type": "text", + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, Roman Ring, Eliza Rutherford, Serkan Cabi, Tengda Han, Zhitao Gong, Sina Samangooei, Marianne Monteiro, Jacob Menick, Sebastian Borgeaud, Andrew Brock, Aida Nematzadeh, Sahand Sharifzadeh, Mikolaj Binkowski, Ricardo Barreira, Oriol Vinyals, Andrew Zisserman, and Karen Simonyan. 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Mucko: multi-layer cross-modal knowledge reasoning for fact-based visual question answering. arXiv preprint arXiv:2006.09073, 2020. 2" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2975" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 12 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/PromptStyler_ Prompt-driven Style Generation for Source-free Domain Generalization/f8d2a45d-4c84-4d88-913c-50e0d9fbe4a8_content_list.json b/2023/PromptStyler_ Prompt-driven Style Generation for Source-free Domain Generalization/f8d2a45d-4c84-4d88-913c-50e0d9fbe4a8_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..b327021f96658f75658e9de4497c217dd3fc055e --- /dev/null +++ b/2023/PromptStyler_ Prompt-driven Style Generation for Source-free Domain Generalization/f8d2a45d-4c84-4d88-913c-50e0d9fbe4a8_content_list.json @@ -0,0 +1,1594 @@ +[ + { + "type": "text", + "text": "PromptStyler: Prompt-driven Style Generation for Source-free Domain Generalization", + "text_level": 1, + "bbox": [ + 245, + 130, + 725, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Junhyeong Cho $^{1}$ Gilhyun Nam $^{1}$ Sungyeon Kim $^{2}$ Hunmin Yang $^{1,3}$ Suha Kwak $^{2}$ $^{1}$ ADD $^{2}$ POSTECH $^{3}$ KAIST \nhttps://PromptStyler.github.io", + "bbox": [ + 133, + 202, + 834, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In a joint vision-language space, a text feature (e.g., from \"a photo of a dog\") could effectively represent its relevant image features (e.g., from dog photos). Also, a recent study has demonstrated the cross-modal transferability phenomenon of this joint space. From these observations, we propose PromptStyler which simulates various distribution shifts in the joint space by synthesizing diverse styles via prompts without using any images to deal with source-free domain generalization. The proposed method learns to generate a variety of style features (from \"a $S_*$ style of a\") via learnable style word vectors for pseudo-words $S_*$ . To ensure that learned styles do not distort content information, we force style-content features (from \"a $S_*$ style of a [class]\") to be located nearby their corresponding content features (from \"[class]\") in the joint vision-language space. After learning style word vectors, we train a linear classifier using synthesized style-content features. PromptStyler achieves the state of the art on PACS, VLCS, OfficeHome and DomainNet, even though it does not require any images for training.", + "bbox": [ + 73, + 311, + 473, + 599 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 619, + 209, + 636 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep neural networks are usually trained with the assumption that training and test data are independent and identically distributed, which makes them vulnerable to substantial distribution shifts between training and test data [23, 52]. This susceptibility is considered as one of the major obstacles to their deployment in real-world applications. To enhance their robustness to such distribution shifts, Domain Adaptation (DA) [2, 24, 32, 33, 54, 56, 57, 68] has been studied; it aims at adapting neural networks to a target domain using target domain data available in training. However, such a target domain is often latent in common training scenarios, which considerably limits the application of DA. Recently, a body of research has addressed this limitation by Domain Generalization (DG) [3, 5, 21, 29, 35, 37, 74] that aims to improve model's generalization capability to any unseen domains. It has been a common practice in DG to utilize multiple source domains for learning domain-invariant features [61, 69], but", + "bbox": [ + 75, + 643, + 472, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e5a565637b157782a9d80607cf5b0578cb65a0ea4f6df5086f7c42da621e858b.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 535, + 290, + 890, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/866e4d637a5b4a9f831248aa803b78ee62b3347747ca78768831881749520fb4.jpg", + "image_caption": [ + "(b)", + "Figure 1: Motivation of our method. (a) Text features could effectively represent various image styles in a joint vision-language space. (b) PromptStyler synthesizes diverse styles in a joint vision-language space via learnable style word vectors for pseudo-words $S_{*}$ without using any images." + ], + "image_footnote": [], + "bbox": [ + 537, + 462, + 890, + 628 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "it is unclear which source domains are ideal for DG, since arbitrary unseen domains should be addressed. Furthermore, it is costly and sometimes even infeasible to collect and annotate large-scale multi-source domain data for training.", + "bbox": [ + 496, + 732, + 893, + 794 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We notice that a large-scale pre-trained model might have already observed a great variety of domains and thus can be used as an efficient proxy of actual multiple source domains. From this perspective, we raised a question \"Could we further improve model's generalization capability by simulating various distribution shifts in the latent space of such a large-scale model without using any source domain data?\" If this", + "bbox": [ + 496, + 795, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15702", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b7e0632f0fd96cc7b1ef303d1293082b8acc6fb50817a4b4a1ec1677ffda0dca.jpg", + "image_caption": [ + "Figure 2: Important factors in the proposed method. PromptStyler learns style word vectors for pseudo-words $S_{*}$ which lead to diverse style features (from \"a $S_{*}$ style of a\") while preserving content information encoded in style-content features (from \"a $S_{*}$ style of a [class])\". $\\mathcal{L}_{\\mathrm{style}}$ and $\\mathcal{L}_{\\mathrm{content}}$ are the loss functions used for maximizing style diversity and content consistency in a hyperspherical joint vision-language space (e.g., CLIP [50] latent space)." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 486, + 303 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/14762db21e7aff5a1db84fe2b1d15b30decec8136ce0249ce961c876a8f29113.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 493, + 88, + 890, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "is possible, DG will become immensely practical by effectively and efficiently exploiting such a large-scale model. However, this approach is much more challenging since any actual data of source and target domains are not accessible but only the target task definition (e.g., class names) is given.", + "bbox": [ + 75, + 386, + 470, + 462 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we argue that large-scale vision-language models [26, 50, 64] could shed light on this challenging source-free domain generalization. As conceptually illustrated in Figure 1(a), text features could effectively represent their relevant image features in a joint vision-language space. Despite the modality gap between two modalities in the joint space [39], a recent study has demonstrated the cross-modal transferability phenomenon [67]; we could train a classifier using text features while running an inference with the classifier using image features. This training procedure meets the necessary condition for the source-free domain generalization, i.e., source domain images are not required. Using such a joint vision-language space, we could simulate various distribution shifts via prompts without any images.", + "bbox": [ + 75, + 463, + 468, + 674 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We propose a prompt-driven style generation method, dubbed PromptStyler, which synthesizes diverse styles via learnable word vectors to simulate distribution shifts in a hyperspherical joint vision-language space. PromptStyler is motivated by the observation that a shared style of images could characterize a domain [27, 74] and such a shared style could be captured by a learnable word vector for a pseudoword $S_{*}$ using CLIP [50] with a prompt (\"a painting in the style of $S_{*}$ ) [17]. As shown in Figure 1(b), our method learns a style word vector for $S_{*}$ to represent each style.", + "bbox": [ + 75, + 674, + 468, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To effectively simulate various distribution shifts, we try to maximize style diversity as illustrated in Figure 2. Specifically, our method encourages learnable style word vectors to result in orthogonal style features in the hyperspherical space, where each style feature is obtained from a style prompt", + "bbox": [ + 75, + 824, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "(\"a $S_*$ style of a\") via a pre-trained text encoder. To prevent learned styles from distorting content information, we also consider content consistency as illustrated in Figure 2. Each style-content feature obtained from a style-content prompt (\"a $S_*$ style of a [class]) is forced to be located closer to its corresponding content feature obtained from a content prompt (\"[class]\") than the other content features.", + "bbox": [ + 496, + 386, + 892, + 492 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learned style word vectors are used to synthesize style-content features for training a classifier; these synthesized features could simulate images of known contents with diverse unknown styles in the joint space. These style-content features are fed as input to a linear classifier which is trained by a classification loss using contents (\"[class]\") as their class labels. At inference time, an image encoder extracts image features from input images, which are fed as input to the trained classifier. Note that the text and image encoders are derived from the same pre-trained vision-language model (e.g., CLIP [50]); the text encoder is only involved in training and the image encoder is only involved at inference time.", + "bbox": [ + 496, + 492, + 892, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The proposed method achieves state-of-the-art results on PACS [34], VLCS [15], OfficeHome [60] and DomainNet [48] without using any actual data of source and target domains. It takes just $\\sim 30$ minutes for the entire training using a single RTX 3090 GPU, and our model is $\\sim 2.6\\times$ smaller and $\\sim 243\\times$ faster at inference compared with CLIP [50].", + "bbox": [ + 496, + 674, + 893, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized as follows:", + "bbox": [ + 517, + 763, + 821, + 777 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- This work is the first attempt to synthesize a variety of styles in a joint vision-language space via prompts to effectively tackle source-free domain generalization.", + "- This paper proposes a novel method that effectively simulates images of known contents with diverse unknown styles in a joint vision-language space.", + "- PromptStyler achieves the state of the art on domain generalization benchmarks without using any images." + ], + "bbox": [ + 517, + 779, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15703", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/7ec19ae78c9b78e06912a4acd3f5827b3b6126782538ba36d423ddf742593f7d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SetupSourceTargetTask Definition
DA✓✓✓
DG✓-✓
Source-free DA-✓✓
Source-free DG--✓
", + "bbox": [ + 81, + 88, + 468, + 170 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 1: Different requirements in each setup. Source-free DG only assumes the task definition (i.e., what should be predicted) without requiring source and target domain data.", + "bbox": [ + 76, + 175, + 468, + 220 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 238, + 218, + 255 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Domain Generalization. Model's generalization capability to arbitrary unseen domains is the key factor to successful deployment of neural networks in real-world applications, since substantial distribution shifts between source and target domains could significantly degrade their performance [23, 52]. To this end, Domain Generalization (DG) [4, 5, 10, 16, 21, 29, 35, 37, 44, 45, 61, 69] has been studied. It assumes target domain data are not accessible while using data from source domains. Generally speaking, existing DG methods could be divided into two categories: multi-source DG [3, 12, 36, 42, 43, 51, 55, 63, 73, 74] and single-source DG [14, 38, 49, 62]. Mostly, multi-source DG methods aim to learn domain-invariant features by exploiting available multiple source domains, and single-source DG methods also aim to learn such features by generating diverse domains based on a single domain and then exploiting the synthesized domains.", + "bbox": [ + 76, + 263, + 472, + 505 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Source-free Domain Generalization. In this setup, we are not able to access any source and target domains as summarized in Table 1. Thus, source-free DG is much more challenging than multi-source and single-source DG. From the observation that synthesizing new domains from the given source domain could effectively improve model's generalization capability [27,38,62,72,73], we also try to generate diverse domains but without using any source domains to deal with source-free DG. By leveraging a large-scale pre-trained model which has already seen a great variety of domains, our method could simulate various distribution shifts in the latent space of the large-scale model. This approach has several advantages compared with existing DG methods; source domain images are not required and there is no concern for catastrophic forgetting which might impede model's generalization capability. Also, it would be immensely practical to exploit such a large-scale model for downstream visual recognition tasks, since we only need the task definition.", + "bbox": [ + 76, + 507, + 472, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Large-scale model in Domain Generalization. Recently, several DG methods [5, 53] exploit a large-scale pre-trained model (e.g., CLIP [50]) to leverage its great generalization capability. While training neural networks on available data, CAD [53] and MIRO [5] try to learn robust features using such a large-scale model. Compared with them, the proposed method could learn domain-invariant features using a large-scale pre-trained model without requiring any actual data.", + "bbox": [ + 75, + 780, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Joint vision-language space. Large-scale vision-language models [26, 50, 64] are trained with a great amount of image-text pairs, and achieve state-of-the-art results on downstream visual recognition tasks [20, 41, 66, 70, 71]. By leveraging their joint vision-language spaces, we could also effectively manipulate visual features via prompts [13, 18, 31, 47]. Interestingly, Textual Inversion [17] shows that a learnable style word vector for a pseudo-word $S_{*}$ could capture a shared style of images using CLIP [50] with a prompt (\"a painting in the style of $S_{*}$ \"). From this observation, we argue that learnable style word vectors would be able to seek a variety of styles for simulating various distribution shifts in a joint vision-language space without using any images.", + "bbox": [ + 496, + 90, + 893, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 297, + 591, + 314 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The overall framework of the proposed method is shown in Figure 3, and pseudo-code of PromptStyler is described in Algorithm 1. Our method learns style word vectors to represent a variety of styles in a hyperspherical joint vision-language space (e.g., CLIP [50] latent space). After learning those style word vectors, we train a linear classifier using synthesized style-content features produced by a pre-trained text encoder $T(\\cdot)$ . At inference time, a pre-trained image encoder $I(\\cdot)$ extracts image features from input images, which are fed as input to the trained linear classifier. Thanks to the cross-modal transferability phenomenon of the joint vision-language space [67], this classifier could produce class scores using the image features. Note that we exploit CLIP as our large-scale vision-language model; its image encoder and text encoder are frozen in our entire framework.", + "bbox": [ + 496, + 324, + 893, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Prompt-driven style generation", + "text_level": 1, + "bbox": [ + 500, + 558, + 774, + 574 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An input text prompt is converted to several tokens via a tokenization process, and then such tokens are replaced by their corresponding word vectors via a word lookup process. In PromptStyler, a pseudo-word $S_{i}$ in a prompt is a placeholder which is replaced by a style word vector $\\mathbf{s}_i \\in \\mathbb{R}^D$ during the word lookup process. Note that three kinds of prompts are used in the proposed method: a style prompt $\\mathcal{P}_i^{\\mathrm{style}}$ (\"a $S_{i}$ style of a\"), a content prompt $\\mathcal{P}_m^{\\mathrm{content}}$ (\"[class] $m$ \"), and a style-content prompt $\\mathcal{P}_i^{\\mathrm{style}} \\circ \\mathcal{P}_m^{\\mathrm{content}}$ (\"a $S_{i}$ style of a [class] $m$ \"). $S_{i}$ indicates the placeholder for $i$ -th style word vector and [class] $m$ denotes $m$ -th class name.", + "bbox": [ + 496, + 582, + 893, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Suppose we want to generate $K$ different styles in a joint vision-language space. In this case, the proposed method needs to learn $K$ style word vectors $\\{\\mathbf{s}_i\\}_{i=1}^K$ , where each $\\mathbf{s}_i$ is randomly initialized at the beginning. To effectively simulate various distribution shifts in the joint vision-language space, those style word vectors need to be diverse while not distorting content information when they are exploited in style-content prompts. There are two possible design choices for learning such word vectors: (1) learning each style word vector $\\mathbf{s}_i$ in a sequential manner, or (2) learning all style", + "bbox": [ + 496, + 750, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15704", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5d6b5fea955f54effc6924315ad9121f02bb0063f474b3059c065d3fcbc14752.jpg", + "image_caption": [ + "(i) Prompt-driven style generation" + ], + "image_footnote": [], + "bbox": [ + 78, + 114, + 524, + 324 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a0ac41ba6eafb7f255d2e0c841115d9450a4d2716c206f457ff2dbf18ffb0cea.jpg", + "image_caption": [ + "(ii) Training a linear classifier using diverse styles" + ], + "image_footnote": [ + "Frozen weights $\\ell_2$ normalization layer" + ], + "bbox": [ + 535, + 125, + 885, + 193 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8a9be02778762e0c40bea03a8b2d0dbc0dcd97108b318eb7c3f4e1cc122a2efb.jpg", + "image_caption": [ + "(iii) Inference using the trained classifier", + "Figure 3: PromptStyler learns diverse style word vectors which do not distort content information of style-content prompts. After learning style word vectors, we synthesize style-content features (e.g., from \"a $S_{1}$ style of a dog\") via a pre-trained text encoder for training a linear classifier. The classifier is trained by a classification loss using those synthesized features and their corresponding class labels (e.g., \"dog\"). At inference time, a pre-trained image encoder extracts image features, which are fed as input to the trained classifier. Note that the encoders are derived from the same vision-language model (e.g., CLIP [50])." + ], + "image_footnote": [ + "Frozen weights $\\ell_2$ normalization layer" + ], + "bbox": [ + 562, + 247, + 883, + 319 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "word vectors $\\{\\mathbf{s}_i\\}_{i=1}^K$ in a parallel manner. We choose the former, since it takes much less memory during training. Please refer to the supplementary material (Section A.2) for the empirical justification of our design choice.", + "bbox": [ + 75, + 440, + 468, + 500 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Style diversity loss. To maximize the diversity of $K$ styles in a hyperspherical joint vision-language space, we sequentially learn style word vectors $\\{\\mathbf{s}_i\\}_{i=1}^K$ in such a way that $i$ -th style feature $T(\\mathcal{P}_i^{\\mathrm{style}}) \\in \\mathbb{R}^C$ produced by $i$ -th style word vector $\\mathbf{s}_i$ is orthogonal to $\\{T(\\mathcal{P}_j^{\\mathrm{style}})\\}_{j=1}^{i-1}$ produced by previously learned style word vectors $\\{\\mathbf{s}_j\\}_{j=1}^{i-1}$ . Regarding this, the style diversity loss $\\mathcal{L}_{\\mathrm{style}}$ for learning $i$ -th style word vector $\\mathbf{s}_i$ is computed by", + "bbox": [ + 75, + 500, + 470, + 628 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s t y l e}} = \\frac {1}{i - 1} \\sum_ {j = 1} ^ {i - 1} \\left| \\frac {T \\left(\\mathcal {P} _ {i} ^ {\\text {s t y l e}}\\right)}{\\| T \\left(\\mathcal {P} _ {i} ^ {\\text {s t y l e}}\\right) \\| _ {2}} \\cdot \\frac {T \\left(\\mathcal {P} _ {j} ^ {\\text {s t y l e}}\\right)}{\\| T \\left(\\mathcal {P} _ {j} ^ {\\text {s t y l e}}\\right) \\| _ {2}} \\right|. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 637, + 468, + 680 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This style loss $\\mathcal{L}_{\\mathrm{style}}$ aims to minimize the absolute value of the cosine similarity between $i$ -th style features and each of the existing style features. When the value of this loss becomes zero, it satisfies the orthogonality between $i$ -th style feature and all the existing style features.", + "bbox": [ + 75, + 688, + 468, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Content consistency loss. Learning the style word vectors $\\{\\mathbf{s}_i\\}_{i = 1}^K$ only using the style diversity loss sometimes leads to undesirable outcome, since a learned style $\\mathbf{s}_i$ could substantially distort content information when used to generate a style-content feature $T(\\mathcal{P}_i^{\\mathrm{style}}\\circ \\mathcal{P}_m^{\\mathrm{content}})\\in \\mathbb{R}^C$ . To alleviate this problem, we encourage the content information in the style-content feature to be consistent with its corresponding content feature $T(\\mathcal{P}_m^{\\mathrm{content}})\\in \\mathbb{R}^C$ while learning each $i$ -th style word vector $\\mathbf{s}_i$ . Specifically, each style-content", + "bbox": [ + 76, + 763, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "feature synthesized via $i$ -th style word vector $\\mathbf{s}_i$ should have the highest cosine similarity score with its corresponding content feature. For $i$ -th style word vector $\\mathbf{s}_i$ , a cosine similarity score $z_{imn}$ between a style-content feature with $m$ -th class name and a content feature with $n$ -th class name is computed by", + "bbox": [ + 496, + 440, + 893, + 532 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nz _ {i m n} = \\frac {T \\left(\\mathcal {P} _ {i} ^ {\\text {s t y l e}} \\circ \\mathcal {P} _ {m} ^ {\\text {c o n t e n t}}\\right)}{\\| T \\left(\\mathcal {P} _ {i} ^ {\\text {s t y l e}} \\circ \\mathcal {P} _ {m} ^ {\\text {c o n t e n t}}\\right) \\| _ {2}} \\cdot \\frac {T \\left(\\mathcal {P} _ {n} ^ {\\text {c o n t e n t}}\\right)}{\\| T \\left(\\mathcal {P} _ {n} ^ {\\text {c o n t e n t}}\\right) \\| _ {2}}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 537, + 890, + 575 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Using cosine similarity scores between style-content features and content features, the content consistency loss $\\mathcal{L}_{\\mathrm{content}}$ for learning $i$ -th style word vector $\\mathbf{s}_i$ is computed by", + "bbox": [ + 496, + 579, + 890, + 625 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c o n t e n t}} = - \\frac {1}{N} \\sum_ {m = 1} ^ {N} \\log \\left(\\frac {\\exp \\left(z _ {i m m}\\right)}{\\sum_ {n = 1} ^ {N} \\exp \\left(z _ {i m n}\\right)}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 534, + 630, + 890, + 671 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $N$ denotes the number of classes pre-defined in the target task. This content loss $\\mathcal{L}_{\\mathrm{content}}$ is a contrastive loss which encourages each style-content feature to be located closer to its corresponding content feature so that it forces each $i$ -th style word vector $\\mathbf{s}_i$ to preserve content information when used to synthesize style-content features.", + "bbox": [ + 496, + 675, + 890, + 765 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Total prompt loss. PromptStyler learns $K$ style word vectors $\\{\\mathbf{s}_i\\}_{i=1}^K$ in a sequential manner, where each $i$ -th style word vector $\\mathbf{s}_i$ is learned using both $\\mathcal{L}_{\\mathrm{style}}$ (Eq.(1)) and $\\mathcal{L}_{\\mathrm{content}}$ (Eq.(3)). In the proposed method, the total loss $\\mathcal{L}_{\\mathrm{prompt}}$ for learning $i$ -th style word vector is computed by", + "bbox": [ + 496, + 766, + 893, + 843 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p r o m p t}} = \\mathcal {L} _ {\\text {s t y l e}} + \\mathcal {L} _ {\\text {c o n t e n t}}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 848, + 890, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Using this prompt loss $\\mathcal{L}_{\\mathrm{prompt}}$ , we train $i$ -th style word vector $\\mathbf{s}_i$ for $L$ training iterations.", + "bbox": [ + 496, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15705", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [], + "code_body": "Algorithm 1 PromptStyler \nRequirement: pre-trained text encoder $T(\\cdot)$ , pre-defined $N$ class names in the target task \nInput: number of style word vectors $K$ , number of training iterations $L$ \nOutput: $KN$ style-content features \n # randomly initialize style word vectors \n1: $\\{\\mathbf{s}_i\\}_{i=1}^K \\leftarrow$ random_init( $\\{\\mathbf{s}_i\\}_{i=1}^K$ ) \n # sequentially learn $K$ style word vectors \n2: for $i = 1, 2, \\ldots, K$ do \n # $L$ training iterations for learning each word vector \n3: for iteration $= 1, 2, \\ldots, L$ do \n # compute $\\mathcal{L}_{\\text{style}}$ using $T(\\cdot)$ and word vectors \n4: $\\mathcal{L}_{\\text{style}} \\leftarrow$ style_diversity_loss( $\\mathbf{s}_i$ , $\\{\\mathbf{s}_j\\}_{j=1}^{i-1}$ ) \n # compute $\\mathcal{L}_{\\text{content}}$ using $T(\\cdot)$ and a word vector \n5: $\\mathcal{L}_{\\text{content}} \\leftarrow$ content_consistency_loss( $\\mathbf{s}_i$ ) \n6: $\\mathcal{L}_{\\text{prompt}} \\leftarrow \\mathcal{L}_{\\text{style}} + \\mathcal{L}_{\\text{content}}$ \n7: Update $\\mathbf{s}_i$ using $\\mathcal{L}_{\\text{prompt}}$ by gradient descent \n8: end for \n9: end for \n10: Synthesize $KN$ style-content features using the learned $K$ style word vectors and $N$ class names via $T(\\cdot)$", + "bbox": [ + 76, + 89, + 472, + 433 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Training a linear classifier using diverse styles", + "text_level": 1, + "bbox": [ + 76, + 460, + 464, + 477 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After learning $K$ style word vectors $\\{\\mathbf{s}_i\\}_{i = 1}^K$ , we generate $KN$ style-content features for training a linear classifier. To be specific, we synthesize those features using the learned $K$ styles and pre-defined $N$ classes via the text encoder $T(\\cdot)$ . The linear classifier is trained by a classification loss using $\\ell_2$ -normalized style-content features and their class labels; each class label is the class name used to generate each style-content feature. To effectively leverage the hyperspherical joint vision-language space, we adopt ArcFace [8] loss as our classification loss $\\mathcal{L}_{\\mathrm{class}}$ . Note that ArcFace loss is an angular Softmax loss which computes the cosine similarities between classifier input features and classifier weights with an additive angular margin penalty between classes. This angular margin penalty allows for more discriminative predictions by pushing features from different classes further apart. Thanks to the property, this angular Softmax loss has been widely used in visual recognition tasks [7,9,30,40,65].", + "bbox": [ + 75, + 484, + 473, + 743 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Inference using the trained classifier", + "text_level": 1, + "bbox": [ + 76, + 755, + 393, + 771 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The trained classifier is used with a pre-trained image encoder $I(\\cdot)$ at inference time. Given an input image $\\mathbf{x}$ , the image encoder extracts its image feature $I(\\mathbf{x}) \\in \\mathbb{R}^{C}$ , which is mapped to the hyperspherical joint vision-language space by $\\ell_{2}$ normalization. Then, the trained classifier produces class scores using the $\\ell_{2}$ -normalized image feature. Note that the text encoder $T(\\cdot)$ is not used at inference time, while the image encoder $I(\\cdot)$ is only exploited at inference time.", + "bbox": [ + 75, + 779, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 89, + 633, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For more comprehensive understanding, please refer to the supplementary material (Section B and D).", + "bbox": [ + 500, + 114, + 890, + 146 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Evaluation datasets", + "text_level": 1, + "bbox": [ + 500, + 155, + 687, + 170 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proposed method does not require any actual data for training. To analyze its generalization capability, four domain generalization benchmarks are used for evaluation: PACS [34] (4 domains and 7 classes), VLCS [15] (4 domains and 5 classes), OfficeHome [60] (4 domains and 65 classes) and DomainNet [48] (6 domains and 345 classes). On these benchmarks, we repeat each experiment three times using different random seeds and report average top-1 classification accuracies with standard errors. Unlike the leave-one-domain-out cross-validation evaluation protocol [21], we do not exploit any source domain data for training.", + "bbox": [ + 496, + 179, + 893, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation details", + "text_level": 1, + "bbox": [ + 500, + 354, + 714, + 371 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "PromptStyler is implemented and trained with the same configuration regardless of the evaluation datasets. Training takes about 30 minutes using a single RTX 3090 GPU.", + "bbox": [ + 496, + 378, + 890, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Architecture. We choose CLIP [50] as our large-scale pretrained vision-language model, and use the publicly available pre-trained model. $^{1}$ The text encoder $T(\\cdot)$ used in training is Transformer [59] and the image encoder $I(\\cdot)$ used at inference is ResNet-50 [22] as default setting in experiments; our method is also implemented with ViT-B/16 [11] or ViT-L/14 [11] for further evaluations as shown in Table 2. Note that text and image encoders are derived from the same CLIP model and frozen in the entire pipeline. The dimension of each text feature or image feature is $C = 1024$ when our method is implemented with ResNet-50, while $C = 512$ in the case of ViT-B/16 and $C = 768$ in the case of ViT-L/14.", + "bbox": [ + 496, + 424, + 893, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Learning style word vectors. We follow prompt learning methods [70, 71] when learning the word vectors. Using a zero-mean Gaussian distribution with 0.02 standard deviation, we randomly initialize $K$ style word vectors $\\{\\mathbf{s}_i\\}_{i=1}^K$ , where $K = 80$ . The dimension of each style word vector is $D = 512$ when the proposed method is implemented with ResNet-50 [22] or ViT-B/16 [11], while $D = 768$ in the case of ViT-L/14 [11]. Each $i$ -th style word vector $\\mathbf{s}_i$ is trained by the prompt loss $\\mathcal{L}_{\\mathrm{prompt}}$ for $L = 100$ training iterations using the SGD optimizer with 0.002 learning rate and 0.9 momentum. The number of classes $N$ is pre-defined by each target task definition, e.g., $N = 345$ for DomainNet [48].", + "bbox": [ + 496, + 606, + 893, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training a linear classifier. The classifier is trained for 50 epochs using the SGD optimizer with 0.005 learning rate, 0.9 momentum, and a batch size of 128. In ArcFace [8] loss, its scaling factor is set to 5 with 0.5 angular margin.", + "bbox": [ + 496, + 787, + 893, + 847 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inference. Input images are pre-processed in the same way with the CLIP model; resized to $224 \\times 224$ and normalized.", + "bbox": [ + 496, + 848, + 893, + 877 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "1https://github.com/openai/CLIP", + "bbox": [ + 517, + 886, + 761, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15706", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/4c7f581d90a25ba0ca2bf38257c93d7ac9e23a3261b26f859337f40f820110f9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodConfigurationAccuracy (%)
Source DomainDomain DescriptionPACSVLCSOfficeHomeDomainNetAvg.
ResNet-50 [22] with pre-trained weights on ImageNet [6]
DANN [19]✓-83.6±0.478.6±0.465.9±0.638.3±0.166.6
RSC [25]✓-85.2±0.977.1±0.565.5±0.938.9±0.566.7
MLDG [35]✓-84.9±1.077.2±0.466.8±0.641.2±0.167.5
SagNet [46]✓-86.3±0.277.8±0.568.1±0.140.3±0.168.1
SelfReg [28]✓-85.6±0.477.8±0.967.9±0.742.8±0.068.5
GVRT [44]✓-85.1±0.379.0±0.270.1±0.144.1±0.169.6
MIRO [5]✓-85.4±0.479.0±0.070.5±0.444.3±0.269.8
ResNet-50 [22] with pre-trained weights from CLIP [50]
ZS-CLIP (C) [50]--90.6±0.076.0±0.068.6±0.045.6±0.070.2
CAD [53]✓-90.0±0.681.2±0.670.5±0.345.5±2.171.8
ZS-CLIP (PC) [50]-✓90.7±0.080.1±0.072.0±0.046.2±0.072.3
PromptStyler--93.2±0.082.3±0.173.6±0.149.5±0.074.7
ViT-B/16 [11] with pre-trained weights from CLIP [50]
ZS-CLIP (C) [50]--95.7±0.076.4±0.079.9±0.057.8±0.077.5
MIRO [5]✓-95.682.282.554.078.6
ZS-CLIP (PC) [50]-✓96.1±0.082.4±0.082.3±0.057.7±0.079.6
PromptStyler--97.2±0.182.9±0.083.6±0.059.4±0.080.8
ViT-L/14 [11] with pre-trained weights from CLIP [50]
ZS-CLIP (C) [50]--97.6±0.077.5±0.085.9±0.063.3±0.081.1
ZS-CLIP (PC) [50]-✓98.5±0.082.4±0.086.9±0.064.0±0.083.0
PromptStyler--98.6±0.082.4±0.289.1±0.065.5±0.083.9
", + "bbox": [ + 81, + 88, + 893, + 512 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Evaluations", + "text_level": 1, + "bbox": [ + 75, + 588, + 205, + 603 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Main results. PromptStyler achieves the state of the art in every evaluation on PACS [34], VLCS [15], OfficeHome [60] and DomainNet [48] as shown in Table 2. Note that all existing methods utilize source domain data except for zero-shot CLIP [50] in Table 2. Compared with zero-shot CLIP which generates each text feature using a domain-agnostic prompt (\"[class]\", PromptStyler largely outperforms its records in all evaluations. Our method also shows higher accuracy compared with zero-shot CLIP which produces each text feature using a domain-specific prompt (\"a photo of a [class]\", even though we do not exploit any domain descriptions. These results confirm that the proposed method effectively improves the generalization capability of the chosen pre-trained model, i.e., CLIP, without using any images by simulating various distribution shifts via prompts in its latent space.", + "bbox": [ + 73, + 612, + 470, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Computational evaluations. In Table 3, we compare our PromptStyler and zero-shot CLIP [50] in terms of the number of parameters and inference speed; the inference speed was measured using a single RTX 3090 GPU with a batch size", + "bbox": [ + 75, + 839, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5a3b550a0c373101c0d675e5c4f65033493e7a9fec2a2f2f1c3f0b0814e806bc.jpg", + "table_caption": [ + "Table 2: Comparison with the state-of-the-art domain generalization methods. ZS-CLIP (C) denotes zero-shot CLIP using \"[class]\" as its text prompt, and ZS-CLIP (PC) indicates zero-shot CLIP using \"a photo of a [class]\" as its text prompt. Note that PromptStyler does not exploit any source domain data and domain descriptions." + ], + "table_footnote": [], + "table_body": "
MethodInference Module# ParamsFPS
Image EncoderText Encoder
OfficeHome (65 classes)
ZS-CLIP [50]✓✓102.0M1.6
PromptStyler✓-38.4M72.9
DomainNet (345 classes)
ZS-CLIP [50]✓✓102.0M0.3
PromptStyler✓-38.7M72.9
", + "bbox": [ + 504, + 585, + 890, + 728 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3: The number of parameters and inference speed on OfficeHome [60] and DomainNet [48] using ResNet-50 [22] as an image encoder. Note that CLIP [50] text encoder needs to generate text features as many as the number of classes.", + "bbox": [ + 496, + 732, + 893, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "of 1. Note that we do not exploit a text encoder at inference time, which makes our model $\\sim 2.6 \\times$ smaller and $\\sim 243 \\times$ faster compared with CLIP. Regarding the inference speed, the proposed model is about $45 \\times$ faster for the target task OfficeHome [60] (65 classes) and it is about $243 \\times$ faster for the target task DomainNet [48] (345 classes).", + "bbox": [ + 496, + 809, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15707", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7f2a84d5dfccfb3cb966ba8cc3d766e24359d06ca57f37fb7ee70a35d60a9236.jpg", + "image_caption": [ + "(a) $\\mathcal{L}_{\\mathrm{style}}$" + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 344, + 243 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3b8f69e8e96565e700c30b31ac3ecd4bf4d6cb3a8b7046bf15400ea887a328fe.jpg", + "image_caption": [ + "(b) $\\mathcal{L}_{\\mathrm{content}}$" + ], + "image_footnote": [], + "bbox": [ + 354, + 90, + 614, + 243 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2c93bea5367111625aaeed349e2d76c1493c0b115cafea51078dc4fbc646b969.jpg", + "image_caption": [ + "(c) $\\mathcal{L}_{\\mathrm{style}} + \\mathcal{L}_{\\mathrm{content}}$" + ], + "image_footnote": [], + "bbox": [ + 625, + 90, + 885, + 243 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c920cb1d330be0ab0fa477e01aa864512539d7b86c65db640188f6160a0ea738.jpg", + "image_caption": [ + "Figure 4: t-SNE [58] visualization results for the target task VLCS [15] (5 classes) using synthesized style-content features. We visualize such features obtained from the learned 80 style word vectors $\\{\\mathbf{s}_i\\}_{i=1}^{80}$ and all the 5 classes (bird, car, chair, dog, person). Different colors denote features obtained from different style word vectors, and different shapes indicate features obtained from different class names. We only colorize features from the first 10 styles $\\{\\mathbf{s}_i\\}_{i=1}^{10}$ . Combining the style diversity loss $\\mathcal{L}_{\\text{style}}$ and content consistency loss $\\mathcal{L}_{\\text{content}}$ leads to diverse styles while preserving content information." + ], + "image_footnote": [], + "bbox": [ + 81, + 359, + 209, + 460 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3dd295e1b3285874ae513653efe4afb79f9a382c8e6a17421d7008fa4866e193.jpg", + "image_caption": [ + "Figure 5: Text-to-Image synthesis results using style-content features (from \"a $S_{*}$ style of a cat\") with 6 different style word vectors. By leveraging the proposed method, we could learn a variety of styles while not distorting content information." + ], + "image_footnote": [], + "bbox": [ + 215, + 359, + 346, + 460 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f9e2d8a34fd548d59d5bc703ac5c955c554a1fcfdbb9899ab211cd70b2878d2b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 352, + 359, + 480, + 460 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5afdd5c9b4392033a4d1c1dd2f0ff0a0a6410d9c61b11952e21adf67c440b28a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 359, + 617, + 460 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5d6621cebc43e3eb2fd68b9e36560adcb3f998c0cc7d549ab3ebd6d64c99741c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 624, + 359, + 753, + 460 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/03d646dc348b3f09db2cbee8318ea39e1523286f01c3e656a2d98001b87ce12f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 359, + 888, + 460 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5853a604474f07f38cb505111fc44079db7f607d2cc161e22accd12e10c822db.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
\\( {\\mathcal{L}}_{\\text{style }} \\)\\( {\\mathcal{L}}_{\\text{content }} \\)Accuracy (%)
PACSVLCSOfficeHomeDomainNetAvg.
--92.678.372.248.072.8
✓-92.380.971.548.273.2
-✓92.880.572.448.673.6
✓✓93.282.373.649.574.7
", + "bbox": [ + 81, + 507, + 468, + 599 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "t-SNE visualization results. In Figure 4, we qualitatively evaluate style-content features synthesized for the target task VLCS [15] (5 classes) using t-SNE [58] visualization. As shown in Figure 4(c), PromptStyler generates a variety of styles while not distorting content information; style-content features obtained from the same class name share similar semantics with diverse variations. This result confirms that we could effectively simulate various distribution shifts in the latent space of a large-scale vision-language model by synthesizing diverse styles via learnable style word vectors. Text-to-Image synthesis results. In Figure 5, we visualize style-content features (from \"a $S_*$ style of a cat\") via diffusers library. These results are obtained with 6 different style word vectors, where the word vectors are learned for the target task DomainNet [48] using ViT-L/14 [11] model.", + "bbox": [ + 75, + 651, + 470, + 878 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0bd2988e085fbe37b8ec7eecf6f1aeb1e571e6ef3745e9b7760bfcf164fb414d.jpg", + "table_caption": [ + "Table 4: Ablation study on the style diversity loss $\\mathcal{L}_{\\mathrm{style}}$ and content consistency loss $\\mathcal{L}_{\\mathrm{content}}$ used in the prompt loss." + ], + "table_footnote": [], + "table_body": "
LclassAccuracy (%)
PACSVLCSOfficeHomeDomainNetAvg.
Softmax92.581.272.348.673.7
ArcFace93.282.373.649.574.7
", + "bbox": [ + 504, + 507, + 890, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5: Ablation study on the classification loss $\\mathcal{L}_{\\mathrm{class}}$ used for training a linear classifier in the proposed framework.", + "bbox": [ + 498, + 583, + 890, + 614 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. More analyses", + "text_level": 1, + "bbox": [ + 500, + 635, + 648, + 651 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation study on the prompt loss. In Table 4, we evaluate the effects of $\\mathcal{L}_{\\mathrm{style}}$ and $\\mathcal{L}_{\\mathrm{content}}$ in $\\mathcal{L}_{\\mathrm{prompt}}$ used for learning style words. Interestingly, our method also achieves state-of-the-art results even without using these losses, i.e., the proposed framework (Fig. 3) is substantially effective by itself. Note that randomly initialized style word vectors are already diverse, and CLIP [50] is already good at extracting correct content information from a style-content prompt even without training the word vectors using $\\mathcal{L}_{\\mathrm{content}}$ . When we learn style word vectors using $\\mathcal{L}_{\\mathrm{style}}$ without $\\mathcal{L}_{\\mathrm{content}}$ , style-content features obtained from different class names share more similar features than those from the same class name (Fig. 4(a)). On the other hand, using $\\mathcal{L}_{\\mathrm{content}}$ without $\\mathcal{L}_{\\mathrm{style}}$ leads to less diverse style-content features (Fig. 4(b)). When incorporating both losses, we could generate diverse styles while not distorting content information (Fig. 4(c)).", + "bbox": [ + 496, + 657, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "2https://github.com/huggingface/diffusers", + "bbox": [ + 93, + 886, + 418, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15708", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/db544386c17bca8b0c1ccdd2665feb95f68b96bd9bac8245cb0c03ebebb849dc.jpg", + "image_caption": [ + "Figure 6: Top-1 classification accuracy on the PACS [34], VLCS [15], OfficeHome [60] and DomainNet [48] datasets with regard to the number of learnable style word vectors $K$ ." + ], + "image_footnote": [], + "bbox": [ + 76, + 89, + 281, + 229 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/16aca7536738cc5ffba8c6507e7616ec90bb752a002cdc62b703a173dc6e1cf9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 90, + 483, + 229 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/50868d20456b01dccfa0567fe62d558978604e3b25ceed72bde224e0eca921e4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 90, + 687, + 229 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ca69433126e7948dc9ebab49f11d0ce8306a3ba179aa71666546c07acba1a4f7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 90, + 890, + 229 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6962712cf551db230d27623eff7a7ccc656d107a2456e831722b08c1784741e2.jpg", + "image_caption": [ + "Figure 7: Top-1 classification accuracy on the PACS [34], VLCS [15], OfficeHome [60] and DomainNet [48] datasets with regard to the number of training iterations $L$ for learning each style word vector $\\mathbf{s}_i$ ." + ], + "image_footnote": [], + "bbox": [ + 76, + 267, + 281, + 406 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e49291f220df53107d03e45791827d1eecf1563546c583ffffcf017f10493e31.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 267, + 483, + 407 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0a3903bd3fc277cf36c81c6a6aa6c94859cadbef26bdd1da94f6f5ac4fbf13f4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 267, + 687, + 407 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/27a886adfd7f6849890bc14be963cbb0e298c7b84b9c4ebd17b60a24d92a3095.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 267, + 890, + 407 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8d1541d96a046f23a0b73ecb9c8f3899755efb61f2faf9fa7fe11587e8ddcf87.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodConfigurationAccuracy (%)
Source DomainDomain DescriptionTerra Incognito
ResNet-50 [22] with pre-trained weights on ImageNet [6]
SelfReg [28]✓-47.0±0.3
GVRT [44]✓-48.0±0.2
ResNet-50 [22] with pre-trained weights from CLIP [50]
ZS-CLIP (C) [50]--19.5±0.0
ZS-CLIP (PC) [50]-✓23.8±0.0
PromptStyler--30.5±0.8
", + "bbox": [ + 81, + 450, + 470, + 599 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6: Unsatisfactory results obtained from CLIP [50] without using source domain data from Terra Incognita [1].", + "bbox": [ + 75, + 601, + 468, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation study on the classification loss. In Table 5, we evaluate the effects of the original Softmax loss and the angular Softmax loss (i.e., ArcFace [8]). PromptStyler also achieves the state of the art using the original one, which validates that the performance improvement of our method mainly comes from the proposed framework (Fig. 3). Note that the angular Softmax loss further improves its accuracy by leveraging the hyperspherical joint vision-language space. Effect of the number of styles. We evaluate our method with regard to the number of style word vectors $K$ as shown in Figure 6. Interestingly, our PromptStyler outperforms CLIP [50] using just 5 styles. This evaluation shows that 20 style word vectors are enough to achieve decent results.", + "bbox": [ + 75, + 643, + 468, + 839 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of the number of iterations. We evaluate our method with regard to the number of training iterations $L$ for learning each style word vector as shown in Figure 7. This evaluation shows that 20 iterations are enough to achieve decent results.", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitation", + "text_level": 1, + "bbox": [ + 500, + 452, + 612, + 468 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The performance of our method depends on the quality of the joint vision-language space constructed by the chosen vision-language model. For example, although PromptStyler largely outperforms its base model (i.e., CLIP [50]) in all evaluations, our method shows lower accuracy on the Terra Incognita dataset [1] compared with other methods which utilize several images from the dataset as shown in Table 6. The main reason for this might be due to the low accuracy of CLIP on the dataset. Nevertheless, given that our method consistently outperforms its base model in every evaluation, this limitation could be alleviated with the development of large-scale vision-language models.", + "bbox": [ + 496, + 477, + 893, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 674, + 617, + 689 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have presented a novel method that synthesizes a variety of styles in a joint vision-language space via learnable style words without exploiting any images to deal with source-free domain generalization. PromptStyler simulates various distribution shifts in the latent space of a large-scale pre-trained model, which could effectively improve its generalization capability. The proposed method achieves state-of-the-art results without using any source domain data on multiple domain generalization benchmarks. We hope that future work could apply our method to other tasks using different large-scale vision-language models.", + "bbox": [ + 496, + 698, + 893, + 864 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment. This work was supported by the Agency for Defense Development grant funded by the Korean government.", + "bbox": [ + 500, + 871, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15709", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sara Beery, Grant van Horn, and Pietro Perona. Recognition in Terra Incognita. In Proceedings of the European Conference on Computer Vision (ECCV), 2018.", + "[2] Shai Ben-David, John Blitzer, Koby Crammer, and Fernando Pereira. Analysis of Representations for Domain Adaptation. In Advances in Neural Information Processing Systems (NIPS), 2006.", + "[3] Fabio Maria Carlucci, Antonio D'Innocente, Silvia Bucci, Barbara Caputo, and Tatiana Tommasi. Domain Generalization by Solving Jigsaw Puzzles. 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In International Conference on Learning Representations (ICLR), 2021." + ], + "bbox": [ + 501, + 92, + 893, + 402 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "15712", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/PromptStyler_ Prompt-driven Style Generation for Source-free Domain Generalization/f8d2a45d-4c84-4d88-913c-50e0d9fbe4a8_model.json b/2023/PromptStyler_ Prompt-driven Style Generation for Source-free Domain Generalization/f8d2a45d-4c84-4d88-913c-50e0d9fbe4a8_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b985360d0d88572f56001122cb4bc00137a64924 --- /dev/null +++ b/2023/PromptStyler_ Prompt-driven Style Generation for Source-free Domain Generalization/f8d2a45d-4c84-4d88-913c-50e0d9fbe4a8_model.json @@ -0,0 +1,2477 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.246, + 0.131, + 0.726, + 0.175 + ], + "angle": 0, + "content": "PromptStyler: Prompt-driven Style Generation for Source-free Domain Generalization" + }, + { + "type": "text", + "bbox": [ + 0.135, + 0.203, + 0.836, + 0.258 + ], + "angle": 0, + "content": "Junhyeong Cho\\(^{1}\\) Gilhyun Nam\\(^{1}\\) Sungyeon Kim\\(^{2}\\) Hunmin Yang\\(^{1,3}\\) Suha Kwak\\(^{2}\\) \n\\(^{1}\\)ADD \\(^{2}\\)POSTECH \\(^{3}\\)KAIST \nhttps://PromptStyler.github.io" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.074, + 0.313, + 0.474, + 0.601 + ], + "angle": 0, + "content": "In a joint vision-language space, a text feature (e.g., from \"a photo of a dog\") could effectively represent its relevant image features (e.g., from dog photos). Also, a recent study has demonstrated the cross-modal transferability phenomenon of this joint space. From these observations, we propose PromptStyler which simulates various distribution shifts in the joint space by synthesizing diverse styles via prompts without using any images to deal with source-free domain generalization. The proposed method learns to generate a variety of style features (from \"a \\(S_*\\) style of a\") via learnable style word vectors for pseudo-words \\(S_*\\). To ensure that learned styles do not distort content information, we force style-content features (from \"a \\(S_*\\) style of a [class]\") to be located nearby their corresponding content features (from \"[class]\") in the joint vision-language space. After learning style word vectors, we train a linear classifier using synthesized style-content features. PromptStyler achieves the state of the art on PACS, VLCS, OfficeHome and DomainNet, even though it does not require any images for training." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.621, + 0.21, + 0.637 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Deep neural networks are usually trained with the assumption that training and test data are independent and identically distributed, which makes them vulnerable to substantial distribution shifts between training and test data [23, 52]. This susceptibility is considered as one of the major obstacles to their deployment in real-world applications. To enhance their robustness to such distribution shifts, Domain Adaptation (DA) [2, 24, 32, 33, 54, 56, 57, 68] has been studied; it aims at adapting neural networks to a target domain using target domain data available in training. However, such a target domain is often latent in common training scenarios, which considerably limits the application of DA. Recently, a body of research has addressed this limitation by Domain Generalization (DG) [3, 5, 21, 29, 35, 37, 74] that aims to improve model's generalization capability to any unseen domains. It has been a common practice in DG to utilize multiple source domains for learning domain-invariant features [61, 69], but" + }, + { + "type": "image_caption", + "bbox": [ + 0.503, + 0.368, + 0.529, + 0.385 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.537, + 0.291, + 0.891, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.503, + 0.539, + 0.529, + 0.557 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.539, + 0.463, + 0.891, + 0.629 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.634, + 0.895, + 0.711 + ], + "angle": 0, + "content": "Figure 1: Motivation of our method. (a) Text features could effectively represent various image styles in a joint vision-language space. (b) PromptStyler synthesizes diverse styles in a joint vision-language space via learnable style word vectors for pseudo-words \\( S_{*} \\) without using any images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.895, + 0.795 + ], + "angle": 0, + "content": "it is unclear which source domains are ideal for DG, since arbitrary unseen domains should be addressed. Furthermore, it is costly and sometimes even infeasible to collect and annotate large-scale multi-source domain data for training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.897, + 0.902 + ], + "angle": 0, + "content": "We notice that a large-scale pre-trained model might have already observed a great variety of domains and thus can be used as an efficient proxy of actual multiple source domains. From this perspective, we raised a question \"Could we further improve model's generalization capability by simulating various distribution shifts in the latent space of such a large-scale model without using any source domain data?\" If this" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15702" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.487, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.494, + 0.089, + 0.891, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.308, + 0.894, + 0.37 + ], + "angle": 0, + "content": "Figure 2: Important factors in the proposed method. PromptStyler learns style word vectors for pseudo-words \\( S_{*} \\) which lead to diverse style features (from \"a \\( S_{*} \\) style of a\") while preserving content information encoded in style-content features (from \"a \\( S_{*} \\) style of a [class])\". \\( \\mathcal{L}_{\\mathrm{style}} \\) and \\( \\mathcal{L}_{\\mathrm{content}} \\) are the loss functions used for maximizing style diversity and content consistency in a hyperspherical joint vision-language space (e.g., CLIP [50] latent space)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.387, + 0.471, + 0.463 + ], + "angle": 0, + "content": "is possible, DG will become immensely practical by effectively and efficiently exploiting such a large-scale model. However, this approach is much more challenging since any actual data of source and target domains are not accessible but only the target task definition (e.g., class names) is given." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.464, + 0.47, + 0.675 + ], + "angle": 0, + "content": "In this paper, we argue that large-scale vision-language models [26, 50, 64] could shed light on this challenging source-free domain generalization. As conceptually illustrated in Figure 1(a), text features could effectively represent their relevant image features in a joint vision-language space. Despite the modality gap between two modalities in the joint space [39], a recent study has demonstrated the cross-modal transferability phenomenon [67]; we could train a classifier using text features while running an inference with the classifier using image features. This training procedure meets the necessary condition for the source-free domain generalization, i.e., source domain images are not required. Using such a joint vision-language space, we could simulate various distribution shifts via prompts without any images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.47, + 0.825 + ], + "angle": 0, + "content": "We propose a prompt-driven style generation method, dubbed PromptStyler, which synthesizes diverse styles via learnable word vectors to simulate distribution shifts in a hyperspherical joint vision-language space. PromptStyler is motivated by the observation that a shared style of images could characterize a domain [27, 74] and such a shared style could be captured by a learnable word vector for a pseudoword \\( S_{*} \\) using CLIP [50] with a prompt (\"a painting in the style of \\( S_{*} \\)) [17]. As shown in Figure 1(b), our method learns a style word vector for \\( S_{*} \\) to represent each style." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.902 + ], + "angle": 0, + "content": "To effectively simulate various distribution shifts, we try to maximize style diversity as illustrated in Figure 2. Specifically, our method encourages learnable style word vectors to result in orthogonal style features in the hyperspherical space, where each style feature is obtained from a style prompt" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.893, + 0.493 + ], + "angle": 0, + "content": "(\"a \\( S_* \\) style of a\") via a pre-trained text encoder. To prevent learned styles from distorting content information, we also consider content consistency as illustrated in Figure 2. Each style-content feature obtained from a style-content prompt (\"a \\( S_* \\) style of a [class]) is forced to be located closer to its corresponding content feature obtained from a content prompt (\"[class]\") than the other content features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.893, + 0.674 + ], + "angle": 0, + "content": "Learned style word vectors are used to synthesize style-content features for training a classifier; these synthesized features could simulate images of known contents with diverse unknown styles in the joint space. These style-content features are fed as input to a linear classifier which is trained by a classification loss using contents (\"[class]\") as their class labels. At inference time, an image encoder extracts image features from input images, which are fed as input to the trained classifier. Note that the text and image encoders are derived from the same pre-trained vision-language model (e.g., CLIP [50]); the text encoder is only involved in training and the image encoder is only involved at inference time." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.894, + 0.765 + ], + "angle": 0, + "content": "The proposed method achieves state-of-the-art results on PACS [34], VLCS [15], OfficeHome [60] and DomainNet [48] without using any actual data of source and target domains. It takes just \\(\\sim 30\\) minutes for the entire training using a single RTX 3090 GPU, and our model is \\(\\sim 2.6\\times\\) smaller and \\(\\sim 243\\times\\) faster at inference compared with CLIP [50]." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.765, + 0.822, + 0.779 + ], + "angle": 0, + "content": "Our contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.78, + 0.892, + 0.825 + ], + "angle": 0, + "content": "- This work is the first attempt to synthesize a variety of styles in a joint vision-language space via prompts to effectively tackle source-free domain generalization." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.826, + 0.894, + 0.87 + ], + "angle": 0, + "content": "- This paper proposes a novel method that effectively simulates images of known contents with diverse unknown styles in a joint vision-language space." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "- PromptStyler achieves the state of the art on domain generalization benchmarks without using any images." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.78, + 0.894, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15703" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.47, + 0.171 + ], + "angle": 0, + "content": "
SetupSourceTargetTask Definition
DA✓✓✓
DG✓-✓
Source-free DA-✓✓
Source-free DG--✓
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.176, + 0.47, + 0.222 + ], + "angle": 0, + "content": "Table 1: Different requirements in each setup. Source-free DG only assumes the task definition (i.e., what should be predicted) without requiring source and target domain data." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.239, + 0.22, + 0.256 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.265, + 0.473, + 0.506 + ], + "angle": 0, + "content": "Domain Generalization. Model's generalization capability to arbitrary unseen domains is the key factor to successful deployment of neural networks in real-world applications, since substantial distribution shifts between source and target domains could significantly degrade their performance [23, 52]. To this end, Domain Generalization (DG) [4, 5, 10, 16, 21, 29, 35, 37, 44, 45, 61, 69] has been studied. It assumes target domain data are not accessible while using data from source domains. Generally speaking, existing DG methods could be divided into two categories: multi-source DG [3, 12, 36, 42, 43, 51, 55, 63, 73, 74] and single-source DG [14, 38, 49, 62]. Mostly, multi-source DG methods aim to learn domain-invariant features by exploiting available multiple source domains, and single-source DG methods also aim to learn such features by generating diverse domains based on a single domain and then exploiting the synthesized domains." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.508, + 0.473, + 0.78 + ], + "angle": 0, + "content": "Source-free Domain Generalization. In this setup, we are not able to access any source and target domains as summarized in Table 1. Thus, source-free DG is much more challenging than multi-source and single-source DG. From the observation that synthesizing new domains from the given source domain could effectively improve model's generalization capability [27,38,62,72,73], we also try to generate diverse domains but without using any source domains to deal with source-free DG. By leveraging a large-scale pre-trained model which has already seen a great variety of domains, our method could simulate various distribution shifts in the latent space of the large-scale model. This approach has several advantages compared with existing DG methods; source domain images are not required and there is no concern for catastrophic forgetting which might impede model's generalization capability. Also, it would be immensely practical to exploit such a large-scale model for downstream visual recognition tasks, since we only need the task definition." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Large-scale model in Domain Generalization. Recently, several DG methods [5, 53] exploit a large-scale pre-trained model (e.g., CLIP [50]) to leverage its great generalization capability. While training neural networks on available data, CAD [53] and MIRO [5] try to learn robust features using such a large-scale model. Compared with them, the proposed method could learn domain-invariant features using a large-scale pre-trained model without requiring any actual data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.289 + ], + "angle": 0, + "content": "Joint vision-language space. Large-scale vision-language models [26, 50, 64] are trained with a great amount of image-text pairs, and achieve state-of-the-art results on downstream visual recognition tasks [20, 41, 66, 70, 71]. By leveraging their joint vision-language spaces, we could also effectively manipulate visual features via prompts [13, 18, 31, 47]. Interestingly, Textual Inversion [17] shows that a learnable style word vector for a pseudo-word \\( S_{*} \\) could capture a shared style of images using CLIP [50] with a prompt (\"a painting in the style of \\( S_{*} \\)\"). From this observation, we argue that learnable style word vectors would be able to seek a variety of styles for simulating various distribution shifts in a joint vision-language space without using any images." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.299, + 0.593, + 0.315 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.325, + 0.895, + 0.552 + ], + "angle": 0, + "content": "The overall framework of the proposed method is shown in Figure 3, and pseudo-code of PromptStyler is described in Algorithm 1. Our method learns style word vectors to represent a variety of styles in a hyperspherical joint vision-language space (e.g., CLIP [50] latent space). After learning those style word vectors, we train a linear classifier using synthesized style-content features produced by a pre-trained text encoder \\( T(\\cdot) \\). At inference time, a pre-trained image encoder \\( I(\\cdot) \\) extracts image features from input images, which are fed as input to the trained linear classifier. Thanks to the cross-modal transferability phenomenon of the joint vision-language space [67], this classifier could produce class scores using the image features. Note that we exploit CLIP as our large-scale vision-language model; its image encoder and text encoder are frozen in our entire framework." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.559, + 0.776, + 0.575 + ], + "angle": 0, + "content": "3.1. Prompt-driven style generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.894, + 0.75 + ], + "angle": 0, + "content": "An input text prompt is converted to several tokens via a tokenization process, and then such tokens are replaced by their corresponding word vectors via a word lookup process. In PromptStyler, a pseudo-word \\( S_{i} \\) in a prompt is a placeholder which is replaced by a style word vector \\( \\mathbf{s}_i \\in \\mathbb{R}^D \\) during the word lookup process. Note that three kinds of prompts are used in the proposed method: a style prompt \\( \\mathcal{P}_i^{\\mathrm{style}} \\) (\"a \\( S_{i} \\) style of a\"), a content prompt \\( \\mathcal{P}_m^{\\mathrm{content}} \\) (\"[class] \\( m \\)\"), and a style-content prompt \\( \\mathcal{P}_i^{\\mathrm{style}} \\circ \\mathcal{P}_m^{\\mathrm{content}} \\) (\"a \\( S_{i} \\) style of a [class] \\( m \\)\"). \\( S_{i} \\) indicates the placeholder for \\( i \\)-th style word vector and [class] \\( m \\) denotes \\( m \\)-th class name." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Suppose we want to generate \\(K\\) different styles in a joint vision-language space. In this case, the proposed method needs to learn \\(K\\) style word vectors \\(\\{\\mathbf{s}_i\\}_{i=1}^K\\), where each \\(\\mathbf{s}_i\\) is randomly initialized at the beginning. To effectively simulate various distribution shifts in the joint vision-language space, those style word vectors need to be diverse while not distorting content information when they are exploited in style-content prompts. There are two possible design choices for learning such word vectors: (1) learning each style word vector \\(\\mathbf{s}_i\\) in a sequential manner, or (2) learning all style" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15704" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.182, + 0.095, + 0.422, + 0.111 + ], + "angle": 0, + "content": "(i) Prompt-driven style generation" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.116, + 0.526, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.095, + 0.888, + 0.111 + ], + "angle": 0, + "content": "(ii) Training a linear classifier using diverse styles" + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.125, + 0.887, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.693, + 0.201, + 0.884, + 0.214 + ], + "angle": 0, + "content": "Frozen weights \\(\\ell_2\\) normalization layer" + }, + { + "type": "image_caption", + "bbox": [ + 0.573, + 0.219, + 0.856, + 0.234 + ], + "angle": 0, + "content": "(iii) Inference using the trained classifier" + }, + { + "type": "image", + "bbox": [ + 0.563, + 0.248, + 0.885, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.693, + 0.324, + 0.884, + 0.337 + ], + "angle": 0, + "content": "Frozen weights \\(\\ell_2\\) normalization layer" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.345, + 0.894, + 0.422 + ], + "angle": 0, + "content": "Figure 3: PromptStyler learns diverse style word vectors which do not distort content information of style-content prompts. After learning style word vectors, we synthesize style-content features (e.g., from \"a \\(S_{1}\\) style of a dog\") via a pre-trained text encoder for training a linear classifier. The classifier is trained by a classification loss using those synthesized features and their corresponding class labels (e.g., \"dog\"). At inference time, a pre-trained image encoder extracts image features, which are fed as input to the trained classifier. Note that the encoders are derived from the same vision-language model (e.g., CLIP [50])." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.441, + 0.47, + 0.501 + ], + "angle": 0, + "content": "word vectors \\(\\{\\mathbf{s}_i\\}_{i=1}^K\\) in a parallel manner. We choose the former, since it takes much less memory during training. Please refer to the supplementary material (Section A.2) for the empirical justification of our design choice." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.471, + 0.629 + ], + "angle": 0, + "content": "Style diversity loss. To maximize the diversity of \\( K \\) styles in a hyperspherical joint vision-language space, we sequentially learn style word vectors \\( \\{\\mathbf{s}_i\\}_{i=1}^K \\) in such a way that \\( i \\)-th style feature \\( T(\\mathcal{P}_i^{\\mathrm{style}}) \\in \\mathbb{R}^C \\) produced by \\( i \\)-th style word vector \\( \\mathbf{s}_i \\) is orthogonal to \\( \\{T(\\mathcal{P}_j^{\\mathrm{style}})\\}_{j=1}^{i-1} \\) produced by previously learned style word vectors \\( \\{\\mathbf{s}_j\\}_{j=1}^{i-1} \\). Regarding this, the style diversity loss \\( \\mathcal{L}_{\\mathrm{style}} \\) for learning \\( i \\)-th style word vector \\( \\mathbf{s}_i \\) is computed by" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.638, + 0.47, + 0.681 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s t y l e}} = \\frac {1}{i - 1} \\sum_ {j = 1} ^ {i - 1} \\left| \\frac {T \\left(\\mathcal {P} _ {i} ^ {\\text {s t y l e}}\\right)}{\\| T \\left(\\mathcal {P} _ {i} ^ {\\text {s t y l e}}\\right) \\| _ {2}} \\cdot \\frac {T \\left(\\mathcal {P} _ {j} ^ {\\text {s t y l e}}\\right)}{\\| T \\left(\\mathcal {P} _ {j} ^ {\\text {s t y l e}}\\right) \\| _ {2}} \\right|. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.764 + ], + "angle": 0, + "content": "This style loss \\(\\mathcal{L}_{\\mathrm{style}}\\) aims to minimize the absolute value of the cosine similarity between \\(i\\)-th style features and each of the existing style features. When the value of this loss becomes zero, it satisfies the orthogonality between \\(i\\)-th style feature and all the existing style features." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.765, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Content consistency loss. Learning the style word vectors \\(\\{\\mathbf{s}_i\\}_{i = 1}^K\\) only using the style diversity loss sometimes leads to undesirable outcome, since a learned style \\(\\mathbf{s}_i\\) could substantially distort content information when used to generate a style-content feature \\(T(\\mathcal{P}_i^{\\mathrm{style}}\\circ \\mathcal{P}_m^{\\mathrm{content}})\\in \\mathbb{R}^C\\). To alleviate this problem, we encourage the content information in the style-content feature to be consistent with its corresponding content feature \\(T(\\mathcal{P}_m^{\\mathrm{content}})\\in \\mathbb{R}^C\\) while learning each \\(i\\)-th style word vector \\(\\mathbf{s}_i\\). Specifically, each style-content" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.441, + 0.895, + 0.533 + ], + "angle": 0, + "content": "feature synthesized via \\(i\\)-th style word vector \\(\\mathbf{s}_i\\) should have the highest cosine similarity score with its corresponding content feature. For \\(i\\)-th style word vector \\(\\mathbf{s}_i\\), a cosine similarity score \\(z_{imn}\\) between a style-content feature with \\(m\\)-th class name and a content feature with \\(n\\)-th class name is computed by" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.538, + 0.892, + 0.577 + ], + "angle": 0, + "content": "\\[\nz _ {i m n} = \\frac {T \\left(\\mathcal {P} _ {i} ^ {\\text {s t y l e}} \\circ \\mathcal {P} _ {m} ^ {\\text {c o n t e n t}}\\right)}{\\| T \\left(\\mathcal {P} _ {i} ^ {\\text {s t y l e}} \\circ \\mathcal {P} _ {m} ^ {\\text {c o n t e n t}}\\right) \\| _ {2}} \\cdot \\frac {T \\left(\\mathcal {P} _ {n} ^ {\\text {c o n t e n t}}\\right)}{\\| T \\left(\\mathcal {P} _ {n} ^ {\\text {c o n t e n t}}\\right) \\| _ {2}}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.626 + ], + "angle": 0, + "content": "Using cosine similarity scores between style-content features and content features, the content consistency loss \\(\\mathcal{L}_{\\mathrm{content}}\\) for learning \\(i\\)-th style word vector \\(\\mathbf{s}_i\\) is computed by" + }, + { + "type": "equation", + "bbox": [ + 0.535, + 0.631, + 0.892, + 0.672 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c o n t e n t}} = - \\frac {1}{N} \\sum_ {m = 1} ^ {N} \\log \\left(\\frac {\\exp \\left(z _ {i m m}\\right)}{\\sum_ {n = 1} ^ {N} \\exp \\left(z _ {i m n}\\right)}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.676, + 0.892, + 0.766 + ], + "angle": 0, + "content": "where \\(N\\) denotes the number of classes pre-defined in the target task. This content loss \\(\\mathcal{L}_{\\mathrm{content}}\\) is a contrastive loss which encourages each style-content feature to be located closer to its corresponding content feature so that it forces each \\(i\\)-th style word vector \\(\\mathbf{s}_i\\) to preserve content information when used to synthesize style-content features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.767, + 0.894, + 0.844 + ], + "angle": 0, + "content": "Total prompt loss. PromptStyler learns \\(K\\) style word vectors \\(\\{\\mathbf{s}_i\\}_{i=1}^K\\) in a sequential manner, where each \\(i\\)-th style word vector \\(\\mathbf{s}_i\\) is learned using both \\(\\mathcal{L}_{\\mathrm{style}}\\) (Eq.(1)) and \\(\\mathcal{L}_{\\mathrm{content}}\\) (Eq.(3)). In the proposed method, the total loss \\(\\mathcal{L}_{\\mathrm{prompt}}\\) for learning \\(i\\)-th style word vector is computed by" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.849, + 0.892, + 0.866 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p r o m p t}} = \\mathcal {L} _ {\\text {s t y l e}} + \\mathcal {L} _ {\\text {c o n t e n t}}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Using this prompt loss \\(\\mathcal{L}_{\\mathrm{prompt}}\\), we train \\(i\\)-th style word vector \\(\\mathbf{s}_i\\) for \\(L\\) training iterations." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15705" + } + ], + [ + { + "type": "algorithm", + "bbox": [ + 0.078, + 0.09, + 0.473, + 0.434 + ], + "angle": 0, + "content": "Algorithm 1 PromptStyler \nRequirement: pre-trained text encoder \\(T(\\cdot)\\), pre-defined \\(N\\) class names in the target task \nInput: number of style word vectors \\(K\\), number of training iterations \\(L\\) \nOutput: \\(KN\\) style-content features \n # randomly initialize style word vectors \n1: \\(\\{\\mathbf{s}_i\\}_{i=1}^K \\leftarrow\\) random_init(\\(\\{\\mathbf{s}_i\\}_{i=1}^K\\)) \n # sequentially learn \\(K\\) style word vectors \n2: for \\(i = 1, 2, \\ldots, K\\) do \n # \\(L\\) training iterations for learning each word vector \n3: for iteration \\(= 1, 2, \\ldots, L\\) do \n # compute \\(\\mathcal{L}_{\\text{style}}\\) using \\(T(\\cdot)\\) and word vectors \n4: \\(\\mathcal{L}_{\\text{style}} \\leftarrow\\) style_diversity_loss(\\(\\mathbf{s}_i\\), \\(\\{\\mathbf{s}_j\\}_{j=1}^{i-1}\\)) \n # compute \\(\\mathcal{L}_{\\text{content}}\\) using \\(T(\\cdot)\\) and a word vector \n5: \\(\\mathcal{L}_{\\text{content}} \\leftarrow\\) content_consistency_loss(\\(\\mathbf{s}_i\\)) \n6: \\(\\mathcal{L}_{\\text{prompt}} \\leftarrow \\mathcal{L}_{\\text{style}} + \\mathcal{L}_{\\text{content}}\\) \n7: Update \\(\\mathbf{s}_i\\) using \\(\\mathcal{L}_{\\text{prompt}}\\) by gradient descent \n8: end for \n9: end for \n10: Synthesize \\(KN\\) style-content features using the learned \\(K\\) style word vectors and \\(N\\) class names via \\(T(\\cdot)\\)" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.462, + 0.465, + 0.478 + ], + "angle": 0, + "content": "3.2. Training a linear classifier using diverse styles" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.485, + 0.474, + 0.744 + ], + "angle": 0, + "content": "After learning \\(K\\) style word vectors \\(\\{\\mathbf{s}_i\\}_{i = 1}^K\\), we generate \\(KN\\) style-content features for training a linear classifier. To be specific, we synthesize those features using the learned \\(K\\) styles and pre-defined \\(N\\) classes via the text encoder \\(T(\\cdot)\\). The linear classifier is trained by a classification loss using \\(\\ell_2\\)-normalized style-content features and their class labels; each class label is the class name used to generate each style-content feature. To effectively leverage the hyperspherical joint vision-language space, we adopt ArcFace [8] loss as our classification loss \\(\\mathcal{L}_{\\mathrm{class}}\\). Note that ArcFace loss is an angular Softmax loss which computes the cosine similarities between classifier input features and classifier weights with an additive angular margin penalty between classes. This angular margin penalty allows for more discriminative predictions by pushing features from different classes further apart. Thanks to the property, this angular Softmax loss has been widely used in visual recognition tasks [7,9,30,40,65]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.756, + 0.394, + 0.772 + ], + "angle": 0, + "content": "3.3. Inference using the trained classifier" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.903 + ], + "angle": 0, + "content": "The trained classifier is used with a pre-trained image encoder \\( I(\\cdot) \\) at inference time. Given an input image \\( \\mathbf{x} \\), the image encoder extracts its image feature \\( I(\\mathbf{x}) \\in \\mathbb{R}^{C} \\), which is mapped to the hyperspherical joint vision-language space by \\( \\ell_{2} \\) normalization. Then, the trained classifier produces class scores using the \\( \\ell_{2} \\)-normalized image feature. Note that the text encoder \\( T(\\cdot) \\) is not used at inference time, while the image encoder \\( I(\\cdot) \\) is only exploited at inference time." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.634, + 0.108 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.116, + 0.892, + 0.147 + ], + "angle": 0, + "content": "For more comprehensive understanding, please refer to the supplementary material (Section B and D)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.156, + 0.688, + 0.171 + ], + "angle": 0, + "content": "4.1. Evaluation datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.18, + 0.895, + 0.347 + ], + "angle": 0, + "content": "The proposed method does not require any actual data for training. To analyze its generalization capability, four domain generalization benchmarks are used for evaluation: PACS [34] (4 domains and 7 classes), VLCS [15] (4 domains and 5 classes), OfficeHome [60] (4 domains and 65 classes) and DomainNet [48] (6 domains and 345 classes). On these benchmarks, we repeat each experiment three times using different random seeds and report average top-1 classification accuracies with standard errors. Unlike the leave-one-domain-out cross-validation evaluation protocol [21], we do not exploit any source domain data for training." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.356, + 0.715, + 0.372 + ], + "angle": 0, + "content": "4.2. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.379, + 0.892, + 0.424 + ], + "angle": 0, + "content": "PromptStyler is implemented and trained with the same configuration regardless of the evaluation datasets. Training takes about 30 minutes using a single RTX 3090 GPU." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.425, + 0.895, + 0.606 + ], + "angle": 0, + "content": "Architecture. We choose CLIP [50] as our large-scale pretrained vision-language model, and use the publicly available pre-trained model.\\(^{1}\\) The text encoder \\( T(\\cdot) \\) used in training is Transformer [59] and the image encoder \\( I(\\cdot) \\) used at inference is ResNet-50 [22] as default setting in experiments; our method is also implemented with ViT-B/16 [11] or ViT-L/14 [11] for further evaluations as shown in Table 2. Note that text and image encoders are derived from the same CLIP model and frozen in the entire pipeline. The dimension of each text feature or image feature is \\( C = 1024 \\) when our method is implemented with ResNet-50, while \\( C = 512 \\) in the case of ViT-B/16 and \\( C = 768 \\) in the case of ViT-L/14." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.607, + 0.894, + 0.788 + ], + "angle": 0, + "content": "Learning style word vectors. We follow prompt learning methods [70, 71] when learning the word vectors. Using a zero-mean Gaussian distribution with 0.02 standard deviation, we randomly initialize \\( K \\) style word vectors \\( \\{\\mathbf{s}_i\\}_{i=1}^K \\), where \\( K = 80 \\). The dimension of each style word vector is \\( D = 512 \\) when the proposed method is implemented with ResNet-50 [22] or ViT-B/16 [11], while \\( D = 768 \\) in the case of ViT-L/14 [11]. Each \\( i \\)-th style word vector \\( \\mathbf{s}_i \\) is trained by the prompt loss \\( \\mathcal{L}_{\\mathrm{prompt}} \\) for \\( L = 100 \\) training iterations using the SGD optimizer with 0.002 learning rate and 0.9 momentum. The number of classes \\( N \\) is pre-defined by each target task definition, e.g., \\( N = 345 \\) for DomainNet [48]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.788, + 0.894, + 0.848 + ], + "angle": 0, + "content": "Training a linear classifier. The classifier is trained for 50 epochs using the SGD optimizer with 0.005 learning rate, 0.9 momentum, and a batch size of 128. In ArcFace [8] loss, its scaling factor is set to 5 with 0.5 angular margin." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.849, + 0.894, + 0.878 + ], + "angle": 0, + "content": "Inference. Input images are pre-processed in the same way with the CLIP model; resized to \\(224 \\times 224\\) and normalized." + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.887, + 0.763, + 0.901 + ], + "angle": 0, + "content": "1https://github.com/openai/CLIP" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15706" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.895, + 0.513 + ], + "angle": 0, + "content": "
MethodConfigurationAccuracy (%)
Source DomainDomain DescriptionPACSVLCSOfficeHomeDomainNetAvg.
ResNet-50 [22] with pre-trained weights on ImageNet [6]
DANN [19]✓-83.6±0.478.6±0.465.9±0.638.3±0.166.6
RSC [25]✓-85.2±0.977.1±0.565.5±0.938.9±0.566.7
MLDG [35]✓-84.9±1.077.2±0.466.8±0.641.2±0.167.5
SagNet [46]✓-86.3±0.277.8±0.568.1±0.140.3±0.168.1
SelfReg [28]✓-85.6±0.477.8±0.967.9±0.742.8±0.068.5
GVRT [44]✓-85.1±0.379.0±0.270.1±0.144.1±0.169.6
MIRO [5]✓-85.4±0.479.0±0.070.5±0.444.3±0.269.8
ResNet-50 [22] with pre-trained weights from CLIP [50]
ZS-CLIP (C) [50]--90.6±0.076.0±0.068.6±0.045.6±0.070.2
CAD [53]✓-90.0±0.681.2±0.670.5±0.345.5±2.171.8
ZS-CLIP (PC) [50]-✓90.7±0.080.1±0.072.0±0.046.2±0.072.3
PromptStyler--93.2±0.082.3±0.173.6±0.149.5±0.074.7
ViT-B/16 [11] with pre-trained weights from CLIP [50]
ZS-CLIP (C) [50]--95.7±0.076.4±0.079.9±0.057.8±0.077.5
MIRO [5]✓-95.682.282.554.078.6
ZS-CLIP (PC) [50]-✓96.1±0.082.4±0.082.3±0.057.7±0.079.6
PromptStyler--97.2±0.182.9±0.083.6±0.059.4±0.080.8
ViT-L/14 [11] with pre-trained weights from CLIP [50]
ZS-CLIP (C) [50]--97.6±0.077.5±0.085.9±0.063.3±0.081.1
ZS-CLIP (PC) [50]-✓98.5±0.082.4±0.086.9±0.064.0±0.083.0
PromptStyler--98.6±0.082.4±0.289.1±0.065.5±0.083.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.075, + 0.517, + 0.893, + 0.563 + ], + "angle": 0, + "content": "Table 2: Comparison with the state-of-the-art domain generalization methods. ZS-CLIP (C) denotes zero-shot CLIP using \"[class]\" as its text prompt, and ZS-CLIP (PC) indicates zero-shot CLIP using \"a photo of a [class]\" as its text prompt. Note that PromptStyler does not exploit any source domain data and domain descriptions." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.589, + 0.206, + 0.604 + ], + "angle": 0, + "content": "4.3. Evaluations" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.613, + 0.471, + 0.84 + ], + "angle": 0, + "content": "Main results. PromptStyler achieves the state of the art in every evaluation on PACS [34], VLCS [15], OfficeHome [60] and DomainNet [48] as shown in Table 2. Note that all existing methods utilize source domain data except for zero-shot CLIP [50] in Table 2. Compared with zero-shot CLIP which generates each text feature using a domain-agnostic prompt (\"[class]\", PromptStyler largely outperforms its records in all evaluations. Our method also shows higher accuracy compared with zero-shot CLIP which produces each text feature using a domain-specific prompt (\"a photo of a [class]\", even though we do not exploit any domain descriptions. These results confirm that the proposed method effectively improves the generalization capability of the chosen pre-trained model, i.e., CLIP, without using any images by simulating various distribution shifts via prompts in its latent space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Computational evaluations. In Table 3, we compare our PromptStyler and zero-shot CLIP [50] in terms of the number of parameters and inference speed; the inference speed was measured using a single RTX 3090 GPU with a batch size" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.587, + 0.892, + 0.729 + ], + "angle": 0, + "content": "
MethodInference Module# ParamsFPS
Image EncoderText Encoder
OfficeHome (65 classes)
ZS-CLIP [50]✓✓102.0M1.6
PromptStyler✓-38.4M72.9
DomainNet (345 classes)
ZS-CLIP [50]✓✓102.0M0.3
PromptStyler✓-38.7M72.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.733, + 0.894, + 0.793 + ], + "angle": 0, + "content": "Table 3: The number of parameters and inference speed on OfficeHome [60] and DomainNet [48] using ResNet-50 [22] as an image encoder. Note that CLIP [50] text encoder needs to generate text features as many as the number of classes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.894, + 0.901 + ], + "angle": 0, + "content": "of 1. Note that we do not exploit a text encoder at inference time, which makes our model \\(\\sim 2.6 \\times\\) smaller and \\(\\sim 243 \\times\\) faster compared with CLIP. Regarding the inference speed, the proposed model is about \\(45 \\times\\) faster for the target task OfficeHome [60] (65 classes) and it is about \\(243 \\times\\) faster for the target task DomainNet [48] (345 classes)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15707" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.346, + 0.244 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.176, + 0.25, + 0.253, + 0.271 + ], + "angle": 0, + "content": "(a) \\(\\mathcal{L}_{\\mathrm{style}}\\)" + }, + { + "type": "image", + "bbox": [ + 0.356, + 0.092, + 0.616, + 0.244 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.438, + 0.25, + 0.534, + 0.27 + ], + "angle": 0, + "content": "(b) \\(\\mathcal{L}_{\\mathrm{content}}\\)" + }, + { + "type": "image", + "bbox": [ + 0.626, + 0.092, + 0.887, + 0.244 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.674, + 0.25, + 0.839, + 0.271 + ], + "angle": 0, + "content": "(c) \\(\\mathcal{L}_{\\mathrm{style}} + \\mathcal{L}_{\\mathrm{content}}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.274, + 0.894, + 0.351 + ], + "angle": 0, + "content": "Figure 4: t-SNE [58] visualization results for the target task VLCS [15] (5 classes) using synthesized style-content features. We visualize such features obtained from the learned 80 style word vectors \\(\\{\\mathbf{s}_i\\}_{i=1}^{80}\\) and all the 5 classes (bird, car, chair, dog, person). Different colors denote features obtained from different style word vectors, and different shapes indicate features obtained from different class names. We only colorize features from the first 10 styles \\(\\{\\mathbf{s}_i\\}_{i=1}^{10}\\). Combining the style diversity loss \\(\\mathcal{L}_{\\text{style}}\\) and content consistency loss \\(\\mathcal{L}_{\\text{content}}\\) leads to diverse styles while preserving content information." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.361, + 0.21, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.217, + 0.361, + 0.347, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.361, + 0.482, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.361, + 0.618, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.625, + 0.361, + 0.754, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.361, + 0.89, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.465, + 0.893, + 0.495 + ], + "angle": 0, + "content": "Figure 5: Text-to-Image synthesis results using style-content features (from \"a \\(S_{*}\\) style of a cat\") with 6 different style word vectors. By leveraging the proposed method, we could learn a variety of styles while not distorting content information." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.508, + 0.47, + 0.6 + ], + "angle": 0, + "content": "
\\( {\\mathcal{L}}_{\\text{style }} \\)\\( {\\mathcal{L}}_{\\text{content }} \\)Accuracy (%)
PACSVLCSOfficeHomeDomainNetAvg.
--92.678.372.248.072.8
✓-92.380.971.548.273.2
-✓92.880.572.448.673.6
✓✓93.282.373.649.574.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.605, + 0.47, + 0.636 + ], + "angle": 0, + "content": "Table 4: Ablation study on the style diversity loss \\(\\mathcal{L}_{\\mathrm{style}}\\) and content consistency loss \\(\\mathcal{L}_{\\mathrm{content}}\\) used in the prompt loss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.652, + 0.471, + 0.879 + ], + "angle": 0, + "content": "t-SNE visualization results. In Figure 4, we qualitatively evaluate style-content features synthesized for the target task VLCS [15] (5 classes) using t-SNE [58] visualization. As shown in Figure 4(c), PromptStyler generates a variety of styles while not distorting content information; style-content features obtained from the same class name share similar semantics with diverse variations. This result confirms that we could effectively simulate various distribution shifts in the latent space of a large-scale vision-language model by synthesizing diverse styles via learnable style word vectors. Text-to-Image synthesis results. In Figure 5, we visualize style-content features (from \"a \\(S_*\\) style of a cat\") via diffusers library. These results are obtained with 6 different style word vectors, where the word vectors are learned for the target task DomainNet [48] using ViT-L/14 [11] model." + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.508, + 0.892, + 0.579 + ], + "angle": 0, + "content": "
LclassAccuracy (%)
PACSVLCSOfficeHomeDomainNetAvg.
Softmax92.581.272.348.673.7
ArcFace93.282.373.649.574.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.584, + 0.892, + 0.615 + ], + "angle": 0, + "content": "Table 5: Ablation study on the classification loss \\(\\mathcal{L}_{\\mathrm{class}}\\) used for training a linear classifier in the proposed framework." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.636, + 0.649, + 0.652 + ], + "angle": 0, + "content": "4.4. More analyses" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Ablation study on the prompt loss. In Table 4, we evaluate the effects of \\(\\mathcal{L}_{\\mathrm{style}}\\) and \\(\\mathcal{L}_{\\mathrm{content}}\\) in \\(\\mathcal{L}_{\\mathrm{prompt}}\\) used for learning style words. Interestingly, our method also achieves state-of-the-art results even without using these losses, i.e., the proposed framework (Fig. 3) is substantially effective by itself. Note that randomly initialized style word vectors are already diverse, and CLIP [50] is already good at extracting correct content information from a style-content prompt even without training the word vectors using \\(\\mathcal{L}_{\\mathrm{content}}\\). When we learn style word vectors using \\(\\mathcal{L}_{\\mathrm{style}}\\) without \\(\\mathcal{L}_{\\mathrm{content}}\\), style-content features obtained from different class names share more similar features than those from the same class name (Fig. 4(a)). On the other hand, using \\(\\mathcal{L}_{\\mathrm{content}}\\) without \\(\\mathcal{L}_{\\mathrm{style}}\\) leads to less diverse style-content features (Fig. 4(b)). When incorporating both losses, we could generate diverse styles while not distorting content information (Fig. 4(c))." + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.887, + 0.419, + 0.9 + ], + "angle": 0, + "content": "2https://github.com/huggingface/diffusers" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15708" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.09, + 0.282, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.091, + 0.485, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.091, + 0.688, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.688, + 0.091, + 0.892, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.233, + 0.892, + 0.264 + ], + "angle": 0, + "content": "Figure 6: Top-1 classification accuracy on the PACS [34], VLCS [15], OfficeHome [60] and DomainNet [48] datasets with regard to the number of learnable style word vectors \\( K \\)." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.268, + 0.282, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.268, + 0.485, + 0.408 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.268, + 0.688, + 0.408 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.688, + 0.268, + 0.892, + 0.408 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.41, + 0.892, + 0.441 + ], + "angle": 0, + "content": "Figure 7: Top-1 classification accuracy on the PACS [34], VLCS [15], OfficeHome [60] and DomainNet [48] datasets with regard to the number of training iterations \\( L \\) for learning each style word vector \\( \\mathbf{s}_i \\)." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.452, + 0.472, + 0.6 + ], + "angle": 0, + "content": "
MethodConfigurationAccuracy (%)
Source DomainDomain DescriptionTerra Incognito
ResNet-50 [22] with pre-trained weights on ImageNet [6]
SelfReg [28]✓-47.0±0.3
GVRT [44]✓-48.0±0.2
ResNet-50 [22] with pre-trained weights from CLIP [50]
ZS-CLIP (C) [50]--19.5±0.0
ZS-CLIP (PC) [50]-✓23.8±0.0
PromptStyler--30.5±0.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.602, + 0.47, + 0.634 + ], + "angle": 0, + "content": "Table 6: Unsatisfactory results obtained from CLIP [50] without using source domain data from Terra Incognita [1]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.47, + 0.84 + ], + "angle": 0, + "content": "Ablation study on the classification loss. In Table 5, we evaluate the effects of the original Softmax loss and the angular Softmax loss (i.e., ArcFace [8]). PromptStyler also achieves the state of the art using the original one, which validates that the performance improvement of our method mainly comes from the proposed framework (Fig. 3). Note that the angular Softmax loss further improves its accuracy by leveraging the hyperspherical joint vision-language space. Effect of the number of styles. We evaluate our method with regard to the number of style word vectors \\( K \\) as shown in Figure 6. Interestingly, our PromptStyler outperforms CLIP [50] using just 5 styles. This evaluation shows that 20 style word vectors are enough to achieve decent results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Effect of the number of iterations. We evaluate our method with regard to the number of training iterations \\( L \\) for learning each style word vector as shown in Figure 7. This evaluation shows that 20 iterations are enough to achieve decent results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.453, + 0.614, + 0.469 + ], + "angle": 0, + "content": "5. Limitation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.895, + 0.659 + ], + "angle": 0, + "content": "The performance of our method depends on the quality of the joint vision-language space constructed by the chosen vision-language model. For example, although PromptStyler largely outperforms its base model (i.e., CLIP [50]) in all evaluations, our method shows lower accuracy on the Terra Incognita dataset [1] compared with other methods which utilize several images from the dataset as shown in Table 6. The main reason for this might be due to the low accuracy of CLIP on the dataset. Nevertheless, given that our method consistently outperforms its base model in every evaluation, this limitation could be alleviated with the development of large-scale vision-language models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.675, + 0.619, + 0.69 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.699, + 0.895, + 0.865 + ], + "angle": 0, + "content": "We have presented a novel method that synthesizes a variety of styles in a joint vision-language space via learnable style words without exploiting any images to deal with source-free domain generalization. PromptStyler simulates various distribution shifts in the latent space of a large-scale pre-trained model, which could effectively improve its generalization capability. The proposed method achieves state-of-the-art results without using any source domain data on multiple domain generalization benchmarks. We hope that future work could apply our method to other tasks using different large-scale vision-language models." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.872, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgment. This work was supported by the Agency for Defense Development grant funded by the Korean government." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15709" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.471, + 0.157 + ], + "angle": 0, + "content": "[1] Sara Beery, Grant van Horn, and Pietro Perona. Recognition in Terra Incognita. In Proceedings of the European Conference on Computer Vision (ECCV), 2018." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.472, + 0.213 + ], + "angle": 0, + "content": "[2] Shai Ben-David, John Blitzer, Koby Crammer, and Fernando Pereira. Analysis of Representations for Domain Adaptation. 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Also, a recent study has demonstrated the cross-modal transferability phenomenon of this joint space. From these observations, we propose PromptStyler which simulates various distribution shifts in the joint space by synthesizing diverse styles via prompts without using any images to deal with source-free domain generalization. The proposed method learns to generate a variety of style features (from "a $S_*$ style of a") via learnable style word vectors for pseudo-words $S_*$ . To ensure that learned styles do not distort content information, we force style-content features (from "a $S_*$ style of a [class]") to be located nearby their corresponding content features (from "[class]") in the joint vision-language space. After learning style word vectors, we train a linear classifier using synthesized style-content features. PromptStyler achieves the state of the art on PACS, VLCS, OfficeHome and DomainNet, even though it does not require any images for training. + +# 1. Introduction + +Deep neural networks are usually trained with the assumption that training and test data are independent and identically distributed, which makes them vulnerable to substantial distribution shifts between training and test data [23, 52]. This susceptibility is considered as one of the major obstacles to their deployment in real-world applications. To enhance their robustness to such distribution shifts, Domain Adaptation (DA) [2, 24, 32, 33, 54, 56, 57, 68] has been studied; it aims at adapting neural networks to a target domain using target domain data available in training. However, such a target domain is often latent in common training scenarios, which considerably limits the application of DA. Recently, a body of research has addressed this limitation by Domain Generalization (DG) [3, 5, 21, 29, 35, 37, 74] that aims to improve model's generalization capability to any unseen domains. It has been a common practice in DG to utilize multiple source domains for learning domain-invariant features [61, 69], but + +![](images/e5a565637b157782a9d80607cf5b0578cb65a0ea4f6df5086f7c42da621e858b.jpg) +(a) + +![](images/866e4d637a5b4a9f831248aa803b78ee62b3347747ca78768831881749520fb4.jpg) +(b) +Figure 1: Motivation of our method. (a) Text features could effectively represent various image styles in a joint vision-language space. (b) PromptStyler synthesizes diverse styles in a joint vision-language space via learnable style word vectors for pseudo-words $S_{*}$ without using any images. + +it is unclear which source domains are ideal for DG, since arbitrary unseen domains should be addressed. Furthermore, it is costly and sometimes even infeasible to collect and annotate large-scale multi-source domain data for training. + +We notice that a large-scale pre-trained model might have already observed a great variety of domains and thus can be used as an efficient proxy of actual multiple source domains. From this perspective, we raised a question "Could we further improve model's generalization capability by simulating various distribution shifts in the latent space of such a large-scale model without using any source domain data?" If this + +![](images/b7e0632f0fd96cc7b1ef303d1293082b8acc6fb50817a4b4a1ec1677ffda0dca.jpg) +Figure 2: Important factors in the proposed method. PromptStyler learns style word vectors for pseudo-words $S_{*}$ which lead to diverse style features (from "a $S_{*}$ style of a") while preserving content information encoded in style-content features (from "a $S_{*}$ style of a [class])". $\mathcal{L}_{\mathrm{style}}$ and $\mathcal{L}_{\mathrm{content}}$ are the loss functions used for maximizing style diversity and content consistency in a hyperspherical joint vision-language space (e.g., CLIP [50] latent space). + +![](images/14762db21e7aff5a1db84fe2b1d15b30decec8136ce0249ce961c876a8f29113.jpg) + +is possible, DG will become immensely practical by effectively and efficiently exploiting such a large-scale model. However, this approach is much more challenging since any actual data of source and target domains are not accessible but only the target task definition (e.g., class names) is given. + +In this paper, we argue that large-scale vision-language models [26, 50, 64] could shed light on this challenging source-free domain generalization. As conceptually illustrated in Figure 1(a), text features could effectively represent their relevant image features in a joint vision-language space. Despite the modality gap between two modalities in the joint space [39], a recent study has demonstrated the cross-modal transferability phenomenon [67]; we could train a classifier using text features while running an inference with the classifier using image features. This training procedure meets the necessary condition for the source-free domain generalization, i.e., source domain images are not required. Using such a joint vision-language space, we could simulate various distribution shifts via prompts without any images. + +We propose a prompt-driven style generation method, dubbed PromptStyler, which synthesizes diverse styles via learnable word vectors to simulate distribution shifts in a hyperspherical joint vision-language space. PromptStyler is motivated by the observation that a shared style of images could characterize a domain [27, 74] and such a shared style could be captured by a learnable word vector for a pseudoword $S_{*}$ using CLIP [50] with a prompt ("a painting in the style of $S_{*}$ ) [17]. As shown in Figure 1(b), our method learns a style word vector for $S_{*}$ to represent each style. + +To effectively simulate various distribution shifts, we try to maximize style diversity as illustrated in Figure 2. Specifically, our method encourages learnable style word vectors to result in orthogonal style features in the hyperspherical space, where each style feature is obtained from a style prompt + +("a $S_*$ style of a") via a pre-trained text encoder. To prevent learned styles from distorting content information, we also consider content consistency as illustrated in Figure 2. Each style-content feature obtained from a style-content prompt ("a $S_*$ style of a [class]) is forced to be located closer to its corresponding content feature obtained from a content prompt ("[class]") than the other content features. + +Learned style word vectors are used to synthesize style-content features for training a classifier; these synthesized features could simulate images of known contents with diverse unknown styles in the joint space. These style-content features are fed as input to a linear classifier which is trained by a classification loss using contents ("[class]") as their class labels. At inference time, an image encoder extracts image features from input images, which are fed as input to the trained classifier. Note that the text and image encoders are derived from the same pre-trained vision-language model (e.g., CLIP [50]); the text encoder is only involved in training and the image encoder is only involved at inference time. + +The proposed method achieves state-of-the-art results on PACS [34], VLCS [15], OfficeHome [60] and DomainNet [48] without using any actual data of source and target domains. It takes just $\sim 30$ minutes for the entire training using a single RTX 3090 GPU, and our model is $\sim 2.6\times$ smaller and $\sim 243\times$ faster at inference compared with CLIP [50]. + +Our contributions are summarized as follows: + +- This work is the first attempt to synthesize a variety of styles in a joint vision-language space via prompts to effectively tackle source-free domain generalization. +- This paper proposes a novel method that effectively simulates images of known contents with diverse unknown styles in a joint vision-language space. +- PromptStyler achieves the state of the art on domain generalization benchmarks without using any images. + +
SetupSourceTargetTask Definition
DA✓✓✓
DG✓-✓
Source-free DA-✓✓
Source-free DG--✓
+ +Table 1: Different requirements in each setup. Source-free DG only assumes the task definition (i.e., what should be predicted) without requiring source and target domain data. + +# 2. Related Work + +Domain Generalization. Model's generalization capability to arbitrary unseen domains is the key factor to successful deployment of neural networks in real-world applications, since substantial distribution shifts between source and target domains could significantly degrade their performance [23, 52]. To this end, Domain Generalization (DG) [4, 5, 10, 16, 21, 29, 35, 37, 44, 45, 61, 69] has been studied. It assumes target domain data are not accessible while using data from source domains. Generally speaking, existing DG methods could be divided into two categories: multi-source DG [3, 12, 36, 42, 43, 51, 55, 63, 73, 74] and single-source DG [14, 38, 49, 62]. Mostly, multi-source DG methods aim to learn domain-invariant features by exploiting available multiple source domains, and single-source DG methods also aim to learn such features by generating diverse domains based on a single domain and then exploiting the synthesized domains. + +Source-free Domain Generalization. In this setup, we are not able to access any source and target domains as summarized in Table 1. Thus, source-free DG is much more challenging than multi-source and single-source DG. From the observation that synthesizing new domains from the given source domain could effectively improve model's generalization capability [27,38,62,72,73], we also try to generate diverse domains but without using any source domains to deal with source-free DG. By leveraging a large-scale pre-trained model which has already seen a great variety of domains, our method could simulate various distribution shifts in the latent space of the large-scale model. This approach has several advantages compared with existing DG methods; source domain images are not required and there is no concern for catastrophic forgetting which might impede model's generalization capability. Also, it would be immensely practical to exploit such a large-scale model for downstream visual recognition tasks, since we only need the task definition. + +Large-scale model in Domain Generalization. Recently, several DG methods [5, 53] exploit a large-scale pre-trained model (e.g., CLIP [50]) to leverage its great generalization capability. While training neural networks on available data, CAD [53] and MIRO [5] try to learn robust features using such a large-scale model. Compared with them, the proposed method could learn domain-invariant features using a large-scale pre-trained model without requiring any actual data. + +Joint vision-language space. Large-scale vision-language models [26, 50, 64] are trained with a great amount of image-text pairs, and achieve state-of-the-art results on downstream visual recognition tasks [20, 41, 66, 70, 71]. By leveraging their joint vision-language spaces, we could also effectively manipulate visual features via prompts [13, 18, 31, 47]. Interestingly, Textual Inversion [17] shows that a learnable style word vector for a pseudo-word $S_{*}$ could capture a shared style of images using CLIP [50] with a prompt ("a painting in the style of $S_{*}$ "). From this observation, we argue that learnable style word vectors would be able to seek a variety of styles for simulating various distribution shifts in a joint vision-language space without using any images. + +# 3. Method + +The overall framework of the proposed method is shown in Figure 3, and pseudo-code of PromptStyler is described in Algorithm 1. Our method learns style word vectors to represent a variety of styles in a hyperspherical joint vision-language space (e.g., CLIP [50] latent space). After learning those style word vectors, we train a linear classifier using synthesized style-content features produced by a pre-trained text encoder $T(\cdot)$ . At inference time, a pre-trained image encoder $I(\cdot)$ extracts image features from input images, which are fed as input to the trained linear classifier. Thanks to the cross-modal transferability phenomenon of the joint vision-language space [67], this classifier could produce class scores using the image features. Note that we exploit CLIP as our large-scale vision-language model; its image encoder and text encoder are frozen in our entire framework. + +# 3.1. Prompt-driven style generation + +An input text prompt is converted to several tokens via a tokenization process, and then such tokens are replaced by their corresponding word vectors via a word lookup process. In PromptStyler, a pseudo-word $S_{i}$ in a prompt is a placeholder which is replaced by a style word vector $\mathbf{s}_i \in \mathbb{R}^D$ during the word lookup process. Note that three kinds of prompts are used in the proposed method: a style prompt $\mathcal{P}_i^{\mathrm{style}}$ ("a $S_{i}$ style of a"), a content prompt $\mathcal{P}_m^{\mathrm{content}}$ ("[class] $m$ "), and a style-content prompt $\mathcal{P}_i^{\mathrm{style}} \circ \mathcal{P}_m^{\mathrm{content}}$ ("a $S_{i}$ style of a [class] $m$ "). $S_{i}$ indicates the placeholder for $i$ -th style word vector and [class] $m$ denotes $m$ -th class name. + +Suppose we want to generate $K$ different styles in a joint vision-language space. In this case, the proposed method needs to learn $K$ style word vectors $\{\mathbf{s}_i\}_{i=1}^K$ , where each $\mathbf{s}_i$ is randomly initialized at the beginning. To effectively simulate various distribution shifts in the joint vision-language space, those style word vectors need to be diverse while not distorting content information when they are exploited in style-content prompts. There are two possible design choices for learning such word vectors: (1) learning each style word vector $\mathbf{s}_i$ in a sequential manner, or (2) learning all style + +![](images/5d6b5fea955f54effc6924315ad9121f02bb0063f474b3059c065d3fcbc14752.jpg) +(i) Prompt-driven style generation + +(ii) Training a linear classifier using diverse styles +![](images/a0ac41ba6eafb7f255d2e0c841115d9450a4d2716c206f457ff2dbf18ffb0cea.jpg) +Frozen weights $\ell_2$ normalization layer + +(iii) Inference using the trained classifier +Figure 3: PromptStyler learns diverse style word vectors which do not distort content information of style-content prompts. After learning style word vectors, we synthesize style-content features (e.g., from "a $S_{1}$ style of a dog") via a pre-trained text encoder for training a linear classifier. The classifier is trained by a classification loss using those synthesized features and their corresponding class labels (e.g., "dog"). At inference time, a pre-trained image encoder extracts image features, which are fed as input to the trained classifier. Note that the encoders are derived from the same vision-language model (e.g., CLIP [50]). +![](images/8a9be02778762e0c40bea03a8b2d0dbc0dcd97108b318eb7c3f4e1cc122a2efb.jpg) +Frozen weights $\ell_2$ normalization layer + +word vectors $\{\mathbf{s}_i\}_{i=1}^K$ in a parallel manner. We choose the former, since it takes much less memory during training. Please refer to the supplementary material (Section A.2) for the empirical justification of our design choice. + +Style diversity loss. To maximize the diversity of $K$ styles in a hyperspherical joint vision-language space, we sequentially learn style word vectors $\{\mathbf{s}_i\}_{i=1}^K$ in such a way that $i$ -th style feature $T(\mathcal{P}_i^{\mathrm{style}}) \in \mathbb{R}^C$ produced by $i$ -th style word vector $\mathbf{s}_i$ is orthogonal to $\{T(\mathcal{P}_j^{\mathrm{style}})\}_{j=1}^{i-1}$ produced by previously learned style word vectors $\{\mathbf{s}_j\}_{j=1}^{i-1}$ . Regarding this, the style diversity loss $\mathcal{L}_{\mathrm{style}}$ for learning $i$ -th style word vector $\mathbf{s}_i$ is computed by + +$$ +\mathcal {L} _ {\text {s t y l e}} = \frac {1}{i - 1} \sum_ {j = 1} ^ {i - 1} \left| \frac {T \left(\mathcal {P} _ {i} ^ {\text {s t y l e}}\right)}{\| T \left(\mathcal {P} _ {i} ^ {\text {s t y l e}}\right) \| _ {2}} \cdot \frac {T \left(\mathcal {P} _ {j} ^ {\text {s t y l e}}\right)}{\| T \left(\mathcal {P} _ {j} ^ {\text {s t y l e}}\right) \| _ {2}} \right|. \tag {1} +$$ + +This style loss $\mathcal{L}_{\mathrm{style}}$ aims to minimize the absolute value of the cosine similarity between $i$ -th style features and each of the existing style features. When the value of this loss becomes zero, it satisfies the orthogonality between $i$ -th style feature and all the existing style features. + +Content consistency loss. Learning the style word vectors $\{\mathbf{s}_i\}_{i = 1}^K$ only using the style diversity loss sometimes leads to undesirable outcome, since a learned style $\mathbf{s}_i$ could substantially distort content information when used to generate a style-content feature $T(\mathcal{P}_i^{\mathrm{style}}\circ \mathcal{P}_m^{\mathrm{content}})\in \mathbb{R}^C$ . To alleviate this problem, we encourage the content information in the style-content feature to be consistent with its corresponding content feature $T(\mathcal{P}_m^{\mathrm{content}})\in \mathbb{R}^C$ while learning each $i$ -th style word vector $\mathbf{s}_i$ . Specifically, each style-content + +feature synthesized via $i$ -th style word vector $\mathbf{s}_i$ should have the highest cosine similarity score with its corresponding content feature. For $i$ -th style word vector $\mathbf{s}_i$ , a cosine similarity score $z_{imn}$ between a style-content feature with $m$ -th class name and a content feature with $n$ -th class name is computed by + +$$ +z _ {i m n} = \frac {T \left(\mathcal {P} _ {i} ^ {\text {s t y l e}} \circ \mathcal {P} _ {m} ^ {\text {c o n t e n t}}\right)}{\| T \left(\mathcal {P} _ {i} ^ {\text {s t y l e}} \circ \mathcal {P} _ {m} ^ {\text {c o n t e n t}}\right) \| _ {2}} \cdot \frac {T \left(\mathcal {P} _ {n} ^ {\text {c o n t e n t}}\right)}{\| T \left(\mathcal {P} _ {n} ^ {\text {c o n t e n t}}\right) \| _ {2}}. \tag {2} +$$ + +Using cosine similarity scores between style-content features and content features, the content consistency loss $\mathcal{L}_{\mathrm{content}}$ for learning $i$ -th style word vector $\mathbf{s}_i$ is computed by + +$$ +\mathcal {L} _ {\text {c o n t e n t}} = - \frac {1}{N} \sum_ {m = 1} ^ {N} \log \left(\frac {\exp \left(z _ {i m m}\right)}{\sum_ {n = 1} ^ {N} \exp \left(z _ {i m n}\right)}\right), \tag {3} +$$ + +where $N$ denotes the number of classes pre-defined in the target task. This content loss $\mathcal{L}_{\mathrm{content}}$ is a contrastive loss which encourages each style-content feature to be located closer to its corresponding content feature so that it forces each $i$ -th style word vector $\mathbf{s}_i$ to preserve content information when used to synthesize style-content features. + +Total prompt loss. PromptStyler learns $K$ style word vectors $\{\mathbf{s}_i\}_{i=1}^K$ in a sequential manner, where each $i$ -th style word vector $\mathbf{s}_i$ is learned using both $\mathcal{L}_{\mathrm{style}}$ (Eq.(1)) and $\mathcal{L}_{\mathrm{content}}$ (Eq.(3)). In the proposed method, the total loss $\mathcal{L}_{\mathrm{prompt}}$ for learning $i$ -th style word vector is computed by + +$$ +\mathcal {L} _ {\text {p r o m p t}} = \mathcal {L} _ {\text {s t y l e}} + \mathcal {L} _ {\text {c o n t e n t}}. \tag {4} +$$ + +Using this prompt loss $\mathcal{L}_{\mathrm{prompt}}$ , we train $i$ -th style word vector $\mathbf{s}_i$ for $L$ training iterations. + +Algorithm 1 PromptStyler +Requirement: pre-trained text encoder $T(\cdot)$ , pre-defined $N$ class names in the target task +Input: number of style word vectors $K$ , number of training iterations $L$ +Output: $KN$ style-content features + # randomly initialize style word vectors +1: $\{\mathbf{s}_i\}_{i=1}^K \leftarrow$ random_init( $\{\mathbf{s}_i\}_{i=1}^K$ ) + # sequentially learn $K$ style word vectors +2: for $i = 1, 2, \ldots, K$ do + # $L$ training iterations for learning each word vector +3: for iteration $= 1, 2, \ldots, L$ do + # compute $\mathcal{L}_{\text{style}}$ using $T(\cdot)$ and word vectors +4: $\mathcal{L}_{\text{style}} \leftarrow$ style_diversity_loss( $\mathbf{s}_i$ , $\{\mathbf{s}_j\}_{j=1}^{i-1}$ ) + # compute $\mathcal{L}_{\text{content}}$ using $T(\cdot)$ and a word vector +5: $\mathcal{L}_{\text{content}} \leftarrow$ content_consistency_loss( $\mathbf{s}_i$ ) +6: $\mathcal{L}_{\text{prompt}} \leftarrow \mathcal{L}_{\text{style}} + \mathcal{L}_{\text{content}}$ +7: Update $\mathbf{s}_i$ using $\mathcal{L}_{\text{prompt}}$ by gradient descent +8: end for +9: end for +10: Synthesize $KN$ style-content features using the learned $K$ style word vectors and $N$ class names via $T(\cdot)$ + +# 3.2. Training a linear classifier using diverse styles + +After learning $K$ style word vectors $\{\mathbf{s}_i\}_{i = 1}^K$ , we generate $KN$ style-content features for training a linear classifier. To be specific, we synthesize those features using the learned $K$ styles and pre-defined $N$ classes via the text encoder $T(\cdot)$ . The linear classifier is trained by a classification loss using $\ell_2$ -normalized style-content features and their class labels; each class label is the class name used to generate each style-content feature. To effectively leverage the hyperspherical joint vision-language space, we adopt ArcFace [8] loss as our classification loss $\mathcal{L}_{\mathrm{class}}$ . Note that ArcFace loss is an angular Softmax loss which computes the cosine similarities between classifier input features and classifier weights with an additive angular margin penalty between classes. This angular margin penalty allows for more discriminative predictions by pushing features from different classes further apart. Thanks to the property, this angular Softmax loss has been widely used in visual recognition tasks [7,9,30,40,65]. + +# 3.3. Inference using the trained classifier + +The trained classifier is used with a pre-trained image encoder $I(\cdot)$ at inference time. Given an input image $\mathbf{x}$ , the image encoder extracts its image feature $I(\mathbf{x}) \in \mathbb{R}^{C}$ , which is mapped to the hyperspherical joint vision-language space by $\ell_{2}$ normalization. Then, the trained classifier produces class scores using the $\ell_{2}$ -normalized image feature. Note that the text encoder $T(\cdot)$ is not used at inference time, while the image encoder $I(\cdot)$ is only exploited at inference time. + +# 4. Experiments + +For more comprehensive understanding, please refer to the supplementary material (Section B and D). + +# 4.1. Evaluation datasets + +The proposed method does not require any actual data for training. To analyze its generalization capability, four domain generalization benchmarks are used for evaluation: PACS [34] (4 domains and 7 classes), VLCS [15] (4 domains and 5 classes), OfficeHome [60] (4 domains and 65 classes) and DomainNet [48] (6 domains and 345 classes). On these benchmarks, we repeat each experiment three times using different random seeds and report average top-1 classification accuracies with standard errors. Unlike the leave-one-domain-out cross-validation evaluation protocol [21], we do not exploit any source domain data for training. + +# 4.2. Implementation details + +PromptStyler is implemented and trained with the same configuration regardless of the evaluation datasets. Training takes about 30 minutes using a single RTX 3090 GPU. + +Architecture. We choose CLIP [50] as our large-scale pretrained vision-language model, and use the publicly available pre-trained model. $^{1}$ The text encoder $T(\cdot)$ used in training is Transformer [59] and the image encoder $I(\cdot)$ used at inference is ResNet-50 [22] as default setting in experiments; our method is also implemented with ViT-B/16 [11] or ViT-L/14 [11] for further evaluations as shown in Table 2. Note that text and image encoders are derived from the same CLIP model and frozen in the entire pipeline. The dimension of each text feature or image feature is $C = 1024$ when our method is implemented with ResNet-50, while $C = 512$ in the case of ViT-B/16 and $C = 768$ in the case of ViT-L/14. + +Learning style word vectors. We follow prompt learning methods [70, 71] when learning the word vectors. Using a zero-mean Gaussian distribution with 0.02 standard deviation, we randomly initialize $K$ style word vectors $\{\mathbf{s}_i\}_{i=1}^K$ , where $K = 80$ . The dimension of each style word vector is $D = 512$ when the proposed method is implemented with ResNet-50 [22] or ViT-B/16 [11], while $D = 768$ in the case of ViT-L/14 [11]. Each $i$ -th style word vector $\mathbf{s}_i$ is trained by the prompt loss $\mathcal{L}_{\mathrm{prompt}}$ for $L = 100$ training iterations using the SGD optimizer with 0.002 learning rate and 0.9 momentum. The number of classes $N$ is pre-defined by each target task definition, e.g., $N = 345$ for DomainNet [48]. + +Training a linear classifier. The classifier is trained for 50 epochs using the SGD optimizer with 0.005 learning rate, 0.9 momentum, and a batch size of 128. In ArcFace [8] loss, its scaling factor is set to 5 with 0.5 angular margin. + +Inference. Input images are pre-processed in the same way with the CLIP model; resized to $224 \times 224$ and normalized. + +
MethodConfigurationAccuracy (%)
Source DomainDomain DescriptionPACSVLCSOfficeHomeDomainNetAvg.
ResNet-50 [22] with pre-trained weights on ImageNet [6]
DANN [19]✓-83.6±0.478.6±0.465.9±0.638.3±0.166.6
RSC [25]✓-85.2±0.977.1±0.565.5±0.938.9±0.566.7
MLDG [35]✓-84.9±1.077.2±0.466.8±0.641.2±0.167.5
SagNet [46]✓-86.3±0.277.8±0.568.1±0.140.3±0.168.1
SelfReg [28]✓-85.6±0.477.8±0.967.9±0.742.8±0.068.5
GVRT [44]✓-85.1±0.379.0±0.270.1±0.144.1±0.169.6
MIRO [5]✓-85.4±0.479.0±0.070.5±0.444.3±0.269.8
ResNet-50 [22] with pre-trained weights from CLIP [50]
ZS-CLIP (C) [50]--90.6±0.076.0±0.068.6±0.045.6±0.070.2
CAD [53]✓-90.0±0.681.2±0.670.5±0.345.5±2.171.8
ZS-CLIP (PC) [50]-✓90.7±0.080.1±0.072.0±0.046.2±0.072.3
PromptStyler--93.2±0.082.3±0.173.6±0.149.5±0.074.7
ViT-B/16 [11] with pre-trained weights from CLIP [50]
ZS-CLIP (C) [50]--95.7±0.076.4±0.079.9±0.057.8±0.077.5
MIRO [5]✓-95.682.282.554.078.6
ZS-CLIP (PC) [50]-✓96.1±0.082.4±0.082.3±0.057.7±0.079.6
PromptStyler--97.2±0.182.9±0.083.6±0.059.4±0.080.8
ViT-L/14 [11] with pre-trained weights from CLIP [50]
ZS-CLIP (C) [50]--97.6±0.077.5±0.085.9±0.063.3±0.081.1
ZS-CLIP (PC) [50]-✓98.5±0.082.4±0.086.9±0.064.0±0.083.0
PromptStyler--98.6±0.082.4±0.289.1±0.065.5±0.083.9
+ +# 4.3. Evaluations + +Main results. PromptStyler achieves the state of the art in every evaluation on PACS [34], VLCS [15], OfficeHome [60] and DomainNet [48] as shown in Table 2. Note that all existing methods utilize source domain data except for zero-shot CLIP [50] in Table 2. Compared with zero-shot CLIP which generates each text feature using a domain-agnostic prompt ("[class]", PromptStyler largely outperforms its records in all evaluations. Our method also shows higher accuracy compared with zero-shot CLIP which produces each text feature using a domain-specific prompt ("a photo of a [class]", even though we do not exploit any domain descriptions. These results confirm that the proposed method effectively improves the generalization capability of the chosen pre-trained model, i.e., CLIP, without using any images by simulating various distribution shifts via prompts in its latent space. + +Computational evaluations. In Table 3, we compare our PromptStyler and zero-shot CLIP [50] in terms of the number of parameters and inference speed; the inference speed was measured using a single RTX 3090 GPU with a batch size + +Table 2: Comparison with the state-of-the-art domain generalization methods. ZS-CLIP (C) denotes zero-shot CLIP using "[class]" as its text prompt, and ZS-CLIP (PC) indicates zero-shot CLIP using "a photo of a [class]" as its text prompt. Note that PromptStyler does not exploit any source domain data and domain descriptions. + +
MethodInference Module# ParamsFPS
Image EncoderText Encoder
OfficeHome (65 classes)
ZS-CLIP [50]✓✓102.0M1.6
PromptStyler✓-38.4M72.9
DomainNet (345 classes)
ZS-CLIP [50]✓✓102.0M0.3
PromptStyler✓-38.7M72.9
+ +Table 3: The number of parameters and inference speed on OfficeHome [60] and DomainNet [48] using ResNet-50 [22] as an image encoder. Note that CLIP [50] text encoder needs to generate text features as many as the number of classes. + +of 1. Note that we do not exploit a text encoder at inference time, which makes our model $\sim 2.6 \times$ smaller and $\sim 243 \times$ faster compared with CLIP. Regarding the inference speed, the proposed model is about $45 \times$ faster for the target task OfficeHome [60] (65 classes) and it is about $243 \times$ faster for the target task DomainNet [48] (345 classes). + +![](images/7f2a84d5dfccfb3cb966ba8cc3d766e24359d06ca57f37fb7ee70a35d60a9236.jpg) +(a) $\mathcal{L}_{\mathrm{style}}$ + +![](images/3b8f69e8e96565e700c30b31ac3ecd4bf4d6cb3a8b7046bf15400ea887a328fe.jpg) +(b) $\mathcal{L}_{\mathrm{content}}$ + +![](images/2c93bea5367111625aaeed349e2d76c1493c0b115cafea51078dc4fbc646b969.jpg) +(c) $\mathcal{L}_{\mathrm{style}} + \mathcal{L}_{\mathrm{content}}$ + +![](images/c920cb1d330be0ab0fa477e01aa864512539d7b86c65db640188f6160a0ea738.jpg) +Figure 4: t-SNE [58] visualization results for the target task VLCS [15] (5 classes) using synthesized style-content features. We visualize such features obtained from the learned 80 style word vectors $\{\mathbf{s}_i\}_{i=1}^{80}$ and all the 5 classes (bird, car, chair, dog, person). Different colors denote features obtained from different style word vectors, and different shapes indicate features obtained from different class names. We only colorize features from the first 10 styles $\{\mathbf{s}_i\}_{i=1}^{10}$ . Combining the style diversity loss $\mathcal{L}_{\text{style}}$ and content consistency loss $\mathcal{L}_{\text{content}}$ leads to diverse styles while preserving content information. + +![](images/3dd295e1b3285874ae513653efe4afb79f9a382c8e6a17421d7008fa4866e193.jpg) +Figure 5: Text-to-Image synthesis results using style-content features (from "a $S_{*}$ style of a cat") with 6 different style word vectors. By leveraging the proposed method, we could learn a variety of styles while not distorting content information. + +![](images/f9e2d8a34fd548d59d5bc703ac5c955c554a1fcfdbb9899ab211cd70b2878d2b.jpg) + +![](images/5afdd5c9b4392033a4d1c1dd2f0ff0a0a6410d9c61b11952e21adf67c440b28a.jpg) + +![](images/5d6621cebc43e3eb2fd68b9e36560adcb3f998c0cc7d549ab3ebd6d64c99741c.jpg) + +![](images/03d646dc348b3f09db2cbee8318ea39e1523286f01c3e656a2d98001b87ce12f.jpg) + +
\( {\mathcal{L}}_{\text{style }} \)\( {\mathcal{L}}_{\text{content }} \)Accuracy (%)
PACSVLCSOfficeHomeDomainNetAvg.
--92.678.372.248.072.8
✓-92.380.971.548.273.2
-✓92.880.572.448.673.6
✓✓93.282.373.649.574.7
+ +t-SNE visualization results. In Figure 4, we qualitatively evaluate style-content features synthesized for the target task VLCS [15] (5 classes) using t-SNE [58] visualization. As shown in Figure 4(c), PromptStyler generates a variety of styles while not distorting content information; style-content features obtained from the same class name share similar semantics with diverse variations. This result confirms that we could effectively simulate various distribution shifts in the latent space of a large-scale vision-language model by synthesizing diverse styles via learnable style word vectors. Text-to-Image synthesis results. In Figure 5, we visualize style-content features (from "a $S_*$ style of a cat") via diffusers library. These results are obtained with 6 different style word vectors, where the word vectors are learned for the target task DomainNet [48] using ViT-L/14 [11] model. + +Table 4: Ablation study on the style diversity loss $\mathcal{L}_{\mathrm{style}}$ and content consistency loss $\mathcal{L}_{\mathrm{content}}$ used in the prompt loss. + +
LclassAccuracy (%)
PACSVLCSOfficeHomeDomainNetAvg.
Softmax92.581.272.348.673.7
ArcFace93.282.373.649.574.7
+ +Table 5: Ablation study on the classification loss $\mathcal{L}_{\mathrm{class}}$ used for training a linear classifier in the proposed framework. + +# 4.4. More analyses + +Ablation study on the prompt loss. In Table 4, we evaluate the effects of $\mathcal{L}_{\mathrm{style}}$ and $\mathcal{L}_{\mathrm{content}}$ in $\mathcal{L}_{\mathrm{prompt}}$ used for learning style words. Interestingly, our method also achieves state-of-the-art results even without using these losses, i.e., the proposed framework (Fig. 3) is substantially effective by itself. Note that randomly initialized style word vectors are already diverse, and CLIP [50] is already good at extracting correct content information from a style-content prompt even without training the word vectors using $\mathcal{L}_{\mathrm{content}}$ . When we learn style word vectors using $\mathcal{L}_{\mathrm{style}}$ without $\mathcal{L}_{\mathrm{content}}$ , style-content features obtained from different class names share more similar features than those from the same class name (Fig. 4(a)). On the other hand, using $\mathcal{L}_{\mathrm{content}}$ without $\mathcal{L}_{\mathrm{style}}$ leads to less diverse style-content features (Fig. 4(b)). When incorporating both losses, we could generate diverse styles while not distorting content information (Fig. 4(c)). + +![](images/db544386c17bca8b0c1ccdd2665feb95f68b96bd9bac8245cb0c03ebebb849dc.jpg) +Figure 6: Top-1 classification accuracy on the PACS [34], VLCS [15], OfficeHome [60] and DomainNet [48] datasets with regard to the number of learnable style word vectors $K$ . + +![](images/16aca7536738cc5ffba8c6507e7616ec90bb752a002cdc62b703a173dc6e1cf9.jpg) + +![](images/50868d20456b01dccfa0567fe62d558978604e3b25ceed72bde224e0eca921e4.jpg) + +![](images/ca69433126e7948dc9ebab49f11d0ce8306a3ba179aa71666546c07acba1a4f7.jpg) + +![](images/6962712cf551db230d27623eff7a7ccc656d107a2456e831722b08c1784741e2.jpg) +Figure 7: Top-1 classification accuracy on the PACS [34], VLCS [15], OfficeHome [60] and DomainNet [48] datasets with regard to the number of training iterations $L$ for learning each style word vector $\mathbf{s}_i$ . + +![](images/e49291f220df53107d03e45791827d1eecf1563546c583ffffcf017f10493e31.jpg) + +![](images/0a3903bd3fc277cf36c81c6a6aa6c94859cadbef26bdd1da94f6f5ac4fbf13f4.jpg) + +![](images/27a886adfd7f6849890bc14be963cbb0e298c7b84b9c4ebd17b60a24d92a3095.jpg) + +
MethodConfigurationAccuracy (%)
Source DomainDomain DescriptionTerra Incognito
ResNet-50 [22] with pre-trained weights on ImageNet [6]
SelfReg [28]✓-47.0±0.3
GVRT [44]✓-48.0±0.2
ResNet-50 [22] with pre-trained weights from CLIP [50]
ZS-CLIP (C) [50]--19.5±0.0
ZS-CLIP (PC) [50]-✓23.8±0.0
PromptStyler--30.5±0.8
+ +Table 6: Unsatisfactory results obtained from CLIP [50] without using source domain data from Terra Incognita [1]. + +Ablation study on the classification loss. In Table 5, we evaluate the effects of the original Softmax loss and the angular Softmax loss (i.e., ArcFace [8]). PromptStyler also achieves the state of the art using the original one, which validates that the performance improvement of our method mainly comes from the proposed framework (Fig. 3). Note that the angular Softmax loss further improves its accuracy by leveraging the hyperspherical joint vision-language space. Effect of the number of styles. We evaluate our method with regard to the number of style word vectors $K$ as shown in Figure 6. Interestingly, our PromptStyler outperforms CLIP [50] using just 5 styles. This evaluation shows that 20 style word vectors are enough to achieve decent results. + +Effect of the number of iterations. We evaluate our method with regard to the number of training iterations $L$ for learning each style word vector as shown in Figure 7. This evaluation shows that 20 iterations are enough to achieve decent results. + +# 5. Limitation + +The performance of our method depends on the quality of the joint vision-language space constructed by the chosen vision-language model. For example, although PromptStyler largely outperforms its base model (i.e., CLIP [50]) in all evaluations, our method shows lower accuracy on the Terra Incognita dataset [1] compared with other methods which utilize several images from the dataset as shown in Table 6. The main reason for this might be due to the low accuracy of CLIP on the dataset. Nevertheless, given that our method consistently outperforms its base model in every evaluation, this limitation could be alleviated with the development of large-scale vision-language models. + +# 6. Conclusion + +We have presented a novel method that synthesizes a variety of styles in a joint vision-language space via learnable style words without exploiting any images to deal with source-free domain generalization. PromptStyler simulates various distribution shifts in the latent space of a large-scale pre-trained model, which could effectively improve its generalization capability. The proposed method achieves state-of-the-art results without using any source domain data on multiple domain generalization benchmarks. We hope that future work could apply our method to other tasks using different large-scale vision-language models. + +Acknowledgment. This work was supported by the Agency for Defense Development grant funded by the Korean government. + +# References + +[1] Sara Beery, Grant van Horn, and Pietro Perona. Recognition in Terra Incognita. 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Also, a recent study has demonstrated the cross-modal transferability phenomenon of this joint space. From these observations, we propose PromptStyler which simulates various distribution shifts in the joint space by synthesizing diverse styles via prompts without using any images to deal with source-free domain generalization. The proposed method learns to generate a variety of style features (from \"a " + }, + { + "bbox": [ + 45, + 247, + 290, + 475 + ], + "type": "inline_equation", + "content": "S_*" + }, + { + "bbox": [ + 45, + 247, + 290, + 475 + ], + "type": "text", + "content": " style of a\") via learnable style word vectors for pseudo-words " + }, + { + "bbox": [ + 45, + 247, + 290, + 475 + ], + "type": "inline_equation", + "content": "S_*" + }, + { + "bbox": [ + 45, + 247, + 290, + 475 + ], + "type": "text", + "content": ". To ensure that learned styles do not distort content information, we force style-content features (from \"a " + }, + { + "bbox": [ + 45, + 247, + 290, + 475 + ], + "type": "inline_equation", + "content": "S_*" + }, + { + "bbox": [ + 45, + 247, + 290, + 475 + ], + "type": "text", + "content": " style of a [class]\") to be located nearby their corresponding content features (from \"[class]\") in the joint vision-language space. After learning style word vectors, we train a linear classifier using synthesized style-content features. PromptStyler achieves the state of the art on PACS, VLCS, OfficeHome and DomainNet, even though it does not require any images for training." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 48, + 491, + 128, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 491, + 128, + 504 + ], + "spans": [ + { + "bbox": [ + 48, + 491, + 128, + 504 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": "Deep neural networks are usually trained with the assumption that training and test data are independent and identically distributed, which makes them vulnerable to substantial distribution shifts between training and test data [23, 52]. This susceptibility is considered as one of the major obstacles to their deployment in real-world applications. To enhance their robustness to such distribution shifts, Domain Adaptation (DA) [2, 24, 32, 33, 54, 56, 57, 68] has been studied; it aims at adapting neural networks to a target domain using target domain data available in training. However, such a target domain is often latent in common training scenarios, which considerably limits the application of DA. Recently, a body of research has addressed this limitation by Domain Generalization (DG) [3, 5, 21, 29, 35, 37, 74] that aims to improve model's generalization capability to any unseen domains. It has been a common practice in DG to utilize multiple source domains for learning domain-invariant features [61, 69], but" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 328, + 230, + 545, + 361 + ], + "blocks": [ + { + "bbox": [ + 307, + 291, + 323, + 304 + ], + "lines": [ + { + "bbox": [ + 307, + 291, + 323, + 304 + ], + "spans": [ + { + "bbox": [ + 307, + 291, + 323, + 304 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 328, + 230, + 545, + 361 + ], + "lines": [ + { + "bbox": [ + 328, + 230, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 328, + 230, + 545, + 361 + ], + "type": "image", + "image_path": "e5a565637b157782a9d80607cf5b0578cb65a0ea4f6df5086f7c42da621e858b.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 329, + 366, + 545, + 498 + ], + "blocks": [ + { + "bbox": [ + 307, + 426, + 323, + 441 + ], + "lines": [ + { + "bbox": [ + 307, + 426, + 323, + 441 + ], + "spans": [ + { + "bbox": [ + 307, + 426, + 323, + 441 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 329, + 366, + 545, + 498 + ], + "lines": [ + { + "bbox": [ + 329, + 366, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 329, + 366, + 545, + 498 + ], + "type": "image", + "image_path": "866e4d637a5b4a9f831248aa803b78ee62b3347747ca78768831881749520fb4.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 502, + 547, + 563 + ], + "lines": [ + { + "bbox": [ + 304, + 502, + 547, + 563 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 547, + 563 + ], + "type": "text", + "content": "Figure 1: Motivation of our method. (a) Text features could effectively represent various image styles in a joint vision-language space. (b) PromptStyler synthesizes diverse styles in a joint vision-language space via learnable style word vectors for pseudo-words " + }, + { + "bbox": [ + 304, + 502, + 547, + 563 + ], + "type": "inline_equation", + "content": "S_{*}" + }, + { + "bbox": [ + 304, + 502, + 547, + 563 + ], + "type": "text", + "content": " without using any images." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 580, + 547, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 547, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 547, + 629 + ], + "type": "text", + "content": "it is unclear which source domains are ideal for DG, since arbitrary unseen domains should be addressed. Furthermore, it is costly and sometimes even infeasible to collect and annotate large-scale multi-source domain data for training." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 630, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 548, + 714 + ], + "type": "text", + "content": "We notice that a large-scale pre-trained model might have already observed a great variety of domains and thus can be used as an efficient proxy of actual multiple source domains. From this perspective, we raised a question \"Could we further improve model's generalization capability by simulating various distribution shifts in the latent space of such a large-scale model without using any source domain data?\" If this" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15702" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 298, + 240 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 298, + 240 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 298, + 240 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 298, + 240 + ], + "type": "image", + "image_path": "b7e0632f0fd96cc7b1ef303d1293082b8acc6fb50817a4b4a1ec1677ffda0dca.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 243, + 547, + 293 + ], + "lines": [ + { + "bbox": [ + 45, + 243, + 547, + 293 + ], + "spans": [ + { + "bbox": [ + 45, + 243, + 547, + 293 + ], + "type": "text", + "content": "Figure 2: Important factors in the proposed method. PromptStyler learns style word vectors for pseudo-words " + }, + { + "bbox": [ + 45, + 243, + 547, + 293 + ], + "type": "inline_equation", + "content": "S_{*}" + }, + { + "bbox": [ + 45, + 243, + 547, + 293 + ], + "type": "text", + "content": " which lead to diverse style features (from \"a " + }, + { + "bbox": [ + 45, + 243, + 547, + 293 + ], + "type": "inline_equation", + "content": "S_{*}" + }, + { + "bbox": [ + 45, + 243, + 547, + 293 + ], + "type": "text", + "content": " style of a\") while preserving content information encoded in style-content features (from \"a " + }, + { + "bbox": [ + 45, + 243, + 547, + 293 + ], + "type": "inline_equation", + "content": "S_{*}" + }, + { + "bbox": [ + 45, + 243, + 547, + 293 + ], + "type": "text", + "content": " style of a [class])\". " + }, + { + "bbox": [ + 45, + 243, + 547, + 293 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{style}}" + }, + { + "bbox": [ + 45, + 243, + 547, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 243, + 547, + 293 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{content}}" + }, + { + "bbox": [ + 45, + 243, + 547, + 293 + ], + "type": "text", + "content": " are the loss functions used for maximizing style diversity and content consistency in a hyperspherical joint vision-language space (e.g., CLIP [50] latent space)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 302, + 70, + 545, + 240 + ], + "blocks": [ + { + "bbox": [ + 302, + 70, + 545, + 240 + ], + "lines": [ + { + "bbox": [ + 302, + 70, + 545, + 240 + ], + "spans": [ + { + "bbox": [ + 302, + 70, + 545, + 240 + ], + "type": "image", + "image_path": "14762db21e7aff5a1db84fe2b1d15b30decec8136ce0249ce961c876a8f29113.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 306, + 288, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 306, + 288, + 366 + ], + "spans": [ + { + "bbox": [ + 46, + 306, + 288, + 366 + ], + "type": "text", + "content": "is possible, DG will become immensely practical by effectively and efficiently exploiting such a large-scale model. However, this approach is much more challenging since any actual data of source and target domains are not accessible but only the target task definition (e.g., class names) is given." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 367, + 287, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 367, + 287, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 367, + 287, + 534 + ], + "type": "text", + "content": "In this paper, we argue that large-scale vision-language models [26, 50, 64] could shed light on this challenging source-free domain generalization. As conceptually illustrated in Figure 1(a), text features could effectively represent their relevant image features in a joint vision-language space. Despite the modality gap between two modalities in the joint space [39], a recent study has demonstrated the cross-modal transferability phenomenon [67]; we could train a classifier using text features while running an inference with the classifier using image features. This training procedure meets the necessary condition for the source-free domain generalization, i.e., source domain images are not required. Using such a joint vision-language space, we could simulate various distribution shifts via prompts without any images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 534, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 287, + 653 + ], + "type": "text", + "content": "We propose a prompt-driven style generation method, dubbed PromptStyler, which synthesizes diverse styles via learnable word vectors to simulate distribution shifts in a hyperspherical joint vision-language space. PromptStyler is motivated by the observation that a shared style of images could characterize a domain [27, 74] and such a shared style could be captured by a learnable word vector for a pseudoword " + }, + { + "bbox": [ + 46, + 534, + 287, + 653 + ], + "type": "inline_equation", + "content": "S_{*}" + }, + { + "bbox": [ + 46, + 534, + 287, + 653 + ], + "type": "text", + "content": " using CLIP [50] with a prompt (\"a painting in the style of " + }, + { + "bbox": [ + 46, + 534, + 287, + 653 + ], + "type": "inline_equation", + "content": "S_{*}" + }, + { + "bbox": [ + 46, + 534, + 287, + 653 + ], + "type": "text", + "content": ") [17]. As shown in Figure 1(b), our method learns a style word vector for " + }, + { + "bbox": [ + 46, + 534, + 287, + 653 + ], + "type": "inline_equation", + "content": "S_{*}" + }, + { + "bbox": [ + 46, + 534, + 287, + 653 + ], + "type": "text", + "content": " to represent each style." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "text", + "content": "To effectively simulate various distribution shifts, we try to maximize style diversity as illustrated in Figure 2. Specifically, our method encourages learnable style word vectors to result in orthogonal style features in the hyperspherical space, where each style feature is obtained from a style prompt" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 306, + 546, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 546, + 390 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 546, + 390 + ], + "type": "text", + "content": "(\"a " + }, + { + "bbox": [ + 304, + 306, + 546, + 390 + ], + "type": "inline_equation", + "content": "S_*" + }, + { + "bbox": [ + 304, + 306, + 546, + 390 + ], + "type": "text", + "content": " style of a\") via a pre-trained text encoder. To prevent learned styles from distorting content information, we also consider content consistency as illustrated in Figure 2. Each style-content feature obtained from a style-content prompt (\"a " + }, + { + "bbox": [ + 304, + 306, + 546, + 390 + ], + "type": "inline_equation", + "content": "S_*" + }, + { + "bbox": [ + 304, + 306, + 546, + 390 + ], + "type": "text", + "content": " style of a [class]) is forced to be located closer to its corresponding content feature obtained from a content prompt (\"[class]\") than the other content features." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 390, + 546, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 546, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 546, + 533 + ], + "type": "text", + "content": "Learned style word vectors are used to synthesize style-content features for training a classifier; these synthesized features could simulate images of known contents with diverse unknown styles in the joint space. These style-content features are fed as input to a linear classifier which is trained by a classification loss using contents (\"[class]\") as their class labels. At inference time, an image encoder extracts image features from input images, which are fed as input to the trained classifier. Note that the text and image encoders are derived from the same pre-trained vision-language model (e.g., CLIP [50]); the text encoder is only involved in training and the image encoder is only involved at inference time." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 534, + 547, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 605 + ], + "type": "text", + "content": "The proposed method achieves state-of-the-art results on PACS [34], VLCS [15], OfficeHome [60] and DomainNet [48] without using any actual data of source and target domains. It takes just " + }, + { + "bbox": [ + 304, + 534, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\sim 30" + }, + { + "bbox": [ + 304, + 534, + 547, + 605 + ], + "type": "text", + "content": " minutes for the entire training using a single RTX 3090 GPU, and our model is " + }, + { + "bbox": [ + 304, + 534, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\sim 2.6\\times" + }, + { + "bbox": [ + 304, + 534, + 547, + 605 + ], + "type": "text", + "content": " smaller and " + }, + { + "bbox": [ + 304, + 534, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\sim 243\\times" + }, + { + "bbox": [ + 304, + 534, + 547, + 605 + ], + "type": "text", + "content": " faster at inference compared with CLIP [50]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 605, + 503, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 605, + 503, + 616 + ], + "spans": [ + { + "bbox": [ + 317, + 605, + 503, + 616 + ], + "type": "text", + "content": "Our contributions are summarized as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 617, + 547, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 317, + 617, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 617, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 317, + 617, + 545, + 653 + ], + "type": "text", + "content": "- This work is the first attempt to synthesize a variety of styles in a joint vision-language space via prompts to effectively tackle source-free domain generalization." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 654, + 547, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 654, + 547, + 689 + ], + "spans": [ + { + "bbox": [ + 317, + 654, + 547, + 689 + ], + "type": "text", + "content": "- This paper proposes a novel method that effectively simulates images of known contents with diverse unknown styles in a joint vision-language space." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 689, + 545, + 714 + ], + "type": "text", + "content": "- PromptStyler achieves the state of the art on domain generalization benchmarks without using any images." + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15703" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 287, + 135 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 287, + 135 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 287, + 135 + ], + "type": "table", + "html": "
SetupSourceTargetTask Definition
DA✓✓✓
DG✓-✓
Source-free DA-✓✓
Source-free DG--✓
", + "image_path": "7ec19ae78c9b78e06912a4acd3f5827b3b6126782538ba36d423ddf742593f7d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 139, + 287, + 175 + ], + "lines": [ + { + "bbox": [ + 47, + 139, + 287, + 175 + ], + "spans": [ + { + "bbox": [ + 47, + 139, + 287, + 175 + ], + "type": "text", + "content": "Table 1: Different requirements in each setup. Source-free DG only assumes the task definition (i.e., what should be predicted) without requiring source and target domain data." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 189, + 134, + 202 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 189, + 134, + 202 + ], + "spans": [ + { + "bbox": [ + 47, + 189, + 134, + 202 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 209, + 289, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 209, + 289, + 400 + ], + "spans": [ + { + "bbox": [ + 47, + 209, + 289, + 400 + ], + "type": "text", + "content": "Domain Generalization. Model's generalization capability to arbitrary unseen domains is the key factor to successful deployment of neural networks in real-world applications, since substantial distribution shifts between source and target domains could significantly degrade their performance [23, 52]. To this end, Domain Generalization (DG) [4, 5, 10, 16, 21, 29, 35, 37, 44, 45, 61, 69] has been studied. It assumes target domain data are not accessible while using data from source domains. Generally speaking, existing DG methods could be divided into two categories: multi-source DG [3, 12, 36, 42, 43, 51, 55, 63, 73, 74] and single-source DG [14, 38, 49, 62]. Mostly, multi-source DG methods aim to learn domain-invariant features by exploiting available multiple source domains, and single-source DG methods also aim to learn such features by generating diverse domains based on a single domain and then exploiting the synthesized domains." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 402, + 289, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 402, + 289, + 617 + ], + "spans": [ + { + "bbox": [ + 47, + 402, + 289, + 617 + ], + "type": "text", + "content": "Source-free Domain Generalization. In this setup, we are not able to access any source and target domains as summarized in Table 1. Thus, source-free DG is much more challenging than multi-source and single-source DG. From the observation that synthesizing new domains from the given source domain could effectively improve model's generalization capability [27,38,62,72,73], we also try to generate diverse domains but without using any source domains to deal with source-free DG. By leveraging a large-scale pre-trained model which has already seen a great variety of domains, our method could simulate various distribution shifts in the latent space of the large-scale model. This approach has several advantages compared with existing DG methods; source domain images are not required and there is no concern for catastrophic forgetting which might impede model's generalization capability. Also, it would be immensely practical to exploit such a large-scale model for downstream visual recognition tasks, since we only need the task definition." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": "Large-scale model in Domain Generalization. Recently, several DG methods [5, 53] exploit a large-scale pre-trained model (e.g., CLIP [50]) to leverage its great generalization capability. While training neural networks on available data, CAD [53] and MIRO [5] try to learn robust features using such a large-scale model. Compared with them, the proposed method could learn domain-invariant features using a large-scale pre-trained model without requiring any actual data." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "content": "Joint vision-language space. Large-scale vision-language models [26, 50, 64] are trained with a great amount of image-text pairs, and achieve state-of-the-art results on downstream visual recognition tasks [20, 41, 66, 70, 71]. By leveraging their joint vision-language spaces, we could also effectively manipulate visual features via prompts [13, 18, 31, 47]. Interestingly, Textual Inversion [17] shows that a learnable style word vector for a pseudo-word " + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "inline_equation", + "content": "S_{*}" + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "content": " could capture a shared style of images using CLIP [50] with a prompt (\"a painting in the style of " + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "inline_equation", + "content": "S_{*}" + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "content": "\"). From this observation, we argue that learnable style word vectors would be able to seek a variety of styles for simulating various distribution shifts in a joint vision-language space without using any images." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 236, + 362, + 249 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 236, + 362, + 249 + ], + "spans": [ + { + "bbox": [ + 306, + 236, + 362, + 249 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 257, + 547, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 257, + 547, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 257, + 547, + 437 + ], + "type": "text", + "content": "The overall framework of the proposed method is shown in Figure 3, and pseudo-code of PromptStyler is described in Algorithm 1. Our method learns style word vectors to represent a variety of styles in a hyperspherical joint vision-language space (e.g., CLIP [50] latent space). After learning those style word vectors, we train a linear classifier using synthesized style-content features produced by a pre-trained text encoder " + }, + { + "bbox": [ + 304, + 257, + 547, + 437 + ], + "type": "inline_equation", + "content": "T(\\cdot)" + }, + { + "bbox": [ + 304, + 257, + 547, + 437 + ], + "type": "text", + "content": ". At inference time, a pre-trained image encoder " + }, + { + "bbox": [ + 304, + 257, + 547, + 437 + ], + "type": "inline_equation", + "content": "I(\\cdot)" + }, + { + "bbox": [ + 304, + 257, + 547, + 437 + ], + "type": "text", + "content": " extracts image features from input images, which are fed as input to the trained linear classifier. Thanks to the cross-modal transferability phenomenon of the joint vision-language space [67], this classifier could produce class scores using the image features. Note that we exploit CLIP as our large-scale vision-language model; its image encoder and text encoder are frozen in our entire framework." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 442, + 474, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 442, + 474, + 455 + ], + "spans": [ + { + "bbox": [ + 306, + 442, + 474, + 455 + ], + "type": "text", + "content": "3.1. Prompt-driven style generation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "text", + "content": "An input text prompt is converted to several tokens via a tokenization process, and then such tokens are replaced by their corresponding word vectors via a word lookup process. In PromptStyler, a pseudo-word " + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "text", + "content": " in a prompt is a placeholder which is replaced by a style word vector " + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "text", + "content": " during the word lookup process. Note that three kinds of prompts are used in the proposed method: a style prompt " + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_i^{\\mathrm{style}}" + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "text", + "content": " (\"a " + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "text", + "content": " style of a\"), a content prompt " + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_m^{\\mathrm{content}}" + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "text", + "content": " (\"[class] " + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "text", + "content": "\"), and a style-content prompt " + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_i^{\\mathrm{style}} \\circ \\mathcal{P}_m^{\\mathrm{content}}" + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "text", + "content": " (\"a " + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "text", + "content": " style of a [class] " + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "text", + "content": "\"). " + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "text", + "content": " indicates the placeholder for " + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "text", + "content": "-th style word vector and [class] " + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "text", + "content": " denotes " + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 461, + 547, + 594 + ], + "type": "text", + "content": "-th class name." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": "Suppose we want to generate " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " different styles in a joint vision-language space. In this case, the proposed method needs to learn " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " style word vectors " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{s}_i\\}_{i=1}^K" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": ", where each " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " is randomly initialized at the beginning. To effectively simulate various distribution shifts in the joint vision-language space, those style word vectors need to be diverse while not distorting content information when they are exploited in style-content prompts. There are two possible design choices for learning such word vectors: (1) learning each style word vector " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " in a sequential manner, or (2) learning all style" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15704" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 91, + 321, + 257 + ], + "blocks": [ + { + "bbox": [ + 111, + 75, + 258, + 87 + ], + "lines": [ + { + "bbox": [ + 111, + 75, + 258, + 87 + ], + "spans": [ + { + "bbox": [ + 111, + 75, + 258, + 87 + ], + "type": "text", + "content": "(i) Prompt-driven style generation" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 48, + 91, + 321, + 257 + ], + "lines": [ + { + "bbox": [ + 48, + 91, + 321, + 257 + ], + "spans": [ + { + "bbox": [ + 48, + 91, + 321, + 257 + ], + "type": "image", + "image_path": "5d6b5fea955f54effc6924315ad9121f02bb0063f474b3059c065d3fcbc14752.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 328, + 99, + 542, + 153 + ], + "blocks": [ + { + "bbox": [ + 329, + 75, + 543, + 87 + ], + "lines": [ + { + "bbox": [ + 329, + 75, + 543, + 87 + ], + "spans": [ + { + "bbox": [ + 329, + 75, + 543, + 87 + ], + "type": "text", + "content": "(ii) Training a linear classifier using diverse styles" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 328, + 99, + 542, + 153 + ], + "lines": [ + { + "bbox": [ + 328, + 99, + 542, + 153 + ], + "spans": [ + { + "bbox": [ + 328, + 99, + 542, + 153 + ], + "type": "image", + "image_path": "a0ac41ba6eafb7f255d2e0c841115d9450a4d2716c206f457ff2dbf18ffb0cea.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 424, + 159, + 541, + 169 + ], + "lines": [ + { + "bbox": [ + 424, + 159, + 541, + 169 + ], + "spans": [ + { + "bbox": [ + 424, + 159, + 541, + 169 + ], + "type": "text", + "content": "Frozen weights " + }, + { + "bbox": [ + 424, + 159, + 541, + 169 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 424, + 159, + 541, + 169 + ], + "type": "text", + "content": " normalization layer" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 344, + 196, + 541, + 253 + ], + "blocks": [ + { + "bbox": [ + 350, + 173, + 523, + 185 + ], + "lines": [ + { + "bbox": [ + 350, + 173, + 523, + 185 + ], + "spans": [ + { + "bbox": [ + 350, + 173, + 523, + 185 + ], + "type": "text", + "content": "(iii) Inference using the trained classifier" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 344, + 196, + 541, + 253 + ], + "lines": [ + { + "bbox": [ + 344, + 196, + 541, + 253 + ], + "spans": [ + { + "bbox": [ + 344, + 196, + 541, + 253 + ], + "type": "image", + "image_path": "8a9be02778762e0c40bea03a8b2d0dbc0dcd97108b318eb7c3f4e1cc122a2efb.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 424, + 256, + 541, + 266 + ], + "lines": [ + { + "bbox": [ + 424, + 256, + 541, + 266 + ], + "spans": [ + { + "bbox": [ + 424, + 256, + 541, + 266 + ], + "type": "text", + "content": "Frozen weights " + }, + { + "bbox": [ + 424, + 256, + 541, + 266 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 424, + 256, + 541, + 266 + ], + "type": "text", + "content": " normalization layer" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 46, + 273, + 547, + 334 + ], + "lines": [ + { + "bbox": [ + 46, + 273, + 547, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 547, + 334 + ], + "type": "text", + "content": "Figure 3: PromptStyler learns diverse style word vectors which do not distort content information of style-content prompts. After learning style word vectors, we synthesize style-content features (e.g., from \"a " + }, + { + "bbox": [ + 46, + 273, + 547, + 334 + ], + "type": "inline_equation", + "content": "S_{1}" + }, + { + "bbox": [ + 46, + 273, + 547, + 334 + ], + "type": "text", + "content": " style of a dog\") via a pre-trained text encoder for training a linear classifier. The classifier is trained by a classification loss using those synthesized features and their corresponding class labels (e.g., \"dog\"). At inference time, a pre-trained image encoder extracts image features, which are fed as input to the trained classifier. Note that the encoders are derived from the same vision-language model (e.g., CLIP [50])." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 349, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 349, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 349, + 287, + 396 + ], + "type": "text", + "content": "word vectors " + }, + { + "bbox": [ + 46, + 349, + 287, + 396 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{s}_i\\}_{i=1}^K" + }, + { + "bbox": [ + 46, + 349, + 287, + 396 + ], + "type": "text", + "content": " in a parallel manner. We choose the former, since it takes much less memory during training. Please refer to the supplementary material (Section A.2) for the empirical justification of our design choice." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "text", + "content": "Style diversity loss. To maximize the diversity of " + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "text", + "content": " styles in a hyperspherical joint vision-language space, we sequentially learn style word vectors " + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{s}_i\\}_{i=1}^K" + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "text", + "content": " in such a way that " + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "text", + "content": "-th style feature " + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "inline_equation", + "content": "T(\\mathcal{P}_i^{\\mathrm{style}}) \\in \\mathbb{R}^C" + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "text", + "content": " produced by " + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "text", + "content": "-th style word vector " + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i" + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "text", + "content": " is orthogonal to " + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "inline_equation", + "content": "\\{T(\\mathcal{P}_j^{\\mathrm{style}})\\}_{j=1}^{i-1}" + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "text", + "content": " produced by previously learned style word vectors " + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{s}_j\\}_{j=1}^{i-1}" + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "text", + "content": ". Regarding this, the style diversity loss " + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{style}}" + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "text", + "content": " for learning " + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "text", + "content": "-th style word vector " + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i" + }, + { + "bbox": [ + 46, + 396, + 288, + 498 + ], + "type": "text", + "content": " is computed by" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 53, + 505, + 287, + 539 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 505, + 287, + 539 + ], + "spans": [ + { + "bbox": [ + 53, + 505, + 287, + 539 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s t y l e}} = \\frac {1}{i - 1} \\sum_ {j = 1} ^ {i - 1} \\left| \\frac {T \\left(\\mathcal {P} _ {i} ^ {\\text {s t y l e}}\\right)}{\\| T \\left(\\mathcal {P} _ {i} ^ {\\text {s t y l e}}\\right) \\| _ {2}} \\cdot \\frac {T \\left(\\mathcal {P} _ {j} ^ {\\text {s t y l e}}\\right)}{\\| T \\left(\\mathcal {P} _ {j} ^ {\\text {s t y l e}}\\right) \\| _ {2}} \\right|. \\tag {1}", + "image_path": "0b254bfe01b4e9ab12115b8699468a726b7d070ef0c76972bbd7ea311f214c90.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 545, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 605 + ], + "type": "text", + "content": "This style loss " + }, + { + "bbox": [ + 46, + 545, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{style}}" + }, + { + "bbox": [ + 46, + 545, + 287, + 605 + ], + "type": "text", + "content": " aims to minimize the absolute value of the cosine similarity between " + }, + { + "bbox": [ + 46, + 545, + 287, + 605 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 545, + 287, + 605 + ], + "type": "text", + "content": "-th style features and each of the existing style features. When the value of this loss becomes zero, it satisfies the orthogonality between " + }, + { + "bbox": [ + 46, + 545, + 287, + 605 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 545, + 287, + 605 + ], + "type": "text", + "content": "-th style feature and all the existing style features." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 605, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 288, + 714 + ], + "type": "text", + "content": "Content consistency loss. Learning the style word vectors " + }, + { + "bbox": [ + 47, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{s}_i\\}_{i = 1}^K" + }, + { + "bbox": [ + 47, + 605, + 288, + 714 + ], + "type": "text", + "content": " only using the style diversity loss sometimes leads to undesirable outcome, since a learned style " + }, + { + "bbox": [ + 47, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i" + }, + { + "bbox": [ + 47, + 605, + 288, + 714 + ], + "type": "text", + "content": " could substantially distort content information when used to generate a style-content feature " + }, + { + "bbox": [ + 47, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "T(\\mathcal{P}_i^{\\mathrm{style}}\\circ \\mathcal{P}_m^{\\mathrm{content}})\\in \\mathbb{R}^C" + }, + { + "bbox": [ + 47, + 605, + 288, + 714 + ], + "type": "text", + "content": ". To alleviate this problem, we encourage the content information in the style-content feature to be consistent with its corresponding content feature " + }, + { + "bbox": [ + 47, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "T(\\mathcal{P}_m^{\\mathrm{content}})\\in \\mathbb{R}^C" + }, + { + "bbox": [ + 47, + 605, + 288, + 714 + ], + "type": "text", + "content": " while learning each " + }, + { + "bbox": [ + 47, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 605, + 288, + 714 + ], + "type": "text", + "content": "-th style word vector " + }, + { + "bbox": [ + 47, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i" + }, + { + "bbox": [ + 47, + 605, + 288, + 714 + ], + "type": "text", + "content": ". Specifically, each style-content" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 349, + 547, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 349, + 547, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 349, + 547, + 422 + ], + "type": "text", + "content": "feature synthesized via " + }, + { + "bbox": [ + 304, + 349, + 547, + 422 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 349, + 547, + 422 + ], + "type": "text", + "content": "-th style word vector " + }, + { + "bbox": [ + 304, + 349, + 547, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i" + }, + { + "bbox": [ + 304, + 349, + 547, + 422 + ], + "type": "text", + "content": " should have the highest cosine similarity score with its corresponding content feature. 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This content loss " + }, + { + "bbox": [ + 304, + 535, + 545, + 606 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{content}}" + }, + { + "bbox": [ + 304, + 535, + 545, + 606 + ], + "type": "text", + "content": " is a contrastive loss which encourages each style-content feature to be located closer to its corresponding content feature so that it forces each " + }, + { + "bbox": [ + 304, + 535, + 545, + 606 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 535, + 545, + 606 + ], + "type": "text", + "content": "-th style word vector " + }, + { + "bbox": [ + 304, + 535, + 545, + 606 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i" + }, + { + "bbox": [ + 304, + 535, + 545, + 606 + ], + "type": "text", + "content": " to preserve content information when used to synthesize style-content features." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 607, + 547, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 607, + 547, + 668 + ], + "spans": [ + { + "bbox": [ + 304, + 607, + 547, + 668 + ], + "type": "text", + "content": "Total prompt loss. 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In the proposed method, the total loss " + }, + { + "bbox": [ + 304, + 607, + 547, + 668 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{prompt}}" + }, + { + "bbox": [ + 304, + 607, + 547, + 668 + ], + "type": "text", + "content": " for learning " + }, + { + "bbox": [ + 304, + 607, + 547, + 668 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 607, + 547, + 668 + ], + "type": "text", + "content": "-th style word vector is computed by" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 364, + 672, + 545, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 672, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 364, + 672, + 545, + 685 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p r o m p t}} = \\mathcal {L} _ {\\text {s t y l e}} + \\mathcal {L} _ {\\text {c o n t e n t}}. \\tag {4}", + "image_path": "12249778c56651b0670f46e3f1a91020c014939ba0bcc2112fe00d76cef4ac8a.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "Using this prompt loss " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{prompt}}" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": ", we train " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "-th style word vector " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": " training iterations." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15705" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 47, + 71, + 289, + 343 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": "Algorithm 1 PromptStyler \nRequirement: pre-trained text encoder " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "T(\\cdot)" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": ", pre-defined " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " class names in the target task \nInput: number of style word vectors " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": ", number of training iterations " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " \nOutput: " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "KN" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " style-content features \n # randomly initialize style word vectors \n1: " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{s}_i\\}_{i=1}^K \\leftarrow" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " random_init(" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{s}_i\\}_{i=1}^K" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": ") \n # sequentially learn " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " style word vectors \n2: for " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "i = 1, 2, \\ldots, K" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " do \n # " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " training iterations for learning each word vector \n3: for iteration " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "= 1, 2, \\ldots, L" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " do \n # compute " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{style}}" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "T(\\cdot)" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " and word vectors \n4: " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{style}} \\leftarrow" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " style_diversity_loss(" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{s}_j\\}_{j=1}^{i-1}" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": ") \n # compute " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{content}}" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "T(\\cdot)" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " and a word vector \n5: " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{content}} \\leftarrow" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " content_consistency_loss(" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": ") \n6: " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{prompt}} \\leftarrow \\mathcal{L}_{\\text{style}} + \\mathcal{L}_{\\text{content}}" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " \n7: Update " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{prompt}}" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " by gradient descent \n8: end for \n9: end for \n10: Synthesize " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "KN" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " style-content features using the learned " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " style word vectors and " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "text", + "content": " class names via " + }, + { + "bbox": [ + 47, + 71, + 289, + 343 + ], + "type": "inline_equation", + "content": "T(\\cdot)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_body" + } + ], + "index": 0, + "sub_type": "algorithm" + }, + { + "bbox": [ + 47, + 365, + 284, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 365, + 284, + 378 + ], + "spans": [ + { + "bbox": [ + 47, + 365, + 284, + 378 + ], + "type": "text", + "content": "3.2. Training a linear classifier using diverse styles" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "type": "text", + "content": "After learning " + }, + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "type": "text", + "content": " style word vectors " + }, + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{s}_i\\}_{i = 1}^K" + }, + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "type": "text", + "content": ", we generate " + }, + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "type": "inline_equation", + "content": "KN" + }, + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "type": "text", + "content": " style-content features for training a linear classifier. To be specific, we synthesize those features using the learned " + }, + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "type": "text", + "content": " styles and pre-defined " + }, + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "type": "text", + "content": " classes via the text encoder " + }, + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "type": "inline_equation", + "content": "T(\\cdot)" + }, + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "type": "text", + "content": ". The linear classifier is trained by a classification loss using " + }, + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "type": "text", + "content": "-normalized style-content features and their class labels; each class label is the class name used to generate each style-content feature. To effectively leverage the hyperspherical joint vision-language space, we adopt ArcFace [8] loss as our classification loss " + }, + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{class}}" + }, + { + "bbox": [ + 46, + 384, + 290, + 589 + ], + "type": "text", + "content": ". Note that ArcFace loss is an angular Softmax loss which computes the cosine similarities between classifier input features and classifier weights with an additive angular margin penalty between classes. This angular margin penalty allows for more discriminative predictions by pushing features from different classes further apart. Thanks to the property, this angular Softmax loss has been widely used in visual recognition tasks [7,9,30,40,65]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 598, + 241, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 598, + 241, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 598, + 241, + 611 + ], + "type": "text", + "content": "3.3. Inference using the trained classifier" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": "The trained classifier is used with a pre-trained image encoder " + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "inline_equation", + "content": "I(\\cdot)" + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": " at inference time. Given an input image " + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": ", the image encoder extracts its image feature " + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "inline_equation", + "content": "I(\\mathbf{x}) \\in \\mathbb{R}^{C}" + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": ", which is mapped to the hyperspherical joint vision-language space by " + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\ell_{2}" + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": " normalization. Then, the trained classifier produces class scores using the " + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\ell_{2}" + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": "-normalized image feature. Note that the text encoder " + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "inline_equation", + "content": "T(\\cdot)" + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": " is not used at inference time, while the image encoder " + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "inline_equation", + "content": "I(\\cdot)" + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": " is only exploited at inference time." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 71, + 388, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 388, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 388, + 85 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 91, + 545, + 116 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 91, + 545, + 116 + ], + "spans": [ + { + "bbox": [ + 306, + 91, + 545, + 116 + ], + "type": "text", + "content": "For more comprehensive understanding, please refer to the supplementary material (Section B and D)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 123, + 421, + 135 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 123, + 421, + 135 + ], + "spans": [ + { + "bbox": [ + 306, + 123, + 421, + 135 + ], + "type": "text", + "content": "4.1. Evaluation datasets" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 142, + 547, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 142, + 547, + 274 + ], + "spans": [ + { + "bbox": [ + 304, + 142, + 547, + 274 + ], + "type": "text", + "content": "The proposed method does not require any actual data for training. To analyze its generalization capability, four domain generalization benchmarks are used for evaluation: PACS [34] (4 domains and 7 classes), VLCS [15] (4 domains and 5 classes), OfficeHome [60] (4 domains and 65 classes) and DomainNet [48] (6 domains and 345 classes). On these benchmarks, we repeat each experiment three times using different random seeds and report average top-1 classification accuracies with standard errors. Unlike the leave-one-domain-out cross-validation evaluation protocol [21], we do not exploit any source domain data for training." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 281, + 437, + 294 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 281, + 437, + 294 + ], + "spans": [ + { + "bbox": [ + 306, + 281, + 437, + 294 + ], + "type": "text", + "content": "4.2. Implementation details" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 300, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 545, + 335 + ], + "type": "text", + "content": "PromptStyler is implemented and trained with the same configuration regardless of the evaluation datasets. Training takes about 30 minutes using a single RTX 3090 GPU." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 336, + 547, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 336, + 547, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 336, + 547, + 479 + ], + "type": "text", + "content": "Architecture. We choose CLIP [50] as our large-scale pretrained vision-language model, and use the publicly available pre-trained model." + }, + { + "bbox": [ + 304, + 336, + 547, + 479 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 304, + 336, + 547, + 479 + ], + "type": "text", + "content": " The text encoder " + }, + { + "bbox": [ + 304, + 336, + 547, + 479 + ], + "type": "inline_equation", + "content": "T(\\cdot)" + }, + { + "bbox": [ + 304, + 336, + 547, + 479 + ], + "type": "text", + "content": " used in training is Transformer [59] and the image encoder " + }, + { + "bbox": [ + 304, + 336, + 547, + 479 + ], + "type": "inline_equation", + "content": "I(\\cdot)" + }, + { + "bbox": [ + 304, + 336, + 547, + 479 + ], + "type": "text", + "content": " used at inference is ResNet-50 [22] as default setting in experiments; our method is also implemented with ViT-B/16 [11] or ViT-L/14 [11] for further evaluations as shown in Table 2. Note that text and image encoders are derived from the same CLIP model and frozen in the entire pipeline. The dimension of each text feature or image feature is " + }, + { + "bbox": [ + 304, + 336, + 547, + 479 + ], + "type": "inline_equation", + "content": "C = 1024" + }, + { + "bbox": [ + 304, + 336, + 547, + 479 + ], + "type": "text", + "content": " when our method is implemented with ResNet-50, while " + }, + { + "bbox": [ + 304, + 336, + 547, + 479 + ], + "type": "inline_equation", + "content": "C = 512" + }, + { + "bbox": [ + 304, + 336, + 547, + 479 + ], + "type": "text", + "content": " in the case of ViT-B/16 and " + }, + { + "bbox": [ + 304, + 336, + 547, + 479 + ], + "type": "inline_equation", + "content": "C = 768" + }, + { + "bbox": [ + 304, + 336, + 547, + 479 + ], + "type": "text", + "content": " in the case of ViT-L/14." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "text", + "content": "Learning style word vectors. We follow prompt learning methods [70, 71] when learning the word vectors. Using a zero-mean Gaussian distribution with 0.02 standard deviation, we randomly initialize " + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "text", + "content": " style word vectors " + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{s}_i\\}_{i=1}^K" + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "inline_equation", + "content": "K = 80" + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "text", + "content": ". The dimension of each style word vector is " + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "inline_equation", + "content": "D = 512" + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "text", + "content": " when the proposed method is implemented with ResNet-50 [22] or ViT-B/16 [11], while " + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "inline_equation", + "content": "D = 768" + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "text", + "content": " in the case of ViT-L/14 [11]. Each " + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "text", + "content": "-th style word vector " + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i" + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "text", + "content": " is trained by the prompt loss " + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{prompt}}" + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "inline_equation", + "content": "L = 100" + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "text", + "content": " training iterations using the SGD optimizer with 0.002 learning rate and 0.9 momentum. The number of classes " + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "text", + "content": " is pre-defined by each target task definition, e.g., " + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "inline_equation", + "content": "N = 345" + }, + { + "bbox": [ + 304, + 480, + 547, + 624 + ], + "type": "text", + "content": " for DomainNet [48]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 624, + 547, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 624, + 547, + 671 + ], + "spans": [ + { + "bbox": [ + 304, + 624, + 547, + 671 + ], + "type": "text", + "content": "Training a linear classifier. The classifier is trained for 50 epochs using the SGD optimizer with 0.005 learning rate, 0.9 momentum, and a batch size of 128. In ArcFace [8] loss, its scaling factor is set to 5 with 0.5 angular margin." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 672, + 547, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 672, + 547, + 695 + ], + "spans": [ + { + "bbox": [ + 304, + 672, + 547, + 695 + ], + "type": "text", + "content": "Inference. Input images are pre-processed in the same way with the CLIP model; resized to " + }, + { + "bbox": [ + 304, + 672, + 547, + 695 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 672, + 547, + 695 + ], + "type": "text", + "content": " and normalized." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 317, + 702, + 466, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 702, + 466, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 702, + 466, + 713 + ], + "type": "text", + "content": "1https://github.com/openai/CLIP" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15706" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 547, + 406 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 547, + 406 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 547, + 406 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 547, + 406 + ], + "type": "table", + "html": "
MethodConfigurationAccuracy (%)
Source DomainDomain DescriptionPACSVLCSOfficeHomeDomainNetAvg.
ResNet-50 [22] with pre-trained weights on ImageNet [6]
DANN [19]✓-83.6±0.478.6±0.465.9±0.638.3±0.166.6
RSC [25]✓-85.2±0.977.1±0.565.5±0.938.9±0.566.7
MLDG [35]✓-84.9±1.077.2±0.466.8±0.641.2±0.167.5
SagNet [46]✓-86.3±0.277.8±0.568.1±0.140.3±0.168.1
SelfReg [28]✓-85.6±0.477.8±0.967.9±0.742.8±0.068.5
GVRT [44]✓-85.1±0.379.0±0.270.1±0.144.1±0.169.6
MIRO [5]✓-85.4±0.479.0±0.070.5±0.444.3±0.269.8
ResNet-50 [22] with pre-trained weights from CLIP [50]
ZS-CLIP (C) [50]--90.6±0.076.0±0.068.6±0.045.6±0.070.2
CAD [53]✓-90.0±0.681.2±0.670.5±0.345.5±2.171.8
ZS-CLIP (PC) [50]-✓90.7±0.080.1±0.072.0±0.046.2±0.072.3
PromptStyler--93.2±0.082.3±0.173.6±0.149.5±0.074.7
ViT-B/16 [11] with pre-trained weights from CLIP [50]
ZS-CLIP (C) [50]--95.7±0.076.4±0.079.9±0.057.8±0.077.5
MIRO [5]✓-95.682.282.554.078.6
ZS-CLIP (PC) [50]-✓96.1±0.082.4±0.082.3±0.057.7±0.079.6
PromptStyler--97.2±0.182.9±0.083.6±0.059.4±0.080.8
ViT-L/14 [11] with pre-trained weights from CLIP [50]
ZS-CLIP (C) [50]--97.6±0.077.5±0.085.9±0.063.3±0.081.1
ZS-CLIP (PC) [50]-✓98.5±0.082.4±0.086.9±0.064.0±0.083.0
PromptStyler--98.6±0.082.4±0.289.1±0.065.5±0.083.9
", + "image_path": "4c7f581d90a25ba0ca2bf38257c93d7ac9e23a3261b26f859337f40f820110f9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 466, + 126, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 466, + 126, + 478 + ], + "spans": [ + { + "bbox": [ + 46, + 466, + 126, + 478 + ], + "type": "text", + "content": "4.3. Evaluations" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 485, + 288, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 485, + 288, + 665 + ], + "spans": [ + { + "bbox": [ + 45, + 485, + 288, + 665 + ], + "type": "text", + "content": "Main results. PromptStyler achieves the state of the art in every evaluation on PACS [34], VLCS [15], OfficeHome [60] and DomainNet [48] as shown in Table 2. Note that all existing methods utilize source domain data except for zero-shot CLIP [50] in Table 2. Compared with zero-shot CLIP which generates each text feature using a domain-agnostic prompt (\"[class]\", PromptStyler largely outperforms its records in all evaluations. Our method also shows higher accuracy compared with zero-shot CLIP which produces each text feature using a domain-specific prompt (\"a photo of a [class]\", even though we do not exploit any domain descriptions. These results confirm that the proposed method effectively improves the generalization capability of the chosen pre-trained model, i.e., CLIP, without using any images by simulating various distribution shifts via prompts in its latent space." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "content": "Computational evaluations. In Table 3, we compare our PromptStyler and zero-shot CLIP [50] in terms of the number of parameters and inference speed; the inference speed was measured using a single RTX 3090 GPU with a batch size" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 309, + 464, + 545, + 577 + ], + "blocks": [ + { + "bbox": [ + 45, + 409, + 546, + 445 + ], + "lines": [ + { + "bbox": [ + 45, + 409, + 546, + 445 + ], + "spans": [ + { + "bbox": [ + 45, + 409, + 546, + 445 + ], + "type": "text", + "content": "Table 2: Comparison with the state-of-the-art domain generalization methods. ZS-CLIP (C) denotes zero-shot CLIP using \"[class]\" as its text prompt, and ZS-CLIP (PC) indicates zero-shot CLIP using \"a photo of a [class]\" as its text prompt. Note that PromptStyler does not exploit any source domain data and domain descriptions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 464, + 545, + 577 + ], + "lines": [ + { + "bbox": [ + 309, + 464, + 545, + 577 + ], + "spans": [ + { + "bbox": [ + 309, + 464, + 545, + 577 + ], + "type": "table", + "html": "
MethodInference Module# ParamsFPS
Image EncoderText Encoder
OfficeHome (65 classes)
ZS-CLIP [50]✓✓102.0M1.6
PromptStyler✓-38.4M72.9
DomainNet (345 classes)
ZS-CLIP [50]✓✓102.0M0.3
PromptStyler✓-38.7M72.9
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Note that we do not exploit a text encoder at inference time, which makes our model " + }, + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\sim 2.6 \\times" + }, + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "type": "text", + "content": " smaller and " + }, + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\sim 243 \\times" + }, + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "type": "text", + "content": " faster compared with CLIP. Regarding the inference speed, the proposed model is about " + }, + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "type": "inline_equation", + "content": "45 \\times" + }, + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "type": "text", + "content": " faster for the target task OfficeHome [60] (65 classes) and it is about " + }, + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "type": "inline_equation", + "content": "243 \\times" + }, + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "type": "text", + "content": " faster for the target task DomainNet [48] (345 classes)." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15707" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 211, + 193 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 211, + 193 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 211, + 193 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 211, + 193 + ], + "type": "image", + "image_path": "7f2a84d5dfccfb3cb966ba8cc3d766e24359d06ca57f37fb7ee70a35d60a9236.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 107, + 198, + 154, + 214 + ], + "lines": [ + { + "bbox": [ + 107, + 198, + 154, + 214 + ], + "spans": [ + { + "bbox": [ + 107, + 198, + 154, + 214 + ], + "type": "text", + "content": "(a) " + }, + { + "bbox": [ + 107, + 198, + 154, + 214 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{style}}" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 217, + 72, + 376, + 193 + ], + "blocks": [ + { + "bbox": [ + 217, + 72, + 376, + 193 + ], + "lines": [ + { + "bbox": [ + 217, + 72, + 376, + 193 + ], + "spans": [ + { + "bbox": [ + 217, + 72, + 376, + 193 + ], + "type": "image", + "image_path": "3b8f69e8e96565e700c30b31ac3ecd4bf4d6cb3a8b7046bf15400ea887a328fe.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 268, + 198, + 326, + 213 + ], + "lines": [ + { + "bbox": [ + 268, + 198, + 326, + 213 + ], + "spans": [ + { + "bbox": [ + 268, + 198, + 326, + 213 + ], + "type": "text", + "content": "(b) " + }, + { + "bbox": [ + 268, + 198, + 326, + 213 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{content}}" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 383, + 72, + 542, + 193 + ], + "blocks": [ + { + "bbox": [ + 383, + 72, + 542, + 193 + ], + "lines": [ + { + "bbox": [ + 383, + 72, + 542, + 193 + ], + "spans": [ + { + "bbox": [ + 383, + 72, + 542, + 193 + ], + "type": "image", + "image_path": "2c93bea5367111625aaeed349e2d76c1493c0b115cafea51078dc4fbc646b969.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 412, + 198, + 513, + 214 + ], + "lines": [ + { + "bbox": [ + 412, + 198, + 513, + 214 + ], + "spans": [ + { + "bbox": [ + 412, + 198, + 513, + 214 + ], + "type": "text", + "content": "(c) " + }, + { + "bbox": [ + 412, + 198, + 513, + 214 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{style}} + \\mathcal{L}_{\\mathrm{content}}" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 50, + 285, + 128, + 365 + ], + "blocks": [ + { + "bbox": [ + 46, + 217, + 547, + 277 + ], + "lines": [ + { + "bbox": [ + 46, + 217, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 547, + 277 + ], + "type": "text", + "content": "Figure 4: t-SNE [58] visualization results for the target task VLCS [15] (5 classes) using synthesized style-content features. We visualize such features obtained from the learned 80 style word vectors " + }, + { + "bbox": [ + 46, + 217, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{s}_i\\}_{i=1}^{80}" + }, + { + "bbox": [ + 46, + 217, + 547, + 277 + ], + "type": "text", + "content": " and all the 5 classes (bird, car, chair, dog, person). Different colors denote features obtained from different style word vectors, and different shapes indicate features obtained from different class names. We only colorize features from the first 10 styles " + }, + { + "bbox": [ + 46, + 217, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{s}_i\\}_{i=1}^{10}" + }, + { + "bbox": [ + 46, + 217, + 547, + 277 + ], + "type": "text", + "content": ". Combining the style diversity loss " + }, + { + "bbox": [ + 46, + 217, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{style}}" + }, + { + "bbox": [ + 46, + 217, + 547, + 277 + ], + "type": "text", + "content": " and content consistency loss " + }, + { + "bbox": [ + 46, + 217, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{content}}" + }, + { + "bbox": [ + 46, + 217, + 547, + 277 + ], + "type": "text", + "content": " leads to diverse styles while preserving content information." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 285, + 128, + 365 + ], + "lines": [ + { + "bbox": [ + 50, + 285, + 128, + 365 + ], + "spans": [ + { + "bbox": [ + 50, + 285, + 128, + 365 + ], + "type": "image", + "image_path": "c920cb1d330be0ab0fa477e01aa864512539d7b86c65db640188f6160a0ea738.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 132, + 285, + 212, + 365 + ], + "blocks": [ + { + "bbox": [ + 132, + 285, + 212, + 365 + ], + "lines": [ + { + "bbox": [ + 132, + 285, + 212, + 365 + ], + "spans": [ + { + "bbox": [ + 132, + 285, + 212, + 365 + ], + "type": "image", + "image_path": "3dd295e1b3285874ae513653efe4afb79f9a382c8e6a17421d7008fa4866e193.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 368, + 546, + 392 + ], + "lines": [ + { + "bbox": [ + 46, + 368, + 546, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 368, + 546, + 392 + ], + "type": "text", + "content": "Figure 5: Text-to-Image synthesis results using style-content features (from \"a " + }, + { + "bbox": [ + 46, + 368, + 546, + 392 + ], + "type": "inline_equation", + "content": "S_{*}" + }, + { + "bbox": [ + 46, + 368, + 546, + 392 + ], + "type": "text", + "content": " style of a cat\") with 6 different style word vectors. By leveraging the proposed method, we could learn a variety of styles while not distorting content information." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 216, + 285, + 294, + 365 + ], + "blocks": [ + { + "bbox": [ + 216, + 285, + 294, + 365 + ], + "lines": [ + { + "bbox": [ + 216, + 285, + 294, + 365 + ], + "spans": [ + { + "bbox": [ + 216, + 285, + 294, + 365 + ], + "type": "image", + "image_path": "f9e2d8a34fd548d59d5bc703ac5c955c554a1fcfdbb9899ab211cd70b2878d2b.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 298, + 285, + 378, + 365 + ], + "blocks": [ + { + "bbox": [ + 298, + 285, + 378, + 365 + ], + "lines": [ + { + "bbox": [ + 298, + 285, + 378, + 365 + ], + "spans": [ + { + "bbox": [ + 298, + 285, + 378, + 365 + ], + "type": "image", + "image_path": "5afdd5c9b4392033a4d1c1dd2f0ff0a0a6410d9c61b11952e21adf67c440b28a.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 382, + 285, + 461, + 365 + ], + "blocks": [ + { + "bbox": [ + 382, + 285, + 461, + 365 + ], + "lines": [ + { + "bbox": [ + 382, + 285, + 461, + 365 + ], + "spans": [ + { + "bbox": [ + 382, + 285, + 461, + 365 + ], + "type": "image", + "image_path": "5d6621cebc43e3eb2fd68b9e36560adcb3f998c0cc7d549ab3ebd6d64c99741c.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 465, + 285, + 544, + 365 + ], + "blocks": [ + { + "bbox": [ + 465, + 285, + 544, + 365 + ], + "lines": [ + { + "bbox": [ + 465, + 285, + 544, + 365 + ], + "spans": [ + { + "bbox": [ + 465, + 285, + 544, + 365 + ], + "type": "image", + "image_path": "03d646dc348b3f09db2cbee8318ea39e1523286f01c3e656a2d98001b87ce12f.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 50, + 402, + 287, + 475 + ], + "blocks": [ + { + "bbox": [ + 50, + 402, + 287, + 475 + ], + "lines": [ + { + "bbox": [ + 50, + 402, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 50, + 402, + 287, + 475 + ], + "type": "table", + "html": "
\\( {\\mathcal{L}}_{\\text{style }} \\)\\( {\\mathcal{L}}_{\\text{content }} \\)Accuracy (%)
PACSVLCSOfficeHomeDomainNetAvg.
--92.678.372.248.072.8
✓-92.380.971.548.273.2
-✓92.880.572.448.673.6
✓✓93.282.373.649.574.7
", + "image_path": "5853a604474f07f38cb505111fc44079db7f607d2cc161e22accd12e10c822db.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 516, + 288, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 516, + 288, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 516, + 288, + 696 + ], + "type": "text", + "content": "t-SNE visualization results. In Figure 4, we qualitatively evaluate style-content features synthesized for the target task VLCS [15] (5 classes) using t-SNE [58] visualization. As shown in Figure 4(c), PromptStyler generates a variety of styles while not distorting content information; style-content features obtained from the same class name share similar semantics with diverse variations. This result confirms that we could effectively simulate various distribution shifts in the latent space of a large-scale vision-language model by synthesizing diverse styles via learnable style word vectors. Text-to-Image synthesis results. In Figure 5, we visualize style-content features (from \"a " + }, + { + "bbox": [ + 46, + 516, + 288, + 696 + ], + "type": "inline_equation", + "content": "S_*" + }, + { + "bbox": [ + 46, + 516, + 288, + 696 + ], + "type": "text", + "content": " style of a cat\") via diffusers library. These results are obtained with 6 different style word vectors, where the word vectors are learned for the target task DomainNet [48] using ViT-L/14 [11] model." + } + ] + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 309, + 402, + 545, + 458 + ], + "blocks": [ + { + "bbox": [ + 46, + 479, + 287, + 503 + ], + "lines": [ + { + "bbox": [ + 46, + 479, + 287, + 503 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 287, + 503 + ], + "type": "text", + "content": "Table 4: Ablation study on the style diversity loss " + }, + { + "bbox": [ + 46, + 479, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{style}}" + }, + { + "bbox": [ + 46, + 479, + 287, + 503 + ], + "type": "text", + "content": " and content consistency loss " + }, + { + "bbox": [ + 46, + 479, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{content}}" + }, + { + "bbox": [ + 46, + 479, + 287, + 503 + ], + "type": "text", + "content": " used in the prompt loss." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 402, + 545, + 458 + ], + "lines": [ + { + "bbox": [ + 309, + 402, + 545, + 458 + ], + "spans": [ + { + "bbox": [ + 309, + 402, + 545, + 458 + ], + "type": "table", + "html": "
LclassAccuracy (%)
PACSVLCSOfficeHomeDomainNetAvg.
Softmax92.581.272.348.673.7
ArcFace93.282.373.649.574.7
", + "image_path": "0bd2988e085fbe37b8ec7eecf6f1aeb1e571e6ef3745e9b7760bfcf164fb414d.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 462, + 545, + 487 + ], + "lines": [ + { + "bbox": [ + 305, + 462, + 545, + 487 + ], + "spans": [ + { + "bbox": [ + 305, + 462, + 545, + 487 + ], + "type": "text", + "content": "Table 5: Ablation study on the classification loss " + }, + { + "bbox": [ + 305, + 462, + 545, + 487 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{class}}" + }, + { + "bbox": [ + 305, + 462, + 545, + 487 + ], + "type": "text", + "content": " used for training a linear classifier in the proposed framework." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 503, + 397, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 503, + 397, + 516 + ], + "spans": [ + { + "bbox": [ + 306, + 503, + 397, + 516 + ], + "type": "text", + "content": "4.4. More analyses" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "text", + "content": "Ablation study on the prompt loss. In Table 4, we evaluate the effects of " + }, + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{style}}" + }, + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{content}}" + }, + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{prompt}}" + }, + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "text", + "content": " used for learning style words. Interestingly, our method also achieves state-of-the-art results even without using these losses, i.e., the proposed framework (Fig. 3) is substantially effective by itself. Note that randomly initialized style word vectors are already diverse, and CLIP [50] is already good at extracting correct content information from a style-content prompt even without training the word vectors using " + }, + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{content}}" + }, + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "text", + "content": ". When we learn style word vectors using " + }, + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{style}}" + }, + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "text", + "content": " without " + }, + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{content}}" + }, + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "text", + "content": ", style-content features obtained from different class names share more similar features than those from the same class name (Fig. 4(a)). On the other hand, using " + }, + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{content}}" + }, + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "text", + "content": " without " + }, + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{style}}" + }, + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "text", + "content": " leads to less diverse style-content features (Fig. 4(b)). When incorporating both losses, we could generate diverse styles while not distorting content information (Fig. 4(c))." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 702, + 256, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 702, + 256, + 712 + ], + "spans": [ + { + "bbox": [ + 57, + 702, + 256, + 712 + ], + "type": "text", + "content": "2https://github.com/huggingface/diffusers" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15708" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 71, + 172, + 182 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 172, + 182 + ], + 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MethodConfigurationAccuracy (%)
Source DomainDomain DescriptionTerra Incognito
ResNet-50 [22] with pre-trained weights on ImageNet [6]
SelfReg [28]✓-47.0±0.3
GVRT [44]✓-48.0±0.2
ResNet-50 [22] with pre-trained weights from CLIP [50]
ZS-CLIP (C) [50]--19.5±0.0
ZS-CLIP (PC) [50]-✓23.8±0.0
PromptStyler--30.5±0.8
", + "image_path": "8d1541d96a046f23a0b73ecb9c8f3899755efb61f2faf9fa7fe11587e8ddcf87.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 476, + 287, + 502 + ], + "lines": [ + { + "bbox": [ + 46, + 476, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 476, + 287, + 502 + ], + "type": "text", + "content": "Table 6: Unsatisfactory results obtained from CLIP [50] without using source domain data from Terra Incognita [1]." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 510, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 665 + ], + "type": "text", + "content": "Ablation study on the classification loss. In Table 5, we evaluate the effects of the original Softmax loss and the angular Softmax loss (i.e., ArcFace [8]). PromptStyler also achieves the state of the art using the original one, which validates that the performance improvement of our method mainly comes from the proposed framework (Fig. 3). Note that the angular Softmax loss further improves its accuracy by leveraging the hyperspherical joint vision-language space. Effect of the number of styles. We evaluate our method with regard to the number of style word vectors " + }, + { + "bbox": [ + 46, + 510, + 287, + 665 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 510, + 287, + 665 + ], + "type": "text", + "content": " as shown in Figure 6. Interestingly, our PromptStyler outperforms CLIP [50] using just 5 styles. This evaluation shows that 20 style word vectors are enough to achieve decent results." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "Effect of the number of iterations. We evaluate our method with regard to the number of training iterations " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": " for learning each style word vector as shown in Figure 7. This evaluation shows that 20 iterations are enough to achieve decent results." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 358, + 375, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 358, + 375, + 371 + ], + "spans": [ + { + "bbox": [ + 306, + 358, + 375, + 371 + ], + "type": "text", + "content": "5. Limitation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 378, + 547, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 547, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 547, + 521 + ], + "type": "text", + "content": "The performance of our method depends on the quality of the joint vision-language space constructed by the chosen vision-language model. For example, although PromptStyler largely outperforms its base model (i.e., CLIP [50]) in all evaluations, our method shows lower accuracy on the Terra Incognita dataset [1] compared with other methods which utilize several images from the dataset as shown in Table 6. The main reason for this might be due to the low accuracy of CLIP on the dataset. Nevertheless, given that our method consistently outperforms its base model in every evaluation, this limitation could be alleviated with the development of large-scale vision-language models." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 534, + 378, + 546 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 534, + 378, + 546 + ], + "spans": [ + { + "bbox": [ + 306, + 534, + 378, + 546 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 553, + 547, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 553, + 547, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 553, + 547, + 685 + ], + "type": "text", + "content": "We have presented a novel method that synthesizes a variety of styles in a joint vision-language space via learnable style words without exploiting any images to deal with source-free domain generalization. PromptStyler simulates various distribution shifts in the latent space of a large-scale pre-trained model, which could effectively improve its generalization capability. The proposed method achieves state-of-the-art results without using any source domain data on multiple domain generalization benchmarks. We hope that future work could apply our method to other tasks using different large-scale vision-language models." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 690, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 690, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 690, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgment. This work was supported by the Agency for Defense Development grant funded by the Korean government." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15709" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 288, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 288, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 288, + 124 + ], + "type": "text", + "content": "[1] Sara Beery, Grant van Horn, and Pietro Perona. 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However, limited round communications, scarce representation, and scalability pose significant challenges to its deployment, hindering its full potential. In this paper, we propose 'ProtoFL', Prototypical Representation Distillation based unsupervised Federated Learning to enhance the representation power of a global model and reduce round communication costs. Additionally, we introduce a local one-class classifier based on normalizing flows to improve performance with limited data. Our study represents the first investigation of using FL to improve one-class classification performance. We conduct extensive experiments on five widely used benchmarks, namely MNIST, CIFAR-10, CIFAR-100, ImageNet-30, and Keystroke-Dynamics, to demonstrate the superior performance of our proposed framework over previous methods in the literature.", + "bbox": [ + 75, + 390, + 473, + 661 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 676, + 209, + 691 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, there has been a growing concern about privacy, leading people to hesitate when it comes to uploading their biological data to central data servers. Moreover, companies that possess personal information from users are strictly bound by the General Data Protection Regulation (GDPR) [44]. To address these privacy issues, Federated Learning (FL), an emerging distributed data parallel machine learning approach, has been proposed. FL leverages the decentralized data available on individual clients to collaboratively train a shared global model on a mediator server without the need to share personal data.", + "bbox": [ + 75, + 700, + 468, + 867 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/140e95df5318e9fddcee0848aad2033591d6af2b39de57518930a8e612cee401.jpg", + "image_caption": [ + "Figure 1: Visualization of extreme non-i.i.d. ( $\\alpha = 0.0$ is a concentration parameter of Dirichlet distribution) data based FL schema shows that each device has only the data from its target class not shared among all joined devices, and prototypical representation is distributed separately to corresponding joined clients in secure from a central server." + ], + "image_footnote": [], + "bbox": [ + 500, + 356, + 893, + 545 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In the context of FL, where data is decentralized across individual clients, one-class classification (OCC) can be used. This is because that OCC can determine whether a new example belongs to the target distribution or not. Despite not using data from the non-target class, OCC has shown impressive performance [31, 38, 43, 42, 39, 40, 15, 28]. In computer vision applications, OCC is particularly useful for detecting fraud, defects, and unauthorized users.", + "bbox": [ + 496, + 672, + 890, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent advancements in biometric authentication have highlighted the importance of FL-based OCC in computer vision (e.g., user-defined embedding-based methods [17, 26] and data-driven methods [2, 24, 32]). However, FL-based OCC methods face significant challenges, including high communication costs, limited representation, and unstable learning processes. Additionally, centralized server", + "bbox": [ + 496, + 795, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*These authors contributed equally to this work", + "bbox": [ + 94, + 875, + 367, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author", + "bbox": [ + 96, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "6470", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "based methods [31, 42, 43] may not be suitable for FL-based OCC due to limited computing resources on each device, which are a major obstacle for centralized methods that require substantial computing power.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The limitations inherent in FL-based OCC necessitated the development of a novel approach to address these challenges. In this paper, we aim to attain a more expressive global model without the need for frequent re-training processes between the central server and client devices on a large scale. To achieve this, we propose Prototypical representation distillation based unsupervised Federated Learning (ProtoFL) that distills representation from an off-the-shelf model learned using off-the-shelf datasets, regardless of individual client data. In contrast to traditional FL-based OCC, our proposed ProtoFL approach does not transfer parameters directly to the client, as depicted in Fig. 1. This resolves the issues of frequent round communication costs and the need for extra data due to one-time prototype representation distillation. ProtoFL provides a novel solution to the existing challenges of FL-based OCC, enabling efficient and effective global model updates.", + "bbox": [ + 75, + 152, + 470, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Subsequently, we suggest a novel approach for estimating the density of a target class in a distributed setting using a flow-based one-class classifier [20]. To achieve this, we conduct the estimation on individual client devices, using augmented latent variables for training their distributed models. Our approach leverages two key techniques: maximum likelihood estimation with log-likelihood and a probabilistic similarity loss function that includes $\\mathcal{KL}$ -divergence. By combining the distillation and one-class classification phases, we can effectively handle complex data distributions that are non-independent and nonidentically distributed across individual clients. Our two-phase learning framework is inspired by the success of flow-based models in various applications [20, 11, 40, 1], and we demonstrate its effectiveness in handling complex data distributions in the distributed settings.", + "bbox": [ + 75, + 409, + 468, + 648 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The experimental findings of our proposed method demonstrate superior classification performance compared to both server-based and client-based methods on both image and tabular datasets. Additionally, we have validated the scalability of the learned representation and have shown that the global model learned by the ProtoFL is compatible with existing one-class classifiers as well as our one-class classifier based on the benchmark datasets. Our results indicate that our method is a promising approach for large-scale machine learning tasks that require robust and scalable classification capabilities.", + "bbox": [ + 75, + 648, + 468, + 813 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are described as follows:", + "bbox": [ + 96, + 816, + 380, + 829 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We propose a novel unsupervised federated learning framework that effectively addresses the challenge of insufficient local training data. By leveraging normalizing flows for local classifier learning and prototypical", + "bbox": [ + 94, + 839, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "representation distillation, our approach enables efficient and effective global model updates.", + "bbox": [ + 531, + 90, + 888, + 119 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel prototype-based representation learning method for distilling normal data representation using an off-the-shelf model and dataset. Our approach demonstrates the scalability of the global model, which can be verified by adding new clients in FL-based OCC.", + "- We propose new federated and centralized learning methods for one-class classification, which we evaluate on five widely-used benchmarks. Our experiments show that our methods achieve superior performance compared to existing approaches." + ], + "bbox": [ + 517, + 143, + 890, + 321 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 333, + 640, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "One-class classification Various one-class classification approaches have been proposed and categorized into description-based and representation-based learning. In the description-based methods, Deep-SVDD [31] performs one-class detection by learning a model to map target samples into a center in the latent space, otherwise non-target samples are mapped far from the center. And FCDD [27] proposes an explainable one-class classifier by upsampling based on gaussian sampling. In contrast, representation-based learning methods (DROC [42] and CSI [43]) present a two-step learning framework to learn a representation model through excessive data-augmentation and contrastive loss. The framework either employs a classifier or defines a score function for detecting a target class. Unlike previous centralized server-based approaches, our proposed approach for one-class classification on decentralized learning avoids the risk of personal data leakage by constructing a model using distributed data. To the best of our knowledge, our method is the first to directly address this problem in a decentralized setting.", + "bbox": [ + 496, + 358, + 890, + 660 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Federated learning for local one-class classifier Federated Learning (FL) is a distributed machine learning paradigm that enables collaborative model training without direct data sharing. FL has been applied to one class classification (OCC) tasks for user verification and authentication, with several studies demonstrating promising results. [17, 32, 34]. FedAwS [45] introduces a geometric regularization to learn a global model by utilizing uploaded latent variables of joined clients in a central server. Since the latent variables shared on a server are private data, the FedAwS violates in the setting of FL. FedUV [17] employs independent secret error correcting codes (ECCs) to train a one-class classifier by preventing personal data from sharing among joined clients. The secret codes induce the concise objective of FedUV so that only positive examples are", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "6471", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "required. The FedUV approach was further refined to estimate a center of distribution by FedAA [32] and FedMetric [34], instead of defining hand-designed codes. However, local data on each device is not sufficient to represent a centroid of local data distribution.", + "bbox": [ + 75, + 90, + 468, + 165 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Federated learning for central and client classifiers In authentication systems, client data is often partitioned according to a target class. This results in highly or extremely non-i.i.d. data that poses a significant challenge for FL. This extreme non-i.i.d. means that a concentration parameter of Dirichlet distribution approaches to zero $(\\alpha = 0.0)$ while many federated learning methods [6, 9, 13] assumes non-i.i.d. data with non-zero $(\\alpha \\neq 0.0)$ setting [18, 23, 29, 6, 13, 9].", + "bbox": [ + 75, + 176, + 468, + 313 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unsupervised federated learning methods [23, 29] aggregate local representation models and centroids for achieving a global model and centroid. FedRep [6] shares partitions of a global model to adapt each local heterogeneous data. FedX [13], which utilizes structure knowledge distillation between local and global knowledge relationships, learns meaningful data representation without sharing external data. SphereFed [9] introduced a learned matrix, which is a fixed-classifier for sharing among all participating clients, to transform each local data distribution into the predefined latent space. But, SphereFed requires enormous cost to re-construct and re-distribute a new learned matrix whenever a new client joins. Therefore, we first propose a prototypical representation distillation learning to save communication cost in FL with extreme non-i.i.d. $(\\alpha = 0.0)$ data settings.", + "bbox": [ + 75, + 314, + 468, + 554 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 566, + 202, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Federated Average Learning FedAVG [30], composed of participating clients and a central mediator server, trains a global model by aggregating locally-computed parameters, and broadcasts the updated global model to the clients. In each round, FedAVG updates the global model parameters with local model parameters as follows:", + "bbox": [ + 75, + 592, + 468, + 681 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {g} ^ {t + 1} = \\sum_ {k = 1} ^ {K} \\frac {\\left| D _ {k} \\right|}{\\sum_ {k = 1} ^ {K} \\left| D _ {k} \\right|} \\theta_ {k} ^ {t}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 688, + 468, + 729 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $k \\in \\{1, \\dots, K\\}$ indicates an index of a local client. $\\theta_{g}^{t+1}$ is the parameters of a global model, and $\\theta_{k}^{t}$ is the parameters of the $k^{th}$ local model at a round $t$ . For the balanced updating of the global model $\\theta_{g}^{t+1}$ , $|D_{k}|$ is the number of samples on dataset $D_{k}$ .", + "bbox": [ + 75, + 736, + 468, + 813 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unsupervised Contrastive Learning FL with extreme non-i.i.d. $(\\alpha = 0.0)$ data setting is unavailable to access samples of the other clients. Thus, we simplify the contrastive loss, $\\mathcal{L}_{cntr} = y \\times (1 - d(\\bullet, \\hat{\\bullet})) + (1 - y) \\times \\max(0, d(\\bullet, \\hat{\\bullet}))$ , as follows:", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d} = 1 - d (\\bullet , \\hat {\\bullet}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 113, + 890, + 128 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $d(\\bullet, \\hat{\\bullet})$ is the cosine-similarity $\\frac{\\bullet \\cdot \\hat{\\bullet}}{||\\bullet|| \\cdot ||\\hat{\\bullet}||}$ . We utilize $L_{d}$ as our positive cosine similarity loss for our unsupervised leaning, instead of $\\mathcal{L}_{cntr}$ .", + "bbox": [ + 498, + 138, + 890, + 186 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Normalizing Flows Normalizing flows (NFs) [8] are the statistical methods using the change-of-variable law of probabilities to fit an arbitrary target density $p_R(r)$ by a tractable base distribution with density $p_Z(z)$ and a bijective invertible mapping $\\mathfrak{t}^{-1}: R^D \\to Z^D \\Leftrightarrow \\mathfrak{t}: Z^D \\to R^D$ . According to [33], $\\mathcal{KL}$ -divergence and log-likelihood estimation are employed to optimize the invertible flow-based model $z = \\mathfrak{t}^{-1}(r; \\psi)$ and $r = \\mathfrak{t}(z; \\psi)$ by the target distribution $p_R(r)$ . The bijective invertible mapping is drawn as:", + "bbox": [ + 498, + 196, + 890, + 333 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {D} _ {\\mathcal {K L}} \\left[ \\hat {p} _ {R} (r) \\| p _ {R} (r; \\psi) \\right] \\\\ \\approx - \\mathbb {E} _ {\\hat {p} _ {R} (r)} \\left[ \\log p _ {Z} \\left(\\mathrm {t} ^ {- 1} (r; \\psi)\\right) + \\log | \\det j _ {\\mathrm {t} ^ {- 1}} | \\right] + c o n t, \\tag {3} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 351, + 890, + 401 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $p_R(r;\\psi)$ denotes the likelihood of a model. $\\hat{p}_R$ is the target distribution to learn the model by $\\mathcal{KL}$ -divergence. $p_R(r;\\psi)$ only remains for learning parameters $\\psi$ , and then is replaced by $\\frac{1}{N}\\sum_{i=1}^{N}\\left[\\frac{\\|\\mathfrak{t}^{-1}(r_i)\\|_2^2}{2}-\\log|\\det\\mathfrak{j}_{\\mathfrak{t}^{-1}}|\\right]$ through the training dataset $D_k$ as explained by [11, 20]. The re-written equation is applied to our objective to estimate the log-likelihood of given local data on each device.", + "bbox": [ + 498, + 402, + 890, + 513 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Proposed Method", + "text_level": 1, + "bbox": [ + 500, + 526, + 671, + 542 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we propose a two-phase unsupervised learning framework that combines unsupervised federated learning via distillation of prototypical representations with local classifier learning via leveraging normalizing flows.", + "bbox": [ + 498, + 551, + 890, + 612 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 500, + 619, + 702, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Participating $K$ clients aim to train a global model by aggregating locally-computed parameters $\\phi(\\bullet, \\theta)$ for an one-class classification task without sharing private data among joined clients. Each client has a training dataset $D_{K,N} = \\{x_{k,i}, 1 \\leq i \\leq N, 1 \\leq k \\leq K\\}$ and $N$ is the cardinality of the local data $D_{k,N}$ . Let $\\phi(x_{k,i}; \\theta_k)$ denote the trainable model of the $k^{th}$ client. In particular, we follow the extreme non-i.i.d. $(\\forall_{m,n} D_{m,N} \\cap D_{n,N} = \\emptyset)$ data setting in our FL-based OCC. Different from prior FL settings utilizing either hand-designed codes or additional training datasets, we invent generic representation of the local model $\\phi$ by leveraging the off-the-shelf model $\\mathcal{F}$ and dataset $S$ , and we employ the flow-based model $\\psi$ for the local one-class classifier.", + "bbox": [ + 498, + 642, + 890, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.2. Sequence of procedures", + "text_level": 1, + "bbox": [ + 500, + 847, + 718, + 863 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 2, we describe our proposed method workflow in each phase. $①$ Whenever a new client partici", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "6472", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7a5be14a4fda3165121fd68dc1fafea57d219633c4acc04699148ca443fb93f8.jpg", + "image_caption": [ + "(a) Phase 1: Unsupervised federated learning via prototypical representation distillation" + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 575, + 281 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cfca0dd713e55ee3f8fc71af74ccdee619e4a99ce5c6158299fbd91853c28aa6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 578, + 90, + 890, + 200 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e179ce143316191b6a150dcd5a88078ad437b78877c834bdadb161fb8aae95ac.jpg", + "image_caption": [ + "(b) Phase 2: Local one-class classifier based on NFs", + "Figure 2: Overview of our proposed two-phase learning architecture. $① \\sim$ $④$ indicates the workflows of ProtoFL with all the joined clients to upload parameters of each client and to download the aggregated global model, and $⑤$ represents a local training for the OC-NF. The details of sequences $① \\sim$ $⑤$ are described in Section 4.2. NFs denote normalizing flows." + ], + "image_footnote": [], + "bbox": [ + 578, + 203, + 890, + 281 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "pates in our unsupervised federated learning, all clients join a central mediator server. ② For the $k^{th}$ client, a categorical image $s_k$ is chosen from $\\mathcal{S}$ and transformed into a latent variable $v_k$ by the central mediator server. Both ① and ② occur only once at the first time, and $\\mathcal{V} = \\{v_k, 1 \\leq k \\leq K\\}$ is secretly distributed to the corresponding client. ③ We train the $k^{th}$ local model $\\theta_k$ via the local data $D_{k,N}$ , the distributed prototype representation $v_k$ , cosine similarly loss, and $\\mathcal{KL}$ -divergence loss. ④ A global model $\\theta_g$ is aggregated with all the uploaded local models by FedAVG, and the global model is distributed to all participating clients. ⑤ Once federated representation learning has finished, we train a local one-class classifier based on normalizing flows (OC-NF) by using maximum likelihood and cosine similarity losses. We describe the details of our procedures (① ~ ⑤) in the following subsections.", + "bbox": [ + 75, + 364, + 472, + 608 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Prototypical representation distillation based unsupervised federated learning (ProtoFL)", + "text_level": 1, + "bbox": [ + 76, + 623, + 468, + 655 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We assume $\\mathcal{F}:R^{W\\times H\\times C}\\to R^D$ and $\\phi :R^{W\\times H\\times C}\\to$ $R^D$ indicate the off-the-shelf model and the local model, respectively as illustrated in Fig. 2. For training the local model of the $k^{th}$ client, we augment two views $x_{k,i},\\hat{x}_{k,i}$ from the $i^{th}$ example of the local training data $D_{k,N}$ , and subsequently transform the two samples as follows:", + "bbox": [ + 76, + 661, + 468, + 755 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nr _ {k, i} = \\phi \\left(x _ {k, i}; \\theta_ {k}\\right); \\hat {r} _ {k, i} = \\phi \\left(\\hat {x} _ {k, i}; \\theta_ {k}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 776, + 468, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $r_{k,i}$ and $\\hat{r}_{k,i}$ represent latent variables of the $i^{th}$ example. $\\phi$ is the client model with $k^{th}$ learnable parameters $\\theta_{k}$ . Inspired by SimCLR [5], the two latent variables $r_k$ and $\\hat{r}_k$ must be very close to each other. Given the only positive local data and the constraint, we employ the positive cosine similarity loss(Eq. 2) to learn the local model as follows:", + "bbox": [ + 76, + 809, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p} ^ {\\theta} \\left(\\theta_ {k}\\right) = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left[ 1 - d \\left(r _ {k, i}, \\hat {r} _ {k, i}\\right) \\right], \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 390, + 890, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\theta_{k}$ is optimized by the local data $D_{k,N}$ . To overcome the small cardinality of local data for training the local representative model, we propose the off-the-shelf model with pre-trained parameters $\\mathcal{F}(\\bullet ;\\omega)$ and the off-the-shelf dataset $s_k\\in S_s$ . The off-the-shelf model and dataset are utilized on a central mediator server as depicted:", + "bbox": [ + 498, + 443, + 892, + 534 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nv _ {k} = \\mathcal {F} \\left(s _ {k}; \\omega\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 640, + 547, + 890, + 564 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $s_k$ and $v_k$ represent a prototype example and representation for the $k^{th}$ client. After $\\mathcal{V} = \\{v_k, 1 \\leq k \\leq K\\}$ is distributed to the corresponding client in secret, we train the local model of the $k^{th}$ client to estimate the prototypical target representation $v_k$ . We employ the $\\mathcal{KL}$ -divergence to minimize the discrepancy between two distributions $v_k$ and either $r_k$ or $\\hat{r}_k$ . Therefore, we invent the prototypical distillation loss as follows:", + "bbox": [ + 498, + 577, + 890, + 699 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p d} ^ {\\theta} \\left(\\theta_ {k}\\right) = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left[ \\mathcal {K L} \\left(v _ {k} \\| r _ {k, i}\\right) + \\mathcal {K L} \\left(v _ {k} \\| \\hat {r} _ {k, i}\\right) \\right], \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 712, + 890, + 753 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{KL}(v_k\\| r_{k,i})$ and $\\mathcal{KL}(v_k\\|\\hat{r}_{k,i})$ are equally contributed to our distillation loss. Figure 3 describes the details of Eq. 5 and Eq. 7, and the overall objective of the first phase (phase 1) is defined as follows:", + "bbox": [ + 498, + 766, + 890, + 827 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\phi} \\left(\\theta_ {k}\\right) = (1 - \\alpha) \\times \\mathcal {L} _ {p d} ^ {\\theta} \\left(\\theta_ {k}\\right) + \\alpha \\times \\mathcal {L} _ {p} ^ {\\theta} \\left(\\theta_ {k}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 839, + 890, + 859 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha$ is a balancing weight. In our experiment, $\\alpha$ is empirically set to 0.1.", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "6473", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2ba057b7238259801252892b21079b2808b9781ea196313c777801c6cf5451f7.jpg", + "image_caption": [ + "Figure 3: Illustration of learning a global model with prototypical representation distillation on distributed devices without sharing private data among participating clients." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 349, + 258 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ae7feeadfbbd5a0b3823c2aa76bd276428ab441c3568cbbd7938c5274dbcbbe5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 352, + 88, + 467, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Local one-class classifier via Normalizing Flows (OC-NF)", + "text_level": 1, + "bbox": [ + 76, + 327, + 468, + 358 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After unsupervised federated representation learning for the global model, we leverage a general flow-based model for training the local one-class classifier in each client as shown in Fig. 2. To estimate log-likelihood of transformed latent variables $r_k$ and $\\hat{r}_k$ , we exploit Eq. 3 to learn the probabilistic normalizing flows $\\mathfrak{t}$ through the local dataset $D_{k,N}$ and the local model $\\phi (\\cdot ;\\theta_k)$ on the $k^{th}$ client as follows:", + "bbox": [ + 75, + 367, + 470, + 474 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {m l e} ^ {\\psi} (\\psi_ {k}) \\\\ = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left[ \\frac {\\| \\mathfrak {t} ^ {- 1} (r _ {k , i} ; \\psi_ {k}) \\| _ {2} ^ {2}}{2} - \\log | \\det \\mathfrak {j} _ {k, i} | \\right] + c o n t \\\\ \\approx \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left[ \\frac {\\left\\| z _ {k , i} \\right\\| _ {2} ^ {2}}{2} - \\log | \\det j _ {k, i} | \\right] + c o n t, \\tag {9} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 489, + 468, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $z_{k,i}$ is the estimated distribution as it passes through $\\mathrm{t}^{-1}(r_{k,i};\\psi_k)$ . $r_{k,i}$ is a latent variable from $\\phi (x_{k,i};\\theta)$ . When optimizing the flow-based model, we ignore constants, det and cont. Since $r_{k,i}$ and $\\hat{r}_{k,i}$ are close each other in a latent space, $z_{k,i}$ and $\\hat{z}_{k,i}$ also predict the same distribution so that we introduce the following objective as a regularizer:", + "bbox": [ + 75, + 607, + 468, + 699 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r e g} ^ {\\psi} (\\psi_ {k}) = \\frac {1}{N} \\sum_ {i = 1} ^ {N} [ 1 - d (z _ {k, i}, \\hat {z} _ {k, i}) ], \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 712, + 468, + 753 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $z_{k,i}$ and $\\hat{z}_{k,i}$ are the normal distribution estimated by $\\mathfrak{t}^{-1}((\\phi (x_{k,i};\\theta_k);\\psi_k))$ and $\\mathfrak{t}^{-1}((\\phi (\\hat{x}_{k,i};\\theta_k);\\psi_k))$ respectively. The overall objective of the second phase (phase 2) is composed of Eq. 9 and Eq. 10 as follows:", + "bbox": [ + 76, + 765, + 468, + 825 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {t}} \\left(\\psi_ {k}\\right) = \\mathcal {L} _ {m l e} ^ {\\psi} \\left(\\psi_ {k}\\right) + \\lambda \\times \\mathcal {L} _ {r e g} ^ {\\psi} \\left(\\psi_ {k}\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 838, + 468, + 859 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda$ is a hyper-parameter for effectiveness of regularization. For our experiment, we empirically set $\\lambda$ to 0.01.", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 89, + 633, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we demonstrate the proposed approach on image and tabular benchmarks. We evaluate the performance of our proposed ProtoFL and compare our model with the other FL methods and one-class detectors. And we analyze the impact of new client participation in the context of OCC on FL, as well as ablation studies on each proposed component.", + "bbox": [ + 496, + 114, + 893, + 220 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 231, + 601, + 244 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We thoroughly evaluate our proposed method on several benchmark datasets, including the widely used MNIST [22], CIFAR-10 [21], CIFAR-100 [21], ImageNet-30 [16], and Keystroke-Dynamics [19], to tackle the demanding task of one-class classification. Our evaluation scrutinizes the efficacy, robustness, and scalability of our method, highlighting its strengths in handling real-world scenarios. In case of CIFAR-100, we adopt 20 super-class labels, denoted by CIFAR- $100^{\\ddagger}$ , as suggested in [10] to our experiments. The numbers of categories in the benchmarks are 10, 10, 20, 30, and 51, which are the numbers of participating clients on our federated learning. The vision and tabular based benchmarks for OCC follow a one-vs-rest protocol [10, 42, 43]. In the protocol, a set of samples from one class indicates a target class for one client, whereas a set of samples from the remaining classes represents a non-target class for the remaining clients.", + "bbox": [ + 496, + 253, + 892, + 512 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Experiment Setting", + "text_level": 1, + "bbox": [ + 500, + 521, + 687, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Off-the-shelf model and dataset In the central mediator server, the off-the-shelf dataset and model generate prototypical representation when a new client participates in our unsupervised federated learning. For the off-the-shelf model and dataset, we exploit ArcFace [7] based ResNet-50 backbone [14] and MS-Celeb-1M [12], respectively.", + "bbox": [ + 496, + 544, + 893, + 636 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Architectures In this experiment, we employ ResNet-18/32 backbones [14] to learn the local and global models on our proposed approach. Since batch normalization is detrimental to the performance in federated learning [17] both ResNet-18/32 backbones replace batch- with group-normalization. In the Keystroke Dynamics dataset, we employ multi-layer perceptions as the local and global model, consisting of three linear layers, ReLU, and group-normalization. And we utilize NFs as a local classifier model composed of 8 coupling layers [8].", + "bbox": [ + 496, + 643, + 893, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details In the first phase as described in Algorithm 1, we train our expressive global model based on the FedAvg [30] method with 1 local epoch and 900 communication rounds, using randomly chosen clients from all participating clients. We utilize the RAdam optimizer [25] with betas 0.94 and 0.98, a weight decay 1e-3 and a learning", + "bbox": [ + 496, + 809, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "6474", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 Procedure of our two-phase learning", + "text_level": 1, + "bbox": [ + 80, + 90, + 383, + 104 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Phase 1 (ProtoFL): Start phase 1 for $T$ rounds.", + "bbox": [ + 94, + 109, + 379, + 123 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Initialize and broadcast a global model $\\theta_g^0$ to all joined $K$ clients. Send an acknowledgement (ACK) with prototypical representation $v_{k}$ to the $k^{th}$ client.", + "bbox": [ + 94, + 125, + 467, + 165 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "for $t\\gets 0$ to $T - 1$ do", + "bbox": [ + 94, + 166, + 230, + 176 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {g} ^ {t + 1} \\leftarrow \\text {G L O B A L - T R A I N I N G} (t, \\theta_ {g} ^ {t})\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 178, + 341, + 194 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "end for", + "bbox": [ + 96, + 194, + 142, + 205 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Update the global model $\\theta_g$ with $\\theta_g^T$ .", + "bbox": [ + 96, + 205, + 313, + 220 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "function GLOBAL TRAINING $(t,\\theta_g^t)$ Randomly select $k$ number of clients from $\\{C_k\\}_{k = 1}^K$", + "bbox": [ + 96, + 220, + 429, + 250 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "for $k\\gets 1$ to $K$ do", + "bbox": [ + 117, + 250, + 232, + 260 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\text {B r o a d c a s t} \\theta_ {q} ^ {t} \\text {t o} C _ {k}.\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 262, + 359, + 276 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {k} ^ {t}, \\left| D _ {k, N} \\right| \\leftarrow \\text {C L I E N T - T R A I N I N G} (t, k, \\theta_ {g} ^ {t})\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 276, + 406, + 291 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "end for", + "bbox": [ + 117, + 292, + 163, + 301 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {g} ^ {t + 1} \\leftarrow \\sum_ {k = 1} ^ {K} \\frac {\\left| D _ {k , N} \\right|}{\\sum_ {k = 1} ^ {K} \\left| D _ {k , N} \\right|} \\theta_ {k} ^ {t}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 301, + 302, + 321 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {r e t u r n} \\theta_ {g} ^ {t + 1}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 321, + 189, + 337 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "end function", + "bbox": [ + 96, + 338, + 176, + 348 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "function CLIENT.TrAINING $(t,k,\\theta_g^t)$", + "bbox": [ + 96, + 349, + 343, + 364 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Download the global model $\\theta_g^t$ , and assign it to $\\theta_k^t$", + "bbox": [ + 117, + 364, + 415, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "for $x_{k,i}\\in D_{K,N}$ do", + "bbox": [ + 117, + 378, + 241, + 391 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\phi} \\left(\\theta_ {k} ^ {t}\\right) = (1 - \\alpha) \\times \\mathcal {L} _ {p d} ^ {\\theta} \\left(\\theta_ {k} ^ {t}\\right) + \\alpha \\times \\mathcal {L} _ {p} ^ {\\theta} \\left(\\theta_ {k} ^ {t}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 391, + 411, + 406 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {k} ^ {t} \\leftarrow \\theta_ {k} ^ {t} - \\eta \\nabla \\mathcal {L} _ {\\phi} \\left(\\theta_ {k} ^ {t}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 406, + 277, + 420 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "end for", + "bbox": [ + 117, + 420, + 165, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Calculate the number of the $k^{th}$ client data $D_{k,N}$ .", + "bbox": [ + 117, + 431, + 411, + 446 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "return $\\theta_k^t$ and $|D_{k,N}|$", + "bbox": [ + 117, + 446, + 250, + 460 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "end function", + "bbox": [ + 96, + 462, + 176, + 473 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Phase 2 (OC-NF): All joined clients start Algorithm 2 for OCC.", + "bbox": [ + 94, + 474, + 468, + 502 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Algorithm 2 Procedure of our OC-NF for OCC", + "text_level": 1, + "bbox": [ + 80, + 522, + 370, + 536 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Download the global model $\\theta_{g}$ , and assign it to the $k^{th}$ client model $\\theta_{k}$ . Freeze the global representation model $\\phi (\\bullet ;\\theta_k)$ . Initialize the flow-based model of the $k^{th}$ client $\\mathfrak{t}_{\\psi_k}$ .", + "bbox": [ + 94, + 542, + 468, + 585 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "for $x_{k,i}\\in D_{k,N}$ do", + "bbox": [ + 96, + 585, + 215, + 598 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathfrak {t}} (\\psi_ {k}) = \\mathcal {L} _ {m l e} ^ {\\psi} (\\psi_ {k}) + \\lambda \\times \\mathcal {L} _ {r e g} ^ {\\psi} (\\psi_ {k})\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 598, + 346, + 614 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\psi_ {k} \\leftarrow \\psi_ {k} - \\eta \\nabla \\mathcal {L} _ {\\mathrm {t}} (\\psi_ {k})\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 614, + 259, + 627 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "end for", + "bbox": [ + 96, + 628, + 142, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "rate 1e-6 to learn local models. In the second phase as described in Algorithm 2, we use the SGD optimizer [35] with a learning rate 5e-3 and 5 epochs to learn our one-class classifier. Data augmentations include the set of random processes (crop, horizontal-flip, and gaussian-blur) and color jitter. To evaluate the performance of various methods, we use the area under curve of ROC curve (AUROC) and equal error rate (EER).", + "bbox": [ + 75, + 669, + 468, + 789 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Experimental Results", + "text_level": 1, + "bbox": [ + 76, + 800, + 277, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Image and tabular benchmarks For the image benchmarks, we present the results on MNIST and CIFAR-10 datasets for OCC in extreme non-i.i.d. $(\\alpha = 0.0)$ data setting of FL. Table 1 shows the outstanding result of not only the significantly improved performance but also the", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/569e7470543c4f3c45212685c3a706517941c5cf7d10dd7718b71e09ef24c5a9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodNetworkMNISTCIFAR-10
AUROCRoundAUROCRound
FedAwS [45]ResNet-3299.610K94.1100K
FedUV [17]ResNet-3299.720K87.220K
FedMetric [34]ResNet-3299.610K94.2100K
OursResNet-3299.90.9K95.20.9K
", + "bbox": [ + 501, + 88, + 890, + 162 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1: Performance comparison FL-based methods with our proposed approach on MNIST and CIFAR-10 benchmarks. Our approach outperforms both benchmarks while reducing the communication round cost.", + "bbox": [ + 500, + 164, + 890, + 223 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0dd1a55d12a24d32390d02dcc22416057e356bc5608b8d95963bf765e305ed5c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TypeMethodNetworkCIFAR-10CIFAR-100‡ImageNet-30
AUROCAUROCAUROC
Centralized LearningAE [27]---56.0
OC-SVM [41]-58.863.1-
Geom [10]WRN-16-886.078.7-
Rot [16]ResNet-1889.877.777.9
GOAD [3]ResNet-1885.174.5-
DROC [42]ResNet-1892.586.5-
CSI [43]ResNet-1894.386.691.6
FLOW† [40]ResNet-5095.293.0-
Federated LearningFedUV [17]ResNet-1879.8*55.9*62.8*
FedRep [6]ResNet-1858.2*56.9*56.3*
OursResNet-1895.389.995.4
", + "bbox": [ + 501, + 239, + 890, + 368 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2: AUROC of various centralized and decentralized detection methods on CIFAR-10/100 $\\ddagger$ , and ImageNet-30 for OCC. $\\dagger$ and $*$ denote the usage of a pre-trained model learned on ImageNet-1M and the values from our reimplementation respectively, whereas **bold** and **underline** indicate the best results and the second results, respectively.", + "bbox": [ + 500, + 369, + 890, + 460 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "effective communication cost on FL methods. We found that our proposed method exploits the off-the-shelf model and dataset to compensate the shortage of the local data. For updating a global model every rounds, naive FL methods [45, 17, 34] minimize the distance among the latent variables of the local data and map the distribution of the local data into one secure code designated. Those methods demand the inordinate communication cost and show the limited performance due to the deficiency of the local data on each device and the entangled secure code on latent space. Furthermore, we compare our approach with various centralized methods as depicted in Table 2. Our method outperforms ResNet-18 based methods on CIFAR-10 and ImageNet-30. In case of CIFAR- $100^{\\ddagger}$ , our approach places the second-rank performance comparing with FLOW [40] leveraging the feature extraction of a pre-trained model learned on ImageNet-1M. Note that our proposed method is the first rank among ResNet-18 based methods having no additional training datasets and limited computing resources. Among FL methods, our proposed method accomplishes the consistently improved performance on the image benchmarks.", + "bbox": [ + 496, + 476, + 890, + 806 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the tabular benchmark, we make the comparisons to the centralized methods on the Keystroke-Dynamics dataset for one-class classification as shown in Fig. 4. As the results, we found that our proposed method reduces EER more than two times comparing to prior methods. Training a foundation model as the global model is essential for the", + "bbox": [ + 496, + 810, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6475", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9abafa46d63521f9669385536c2da15fc017c3f58deb949a6f514edd87ee31ed.jpg", + "table_caption": [], + "table_footnote": [ + "Table 3: AUROC of various centralized and decentralized detection methods on CIFAR-10 for one-class classification. We present the AUROC of each class and the mean and standard deviation (std) of AUROC for all classes. $\\dagger$ , bold, and underline denote the usage of a pre-trained model learned on ImageNet-1M, the best results, and the second results, respectively." + ], + "table_body": "
TypeMethodNetworkPlaneCarBirdCatDeerDogForgHorseShipTruckMean (std)
Centralized LearningOC-SVM [41]-65.640.965.350.175.251.271.851.267.948.558.8 (±11.6)
DeepSVDD [37]LeNet61.765.950.859.160.965.767.767.375.973.164.8 (±7.17)
Geom [10]WRN-16-874.795.778.172.487.887.883.495.593.391.386.0 (±8.52)
Rot [16]WRN-16-477.596.987.380.992.790.290.996.595.293.390.1 (±6.52)
GOAD [3]WRN-16-477.296.783.377.787.887.890.096.193.892.088.2 (±6.99)
Rot [16]ResNet-1880.496.485.981.191.389.689.995.995.092.689.8 (±5.75)
GOAD [3]ResNet-1875.594.181.872.083.784.482.993.992.989.585.1 (±7.61)
DROC [42]ResNet-1890.998.988.083.189.990.393.598.296.595.292.5 (±4.95)
CSI [43]ResNet-1889.999.193.186.493.993.295.198.797.995.594.3 (±3.97)
FLOW† [40]ResNet-5096.197.592.689.893.395.798.094.797.896.695.2 (±2.64)
Federated LearningOursResNet-1896.497.992.790.995.892.796.496.497.696.795.3 (±2.38)
", + "bbox": [ + 78, + 89, + 893, + 262 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a1b08468be02d2345e68373c278510ad7b754f63d8c3e6a8d0249698c239072f.jpg", + "image_caption": [ + "Figure 4: Comparison to previous methods of one-class classification on the Keystroke-Dynamics dataset. OC, Manhattan, AE, and MLP denote Outlier Count, Euclidean detector with Manhattan distance, Auto-Encoder, and 4-multi layer perception, respectively, from [19]. $\\mathbb{I}$ denotes a standard deviation." + ], + "image_footnote": [], + "bbox": [ + 138, + 321, + 405, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "OCC task instead of the various architectures and distance metrics to achieve notably improved performance.", + "bbox": [ + 75, + 585, + 468, + 617 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Centralized vs Federated learning As shown in Table 3, we compare our proposed method with the centralized learning based methods because there is no previous FL method studying sufficiently analysis results for CIFAR-10. Our proposed approach outperforms the previous methods in terms of the overall mean and standard deviation because we collaboratively train our global model to represent all classes by the distributively-learned local models, and then we apply our non-biased global model to transform raw data into latent spaces for learning a local one-class classifier in each client as shown in Fig. 5. In case of each class, this method shows the first and second-placed performance in 8 out of 10, whereas FLOW [40] and CSI [43] show the first and second-placed performance in 4 and 5 out of 10, which indicates that our collaboratively learned global model avoids over-fitting problem for each client.", + "bbox": [ + 75, + 622, + 470, + 864 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Scalability of representation In this setup on CIFAR $\\mathbf{100}^{\\ddagger}$ , let $\\gamma$ indicate the number of new joined clients for", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b62a5af6cda63507628c96eb7696c00718c5f9304f1c36edb4bc59edd15b3877.jpg", + "image_caption": [ + "Figure 5: Analysis the scalability of our global model learned by ProtoFL through new clients on CIFAR-100‡ dataset. Our approach modestly overcomes the other methods [6, 17, 23] in FL with extreme non-i.i.d. $(\\alpha = 0.0)$ data. $\\gamma$ and $\\mathbb{I}$ denote the number of new joined clients and a standard deviation each." + ], + "image_footnote": [], + "bbox": [ + 562, + 321, + 826, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "one-class classification, and $20 - \\gamma$ represent the number of clients who participating in FL. To optimize the local classifier parameters of the new client, the new client downloads the global model as described in Algorithm 2. Note that we are the first to consider the effects of joining new clients. As presented in Fig. 5, we demonstrate the effectiveness for scalability of the learned representation as our global model through experiments and comparisons. Although new clients have increased, all federated learning methods suffer from degraded performances. However, our proposed method shows more scalability with respect to a new joiner than the others [17, 6, 23]. In addition, FedRep [6] and LG-FedAvg [23] are meaningless to support new clients. Thus, our method presents an novel property validating new joiners performance in FL.", + "bbox": [ + 496, + 589, + 893, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 830, + 665, + 845 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conducted ablation studies on CIFAR-10/100 $\\ddagger$ and ImageNet-30 (i) to verify the phase 1 and the phase 2, (ii) to explore the contribution of each component in our method,", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "6476", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ef9634e66362ee6b1aad472204c4a83621a9904d7df19bf3e13693361b633c75.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Phase 1Phase 2CIFAR-10CIFAR-100‡ImageNet-30Mean
Ours \n(ProtoFL)KDE94.588.994.092.3
GDE94.388.692.891.9
OC-SVM97.186.990.891.6
Ours (OC-NF)95.389.995.493.5
", + "bbox": [ + 78, + 88, + 467, + 143 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/85a01f90ca4e2701336e395ec7d811a686c5b2b525739d67cac11acdf4e0fcce.jpg", + "table_caption": [ + "Table 4: Ablation study of various classifiers on CIFAR-10, CIFAR- $100^{\\ddagger}$ , and ImageNet-30 with our representative global model. The performance is evaluated by AUROC." + ], + "table_footnote": [], + "table_body": "
MethodPhase 1Phase 2CIFAR-10‡ImageNet-30
LθpdLθpLψmleLψregAUROCAUROC
Ours w/o Lθpd, Lψreg✓✓48.950.2
Ours w/o Lθp, Lψreg✓✓87.091.1
Ours w/o Lψreg✓✓✓89.694.4
Ours✓✓✓✓89.995.4
", + "bbox": [ + 78, + 204, + 467, + 273 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5: Ablation study on CIFAR-100† and ImageNet-30 to evaluate each component in the individual phase.", + "bbox": [ + 76, + 275, + 467, + 305 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and (iii) to investigate the effectiveness of the off-the-shelf model in respect of the various off-the-shelf datasets.", + "bbox": [ + 76, + 319, + 467, + 349 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analyses of our global- and classifier- model With fixed our global model learned by joined clients in advance, we compared our proposed local one-class classifier via normalizing flows (OC-NF) with the prior one-class classifiers for the usability of the global model. As shown in Table 4, we observed the superiority of the global model and the local classifier either each or both comparing to the previous detectors [4, 41] non-parametric kernel density estimation, parametric gaussian density estimation, and one-class SVM (KDE, GDE, and OC-SVM).", + "bbox": [ + 76, + 359, + 467, + 511 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analyses of each component To analyze the effect of our proposed objective for each phase, we separated the representation objective of the phase 1 into distilling loss $\\mathcal{L}_{pd}^{\\theta}$ and similarity loss $\\mathcal{L}_p^\\theta$ , and the classification objective of the phase 2 into maximum likelihood $\\mathcal{L}_{mle}^{\\psi}$ and regularizer $\\mathcal{L}_{reg}^{\\psi}$ to show the importance in Table 5. Thus, we confirmed that each of them is the essential terms for the improving performance, and also observed the best results when all of them were used on CIFAR- $100^{\\ddagger}$ and ImageNet30. In case of ImageNet-30, the improved performance indicates the effectiveness of this regularizer. As shown in Fig. 6, we found that our representative global model, trained without this distilling loss $\\mathcal{L}_{pd}^{\\theta}$ , leads the drastically impoverished representation.", + "bbox": [ + 76, + 522, + 467, + 738 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analyses of distilling representation With the FL setting, we employ cosine similarity $S_{c}$ as a criterion for selecting the off-the-shelf models as shown in left of Fig. 7, and evaluated the performance based on various $S_{c}$ on all the benchmarks as shown in right of Fig. 7. Our proposed ProtoFL achieves the significantly improved performance comparing to FedUV since the ProtoFL is robust to the increased clients for one-class classification, and the results show that lower $S_{c}$ indicate more discriminative features. Note, distributing the prototypical representation in secure", + "bbox": [ + 76, + 750, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/32ba4430cb19059812eb61a9196cd790fc35a21ecdabd7d340a2495f95d0ce50.jpg", + "image_caption": [ + "(a) Ours w/o $L_{pd}^{\\theta}, L_{reg}^{\\psi}$" + ], + "image_footnote": [], + "bbox": [ + 504, + 92, + 624, + 178 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/37155c805f098edcafee61fa1a6ff6869fc6cf7c0630a3181612bed1cdedba57.jpg", + "image_caption": [ + "(b) Ours w/o $L_{p}^{\\theta}, L_{reg}^{\\theta}$" + ], + "image_footnote": [], + "bbox": [ + 630, + 92, + 746, + 178 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a7a1f43994dddc32a01c1a68ae7af412364a98c539dc09141370edcb3fa48f8a.jpg", + "image_caption": [ + "(c) Ours", + "Figure 6: Visualization of latent-features using t-sne for our global model learned (Phase 1) with either each component or all. Score in each figure denote the silhouette values [36]." + ], + "image_footnote": [], + "bbox": [ + 753, + 93, + 888, + 178 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "is important to overcome the shortage of training data, limited round communications, and greater number of clients.", + "bbox": [ + 500, + 260, + 888, + 289 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8a1abffb0191da7e8383ea7cf16f9644b422ef11b1c0d91f2169d2dd80f104a5.jpg", + "image_caption": [ + "Figure 7: Left : Each score denotes cosine similarity $S_{c}$ between the various off-the-shelf datasets and models. Right : Performance comparison among the various global models whose off-the-shelf model is different. C and I denote CIFAR and ImageNet benchmarks." + ], + "image_footnote": [], + "bbox": [ + 493, + 291, + 658, + 436 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/acf3171f50444f8b4c79bc24f5cdff37d6eecac912fe68817cef9f9d9d82a54f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 678, + 291, + 883, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 532, + 617, + 547 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We proposed ProtoFL, a method for achieving effective round cost and scalability representation in extreme non-i.i.d. data based FL. By utilizing an off-the-shelf model and dataset to distribute prototypical independent representations, we were able to learn a global model with all joined clients and optimize the flow-based classifier of each client. Our proposed method outperforms FL methods with efficient communication cost and presents a novel property of scalability of representation, validating new joiners' performance in FL. We believe that our method and experimental details could be adapted to handle further problems in both federated and centralized learning based one-class classification.", + "bbox": [ + 496, + 559, + 890, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 763, + 666, + 780 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by KakaoBank Corp., and Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. 2022-0-00320, Artificial intelligence research about cross-modal dialogue modeling for one-on-one multi-modal interactions). In particular, we would like to thank the designer Eunha Lim (milkyway-mind@naver.com) for well-presented Figures 1, 2, and 3.", + "bbox": [ + 496, + 780, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "6477", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Unsupervised video anomaly detection via normalizing flows with implicit latent features. Pattern Recognition, 129:108703, 2022. 2", + "[2] Divyansh Aggarwal, Jiayu Zhou, and Anil K. Jain. Fedface: Collaborative learning of face recognition model. In IJCB, 2021. 1", + "[3] Liron Bergman and Yedid Hoshen. Classification-based anomaly detection for general data. arXiv preprint arXiv:2005.02359, 2020. 6, 7", + "[4] Markus M Breunig, Hans-Peter Kriegel, Raymond T Ng, and Jörg Sander. 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PMLR, 2020. 2, 6" + ], + "bbox": [ + 78, + 90, + 468, + 782 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "6479", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/ProtoFL_ Unsupervised Federated Learning via Prototypical Distillation/c82e3c6e-4735-400a-b460-81642c25b787_model.json b/2023/ProtoFL_ Unsupervised Federated Learning via Prototypical Distillation/c82e3c6e-4735-400a-b460-81642c25b787_model.json new file mode 100644 index 0000000000000000000000000000000000000000..6e55ea9e933ee48428e4ae04478fe409ebde8c4f --- /dev/null +++ b/2023/ProtoFL_ Unsupervised Federated Learning via Prototypical Distillation/c82e3c6e-4735-400a-b460-81642c25b787_model.json @@ -0,0 +1,2497 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.119, + 0.131, + 0.846, + 0.154 + ], + "angle": 0, + "content": "ProtoFL: Unsupervised Federated Learning via Prototypical Distillation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.188, + 0.892, + 0.209 + ], + "angle": 0, + "content": "Hansol Kim\\*1, Youngjun Kwak\\*12, Minyoung Jung3, Jinho Shin1, Youngsung Kim4, and Changick Kim" + }, + { + "type": "text", + "bbox": [ + 0.356, + 0.22, + 0.616, + 0.238 + ], + "angle": 0, + "content": "\\(^{1}\\)KakaoBank Corp., South Korea" + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.238, + 0.725, + 0.255 + ], + "angle": 0, + "content": "\\(^{2}\\)Department of Electrical Engineering, KAIST, South Korea" + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.255, + 0.725, + 0.273 + ], + "angle": 0, + "content": "\\(^{3}\\)KETI, Korea Electronics Technology Institute, South Korea" + }, + { + "type": "text", + "bbox": [ + 0.366, + 0.273, + 0.605, + 0.29 + ], + "angle": 0, + "content": "4Inha University, South Korea" + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.29, + 0.868, + 0.305 + ], + "angle": 0, + "content": "{han.kim,vivaan.yjkwak,william.shin}@lab.kakaobank.com,{yjk.kwak,changick}@kaist.ac.kr," + }, + { + "type": "text", + "bbox": [ + 0.301, + 0.305, + 0.663, + 0.318 + ], + "angle": 0, + "content": "minyoung.jung@keti.re.kr,y.kim@inha.ac.kr" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.359, + 0.314, + 0.375 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.391, + 0.474, + 0.662 + ], + "angle": 0, + "content": "Federated learning (FL) is a promising approach for enhancing data privacy preservation, particularly for authentication systems. However, limited round communications, scarce representation, and scalability pose significant challenges to its deployment, hindering its full potential. In this paper, we propose 'ProtoFL', Prototypical Representation Distillation based unsupervised Federated Learning to enhance the representation power of a global model and reduce round communication costs. Additionally, we introduce a local one-class classifier based on normalizing flows to improve performance with limited data. Our study represents the first investigation of using FL to improve one-class classification performance. We conduct extensive experiments on five widely used benchmarks, namely MNIST, CIFAR-10, CIFAR-100, ImageNet-30, and Keystroke-Dynamics, to demonstrate the superior performance of our proposed framework over previous methods in the literature." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.677, + 0.21, + 0.693 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.702, + 0.47, + 0.868 + ], + "angle": 0, + "content": "In recent years, there has been a growing concern about privacy, leading people to hesitate when it comes to uploading their biological data to central data servers. Moreover, companies that possess personal information from users are strictly bound by the General Data Protection Regulation (GDPR) [44]. To address these privacy issues, Federated Learning (FL), an emerging distributed data parallel machine learning approach, has been proposed. FL leverages the decentralized data available on individual clients to collaboratively train a shared global model on a mediator server without the need to share personal data." + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.357, + 0.895, + 0.546 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.553, + 0.895, + 0.646 + ], + "angle": 0, + "content": "Figure 1: Visualization of extreme non-i.i.d. (\\(\\alpha = 0.0\\) is a concentration parameter of Dirichlet distribution) data based FL schema shows that each device has only the data from its target class not shared among all joined devices, and prototypical representation is distributed separately to corresponding joined clients in secure from a central server." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.794 + ], + "angle": 0, + "content": "In the context of FL, where data is decentralized across individual clients, one-class classification (OCC) can be used. This is because that OCC can determine whether a new example belongs to the target distribution or not. Despite not using data from the non-target class, OCC has shown impressive performance [31, 38, 43, 42, 39, 40, 15, 28]. In computer vision applications, OCC is particularly useful for detecting fraud, defects, and unauthorized users." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Recent advancements in biometric authentication have highlighted the importance of FL-based OCC in computer vision (e.g., user-defined embedding-based methods [17, 26] and data-driven methods [2, 24, 32]). However, FL-based OCC methods face significant challenges, including high communication costs, limited representation, and unstable learning processes. Additionally, centralized server" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.368, + 0.888 + ], + "angle": 0, + "content": "*These authors contributed equally to this work" + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.221, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.368, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6470" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "based methods [31, 42, 43] may not be suitable for FL-based OCC due to limited computing resources on each device, which are a major obstacle for centralized methods that require substantial computing power." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.153, + 0.471, + 0.408 + ], + "angle": 0, + "content": "The limitations inherent in FL-based OCC necessitated the development of a novel approach to address these challenges. In this paper, we aim to attain a more expressive global model without the need for frequent re-training processes between the central server and client devices on a large scale. To achieve this, we propose Prototypical representation distillation based unsupervised Federated Learning (ProtoFL) that distills representation from an off-the-shelf model learned using off-the-shelf datasets, regardless of individual client data. In contrast to traditional FL-based OCC, our proposed ProtoFL approach does not transfer parameters directly to the client, as depicted in Fig. 1. This resolves the issues of frequent round communication costs and the need for extra data due to one-time prototype representation distillation. ProtoFL provides a novel solution to the existing challenges of FL-based OCC, enabling efficient and effective global model updates." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.47, + 0.649 + ], + "angle": 0, + "content": "Subsequently, we suggest a novel approach for estimating the density of a target class in a distributed setting using a flow-based one-class classifier [20]. To achieve this, we conduct the estimation on individual client devices, using augmented latent variables for training their distributed models. Our approach leverages two key techniques: maximum likelihood estimation with log-likelihood and a probabilistic similarity loss function that includes \\(\\mathcal{KL}\\)-divergence. By combining the distillation and one-class classification phases, we can effectively handle complex data distributions that are non-independent and nonidentically distributed across individual clients. Our two-phase learning framework is inspired by the success of flow-based models in various applications [20, 11, 40, 1], and we demonstrate its effectiveness in handling complex data distributions in the distributed settings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.65, + 0.47, + 0.814 + ], + "angle": 0, + "content": "The experimental findings of our proposed method demonstrate superior classification performance compared to both server-based and client-based methods on both image and tabular datasets. Additionally, we have validated the scalability of the learned representation and have shown that the global model learned by the ProtoFL is compatible with existing one-class classifiers as well as our one-class classifier based on the benchmark datasets. Our results indicate that our method is a promising approach for large-scale machine learning tasks that require robust and scalable classification capabilities." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.817, + 0.382, + 0.83 + ], + "angle": 0, + "content": "Our contributions are described as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.84, + 0.47, + 0.901 + ], + "angle": 0, + "content": "- We propose a novel unsupervised federated learning framework that effectively addresses the challenge of insufficient local training data. By leveraging normalizing flows for local classifier learning and prototypical" + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.092, + 0.89, + 0.121 + ], + "angle": 0, + "content": "representation distillation, our approach enables efficient and effective global model updates." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.145, + 0.892, + 0.236 + ], + "angle": 0, + "content": "- We propose a novel prototype-based representation learning method for distilling normal data representation using an off-the-shelf model and dataset. Our approach demonstrates the scalability of the global model, which can be verified by adding new clients in FL-based OCC." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.247, + 0.892, + 0.323 + ], + "angle": 0, + "content": "- We propose new federated and centralized learning methods for one-class classification, which we evaluate on five widely-used benchmarks. Our experiments show that our methods achieve superior performance compared to existing approaches." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.145, + 0.892, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.334, + 0.642, + 0.35 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.359, + 0.892, + 0.661 + ], + "angle": 0, + "content": "One-class classification Various one-class classification approaches have been proposed and categorized into description-based and representation-based learning. In the description-based methods, Deep-SVDD [31] performs one-class detection by learning a model to map target samples into a center in the latent space, otherwise non-target samples are mapped far from the center. And FCDD [27] proposes an explainable one-class classifier by upsampling based on gaussian sampling. In contrast, representation-based learning methods (DROC [42] and CSI [43]) present a two-step learning framework to learn a representation model through excessive data-augmentation and contrastive loss. The framework either employs a classifier or defines a score function for detecting a target class. Unlike previous centralized server-based approaches, our proposed approach for one-class classification on decentralized learning avoids the risk of personal data leakage by constructing a model using distributed data. To the best of our knowledge, our method is the first to directly address this problem in a decentralized setting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Federated learning for local one-class classifier Federated Learning (FL) is a distributed machine learning paradigm that enables collaborative model training without direct data sharing. FL has been applied to one class classification (OCC) tasks for user verification and authentication, with several studies demonstrating promising results. [17, 32, 34]. FedAwS [45] introduces a geometric regularization to learn a global model by utilizing uploaded latent variables of joined clients in a central server. Since the latent variables shared on a server are private data, the FedAwS violates in the setting of FL. FedUV [17] employs independent secret error correcting codes (ECCs) to train a one-class classifier by preventing personal data from sharing among joined clients. The secret codes induce the concise objective of FedUV so that only positive examples are" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "6471" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.166 + ], + "angle": 0, + "content": "required. The FedUV approach was further refined to estimate a center of distribution by FedAA [32] and FedMetric [34], instead of defining hand-designed codes. However, local data on each device is not sufficient to represent a centroid of local data distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.178, + 0.469, + 0.314 + ], + "angle": 0, + "content": "Federated learning for central and client classifiers In authentication systems, client data is often partitioned according to a target class. This results in highly or extremely non-i.i.d. data that poses a significant challenge for FL. This extreme non-i.i.d. means that a concentration parameter of Dirichlet distribution approaches to zero \\((\\alpha = 0.0)\\) while many federated learning methods [6, 9, 13] assumes non-i.i.d. data with non-zero \\((\\alpha \\neq 0.0)\\) setting [18, 23, 29, 6, 13, 9]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.315, + 0.47, + 0.555 + ], + "angle": 0, + "content": "Unsupervised federated learning methods [23, 29] aggregate local representation models and centroids for achieving a global model and centroid. FedRep [6] shares partitions of a global model to adapt each local heterogeneous data. FedX [13], which utilizes structure knowledge distillation between local and global knowledge relationships, learns meaningful data representation without sharing external data. SphereFed [9] introduced a learned matrix, which is a fixed-classifier for sharing among all participating clients, to transform each local data distribution into the predefined latent space. But, SphereFed requires enormous cost to re-construct and re-distribute a new learned matrix whenever a new client joins. Therefore, we first propose a prototypical representation distillation learning to save communication cost in FL with extreme non-i.i.d. \\((\\alpha = 0.0)\\) data settings." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.567, + 0.204, + 0.584 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.593, + 0.469, + 0.683 + ], + "angle": 0, + "content": "Federated Average Learning FedAVG [30], composed of participating clients and a central mediator server, trains a global model by aggregating locally-computed parameters, and broadcasts the updated global model to the clients. In each round, FedAVG updates the global model parameters with local model parameters as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.689, + 0.47, + 0.731 + ], + "angle": 0, + "content": "\\[\n\\theta_ {g} ^ {t + 1} = \\sum_ {k = 1} ^ {K} \\frac {\\left| D _ {k} \\right|}{\\sum_ {k = 1} ^ {K} \\left| D _ {k} \\right|} \\theta_ {k} ^ {t}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.737, + 0.469, + 0.814 + ], + "angle": 0, + "content": "where \\( k \\in \\{1, \\dots, K\\} \\) indicates an index of a local client. \\( \\theta_{g}^{t+1} \\) is the parameters of a global model, and \\( \\theta_{k}^{t} \\) is the parameters of the \\( k^{th} \\) local model at a round \\( t \\). For the balanced updating of the global model \\( \\theta_{g}^{t+1} \\), \\( |D_{k}| \\) is the number of samples on dataset \\( D_{k} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Unsupervised Contrastive Learning FL with extreme non-i.i.d. \\((\\alpha = 0.0)\\) data setting is unavailable to access samples of the other clients. Thus, we simplify the contrastive loss, \\(\\mathcal{L}_{cntr} = y \\times (1 - d(\\bullet, \\hat{\\bullet})) + (1 - y) \\times \\max(0, d(\\bullet, \\hat{\\bullet}))\\), as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.635, + 0.114, + 0.892, + 0.13 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d} = 1 - d (\\bullet , \\hat {\\bullet}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.139, + 0.892, + 0.187 + ], + "angle": 0, + "content": "where \\(d(\\bullet, \\hat{\\bullet})\\) is the cosine-similarity \\(\\frac{\\bullet \\cdot \\hat{\\bullet}}{||\\bullet|| \\cdot ||\\hat{\\bullet}||}\\). We utilize \\(L_{d}\\) as our positive cosine similarity loss for our unsupervised leaning, instead of \\(\\mathcal{L}_{cntr}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.197, + 0.892, + 0.334 + ], + "angle": 0, + "content": "Normalizing Flows Normalizing flows (NFs) [8] are the statistical methods using the change-of-variable law of probabilities to fit an arbitrary target density \\( p_R(r) \\) by a tractable base distribution with density \\( p_Z(z) \\) and a bijective invertible mapping \\( \\mathfrak{t}^{-1}: R^D \\to Z^D \\Leftrightarrow \\mathfrak{t}: Z^D \\to R^D \\). According to [33], \\( \\mathcal{KL} \\)-divergence and log-likelihood estimation are employed to optimize the invertible flow-based model \\( z = \\mathfrak{t}^{-1}(r; \\psi) \\) and \\( r = \\mathfrak{t}(z; \\psi) \\) by the target distribution \\( p_R(r) \\). The bijective invertible mapping is drawn as:" + }, + { + "type": "equation", + "bbox": [ + 0.511, + 0.352, + 0.891, + 0.402 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {D} _ {\\mathcal {K L}} \\left[ \\hat {p} _ {R} (r) \\| p _ {R} (r; \\psi) \\right] \\\\ \\approx - \\mathbb {E} _ {\\hat {p} _ {R} (r)} \\left[ \\log p _ {Z} \\left(\\mathrm {t} ^ {- 1} (r; \\psi)\\right) + \\log | \\det j _ {\\mathrm {t} ^ {- 1}} | \\right] + c o n t, \\tag {3} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.403, + 0.892, + 0.515 + ], + "angle": 0, + "content": "where \\(p_R(r;\\psi)\\) denotes the likelihood of a model. \\(\\hat{p}_R\\) is the target distribution to learn the model by \\(\\mathcal{KL}\\)-divergence. \\(p_R(r;\\psi)\\) only remains for learning parameters \\(\\psi\\), and then is replaced by \\(\\frac{1}{N}\\sum_{i=1}^{N}\\left[\\frac{\\|\\mathfrak{t}^{-1}(r_i)\\|_2^2}{2}-\\log|\\det\\mathfrak{j}_{\\mathfrak{t}^{-1}}|\\right]\\) through the training dataset \\(D_k\\) as explained by [11, 20]. The re-written equation is applied to our objective to estimate the log-likelihood of given local data on each device." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.527, + 0.673, + 0.544 + ], + "angle": 0, + "content": "4. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.553, + 0.892, + 0.613 + ], + "angle": 0, + "content": "In this section, we propose a two-phase unsupervised learning framework that combines unsupervised federated learning via distillation of prototypical representations with local classifier learning via leveraging normalizing flows." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.62, + 0.704, + 0.635 + ], + "angle": 0, + "content": "4.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.643, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Participating \\(K\\) clients aim to train a global model by aggregating locally-computed parameters \\(\\phi(\\bullet, \\theta)\\) for an one-class classification task without sharing private data among joined clients. Each client has a training dataset \\(D_{K,N} = \\{x_{k,i}, 1 \\leq i \\leq N, 1 \\leq k \\leq K\\}\\) and \\(N\\) is the cardinality of the local data \\(D_{k,N}\\). Let \\(\\phi(x_{k,i}; \\theta_k)\\) denote the trainable model of the \\(k^{th}\\) client. In particular, we follow the extreme non-i.i.d. \\((\\forall_{m,n} D_{m,N} \\cap D_{n,N} = \\emptyset)\\) data setting in our FL-based OCC. Different from prior FL settings utilizing either hand-designed codes or additional training datasets, we invent generic representation of the local model \\(\\phi\\) by leveraging the off-the-shelf model \\(\\mathcal{F}\\) and dataset \\(S\\), and we employ the flow-based model \\(\\psi\\) for the local one-class classifier." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.719, + 0.864 + ], + "angle": 0, + "content": "4.2. Sequence of procedures" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As shown in Fig. 2, we describe our proposed method workflow in each phase. \\(①\\) Whenever a new client partici" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6472" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.576, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.081, + 0.283, + 0.574, + 0.298 + ], + "angle": 0, + "content": "(a) Phase 1: Unsupervised federated learning via prototypical representation distillation" + }, + { + "type": "image", + "bbox": [ + 0.58, + 0.091, + 0.892, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.58, + 0.204, + 0.891, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.59, + 0.284, + 0.882, + 0.298 + ], + "angle": 0, + "content": "(b) Phase 2: Local one-class classifier based on NFs" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.305, + 0.894, + 0.352 + ], + "angle": 0, + "content": "Figure 2: Overview of our proposed two-phase learning architecture. \\(① \\sim\\) \\(④\\) indicates the workflows of ProtoFL with all the joined clients to upload parameters of each client and to download the aggregated global model, and \\(⑤\\) represents a local training for the OC-NF. The details of sequences \\(① \\sim\\) \\(⑤\\) are described in Section 4.2. NFs denote normalizing flows." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.473, + 0.609 + ], + "angle": 0, + "content": "pates in our unsupervised federated learning, all clients join a central mediator server. ② For the \\(k^{th}\\) client, a categorical image \\(s_k\\) is chosen from \\(\\mathcal{S}\\) and transformed into a latent variable \\(v_k\\) by the central mediator server. Both ① and ② occur only once at the first time, and \\(\\mathcal{V} = \\{v_k, 1 \\leq k \\leq K\\}\\) is secretly distributed to the corresponding client. ③ We train the \\(k^{th}\\) local model \\(\\theta_k\\) via the local data \\(D_{k,N}\\), the distributed prototype representation \\(v_k\\), cosine similarly loss, and \\(\\mathcal{KL}\\)-divergence loss. ④ A global model \\(\\theta_g\\) is aggregated with all the uploaded local models by FedAVG, and the global model is distributed to all participating clients. ⑤ Once federated representation learning has finished, we train a local one-class classifier based on normalizing flows (OC-NF) by using maximum likelihood and cosine similarity losses. We describe the details of our procedures (① ~ ⑤) in the following subsections." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.624, + 0.47, + 0.656 + ], + "angle": 0, + "content": "4.3. Prototypical representation distillation based unsupervised federated learning (ProtoFL)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.662, + 0.47, + 0.756 + ], + "angle": 0, + "content": "We assume \\(\\mathcal{F}:R^{W\\times H\\times C}\\to R^D\\) and \\(\\phi :R^{W\\times H\\times C}\\to\\) \\(R^D\\) indicate the off-the-shelf model and the local model, respectively as illustrated in Fig. 2. For training the local model of the \\(k^{th}\\) client, we augment two views \\(x_{k,i},\\hat{x}_{k,i}\\) from the \\(i^{th}\\) example of the local training data \\(D_{k,N}\\), and subsequently transform the two samples as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.777, + 0.47, + 0.793 + ], + "angle": 0, + "content": "\\[\nr _ {k, i} = \\phi \\left(x _ {k, i}; \\theta_ {k}\\right); \\hat {r} _ {k, i} = \\phi \\left(\\hat {x} _ {k, i}; \\theta_ {k}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.81, + 0.471, + 0.902 + ], + "angle": 0, + "content": "where \\( r_{k,i} \\) and \\( \\hat{r}_{k,i} \\) represent latent variables of the \\( i^{th} \\) example. \\( \\phi \\) is the client model with \\( k^{th} \\) learnable parameters \\( \\theta_{k} \\). Inspired by SimCLR [5], the two latent variables \\( r_k \\) and \\( \\hat{r}_k \\) must be very close to each other. Given the only positive local data and the constraint, we employ the positive cosine similarity loss(Eq. 2) to learn the local model as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.391, + 0.892, + 0.432 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p} ^ {\\theta} \\left(\\theta_ {k}\\right) = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left[ 1 - d \\left(r _ {k, i}, \\hat {r} _ {k, i}\\right) \\right], \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.444, + 0.893, + 0.535 + ], + "angle": 0, + "content": "where \\(\\theta_{k}\\) is optimized by the local data \\(D_{k,N}\\). To overcome the small cardinality of local data for training the local representative model, we propose the off-the-shelf model with pre-trained parameters \\(\\mathcal{F}(\\bullet ;\\omega)\\) and the off-the-shelf dataset \\(s_k\\in S_s\\). The off-the-shelf model and dataset are utilized on a central mediator server as depicted:" + }, + { + "type": "equation", + "bbox": [ + 0.642, + 0.549, + 0.892, + 0.565 + ], + "angle": 0, + "content": "\\[\nv _ {k} = \\mathcal {F} \\left(s _ {k}; \\omega\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.578, + 0.892, + 0.7 + ], + "angle": 0, + "content": "where \\( s_k \\) and \\( v_k \\) represent a prototype example and representation for the \\( k^{th} \\) client. After \\( \\mathcal{V} = \\{v_k, 1 \\leq k \\leq K\\} \\) is distributed to the corresponding client in secret, we train the local model of the \\( k^{th} \\) client to estimate the prototypical target representation \\( v_k \\). We employ the \\( \\mathcal{KL} \\)-divergence to minimize the discrepancy between two distributions \\( v_k \\) and either \\( r_k \\) or \\( \\hat{r}_k \\). Therefore, we invent the prototypical distillation loss as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.519, + 0.713, + 0.892, + 0.754 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p d} ^ {\\theta} \\left(\\theta_ {k}\\right) = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left[ \\mathcal {K L} \\left(v _ {k} \\| r _ {k, i}\\right) + \\mathcal {K L} \\left(v _ {k} \\| \\hat {r} _ {k, i}\\right) \\right], \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.767, + 0.892, + 0.828 + ], + "angle": 0, + "content": "where \\(\\mathcal{KL}(v_k\\| r_{k,i})\\) and \\(\\mathcal{KL}(v_k\\|\\hat{r}_{k,i})\\) are equally contributed to our distillation loss. Figure 3 describes the details of Eq. 5 and Eq. 7, and the overall objective of the first phase (phase 1) is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.84, + 0.892, + 0.86 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\phi} \\left(\\theta_ {k}\\right) = (1 - \\alpha) \\times \\mathcal {L} _ {p d} ^ {\\theta} \\left(\\theta_ {k}\\right) + \\alpha \\times \\mathcal {L} _ {p} ^ {\\theta} \\left(\\theta_ {k}\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is a balancing weight. In our experiment, \\(\\alpha\\) is empirically set to 0.1." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6473" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.351, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.089, + 0.468, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.267, + 0.47, + 0.314 + ], + "angle": 0, + "content": "Figure 3: Illustration of learning a global model with prototypical representation distillation on distributed devices without sharing private data among participating clients." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.328, + 0.47, + 0.359 + ], + "angle": 0, + "content": "4.4. Local one-class classifier via Normalizing Flows (OC-NF)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.368, + 0.471, + 0.475 + ], + "angle": 0, + "content": "After unsupervised federated representation learning for the global model, we leverage a general flow-based model for training the local one-class classifier in each client as shown in Fig. 2. To estimate log-likelihood of transformed latent variables \\( r_k \\) and \\( \\hat{r}_k \\), we exploit Eq. 3 to learn the probabilistic normalizing flows \\( \\mathfrak{t} \\) through the local dataset \\( D_{k,N} \\) and the local model \\( \\phi (\\cdot ;\\theta_k) \\) on the \\( k^{th} \\) client as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.49, + 0.469, + 0.597 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {m l e} ^ {\\psi} (\\psi_ {k}) \\\\ = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left[ \\frac {\\| \\mathfrak {t} ^ {- 1} (r _ {k , i} ; \\psi_ {k}) \\| _ {2} ^ {2}}{2} - \\log | \\det \\mathfrak {j} _ {k, i} | \\right] + c o n t \\\\ \\approx \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left[ \\frac {\\left\\| z _ {k , i} \\right\\| _ {2} ^ {2}}{2} - \\log | \\det j _ {k, i} | \\right] + c o n t, \\tag {9} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.47, + 0.7 + ], + "angle": 0, + "content": "where \\( z_{k,i} \\) is the estimated distribution as it passes through \\( \\mathrm{t}^{-1}(r_{k,i};\\psi_k) \\). \\( r_{k,i} \\) is a latent variable from \\( \\phi (x_{k,i};\\theta) \\). When optimizing the flow-based model, we ignore constants, det and cont. Since \\( r_{k,i} \\) and \\( \\hat{r}_{k,i} \\) are close each other in a latent space, \\( z_{k,i} \\) and \\( \\hat{z}_{k,i} \\) also predict the same distribution so that we introduce the following objective as a regularizer:" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.713, + 0.47, + 0.755 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r e g} ^ {\\psi} (\\psi_ {k}) = \\frac {1}{N} \\sum_ {i = 1} ^ {N} [ 1 - d (z _ {k, i}, \\hat {z} _ {k, i}) ], \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.766, + 0.469, + 0.827 + ], + "angle": 0, + "content": "where \\(z_{k,i}\\) and \\(\\hat{z}_{k,i}\\) are the normal distribution estimated by \\(\\mathfrak{t}^{-1}((\\phi (x_{k,i};\\theta_k);\\psi_k))\\) and \\(\\mathfrak{t}^{-1}((\\phi (\\hat{x}_{k,i};\\theta_k);\\psi_k))\\) respectively. The overall objective of the second phase (phase 2) is composed of Eq. 9 and Eq. 10 as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.839, + 0.469, + 0.86 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {t}} \\left(\\psi_ {k}\\right) = \\mathcal {L} _ {m l e} ^ {\\psi} \\left(\\psi_ {k}\\right) + \\lambda \\times \\mathcal {L} _ {r e g} ^ {\\psi} \\left(\\psi_ {k}\\right), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is a hyper-parameter for effectiveness of regularization. For our experiment, we empirically set \\(\\lambda\\) to 0.01." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.634, + 0.108 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.116, + 0.894, + 0.222 + ], + "angle": 0, + "content": "In this section, we demonstrate the proposed approach on image and tabular benchmarks. We evaluate the performance of our proposed ProtoFL and compare our model with the other FL methods and one-class detectors. And we analyze the impact of new client participation in the context of OCC on FL, as well as ablation studies on each proposed component." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.232, + 0.602, + 0.246 + ], + "angle": 0, + "content": "5.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.255, + 0.893, + 0.513 + ], + "angle": 0, + "content": "We thoroughly evaluate our proposed method on several benchmark datasets, including the widely used MNIST [22], CIFAR-10 [21], CIFAR-100 [21], ImageNet-30 [16], and Keystroke-Dynamics [19], to tackle the demanding task of one-class classification. Our evaluation scrutinizes the efficacy, robustness, and scalability of our method, highlighting its strengths in handling real-world scenarios. In case of CIFAR-100, we adopt 20 super-class labels, denoted by CIFAR- \\(100^{\\ddagger}\\), as suggested in [10] to our experiments. The numbers of categories in the benchmarks are 10, 10, 20, 30, and 51, which are the numbers of participating clients on our federated learning. The vision and tabular based benchmarks for OCC follow a one-vs-rest protocol [10, 42, 43]. In the protocol, a set of samples from one class indicates a target class for one client, whereas a set of samples from the remaining classes represents a non-target class for the remaining clients." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.522, + 0.688, + 0.539 + ], + "angle": 0, + "content": "5.2. Experiment Setting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.545, + 0.894, + 0.637 + ], + "angle": 0, + "content": "Off-the-shelf model and dataset In the central mediator server, the off-the-shelf dataset and model generate prototypical representation when a new client participates in our unsupervised federated learning. For the off-the-shelf model and dataset, we exploit ArcFace [7] based ResNet-50 backbone [14] and MS-Celeb-1M [12], respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.894, + 0.795 + ], + "angle": 0, + "content": "Architectures In this experiment, we employ ResNet-18/32 backbones [14] to learn the local and global models on our proposed approach. Since batch normalization is detrimental to the performance in federated learning [17] both ResNet-18/32 backbones replace batch- with group-normalization. In the Keystroke Dynamics dataset, we employ multi-layer perceptions as the local and global model, consisting of three linear layers, ReLU, and group-normalization. And we utilize NFs as a local classifier model composed of 8 coupling layers [8]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Implementation details In the first phase as described in Algorithm 1, we train our expressive global model based on the FedAvg [30] method with 1 local epoch and 900 communication rounds, using randomly chosen clients from all participating clients. We utilize the RAdam optimizer [25] with betas 0.94 and 0.98, a weight decay 1e-3 and a learning" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6474" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.081, + 0.092, + 0.385, + 0.106 + ], + "angle": 0, + "content": "Algorithm 1 Procedure of our two-phase learning" + }, + { + "type": "text", + "bbox": [ + 0.095, + 0.111, + 0.38, + 0.124 + ], + "angle": 0, + "content": "Phase 1 (ProtoFL): Start phase 1 for \\(T\\) rounds." + }, + { + "type": "text", + "bbox": [ + 0.095, + 0.125, + 0.468, + 0.166 + ], + "angle": 0, + "content": "Initialize and broadcast a global model \\(\\theta_g^0\\) to all joined \\(K\\) clients. Send an acknowledgement (ACK) with prototypical representation \\(v_{k}\\) to the \\(k^{th}\\) client." + }, + { + "type": "text", + "bbox": [ + 0.095, + 0.167, + 0.232, + 0.178 + ], + "angle": 0, + "content": "for \\(t\\gets 0\\) to \\(T - 1\\) do" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.179, + 0.342, + 0.195 + ], + "angle": 0, + "content": "\\[\n\\theta_ {g} ^ {t + 1} \\leftarrow \\text {G L O B A L - T R A I N I N G} (t, \\theta_ {g} ^ {t})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.195, + 0.143, + 0.206 + ], + "angle": 0, + "content": "end for" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.207, + 0.314, + 0.222 + ], + "angle": 0, + "content": "Update the global model \\(\\theta_g\\) with \\(\\theta_g^T\\)." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.222, + 0.431, + 0.25 + ], + "angle": 0, + "content": "function GLOBAL TRAINING \\((t,\\theta_g^t)\\) Randomly select \\(k\\) number of clients from \\(\\{C_k\\}_{k = 1}^K\\)" + }, + { + "type": "text", + "bbox": [ + 0.118, + 0.251, + 0.233, + 0.261 + ], + "angle": 0, + "content": "for \\(k\\gets 1\\) to \\(K\\) do" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.263, + 0.36, + 0.277 + ], + "angle": 0, + "content": "\\[\n\\text {B r o a d c a s t} \\theta_ {q} ^ {t} \\text {t o} C _ {k}.\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.277, + 0.407, + 0.292 + ], + "angle": 0, + "content": "\\[\n\\theta_ {k} ^ {t}, \\left| D _ {k, N} \\right| \\leftarrow \\text {C L I E N T - T R A I N I N G} (t, k, \\theta_ {g} ^ {t})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.118, + 0.293, + 0.165, + 0.302 + ], + "angle": 0, + "content": "end for" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.302, + 0.303, + 0.323 + ], + "angle": 0, + "content": "\\[\n\\theta_ {g} ^ {t + 1} \\leftarrow \\sum_ {k = 1} ^ {K} \\frac {\\left| D _ {k , N} \\right|}{\\sum_ {k = 1} ^ {K} \\left| D _ {k , N} \\right|} \\theta_ {k} ^ {t}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.323, + 0.19, + 0.338 + ], + "angle": 0, + "content": "\\[\n\\mathrm {r e t u r n} \\theta_ {g} ^ {t + 1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.339, + 0.177, + 0.349 + ], + "angle": 0, + "content": "end function" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.351, + 0.344, + 0.366 + ], + "angle": 0, + "content": "function CLIENT.TrAINING \\((t,k,\\theta_g^t)\\)" + }, + { + "type": "text", + "bbox": [ + 0.118, + 0.366, + 0.416, + 0.38 + ], + "angle": 0, + "content": "Download the global model \\(\\theta_g^t\\), and assign it to \\(\\theta_k^t\\)" + }, + { + "type": "text", + "bbox": [ + 0.118, + 0.38, + 0.242, + 0.392 + ], + "angle": 0, + "content": "for \\(x_{k,i}\\in D_{K,N}\\) do" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.392, + 0.412, + 0.407 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\phi} \\left(\\theta_ {k} ^ {t}\\right) = (1 - \\alpha) \\times \\mathcal {L} _ {p d} ^ {\\theta} \\left(\\theta_ {k} ^ {t}\\right) + \\alpha \\times \\mathcal {L} _ {p} ^ {\\theta} \\left(\\theta_ {k} ^ {t}\\right)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.407, + 0.278, + 0.421 + ], + "angle": 0, + "content": "\\[\n\\theta_ {k} ^ {t} \\leftarrow \\theta_ {k} ^ {t} - \\eta \\nabla \\mathcal {L} _ {\\phi} \\left(\\theta_ {k} ^ {t}\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.118, + 0.421, + 0.166, + 0.432 + ], + "angle": 0, + "content": "end for" + }, + { + "type": "text", + "bbox": [ + 0.118, + 0.433, + 0.412, + 0.448 + ], + "angle": 0, + "content": "Calculate the number of the \\(k^{th}\\) client data \\(D_{k,N}\\)." + }, + { + "type": "text", + "bbox": [ + 0.118, + 0.448, + 0.25, + 0.462 + ], + "angle": 0, + "content": "return \\(\\theta_k^t\\) and \\(|D_{k,N}|\\)" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.463, + 0.177, + 0.474 + ], + "angle": 0, + "content": "end function" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.476, + 0.469, + 0.503 + ], + "angle": 0, + "content": "Phase 2 (OC-NF): All joined clients start Algorithm 2 for OCC." + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.523, + 0.371, + 0.537 + ], + "angle": 0, + "content": "Algorithm 2 Procedure of our OC-NF for OCC" + }, + { + "type": "text", + "bbox": [ + 0.095, + 0.543, + 0.469, + 0.586 + ], + "angle": 0, + "content": "Download the global model \\(\\theta_{g}\\), and assign it to the \\(k^{th}\\) client model \\(\\theta_{k}\\). Freeze the global representation model \\(\\phi (\\bullet ;\\theta_k)\\). Initialize the flow-based model of the \\(k^{th}\\) client \\(\\mathfrak{t}_{\\psi_k}\\)." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.587, + 0.217, + 0.599 + ], + "angle": 0, + "content": "for \\(x_{k,i}\\in D_{k,N}\\) do" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.599, + 0.348, + 0.615 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathfrak {t}} (\\psi_ {k}) = \\mathcal {L} _ {m l e} ^ {\\psi} (\\psi_ {k}) + \\lambda \\times \\mathcal {L} _ {r e g} ^ {\\psi} (\\psi_ {k})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.615, + 0.261, + 0.628 + ], + "angle": 0, + "content": "\\[\n\\psi_ {k} \\leftarrow \\psi_ {k} - \\eta \\nabla \\mathcal {L} _ {\\mathrm {t}} (\\psi_ {k})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.629, + 0.143, + 0.639 + ], + "angle": 0, + "content": "end for" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.67, + 0.47, + 0.79 + ], + "angle": 0, + "content": "rate 1e-6 to learn local models. In the second phase as described in Algorithm 2, we use the SGD optimizer [35] with a learning rate 5e-3 and 5 epochs to learn our one-class classifier. Data augmentations include the set of random processes (crop, horizontal-flip, and gaussian-blur) and color jitter. To evaluate the performance of various methods, we use the area under curve of ROC curve (AUROC) and equal error rate (EER)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.801, + 0.279, + 0.817 + ], + "angle": 0, + "content": "5.3. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Image and tabular benchmarks For the image benchmarks, we present the results on MNIST and CIFAR-10 datasets for OCC in extreme non-i.i.d. \\((\\alpha = 0.0)\\) data setting of FL. Table 1 shows the outstanding result of not only the significantly improved performance but also the" + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.089, + 0.892, + 0.164 + ], + "angle": 0, + "content": "
MethodNetworkMNISTCIFAR-10
AUROCRoundAUROCRound
FedAwS [45]ResNet-3299.610K94.1100K
FedUV [17]ResNet-3299.720K87.220K
FedMetric [34]ResNet-3299.610K94.2100K
OursResNet-3299.90.9K95.20.9K
" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.165, + 0.892, + 0.224 + ], + "angle": 0, + "content": "Table 1: Performance comparison FL-based methods with our proposed approach on MNIST and CIFAR-10 benchmarks. Our approach outperforms both benchmarks while reducing the communication round cost." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.241, + 0.892, + 0.369 + ], + "angle": 0, + "content": "
TypeMethodNetworkCIFAR-10CIFAR-100‡ImageNet-30
AUROCAUROCAUROC
Centralized LearningAE [27]---56.0
OC-SVM [41]-58.863.1-
Geom [10]WRN-16-886.078.7-
Rot [16]ResNet-1889.877.777.9
GOAD [3]ResNet-1885.174.5-
DROC [42]ResNet-1892.586.5-
CSI [43]ResNet-1894.386.691.6
FLOW† [40]ResNet-5095.293.0-
Federated LearningFedUV [17]ResNet-1879.8*55.9*62.8*
FedRep [6]ResNet-1858.2*56.9*56.3*
OursResNet-1895.389.995.4
" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.371, + 0.892, + 0.461 + ], + "angle": 0, + "content": "Table 2: AUROC of various centralized and decentralized detection methods on CIFAR-10/100\\(\\ddagger\\), and ImageNet-30 for OCC. \\(\\dagger\\) and \\(*\\) denote the usage of a pre-trained model learned on ImageNet-1M and the values from our reimplementation respectively, whereas **bold** and **underline** indicate the best results and the second results, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.892, + 0.808 + ], + "angle": 0, + "content": "effective communication cost on FL methods. We found that our proposed method exploits the off-the-shelf model and dataset to compensate the shortage of the local data. For updating a global model every rounds, naive FL methods [45, 17, 34] minimize the distance among the latent variables of the local data and map the distribution of the local data into one secure code designated. Those methods demand the inordinate communication cost and show the limited performance due to the deficiency of the local data on each device and the entangled secure code on latent space. Furthermore, we compare our approach with various centralized methods as depicted in Table 2. Our method outperforms ResNet-18 based methods on CIFAR-10 and ImageNet-30. In case of CIFAR- \\(100^{\\ddagger}\\), our approach places the second-rank performance comparing with FLOW [40] leveraging the feature extraction of a pre-trained model learned on ImageNet-1M. Note that our proposed method is the first rank among ResNet-18 based methods having no additional training datasets and limited computing resources. Among FL methods, our proposed method accomplishes the consistently improved performance on the image benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.9 + ], + "angle": 0, + "content": "For the tabular benchmark, we make the comparisons to the centralized methods on the Keystroke-Dynamics dataset for one-class classification as shown in Fig. 4. As the results, we found that our proposed method reduces EER more than two times comparing to prior methods. Training a foundation model as the global model is essential for the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.957 + ], + "angle": 0, + "content": "6475" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.09, + 0.894, + 0.263 + ], + "angle": 0, + "content": "
TypeMethodNetworkPlaneCarBirdCatDeerDogForgHorseShipTruckMean (std)
Centralized LearningOC-SVM [41]-65.640.965.350.175.251.271.851.267.948.558.8 (±11.6)
DeepSVDD [37]LeNet61.765.950.859.160.965.767.767.375.973.164.8 (±7.17)
Geom [10]WRN-16-874.795.778.172.487.887.883.495.593.391.386.0 (±8.52)
Rot [16]WRN-16-477.596.987.380.992.790.290.996.595.293.390.1 (±6.52)
GOAD [3]WRN-16-477.296.783.377.787.887.890.096.193.892.088.2 (±6.99)
Rot [16]ResNet-1880.496.485.981.191.389.689.995.995.092.689.8 (±5.75)
GOAD [3]ResNet-1875.594.181.872.083.784.482.993.992.989.585.1 (±7.61)
DROC [42]ResNet-1890.998.988.083.189.990.393.598.296.595.292.5 (±4.95)
CSI [43]ResNet-1889.999.193.186.493.993.295.198.797.995.594.3 (±3.97)
FLOW† [40]ResNet-5096.197.592.689.893.395.798.094.797.896.695.2 (±2.64)
Federated LearningOursResNet-1896.497.992.790.995.892.796.496.497.696.795.3 (±2.38)
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.263, + 0.893, + 0.309 + ], + "angle": 0, + "content": "Table 3: AUROC of various centralized and decentralized detection methods on CIFAR-10 for one-class classification. We present the AUROC of each class and the mean and standard deviation (std) of AUROC for all classes. \\(\\dagger\\), bold, and underline denote the usage of a pre-trained model learned on ImageNet-1M, the best results, and the second results, respectively." + }, + { + "type": "image", + "bbox": [ + 0.14, + 0.323, + 0.406, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.476, + 0.471, + 0.566 + ], + "angle": 0, + "content": "Figure 4: Comparison to previous methods of one-class classification on the Keystroke-Dynamics dataset. OC, Manhattan, AE, and MLP denote Outlier Count, Euclidean detector with Manhattan distance, Auto-Encoder, and 4-multi layer perception, respectively, from [19]. \\(\\mathbb{I}\\) denotes a standard deviation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.587, + 0.47, + 0.618 + ], + "angle": 0, + "content": "OCC task instead of the various architectures and distance metrics to achieve notably improved performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.623, + 0.471, + 0.866 + ], + "angle": 0, + "content": "Centralized vs Federated learning As shown in Table 3, we compare our proposed method with the centralized learning based methods because there is no previous FL method studying sufficiently analysis results for CIFAR-10. Our proposed approach outperforms the previous methods in terms of the overall mean and standard deviation because we collaboratively train our global model to represent all classes by the distributively-learned local models, and then we apply our non-biased global model to transform raw data into latent spaces for learning a local one-class classifier in each client as shown in Fig. 5. In case of each class, this method shows the first and second-placed performance in 8 out of 10, whereas FLOW [40] and CSI [43] show the first and second-placed performance in 4 and 5 out of 10, which indicates that our collaboratively learned global model avoids over-fitting problem for each client." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Scalability of representation In this setup on CIFAR\\(\\mathbf{100}^{\\ddagger}\\), let \\(\\gamma\\) indicate the number of new joined clients for" + }, + { + "type": "image", + "bbox": [ + 0.563, + 0.323, + 0.828, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.475, + 0.893, + 0.567 + ], + "angle": 0, + "content": "Figure 5: Analysis the scalability of our global model learned by ProtoFL through new clients on CIFAR-100‡ dataset. Our approach modestly overcomes the other methods [6, 17, 23] in FL with extreme non-i.i.d. \\((\\alpha = 0.0)\\) data. \\(\\gamma\\) and \\(\\mathbb{I}\\) denote the number of new joined clients and a standard deviation each." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.59, + 0.895, + 0.818 + ], + "angle": 0, + "content": "one-class classification, and \\(20 - \\gamma\\) represent the number of clients who participating in FL. To optimize the local classifier parameters of the new client, the new client downloads the global model as described in Algorithm 2. Note that we are the first to consider the effects of joining new clients. As presented in Fig. 5, we demonstrate the effectiveness for scalability of the learned representation as our global model through experiments and comparisons. Although new clients have increased, all federated learning methods suffer from degraded performances. However, our proposed method shows more scalability with respect to a new joiner than the others [17, 6, 23]. In addition, FedRep [6] and LG-FedAvg [23] are meaningless to support new clients. Thus, our method presents an novel property validating new joiners performance in FL." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.666, + 0.846 + ], + "angle": 0, + "content": "5.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.855, + 0.894, + 0.903 + ], + "angle": 0, + "content": "We conducted ablation studies on CIFAR-10/100\\(\\ddagger\\) and ImageNet-30 (i) to verify the phase 1 and the phase 2, (ii) to explore the contribution of each component in our method," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "6476" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.468, + 0.144 + ], + "angle": 0, + "content": "
Phase 1Phase 2CIFAR-10CIFAR-100‡ImageNet-30Mean
Ours \n(ProtoFL)KDE94.588.994.092.3
GDE94.388.692.891.9
OC-SVM97.186.990.891.6
Ours (OC-NF)95.389.995.493.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.145, + 0.468, + 0.19 + ], + "angle": 0, + "content": "Table 4: Ablation study of various classifiers on CIFAR-10, CIFAR- \\(100^{\\ddagger}\\), and ImageNet-30 with our representative global model. The performance is evaluated by AUROC." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.205, + 0.468, + 0.274 + ], + "angle": 0, + "content": "
MethodPhase 1Phase 2CIFAR-10‡ImageNet-30
LθpdLθpLψmleLψregAUROCAUROC
Ours w/o Lθpd, Lψreg✓✓48.950.2
Ours w/o Lθp, Lψreg✓✓87.091.1
Ours w/o Lψreg✓✓✓89.694.4
Ours✓✓✓✓89.995.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.276, + 0.468, + 0.306 + ], + "angle": 0, + "content": "Table 5: Ablation study on CIFAR-100† and ImageNet-30 to evaluate each component in the individual phase." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.32, + 0.468, + 0.351 + ], + "angle": 0, + "content": "and (iii) to investigate the effectiveness of the off-the-shelf model in respect of the various off-the-shelf datasets." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.361, + 0.468, + 0.512 + ], + "angle": 0, + "content": "Analyses of our global- and classifier- model With fixed our global model learned by joined clients in advance, we compared our proposed local one-class classifier via normalizing flows (OC-NF) with the prior one-class classifiers for the usability of the global model. As shown in Table 4, we observed the superiority of the global model and the local classifier either each or both comparing to the previous detectors [4, 41] non-parametric kernel density estimation, parametric gaussian density estimation, and one-class SVM (KDE, GDE, and OC-SVM)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.523, + 0.468, + 0.739 + ], + "angle": 0, + "content": "Analyses of each component To analyze the effect of our proposed objective for each phase, we separated the representation objective of the phase 1 into distilling loss \\(\\mathcal{L}_{pd}^{\\theta}\\) and similarity loss \\(\\mathcal{L}_p^\\theta\\), and the classification objective of the phase 2 into maximum likelihood \\(\\mathcal{L}_{mle}^{\\psi}\\) and regularizer \\(\\mathcal{L}_{reg}^{\\psi}\\) to show the importance in Table 5. Thus, we confirmed that each of them is the essential terms for the improving performance, and also observed the best results when all of them were used on CIFAR- \\(100^{\\ddagger}\\) and ImageNet30. In case of ImageNet-30, the improved performance indicates the effectiveness of this regularizer. As shown in Fig. 6, we found that our representative global model, trained without this distilling loss \\(\\mathcal{L}_{pd}^{\\theta}\\), leads the drastically impoverished representation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.75, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Analyses of distilling representation With the FL setting, we employ cosine similarity \\(S_{c}\\) as a criterion for selecting the off-the-shelf models as shown in left of Fig. 7, and evaluated the performance based on various \\(S_{c}\\) on all the benchmarks as shown in right of Fig. 7. Our proposed ProtoFL achieves the significantly improved performance comparing to FedUV since the ProtoFL is robust to the increased clients for one-class classification, and the results show that lower \\(S_{c}\\) indicate more discriminative features. Note, distributing the prototypical representation in secure" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.093, + 0.625, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.507, + 0.18, + 0.625, + 0.196 + ], + "angle": 0, + "content": "(a) Ours w/o \\( L_{pd}^{\\theta}, L_{reg}^{\\psi} \\)" + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.093, + 0.747, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.631, + 0.18, + 0.748, + 0.196 + ], + "angle": 0, + "content": "(b) Ours w/o \\(L_{p}^{\\theta}, L_{reg}^{\\theta}\\)" + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.094, + 0.889, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.789, + 0.182, + 0.832, + 0.194 + ], + "angle": 0, + "content": "(c) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.202, + 0.892, + 0.247 + ], + "angle": 0, + "content": "Figure 6: Visualization of latent-features using t-sne for our global model learned (Phase 1) with either each component or all. Score in each figure denote the silhouette values [36]." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.261, + 0.89, + 0.29 + ], + "angle": 0, + "content": "is important to overcome the shortage of training data, limited round communications, and greater number of clients." + }, + { + "type": "image", + "bbox": [ + 0.494, + 0.292, + 0.66, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.679, + 0.292, + 0.884, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.446, + 0.891, + 0.521 + ], + "angle": 0, + "content": "Figure 7: Left : Each score denotes cosine similarity \\( S_{c} \\) between the various off-the-shelf datasets and models. Right : Performance comparison among the various global models whose off-the-shelf model is different. C and I denote CIFAR and ImageNet benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.534, + 0.618, + 0.549 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.56, + 0.892, + 0.755 + ], + "angle": 0, + "content": "We proposed ProtoFL, a method for achieving effective round cost and scalability representation in extreme non-i.i.d. data based FL. By utilizing an off-the-shelf model and dataset to distribute prototypical independent representations, we were able to learn a global model with all joined clients and optimize the flow-based classifier of each client. Our proposed method outperforms FL methods with efficient communication cost and presents a novel property of scalability of representation, validating new joiners' performance in FL. We believe that our method and experimental details could be adapted to handle further problems in both federated and centralized learning based one-class classification." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.765, + 0.667, + 0.781 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was supported by KakaoBank Corp., and Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. 2022-0-00320, Artificial intelligence research about cross-modal dialogue modeling for one-on-one multi-modal interactions). In particular, we would like to thank the designer Eunha Lim (milkyway-mind@naver.com) for well-presented Figures 1, 2, and 3." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.957 + ], + "angle": 0, + "content": "6477" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] Unsupervised video anomaly detection via normalizing flows with implicit latent features. Pattern Recognition, 129:108703, 2022. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.159, + 0.468, + 0.2 + ], + "angle": 0, + "content": "[2] Divyansh Aggarwal, Jiayu Zhou, and Anil K. Jain. Fedface: Collaborative learning of face recognition model. 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PMLR, 2020. 2, 6" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.784 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6479" + } + ] +] \ No newline at end of file diff --git a/2023/ProtoFL_ Unsupervised Federated Learning via Prototypical Distillation/c82e3c6e-4735-400a-b460-81642c25b787_origin.pdf b/2023/ProtoFL_ Unsupervised Federated Learning via Prototypical Distillation/c82e3c6e-4735-400a-b460-81642c25b787_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d48b813e3339000081e2baba7a1a1eb044e5adf9 --- /dev/null +++ b/2023/ProtoFL_ Unsupervised Federated Learning via Prototypical Distillation/c82e3c6e-4735-400a-b460-81642c25b787_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6c8c83f82640b5bbee9bec3268d2e0f009abac65b2a26727ed8c0fcf8890b5b4 +size 6585296 diff --git a/2023/ProtoFL_ Unsupervised Federated Learning via Prototypical Distillation/full.md b/2023/ProtoFL_ Unsupervised Federated Learning via Prototypical Distillation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..17bacd0f165a7f25b134bc44411560e876d8d215 --- /dev/null +++ b/2023/ProtoFL_ Unsupervised Federated Learning via Prototypical Distillation/full.md @@ -0,0 +1,397 @@ +# ProtoFL: Unsupervised Federated Learning via Prototypical Distillation + +Hansol Kim\*1, Youngjun Kwak\*12, Minyoung Jung3, Jinho Shin1, Youngsung Kim4, and Changick Kim + +$^{1}$ KakaoBank Corp., South Korea + +$^{2}$ Department of Electrical Engineering, KAIST, South Korea + +$^{3}$ KETI, Korea Electronics Technology Institute, South Korea + +4Inha University, South Korea + +{han.kim,vivaan.yjkwak,william.shin}@lab.kakaobank.com,{yjk.kwak,changick}@kaist.ac.kr, + +minyoung.jung@keti.re.kr,y.kim@inha.ac.kr + +# Abstract + +Federated learning (FL) is a promising approach for enhancing data privacy preservation, particularly for authentication systems. However, limited round communications, scarce representation, and scalability pose significant challenges to its deployment, hindering its full potential. In this paper, we propose 'ProtoFL', Prototypical Representation Distillation based unsupervised Federated Learning to enhance the representation power of a global model and reduce round communication costs. Additionally, we introduce a local one-class classifier based on normalizing flows to improve performance with limited data. Our study represents the first investigation of using FL to improve one-class classification performance. We conduct extensive experiments on five widely used benchmarks, namely MNIST, CIFAR-10, CIFAR-100, ImageNet-30, and Keystroke-Dynamics, to demonstrate the superior performance of our proposed framework over previous methods in the literature. + +# 1. Introduction + +In recent years, there has been a growing concern about privacy, leading people to hesitate when it comes to uploading their biological data to central data servers. Moreover, companies that possess personal information from users are strictly bound by the General Data Protection Regulation (GDPR) [44]. To address these privacy issues, Federated Learning (FL), an emerging distributed data parallel machine learning approach, has been proposed. FL leverages the decentralized data available on individual clients to collaboratively train a shared global model on a mediator server without the need to share personal data. + +![](images/140e95df5318e9fddcee0848aad2033591d6af2b39de57518930a8e612cee401.jpg) +Figure 1: Visualization of extreme non-i.i.d. ( $\alpha = 0.0$ is a concentration parameter of Dirichlet distribution) data based FL schema shows that each device has only the data from its target class not shared among all joined devices, and prototypical representation is distributed separately to corresponding joined clients in secure from a central server. + +In the context of FL, where data is decentralized across individual clients, one-class classification (OCC) can be used. This is because that OCC can determine whether a new example belongs to the target distribution or not. Despite not using data from the non-target class, OCC has shown impressive performance [31, 38, 43, 42, 39, 40, 15, 28]. In computer vision applications, OCC is particularly useful for detecting fraud, defects, and unauthorized users. + +Recent advancements in biometric authentication have highlighted the importance of FL-based OCC in computer vision (e.g., user-defined embedding-based methods [17, 26] and data-driven methods [2, 24, 32]). However, FL-based OCC methods face significant challenges, including high communication costs, limited representation, and unstable learning processes. Additionally, centralized server + +based methods [31, 42, 43] may not be suitable for FL-based OCC due to limited computing resources on each device, which are a major obstacle for centralized methods that require substantial computing power. + +The limitations inherent in FL-based OCC necessitated the development of a novel approach to address these challenges. In this paper, we aim to attain a more expressive global model without the need for frequent re-training processes between the central server and client devices on a large scale. To achieve this, we propose Prototypical representation distillation based unsupervised Federated Learning (ProtoFL) that distills representation from an off-the-shelf model learned using off-the-shelf datasets, regardless of individual client data. In contrast to traditional FL-based OCC, our proposed ProtoFL approach does not transfer parameters directly to the client, as depicted in Fig. 1. This resolves the issues of frequent round communication costs and the need for extra data due to one-time prototype representation distillation. ProtoFL provides a novel solution to the existing challenges of FL-based OCC, enabling efficient and effective global model updates. + +Subsequently, we suggest a novel approach for estimating the density of a target class in a distributed setting using a flow-based one-class classifier [20]. To achieve this, we conduct the estimation on individual client devices, using augmented latent variables for training their distributed models. Our approach leverages two key techniques: maximum likelihood estimation with log-likelihood and a probabilistic similarity loss function that includes $\mathcal{KL}$ -divergence. By combining the distillation and one-class classification phases, we can effectively handle complex data distributions that are non-independent and nonidentically distributed across individual clients. Our two-phase learning framework is inspired by the success of flow-based models in various applications [20, 11, 40, 1], and we demonstrate its effectiveness in handling complex data distributions in the distributed settings. + +The experimental findings of our proposed method demonstrate superior classification performance compared to both server-based and client-based methods on both image and tabular datasets. Additionally, we have validated the scalability of the learned representation and have shown that the global model learned by the ProtoFL is compatible with existing one-class classifiers as well as our one-class classifier based on the benchmark datasets. Our results indicate that our method is a promising approach for large-scale machine learning tasks that require robust and scalable classification capabilities. + +Our contributions are described as follows: + +- We propose a novel unsupervised federated learning framework that effectively addresses the challenge of insufficient local training data. By leveraging normalizing flows for local classifier learning and prototypical + +representation distillation, our approach enables efficient and effective global model updates. + +- We propose a novel prototype-based representation learning method for distilling normal data representation using an off-the-shelf model and dataset. Our approach demonstrates the scalability of the global model, which can be verified by adding new clients in FL-based OCC. +- We propose new federated and centralized learning methods for one-class classification, which we evaluate on five widely-used benchmarks. Our experiments show that our methods achieve superior performance compared to existing approaches. + +# 2. Related Work + +One-class classification Various one-class classification approaches have been proposed and categorized into description-based and representation-based learning. In the description-based methods, Deep-SVDD [31] performs one-class detection by learning a model to map target samples into a center in the latent space, otherwise non-target samples are mapped far from the center. And FCDD [27] proposes an explainable one-class classifier by upsampling based on gaussian sampling. In contrast, representation-based learning methods (DROC [42] and CSI [43]) present a two-step learning framework to learn a representation model through excessive data-augmentation and contrastive loss. The framework either employs a classifier or defines a score function for detecting a target class. Unlike previous centralized server-based approaches, our proposed approach for one-class classification on decentralized learning avoids the risk of personal data leakage by constructing a model using distributed data. To the best of our knowledge, our method is the first to directly address this problem in a decentralized setting. + +Federated learning for local one-class classifier Federated Learning (FL) is a distributed machine learning paradigm that enables collaborative model training without direct data sharing. FL has been applied to one class classification (OCC) tasks for user verification and authentication, with several studies demonstrating promising results. [17, 32, 34]. FedAwS [45] introduces a geometric regularization to learn a global model by utilizing uploaded latent variables of joined clients in a central server. Since the latent variables shared on a server are private data, the FedAwS violates in the setting of FL. FedUV [17] employs independent secret error correcting codes (ECCs) to train a one-class classifier by preventing personal data from sharing among joined clients. The secret codes induce the concise objective of FedUV so that only positive examples are + +required. The FedUV approach was further refined to estimate a center of distribution by FedAA [32] and FedMetric [34], instead of defining hand-designed codes. However, local data on each device is not sufficient to represent a centroid of local data distribution. + +Federated learning for central and client classifiers In authentication systems, client data is often partitioned according to a target class. This results in highly or extremely non-i.i.d. data that poses a significant challenge for FL. This extreme non-i.i.d. means that a concentration parameter of Dirichlet distribution approaches to zero $(\alpha = 0.0)$ while many federated learning methods [6, 9, 13] assumes non-i.i.d. data with non-zero $(\alpha \neq 0.0)$ setting [18, 23, 29, 6, 13, 9]. + +Unsupervised federated learning methods [23, 29] aggregate local representation models and centroids for achieving a global model and centroid. FedRep [6] shares partitions of a global model to adapt each local heterogeneous data. FedX [13], which utilizes structure knowledge distillation between local and global knowledge relationships, learns meaningful data representation without sharing external data. SphereFed [9] introduced a learned matrix, which is a fixed-classifier for sharing among all participating clients, to transform each local data distribution into the predefined latent space. But, SphereFed requires enormous cost to re-construct and re-distribute a new learned matrix whenever a new client joins. Therefore, we first propose a prototypical representation distillation learning to save communication cost in FL with extreme non-i.i.d. $(\alpha = 0.0)$ data settings. + +# 3. Preliminary + +Federated Average Learning FedAVG [30], composed of participating clients and a central mediator server, trains a global model by aggregating locally-computed parameters, and broadcasts the updated global model to the clients. In each round, FedAVG updates the global model parameters with local model parameters as follows: + +$$ +\theta_ {g} ^ {t + 1} = \sum_ {k = 1} ^ {K} \frac {\left| D _ {k} \right|}{\sum_ {k = 1} ^ {K} \left| D _ {k} \right|} \theta_ {k} ^ {t}, \tag {1} +$$ + +where $k \in \{1, \dots, K\}$ indicates an index of a local client. $\theta_{g}^{t+1}$ is the parameters of a global model, and $\theta_{k}^{t}$ is the parameters of the $k^{th}$ local model at a round $t$ . For the balanced updating of the global model $\theta_{g}^{t+1}$ , $|D_{k}|$ is the number of samples on dataset $D_{k}$ . + +Unsupervised Contrastive Learning FL with extreme non-i.i.d. $(\alpha = 0.0)$ data setting is unavailable to access samples of the other clients. Thus, we simplify the contrastive loss, $\mathcal{L}_{cntr} = y \times (1 - d(\bullet, \hat{\bullet})) + (1 - y) \times \max(0, d(\bullet, \hat{\bullet}))$ , as follows: + +$$ +\mathcal {L} _ {d} = 1 - d (\bullet , \hat {\bullet}), \tag {2} +$$ + +where $d(\bullet, \hat{\bullet})$ is the cosine-similarity $\frac{\bullet \cdot \hat{\bullet}}{||\bullet|| \cdot ||\hat{\bullet}||}$ . We utilize $L_{d}$ as our positive cosine similarity loss for our unsupervised leaning, instead of $\mathcal{L}_{cntr}$ . + +Normalizing Flows Normalizing flows (NFs) [8] are the statistical methods using the change-of-variable law of probabilities to fit an arbitrary target density $p_R(r)$ by a tractable base distribution with density $p_Z(z)$ and a bijective invertible mapping $\mathfrak{t}^{-1}: R^D \to Z^D \Leftrightarrow \mathfrak{t}: Z^D \to R^D$ . According to [33], $\mathcal{KL}$ -divergence and log-likelihood estimation are employed to optimize the invertible flow-based model $z = \mathfrak{t}^{-1}(r; \psi)$ and $r = \mathfrak{t}(z; \psi)$ by the target distribution $p_R(r)$ . The bijective invertible mapping is drawn as: + +$$ +\begin{array}{l} \mathcal {D} _ {\mathcal {K L}} \left[ \hat {p} _ {R} (r) \| p _ {R} (r; \psi) \right] \\ \approx - \mathbb {E} _ {\hat {p} _ {R} (r)} \left[ \log p _ {Z} \left(\mathrm {t} ^ {- 1} (r; \psi)\right) + \log | \det j _ {\mathrm {t} ^ {- 1}} | \right] + c o n t, \tag {3} \\ \end{array} +$$ + +where $p_R(r;\psi)$ denotes the likelihood of a model. $\hat{p}_R$ is the target distribution to learn the model by $\mathcal{KL}$ -divergence. $p_R(r;\psi)$ only remains for learning parameters $\psi$ , and then is replaced by $\frac{1}{N}\sum_{i=1}^{N}\left[\frac{\|\mathfrak{t}^{-1}(r_i)\|_2^2}{2}-\log|\det\mathfrak{j}_{\mathfrak{t}^{-1}}|\right]$ through the training dataset $D_k$ as explained by [11, 20]. The re-written equation is applied to our objective to estimate the log-likelihood of given local data on each device. + +# 4. Proposed Method + +In this section, we propose a two-phase unsupervised learning framework that combines unsupervised federated learning via distillation of prototypical representations with local classifier learning via leveraging normalizing flows. + +# 4.1. Problem Formulation + +Participating $K$ clients aim to train a global model by aggregating locally-computed parameters $\phi(\bullet, \theta)$ for an one-class classification task without sharing private data among joined clients. Each client has a training dataset $D_{K,N} = \{x_{k,i}, 1 \leq i \leq N, 1 \leq k \leq K\}$ and $N$ is the cardinality of the local data $D_{k,N}$ . Let $\phi(x_{k,i}; \theta_k)$ denote the trainable model of the $k^{th}$ client. In particular, we follow the extreme non-i.i.d. $(\forall_{m,n} D_{m,N} \cap D_{n,N} = \emptyset)$ data setting in our FL-based OCC. Different from prior FL settings utilizing either hand-designed codes or additional training datasets, we invent generic representation of the local model $\phi$ by leveraging the off-the-shelf model $\mathcal{F}$ and dataset $S$ , and we employ the flow-based model $\psi$ for the local one-class classifier. + +# 4.2. Sequence of procedures + +As shown in Fig. 2, we describe our proposed method workflow in each phase. $①$ Whenever a new client partici + +![](images/7a5be14a4fda3165121fd68dc1fafea57d219633c4acc04699148ca443fb93f8.jpg) +(a) Phase 1: Unsupervised federated learning via prototypical representation distillation + +![](images/cfca0dd713e55ee3f8fc71af74ccdee619e4a99ce5c6158299fbd91853c28aa6.jpg) + +![](images/e179ce143316191b6a150dcd5a88078ad437b78877c834bdadb161fb8aae95ac.jpg) +(b) Phase 2: Local one-class classifier based on NFs +Figure 2: Overview of our proposed two-phase learning architecture. $① \sim$ $④$ indicates the workflows of ProtoFL with all the joined clients to upload parameters of each client and to download the aggregated global model, and $⑤$ represents a local training for the OC-NF. The details of sequences $① \sim$ $⑤$ are described in Section 4.2. NFs denote normalizing flows. + +pates in our unsupervised federated learning, all clients join a central mediator server. ② For the $k^{th}$ client, a categorical image $s_k$ is chosen from $\mathcal{S}$ and transformed into a latent variable $v_k$ by the central mediator server. Both ① and ② occur only once at the first time, and $\mathcal{V} = \{v_k, 1 \leq k \leq K\}$ is secretly distributed to the corresponding client. ③ We train the $k^{th}$ local model $\theta_k$ via the local data $D_{k,N}$ , the distributed prototype representation $v_k$ , cosine similarly loss, and $\mathcal{KL}$ -divergence loss. ④ A global model $\theta_g$ is aggregated with all the uploaded local models by FedAVG, and the global model is distributed to all participating clients. ⑤ Once federated representation learning has finished, we train a local one-class classifier based on normalizing flows (OC-NF) by using maximum likelihood and cosine similarity losses. We describe the details of our procedures (① ~ ⑤) in the following subsections. + +# 4.3. Prototypical representation distillation based unsupervised federated learning (ProtoFL) + +We assume $\mathcal{F}:R^{W\times H\times C}\to R^D$ and $\phi :R^{W\times H\times C}\to$ $R^D$ indicate the off-the-shelf model and the local model, respectively as illustrated in Fig. 2. For training the local model of the $k^{th}$ client, we augment two views $x_{k,i},\hat{x}_{k,i}$ from the $i^{th}$ example of the local training data $D_{k,N}$ , and subsequently transform the two samples as follows: + +$$ +r _ {k, i} = \phi \left(x _ {k, i}; \theta_ {k}\right); \hat {r} _ {k, i} = \phi \left(\hat {x} _ {k, i}; \theta_ {k}\right), \tag {4} +$$ + +where $r_{k,i}$ and $\hat{r}_{k,i}$ represent latent variables of the $i^{th}$ example. $\phi$ is the client model with $k^{th}$ learnable parameters $\theta_{k}$ . Inspired by SimCLR [5], the two latent variables $r_k$ and $\hat{r}_k$ must be very close to each other. Given the only positive local data and the constraint, we employ the positive cosine similarity loss(Eq. 2) to learn the local model as follows: + +$$ +\mathcal {L} _ {p} ^ {\theta} \left(\theta_ {k}\right) = \frac {1}{N} \sum_ {i = 1} ^ {N} \left[ 1 - d \left(r _ {k, i}, \hat {r} _ {k, i}\right) \right], \tag {5} +$$ + +where $\theta_{k}$ is optimized by the local data $D_{k,N}$ . To overcome the small cardinality of local data for training the local representative model, we propose the off-the-shelf model with pre-trained parameters $\mathcal{F}(\bullet ;\omega)$ and the off-the-shelf dataset $s_k\in S_s$ . The off-the-shelf model and dataset are utilized on a central mediator server as depicted: + +$$ +v _ {k} = \mathcal {F} \left(s _ {k}; \omega\right), \tag {6} +$$ + +where $s_k$ and $v_k$ represent a prototype example and representation for the $k^{th}$ client. After $\mathcal{V} = \{v_k, 1 \leq k \leq K\}$ is distributed to the corresponding client in secret, we train the local model of the $k^{th}$ client to estimate the prototypical target representation $v_k$ . We employ the $\mathcal{KL}$ -divergence to minimize the discrepancy between two distributions $v_k$ and either $r_k$ or $\hat{r}_k$ . Therefore, we invent the prototypical distillation loss as follows: + +$$ +\mathcal {L} _ {p d} ^ {\theta} \left(\theta_ {k}\right) = \frac {1}{N} \sum_ {i = 1} ^ {N} \left[ \mathcal {K L} \left(v _ {k} \| r _ {k, i}\right) + \mathcal {K L} \left(v _ {k} \| \hat {r} _ {k, i}\right) \right], \tag {7} +$$ + +where $\mathcal{KL}(v_k\| r_{k,i})$ and $\mathcal{KL}(v_k\|\hat{r}_{k,i})$ are equally contributed to our distillation loss. Figure 3 describes the details of Eq. 5 and Eq. 7, and the overall objective of the first phase (phase 1) is defined as follows: + +$$ +\mathcal {L} _ {\phi} \left(\theta_ {k}\right) = (1 - \alpha) \times \mathcal {L} _ {p d} ^ {\theta} \left(\theta_ {k}\right) + \alpha \times \mathcal {L} _ {p} ^ {\theta} \left(\theta_ {k}\right), \tag {8} +$$ + +where $\alpha$ is a balancing weight. In our experiment, $\alpha$ is empirically set to 0.1. + +![](images/2ba057b7238259801252892b21079b2808b9781ea196313c777801c6cf5451f7.jpg) +Figure 3: Illustration of learning a global model with prototypical representation distillation on distributed devices without sharing private data among participating clients. + +![](images/ae7feeadfbbd5a0b3823c2aa76bd276428ab441c3568cbbd7938c5274dbcbbe5.jpg) + +# 4.4. Local one-class classifier via Normalizing Flows (OC-NF) + +After unsupervised federated representation learning for the global model, we leverage a general flow-based model for training the local one-class classifier in each client as shown in Fig. 2. To estimate log-likelihood of transformed latent variables $r_k$ and $\hat{r}_k$ , we exploit Eq. 3 to learn the probabilistic normalizing flows $\mathfrak{t}$ through the local dataset $D_{k,N}$ and the local model $\phi (\cdot ;\theta_k)$ on the $k^{th}$ client as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {m l e} ^ {\psi} (\psi_ {k}) \\ = \frac {1}{N} \sum_ {i = 1} ^ {N} \left[ \frac {\| \mathfrak {t} ^ {- 1} (r _ {k , i} ; \psi_ {k}) \| _ {2} ^ {2}}{2} - \log | \det \mathfrak {j} _ {k, i} | \right] + c o n t \\ \approx \frac {1}{N} \sum_ {i = 1} ^ {N} \left[ \frac {\left\| z _ {k , i} \right\| _ {2} ^ {2}}{2} - \log | \det j _ {k, i} | \right] + c o n t, \tag {9} \\ \end{array} +$$ + +where $z_{k,i}$ is the estimated distribution as it passes through $\mathrm{t}^{-1}(r_{k,i};\psi_k)$ . $r_{k,i}$ is a latent variable from $\phi (x_{k,i};\theta)$ . When optimizing the flow-based model, we ignore constants, det and cont. Since $r_{k,i}$ and $\hat{r}_{k,i}$ are close each other in a latent space, $z_{k,i}$ and $\hat{z}_{k,i}$ also predict the same distribution so that we introduce the following objective as a regularizer: + +$$ +\mathcal {L} _ {r e g} ^ {\psi} (\psi_ {k}) = \frac {1}{N} \sum_ {i = 1} ^ {N} [ 1 - d (z _ {k, i}, \hat {z} _ {k, i}) ], \tag {10} +$$ + +where $z_{k,i}$ and $\hat{z}_{k,i}$ are the normal distribution estimated by $\mathfrak{t}^{-1}((\phi (x_{k,i};\theta_k);\psi_k))$ and $\mathfrak{t}^{-1}((\phi (\hat{x}_{k,i};\theta_k);\psi_k))$ respectively. The overall objective of the second phase (phase 2) is composed of Eq. 9 and Eq. 10 as follows: + +$$ +\mathcal {L} _ {\mathrm {t}} \left(\psi_ {k}\right) = \mathcal {L} _ {m l e} ^ {\psi} \left(\psi_ {k}\right) + \lambda \times \mathcal {L} _ {r e g} ^ {\psi} \left(\psi_ {k}\right), \tag {11} +$$ + +where $\lambda$ is a hyper-parameter for effectiveness of regularization. For our experiment, we empirically set $\lambda$ to 0.01. + +# 5. Experiments + +In this section, we demonstrate the proposed approach on image and tabular benchmarks. We evaluate the performance of our proposed ProtoFL and compare our model with the other FL methods and one-class detectors. And we analyze the impact of new client participation in the context of OCC on FL, as well as ablation studies on each proposed component. + +# 5.1. Datasets + +We thoroughly evaluate our proposed method on several benchmark datasets, including the widely used MNIST [22], CIFAR-10 [21], CIFAR-100 [21], ImageNet-30 [16], and Keystroke-Dynamics [19], to tackle the demanding task of one-class classification. Our evaluation scrutinizes the efficacy, robustness, and scalability of our method, highlighting its strengths in handling real-world scenarios. In case of CIFAR-100, we adopt 20 super-class labels, denoted by CIFAR- $100^{\ddagger}$ , as suggested in [10] to our experiments. The numbers of categories in the benchmarks are 10, 10, 20, 30, and 51, which are the numbers of participating clients on our federated learning. The vision and tabular based benchmarks for OCC follow a one-vs-rest protocol [10, 42, 43]. In the protocol, a set of samples from one class indicates a target class for one client, whereas a set of samples from the remaining classes represents a non-target class for the remaining clients. + +# 5.2. Experiment Setting + +Off-the-shelf model and dataset In the central mediator server, the off-the-shelf dataset and model generate prototypical representation when a new client participates in our unsupervised federated learning. For the off-the-shelf model and dataset, we exploit ArcFace [7] based ResNet-50 backbone [14] and MS-Celeb-1M [12], respectively. + +Architectures In this experiment, we employ ResNet-18/32 backbones [14] to learn the local and global models on our proposed approach. Since batch normalization is detrimental to the performance in federated learning [17] both ResNet-18/32 backbones replace batch- with group-normalization. In the Keystroke Dynamics dataset, we employ multi-layer perceptions as the local and global model, consisting of three linear layers, ReLU, and group-normalization. And we utilize NFs as a local classifier model composed of 8 coupling layers [8]. + +Implementation details In the first phase as described in Algorithm 1, we train our expressive global model based on the FedAvg [30] method with 1 local epoch and 900 communication rounds, using randomly chosen clients from all participating clients. We utilize the RAdam optimizer [25] with betas 0.94 and 0.98, a weight decay 1e-3 and a learning + +# Algorithm 1 Procedure of our two-phase learning + +Phase 1 (ProtoFL): Start phase 1 for $T$ rounds. + +Initialize and broadcast a global model $\theta_g^0$ to all joined $K$ clients. Send an acknowledgement (ACK) with prototypical representation $v_{k}$ to the $k^{th}$ client. + +for $t\gets 0$ to $T - 1$ do + +$$ +\theta_ {g} ^ {t + 1} \leftarrow \text {G L O B A L - T R A I N I N G} (t, \theta_ {g} ^ {t}) +$$ + +end for + +Update the global model $\theta_g$ with $\theta_g^T$ . + +function GLOBAL TRAINING $(t,\theta_g^t)$ Randomly select $k$ number of clients from $\{C_k\}_{k = 1}^K$ + +for $k\gets 1$ to $K$ do + +$$ +\text {B r o a d c a s t} \theta_ {q} ^ {t} \text {t o} C _ {k}. +$$ + +$$ +\theta_ {k} ^ {t}, \left| D _ {k, N} \right| \leftarrow \text {C L I E N T - T R A I N I N G} (t, k, \theta_ {g} ^ {t}) +$$ + +end for + +$$ +\theta_ {g} ^ {t + 1} \leftarrow \sum_ {k = 1} ^ {K} \frac {\left| D _ {k , N} \right|}{\sum_ {k = 1} ^ {K} \left| D _ {k , N} \right|} \theta_ {k} ^ {t} +$$ + +$$ +\mathrm {r e t u r n} \theta_ {g} ^ {t + 1} +$$ + +end function + +function CLIENT.TrAINING $(t,k,\theta_g^t)$ + +Download the global model $\theta_g^t$ , and assign it to $\theta_k^t$ + +for $x_{k,i}\in D_{K,N}$ do + +$$ +\mathcal {L} _ {\phi} \left(\theta_ {k} ^ {t}\right) = (1 - \alpha) \times \mathcal {L} _ {p d} ^ {\theta} \left(\theta_ {k} ^ {t}\right) + \alpha \times \mathcal {L} _ {p} ^ {\theta} \left(\theta_ {k} ^ {t}\right) +$$ + +$$ +\theta_ {k} ^ {t} \leftarrow \theta_ {k} ^ {t} - \eta \nabla \mathcal {L} _ {\phi} \left(\theta_ {k} ^ {t}\right) +$$ + +end for + +Calculate the number of the $k^{th}$ client data $D_{k,N}$ . + +return $\theta_k^t$ and $|D_{k,N}|$ + +end function + +Phase 2 (OC-NF): All joined clients start Algorithm 2 for OCC. + +# Algorithm 2 Procedure of our OC-NF for OCC + +Download the global model $\theta_{g}$ , and assign it to the $k^{th}$ client model $\theta_{k}$ . Freeze the global representation model $\phi (\bullet ;\theta_k)$ . Initialize the flow-based model of the $k^{th}$ client $\mathfrak{t}_{\psi_k}$ . + +for $x_{k,i}\in D_{k,N}$ do + +$$ +\mathcal {L} _ {\mathfrak {t}} (\psi_ {k}) = \mathcal {L} _ {m l e} ^ {\psi} (\psi_ {k}) + \lambda \times \mathcal {L} _ {r e g} ^ {\psi} (\psi_ {k}) +$$ + +$$ +\psi_ {k} \leftarrow \psi_ {k} - \eta \nabla \mathcal {L} _ {\mathrm {t}} (\psi_ {k}) +$$ + +end for + +rate 1e-6 to learn local models. In the second phase as described in Algorithm 2, we use the SGD optimizer [35] with a learning rate 5e-3 and 5 epochs to learn our one-class classifier. Data augmentations include the set of random processes (crop, horizontal-flip, and gaussian-blur) and color jitter. To evaluate the performance of various methods, we use the area under curve of ROC curve (AUROC) and equal error rate (EER). + +# 5.3. Experimental Results + +Image and tabular benchmarks For the image benchmarks, we present the results on MNIST and CIFAR-10 datasets for OCC in extreme non-i.i.d. $(\alpha = 0.0)$ data setting of FL. Table 1 shows the outstanding result of not only the significantly improved performance but also the + +
MethodNetworkMNISTCIFAR-10
AUROCRoundAUROCRound
FedAwS [45]ResNet-3299.610K94.1100K
FedUV [17]ResNet-3299.720K87.220K
FedMetric [34]ResNet-3299.610K94.2100K
OursResNet-3299.90.9K95.20.9K
+ +Table 1: Performance comparison FL-based methods with our proposed approach on MNIST and CIFAR-10 benchmarks. Our approach outperforms both benchmarks while reducing the communication round cost. + +
TypeMethodNetworkCIFAR-10CIFAR-100‡ImageNet-30
AUROCAUROCAUROC
Centralized LearningAE [27]---56.0
OC-SVM [41]-58.863.1-
Geom [10]WRN-16-886.078.7-
Rot [16]ResNet-1889.877.777.9
GOAD [3]ResNet-1885.174.5-
DROC [42]ResNet-1892.586.5-
CSI [43]ResNet-1894.386.691.6
FLOW† [40]ResNet-5095.293.0-
Federated LearningFedUV [17]ResNet-1879.8*55.9*62.8*
FedRep [6]ResNet-1858.2*56.9*56.3*
OursResNet-1895.389.995.4
+ +Table 2: AUROC of various centralized and decentralized detection methods on CIFAR-10/100 $\ddagger$ , and ImageNet-30 for OCC. $\dagger$ and $*$ denote the usage of a pre-trained model learned on ImageNet-1M and the values from our reimplementation respectively, whereas **bold** and **underline** indicate the best results and the second results, respectively. + +effective communication cost on FL methods. We found that our proposed method exploits the off-the-shelf model and dataset to compensate the shortage of the local data. For updating a global model every rounds, naive FL methods [45, 17, 34] minimize the distance among the latent variables of the local data and map the distribution of the local data into one secure code designated. Those methods demand the inordinate communication cost and show the limited performance due to the deficiency of the local data on each device and the entangled secure code on latent space. Furthermore, we compare our approach with various centralized methods as depicted in Table 2. Our method outperforms ResNet-18 based methods on CIFAR-10 and ImageNet-30. In case of CIFAR- $100^{\ddagger}$ , our approach places the second-rank performance comparing with FLOW [40] leveraging the feature extraction of a pre-trained model learned on ImageNet-1M. Note that our proposed method is the first rank among ResNet-18 based methods having no additional training datasets and limited computing resources. Among FL methods, our proposed method accomplishes the consistently improved performance on the image benchmarks. + +For the tabular benchmark, we make the comparisons to the centralized methods on the Keystroke-Dynamics dataset for one-class classification as shown in Fig. 4. As the results, we found that our proposed method reduces EER more than two times comparing to prior methods. Training a foundation model as the global model is essential for the + +
TypeMethodNetworkPlaneCarBirdCatDeerDogForgHorseShipTruckMean (std)
Centralized LearningOC-SVM [41]-65.640.965.350.175.251.271.851.267.948.558.8 (±11.6)
DeepSVDD [37]LeNet61.765.950.859.160.965.767.767.375.973.164.8 (±7.17)
Geom [10]WRN-16-874.795.778.172.487.887.883.495.593.391.386.0 (±8.52)
Rot [16]WRN-16-477.596.987.380.992.790.290.996.595.293.390.1 (±6.52)
GOAD [3]WRN-16-477.296.783.377.787.887.890.096.193.892.088.2 (±6.99)
Rot [16]ResNet-1880.496.485.981.191.389.689.995.995.092.689.8 (±5.75)
GOAD [3]ResNet-1875.594.181.872.083.784.482.993.992.989.585.1 (±7.61)
DROC [42]ResNet-1890.998.988.083.189.990.393.598.296.595.292.5 (±4.95)
CSI [43]ResNet-1889.999.193.186.493.993.295.198.797.995.594.3 (±3.97)
FLOW† [40]ResNet-5096.197.592.689.893.395.798.094.797.896.695.2 (±2.64)
Federated LearningOursResNet-1896.497.992.790.995.892.796.496.497.696.795.3 (±2.38)
+ +Table 3: AUROC of various centralized and decentralized detection methods on CIFAR-10 for one-class classification. We present the AUROC of each class and the mean and standard deviation (std) of AUROC for all classes. $\dagger$ , bold, and underline denote the usage of a pre-trained model learned on ImageNet-1M, the best results, and the second results, respectively. + +![](images/a1b08468be02d2345e68373c278510ad7b754f63d8c3e6a8d0249698c239072f.jpg) +Figure 4: Comparison to previous methods of one-class classification on the Keystroke-Dynamics dataset. OC, Manhattan, AE, and MLP denote Outlier Count, Euclidean detector with Manhattan distance, Auto-Encoder, and 4-multi layer perception, respectively, from [19]. $\mathbb{I}$ denotes a standard deviation. + +OCC task instead of the various architectures and distance metrics to achieve notably improved performance. + +Centralized vs Federated learning As shown in Table 3, we compare our proposed method with the centralized learning based methods because there is no previous FL method studying sufficiently analysis results for CIFAR-10. Our proposed approach outperforms the previous methods in terms of the overall mean and standard deviation because we collaboratively train our global model to represent all classes by the distributively-learned local models, and then we apply our non-biased global model to transform raw data into latent spaces for learning a local one-class classifier in each client as shown in Fig. 5. In case of each class, this method shows the first and second-placed performance in 8 out of 10, whereas FLOW [40] and CSI [43] show the first and second-placed performance in 4 and 5 out of 10, which indicates that our collaboratively learned global model avoids over-fitting problem for each client. + +Scalability of representation In this setup on CIFAR $\mathbf{100}^{\ddagger}$ , let $\gamma$ indicate the number of new joined clients for + +![](images/b62a5af6cda63507628c96eb7696c00718c5f9304f1c36edb4bc59edd15b3877.jpg) +Figure 5: Analysis the scalability of our global model learned by ProtoFL through new clients on CIFAR-100‡ dataset. Our approach modestly overcomes the other methods [6, 17, 23] in FL with extreme non-i.i.d. $(\alpha = 0.0)$ data. $\gamma$ and $\mathbb{I}$ denote the number of new joined clients and a standard deviation each. + +one-class classification, and $20 - \gamma$ represent the number of clients who participating in FL. To optimize the local classifier parameters of the new client, the new client downloads the global model as described in Algorithm 2. Note that we are the first to consider the effects of joining new clients. As presented in Fig. 5, we demonstrate the effectiveness for scalability of the learned representation as our global model through experiments and comparisons. Although new clients have increased, all federated learning methods suffer from degraded performances. However, our proposed method shows more scalability with respect to a new joiner than the others [17, 6, 23]. In addition, FedRep [6] and LG-FedAvg [23] are meaningless to support new clients. Thus, our method presents an novel property validating new joiners performance in FL. + +# 5.4. Ablation Studies + +We conducted ablation studies on CIFAR-10/100 $\ddagger$ and ImageNet-30 (i) to verify the phase 1 and the phase 2, (ii) to explore the contribution of each component in our method, + +
Phase 1Phase 2CIFAR-10CIFAR-100‡ImageNet-30Mean
Ours +(ProtoFL)KDE94.588.994.092.3
GDE94.388.692.891.9
OC-SVM97.186.990.891.6
Ours (OC-NF)95.389.995.493.5
+ +Table 4: Ablation study of various classifiers on CIFAR-10, CIFAR- $100^{\ddagger}$ , and ImageNet-30 with our representative global model. The performance is evaluated by AUROC. + +
MethodPhase 1Phase 2CIFAR-10‡ImageNet-30
LθpdLθpLψmleLψregAUROCAUROC
Ours w/o Lθpd, Lψreg✓✓48.950.2
Ours w/o Lθp, Lψreg✓✓87.091.1
Ours w/o Lψreg✓✓✓89.694.4
Ours✓✓✓✓89.995.4
+ +Table 5: Ablation study on CIFAR-100† and ImageNet-30 to evaluate each component in the individual phase. + +and (iii) to investigate the effectiveness of the off-the-shelf model in respect of the various off-the-shelf datasets. + +Analyses of our global- and classifier- model With fixed our global model learned by joined clients in advance, we compared our proposed local one-class classifier via normalizing flows (OC-NF) with the prior one-class classifiers for the usability of the global model. As shown in Table 4, we observed the superiority of the global model and the local classifier either each or both comparing to the previous detectors [4, 41] non-parametric kernel density estimation, parametric gaussian density estimation, and one-class SVM (KDE, GDE, and OC-SVM). + +Analyses of each component To analyze the effect of our proposed objective for each phase, we separated the representation objective of the phase 1 into distilling loss $\mathcal{L}_{pd}^{\theta}$ and similarity loss $\mathcal{L}_p^\theta$ , and the classification objective of the phase 2 into maximum likelihood $\mathcal{L}_{mle}^{\psi}$ and regularizer $\mathcal{L}_{reg}^{\psi}$ to show the importance in Table 5. Thus, we confirmed that each of them is the essential terms for the improving performance, and also observed the best results when all of them were used on CIFAR- $100^{\ddagger}$ and ImageNet30. In case of ImageNet-30, the improved performance indicates the effectiveness of this regularizer. As shown in Fig. 6, we found that our representative global model, trained without this distilling loss $\mathcal{L}_{pd}^{\theta}$ , leads the drastically impoverished representation. + +Analyses of distilling representation With the FL setting, we employ cosine similarity $S_{c}$ as a criterion for selecting the off-the-shelf models as shown in left of Fig. 7, and evaluated the performance based on various $S_{c}$ on all the benchmarks as shown in right of Fig. 7. Our proposed ProtoFL achieves the significantly improved performance comparing to FedUV since the ProtoFL is robust to the increased clients for one-class classification, and the results show that lower $S_{c}$ indicate more discriminative features. Note, distributing the prototypical representation in secure + +![](images/32ba4430cb19059812eb61a9196cd790fc35a21ecdabd7d340a2495f95d0ce50.jpg) +(a) Ours w/o $L_{pd}^{\theta}, L_{reg}^{\psi}$ + +![](images/37155c805f098edcafee61fa1a6ff6869fc6cf7c0630a3181612bed1cdedba57.jpg) +(b) Ours w/o $L_{p}^{\theta}, L_{reg}^{\theta}$ + +![](images/a7a1f43994dddc32a01c1a68ae7af412364a98c539dc09141370edcb3fa48f8a.jpg) +(c) Ours +Figure 6: Visualization of latent-features using t-sne for our global model learned (Phase 1) with either each component or all. Score in each figure denote the silhouette values [36]. + +is important to overcome the shortage of training data, limited round communications, and greater number of clients. + +![](images/8a1abffb0191da7e8383ea7cf16f9644b422ef11b1c0d91f2169d2dd80f104a5.jpg) +Figure 7: Left : Each score denotes cosine similarity $S_{c}$ between the various off-the-shelf datasets and models. Right : Performance comparison among the various global models whose off-the-shelf model is different. C and I denote CIFAR and ImageNet benchmarks. + +![](images/acf3171f50444f8b4c79bc24f5cdff37d6eecac912fe68817cef9f9d9d82a54f.jpg) + +# 6. Conclusion + +We proposed ProtoFL, a method for achieving effective round cost and scalability representation in extreme non-i.i.d. data based FL. By utilizing an off-the-shelf model and dataset to distribute prototypical independent representations, we were able to learn a global model with all joined clients and optimize the flow-based classifier of each client. Our proposed method outperforms FL methods with efficient communication cost and presents a novel property of scalability of representation, validating new joiners' performance in FL. We believe that our method and experimental details could be adapted to handle further problems in both federated and centralized learning based one-class classification. + +# Acknowledgements + +This work was supported by KakaoBank Corp., and Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. 2022-0-00320, Artificial intelligence research about cross-modal dialogue modeling for one-on-one multi-modal interactions). In particular, we would like to thank the designer Eunha Lim (milkyway-mind@naver.com) for well-presented Figures 1, 2, and 3. + +# References + +[1] Unsupervised video anomaly detection via normalizing flows with implicit latent features. Pattern Recognition, 129:108703, 2022. 2 +[2] Divyansh Aggarwal, Jiayu Zhou, and Anil K. Jain. Fedface: Collaborative learning of face recognition model. In IJCB, 2021. 1 +[3] Liron Bergman and Yedid Hoshen. 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However, limited round communications, scarce representation, and scalability pose significant challenges to its deployment, hindering its full potential. In this paper, we propose 'ProtoFL', Prototypical Representation Distillation based unsupervised Federated Learning to enhance the representation power of a global model and reduce round communication costs. Additionally, we introduce a local one-class classifier based on normalizing flows to improve performance with limited data. Our study represents the first investigation of using FL to improve one-class classification performance. 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(" + }, + { + "bbox": [ + 304, + 437, + 547, + 511 + ], + "type": "inline_equation", + "content": "\\alpha = 0.0" + }, + { + "bbox": [ + 304, + 437, + 547, + 511 + ], + "type": "text", + "content": " is a concentration parameter of Dirichlet distribution) data based FL schema shows that each device has only the data from its target class not shared among all joined devices, and prototypical representation is distributed separately to corresponding joined clients in secure from a central server." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 533, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 628 + ], + "type": "text", + "content": "In the context of FL, where data is decentralized across individual clients, one-class classification (OCC) can be used. This is because that OCC can determine whether a new example belongs to the target distribution or not. Despite not using data from the non-target class, OCC has shown impressive performance [31, 38, 43, 42, 39, 40, 15, 28]. In computer vision applications, OCC is particularly useful for detecting fraud, defects, and unauthorized users." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": "Recent advancements in biometric authentication have highlighted the importance of FL-based OCC in computer vision (e.g., user-defined embedding-based methods [17, 26] and data-driven methods [2, 24, 32]). However, FL-based OCC methods face significant challenges, including high communication costs, limited representation, and unstable learning processes. Additionally, centralized server" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 225, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 225, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 225, + 703 + ], + "type": "text", + "content": "*These authors contributed equally to this work" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "text", + "content": "† Corresponding author" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6470" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "based methods [31, 42, 43] may not be suitable for FL-based OCC due to limited computing resources on each device, which are a major obstacle for centralized methods that require substantial computing power." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 121, + 288, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 288, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 288, + 323 + ], + "type": "text", + "content": "The limitations inherent in FL-based OCC necessitated the development of a novel approach to address these challenges. In this paper, we aim to attain a more expressive global model without the need for frequent re-training processes between the central server and client devices on a large scale. To achieve this, we propose Prototypical representation distillation based unsupervised Federated Learning (ProtoFL) that distills representation from an off-the-shelf model learned using off-the-shelf datasets, regardless of individual client data. In contrast to traditional FL-based OCC, our proposed ProtoFL approach does not transfer parameters directly to the client, as depicted in Fig. 1. This resolves the issues of frequent round communication costs and the need for extra data due to one-time prototype representation distillation. ProtoFL provides a novel solution to the existing challenges of FL-based OCC, enabling efficient and effective global model updates." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 324, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 287, + 514 + ], + "type": "text", + "content": "Subsequently, we suggest a novel approach for estimating the density of a target class in a distributed setting using a flow-based one-class classifier [20]. To achieve this, we conduct the estimation on individual client devices, using augmented latent variables for training their distributed models. Our approach leverages two key techniques: maximum likelihood estimation with log-likelihood and a probabilistic similarity loss function that includes " + }, + { + "bbox": [ + 46, + 324, + 287, + 514 + ], + "type": "inline_equation", + "content": "\\mathcal{KL}" + }, + { + "bbox": [ + 46, + 324, + 287, + 514 + ], + "type": "text", + "content": "-divergence. By combining the distillation and one-class classification phases, we can effectively handle complex data distributions that are non-independent and nonidentically distributed across individual clients. Our two-phase learning framework is inspired by the success of flow-based models in various applications [20, 11, 40, 1], and we demonstrate its effectiveness in handling complex data distributions in the distributed settings." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 514, + 287, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 514, + 287, + 644 + ], + "spans": [ + { + "bbox": [ + 46, + 514, + 287, + 644 + ], + "type": "text", + "content": "The experimental findings of our proposed method demonstrate superior classification performance compared to both server-based and client-based methods on both image and tabular datasets. Additionally, we have validated the scalability of the learned representation and have shown that the global model learned by the ProtoFL is compatible with existing one-class classifiers as well as our one-class classifier based on the benchmark datasets. Our results indicate that our method is a promising approach for large-scale machine learning tasks that require robust and scalable classification capabilities." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 647, + 233, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 647, + 233, + 657 + ], + "spans": [ + { + "bbox": [ + 59, + 647, + 233, + 657 + ], + "type": "text", + "content": "Our contributions are described as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 665, + 287, + 713 + ], + "type": "text", + "content": "- We propose a novel unsupervised federated learning framework that effectively addresses the challenge of insufficient local training data. By leveraging normalizing flows for local classifier learning and prototypical" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 325, + 72, + 544, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 72, + 544, + 95 + ], + "spans": [ + { + "bbox": [ + 325, + 72, + 544, + 95 + ], + "type": "text", + "content": "representation distillation, our approach enables efficient and effective global model updates." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 114, + 545, + 255 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 317, + 114, + 545, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 114, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 317, + 114, + 545, + 186 + ], + "type": "text", + "content": "- We propose a novel prototype-based representation learning method for distilling normal data representation using an off-the-shelf model and dataset. Our approach demonstrates the scalability of the global model, which can be verified by adding new clients in FL-based OCC." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 195, + 545, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 195, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 317, + 195, + 545, + 255 + ], + "type": "text", + "content": "- We propose new federated and centralized learning methods for one-class classification, which we evaluate on five widely-used benchmarks. Our experiments show that our methods achieve superior performance compared to existing approaches." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 264, + 392, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 264, + 392, + 277 + ], + "spans": [ + { + "bbox": [ + 306, + 264, + 392, + 277 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 284, + 545, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 284, + 545, + 523 + ], + "spans": [ + { + "bbox": [ + 304, + 284, + 545, + 523 + ], + "type": "text", + "content": "One-class classification Various one-class classification approaches have been proposed and categorized into description-based and representation-based learning. In the description-based methods, Deep-SVDD [31] performs one-class detection by learning a model to map target samples into a center in the latent space, otherwise non-target samples are mapped far from the center. And FCDD [27] proposes an explainable one-class classifier by upsampling based on gaussian sampling. In contrast, representation-based learning methods (DROC [42] and CSI [43]) present a two-step learning framework to learn a representation model through excessive data-augmentation and contrastive loss. The framework either employs a classifier or defines a score function for detecting a target class. Unlike previous centralized server-based approaches, our proposed approach for one-class classification on decentralized learning avoids the risk of personal data leakage by constructing a model using distributed data. To the best of our knowledge, our method is the first to directly address this problem in a decentralized setting." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "Federated learning for local one-class classifier Federated Learning (FL) is a distributed machine learning paradigm that enables collaborative model training without direct data sharing. FL has been applied to one class classification (OCC) tasks for user verification and authentication, with several studies demonstrating promising results. [17, 32, 34]. FedAwS [45] introduces a geometric regularization to learn a global model by utilizing uploaded latent variables of joined clients in a central server. Since the latent variables shared on a server are private data, the FedAwS violates in the setting of FL. FedUV [17] employs independent secret error correcting codes (ECCs) to train a one-class classifier by preventing personal data from sharing among joined clients. The secret codes induce the concise objective of FedUV so that only positive examples are" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "6471" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "content": "required. The FedUV approach was further refined to estimate a center of distribution by FedAA [32] and FedMetric [34], instead of defining hand-designed codes. However, local data on each device is not sufficient to represent a centroid of local data distribution." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 140, + 287, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 140, + 287, + 248 + ], + "spans": [ + { + "bbox": [ + 46, + 140, + 287, + 248 + ], + "type": "text", + "content": "Federated learning for central and client classifiers In authentication systems, client data is often partitioned according to a target class. This results in highly or extremely non-i.i.d. data that poses a significant challenge for FL. This extreme non-i.i.d. means that a concentration parameter of Dirichlet distribution approaches to zero " + }, + { + "bbox": [ + 46, + 140, + 287, + 248 + ], + "type": "inline_equation", + "content": "(\\alpha = 0.0)" + }, + { + "bbox": [ + 46, + 140, + 287, + 248 + ], + "type": "text", + "content": " while many federated learning methods [6, 9, 13] assumes non-i.i.d. data with non-zero " + }, + { + "bbox": [ + 46, + 140, + 287, + 248 + ], + "type": "inline_equation", + "content": "(\\alpha \\neq 0.0)" + }, + { + "bbox": [ + 46, + 140, + 287, + 248 + ], + "type": "text", + "content": " setting [18, 23, 29, 6, 13, 9]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 249, + 287, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 249, + 287, + 439 + ], + "spans": [ + { + "bbox": [ + 46, + 249, + 287, + 439 + ], + "type": "text", + "content": "Unsupervised federated learning methods [23, 29] aggregate local representation models and centroids for achieving a global model and centroid. FedRep [6] shares partitions of a global model to adapt each local heterogeneous data. FedX [13], which utilizes structure knowledge distillation between local and global knowledge relationships, learns meaningful data representation without sharing external data. SphereFed [9] introduced a learned matrix, which is a fixed-classifier for sharing among all participating clients, to transform each local data distribution into the predefined latent space. But, SphereFed requires enormous cost to re-construct and re-distribute a new learned matrix whenever a new client joins. Therefore, we first propose a prototypical representation distillation learning to save communication cost in FL with extreme non-i.i.d. " + }, + { + "bbox": [ + 46, + 249, + 287, + 439 + ], + "type": "inline_equation", + "content": "(\\alpha = 0.0)" + }, + { + "bbox": [ + 46, + 249, + 287, + 439 + ], + "type": "text", + "content": " data settings." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 449, + 124, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 449, + 124, + 462 + ], + "spans": [ + { + "bbox": [ + 47, + 449, + 124, + 462 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 469, + 287, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 469, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 469, + 287, + 540 + ], + "type": "text", + "content": "Federated Average Learning FedAVG [30], composed of participating clients and a central mediator server, trains a global model by aggregating locally-computed parameters, and broadcasts the updated global model to the clients. In each round, FedAVG updates the global model parameters with local model parameters as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 110, + 545, + 287, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 545, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 110, + 545, + 287, + 578 + ], + "type": "interline_equation", + "content": "\\theta_ {g} ^ {t + 1} = \\sum_ {k = 1} ^ {K} \\frac {\\left| D _ {k} \\right|}{\\sum_ {k = 1} ^ {K} \\left| D _ {k} \\right|} \\theta_ {k} ^ {t}, \\tag {1}", + "image_path": "85ab46505710a453d61e06ac2abb32dcae9a88bdcd0d2c6a1a6c798719cee291.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "spans": [ + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "type": "inline_equation", + "content": "k \\in \\{1, \\dots, K\\}" + }, + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "type": "text", + "content": " indicates an index of a local client. " + }, + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "type": "inline_equation", + "content": "\\theta_{g}^{t+1}" + }, + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "type": "text", + "content": " is the parameters of a global model, and " + }, + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "type": "inline_equation", + "content": "\\theta_{k}^{t}" + }, + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "type": "text", + "content": " is the parameters of the " + }, + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "type": "text", + "content": " local model at a round " + }, + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "type": "text", + "content": ". For the balanced updating of the global model " + }, + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "type": "inline_equation", + "content": "\\theta_{g}^{t+1}" + }, + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "type": "inline_equation", + "content": "|D_{k}|" + }, + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "type": "text", + "content": " is the number of samples on dataset " + }, + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "type": "inline_equation", + "content": "D_{k}" + }, + { + "bbox": [ + 46, + 583, + 287, + 644 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "Unsupervised Contrastive Learning FL with extreme non-i.i.d. " + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "(\\alpha = 0.0)" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": " data setting is unavailable to access samples of the other clients. Thus, we simplify the contrastive loss, " + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cntr} = y \\times (1 - d(\\bullet, \\hat{\\bullet})) + (1 - y) \\times \\max(0, d(\\bullet, \\hat{\\bullet}))" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": ", as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 388, + 90, + 545, + 102 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 90, + 545, + 102 + ], + "spans": [ + { + "bbox": [ + 388, + 90, + 545, + 102 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d} = 1 - d (\\bullet , \\hat {\\bullet}), \\tag {2}", + "image_path": "1845f8adf4cc20a66f39afaa0af02d451fad3e268af6f2123b7f394ba31d94e1.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 110, + 545, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 110, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 305, + 110, + 545, + 148 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 110, + 545, + 148 + ], + "type": "inline_equation", + "content": "d(\\bullet, \\hat{\\bullet})" + }, + { + "bbox": [ + 305, + 110, + 545, + 148 + ], + "type": "text", + "content": " is the cosine-similarity " + }, + { + "bbox": [ + 305, + 110, + 545, + 148 + ], + "type": "inline_equation", + "content": "\\frac{\\bullet \\cdot \\hat{\\bullet}}{||\\bullet|| \\cdot ||\\hat{\\bullet}||}" + }, + { + "bbox": [ + 305, + 110, + 545, + 148 + ], + "type": "text", + "content": ". We utilize " + }, + { + "bbox": [ + 305, + 110, + 545, + 148 + ], + "type": "inline_equation", + "content": "L_{d}" + }, + { + "bbox": [ + 305, + 110, + 545, + 148 + ], + "type": "text", + "content": " as our positive cosine similarity loss for our unsupervised leaning, instead of " + }, + { + "bbox": [ + 305, + 110, + 545, + 148 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cntr}" + }, + { + "bbox": [ + 305, + 110, + 545, + 148 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 156, + 545, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 156, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 305, + 156, + 545, + 264 + ], + "type": "text", + "content": "Normalizing Flows Normalizing flows (NFs) [8] are the statistical methods using the change-of-variable law of probabilities to fit an arbitrary target density " + }, + { + "bbox": [ + 305, + 156, + 545, + 264 + ], + "type": "inline_equation", + "content": "p_R(r)" + }, + { + "bbox": [ + 305, + 156, + 545, + 264 + ], + "type": "text", + "content": " by a tractable base distribution with density " + }, + { + "bbox": [ + 305, + 156, + 545, + 264 + ], + "type": "inline_equation", + "content": "p_Z(z)" + }, + { + "bbox": [ + 305, + 156, + 545, + 264 + ], + "type": "text", + "content": " and a bijective invertible mapping " + }, + { + "bbox": [ + 305, + 156, + 545, + 264 + ], + "type": "inline_equation", + "content": "\\mathfrak{t}^{-1}: R^D \\to Z^D \\Leftrightarrow \\mathfrak{t}: Z^D \\to R^D" + }, + { + "bbox": [ + 305, + 156, + 545, + 264 + ], + "type": "text", + "content": ". According to [33], " + }, + { + "bbox": [ + 305, + 156, + 545, + 264 + ], + "type": "inline_equation", + "content": "\\mathcal{KL}" + }, + { + "bbox": [ + 305, + 156, + 545, + 264 + ], + "type": "text", + "content": "-divergence and log-likelihood estimation are employed to optimize the invertible flow-based model " + }, + { + "bbox": [ + 305, + 156, + 545, + 264 + ], + "type": "inline_equation", + "content": "z = \\mathfrak{t}^{-1}(r; \\psi)" + }, + { + "bbox": [ + 305, + 156, + 545, + 264 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 156, + 545, + 264 + ], + "type": "inline_equation", + "content": "r = \\mathfrak{t}(z; \\psi)" + }, + { + "bbox": [ + 305, + 156, + 545, + 264 + ], + "type": "text", + "content": " by the target distribution " + }, + { + "bbox": [ + 305, + 156, + 545, + 264 + ], + "type": "inline_equation", + "content": "p_R(r)" + }, + { + "bbox": [ + 305, + 156, + 545, + 264 + ], + "type": "text", + "content": ". The bijective invertible mapping is drawn as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 278, + 545, + 318 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 278, + 545, + 318 + ], + "spans": [ + { + "bbox": [ + 312, + 278, + 545, + 318 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {D} _ {\\mathcal {K L}} \\left[ \\hat {p} _ {R} (r) \\| p _ {R} (r; \\psi) \\right] \\\\ \\approx - \\mathbb {E} _ {\\hat {p} _ {R} (r)} \\left[ \\log p _ {Z} \\left(\\mathrm {t} ^ {- 1} (r; \\psi)\\right) + \\log | \\det j _ {\\mathrm {t} ^ {- 1}} | \\right] + c o n t, \\tag {3} \\\\ \\end{array}", + "image_path": "3573e04b1cbfe70da8c2d46a09c1b4e87595a7a954a2370af0e4bc5cccde4af3.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 319, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 319, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 305, + 319, + 545, + 407 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 319, + 545, + 407 + ], + "type": "inline_equation", + "content": "p_R(r;\\psi)" + }, + { + "bbox": [ + 305, + 319, + 545, + 407 + ], + "type": "text", + "content": " denotes the likelihood of a model. " + }, + { + "bbox": [ + 305, + 319, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\hat{p}_R" + }, + { + "bbox": [ + 305, + 319, + 545, + 407 + ], + "type": "text", + "content": " is the target distribution to learn the model by " + }, + { + "bbox": [ + 305, + 319, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\mathcal{KL}" + }, + { + "bbox": [ + 305, + 319, + 545, + 407 + ], + "type": "text", + "content": "-divergence. " + }, + { + "bbox": [ + 305, + 319, + 545, + 407 + ], + "type": "inline_equation", + "content": "p_R(r;\\psi)" + }, + { + "bbox": [ + 305, + 319, + 545, + 407 + ], + "type": "text", + "content": " only remains for learning parameters " + }, + { + "bbox": [ + 305, + 319, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 305, + 319, + 545, + 407 + ], + "type": "text", + "content": ", and then is replaced by " + }, + { + "bbox": [ + 305, + 319, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\frac{1}{N}\\sum_{i=1}^{N}\\left[\\frac{\\|\\mathfrak{t}^{-1}(r_i)\\|_2^2}{2}-\\log|\\det\\mathfrak{j}_{\\mathfrak{t}^{-1}}|\\right]" + }, + { + "bbox": [ + 305, + 319, + 545, + 407 + ], + "type": "text", + "content": " through the training dataset " + }, + { + "bbox": [ + 305, + 319, + 545, + 407 + ], + "type": "inline_equation", + "content": "D_k" + }, + { + "bbox": [ + 305, + 319, + 545, + 407 + ], + "type": "text", + "content": " as explained by [11, 20]. The re-written equation is applied to our objective to estimate the log-likelihood of given local data on each device." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 417, + 411, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 417, + 411, + 430 + ], + "spans": [ + { + "bbox": [ + 306, + 417, + 411, + 430 + ], + "type": "text", + "content": "4. Proposed Method" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 437, + 545, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 437, + 545, + 485 + ], + "spans": [ + { + "bbox": [ + 305, + 437, + 545, + 485 + ], + "type": "text", + "content": "In this section, we propose a two-phase unsupervised learning framework that combines unsupervised federated learning via distillation of prototypical representations with local classifier learning via leveraging normalizing flows." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 491, + 430, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 430, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 430, + 502 + ], + "type": "text", + "content": "4.1. Problem Formulation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "text", + "content": "Participating " + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "text", + "content": " clients aim to train a global model by aggregating locally-computed parameters " + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\phi(\\bullet, \\theta)" + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "text", + "content": " for an one-class classification task without sharing private data among joined clients. Each client has a training dataset " + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "D_{K,N} = \\{x_{k,i}, 1 \\leq i \\leq N, 1 \\leq k \\leq K\\}" + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "text", + "content": " is the cardinality of the local data " + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "D_{k,N}" + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\phi(x_{k,i}; \\theta_k)" + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "text", + "content": " denote the trainable model of the " + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "text", + "content": " client. In particular, we follow the extreme non-i.i.d. " + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "(\\forall_{m,n} D_{m,N} \\cap D_{n,N} = \\emptyset)" + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "text", + "content": " data setting in our FL-based OCC. Different from prior FL settings utilizing either hand-designed codes or additional training datasets, we invent generic representation of the local model " + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "text", + "content": " by leveraging the off-the-shelf model " + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "text", + "content": " and dataset " + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "text", + "content": ", and we employ the flow-based model " + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 305, + 509, + 545, + 665 + ], + "type": "text", + "content": " for the local one-class classifier." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 671, + 440, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 440, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 440, + 684 + ], + "type": "text", + "content": "4.2. Sequence of procedures" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "As shown in Fig. 2, we describe our proposed method workflow in each phase. " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "①" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": " Whenever a new client partici" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6472" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 352, + 223 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 352, + 223 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 352, + 223 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 352, + 223 + ], + "type": "image", + "image_path": "7a5be14a4fda3165121fd68dc1fafea57d219633c4acc04699148ca443fb93f8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 49, + 224, + 351, + 236 + ], + "lines": [ + { + "bbox": [ + 49, + 224, + 351, + 236 + ], + "spans": [ + { + "bbox": [ + 49, + 224, + 351, + 236 + ], + "type": "text", + "content": "(a) Phase 1: Unsupervised federated learning via prototypical representation distillation" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 354, + 72, + 545, + 159 + ], + "blocks": [ + { + "bbox": [ + 354, + 72, + 545, + 159 + ], + "lines": [ + { + "bbox": [ + 354, + 72, + 545, + 159 + ], + "spans": [ + { + "bbox": [ + 354, + 72, + 545, + 159 + ], + "type": "image", + "image_path": "cfca0dd713e55ee3f8fc71af74ccdee619e4a99ce5c6158299fbd91853c28aa6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 354, + 161, + 545, + 223 + ], + "blocks": [ + { + "bbox": [ + 354, + 161, + 545, + 223 + ], + "lines": [ + { + "bbox": [ + 354, + 161, + 545, + 223 + ], + "spans": [ + { + "bbox": [ + 354, + 161, + 545, + 223 + ], + "type": "image", + "image_path": "e179ce143316191b6a150dcd5a88078ad437b78877c834bdadb161fb8aae95ac.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 361, + 224, + 539, + 236 + ], + "lines": [ + { + "bbox": [ + 361, + 224, + 539, + 236 + ], + "spans": [ + { + "bbox": [ + 361, + 224, + 539, + 236 + ], + "type": "text", + "content": "(b) Phase 2: Local one-class classifier based on NFs" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 241, + 547, + 278 + ], + "lines": [ + { + "bbox": [ + 46, + 241, + 547, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 547, + 278 + ], + "type": "text", + "content": "Figure 2: Overview of our proposed two-phase learning architecture. " + }, + { + "bbox": [ + 46, + 241, + 547, + 278 + ], + "type": "inline_equation", + "content": "① \\sim" + }, + { + "bbox": [ + 46, + 241, + 547, + 278 + ], + "type": "inline_equation", + "content": "④" + }, + { + "bbox": [ + 46, + 241, + 547, + 278 + ], + "type": "text", + "content": " indicates the workflows of ProtoFL with all the joined clients to upload parameters of each client and to download the aggregated global model, and " + }, + { + "bbox": [ + 46, + 241, + 547, + 278 + ], + "type": "inline_equation", + "content": "⑤" + }, + { + "bbox": [ + 46, + 241, + 547, + 278 + ], + "type": "text", + "content": " represents a local training for the OC-NF. The details of sequences " + }, + { + "bbox": [ + 46, + 241, + 547, + 278 + ], + "type": "inline_equation", + "content": "① \\sim" + }, + { + "bbox": [ + 46, + 241, + 547, + 278 + ], + "type": "inline_equation", + "content": "⑤" + }, + { + "bbox": [ + 46, + 241, + 547, + 278 + ], + "type": "text", + "content": " are described in Section 4.2. NFs denote normalizing flows." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "text", + "content": "pates in our unsupervised federated learning, all clients join a central mediator server. ② For the " + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "text", + "content": " client, a categorical image " + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "inline_equation", + "content": "s_k" + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "text", + "content": " is chosen from " + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "text", + "content": " and transformed into a latent variable " + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "inline_equation", + "content": "v_k" + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "text", + "content": " by the central mediator server. Both ① and ② occur only once at the first time, and " + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = \\{v_k, 1 \\leq k \\leq K\\}" + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "text", + "content": " is secretly distributed to the corresponding client. ③ We train the " + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "text", + "content": " local model " + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "inline_equation", + "content": "\\theta_k" + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "text", + "content": " via the local data " + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "inline_equation", + "content": "D_{k,N}" + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "text", + "content": ", the distributed prototype representation " + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "inline_equation", + "content": "v_k" + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "text", + "content": ", cosine similarly loss, and " + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "inline_equation", + "content": "\\mathcal{KL}" + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "text", + "content": "-divergence loss. ④ A global model " + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "inline_equation", + "content": "\\theta_g" + }, + { + "bbox": [ + 46, + 289, + 289, + 482 + ], + "type": "text", + "content": " is aggregated with all the uploaded local models by FedAVG, and the global model is distributed to all participating clients. ⑤ Once federated representation learning has finished, we train a local one-class classifier based on normalizing flows (OC-NF) by using maximum likelihood and cosine similarity losses. We describe the details of our procedures (① ~ ⑤) in the following subsections." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 494, + 287, + 519 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 494, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 47, + 494, + 287, + 519 + ], + "type": "text", + "content": "4.3. Prototypical representation distillation based unsupervised federated learning (ProtoFL)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 524, + 287, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 524, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 524, + 287, + 598 + ], + "type": "text", + "content": "We assume " + }, + { + "bbox": [ + 47, + 524, + 287, + 598 + ], + "type": "inline_equation", + "content": "\\mathcal{F}:R^{W\\times H\\times C}\\to R^D" + }, + { + "bbox": [ + 47, + 524, + 287, + 598 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 524, + 287, + 598 + ], + "type": "inline_equation", + "content": "\\phi :R^{W\\times H\\times C}\\to" + }, + { + "bbox": [ + 47, + 524, + 287, + 598 + ], + "type": "inline_equation", + "content": "R^D" + }, + { + "bbox": [ + 47, + 524, + 287, + 598 + ], + "type": "text", + "content": " indicate the off-the-shelf model and the local model, respectively as illustrated in Fig. 2. For training the local model of the " + }, + { + "bbox": [ + 47, + 524, + 287, + 598 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 47, + 524, + 287, + 598 + ], + "type": "text", + "content": " client, we augment two views " + }, + { + "bbox": [ + 47, + 524, + 287, + 598 + ], + "type": "inline_equation", + "content": "x_{k,i},\\hat{x}_{k,i}" + }, + { + "bbox": [ + 47, + 524, + 287, + 598 + ], + "type": "text", + "content": " from the " + }, + { + "bbox": [ + 47, + 524, + 287, + 598 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 47, + 524, + 287, + 598 + ], + "type": "text", + "content": " example of the local training data " + }, + { + "bbox": [ + 47, + 524, + 287, + 598 + ], + "type": "inline_equation", + "content": "D_{k,N}" + }, + { + "bbox": [ + 47, + 524, + 287, + 598 + ], + "type": "text", + "content": ", and subsequently transform the two samples as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 88, + 615, + 287, + 628 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 615, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 88, + 615, + 287, + 628 + ], + "type": "interline_equation", + "content": "r _ {k, i} = \\phi \\left(x _ {k, i}; \\theta_ {k}\\right); \\hat {r} _ {k, i} = \\phi \\left(\\hat {x} _ {k, i}; \\theta_ {k}\\right), \\tag {4}", + "image_path": "7f881b0df25d966550992e8b4babf75b566b280d59da3908e288cc71582bf517.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "r_{k,i}" + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\hat{r}_{k,i}" + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "text", + "content": " represent latent variables of the " + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "text", + "content": " example. " + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "text", + "content": " is the client model with " + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "text", + "content": " learnable parameters " + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\theta_{k}" + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "text", + "content": ". Inspired by SimCLR [5], the two latent variables " + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "r_k" + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\hat{r}_k" + }, + { + "bbox": [ + 47, + 641, + 288, + 714 + ], + "type": "text", + "content": " must be very close to each other. Given the only positive local data and the constraint, we employ the positive cosine similarity loss(Eq. 2) to learn the local model as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 351, + 309, + 545, + 342 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 309, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 351, + 309, + 545, + 342 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p} ^ {\\theta} \\left(\\theta_ {k}\\right) = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left[ 1 - d \\left(r _ {k, i}, \\hat {r} _ {k, i}\\right) \\right], \\tag {5}", + "image_path": "a5a6753d78f476351b33bc5f28b7f1afa055e236956158f830ee6a8d3fa33e12.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 351, + 546, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 351, + 546, + 423 + ], + "spans": [ + { + "bbox": [ + 305, + 351, + 546, + 423 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 351, + 546, + 423 + ], + "type": "inline_equation", + "content": "\\theta_{k}" + }, + { + "bbox": [ + 305, + 351, + 546, + 423 + ], + "type": "text", + "content": " is optimized by the local data " + }, + { + "bbox": [ + 305, + 351, + 546, + 423 + ], + "type": "inline_equation", + "content": "D_{k,N}" + }, + { + "bbox": [ + 305, + 351, + 546, + 423 + ], + "type": "text", + "content": ". To overcome the small cardinality of local data for training the local representative model, we propose the off-the-shelf model with pre-trained parameters " + }, + { + "bbox": [ + 305, + 351, + 546, + 423 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(\\bullet ;\\omega)" + }, + { + "bbox": [ + 305, + 351, + 546, + 423 + ], + "type": "text", + "content": " and the off-the-shelf dataset " + }, + { + "bbox": [ + 305, + 351, + 546, + 423 + ], + "type": "inline_equation", + "content": "s_k\\in S_s" + }, + { + "bbox": [ + 305, + 351, + 546, + 423 + ], + "type": "text", + "content": ". The off-the-shelf model and dataset are utilized on a central mediator server as depicted:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 392, + 434, + 545, + 447 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 392, + 434, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 392, + 434, + 545, + 447 + ], + "type": "interline_equation", + "content": "v _ {k} = \\mathcal {F} \\left(s _ {k}; \\omega\\right), \\tag {6}", + "image_path": "9618d948abb533d2557bfe929011727977b5b396955f9435a76c45f197b81b5b.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "spans": [ + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "inline_equation", + "content": "s_k" + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "inline_equation", + "content": "v_k" + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "text", + "content": " represent a prototype example and representation for the " + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "text", + "content": " client. After " + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = \\{v_k, 1 \\leq k \\leq K\\}" + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "text", + "content": " is distributed to the corresponding client in secret, we train the local model of the " + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "text", + "content": " client to estimate the prototypical target representation " + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "inline_equation", + "content": "v_k" + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "text", + "content": ". We employ the " + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "inline_equation", + "content": "\\mathcal{KL}" + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "text", + "content": "-divergence to minimize the discrepancy between two distributions " + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "inline_equation", + "content": "v_k" + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "text", + "content": " and either " + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "inline_equation", + "content": "r_k" + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "inline_equation", + "content": "\\hat{r}_k" + }, + { + "bbox": [ + 305, + 457, + 545, + 554 + ], + "type": "text", + "content": ". Therefore, we invent the prototypical distillation loss as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 564, + 545, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 564, + 545, + 597 + ], + "spans": [ + { + "bbox": [ + 317, + 564, + 545, + 597 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p d} ^ {\\theta} \\left(\\theta_ {k}\\right) = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left[ \\mathcal {K L} \\left(v _ {k} \\| r _ {k, i}\\right) + \\mathcal {K L} \\left(v _ {k} \\| \\hat {r} _ {k, i}\\right) \\right], \\tag {7}", + "image_path": "0fc275915451fc376a34a495f19a954375f6df8d44478cb70d82d6f51d5c4775.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 607, + 545, + 655 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 607, + 545, + 655 + ], + "spans": [ + { + "bbox": [ + 305, + 607, + 545, + 655 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 607, + 545, + 655 + ], + "type": "inline_equation", + "content": "\\mathcal{KL}(v_k\\| r_{k,i})" + }, + { + "bbox": [ + 305, + 607, + 545, + 655 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 607, + 545, + 655 + ], + "type": "inline_equation", + "content": "\\mathcal{KL}(v_k\\|\\hat{r}_{k,i})" + }, + { + "bbox": [ + 305, + 607, + 545, + 655 + ], + "type": "text", + "content": " are equally contributed to our distillation loss. Figure 3 describes the details of Eq. 5 and Eq. 7, and the overall objective of the first phase (phase 1) is defined as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 333, + 665, + 545, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 665, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 333, + 665, + 545, + 681 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\phi} \\left(\\theta_ {k}\\right) = (1 - \\alpha) \\times \\mathcal {L} _ {p d} ^ {\\theta} \\left(\\theta_ {k}\\right) + \\alpha \\times \\mathcal {L} _ {p} ^ {\\theta} \\left(\\theta_ {k}\\right), \\tag {8}", + "image_path": "3423564be86e8eefa8f56169cd7791a3bc54e3a71b9b94a8a417c06cac1c8931.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " is a balancing weight. In our experiment, " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " is empirically set to 0.1." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6473" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 214, + 205 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 214, + 205 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 214, + 205 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 214, + 205 + ], + "type": "image", + "image_path": "2ba057b7238259801252892b21079b2808b9781ea196313c777801c6cf5451f7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 211, + 287, + 248 + ], + "lines": [ + { + "bbox": [ + 46, + 211, + 287, + 248 + ], + "spans": [ + { + "bbox": [ + 46, + 211, + 287, + 248 + ], + "type": "text", + "content": "Figure 3: Illustration of learning a global model with prototypical representation distillation on distributed devices without sharing private data among participating clients." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 216, + 70, + 286, + 205 + ], + "blocks": [ + { + "bbox": [ + 216, + 70, + 286, + 205 + ], + "lines": [ + { + "bbox": [ + 216, + 70, + 286, + 205 + ], + "spans": [ + { + "bbox": [ + 216, + 70, + 286, + 205 + ], + "type": "image", + "image_path": "ae7feeadfbbd5a0b3823c2aa76bd276428ab441c3568cbbd7938c5274dbcbbe5.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 259, + 287, + 284 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 259, + 287, + 284 + ], + "spans": [ + { + "bbox": [ + 47, + 259, + 287, + 284 + ], + "type": "text", + "content": "4.4. Local one-class classifier via Normalizing Flows (OC-NF)" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 291, + 288, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 291, + 288, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 291, + 288, + 376 + ], + "type": "text", + "content": "After unsupervised federated representation learning for the global model, we leverage a general flow-based model for training the local one-class classifier in each client as shown in Fig. 2. To estimate log-likelihood of transformed latent variables " + }, + { + "bbox": [ + 46, + 291, + 288, + 376 + ], + "type": "inline_equation", + "content": "r_k" + }, + { + "bbox": [ + 46, + 291, + 288, + 376 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 291, + 288, + 376 + ], + "type": "inline_equation", + "content": "\\hat{r}_k" + }, + { + "bbox": [ + 46, + 291, + 288, + 376 + ], + "type": "text", + "content": ", we exploit Eq. 3 to learn the probabilistic normalizing flows " + }, + { + "bbox": [ + 46, + 291, + 288, + 376 + ], + "type": "inline_equation", + "content": "\\mathfrak{t}" + }, + { + "bbox": [ + 46, + 291, + 288, + 376 + ], + "type": "text", + "content": " through the local dataset " + }, + { + "bbox": [ + 46, + 291, + 288, + 376 + ], + "type": "inline_equation", + "content": "D_{k,N}" + }, + { + "bbox": [ + 46, + 291, + 288, + 376 + ], + "type": "text", + "content": " and the local model " + }, + { + "bbox": [ + 46, + 291, + 288, + 376 + ], + "type": "inline_equation", + "content": "\\phi (\\cdot ;\\theta_k)" + }, + { + "bbox": [ + 46, + 291, + 288, + 376 + ], + "type": "text", + "content": " on the " + }, + { + "bbox": [ + 46, + 291, + 288, + 376 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 46, + 291, + 288, + 376 + ], + "type": "text", + "content": " client as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 62, + 388, + 287, + 472 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 388, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 62, + 388, + 287, + 472 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {m l e} ^ {\\psi} (\\psi_ {k}) \\\\ = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left[ \\frac {\\| \\mathfrak {t} ^ {- 1} (r _ {k , i} ; \\psi_ {k}) \\| _ {2} ^ {2}}{2} - \\log | \\det \\mathfrak {j} _ {k, i} | \\right] + c o n t \\\\ \\approx \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left[ \\frac {\\left\\| z _ {k , i} \\right\\| _ {2} ^ {2}}{2} - \\log | \\det j _ {k, i} | \\right] + c o n t, \\tag {9} \\\\ \\end{array}", + "image_path": "d0a1fe9c4c8e004228251c68468bc769a229bc6934411cc33720cbc25de71f45.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "type": "inline_equation", + "content": "z_{k,i}" + }, + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "type": "text", + "content": " is the estimated distribution as it passes through " + }, + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "type": "inline_equation", + "content": "\\mathrm{t}^{-1}(r_{k,i};\\psi_k)" + }, + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "type": "inline_equation", + "content": "r_{k,i}" + }, + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "type": "text", + "content": " is a latent variable from " + }, + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "type": "inline_equation", + "content": "\\phi (x_{k,i};\\theta)" + }, + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "type": "text", + "content": ". When optimizing the flow-based model, we ignore constants, det and cont. Since " + }, + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "type": "inline_equation", + "content": "r_{k,i}" + }, + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "type": "inline_equation", + "content": "\\hat{r}_{k,i}" + }, + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "type": "text", + "content": " are close each other in a latent space, " + }, + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "type": "inline_equation", + "content": "z_{k,i}" + }, + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "type": "inline_equation", + "content": "\\hat{z}_{k,i}" + }, + { + "bbox": [ + 46, + 481, + 287, + 554 + ], + "type": "text", + "content": " also predict the same distribution so that we introduce the following objective as a regularizer:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 88, + 564, + 287, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 564, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 88, + 564, + 287, + 597 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r e g} ^ {\\psi} (\\psi_ {k}) = \\frac {1}{N} \\sum_ {i = 1} ^ {N} [ 1 - d (z _ {k, i}, \\hat {z} _ {k, i}) ], \\tag {10}", + "image_path": "8de85392dc09342c93bd7fdd7c496ff7e38974754f92f43719c0d647753617f3.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 606, + 287, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 606, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 47, + 606, + 287, + 654 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 606, + 287, + 654 + ], + "type": "inline_equation", + "content": "z_{k,i}" + }, + { + "bbox": [ + 47, + 606, + 287, + 654 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 606, + 287, + 654 + ], + "type": "inline_equation", + "content": "\\hat{z}_{k,i}" + }, + { + "bbox": [ + 47, + 606, + 287, + 654 + ], + "type": "text", + "content": " are the normal distribution estimated by " + }, + { + "bbox": [ + 47, + 606, + 287, + 654 + ], + "type": "inline_equation", + "content": "\\mathfrak{t}^{-1}((\\phi (x_{k,i};\\theta_k);\\psi_k))" + }, + { + "bbox": [ + 47, + 606, + 287, + 654 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 606, + 287, + 654 + ], + "type": "inline_equation", + "content": "\\mathfrak{t}^{-1}((\\phi (\\hat{x}_{k,i};\\theta_k);\\psi_k))" + }, + { + "bbox": [ + 47, + 606, + 287, + 654 + ], + "type": "text", + "content": " respectively. The overall objective of the second phase (phase 2) is composed of Eq. 9 and Eq. 10 as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 88, + 664, + 287, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 664, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 88, + 664, + 287, + 681 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {t}} \\left(\\psi_ {k}\\right) = \\mathcal {L} _ {m l e} ^ {\\psi} \\left(\\psi_ {k}\\right) + \\lambda \\times \\mathcal {L} _ {r e g} ^ {\\psi} \\left(\\psi_ {k}\\right), \\tag {11}", + "image_path": "cc994aced3fb884f6b54791cbf395ebe95bd653ee2e62b1c5f99f65a71fe1195.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " is a hyper-parameter for effectiveness of regularization. For our experiment, we empirically set " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " to 0.01." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 71, + 388, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 388, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 388, + 85 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 91, + 547, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 175 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 175 + ], + "type": "text", + "content": "In this section, we demonstrate the proposed approach on image and tabular benchmarks. We evaluate the performance of our proposed ProtoFL and compare our model with the other FL methods and one-class detectors. And we analyze the impact of new client participation in the context of OCC on FL, as well as ablation studies on each proposed component." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 183, + 368, + 194 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 183, + 368, + 194 + ], + "spans": [ + { + "bbox": [ + 306, + 183, + 368, + 194 + ], + "type": "text", + "content": "5.1. Datasets" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 201, + 546, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 201, + 546, + 406 + ], + "spans": [ + { + "bbox": [ + 304, + 201, + 546, + 406 + ], + "type": "text", + "content": "We thoroughly evaluate our proposed method on several benchmark datasets, including the widely used MNIST [22], CIFAR-10 [21], CIFAR-100 [21], ImageNet-30 [16], and Keystroke-Dynamics [19], to tackle the demanding task of one-class classification. Our evaluation scrutinizes the efficacy, robustness, and scalability of our method, highlighting its strengths in handling real-world scenarios. In case of CIFAR-100, we adopt 20 super-class labels, denoted by CIFAR- " + }, + { + "bbox": [ + 304, + 201, + 546, + 406 + ], + "type": "inline_equation", + "content": "100^{\\ddagger}" + }, + { + "bbox": [ + 304, + 201, + 546, + 406 + ], + "type": "text", + "content": ", as suggested in [10] to our experiments. The numbers of categories in the benchmarks are 10, 10, 20, 30, and 51, which are the numbers of participating clients on our federated learning. The vision and tabular based benchmarks for OCC follow a one-vs-rest protocol [10, 42, 43]. In the protocol, a set of samples from one class indicates a target class for one client, whereas a set of samples from the remaining classes represents a non-target class for the remaining clients." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 413, + 421, + 426 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 413, + 421, + 426 + ], + "spans": [ + { + "bbox": [ + 306, + 413, + 421, + 426 + ], + "type": "text", + "content": "5.2. Experiment Setting" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 431, + 547, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 431, + 547, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 431, + 547, + 504 + ], + "type": "text", + "content": "Off-the-shelf model and dataset In the central mediator server, the off-the-shelf dataset and model generate prototypical representation when a new client participates in our unsupervised federated learning. For the off-the-shelf model and dataset, we exploit ArcFace [7] based ResNet-50 backbone [14] and MS-Celeb-1M [12], respectively." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 510, + 547, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 629 + ], + "type": "text", + "content": "Architectures In this experiment, we employ ResNet-18/32 backbones [14] to learn the local and global models on our proposed approach. Since batch normalization is detrimental to the performance in federated learning [17] both ResNet-18/32 backbones replace batch- with group-normalization. In the Keystroke Dynamics dataset, we employ multi-layer perceptions as the local and global model, consisting of three linear layers, ReLU, and group-normalization. And we utilize NFs as a local classifier model composed of 8 coupling layers [8]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 641, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 714 + ], + "type": "text", + "content": "Implementation details In the first phase as described in Algorithm 1, we train our expressive global model based on the FedAvg [30] method with 1 local epoch and 900 communication rounds, using randomly chosen clients from all participating clients. 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In the second phase as described in Algorithm 2, we use the SGD optimizer [35] with a learning rate 5e-3 and 5 epochs to learn our one-class classifier. Data augmentations include the set of random processes (crop, horizontal-flip, and gaussian-blur) and color jitter. To evaluate the performance of various methods, we use the area under curve of ROC curve (AUROC) and equal error rate (EER)." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 47, + 634, + 170, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 170, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 170, + 647 + ], + "type": "text", + "content": "5.3. Experimental Results" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "Image and tabular benchmarks For the image benchmarks, we present the results on MNIST and CIFAR-10 datasets for OCC in extreme non-i.i.d. " + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "(\\alpha = 0.0)" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": " data setting of FL. Table 1 shows the outstanding result of not only the significantly improved performance but also the" + } + ] + } + ], + "index": 33 + }, + { + "type": "table", + "bbox": [ + 307, + 70, + 545, + 129 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 129 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 129 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 129 + ], + "type": "table", + "html": "
MethodNetworkMNISTCIFAR-10
AUROCRoundAUROCRound
FedAwS [45]ResNet-3299.610K94.1100K
FedUV [17]ResNet-3299.720K87.220K
FedMetric [34]ResNet-3299.610K94.2100K
OursResNet-3299.90.9K95.20.9K
", + "image_path": "569e7470543c4f3c45212685c3a706517941c5cf7d10dd7718b71e09ef24c5a9.jpg" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "table_body" + } + ], + "index": 34 + }, + { + "bbox": [ + 306, + 130, + 545, + 177 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 130, + 545, + 177 + ], + "spans": [ + { + "bbox": [ + 306, + 130, + 545, + 177 + ], + "type": "text", + "content": "Table 1: Performance comparison FL-based methods with our proposed approach on MNIST and CIFAR-10 benchmarks. Our approach outperforms both benchmarks while reducing the communication round cost." + } + ] + } + ], + "index": 35 + }, + { + "type": "table", + "bbox": [ + 307, + 190, + 545, + 292 + ], + "blocks": [ + { + "bbox": [ + 307, + 190, + 545, + 292 + ], + "lines": [ + { + "bbox": [ + 307, + 190, + 545, + 292 + ], + "spans": [ + { + "bbox": [ + 307, + 190, + 545, + 292 + ], + "type": "table", + "html": "
TypeMethodNetworkCIFAR-10CIFAR-100‡ImageNet-30
AUROCAUROCAUROC
Centralized LearningAE [27]---56.0
OC-SVM [41]-58.863.1-
Geom [10]WRN-16-886.078.7-
Rot [16]ResNet-1889.877.777.9
GOAD [3]ResNet-1885.174.5-
DROC [42]ResNet-1892.586.5-
CSI [43]ResNet-1894.386.691.6
FLOW† [40]ResNet-5095.293.0-
Federated LearningFedUV [17]ResNet-1879.8*55.9*62.8*
FedRep [6]ResNet-1858.2*56.9*56.3*
OursResNet-1895.389.995.4
", + "image_path": "0dd1a55d12a24d32390d02dcc22416057e356bc5608b8d95963bf765e305ed5c.jpg" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "table_body" + } + ], + "index": 36 + }, + { + "bbox": [ + 306, + 293, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 293, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 306, + 293, + 545, + 365 + ], + "type": "text", + "content": "Table 2: AUROC of various centralized and decentralized detection methods on CIFAR-10/100" + }, + { + "bbox": [ + 306, + 293, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\ddagger" + }, + { + "bbox": [ + 306, + 293, + 545, + 365 + ], + "type": "text", + "content": ", and ImageNet-30 for OCC. " + }, + { + "bbox": [ + 306, + 293, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 306, + 293, + 545, + 365 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 293, + 545, + 365 + ], + "type": "inline_equation", + "content": "*" + }, + { + "bbox": [ + 306, + 293, + 545, + 365 + ], + "type": "text", + "content": " denote the usage of a pre-trained model learned on ImageNet-1M and the values from our reimplementation respectively, whereas **bold** and **underline** indicate the best results and the second results, respectively." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 377, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 545, + 639 + ], + "type": "text", + "content": "effective communication cost on FL methods. We found that our proposed method exploits the off-the-shelf model and dataset to compensate the shortage of the local data. For updating a global model every rounds, naive FL methods [45, 17, 34] minimize the distance among the latent variables of the local data and map the distribution of the local data into one secure code designated. Those methods demand the inordinate communication cost and show the limited performance due to the deficiency of the local data on each device and the entangled secure code on latent space. Furthermore, we compare our approach with various centralized methods as depicted in Table 2. Our method outperforms ResNet-18 based methods on CIFAR-10 and ImageNet-30. In case of CIFAR- " + }, + { + "bbox": [ + 304, + 377, + 545, + 639 + ], + "type": "inline_equation", + "content": "100^{\\ddagger}" + }, + { + "bbox": [ + 304, + 377, + 545, + 639 + ], + "type": "text", + "content": ", our approach places the second-rank performance comparing with FLOW [40] leveraging the feature extraction of a pre-trained model learned on ImageNet-1M. Note that our proposed method is the first rank among ResNet-18 based methods having no additional training datasets and limited computing resources. Among FL methods, our proposed method accomplishes the consistently improved performance on the image benchmarks." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": "For the tabular benchmark, we make the comparisons to the centralized methods on the Keystroke-Dynamics dataset for one-class classification as shown in Fig. 4. As the results, we found that our proposed method reduces EER more than two times comparing to prior methods. Training a foundation model as the global model is essential for the" + } + ] + } + ], + "index": 39 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6475" + } + ] + } + ], + "index": 40 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 71, + 547, + 208 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 547, + 208 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 547, + 208 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 547, + 208 + ], + "type": "table", + "html": "
TypeMethodNetworkPlaneCarBirdCatDeerDogForgHorseShipTruckMean (std)
Centralized LearningOC-SVM [41]-65.640.965.350.175.251.271.851.267.948.558.8 (±11.6)
DeepSVDD [37]LeNet61.765.950.859.160.965.767.767.375.973.164.8 (±7.17)
Geom [10]WRN-16-874.795.778.172.487.887.883.495.593.391.386.0 (±8.52)
Rot [16]WRN-16-477.596.987.380.992.790.290.996.595.293.390.1 (±6.52)
GOAD [3]WRN-16-477.296.783.377.787.887.890.096.193.892.088.2 (±6.99)
Rot [16]ResNet-1880.496.485.981.191.389.689.995.995.092.689.8 (±5.75)
GOAD [3]ResNet-1875.594.181.872.083.784.482.993.992.989.585.1 (±7.61)
DROC [42]ResNet-1890.998.988.083.189.990.393.598.296.595.292.5 (±4.95)
CSI [43]ResNet-1889.999.193.186.493.993.295.198.797.995.594.3 (±3.97)
FLOW† [40]ResNet-5096.197.592.689.893.395.798.094.797.896.695.2 (±2.64)
Federated LearningOursResNet-1896.497.992.790.995.892.796.496.497.696.795.3 (±2.38)
", + "image_path": "9abafa46d63521f9669385536c2da15fc017c3f58deb949a6f514edd87ee31ed.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 208, + 546, + 244 + ], + "lines": [ + { + "bbox": [ + 46, + 208, + 546, + 244 + ], + "spans": [ + { + "bbox": [ + 46, + 208, + 546, + 244 + ], + "type": "text", + "content": "Table 3: AUROC of various centralized and decentralized detection methods on CIFAR-10 for one-class classification. We present the AUROC of each class and the mean and standard deviation (std) of AUROC for all classes. " + }, + { + "bbox": [ + 46, + 208, + 546, + 244 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 46, + 208, + 546, + 244 + ], + "type": "text", + "content": ", bold, and underline denote the usage of a pre-trained model learned on ImageNet-1M, the best results, and the second results, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 85, + 255, + 248, + 373 + ], + "blocks": [ + { + "bbox": [ + 85, + 255, + 248, + 373 + ], + "lines": [ + { + "bbox": [ + 85, + 255, + 248, + 373 + ], + "spans": [ + { + "bbox": [ + 85, + 255, + 248, + 373 + ], + "type": "image", + "image_path": "a1b08468be02d2345e68373c278510ad7b754f63d8c3e6a8d0249698c239072f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 376, + 288, + 448 + ], + "lines": [ + { + "bbox": [ + 46, + 376, + 288, + 448 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 288, + 448 + ], + "type": "text", + "content": "Figure 4: Comparison to previous methods of one-class classification on the Keystroke-Dynamics dataset. OC, Manhattan, AE, and MLP denote Outlier Count, Euclidean detector with Manhattan distance, Auto-Encoder, and 4-multi layer perception, respectively, from [19]. " + }, + { + "bbox": [ + 46, + 376, + 288, + 448 + ], + "type": "inline_equation", + "content": "\\mathbb{I}" + }, + { + "bbox": [ + 46, + 376, + 288, + 448 + ], + "type": "text", + "content": " denotes a standard deviation." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 464, + 287, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 489 + ], + "type": "text", + "content": "OCC task instead of the various architectures and distance metrics to achieve notably improved performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 493, + 288, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 493, + 288, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 493, + 288, + 685 + ], + "type": "text", + "content": "Centralized vs Federated learning As shown in Table 3, we compare our proposed method with the centralized learning based methods because there is no previous FL method studying sufficiently analysis results for CIFAR-10. Our proposed approach outperforms the previous methods in terms of the overall mean and standard deviation because we collaboratively train our global model to represent all classes by the distributively-learned local models, and then we apply our non-biased global model to transform raw data into latent spaces for learning a local one-class classifier in each client as shown in Fig. 5. In case of each class, this method shows the first and second-placed performance in 8 out of 10, whereas FLOW [40] and CSI [43] show the first and second-placed performance in 4 and 5 out of 10, which indicates that our collaboratively learned global model avoids over-fitting problem for each client." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "Scalability of representation In this setup on CIFAR" + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{100}^{\\ddagger}" + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": ", let " + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": " indicate the number of new joined clients for" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 344, + 255, + 506, + 373 + ], + "blocks": [ + { + "bbox": [ + 344, + 255, + 506, + 373 + ], + "lines": [ + { + "bbox": [ + 344, + 255, + 506, + 373 + ], + "spans": [ + { + "bbox": [ + 344, + 255, + 506, + 373 + ], + "type": "image", + "image_path": "b62a5af6cda63507628c96eb7696c00718c5f9304f1c36edb4bc59edd15b3877.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 376, + 546, + 449 + ], + "lines": [ + { + "bbox": [ + 304, + 376, + 546, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 546, + 449 + ], + "type": "text", + "content": "Figure 5: Analysis the scalability of our global model learned by ProtoFL through new clients on CIFAR-100‡ dataset. Our approach modestly overcomes the other methods [6, 17, 23] in FL with extreme non-i.i.d. " + }, + { + "bbox": [ + 304, + 376, + 546, + 449 + ], + "type": "inline_equation", + "content": "(\\alpha = 0.0)" + }, + { + "bbox": [ + 304, + 376, + 546, + 449 + ], + "type": "text", + "content": " data. " + }, + { + "bbox": [ + 304, + 376, + 546, + 449 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 376, + 546, + 449 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 376, + 546, + 449 + ], + "type": "inline_equation", + "content": "\\mathbb{I}" + }, + { + "bbox": [ + 304, + 376, + 546, + 449 + ], + "type": "text", + "content": " denote the number of new joined clients and a standard deviation each." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 467, + 547, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 467, + 547, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 467, + 547, + 647 + ], + "type": "text", + "content": "one-class classification, and " + }, + { + "bbox": [ + 304, + 467, + 547, + 647 + ], + "type": "inline_equation", + "content": "20 - \\gamma" + }, + { + "bbox": [ + 304, + 467, + 547, + 647 + ], + "type": "text", + "content": " represent the number of clients who participating in FL. To optimize the local classifier parameters of the new client, the new client downloads the global model as described in Algorithm 2. Note that we are the first to consider the effects of joining new clients. As presented in Fig. 5, we demonstrate the effectiveness for scalability of the learned representation as our global model through experiments and comparisons. Although new clients have increased, all federated learning methods suffer from degraded performances. However, our proposed method shows more scalability with respect to a new joiner than the others [17, 6, 23]. In addition, FedRep [6] and LG-FedAvg [23] are meaningless to support new clients. Thus, our method presents an novel property validating new joiners performance in FL." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 658, + 407, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 407, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 407, + 670 + ], + "type": "text", + "content": "5.4. Ablation Studies" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "We conducted ablation studies on CIFAR-10/100" + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\ddagger" + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": " and ImageNet-30 (i) to verify the phase 1 and the phase 2, (ii) to explore the contribution of each component in our method," + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "6476" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 286, + 114 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 286, + 114 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 286, + 114 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 286, + 114 + ], + "type": "table", + "html": "
Phase 1Phase 2CIFAR-10CIFAR-100‡ImageNet-30Mean
Ours \n(ProtoFL)KDE94.588.994.092.3
GDE94.388.692.891.9
OC-SVM97.186.990.891.6
Ours (OC-NF)95.389.995.493.5
", + "image_path": "ef9634e66362ee6b1aad472204c4a83621a9904d7df19bf3e13693361b633c75.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 162, + 286, + 217 + ], + "blocks": [ + { + "bbox": [ + 47, + 114, + 286, + 150 + ], + "lines": [ + { + "bbox": [ + 47, + 114, + 286, + 150 + ], + "spans": [ + { + "bbox": [ + 47, + 114, + 286, + 150 + ], + "type": "text", + "content": "Table 4: Ablation study of various classifiers on CIFAR-10, CIFAR- " + }, + { + "bbox": [ + 47, + 114, + 286, + 150 + ], + "type": "inline_equation", + "content": "100^{\\ddagger}" + }, + { + "bbox": [ + 47, + 114, + 286, + 150 + ], + "type": "text", + "content": ", and ImageNet-30 with our representative global model. The performance is evaluated by AUROC." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 162, + 286, + 217 + ], + "lines": [ + { + "bbox": [ + 48, + 162, + 286, + 217 + ], + "spans": [ + { + "bbox": [ + 48, + 162, + 286, + 217 + ], + "type": "table", + "html": "
MethodPhase 1Phase 2CIFAR-10‡ImageNet-30
LθpdLθpLψmleLψregAUROCAUROC
Ours w/o Lθpd, Lψreg✓✓48.950.2
Ours w/o Lθp, Lψreg✓✓87.091.1
Ours w/o Lψreg✓✓✓89.694.4
Ours✓✓✓✓89.995.4
", + "image_path": "85a01f90ca4e2701336e395ec7d811a686c5b2b525739d67cac11acdf4e0fcce.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 218, + 286, + 242 + ], + "lines": [ + { + "bbox": [ + 47, + 218, + 286, + 242 + ], + "spans": [ + { + "bbox": [ + 47, + 218, + 286, + 242 + ], + "type": "text", + "content": "Table 5: Ablation study on CIFAR-100† and ImageNet-30 to evaluate each component in the individual phase." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 253, + 286, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 253, + 286, + 277 + ], + "spans": [ + { + "bbox": [ + 47, + 253, + 286, + 277 + ], + "type": "text", + "content": "and (iii) to investigate the effectiveness of the off-the-shelf model in respect of the various off-the-shelf datasets." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 285, + 286, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 285, + 286, + 405 + ], + "spans": [ + { + "bbox": [ + 47, + 285, + 286, + 405 + ], + "type": "text", + "content": "Analyses of our global- and classifier- model With fixed our global model learned by joined clients in advance, we compared our proposed local one-class classifier via normalizing flows (OC-NF) with the prior one-class classifiers for the usability of the global model. As shown in Table 4, we observed the superiority of the global model and the local classifier either each or both comparing to the previous detectors [4, 41] non-parametric kernel density estimation, parametric gaussian density estimation, and one-class SVM (KDE, GDE, and OC-SVM)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 414, + 286, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 414, + 286, + 585 + ], + "spans": [ + { + "bbox": [ + 47, + 414, + 286, + 585 + ], + "type": "text", + "content": "Analyses of each component To analyze the effect of our proposed objective for each phase, we separated the representation objective of the phase 1 into distilling loss " + }, + { + "bbox": [ + 47, + 414, + 286, + 585 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{pd}^{\\theta}" + }, + { + "bbox": [ + 47, + 414, + 286, + 585 + ], + "type": "text", + "content": " and similarity loss " + }, + { + "bbox": [ + 47, + 414, + 286, + 585 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_p^\\theta" + }, + { + "bbox": [ + 47, + 414, + 286, + 585 + ], + "type": "text", + "content": ", and the classification objective of the phase 2 into maximum likelihood " + }, + { + "bbox": [ + 47, + 414, + 286, + 585 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{mle}^{\\psi}" + }, + { + "bbox": [ + 47, + 414, + 286, + 585 + ], + "type": "text", + "content": " and regularizer " + }, + { + "bbox": [ + 47, + 414, + 286, + 585 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{reg}^{\\psi}" + }, + { + "bbox": [ + 47, + 414, + 286, + 585 + ], + "type": "text", + "content": " to show the importance in Table 5. Thus, we confirmed that each of them is the essential terms for the improving performance, and also observed the best results when all of them were used on CIFAR- " + }, + { + "bbox": [ + 47, + 414, + 286, + 585 + ], + "type": "inline_equation", + "content": "100^{\\ddagger}" + }, + { + "bbox": [ + 47, + 414, + 286, + 585 + ], + "type": "text", + "content": " and ImageNet30. In case of ImageNet-30, the improved performance indicates the effectiveness of this regularizer. As shown in Fig. 6, we found that our representative global model, trained without this distilling loss " + }, + { + "bbox": [ + 47, + 414, + 286, + 585 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{pd}^{\\theta}" + }, + { + "bbox": [ + 47, + 414, + 286, + 585 + ], + "type": "text", + "content": ", leads the drastically impoverished representation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 594, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 594, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 594, + 286, + 713 + ], + "type": "text", + "content": "Analyses of distilling representation With the FL setting, we employ cosine similarity " + }, + { + "bbox": [ + 47, + 594, + 286, + 713 + ], + "type": "inline_equation", + "content": "S_{c}" + }, + { + "bbox": [ + 47, + 594, + 286, + 713 + ], + "type": "text", + "content": " as a criterion for selecting the off-the-shelf models as shown in left of Fig. 7, and evaluated the performance based on various " + }, + { + "bbox": [ + 47, + 594, + 286, + 713 + ], + "type": "inline_equation", + "content": "S_{c}" + }, + { + "bbox": [ + 47, + 594, + 286, + 713 + ], + "type": "text", + "content": " on all the benchmarks as shown in right of Fig. 7. Our proposed ProtoFL achieves the significantly improved performance comparing to FedUV since the ProtoFL is robust to the increased clients for one-class classification, and the results show that lower " + }, + { + "bbox": [ + 47, + 594, + 286, + 713 + ], + "type": "inline_equation", + "content": "S_{c}" + }, + { + "bbox": [ + 47, + 594, + 286, + 713 + ], + "type": "text", + "content": " indicate more discriminative features. Note, distributing the prototypical representation in secure" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 309, + 73, + 382, + 141 + ], + "blocks": [ + { + "bbox": [ + 309, + 73, + 382, + 141 + ], + "lines": [ + { + "bbox": [ + 309, + 73, + 382, + 141 + ], + "spans": [ + { + "bbox": [ + 309, + 73, + 382, + 141 + ], + "type": "image", + "image_path": "32ba4430cb19059812eb61a9196cd790fc35a21ecdabd7d340a2495f95d0ce50.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 310, + 142, + 382, + 155 + ], + "lines": [ + { + "bbox": [ + 310, + 142, + 382, + 155 + ], + "spans": [ + { + "bbox": [ + 310, + 142, + 382, + 155 + ], + "type": "text", + "content": "(a) Ours w/o " + }, + { + "bbox": [ + 310, + 142, + 382, + 155 + ], + "type": "inline_equation", + "content": "L_{pd}^{\\theta}, L_{reg}^{\\psi}" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 386, + 73, + 457, + 141 + ], + "blocks": [ + { + "bbox": [ + 386, + 73, + 457, + 141 + ], + "lines": [ + { + "bbox": [ + 386, + 73, + 457, + 141 + ], + "spans": [ + { + "bbox": [ + 386, + 73, + 457, + 141 + ], + "type": "image", + "image_path": "37155c805f098edcafee61fa1a6ff6869fc6cf7c0630a3181612bed1cdedba57.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 386, + 142, + 457, + 155 + ], + "lines": [ + { + "bbox": [ + 386, + 142, + 457, + 155 + ], + "spans": [ + { + "bbox": [ + 386, + 142, + 457, + 155 + ], + "type": "text", + "content": "(b) Ours w/o " + }, + { + "bbox": [ + 386, + 142, + 457, + 155 + ], + "type": "inline_equation", + "content": "L_{p}^{\\theta}, L_{reg}^{\\theta}" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 461, + 74, + 544, + 141 + ], + "blocks": [ + { + "bbox": [ + 461, + 74, + 544, + 141 + ], + "lines": [ + { + "bbox": [ + 461, + 74, + 544, + 141 + ], + "spans": [ + { + "bbox": [ + 461, + 74, + 544, + 141 + ], + "type": "image", + "image_path": "a7a1f43994dddc32a01c1a68ae7af412364a98c539dc09141370edcb3fa48f8a.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 482, + 144, + 509, + 153 + ], + "lines": [ + { + "bbox": [ + 482, + 144, + 509, + 153 + ], + "spans": [ + { + "bbox": [ + 482, + 144, + 509, + 153 + ], + "type": "text", + "content": "(c) Ours" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 159, + 545, + 195 + ], + "lines": [ + { + "bbox": [ + 306, + 159, + 545, + 195 + ], + "spans": [ + { + "bbox": [ + 306, + 159, + 545, + 195 + ], + "type": "text", + "content": "Figure 6: Visualization of latent-features using t-sne for our global model learned (Phase 1) with either each component or all. Score in each figure denote the silhouette values [36]." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 206, + 544, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 206, + 544, + 229 + ], + "spans": [ + { + "bbox": [ + 306, + 206, + 544, + 229 + ], + "type": "text", + "content": "is important to overcome the shortage of training data, limited round communications, and greater number of clients." + } + ] + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 302, + 231, + 403, + 346 + ], + "blocks": [ + { + "bbox": [ + 302, + 231, + 403, + 346 + ], + "lines": [ + { + "bbox": [ + 302, + 231, + 403, + 346 + ], + "spans": [ + { + "bbox": [ + 302, + 231, + 403, + 346 + ], + "type": "image", + "image_path": "8a1abffb0191da7e8383ea7cf16f9644b422ef11b1c0d91f2169d2dd80f104a5.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 353, + 545, + 412 + ], + "lines": [ + { + "bbox": [ + 306, + 353, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 306, + 353, + 545, + 412 + ], + "type": "text", + "content": "Figure 7: Left : Each score denotes cosine similarity " + }, + { + "bbox": [ + 306, + 353, + 545, + 412 + ], + "type": "inline_equation", + "content": "S_{c}" + }, + { + "bbox": [ + 306, + 353, + 545, + 412 + ], + "type": "text", + "content": " between the various off-the-shelf datasets and models. Right : Performance comparison among the various global models whose off-the-shelf model is different. C and I denote CIFAR and ImageNet benchmarks." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 415, + 231, + 541, + 346 + ], + "blocks": [ + { + "bbox": [ + 415, + 231, + 541, + 346 + ], + "lines": [ + { + "bbox": [ + 415, + 231, + 541, + 346 + ], + "spans": [ + { + "bbox": [ + 415, + 231, + 541, + 346 + ], + "type": "image", + "image_path": "acf3171f50444f8b4c79bc24f5cdff37d6eecac912fe68817cef9f9d9d82a54f.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 422, + 378, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 422, + 378, + 434 + ], + "spans": [ + { + "bbox": [ + 306, + 422, + 378, + 434 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 443, + 545, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 443, + 545, + 597 + ], + "spans": [ + { + "bbox": [ + 304, + 443, + 545, + 597 + ], + "type": "text", + "content": "We proposed ProtoFL, a method for achieving effective round cost and scalability representation in extreme non-i.i.d. data based FL. By utilizing an off-the-shelf model and dataset to distribute prototypical independent representations, we were able to learn a global model with all joined clients and optimize the flow-based classifier of each client. Our proposed method outperforms FL methods with efficient communication cost and presents a novel property of scalability of representation, validating new joiners' performance in FL. We believe that our method and experimental details could be adapted to handle further problems in both federated and centralized learning based one-class classification." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 605, + 408, + 618 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 605, + 408, + 618 + ], + "spans": [ + { + "bbox": [ + 306, + 605, + 408, + 618 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": "This work was supported by KakaoBank Corp., and Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. 2022-0-00320, Artificial intelligence research about cross-modal dialogue modeling for one-on-one multi-modal interactions). In particular, we would like to thank the designer Eunha Lim (milkyway-mind@naver.com) for well-presented Figures 1, 2, and 3." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6477" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "text", + "content": "[1] Unsupervised video anomaly detection via normalizing flows with implicit latent features. 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Recent advances in point cloud segmentation distill knowledge from strictly aligned point-pixel fusion features while leaving a large number of unmatched image pixels unexplored and unmatched LiDAR points under-benefited. In this paper, we propose a novel approach, named ProtoTransfer, which not only fully exploits image representations but also transfers the learned multi-modal knowledge to all point cloud features. Specifically, based on the basic multi-modal learning framework, we build up a class-wise prototype bank from the strictly-aligned fusion features and encourage all the point cloud features to learn from the prototypes during model training. Moreover, to exploit the massive unmatched point and pixel features, we use a pseudo-labeling scheme and further accumulate these features into the class-wise prototype bank with a carefully designed fusion strategy. Without bells and whistles, our approach demonstrates superior performance over the published state-of-the-arts on two large-scale benchmarks, i.e., nuScenes and SemanticKITTI, and ranks 2nd on the competitive nuScenes Lidarseg challenge leaderboard.", + "bbox": [ + 75, + 319, + 473, + 698 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 727, + 209, + 742 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semantic segmentation on point cloud [6, 15, 37, 40] has attracted increasing attention from the computer vision community for its crucial role in scene understanding of 3D space. Although LiDAR point cloud can provide accurate location and depth information of interested scenes, the sparse and textureless shortages inevitably restrict its semantic segmentation performance. On the other hand, 2D images consist of dense pixels with rich color and subtle", + "bbox": [ + 75, + 753, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1d5e040b3edb48bc236cb7e5381956b02698f9e285487356db8d16db4a0c7738.jpg", + "image_caption": [ + "(a) Point-pixel matching and feature fusion" + ], + "image_footnote": [], + "bbox": [ + 522, + 285, + 883, + 382 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8e7ea3925b02ca12dcd239659ff378a67ab193eb802ea310579795199fde9e26.jpg", + "image_caption": [ + "(b) Distillation-based methods" + ], + "image_footnote": [], + "bbox": [ + 511, + 397, + 694, + 539 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1a56e680051605d8b9940b1f2831c21b5867b3da7832961dd3b7ae9f680f7a76.jpg", + "image_caption": [ + "(c) Our ProtoTransfer", + "Figure 1. (a) Point-pixel matching and feature fusion: only features of strictly matched point-pixel pairs can be fused. (b) Distillation-based methods are only performed between fusion prediction and the corresponding matched point prediction while other unmatched points have no chance to mimic the fusion prediction. (c) Our ProtoTransfer performs knowledge transfer from prototype bank to all point features directly without being restricted by matching requirements. The prototype bank is updated using fusion, point, and unmatched image features." + ], + "image_footnote": [], + "bbox": [ + 707, + 397, + 888, + 537 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "textures [34]. Therefore, incorporating these two complementary modals altogether can be a more plausible solution.", + "bbox": [ + 496, + 700, + 890, + 732 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, there are mainly two stream approaches of utilizing multi-modal data, i.e., fusion-based methods [10, 50] and distillation-based methods [42]. The former methods project point clouds to the camera coordinate to obtain a point-to-pixel mapping, based on which point features are fused with corresponding image features to produce the final point-wise segmentation during both the training and evaluation phases. Although robust and accurate segments are achieved by fusing different sensors, the fusion-based methods may suffer from heavy memory and time consumption for processing these two modal data simul", + "bbox": [ + 496, + 734, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Corresponding author.", + "bbox": [ + 94, + 887, + 225, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3337", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "taneously. In order to benefit from multi-modal fusion while bypassing the computation burden, the latter methods [42] propose to utilize the distillation technique to transfer knowledge learned from cross-modal fusion at the training stage and discard the fusion module for evaluation. The impressive segmentation performance suggests the feasibility of the methods in this stream. Therefore, this paper further explores this research direction.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unlike common distillation approaches in image classification tasks [14, 44], distilling from multi-modal to the single LiDAR modal may meet quite different pitfalls: (1) Not all LiDAR points can be used in knowledge distillation because LiDAR-to-image is partially matched. Due to the difference in the way sensors collect data, not all the LiDAR points can be aligned to the dense image pixels. For example, we empirically find that only around $16.07\\%$ LiDAR points in SemanticKITTI dataset can be matched to corresponding image pixels, and Fig. 1(a) also demonstrates this observation. Thus, classic logit-/probability-style distillation strategies [42] can only be performed on the well-aligned point clouds, leading to a sub-optimal knowledge distillation. (2) Massive image pixels are overlooked. Since only partial image pixels1 will contribute to the modal fusion based on the above matching constraints, a large number of pixels are not used in knowledge distillation, resulting in a great loss of rich semantic information in dense pixels.", + "bbox": [ + 75, + 212, + 472, + 484 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "In this paper, we propose a novel approach for point cloud semantic segmentation which successfully avoids the above pitfalls. Specifically, following the existing work [17, 34, 42], we first construct a modal fusion module to combine the feature representations of matched LiDAR points and image pixels. Next, in order to transfer the knowledge from the fusion module to each point feature representation, we create a class-wise prototype bank to accumulate the fusion features learned in the fusion module and encourage the similarity between features of all LiDAR points and corresponding-class prototypes as high as possible. By this means, every LiDAR point has a fair chance to mimic the fusion features as shown in Fig. 1(c), and we dub our method as ProtoTransfer. Moreover, to make full use of semantic information inherited in dense image pixels, we propose to incorporate the image features into the class-wise prototype bank through a cleverly designed fusion strategy. Since images in the point cloud semantic segmentation datasets usually lack per-pixel annotations, we further use a pseudo-labeling scheme to generate pseudolabels for each pixel and thus make the update of pixelfeature into class-wise prototypes become possible. In summary, the main contributions of this paper are three aspects:", + "- We investigate the pitfalls of point cloud semantic segmentation on distillation-based methods and find that a" + ], + "bbox": [ + 75, + 484, + 472, + 863 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "large number of image features are not well-utilized and point features are not well distillation-benefited.", + "bbox": [ + 500, + 90, + 890, + 119 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce the prototype bank concept into point cloud semantic segmentation and propose a novel approach ProtoTransfer to successfully overcome the above pitfalls.", + "- We conduct experiments on both SemanticKITTI and nuScenes benchmarks to demonstrate the effectiveness of our approach and also achieve a 2nd place on the competitive nuScenes Lidarseg leaderboard." + ], + "bbox": [ + 498, + 122, + 893, + 228 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 244, + 640, + 260 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-Modal 3D Semantic Segmentation. Since different modal can provide complimentary information to each other, multi-modal point cloud semantic segmentation attracts increasing attention [8, 20, 24]. RGBAL [8] casts RGB images to a polar-grid mapping representation and designs an early-mid-level hybrid fusion architecture. Recently, PMF [50] projects LiDAR points to camera coordinates, which is called perspective projection [25]. Then, they use two 2D U-net [27] to extract the image and point features. The multi-scale image and point features in both U-nets are fused to produce better segmentation results. Though satisfactory performance are achieved, these methods need multi-modal inputs during both training and inference phases, which is time-/memory-consuming.", + "bbox": [ + 496, + 270, + 890, + 482 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Prototype Networks. Prototype-based learning methods has been widely used in machine learning [9, 11, 28]. Recently, a surge of attention is paid to employ prototype networks on various tasks, presenting great potential in few-shot learning [29] and zero-shot learning[18, 36]. Moreover, [48] shows a prototype view of image semantic segmentation network. Another prototype-based semisupervised method is also proposed [39]. Our work sheds light on the possibility of using prototypes for knowledge transfer from multi-modal to single-modal.", + "bbox": [ + 496, + 487, + 890, + 638 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Cross-Modal Knowledge Transfer. Knowledge distillation, first proposed by Hinton et al. [14], is a common knowledge transfer method, which pushes the student network mimic the soft logits of the teacher network. Very recently, knowledge distillation is introduced into perception tasks in autonomous driving, such as 3D object detection [7, 19, 46] and point cloud segmentation [42]. During training, they use distillation to transfer multi-modal knowledge learned by the multi-modal teacher to a single-modal student. However, these methods suffers from strict point-pixel alignment, leading to massive unmatched image pixels unexplored and points under-benefited. Our work performs knowledge transfer in another way. Contrary to [42], we construct a prototype bank from fusion and unmatched image features and encourage all the point cloud features to learn from the prototypes during model training, thus fully exploiting and transferring multi-modal knowledge.", + "bbox": [ + 496, + 643, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "${}^{1}$ Only $5\\%$ image pixels are matched to LiDAR points for a typical 32-beam LiDAR scanner as presented in BEVFusion [22].", + "bbox": [ + 76, + 875, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3338", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f7760b27618bfcd3afac9a6bbd5472f1b5c0cd1f1ba8a285d164a95734adbe83.jpg", + "image_caption": [ + "Figure 2. Pipeline overview of our ProtoTransfer. The model first uses modal-specific backbones to generate image features $F^{2\\mathrm{d}}$ and point features $F^{3\\mathrm{d}}$ and feeds them into the point-pixel matching module to generate matched point feature $F^{3\\mathrm{d},\\mathrm{m}}$ , matched and unmatched image features $F^{2\\mathrm{d},\\mathrm{m}}$ and $F^{2\\mathrm{d},\\mathrm{u}}$ , respectively. Then modal-specific segmentation heads are used to produce predictions for loss calculation, i.e., $\\mathcal{L}^{3\\mathrm{d}}, \\mathcal{L}^{2\\mathrm{d}}$ and $\\mathcal{L}^{\\mathrm{fuse}}$ , where $\\mathcal{L}^{\\mathrm{fuse}}$ will update the feature $F^{\\mathrm{fuse}}$ fused from $F^{2\\mathrm{d},\\mathrm{m}}$ and $F^{3\\mathrm{d},\\mathrm{m}}$ . To take advantage of the fusion features, we introduce a class-wise prototype bank whose input source includes features $F^{3\\mathrm{d}}$ , $F^{\\mathrm{fuse}}$ and $F^{2\\mathrm{d},\\mathrm{u}}$ and propose a loss $\\mathcal{L}^{\\mathrm{proto}}$ to transfer fusion knowledge to all point features. Please note 2D&Fusion GT is derived from the 3D GT based on point-pixel matching." + ], + "image_footnote": [], + "bbox": [ + 99, + 85, + 872, + 280 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 378, + 212, + 396 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Framework Overview", + "text_level": 1, + "bbox": [ + 76, + 402, + 282, + 419 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a LiDAR point cloud frame with $N$ unordered points $P = \\{p_i\\in \\mathbb{R}^{d_{\\mathrm{in}}}\\}_{i = 1}^N$ where $d_{\\mathrm{in}}$ is input feature dimension, the goal of point cloud semantic segmentation is to assign a single class label $c\\in \\{1,2\\dots ,C\\}$ to each point. To make up for the sparsity and lack of texture of point clouds collected in outdoor scenes [42], the other modal of the corresponding scenes, raw images $I\\in \\mathbb{R}^{W\\times H\\times 3}$ , where $W,H$ denote the resolution of a given image, are also provided for model learning to achieve a better segmentation performance.", + "bbox": [ + 75, + 426, + 470, + 577 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As the overall structure presented in Fig. 2, the main contributions of our approach are (1) introducing a class-wise prototype bank for knowledge transfer from a fusion modal to all LiDAR points and (2) proposing to make full use of image features to enhance the prototype quality. Specifically, paired point cloud and image are first fed into modal-specific backbones to extract feature representations respectively. Next, based on the given LiDAR-to-image transformation matrix, features are fused for matched LiDAR point and corresponding image pixels, as done in previous modal-fusion-related work [17, 34, 42]. Due to the differing data acquisition mechanisms of different modal sensors, the matching rate between LiDAR points and image pixels is often quite low. Instead of distilling knowledge solely for the limited matched LiDAR points, we propose a novel knowledge transfer module that can enable unmatched points to also benefit from fused feature representations. With this framework, we explore and exploit unmatched image pixels to further enhance the overall point", + "bbox": [ + 75, + 579, + 468, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "cloud segmentation performance.", + "bbox": [ + 500, + 380, + 723, + 395 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "During inference, the enhanced point cloud segmentation branch can produce accurate segmentation results without the image backbone and multi-modal fusion, and thus challenges can be tackled within a real-time speed.", + "bbox": [ + 496, + 396, + 890, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Cross-Modal Prototype Transfer", + "text_level": 1, + "bbox": [ + 500, + 463, + 785, + 479 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Considering the data structures of point cloud and image pixels are totally different, various network architectures are utilized to extract feature representations for the two modal inputs independently. Specifically, ResNet34 [13] encoder and FCN [23] decoder are used for 2D images to extract dense-grid features $F^{2\\mathrm{d}} \\in \\mathbb{R}^{W \\times H \\times D_{2\\mathrm{d}}}$ , and a sparse convolution [12] based hierarchical point-voxel backbone [42] are designed for 3D point cloud to generate point-wise features $F^{3\\mathrm{d}} \\in \\mathbb{R}^{N \\times D_{3\\mathrm{d}}}$ . Since LiDAR points and image pixels are not naturally aligned due to the differences in data collection of LiDAR and camera devices, LiDAR-camera transformation matrix is used to find the point-to-pixel correspondence3 and further obtain the matched pixel feature $F^{2\\mathrm{d\\_m}}$ and matched point features $F^{2\\mathrm{d\\_m}}$ . Following the previous work [42], we concatenate the matched point-pixel features and use a multi-layer perceptron (MLP) to obtain the fusion feature", + "bbox": [ + 496, + 486, + 892, + 742 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nF ^ {\\mathrm {f u s e}} = \\operatorname {M L P} \\left(\\operatorname {c a t} \\left(F ^ {2 \\mathrm {d}. \\mathrm {m}}, F ^ {3 \\mathrm {d}. \\mathrm {m}}\\right)\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 747, + 890, + 767 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\odot$ is Hadamard product of two matrices. The MLP is used to reduce feature dimension to $D_{3\\mathrm{d}}$ and obtain $F^{\\mathrm{fuse}}$ . With LiDAR per-point ground truth $Y^{3\\mathrm{d}}$ , the fusion branch is got supervised", + "bbox": [ + 496, + 771, + 890, + 830 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} ^ {\\text {f u s e}} = \\mathcal {L} _ {\\mathrm {C E}} \\left(h ^ {\\text {f u s e}} \\left(F ^ {\\text {f u s e}}\\right), \\hat {Y}\\right) + \\mathcal {L} _ {\\text {L o v a s z}} \\left(h ^ {\\text {f u s e}} \\left(F ^ {\\text {f u s e}}\\right), \\hat {Y}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 835, + 890, + 868 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "2Input feature normally contains Cartesian coordinates, intensity of returning laser beam, colors, etc.", + "bbox": [ + 76, + 875, + 468, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "3Detailed point-to-pixel mapping mechanism is provided in supplementary material.", + "bbox": [ + 500, + 875, + 890, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3339", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $h^{\\mathrm{fuse}}$ is the segmentation head of fusion branch. $\\hat{Y}$ is the subset of $Y^{3\\mathrm{d}}$ , representing the ground truth for matched points. $\\mathcal{L}_{\\mathrm{CE}}$ and $\\mathcal{L}_{\\mathrm{Lovasz}}$ denote the cross entropy loss and the IoU-style Lovasz loss [3] respectively.", + "bbox": [ + 75, + 89, + 468, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Attributed to the integration of rich semantic information from 2D images, the segmentation performance of the fusion branch is superior to the LiDAR-sole branch (the bottom branch in Fig. 2). In order to make a single LiDAR point cloud segmentation benefit from the fusion branch, one straightforward way is to introduce a knowledge distillation loss between these two branches, as done in [42]. However, due to the matched point-pixel being limited, only partial point features can benefit from the fusion features and leave massive unmatched points under-benefited.", + "bbox": [ + 75, + 152, + 467, + 303 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To bypass the strict matching restriction, we introduce a class-wise prototype bank to accumulate the fusion features during model optimization. Such a prototype bank can be served as a parameter-free segmentation head to regularize the distribution of all point features with LiDAR ground truth", + "bbox": [ + 75, + 303, + 467, + 393 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} ^ {\\text {p r o t o}} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathcal {L} _ {\\mathrm {C E}} \\left(p _ {c _ {i}}, c _ {i}\\right) + \\mathcal {L} _ {\\text {L o v a s z}} \\left(p _ {c _ {i}}, c _ {i}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 404, + 467, + 445 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $p_{c_i} \\coloneqq p(y = c_i | F_i^{3\\mathrm{d}}) = \\frac{\\exp(\\cos(\\mathsf{p}_{c_i}, F_i^{3\\mathrm{d}}) / T)}{\\sum_{j=1}^{C} \\exp(\\cos(\\mathsf{p}_j, F_i^{3\\mathrm{d}}) / T)}$", + "bbox": [ + 76, + 448, + 483, + 488 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $F_{i}^{3\\mathrm{d}}$ and $c_{i}$ denote the feature and semantic label of $i$ -th point respectively. $\\mathsf{p}_{c_i} \\in \\mathbb{R}^{D_{3\\mathrm{d}}}$ represents the prototype in class $c_{i}$ . $\\cos$ is the cosine function to calculate the similarity of the prototype and point feature. $T$ is the temperature parameter to adjust the scale of similarity measurement and is empirically set to 0.1 in our study.", + "bbox": [ + 75, + 500, + 467, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The proposed cross-modal prototype-based knowledge transfer module encourages the point features to be close to the same-class prototype while staying far away from other-class prototypes. Therefore, through the class-wise prototype bank as a bridge, we successfully transfer the knowledge learned from the fusion feature to the whole point cloud and we term our method as ProtoTransfer.", + "bbox": [ + 75, + 592, + 467, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Prototype Bank Initialization and Update", + "text_level": 1, + "bbox": [ + 76, + 709, + 431, + 726 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our work, the prototype bank is designed to be non-parametric and non-learnable and thus the quality of the prototype bank plays a critical role in the success of cross-modal knowledge transfer. Instead of using random vectors to initialize the prototype bank at the beginning of model training, we propose to use the fusion features of the first few iterations to warm up the class-wise prototype bank for a stable optimization procedure.", + "bbox": [ + 75, + 733, + 467, + 853 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Meanwhile, since the initial prototype bank can not capture the distribution of fusion features, we also dynamically update the prototype bank throughout the training stage.", + "bbox": [ + 75, + 854, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/022dc0f98c60065388fe9216e2fa563993a6529663510b900aedb37c5bf751d7.jpg", + "image_caption": [ + "Figure 3. Prototype bank update demonstration. The fusion feature $F^{\\mathrm{fuse}}$ , unmatched image feature $F^{2\\mathrm{d.u}}$ and point feature $F^{3\\mathrm{d}}$ are respectively clustered into class-wise feature sets using corresponding GT or pseudo-label obtained with Eq. (6). Then the feature sets are class-wise averaged to produce class-mean embeddings. $\\bar{F}^{2\\mathrm{d.u}}$ and $\\bar{F}^{3\\mathrm{d}}$ are fused to get $\\bar{F}^{\\mathrm{fuse\\_u}}$ . Finally, both $\\bar{F}^{\\mathrm{fuse}}$ and $\\bar{F}^{\\mathrm{fuse\\_u}}$ are accumulated into the class-wise prototype bank." + ], + "image_footnote": [], + "bbox": [ + 509, + 87, + 880, + 294 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given all fusion features $\\{F_i^{\\mathrm{fuse}}\\}$ , we can use their corresponding class labels $\\{c_i\\}$ to cluster the fusion features into class-wise feature set. As shown in the top branch of Fig. 3, the fusion feature set of class $k$ can be obtained by", + "bbox": [ + 498, + 402, + 890, + 464 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Omega_ {k} ^ {\\text {f u s e}} = \\left\\{F _ {i} ^ {\\text {f u s e}} \\mid c _ {i} = k \\right\\}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 470, + 890, + 491 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We then use the moving average trick to update the class-specific prototype $\\mathfrak{p}_k$ of class $k$", + "bbox": [ + 498, + 498, + 888, + 529 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {p} _ {k} \\leftarrow \\alpha \\cdot \\mathbf {p} _ {k} + (1 - \\alpha) \\cdot \\bar {F} _ {k} ^ {\\text {f u s e}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 537, + 890, + 555 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\bar{F}_k^{\\mathrm{fuse}} = \\frac{1}{\\|\\Omega_k^{\\mathrm{fuse}}\\|}\\sum_j\\Omega_{k,j}^{\\mathrm{fuse}}$", + "bbox": [ + 571, + 556, + 818, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha$ is a fixed hyper-parameter to control the prototype update speed and is empirically set as 0.999 in our study. $\\bar{F}_k^{\\mathrm{fuse}}$ is the class-mean embedding of fusion features in class $k$ .", + "bbox": [ + 498, + 597, + 890, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Unmatched Image Features Exploration and Exploitation", + "text_level": 1, + "bbox": [ + 498, + 665, + 888, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although prototype-based knowledge transfer has helped all point features benefit from the fusion features and enhanced the point segmentation performance, the fusion features, which are the knowledge source of the prototype bank, are only available on matched point-pixel pairs. Since the point-pixel matching rate is quite low, the rich semantic information lying in a large amount of unmatched image pixels is not explored and exploited.", + "bbox": [ + 496, + 704, + 890, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, the exploitation of unmatched image pixels is non-trivial and there are at least two challenges: 1) Naturally lacking matching points for modal fusion. Since modal fusion requires well-matched point-pixel features, it is difficult to construct matching points for unmatched pixels.", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3340", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2) Hardly obtaining semantic labels of unmatched pixels. Since 2D images are provided without annotations and it can be costly to additionally annotate these dense pixels, the semantic labels of unlabeled pixels are thus unknown without the matching correspondence from the LiDAR point cloud ground truth.", + "bbox": [ + 75, + 90, + 467, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on our proposed cross-modal prototype transfer framework, we further design a novel strategy to incorporate the unmatched pixel features into the prototype bank to improve the transferred knowledge, and Fig. 3 presents an overview. Specifically, in order to solve the challenge 2), we formulate the image pixel class label generation problem as a weakly-/semi-supervised task [5, 30], i.e., taking the LiDAR-to-image matched pixels as labeled samples and taking other unmatched pixels as unlabeled ones. Considering the segmentation head $h^{2d}$ for image input has been optimized on features of matched pixels4, we can generate posterior probability estimation for unmatched pixels", + "bbox": [ + 75, + 181, + 467, + 363 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np (y | F ^ {2 d. u}) = \\operatorname {s o f t m a x} \\left(h ^ {2 d} \\left(F ^ {2 d. u}\\right)\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 378, + 395, + 397 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $F^{2\\mathrm{d.u}}$ is the features of unmatched pixels. Then the pseudo-labels can be obtained for these unmatched pixels when their maximal posterior probability is greater than a pre-defined confidence threshold $\\delta$ (set as 0.8 in our study)", + "bbox": [ + 75, + 402, + 467, + 465 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ny ^ {2 \\mathrm {d} - \\mathrm {u}} = \\operatorname {a r g m a x} _ {c} p (y = c | F ^ {2 \\mathrm {d} - \\mathrm {u}}), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 491, + 467, + 508 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {o n l y i f} \\quad p (y = y ^ {2 d. u} | F ^ {2 d. u}) \\geq \\delta .\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 512, + 383, + 529 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given the pseudo-labeled unmatched pixels, it is still non-trivial to fuse the features of unmatched pixels and points due to the challenge 1) mentioned above. One straightforward way is to directly add the features of unmatched pixels to the prototype bank, empirical results in Tab. 4 show that this simple way can not bring a performance gain and we postulate that it may be caused by the distribution gap between image features and prototypes. Alternatively, we propose to first calculate a class-mean embedding $\\bar{F}_k^{2\\mathrm{d\\_u}}$ of unmatched pixel features in the same pseudo-label $k$", + "bbox": [ + 75, + 542, + 467, + 709 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {F} _ {k} ^ {\\mathrm {2 d \\_ u}} = \\frac {1}{\\| \\Omega_ {k} ^ {\\mathrm {2 d \\_ u}} \\|} \\sum_ {j} \\Omega_ {k, j} ^ {\\mathrm {2 d \\_ u}},\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 720, + 344, + 753 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {w h e r e} \\quad \\Omega_ {k} ^ {2 d. u} = \\left\\{F _ {i} ^ {2 d. u} \\mid y _ {i} ^ {2 d. u} = k \\right\\},\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 756, + 401, + 773 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\Omega_{k}^{2\\mathrm{d.u}}$ is class-wise unmatched image feature set and is obtained using pseudo labels but not ground-truth as in Eq. (4). And the class-mean embedding $\\bar{F}^{3\\mathrm{d}}$ of point features can be obtained from $F^{3\\mathrm{d}}$ with LiDAR ground truth. Then, modal fusion can be performed between class-mean embeddings", + "bbox": [ + 75, + 787, + 467, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "of the same class", + "bbox": [ + 500, + 90, + 614, + 104 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {F} ^ {\\text {f u s e - u}} = \\operatorname {M L P} \\left(\\operatorname {c a t} \\left(\\bar {F} ^ {2 \\mathrm {d} - \\mathrm {u}}, \\bar {F} ^ {3 \\mathrm {d}}\\right)\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 114, + 890, + 133 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the MLP shares parameter with the one in Eq. (1). Finally, the class-wise prototype bank updating in Eq. (5) can be extended as", + "bbox": [ + 498, + 145, + 890, + 189 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathfrak {p} _ {k} \\leftarrow \\alpha \\cdot \\mathfrak {p} _ {k} + (1 - \\alpha) \\cdot (\\lambda \\cdot \\bar {F} _ {k} ^ {\\text {f u s e}} + (1 - \\lambda) \\cdot \\bar {F} _ {k} ^ {\\text {f u s e - u}}), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 200, + 890, + 218 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda$ is the balance weight of these two fusion features.", + "bbox": [ + 498, + 229, + 885, + 243 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since the pseudo-labeling scheme for unmatched pixels may not be activated at the beginning of model training, the prototype bank is still initialized with the method mentioned in Sec. 3.3.", + "bbox": [ + 496, + 244, + 890, + 303 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Overall Objective Function", + "text_level": 1, + "bbox": [ + 498, + 314, + 745, + 330 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Apart from the loss terms in Eq. (2) and Eq. (3), we also have separate losses $\\mathcal{L}^{3\\mathrm{d}}$ and $\\mathcal{L}^{2\\mathrm{d}}$ for LiDAR point cloud input and image input respectively. Both of these two losses are composed of a cross-entropy loss and a Lovasz loss as those in Eq. (2). Finally, the overall object function is the weighted sum of these loss terms", + "bbox": [ + 496, + 337, + 890, + 426 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\omega^ {\\mathrm {3 d}} \\mathcal {L} ^ {\\mathrm {3 d}} + \\omega^ {\\mathrm {2 d}} \\mathcal {L} ^ {\\mathrm {2 d}} + \\omega^ {\\text {f u s e}} \\mathcal {L} ^ {\\text {f u s e}} + \\omega^ {\\text {p r o t o}} \\mathcal {L} ^ {\\text {p r o t o}},\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 436, + 872, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we empirically set $\\omega^{3\\mathrm{d}} = 2.0$ and $\\omega^{2\\mathrm{d}} = \\omega^{\\mathrm{fuse}} = \\omega^{\\mathrm{proto}} = 1.0$ in our study.", + "bbox": [ + 498, + 465, + 890, + 496 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 510, + 630, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we first provide details of our experimental setup. Then we evaluate ProtoTransfer on both nuScenes dataset and SemanticKITTI dataset. Finally, extensive ablation studies of our approach are presented.", + "bbox": [ + 496, + 536, + 890, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 604, + 689, + 622 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. NuScenes [4] collects 1000 driving scenes from various locations in Boston and Singapore using 1 LiDAR and 6 cameras covering $360^{\\circ}$ FoV. According to the official setting, it is split into training, validation and test set as 700, 150 and 150 scenes. For point cloud semantic segmentation task, it annotates labels for 16 classes under different traffic and weather conditions. SemanticKITTI [2] contains 22 LiDAR sequences numbered from 00 to 21, in which sequence 08 is officially selected as validation set, sequence 00-10 except 08 is training set and 11-21 is test set. Unlike nuScenes, SemanticKITTI has only two front-view cameras.", + "bbox": [ + 496, + 628, + 890, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metric. Following previous work [49, 42], we calculate intersection-over-union (IoU) of each class and mean IoU (mIoU) of all classes, which is formulated as $\\mathrm{mIoU} = \\frac{1}{C}\\sum_{c = 1}^{C}\\frac{\\mathrm{TP}_c}{\\mathrm{TP}_c + \\mathrm{FP}_c + \\mathrm{FN}_c}$ , where $\\mathrm{TP}_c$ , $\\mathrm{FP}_c$ and $\\mathrm{TP}_c$ denotes the number of true positive, false positive and false negative points of class $c$ .", + "bbox": [ + 496, + 810, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "4Please note that the segmentation head for 2D images already exists in our training framework.", + "bbox": [ + 75, + 875, + 467, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3341", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/79d852b50b13ab73c064719eefd8420e42d7572fd0b9fc5e8a0bb5c2d91a714b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsinputmIoUbarrierbicyclebuscarconstructionmotorcyclepedestriantraffic conetrailertruckdrivableother flatsidewalkterrainmannadevegetationLatency (ms)
PolarNet [45]L69.472.216.877.086.551.169.764.854.169.763.596.667.177.772.187.184.5-
JS3C-Net [41]L73.680.126.287.884.555.272.671.366.376.871.296.864.576.974.187.586.1-
Cylinder3D [47]L77.282.829.884.389.463.079.377.273.484.669.197.770.280.375.590.487.663
AMVNet [21]L77.380.632.081.788.967.184.376.173.584.967.397.567.479.475.591.588.785
SPVCNN [31]L77.480.030.091.990.864.779.075.670.981.074.697.469.280.076.189.387.163
(AF)2-S3Net [6]L78.378.952.289.984.277.474.377.372.083.973.897.166.577.574.087.786.8270
PMF [50]L+C77.082.040.081.088.064.079.080.076.081.067.097.068.078.074.090.088.0125*
2D3DNet [10]L+C80.083.059.488.085.163.784.482.076.084.871.996.967.479.876.092.189.2-
2DPASS [42]L80.881.755.392.091.873.386.578.572.584.775.597.669.179.975.590.288.044
ProtoTransfer [Ours]L82.181.155.593.991.577.987.382.778.985.176.597.669.879.675.991.589.144
", + "bbox": [ + 81, + 88, + 890, + 253 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ed41365256d76f7c1b4a1c7aa0bd42c8e1b66e6019061cf424f7878ca1eebd68.jpg", + "table_caption": [ + "Table 1. Semantic segmentation results on nuScenes test set. Methods published before the submission deadline (08/03/2023) are listed. L and C respectively denote LiDAR and camera. * The latency of PMF [50] is tested without TensorRT acceleration. The bold numbers indicate the best results, and the blue numbers indicate the second best results." + ], + "table_footnote": [], + "table_body": "
MethodmIoUroadsidewalkparkingother-groundbuildingcartruckbicyclemotorcycleother-vehiclevegetationtrunkterrainpersonbicyclistmotorcyclistfencepoletraffic signlatency (ms)
SqueezeSegV2 [35]39.788.667.645.817.773.781.813.418.517.914.071.835.860.220.125.13.941.120.226.3-
DarkNet53Seg [2]49.991.874.664.827.984.186.425.524.532.722.678.350.164.036.233.64.755.038.952.2-
RangeNet53++ [25]52.291.875.265.027.887.491.425.725.734.423.080.555.164.638.338.84.858.647.955.983.3
3D-MiniNet [1]55.891.674.564.225.489.490.528.542.342.129.482.860.866.747.844.114.560.848.056.6-
SqueezeSegV3 [38]55.991.774.863.426.489.092.529.638.736.533.082.058.765.445.646.220.159.449.658.9238
PointNet++ [26]20.172.041.818.75.662.353.70.91.90.20.246.513.830.00.91.00.016.96.08.95900
TangentConv [32]40.983.963.933.415.483.490.815.22.716.512.179.549.358.123.028.48.149.035.828.53000
PointASNL [43]46.887.474.324.31.883.187.939.00.025.129.284.152.270.634.257.60.043.957.836.9-
RandLA-Net [16]55.990.574.061.824.589.794.243.929.832.239.183.863.668.648.447.49.460.451.050.7880
KPConv [33]58.890.372.761.331.590.595.033.430.242.544.384.869.269.161.561.611.864.256.447.4-
PolarNet [45]54.390.874.461.721.790.093.822.940.330.128.584.065.567.843.240.25.661.351.857.562
JS3C-Net [41]66.088.972.161.931.992.595.854.359.352.946.084.569.867.969.565.439.970.860.768.7471
SPVNAS [31]67.090.275.467.621.891.697.256.650.650.458.086.173.471.067.467.150.366.964.367.3259
Cylinder3D [47]68.992.277.065.032.390.797.150.867.663.858.585.672.569.873.769.248.066.562.466.2131
RPVNet [40]70.393.480.770.333.393.597.644.268.468.761.186.575.171.775.974.443.472.164.861.4168
(AF)2-S3Net [6]70.892.076.266.845.892.594.340.263.081.440.078.668.063.176.481.777.769.664.073.3-
2DPASS [42]72.989.774.767.440.093.597.061.163.663.461.586.273.971.077.981.374.172.965.070.462
ProtoTransfer [Ours]73.691.577.571.542.892.997.557.168.476.068.086.774.872.680.076.061.470.765.866.762
", + "bbox": [ + 81, + 301, + 890, + 540 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Semantic segmentation results on SemanticKITTI test set. Methods published before the submission deadline (08/03/2023) are listed. The bold numbers indicate the best results, and the blue numbers indicate the second best results.", + "bbox": [ + 76, + 541, + 890, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In order to have a fair comparison, most of the experimental setup and implementations are identical to the recent work [42]. During the model evaluation, the same test-time augmentation as in [42] is also used in our study.", + "bbox": [ + 76, + 579, + 468, + 640 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Results on Benchmarks", + "text_level": 1, + "bbox": [ + 76, + 650, + 294, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare the results of our ProtoTransfer with the published state-of-the-art methods on two large-scale benchmarks, i.e., nuScenes [4] and SemanticKITTI [2].", + "bbox": [ + 75, + 672, + 468, + 718 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "NuScenes. As shown in Tab. 1, ProtoTransfer successfully outperforms all existing methods in terms of both mIoU and latency, demonstrating its efficacy and efficiency. Moreover, our ProtoTransfer not only outperforms single-modal approaches, but also surprisingly surpasses fusion-based methods which require both of LiDAR point clouds and images covering the whole FoV as input for the inference stage. In contrast, our method ProtoTransfer only takes point clouds as input and produces superior segmentation results. Compared to the recently proposed distillation-based method 2DPASS [42], our ProtoTransfer achieves $1.3\\%$ performance gain, showing the success of explor", + "bbox": [ + 75, + 719, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ing prototypes for knowledge transfer from multi-modal to single-modal. Besides, according to Tab. 1, we can find that our ProtoTransfer performs best on classes of small size and with sparse points, such as traffic-cone, motorcycle and construction vehicle, showing great potential in real-world practice.", + "bbox": [ + 496, + 579, + 890, + 669 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SemanticKITTI. We compare our ProtoTransfer with several previous state-of-the-arts works. From Tab. 2, we can see that our proposed ProtoTransfer still achieves the best performance among these methods, leaving a margin of $0.7\\%$ compared with the distillation-based 2DPASS [42]. Similarly, ProtoTransfer achieves the best results on classes of small objects such as person and bicycle.", + "bbox": [ + 496, + 670, + 890, + 776 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Qualitative Evaluation", + "text_level": 1, + "bbox": [ + 500, + 786, + 709, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We visualize the segmentation results on nuScenes validation set in Fig. 4. As can be observed, our ProtoTransfer achieves the most minor error prediction compared with the two comparison methods. In the first row of Fig. 4, the car and bus are close to each other, neither the baseline method nor the 2DPASS approach can produce an accurate segmen", + "bbox": [ + 496, + 810, + 890, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3342", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/00a113ed776bbe753ab91d9a3a760b4936025cd13d7d2789627d298a79ab7eb6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 125, + 92, + 305, + 193 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3a77602ddeb243d5a11bcdf9015ec203ba7c8d686360129a295c12ce7e11622c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 125, + 193, + 303, + 287 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5b7e755d21d945ef46a16cba02b43dbb7f285ebaa2865de22aab4405d780d2df.jpg", + "image_caption": [ + "(a) Error by baseline" + ], + "image_footnote": [], + "bbox": [ + 125, + 287, + 303, + 386 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c1505c94d54497f7979495736ee8162476ae7fd575d33af8df69cf11a0916be7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 305, + 92, + 485, + 191 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ed0f7c2726b947d2b725efb94feb9e4e29d2f698ce66c9367adb6794b9880092.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 305, + 191, + 483, + 287 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/44142d1a64538ecc71734ac50a7547949a079ee83b0a3a0a10cc51e5e71f6ca0.jpg", + "image_caption": [ + "(b) Error by 2DPASS" + ], + "image_footnote": [], + "bbox": [ + 305, + 287, + 483, + 386 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6e9aec90110f0c2e2e4fa03a5cc1e1598a07a280fd05ff087c684f1a96306538.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 485, + 92, + 665, + 191 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/05957da15639b2d6815ef5ba29f47eb95bbf0b706ed9dad07f88d919406e7993.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 485, + 191, + 665, + 287 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/756f62ab06194b300d2e17acbb095c023eb357ef2ceb36205ea98712c865e9d7.jpg", + "image_caption": [ + "Figure 4. Qualitative results on nuScenes Lidarseg validation set. Red points are in red. Compared to baseline and the recently proposed distillation-based method 2DPASS [42], our ProtoTransfer achieves better segmentation on region boundaries (the first row), far objects (the second row) and small objects (the third row), thanks to the fully exploited and transferred multi-modal knowledge." + ], + "image_footnote": [], + "bbox": [ + 485, + 287, + 665, + 386 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/26b1bf5f6cce501c610161c63f1570736f148072cbc641504982d0dadab00e5d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 666, + 92, + 844, + 191 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f5f1f6eee9524e741ea315fbf11679dfae27a36c77492dc1532c49df614123af.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 666, + 191, + 844, + 287 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/892be72b976e8ee8880150fd5cc17fa2aff98262425264ad59a3f9904d3c4e11.jpg", + "image_caption": [ + "(c) Error by ProtoTransfer", + "(d) Ground-truth" + ], + "image_footnote": [], + "bbox": [ + 666, + 287, + 844, + 386 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8c9849ee4a4ae443fbdaba8c393c11728cdc45e05268158521d9f31450ea6d36.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
baselineLprotoupdate proto. bankmIoU
✓76.21
✓✓76.50
✓✓✓80.51
", + "bbox": [ + 120, + 459, + 424, + 520 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tation for the points in the class of car, while our ProtoTransfer precisely segments all points belonging to the car. The second row displays a car far away from the ego-car, both of the two comparing methods mispredict the point clouds in the head area of the car and ProtoTransfer segments the car points perfectly again. The last row presents a pedestrian with only several LiDAR points. Thanks to the fully exploited and transferred multi-modal knowledge, our ProtoTransfer obtains the most accurate segmentation.", + "bbox": [ + 75, + 546, + 468, + 681 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 691, + 240, + 705 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we present comprehensive ablation studies to examine the efficacy of each component in ProtoTransfer, ways of prototype bank construction, and distribution of feature representations. All the ablation studies are conducted on the nuScenes validation set.", + "bbox": [ + 75, + 714, + 468, + 789 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effects of each component. As shown in Tab. 3, introducing the proposed prototype-based loss term $\\mathcal{L}^{\\mathrm{proto}}$ into the naive baseline method without updating the prototype bank can only bring minor performance gain. When the prototype bank is dynamically updated with the strategy presented in Sec. 3.4, the segmentation performance is significantly boosted which obviously demonstrates that the qual", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/692d4eef02b8530a9638ce61eaaa091cf9cc228f27e3d512113cb1d974a878b4.jpg", + "table_caption": [ + "Table 3. Ablation study of each component in our ProtoTransfer." + ], + "table_footnote": [], + "table_body": "
F3dF2dFfuseFfuse_umIoU
baseline76.21
(a)✓76.97
(b)✓75.35
(c)✓78.65
(d)✓✓77.11
(e)✓✓75.67
(f)✓✓✓75.58
(g)✓79.83
(h)✓✓80.51
", + "bbox": [ + 535, + 459, + 857, + 607 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Abaltion study of inputs of prototype bank.", + "bbox": [ + 539, + 607, + 849, + 619 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ity of the prototype bank is critical.", + "bbox": [ + 500, + 633, + 733, + 648 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Input Source of Prototype Bank. As presented in Sec. 3, the inputs of the prototype bank include point-pixel fusion features, image features and point features. Tab. 4 shows an ablation study on the effect of different input combinations on final segmentation performance. As can be observed, building up the prototype bank using only point cloud features (a) can generate a $0.76\\%$ performance gain over the baseline. We think it is because prototypes constructed from only point features can serve as cluster centers and using the proposed prototype-based loss $\\mathcal{L}^{\\mathrm{proto}}$ can help point features become more discriminative as they are pushed to be closer to their cluster centers. However, only accumulating image features into the prototype bank leads to a $0.86\\%$ performance drop, we postulate it may be because there is", + "bbox": [ + 496, + 652, + 890, + 864 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "5Please note the pseudo-labeling scheme presented in Sec. 3.4 can also be used here to exploit unmatched image features.", + "bbox": [ + 500, + 875, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3343", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b533604ffbec4c3809655b0f95b55a4d38896115ced4452cee2848a8e91f7d94.jpg", + "image_caption": [ + "Figure 5. Ablation study of $\\lambda$ in Eq. (8). $\\lambda = 0.2$ is set as default in ProtoTransfer." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 462, + 284 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "a distribution gap between image features and point cloud features and thus it is unwise to force point cloud features to imitate image feature cluster centers. On the contrary, when fusing the point-pixel matched features and only using the fusion features for the prototype bank (c) excels $2.44\\%$ over the baseline, demonstrating the effectiveness of knowledge transfer from multi-modal to the single LiDAR modal. As shown by Tab. 4 (h), when the fusion features $\\bar{F}^{\\mathrm{fuse}}$ and $\\bar{F}^{\\mathrm{fuse.u}}$ are fully explored and accumulated into the prototype bank, our ProtoTransfer reaches the best mIoU of $80.51\\%$ . This ablation study clearly shows that the input source plays a key role in the quality of the prototype bank.", + "bbox": [ + 75, + 329, + 472, + 511 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fusion Strategy of Features for Prototype Bank. As illustrated in Fig. 3 and Sec. 3.4, we calculate class-mean embeddings for the unmatched pixel features and point features, respectively. Then we concatenate these two embeddings and fuse them by reusing the MLP in Eq. (1). The fused embedding $\\bar{F}^{\\mathrm{fuse - u}}$ is finally accumulated to the prototype bank together with the point-pixel matched fusion features $\\bar{F}^{\\mathrm{fuse}}$ . To demonstrate the improvement not only comes from the additional image and point features but also comes from the cleverly designed fusion strategy, we use a naive way to have an investigation, i.e., any combinations among the point-pixel naturally matched fusion feature $\\bar{F}^{\\mathrm{fuse}}$ , image feature $F^{2\\mathrm{d}}$ and point feature $F^{3\\mathrm{d}}$ in the way of simple summation and use moving average to accumulate them into the prototype bank as presented in Tab. 4 (d)~(f). We can find that this naive summation of all three features (f) reduces the mIoU to $75.58\\%$ . We owe this to the large distribution gap between different kinds of features which cannot be handled in the naive sum-up way. In contrast, our ProtoTransfer reuses the MLP to map the unmatched image features to the fusion feature space, thus successfully bypassing this problem.", + "bbox": [ + 75, + 516, + 472, + 849 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of $\\lambda$ Selection. We have experimented with different values of $\\lambda$ in Eq. (8) and the results are presented in Fig. 5. As can be observed, our ProtoTransfer achieves the best per", + "bbox": [ + 76, + 854, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d6bedc6fa8642665921e95eca479f2782236ef1410cdbb821889a22556cf517c.jpg", + "image_caption": [ + "(a) Baseline" + ], + "image_footnote": [], + "bbox": [ + 516, + 95, + 697, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/04fe9a0c7caa404b034f7218f2493af58a36a39170147a2e5d2078283866e200.jpg", + "image_caption": [ + "(b) ProtoTransfer", + "Figure 6. Feature representation visualization of (a) the baseline and (b) our ProtoTransfer. Outlier points have been pointed out by the red arrow. The displayed category ID and their corresponding semantic category is {1: \"barrier\", 2: \"bicycle\", 3: \"bus\", 8: \"traffic cone\", 9: \"trailer\", 10: \"truck)}." + ], + "image_footnote": [], + "bbox": [ + 705, + 95, + 888, + 205 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "formance when $\\lambda = 0.2$ which reveals that the unmatched-pixel-feature-based fusion embedding $\\bar{F}^{\\mathrm{fuse\\_u}}$ plays a more important role. Note that when $\\lambda = 0$ , i.e., using only $\\bar{F}^{\\mathrm{fuse\\_u}}$ , is able to achieve a satisfactory segmentation accuracy, demonstrating the benefits brought by the unmatched image features.", + "bbox": [ + 496, + 316, + 893, + 409 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Distribution of Feature Representation. The essence of introducing the prototype-based loss term $\\mathcal{L}^{\\mathrm{proto}}$ in our method is to encourage the point features to be close to the same-class multi-modal prototype while staying far away from the other-class prototypes. Hence, it is important to study the impact of prototypes on feature distribution. As can be observed in Fig. 6 (a), outlier points appear in the feature distribution of the baseline method, while our ProtoTransfer is able to produce more compact feature distributions for all semantic classes, demonstrating the effectiveness of our method.", + "bbox": [ + 496, + 421, + 893, + 588 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 614, + 619, + 631 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work presents a cross-modal knowledge transfer method dubbed ProtoTransfer for point cloud semantic segmentation. ProtoTransfer achieves remarkable segmentation performance but keep a single LiDAR inference speed. By accumulating the fusion features into a prototype bank, all LiDAR points can learn from their class-specific prototypes, thus being well benefited. The unmatched image features are further explored and exploited via a pseudolabeling scheme and a novel prototype bank update strategy. Through extensive experimental results on nuScenes and SemanticKITTI dataset, the efficacy of our method has been successfully demonstrated.", + "bbox": [ + 496, + 645, + 893, + 828 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported by Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), and the Fundamental Research Funds for the Central Universities.", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3344", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Inigo Alonso, Luis Riazuelo, Luis Montesano, and Ana C Murillo. 3d-mininet: Learning a 2d representation from point clouds for fast and efficient 3d lidar semantic segmentation. arXiv preprint arXiv:2002.10893, 2020.", + "[2] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Jurgen Gall. Semantickitti: A dataset for semantic scene understanding of lidar sequences. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 16280-16290, 2021." + ], + "bbox": [ + 78, + 90, + 468, + 218 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "3347", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/ProtoTransfer_ Cross-Modal Prototype Transfer for Point Cloud Segmentation/4c052c14-482f-4c6c-bea8-5d4ef790aea8_model.json b/2023/ProtoTransfer_ Cross-Modal Prototype Transfer for Point Cloud Segmentation/4c052c14-482f-4c6c-bea8-5d4ef790aea8_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b20d3b850fe1c72ca59abd5a59f84245f5d1e360 --- /dev/null +++ b/2023/ProtoTransfer_ Cross-Modal Prototype Transfer for Point Cloud Segmentation/4c052c14-482f-4c6c-bea8-5d4ef790aea8_model.json @@ -0,0 +1,2455 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.088, + 0.131, + 0.882, + 0.153 + ], + "angle": 0, + "content": "ProtoTransfer: Cross-Modal Prototype Transfer for Point Cloud Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.321, + 0.18, + 0.654, + 0.199 + ], + "angle": 0, + "content": "Pin Tang\\(^{1}\\) Hai-Ming Xu\\(^{2}\\) Chao Ma\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.15, + 0.199, + 0.82, + 0.217 + ], + "angle": 0, + "content": "1 MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University" + }, + { + "type": "text", + "bbox": [ + 0.218, + 0.217, + 0.751, + 0.235 + ], + "angle": 0, + "content": "\\(^{2}\\) Australian Institute for Machine Learning, University of Adelaide" + }, + { + "type": "text", + "bbox": [ + 0.228, + 0.237, + 0.741, + 0.252 + ], + "angle": 0, + "content": "{pin.tang,chaoma}@sjtu.edu.cn，hai-ming.xu@adelaide.edu.au" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.474, + 0.699 + ], + "angle": 0, + "content": "Knowledge transfer from multi-modal, i.e., LiDAR points and images, to a single LiDAR modal can take advantage of complimentary information from modal-fusion but keep a single modal inference speed, showing a promising direction for point cloud semantic segmentation in autonomous driving. Recent advances in point cloud segmentation distill knowledge from strictly aligned point-pixel fusion features while leaving a large number of unmatched image pixels unexplored and unmatched LiDAR points under-benefited. In this paper, we propose a novel approach, named ProtoTransfer, which not only fully exploits image representations but also transfers the learned multi-modal knowledge to all point cloud features. Specifically, based on the basic multi-modal learning framework, we build up a class-wise prototype bank from the strictly-aligned fusion features and encourage all the point cloud features to learn from the prototypes during model training. Moreover, to exploit the massive unmatched point and pixel features, we use a pseudo-labeling scheme and further accumulate these features into the class-wise prototype bank with a carefully designed fusion strategy. Without bells and whistles, our approach demonstrates superior performance over the published state-of-the-arts on two large-scale benchmarks, i.e., nuScenes and SemanticKITTI, and ranks 2nd on the competitive nuScenes Lidarseg challenge leaderboard." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.728, + 0.21, + 0.743 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.754, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Semantic segmentation on point cloud [6, 15, 37, 40] has attracted increasing attention from the computer vision community for its crucial role in scene understanding of 3D space. Although LiDAR point cloud can provide accurate location and depth information of interested scenes, the sparse and textureless shortages inevitably restrict its semantic segmentation performance. On the other hand, 2D images consist of dense pixels with rich color and subtle" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.286, + 0.884, + 0.383 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.595, + 0.385, + 0.807, + 0.396 + ], + "angle": 0, + "content": "(a) Point-pixel matching and feature fusion" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.398, + 0.695, + 0.54 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.526, + 0.544, + 0.675, + 0.554 + ], + "angle": 0, + "content": "(b) Distillation-based methods" + }, + { + "type": "image", + "bbox": [ + 0.708, + 0.398, + 0.889, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.735, + 0.544, + 0.846, + 0.555 + ], + "angle": 0, + "content": "(c) Our ProtoTransfer" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.558, + 0.892, + 0.684 + ], + "angle": 0, + "content": "Figure 1. (a) Point-pixel matching and feature fusion: only features of strictly matched point-pixel pairs can be fused. (b) Distillation-based methods are only performed between fusion prediction and the corresponding matched point prediction while other unmatched points have no chance to mimic the fusion prediction. (c) Our ProtoTransfer performs knowledge transfer from prototype bank to all point features directly without being restricted by matching requirements. The prototype bank is updated using fusion, point, and unmatched image features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.701, + 0.892, + 0.733 + ], + "angle": 0, + "content": "textures [34]. Therefore, incorporating these two complementary modals altogether can be a more plausible solution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Recently, there are mainly two stream approaches of utilizing multi-modal data, i.e., fusion-based methods [10, 50] and distillation-based methods [42]. The former methods project point clouds to the camera coordinate to obtain a point-to-pixel mapping, based on which point features are fused with corresponding image features to produce the final point-wise segmentation during both the training and evaluation phases. Although robust and accurate segments are achieved by fusing different sensors, the fusion-based methods may suffer from heavy memory and time consumption for processing these two modal data simul" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.227, + 0.901 + ], + "angle": 0, + "content": "* Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3337" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "taneously. In order to benefit from multi-modal fusion while bypassing the computation burden, the latter methods [42] propose to utilize the distillation technique to transfer knowledge learned from cross-modal fusion at the training stage and discard the fusion module for evaluation. The impressive segmentation performance suggests the feasibility of the methods in this stream. Therefore, this paper further explores this research direction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.473, + 0.485 + ], + "angle": 0, + "content": "Unlike common distillation approaches in image classification tasks [14, 44], distilling from multi-modal to the single LiDAR modal may meet quite different pitfalls: (1) Not all LiDAR points can be used in knowledge distillation because LiDAR-to-image is partially matched. Due to the difference in the way sensors collect data, not all the LiDAR points can be aligned to the dense image pixels. For example, we empirically find that only around \\(16.07\\%\\) LiDAR points in SemanticKITTI dataset can be matched to corresponding image pixels, and Fig. 1(a) also demonstrates this observation. Thus, classic logit-/probability-style distillation strategies [42] can only be performed on the well-aligned point clouds, leading to a sub-optimal knowledge distillation. (2) Massive image pixels are overlooked. Since only partial image pixels1 will contribute to the modal fusion based on the above matching constraints, a large number of pixels are not used in knowledge distillation, resulting in a great loss of rich semantic information in dense pixels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.473, + 0.833 + ], + "angle": 0, + "content": "In this paper, we propose a novel approach for point cloud semantic segmentation which successfully avoids the above pitfalls. Specifically, following the existing work [17, 34, 42], we first construct a modal fusion module to combine the feature representations of matched LiDAR points and image pixels. Next, in order to transfer the knowledge from the fusion module to each point feature representation, we create a class-wise prototype bank to accumulate the fusion features learned in the fusion module and encourage the similarity between features of all LiDAR points and corresponding-class prototypes as high as possible. By this means, every LiDAR point has a fair chance to mimic the fusion features as shown in Fig. 1(c), and we dub our method as ProtoTransfer. Moreover, to make full use of semantic information inherited in dense image pixels, we propose to incorporate the image features into the class-wise prototype bank through a cleverly designed fusion strategy. Since images in the point cloud semantic segmentation datasets usually lack per-pixel annotations, we further use a pseudo-labeling scheme to generate pseudolabels for each pixel and thus make the update of pixelfeature into class-wise prototypes become possible. In summary, the main contributions of this paper are three aspects:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.834, + 0.472, + 0.864 + ], + "angle": 0, + "content": "- We investigate the pitfalls of point cloud semantic segmentation on distillation-based methods and find that a" + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.486, + 0.473, + 0.864 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "large number of image features are not well-utilized and point features are not well distillation-benefited." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.123, + 0.894, + 0.168 + ], + "angle": 0, + "content": "- We introduce the prototype bank concept into point cloud semantic segmentation and propose a novel approach ProtoTransfer to successfully overcome the above pitfalls." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.169, + 0.895, + 0.229 + ], + "angle": 0, + "content": "- We conduct experiments on both SemanticKITTI and nuScenes benchmarks to demonstrate the effectiveness of our approach and also achieve a 2nd place on the competitive nuScenes Lidarseg leaderboard." + }, + { + "type": "list", + "bbox": [ + 0.499, + 0.123, + 0.895, + 0.229 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.245, + 0.642, + 0.261 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.271, + 0.892, + 0.483 + ], + "angle": 0, + "content": "Multi-Modal 3D Semantic Segmentation. Since different modal can provide complimentary information to each other, multi-modal point cloud semantic segmentation attracts increasing attention [8, 20, 24]. RGBAL [8] casts RGB images to a polar-grid mapping representation and designs an early-mid-level hybrid fusion architecture. Recently, PMF [50] projects LiDAR points to camera coordinates, which is called perspective projection [25]. Then, they use two 2D U-net [27] to extract the image and point features. The multi-scale image and point features in both U-nets are fused to produce better segmentation results. Though satisfactory performance are achieved, these methods need multi-modal inputs during both training and inference phases, which is time-/memory-consuming." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.488, + 0.892, + 0.639 + ], + "angle": 0, + "content": "Prototype Networks. Prototype-based learning methods has been widely used in machine learning [9, 11, 28]. Recently, a surge of attention is paid to employ prototype networks on various tasks, presenting great potential in few-shot learning [29] and zero-shot learning[18, 36]. Moreover, [48] shows a prototype view of image semantic segmentation network. Another prototype-based semisupervised method is also proposed [39]. Our work sheds light on the possibility of using prototypes for knowledge transfer from multi-modal to single-modal." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Cross-Modal Knowledge Transfer. Knowledge distillation, first proposed by Hinton et al. [14], is a common knowledge transfer method, which pushes the student network mimic the soft logits of the teacher network. Very recently, knowledge distillation is introduced into perception tasks in autonomous driving, such as 3D object detection [7, 19, 46] and point cloud segmentation [42]. During training, they use distillation to transfer multi-modal knowledge learned by the multi-modal teacher to a single-modal student. However, these methods suffers from strict point-pixel alignment, leading to massive unmatched image pixels unexplored and points under-benefited. Our work performs knowledge transfer in another way. Contrary to [42], we construct a prototype bank from fusion and unmatched image features and encourage all the point cloud features to learn from the prototypes during model training, thus fully exploiting and transferring multi-modal knowledge." + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.47, + 0.901 + ], + "angle": 0, + "content": "\\( {}^{1} \\) Only \\( 5\\% \\) image pixels are matched to LiDAR points for a typical 32-beam LiDAR scanner as presented in BEVFusion [22]." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3338" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.087, + 0.873, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.285, + 0.895, + 0.373 + ], + "angle": 0, + "content": "Figure 2. Pipeline overview of our ProtoTransfer. The model first uses modal-specific backbones to generate image features \\( F^{2\\mathrm{d}} \\) and point features \\( F^{3\\mathrm{d}} \\) and feeds them into the point-pixel matching module to generate matched point feature \\( F^{3\\mathrm{d},\\mathrm{m}} \\), matched and unmatched image features \\( F^{2\\mathrm{d},\\mathrm{m}} \\) and \\( F^{2\\mathrm{d},\\mathrm{u}} \\), respectively. Then modal-specific segmentation heads are used to produce predictions for loss calculation, i.e., \\( \\mathcal{L}^{3\\mathrm{d}}, \\mathcal{L}^{2\\mathrm{d}} \\) and \\( \\mathcal{L}^{\\mathrm{fuse}} \\), where \\( \\mathcal{L}^{\\mathrm{fuse}} \\) will update the feature \\( F^{\\mathrm{fuse}} \\) fused from \\( F^{2\\mathrm{d},\\mathrm{m}} \\) and \\( F^{3\\mathrm{d},\\mathrm{m}} \\). To take advantage of the fusion features, we introduce a class-wise prototype bank whose input source includes features \\( F^{3\\mathrm{d}} \\), \\( F^{\\mathrm{fuse}} \\) and \\( F^{2\\mathrm{d},\\mathrm{u}} \\) and propose a loss \\( \\mathcal{L}^{\\mathrm{proto}} \\) to transfer fusion knowledge to all point features. Please note 2D&Fusion GT is derived from the 3D GT based on point-pixel matching." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.38, + 0.213, + 0.397 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.404, + 0.283, + 0.42 + ], + "angle": 0, + "content": "3.1. Framework Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.428, + 0.471, + 0.578 + ], + "angle": 0, + "content": "Given a LiDAR point cloud frame with \\(N\\) unordered points \\(P = \\{p_i\\in \\mathbb{R}^{d_{\\mathrm{in}}}\\}_{i = 1}^N\\) where \\(d_{\\mathrm{in}}\\) is input feature dimension, the goal of point cloud semantic segmentation is to assign a single class label \\(c\\in \\{1,2\\dots ,C\\}\\) to each point. To make up for the sparsity and lack of texture of point clouds collected in outdoor scenes [42], the other modal of the corresponding scenes, raw images \\(I\\in \\mathbb{R}^{W\\times H\\times 3}\\), where \\(W,H\\) denote the resolution of a given image, are also provided for model learning to achieve a better segmentation performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.47, + 0.867 + ], + "angle": 0, + "content": "As the overall structure presented in Fig. 2, the main contributions of our approach are (1) introducing a class-wise prototype bank for knowledge transfer from a fusion modal to all LiDAR points and (2) proposing to make full use of image features to enhance the prototype quality. Specifically, paired point cloud and image are first fed into modal-specific backbones to extract feature representations respectively. Next, based on the given LiDAR-to-image transformation matrix, features are fused for matched LiDAR point and corresponding image pixels, as done in previous modal-fusion-related work [17, 34, 42]. Due to the differing data acquisition mechanisms of different modal sensors, the matching rate between LiDAR points and image pixels is often quite low. Instead of distilling knowledge solely for the limited matched LiDAR points, we propose a novel knowledge transfer module that can enable unmatched points to also benefit from fused feature representations. With this framework, we explore and exploit unmatched image pixels to further enhance the overall point" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.381, + 0.724, + 0.396 + ], + "angle": 0, + "content": "cloud segmentation performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.397, + 0.892, + 0.457 + ], + "angle": 0, + "content": "During inference, the enhanced point cloud segmentation branch can produce accurate segmentation results without the image backbone and multi-modal fusion, and thus challenges can be tackled within a real-time speed." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.464, + 0.787, + 0.48 + ], + "angle": 0, + "content": "3.2. Cross-Modal Prototype Transfer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.487, + 0.893, + 0.743 + ], + "angle": 0, + "content": "Considering the data structures of point cloud and image pixels are totally different, various network architectures are utilized to extract feature representations for the two modal inputs independently. Specifically, ResNet34 [13] encoder and FCN [23] decoder are used for 2D images to extract dense-grid features \\( F^{2\\mathrm{d}} \\in \\mathbb{R}^{W \\times H \\times D_{2\\mathrm{d}}} \\), and a sparse convolution [12] based hierarchical point-voxel backbone [42] are designed for 3D point cloud to generate point-wise features \\( F^{3\\mathrm{d}} \\in \\mathbb{R}^{N \\times D_{3\\mathrm{d}}} \\). Since LiDAR points and image pixels are not naturally aligned due to the differences in data collection of LiDAR and camera devices, LiDAR-camera transformation matrix is used to find the point-to-pixel correspondence3 and further obtain the matched pixel feature \\( F^{2\\mathrm{d\\_m}} \\) and matched point features \\( F^{2\\mathrm{d\\_m}} \\). Following the previous work [42], we concatenate the matched point-pixel features and use a multi-layer perceptron (MLP) to obtain the fusion feature" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.748, + 0.892, + 0.768 + ], + "angle": 0, + "content": "\\[\nF ^ {\\mathrm {f u s e}} = \\operatorname {M L P} \\left(\\operatorname {c a t} \\left(F ^ {2 \\mathrm {d}. \\mathrm {m}}, F ^ {3 \\mathrm {d}. \\mathrm {m}}\\right)\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.772, + 0.892, + 0.832 + ], + "angle": 0, + "content": "where \\(\\odot\\) is Hadamard product of two matrices. The MLP is used to reduce feature dimension to \\(D_{3\\mathrm{d}}\\) and obtain \\(F^{\\mathrm{fuse}}\\). With LiDAR per-point ground truth \\(Y^{3\\mathrm{d}}\\), the fusion branch is got supervised" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.836, + 0.892, + 0.869 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} ^ {\\text {f u s e}} = \\mathcal {L} _ {\\mathrm {C E}} \\left(h ^ {\\text {f u s e}} \\left(F ^ {\\text {f u s e}}\\right), \\hat {Y}\\right) + \\mathcal {L} _ {\\text {L o v a s z}} \\left(h ^ {\\text {f u s e}} \\left(F ^ {\\text {f u s e}}\\right), \\hat {Y}\\right) \\tag {2}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.47, + 0.9 + ], + "angle": 0, + "content": "2Input feature normally contains Cartesian coordinates, intensity of returning laser beam, colors, etc." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.9 + ], + "angle": 0, + "content": "3Detailed point-to-pixel mapping mechanism is provided in supplementary material." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3339" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.09, + 0.47, + 0.152 + ], + "angle": 0, + "content": "where \\( h^{\\mathrm{fuse}} \\) is the segmentation head of fusion branch. \\( \\hat{Y} \\) is the subset of \\( Y^{3\\mathrm{d}} \\), representing the ground truth for matched points. \\( \\mathcal{L}_{\\mathrm{CE}} \\) and \\( \\mathcal{L}_{\\mathrm{Lovasz}} \\) denote the cross entropy loss and the IoU-style Lovasz loss [3] respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.153, + 0.468, + 0.304 + ], + "angle": 0, + "content": "Attributed to the integration of rich semantic information from 2D images, the segmentation performance of the fusion branch is superior to the LiDAR-sole branch (the bottom branch in Fig. 2). In order to make a single LiDAR point cloud segmentation benefit from the fusion branch, one straightforward way is to introduce a knowledge distillation loss between these two branches, as done in [42]. However, due to the matched point-pixel being limited, only partial point features can benefit from the fusion features and leave massive unmatched points under-benefited." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.468, + 0.395 + ], + "angle": 0, + "content": "To bypass the strict matching restriction, we introduce a class-wise prototype bank to accumulate the fusion features during model optimization. Such a prototype bank can be served as a parameter-free segmentation head to regularize the distribution of all point features with LiDAR ground truth" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.405, + 0.468, + 0.446 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} ^ {\\text {p r o t o}} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathcal {L} _ {\\mathrm {C E}} \\left(p _ {c _ {i}}, c _ {i}\\right) + \\mathcal {L} _ {\\text {L o v a s z}} \\left(p _ {c _ {i}}, c _ {i}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.449, + 0.484, + 0.489 + ], + "angle": 0, + "content": "where \\(p_{c_i} \\coloneqq p(y = c_i | F_i^{3\\mathrm{d}}) = \\frac{\\exp(\\cos(\\mathsf{p}_{c_i}, F_i^{3\\mathrm{d}}) / T)}{\\sum_{j=1}^{C} \\exp(\\cos(\\mathsf{p}_j, F_i^{3\\mathrm{d}}) / T)}\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.468, + 0.592 + ], + "angle": 0, + "content": "where \\(F_{i}^{3\\mathrm{d}}\\) and \\(c_{i}\\) denote the feature and semantic label of \\(i\\)-th point respectively. \\(\\mathsf{p}_{c_i} \\in \\mathbb{R}^{D_{3\\mathrm{d}}}\\) represents the prototype in class \\(c_{i}\\). \\(\\cos\\) is the cosine function to calculate the similarity of the prototype and point feature. \\(T\\) is the temperature parameter to adjust the scale of similarity measurement and is empirically set to 0.1 in our study." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.593, + 0.468, + 0.698 + ], + "angle": 0, + "content": "The proposed cross-modal prototype-based knowledge transfer module encourages the point features to be close to the same-class prototype while staying far away from other-class prototypes. Therefore, through the class-wise prototype bank as a bridge, we successfully transfer the knowledge learned from the fusion feature to the whole point cloud and we term our method as ProtoTransfer." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.71, + 0.432, + 0.727 + ], + "angle": 0, + "content": "3.3. Prototype Bank Initialization and Update" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.734, + 0.468, + 0.854 + ], + "angle": 0, + "content": "In our work, the prototype bank is designed to be non-parametric and non-learnable and thus the quality of the prototype bank plays a critical role in the success of cross-modal knowledge transfer. Instead of using random vectors to initialize the prototype bank at the beginning of model training, we propose to use the fusion features of the first few iterations to warm up the class-wise prototype bank for a stable optimization procedure." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Meanwhile, since the initial prototype bank can not capture the distribution of fusion features, we also dynamically update the prototype bank throughout the training stage." + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.088, + 0.882, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.297, + 0.892, + 0.395 + ], + "angle": 0, + "content": "Figure 3. Prototype bank update demonstration. The fusion feature \\( F^{\\mathrm{fuse}} \\), unmatched image feature \\( F^{2\\mathrm{d.u}} \\) and point feature \\( F^{3\\mathrm{d}} \\) are respectively clustered into class-wise feature sets using corresponding GT or pseudo-label obtained with Eq. (6). Then the feature sets are class-wise averaged to produce class-mean embeddings. \\( \\bar{F}^{2\\mathrm{d.u}} \\) and \\( \\bar{F}^{3\\mathrm{d}} \\) are fused to get \\( \\bar{F}^{\\mathrm{fuse\\_u}} \\). Finally, both \\( \\bar{F}^{\\mathrm{fuse}} \\) and \\( \\bar{F}^{\\mathrm{fuse\\_u}} \\) are accumulated into the class-wise prototype bank." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.403, + 0.892, + 0.465 + ], + "angle": 0, + "content": "Given all fusion features \\(\\{F_i^{\\mathrm{fuse}}\\}\\), we can use their corresponding class labels \\(\\{c_i\\}\\) to cluster the fusion features into class-wise feature set. As shown in the top branch of Fig. 3, the fusion feature set of class \\(k\\) can be obtained by" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.472, + 0.891, + 0.492 + ], + "angle": 0, + "content": "\\[\n\\Omega_ {k} ^ {\\text {f u s e}} = \\left\\{F _ {i} ^ {\\text {f u s e}} \\mid c _ {i} = k \\right\\}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.499, + 0.89, + 0.53 + ], + "angle": 0, + "content": "We then use the moving average trick to update the class-specific prototype \\(\\mathfrak{p}_k\\) of class \\(k\\)" + }, + { + "type": "equation", + "bbox": [ + 0.572, + 0.538, + 0.891, + 0.556 + ], + "angle": 0, + "content": "\\[\n\\mathbf {p} _ {k} \\leftarrow \\alpha \\cdot \\mathbf {p} _ {k} + (1 - \\alpha) \\cdot \\bar {F} _ {k} ^ {\\text {f u s e}}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.573, + 0.558, + 0.819, + 0.591 + ], + "angle": 0, + "content": "where \\(\\bar{F}_k^{\\mathrm{fuse}} = \\frac{1}{\\|\\Omega_k^{\\mathrm{fuse}}\\|}\\sum_j\\Omega_{k,j}^{\\mathrm{fuse}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.598, + 0.892, + 0.657 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is a fixed hyper-parameter to control the prototype update speed and is empirically set as 0.999 in our study. \\(\\bar{F}_k^{\\mathrm{fuse}}\\) is the class-mean embedding of fusion features in class \\(k\\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.666, + 0.89, + 0.698 + ], + "angle": 0, + "content": "3.4. Unmatched Image Features Exploration and Exploitation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.825 + ], + "angle": 0, + "content": "Although prototype-based knowledge transfer has helped all point features benefit from the fusion features and enhanced the point segmentation performance, the fusion features, which are the knowledge source of the prototype bank, are only available on matched point-pixel pairs. Since the point-pixel matching rate is quite low, the rich semantic information lying in a large amount of unmatched image pixels is not explored and exploited." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "However, the exploitation of unmatched image pixels is non-trivial and there are at least two challenges: 1) Naturally lacking matching points for modal fusion. Since modal fusion requires well-matched point-pixel features, it is difficult to construct matching points for unmatched pixels." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3340" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.182 + ], + "angle": 0, + "content": "2) Hardly obtaining semantic labels of unmatched pixels. Since 2D images are provided without annotations and it can be costly to additionally annotate these dense pixels, the semantic labels of unlabeled pixels are thus unknown without the matching correspondence from the LiDAR point cloud ground truth." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.468, + 0.364 + ], + "angle": 0, + "content": "Based on our proposed cross-modal prototype transfer framework, we further design a novel strategy to incorporate the unmatched pixel features into the prototype bank to improve the transferred knowledge, and Fig. 3 presents an overview. Specifically, in order to solve the challenge 2), we formulate the image pixel class label generation problem as a weakly-/semi-supervised task [5, 30], i.e., taking the LiDAR-to-image matched pixels as labeled samples and taking other unmatched pixels as unlabeled ones. Considering the segmentation head \\( h^{2d} \\) for image input has been optimized on features of matched pixels4, we can generate posterior probability estimation for unmatched pixels" + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.379, + 0.397, + 0.398 + ], + "angle": 0, + "content": "\\[\np (y | F ^ {2 d. u}) = \\operatorname {s o f t m a x} \\left(h ^ {2 d} \\left(F ^ {2 d. u}\\right)\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.404, + 0.468, + 0.466 + ], + "angle": 0, + "content": "where \\( F^{2\\mathrm{d.u}} \\) is the features of unmatched pixels. Then the pseudo-labels can be obtained for these unmatched pixels when their maximal posterior probability is greater than a pre-defined confidence threshold \\( \\delta \\) (set as 0.8 in our study)" + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.492, + 0.468, + 0.51 + ], + "angle": 0, + "content": "\\[\ny ^ {2 \\mathrm {d} - \\mathrm {u}} = \\operatorname {a r g m a x} _ {c} p (y = c | F ^ {2 \\mathrm {d} - \\mathrm {u}}), \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.513, + 0.385, + 0.53 + ], + "angle": 0, + "content": "\\[\n\\text {o n l y i f} \\quad p (y = y ^ {2 d. u} | F ^ {2 d. u}) \\geq \\delta .\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.544, + 0.468, + 0.71 + ], + "angle": 0, + "content": "Given the pseudo-labeled unmatched pixels, it is still non-trivial to fuse the features of unmatched pixels and points due to the challenge 1) mentioned above. One straightforward way is to directly add the features of unmatched pixels to the prototype bank, empirical results in Tab. 4 show that this simple way can not bring a performance gain and we postulate that it may be caused by the distribution gap between image features and prototypes. Alternatively, we propose to first calculate a class-mean embedding \\(\\bar{F}_k^{2\\mathrm{d\\_u}}\\) of unmatched pixel features in the same pseudo-label \\(k\\)" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.722, + 0.345, + 0.755 + ], + "angle": 0, + "content": "\\[\n\\bar {F} _ {k} ^ {\\mathrm {2 d \\_ u}} = \\frac {1}{\\| \\Omega_ {k} ^ {\\mathrm {2 d \\_ u}} \\|} \\sum_ {j} \\Omega_ {k, j} ^ {\\mathrm {2 d \\_ u}},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.757, + 0.403, + 0.775 + ], + "angle": 0, + "content": "\\[\n\\text {w h e r e} \\quad \\Omega_ {k} ^ {2 d. u} = \\left\\{F _ {i} ^ {2 d. u} \\mid y _ {i} ^ {2 d. u} = k \\right\\},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.788, + 0.468, + 0.864 + ], + "angle": 0, + "content": "\\(\\Omega_{k}^{2\\mathrm{d.u}}\\) is class-wise unmatched image feature set and is obtained using pseudo labels but not ground-truth as in Eq. (4). And the class-mean embedding \\(\\bar{F}^{3\\mathrm{d}}\\) of point features can be obtained from \\(F^{3\\mathrm{d}}\\) with LiDAR ground truth. Then, modal fusion can be performed between class-mean embeddings" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.468, + 0.9 + ], + "angle": 0, + "content": "4Please note that the segmentation head for 2D images already exists in our training framework." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.616, + 0.105 + ], + "angle": 0, + "content": "of the same class" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.116, + 0.891, + 0.135 + ], + "angle": 0, + "content": "\\[\n\\bar {F} ^ {\\text {f u s e - u}} = \\operatorname {M L P} \\left(\\operatorname {c a t} \\left(\\bar {F} ^ {2 \\mathrm {d} - \\mathrm {u}}, \\bar {F} ^ {3 \\mathrm {d}}\\right)\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.146, + 0.892, + 0.19 + ], + "angle": 0, + "content": "where the MLP shares parameter with the one in Eq. (1). Finally, the class-wise prototype bank updating in Eq. (5) can be extended as" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.201, + 0.891, + 0.219 + ], + "angle": 0, + "content": "\\[\n\\mathfrak {p} _ {k} \\leftarrow \\alpha \\cdot \\mathfrak {p} _ {k} + (1 - \\alpha) \\cdot (\\lambda \\cdot \\bar {F} _ {k} ^ {\\text {f u s e}} + (1 - \\lambda) \\cdot \\bar {F} _ {k} ^ {\\text {f u s e - u}}), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.23, + 0.887, + 0.244 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is the balance weight of these two fusion features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.245, + 0.892, + 0.304 + ], + "angle": 0, + "content": "Since the pseudo-labeling scheme for unmatched pixels may not be activated at the beginning of model training, the prototype bank is still initialized with the method mentioned in Sec. 3.3." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.315, + 0.746, + 0.331 + ], + "angle": 0, + "content": "3.5. Overall Objective Function" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.338, + 0.892, + 0.428 + ], + "angle": 0, + "content": "Apart from the loss terms in Eq. (2) and Eq. (3), we also have separate losses \\(\\mathcal{L}^{3\\mathrm{d}}\\) and \\(\\mathcal{L}^{2\\mathrm{d}}\\) for LiDAR point cloud input and image input respectively. Both of these two losses are composed of a cross-entropy loss and a Lovasz loss as those in Eq. (2). Finally, the overall object function is the weighted sum of these loss terms" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.438, + 0.874, + 0.456 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\omega^ {\\mathrm {3 d}} \\mathcal {L} ^ {\\mathrm {3 d}} + \\omega^ {\\mathrm {2 d}} \\mathcal {L} ^ {\\mathrm {2 d}} + \\omega^ {\\text {f u s e}} \\mathcal {L} ^ {\\text {f u s e}} + \\omega^ {\\text {p r o t o}} \\mathcal {L} ^ {\\text {p r o t o}},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.467, + 0.891, + 0.497 + ], + "angle": 0, + "content": "where we empirically set \\(\\omega^{3\\mathrm{d}} = 2.0\\) and \\(\\omega^{2\\mathrm{d}} = \\omega^{\\mathrm{fuse}} = \\omega^{\\mathrm{proto}} = 1.0\\) in our study." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.511, + 0.632, + 0.528 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.891, + 0.597 + ], + "angle": 0, + "content": "In this section, we first provide details of our experimental setup. Then we evaluate ProtoTransfer on both nuScenes dataset and SemanticKITTI dataset. Finally, extensive ablation studies of our approach are presented." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.606, + 0.69, + 0.623 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.809 + ], + "angle": 0, + "content": "Datasets. NuScenes [4] collects 1000 driving scenes from various locations in Boston and Singapore using 1 LiDAR and 6 cameras covering \\(360^{\\circ}\\) FoV. According to the official setting, it is split into training, validation and test set as 700, 150 and 150 scenes. For point cloud semantic segmentation task, it annotates labels for 16 classes under different traffic and weather conditions. SemanticKITTI [2] contains 22 LiDAR sequences numbered from 00 to 21, in which sequence 08 is officially selected as validation set, sequence 00-10 except 08 is training set and 11-21 is test set. Unlike nuScenes, SemanticKITTI has only two front-view cameras." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Evaluation Metric. Following previous work [49, 42], we calculate intersection-over-union (IoU) of each class and mean IoU (mIoU) of all classes, which is formulated as \\(\\mathrm{mIoU} = \\frac{1}{C}\\sum_{c = 1}^{C}\\frac{\\mathrm{TP}_c}{\\mathrm{TP}_c + \\mathrm{FP}_c + \\mathrm{FN}_c}\\), where \\(\\mathrm{TP}_c\\), \\(\\mathrm{FP}_c\\) and \\(\\mathrm{TP}_c\\) denotes the number of true positive, false positive and false negative points of class \\(c\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "3341" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.255 + ], + "angle": 0, + "content": "
MethodsinputmIoUbarrierbicyclebuscarconstructionmotorcyclepedestriantraffic conetrailertruckdrivableother flatsidewalkterrainmannadevegetationLatency (ms)
PolarNet [45]L69.472.216.877.086.551.169.764.854.169.763.596.667.177.772.187.184.5-
JS3C-Net [41]L73.680.126.287.884.555.272.671.366.376.871.296.864.576.974.187.586.1-
Cylinder3D [47]L77.282.829.884.389.463.079.377.273.484.669.197.770.280.375.590.487.663
AMVNet [21]L77.380.632.081.788.967.184.376.173.584.967.397.567.479.475.591.588.785
SPVCNN [31]L77.480.030.091.990.864.779.075.670.981.074.697.469.280.076.189.387.163
(AF)2-S3Net [6]L78.378.952.289.984.277.474.377.372.083.973.897.166.577.574.087.786.8270
PMF [50]L+C77.082.040.081.088.064.079.080.076.081.067.097.068.078.074.090.088.0125*
2D3DNet [10]L+C80.083.059.488.085.163.784.482.076.084.871.996.967.479.876.092.189.2-
2DPASS [42]L80.881.755.392.091.873.386.578.572.584.775.597.669.179.975.590.288.044
ProtoTransfer [Ours]L82.181.155.593.991.577.987.382.778.985.176.597.669.879.675.991.589.144
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.256, + 0.892, + 0.296 + ], + "angle": 0, + "content": "Table 1. Semantic segmentation results on nuScenes test set. Methods published before the submission deadline (08/03/2023) are listed. L and C respectively denote LiDAR and camera. * The latency of PMF [50] is tested without TensorRT acceleration. The bold numbers indicate the best results, and the blue numbers indicate the second best results." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.302, + 0.891, + 0.541 + ], + "angle": 0, + "content": "
MethodmIoUroadsidewalkparkingother-groundbuildingcartruckbicyclemotorcycleother-vehiclevegetationtrunkterrainpersonbicyclistmotorcyclistfencepoletraffic signlatency (ms)
SqueezeSegV2 [35]39.788.667.645.817.773.781.813.418.517.914.071.835.860.220.125.13.941.120.226.3-
DarkNet53Seg [2]49.991.874.664.827.984.186.425.524.532.722.678.350.164.036.233.64.755.038.952.2-
RangeNet53++ [25]52.291.875.265.027.887.491.425.725.734.423.080.555.164.638.338.84.858.647.955.983.3
3D-MiniNet [1]55.891.674.564.225.489.490.528.542.342.129.482.860.866.747.844.114.560.848.056.6-
SqueezeSegV3 [38]55.991.774.863.426.489.092.529.638.736.533.082.058.765.445.646.220.159.449.658.9238
PointNet++ [26]20.172.041.818.75.662.353.70.91.90.20.246.513.830.00.91.00.016.96.08.95900
TangentConv [32]40.983.963.933.415.483.490.815.22.716.512.179.549.358.123.028.48.149.035.828.53000
PointASNL [43]46.887.474.324.31.883.187.939.00.025.129.284.152.270.634.257.60.043.957.836.9-
RandLA-Net [16]55.990.574.061.824.589.794.243.929.832.239.183.863.668.648.447.49.460.451.050.7880
KPConv [33]58.890.372.761.331.590.595.033.430.242.544.384.869.269.161.561.611.864.256.447.4-
PolarNet [45]54.390.874.461.721.790.093.822.940.330.128.584.065.567.843.240.25.661.351.857.562
JS3C-Net [41]66.088.972.161.931.992.595.854.359.352.946.084.569.867.969.565.439.970.860.768.7471
SPVNAS [31]67.090.275.467.621.891.697.256.650.650.458.086.173.471.067.467.150.366.964.367.3259
Cylinder3D [47]68.992.277.065.032.390.797.150.867.663.858.585.672.569.873.769.248.066.562.466.2131
RPVNet [40]70.393.480.770.333.393.597.644.268.468.761.186.575.171.775.974.443.472.164.861.4168
(AF)2-S3Net [6]70.892.076.266.845.892.594.340.263.081.440.078.668.063.176.481.777.769.664.073.3-
2DPASS [42]72.989.774.767.440.093.597.061.163.663.461.586.273.971.077.981.374.172.965.070.462
ProtoTransfer [Ours]73.691.577.571.542.892.997.557.168.476.068.086.774.872.680.076.061.470.765.866.762
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.542, + 0.892, + 0.568 + ], + "angle": 0, + "content": "Table 2. Semantic segmentation results on SemanticKITTI test set. Methods published before the submission deadline (08/03/2023) are listed. The bold numbers indicate the best results, and the blue numbers indicate the second best results." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.58, + 0.47, + 0.641 + ], + "angle": 0, + "content": "In order to have a fair comparison, most of the experimental setup and implementations are identical to the recent work [42]. During the model evaluation, the same test-time augmentation as in [42] is also used in our study." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.651, + 0.295, + 0.667 + ], + "angle": 0, + "content": "4.2. Results on Benchmarks" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.469, + 0.719 + ], + "angle": 0, + "content": "We compare the results of our ProtoTransfer with the published state-of-the-art methods on two large-scale benchmarks, i.e., nuScenes [4] and SemanticKITTI [2]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.902 + ], + "angle": 0, + "content": "NuScenes. As shown in Tab. 1, ProtoTransfer successfully outperforms all existing methods in terms of both mIoU and latency, demonstrating its efficacy and efficiency. Moreover, our ProtoTransfer not only outperforms single-modal approaches, but also surprisingly surpasses fusion-based methods which require both of LiDAR point clouds and images covering the whole FoV as input for the inference stage. In contrast, our method ProtoTransfer only takes point clouds as input and produces superior segmentation results. Compared to the recently proposed distillation-based method 2DPASS [42], our ProtoTransfer achieves \\(1.3\\%\\) performance gain, showing the success of explor" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.67 + ], + "angle": 0, + "content": "ing prototypes for knowledge transfer from multi-modal to single-modal. Besides, according to Tab. 1, we can find that our ProtoTransfer performs best on classes of small size and with sparse points, such as traffic-cone, motorcycle and construction vehicle, showing great potential in real-world practice." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.892, + 0.777 + ], + "angle": 0, + "content": "SemanticKITTI. We compare our ProtoTransfer with several previous state-of-the-arts works. From Tab. 2, we can see that our proposed ProtoTransfer still achieves the best performance among these methods, leaving a margin of \\(0.7\\%\\) compared with the distillation-based 2DPASS [42]. Similarly, ProtoTransfer achieves the best results on classes of small objects such as person and bicycle." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.71, + 0.803 + ], + "angle": 0, + "content": "4.3. Qualitative Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.903 + ], + "angle": 0, + "content": "We visualize the segmentation results on nuScenes validation set in Fig. 4. As can be observed, our ProtoTransfer achieves the most minor error prediction compared with the two comparison methods. In the first row of Fig. 4, the car and bus are close to each other, neither the baseline method nor the 2DPASS approach can produce an accurate segmen" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3342" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.127, + 0.093, + 0.306, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.126, + 0.194, + 0.305, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.126, + 0.289, + 0.305, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.144, + 0.39, + 0.273, + 0.403 + ], + "angle": 0, + "content": "(a) Error by baseline" + }, + { + "type": "image", + "bbox": [ + 0.306, + 0.093, + 0.486, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.306, + 0.193, + 0.485, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.306, + 0.289, + 0.485, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.335, + 0.39, + 0.466, + 0.403 + ], + "angle": 0, + "content": "(b) Error by 2DPASS" + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.093, + 0.666, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.193, + 0.666, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.289, + 0.666, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.496, + 0.39, + 0.661, + 0.403 + ], + "angle": 0, + "content": "(c) Error by ProtoTransfer" + }, + { + "type": "image", + "bbox": [ + 0.668, + 0.093, + 0.846, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.668, + 0.193, + 0.846, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.668, + 0.289, + 0.846, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.701, + 0.39, + 0.807, + 0.403 + ], + "angle": 0, + "content": "(d) Ground-truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.409, + 0.893, + 0.451 + ], + "angle": 0, + "content": "Figure 4. Qualitative results on nuScenes Lidarseg validation set. Red points are in red. Compared to baseline and the recently proposed distillation-based method 2DPASS [42], our ProtoTransfer achieves better segmentation on region boundaries (the first row), far objects (the second row) and small objects (the third row), thanks to the fully exploited and transferred multi-modal knowledge." + }, + { + "type": "table", + "bbox": [ + 0.122, + 0.46, + 0.426, + 0.521 + ], + "angle": 0, + "content": "
baselineLprotoupdate proto. bankmIoU
✓76.21
✓✓76.50
✓✓✓80.51
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.52, + 0.46, + 0.533 + ], + "angle": 0, + "content": "Table 3. Ablation study of each component in our ProtoTransfer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.547, + 0.47, + 0.682 + ], + "angle": 0, + "content": "tation for the points in the class of car, while our ProtoTransfer precisely segments all points belonging to the car. The second row displays a car far away from the ego-car, both of the two comparing methods mispredict the point clouds in the head area of the car and ProtoTransfer segments the car points perfectly again. The last row presents a pedestrian with only several LiDAR points. Thanks to the fully exploited and transferred multi-modal knowledge, our ProtoTransfer obtains the most accurate segmentation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.692, + 0.241, + 0.707 + ], + "angle": 0, + "content": "4.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.715, + 0.469, + 0.79 + ], + "angle": 0, + "content": "In this section, we present comprehensive ablation studies to examine the efficacy of each component in ProtoTransfer, ways of prototype bank construction, and distribution of feature representations. All the ablation studies are conducted on the nuScenes validation set." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Effects of each component. As shown in Tab. 3, introducing the proposed prototype-based loss term \\(\\mathcal{L}^{\\mathrm{proto}}\\) into the naive baseline method without updating the prototype bank can only bring minor performance gain. When the prototype bank is dynamically updated with the strategy presented in Sec. 3.4, the segmentation performance is significantly boosted which obviously demonstrates that the qual" + }, + { + "type": "table", + "bbox": [ + 0.536, + 0.46, + 0.858, + 0.608 + ], + "angle": 0, + "content": "
F3dF2dFfuseFfuse_umIoU
baseline76.21
(a)✓76.97
(b)✓75.35
(c)✓78.65
(d)✓✓77.11
(e)✓✓75.67
(f)✓✓✓75.58
(g)✓79.83
(h)✓✓80.51
" + }, + { + "type": "table_caption", + "bbox": [ + 0.54, + 0.608, + 0.85, + 0.621 + ], + "angle": 0, + "content": "Table 4. Abaltion study of inputs of prototype bank." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.634, + 0.734, + 0.649 + ], + "angle": 0, + "content": "ity of the prototype bank is critical." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.653, + 0.892, + 0.865 + ], + "angle": 0, + "content": "Input Source of Prototype Bank. As presented in Sec. 3, the inputs of the prototype bank include point-pixel fusion features, image features and point features. Tab. 4 shows an ablation study on the effect of different input combinations on final segmentation performance. As can be observed, building up the prototype bank using only point cloud features (a) can generate a \\(0.76\\%\\) performance gain over the baseline. We think it is because prototypes constructed from only point features can serve as cluster centers and using the proposed prototype-based loss \\(\\mathcal{L}^{\\mathrm{proto}}\\) can help point features become more discriminative as they are pushed to be closer to their cluster centers. However, only accumulating image features into the prototype bank leads to a \\(0.86\\%\\) performance drop, we postulate it may be because there is" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.9 + ], + "angle": 0, + "content": "5Please note the pseudo-labeling scheme presented in Sec. 3.4 can also be used here to exploit unmatched image features." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3343" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.464, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.288, + 0.47, + 0.318 + ], + "angle": 0, + "content": "Figure 5. Ablation study of \\(\\lambda\\) in Eq. (8). \\(\\lambda = 0.2\\) is set as default in ProtoTransfer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.473, + 0.512 + ], + "angle": 0, + "content": "a distribution gap between image features and point cloud features and thus it is unwise to force point cloud features to imitate image feature cluster centers. On the contrary, when fusing the point-pixel matched features and only using the fusion features for the prototype bank (c) excels \\(2.44\\%\\) over the baseline, demonstrating the effectiveness of knowledge transfer from multi-modal to the single LiDAR modal. As shown by Tab. 4 (h), when the fusion features \\(\\bar{F}^{\\mathrm{fuse}}\\) and \\(\\bar{F}^{\\mathrm{fuse.u}}\\) are fully explored and accumulated into the prototype bank, our ProtoTransfer reaches the best mIoU of \\(80.51\\%\\). This ablation study clearly shows that the input source plays a key role in the quality of the prototype bank." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.473, + 0.851 + ], + "angle": 0, + "content": "Fusion Strategy of Features for Prototype Bank. As illustrated in Fig. 3 and Sec. 3.4, we calculate class-mean embeddings for the unmatched pixel features and point features, respectively. Then we concatenate these two embeddings and fuse them by reusing the MLP in Eq. (1). The fused embedding \\(\\bar{F}^{\\mathrm{fuse - u}}\\) is finally accumulated to the prototype bank together with the point-pixel matched fusion features \\(\\bar{F}^{\\mathrm{fuse}}\\). To demonstrate the improvement not only comes from the additional image and point features but also comes from the cleverly designed fusion strategy, we use a naive way to have an investigation, i.e., any combinations among the point-pixel naturally matched fusion feature \\(\\bar{F}^{\\mathrm{fuse}}\\), image feature \\(F^{2\\mathrm{d}}\\) and point feature \\(F^{3\\mathrm{d}}\\) in the way of simple summation and use moving average to accumulate them into the prototype bank as presented in Tab. 4 (d)~(f). We can find that this naive summation of all three features (f) reduces the mIoU to \\(75.58\\%\\). We owe this to the large distribution gap between different kinds of features which cannot be handled in the naive sum-up way. In contrast, our ProtoTransfer reuses the MLP to map the unmatched image features to the fusion feature space, thus successfully bypassing this problem." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Effect of \\(\\lambda\\) Selection. We have experimented with different values of \\(\\lambda\\) in Eq. (8) and the results are presented in Fig. 5. As can be observed, our ProtoTransfer achieves the best per" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.097, + 0.698, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.576, + 0.211, + 0.643, + 0.223 + ], + "angle": 0, + "content": "(a) Baseline" + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.097, + 0.89, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.751, + 0.211, + 0.851, + 0.223 + ], + "angle": 0, + "content": "(b) ProtoTransfer" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.226, + 0.895, + 0.298 + ], + "angle": 0, + "content": "Figure 6. Feature representation visualization of (a) the baseline and (b) our ProtoTransfer. Outlier points have been pointed out by the red arrow. The displayed category ID and their corresponding semantic category is {1: \"barrier\", 2: \"bicycle\", 3: \"bus\", 8: \"traffic cone\", 9: \"trailer\", 10: \"truck)}." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.318, + 0.895, + 0.41 + ], + "angle": 0, + "content": "formance when \\(\\lambda = 0.2\\) which reveals that the unmatched-pixel-feature-based fusion embedding \\(\\bar{F}^{\\mathrm{fuse\\_u}}\\) plays a more important role. Note that when \\(\\lambda = 0\\), i.e., using only \\(\\bar{F}^{\\mathrm{fuse\\_u}}\\), is able to achieve a satisfactory segmentation accuracy, demonstrating the benefits brought by the unmatched image features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.422, + 0.895, + 0.589 + ], + "angle": 0, + "content": "Distribution of Feature Representation. The essence of introducing the prototype-based loss term \\(\\mathcal{L}^{\\mathrm{proto}}\\) in our method is to encourage the point features to be close to the same-class multi-modal prototype while staying far away from the other-class prototypes. Hence, it is important to study the impact of prototypes on feature distribution. As can be observed in Fig. 6 (a), outlier points appear in the feature distribution of the baseline method, while our ProtoTransfer is able to produce more compact feature distributions for all semantic classes, demonstrating the effectiveness of our method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.616, + 0.62, + 0.632 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.646, + 0.895, + 0.829 + ], + "angle": 0, + "content": "This work presents a cross-modal knowledge transfer method dubbed ProtoTransfer for point cloud semantic segmentation. ProtoTransfer achieves remarkable segmentation performance but keep a single LiDAR inference speed. By accumulating the fusion features into a prototype bank, all LiDAR points can learn from their class-specific prototypes, thus being well benefited. The unmatched image features are further explored and exploited via a pseudolabeling scheme and a novel prototype bank update strategy. Through extensive experimental results on nuScenes and SemanticKITTI dataset, the efficacy of our method has been successfully demonstrated." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported by Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), and the Fundamental Research Funds for the Central Universities." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "3344" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Inigo Alonso, Luis Riazuelo, Luis Montesano, and Ana C Murillo. 3d-mininet: Learning a 2d representation from point clouds for fast and efficient 3d lidar semantic segmentation. arXiv preprint arXiv:2002.10893, 2020." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.174, + 0.472, + 0.243 + ], + "angle": 0, + "content": "[2] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Jurgen Gall. 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Recent advances in point cloud segmentation distill knowledge from strictly aligned point-pixel fusion features while leaving a large number of unmatched image pixels unexplored and unmatched LiDAR points under-benefited. In this paper, we propose a novel approach, named ProtoTransfer, which not only fully exploits image representations but also transfers the learned multi-modal knowledge to all point cloud features. Specifically, based on the basic multi-modal learning framework, we build up a class-wise prototype bank from the strictly-aligned fusion features and encourage all the point cloud features to learn from the prototypes during model training. Moreover, to exploit the massive unmatched point and pixel features, we use a pseudo-labeling scheme and further accumulate these features into the class-wise prototype bank with a carefully designed fusion strategy. Without bells and whistles, our approach demonstrates superior performance over the published state-of-the-arts on two large-scale benchmarks, i.e., nuScenes and SemanticKITTI, and ranks 2nd on the competitive nuScenes Lidarseg challenge leaderboard. + +# 1. Introduction + +Semantic segmentation on point cloud [6, 15, 37, 40] has attracted increasing attention from the computer vision community for its crucial role in scene understanding of 3D space. Although LiDAR point cloud can provide accurate location and depth information of interested scenes, the sparse and textureless shortages inevitably restrict its semantic segmentation performance. On the other hand, 2D images consist of dense pixels with rich color and subtle + +![](images/1d5e040b3edb48bc236cb7e5381956b02698f9e285487356db8d16db4a0c7738.jpg) +(a) Point-pixel matching and feature fusion + +![](images/8e7ea3925b02ca12dcd239659ff378a67ab193eb802ea310579795199fde9e26.jpg) +(b) Distillation-based methods + +![](images/1a56e680051605d8b9940b1f2831c21b5867b3da7832961dd3b7ae9f680f7a76.jpg) +(c) Our ProtoTransfer +Figure 1. (a) Point-pixel matching and feature fusion: only features of strictly matched point-pixel pairs can be fused. (b) Distillation-based methods are only performed between fusion prediction and the corresponding matched point prediction while other unmatched points have no chance to mimic the fusion prediction. (c) Our ProtoTransfer performs knowledge transfer from prototype bank to all point features directly without being restricted by matching requirements. The prototype bank is updated using fusion, point, and unmatched image features. + +textures [34]. Therefore, incorporating these two complementary modals altogether can be a more plausible solution. + +Recently, there are mainly two stream approaches of utilizing multi-modal data, i.e., fusion-based methods [10, 50] and distillation-based methods [42]. The former methods project point clouds to the camera coordinate to obtain a point-to-pixel mapping, based on which point features are fused with corresponding image features to produce the final point-wise segmentation during both the training and evaluation phases. Although robust and accurate segments are achieved by fusing different sensors, the fusion-based methods may suffer from heavy memory and time consumption for processing these two modal data simul + +taneously. In order to benefit from multi-modal fusion while bypassing the computation burden, the latter methods [42] propose to utilize the distillation technique to transfer knowledge learned from cross-modal fusion at the training stage and discard the fusion module for evaluation. The impressive segmentation performance suggests the feasibility of the methods in this stream. Therefore, this paper further explores this research direction. + +Unlike common distillation approaches in image classification tasks [14, 44], distilling from multi-modal to the single LiDAR modal may meet quite different pitfalls: (1) Not all LiDAR points can be used in knowledge distillation because LiDAR-to-image is partially matched. Due to the difference in the way sensors collect data, not all the LiDAR points can be aligned to the dense image pixels. For example, we empirically find that only around $16.07\%$ LiDAR points in SemanticKITTI dataset can be matched to corresponding image pixels, and Fig. 1(a) also demonstrates this observation. Thus, classic logit-/probability-style distillation strategies [42] can only be performed on the well-aligned point clouds, leading to a sub-optimal knowledge distillation. (2) Massive image pixels are overlooked. Since only partial image pixels1 will contribute to the modal fusion based on the above matching constraints, a large number of pixels are not used in knowledge distillation, resulting in a great loss of rich semantic information in dense pixels. + +In this paper, we propose a novel approach for point cloud semantic segmentation which successfully avoids the above pitfalls. Specifically, following the existing work [17, 34, 42], we first construct a modal fusion module to combine the feature representations of matched LiDAR points and image pixels. Next, in order to transfer the knowledge from the fusion module to each point feature representation, we create a class-wise prototype bank to accumulate the fusion features learned in the fusion module and encourage the similarity between features of all LiDAR points and corresponding-class prototypes as high as possible. By this means, every LiDAR point has a fair chance to mimic the fusion features as shown in Fig. 1(c), and we dub our method as ProtoTransfer. Moreover, to make full use of semantic information inherited in dense image pixels, we propose to incorporate the image features into the class-wise prototype bank through a cleverly designed fusion strategy. Since images in the point cloud semantic segmentation datasets usually lack per-pixel annotations, we further use a pseudo-labeling scheme to generate pseudolabels for each pixel and thus make the update of pixelfeature into class-wise prototypes become possible. In summary, the main contributions of this paper are three aspects: +- We investigate the pitfalls of point cloud semantic segmentation on distillation-based methods and find that a + +large number of image features are not well-utilized and point features are not well distillation-benefited. + +- We introduce the prototype bank concept into point cloud semantic segmentation and propose a novel approach ProtoTransfer to successfully overcome the above pitfalls. +- We conduct experiments on both SemanticKITTI and nuScenes benchmarks to demonstrate the effectiveness of our approach and also achieve a 2nd place on the competitive nuScenes Lidarseg leaderboard. + +# 2. Related Work + +Multi-Modal 3D Semantic Segmentation. Since different modal can provide complimentary information to each other, multi-modal point cloud semantic segmentation attracts increasing attention [8, 20, 24]. RGBAL [8] casts RGB images to a polar-grid mapping representation and designs an early-mid-level hybrid fusion architecture. Recently, PMF [50] projects LiDAR points to camera coordinates, which is called perspective projection [25]. Then, they use two 2D U-net [27] to extract the image and point features. The multi-scale image and point features in both U-nets are fused to produce better segmentation results. Though satisfactory performance are achieved, these methods need multi-modal inputs during both training and inference phases, which is time-/memory-consuming. + +Prototype Networks. Prototype-based learning methods has been widely used in machine learning [9, 11, 28]. Recently, a surge of attention is paid to employ prototype networks on various tasks, presenting great potential in few-shot learning [29] and zero-shot learning[18, 36]. Moreover, [48] shows a prototype view of image semantic segmentation network. Another prototype-based semisupervised method is also proposed [39]. Our work sheds light on the possibility of using prototypes for knowledge transfer from multi-modal to single-modal. + +Cross-Modal Knowledge Transfer. Knowledge distillation, first proposed by Hinton et al. [14], is a common knowledge transfer method, which pushes the student network mimic the soft logits of the teacher network. Very recently, knowledge distillation is introduced into perception tasks in autonomous driving, such as 3D object detection [7, 19, 46] and point cloud segmentation [42]. During training, they use distillation to transfer multi-modal knowledge learned by the multi-modal teacher to a single-modal student. However, these methods suffers from strict point-pixel alignment, leading to massive unmatched image pixels unexplored and points under-benefited. Our work performs knowledge transfer in another way. Contrary to [42], we construct a prototype bank from fusion and unmatched image features and encourage all the point cloud features to learn from the prototypes during model training, thus fully exploiting and transferring multi-modal knowledge. + +![](images/f7760b27618bfcd3afac9a6bbd5472f1b5c0cd1f1ba8a285d164a95734adbe83.jpg) +Figure 2. Pipeline overview of our ProtoTransfer. The model first uses modal-specific backbones to generate image features $F^{2\mathrm{d}}$ and point features $F^{3\mathrm{d}}$ and feeds them into the point-pixel matching module to generate matched point feature $F^{3\mathrm{d},\mathrm{m}}$ , matched and unmatched image features $F^{2\mathrm{d},\mathrm{m}}$ and $F^{2\mathrm{d},\mathrm{u}}$ , respectively. Then modal-specific segmentation heads are used to produce predictions for loss calculation, i.e., $\mathcal{L}^{3\mathrm{d}}, \mathcal{L}^{2\mathrm{d}}$ and $\mathcal{L}^{\mathrm{fuse}}$ , where $\mathcal{L}^{\mathrm{fuse}}$ will update the feature $F^{\mathrm{fuse}}$ fused from $F^{2\mathrm{d},\mathrm{m}}$ and $F^{3\mathrm{d},\mathrm{m}}$ . To take advantage of the fusion features, we introduce a class-wise prototype bank whose input source includes features $F^{3\mathrm{d}}$ , $F^{\mathrm{fuse}}$ and $F^{2\mathrm{d},\mathrm{u}}$ and propose a loss $\mathcal{L}^{\mathrm{proto}}$ to transfer fusion knowledge to all point features. Please note 2D&Fusion GT is derived from the 3D GT based on point-pixel matching. + +# 3. Methodology + +# 3.1. Framework Overview + +Given a LiDAR point cloud frame with $N$ unordered points $P = \{p_i\in \mathbb{R}^{d_{\mathrm{in}}}\}_{i = 1}^N$ where $d_{\mathrm{in}}$ is input feature dimension, the goal of point cloud semantic segmentation is to assign a single class label $c\in \{1,2\dots ,C\}$ to each point. To make up for the sparsity and lack of texture of point clouds collected in outdoor scenes [42], the other modal of the corresponding scenes, raw images $I\in \mathbb{R}^{W\times H\times 3}$ , where $W,H$ denote the resolution of a given image, are also provided for model learning to achieve a better segmentation performance. + +As the overall structure presented in Fig. 2, the main contributions of our approach are (1) introducing a class-wise prototype bank for knowledge transfer from a fusion modal to all LiDAR points and (2) proposing to make full use of image features to enhance the prototype quality. Specifically, paired point cloud and image are first fed into modal-specific backbones to extract feature representations respectively. Next, based on the given LiDAR-to-image transformation matrix, features are fused for matched LiDAR point and corresponding image pixels, as done in previous modal-fusion-related work [17, 34, 42]. Due to the differing data acquisition mechanisms of different modal sensors, the matching rate between LiDAR points and image pixels is often quite low. Instead of distilling knowledge solely for the limited matched LiDAR points, we propose a novel knowledge transfer module that can enable unmatched points to also benefit from fused feature representations. With this framework, we explore and exploit unmatched image pixels to further enhance the overall point + +cloud segmentation performance. + +During inference, the enhanced point cloud segmentation branch can produce accurate segmentation results without the image backbone and multi-modal fusion, and thus challenges can be tackled within a real-time speed. + +# 3.2. Cross-Modal Prototype Transfer + +Considering the data structures of point cloud and image pixels are totally different, various network architectures are utilized to extract feature representations for the two modal inputs independently. Specifically, ResNet34 [13] encoder and FCN [23] decoder are used for 2D images to extract dense-grid features $F^{2\mathrm{d}} \in \mathbb{R}^{W \times H \times D_{2\mathrm{d}}}$ , and a sparse convolution [12] based hierarchical point-voxel backbone [42] are designed for 3D point cloud to generate point-wise features $F^{3\mathrm{d}} \in \mathbb{R}^{N \times D_{3\mathrm{d}}}$ . Since LiDAR points and image pixels are not naturally aligned due to the differences in data collection of LiDAR and camera devices, LiDAR-camera transformation matrix is used to find the point-to-pixel correspondence3 and further obtain the matched pixel feature $F^{2\mathrm{d\_m}}$ and matched point features $F^{2\mathrm{d\_m}}$ . Following the previous work [42], we concatenate the matched point-pixel features and use a multi-layer perceptron (MLP) to obtain the fusion feature + +$$ +F ^ {\mathrm {f u s e}} = \operatorname {M L P} \left(\operatorname {c a t} \left(F ^ {2 \mathrm {d}. \mathrm {m}}, F ^ {3 \mathrm {d}. \mathrm {m}}\right)\right) \tag {1} +$$ + +where $\odot$ is Hadamard product of two matrices. The MLP is used to reduce feature dimension to $D_{3\mathrm{d}}$ and obtain $F^{\mathrm{fuse}}$ . With LiDAR per-point ground truth $Y^{3\mathrm{d}}$ , the fusion branch is got supervised + +$$ +\mathcal {L} ^ {\text {f u s e}} = \mathcal {L} _ {\mathrm {C E}} \left(h ^ {\text {f u s e}} \left(F ^ {\text {f u s e}}\right), \hat {Y}\right) + \mathcal {L} _ {\text {L o v a s z}} \left(h ^ {\text {f u s e}} \left(F ^ {\text {f u s e}}\right), \hat {Y}\right) \tag {2} +$$ + +where $h^{\mathrm{fuse}}$ is the segmentation head of fusion branch. $\hat{Y}$ is the subset of $Y^{3\mathrm{d}}$ , representing the ground truth for matched points. $\mathcal{L}_{\mathrm{CE}}$ and $\mathcal{L}_{\mathrm{Lovasz}}$ denote the cross entropy loss and the IoU-style Lovasz loss [3] respectively. + +Attributed to the integration of rich semantic information from 2D images, the segmentation performance of the fusion branch is superior to the LiDAR-sole branch (the bottom branch in Fig. 2). In order to make a single LiDAR point cloud segmentation benefit from the fusion branch, one straightforward way is to introduce a knowledge distillation loss between these two branches, as done in [42]. However, due to the matched point-pixel being limited, only partial point features can benefit from the fusion features and leave massive unmatched points under-benefited. + +To bypass the strict matching restriction, we introduce a class-wise prototype bank to accumulate the fusion features during model optimization. Such a prototype bank can be served as a parameter-free segmentation head to regularize the distribution of all point features with LiDAR ground truth + +$$ +\mathcal {L} ^ {\text {p r o t o}} = \frac {1}{N} \sum_ {i = 1} ^ {N} \mathcal {L} _ {\mathrm {C E}} \left(p _ {c _ {i}}, c _ {i}\right) + \mathcal {L} _ {\text {L o v a s z}} \left(p _ {c _ {i}}, c _ {i}\right), \tag {3} +$$ + +where $p_{c_i} \coloneqq p(y = c_i | F_i^{3\mathrm{d}}) = \frac{\exp(\cos(\mathsf{p}_{c_i}, F_i^{3\mathrm{d}}) / T)}{\sum_{j=1}^{C} \exp(\cos(\mathsf{p}_j, F_i^{3\mathrm{d}}) / T)}$ + +where $F_{i}^{3\mathrm{d}}$ and $c_{i}$ denote the feature and semantic label of $i$ -th point respectively. $\mathsf{p}_{c_i} \in \mathbb{R}^{D_{3\mathrm{d}}}$ represents the prototype in class $c_{i}$ . $\cos$ is the cosine function to calculate the similarity of the prototype and point feature. $T$ is the temperature parameter to adjust the scale of similarity measurement and is empirically set to 0.1 in our study. + +The proposed cross-modal prototype-based knowledge transfer module encourages the point features to be close to the same-class prototype while staying far away from other-class prototypes. Therefore, through the class-wise prototype bank as a bridge, we successfully transfer the knowledge learned from the fusion feature to the whole point cloud and we term our method as ProtoTransfer. + +# 3.3. Prototype Bank Initialization and Update + +In our work, the prototype bank is designed to be non-parametric and non-learnable and thus the quality of the prototype bank plays a critical role in the success of cross-modal knowledge transfer. Instead of using random vectors to initialize the prototype bank at the beginning of model training, we propose to use the fusion features of the first few iterations to warm up the class-wise prototype bank for a stable optimization procedure. + +Meanwhile, since the initial prototype bank can not capture the distribution of fusion features, we also dynamically update the prototype bank throughout the training stage. + +![](images/022dc0f98c60065388fe9216e2fa563993a6529663510b900aedb37c5bf751d7.jpg) +Figure 3. Prototype bank update demonstration. The fusion feature $F^{\mathrm{fuse}}$ , unmatched image feature $F^{2\mathrm{d.u}}$ and point feature $F^{3\mathrm{d}}$ are respectively clustered into class-wise feature sets using corresponding GT or pseudo-label obtained with Eq. (6). Then the feature sets are class-wise averaged to produce class-mean embeddings. $\bar{F}^{2\mathrm{d.u}}$ and $\bar{F}^{3\mathrm{d}}$ are fused to get $\bar{F}^{\mathrm{fuse\_u}}$ . Finally, both $\bar{F}^{\mathrm{fuse}}$ and $\bar{F}^{\mathrm{fuse\_u}}$ are accumulated into the class-wise prototype bank. + +Given all fusion features $\{F_i^{\mathrm{fuse}}\}$ , we can use their corresponding class labels $\{c_i\}$ to cluster the fusion features into class-wise feature set. As shown in the top branch of Fig. 3, the fusion feature set of class $k$ can be obtained by + +$$ +\Omega_ {k} ^ {\text {f u s e}} = \left\{F _ {i} ^ {\text {f u s e}} \mid c _ {i} = k \right\}. \tag {4} +$$ + +We then use the moving average trick to update the class-specific prototype $\mathfrak{p}_k$ of class $k$ + +$$ +\mathbf {p} _ {k} \leftarrow \alpha \cdot \mathbf {p} _ {k} + (1 - \alpha) \cdot \bar {F} _ {k} ^ {\text {f u s e}}, \tag {5} +$$ + +where $\bar{F}_k^{\mathrm{fuse}} = \frac{1}{\|\Omega_k^{\mathrm{fuse}}\|}\sum_j\Omega_{k,j}^{\mathrm{fuse}}$ + +where $\alpha$ is a fixed hyper-parameter to control the prototype update speed and is empirically set as 0.999 in our study. $\bar{F}_k^{\mathrm{fuse}}$ is the class-mean embedding of fusion features in class $k$ . + +# 3.4. Unmatched Image Features Exploration and Exploitation + +Although prototype-based knowledge transfer has helped all point features benefit from the fusion features and enhanced the point segmentation performance, the fusion features, which are the knowledge source of the prototype bank, are only available on matched point-pixel pairs. Since the point-pixel matching rate is quite low, the rich semantic information lying in a large amount of unmatched image pixels is not explored and exploited. + +However, the exploitation of unmatched image pixels is non-trivial and there are at least two challenges: 1) Naturally lacking matching points for modal fusion. Since modal fusion requires well-matched point-pixel features, it is difficult to construct matching points for unmatched pixels. + +2) Hardly obtaining semantic labels of unmatched pixels. Since 2D images are provided without annotations and it can be costly to additionally annotate these dense pixels, the semantic labels of unlabeled pixels are thus unknown without the matching correspondence from the LiDAR point cloud ground truth. + +Based on our proposed cross-modal prototype transfer framework, we further design a novel strategy to incorporate the unmatched pixel features into the prototype bank to improve the transferred knowledge, and Fig. 3 presents an overview. Specifically, in order to solve the challenge 2), we formulate the image pixel class label generation problem as a weakly-/semi-supervised task [5, 30], i.e., taking the LiDAR-to-image matched pixels as labeled samples and taking other unmatched pixels as unlabeled ones. Considering the segmentation head $h^{2d}$ for image input has been optimized on features of matched pixels4, we can generate posterior probability estimation for unmatched pixels + +$$ +p (y | F ^ {2 d. u}) = \operatorname {s o f t m a x} \left(h ^ {2 d} \left(F ^ {2 d. u}\right)\right), +$$ + +where $F^{2\mathrm{d.u}}$ is the features of unmatched pixels. Then the pseudo-labels can be obtained for these unmatched pixels when their maximal posterior probability is greater than a pre-defined confidence threshold $\delta$ (set as 0.8 in our study) + +$$ +y ^ {2 \mathrm {d} - \mathrm {u}} = \operatorname {a r g m a x} _ {c} p (y = c | F ^ {2 \mathrm {d} - \mathrm {u}}), \tag {6} +$$ + +$$ +\text {o n l y i f} \quad p (y = y ^ {2 d. u} | F ^ {2 d. u}) \geq \delta . +$$ + +Given the pseudo-labeled unmatched pixels, it is still non-trivial to fuse the features of unmatched pixels and points due to the challenge 1) mentioned above. One straightforward way is to directly add the features of unmatched pixels to the prototype bank, empirical results in Tab. 4 show that this simple way can not bring a performance gain and we postulate that it may be caused by the distribution gap between image features and prototypes. Alternatively, we propose to first calculate a class-mean embedding $\bar{F}_k^{2\mathrm{d\_u}}$ of unmatched pixel features in the same pseudo-label $k$ + +$$ +\bar {F} _ {k} ^ {\mathrm {2 d \_ u}} = \frac {1}{\| \Omega_ {k} ^ {\mathrm {2 d \_ u}} \|} \sum_ {j} \Omega_ {k, j} ^ {\mathrm {2 d \_ u}}, +$$ + +$$ +\text {w h e r e} \quad \Omega_ {k} ^ {2 d. u} = \left\{F _ {i} ^ {2 d. u} \mid y _ {i} ^ {2 d. u} = k \right\}, +$$ + +$\Omega_{k}^{2\mathrm{d.u}}$ is class-wise unmatched image feature set and is obtained using pseudo labels but not ground-truth as in Eq. (4). And the class-mean embedding $\bar{F}^{3\mathrm{d}}$ of point features can be obtained from $F^{3\mathrm{d}}$ with LiDAR ground truth. Then, modal fusion can be performed between class-mean embeddings + +of the same class + +$$ +\bar {F} ^ {\text {f u s e - u}} = \operatorname {M L P} \left(\operatorname {c a t} \left(\bar {F} ^ {2 \mathrm {d} - \mathrm {u}}, \bar {F} ^ {3 \mathrm {d}}\right)\right), \tag {7} +$$ + +where the MLP shares parameter with the one in Eq. (1). Finally, the class-wise prototype bank updating in Eq. (5) can be extended as + +$$ +\mathfrak {p} _ {k} \leftarrow \alpha \cdot \mathfrak {p} _ {k} + (1 - \alpha) \cdot (\lambda \cdot \bar {F} _ {k} ^ {\text {f u s e}} + (1 - \lambda) \cdot \bar {F} _ {k} ^ {\text {f u s e - u}}), \tag {8} +$$ + +where $\lambda$ is the balance weight of these two fusion features. + +Since the pseudo-labeling scheme for unmatched pixels may not be activated at the beginning of model training, the prototype bank is still initialized with the method mentioned in Sec. 3.3. + +# 3.5. Overall Objective Function + +Apart from the loss terms in Eq. (2) and Eq. (3), we also have separate losses $\mathcal{L}^{3\mathrm{d}}$ and $\mathcal{L}^{2\mathrm{d}}$ for LiDAR point cloud input and image input respectively. Both of these two losses are composed of a cross-entropy loss and a Lovasz loss as those in Eq. (2). Finally, the overall object function is the weighted sum of these loss terms + +$$ +\mathcal {L} = \omega^ {\mathrm {3 d}} \mathcal {L} ^ {\mathrm {3 d}} + \omega^ {\mathrm {2 d}} \mathcal {L} ^ {\mathrm {2 d}} + \omega^ {\text {f u s e}} \mathcal {L} ^ {\text {f u s e}} + \omega^ {\text {p r o t o}} \mathcal {L} ^ {\text {p r o t o}}, +$$ + +where we empirically set $\omega^{3\mathrm{d}} = 2.0$ and $\omega^{2\mathrm{d}} = \omega^{\mathrm{fuse}} = \omega^{\mathrm{proto}} = 1.0$ in our study. + +# 4. Experiments + +In this section, we first provide details of our experimental setup. Then we evaluate ProtoTransfer on both nuScenes dataset and SemanticKITTI dataset. Finally, extensive ablation studies of our approach are presented. + +# 4.1. Experimental Setup + +Datasets. NuScenes [4] collects 1000 driving scenes from various locations in Boston and Singapore using 1 LiDAR and 6 cameras covering $360^{\circ}$ FoV. According to the official setting, it is split into training, validation and test set as 700, 150 and 150 scenes. For point cloud semantic segmentation task, it annotates labels for 16 classes under different traffic and weather conditions. SemanticKITTI [2] contains 22 LiDAR sequences numbered from 00 to 21, in which sequence 08 is officially selected as validation set, sequence 00-10 except 08 is training set and 11-21 is test set. Unlike nuScenes, SemanticKITTI has only two front-view cameras. + +Evaluation Metric. Following previous work [49, 42], we calculate intersection-over-union (IoU) of each class and mean IoU (mIoU) of all classes, which is formulated as $\mathrm{mIoU} = \frac{1}{C}\sum_{c = 1}^{C}\frac{\mathrm{TP}_c}{\mathrm{TP}_c + \mathrm{FP}_c + \mathrm{FN}_c}$ , where $\mathrm{TP}_c$ , $\mathrm{FP}_c$ and $\mathrm{TP}_c$ denotes the number of true positive, false positive and false negative points of class $c$ . + +
MethodsinputmIoUbarrierbicyclebuscarconstructionmotorcyclepedestriantraffic conetrailertruckdrivableother flatsidewalkterrainmannadevegetationLatency (ms)
PolarNet [45]L69.472.216.877.086.551.169.764.854.169.763.596.667.177.772.187.184.5-
JS3C-Net [41]L73.680.126.287.884.555.272.671.366.376.871.296.864.576.974.187.586.1-
Cylinder3D [47]L77.282.829.884.389.463.079.377.273.484.669.197.770.280.375.590.487.663
AMVNet [21]L77.380.632.081.788.967.184.376.173.584.967.397.567.479.475.591.588.785
SPVCNN [31]L77.480.030.091.990.864.779.075.670.981.074.697.469.280.076.189.387.163
(AF)2-S3Net [6]L78.378.952.289.984.277.474.377.372.083.973.897.166.577.574.087.786.8270
PMF [50]L+C77.082.040.081.088.064.079.080.076.081.067.097.068.078.074.090.088.0125*
2D3DNet [10]L+C80.083.059.488.085.163.784.482.076.084.871.996.967.479.876.092.189.2-
2DPASS [42]L80.881.755.392.091.873.386.578.572.584.775.597.669.179.975.590.288.044
ProtoTransfer [Ours]L82.181.155.593.991.577.987.382.778.985.176.597.669.879.675.991.589.144
+ +Table 1. Semantic segmentation results on nuScenes test set. Methods published before the submission deadline (08/03/2023) are listed. L and C respectively denote LiDAR and camera. * The latency of PMF [50] is tested without TensorRT acceleration. The bold numbers indicate the best results, and the blue numbers indicate the second best results. + +
MethodmIoUroadsidewalkparkingother-groundbuildingcartruckbicyclemotorcycleother-vehiclevegetationtrunkterrainpersonbicyclistmotorcyclistfencepoletraffic signlatency (ms)
SqueezeSegV2 [35]39.788.667.645.817.773.781.813.418.517.914.071.835.860.220.125.13.941.120.226.3-
DarkNet53Seg [2]49.991.874.664.827.984.186.425.524.532.722.678.350.164.036.233.64.755.038.952.2-
RangeNet53++ [25]52.291.875.265.027.887.491.425.725.734.423.080.555.164.638.338.84.858.647.955.983.3
3D-MiniNet [1]55.891.674.564.225.489.490.528.542.342.129.482.860.866.747.844.114.560.848.056.6-
SqueezeSegV3 [38]55.991.774.863.426.489.092.529.638.736.533.082.058.765.445.646.220.159.449.658.9238
PointNet++ [26]20.172.041.818.75.662.353.70.91.90.20.246.513.830.00.91.00.016.96.08.95900
TangentConv [32]40.983.963.933.415.483.490.815.22.716.512.179.549.358.123.028.48.149.035.828.53000
PointASNL [43]46.887.474.324.31.883.187.939.00.025.129.284.152.270.634.257.60.043.957.836.9-
RandLA-Net [16]55.990.574.061.824.589.794.243.929.832.239.183.863.668.648.447.49.460.451.050.7880
KPConv [33]58.890.372.761.331.590.595.033.430.242.544.384.869.269.161.561.611.864.256.447.4-
PolarNet [45]54.390.874.461.721.790.093.822.940.330.128.584.065.567.843.240.25.661.351.857.562
JS3C-Net [41]66.088.972.161.931.992.595.854.359.352.946.084.569.867.969.565.439.970.860.768.7471
SPVNAS [31]67.090.275.467.621.891.697.256.650.650.458.086.173.471.067.467.150.366.964.367.3259
Cylinder3D [47]68.992.277.065.032.390.797.150.867.663.858.585.672.569.873.769.248.066.562.466.2131
RPVNet [40]70.393.480.770.333.393.597.644.268.468.761.186.575.171.775.974.443.472.164.861.4168
(AF)2-S3Net [6]70.892.076.266.845.892.594.340.263.081.440.078.668.063.176.481.777.769.664.073.3-
2DPASS [42]72.989.774.767.440.093.597.061.163.663.461.586.273.971.077.981.374.172.965.070.462
ProtoTransfer [Ours]73.691.577.571.542.892.997.557.168.476.068.086.774.872.680.076.061.470.765.866.762
+ +Table 2. Semantic segmentation results on SemanticKITTI test set. Methods published before the submission deadline (08/03/2023) are listed. The bold numbers indicate the best results, and the blue numbers indicate the second best results. + +In order to have a fair comparison, most of the experimental setup and implementations are identical to the recent work [42]. During the model evaluation, the same test-time augmentation as in [42] is also used in our study. + +# 4.2. Results on Benchmarks + +We compare the results of our ProtoTransfer with the published state-of-the-art methods on two large-scale benchmarks, i.e., nuScenes [4] and SemanticKITTI [2]. + +NuScenes. As shown in Tab. 1, ProtoTransfer successfully outperforms all existing methods in terms of both mIoU and latency, demonstrating its efficacy and efficiency. Moreover, our ProtoTransfer not only outperforms single-modal approaches, but also surprisingly surpasses fusion-based methods which require both of LiDAR point clouds and images covering the whole FoV as input for the inference stage. In contrast, our method ProtoTransfer only takes point clouds as input and produces superior segmentation results. Compared to the recently proposed distillation-based method 2DPASS [42], our ProtoTransfer achieves $1.3\%$ performance gain, showing the success of explor + +ing prototypes for knowledge transfer from multi-modal to single-modal. Besides, according to Tab. 1, we can find that our ProtoTransfer performs best on classes of small size and with sparse points, such as traffic-cone, motorcycle and construction vehicle, showing great potential in real-world practice. + +SemanticKITTI. We compare our ProtoTransfer with several previous state-of-the-arts works. From Tab. 2, we can see that our proposed ProtoTransfer still achieves the best performance among these methods, leaving a margin of $0.7\%$ compared with the distillation-based 2DPASS [42]. Similarly, ProtoTransfer achieves the best results on classes of small objects such as person and bicycle. + +# 4.3. Qualitative Evaluation + +We visualize the segmentation results on nuScenes validation set in Fig. 4. As can be observed, our ProtoTransfer achieves the most minor error prediction compared with the two comparison methods. In the first row of Fig. 4, the car and bus are close to each other, neither the baseline method nor the 2DPASS approach can produce an accurate segmen + +![](images/00a113ed776bbe753ab91d9a3a760b4936025cd13d7d2789627d298a79ab7eb6.jpg) + +![](images/3a77602ddeb243d5a11bcdf9015ec203ba7c8d686360129a295c12ce7e11622c.jpg) + +![](images/5b7e755d21d945ef46a16cba02b43dbb7f285ebaa2865de22aab4405d780d2df.jpg) +(a) Error by baseline + +![](images/c1505c94d54497f7979495736ee8162476ae7fd575d33af8df69cf11a0916be7.jpg) + +![](images/ed0f7c2726b947d2b725efb94feb9e4e29d2f698ce66c9367adb6794b9880092.jpg) + +![](images/44142d1a64538ecc71734ac50a7547949a079ee83b0a3a0a10cc51e5e71f6ca0.jpg) +(b) Error by 2DPASS + +![](images/6e9aec90110f0c2e2e4fa03a5cc1e1598a07a280fd05ff087c684f1a96306538.jpg) + +![](images/05957da15639b2d6815ef5ba29f47eb95bbf0b706ed9dad07f88d919406e7993.jpg) + +![](images/756f62ab06194b300d2e17acbb095c023eb357ef2ceb36205ea98712c865e9d7.jpg) +Figure 4. Qualitative results on nuScenes Lidarseg validation set. Red points are in red. Compared to baseline and the recently proposed distillation-based method 2DPASS [42], our ProtoTransfer achieves better segmentation on region boundaries (the first row), far objects (the second row) and small objects (the third row), thanks to the fully exploited and transferred multi-modal knowledge. + +![](images/26b1bf5f6cce501c610161c63f1570736f148072cbc641504982d0dadab00e5d.jpg) + +![](images/f5f1f6eee9524e741ea315fbf11679dfae27a36c77492dc1532c49df614123af.jpg) + +![](images/892be72b976e8ee8880150fd5cc17fa2aff98262425264ad59a3f9904d3c4e11.jpg) +(c) Error by ProtoTransfer +(d) Ground-truth + +
baselineLprotoupdate proto. bankmIoU
✓76.21
✓✓76.50
✓✓✓80.51
+ +tation for the points in the class of car, while our ProtoTransfer precisely segments all points belonging to the car. The second row displays a car far away from the ego-car, both of the two comparing methods mispredict the point clouds in the head area of the car and ProtoTransfer segments the car points perfectly again. The last row presents a pedestrian with only several LiDAR points. Thanks to the fully exploited and transferred multi-modal knowledge, our ProtoTransfer obtains the most accurate segmentation. + +# 4.4. Ablation Studies + +In this section, we present comprehensive ablation studies to examine the efficacy of each component in ProtoTransfer, ways of prototype bank construction, and distribution of feature representations. All the ablation studies are conducted on the nuScenes validation set. + +Effects of each component. As shown in Tab. 3, introducing the proposed prototype-based loss term $\mathcal{L}^{\mathrm{proto}}$ into the naive baseline method without updating the prototype bank can only bring minor performance gain. When the prototype bank is dynamically updated with the strategy presented in Sec. 3.4, the segmentation performance is significantly boosted which obviously demonstrates that the qual + +Table 3. Ablation study of each component in our ProtoTransfer. + +
F3dF2dFfuseFfuse_umIoU
baseline76.21
(a)✓76.97
(b)✓75.35
(c)✓78.65
(d)✓✓77.11
(e)✓✓75.67
(f)✓✓✓75.58
(g)✓79.83
(h)✓✓80.51
+ +Table 4. Abaltion study of inputs of prototype bank. + +ity of the prototype bank is critical. + +Input Source of Prototype Bank. As presented in Sec. 3, the inputs of the prototype bank include point-pixel fusion features, image features and point features. Tab. 4 shows an ablation study on the effect of different input combinations on final segmentation performance. As can be observed, building up the prototype bank using only point cloud features (a) can generate a $0.76\%$ performance gain over the baseline. We think it is because prototypes constructed from only point features can serve as cluster centers and using the proposed prototype-based loss $\mathcal{L}^{\mathrm{proto}}$ can help point features become more discriminative as they are pushed to be closer to their cluster centers. However, only accumulating image features into the prototype bank leads to a $0.86\%$ performance drop, we postulate it may be because there is + +![](images/b533604ffbec4c3809655b0f95b55a4d38896115ced4452cee2848a8e91f7d94.jpg) +Figure 5. Ablation study of $\lambda$ in Eq. (8). $\lambda = 0.2$ is set as default in ProtoTransfer. + +a distribution gap between image features and point cloud features and thus it is unwise to force point cloud features to imitate image feature cluster centers. On the contrary, when fusing the point-pixel matched features and only using the fusion features for the prototype bank (c) excels $2.44\%$ over the baseline, demonstrating the effectiveness of knowledge transfer from multi-modal to the single LiDAR modal. As shown by Tab. 4 (h), when the fusion features $\bar{F}^{\mathrm{fuse}}$ and $\bar{F}^{\mathrm{fuse.u}}$ are fully explored and accumulated into the prototype bank, our ProtoTransfer reaches the best mIoU of $80.51\%$ . This ablation study clearly shows that the input source plays a key role in the quality of the prototype bank. + +Fusion Strategy of Features for Prototype Bank. As illustrated in Fig. 3 and Sec. 3.4, we calculate class-mean embeddings for the unmatched pixel features and point features, respectively. Then we concatenate these two embeddings and fuse them by reusing the MLP in Eq. (1). The fused embedding $\bar{F}^{\mathrm{fuse - u}}$ is finally accumulated to the prototype bank together with the point-pixel matched fusion features $\bar{F}^{\mathrm{fuse}}$ . To demonstrate the improvement not only comes from the additional image and point features but also comes from the cleverly designed fusion strategy, we use a naive way to have an investigation, i.e., any combinations among the point-pixel naturally matched fusion feature $\bar{F}^{\mathrm{fuse}}$ , image feature $F^{2\mathrm{d}}$ and point feature $F^{3\mathrm{d}}$ in the way of simple summation and use moving average to accumulate them into the prototype bank as presented in Tab. 4 (d)~(f). We can find that this naive summation of all three features (f) reduces the mIoU to $75.58\%$ . We owe this to the large distribution gap between different kinds of features which cannot be handled in the naive sum-up way. In contrast, our ProtoTransfer reuses the MLP to map the unmatched image features to the fusion feature space, thus successfully bypassing this problem. + +Effect of $\lambda$ Selection. We have experimented with different values of $\lambda$ in Eq. (8) and the results are presented in Fig. 5. As can be observed, our ProtoTransfer achieves the best per + +![](images/d6bedc6fa8642665921e95eca479f2782236ef1410cdbb821889a22556cf517c.jpg) +(a) Baseline + +![](images/04fe9a0c7caa404b034f7218f2493af58a36a39170147a2e5d2078283866e200.jpg) +(b) ProtoTransfer +Figure 6. Feature representation visualization of (a) the baseline and (b) our ProtoTransfer. Outlier points have been pointed out by the red arrow. The displayed category ID and their corresponding semantic category is {1: "barrier", 2: "bicycle", 3: "bus", 8: "traffic cone", 9: "trailer", 10: "truck)}. + +formance when $\lambda = 0.2$ which reveals that the unmatched-pixel-feature-based fusion embedding $\bar{F}^{\mathrm{fuse\_u}}$ plays a more important role. Note that when $\lambda = 0$ , i.e., using only $\bar{F}^{\mathrm{fuse\_u}}$ , is able to achieve a satisfactory segmentation accuracy, demonstrating the benefits brought by the unmatched image features. + +Distribution of Feature Representation. The essence of introducing the prototype-based loss term $\mathcal{L}^{\mathrm{proto}}$ in our method is to encourage the point features to be close to the same-class multi-modal prototype while staying far away from the other-class prototypes. Hence, it is important to study the impact of prototypes on feature distribution. As can be observed in Fig. 6 (a), outlier points appear in the feature distribution of the baseline method, while our ProtoTransfer is able to produce more compact feature distributions for all semantic classes, demonstrating the effectiveness of our method. + +# 5. Conclusion + +This work presents a cross-modal knowledge transfer method dubbed ProtoTransfer for point cloud semantic segmentation. ProtoTransfer achieves remarkable segmentation performance but keep a single LiDAR inference speed. By accumulating the fusion features into a prototype bank, all LiDAR points can learn from their class-specific prototypes, thus being well benefited. The unmatched image features are further explored and exploited via a pseudolabeling scheme and a novel prototype bank update strategy. Through extensive experimental results on nuScenes and SemanticKITTI dataset, the efficacy of our method has been successfully demonstrated. + +Acknowledgements. This work was supported by Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), and the Fundamental Research Funds for the Central Universities. + +# References + +[1] Inigo Alonso, Luis Riazuelo, Luis Montesano, and Ana C Murillo. 3d-mininet: Learning a 2d representation from point clouds for fast and efficient 3d lidar semantic segmentation. arXiv preprint arXiv:2002.10893, 2020. +[2] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Jurgen Gall. Semantickitti: A dataset for semantic scene understanding of lidar sequences. In Proceedings of the IEEE International Conference on Computer Vision, pages 9297-9307, 2019. +[3] Maxim Berman, Amal Rannen Triki, and Matthew B Blaschko. The lovasz-softmax loss: A tractable surrogate for the optimization of the intersection-over-union measure in neural networks. 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Recent advances in point cloud segmentation distill knowledge from strictly aligned point-pixel fusion features while leaving a large number of unmatched image pixels unexplored and unmatched LiDAR points under-benefited. In this paper, we propose a novel approach, named ProtoTransfer, which not only fully exploits image representations but also transfers the learned multi-modal knowledge to all point cloud features. Specifically, based on the basic multi-modal learning framework, we build up a class-wise prototype bank from the strictly-aligned fusion features and encourage all the point cloud features to learn from the prototypes during model training. Moreover, to exploit the massive unmatched point and pixel features, we use a pseudo-labeling scheme and further accumulate these features into the class-wise prototype bank with a carefully designed fusion strategy. Without bells and whistles, our approach demonstrates superior performance over the published state-of-the-arts on two large-scale benchmarks, i.e., nuScenes and SemanticKITTI, and ranks 2nd on the competitive nuScenes Lidarseg challenge leaderboard." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 576, + 128, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 576, + 128, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 576, + 128, + 588 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 597, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 287, + 693 + ], + "type": "text", + "content": "Semantic segmentation on point cloud [6, 15, 37, 40] has attracted increasing attention from the computer vision community for its crucial role in scene understanding of 3D space. Although LiDAR point cloud can provide accurate location and depth information of interested scenes, the sparse and textureless shortages inevitably restrict its semantic segmentation performance. On the other hand, 2D images consist of dense pixels with rich color and subtle" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 320, + 226, + 541, + 303 + ], + "blocks": [ + { + "bbox": [ + 320, + 226, + 541, + 303 + ], + "lines": [ + { + "bbox": [ + 320, + 226, + 541, + 303 + ], + "spans": [ + { + "bbox": [ + 320, + 226, + 541, + 303 + ], + "type": "image", + "image_path": "1d5e040b3edb48bc236cb7e5381956b02698f9e285487356db8d16db4a0c7738.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 364, + 304, + 493, + 313 + ], + "lines": [ + { + "bbox": [ + 364, + 304, + 493, + 313 + ], + "spans": [ + { + "bbox": [ + 364, + 304, + 493, + 313 + ], + "type": "text", + "content": "(a) Point-pixel matching and feature fusion" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 313, + 315, + 425, + 427 + ], + "blocks": [ + { + "bbox": [ + 313, + 315, + 425, + 427 + ], + "lines": [ + { + "bbox": [ + 313, + 315, + 425, + 427 + ], + "spans": [ + { + "bbox": [ + 313, + 315, + 425, + 427 + ], + "type": "image", + "image_path": "8e7ea3925b02ca12dcd239659ff378a67ab193eb802ea310579795199fde9e26.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 321, + 430, + 413, + 438 + ], + "lines": [ + { + "bbox": [ + 321, + 430, + 413, + 438 + ], + "spans": [ + { + "bbox": [ + 321, + 430, + 413, + 438 + ], + "type": "text", + "content": "(b) Distillation-based methods" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 433, + 315, + 544, + 426 + ], + "blocks": [ + { + "bbox": [ + 433, + 315, + 544, + 426 + ], + "lines": [ + { + "bbox": [ + 433, + 315, + 544, + 426 + ], + "spans": [ + { + "bbox": [ + 433, + 315, + 544, + 426 + ], + "type": "image", + "image_path": "1a56e680051605d8b9940b1f2831c21b5867b3da7832961dd3b7ae9f680f7a76.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 449, + 430, + 517, + 439 + ], + "lines": [ + { + "bbox": [ + 449, + 430, + 517, + 439 + ], + "spans": [ + { + "bbox": [ + 449, + 430, + 517, + 439 + ], + "type": "text", + "content": "(c) Our ProtoTransfer" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 441, + 545, + 541 + ], + "lines": [ + { + "bbox": [ + 304, + 441, + 545, + 541 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 545, + 541 + ], + "type": "text", + "content": "Figure 1. (a) Point-pixel matching and feature fusion: only features of strictly matched point-pixel pairs can be fused. (b) Distillation-based methods are only performed between fusion prediction and the corresponding matched point prediction while other unmatched points have no chance to mimic the fusion prediction. (c) Our ProtoTransfer performs knowledge transfer from prototype bank to all point features directly without being restricted by matching requirements. The prototype bank is updated using fusion, point, and unmatched image features." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 555, + 545, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 545, + 580 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 545, + 580 + ], + "type": "text", + "content": "textures [34]. Therefore, incorporating these two complementary modals altogether can be a more plausible solution." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": "Recently, there are mainly two stream approaches of utilizing multi-modal data, i.e., fusion-based methods [10, 50] and distillation-based methods [42]. The former methods project point clouds to the camera coordinate to obtain a point-to-pixel mapping, based on which point features are fused with corresponding image features to produce the final point-wise segmentation during both the training and evaluation phases. Although robust and accurate segments are achieved by fusing different sensors, the fusion-based methods may suffer from heavy memory and time consumption for processing these two modal data simul" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 138, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 138, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 138, + 713 + ], + "type": "text", + "content": "* Corresponding author." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3337" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "taneously. In order to benefit from multi-modal fusion while bypassing the computation burden, the latter methods [42] propose to utilize the distillation technique to transfer knowledge learned from cross-modal fusion at the training stage and discard the fusion module for evaluation. The impressive segmentation performance suggests the feasibility of the methods in this stream. Therefore, this paper further explores this research direction." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 289, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 289, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 289, + 384 + ], + "type": "text", + "content": "Unlike common distillation approaches in image classification tasks [14, 44], distilling from multi-modal to the single LiDAR modal may meet quite different pitfalls: (1) Not all LiDAR points can be used in knowledge distillation because LiDAR-to-image is partially matched. Due to the difference in the way sensors collect data, not all the LiDAR points can be aligned to the dense image pixels. For example, we empirically find that only around " + }, + { + "bbox": [ + 46, + 168, + 289, + 384 + ], + "type": "inline_equation", + "content": "16.07\\%" + }, + { + "bbox": [ + 46, + 168, + 289, + 384 + ], + "type": "text", + "content": " LiDAR points in SemanticKITTI dataset can be matched to corresponding image pixels, and Fig. 1(a) also demonstrates this observation. Thus, classic logit-/probability-style distillation strategies [42] can only be performed on the well-aligned point clouds, leading to a sub-optimal knowledge distillation. (2) Massive image pixels are overlooked. Since only partial image pixels1 will contribute to the modal fusion based on the above matching constraints, a large number of pixels are not used in knowledge distillation, resulting in a great loss of rich semantic information in dense pixels." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 384, + 289, + 684 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 46, + 384, + 289, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 289, + 659 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 289, + 659 + ], + "type": "text", + "content": "In this paper, we propose a novel approach for point cloud semantic segmentation which successfully avoids the above pitfalls. Specifically, following the existing work [17, 34, 42], we first construct a modal fusion module to combine the feature representations of matched LiDAR points and image pixels. Next, in order to transfer the knowledge from the fusion module to each point feature representation, we create a class-wise prototype bank to accumulate the fusion features learned in the fusion module and encourage the similarity between features of all LiDAR points and corresponding-class prototypes as high as possible. By this means, every LiDAR point has a fair chance to mimic the fusion features as shown in Fig. 1(c), and we dub our method as ProtoTransfer. Moreover, to make full use of semantic information inherited in dense image pixels, we propose to incorporate the image features into the class-wise prototype bank through a cleverly designed fusion strategy. Since images in the point cloud semantic segmentation datasets usually lack per-pixel annotations, we further use a pseudo-labeling scheme to generate pseudolabels for each pixel and thus make the update of pixelfeature into class-wise prototypes become possible. In summary, the main contributions of this paper are three aspects:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 660, + 288, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 660, + 288, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 660, + 288, + 684 + ], + "type": "text", + "content": "- We investigate the pitfalls of point cloud semantic segmentation on distillation-based methods and find that a" + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 95 + ], + "type": "text", + "content": "large number of image features are not well-utilized and point features are not well distillation-benefited." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 97, + 547, + 181 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 305, + 97, + 547, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 97, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 305, + 97, + 547, + 133 + ], + "type": "text", + "content": "- We introduce the prototype bank concept into point cloud semantic segmentation and propose a novel approach ProtoTransfer to successfully overcome the above pitfalls." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 133, + 547, + 181 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 133, + 547, + 181 + ], + "spans": [ + { + "bbox": [ + 305, + 133, + 547, + 181 + ], + "type": "text", + "content": "- We conduct experiments on both SemanticKITTI and nuScenes benchmarks to demonstrate the effectiveness of our approach and also achieve a 2nd place on the competitive nuScenes Lidarseg leaderboard." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 194, + 392, + 206 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 194, + 392, + 206 + ], + "spans": [ + { + "bbox": [ + 306, + 194, + 392, + 206 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 214, + 545, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 214, + 545, + 382 + ], + "spans": [ + { + "bbox": [ + 304, + 214, + 545, + 382 + ], + "type": "text", + "content": "Multi-Modal 3D Semantic Segmentation. Since different modal can provide complimentary information to each other, multi-modal point cloud semantic segmentation attracts increasing attention [8, 20, 24]. RGBAL [8] casts RGB images to a polar-grid mapping representation and designs an early-mid-level hybrid fusion architecture. Recently, PMF [50] projects LiDAR points to camera coordinates, which is called perspective projection [25]. Then, they use two 2D U-net [27] to extract the image and point features. The multi-scale image and point features in both U-nets are fused to produce better segmentation results. Though satisfactory performance are achieved, these methods need multi-modal inputs during both training and inference phases, which is time-/memory-consuming." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 386, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 386, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 545, + 506 + ], + "type": "text", + "content": "Prototype Networks. Prototype-based learning methods has been widely used in machine learning [9, 11, 28]. Recently, a surge of attention is paid to employ prototype networks on various tasks, presenting great potential in few-shot learning [29] and zero-shot learning[18, 36]. Moreover, [48] shows a prototype view of image semantic segmentation network. Another prototype-based semisupervised method is also proposed [39]. Our work sheds light on the possibility of using prototypes for knowledge transfer from multi-modal to single-modal." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": "Cross-Modal Knowledge Transfer. Knowledge distillation, first proposed by Hinton et al. [14], is a common knowledge transfer method, which pushes the student network mimic the soft logits of the teacher network. Very recently, knowledge distillation is introduced into perception tasks in autonomous driving, such as 3D object detection [7, 19, 46] and point cloud segmentation [42]. During training, they use distillation to transfer multi-modal knowledge learned by the multi-modal teacher to a single-modal student. However, these methods suffers from strict point-pixel alignment, leading to massive unmatched image pixels unexplored and points under-benefited. Our work performs knowledge transfer in another way. Contrary to [42], we construct a prototype bank from fusion and unmatched image features and encourage all the point cloud features to learn from the prototypes during model training, thus fully exploiting and transferring multi-modal knowledge." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "inline_equation", + "content": "{}^{1}" + }, + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "text", + "content": " Only " + }, + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "text", + "content": " image pixels are matched to LiDAR points for a typical 32-beam LiDAR scanner as presented in BEVFusion [22]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3338" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 68, + 534, + 222 + ], + "blocks": [ + { + "bbox": [ + 61, + 68, + 534, + 222 + ], + "lines": [ + { + "bbox": [ + 61, + 68, + 534, + 222 + ], + "spans": [ + { + "bbox": [ + 61, + 68, + 534, + 222 + ], + "type": "image", + "image_path": "f7760b27618bfcd3afac9a6bbd5472f1b5c0cd1f1ba8a285d164a95734adbe83.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "lines": [ + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "spans": [ + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "text", + "content": "Figure 2. Pipeline overview of our ProtoTransfer. The model first uses modal-specific backbones to generate image features " + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "inline_equation", + "content": "F^{2\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "text", + "content": " and point features " + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "inline_equation", + "content": "F^{3\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "text", + "content": " and feeds them into the point-pixel matching module to generate matched point feature " + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "inline_equation", + "content": "F^{3\\mathrm{d},\\mathrm{m}}" + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "text", + "content": ", matched and unmatched image features " + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "inline_equation", + "content": "F^{2\\mathrm{d},\\mathrm{m}}" + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "inline_equation", + "content": "F^{2\\mathrm{d},\\mathrm{u}}" + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "text", + "content": ", respectively. Then modal-specific segmentation heads are used to produce predictions for loss calculation, i.e., " + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^{3\\mathrm{d}}, \\mathcal{L}^{2\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^{\\mathrm{fuse}}" + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^{\\mathrm{fuse}}" + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "text", + "content": " will update the feature " + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "inline_equation", + "content": "F^{\\mathrm{fuse}}" + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "text", + "content": " fused from " + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "inline_equation", + "content": "F^{2\\mathrm{d},\\mathrm{m}}" + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "inline_equation", + "content": "F^{3\\mathrm{d},\\mathrm{m}}" + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "text", + "content": ". To take advantage of the fusion features, we introduce a class-wise prototype bank whose input source includes features " + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "inline_equation", + "content": "F^{3\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "inline_equation", + "content": "F^{\\mathrm{fuse}}" + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "inline_equation", + "content": "F^{2\\mathrm{d},\\mathrm{u}}" + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "text", + "content": " and propose a loss " + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^{\\mathrm{proto}}" + }, + { + "bbox": [ + 46, + 225, + 547, + 295 + ], + "type": "text", + "content": " to transfer fusion knowledge to all point features. Please note 2D&Fusion GT is derived from the 3D GT based on point-pixel matching." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 300, + 130, + 314 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 130, + 314 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 130, + 314 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 319, + 173, + 332 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 319, + 173, + 332 + ], + "spans": [ + { + "bbox": [ + 47, + 319, + 173, + 332 + ], + "type": "text", + "content": "3.1. Framework Overview" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 338, + 288, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 288, + 457 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 288, + 457 + ], + "type": "text", + "content": "Given a LiDAR point cloud frame with " + }, + { + "bbox": [ + 46, + 338, + 288, + 457 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 338, + 288, + 457 + ], + "type": "text", + "content": " unordered points " + }, + { + "bbox": [ + 46, + 338, + 288, + 457 + ], + "type": "inline_equation", + "content": "P = \\{p_i\\in \\mathbb{R}^{d_{\\mathrm{in}}}\\}_{i = 1}^N" + }, + { + "bbox": [ + 46, + 338, + 288, + 457 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 338, + 288, + 457 + ], + "type": "inline_equation", + "content": "d_{\\mathrm{in}}" + }, + { + "bbox": [ + 46, + 338, + 288, + 457 + ], + "type": "text", + "content": " is input feature dimension, the goal of point cloud semantic segmentation is to assign a single class label " + }, + { + "bbox": [ + 46, + 338, + 288, + 457 + ], + "type": "inline_equation", + "content": "c\\in \\{1,2\\dots ,C\\}" + }, + { + "bbox": [ + 46, + 338, + 288, + 457 + ], + "type": "text", + "content": " to each point. To make up for the sparsity and lack of texture of point clouds collected in outdoor scenes [42], the other modal of the corresponding scenes, raw images " + }, + { + "bbox": [ + 46, + 338, + 288, + 457 + ], + "type": "inline_equation", + "content": "I\\in \\mathbb{R}^{W\\times H\\times 3}" + }, + { + "bbox": [ + 46, + 338, + 288, + 457 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 338, + 288, + 457 + ], + "type": "inline_equation", + "content": "W,H" + }, + { + "bbox": [ + 46, + 338, + 288, + 457 + ], + "type": "text", + "content": " denote the resolution of a given image, are also provided for model learning to achieve a better segmentation performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 459, + 287, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 287, + 686 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 287, + 686 + ], + "type": "text", + "content": "As the overall structure presented in Fig. 2, the main contributions of our approach are (1) introducing a class-wise prototype bank for knowledge transfer from a fusion modal to all LiDAR points and (2) proposing to make full use of image features to enhance the prototype quality. Specifically, paired point cloud and image are first fed into modal-specific backbones to extract feature representations respectively. Next, based on the given LiDAR-to-image transformation matrix, features are fused for matched LiDAR point and corresponding image pixels, as done in previous modal-fusion-related work [17, 34, 42]. Due to the differing data acquisition mechanisms of different modal sensors, the matching rate between LiDAR points and image pixels is often quite low. Instead of distilling knowledge solely for the limited matched LiDAR points, we propose a novel knowledge transfer module that can enable unmatched points to also benefit from fused feature representations. With this framework, we explore and exploit unmatched image pixels to further enhance the overall point" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 301, + 443, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 301, + 443, + 313 + ], + "spans": [ + { + "bbox": [ + 306, + 301, + 443, + 313 + ], + "type": "text", + "content": "cloud segmentation performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 314, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 314, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 545, + 361 + ], + "type": "text", + "content": "During inference, the enhanced point cloud segmentation branch can produce accurate segmentation results without the image backbone and multi-modal fusion, and thus challenges can be tackled within a real-time speed." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 367, + 481, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 367, + 481, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 367, + 481, + 380 + ], + "type": "text", + "content": "3.2. Cross-Modal Prototype Transfer" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 385, + 546, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 385, + 546, + 588 + ], + "spans": [ + { + "bbox": [ + 304, + 385, + 546, + 588 + ], + "type": "text", + "content": "Considering the data structures of point cloud and image pixels are totally different, various network architectures are utilized to extract feature representations for the two modal inputs independently. Specifically, ResNet34 [13] encoder and FCN [23] decoder are used for 2D images to extract dense-grid features " + }, + { + "bbox": [ + 304, + 385, + 546, + 588 + ], + "type": "inline_equation", + "content": "F^{2\\mathrm{d}} \\in \\mathbb{R}^{W \\times H \\times D_{2\\mathrm{d}}}" + }, + { + "bbox": [ + 304, + 385, + 546, + 588 + ], + "type": "text", + "content": ", and a sparse convolution [12] based hierarchical point-voxel backbone [42] are designed for 3D point cloud to generate point-wise features " + }, + { + "bbox": [ + 304, + 385, + 546, + 588 + ], + "type": "inline_equation", + "content": "F^{3\\mathrm{d}} \\in \\mathbb{R}^{N \\times D_{3\\mathrm{d}}}" + }, + { + "bbox": [ + 304, + 385, + 546, + 588 + ], + "type": "text", + "content": ". Since LiDAR points and image pixels are not naturally aligned due to the differences in data collection of LiDAR and camera devices, LiDAR-camera transformation matrix is used to find the point-to-pixel correspondence3 and further obtain the matched pixel feature " + }, + { + "bbox": [ + 304, + 385, + 546, + 588 + ], + "type": "inline_equation", + "content": "F^{2\\mathrm{d\\_m}}" + }, + { + "bbox": [ + 304, + 385, + 546, + 588 + ], + "type": "text", + "content": " and matched point features " + }, + { + "bbox": [ + 304, + 385, + 546, + 588 + ], + "type": "inline_equation", + "content": "F^{2\\mathrm{d\\_m}}" + }, + { + "bbox": [ + 304, + 385, + 546, + 588 + ], + "type": "text", + "content": ". Following the previous work [42], we concatenate the matched point-pixel features and use a multi-layer perceptron (MLP) to obtain the fusion feature" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 352, + 592, + 545, + 608 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 592, + 545, + 608 + ], + "spans": [ + { + "bbox": [ + 352, + 592, + 545, + 608 + ], + "type": "interline_equation", + "content": "F ^ {\\mathrm {f u s e}} = \\operatorname {M L P} \\left(\\operatorname {c a t} \\left(F ^ {2 \\mathrm {d}. \\mathrm {m}}, F ^ {3 \\mathrm {d}. \\mathrm {m}}\\right)\\right) \\tag {1}", + "image_path": "89a9b09ac20b3fd6f6c35c621a4a9bb34c9005f9eb73218fd180cdb26c048d78.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 611, + 545, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 611, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 304, + 611, + 545, + 658 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 611, + 545, + 658 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 304, + 611, + 545, + 658 + ], + "type": "text", + "content": " is Hadamard product of two matrices. The MLP is used to reduce feature dimension to " + }, + { + "bbox": [ + 304, + 611, + 545, + 658 + ], + "type": "inline_equation", + "content": "D_{3\\mathrm{d}}" + }, + { + "bbox": [ + 304, + 611, + 545, + 658 + ], + "type": "text", + "content": " and obtain " + }, + { + "bbox": [ + 304, + 611, + 545, + 658 + ], + "type": "inline_equation", + "content": "F^{\\mathrm{fuse}}" + }, + { + "bbox": [ + 304, + 611, + 545, + 658 + ], + "type": "text", + "content": ". With LiDAR per-point ground truth " + }, + { + "bbox": [ + 304, + 611, + 545, + 658 + ], + "type": "inline_equation", + "content": "Y^{3\\mathrm{d}}" + }, + { + "bbox": [ + 304, + 611, + 545, + 658 + ], + "type": "text", + "content": ", the fusion branch is got supervised" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 662, + 545, + 688 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 662, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 306, + 662, + 545, + 688 + ], + "type": "interline_equation", + "content": "\\mathcal {L} ^ {\\text {f u s e}} = \\mathcal {L} _ {\\mathrm {C E}} \\left(h ^ {\\text {f u s e}} \\left(F ^ {\\text {f u s e}}\\right), \\hat {Y}\\right) + \\mathcal {L} _ {\\text {L o v a s z}} \\left(h ^ {\\text {f u s e}} \\left(F ^ {\\text {f u s e}}\\right), \\hat {Y}\\right) \\tag {2}", + "image_path": "06d2067501dcbe0252111f01ff581b240aebcc5ecfab1f3c4d89c18df23f8662.jpg" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "text", + "content": "2Input feature normally contains Cartesian coordinates, intensity of returning laser beam, colors, etc." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "text", + "content": "3Detailed point-to-pixel mapping mechanism is provided in supplementary material." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3339" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "inline_equation", + "content": "h^{\\mathrm{fuse}}" + }, + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "text", + "content": " is the segmentation head of fusion branch. " + }, + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "inline_equation", + "content": "\\hat{Y}" + }, + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "text", + "content": " is the subset of " + }, + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "inline_equation", + "content": "Y^{3\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "text", + "content": ", representing the ground truth for matched points. " + }, + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{CE}}" + }, + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{Lovasz}}" + }, + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "text", + "content": " denote the cross entropy loss and the IoU-style Lovasz loss [3] respectively." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 121, + 286, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 286, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 286, + 240 + ], + "type": "text", + "content": "Attributed to the integration of rich semantic information from 2D images, the segmentation performance of the fusion branch is superior to the LiDAR-sole branch (the bottom branch in Fig. 2). In order to make a single LiDAR point cloud segmentation benefit from the fusion branch, one straightforward way is to introduce a knowledge distillation loss between these two branches, as done in [42]. However, due to the matched point-pixel being limited, only partial point features can benefit from the fusion features and leave massive unmatched points under-benefited." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 240, + 286, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 240, + 286, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 286, + 312 + ], + "type": "text", + "content": "To bypass the strict matching restriction, we introduce a class-wise prototype bank to accumulate the fusion features during model optimization. Such a prototype bank can be served as a parameter-free segmentation head to regularize the distribution of all point features with LiDAR ground truth" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 320, + 286, + 353 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 320, + 286, + 353 + ], + "spans": [ + { + "bbox": [ + 47, + 320, + 286, + 353 + ], + "type": "interline_equation", + "content": "\\mathcal {L} ^ {\\text {p r o t o}} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathcal {L} _ {\\mathrm {C E}} \\left(p _ {c _ {i}}, c _ {i}\\right) + \\mathcal {L} _ {\\text {L o v a s z}} \\left(p _ {c _ {i}}, c _ {i}\\right), \\tag {3}", + "image_path": "62f4a98f3a0922129c49f57d7a83e0ed7ba91c6f696e2a50b8e6a1d2b6c46ed7.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 355, + 296, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 355, + 296, + 387 + ], + "spans": [ + { + "bbox": [ + 47, + 355, + 296, + 387 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 355, + 296, + 387 + ], + "type": "inline_equation", + "content": "p_{c_i} \\coloneqq p(y = c_i | F_i^{3\\mathrm{d}}) = \\frac{\\exp(\\cos(\\mathsf{p}_{c_i}, F_i^{3\\mathrm{d}}) / T)}{\\sum_{j=1}^{C} \\exp(\\cos(\\mathsf{p}_j, F_i^{3\\mathrm{d}}) / T)}" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 396, + 286, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 286, + 468 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 286, + 468 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 396, + 286, + 468 + ], + "type": "inline_equation", + "content": "F_{i}^{3\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 396, + 286, + 468 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 396, + 286, + 468 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 46, + 396, + 286, + 468 + ], + "type": "text", + "content": " denote the feature and semantic label of " + }, + { + "bbox": [ + 46, + 396, + 286, + 468 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 396, + 286, + 468 + ], + "type": "text", + "content": "-th point respectively. " + }, + { + "bbox": [ + 46, + 396, + 286, + 468 + ], + "type": "inline_equation", + "content": "\\mathsf{p}_{c_i} \\in \\mathbb{R}^{D_{3\\mathrm{d}}}" + }, + { + "bbox": [ + 46, + 396, + 286, + 468 + ], + "type": "text", + "content": " represents the prototype in class " + }, + { + "bbox": [ + 46, + 396, + 286, + 468 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 46, + 396, + 286, + 468 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 396, + 286, + 468 + ], + "type": "inline_equation", + "content": "\\cos" + }, + { + "bbox": [ + 46, + 396, + 286, + 468 + ], + "type": "text", + "content": " is the cosine function to calculate the similarity of the prototype and point feature. " + }, + { + "bbox": [ + 46, + 396, + 286, + 468 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 396, + 286, + 468 + ], + "type": "text", + "content": " is the temperature parameter to adjust the scale of similarity measurement and is empirically set to 0.1 in our study." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 469, + 286, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 469, + 286, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 469, + 286, + 552 + ], + "type": "text", + "content": "The proposed cross-modal prototype-based knowledge transfer module encourages the point features to be close to the same-class prototype while staying far away from other-class prototypes. Therefore, through the class-wise prototype bank as a bridge, we successfully transfer the knowledge learned from the fusion feature to the whole point cloud and we term our method as ProtoTransfer." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 562, + 264, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 264, + 575 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 264, + 575 + ], + "type": "text", + "content": "3.3. Prototype Bank Initialization and Update" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 581, + 286, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 581, + 286, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 581, + 286, + 676 + ], + "type": "text", + "content": "In our work, the prototype bank is designed to be non-parametric and non-learnable and thus the quality of the prototype bank plays a critical role in the success of cross-modal knowledge transfer. Instead of using random vectors to initialize the prototype bank at the beginning of model training, we propose to use the fusion features of the first few iterations to warm up the class-wise prototype bank for a stable optimization procedure." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": "Meanwhile, since the initial prototype bank can not capture the distribution of fusion features, we also dynamically update the prototype bank throughout the training stage." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 312, + 69, + 539, + 233 + ], + "blocks": [ + { + "bbox": [ + 312, + 69, + 539, + 233 + ], + "lines": [ + { + "bbox": [ + 312, + 69, + 539, + 233 + ], + "spans": [ + { + "bbox": [ + 312, + 69, + 539, + 233 + ], + "type": "image", + "image_path": "022dc0f98c60065388fe9216e2fa563993a6529663510b900aedb37c5bf751d7.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "lines": [ + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "type": "text", + "content": "Figure 3. Prototype bank update demonstration. The fusion feature " + }, + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "type": "inline_equation", + "content": "F^{\\mathrm{fuse}}" + }, + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "type": "text", + "content": ", unmatched image feature " + }, + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "type": "inline_equation", + "content": "F^{2\\mathrm{d.u}}" + }, + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "type": "text", + "content": " and point feature " + }, + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "type": "inline_equation", + "content": "F^{3\\mathrm{d}}" + }, + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "type": "text", + "content": " are respectively clustered into class-wise feature sets using corresponding GT or pseudo-label obtained with Eq. (6). Then the feature sets are class-wise averaged to produce class-mean embeddings. " + }, + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\bar{F}^{2\\mathrm{d.u}}" + }, + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\bar{F}^{3\\mathrm{d}}" + }, + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "type": "text", + "content": " are fused to get " + }, + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\bar{F}^{\\mathrm{fuse\\_u}}" + }, + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "type": "text", + "content": ". Finally, both " + }, + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\bar{F}^{\\mathrm{fuse}}" + }, + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\bar{F}^{\\mathrm{fuse\\_u}}" + }, + { + "bbox": [ + 305, + 235, + 545, + 312 + ], + "type": "text", + "content": " are accumulated into the class-wise prototype bank." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 319, + 545, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 319, + 545, + 368 + ], + "spans": [ + { + "bbox": [ + 305, + 319, + 545, + 368 + ], + "type": "text", + "content": "Given all fusion features " + }, + { + "bbox": [ + 305, + 319, + 545, + 368 + ], + "type": "inline_equation", + "content": "\\{F_i^{\\mathrm{fuse}}\\}" + }, + { + "bbox": [ + 305, + 319, + 545, + 368 + ], + "type": "text", + "content": ", we can use their corresponding class labels " + }, + { + "bbox": [ + 305, + 319, + 545, + 368 + ], + "type": "inline_equation", + "content": "\\{c_i\\}" + }, + { + "bbox": [ + 305, + 319, + 545, + 368 + ], + "type": "text", + "content": " to cluster the fusion features into class-wise feature set. As shown in the top branch of Fig. 3, the fusion feature set of class " + }, + { + "bbox": [ + 305, + 319, + 545, + 368 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 319, + 545, + 368 + ], + "type": "text", + "content": " can be obtained by" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 372, + 373, + 545, + 389 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 373, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 372, + 373, + 545, + 389 + ], + "type": "interline_equation", + "content": "\\Omega_ {k} ^ {\\text {f u s e}} = \\left\\{F _ {i} ^ {\\text {f u s e}} \\mid c _ {i} = k \\right\\}. \\tag {4}", + "image_path": "226ca57aca060e8cd310639ae9aed928fb2c776a993b681bcf379b7d83fcaf9e.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 395, + 544, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 395, + 544, + 419 + ], + "spans": [ + { + "bbox": [ + 305, + 395, + 544, + 419 + ], + "type": "text", + "content": "We then use the moving average trick to update the class-specific prototype " + }, + { + "bbox": [ + 305, + 395, + 544, + 419 + ], + "type": "inline_equation", + "content": "\\mathfrak{p}_k" + }, + { + "bbox": [ + 305, + 395, + 544, + 419 + ], + "type": "text", + "content": " of class " + }, + { + "bbox": [ + 305, + 395, + 544, + 419 + ], + "type": "inline_equation", + "content": "k" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 350, + 426, + 545, + 440 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 426, + 545, + 440 + ], + "spans": [ + { + "bbox": [ + 350, + 426, + 545, + 440 + ], + "type": "interline_equation", + "content": "\\mathbf {p} _ {k} \\leftarrow \\alpha \\cdot \\mathbf {p} _ {k} + (1 - \\alpha) \\cdot \\bar {F} _ {k} ^ {\\text {f u s e}}, \\tag {5}", + "image_path": "98ae5f0a1d5444cd49dc4ab2b8ce0031d9cf64867bc55e85f5b53f34bc559e9e.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 350, + 441, + 501, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 441, + 501, + 468 + ], + "spans": [ + { + "bbox": [ + 350, + 441, + 501, + 468 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 350, + 441, + 501, + 468 + ], + "type": "inline_equation", + "content": "\\bar{F}_k^{\\mathrm{fuse}} = \\frac{1}{\\|\\Omega_k^{\\mathrm{fuse}}\\|}\\sum_j\\Omega_{k,j}^{\\mathrm{fuse}}" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 473, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 473, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 305, + 473, + 545, + 520 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 473, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 473, + 545, + 520 + ], + "type": "text", + "content": " is a fixed hyper-parameter to control the prototype update speed and is empirically set as 0.999 in our study. " + }, + { + "bbox": [ + 305, + 473, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\bar{F}_k^{\\mathrm{fuse}}" + }, + { + "bbox": [ + 305, + 473, + 545, + 520 + ], + "type": "text", + "content": " is the class-mean embedding of fusion features in class " + }, + { + "bbox": [ + 305, + 473, + 545, + 520 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 473, + 545, + 520 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 527, + 544, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 527, + 544, + 552 + ], + "spans": [ + { + "bbox": [ + 305, + 527, + 544, + 552 + ], + "type": "text", + "content": "3.4. Unmatched Image Features Exploration and Exploitation" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 558, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 653 + ], + "type": "text", + "content": "Although prototype-based knowledge transfer has helped all point features benefit from the fusion features and enhanced the point segmentation performance, the fusion features, which are the knowledge source of the prototype bank, are only available on matched point-pixel pairs. Since the point-pixel matching rate is quite low, the rich semantic information lying in a large amount of unmatched image pixels is not explored and exploited." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "However, the exploitation of unmatched image pixels is non-trivial and there are at least two challenges: 1) Naturally lacking matching points for modal fusion. Since modal fusion requires well-matched point-pixel features, it is difficult to construct matching points for unmatched pixels." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3340" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "type": "text", + "content": "2) Hardly obtaining semantic labels of unmatched pixels. Since 2D images are provided without annotations and it can be costly to additionally annotate these dense pixels, the semantic labels of unlabeled pixels are thus unknown without the matching correspondence from the LiDAR point cloud ground truth." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 286, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 286, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 286, + 288 + ], + "type": "text", + "content": "Based on our proposed cross-modal prototype transfer framework, we further design a novel strategy to incorporate the unmatched pixel features into the prototype bank to improve the transferred knowledge, and Fig. 3 presents an overview. Specifically, in order to solve the challenge 2), we formulate the image pixel class label generation problem as a weakly-/semi-supervised task [5, 30], i.e., taking the LiDAR-to-image matched pixels as labeled samples and taking other unmatched pixels as unlabeled ones. Considering the segmentation head " + }, + { + "bbox": [ + 46, + 144, + 286, + 288 + ], + "type": "inline_equation", + "content": "h^{2d}" + }, + { + "bbox": [ + 46, + 144, + 286, + 288 + ], + "type": "text", + "content": " for image input has been optimized on features of matched pixels4, we can generate posterior probability estimation for unmatched pixels" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 89, + 300, + 242, + 315 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 300, + 242, + 315 + ], + "spans": [ + { + "bbox": [ + 89, + 300, + 242, + 315 + ], + "type": "interline_equation", + "content": "p (y | F ^ {2 d. u}) = \\operatorname {s o f t m a x} \\left(h ^ {2 d} \\left(F ^ {2 d. u}\\right)\\right),", + "image_path": "9686684569b42c3eb6f82546c8c9360fef585b24c1014f104f0ca94818e61bce.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 319, + 286, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 286, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 286, + 369 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 319, + 286, + 369 + ], + "type": "inline_equation", + "content": "F^{2\\mathrm{d.u}}" + }, + { + "bbox": [ + 46, + 319, + 286, + 369 + ], + "type": "text", + "content": " is the features of unmatched pixels. Then the pseudo-labels can be obtained for these unmatched pixels when their maximal posterior probability is greater than a pre-defined confidence threshold " + }, + { + "bbox": [ + 46, + 319, + 286, + 369 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 319, + 286, + 369 + ], + "type": "text", + "content": " (set as 0.8 in our study)" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 96, + 389, + 286, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 389, + 286, + 403 + ], + "spans": [ + { + "bbox": [ + 96, + 389, + 286, + 403 + ], + "type": "interline_equation", + "content": "y ^ {2 \\mathrm {d} - \\mathrm {u}} = \\operatorname {a r g m a x} _ {c} p (y = c | F ^ {2 \\mathrm {d} - \\mathrm {u}}), \\tag {6}", + "image_path": "8115e28c812b1db5dea6105bde3ce0d4275ea29f5ba295be1716a4d2f37f61f7.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 96, + 406, + 235, + 419 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 406, + 235, + 419 + ], + "spans": [ + { + "bbox": [ + 96, + 406, + 235, + 419 + ], + "type": "interline_equation", + "content": "\\text {o n l y i f} \\quad p (y = y ^ {2 d. u} | F ^ {2 d. u}) \\geq \\delta .", + "image_path": "4c49276926ae9d76f94d2762bbb7babc4b4901b64573e208d66a8672f54a7225.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 430, + 286, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 286, + 562 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 286, + 562 + ], + "type": "text", + "content": "Given the pseudo-labeled unmatched pixels, it is still non-trivial to fuse the features of unmatched pixels and points due to the challenge 1) mentioned above. One straightforward way is to directly add the features of unmatched pixels to the prototype bank, empirical results in Tab. 4 show that this simple way can not bring a performance gain and we postulate that it may be caused by the distribution gap between image features and prototypes. Alternatively, we propose to first calculate a class-mean embedding " + }, + { + "bbox": [ + 46, + 430, + 286, + 562 + ], + "type": "inline_equation", + "content": "\\bar{F}_k^{2\\mathrm{d\\_u}}" + }, + { + "bbox": [ + 46, + 430, + 286, + 562 + ], + "type": "text", + "content": " of unmatched pixel features in the same pseudo-label " + }, + { + "bbox": [ + 46, + 430, + 286, + 562 + ], + "type": "inline_equation", + "content": "k" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 86, + 571, + 211, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 571, + 211, + 597 + ], + "spans": [ + { + "bbox": [ + 86, + 571, + 211, + 597 + ], + "type": "interline_equation", + "content": "\\bar {F} _ {k} ^ {\\mathrm {2 d \\_ u}} = \\frac {1}{\\| \\Omega_ {k} ^ {\\mathrm {2 d \\_ u}} \\|} \\sum_ {j} \\Omega_ {k, j} ^ {\\mathrm {2 d \\_ u}},", + "image_path": "a8359fb7329718e7b98af3d076b3ee11ff63ebb918d4563af153d4dae401ee47.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 87, + 599, + 246, + 613 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 599, + 246, + 613 + ], + "spans": [ + { + "bbox": [ + 87, + 599, + 246, + 613 + ], + "type": "interline_equation", + "content": "\\text {w h e r e} \\quad \\Omega_ {k} ^ {2 d. u} = \\left\\{F _ {i} ^ {2 d. u} \\mid y _ {i} ^ {2 d. u} = k \\right\\},", + "image_path": "92ec65896e80cfa23b8b2516c713b2bc8d12c011af9cdfa42ff7df2306e5c1b5.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 624, + 286, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 624, + 286, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 624, + 286, + 684 + ], + "type": "inline_equation", + "content": "\\Omega_{k}^{2\\mathrm{d.u}}" + }, + { + "bbox": [ + 46, + 624, + 286, + 684 + ], + "type": "text", + "content": " is class-wise unmatched image feature set and is obtained using pseudo labels but not ground-truth as in Eq. (4). And the class-mean embedding " + }, + { + "bbox": [ + 46, + 624, + 286, + 684 + ], + "type": "inline_equation", + "content": "\\bar{F}^{3\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 624, + 286, + 684 + ], + "type": "text", + "content": " of point features can be obtained from " + }, + { + "bbox": [ + 46, + 624, + 286, + 684 + ], + "type": "inline_equation", + "content": "F^{3\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 624, + 286, + 684 + ], + "type": "text", + "content": " with LiDAR ground truth. Then, modal fusion can be performed between class-mean embeddings" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 72, + 376, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 376, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 376, + 83 + ], + "type": "text", + "content": "of the same class" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 351, + 91, + 545, + 106 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 91, + 545, + 106 + ], + "spans": [ + { + "bbox": [ + 351, + 91, + 545, + 106 + ], + "type": "interline_equation", + "content": "\\bar {F} ^ {\\text {f u s e - u}} = \\operatorname {M L P} \\left(\\operatorname {c a t} \\left(\\bar {F} ^ {2 \\mathrm {d} - \\mathrm {u}}, \\bar {F} ^ {3 \\mathrm {d}}\\right)\\right), \\tag {7}", + "image_path": "f68d609ab0465ec738ed737f2f515221932bb79e6a841e37bbac2dec33e91f6a.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 115, + 545, + 150 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 115, + 545, + 150 + ], + "spans": [ + { + "bbox": [ + 305, + 115, + 545, + 150 + ], + "type": "text", + "content": "where the MLP shares parameter with the one in Eq. (1). Finally, the class-wise prototype bank updating in Eq. (5) can be extended as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 310, + 159, + 545, + 173 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 159, + 545, + 173 + ], + "spans": [ + { + "bbox": [ + 310, + 159, + 545, + 173 + ], + "type": "interline_equation", + "content": "\\mathfrak {p} _ {k} \\leftarrow \\alpha \\cdot \\mathfrak {p} _ {k} + (1 - \\alpha) \\cdot (\\lambda \\cdot \\bar {F} _ {k} ^ {\\text {f u s e}} + (1 - \\lambda) \\cdot \\bar {F} _ {k} ^ {\\text {f u s e - u}}), \\tag {8}", + "image_path": "0532bce1d6b817741ea647c346ca1ebb9723a4aa270f69c85e23ed07b3ac4c7c.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 182, + 542, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 182, + 542, + 193 + ], + "spans": [ + { + "bbox": [ + 305, + 182, + 542, + 193 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 182, + 542, + 193 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 182, + 542, + 193 + ], + "type": "text", + "content": " is the balance weight of these two fusion features." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 194, + 545, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 194, + 545, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 545, + 240 + ], + "type": "text", + "content": "Since the pseudo-labeling scheme for unmatched pixels may not be activated at the beginning of model training, the prototype bank is still initialized with the method mentioned in Sec. 3.3." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 249, + 456, + 262 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 249, + 456, + 262 + ], + "spans": [ + { + "bbox": [ + 305, + 249, + 456, + 262 + ], + "type": "text", + "content": "3.5. Overall Objective Function" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 267, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 267, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 304, + 267, + 545, + 338 + ], + "type": "text", + "content": "Apart from the loss terms in Eq. (2) and Eq. (3), we also have separate losses " + }, + { + "bbox": [ + 304, + 267, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^{3\\mathrm{d}}" + }, + { + "bbox": [ + 304, + 267, + 545, + 338 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 267, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^{2\\mathrm{d}}" + }, + { + "bbox": [ + 304, + 267, + 545, + 338 + ], + "type": "text", + "content": " for LiDAR point cloud input and image input respectively. Both of these two losses are composed of a cross-entropy loss and a Lovasz loss as those in Eq. (2). Finally, the overall object function is the weighted sum of these loss terms" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 316, + 346, + 534, + 361 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 346, + 534, + 361 + ], + "spans": [ + { + "bbox": [ + 316, + 346, + 534, + 361 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\omega^ {\\mathrm {3 d}} \\mathcal {L} ^ {\\mathrm {3 d}} + \\omega^ {\\mathrm {2 d}} \\mathcal {L} ^ {\\mathrm {2 d}} + \\omega^ {\\text {f u s e}} \\mathcal {L} ^ {\\text {f u s e}} + \\omega^ {\\text {p r o t o}} \\mathcal {L} ^ {\\text {p r o t o}},", + "image_path": "c0ad6edf47c044bb92dd21d31ea5686a64e36cbf0e99f7dc21ad3b7bf08a9ed1.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 369, + 545, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 369, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 305, + 369, + 545, + 393 + ], + "type": "text", + "content": "where we empirically set " + }, + { + "bbox": [ + 305, + 369, + 545, + 393 + ], + "type": "inline_equation", + "content": "\\omega^{3\\mathrm{d}} = 2.0" + }, + { + "bbox": [ + 305, + 369, + 545, + 393 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 369, + 545, + 393 + ], + "type": "inline_equation", + "content": "\\omega^{2\\mathrm{d}} = \\omega^{\\mathrm{fuse}} = \\omega^{\\mathrm{proto}} = 1.0" + }, + { + "bbox": [ + 305, + 369, + 545, + 393 + ], + "type": "text", + "content": " in our study." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 404, + 386, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 404, + 386, + 418 + ], + "spans": [ + { + "bbox": [ + 306, + 404, + 386, + 418 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 425, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 545, + 472 + ], + "type": "text", + "content": "In this section, we first provide details of our experimental setup. Then we evaluate ProtoTransfer on both nuScenes dataset and SemanticKITTI dataset. Finally, extensive ablation studies of our approach are presented." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 479, + 422, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 422, + 493 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 422, + 493 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 498, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 640 + ], + "type": "text", + "content": "Datasets. NuScenes [4] collects 1000 driving scenes from various locations in Boston and Singapore using 1 LiDAR and 6 cameras covering " + }, + { + "bbox": [ + 304, + 498, + 545, + 640 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 498, + 545, + 640 + ], + "type": "text", + "content": " FoV. According to the official setting, it is split into training, validation and test set as 700, 150 and 150 scenes. For point cloud semantic segmentation task, it annotates labels for 16 classes under different traffic and weather conditions. SemanticKITTI [2] contains 22 LiDAR sequences numbered from 00 to 21, in which sequence 08 is officially selected as validation set, sequence 00-10 except 08 is training set and 11-21 is test set. Unlike nuScenes, SemanticKITTI has only two front-view cameras." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": "Evaluation Metric. Following previous work [49, 42], we calculate intersection-over-union (IoU) of each class and mean IoU (mIoU) of all classes, which is formulated as " + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathrm{mIoU} = \\frac{1}{C}\\sum_{c = 1}^{C}\\frac{\\mathrm{TP}_c}{\\mathrm{TP}_c + \\mathrm{FP}_c + \\mathrm{FN}_c}" + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathrm{TP}_c" + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathrm{FP}_c" + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathrm{TP}_c" + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": " denotes the number of true positive, false positive and false negative points of class " + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 693, + 286, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 286, + 712 + ], + "type": "text", + "content": "4Please note that the segmentation head for 2D images already exists in our training framework." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "3341" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 545, + 201 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 201 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 201 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 201 + ], + "type": "table", + "html": "
MethodsinputmIoUbarrierbicyclebuscarconstructionmotorcyclepedestriantraffic conetrailertruckdrivableother flatsidewalkterrainmannadevegetationLatency (ms)
PolarNet [45]L69.472.216.877.086.551.169.764.854.169.763.596.667.177.772.187.184.5-
JS3C-Net [41]L73.680.126.287.884.555.272.671.366.376.871.296.864.576.974.187.586.1-
Cylinder3D [47]L77.282.829.884.389.463.079.377.273.484.669.197.770.280.375.590.487.663
AMVNet [21]L77.380.632.081.788.967.184.376.173.584.967.397.567.479.475.591.588.785
SPVCNN [31]L77.480.030.091.990.864.779.075.670.981.074.697.469.280.076.189.387.163
(AF)2-S3Net [6]L78.378.952.289.984.277.474.377.372.083.973.897.166.577.574.087.786.8270
PMF [50]L+C77.082.040.081.088.064.079.080.076.081.067.097.068.078.074.090.088.0125*
2D3DNet [10]L+C80.083.059.488.085.163.784.482.076.084.871.996.967.479.876.092.189.2-
2DPASS [42]L80.881.755.392.091.873.386.578.572.584.775.597.669.179.975.590.288.044
ProtoTransfer [Ours]L82.181.155.593.991.577.987.382.778.985.176.597.669.879.675.991.589.144
", + "image_path": "79d852b50b13ab73c064719eefd8420e42d7572fd0b9fc5e8a0bb5c2d91a714b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 239, + 545, + 428 + ], + "blocks": [ + { + "bbox": [ + 47, + 202, + 545, + 234 + ], + "lines": [ + { + "bbox": [ + 47, + 202, + 545, + 234 + ], + "spans": [ + { + "bbox": [ + 47, + 202, + 545, + 234 + ], + "type": "text", + "content": "Table 1. Semantic segmentation results on nuScenes test set. Methods published before the submission deadline (08/03/2023) are listed. L and C respectively denote LiDAR and camera. * The latency of PMF [50] is tested without TensorRT acceleration. The bold numbers indicate the best results, and the blue numbers indicate the second best results." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 239, + 545, + 428 + ], + "lines": [ + { + "bbox": [ + 50, + 239, + 545, + 428 + ], + "spans": [ + { + "bbox": [ + 50, + 239, + 545, + 428 + ], + "type": "table", + "html": "
MethodmIoUroadsidewalkparkingother-groundbuildingcartruckbicyclemotorcycleother-vehiclevegetationtrunkterrainpersonbicyclistmotorcyclistfencepoletraffic signlatency (ms)
SqueezeSegV2 [35]39.788.667.645.817.773.781.813.418.517.914.071.835.860.220.125.13.941.120.226.3-
DarkNet53Seg [2]49.991.874.664.827.984.186.425.524.532.722.678.350.164.036.233.64.755.038.952.2-
RangeNet53++ [25]52.291.875.265.027.887.491.425.725.734.423.080.555.164.638.338.84.858.647.955.983.3
3D-MiniNet [1]55.891.674.564.225.489.490.528.542.342.129.482.860.866.747.844.114.560.848.056.6-
SqueezeSegV3 [38]55.991.774.863.426.489.092.529.638.736.533.082.058.765.445.646.220.159.449.658.9238
PointNet++ [26]20.172.041.818.75.662.353.70.91.90.20.246.513.830.00.91.00.016.96.08.95900
TangentConv [32]40.983.963.933.415.483.490.815.22.716.512.179.549.358.123.028.48.149.035.828.53000
PointASNL [43]46.887.474.324.31.883.187.939.00.025.129.284.152.270.634.257.60.043.957.836.9-
RandLA-Net [16]55.990.574.061.824.589.794.243.929.832.239.183.863.668.648.447.49.460.451.050.7880
KPConv [33]58.890.372.761.331.590.595.033.430.242.544.384.869.269.161.561.611.864.256.447.4-
PolarNet [45]54.390.874.461.721.790.093.822.940.330.128.584.065.567.843.240.25.661.351.857.562
JS3C-Net [41]66.088.972.161.931.992.595.854.359.352.946.084.569.867.969.565.439.970.860.768.7471
SPVNAS [31]67.090.275.467.621.891.697.256.650.650.458.086.173.471.067.467.150.366.964.367.3259
Cylinder3D [47]68.992.277.065.032.390.797.150.867.663.858.585.672.569.873.769.248.066.562.466.2131
RPVNet [40]70.393.480.770.333.393.597.644.268.468.761.186.575.171.775.974.443.472.164.861.4168
(AF)2-S3Net [6]70.892.076.266.845.892.594.340.263.081.440.078.668.063.176.481.777.769.664.073.3-
2DPASS [42]72.989.774.767.440.093.597.061.163.663.461.586.273.971.077.981.374.172.965.070.462
ProtoTransfer [Ours]73.691.577.571.542.892.997.557.168.476.068.086.774.872.680.076.061.470.765.866.762
", + "image_path": "ed41365256d76f7c1b4a1c7aa0bd42c8e1b66e6019061cf424f7878ca1eebd68.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 429, + 545, + 449 + ], + "lines": [ + { + "bbox": [ + 47, + 429, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 47, + 429, + 545, + 449 + ], + "type": "text", + "content": "Table 2. Semantic segmentation results on SemanticKITTI test set. Methods published before the submission deadline (08/03/2023) are listed. The bold numbers indicate the best results, and the blue numbers indicate the second best results." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 459, + 287, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 459, + 287, + 507 + ], + "spans": [ + { + "bbox": [ + 47, + 459, + 287, + 507 + ], + "type": "text", + "content": "In order to have a fair comparison, most of the experimental setup and implementations are identical to the recent work [42]. During the model evaluation, the same test-time augmentation as in [42] is also used in our study." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 515, + 180, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 515, + 180, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 515, + 180, + 528 + ], + "type": "text", + "content": "4.2. Results on Benchmarks" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 533, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 569 + ], + "type": "text", + "content": "We compare the results of our ProtoTransfer with the published state-of-the-art methods on two large-scale benchmarks, i.e., nuScenes [4] and SemanticKITTI [2]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "content": "NuScenes. As shown in Tab. 1, ProtoTransfer successfully outperforms all existing methods in terms of both mIoU and latency, demonstrating its efficacy and efficiency. Moreover, our ProtoTransfer not only outperforms single-modal approaches, but also surprisingly surpasses fusion-based methods which require both of LiDAR point clouds and images covering the whole FoV as input for the inference stage. In contrast, our method ProtoTransfer only takes point clouds as input and produces superior segmentation results. Compared to the recently proposed distillation-based method 2DPASS [42], our ProtoTransfer achieves " + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "inline_equation", + "content": "1.3\\%" + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "content": " performance gain, showing the success of explor" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 459, + 545, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 530 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 530 + ], + "type": "text", + "content": "ing prototypes for knowledge transfer from multi-modal to single-modal. Besides, according to Tab. 1, we can find that our ProtoTransfer performs best on classes of small size and with sparse points, such as traffic-cone, motorcycle and construction vehicle, showing great potential in real-world practice." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 531, + 545, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 545, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 545, + 615 + ], + "type": "text", + "content": "SemanticKITTI. We compare our ProtoTransfer with several previous state-of-the-arts works. From Tab. 2, we can see that our proposed ProtoTransfer still achieves the best performance among these methods, leaving a margin of " + }, + { + "bbox": [ + 304, + 531, + 545, + 615 + ], + "type": "inline_equation", + "content": "0.7\\%" + }, + { + "bbox": [ + 304, + 531, + 545, + 615 + ], + "type": "text", + "content": " compared with the distillation-based 2DPASS [42]. Similarly, ProtoTransfer achieves the best results on classes of small objects such as person and bicycle." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 623, + 434, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 434, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 434, + 635 + ], + "type": "text", + "content": "4.3. Qualitative Evaluation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 642, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 715 + ], + "type": "text", + "content": "We visualize the segmentation results on nuScenes validation set in Fig. 4. As can be observed, our ProtoTransfer achieves the most minor error prediction compared with the two comparison methods. In the first row of Fig. 4, the car and bus are close to each other, neither the baseline method nor the 2DPASS approach can produce an accurate segmen" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3342" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 77, + 73, + 187, + 153 + ], + "blocks": [ + { + "bbox": [ + 77, + 73, + 187, + 153 + ], + "lines": [ + { + "bbox": [ + 77, + 73, + 187, + 153 + ], + "spans": [ + { + "bbox": [ + 77, + 73, + 187, + 153 + ], + "type": "image", + "image_path": "00a113ed776bbe753ab91d9a3a760b4936025cd13d7d2789627d298a79ab7eb6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" 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Qualitative results on nuScenes Lidarseg validation set. Red points are in red. Compared to baseline and the recently proposed distillation-based method 2DPASS [42], our ProtoTransfer achieves better segmentation on region boundaries (the first row), far objects (the second row) and small objects (the third row), thanks to the fully exploited and transferred multi-modal knowledge." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 408, + 73, + 517, + 152 + ], + "blocks": [ + { + "bbox": [ + 408, + 73, + 517, + 152 + ], + "lines": [ + { + "bbox": [ + 408, + 73, + 517, + 152 + ], + "spans": [ + { + "bbox": [ + 408, + 73, + 517, + 152 + ], + "type": "image", + "image_path": "26b1bf5f6cce501c610161c63f1570736f148072cbc641504982d0dadab00e5d.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 408, + 152, + 517, + 228 + ], + "blocks": [ + { + "bbox": [ + 408, + 152, + 517, + 228 + ], + "lines": [ + { + "bbox": [ + 408, + 152, + 517, + 228 + ], + "spans": [ + { + "bbox": [ + 408, + 152, + 517, + 228 + ], + "type": "image", + "image_path": "f5f1f6eee9524e741ea315fbf11679dfae27a36c77492dc1532c49df614123af.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 408, + 228, + 517, + 306 + ], + "blocks": [ + { + "bbox": [ + 303, + 308, + 404, + 319 + ], + "lines": [ + { + "bbox": [ + 303, + 308, + 404, + 319 + ], + "spans": [ + { + "bbox": [ + 303, + 308, + 404, + 319 + ], + "type": "text", + "content": "(c) Error by ProtoTransfer" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 408, + 228, + 517, + 306 + ], + "lines": [ + { + "bbox": [ + 408, + 228, + 517, + 306 + ], + "spans": [ + { + "bbox": [ + 408, + 228, + 517, + 306 + ], + "type": "image", + "image_path": "892be72b976e8ee8880150fd5cc17fa2aff98262425264ad59a3f9904d3c4e11.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 429, + 308, + 493, + 319 + ], + "lines": [ + { + "bbox": [ + 429, + 308, + 493, + 319 + ], + "spans": [ + { + "bbox": [ + 429, + 308, + 493, + 319 + ], + "type": "text", + "content": "(d) Ground-truth" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 74, + 364, + 260, + 412 + ], + "blocks": [ + { + "bbox": [ + 74, + 364, + 260, + 412 + ], + "lines": [ + { + "bbox": [ + 74, + 364, + 260, + 412 + ], + "spans": [ + { + "bbox": [ + 74, + 364, + 260, + 412 + ], + "type": "table", + "html": "
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Abaltion study of inputs of prototype bank." + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 502, + 449, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 502, + 449, + 514 + ], + "spans": [ + { + "bbox": [ + 306, + 502, + 449, + 514 + ], + "type": "text", + "content": "ity of the prototype bank is critical." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "text", + "content": "Input Source of Prototype Bank. As presented in Sec. 3, the inputs of the prototype bank include point-pixel fusion features, image features and point features. Tab. 4 shows an ablation study on the effect of different input combinations on final segmentation performance. As can be observed, building up the prototype bank using only point cloud features (a) can generate a " + }, + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "inline_equation", + "content": "0.76\\%" + }, + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "text", + "content": " performance gain over the baseline. We think it is because prototypes constructed from only point features can serve as cluster centers and using the proposed prototype-based loss " + }, + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^{\\mathrm{proto}}" + }, + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "text", + "content": " can help point features become more discriminative as they are pushed to be closer to their cluster centers. However, only accumulating image features into the prototype bank leads to a " + }, + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "inline_equation", + "content": "0.86\\%" + }, + { + "bbox": [ + 304, + 517, + 545, + 685 + ], + "type": "text", + "content": " performance drop, we postulate it may be because there is" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "text", + "content": "5Please note the pseudo-labeling scheme presented in Sec. 3.4 can also be used here to exploit unmatched image features." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3343" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 283, + 225 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 283, + 225 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 283, + 225 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 283, + 225 + ], + "type": "image", + "image_path": "b533604ffbec4c3809655b0f95b55a4d38896115ced4452cee2848a8e91f7d94.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 228, + 287, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 228, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 287, + 251 + ], + "type": "text", + "content": "Figure 5. Ablation study of " + }, + { + "bbox": [ + 46, + 228, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 228, + 287, + 251 + ], + "type": "text", + "content": " in Eq. (8). " + }, + { + "bbox": [ + 46, + 228, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\lambda = 0.2" + }, + { + "bbox": [ + 46, + 228, + 287, + 251 + ], + "type": "text", + "content": " is set as default in ProtoTransfer." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 261, + 289, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 289, + 405 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 289, + 405 + ], + "type": "text", + "content": "a distribution gap between image features and point cloud features and thus it is unwise to force point cloud features to imitate image feature cluster centers. On the contrary, when fusing the point-pixel matched features and only using the fusion features for the prototype bank (c) excels " + }, + { + "bbox": [ + 46, + 261, + 289, + 405 + ], + "type": "inline_equation", + "content": "2.44\\%" + }, + { + "bbox": [ + 46, + 261, + 289, + 405 + ], + "type": "text", + "content": " over the baseline, demonstrating the effectiveness of knowledge transfer from multi-modal to the single LiDAR modal. As shown by Tab. 4 (h), when the fusion features " + }, + { + "bbox": [ + 46, + 261, + 289, + 405 + ], + "type": "inline_equation", + "content": "\\bar{F}^{\\mathrm{fuse}}" + }, + { + "bbox": [ + 46, + 261, + 289, + 405 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 261, + 289, + 405 + ], + "type": "inline_equation", + "content": "\\bar{F}^{\\mathrm{fuse.u}}" + }, + { + "bbox": [ + 46, + 261, + 289, + 405 + ], + "type": "text", + "content": " are fully explored and accumulated into the prototype bank, our ProtoTransfer reaches the best mIoU of " + }, + { + "bbox": [ + 46, + 261, + 289, + 405 + ], + "type": "inline_equation", + "content": "80.51\\%" + }, + { + "bbox": [ + 46, + 261, + 289, + 405 + ], + "type": "text", + "content": ". This ablation study clearly shows that the input source plays a key role in the quality of the prototype bank." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "type": "text", + "content": "Fusion Strategy of Features for Prototype Bank. As illustrated in Fig. 3 and Sec. 3.4, we calculate class-mean embeddings for the unmatched pixel features and point features, respectively. Then we concatenate these two embeddings and fuse them by reusing the MLP in Eq. (1). The fused embedding " + }, + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "type": "inline_equation", + "content": "\\bar{F}^{\\mathrm{fuse - u}}" + }, + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "type": "text", + "content": " is finally accumulated to the prototype bank together with the point-pixel matched fusion features " + }, + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "type": "inline_equation", + "content": "\\bar{F}^{\\mathrm{fuse}}" + }, + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "type": "text", + "content": ". To demonstrate the improvement not only comes from the additional image and point features but also comes from the cleverly designed fusion strategy, we use a naive way to have an investigation, i.e., any combinations among the point-pixel naturally matched fusion feature " + }, + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "type": "inline_equation", + "content": "\\bar{F}^{\\mathrm{fuse}}" + }, + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "type": "text", + "content": ", image feature " + }, + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "type": "inline_equation", + "content": "F^{2\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "type": "text", + "content": " and point feature " + }, + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "type": "inline_equation", + "content": "F^{3\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "type": "text", + "content": " in the way of simple summation and use moving average to accumulate them into the prototype bank as presented in Tab. 4 (d)~(f). We can find that this naive summation of all three features (f) reduces the mIoU to " + }, + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "type": "inline_equation", + "content": "75.58\\%" + }, + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "type": "text", + "content": ". We owe this to the large distribution gap between different kinds of features which cannot be handled in the naive sum-up way. In contrast, our ProtoTransfer reuses the MLP to map the unmatched image features to the fusion feature space, thus successfully bypassing this problem." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": "Effect of " + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": " Selection. We have experimented with different values of " + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": " in Eq. (8) and the results are presented in Fig. 5. As can be observed, our ProtoTransfer achieves the best per" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 316, + 76, + 427, + 163 + ], + "blocks": [ + { + "bbox": [ + 316, + 76, + 427, + 163 + ], + "lines": [ + { + "bbox": [ + 316, + 76, + 427, + 163 + ], + "spans": [ + { + "bbox": [ + 316, + 76, + 427, + 163 + ], + "type": "image", + "image_path": "d6bedc6fa8642665921e95eca479f2782236ef1410cdbb821889a22556cf517c.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 352, + 167, + 393, + 176 + ], + "lines": [ + { + "bbox": [ + 352, + 167, + 393, + 176 + ], + "spans": [ + { + "bbox": [ + 352, + 167, + 393, + 176 + ], + "type": "text", + "content": "(a) Baseline" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 432, + 76, + 544, + 163 + ], + "blocks": [ + { + "bbox": [ + 432, + 76, + 544, + 163 + ], + "lines": [ + { + "bbox": [ + 432, + 76, + 544, + 163 + ], + "spans": [ + { + "bbox": [ + 432, + 76, + 544, + 163 + ], + "type": "image", + "image_path": "04fe9a0c7caa404b034f7218f2493af58a36a39170147a2e5d2078283866e200.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 459, + 167, + 520, + 176 + ], + "lines": [ + { + "bbox": [ + 459, + 167, + 520, + 176 + ], + "spans": [ + { + "bbox": [ + 459, + 167, + 520, + 176 + ], + "type": "text", + "content": "(b) ProtoTransfer" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 178, + 547, + 236 + ], + "lines": [ + { + "bbox": [ + 304, + 178, + 547, + 236 + ], + "spans": [ + { + "bbox": [ + 304, + 178, + 547, + 236 + ], + "type": "text", + "content": "Figure 6. Feature representation visualization of (a) the baseline and (b) our ProtoTransfer. Outlier points have been pointed out by the red arrow. The displayed category ID and their corresponding semantic category is {1: \"barrier\", 2: \"bicycle\", 3: \"bus\", 8: \"traffic cone\", 9: \"trailer\", 10: \"truck)}." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 251, + 547, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 547, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 547, + 324 + ], + "type": "text", + "content": "formance when " + }, + { + "bbox": [ + 304, + 251, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\lambda = 0.2" + }, + { + "bbox": [ + 304, + 251, + 547, + 324 + ], + "type": "text", + "content": " which reveals that the unmatched-pixel-feature-based fusion embedding " + }, + { + "bbox": [ + 304, + 251, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\bar{F}^{\\mathrm{fuse\\_u}}" + }, + { + "bbox": [ + 304, + 251, + 547, + 324 + ], + "type": "text", + "content": " plays a more important role. Note that when " + }, + { + "bbox": [ + 304, + 251, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\lambda = 0" + }, + { + "bbox": [ + 304, + 251, + 547, + 324 + ], + "type": "text", + "content": ", i.e., using only " + }, + { + "bbox": [ + 304, + 251, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\bar{F}^{\\mathrm{fuse\\_u}}" + }, + { + "bbox": [ + 304, + 251, + 547, + 324 + ], + "type": "text", + "content": ", is able to achieve a satisfactory segmentation accuracy, demonstrating the benefits brought by the unmatched image features." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 334, + 547, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 334, + 547, + 466 + ], + "spans": [ + { + "bbox": [ + 304, + 334, + 547, + 466 + ], + "type": "text", + "content": "Distribution of Feature Representation. The essence of introducing the prototype-based loss term " + }, + { + "bbox": [ + 304, + 334, + 547, + 466 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^{\\mathrm{proto}}" + }, + { + "bbox": [ + 304, + 334, + 547, + 466 + ], + "type": "text", + "content": " in our method is to encourage the point features to be close to the same-class multi-modal prototype while staying far away from the other-class prototypes. Hence, it is important to study the impact of prototypes on feature distribution. As can be observed in Fig. 6 (a), outlier points appear in the feature distribution of the baseline method, while our ProtoTransfer is able to produce more compact feature distributions for all semantic classes, demonstrating the effectiveness of our method." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 487, + 379, + 500 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 487, + 379, + 500 + ], + "spans": [ + { + "bbox": [ + 306, + 487, + 379, + 500 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 511, + 547, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 511, + 547, + 656 + ], + "spans": [ + { + "bbox": [ + 304, + 511, + 547, + 656 + ], + "type": "text", + "content": "This work presents a cross-modal knowledge transfer method dubbed ProtoTransfer for point cloud semantic segmentation. ProtoTransfer achieves remarkable segmentation performance but keep a single LiDAR inference speed. By accumulating the fusion features into a prototype bank, all LiDAR points can learn from their class-specific prototypes, thus being well benefited. The unmatched image features are further explored and exploited via a pseudolabeling scheme and a novel prototype bank update strategy. Through extensive experimental results on nuScenes and SemanticKITTI dataset, the efficacy of our method has been successfully demonstrated." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgements. This work was supported by Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), and the Fundamental Research Funds for the Central Universities." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "3344" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 135 + ], + "type": "text", + "content": "[1] Inigo Alonso, Luis Riazuelo, Luis Montesano, and Ana C Murillo. 3d-mininet: Learning a 2d representation from point clouds for fast and efficient 3d lidar semantic segmentation. arXiv preprint arXiv:2002.10893, 2020." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 137, + 288, + 192 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 137, + 288, + 192 + ], + "spans": [ + { + "bbox": [ + 53, + 137, + 288, + 192 + ], + "type": "text", + "content": "[2] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Jurgen Gall. 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In NECIL methods, prototypical representations are usually stored, which inject information from former classes to resist catastrophic forgetting in subsequent incremental learning. However, since the model continuously learns new knowledge, the stored prototypical representations cannot correctly model the properties of old classes in the existence of knowledge updates. To address this problem, we propose a novel prototype reminiscence mechanism that incorporates the previous class prototypes with arriving new class features to dynamically reshape old class feature distributions thus preserving the decision boundaries of previous tasks. In addition, to improve the model generalization on both newly arriving classes and old classes, we contribute an augmented asymmetric knowledge aggregation approach, which aggregates the overall knowledge of the current task and extracts the valuable knowledge of the past tasks, on top of self-supervised label augmentation. Experimental results on three benchmarks suggest the superior performance of our approach over the SOTA methods.", + "bbox": [ + 75, + 353, + 473, + 659 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 77, + 681, + 208, + 695 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, deep neural networks have achieved great success on various tasks. In dynamic and open environments, deep models also require the ability to continuously learn new tasks as the input stream is updated. Hence, class-incremental learning (CIL), which aims to learn a unified classifier that can classify all seen classes under progressive changes in the classes to be learned, has attracted extensive attention [30, 41, 16, 47, 31, 28].", + "bbox": [ + 75, + 705, + 468, + 815 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As new data becomes available, it is computationally expensive to jointly retrain the model with new and old class", + "bbox": [ + 75, + 815, + 468, + 844 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/61435a7e68d6b1d3ca58c68b63e86f1f127444db2709525d6230656ba363be58.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 507, + 324, + 890, + 404 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b8f79e6cd48897686028572c4979d0eba37bec46e2adb11fccb2d20bcb334a50.jpg", + "image_caption": [ + "Figure 1. Idea illustration. (a) Joint training with abundant samples. (b) Baseline: Updating the model with the memorized prototype and new data, which narrows the decision boundary of the old classes. (c) Gaussian Noise Augmentation [66]: The decision boundary of the old class is retained, but it introduces an overlap between the old and new class distributions due to the change in representation space. (d) With prototype reminiscence, newly learned information can be injected while reshaping the feature distribution of past data to reduce overlap and resist forgetting." + ], + "image_footnote": [], + "bbox": [ + 502, + 407, + 890, + 505 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "samples. Worse still, the old class samples could not be fully accessible. In this case, an alternative is to fine-tune the model on new data, yet catastrophic forgetting [38, 15] will be a serious challenge. The decision boundary of the unified classifier would be significantly changed and biased towards the new classes. Conversely, another direction is to fix the feature embedding space of a trained model, which suffers from frustrating generalization ability and thus performs poorly on new tasks, i.e., the plasticity of the model is greatly degraded.", + "bbox": [ + 497, + 631, + 892, + 769 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To overcome the catastrophic forgetting issue, many CIL methods [42, 8, 6, 56, 2, 53] store a fraction of the old data in memory and replay them in subsequent incremental phases to maintain the existing knowledge. Unfortunately, storing data poses privacy concerns and comes at a sharp cost to memory and computation. In this paper, we follow a paradigm holding for more extensive applications,", + "bbox": [ + 497, + 769, + 892, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 129, + 49, + 200, + 84 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation.", + "bbox": [ + 253, + 48, + 789, + 61 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "Except for this watermark, it is identical to the accepted version;", + "bbox": [ + 332, + 62, + 709, + 74 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 304, + 74, + 739, + 87 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author: Mang Ye (yemang@whu.edu.cn)", + "bbox": [ + 94, + 853, + 403, + 866 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1772", + "bbox": [ + 468, + 887, + 500, + 897 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "termed non-exemplar class-incremental learning (NECIL) [66, 67], which solves the catastrophic forgetting problem in CIL scenario without preserving old class samples.", + "bbox": [ + 75, + 125, + 468, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For NECIL, a natural substitute for storing data is to generate pseudo-samples of previous classes by deep generative models [62, 54, 46, 49, 57] such as GAN [4, 17]. However, it is unstable and ineffective to train generative models for non-stationary data streams [65]. Catastrophic forgetting can also have a negative impact on the generative model resulting in a simultaneous decrease in the effectiveness of both models. Instead of focusing on old data, some works turn to estimating model parameters that are important for previous tasks and constraining their changes [23, 61, 3]. Nevertheless, the constraints on the model parameters lead to poor generalization ability to long-sequence tasks. Besides, several studies propose to dynamically expand the network structure during the process of incremental learning [44, 58, 59, 37, 64]. Although this strategy can efficiently handle long sequences of tasks and ultimately maintain the performance of the old classes, the computational resource requirements associated with creating and storing additional network components and reasoning about multiple forward propagations are frustrating.", + "bbox": [ + 75, + 169, + 468, + 445 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, some prototype-based NECIL methods have achieved impressive performance [66, 67, 60, 50]. They use prototypical representations (typically the class mean in the deep feature space) memorized for each old class to model the feature distribution of past data and inject information from the previous classes in subsequent incremental learning. Rather than storing samples, this strategy is more memory efficient and privacy secure. Nevertheless, as shown in Fig. 1 (b), direct training with saved prototypes and current data struggles to prevent the collapse of decision boundaries, due to the lack of old class features. Some works augment the prototypes by adding Gaussian noise [66] or over-sampling [67] to enrich old class features. However, updates of the model on continuous data streams could lead to inevitable changes in the representation of old classes, making the saved prototypes increasingly outdated.", + "bbox": [ + 75, + 448, + 468, + 668 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The feature distribution simulated by the above strategies cannot accommodate such changes due to the missing consideration of knowledge updates. It could result in overlap between the distributions of different classes, especially between new and old classes, as shown in Fig. 1 (c). Consequently, combining newly acquired information with stored prototypes to dynamically model past data distributions is crucial to resist catastrophic forgetting in NECIL.", + "bbox": [ + 75, + 669, + 468, + 781 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address this challenge, we propose a prototype reminiscence mechanism to track the evolution of the old class representations by injecting new knowledge from the updating network while reshaping the feature distribution. Specifically, we perform a random bidirectional interpolation operation between the extracted new class features and", + "bbox": [ + 75, + 783, + 468, + 866 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ac65a3b24c9faa1c01b41c7953b4088123479b7ccd901f6fa898832665249713.jpg", + "image_caption": [ + "Figure 2. We introduce self-supervised label augmentation to learn generalizable and transferable representations. The knowledge of the self-supervised classifier is aggregated and transferred to another classifier to take full advantage of it." + ], + "image_footnote": [], + "bbox": [ + 534, + 124, + 858, + 404 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the saved old class prototypes to enrich old class features. As shown in Fig. 1 (d), it expands the prototype to protect the decision boundaries of old classes and to counteract catastrophic forgetting. Since the feature distribution of past tasks is dynamically adjusted to the current representation space, the overlap between the old and new classes is reduced. Thus, the discrimination and balance between the old and new classes are maintained. Cooperating with the well-known knowledge distillation (KD) [20, 19], the mismatch between the preserved prototypes and the continuously updated network is alleviated.", + "bbox": [ + 497, + 475, + 890, + 627 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In addition to dealing with catastrophic forgetting, when new data arrives, performance on the current task is also of great concern, necessitating the plasticity of the incremental learner. This mainly involves two aspects: learning generalizable and transferable representations, fully utilizing the information from new data. Previous works [66, 55] have achieved good progress on the first aspect by self-supervised label augmentation [27], however they ordinarily disregard the second. The new task contains abundant information that the network has never encountered and will have a stronger influence on model updates. Improving the plasticity of the model from continuous data streams requires a simultaneous approach from both aspects.", + "bbox": [ + 497, + 629, + 890, + 809 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To solve this bottleneck, we contribute an augmented asymmetric knowledge aggregation approach to enhance the plasticity of the model noninvasively. Taking inspiration from [24, 27], we first augment the new classes with", + "bbox": [ + 497, + 809, + 890, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1773", + "bbox": [ + 468, + 887, + 500, + 897 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "rotation as self-supervision, which requires the model to acquire task-agnostic representations to improve its generalization ability. Furthermore, as illustrated in Fig. 2, we selectively aggregate the valuable knowledge in the augmented classifier—valid weights of past tasks are extracted, and the information captured on the current task is sufficiently exploited. This asymmetric knowledge aggregation scheme can condense the knowledge learned via self-supervised label augmentation (SLA) to make the classifier more purified. It further improves the incremental learner's performance on the new tasks without discrimination scari-fication on old classes.", + "bbox": [ + 75, + 125, + 472, + 290 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To summarize, our main contributions are as follows:", + "bbox": [ + 95, + 292, + 448, + 305 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a simple yet effective method of prototype reminiscence for NECIL, which models feature distribution for the past data in a continuously updated representation space to resist catastrophic forgetting.", + "- We contribute augmented asymmetric knowledge aggregation, which learns task-agnostic representations and fully captures the newly acquired knowledge to improve the plasticity of incremental learners.", + "- Extensive experiments on three benchmarks demonstrate that our method achieves state-of-the-art performance. We also provide a detailed ablation study to analyze the influence of each component." + ], + "bbox": [ + 95, + 315, + 468, + 503 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 75, + 517, + 218, + 530 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Class-Incremental Learning", + "text_level": 1, + "bbox": [ + 75, + 540, + 329, + 555 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Current CIL methods can be roughly divided into three categories: rehearsal-based methods, regularization-based methods and structure-based methods.", + "bbox": [ + 75, + 561, + 468, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Rehearsal-based methods maintain the distribution of old classes by saving exemplars of fixed memory size to jointly train the model with current data. Based on the saved samples, some works investigate knowledge distillation to prevent forgetting [56, 42, 13], while others try to combine regularization of gradients and rehearsal to make more efficient use of the preserved data [43, 34, 11]. In addition, several papers have studied the impact of memory management schemes [5, 22, 33]. Regularization-based methods identify the key model parameters for the previous tasks, penalizing their changes when learning the current task [23, 61, 3, 40]. The difference between these methods is the association of each network parameter with importance weights stored in incremental learning. Structure-based methods dynamically modify the network architecture to maintain existing knowledge and adapt to new tasks. They usually expand the network structure in depth or width when facing a new task [59, 21, 29, 58], or mask parts of the network for different tasks [45, 36, 1].", + "bbox": [ + 75, + 603, + 472, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, some works have researched the use of class prototypes to implement non-exemplar class-incremental learning [66, 60, 67, 50], which somewhat reduces the issues of data privacy security and memory constraints. Yu et al. [60] approximate and compensate for the semantic drift of previous tasks during the training of the new task. Based on this, Toldo et al. [50] propose to jointly exploit semantic drift and feature drift to update the representations of past classes. Apart from investigating the evolution of prototypes as incremental learning occurs, there are some studies that focus on the ways to model past data distributions by prototypes [66, 67]. Note that this strategy is orthogonal to the above methods for drift estimation, and our method falls into this category. Zhu et al. [66] introduce Gaussian noise to augment the prototype to restrain the decision boundaries of old classes. Zhu et al. [67] propose a prototype selection mechanism that uses samples of the new data similar to the old classes for distillation to reduce confusion between the newly added classes and the original classes.", + "bbox": [ + 497, + 125, + 890, + 388 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Self-supervised Learning in CIL", + "text_level": 1, + "bbox": [ + 497, + 396, + 784, + 410 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The objective of self-supervised learning (SSL) is to acquire transferable representations that are applicable for other tasks. This coincides with the need for IL to inhibit task-level overfitting phenomenon and rapidly adapt to new tasks. Hence, some works explore improving the quality of the learned representations by SSL in the CIL setting [66, 55, 7, 14]. Wu et al. [55] learn class-independent knowledge and multi-perspective knowledge by SSL to make a trade-off between gaining new information and maintaining old knowledge. Fini et al. [14] attempt to seamlessly convert the existing self-supervised loss function into distillation mechanisms plugged into the CIL framework. It also points out that simply introducing SSL can approach or outperform supervised learning in the CIL setting, while this is not always the case for other settings (data-incremental and domain-incremental). Zhu et al. [66] provide better initialization for learning the next task by using rotation as self-supervised information for label augmentation to reduce forgetting from model updates. Our SLA is implemented in the same way as the SSL in [66]. On top of [66], we further improve the upper bound of the incremental learner's understanding of new tasks.", + "bbox": [ + 497, + 416, + 890, + 720 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 497, + 732, + 636, + 749 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Problem Statement. In this paper, we consider nonexemplar class-incremental learning (NECIL), where no samples from old classes are stored. The training data for the incremental task $t \\in \\{1, \\dots, T\\}$ is denoted as $D_{t} = \\{X_{t}, Y_{t}\\} = \\{x_{t}^{i}, y_{t}^{i}\\}_{i=1}^{n_{t}}$ , where $n_{t}$ , $x_{t}^{i}$ and $y_{t}^{i} \\in C_{t}$ represent the number of training samples, an input sample and its corresponding label for task $t$ , respectively. $C_{t}$ is the class set of task $t$ and all the incremental classes are disjoint, i.e.,", + "bbox": [ + 497, + 755, + 890, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1774", + "bbox": [ + 468, + 887, + 500, + 897 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/296947040fa00f334cdf5ed32a8e938a888c90ae2f080acead9c5e03f8ba75ff.jpg", + "image_caption": [ + "Figure 3. Illustration of our method for NECIL. The classes of current task are augmented by rotation transformation [27]. We expand the stored prototype by prototype reminiscence in the deep feature space to generate the same number of old class features as the batch size each time. During the evaluation, only the current feature extractor $\\mathcal{F}_t$ and the refined classifier $\\mathcal{G}_o$ are used." + ], + "image_footnote": [], + "bbox": [ + 82, + 124, + 529, + 368 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/86f1e99f6b36baa18d8b42f28449338372084cef72f61bec683e1916dae92a6f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 532, + 124, + 885, + 368 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$C_1 \\cap \\ldots \\cap C_i = \\emptyset$ . We represent the model with two components: a feature extractor $\\mathcal{F}$ with parameters $\\theta$ and a unified classifier $\\mathcal{G}$ with parameters $\\varphi$ . The goal is to find a classification model minimized for some loss function $\\mathcal{L}(\\cdot, \\cdot)$ :", + "bbox": [ + 75, + 418, + 470, + 475 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\theta , \\varphi} {\\operatorname {a r g m i n}} \\sum_ {t = 1} ^ {C _ {t}} \\mathbb {E} _ {\\left(x _ {t} ^ {i}, y _ {t} ^ {i}\\right) \\sim D _ {t}} \\left[ \\mathcal {L} \\left(y _ {t} ^ {i}, \\mathcal {G} \\left(\\mathcal {F} \\left(x _ {t} ^ {i}; \\theta\\right); \\varphi\\right)\\right) \\right]. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 95, + 488, + 468, + 526 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As other class-incremental methods, the algorithm has no access to the task label $t$ and is expected to classify all observed classes $C_{total} = \\{C_1,\\dots ,C_t\\}$ at any given point.", + "bbox": [ + 75, + 532, + 468, + 573 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Overview of Framework. Fig. 3 shows an overview of our method. The classes of the current task are augmented by rotation transformation [27] and the augmented data is fed to the feature extractors. For each old class, we memorize a class-representative prototype. Then the prototype reminiscence uses the extracted new class features and the stored old class prototypes to generate old class features for joint training. We aggregate the knowledge from the classifier $\\mathcal{G}_S$ learned with SLA and transfer it to another classifier $\\mathcal{G}_O$ that only recognizes classes without augmentation. At test time, the current feature extractor $\\mathcal{F}_t$ and the refined classifier $\\mathcal{G}_O$ are used for evaluation.", + "bbox": [ + 75, + 573, + 470, + 739 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Prototype Reminiscence", + "text_level": 1, + "bbox": [ + 75, + 747, + 299, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At each incremental phase of task $t$ , only $D_{t}$ is available in the NECIL setting. Following [66, 60], when learning a new task, we compute and memorize one prototype in the deep feature space for each class:", + "bbox": [ + 75, + 768, + 468, + 824 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP _ {t, k _ {n e w}} = \\frac {1}{N _ {t , c _ {n e w}}} \\sum_ {n = 1} ^ {N _ {t, c _ {n e w}}} \\mathcal {F} \\left(\\mathbf {X} _ {t, c _ {n e w}}; \\theta_ {t}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 830, + 468, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $c_{new} \\in C_{new} = C_t$ is one class of the current task. To alleviate the catastrophic forgetting, the model is trained jointly on the memorized prototypes $\\{P_{old}^1, \\ldots, P_{old}^{|C_{old}|}\\}$ and current data $D_t$ , where $C_{old} = C_1 \\cup \\ldots \\cup C_{t-1}$ denotes the set of past classes.", + "bbox": [ + 497, + 418, + 890, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Whereas prototypes can inject information of past classes in training, the decision boundaries are narrowed due to the lack of rich old class features. Moreover, as the model continuously learns new data, the deep representation space is changing, which poses a challenge to reproduce the properties of old classes. To this end, we propose a prototype reminiscence strategy to dynamically model the feature distribution of past data in an updating representation space. Our strategy is based on a simple yet effective interpolation operation. In general, as shown in Fig. 3, we randomly select a prototype of the old classes $P_{old}^{n} \\in \\{P_{old}^{1}, \\dots, P_{old}^{|C_{old}|}\\}$ and a feature of the new classes $F_{new}^{m} \\in \\{F_{new}^{1}, \\dots, F_{new}^{B}\\}$ , where $B$ is the batch size. Then we perform a random bidirectional interpolation operation between $P_{old}^{n}$ and $F_{new}^{m}$ :", + "bbox": [ + 497, + 490, + 892, + 700 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF _ {o l d} ^ {n} = \\left\\{ \\begin{array}{l} (1 - \\lambda) \\left(P _ {o l d} ^ {n}\\right) + \\lambda \\left(F _ {n e w} ^ {m}\\right), p _ {e} < 0. 5 \\\\ (1 + \\lambda) \\left(P _ {o l d} ^ {n}\\right) - \\lambda \\left(F _ {n e w} ^ {m}\\right), o t h e r w i s e \\end{array} \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 704, + 890, + 736 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $F_{old}^{n}$ is the feature generated in the current representation space that has the same label as $P_{old}^{n}$ and $p_e$ is randomly sampled from [0, 1). Considering the design principle of mixup [63, 52], we ensure that the coefficient summary of the two terms for the prototype reminiscence is equal to 1. Different from them, our prototype reminiscence introduces an extrapolation operation, which avoids the generated features being concentrated on one side of the decision boundary. Meanwhile, we choose", + "bbox": [ + 497, + 741, + 890, + 866 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1775", + "bbox": [ + 468, + 887, + 500, + 897 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\lambda \\sim \\mathrm{Beta}(0.5, 0.5) \\in [0, \\eta]$ , where $\\eta$ is a threshold value to control the maximum distance between the generated old class features and the corresponding prototype for avoiding outliers. To make a fair comparison, as in [66], we generate the same number of old class features as the batch size for each batch of new data.", + "bbox": [ + 75, + 125, + 468, + 207 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Augmented Asymmetric Knowledge Aggregation", + "text_level": 1, + "bbox": [ + 77, + 216, + 468, + 244 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While counteracting forgetting, incremental learners also need to adapt to new tasks. We design an augmented asymmetric knowledge aggregation scheme that endows the model with stronger plasticity. First, we augment the current classes as in [27]. For the current task, the N-way classification problem is extended into a 4N-way classification problem. Specifically, the input data for each class is rotated by $90^{\\circ}$ , $180^{\\circ}$ , and $270^{\\circ}$ to produce three new classes:", + "bbox": [ + 75, + 251, + 468, + 362 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {x} _ {t} ^ {i} = \\left\\{x _ {t} ^ {i, j} \\right\\} _ {j = 0} ^ {3} = \\left\\{r o t a t e (x _ {t} ^ {i}, j \\times 9 0 ^ {\\circ}) \\right\\} _ {j = 0} ^ {3}, \\quad (4)\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 368, + 468, + 391 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and we allocate new labels $y_{t}^{i}$ to the augmented data:", + "bbox": [ + 75, + 393, + 426, + 408 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {y} _ {t} ^ {i} = \\left\\{y _ {t} ^ {i} \\times 4 + j \\right\\} _ {j = 0} ^ {3}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 412, + 468, + 433 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Compared to the widely used 4-way self-supervised task, the above approach removes unnecessary invariant properties when learning both the original task and the self-supervised task simultaneously, thereby reducing the loss of discriminative information while obtaining generalizable and transferable representations [27].", + "bbox": [ + 75, + 437, + 468, + 519 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, for NECIL, the self-supervised label augmentation can only be applied to new classes (past data is not available). Borrowing from some works [39, 48], the classification weight $w_{c,j}$ is denoted as a proxy, where $c \\in C_{total}$ and $j$ represents different rotation transformations. In the subsequent incremental learning, the proxies for the augmented classes $(90^{\\circ}, 180^{\\circ}, 270^{\\circ})$ of the previous tasks gradually fail, leading to redundancy within the classifier. When using the cross-entropy loss for optimization, all augmented classes are viewed independently, and the relationship between them is not explored. Moreover, only the predictions of the non-augmented classes $(0^{\\circ})$ are considered valid during testing [66], which leads to a large amount of information valuable for the current task being discarded.", + "bbox": [ + 75, + 519, + 468, + 712 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To precisely utilize the valuable knowledge obtained from the above self-supervised label augmentation, we propose an asymmetric knowledge aggregation approach for NECIL. Concretely, for the past tasks, we take in the knowledge of the proxies associated with the original classes:", + "bbox": [ + 75, + 712, + 468, + 781 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} _ {a g g} (c \\mid F _ {o l d}) = \\frac {\\exp \\left(w _ {c , 0} ^ {T} F _ {o l d}\\right)}{\\sum_ {k = 1} ^ {K} \\exp \\left(w _ {k , 0} ^ {T} F _ {o l d}\\right)}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 136, + 783, + 468, + 823 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $K = |C_{total}|$ , $w$ is the proxy of $\\mathcal{G}_S$ and $F_{old}$ is the feature generated by prototype reminiscence. For the current task, the conditional probabilities corresponding to all", + "bbox": [ + 75, + 824, + 468, + 866 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "transformations of each class are aggregated:", + "bbox": [ + 499, + 125, + 798, + 140 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} _ {a g g} (c | \\tilde {F _ {n e w}}) = \\frac {\\exp \\left(\\frac {1}{4} \\sum_ {j = 0} ^ {3} w _ {c , j} ^ {T} F _ {n e w} ^ {j}\\right)}{\\sum_ {k = 1} ^ {K} \\exp \\left(\\frac {1}{4} \\sum_ {j = 0} ^ {3} w _ {k , j} ^ {T} F _ {n e w} ^ {j}\\right)}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 143, + 890, + 192 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $F_{new}^{\\tilde{F}} = \\{F_{new}^{j}\\}_{j=0}^{3}$ represents the set of features extracted from the augmented exemplars $\\tilde{x}_t^i$ by current model $\\mathcal{F}_t$ . As presented in Fig. 3, we transfer the aggregated knowledge to another classifier $\\mathcal{G}_O$ , which only needs to distinguish between non-augmented classes. The loss function $\\mathcal{L}_{ka}$ can be expressed as follows:", + "bbox": [ + 497, + 199, + 890, + 286 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {k a} = K L D \\left(\\mathcal {P} _ {a g g} (\\cdot | F) \\| \\mathcal {G} _ {O} (F; \\phi)\\right), \\\\ = \\mathcal {P} _ {a g g} (\\cdot | F) \\log \\frac {\\mathcal {P} _ {a g g} (\\cdot | F)}{\\mathcal {G} _ {O} (F ; \\phi)} \\tag {8} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 569, + 288, + 890, + 336 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\phi$ denotes the parameters of $\\mathcal{G}_O$ and $KLD(\\cdot|\\cdot)$ is the Kullback-Leibler divergence. The knowledge learned from the new data is utilized as much as possible and the invalid weights are discarded to obtain a more refined classifier. During testing inference, only the classifier $\\mathcal{G}_O$ is used.", + "bbox": [ + 497, + 342, + 890, + 413 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Integrated Optimization Objective", + "text_level": 1, + "bbox": [ + 499, + 419, + 801, + 434 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspiring ourselves from [66], we employ the well-known knowledge distillation (KD) [68, 19] to regularize the feature extractor. Specifically, we minimize the Euclidean distance between the features of new data extracted by current model $\\mathcal{F}_t$ and that of previous model $\\mathcal{F}_{t - 1}$ to constrain the feature extractor, which can be formulated as:", + "bbox": [ + 497, + 440, + 890, + 523 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {k d} = \\left\\| \\mathcal {F} _ {t} \\left(\\tilde {x} _ {t} ^ {i}; \\theta_ {t}\\right) - \\mathcal {F} _ {t - 1} \\left(\\tilde {x} _ {t} ^ {i}; \\theta_ {t - 1}\\right) \\right\\| _ {2}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 561, + 528, + 890, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the assistance of prototype reminiscence, the disparity between the stored prototype and the updated model can be significantly mitigated. We also calculate the cross-entropy loss for $\\mathcal{G}_S$ and $\\mathcal{G}_O$ , respectively. With these considerations above, the total loss function $\\mathcal{L}_{total}$ can be expressed as:", + "bbox": [ + 497, + 549, + 890, + 619 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {n e w}} = \\mathcal {L} _ {c e} \\left(\\mathcal {G} _ {S} \\left(\\tilde {\\mathcal {F}} _ {t} \\left(\\tilde {x _ {t} ^ {i}}; \\theta_ {t}\\right); \\varphi_ {t}\\right)\\right) \\tag {10} \\\\ + \\mathcal {L} _ {c e} \\left(\\mathcal {G} _ {O} \\left(\\mathcal {F} _ {t} \\left(\\tilde {x _ {t} ^ {\\prime}}; \\theta_ {t}\\right); \\phi_ {t}\\right)\\right) + \\mathcal {L} _ {k a}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 635, + 890, + 674 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {o l d} = \\mathcal {L} _ {c e} \\left(\\mathcal {G} _ {S} \\left(F _ {o l d} ^ {i}; \\varphi_ {t}\\right)\\right) \\tag {11} \\\\ + \\mathcal {L} _ {c e} \\left(\\mathcal {G} _ {O} \\left(F _ {o l d} ^ {i}\\right); \\phi_ {t})\\right) + \\mathcal {L} _ {k a}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 676, + 890, + 711 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {n e w}} + \\alpha \\mathcal {L} _ {\\text {o l d}} + \\gamma \\mathcal {L} _ {\\text {k d}}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 536, + 714, + 890, + 730 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{new}$ is the loss of new data $\\tilde{x}_t^i$ , $\\mathcal{L}_{old}$ is the loss of the feature $F_{old}^{i}$ generated by prototype reminiscence. The loss weights $\\alpha$ and $\\gamma$ are both set to 15 in our experiments.", + "bbox": [ + 497, + 739, + 890, + 783 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 499, + 794, + 631, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setting", + "text_level": 1, + "bbox": [ + 499, + 817, + 699, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. To evaluate the performance of our method, we conduct sufficient experiments on three benchmarks includ", + "bbox": [ + 499, + 838, + 890, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1776", + "bbox": [ + 468, + 887, + 500, + 897 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/2ac9860766d1c512fc9c04bd5895b6d2ce894c4f4d1548d8f51ecfdf03db2bae.jpg", + "table_caption": [ + "Table 1. Quantitative comparisons of the average incremental accuracy (%) with other methods at different task number settings on CIFAR-100, TinyImageNet, and ImageNet-Subset. $E = {20}$ represents exemplar-based methods and storing 20 exemplars for each old class. $E = 0$ represents non-exemplar methods. The relative improvement compared to the SOTA NECIL method is shown by the red footnotes." + ], + "table_footnote": [], + "table_body": "
MethodsCIFAR-100TinyImageNetImageNet-Subset
5 phases10 phases20 phases5 phases10 phases20 phases10 phases
E=20iCaRL-CNN51.0748.6644.4334.6431.1527.9050.53
iCaRL-NCM [42]58.5654.1950.5145.8643.2938.0460.79
EEIL [9]60.3756.0552.3447.1245.0140.5063.34
UCIR [20]63.7862.3959.0749.1548.5242.8366.16
DER [58]73.2172.8169.97———75.36
E=0EWC [23]24.4821.2015.8918.8015.7712.3920.40
LwFMC [42]45.9327.4320.0729.1223.1017.4331.18
MUC [32]49.4230.1921.2732.5826.6121.9535.07
SDC [60]56.7757.0058.90———61.12
PASS [66]63.4761.8458.0949.5547.2942.0761.80
SSRE [67]65.8865.0461.7050.3948.9348.1767.69
Ours70.02+4.1468.86+3.8265.86+4.1653.32+2.9352.61+3.6849.83+1.6668.98+1.29
", + "bbox": [ + 80, + 159, + 884, + 343 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ing CIFAR-100 [25], TinyImageNet [26] and ImageNet-Subset (random seed 1993) [12]. For CIFAR-100 and TinyImageNet there are three incremental settings (5, 10, and 20 phases) and for ImageNet-Subset there is one (10 phases). For the sequencing and division of all dataset classes, we strictly follow the specification in [66].", + "bbox": [ + 75, + 350, + 468, + 434 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. Following [66], we use ResNet-18 [18] as the backbone network. The model is trained for 100 epochs on each new task. For comparisons on all datasets, the threshold of our prototype reminiscence is set to 0.6. During training, the batch size is set to 128 and the model is optimized by the Adam optimizer with $\\beta_{1} = 0.9$ , $\\beta_{2} = 0.999$ and $\\epsilon = 1e^{-8}$ (weight decay 2e-4). The initial learning rate is 0.001 and is adjusted with the cosine annealing algorithm [35] with a period of 32 epochs.", + "bbox": [ + 75, + 434, + 468, + 559 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics. As with [66], we employ average incremental accuracy [42] and average forgetting [10] as the evaluation metric. The average incremental accuracy is defined as the average of the accuracies over seen classes across all incremental phases (including the first phase), which reflects the overall incremental performance of the method. The average forgetting is the average difference between the peak task accuracy and the final task accuracy after incremental learning is completed, and the lower value represents better performance.", + "bbox": [ + 75, + 560, + 468, + 698 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with SOTA", + "text_level": 1, + "bbox": [ + 75, + 705, + 297, + 720 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our method with the state-of-the-art (SOTA) methods of NECIL (EWC [23], LwF_MC [42], MUC [32], SDC [60], PASS [66] and SSRE [67]) and several classical exemplar-based CIL approaches (iCaRL [42], EEIL [9] and UCIR [20]). The results reported for PASS are obtained with self-supervised learning. We reproduce the SSRE with label augmentation in the supplementary materials. As adopted in [67], we memorize 20 samples for the exemplar-based methods.", + "bbox": [ + 75, + 726, + 468, + 851 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Accuracy and forgetting. The quantitative comparisons", + "bbox": [ + 95, + 852, + 468, + 866 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/52e426f7c4e3e44d9e6e6acc485a79e591f3c03945f41655c2c97aae927c428e.jpg", + "table_caption": [ + "Table 2. Results of average forgetting on 5, 10 and 20 phases." + ], + "table_footnote": [], + "table_body": "
MethodsCIFAR-100TinyImageNet
5102051020
iCaRL-CNN42.1345.6943.5436.8936.7045.12
iCaRL-NCM24.9028.3235.5327.1528.8937.40
EEIL23.3626.6532.4025.5625.5135.04
UCIR21.0025.1228.6520.6122.2533.74
LwFMC44.2350.4755.4654.2654.3763.54
MUC40.2847.5652.6551.4650.2158.00
PASS25.2030.2530.6118.0423.1130.55
SSRE18.3719.4819.009.1714.0614.20
Ours12.5914.6517.3911.8413.9518.51
Ours w/o AKA7.186.4210.304.575.109.05
", + "bbox": [ + 500, + 359, + 897, + 496 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "of the average incremental accuracy are reported in Tab. 1. Compared to the suboptimal NECIL method (SSRE), we improve the accuracy on CIFAR-100, TinyImageNet and ImageNetSubset by $6.30\\%$ , $5.59\\%$ , and $1.91\\%$ , respectively. Moreover, our method shows competitive or even better performance than the classical exemplar-based methods. Certainly, it still slightly inferior to the SOTA exemplar-based method DER [58]. In Fig. 4 we show the accuracy change curves on three benchmarks. Our method is superior at almost all phases, achieving a better balance between stability and plasticity. To further evaluate the above methods, we provide the results of average forgetting in Tab. 2, where our method also performs superiorly. In addition, since the proposed asymmetric knowledge aggregation (AKA) improves the classification accuracy on the current task, the forgetting metric is increased, however this is harmless to overall performance. We will report more analysis in the following and supplementary materials. Experimental results show that our approach can mitigate catastrophic forgetting despite the lack of past task data, which is a more privacy-safe and memory-friendly manner to achieve CIL.", + "bbox": [ + 497, + 503, + 890, + 793 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 499, + 802, + 653, + 817 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we conduct several ablation studies on the proposed method. To better analyze the impact of the core designs, our approach is divided into three compo", + "bbox": [ + 497, + 824, + 892, + 866 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1777", + "bbox": [ + 468, + 887, + 500, + 897 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1a93b4399b3cbc81db839218245190045e0234094af61aff710493fbc422cd9a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 122, + 285, + 235 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6dfb9cba030c3399923ddda21bda3cebbc2d0b94bfdac529573ca091045bd150.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 122, + 485, + 233 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/62fc92677b026b68b08ff7366fc57c4df721bd826f53742c4985071957014b64.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 495, + 122, + 687, + 233 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1cca4e323c647fbb69f2cf4829a03959acc53524841a783d271f3e68ee875804.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 147, + 870, + 212 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4d6a06f8c3cd09bcaaeb9a74391dce3f49bdb255a91bf0da2ecd6baf4c819dc0.jpg", + "image_caption": [ + "Figure 4. Illustration of the classification accuracy changes as tasks are being learned on CIFAR-100, TinyImageNet and ImageNet-Subset, which contains the complete curves. Precise data of our method is presented in the supplementary materials." + ], + "image_footnote": [], + "bbox": [ + 80, + 239, + 285, + 359 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fa6030409957229536ab8144b33bb10ebbee21502c2d522422b63d516752d2e0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 239, + 485, + 359 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4fc92919e116aa6bcff82370aa6c0860bf5e4831303dcad7ae5ca04ec9b6bb4e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 497, + 239, + 687, + 359 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8ca0894e4222ab6d2425584a4aacf2d2148f2c5c227424a938ab30aee8a09185.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 239, + 887, + 359 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b6a272adb0549a7f5994e9c4f161326c6c244c7d19c265bc95bb1f46ca419111.jpg", + "table_caption": [ + "Table 3. Ablation study (in average incremental accuracy) of our method on CIFAR-100 and TinyImageNet datasets." + ], + "table_footnote": [], + "table_body": "
ComponentsCIFAR-100TinyImageNet
PRSLAAKA5 phases10 phases20 phases5 phases10 phases20 phases
56.2751.0243.9837.9332.4423.98
✓66.2163.8057.3145.8544.0435.93
✓61.2759.5955.1446.6543.8838.13
✓✓68.4867.5665.0352.1551.6749.30
✓✓✓70.0268.8665.8653.3252.6149.83
", + "bbox": [ + 122, + 404, + 838, + 507 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/57077b2120d55956c119e0c082a92a954a06b5398a5d2b4bd237e23f969e835c.jpg", + "image_caption": [ + "Figure 5. Influence of the threshold in prototype reminiscence." + ], + "image_footnote": [], + "bbox": [ + 100, + 516, + 443, + 676 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "nents: prototype reminiscence (PR), self-supervised label augmentation (SLA) and asymmetric knowledge aggregation (AKA). As a general trick, KD was used in all experimental settings. To explicitly illustrate the effectiveness of PR, in the baseline model we save the prototypes and directly use them for training. As shown in the $1^{st}$ and $2^{nd}$ rows of Tab. 3, PR successfully maintains the discrimination and balance between the old and new classes and makes an impressive progress on the baseline model. When SLA acts on the baseline model alone, it is effective, but there is still a bias in the classifier, while using it with PR achieves promising results. AKA and SLA are adopted as a whole.", + "bbox": [ + 75, + 700, + 468, + 866 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In addition to the overall performance improvement, AKA is more about enhancing the model's understanding of the new task to satisfy the latest business requirements.", + "bbox": [ + 499, + 517, + 890, + 559 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To investigate the sensitivity of the threshold $\\eta$ in our prototype reminiscence, we plot its fluctuation curve on CIFAR-100 dataset. As presented in Fig. 5, when $\\eta$ is low, the generated old class features are restricted to concentrate around the preserved prototypes thus lacking the ability to adapt to the changes of the representation space, which results in poor performance. As the constraint is relaxed ( $\\eta$ increases), the effect of PR gradually comes into its own and peaks in performance at about $\\eta = 0.6$ . When the threshold continues to increase, the performance gain from PR starts to diminish because as the constraint fades away, the number of outlier features generated by PR gradually increases, which disturbs the learning of the model.", + "bbox": [ + 497, + 560, + 890, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Analysis", + "text_level": 1, + "bbox": [ + 499, + 748, + 601, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visualization. To demonstrate the advantages of our prototype reminiscence, we visualise the 2D embeddings of feature vectors with t-SNE [51]. In Fig. 6 (c) and (d), the old class features are generated by the stored prototypes. Compared with fine-tuning, the confusion of old class features is alleviated in the results of Gaussian noise augmentation. However, the overlap between the distributions of different", + "bbox": [ + 497, + 769, + 892, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1778", + "bbox": [ + 468, + 887, + 500, + 897 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/aadac86b2364d8127afabbcd24d59af9a706816e6951e1f30fd0d3174624915e.jpg", + "image_caption": [ + "(a) Initial Phase" + ], + "image_footnote": [], + "bbox": [ + 87, + 122, + 267, + 225 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f5ad0d8978c7c409ddfbfef28eb6e183af4419de9d4362f702ed13fb6fd12883.jpg", + "image_caption": [ + "(b) Finetuning" + ], + "image_footnote": [], + "bbox": [ + 275, + 123, + 455, + 225 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c5152f78a0a7279076f48e153b2fb4c95903f064012415578b92d879000cf986.jpg", + "image_caption": [ + "(c) Gaussian Noise Augmentation" + ], + "image_footnote": [], + "bbox": [ + 87, + 238, + 267, + 333 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ad601d821c7c92f1990042a930846170d7d15e62e7f4bd0c98976da907fa5deb.jpg", + "image_caption": [ + "(d) Prototype Reminiscence" + ], + "image_footnote": [], + "bbox": [ + 275, + 238, + 455, + 333 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ab0db62b14133d9c28fade7251a6244010a99f0990fd1d41fdf76745d40cdb18.jpg", + "image_caption": [ + "Figure 6. Visualization of different augmentation schemes.", + "(a) Finetuning", + "Figure 7. The comparison of confusion matrix of finetuning, iCaRL and our method on CIFAR-100 (10 phases)." + ], + "image_footnote": [], + "bbox": [ + 78, + 359, + 205, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/758adda0148ad68cce97cf41348b3382f62a1da0c4f82be9cc4f815784ccc8c8.jpg", + "image_caption": [ + "(b) iCaRL" + ], + "image_footnote": [], + "bbox": [ + 211, + 359, + 324, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5a76e810a74cead764772aa1f5a8b2d4ef57553dc486fb238d39c069a29bac17.jpg", + "image_caption": [ + "(c) Ours" + ], + "image_footnote": [], + "bbox": [ + 332, + 359, + 467, + 441 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "classes is still significant, and in particular the confusion between the generated features. Instead, the feature distributions of different old classes reshaped by our method are relatively dispersed among each other.", + "bbox": [ + 75, + 490, + 468, + 545 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Classification bias of the model. To evaluate the performance differences between the old and new classes, we compared the confusion matrix of finetuning, iCaRL and our method on CIFAR-100. As shown in Fig. 7, since samples of old classes are not available, finetuning tends to classify the samples into new classes. The confusion is alleviated by iCaRL, but still shows a preference for new classes. The confusion matrix of our method exhibits better overall performance without favouring old or new classes. Thanks to PR and AKA, the classification bias between old and new classes is well handled.", + "bbox": [ + 75, + 547, + 468, + 698 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The role of asymmetric knowledge aggregation. To better illustrate the role of the asymmetric knowledge aggregation, we compare the changes in classification accuracy for the initial task during subsequent incremental learning, and the performance on each new task in the presence or absence of AKA. The results for the three settings on CIFAR100 are shown in Fig. 8. On the one hand, the performance degradation in the initial task caused by the introduction of AKA is negligible; on the other hand, the discrimination of new classes is considerably improved. As analyzed in the introduction, AKA can improve the model's understanding of new tasks as non-destructively as possible.", + "bbox": [ + 75, + 700, + 468, + 866 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/10147fedf265c9181e8fcdaf6ed42f86c299c836316fc3c5f049cf87096c1e58.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 502, + 123, + 700, + 225 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e8453a93d9cc38dc040f20a2ae2da20f8c4964320ac6b8155d7409ab0ea79266.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 704, + 124, + 887, + 225 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5ae56df30d9b202fa2459ecd2ba9f6f8403e6a36292d422294a8fd6b8e179cbc.jpg", + "image_caption": [ + "CIFAR-100 (10 phases)" + ], + "image_footnote": [], + "bbox": [ + 502, + 239, + 697, + 323 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e2891e1f7b2a10b4b7bb0de69ac093762da7ef12e2a34ab91a7a6090c0815469.jpg", + "image_caption": [ + "CIFAR-100 (10 phases)" + ], + "image_footnote": [], + "bbox": [ + 704, + 239, + 887, + 323 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9c06c2f4009b147b4c7fe01fb9f7324b57254b1d4acc18d4bb1f8b5bee743399.jpg", + "image_caption": [ + "CIFAR-100 (20 phases)", + "Figure 8. The first column is the classification accuracy on the initial task, which changes with the incremental phase. The second column shows the change in classification accuracy on the new task. The proposed knowledge aggregation allows better learning of new tasks with little impact on existing knowledge." + ], + "image_footnote": [], + "bbox": [ + 502, + 337, + 697, + 427 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7690fc172bf6dc811de44a56b1121791395627ec4228f087e5709c13b575ec1a.jpg", + "image_caption": [ + "CIFAR-100 (20 phases)" + ], + "image_footnote": [], + "bbox": [ + 704, + 337, + 887, + 427 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 499, + 503, + 616, + 516 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we address the NECIL issue from two perspectives of resisting catastrophic forgetting and boosting plasticity of the model, proposing prototype reminiscence and augmented asymmetric knowledge aggregation, respectively. In particular, we pay attention to the performance of the incremental learner on new tasks which often represent the latest business requirements, and design an asymmetric knowledge aggregation strategy for better adaptation to new tasks. Extensive evaluations demonstrate that our approach outperforms the SOTA NECIL methods and shows strong competitiveness with classical exemplar-based methods in the absence of stored samples.", + "bbox": [ + 497, + 520, + 890, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. For each prototype reminiscence, the prototype and the feature are selected randomly. When the selected prototype and feature are less similar (i.e., farther apart in the feature space), there may be outliers in the generated features of old classes. Exploring the impact of outliers on training may be of interest.", + "bbox": [ + 497, + 686, + 890, + 769 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work is partially supported by the Key Research and Development Program of Hubei Province (2021BAA187), National Natural Science Foundation of China under Grant (62176188), Zhejiang lab (NO.2022NF0AB01), the Special Fund of Hubei Luojia Laboratory (220100015) and CAAI-Huawei MindSpore Open Fund.", + "bbox": [ + 497, + 769, + 890, + 866 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1779", + "bbox": [ + 468, + 887, + 500, + 897 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 124, + 171, + 138 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Davide Abati, Jakub Tomczak, Tijmen Blankevoort, Simone Calderara, Rita Cucchiara, and Babak Ehteshami Bejnordi. Conditional channel gated networks for task-aware continual learning. In CVPR, pages 3931-3940, 2020. 3", + "[2] Hongjoon Ahn, Jihwan Kwak, Subin Lim, Hyeonsu Bang, Hyojun Kim, and Taesup Moon. 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NeurIPS, 31, 2018. 5" + ], + "bbox": [ + 502, + 125, + 890, + 853 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "1781", + "bbox": [ + 468, + 887, + 499, + 897 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Prototype Reminiscence and Augmented Asymmetric Knowledge Aggregation for Non-Exemplar Class-Incremental Learning/f06e28ba-39c2-463d-9177-75781355ca62_model.json b/2023/Prototype Reminiscence and Augmented Asymmetric Knowledge Aggregation for Non-Exemplar Class-Incremental Learning/f06e28ba-39c2-463d-9177-75781355ca62_model.json new file mode 100644 index 0000000000000000000000000000000000000000..eea8019f9e232f28799411f189653a3fdfc43aff --- /dev/null +++ b/2023/Prototype Reminiscence and Augmented Asymmetric Knowledge Aggregation for Non-Exemplar Class-Incremental Learning/f06e28ba-39c2-463d-9177-75781355ca62_model.json @@ -0,0 +1,2618 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.13, + 0.051, + 0.201, + 0.085 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.254, + 0.049, + 0.79, + 0.062 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation." + }, + { + "type": "header", + "bbox": [ + 0.334, + 0.063, + 0.71, + 0.075 + ], + "angle": 0, + "content": "Except for this watermark, it is identical to the accepted version;" + }, + { + "type": "header", + "bbox": [ + 0.305, + 0.076, + 0.74, + 0.088 + ], + "angle": 0, + "content": "the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.162, + 0.877, + 0.205 + ], + "angle": 0, + "content": "Prototype Reminiscence and Augmented Asymmetric Knowledge Aggregation for Non-Exemplar Class-Incremental Learning" + }, + { + "type": "text", + "bbox": [ + 0.369, + 0.228, + 0.594, + 0.246 + ], + "angle": 0, + "content": "Wuxuan Shi\\(^{1}\\), Mang Ye\\(^{1,2*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.232, + 0.246, + 0.74, + 0.261 + ], + "angle": 0, + "content": "\\(^{1}\\)School of Computer Science, Wuhan University, Wuhan, China" + }, + { + "type": "text", + "bbox": [ + 0.319, + 0.262, + 0.652, + 0.278 + ], + "angle": 0, + "content": "\\(^{2}\\) Hubei Luojia Laboratory, Wuhan, China" + }, + { + "type": "text", + "bbox": [ + 0.302, + 0.28, + 0.667, + 0.294 + ], + "angle": 0, + "content": "https://shiwuxuan.github.io/PRAKA-project" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.325, + 0.314, + 0.34 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.355, + 0.474, + 0.66 + ], + "angle": 0, + "content": "Non-exemplar class-incremental learning (NECIL) requires deep models to maintain existing knowledge while continuously learning new classes without saving old class samples. In NECIL methods, prototypical representations are usually stored, which inject information from former classes to resist catastrophic forgetting in subsequent incremental learning. However, since the model continuously learns new knowledge, the stored prototypical representations cannot correctly model the properties of old classes in the existence of knowledge updates. To address this problem, we propose a novel prototype reminiscence mechanism that incorporates the previous class prototypes with arriving new class features to dynamically reshape old class feature distributions thus preserving the decision boundaries of previous tasks. In addition, to improve the model generalization on both newly arriving classes and old classes, we contribute an augmented asymmetric knowledge aggregation approach, which aggregates the overall knowledge of the current task and extracts the valuable knowledge of the past tasks, on top of self-supervised label augmentation. Experimental results on three benchmarks suggest the superior performance of our approach over the SOTA methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.682, + 0.21, + 0.697 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.706, + 0.47, + 0.816 + ], + "angle": 0, + "content": "In recent years, deep neural networks have achieved great success on various tasks. In dynamic and open environments, deep models also require the ability to continuously learn new tasks as the input stream is updated. Hence, class-incremental learning (CIL), which aims to learn a unified classifier that can classify all seen classes under progressive changes in the classes to be learned, has attracted extensive attention [30, 41, 16, 47, 31, 28]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.817, + 0.47, + 0.845 + ], + "angle": 0, + "content": "As new data becomes available, it is computationally expensive to jointly retrain the model with new and old class" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.325, + 0.891, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.408, + 0.891, + 0.506 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.507, + 0.893, + 0.622 + ], + "angle": 0, + "content": "Figure 1. Idea illustration. (a) Joint training with abundant samples. (b) Baseline: Updating the model with the memorized prototype and new data, which narrows the decision boundary of the old classes. (c) Gaussian Noise Augmentation [66]: The decision boundary of the old class is retained, but it introduces an overlap between the old and new class distributions due to the change in representation space. (d) With prototype reminiscence, newly learned information can be injected while reshaping the feature distribution of past data to reduce overlap and resist forgetting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.632, + 0.893, + 0.77 + ], + "angle": 0, + "content": "samples. Worse still, the old class samples could not be fully accessible. In this case, an alternative is to fine-tune the model on new data, yet catastrophic forgetting [38, 15] will be a serious challenge. The decision boundary of the unified classifier would be significantly changed and biased towards the new classes. Conversely, another direction is to fix the feature embedding space of a trained model, which suffers from frustrating generalization ability and thus performs poorly on new tasks, i.e., the plasticity of the model is greatly degraded." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.77, + 0.894, + 0.868 + ], + "angle": 0, + "content": "To overcome the catastrophic forgetting issue, many CIL methods [42, 8, 6, 56, 2, 53] store a fraction of the old data in memory and replay them in subsequent incremental phases to maintain the existing knowledge. Unfortunately, storing data poses privacy concerns and comes at a sharp cost to memory and computation. In this paper, we follow a paradigm holding for more extensive applications," + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.854, + 0.405, + 0.867 + ], + "angle": 0, + "content": "*Corresponding Author: Mang Ye (yemang@whu.edu.cn)" + }, + { + "type": "page_number", + "bbox": [ + 0.47, + 0.888, + 0.502, + 0.899 + ], + "angle": 0, + "content": "1772" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.127, + 0.47, + 0.168 + ], + "angle": 0, + "content": "termed non-exemplar class-incremental learning (NECIL) [66, 67], which solves the catastrophic forgetting problem in CIL scenario without preserving old class samples." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.17, + 0.47, + 0.446 + ], + "angle": 0, + "content": "For NECIL, a natural substitute for storing data is to generate pseudo-samples of previous classes by deep generative models [62, 54, 46, 49, 57] such as GAN [4, 17]. However, it is unstable and ineffective to train generative models for non-stationary data streams [65]. Catastrophic forgetting can also have a negative impact on the generative model resulting in a simultaneous decrease in the effectiveness of both models. Instead of focusing on old data, some works turn to estimating model parameters that are important for previous tasks and constraining their changes [23, 61, 3]. Nevertheless, the constraints on the model parameters lead to poor generalization ability to long-sequence tasks. Besides, several studies propose to dynamically expand the network structure during the process of incremental learning [44, 58, 59, 37, 64]. Although this strategy can efficiently handle long sequences of tasks and ultimately maintain the performance of the old classes, the computational resource requirements associated with creating and storing additional network components and reasoning about multiple forward propagations are frustrating." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.449, + 0.47, + 0.669 + ], + "angle": 0, + "content": "Recently, some prototype-based NECIL methods have achieved impressive performance [66, 67, 60, 50]. They use prototypical representations (typically the class mean in the deep feature space) memorized for each old class to model the feature distribution of past data and inject information from the previous classes in subsequent incremental learning. Rather than storing samples, this strategy is more memory efficient and privacy secure. Nevertheless, as shown in Fig. 1 (b), direct training with saved prototypes and current data struggles to prevent the collapse of decision boundaries, due to the lack of old class features. Some works augment the prototypes by adding Gaussian noise [66] or over-sampling [67] to enrich old class features. However, updates of the model on continuous data streams could lead to inevitable changes in the representation of old classes, making the saved prototypes increasingly outdated." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.671, + 0.47, + 0.782 + ], + "angle": 0, + "content": "The feature distribution simulated by the above strategies cannot accommodate such changes due to the missing consideration of knowledge updates. It could result in overlap between the distributions of different classes, especially between new and old classes, as shown in Fig. 1 (c). Consequently, combining newly acquired information with stored prototypes to dynamically model past data distributions is crucial to resist catastrophic forgetting in NECIL." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.784, + 0.47, + 0.867 + ], + "angle": 0, + "content": "To address this challenge, we propose a prototype reminiscence mechanism to track the evolution of the old class representations by injecting new knowledge from the updating network while reshaping the feature distribution. Specifically, we perform a random bidirectional interpolation operation between the extracted new class features and" + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.125, + 0.86, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.41, + 0.893, + 0.462 + ], + "angle": 0, + "content": "Figure 2. We introduce self-supervised label augmentation to learn generalizable and transferable representations. The knowledge of the self-supervised classifier is aggregated and transferred to another classifier to take full advantage of it." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.892, + 0.628 + ], + "angle": 0, + "content": "the saved old class prototypes to enrich old class features. As shown in Fig. 1 (d), it expands the prototype to protect the decision boundaries of old classes and to counteract catastrophic forgetting. Since the feature distribution of past tasks is dynamically adjusted to the current representation space, the overlap between the old and new classes is reduced. Thus, the discrimination and balance between the old and new classes are maintained. Cooperating with the well-known knowledge distillation (KD) [20, 19], the mismatch between the preserved prototypes and the continuously updated network is alleviated." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.892, + 0.81 + ], + "angle": 0, + "content": "In addition to dealing with catastrophic forgetting, when new data arrives, performance on the current task is also of great concern, necessitating the plasticity of the incremental learner. This mainly involves two aspects: learning generalizable and transferable representations, fully utilizing the information from new data. Previous works [66, 55] have achieved good progress on the first aspect by self-supervised label augmentation [27], however they ordinarily disregard the second. The new task contains abundant information that the network has never encountered and will have a stronger influence on model updates. Improving the plasticity of the model from continuous data streams requires a simultaneous approach from both aspects." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.811, + 0.892, + 0.867 + ], + "angle": 0, + "content": "To solve this bottleneck, we contribute an augmented asymmetric knowledge aggregation approach to enhance the plasticity of the model noninvasively. Taking inspiration from [24, 27], we first augment the new classes with" + }, + { + "type": "page_number", + "bbox": [ + 0.47, + 0.888, + 0.501, + 0.898 + ], + "angle": 0, + "content": "1773" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.127, + 0.473, + 0.291 + ], + "angle": 0, + "content": "rotation as self-supervision, which requires the model to acquire task-agnostic representations to improve its generalization ability. Furthermore, as illustrated in Fig. 2, we selectively aggregate the valuable knowledge in the augmented classifier—valid weights of past tasks are extracted, and the information captured on the current task is sufficiently exploited. This asymmetric knowledge aggregation scheme can condense the knowledge learned via self-supervised label augmentation (SLA) to make the classifier more purified. It further improves the incremental learner's performance on the new tasks without discrimination scari-fication on old classes." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.293, + 0.45, + 0.306 + ], + "angle": 0, + "content": "To summarize, our main contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.317, + 0.469, + 0.372 + ], + "angle": 0, + "content": "- We propose a simple yet effective method of prototype reminiscence for NECIL, which models feature distribution for the past data in a continuously updated representation space to resist catastrophic forgetting." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.383, + 0.469, + 0.437 + ], + "angle": 0, + "content": "- We contribute augmented asymmetric knowledge aggregation, which learns task-agnostic representations and fully captures the newly acquired knowledge to improve the plasticity of incremental learners." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.449, + 0.469, + 0.504 + ], + "angle": 0, + "content": "- Extensive experiments on three benchmarks demonstrate that our method achieves state-of-the-art performance. We also provide a detailed ablation study to analyze the influence of each component." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.317, + 0.469, + 0.504 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.518, + 0.219, + 0.532 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.541, + 0.33, + 0.556 + ], + "angle": 0, + "content": "2.1. Class-Incremental Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.562, + 0.47, + 0.603 + ], + "angle": 0, + "content": "Current CIL methods can be roughly divided into three categories: rehearsal-based methods, regularization-based methods and structure-based methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.604, + 0.473, + 0.867 + ], + "angle": 0, + "content": "Rehearsal-based methods maintain the distribution of old classes by saving exemplars of fixed memory size to jointly train the model with current data. Based on the saved samples, some works investigate knowledge distillation to prevent forgetting [56, 42, 13], while others try to combine regularization of gradients and rehearsal to make more efficient use of the preserved data [43, 34, 11]. In addition, several papers have studied the impact of memory management schemes [5, 22, 33]. Regularization-based methods identify the key model parameters for the previous tasks, penalizing their changes when learning the current task [23, 61, 3, 40]. The difference between these methods is the association of each network parameter with importance weights stored in incremental learning. Structure-based methods dynamically modify the network architecture to maintain existing knowledge and adapt to new tasks. They usually expand the network structure in depth or width when facing a new task [59, 21, 29, 58], or mask parts of the network for different tasks [45, 36, 1]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.127, + 0.892, + 0.389 + ], + "angle": 0, + "content": "Recently, some works have researched the use of class prototypes to implement non-exemplar class-incremental learning [66, 60, 67, 50], which somewhat reduces the issues of data privacy security and memory constraints. Yu et al. [60] approximate and compensate for the semantic drift of previous tasks during the training of the new task. Based on this, Toldo et al. [50] propose to jointly exploit semantic drift and feature drift to update the representations of past classes. Apart from investigating the evolution of prototypes as incremental learning occurs, there are some studies that focus on the ways to model past data distributions by prototypes [66, 67]. Note that this strategy is orthogonal to the above methods for drift estimation, and our method falls into this category. Zhu et al. [66] introduce Gaussian noise to augment the prototype to restrain the decision boundaries of old classes. Zhu et al. [67] propose a prototype selection mechanism that uses samples of the new data similar to the old classes for distillation to reduce confusion between the newly added classes and the original classes." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.397, + 0.785, + 0.412 + ], + "angle": 0, + "content": "2.2. Self-supervised Learning in CIL" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.417, + 0.892, + 0.722 + ], + "angle": 0, + "content": "The objective of self-supervised learning (SSL) is to acquire transferable representations that are applicable for other tasks. This coincides with the need for IL to inhibit task-level overfitting phenomenon and rapidly adapt to new tasks. Hence, some works explore improving the quality of the learned representations by SSL in the CIL setting [66, 55, 7, 14]. Wu et al. [55] learn class-independent knowledge and multi-perspective knowledge by SSL to make a trade-off between gaining new information and maintaining old knowledge. Fini et al. [14] attempt to seamlessly convert the existing self-supervised loss function into distillation mechanisms plugged into the CIL framework. It also points out that simply introducing SSL can approach or outperform supervised learning in the CIL setting, while this is not always the case for other settings (data-incremental and domain-incremental). Zhu et al. [66] provide better initialization for learning the next task by using rotation as self-supervised information for label augmentation to reduce forgetting from model updates. Our SLA is implemented in the same way as the SSL in [66]. On top of [66], we further improve the upper bound of the incremental learner's understanding of new tasks." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.733, + 0.637, + 0.75 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.756, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Problem Statement. In this paper, we consider nonexemplar class-incremental learning (NECIL), where no samples from old classes are stored. The training data for the incremental task \\( t \\in \\{1, \\dots, T\\} \\) is denoted as \\( D_{t} = \\{X_{t}, Y_{t}\\} = \\{x_{t}^{i}, y_{t}^{i}\\}_{i=1}^{n_{t}} \\), where \\( n_{t} \\), \\( x_{t}^{i} \\) and \\( y_{t}^{i} \\in C_{t} \\) represent the number of training samples, an input sample and its corresponding label for task \\( t \\), respectively. \\( C_{t} \\) is the class set of task \\( t \\) and all the incremental classes are disjoint, i.e.," + }, + { + "type": "page_number", + "bbox": [ + 0.47, + 0.888, + 0.502, + 0.899 + ], + "angle": 0, + "content": "1774" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.125, + 0.531, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.125, + 0.887, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.37, + 0.893, + 0.409 + ], + "angle": 0, + "content": "Figure 3. Illustration of our method for NECIL. The classes of current task are augmented by rotation transformation [27]. We expand the stored prototype by prototype reminiscence in the deep feature space to generate the same number of old class features as the batch size each time. During the evaluation, only the current feature extractor \\(\\mathcal{F}_t\\) and the refined classifier \\(\\mathcal{G}_o\\) are used." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.419, + 0.471, + 0.476 + ], + "angle": 0, + "content": "\\(C_1 \\cap \\ldots \\cap C_i = \\emptyset\\). We represent the model with two components: a feature extractor \\(\\mathcal{F}\\) with parameters \\(\\theta\\) and a unified classifier \\(\\mathcal{G}\\) with parameters \\(\\varphi\\). The goal is to find a classification model minimized for some loss function \\(\\mathcal{L}(\\cdot, \\cdot)\\):" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.489, + 0.47, + 0.527 + ], + "angle": 0, + "content": "\\[\n\\underset {\\theta , \\varphi} {\\operatorname {a r g m i n}} \\sum_ {t = 1} ^ {C _ {t}} \\mathbb {E} _ {\\left(x _ {t} ^ {i}, y _ {t} ^ {i}\\right) \\sim D _ {t}} \\left[ \\mathcal {L} \\left(y _ {t} ^ {i}, \\mathcal {G} \\left(\\mathcal {F} \\left(x _ {t} ^ {i}; \\theta\\right); \\varphi\\right)\\right) \\right]. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.533, + 0.47, + 0.574 + ], + "angle": 0, + "content": "As other class-incremental methods, the algorithm has no access to the task label \\( t \\) and is expected to classify all observed classes \\( C_{total} = \\{C_1,\\dots ,C_t\\} \\) at any given point." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.574, + 0.471, + 0.74 + ], + "angle": 0, + "content": "Overview of Framework. Fig. 3 shows an overview of our method. The classes of the current task are augmented by rotation transformation [27] and the augmented data is fed to the feature extractors. For each old class, we memorize a class-representative prototype. Then the prototype reminiscence uses the extracted new class features and the stored old class prototypes to generate old class features for joint training. We aggregate the knowledge from the classifier \\(\\mathcal{G}_S\\) learned with SLA and transfer it to another classifier \\(\\mathcal{G}_O\\) that only recognizes classes without augmentation. At test time, the current feature extractor \\(\\mathcal{F}_t\\) and the refined classifier \\(\\mathcal{G}_O\\) are used for evaluation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.748, + 0.3, + 0.763 + ], + "angle": 0, + "content": "3.1. Prototype Reminiscence" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.769, + 0.47, + 0.825 + ], + "angle": 0, + "content": "At each incremental phase of task \\( t \\), only \\( D_{t} \\) is available in the NECIL setting. Following [66, 60], when learning a new task, we compute and memorize one prototype in the deep feature space for each class:" + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.831, + 0.47, + 0.87 + ], + "angle": 0, + "content": "\\[\nP _ {t, k _ {n e w}} = \\frac {1}{N _ {t , c _ {n e w}}} \\sum_ {n = 1} ^ {N _ {t, c _ {n e w}}} \\mathcal {F} \\left(\\mathbf {X} _ {t, c _ {n e w}}; \\theta_ {t}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.419, + 0.892, + 0.49 + ], + "angle": 0, + "content": "where \\( c_{new} \\in C_{new} = C_t \\) is one class of the current task. To alleviate the catastrophic forgetting, the model is trained jointly on the memorized prototypes \\( \\{P_{old}^1, \\ldots, P_{old}^{|C_{old}|}\\} \\) and current data \\( D_t \\), where \\( C_{old} = C_1 \\cup \\ldots \\cup C_{t-1} \\) denotes the set of past classes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.491, + 0.893, + 0.701 + ], + "angle": 0, + "content": "Whereas prototypes can inject information of past classes in training, the decision boundaries are narrowed due to the lack of rich old class features. Moreover, as the model continuously learns new data, the deep representation space is changing, which poses a challenge to reproduce the properties of old classes. To this end, we propose a prototype reminiscence strategy to dynamically model the feature distribution of past data in an updating representation space. Our strategy is based on a simple yet effective interpolation operation. In general, as shown in Fig. 3, we randomly select a prototype of the old classes \\( P_{old}^{n} \\in \\{P_{old}^{1}, \\dots, P_{old}^{|C_{old}|}\\} \\) and a feature of the new classes \\( F_{new}^{m} \\in \\{F_{new}^{1}, \\dots, F_{new}^{B}\\} \\), where \\( B \\) is the batch size. Then we perform a random bidirectional interpolation operation between \\( P_{old}^{n} \\) and \\( F_{new}^{m} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.705, + 0.892, + 0.737 + ], + "angle": 0, + "content": "\\[\nF _ {o l d} ^ {n} = \\left\\{ \\begin{array}{l} (1 - \\lambda) \\left(P _ {o l d} ^ {n}\\right) + \\lambda \\left(F _ {n e w} ^ {m}\\right), p _ {e} < 0. 5 \\\\ (1 + \\lambda) \\left(P _ {o l d} ^ {n}\\right) - \\lambda \\left(F _ {n e w} ^ {m}\\right), o t h e r w i s e \\end{array} \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.742, + 0.892, + 0.867 + ], + "angle": 0, + "content": "where \\( F_{old}^{n} \\) is the feature generated in the current representation space that has the same label as \\( P_{old}^{n} \\) and \\( p_e \\) is randomly sampled from [0, 1). Considering the design principle of mixup [63, 52], we ensure that the coefficient summary of the two terms for the prototype reminiscence is equal to 1. Different from them, our prototype reminiscence introduces an extrapolation operation, which avoids the generated features being concentrated on one side of the decision boundary. Meanwhile, we choose" + }, + { + "type": "page_number", + "bbox": [ + 0.47, + 0.888, + 0.501, + 0.899 + ], + "angle": 0, + "content": "1775" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.126, + 0.47, + 0.209 + ], + "angle": 0, + "content": "\\(\\lambda \\sim \\mathrm{Beta}(0.5, 0.5) \\in [0, \\eta]\\), where \\(\\eta\\) is a threshold value to control the maximum distance between the generated old class features and the corresponding prototype for avoiding outliers. To make a fair comparison, as in [66], we generate the same number of old class features as the batch size for each batch of new data." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.217, + 0.469, + 0.245 + ], + "angle": 0, + "content": "3.2. Augmented Asymmetric Knowledge Aggregation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.252, + 0.469, + 0.363 + ], + "angle": 0, + "content": "While counteracting forgetting, incremental learners also need to adapt to new tasks. We design an augmented asymmetric knowledge aggregation scheme that endows the model with stronger plasticity. First, we augment the current classes as in [27]. For the current task, the N-way classification problem is extended into a 4N-way classification problem. Specifically, the input data for each class is rotated by \\(90^{\\circ}\\), \\(180^{\\circ}\\), and \\(270^{\\circ}\\) to produce three new classes:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.369, + 0.469, + 0.392 + ], + "angle": 0, + "content": "\\[\n\\tilde {x} _ {t} ^ {i} = \\left\\{x _ {t} ^ {i, j} \\right\\} _ {j = 0} ^ {3} = \\left\\{r o t a t e (x _ {t} ^ {i}, j \\times 9 0 ^ {\\circ}) \\right\\} _ {j = 0} ^ {3}, \\quad (4)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.394, + 0.427, + 0.409 + ], + "angle": 0, + "content": "and we allocate new labels \\( y_{t}^{i} \\) to the augmented data:" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.413, + 0.469, + 0.434 + ], + "angle": 0, + "content": "\\[\n\\tilde {y} _ {t} ^ {i} = \\left\\{y _ {t} ^ {i} \\times 4 + j \\right\\} _ {j = 0} ^ {3}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.438, + 0.469, + 0.52 + ], + "angle": 0, + "content": "Compared to the widely used 4-way self-supervised task, the above approach removes unnecessary invariant properties when learning both the original task and the self-supervised task simultaneously, thereby reducing the loss of discriminative information while obtaining generalizable and transferable representations [27]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.469, + 0.713 + ], + "angle": 0, + "content": "However, for NECIL, the self-supervised label augmentation can only be applied to new classes (past data is not available). Borrowing from some works [39, 48], the classification weight \\( w_{c,j} \\) is denoted as a proxy, where \\( c \\in C_{total} \\) and \\( j \\) represents different rotation transformations. In the subsequent incremental learning, the proxies for the augmented classes \\( (90^{\\circ}, 180^{\\circ}, 270^{\\circ}) \\) of the previous tasks gradually fail, leading to redundancy within the classifier. When using the cross-entropy loss for optimization, all augmented classes are viewed independently, and the relationship between them is not explored. Moreover, only the predictions of the non-augmented classes \\( (0^{\\circ}) \\) are considered valid during testing [66], which leads to a large amount of information valuable for the current task being discarded." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.713, + 0.469, + 0.782 + ], + "angle": 0, + "content": "To precisely utilize the valuable knowledge obtained from the above self-supervised label augmentation, we propose an asymmetric knowledge aggregation approach for NECIL. Concretely, for the past tasks, we take in the knowledge of the proxies associated with the original classes:" + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.784, + 0.469, + 0.824 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} _ {a g g} (c \\mid F _ {o l d}) = \\frac {\\exp \\left(w _ {c , 0} ^ {T} F _ {o l d}\\right)}{\\sum_ {k = 1} ^ {K} \\exp \\left(w _ {k , 0} ^ {T} F _ {o l d}\\right)}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.469, + 0.867 + ], + "angle": 0, + "content": "where \\(K = |C_{total}|\\), \\(w\\) is the proxy of \\(\\mathcal{G}_S\\) and \\(F_{old}\\) is the feature generated by prototype reminiscence. For the current task, the conditional probabilities corresponding to all" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.127, + 0.799, + 0.141 + ], + "angle": 0, + "content": "transformations of each class are aggregated:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.144, + 0.892, + 0.193 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} _ {a g g} (c | \\tilde {F _ {n e w}}) = \\frac {\\exp \\left(\\frac {1}{4} \\sum_ {j = 0} ^ {3} w _ {c , j} ^ {T} F _ {n e w} ^ {j}\\right)}{\\sum_ {k = 1} ^ {K} \\exp \\left(\\frac {1}{4} \\sum_ {j = 0} ^ {3} w _ {k , j} ^ {T} F _ {n e w} ^ {j}\\right)}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.2, + 0.892, + 0.287 + ], + "angle": 0, + "content": "where \\( F_{new}^{\\tilde{F}} = \\{F_{new}^{j}\\}_{j=0}^{3} \\) represents the set of features extracted from the augmented exemplars \\( \\tilde{x}_t^i \\) by current model \\( \\mathcal{F}_t \\). As presented in Fig. 3, we transfer the aggregated knowledge to another classifier \\( \\mathcal{G}_O \\), which only needs to distinguish between non-augmented classes. The loss function \\( \\mathcal{L}_{ka} \\) can be expressed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.289, + 0.891, + 0.337 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {k a} = K L D \\left(\\mathcal {P} _ {a g g} (\\cdot | F) \\| \\mathcal {G} _ {O} (F; \\phi)\\right), \\\\ = \\mathcal {P} _ {a g g} (\\cdot | F) \\log \\frac {\\mathcal {P} _ {a g g} (\\cdot | F)}{\\mathcal {G} _ {O} (F ; \\phi)} \\tag {8} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.343, + 0.892, + 0.414 + ], + "angle": 0, + "content": "where \\(\\phi\\) denotes the parameters of \\(\\mathcal{G}_O\\) and \\(KLD(\\cdot|\\cdot)\\) is the Kullback-Leibler divergence. The knowledge learned from the new data is utilized as much as possible and the invalid weights are discarded to obtain a more refined classifier. During testing inference, only the classifier \\(\\mathcal{G}_O\\) is used." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.42, + 0.802, + 0.435 + ], + "angle": 0, + "content": "3.3. Integrated Optimization Objective" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.441, + 0.892, + 0.524 + ], + "angle": 0, + "content": "Inspiring ourselves from [66], we employ the well-known knowledge distillation (KD) [68, 19] to regularize the feature extractor. Specifically, we minimize the Euclidean distance between the features of new data extracted by current model \\(\\mathcal{F}_t\\) and that of previous model \\(\\mathcal{F}_{t - 1}\\) to constrain the feature extractor, which can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.529, + 0.891, + 0.548 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {k d} = \\left\\| \\mathcal {F} _ {t} \\left(\\tilde {x} _ {t} ^ {i}; \\theta_ {t}\\right) - \\mathcal {F} _ {t - 1} \\left(\\tilde {x} _ {t} ^ {i}; \\theta_ {t - 1}\\right) \\right\\| _ {2}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.551, + 0.892, + 0.621 + ], + "angle": 0, + "content": "With the assistance of prototype reminiscence, the disparity between the stored prototype and the updated model can be significantly mitigated. We also calculate the cross-entropy loss for \\(\\mathcal{G}_S\\) and \\(\\mathcal{G}_O\\), respectively. With these considerations above, the total loss function \\(\\mathcal{L}_{total}\\) can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.541, + 0.636, + 0.891, + 0.675 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {n e w}} = \\mathcal {L} _ {c e} \\left(\\mathcal {G} _ {S} \\left(\\tilde {\\mathcal {F}} _ {t} \\left(\\tilde {x _ {t} ^ {i}}; \\theta_ {t}\\right); \\varphi_ {t}\\right)\\right) \\tag {10} \\\\ + \\mathcal {L} _ {c e} \\left(\\mathcal {G} _ {O} \\left(\\mathcal {F} _ {t} \\left(\\tilde {x _ {t} ^ {\\prime}}; \\theta_ {t}\\right); \\phi_ {t}\\right)\\right) + \\mathcal {L} _ {k a}, \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.548, + 0.678, + 0.891, + 0.712 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {o l d} = \\mathcal {L} _ {c e} \\left(\\mathcal {G} _ {S} \\left(F _ {o l d} ^ {i}; \\varphi_ {t}\\right)\\right) \\tag {11} \\\\ + \\mathcal {L} _ {c e} \\left(\\mathcal {G} _ {O} \\left(F _ {o l d} ^ {i}\\right); \\phi_ {t})\\right) + \\mathcal {L} _ {k a}, \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.716, + 0.891, + 0.731 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {n e w}} + \\alpha \\mathcal {L} _ {\\text {o l d}} + \\gamma \\mathcal {L} _ {\\text {k d}}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.741, + 0.892, + 0.784 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{new}\\) is the loss of new data \\(\\tilde{x}_t^i\\), \\(\\mathcal{L}_{old}\\) is the loss of the feature \\(F_{old}^{i}\\) generated by prototype reminiscence. The loss weights \\(\\alpha\\) and \\(\\gamma\\) are both set to 15 in our experiments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.795, + 0.632, + 0.81 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.818, + 0.7, + 0.833 + ], + "angle": 0, + "content": "4.1. Experimental Setting" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.839, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Dataset. To evaluate the performance of our method, we conduct sufficient experiments on three benchmarks includ" + }, + { + "type": "page_number", + "bbox": [ + 0.47, + 0.888, + 0.502, + 0.899 + ], + "angle": 0, + "content": "1776" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.123, + 0.894, + 0.16 + ], + "angle": 0, + "content": "Table 1. Quantitative comparisons of the average incremental accuracy (%) with other methods at different task number settings on CIFAR-100, TinyImageNet, and ImageNet-Subset. \\( E = {20} \\) represents exemplar-based methods and storing 20 exemplars for each old class. \\( E = 0 \\) represents non-exemplar methods. The relative improvement compared to the SOTA NECIL method is shown by the red footnotes." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.16, + 0.885, + 0.344 + ], + "angle": 0, + "content": "
MethodsCIFAR-100TinyImageNetImageNet-Subset
5 phases10 phases20 phases5 phases10 phases20 phases10 phases
E=20iCaRL-CNN51.0748.6644.4334.6431.1527.9050.53
iCaRL-NCM [42]58.5654.1950.5145.8643.2938.0460.79
EEIL [9]60.3756.0552.3447.1245.0140.5063.34
UCIR [20]63.7862.3959.0749.1548.5242.8366.16
DER [58]73.2172.8169.97———75.36
E=0EWC [23]24.4821.2015.8918.8015.7712.3920.40
LwFMC [42]45.9327.4320.0729.1223.1017.4331.18
MUC [32]49.4230.1921.2732.5826.6121.9535.07
SDC [60]56.7757.0058.90———61.12
PASS [66]63.4761.8458.0949.5547.2942.0761.80
SSRE [67]65.8865.0461.7050.3948.9348.1767.69
Ours70.02+4.1468.86+3.8265.86+4.1653.32+2.9352.61+3.6849.83+1.6668.98+1.29
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.351, + 0.47, + 0.435 + ], + "angle": 0, + "content": "ing CIFAR-100 [25], TinyImageNet [26] and ImageNet-Subset (random seed 1993) [12]. For CIFAR-100 and TinyImageNet there are three incremental settings (5, 10, and 20 phases) and for ImageNet-Subset there is one (10 phases). For the sequencing and division of all dataset classes, we strictly follow the specification in [66]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.435, + 0.47, + 0.56 + ], + "angle": 0, + "content": "Implementation details. Following [66], we use ResNet-18 [18] as the backbone network. The model is trained for 100 epochs on each new task. For comparisons on all datasets, the threshold of our prototype reminiscence is set to 0.6. During training, the batch size is set to 128 and the model is optimized by the Adam optimizer with \\(\\beta_{1} = 0.9\\), \\(\\beta_{2} = 0.999\\) and \\(\\epsilon = 1e^{-8}\\) (weight decay 2e-4). The initial learning rate is 0.001 and is adjusted with the cosine annealing algorithm [35] with a period of 32 epochs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.47, + 0.699 + ], + "angle": 0, + "content": "Evaluation metrics. As with [66], we employ average incremental accuracy [42] and average forgetting [10] as the evaluation metric. The average incremental accuracy is defined as the average of the accuracies over seen classes across all incremental phases (including the first phase), which reflects the overall incremental performance of the method. The average forgetting is the average difference between the peak task accuracy and the final task accuracy after incremental learning is completed, and the lower value represents better performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.706, + 0.298, + 0.721 + ], + "angle": 0, + "content": "4.2. Comparison with SOTA" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.728, + 0.47, + 0.852 + ], + "angle": 0, + "content": "We compare our method with the state-of-the-art (SOTA) methods of NECIL (EWC [23], LwF_MC [42], MUC [32], SDC [60], PASS [66] and SSRE [67]) and several classical exemplar-based CIL approaches (iCaRL [42], EEIL [9] and UCIR [20]). The results reported for PASS are obtained with self-supervised learning. We reproduce the SSRE with label augmentation in the supplementary materials. As adopted in [67], we memorize 20 samples for the exemplar-based methods." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.853, + 0.469, + 0.868 + ], + "angle": 0, + "content": "Accuracy and forgetting. The quantitative comparisons" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.349, + 0.865, + 0.361 + ], + "angle": 0, + "content": "Table 2. Results of average forgetting on 5, 10 and 20 phases." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.361, + 0.898, + 0.497 + ], + "angle": 0, + "content": "
MethodsCIFAR-100TinyImageNet
5102051020
iCaRL-CNN42.1345.6943.5436.8936.7045.12
iCaRL-NCM24.9028.3235.5327.1528.8937.40
EEIL23.3626.6532.4025.5625.5135.04
UCIR21.0025.1228.6520.6122.2533.74
LwFMC44.2350.4755.4654.2654.3763.54
MUC40.2847.5652.6551.4650.2158.00
PASS25.2030.2530.6118.0423.1130.55
SSRE18.3719.4819.009.1714.0614.20
Ours12.5914.6517.3911.8413.9518.51
Ours w/o AKA7.186.4210.304.575.109.05
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.504, + 0.892, + 0.794 + ], + "angle": 0, + "content": "of the average incremental accuracy are reported in Tab. 1. Compared to the suboptimal NECIL method (SSRE), we improve the accuracy on CIFAR-100, TinyImageNet and ImageNetSubset by \\(6.30\\%\\), \\(5.59\\%\\), and \\(1.91\\%\\), respectively. Moreover, our method shows competitive or even better performance than the classical exemplar-based methods. Certainly, it still slightly inferior to the SOTA exemplar-based method DER [58]. In Fig. 4 we show the accuracy change curves on three benchmarks. Our method is superior at almost all phases, achieving a better balance between stability and plasticity. To further evaluate the above methods, we provide the results of average forgetting in Tab. 2, where our method also performs superiorly. In addition, since the proposed asymmetric knowledge aggregation (AKA) improves the classification accuracy on the current task, the forgetting metric is increased, however this is harmless to overall performance. We will report more analysis in the following and supplementary materials. Experimental results show that our approach can mitigate catastrophic forgetting despite the lack of past task data, which is a more privacy-safe and memory-friendly manner to achieve CIL." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.803, + 0.655, + 0.818 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.893, + 0.868 + ], + "angle": 0, + "content": "In this section, we conduct several ablation studies on the proposed method. To better analyze the impact of the core designs, our approach is divided into three compo" + }, + { + "type": "page_number", + "bbox": [ + 0.47, + 0.888, + 0.502, + 0.899 + ], + "angle": 0, + "content": "1777" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.123, + 0.286, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.123, + 0.487, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.497, + 0.123, + 0.688, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.148, + 0.872, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.24, + 0.286, + 0.361 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.24, + 0.487, + 0.361 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.498, + 0.24, + 0.688, + 0.361 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.24, + 0.888, + 0.361 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.364, + 0.893, + 0.39 + ], + "angle": 0, + "content": "Figure 4. Illustration of the classification accuracy changes as tasks are being learned on CIFAR-100, TinyImageNet and ImageNet-Subset, which contains the complete curves. Precise data of our method is presented in the supplementary materials." + }, + { + "type": "table_caption", + "bbox": [ + 0.14, + 0.393, + 0.829, + 0.405 + ], + "angle": 0, + "content": "Table 3. Ablation study (in average incremental accuracy) of our method on CIFAR-100 and TinyImageNet datasets." + }, + { + "type": "table", + "bbox": [ + 0.124, + 0.405, + 0.84, + 0.508 + ], + "angle": 0, + "content": "
ComponentsCIFAR-100TinyImageNet
PRSLAAKA5 phases10 phases20 phases5 phases10 phases20 phases
56.2751.0243.9837.9332.4423.98
✓66.2163.8057.3145.8544.0435.93
✓61.2759.5955.1446.6543.8838.13
✓✓68.4867.5665.0352.1551.6749.30
✓✓✓70.0268.8665.8653.3252.6149.83
" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.517, + 0.445, + 0.678 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.681, + 0.448, + 0.695 + ], + "angle": 0, + "content": "Figure 5. Influence of the threshold in prototype reminiscence." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.701, + 0.47, + 0.867 + ], + "angle": 0, + "content": "nents: prototype reminiscence (PR), self-supervised label augmentation (SLA) and asymmetric knowledge aggregation (AKA). As a general trick, KD was used in all experimental settings. To explicitly illustrate the effectiveness of PR, in the baseline model we save the prototypes and directly use them for training. As shown in the \\(1^{st}\\) and \\(2^{nd}\\) rows of Tab. 3, PR successfully maintains the discrimination and balance between the old and new classes and makes an impressive progress on the baseline model. When SLA acts on the baseline model alone, it is effective, but there is still a bias in the classifier, while using it with PR achieves promising results. AKA and SLA are adopted as a whole." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.519, + 0.891, + 0.56 + ], + "angle": 0, + "content": "In addition to the overall performance improvement, AKA is more about enhancing the model's understanding of the new task to satisfy the latest business requirements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.741 + ], + "angle": 0, + "content": "To investigate the sensitivity of the threshold \\(\\eta\\) in our prototype reminiscence, we plot its fluctuation curve on CIFAR-100 dataset. As presented in Fig. 5, when \\(\\eta\\) is low, the generated old class features are restricted to concentrate around the preserved prototypes thus lacking the ability to adapt to the changes of the representation space, which results in poor performance. As the constraint is relaxed (\\(\\eta\\) increases), the effect of PR gradually comes into its own and peaks in performance at about \\(\\eta = 0.6\\). When the threshold continues to increase, the performance gain from PR starts to diminish because as the constraint fades away, the number of outlier features generated by PR gradually increases, which disturbs the learning of the model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.749, + 0.602, + 0.763 + ], + "angle": 0, + "content": "4.4. Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.77, + 0.893, + 0.867 + ], + "angle": 0, + "content": "Visualization. To demonstrate the advantages of our prototype reminiscence, we visualise the 2D embeddings of feature vectors with t-SNE [51]. In Fig. 6 (c) and (d), the old class features are generated by the stored prototypes. Compared with fine-tuning, the confusion of old class features is alleviated in the results of Gaussian noise augmentation. However, the overlap between the distributions of different" + }, + { + "type": "page_number", + "bbox": [ + 0.47, + 0.888, + 0.502, + 0.898 + ], + "angle": 0, + "content": "1778" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.123, + 0.268, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.14, + 0.227, + 0.216, + 0.236 + ], + "angle": 0, + "content": "(a) Initial Phase" + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.124, + 0.457, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.332, + 0.227, + 0.401, + 0.236 + ], + "angle": 0, + "content": "(b) Finetuning" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.239, + 0.268, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.335, + 0.255, + 0.345 + ], + "angle": 0, + "content": "(c) Gaussian Noise Augmentation" + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.239, + 0.457, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.301, + 0.335, + 0.43, + 0.345 + ], + "angle": 0, + "content": "(d) Prototype Reminiscence" + }, + { + "type": "image_caption", + "bbox": [ + 0.099, + 0.346, + 0.446, + 0.358 + ], + "angle": 0, + "content": "Figure 6. Visualization of different augmentation schemes." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.361, + 0.206, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.115, + 0.443, + 0.18, + 0.452 + ], + "angle": 0, + "content": "(a) Finetuning" + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.361, + 0.326, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.245, + 0.443, + 0.291, + 0.452 + ], + "angle": 0, + "content": "(b) iCaRL" + }, + { + "type": "image", + "bbox": [ + 0.333, + 0.361, + 0.468, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.378, + 0.443, + 0.416, + 0.452 + ], + "angle": 0, + "content": "(c) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.453, + 0.468, + 0.478 + ], + "angle": 0, + "content": "Figure 7. The comparison of confusion matrix of finetuning, iCaRL and our method on CIFAR-100 (10 phases)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.469, + 0.546 + ], + "angle": 0, + "content": "classes is still significant, and in particular the confusion between the generated features. Instead, the feature distributions of different old classes reshaped by our method are relatively dispersed among each other." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.548, + 0.469, + 0.699 + ], + "angle": 0, + "content": "Classification bias of the model. To evaluate the performance differences between the old and new classes, we compared the confusion matrix of finetuning, iCaRL and our method on CIFAR-100. As shown in Fig. 7, since samples of old classes are not available, finetuning tends to classify the samples into new classes. The confusion is alleviated by iCaRL, but still shows a preference for new classes. The confusion matrix of our method exhibits better overall performance without favouring old or new classes. Thanks to PR and AKA, the classification bias between old and new classes is well handled." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.701, + 0.47, + 0.867 + ], + "angle": 0, + "content": "The role of asymmetric knowledge aggregation. To better illustrate the role of the asymmetric knowledge aggregation, we compare the changes in classification accuracy for the initial task during subsequent incremental learning, and the performance on each new task in the presence or absence of AKA. The results for the three settings on CIFAR100 are shown in Fig. 8. On the one hand, the performance degradation in the initial task caused by the introduction of AKA is negligible; on the other hand, the discrimination of new classes is considerably improved. As analyzed in the introduction, AKA can improve the model's understanding of new tasks as non-destructively as possible." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.124, + 0.701, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.564, + 0.232, + 0.659, + 0.241 + ], + "angle": 0, + "content": "CIFAR-100 (10 phases)" + }, + { + "type": "image", + "bbox": [ + 0.705, + 0.125, + 0.889, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.75, + 0.232, + 0.845, + 0.241 + ], + "angle": 0, + "content": "CIFAR-100 (10 phases)" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.241, + 0.699, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.561, + 0.329, + 0.655, + 0.338 + ], + "angle": 0, + "content": "CIFAR-100 (20 phases)" + }, + { + "type": "image", + "bbox": [ + 0.705, + 0.241, + 0.888, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.753, + 0.329, + 0.847, + 0.338 + ], + "angle": 0, + "content": "CIFAR-100 (20 phases)" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.338, + 0.699, + 0.428 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.705, + 0.338, + 0.888, + 0.428 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.43, + 0.892, + 0.493 + ], + "angle": 0, + "content": "Figure 8. The first column is the classification accuracy on the initial task, which changes with the incremental phase. The second column shows the change in classification accuracy on the new task. The proposed knowledge aggregation allows better learning of new tasks with little impact on existing knowledge." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.504, + 0.618, + 0.517 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.892, + 0.687 + ], + "angle": 0, + "content": "In this work, we address the NECIL issue from two perspectives of resisting catastrophic forgetting and boosting plasticity of the model, proposing prototype reminiscence and augmented asymmetric knowledge aggregation, respectively. In particular, we pay attention to the performance of the incremental learner on new tasks which often represent the latest business requirements, and design an asymmetric knowledge aggregation strategy for better adaptation to new tasks. Extensive evaluations demonstrate that our approach outperforms the SOTA NECIL methods and shows strong competitiveness with classical exemplar-based methods in the absence of stored samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.892, + 0.77 + ], + "angle": 0, + "content": "Limitations. For each prototype reminiscence, the prototype and the feature are selected randomly. When the selected prototype and feature are less similar (i.e., farther apart in the feature space), there may be outliers in the generated features of old classes. Exploring the impact of outliers on training may be of interest." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.77, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Acknowledgement. This work is partially supported by the Key Research and Development Program of Hubei Province (2021BAA187), National Natural Science Foundation of China under Grant (62176188), Zhejiang lab (NO.2022NF0AB01), the Special Fund of Hubei Luojia Laboratory (220100015) and CAAI-Huawei MindSpore Open Fund." + }, + { + "type": "page_number", + "bbox": [ + 0.47, + 0.888, + 0.502, + 0.899 + ], + "angle": 0, + "content": "1779" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.125, + 0.173, + 0.139 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.148, + 0.469, + 0.199 + ], + "angle": 0, + "content": "[1] Davide Abati, Jakub Tomczak, Tijmen Blankevoort, Simone Calderara, Rita Cucchiara, and Babak Ehteshami Bejnordi. Conditional channel gated networks for task-aware continual learning. 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NeurIPS, 31, 2018. 5" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.127, + 0.892, + 0.855 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.47, + 0.888, + 0.5, + 0.898 + ], + "angle": 0, + "content": "1781" + } + ] +] \ No newline at end of file diff --git a/2023/Prototype Reminiscence and Augmented Asymmetric Knowledge Aggregation for Non-Exemplar Class-Incremental Learning/f06e28ba-39c2-463d-9177-75781355ca62_origin.pdf b/2023/Prototype Reminiscence and Augmented Asymmetric Knowledge Aggregation for Non-Exemplar Class-Incremental Learning/f06e28ba-39c2-463d-9177-75781355ca62_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..cb5b77e7c61519adcd3cab58979bf9660518af5b --- /dev/null +++ b/2023/Prototype Reminiscence and Augmented Asymmetric Knowledge Aggregation for Non-Exemplar Class-Incremental Learning/f06e28ba-39c2-463d-9177-75781355ca62_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:02bf5dd1c319c7fa442f6c9660322ce266655442397fadd6ae138260e75cb32a +size 697654 diff --git a/2023/Prototype Reminiscence and Augmented Asymmetric Knowledge Aggregation for Non-Exemplar Class-Incremental Learning/full.md b/2023/Prototype Reminiscence and Augmented Asymmetric Knowledge Aggregation for Non-Exemplar Class-Incremental Learning/full.md new file mode 100644 index 0000000000000000000000000000000000000000..58379e868559a808cd52e9464efcd610f90c2714 --- /dev/null +++ b/2023/Prototype Reminiscence and Augmented Asymmetric Knowledge Aggregation for Non-Exemplar Class-Incremental Learning/full.md @@ -0,0 +1,368 @@ +# Prototype Reminiscence and Augmented Asymmetric Knowledge Aggregation for Non-Exemplar Class-Incremental Learning + +Wuxuan Shi $^{1}$ , Mang Ye $^{1,2*}$ + +$^{1}$ School of Computer Science, Wuhan University, Wuhan, China + +$^{2}$ Hubei Luojia Laboratory, Wuhan, China + +https://shiwuxuan.github.io/PRAKA-project + +# Abstract + +Non-exemplar class-incremental learning (NECIL) requires deep models to maintain existing knowledge while continuously learning new classes without saving old class samples. In NECIL methods, prototypical representations are usually stored, which inject information from former classes to resist catastrophic forgetting in subsequent incremental learning. However, since the model continuously learns new knowledge, the stored prototypical representations cannot correctly model the properties of old classes in the existence of knowledge updates. To address this problem, we propose a novel prototype reminiscence mechanism that incorporates the previous class prototypes with arriving new class features to dynamically reshape old class feature distributions thus preserving the decision boundaries of previous tasks. In addition, to improve the model generalization on both newly arriving classes and old classes, we contribute an augmented asymmetric knowledge aggregation approach, which aggregates the overall knowledge of the current task and extracts the valuable knowledge of the past tasks, on top of self-supervised label augmentation. Experimental results on three benchmarks suggest the superior performance of our approach over the SOTA methods. + +# 1. Introduction + +In recent years, deep neural networks have achieved great success on various tasks. In dynamic and open environments, deep models also require the ability to continuously learn new tasks as the input stream is updated. Hence, class-incremental learning (CIL), which aims to learn a unified classifier that can classify all seen classes under progressive changes in the classes to be learned, has attracted extensive attention [30, 41, 16, 47, 31, 28]. + +As new data becomes available, it is computationally expensive to jointly retrain the model with new and old class + +![](images/61435a7e68d6b1d3ca58c68b63e86f1f127444db2709525d6230656ba363be58.jpg) + +![](images/b8f79e6cd48897686028572c4979d0eba37bec46e2adb11fccb2d20bcb334a50.jpg) +Figure 1. Idea illustration. (a) Joint training with abundant samples. (b) Baseline: Updating the model with the memorized prototype and new data, which narrows the decision boundary of the old classes. (c) Gaussian Noise Augmentation [66]: The decision boundary of the old class is retained, but it introduces an overlap between the old and new class distributions due to the change in representation space. (d) With prototype reminiscence, newly learned information can be injected while reshaping the feature distribution of past data to reduce overlap and resist forgetting. + +samples. Worse still, the old class samples could not be fully accessible. In this case, an alternative is to fine-tune the model on new data, yet catastrophic forgetting [38, 15] will be a serious challenge. The decision boundary of the unified classifier would be significantly changed and biased towards the new classes. Conversely, another direction is to fix the feature embedding space of a trained model, which suffers from frustrating generalization ability and thus performs poorly on new tasks, i.e., the plasticity of the model is greatly degraded. + +To overcome the catastrophic forgetting issue, many CIL methods [42, 8, 6, 56, 2, 53] store a fraction of the old data in memory and replay them in subsequent incremental phases to maintain the existing knowledge. Unfortunately, storing data poses privacy concerns and comes at a sharp cost to memory and computation. In this paper, we follow a paradigm holding for more extensive applications, + +termed non-exemplar class-incremental learning (NECIL) [66, 67], which solves the catastrophic forgetting problem in CIL scenario without preserving old class samples. + +For NECIL, a natural substitute for storing data is to generate pseudo-samples of previous classes by deep generative models [62, 54, 46, 49, 57] such as GAN [4, 17]. However, it is unstable and ineffective to train generative models for non-stationary data streams [65]. Catastrophic forgetting can also have a negative impact on the generative model resulting in a simultaneous decrease in the effectiveness of both models. Instead of focusing on old data, some works turn to estimating model parameters that are important for previous tasks and constraining their changes [23, 61, 3]. Nevertheless, the constraints on the model parameters lead to poor generalization ability to long-sequence tasks. Besides, several studies propose to dynamically expand the network structure during the process of incremental learning [44, 58, 59, 37, 64]. Although this strategy can efficiently handle long sequences of tasks and ultimately maintain the performance of the old classes, the computational resource requirements associated with creating and storing additional network components and reasoning about multiple forward propagations are frustrating. + +Recently, some prototype-based NECIL methods have achieved impressive performance [66, 67, 60, 50]. They use prototypical representations (typically the class mean in the deep feature space) memorized for each old class to model the feature distribution of past data and inject information from the previous classes in subsequent incremental learning. Rather than storing samples, this strategy is more memory efficient and privacy secure. Nevertheless, as shown in Fig. 1 (b), direct training with saved prototypes and current data struggles to prevent the collapse of decision boundaries, due to the lack of old class features. Some works augment the prototypes by adding Gaussian noise [66] or over-sampling [67] to enrich old class features. However, updates of the model on continuous data streams could lead to inevitable changes in the representation of old classes, making the saved prototypes increasingly outdated. + +The feature distribution simulated by the above strategies cannot accommodate such changes due to the missing consideration of knowledge updates. It could result in overlap between the distributions of different classes, especially between new and old classes, as shown in Fig. 1 (c). Consequently, combining newly acquired information with stored prototypes to dynamically model past data distributions is crucial to resist catastrophic forgetting in NECIL. + +To address this challenge, we propose a prototype reminiscence mechanism to track the evolution of the old class representations by injecting new knowledge from the updating network while reshaping the feature distribution. Specifically, we perform a random bidirectional interpolation operation between the extracted new class features and + +![](images/ac65a3b24c9faa1c01b41c7953b4088123479b7ccd901f6fa898832665249713.jpg) +Figure 2. We introduce self-supervised label augmentation to learn generalizable and transferable representations. The knowledge of the self-supervised classifier is aggregated and transferred to another classifier to take full advantage of it. + +the saved old class prototypes to enrich old class features. As shown in Fig. 1 (d), it expands the prototype to protect the decision boundaries of old classes and to counteract catastrophic forgetting. Since the feature distribution of past tasks is dynamically adjusted to the current representation space, the overlap between the old and new classes is reduced. Thus, the discrimination and balance between the old and new classes are maintained. Cooperating with the well-known knowledge distillation (KD) [20, 19], the mismatch between the preserved prototypes and the continuously updated network is alleviated. + +In addition to dealing with catastrophic forgetting, when new data arrives, performance on the current task is also of great concern, necessitating the plasticity of the incremental learner. This mainly involves two aspects: learning generalizable and transferable representations, fully utilizing the information from new data. Previous works [66, 55] have achieved good progress on the first aspect by self-supervised label augmentation [27], however they ordinarily disregard the second. The new task contains abundant information that the network has never encountered and will have a stronger influence on model updates. Improving the plasticity of the model from continuous data streams requires a simultaneous approach from both aspects. + +To solve this bottleneck, we contribute an augmented asymmetric knowledge aggregation approach to enhance the plasticity of the model noninvasively. Taking inspiration from [24, 27], we first augment the new classes with + +rotation as self-supervision, which requires the model to acquire task-agnostic representations to improve its generalization ability. Furthermore, as illustrated in Fig. 2, we selectively aggregate the valuable knowledge in the augmented classifier—valid weights of past tasks are extracted, and the information captured on the current task is sufficiently exploited. This asymmetric knowledge aggregation scheme can condense the knowledge learned via self-supervised label augmentation (SLA) to make the classifier more purified. It further improves the incremental learner's performance on the new tasks without discrimination scari-fication on old classes. + +To summarize, our main contributions are as follows: + +- We propose a simple yet effective method of prototype reminiscence for NECIL, which models feature distribution for the past data in a continuously updated representation space to resist catastrophic forgetting. +- We contribute augmented asymmetric knowledge aggregation, which learns task-agnostic representations and fully captures the newly acquired knowledge to improve the plasticity of incremental learners. +- Extensive experiments on three benchmarks demonstrate that our method achieves state-of-the-art performance. We also provide a detailed ablation study to analyze the influence of each component. + +# 2. Related Work + +# 2.1. Class-Incremental Learning + +Current CIL methods can be roughly divided into three categories: rehearsal-based methods, regularization-based methods and structure-based methods. + +Rehearsal-based methods maintain the distribution of old classes by saving exemplars of fixed memory size to jointly train the model with current data. Based on the saved samples, some works investigate knowledge distillation to prevent forgetting [56, 42, 13], while others try to combine regularization of gradients and rehearsal to make more efficient use of the preserved data [43, 34, 11]. In addition, several papers have studied the impact of memory management schemes [5, 22, 33]. Regularization-based methods identify the key model parameters for the previous tasks, penalizing their changes when learning the current task [23, 61, 3, 40]. The difference between these methods is the association of each network parameter with importance weights stored in incremental learning. Structure-based methods dynamically modify the network architecture to maintain existing knowledge and adapt to new tasks. They usually expand the network structure in depth or width when facing a new task [59, 21, 29, 58], or mask parts of the network for different tasks [45, 36, 1]. + +Recently, some works have researched the use of class prototypes to implement non-exemplar class-incremental learning [66, 60, 67, 50], which somewhat reduces the issues of data privacy security and memory constraints. Yu et al. [60] approximate and compensate for the semantic drift of previous tasks during the training of the new task. Based on this, Toldo et al. [50] propose to jointly exploit semantic drift and feature drift to update the representations of past classes. Apart from investigating the evolution of prototypes as incremental learning occurs, there are some studies that focus on the ways to model past data distributions by prototypes [66, 67]. Note that this strategy is orthogonal to the above methods for drift estimation, and our method falls into this category. Zhu et al. [66] introduce Gaussian noise to augment the prototype to restrain the decision boundaries of old classes. Zhu et al. [67] propose a prototype selection mechanism that uses samples of the new data similar to the old classes for distillation to reduce confusion between the newly added classes and the original classes. + +# 2.2. Self-supervised Learning in CIL + +The objective of self-supervised learning (SSL) is to acquire transferable representations that are applicable for other tasks. This coincides with the need for IL to inhibit task-level overfitting phenomenon and rapidly adapt to new tasks. Hence, some works explore improving the quality of the learned representations by SSL in the CIL setting [66, 55, 7, 14]. Wu et al. [55] learn class-independent knowledge and multi-perspective knowledge by SSL to make a trade-off between gaining new information and maintaining old knowledge. Fini et al. [14] attempt to seamlessly convert the existing self-supervised loss function into distillation mechanisms plugged into the CIL framework. It also points out that simply introducing SSL can approach or outperform supervised learning in the CIL setting, while this is not always the case for other settings (data-incremental and domain-incremental). Zhu et al. [66] provide better initialization for learning the next task by using rotation as self-supervised information for label augmentation to reduce forgetting from model updates. Our SLA is implemented in the same way as the SSL in [66]. On top of [66], we further improve the upper bound of the incremental learner's understanding of new tasks. + +# 3. Methodology + +Problem Statement. In this paper, we consider nonexemplar class-incremental learning (NECIL), where no samples from old classes are stored. The training data for the incremental task $t \in \{1, \dots, T\}$ is denoted as $D_{t} = \{X_{t}, Y_{t}\} = \{x_{t}^{i}, y_{t}^{i}\}_{i=1}^{n_{t}}$ , where $n_{t}$ , $x_{t}^{i}$ and $y_{t}^{i} \in C_{t}$ represent the number of training samples, an input sample and its corresponding label for task $t$ , respectively. $C_{t}$ is the class set of task $t$ and all the incremental classes are disjoint, i.e., + +![](images/296947040fa00f334cdf5ed32a8e938a888c90ae2f080acead9c5e03f8ba75ff.jpg) +Figure 3. Illustration of our method for NECIL. The classes of current task are augmented by rotation transformation [27]. We expand the stored prototype by prototype reminiscence in the deep feature space to generate the same number of old class features as the batch size each time. During the evaluation, only the current feature extractor $\mathcal{F}_t$ and the refined classifier $\mathcal{G}_o$ are used. + +![](images/86f1e99f6b36baa18d8b42f28449338372084cef72f61bec683e1916dae92a6f.jpg) + +$C_1 \cap \ldots \cap C_i = \emptyset$ . We represent the model with two components: a feature extractor $\mathcal{F}$ with parameters $\theta$ and a unified classifier $\mathcal{G}$ with parameters $\varphi$ . The goal is to find a classification model minimized for some loss function $\mathcal{L}(\cdot, \cdot)$ : + +$$ +\underset {\theta , \varphi} {\operatorname {a r g m i n}} \sum_ {t = 1} ^ {C _ {t}} \mathbb {E} _ {\left(x _ {t} ^ {i}, y _ {t} ^ {i}\right) \sim D _ {t}} \left[ \mathcal {L} \left(y _ {t} ^ {i}, \mathcal {G} \left(\mathcal {F} \left(x _ {t} ^ {i}; \theta\right); \varphi\right)\right) \right]. \tag {1} +$$ + +As other class-incremental methods, the algorithm has no access to the task label $t$ and is expected to classify all observed classes $C_{total} = \{C_1,\dots ,C_t\}$ at any given point. + +Overview of Framework. Fig. 3 shows an overview of our method. The classes of the current task are augmented by rotation transformation [27] and the augmented data is fed to the feature extractors. For each old class, we memorize a class-representative prototype. Then the prototype reminiscence uses the extracted new class features and the stored old class prototypes to generate old class features for joint training. We aggregate the knowledge from the classifier $\mathcal{G}_S$ learned with SLA and transfer it to another classifier $\mathcal{G}_O$ that only recognizes classes without augmentation. At test time, the current feature extractor $\mathcal{F}_t$ and the refined classifier $\mathcal{G}_O$ are used for evaluation. + +# 3.1. Prototype Reminiscence + +At each incremental phase of task $t$ , only $D_{t}$ is available in the NECIL setting. Following [66, 60], when learning a new task, we compute and memorize one prototype in the deep feature space for each class: + +$$ +P _ {t, k _ {n e w}} = \frac {1}{N _ {t , c _ {n e w}}} \sum_ {n = 1} ^ {N _ {t, c _ {n e w}}} \mathcal {F} \left(\mathbf {X} _ {t, c _ {n e w}}; \theta_ {t}\right), \tag {2} +$$ + +where $c_{new} \in C_{new} = C_t$ is one class of the current task. To alleviate the catastrophic forgetting, the model is trained jointly on the memorized prototypes $\{P_{old}^1, \ldots, P_{old}^{|C_{old}|}\}$ and current data $D_t$ , where $C_{old} = C_1 \cup \ldots \cup C_{t-1}$ denotes the set of past classes. + +Whereas prototypes can inject information of past classes in training, the decision boundaries are narrowed due to the lack of rich old class features. Moreover, as the model continuously learns new data, the deep representation space is changing, which poses a challenge to reproduce the properties of old classes. To this end, we propose a prototype reminiscence strategy to dynamically model the feature distribution of past data in an updating representation space. Our strategy is based on a simple yet effective interpolation operation. In general, as shown in Fig. 3, we randomly select a prototype of the old classes $P_{old}^{n} \in \{P_{old}^{1}, \dots, P_{old}^{|C_{old}|}\}$ and a feature of the new classes $F_{new}^{m} \in \{F_{new}^{1}, \dots, F_{new}^{B}\}$ , where $B$ is the batch size. Then we perform a random bidirectional interpolation operation between $P_{old}^{n}$ and $F_{new}^{m}$ : + +$$ +F _ {o l d} ^ {n} = \left\{ \begin{array}{l} (1 - \lambda) \left(P _ {o l d} ^ {n}\right) + \lambda \left(F _ {n e w} ^ {m}\right), p _ {e} < 0. 5 \\ (1 + \lambda) \left(P _ {o l d} ^ {n}\right) - \lambda \left(F _ {n e w} ^ {m}\right), o t h e r w i s e \end{array} \right. \tag {3} +$$ + +where $F_{old}^{n}$ is the feature generated in the current representation space that has the same label as $P_{old}^{n}$ and $p_e$ is randomly sampled from [0, 1). Considering the design principle of mixup [63, 52], we ensure that the coefficient summary of the two terms for the prototype reminiscence is equal to 1. Different from them, our prototype reminiscence introduces an extrapolation operation, which avoids the generated features being concentrated on one side of the decision boundary. Meanwhile, we choose + +$\lambda \sim \mathrm{Beta}(0.5, 0.5) \in [0, \eta]$ , where $\eta$ is a threshold value to control the maximum distance between the generated old class features and the corresponding prototype for avoiding outliers. To make a fair comparison, as in [66], we generate the same number of old class features as the batch size for each batch of new data. + +# 3.2. Augmented Asymmetric Knowledge Aggregation + +While counteracting forgetting, incremental learners also need to adapt to new tasks. We design an augmented asymmetric knowledge aggregation scheme that endows the model with stronger plasticity. First, we augment the current classes as in [27]. For the current task, the N-way classification problem is extended into a 4N-way classification problem. Specifically, the input data for each class is rotated by $90^{\circ}$ , $180^{\circ}$ , and $270^{\circ}$ to produce three new classes: + +$$ +\tilde {x} _ {t} ^ {i} = \left\{x _ {t} ^ {i, j} \right\} _ {j = 0} ^ {3} = \left\{r o t a t e (x _ {t} ^ {i}, j \times 9 0 ^ {\circ}) \right\} _ {j = 0} ^ {3}, \quad (4) +$$ + +and we allocate new labels $y_{t}^{i}$ to the augmented data: + +$$ +\tilde {y} _ {t} ^ {i} = \left\{y _ {t} ^ {i} \times 4 + j \right\} _ {j = 0} ^ {3}. \tag {5} +$$ + +Compared to the widely used 4-way self-supervised task, the above approach removes unnecessary invariant properties when learning both the original task and the self-supervised task simultaneously, thereby reducing the loss of discriminative information while obtaining generalizable and transferable representations [27]. + +However, for NECIL, the self-supervised label augmentation can only be applied to new classes (past data is not available). Borrowing from some works [39, 48], the classification weight $w_{c,j}$ is denoted as a proxy, where $c \in C_{total}$ and $j$ represents different rotation transformations. In the subsequent incremental learning, the proxies for the augmented classes $(90^{\circ}, 180^{\circ}, 270^{\circ})$ of the previous tasks gradually fail, leading to redundancy within the classifier. When using the cross-entropy loss for optimization, all augmented classes are viewed independently, and the relationship between them is not explored. Moreover, only the predictions of the non-augmented classes $(0^{\circ})$ are considered valid during testing [66], which leads to a large amount of information valuable for the current task being discarded. + +To precisely utilize the valuable knowledge obtained from the above self-supervised label augmentation, we propose an asymmetric knowledge aggregation approach for NECIL. Concretely, for the past tasks, we take in the knowledge of the proxies associated with the original classes: + +$$ +\mathcal {P} _ {a g g} (c \mid F _ {o l d}) = \frac {\exp \left(w _ {c , 0} ^ {T} F _ {o l d}\right)}{\sum_ {k = 1} ^ {K} \exp \left(w _ {k , 0} ^ {T} F _ {o l d}\right)}, \tag {6} +$$ + +where $K = |C_{total}|$ , $w$ is the proxy of $\mathcal{G}_S$ and $F_{old}$ is the feature generated by prototype reminiscence. For the current task, the conditional probabilities corresponding to all + +transformations of each class are aggregated: + +$$ +\mathcal {P} _ {a g g} (c | \tilde {F _ {n e w}}) = \frac {\exp \left(\frac {1}{4} \sum_ {j = 0} ^ {3} w _ {c , j} ^ {T} F _ {n e w} ^ {j}\right)}{\sum_ {k = 1} ^ {K} \exp \left(\frac {1}{4} \sum_ {j = 0} ^ {3} w _ {k , j} ^ {T} F _ {n e w} ^ {j}\right)}, \tag {7} +$$ + +where $F_{new}^{\tilde{F}} = \{F_{new}^{j}\}_{j=0}^{3}$ represents the set of features extracted from the augmented exemplars $\tilde{x}_t^i$ by current model $\mathcal{F}_t$ . As presented in Fig. 3, we transfer the aggregated knowledge to another classifier $\mathcal{G}_O$ , which only needs to distinguish between non-augmented classes. The loss function $\mathcal{L}_{ka}$ can be expressed as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {k a} = K L D \left(\mathcal {P} _ {a g g} (\cdot | F) \| \mathcal {G} _ {O} (F; \phi)\right), \\ = \mathcal {P} _ {a g g} (\cdot | F) \log \frac {\mathcal {P} _ {a g g} (\cdot | F)}{\mathcal {G} _ {O} (F ; \phi)} \tag {8} \\ \end{array} +$$ + +where $\phi$ denotes the parameters of $\mathcal{G}_O$ and $KLD(\cdot|\cdot)$ is the Kullback-Leibler divergence. The knowledge learned from the new data is utilized as much as possible and the invalid weights are discarded to obtain a more refined classifier. During testing inference, only the classifier $\mathcal{G}_O$ is used. + +# 3.3. Integrated Optimization Objective + +Inspiring ourselves from [66], we employ the well-known knowledge distillation (KD) [68, 19] to regularize the feature extractor. Specifically, we minimize the Euclidean distance between the features of new data extracted by current model $\mathcal{F}_t$ and that of previous model $\mathcal{F}_{t - 1}$ to constrain the feature extractor, which can be formulated as: + +$$ +\mathcal {L} _ {k d} = \left\| \mathcal {F} _ {t} \left(\tilde {x} _ {t} ^ {i}; \theta_ {t}\right) - \mathcal {F} _ {t - 1} \left(\tilde {x} _ {t} ^ {i}; \theta_ {t - 1}\right) \right\| _ {2}. \tag {9} +$$ + +With the assistance of prototype reminiscence, the disparity between the stored prototype and the updated model can be significantly mitigated. We also calculate the cross-entropy loss for $\mathcal{G}_S$ and $\mathcal{G}_O$ , respectively. With these considerations above, the total loss function $\mathcal{L}_{total}$ can be expressed as: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {n e w}} = \mathcal {L} _ {c e} \left(\mathcal {G} _ {S} \left(\tilde {\mathcal {F}} _ {t} \left(\tilde {x _ {t} ^ {i}}; \theta_ {t}\right); \varphi_ {t}\right)\right) \tag {10} \\ + \mathcal {L} _ {c e} \left(\mathcal {G} _ {O} \left(\mathcal {F} _ {t} \left(\tilde {x _ {t} ^ {\prime}}; \theta_ {t}\right); \phi_ {t}\right)\right) + \mathcal {L} _ {k a}, \\ \end{array} +$$ + +$$ +\begin{array}{l} \mathcal {L} _ {o l d} = \mathcal {L} _ {c e} \left(\mathcal {G} _ {S} \left(F _ {o l d} ^ {i}; \varphi_ {t}\right)\right) \tag {11} \\ + \mathcal {L} _ {c e} \left(\mathcal {G} _ {O} \left(F _ {o l d} ^ {i}\right); \phi_ {t})\right) + \mathcal {L} _ {k a}, \\ \end{array} +$$ + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {n e w}} + \alpha \mathcal {L} _ {\text {o l d}} + \gamma \mathcal {L} _ {\text {k d}}, \tag {12} +$$ + +where $\mathcal{L}_{new}$ is the loss of new data $\tilde{x}_t^i$ , $\mathcal{L}_{old}$ is the loss of the feature $F_{old}^{i}$ generated by prototype reminiscence. The loss weights $\alpha$ and $\gamma$ are both set to 15 in our experiments. + +# 4. Experiments + +# 4.1. Experimental Setting + +Dataset. To evaluate the performance of our method, we conduct sufficient experiments on three benchmarks includ + +Table 1. Quantitative comparisons of the average incremental accuracy (%) with other methods at different task number settings on CIFAR-100, TinyImageNet, and ImageNet-Subset. $E = {20}$ represents exemplar-based methods and storing 20 exemplars for each old class. $E = 0$ represents non-exemplar methods. The relative improvement compared to the SOTA NECIL method is shown by the red footnotes. + +
MethodsCIFAR-100TinyImageNetImageNet-Subset
5 phases10 phases20 phases5 phases10 phases20 phases10 phases
E=20iCaRL-CNN51.0748.6644.4334.6431.1527.9050.53
iCaRL-NCM [42]58.5654.1950.5145.8643.2938.0460.79
EEIL [9]60.3756.0552.3447.1245.0140.5063.34
UCIR [20]63.7862.3959.0749.1548.5242.8366.16
DER [58]73.2172.8169.97———75.36
E=0EWC [23]24.4821.2015.8918.8015.7712.3920.40
LwFMC [42]45.9327.4320.0729.1223.1017.4331.18
MUC [32]49.4230.1921.2732.5826.6121.9535.07
SDC [60]56.7757.0058.90———61.12
PASS [66]63.4761.8458.0949.5547.2942.0761.80
SSRE [67]65.8865.0461.7050.3948.9348.1767.69
Ours70.02+4.1468.86+3.8265.86+4.1653.32+2.9352.61+3.6849.83+1.6668.98+1.29
+ +ing CIFAR-100 [25], TinyImageNet [26] and ImageNet-Subset (random seed 1993) [12]. For CIFAR-100 and TinyImageNet there are three incremental settings (5, 10, and 20 phases) and for ImageNet-Subset there is one (10 phases). For the sequencing and division of all dataset classes, we strictly follow the specification in [66]. + +Implementation details. Following [66], we use ResNet-18 [18] as the backbone network. The model is trained for 100 epochs on each new task. For comparisons on all datasets, the threshold of our prototype reminiscence is set to 0.6. During training, the batch size is set to 128 and the model is optimized by the Adam optimizer with $\beta_{1} = 0.9$ , $\beta_{2} = 0.999$ and $\epsilon = 1e^{-8}$ (weight decay 2e-4). The initial learning rate is 0.001 and is adjusted with the cosine annealing algorithm [35] with a period of 32 epochs. + +Evaluation metrics. As with [66], we employ average incremental accuracy [42] and average forgetting [10] as the evaluation metric. The average incremental accuracy is defined as the average of the accuracies over seen classes across all incremental phases (including the first phase), which reflects the overall incremental performance of the method. The average forgetting is the average difference between the peak task accuracy and the final task accuracy after incremental learning is completed, and the lower value represents better performance. + +# 4.2. Comparison with SOTA + +We compare our method with the state-of-the-art (SOTA) methods of NECIL (EWC [23], LwF_MC [42], MUC [32], SDC [60], PASS [66] and SSRE [67]) and several classical exemplar-based CIL approaches (iCaRL [42], EEIL [9] and UCIR [20]). The results reported for PASS are obtained with self-supervised learning. We reproduce the SSRE with label augmentation in the supplementary materials. As adopted in [67], we memorize 20 samples for the exemplar-based methods. + +Accuracy and forgetting. The quantitative comparisons + +Table 2. Results of average forgetting on 5, 10 and 20 phases. + +
MethodsCIFAR-100TinyImageNet
5102051020
iCaRL-CNN42.1345.6943.5436.8936.7045.12
iCaRL-NCM24.9028.3235.5327.1528.8937.40
EEIL23.3626.6532.4025.5625.5135.04
UCIR21.0025.1228.6520.6122.2533.74
LwFMC44.2350.4755.4654.2654.3763.54
MUC40.2847.5652.6551.4650.2158.00
PASS25.2030.2530.6118.0423.1130.55
SSRE18.3719.4819.009.1714.0614.20
Ours12.5914.6517.3911.8413.9518.51
Ours w/o AKA7.186.4210.304.575.109.05
+ +of the average incremental accuracy are reported in Tab. 1. Compared to the suboptimal NECIL method (SSRE), we improve the accuracy on CIFAR-100, TinyImageNet and ImageNetSubset by $6.30\%$ , $5.59\%$ , and $1.91\%$ , respectively. Moreover, our method shows competitive or even better performance than the classical exemplar-based methods. Certainly, it still slightly inferior to the SOTA exemplar-based method DER [58]. In Fig. 4 we show the accuracy change curves on three benchmarks. Our method is superior at almost all phases, achieving a better balance between stability and plasticity. To further evaluate the above methods, we provide the results of average forgetting in Tab. 2, where our method also performs superiorly. In addition, since the proposed asymmetric knowledge aggregation (AKA) improves the classification accuracy on the current task, the forgetting metric is increased, however this is harmless to overall performance. We will report more analysis in the following and supplementary materials. Experimental results show that our approach can mitigate catastrophic forgetting despite the lack of past task data, which is a more privacy-safe and memory-friendly manner to achieve CIL. + +# 4.3. Ablation Study + +In this section, we conduct several ablation studies on the proposed method. To better analyze the impact of the core designs, our approach is divided into three compo + +![](images/1a93b4399b3cbc81db839218245190045e0234094af61aff710493fbc422cd9a.jpg) + +![](images/6dfb9cba030c3399923ddda21bda3cebbc2d0b94bfdac529573ca091045bd150.jpg) + +![](images/62fc92677b026b68b08ff7366fc57c4df721bd826f53742c4985071957014b64.jpg) + +![](images/1cca4e323c647fbb69f2cf4829a03959acc53524841a783d271f3e68ee875804.jpg) + +![](images/4d6a06f8c3cd09bcaaeb9a74391dce3f49bdb255a91bf0da2ecd6baf4c819dc0.jpg) +Figure 4. Illustration of the classification accuracy changes as tasks are being learned on CIFAR-100, TinyImageNet and ImageNet-Subset, which contains the complete curves. Precise data of our method is presented in the supplementary materials. + +![](images/fa6030409957229536ab8144b33bb10ebbee21502c2d522422b63d516752d2e0.jpg) + +![](images/4fc92919e116aa6bcff82370aa6c0860bf5e4831303dcad7ae5ca04ec9b6bb4e.jpg) + +![](images/8ca0894e4222ab6d2425584a4aacf2d2148f2c5c227424a938ab30aee8a09185.jpg) + +Table 3. Ablation study (in average incremental accuracy) of our method on CIFAR-100 and TinyImageNet datasets. + +
ComponentsCIFAR-100TinyImageNet
PRSLAAKA5 phases10 phases20 phases5 phases10 phases20 phases
56.2751.0243.9837.9332.4423.98
✓66.2163.8057.3145.8544.0435.93
✓61.2759.5955.1446.6543.8838.13
✓✓68.4867.5665.0352.1551.6749.30
✓✓✓70.0268.8665.8653.3252.6149.83
+ +![](images/57077b2120d55956c119e0c082a92a954a06b5398a5d2b4bd237e23f969e835c.jpg) +Figure 5. Influence of the threshold in prototype reminiscence. + +nents: prototype reminiscence (PR), self-supervised label augmentation (SLA) and asymmetric knowledge aggregation (AKA). As a general trick, KD was used in all experimental settings. To explicitly illustrate the effectiveness of PR, in the baseline model we save the prototypes and directly use them for training. As shown in the $1^{st}$ and $2^{nd}$ rows of Tab. 3, PR successfully maintains the discrimination and balance between the old and new classes and makes an impressive progress on the baseline model. When SLA acts on the baseline model alone, it is effective, but there is still a bias in the classifier, while using it with PR achieves promising results. AKA and SLA are adopted as a whole. + +In addition to the overall performance improvement, AKA is more about enhancing the model's understanding of the new task to satisfy the latest business requirements. + +To investigate the sensitivity of the threshold $\eta$ in our prototype reminiscence, we plot its fluctuation curve on CIFAR-100 dataset. As presented in Fig. 5, when $\eta$ is low, the generated old class features are restricted to concentrate around the preserved prototypes thus lacking the ability to adapt to the changes of the representation space, which results in poor performance. As the constraint is relaxed ( $\eta$ increases), the effect of PR gradually comes into its own and peaks in performance at about $\eta = 0.6$ . When the threshold continues to increase, the performance gain from PR starts to diminish because as the constraint fades away, the number of outlier features generated by PR gradually increases, which disturbs the learning of the model. + +# 4.4. Analysis + +Visualization. To demonstrate the advantages of our prototype reminiscence, we visualise the 2D embeddings of feature vectors with t-SNE [51]. In Fig. 6 (c) and (d), the old class features are generated by the stored prototypes. Compared with fine-tuning, the confusion of old class features is alleviated in the results of Gaussian noise augmentation. However, the overlap between the distributions of different + +![](images/aadac86b2364d8127afabbcd24d59af9a706816e6951e1f30fd0d3174624915e.jpg) +(a) Initial Phase + +![](images/f5ad0d8978c7c409ddfbfef28eb6e183af4419de9d4362f702ed13fb6fd12883.jpg) +(b) Finetuning + +![](images/c5152f78a0a7279076f48e153b2fb4c95903f064012415578b92d879000cf986.jpg) +(c) Gaussian Noise Augmentation + +![](images/ad601d821c7c92f1990042a930846170d7d15e62e7f4bd0c98976da907fa5deb.jpg) +(d) Prototype Reminiscence + +![](images/ab0db62b14133d9c28fade7251a6244010a99f0990fd1d41fdf76745d40cdb18.jpg) +Figure 6. Visualization of different augmentation schemes. +(a) Finetuning +Figure 7. The comparison of confusion matrix of finetuning, iCaRL and our method on CIFAR-100 (10 phases). + +![](images/758adda0148ad68cce97cf41348b3382f62a1da0c4f82be9cc4f815784ccc8c8.jpg) +(b) iCaRL + +![](images/5a76e810a74cead764772aa1f5a8b2d4ef57553dc486fb238d39c069a29bac17.jpg) +(c) Ours + +classes is still significant, and in particular the confusion between the generated features. Instead, the feature distributions of different old classes reshaped by our method are relatively dispersed among each other. + +Classification bias of the model. To evaluate the performance differences between the old and new classes, we compared the confusion matrix of finetuning, iCaRL and our method on CIFAR-100. As shown in Fig. 7, since samples of old classes are not available, finetuning tends to classify the samples into new classes. The confusion is alleviated by iCaRL, but still shows a preference for new classes. The confusion matrix of our method exhibits better overall performance without favouring old or new classes. Thanks to PR and AKA, the classification bias between old and new classes is well handled. + +The role of asymmetric knowledge aggregation. To better illustrate the role of the asymmetric knowledge aggregation, we compare the changes in classification accuracy for the initial task during subsequent incremental learning, and the performance on each new task in the presence or absence of AKA. The results for the three settings on CIFAR100 are shown in Fig. 8. On the one hand, the performance degradation in the initial task caused by the introduction of AKA is negligible; on the other hand, the discrimination of new classes is considerably improved. As analyzed in the introduction, AKA can improve the model's understanding of new tasks as non-destructively as possible. + +![](images/10147fedf265c9181e8fcdaf6ed42f86c299c836316fc3c5f049cf87096c1e58.jpg) + +![](images/e8453a93d9cc38dc040f20a2ae2da20f8c4964320ac6b8155d7409ab0ea79266.jpg) + +![](images/5ae56df30d9b202fa2459ecd2ba9f6f8403e6a36292d422294a8fd6b8e179cbc.jpg) +CIFAR-100 (10 phases) + +![](images/e2891e1f7b2a10b4b7bb0de69ac093762da7ef12e2a34ab91a7a6090c0815469.jpg) +CIFAR-100 (10 phases) + +![](images/9c06c2f4009b147b4c7fe01fb9f7324b57254b1d4acc18d4bb1f8b5bee743399.jpg) +CIFAR-100 (20 phases) +Figure 8. The first column is the classification accuracy on the initial task, which changes with the incremental phase. The second column shows the change in classification accuracy on the new task. The proposed knowledge aggregation allows better learning of new tasks with little impact on existing knowledge. + +![](images/7690fc172bf6dc811de44a56b1121791395627ec4228f087e5709c13b575ec1a.jpg) +CIFAR-100 (20 phases) + +# 5. Conclusion + +In this work, we address the NECIL issue from two perspectives of resisting catastrophic forgetting and boosting plasticity of the model, proposing prototype reminiscence and augmented asymmetric knowledge aggregation, respectively. In particular, we pay attention to the performance of the incremental learner on new tasks which often represent the latest business requirements, and design an asymmetric knowledge aggregation strategy for better adaptation to new tasks. Extensive evaluations demonstrate that our approach outperforms the SOTA NECIL methods and shows strong competitiveness with classical exemplar-based methods in the absence of stored samples. + +Limitations. For each prototype reminiscence, the prototype and the feature are selected randomly. When the selected prototype and feature are less similar (i.e., farther apart in the feature space), there may be outliers in the generated features of old classes. Exploring the impact of outliers on training may be of interest. + +Acknowledgement. This work is partially supported by the Key Research and Development Program of Hubei Province (2021BAA187), National Natural Science Foundation of China under Grant (62176188), Zhejiang lab (NO.2022NF0AB01), the Special Fund of Hubei Luojia Laboratory (220100015) and CAAI-Huawei MindSpore Open Fund. + +# References + +[1] Davide Abati, Jakub Tomczak, Tijmen Blankevoort, Simone Calderara, Rita Cucchiara, and Babak Ehteshami Bejnordi. Conditional channel gated networks for task-aware continual learning. In CVPR, pages 3931-3940, 2020. 3 +[2] Hongjoon Ahn, Jihwan Kwak, Subin Lim, Hyeonsu Bang, Hyojun Kim, and Taesup Moon. 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NeurIPS, 31, 2018. 5 \ No newline at end of file diff --git a/2023/Prototype Reminiscence and Augmented Asymmetric Knowledge Aggregation for Non-Exemplar Class-Incremental Learning/images.zip b/2023/Prototype Reminiscence and Augmented Asymmetric Knowledge Aggregation for Non-Exemplar Class-Incremental Learning/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..609984bbb32513c071a223a767ba632f3ab3d63c --- /dev/null +++ b/2023/Prototype Reminiscence and Augmented Asymmetric Knowledge Aggregation for Non-Exemplar Class-Incremental Learning/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3ba473b3548f46fc5a3ecd7e419c19ae4ba806b380c96918a73520152cf2449c +size 698748 diff --git a/2023/Prototype Reminiscence and Augmented Asymmetric Knowledge Aggregation for Non-Exemplar Class-Incremental Learning/layout.json b/2023/Prototype Reminiscence and Augmented Asymmetric Knowledge Aggregation for Non-Exemplar Class-Incremental Learning/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..335196ba2f1085ebf04acbfd0d6d58684e04a252 --- /dev/null +++ b/2023/Prototype Reminiscence and Augmented Asymmetric Knowledge Aggregation for Non-Exemplar Class-Incremental Learning/layout.json @@ -0,0 +1,9914 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 55, + 136, + 521, + 172 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 136, + 521, + 172 + ], + "spans": [ + { + "bbox": [ + 55, + 136, + 521, + 172 + ], + "type": "text", + "content": "Prototype Reminiscence and Augmented Asymmetric Knowledge Aggregation for Non-Exemplar Class-Incremental Learning" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 219, + 191, + 353, + 207 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 219, + 191, + 353, + 207 + ], + "spans": [ + { + "bbox": [ + 219, + 191, + 353, + 207 + ], + "type": "text", + "content": "Wuxuan Shi" + }, + { + "bbox": [ + 219, + 191, + 353, + 207 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 219, + 191, + 353, + 207 + ], + "type": "text", + "content": ", Mang Ye" + }, + { + "bbox": [ + 219, + 191, + 353, + 207 + ], + "type": "inline_equation", + "content": "^{1,2*}" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 138, + 207, + 440, + 219 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 207, + 440, + 219 + ], + "spans": [ + { + "bbox": [ + 138, + 207, + 440, + 219 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 138, + 207, + 440, + 219 + ], + "type": "text", + "content": "School of Computer Science, Wuhan University, Wuhan, China" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 189, + 220, + 387, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 189, + 220, + 387, + 234 + ], + "spans": [ + { + "bbox": [ + 189, + 220, + 387, + 234 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 189, + 220, + 387, + 234 + ], + "type": "text", + "content": " Hubei Luojia Laboratory, Wuhan, China" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 179, + 235, + 396, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 179, + 235, + 396, + 247 + ], + "spans": [ + { + "bbox": [ + 179, + 235, + 396, + 247 + ], + "type": "text", + "content": "https://shiwuxuan.github.io/PRAKA-project" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 139, + 273, + 186, + 286 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 273, + 186, + 286 + ], + "spans": [ + { + "bbox": [ + 139, + 273, + 186, + 286 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 298, + 282, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 298, + 282, + 555 + ], + "spans": [ + { + "bbox": [ + 45, + 298, + 282, + 555 + ], + "type": "text", + "content": "Non-exemplar class-incremental learning (NECIL) requires deep models to maintain existing knowledge while continuously learning new classes without saving old class samples. In NECIL methods, prototypical representations are usually stored, which inject information from former classes to resist catastrophic forgetting in subsequent incremental learning. However, since the model continuously learns new knowledge, the stored prototypical representations cannot correctly model the properties of old classes in the existence of knowledge updates. To address this problem, we propose a novel prototype reminiscence mechanism that incorporates the previous class prototypes with arriving new class features to dynamically reshape old class feature distributions thus preserving the decision boundaries of previous tasks. In addition, to improve the model generalization on both newly arriving classes and old classes, we contribute an augmented asymmetric knowledge aggregation approach, which aggregates the overall knowledge of the current task and extracts the valuable knowledge of the past tasks, on top of self-supervised label augmentation. Experimental results on three benchmarks suggest the superior performance of our approach over the SOTA methods." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 574, + 124, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 124, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 124, + 586 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 45, + 594, + 279, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 594, + 279, + 687 + ], + "spans": [ + { + "bbox": [ + 45, + 594, + 279, + 687 + ], + "type": "text", + "content": "In recent years, deep neural networks have achieved great success on various tasks. In dynamic and open environments, deep models also require the ability to continuously learn new tasks as the input stream is updated. Hence, class-incremental learning (CIL), which aims to learn a unified classifier that can classify all seen classes under progressive changes in the classes to be learned, has attracted extensive attention [30, 41, 16, 47, 31, 28]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 45, + 687, + 279, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 687, + 279, + 711 + ], + "spans": [ + { + "bbox": [ + 45, + 687, + 279, + 711 + ], + "type": "text", + "content": "As new data becomes available, it is computationally expensive to jointly retrain the model with new and old class" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 302, + 273, + 530, + 341 + ], + "blocks": [ + { + "bbox": [ + 302, + 273, + 530, + 341 + ], + "lines": [ + { + "bbox": [ + 302, + 273, + 530, + 341 + ], + "spans": [ + { + "bbox": [ + 302, + 273, + 530, + 341 + ], + "type": "image", + "image_path": "61435a7e68d6b1d3ca58c68b63e86f1f127444db2709525d6230656ba363be58.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 299, + 343, + 530, + 426 + ], + "blocks": [ + { + "bbox": [ + 299, + 343, + 530, + 426 + ], + "lines": [ + { + "bbox": [ + 299, + 343, + 530, + 426 + ], + "spans": [ + { + "bbox": [ + 299, + 343, + 530, + 426 + ], + "type": "image", + "image_path": "b8f79e6cd48897686028572c4979d0eba37bec46e2adb11fccb2d20bcb334a50.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 426, + 531, + 523 + ], + "lines": [ + { + "bbox": [ + 296, + 426, + 531, + 523 + ], + "spans": [ + { + "bbox": [ + 296, + 426, + 531, + 523 + ], + "type": "text", + "content": "Figure 1. Idea illustration. (a) Joint training with abundant samples. (b) Baseline: Updating the model with the memorized prototype and new data, which narrows the decision boundary of the old classes. (c) Gaussian Noise Augmentation [66]: The decision boundary of the old class is retained, but it introduces an overlap between the old and new class distributions due to the change in representation space. (d) With prototype reminiscence, newly learned information can be injected while reshaping the feature distribution of past data to reduce overlap and resist forgetting." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 532, + 531, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 532, + 531, + 648 + ], + "spans": [ + { + "bbox": [ + 296, + 532, + 531, + 648 + ], + "type": "text", + "content": "samples. Worse still, the old class samples could not be fully accessible. In this case, an alternative is to fine-tune the model on new data, yet catastrophic forgetting [38, 15] will be a serious challenge. The decision boundary of the unified classifier would be significantly changed and biased towards the new classes. Conversely, another direction is to fix the feature embedding space of a trained model, which suffers from frustrating generalization ability and thus performs poorly on new tasks, i.e., the plasticity of the model is greatly degraded." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 648, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 648, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 648, + 531, + 730 + ], + "type": "text", + "content": "To overcome the catastrophic forgetting issue, many CIL methods [42, 8, 6, 56, 2, 53] store a fraction of the old data in memory and replay them in subsequent incremental phases to maintain the existing knowledge. Unfortunately, storing data poses privacy concerns and comes at a sharp cost to memory and computation. In this paper, we follow a paradigm holding for more extensive applications," + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 77, + 42, + 119, + 71 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 42, + 119, + 71 + ], + "spans": [ + { + "bbox": [ + 77, + 42, + 119, + 71 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 151, + 41, + 470, + 52 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 41, + 470, + 52 + ], + "spans": [ + { + "bbox": [ + 151, + 41, + 470, + 52 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 198, + 53, + 422, + 63 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 198, + 53, + 422, + 63 + ], + "spans": [ + { + "bbox": [ + 198, + 53, + 422, + 63 + ], + "type": "text", + "content": "Except for this watermark, it is identical to the accepted version;" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 181, + 63, + 440, + 74 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 181, + 63, + 440, + 74 + ], + "spans": [ + { + "bbox": [ + 181, + 63, + 440, + 74 + ], + "type": "text", + "content": "the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 719, + 240, + 730 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 719, + 240, + 730 + ], + "spans": [ + { + "bbox": [ + 56, + 719, + 240, + 730 + ], + "type": "text", + "content": "*Corresponding Author: Mang Ye (yemang@whu.edu.cn)" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "text", + "content": "1772" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 279, + 141 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 279, + 141 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 279, + 141 + ], + "type": "text", + "content": "termed non-exemplar class-incremental learning (NECIL) [66, 67], which solves the catastrophic forgetting problem in CIL scenario without preserving old class samples." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 143, + 279, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 143, + 279, + 375 + ], + "spans": [ + { + "bbox": [ + 45, + 143, + 279, + 375 + ], + "type": "text", + "content": "For NECIL, a natural substitute for storing data is to generate pseudo-samples of previous classes by deep generative models [62, 54, 46, 49, 57] such as GAN [4, 17]. However, it is unstable and ineffective to train generative models for non-stationary data streams [65]. Catastrophic forgetting can also have a negative impact on the generative model resulting in a simultaneous decrease in the effectiveness of both models. Instead of focusing on old data, some works turn to estimating model parameters that are important for previous tasks and constraining their changes [23, 61, 3]. Nevertheless, the constraints on the model parameters lead to poor generalization ability to long-sequence tasks. Besides, several studies propose to dynamically expand the network structure during the process of incremental learning [44, 58, 59, 37, 64]. Although this strategy can efficiently handle long sequences of tasks and ultimately maintain the performance of the old classes, the computational resource requirements associated with creating and storing additional network components and reasoning about multiple forward propagations are frustrating." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 378, + 279, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 378, + 279, + 563 + ], + "spans": [ + { + "bbox": [ + 45, + 378, + 279, + 563 + ], + "type": "text", + "content": "Recently, some prototype-based NECIL methods have achieved impressive performance [66, 67, 60, 50]. They use prototypical representations (typically the class mean in the deep feature space) memorized for each old class to model the feature distribution of past data and inject information from the previous classes in subsequent incremental learning. Rather than storing samples, this strategy is more memory efficient and privacy secure. Nevertheless, as shown in Fig. 1 (b), direct training with saved prototypes and current data struggles to prevent the collapse of decision boundaries, due to the lack of old class features. Some works augment the prototypes by adding Gaussian noise [66] or over-sampling [67] to enrich old class features. However, updates of the model on continuous data streams could lead to inevitable changes in the representation of old classes, making the saved prototypes increasingly outdated." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 564, + 279, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 564, + 279, + 658 + ], + "spans": [ + { + "bbox": [ + 45, + 564, + 279, + 658 + ], + "type": "text", + "content": "The feature distribution simulated by the above strategies cannot accommodate such changes due to the missing consideration of knowledge updates. It could result in overlap between the distributions of different classes, especially between new and old classes, as shown in Fig. 1 (c). Consequently, combining newly acquired information with stored prototypes to dynamically model past data distributions is crucial to resist catastrophic forgetting in NECIL." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "content": "To address this challenge, we propose a prototype reminiscence mechanism to track the evolution of the old class representations by injecting new knowledge from the updating network while reshaping the feature distribution. Specifically, we perform a random bidirectional interpolation operation between the extracted new class features and" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 318, + 105, + 511, + 341 + ], + "blocks": [ + { + "bbox": [ + 318, + 105, + 511, + 341 + ], + "lines": [ + { + "bbox": [ + 318, + 105, + 511, + 341 + ], + "spans": [ + { + "bbox": [ + 318, + 105, + 511, + 341 + ], + "type": "image", + "image_path": "ac65a3b24c9faa1c01b41c7953b4088123479b7ccd901f6fa898832665249713.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 345, + 531, + 389 + ], + "lines": [ + { + "bbox": [ + 296, + 345, + 531, + 389 + ], + "spans": [ + { + "bbox": [ + 296, + 345, + 531, + 389 + ], + "type": "text", + "content": "Figure 2. We introduce self-supervised label augmentation to learn generalizable and transferable representations. The knowledge of the self-supervised classifier is aggregated and transferred to another classifier to take full advantage of it." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 296, + 400, + 530, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 400, + 530, + 528 + ], + "spans": [ + { + "bbox": [ + 296, + 400, + 530, + 528 + ], + "type": "text", + "content": "the saved old class prototypes to enrich old class features. As shown in Fig. 1 (d), it expands the prototype to protect the decision boundaries of old classes and to counteract catastrophic forgetting. Since the feature distribution of past tasks is dynamically adjusted to the current representation space, the overlap between the old and new classes is reduced. Thus, the discrimination and balance between the old and new classes are maintained. Cooperating with the well-known knowledge distillation (KD) [20, 19], the mismatch between the preserved prototypes and the continuously updated network is alleviated." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 530, + 530, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 530, + 530, + 682 + ], + "spans": [ + { + "bbox": [ + 296, + 530, + 530, + 682 + ], + "type": "text", + "content": "In addition to dealing with catastrophic forgetting, when new data arrives, performance on the current task is also of great concern, necessitating the plasticity of the incremental learner. This mainly involves two aspects: learning generalizable and transferable representations, fully utilizing the information from new data. Previous works [66, 55] have achieved good progress on the first aspect by self-supervised label augmentation [27], however they ordinarily disregard the second. The new task contains abundant information that the network has never encountered and will have a stronger influence on model updates. Improving the plasticity of the model from continuous data streams requires a simultaneous approach from both aspects." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 682, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 682, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 682, + 530, + 730 + ], + "type": "text", + "content": "To solve this bottleneck, we contribute an augmented asymmetric knowledge aggregation approach to enhance the plasticity of the model noninvasively. Taking inspiration from [24, 27], we first augment the new classes with" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "text", + "content": "1773" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 281, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 281, + 245 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 281, + 245 + ], + "type": "text", + "content": "rotation as self-supervision, which requires the model to acquire task-agnostic representations to improve its generalization ability. Furthermore, as illustrated in Fig. 2, we selectively aggregate the valuable knowledge in the augmented classifier—valid weights of past tasks are extracted, and the information captured on the current task is sufficiently exploited. This asymmetric knowledge aggregation scheme can condense the knowledge learned via self-supervised label augmentation (SLA) to make the classifier more purified. It further improves the incremental learner's performance on the new tasks without discrimination scari-fication on old classes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 246, + 267, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 246, + 267, + 257 + ], + "spans": [ + { + "bbox": [ + 57, + 246, + 267, + 257 + ], + "type": "text", + "content": "To summarize, our main contributions are as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 266, + 279, + 424 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 57, + 266, + 279, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 266, + 279, + 313 + ], + "spans": [ + { + "bbox": [ + 57, + 266, + 279, + 313 + ], + "type": "text", + "content": "- We propose a simple yet effective method of prototype reminiscence for NECIL, which models feature distribution for the past data in a continuously updated representation space to resist catastrophic forgetting." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 322, + 279, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 322, + 279, + 367 + ], + "spans": [ + { + "bbox": [ + 57, + 322, + 279, + 367 + ], + "type": "text", + "content": "- We contribute augmented asymmetric knowledge aggregation, which learns task-agnostic representations and fully captures the newly acquired knowledge to improve the plasticity of incremental learners." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 57, + 378, + 279, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 378, + 279, + 424 + ], + "spans": [ + { + "bbox": [ + 57, + 378, + 279, + 424 + ], + "type": "text", + "content": "- Extensive experiments on three benchmarks demonstrate that our method achieves state-of-the-art performance. We also provide a detailed ablation study to analyze the influence of each component." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 45, + 436, + 130, + 447 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 436, + 130, + 447 + ], + "spans": [ + { + "bbox": [ + 45, + 436, + 130, + 447 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 455, + 196, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 455, + 196, + 468 + ], + "spans": [ + { + "bbox": [ + 45, + 455, + 196, + 468 + ], + "type": "text", + "content": "2.1. Class-Incremental Learning" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 473, + 279, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 473, + 279, + 507 + ], + "spans": [ + { + "bbox": [ + 45, + 473, + 279, + 507 + ], + "type": "text", + "content": "Current CIL methods can be roughly divided into three categories: rehearsal-based methods, regularization-based methods and structure-based methods." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 508, + 281, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 508, + 281, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 508, + 281, + 730 + ], + "type": "text", + "content": "Rehearsal-based methods maintain the distribution of old classes by saving exemplars of fixed memory size to jointly train the model with current data. Based on the saved samples, some works investigate knowledge distillation to prevent forgetting [56, 42, 13], while others try to combine regularization of gradients and rehearsal to make more efficient use of the preserved data [43, 34, 11]. In addition, several papers have studied the impact of memory management schemes [5, 22, 33]. Regularization-based methods identify the key model parameters for the previous tasks, penalizing their changes when learning the current task [23, 61, 3, 40]. The difference between these methods is the association of each network parameter with importance weights stored in incremental learning. Structure-based methods dynamically modify the network architecture to maintain existing knowledge and adapt to new tasks. They usually expand the network structure in depth or width when facing a new task [59, 21, 29, 58], or mask parts of the network for different tasks [45, 36, 1]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 106, + 530, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 327 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 327 + ], + "type": "text", + "content": "Recently, some works have researched the use of class prototypes to implement non-exemplar class-incremental learning [66, 60, 67, 50], which somewhat reduces the issues of data privacy security and memory constraints. Yu et al. [60] approximate and compensate for the semantic drift of previous tasks during the training of the new task. Based on this, Toldo et al. [50] propose to jointly exploit semantic drift and feature drift to update the representations of past classes. Apart from investigating the evolution of prototypes as incremental learning occurs, there are some studies that focus on the ways to model past data distributions by prototypes [66, 67]. Note that this strategy is orthogonal to the above methods for drift estimation, and our method falls into this category. Zhu et al. [66] introduce Gaussian noise to augment the prototype to restrain the decision boundaries of old classes. Zhu et al. [67] propose a prototype selection mechanism that uses samples of the new data similar to the old classes for distillation to reduce confusion between the newly added classes and the original classes." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 334, + 467, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 334, + 467, + 346 + ], + "spans": [ + { + "bbox": [ + 296, + 334, + 467, + 346 + ], + "type": "text", + "content": "2.2. Self-supervised Learning in CIL" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 351, + 530, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 351, + 530, + 607 + ], + "spans": [ + { + "bbox": [ + 296, + 351, + 530, + 607 + ], + "type": "text", + "content": "The objective of self-supervised learning (SSL) is to acquire transferable representations that are applicable for other tasks. This coincides with the need for IL to inhibit task-level overfitting phenomenon and rapidly adapt to new tasks. Hence, some works explore improving the quality of the learned representations by SSL in the CIL setting [66, 55, 7, 14]. Wu et al. [55] learn class-independent knowledge and multi-perspective knowledge by SSL to make a trade-off between gaining new information and maintaining old knowledge. Fini et al. [14] attempt to seamlessly convert the existing self-supervised loss function into distillation mechanisms plugged into the CIL framework. It also points out that simply introducing SSL can approach or outperform supervised learning in the CIL setting, while this is not always the case for other settings (data-incremental and domain-incremental). Zhu et al. [66] provide better initialization for learning the next task by using rotation as self-supervised information for label augmentation to reduce forgetting from model updates. Our SLA is implemented in the same way as the SSL in [66]. On top of [66], we further improve the upper bound of the incremental learner's understanding of new tasks." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 617, + 379, + 631 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 617, + 379, + 631 + ], + "spans": [ + { + "bbox": [ + 296, + 617, + 379, + 631 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": "Problem Statement. In this paper, we consider nonexemplar class-incremental learning (NECIL), where no samples from old classes are stored. The training data for the incremental task " + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "inline_equation", + "content": "t \\in \\{1, \\dots, T\\}" + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": " is denoted as " + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "inline_equation", + "content": "D_{t} = \\{X_{t}, Y_{t}\\} = \\{x_{t}^{i}, y_{t}^{i}\\}_{i=1}^{n_{t}}" + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "inline_equation", + "content": "n_{t}" + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "inline_equation", + "content": "x_{t}^{i}" + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "inline_equation", + "content": "y_{t}^{i} \\in C_{t}" + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": " represent the number of training samples, an input sample and its corresponding label for task " + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": ", respectively. " + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "inline_equation", + "content": "C_{t}" + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": " is the class set of task " + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": " and all the incremental classes are disjoint, i.e.," + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "text", + "content": "1774" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 105, + 315, + 310 + ], + "blocks": [ + { + "bbox": [ + 49, + 105, + 315, + 310 + ], + "lines": [ + { + "bbox": [ + 49, + 105, + 315, + 310 + ], + "spans": [ + { + "bbox": [ + 49, + 105, + 315, + 310 + ], + "type": "image", + "image_path": "296947040fa00f334cdf5ed32a8e938a888c90ae2f080acead9c5e03f8ba75ff.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 311, + 531, + 344 + ], + "lines": [ + { + "bbox": [ + 45, + 311, + 531, + 344 + ], + "spans": [ + { + "bbox": [ + 45, + 311, + 531, + 344 + ], + "type": "text", + "content": "Figure 3. Illustration of our method for NECIL. The classes of current task are augmented by rotation transformation [27]. We expand the stored prototype by prototype reminiscence in the deep feature space to generate the same number of old class features as the batch size each time. During the evaluation, only the current feature extractor " + }, + { + "bbox": [ + 45, + 311, + 531, + 344 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_t" + }, + { + "bbox": [ + 45, + 311, + 531, + 344 + ], + "type": "text", + "content": " and the refined classifier " + }, + { + "bbox": [ + 45, + 311, + 531, + 344 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_o" + }, + { + "bbox": [ + 45, + 311, + 531, + 344 + ], + "type": "text", + "content": " are used." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 317, + 105, + 527, + 310 + ], + "blocks": [ + { + "bbox": [ + 317, + 105, + 527, + 310 + ], + "lines": [ + { + "bbox": [ + 317, + 105, + 527, + 310 + ], + "spans": [ + { + "bbox": [ + 317, + 105, + 527, + 310 + ], + "type": "image", + "image_path": "86f1e99f6b36baa18d8b42f28449338372084cef72f61bec683e1916dae92a6f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 352, + 280, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 352, + 280, + 400 + ], + "spans": [ + { + "bbox": [ + 45, + 352, + 280, + 400 + ], + "type": "inline_equation", + "content": "C_1 \\cap \\ldots \\cap C_i = \\emptyset" + }, + { + "bbox": [ + 45, + 352, + 280, + 400 + ], + "type": "text", + "content": ". We represent the model with two components: a feature extractor " + }, + { + "bbox": [ + 45, + 352, + 280, + 400 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 45, + 352, + 280, + 400 + ], + "type": "text", + "content": " with parameters " + }, + { + "bbox": [ + 45, + 352, + 280, + 400 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 45, + 352, + 280, + 400 + ], + "type": "text", + "content": " and a unified classifier " + }, + { + "bbox": [ + 45, + 352, + 280, + 400 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 45, + 352, + 280, + 400 + ], + "type": "text", + "content": " with parameters " + }, + { + "bbox": [ + 45, + 352, + 280, + 400 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 45, + 352, + 280, + 400 + ], + "type": "text", + "content": ". The goal is to find a classification model minimized for some loss function " + }, + { + "bbox": [ + 45, + 352, + 280, + 400 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 45, + 352, + 280, + 400 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 57, + 411, + 279, + 443 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 411, + 279, + 443 + ], + "spans": [ + { + "bbox": [ + 57, + 411, + 279, + 443 + ], + "type": "interline_equation", + "content": "\\underset {\\theta , \\varphi} {\\operatorname {a r g m i n}} \\sum_ {t = 1} ^ {C _ {t}} \\mathbb {E} _ {\\left(x _ {t} ^ {i}, y _ {t} ^ {i}\\right) \\sim D _ {t}} \\left[ \\mathcal {L} \\left(y _ {t} ^ {i}, \\mathcal {G} \\left(\\mathcal {F} \\left(x _ {t} ^ {i}; \\theta\\right); \\varphi\\right)\\right) \\right]. \\tag {1}", + "image_path": "05158991e0907d28dfb35cc88e6fa3959dc64783de9e5f6141076028a94556ee.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 448, + 279, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 448, + 279, + 483 + ], + "spans": [ + { + "bbox": [ + 45, + 448, + 279, + 483 + ], + "type": "text", + "content": "As other class-incremental methods, the algorithm has no access to the task label " + }, + { + "bbox": [ + 45, + 448, + 279, + 483 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 45, + 448, + 279, + 483 + ], + "type": "text", + "content": " and is expected to classify all observed classes " + }, + { + "bbox": [ + 45, + 448, + 279, + 483 + ], + "type": "inline_equation", + "content": "C_{total} = \\{C_1,\\dots ,C_t\\}" + }, + { + "bbox": [ + 45, + 448, + 279, + 483 + ], + "type": "text", + "content": " at any given point." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 483, + 280, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 483, + 280, + 623 + ], + "spans": [ + { + "bbox": [ + 45, + 483, + 280, + 623 + ], + "type": "text", + "content": "Overview of Framework. Fig. 3 shows an overview of our method. The classes of the current task are augmented by rotation transformation [27] and the augmented data is fed to the feature extractors. For each old class, we memorize a class-representative prototype. Then the prototype reminiscence uses the extracted new class features and the stored old class prototypes to generate old class features for joint training. We aggregate the knowledge from the classifier " + }, + { + "bbox": [ + 45, + 483, + 280, + 623 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_S" + }, + { + "bbox": [ + 45, + 483, + 280, + 623 + ], + "type": "text", + "content": " learned with SLA and transfer it to another classifier " + }, + { + "bbox": [ + 45, + 483, + 280, + 623 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_O" + }, + { + "bbox": [ + 45, + 483, + 280, + 623 + ], + "type": "text", + "content": " that only recognizes classes without augmentation. At test time, the current feature extractor " + }, + { + "bbox": [ + 45, + 483, + 280, + 623 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_t" + }, + { + "bbox": [ + 45, + 483, + 280, + 623 + ], + "type": "text", + "content": " and the refined classifier " + }, + { + "bbox": [ + 45, + 483, + 280, + 623 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_O" + }, + { + "bbox": [ + 45, + 483, + 280, + 623 + ], + "type": "text", + "content": " are used for evaluation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 629, + 178, + 642 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 629, + 178, + 642 + ], + "spans": [ + { + "bbox": [ + 45, + 629, + 178, + 642 + ], + "type": "text", + "content": "3.1. Prototype Reminiscence" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 647, + 279, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 647, + 279, + 694 + ], + "spans": [ + { + "bbox": [ + 45, + 647, + 279, + 694 + ], + "type": "text", + "content": "At each incremental phase of task " + }, + { + "bbox": [ + 45, + 647, + 279, + 694 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 45, + 647, + 279, + 694 + ], + "type": "text", + "content": ", only " + }, + { + "bbox": [ + 45, + 647, + 279, + 694 + ], + "type": "inline_equation", + "content": "D_{t}" + }, + { + "bbox": [ + 45, + 647, + 279, + 694 + ], + "type": "text", + "content": " is available in the NECIL setting. Following [66, 60], when learning a new task, we compute and memorize one prototype in the deep feature space for each class:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 76, + 699, + 279, + 732 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 699, + 279, + 732 + ], + "spans": [ + { + "bbox": [ + 76, + 699, + 279, + 732 + ], + "type": "interline_equation", + "content": "P _ {t, k _ {n e w}} = \\frac {1}{N _ {t , c _ {n e w}}} \\sum_ {n = 1} ^ {N _ {t, c _ {n e w}}} \\mathcal {F} \\left(\\mathbf {X} _ {t, c _ {n e w}}; \\theta_ {t}\\right), \\tag {2}", + "image_path": "91d4b851234fab7aabf7b5285510950599327d20712e93a678285106b73ef7e2.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 352, + 530, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 352, + 530, + 412 + ], + "spans": [ + { + "bbox": [ + 296, + 352, + 530, + 412 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 352, + 530, + 412 + ], + "type": "inline_equation", + "content": "c_{new} \\in C_{new} = C_t" + }, + { + "bbox": [ + 296, + 352, + 530, + 412 + ], + "type": "text", + "content": " is one class of the current task. To alleviate the catastrophic forgetting, the model is trained jointly on the memorized prototypes " + }, + { + "bbox": [ + 296, + 352, + 530, + 412 + ], + "type": "inline_equation", + "content": "\\{P_{old}^1, \\ldots, P_{old}^{|C_{old}|}\\}" + }, + { + "bbox": [ + 296, + 352, + 530, + 412 + ], + "type": "text", + "content": " and current data " + }, + { + "bbox": [ + 296, + 352, + 530, + 412 + ], + "type": "inline_equation", + "content": "D_t" + }, + { + "bbox": [ + 296, + 352, + 530, + 412 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 296, + 352, + 530, + 412 + ], + "type": "inline_equation", + "content": "C_{old} = C_1 \\cup \\ldots \\cup C_{t-1}" + }, + { + "bbox": [ + 296, + 352, + 530, + 412 + ], + "type": "text", + "content": " denotes the set of past classes." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 413, + 531, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 413, + 531, + 590 + ], + "spans": [ + { + "bbox": [ + 296, + 413, + 531, + 590 + ], + "type": "text", + "content": "Whereas prototypes can inject information of past classes in training, the decision boundaries are narrowed due to the lack of rich old class features. Moreover, as the model continuously learns new data, the deep representation space is changing, which poses a challenge to reproduce the properties of old classes. To this end, we propose a prototype reminiscence strategy to dynamically model the feature distribution of past data in an updating representation space. Our strategy is based on a simple yet effective interpolation operation. In general, as shown in Fig. 3, we randomly select a prototype of the old classes " + }, + { + "bbox": [ + 296, + 413, + 531, + 590 + ], + "type": "inline_equation", + "content": "P_{old}^{n} \\in \\{P_{old}^{1}, \\dots, P_{old}^{|C_{old}|}\\}" + }, + { + "bbox": [ + 296, + 413, + 531, + 590 + ], + "type": "text", + "content": " and a feature of the new classes " + }, + { + "bbox": [ + 296, + 413, + 531, + 590 + ], + "type": "inline_equation", + "content": "F_{new}^{m} \\in \\{F_{new}^{1}, \\dots, F_{new}^{B}\\}" + }, + { + "bbox": [ + 296, + 413, + 531, + 590 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 296, + 413, + 531, + 590 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 296, + 413, + 531, + 590 + ], + "type": "text", + "content": " is the batch size. Then we perform a random bidirectional interpolation operation between " + }, + { + "bbox": [ + 296, + 413, + 531, + 590 + ], + "type": "inline_equation", + "content": "P_{old}^{n}" + }, + { + "bbox": [ + 296, + 413, + 531, + 590 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 413, + 531, + 590 + ], + "type": "inline_equation", + "content": "F_{new}^{m}" + }, + { + "bbox": [ + 296, + 413, + 531, + 590 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 593, + 530, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 593, + 530, + 620 + ], + "spans": [ + { + "bbox": [ + 306, + 593, + 530, + 620 + ], + "type": "interline_equation", + "content": "F _ {o l d} ^ {n} = \\left\\{ \\begin{array}{l} (1 - \\lambda) \\left(P _ {o l d} ^ {n}\\right) + \\lambda \\left(F _ {n e w} ^ {m}\\right), p _ {e} < 0. 5 \\\\ (1 + \\lambda) \\left(P _ {o l d} ^ {n}\\right) - \\lambda \\left(F _ {n e w} ^ {m}\\right), o t h e r w i s e \\end{array} \\right. \\tag {3}", + "image_path": "89f6a914f6f2fc2d39666ef714e7709f9799293051aa77921a5abcf3e332c160.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "F_{old}^{n}" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": " is the feature generated in the current representation space that has the same label as " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "P_{old}^{n}" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "inline_equation", + "content": "p_e" + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": " is randomly sampled from [0, 1). Considering the design principle of mixup [63, 52], we ensure that the coefficient summary of the two terms for the prototype reminiscence is equal to 1. Different from them, our prototype reminiscence introduces an extrapolation operation, which avoids the generated features being concentrated on one side of the decision boundary. Meanwhile, we choose" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "text", + "content": "1775" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 279, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 279, + 175 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 279, + 175 + ], + "type": "inline_equation", + "content": "\\lambda \\sim \\mathrm{Beta}(0.5, 0.5) \\in [0, \\eta]" + }, + { + "bbox": [ + 45, + 106, + 279, + 175 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 45, + 106, + 279, + 175 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 45, + 106, + 279, + 175 + ], + "type": "text", + "content": " is a threshold value to control the maximum distance between the generated old class features and the corresponding prototype for avoiding outliers. To make a fair comparison, as in [66], we generate the same number of old class features as the batch size for each batch of new data." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 182, + 279, + 206 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 279, + 206 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 279, + 206 + ], + "type": "text", + "content": "3.2. Augmented Asymmetric Knowledge Aggregation" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 212, + 279, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 212, + 279, + 305 + ], + "spans": [ + { + "bbox": [ + 45, + 212, + 279, + 305 + ], + "type": "text", + "content": "While counteracting forgetting, incremental learners also need to adapt to new tasks. We design an augmented asymmetric knowledge aggregation scheme that endows the model with stronger plasticity. First, we augment the current classes as in [27]. For the current task, the N-way classification problem is extended into a 4N-way classification problem. Specifically, the input data for each class is rotated by " + }, + { + "bbox": [ + 45, + 212, + 279, + 305 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 45, + 212, + 279, + 305 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 212, + 279, + 305 + ], + "type": "inline_equation", + "content": "180^{\\circ}" + }, + { + "bbox": [ + 45, + 212, + 279, + 305 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 45, + 212, + 279, + 305 + ], + "type": "inline_equation", + "content": "270^{\\circ}" + }, + { + "bbox": [ + 45, + 212, + 279, + 305 + ], + "type": "text", + "content": " to produce three new classes:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 71, + 310, + 279, + 330 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 310, + 279, + 330 + ], + "spans": [ + { + "bbox": [ + 71, + 310, + 279, + 330 + ], + "type": "interline_equation", + "content": "\\tilde {x} _ {t} ^ {i} = \\left\\{x _ {t} ^ {i, j} \\right\\} _ {j = 0} ^ {3} = \\left\\{r o t a t e (x _ {t} ^ {i}, j \\times 9 0 ^ {\\circ}) \\right\\} _ {j = 0} ^ {3}, \\quad (4)", + "image_path": "13ff0d8704c8eeabae3e4ac70775f3e7ac4d9614e33a0926db03e64460907a39.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 331, + 254, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 331, + 254, + 344 + ], + "spans": [ + { + "bbox": [ + 45, + 331, + 254, + 344 + ], + "type": "text", + "content": "and we allocate new labels " + }, + { + "bbox": [ + 45, + 331, + 254, + 344 + ], + "type": "inline_equation", + "content": "y_{t}^{i}" + }, + { + "bbox": [ + 45, + 331, + 254, + 344 + ], + "type": "text", + "content": " to the augmented data:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 114, + 347, + 279, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 347, + 279, + 365 + ], + "spans": [ + { + "bbox": [ + 114, + 347, + 279, + 365 + ], + "type": "interline_equation", + "content": "\\tilde {y} _ {t} ^ {i} = \\left\\{y _ {t} ^ {i} \\times 4 + j \\right\\} _ {j = 0} ^ {3}. \\tag {5}", + "image_path": "bedeed86059200be9192c390024c44b547131331b93f18e64e7356e24db9dbe7.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 368, + 279, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 368, + 279, + 437 + ], + "spans": [ + { + "bbox": [ + 45, + 368, + 279, + 437 + ], + "type": "text", + "content": "Compared to the widely used 4-way self-supervised task, the above approach removes unnecessary invariant properties when learning both the original task and the self-supervised task simultaneously, thereby reducing the loss of discriminative information while obtaining generalizable and transferable representations [27]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 437, + 279, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 437, + 279, + 600 + ], + "spans": [ + { + "bbox": [ + 45, + 437, + 279, + 600 + ], + "type": "text", + "content": "However, for NECIL, the self-supervised label augmentation can only be applied to new classes (past data is not available). Borrowing from some works [39, 48], the classification weight " + }, + { + "bbox": [ + 45, + 437, + 279, + 600 + ], + "type": "inline_equation", + "content": "w_{c,j}" + }, + { + "bbox": [ + 45, + 437, + 279, + 600 + ], + "type": "text", + "content": " is denoted as a proxy, where " + }, + { + "bbox": [ + 45, + 437, + 279, + 600 + ], + "type": "inline_equation", + "content": "c \\in C_{total}" + }, + { + "bbox": [ + 45, + 437, + 279, + 600 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 437, + 279, + 600 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 45, + 437, + 279, + 600 + ], + "type": "text", + "content": " represents different rotation transformations. In the subsequent incremental learning, the proxies for the augmented classes " + }, + { + "bbox": [ + 45, + 437, + 279, + 600 + ], + "type": "inline_equation", + "content": "(90^{\\circ}, 180^{\\circ}, 270^{\\circ})" + }, + { + "bbox": [ + 45, + 437, + 279, + 600 + ], + "type": "text", + "content": " of the previous tasks gradually fail, leading to redundancy within the classifier. When using the cross-entropy loss for optimization, all augmented classes are viewed independently, and the relationship between them is not explored. Moreover, only the predictions of the non-augmented classes " + }, + { + "bbox": [ + 45, + 437, + 279, + 600 + ], + "type": "inline_equation", + "content": "(0^{\\circ})" + }, + { + "bbox": [ + 45, + 437, + 279, + 600 + ], + "type": "text", + "content": " are considered valid during testing [66], which leads to a large amount of information valuable for the current task being discarded." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 600, + 279, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 600, + 279, + 658 + ], + "spans": [ + { + "bbox": [ + 45, + 600, + 279, + 658 + ], + "type": "text", + "content": "To precisely utilize the valuable knowledge obtained from the above self-supervised label augmentation, we propose an asymmetric knowledge aggregation approach for NECIL. Concretely, for the past tasks, we take in the knowledge of the proxies associated with the original classes:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 81, + 660, + 279, + 693 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 660, + 279, + 693 + ], + "spans": [ + { + "bbox": [ + 81, + 660, + 279, + 693 + ], + "type": "interline_equation", + "content": "\\mathcal {P} _ {a g g} (c \\mid F _ {o l d}) = \\frac {\\exp \\left(w _ {c , 0} ^ {T} F _ {o l d}\\right)}{\\sum_ {k = 1} ^ {K} \\exp \\left(w _ {k , 0} ^ {T} F _ {o l d}\\right)}, \\tag {6}", + "image_path": "1948a99c8f6306e690420ce5c6a2041755df5750846a510325b6c2c91d01f7bf.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "inline_equation", + "content": "K = |C_{total}|" + }, + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "text", + "content": " is the proxy of " + }, + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_S" + }, + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "inline_equation", + "content": "F_{old}" + }, + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "text", + "content": " is the feature generated by prototype reminiscence. For the current task, the conditional probabilities corresponding to all" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 297, + 106, + 475, + 118 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 106, + 475, + 118 + ], + "spans": [ + { + "bbox": [ + 297, + 106, + 475, + 118 + ], + "type": "text", + "content": "transformations of each class are aggregated:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 308, + 121, + 530, + 162 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 121, + 530, + 162 + ], + "spans": [ + { + "bbox": [ + 308, + 121, + 530, + 162 + ], + "type": "interline_equation", + "content": "\\mathcal {P} _ {a g g} (c | \\tilde {F _ {n e w}}) = \\frac {\\exp \\left(\\frac {1}{4} \\sum_ {j = 0} ^ {3} w _ {c , j} ^ {T} F _ {n e w} ^ {j}\\right)}{\\sum_ {k = 1} ^ {K} \\exp \\left(\\frac {1}{4} \\sum_ {j = 0} ^ {3} w _ {k , j} ^ {T} F _ {n e w} ^ {j}\\right)}, \\tag {7}", + "image_path": "3ac52082476af5a983dc619716db847efa7d9f384b1d3aa11e67c8194b5d2a29.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 168, + 530, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 168, + 530, + 241 + ], + "spans": [ + { + "bbox": [ + 296, + 168, + 530, + 241 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 168, + 530, + 241 + ], + "type": "inline_equation", + "content": "F_{new}^{\\tilde{F}} = \\{F_{new}^{j}\\}_{j=0}^{3}" + }, + { + "bbox": [ + 296, + 168, + 530, + 241 + ], + "type": "text", + "content": " represents the set of features extracted from the augmented exemplars " + }, + { + "bbox": [ + 296, + 168, + 530, + 241 + ], + "type": "inline_equation", + "content": "\\tilde{x}_t^i" + }, + { + "bbox": [ + 296, + 168, + 530, + 241 + ], + "type": "text", + "content": " by current model " + }, + { + "bbox": [ + 296, + 168, + 530, + 241 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_t" + }, + { + "bbox": [ + 296, + 168, + 530, + 241 + ], + "type": "text", + "content": ". As presented in Fig. 3, we transfer the aggregated knowledge to another classifier " + }, + { + "bbox": [ + 296, + 168, + 530, + 241 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_O" + }, + { + "bbox": [ + 296, + 168, + 530, + 241 + ], + "type": "text", + "content": ", which only needs to distinguish between non-augmented classes. The loss function " + }, + { + "bbox": [ + 296, + 168, + 530, + 241 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ka}" + }, + { + "bbox": [ + 296, + 168, + 530, + 241 + ], + "type": "text", + "content": " can be expressed as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 339, + 243, + 530, + 283 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 243, + 530, + 283 + ], + "spans": [ + { + "bbox": [ + 339, + 243, + 530, + 283 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {k a} = K L D \\left(\\mathcal {P} _ {a g g} (\\cdot | F) \\| \\mathcal {G} _ {O} (F; \\phi)\\right), \\\\ = \\mathcal {P} _ {a g g} (\\cdot | F) \\log \\frac {\\mathcal {P} _ {a g g} (\\cdot | F)}{\\mathcal {G} _ {O} (F ; \\phi)} \\tag {8} \\\\ \\end{array}", + "image_path": "f1a594ec71a9485d3da6f8441cdb2e92cba30cffd4eb5ce283c183bd49005688.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 288, + 530, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 288, + 530, + 348 + ], + "spans": [ + { + "bbox": [ + 296, + 288, + 530, + 348 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 288, + 530, + 348 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 296, + 288, + 530, + 348 + ], + "type": "text", + "content": " denotes the parameters of " + }, + { + "bbox": [ + 296, + 288, + 530, + 348 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_O" + }, + { + "bbox": [ + 296, + 288, + 530, + 348 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 288, + 530, + 348 + ], + "type": "inline_equation", + "content": "KLD(\\cdot|\\cdot)" + }, + { + "bbox": [ + 296, + 288, + 530, + 348 + ], + "type": "text", + "content": " is the Kullback-Leibler divergence. The knowledge learned from the new data is utilized as much as possible and the invalid weights are discarded to obtain a more refined classifier. During testing inference, only the classifier " + }, + { + "bbox": [ + 296, + 288, + 530, + 348 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_O" + }, + { + "bbox": [ + 296, + 288, + 530, + 348 + ], + "type": "text", + "content": " is used." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 297, + 353, + 477, + 366 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 353, + 477, + 366 + ], + "spans": [ + { + "bbox": [ + 297, + 353, + 477, + 366 + ], + "type": "text", + "content": "3.3. Integrated Optimization Objective" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 371, + 530, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 371, + 530, + 441 + ], + "spans": [ + { + "bbox": [ + 296, + 371, + 530, + 441 + ], + "type": "text", + "content": "Inspiring ourselves from [66], we employ the well-known knowledge distillation (KD) [68, 19] to regularize the feature extractor. Specifically, we minimize the Euclidean distance between the features of new data extracted by current model " + }, + { + "bbox": [ + 296, + 371, + 530, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_t" + }, + { + "bbox": [ + 296, + 371, + 530, + 441 + ], + "type": "text", + "content": " and that of previous model " + }, + { + "bbox": [ + 296, + 371, + 530, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{t - 1}" + }, + { + "bbox": [ + 296, + 371, + 530, + 441 + ], + "type": "text", + "content": " to constrain the feature extractor, which can be formulated as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 334, + 445, + 530, + 461 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 445, + 530, + 461 + ], + "spans": [ + { + "bbox": [ + 334, + 445, + 530, + 461 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {k d} = \\left\\| \\mathcal {F} _ {t} \\left(\\tilde {x} _ {t} ^ {i}; \\theta_ {t}\\right) - \\mathcal {F} _ {t - 1} \\left(\\tilde {x} _ {t} ^ {i}; \\theta_ {t - 1}\\right) \\right\\| _ {2}. \\tag {9}", + "image_path": "1110a661e8b4e501dd872b2893daa334551c22cbee6a89a4b4a7b3b5644d70b4.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 296, + 463, + 530, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 463, + 530, + 522 + ], + "spans": [ + { + "bbox": [ + 296, + 463, + 530, + 522 + ], + "type": "text", + "content": "With the assistance of prototype reminiscence, the disparity between the stored prototype and the updated model can be significantly mitigated. We also calculate the cross-entropy loss for " + }, + { + "bbox": [ + 296, + 463, + 530, + 522 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_S" + }, + { + "bbox": [ + 296, + 463, + 530, + 522 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 463, + 530, + 522 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_O" + }, + { + "bbox": [ + 296, + 463, + 530, + 522 + ], + "type": "text", + "content": ", respectively. With these considerations above, the total loss function " + }, + { + "bbox": [ + 296, + 463, + 530, + 522 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{total}" + }, + { + "bbox": [ + 296, + 463, + 530, + 522 + ], + "type": "text", + "content": " can be expressed as:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 321, + 535, + 530, + 568 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 535, + 530, + 568 + ], + "spans": [ + { + "bbox": [ + 321, + 535, + 530, + 568 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {n e w}} = \\mathcal {L} _ {c e} \\left(\\mathcal {G} _ {S} \\left(\\tilde {\\mathcal {F}} _ {t} \\left(\\tilde {x _ {t} ^ {i}}; \\theta_ {t}\\right); \\varphi_ {t}\\right)\\right) \\tag {10} \\\\ + \\mathcal {L} _ {c e} \\left(\\mathcal {G} _ {O} \\left(\\mathcal {F} _ {t} \\left(\\tilde {x _ {t} ^ {\\prime}}; \\theta_ {t}\\right); \\phi_ {t}\\right)\\right) + \\mathcal {L} _ {k a}, \\\\ \\end{array}", + "image_path": "13b7a5c9b640219eda952ae849fbe3edef1591cca0ef5aa396690ae64ab081a6.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 326, + 570, + 530, + 599 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 570, + 530, + 599 + ], + "spans": [ + { + "bbox": [ + 326, + 570, + 530, + 599 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {o l d} = \\mathcal {L} _ {c e} \\left(\\mathcal {G} _ {S} \\left(F _ {o l d} ^ {i}; \\varphi_ {t}\\right)\\right) \\tag {11} \\\\ + \\mathcal {L} _ {c e} \\left(\\mathcal {G} _ {O} \\left(F _ {o l d} ^ {i}\\right); \\phi_ {t})\\right) + \\mathcal {L} _ {k a}, \\\\ \\end{array}", + "image_path": "e16983c74623519fc0a4e99158904cd0c48fcc323ab587e5ce9d789afc64fc81.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 319, + 602, + 530, + 615 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 602, + 530, + 615 + ], + "spans": [ + { + "bbox": [ + 319, + 602, + 530, + 615 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {n e w}} + \\alpha \\mathcal {L} _ {\\text {o l d}} + \\gamma \\mathcal {L} _ {\\text {k d}}, \\tag {12}", + "image_path": "f6e51c4a087968e696da6b420fd8aa64aa645ed86c6c573288e166d20892e284.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 296, + 623, + 530, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 623, + 530, + 660 + ], + "spans": [ + { + "bbox": [ + 296, + 623, + 530, + 660 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 623, + 530, + 660 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{new}" + }, + { + "bbox": [ + 296, + 623, + 530, + 660 + ], + "type": "text", + "content": " is the loss of new data " + }, + { + "bbox": [ + 296, + 623, + 530, + 660 + ], + "type": "inline_equation", + "content": "\\tilde{x}_t^i" + }, + { + "bbox": [ + 296, + 623, + 530, + 660 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 623, + 530, + 660 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{old}" + }, + { + "bbox": [ + 296, + 623, + 530, + 660 + ], + "type": "text", + "content": " is the loss of the feature " + }, + { + "bbox": [ + 296, + 623, + 530, + 660 + ], + "type": "inline_equation", + "content": "F_{old}^{i}" + }, + { + "bbox": [ + 296, + 623, + 530, + 660 + ], + "type": "text", + "content": " generated by prototype reminiscence. The loss weights " + }, + { + "bbox": [ + 296, + 623, + 530, + 660 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 296, + 623, + 530, + 660 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 623, + 530, + 660 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 296, + 623, + 530, + 660 + ], + "type": "text", + "content": " are both set to 15 in our experiments." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 297, + 669, + 376, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 669, + 376, + 682 + ], + "spans": [ + { + "bbox": [ + 297, + 669, + 376, + 682 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 297, + 688, + 416, + 701 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 688, + 416, + 701 + ], + "spans": [ + { + "bbox": [ + 297, + 688, + 416, + 701 + ], + "type": "text", + "content": "4.1. Experimental Setting" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 297, + 706, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 706, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 297, + 706, + 530, + 730 + ], + "type": "text", + "content": "Dataset. To evaluate the performance of our method, we conduct sufficient experiments on three benchmarks includ" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "text", + "content": "1776" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 134, + 526, + 289 + ], + "blocks": [ + { + "bbox": [ + 46, + 103, + 531, + 134 + ], + "lines": [ + { + "bbox": [ + 46, + 103, + 531, + 134 + ], + "spans": [ + { + "bbox": [ + 46, + 103, + 531, + 134 + ], + "type": "text", + "content": "Table 1. Quantitative comparisons of the average incremental accuracy (%) with other methods at different task number settings on CIFAR-100, TinyImageNet, and ImageNet-Subset. " + }, + { + "bbox": [ + 46, + 103, + 531, + 134 + ], + "type": "inline_equation", + "content": "E = {20}" + }, + { + "bbox": [ + 46, + 103, + 531, + 134 + ], + "type": "text", + "content": " represents exemplar-based methods and storing 20 exemplars for each old class. " + }, + { + "bbox": [ + 46, + 103, + 531, + 134 + ], + "type": "inline_equation", + "content": "E = 0" + }, + { + "bbox": [ + 46, + 103, + 531, + 134 + ], + "type": "text", + "content": " represents non-exemplar methods. The relative improvement compared to the SOTA NECIL method is shown by the red footnotes." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 134, + 526, + 289 + ], + "lines": [ + { + "bbox": [ + 48, + 134, + 526, + 289 + ], + "spans": [ + { + "bbox": [ + 48, + 134, + 526, + 289 + ], + "type": "table", + "html": "
MethodsCIFAR-100TinyImageNetImageNet-Subset
5 phases10 phases20 phases5 phases10 phases20 phases10 phases
E=20iCaRL-CNN51.0748.6644.4334.6431.1527.9050.53
iCaRL-NCM [42]58.5654.1950.5145.8643.2938.0460.79
EEIL [9]60.3756.0552.3447.1245.0140.5063.34
UCIR [20]63.7862.3959.0749.1548.5242.8366.16
DER [58]73.2172.8169.97———75.36
E=0EWC [23]24.4821.2015.8918.8015.7712.3920.40
LwFMC [42]45.9327.4320.0729.1223.1017.4331.18
MUC [32]49.4230.1921.2732.5826.6121.9535.07
SDC [60]56.7757.0058.90———61.12
PASS [66]63.4761.8458.0949.5547.2942.0761.80
SSRE [67]65.8865.0461.7050.3948.9348.1767.69
Ours70.02+4.1468.86+3.8265.86+4.1653.32+2.9352.61+3.6849.83+1.6668.98+1.29
", + "image_path": "2ac9860766d1c512fc9c04bd5895b6d2ce894c4f4d1548d8f51ecfdf03db2bae.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 295, + 279, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 295, + 279, + 366 + ], + "spans": [ + { + "bbox": [ + 45, + 295, + 279, + 366 + ], + "type": "text", + "content": "ing CIFAR-100 [25], TinyImageNet [26] and ImageNet-Subset (random seed 1993) [12]. For CIFAR-100 and TinyImageNet there are three incremental settings (5, 10, and 20 phases) and for ImageNet-Subset there is one (10 phases). For the sequencing and division of all dataset classes, we strictly follow the specification in [66]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 366, + 279, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 366, + 279, + 471 + ], + "spans": [ + { + "bbox": [ + 45, + 366, + 279, + 471 + ], + "type": "text", + "content": "Implementation details. Following [66], we use ResNet-18 [18] as the backbone network. The model is trained for 100 epochs on each new task. For comparisons on all datasets, the threshold of our prototype reminiscence is set to 0.6. During training, the batch size is set to 128 and the model is optimized by the Adam optimizer with " + }, + { + "bbox": [ + 45, + 366, + 279, + 471 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 45, + 366, + 279, + 471 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 366, + 279, + 471 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 45, + 366, + 279, + 471 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 366, + 279, + 471 + ], + "type": "inline_equation", + "content": "\\epsilon = 1e^{-8}" + }, + { + "bbox": [ + 45, + 366, + 279, + 471 + ], + "type": "text", + "content": " (weight decay 2e-4). The initial learning rate is 0.001 and is adjusted with the cosine annealing algorithm [35] with a period of 32 epochs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 472, + 279, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 472, + 279, + 588 + ], + "spans": [ + { + "bbox": [ + 45, + 472, + 279, + 588 + ], + "type": "text", + "content": "Evaluation metrics. As with [66], we employ average incremental accuracy [42] and average forgetting [10] as the evaluation metric. The average incremental accuracy is defined as the average of the accuracies over seen classes across all incremental phases (including the first phase), which reflects the overall incremental performance of the method. The average forgetting is the average difference between the peak task accuracy and the final task accuracy after incremental learning is completed, and the lower value represents better performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 594, + 177, + 607 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 594, + 177, + 607 + ], + "spans": [ + { + "bbox": [ + 45, + 594, + 177, + 607 + ], + "type": "text", + "content": "4.2. Comparison with SOTA" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 612, + 279, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 612, + 279, + 717 + ], + "spans": [ + { + "bbox": [ + 45, + 612, + 279, + 717 + ], + "type": "text", + "content": "We compare our method with the state-of-the-art (SOTA) methods of NECIL (EWC [23], LwF_MC [42], MUC [32], SDC [60], PASS [66] and SSRE [67]) and several classical exemplar-based CIL approaches (iCaRL [42], EEIL [9] and UCIR [20]). The results reported for PASS are obtained with self-supervised learning. We reproduce the SSRE with label augmentation in the supplementary materials. As adopted in [67], we memorize 20 samples for the exemplar-based methods." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 57, + 718, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 718, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 57, + 718, + 279, + 730 + ], + "type": "text", + "content": "Accuracy and forgetting. The quantitative comparisons" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 298, + 303, + 534, + 418 + ], + "blocks": [ + { + "bbox": [ + 297, + 293, + 514, + 303 + ], + "lines": [ + { + "bbox": [ + 297, + 293, + 514, + 303 + ], + "spans": [ + { + "bbox": [ + 297, + 293, + 514, + 303 + ], + "type": "text", + "content": "Table 2. Results of average forgetting on 5, 10 and 20 phases." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 298, + 303, + 534, + 418 + ], + "lines": [ + { + "bbox": [ + 298, + 303, + 534, + 418 + ], + "spans": [ + { + "bbox": [ + 298, + 303, + 534, + 418 + ], + "type": "table", + "html": "
MethodsCIFAR-100TinyImageNet
5102051020
iCaRL-CNN42.1345.6943.5436.8936.7045.12
iCaRL-NCM24.9028.3235.5327.1528.8937.40
EEIL23.3626.6532.4025.5625.5135.04
UCIR21.0025.1228.6520.6122.2533.74
LwFMC44.2350.4755.4654.2654.3763.54
MUC40.2847.5652.6551.4650.2158.00
PASS25.2030.2530.6118.0423.1130.55
SSRE18.3719.4819.009.1714.0614.20
Ours12.5914.6517.3911.8413.9518.51
Ours w/o AKA7.186.4210.304.575.109.05
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Compared to the suboptimal NECIL method (SSRE), we improve the accuracy on CIFAR-100, TinyImageNet and ImageNetSubset by " + }, + { + "bbox": [ + 296, + 424, + 530, + 668 + ], + "type": "inline_equation", + "content": "6.30\\%" + }, + { + "bbox": [ + 296, + 424, + 530, + 668 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 424, + 530, + 668 + ], + "type": "inline_equation", + "content": "5.59\\%" + }, + { + "bbox": [ + 296, + 424, + 530, + 668 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 296, + 424, + 530, + 668 + ], + "type": "inline_equation", + "content": "1.91\\%" + }, + { + "bbox": [ + 296, + 424, + 530, + 668 + ], + "type": "text", + "content": ", respectively. Moreover, our method shows competitive or even better performance than the classical exemplar-based methods. Certainly, it still slightly inferior to the SOTA exemplar-based method DER [58]. In Fig. 4 we show the accuracy change curves on three benchmarks. Our method is superior at almost all phases, achieving a better balance between stability and plasticity. To further evaluate the above methods, we provide the results of average forgetting in Tab. 2, where our method also performs superiorly. In addition, since the proposed asymmetric knowledge aggregation (AKA) improves the classification accuracy on the current task, the forgetting metric is increased, however this is harmless to overall performance. We will report more analysis in the following and supplementary materials. Experimental results show that our approach can mitigate catastrophic forgetting despite the lack of past task data, which is a more privacy-safe and memory-friendly manner to achieve CIL." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 297, + 676, + 389, + 688 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 676, + 389, + 688 + ], + "spans": [ + { + "bbox": [ + 297, + 676, + 389, + 688 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 694, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 694, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 694, + 531, + 730 + ], + "type": "text", + "content": "In this section, we conduct several ablation studies on the proposed method. To better analyze the impact of the core designs, our approach is divided into three compo" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "text", + "content": "1777" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 103, + 170, + 198 + ], + "blocks": [ + { + "bbox": [ + 48, + 103, + 170, + 198 + ], + "lines": [ + { + "bbox": [ + 48, + 103, + 170, + 198 + ], + "spans": [ + { + "bbox": [ + 48, + 103, + 170, + 198 + ], + "type": "image", + "image_path": "1a93b4399b3cbc81db839218245190045e0234094af61aff710493fbc422cd9a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 176, + 103, + 289, + 197 + ], + "blocks": [ + { + "bbox": [ + 176, + 103, + 289, + 197 + ], + "lines": [ + { + "bbox": [ + 176, + 103, + 289, + 197 + ], + "spans": [ + { + "bbox": [ + 176, + 103, + 289, + 197 + ], + "type": "image", + "image_path": "6dfb9cba030c3399923ddda21bda3cebbc2d0b94bfdac529573ca091045bd150.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 295, + 103, + 409, + 197 + ], + "blocks": [ + { + "bbox": [ + 295, + 103, + 409, + 197 + ], + "lines": [ + { + "bbox": [ + 295, + 103, + 409, + 197 + ], + "spans": [ + { + "bbox": [ + 295, + 103, + 409, + 197 + ], + "type": "image", + "image_path": "62fc92677b026b68b08ff7366fc57c4df721bd826f53742c4985071957014b64.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 420, + 124, + 518, + 179 + ], + "blocks": [ + { + "bbox": [ + 420, + 124, + 518, + 179 + ], + "lines": [ + { + "bbox": [ + 420, + 124, + 518, + 179 + ], + "spans": [ + { + "bbox": [ + 420, + 124, + 518, + 179 + ], + "type": "image", + "image_path": "1cca4e323c647fbb69f2cf4829a03959acc53524841a783d271f3e68ee875804.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 48, + 202, + 170, + 303 + ], + "blocks": [ + { + "bbox": [ + 48, + 202, + 170, + 303 + ], + "lines": [ + { + "bbox": [ + 48, + 202, + 170, + 303 + ], + "spans": [ + { + "bbox": [ + 48, + 202, + 170, + 303 + ], + "type": "image", + "image_path": "4d6a06f8c3cd09bcaaeb9a74391dce3f49bdb255a91bf0da2ecd6baf4c819dc0.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 306, + 531, + 328 + ], + "lines": [ + { + "bbox": [ + 45, + 306, + 531, + 328 + ], + "spans": [ + { + "bbox": [ + 45, + 306, + 531, + 328 + ], + "type": "text", + "content": "Figure 4. Illustration of the classification accuracy changes as tasks are being learned on CIFAR-100, TinyImageNet and ImageNet-Subset, which contains the complete curves. 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Ablation study (in average incremental accuracy) of our method on CIFAR-100 and TinyImageNet datasets." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 73, + 341, + 499, + 427 + ], + "lines": [ + { + "bbox": [ + 73, + 341, + 499, + 427 + ], + "spans": [ + { + "bbox": [ + 73, + 341, + 499, + 427 + ], + "type": "table", + "html": "
ComponentsCIFAR-100TinyImageNet
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", + "image_path": "b6a272adb0549a7f5994e9c4f161326c6c244c7d19c265bc95bb1f46ca419111.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 60, + 435, + 264, + 570 + ], + "blocks": [ + { + "bbox": [ + 60, + 435, + 264, + 570 + ], + "lines": [ + { + "bbox": [ + 60, + 435, + 264, + 570 + ], + "spans": [ + { + "bbox": [ + 60, + 435, + 264, + 570 + ], + "type": "image", + "image_path": "57077b2120d55956c119e0c082a92a954a06b5398a5d2b4bd237e23f969e835c.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 573, + 266, + 585 + ], + "lines": [ + { + "bbox": [ + 45, + 573, + 266, + 585 + ], + "spans": [ + { + "bbox": [ + 45, + 573, + 266, + 585 + ], + "type": "text", + "content": "Figure 5. Influence of the threshold in prototype reminiscence." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 45, + 590, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 590, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 590, + 279, + 730 + ], + "type": "text", + "content": "nents: prototype reminiscence (PR), self-supervised label augmentation (SLA) and asymmetric knowledge aggregation (AKA). As a general trick, KD was used in all experimental settings. To explicitly illustrate the effectiveness of PR, in the baseline model we save the prototypes and directly use them for training. As shown in the " + }, + { + "bbox": [ + 45, + 590, + 279, + 730 + ], + "type": "inline_equation", + "content": "1^{st}" + }, + { + "bbox": [ + 45, + 590, + 279, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 590, + 279, + 730 + ], + "type": "inline_equation", + "content": "2^{nd}" + }, + { + "bbox": [ + 45, + 590, + 279, + 730 + ], + "type": "text", + "content": " rows of Tab. 3, PR successfully maintains the discrimination and balance between the old and new classes and makes an impressive progress on the baseline model. When SLA acts on the baseline model alone, it is effective, but there is still a bias in the classifier, while using it with PR achieves promising results. AKA and SLA are adopted as a whole." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 297, + 436, + 530, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 436, + 530, + 471 + ], + "spans": [ + { + "bbox": [ + 297, + 436, + 530, + 471 + ], + "type": "text", + "content": "In addition to the overall performance improvement, AKA is more about enhancing the model's understanding of the new task to satisfy the latest business requirements." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 472, + 530, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 472, + 530, + 623 + ], + "spans": [ + { + "bbox": [ + 296, + 472, + 530, + 623 + ], + "type": "text", + "content": "To investigate the sensitivity of the threshold " + }, + { + "bbox": [ + 296, + 472, + 530, + 623 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 296, + 472, + 530, + 623 + ], + "type": "text", + "content": " in our prototype reminiscence, we plot its fluctuation curve on CIFAR-100 dataset. As presented in Fig. 5, when " + }, + { + "bbox": [ + 296, + 472, + 530, + 623 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 296, + 472, + 530, + 623 + ], + "type": "text", + "content": " is low, the generated old class features are restricted to concentrate around the preserved prototypes thus lacking the ability to adapt to the changes of the representation space, which results in poor performance. As the constraint is relaxed (" + }, + { + "bbox": [ + 296, + 472, + 530, + 623 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 296, + 472, + 530, + 623 + ], + "type": "text", + "content": " increases), the effect of PR gradually comes into its own and peaks in performance at about " + }, + { + "bbox": [ + 296, + 472, + 530, + 623 + ], + "type": "inline_equation", + "content": "\\eta = 0.6" + }, + { + "bbox": [ + 296, + 472, + 530, + 623 + ], + "type": "text", + "content": ". When the threshold continues to increase, the performance gain from PR starts to diminish because as the constraint fades away, the number of outlier features generated by PR gradually increases, which disturbs the learning of the model." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 297, + 630, + 358, + 642 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 630, + 358, + 642 + ], + "spans": [ + { + "bbox": [ + 297, + 630, + 358, + 642 + ], + "type": "text", + "content": "4.4. Analysis" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 648, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 648, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 648, + 531, + 730 + ], + "type": "text", + "content": "Visualization. To demonstrate the advantages of our prototype reminiscence, we visualise the 2D embeddings of feature vectors with t-SNE [51]. In Fig. 6 (c) and (d), the old class features are generated by the stored prototypes. Compared with fine-tuning, the confusion of old class features is alleviated in the results of Gaussian noise augmentation. However, the overlap between the distributions of different" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "text", + "content": "1778" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 103, + 159, + 190 + ], + "blocks": [ + { + "bbox": [ + 52, + 103, + 159, + 190 + ], + "lines": [ + { + "bbox": [ + 52, + 103, + 159, + 190 + ], + "spans": [ + { + "bbox": [ + 52, + 103, + 159, + 190 + ], + "type": "image", + "image_path": "aadac86b2364d8127afabbcd24d59af9a706816e6951e1f30fd0d3174624915e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 83, + 191, + 128, + 198 + ], + "lines": [ + { + "bbox": [ + 83, + 191, + 128, + 198 + ], + "spans": [ + { + "bbox": [ + 83, + 191, + 128, + 198 + ], + "type": "text", + "content": "(a) Initial Phase" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 164, + 104, + 271, + 190 + ], + "blocks": [ + { + "bbox": [ + 164, + 104, + 271, + 190 + ], + "lines": [ + { + "bbox": [ + 164, + 104, + 271, + 190 + ], + "spans": [ + { + "bbox": [ + 164, + 104, + 271, + 190 + ], + "type": "image", + "image_path": "f5ad0d8978c7c409ddfbfef28eb6e183af4419de9d4362f702ed13fb6fd12883.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 197, + 191, + 238, + 198 + ], + "lines": [ + { + "bbox": [ + 197, + 191, + 238, + 198 + ], + "spans": [ + { + "bbox": [ + 197, + 191, + 238, + 198 + ], + "type": "text", + "content": "(b) Finetuning" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 52, + 201, + 159, + 281 + ], + "blocks": [ + { + "bbox": [ + 52, + 201, + 159, + 281 + ], + "lines": [ + { + "bbox": [ + 52, + 201, + 159, + 281 + ], + "spans": [ + { + "bbox": [ + 52, + 201, + 159, + 281 + ], + "type": "image", + "image_path": "c5152f78a0a7279076f48e153b2fb4c95903f064012415578b92d879000cf986.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 59, + 282, + 151, + 290 + ], + "lines": [ + { + "bbox": [ + 59, + 282, + 151, + 290 + ], + "spans": [ + { + "bbox": [ + 59, + 282, + 151, + 290 + ], + "type": "text", + "content": "(c) Gaussian Noise Augmentation" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 164, + 201, + 271, + 281 + ], + "blocks": [ + { + "bbox": [ + 164, + 201, + 271, + 281 + ], + "lines": [ + { + "bbox": [ + 164, + 201, + 271, + 281 + ], + "spans": [ + { + "bbox": [ + 164, + 201, + 271, + 281 + ], + "type": "image", + "image_path": "ad601d821c7c92f1990042a930846170d7d15e62e7f4bd0c98976da907fa5deb.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 179, + 282, + 255, + 290 + ], + "lines": [ + { + "bbox": [ + 179, + 282, + 255, + 290 + ], + "spans": [ + { + "bbox": [ + 179, + 282, + 255, + 290 + ], + "type": "text", + "content": "(d) Prototype Reminiscence" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 47, + 303, + 122, + 372 + ], + "blocks": [ + { + "bbox": [ + 58, + 291, + 265, + 301 + ], + "lines": [ + { + "bbox": [ + 58, + 291, + 265, + 301 + ], + "spans": [ + { + "bbox": [ + 58, + 291, + 265, + 301 + ], + "type": "text", + "content": "Figure 6. Visualization of different augmentation schemes." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 303, + 122, + 372 + ], + "lines": [ + { + "bbox": [ + 47, + 303, + 122, + 372 + ], + "spans": [ + { + "bbox": [ + 47, + 303, + 122, + 372 + ], + "type": "image", + "image_path": "ab0db62b14133d9c28fade7251a6244010a99f0990fd1d41fdf76745d40cdb18.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 68, + 373, + 107, + 380 + ], + "lines": [ + { + "bbox": [ + 68, + 373, + 107, + 380 + ], + "spans": [ + { + "bbox": [ + 68, + 373, + 107, + 380 + ], + "type": "text", + "content": "(a) Finetuning" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 381, + 278, + 402 + ], + "lines": [ + { + "bbox": [ + 45, + 381, + 278, + 402 + ], + "spans": [ + { + "bbox": [ + 45, + 381, + 278, + 402 + ], + "type": "text", + "content": "Figure 7. The comparison of confusion matrix of finetuning, iCaRL and our method on CIFAR-100 (10 phases)." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 126, + 303, + 193, + 372 + ], + "blocks": [ + { + "bbox": [ + 126, + 303, + 193, + 372 + ], + "lines": [ + { + "bbox": [ + 126, + 303, + 193, + 372 + ], + "spans": [ + { + "bbox": [ + 126, + 303, + 193, + 372 + ], + "type": "image", + "image_path": "758adda0148ad68cce97cf41348b3382f62a1da0c4f82be9cc4f815784ccc8c8.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 145, + 373, + 173, + 380 + ], + "lines": [ + { + "bbox": [ + 145, + 373, + 173, + 380 + ], + "spans": [ + { + "bbox": [ + 145, + 373, + 173, + 380 + ], + "type": "text", + "content": "(b) iCaRL" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 198, + 303, + 278, + 372 + ], + "blocks": [ + { + "bbox": [ + 198, + 303, + 278, + 372 + ], + "lines": [ + { + "bbox": [ + 198, + 303, + 278, + 372 + ], + "spans": [ + { + "bbox": [ + 198, + 303, + 278, + 372 + ], + "type": "image", + "image_path": "5a76e810a74cead764772aa1f5a8b2d4ef57553dc486fb238d39c069a29bac17.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 224, + 373, + 247, + 380 + ], + "lines": [ + { + "bbox": [ + 224, + 373, + 247, + 380 + ], + "spans": [ + { + "bbox": [ + 224, + 373, + 247, + 380 + ], + "type": "text", + "content": "(c) Ours" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 45, + 413, + 279, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 413, + 279, + 459 + ], + "spans": [ + { + "bbox": [ + 45, + 413, + 279, + 459 + ], + "type": "text", + "content": "classes is still significant, and in particular the confusion between the generated features. Instead, the feature distributions of different old classes reshaped by our method are relatively dispersed among each other." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 45, + 461, + 279, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 461, + 279, + 588 + ], + "spans": [ + { + "bbox": [ + 45, + 461, + 279, + 588 + ], + "type": "text", + "content": "Classification bias of the model. To evaluate the performance differences between the old and new classes, we compared the confusion matrix of finetuning, iCaRL and our method on CIFAR-100. As shown in Fig. 7, since samples of old classes are not available, finetuning tends to classify the samples into new classes. The confusion is alleviated by iCaRL, but still shows a preference for new classes. The confusion matrix of our method exhibits better overall performance without favouring old or new classes. Thanks to PR and AKA, the classification bias between old and new classes is well handled." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 45, + 590, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 590, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 590, + 279, + 730 + ], + "type": "text", + "content": "The role of asymmetric knowledge aggregation. To better illustrate the role of the asymmetric knowledge aggregation, we compare the changes in classification accuracy for the initial task during subsequent incremental learning, and the performance on each new task in the presence or absence of AKA. The results for the three settings on CIFAR100 are shown in Fig. 8. On the one hand, the performance degradation in the initial task caused by the introduction of AKA is negligible; on the other hand, the discrimination of new classes is considerably improved. As analyzed in the introduction, AKA can improve the model's understanding of new tasks as non-destructively as possible." + } + ] + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 299, + 104, + 417, + 190 + ], + "blocks": [ + { + "bbox": [ + 299, + 104, + 417, + 190 + ], + "lines": [ + { + "bbox": [ + 299, + 104, + 417, + 190 + ], + "spans": [ + { + "bbox": [ + 299, + 104, + 417, + 190 + ], + "type": "image", + "image_path": "10147fedf265c9181e8fcdaf6ed42f86c299c836316fc3c5f049cf87096c1e58.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 419, + 105, + 528, + 190 + ], + "blocks": [ + { + "bbox": [ + 419, + 105, + 528, + 190 + ], + "lines": [ + { + "bbox": [ + 419, + 105, + 528, + 190 + ], + "spans": [ + { + "bbox": [ + 419, + 105, + 528, + 190 + ], + "type": "image", + "image_path": "e8453a93d9cc38dc040f20a2ae2da20f8c4964320ac6b8155d7409ab0ea79266.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 299, + 202, + 415, + 272 + ], + "blocks": [ + { + "bbox": [ + 335, + 195, + 392, + 202 + ], + "lines": [ + { + "bbox": [ + 335, + 195, + 392, + 202 + ], + "spans": [ + { + "bbox": [ + 335, + 195, + 392, + 202 + ], + "type": "text", + "content": "CIFAR-100 (10 phases)" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 299, + 202, + 415, + 272 + ], + "lines": [ + { + "bbox": [ + 299, + 202, + 415, + 272 + ], + "spans": [ + { + "bbox": [ + 299, + 202, + 415, + 272 + ], + "type": "image", + "image_path": "5ae56df30d9b202fa2459ecd2ba9f6f8403e6a36292d422294a8fd6b8e179cbc.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 419, + 202, + 528, + 272 + ], + "blocks": [ + { + "bbox": [ + 446, + 195, + 502, + 202 + ], + "lines": [ + { + "bbox": [ + 446, + 195, + 502, + 202 + ], + "spans": [ + { + "bbox": [ + 446, + 195, + 502, + 202 + ], + "type": "text", + "content": "CIFAR-100 (10 phases)" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 419, + 202, + 528, + 272 + ], + "lines": [ + { + "bbox": [ + 419, + 202, + 528, + 272 + ], + "spans": [ + { + "bbox": [ + 419, + 202, + 528, + 272 + ], + "type": "image", + "image_path": "e2891e1f7b2a10b4b7bb0de69ac093762da7ef12e2a34ab91a7a6090c0815469.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + } + ], + "index": 25 + }, + { + "type": "image", + "bbox": [ + 299, + 284, + 415, + 360 + ], + "blocks": [ + { + "bbox": [ + 333, + 277, + 389, + 284 + ], + "lines": [ + { + "bbox": [ + 333, + 277, + 389, + 284 + ], + "spans": [ + { + "bbox": [ + 333, + 277, + 389, + 284 + ], + "type": "text", + "content": "CIFAR-100 (20 phases)" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 299, + 284, + 415, + 360 + ], + "lines": [ + { + "bbox": [ + 299, + 284, + 415, + 360 + ], + "spans": [ + { + "bbox": [ + 299, + 284, + 415, + 360 + ], + "type": "image", + "image_path": "9c06c2f4009b147b4c7fe01fb9f7324b57254b1d4acc18d4bb1f8b5bee743399.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 362, + 530, + 415 + ], + "lines": [ + { + "bbox": [ + 296, + 362, + 530, + 415 + ], + "spans": [ + { + "bbox": [ + 296, + 362, + 530, + 415 + ], + "type": "text", + "content": "Figure 8. The first column is the classification accuracy on the initial task, which changes with the incremental phase. The second column shows the change in classification accuracy on the new task. The proposed knowledge aggregation allows better learning of new tasks with little impact on existing knowledge." + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + } + ], + "index": 27 + }, + { + "type": "image", + "bbox": [ + 419, + 284, + 528, + 360 + ], + "blocks": [ + { + "bbox": [ + 448, + 277, + 503, + 284 + ], + "lines": [ + { + "bbox": [ + 448, + 277, + 503, + 284 + ], + "spans": [ + { + "bbox": [ + 448, + 277, + 503, + 284 + ], + "type": "text", + "content": "CIFAR-100 (20 phases)" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 419, + 284, + 528, + 360 + ], + "lines": [ + { + "bbox": [ + 419, + 284, + 528, + 360 + ], + "spans": [ + { + "bbox": [ + 419, + 284, + 528, + 360 + ], + "type": "image", + "image_path": "7690fc172bf6dc811de44a56b1121791395627ec4228f087e5709c13b575ec1a.jpg" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_body" + } + ], + "index": 28 + }, + { + "bbox": [ + 297, + 424, + 367, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 424, + 367, + 435 + ], + "spans": [ + { + "bbox": [ + 297, + 424, + 367, + 435 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 296, + 438, + 530, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 438, + 530, + 578 + ], + "spans": [ + { + "bbox": [ + 296, + 438, + 530, + 578 + ], + "type": "text", + "content": "In this work, we address the NECIL issue from two perspectives of resisting catastrophic forgetting and boosting plasticity of the model, proposing prototype reminiscence and augmented asymmetric knowledge aggregation, respectively. In particular, we pay attention to the performance of the incremental learner on new tasks which often represent the latest business requirements, and design an asymmetric knowledge aggregation strategy for better adaptation to new tasks. Extensive evaluations demonstrate that our approach outperforms the SOTA NECIL methods and shows strong competitiveness with classical exemplar-based methods in the absence of stored samples." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 296, + 578, + 530, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 578, + 530, + 648 + ], + "spans": [ + { + "bbox": [ + 296, + 578, + 530, + 648 + ], + "type": "text", + "content": "Limitations. For each prototype reminiscence, the prototype and the feature are selected randomly. When the selected prototype and feature are less similar (i.e., farther apart in the feature space), there may be outliers in the generated features of old classes. Exploring the impact of outliers on training may be of interest." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 296, + 648, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 648, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 648, + 530, + 730 + ], + "type": "text", + "content": "Acknowledgement. This work is partially supported by the Key Research and Development Program of Hubei Province (2021BAA187), National Natural Science Foundation of China under Grant (62176188), Zhejiang lab (NO.2022NF0AB01), the Special Fund of Hubei Luojia Laboratory (220100015) and CAAI-Huawei MindSpore Open Fund." + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "text", + "content": "1779" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 124, + 279, + 730 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 51, + 124, + 279, + 167 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 124, + 279, + 167 + ], + "spans": [ + { + "bbox": [ + 51, + 124, + 279, + 167 + ], + "type": "text", + "content": "[1] Davide Abati, Jakub Tomczak, Tijmen Blankevoort, Simone Calderara, Rita Cucchiara, and Babak Ehteshami Bejnordi. 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NeurIPS, 31, 2018. 5" + } + ] + } + ], + "index": 35 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 747, + 297, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 747, + 297, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 747, + 297, + 756 + ], + "type": "text", + "content": "1781" + } + ] + } + ], + "index": 37 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Prototype-based Dataset Comparison/02a62e7f-ba00-4044-92de-55f8e976a093_content_list.json b/2023/Prototype-based Dataset Comparison/02a62e7f-ba00-4044-92de-55f8e976a093_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..3e358580ed77336bacc6f9451947027e8136516a --- /dev/null +++ b/2023/Prototype-based Dataset Comparison/02a62e7f-ba00-4044-92de-55f8e976a093_content_list.json @@ -0,0 +1,2520 @@ +[ + { + "type": "text", + "text": "Prototype-based Dataset Comparison", + "text_level": 1, + "bbox": [ + 295, + 130, + 674, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Nanne van Noord \nUniversity of Amsterdam", + "bbox": [ + 383, + 181, + 584, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "n.j.e.vannoord@uva.nl", + "bbox": [ + 390, + 219, + 578, + 232 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dataset-specific Prototypes", + "text_level": 1, + "bbox": [ + 189, + 270, + 392, + 286 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shared Prototype", + "text_level": 1, + "bbox": [ + 632, + 270, + 763, + 286 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/799e77ec529e22da1202c02e0346720bb57cab9de8bce83a89815b4536b32caa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 290, + 176, + 339 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/126ecd00c28018c5755a077a5ff840b95d23a348a5cbd1ec256fe156a3ddaf85.jpg", + "image_caption": [ + "Figure 1: Prototypes discovered with ProtoSim. By training on both datasets ProtoSim is able to discover prototypes that are dataset specific or shared. From left to right: ImageNet specific “Wedding”, PASS specific “sunset skyline”, and shared “viaduct” prototypes." + ], + "image_footnote": [], + "bbox": [ + 184, + 290, + 279, + 339 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a8204d7fa91adbdf1ab92a48b767802ed9b7d10fb365f318317e9dbeeee0bb66.jpg", + "image_caption": [ + "ImageNet" + ], + "image_footnote": [], + "bbox": [ + 84, + 345, + 176, + 395 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bc95ddf6aa0484d33c242c21b332e5264a1c7c5c85a21a6628f802a9a14fcd16.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 186, + 345, + 279, + 395 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3afe4e514435a99d70c55a3bc169d77df92080e5a0ef9d5f9124bd5511a1f981.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 297, + 387, + 339 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/17d7d394fc8bfc1e52e73f3f3172c134e3e8539e612bcef41fbf7baa09fef0fa.jpg", + "image_caption": [ + "PASS" + ], + "image_footnote": [], + "bbox": [ + 295, + 340, + 387, + 395 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ac0b6bbeff86710511cb88801425bada35c2919ee13ae3b7a9f5c4dc0ad342b2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 374, + 289, + 488, + 395 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/82aaa4644bab16352c1ef21b6ab4804c18532d8cdff3b99294d8dcd9cbbd0f58.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 297, + 599, + 339 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/381a65a017042c64b6bf510aaca2525edd311676979bac35fd325e37d65a6cd3.jpg", + "image_caption": [ + "ImageNet" + ], + "image_footnote": [], + "bbox": [ + 506, + 344, + 598, + 395 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c8e934e539f2ac5281bfa6dcdecb9562dd838e3537b341b9201b676303ae0f54.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 607, + 297, + 700, + 339 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/98318653b639a4c2e60e01b50d02aad80c09fbbffd1a749f98dc27c00be2f6ef.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 607, + 344, + 700, + 395 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6ad907ad43aff95263b3e70ac79c94aedf224482beab96a0975ba940db3f2c14.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 718, + 289, + 787, + 339 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 709, + 351, + 792, + 395 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/384920f5d57cde2b01e55668ca674fa5e0ebdcf9b77fb6919713a4525d89e36c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 805, + 292, + 887, + 339 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ef6898b5ba3c74feaa177bc0886f01b8b2177f599aff21fa3b6229d8cec895ea.jpg", + "image_caption": [ + "PASS" + ], + "image_footnote": [], + "bbox": [ + 709, + 351, + 794, + 395 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/18267aabae9556211dc7b311525332adcaa81491280d7fda87eb0a946b2b7ebe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 805, + 353, + 888, + 395 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 487, + 313, + 503 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dataset summarisation is a fruitful approach to dataset inspection. However, when applied to a single dataset the discovery of visual concepts is restricted to those most prominent. We argue that a comparative approach can expand upon this paradigm to enable richer forms of dataset inspection that go beyond the most prominent concepts.", + "bbox": [ + 75, + 521, + 468, + 611 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To enable dataset comparison we present a module that learns concept-level prototypes across datasets. We leverage self-supervised learning to discover these prototypes without supervision, and we demonstrate the benefits of our approach in two case-studies. Our findings show that dataset comparison extends dataset inspection and we hope to encourage more works in this direction. Code and usage instructions available at https://github.com/Nanne/ProtoSim", + "bbox": [ + 75, + 613, + 472, + 750 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 782, + 209, + 797 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image datasets are crucial for Computer Vision and due to the algorithms' need for more data they are ever growing in size. At the same time datasets are a major source of bias leading to negative social impact [29, 30]. Unfortunately, it is challenging to determine what is contained in a dataset as their large size combined with the visual nature of the", + "bbox": [ + 75, + 809, + 470, + 900 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "data makes manual inspection infeasible. To support users and developers of large-scale datasets in ensuring that the datasets match their usage and design goals it is necessary to develop better tools for dataset inspection.", + "bbox": [ + 496, + 489, + 892, + 549 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A promising direction for generic dataset inspection is found in highly effective approaches that have been proposed for summarisation [35, 9, 14, 44, 24]. A major benefit of these approaches is that they enable explorative dataset inspection without needing supervised pretraining. However, a limitation of these approaches is that they use frequency as a proxy for importance, and on a single dataset therefore only discover those visual concepts which are most prominent. As such, we argue that a comparative approach, which enables discovery of a wider and more diverse range of concepts, is necessary to effectively perform dataset inspection. For instance, the PASS dataset [1] is designed as an ImageNet [32] alternative whilst containing no people, as such it provides us with a testable hypothesis that is comparative in nature. Namely, when comparing these two datasets there should be a disjoint set of visual people-centric concepts that are only found in ImageNet. In a case study we will verify this hypothesis, and demonstrate that dataset comparison can lead to new insights.", + "bbox": [ + 496, + 551, + 892, + 838 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Moreover, an additional limitation of existing summarisation approaches is that they decouple the summarisation process from representation learning, and treat these as two distinct steps by performing the summarisation on a", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1944", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "pre-defined feature basis, such as GIST descriptors in [35] or LDA clusters in [31]. As recent work on incorporating prototypes into a network's reasoning process has been shown to aid interpretability [23, 6, 33, 13, 45], we propose that this may also be a promising direction for end-to-end dataset comparison. Therefore, we introduce a method for prototype-based dataset comparison, which discovers the visual concepts in a dataset in an end-to-end fashion.", + "bbox": [ + 75, + 90, + 468, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Dataset prototypes are similar to cluster centroids in that they represent latent points in the feature space that are to be discovered. However, in clustering, similar to prior work on dataset summarisation, these centroids are discovered in a step that is decoupled from learning the feature representations. Whilst some recent works have explored forms of deep clustering [40, 11, 22], they still involve two separate optimisation goals. For example, by having one loss focused on the feature representation and another on clustering [11]. Instead, we propose a simple module ProtoSim that can be integrated into a deep network without changing how it is optimised. To demonstrate this, we add ProtoSim to a Vision Transformer (ViT) [10] and show that it can effectively discover visual concepts across datasets in a self-supervised setting.", + "bbox": [ + 75, + 213, + 470, + 439 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Overall, we make the following contributions:", + "bbox": [ + 96, + 441, + 401, + 455 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce dataset comparison, a new approach for inspecting datasets.", + "- To enable dataset comparison we present ProtoSim, a module for integrated learning of dataset prototypes.", + "- With two case-studies we demonstrate how dataset comparison can be used to gain new insight into datasets." + ], + "bbox": [ + 96, + 460, + 468, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 76, + 599, + 215, + 616 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Dataset comparison through prototypes is a largely unexplored area of research, but it is similar in spirit to dataset distillation [47, 5] which seeks to distill the knowledge from a large dataset into a small dataset. Most works in dataset distillation generate synthetic examples, as opposed to selecting a set of data instances, to construct the small dataset. These synthetic examples could be considered dataset prototypes, as they represent an aggregate of information that is central to the dataset. A key difference between such prototypes and the prototypes considered in this work, is that the distilled synthetic examples are instance-level prototypes (i.e., complete images that may represent multiple concepts), whereas in this work the aim is to discover concept-level prototypes, which may correspond to global concepts or part-level concepts.", + "bbox": [ + 75, + 628, + 468, + 853 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the remainder of this section we will further explore how dataset comparison relates to dataset summarisation, prototype learning, and deep clustering.", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Dataset Summarisation", + "text_level": 1, + "bbox": [ + 500, + 90, + 718, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Manual browsing is a reliable manner to determine what is contained in a dataset, however, browsing even a subset of the data can be time-consuming, which has led to a line of work on dataset summarisation [31, 9, 14, 44, 24]. The aim of dataset summarisation is to find underlying structure or patterns that are shared between data instances to give an overview of what is contained in a dataset.", + "bbox": [ + 496, + 113, + 890, + 218 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "An important modeling choice for dataset summarisation is the basis on top of which the patterns are found. Work on mid-level pattern mining aims to find discriminative and representative patches and use these as visual primitive for further analysis [34]. Mid-level pattern mining aims to distinguish itself from \"visual word\" approaches [36], which were found to mainly capture low-level patterns such as edges and corners [34, 9]. Two notable patch-based approaches are the dataset fingerprinting approach by [31] and the what makes Paris look like Paris? approach by [9]. Patch-based approaches aim to circumvent the limitations of visual words by starting with larger visual structure (i.e., patches at multiple scales). Due to the limitations of pixel-space representations patches cannot be used directly for analysis, instead initial patch-based approaches used feature extractors such as HOG [34, 9] and Convolutional Neural Network (CNN) activations in later works [24]. Using patches has been shown to help steer the results towards more semantically meaningful visual elements, yet they are still restrictive in representational power and in terms of shape (i.e., patches must be rectangular). Moreover, although the starting point is a patch, the features extracted largely determine what the pattern represents and the features are not intrinsically explainable, necessitating posthoc explanations. In contrast, we propose to add ProtoSim to a ViT architecture, which can learn to recognise visual elements of arbitrary shapes and sizes, whilst still focusing on semantically meaningful concepts.", + "bbox": [ + 496, + 219, + 892, + 642 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Prototype Learning", + "text_level": 1, + "bbox": [ + 500, + 650, + 687, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Prototype-based approaches can be categorised into two areas, the first aims to learn prototypes which represent high-level semantic concepts (i.e., classes) to support zero or few-shot learning [18, 28, 37]. The second area is concerned with finding recurring visual elements and are increasingly used for model explainability [23, 6, 21, 39, 13, 20, 42, 45]. As opposed to post-hoc explainability methods, prototypes are integral to the network and provide explanations of the network's reasoning process [6]. Our approach is part of this second area and we will focus the discussion on integral prototypes for recurring visual elements.", + "bbox": [ + 496, + 674, + 890, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Integral prototypes have been shown to be effective for supervised multi-class classification [6, 13, 20, 21], deepfake detection [39], and semantic segmentation [48]. In the literature we can recognise two branches of work on integral", + "bbox": [ + 496, + 840, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1945", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "prototypes, the first builds on ProtoPnet [23, 6] and the second on Concept Bottleneck Models (CBM) [13, 20]. Common across these approaches is that they add a layer preceding the output layer that maps the extracted features to prototypes (or concepts) and produce the final output based on the affinity to these prototypes. The logic is thus that because the prototypes are recognisable entities, the prediction is explained by the affinity to the prototypes. The main difference between these branches is that in ProtoPnet-like approaches the prototypes are latent vectors in the embedding space that are learnt end-to-end, whereas CBM approaches use a pre-defined concept library.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, these prior approaches all focus on a supervised setting and learn per-class prototypes or concepts, which is severely limiting for dataset summarisation. Instead, we propose to leverage a self-supervised loss to learn prototypes that are not class specific and can represent any visual concept that is present in the data. In particular, our prototypes may represent class-level concepts or segment-level concepts as in CBM [13], but we learn them without concept-level supervision. Previous works learned prototypes for the features at each location in the convolutional output of a Convolutional Neural Network (CNN) backbone [6, 21, 39]. This restricts the spatial extent of the prototypes to size of the receptive field. Additionally, in CNN the output is typically spatially averaged to achieve a global image representation, however, as this is not done for CNN-based prototype approaches they can only learn local and not global prototypes. Instead, we use Vision Transformers (ViT) [10], as they offer solutions for both aforementioned issues capturing local and global concepts of various spatial extents.", + "bbox": [ + 75, + 276, + 472, + 578 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Deep Clustering", + "text_level": 1, + "bbox": [ + 76, + 598, + 238, + 614 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Clustering relates to learning prototypes or concepts in that it has been used to define the library of concept CBM [13], and to an extent the underlying principles match the goal of clustering. In particular, in deep clustering [40, 11, 22] the centroids are learned iteratively, resulting in them being conceptually close to prototypes or CBM-concepts. However, in prior works on deep clustering [40, 11, 22] the clustering objective is separate from the feature representation, whereas in prototype-based approaches the final output is determined by projecting the input to the prototype subspace.", + "bbox": [ + 75, + 625, + 468, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Another key difference is that by making the prototypes integral to the reasoning process, as in CBM [13] or ProtoP-net [6], it is ensured that the prototypes are of meaningful to the final output. Post-hoc clustering, or as part of a separate objective, may lead to overrepresentation of clusters which capture meaningless information, e.g., orthogonal to the objective that was used to obtain the feature representation.", + "bbox": [ + 75, + 795, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Dataset Comparison", + "text_level": 1, + "bbox": [ + 500, + 89, + 696, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a collection of datasets $X = \\{\\chi_i\\}_{i=1}^{|X|}$ the aim of prototype-based dataset comparison is to discover a set of prototypes $p \\in \\mathbb{R}^{K \\times D}$ that represent visual concepts that may occur predominantly in only one dataset (i.e. dataset-specific prototypes) or visual concepts which occur in two or more datasets (i.e. shared prototypes). An illustration of the dataset comparison workflow is shown in Figure 2.", + "bbox": [ + 496, + 114, + 893, + 223 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We argue that a comparative approach to dataset summarisation, i.e., dataset comparison is vital for gaining insights into datasets. In particular, if $C_*$ is the set of all possible visual concepts, and $C_i$ the visual concepts in ImageNet, then $C_i \\subset C_*$ . Given these sets, $C_i$ is a perfect description of what is contained in ImageNet, and the difference $C_* - C_i$ perfectly describes what is not contained in ImageNet. However, as we do not have access to $C_*$ and we have no guaranteed manner of discovering $C_i$ , we can at best learn a set of prototypes $\\hat{C}_i$ that approximates $C_i$ .", + "bbox": [ + 496, + 223, + 893, + 375 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As it is an approximation it cannot be concluded from $\\hat{C}_i$ that a concept is not in $C_i$ . For example, PASS is designed to not contain humans (i.e., no humans in $C_p$ ), but based on $\\hat{C}_p$ it cannot be stated with certainty that no humans are found in PASS, only that no human-centric concepts were discovered. To overcome this limitation we propose to jointly learn $\\hat{C}_i$ and $\\hat{C}_p$ . Thereby, if we know a concept is in $\\hat{C}_i$ and not in $\\hat{C}_p$ , we can reasonably conclude that the concept is not in $C_p$ either.", + "bbox": [ + 496, + 373, + 893, + 515 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/36a19db9befefe9249ad63f316577839ecfda8f431da25fb811cfdbd28a62624.jpg", + "image_caption": [ + "Figure 2: Overview of the dataset comparison workflow. Datasets are mapped to the prototype embedding space, from where we can inspect and compare individual prototypes." + ], + "image_footnote": [], + "bbox": [ + 506, + 527, + 880, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Through dataset comparison we are thus able to answer questions that could not be answered by only considering a single dataset, thereby creating new possibilities for dataset inspection for hypothesis verification or comparative exploration.", + "bbox": [ + 496, + 747, + 893, + 823 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Prototype Evaluation", + "text_level": 1, + "bbox": [ + 500, + 832, + 700, + 848 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "How to evaluate the prototypes learnt for dataset comparison (or summarisation) is an open problem, as the groundtruth for which visual concepts are contained in the dataset", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1946", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9c7ff26deebc6d53330ef3fa4cce5115a56171801309afd41c4e6b506d5cd965.jpg", + "image_caption": [ + "Figure 3: Examples of low-level visual properties discovered with ProtoSim: motion blur (top) and a shallow depth of field (bottom)." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 467, + 176 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "are unknown. Nonetheless, we can leverage the comparative approach by verifying whether the prototypes found match the design goals of the datasets. For instance, as PASS was designed not to contain humans we can explore whether the human-centric prototypes learnt from ImageNet indeed do not occur in PASS. This manner of evaluation forms the basis of our first case study.", + "bbox": [ + 75, + 270, + 467, + 376 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Generally, we consider the prototypes $p$ to be of high-quality when they are distinct and meaningful. Distinct prototypes are able to independently represent a visual concept, this is in contrast to, for example, sparse coding [46] where the aim is to find basis vectors that represent the input through linear combinations. The set of prototypes is meaningful when it can be used to discriminate images within and across the datasets from one another. Requiring that the prototypes are discriminative helps avoid trivial solutions. We can quantitatively measure how discriminative the prototypes are by evaluating them with downstream tasks.", + "bbox": [ + 75, + 378, + 467, + 545 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To ensure that the prototypes are distinct we design our method ProtoSim to perform hard assignment of the prototypes, and by optimising the prototypes with contrastive SSL we ensure that they are discriminative. This alignment between the design of the method (more details in Section 4) and the goal of dataset comparison helps us make certain the prototypes are of high-quality.", + "bbox": [ + 75, + 549, + 467, + 654 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Types of Prototypes", + "text_level": 1, + "bbox": [ + 76, + 674, + 264, + 690 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Within the set of prototypes we can recognise different types of prototypes depending on how they occur across the datasets. For instance, a prototype $p_i$ may be considered dataset-specific when over $95\\%$ of its occurrences are only found in a single dataset. By definition, any prototype which is not dataset-specific would then be considered shared. However, various degrees of 'sharedness' may occur depending on the overlap between datasets.", + "bbox": [ + 75, + 700, + 467, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In theory it may be possible for the datasets in $X$ to be fully distinct, resulting in only dataset-specific prototypes. In practice, we find that prototypes may represent various basic visual properties (see Figure 3), resulting in shared prototypes even when the datasets differ semantically.", + "bbox": [ + 75, + 824, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Prototype-based Learning", + "text_level": 1, + "bbox": [ + 500, + 89, + 741, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We propose ProtoSim a simple module that can inserted in ViT architectures to enable dataset comparison through integral prototype-based learning. ProtoSim differs from previous prototype layers in three ways, firstly, the prototypes learned with ProtoSim are distinct (as opposed to linear mixtures), secondly, ProtoSim is specifically designed for ViT architectures and learns prototypes from a set of tokens, rather than a single embedding vector. Lastly, the prototypes in ProtoSim are not class-specific, instead we learn a single pool of prototypes that may occur in any image.", + "bbox": [ + 496, + 114, + 890, + 266 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. ProtoSim", + "text_level": 1, + "bbox": [ + 500, + 273, + 609, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to learn which visual concepts are present in a dataset we aim to optimise a set of $K$ learnable prototypes $p \\in \\mathbb{R}^{K \\times D}$ . By designing the prototypes to be part of a prototype layer (i.e. ProtoSim) we can directly optimise them in and end-to-end fashion as part of ViT that we add the layer to. Specifically, given the token embeddings $z \\in \\mathbb{R}^{N + 1 \\times D}$ produced by a ViT, ProtoSim maps these to the prototype embeddings $\\hat{z} \\in \\mathbb{R}^{N + 1 \\times D}$ , where $D$ is the token vector size. During this mapping each token is replaced with the most similar prototype in $p$ .", + "bbox": [ + 496, + 296, + 890, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In [23, 6] the similarity to each of the class-specific prototypes is determined by calculating the squared $L^2$ distance and selecting the closest prototype with a max operation. Because our aim is to find prototypes that recur in the entire dataset, instead of finding class-specific prototypes, we propose a surprisingly simple formulation of this process by using a reversed version of dot-product attention [25] to efficiently calculate attention across all the prototypes:", + "bbox": [ + 496, + 446, + 890, + 568 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\na = \\operatorname {s o f t m a x} \\left(p z ^ {\\intercal}\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 574, + 890, + 590 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {z} = a ^ {\\intercal} p. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 593, + 890, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here the attention mask $a$ represents the soft-assignment of prototypes to tokens, as such each token embedding $\\hat{z}$ is a linear combination of prototypes. This is not desirable as our aim is to learn distinct prototypes which independently represent a visual concept, as this enables better summarisation and greater interpretability. To obtain a hard assignment we replace the softmax operation in Equation 1 with gumbel-softmax [17]:", + "bbox": [ + 496, + 614, + 890, + 734 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\na = \\operatorname {g u m b e l - s o f t m a x} (p z ^ {\\intercal}). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 742, + 890, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For simplicity we drop the temperature parameter, as it empirically does not meaningfully influence performance and can be kept fixed at 1. The benefit of gumbel-softmax is that it maintains gradient-flow whilst enabling hard attention. Based on this modification $a$ now represents a hard assignment matrix which is used to replace each token with a prototype. As a visual concept can occur across multiple spatial locations there is no constraint on how often a prototype can be assigned.", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1947", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Backbone", + "text_level": 1, + "bbox": [ + 76, + 90, + 189, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Whilst ProtoSim functions as a generic network module, with the only requirement being an a two-dimensional input of $K \\times D$ , we specifically apply it to ViT in this work as these offer some benefits over CNN. In particular, in ViT all tokens can share information with all other tokens, as such there is no restriction on the spatial extent of the learned prototypes. Moreover, whilst most tokens in a ViT represent some spatial region of the image (i.e. patch tokens), the class token takes on the role of a global image representation. This allows us to learn prototypes that are local (i.e. only assigned to patch tokens) and global (i.e. only assigned to the class token) without modifying the architecture.", + "bbox": [ + 75, + 113, + 468, + 296 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ProtoSim is placed at the end of the backbone ViT in the network architecture. Formally, the input $x \\in \\mathbb{R}^{H \\times W \\times C}$ is divided into flattened patch tokens $x_{p} \\in \\mathbb{R}^{N \\times (P^{2} \\cdot C)}$ , where $H, W,$ and $C$ are the height, width, and channel dimensionality of the input and $P$ the patch size hyperparameter. In addition to $N$ patch tokens, a learnable class token $x_{class}$ is prepended to input. No class labels are used during training, but we retain the ViT terminology of referring to this as a class token. After the embedding phase the tokens are passed through a series of transformer blocks resulting in the token embeddings $z \\in \\mathbb{R}^{N + 1 \\times D}$ , where $D$ is the embedded token vector size. $z$ is passed through the ProtoSim layer resulting in the prototype embeddings $\\hat{z}$ .", + "bbox": [ + 75, + 296, + 470, + 494 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Training Objective", + "text_level": 1, + "bbox": [ + 76, + 503, + 259, + 522 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The training objective determines the prototypes. For instance, a classification-based objective results in prototypes that are indicative of the classes (as in ProtoPnet [6] or CBM [20]). Yet, such an objective may result in a poor coverage of concepts that are not part of the annotated classes. Because we strive for good coverage we focus on a Contrastive Self-Supervised Learning (Contrastive SSL) objective. In particular, because Constrastive SSL optimises for fine-grained discrimination between images (rather than classes) and has been shown to be perform well on a variety of downstream tasks [7].", + "bbox": [ + 75, + 527, + 468, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "From the recently proposed Contrastive SSL methods [16, 15, 7, 8, 3, 4], only DINO [4] has been specifically designed to work with ViT. As such, we minimise the DINO loss as the training objective:", + "bbox": [ + 75, + 695, + 468, + 756 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta_ {s}} \\sum_ {x \\in \\{x _ {1} ^ {g}, x _ {2} ^ {g} \\}} \\sum_ { \\begin{array}{c} x ^ {\\prime} \\in V \\\\ x ^ {\\prime} \\neq x \\end{array} } H (P _ {t} (x), P _ {s} (x ^ {\\prime})), \\qquad (4)\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 767, + 468, + 811 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $H(a,b) = -a\\log b$ , $x_1^g$ and $x_2^g$ are two large crops from the input, $V$ a set of data-augmented smaller crops, and $P_t$ and $P_s$ are the teacher and student networks respectively, each with a ProtoSim layer added to the backbone. We refer to the excellent work by [4] for further details.", + "bbox": [ + 75, + 824, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Case Studies", + "text_level": 1, + "bbox": [ + 500, + 89, + 632, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section we present two case studies, the first is a comparison between two datasets (i.e., two-way dataset comparison) aimed at determining how the PASS [1] dataset differs from ImageNet [32]. Because the design goal of PASS was to present an alternative for ImageNet that does not contain humans we test whether this is achieved successfully. The second case study focuses on a three-way dataset comparison scenario wherein we explore how three artwork datasets differ. These three datasets were designed for different tasks and contain images from different museum collections, as such based on these meta properties of the datasets it is challenging to determine how they actually relate. With these two case studies we put the two main applications of dataset comparison to the test, verifying a design goal of a dataset, and exploring unknown datasets. In addition, in Supplementary Section A we demonstrate how ProtoSim can also be used on a single dataset.", + "bbox": [ + 496, + 114, + 893, + 372 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 380, + 602, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the first case study we focus on ImageNet and PASS, we briefly describe both:", + "bbox": [ + 500, + 402, + 890, + 433 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- ImageNet [32] is a widely used dataset available in two versions: ImageNet-21K and ImageNet-1K. In this work we focus on ImageNet-1K consisting of approximately 1.2 million training images and 1000 classes. Despite how widely used it is, and how influential it has been, ImageNet-1K has also been criticised for its biased depictions of persons [30].", + "- PASS [1] is a recently proposed alternative for ImageNet with the intention of not containing persons to avoid the issues in ImageNet. PASS contains approximately 1.4 million unlabeled images and can only be used for self-supervised training." + ], + "bbox": [ + 517, + 443, + 890, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the second case study we focus on three artwork datasets that have been used for a variety of different tasks:", + "bbox": [ + 500, + 645, + 890, + 675 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- MET [43] is a dataset designed for instance-level recognition, its training set contains over 400k images from more than 224k different objects held by the Metropolitan Museum of Art in New York.", + "- Rijksmuseum [27] presents a set of tasks which are museum-centric, focusing on predicting various types of metadata (i.e., artist, object-type, material usage, and creation year). It consists of 110k images obtained from collections held by the Rijksmuseum in Amsterdam.", + "- SemArt [12] consists of images collected from the Web Gallery of Art a virtual museum with predominantly European fine-art. The SemArt dataset contains" + ], + "bbox": [ + 517, + 685, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1948", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "21k images described with similar metadata as the Rijksmuseum dataset, but in addition also has textual descriptions in the form of artistic comments.", + "bbox": [ + 109, + 90, + 467, + 135 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The available metadata for these three artwork datasets differs, but notably none of these datasets have been described with semantic classes as, for example, found in ImageNet. As such, we do not have prior information about what type of visual concepts are represented in the artwork datasets.", + "bbox": [ + 76, + 150, + 467, + 239 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Experimental setup", + "text_level": 1, + "bbox": [ + 76, + 252, + 264, + 268 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The backbone used is the DeIT-S model [38] with a patch size of $16 \\times 16$ . The parameters of the backbone are fixed during prototype learning and training is done on a single NVIDIA RTX 3090 with a batch size of 128 and learning rate of $5\\mathrm{e} - 5$ for 20 epochs. For the first 15 epochs we train with soft gumbel-softmax, after which we switch the student to the hard 'straight-through' gumbel-softmax, to ensure more independent prototypes. In line with previous works (e.g., [2, 26]) we set $K$ to 8192.", + "bbox": [ + 75, + 276, + 467, + 411 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For quantitative evaluation we follow the standard procedure of training a linear classifier on frozen features [4, 16]. We freeze the backbone and the ProtoSim layer and then train a linear classifier for 20 epochs with a learning rate of 0.001 and a batch size of 256.", + "bbox": [ + 76, + 412, + 467, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Two-way Dataset Comparison", + "text_level": 1, + "bbox": [ + 76, + 500, + 344, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the two-way dataset comparison case study we focus on the PASS and ImageNet datasets, to this end we learn prototypes on the union of these two datasets, which we refer to as the PassNet dataset, and present the results in this section. All results in this section are obtained with ProtoSim trained on top of the DINO backbone pretrained on ImageNet. A key finding of this comparison is that ProtoSim learns both dataset-specific prototypes (i.e., prototypes that predominantly activate for one dataset) and shared prototypes (i.e., prototypes that occur frequently in both datasets). In Figure 4 we show nine prototypes which are predominantly found in ImageNet, PASS, or are shared equally among both datasets. Additional examples of prototypes are shown in the supplementary material.", + "bbox": [ + 75, + 522, + 467, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The prototypes that are predominantly found in ImageNet contain people (i.e., over $99\\%$ of images for which they activate are found in ImageNet). However, despite its design goal we do find persons for these prototypes in PASS. The Persons at the beach prototype (first row) contains a man holding a beach-ball photographed from the back, and the Uncovered legs/arms prototype (third row) is found in (nude) statues and a faded Polaroid of a person. The only two PASS images for the Sports-ball prototype (second row) just depict the field and a ball, suggesting that the prototype captures more than just persons.", + "bbox": [ + 75, + 734, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The prototypes that are predominantly found in PASS depict concepts or objects that are not found among the 1000 ImageNet categories. Nonetheless, these predominantly PASS prototypes can be found in some ImageNet images where the annotated object is a (small) part of the image. From left to right for row four to six we find the following ImageNet categories: European Gallinule, Ant, Wheelbarrow, Turnstile, Barn, and Headland. We would describe the prototypes in these rows as capturing Flowers, a View down narrow alley, and Sunset with silhouetted foreground respectively. In general, the PASS prototypes that predominantly concern vista or landscape images, which on occasion contain objects from ImageNet categories.", + "bbox": [ + 496, + 90, + 890, + 287 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the prototype in the second row of Figure 4 we measure how it is spatially distributed and visualise this for the four ImageNet images in Figure 5. Visualising the attention maps of this prototype shows that the main activations are indeed for the leg and arm areas of the persons depicted. Other parts of the persons receive much less attention than these uncovered areas. Although this is a predominantly ImageNet prototype, and is therefore commonly found in instances of the 'miniskirt' and 'bikini' categories, it is also found in PASS, including in images of mannequins, artworks, and anime of primarily feminine characters.", + "bbox": [ + 496, + 287, + 890, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Overall, we can conclude that the two-way comparison is highly successful, not only are we able to verify that depictions of humans in PASS are practically non-existent, but by edge-cases we are able to demonstrate the strength of the prototypes. Moreover, based on the discovered prototypes we also gain insights into how these datasets differ, with PASS containing many more vistas and landscapes, whereas ImageNet is strongly object-centric. As such we can conclude that while there is an overlap, PASS differs in more respects from ImageNet than just the presence of humans - which may cast doubt on its status as an ImageNet replacement.", + "bbox": [ + 496, + 455, + 890, + 637 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3c609441cb11035b94b7ef65e810a278b32fe518376fe19b415e4bc261852645.jpg", + "table_caption": [ + "Table 1: Performance for linear classifier on ImageNet." + ], + "table_footnote": [], + "table_body": "
Train setBackboneKAccuracy
ImageNetDINO [4]819264.8
PASSPASS-DINO [1]819220.4
PassNet (I+P)DINO [4]819253.2
PassNet (P+I)PASS-DINO [1]819215.9
ImageNetDINO [4]102454.7
ImageNetDINO [4]409663.7
", + "bbox": [ + 501, + 679, + 875, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative analysis. We perform two quantitative analyses. Firstly, we explore the loss value of each model during training and compare it to the diversity of the prototypes, as measured by the average cosine distance between the prototype weights. Secondly, we train a linear classifier on top of each of the backbones to perform ImageNet clas", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1949", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c80bbc75a3abef34b35710ee859acbffc6bf260e29bcbd246afe94ae6ea595c2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 130, + 114, + 243, + 176 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9803b847478edbafe40da8b27e13699e9247dfd2522afa02a9937122bc38efd3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 259, + 104, + 352, + 175 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/00222b6416b3a9c7536ad7d1d3f0463fb749ab1702f78cc9234de2ce41b4baf5.jpg", + "image_caption": [ + "ImageNet prototypes" + ], + "image_footnote": [], + "bbox": [ + 370, + 117, + 478, + 175 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/94cb6aed37fd3df3d36c4baea47ba439f9d3c84bc0f6003f87cf7de6ebb9c373.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 109, + 596, + 175 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cc285b3d0b97ecd162767eae8eda16dee3fdd11772834c0e2790151fe11edd38.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 629, + 107, + 697, + 175 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bbdd331cc5851fed85497831aeaba8efe4498a5c42483cd17c2fd81d9a4b13bc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 727, + 123, + 836, + 175 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4f11a057d69c4f03e02f9495ef583f5a73e1e529bf3a60a0f54a7554047fa1ba.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 132, + 183, + 241, + 241 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": 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The last two columns for rows one through six show some of the few examples found in the other dataset. The last three rows show prototypes common in both with examples of ImageNet in the left three columns, and examples in the right three." + ], + "image_footnote": [], + "bbox": [ + 130, + 738, + 240, + 796 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e03821feff5e6592738b89692d383d2c68ee076baf14c7b18825b98091d67fa0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 251, + 732, + 357, + 795 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d15cc0bdc86321c3d8e723bbb32ad0fd7117c3c25484b06084bec3b47a300db3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 369, + 732, + 477, + 795 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/67c89a5320b64a28c007d6002d979eb5be35eab6b0d883bb29080b3ce99c8ddb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 493, + 738, + 602, + 795 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f5c951372b267d28fd48d956e2de99045f7ddfba02782408ddca7e33cf0f8cdd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 611, + 739, + 718, + 795 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9152648ec114cdcdc03bbd8c7b37568f6772a0e9906cb00cb4962fe0b375936d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 730, + 739, + 838, + 795 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1950", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7d4a712213c49814e13958b13fa9017d7b1ef0f3e006197e348b3286f10c3cb9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 101, + 89, + 155, + 150 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bbceb2e0736191fe00f490b5d197ffff59b58a944f46d757cde1a04b32a368d3.jpg", + "image_caption": [ + "Figure 5: Attention maps for the four ImageNet images for the Uncovered legs/arms prototype in Figure 4." + ], + "image_footnote": [], + "bbox": [ + 86, + 167, + 169, + 215 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/32ff41bc4db8bb02dc9d78d906eb852012a0b4e638a310520f18dfa5f90e9c5d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 187, + 90, + 263, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/004391f7cd35dde08d671075a42ca21c0a96d1ad0e9ee0673a45bc2089b95a76.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 187, + 154, + 263, + 212 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b31840e82ee21f409ef36d017ed63779b2ba54864fb5f5a088c9321154b6113d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 109, + 361, + 150 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/07e27ebe519429371dd94bd5d912d756b1dbd546be38ffb33a7625301c31d58c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 179, + 361, + 214 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/80e75a2e5e5050b60be0932b35ce1eb7524bf94536b8a8ea95d46af909b17233.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 382, + 90, + 455, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dcb18a7e60ea44a1891917928f94f1294dafb7dffdece0a167d87cccf2b0d82b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 382, + 154, + 455, + 212 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "sification. For these evaluations we compare between two different backbones, one pre-trained on ImageNet [4] and one pre-trained on PASS [1]. Results reported on PassNet are described as either $(\\mathrm{I} + \\mathrm{P})$ for the ImageNet pre-trained backbone, or $\\mathrm{P} + \\mathrm{I}$ for the PASS pre-trained backbone.", + "bbox": [ + 75, + 285, + 468, + 359 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 1 shows the performance on the ImageNet validation set for a linear classifier trained on top of fixed backbones. We observe that pre-training on ImageNet (unsurprisingly) leads to the best downstream performance on ImageNet, and that training on PASS leads to lower performance. Similarly, for the two backbones we find that the ImageNet pre-trained backbone performs much better. Nonetheless, we see degraded performance for training on PassNet versus ImageNet. The last two rows of Table 1 show that increasing the $K$ value benefits performance, due to computational complexity and diminishing returns no values above 8192 were tested. In conclusion, our quantitative evaluation confirms our modelling choices of using the ImageNet pre-trained backbone with 8192 prototypes, and we will use this configuration for the second case study as well.", + "bbox": [ + 75, + 361, + 468, + 602 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/39ff7cdcb8742f4d536e413fe1ad53b07451f10e04260fa1915d40a3edee2c61.jpg", + "image_caption": [ + "Figure 6: Training loss (left) and average cosine similarity (right) during prototype training. PassNet results $\\mathrm{P} + \\mathrm{I}$ are obtained PASS-DINO backbone and $\\mathrm{I} + \\mathrm{P}$ with the DINO backbone." + ], + "image_footnote": [], + "bbox": [ + 89, + 612, + 267, + 718 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6ecab230bf582637f070de7f053ca80d59804818b1434461d10c4c36504da765.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 271, + 613, + 455, + 718 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The results in Figure 6 show the training loss and the average cosine similarity between prototypes as training progresses. In both plots we see two groupings of two lines that follow the same pattern. For all models we can see that switching to the hard gumbel-softmax leads to a bump in the loss, but except for $\\mathrm{P} + \\mathrm{I}$ this bump levels off quickly.", + "bbox": [ + 75, + 809, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Three-way Dataset Comparison", + "text_level": 1, + "bbox": [ + 500, + 90, + 781, + 107 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In the second case study we perform a three-way dataset comparison between the MET, Rijksmuseum, and SemArt datasets. The aim of this comparison is highly exploratory, unlike ImageNet, none of these datasets have pre-defined classes, as such it is not obvious what visual concepts are represented. In Figure 7 we show nine prototypes discovered with ProtoSim, the first three pairs of prototypes are dataset-specific and are predominantly found in the MET, Rijksmuseum, and SemArt respectively. These prototypes were randomly selected from the most dataset-specific prototypes and give a good indication of what is contained in these datasets. The MET dataset contains many 3D objects and often multiple photographs are taken from different angles, as such the first prototype represents Top-down views of vases. The second MET prototype depicts Egyptian wall carvings, which were photographed under raking light to emphasise the height differences across the surface.", + "bbox": [ + 496, + 113, + 890, + 369 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The Rijksmuseum dataset contains many prints or drawings on paper, whilst this is something that can be learnt from the material type overview in [27], the two prototypes depicted show two different groups of visual concepts. The first Rijksmuseum prototype depicts natural history drawings, whereas the second is found in side view portraits. Se-mArt on the other hand consists of mostly fine-art paintings, with the first prototype capturing a stylistic visual concept of Renaissance paintings, the second prototype is a more concrete semantic concept, namely dogs.", + "bbox": [ + 496, + 369, + 890, + 522 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Just by exploring the dataset-specific datasets we already get a much better understanding of what is contained in these datasets and what makes them unique. In addition, when we then analyse the shared prototypes we can see that these differences largely persist across different visual concepts. The first shared prototype is of various animals, notably we see that the prototype is not sensitive to material differences, returning both drawings and paintings. The same observation is made for the second shared prototype of baskets, which is matched to drawings, paintings, and photographs of actual baskets. This ability to generalise across modalities is also observed in the third shared prototype of brass instruments, which matches actual instruments and realistic paintings containing similar instruments.", + "bbox": [ + 496, + 523, + 890, + 733 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Based on the three-way dataset comparison we find that there are degrees of overlap between the datasets, generally we would see that the MET and Rijksmuseum datasets are most similar in types of objects, where MET has a greater focus on physical objects and Rijksmuseum on prints and drawings. Because these two datasets have a relatively small proportion of paintings the similarity with the SemArt dataset is less, nonetheless, we can observe that in terms of visual concepts these datasets represent similar things. In Appendix Section C we show additional prototypes discovered for these artwork datasets.", + "bbox": [ + 496, + 734, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1951", + "bbox": [ + 483, + 944, + 513, + 955 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4b54cca991050a9bdc1cc85bf6801501086966877cbdfb7769f68402bae78505.jpg", + "image_caption": [ + "MET prototypes" + ], + "image_footnote": [], + "bbox": [ + 84, + 104, + 460, + 354 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/b158d5abd036f4e300c09b3d949283355a0484b1f2e72d856332f7df4d28ab10.jpg", + "image_caption": [ + "SemArt prototypes" + ], + "image_footnote": [], + "bbox": [ + 94, + 383, + 457, + 523 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/9af90c233ef8a0c4b5975ad4d52a8432f0371a2887cc19c52a267b6c12babc4d.jpg", + "image_caption": [ + "Shared prototypes", + "Figure 7: Example images for nine prototypes, the first six rows are divided in three pairs of prototypes predominantly found in MET, Rijksmuseum, or SemArt respectively. The last three rows show prototypes common across the datasets. Examples with a pink, green, and blue background belong to the MET, Rijksmuseum, or Semart datasets respectively." + ], + "image_footnote": [], + "bbox": [ + 86, + 555, + 457, + 753 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Discussion", + "text_level": 1, + "bbox": [ + 500, + 89, + 612, + 104 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The prototypes obtained with ProtoSim enable dataset comparison, nonetheless, there are two limitations. Firstly, although explanation methods based on visual examples are preferred for visual data [19], there is a mandatory manual inference step to determine what a prototype represents. Whilst previous methods suffer from the same limitation [6, 21] ProtoSim does offer an advantage in that the attention maps can be visualised (i.e., Figure 5). Based on example images and their attention maps it becomes possible to be relatively certain about what the prototype represents.", + "bbox": [ + 496, + 114, + 890, + 266 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Secondly, whilst the ViT backbone can be replaced, for our experiments we found the best results with an ImageNet pre-trained backbone. Since this dataset is one of the ones being compared, but also because this dataset has known biases [41] the choice for a ImageNet pre-trained backbone may influence the prototypes learned. During experiments no such influence was observed, instead it appears ProtoSim is flexible in learning diverse prototypes, nonetheless further investigation is necessary.", + "bbox": [ + 496, + 266, + 892, + 402 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 417, + 617, + 431 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this work we presented dataset comparison as a new direction for dataset inspection. To enable dataset comparison across large-scale datasets we introduce ProtoSim which leverages integral prototype-based learning and self-supervised learning to discover visual concepts across datasets. To evaluate our proposed approach we perform two case studies, in the first we compare the PASS and ImageNet datasets, and in the second we perform a three-way comparison between artwork datasets.", + "bbox": [ + 496, + 441, + 890, + 577 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Based on these case studies we find that we can gain new insights into the datasets. In the first case study we find that ImageNet indeed contains many more images with persons, which is in line with the design goal of PASS. However, we still discovered partial and non-photorealistic depictions of persons in PASS, which were not discovered in its person-focused dataset curation process. When comparing the artwork datasets we find that each has a unique focus, but also that various semantic concepts are shared between them.", + "bbox": [ + 496, + 579, + 890, + 714 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Overall, we presented an initial exploration of dataset comparison that will hopefully lead to greater attention for this topic, as it is becoming increasingly necessary to improve dataset inspection techniques.", + "bbox": [ + 496, + 715, + 890, + 775 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 790, + 596, + 805 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Yuki M Asano, Christian Rupprecht, Andrew Zisserman, and Andrea Vedaldi. 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IEEE. 2" + ], + "bbox": [ + 501, + 92, + 890, + 246 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "1954", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Prototype-based Dataset Comparison/02a62e7f-ba00-4044-92de-55f8e976a093_model.json b/2023/Prototype-based Dataset Comparison/02a62e7f-ba00-4044-92de-55f8e976a093_model.json new file mode 100644 index 0000000000000000000000000000000000000000..a2d294019d236d2148d8117662e11e4cbd00c05d --- /dev/null +++ b/2023/Prototype-based Dataset Comparison/02a62e7f-ba00-4044-92de-55f8e976a093_model.json @@ -0,0 +1,3060 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.296, + 0.131, + 0.676, + 0.154 + ], + "angle": 0, + "content": "Prototype-based Dataset Comparison" + }, + { + "type": "text", + "bbox": [ + 0.384, + 0.182, + 0.586, + 0.216 + ], + "angle": 0, + "content": "Nanne van Noord \nUniversity of Amsterdam" + }, + { + "type": "text", + "bbox": [ + 0.391, + 0.22, + 0.579, + 0.233 + ], + "angle": 0, + "content": "n.j.e.vannoord@uva.nl" + }, + { + "type": "title", + "bbox": [ + 0.19, + 0.271, + 0.393, + 0.287 + ], + "angle": 0, + "content": "Dataset-specific Prototypes" + }, + { + "type": "title", + "bbox": [ + 0.633, + 0.271, + 0.764, + 0.287 + ], + "angle": 0, + "content": "Shared Prototype" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.291, + 0.178, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.186, + 0.291, + 0.28, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.347, + 0.178, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.187, + 0.346, + 0.28, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.15, + 0.399, + 0.223, + 0.414 + ], + "angle": 0, + "content": "ImageNet" + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.298, + 0.388, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.342, + 0.388, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.375, + 0.29, + 0.49, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.375, + 0.399, + 0.42, + 0.412 + ], + "angle": 0, + "content": "PASS" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.298, + 0.6, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.345, + 0.599, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.568, + 0.399, + 0.641, + 0.414 + ], + "angle": 0, + "content": "ImageNet" + }, + { + "type": "image", + "bbox": [ + 0.609, + 0.298, + 0.701, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.609, + 0.345, + 0.701, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.719, + 0.29, + 0.788, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.352, + 0.794, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.806, + 0.294, + 0.888, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.352, + 0.795, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.806, + 0.354, + 0.889, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.778, + 0.399, + 0.822, + 0.412 + ], + "angle": 0, + "content": "PASS" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.43, + 0.894, + 0.476 + ], + "angle": 0, + "content": "Figure 1: Prototypes discovered with ProtoSim. By training on both datasets ProtoSim is able to discover prototypes that are dataset specific or shared. From left to right: ImageNet specific “Wedding”, PASS specific “sunset skyline”, and shared “viaduct” prototypes." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.488, + 0.314, + 0.504 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.47, + 0.612 + ], + "angle": 0, + "content": "Dataset summarisation is a fruitful approach to dataset inspection. However, when applied to a single dataset the discovery of visual concepts is restricted to those most prominent. We argue that a comparative approach can expand upon this paradigm to enable richer forms of dataset inspection that go beyond the most prominent concepts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.473, + 0.75 + ], + "angle": 0, + "content": "To enable dataset comparison we present a module that learns concept-level prototypes across datasets. We leverage self-supervised learning to discover these prototypes without supervision, and we demonstrate the benefits of our approach in two case-studies. Our findings show that dataset comparison extends dataset inspection and we hope to encourage more works in this direction. Code and usage instructions available at https://github.com/Nanne/ProtoSim" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.784, + 0.21, + 0.799 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Image datasets are crucial for Computer Vision and due to the algorithms' need for more data they are ever growing in size. At the same time datasets are a major source of bias leading to negative social impact [29, 30]. Unfortunately, it is challenging to determine what is contained in a dataset as their large size combined with the visual nature of the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.893, + 0.55 + ], + "angle": 0, + "content": "data makes manual inspection infeasible. To support users and developers of large-scale datasets in ensuring that the datasets match their usage and design goals it is necessary to develop better tools for dataset inspection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.893, + 0.839 + ], + "angle": 0, + "content": "A promising direction for generic dataset inspection is found in highly effective approaches that have been proposed for summarisation [35, 9, 14, 44, 24]. A major benefit of these approaches is that they enable explorative dataset inspection without needing supervised pretraining. However, a limitation of these approaches is that they use frequency as a proxy for importance, and on a single dataset therefore only discover those visual concepts which are most prominent. As such, we argue that a comparative approach, which enables discovery of a wider and more diverse range of concepts, is necessary to effectively perform dataset inspection. For instance, the PASS dataset [1] is designed as an ImageNet [32] alternative whilst containing no people, as such it provides us with a testable hypothesis that is comparative in nature. Namely, when comparing these two datasets there should be a disjoint set of visual people-centric concepts that are only found in ImageNet. In a case study we will verify this hypothesis, and demonstrate that dataset comparison can lead to new insights." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Moreover, an additional limitation of existing summarisation approaches is that they decouple the summarisation process from representation learning, and treat these as two distinct steps by performing the summarisation on a" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1944" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.212 + ], + "angle": 0, + "content": "pre-defined feature basis, such as GIST descriptors in [35] or LDA clusters in [31]. As recent work on incorporating prototypes into a network's reasoning process has been shown to aid interpretability [23, 6, 33, 13, 45], we propose that this may also be a promising direction for end-to-end dataset comparison. Therefore, we introduce a method for prototype-based dataset comparison, which discovers the visual concepts in a dataset in an end-to-end fashion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.214, + 0.471, + 0.44 + ], + "angle": 0, + "content": "Dataset prototypes are similar to cluster centroids in that they represent latent points in the feature space that are to be discovered. However, in clustering, similar to prior work on dataset summarisation, these centroids are discovered in a step that is decoupled from learning the feature representations. Whilst some recent works have explored forms of deep clustering [40, 11, 22], they still involve two separate optimisation goals. For example, by having one loss focused on the feature representation and another on clustering [11]. Instead, we propose a simple module ProtoSim that can be integrated into a deep network without changing how it is optimised. To demonstrate this, we add ProtoSim to a Vision Transformer (ViT) [10] and show that it can effectively discover visual concepts across datasets in a self-supervised setting." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.442, + 0.402, + 0.456 + ], + "angle": 0, + "content": "Overall, we make the following contributions:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.461, + 0.469, + 0.49 + ], + "angle": 0, + "content": "- We introduce dataset comparison, a new approach for inspecting datasets." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.5, + 0.469, + 0.53 + ], + "angle": 0, + "content": "- To enable dataset comparison we present ProtoSim, a module for integrated learning of dataset prototypes." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.539, + 0.469, + 0.582 + ], + "angle": 0, + "content": "- With two case-studies we demonstrate how dataset comparison can be used to gain new insight into datasets." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.461, + 0.469, + 0.582 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.601, + 0.216, + 0.617 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.469, + 0.854 + ], + "angle": 0, + "content": "Dataset comparison through prototypes is a largely unexplored area of research, but it is similar in spirit to dataset distillation [47, 5] which seeks to distill the knowledge from a large dataset into a small dataset. Most works in dataset distillation generate synthetic examples, as opposed to selecting a set of data instances, to construct the small dataset. These synthetic examples could be considered dataset prototypes, as they represent an aggregate of information that is central to the dataset. A key difference between such prototypes and the prototypes considered in this work, is that the distilled synthetic examples are instance-level prototypes (i.e., complete images that may represent multiple concepts), whereas in this work the aim is to discover concept-level prototypes, which may correspond to global concepts or part-level concepts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "In the remainder of this section we will further explore how dataset comparison relates to dataset summarisation, prototype learning, and deep clustering." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.719, + 0.107 + ], + "angle": 0, + "content": "2.1. Dataset Summarisation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.219 + ], + "angle": 0, + "content": "Manual browsing is a reliable manner to determine what is contained in a dataset, however, browsing even a subset of the data can be time-consuming, which has led to a line of work on dataset summarisation [31, 9, 14, 44, 24]. The aim of dataset summarisation is to find underlying structure or patterns that are shared between data instances to give an overview of what is contained in a dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.22, + 0.893, + 0.643 + ], + "angle": 0, + "content": "An important modeling choice for dataset summarisation is the basis on top of which the patterns are found. Work on mid-level pattern mining aims to find discriminative and representative patches and use these as visual primitive for further analysis [34]. Mid-level pattern mining aims to distinguish itself from \"visual word\" approaches [36], which were found to mainly capture low-level patterns such as edges and corners [34, 9]. Two notable patch-based approaches are the dataset fingerprinting approach by [31] and the what makes Paris look like Paris? approach by [9]. Patch-based approaches aim to circumvent the limitations of visual words by starting with larger visual structure (i.e., patches at multiple scales). Due to the limitations of pixel-space representations patches cannot be used directly for analysis, instead initial patch-based approaches used feature extractors such as HOG [34, 9] and Convolutional Neural Network (CNN) activations in later works [24]. Using patches has been shown to help steer the results towards more semantically meaningful visual elements, yet they are still restrictive in representational power and in terms of shape (i.e., patches must be rectangular). Moreover, although the starting point is a patch, the features extracted largely determine what the pattern represents and the features are not intrinsically explainable, necessitating posthoc explanations. In contrast, we propose to add ProtoSim to a ViT architecture, which can learn to recognise visual elements of arbitrary shapes and sizes, whilst still focusing on semantically meaningful concepts." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.688, + 0.668 + ], + "angle": 0, + "content": "2.2. Prototype Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Prototype-based approaches can be categorised into two areas, the first aims to learn prototypes which represent high-level semantic concepts (i.e., classes) to support zero or few-shot learning [18, 28, 37]. The second area is concerned with finding recurring visual elements and are increasingly used for model explainability [23, 6, 21, 39, 13, 20, 42, 45]. As opposed to post-hoc explainability methods, prototypes are integral to the network and provide explanations of the network's reasoning process [6]. Our approach is part of this second area and we will focus the discussion on integral prototypes for recurring visual elements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Integral prototypes have been shown to be effective for supervised multi-class classification [6, 13, 20, 21], deepfake detection [39], and semantic segmentation [48]. In the literature we can recognise two branches of work on integral" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1945" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "prototypes, the first builds on ProtoPnet [23, 6] and the second on Concept Bottleneck Models (CBM) [13, 20]. Common across these approaches is that they add a layer preceding the output layer that maps the extracted features to prototypes (or concepts) and produce the final output based on the affinity to these prototypes. The logic is thus that because the prototypes are recognisable entities, the prediction is explained by the affinity to the prototypes. The main difference between these branches is that in ProtoPnet-like approaches the prototypes are latent vectors in the embedding space that are learnt end-to-end, whereas CBM approaches use a pre-defined concept library." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.277, + 0.473, + 0.579 + ], + "angle": 0, + "content": "However, these prior approaches all focus on a supervised setting and learn per-class prototypes or concepts, which is severely limiting for dataset summarisation. Instead, we propose to leverage a self-supervised loss to learn prototypes that are not class specific and can represent any visual concept that is present in the data. In particular, our prototypes may represent class-level concepts or segment-level concepts as in CBM [13], but we learn them without concept-level supervision. Previous works learned prototypes for the features at each location in the convolutional output of a Convolutional Neural Network (CNN) backbone [6, 21, 39]. This restricts the spatial extent of the prototypes to size of the receptive field. Additionally, in CNN the output is typically spatially averaged to achieve a global image representation, however, as this is not done for CNN-based prototype approaches they can only learn local and not global prototypes. Instead, we use Vision Transformers (ViT) [10], as they offer solutions for both aforementioned issues capturing local and global concepts of various spatial extents." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.599, + 0.24, + 0.615 + ], + "angle": 0, + "content": "2.3. Deep Clustering" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.47, + 0.793 + ], + "angle": 0, + "content": "Clustering relates to learning prototypes or concepts in that it has been used to define the library of concept CBM [13], and to an extent the underlying principles match the goal of clustering. In particular, in deep clustering [40, 11, 22] the centroids are learned iteratively, resulting in them being conceptually close to prototypes or CBM-concepts. However, in prior works on deep clustering [40, 11, 22] the clustering objective is separate from the feature representation, whereas in prototype-based approaches the final output is determined by projecting the input to the prototype subspace." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Another key difference is that by making the prototypes integral to the reasoning process, as in CBM [13] or ProtoP-net [6], it is ensured that the prototypes are of meaningful to the final output. Post-hoc clustering, or as part of a separate objective, may lead to overrepresentation of clusters which capture meaningless information, e.g., orthogonal to the objective that was used to obtain the feature representation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.697, + 0.108 + ], + "angle": 0, + "content": "3. Dataset Comparison" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.895, + 0.224 + ], + "angle": 0, + "content": "Given a collection of datasets \\( X = \\{\\chi_i\\}_{i=1}^{|X|} \\) the aim of prototype-based dataset comparison is to discover a set of prototypes \\( p \\in \\mathbb{R}^{K \\times D} \\) that represent visual concepts that may occur predominantly in only one dataset (i.e. dataset-specific prototypes) or visual concepts which occur in two or more datasets (i.e. shared prototypes). An illustration of the dataset comparison workflow is shown in Figure 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.224, + 0.895, + 0.375 + ], + "angle": 0, + "content": "We argue that a comparative approach to dataset summarisation, i.e., dataset comparison is vital for gaining insights into datasets. In particular, if \\( C_* \\) is the set of all possible visual concepts, and \\( C_i \\) the visual concepts in ImageNet, then \\( C_i \\subset C_* \\). Given these sets, \\( C_i \\) is a perfect description of what is contained in ImageNet, and the difference \\( C_* - C_i \\) perfectly describes what is not contained in ImageNet. However, as we do not have access to \\( C_* \\) and we have no guaranteed manner of discovering \\( C_i \\), we can at best learn a set of prototypes \\( \\hat{C}_i \\) that approximates \\( C_i \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.374, + 0.895, + 0.516 + ], + "angle": 0, + "content": "As it is an approximation it cannot be concluded from \\(\\hat{C}_i\\) that a concept is not in \\(C_i\\). For example, PASS is designed to not contain humans (i.e., no humans in \\(C_p\\)), but based on \\(\\hat{C}_p\\) it cannot be stated with certainty that no humans are found in PASS, only that no human-centric concepts were discovered. To overcome this limitation we propose to jointly learn \\(\\hat{C}_i\\) and \\(\\hat{C}_p\\). Thereby, if we know a concept is in \\(\\hat{C}_i\\) and not in \\(\\hat{C}_p\\), we can reasonably conclude that the concept is not in \\(C_p\\) either." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.528, + 0.882, + 0.657 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.672, + 0.894, + 0.735 + ], + "angle": 0, + "content": "Figure 2: Overview of the dataset comparison workflow. Datasets are mapped to the prototype embedding space, from where we can inspect and compare individual prototypes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.748, + 0.895, + 0.824 + ], + "angle": 0, + "content": "Through dataset comparison we are thus able to answer questions that could not be answered by only considering a single dataset, thereby creating new possibilities for dataset inspection for hypothesis verification or comparative exploration." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.702, + 0.849 + ], + "angle": 0, + "content": "3.1. Prototype Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "How to evaluate the prototypes learnt for dataset comparison (or summarisation) is an open problem, as the groundtruth for which visual concepts are contained in the dataset" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1946" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.468, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.192, + 0.47, + 0.237 + ], + "angle": 0, + "content": "Figure 3: Examples of low-level visual properties discovered with ProtoSim: motion blur (top) and a shallow depth of field (bottom)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.271, + 0.468, + 0.377 + ], + "angle": 0, + "content": "are unknown. Nonetheless, we can leverage the comparative approach by verifying whether the prototypes found match the design goals of the datasets. For instance, as PASS was designed not to contain humans we can explore whether the human-centric prototypes learnt from ImageNet indeed do not occur in PASS. This manner of evaluation forms the basis of our first case study." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.38, + 0.468, + 0.546 + ], + "angle": 0, + "content": "Generally, we consider the prototypes \\( p \\) to be of high-quality when they are distinct and meaningful. Distinct prototypes are able to independently represent a visual concept, this is in contrast to, for example, sparse coding [46] where the aim is to find basis vectors that represent the input through linear combinations. The set of prototypes is meaningful when it can be used to discriminate images within and across the datasets from one another. Requiring that the prototypes are discriminative helps avoid trivial solutions. We can quantitatively measure how discriminative the prototypes are by evaluating them with downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.468, + 0.655 + ], + "angle": 0, + "content": "To ensure that the prototypes are distinct we design our method ProtoSim to perform hard assignment of the prototypes, and by optimising the prototypes with contrastive SSL we ensure that they are discriminative. This alignment between the design of the method (more details in Section 4) and the goal of dataset comparison helps us make certain the prototypes are of high-quality." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.675, + 0.265, + 0.691 + ], + "angle": 0, + "content": "3.2. Types of Prototypes" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.701, + 0.468, + 0.822 + ], + "angle": 0, + "content": "Within the set of prototypes we can recognise different types of prototypes depending on how they occur across the datasets. For instance, a prototype \\( p_i \\) may be considered dataset-specific when over \\( 95\\% \\) of its occurrences are only found in a single dataset. By definition, any prototype which is not dataset-specific would then be considered shared. However, various degrees of 'sharedness' may occur depending on the overlap between datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.901 + ], + "angle": 0, + "content": "In theory it may be possible for the datasets in \\( X \\) to be fully distinct, resulting in only dataset-specific prototypes. In practice, we find that prototypes may represent various basic visual properties (see Figure 3), resulting in shared prototypes even when the datasets differ semantically." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.743, + 0.108 + ], + "angle": 0, + "content": "4. Prototype-based Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.892, + 0.267 + ], + "angle": 0, + "content": "We propose ProtoSim a simple module that can inserted in ViT architectures to enable dataset comparison through integral prototype-based learning. ProtoSim differs from previous prototype layers in three ways, firstly, the prototypes learned with ProtoSim are distinct (as opposed to linear mixtures), secondly, ProtoSim is specifically designed for ViT architectures and learns prototypes from a set of tokens, rather than a single embedding vector. Lastly, the prototypes in ProtoSim are not class-specific, instead we learn a single pool of prototypes that may occur in any image." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.274, + 0.61, + 0.288 + ], + "angle": 0, + "content": "4.1. ProtoSim" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.297, + 0.892, + 0.447 + ], + "angle": 0, + "content": "In order to learn which visual concepts are present in a dataset we aim to optimise a set of \\(K\\) learnable prototypes \\(p \\in \\mathbb{R}^{K \\times D}\\). By designing the prototypes to be part of a prototype layer (i.e. ProtoSim) we can directly optimise them in and end-to-end fashion as part of ViT that we add the layer to. Specifically, given the token embeddings \\(z \\in \\mathbb{R}^{N + 1 \\times D}\\) produced by a ViT, ProtoSim maps these to the prototype embeddings \\(\\hat{z} \\in \\mathbb{R}^{N + 1 \\times D}\\), where \\(D\\) is the token vector size. During this mapping each token is replaced with the most similar prototype in \\(p\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.892, + 0.569 + ], + "angle": 0, + "content": "In [23, 6] the similarity to each of the class-specific prototypes is determined by calculating the squared \\( L^2 \\) distance and selecting the closest prototype with a max operation. Because our aim is to find prototypes that recur in the entire dataset, instead of finding class-specific prototypes, we propose a surprisingly simple formulation of this process by using a reversed version of dot-product attention [25] to efficiently calculate attention across all the prototypes:" + }, + { + "type": "equation", + "bbox": [ + 0.627, + 0.575, + 0.891, + 0.591 + ], + "angle": 0, + "content": "\\[\na = \\operatorname {s o f t m a x} \\left(p z ^ {\\intercal}\\right) \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.629, + 0.594, + 0.891, + 0.61 + ], + "angle": 0, + "content": "\\[\n\\hat {z} = a ^ {\\intercal} p. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.616, + 0.892, + 0.736 + ], + "angle": 0, + "content": "Here the attention mask \\( a \\) represents the soft-assignment of prototypes to tokens, as such each token embedding \\( \\hat{z} \\) is a linear combination of prototypes. This is not desirable as our aim is to learn distinct prototypes which independently represent a visual concept, as this enables better summarisation and greater interpretability. To obtain a hard assignment we replace the softmax operation in Equation 1 with gumbel-softmax [17]:" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.743, + 0.891, + 0.759 + ], + "angle": 0, + "content": "\\[\na = \\operatorname {g u m b e l - s o f t m a x} (p z ^ {\\intercal}). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "For simplicity we drop the temperature parameter, as it empirically does not meaningfully influence performance and can be kept fixed at 1. The benefit of gumbel-softmax is that it maintains gradient-flow whilst enabling hard attention. Based on this modification \\( a \\) now represents a hard assignment matrix which is used to replace each token with a prototype. As a visual concept can occur across multiple spatial locations there is no constraint on how often a prototype can be assigned." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1947" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.191, + 0.105 + ], + "angle": 0, + "content": "4.2. Backbone" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.47, + 0.297 + ], + "angle": 0, + "content": "Whilst ProtoSim functions as a generic network module, with the only requirement being an a two-dimensional input of \\( K \\times D \\), we specifically apply it to ViT in this work as these offer some benefits over CNN. In particular, in ViT all tokens can share information with all other tokens, as such there is no restriction on the spatial extent of the learned prototypes. Moreover, whilst most tokens in a ViT represent some spatial region of the image (i.e. patch tokens), the class token takes on the role of a global image representation. This allows us to learn prototypes that are local (i.e. only assigned to patch tokens) and global (i.e. only assigned to the class token) without modifying the architecture." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.297, + 0.471, + 0.495 + ], + "angle": 0, + "content": "ProtoSim is placed at the end of the backbone ViT in the network architecture. Formally, the input \\( x \\in \\mathbb{R}^{H \\times W \\times C} \\) is divided into flattened patch tokens \\( x_{p} \\in \\mathbb{R}^{N \\times (P^{2} \\cdot C)} \\), where \\( H, W, \\) and \\( C \\) are the height, width, and channel dimensionality of the input and \\( P \\) the patch size hyperparameter. In addition to \\( N \\) patch tokens, a learnable class token \\( x_{class} \\) is prepended to input. No class labels are used during training, but we retain the ViT terminology of referring to this as a class token. After the embedding phase the tokens are passed through a series of transformer blocks resulting in the token embeddings \\( z \\in \\mathbb{R}^{N + 1 \\times D} \\), where \\( D \\) is the embedded token vector size. \\( z \\) is passed through the ProtoSim layer resulting in the prototype embeddings \\( \\hat{z} \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.505, + 0.26, + 0.523 + ], + "angle": 0, + "content": "4.3. Training Objective" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.529, + 0.47, + 0.695 + ], + "angle": 0, + "content": "The training objective determines the prototypes. For instance, a classification-based objective results in prototypes that are indicative of the classes (as in ProtoPnet [6] or CBM [20]). Yet, such an objective may result in a poor coverage of concepts that are not part of the annotated classes. Because we strive for good coverage we focus on a Contrastive Self-Supervised Learning (Contrastive SSL) objective. In particular, because Constrastive SSL optimises for fine-grained discrimination between images (rather than classes) and has been shown to be perform well on a variety of downstream tasks [7]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.696, + 0.47, + 0.757 + ], + "angle": 0, + "content": "From the recently proposed Contrastive SSL methods [16, 15, 7, 8, 3, 4], only DINO [4] has been specifically designed to work with ViT. As such, we minimise the DINO loss as the training objective:" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.768, + 0.47, + 0.813 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta_ {s}} \\sum_ {x \\in \\{x _ {1} ^ {g}, x _ {2} ^ {g} \\}} \\sum_ { \\begin{array}{c} x ^ {\\prime} \\in V \\\\ x ^ {\\prime} \\neq x \\end{array} } H (P _ {t} (x), P _ {s} (x ^ {\\prime})), \\qquad (4)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\( H(a,b) = -a\\log b \\), \\( x_1^g \\) and \\( x_2^g \\) are two large crops from the input, \\( V \\) a set of data-augmented smaller crops, and \\( P_t \\) and \\( P_s \\) are the teacher and student networks respectively, each with a ProtoSim layer added to the backbone. We refer to the excellent work by [4] for further details." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.633, + 0.106 + ], + "angle": 0, + "content": "5. Case Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.895, + 0.373 + ], + "angle": 0, + "content": "In this section we present two case studies, the first is a comparison between two datasets (i.e., two-way dataset comparison) aimed at determining how the PASS [1] dataset differs from ImageNet [32]. Because the design goal of PASS was to present an alternative for ImageNet that does not contain humans we test whether this is achieved successfully. The second case study focuses on a three-way dataset comparison scenario wherein we explore how three artwork datasets differ. These three datasets were designed for different tasks and contain images from different museum collections, as such based on these meta properties of the datasets it is challenging to determine how they actually relate. With these two case studies we put the two main applications of dataset comparison to the test, verifying a design goal of a dataset, and exploring unknown datasets. In addition, in Supplementary Section A we demonstrate how ProtoSim can also be used on a single dataset." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.381, + 0.603, + 0.395 + ], + "angle": 0, + "content": "5.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.404, + 0.892, + 0.434 + ], + "angle": 0, + "content": "For the first case study we focus on ImageNet and PASS, we briefly describe both:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.444, + 0.892, + 0.552 + ], + "angle": 0, + "content": "- ImageNet [32] is a widely used dataset available in two versions: ImageNet-21K and ImageNet-1K. In this work we focus on ImageNet-1K consisting of approximately 1.2 million training images and 1000 classes. Despite how widely used it is, and how influential it has been, ImageNet-1K has also been criticised for its biased depictions of persons [30]." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.56, + 0.892, + 0.635 + ], + "angle": 0, + "content": "- PASS [1] is a recently proposed alternative for ImageNet with the intention of not containing persons to avoid the issues in ImageNet. PASS contains approximately 1.4 million unlabeled images and can only be used for self-supervised training." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.444, + 0.892, + 0.635 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.646, + 0.892, + 0.676 + ], + "angle": 0, + "content": "In the second case study we focus on three artwork datasets that have been used for a variety of different tasks:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.686, + 0.892, + 0.747 + ], + "angle": 0, + "content": "- MET [43] is a dataset designed for instance-level recognition, its training set contains over 400k images from more than 224k different objects held by the Metropolitan Museum of Art in New York." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.756, + 0.892, + 0.845 + ], + "angle": 0, + "content": "- Rijksmuseum [27] presents a set of tasks which are museum-centric, focusing on predicting various types of metadata (i.e., artist, object-type, material usage, and creation year). It consists of 110k images obtained from collections held by the Rijksmuseum in Amsterdam." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "- SemArt [12] consists of images collected from the Web Gallery of Art a virtual museum with predominantly European fine-art. The SemArt dataset contains" + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.686, + 0.892, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1948" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.11, + 0.092, + 0.468, + 0.136 + ], + "angle": 0, + "content": "21k images described with similar metadata as the Rijksmuseum dataset, but in addition also has textual descriptions in the form of artistic comments." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.151, + 0.468, + 0.241 + ], + "angle": 0, + "content": "The available metadata for these three artwork datasets differs, but notably none of these datasets have been described with semantic classes as, for example, found in ImageNet. As such, we do not have prior information about what type of visual concepts are represented in the artwork datasets." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.253, + 0.265, + 0.269 + ], + "angle": 0, + "content": "5.2. Experimental setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.277, + 0.468, + 0.412 + ], + "angle": 0, + "content": "The backbone used is the DeIT-S model [38] with a patch size of \\(16 \\times 16\\). The parameters of the backbone are fixed during prototype learning and training is done on a single NVIDIA RTX 3090 with a batch size of 128 and learning rate of \\(5\\mathrm{e} - 5\\) for 20 epochs. For the first 15 epochs we train with soft gumbel-softmax, after which we switch the student to the hard 'straight-through' gumbel-softmax, to ensure more independent prototypes. In line with previous works (e.g., [2, 26]) we set \\(K\\) to 8192." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.413, + 0.468, + 0.486 + ], + "angle": 0, + "content": "For quantitative evaluation we follow the standard procedure of training a linear classifier on frozen features [4, 16]. We freeze the backbone and the ProtoSim layer and then train a linear classifier for 20 epochs with a learning rate of 0.001 and a batch size of 256." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.5, + 0.345, + 0.515 + ], + "angle": 0, + "content": "5.3. Two-way Dataset Comparison" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.468, + 0.734 + ], + "angle": 0, + "content": "For the two-way dataset comparison case study we focus on the PASS and ImageNet datasets, to this end we learn prototypes on the union of these two datasets, which we refer to as the PassNet dataset, and present the results in this section. All results in this section are obtained with ProtoSim trained on top of the DINO backbone pretrained on ImageNet. A key finding of this comparison is that ProtoSim learns both dataset-specific prototypes (i.e., prototypes that predominantly activate for one dataset) and shared prototypes (i.e., prototypes that occur frequently in both datasets). In Figure 4 we show nine prototypes which are predominantly found in ImageNet, PASS, or are shared equally among both datasets. Additional examples of prototypes are shown in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.468, + 0.901 + ], + "angle": 0, + "content": "The prototypes that are predominantly found in ImageNet contain people (i.e., over \\(99\\%\\) of images for which they activate are found in ImageNet). However, despite its design goal we do find persons for these prototypes in PASS. The Persons at the beach prototype (first row) contains a man holding a beach-ball photographed from the back, and the Uncovered legs/arms prototype (third row) is found in (nude) statues and a faded Polaroid of a person. The only two PASS images for the Sports-ball prototype (second row) just depict the field and a ball, suggesting that the prototype captures more than just persons." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.288 + ], + "angle": 0, + "content": "The prototypes that are predominantly found in PASS depict concepts or objects that are not found among the 1000 ImageNet categories. Nonetheless, these predominantly PASS prototypes can be found in some ImageNet images where the annotated object is a (small) part of the image. From left to right for row four to six we find the following ImageNet categories: European Gallinule, Ant, Wheelbarrow, Turnstile, Barn, and Headland. We would describe the prototypes in these rows as capturing Flowers, a View down narrow alley, and Sunset with silhouetted foreground respectively. In general, the PASS prototypes that predominantly concern vista or landscape images, which on occasion contain objects from ImageNet categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.892, + 0.456 + ], + "angle": 0, + "content": "For the prototype in the second row of Figure 4 we measure how it is spatially distributed and visualise this for the four ImageNet images in Figure 5. Visualising the attention maps of this prototype shows that the main activations are indeed for the leg and arm areas of the persons depicted. Other parts of the persons receive much less attention than these uncovered areas. Although this is a predominantly ImageNet prototype, and is therefore commonly found in instances of the 'miniskirt' and 'bikini' categories, it is also found in PASS, including in images of mannequins, artworks, and anime of primarily feminine characters." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.892, + 0.638 + ], + "angle": 0, + "content": "Overall, we can conclude that the two-way comparison is highly successful, not only are we able to verify that depictions of humans in PASS are practically non-existent, but by edge-cases we are able to demonstrate the strength of the prototypes. Moreover, based on the discovered prototypes we also gain insights into how these datasets differ, with PASS containing many more vistas and landscapes, whereas ImageNet is strongly object-centric. As such we can conclude that while there is an overlap, PASS differs in more respects from ImageNet than just the presence of humans - which may cast doubt on its status as an ImageNet replacement." + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.655, + 0.877, + 0.671 + ], + "angle": 0, + "content": "Table 1: Performance for linear classifier on ImageNet." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.68, + 0.877, + 0.793 + ], + "angle": 0, + "content": "
Train setBackboneKAccuracy
ImageNetDINO [4]819264.8
PASSPASS-DINO [1]819220.4
PassNet (I+P)DINO [4]819253.2
PassNet (P+I)PASS-DINO [1]819215.9
ImageNetDINO [4]102454.7
ImageNetDINO [4]409663.7
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Quantitative analysis. We perform two quantitative analyses. Firstly, we explore the loss value of each model during training and compare it to the diversity of the prototypes, as measured by the average cosine distance between the prototype weights. Secondly, we train a linear classifier on top of each of the backbones to perform ImageNet clas" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1949" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.409, + 0.09, + 0.563, + 0.105 + ], + "angle": 0, + "content": "ImageNet prototypes" + }, + { + "type": "image", + "bbox": [ + 0.131, + 0.116, + 0.245, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.26, + 0.106, + 0.353, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.371, + 0.118, + 0.48, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.111, + 0.597, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.108, + 0.699, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.728, + 0.124, + 0.837, + 0.176 + ], + 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], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.263, + 0.597, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.639, + 0.244, + 0.691, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.753, + 0.244, + 0.813, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.423, + 0.316, + 0.548, + 0.332 + ], + "angle": 0, + "content": "PASS prototypes" + }, + { + "type": "image", + "bbox": [ + 0.132, + 0.34, + 0.241, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.251, + 0.334, + 0.359, + 0.398 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.369, + 0.34, + 0.478, + 0.398 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.341, + 0.596, + 0.398 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.612, + 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"type": "image", + "bbox": [ + 0.132, + 0.739, + 0.241, + 0.797 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.252, + 0.733, + 0.359, + 0.796 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.37, + 0.733, + 0.478, + 0.796 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.494, + 0.739, + 0.603, + 0.796 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.612, + 0.741, + 0.72, + 0.796 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.74, + 0.839, + 0.796 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.818, + 0.894, + 0.88 + ], + "angle": 0, + "content": "Figure 4: Example images for nine prototypes, each three rows showing predominantly ImageNet, predominantly PASS, and Shared prototypes respectively. The last two columns for rows one through six show some of the few examples found in the other dataset. The last three rows show prototypes common in both with examples of ImageNet in the left three columns, and examples in the right three." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1950" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.09, + 0.156, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.168, + 0.17, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.188, + 0.091, + 0.264, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.189, + 0.155, + 0.264, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.111, + 0.362, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.18, + 0.362, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.383, + 0.091, + 0.457, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.383, + 0.155, + 0.457, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.23, + 0.47, + 0.262 + ], + "angle": 0, + "content": "Figure 5: Attention maps for the four ImageNet images for the Uncovered legs/arms prototype in Figure 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.286, + 0.469, + 0.361 + ], + "angle": 0, + "content": "sification. For these evaluations we compare between two different backbones, one pre-trained on ImageNet [4] and one pre-trained on PASS [1]. Results reported on PassNet are described as either \\((\\mathrm{I} + \\mathrm{P})\\) for the ImageNet pre-trained backbone, or \\(\\mathrm{P} + \\mathrm{I}\\) for the PASS pre-trained backbone." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.362, + 0.47, + 0.603 + ], + "angle": 0, + "content": "Table 1 shows the performance on the ImageNet validation set for a linear classifier trained on top of fixed backbones. We observe that pre-training on ImageNet (unsurprisingly) leads to the best downstream performance on ImageNet, and that training on PASS leads to lower performance. Similarly, for the two backbones we find that the ImageNet pre-trained backbone performs much better. Nonetheless, we see degraded performance for training on PassNet versus ImageNet. The last two rows of Table 1 show that increasing the \\( K \\) value benefits performance, due to computational complexity and diminishing returns no values above 8192 were tested. In conclusion, our quantitative evaluation confirms our modelling choices of using the ImageNet pre-trained backbone with 8192 prototypes, and we will use this configuration for the second case study as well." + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.613, + 0.269, + 0.719 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.272, + 0.614, + 0.456, + 0.719 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.731, + 0.47, + 0.792 + ], + "angle": 0, + "content": "Figure 6: Training loss (left) and average cosine similarity (right) during prototype training. PassNet results \\(\\mathrm{P} + \\mathrm{I}\\) are obtained PASS-DINO backbone and \\(\\mathrm{I} + \\mathrm{P}\\) with the DINO backbone." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.903 + ], + "angle": 0, + "content": "The results in Figure 6 show the training loss and the average cosine similarity between prototypes as training progresses. In both plots we see two groupings of two lines that follow the same pattern. For all models we can see that switching to the hard gumbel-softmax leads to a bump in the loss, but except for \\(\\mathrm{P} + \\mathrm{I}\\) this bump levels off quickly." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.782, + 0.108 + ], + "angle": 0, + "content": "5.4. Three-way Dataset Comparison" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.37 + ], + "angle": 0, + "content": "In the second case study we perform a three-way dataset comparison between the MET, Rijksmuseum, and SemArt datasets. The aim of this comparison is highly exploratory, unlike ImageNet, none of these datasets have pre-defined classes, as such it is not obvious what visual concepts are represented. In Figure 7 we show nine prototypes discovered with ProtoSim, the first three pairs of prototypes are dataset-specific and are predominantly found in the MET, Rijksmuseum, and SemArt respectively. These prototypes were randomly selected from the most dataset-specific prototypes and give a good indication of what is contained in these datasets. The MET dataset contains many 3D objects and often multiple photographs are taken from different angles, as such the first prototype represents Top-down views of vases. The second MET prototype depicts Egyptian wall carvings, which were photographed under raking light to emphasise the height differences across the surface." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.371, + 0.892, + 0.523 + ], + "angle": 0, + "content": "The Rijksmuseum dataset contains many prints or drawings on paper, whilst this is something that can be learnt from the material type overview in [27], the two prototypes depicted show two different groups of visual concepts. The first Rijksmuseum prototype depicts natural history drawings, whereas the second is found in side view portraits. Se-mArt on the other hand consists of mostly fine-art paintings, with the first prototype capturing a stylistic visual concept of Renaissance paintings, the second prototype is a more concrete semantic concept, namely dogs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.734 + ], + "angle": 0, + "content": "Just by exploring the dataset-specific datasets we already get a much better understanding of what is contained in these datasets and what makes them unique. In addition, when we then analyse the shared prototypes we can see that these differences largely persist across different visual concepts. The first shared prototype is of various animals, notably we see that the prototype is not sensitive to material differences, returning both drawings and paintings. The same observation is made for the second shared prototype of baskets, which is matched to drawings, paintings, and photographs of actual baskets. This ability to generalise across modalities is also observed in the third shared prototype of brass instruments, which matches actual instruments and realistic paintings containing similar instruments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Based on the three-way dataset comparison we find that there are degrees of overlap between the datasets, generally we would see that the MET and Rijksmuseum datasets are most similar in types of objects, where MET has a greater focus on physical objects and Rijksmuseum on prints and drawings. Because these two datasets have a relatively small proportion of paintings the similarity with the SemArt dataset is less, nonetheless, we can observe that in terms of visual concepts these datasets represent similar things. In Appendix Section C we show additional prototypes discovered for these artwork datasets." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1951" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.215, + 0.089, + 0.333, + 0.104 + ], + "angle": 0, + "content": "MET prototypes" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.105, + 0.461, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.205, + 0.368, + 0.343, + 0.383 + ], + "angle": 0, + "content": "SemArt prototypes" + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.384, + 0.458, + 0.525 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.204, + 0.54, + 0.34, + 0.555 + ], + "angle": 0, + "content": "Shared prototypes" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.556, + 0.458, + 0.755 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.764, + 0.47, + 0.869 + ], + "angle": 0, + "content": "Figure 7: Example images for nine prototypes, the first six rows are divided in three pairs of prototypes predominantly found in MET, Rijksmuseum, or SemArt respectively. The last three rows show prototypes common across the datasets. Examples with a pink, green, and blue background belong to the MET, Rijksmuseum, or Semart datasets respectively." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.614, + 0.105 + ], + "angle": 0, + "content": "6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.116, + 0.892, + 0.267 + ], + "angle": 0, + "content": "The prototypes obtained with ProtoSim enable dataset comparison, nonetheless, there are two limitations. Firstly, although explanation methods based on visual examples are preferred for visual data [19], there is a mandatory manual inference step to determine what a prototype represents. Whilst previous methods suffer from the same limitation [6, 21] ProtoSim does offer an advantage in that the attention maps can be visualised (i.e., Figure 5). Based on example images and their attention maps it becomes possible to be relatively certain about what the prototype represents." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.267, + 0.893, + 0.403 + ], + "angle": 0, + "content": "Secondly, whilst the ViT backbone can be replaced, for our experiments we found the best results with an ImageNet pre-trained backbone. Since this dataset is one of the ones being compared, but also because this dataset has known biases [41] the choice for a ImageNet pre-trained backbone may influence the prototypes learned. During experiments no such influence was observed, instead it appears ProtoSim is flexible in learning diverse prototypes, nonetheless further investigation is necessary." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.418, + 0.618, + 0.432 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.443, + 0.892, + 0.578 + ], + "angle": 0, + "content": "In this work we presented dataset comparison as a new direction for dataset inspection. To enable dataset comparison across large-scale datasets we introduce ProtoSim which leverages integral prototype-based learning and self-supervised learning to discover visual concepts across datasets. To evaluate our proposed approach we perform two case studies, in the first we compare the PASS and ImageNet datasets, and in the second we perform a three-way comparison between artwork datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.715 + ], + "angle": 0, + "content": "Based on these case studies we find that we can gain new insights into the datasets. In the first case study we find that ImageNet indeed contains many more images with persons, which is in line with the design goal of PASS. However, we still discovered partial and non-photorealistic depictions of persons in PASS, which were not discovered in its person-focused dataset curation process. When comparing the artwork datasets we find that each has a unique focus, but also that various semantic concepts are shared between them." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.716, + 0.892, + 0.776 + ], + "angle": 0, + "content": "Overall, we presented an initial exploration of dataset comparison that will hopefully lead to greater attention for this topic, as it is becoming increasingly necessary to improve dataset inspection techniques." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.791, + 0.597, + 0.806 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.816, + 0.892, + 0.871 + ], + "angle": 0, + "content": "[1] Yuki M Asano, Christian Rupprecht, Andrew Zisserman, and Andrea Vedaldi. 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IEEE. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1954" + } + ] +] \ No newline at end of file diff --git a/2023/Prototype-based Dataset Comparison/02a62e7f-ba00-4044-92de-55f8e976a093_origin.pdf b/2023/Prototype-based Dataset Comparison/02a62e7f-ba00-4044-92de-55f8e976a093_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d413b511b7230ae30c006eac57f365854c2033c4 --- /dev/null +++ b/2023/Prototype-based Dataset Comparison/02a62e7f-ba00-4044-92de-55f8e976a093_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5da27dc874a5b329954a2c21c19b1a43587458f69b638f7c3b723bb7d7fd00d6 +size 9660165 diff --git a/2023/Prototype-based Dataset Comparison/full.md b/2023/Prototype-based Dataset Comparison/full.md new file mode 100644 index 0000000000000000000000000000000000000000..0058b2f4a609ab1c9f55ca3348df9f313fe08081 --- /dev/null +++ b/2023/Prototype-based Dataset Comparison/full.md @@ -0,0 +1,450 @@ +# Prototype-based Dataset Comparison + +Nanne van Noord +University of Amsterdam + +n.j.e.vannoord@uva.nl + +# Dataset-specific Prototypes + +# Shared Prototype + +![](images/799e77ec529e22da1202c02e0346720bb57cab9de8bce83a89815b4536b32caa.jpg) + +![](images/126ecd00c28018c5755a077a5ff840b95d23a348a5cbd1ec256fe156a3ddaf85.jpg) +Figure 1: Prototypes discovered with ProtoSim. By training on both datasets ProtoSim is able to discover prototypes that are dataset specific or shared. From left to right: ImageNet specific “Wedding”, PASS specific “sunset skyline”, and shared “viaduct” prototypes. + +![](images/a8204d7fa91adbdf1ab92a48b767802ed9b7d10fb365f318317e9dbeeee0bb66.jpg) +ImageNet + +![](images/bc95ddf6aa0484d33c242c21b332e5264a1c7c5c85a21a6628f802a9a14fcd16.jpg) + +![](images/3afe4e514435a99d70c55a3bc169d77df92080e5a0ef9d5f9124bd5511a1f981.jpg) + +![](images/17d7d394fc8bfc1e52e73f3f3172c134e3e8539e612bcef41fbf7baa09fef0fa.jpg) +PASS + +![](images/ac0b6bbeff86710511cb88801425bada35c2919ee13ae3b7a9f5c4dc0ad342b2.jpg) + +![](images/82aaa4644bab16352c1ef21b6ab4804c18532d8cdff3b99294d8dcd9cbbd0f58.jpg) + +![](images/381a65a017042c64b6bf510aaca2525edd311676979bac35fd325e37d65a6cd3.jpg) +ImageNet + +![](images/c8e934e539f2ac5281bfa6dcdecb9562dd838e3537b341b9201b676303ae0f54.jpg) + +![](images/98318653b639a4c2e60e01b50d02aad80c09fbbffd1a749f98dc27c00be2f6ef.jpg) + +![](images/6ad907ad43aff95263b3e70ac79c94aedf224482beab96a0975ba940db3f2c14.jpg) + +![](images/384920f5d57cde2b01e55668ca674fa5e0ebdcf9b77fb6919713a4525d89e36c.jpg) + +![](images/ef6898b5ba3c74feaa177bc0886f01b8b2177f599aff21fa3b6229d8cec895ea.jpg) +PASS + +![](images/18267aabae9556211dc7b311525332adcaa81491280d7fda87eb0a946b2b7ebe.jpg) + +# Abstract + +Dataset summarisation is a fruitful approach to dataset inspection. However, when applied to a single dataset the discovery of visual concepts is restricted to those most prominent. We argue that a comparative approach can expand upon this paradigm to enable richer forms of dataset inspection that go beyond the most prominent concepts. + +To enable dataset comparison we present a module that learns concept-level prototypes across datasets. We leverage self-supervised learning to discover these prototypes without supervision, and we demonstrate the benefits of our approach in two case-studies. Our findings show that dataset comparison extends dataset inspection and we hope to encourage more works in this direction. Code and usage instructions available at https://github.com/Nanne/ProtoSim + +# 1. Introduction + +Image datasets are crucial for Computer Vision and due to the algorithms' need for more data they are ever growing in size. At the same time datasets are a major source of bias leading to negative social impact [29, 30]. Unfortunately, it is challenging to determine what is contained in a dataset as their large size combined with the visual nature of the + +data makes manual inspection infeasible. To support users and developers of large-scale datasets in ensuring that the datasets match their usage and design goals it is necessary to develop better tools for dataset inspection. + +A promising direction for generic dataset inspection is found in highly effective approaches that have been proposed for summarisation [35, 9, 14, 44, 24]. A major benefit of these approaches is that they enable explorative dataset inspection without needing supervised pretraining. However, a limitation of these approaches is that they use frequency as a proxy for importance, and on a single dataset therefore only discover those visual concepts which are most prominent. As such, we argue that a comparative approach, which enables discovery of a wider and more diverse range of concepts, is necessary to effectively perform dataset inspection. For instance, the PASS dataset [1] is designed as an ImageNet [32] alternative whilst containing no people, as such it provides us with a testable hypothesis that is comparative in nature. Namely, when comparing these two datasets there should be a disjoint set of visual people-centric concepts that are only found in ImageNet. In a case study we will verify this hypothesis, and demonstrate that dataset comparison can lead to new insights. + +Moreover, an additional limitation of existing summarisation approaches is that they decouple the summarisation process from representation learning, and treat these as two distinct steps by performing the summarisation on a + +pre-defined feature basis, such as GIST descriptors in [35] or LDA clusters in [31]. As recent work on incorporating prototypes into a network's reasoning process has been shown to aid interpretability [23, 6, 33, 13, 45], we propose that this may also be a promising direction for end-to-end dataset comparison. Therefore, we introduce a method for prototype-based dataset comparison, which discovers the visual concepts in a dataset in an end-to-end fashion. + +Dataset prototypes are similar to cluster centroids in that they represent latent points in the feature space that are to be discovered. However, in clustering, similar to prior work on dataset summarisation, these centroids are discovered in a step that is decoupled from learning the feature representations. Whilst some recent works have explored forms of deep clustering [40, 11, 22], they still involve two separate optimisation goals. For example, by having one loss focused on the feature representation and another on clustering [11]. Instead, we propose a simple module ProtoSim that can be integrated into a deep network without changing how it is optimised. To demonstrate this, we add ProtoSim to a Vision Transformer (ViT) [10] and show that it can effectively discover visual concepts across datasets in a self-supervised setting. + +Overall, we make the following contributions: + +- We introduce dataset comparison, a new approach for inspecting datasets. +- To enable dataset comparison we present ProtoSim, a module for integrated learning of dataset prototypes. +- With two case-studies we demonstrate how dataset comparison can be used to gain new insight into datasets. + +# 2. Related work + +Dataset comparison through prototypes is a largely unexplored area of research, but it is similar in spirit to dataset distillation [47, 5] which seeks to distill the knowledge from a large dataset into a small dataset. Most works in dataset distillation generate synthetic examples, as opposed to selecting a set of data instances, to construct the small dataset. These synthetic examples could be considered dataset prototypes, as they represent an aggregate of information that is central to the dataset. A key difference between such prototypes and the prototypes considered in this work, is that the distilled synthetic examples are instance-level prototypes (i.e., complete images that may represent multiple concepts), whereas in this work the aim is to discover concept-level prototypes, which may correspond to global concepts or part-level concepts. + +In the remainder of this section we will further explore how dataset comparison relates to dataset summarisation, prototype learning, and deep clustering. + +# 2.1. Dataset Summarisation + +Manual browsing is a reliable manner to determine what is contained in a dataset, however, browsing even a subset of the data can be time-consuming, which has led to a line of work on dataset summarisation [31, 9, 14, 44, 24]. The aim of dataset summarisation is to find underlying structure or patterns that are shared between data instances to give an overview of what is contained in a dataset. + +An important modeling choice for dataset summarisation is the basis on top of which the patterns are found. Work on mid-level pattern mining aims to find discriminative and representative patches and use these as visual primitive for further analysis [34]. Mid-level pattern mining aims to distinguish itself from "visual word" approaches [36], which were found to mainly capture low-level patterns such as edges and corners [34, 9]. Two notable patch-based approaches are the dataset fingerprinting approach by [31] and the what makes Paris look like Paris? approach by [9]. Patch-based approaches aim to circumvent the limitations of visual words by starting with larger visual structure (i.e., patches at multiple scales). Due to the limitations of pixel-space representations patches cannot be used directly for analysis, instead initial patch-based approaches used feature extractors such as HOG [34, 9] and Convolutional Neural Network (CNN) activations in later works [24]. Using patches has been shown to help steer the results towards more semantically meaningful visual elements, yet they are still restrictive in representational power and in terms of shape (i.e., patches must be rectangular). Moreover, although the starting point is a patch, the features extracted largely determine what the pattern represents and the features are not intrinsically explainable, necessitating posthoc explanations. In contrast, we propose to add ProtoSim to a ViT architecture, which can learn to recognise visual elements of arbitrary shapes and sizes, whilst still focusing on semantically meaningful concepts. + +# 2.2. Prototype Learning + +Prototype-based approaches can be categorised into two areas, the first aims to learn prototypes which represent high-level semantic concepts (i.e., classes) to support zero or few-shot learning [18, 28, 37]. The second area is concerned with finding recurring visual elements and are increasingly used for model explainability [23, 6, 21, 39, 13, 20, 42, 45]. As opposed to post-hoc explainability methods, prototypes are integral to the network and provide explanations of the network's reasoning process [6]. Our approach is part of this second area and we will focus the discussion on integral prototypes for recurring visual elements. + +Integral prototypes have been shown to be effective for supervised multi-class classification [6, 13, 20, 21], deepfake detection [39], and semantic segmentation [48]. In the literature we can recognise two branches of work on integral + +prototypes, the first builds on ProtoPnet [23, 6] and the second on Concept Bottleneck Models (CBM) [13, 20]. Common across these approaches is that they add a layer preceding the output layer that maps the extracted features to prototypes (or concepts) and produce the final output based on the affinity to these prototypes. The logic is thus that because the prototypes are recognisable entities, the prediction is explained by the affinity to the prototypes. The main difference between these branches is that in ProtoPnet-like approaches the prototypes are latent vectors in the embedding space that are learnt end-to-end, whereas CBM approaches use a pre-defined concept library. + +However, these prior approaches all focus on a supervised setting and learn per-class prototypes or concepts, which is severely limiting for dataset summarisation. Instead, we propose to leverage a self-supervised loss to learn prototypes that are not class specific and can represent any visual concept that is present in the data. In particular, our prototypes may represent class-level concepts or segment-level concepts as in CBM [13], but we learn them without concept-level supervision. Previous works learned prototypes for the features at each location in the convolutional output of a Convolutional Neural Network (CNN) backbone [6, 21, 39]. This restricts the spatial extent of the prototypes to size of the receptive field. Additionally, in CNN the output is typically spatially averaged to achieve a global image representation, however, as this is not done for CNN-based prototype approaches they can only learn local and not global prototypes. Instead, we use Vision Transformers (ViT) [10], as they offer solutions for both aforementioned issues capturing local and global concepts of various spatial extents. + +# 2.3. Deep Clustering + +Clustering relates to learning prototypes or concepts in that it has been used to define the library of concept CBM [13], and to an extent the underlying principles match the goal of clustering. In particular, in deep clustering [40, 11, 22] the centroids are learned iteratively, resulting in them being conceptually close to prototypes or CBM-concepts. However, in prior works on deep clustering [40, 11, 22] the clustering objective is separate from the feature representation, whereas in prototype-based approaches the final output is determined by projecting the input to the prototype subspace. + +Another key difference is that by making the prototypes integral to the reasoning process, as in CBM [13] or ProtoP-net [6], it is ensured that the prototypes are of meaningful to the final output. Post-hoc clustering, or as part of a separate objective, may lead to overrepresentation of clusters which capture meaningless information, e.g., orthogonal to the objective that was used to obtain the feature representation. + +# 3. Dataset Comparison + +Given a collection of datasets $X = \{\chi_i\}_{i=1}^{|X|}$ the aim of prototype-based dataset comparison is to discover a set of prototypes $p \in \mathbb{R}^{K \times D}$ that represent visual concepts that may occur predominantly in only one dataset (i.e. dataset-specific prototypes) or visual concepts which occur in two or more datasets (i.e. shared prototypes). An illustration of the dataset comparison workflow is shown in Figure 2. + +We argue that a comparative approach to dataset summarisation, i.e., dataset comparison is vital for gaining insights into datasets. In particular, if $C_*$ is the set of all possible visual concepts, and $C_i$ the visual concepts in ImageNet, then $C_i \subset C_*$ . Given these sets, $C_i$ is a perfect description of what is contained in ImageNet, and the difference $C_* - C_i$ perfectly describes what is not contained in ImageNet. However, as we do not have access to $C_*$ and we have no guaranteed manner of discovering $C_i$ , we can at best learn a set of prototypes $\hat{C}_i$ that approximates $C_i$ . + +As it is an approximation it cannot be concluded from $\hat{C}_i$ that a concept is not in $C_i$ . For example, PASS is designed to not contain humans (i.e., no humans in $C_p$ ), but based on $\hat{C}_p$ it cannot be stated with certainty that no humans are found in PASS, only that no human-centric concepts were discovered. To overcome this limitation we propose to jointly learn $\hat{C}_i$ and $\hat{C}_p$ . Thereby, if we know a concept is in $\hat{C}_i$ and not in $\hat{C}_p$ , we can reasonably conclude that the concept is not in $C_p$ either. + +![](images/36a19db9befefe9249ad63f316577839ecfda8f431da25fb811cfdbd28a62624.jpg) +Figure 2: Overview of the dataset comparison workflow. Datasets are mapped to the prototype embedding space, from where we can inspect and compare individual prototypes. + +Through dataset comparison we are thus able to answer questions that could not be answered by only considering a single dataset, thereby creating new possibilities for dataset inspection for hypothesis verification or comparative exploration. + +# 3.1. Prototype Evaluation + +How to evaluate the prototypes learnt for dataset comparison (or summarisation) is an open problem, as the groundtruth for which visual concepts are contained in the dataset + +![](images/9c7ff26deebc6d53330ef3fa4cce5115a56171801309afd41c4e6b506d5cd965.jpg) +Figure 3: Examples of low-level visual properties discovered with ProtoSim: motion blur (top) and a shallow depth of field (bottom). + +are unknown. Nonetheless, we can leverage the comparative approach by verifying whether the prototypes found match the design goals of the datasets. For instance, as PASS was designed not to contain humans we can explore whether the human-centric prototypes learnt from ImageNet indeed do not occur in PASS. This manner of evaluation forms the basis of our first case study. + +Generally, we consider the prototypes $p$ to be of high-quality when they are distinct and meaningful. Distinct prototypes are able to independently represent a visual concept, this is in contrast to, for example, sparse coding [46] where the aim is to find basis vectors that represent the input through linear combinations. The set of prototypes is meaningful when it can be used to discriminate images within and across the datasets from one another. Requiring that the prototypes are discriminative helps avoid trivial solutions. We can quantitatively measure how discriminative the prototypes are by evaluating them with downstream tasks. + +To ensure that the prototypes are distinct we design our method ProtoSim to perform hard assignment of the prototypes, and by optimising the prototypes with contrastive SSL we ensure that they are discriminative. This alignment between the design of the method (more details in Section 4) and the goal of dataset comparison helps us make certain the prototypes are of high-quality. + +# 3.2. Types of Prototypes + +Within the set of prototypes we can recognise different types of prototypes depending on how they occur across the datasets. For instance, a prototype $p_i$ may be considered dataset-specific when over $95\%$ of its occurrences are only found in a single dataset. By definition, any prototype which is not dataset-specific would then be considered shared. However, various degrees of 'sharedness' may occur depending on the overlap between datasets. + +In theory it may be possible for the datasets in $X$ to be fully distinct, resulting in only dataset-specific prototypes. In practice, we find that prototypes may represent various basic visual properties (see Figure 3), resulting in shared prototypes even when the datasets differ semantically. + +# 4. Prototype-based Learning + +We propose ProtoSim a simple module that can inserted in ViT architectures to enable dataset comparison through integral prototype-based learning. ProtoSim differs from previous prototype layers in three ways, firstly, the prototypes learned with ProtoSim are distinct (as opposed to linear mixtures), secondly, ProtoSim is specifically designed for ViT architectures and learns prototypes from a set of tokens, rather than a single embedding vector. Lastly, the prototypes in ProtoSim are not class-specific, instead we learn a single pool of prototypes that may occur in any image. + +# 4.1. ProtoSim + +In order to learn which visual concepts are present in a dataset we aim to optimise a set of $K$ learnable prototypes $p \in \mathbb{R}^{K \times D}$ . By designing the prototypes to be part of a prototype layer (i.e. ProtoSim) we can directly optimise them in and end-to-end fashion as part of ViT that we add the layer to. Specifically, given the token embeddings $z \in \mathbb{R}^{N + 1 \times D}$ produced by a ViT, ProtoSim maps these to the prototype embeddings $\hat{z} \in \mathbb{R}^{N + 1 \times D}$ , where $D$ is the token vector size. During this mapping each token is replaced with the most similar prototype in $p$ . + +In [23, 6] the similarity to each of the class-specific prototypes is determined by calculating the squared $L^2$ distance and selecting the closest prototype with a max operation. Because our aim is to find prototypes that recur in the entire dataset, instead of finding class-specific prototypes, we propose a surprisingly simple formulation of this process by using a reversed version of dot-product attention [25] to efficiently calculate attention across all the prototypes: + +$$ +a = \operatorname {s o f t m a x} \left(p z ^ {\intercal}\right) \tag {1} +$$ + +$$ +\hat {z} = a ^ {\intercal} p. \tag {2} +$$ + +Here the attention mask $a$ represents the soft-assignment of prototypes to tokens, as such each token embedding $\hat{z}$ is a linear combination of prototypes. This is not desirable as our aim is to learn distinct prototypes which independently represent a visual concept, as this enables better summarisation and greater interpretability. To obtain a hard assignment we replace the softmax operation in Equation 1 with gumbel-softmax [17]: + +$$ +a = \operatorname {g u m b e l - s o f t m a x} (p z ^ {\intercal}). \tag {3} +$$ + +For simplicity we drop the temperature parameter, as it empirically does not meaningfully influence performance and can be kept fixed at 1. The benefit of gumbel-softmax is that it maintains gradient-flow whilst enabling hard attention. Based on this modification $a$ now represents a hard assignment matrix which is used to replace each token with a prototype. As a visual concept can occur across multiple spatial locations there is no constraint on how often a prototype can be assigned. + +# 4.2. Backbone + +Whilst ProtoSim functions as a generic network module, with the only requirement being an a two-dimensional input of $K \times D$ , we specifically apply it to ViT in this work as these offer some benefits over CNN. In particular, in ViT all tokens can share information with all other tokens, as such there is no restriction on the spatial extent of the learned prototypes. Moreover, whilst most tokens in a ViT represent some spatial region of the image (i.e. patch tokens), the class token takes on the role of a global image representation. This allows us to learn prototypes that are local (i.e. only assigned to patch tokens) and global (i.e. only assigned to the class token) without modifying the architecture. + +ProtoSim is placed at the end of the backbone ViT in the network architecture. Formally, the input $x \in \mathbb{R}^{H \times W \times C}$ is divided into flattened patch tokens $x_{p} \in \mathbb{R}^{N \times (P^{2} \cdot C)}$ , where $H, W,$ and $C$ are the height, width, and channel dimensionality of the input and $P$ the patch size hyperparameter. In addition to $N$ patch tokens, a learnable class token $x_{class}$ is prepended to input. No class labels are used during training, but we retain the ViT terminology of referring to this as a class token. After the embedding phase the tokens are passed through a series of transformer blocks resulting in the token embeddings $z \in \mathbb{R}^{N + 1 \times D}$ , where $D$ is the embedded token vector size. $z$ is passed through the ProtoSim layer resulting in the prototype embeddings $\hat{z}$ . + +# 4.3. Training Objective + +The training objective determines the prototypes. For instance, a classification-based objective results in prototypes that are indicative of the classes (as in ProtoPnet [6] or CBM [20]). Yet, such an objective may result in a poor coverage of concepts that are not part of the annotated classes. Because we strive for good coverage we focus on a Contrastive Self-Supervised Learning (Contrastive SSL) objective. In particular, because Constrastive SSL optimises for fine-grained discrimination between images (rather than classes) and has been shown to be perform well on a variety of downstream tasks [7]. + +From the recently proposed Contrastive SSL methods [16, 15, 7, 8, 3, 4], only DINO [4] has been specifically designed to work with ViT. As such, we minimise the DINO loss as the training objective: + +$$ +\min _ {\theta_ {s}} \sum_ {x \in \{x _ {1} ^ {g}, x _ {2} ^ {g} \}} \sum_ { \begin{array}{c} x ^ {\prime} \in V \\ x ^ {\prime} \neq x \end{array} } H (P _ {t} (x), P _ {s} (x ^ {\prime})), \qquad (4) +$$ + +where $H(a,b) = -a\log b$ , $x_1^g$ and $x_2^g$ are two large crops from the input, $V$ a set of data-augmented smaller crops, and $P_t$ and $P_s$ are the teacher and student networks respectively, each with a ProtoSim layer added to the backbone. We refer to the excellent work by [4] for further details. + +# 5. Case Studies + +In this section we present two case studies, the first is a comparison between two datasets (i.e., two-way dataset comparison) aimed at determining how the PASS [1] dataset differs from ImageNet [32]. Because the design goal of PASS was to present an alternative for ImageNet that does not contain humans we test whether this is achieved successfully. The second case study focuses on a three-way dataset comparison scenario wherein we explore how three artwork datasets differ. These three datasets were designed for different tasks and contain images from different museum collections, as such based on these meta properties of the datasets it is challenging to determine how they actually relate. With these two case studies we put the two main applications of dataset comparison to the test, verifying a design goal of a dataset, and exploring unknown datasets. In addition, in Supplementary Section A we demonstrate how ProtoSim can also be used on a single dataset. + +# 5.1. Datasets + +For the first case study we focus on ImageNet and PASS, we briefly describe both: + +- ImageNet [32] is a widely used dataset available in two versions: ImageNet-21K and ImageNet-1K. In this work we focus on ImageNet-1K consisting of approximately 1.2 million training images and 1000 classes. Despite how widely used it is, and how influential it has been, ImageNet-1K has also been criticised for its biased depictions of persons [30]. +- PASS [1] is a recently proposed alternative for ImageNet with the intention of not containing persons to avoid the issues in ImageNet. PASS contains approximately 1.4 million unlabeled images and can only be used for self-supervised training. + +In the second case study we focus on three artwork datasets that have been used for a variety of different tasks: + +- MET [43] is a dataset designed for instance-level recognition, its training set contains over 400k images from more than 224k different objects held by the Metropolitan Museum of Art in New York. +- Rijksmuseum [27] presents a set of tasks which are museum-centric, focusing on predicting various types of metadata (i.e., artist, object-type, material usage, and creation year). It consists of 110k images obtained from collections held by the Rijksmuseum in Amsterdam. +- SemArt [12] consists of images collected from the Web Gallery of Art a virtual museum with predominantly European fine-art. The SemArt dataset contains + +21k images described with similar metadata as the Rijksmuseum dataset, but in addition also has textual descriptions in the form of artistic comments. + +The available metadata for these three artwork datasets differs, but notably none of these datasets have been described with semantic classes as, for example, found in ImageNet. As such, we do not have prior information about what type of visual concepts are represented in the artwork datasets. + +# 5.2. Experimental setup + +The backbone used is the DeIT-S model [38] with a patch size of $16 \times 16$ . The parameters of the backbone are fixed during prototype learning and training is done on a single NVIDIA RTX 3090 with a batch size of 128 and learning rate of $5\mathrm{e} - 5$ for 20 epochs. For the first 15 epochs we train with soft gumbel-softmax, after which we switch the student to the hard 'straight-through' gumbel-softmax, to ensure more independent prototypes. In line with previous works (e.g., [2, 26]) we set $K$ to 8192. + +For quantitative evaluation we follow the standard procedure of training a linear classifier on frozen features [4, 16]. We freeze the backbone and the ProtoSim layer and then train a linear classifier for 20 epochs with a learning rate of 0.001 and a batch size of 256. + +# 5.3. Two-way Dataset Comparison + +For the two-way dataset comparison case study we focus on the PASS and ImageNet datasets, to this end we learn prototypes on the union of these two datasets, which we refer to as the PassNet dataset, and present the results in this section. All results in this section are obtained with ProtoSim trained on top of the DINO backbone pretrained on ImageNet. A key finding of this comparison is that ProtoSim learns both dataset-specific prototypes (i.e., prototypes that predominantly activate for one dataset) and shared prototypes (i.e., prototypes that occur frequently in both datasets). In Figure 4 we show nine prototypes which are predominantly found in ImageNet, PASS, or are shared equally among both datasets. Additional examples of prototypes are shown in the supplementary material. + +The prototypes that are predominantly found in ImageNet contain people (i.e., over $99\%$ of images for which they activate are found in ImageNet). However, despite its design goal we do find persons for these prototypes in PASS. The Persons at the beach prototype (first row) contains a man holding a beach-ball photographed from the back, and the Uncovered legs/arms prototype (third row) is found in (nude) statues and a faded Polaroid of a person. The only two PASS images for the Sports-ball prototype (second row) just depict the field and a ball, suggesting that the prototype captures more than just persons. + +The prototypes that are predominantly found in PASS depict concepts or objects that are not found among the 1000 ImageNet categories. Nonetheless, these predominantly PASS prototypes can be found in some ImageNet images where the annotated object is a (small) part of the image. From left to right for row four to six we find the following ImageNet categories: European Gallinule, Ant, Wheelbarrow, Turnstile, Barn, and Headland. We would describe the prototypes in these rows as capturing Flowers, a View down narrow alley, and Sunset with silhouetted foreground respectively. In general, the PASS prototypes that predominantly concern vista or landscape images, which on occasion contain objects from ImageNet categories. + +For the prototype in the second row of Figure 4 we measure how it is spatially distributed and visualise this for the four ImageNet images in Figure 5. Visualising the attention maps of this prototype shows that the main activations are indeed for the leg and arm areas of the persons depicted. Other parts of the persons receive much less attention than these uncovered areas. Although this is a predominantly ImageNet prototype, and is therefore commonly found in instances of the 'miniskirt' and 'bikini' categories, it is also found in PASS, including in images of mannequins, artworks, and anime of primarily feminine characters. + +Overall, we can conclude that the two-way comparison is highly successful, not only are we able to verify that depictions of humans in PASS are practically non-existent, but by edge-cases we are able to demonstrate the strength of the prototypes. Moreover, based on the discovered prototypes we also gain insights into how these datasets differ, with PASS containing many more vistas and landscapes, whereas ImageNet is strongly object-centric. As such we can conclude that while there is an overlap, PASS differs in more respects from ImageNet than just the presence of humans - which may cast doubt on its status as an ImageNet replacement. + +Table 1: Performance for linear classifier on ImageNet. + +
Train setBackboneKAccuracy
ImageNetDINO [4]819264.8
PASSPASS-DINO [1]819220.4
PassNet (I+P)DINO [4]819253.2
PassNet (P+I)PASS-DINO [1]819215.9
ImageNetDINO [4]102454.7
ImageNetDINO [4]409663.7
+ +Quantitative analysis. We perform two quantitative analyses. Firstly, we explore the loss value of each model during training and compare it to the diversity of the prototypes, as measured by the average cosine distance between the prototype weights. Secondly, we train a linear classifier on top of each of the backbones to perform ImageNet clas + +![](images/c80bbc75a3abef34b35710ee859acbffc6bf260e29bcbd246afe94ae6ea595c2.jpg) + +![](images/9803b847478edbafe40da8b27e13699e9247dfd2522afa02a9937122bc38efd3.jpg) + +![](images/00222b6416b3a9c7536ad7d1d3f0463fb749ab1702f78cc9234de2ce41b4baf5.jpg) +ImageNet prototypes + +![](images/94cb6aed37fd3df3d36c4baea47ba439f9d3c84bc0f6003f87cf7de6ebb9c373.jpg) + +![](images/cc285b3d0b97ecd162767eae8eda16dee3fdd11772834c0e2790151fe11edd38.jpg) + +![](images/bbdd331cc5851fed85497831aeaba8efe4498a5c42483cd17c2fd81d9a4b13bc.jpg) + +![](images/4f11a057d69c4f03e02f9495ef583f5a73e1e529bf3a60a0f54a7554047fa1ba.jpg) + +![](images/70f9ee76d08888ea27b99611907af00d4592e78654a996d7d0951b934233b1a8.jpg) + +![](images/83b3a3a484ca452c029fb67624bfcd3e1db969deed19f1c3e9e41b355c789f5a.jpg) + +![](images/40fda8c9c82df060be5543129feafa0631f89d6292e8c33c43d8155cc8efca1e.jpg) + +![](images/4ac73a01d3e60ea8e51d1191640268f708b5ead41c5375d26d515dfbccc8756f.jpg) + +![](images/9f23c6d6ec7c8d2a3eafb21cb643df147006fe3b2acf889a1d49765228b8646e.jpg) + +![](images/5e1645594f55d40b7575af225f9e673b85133a926eae432420c0f473e22d3047.jpg) + +![](images/906bff753491e75a773a0b2199bf1c05fa61df2c23f59bf7ec327af4648b2a17.jpg) + +![](images/03c9bc346ecadb3f95829d74b83ad5a435e4656632b019fd28c5b037e09dff14.jpg) +PASS prototypes + +![](images/c025bb7357f44f2fcf031dda560f9105210d9073ae23ddb53eb202bc650e4298.jpg) + +![](images/e99efab4cacd17624e40771bfd29ea240939c5a84b27bc1f6f09c10e51db19a2.jpg) + +![](images/b008180b6a6e8ed3fe02e37d602de13c384dc00b588736cdea97e9fd7f1c443d.jpg) + +![](images/ae7174d545b77b3f97daa4f20f4669ff970cb3f6430afe34d4e6b68206279a10.jpg) + +![](images/f469b8ab27659ae9c11a26bc382b9e702cfaf0ca9a4439ffd67e95ffabc552c2.jpg) + +![](images/4c97c514006f19fd7cef1bafc990155aade60d3da72ed285cffc963eafd71b4f.jpg) + +![](images/23f2d24c3c6d29c4ba65f400a74d5e574c0e3ae48be0305d003053d5bb8c73d5.jpg) + +![](images/ed2bd1e557afd87d8f648d009cc5528c1517891e8ce788fd3dcf6b25a602fda5.jpg) + +![](images/ee4a661e69abd778bcccc9474a1fb50be0560c0558d7d4ce14015195682d4a25.jpg) + +![](images/fac513f4300be6f2609487560b9ce443bfd0e958877b6d892f29cb1522d5ad2c.jpg) + +![](images/c10fae786b158210a47eb31380f76c2c34cc3d8de40ea669bd534e8b2aee6c33.jpg) + +![](images/1ef62682390f14989886528c8ee0b9da76050b41d65562d550a911aff7922633.jpg) + +![](images/4120d37d2a945623bad47e1e7b2a2f8f2bc91965906fab734e73152f23fabb34.jpg) + +![](images/446b25cfe80881c3995bb25c795db6d16bc3241d98da7172023394d603231511.jpg) + +![](images/35891a9c855ab94a8da93360cddbdc58dbd82242c7e40f551701b577d20ad287.jpg) + +![](images/cfdccc5a29249f47334d2314e4fc2bbcc7322bda3b0a155abe0505165d88baa8.jpg) + +![](images/87b11e95388c2f4cc32afde9c44d16978988937aee30bcdc5e9a0bc196a7584b.jpg) + +![](images/577dae3e26e74117a4515618ca308f79766d4c211d680cb4cb2d4c9c5878f4d3.jpg) + +![](images/87a47b133a65e2f72f49e7c964c51c86d925978e0285afaa75a45fe29870fdbd.jpg) + +![](images/8131ea0aead303dbea000794f33719069b4cabc63131982a9db7847589eb10aa.jpg) + +![](images/585436a345a87a8df5e1b7bc8d677cbdef76b0a8cc9bc7562a7f25cbba334591.jpg) + +![](images/a2c60890b9db408110edc38260f4db8c74a98473400cfe74c203a2afcec2df48.jpg) + +![](images/dcebac5dba7637e4bd41d3d5cebfa8f3d1f319b368ce4d7a8e11aad3c0390b63.jpg) + +![](images/8b7a99b57e5bcc4c56ac2c3956ed4104c677874391fabfff5d10b69202bd0c53.jpg) +Shared prototypes + +![](images/20d5e3b6e67381dfb33eed49654f809a2dfc271619653cf137d1fa01506b1998.jpg) + +![](images/08249587f51c93d8a68d3572abba79a997dbefd84d198ac46b8cf1a603abb78c.jpg) + +![](images/886f822c97a8b3950b9649f4fc6b6b401ae394c12dd89984a8ab8faab4daa9c1.jpg) + +![](images/837f59367104cfb7f07f91cea95083672a3b4dcc93052537bebce45a055b922a.jpg) + +![](images/fb5b811c66996def5d21ac1108681b391043db225bb986bac728575b1b6c3e82.jpg) + +![](images/0d31c5ba3e1e9ab37081a3ac13750349d84dc72ed0415972da8d2843f3fd26e3.jpg) + +![](images/202fdda764b1f61cc841b3a01a854b6ae4d7d6f9659662d226d78470c1899541.jpg) + +![](images/12d68761de45c75489787e3b431162a4d33acce6b8e1b5425e48ea88577adc5b.jpg) + +![](images/e78ec2add5e85a613900cf337ffa38e0c5adc5e29633ad1122a4b30f56b78039.jpg) + +![](images/1bfaf6e09d272d56d96426a273419d438339a3d4f1a848bdc7b6ad73e93b4bc1.jpg) +Figure 4: Example images for nine prototypes, each three rows showing predominantly ImageNet, predominantly PASS, and Shared prototypes respectively. The last two columns for rows one through six show some of the few examples found in the other dataset. The last three rows show prototypes common in both with examples of ImageNet in the left three columns, and examples in the right three. + +![](images/e03821feff5e6592738b89692d383d2c68ee076baf14c7b18825b98091d67fa0.jpg) + +![](images/d15cc0bdc86321c3d8e723bbb32ad0fd7117c3c25484b06084bec3b47a300db3.jpg) + +![](images/67c89a5320b64a28c007d6002d979eb5be35eab6b0d883bb29080b3ce99c8ddb.jpg) + +![](images/f5c951372b267d28fd48d956e2de99045f7ddfba02782408ddca7e33cf0f8cdd.jpg) + +![](images/9152648ec114cdcdc03bbd8c7b37568f6772a0e9906cb00cb4962fe0b375936d.jpg) + +![](images/7d4a712213c49814e13958b13fa9017d7b1ef0f3e006197e348b3286f10c3cb9.jpg) + +![](images/bbceb2e0736191fe00f490b5d197ffff59b58a944f46d757cde1a04b32a368d3.jpg) +Figure 5: Attention maps for the four ImageNet images for the Uncovered legs/arms prototype in Figure 4. + +![](images/32ff41bc4db8bb02dc9d78d906eb852012a0b4e638a310520f18dfa5f90e9c5d.jpg) + +![](images/004391f7cd35dde08d671075a42ca21c0a96d1ad0e9ee0673a45bc2089b95a76.jpg) + +![](images/b31840e82ee21f409ef36d017ed63779b2ba54864fb5f5a088c9321154b6113d.jpg) + +![](images/07e27ebe519429371dd94bd5d912d756b1dbd546be38ffb33a7625301c31d58c.jpg) + +![](images/80e75a2e5e5050b60be0932b35ce1eb7524bf94536b8a8ea95d46af909b17233.jpg) + +![](images/dcb18a7e60ea44a1891917928f94f1294dafb7dffdece0a167d87cccf2b0d82b.jpg) + +sification. For these evaluations we compare between two different backbones, one pre-trained on ImageNet [4] and one pre-trained on PASS [1]. Results reported on PassNet are described as either $(\mathrm{I} + \mathrm{P})$ for the ImageNet pre-trained backbone, or $\mathrm{P} + \mathrm{I}$ for the PASS pre-trained backbone. + +Table 1 shows the performance on the ImageNet validation set for a linear classifier trained on top of fixed backbones. We observe that pre-training on ImageNet (unsurprisingly) leads to the best downstream performance on ImageNet, and that training on PASS leads to lower performance. Similarly, for the two backbones we find that the ImageNet pre-trained backbone performs much better. Nonetheless, we see degraded performance for training on PassNet versus ImageNet. The last two rows of Table 1 show that increasing the $K$ value benefits performance, due to computational complexity and diminishing returns no values above 8192 were tested. In conclusion, our quantitative evaluation confirms our modelling choices of using the ImageNet pre-trained backbone with 8192 prototypes, and we will use this configuration for the second case study as well. + +![](images/39ff7cdcb8742f4d536e413fe1ad53b07451f10e04260fa1915d40a3edee2c61.jpg) +Figure 6: Training loss (left) and average cosine similarity (right) during prototype training. PassNet results $\mathrm{P} + \mathrm{I}$ are obtained PASS-DINO backbone and $\mathrm{I} + \mathrm{P}$ with the DINO backbone. + +![](images/6ecab230bf582637f070de7f053ca80d59804818b1434461d10c4c36504da765.jpg) + +The results in Figure 6 show the training loss and the average cosine similarity between prototypes as training progresses. In both plots we see two groupings of two lines that follow the same pattern. For all models we can see that switching to the hard gumbel-softmax leads to a bump in the loss, but except for $\mathrm{P} + \mathrm{I}$ this bump levels off quickly. + +# 5.4. Three-way Dataset Comparison + +In the second case study we perform a three-way dataset comparison between the MET, Rijksmuseum, and SemArt datasets. The aim of this comparison is highly exploratory, unlike ImageNet, none of these datasets have pre-defined classes, as such it is not obvious what visual concepts are represented. In Figure 7 we show nine prototypes discovered with ProtoSim, the first three pairs of prototypes are dataset-specific and are predominantly found in the MET, Rijksmuseum, and SemArt respectively. These prototypes were randomly selected from the most dataset-specific prototypes and give a good indication of what is contained in these datasets. The MET dataset contains many 3D objects and often multiple photographs are taken from different angles, as such the first prototype represents Top-down views of vases. The second MET prototype depicts Egyptian wall carvings, which were photographed under raking light to emphasise the height differences across the surface. + +The Rijksmuseum dataset contains many prints or drawings on paper, whilst this is something that can be learnt from the material type overview in [27], the two prototypes depicted show two different groups of visual concepts. The first Rijksmuseum prototype depicts natural history drawings, whereas the second is found in side view portraits. Se-mArt on the other hand consists of mostly fine-art paintings, with the first prototype capturing a stylistic visual concept of Renaissance paintings, the second prototype is a more concrete semantic concept, namely dogs. + +Just by exploring the dataset-specific datasets we already get a much better understanding of what is contained in these datasets and what makes them unique. In addition, when we then analyse the shared prototypes we can see that these differences largely persist across different visual concepts. The first shared prototype is of various animals, notably we see that the prototype is not sensitive to material differences, returning both drawings and paintings. The same observation is made for the second shared prototype of baskets, which is matched to drawings, paintings, and photographs of actual baskets. This ability to generalise across modalities is also observed in the third shared prototype of brass instruments, which matches actual instruments and realistic paintings containing similar instruments. + +Based on the three-way dataset comparison we find that there are degrees of overlap between the datasets, generally we would see that the MET and Rijksmuseum datasets are most similar in types of objects, where MET has a greater focus on physical objects and Rijksmuseum on prints and drawings. Because these two datasets have a relatively small proportion of paintings the similarity with the SemArt dataset is less, nonetheless, we can observe that in terms of visual concepts these datasets represent similar things. In Appendix Section C we show additional prototypes discovered for these artwork datasets. + +![](images/4b54cca991050a9bdc1cc85bf6801501086966877cbdfb7769f68402bae78505.jpg) +MET prototypes + +![](images/b158d5abd036f4e300c09b3d949283355a0484b1f2e72d856332f7df4d28ab10.jpg) +SemArt prototypes + +![](images/9af90c233ef8a0c4b5975ad4d52a8432f0371a2887cc19c52a267b6c12babc4d.jpg) +Shared prototypes +Figure 7: Example images for nine prototypes, the first six rows are divided in three pairs of prototypes predominantly found in MET, Rijksmuseum, or SemArt respectively. The last three rows show prototypes common across the datasets. Examples with a pink, green, and blue background belong to the MET, Rijksmuseum, or Semart datasets respectively. + +# 6. Discussion + +The prototypes obtained with ProtoSim enable dataset comparison, nonetheless, there are two limitations. Firstly, although explanation methods based on visual examples are preferred for visual data [19], there is a mandatory manual inference step to determine what a prototype represents. Whilst previous methods suffer from the same limitation [6, 21] ProtoSim does offer an advantage in that the attention maps can be visualised (i.e., Figure 5). Based on example images and their attention maps it becomes possible to be relatively certain about what the prototype represents. + +Secondly, whilst the ViT backbone can be replaced, for our experiments we found the best results with an ImageNet pre-trained backbone. Since this dataset is one of the ones being compared, but also because this dataset has known biases [41] the choice for a ImageNet pre-trained backbone may influence the prototypes learned. During experiments no such influence was observed, instead it appears ProtoSim is flexible in learning diverse prototypes, nonetheless further investigation is necessary. + +# 7. Conclusion + +In this work we presented dataset comparison as a new direction for dataset inspection. To enable dataset comparison across large-scale datasets we introduce ProtoSim which leverages integral prototype-based learning and self-supervised learning to discover visual concepts across datasets. To evaluate our proposed approach we perform two case studies, in the first we compare the PASS and ImageNet datasets, and in the second we perform a three-way comparison between artwork datasets. + +Based on these case studies we find that we can gain new insights into the datasets. In the first case study we find that ImageNet indeed contains many more images with persons, which is in line with the design goal of PASS. 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"bbox": [ + 46, + 413, + 287, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 484 + ], + "type": "text", + "content": "Dataset summarisation is a fruitful approach to dataset inspection. However, when applied to a single dataset the discovery of visual concepts is restricted to those most prominent. We argue that a comparative approach can expand upon this paradigm to enable richer forms of dataset inspection that go beyond the most prominent concepts." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 46, + 486, + 289, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 289, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 289, + 594 + ], + "type": "text", + "content": "To enable dataset comparison we present a module that learns concept-level prototypes across datasets. We leverage self-supervised learning to discover these prototypes without supervision, and we demonstrate the benefits of our approach in two case-studies. Our findings show that dataset comparison extends dataset inspection and we hope to encourage more works in this direction. Code and usage instructions available at https://github.com/Nanne/ProtoSim" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 47, + 620, + 128, + 632 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 620, + 128, + 632 + ], + "spans": [ + { + "bbox": [ + 47, + 620, + 128, + 632 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "content": "Image datasets are crucial for Computer Vision and due to the algorithms' need for more data they are ever growing in size. At the same time datasets are a major source of bias leading to negative social impact [29, 30]. Unfortunately, it is challenging to determine what is contained in a dataset as their large size combined with the visual nature of the" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 388, + 546, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 546, + 435 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 546, + 435 + ], + "type": "text", + "content": "data makes manual inspection infeasible. To support users and developers of large-scale datasets in ensuring that the datasets match their usage and design goals it is necessary to develop better tools for dataset inspection." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 304, + 437, + 546, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 546, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 546, + 664 + ], + "type": "text", + "content": "A promising direction for generic dataset inspection is found in highly effective approaches that have been proposed for summarisation [35, 9, 14, 44, 24]. A major benefit of these approaches is that they enable explorative dataset inspection without needing supervised pretraining. However, a limitation of these approaches is that they use frequency as a proxy for importance, and on a single dataset therefore only discover those visual concepts which are most prominent. As such, we argue that a comparative approach, which enables discovery of a wider and more diverse range of concepts, is necessary to effectively perform dataset inspection. For instance, the PASS dataset [1] is designed as an ImageNet [32] alternative whilst containing no people, as such it provides us with a testable hypothesis that is comparative in nature. Namely, when comparing these two datasets there should be a disjoint set of visual people-centric concepts that are only found in ImageNet. In a case study we will verify this hypothesis, and demonstrate that dataset comparison can lead to new insights." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Moreover, an additional limitation of existing summarisation approaches is that they decouple the summarisation process from representation learning, and treat these as two distinct steps by performing the summarisation on a" + } + ] + } + ], + "index": 35 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1944" + } + ] + } + ], + "index": 36 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": "pre-defined feature basis, such as GIST descriptors in [35] or LDA clusters in [31]. As recent work on incorporating prototypes into a network's reasoning process has been shown to aid interpretability [23, 6, 33, 13, 45], we propose that this may also be a promising direction for end-to-end dataset comparison. Therefore, we introduce a method for prototype-based dataset comparison, which discovers the visual concepts in a dataset in an end-to-end fashion." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 169, + 288, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 169, + 288, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 169, + 288, + 348 + ], + "type": "text", + "content": "Dataset prototypes are similar to cluster centroids in that they represent latent points in the feature space that are to be discovered. However, in clustering, similar to prior work on dataset summarisation, these centroids are discovered in a step that is decoupled from learning the feature representations. Whilst some recent works have explored forms of deep clustering [40, 11, 22], they still involve two separate optimisation goals. For example, by having one loss focused on the feature representation and another on clustering [11]. Instead, we propose a simple module ProtoSim that can be integrated into a deep network without changing how it is optimised. To demonstrate this, we add ProtoSim to a Vision Transformer (ViT) [10] and show that it can effectively discover visual concepts across datasets in a self-supervised setting." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 350, + 246, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 350, + 246, + 361 + ], + "spans": [ + { + "bbox": [ + 59, + 350, + 246, + 361 + ], + "type": "text", + "content": "Overall, we make the following contributions:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 365, + 287, + 460 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 59, + 365, + 287, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 365, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 59, + 365, + 287, + 388 + ], + "type": "text", + "content": "- We introduce dataset comparison, a new approach for inspecting datasets." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 396, + 287, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 396, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 59, + 396, + 287, + 419 + ], + "type": "text", + "content": "- To enable dataset comparison we present ProtoSim, a module for integrated learning of dataset prototypes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 426, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 426, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 59, + 426, + 287, + 460 + ], + "type": "text", + "content": "- With two case-studies we demonstrate how dataset comparison can be used to gain new insight into datasets." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 475, + 132, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 475, + 132, + 488 + ], + "spans": [ + { + "bbox": [ + 47, + 475, + 132, + 488 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 498, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 676 + ], + "type": "text", + "content": "Dataset comparison through prototypes is a largely unexplored area of research, but it is similar in spirit to dataset distillation [47, 5] which seeks to distill the knowledge from a large dataset into a small dataset. Most works in dataset distillation generate synthetic examples, as opposed to selecting a set of data instances, to construct the small dataset. These synthetic examples could be considered dataset prototypes, as they represent an aggregate of information that is central to the dataset. A key difference between such prototypes and the prototypes considered in this work, is that the distilled synthetic examples are instance-level prototypes (i.e., complete images that may represent multiple concepts), whereas in this work the aim is to discover concept-level prototypes, which may correspond to global concepts or part-level concepts." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "In the remainder of this section we will further explore how dataset comparison relates to dataset summarisation, prototype learning, and deep clustering." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 72, + 440, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 440, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 440, + 84 + ], + "type": "text", + "content": "2.1. Dataset Summarisation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 90, + 545, + 173 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 173 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 173 + ], + "type": "text", + "content": "Manual browsing is a reliable manner to determine what is contained in a dataset, however, browsing even a subset of the data can be time-consuming, which has led to a line of work on dataset summarisation [31, 9, 14, 44, 24]. The aim of dataset summarisation is to find underlying structure or patterns that are shared between data instances to give an overview of what is contained in a dataset." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 174, + 546, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 174, + 546, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 174, + 546, + 509 + ], + "type": "text", + "content": "An important modeling choice for dataset summarisation is the basis on top of which the patterns are found. Work on mid-level pattern mining aims to find discriminative and representative patches and use these as visual primitive for further analysis [34]. Mid-level pattern mining aims to distinguish itself from \"visual word\" approaches [36], which were found to mainly capture low-level patterns such as edges and corners [34, 9]. Two notable patch-based approaches are the dataset fingerprinting approach by [31] and the what makes Paris look like Paris? approach by [9]. Patch-based approaches aim to circumvent the limitations of visual words by starting with larger visual structure (i.e., patches at multiple scales). Due to the limitations of pixel-space representations patches cannot be used directly for analysis, instead initial patch-based approaches used feature extractors such as HOG [34, 9] and Convolutional Neural Network (CNN) activations in later works [24]. Using patches has been shown to help steer the results towards more semantically meaningful visual elements, yet they are still restrictive in representational power and in terms of shape (i.e., patches must be rectangular). Moreover, although the starting point is a patch, the features extracted largely determine what the pattern represents and the features are not intrinsically explainable, necessitating posthoc explanations. In contrast, we propose to add ProtoSim to a ViT architecture, which can learn to recognise visual elements of arbitrary shapes and sizes, whilst still focusing on semantically meaningful concepts." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 515, + 421, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 421, + 529 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 421, + 529 + ], + "type": "text", + "content": "2.2. Prototype Learning" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 534, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 665 + ], + "type": "text", + "content": "Prototype-based approaches can be categorised into two areas, the first aims to learn prototypes which represent high-level semantic concepts (i.e., classes) to support zero or few-shot learning [18, 28, 37]. The second area is concerned with finding recurring visual elements and are increasingly used for model explainability [23, 6, 21, 39, 13, 20, 42, 45]. As opposed to post-hoc explainability methods, prototypes are integral to the network and provide explanations of the network's reasoning process [6]. Our approach is part of this second area and we will focus the discussion on integral prototypes for recurring visual elements." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": "Integral prototypes have been shown to be effective for supervised multi-class classification [6, 13, 20, 21], deepfake detection [39], and semantic segmentation [48]. In the literature we can recognise two branches of work on integral" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1945" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "prototypes, the first builds on ProtoPnet [23, 6] and the second on Concept Bottleneck Models (CBM) [13, 20]. Common across these approaches is that they add a layer preceding the output layer that maps the extracted features to prototypes (or concepts) and produce the final output based on the affinity to these prototypes. The logic is thus that because the prototypes are recognisable entities, the prediction is explained by the affinity to the prototypes. The main difference between these branches is that in ProtoPnet-like approaches the prototypes are latent vectors in the embedding space that are learnt end-to-end, whereas CBM approaches use a pre-defined concept library." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 219, + 289, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 219, + 289, + 458 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 289, + 458 + ], + "type": "text", + "content": "However, these prior approaches all focus on a supervised setting and learn per-class prototypes or concepts, which is severely limiting for dataset summarisation. Instead, we propose to leverage a self-supervised loss to learn prototypes that are not class specific and can represent any visual concept that is present in the data. In particular, our prototypes may represent class-level concepts or segment-level concepts as in CBM [13], but we learn them without concept-level supervision. Previous works learned prototypes for the features at each location in the convolutional output of a Convolutional Neural Network (CNN) backbone [6, 21, 39]. This restricts the spatial extent of the prototypes to size of the receptive field. Additionally, in CNN the output is typically spatially averaged to achieve a global image representation, however, as this is not done for CNN-based prototype approaches they can only learn local and not global prototypes. Instead, we use Vision Transformers (ViT) [10], as they offer solutions for both aforementioned issues capturing local and global concepts of various spatial extents." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 474, + 146, + 487 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 474, + 146, + 487 + ], + "spans": [ + { + "bbox": [ + 47, + 474, + 146, + 487 + ], + "type": "text", + "content": "2.3. Deep Clustering" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 495, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 287, + 628 + ], + "type": "text", + "content": "Clustering relates to learning prototypes or concepts in that it has been used to define the library of concept CBM [13], and to an extent the underlying principles match the goal of clustering. In particular, in deep clustering [40, 11, 22] the centroids are learned iteratively, resulting in them being conceptually close to prototypes or CBM-concepts. However, in prior works on deep clustering [40, 11, 22] the clustering objective is separate from the feature representation, whereas in prototype-based approaches the final output is determined by projecting the input to the prototype subspace." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": "Another key difference is that by making the prototypes integral to the reasoning process, as in CBM [13] or ProtoP-net [6], it is ensured that the prototypes are of meaningful to the final output. Post-hoc clustering, or as part of a separate objective, may lead to overrepresentation of clusters which capture meaningless information, e.g., orthogonal to the objective that was used to obtain the feature representation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 71, + 426, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 426, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 426, + 85 + ], + "type": "text", + "content": "3. Dataset Comparison" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 91, + 547, + 177 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 177 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 177 + ], + "type": "text", + "content": "Given a collection of datasets " + }, + { + "bbox": [ + 304, + 91, + 547, + 177 + ], + "type": "inline_equation", + "content": "X = \\{\\chi_i\\}_{i=1}^{|X|}" + }, + { + "bbox": [ + 304, + 91, + 547, + 177 + ], + "type": "text", + "content": " the aim of prototype-based dataset comparison is to discover a set of prototypes " + }, + { + "bbox": [ + 304, + 91, + 547, + 177 + ], + "type": "inline_equation", + "content": "p \\in \\mathbb{R}^{K \\times D}" + }, + { + "bbox": [ + 304, + 91, + 547, + 177 + ], + "type": "text", + "content": " that represent visual concepts that may occur predominantly in only one dataset (i.e. dataset-specific prototypes) or visual concepts which occur in two or more datasets (i.e. shared prototypes). An illustration of the dataset comparison workflow is shown in Figure 2." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "spans": [ + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "text", + "content": "We argue that a comparative approach to dataset summarisation, i.e., dataset comparison is vital for gaining insights into datasets. In particular, if " + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "inline_equation", + "content": "C_*" + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "text", + "content": " is the set of all possible visual concepts, and " + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "text", + "content": " the visual concepts in ImageNet, then " + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "inline_equation", + "content": "C_i \\subset C_*" + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "text", + "content": ". Given these sets, " + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "text", + "content": " is a perfect description of what is contained in ImageNet, and the difference " + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "inline_equation", + "content": "C_* - C_i" + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "text", + "content": " perfectly describes what is not contained in ImageNet. However, as we do not have access to " + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "inline_equation", + "content": "C_*" + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "text", + "content": " and we have no guaranteed manner of discovering " + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "text", + "content": ", we can at best learn a set of prototypes " + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "inline_equation", + "content": "\\hat{C}_i" + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "text", + "content": " that approximates " + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 304, + 177, + 547, + 297 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "spans": [ + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "text", + "content": "As it is an approximation it cannot be concluded from " + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "inline_equation", + "content": "\\hat{C}_i" + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "text", + "content": " that a concept is not in " + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "text", + "content": ". For example, PASS is designed to not contain humans (i.e., no humans in " + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "inline_equation", + "content": "C_p" + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "text", + "content": "), but based on " + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "inline_equation", + "content": "\\hat{C}_p" + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "text", + "content": " it cannot be stated with certainty that no humans are found in PASS, only that no human-centric concepts were discovered. To overcome this limitation we propose to jointly learn " + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "inline_equation", + "content": "\\hat{C}_i" + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "inline_equation", + "content": "\\hat{C}_p" + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "text", + "content": ". Thereby, if we know a concept is in " + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "inline_equation", + "content": "\\hat{C}_i" + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "text", + "content": " and not in " + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "inline_equation", + "content": "\\hat{C}_p" + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "text", + "content": ", we can reasonably conclude that the concept is not in " + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "inline_equation", + "content": "C_p" + }, + { + "bbox": [ + 304, + 296, + 547, + 408 + ], + "type": "text", + "content": " either." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 418, + 539, + 520 + ], + "blocks": [ + { + "bbox": [ + 310, + 418, + 539, + 520 + ], + "lines": [ + { + "bbox": [ + 310, + 418, + 539, + 520 + ], + "spans": [ + { + "bbox": [ + 310, + 418, + 539, + 520 + ], + "type": "image", + "image_path": "36a19db9befefe9249ad63f316577839ecfda8f431da25fb811cfdbd28a62624.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 532, + 547, + 582 + ], + "lines": [ + { + "bbox": [ + 304, + 532, + 547, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 547, + 582 + ], + "type": "text", + "content": "Figure 2: Overview of the dataset comparison workflow. Datasets are mapped to the prototype embedding space, from where we can inspect and compare individual prototypes." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 592, + 547, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 592, + 547, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 592, + 547, + 652 + ], + "type": "text", + "content": "Through dataset comparison we are thus able to answer questions that could not be answered by only considering a single dataset, thereby creating new possibilities for dataset inspection for hypothesis verification or comparative exploration." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 659, + 429, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 429, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 429, + 672 + ], + "type": "text", + "content": "3.1. Prototype Evaluation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "How to evaluate the prototypes learnt for dataset comparison (or summarisation) is an open problem, as the groundtruth for which visual concepts are contained in the dataset" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1946" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 286, + 140 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 286, + 140 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 286, + 140 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 286, + 140 + ], + "type": "image", + "image_path": "9c7ff26deebc6d53330ef3fa4cce5115a56171801309afd41c4e6b506d5cd965.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 152, + 287, + 187 + ], + "lines": [ + { + "bbox": [ + 46, + 152, + 287, + 187 + ], + "spans": [ + { + "bbox": [ + 46, + 152, + 287, + 187 + ], + "type": "text", + "content": "Figure 3: Examples of low-level visual properties discovered with ProtoSim: motion blur (top) and a shallow depth of field (bottom)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 214, + 286, + 298 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 214, + 286, + 298 + ], + "spans": [ + { + "bbox": [ + 46, + 214, + 286, + 298 + ], + "type": "text", + "content": "are unknown. Nonetheless, we can leverage the comparative approach by verifying whether the prototypes found match the design goals of the datasets. For instance, as PASS was designed not to contain humans we can explore whether the human-centric prototypes learnt from ImageNet indeed do not occur in PASS. This manner of evaluation forms the basis of our first case study." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 300, + 286, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 286, + 432 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 286, + 432 + ], + "type": "text", + "content": "Generally, we consider the prototypes " + }, + { + "bbox": [ + 46, + 300, + 286, + 432 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 300, + 286, + 432 + ], + "type": "text", + "content": " to be of high-quality when they are distinct and meaningful. Distinct prototypes are able to independently represent a visual concept, this is in contrast to, for example, sparse coding [46] where the aim is to find basis vectors that represent the input through linear combinations. The set of prototypes is meaningful when it can be used to discriminate images within and across the datasets from one another. Requiring that the prototypes are discriminative helps avoid trivial solutions. We can quantitatively measure how discriminative the prototypes are by evaluating them with downstream tasks." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 435, + 286, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 286, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 286, + 518 + ], + "type": "text", + "content": "To ensure that the prototypes are distinct we design our method ProtoSim to perform hard assignment of the prototypes, and by optimising the prototypes with contrastive SSL we ensure that they are discriminative. This alignment between the design of the method (more details in Section 4) and the goal of dataset comparison helps us make certain the prototypes are of high-quality." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 534, + 162, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 534, + 162, + 547 + ], + "spans": [ + { + "bbox": [ + 47, + 534, + 162, + 547 + ], + "type": "text", + "content": "3.2. Types of Prototypes" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 555, + 286, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 286, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 286, + 651 + ], + "type": "text", + "content": "Within the set of prototypes we can recognise different types of prototypes depending on how they occur across the datasets. For instance, a prototype " + }, + { + "bbox": [ + 46, + 555, + 286, + 651 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 46, + 555, + 286, + 651 + ], + "type": "text", + "content": " may be considered dataset-specific when over " + }, + { + "bbox": [ + 46, + 555, + 286, + 651 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 46, + 555, + 286, + 651 + ], + "type": "text", + "content": " of its occurrences are only found in a single dataset. By definition, any prototype which is not dataset-specific would then be considered shared. However, various degrees of 'sharedness' may occur depending on the overlap between datasets." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "content": "In theory it may be possible for the datasets in " + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "content": " to be fully distinct, resulting in only dataset-specific prototypes. In practice, we find that prototypes may represent various basic visual properties (see Figure 3), resulting in shared prototypes even when the datasets differ semantically." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 71, + 454, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 454, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 454, + 85 + ], + "type": "text", + "content": "4. Prototype-based Learning" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 91, + 545, + 211 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 211 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 211 + ], + "type": "text", + "content": "We propose ProtoSim a simple module that can inserted in ViT architectures to enable dataset comparison through integral prototype-based learning. ProtoSim differs from previous prototype layers in three ways, firstly, the prototypes learned with ProtoSim are distinct (as opposed to linear mixtures), secondly, ProtoSim is specifically designed for ViT architectures and learns prototypes from a set of tokens, rather than a single embedding vector. Lastly, the prototypes in ProtoSim are not class-specific, instead we learn a single pool of prototypes that may occur in any image." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 217, + 373, + 228 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 217, + 373, + 228 + ], + "spans": [ + { + "bbox": [ + 306, + 217, + 373, + 228 + ], + "type": "text", + "content": "4.1. ProtoSim" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 235, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 235, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 235, + 545, + 354 + ], + "type": "text", + "content": "In order to learn which visual concepts are present in a dataset we aim to optimise a set of " + }, + { + "bbox": [ + 304, + 235, + 545, + 354 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 235, + 545, + 354 + ], + "type": "text", + "content": " learnable prototypes " + }, + { + "bbox": [ + 304, + 235, + 545, + 354 + ], + "type": "inline_equation", + "content": "p \\in \\mathbb{R}^{K \\times D}" + }, + { + "bbox": [ + 304, + 235, + 545, + 354 + ], + "type": "text", + "content": ". By designing the prototypes to be part of a prototype layer (i.e. ProtoSim) we can directly optimise them in and end-to-end fashion as part of ViT that we add the layer to. Specifically, given the token embeddings " + }, + { + "bbox": [ + 304, + 235, + 545, + 354 + ], + "type": "inline_equation", + "content": "z \\in \\mathbb{R}^{N + 1 \\times D}" + }, + { + "bbox": [ + 304, + 235, + 545, + 354 + ], + "type": "text", + "content": " produced by a ViT, ProtoSim maps these to the prototype embeddings " + }, + { + "bbox": [ + 304, + 235, + 545, + 354 + ], + "type": "inline_equation", + "content": "\\hat{z} \\in \\mathbb{R}^{N + 1 \\times D}" + }, + { + "bbox": [ + 304, + 235, + 545, + 354 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 235, + 545, + 354 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 235, + 545, + 354 + ], + "type": "text", + "content": " is the token vector size. During this mapping each token is replaced with the most similar prototype in " + }, + { + "bbox": [ + 304, + 235, + 545, + 354 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 235, + 545, + 354 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 354, + 545, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 450 + ], + "type": "text", + "content": "In [23, 6] the similarity to each of the class-specific prototypes is determined by calculating the squared " + }, + { + "bbox": [ + 304, + 354, + 545, + 450 + ], + "type": "inline_equation", + "content": "L^2" + }, + { + "bbox": [ + 304, + 354, + 545, + 450 + ], + "type": "text", + "content": " distance and selecting the closest prototype with a max operation. Because our aim is to find prototypes that recur in the entire dataset, instead of finding class-specific prototypes, we propose a surprisingly simple formulation of this process by using a reversed version of dot-product attention [25] to efficiently calculate attention across all the prototypes:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 383, + 455, + 545, + 468 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 455, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 383, + 455, + 545, + 468 + ], + "type": "interline_equation", + "content": "a = \\operatorname {s o f t m a x} \\left(p z ^ {\\intercal}\\right) \\tag {1}", + "image_path": "cf747df9582add38b61631069bcc469c159439bdf383953eed8e79d474dbe612.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 384, + 470, + 545, + 483 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 470, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 384, + 470, + 545, + 483 + ], + "type": "interline_equation", + "content": "\\hat {z} = a ^ {\\intercal} p. \\tag {2}", + "image_path": "a91f277acbde52593baf4afcb0e5e92f996a4596e125a1955b8352d90dbebbd2.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 487, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 487, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 545, + 582 + ], + "type": "text", + "content": "Here the attention mask " + }, + { + "bbox": [ + 304, + 487, + 545, + 582 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 487, + 545, + 582 + ], + "type": "text", + "content": " represents the soft-assignment of prototypes to tokens, as such each token embedding " + }, + { + "bbox": [ + 304, + 487, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\hat{z}" + }, + { + "bbox": [ + 304, + 487, + 545, + 582 + ], + "type": "text", + "content": " is a linear combination of prototypes. This is not desirable as our aim is to learn distinct prototypes which independently represent a visual concept, as this enables better summarisation and greater interpretability. To obtain a hard assignment we replace the softmax operation in Equation 1 with gumbel-softmax [17]:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 365, + 588, + 545, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 588, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 365, + 588, + 545, + 601 + ], + "type": "interline_equation", + "content": "a = \\operatorname {g u m b e l - s o f t m a x} (p z ^ {\\intercal}). \\tag {3}", + "image_path": "98c7e57d2cf20c5f6440bc261add6d498022fee1daad3483428e7c33f5f0f41f.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "For simplicity we drop the temperature parameter, as it empirically does not meaningfully influence performance and can be kept fixed at 1. The benefit of gumbel-softmax is that it maintains gradient-flow whilst enabling hard attention. Based on this modification " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " now represents a hard assignment matrix which is used to replace each token with a prototype. As a visual concept can occur across multiple spatial locations there is no constraint on how often a prototype can be assigned." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1947" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 116, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 116, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 116, + 83 + ], + "type": "text", + "content": "4.2. Backbone" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 287, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 287, + 235 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 287, + 235 + ], + "type": "text", + "content": "Whilst ProtoSim functions as a generic network module, with the only requirement being an a two-dimensional input of " + }, + { + "bbox": [ + 46, + 90, + 287, + 235 + ], + "type": "inline_equation", + "content": "K \\times D" + }, + { + "bbox": [ + 46, + 90, + 287, + 235 + ], + "type": "text", + "content": ", we specifically apply it to ViT in this work as these offer some benefits over CNN. In particular, in ViT all tokens can share information with all other tokens, as such there is no restriction on the spatial extent of the learned prototypes. Moreover, whilst most tokens in a ViT represent some spatial region of the image (i.e. patch tokens), the class token takes on the role of a global image representation. This allows us to learn prototypes that are local (i.e. only assigned to patch tokens) and global (i.e. only assigned to the class token) without modifying the architecture." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "text", + "content": "ProtoSim is placed at the end of the backbone ViT in the network architecture. Formally, the input " + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "inline_equation", + "content": "x \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "text", + "content": " is divided into flattened patch tokens " + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "inline_equation", + "content": "x_{p} \\in \\mathbb{R}^{N \\times (P^{2} \\cdot C)}" + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "inline_equation", + "content": "H, W," + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "text", + "content": " are the height, width, and channel dimensionality of the input and " + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "text", + "content": " the patch size hyperparameter. In addition to " + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "text", + "content": " patch tokens, a learnable class token " + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "inline_equation", + "content": "x_{class}" + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "text", + "content": " is prepended to input. No class labels are used during training, but we retain the ViT terminology of referring to this as a class token. After the embedding phase the tokens are passed through a series of transformer blocks resulting in the token embeddings " + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "inline_equation", + "content": "z \\in \\mathbb{R}^{N + 1 \\times D}" + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "text", + "content": " is the embedded token vector size. " + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "text", + "content": " is passed through the ProtoSim layer resulting in the prototype embeddings " + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "inline_equation", + "content": "\\hat{z}" + }, + { + "bbox": [ + 46, + 235, + 288, + 392 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 399, + 159, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 399, + 159, + 414 + ], + "spans": [ + { + "bbox": [ + 47, + 399, + 159, + 414 + ], + "type": "text", + "content": "4.3. Training Objective" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 418, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 287, + 550 + ], + "type": "text", + "content": "The training objective determines the prototypes. For instance, a classification-based objective results in prototypes that are indicative of the classes (as in ProtoPnet [6] or CBM [20]). Yet, such an objective may result in a poor coverage of concepts that are not part of the annotated classes. Because we strive for good coverage we focus on a Contrastive Self-Supervised Learning (Contrastive SSL) objective. In particular, because Constrastive SSL optimises for fine-grained discrimination between images (rather than classes) and has been shown to be perform well on a variety of downstream tasks [7]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 551, + 287, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 551, + 287, + 599 + ], + "spans": [ + { + "bbox": [ + 46, + 551, + 287, + 599 + ], + "type": "text", + "content": "From the recently proposed Contrastive SSL methods [16, 15, 7, 8, 3, 4], only DINO [4] has been specifically designed to work with ViT. As such, we minimise the DINO loss as the training objective:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 78, + 608, + 287, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 608, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 78, + 608, + 287, + 643 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta_ {s}} \\sum_ {x \\in \\{x _ {1} ^ {g}, x _ {2} ^ {g} \\}} \\sum_ { \\begin{array}{c} x ^ {\\prime} \\in V \\\\ x ^ {\\prime} \\neq x \\end{array} } H (P _ {t} (x), P _ {s} (x ^ {\\prime})), \\qquad (4)", + "image_path": "02c2af1ca3a5853755c06bf1ec60db7435ff1e978c84fed01160e290146044de.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "H(a,b) = -a\\log b" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "x_1^g" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "x_2^g" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " are two large crops from the input, " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " a set of data-augmented smaller crops, and " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "P_t" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "P_s" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " are the teacher and student networks respectively, each with a ProtoSim layer added to the backbone. We refer to the excellent work by [4] for further details." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 71, + 387, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 387, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 387, + 83 + ], + "type": "text", + "content": "5. Case Studies" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 91, + 547, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 295 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 295 + ], + "type": "text", + "content": "In this section we present two case studies, the first is a comparison between two datasets (i.e., two-way dataset comparison) aimed at determining how the PASS [1] dataset differs from ImageNet [32]. Because the design goal of PASS was to present an alternative for ImageNet that does not contain humans we test whether this is achieved successfully. The second case study focuses on a three-way dataset comparison scenario wherein we explore how three artwork datasets differ. These three datasets were designed for different tasks and contain images from different museum collections, as such based on these meta properties of the datasets it is challenging to determine how they actually relate. With these two case studies we put the two main applications of dataset comparison to the test, verifying a design goal of a dataset, and exploring unknown datasets. In addition, in Supplementary Section A we demonstrate how ProtoSim can also be used on a single dataset." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 301, + 369, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 301, + 369, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 301, + 369, + 312 + ], + "type": "text", + "content": "5.1. Datasets" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 319, + 545, + 343 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 319, + 545, + 343 + ], + "spans": [ + { + "bbox": [ + 306, + 319, + 545, + 343 + ], + "type": "text", + "content": "For the first case study we focus on ImageNet and PASS, we briefly describe both:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 351, + 545, + 502 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 317, + 351, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 351, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 317, + 351, + 545, + 437 + ], + "type": "text", + "content": "- ImageNet [32] is a widely used dataset available in two versions: ImageNet-21K and ImageNet-1K. In this work we focus on ImageNet-1K consisting of approximately 1.2 million training images and 1000 classes. Despite how widely used it is, and how influential it has been, ImageNet-1K has also been criticised for its biased depictions of persons [30]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 443, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 443, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 317, + 443, + 545, + 502 + ], + "type": "text", + "content": "- PASS [1] is a recently proposed alternative for ImageNet with the intention of not containing persons to avoid the issues in ImageNet. PASS contains approximately 1.4 million unlabeled images and can only be used for self-supervised training." + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 511, + 545, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 511, + 545, + 535 + ], + "spans": [ + { + "bbox": [ + 306, + 511, + 545, + 535 + ], + "type": "text", + "content": "In the second case study we focus on three artwork datasets that have been used for a variety of different tasks:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 543, + 545, + 713 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 317, + 543, + 545, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 543, + 545, + 591 + ], + "spans": [ + { + "bbox": [ + 317, + 543, + 545, + 591 + ], + "type": "text", + "content": "- MET [43] is a dataset designed for instance-level recognition, its training set contains over 400k images from more than 224k different objects held by the Metropolitan Museum of Art in New York." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 598, + 545, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 598, + 545, + 669 + ], + "spans": [ + { + "bbox": [ + 317, + 598, + 545, + 669 + ], + "type": "text", + "content": "- Rijksmuseum [27] presents a set of tasks which are museum-centric, focusing on predicting various types of metadata (i.e., artist, object-type, material usage, and creation year). It consists of 110k images obtained from collections held by the Rijksmuseum in Amsterdam." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 317, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 677, + 545, + 713 + ], + "type": "text", + "content": "- SemArt [12] consists of images collected from the Web Gallery of Art a virtual museum with predominantly European fine-art. The SemArt dataset contains" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1948" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 67, + 72, + 286, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 72, + 286, + 107 + ], + "spans": [ + { + "bbox": [ + 67, + 72, + 286, + 107 + ], + "type": "text", + "content": "21k images described with similar metadata as the Rijksmuseum dataset, but in addition also has textual descriptions in the form of artistic comments." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 119, + 286, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 119, + 286, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 119, + 286, + 190 + ], + "type": "text", + "content": "The available metadata for these three artwork datasets differs, but notably none of these datasets have been described with semantic classes as, for example, found in ImageNet. As such, we do not have prior information about what type of visual concepts are represented in the artwork datasets." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 200, + 162, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 200, + 162, + 213 + ], + "spans": [ + { + "bbox": [ + 47, + 200, + 162, + 213 + ], + "type": "text", + "content": "5.2. Experimental setup" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 219, + 286, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 219, + 286, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 286, + 326 + ], + "type": "text", + "content": "The backbone used is the DeIT-S model [38] with a patch size of " + }, + { + "bbox": [ + 46, + 219, + 286, + 326 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 46, + 219, + 286, + 326 + ], + "type": "text", + "content": ". The parameters of the backbone are fixed during prototype learning and training is done on a single NVIDIA RTX 3090 with a batch size of 128 and learning rate of " + }, + { + "bbox": [ + 46, + 219, + 286, + 326 + ], + "type": "inline_equation", + "content": "5\\mathrm{e} - 5" + }, + { + "bbox": [ + 46, + 219, + 286, + 326 + ], + "type": "text", + "content": " for 20 epochs. For the first 15 epochs we train with soft gumbel-softmax, after which we switch the student to the hard 'straight-through' gumbel-softmax, to ensure more independent prototypes. In line with previous works (e.g., [2, 26]) we set " + }, + { + "bbox": [ + 46, + 219, + 286, + 326 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 219, + 286, + 326 + ], + "type": "text", + "content": " to 8192." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 327, + 286, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 327, + 286, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 327, + 286, + 384 + ], + "type": "text", + "content": "For quantitative evaluation we follow the standard procedure of training a linear classifier on frozen features [4, 16]. We freeze the backbone and the ProtoSim layer and then train a linear classifier for 20 epochs with a learning rate of 0.001 and a batch size of 256." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 396, + 211, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 211, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 211, + 407 + ], + "type": "text", + "content": "5.3. Two-way Dataset Comparison" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 414, + 286, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 286, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 286, + 581 + ], + "type": "text", + "content": "For the two-way dataset comparison case study we focus on the PASS and ImageNet datasets, to this end we learn prototypes on the union of these two datasets, which we refer to as the PassNet dataset, and present the results in this section. All results in this section are obtained with ProtoSim trained on top of the DINO backbone pretrained on ImageNet. A key finding of this comparison is that ProtoSim learns both dataset-specific prototypes (i.e., prototypes that predominantly activate for one dataset) and shared prototypes (i.e., prototypes that occur frequently in both datasets). In Figure 4 we show nine prototypes which are predominantly found in ImageNet, PASS, or are shared equally among both datasets. Additional examples of prototypes are shown in the supplementary material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": "The prototypes that are predominantly found in ImageNet contain people (i.e., over " + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "inline_equation", + "content": "99\\%" + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": " of images for which they activate are found in ImageNet). However, despite its design goal we do find persons for these prototypes in PASS. The Persons at the beach prototype (first row) contains a man holding a beach-ball photographed from the back, and the Uncovered legs/arms prototype (third row) is found in (nude) statues and a faded Polaroid of a person. The only two PASS images for the Sports-ball prototype (second row) just depict the field and a ball, suggesting that the prototype captures more than just persons." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "The prototypes that are predominantly found in PASS depict concepts or objects that are not found among the 1000 ImageNet categories. Nonetheless, these predominantly PASS prototypes can be found in some ImageNet images where the annotated object is a (small) part of the image. From left to right for row four to six we find the following ImageNet categories: European Gallinule, Ant, Wheelbarrow, Turnstile, Barn, and Headland. We would describe the prototypes in these rows as capturing Flowers, a View down narrow alley, and Sunset with silhouetted foreground respectively. In general, the PASS prototypes that predominantly concern vista or landscape images, which on occasion contain objects from ImageNet categories." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 228, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 361 + ], + "type": "text", + "content": "For the prototype in the second row of Figure 4 we measure how it is spatially distributed and visualise this for the four ImageNet images in Figure 5. Visualising the attention maps of this prototype shows that the main activations are indeed for the leg and arm areas of the persons depicted. Other parts of the persons receive much less attention than these uncovered areas. Although this is a predominantly ImageNet prototype, and is therefore commonly found in instances of the 'miniskirt' and 'bikini' categories, it is also found in PASS, including in images of mannequins, artworks, and anime of primarily feminine characters." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 361, + 545, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 505 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 505 + ], + "type": "text", + "content": "Overall, we can conclude that the two-way comparison is highly successful, not only are we able to verify that depictions of humans in PASS are practically non-existent, but by edge-cases we are able to demonstrate the strength of the prototypes. Moreover, based on the discovered prototypes we also gain insights into how these datasets differ, with PASS containing many more vistas and landscapes, whereas ImageNet is strongly object-centric. As such we can conclude that while there is an overlap, PASS differs in more respects from ImageNet than just the presence of humans - which may cast doubt on its status as an ImageNet replacement." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 307, + 538, + 536, + 628 + ], + "blocks": [ + { + "bbox": [ + 313, + 518, + 536, + 531 + ], + "lines": [ + { + "bbox": [ + 313, + 518, + 536, + 531 + ], + "spans": [ + { + "bbox": [ + 313, + 518, + 536, + 531 + ], + "type": "text", + "content": "Table 1: Performance for linear classifier on ImageNet." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 538, + 536, + 628 + ], + "lines": [ + { + "bbox": [ + 307, + 538, + 536, + 628 + ], + "spans": [ + { + "bbox": [ + 307, + 538, + 536, + 628 + ], + "type": "table", + "html": "
Train setBackboneKAccuracy
ImageNetDINO [4]819264.8
PASSPASS-DINO [1]819220.4
PassNet (I+P)DINO [4]819253.2
PassNet (P+I)PASS-DINO [1]819215.9
ImageNetDINO [4]102454.7
ImageNetDINO [4]409663.7
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Secondly, we train a linear classifier on top of each of the backbones to perform ImageNet clas" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1949" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 80, + 91, + 149, + 140 + ], + "blocks": [ + { + "bbox": [ + 80, + 91, + 149, + 140 + ], + "lines": [ + { + "bbox": [ + 80, + 91, + 149, + 140 + ], + "spans": [ + { + "bbox": [ + 80, + 91, + 149, + 140 + ], + "type": "image", + "image_path": "c80bbc75a3abef34b35710ee859acbffc6bf260e29bcbd246afe94ae6ea595c2.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + 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For these evaluations we compare between two different backbones, one pre-trained on ImageNet [4] and one pre-trained on PASS [1]. Results reported on PassNet are described as either " + }, + { + "bbox": [ + 46, + 226, + 287, + 285 + ], + "type": "inline_equation", + "content": "(\\mathrm{I} + \\mathrm{P})" + }, + { + "bbox": [ + 46, + 226, + 287, + 285 + ], + "type": "text", + "content": " for the ImageNet pre-trained backbone, or " + }, + { + "bbox": [ + 46, + 226, + 287, + 285 + ], + "type": "inline_equation", + "content": "\\mathrm{P} + \\mathrm{I}" + }, + { + "bbox": [ + 46, + 226, + 287, + 285 + ], + "type": "text", + "content": " for the PASS pre-trained backbone." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 286, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 286, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 286, + 287, + 477 + ], + "type": "text", + "content": "Table 1 shows the performance on the ImageNet validation set for a linear classifier trained on top of fixed backbones. We observe that pre-training on ImageNet (unsurprisingly) leads to the best downstream performance on ImageNet, and that training on PASS leads to lower performance. Similarly, for the two backbones we find that the ImageNet pre-trained backbone performs much better. Nonetheless, we see degraded performance for training on PassNet versus ImageNet. The last two rows of Table 1 show that increasing the " + }, + { + "bbox": [ + 46, + 286, + 287, + 477 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 286, + 287, + 477 + ], + "type": "text", + "content": " value benefits performance, due to computational complexity and diminishing returns no values above 8192 were tested. In conclusion, our quantitative evaluation confirms our modelling choices of using the ImageNet pre-trained backbone with 8192 prototypes, and we will use this configuration for the second case study as well." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 55, + 485, + 164, + 569 + ], + "blocks": [ + { + "bbox": [ + 55, + 485, + 164, + 569 + ], + "lines": [ + { + "bbox": [ + 55, + 485, + 164, + 569 + ], + "spans": [ + { + "bbox": [ + 55, + 485, + 164, + 569 + ], + "type": "image", + "image_path": "39ff7cdcb8742f4d536e413fe1ad53b07451f10e04260fa1915d40a3edee2c61.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "lines": [ + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "text", + "content": "Figure 6: Training loss (left) and average cosine similarity (right) during prototype training. PassNet results " + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "inline_equation", + "content": "\\mathrm{P} + \\mathrm{I}" + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "text", + "content": " are obtained PASS-DINO backbone and " + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "inline_equation", + "content": "\\mathrm{I} + \\mathrm{P}" + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "text", + "content": " with the DINO backbone." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 166, + 486, + 279, + 569 + ], + "blocks": [ + { + "bbox": [ + 166, + 486, + 279, + 569 + ], + "lines": [ + { + "bbox": [ + 166, + 486, + 279, + 569 + ], + "spans": [ + { + "bbox": [ + 166, + 486, + 279, + 569 + ], + "type": "image", + "image_path": "6ecab230bf582637f070de7f053ca80d59804818b1434461d10c4c36504da765.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "type": "text", + "content": "The results in Figure 6 show the training loss and the average cosine similarity between prototypes as training progresses. In both plots we see two groupings of two lines that follow the same pattern. For all models we can see that switching to the hard gumbel-softmax leads to a bump in the loss, but except for " + }, + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{P} + \\mathrm{I}" + }, + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "type": "text", + "content": " this bump levels off quickly." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 72, + 478, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 478, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 478, + 85 + ], + "type": "text", + "content": "5.4. Three-way Dataset Comparison" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 90, + 545, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 293 + ], + "type": "text", + "content": "In the second case study we perform a three-way dataset comparison between the MET, Rijksmuseum, and SemArt datasets. The aim of this comparison is highly exploratory, unlike ImageNet, none of these datasets have pre-defined classes, as such it is not obvious what visual concepts are represented. In Figure 7 we show nine prototypes discovered with ProtoSim, the first three pairs of prototypes are dataset-specific and are predominantly found in the MET, Rijksmuseum, and SemArt respectively. These prototypes were randomly selected from the most dataset-specific prototypes and give a good indication of what is contained in these datasets. The MET dataset contains many 3D objects and often multiple photographs are taken from different angles, as such the first prototype represents Top-down views of vases. The second MET prototype depicts Egyptian wall carvings, which were photographed under raking light to emphasise the height differences across the surface." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 293, + 545, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 545, + 414 + ], + "type": "text", + "content": "The Rijksmuseum dataset contains many prints or drawings on paper, whilst this is something that can be learnt from the material type overview in [27], the two prototypes depicted show two different groups of visual concepts. The first Rijksmuseum prototype depicts natural history drawings, whereas the second is found in side view portraits. Se-mArt on the other hand consists of mostly fine-art paintings, with the first prototype capturing a stylistic visual concept of Renaissance paintings, the second prototype is a more concrete semantic concept, namely dogs." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 415, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 581 + ], + "type": "text", + "content": "Just by exploring the dataset-specific datasets we already get a much better understanding of what is contained in these datasets and what makes them unique. In addition, when we then analyse the shared prototypes we can see that these differences largely persist across different visual concepts. The first shared prototype is of various animals, notably we see that the prototype is not sensitive to material differences, returning both drawings and paintings. The same observation is made for the second shared prototype of baskets, which is matched to drawings, paintings, and photographs of actual baskets. This ability to generalise across modalities is also observed in the third shared prototype of brass instruments, which matches actual instruments and realistic paintings containing similar instruments." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 582, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 712 + ], + "type": "text", + "content": "Based on the three-way dataset comparison we find that there are degrees of overlap between the datasets, generally we would see that the MET and Rijksmuseum datasets are most similar in types of objects, where MET has a greater focus on physical objects and Rijksmuseum on prints and drawings. Because these two datasets have a relatively small proportion of paintings the similarity with the SemArt dataset is less, nonetheless, we can observe that in terms of visual concepts these datasets represent similar things. In Appendix Section C we show additional prototypes discovered for these artwork datasets." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "text", + "content": "1951" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 83, + 282, + 281 + ], + "blocks": [ + { + "bbox": [ + 131, + 70, + 203, + 82 + ], + "lines": [ + { + "bbox": [ + 131, + 70, + 203, + 82 + ], + "spans": [ + { + "bbox": [ + 131, + 70, + 203, + 82 + ], + "type": "text", + "content": "MET prototypes" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 52, + 83, + 282, + 281 + ], + "lines": [ + { + "bbox": [ + 52, + 83, + 282, + 281 + ], + "spans": [ + { + "bbox": [ + 52, + 83, + 282, + 281 + ], + "type": "image", + "image_path": "4b54cca991050a9bdc1cc85bf6801501086966877cbdfb7769f68402bae78505.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 58, + 304, + 280, + 415 + ], + "blocks": [ + { + "bbox": [ + 125, + 291, + 209, + 303 + ], + "lines": [ + { + "bbox": [ + 125, + 291, + 209, + 303 + ], + "spans": [ + { + "bbox": [ + 125, + 291, + 209, + 303 + ], + "type": "text", + "content": "SemArt prototypes" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 58, + 304, + 280, + 415 + ], + "lines": [ + { + "bbox": [ + 58, + 304, + 280, + 415 + ], + "spans": [ + { + "bbox": [ + 58, + 304, + 280, + 415 + ], + "type": "image", + "image_path": "b158d5abd036f4e300c09b3d949283355a0484b1f2e72d856332f7df4d28ab10.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 53, + 440, + 280, + 597 + ], + "blocks": [ + { + "bbox": [ + 124, + 427, + 208, + 439 + ], + "lines": [ + { + "bbox": [ + 124, + 427, + 208, + 439 + ], + "spans": [ + { + "bbox": [ + 124, + 427, + 208, + 439 + ], + "type": "text", + "content": "Shared prototypes" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 53, + 440, + 280, + 597 + ], + "lines": [ + { + "bbox": [ + 53, + 440, + 280, + 597 + ], + "spans": [ + { + "bbox": [ + 53, + 440, + 280, + 597 + ], + "type": "image", + "image_path": "9af90c233ef8a0c4b5975ad4d52a8432f0371a2887cc19c52a267b6c12babc4d.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "type": "text", + "content": "Figure 7: Example images for nine prototypes, the first six rows are divided in three pairs of prototypes predominantly found in MET, Rijksmuseum, or SemArt respectively. The last three rows show prototypes common across the datasets. Examples with a pink, green, and blue background belong to the MET, Rijksmuseum, or Semart datasets respectively." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 71, + 375, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 375, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 375, + 83 + ], + "type": "text", + "content": "6. Discussion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 91, + 545, + 211 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 211 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 211 + ], + "type": "text", + "content": "The prototypes obtained with ProtoSim enable dataset comparison, nonetheless, there are two limitations. Firstly, although explanation methods based on visual examples are preferred for visual data [19], there is a mandatory manual inference step to determine what a prototype represents. Whilst previous methods suffer from the same limitation [6, 21] ProtoSim does offer an advantage in that the attention maps can be visualised (i.e., Figure 5). Based on example images and their attention maps it becomes possible to be relatively certain about what the prototype represents." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 211, + 546, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 211, + 546, + 319 + ], + "spans": [ + { + "bbox": [ + 304, + 211, + 546, + 319 + ], + "type": "text", + "content": "Secondly, whilst the ViT backbone can be replaced, for our experiments we found the best results with an ImageNet pre-trained backbone. Since this dataset is one of the ones being compared, but also because this dataset has known biases [41] the choice for a ImageNet pre-trained backbone may influence the prototypes learned. During experiments no such influence was observed, instead it appears ProtoSim is flexible in learning diverse prototypes, nonetheless further investigation is necessary." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 331, + 378, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 331, + 378, + 342 + ], + "spans": [ + { + "bbox": [ + 306, + 331, + 378, + 342 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 350, + 545, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 545, + 457 + ], + "type": "text", + "content": "In this work we presented dataset comparison as a new direction for dataset inspection. To enable dataset comparison across large-scale datasets we introduce ProtoSim which leverages integral prototype-based learning and self-supervised learning to discover visual concepts across datasets. To evaluate our proposed approach we perform two case studies, in the first we compare the PASS and ImageNet datasets, and in the second we perform a three-way comparison between artwork datasets." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 459, + 545, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 566 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 566 + ], + "type": "text", + "content": "Based on these case studies we find that we can gain new insights into the datasets. In the first case study we find that ImageNet indeed contains many more images with persons, which is in line with the design goal of PASS. However, we still discovered partial and non-photorealistic depictions of persons in PASS, which were not discovered in its person-focused dataset curation process. When comparing the artwork datasets we find that each has a unique focus, but also that various semantic concepts are shared between them." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 567, + 545, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 545, + 614 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 545, + 614 + ], + "type": "text", + "content": "Overall, we presented an initial exploration of dataset comparison that will hopefully lead to greater attention for this topic, as it is becoming increasingly necessary to improve dataset inspection techniques." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 626, + 365, + 638 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 626, + 365, + 638 + ], + "spans": [ + { + "bbox": [ + 306, + 626, + 365, + 638 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 310, + 646, + 545, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 310, + 646, + 545, + 689 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 646, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 310, + 646, + 545, + 689 + ], + "type": "text", + "content": "[1] Yuki M Asano, Christian Rupprecht, Andrew Zisserman, and Andrea Vedaldi. 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However, previous TFSL methods usually encode uniform prior that all the classes within query samples are equally likely, which is biased in imbalanced TFSL and causes severe performance degradation. Given this pivotal issue, in this work, we propose a novel Conditional Transport (CT) based imbalanced TFSL model called Prototypes-oriented Unbiased Transfer Model (PUTM) to fully exploit unbiased statistics of imbalanced query samples, which employs forward and backward navigators as transport matrices to balance the prior of query samples per class between uniform and adaptive data-driven distributions. For efficiently transferring statistics learned by CT, we further derive a closed form solution to refine prototypes based on MAP given the learned navigators. The above two steps of discovering and transferring unbiased statistics follow an iterative manner, formulating our EM-based solver. Experimental results on four standard benchmarks including miniImageNet, tieredImageNet, CUB, and CIFAR-FS demonstrate superiority of our model in class-imbalanced generalization1.", + "bbox": [ + 75, + 327, + 473, + 659 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 686, + 209, + 702 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep learning based methods have gained a great success in many real-world applications, such as image classification [10, 25, 36], natural language processing [3, 32, 38], and so on, thanks to its powerful nonlinear representation ability [18, 24]. However, their outstanding performances heavily rely on large-scale annotated training data [6, 16]. When it comes to high cost of collecting and annotating a large amount of data, a major research effort is being dedicated to low data regimes, in which overfitting occurs in optimizing deep learning architectures. Few-shot Learning (FSL) tackles these challenges and has triggered substantial interests", + "bbox": [ + 75, + 712, + 470, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4221e7dcb0b2f0338e3e0b5f6fd7e0f9e1b63c1af0d0689d3a688bf27faca9c0.jpg", + "image_caption": [ + "Figure 1: 5-way 1-shot image classification results with miniImageNet [22] dataset on 3000 tasks. Our model achieves the best accuracy in a wide range of imbalanced coefficients compared with PT-MAP [11] and $\\alpha$ -TIM [29]." + ], + "image_footnote": [], + "bbox": [ + 503, + 295, + 883, + 448 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "within the community [8, 20], it aims to train a model from the base classes so as to generalize on the tasks sampled from the novel classes that were never seen during training. There are two major lines of works from the perspective of inference paradigms, namely inductive methods [26, 4] and their transductive counterparts [7, 23]. Both of them adopt well trained models for evaluating new tasks sampled from the novel classes. The former ones only utilize support samples in a supervised way while the later ones leverage both support and query samples in a semi-supervised manner.", + "bbox": [ + 496, + 550, + 893, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Transductive inference is widely used in FSL since it can sufficiently discover statistics of query samples compared with its inductive peer. As a representative example, Hu et al. [11] propose PT-MAP for first employing Wide ResNet (WRN) [36] trained with S2M2 [19] on base classes to extract features of new tasks, and then adjusting prototypes from novel classes by aggregating similar query samples per class with the help of transport matrix derived from the Sinkhorn algorithm [5]. Setting marginal distributions of prototypes as uniform encodes strong prior that all the classes within query samples are equally likely, although, it works pretty well in perfectly class-balanced query samples. However, it is proven to be detrimental in class-imbalanced", + "bbox": [ + 496, + 703, + 895, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 805, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1Our code is available at https://github.com/RashLog/PUTM", + "bbox": [ + 94, + 886, + 416, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16317", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "applications where query samples come with arbitrary and unknown label marginals [21], and classification accuracy drops dramatically, as shown in Fig. 1. To narrow this gap, Veilleux et al. [29] propose $\\alpha$ -TIM for handling class-distribution variations effectively. Unfortunately, we have observed the phenomena as shown in Fig. 1 that $\\alpha$ -TIM can not achieve consistent improvement in various class-imbalanced levels, thus restricting its real-world applications. Most recently, other more complicated methods are also be arisen [14, 12]. Hu et al. [12] propose a clustering method for capturing the class-wise distributions properly.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, for class-imbalanced TFSL, we develop a novel and simple Prototypes-oriented Unbiased Transfer Model (PUTM). It firstly constructs transferable class-wise prototypes iteratively for capturing the unbiased statistics within class-imbalanced query samples. Then it performs few-shot classification via the similarities between prototypes and query samples when the transfer arrives at convergence. The key to obtain unbiased transferable statistics is estimating class-wise marginal distributions precisely [14]. To achieve this, instead of utilizing doubly stochastic transport matrix constrained with fixed uniform-distributed marginal prior between prototypes and query samples as PT-MAP does, we employ task-adaptive forward and backward transport matrices with learnable marginal priors constrained by minimizing Conditional Transport (CT) distance [39] between prototypes and query samples. CT is a tool for measuring the cost in transporting the mass in one distribution to match another in an exchangeable but asymmetrical manner given a specific point-to-point cost function and an estimizable forward and backward transport matrices, also called navigators in the CT scope. To better calibrate prototypes with the help of learned transport matrices and query samples, we further derive a closed-form solution to refine prototypes based on MAP in an iterative manner. Decisions are finally made using the combination of forward and backward transport matrices when the iteration converges. Experiments on four benchmarks demonstrate that our proposed PUTM can learn task-adaptive prior in various class-imbalanced coefficients, paving a new way to transfer the unbiased statistics of query samples to prototypes.", + "bbox": [ + 75, + 257, + 472, + 710 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be summarized as follows:", + "bbox": [ + 96, + 710, + 421, + 724 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We find that the performance of class-imbalanced FSL heavily relies on the accurate estimation of class-wise marginal distribution. Meanwhile, we are the first one to find that there exists a nature connection between CT theory and such marginal distribution estimation.", + "- We propose a novel and simple PUTM for class-imbalanced FSL based on connections mentioned above. It firstly embeds CT distance to measure the differences between prototypes and query samples for achieving better task-adaptive unbiased statistic migra" + ], + "bbox": [ + 94, + 737, + 472, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tion elegantly. Then it calibrates prototypes using the transferred statistics in an iterative manner.", + "bbox": [ + 529, + 90, + 890, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We provide extensive experiments and comparisons on four standard benchmarks for verifying that our model achieves competitive results on both class-balanced and class-imbalanced (in a wide range of imbalanced coefficients) FSL settings.", + "bbox": [ + 517, + 132, + 893, + 207 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Task Formulation", + "text_level": 1, + "bbox": [ + 500, + 220, + 674, + 237 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We divide the whole annotated dataset into two disjoint subsets: a base set $\\mathcal{D}_{\\text{base}}$ with $\\mathcal{B}$ classes and a novel set $\\mathcal{D}_{\\text{novel}}$ with $\\mathcal{N}$ classes. To build a common N-way K-shot task [30, 26], we first randomly sample N classes from $\\mathcal{N}$ novel classes, and then pick K samples per class for the support set $S = \\{\\pmb{x}_{i,j}^{s}, \\pmb{y}_{i,j}^{s}\\}_{i=1,j=1}^{N,K}$ to train or fine-tune the model. Finally, $K_{i}'$ query samples being non-overlapped with support samples per class are randomly picked from the $N$ support classes for evaluating the performance of the model, formulating query set as $\\mathcal{Q} = \\{\\pmb{x}_{i,j}^{q}, \\pmb{y}_{i,j}^{q}\\}_{i=1,j=1}^{N,K_{i}'}$ . For simplicity, we set $M = \\sum_{i=1}^{N} K_{i}'$ .", + "bbox": [ + 498, + 246, + 893, + 419 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Class-imbalanced TFSL: Veilleux et al. [29] figure out that the number of query samples per class should be arbitrary and unknown instead of being strictly equal. That is $K'$ is a function of class and changes with class indexes. To describe such behavior, they develop a class marginal with Dirichlet distribution for generating query samples. Specifically, the class-wise marginal distribution of query samples per task $p$ are determined by:", + "bbox": [ + 498, + 420, + 893, + 541 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nf _ {D i r} (\\boldsymbol {p}; \\boldsymbol {a}) = \\frac {1}{B (\\boldsymbol {\\alpha})} \\prod_ {i = 1} ^ {N} p _ {i} ^ {\\alpha_ {i} - 1} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 551, + 893, + 594 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\pmb{p} = (p_{1},\\dots,p_{N})$ stands for class-wise distribution, $\\alpha = (\\alpha_{1},\\dots,\\alpha_{N})$ denotes Dirichlet-distributed parameter controlling imbalanced ratio of query samples, $B(\\pmb{a}) = \\frac{\\prod_{i=1}^{N}\\Gamma(a_{i})}{\\Gamma(\\sum_{i=1}^{N}a_{i})}$ represents multivariate Beta function, and $\\Gamma(\\cdot)$ is Gamma function. Smaller $\\pmb{a}$ means higher imbalanced level, and vice versa. Taking $\\alpha = 2$ as an example, total number of query samples is 75, then the number of query samples per class could be distributed as $K' = [10,5,2,35,18]$ , which is more realistic compared with the class-balanced situation whose $K_i' = 15, i = 1,\\dots,N$ . Besides, it also poses some difficulties such as overfitting to the classes whose query samples are extremely few.", + "bbox": [ + 498, + 604, + 893, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Our Model", + "text_level": 1, + "bbox": [ + 500, + 806, + 619, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Overall Method", + "text_level": 1, + "bbox": [ + 500, + 830, + 658, + 847 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose a novel model called PUTM for class-imbalanced transductive few-shot image classification. Considering the correlations between support and", + "bbox": [ + 498, + 854, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16318", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/deebc978bdb1dd8874d9ba6d9dcfed99153ded6777929cf9b90f917092eb7f52.jpg", + "image_caption": [ + "Figure 2: Illustration of the our model. Tasks are generated from Dirichlet-distributed generator parameterized by $\\mathbf{a}$ . We first adopt a well trained feature extractor [19] and a channel-wise feature adaptation [35] to obtain the input features. Transductive inference is then conducted on the pre-processed features by: i) optimizing the transport matrices using CT; ii) refining the class-wise prototypes via MAP statistics aggregation; iii) making predictions after the above two steps iterate until convergence." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 893, + 280 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "query samples, it is reasonable to refine the representations of class-wise prototypes initialized by support samples with the statistics of query samples. At this moment, the key is how to transfer the unbiased statistics from query samples to prototypes for achieving the best calibration. Moreover, the class-imbalanced setting is more challenging due to its unknown and arbitrary prior distribution of query samples. To address this challenge, we pioneered to depict the important but unknown prior with well-defined CT theory. Specifically, the prior could be measured by the transport mass from query samples to each prototype by summing the combination of forward and backward transport matrices optimized by CT loss along every query sample. Given the well-optimized prior, a prototype refinement algorithm is easy to be derived according to the MAP criterion. Considering the fact that the discriminative prototypes and well-optimized prior are coupled, we further employ an EM-solver to transfer the unbiased statistics efficiently and precisely. The overview of the proposed method can be found in Fig. 2.", + "bbox": [ + 75, + 376, + 472, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. CT Theory", + "text_level": 1, + "bbox": [ + 76, + 700, + 199, + 718 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "CT [39] is a powerful tool developed for measuring distance between any two probability distributions most recently, the effectiveness of which is mostly verified on deep generative models [13, 27] and multi-label classification [15]. In this work, we expand the territory of CT for discrete distributions under class-imbalanced TFSL. Denote $p(x) = \\sum_{i=1}^{n} a_i \\delta_{x_i}$ and $q(y) = \\sum_{j=1}^{m} b_j \\delta_{y_j}$ as source and target discrete distributions with $n$ and $m$ points, respectively. $\\pmb{a} \\in \\Delta^n$ and $\\pmb{b} \\in \\Delta^m$ , where $\\Delta^n$ and $\\Delta^m$ separately denote the probability simplex of $\\mathbb{R}^n$ and $\\mathbb{R}^m$ . The CT distance between $p(x)$ and $q(y)$ can be expressed as a combination", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "of forward CT $\\mathcal{C}_{\\phi}(x\\to y)$ and a backward CT $\\mathcal{C}_{\\phi}(x\\gets y)$", + "bbox": [ + 498, + 376, + 885, + 393 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {C} _ {\\phi , \\rho} (p, q) = \\min _ {\\phi} \\sum_ {x \\in p, y \\in q} \\rho \\mathcal {C} _ {\\phi} (x \\rightarrow y) + (1 - \\rho) \\mathcal {C} _ {\\phi} (x \\leftarrow y) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 402, + 892, + 433 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\phi$ is parameters of CT, $\\rho$ is the trade-off factor controlling the strengths between the forward and backward CTs. To better understand how the CT works when minimizing Eq. 2, we take the forward CT as an example:", + "bbox": [ + 496, + 441, + 893, + 503 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {C} _ {\\phi} (x \\rightarrow y) = \\mathbb {E} _ {y 1: m \\sim q} \\mathbb {E} _ {x \\sim p} \\left[ \\sum_ {j = 1} ^ {m} c (x, y _ {j}) \\hat {\\pi} _ {m} \\left(y _ {j} \\mid x, \\phi\\right)\\right] \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 512, + 892, + 549 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $c(\\cdot, \\cdot)$ could be some well defined distance functions, such as Euclidean or Cosine, $\\hat{\\pi}_m(y_j|x, \\phi)$ is forward transport matrix, also called forward navigator in the scope of CT, satisfying $\\sum_{j=1}^{m} \\hat{\\pi}_m(y_j|x, \\phi) = 1$ , it describes the possibility of transporting $x$ to $y_j$ and can be formulated as:", + "bbox": [ + 496, + 559, + 893, + 636 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\pi} _ {m} \\left(y _ {j} \\mid x, \\phi\\right) = \\frac {e ^ {- d _ {\\phi} \\left(x , y _ {j}\\right)}}{\\sum_ {j ^ {\\prime}} ^ {m} e ^ {- d _ {\\phi} \\left(x , y _ {j ^ {\\prime}}\\right)}} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 645, + 892, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $d_{\\phi}(\\cdot, \\cdot)$ represents measurement function, such as MLP implemented by Zheng et al. [39]. The forward CT can be interpreted as the expected cost to stochastically transport a random source point $x$ to one of the $m$ randomly instantiated \"anchors\" of the target distribution. By minimizing Eq. 3, an unbiased statistical estimation of the two distributions arrives. Proofs can be found in Zheng et al. [39]. Hence, it is reasonable to transfer statistics of one distribution to another.", + "bbox": [ + 496, + 685, + 893, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. PUTM", + "text_level": 1, + "bbox": [ + 500, + 816, + 589, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our proposed PUTM aims to exploit discriminative statistics from query samples for reducing the gap between the estimated prototypes and their ground truth prototypes. However, the ground truth prototypes are always intractable in", + "bbox": [ + 496, + 839, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16319", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "practice. A reasonable approach to obtain unbiased prototypes is to aggregate discriminative statistics from both support and query samples following a semi-supervised manner [37]. Different from the standard semi-supervised problems, the query samples are usually limited per class, especially in class-imbalanced case. Follow up, we present the importance of unbiased transfer in semi-supervised FSL setting, the algorithm of realizing unbiased exploitation with CT and transductive inference with unbiased transfer in turn.", + "bbox": [ + 75, + 90, + 472, + 224 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.1 Unbiased Statistics Transfer Matters in TFSL", + "text_level": 1, + "bbox": [ + 76, + 244, + 449, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a few-shot task, unbiased prototypes arrives if and only if the aggregated query samples are noiseless, which should heavily rely on the unbiased statistics transfer. Leveraging similarities between query samples and prototypes is a common way to realize statistics transfer in transductive few-shot image classification. Given the transport matrix $\\pi^n\\in \\mathbb{R}^{M\\times N}$ at the $n$ -th iteration, it measures the closeness of prototypes $\\{c_i^n\\}_{i = 1}^N$ and query samples $\\{\\pmb{x}_{i,j}^q\\}_{j = 1}^{K_i'}$ For simplicity, we rewrite all query samples as $\\{\\pmb{x}_r^q\\}_{r = 1}^M$ . Thus, the refined prototypes $\\{c_i^{n + 1}\\}_{i = 1}^N$ can be expressed as:", + "bbox": [ + 75, + 268, + 472, + 425 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {c} _ {i} ^ {n + 1} = \\frac {\\sum_ {r = 1} ^ {M} \\boldsymbol {\\pi} _ {r , i} ^ {n} \\boldsymbol {x} _ {r} ^ {q} + \\sum_ {j = 1} ^ {K} \\boldsymbol {x} _ {i , j} ^ {s}}{\\sum_ {r ^ {\\prime} = 1} ^ {M} \\boldsymbol {\\pi} _ {r ^ {\\prime} , i} ^ {n} + K}, \\quad i = 1, \\dots , N \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 431, + 468, + 469 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\pi_{r,i}^{n} = \\frac{e^{-d_{\\phi}(\\pmb{x}_{r}^{q},\\pmb{c}_{i}^{n})}}{\\sum_{r^{\\prime} = 1}^{M}e^{-d_{\\phi}(\\pmb{x}_{r^{\\prime}}^{q},\\pmb{c}_{i}^{n})}}, d_{\\phi}(\\cdot ,\\cdot)$ denotes the well defined measurement function, and we denote optimal transport matrix as $\\pi^{*}$ . To guarantee the unbiased refinement of prototypes, $\\pi^{*}$ need to be precise, which is usually difficult to be satisfied in practice. Fortunately, partial noisy is tolerable. For example, given 15 query samples per class, a few wrong transferring such as 1 or 2 samples is tolerable in calibrating prototypes. As for class-imbalanced case, a tiny mistake may result in disastrous consequence on prototypes calibration. For the classes having only 1 or 2 query samples, the tolerances of error transmissions should be extremely low. Therefore, to improve the robustness of calibrated prototypes in class-imbalanced TFSL, transferring unbiased statistics of query samples with $\\pi^{*}$ becomes crucial.", + "bbox": [ + 75, + 476, + 472, + 699 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "There are mainly two lines of works in defining $\\pi^{*}$ : i) Liu et al. [17] employ Cosine function [17]; ii) Hu et al. [11] use Optimal Transport (OT). Cosine function may not powerful enough to fully reflect the relationships between prototypes and query samples since it ignores various importance between each two points. OT describes a doubly stochastic transport matrix such that $\\Pi(p, q) = \\{\\pi^{*} | \\sum_{r=1}^{M} \\pi_{r,i}^{*} = a_{i}, \\sum_{i=1}^{N} \\pi_{r,i}^{*} = b_{r}\\}$ . Unfortunately, we usually do not have any priors on distributions of $p$ and $q$ , thus, we usually have $a_{i} = \\frac{1}{N}, i = 1, \\dots, N$ and $b_{r} = \\frac{1}{M}, r = 1, \\dots, M$ , which should be contradictory to class-imbalanced setting. For example, once we employ Dirichlet distribution with $\\alpha = 2_{N}$ to mimic the generation of query samples, $a_{i} = \\frac{1}{N}$ will never", + "bbox": [ + 75, + 700, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "fit the data. According to the analysis of CT, it replaces the uniform constraint on prior distribution of classes derived from query samples with a data-driven manner, thus ensuring to transfer the unbiased statistics more flexible and efficient.", + "bbox": [ + 496, + 90, + 893, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.2 Unbiased Statistics Exploitation with CT", + "text_level": 1, + "bbox": [ + 498, + 169, + 839, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As we can see, CT has an appealing property of exploiting unbiased statistics thanks to its task-adaptive prior rather than uniform-distributed one as OT. Here after, we present details of achieving such unbiased exploitation with CT.", + "bbox": [ + 496, + 193, + 893, + 253 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 2, given a class-imbalanced few-shot task in Sec. 2, we first employ a well-trained feature extractor $f_{\\theta^{*}}(\\cdot)$ to get features of support and query samples as $f_{i,j}^{s} = f_{\\theta^{*}}(\\pmb{x}_{i,j}^{s})$ and $f_{r}^{q} = f_{\\theta^{*}}(\\pmb{x}_{r}^{q})$ , where $\\theta^{*}$ is the set of optimized parameters, being fixed after training on the base classes following Mangla et al. [19]. Then, we conduct channel attention with preprocessing developed by Yang et al. [35]. Finally, unbiased statistics exploitation is realized by optimizing transport matrices constrained by CT theory.", + "bbox": [ + 496, + 253, + 893, + 388 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, the initial prototypes are averaged on the features of support set as $\\pmb{c}_i^0 = \\frac{1}{K}\\sum_{j = 1}^{K}f_{i,j}^s$ , $i = 1,\\dots,N$ where the superscript of $\\{c_i^0\\}_{i = 1}^N$ describes the generation of prototypes is zero. They will be updated subsequently, detailed in Sec. 3.3.3. At this moment, we treat $\\{c_i^0\\}_{i = 1}^N$ and $\\{f_r^q\\}_{r = 1}^M$ as samples from the two discrete distributions, and utilizing CT to learn the transport matrices for exploiting unbiased statistics. According to the analysis of Eq. 2, an unbiased sample estimate of CT given query features $\\{f_r^q\\}_{r = 1}^M$ and prototypes $\\{c_i^0\\}_{i = 1}^N$ can be expressed as:", + "bbox": [ + 498, + 390, + 893, + 544 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\phi , \\boldsymbol {\\theta} ^ {*}, \\rho} \\left(f _ {1: M} ^ {q}, \\boldsymbol {c} _ {1: N} ^ {0}\\right) = \\sum_ {i = 1} ^ {N} \\sum_ {r = 1} ^ {M} c \\left(\\boldsymbol {c} _ {i} ^ {0}, f _ {r} ^ {q}\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 553, + 890, + 595 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n(\\frac {\\rho}{M} \\hat {\\pi} _ {N} (\\pmb {c} _ {i} ^ {0} | f _ {r} ^ {q}, \\phi) + \\frac {1 - \\rho}{N} \\hat {\\pi} _ {M} (f _ {r} ^ {q} | \\pmb {c} _ {i} ^ {0}, \\phi))\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 598, + 864, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\hat{\\pi}_N$ and $\\hat{\\pi}_M$ separately denote the forward and backward transport matrices. Again substituting query features $\\{f_r^q\\}_{r=1}^M$ and prototypes $\\{c_i^0\\}_{i=1}^N$ into Eq. 4, we have:", + "bbox": [ + 500, + 635, + 893, + 681 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\pi} _ {N} \\left(\\boldsymbol {c} _ {i} ^ {0} \\mid f _ {r} ^ {q}, \\phi\\right) = \\frac {e ^ {- d _ {\\phi} \\left(f _ {r} ^ {q} , \\boldsymbol {c} _ {i} ^ {0}\\right)}}{\\sum_ {i ^ {\\prime} = 1} ^ {N} e ^ {- d _ {\\phi} \\left(f _ {r} ^ {q} , \\boldsymbol {c} _ {i ^ {\\prime}} ^ {0}\\right)}} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 691, + 890, + 729 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {\\pi}} _ {M} \\left(f _ {r} ^ {q} \\mid \\boldsymbol {c} _ {i} ^ {0}, \\phi\\right) = \\frac {e ^ {- d _ {\\phi} \\left(f _ {r} ^ {q} , \\boldsymbol {c} _ {i} ^ {0}\\right)}}{\\sum_ {r ^ {\\prime} = 1} ^ {M} e ^ {- d _ {\\phi} \\left(f _ {r ^ {\\prime}} ^ {q} , \\boldsymbol {c} _ {i} ^ {0}\\right)}} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 732, + 890, + 771 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The forward transport matrix represents the probability of query samples belonging to the corresponding support classes. The two transport matrices with the optimal parameter $\\phi^{*}$ can be obtained by minimizing the approximated CT estimation of Eq. 6. Once $\\hat{\\pi}_N^*$ and $\\hat{\\pi}_M^*$ with the optimal $\\phi^{*}$ are obtained, the transport matrix described in Sec. 3.3.1 for unbiased statistics exploitation can be naturally realized. To better understand this, we depict the mechanisms of the", + "bbox": [ + 496, + 779, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16320", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Work flow of PUTM for one task." + ], + "code_body": "Input: Support samples $\\{\\pmb{x}_{i,j}^{s}\\}_{i,j = 1}^{N,K}$ and class-imbalanced query samples $\\{\\pmb{x}_r^q\\}_{r = 1}^M$ generated from Dirichlet distribution with parameter $\\alpha$ , a well-trained feature extractor $f_{\\theta^{*}}(\\cdot)$ Parameters: Distance measurement function $d_{\\phi}(\\cdot ,\\cdot)$ Initialization Hyper-parameters $\\alpha$ $\\rho$ $\\lambda$ , and learning schedule for updating $\\phi$ ; Initialize prototypes $c_{i}^{0} = \\frac{1}{K}\\sum_{j = 1}^{K}f_{i,j}^{s},i = 1,\\ldots ,N;$ for n=1: $n_{steps}$ do Initialize parameters $\\phi$ $\\phi^{*}\\gets argmin_{\\phi}\\mathcal{L}_{\\phi ,\\theta^{*},\\rho}(f_{1:M}^{q},c_{1:N}^{n})$ Refining prototypes $c_{1:N}^{n + 1}$ using Eq. 11 based on $c_{1:N}^{n}$ end for Evaluating performance using Eq. 12; Output Parameters $\\{\\phi^{*},c_{1:N}^{n_{step}}\\}$", + "bbox": [ + 89, + 109, + 468, + 311 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "transport matrices developed above from three perspectives: 1) the distance function in transport matrices is implemented with DNNs, hence, they are able to learn a comprehensive distance metric beyond a simple Cosine function; 2) the CT distance is proven to be unbiased given samples of two distributions $p$ and $q$ in [39]; 3) The forward transport matrix holds free for sum along query samples given a specific prototype, namely, $\\sum_{r=1}^{M} \\hat{\\pi}_N(c_i^0 | f_r^q, \\phi^*) = C$ , and $C$ is not restricted to be equal for each class, thus embedding task-adaptive prior instead of uniform distribution as PT-MAP [11] does. On the other hand, the backward transport matrix holds tight for sum along query samples given a specific prototype, that is, $\\sum_{r=1}^{M} \\hat{\\pi}_M(f_r^q | c_i^0, \\phi^*) = 1$ , hence, uniform-distributed prior holds, and it is proven to be underfitting in class-imbalanced case [29]. In practice, we employ a trade-off to balance the strengths of the two transport matrices by summing them together with a soft coefficient $\\rho$ . For simplicity, we only use the forward transport matrix in the rest of the work.", + "bbox": [ + 75, + 339, + 472, + 612 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.3 Unbiased Statistics Transfer with EM-Solver", + "text_level": 1, + "bbox": [ + 76, + 628, + 442, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Once the forward transport matrix $\\hat{\\pi}_N^*$ is obtained by minimizing Eq. 6, it is straightforward to derive the refined prototypes by substituting $\\hat{\\pi}_N^*$ into Eq. 5:", + "bbox": [ + 75, + 652, + 470, + 700 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {c} _ {i} ^ {\\prime} = \\frac {\\sum_ {r = 1} ^ {M} \\hat {\\pi} _ {N , r , i} ^ {*} f _ {r} ^ {q} + \\sum_ {j = 1} ^ {K} f _ {i , j} ^ {s}}{K + \\sum_ {r = 1} ^ {M} \\hat {\\pi} _ {N , r , i} ^ {*}}, \\quad i = 1, \\dots , N \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 710, + 470, + 753 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It is worth noting that once the optimal parameters $\\phi^{*}$ are arrived, the only parameters left for optimizing are prototypes. Recalling our objective in Eq. 6, it is easy to find that the optimal prototypes at this moment could also be derived by $\\frac{\\partial\\mathcal{L}_{\\phi^{*},\\theta^{*},\\rho}}{\\partial c_{1:N}^{0}}$ , thereby Eq. 9 could be derived. Instead of directly calibrating class-wise prototypes, We employ an inertia parameter $\\alpha$ to update prototypes proportionally:", + "bbox": [ + 75, + 762, + 472, + 875 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {c} _ {i} ^ {1} = \\boldsymbol {c} _ {i} ^ {0} + \\alpha \\left(\\boldsymbol {c} _ {i} ^ {\\prime} - \\boldsymbol {c} _ {i} ^ {0}\\right), \\quad i = 1, \\dots , N \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 883, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Right now, recursive expression emerges for updating prototypes according to Eq. 10:", + "bbox": [ + 498, + 90, + 893, + 122 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {c} _ {i} ^ {n + 1} = \\boldsymbol {c} _ {i} ^ {n} + \\alpha \\left(\\boldsymbol {c} _ {i} ^ {\\prime} - \\boldsymbol {c} _ {i} ^ {n}\\right), \\quad i = 1, \\dots , N \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 130, + 893, + 148 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As we can see: i) updating the forward transport matrix $\\hat{\\pi}_N^*$ and prototypes $c_{1:N}^n$ are coupled; ii) $\\hat{\\pi}_N^*$ is a random variable determined by $\\phi$ while $c_{1:N}^n$ is an unknown but deterministic variable. These two facts meet conditions of implementing EM optimization, and we formulate our EM-Solver as follows: i) E Step, updating $\\hat{\\pi}_N^*$ by minimizing Eq. 6 while keeping $c_{1:N}^n$ fixed; ii) M Step, updating $c_{1:N}^n$ by minimizing Eq. 6 while keeping $\\hat{\\pi}_N^*$ fixed. Besides, it is worth noting that at each iteration, $\\phi^*$ need to be reinitialized. The pseudo code is provided in Alg. 1.", + "bbox": [ + 496, + 157, + 893, + 309 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After $n_{step}$ loops between estimating $\\hat{\\pi}_N^*$ and refining $c_{1:N}^n$ , the decision per sample is finally made by:", + "bbox": [ + 498, + 309, + 890, + 340 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ny _ {r} ^ {q} = \\max _ {i \\in [ 1: N ]} \\hat {\\pi} _ {N} \\left(\\boldsymbol {c} _ {i} ^ {n _ {\\text {s t e p}}} \\mid f _ {r} ^ {q}, \\phi^ {*}\\right), \\quad r = 1, \\dots , M \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 348, + 892, + 375 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Statistic results of average accuracy are usually conducted using query samples on various of different tasks.", + "bbox": [ + 498, + 383, + 890, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Complexity Analysis", + "text_level": 1, + "bbox": [ + 500, + 422, + 694, + 438 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\phi$ is implemented with MLP in our work. Taking a two-layers MLP for example, namely, $d_{f} \\rightarrow d_{1}^{\\phi} \\rightarrow d_{2}^{\\phi}$ . For $T$ tasks, computational complexity originally takes $\\mathcal{O}(T \\times \\max \\{NM \\times d_{f} \\times d_{1}^{\\phi}, NM \\times d_{1}^{\\phi} \\times d_{2}^{\\phi}\\})$ . In practice, $T$ is usually set to be large enough for reliable results, thus resulting in time-consuming evaluation of our model. To mitigate the real-time issue, we trade space for time by paralleling our proposed PUTM among all tasks. Therefore, the computational complexity is reduced to $\\mathcal{O}(\\max \\{NM \\times d_{f} \\times d_{1}^{\\phi}, NM \\times d_{1}^{\\phi} \\times d_{2}^{\\phi}\\})$ . Besides, we can further control the size of MLP, that is $\\{d_{i}^{\\phi}\\}_{i=1}^{2}$ , to achieve a trade-off between accuracy and real-time efficiency.", + "bbox": [ + 496, + 444, + 893, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 641, + 633, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 666, + 689, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines: We mainly compare our model with some recently proposed State-Of-The-Art (SOTA) methods on one Nvidia RTX 3090 GPU. For inductive methods, we adopt Baseline/Baseline $(++)$ [4], ProtoNet [26], Simpleshot [33], and HOT [9] in inductive. For transductive methods, we adopt PT-MAP [11], LaplacianShot [40], TIM[2], BD-CSPN [17], $\\alpha$ -TIM [29], iLPC [14], and BAVAR [12].", + "bbox": [ + 496, + 688, + 893, + 795 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets: We evaluate our model on four benchmarks including miniImageNet [22], tieredImageNet [23], CUB [31], and CIFAR-FS [1]. MiniImageNet is randomly chosen from ILSVRC-12 dataset [6] and it contains 100 classes with 600 images per class, the resolution of which is $84 \\times 84 \\times 3$ . Following previous works [22, 29, 11, 35], the dataset is split into 64 base classes, 16 validation classes, and", + "bbox": [ + 496, + 795, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16321", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/5771361a0181e54271e590a1ac27a03d60b389c1f1f5319739d32da0bc228eec.jpg", + "table_caption": [ + "Table 1: Classification accuracy (%) of SOTA methods on class-imbalanced and class-balanced settings with different datasets and backbones. For imbalanced case, query samples are generated following a Dirichlet distribution with $\\alpha = 2_{N}$ . Results are averaged over 3000 tasks with $95\\%$ confidence intervals. Results with superscript $\\dagger$ are our re-implementations based on the code provided by Veilleux et al. [29]. The best and the second best scores are marked in bold and blue, respectively." + ], + "table_footnote": [], + "table_body": "
SettingMethodmini-ImageNet (WRN/WRN$)CUB (RN18/WRN$)tiered-ImageNet (WRN/WRN$)CIFAR-FS (WRN$)
1-shot3-shot5-shot1-shot3-shot5-shot1-shot3-shot5-shot1-shot3-shot5-shot
Induct. (%)Imbalanced & BalancedBaseline (ICLR'19)62.2/62.8†76.9†/77.3†81.9/82.9†64.6/70.7†82.3†/87.3†86.9/90.0†64.6/63.6†80.0†/83.0†84.9/87.2†69.5†83.9†86.7†
Baseline++ (ICLR'19)64.5/64.8†77.5†/78.4†82.1/82.7†69.4/81.7†83.3†/89.4†87.1/91.2†68.7/66.9†80.9†/78.7†85.4/82.2†74.9†85.0†87.4†
ProtoNet (NeurIPS'17)61.2/62.5†76.9†/77.2†81.1/81.4†63.1†/69.6†82.3†/85.6†85.4†/88.8†63.5†/64.2†79.9†/80.1†84.1†/84.0†69.5†83.8†86.7†
Simpleshot (ARXIV)66.2/67.1†77.6†/78.2†82.4/83.3†70.6/81.7†83.6†/89.5†87.5/91.4†70.7/71.4†81.3†/84.2†85.9/87.5†75.2†84.7†87.4†
HOT (NeurIPS'22)66.3†/69.178.5†/79.8†82.8†/84.474.5†/81.285.4†/88.2†87.8†/91.574.1†/75.982.6†/83.9†85.4†/87.375.485.3†87.5
Transduct. (%)ImbalancedPT-MAP (ARXIV)60.6/63.2†65.9†/68.0†66.8/69.3†65.1/69.8†71.2†/73.2†71.3/74.3†65.1/67.8†69.1†/72.0†71.0/73.2†65.9†69.3†70.3†
LaplacianShot (ICML'20)68.1/69.8†78.8†/79.2†83.2/83.6†73.7/84.2†85.7†/90.4†87.7/91.4†73.5/72.6†82.6†/85.0†86.8/87.7†78.3†86.1†87.3†
TIM (NeurIPS'20)69.8/70.9†79.7†/80.7†81.6/83.2†74.8/82.8†84.8†/89.1†86.9/90.5†75.8/77.8†82.5†/86.3†85.4/88.3†77.0†84.6†86.2†
BD-CSPN (ECCV'20)70.4/71.2†77.1†/78.6†82.3/83.4†74.5/85.1†85.7†/90.5†87.1/91.5†75.4/76.3†82.5†/85.0†85.9/87.2†79.1†86.0†87.3†
α-TIM (NeurIPS'2021)69.8/70.9†80.4†/81.1†84.8/84.9†75.7/83.6†87.3†/91.2†89.8/92.8†76.0/77.7†83.6†/86.6†87.8/89.9†78.1†87.2†88.9†
iLPC (ICCV'21)71.5†/74.3†78.6†/81.1†81.0†/83.3†78.7†/86.4†85.6†/90.1†86.9†/90.8†76.6†/81.6†83.2†/87.5†85.1†/89.0†80.8†85.4†86.5†
BAVAR (AISTATS'23)74.1/74.2†82.6†/82.6†85.5/85.6†82.0/85.7†89.2†/89.8†90.7/90.8†77.5/80.6†84.8†/87.2†87.5/89.3†81.8†87.0†87.9†
PUTM (Ours)70.9/73.880.5/82.984.6/85.778.9/86.987.8/91.389.3/92.275.0/81.183.6/88.486.0/90.481.487.388.6
BalancedPT-MAP (ARXIV)78.9/82.5†86.3†/87.5†86.6/88.6†85.5/92.0†90.5†/94.0†91.3/94.3†84.6/88.1†88.2†/91.8†90.0/92.5†87.6†90.5†90.9†
LaplacianShot (ICML'20)72.9/73.4†79.0†/80.5†83.8/84.2†78.9/87.5†86.7†/90.4†88.8/92.3†78.8/78.7†84.6†/85.6†87.3/87.0†82.1†86.3†86.8†
TIM (NeurIPS'20)74.6/77.6†85.5†/86.0†85.9/88.0†80.3/88.1†89.8†/93.0†90.5/94.0†80.3/83.8†87.7†/90.6†88.9/92.1†83.0†89.5†90.5†
BD-CSPN (ECCV'20)72.5/73.8†79.2†/80.7†83.7/85.3†77.9/87.3†86.9†/91.4†88.9/92.4†77.7/78.7†84.5†/86.4†87.4/88.3†81.6†87.4†88.6†
α-TIM (NeurIPS'2021)71.0/71.5†76.8†/77.7†82.4/83.3†77.2†/84.9†85.1†/90.2†87.6†/91.2†75.1†/78.9†80.6†/84.4†85.3†/88.2†79.7†85.7†87.9†
iLPC (ICCV'21)75.5†/77.8†82.0†/83.9†83.9†/85.7†82.4†/89.6†87.9†/92.3†88.9†/93.0†81.0†/85.5†86.4†/89.8†87.5†/90.9†84.8†88.6†89.2†
BAVAR (AISTATS'23)78.5/78.5†84.8†/84.9†87.4/87.7†85.6/89.0†90.8†/91.7†91.4/92.1†81.5/84.7†87.4†/89.3†88.3/90.3†85.0†88.4†88.9†
PUTM(Ours)78.4/81.484.9/86.786.5/88.184.9/91.289.2/93.390.1/93.781.6/86.886.9/90.788.6/92.286.489.590.4
", + "bbox": [ + 80, + 161, + 890, + 386 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/03f36be5589b3e7217c55def4c04ce9fbd84dcc621e097d8ea5193aff6247575.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 81, + 398, + 330, + 531 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b1e240b3e1a7705cc135e6eccc763daa6b6161085835fd78ab617d6092a67cf9.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 351, + 398, + 609, + 530 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a1ce3d03635b385abb5ab7dd482800a036f12a9107fa72ca52cd43b2264aeff3.jpg", + "image_caption": [ + "(c)", + "Figure 3: (a)-(b): The t-SNE [28] visualizations before (middle) and after (left) calibration on a 5-way 1-shot miniImageNet task. Pentagrams are prototypes while solid dots are query features. Classes change and best view in colors. (c): Impact of forward and backward transport matrices in calibrating prototypes on miniImageNet over 3000 5-way 1-shot tasks." + ], + "image_footnote": [], + "bbox": [ + 633, + 398, + 890, + 537 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "20 novel classes. TieredImageNet [23] is also a subset of ILSVRC-12 dataset, which is larger than miniImageNet. It contains 608 classes sampled from a hierarchical category structure with around 1281 images per class. Following the previous work [23], we split the dataset into 351 base classes, 97 validation classes, and 160 novel classes. The resolution is also $84 \\times 84 \\times 3$ . CUB is a fine-grained dataset, containing 200 classes of birds with around 60 images per class. And the resolution is still $84 \\times 84 \\times 3$ . We adopt 100 base classes, 50 validation classes, and 50 novel classes following [4]. CIFAR-FS consists of all 100 classes from CIFAR-100 [34], whose classes are randomly split into 64 base classes, 16 classes, and 20 novel classes. Each class contains 600 images of size $32 \\times 32 \\times 3$ .", + "bbox": [ + 75, + 638, + 472, + 851 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details: We use pre-trained backbones for extracting visual features of four benchmarks, as shown in Table. 1. WRN and RN18 are separately WideResNet-28-", + "bbox": [ + 75, + 854, + 472, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "10 and ResNet-18 pre-trained with standard classification loss [29]. WRN $\\S$ is WideResNet-28-10 pre-trained with self-supervised loss [19]. Besides, we employ log transform, a channel-wise feature adaptation, introduced in Yang et al. [35] to pre-process the pre-extracted features. The distance function $\\phi$ is instantiated as a two-layers MLP activated with LeakyReLU whose architecture is $[d_f, 128, 64, 1]$ . As for hyper-parameters, we mainly set $\\beta = 0.5$ , $\\alpha = 0.1$ , $\\rho = 0.2$ . The reported results are averaged over 3000 tasks.", + "bbox": [ + 496, + 638, + 893, + 776 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Main Results", + "text_level": 1, + "bbox": [ + 500, + 786, + 638, + 800 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative results: The classification results on miniImageNet, tieredImageNet, CUB, and CIFAR-FS are reported in Table 1, according to which five-fold observations can be drawn: 1) inductive methods are not bothered by class-imbalanced problem since they do not leverage transferable statistics of query samples; 2) most transductive methods", + "bbox": [ + 496, + 809, + 895, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16322", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e8520dc25383a3eb2b6efef5b65fdc2b7a19db726b824beffa9ebda40b8fd5cc.jpg", + "image_caption": [ + "Figure 4: Case studies for 5-way 5-shots tasks on CUB [31] (left) and miniImageNet (right). Comparisons between unnormalized prior distribution (true number of query samples counting for each class) and unnormalized posterior distribution (estimated number of query samples counting by the well optimized forward transport matrix for each class)." + ], + "image_footnote": [], + "bbox": [ + 68, + 88, + 272, + 195 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c2bc6762adbc84335fc53b3432e498d319753588350ba5b533bcbfe7c9da7f09.jpg", + "image_caption": [ + "Figure 5: 5-way 5-shot classification accuracy on miniImageNet and CUB of transductive methods versus imbalance level, lower $\\alpha$ corresponds to severer class imbalance." + ], + "image_footnote": [], + "bbox": [ + 276, + 88, + 478, + 196 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "still outperform the inductive peers in class-imbalanced setting, which implies that there exists a trade-off between extra statistics conveyed by class-imbalanced query samples and algorithm bias; 3) results of features extracted by WRN $\\S$ usually outperforms those by WRN or RN18, it indicates that self-supervised learning is helpful in obtaining generalized representations in class-imbalanced and class-balanced FSL applications; 4) most existed transductive inference methods suffer from performance cliff since their mismatch between data distribution and prior distribution. For example, TIM implicitly introduces uniform prior on query samples by using entropy regularization since minimizing entropy-based regularization is equivalent to minimizing the KL divergence between the predicted marginal distribution and uniform distribution. Hence, data distribution and model bias are unsuitable, leading to poor accuracy. Fortunately, such kind of mismatch can be eased by re-weighting in [29]. On the contrary, PT-MAP holds a strong but unmodified uniformly distributed prior on its transport matrix. Therefore, results of TIM are robuster than those of PT-MAP; 5) our proposed method outperforms most of the transductive methods and achieves competitive results with some most recently proposed methods, such as $\\alpha$ -TIM, iLPC and BAVAR. It indicates that prototype refinement benefits from the well optimized transport matrices when shot number is low. Moreover, compared with iLPC and BAVAR, on the one hand, our model is easy to implement. On the other hand, BAVAR heavily relies on prior of imbalanced ratio $\\alpha$ in class-imbalanced case while iLPC depends on uniform prior in class-balanced case [12], importantly however, our model is free of these priors, making it suitable for real-world applications when we have no idea on class distributions.", + "bbox": [ + 76, + 325, + 472, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitatively analysis: To qualitatively illustrate the evolution of prototypes of our model, we map prototypes and query features of one task into a 2-D subspace with t-distributed Stochastic Neighbor Embedding (t-SNE) [28], it is a non-linear dimensional reduction technique well-suited for embedding high-dimensional data into a low-dimensional", + "bbox": [ + 75, + 810, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9f5da9ddfb275610243ae1e2beb650110964e6496e8595ce92af91b504d1ce98.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 88, + 689, + 209 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5b00c9dbd6b1a6fc6f1a8ee2fbd614df8d9147a7bd0c0101073eadbb3e0c3a46.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 88, + 901, + 209 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4b117b8f5e5e6d7912a0957bbd664cc2f80691a425a127835f2e8dfa36016642.jpg", + "table_caption": [ + "Table 2: End-to-end real-time efficiencies (s) of 5-way 1-shot on CUB with two backbones averaged on 100 tasks." + ], + "table_footnote": [], + "table_body": "
Backboneα - TIM (NeurIPS'21)iLPC (ICCV'21)BAVAR (AISTATS'23)Ours
RN185.64.63.42.9
WRN6.24.73.63.7
", + "bbox": [ + 504, + 321, + 888, + 388 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "space. As we can see from Fig. 3, due to class-imbalanced issue, although prototypes can not match their corresponding class centers well at beginning, they become consistent with the ground truth centers after refinement using our proposed method, verifying the effectiveness of our PUTM in dealing with unknown and arbitrary prior situation.", + "bbox": [ + 496, + 414, + 893, + 506 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Model Analysis", + "text_level": 1, + "bbox": [ + 500, + 513, + 656, + 531 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Forward transport V.S. backward transport: As discussed in Sec. 3.3.2, the forward and backward transport matrices put different priors of $\\{a_i\\}_{i=1}^N$ . Namely, we do not restrict uniform distribution in the forward transport and enable it to be adaptive to data-driven class distribution. On the contrary, prior in the backward transport is always assumed to be $\\frac{1}{N}$ . Therefore, we employ the forward transport for predictions to meet the class-imbalanced essence, the efficiency is illustrated in Fig. 4, it depicts that the predicted distribution is consistent with the true distribution. Moreover, we conduct an extra experiment to verify the opposite direction of the two transport matrices, results are illustrated in Fig. 3, where we separately use the forward transport and the backward transport to calibrate the prototypes over 3000 tasks. According to the results, we find that, from a statistical point of view, the backward transport does harm the efficient migration from the class-imbalanced query samples.", + "bbox": [ + 496, + 537, + 895, + 794 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Robustness of imbalanced coefficients: An important point in this work is that our model is robust for various class-imbalanced coefficients, which is vital and crucial for real-world applications since we usually do not know whether the few-shot tasks are balanced or not in advance, thus, we could not know what kind of methods are suitable for describing the samples distribution of tasks. Once they are", + "bbox": [ + 496, + 795, + 895, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16323", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/31de3a57fe62b36349fc65422bb829107d7a86eccc89cb737914971922bc4fb6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 88, + 344, + 213 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/40d73d77e591d28f618fb87f29e90ee2d1dcaa757ad0940aeea7b377e568bace.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 87, + 616, + 213 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7625139324fac253e27f9d27d8039a52cba1acba48db366165cb100f4262c3fa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 625, + 88, + 890, + 212 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/97375bd9f791c9ee9a48ed1ee0674f95378f49b3323be29c19ebdbb12d477929.jpg", + "image_caption": [ + "Figure 6: Sensitivity analysis of our model to hyper-parameters including log transform $\\beta$ , CT coefficient $\\rho$ , and inertia $\\alpha$ . Results are obtained with WRN8 and are reported on both validation and test sets. Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 78, + 215, + 344, + 340 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c8c618a05c2cab20e3f21c6c2d80903b8512108f50151a6fc69185e8c9cf3e5b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 215, + 616, + 340 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3961bb3cd77757ffe3a0de41e992f0d7ed4011378782c1fb2f8c05b2b2784868.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 625, + 215, + 890, + 339 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "unmatched, horrible performance degradation would happen, such as PT-MAP does. We verify the robustness of our model with a wide range of imbalanced coefficients as shown in Fig. 5, where $\\alpha$ changes from 1 to 6. The performance of most methods decreases as $\\alpha$ decreasing because smaller $\\alpha$ indicates more imbalanced distribution of query samples, thus making tasks harder. On the contrary, performances of LaplacianShot and $\\alpha$ -TIM drop obviously as $\\alpha$ increases. Our model achieves consistent improvement and reasonable trend in a wide range of $\\alpha$ , we attribute this to the introduction of adaptive transport matrices, which enables PUTM to fit the class distributions precisely and flexibly.", + "bbox": [ + 75, + 409, + 470, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Sensitivity of hyper-parameters: To further verify the robustness of our model, we validate the sensitivity of PUTM to different hyper-parameters introduced in Sec. 4.1, and results are reported in Fig. 6. Generally speaking, the tendencies on validation and test sets are same. Besides there are three-fold observations: i) CT coefficient is less sensitive than log transform and inertia; ii) log transform controls the strength of channel-wise attention, which is proven to be important especially in few-shot case, thus it affects performance mostly; iii) inertia reflects the bottleneck of information flow from the aggregated prototypes to the refined prototypes. Bigger or smaller value of inertia is helpless for robust transfer since refinement of prototypes is associated with transport matrices. Namely, if the matrices are not well-optimized, a big inertia may cause algorithm to fall into a local optimum and vice versa.", + "bbox": [ + 75, + 594, + 470, + 835 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Real-time efficiency: To verify the efficiency of PUTM, we conduct parallel versions of $\\alpha$ -TIM, iLPC, and BAVAR based on their official implementations with the same machine. Results are reported in Table. 2, as we can see that our", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "model consumes less time using RN18 and achieves competitive results using WRN. And we attribute this to the fact that : i) both $\\alpha$ -TIM and iLPC employ Sinkhorn algorithm to solve the Optimal Transport (OT) problem involving thousands of inner loop, and it is a kind of time consuming; ; ii) our EM-Solver might be more efficient for dealing with the class-imbalanced TFSL since it imposes potential capability for modeling such unknown distribution with CT theory.", + "bbox": [ + 496, + 409, + 893, + 531 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and Future Works", + "text_level": 1, + "bbox": [ + 498, + 545, + 777, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose a novel model called PUTM with EM-Solver based on CT theory for both class-imbalanced and class-balanced TFSL in this work according to an important observation that CT has a natural connection with unknown and arbitrary class prior problem. Specifically, PUTM exploits transferable statistics with CT for refining biased prototypes solved by EM to capture the unbiased statistics within imbalanced query samples. Extensive experiments on standard benchmarks verify the effectiveness of our model in both class-imbalanced and class-balanced few-shot applications. In the future, we will explore the applicability of PUTM on more problem settings and applications, such as multi-domain few-shot classification and few-shot object detection.", + "bbox": [ + 496, + 571, + 893, + 768 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 784, + 679, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant U21B2006; in part by Shaanxi Youth Innovation Team Project; in part by the National NSFC under Grant 82172860; in part by the National NSFC under Grant 6220010437; in part by the Fundation of Aerospace under Grant SAST2021-", + "bbox": [ + 496, + 809, + 895, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16324", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "012. We also thanks Dandan Guo and He Zhao for their constructive comments on transductive few-shot learning, we thanks Zhisong Zhang for his very initial exploration on class-imbalanced few-shot image classification, we thanks Dongsheng Wang for his passion discussions on CT.", + "bbox": [ + 76, + 90, + 472, + 167 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 180, + 173, + 196 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Luca Bertinetto, Joao F Henriques, Philip HS Torr, and Andrea Vedaldi. Meta-learning with differentiable closed-form solvers. arXiv preprint arXiv:1805.08136, 2018.", + "[2] Malik Boudiaf, Imtiaz Ziko, Jérôme Rony, José Dolz, Pablo Piantanida, and Ismail Ben Ayed. Information maximization for few-shot learning. 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PMLR, 2020." + ], + "bbox": [ + 78, + 90, + 470, + 771 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "16326", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Prototypes-oriented Transductive Few-shot Learning with Conditional Transport/e3d7c832-dffc-42b7-b29a-faccf7386804_model.json b/2023/Prototypes-oriented Transductive Few-shot Learning with Conditional Transport/e3d7c832-dffc-42b7-b29a-faccf7386804_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e42f1bec7db299e105f6ce9d684fef135adaa7bf --- /dev/null +++ b/2023/Prototypes-oriented Transductive Few-shot Learning with Conditional Transport/e3d7c832-dffc-42b7-b29a-faccf7386804_model.json @@ -0,0 +1,2002 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.807, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.131, + 0.892, + 0.153 + ], + "angle": 0, + "content": "Prototypes-oriented Transductive Few-shot Learning with Conditional Transport" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.189, + 0.93, + 0.244 + ], + "angle": 0, + "content": "Long Tian\\(^{1}\\), Jingyi Feng\\(^{1}\\), Xiaoqiang Chai\\(^{1}\\), Wenchao Chen\\(^{2,\\text{图}}\\), Liming Wang\\(^{1}\\), Xiyang Liu\\(^{1}\\), Bo Chen\\(^{2}\\) \n\\(^{1}\\) National Pilot School of Software Engineering, \\(^{2}\\) National Key Laboratory of Radar Signal Processing \n\\(^{1,2}\\) Xidian University, Xi'an, Shanxi 710071, China" + }, + { + "type": "text", + "bbox": [ + 0.325, + 0.246, + 0.694, + 0.26 + ], + "angle": 0, + "content": "Email: {tianlong, wcchen}_xidian@163.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.296, + 0.314, + 0.312 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.328, + 0.474, + 0.66 + ], + "angle": 0, + "content": "Transductive Few-Shot Learning (TFSL) has recently attracted increasing attention since it typically outperforms its inductive peer by leveraging statistics of query samples. However, previous TFSL methods usually encode uniform prior that all the classes within query samples are equally likely, which is biased in imbalanced TFSL and causes severe performance degradation. Given this pivotal issue, in this work, we propose a novel Conditional Transport (CT) based imbalanced TFSL model called Prototypes-oriented Unbiased Transfer Model (PUTM) to fully exploit unbiased statistics of imbalanced query samples, which employs forward and backward navigators as transport matrices to balance the prior of query samples per class between uniform and adaptive data-driven distributions. For efficiently transferring statistics learned by CT, we further derive a closed form solution to refine prototypes based on MAP given the learned navigators. The above two steps of discovering and transferring unbiased statistics follow an iterative manner, formulating our EM-based solver. Experimental results on four standard benchmarks including miniImageNet, tieredImageNet, CUB, and CIFAR-FS demonstrate superiority of our model in class-imbalanced generalization1." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.687, + 0.21, + 0.703 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.713, + 0.471, + 0.879 + ], + "angle": 0, + "content": "Deep learning based methods have gained a great success in many real-world applications, such as image classification [10, 25, 36], natural language processing [3, 32, 38], and so on, thanks to its powerful nonlinear representation ability [18, 24]. However, their outstanding performances heavily rely on large-scale annotated training data [6, 16]. When it comes to high cost of collecting and annotating a large amount of data, a major research effort is being dedicated to low data regimes, in which overfitting occurs in optimizing deep learning architectures. Few-shot Learning (FSL) tackles these challenges and has triggered substantial interests" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.296, + 0.885, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.457, + 0.895, + 0.518 + ], + "angle": 0, + "content": "Figure 1: 5-way 1-shot image classification results with miniImageNet [22] dataset on 3000 tasks. Our model achieves the best accuracy in a wide range of imbalanced coefficients compared with PT-MAP [11] and \\(\\alpha\\)-TIM [29]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.551, + 0.895, + 0.702 + ], + "angle": 0, + "content": "within the community [8, 20], it aims to train a model from the base classes so as to generalize on the tasks sampled from the novel classes that were never seen during training. There are two major lines of works from the perspective of inference paradigms, namely inductive methods [26, 4] and their transductive counterparts [7, 23]. Both of them adopt well trained models for evaluating new tasks sampled from the novel classes. The former ones only utilize support samples in a supervised way while the later ones leverage both support and query samples in a semi-supervised manner." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.897, + 0.901 + ], + "angle": 0, + "content": "Transductive inference is widely used in FSL since it can sufficiently discover statistics of query samples compared with its inductive peer. As a representative example, Hu et al. [11] propose PT-MAP for first employing Wide ResNet (WRN) [36] trained with S2M2 [19] on base classes to extract features of new tasks, and then adjusting prototypes from novel classes by aggregating similar query samples per class with the help of transport matrix derived from the Sinkhorn algorithm [5]. Setting marginal distributions of prototypes as uniform encodes strong prior that all the classes within query samples are equally likely, although, it works pretty well in perfectly class-balanced query samples. However, it is proven to be detrimental in class-imbalanced" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.418, + 0.901 + ], + "angle": 0, + "content": "1Our code is available at https://github.com/RashLog/PUTM" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16317" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "applications where query samples come with arbitrary and unknown label marginals [21], and classification accuracy drops dramatically, as shown in Fig. 1. To narrow this gap, Veilleux et al. [29] propose \\(\\alpha\\)-TIM for handling class-distribution variations effectively. Unfortunately, we have observed the phenomena as shown in Fig. 1 that \\(\\alpha\\)-TIM can not achieve consistent improvement in various class-imbalanced levels, thus restricting its real-world applications. Most recently, other more complicated methods are also be arisen [14, 12]. Hu et al. [12] propose a clustering method for capturing the class-wise distributions properly." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.258, + 0.473, + 0.711 + ], + "angle": 0, + "content": "To this end, for class-imbalanced TFSL, we develop a novel and simple Prototypes-oriented Unbiased Transfer Model (PUTM). It firstly constructs transferable class-wise prototypes iteratively for capturing the unbiased statistics within class-imbalanced query samples. Then it performs few-shot classification via the similarities between prototypes and query samples when the transfer arrives at convergence. The key to obtain unbiased transferable statistics is estimating class-wise marginal distributions precisely [14]. To achieve this, instead of utilizing doubly stochastic transport matrix constrained with fixed uniform-distributed marginal prior between prototypes and query samples as PT-MAP does, we employ task-adaptive forward and backward transport matrices with learnable marginal priors constrained by minimizing Conditional Transport (CT) distance [39] between prototypes and query samples. CT is a tool for measuring the cost in transporting the mass in one distribution to match another in an exchangeable but asymmetrical manner given a specific point-to-point cost function and an estimizable forward and backward transport matrices, also called navigators in the CT scope. To better calibrate prototypes with the help of learned transport matrices and query samples, we further derive a closed-form solution to refine prototypes based on MAP in an iterative manner. Decisions are finally made using the combination of forward and backward transport matrices when the iteration converges. Experiments on four benchmarks demonstrate that our proposed PUTM can learn task-adaptive prior in various class-imbalanced coefficients, paving a new way to transfer the unbiased statistics of query samples to prototypes." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.712, + 0.423, + 0.726 + ], + "angle": 0, + "content": "Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.738, + 0.47, + 0.814 + ], + "angle": 0, + "content": "- We find that the performance of class-imbalanced FSL heavily relies on the accurate estimation of class-wise marginal distribution. Meanwhile, we are the first one to find that there exists a nature connection between CT theory and such marginal distribution estimation." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.825, + 0.473, + 0.902 + ], + "angle": 0, + "content": "- We propose a novel and simple PUTM for class-imbalanced FSL based on connections mentioned above. It firstly embeds CT distance to measure the differences between prototypes and query samples for achieving better task-adaptive unbiased statistic migra" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.738, + 0.473, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "tion elegantly. Then it calibrates prototypes using the transferred statistics in an iterative manner." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.133, + 0.895, + 0.208 + ], + "angle": 0, + "content": "- We provide extensive experiments and comparisons on four standard benchmarks for verifying that our model achieves competitive results on both class-balanced and class-imbalanced (in a wide range of imbalanced coefficients) FSL settings." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.222, + 0.676, + 0.238 + ], + "angle": 0, + "content": "2. Task Formulation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.247, + 0.895, + 0.42 + ], + "angle": 0, + "content": "We divide the whole annotated dataset into two disjoint subsets: a base set \\(\\mathcal{D}_{\\text{base}}\\) with \\(\\mathcal{B}\\) classes and a novel set \\(\\mathcal{D}_{\\text{novel}}\\) with \\(\\mathcal{N}\\) classes. To build a common N-way K-shot task [30, 26], we first randomly sample N classes from \\(\\mathcal{N}\\) novel classes, and then pick K samples per class for the support set \\(S = \\{\\pmb{x}_{i,j}^{s}, \\pmb{y}_{i,j}^{s}\\}_{i=1,j=1}^{N,K}\\) to train or fine-tune the model. Finally, \\(K_{i}'\\) query samples being non-overlapped with support samples per class are randomly picked from the \\(N\\) support classes for evaluating the performance of the model, formulating query set as \\(\\mathcal{Q} = \\{\\pmb{x}_{i,j}^{q}, \\pmb{y}_{i,j}^{q}\\}_{i=1,j=1}^{N,K_{i}'}\\). For simplicity, we set \\(M = \\sum_{i=1}^{N} K_{i}'\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.421, + 0.895, + 0.542 + ], + "angle": 0, + "content": "Class-imbalanced TFSL: Veilleux et al. [29] figure out that the number of query samples per class should be arbitrary and unknown instead of being strictly equal. That is \\( K' \\) is a function of class and changes with class indexes. To describe such behavior, they develop a class marginal with Dirichlet distribution for generating query samples. Specifically, the class-wise marginal distribution of query samples per task \\( p \\) are determined by:" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.553, + 0.895, + 0.595 + ], + "angle": 0, + "content": "\\[\nf _ {D i r} (\\boldsymbol {p}; \\boldsymbol {a}) = \\frac {1}{B (\\boldsymbol {\\alpha})} \\prod_ {i = 1} ^ {N} p _ {i} ^ {\\alpha_ {i} - 1} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.606, + 0.895, + 0.793 + ], + "angle": 0, + "content": "where \\(\\pmb{p} = (p_{1},\\dots,p_{N})\\) stands for class-wise distribution, \\(\\alpha = (\\alpha_{1},\\dots,\\alpha_{N})\\) denotes Dirichlet-distributed parameter controlling imbalanced ratio of query samples, \\(B(\\pmb{a}) = \\frac{\\prod_{i=1}^{N}\\Gamma(a_{i})}{\\Gamma(\\sum_{i=1}^{N}a_{i})}\\) represents multivariate Beta function, and \\(\\Gamma(\\cdot)\\) is Gamma function. Smaller \\(\\pmb{a}\\) means higher imbalanced level, and vice versa. Taking \\(\\alpha = 2\\) as an example, total number of query samples is 75, then the number of query samples per class could be distributed as \\(K' = [10,5,2,35,18]\\), which is more realistic compared with the class-balanced situation whose \\(K_i' = 15, i = 1,\\dots,N\\). Besides, it also poses some difficulties such as overfitting to the classes whose query samples are extremely few." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.808, + 0.62, + 0.823 + ], + "angle": 0, + "content": "3. Our Model" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.66, + 0.848 + ], + "angle": 0, + "content": "3.1. Overall Method" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.902 + ], + "angle": 0, + "content": "In this work, we propose a novel model called PUTM for class-imbalanced transductive few-shot image classification. Considering the correlations between support and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16318" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.895, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.289, + 0.895, + 0.352 + ], + "angle": 0, + "content": "Figure 2: Illustration of the our model. Tasks are generated from Dirichlet-distributed generator parameterized by \\( \\mathbf{a} \\). We first adopt a well trained feature extractor [19] and a channel-wise feature adaptation [35] to obtain the input features. Transductive inference is then conducted on the pre-processed features by: i) optimizing the transport matrices using CT; ii) refining the class-wise prototypes via MAP statistics aggregation; iii) making predictions after the above two steps iterate until convergence." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.377, + 0.473, + 0.665 + ], + "angle": 0, + "content": "query samples, it is reasonable to refine the representations of class-wise prototypes initialized by support samples with the statistics of query samples. At this moment, the key is how to transfer the unbiased statistics from query samples to prototypes for achieving the best calibration. Moreover, the class-imbalanced setting is more challenging due to its unknown and arbitrary prior distribution of query samples. To address this challenge, we pioneered to depict the important but unknown prior with well-defined CT theory. Specifically, the prior could be measured by the transport mass from query samples to each prototype by summing the combination of forward and backward transport matrices optimized by CT loss along every query sample. Given the well-optimized prior, a prototype refinement algorithm is easy to be derived according to the MAP criterion. Considering the fact that the discriminative prototypes and well-optimized prior are coupled, we further employ an EM-solver to transfer the unbiased statistics efficiently and precisely. The overview of the proposed method can be found in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.702, + 0.2, + 0.719 + ], + "angle": 0, + "content": "3.2. CT Theory" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.903 + ], + "angle": 0, + "content": "CT [39] is a powerful tool developed for measuring distance between any two probability distributions most recently, the effectiveness of which is mostly verified on deep generative models [13, 27] and multi-label classification [15]. In this work, we expand the territory of CT for discrete distributions under class-imbalanced TFSL. Denote \\( p(x) = \\sum_{i=1}^{n} a_i \\delta_{x_i} \\) and \\( q(y) = \\sum_{j=1}^{m} b_j \\delta_{y_j} \\) as source and target discrete distributions with \\( n \\) and \\( m \\) points, respectively. \\( \\pmb{a} \\in \\Delta^n \\) and \\( \\pmb{b} \\in \\Delta^m \\), where \\( \\Delta^n \\) and \\( \\Delta^m \\) separately denote the probability simplex of \\( \\mathbb{R}^n \\) and \\( \\mathbb{R}^m \\). The CT distance between \\( p(x) \\) and \\( q(y) \\) can be expressed as a combination" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.377, + 0.887, + 0.394 + ], + "angle": 0, + "content": "of forward CT \\(\\mathcal{C}_{\\phi}(x\\to y)\\) and a backward CT \\(\\mathcal{C}_{\\phi}(x\\gets y)\\)" + }, + { + "type": "equation", + "bbox": [ + 0.506, + 0.403, + 0.893, + 0.434 + ], + "angle": 0, + "content": "\\[\n\\mathcal {C} _ {\\phi , \\rho} (p, q) = \\min _ {\\phi} \\sum_ {x \\in p, y \\in q} \\rho \\mathcal {C} _ {\\phi} (x \\rightarrow y) + (1 - \\rho) \\mathcal {C} _ {\\phi} (x \\leftarrow y) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.443, + 0.895, + 0.504 + ], + "angle": 0, + "content": "where \\(\\phi\\) is parameters of CT, \\(\\rho\\) is the trade-off factor controlling the strengths between the forward and backward CTs. To better understand how the CT works when minimizing Eq. 2, we take the forward CT as an example:" + }, + { + "type": "equation", + "bbox": [ + 0.511, + 0.513, + 0.893, + 0.55 + ], + "angle": 0, + "content": "\\[\n\\mathcal {C} _ {\\phi} (x \\rightarrow y) = \\mathbb {E} _ {y 1: m \\sim q} \\mathbb {E} _ {x \\sim p} \\left[ \\sum_ {j = 1} ^ {m} c (x, y _ {j}) \\hat {\\pi} _ {m} \\left(y _ {j} \\mid x, \\phi\\right)\\right] \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.56, + 0.895, + 0.637 + ], + "angle": 0, + "content": "where \\(c(\\cdot, \\cdot)\\) could be some well defined distance functions, such as Euclidean or Cosine, \\(\\hat{\\pi}_m(y_j|x, \\phi)\\) is forward transport matrix, also called forward navigator in the scope of CT, satisfying \\(\\sum_{j=1}^{m} \\hat{\\pi}_m(y_j|x, \\phi) = 1\\), it describes the possibility of transporting \\(x\\) to \\(y_j\\) and can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.593, + 0.646, + 0.893, + 0.682 + ], + "angle": 0, + "content": "\\[\n\\hat {\\pi} _ {m} \\left(y _ {j} \\mid x, \\phi\\right) = \\frac {e ^ {- d _ {\\phi} \\left(x , y _ {j}\\right)}}{\\sum_ {j ^ {\\prime}} ^ {m} e ^ {- d _ {\\phi} \\left(x , y _ {j ^ {\\prime}}\\right)}} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.686, + 0.895, + 0.807 + ], + "angle": 0, + "content": "where \\(d_{\\phi}(\\cdot, \\cdot)\\) represents measurement function, such as MLP implemented by Zheng et al. [39]. The forward CT can be interpreted as the expected cost to stochastically transport a random source point \\(x\\) to one of the \\(m\\) randomly instantiated \"anchors\" of the target distribution. By minimizing Eq. 3, an unbiased statistical estimation of the two distributions arrives. Proofs can be found in Zheng et al. [39]. Hence, it is reasonable to transfer statistics of one distribution to another." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.591, + 0.832 + ], + "angle": 0, + "content": "3.3. PUTM" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Our proposed PUTM aims to exploit discriminative statistics from query samples for reducing the gap between the estimated prototypes and their ground truth prototypes. However, the ground truth prototypes are always intractable in" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16319" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.226 + ], + "angle": 0, + "content": "practice. A reasonable approach to obtain unbiased prototypes is to aggregate discriminative statistics from both support and query samples following a semi-supervised manner [37]. Different from the standard semi-supervised problems, the query samples are usually limited per class, especially in class-imbalanced case. Follow up, we present the importance of unbiased transfer in semi-supervised FSL setting, the algorithm of realizing unbiased exploitation with CT and transductive inference with unbiased transfer in turn." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.245, + 0.45, + 0.26 + ], + "angle": 0, + "content": "3.3.1 Unbiased Statistics Transfer Matters in TFSL" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.269, + 0.473, + 0.426 + ], + "angle": 0, + "content": "Given a few-shot task, unbiased prototypes arrives if and only if the aggregated query samples are noiseless, which should heavily rely on the unbiased statistics transfer. Leveraging similarities between query samples and prototypes is a common way to realize statistics transfer in transductive few-shot image classification. Given the transport matrix \\(\\pi^n\\in \\mathbb{R}^{M\\times N}\\) at the \\(n\\) -th iteration, it measures the closeness of prototypes \\(\\{c_i^n\\}_{i = 1}^N\\) and query samples \\(\\{\\pmb{x}_{i,j}^q\\}_{j = 1}^{K_i'}\\) For simplicity, we rewrite all query samples as \\(\\{\\pmb{x}_r^q\\}_{r = 1}^M\\) . Thus, the refined prototypes \\(\\{c_i^{n + 1}\\}_{i = 1}^N\\) can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.113, + 0.432, + 0.47, + 0.47 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {c} _ {i} ^ {n + 1} = \\frac {\\sum_ {r = 1} ^ {M} \\boldsymbol {\\pi} _ {r , i} ^ {n} \\boldsymbol {x} _ {r} ^ {q} + \\sum_ {j = 1} ^ {K} \\boldsymbol {x} _ {i , j} ^ {s}}{\\sum_ {r ^ {\\prime} = 1} ^ {M} \\boldsymbol {\\pi} _ {r ^ {\\prime} , i} ^ {n} + K}, \\quad i = 1, \\dots , N \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.473, + 0.7 + ], + "angle": 0, + "content": "where \\(\\pi_{r,i}^{n} = \\frac{e^{-d_{\\phi}(\\pmb{x}_{r}^{q},\\pmb{c}_{i}^{n})}}{\\sum_{r^{\\prime} = 1}^{M}e^{-d_{\\phi}(\\pmb{x}_{r^{\\prime}}^{q},\\pmb{c}_{i}^{n})}}, d_{\\phi}(\\cdot ,\\cdot)\\) denotes the well defined measurement function, and we denote optimal transport matrix as \\(\\pi^{*}\\). To guarantee the unbiased refinement of prototypes, \\(\\pi^{*}\\) need to be precise, which is usually difficult to be satisfied in practice. Fortunately, partial noisy is tolerable. For example, given 15 query samples per class, a few wrong transferring such as 1 or 2 samples is tolerable in calibrating prototypes. As for class-imbalanced case, a tiny mistake may result in disastrous consequence on prototypes calibration. For the classes having only 1 or 2 query samples, the tolerances of error transmissions should be extremely low. Therefore, to improve the robustness of calibrated prototypes in class-imbalanced TFSL, transferring unbiased statistics of query samples with \\(\\pi^{*}\\) becomes crucial." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.702, + 0.473, + 0.904 + ], + "angle": 0, + "content": "There are mainly two lines of works in defining \\(\\pi^{*}\\): i) Liu et al. [17] employ Cosine function [17]; ii) Hu et al. [11] use Optimal Transport (OT). Cosine function may not powerful enough to fully reflect the relationships between prototypes and query samples since it ignores various importance between each two points. OT describes a doubly stochastic transport matrix such that \\(\\Pi(p, q) = \\{\\pi^{*} | \\sum_{r=1}^{M} \\pi_{r,i}^{*} = a_{i}, \\sum_{i=1}^{N} \\pi_{r,i}^{*} = b_{r}\\}\\). Unfortunately, we usually do not have any priors on distributions of \\(p\\) and \\(q\\), thus, we usually have \\(a_{i} = \\frac{1}{N}, i = 1, \\dots, N\\) and \\(b_{r} = \\frac{1}{M}, r = 1, \\dots, M\\), which should be contradictory to class-imbalanced setting. For example, once we employ Dirichlet distribution with \\(\\alpha = 2_{N}\\) to mimic the generation of query samples, \\(a_{i} = \\frac{1}{N}\\) will never" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.152 + ], + "angle": 0, + "content": "fit the data. According to the analysis of CT, it replaces the uniform constraint on prior distribution of classes derived from query samples with a data-driven manner, thus ensuring to transfer the unbiased statistics more flexible and efficient." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.17, + 0.84, + 0.187 + ], + "angle": 0, + "content": "3.3.2 Unbiased Statistics Exploitation with CT" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.194, + 0.894, + 0.254 + ], + "angle": 0, + "content": "As we can see, CT has an appealing property of exploiting unbiased statistics thanks to its task-adaptive prior rather than uniform-distributed one as OT. Here after, we present details of achieving such unbiased exploitation with CT." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.255, + 0.895, + 0.39 + ], + "angle": 0, + "content": "As shown in Fig. 2, given a class-imbalanced few-shot task in Sec. 2, we first employ a well-trained feature extractor \\(f_{\\theta^{*}}(\\cdot)\\) to get features of support and query samples as \\(f_{i,j}^{s} = f_{\\theta^{*}}(\\pmb{x}_{i,j}^{s})\\) and \\(f_{r}^{q} = f_{\\theta^{*}}(\\pmb{x}_{r}^{q})\\), where \\(\\theta^{*}\\) is the set of optimized parameters, being fixed after training on the base classes following Mangla et al. [19]. Then, we conduct channel attention with preprocessing developed by Yang et al. [35]. Finally, unbiased statistics exploitation is realized by optimizing transport matrices constrained by CT theory." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.391, + 0.894, + 0.545 + ], + "angle": 0, + "content": "Specifically, the initial prototypes are averaged on the features of support set as \\( \\pmb{c}_i^0 = \\frac{1}{K}\\sum_{j = 1}^{K}f_{i,j}^s \\), \\( i = 1,\\dots,N \\) where the superscript of \\( \\{c_i^0\\}_{i = 1}^N \\) describes the generation of prototypes is zero. They will be updated subsequently, detailed in Sec. 3.3.3. At this moment, we treat \\( \\{c_i^0\\}_{i = 1}^N \\) and \\( \\{f_r^q\\}_{r = 1}^M \\) as samples from the two discrete distributions, and utilizing CT to learn the transport matrices for exploiting unbiased statistics. According to the analysis of Eq. 2, an unbiased sample estimate of CT given query features \\( \\{f_r^q\\}_{r = 1}^M \\) and prototypes \\( \\{c_i^0\\}_{i = 1}^N \\) can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.554, + 0.892, + 0.597 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\phi , \\boldsymbol {\\theta} ^ {*}, \\rho} \\left(f _ {1: M} ^ {q}, \\boldsymbol {c} _ {1: N} ^ {0}\\right) = \\sum_ {i = 1} ^ {N} \\sum_ {r = 1} ^ {M} c \\left(\\boldsymbol {c} _ {i} ^ {0}, f _ {r} ^ {q}\\right). \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.599, + 0.866, + 0.627 + ], + "angle": 0, + "content": "\\[\n(\\frac {\\rho}{M} \\hat {\\pi} _ {N} (\\pmb {c} _ {i} ^ {0} | f _ {r} ^ {q}, \\phi) + \\frac {1 - \\rho}{N} \\hat {\\pi} _ {M} (f _ {r} ^ {q} | \\pmb {c} _ {i} ^ {0}, \\phi))\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.636, + 0.895, + 0.683 + ], + "angle": 0, + "content": "where \\(\\hat{\\pi}_N\\) and \\(\\hat{\\pi}_M\\) separately denote the forward and backward transport matrices. Again substituting query features \\(\\{f_r^q\\}_{r=1}^M\\) and prototypes \\(\\{c_i^0\\}_{i=1}^N\\) into Eq. 4, we have:" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.692, + 0.892, + 0.731 + ], + "angle": 0, + "content": "\\[\n\\hat {\\pi} _ {N} \\left(\\boldsymbol {c} _ {i} ^ {0} \\mid f _ {r} ^ {q}, \\phi\\right) = \\frac {e ^ {- d _ {\\phi} \\left(f _ {r} ^ {q} , \\boldsymbol {c} _ {i} ^ {0}\\right)}}{\\sum_ {i ^ {\\prime} = 1} ^ {N} e ^ {- d _ {\\phi} \\left(f _ {r} ^ {q} , \\boldsymbol {c} _ {i ^ {\\prime}} ^ {0}\\right)}} \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.733, + 0.892, + 0.772 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {\\pi}} _ {M} \\left(f _ {r} ^ {q} \\mid \\boldsymbol {c} _ {i} ^ {0}, \\phi\\right) = \\frac {e ^ {- d _ {\\phi} \\left(f _ {r} ^ {q} , \\boldsymbol {c} _ {i} ^ {0}\\right)}}{\\sum_ {r ^ {\\prime} = 1} ^ {M} e ^ {- d _ {\\phi} \\left(f _ {r ^ {\\prime}} ^ {q} , \\boldsymbol {c} _ {i} ^ {0}\\right)}} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.901 + ], + "angle": 0, + "content": "The forward transport matrix represents the probability of query samples belonging to the corresponding support classes. The two transport matrices with the optimal parameter \\(\\phi^{*}\\) can be obtained by minimizing the approximated CT estimation of Eq. 6. Once \\(\\hat{\\pi}_N^*\\) and \\(\\hat{\\pi}_M^*\\) with the optimal \\(\\phi^{*}\\) are obtained, the transport matrix described in Sec. 3.3.1 for unbiased statistics exploitation can be naturally realized. To better understand this, we depict the mechanisms of the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16320" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.079, + 0.092, + 0.391, + 0.106 + ], + "angle": 0, + "content": "Algorithm 1 Work flow of PUTM for one task." + }, + { + "type": "algorithm", + "bbox": [ + 0.09, + 0.111, + 0.47, + 0.313 + ], + "angle": 0, + "content": "Input: Support samples \\(\\{\\pmb{x}_{i,j}^{s}\\}_{i,j = 1}^{N,K}\\) and class-imbalanced query samples \\(\\{\\pmb{x}_r^q\\}_{r = 1}^M\\) generated from Dirichlet distribution with parameter \\(\\alpha\\) , a well-trained feature extractor \\(f_{\\theta^{*}}(\\cdot)\\) Parameters: Distance measurement function \\(d_{\\phi}(\\cdot ,\\cdot)\\) Initialization Hyper-parameters \\(\\alpha\\) \\(\\rho\\) \\(\\lambda\\) , and learning schedule for updating \\(\\phi\\) ; Initialize prototypes \\(c_{i}^{0} = \\frac{1}{K}\\sum_{j = 1}^{K}f_{i,j}^{s},i = 1,\\ldots ,N;\\) for n=1: \\(n_{steps}\\) do Initialize parameters \\(\\phi\\) \\(\\phi^{*}\\gets argmin_{\\phi}\\mathcal{L}_{\\phi ,\\theta^{*},\\rho}(f_{1:M}^{q},c_{1:N}^{n})\\) Refining prototypes \\(c_{1:N}^{n + 1}\\) using Eq. 11 based on \\(c_{1:N}^{n}\\) end for Evaluating performance using Eq. 12; Output Parameters \\(\\{\\phi^{*},c_{1:N}^{n_{step}}\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.34, + 0.473, + 0.613 + ], + "angle": 0, + "content": "transport matrices developed above from three perspectives: 1) the distance function in transport matrices is implemented with DNNs, hence, they are able to learn a comprehensive distance metric beyond a simple Cosine function; 2) the CT distance is proven to be unbiased given samples of two distributions \\( p \\) and \\( q \\) in [39]; 3) The forward transport matrix holds free for sum along query samples given a specific prototype, namely, \\( \\sum_{r=1}^{M} \\hat{\\pi}_N(c_i^0 | f_r^q, \\phi^*) = C \\), and \\( C \\) is not restricted to be equal for each class, thus embedding task-adaptive prior instead of uniform distribution as PT-MAP [11] does. On the other hand, the backward transport matrix holds tight for sum along query samples given a specific prototype, that is, \\( \\sum_{r=1}^{M} \\hat{\\pi}_M(f_r^q | c_i^0, \\phi^*) = 1 \\), hence, uniform-distributed prior holds, and it is proven to be underfitting in class-imbalanced case [29]. In practice, we employ a trade-off to balance the strengths of the two transport matrices by summing them together with a soft coefficient \\( \\rho \\). For simplicity, we only use the forward transport matrix in the rest of the work." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.63, + 0.443, + 0.645 + ], + "angle": 0, + "content": "3.3.3 Unbiased Statistics Transfer with EM-Solver" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.654, + 0.472, + 0.701 + ], + "angle": 0, + "content": "Once the forward transport matrix \\(\\hat{\\pi}_N^*\\) is obtained by minimizing Eq. 6, it is straightforward to derive the refined prototypes by substituting \\(\\hat{\\pi}_N^*\\) into Eq. 5:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.711, + 0.472, + 0.754 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {c} _ {i} ^ {\\prime} = \\frac {\\sum_ {r = 1} ^ {M} \\hat {\\pi} _ {N , r , i} ^ {*} f _ {r} ^ {q} + \\sum_ {j = 1} ^ {K} f _ {i , j} ^ {s}}{K + \\sum_ {r = 1} ^ {M} \\hat {\\pi} _ {N , r , i} ^ {*}}, \\quad i = 1, \\dots , N \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.763, + 0.473, + 0.875 + ], + "angle": 0, + "content": "It is worth noting that once the optimal parameters \\(\\phi^{*}\\) are arrived, the only parameters left for optimizing are prototypes. Recalling our objective in Eq. 6, it is easy to find that the optimal prototypes at this moment could also be derived by \\(\\frac{\\partial\\mathcal{L}_{\\phi^{*},\\theta^{*},\\rho}}{\\partial c_{1:N}^{0}}\\), thereby Eq. 9 could be derived. Instead of directly calibrating class-wise prototypes, We employ an inertia parameter \\(\\alpha\\) to update prototypes proportionally:" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.884, + 0.472, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {c} _ {i} ^ {1} = \\boldsymbol {c} _ {i} ^ {0} + \\alpha \\left(\\boldsymbol {c} _ {i} ^ {\\prime} - \\boldsymbol {c} _ {i} ^ {0}\\right), \\quad i = 1, \\dots , N \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.895, + 0.123 + ], + "angle": 0, + "content": "Right now, recursive expression emerges for updating prototypes according to Eq. 10:" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.131, + 0.894, + 0.15 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {c} _ {i} ^ {n + 1} = \\boldsymbol {c} _ {i} ^ {n} + \\alpha \\left(\\boldsymbol {c} _ {i} ^ {\\prime} - \\boldsymbol {c} _ {i} ^ {n}\\right), \\quad i = 1, \\dots , N \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.159, + 0.895, + 0.31 + ], + "angle": 0, + "content": "As we can see: i) updating the forward transport matrix \\(\\hat{\\pi}_N^*\\) and prototypes \\(c_{1:N}^n\\) are coupled; ii) \\(\\hat{\\pi}_N^*\\) is a random variable determined by \\(\\phi\\) while \\(c_{1:N}^n\\) is an unknown but deterministic variable. These two facts meet conditions of implementing EM optimization, and we formulate our EM-Solver as follows: i) E Step, updating \\(\\hat{\\pi}_N^*\\) by minimizing Eq. 6 while keeping \\(c_{1:N}^n\\) fixed; ii) M Step, updating \\(c_{1:N}^n\\) by minimizing Eq. 6 while keeping \\(\\hat{\\pi}_N^*\\) fixed. Besides, it is worth noting that at each iteration, \\(\\phi^*\\) need to be reinitialized. The pseudo code is provided in Alg. 1." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.31, + 0.892, + 0.342 + ], + "angle": 0, + "content": "After \\( n_{step} \\) loops between estimating \\( \\hat{\\pi}_N^* \\) and refining \\( c_{1:N}^n \\), the decision per sample is finally made by:" + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.349, + 0.893, + 0.375 + ], + "angle": 0, + "content": "\\[\ny _ {r} ^ {q} = \\max _ {i \\in [ 1: N ]} \\hat {\\pi} _ {N} \\left(\\boldsymbol {c} _ {i} ^ {n _ {\\text {s t e p}}} \\mid f _ {r} ^ {q}, \\phi^ {*}\\right), \\quad r = 1, \\dots , M \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.384, + 0.892, + 0.414 + ], + "angle": 0, + "content": "Statistic results of average accuracy are usually conducted using query samples on various of different tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.423, + 0.696, + 0.439 + ], + "angle": 0, + "content": "3.4. Complexity Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.445, + 0.895, + 0.63 + ], + "angle": 0, + "content": "\\(\\phi\\) is implemented with MLP in our work. Taking a two-layers MLP for example, namely, \\(d_{f} \\rightarrow d_{1}^{\\phi} \\rightarrow d_{2}^{\\phi}\\). For \\(T\\) tasks, computational complexity originally takes \\(\\mathcal{O}(T \\times \\max \\{NM \\times d_{f} \\times d_{1}^{\\phi}, NM \\times d_{1}^{\\phi} \\times d_{2}^{\\phi}\\})\\). In practice, \\(T\\) is usually set to be large enough for reliable results, thus resulting in time-consuming evaluation of our model. To mitigate the real-time issue, we trade space for time by paralleling our proposed PUTM among all tasks. Therefore, the computational complexity is reduced to \\(\\mathcal{O}(\\max \\{NM \\times d_{f} \\times d_{1}^{\\phi}, NM \\times d_{1}^{\\phi} \\times d_{2}^{\\phi}\\})\\). Besides, we can further control the size of MLP, that is \\(\\{d_{i}^{\\phi}\\}_{i=1}^{2}\\), to achieve a trade-off between accuracy and real-time efficiency." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.642, + 0.634, + 0.659 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.667, + 0.691, + 0.683 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.894, + 0.796 + ], + "angle": 0, + "content": "Baselines: We mainly compare our model with some recently proposed State-Of-The-Art (SOTA) methods on one Nvidia RTX 3090 GPU. For inductive methods, we adopt Baseline/Baseline \\((++)\\) [4], ProtoNet [26], Simpleshot [33], and HOT [9] in inductive. For transductive methods, we adopt PT-MAP [11], LaplacianShot [40], TIM[2], BD-CSPN [17], \\(\\alpha\\)-TIM [29], iLPC [14], and BAVAR [12]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Datasets: We evaluate our model on four benchmarks including miniImageNet [22], tieredImageNet [23], CUB [31], and CIFAR-FS [1]. MiniImageNet is randomly chosen from ILSVRC-12 dataset [6] and it contains 100 classes with 600 images per class, the resolution of which is \\(84 \\times 84 \\times 3\\). Following previous works [22, 29, 11, 35], the dataset is split into 64 base classes, 16 validation classes, and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16321" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.152 + ], + "angle": 0, + "content": "Table 1: Classification accuracy (%) of SOTA methods on class-imbalanced and class-balanced settings with different datasets and backbones. For imbalanced case, query samples are generated following a Dirichlet distribution with \\(\\alpha = 2_{N}\\). Results are averaged over 3000 tasks with \\(95\\%\\) confidence intervals. Results with superscript \\(\\dagger\\) are our re-implementations based on the code provided by Veilleux et al. [29]. The best and the second best scores are marked in bold and blue, respectively." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.162, + 0.892, + 0.387 + ], + "angle": 0, + "content": "
SettingMethodmini-ImageNet (WRN/WRN$)CUB (RN18/WRN$)tiered-ImageNet (WRN/WRN$)CIFAR-FS (WRN$)
1-shot3-shot5-shot1-shot3-shot5-shot1-shot3-shot5-shot1-shot3-shot5-shot
Induct. (%)Imbalanced & BalancedBaseline (ICLR'19)62.2/62.8†76.9†/77.3†81.9/82.9†64.6/70.7†82.3†/87.3†86.9/90.0†64.6/63.6†80.0†/83.0†84.9/87.2†69.5†83.9†86.7†
Baseline++ (ICLR'19)64.5/64.8†77.5†/78.4†82.1/82.7†69.4/81.7†83.3†/89.4†87.1/91.2†68.7/66.9†80.9†/78.7†85.4/82.2†74.9†85.0†87.4†
ProtoNet (NeurIPS'17)61.2/62.5†76.9†/77.2†81.1/81.4†63.1†/69.6†82.3†/85.6†85.4†/88.8†63.5†/64.2†79.9†/80.1†84.1†/84.0†69.5†83.8†86.7†
Simpleshot (ARXIV)66.2/67.1†77.6†/78.2†82.4/83.3†70.6/81.7†83.6†/89.5†87.5/91.4†70.7/71.4†81.3†/84.2†85.9/87.5†75.2†84.7†87.4†
HOT (NeurIPS'22)66.3†/69.178.5†/79.8†82.8†/84.474.5†/81.285.4†/88.2†87.8†/91.574.1†/75.982.6†/83.9†85.4†/87.375.485.3†87.5
Transduct. (%)ImbalancedPT-MAP (ARXIV)60.6/63.2†65.9†/68.0†66.8/69.3†65.1/69.8†71.2†/73.2†71.3/74.3†65.1/67.8†69.1†/72.0†71.0/73.2†65.9†69.3†70.3†
LaplacianShot (ICML'20)68.1/69.8†78.8†/79.2†83.2/83.6†73.7/84.2†85.7†/90.4†87.7/91.4†73.5/72.6†82.6†/85.0†86.8/87.7†78.3†86.1†87.3†
TIM (NeurIPS'20)69.8/70.9†79.7†/80.7†81.6/83.2†74.8/82.8†84.8†/89.1†86.9/90.5†75.8/77.8†82.5†/86.3†85.4/88.3†77.0†84.6†86.2†
BD-CSPN (ECCV'20)70.4/71.2†77.1†/78.6†82.3/83.4†74.5/85.1†85.7†/90.5†87.1/91.5†75.4/76.3†82.5†/85.0†85.9/87.2†79.1†86.0†87.3†
α-TIM (NeurIPS'2021)69.8/70.9†80.4†/81.1†84.8/84.9†75.7/83.6†87.3†/91.2†89.8/92.8†76.0/77.7†83.6†/86.6†87.8/89.9†78.1†87.2†88.9†
iLPC (ICCV'21)71.5†/74.3†78.6†/81.1†81.0†/83.3†78.7†/86.4†85.6†/90.1†86.9†/90.8†76.6†/81.6†83.2†/87.5†85.1†/89.0†80.8†85.4†86.5†
BAVAR (AISTATS'23)74.1/74.2†82.6†/82.6†85.5/85.6†82.0/85.7†89.2†/89.8†90.7/90.8†77.5/80.6†84.8†/87.2†87.5/89.3†81.8†87.0†87.9†
PUTM (Ours)70.9/73.880.5/82.984.6/85.778.9/86.987.8/91.389.3/92.275.0/81.183.6/88.486.0/90.481.487.388.6
BalancedPT-MAP (ARXIV)78.9/82.5†86.3†/87.5†86.6/88.6†85.5/92.0†90.5†/94.0†91.3/94.3†84.6/88.1†88.2†/91.8†90.0/92.5†87.6†90.5†90.9†
LaplacianShot (ICML'20)72.9/73.4†79.0†/80.5†83.8/84.2†78.9/87.5†86.7†/90.4†88.8/92.3†78.8/78.7†84.6†/85.6†87.3/87.0†82.1†86.3†86.8†
TIM (NeurIPS'20)74.6/77.6†85.5†/86.0†85.9/88.0†80.3/88.1†89.8†/93.0†90.5/94.0†80.3/83.8†87.7†/90.6†88.9/92.1†83.0†89.5†90.5†
BD-CSPN (ECCV'20)72.5/73.8†79.2†/80.7†83.7/85.3†77.9/87.3†86.9†/91.4†88.9/92.4†77.7/78.7†84.5†/86.4†87.4/88.3†81.6†87.4†88.6†
α-TIM (NeurIPS'2021)71.0/71.5†76.8†/77.7†82.4/83.3†77.2†/84.9†85.1†/90.2†87.6†/91.2†75.1†/78.9†80.6†/84.4†85.3†/88.2†79.7†85.7†87.9†
iLPC (ICCV'21)75.5†/77.8†82.0†/83.9†83.9†/85.7†82.4†/89.6†87.9†/92.3†88.9†/93.0†81.0†/85.5†86.4†/89.8†87.5†/90.9†84.8†88.6†89.2†
BAVAR (AISTATS'23)78.5/78.5†84.8†/84.9†87.4/87.7†85.6/89.0†90.8†/91.7†91.4/92.1†81.5/84.7†87.4†/89.3†88.3/90.3†85.0†88.4†88.9†
PUTM(Ours)78.4/81.484.9/86.786.5/88.184.9/91.289.2/93.390.1/93.781.6/86.886.9/90.788.6/92.286.489.590.4
" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.399, + 0.331, + 0.532 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.197, + 0.543, + 0.225, + 0.556 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.399, + 0.611, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.473, + 0.542, + 0.503, + 0.556 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.399, + 0.891, + 0.538 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.761, + 0.543, + 0.788, + 0.556 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.568, + 0.897, + 0.614 + ], + "angle": 0, + "content": "Figure 3: (a)-(b): The t-SNE [28] visualizations before (middle) and after (left) calibration on a 5-way 1-shot miniImageNet task. Pentagrams are prototypes while solid dots are query features. Classes change and best view in colors. (c): Impact of forward and backward transport matrices in calibrating prototypes on miniImageNet over 3000 5-way 1-shot tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.64, + 0.473, + 0.852 + ], + "angle": 0, + "content": "20 novel classes. TieredImageNet [23] is also a subset of ILSVRC-12 dataset, which is larger than miniImageNet. It contains 608 classes sampled from a hierarchical category structure with around 1281 images per class. Following the previous work [23], we split the dataset into 351 base classes, 97 validation classes, and 160 novel classes. The resolution is also \\(84 \\times 84 \\times 3\\). CUB is a fine-grained dataset, containing 200 classes of birds with around 60 images per class. And the resolution is still \\(84 \\times 84 \\times 3\\). We adopt 100 base classes, 50 validation classes, and 50 novel classes following [4]. CIFAR-FS consists of all 100 classes from CIFAR-100 [34], whose classes are randomly split into 64 base classes, 16 classes, and 20 novel classes. Each class contains 600 images of size \\(32 \\times 32 \\times 3\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.473, + 0.901 + ], + "angle": 0, + "content": "Implementation details: We use pre-trained backbones for extracting visual features of four benchmarks, as shown in Table. 1. WRN and RN18 are separately WideResNet-28-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.895, + 0.777 + ], + "angle": 0, + "content": "10 and ResNet-18 pre-trained with standard classification loss [29]. WRN\\(\\S\\) is WideResNet-28-10 pre-trained with self-supervised loss [19]. Besides, we employ log transform, a channel-wise feature adaptation, introduced in Yang et al. [35] to pre-process the pre-extracted features. The distance function \\(\\phi\\) is instantiated as a two-layers MLP activated with LeakyReLU whose architecture is \\([d_f, 128, 64, 1]\\). As for hyper-parameters, we mainly set \\(\\beta = 0.5\\), \\(\\alpha = 0.1\\), \\(\\rho = 0.2\\). The reported results are averaged over 3000 tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.64, + 0.801 + ], + "angle": 0, + "content": "4.2. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.896, + 0.901 + ], + "angle": 0, + "content": "Quantitative results: The classification results on miniImageNet, tieredImageNet, CUB, and CIFAR-FS are reported in Table 1, according to which five-fold observations can be drawn: 1) inductive methods are not bothered by class-imbalanced problem since they do not leverage transferable statistics of query samples; 2) most transductive methods" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16322" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.07, + 0.089, + 0.273, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.089, + 0.48, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.206, + 0.473, + 0.299 + ], + "angle": 0, + "content": "Figure 4: Case studies for 5-way 5-shots tasks on CUB [31] (left) and miniImageNet (right). Comparisons between unnormalized prior distribution (true number of query samples counting for each class) and unnormalized posterior distribution (estimated number of query samples counting by the well optimized forward transport matrix for each class)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.326, + 0.473, + 0.81 + ], + "angle": 0, + "content": "still outperform the inductive peers in class-imbalanced setting, which implies that there exists a trade-off between extra statistics conveyed by class-imbalanced query samples and algorithm bias; 3) results of features extracted by WRN\\(\\S\\) usually outperforms those by WRN or RN18, it indicates that self-supervised learning is helpful in obtaining generalized representations in class-imbalanced and class-balanced FSL applications; 4) most existed transductive inference methods suffer from performance cliff since their mismatch between data distribution and prior distribution. For example, TIM implicitly introduces uniform prior on query samples by using entropy regularization since minimizing entropy-based regularization is equivalent to minimizing the KL divergence between the predicted marginal distribution and uniform distribution. Hence, data distribution and model bias are unsuitable, leading to poor accuracy. Fortunately, such kind of mismatch can be eased by re-weighting in [29]. On the contrary, PT-MAP holds a strong but unmodified uniformly distributed prior on its transport matrix. Therefore, results of TIM are robuster than those of PT-MAP; 5) our proposed method outperforms most of the transductive methods and achieves competitive results with some most recently proposed methods, such as \\(\\alpha\\)-TIM, iLPC and BAVAR. It indicates that prototype refinement benefits from the well optimized transport matrices when shot number is low. Moreover, compared with iLPC and BAVAR, on the one hand, our model is easy to implement. On the other hand, BAVAR heavily relies on prior of imbalanced ratio \\(\\alpha\\) in class-imbalanced case while iLPC depends on uniform prior in class-balanced case [12], importantly however, our model is free of these priors, making it suitable for real-world applications when we have no idea on class distributions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Qualitatively analysis: To qualitatively illustrate the evolution of prototypes of our model, we map prototypes and query features of one task into a 2-D subspace with t-distributed Stochastic Neighbor Embedding (t-SNE) [28], it is a non-linear dimensional reduction technique well-suited for embedding high-dimensional data into a low-dimensional" + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.089, + 0.691, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.089, + 0.903, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.221, + 0.896, + 0.268 + ], + "angle": 0, + "content": "Figure 5: 5-way 5-shot classification accuracy on miniImageNet and CUB of transductive methods versus imbalance level, lower \\(\\alpha\\) corresponds to severer class imbalance." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.282, + 0.895, + 0.313 + ], + "angle": 0, + "content": "Table 2: End-to-end real-time efficiencies (s) of 5-way 1-shot on CUB with two backbones averaged on 100 tasks." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.323, + 0.89, + 0.39 + ], + "angle": 0, + "content": "
Backboneα - TIM (NeurIPS'21)iLPC (ICCV'21)BAVAR (AISTATS'23)Ours
RN185.64.63.42.9
WRN6.24.73.63.7
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.895, + 0.507 + ], + "angle": 0, + "content": "space. As we can see from Fig. 3, due to class-imbalanced issue, although prototypes can not match their corresponding class centers well at beginning, they become consistent with the ground truth centers after refinement using our proposed method, verifying the effectiveness of our PUTM in dealing with unknown and arbitrary prior situation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.515, + 0.657, + 0.532 + ], + "angle": 0, + "content": "4.3. Model Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.896, + 0.795 + ], + "angle": 0, + "content": "Forward transport V.S. backward transport: As discussed in Sec. 3.3.2, the forward and backward transport matrices put different priors of \\(\\{a_i\\}_{i=1}^N\\). Namely, we do not restrict uniform distribution in the forward transport and enable it to be adaptive to data-driven class distribution. On the contrary, prior in the backward transport is always assumed to be \\(\\frac{1}{N}\\). Therefore, we employ the forward transport for predictions to meet the class-imbalanced essence, the efficiency is illustrated in Fig. 4, it depicts that the predicted distribution is consistent with the true distribution. Moreover, we conduct an extra experiment to verify the opposite direction of the two transport matrices, results are illustrated in Fig. 3, where we separately use the forward transport and the backward transport to calibrate the prototypes over 3000 tasks. According to the results, we find that, from a statistical point of view, the backward transport does harm the efficient migration from the class-imbalanced query samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Robustness of imbalanced coefficients: An important point in this work is that our model is robust for various class-imbalanced coefficients, which is vital and crucial for real-world applications since we usually do not know whether the few-shot tasks are balanced or not in advance, thus, we could not know what kind of methods are suitable for describing the samples distribution of tasks. Once they are" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16323" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.345, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.088, + 0.617, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.626, + 0.089, + 0.891, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.216, + 0.345, + 0.342 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.216, + 0.617, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.626, + 0.216, + 0.891, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.352, + 0.894, + 0.385 + ], + "angle": 0, + "content": "Figure 6: Sensitivity analysis of our model to hyper-parameters including log transform \\(\\beta\\), CT coefficient \\(\\rho\\), and inertia \\(\\alpha\\). Results are obtained with WRN8 and are reported on both validation and test sets. Best viewed in color." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.471, + 0.59 + ], + "angle": 0, + "content": "unmatched, horrible performance degradation would happen, such as PT-MAP does. We verify the robustness of our model with a wide range of imbalanced coefficients as shown in Fig. 5, where \\(\\alpha\\) changes from 1 to 6. The performance of most methods decreases as \\(\\alpha\\) decreasing because smaller \\(\\alpha\\) indicates more imbalanced distribution of query samples, thus making tasks harder. On the contrary, performances of LaplacianShot and \\(\\alpha\\)-TIM drop obviously as \\(\\alpha\\) increases. Our model achieves consistent improvement and reasonable trend in a wide range of \\(\\alpha\\), we attribute this to the introduction of adaptive transport matrices, which enables PUTM to fit the class distributions precisely and flexibly." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.471, + 0.837 + ], + "angle": 0, + "content": "Sensitivity of hyper-parameters: To further verify the robustness of our model, we validate the sensitivity of PUTM to different hyper-parameters introduced in Sec. 4.1, and results are reported in Fig. 6. Generally speaking, the tendencies on validation and test sets are same. Besides there are three-fold observations: i) CT coefficient is less sensitive than log transform and inertia; ii) log transform controls the strength of channel-wise attention, which is proven to be important especially in few-shot case, thus it affects performance mostly; iii) inertia reflects the bottleneck of information flow from the aggregated prototypes to the refined prototypes. Bigger or smaller value of inertia is helpless for robust transfer since refinement of prototypes is associated with transport matrices. Namely, if the matrices are not well-optimized, a big inertia may cause algorithm to fall into a local optimum and vice versa." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Real-time efficiency: To verify the efficiency of PUTM, we conduct parallel versions of \\(\\alpha\\)-TIM, iLPC, and BAVAR based on their official implementations with the same machine. Results are reported in Table. 2, as we can see that our" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.895, + 0.532 + ], + "angle": 0, + "content": "model consumes less time using RN18 and achieves competitive results using WRN. And we attribute this to the fact that : i) both \\(\\alpha\\)-TIM and iLPC employ Sinkhorn algorithm to solve the Optimal Transport (OT) problem involving thousands of inner loop, and it is a kind of time consuming; ; ii) our EM-Solver might be more efficient for dealing with the class-imbalanced TFSL since it imposes potential capability for modeling such unknown distribution with CT theory." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.546, + 0.779, + 0.563 + ], + "angle": 0, + "content": "5. Conclusion and Future Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.572, + 0.895, + 0.77 + ], + "angle": 0, + "content": "We propose a novel model called PUTM with EM-Solver based on CT theory for both class-imbalanced and class-balanced TFSL in this work according to an important observation that CT has a natural connection with unknown and arbitrary class prior problem. Specifically, PUTM exploits transferable statistics with CT for refining biased prototypes solved by EM to capture the unbiased statistics within imbalanced query samples. Extensive experiments on standard benchmarks verify the effectiveness of our model in both class-imbalanced and class-balanced few-shot applications. In the future, we will explore the applicability of PUTM on more problem settings and applications, such as multi-domain few-shot classification and few-shot object detection." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.785, + 0.681, + 0.803 + ], + "angle": 0, + "content": "6. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.897, + 0.903 + ], + "angle": 0, + "content": "This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant U21B2006; in part by Shaanxi Youth Innovation Team Project; in part by the National NSFC under Grant 82172860; in part by the National NSFC under Grant 6220010437; in part by the Fundation of Aerospace under Grant SAST2021-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16324" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.168 + ], + "angle": 0, + "content": "012. We also thanks Dandan Guo and He Zhao for their constructive comments on transductive few-shot learning, we thanks Zhisong Zhang for his very initial exploration on class-imbalanced few-shot image classification, we thanks Dongsheng Wang for his passion discussions on CT." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.181, + 0.174, + 0.197 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.206, + 0.47, + 0.248 + ], + "angle": 0, + "content": "[1] Luca Bertinetto, Joao F Henriques, Philip HS Torr, and Andrea Vedaldi. Meta-learning with differentiable closed-form solvers. arXiv preprint arXiv:1805.08136, 2018." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.248, + 0.472, + 0.304 + ], + "angle": 0, + "content": "[2] Malik Boudiaf, Imtiaz Ziko, Jérôme Rony, José Dolz, Pablo Piantanida, and Ismail Ben Ayed. Information maximization for few-shot learning. 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However, previous TFSL methods usually encode uniform prior that all the classes within query samples are equally likely, which is biased in imbalanced TFSL and causes severe performance degradation. Given this pivotal issue, in this work, we propose a novel Conditional Transport (CT) based imbalanced TFSL model called Prototypes-oriented Unbiased Transfer Model (PUTM) to fully exploit unbiased statistics of imbalanced query samples, which employs forward and backward navigators as transport matrices to balance the prior of query samples per class between uniform and adaptive data-driven distributions. For efficiently transferring statistics learned by CT, we further derive a closed form solution to refine prototypes based on MAP given the learned navigators. The above two steps of discovering and transferring unbiased statistics follow an iterative manner, formulating our EM-based solver. Experimental results on four standard benchmarks including miniImageNet, tieredImageNet, CUB, and CIFAR-FS demonstrate superiority of our model in class-imbalanced generalization1. + +# 1. Introduction + +Deep learning based methods have gained a great success in many real-world applications, such as image classification [10, 25, 36], natural language processing [3, 32, 38], and so on, thanks to its powerful nonlinear representation ability [18, 24]. However, their outstanding performances heavily rely on large-scale annotated training data [6, 16]. When it comes to high cost of collecting and annotating a large amount of data, a major research effort is being dedicated to low data regimes, in which overfitting occurs in optimizing deep learning architectures. Few-shot Learning (FSL) tackles these challenges and has triggered substantial interests + +![](images/4221e7dcb0b2f0338e3e0b5f6fd7e0f9e1b63c1af0d0689d3a688bf27faca9c0.jpg) +Figure 1: 5-way 1-shot image classification results with miniImageNet [22] dataset on 3000 tasks. Our model achieves the best accuracy in a wide range of imbalanced coefficients compared with PT-MAP [11] and $\alpha$ -TIM [29]. + +within the community [8, 20], it aims to train a model from the base classes so as to generalize on the tasks sampled from the novel classes that were never seen during training. There are two major lines of works from the perspective of inference paradigms, namely inductive methods [26, 4] and their transductive counterparts [7, 23]. Both of them adopt well trained models for evaluating new tasks sampled from the novel classes. The former ones only utilize support samples in a supervised way while the later ones leverage both support and query samples in a semi-supervised manner. + +Transductive inference is widely used in FSL since it can sufficiently discover statistics of query samples compared with its inductive peer. As a representative example, Hu et al. [11] propose PT-MAP for first employing Wide ResNet (WRN) [36] trained with S2M2 [19] on base classes to extract features of new tasks, and then adjusting prototypes from novel classes by aggregating similar query samples per class with the help of transport matrix derived from the Sinkhorn algorithm [5]. Setting marginal distributions of prototypes as uniform encodes strong prior that all the classes within query samples are equally likely, although, it works pretty well in perfectly class-balanced query samples. However, it is proven to be detrimental in class-imbalanced + +applications where query samples come with arbitrary and unknown label marginals [21], and classification accuracy drops dramatically, as shown in Fig. 1. To narrow this gap, Veilleux et al. [29] propose $\alpha$ -TIM for handling class-distribution variations effectively. Unfortunately, we have observed the phenomena as shown in Fig. 1 that $\alpha$ -TIM can not achieve consistent improvement in various class-imbalanced levels, thus restricting its real-world applications. Most recently, other more complicated methods are also be arisen [14, 12]. Hu et al. [12] propose a clustering method for capturing the class-wise distributions properly. + +To this end, for class-imbalanced TFSL, we develop a novel and simple Prototypes-oriented Unbiased Transfer Model (PUTM). It firstly constructs transferable class-wise prototypes iteratively for capturing the unbiased statistics within class-imbalanced query samples. Then it performs few-shot classification via the similarities between prototypes and query samples when the transfer arrives at convergence. The key to obtain unbiased transferable statistics is estimating class-wise marginal distributions precisely [14]. To achieve this, instead of utilizing doubly stochastic transport matrix constrained with fixed uniform-distributed marginal prior between prototypes and query samples as PT-MAP does, we employ task-adaptive forward and backward transport matrices with learnable marginal priors constrained by minimizing Conditional Transport (CT) distance [39] between prototypes and query samples. CT is a tool for measuring the cost in transporting the mass in one distribution to match another in an exchangeable but asymmetrical manner given a specific point-to-point cost function and an estimizable forward and backward transport matrices, also called navigators in the CT scope. To better calibrate prototypes with the help of learned transport matrices and query samples, we further derive a closed-form solution to refine prototypes based on MAP in an iterative manner. Decisions are finally made using the combination of forward and backward transport matrices when the iteration converges. Experiments on four benchmarks demonstrate that our proposed PUTM can learn task-adaptive prior in various class-imbalanced coefficients, paving a new way to transfer the unbiased statistics of query samples to prototypes. + +Our contributions can be summarized as follows: + +- We find that the performance of class-imbalanced FSL heavily relies on the accurate estimation of class-wise marginal distribution. Meanwhile, we are the first one to find that there exists a nature connection between CT theory and such marginal distribution estimation. +- We propose a novel and simple PUTM for class-imbalanced FSL based on connections mentioned above. It firstly embeds CT distance to measure the differences between prototypes and query samples for achieving better task-adaptive unbiased statistic migra + +tion elegantly. Then it calibrates prototypes using the transferred statistics in an iterative manner. + +- We provide extensive experiments and comparisons on four standard benchmarks for verifying that our model achieves competitive results on both class-balanced and class-imbalanced (in a wide range of imbalanced coefficients) FSL settings. + +# 2. Task Formulation + +We divide the whole annotated dataset into two disjoint subsets: a base set $\mathcal{D}_{\text{base}}$ with $\mathcal{B}$ classes and a novel set $\mathcal{D}_{\text{novel}}$ with $\mathcal{N}$ classes. To build a common N-way K-shot task [30, 26], we first randomly sample N classes from $\mathcal{N}$ novel classes, and then pick K samples per class for the support set $S = \{\pmb{x}_{i,j}^{s}, \pmb{y}_{i,j}^{s}\}_{i=1,j=1}^{N,K}$ to train or fine-tune the model. Finally, $K_{i}'$ query samples being non-overlapped with support samples per class are randomly picked from the $N$ support classes for evaluating the performance of the model, formulating query set as $\mathcal{Q} = \{\pmb{x}_{i,j}^{q}, \pmb{y}_{i,j}^{q}\}_{i=1,j=1}^{N,K_{i}'}$ . For simplicity, we set $M = \sum_{i=1}^{N} K_{i}'$ . + +Class-imbalanced TFSL: Veilleux et al. [29] figure out that the number of query samples per class should be arbitrary and unknown instead of being strictly equal. That is $K'$ is a function of class and changes with class indexes. To describe such behavior, they develop a class marginal with Dirichlet distribution for generating query samples. Specifically, the class-wise marginal distribution of query samples per task $p$ are determined by: + +$$ +f _ {D i r} (\boldsymbol {p}; \boldsymbol {a}) = \frac {1}{B (\boldsymbol {\alpha})} \prod_ {i = 1} ^ {N} p _ {i} ^ {\alpha_ {i} - 1} \tag {1} +$$ + +where $\pmb{p} = (p_{1},\dots,p_{N})$ stands for class-wise distribution, $\alpha = (\alpha_{1},\dots,\alpha_{N})$ denotes Dirichlet-distributed parameter controlling imbalanced ratio of query samples, $B(\pmb{a}) = \frac{\prod_{i=1}^{N}\Gamma(a_{i})}{\Gamma(\sum_{i=1}^{N}a_{i})}$ represents multivariate Beta function, and $\Gamma(\cdot)$ is Gamma function. Smaller $\pmb{a}$ means higher imbalanced level, and vice versa. Taking $\alpha = 2$ as an example, total number of query samples is 75, then the number of query samples per class could be distributed as $K' = [10,5,2,35,18]$ , which is more realistic compared with the class-balanced situation whose $K_i' = 15, i = 1,\dots,N$ . Besides, it also poses some difficulties such as overfitting to the classes whose query samples are extremely few. + +# 3. Our Model + +# 3.1. Overall Method + +In this work, we propose a novel model called PUTM for class-imbalanced transductive few-shot image classification. Considering the correlations between support and + +![](images/deebc978bdb1dd8874d9ba6d9dcfed99153ded6777929cf9b90f917092eb7f52.jpg) +Figure 2: Illustration of the our model. Tasks are generated from Dirichlet-distributed generator parameterized by $\mathbf{a}$ . We first adopt a well trained feature extractor [19] and a channel-wise feature adaptation [35] to obtain the input features. Transductive inference is then conducted on the pre-processed features by: i) optimizing the transport matrices using CT; ii) refining the class-wise prototypes via MAP statistics aggregation; iii) making predictions after the above two steps iterate until convergence. + +query samples, it is reasonable to refine the representations of class-wise prototypes initialized by support samples with the statistics of query samples. At this moment, the key is how to transfer the unbiased statistics from query samples to prototypes for achieving the best calibration. Moreover, the class-imbalanced setting is more challenging due to its unknown and arbitrary prior distribution of query samples. To address this challenge, we pioneered to depict the important but unknown prior with well-defined CT theory. Specifically, the prior could be measured by the transport mass from query samples to each prototype by summing the combination of forward and backward transport matrices optimized by CT loss along every query sample. Given the well-optimized prior, a prototype refinement algorithm is easy to be derived according to the MAP criterion. Considering the fact that the discriminative prototypes and well-optimized prior are coupled, we further employ an EM-solver to transfer the unbiased statistics efficiently and precisely. The overview of the proposed method can be found in Fig. 2. + +# 3.2. CT Theory + +CT [39] is a powerful tool developed for measuring distance between any two probability distributions most recently, the effectiveness of which is mostly verified on deep generative models [13, 27] and multi-label classification [15]. In this work, we expand the territory of CT for discrete distributions under class-imbalanced TFSL. Denote $p(x) = \sum_{i=1}^{n} a_i \delta_{x_i}$ and $q(y) = \sum_{j=1}^{m} b_j \delta_{y_j}$ as source and target discrete distributions with $n$ and $m$ points, respectively. $\pmb{a} \in \Delta^n$ and $\pmb{b} \in \Delta^m$ , where $\Delta^n$ and $\Delta^m$ separately denote the probability simplex of $\mathbb{R}^n$ and $\mathbb{R}^m$ . The CT distance between $p(x)$ and $q(y)$ can be expressed as a combination + +of forward CT $\mathcal{C}_{\phi}(x\to y)$ and a backward CT $\mathcal{C}_{\phi}(x\gets y)$ + +$$ +\mathcal {C} _ {\phi , \rho} (p, q) = \min _ {\phi} \sum_ {x \in p, y \in q} \rho \mathcal {C} _ {\phi} (x \rightarrow y) + (1 - \rho) \mathcal {C} _ {\phi} (x \leftarrow y) \tag {2} +$$ + +where $\phi$ is parameters of CT, $\rho$ is the trade-off factor controlling the strengths between the forward and backward CTs. To better understand how the CT works when minimizing Eq. 2, we take the forward CT as an example: + +$$ +\mathcal {C} _ {\phi} (x \rightarrow y) = \mathbb {E} _ {y 1: m \sim q} \mathbb {E} _ {x \sim p} \left[ \sum_ {j = 1} ^ {m} c (x, y _ {j}) \hat {\pi} _ {m} \left(y _ {j} \mid x, \phi\right)\right] \tag {3} +$$ + +where $c(\cdot, \cdot)$ could be some well defined distance functions, such as Euclidean or Cosine, $\hat{\pi}_m(y_j|x, \phi)$ is forward transport matrix, also called forward navigator in the scope of CT, satisfying $\sum_{j=1}^{m} \hat{\pi}_m(y_j|x, \phi) = 1$ , it describes the possibility of transporting $x$ to $y_j$ and can be formulated as: + +$$ +\hat {\pi} _ {m} \left(y _ {j} \mid x, \phi\right) = \frac {e ^ {- d _ {\phi} \left(x , y _ {j}\right)}}{\sum_ {j ^ {\prime}} ^ {m} e ^ {- d _ {\phi} \left(x , y _ {j ^ {\prime}}\right)}} \tag {4} +$$ + +where $d_{\phi}(\cdot, \cdot)$ represents measurement function, such as MLP implemented by Zheng et al. [39]. The forward CT can be interpreted as the expected cost to stochastically transport a random source point $x$ to one of the $m$ randomly instantiated "anchors" of the target distribution. By minimizing Eq. 3, an unbiased statistical estimation of the two distributions arrives. Proofs can be found in Zheng et al. [39]. Hence, it is reasonable to transfer statistics of one distribution to another. + +# 3.3. PUTM + +Our proposed PUTM aims to exploit discriminative statistics from query samples for reducing the gap between the estimated prototypes and their ground truth prototypes. However, the ground truth prototypes are always intractable in + +practice. A reasonable approach to obtain unbiased prototypes is to aggregate discriminative statistics from both support and query samples following a semi-supervised manner [37]. Different from the standard semi-supervised problems, the query samples are usually limited per class, especially in class-imbalanced case. Follow up, we present the importance of unbiased transfer in semi-supervised FSL setting, the algorithm of realizing unbiased exploitation with CT and transductive inference with unbiased transfer in turn. + +# 3.3.1 Unbiased Statistics Transfer Matters in TFSL + +Given a few-shot task, unbiased prototypes arrives if and only if the aggregated query samples are noiseless, which should heavily rely on the unbiased statistics transfer. Leveraging similarities between query samples and prototypes is a common way to realize statistics transfer in transductive few-shot image classification. Given the transport matrix $\pi^n\in \mathbb{R}^{M\times N}$ at the $n$ -th iteration, it measures the closeness of prototypes $\{c_i^n\}_{i = 1}^N$ and query samples $\{\pmb{x}_{i,j}^q\}_{j = 1}^{K_i'}$ For simplicity, we rewrite all query samples as $\{\pmb{x}_r^q\}_{r = 1}^M$ . Thus, the refined prototypes $\{c_i^{n + 1}\}_{i = 1}^N$ can be expressed as: + +$$ +\boldsymbol {c} _ {i} ^ {n + 1} = \frac {\sum_ {r = 1} ^ {M} \boldsymbol {\pi} _ {r , i} ^ {n} \boldsymbol {x} _ {r} ^ {q} + \sum_ {j = 1} ^ {K} \boldsymbol {x} _ {i , j} ^ {s}}{\sum_ {r ^ {\prime} = 1} ^ {M} \boldsymbol {\pi} _ {r ^ {\prime} , i} ^ {n} + K}, \quad i = 1, \dots , N \tag {5} +$$ + +where $\pi_{r,i}^{n} = \frac{e^{-d_{\phi}(\pmb{x}_{r}^{q},\pmb{c}_{i}^{n})}}{\sum_{r^{\prime} = 1}^{M}e^{-d_{\phi}(\pmb{x}_{r^{\prime}}^{q},\pmb{c}_{i}^{n})}}, d_{\phi}(\cdot ,\cdot)$ denotes the well defined measurement function, and we denote optimal transport matrix as $\pi^{*}$ . To guarantee the unbiased refinement of prototypes, $\pi^{*}$ need to be precise, which is usually difficult to be satisfied in practice. Fortunately, partial noisy is tolerable. For example, given 15 query samples per class, a few wrong transferring such as 1 or 2 samples is tolerable in calibrating prototypes. As for class-imbalanced case, a tiny mistake may result in disastrous consequence on prototypes calibration. For the classes having only 1 or 2 query samples, the tolerances of error transmissions should be extremely low. Therefore, to improve the robustness of calibrated prototypes in class-imbalanced TFSL, transferring unbiased statistics of query samples with $\pi^{*}$ becomes crucial. + +There are mainly two lines of works in defining $\pi^{*}$ : i) Liu et al. [17] employ Cosine function [17]; ii) Hu et al. [11] use Optimal Transport (OT). Cosine function may not powerful enough to fully reflect the relationships between prototypes and query samples since it ignores various importance between each two points. OT describes a doubly stochastic transport matrix such that $\Pi(p, q) = \{\pi^{*} | \sum_{r=1}^{M} \pi_{r,i}^{*} = a_{i}, \sum_{i=1}^{N} \pi_{r,i}^{*} = b_{r}\}$ . Unfortunately, we usually do not have any priors on distributions of $p$ and $q$ , thus, we usually have $a_{i} = \frac{1}{N}, i = 1, \dots, N$ and $b_{r} = \frac{1}{M}, r = 1, \dots, M$ , which should be contradictory to class-imbalanced setting. For example, once we employ Dirichlet distribution with $\alpha = 2_{N}$ to mimic the generation of query samples, $a_{i} = \frac{1}{N}$ will never + +fit the data. According to the analysis of CT, it replaces the uniform constraint on prior distribution of classes derived from query samples with a data-driven manner, thus ensuring to transfer the unbiased statistics more flexible and efficient. + +# 3.3.2 Unbiased Statistics Exploitation with CT + +As we can see, CT has an appealing property of exploiting unbiased statistics thanks to its task-adaptive prior rather than uniform-distributed one as OT. Here after, we present details of achieving such unbiased exploitation with CT. + +As shown in Fig. 2, given a class-imbalanced few-shot task in Sec. 2, we first employ a well-trained feature extractor $f_{\theta^{*}}(\cdot)$ to get features of support and query samples as $f_{i,j}^{s} = f_{\theta^{*}}(\pmb{x}_{i,j}^{s})$ and $f_{r}^{q} = f_{\theta^{*}}(\pmb{x}_{r}^{q})$ , where $\theta^{*}$ is the set of optimized parameters, being fixed after training on the base classes following Mangla et al. [19]. Then, we conduct channel attention with preprocessing developed by Yang et al. [35]. Finally, unbiased statistics exploitation is realized by optimizing transport matrices constrained by CT theory. + +Specifically, the initial prototypes are averaged on the features of support set as $\pmb{c}_i^0 = \frac{1}{K}\sum_{j = 1}^{K}f_{i,j}^s$ , $i = 1,\dots,N$ where the superscript of $\{c_i^0\}_{i = 1}^N$ describes the generation of prototypes is zero. They will be updated subsequently, detailed in Sec. 3.3.3. At this moment, we treat $\{c_i^0\}_{i = 1}^N$ and $\{f_r^q\}_{r = 1}^M$ as samples from the two discrete distributions, and utilizing CT to learn the transport matrices for exploiting unbiased statistics. According to the analysis of Eq. 2, an unbiased sample estimate of CT given query features $\{f_r^q\}_{r = 1}^M$ and prototypes $\{c_i^0\}_{i = 1}^N$ can be expressed as: + +$$ +\mathcal {L} _ {\phi , \boldsymbol {\theta} ^ {*}, \rho} \left(f _ {1: M} ^ {q}, \boldsymbol {c} _ {1: N} ^ {0}\right) = \sum_ {i = 1} ^ {N} \sum_ {r = 1} ^ {M} c \left(\boldsymbol {c} _ {i} ^ {0}, f _ {r} ^ {q}\right). \tag {6} +$$ + +$$ +(\frac {\rho}{M} \hat {\pi} _ {N} (\pmb {c} _ {i} ^ {0} | f _ {r} ^ {q}, \phi) + \frac {1 - \rho}{N} \hat {\pi} _ {M} (f _ {r} ^ {q} | \pmb {c} _ {i} ^ {0}, \phi)) +$$ + +where $\hat{\pi}_N$ and $\hat{\pi}_M$ separately denote the forward and backward transport matrices. Again substituting query features $\{f_r^q\}_{r=1}^M$ and prototypes $\{c_i^0\}_{i=1}^N$ into Eq. 4, we have: + +$$ +\hat {\pi} _ {N} \left(\boldsymbol {c} _ {i} ^ {0} \mid f _ {r} ^ {q}, \phi\right) = \frac {e ^ {- d _ {\phi} \left(f _ {r} ^ {q} , \boldsymbol {c} _ {i} ^ {0}\right)}}{\sum_ {i ^ {\prime} = 1} ^ {N} e ^ {- d _ {\phi} \left(f _ {r} ^ {q} , \boldsymbol {c} _ {i ^ {\prime}} ^ {0}\right)}} \tag {7} +$$ + +$$ +\hat {\boldsymbol {\pi}} _ {M} \left(f _ {r} ^ {q} \mid \boldsymbol {c} _ {i} ^ {0}, \phi\right) = \frac {e ^ {- d _ {\phi} \left(f _ {r} ^ {q} , \boldsymbol {c} _ {i} ^ {0}\right)}}{\sum_ {r ^ {\prime} = 1} ^ {M} e ^ {- d _ {\phi} \left(f _ {r ^ {\prime}} ^ {q} , \boldsymbol {c} _ {i} ^ {0}\right)}} \tag {8} +$$ + +The forward transport matrix represents the probability of query samples belonging to the corresponding support classes. The two transport matrices with the optimal parameter $\phi^{*}$ can be obtained by minimizing the approximated CT estimation of Eq. 6. Once $\hat{\pi}_N^*$ and $\hat{\pi}_M^*$ with the optimal $\phi^{*}$ are obtained, the transport matrix described in Sec. 3.3.1 for unbiased statistics exploitation can be naturally realized. To better understand this, we depict the mechanisms of the + +Algorithm 1 Work flow of PUTM for one task. +Input: Support samples $\{\pmb{x}_{i,j}^{s}\}_{i,j = 1}^{N,K}$ and class-imbalanced query samples $\{\pmb{x}_r^q\}_{r = 1}^M$ generated from Dirichlet distribution with parameter $\alpha$ , a well-trained feature extractor $f_{\theta^{*}}(\cdot)$ Parameters: Distance measurement function $d_{\phi}(\cdot ,\cdot)$ Initialization Hyper-parameters $\alpha$ $\rho$ $\lambda$ , and learning schedule for updating $\phi$ ; Initialize prototypes $c_{i}^{0} = \frac{1}{K}\sum_{j = 1}^{K}f_{i,j}^{s},i = 1,\ldots ,N;$ for n=1: $n_{steps}$ do Initialize parameters $\phi$ $\phi^{*}\gets argmin_{\phi}\mathcal{L}_{\phi ,\theta^{*},\rho}(f_{1:M}^{q},c_{1:N}^{n})$ Refining prototypes $c_{1:N}^{n + 1}$ using Eq. 11 based on $c_{1:N}^{n}$ end for Evaluating performance using Eq. 12; Output Parameters $\{\phi^{*},c_{1:N}^{n_{step}}\}$ + +transport matrices developed above from three perspectives: 1) the distance function in transport matrices is implemented with DNNs, hence, they are able to learn a comprehensive distance metric beyond a simple Cosine function; 2) the CT distance is proven to be unbiased given samples of two distributions $p$ and $q$ in [39]; 3) The forward transport matrix holds free for sum along query samples given a specific prototype, namely, $\sum_{r=1}^{M} \hat{\pi}_N(c_i^0 | f_r^q, \phi^*) = C$ , and $C$ is not restricted to be equal for each class, thus embedding task-adaptive prior instead of uniform distribution as PT-MAP [11] does. On the other hand, the backward transport matrix holds tight for sum along query samples given a specific prototype, that is, $\sum_{r=1}^{M} \hat{\pi}_M(f_r^q | c_i^0, \phi^*) = 1$ , hence, uniform-distributed prior holds, and it is proven to be underfitting in class-imbalanced case [29]. In practice, we employ a trade-off to balance the strengths of the two transport matrices by summing them together with a soft coefficient $\rho$ . For simplicity, we only use the forward transport matrix in the rest of the work. + +# 3.3.3 Unbiased Statistics Transfer with EM-Solver + +Once the forward transport matrix $\hat{\pi}_N^*$ is obtained by minimizing Eq. 6, it is straightforward to derive the refined prototypes by substituting $\hat{\pi}_N^*$ into Eq. 5: + +$$ +\boldsymbol {c} _ {i} ^ {\prime} = \frac {\sum_ {r = 1} ^ {M} \hat {\pi} _ {N , r , i} ^ {*} f _ {r} ^ {q} + \sum_ {j = 1} ^ {K} f _ {i , j} ^ {s}}{K + \sum_ {r = 1} ^ {M} \hat {\pi} _ {N , r , i} ^ {*}}, \quad i = 1, \dots , N \tag {9} +$$ + +It is worth noting that once the optimal parameters $\phi^{*}$ are arrived, the only parameters left for optimizing are prototypes. Recalling our objective in Eq. 6, it is easy to find that the optimal prototypes at this moment could also be derived by $\frac{\partial\mathcal{L}_{\phi^{*},\theta^{*},\rho}}{\partial c_{1:N}^{0}}$ , thereby Eq. 9 could be derived. Instead of directly calibrating class-wise prototypes, We employ an inertia parameter $\alpha$ to update prototypes proportionally: + +$$ +\boldsymbol {c} _ {i} ^ {1} = \boldsymbol {c} _ {i} ^ {0} + \alpha \left(\boldsymbol {c} _ {i} ^ {\prime} - \boldsymbol {c} _ {i} ^ {0}\right), \quad i = 1, \dots , N \tag {10} +$$ + +Right now, recursive expression emerges for updating prototypes according to Eq. 10: + +$$ +\boldsymbol {c} _ {i} ^ {n + 1} = \boldsymbol {c} _ {i} ^ {n} + \alpha \left(\boldsymbol {c} _ {i} ^ {\prime} - \boldsymbol {c} _ {i} ^ {n}\right), \quad i = 1, \dots , N \tag {11} +$$ + +As we can see: i) updating the forward transport matrix $\hat{\pi}_N^*$ and prototypes $c_{1:N}^n$ are coupled; ii) $\hat{\pi}_N^*$ is a random variable determined by $\phi$ while $c_{1:N}^n$ is an unknown but deterministic variable. These two facts meet conditions of implementing EM optimization, and we formulate our EM-Solver as follows: i) E Step, updating $\hat{\pi}_N^*$ by minimizing Eq. 6 while keeping $c_{1:N}^n$ fixed; ii) M Step, updating $c_{1:N}^n$ by minimizing Eq. 6 while keeping $\hat{\pi}_N^*$ fixed. Besides, it is worth noting that at each iteration, $\phi^*$ need to be reinitialized. The pseudo code is provided in Alg. 1. + +After $n_{step}$ loops between estimating $\hat{\pi}_N^*$ and refining $c_{1:N}^n$ , the decision per sample is finally made by: + +$$ +y _ {r} ^ {q} = \max _ {i \in [ 1: N ]} \hat {\pi} _ {N} \left(\boldsymbol {c} _ {i} ^ {n _ {\text {s t e p}}} \mid f _ {r} ^ {q}, \phi^ {*}\right), \quad r = 1, \dots , M \tag {12} +$$ + +Statistic results of average accuracy are usually conducted using query samples on various of different tasks. + +# 3.4. Complexity Analysis + +$\phi$ is implemented with MLP in our work. Taking a two-layers MLP for example, namely, $d_{f} \rightarrow d_{1}^{\phi} \rightarrow d_{2}^{\phi}$ . For $T$ tasks, computational complexity originally takes $\mathcal{O}(T \times \max \{NM \times d_{f} \times d_{1}^{\phi}, NM \times d_{1}^{\phi} \times d_{2}^{\phi}\})$ . In practice, $T$ is usually set to be large enough for reliable results, thus resulting in time-consuming evaluation of our model. To mitigate the real-time issue, we trade space for time by paralleling our proposed PUTM among all tasks. Therefore, the computational complexity is reduced to $\mathcal{O}(\max \{NM \times d_{f} \times d_{1}^{\phi}, NM \times d_{1}^{\phi} \times d_{2}^{\phi}\})$ . Besides, we can further control the size of MLP, that is $\{d_{i}^{\phi}\}_{i=1}^{2}$ , to achieve a trade-off between accuracy and real-time efficiency. + +# 4. Experiments + +# 4.1. Experimental Setup + +Baselines: We mainly compare our model with some recently proposed State-Of-The-Art (SOTA) methods on one Nvidia RTX 3090 GPU. For inductive methods, we adopt Baseline/Baseline $(++)$ [4], ProtoNet [26], Simpleshot [33], and HOT [9] in inductive. For transductive methods, we adopt PT-MAP [11], LaplacianShot [40], TIM[2], BD-CSPN [17], $\alpha$ -TIM [29], iLPC [14], and BAVAR [12]. + +Datasets: We evaluate our model on four benchmarks including miniImageNet [22], tieredImageNet [23], CUB [31], and CIFAR-FS [1]. MiniImageNet is randomly chosen from ILSVRC-12 dataset [6] and it contains 100 classes with 600 images per class, the resolution of which is $84 \times 84 \times 3$ . Following previous works [22, 29, 11, 35], the dataset is split into 64 base classes, 16 validation classes, and + +Table 1: Classification accuracy (%) of SOTA methods on class-imbalanced and class-balanced settings with different datasets and backbones. For imbalanced case, query samples are generated following a Dirichlet distribution with $\alpha = 2_{N}$ . Results are averaged over 3000 tasks with $95\%$ confidence intervals. Results with superscript $\dagger$ are our re-implementations based on the code provided by Veilleux et al. [29]. The best and the second best scores are marked in bold and blue, respectively. + +
SettingMethodmini-ImageNet (WRN/WRN$)CUB (RN18/WRN$)tiered-ImageNet (WRN/WRN$)CIFAR-FS (WRN$)
1-shot3-shot5-shot1-shot3-shot5-shot1-shot3-shot5-shot1-shot3-shot5-shot
Induct. (%)Imbalanced & BalancedBaseline (ICLR'19)62.2/62.8†76.9†/77.3†81.9/82.9†64.6/70.7†82.3†/87.3†86.9/90.0†64.6/63.6†80.0†/83.0†84.9/87.2†69.5†83.9†86.7†
Baseline++ (ICLR'19)64.5/64.8†77.5†/78.4†82.1/82.7†69.4/81.7†83.3†/89.4†87.1/91.2†68.7/66.9†80.9†/78.7†85.4/82.2†74.9†85.0†87.4†
ProtoNet (NeurIPS'17)61.2/62.5†76.9†/77.2†81.1/81.4†63.1†/69.6†82.3†/85.6†85.4†/88.8†63.5†/64.2†79.9†/80.1†84.1†/84.0†69.5†83.8†86.7†
Simpleshot (ARXIV)66.2/67.1†77.6†/78.2†82.4/83.3†70.6/81.7†83.6†/89.5†87.5/91.4†70.7/71.4†81.3†/84.2†85.9/87.5†75.2†84.7†87.4†
HOT (NeurIPS'22)66.3†/69.178.5†/79.8†82.8†/84.474.5†/81.285.4†/88.2†87.8†/91.574.1†/75.982.6†/83.9†85.4†/87.375.485.3†87.5
Transduct. (%)ImbalancedPT-MAP (ARXIV)60.6/63.2†65.9†/68.0†66.8/69.3†65.1/69.8†71.2†/73.2†71.3/74.3†65.1/67.8†69.1†/72.0†71.0/73.2†65.9†69.3†70.3†
LaplacianShot (ICML'20)68.1/69.8†78.8†/79.2†83.2/83.6†73.7/84.2†85.7†/90.4†87.7/91.4†73.5/72.6†82.6†/85.0†86.8/87.7†78.3†86.1†87.3†
TIM (NeurIPS'20)69.8/70.9†79.7†/80.7†81.6/83.2†74.8/82.8†84.8†/89.1†86.9/90.5†75.8/77.8†82.5†/86.3†85.4/88.3†77.0†84.6†86.2†
BD-CSPN (ECCV'20)70.4/71.2†77.1†/78.6†82.3/83.4†74.5/85.1†85.7†/90.5†87.1/91.5†75.4/76.3†82.5†/85.0†85.9/87.2†79.1†86.0†87.3†
α-TIM (NeurIPS'2021)69.8/70.9†80.4†/81.1†84.8/84.9†75.7/83.6†87.3†/91.2†89.8/92.8†76.0/77.7†83.6†/86.6†87.8/89.9†78.1†87.2†88.9†
iLPC (ICCV'21)71.5†/74.3†78.6†/81.1†81.0†/83.3†78.7†/86.4†85.6†/90.1†86.9†/90.8†76.6†/81.6†83.2†/87.5†85.1†/89.0†80.8†85.4†86.5†
BAVAR (AISTATS'23)74.1/74.2†82.6†/82.6†85.5/85.6†82.0/85.7†89.2†/89.8†90.7/90.8†77.5/80.6†84.8†/87.2†87.5/89.3†81.8†87.0†87.9†
PUTM (Ours)70.9/73.880.5/82.984.6/85.778.9/86.987.8/91.389.3/92.275.0/81.183.6/88.486.0/90.481.487.388.6
BalancedPT-MAP (ARXIV)78.9/82.5†86.3†/87.5†86.6/88.6†85.5/92.0†90.5†/94.0†91.3/94.3†84.6/88.1†88.2†/91.8†90.0/92.5†87.6†90.5†90.9†
LaplacianShot (ICML'20)72.9/73.4†79.0†/80.5†83.8/84.2†78.9/87.5†86.7†/90.4†88.8/92.3†78.8/78.7†84.6†/85.6†87.3/87.0†82.1†86.3†86.8†
TIM (NeurIPS'20)74.6/77.6†85.5†/86.0†85.9/88.0†80.3/88.1†89.8†/93.0†90.5/94.0†80.3/83.8†87.7†/90.6†88.9/92.1†83.0†89.5†90.5†
BD-CSPN (ECCV'20)72.5/73.8†79.2†/80.7†83.7/85.3†77.9/87.3†86.9†/91.4†88.9/92.4†77.7/78.7†84.5†/86.4†87.4/88.3†81.6†87.4†88.6†
α-TIM (NeurIPS'2021)71.0/71.5†76.8†/77.7†82.4/83.3†77.2†/84.9†85.1†/90.2†87.6†/91.2†75.1†/78.9†80.6†/84.4†85.3†/88.2†79.7†85.7†87.9†
iLPC (ICCV'21)75.5†/77.8†82.0†/83.9†83.9†/85.7†82.4†/89.6†87.9†/92.3†88.9†/93.0†81.0†/85.5†86.4†/89.8†87.5†/90.9†84.8†88.6†89.2†
BAVAR (AISTATS'23)78.5/78.5†84.8†/84.9†87.4/87.7†85.6/89.0†90.8†/91.7†91.4/92.1†81.5/84.7†87.4†/89.3†88.3/90.3†85.0†88.4†88.9†
PUTM(Ours)78.4/81.484.9/86.786.5/88.184.9/91.289.2/93.390.1/93.781.6/86.886.9/90.788.6/92.286.489.590.4
+ +![](images/03f36be5589b3e7217c55def4c04ce9fbd84dcc621e097d8ea5193aff6247575.jpg) +(a) + +![](images/b1e240b3e1a7705cc135e6eccc763daa6b6161085835fd78ab617d6092a67cf9.jpg) +(b) + +![](images/a1ce3d03635b385abb5ab7dd482800a036f12a9107fa72ca52cd43b2264aeff3.jpg) +(c) +Figure 3: (a)-(b): The t-SNE [28] visualizations before (middle) and after (left) calibration on a 5-way 1-shot miniImageNet task. Pentagrams are prototypes while solid dots are query features. Classes change and best view in colors. (c): Impact of forward and backward transport matrices in calibrating prototypes on miniImageNet over 3000 5-way 1-shot tasks. + +20 novel classes. TieredImageNet [23] is also a subset of ILSVRC-12 dataset, which is larger than miniImageNet. It contains 608 classes sampled from a hierarchical category structure with around 1281 images per class. Following the previous work [23], we split the dataset into 351 base classes, 97 validation classes, and 160 novel classes. The resolution is also $84 \times 84 \times 3$ . CUB is a fine-grained dataset, containing 200 classes of birds with around 60 images per class. And the resolution is still $84 \times 84 \times 3$ . We adopt 100 base classes, 50 validation classes, and 50 novel classes following [4]. CIFAR-FS consists of all 100 classes from CIFAR-100 [34], whose classes are randomly split into 64 base classes, 16 classes, and 20 novel classes. Each class contains 600 images of size $32 \times 32 \times 3$ . + +Implementation details: We use pre-trained backbones for extracting visual features of four benchmarks, as shown in Table. 1. WRN and RN18 are separately WideResNet-28- + +10 and ResNet-18 pre-trained with standard classification loss [29]. WRN $\S$ is WideResNet-28-10 pre-trained with self-supervised loss [19]. Besides, we employ log transform, a channel-wise feature adaptation, introduced in Yang et al. [35] to pre-process the pre-extracted features. The distance function $\phi$ is instantiated as a two-layers MLP activated with LeakyReLU whose architecture is $[d_f, 128, 64, 1]$ . As for hyper-parameters, we mainly set $\beta = 0.5$ , $\alpha = 0.1$ , $\rho = 0.2$ . The reported results are averaged over 3000 tasks. + +# 4.2. Main Results + +Quantitative results: The classification results on miniImageNet, tieredImageNet, CUB, and CIFAR-FS are reported in Table 1, according to which five-fold observations can be drawn: 1) inductive methods are not bothered by class-imbalanced problem since they do not leverage transferable statistics of query samples; 2) most transductive methods + +![](images/e8520dc25383a3eb2b6efef5b65fdc2b7a19db726b824beffa9ebda40b8fd5cc.jpg) +Figure 4: Case studies for 5-way 5-shots tasks on CUB [31] (left) and miniImageNet (right). Comparisons between unnormalized prior distribution (true number of query samples counting for each class) and unnormalized posterior distribution (estimated number of query samples counting by the well optimized forward transport matrix for each class). + +![](images/c2bc6762adbc84335fc53b3432e498d319753588350ba5b533bcbfe7c9da7f09.jpg) +Figure 5: 5-way 5-shot classification accuracy on miniImageNet and CUB of transductive methods versus imbalance level, lower $\alpha$ corresponds to severer class imbalance. + +still outperform the inductive peers in class-imbalanced setting, which implies that there exists a trade-off between extra statistics conveyed by class-imbalanced query samples and algorithm bias; 3) results of features extracted by WRN $\S$ usually outperforms those by WRN or RN18, it indicates that self-supervised learning is helpful in obtaining generalized representations in class-imbalanced and class-balanced FSL applications; 4) most existed transductive inference methods suffer from performance cliff since their mismatch between data distribution and prior distribution. For example, TIM implicitly introduces uniform prior on query samples by using entropy regularization since minimizing entropy-based regularization is equivalent to minimizing the KL divergence between the predicted marginal distribution and uniform distribution. Hence, data distribution and model bias are unsuitable, leading to poor accuracy. Fortunately, such kind of mismatch can be eased by re-weighting in [29]. On the contrary, PT-MAP holds a strong but unmodified uniformly distributed prior on its transport matrix. Therefore, results of TIM are robuster than those of PT-MAP; 5) our proposed method outperforms most of the transductive methods and achieves competitive results with some most recently proposed methods, such as $\alpha$ -TIM, iLPC and BAVAR. It indicates that prototype refinement benefits from the well optimized transport matrices when shot number is low. Moreover, compared with iLPC and BAVAR, on the one hand, our model is easy to implement. On the other hand, BAVAR heavily relies on prior of imbalanced ratio $\alpha$ in class-imbalanced case while iLPC depends on uniform prior in class-balanced case [12], importantly however, our model is free of these priors, making it suitable for real-world applications when we have no idea on class distributions. + +Qualitatively analysis: To qualitatively illustrate the evolution of prototypes of our model, we map prototypes and query features of one task into a 2-D subspace with t-distributed Stochastic Neighbor Embedding (t-SNE) [28], it is a non-linear dimensional reduction technique well-suited for embedding high-dimensional data into a low-dimensional + +![](images/9f5da9ddfb275610243ae1e2beb650110964e6496e8595ce92af91b504d1ce98.jpg) + +![](images/5b00c9dbd6b1a6fc6f1a8ee2fbd614df8d9147a7bd0c0101073eadbb3e0c3a46.jpg) + +Table 2: End-to-end real-time efficiencies (s) of 5-way 1-shot on CUB with two backbones averaged on 100 tasks. + +
Backboneα - TIM (NeurIPS'21)iLPC (ICCV'21)BAVAR (AISTATS'23)Ours
RN185.64.63.42.9
WRN6.24.73.63.7
+ +space. As we can see from Fig. 3, due to class-imbalanced issue, although prototypes can not match their corresponding class centers well at beginning, they become consistent with the ground truth centers after refinement using our proposed method, verifying the effectiveness of our PUTM in dealing with unknown and arbitrary prior situation. + +# 4.3. Model Analysis + +Forward transport V.S. backward transport: As discussed in Sec. 3.3.2, the forward and backward transport matrices put different priors of $\{a_i\}_{i=1}^N$ . Namely, we do not restrict uniform distribution in the forward transport and enable it to be adaptive to data-driven class distribution. On the contrary, prior in the backward transport is always assumed to be $\frac{1}{N}$ . Therefore, we employ the forward transport for predictions to meet the class-imbalanced essence, the efficiency is illustrated in Fig. 4, it depicts that the predicted distribution is consistent with the true distribution. Moreover, we conduct an extra experiment to verify the opposite direction of the two transport matrices, results are illustrated in Fig. 3, where we separately use the forward transport and the backward transport to calibrate the prototypes over 3000 tasks. According to the results, we find that, from a statistical point of view, the backward transport does harm the efficient migration from the class-imbalanced query samples. + +Robustness of imbalanced coefficients: An important point in this work is that our model is robust for various class-imbalanced coefficients, which is vital and crucial for real-world applications since we usually do not know whether the few-shot tasks are balanced or not in advance, thus, we could not know what kind of methods are suitable for describing the samples distribution of tasks. Once they are + +![](images/31de3a57fe62b36349fc65422bb829107d7a86eccc89cb737914971922bc4fb6.jpg) + +![](images/40d73d77e591d28f618fb87f29e90ee2d1dcaa757ad0940aeea7b377e568bace.jpg) + +![](images/7625139324fac253e27f9d27d8039a52cba1acba48db366165cb100f4262c3fa.jpg) + +![](images/97375bd9f791c9ee9a48ed1ee0674f95378f49b3323be29c19ebdbb12d477929.jpg) +Figure 6: Sensitivity analysis of our model to hyper-parameters including log transform $\beta$ , CT coefficient $\rho$ , and inertia $\alpha$ . Results are obtained with WRN8 and are reported on both validation and test sets. Best viewed in color. + +![](images/c8c618a05c2cab20e3f21c6c2d80903b8512108f50151a6fc69185e8c9cf3e5b.jpg) + +![](images/3961bb3cd77757ffe3a0de41e992f0d7ed4011378782c1fb2f8c05b2b2784868.jpg) + +unmatched, horrible performance degradation would happen, such as PT-MAP does. We verify the robustness of our model with a wide range of imbalanced coefficients as shown in Fig. 5, where $\alpha$ changes from 1 to 6. The performance of most methods decreases as $\alpha$ decreasing because smaller $\alpha$ indicates more imbalanced distribution of query samples, thus making tasks harder. On the contrary, performances of LaplacianShot and $\alpha$ -TIM drop obviously as $\alpha$ increases. Our model achieves consistent improvement and reasonable trend in a wide range of $\alpha$ , we attribute this to the introduction of adaptive transport matrices, which enables PUTM to fit the class distributions precisely and flexibly. + +Sensitivity of hyper-parameters: To further verify the robustness of our model, we validate the sensitivity of PUTM to different hyper-parameters introduced in Sec. 4.1, and results are reported in Fig. 6. Generally speaking, the tendencies on validation and test sets are same. Besides there are three-fold observations: i) CT coefficient is less sensitive than log transform and inertia; ii) log transform controls the strength of channel-wise attention, which is proven to be important especially in few-shot case, thus it affects performance mostly; iii) inertia reflects the bottleneck of information flow from the aggregated prototypes to the refined prototypes. Bigger or smaller value of inertia is helpless for robust transfer since refinement of prototypes is associated with transport matrices. Namely, if the matrices are not well-optimized, a big inertia may cause algorithm to fall into a local optimum and vice versa. + +Real-time efficiency: To verify the efficiency of PUTM, we conduct parallel versions of $\alpha$ -TIM, iLPC, and BAVAR based on their official implementations with the same machine. Results are reported in Table. 2, as we can see that our + +model consumes less time using RN18 and achieves competitive results using WRN. And we attribute this to the fact that : i) both $\alpha$ -TIM and iLPC employ Sinkhorn algorithm to solve the Optimal Transport (OT) problem involving thousands of inner loop, and it is a kind of time consuming; ; ii) our EM-Solver might be more efficient for dealing with the class-imbalanced TFSL since it imposes potential capability for modeling such unknown distribution with CT theory. + +# 5. Conclusion and Future Works + +We propose a novel model called PUTM with EM-Solver based on CT theory for both class-imbalanced and class-balanced TFSL in this work according to an important observation that CT has a natural connection with unknown and arbitrary class prior problem. Specifically, PUTM exploits transferable statistics with CT for refining biased prototypes solved by EM to capture the unbiased statistics within imbalanced query samples. Extensive experiments on standard benchmarks verify the effectiveness of our model in both class-imbalanced and class-balanced few-shot applications. In the future, we will explore the applicability of PUTM on more problem settings and applications, such as multi-domain few-shot classification and few-shot object detection. + +# 6. Acknowledgement + +This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant U21B2006; in part by Shaanxi Youth Innovation Team Project; in part by the National NSFC under Grant 82172860; in part by the National NSFC under Grant 6220010437; in part by the Fundation of Aerospace under Grant SAST2021- + +012. 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PMLR, 2020. \ No newline at end of file diff --git a/2023/Prototypes-oriented Transductive Few-shot Learning with Conditional Transport/images.zip b/2023/Prototypes-oriented Transductive Few-shot Learning with Conditional Transport/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..6826947b60881a93b646341d79c6704f17f5ea21 --- /dev/null +++ b/2023/Prototypes-oriented Transductive Few-shot Learning with Conditional Transport/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a878b0292f72c5a4d0ee7f58f84c31be3c28ae2c8db5e8e361989563a9c44d64 +size 562941 diff --git a/2023/Prototypes-oriented Transductive Few-shot Learning with Conditional Transport/layout.json b/2023/Prototypes-oriented Transductive Few-shot Learning with Conditional Transport/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..49c39740594bab40c2f73956bfc66ac60576884a --- /dev/null +++ b/2023/Prototypes-oriented Transductive Few-shot Learning with Conditional Transport/layout.json @@ -0,0 +1,9622 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 48, + 103, + 545, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 103, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 48, + 103, + 545, + 121 + ], + "type": "text", + "content": "Prototypes-oriented Transductive Few-shot Learning with Conditional Transport" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "spans": [ + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "text", + "content": "Long Tian" + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "text", + "content": ", Jingyi Feng" + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "text", + "content": ", Xiaoqiang Chai" + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "text", + "content": ", Wenchao Chen" + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "inline_equation", + "content": "^{2,\\text{图}}" + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "text", + "content": ", Liming Wang" + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "text", + "content": ", Xiyang Liu" + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "text", + "content": ", Bo Chen" + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "text", + "content": " National Pilot School of Software Engineering, " + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "text", + "content": " National Key Laboratory of Radar Signal Processing \n" + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 52, + 149, + 569, + 193 + ], + "type": "text", + "content": " Xidian University, Xi'an, Shanxi 710071, China" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 198, + 194, + 424, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 198, + 194, + 424, + 205 + ], + "spans": [ + { + "bbox": [ + 198, + 194, + 424, + 205 + ], + "type": "text", + "content": "Email: {tianlong, wcchen}_xidian@163.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 234, + 192, + 247 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 234, + 192, + 247 + ], + "spans": [ + { + "bbox": [ + 143, + 234, + 192, + 247 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 259, + 290, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 259, + 290, + 522 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 290, + 522 + ], + "type": "text", + "content": "Transductive Few-Shot Learning (TFSL) has recently attracted increasing attention since it typically outperforms its inductive peer by leveraging statistics of query samples. However, previous TFSL methods usually encode uniform prior that all the classes within query samples are equally likely, which is biased in imbalanced TFSL and causes severe performance degradation. Given this pivotal issue, in this work, we propose a novel Conditional Transport (CT) based imbalanced TFSL model called Prototypes-oriented Unbiased Transfer Model (PUTM) to fully exploit unbiased statistics of imbalanced query samples, which employs forward and backward navigators as transport matrices to balance the prior of query samples per class between uniform and adaptive data-driven distributions. For efficiently transferring statistics learned by CT, we further derive a closed form solution to refine prototypes based on MAP given the learned navigators. The above two steps of discovering and transferring unbiased statistics follow an iterative manner, formulating our EM-based solver. Experimental results on four standard benchmarks including miniImageNet, tieredImageNet, CUB, and CIFAR-FS demonstrate superiority of our model in class-imbalanced generalization1." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 544, + 128, + 556 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 128, + 556 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 128, + 556 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 564, + 288, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 564, + 288, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 564, + 288, + 696 + ], + "type": "text", + "content": "Deep learning based methods have gained a great success in many real-world applications, such as image classification [10, 25, 36], natural language processing [3, 32, 38], and so on, thanks to its powerful nonlinear representation ability [18, 24]. However, their outstanding performances heavily rely on large-scale annotated training data [6, 16]. When it comes to high cost of collecting and annotating a large amount of data, a major research effort is being dedicated to low data regimes, in which overfitting occurs in optimizing deep learning architectures. Few-shot Learning (FSL) tackles these challenges and has triggered substantial interests" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 308, + 234, + 541, + 355 + ], + "blocks": [ + { + "bbox": [ + 308, + 234, + 541, + 355 + ], + "lines": [ + { + "bbox": [ + 308, + 234, + 541, + 355 + ], + "spans": [ + { + "bbox": [ + 308, + 234, + 541, + 355 + ], + "type": "image", + "image_path": "4221e7dcb0b2f0338e3e0b5f6fd7e0f9e1b63c1af0d0689d3a688bf27faca9c0.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 361, + 547, + 410 + ], + "lines": [ + { + "bbox": [ + 305, + 361, + 547, + 410 + ], + "spans": [ + { + "bbox": [ + 305, + 361, + 547, + 410 + ], + "type": "text", + "content": "Figure 1: 5-way 1-shot image classification results with miniImageNet [22] dataset on 3000 tasks. Our model achieves the best accuracy in a wide range of imbalanced coefficients compared with PT-MAP [11] and " + }, + { + "bbox": [ + 305, + 361, + 547, + 410 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 361, + 547, + 410 + ], + "type": "text", + "content": "-TIM [29]." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 436, + 547, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 436, + 547, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 436, + 547, + 555 + ], + "type": "text", + "content": "within the community [8, 20], it aims to train a model from the base classes so as to generalize on the tasks sampled from the novel classes that were never seen during training. There are two major lines of works from the perspective of inference paradigms, namely inductive methods [26, 4] and their transductive counterparts [7, 23]. Both of them adopt well trained models for evaluating new tasks sampled from the novel classes. The former ones only utilize support samples in a supervised way while the later ones leverage both support and query samples in a semi-supervised manner." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 557, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 548, + 713 + ], + "type": "text", + "content": "Transductive inference is widely used in FSL since it can sufficiently discover statistics of query samples compared with its inductive peer. As a representative example, Hu et al. [11] propose PT-MAP for first employing Wide ResNet (WRN) [36] trained with S2M2 [19] on base classes to extract features of new tasks, and then adjusting prototypes from novel classes by aggregating similar query samples per class with the help of transport matrix derived from the Sinkhorn algorithm [5]. Setting marginal distributions of prototypes as uniform encodes strong prior that all the classes within query samples are equally likely, although, it works pretty well in perfectly class-balanced query samples. However, it is proven to be detrimental in class-imbalanced" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 255, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 255, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 255, + 713 + ], + "type": "text", + "content": "1Our code is available at https://github.com/RashLog/PUTM" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16317" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "applications where query samples come with arbitrary and unknown label marginals [21], and classification accuracy drops dramatically, as shown in Fig. 1. To narrow this gap, Veilleux et al. [29] propose " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "-TIM for handling class-distribution variations effectively. Unfortunately, we have observed the phenomena as shown in Fig. 1 that " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "-TIM can not achieve consistent improvement in various class-imbalanced levels, thus restricting its real-world applications. Most recently, other more complicated methods are also be arisen [14, 12]. Hu et al. [12] propose a clustering method for capturing the class-wise distributions properly." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 204, + 289, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 204, + 289, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 289, + 563 + ], + "type": "text", + "content": "To this end, for class-imbalanced TFSL, we develop a novel and simple Prototypes-oriented Unbiased Transfer Model (PUTM). It firstly constructs transferable class-wise prototypes iteratively for capturing the unbiased statistics within class-imbalanced query samples. Then it performs few-shot classification via the similarities between prototypes and query samples when the transfer arrives at convergence. The key to obtain unbiased transferable statistics is estimating class-wise marginal distributions precisely [14]. To achieve this, instead of utilizing doubly stochastic transport matrix constrained with fixed uniform-distributed marginal prior between prototypes and query samples as PT-MAP does, we employ task-adaptive forward and backward transport matrices with learnable marginal priors constrained by minimizing Conditional Transport (CT) distance [39] between prototypes and query samples. CT is a tool for measuring the cost in transporting the mass in one distribution to match another in an exchangeable but asymmetrical manner given a specific point-to-point cost function and an estimizable forward and backward transport matrices, also called navigators in the CT scope. To better calibrate prototypes with the help of learned transport matrices and query samples, we further derive a closed-form solution to refine prototypes based on MAP in an iterative manner. Decisions are finally made using the combination of forward and backward transport matrices when the iteration converges. Experiments on four benchmarks demonstrate that our proposed PUTM can learn task-adaptive prior in various class-imbalanced coefficients, paving a new way to transfer the unbiased statistics of query samples to prototypes." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 563, + 258, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 563, + 258, + 574 + ], + "spans": [ + { + "bbox": [ + 59, + 563, + 258, + 574 + ], + "type": "text", + "content": "Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 584, + 289, + 714 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 58, + 584, + 287, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 584, + 287, + 644 + ], + "spans": [ + { + "bbox": [ + 58, + 584, + 287, + 644 + ], + "type": "text", + "content": "- We find that the performance of class-imbalanced FSL heavily relies on the accurate estimation of class-wise marginal distribution. Meanwhile, we are the first one to find that there exists a nature connection between CT theory and such marginal distribution estimation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 653, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 653, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 653, + 289, + 714 + ], + "type": "text", + "content": "- We propose a novel and simple PUTM for class-imbalanced FSL based on connections mentioned above. It firstly embeds CT distance to measure the differences between prototypes and query samples for achieving better task-adaptive unbiased statistic migra" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 324, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 324, + 72, + 545, + 96 + ], + "type": "text", + "content": "tion elegantly. Then it calibrates prototypes using the transferred statistics in an iterative manner." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 105, + 547, + 164 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 105, + 547, + 164 + ], + "spans": [ + { + "bbox": [ + 317, + 105, + 547, + 164 + ], + "type": "text", + "content": "- We provide extensive experiments and comparisons on four standard benchmarks for verifying that our model achieves competitive results on both class-balanced and class-imbalanced (in a wide range of imbalanced coefficients) FSL settings." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 175, + 413, + 188 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 175, + 413, + 188 + ], + "spans": [ + { + "bbox": [ + 306, + 175, + 413, + 188 + ], + "type": "text", + "content": "2. Task Formulation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "spans": [ + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "text", + "content": "We divide the whole annotated dataset into two disjoint subsets: a base set " + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\text{base}}" + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "text", + "content": " classes and a novel set " + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\text{novel}}" + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "text", + "content": " classes. To build a common N-way K-shot task [30, 26], we first randomly sample N classes from " + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "text", + "content": " novel classes, and then pick K samples per class for the support set " + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "inline_equation", + "content": "S = \\{\\pmb{x}_{i,j}^{s}, \\pmb{y}_{i,j}^{s}\\}_{i=1,j=1}^{N,K}" + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "text", + "content": " to train or fine-tune the model. Finally, " + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "inline_equation", + "content": "K_{i}'" + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "text", + "content": " query samples being non-overlapped with support samples per class are randomly picked from the " + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "text", + "content": " support classes for evaluating the performance of the model, formulating query set as " + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "inline_equation", + "content": "\\mathcal{Q} = \\{\\pmb{x}_{i,j}^{q}, \\pmb{y}_{i,j}^{q}\\}_{i=1,j=1}^{N,K_{i}'}" + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "text", + "content": ". For simplicity, we set " + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "inline_equation", + "content": "M = \\sum_{i=1}^{N} K_{i}'" + }, + { + "bbox": [ + 305, + 195, + 547, + 332 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 333, + 547, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 333, + 547, + 429 + ], + "spans": [ + { + "bbox": [ + 305, + 333, + 547, + 429 + ], + "type": "text", + "content": "Class-imbalanced TFSL: Veilleux et al. [29] figure out that the number of query samples per class should be arbitrary and unknown instead of being strictly equal. That is " + }, + { + "bbox": [ + 305, + 333, + 547, + 429 + ], + "type": "inline_equation", + "content": "K'" + }, + { + "bbox": [ + 305, + 333, + 547, + 429 + ], + "type": "text", + "content": " is a function of class and changes with class indexes. To describe such behavior, they develop a class marginal with Dirichlet distribution for generating query samples. Specifically, the class-wise marginal distribution of query samples per task " + }, + { + "bbox": [ + 305, + 333, + 547, + 429 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 305, + 333, + 547, + 429 + ], + "type": "text", + "content": " are determined by:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 362, + 437, + 547, + 471 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 437, + 547, + 471 + ], + "spans": [ + { + "bbox": [ + 362, + 437, + 547, + 471 + ], + "type": "interline_equation", + "content": "f _ {D i r} (\\boldsymbol {p}; \\boldsymbol {a}) = \\frac {1}{B (\\boldsymbol {\\alpha})} \\prod_ {i = 1} ^ {N} p _ {i} ^ {\\alpha_ {i} - 1} \\tag {1}", + "image_path": "1081f8587234e03f0fd67eecfa65e83317204105171c9b576bc6389d01ca259b.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "type": "inline_equation", + "content": "\\pmb{p} = (p_{1},\\dots,p_{N})" + }, + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "type": "text", + "content": " stands for class-wise distribution, " + }, + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "type": "inline_equation", + "content": "\\alpha = (\\alpha_{1},\\dots,\\alpha_{N})" + }, + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "type": "text", + "content": " denotes Dirichlet-distributed parameter controlling imbalanced ratio of query samples, " + }, + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "type": "inline_equation", + "content": "B(\\pmb{a}) = \\frac{\\prod_{i=1}^{N}\\Gamma(a_{i})}{\\Gamma(\\sum_{i=1}^{N}a_{i})}" + }, + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "type": "text", + "content": " represents multivariate Beta function, and " + }, + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "type": "inline_equation", + "content": "\\Gamma(\\cdot)" + }, + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "type": "text", + "content": " is Gamma function. Smaller " + }, + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "type": "inline_equation", + "content": "\\pmb{a}" + }, + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "type": "text", + "content": " means higher imbalanced level, and vice versa. Taking " + }, + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "type": "inline_equation", + "content": "\\alpha = 2" + }, + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "type": "text", + "content": " as an example, total number of query samples is 75, then the number of query samples per class could be distributed as " + }, + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "type": "inline_equation", + "content": "K' = [10,5,2,35,18]" + }, + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "type": "text", + "content": ", which is more realistic compared with the class-balanced situation whose " + }, + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "type": "inline_equation", + "content": "K_i' = 15, i = 1,\\dots,N" + }, + { + "bbox": [ + 305, + 479, + 547, + 628 + ], + "type": "text", + "content": ". Besides, it also poses some difficulties such as overfitting to the classes whose query samples are extremely few." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 639, + 379, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 639, + 379, + 651 + ], + "spans": [ + { + "bbox": [ + 306, + 639, + 379, + 651 + ], + "type": "text", + "content": "3. Our Model" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 658, + 403, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 403, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 403, + 671 + ], + "type": "text", + "content": "3.1. Overall Method" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 677, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 714 + ], + "type": "text", + "content": "In this work, we propose a novel model called PUTM for class-imbalanced transductive few-shot image classification. Considering the correlations between support and" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16318" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 547, + 222 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 547, + 222 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 547, + 222 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 547, + 222 + ], + "type": "image", + "image_path": "deebc978bdb1dd8874d9ba6d9dcfed99153ded6777929cf9b90f917092eb7f52.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 228, + 547, + 278 + ], + "lines": [ + { + "bbox": [ + 46, + 228, + 547, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 547, + 278 + ], + "type": "text", + "content": "Figure 2: Illustration of the our model. Tasks are generated from Dirichlet-distributed generator parameterized by " + }, + { + "bbox": [ + 46, + 228, + 547, + 278 + ], + "type": "inline_equation", + "content": "\\mathbf{a}" + }, + { + "bbox": [ + 46, + 228, + 547, + 278 + ], + "type": "text", + "content": ". We first adopt a well trained feature extractor [19] and a channel-wise feature adaptation [35] to obtain the input features. Transductive inference is then conducted on the pre-processed features by: i) optimizing the transport matrices using CT; ii) refining the class-wise prototypes via MAP statistics aggregation; iii) making predictions after the above two steps iterate until convergence." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 298, + 289, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 298, + 289, + 526 + ], + "spans": [ + { + "bbox": [ + 46, + 298, + 289, + 526 + ], + "type": "text", + "content": "query samples, it is reasonable to refine the representations of class-wise prototypes initialized by support samples with the statistics of query samples. At this moment, the key is how to transfer the unbiased statistics from query samples to prototypes for achieving the best calibration. Moreover, the class-imbalanced setting is more challenging due to its unknown and arbitrary prior distribution of query samples. To address this challenge, we pioneered to depict the important but unknown prior with well-defined CT theory. Specifically, the prior could be measured by the transport mass from query samples to each prototype by summing the combination of forward and backward transport matrices optimized by CT loss along every query sample. Given the well-optimized prior, a prototype refinement algorithm is easy to be derived according to the MAP criterion. Considering the fact that the discriminative prototypes and well-optimized prior are coupled, we further employ an EM-solver to transfer the unbiased statistics efficiently and precisely. The overview of the proposed method can be found in Fig. 2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 555, + 122, + 569 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 555, + 122, + 569 + ], + "spans": [ + { + "bbox": [ + 47, + 555, + 122, + 569 + ], + "type": "text", + "content": "3.2. CT Theory" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "CT [39] is a powerful tool developed for measuring distance between any two probability distributions most recently, the effectiveness of which is mostly verified on deep generative models [13, 27] and multi-label classification [15]. In this work, we expand the territory of CT for discrete distributions under class-imbalanced TFSL. Denote " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "p(x) = \\sum_{i=1}^{n} a_i \\delta_{x_i}" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "q(y) = \\sum_{j=1}^{m} b_j \\delta_{y_j}" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " as source and target discrete distributions with " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " points, respectively. " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{a} \\in \\Delta^n" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{b} \\in \\Delta^m" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\Delta^n" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\Delta^m" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " separately denote the probability simplex of " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^n" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^m" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": ". The CT distance between " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "p(x)" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "q(y)" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " can be expressed as a combination" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 298, + 542, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 298, + 542, + 312 + ], + "spans": [ + { + "bbox": [ + 305, + 298, + 542, + 312 + ], + "type": "text", + "content": "of forward CT " + }, + { + "bbox": [ + 305, + 298, + 542, + 312 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{\\phi}(x\\to y)" + }, + { + "bbox": [ + 305, + 298, + 542, + 312 + ], + "type": "text", + "content": " and a backward CT " + }, + { + "bbox": [ + 305, + 298, + 542, + 312 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{\\phi}(x\\gets y)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 309, + 319, + 546, + 343 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 319, + 546, + 343 + ], + "spans": [ + { + "bbox": [ + 309, + 319, + 546, + 343 + ], + "type": "interline_equation", + "content": "\\mathcal {C} _ {\\phi , \\rho} (p, q) = \\min _ {\\phi} \\sum_ {x \\in p, y \\in q} \\rho \\mathcal {C} _ {\\phi} (x \\rightarrow y) + (1 - \\rho) \\mathcal {C} _ {\\phi} (x \\leftarrow y) \\tag {2}", + "image_path": "13ee1bb40147966610a0775186138ee057a40b8fb7e850ab6b0d9ad4d5bdedf1.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 350, + 547, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 547, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 547, + 399 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 350, + 547, + 399 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 350, + 547, + 399 + ], + "type": "text", + "content": " is parameters of CT, " + }, + { + "bbox": [ + 304, + 350, + 547, + 399 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 350, + 547, + 399 + ], + "type": "text", + "content": " is the trade-off factor controlling the strengths between the forward and backward CTs. To better understand how the CT works when minimizing Eq. 2, we take the forward CT as an example:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 312, + 406, + 546, + 435 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 406, + 546, + 435 + ], + "spans": [ + { + "bbox": [ + 312, + 406, + 546, + 435 + ], + "type": "interline_equation", + "content": "\\mathcal {C} _ {\\phi} (x \\rightarrow y) = \\mathbb {E} _ {y 1: m \\sim q} \\mathbb {E} _ {x \\sim p} \\left[ \\sum_ {j = 1} ^ {m} c (x, y _ {j}) \\hat {\\pi} _ {m} \\left(y _ {j} \\mid x, \\phi\\right)\\right] \\tag {3}", + "image_path": "64a8dc91067586f35fa4140b3fd72a951993340f825581329206baaca153ebab.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 443, + 547, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 443, + 547, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 443, + 547, + 504 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 443, + 547, + 504 + ], + "type": "inline_equation", + "content": "c(\\cdot, \\cdot)" + }, + { + "bbox": [ + 304, + 443, + 547, + 504 + ], + "type": "text", + "content": " could be some well defined distance functions, such as Euclidean or Cosine, " + }, + { + "bbox": [ + 304, + 443, + 547, + 504 + ], + "type": "inline_equation", + "content": "\\hat{\\pi}_m(y_j|x, \\phi)" + }, + { + "bbox": [ + 304, + 443, + 547, + 504 + ], + "type": "text", + "content": " is forward transport matrix, also called forward navigator in the scope of CT, satisfying " + }, + { + "bbox": [ + 304, + 443, + 547, + 504 + ], + "type": "inline_equation", + "content": "\\sum_{j=1}^{m} \\hat{\\pi}_m(y_j|x, \\phi) = 1" + }, + { + "bbox": [ + 304, + 443, + 547, + 504 + ], + "type": "text", + "content": ", it describes the possibility of transporting " + }, + { + "bbox": [ + 304, + 443, + 547, + 504 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 443, + 547, + 504 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 443, + 547, + 504 + ], + "type": "inline_equation", + "content": "y_j" + }, + { + "bbox": [ + 304, + 443, + 547, + 504 + ], + "type": "text", + "content": " and can be formulated as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 362, + 511, + 546, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 511, + 546, + 540 + ], + "spans": [ + { + "bbox": [ + 362, + 511, + 546, + 540 + ], + "type": "interline_equation", + "content": "\\hat {\\pi} _ {m} \\left(y _ {j} \\mid x, \\phi\\right) = \\frac {e ^ {- d _ {\\phi} \\left(x , y _ {j}\\right)}}{\\sum_ {j ^ {\\prime}} ^ {m} e ^ {- d _ {\\phi} \\left(x , y _ {j ^ {\\prime}}\\right)}} \\tag {4}", + "image_path": "1b1e66e1750abc6b75eb20426086ca8bb517cf215a8a257d63a6cb6a3ce8d95a.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 543, + 547, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 543, + 547, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 543, + 547, + 639 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 543, + 547, + 639 + ], + "type": "inline_equation", + "content": "d_{\\phi}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 304, + 543, + 547, + 639 + ], + "type": "text", + "content": " represents measurement function, such as MLP implemented by Zheng et al. [39]. The forward CT can be interpreted as the expected cost to stochastically transport a random source point " + }, + { + "bbox": [ + 304, + 543, + 547, + 639 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 543, + 547, + 639 + ], + "type": "text", + "content": " to one of the " + }, + { + "bbox": [ + 304, + 543, + 547, + 639 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 543, + 547, + 639 + ], + "type": "text", + "content": " randomly instantiated \"anchors\" of the target distribution. By minimizing Eq. 3, an unbiased statistical estimation of the two distributions arrives. Proofs can be found in Zheng et al. [39]. Hence, it is reasonable to transfer statistics of one distribution to another." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 647, + 361, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 361, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 361, + 658 + ], + "type": "text", + "content": "3.3. PUTM" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": "Our proposed PUTM aims to exploit discriminative statistics from query samples for reducing the gap between the estimated prototypes and their ground truth prototypes. However, the ground truth prototypes are always intractable in" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16319" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 178 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 178 + ], + "type": "text", + "content": "practice. A reasonable approach to obtain unbiased prototypes is to aggregate discriminative statistics from both support and query samples following a semi-supervised manner [37]. Different from the standard semi-supervised problems, the query samples are usually limited per class, especially in class-imbalanced case. Follow up, we present the importance of unbiased transfer in semi-supervised FSL setting, the algorithm of realizing unbiased exploitation with CT and transductive inference with unbiased transfer in turn." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 194, + 275, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 194, + 275, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 194, + 275, + 205 + ], + "type": "text", + "content": "3.3.1 Unbiased Statistics Transfer Matters in TFSL" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 213, + 289, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 213, + 289, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 289, + 337 + ], + "type": "text", + "content": "Given a few-shot task, unbiased prototypes arrives if and only if the aggregated query samples are noiseless, which should heavily rely on the unbiased statistics transfer. Leveraging similarities between query samples and prototypes is a common way to realize statistics transfer in transductive few-shot image classification. Given the transport matrix " + }, + { + "bbox": [ + 46, + 213, + 289, + 337 + ], + "type": "inline_equation", + "content": "\\pi^n\\in \\mathbb{R}^{M\\times N}" + }, + { + "bbox": [ + 46, + 213, + 289, + 337 + ], + "type": "text", + "content": " at the " + }, + { + "bbox": [ + 46, + 213, + 289, + 337 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 213, + 289, + 337 + ], + "type": "text", + "content": " -th iteration, it measures the closeness of prototypes " + }, + { + "bbox": [ + 46, + 213, + 289, + 337 + ], + "type": "inline_equation", + "content": "\\{c_i^n\\}_{i = 1}^N" + }, + { + "bbox": [ + 46, + 213, + 289, + 337 + ], + "type": "text", + "content": " and query samples " + }, + { + "bbox": [ + 46, + 213, + 289, + 337 + ], + "type": "inline_equation", + "content": "\\{\\pmb{x}_{i,j}^q\\}_{j = 1}^{K_i'}" + }, + { + "bbox": [ + 46, + 213, + 289, + 337 + ], + "type": "text", + "content": " For simplicity, we rewrite all query samples as " + }, + { + "bbox": [ + 46, + 213, + 289, + 337 + ], + "type": "inline_equation", + "content": "\\{\\pmb{x}_r^q\\}_{r = 1}^M" + }, + { + "bbox": [ + 46, + 213, + 289, + 337 + ], + "type": "text", + "content": " . Thus, the refined prototypes " + }, + { + "bbox": [ + 46, + 213, + 289, + 337 + ], + "type": "inline_equation", + "content": "\\{c_i^{n + 1}\\}_{i = 1}^N" + }, + { + "bbox": [ + 46, + 213, + 289, + 337 + ], + "type": "text", + "content": " can be expressed as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 342, + 287, + 372 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 342, + 287, + 372 + ], + "spans": [ + { + "bbox": [ + 69, + 342, + 287, + 372 + ], + "type": "interline_equation", + "content": "\\boldsymbol {c} _ {i} ^ {n + 1} = \\frac {\\sum_ {r = 1} ^ {M} \\boldsymbol {\\pi} _ {r , i} ^ {n} \\boldsymbol {x} _ {r} ^ {q} + \\sum_ {j = 1} ^ {K} \\boldsymbol {x} _ {i , j} ^ {s}}{\\sum_ {r ^ {\\prime} = 1} ^ {M} \\boldsymbol {\\pi} _ {r ^ {\\prime} , i} ^ {n} + K}, \\quad i = 1, \\dots , N \\tag {5}", + "image_path": "e733c7449d7be70f7f4636b3ca30e72f133081da397b1ac499fd240b4219700c.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 377, + 289, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 289, + 554 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 289, + 554 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 377, + 289, + 554 + ], + "type": "inline_equation", + "content": "\\pi_{r,i}^{n} = \\frac{e^{-d_{\\phi}(\\pmb{x}_{r}^{q},\\pmb{c}_{i}^{n})}}{\\sum_{r^{\\prime} = 1}^{M}e^{-d_{\\phi}(\\pmb{x}_{r^{\\prime}}^{q},\\pmb{c}_{i}^{n})}}, d_{\\phi}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 46, + 377, + 289, + 554 + ], + "type": "text", + "content": " denotes the well defined measurement function, and we denote optimal transport matrix as " + }, + { + "bbox": [ + 46, + 377, + 289, + 554 + ], + "type": "inline_equation", + "content": "\\pi^{*}" + }, + { + "bbox": [ + 46, + 377, + 289, + 554 + ], + "type": "text", + "content": ". To guarantee the unbiased refinement of prototypes, " + }, + { + "bbox": [ + 46, + 377, + 289, + 554 + ], + "type": "inline_equation", + "content": "\\pi^{*}" + }, + { + "bbox": [ + 46, + 377, + 289, + 554 + ], + "type": "text", + "content": " need to be precise, which is usually difficult to be satisfied in practice. Fortunately, partial noisy is tolerable. For example, given 15 query samples per class, a few wrong transferring such as 1 or 2 samples is tolerable in calibrating prototypes. As for class-imbalanced case, a tiny mistake may result in disastrous consequence on prototypes calibration. For the classes having only 1 or 2 query samples, the tolerances of error transmissions should be extremely low. Therefore, to improve the robustness of calibrated prototypes in class-imbalanced TFSL, transferring unbiased statistics of query samples with " + }, + { + "bbox": [ + 46, + 377, + 289, + 554 + ], + "type": "inline_equation", + "content": "\\pi^{*}" + }, + { + "bbox": [ + 46, + 377, + 289, + 554 + ], + "type": "text", + "content": " becomes crucial." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "type": "text", + "content": "There are mainly two lines of works in defining " + }, + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\pi^{*}" + }, + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "type": "text", + "content": ": i) Liu et al. [17] employ Cosine function [17]; ii) Hu et al. [11] use Optimal Transport (OT). Cosine function may not powerful enough to fully reflect the relationships between prototypes and query samples since it ignores various importance between each two points. OT describes a doubly stochastic transport matrix such that " + }, + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\Pi(p, q) = \\{\\pi^{*} | \\sum_{r=1}^{M} \\pi_{r,i}^{*} = a_{i}, \\sum_{i=1}^{N} \\pi_{r,i}^{*} = b_{r}\\}" + }, + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "type": "text", + "content": ". Unfortunately, we usually do not have any priors on distributions of " + }, + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "type": "text", + "content": ", thus, we usually have " + }, + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "type": "inline_equation", + "content": "a_{i} = \\frac{1}{N}, i = 1, \\dots, N" + }, + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "type": "inline_equation", + "content": "b_{r} = \\frac{1}{M}, r = 1, \\dots, M" + }, + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "type": "text", + "content": ", which should be contradictory to class-imbalanced setting. For example, once we employ Dirichlet distribution with " + }, + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\alpha = 2_{N}" + }, + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "type": "text", + "content": " to mimic the generation of query samples, " + }, + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "type": "inline_equation", + "content": "a_{i} = \\frac{1}{N}" + }, + { + "bbox": [ + 46, + 555, + 289, + 715 + ], + "type": "text", + "content": " will never" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "text", + "content": "fit the data. According to the analysis of CT, it replaces the uniform constraint on prior distribution of classes derived from query samples with a data-driven manner, thus ensuring to transfer the unbiased statistics more flexible and efficient." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 134, + 514, + 148 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 134, + 514, + 148 + ], + "spans": [ + { + "bbox": [ + 305, + 134, + 514, + 148 + ], + "type": "text", + "content": "3.3.2 Unbiased Statistics Exploitation with CT" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 153, + 547, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 153, + 547, + 201 + ], + "spans": [ + { + "bbox": [ + 304, + 153, + 547, + 201 + ], + "type": "text", + "content": "As we can see, CT has an appealing property of exploiting unbiased statistics thanks to its task-adaptive prior rather than uniform-distributed one as OT. Here after, we present details of achieving such unbiased exploitation with CT." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 201, + 547, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 201, + 547, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 201, + 547, + 308 + ], + "type": "text", + "content": "As shown in Fig. 2, given a class-imbalanced few-shot task in Sec. 2, we first employ a well-trained feature extractor " + }, + { + "bbox": [ + 304, + 201, + 547, + 308 + ], + "type": "inline_equation", + "content": "f_{\\theta^{*}}(\\cdot)" + }, + { + "bbox": [ + 304, + 201, + 547, + 308 + ], + "type": "text", + "content": " to get features of support and query samples as " + }, + { + "bbox": [ + 304, + 201, + 547, + 308 + ], + "type": "inline_equation", + "content": "f_{i,j}^{s} = f_{\\theta^{*}}(\\pmb{x}_{i,j}^{s})" + }, + { + "bbox": [ + 304, + 201, + 547, + 308 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 201, + 547, + 308 + ], + "type": "inline_equation", + "content": "f_{r}^{q} = f_{\\theta^{*}}(\\pmb{x}_{r}^{q})" + }, + { + "bbox": [ + 304, + 201, + 547, + 308 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 201, + 547, + 308 + ], + "type": "inline_equation", + "content": "\\theta^{*}" + }, + { + "bbox": [ + 304, + 201, + 547, + 308 + ], + "type": "text", + "content": " is the set of optimized parameters, being fixed after training on the base classes following Mangla et al. [19]. Then, we conduct channel attention with preprocessing developed by Yang et al. [35]. Finally, unbiased statistics exploitation is realized by optimizing transport matrices constrained by CT theory." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 309, + 547, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 309, + 547, + 431 + ], + "spans": [ + { + "bbox": [ + 305, + 309, + 547, + 431 + ], + "type": "text", + "content": "Specifically, the initial prototypes are averaged on the features of support set as " + }, + { + "bbox": [ + 305, + 309, + 547, + 431 + ], + "type": "inline_equation", + "content": "\\pmb{c}_i^0 = \\frac{1}{K}\\sum_{j = 1}^{K}f_{i,j}^s" + }, + { + "bbox": [ + 305, + 309, + 547, + 431 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 309, + 547, + 431 + ], + "type": "inline_equation", + "content": "i = 1,\\dots,N" + }, + { + "bbox": [ + 305, + 309, + 547, + 431 + ], + "type": "text", + "content": " where the superscript of " + }, + { + "bbox": [ + 305, + 309, + 547, + 431 + ], + "type": "inline_equation", + "content": "\\{c_i^0\\}_{i = 1}^N" + }, + { + "bbox": [ + 305, + 309, + 547, + 431 + ], + "type": "text", + "content": " describes the generation of prototypes is zero. They will be updated subsequently, detailed in Sec. 3.3.3. At this moment, we treat " + }, + { + "bbox": [ + 305, + 309, + 547, + 431 + ], + "type": "inline_equation", + "content": "\\{c_i^0\\}_{i = 1}^N" + }, + { + "bbox": [ + 305, + 309, + 547, + 431 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 309, + 547, + 431 + ], + "type": "inline_equation", + "content": "\\{f_r^q\\}_{r = 1}^M" + }, + { + "bbox": [ + 305, + 309, + 547, + 431 + ], + "type": "text", + "content": " as samples from the two discrete distributions, and utilizing CT to learn the transport matrices for exploiting unbiased statistics. According to the analysis of Eq. 2, an unbiased sample estimate of CT given query features " + }, + { + "bbox": [ + 305, + 309, + 547, + 431 + ], + "type": "inline_equation", + "content": "\\{f_r^q\\}_{r = 1}^M" + }, + { + "bbox": [ + 305, + 309, + 547, + 431 + ], + "type": "text", + "content": " and prototypes " + }, + { + "bbox": [ + 305, + 309, + 547, + 431 + ], + "type": "inline_equation", + "content": "\\{c_i^0\\}_{i = 1}^N" + }, + { + "bbox": [ + 305, + 309, + 547, + 431 + ], + "type": "text", + "content": " can be expressed as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 438, + 545, + 472 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 438, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 312, + 438, + 545, + 472 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\phi , \\boldsymbol {\\theta} ^ {*}, \\rho} \\left(f _ {1: M} ^ {q}, \\boldsymbol {c} _ {1: N} ^ {0}\\right) = \\sum_ {i = 1} ^ {N} \\sum_ {r = 1} ^ {M} c \\left(\\boldsymbol {c} _ {i} ^ {0}, f _ {r} ^ {q}\\right). \\tag {6}", + "image_path": "590b4709040a784625eb3f1260dd9fe192f4f869d36bcde2a36e9951db066c9c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 354, + 474, + 529, + 496 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 474, + 529, + 496 + ], + "spans": [ + { + "bbox": [ + 354, + 474, + 529, + 496 + ], + "type": "interline_equation", + "content": "(\\frac {\\rho}{M} \\hat {\\pi} _ {N} (\\pmb {c} _ {i} ^ {0} | f _ {r} ^ {q}, \\phi) + \\frac {1 - \\rho}{N} \\hat {\\pi} _ {M} (f _ {r} ^ {q} | \\pmb {c} _ {i} ^ {0}, \\phi))", + "image_path": "882b279535eed45d58062a8a594e4d0fac629476c5aa42ea7e3c6874e15d83c4.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 503, + 547, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 503, + 547, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 503, + 547, + 540 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 503, + 547, + 540 + ], + "type": "inline_equation", + "content": "\\hat{\\pi}_N" + }, + { + "bbox": [ + 306, + 503, + 547, + 540 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 503, + 547, + 540 + ], + "type": "inline_equation", + "content": "\\hat{\\pi}_M" + }, + { + "bbox": [ + 306, + 503, + 547, + 540 + ], + "type": "text", + "content": " separately denote the forward and backward transport matrices. Again substituting query features " + }, + { + "bbox": [ + 306, + 503, + 547, + 540 + ], + "type": "inline_equation", + "content": "\\{f_r^q\\}_{r=1}^M" + }, + { + "bbox": [ + 306, + 503, + 547, + 540 + ], + "type": "text", + "content": " and prototypes " + }, + { + "bbox": [ + 306, + 503, + 547, + 540 + ], + "type": "inline_equation", + "content": "\\{c_i^0\\}_{i=1}^N" + }, + { + "bbox": [ + 306, + 503, + 547, + 540 + ], + "type": "text", + "content": " into Eq. 4, we have:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 348, + 548, + 545, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 548, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 348, + 548, + 545, + 578 + ], + "type": "interline_equation", + "content": "\\hat {\\pi} _ {N} \\left(\\boldsymbol {c} _ {i} ^ {0} \\mid f _ {r} ^ {q}, \\phi\\right) = \\frac {e ^ {- d _ {\\phi} \\left(f _ {r} ^ {q} , \\boldsymbol {c} _ {i} ^ {0}\\right)}}{\\sum_ {i ^ {\\prime} = 1} ^ {N} e ^ {- d _ {\\phi} \\left(f _ {r} ^ {q} , \\boldsymbol {c} _ {i ^ {\\prime}} ^ {0}\\right)}} \\tag {7}", + "image_path": "a94e76e677de504eac7dc86dc6926fee3714f7ec741e25315a96a32427b9d5d3.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 349, + 580, + 545, + 611 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 580, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 349, + 580, + 545, + 611 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {\\pi}} _ {M} \\left(f _ {r} ^ {q} \\mid \\boldsymbol {c} _ {i} ^ {0}, \\phi\\right) = \\frac {e ^ {- d _ {\\phi} \\left(f _ {r} ^ {q} , \\boldsymbol {c} _ {i} ^ {0}\\right)}}{\\sum_ {r ^ {\\prime} = 1} ^ {M} e ^ {- d _ {\\phi} \\left(f _ {r ^ {\\prime}} ^ {q} , \\boldsymbol {c} _ {i} ^ {0}\\right)}} \\tag {8}", + "image_path": "af8f835c2b7086b9e50511995ed64057d2f87dcc3c1bbea0118062911bb4b053.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": "The forward transport matrix represents the probability of query samples belonging to the corresponding support classes. The two transport matrices with the optimal parameter " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\phi^{*}" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": " can be obtained by minimizing the approximated CT estimation of Eq. 6. Once " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\pi}_N^*" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\pi}_M^*" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": " with the optimal " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\phi^{*}" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": " are obtained, the transport matrix described in Sec. 3.3.1 for unbiased statistics exploitation can be naturally realized. To better understand this, we depict the mechanisms of the" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16320" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 55, + 87, + 287, + 247 + ], + "blocks": [ + { + "bbox": [ + 48, + 72, + 239, + 83 + ], + "lines": [ + { + "bbox": [ + 48, + 72, + 239, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 239, + 83 + ], + "type": "text", + "content": "Algorithm 1 Work flow of PUTM for one task." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "lines": [ + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "spans": [ + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "text", + "content": "Input: Support samples " + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "inline_equation", + "content": "\\{\\pmb{x}_{i,j}^{s}\\}_{i,j = 1}^{N,K}" + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "text", + "content": " and class-imbalanced query samples " + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "inline_equation", + "content": "\\{\\pmb{x}_r^q\\}_{r = 1}^M" + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "text", + "content": " generated from Dirichlet distribution with parameter " + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "text", + "content": " , a well-trained feature extractor " + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "inline_equation", + "content": "f_{\\theta^{*}}(\\cdot)" + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "text", + "content": " Parameters: Distance measurement function " + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "inline_equation", + "content": "d_{\\phi}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "text", + "content": " Initialization Hyper-parameters " + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "text", + "content": " , and learning schedule for updating " + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "text", + "content": " ; Initialize prototypes " + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "inline_equation", + "content": "c_{i}^{0} = \\frac{1}{K}\\sum_{j = 1}^{K}f_{i,j}^{s},i = 1,\\ldots ,N;" + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "text", + "content": " for n=1: " + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "inline_equation", + "content": "n_{steps}" + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "text", + "content": " do Initialize parameters " + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "inline_equation", + "content": "\\phi^{*}\\gets argmin_{\\phi}\\mathcal{L}_{\\phi ,\\theta^{*},\\rho}(f_{1:M}^{q},c_{1:N}^{n})" + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "text", + "content": " Refining prototypes " + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "inline_equation", + "content": "c_{1:N}^{n + 1}" + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "text", + "content": " using Eq. 11 based on " + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "inline_equation", + "content": "c_{1:N}^{n}" + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "text", + "content": " end for Evaluating performance using Eq. 12; Output Parameters " + }, + { + "bbox": [ + 55, + 87, + 287, + 247 + ], + "type": "inline_equation", + "content": "\\{\\phi^{*},c_{1:N}^{n_{step}}\\}" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "algorithm" + }, + { + "bbox": [ + 46, + 269, + 289, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 269, + 289, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 269, + 289, + 485 + ], + "type": "text", + "content": "transport matrices developed above from three perspectives: 1) the distance function in transport matrices is implemented with DNNs, hence, they are able to learn a comprehensive distance metric beyond a simple Cosine function; 2) the CT distance is proven to be unbiased given samples of two distributions " + }, + { + "bbox": [ + 46, + 269, + 289, + 485 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 269, + 289, + 485 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 269, + 289, + 485 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 269, + 289, + 485 + ], + "type": "text", + "content": " in [39]; 3) The forward transport matrix holds free for sum along query samples given a specific prototype, namely, " + }, + { + "bbox": [ + 46, + 269, + 289, + 485 + ], + "type": "inline_equation", + "content": "\\sum_{r=1}^{M} \\hat{\\pi}_N(c_i^0 | f_r^q, \\phi^*) = C" + }, + { + "bbox": [ + 46, + 269, + 289, + 485 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 269, + 289, + 485 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 269, + 289, + 485 + ], + "type": "text", + "content": " is not restricted to be equal for each class, thus embedding task-adaptive prior instead of uniform distribution as PT-MAP [11] does. On the other hand, the backward transport matrix holds tight for sum along query samples given a specific prototype, that is, " + }, + { + "bbox": [ + 46, + 269, + 289, + 485 + ], + "type": "inline_equation", + "content": "\\sum_{r=1}^{M} \\hat{\\pi}_M(f_r^q | c_i^0, \\phi^*) = 1" + }, + { + "bbox": [ + 46, + 269, + 289, + 485 + ], + "type": "text", + "content": ", hence, uniform-distributed prior holds, and it is proven to be underfitting in class-imbalanced case [29]. In practice, we employ a trade-off to balance the strengths of the two transport matrices by summing them together with a soft coefficient " + }, + { + "bbox": [ + 46, + 269, + 289, + 485 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 269, + 289, + 485 + ], + "type": "text", + "content": ". For simplicity, we only use the forward transport matrix in the rest of the work." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 498, + 271, + 510 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 271, + 510 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 271, + 510 + ], + "type": "text", + "content": "3.3.3 Unbiased Statistics Transfer with EM-Solver" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 517, + 288, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 517, + 288, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 517, + 288, + 555 + ], + "type": "text", + "content": "Once the forward transport matrix " + }, + { + "bbox": [ + 46, + 517, + 288, + 555 + ], + "type": "inline_equation", + "content": "\\hat{\\pi}_N^*" + }, + { + "bbox": [ + 46, + 517, + 288, + 555 + ], + "type": "text", + "content": " is obtained by minimizing Eq. 6, it is straightforward to derive the refined prototypes by substituting " + }, + { + "bbox": [ + 46, + 517, + 288, + 555 + ], + "type": "inline_equation", + "content": "\\hat{\\pi}_N^*" + }, + { + "bbox": [ + 46, + 517, + 288, + 555 + ], + "type": "text", + "content": " into Eq. 5:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 563, + 288, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 563, + 288, + 597 + ], + "spans": [ + { + "bbox": [ + 59, + 563, + 288, + 597 + ], + "type": "interline_equation", + "content": "\\boldsymbol {c} _ {i} ^ {\\prime} = \\frac {\\sum_ {r = 1} ^ {M} \\hat {\\pi} _ {N , r , i} ^ {*} f _ {r} ^ {q} + \\sum_ {j = 1} ^ {K} f _ {i , j} ^ {s}}{K + \\sum_ {r = 1} ^ {M} \\hat {\\pi} _ {N , r , i} ^ {*}}, \\quad i = 1, \\dots , N \\tag {9}", + "image_path": "43b9b9725c28ec1317159e0457d53c4934286c3f78b2c727ba8611bdc5fee833.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 604, + 289, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 604, + 289, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 604, + 289, + 693 + ], + "type": "text", + "content": "It is worth noting that once the optimal parameters " + }, + { + "bbox": [ + 46, + 604, + 289, + 693 + ], + "type": "inline_equation", + "content": "\\phi^{*}" + }, + { + "bbox": [ + 46, + 604, + 289, + 693 + ], + "type": "text", + "content": " are arrived, the only parameters left for optimizing are prototypes. Recalling our objective in Eq. 6, it is easy to find that the optimal prototypes at this moment could also be derived by " + }, + { + "bbox": [ + 46, + 604, + 289, + 693 + ], + "type": "inline_equation", + "content": "\\frac{\\partial\\mathcal{L}_{\\phi^{*},\\theta^{*},\\rho}}{\\partial c_{1:N}^{0}}" + }, + { + "bbox": [ + 46, + 604, + 289, + 693 + ], + "type": "text", + "content": ", thereby Eq. 9 could be derived. Instead of directly calibrating class-wise prototypes, We employ an inertia parameter " + }, + { + "bbox": [ + 46, + 604, + 289, + 693 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 604, + 289, + 693 + ], + "type": "text", + "content": " to update prototypes proportionally:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 89, + 700, + 288, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 700, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 89, + 700, + 288, + 715 + ], + "type": "interline_equation", + "content": "\\boldsymbol {c} _ {i} ^ {1} = \\boldsymbol {c} _ {i} ^ {0} + \\alpha \\left(\\boldsymbol {c} _ {i} ^ {\\prime} - \\boldsymbol {c} _ {i} ^ {0}\\right), \\quad i = 1, \\dots , N \\tag {10}", + "image_path": "bedf76f51530f230576c90c93597f6d4e347b70a0b242dfae44d1375a86d2cfa.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 547, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 547, + 97 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 547, + 97 + ], + "type": "text", + "content": "Right now, recursive expression emerges for updating prototypes according to Eq. 10:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 341, + 103, + 547, + 118 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 103, + 547, + 118 + ], + "spans": [ + { + "bbox": [ + 341, + 103, + 547, + 118 + ], + "type": "interline_equation", + "content": "\\boldsymbol {c} _ {i} ^ {n + 1} = \\boldsymbol {c} _ {i} ^ {n} + \\alpha \\left(\\boldsymbol {c} _ {i} ^ {\\prime} - \\boldsymbol {c} _ {i} ^ {n}\\right), \\quad i = 1, \\dots , N \\tag {11}", + "image_path": "8f1614276f749d883c77f0b11b366bf2ec4966c73d4b61f89fefa585ea5dbb77.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "spans": [ + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "text", + "content": "As we can see: i) updating the forward transport matrix " + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "inline_equation", + "content": "\\hat{\\pi}_N^*" + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "text", + "content": " and prototypes " + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "inline_equation", + "content": "c_{1:N}^n" + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "text", + "content": " are coupled; ii) " + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "inline_equation", + "content": "\\hat{\\pi}_N^*" + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "text", + "content": " is a random variable determined by " + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "text", + "content": " while " + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "inline_equation", + "content": "c_{1:N}^n" + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "text", + "content": " is an unknown but deterministic variable. These two facts meet conditions of implementing EM optimization, and we formulate our EM-Solver as follows: i) E Step, updating " + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "inline_equation", + "content": "\\hat{\\pi}_N^*" + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "text", + "content": " by minimizing Eq. 6 while keeping " + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "inline_equation", + "content": "c_{1:N}^n" + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "text", + "content": " fixed; ii) M Step, updating " + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "inline_equation", + "content": "c_{1:N}^n" + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "text", + "content": " by minimizing Eq. 6 while keeping " + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "inline_equation", + "content": "\\hat{\\pi}_N^*" + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "text", + "content": " fixed. Besides, it is worth noting that at each iteration, " + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "inline_equation", + "content": "\\phi^*" + }, + { + "bbox": [ + 304, + 125, + 547, + 245 + ], + "type": "text", + "content": " need to be reinitialized. The pseudo code is provided in Alg. 1." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 245, + 545, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 245, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 305, + 245, + 545, + 270 + ], + "type": "text", + "content": "After " + }, + { + "bbox": [ + 305, + 245, + 545, + 270 + ], + "type": "inline_equation", + "content": "n_{step}" + }, + { + "bbox": [ + 305, + 245, + 545, + 270 + ], + "type": "text", + "content": " loops between estimating " + }, + { + "bbox": [ + 305, + 245, + 545, + 270 + ], + "type": "inline_equation", + "content": "\\hat{\\pi}_N^*" + }, + { + "bbox": [ + 305, + 245, + 545, + 270 + ], + "type": "text", + "content": " and refining " + }, + { + "bbox": [ + 305, + 245, + 545, + 270 + ], + "type": "inline_equation", + "content": "c_{1:N}^n" + }, + { + "bbox": [ + 305, + 245, + 545, + 270 + ], + "type": "text", + "content": ", the decision per sample is finally made by:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 320, + 276, + 546, + 297 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 276, + 546, + 297 + ], + "spans": [ + { + "bbox": [ + 320, + 276, + 546, + 297 + ], + "type": "interline_equation", + "content": "y _ {r} ^ {q} = \\max _ {i \\in [ 1: N ]} \\hat {\\pi} _ {N} \\left(\\boldsymbol {c} _ {i} ^ {n _ {\\text {s t e p}}} \\mid f _ {r} ^ {q}, \\phi^ {*}\\right), \\quad r = 1, \\dots , M \\tag {12}", + "image_path": "35cbf2db694a14cbe168ab27dcb1ecb9f9c6a14277a0a07b010d14c581973ebe.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 304, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 304, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 545, + 327 + ], + "type": "text", + "content": "Statistic results of average accuracy are usually conducted using query samples on various of different tasks." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 335, + 425, + 347 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 335, + 425, + 347 + ], + "spans": [ + { + "bbox": [ + 306, + 335, + 425, + 347 + ], + "type": "text", + "content": "3.4. Complexity Analysis" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 352, + 547, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 352, + 547, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 352, + 547, + 498 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 352, + 547, + 498 + ], + "type": "text", + "content": " is implemented with MLP in our work. Taking a two-layers MLP for example, namely, " + }, + { + "bbox": [ + 304, + 352, + 547, + 498 + ], + "type": "inline_equation", + "content": "d_{f} \\rightarrow d_{1}^{\\phi} \\rightarrow d_{2}^{\\phi}" + }, + { + "bbox": [ + 304, + 352, + 547, + 498 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 304, + 352, + 547, + 498 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 352, + 547, + 498 + ], + "type": "text", + "content": " tasks, computational complexity originally takes " + }, + { + "bbox": [ + 304, + 352, + 547, + 498 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(T \\times \\max \\{NM \\times d_{f} \\times d_{1}^{\\phi}, NM \\times d_{1}^{\\phi} \\times d_{2}^{\\phi}\\})" + }, + { + "bbox": [ + 304, + 352, + 547, + 498 + ], + "type": "text", + "content": ". In practice, " + }, + { + "bbox": [ + 304, + 352, + 547, + 498 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 352, + 547, + 498 + ], + "type": "text", + "content": " is usually set to be large enough for reliable results, thus resulting in time-consuming evaluation of our model. To mitigate the real-time issue, we trade space for time by paralleling our proposed PUTM among all tasks. Therefore, the computational complexity is reduced to " + }, + { + "bbox": [ + 304, + 352, + 547, + 498 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\max \\{NM \\times d_{f} \\times d_{1}^{\\phi}, NM \\times d_{1}^{\\phi} \\times d_{2}^{\\phi}\\})" + }, + { + "bbox": [ + 304, + 352, + 547, + 498 + ], + "type": "text", + "content": ". Besides, we can further control the size of MLP, that is " + }, + { + "bbox": [ + 304, + 352, + 547, + 498 + ], + "type": "inline_equation", + "content": "\\{d_{i}^{\\phi}\\}_{i=1}^{2}" + }, + { + "bbox": [ + 304, + 352, + 547, + 498 + ], + "type": "text", + "content": ", to achieve a trade-off between accuracy and real-time efficiency." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 508, + 388, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 508, + 388, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 508, + 388, + 521 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 528, + 422, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 528, + 422, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 528, + 422, + 540 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 545, + 547, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 630 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 630 + ], + "type": "text", + "content": "Baselines: We mainly compare our model with some recently proposed State-Of-The-Art (SOTA) methods on one Nvidia RTX 3090 GPU. For inductive methods, we adopt Baseline/Baseline " + }, + { + "bbox": [ + 304, + 545, + 547, + 630 + ], + "type": "inline_equation", + "content": "(++)" + }, + { + "bbox": [ + 304, + 545, + 547, + 630 + ], + "type": "text", + "content": " [4], ProtoNet [26], Simpleshot [33], and HOT [9] in inductive. For transductive methods, we adopt PT-MAP [11], LaplacianShot [40], TIM[2], BD-CSPN [17], " + }, + { + "bbox": [ + 304, + 545, + 547, + 630 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 545, + 547, + 630 + ], + "type": "text", + "content": "-TIM [29], iLPC [14], and BAVAR [12]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": "Datasets: We evaluate our model on four benchmarks including miniImageNet [22], tieredImageNet [23], CUB [31], and CIFAR-FS [1]. MiniImageNet is randomly chosen from ILSVRC-12 dataset [6] and it contains 100 classes with 600 images per class, the resolution of which is " + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "inline_equation", + "content": "84 \\times 84 \\times 3" + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": ". Following previous works [22, 29, 11, 35], the dataset is split into 64 base classes, 16 validation classes, and" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16321" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 128, + 545, + 306 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 120 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 120 + ], + "type": "text", + "content": "Table 1: Classification accuracy (%) of SOTA methods on class-imbalanced and class-balanced settings with different datasets and backbones. For imbalanced case, query samples are generated following a Dirichlet distribution with " + }, + { + "bbox": [ + 46, + 70, + 547, + 120 + ], + "type": "inline_equation", + "content": "\\alpha = 2_{N}" + }, + { + "bbox": [ + 46, + 70, + 547, + 120 + ], + "type": "text", + "content": ". Results are averaged over 3000 tasks with " + }, + { + "bbox": [ + 46, + 70, + 547, + 120 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 46, + 70, + 547, + 120 + ], + "type": "text", + "content": " confidence intervals. Results with superscript " + }, + { + "bbox": [ + 46, + 70, + 547, + 120 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 46, + 70, + 547, + 120 + ], + "type": "text", + "content": " are our re-implementations based on the code provided by Veilleux et al. [29]. The best and the second best scores are marked in bold and blue, respectively." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 128, + 545, + 306 + ], + "lines": [ + { + "bbox": [ + 49, + 128, + 545, + 306 + ], + "spans": [ + { + "bbox": [ + 49, + 128, + 545, + 306 + ], + "type": "table", + "html": "
SettingMethodmini-ImageNet (WRN/WRN$)CUB (RN18/WRN$)tiered-ImageNet (WRN/WRN$)CIFAR-FS (WRN$)
1-shot3-shot5-shot1-shot3-shot5-shot1-shot3-shot5-shot1-shot3-shot5-shot
Induct. (%)Imbalanced & BalancedBaseline (ICLR'19)62.2/62.8†76.9†/77.3†81.9/82.9†64.6/70.7†82.3†/87.3†86.9/90.0†64.6/63.6†80.0†/83.0†84.9/87.2†69.5†83.9†86.7†
Baseline++ (ICLR'19)64.5/64.8†77.5†/78.4†82.1/82.7†69.4/81.7†83.3†/89.4†87.1/91.2†68.7/66.9†80.9†/78.7†85.4/82.2†74.9†85.0†87.4†
ProtoNet (NeurIPS'17)61.2/62.5†76.9†/77.2†81.1/81.4†63.1†/69.6†82.3†/85.6†85.4†/88.8†63.5†/64.2†79.9†/80.1†84.1†/84.0†69.5†83.8†86.7†
Simpleshot (ARXIV)66.2/67.1†77.6†/78.2†82.4/83.3†70.6/81.7†83.6†/89.5†87.5/91.4†70.7/71.4†81.3†/84.2†85.9/87.5†75.2†84.7†87.4†
HOT (NeurIPS'22)66.3†/69.178.5†/79.8†82.8†/84.474.5†/81.285.4†/88.2†87.8†/91.574.1†/75.982.6†/83.9†85.4†/87.375.485.3†87.5
Transduct. (%)ImbalancedPT-MAP (ARXIV)60.6/63.2†65.9†/68.0†66.8/69.3†65.1/69.8†71.2†/73.2†71.3/74.3†65.1/67.8†69.1†/72.0†71.0/73.2†65.9†69.3†70.3†
LaplacianShot (ICML'20)68.1/69.8†78.8†/79.2†83.2/83.6†73.7/84.2†85.7†/90.4†87.7/91.4†73.5/72.6†82.6†/85.0†86.8/87.7†78.3†86.1†87.3†
TIM (NeurIPS'20)69.8/70.9†79.7†/80.7†81.6/83.2†74.8/82.8†84.8†/89.1†86.9/90.5†75.8/77.8†82.5†/86.3†85.4/88.3†77.0†84.6†86.2†
BD-CSPN (ECCV'20)70.4/71.2†77.1†/78.6†82.3/83.4†74.5/85.1†85.7†/90.5†87.1/91.5†75.4/76.3†82.5†/85.0†85.9/87.2†79.1†86.0†87.3†
α-TIM (NeurIPS'2021)69.8/70.9†80.4†/81.1†84.8/84.9†75.7/83.6†87.3†/91.2†89.8/92.8†76.0/77.7†83.6†/86.6†87.8/89.9†78.1†87.2†88.9†
iLPC (ICCV'21)71.5†/74.3†78.6†/81.1†81.0†/83.3†78.7†/86.4†85.6†/90.1†86.9†/90.8†76.6†/81.6†83.2†/87.5†85.1†/89.0†80.8†85.4†86.5†
BAVAR (AISTATS'23)74.1/74.2†82.6†/82.6†85.5/85.6†82.0/85.7†89.2†/89.8†90.7/90.8†77.5/80.6†84.8†/87.2†87.5/89.3†81.8†87.0†87.9†
PUTM (Ours)70.9/73.880.5/82.984.6/85.778.9/86.987.8/91.389.3/92.275.0/81.183.6/88.486.0/90.481.487.388.6
BalancedPT-MAP (ARXIV)78.9/82.5†86.3†/87.5†86.6/88.6†85.5/92.0†90.5†/94.0†91.3/94.3†84.6/88.1†88.2†/91.8†90.0/92.5†87.6†90.5†90.9†
LaplacianShot (ICML'20)72.9/73.4†79.0†/80.5†83.8/84.2†78.9/87.5†86.7†/90.4†88.8/92.3†78.8/78.7†84.6†/85.6†87.3/87.0†82.1†86.3†86.8†
TIM (NeurIPS'20)74.6/77.6†85.5†/86.0†85.9/88.0†80.3/88.1†89.8†/93.0†90.5/94.0†80.3/83.8†87.7†/90.6†88.9/92.1†83.0†89.5†90.5†
BD-CSPN (ECCV'20)72.5/73.8†79.2†/80.7†83.7/85.3†77.9/87.3†86.9†/91.4†88.9/92.4†77.7/78.7†84.5†/86.4†87.4/88.3†81.6†87.4†88.6†
α-TIM (NeurIPS'2021)71.0/71.5†76.8†/77.7†82.4/83.3†77.2†/84.9†85.1†/90.2†87.6†/91.2†75.1†/78.9†80.6†/84.4†85.3†/88.2†79.7†85.7†87.9†
iLPC (ICCV'21)75.5†/77.8†82.0†/83.9†83.9†/85.7†82.4†/89.6†87.9†/92.3†88.9†/93.0†81.0†/85.5†86.4†/89.8†87.5†/90.9†84.8†88.6†89.2†
BAVAR (AISTATS'23)78.5/78.5†84.8†/84.9†87.4/87.7†85.6/89.0†90.8†/91.7†91.4/92.1†81.5/84.7†87.4†/89.3†88.3/90.3†85.0†88.4†88.9†
PUTM(Ours)78.4/81.484.9/86.786.5/88.184.9/91.289.2/93.390.1/93.781.6/86.886.9/90.788.6/92.286.489.590.4
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Pentagrams are prototypes while solid dots are query features. Classes change and best view in colors. (c): Impact of forward and backward transport matrices in calibrating prototypes on miniImageNet over 3000 5-way 1-shot tasks." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 506, + 289, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 506, + 289, + 674 + ], + "spans": [ + { + "bbox": [ + 46, + 506, + 289, + 674 + ], + "type": "text", + "content": "20 novel classes. TieredImageNet [23] is also a subset of ILSVRC-12 dataset, which is larger than miniImageNet. It contains 608 classes sampled from a hierarchical category structure with around 1281 images per class. Following the previous work [23], we split the dataset into 351 base classes, 97 validation classes, and 160 novel classes. The resolution is also " + }, + { + "bbox": [ + 46, + 506, + 289, + 674 + ], + "type": "inline_equation", + "content": "84 \\times 84 \\times 3" + }, + { + "bbox": [ + 46, + 506, + 289, + 674 + ], + "type": "text", + "content": ". CUB is a fine-grained dataset, containing 200 classes of birds with around 60 images per class. And the resolution is still " + }, + { + "bbox": [ + 46, + 506, + 289, + 674 + ], + "type": "inline_equation", + "content": "84 \\times 84 \\times 3" + }, + { + "bbox": [ + 46, + 506, + 289, + 674 + ], + "type": "text", + "content": ". We adopt 100 base classes, 50 validation classes, and 50 novel classes following [4]. CIFAR-FS consists of all 100 classes from CIFAR-100 [34], whose classes are randomly split into 64 base classes, 16 classes, and 20 novel classes. Each class contains 600 images of size " + }, + { + "bbox": [ + 46, + 506, + 289, + 674 + ], + "type": "inline_equation", + "content": "32 \\times 32 \\times 3" + }, + { + "bbox": [ + 46, + 506, + 289, + 674 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 677, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 289, + 713 + ], + "type": "text", + "content": "Implementation details: We use pre-trained backbones for extracting visual features of four benchmarks, as shown in Table. 1. WRN and RN18 are separately WideResNet-28-" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 506, + 547, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 547, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 547, + 615 + ], + "type": "text", + "content": "10 and ResNet-18 pre-trained with standard classification loss [29]. WRN" + }, + { + "bbox": [ + 304, + 506, + 547, + 615 + ], + "type": "inline_equation", + "content": "\\S" + }, + { + "bbox": [ + 304, + 506, + 547, + 615 + ], + "type": "text", + "content": " is WideResNet-28-10 pre-trained with self-supervised loss [19]. Besides, we employ log transform, a channel-wise feature adaptation, introduced in Yang et al. [35] to pre-process the pre-extracted features. The distance function " + }, + { + "bbox": [ + 304, + 506, + 547, + 615 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 506, + 547, + 615 + ], + "type": "text", + "content": " is instantiated as a two-layers MLP activated with LeakyReLU whose architecture is " + }, + { + "bbox": [ + 304, + 506, + 547, + 615 + ], + "type": "inline_equation", + "content": "[d_f, 128, 64, 1]" + }, + { + "bbox": [ + 304, + 506, + 547, + 615 + ], + "type": "text", + "content": ". As for hyper-parameters, we mainly set " + }, + { + "bbox": [ + 304, + 506, + 547, + 615 + ], + "type": "inline_equation", + "content": "\\beta = 0.5" + }, + { + "bbox": [ + 304, + 506, + 547, + 615 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 506, + 547, + 615 + ], + "type": "inline_equation", + "content": "\\alpha = 0.1" + }, + { + "bbox": [ + 304, + 506, + 547, + 615 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 506, + 547, + 615 + ], + "type": "inline_equation", + "content": "\\rho = 0.2" + }, + { + "bbox": [ + 304, + 506, + 547, + 615 + ], + "type": "text", + "content": ". The reported results are averaged over 3000 tasks." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 623, + 391, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 391, + 634 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 391, + 634 + ], + "type": "text", + "content": "4.2. Main Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 641, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 548, + 713 + ], + "type": "text", + "content": "Quantitative results: The classification results on miniImageNet, tieredImageNet, CUB, and CIFAR-FS are reported in Table 1, according to which five-fold observations can be drawn: 1) inductive methods are not bothered by class-imbalanced problem since they do not leverage transferable statistics of query samples; 2) most transductive methods" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16322" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 42, + 70, + 167, + 155 + ], + "blocks": [ + { + "bbox": [ + 42, + 70, + 167, + 155 + ], + "lines": [ + { + "bbox": [ + 42, + 70, + 167, + 155 + ], + "spans": [ + { + "bbox": [ + 42, + 70, + 167, + 155 + ], + "type": "image", + "image_path": "e8520dc25383a3eb2b6efef5b65fdc2b7a19db726b824beffa9ebda40b8fd5cc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 163, + 289, + 236 + ], + "lines": [ + { + "bbox": [ + 46, + 163, + 289, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 289, + 236 + ], + "type": "text", + "content": "Figure 4: Case studies for 5-way 5-shots tasks on CUB [31] (left) and miniImageNet (right). Comparisons between unnormalized prior distribution (true number of query samples counting for each class) and unnormalized posterior distribution (estimated number of query samples counting by the well optimized forward transport matrix for each class)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 169, + 70, + 293, + 156 + ], + "blocks": [ + { + "bbox": [ + 169, + 70, + 293, + 156 + ], + "lines": [ + { + "bbox": [ + 169, + 70, + 293, + 156 + ], + "spans": [ + { + "bbox": [ + 169, + 70, + 293, + 156 + ], + "type": "image", + "image_path": "c2bc6762adbc84335fc53b3432e498d319753588350ba5b533bcbfe7c9da7f09.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 175, + 548, + 212 + ], + "lines": [ + { + "bbox": [ + 304, + 175, + 548, + 212 + ], + "spans": [ + { + "bbox": [ + 304, + 175, + 548, + 212 + ], + "type": "text", + "content": "Figure 5: 5-way 5-shot classification accuracy on miniImageNet and CUB of transductive methods versus imbalance level, lower " + }, + { + "bbox": [ + 304, + 175, + 548, + 212 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 175, + 548, + 212 + ], + "type": "text", + "content": " corresponds to severer class imbalance." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 258, + 289, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 258, + 289, + 641 + ], + "spans": [ + { + "bbox": [ + 47, + 258, + 289, + 641 + ], + "type": "text", + "content": "still outperform the inductive peers in class-imbalanced setting, which implies that there exists a trade-off between extra statistics conveyed by class-imbalanced query samples and algorithm bias; 3) results of features extracted by WRN" + }, + { + "bbox": [ + 47, + 258, + 289, + 641 + ], + "type": "inline_equation", + "content": "\\S" + }, + { + "bbox": [ + 47, + 258, + 289, + 641 + ], + "type": "text", + "content": " usually outperforms those by WRN or RN18, it indicates that self-supervised learning is helpful in obtaining generalized representations in class-imbalanced and class-balanced FSL applications; 4) most existed transductive inference methods suffer from performance cliff since their mismatch between data distribution and prior distribution. For example, TIM implicitly introduces uniform prior on query samples by using entropy regularization since minimizing entropy-based regularization is equivalent to minimizing the KL divergence between the predicted marginal distribution and uniform distribution. Hence, data distribution and model bias are unsuitable, leading to poor accuracy. Fortunately, such kind of mismatch can be eased by re-weighting in [29]. On the contrary, PT-MAP holds a strong but unmodified uniformly distributed prior on its transport matrix. Therefore, results of TIM are robuster than those of PT-MAP; 5) our proposed method outperforms most of the transductive methods and achieves competitive results with some most recently proposed methods, such as " + }, + { + "bbox": [ + 47, + 258, + 289, + 641 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 258, + 289, + 641 + ], + "type": "text", + "content": "-TIM, iLPC and BAVAR. It indicates that prototype refinement benefits from the well optimized transport matrices when shot number is low. Moreover, compared with iLPC and BAVAR, on the one hand, our model is easy to implement. On the other hand, BAVAR heavily relies on prior of imbalanced ratio " + }, + { + "bbox": [ + 47, + 258, + 289, + 641 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 258, + 289, + 641 + ], + "type": "text", + "content": " in class-imbalanced case while iLPC depends on uniform prior in class-balanced case [12], importantly however, our model is free of these priors, making it suitable for real-world applications when we have no idea on class distributions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 642, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 289, + 715 + ], + "type": "text", + "content": "Qualitatively analysis: To qualitatively illustrate the evolution of prototypes of our model, we map prototypes and query features of one task into a 2-D subspace with t-distributed Stochastic Neighbor Embedding (t-SNE) [28], it is a non-linear dimensional reduction technique well-suited for embedding high-dimensional data into a low-dimensional" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 301, + 70, + 422, + 166 + ], + "blocks": [ + { + "bbox": [ + 301, + 70, + 422, + 166 + ], + "lines": [ + { + "bbox": [ + 301, + 70, + 422, + 166 + ], + "spans": [ + { + "bbox": [ + 301, + 70, + 422, + 166 + ], + "type": "image", + "image_path": "9f5da9ddfb275610243ae1e2beb650110964e6496e8595ce92af91b504d1ce98.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 429, + 70, + 552, + 166 + ], + "blocks": [ + { + "bbox": [ + 429, + 70, + 552, + 166 + ], + "lines": [ + { + "bbox": [ + 429, + 70, + 552, + 166 + ], + "spans": [ + { + "bbox": [ + 429, + 70, + 552, + 166 + ], + "type": "image", + "image_path": "5b00c9dbd6b1a6fc6f1a8ee2fbd614df8d9147a7bd0c0101073eadbb3e0c3a46.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 309, + 255, + 544, + 308 + ], + "blocks": [ + { + "bbox": [ + 305, + 223, + 547, + 247 + ], + "lines": [ + { + "bbox": [ + 305, + 223, + 547, + 247 + ], + "spans": [ + { + "bbox": [ + 305, + 223, + 547, + 247 + ], + "type": "text", + "content": "Table 2: End-to-end real-time efficiencies (s) of 5-way 1-shot on CUB with two backbones averaged on 100 tasks." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 255, + 544, + 308 + ], + "lines": [ + { + "bbox": [ + 309, + 255, + 544, + 308 + ], + "spans": [ + { + "bbox": [ + 309, + 255, + 544, + 308 + ], + "type": "table", + "html": "
Backboneα - TIM (NeurIPS'21)iLPC (ICCV'21)BAVAR (AISTATS'23)Ours
RN185.64.63.42.9
WRN6.24.73.63.7
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As we can see from Fig. 3, due to class-imbalanced issue, although prototypes can not match their corresponding class centers well at beginning, they become consistent with the ground truth centers after refinement using our proposed method, verifying the effectiveness of our PUTM in dealing with unknown and arbitrary prior situation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 407, + 402, + 421 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 407, + 402, + 421 + ], + "spans": [ + { + "bbox": [ + 306, + 407, + 402, + 421 + ], + "type": "text", + "content": "4.3. Model Analysis" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 426, + 548, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 548, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 548, + 629 + ], + "type": "text", + "content": "Forward transport V.S. backward transport: As discussed in Sec. 3.3.2, the forward and backward transport matrices put different priors of " + }, + { + "bbox": [ + 304, + 426, + 548, + 629 + ], + "type": "inline_equation", + "content": "\\{a_i\\}_{i=1}^N" + }, + { + "bbox": [ + 304, + 426, + 548, + 629 + ], + "type": "text", + "content": ". Namely, we do not restrict uniform distribution in the forward transport and enable it to be adaptive to data-driven class distribution. On the contrary, prior in the backward transport is always assumed to be " + }, + { + "bbox": [ + 304, + 426, + 548, + 629 + ], + "type": "inline_equation", + "content": "\\frac{1}{N}" + }, + { + "bbox": [ + 304, + 426, + 548, + 629 + ], + "type": "text", + "content": ". Therefore, we employ the forward transport for predictions to meet the class-imbalanced essence, the efficiency is illustrated in Fig. 4, it depicts that the predicted distribution is consistent with the true distribution. Moreover, we conduct an extra experiment to verify the opposite direction of the two transport matrices, results are illustrated in Fig. 3, where we separately use the forward transport and the backward transport to calibrate the prototypes over 3000 tasks. According to the results, we find that, from a statistical point of view, the backward transport does harm the efficient migration from the class-imbalanced query samples." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 630, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 548, + 715 + ], + "type": "text", + "content": "Robustness of imbalanced coefficients: An important point in this work is that our model is robust for various class-imbalanced coefficients, which is vital and crucial for real-world applications since we usually do not know whether the few-shot tasks are balanced or not in advance, thus, we could not know what kind of methods are suitable for describing the samples distribution of tasks. Once they are" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16323" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 211, + 169 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 211, + 169 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 211, + 169 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 211, + 169 + ], + "type": "image", + "image_path": "31de3a57fe62b36349fc65422bb829107d7a86eccc89cb737914971922bc4fb6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 215, + 69, + 377, + 169 + ], + "blocks": [ + { + "bbox": [ + 215, + 69, + 377, + 169 + ], + "lines": [ + { + "bbox": [ + 215, + 69, + 377, + 169 + ], + "spans": [ + { + "bbox": [ + 215, + 69, + 377, + 169 + ], + "type": "image", + "image_path": "40d73d77e591d28f618fb87f29e90ee2d1dcaa757ad0940aeea7b377e568bace.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 383, + 70, + 545, + 168 + ], + "blocks": [ + { + "bbox": [ + 383, + 70, + 545, + 168 + ], + "lines": [ + { + "bbox": [ + 383, + 70, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 383, + 70, + 545, + 168 + ], + "type": "image", + "image_path": "7625139324fac253e27f9d27d8039a52cba1acba48db366165cb100f4262c3fa.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 48, + 171, + 211, + 270 + ], + "blocks": [ + { + "bbox": [ + 48, + 171, + 211, + 270 + ], + "lines": [ + { + "bbox": [ + 48, + 171, + 211, + 270 + ], + "spans": [ + { + "bbox": [ + 48, + 171, + 211, + 270 + ], + "type": "image", + "image_path": "97375bd9f791c9ee9a48ed1ee0674f95378f49b3323be29c19ebdbb12d477929.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 278, + 547, + 304 + ], + "lines": [ + { + "bbox": [ + 46, + 278, + 547, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 547, + 304 + ], + "type": "text", + "content": "Figure 6: Sensitivity analysis of our model to hyper-parameters including log transform " + }, + { + "bbox": [ + 46, + 278, + 547, + 304 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 278, + 547, + 304 + ], + "type": "text", + "content": ", CT coefficient " + }, + { + "bbox": [ + 46, + 278, + 547, + 304 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 278, + 547, + 304 + ], + "type": "text", + "content": ", and inertia " + }, + { + "bbox": [ + 46, + 278, + 547, + 304 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 278, + 547, + 304 + ], + "type": "text", + "content": ". Results are obtained with WRN8 and are reported on both validation and test sets. Best viewed in color." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 215, + 171, + 377, + 270 + ], + "blocks": [ + { + "bbox": [ + 215, + 171, + 377, + 270 + ], + "lines": [ + { + "bbox": [ + 215, + 171, + 377, + 270 + ], + "spans": [ + { + "bbox": [ + 215, + 171, + 377, + 270 + ], + "type": "image", + "image_path": "c8c618a05c2cab20e3f21c6c2d80903b8512108f50151a6fc69185e8c9cf3e5b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 383, + 171, + 545, + 269 + ], + "blocks": [ + { + "bbox": [ + 383, + 171, + 545, + 269 + ], + "lines": [ + { + "bbox": [ + 383, + 171, + 545, + 269 + ], + "spans": [ + { + "bbox": [ + 383, + 171, + 545, + 269 + ], + "type": "image", + "image_path": "3961bb3cd77757ffe3a0de41e992f0d7ed4011378782c1fb2f8c05b2b2784868.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 324, + 288, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 288, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 288, + 467 + ], + "type": "text", + "content": "unmatched, horrible performance degradation would happen, such as PT-MAP does. We verify the robustness of our model with a wide range of imbalanced coefficients as shown in Fig. 5, where " + }, + { + "bbox": [ + 46, + 324, + 288, + 467 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 324, + 288, + 467 + ], + "type": "text", + "content": " changes from 1 to 6. The performance of most methods decreases as " + }, + { + "bbox": [ + 46, + 324, + 288, + 467 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 324, + 288, + 467 + ], + "type": "text", + "content": " decreasing because smaller " + }, + { + "bbox": [ + 46, + 324, + 288, + 467 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 324, + 288, + 467 + ], + "type": "text", + "content": " indicates more imbalanced distribution of query samples, thus making tasks harder. On the contrary, performances of LaplacianShot and " + }, + { + "bbox": [ + 46, + 324, + 288, + 467 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 324, + 288, + 467 + ], + "type": "text", + "content": "-TIM drop obviously as " + }, + { + "bbox": [ + 46, + 324, + 288, + 467 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 324, + 288, + 467 + ], + "type": "text", + "content": " increases. Our model achieves consistent improvement and reasonable trend in a wide range of " + }, + { + "bbox": [ + 46, + 324, + 288, + 467 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 324, + 288, + 467 + ], + "type": "text", + "content": ", we attribute this to the introduction of adaptive transport matrices, which enables PUTM to fit the class distributions precisely and flexibly." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 471, + 288, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 288, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 288, + 662 + ], + "type": "text", + "content": "Sensitivity of hyper-parameters: To further verify the robustness of our model, we validate the sensitivity of PUTM to different hyper-parameters introduced in Sec. 4.1, and results are reported in Fig. 6. Generally speaking, the tendencies on validation and test sets are same. Besides there are three-fold observations: i) CT coefficient is less sensitive than log transform and inertia; ii) log transform controls the strength of channel-wise attention, which is proven to be important especially in few-shot case, thus it affects performance mostly; iii) inertia reflects the bottleneck of information flow from the aggregated prototypes to the refined prototypes. Bigger or smaller value of inertia is helpless for robust transfer since refinement of prototypes is associated with transport matrices. Namely, if the matrices are not well-optimized, a big inertia may cause algorithm to fall into a local optimum and vice versa." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Real-time efficiency: To verify the efficiency of PUTM, we conduct parallel versions of " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "-TIM, iLPC, and BAVAR based on their official implementations with the same machine. Results are reported in Table. 2, as we can see that our" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 324, + 547, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 547, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 547, + 421 + ], + "type": "text", + "content": "model consumes less time using RN18 and achieves competitive results using WRN. And we attribute this to the fact that : i) both " + }, + { + "bbox": [ + 304, + 324, + 547, + 421 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 324, + 547, + 421 + ], + "type": "text", + "content": "-TIM and iLPC employ Sinkhorn algorithm to solve the Optimal Transport (OT) problem involving thousands of inner loop, and it is a kind of time consuming; ; ii) our EM-Solver might be more efficient for dealing with the class-imbalanced TFSL since it imposes potential capability for modeling such unknown distribution with CT theory." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 432, + 476, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 432, + 476, + 445 + ], + "spans": [ + { + "bbox": [ + 305, + 432, + 476, + 445 + ], + "type": "text", + "content": "5. Conclusion and Future Works" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 453, + 547, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 547, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 547, + 609 + ], + "type": "text", + "content": "We propose a novel model called PUTM with EM-Solver based on CT theory for both class-imbalanced and class-balanced TFSL in this work according to an important observation that CT has a natural connection with unknown and arbitrary class prior problem. Specifically, PUTM exploits transferable statistics with CT for refining biased prototypes solved by EM to capture the unbiased statistics within imbalanced query samples. Extensive experiments on standard benchmarks verify the effectiveness of our model in both class-imbalanced and class-balanced few-shot applications. In the future, we will explore the applicability of PUTM on more problem settings and applications, such as multi-domain few-shot classification and few-shot object detection." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 621, + 416, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 416, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 416, + 635 + ], + "type": "text", + "content": "6. Acknowledgement" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 641, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 548, + 715 + ], + "type": "text", + "content": "This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant U21B2006; in part by Shaanxi Youth Innovation Team Project; in part by the National NSFC under Grant 82172860; in part by the National NSFC under Grant 6220010437; in part by the Fundation of Aerospace under Grant SAST2021-" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16324" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 133 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 133 + ], + "type": "text", + "content": "012. We also thanks Dandan Guo and He Zhao for their constructive comments on transductive few-shot learning, we thanks Zhisong Zhang for his very initial exploration on class-imbalanced few-shot image classification, we thanks Dongsheng Wang for his passion discussions on CT." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 143, + 106, + 156 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 143, + 106, + 156 + ], + "spans": [ + { + "bbox": [ + 48, + 143, + 106, + 156 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 163, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 163, + 287, + 196 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 163, + 287, + 196 + ], + "spans": [ + { + "bbox": [ + 53, + 163, + 287, + 196 + ], + "type": "text", + "content": "[1] Luca Bertinetto, Joao F Henriques, Philip HS Torr, and Andrea Vedaldi. 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PMLR, 2020." + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "16326" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Prototypical Kernel Learning and Open-set Foreground Perception for Generalized Few-shot Semantic Segmentation/ae5d3fad-adfb-4c23-912c-f33a2a374a40_content_list.json b/2023/Prototypical Kernel Learning and Open-set Foreground Perception for Generalized Few-shot Semantic Segmentation/ae5d3fad-adfb-4c23-912c-f33a2a374a40_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..617245199864c817081d4a3bedf87500e3fab143 --- /dev/null +++ b/2023/Prototypical Kernel Learning and Open-set Foreground Perception for Generalized Few-shot Semantic Segmentation/ae5d3fad-adfb-4c23-912c-f33a2a374a40_content_list.json @@ -0,0 +1,1569 @@ +[ + { + "type": "text", + "text": "Prototypical Kernel Learning and Open-set Foreground Perception for Generalized Few-shot Semantic Segmentation", + "text_level": 1, + "bbox": [ + 129, + 130, + 841, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Kai Huang, Feigege Wang, Ye Xi, Yutao Gao", + "bbox": [ + 303, + 203, + 663, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Alibaba Group", + "bbox": [ + 424, + 222, + 545, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "zhouwan.hk, feigege.wfgg, yx150449, yutao.gao@alibaba-inc.com", + "bbox": [ + 212, + 241, + 754, + 255 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Generalized Few-shot Semantic Segmentation (GFSS) extends Few-shot Semantic Segmentation (FSS) to simultaneously segment unseen classes and seen classes during evaluation. Previous works leverage additional branch or prototypical aggregation to eliminate the constrained setting of FSS. However, representation division and embedding prejudice, which heavily results in poor performance of GFSS, have not been synthetical considered. We address the aforementioned problems by jointing the prototypical kernel learning and open-set foreground perception. Specifically, a group of learnable kernels is proposed to perform segmentation with each kernel in charge of a stuff class. Then, we explore to merge the prototypical learning to the update of base-class kernels, which is consistent with the prototype knowledge aggregation of few-shot novel classes. In addition, a foreground contextual perception module cooperating with conditional bias based inference is adopted to perform class-agnostic as well as open-set foreground detection, thus to mitigate the embedding prejudice and prevent novel targets from being misclassified as background. Moreover, we also adjust our method to the Class Incremental Few-shot Semantic Segmentation (CIFSS) which takes the knowledge of novel classes in a incremental stream. Extensive experiments on PASCAL-5 $^i$ and COCO-20 $^i$ datasets demonstrate that our method performs better than previous state-of-the-art.", + "bbox": [ + 76, + 325, + 473, + 718 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 752, + 209, + 767 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Few-shot semantic segmentation [25, 39, 2, 15] aims to handle the situation of only sparse annotated data available, which perplexes most normal semantic segmentation methods. Inherited from the superiority of few-shot learning, the FSS methods can quickly be expended to unseen domains with only few labeled samples. Typically, most FSS methods are built on episode-based meta-learning [27], each episode data contains a support set and a query set shared", + "bbox": [ + 75, + 780, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d8d2c856a81604d88e674062da6ed4677eaaaf048ef227018146fd7b87c8e931.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 292, + 908, + 358 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2c2d6ff724bb91cae821e521e0145d452b6880bfc538829622d91b04f51c5a6c.jpg", + "image_caption": [ + "Novel-class Image" + ], + "image_footnote": [], + "bbox": [ + 504, + 359, + 908, + 412 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/270f84ab681739917af3e31302fd6ef7e7a6e3653f80d8fd49a55a935598434d.jpg", + "image_caption": [ + "Representation Division", + "Figure 1. Illustration of our motivation. (a) shows the generation of base-class representation vectors, it learns from abundant base-class images. (b) is the process of novel-class prototypes, which are aggregated by the lightweight feature pooling since few samples available. (c) demonstrates the representation division and embedding prejudice problem existed in current GFSS." + ], + "image_footnote": [], + "bbox": [ + 504, + 420, + 710, + 474 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/483a04c09be2ccf71bb9c9d7aeb5b06049491705e27831bf65c986dbbfd76190.jpg", + "image_caption": [ + "Embedding Prejudice" + ], + "image_footnote": [], + "bbox": [ + 718, + 421, + 905, + 474 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "with same classes. In general, the support set consists of few support images with pixel-wise annotations. The models are supported to learn a generic meta-learner with abundant episodic data sampled from the base classes, and adopt to novel classes with the guidance of the support set. However, the majority of current FSS methods can not escape from the limitation of support set, in which specific as well as single novel class annotations are needed corresponding to query images during the inference. Another weakness is that models can only segment the specific novel class of support set while lack the identification of base classes or multi-novel classes. The recent work [15] leverages the prediction of base classes with a base learner, and thus gives a mask region, which instructs the area does not need to be segmented, to guide the recognition of novel concepts. Despite the significant improvement has been made in base classes, the issue of heavily relying on the support samples with the same classes for each query image still exists.", + "bbox": [ + 496, + 597, + 893, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To this end, Generalized Few-shot Semantic Segmentation (GFSS) was proposed [28] where novel classes are", + "bbox": [ + 500, + 869, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19256", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "aforehand registered to the vanilla model learned from the base classes, making it possible to segment the base and novel simultaneously without extra information in the inference phase. The typical similarity metric enables a more flexible way to expand novel classes with few annotated samples above the base classes. It can directly perform the inference the same as normal segmentation models, with no need of the prerequisite which informs the target classes contained in query images. Regardless, there are still two challenges in GFSS as shown in Fig.1(c): 1) The representation division between base-class and novel-class blocks the accurate predictions, where the former are learned from sufficient data and the latter are aggregated from limited samples with feature pooling approaches; 2) the prejudice of feature embedding makes the novel-class pixels have the tendency to be identified as varied background, since the feature extractor is trained in base classes.", + "bbox": [ + 75, + 90, + 472, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose to joint prototypical kernel learning and open-set foreground perception to address the above-mentioned problems. It exploits a base-class kernel update schema by applying the pixel assembled feature of each input image to extra supervise the update of base-class kernels. Apart from the normal update with abundant base-class samples, those kernels are endowed with the ability of prototypical representation by the prototypical kernel update, which is consistent with the knowledge aggregation of novel-class with few labeled data. To mitigate the feature embedding preconception, we leverage the common feature patterns cross multi-class targets by an open-set foreground perception, which serves the purpose to offer the class-agnostic as well as open-set foreground prediction. Finally, a conditional bias based inference is proposed to assemble the class-wise prediction and the binary foreground prediction. Furthermore, we expand our method from the GFSS to class incremental few-shot segmentation which registers novel classes with an incremental stream.", + "bbox": [ + 75, + 347, + 472, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our primary contributions can be summarized as: 1) we present a prototypical kernel learning for maintaining the representation consistency between base-class and novel-class by the notion of kernel; 2) we propose to learn the class-agnostic foreground perception cross the multi-class targets to mitigate the feature embedding preconception, and devise a conditional bias based inference for ensemble prediction; 3) extensive experiments on GFSS and CIFSS demonstrate that the proposed method achieves higher performance compared with other approaches.", + "bbox": [ + 75, + 635, + 472, + 787 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 799, + 218, + 814 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Few-shot Segmentation aims to give a dense pixel prediction for the query images with only a few annotated support images available. The most recent methods adopt two-branch paradigm, i.e., a support branch for target classes prototypical representation and a query branch", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "for feature pairs comparison. Typically, the support branch is performed by the mask-involved feature pooling, such as masked average pooling [26], dynamic kernel generation [18]. The query branch tries to strengthen the metric ability between support prototypes and query feature, with directly pixel similarity [5], convolutional correlation [18, 19], attention-based interaction [36, 40] and so on. However, limited by the instance-based feature comparison of query branch, those methods can not handle on the GFSS scene, in which both base classes and novel classes are included to validation. BAM [15] introduces a base learner module for highly reliable base classes segmentation, and further incorporates into the meta prediction with an ensemble module. Nevertheless, it still needs specific support data and only works with single novel class for each query task. CAPL [28] proposes a novel class registration phase to register the novel information to base classifier, making it possible to be qualified for the segmentation of both base and multi-novel classes without additional support samples.", + "bbox": [ + 496, + 90, + 893, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Prototypical Learning is meant to excavate or utilize the representative examples directly with the exemplar-driven pattern. Owing to the needs of representation with limited data, the prototypical learning methods have been widely used in many few-shot tasks [27, 14, 5, 41], especially few-shot segmentation [32, 48]. A typical delegate is the prototype-based framework, in which annotated support data is class-wise aggregated as prototypes and then guide the segmentation of query samples. The prototypical learning of FSS can be roughly divided into implicit and explicit. The implicit methods mainly focus on the embedding learning and tend to use the feature pooling approaches, such as masked average pooling [26], attention-based aggregation [36] and kernel generation [18]. While the explicit way is to construct learnable prototypes, so that the labeled instances [48] or meta episode data [37] can react it directly.", + "bbox": [ + 496, + 382, + 893, + 625 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Foreground Modeling has gained rapid development with the effectiveness of targets detection. The most representative methods are class activation mapping and its variants [47, 24, 31], which are early used for feature visualization [47] and further as the rough foreground mask to initialize the progressive inception of many weak-supervised approaches [6, 4]. Later, salient detection [23, 46, 33] has been raised for binary segmentation tasks, with the strong ability of flexible saliency perception. The mainstream salient works only consider the intra interaction on each single image separately, which suffer from obscure and coarse results. Co-salient [42, 9] extends the separate mode to co-exploration within the image group, while extra information, e.g., edge [8], class-wise gradient [44], is always needed for discriminative feature learning. In this work, we propose to learn the common foreground patterns cross multi-class group instances, so as to directly promote to the detection of novel targets without class limitation.", + "bbox": [ + 496, + 628, + 895, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19257", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/6cb4cdeb58dd09f8703ad8a91ed744248bd4555907975f325fae9cee8bcb6845.jpg", + "image_caption": [ + "Figure 2. Overview of training framework. For the upper branch, the learnable base-class kernels are optimized by the Prototypical Kernel Learning (PKL). The down branch, named as Foreground Contextual Perception (FCP), is constructed to learn the open-set foreground detection by leveraging the contextual feature patterns cross multi-class targets. Batch is omitted in PKL for better display." + ], + "image_footnote": [], + "bbox": [ + 76, + 87, + 893, + 315 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 383, + 169, + 398 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Task Formulation", + "text_level": 1, + "bbox": [ + 76, + 409, + 250, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generalized few-shot segmentation is designed to quickly integrate unseen classes into a segmentation model with only a few annotated data. It aims to actualize segmentation tasks on novel classes with limited labeled samples and base classes with sufficient labeled data simultaneously. GFSS model learns the basal knowledge from the base classes set $C_{\\text{base}}$ , and novel classes set $C_{\\text{novel}}$ is registered to this base model with a few labeled data. There are no overlap between the base and novel classes set, i.e., $C_{\\text{base}} \\cap C_{\\text{novel}} = \\emptyset$ . In the inference process, the model should be qualified to the segmentation of the union set $C_{\\text{base}} \\cup C_{\\text{novel}}$ . Different from the normal FSS which are specific to the modeling of few-shot learner, GFSS is proposed to explore the possibility of empowering the few-shot learning ability to a vanilla segmentation model.", + "bbox": [ + 75, + 431, + 473, + 659 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Overview", + "text_level": 1, + "bbox": [ + 76, + 666, + 187, + 679 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The overall architectures for training and inference are shown in Fig. 2 and Fig. 4, which mainly consists of three components: Prototypical Kernel Learning (PKL), Foreground Contextual Perception (FCP) and Conditional Bias Based Inference (CBBI). The feature of input is respectively fed to two branches. For the upper branch, we employ the PKL to dynamically get the refined base-class kernels specific to the assembled feature of input image, and the class-wise predictions are produced by applying those kernels to the pixel features. For the down branch, the binary foreground prediction is decoded by the FCP which incorporates relevant contextual patterns cross multi-classes. The final prediction masks are obtained by combining the predictions of these two branch with the CBBI.", + "bbox": [ + 75, + 689, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Prototypical Kernel Learning Module", + "text_level": 1, + "bbox": [ + 500, + 383, + 826, + 402 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by the dynamic kernel [11, 34, 43] in semantic segmentation, which possess better representation ability than convolution kernels with flexible structures [35] or roles [16], we extend this to GFSS task by adopting prototypical kernel learning to maintain the representation consistency of base-class and novel-class.", + "bbox": [ + 496, + 409, + 890, + 498 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Specifically, $N_{b}$ learnable kernels $K_{b} \\in \\mathbb{R}^{N_{b} \\times C}$ are constructed to represent the knowledge of $N_{b}$ base classes, in which the convolution between these kernels and feature maps is taken on the segmentation basis. Concretely, given the input feature maps $\\mathcal{F} \\in \\mathbb{R}^{B \\times C \\times H \\times W}$ of $B$ input images, the semantic segmentation output is formulated as:", + "bbox": [ + 496, + 500, + 890, + 590 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nS = \\operatorname {s o f t m a x} \\left(K _ {b} * \\mathcal {F}\\right), S \\in \\mathbb {R} ^ {B \\times N _ {b} \\times H \\times W}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 602, + 890, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $C$ , $H$ , and $W$ indicate the number of channels, height, and width of the feature map respectively, and $N_{b}$ is the number of classes in base-class set.", + "bbox": [ + 496, + 633, + 890, + 678 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Pixel Feature Assembling. As the segmentation output of each kernel can reflect the class-wise pixel-to-prototype mapping, the pixel feature assembling is performed by aggregating the input feature with the pseudo semantic segmentation masks as:", + "bbox": [ + 496, + 679, + 890, + 753 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nP _ {m b} = \\sum_ {x} ^ {H} \\sum_ {y} ^ {W} S (x, y) \\cdot \\mathcal {F} (x, y), P _ {m b} \\in \\mathbb {R} ^ {B \\times N _ {b} \\times C}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 758, + 890, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The generation of $P_{mb}$ are analogous to the novel-class feature aggregation with few labeled samples, which takes the ability of prototypical representation.", + "bbox": [ + 496, + 809, + 890, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Prototypical Kernel Update. Ordinarily, the kernel of base-class learn the general perception from abundant annotated samples, it would be broader and more inclusive", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19258", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "than the novel-class kernels learned from few data, which exists representation division. Those ambiguous instances, e.g., the novel classes samples, are more predisposed to be caught by the base-class kernels. Thus, the prototypical kernel update is proposed to adapt the base-class kernels to few-shot task with extra one-off update specific to each input:", + "bbox": [ + 75, + 90, + 472, + 195 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {K} _ {b} = K _ {b} - \\alpha \\nabla_ {K _ {b}} \\mathcal {L} (K _ {b}) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 196, + 468, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\nabla_{K_b}\\mathcal{L}(K_b) = \\nabla_{K_b}(K_b - P_{mb}^i)^2$ is the gradient descent of the mean squared error loss between $K_{b}$ and the assembled feature of $i$ -th images $P_{mb}^{i}$ , $\\alpha$ is the adaptation learning rate, which denotes as kernel-to-prototype similarity with the restraint of ReLU function that insures constant positive:", + "bbox": [ + 75, + 217, + 468, + 308 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha = \\operatorname {R e L U} \\left(\\operatorname {c o s i n e} \\left(K _ {b}, P _ {m b} ^ {i}\\right)\\right), \\alpha \\in \\mathbb {R} ^ {1 \\times N _ {b}}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 316, + 468, + 334 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The adaptation learning rate is designed to adaptive filter out ineffective gradient signals caused by those classes do not exist in this image. Since the classes existed in input image are a subset of base-class set, the pixel feature assembling of those missing classes is invalid and will lead to incorrect kernel update. The adaptation learning rate will decay to near zero to block the ineffective update as the kernel-to-prototype similarities are low. Finally, The predicted segmentation mask is obtained by:", + "bbox": [ + 75, + 343, + 468, + 479 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM (x, y) = \\underset {i} {\\arg \\max } \\tilde {S} ^ {i} (x, y), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 486, + 468, + 510 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tilde{S}^i (x,y)$ is the score map between the updated base-class kernels and the feature maps followed by Eq. (1).", + "bbox": [ + 75, + 521, + 468, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Foreground Contextual Perception Module", + "text_level": 1, + "bbox": [ + 76, + 560, + 444, + 575 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The aforementioned PKL module aims to adjust the general base-class kernels to few-shot scenario with assembled prototypical feature, so that the representation divergence between base and novel classes is mitigated. While the perception ability of novel foreground targets remains poor with the limitation of backbone training, where only the base-class data is sufficiently accessible. Inspired by the episode-based paradigm in various few-shot learning [30, 25, 14], which can boost the model to adapt to unknown scenes, we propose a foreground contextual perception module to perform the open-set foreground perception. The batch group of images sampled from the base categories set can be considered as a pseudo episode, in which each batch group is randomly mixed with the samples of different base-class targets. The FCP module aims to mine common foreground patterns cross multi-class samples with abundant pseudo episode, thus possesses the ability of class-agnostic perception and prevents novel targets from being misclassified as background.", + "bbox": [ + 75, + 583, + 468, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Hybrid Pooling. As shown in Fig.3, the feature maps of pseudo episode are first passed by two independent lin", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ba728494f7e3a2302a0692410198f78f87a1f707649c8648c3f402270b156ba5.jpg", + "image_caption": [ + "Figure 3. Illustration of the Hybrid Pooling in FCP module." + ], + "image_footnote": [], + "bbox": [ + 501, + 89, + 908, + 202 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ear mappings, and the pixel-wise correlation is calculated within the feature map groups:", + "bbox": [ + 498, + 251, + 890, + 282 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA ^ {b} = \\Phi (\\mathcal {F}) ^ {T} \\Theta (\\mathcal {F} _ {b}) \\in \\mathbb {R} ^ {B \\times H W \\times H W}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 287, + 890, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Phi$ and $\\Theta$ represent $1\\times 1$ convolution layers, $\\mathcal{F}_b$ is the $b$ -th feature map, and $A^b$ denotes the pixel-wise correlation between the $b$ -th feature map and whole pseudo episode. The first dimension of $A^b$ indicates all images of pseudo episode, while the second and third dimensions mean the total feature pixels of each image in pseudo episode and the total feature pixels of query. The reshaping and transposing operations of matrix dimension are omitted for the simplification of presentation. A max pooling and average pooling are separately acted on the second and first dimensions to obtain a more representative correlation $\\bar{A}\\in \\mathbb{R}^{B\\times H\\times W}$ . It is worth mentioning that performing max pooling on pixel dimension can help to find out discriminative correlation pairs, and average pooling on image dimension is supported to learn the common foreground feature patterns.", + "bbox": [ + 496, + 314, + 890, + 541 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Foreground Correlation Responses. The correlation normalized by a softmax layer is truncated as the correlation mask $M_{corr}$ :", + "bbox": [ + 498, + 544, + 890, + 589 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM _ {c o r r} (h, w) = \\mathbb {1} (\\bar {A} (h, w) > 0. 5), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 598, + 890, + 614 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbb{1}(*)$ is the binary indicator that outputs 1 when $^*$ is true 0 otherwise, $h$ and $w$ are the height index and width index with the limitation of $H$ and $W$ . Although the correlation mask can embody the most discriminative feature pixel position, the relation response of other positions are discarded with the consideration of computational complexity. A sharp correlation information may carry more hard noisy, which blocks the learning of FCP module. Therefore, the spacial weighted Global Average Pooling (wGAP) [39, 38] of the correlation mask together with the normalized original feature maps is introduced to obtain a more robust correlation prototypes as:", + "bbox": [ + 496, + 622, + 890, + 804 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {w G P A} = \\frac {\\sum_ {h , w} \\| \\mathcal {F} (h , w) \\| _ {2} M _ {c o r r} (h , w)}{\\sum_ {h , w} M _ {c o r r} (h , w)} \\in \\mathbb {R} ^ {B \\times C}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 810, + 890, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\| * \\|_2$ is the L2 normalization. The correlation prototypes reflect the positive relations between the pixel and whole image pixels within the pseudo episode. The refined", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19259", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "correlation responses can be obtained by applying the correlation prototypes to the original feature maps as:", + "bbox": [ + 76, + 90, + 468, + 122 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {R} (h, w) = \\frac {1}{B} \\sum_ {i = 1} ^ {B} p _ {w G P A} \\| \\mathcal {F} (h, w) \\| _ {2}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 128, + 468, + 170 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Compared to the pixel-wise correlation referred to Eq. (6), the refined correlation responses are more robust with fewer sharp noises, as well as more accurate foreground perception. The final binary foreground masks are predicted by decoding the residual features:", + "bbox": [ + 76, + 176, + 468, + 252 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nM _ {f} = \\mathbb {D} (\\mathcal {F} + \\mathcal {F} \\times \\mathcal {R}), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 260, + 468, + 277 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbb{D}$ represents a correlation decoder built with the four cascaded convolutional layers.", + "bbox": [ + 76, + 285, + 468, + 315 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Training Loss and Novel Classes Registration", + "text_level": 1, + "bbox": [ + 76, + 329, + 460, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training Loss. The loss for training our model consists of two parts corresponding to the PKL module and FCP module respectively. The loss function for PKL module is illustrated as:", + "bbox": [ + 76, + 354, + 468, + 414 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c e} = \\frac {1}{H W} \\sum_ {x, y} \\sum_ {p ^ {i} \\in P _ {t s}} \\mathbb {1} [ M ^ {x, y} = i ] \\log \\hat {S} _ {c} ^ {x, y}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 419, + 468, + 457 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbb{1}(*)$ is the binary indicator same as Eq. (7). We adopt the IoU loss [23] to train the FCP module as:", + "bbox": [ + 76, + 465, + 468, + 496 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i o u} = \\frac {1}{B} \\sum_ {b = 1} ^ {B} \\left(1 - \\frac {\\hat {Y} \\cap Y}{\\hat {Y} \\cup Y}\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 503, + 468, + 544 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{Y}$ is the binary predictions and $Y$ is the ground truth. Finally, the total end-to-end loss over the batch is:", + "bbox": [ + 76, + 553, + 467, + 584 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\lambda \\sum_ {b \\in B} \\mathcal {L} _ {c e} ^ {b} + (1 - \\lambda) \\mathcal {L} _ {i o u}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 160, + 592, + 468, + 625 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda$ is utilized to balance the loss functions.", + "bbox": [ + 76, + 631, + 395, + 645 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Novel Classes Registration. After training, the novel-class kernels $K_{n} \\in \\mathbb{R}^{N_{n} \\times C}$ can be obtained by passing the support images of novel classes to the frozen feature extraction, following with the class-wise averaged wGAP referred to Eq. (8). Then, the novel classes knowledge is registered to the model by concatenating the novel-class kernels to the updated base-class kernels:", + "bbox": [ + 76, + 648, + 468, + 753 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nK _ {w} = \\operatorname {C o n c a t} \\left(\\left[ K _ {b}, K _ {n} \\right]\\right), K _ {w} \\in \\mathbb {R} ^ {\\left(N _ {b} + N _ {n}\\right) \\times C}. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 760, + 468, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Conditional Bias Based Inference", + "text_level": 1, + "bbox": [ + 76, + 801, + 369, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given the input test image $I$ , the final decision of position $\\mathbf{p}$ is defined as follows:", + "bbox": [ + 76, + 825, + 468, + 856 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nO _ {I} (\\mathbf {p}) = \\left\\{ \\begin{array}{l l} \\max \\left(c _ {1 \\mathrm {s t}}, c _ {2 \\mathrm {n d}} + b\\right), & O _ {s} (\\mathbf {p}) = = 1 \\\\ c _ {1 \\mathrm {s t}}, & \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 864, + 468, + 904 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/fe0383e32c8e6d1bc7e4c9c428e8ae92eacc3f518a408de82a37daa886c69d55.jpg", + "image_caption": [ + "Figure 4. Framework of the CBBI. We perform the FAH module with only itself contained in the pseudo episode." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 908, + 200 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $c_{1\\mathrm{st}}$ and $c_{2\\mathrm{nd}}$ are the first and second candidates according to the class-wise similarity, $O_s$ indicates the output of FCP module and $b$ is the constant of bias.", + "bbox": [ + 496, + 256, + 890, + 301 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Fig. 4, the refined meta specific prototypes are obtained by feeding the feature map of test image together with the class-wise prototypes to the PKL module. With the concerns of consistency and noise accumulation, we only update the base-class prototypes. Then, the class-wise predictions $O_{p}$ are calculated by the cosine similarity between the updated whole-class prototypes and query feature maps. The first and second candidate masks are the value of Top2 maps along with the class dimension of $O_{p}$ .", + "bbox": [ + 496, + 301, + 890, + 436 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the branch of conditional bias generation, the open-set foreground mask $O_{s}$ can be obtained by the FCP module. A pointwise multiplication between it and the second candidate mask is adopted to obtain the conditional bias mask $O_{sp}^{2}$ . Then, the second candidate mask is recalculated as:", + "bbox": [ + 496, + 438, + 890, + 525 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {O} _ {p} ^ {2} (\\mathbf {p}) = O _ {p} ^ {2} (\\mathbf {p}) + b \\cdot O _ {s p} ^ {2} (\\mathbf {p}). \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 526, + 890, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The final output can be obtained by the maximum argument between the first and second candidate masks.", + "bbox": [ + 496, + 550, + 890, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.7. Extension to Class Incremental FSS", + "text_level": 1, + "bbox": [ + 500, + 590, + 808, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following the incremental learning in other few-shot tasks [10, 22], we give the definition of class incremental setting in few-shot segmentation. The Class Incremental Few-shot Semantic Segmentation (CIFSS) shares the same classes set with GFSS, in which there are base classes set $C_{\\text{base}}$ with adequate data available and novel classes set $C_{\\text{novel}}$ with a small amount of annotated data. Different from the one-off task of novel classes in GFSS, CIFSS focuses on the novel classes in a session stream. The model learns from the base session $S_{b}$ with the base classes and adapts to novel classes with insufficient samples in sequential, i.e., the sequence session $\\{S_{n}^{1}, \\dots, S_{n}^{T}\\}$ with the novel classes. It is critical to mention that we can only access to the data of $t$ -th session when attaching this session, and there is no overlap within these novel sessions. The performance of model with current session $S_{n}^{t}$ is evaluated on the test samples of $S_{n}^{t}$ and the previous sessions $\\{S_{n}^{1}, \\dots, S_{n}^{t-1}\\}$ . The GFSS can be viewed as a exception constructed with only base session and one novel session.", + "bbox": [ + 496, + 613, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19260", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Owing to the extensible kernel and the mechanism of novel classes registration, the proposed model can be easy expanded to CIFSS. Similar to the training of GFSS, we learn the PKL and FCP module in the base session and all parameters are fixed during the sequence novel sessions. There are a series of novel classes registration processes corresponding to incremental classes learning with serialized novel sessions. To be specific, assume $K_w^t$ is the whole-class kernels of $t$ -th session, the extended kernels of next session $K_w^{t+1}$ is obtained by concatenating the novel session kernels $K_n^{t+1}$ :", + "bbox": [ + 75, + 90, + 472, + 258 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nK _ {w} ^ {t + 1} = \\operatorname {C o n c a t} \\left(\\left[ K _ {w} ^ {t}, K _ {n} ^ {t + 1} \\right]\\right), \\in \\mathbb {R} ^ {\\left(N _ {w} ^ {t} + N _ {n} ^ {t + 1}\\right) \\times C}, \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 265, + 468, + 286 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where the calculation of $K_{n}^{t + 1}$ is the same with novel classes registration of GFSS referred to 3.5. In the inference process, only the kernels of base session are passed to the PKL module, and all the kernels of few-shot sessions are treated as a novel whole in the CBBI.", + "bbox": [ + 75, + 291, + 470, + 367 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 383, + 209, + 400 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 407, + 294, + 424 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. Following [28], we evaluate the proposed method on two public datasets, i.e., PASCAL- $5^{i}$ and COCO- $20^{i}$ . PASCAL- $5^{i}$ is modified from PASCAL VOC [7] with extra mask annotations from Semantic Boundaries Dataset (SBD) [12] dataset, it has 20 object classes and one background class. COCO- $20^{i}$ consists of MS COCO [17] with 80 object classes and one background class for segmentation. In terms of GFSS, all the object classes are evenly divided into four folds: $\\{5^{i}, i \\in \\{0,1,2,3\\}\\}$ for PASCAL- $5^{i}$ and $\\{20^{i}, i \\in \\{0,1,2,3\\}\\}$ for COCO- $20^{i}$ . The rest object classes as well as background are treated as base classes, where the object classes of specific fold are conducted as novel classes. Models are directly evaluated on the validation set with both base and novel classes simultaneously. In terms of CIFSS, it shares the same fold division with GFSS. The object classes of specific fold are evenly divided into five novel sessions, while the rest object classes and the background class are included into the base session. On PASCAL- $5^{i}$ , there are 16 object classes in base session and 1 novel object class for each incremental session. As for COCO- $20^{i}$ , the number of object classes in base session is 61 and novel object classes in each incremental session is 5. We evaluate the CIFSS models on the classes belonging to base session, current and previous incremental novel sessions with the validation set.", + "bbox": [ + 75, + 431, + 472, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics. Similar to [28], we use mean Intersection over Union ( $mIoU$ ) for base classes as well as base session $mIoU_{\\mathcal{B}}$ and novel classes as well as incremental novel sessions $mIoU_{\\mathcal{N}}$ . As for GFSS setting, we also provide the overall $mIoU$ with all classes denoted by $mIoU_{\\mathcal{O}}$ . Since the base classes are the vast majority, the arithmetic", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3c4e7b48b9e86fe386114fe74f00dbe0845f277eede47e34f832ee95dc5e1ea4.jpg", + "table_caption": [ + "Table 1. Quantitative results with GFSS setting on PASCAL-5 $^i$ and COCO-20 $^i$ . Best-performing results are highlighted in bold." + ], + "table_footnote": [], + "table_body": "
Methods1-shot5-shot
mIoU_BmIoU_NmIoU_OhIoUmIoU_BmIoU_NmIoU_OhIoU
PASCAL-5^i
CANet [39]8.732.427.233.799.051.527.262.60
PFENet [29]8.322.676.974.048.831.897.183.11
SCL [38]8.882.447.353.839.111.837.383.05
PANet [32]31.8811.2526.9716.6332.9515.2528.7420.85
BAM [15]64.6517.0653.3227.0065.2819.9954.5030.61
CAPL [28]65.4818.8554.3829.2766.1422.4155.7231.96
Ours68.8426.9058.8637.8369.2234.4061.1845.42
COCO-20^i
Baseline [28]36.685.8429.0610.0136.917.2629.5912.13
BAM [15]44.086.7434.8611.6946.1011.2137.4918.03
CAPL [28]44.617.0535.4612.1845.2411.0536.8017.76
Ours46.3611.0437.7117.8346.7714.9138.9022.61
", + "bbox": [ + 503, + 116, + 906, + 305 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "mean might be dominated by $m\\mathrm{IoU}_{\\mathcal{B}}$ [1]. We adopt the harmonic mean $h\\mathrm{IoU}$ of $m\\mathrm{IoU}_{\\mathcal{B}}$ and $m\\mathrm{IoU}_{\\mathcal{N}}$ which can emphasize the impact of novel classes.", + "bbox": [ + 496, + 332, + 890, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training details. For fair comparison, the PSPNet [45] with RestNet50 [13] is adopted as our feature extractor, which is the same as most FSS and GFSS methods, and we train our model for 50 epochs both on PASCAL- $5^{i}$ and COCO- $20^{i}$ . The model is optimized by the SGD with an initial learning rate of 2.5e-3, where momentum is 0.9 and the weight decay is set to 1e-4. All images together with the masks are all resized to $473 \\times 473$ for training and tested with their original sizes. The $\\lambda$ of loss function is set to 0.6 and the bias value $b$ of CBBI is 0.5. We obtain the specific split results by averaging over five different random seeds, and the final reported results are averaged with all splits.", + "bbox": [ + 496, + 378, + 892, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparisons", + "text_level": 1, + "bbox": [ + 500, + 573, + 638, + 589 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "GFSS Setting. Table 1 shows the 1-shot and 5-shot quantitative results of different methods on PASCAL- $5^{i}$ and $\\mathrm{COCO - }20^{i}$ . It can be found that the proposed method shows substantial gains compared with the advanced approaches and achieves the state-of-the-art performance of all GFSS settings and datasets. As for the overall mIoU on PASCAL- $5^{i}$ , the proposed method exceeds the CAPL [28] by $4.48\\%$ and $5.46\\%$ for 1-shot setting and 5-shot setting respectively. With the significant improvement on novel classes, our method surpasses the CAPL [28] by $8.56\\%$ and $13.46\\%$ hIoU, demonstrating the superiority of the proposed method. Meanwhile, better performance on novel classes can also weaken the confusion between base classes and novel classes and improve the mIoU $_{\\mathcal{B}}$ .", + "bbox": [ + 496, + 597, + 893, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CIFSS Setting. We compare our method with the following modified approaches as: 1) the relevant incremental few-shot learning methods, such as PIFS [3] and iFS-RCNN [20]; 2) the current FSS and GFSS methods, i.e., PFENet [29], BAM [15] and CAPL [28]. From Table 2, our method shows substantial gains compared with existing approaches.", + "bbox": [ + 496, + 809, + 893, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19261", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/84e9cdb84cbce1ac6a866fbf767912e0771e8d38cb819c90be8f0b0415913ed4.jpg", + "table_caption": [ + "Table 2. 1-shot Quantitative results with CIFSS setting on the PASCAL-5 $^i$ and COCO-20 $^i$ . Best-performing results are highlighted in bold. * We use the weights of PSPNet [45] backbone pretrained on base classes as the same as the BAM [15]." + ], + "table_footnote": [], + "table_body": "
DatasetsMethodssession 0session 1session 2session 3session 4session 5
mIoU_BmIoU_BmIoU_NhIoUmIoU_BmIoU_NhIoUmIoU_BmIoU_NhIoUmIoU_BmIoU_NhIoU
PASCAL-5iPFENet* [29]74.4367.2110.3417.9266.6214.1223.3064.9711.1218.9965.7712.0820.4162.5011.0818.82
iFS-RCNN [20]72.4367.7111.0819.0467.1716.6326.6665.5112.9421.6165.4811.7519.9263.3612.3920.73
CAPL [28]74.8670.5117.9428.6069.0721.1132.3467.8918.0328.4967.1419.5730.3165.5319.0829.55
PIFS [3]75.0471.1619.4930.6069.8024.3336.0868.0519.9230.8268.4421.0832.2365.8320.9931.83
Our75.4972.9324.6036.7971.2129.3241.5470.7625.7537.7669.9826.1137.8868.4027.2839.00
COCO-20iPFENet* [29]54.1145.794.337.9144.585.189.2843.073.366.2342.405.649.9641.995.059.02
iFS-RCNN [20]53.4250.435.039.1545.526.6011.5343.865.079.0943.377.1112.2242.836.6311.48
CAPL [28]54.4350.256.6911.8146.677.0412.2345.925.539.8744.087.7713.2143.857.5112.82
BAM [15]54.8052.048.8315.1049.018.9415.1247.037.0312.2345.569.1915.2944.488.8314.73
PIFS [3]54.2751.598.9015.1848.529.5315.9346.966.9412.0945.699.9316.3144.278.8014.68
Our54.3951.7811.4718.5548.3311.2218.0847.289.6115.8946.2511.4718.3345.2410.7417.31
", + "bbox": [ + 80, + 116, + 906, + 250 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0d1abf64b548844d88c8d6e8e20045340c2deb7022eba3d522e89ac22e0924b5.jpg", + "table_caption": [ + "Table 3. Ablation Study of the effect with different components." + ], + "table_footnote": [], + "table_body": "
PKLFCPCBBI1-shot5-shot
mIoU_BmIoU_NhIoUmIoU_BmIoU_NhIoU
61.2214.5023.4562.0719.7329.94
✓66.8222.9534.1767.7329.1840.79
✓64.4916.7326.5765.2823.3934.44
✓✓67.7323.5834.9868.0531.4543.02
✓✓✓68.8426.9037.8369.2234.4045.42
", + "bbox": [ + 80, + 286, + 475, + 388 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Since majority approaches adopt analogous backbone, we get similar performance in the session 0, which only construct with base classes. The superiority of our method both in base and novel classes continues to emerge as the novel session increased. It partly embodies the significant benefit of our old and novel classes knowledge ensemble mechanism, and partly verifies that the improvement on novel classes can result better performance of base classes as well.", + "bbox": [ + 75, + 415, + 468, + 536 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 545, + 240, + 559 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Component-wise Effectiveness. We ablate the three major components of proposed method in Table 3: prototypical kernel learning module, foreground contextual perception module and conditional bias based inference. We use the PSPNet [45] modified with learnable kernels as the baseline, in which simple concat operation is conducted between base-class and novel-class kernels. We can see that adding either one of PKL module or FTP module brings substantial improvement compared with the baseline. It means the proposed two modules are indeed beneficial to the novel classes learning in few-shot scenarios, and can mitigate the knowledge division with the extremely class-imbalanced GFSS setting. Moreover, it worth noting that the FTP module explicit plays a vital role in providing the general foreground information, the implicit effect is to boost the feature expression of unknown targets. Fig. 5 shows the qualitative results, which straightforward embodies the effectiveness of proposed method.", + "bbox": [ + 75, + 568, + 468, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Prototypical Kernel Learning Module. The motivation of PKL module is to empower the prototypical ability for base-class kernels, so as to maintain the consistency with the registered novel classes, which is also prototypical aggregated", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/62abb2f0248a31a4e238e91f54875938f7b5025a543d64d8994c718d6df081a3.jpg", + "table_caption": [ + "Table 4. Ablation performances of the proposed method. fixedALR means using fixed learning rate referred to Eq. (3). $\\mathrm{pixel}_{AP\\rightarrow MP}$ indicates replacing average pooling with max pooling in pixel dimension referred to Eq. (6), and $\\mathrm{image}_{MP\\rightarrow AP}$ is the similar replacement in image dimension. $uCBBI$ and $cCBBI$ denote the unconditional form and learnable convolution form for CBBI." + ], + "table_footnote": [], + "table_body": "
Settings1-shot5-shot
mIoUBmIoUNhIoUmIoUBmIoUNhIoU
w/o PKL64.4916.7326.5765.2823.3934.44
fixedALR66.9020.4831.3667.7226.0837.66
concat+AP65.9119.4130.0066.8625.5136.93
concat+LP66.2721.1932.1167.7126.8938.49
w/o FCP66.8222.9534.1767.7329.1840.79
pixelAP→MP65.9422.3133.3466.4228.9140.28
imageMP→AP65.0521.9432.8166.1828.3039.65
GradCAM [24]66.9423.3634.7468.0829.8041.46
PAGENet [33]67.5724.8036.2868.8331.7043.41
MINet [21]67.8924.9936.5368.6531.4743.16
w/o CBBI67.7323.5834.9868.0531.4543.02
uCBBI66.2920.8331.7067.1325.3836.83
cCBBI65.5318.8629.2966.9023.3934.66
Ours68.8426.9037.8369.2234.4045.42
", + "bbox": [ + 504, + 354, + 895, + 590 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "from limited data. We replace the PKL with directly adopting the base-class kernels to the input feature maps as our baseline. As shown in the upside of Table 4, we first construct the ablation studies on the adaptation learning rate, it is clear that the fixed learning rate brings worse results with the distraction of noisy gradient signals during the prototypical kernel update. Meanwhile, we introduce several alternative prototype fusion approaches which are performed by the adaptive pooling (AP) or liner projection (LP) after the channel-wise concat operation between $K_{b}$ and $P_{mb}$ . The results show that our method with the proposed prototypical kernel update remarkably outperforms the aforementioned approaches. It can strike a better balance between generality and specificity, especially for novel targets in generalized inference process, thus is more suitable to the GFSS.", + "bbox": [ + 496, + 625, + 893, + 851 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Foreground Contextual Perception module. The FCP aims to offer a general foreground detection which helps to the mining of novel targets. Similarly, the model with-", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19262", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dd16e4961766a5d942c4b8378dd725c098329bfcb9f11ddca08ed835cd75310d.jpg", + "image_caption": [ + "Figure 5. Qualitative results of our method, ablation of each components, BAM [15] and CAPL [28] on PASCAL- $5^{i}$ benchmark." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 893, + 277 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "out FCP is conducted as the baseline, as well as replacing the CBBI with normal inference. The middle part of Table 4 demonstrates the ablation results of the pixel-wise group correlation aggregation referred to Eq. (6), which is the key of FCP, as well as the comparison with other alternative foreground detection approaches. Using average pooling on pixel dimension of the pixel-wise group correlation tends to introduce more background noisy, leading to worse performance. We also compare our FCP with CAM-based and well-designed salient object detection approaches. Since the CAM-based methods are heavily relied on the extra classes information, such as class-wise gradients [24] or activation values [31], it lacks the ability of novel classes detection. Similar deficiency also lies in other well-designed salient detection methods, e.g., PAGENet [33] and MINet [21], which only consider the interaction within specific classes and lose the generality of foreground detection. The FCP pays more attention to the robust and universal feature patterns with abundant pseudo episode, thus is more easy to generalize to novel targets.", + "bbox": [ + 75, + 319, + 472, + 622 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conditional Bias Based Inference. In our method, the CBBI plays a role in combining the outputs of the PKL module and the FTP module. We also experiment on the way of fusing those outputs in the bottom part of Table 4. When the class-agnostic foreground mask predicted by the FTP module is utilized with unconditional form, the performance gets worse with the interference of background prediction. We also replace the strategy based inference with learnable convolution structure with end-to-end training, the underperform results indicate that introducing parameterized inference module may heavy the optimization of model and even block the learning of other modules.", + "bbox": [ + 75, + 625, + 468, + 806 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Performance distinction between PASCAL-5 $^i$ and COCO-20 $^i$ . We further investigate the improvement gap between PASCAL-5i and COCO-20i referred to Table 1, e.g., $8.05\\%$ v.s. $3.99\\%$ exceed CAPL [28] on mIoU of novel classes. The most obvious difference between these two datasets is that coco-20i contains larger classes set than", + "bbox": [ + 75, + 809, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/81e604c382881bb36882dcb4a4c20465dc305345a8d2dc98b9186f0fa36fd21d.jpg", + "table_caption": [ + "Table 5. Results on the subset of COCO. $a + b/c$ indicates the combination of classes, where $a$ is the number of base classes, $b = 1$ represents the background class and $c$ is the number of novel classes." + ], + "table_footnote": [], + "table_body": "
Methods15+1/530+1/1045+1/1560+1/20
mIoUBmIoUNmIoUBmIoUNmIoUBmIoUNmIoUBmIoUN
Baseline [28]51.1910.0847.748.2241.377.1036.685.84
CAPL [28]63.3916.0857.2213.3950.0810.1644.617.05
Ours66.7023.7659.4818.9152.0114.2746.3611.04
Improvement+3.31+7.76+2.26+5.52+1.92+4.11+1.75+3.99
", + "bbox": [ + 503, + 357, + 898, + 429 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "PASCAL-5 $^i$ . Thus, we design the ablation experiments with gradually enlarging the subset of COCO, which is started from a similar scale with PASCAL-5 $^i$ . As shown in Table 5, we find parallel improvements are raised when the scale and distribution of classes are similar to PASCAL-5 $^i$ , and as the number of classes increasing, the gaps are reduced. Comparable phenomenon also happens on the contrast between the CAPL [28] and baseline, indicating the common issue that the effect of GFSS model may get weakened as the scale of classes set increases.", + "bbox": [ + 496, + 459, + 893, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 631, + 619, + 645 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we have proposed to leverage the prototypical kernel learning and open-set foreground perception for generalized few-shot semantic segmentation. Special to two of major issues existed in current GFSS, i.e., representation division and embedding prejudice. We offer an effective scheme with three components, which are PKL, FCP and CBBI. To maintain the prototypical representation consistency and prevent novel targets from being misclassified as background, the PKL and FCP are proposed to perform adaptive prototypical kernel update and open-set targets detection, respectively. Moreover, the CBBI is designed for the ensemble of the aforementioned two modules and offers the final prediction. Besides, we further extend the GFSS to CIFSS which is more challenging with incremental stream of novel classes. Extensive experiments demonstrate that the proposed method achieves state-of-the-art results.", + "bbox": [ + 496, + 659, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19263", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Donghyeon Baek, Youngmin Oh, and Bumsub Ham. Exploiting a joint embedding space for generalized zero-shot semantic segmentation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 9536-9545, 2021. 6", + "[2] Malik Boudiaf, Hoel Kervadec, Ziko Imtiaz Masud, Pablo Piantanida, Ismail Ben Ayed, and Jose Dolz. Few-shot segmentation without meta-learning: A good transductive inference is all you need? 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2582-2593, 2022. 2" + ], + "bbox": [ + 501, + 92, + 890, + 795 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "19265", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Prototypical Kernel Learning and Open-set Foreground Perception for Generalized Few-shot Semantic Segmentation/ae5d3fad-adfb-4c23-912c-f33a2a374a40_model.json b/2023/Prototypical Kernel Learning and Open-set Foreground Perception for Generalized Few-shot Semantic Segmentation/ae5d3fad-adfb-4c23-912c-f33a2a374a40_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c1e91420d12f54b0420f3162fa777ed352810514 --- /dev/null +++ b/2023/Prototypical Kernel Learning and Open-set Foreground Perception for Generalized Few-shot Semantic Segmentation/ae5d3fad-adfb-4c23-912c-f33a2a374a40_model.json @@ -0,0 +1,2123 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.13, + 0.131, + 0.842, + 0.177 + ], + "angle": 0, + "content": "Prototypical Kernel Learning and Open-set Foreground Perception for Generalized Few-shot Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.305, + 0.204, + 0.665, + 0.222 + ], + "angle": 0, + "content": "Kai Huang, Feigege Wang, Ye Xi, Yutao Gao" + }, + { + "type": "text", + "bbox": [ + 0.425, + 0.223, + 0.546, + 0.24 + ], + "angle": 0, + "content": "Alibaba Group" + }, + { + "type": "text", + "bbox": [ + 0.214, + 0.242, + 0.756, + 0.256 + ], + "angle": 0, + "content": "zhouwan.hk, feigege.wfgg, yx150449, yutao.gao@alibaba-inc.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.326, + 0.474, + 0.719 + ], + "angle": 0, + "content": "Generalized Few-shot Semantic Segmentation (GFSS) extends Few-shot Semantic Segmentation (FSS) to simultaneously segment unseen classes and seen classes during evaluation. Previous works leverage additional branch or prototypical aggregation to eliminate the constrained setting of FSS. However, representation division and embedding prejudice, which heavily results in poor performance of GFSS, have not been synthetical considered. We address the aforementioned problems by jointing the prototypical kernel learning and open-set foreground perception. Specifically, a group of learnable kernels is proposed to perform segmentation with each kernel in charge of a stuff class. Then, we explore to merge the prototypical learning to the update of base-class kernels, which is consistent with the prototype knowledge aggregation of few-shot novel classes. In addition, a foreground contextual perception module cooperating with conditional bias based inference is adopted to perform class-agnostic as well as open-set foreground detection, thus to mitigate the embedding prejudice and prevent novel targets from being misclassified as background. Moreover, we also adjust our method to the Class Incremental Few-shot Semantic Segmentation (CIFSS) which takes the knowledge of novel classes in a incremental stream. Extensive experiments on PASCAL-5\\(^i\\) and COCO-20\\(^i\\) datasets demonstrate that our method performs better than previous state-of-the-art." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.753, + 0.21, + 0.768 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Few-shot semantic segmentation [25, 39, 2, 15] aims to handle the situation of only sparse annotated data available, which perplexes most normal semantic segmentation methods. Inherited from the superiority of few-shot learning, the FSS methods can quickly be expended to unseen domains with only few labeled samples. Typically, most FSS methods are built on episode-based meta-learning [27], each episode data contains a support set and a query set shared" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.293, + 0.91, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.36, + 0.909, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.413, + 0.605, + 0.421 + ], + "angle": 0, + "content": "Novel-class Image" + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.421, + 0.712, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.575, + 0.475, + 0.666, + 0.483 + ], + "angle": 0, + "content": "Representation Division" + }, + { + "type": "image", + "bbox": [ + 0.72, + 0.422, + 0.906, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.771, + 0.475, + 0.851, + 0.484 + ], + "angle": 0, + "content": "Embedding Prejudice" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.487, + 0.895, + 0.571 + ], + "angle": 0, + "content": "Figure 1. Illustration of our motivation. (a) shows the generation of base-class representation vectors, it learns from abundant base-class images. (b) is the process of novel-class prototypes, which are aggregated by the lightweight feature pooling since few samples available. (c) demonstrates the representation division and embedding prejudice problem existed in current GFSS." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.895, + 0.87 + ], + "angle": 0, + "content": "with same classes. In general, the support set consists of few support images with pixel-wise annotations. The models are supported to learn a generic meta-learner with abundant episodic data sampled from the base classes, and adopt to novel classes with the guidance of the support set. However, the majority of current FSS methods can not escape from the limitation of support set, in which specific as well as single novel class annotations are needed corresponding to query images during the inference. Another weakness is that models can only segment the specific novel class of support set while lack the identification of base classes or multi-novel classes. The recent work [15] leverages the prediction of base classes with a base learner, and thus gives a mask region, which instructs the area does not need to be segmented, to guide the recognition of novel concepts. Despite the significant improvement has been made in base classes, the issue of heavily relying on the support samples with the same classes for each query image still exists." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.894, + 0.901 + ], + "angle": 0, + "content": "To this end, Generalized Few-shot Semantic Segmentation (GFSS) was proposed [28] where novel classes are" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19256" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.348 + ], + "angle": 0, + "content": "aforehand registered to the vanilla model learned from the base classes, making it possible to segment the base and novel simultaneously without extra information in the inference phase. The typical similarity metric enables a more flexible way to expand novel classes with few annotated samples above the base classes. It can directly perform the inference the same as normal segmentation models, with no need of the prerequisite which informs the target classes contained in query images. Regardless, there are still two challenges in GFSS as shown in Fig.1(c): 1) The representation division between base-class and novel-class blocks the accurate predictions, where the former are learned from sufficient data and the latter are aggregated from limited samples with feature pooling approaches; 2) the prejudice of feature embedding makes the novel-class pixels have the tendency to be identified as varied background, since the feature extractor is trained in base classes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.473, + 0.635 + ], + "angle": 0, + "content": "In this work, we propose to joint prototypical kernel learning and open-set foreground perception to address the above-mentioned problems. It exploits a base-class kernel update schema by applying the pixel assembled feature of each input image to extra supervise the update of base-class kernels. Apart from the normal update with abundant base-class samples, those kernels are endowed with the ability of prototypical representation by the prototypical kernel update, which is consistent with the knowledge aggregation of novel-class with few labeled data. To mitigate the feature embedding preconception, we leverage the common feature patterns cross multi-class targets by an open-set foreground perception, which serves the purpose to offer the class-agnostic as well as open-set foreground prediction. Finally, a conditional bias based inference is proposed to assemble the class-wise prediction and the binary foreground prediction. Furthermore, we expand our method from the GFSS to class incremental few-shot segmentation which registers novel classes with an incremental stream." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.636, + 0.473, + 0.788 + ], + "angle": 0, + "content": "In summary, our primary contributions can be summarized as: 1) we present a prototypical kernel learning for maintaining the representation consistency between base-class and novel-class by the notion of kernel; 2) we propose to learn the class-agnostic foreground perception cross the multi-class targets to mitigate the feature embedding preconception, and devise a conditional bias based inference for ensemble prediction; 3) extensive experiments on GFSS and CIFSS demonstrate that the proposed method achieves higher performance compared with other approaches." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.8, + 0.22, + 0.815 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Few-shot Segmentation aims to give a dense pixel prediction for the query images with only a few annotated support images available. The most recent methods adopt two-branch paradigm, i.e., a support branch for target classes prototypical representation and a query branch" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.895, + 0.38 + ], + "angle": 0, + "content": "for feature pairs comparison. Typically, the support branch is performed by the mask-involved feature pooling, such as masked average pooling [26], dynamic kernel generation [18]. The query branch tries to strengthen the metric ability between support prototypes and query feature, with directly pixel similarity [5], convolutional correlation [18, 19], attention-based interaction [36, 40] and so on. However, limited by the instance-based feature comparison of query branch, those methods can not handle on the GFSS scene, in which both base classes and novel classes are included to validation. BAM [15] introduces a base learner module for highly reliable base classes segmentation, and further incorporates into the meta prediction with an ensemble module. Nevertheless, it still needs specific support data and only works with single novel class for each query task. CAPL [28] proposes a novel class registration phase to register the novel information to base classifier, making it possible to be qualified for the segmentation of both base and multi-novel classes without additional support samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.383, + 0.895, + 0.626 + ], + "angle": 0, + "content": "Prototypical Learning is meant to excavate or utilize the representative examples directly with the exemplar-driven pattern. Owing to the needs of representation with limited data, the prototypical learning methods have been widely used in many few-shot tasks [27, 14, 5, 41], especially few-shot segmentation [32, 48]. A typical delegate is the prototype-based framework, in which annotated support data is class-wise aggregated as prototypes and then guide the segmentation of query samples. The prototypical learning of FSS can be roughly divided into implicit and explicit. The implicit methods mainly focus on the embedding learning and tend to use the feature pooling approaches, such as masked average pooling [26], attention-based aggregation [36] and kernel generation [18]. While the explicit way is to construct learnable prototypes, so that the labeled instances [48] or meta episode data [37] can react it directly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.897, + 0.902 + ], + "angle": 0, + "content": "Foreground Modeling has gained rapid development with the effectiveness of targets detection. The most representative methods are class activation mapping and its variants [47, 24, 31], which are early used for feature visualization [47] and further as the rough foreground mask to initialize the progressive inception of many weak-supervised approaches [6, 4]. Later, salient detection [23, 46, 33] has been raised for binary segmentation tasks, with the strong ability of flexible saliency perception. The mainstream salient works only consider the intra interaction on each single image separately, which suffer from obscure and coarse results. Co-salient [42, 9] extends the separate mode to co-exploration within the image group, while extra information, e.g., edge [8], class-wise gradient [44], is always needed for discriminative feature learning. In this work, we propose to learn the common foreground patterns cross multi-class group instances, so as to directly promote to the detection of novel targets without class limitation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19257" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.088, + 0.895, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.319, + 0.895, + 0.364 + ], + "angle": 0, + "content": "Figure 2. Overview of training framework. For the upper branch, the learnable base-class kernels are optimized by the Prototypical Kernel Learning (PKL). The down branch, named as Foreground Contextual Perception (FCP), is constructed to learn the open-set foreground detection by leveraging the contextual feature patterns cross multi-class targets. Batch is omitted in PKL for better display." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.385, + 0.17, + 0.4 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.41, + 0.251, + 0.424 + ], + "angle": 0, + "content": "3.1. Task Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.474, + 0.66 + ], + "angle": 0, + "content": "Generalized few-shot segmentation is designed to quickly integrate unseen classes into a segmentation model with only a few annotated data. It aims to actualize segmentation tasks on novel classes with limited labeled samples and base classes with sufficient labeled data simultaneously. GFSS model learns the basal knowledge from the base classes set \\( C_{\\text{base}} \\), and novel classes set \\( C_{\\text{novel}} \\) is registered to this base model with a few labeled data. There are no overlap between the base and novel classes set, i.e., \\( C_{\\text{base}} \\cap C_{\\text{novel}} = \\emptyset \\). In the inference process, the model should be qualified to the segmentation of the union set \\( C_{\\text{base}} \\cup C_{\\text{novel}} \\). Different from the normal FSS which are specific to the modeling of few-shot learner, GFSS is proposed to explore the possibility of empowering the few-shot learning ability to a vanilla segmentation model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.667, + 0.188, + 0.68 + ], + "angle": 0, + "content": "3.2. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.471, + 0.901 + ], + "angle": 0, + "content": "The overall architectures for training and inference are shown in Fig. 2 and Fig. 4, which mainly consists of three components: Prototypical Kernel Learning (PKL), Foreground Contextual Perception (FCP) and Conditional Bias Based Inference (CBBI). The feature of input is respectively fed to two branches. For the upper branch, we employ the PKL to dynamically get the refined base-class kernels specific to the assembled feature of input image, and the class-wise predictions are produced by applying those kernels to the pixel features. For the down branch, the binary foreground prediction is decoded by the FCP which incorporates relevant contextual patterns cross multi-classes. The final prediction masks are obtained by combining the predictions of these two branch with the CBBI." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.385, + 0.827, + 0.403 + ], + "angle": 0, + "content": "3.3. Prototypical Kernel Learning Module" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.892, + 0.499 + ], + "angle": 0, + "content": "Inspired by the dynamic kernel [11, 34, 43] in semantic segmentation, which possess better representation ability than convolution kernels with flexible structures [35] or roles [16], we extend this to GFSS task by adopting prototypical kernel learning to maintain the representation consistency of base-class and novel-class." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.5, + 0.892, + 0.592 + ], + "angle": 0, + "content": "Specifically, \\(N_{b}\\) learnable kernels \\(K_{b} \\in \\mathbb{R}^{N_{b} \\times C}\\) are constructed to represent the knowledge of \\(N_{b}\\) base classes, in which the convolution between these kernels and feature maps is taken on the segmentation basis. Concretely, given the input feature maps \\(\\mathcal{F} \\in \\mathbb{R}^{B \\times C \\times H \\times W}\\) of \\(B\\) input images, the semantic segmentation output is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.603, + 0.892, + 0.621 + ], + "angle": 0, + "content": "\\[\nS = \\operatorname {s o f t m a x} \\left(K _ {b} * \\mathcal {F}\\right), S \\in \\mathbb {R} ^ {B \\times N _ {b} \\times H \\times W}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.634, + 0.892, + 0.679 + ], + "angle": 0, + "content": "where \\(C\\), \\(H\\), and \\(W\\) indicate the number of channels, height, and width of the feature map respectively, and \\(N_{b}\\) is the number of classes in base-class set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.68, + 0.892, + 0.755 + ], + "angle": 0, + "content": "Pixel Feature Assembling. As the segmentation output of each kernel can reflect the class-wise pixel-to-prototype mapping, the pixel feature assembling is performed by aggregating the input feature with the pseudo semantic segmentation masks as:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.76, + 0.892, + 0.803 + ], + "angle": 0, + "content": "\\[\nP _ {m b} = \\sum_ {x} ^ {H} \\sum_ {y} ^ {W} S (x, y) \\cdot \\mathcal {F} (x, y), P _ {m b} \\in \\mathbb {R} ^ {B \\times N _ {b} \\times C}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.856 + ], + "angle": 0, + "content": "The generation of \\( P_{mb} \\) are analogous to the novel-class feature aggregation with few labeled samples, which takes the ability of prototypical representation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Prototypical Kernel Update. Ordinarily, the kernel of base-class learn the general perception from abundant annotated samples, it would be broader and more inclusive" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19258" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.196 + ], + "angle": 0, + "content": "than the novel-class kernels learned from few data, which exists representation division. Those ambiguous instances, e.g., the novel classes samples, are more predisposed to be caught by the base-class kernels. Thus, the prototypical kernel update is proposed to adapt the base-class kernels to few-shot task with extra one-off update specific to each input:" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.197, + 0.47, + 0.213 + ], + "angle": 0, + "content": "\\[\n\\tilde {K} _ {b} = K _ {b} - \\alpha \\nabla_ {K _ {b}} \\mathcal {L} (K _ {b}) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.218, + 0.47, + 0.309 + ], + "angle": 0, + "content": "where \\(\\nabla_{K_b}\\mathcal{L}(K_b) = \\nabla_{K_b}(K_b - P_{mb}^i)^2\\) is the gradient descent of the mean squared error loss between \\(K_{b}\\) and the assembled feature of \\(i\\)-th images \\(P_{mb}^{i}\\), \\(\\alpha\\) is the adaptation learning rate, which denotes as kernel-to-prototype similarity with the restraint of ReLU function that insures constant positive:" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.318, + 0.469, + 0.335 + ], + "angle": 0, + "content": "\\[\n\\alpha = \\operatorname {R e L U} \\left(\\operatorname {c o s i n e} \\left(K _ {b}, P _ {m b} ^ {i}\\right)\\right), \\alpha \\in \\mathbb {R} ^ {1 \\times N _ {b}}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.344, + 0.47, + 0.48 + ], + "angle": 0, + "content": "The adaptation learning rate is designed to adaptive filter out ineffective gradient signals caused by those classes do not exist in this image. Since the classes existed in input image are a subset of base-class set, the pixel feature assembling of those missing classes is invalid and will lead to incorrect kernel update. The adaptation learning rate will decay to near zero to block the ineffective update as the kernel-to-prototype similarities are low. Finally, The predicted segmentation mask is obtained by:" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.487, + 0.469, + 0.511 + ], + "angle": 0, + "content": "\\[\nM (x, y) = \\underset {i} {\\arg \\max } \\tilde {S} ^ {i} (x, y), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.469, + 0.553 + ], + "angle": 0, + "content": "where \\(\\tilde{S}^i (x,y)\\) is the score map between the updated base-class kernels and the feature maps followed by Eq. (1)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.561, + 0.445, + 0.577 + ], + "angle": 0, + "content": "3.4. Foreground Contextual Perception Module" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.47, + 0.87 + ], + "angle": 0, + "content": "The aforementioned PKL module aims to adjust the general base-class kernels to few-shot scenario with assembled prototypical feature, so that the representation divergence between base and novel classes is mitigated. While the perception ability of novel foreground targets remains poor with the limitation of backbone training, where only the base-class data is sufficiently accessible. Inspired by the episode-based paradigm in various few-shot learning [30, 25, 14], which can boost the model to adapt to unknown scenes, we propose a foreground contextual perception module to perform the open-set foreground perception. The batch group of images sampled from the base categories set can be considered as a pseudo episode, in which each batch group is randomly mixed with the samples of different base-class targets. The FCP module aims to mine common foreground patterns cross multi-class samples with abundant pseudo episode, thus possesses the ability of class-agnostic perception and prevents novel targets from being misclassified as background." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Hybrid Pooling. As shown in Fig.3, the feature maps of pseudo episode are first passed by two independent lin" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.09, + 0.91, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.205, + 0.855, + 0.219 + ], + "angle": 0, + "content": "Figure 3. Illustration of the Hybrid Pooling in FCP module." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.252, + 0.892, + 0.283 + ], + "angle": 0, + "content": "ear mappings, and the pixel-wise correlation is calculated within the feature map groups:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.288, + 0.892, + 0.308 + ], + "angle": 0, + "content": "\\[\nA ^ {b} = \\Phi (\\mathcal {F}) ^ {T} \\Theta (\\mathcal {F} _ {b}) \\in \\mathbb {R} ^ {B \\times H W \\times H W}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.315, + 0.892, + 0.542 + ], + "angle": 0, + "content": "where \\(\\Phi\\) and \\(\\Theta\\) represent \\(1\\times 1\\) convolution layers, \\(\\mathcal{F}_b\\) is the \\(b\\)-th feature map, and \\(A^b\\) denotes the pixel-wise correlation between the \\(b\\)-th feature map and whole pseudo episode. The first dimension of \\(A^b\\) indicates all images of pseudo episode, while the second and third dimensions mean the total feature pixels of each image in pseudo episode and the total feature pixels of query. The reshaping and transposing operations of matrix dimension are omitted for the simplification of presentation. A max pooling and average pooling are separately acted on the second and first dimensions to obtain a more representative correlation \\(\\bar{A}\\in \\mathbb{R}^{B\\times H\\times W}\\). It is worth mentioning that performing max pooling on pixel dimension can help to find out discriminative correlation pairs, and average pooling on image dimension is supported to learn the common foreground feature patterns." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.545, + 0.892, + 0.59 + ], + "angle": 0, + "content": "Foreground Correlation Responses. The correlation normalized by a softmax layer is truncated as the correlation mask \\( M_{corr} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.599, + 0.891, + 0.615 + ], + "angle": 0, + "content": "\\[\nM _ {c o r r} (h, w) = \\mathbb {1} (\\bar {A} (h, w) > 0. 5), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.623, + 0.892, + 0.805 + ], + "angle": 0, + "content": "where \\(\\mathbb{1}(*)\\) is the binary indicator that outputs 1 when \\(^*\\) is true 0 otherwise, \\(h\\) and \\(w\\) are the height index and width index with the limitation of \\(H\\) and \\(W\\). Although the correlation mask can embody the most discriminative feature pixel position, the relation response of other positions are discarded with the consideration of computational complexity. A sharp correlation information may carry more hard noisy, which blocks the learning of FCP module. Therefore, the spacial weighted Global Average Pooling (wGAP) [39, 38] of the correlation mask together with the normalized original feature maps is introduced to obtain a more robust correlation prototypes as:" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.811, + 0.892, + 0.849 + ], + "angle": 0, + "content": "\\[\np _ {w G P A} = \\frac {\\sum_ {h , w} \\| \\mathcal {F} (h , w) \\| _ {2} M _ {c o r r} (h , w)}{\\sum_ {h , w} M _ {c o r r} (h , w)} \\in \\mathbb {R} ^ {B \\times C}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\( \\| * \\|_2 \\) is the L2 normalization. The correlation prototypes reflect the positive relations between the pixel and whole image pixels within the pseudo episode. The refined" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19259" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.123 + ], + "angle": 0, + "content": "correlation responses can be obtained by applying the correlation prototypes to the original feature maps as:" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.129, + 0.47, + 0.171 + ], + "angle": 0, + "content": "\\[\n\\mathcal {R} (h, w) = \\frac {1}{B} \\sum_ {i = 1} ^ {B} p _ {w G P A} \\| \\mathcal {F} (h, w) \\| _ {2}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.178, + 0.469, + 0.253 + ], + "angle": 0, + "content": "Compared to the pixel-wise correlation referred to Eq. (6), the refined correlation responses are more robust with fewer sharp noises, as well as more accurate foreground perception. The final binary foreground masks are predicted by decoding the residual features:" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.261, + 0.469, + 0.278 + ], + "angle": 0, + "content": "\\[\nM _ {f} = \\mathbb {D} (\\mathcal {F} + \\mathcal {F} \\times \\mathcal {R}), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.286, + 0.469, + 0.316 + ], + "angle": 0, + "content": "where \\(\\mathbb{D}\\) represents a correlation decoder built with the four cascaded convolutional layers." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.33, + 0.462, + 0.347 + ], + "angle": 0, + "content": "3.5. Training Loss and Novel Classes Registration" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.355, + 0.469, + 0.415 + ], + "angle": 0, + "content": "Training Loss. The loss for training our model consists of two parts corresponding to the PKL module and FCP module respectively. The loss function for PKL module is illustrated as:" + }, + { + "type": "equation", + "bbox": [ + 0.108, + 0.42, + 0.469, + 0.458 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c e} = \\frac {1}{H W} \\sum_ {x, y} \\sum_ {p ^ {i} \\in P _ {t s}} \\mathbb {1} [ M ^ {x, y} = i ] \\log \\hat {S} _ {c} ^ {x, y}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.466, + 0.469, + 0.497 + ], + "angle": 0, + "content": "where \\(\\mathbb{1}(*)\\) is the binary indicator same as Eq. (7). We adopt the IoU loss [23] to train the FCP module as:" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.504, + 0.469, + 0.545 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i o u} = \\frac {1}{B} \\sum_ {b = 1} ^ {B} \\left(1 - \\frac {\\hat {Y} \\cap Y}{\\hat {Y} \\cup Y}\\right), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.554, + 0.468, + 0.585 + ], + "angle": 0, + "content": "where \\(\\hat{Y}\\) is the binary predictions and \\(Y\\) is the ground truth. Finally, the total end-to-end loss over the batch is:" + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.593, + 0.469, + 0.625 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\lambda \\sum_ {b \\in B} \\mathcal {L} _ {c e} ^ {b} + (1 - \\lambda) \\mathcal {L} _ {i o u}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.632, + 0.397, + 0.646 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is utilized to balance the loss functions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.649, + 0.469, + 0.754 + ], + "angle": 0, + "content": "Novel Classes Registration. After training, the novel-class kernels \\( K_{n} \\in \\mathbb{R}^{N_{n} \\times C} \\) can be obtained by passing the support images of novel classes to the frozen feature extraction, following with the class-wise averaged wGAP referred to Eq. (8). Then, the novel classes knowledge is registered to the model by concatenating the novel-class kernels to the updated base-class kernels:" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.761, + 0.469, + 0.78 + ], + "angle": 0, + "content": "\\[\nK _ {w} = \\operatorname {C o n c a t} \\left(\\left[ K _ {b}, K _ {n} \\right]\\right), K _ {w} \\in \\mathbb {R} ^ {\\left(N _ {b} + N _ {n}\\right) \\times C}. \\tag {14}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.802, + 0.37, + 0.817 + ], + "angle": 0, + "content": "3.6. Conditional Bias Based Inference" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.827, + 0.469, + 0.857 + ], + "angle": 0, + "content": "Given the input test image \\(I\\), the final decision of position \\(\\mathbf{p}\\) is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.865, + 0.469, + 0.905 + ], + "angle": 0, + "content": "\\[\nO _ {I} (\\mathbf {p}) = \\left\\{ \\begin{array}{l l} \\max \\left(c _ {1 \\mathrm {s t}}, c _ {2 \\mathrm {n d}} + b\\right), & O _ {s} (\\mathbf {p}) = = 1 \\\\ c _ {1 \\mathrm {s t}}, & \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {15}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.91, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.204, + 0.892, + 0.233 + ], + "angle": 0, + "content": "Figure 4. Framework of the CBBI. We perform the FAH module with only itself contained in the pseudo episode." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.257, + 0.892, + 0.302 + ], + "angle": 0, + "content": "where \\( c_{1\\mathrm{st}} \\) and \\( c_{2\\mathrm{nd}} \\) are the first and second candidates according to the class-wise similarity, \\( O_s \\) indicates the output of FCP module and \\( b \\) is the constant of bias." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.303, + 0.892, + 0.438 + ], + "angle": 0, + "content": "As shown in Fig. 4, the refined meta specific prototypes are obtained by feeding the feature map of test image together with the class-wise prototypes to the PKL module. With the concerns of consistency and noise accumulation, we only update the base-class prototypes. Then, the class-wise predictions \\( O_{p} \\) are calculated by the cosine similarity between the updated whole-class prototypes and query feature maps. The first and second candidate masks are the value of Top2 maps along with the class dimension of \\( O_{p} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.892, + 0.526 + ], + "angle": 0, + "content": "For the branch of conditional bias generation, the open-set foreground mask \\( O_{s} \\) can be obtained by the FCP module. A pointwise multiplication between it and the second candidate mask is adopted to obtain the conditional bias mask \\( O_{sp}^{2} \\). Then, the second candidate mask is recalculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.527, + 0.891, + 0.547 + ], + "angle": 0, + "content": "\\[\n\\hat {O} _ {p} ^ {2} (\\mathbf {p}) = O _ {p} ^ {2} (\\mathbf {p}) + b \\cdot O _ {s p} ^ {2} (\\mathbf {p}). \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.551, + 0.892, + 0.581 + ], + "angle": 0, + "content": "The final output can be obtained by the maximum argument between the first and second candidate masks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.591, + 0.81, + 0.606 + ], + "angle": 0, + "content": "3.7. Extension to Class Incremental FSS" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Following the incremental learning in other few-shot tasks [10, 22], we give the definition of class incremental setting in few-shot segmentation. The Class Incremental Few-shot Semantic Segmentation (CIFSS) shares the same classes set with GFSS, in which there are base classes set \\( C_{\\text{base}} \\) with adequate data available and novel classes set \\( C_{\\text{novel}} \\) with a small amount of annotated data. Different from the one-off task of novel classes in GFSS, CIFSS focuses on the novel classes in a session stream. The model learns from the base session \\( S_{b} \\) with the base classes and adapts to novel classes with insufficient samples in sequential, i.e., the sequence session \\( \\{S_{n}^{1}, \\dots, S_{n}^{T}\\} \\) with the novel classes. It is critical to mention that we can only access to the data of \\( t \\)-th session when attaching this session, and there is no overlap within these novel sessions. The performance of model with current session \\( S_{n}^{t} \\) is evaluated on the test samples of \\( S_{n}^{t} \\) and the previous sessions \\( \\{S_{n}^{1}, \\dots, S_{n}^{t-1}\\} \\). The GFSS can be viewed as a exception constructed with only base session and one novel session." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19260" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.259 + ], + "angle": 0, + "content": "Owing to the extensible kernel and the mechanism of novel classes registration, the proposed model can be easy expanded to CIFSS. Similar to the training of GFSS, we learn the PKL and FCP module in the base session and all parameters are fixed during the sequence novel sessions. There are a series of novel classes registration processes corresponding to incremental classes learning with serialized novel sessions. To be specific, assume \\( K_w^t \\) is the whole-class kernels of \\( t \\)-th session, the extended kernels of next session \\( K_w^{t+1} \\) is obtained by concatenating the novel session kernels \\( K_n^{t+1} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.096, + 0.266, + 0.47, + 0.287 + ], + "angle": 0, + "content": "\\[\nK _ {w} ^ {t + 1} = \\operatorname {C o n c a t} \\left(\\left[ K _ {w} ^ {t}, K _ {n} ^ {t + 1} \\right]\\right), \\in \\mathbb {R} ^ {\\left(N _ {w} ^ {t} + N _ {n} ^ {t + 1}\\right) \\times C}, \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.292, + 0.471, + 0.368 + ], + "angle": 0, + "content": "where the calculation of \\( K_{n}^{t + 1} \\) is the same with novel classes registration of GFSS referred to 3.5. In the inference process, only the kernels of base session are passed to the PKL module, and all the kernels of few-shot sessions are treated as a novel whole in the CBBI." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.384, + 0.21, + 0.401 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.409, + 0.295, + 0.425 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.473, + 0.809 + ], + "angle": 0, + "content": "Dataset. Following [28], we evaluate the proposed method on two public datasets, i.e., PASCAL- \\(5^{i}\\) and COCO- \\(20^{i}\\). PASCAL- \\(5^{i}\\) is modified from PASCAL VOC [7] with extra mask annotations from Semantic Boundaries Dataset (SBD) [12] dataset, it has 20 object classes and one background class. COCO- \\(20^{i}\\) consists of MS COCO [17] with 80 object classes and one background class for segmentation. In terms of GFSS, all the object classes are evenly divided into four folds: \\(\\{5^{i}, i \\in \\{0,1,2,3\\}\\}\\) for PASCAL- \\(5^{i}\\) and \\(\\{20^{i}, i \\in \\{0,1,2,3\\}\\}\\) for COCO- \\(20^{i}\\). The rest object classes as well as background are treated as base classes, where the object classes of specific fold are conducted as novel classes. Models are directly evaluated on the validation set with both base and novel classes simultaneously. In terms of CIFSS, it shares the same fold division with GFSS. The object classes of specific fold are evenly divided into five novel sessions, while the rest object classes and the background class are included into the base session. On PASCAL- \\(5^{i}\\), there are 16 object classes in base session and 1 novel object class for each incremental session. As for COCO- \\(20^{i}\\), the number of object classes in base session is 61 and novel object classes in each incremental session is 5. We evaluate the CIFSS models on the classes belonging to base session, current and previous incremental novel sessions with the validation set." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Evaluation metrics. Similar to [28], we use mean Intersection over Union (\\(mIoU\\)) for base classes as well as base session \\(mIoU_{\\mathcal{B}}\\) and novel classes as well as incremental novel sessions \\(mIoU_{\\mathcal{N}}\\). As for GFSS setting, we also provide the overall \\(mIoU\\) with all classes denoted by \\(mIoU_{\\mathcal{O}}\\). Since the base classes are the vast majority, the arithmetic" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.09, + 0.892, + 0.117 + ], + "angle": 0, + "content": "Table 1. Quantitative results with GFSS setting on PASCAL-5\\(^i\\) and COCO-20\\(^i\\). Best-performing results are highlighted in bold." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.117, + 0.908, + 0.306 + ], + "angle": 0, + "content": "
Methods1-shot5-shot
mIoU_BmIoU_NmIoU_OhIoUmIoU_BmIoU_NmIoU_OhIoU
PASCAL-5^i
CANet [39]8.732.427.233.799.051.527.262.60
PFENet [29]8.322.676.974.048.831.897.183.11
SCL [38]8.882.447.353.839.111.837.383.05
PANet [32]31.8811.2526.9716.6332.9515.2528.7420.85
BAM [15]64.6517.0653.3227.0065.2819.9954.5030.61
CAPL [28]65.4818.8554.3829.2766.1422.4155.7231.96
Ours68.8426.9058.8637.8369.2234.4061.1845.42
COCO-20^i
Baseline [28]36.685.8429.0610.0136.917.2629.5912.13
BAM [15]44.086.7434.8611.6946.1011.2137.4918.03
CAPL [28]44.617.0535.4612.1845.2411.0536.8017.76
Ours46.3611.0437.7117.8346.7714.9138.9022.61
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.333, + 0.892, + 0.379 + ], + "angle": 0, + "content": "mean might be dominated by \\(m\\mathrm{IoU}_{\\mathcal{B}}\\) [1]. We adopt the harmonic mean \\(h\\mathrm{IoU}\\) of \\(m\\mathrm{IoU}_{\\mathcal{B}}\\) and \\(m\\mathrm{IoU}_{\\mathcal{N}}\\) which can emphasize the impact of novel classes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.379, + 0.893, + 0.562 + ], + "angle": 0, + "content": "Training details. For fair comparison, the PSPNet [45] with RestNet50 [13] is adopted as our feature extractor, which is the same as most FSS and GFSS methods, and we train our model for 50 epochs both on PASCAL- \\(5^{i}\\) and COCO- \\(20^{i}\\). The model is optimized by the SGD with an initial learning rate of 2.5e-3, where momentum is 0.9 and the weight decay is set to 1e-4. All images together with the masks are all resized to \\(473 \\times 473\\) for training and tested with their original sizes. The \\(\\lambda\\) of loss function is set to 0.6 and the bias value \\(b\\) of CBBI is 0.5. We obtain the specific split results by averaging over five different random seeds, and the final reported results are averaged with all splits." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.574, + 0.64, + 0.59 + ], + "angle": 0, + "content": "4.2. Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.895, + 0.809 + ], + "angle": 0, + "content": "GFSS Setting. Table 1 shows the 1-shot and 5-shot quantitative results of different methods on PASCAL- \\(5^{i}\\) and \\(\\mathrm{COCO - }20^{i}\\). It can be found that the proposed method shows substantial gains compared with the advanced approaches and achieves the state-of-the-art performance of all GFSS settings and datasets. As for the overall mIoU on PASCAL- \\(5^{i}\\), the proposed method exceeds the CAPL [28] by \\(4.48\\%\\) and \\(5.46\\%\\) for 1-shot setting and 5-shot setting respectively. With the significant improvement on novel classes, our method surpasses the CAPL [28] by \\(8.56\\%\\) and \\(13.46\\%\\) hIoU, demonstrating the superiority of the proposed method. Meanwhile, better performance on novel classes can also weaken the confusion between base classes and novel classes and improve the mIoU\\(_{\\mathcal{B}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.894, + 0.902 + ], + "angle": 0, + "content": "CIFSS Setting. We compare our method with the following modified approaches as: 1) the relevant incremental few-shot learning methods, such as PIFS [3] and iFS-RCNN [20]; 2) the current FSS and GFSS methods, i.e., PFENet [29], BAM [15] and CAPL [28]. From Table 2, our method shows substantial gains compared with existing approaches." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19261" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.09, + 0.892, + 0.117 + ], + "angle": 0, + "content": "Table 2. 1-shot Quantitative results with CIFSS setting on the PASCAL-5\\(^i\\) and COCO-20\\(^i\\). Best-performing results are highlighted in bold. * We use the weights of PSPNet [45] backbone pretrained on base classes as the same as the BAM [15]." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.117, + 0.908, + 0.251 + ], + "angle": 0, + "content": "
DatasetsMethodssession 0session 1session 2session 3session 4session 5
mIoU_BmIoU_BmIoU_NhIoUmIoU_BmIoU_NhIoUmIoU_BmIoU_NhIoUmIoU_BmIoU_NhIoU
PASCAL-5iPFENet* [29]74.4367.2110.3417.9266.6214.1223.3064.9711.1218.9965.7712.0820.4162.5011.0818.82
iFS-RCNN [20]72.4367.7111.0819.0467.1716.6326.6665.5112.9421.6165.4811.7519.9263.3612.3920.73
CAPL [28]74.8670.5117.9428.6069.0721.1132.3467.8918.0328.4967.1419.5730.3165.5319.0829.55
PIFS [3]75.0471.1619.4930.6069.8024.3336.0868.0519.9230.8268.4421.0832.2365.8320.9931.83
Our75.4972.9324.6036.7971.2129.3241.5470.7625.7537.7669.9826.1137.8868.4027.2839.00
COCO-20iPFENet* [29]54.1145.794.337.9144.585.189.2843.073.366.2342.405.649.9641.995.059.02
iFS-RCNN [20]53.4250.435.039.1545.526.6011.5343.865.079.0943.377.1112.2242.836.6311.48
CAPL [28]54.4350.256.6911.8146.677.0412.2345.925.539.8744.087.7713.2143.857.5112.82
BAM [15]54.8052.048.8315.1049.018.9415.1247.037.0312.2345.569.1915.2944.488.8314.73
PIFS [3]54.2751.598.9015.1848.529.5315.9346.966.9412.0945.699.9316.3144.278.8014.68
Our54.3951.7811.4718.5548.3311.2218.0847.289.6115.8946.2511.4718.3345.2410.7417.31
" + }, + { + "type": "table_caption", + "bbox": [ + 0.079, + 0.274, + 0.457, + 0.287 + ], + "angle": 0, + "content": "Table 3. Ablation Study of the effect with different components." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.287, + 0.477, + 0.389 + ], + "angle": 0, + "content": "
PKLFCPCBBI1-shot5-shot
mIoU_BmIoU_NhIoUmIoU_BmIoU_NhIoU
61.2214.5023.4562.0719.7329.94
✓66.8222.9534.1767.7329.1840.79
✓64.4916.7326.5765.2823.3934.44
✓✓67.7323.5834.9868.0531.4543.02
✓✓✓68.8426.9037.8369.2234.4045.42
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.416, + 0.47, + 0.537 + ], + "angle": 0, + "content": "Since majority approaches adopt analogous backbone, we get similar performance in the session 0, which only construct with base classes. The superiority of our method both in base and novel classes continues to emerge as the novel session increased. It partly embodies the significant benefit of our old and novel classes knowledge ensemble mechanism, and partly verifies that the improvement on novel classes can result better performance of base classes as well." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.546, + 0.241, + 0.56 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.84 + ], + "angle": 0, + "content": "Component-wise Effectiveness. We ablate the three major components of proposed method in Table 3: prototypical kernel learning module, foreground contextual perception module and conditional bias based inference. We use the PSPNet [45] modified with learnable kernels as the baseline, in which simple concat operation is conducted between base-class and novel-class kernels. We can see that adding either one of PKL module or FTP module brings substantial improvement compared with the baseline. It means the proposed two modules are indeed beneficial to the novel classes learning in few-shot scenarios, and can mitigate the knowledge division with the extremely class-imbalanced GFSS setting. Moreover, it worth noting that the FTP module explicit plays a vital role in providing the general foreground information, the implicit effect is to boost the feature expression of unknown targets. Fig. 5 shows the qualitative results, which straightforward embodies the effectiveness of proposed method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Prototypical Kernel Learning Module. The motivation of PKL module is to empower the prototypical ability for base-class kernels, so as to maintain the consistency with the registered novel classes, which is also prototypical aggregated" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.274, + 0.895, + 0.356 + ], + "angle": 0, + "content": "Table 4. Ablation performances of the proposed method. fixedALR means using fixed learning rate referred to Eq. (3). \\(\\mathrm{pixel}_{AP\\rightarrow MP}\\) indicates replacing average pooling with max pooling in pixel dimension referred to Eq. (6), and \\(\\mathrm{image}_{MP\\rightarrow AP}\\) is the similar replacement in image dimension. \\(uCBBI\\) and \\(cCBBI\\) denote the unconditional form and learnable convolution form for CBBI." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.356, + 0.897, + 0.591 + ], + "angle": 0, + "content": "
Settings1-shot5-shot
mIoUBmIoUNhIoUmIoUBmIoUNhIoU
w/o PKL64.4916.7326.5765.2823.3934.44
fixedALR66.9020.4831.3667.7226.0837.66
concat+AP65.9119.4130.0066.8625.5136.93
concat+LP66.2721.1932.1167.7126.8938.49
w/o FCP66.8222.9534.1767.7329.1840.79
pixelAP→MP65.9422.3133.3466.4228.9140.28
imageMP→AP65.0521.9432.8166.1828.3039.65
GradCAM [24]66.9423.3634.7468.0829.8041.46
PAGENet [33]67.5724.8036.2868.8331.7043.41
MINet [21]67.8924.9936.5368.6531.4743.16
w/o CBBI67.7323.5834.9868.0531.4543.02
uCBBI66.2920.8331.7067.1325.3836.83
cCBBI65.5318.8629.2966.9023.3934.66
Ours68.8426.9037.8369.2234.4045.42
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.895, + 0.852 + ], + "angle": 0, + "content": "from limited data. We replace the PKL with directly adopting the base-class kernels to the input feature maps as our baseline. As shown in the upside of Table 4, we first construct the ablation studies on the adaptation learning rate, it is clear that the fixed learning rate brings worse results with the distraction of noisy gradient signals during the prototypical kernel update. Meanwhile, we introduce several alternative prototype fusion approaches which are performed by the adaptive pooling (AP) or liner projection (LP) after the channel-wise concat operation between \\( K_{b} \\) and \\( P_{mb} \\). The results show that our method with the proposed prototypical kernel update remarkably outperforms the aforementioned approaches. It can strike a better balance between generality and specificity, especially for novel targets in generalized inference process, thus is more suitable to the GFSS." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Foreground Contextual Perception module. The FCP aims to offer a general foreground detection which helps to the mining of novel targets. Similarly, the model with-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19262" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.895, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.104, + 0.28, + 0.865, + 0.296 + ], + "angle": 0, + "content": "Figure 5. Qualitative results of our method, ablation of each components, BAM [15] and CAPL [28] on PASCAL- \\(5^{i}\\) benchmark." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.473, + 0.623 + ], + "angle": 0, + "content": "out FCP is conducted as the baseline, as well as replacing the CBBI with normal inference. The middle part of Table 4 demonstrates the ablation results of the pixel-wise group correlation aggregation referred to Eq. (6), which is the key of FCP, as well as the comparison with other alternative foreground detection approaches. Using average pooling on pixel dimension of the pixel-wise group correlation tends to introduce more background noisy, leading to worse performance. We also compare our FCP with CAM-based and well-designed salient object detection approaches. Since the CAM-based methods are heavily relied on the extra classes information, such as class-wise gradients [24] or activation values [31], it lacks the ability of novel classes detection. Similar deficiency also lies in other well-designed salient detection methods, e.g., PAGENet [33] and MINet [21], which only consider the interaction within specific classes and lose the generality of foreground detection. The FCP pays more attention to the robust and universal feature patterns with abundant pseudo episode, thus is more easy to generalize to novel targets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.47, + 0.807 + ], + "angle": 0, + "content": "Conditional Bias Based Inference. In our method, the CBBI plays a role in combining the outputs of the PKL module and the FTP module. We also experiment on the way of fusing those outputs in the bottom part of Table 4. When the class-agnostic foreground mask predicted by the FTP module is utilized with unconditional form, the performance gets worse with the interference of background prediction. We also replace the strategy based inference with learnable convolution structure with end-to-end training, the underperform results indicate that introducing parameterized inference module may heavy the optimization of model and even block the learning of other modules." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Performance distinction between PASCAL-5\\(^i\\) and COCO-20\\(^i\\). We further investigate the improvement gap between PASCAL-5i and COCO-20i referred to Table 1, e.g., \\(8.05\\%\\) v.s. \\(3.99\\%\\) exceed CAPL [28] on mIoU of novel classes. The most obvious difference between these two datasets is that coco-20i contains larger classes set than" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.316, + 0.896, + 0.357 + ], + "angle": 0, + "content": "Table 5. Results on the subset of COCO. \\( a + b/c \\) indicates the combination of classes, where \\( a \\) is the number of base classes, \\( b = 1 \\) represents the background class and \\( c \\) is the number of novel classes." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.358, + 0.9, + 0.43 + ], + "angle": 0, + "content": "
Methods15+1/530+1/1045+1/1560+1/20
mIoUBmIoUNmIoUBmIoUNmIoUBmIoUNmIoUBmIoUN
Baseline [28]51.1910.0847.748.2241.377.1036.685.84
CAPL [28]63.3916.0857.2213.3950.0810.1644.617.05
Ours66.7023.7659.4818.9152.0114.2746.3611.04
Improvement+3.31+7.76+2.26+5.52+1.92+4.11+1.75+3.99
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.895, + 0.611 + ], + "angle": 0, + "content": "PASCAL-5\\(^i\\). Thus, we design the ablation experiments with gradually enlarging the subset of COCO, which is started from a similar scale with PASCAL-5\\(^i\\). As shown in Table 5, we find parallel improvements are raised when the scale and distribution of classes are similar to PASCAL-5\\(^i\\), and as the number of classes increasing, the gaps are reduced. Comparable phenomenon also happens on the contrast between the CAPL [28] and baseline, indicating the common issue that the effect of GFSS model may get weakened as the scale of classes set increases." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.632, + 0.62, + 0.646 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In this work, we have proposed to leverage the prototypical kernel learning and open-set foreground perception for generalized few-shot semantic segmentation. Special to two of major issues existed in current GFSS, i.e., representation division and embedding prejudice. We offer an effective scheme with three components, which are PKL, FCP and CBBI. To maintain the prototypical representation consistency and prevent novel targets from being misclassified as background, the PKL and FCP are proposed to perform adaptive prototypical kernel update and open-set targets detection, respectively. Moreover, the CBBI is designed for the ensemble of the aforementioned two modules and offers the final prediction. Besides, we further extend the GFSS to CIFSS which is more challenging with incremental stream of novel classes. Extensive experiments demonstrate that the proposed method achieves state-of-the-art results." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19263" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Donghyeon Baek, Youngmin Oh, and Bumsub Ham. Exploiting a joint embedding space for generalized zero-shot semantic segmentation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 9536-9545, 2021. 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.187, + 0.472, + 0.27 + ], + "angle": 0, + "content": "[2] Malik Boudiaf, Hoel Kervadec, Ziko Imtiaz Masud, Pablo Piantanida, Ismail Ben Ayed, and Jose Dolz. Few-shot segmentation without meta-learning: A good transductive inference is all you need? 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Previous works leverage additional branch or prototypical aggregation to eliminate the constrained setting of FSS. However, representation division and embedding prejudice, which heavily results in poor performance of GFSS, have not been synthetical considered. We address the aforementioned problems by jointing the prototypical kernel learning and open-set foreground perception. Specifically, a group of learnable kernels is proposed to perform segmentation with each kernel in charge of a stuff class. Then, we explore to merge the prototypical learning to the update of base-class kernels, which is consistent with the prototype knowledge aggregation of few-shot novel classes. In addition, a foreground contextual perception module cooperating with conditional bias based inference is adopted to perform class-agnostic as well as open-set foreground detection, thus to mitigate the embedding prejudice and prevent novel targets from being misclassified as background. Moreover, we also adjust our method to the Class Incremental Few-shot Semantic Segmentation (CIFSS) which takes the knowledge of novel classes in a incremental stream. Extensive experiments on PASCAL-5 $^i$ and COCO-20 $^i$ datasets demonstrate that our method performs better than previous state-of-the-art. + +# 1. Introduction + +Few-shot semantic segmentation [25, 39, 2, 15] aims to handle the situation of only sparse annotated data available, which perplexes most normal semantic segmentation methods. Inherited from the superiority of few-shot learning, the FSS methods can quickly be expended to unseen domains with only few labeled samples. Typically, most FSS methods are built on episode-based meta-learning [27], each episode data contains a support set and a query set shared + +![](images/d8d2c856a81604d88e674062da6ed4677eaaaf048ef227018146fd7b87c8e931.jpg) + +![](images/2c2d6ff724bb91cae821e521e0145d452b6880bfc538829622d91b04f51c5a6c.jpg) +Novel-class Image + +![](images/270f84ab681739917af3e31302fd6ef7e7a6e3653f80d8fd49a55a935598434d.jpg) +Representation Division +Figure 1. Illustration of our motivation. (a) shows the generation of base-class representation vectors, it learns from abundant base-class images. (b) is the process of novel-class prototypes, which are aggregated by the lightweight feature pooling since few samples available. (c) demonstrates the representation division and embedding prejudice problem existed in current GFSS. + +![](images/483a04c09be2ccf71bb9c9d7aeb5b06049491705e27831bf65c986dbbfd76190.jpg) +Embedding Prejudice + +with same classes. In general, the support set consists of few support images with pixel-wise annotations. The models are supported to learn a generic meta-learner with abundant episodic data sampled from the base classes, and adopt to novel classes with the guidance of the support set. However, the majority of current FSS methods can not escape from the limitation of support set, in which specific as well as single novel class annotations are needed corresponding to query images during the inference. Another weakness is that models can only segment the specific novel class of support set while lack the identification of base classes or multi-novel classes. The recent work [15] leverages the prediction of base classes with a base learner, and thus gives a mask region, which instructs the area does not need to be segmented, to guide the recognition of novel concepts. Despite the significant improvement has been made in base classes, the issue of heavily relying on the support samples with the same classes for each query image still exists. + +To this end, Generalized Few-shot Semantic Segmentation (GFSS) was proposed [28] where novel classes are + +aforehand registered to the vanilla model learned from the base classes, making it possible to segment the base and novel simultaneously without extra information in the inference phase. The typical similarity metric enables a more flexible way to expand novel classes with few annotated samples above the base classes. It can directly perform the inference the same as normal segmentation models, with no need of the prerequisite which informs the target classes contained in query images. Regardless, there are still two challenges in GFSS as shown in Fig.1(c): 1) The representation division between base-class and novel-class blocks the accurate predictions, where the former are learned from sufficient data and the latter are aggregated from limited samples with feature pooling approaches; 2) the prejudice of feature embedding makes the novel-class pixels have the tendency to be identified as varied background, since the feature extractor is trained in base classes. + +In this work, we propose to joint prototypical kernel learning and open-set foreground perception to address the above-mentioned problems. It exploits a base-class kernel update schema by applying the pixel assembled feature of each input image to extra supervise the update of base-class kernels. Apart from the normal update with abundant base-class samples, those kernels are endowed with the ability of prototypical representation by the prototypical kernel update, which is consistent with the knowledge aggregation of novel-class with few labeled data. To mitigate the feature embedding preconception, we leverage the common feature patterns cross multi-class targets by an open-set foreground perception, which serves the purpose to offer the class-agnostic as well as open-set foreground prediction. Finally, a conditional bias based inference is proposed to assemble the class-wise prediction and the binary foreground prediction. Furthermore, we expand our method from the GFSS to class incremental few-shot segmentation which registers novel classes with an incremental stream. + +In summary, our primary contributions can be summarized as: 1) we present a prototypical kernel learning for maintaining the representation consistency between base-class and novel-class by the notion of kernel; 2) we propose to learn the class-agnostic foreground perception cross the multi-class targets to mitigate the feature embedding preconception, and devise a conditional bias based inference for ensemble prediction; 3) extensive experiments on GFSS and CIFSS demonstrate that the proposed method achieves higher performance compared with other approaches. + +# 2. Related Work + +Few-shot Segmentation aims to give a dense pixel prediction for the query images with only a few annotated support images available. The most recent methods adopt two-branch paradigm, i.e., a support branch for target classes prototypical representation and a query branch + +for feature pairs comparison. Typically, the support branch is performed by the mask-involved feature pooling, such as masked average pooling [26], dynamic kernel generation [18]. The query branch tries to strengthen the metric ability between support prototypes and query feature, with directly pixel similarity [5], convolutional correlation [18, 19], attention-based interaction [36, 40] and so on. However, limited by the instance-based feature comparison of query branch, those methods can not handle on the GFSS scene, in which both base classes and novel classes are included to validation. BAM [15] introduces a base learner module for highly reliable base classes segmentation, and further incorporates into the meta prediction with an ensemble module. Nevertheless, it still needs specific support data and only works with single novel class for each query task. CAPL [28] proposes a novel class registration phase to register the novel information to base classifier, making it possible to be qualified for the segmentation of both base and multi-novel classes without additional support samples. + +Prototypical Learning is meant to excavate or utilize the representative examples directly with the exemplar-driven pattern. Owing to the needs of representation with limited data, the prototypical learning methods have been widely used in many few-shot tasks [27, 14, 5, 41], especially few-shot segmentation [32, 48]. A typical delegate is the prototype-based framework, in which annotated support data is class-wise aggregated as prototypes and then guide the segmentation of query samples. The prototypical learning of FSS can be roughly divided into implicit and explicit. The implicit methods mainly focus on the embedding learning and tend to use the feature pooling approaches, such as masked average pooling [26], attention-based aggregation [36] and kernel generation [18]. While the explicit way is to construct learnable prototypes, so that the labeled instances [48] or meta episode data [37] can react it directly. + +Foreground Modeling has gained rapid development with the effectiveness of targets detection. The most representative methods are class activation mapping and its variants [47, 24, 31], which are early used for feature visualization [47] and further as the rough foreground mask to initialize the progressive inception of many weak-supervised approaches [6, 4]. Later, salient detection [23, 46, 33] has been raised for binary segmentation tasks, with the strong ability of flexible saliency perception. The mainstream salient works only consider the intra interaction on each single image separately, which suffer from obscure and coarse results. Co-salient [42, 9] extends the separate mode to co-exploration within the image group, while extra information, e.g., edge [8], class-wise gradient [44], is always needed for discriminative feature learning. In this work, we propose to learn the common foreground patterns cross multi-class group instances, so as to directly promote to the detection of novel targets without class limitation. + +![](images/6cb4cdeb58dd09f8703ad8a91ed744248bd4555907975f325fae9cee8bcb6845.jpg) +Figure 2. Overview of training framework. For the upper branch, the learnable base-class kernels are optimized by the Prototypical Kernel Learning (PKL). The down branch, named as Foreground Contextual Perception (FCP), is constructed to learn the open-set foreground detection by leveraging the contextual feature patterns cross multi-class targets. Batch is omitted in PKL for better display. + +# 3. Method + +# 3.1. Task Formulation + +Generalized few-shot segmentation is designed to quickly integrate unseen classes into a segmentation model with only a few annotated data. It aims to actualize segmentation tasks on novel classes with limited labeled samples and base classes with sufficient labeled data simultaneously. GFSS model learns the basal knowledge from the base classes set $C_{\text{base}}$ , and novel classes set $C_{\text{novel}}$ is registered to this base model with a few labeled data. There are no overlap between the base and novel classes set, i.e., $C_{\text{base}} \cap C_{\text{novel}} = \emptyset$ . In the inference process, the model should be qualified to the segmentation of the union set $C_{\text{base}} \cup C_{\text{novel}}$ . Different from the normal FSS which are specific to the modeling of few-shot learner, GFSS is proposed to explore the possibility of empowering the few-shot learning ability to a vanilla segmentation model. + +# 3.2. Overview + +The overall architectures for training and inference are shown in Fig. 2 and Fig. 4, which mainly consists of three components: Prototypical Kernel Learning (PKL), Foreground Contextual Perception (FCP) and Conditional Bias Based Inference (CBBI). The feature of input is respectively fed to two branches. For the upper branch, we employ the PKL to dynamically get the refined base-class kernels specific to the assembled feature of input image, and the class-wise predictions are produced by applying those kernels to the pixel features. For the down branch, the binary foreground prediction is decoded by the FCP which incorporates relevant contextual patterns cross multi-classes. The final prediction masks are obtained by combining the predictions of these two branch with the CBBI. + +# 3.3. Prototypical Kernel Learning Module + +Inspired by the dynamic kernel [11, 34, 43] in semantic segmentation, which possess better representation ability than convolution kernels with flexible structures [35] or roles [16], we extend this to GFSS task by adopting prototypical kernel learning to maintain the representation consistency of base-class and novel-class. + +Specifically, $N_{b}$ learnable kernels $K_{b} \in \mathbb{R}^{N_{b} \times C}$ are constructed to represent the knowledge of $N_{b}$ base classes, in which the convolution between these kernels and feature maps is taken on the segmentation basis. Concretely, given the input feature maps $\mathcal{F} \in \mathbb{R}^{B \times C \times H \times W}$ of $B$ input images, the semantic segmentation output is formulated as: + +$$ +S = \operatorname {s o f t m a x} \left(K _ {b} * \mathcal {F}\right), S \in \mathbb {R} ^ {B \times N _ {b} \times H \times W}, \tag {1} +$$ + +where $C$ , $H$ , and $W$ indicate the number of channels, height, and width of the feature map respectively, and $N_{b}$ is the number of classes in base-class set. + +Pixel Feature Assembling. As the segmentation output of each kernel can reflect the class-wise pixel-to-prototype mapping, the pixel feature assembling is performed by aggregating the input feature with the pseudo semantic segmentation masks as: + +$$ +P _ {m b} = \sum_ {x} ^ {H} \sum_ {y} ^ {W} S (x, y) \cdot \mathcal {F} (x, y), P _ {m b} \in \mathbb {R} ^ {B \times N _ {b} \times C}. \tag {2} +$$ + +The generation of $P_{mb}$ are analogous to the novel-class feature aggregation with few labeled samples, which takes the ability of prototypical representation. + +Prototypical Kernel Update. Ordinarily, the kernel of base-class learn the general perception from abundant annotated samples, it would be broader and more inclusive + +than the novel-class kernels learned from few data, which exists representation division. Those ambiguous instances, e.g., the novel classes samples, are more predisposed to be caught by the base-class kernels. Thus, the prototypical kernel update is proposed to adapt the base-class kernels to few-shot task with extra one-off update specific to each input: + +$$ +\tilde {K} _ {b} = K _ {b} - \alpha \nabla_ {K _ {b}} \mathcal {L} (K _ {b}) \tag {3} +$$ + +where $\nabla_{K_b}\mathcal{L}(K_b) = \nabla_{K_b}(K_b - P_{mb}^i)^2$ is the gradient descent of the mean squared error loss between $K_{b}$ and the assembled feature of $i$ -th images $P_{mb}^{i}$ , $\alpha$ is the adaptation learning rate, which denotes as kernel-to-prototype similarity with the restraint of ReLU function that insures constant positive: + +$$ +\alpha = \operatorname {R e L U} \left(\operatorname {c o s i n e} \left(K _ {b}, P _ {m b} ^ {i}\right)\right), \alpha \in \mathbb {R} ^ {1 \times N _ {b}}. \tag {4} +$$ + +The adaptation learning rate is designed to adaptive filter out ineffective gradient signals caused by those classes do not exist in this image. Since the classes existed in input image are a subset of base-class set, the pixel feature assembling of those missing classes is invalid and will lead to incorrect kernel update. The adaptation learning rate will decay to near zero to block the ineffective update as the kernel-to-prototype similarities are low. Finally, The predicted segmentation mask is obtained by: + +$$ +M (x, y) = \underset {i} {\arg \max } \tilde {S} ^ {i} (x, y), \tag {5} +$$ + +where $\tilde{S}^i (x,y)$ is the score map between the updated base-class kernels and the feature maps followed by Eq. (1). + +# 3.4. Foreground Contextual Perception Module + +The aforementioned PKL module aims to adjust the general base-class kernels to few-shot scenario with assembled prototypical feature, so that the representation divergence between base and novel classes is mitigated. While the perception ability of novel foreground targets remains poor with the limitation of backbone training, where only the base-class data is sufficiently accessible. Inspired by the episode-based paradigm in various few-shot learning [30, 25, 14], which can boost the model to adapt to unknown scenes, we propose a foreground contextual perception module to perform the open-set foreground perception. The batch group of images sampled from the base categories set can be considered as a pseudo episode, in which each batch group is randomly mixed with the samples of different base-class targets. The FCP module aims to mine common foreground patterns cross multi-class samples with abundant pseudo episode, thus possesses the ability of class-agnostic perception and prevents novel targets from being misclassified as background. + +Hybrid Pooling. As shown in Fig.3, the feature maps of pseudo episode are first passed by two independent lin + +![](images/ba728494f7e3a2302a0692410198f78f87a1f707649c8648c3f402270b156ba5.jpg) +Figure 3. Illustration of the Hybrid Pooling in FCP module. + +ear mappings, and the pixel-wise correlation is calculated within the feature map groups: + +$$ +A ^ {b} = \Phi (\mathcal {F}) ^ {T} \Theta (\mathcal {F} _ {b}) \in \mathbb {R} ^ {B \times H W \times H W}, \tag {6} +$$ + +where $\Phi$ and $\Theta$ represent $1\times 1$ convolution layers, $\mathcal{F}_b$ is the $b$ -th feature map, and $A^b$ denotes the pixel-wise correlation between the $b$ -th feature map and whole pseudo episode. The first dimension of $A^b$ indicates all images of pseudo episode, while the second and third dimensions mean the total feature pixels of each image in pseudo episode and the total feature pixels of query. The reshaping and transposing operations of matrix dimension are omitted for the simplification of presentation. A max pooling and average pooling are separately acted on the second and first dimensions to obtain a more representative correlation $\bar{A}\in \mathbb{R}^{B\times H\times W}$ . It is worth mentioning that performing max pooling on pixel dimension can help to find out discriminative correlation pairs, and average pooling on image dimension is supported to learn the common foreground feature patterns. + +Foreground Correlation Responses. The correlation normalized by a softmax layer is truncated as the correlation mask $M_{corr}$ : + +$$ +M _ {c o r r} (h, w) = \mathbb {1} (\bar {A} (h, w) > 0. 5), \tag {7} +$$ + +where $\mathbb{1}(*)$ is the binary indicator that outputs 1 when $^*$ is true 0 otherwise, $h$ and $w$ are the height index and width index with the limitation of $H$ and $W$ . Although the correlation mask can embody the most discriminative feature pixel position, the relation response of other positions are discarded with the consideration of computational complexity. A sharp correlation information may carry more hard noisy, which blocks the learning of FCP module. Therefore, the spacial weighted Global Average Pooling (wGAP) [39, 38] of the correlation mask together with the normalized original feature maps is introduced to obtain a more robust correlation prototypes as: + +$$ +p _ {w G P A} = \frac {\sum_ {h , w} \| \mathcal {F} (h , w) \| _ {2} M _ {c o r r} (h , w)}{\sum_ {h , w} M _ {c o r r} (h , w)} \in \mathbb {R} ^ {B \times C}, \tag {8} +$$ + +where $\| * \|_2$ is the L2 normalization. The correlation prototypes reflect the positive relations between the pixel and whole image pixels within the pseudo episode. The refined + +correlation responses can be obtained by applying the correlation prototypes to the original feature maps as: + +$$ +\mathcal {R} (h, w) = \frac {1}{B} \sum_ {i = 1} ^ {B} p _ {w G P A} \| \mathcal {F} (h, w) \| _ {2}. \tag {9} +$$ + +Compared to the pixel-wise correlation referred to Eq. (6), the refined correlation responses are more robust with fewer sharp noises, as well as more accurate foreground perception. The final binary foreground masks are predicted by decoding the residual features: + +$$ +M _ {f} = \mathbb {D} (\mathcal {F} + \mathcal {F} \times \mathcal {R}), \tag {10} +$$ + +where $\mathbb{D}$ represents a correlation decoder built with the four cascaded convolutional layers. + +# 3.5. Training Loss and Novel Classes Registration + +Training Loss. The loss for training our model consists of two parts corresponding to the PKL module and FCP module respectively. The loss function for PKL module is illustrated as: + +$$ +\mathcal {L} _ {c e} = \frac {1}{H W} \sum_ {x, y} \sum_ {p ^ {i} \in P _ {t s}} \mathbb {1} [ M ^ {x, y} = i ] \log \hat {S} _ {c} ^ {x, y}, \tag {11} +$$ + +where $\mathbb{1}(*)$ is the binary indicator same as Eq. (7). We adopt the IoU loss [23] to train the FCP module as: + +$$ +\mathcal {L} _ {i o u} = \frac {1}{B} \sum_ {b = 1} ^ {B} \left(1 - \frac {\hat {Y} \cap Y}{\hat {Y} \cup Y}\right), \tag {12} +$$ + +where $\hat{Y}$ is the binary predictions and $Y$ is the ground truth. Finally, the total end-to-end loss over the batch is: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \lambda \sum_ {b \in B} \mathcal {L} _ {c e} ^ {b} + (1 - \lambda) \mathcal {L} _ {i o u}, \tag {13} +$$ + +where $\lambda$ is utilized to balance the loss functions. + +Novel Classes Registration. After training, the novel-class kernels $K_{n} \in \mathbb{R}^{N_{n} \times C}$ can be obtained by passing the support images of novel classes to the frozen feature extraction, following with the class-wise averaged wGAP referred to Eq. (8). Then, the novel classes knowledge is registered to the model by concatenating the novel-class kernels to the updated base-class kernels: + +$$ +K _ {w} = \operatorname {C o n c a t} \left(\left[ K _ {b}, K _ {n} \right]\right), K _ {w} \in \mathbb {R} ^ {\left(N _ {b} + N _ {n}\right) \times C}. \tag {14} +$$ + +# 3.6. Conditional Bias Based Inference + +Given the input test image $I$ , the final decision of position $\mathbf{p}$ is defined as follows: + +$$ +O _ {I} (\mathbf {p}) = \left\{ \begin{array}{l l} \max \left(c _ {1 \mathrm {s t}}, c _ {2 \mathrm {n d}} + b\right), & O _ {s} (\mathbf {p}) = = 1 \\ c _ {1 \mathrm {s t}}, & \text {o t h e r w i s e} \end{array} , \right. \tag {15} +$$ + +![](images/fe0383e32c8e6d1bc7e4c9c428e8ae92eacc3f518a408de82a37daa886c69d55.jpg) +Figure 4. Framework of the CBBI. We perform the FAH module with only itself contained in the pseudo episode. + +where $c_{1\mathrm{st}}$ and $c_{2\mathrm{nd}}$ are the first and second candidates according to the class-wise similarity, $O_s$ indicates the output of FCP module and $b$ is the constant of bias. + +As shown in Fig. 4, the refined meta specific prototypes are obtained by feeding the feature map of test image together with the class-wise prototypes to the PKL module. With the concerns of consistency and noise accumulation, we only update the base-class prototypes. Then, the class-wise predictions $O_{p}$ are calculated by the cosine similarity between the updated whole-class prototypes and query feature maps. The first and second candidate masks are the value of Top2 maps along with the class dimension of $O_{p}$ . + +For the branch of conditional bias generation, the open-set foreground mask $O_{s}$ can be obtained by the FCP module. A pointwise multiplication between it and the second candidate mask is adopted to obtain the conditional bias mask $O_{sp}^{2}$ . Then, the second candidate mask is recalculated as: + +$$ +\hat {O} _ {p} ^ {2} (\mathbf {p}) = O _ {p} ^ {2} (\mathbf {p}) + b \cdot O _ {s p} ^ {2} (\mathbf {p}). \tag {16} +$$ + +The final output can be obtained by the maximum argument between the first and second candidate masks. + +# 3.7. Extension to Class Incremental FSS + +Following the incremental learning in other few-shot tasks [10, 22], we give the definition of class incremental setting in few-shot segmentation. The Class Incremental Few-shot Semantic Segmentation (CIFSS) shares the same classes set with GFSS, in which there are base classes set $C_{\text{base}}$ with adequate data available and novel classes set $C_{\text{novel}}$ with a small amount of annotated data. Different from the one-off task of novel classes in GFSS, CIFSS focuses on the novel classes in a session stream. The model learns from the base session $S_{b}$ with the base classes and adapts to novel classes with insufficient samples in sequential, i.e., the sequence session $\{S_{n}^{1}, \dots, S_{n}^{T}\}$ with the novel classes. It is critical to mention that we can only access to the data of $t$ -th session when attaching this session, and there is no overlap within these novel sessions. The performance of model with current session $S_{n}^{t}$ is evaluated on the test samples of $S_{n}^{t}$ and the previous sessions $\{S_{n}^{1}, \dots, S_{n}^{t-1}\}$ . The GFSS can be viewed as a exception constructed with only base session and one novel session. + +Owing to the extensible kernel and the mechanism of novel classes registration, the proposed model can be easy expanded to CIFSS. Similar to the training of GFSS, we learn the PKL and FCP module in the base session and all parameters are fixed during the sequence novel sessions. There are a series of novel classes registration processes corresponding to incremental classes learning with serialized novel sessions. To be specific, assume $K_w^t$ is the whole-class kernels of $t$ -th session, the extended kernels of next session $K_w^{t+1}$ is obtained by concatenating the novel session kernels $K_n^{t+1}$ : + +$$ +K _ {w} ^ {t + 1} = \operatorname {C o n c a t} \left(\left[ K _ {w} ^ {t}, K _ {n} ^ {t + 1} \right]\right), \in \mathbb {R} ^ {\left(N _ {w} ^ {t} + N _ {n} ^ {t + 1}\right) \times C}, \tag {17} +$$ + +where the calculation of $K_{n}^{t + 1}$ is the same with novel classes registration of GFSS referred to 3.5. In the inference process, only the kernels of base session are passed to the PKL module, and all the kernels of few-shot sessions are treated as a novel whole in the CBBI. + +# 4. Experiments + +# 4.1. Implementation Details + +Dataset. Following [28], we evaluate the proposed method on two public datasets, i.e., PASCAL- $5^{i}$ and COCO- $20^{i}$ . PASCAL- $5^{i}$ is modified from PASCAL VOC [7] with extra mask annotations from Semantic Boundaries Dataset (SBD) [12] dataset, it has 20 object classes and one background class. COCO- $20^{i}$ consists of MS COCO [17] with 80 object classes and one background class for segmentation. In terms of GFSS, all the object classes are evenly divided into four folds: $\{5^{i}, i \in \{0,1,2,3\}\}$ for PASCAL- $5^{i}$ and $\{20^{i}, i \in \{0,1,2,3\}\}$ for COCO- $20^{i}$ . The rest object classes as well as background are treated as base classes, where the object classes of specific fold are conducted as novel classes. Models are directly evaluated on the validation set with both base and novel classes simultaneously. In terms of CIFSS, it shares the same fold division with GFSS. The object classes of specific fold are evenly divided into five novel sessions, while the rest object classes and the background class are included into the base session. On PASCAL- $5^{i}$ , there are 16 object classes in base session and 1 novel object class for each incremental session. As for COCO- $20^{i}$ , the number of object classes in base session is 61 and novel object classes in each incremental session is 5. We evaluate the CIFSS models on the classes belonging to base session, current and previous incremental novel sessions with the validation set. + +Evaluation metrics. Similar to [28], we use mean Intersection over Union ( $mIoU$ ) for base classes as well as base session $mIoU_{\mathcal{B}}$ and novel classes as well as incremental novel sessions $mIoU_{\mathcal{N}}$ . As for GFSS setting, we also provide the overall $mIoU$ with all classes denoted by $mIoU_{\mathcal{O}}$ . Since the base classes are the vast majority, the arithmetic + +Table 1. Quantitative results with GFSS setting on PASCAL-5 $^i$ and COCO-20 $^i$ . Best-performing results are highlighted in bold. + +
Methods1-shot5-shot
mIoU_BmIoU_NmIoU_OhIoUmIoU_BmIoU_NmIoU_OhIoU
PASCAL-5^i
CANet [39]8.732.427.233.799.051.527.262.60
PFENet [29]8.322.676.974.048.831.897.183.11
SCL [38]8.882.447.353.839.111.837.383.05
PANet [32]31.8811.2526.9716.6332.9515.2528.7420.85
BAM [15]64.6517.0653.3227.0065.2819.9954.5030.61
CAPL [28]65.4818.8554.3829.2766.1422.4155.7231.96
Ours68.8426.9058.8637.8369.2234.4061.1845.42
COCO-20^i
Baseline [28]36.685.8429.0610.0136.917.2629.5912.13
BAM [15]44.086.7434.8611.6946.1011.2137.4918.03
CAPL [28]44.617.0535.4612.1845.2411.0536.8017.76
Ours46.3611.0437.7117.8346.7714.9138.9022.61
+ +mean might be dominated by $m\mathrm{IoU}_{\mathcal{B}}$ [1]. We adopt the harmonic mean $h\mathrm{IoU}$ of $m\mathrm{IoU}_{\mathcal{B}}$ and $m\mathrm{IoU}_{\mathcal{N}}$ which can emphasize the impact of novel classes. + +Training details. For fair comparison, the PSPNet [45] with RestNet50 [13] is adopted as our feature extractor, which is the same as most FSS and GFSS methods, and we train our model for 50 epochs both on PASCAL- $5^{i}$ and COCO- $20^{i}$ . The model is optimized by the SGD with an initial learning rate of 2.5e-3, where momentum is 0.9 and the weight decay is set to 1e-4. All images together with the masks are all resized to $473 \times 473$ for training and tested with their original sizes. The $\lambda$ of loss function is set to 0.6 and the bias value $b$ of CBBI is 0.5. We obtain the specific split results by averaging over five different random seeds, and the final reported results are averaged with all splits. + +# 4.2. Comparisons + +GFSS Setting. Table 1 shows the 1-shot and 5-shot quantitative results of different methods on PASCAL- $5^{i}$ and $\mathrm{COCO - }20^{i}$ . It can be found that the proposed method shows substantial gains compared with the advanced approaches and achieves the state-of-the-art performance of all GFSS settings and datasets. As for the overall mIoU on PASCAL- $5^{i}$ , the proposed method exceeds the CAPL [28] by $4.48\%$ and $5.46\%$ for 1-shot setting and 5-shot setting respectively. With the significant improvement on novel classes, our method surpasses the CAPL [28] by $8.56\%$ and $13.46\%$ hIoU, demonstrating the superiority of the proposed method. Meanwhile, better performance on novel classes can also weaken the confusion between base classes and novel classes and improve the mIoU $_{\mathcal{B}}$ . + +CIFSS Setting. We compare our method with the following modified approaches as: 1) the relevant incremental few-shot learning methods, such as PIFS [3] and iFS-RCNN [20]; 2) the current FSS and GFSS methods, i.e., PFENet [29], BAM [15] and CAPL [28]. From Table 2, our method shows substantial gains compared with existing approaches. + +Table 2. 1-shot Quantitative results with CIFSS setting on the PASCAL-5 $^i$ and COCO-20 $^i$ . Best-performing results are highlighted in bold. * We use the weights of PSPNet [45] backbone pretrained on base classes as the same as the BAM [15]. + +
DatasetsMethodssession 0session 1session 2session 3session 4session 5
mIoU_BmIoU_BmIoU_NhIoUmIoU_BmIoU_NhIoUmIoU_BmIoU_NhIoUmIoU_BmIoU_NhIoU
PASCAL-5iPFENet* [29]74.4367.2110.3417.9266.6214.1223.3064.9711.1218.9965.7712.0820.4162.5011.0818.82
iFS-RCNN [20]72.4367.7111.0819.0467.1716.6326.6665.5112.9421.6165.4811.7519.9263.3612.3920.73
CAPL [28]74.8670.5117.9428.6069.0721.1132.3467.8918.0328.4967.1419.5730.3165.5319.0829.55
PIFS [3]75.0471.1619.4930.6069.8024.3336.0868.0519.9230.8268.4421.0832.2365.8320.9931.83
Our75.4972.9324.6036.7971.2129.3241.5470.7625.7537.7669.9826.1137.8868.4027.2839.00
COCO-20iPFENet* [29]54.1145.794.337.9144.585.189.2843.073.366.2342.405.649.9641.995.059.02
iFS-RCNN [20]53.4250.435.039.1545.526.6011.5343.865.079.0943.377.1112.2242.836.6311.48
CAPL [28]54.4350.256.6911.8146.677.0412.2345.925.539.8744.087.7713.2143.857.5112.82
BAM [15]54.8052.048.8315.1049.018.9415.1247.037.0312.2345.569.1915.2944.488.8314.73
PIFS [3]54.2751.598.9015.1848.529.5315.9346.966.9412.0945.699.9316.3144.278.8014.68
Our54.3951.7811.4718.5548.3311.2218.0847.289.6115.8946.2511.4718.3345.2410.7417.31
+ +Table 3. Ablation Study of the effect with different components. + +
PKLFCPCBBI1-shot5-shot
mIoU_BmIoU_NhIoUmIoU_BmIoU_NhIoU
61.2214.5023.4562.0719.7329.94
✓66.8222.9534.1767.7329.1840.79
✓64.4916.7326.5765.2823.3934.44
✓✓67.7323.5834.9868.0531.4543.02
✓✓✓68.8426.9037.8369.2234.4045.42
+ +Since majority approaches adopt analogous backbone, we get similar performance in the session 0, which only construct with base classes. The superiority of our method both in base and novel classes continues to emerge as the novel session increased. It partly embodies the significant benefit of our old and novel classes knowledge ensemble mechanism, and partly verifies that the improvement on novel classes can result better performance of base classes as well. + +# 4.3. Ablation Studies + +Component-wise Effectiveness. We ablate the three major components of proposed method in Table 3: prototypical kernel learning module, foreground contextual perception module and conditional bias based inference. We use the PSPNet [45] modified with learnable kernels as the baseline, in which simple concat operation is conducted between base-class and novel-class kernels. We can see that adding either one of PKL module or FTP module brings substantial improvement compared with the baseline. It means the proposed two modules are indeed beneficial to the novel classes learning in few-shot scenarios, and can mitigate the knowledge division with the extremely class-imbalanced GFSS setting. Moreover, it worth noting that the FTP module explicit plays a vital role in providing the general foreground information, the implicit effect is to boost the feature expression of unknown targets. Fig. 5 shows the qualitative results, which straightforward embodies the effectiveness of proposed method. + +Prototypical Kernel Learning Module. The motivation of PKL module is to empower the prototypical ability for base-class kernels, so as to maintain the consistency with the registered novel classes, which is also prototypical aggregated + +Table 4. Ablation performances of the proposed method. fixedALR means using fixed learning rate referred to Eq. (3). $\mathrm{pixel}_{AP\rightarrow MP}$ indicates replacing average pooling with max pooling in pixel dimension referred to Eq. (6), and $\mathrm{image}_{MP\rightarrow AP}$ is the similar replacement in image dimension. $uCBBI$ and $cCBBI$ denote the unconditional form and learnable convolution form for CBBI. + +
Settings1-shot5-shot
mIoUBmIoUNhIoUmIoUBmIoUNhIoU
w/o PKL64.4916.7326.5765.2823.3934.44
fixedALR66.9020.4831.3667.7226.0837.66
concat+AP65.9119.4130.0066.8625.5136.93
concat+LP66.2721.1932.1167.7126.8938.49
w/o FCP66.8222.9534.1767.7329.1840.79
pixelAP→MP65.9422.3133.3466.4228.9140.28
imageMP→AP65.0521.9432.8166.1828.3039.65
GradCAM [24]66.9423.3634.7468.0829.8041.46
PAGENet [33]67.5724.8036.2868.8331.7043.41
MINet [21]67.8924.9936.5368.6531.4743.16
w/o CBBI67.7323.5834.9868.0531.4543.02
uCBBI66.2920.8331.7067.1325.3836.83
cCBBI65.5318.8629.2966.9023.3934.66
Ours68.8426.9037.8369.2234.4045.42
+ +from limited data. We replace the PKL with directly adopting the base-class kernels to the input feature maps as our baseline. As shown in the upside of Table 4, we first construct the ablation studies on the adaptation learning rate, it is clear that the fixed learning rate brings worse results with the distraction of noisy gradient signals during the prototypical kernel update. Meanwhile, we introduce several alternative prototype fusion approaches which are performed by the adaptive pooling (AP) or liner projection (LP) after the channel-wise concat operation between $K_{b}$ and $P_{mb}$ . The results show that our method with the proposed prototypical kernel update remarkably outperforms the aforementioned approaches. It can strike a better balance between generality and specificity, especially for novel targets in generalized inference process, thus is more suitable to the GFSS. + +Foreground Contextual Perception module. The FCP aims to offer a general foreground detection which helps to the mining of novel targets. Similarly, the model with- + +![](images/dd16e4961766a5d942c4b8378dd725c098329bfcb9f11ddca08ed835cd75310d.jpg) +Figure 5. Qualitative results of our method, ablation of each components, BAM [15] and CAPL [28] on PASCAL- $5^{i}$ benchmark. + +out FCP is conducted as the baseline, as well as replacing the CBBI with normal inference. The middle part of Table 4 demonstrates the ablation results of the pixel-wise group correlation aggregation referred to Eq. (6), which is the key of FCP, as well as the comparison with other alternative foreground detection approaches. Using average pooling on pixel dimension of the pixel-wise group correlation tends to introduce more background noisy, leading to worse performance. We also compare our FCP with CAM-based and well-designed salient object detection approaches. Since the CAM-based methods are heavily relied on the extra classes information, such as class-wise gradients [24] or activation values [31], it lacks the ability of novel classes detection. Similar deficiency also lies in other well-designed salient detection methods, e.g., PAGENet [33] and MINet [21], which only consider the interaction within specific classes and lose the generality of foreground detection. The FCP pays more attention to the robust and universal feature patterns with abundant pseudo episode, thus is more easy to generalize to novel targets. + +Conditional Bias Based Inference. In our method, the CBBI plays a role in combining the outputs of the PKL module and the FTP module. We also experiment on the way of fusing those outputs in the bottom part of Table 4. When the class-agnostic foreground mask predicted by the FTP module is utilized with unconditional form, the performance gets worse with the interference of background prediction. We also replace the strategy based inference with learnable convolution structure with end-to-end training, the underperform results indicate that introducing parameterized inference module may heavy the optimization of model and even block the learning of other modules. + +Performance distinction between PASCAL-5 $^i$ and COCO-20 $^i$ . We further investigate the improvement gap between PASCAL-5i and COCO-20i referred to Table 1, e.g., $8.05\%$ v.s. $3.99\%$ exceed CAPL [28] on mIoU of novel classes. The most obvious difference between these two datasets is that coco-20i contains larger classes set than + +Table 5. Results on the subset of COCO. $a + b/c$ indicates the combination of classes, where $a$ is the number of base classes, $b = 1$ represents the background class and $c$ is the number of novel classes. + +
Methods15+1/530+1/1045+1/1560+1/20
mIoUBmIoUNmIoUBmIoUNmIoUBmIoUNmIoUBmIoUN
Baseline [28]51.1910.0847.748.2241.377.1036.685.84
CAPL [28]63.3916.0857.2213.3950.0810.1644.617.05
Ours66.7023.7659.4818.9152.0114.2746.3611.04
Improvement+3.31+7.76+2.26+5.52+1.92+4.11+1.75+3.99
+ +PASCAL-5 $^i$ . Thus, we design the ablation experiments with gradually enlarging the subset of COCO, which is started from a similar scale with PASCAL-5 $^i$ . As shown in Table 5, we find parallel improvements are raised when the scale and distribution of classes are similar to PASCAL-5 $^i$ , and as the number of classes increasing, the gaps are reduced. Comparable phenomenon also happens on the contrast between the CAPL [28] and baseline, indicating the common issue that the effect of GFSS model may get weakened as the scale of classes set increases. + +# 5. Conclusion + +In this work, we have proposed to leverage the prototypical kernel learning and open-set foreground perception for generalized few-shot semantic segmentation. Special to two of major issues existed in current GFSS, i.e., representation division and embedding prejudice. We offer an effective scheme with three components, which are PKL, FCP and CBBI. 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Typically, most FSS methods are built on episode-based meta-learning [27], each episode data contains a support set and a query set shared" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 232, + 556, + 284 + ], + "blocks": [ + { + "bbox": [ + 310, + 232, + 556, + 284 + ], + "lines": [ + { + "bbox": [ + 310, + 232, + 556, + 284 + ], + "spans": [ + { + "bbox": [ + 310, + 232, + 556, + 284 + ], + "type": "image", + "image_path": "d8d2c856a81604d88e674062da6ed4677eaaaf048ef227018146fd7b87c8e931.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 309, + 285, + 556, + 327 + ], + "blocks": [ + { + "bbox": [ + 309, + 285, + 556, + 327 + ], + "lines": [ + { + "bbox": [ + 309, + 285, + 556, + 327 + ], + "spans": [ + { + "bbox": [ + 309, + 285, + 556, + 327 + ], + "type": "image", + "image_path": "2c2d6ff724bb91cae821e521e0145d452b6880bfc538829622d91b04f51c5a6c.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 326, + 327, + 370, + 333 + ], + "lines": [ + { + "bbox": [ + 326, + 327, + 370, + 333 + ], + "spans": [ + { + "bbox": [ + 326, + 327, + 370, + 333 + ], + "type": "text", + "content": "Novel-class Image" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 309, + 333, + 435, + 376 + ], + "blocks": [ + { + "bbox": [ + 309, + 333, + 435, + 376 + ], + "lines": [ + { + "bbox": [ + 309, + 333, + 435, + 376 + ], + "spans": [ + { + "bbox": [ + 309, + 333, + 435, + 376 + ], + "type": "image", + "image_path": "270f84ab681739917af3e31302fd6ef7e7a6e3653f80d8fd49a55a935598434d.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 351, + 376, + 407, + 382 + ], + "lines": [ + { + "bbox": [ + 351, + 376, + 407, + 382 + ], + "spans": [ + { + "bbox": [ + 351, + 376, + 407, + 382 + ], + "type": "text", + "content": "Representation Division" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 385, + 547, + 452 + ], + "lines": [ + { + "bbox": [ + 305, + 385, + 547, + 452 + ], + "spans": [ + { + "bbox": [ + 305, + 385, + 547, + 452 + ], + "type": "text", + "content": "Figure 1. Illustration of our motivation. (a) shows the generation of base-class representation vectors, it learns from abundant base-class images. (b) is the process of novel-class prototypes, which are aggregated by the lightweight feature pooling since few samples available. (c) demonstrates the representation division and embedding prejudice problem existed in current GFSS." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 440, + 334, + 554, + 376 + ], + "blocks": [ + { + "bbox": [ + 440, + 334, + 554, + 376 + ], + "lines": [ + { + "bbox": [ + 440, + 334, + 554, + 376 + ], + "spans": [ + { + "bbox": [ + 440, + 334, + 554, + 376 + ], + "type": "image", + "image_path": "483a04c09be2ccf71bb9c9d7aeb5b06049491705e27831bf65c986dbbfd76190.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 471, + 376, + 520, + 383 + ], + "lines": [ + { + "bbox": [ + 471, + 376, + 520, + 383 + ], + "spans": [ + { + "bbox": [ + 471, + 376, + 520, + 383 + ], + "type": "text", + "content": "Embedding Prejudice" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 473, + 547, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 547, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 547, + 689 + ], + "type": "text", + "content": "with same classes. In general, the support set consists of few support images with pixel-wise annotations. The models are supported to learn a generic meta-learner with abundant episodic data sampled from the base classes, and adopt to novel classes with the guidance of the support set. However, the majority of current FSS methods can not escape from the limitation of support set, in which specific as well as single novel class annotations are needed corresponding to query images during the inference. Another weakness is that models can only segment the specific novel class of support set while lack the identification of base classes or multi-novel classes. The recent work [15] leverages the prediction of base classes with a base learner, and thus gives a mask region, which instructs the area does not need to be segmented, to guide the recognition of novel concepts. Despite the significant improvement has been made in base classes, the issue of heavily relying on the support samples with the same classes for each query image still exists." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "type": "text", + "content": "To this end, Generalized Few-shot Semantic Segmentation (GFSS) was proposed [28] where novel classes are" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19256" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": "aforehand registered to the vanilla model learned from the base classes, making it possible to segment the base and novel simultaneously without extra information in the inference phase. The typical similarity metric enables a more flexible way to expand novel classes with few annotated samples above the base classes. It can directly perform the inference the same as normal segmentation models, with no need of the prerequisite which informs the target classes contained in query images. Regardless, there are still two challenges in GFSS as shown in Fig.1(c): 1) The representation division between base-class and novel-class blocks the accurate predictions, where the former are learned from sufficient data and the latter are aggregated from limited samples with feature pooling approaches; 2) the prejudice of feature embedding makes the novel-class pixels have the tendency to be identified as varied background, since the feature extractor is trained in base classes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 275, + 289, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 289, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 289, + 502 + ], + "type": "text", + "content": "In this work, we propose to joint prototypical kernel learning and open-set foreground perception to address the above-mentioned problems. It exploits a base-class kernel update schema by applying the pixel assembled feature of each input image to extra supervise the update of base-class kernels. Apart from the normal update with abundant base-class samples, those kernels are endowed with the ability of prototypical representation by the prototypical kernel update, which is consistent with the knowledge aggregation of novel-class with few labeled data. To mitigate the feature embedding preconception, we leverage the common feature patterns cross multi-class targets by an open-set foreground perception, which serves the purpose to offer the class-agnostic as well as open-set foreground prediction. Finally, a conditional bias based inference is proposed to assemble the class-wise prediction and the binary foreground prediction. Furthermore, we expand our method from the GFSS to class incremental few-shot segmentation which registers novel classes with an incremental stream." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 503, + 289, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 503, + 289, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 503, + 289, + 624 + ], + "type": "text", + "content": "In summary, our primary contributions can be summarized as: 1) we present a prototypical kernel learning for maintaining the representation consistency between base-class and novel-class by the notion of kernel; 2) we propose to learn the class-agnostic foreground perception cross the multi-class targets to mitigate the feature embedding preconception, and devise a conditional bias based inference for ensemble prediction; 3) extensive experiments on GFSS and CIFSS demonstrate that the proposed method achieves higher performance compared with other approaches." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 633, + 134, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 633, + 134, + 645 + ], + "spans": [ + { + "bbox": [ + 47, + 633, + 134, + 645 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "Few-shot Segmentation aims to give a dense pixel prediction for the query images with only a few annotated support images available. The most recent methods adopt two-branch paradigm, i.e., a support branch for target classes prototypical representation and a query branch" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "content": "for feature pairs comparison. Typically, the support branch is performed by the mask-involved feature pooling, such as masked average pooling [26], dynamic kernel generation [18]. The query branch tries to strengthen the metric ability between support prototypes and query feature, with directly pixel similarity [5], convolutional correlation [18, 19], attention-based interaction [36, 40] and so on. However, limited by the instance-based feature comparison of query branch, those methods can not handle on the GFSS scene, in which both base classes and novel classes are included to validation. BAM [15] introduces a base learner module for highly reliable base classes segmentation, and further incorporates into the meta prediction with an ensemble module. Nevertheless, it still needs specific support data and only works with single novel class for each query task. CAPL [28] proposes a novel class registration phase to register the novel information to base classifier, making it possible to be qualified for the segmentation of both base and multi-novel classes without additional support samples." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 303, + 547, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 303, + 547, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 303, + 547, + 495 + ], + "type": "text", + "content": "Prototypical Learning is meant to excavate or utilize the representative examples directly with the exemplar-driven pattern. Owing to the needs of representation with limited data, the prototypical learning methods have been widely used in many few-shot tasks [27, 14, 5, 41], especially few-shot segmentation [32, 48]. A typical delegate is the prototype-based framework, in which annotated support data is class-wise aggregated as prototypes and then guide the segmentation of query samples. The prototypical learning of FSS can be roughly divided into implicit and explicit. The implicit methods mainly focus on the embedding learning and tend to use the feature pooling approaches, such as masked average pooling [26], attention-based aggregation [36] and kernel generation [18]. While the explicit way is to construct learnable prototypes, so that the labeled instances [48] or meta episode data [37] can react it directly." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "content": "Foreground Modeling has gained rapid development with the effectiveness of targets detection. The most representative methods are class activation mapping and its variants [47, 24, 31], which are early used for feature visualization [47] and further as the rough foreground mask to initialize the progressive inception of many weak-supervised approaches [6, 4]. Later, salient detection [23, 46, 33] has been raised for binary segmentation tasks, with the strong ability of flexible saliency perception. The mainstream salient works only consider the intra interaction on each single image separately, which suffer from obscure and coarse results. Co-salient [42, 9] extends the separate mode to co-exploration within the image group, while extra information, e.g., edge [8], class-wise gradient [44], is always needed for discriminative feature learning. In this work, we propose to learn the common foreground patterns cross multi-class group instances, so as to directly promote to the detection of novel targets without class limitation." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19257" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 69, + 547, + 250 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 547, + 250 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 547, + 250 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 547, + 250 + ], + "type": "image", + "image_path": "6cb4cdeb58dd09f8703ad8a91ed744248bd4555907975f325fae9cee8bcb6845.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 252, + 547, + 288 + ], + "lines": [ + { + "bbox": [ + 46, + 252, + 547, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 547, + 288 + ], + "type": "text", + "content": "Figure 2. Overview of training framework. For the upper branch, the learnable base-class kernels are optimized by the Prototypical Kernel Learning (PKL). The down branch, named as Foreground Contextual Perception (FCP), is constructed to learn the open-set foreground detection by leveraging the contextual feature patterns cross multi-class targets. Batch is omitted in PKL for better display." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 304, + 104, + 316 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 304, + 104, + 316 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 104, + 316 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 324, + 153, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 324, + 153, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 324, + 153, + 335 + ], + "type": "text", + "content": "3.1. Task Formulation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 342, + 290, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 290, + 522 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 290, + 522 + ], + "type": "text", + "content": "Generalized few-shot segmentation is designed to quickly integrate unseen classes into a segmentation model with only a few annotated data. It aims to actualize segmentation tasks on novel classes with limited labeled samples and base classes with sufficient labeled data simultaneously. GFSS model learns the basal knowledge from the base classes set " + }, + { + "bbox": [ + 46, + 342, + 290, + 522 + ], + "type": "inline_equation", + "content": "C_{\\text{base}}" + }, + { + "bbox": [ + 46, + 342, + 290, + 522 + ], + "type": "text", + "content": ", and novel classes set " + }, + { + "bbox": [ + 46, + 342, + 290, + 522 + ], + "type": "inline_equation", + "content": "C_{\\text{novel}}" + }, + { + "bbox": [ + 46, + 342, + 290, + 522 + ], + "type": "text", + "content": " is registered to this base model with a few labeled data. There are no overlap between the base and novel classes set, i.e., " + }, + { + "bbox": [ + 46, + 342, + 290, + 522 + ], + "type": "inline_equation", + "content": "C_{\\text{base}} \\cap C_{\\text{novel}} = \\emptyset" + }, + { + "bbox": [ + 46, + 342, + 290, + 522 + ], + "type": "text", + "content": ". In the inference process, the model should be qualified to the segmentation of the union set " + }, + { + "bbox": [ + 46, + 342, + 290, + 522 + ], + "type": "inline_equation", + "content": "C_{\\text{base}} \\cup C_{\\text{novel}}" + }, + { + "bbox": [ + 46, + 342, + 290, + 522 + ], + "type": "text", + "content": ". Different from the normal FSS which are specific to the modeling of few-shot learner, GFSS is proposed to explore the possibility of empowering the few-shot learning ability to a vanilla segmentation model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 528, + 115, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 528, + 115, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 528, + 115, + 538 + ], + "type": "text", + "content": "3.2. Overview" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "type": "text", + "content": "The overall architectures for training and inference are shown in Fig. 2 and Fig. 4, which mainly consists of three components: Prototypical Kernel Learning (PKL), Foreground Contextual Perception (FCP) and Conditional Bias Based Inference (CBBI). The feature of input is respectively fed to two branches. For the upper branch, we employ the PKL to dynamically get the refined base-class kernels specific to the assembled feature of input image, and the class-wise predictions are produced by applying those kernels to the pixel features. For the down branch, the binary foreground prediction is decoded by the FCP which incorporates relevant contextual patterns cross multi-classes. The final prediction masks are obtained by combining the predictions of these two branch with the CBBI." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 304, + 506, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 304, + 506, + 319 + ], + "spans": [ + { + "bbox": [ + 306, + 304, + 506, + 319 + ], + "type": "text", + "content": "3.3. Prototypical Kernel Learning Module" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 324, + 545, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 545, + 395 + ], + "type": "text", + "content": "Inspired by the dynamic kernel [11, 34, 43] in semantic segmentation, which possess better representation ability than convolution kernels with flexible structures [35] or roles [16], we extend this to GFSS task by adopting prototypical kernel learning to maintain the representation consistency of base-class and novel-class." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 396, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 545, + 468 + ], + "type": "text", + "content": "Specifically, " + }, + { + "bbox": [ + 304, + 396, + 545, + 468 + ], + "type": "inline_equation", + "content": "N_{b}" + }, + { + "bbox": [ + 304, + 396, + 545, + 468 + ], + "type": "text", + "content": " learnable kernels " + }, + { + "bbox": [ + 304, + 396, + 545, + 468 + ], + "type": "inline_equation", + "content": "K_{b} \\in \\mathbb{R}^{N_{b} \\times C}" + }, + { + "bbox": [ + 304, + 396, + 545, + 468 + ], + "type": "text", + "content": " are constructed to represent the knowledge of " + }, + { + "bbox": [ + 304, + 396, + 545, + 468 + ], + "type": "inline_equation", + "content": "N_{b}" + }, + { + "bbox": [ + 304, + 396, + 545, + 468 + ], + "type": "text", + "content": " base classes, in which the convolution between these kernels and feature maps is taken on the segmentation basis. Concretely, given the input feature maps " + }, + { + "bbox": [ + 304, + 396, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\mathcal{F} \\in \\mathbb{R}^{B \\times C \\times H \\times W}" + }, + { + "bbox": [ + 304, + 396, + 545, + 468 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 396, + 545, + 468 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 396, + 545, + 468 + ], + "type": "text", + "content": " input images, the semantic segmentation output is formulated as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 336, + 477, + 545, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 477, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 336, + 477, + 545, + 491 + ], + "type": "interline_equation", + "content": "S = \\operatorname {s o f t m a x} \\left(K _ {b} * \\mathcal {F}\\right), S \\in \\mathbb {R} ^ {B \\times N _ {b} \\times H \\times W}, \\tag {1}", + "image_path": "7b71efa407f163a53e0165e3653b89a6c45a7c853cee3647734937ed893d138c.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 502, + 545, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 545, + 537 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 545, + 537 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 502, + 545, + 537 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 502, + 545, + 537 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 502, + 545, + 537 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 502, + 545, + 537 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 502, + 545, + 537 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 502, + 545, + 537 + ], + "type": "text", + "content": " indicate the number of channels, height, and width of the feature map respectively, and " + }, + { + "bbox": [ + 304, + 502, + 545, + 537 + ], + "type": "inline_equation", + "content": "N_{b}" + }, + { + "bbox": [ + 304, + 502, + 545, + 537 + ], + "type": "text", + "content": " is the number of classes in base-class set." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 538, + 545, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 538, + 545, + 597 + ], + "spans": [ + { + "bbox": [ + 304, + 538, + 545, + 597 + ], + "type": "text", + "content": "Pixel Feature Assembling. As the segmentation output of each kernel can reflect the class-wise pixel-to-prototype mapping, the pixel feature assembling is performed by aggregating the input feature with the pseudo semantic segmentation masks as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 601, + 545, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 601, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 315, + 601, + 545, + 635 + ], + "type": "interline_equation", + "content": "P _ {m b} = \\sum_ {x} ^ {H} \\sum_ {y} ^ {W} S (x, y) \\cdot \\mathcal {F} (x, y), P _ {m b} \\in \\mathbb {R} ^ {B \\times N _ {b} \\times C}. \\tag {2}", + "image_path": "0d6c75d685a3e211974a05bca37217a6a3342bc260a6cd19af649f24925befde.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 641, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 677 + ], + "type": "text", + "content": "The generation of " + }, + { + "bbox": [ + 304, + 641, + 545, + 677 + ], + "type": "inline_equation", + "content": "P_{mb}" + }, + { + "bbox": [ + 304, + 641, + 545, + 677 + ], + "type": "text", + "content": " are analogous to the novel-class feature aggregation with few labeled samples, which takes the ability of prototypical representation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "Prototypical Kernel Update. Ordinarily, the kernel of base-class learn the general perception from abundant annotated samples, it would be broader and more inclusive" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19258" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 155 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 155 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 155 + ], + "type": "text", + "content": "than the novel-class kernels learned from few data, which exists representation division. Those ambiguous instances, e.g., the novel classes samples, are more predisposed to be caught by the base-class kernels. Thus, the prototypical kernel update is proposed to adapt the base-class kernels to few-shot task with extra one-off update specific to each input:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 113, + 156, + 287, + 168 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 156, + 287, + 168 + ], + "spans": [ + { + "bbox": [ + 113, + 156, + 287, + 168 + ], + "type": "interline_equation", + "content": "\\tilde {K} _ {b} = K _ {b} - \\alpha \\nabla_ {K _ {b}} \\mathcal {L} (K _ {b}) \\tag {3}", + "image_path": "d7c309fb1cfaef539149e1de0849d609c0f664283147d65beb5d2d343881d77b.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 172, + 287, + 244 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 172, + 287, + 244 + ], + "spans": [ + { + "bbox": [ + 46, + 172, + 287, + 244 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 172, + 287, + 244 + ], + "type": "inline_equation", + "content": "\\nabla_{K_b}\\mathcal{L}(K_b) = \\nabla_{K_b}(K_b - P_{mb}^i)^2" + }, + { + "bbox": [ + 46, + 172, + 287, + 244 + ], + "type": "text", + "content": " is the gradient descent of the mean squared error loss between " + }, + { + "bbox": [ + 46, + 172, + 287, + 244 + ], + "type": "inline_equation", + "content": "K_{b}" + }, + { + "bbox": [ + 46, + 172, + 287, + 244 + ], + "type": "text", + "content": " and the assembled feature of " + }, + { + "bbox": [ + 46, + 172, + 287, + 244 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 172, + 287, + 244 + ], + "type": "text", + "content": "-th images " + }, + { + "bbox": [ + 46, + 172, + 287, + 244 + ], + "type": "inline_equation", + "content": "P_{mb}^{i}" + }, + { + "bbox": [ + 46, + 172, + 287, + 244 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 172, + 287, + 244 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 172, + 287, + 244 + ], + "type": "text", + "content": " is the adaptation learning rate, which denotes as kernel-to-prototype similarity with the restraint of ReLU function that insures constant positive:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 78, + 251, + 287, + 265 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 251, + 287, + 265 + ], + "spans": [ + { + "bbox": [ + 78, + 251, + 287, + 265 + ], + "type": "interline_equation", + "content": "\\alpha = \\operatorname {R e L U} \\left(\\operatorname {c o s i n e} \\left(K _ {b}, P _ {m b} ^ {i}\\right)\\right), \\alpha \\in \\mathbb {R} ^ {1 \\times N _ {b}}. \\tag {4}", + "image_path": "24ded96dc196a1cd4b01bdae062463cd7b2be7b9f2731c622fbf02149b3c73a6.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 272, + 287, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 272, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 272, + 287, + 380 + ], + "type": "text", + "content": "The adaptation learning rate is designed to adaptive filter out ineffective gradient signals caused by those classes do not exist in this image. Since the classes existed in input image are a subset of base-class set, the pixel feature assembling of those missing classes is invalid and will lead to incorrect kernel update. The adaptation learning rate will decay to near zero to block the ineffective update as the kernel-to-prototype similarities are low. Finally, The predicted segmentation mask is obtained by:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 385, + 287, + 404 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 385, + 287, + 404 + ], + "spans": [ + { + "bbox": [ + 106, + 385, + 287, + 404 + ], + "type": "interline_equation", + "content": "M (x, y) = \\underset {i} {\\arg \\max } \\tilde {S} ^ {i} (x, y), \\tag {5}", + "image_path": "de64ba2e86a299d1ee7840a197840b4fc766be600527859ac099c383eee626a1.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 413, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 437 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 413, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\tilde{S}^i (x,y)" + }, + { + "bbox": [ + 46, + 413, + 287, + 437 + ], + "type": "text", + "content": " is the score map between the updated base-class kernels and the feature maps followed by Eq. (1)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 444, + 272, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 444, + 272, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 444, + 272, + 456 + ], + "type": "text", + "content": "3.4. Foreground Contextual Perception Module" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 462, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 287, + 689 + ], + "type": "text", + "content": "The aforementioned PKL module aims to adjust the general base-class kernels to few-shot scenario with assembled prototypical feature, so that the representation divergence between base and novel classes is mitigated. While the perception ability of novel foreground targets remains poor with the limitation of backbone training, where only the base-class data is sufficiently accessible. Inspired by the episode-based paradigm in various few-shot learning [30, 25, 14], which can boost the model to adapt to unknown scenes, we propose a foreground contextual perception module to perform the open-set foreground perception. The batch group of images sampled from the base categories set can be considered as a pseudo episode, in which each batch group is randomly mixed with the samples of different base-class targets. The FCP module aims to mine common foreground patterns cross multi-class samples with abundant pseudo episode, thus possesses the ability of class-agnostic perception and prevents novel targets from being misclassified as background." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Hybrid Pooling. As shown in Fig.3, the feature maps of pseudo episode are first passed by two independent lin" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 71, + 556, + 160 + ], + "blocks": [ + { + "bbox": [ + 307, + 71, + 556, + 160 + ], + "lines": [ + { + "bbox": [ + 307, + 71, + 556, + 160 + ], + "spans": [ + { + "bbox": [ + 307, + 71, + 556, + 160 + ], + "type": "image", + "image_path": "ba728494f7e3a2302a0692410198f78f87a1f707649c8648c3f402270b156ba5.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 162, + 523, + 173 + ], + "lines": [ + { + "bbox": [ + 306, + 162, + 523, + 173 + ], + "spans": [ + { + "bbox": [ + 306, + 162, + 523, + 173 + ], + "type": "text", + "content": "Figure 3. Illustration of the Hybrid Pooling in FCP module." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 199, + 545, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 199, + 545, + 224 + ], + "spans": [ + { + "bbox": [ + 305, + 199, + 545, + 224 + ], + "type": "text", + "content": "ear mappings, and the pixel-wise correlation is calculated within the feature map groups:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 347, + 228, + 545, + 243 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 228, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 347, + 228, + 545, + 243 + ], + "type": "interline_equation", + "content": "A ^ {b} = \\Phi (\\mathcal {F}) ^ {T} \\Theta (\\mathcal {F} _ {b}) \\in \\mathbb {R} ^ {B \\times H W \\times H W}, \\tag {6}", + "image_path": "214cee1c5fa79ba3d57041f240abd8449d13d70f6bed6e74495ce2259da2a907.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "spans": [ + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "text", + "content": " represent " + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "text", + "content": " convolution layers, " + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_b" + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "text", + "content": "-th feature map, and " + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "inline_equation", + "content": "A^b" + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "text", + "content": " denotes the pixel-wise correlation between the " + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "text", + "content": "-th feature map and whole pseudo episode. The first dimension of " + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "inline_equation", + "content": "A^b" + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "text", + "content": " indicates all images of pseudo episode, while the second and third dimensions mean the total feature pixels of each image in pseudo episode and the total feature pixels of query. The reshaping and transposing operations of matrix dimension are omitted for the simplification of presentation. A max pooling and average pooling are separately acted on the second and first dimensions to obtain a more representative correlation " + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "inline_equation", + "content": "\\bar{A}\\in \\mathbb{R}^{B\\times H\\times W}" + }, + { + "bbox": [ + 304, + 249, + 545, + 429 + ], + "type": "text", + "content": ". It is worth mentioning that performing max pooling on pixel dimension can help to find out discriminative correlation pairs, and average pooling on image dimension is supported to learn the common foreground feature patterns." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 431, + 545, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 431, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 305, + 431, + 545, + 467 + ], + "type": "text", + "content": "Foreground Correlation Responses. The correlation normalized by a softmax layer is truncated as the correlation mask " + }, + { + "bbox": [ + 305, + 431, + 545, + 467 + ], + "type": "inline_equation", + "content": "M_{corr}" + }, + { + "bbox": [ + 305, + 431, + 545, + 467 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 356, + 474, + 545, + 487 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 474, + 545, + 487 + ], + "spans": [ + { + "bbox": [ + 356, + 474, + 545, + 487 + ], + "type": "interline_equation", + "content": "M _ {c o r r} (h, w) = \\mathbb {1} (\\bar {A} (h, w) > 0. 5), \\tag {7}", + "image_path": "96ee2ea12b652a60739fe766ab8ba8107a0adab3424e9053a910266e6aa0f5db.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 493, + 545, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 493, + 545, + 637 + ], + "spans": [ + { + "bbox": [ + 304, + 493, + 545, + 637 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 493, + 545, + 637 + ], + "type": "inline_equation", + "content": "\\mathbb{1}(*)" + }, + { + "bbox": [ + 304, + 493, + 545, + 637 + ], + "type": "text", + "content": " is the binary indicator that outputs 1 when " + }, + { + "bbox": [ + 304, + 493, + 545, + 637 + ], + "type": "inline_equation", + "content": "^*" + }, + { + "bbox": [ + 304, + 493, + 545, + 637 + ], + "type": "text", + "content": " is true 0 otherwise, " + }, + { + "bbox": [ + 304, + 493, + 545, + 637 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 493, + 545, + 637 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 493, + 545, + 637 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 493, + 545, + 637 + ], + "type": "text", + "content": " are the height index and width index with the limitation of " + }, + { + "bbox": [ + 304, + 493, + 545, + 637 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 493, + 545, + 637 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 493, + 545, + 637 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 493, + 545, + 637 + ], + "type": "text", + "content": ". Although the correlation mask can embody the most discriminative feature pixel position, the relation response of other positions are discarded with the consideration of computational complexity. A sharp correlation information may carry more hard noisy, which blocks the learning of FCP module. Therefore, the spacial weighted Global Average Pooling (wGAP) [39, 38] of the correlation mask together with the normalized original feature maps is introduced to obtain a more robust correlation prototypes as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 318, + 642, + 545, + 672 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 642, + 545, + 672 + ], + "spans": [ + { + "bbox": [ + 318, + 642, + 545, + 672 + ], + "type": "interline_equation", + "content": "p _ {w G P A} = \\frac {\\sum_ {h , w} \\| \\mathcal {F} (h , w) \\| _ {2} M _ {c o r r} (h , w)}{\\sum_ {h , w} M _ {c o r r} (h , w)} \\in \\mathbb {R} ^ {B \\times C}, \\tag {8}", + "image_path": "319cd91ac69c596c5933ce65cd36324421cad0ec275b14b68c36367a2ab55a6c.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\| * \\|_2" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": " is the L2 normalization. The correlation prototypes reflect the positive relations between the pixel and whole image pixels within the pseudo episode. The refined" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19259" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "content": "correlation responses can be obtained by applying the correlation prototypes to the original feature maps as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 91, + 102, + 287, + 135 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 102, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 91, + 102, + 287, + 135 + ], + "type": "interline_equation", + "content": "\\mathcal {R} (h, w) = \\frac {1}{B} \\sum_ {i = 1} ^ {B} p _ {w G P A} \\| \\mathcal {F} (h, w) \\| _ {2}. \\tag {9}", + "image_path": "b55a8b54022fbaac2d6fe825c14092a9c9cc85cb087886080b2c81b94b4dd6a4.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 140, + 287, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 140, + 287, + 200 + ], + "spans": [ + { + "bbox": [ + 47, + 140, + 287, + 200 + ], + "type": "text", + "content": "Compared to the pixel-wise correlation referred to Eq. (6), the refined correlation responses are more robust with fewer sharp noises, as well as more accurate foreground perception. The final binary foreground masks are predicted by decoding the residual features:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 118, + 206, + 287, + 220 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 206, + 287, + 220 + ], + "spans": [ + { + "bbox": [ + 118, + 206, + 287, + 220 + ], + "type": "interline_equation", + "content": "M _ {f} = \\mathbb {D} (\\mathcal {F} + \\mathcal {F} \\times \\mathcal {R}), \\tag {10}", + "image_path": "3e993baee19c70c75376889d17230d2257b62a75bbf09ce725d6ba55e09ce843.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 226, + 287, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 226, + 287, + 250 + ], + "spans": [ + { + "bbox": [ + 47, + 226, + 287, + 250 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 226, + 287, + 250 + ], + "type": "inline_equation", + "content": "\\mathbb{D}" + }, + { + "bbox": [ + 47, + 226, + 287, + 250 + ], + "type": "text", + "content": " represents a correlation decoder built with the four cascaded convolutional layers." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 261, + 282, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 261, + 282, + 274 + ], + "spans": [ + { + "bbox": [ + 47, + 261, + 282, + 274 + ], + "type": "text", + "content": "3.5. Training Loss and Novel Classes Registration" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 281, + 287, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 281, + 287, + 328 + ], + "spans": [ + { + "bbox": [ + 47, + 281, + 287, + 328 + ], + "type": "text", + "content": "Training Loss. The loss for training our model consists of two parts corresponding to the PKL module and FCP module respectively. The loss function for PKL module is illustrated as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 66, + 332, + 287, + 362 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 332, + 287, + 362 + ], + "spans": [ + { + "bbox": [ + 66, + 332, + 287, + 362 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c e} = \\frac {1}{H W} \\sum_ {x, y} \\sum_ {p ^ {i} \\in P _ {t s}} \\mathbb {1} [ M ^ {x, y} = i ] \\log \\hat {S} _ {c} ^ {x, y}, \\tag {11}", + "image_path": "8ff66f9ad25a606e8819c762b1307db3d009c5be4b3f1edd02ca84489a62f1c7.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 369, + 287, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 369, + 287, + 393 + ], + "spans": [ + { + "bbox": [ + 47, + 369, + 287, + 393 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 369, + 287, + 393 + ], + "type": "inline_equation", + "content": "\\mathbb{1}(*)" + }, + { + "bbox": [ + 47, + 369, + 287, + 393 + ], + "type": "text", + "content": " is the binary indicator same as Eq. (7). We adopt the IoU loss [23] to train the FCP module as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 108, + 399, + 287, + 431 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 399, + 287, + 431 + ], + "spans": [ + { + "bbox": [ + 108, + 399, + 287, + 431 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i o u} = \\frac {1}{B} \\sum_ {b = 1} ^ {B} \\left(1 - \\frac {\\hat {Y} \\cap Y}{\\hat {Y} \\cup Y}\\right), \\tag {12}", + "image_path": "f39a62499f2513a5eefe332c300280e559c69aabda968381ef6097295accc896.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 438, + 286, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 438, + 286, + 463 + ], + "spans": [ + { + "bbox": [ + 47, + 438, + 286, + 463 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 438, + 286, + 463 + ], + "type": "inline_equation", + "content": "\\hat{Y}" + }, + { + "bbox": [ + 47, + 438, + 286, + 463 + ], + "type": "text", + "content": " is the binary predictions and " + }, + { + "bbox": [ + 47, + 438, + 286, + 463 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 47, + 438, + 286, + 463 + ], + "type": "text", + "content": " is the ground truth. Finally, the total end-to-end loss over the batch is:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 98, + 469, + 287, + 495 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 469, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 98, + 469, + 287, + 495 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\lambda \\sum_ {b \\in B} \\mathcal {L} _ {c e} ^ {b} + (1 - \\lambda) \\mathcal {L} _ {i o u}, \\tag {13}", + "image_path": "d99dbdddad32c88cd235767249aeba03e9badc8f00afaaedd615520133f7e377.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 500, + 242, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 500, + 242, + 511 + ], + "spans": [ + { + "bbox": [ + 47, + 500, + 242, + 511 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 500, + 242, + 511 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 500, + 242, + 511 + ], + "type": "text", + "content": " is utilized to balance the loss functions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 514, + 287, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 287, + 597 + ], + "type": "text", + "content": "Novel Classes Registration. After training, the novel-class kernels " + }, + { + "bbox": [ + 47, + 514, + 287, + 597 + ], + "type": "inline_equation", + "content": "K_{n} \\in \\mathbb{R}^{N_{n} \\times C}" + }, + { + "bbox": [ + 47, + 514, + 287, + 597 + ], + "type": "text", + "content": " can be obtained by passing the support images of novel classes to the frozen feature extraction, following with the class-wise averaged wGAP referred to Eq. (8). Then, the novel classes knowledge is registered to the model by concatenating the novel-class kernels to the updated base-class kernels:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 64, + 602, + 287, + 617 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 602, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 64, + 602, + 287, + 617 + ], + "type": "interline_equation", + "content": "K _ {w} = \\operatorname {C o n c a t} \\left(\\left[ K _ {b}, K _ {n} \\right]\\right), K _ {w} \\in \\mathbb {R} ^ {\\left(N _ {b} + N _ {n}\\right) \\times C}. \\tag {14}", + "image_path": "d88fff2deebca7434e125c01d1f195c9d38487d052b337976381b7e80df11ce0.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 635, + 226, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 226, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 226, + 647 + ], + "type": "text", + "content": "3.6. Conditional Bias Based Inference" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 654, + 287, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 287, + 678 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 287, + 678 + ], + "type": "text", + "content": "Given the input test image " + }, + { + "bbox": [ + 47, + 654, + 287, + 678 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 47, + 654, + 287, + 678 + ], + "type": "text", + "content": ", the final decision of position " + }, + { + "bbox": [ + 47, + 654, + 287, + 678 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 47, + 654, + 287, + 678 + ], + "type": "text", + "content": " is defined as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 60, + 685, + 287, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 685, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 60, + 685, + 287, + 716 + ], + "type": "interline_equation", + "content": "O _ {I} (\\mathbf {p}) = \\left\\{ \\begin{array}{l l} \\max \\left(c _ {1 \\mathrm {s t}}, c _ {2 \\mathrm {n d}} + b\\right), & O _ {s} (\\mathbf {p}) = = 1 \\\\ c _ {1 \\mathrm {s t}}, & \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {15}", + "image_path": "46d0946b0bf7530c947bdd66b4a8c9e1c8771ecd0a2450a7163cc674a9d9c788.jpg" + } + ] + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 556, + 159 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 556, + 159 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 556, + 159 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 556, + 159 + ], + "type": "image", + "image_path": "fe0383e32c8e6d1bc7e4c9c428e8ae92eacc3f518a408de82a37daa886c69d55.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 161, + 545, + 184 + ], + "lines": [ + { + "bbox": [ + 306, + 161, + 545, + 184 + ], + "spans": [ + { + "bbox": [ + 306, + 161, + 545, + 184 + ], + "type": "text", + "content": "Figure 4. Framework of the CBBI. We perform the FAH module with only itself contained in the pseudo episode." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 203, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 203, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 203, + 545, + 239 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 203, + 545, + 239 + ], + "type": "inline_equation", + "content": "c_{1\\mathrm{st}}" + }, + { + "bbox": [ + 304, + 203, + 545, + 239 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 203, + 545, + 239 + ], + "type": "inline_equation", + "content": "c_{2\\mathrm{nd}}" + }, + { + "bbox": [ + 304, + 203, + 545, + 239 + ], + "type": "text", + "content": " are the first and second candidates according to the class-wise similarity, " + }, + { + "bbox": [ + 304, + 203, + 545, + 239 + ], + "type": "inline_equation", + "content": "O_s" + }, + { + "bbox": [ + 304, + 203, + 545, + 239 + ], + "type": "text", + "content": " indicates the output of FCP module and " + }, + { + "bbox": [ + 304, + 203, + 545, + 239 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 203, + 545, + 239 + ], + "type": "text", + "content": " is the constant of bias." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "text", + "content": "As shown in Fig. 4, the refined meta specific prototypes are obtained by feeding the feature map of test image together with the class-wise prototypes to the PKL module. With the concerns of consistency and noise accumulation, we only update the base-class prototypes. Then, the class-wise predictions " + }, + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "inline_equation", + "content": "O_{p}" + }, + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "text", + "content": " are calculated by the cosine similarity between the updated whole-class prototypes and query feature maps. The first and second candidate masks are the value of Top2 maps along with the class dimension of " + }, + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "inline_equation", + "content": "O_{p}" + }, + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 347, + 545, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 545, + 416 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 545, + 416 + ], + "type": "text", + "content": "For the branch of conditional bias generation, the open-set foreground mask " + }, + { + "bbox": [ + 304, + 347, + 545, + 416 + ], + "type": "inline_equation", + "content": "O_{s}" + }, + { + "bbox": [ + 304, + 347, + 545, + 416 + ], + "type": "text", + "content": " can be obtained by the FCP module. A pointwise multiplication between it and the second candidate mask is adopted to obtain the conditional bias mask " + }, + { + "bbox": [ + 304, + 347, + 545, + 416 + ], + "type": "inline_equation", + "content": "O_{sp}^{2}" + }, + { + "bbox": [ + 304, + 347, + 545, + 416 + ], + "type": "text", + "content": ". Then, the second candidate mask is recalculated as:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 362, + 417, + 545, + 433 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 417, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 362, + 417, + 545, + 433 + ], + "type": "interline_equation", + "content": "\\hat {O} _ {p} ^ {2} (\\mathbf {p}) = O _ {p} ^ {2} (\\mathbf {p}) + b \\cdot O _ {s p} ^ {2} (\\mathbf {p}). \\tag {16}", + "image_path": "901e06ee7f837931fe9a22975d2fbe99c8f7faa3703fb0783a0853e0afb90f34.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 436, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 436, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 436, + 545, + 460 + ], + "type": "text", + "content": "The final output can be obtained by the maximum argument between the first and second candidate masks." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 468, + 495, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 468, + 495, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 468, + 495, + 479 + ], + "type": "text", + "content": "3.7. Extension to Class Incremental FSS" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "content": "Following the incremental learning in other few-shot tasks [10, 22], we give the definition of class incremental setting in few-shot segmentation. The Class Incremental Few-shot Semantic Segmentation (CIFSS) shares the same classes set with GFSS, in which there are base classes set " + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "inline_equation", + "content": "C_{\\text{base}}" + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "content": " with adequate data available and novel classes set " + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "inline_equation", + "content": "C_{\\text{novel}}" + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "content": " with a small amount of annotated data. Different from the one-off task of novel classes in GFSS, CIFSS focuses on the novel classes in a session stream. The model learns from the base session " + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "inline_equation", + "content": "S_{b}" + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "content": " with the base classes and adapts to novel classes with insufficient samples in sequential, i.e., the sequence session " + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\{S_{n}^{1}, \\dots, S_{n}^{T}\\}" + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "content": " with the novel classes. It is critical to mention that we can only access to the data of " + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "content": "-th session when attaching this session, and there is no overlap within these novel sessions. The performance of model with current session " + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "inline_equation", + "content": "S_{n}^{t}" + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "content": " is evaluated on the test samples of " + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "inline_equation", + "content": "S_{n}^{t}" + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "content": " and the previous sessions " + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\{S_{n}^{1}, \\dots, S_{n}^{t-1}\\}" + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "content": ". The GFSS can be viewed as a exception constructed with only base session and one novel session." + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19260" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "text", + "content": "Owing to the extensible kernel and the mechanism of novel classes registration, the proposed model can be easy expanded to CIFSS. Similar to the training of GFSS, we learn the PKL and FCP module in the base session and all parameters are fixed during the sequence novel sessions. There are a series of novel classes registration processes corresponding to incremental classes learning with serialized novel sessions. To be specific, assume " + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "K_w^t" + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "text", + "content": " is the whole-class kernels of " + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "text", + "content": "-th session, the extended kernels of next session " + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "K_w^{t+1}" + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "text", + "content": " is obtained by concatenating the novel session kernels " + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "K_n^{t+1}" + }, + { + "bbox": [ + 46, + 72, + 289, + 205 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 58, + 210, + 287, + 227 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 210, + 287, + 227 + ], + "spans": [ + { + "bbox": [ + 58, + 210, + 287, + 227 + ], + "type": "interline_equation", + "content": "K _ {w} ^ {t + 1} = \\operatorname {C o n c a t} \\left(\\left[ K _ {w} ^ {t}, K _ {n} ^ {t + 1} \\right]\\right), \\in \\mathbb {R} ^ {\\left(N _ {w} ^ {t} + N _ {n} ^ {t + 1}\\right) \\times C}, \\tag {17}", + "image_path": "7d1e5ea135f16aa908e0577e842a6db9a557c0d039886cfb907113dd8875ce0a.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 231, + 288, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 231, + 288, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 231, + 288, + 291 + ], + "type": "text", + "content": "where the calculation of " + }, + { + "bbox": [ + 46, + 231, + 288, + 291 + ], + "type": "inline_equation", + "content": "K_{n}^{t + 1}" + }, + { + "bbox": [ + 46, + 231, + 288, + 291 + ], + "type": "text", + "content": " is the same with novel classes registration of GFSS referred to 3.5. In the inference process, only the kernels of base session are passed to the PKL module, and all the kernels of few-shot sessions are treated as a novel whole in the CBBI." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 304, + 128, + 317 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 304, + 128, + 317 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 128, + 317 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 323, + 180, + 336 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 180, + 336 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 180, + 336 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "text", + "content": "Dataset. Following [28], we evaluate the proposed method on two public datasets, i.e., PASCAL- " + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "inline_equation", + "content": "5^{i}" + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "text", + "content": " and COCO- " + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "inline_equation", + "content": "20^{i}" + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "text", + "content": ". PASCAL- " + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "inline_equation", + "content": "5^{i}" + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "text", + "content": " is modified from PASCAL VOC [7] with extra mask annotations from Semantic Boundaries Dataset (SBD) [12] dataset, it has 20 object classes and one background class. COCO- " + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "inline_equation", + "content": "20^{i}" + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "text", + "content": " consists of MS COCO [17] with 80 object classes and one background class for segmentation. In terms of GFSS, all the object classes are evenly divided into four folds: " + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "inline_equation", + "content": "\\{5^{i}, i \\in \\{0,1,2,3\\}\\}" + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "text", + "content": " for PASCAL- " + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "inline_equation", + "content": "5^{i}" + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "inline_equation", + "content": "\\{20^{i}, i \\in \\{0,1,2,3\\}\\}" + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "text", + "content": " for COCO- " + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "inline_equation", + "content": "20^{i}" + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "text", + "content": ". The rest object classes as well as background are treated as base classes, where the object classes of specific fold are conducted as novel classes. Models are directly evaluated on the validation set with both base and novel classes simultaneously. In terms of CIFSS, it shares the same fold division with GFSS. The object classes of specific fold are evenly divided into five novel sessions, while the rest object classes and the background class are included into the base session. On PASCAL- " + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "inline_equation", + "content": "5^{i}" + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "text", + "content": ", there are 16 object classes in base session and 1 novel object class for each incremental session. As for COCO- " + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "inline_equation", + "content": "20^{i}" + }, + { + "bbox": [ + 46, + 342, + 289, + 640 + ], + "type": "text", + "content": ", the number of object classes in base session is 61 and novel object classes in each incremental session is 5. We evaluate the CIFSS models on the classes belonging to base session, current and previous incremental novel sessions with the validation set." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "Evaluation metrics. Similar to [28], we use mean Intersection over Union (" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "mIoU" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": ") for base classes as well as base session " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "mIoU_{\\mathcal{B}}" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " and novel classes as well as incremental novel sessions " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "mIoU_{\\mathcal{N}}" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": ". As for GFSS setting, we also provide the overall " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "mIoU" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " with all classes denoted by " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "mIoU_{\\mathcal{O}}" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": ". Since the base classes are the vast majority, the arithmetic" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 308, + 92, + 555, + 242 + ], + "blocks": [ + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "lines": [ + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "type": "text", + "content": "Table 1. Quantitative results with GFSS setting on PASCAL-5" + }, + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "type": "inline_equation", + "content": "^i" + }, + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "type": "text", + "content": " and COCO-20" + }, + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "type": "inline_equation", + "content": "^i" + }, + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "type": "text", + "content": ". Best-performing results are highlighted in bold." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 92, + 555, + 242 + ], + "lines": [ + { + "bbox": [ + 308, + 92, + 555, + 242 + ], + "spans": [ + { + "bbox": [ + 308, + 92, + 555, + 242 + ], + "type": "table", + "html": "
Methods1-shot5-shot
mIoU_BmIoU_NmIoU_OhIoUmIoU_BmIoU_NmIoU_OhIoU
PASCAL-5^i
CANet [39]8.732.427.233.799.051.527.262.60
PFENet [29]8.322.676.974.048.831.897.183.11
SCL [38]8.882.447.353.839.111.837.383.05
PANet [32]31.8811.2526.9716.6332.9515.2528.7420.85
BAM [15]64.6517.0653.3227.0065.2819.9954.5030.61
CAPL [28]65.4818.8554.3829.2766.1422.4155.7231.96
Ours68.8426.9058.8637.8369.2234.4061.1845.42
COCO-20^i
Baseline [28]36.685.8429.0610.0136.917.2629.5912.13
BAM [15]44.086.7434.8611.6946.1011.2137.4918.03
CAPL [28]44.617.0535.4612.1845.2411.0536.8017.76
Ours46.3611.0437.7117.8346.7714.9138.9022.61
", + "image_path": "3c4e7b48b9e86fe386114fe74f00dbe0845f277eede47e34f832ee95dc5e1ea4.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 263, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 263, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 263, + 545, + 300 + ], + "type": "text", + "content": "mean might be dominated by " + }, + { + "bbox": [ + 304, + 263, + 545, + 300 + ], + "type": "inline_equation", + "content": "m\\mathrm{IoU}_{\\mathcal{B}}" + }, + { + "bbox": [ + 304, + 263, + 545, + 300 + ], + "type": "text", + "content": " [1]. We adopt the harmonic mean " + }, + { + "bbox": [ + 304, + 263, + 545, + 300 + ], + "type": "inline_equation", + "content": "h\\mathrm{IoU}" + }, + { + "bbox": [ + 304, + 263, + 545, + 300 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 263, + 545, + 300 + ], + "type": "inline_equation", + "content": "m\\mathrm{IoU}_{\\mathcal{B}}" + }, + { + "bbox": [ + 304, + 263, + 545, + 300 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 263, + 545, + 300 + ], + "type": "inline_equation", + "content": "m\\mathrm{IoU}_{\\mathcal{N}}" + }, + { + "bbox": [ + 304, + 263, + 545, + 300 + ], + "type": "text", + "content": " which can emphasize the impact of novel classes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 300, + 546, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 546, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 546, + 445 + ], + "type": "text", + "content": "Training details. For fair comparison, the PSPNet [45] with RestNet50 [13] is adopted as our feature extractor, which is the same as most FSS and GFSS methods, and we train our model for 50 epochs both on PASCAL- " + }, + { + "bbox": [ + 304, + 300, + 546, + 445 + ], + "type": "inline_equation", + "content": "5^{i}" + }, + { + "bbox": [ + 304, + 300, + 546, + 445 + ], + "type": "text", + "content": " and COCO- " + }, + { + "bbox": [ + 304, + 300, + 546, + 445 + ], + "type": "inline_equation", + "content": "20^{i}" + }, + { + "bbox": [ + 304, + 300, + 546, + 445 + ], + "type": "text", + "content": ". The model is optimized by the SGD with an initial learning rate of 2.5e-3, where momentum is 0.9 and the weight decay is set to 1e-4. All images together with the masks are all resized to " + }, + { + "bbox": [ + 304, + 300, + 546, + 445 + ], + "type": "inline_equation", + "content": "473 \\times 473" + }, + { + "bbox": [ + 304, + 300, + 546, + 445 + ], + "type": "text", + "content": " for training and tested with their original sizes. The " + }, + { + "bbox": [ + 304, + 300, + 546, + 445 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 300, + 546, + 445 + ], + "type": "text", + "content": " of loss function is set to 0.6 and the bias value " + }, + { + "bbox": [ + 304, + 300, + 546, + 445 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 300, + 546, + 445 + ], + "type": "text", + "content": " of CBBI is 0.5. We obtain the specific split results by averaging over five different random seeds, and the final reported results are averaged with all splits." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 454, + 391, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 454, + 391, + 467 + ], + "spans": [ + { + "bbox": [ + 306, + 454, + 391, + 467 + ], + "type": "text", + "content": "4.2. Comparisons" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "type": "text", + "content": "GFSS Setting. Table 1 shows the 1-shot and 5-shot quantitative results of different methods on PASCAL- " + }, + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "type": "inline_equation", + "content": "5^{i}" + }, + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "type": "inline_equation", + "content": "\\mathrm{COCO - }20^{i}" + }, + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "type": "text", + "content": ". It can be found that the proposed method shows substantial gains compared with the advanced approaches and achieves the state-of-the-art performance of all GFSS settings and datasets. As for the overall mIoU on PASCAL- " + }, + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "type": "inline_equation", + "content": "5^{i}" + }, + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "type": "text", + "content": ", the proposed method exceeds the CAPL [28] by " + }, + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "type": "inline_equation", + "content": "4.48\\%" + }, + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "type": "inline_equation", + "content": "5.46\\%" + }, + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "type": "text", + "content": " for 1-shot setting and 5-shot setting respectively. With the significant improvement on novel classes, our method surpasses the CAPL [28] by " + }, + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "type": "inline_equation", + "content": "8.56\\%" + }, + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "type": "inline_equation", + "content": "13.46\\%" + }, + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "type": "text", + "content": " hIoU, demonstrating the superiority of the proposed method. Meanwhile, better performance on novel classes can also weaken the confusion between base classes and novel classes and improve the mIoU" + }, + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "type": "inline_equation", + "content": "_{\\mathcal{B}}" + }, + { + "bbox": [ + 304, + 473, + 547, + 640 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 641, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 714 + ], + "type": "text", + "content": "CIFSS Setting. We compare our method with the following modified approaches as: 1) the relevant incremental few-shot learning methods, such as PIFS [3] and iFS-RCNN [20]; 2) the current FSS and GFSS methods, i.e., PFENet [29], BAM [15] and CAPL [28]. From Table 2, our method shows substantial gains compared with existing approaches." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19261" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 92, + 555, + 198 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 545, + 92 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 545, + 92 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 545, + 92 + ], + "type": "text", + "content": "Table 2. 1-shot Quantitative results with CIFSS setting on the PASCAL-5" + }, + { + "bbox": [ + 47, + 71, + 545, + 92 + ], + "type": "inline_equation", + "content": "^i" + }, + { + "bbox": [ + 47, + 71, + 545, + 92 + ], + "type": "text", + "content": " and COCO-20" + }, + { + "bbox": [ + 47, + 71, + 545, + 92 + ], + "type": "inline_equation", + "content": "^i" + }, + { + "bbox": [ + 47, + 71, + 545, + 92 + ], + "type": "text", + "content": ". Best-performing results are highlighted in bold. * We use the weights of PSPNet [45] backbone pretrained on base classes as the same as the BAM [15]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 92, + 555, + 198 + ], + "lines": [ + { + "bbox": [ + 49, + 92, + 555, + 198 + ], + "spans": [ + { + "bbox": [ + 49, + 92, + 555, + 198 + ], + "type": "table", + "html": "
DatasetsMethodssession 0session 1session 2session 3session 4session 5
mIoU_BmIoU_BmIoU_NhIoUmIoU_BmIoU_NhIoUmIoU_BmIoU_NhIoUmIoU_BmIoU_NhIoU
PASCAL-5iPFENet* [29]74.4367.2110.3417.9266.6214.1223.3064.9711.1218.9965.7712.0820.4162.5011.0818.82
iFS-RCNN [20]72.4367.7111.0819.0467.1716.6326.6665.5112.9421.6165.4811.7519.9263.3612.3920.73
CAPL [28]74.8670.5117.9428.6069.0721.1132.3467.8918.0328.4967.1419.5730.3165.5319.0829.55
PIFS [3]75.0471.1619.4930.6069.8024.3336.0868.0519.9230.8268.4421.0832.2365.8320.9931.83
Our75.4972.9324.6036.7971.2129.3241.5470.7625.7537.7669.9826.1137.8868.4027.2839.00
COCO-20iPFENet* [29]54.1145.794.337.9144.585.189.2843.073.366.2342.405.649.9641.995.059.02
iFS-RCNN [20]53.4250.435.039.1545.526.6011.5343.865.079.0943.377.1112.2242.836.6311.48
CAPL [28]54.4350.256.6911.8146.677.0412.2345.925.539.8744.087.7713.2143.857.5112.82
BAM [15]54.8052.048.8315.1049.018.9415.1247.037.0312.2345.569.1915.2944.488.8314.73
PIFS [3]54.2751.598.9015.1848.529.5315.9346.966.9412.0945.699.9316.3144.278.8014.68
Our54.3951.7811.4718.5548.3311.2218.0847.289.6115.8946.2511.4718.3345.2410.7417.31
", + "image_path": "84e9cdb84cbce1ac6a866fbf767912e0771e8d38cb819c90be8f0b0415913ed4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 49, + 227, + 291, + 308 + ], + "blocks": [ + { + "bbox": [ + 48, + 217, + 279, + 227 + ], + "lines": [ + { + "bbox": [ + 48, + 217, + 279, + 227 + ], + "spans": [ + { + "bbox": [ + 48, + 217, + 279, + 227 + ], + "type": "text", + "content": "Table 3. Ablation Study of the effect with different components." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 227, + 291, + 308 + ], + "lines": [ + { + "bbox": [ + 49, + 227, + 291, + 308 + ], + "spans": [ + { + "bbox": [ + 49, + 227, + 291, + 308 + ], + "type": "table", + "html": "
PKLFCPCBBI1-shot5-shot
mIoU_BmIoU_NhIoUmIoU_BmIoU_NhIoU
61.2214.5023.4562.0719.7329.94
✓66.8222.9534.1767.7329.1840.79
✓64.4916.7326.5765.2823.3934.44
✓✓67.7323.5834.9868.0531.4543.02
✓✓✓68.8426.9037.8369.2234.4045.42
", + "image_path": "0d1abf64b548844d88c8d6e8e20045340c2deb7022eba3d522e89ac22e0924b5.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 329, + 287, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 329, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 287, + 425 + ], + "type": "text", + "content": "Since majority approaches adopt analogous backbone, we get similar performance in the session 0, which only construct with base classes. The superiority of our method both in base and novel classes continues to emerge as the novel session increased. It partly embodies the significant benefit of our old and novel classes knowledge ensemble mechanism, and partly verifies that the improvement on novel classes can result better performance of base classes as well." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 432, + 147, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 432, + 147, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 432, + 147, + 443 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 450, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 665 + ], + "type": "text", + "content": "Component-wise Effectiveness. We ablate the three major components of proposed method in Table 3: prototypical kernel learning module, foreground contextual perception module and conditional bias based inference. We use the PSPNet [45] modified with learnable kernels as the baseline, in which simple concat operation is conducted between base-class and novel-class kernels. We can see that adding either one of PKL module or FTP module brings substantial improvement compared with the baseline. It means the proposed two modules are indeed beneficial to the novel classes learning in few-shot scenarios, and can mitigate the knowledge division with the extremely class-imbalanced GFSS setting. Moreover, it worth noting that the FTP module explicit plays a vital role in providing the general foreground information, the implicit effect is to boost the feature expression of unknown targets. Fig. 5 shows the qualitative results, which straightforward embodies the effectiveness of proposed method." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Prototypical Kernel Learning Module. The motivation of PKL module is to empower the prototypical ability for base-class kernels, so as to maintain the consistency with the registered novel classes, which is also prototypical aggregated" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 309, + 281, + 548, + 468 + ], + "blocks": [ + { + "bbox": [ + 304, + 217, + 547, + 281 + ], + "lines": [ + { + "bbox": [ + 304, + 217, + 547, + 281 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 547, + 281 + ], + "type": "text", + "content": "Table 4. Ablation performances of the proposed method. fixedALR means using fixed learning rate referred to Eq. (3). " + }, + { + "bbox": [ + 304, + 217, + 547, + 281 + ], + "type": "inline_equation", + "content": "\\mathrm{pixel}_{AP\\rightarrow MP}" + }, + { + "bbox": [ + 304, + 217, + 547, + 281 + ], + "type": "text", + "content": " indicates replacing average pooling with max pooling in pixel dimension referred to Eq. (6), and " + }, + { + "bbox": [ + 304, + 217, + 547, + 281 + ], + "type": "inline_equation", + "content": "\\mathrm{image}_{MP\\rightarrow AP}" + }, + { + "bbox": [ + 304, + 217, + 547, + 281 + ], + "type": "text", + "content": " is the similar replacement in image dimension. " + }, + { + "bbox": [ + 304, + 217, + 547, + 281 + ], + "type": "inline_equation", + "content": "uCBBI" + }, + { + "bbox": [ + 304, + 217, + 547, + 281 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 217, + 547, + 281 + ], + "type": "inline_equation", + "content": "cCBBI" + }, + { + "bbox": [ + 304, + 217, + 547, + 281 + ], + "type": "text", + "content": " denote the unconditional form and learnable convolution form for CBBI." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 281, + 548, + 468 + ], + "lines": [ + { + "bbox": [ + 309, + 281, + 548, + 468 + ], + "spans": [ + { + "bbox": [ + 309, + 281, + 548, + 468 + ], + "type": "table", + "html": "
Settings1-shot5-shot
mIoUBmIoUNhIoUmIoUBmIoUNhIoU
w/o PKL64.4916.7326.5765.2823.3934.44
fixedALR66.9020.4831.3667.7226.0837.66
concat+AP65.9119.4130.0066.8625.5136.93
concat+LP66.2721.1932.1167.7126.8938.49
w/o FCP66.8222.9534.1767.7329.1840.79
pixelAP→MP65.9422.3133.3466.4228.9140.28
imageMP→AP65.0521.9432.8166.1828.3039.65
GradCAM [24]66.9423.3634.7468.0829.8041.46
PAGENet [33]67.5724.8036.2868.8331.7043.41
MINet [21]67.8924.9936.5368.6531.4743.16
w/o CBBI67.7323.5834.9868.0531.4543.02
uCBBI66.2920.8331.7067.1325.3836.83
cCBBI65.5318.8629.2966.9023.3934.66
Ours68.8426.9037.8369.2234.4045.42
", + "image_path": "62abb2f0248a31a4e238e91f54875938f7b5025a543d64d8994c718d6df081a3.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 495, + 547, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 547, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 547, + 674 + ], + "type": "text", + "content": "from limited data. We replace the PKL with directly adopting the base-class kernels to the input feature maps as our baseline. As shown in the upside of Table 4, we first construct the ablation studies on the adaptation learning rate, it is clear that the fixed learning rate brings worse results with the distraction of noisy gradient signals during the prototypical kernel update. Meanwhile, we introduce several alternative prototype fusion approaches which are performed by the adaptive pooling (AP) or liner projection (LP) after the channel-wise concat operation between " + }, + { + "bbox": [ + 304, + 495, + 547, + 674 + ], + "type": "inline_equation", + "content": "K_{b}" + }, + { + "bbox": [ + 304, + 495, + 547, + 674 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 495, + 547, + 674 + ], + "type": "inline_equation", + "content": "P_{mb}" + }, + { + "bbox": [ + 304, + 495, + 547, + 674 + ], + "type": "text", + "content": ". The results show that our method with the proposed prototypical kernel update remarkably outperforms the aforementioned approaches. It can strike a better balance between generality and specificity, especially for novel targets in generalized inference process, thus is more suitable to the GFSS." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "Foreground Contextual Perception module. The FCP aims to offer a general foreground detection which helps to the mining of novel targets. Similarly, the model with-" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19262" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 547, + 220 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 547, + 220 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 547, + 220 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 547, + 220 + ], + "type": "image", + "image_path": "dd16e4961766a5d942c4b8378dd725c098329bfcb9f11ddca08ed835cd75310d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 63, + 221, + 529, + 234 + ], + "lines": [ + { + "bbox": [ + 63, + 221, + 529, + 234 + ], + "spans": [ + { + "bbox": [ + 63, + 221, + 529, + 234 + ], + "type": "text", + "content": "Figure 5. Qualitative results of our method, ablation of each components, BAM [15] and CAPL [28] on PASCAL- " + }, + { + "bbox": [ + 63, + 221, + 529, + 234 + ], + "type": "inline_equation", + "content": "5^{i}" + }, + { + "bbox": [ + 63, + 221, + 529, + 234 + ], + "type": "text", + "content": " benchmark." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 253, + 289, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 289, + 493 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 289, + 493 + ], + "type": "text", + "content": "out FCP is conducted as the baseline, as well as replacing the CBBI with normal inference. The middle part of Table 4 demonstrates the ablation results of the pixel-wise group correlation aggregation referred to Eq. (6), which is the key of FCP, as well as the comparison with other alternative foreground detection approaches. Using average pooling on pixel dimension of the pixel-wise group correlation tends to introduce more background noisy, leading to worse performance. We also compare our FCP with CAM-based and well-designed salient object detection approaches. Since the CAM-based methods are heavily relied on the extra classes information, such as class-wise gradients [24] or activation values [31], it lacks the ability of novel classes detection. Similar deficiency also lies in other well-designed salient detection methods, e.g., PAGENet [33] and MINet [21], which only consider the interaction within specific classes and lose the generality of foreground detection. The FCP pays more attention to the robust and universal feature patterns with abundant pseudo episode, thus is more easy to generalize to novel targets." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 495, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 287, + 639 + ], + "type": "text", + "content": "Conditional Bias Based Inference. In our method, the CBBI plays a role in combining the outputs of the PKL module and the FTP module. We also experiment on the way of fusing those outputs in the bottom part of Table 4. When the class-agnostic foreground mask predicted by the FTP module is utilized with unconditional form, the performance gets worse with the interference of background prediction. We also replace the strategy based inference with learnable convolution structure with end-to-end training, the underperform results indicate that introducing parameterized inference module may heavy the optimization of model and even block the learning of other modules." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": "Performance distinction between PASCAL-5" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "^i" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": " and COCO-20" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "^i" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": ". We further investigate the improvement gap between PASCAL-5i and COCO-20i referred to Table 1, e.g., " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "8.05\\%" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": " v.s. " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "3.99\\%" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": " exceed CAPL [28] on mIoU of novel classes. The most obvious difference between these two datasets is that coco-20i contains larger classes set than" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 308, + 283, + 550, + 340 + ], + "blocks": [ + { + "bbox": [ + 305, + 250, + 548, + 282 + ], + "lines": [ + { + "bbox": [ + 305, + 250, + 548, + 282 + ], + "spans": [ + { + "bbox": [ + 305, + 250, + 548, + 282 + ], + "type": "text", + "content": "Table 5. Results on the subset of COCO. " + }, + { + "bbox": [ + 305, + 250, + 548, + 282 + ], + "type": "inline_equation", + "content": "a + b/c" + }, + { + "bbox": [ + 305, + 250, + 548, + 282 + ], + "type": "text", + "content": " indicates the combination of classes, where " + }, + { + "bbox": [ + 305, + 250, + 548, + 282 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 305, + 250, + 548, + 282 + ], + "type": "text", + "content": " is the number of base classes, " + }, + { + "bbox": [ + 305, + 250, + 548, + 282 + ], + "type": "inline_equation", + "content": "b = 1" + }, + { + "bbox": [ + 305, + 250, + 548, + 282 + ], + "type": "text", + "content": " represents the background class and " + }, + { + "bbox": [ + 305, + 250, + 548, + 282 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 305, + 250, + 548, + 282 + ], + "type": "text", + "content": " is the number of novel classes." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 283, + 550, + 340 + ], + "lines": [ + { + "bbox": [ + 308, + 283, + 550, + 340 + ], + "spans": [ + { + "bbox": [ + 308, + 283, + 550, + 340 + ], + "type": "table", + "html": "
Methods15+1/530+1/1045+1/1560+1/20
mIoUBmIoUNmIoUBmIoUNmIoUBmIoUNmIoUBmIoUN
Baseline [28]51.1910.0847.748.2241.377.1036.685.84
CAPL [28]63.3916.0857.2213.3950.0810.1644.617.05
Ours66.7023.7659.4818.9152.0114.2746.3611.04
Improvement+3.31+7.76+2.26+5.52+1.92+4.11+1.75+3.99
", + "image_path": "81e604c382881bb36882dcb4a4c20465dc305345a8d2dc98b9186f0fa36fd21d.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 364, + 547, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 547, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 547, + 483 + ], + "type": "text", + "content": "PASCAL-5" + }, + { + "bbox": [ + 304, + 364, + 547, + 483 + ], + "type": "inline_equation", + "content": "^i" + }, + { + "bbox": [ + 304, + 364, + 547, + 483 + ], + "type": "text", + "content": ". Thus, we design the ablation experiments with gradually enlarging the subset of COCO, which is started from a similar scale with PASCAL-5" + }, + { + "bbox": [ + 304, + 364, + 547, + 483 + ], + "type": "inline_equation", + "content": "^i" + }, + { + "bbox": [ + 304, + 364, + 547, + 483 + ], + "type": "text", + "content": ". As shown in Table 5, we find parallel improvements are raised when the scale and distribution of classes are similar to PASCAL-5" + }, + { + "bbox": [ + 304, + 364, + 547, + 483 + ], + "type": "inline_equation", + "content": "^i" + }, + { + "bbox": [ + 304, + 364, + 547, + 483 + ], + "type": "text", + "content": ", and as the number of classes increasing, the gaps are reduced. Comparable phenomenon also happens on the contrast between the CAPL [28] and baseline, indicating the common issue that the effect of GFSS model may get weakened as the scale of classes set increases." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 500, + 379, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 500, + 379, + 511 + ], + "spans": [ + { + "bbox": [ + 306, + 500, + 379, + 511 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "type": "text", + "content": "In this work, we have proposed to leverage the prototypical kernel learning and open-set foreground perception for generalized few-shot semantic segmentation. Special to two of major issues existed in current GFSS, i.e., representation division and embedding prejudice. We offer an effective scheme with three components, which are PKL, FCP and CBBI. To maintain the prototypical representation consistency and prevent novel targets from being misclassified as background, the PKL and FCP are proposed to perform adaptive prototypical kernel update and open-set targets detection, respectively. Moreover, the CBBI is designed for the ensemble of the aforementioned two modules and offers the final prediction. Besides, we further extend the GFSS to CIFSS which is more challenging with incremental stream of novel classes. Extensive experiments demonstrate that the proposed method achieves state-of-the-art results." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19263" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Donghyeon Baek, Youngmin Oh, and Bumsub Ham. 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Rethinking semantic segmentation: A prototype view. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2582-2593, 2022. 2" + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19265" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Prototypical Mixing and Retrieval-Based Refinement for Label Noise-Resistant Image Retrieval/ec71d51a-9735-4817-bbda-a4f4fe8a6bfa_content_list.json b/2023/Prototypical Mixing and Retrieval-Based Refinement for Label Noise-Resistant Image Retrieval/ec71d51a-9735-4817-bbda-a4f4fe8a6bfa_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..0db0896151144baaf297d9823cf94d99c8ab7350 --- /dev/null +++ b/2023/Prototypical Mixing and Retrieval-Based Refinement for Label Noise-Resistant Image Retrieval/ec71d51a-9735-4817-bbda-a4f4fe8a6bfa_content_list.json @@ -0,0 +1,1700 @@ +[ + { + "type": "text", + "text": "Prototypical Mixing and Retrieval-based Refinement for Label Noise-resistant Image Retrieval", + "text_level": 1, + "bbox": [ + 94, + 128, + 877, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xinlong Yang $^{1*}$ , Haixin Wang $^{1*}$ , Jinan Sun $^{1}$ , Shikun Zhang $^{1}$ , Chong Chen $^{1}$", + "bbox": [ + 187, + 214, + 779, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xian-Sheng Hua², Xiao Luo³†", + "bbox": [ + 362, + 244, + 604, + 263 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Peking University $^{2}$ Terminus Group $^{3}$ University of California, Los Angeles $\\{\\mathrm{xinlong.yang, wang.hx}\\} @$ stu.pku.edu.cn, $\\{\\mathrm{sjn, zhangsk}\\} @$ pu.edu.cn, cheung1990@126.com, huaxiansheng@gmail.com, xiaoluo@cs.ucla.edu", + "bbox": [ + 104, + 275, + 864, + 330 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 375, + 313, + 391 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Label noise is pervasive in real-world applications, which influences the optimization of neural network models. This paper investigates a realistic but understudied problem of image retrieval under label noise, which could lead to severe overfitting or memorization of noisy samples during optimization. Moreover, identifying noisy samples correctly is still a challenging problem for retrieval models. In this paper, we propose a novel approach called Prototypical Mixing and Retrieval-based Refinement (TITAN) for label noise-resistant image retrieval, which corrects label noise and mitigates the effects of the memorization simultaneously. Specifically, we first characterize numerous prototypes with Gaussian distributions in the hidden space, which would direct the Mixing procedure in providing synthesized samples. These samples are fed into a similarity learning framework with varying emphasis based on the prototypical structure to learn semantics with reduced overfitting. In addition, we retrieve comparable samples for each prototype from simple to complex, which refine noisy samples in an accurate and class-balanced manner. Comprehensive experiments on five benchmark datasets demonstrate the superiority of our proposed TITAN compared with various competing baselines.", + "bbox": [ + 76, + 407, + 472, + 755 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 786, + 209, + 801 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Content-based image retrieval has been an essential research area in computer vision [7], with various applications in search engineering [49, 13] and medical image analysis [19]. Content-based image retrieval can be divided", + "bbox": [ + 76, + 813, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "into instance-level retrieval [1, 62] and category-level retrieval [45, 43, 53]. The former focuses on capturing the same instance in different environments. In recent years, category-level retrieval has gained popularity by delivering samples from a massive database with results grouped by the same category as the query [36].", + "bbox": [ + 500, + 376, + 890, + 467 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The core of successful category-level retrieval is to map instances to data points in the feature space while preserving similarity connections. The majority of current approaches focus on similarity learning [46, 35], which use pairwise [30] and triplet [16, 50] objectives to maintain semantics in the embedding space. These approaches promote the proximity of semantically similar samples in the embedding space and the separation of semantically different samples. An alternative strategy is to utilize proxies [53, 36, 21, 14]. These methods map each class into the deep feature space to guide semantics learning in a pointwise manner. A few of studies use binary descriptors to improve efficiency [44, 56], which results in a candidate set followed by further refinement for precise image retrieval.", + "bbox": [ + 496, + 472, + 892, + 684 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite their considerable success, these retrieval systems often presume that the semantic labels in the training set are accurate. In real-world applications, this assumption could be invalidated by the possibility of annotation mistakes and inadequate automated collecting tactics [47, 54]. For instance, web-based sources often include tags and captions, which are usually utilized to provide label information for convenience. These approaches could generate extensive label noise to collected datasets. To address this issue, this work studies a practical topic named image retrieval with label noise. Although there are extensive papers to study the problem of robust learning in classification tasks [29, 12, 25], retrieval models under label noise are still underexplored with unsatisfactory performance in practice.", + "bbox": [ + 496, + 689, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 805, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution. †Corresponding author.", + "bbox": [ + 94, + 886, + 333, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11239", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/eaf01e6295403911afaebb022aec3f31d702e991ad3c779fc6a123ee6f8b86f7.jpg", + "image_caption": [ + "Figure 1. Two Mixing mechanisms are demonstrated including the standard Mixup (top) and our prototypical Mixing (bottom)." + ], + "image_footnote": [], + "bbox": [ + 96, + 94, + 450, + 258 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, developing a label-noise resistant retrieval model is challenging due to two reasons: (1) Erroneous supervision. Extensive label noise could result in erroneous supervision information, resulting in a significant decline in retrieval performance. In literature, a few works propose to refine noisy samples for effective image retrieval [28, 18]. For example, PRISM [28] estimates the probability of an example being clean with the help of a memory bank. However, they are prone to result in biased and overconfident refinement due to their point-wise calculation [60]. (2) Serious Memorization. Although deep neural networks tend to learn generalized patterns at the beginning stage, the overfitting or memorization of noisy data would compromise the optimization process gradually [57]. As a consequence, a robust optimization objective is anticipated to improve the retrieval performance.", + "bbox": [ + 75, + 310, + 468, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this study, we propose a novel retrieval method named Prototypical Mixing and Retrieval-based Refinement (TITAN) for label noise-resistant image retrieval. The essence of our TITAN is to measure the distributions of different prototypes in the hidden space. Note that Mixup [58] can generate synthesis samples, which follows the Vicinal Risk Minimization (VRM) [5] principle with high generalization capability. Here, synthetic samples are generated by merging the original data with samples from the respective prototypical distributions, hence avoiding the possible overfitting of noisy samples. Compared with standard Mixup [58], our prototypical Mixing considers more about the hidden structure and does not require mixing different labels. Afterward, we build a similarity learning framework that optimizes the similarity between samples with the same label against using different emphases inferred from prototypical distributions. In addition, to filter potential noisy data, we retrieve comparable samples for each prototype [55]. The identical retrieval number for different prototypes with curriculum learning [2] promises accurate and class-balanced label refinement. Finally, we involve in learning to cluster to enhance the discriminability for effective image retrieval. Comprehensive experiments on a variety of datasets verify", + "bbox": [ + 75, + 551, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the superiority of our TITAN by comparing it to a number of benchmarks. The contribution of this paper can be summarized as follows:", + "bbox": [ + 496, + 90, + 890, + 135 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- This paper studies a less-explored but practical problem named label noise-resistant image retrieval and proposes a novel method named TITAN for this problem.", + "- On the one hand, TITAN measures the distributions of different prototypes and then generates synthesis data to prevent the memorization of noisy samples. On the other hand, TITAN retrieves comparable samples for each prototype from easy to hard, promising accurate and class-balanced label refinement.", + "- Extensive experiments on five benchmark datasets demonstrate the superiority of our TITAN compared with various baseline methods in different settings." + ], + "bbox": [ + 500, + 146, + 893, + 351 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 364, + 640, + 380 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Context-based Image Retrieval", + "text_level": 1, + "bbox": [ + 500, + 388, + 774, + 406 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As a basic research topic in computer vision and multimedia communities, context-based image retrieval can be separated into instance-level retrieval [1, 62] and category-level retrieval [45, 43, 53]. Recent years have seen an increasing interest in category-level retrieval, which can be further divided into similarity-based [46, 35] and proxy-based approaches [53, 36, 21, 14]. Similarity-based approaches utilize similarity relationships to generate positive and negative pairs, which are then combined with pairwise [30] and triplet [16, 50] losses to optimize deep neural networks. For instance, GSS [27] tries to distinguish the pairwise similarity in the whole dataset in an unsupervised manner. In contrast, proxy-based approaches map labels into the embedding space before minimizing the distance between deep features and their respective proxies. Hashing-based search engines are also in great demand due to their high efficiency [44, 56]. Nevertheless, these approaches do not often account for label noise in real-world datasets. In contrast, we investigate the issue of label noise-resistant image retrieval and develop a novel framework named TITAN to address it.", + "bbox": [ + 496, + 412, + 890, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Learning with Label Noise", + "text_level": 1, + "bbox": [ + 500, + 739, + 740, + 757 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learning with label noise has been intensive in a variety of tasks including image segmentation [32], saliency detection [59], and network analysis [9]. A range of works proposes robust losses to potential label noise [11, 10]. For example, RINCE [8] modifies the formula for contrastive learning, which achieves robust performance under noisy augmented views. Another line of this topic is to choose samples with noisy labels and clean them [15, 48, 31, 24, 61, 37, 20]. Early attempts usually put forward a threshold,", + "bbox": [ + 496, + 763, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11240", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e100f3b38080bd47c77126ed46e275b12d8810736c9869e9d06ab5844fa9406c.jpg", + "image_caption": [ + "Figure 2. An overview of the proposed TITAN. TITAN first estimates the distributions of prototypes for each class, from which we sample features for Mixing to generate virtual features. Moreover, TITAN retrieves different samples for every prototype to refine noisy samples. The final losses are composed of both similarity learning and clustering losses." + ], + "image_footnote": [], + "bbox": [ + 86, + 89, + 890, + 388 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and samples with losses above the threshold are deemed noisy. Co-teaching [15] optimizes two networks concurrently by utilizing small-loss examples from one network to optimize the other network. A few of works attempt to extend robust learning into image retrieval by identifying noisy samples based on similarity [28, 18]. However, these works still neglect the overfitting of noisy samples, and refinement procedures of label noise remain to be biased and overconfident, especially when the amount of noisy data increases. In this paper, we incorporate prototypical Mixing into a similarity learning framework to ease the overfitting of noisy data. To ensure that the labels are assigned correctly and balance class sizes, we also filter noisy samples according to the retrieval process.", + "bbox": [ + 75, + 450, + 472, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 691, + 202, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Definition", + "text_level": 1, + "bbox": [ + 76, + 720, + 259, + 736 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We start by giving the problem definition. Denote the training set as $\\mathcal{D} = \\{(x_i, y_i)\\}_{i=1}^n$ where $x_i$ is the $i$ -th sample and $y_i$ is its observe labels. $n$ represents the data size. We aim to learn a mapping to project data points into an embedding space where similar image pairs should be mapped into similar deep features and vice versa. In our settings, we assume that the observed labels could be wrong, which increases the difficulty of discriminative feature learning. To evaluate our model, we would retrieve similar examples in the database for the given query sample.", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Overview", + "text_level": 1, + "bbox": [ + 500, + 449, + 609, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Learning effective image representations under label noise requires us to reduce the extreme overfitting of noisy samples and clean up noisy labels in the dataset. Here, we propose a novel method named TITAN for this problem. Following previous works [18, 28], our TITAN modifies a popular classification network (e.g., VGG-F and ResNet50) by adding an MLP layer in place of its head to provide deep features, i.e., $\\pmb{h} = H(F(\\pmb{x}))$ where $F(\\cdot)$ is the feature extractor and $H(\\cdot)$ is the MLP head. As illustrated in Figure 2, our model consists of two essential components: (1) Prototypical Mixing, which characterizes prototypes using Gaussian distributions and then generates virtual samples by incorporating prototype information to relieve the memorization of noisy samples; (2) Retrieval-based Refinement, which retrieves similar samples for every prototype to further refine noisy samples in a balanced way. Then, we elaborate on the details of our TITAN.", + "bbox": [ + 496, + 473, + 893, + 731 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Prototypical Mixing for Robust Representation Learning", + "text_level": 1, + "bbox": [ + 498, + 739, + 890, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The overfitting of neural networks is a major challenge in deep representation learning [57]. As a consequence, we must enhance the generalization capacity of the model. Here, we first characterize the prototypes of various classes using different Gaussian distributions before developing a Mixing technique that blends hidden features with samples derived from these prototypes.", + "bbox": [ + 496, + 779, + 890, + 885 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In detail, we characterize the distribution of each class in", + "bbox": [ + 517, + 885, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11241", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the prototype as a latent Gaussian distribution $N(\\pmb{\\mu}_c, \\pmb{\\Sigma}_c)$ , and every related hidden feature can be thought of as a sample from the Gaussian distribution [26]. Note that even if these samples could be noisy, the centroid measurement of the distribution is still reliable since all the samples are considered together with potential label noise neutralized. In particular, we measure the centroid and the corresponding covariance matrix based on these samples. In formulation, denote the hidden feature of $\\pmb{x}_i$ as $\\pmb{z}_i$ , we have the estimated mean vector $\\pmb{\\mu}_c$ and the covariance matrix $\\pmb{\\Sigma}_c$ of the $c$ -th class in the formulation of:", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\mu} _ {c} = \\frac {\\sum_ {i = 1} ^ {N} \\mathbf {1} _ {y _ {i} = c} \\boldsymbol {z} _ {i}}{\\sum_ {i = 1} ^ {N} \\mathbf {1} _ {y _ {i} = c}}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 268, + 468, + 308 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Sigma} _ {c} = \\frac {\\sum_ {i = 1} ^ {N} \\mathbf {1} _ {y _ {i} = c} (\\boldsymbol {z} _ {i} - \\boldsymbol {\\mu} _ {c}) (\\boldsymbol {z} _ {i} - \\boldsymbol {\\mu} _ {c}) ^ {T}}{\\sum_ {i = 1} ^ {N} \\mathbf {1} _ {y _ {i} = c}}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 313, + 468, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, we generate a virtual sample from the distribution, which would be combined with the original sample. In formulation, we first select the prototype with the maximal probability for each sample, i.e.,", + "bbox": [ + 76, + 358, + 468, + 419 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {i} = \\arg \\max _ {c} \\frac {1}{\\sqrt {(2 \\pi) ^ {d} | \\boldsymbol {\\Sigma} _ {c} |}} \\mathrm {e} ^ {- \\frac {1}{2} (\\boldsymbol {z} _ {i} - \\boldsymbol {\\mu} _ {c}) ^ {\\mathrm {T}} \\boldsymbol {\\Sigma} _ {c} ^ {- 1} (\\boldsymbol {z} _ {i} - \\boldsymbol {\\mu} _ {c})}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 429, + 468, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $d$ denotes the hidden dimension. The mixed hidden feature can be written as:", + "bbox": [ + 76, + 474, + 468, + 503 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {z} _ {i} ^ {+} = \\lambda \\boldsymbol {z} _ {i} + (1 - \\lambda) \\boldsymbol {z} _ {i} ^ {\\prime}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 515, + 468, + 534 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\boldsymbol{z}_i'$ is randomly generated from $N(\\boldsymbol{\\mu}_{\\hat{y}_i}, \\boldsymbol{\\Sigma}_{\\hat{y}_i})$ , $\\boldsymbol{z}_i = F(\\boldsymbol{x}_i)$ and $\\boldsymbol{x}_i$ denotes the original image sample. $\\lambda$ is a coefficient selected from a Beta distribution following previous works:", + "bbox": [ + 76, + 544, + 468, + 604 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\lambda \\sim B e t a (\\alpha , \\beta) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 604, + 468, + 622 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha$ and $\\beta$ are two parameters both set to 2 empirically. To simplify the calculation, we adopt a diagonal $\\Sigma_{c}$ for each distribution with the neglection of the covariance.", + "bbox": [ + 75, + 628, + 468, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Advantages of Prototypical Mixing. Similarly to standard Mixup, our prototypical Mixing also generates synthetic samples, extending the Empirical Risk Minimization (ERM) principle [41] to the Vicinal Risk Minimization (VRM) principle [5]. In this way, our TITAN has a strong capacity for generalization and is resistant to the memorization of noisy examples. Moreover, our prototypical Mixing does not need to combine labels to generate synthetic labels, which could be biased since the label space contains distinct relationships. Lastly, our TITAN adequately explores prototypical structures in the hidden space, which can serve as implicit label correction.", + "bbox": [ + 75, + 674, + 468, + 853 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we include the mixed samples into a framework for deep representation learning that maintains similarity. Here, we concatenate the hidden feature with the mixed feature", + "bbox": [ + 75, + 854, + 468, + 898 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "into a mini-batch and maximize the similarity between deep features of positive pairs compared with negative pairs. The positives for $z_{i}^{+}$ are mini-batch samples sharing the same label, i.e., $z_{j}^{+}$ with $y_{i} = y_{j}$ . In formulation, given the minibatch $\\mathcal{B}$ , the index of positives for $z_{i}^{+}$ is written as:", + "bbox": [ + 496, + 90, + 890, + 170 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Pi (i) = \\{j | \\boldsymbol {x} _ {j} \\in \\mathcal {B}, y _ {i} = y _ {j} \\}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 181, + 890, + 199 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following previous works [38, 6], the negatives are all the other samples in a mini-batch, then the similarity learning objective is constructed as:", + "bbox": [ + 496, + 209, + 890, + 255 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {S L} = - \\sum_ {\\boldsymbol {x} _ {i} \\in \\mathcal {B}} \\frac {1}{| \\Pi (i) |} \\sum_ {j \\in \\Pi (i)} \\log \\frac {\\exp \\left(\\boldsymbol {h} _ {i} ^ {+} \\cdot \\boldsymbol {h} _ {j} ^ {+} / \\tau\\right)}{\\sum_ {\\boldsymbol {x} _ {j ^ {\\prime}} \\in \\mathcal {B}} \\exp \\left(\\boldsymbol {h} _ {i} ^ {+} \\cdot \\boldsymbol {h} _ {j ^ {\\prime}} ^ {+} / \\tau\\right)} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 265, + 895, + 323 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\pmb{h}_i^+ = H(\\pmb{z}_i^+)$ maps the hidden feature into the target space and $\\tau$ is a temperature parameter preset to 0.5 as in [38]. Moreover, we also incorporate the probabilities in Eqn. 3 as the confidence scores, which gives more emphasis on samples with high confidence. Consequently, we alleviate the effect of unreliable mixed data and enlarge the range of sample weights. In other words, sample weights are assigned more heavily to reliable samples. Let $\\pmb{w}_i = \\frac{1}{\\sqrt{(2\\pi)^d|\\pmb{\\Sigma}_{\\hat{y}_i}|}}\\mathrm{e}^{-\\frac{1}{2} (\\pmb{z}_i - \\pmb{\\mu}_{\\hat{y}_i})^\\mathrm{T}\\pmb{\\Sigma}_c^{-1}(\\pmb{z}_i - \\pmb{\\mu}_{\\hat{y}_i})}$ denote the confidence score, and we rewrite Eqn. 7 as:", + "bbox": [ + 496, + 323, + 890, + 482 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {S L} = - \\sum_ {\\boldsymbol {x} _ {i} \\in \\mathcal {B}} \\frac {\\boldsymbol {w} _ {i}}{| \\Pi (i) |} \\sum_ {j \\in \\Pi (i)} \\log \\frac {\\exp \\left(\\boldsymbol {h} _ {i} ^ {+} \\cdot \\boldsymbol {h} _ {j} ^ {+} / \\tau\\right)}{\\sum_ {\\boldsymbol {x} _ {j ^ {\\prime}} \\in \\mathcal {B}} \\exp \\left(\\boldsymbol {h} _ {i} ^ {+} \\cdot \\boldsymbol {h} _ {j ^ {\\prime}} ^ {+} / \\tau\\right)}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 492, + 901, + 549 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Compared with proxy-based methods [53, 36, 21, 14], our similarity learning-based objective makes use of pairwise labels, which can be more accurate due to the following reason. Even if two labels in a positive pair are both incorrect, there is still a chance that they share the same semantics [51]. Our Mixing strategy further relieves the memorization of noisy samples, producing label noise-resistant and similarity-preserving deep features.", + "bbox": [ + 496, + 550, + 890, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Retrieval-based Refinement with Curriculum Learning", + "text_level": 1, + "bbox": [ + 500, + 680, + 890, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We need to identify and refine those noisy samples to thoroughly get rid of label noise for better performances [53, 36, 21, 14]. Traditional classification techniques consider samples with small training losses to be clean samples [15], and they often introduce a threshold to distinguish between clean and noisy data. Nevertheless, we are unable to directly obtain losses for various samples in the similarity learning framework. Even worse, a low threshold could exclude too many noisy samples resulting in potential underfitting, while a high threshold may have a limited capacity to filter noisy data. These point-wise methods could also be biased to refine noisy samples into easy", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11242", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "classes with small losses [33]. To address the problems, we provide a retrieval-based refinement module, which retrieves comparable samples for each prototype with curriculum learning [2] for precise and balanced refinement.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In particular, we view the centroid of each prototype as a query and retrieve $K$ samples in the dataset based on the Euclidean distance. For these retrieved samples, we regard them as clean if their labels are not consistent with their queries, otherwise refine their labels. In formulation, the refined datasets can be written as below:", + "bbox": [ + 75, + 152, + 470, + 242 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\mathcal {D}} = \\cup_ {c = 1} ^ {C} \\left\\{\\left(\\boldsymbol {x} _ {i}, c\\right) \\mid \\boldsymbol {z} _ {i} \\in N N \\left(\\boldsymbol {\\mu} _ {c}\\right) \\right\\} \\tag {9} \\\\ \\cup \\left\\{\\left(\\boldsymbol {x} _ {i}, y _ {i}\\right) \\mid \\boldsymbol {z} _ {i} \\notin \\cup_ {c = 1} ^ {C} N N \\left(\\boldsymbol {\\mu} _ {c}\\right) \\right\\}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 251, + 468, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $NN(\\cdot)$ denotes the set of top $K$ nearest samples in the datasets. Here we set the same $K$ for every prototype, which generates an accurate and balanced dataset after refinement. In comparison, clean sample selection based on losses could lean toward selecting clean samples from easy classes. Moreover, we propose to increase the retrieval number $K$ gradually following the principle of curriculum learning, which refines noisy samples from easy to hard. To be specific, we have different $K_{t}$ at the $t$ -th cycle:", + "bbox": [ + 75, + 303, + 470, + 440 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nK _ {t} = \\frac {t}{T} K _ {\\max }, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 450, + 468, + 479 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $T$ denotes the total number of cycles and $K_{max}$ denotes the maximal retrieval number. To increase framework efficiency, we would conduct retrieval-based refinement at the beginning of each cycle.", + "bbox": [ + 75, + 489, + 468, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Summary", + "text_level": 1, + "bbox": [ + 76, + 561, + 191, + 578 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Learn to Cluster. Finally, we enhance the discriminability of hidden features by learning to cluster [40]. This is accomplished by enforcing the accumulation of hidden features around their corresponding centroids. Here, we maximize the similarity between hidden features and their corresponding prototypes compared with the other prototypes by proposing the following objective:", + "bbox": [ + 75, + 585, + 468, + 691 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {C} = - \\sum_ {\\boldsymbol {x} _ {i} \\in \\mathcal {B}} \\log \\frac {\\exp \\left(\\boldsymbol {z} _ {i} \\cdot \\boldsymbol {\\mu} _ {y _ {i}} / \\tau\\right)}{\\sum_ {c = 1} ^ {C} \\exp \\left(\\boldsymbol {z} _ {i} \\cdot \\boldsymbol {\\mu} _ {c} / \\tau\\right)}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 702, + 468, + 741 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then the final objective is summarized by combining both two losses as follows:", + "bbox": [ + 75, + 752, + 468, + 781 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {S L} + \\eta \\mathcal {L} _ {C}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 796, + 468, + 811 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\eta$ is a parameter to balance two losses. In practice, we would first warm up the neural network without conducting Mixing and then perform prototypical Mixing and retrieval-based refinement gradually. We would demonstrate the whole algorithm in Algorithm 1.", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Training Algorithm of TITAN" + ], + "code_body": "Require: Dataset $\\mathcal{D}$ ; Iteration number $T$ Max retrieval number $K_{max}$ \nEnsure: The composited projector $H(F(\\cdot))$ . \n1:Warm up the projector; \n2:repeat \n3: Update the retrieval number $K_{t}$ using Eqn. 10 \n4: Estimate the distribution for every prototype using Eqn. 1 and Eqn. 2; \n5:Refine the dataset using Eqn.9; \n6:for $k = 1,2,\\dots ,k_{max}$ do \n7: Sample $\\mathcal{B}\\subset \\hat{\\mathcal{D}}$ to construct a mini-batch; \n8: Generate synthetic samples using Eqn. 4; \n9: Calculate the loss objective by Eqn. 12; \n10: Update the network parameters by backpropagata tion; \n11: end for \n12: until convergence", + "bbox": [ + 500, + 108, + 890, + 366 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 500, + 395, + 624, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Settings", + "text_level": 1, + "bbox": [ + 500, + 421, + 596, + 436 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. In order to evaluate the TITAN, we utilize four widely used datasets with various levels of granularity and size and one real-world noisy dataset. The concrete experimental setting is depicted in the Appendix. CIFAR10 [23] contains a total of 60k colorful images in 10 categories. CUB200-2011 [42] is the most common dataset utilized for fine-grained visual classification tasks and contains 11,788 images of 200 subcategories related to bird species. CARS196 [22] includes 16,185 samples of 196 distinct categories of car models. FLICKR25K [17] contains more coarsely grained categories and is more generalized. Cars98N [28] is a real-world noisy benchmark, it's built by collecting 9,558 examples for 98 car models from Pinterest. Normally the noisy examples in Cars98N usually consist of the car parts, the interior of the car, or pictures of other car models.", + "bbox": [ + 496, + 445, + 890, + 685 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To investigate the noise-resistant ability, we firstly synthesize two kinds of artificial noise labels, Symmetric and Pairflip, added to the training set of the none real-world noise dataset. Following [28], we vary the noise ratio with three degrees: $10\\%$ , $20\\%$ , and $50\\%$ respectively. Symmetric noise [34] simply flips labels between classes uniformly while Pairflip noise [34] similarly assigns the corrupted label to each nearby class.", + "bbox": [ + 496, + 688, + 890, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. We compare our TITAN with eight baselines that have excellent performances in their corresponding field. Concretely, three of these methods are standard retrieval approaches (i.e., Fast-AP [4], Smooth-AP [3] and Proxy-Anor [21]), two are robust noise-resistant approaches (i.e., REL [52] and Jo-SRC [54]), one is noise", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11243", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/e82a2285162bb2594d83327e55b55a39f0c74b23b85aec8daef6139f9294da2d.jpg", + "table_caption": [ + "Table 1. The MAP@R scores implemented on 512-dimensional feature vectors for retrieval on CIFAR10, CUB, CARS, and FlickR25K with three degrees of symmetric label noise." + ], + "table_footnote": [], + "table_body": "
MethodCIFAR10CUB200CARS196FLICKR25K
0.10.20.50.10.20.50.10.20.50.10.20.5
FastAP85.0783.4065.9213.8512.818.6310.789.286.4788.9588.5987.50
SmoothAP84.4881.3870.1112.7111.789.789.708.826.1986.3785.2082.30
Proxy-Anchor87.2078.0469.2316.7015.8610.1112.2111.115.3389.1288.6987.79
Jo-SRC87.5885.5572.8615.9714.9112.9112.7411.097.1091.0190.2289.43
REL86.8184.7671.9015.7815.6713.8614.0213.337.9691.5991.4490.60
HEART85.3683.1571.6517.1015.7912.0015.3013.598.6492.1191.8191.01
T-SINT87.3886.2672.8717.9017.3614.3414.4113.019.8990.7990.4587.65
PRISM87.6586.2373.0518.1217.7915.2916.9915.8810.0292.4292.1291.23
TITAN (Ours)89.0188.0175.8619.1118.6916.9017.6416.3611.3794.3393.8993.07
", + "bbox": [ + 81, + 114, + 890, + 313 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/476035a0cdd7af85e6570a36a67c6c1b15e0ae7883dd152e78d0968bd4974c06.jpg", + "table_caption": [ + "Table 2. The MAP@R scores implemented on 512-dimensional feature vectors for retrieval on CIFAR10, CUB, CARS, and FLICKR25K with three degrees of pairflip label noise." + ], + "table_footnote": [], + "table_body": "
MethodCIFAR10CUB200CARS196FLICKR25K
0.10.20.50.10.20.50.10.20.50.10.20.5
FastAP77.4276.5256.2714.0612.4211.0610.608.536.3687.5387.1685.22
SmoothAP76.1574.5555.8612.1211.4210.5610.629.556.8485.3085.1885.02
Proxy-Anor75.5573.8257.6516.0815.1112.1613.5211.458.6190.1989.2688.23
Jo-SRC78.5276.2457.7715.9214.5513.4514.4813.439.2091.6391.6090.11
REL75.8375.1258.7215.7614.7813.0512.5011.729.0991.4690.7889.19
HEART77.8276.1158.5516.2615.3313.0713.5813.368.7791.7691.7290.99
T-SINT79.1977.9455.3916.5116.1414.2614.4513.699.0791.6290.7489.71
PRISM80.4380.3262.0517.1315.8313.1315.4615.159.3892.4492.2790.91
TITAN (Ours)83.8982.9967.8818.2917.3615.7316.9815.8210.1494.0593.9093.18
", + "bbox": [ + 81, + 352, + 890, + 537 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "robust hash retrieval method (i.e., HEART [38]), two are noise-robust retrieval methods (i.e., T-SINT [18] and PRISM [28]).", + "bbox": [ + 76, + 563, + 468, + 609 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1caba4feb601873668e0bd4a3bb3a91a0d4a12a8baa9a7ca2f97ff399f73ce81.jpg", + "table_caption": [ + "Table 3. The MAP@R scores implemented on 512-dimensional feature vectors for retrieval on Cars98N." + ], + "table_footnote": [], + "table_body": "
MethodTITAN(Ours)T-SINTPRISMHEARTRELFastAP
Cars98N7.036.536.255.545.385.06
", + "bbox": [ + 81, + 648, + 470, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Criterion. Following [28, 18], we mainly employ Mean Average Precision@R (MAP@R) as our criterion for evaluation. MAP@R metric is a widely used measure of average accuracy for multiple queries and is a common metric for evaluating the quality of retrieval systems. Note that the value of R is not a fixed value for all benchmarks, it is equal to the largest number of samples among all categories in the corresponding retrieved set of the benchmark.", + "bbox": [ + 75, + 702, + 468, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We implement our method using PyTorch with an NVIDIA 3090 GPU. We adopt mini-batch Adam for our model training. The mini-batch size is set to 64 and the learning rate for our model is fixed at $5 \\times 10^{-5}$ .", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "All the images are resized to $224 \\times 224$ , and the training images have a $50\\%$ chance of being randomly flipped horizontally. In all experiments, we use ResNet18 as the feature extractor with the feature dimension being 512, and following [28] we use L2 normalization to make the output of the neural network be on the unit hypersphere for brief distance measurement. In particular, we also choose ResNet18 instead of CLIP as the teacher model when reimplementing T-SINT for a fair comparison.", + "bbox": [ + 496, + 563, + 890, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experimental Results", + "text_level": 1, + "bbox": [ + 500, + 710, + 700, + 726 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Comparison. Table 1 and Table 2 display the MAP@R results on CIFAR10, CARS, CUB, and FLICKR25K under Symmetric/Pairflip label noise specifically with noise rate being 0.1, 0.2, and 0.5. From these experimental results we can make the following observations: (1) The AP-based retrieval methods (i.e., FastAP and SmoothAP) often fail to perform as well as proxy-based retrieval methods in most cases. This may be due to the proxy-based approach's use of the feature centers of each class to protect metric learning from label noise. (2) The noise-resistant classification methods (i.e., Jo-SRC", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11244", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f670e3916558421739ffc6e10147c4d0acbbf7a94af76a89f107e863f75fc25d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 94, + 269, + 224 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5a71086040b4ec1b0ef3b6c358ad54599f07d958dc35041c665ba9ad81d7de43.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 93, + 468, + 227 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4e51d28052af5336e455600b53fcecaf9dd5a44a95b8eb0a353fd0d986581ef2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 229, + 269, + 363 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/eb68eb881a9910bf06312cc8825c89a82829fca3fd2874a17417c9813563e61e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 229, + 468, + 363 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/deb5a0a7b924e90c4f4b71c6fd5264a129cd112a4756171aab1223374c073308.jpg", + "image_caption": [ + "Figure 3. The P-R curves are plotted in the left column and Top-N precision curves are in the right column." + ], + "image_footnote": [], + "bbox": [ + 86, + 366, + 269, + 500 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5e1f7d7c355770915aec9deaba5b5f930e4413bafc6979b9e3443244a4cf22e9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 366, + 468, + 500 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and REL) achieve limited performance increases compared with standard retrieval methods, which illustrates that point-based classification approaches are not suitable for retrieval tasks under label noise and special techniques need to be designed to solve the problem. (3) Our proposed TITAN achieves the best scores on all the benchmarks with different settings. For CUB200, our TITAN obtain an improvement of $5.46\\%$ , $5.05\\%$ , and $9.52\\%$ over the best baseline PRISM under symmetric label noise with noise rate being 0.1, 0.2, 0.5 respectively. For CARS and FLICKR25K, our TITAN outperforms competitive baseline T-SINT by $21.04\\%$ and $4.66\\%$ in terms of average MAP@R scores under symmetric noise with different noise degrees. And the same tendency can also be observed on CIFAR10 under both noise label settings. The exceptional performance of our TITAN can be attributed to two primary factors. On the one hand, we improve the accuracy of noisy sample refinement by using retrieval-based refinement with curriculum learning instead of point-wise refinement. Our model, on the other hand, is enhanced by prototypical mixing technology that prevents it from memorizing noisy data, which facilitates semantic learning.", + "bbox": [ + 75, + 551, + 470, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3 displays the performance on Cars98N with real", + "bbox": [ + 96, + 885, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/094a3ca1d3f9dec8f20d4fa542300bb8aaa4623f311ae75a5ddead5345abb2b8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 93, + 702, + 232 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6e78dd18fbc5938dbe61b3a5ecc6db6f901447df9d65db0fa86e0e2cdb777e7c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 92, + 895, + 232 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f85ea0a949bdaaa831c8095dbc499aa584e1a7423d03a72d43bf6d6077c8c97a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 234, + 700, + 375 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/617f6b80a287fcfccaf9964521f41ff9892a99aec2142f6f9caed9e2e0f692f1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 234, + 895, + 375 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e53fb4323937cd3844ce3c7c221a2e412727ffa4089e82c8e2d8dde78a805831.jpg", + "image_caption": [ + "Figure 4. The MAP@R scores w.r.t. different noise rates. Results with Symmetric noise are plotted in the left column while results with Pairflip noise are plotted in the right column." + ], + "image_footnote": [], + "bbox": [ + 509, + 378, + 700, + 518 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6b526fbb852aa6bd06a6834e2e9604c4fe4b4443e38f4df20ffc973943883e4b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 378, + 895, + 518 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/79a7edeb86175b56f787a74a3227979bb2a18a19918d2b4854c653a4b918f85c.jpg", + "image_caption": [ + "Figure 5. The MAP@R scores of TITAN and PRISM implemented on CUB and Fickr25k with varying hidden dimensions while the noise rate is set to $10\\%$ ." + ], + "image_footnote": [], + "bbox": [ + 501, + 573, + 697, + 715 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/09cd0f7b4dc71929ecadec5c6250b6837084b64eacd744b452561377308c0635.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 573, + 898, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "world label noise. From these results, we can observe that TITAN also achieves significantly better performance in real-world settings, which demonstrates the generalizability and superiority of our approach.", + "bbox": [ + 496, + 777, + 890, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative Comparison. Additionally, we plot the P-R curves and TopN-precision curves of the proposed TITAN and other compared methods with 512-dimensional feature vectors on three benchmarks in Figure 3. In the P-R curve,", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11245", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cb04dac45b766c785c81e13a15543428e606df929cf4c2f2869fdf9b0c5d188f.jpg", + "table_caption": [ + "Table 4. Ablation results on CIFAR10, CUB, CARS, and FLICKR25K with noise rate being 0.1." + ], + "table_footnote": [], + "table_body": "
MethodCIFAR10CUB200CARS196FLICKR25K
TITAN w/o LSL85.0417.0515.8291.98
TITAN w/o LC84.3316.6715.2491.23
TITAN w/o M87.5618.2516.1392.65
TITAN w/o R87.7818.0516.0892.11
TITAN w/o w88.5418.7717.2493.97
TITAN (full)89.0119.1117.6494.33
", + "bbox": [ + 80, + 114, + 470, + 212 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the area enclosed by the curve corresponding to our method is significantly larger than the remaining three baselines, which indicates that our method has better retrieval performance. In the curve of topN-precision, our method keeps the highest accuracy rate as the number of retrieved samples increases, especially when the number of returned samples is around 100. Overall, we have the conclusion based on these visualization results that when coming to actual image retrieval, Titan can achieve promising retrieval performances.", + "bbox": [ + 75, + 229, + 468, + 380 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Noise Degree Analysis. We plot the performance trends under two different types of noise variation, especially for the high noise rate in Figure 4. This result indicates that the performance of PRISM decreases rapidly with an increase in noise, as PRISM is unable to construct a clean memory bank at the beginning if the noise ratio is too high. Even with a high noise ratio, our proposed TITAN is still able to deliver the best performance. Due to curriculum learning and blending the semantic information of the prototype with the sample features, we gradually construct a relatively accurate prototype for semantic learning. In general, our TITAN achieves great performance under various noise ratios, demonstrating the robustness and superiority of our proposed TITAN.", + "bbox": [ + 75, + 381, + 468, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Feature Dimension Analysis. Figure 5 shows the MAP@R results of TITAN and PRISM methods implemented on CUB and FLICKR25k with feature dimensions varying from 128 to 2048. It can be found that the MAP@R value has a small decrease in both 128 and 2048 dimensions for TITAN, while for PRISM there is no obvious pattern of change. In general, probably because of the L2 normalization, the MAP@R value does not change much with the increase of hidden dimension. Note that our method outperforms the PRISM for all the cases, which proves the robustness of our method.", + "bbox": [ + 75, + 593, + 468, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 770, + 230, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present an ablation study to investigate the effectiveness of the important inner module in our proposed TITAN and the experiment results are shown in Table 4. Specifically, we design the following model variants as: (1) TITAN w/o $\\mathcal{L}_{SL}$ removes similarity learning loss for denoising in Eqn. 7. (2) TITAN w/o $\\mathcal{L}_C$ removes cluster learning loss for retrieval in Eqn. 11. (3) TITAN w/o M removes", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the sampled virtual feature in Eqn. 4. (4) TITAN w/o R removes the retrieval-based refinement procedure. (5) TITAN w/o $\\mathbf{w}$ removes confidence scores in Eqn. 8. From these results, we can draw some observations as follows: First, TITAN w/o $\\mathcal{L}_C$ has lower MAP@R scores than TITAN w/o $\\mathcal{L}_{SL}$ , perhaps because in the case of a large number of sample categories in the training set, using a small batch size will lead to few positive sample pairs in the mini-batch, which will affect the learning of similarity. Second, TITAN w/o M performs worse than TITAN, which indicates that our use of prototypical mixing is effective, it makes the feature representation more robust and alleviates the overfitting of the model to dirty data to some extent. Third, MAP@R values corresponding to TITAN w/o R drop by about the same amount as TITAN w/o M, which proves that Retrieval-based refinement is an important and influential module in our proposed TITAN, it provides an effective way to refine noisy samples for pairwise similarity learning framework in retrieval tasks. Finally, the slightly lower performance of TITAN w/o $\\mathbf{w}$ compared to TITAN suggests that confidence scores can improve performance by attenuating the impact of unreliable mixed samples.", + "bbox": [ + 496, + 90, + 893, + 425 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/451947d65c4c6e0303dc65d3bd7e96cef23cf453290d3b755ed32ac616b1762d.jpg", + "image_caption": [ + "Figure 6. Sensitivity analysis of two hyper-parameters on CUB." + ], + "image_footnote": [], + "bbox": [ + 501, + 439, + 697, + 579 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/548ea1d1cd875c9bd223b0773cd444759b0773a594c94cde6ee681cd5aa3d4f5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 439, + 890, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Sensitivity Analysis", + "text_level": 1, + "bbox": [ + 500, + 619, + 687, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We investigate the effect of hyper-parameters $\\eta$ and $K_{max}$ on model retrieval performance on CUB with different noise rates. The loss balance coefficient $\\eta$ controls the weight between different losses, firstly we vary $\\eta$ in [0.1,0.3,0.5,0.8,1.0] with other parameters fixed, Figure 6 illustrates the experimental results, we can find that performance of our method is not sensitive to $\\eta$ when it varies from 0.5 to 1.0, which demonstrates that the convergence of our proposed algorithm is stable. Moreover, we fix all other parameters and change $K_{max}$ in [5,10,15,20,25,30], which controls the max retrieval number of each prototype, as shown in Figure 6, the MAP@R results decrease when $K_{max}$ is set in [25,30], the potential reason is that a high $K_{max}$ will cause more samples to change their labels, but our constructed prototype is not completely reliable at the early stage of training, this leads to refinement which may in turn increase the noise rate. From the analysis, we set $\\eta$", + "bbox": [ + 496, + 643, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11246", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "as 0.8 and $K_{max}$ as 20 respectively for the proposed TITAN as default.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.5. Case Study", + "text_level": 1, + "bbox": [ + 76, + 133, + 200, + 150 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We present the top ten images retrieved by PRISM and the proposed TITAN on FLICKR25K. As depicted in Figure 7, the examples enclosed in green boxes represent accurate results, whereas those enclosed in red boxes are wrong results. Additionally, we have labeled the category of each image below it. It is evident that the proposed approach yields significantly more relevant and precise retrieval outcomes for the given queries, demonstrating the superiority of our methodology in handling realistic scenarios.", + "bbox": [ + 75, + 157, + 472, + 295 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/364d2a5f0bd538b22d636f63482a897032a959ad9abcbf91b6b966fc6dd4742c.jpg", + "image_caption": [ + "Figure 7. Example of the Top10 returned images with 512-dimensional feature on FLICKR25K." + ], + "image_footnote": [], + "bbox": [ + 81, + 311, + 486, + 452 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.6. Visulaization Analysis", + "text_level": 1, + "bbox": [ + 76, + 507, + 284, + 523 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "T-SNE Visualization. We adopt T-Distributed Stochastic Neighbor Embedding (T-SNE) [39] to compress the dense feature vectors into the two-dimensional plane to visualize the correlations between the features embedded and their one-hot labels, which come from the feature space and the label space respectively. Figure 8 illustrates the visualization of dense vectors generated by our method and the competitive baselines, i.e., PRISM and Jo-SRC. Compared with the two baselines, our method can generate actually compact clusters and can separate each category more clearly while at the same time bringing feature vectors with similar semantic information closer together. This visualization shows that our method can generate dense features that are more discriminative, which could facilitate better image retrieval.", + "bbox": [ + 75, + 532, + 472, + 758 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/0bf1f41a97bebe19f6f8cb974e95c906a0a2d0a76aff20200cfa192f8879cfbe.jpg", + "image_caption": [ + "Figure 8. The t-SNE visualization of 512-dimensional feature vectors on CIFAR10." + ], + "image_footnote": [], + "bbox": [ + 84, + 773, + 480, + 866 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 89, + 619, + 106 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This paper studies a practical but less-explored problem of label noise-resistant image retrieval and proposes a novel method TITAN, which simultaneously corrects label noise and mitigates the impacts of memorization to solve the problem. We describe different prototypes with Gaussian distributions in the hidden space, which directs Mixing to generate synthetic samples. In addition, we collect similar samples for each prototype ranging from easy to hard during optimization, which refines noisy samples in a precise and class-balanced way. Extensive experiments on five benchmark datasets reveal that our proposed TITAN can outperform various state-of-the-art methods. In future works, we would extend our TITAN to more scenarios such as learning to hash and cross-modal retrieval.", + "bbox": [ + 496, + 116, + 893, + 328 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 347, + 596, + 363 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Artem Babenko and Victor Lempitsky. Aggregating local deep features for image retrieval. 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IEEE Transactions on Pattern Analysis and Machine Intelligence, 40(5):1224-1244, 2017. 1, 2" + ], + "bbox": [ + 501, + 92, + 890, + 246 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "11249", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Prototypical Mixing and Retrieval-Based Refinement for Label Noise-Resistant Image Retrieval/ec71d51a-9735-4817-bbda-a4f4fe8a6bfa_model.json b/2023/Prototypical Mixing and Retrieval-Based Refinement for Label Noise-Resistant Image Retrieval/ec71d51a-9735-4817-bbda-a4f4fe8a6bfa_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e0377c25ccc7fa1fd986f9f2238ac3d832ec9a81 --- /dev/null +++ b/2023/Prototypical Mixing and Retrieval-Based Refinement for Label Noise-Resistant Image Retrieval/ec71d51a-9735-4817-bbda-a4f4fe8a6bfa_model.json @@ -0,0 +1,2400 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.807, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.095, + 0.13, + 0.878, + 0.175 + ], + "angle": 0, + "content": "Prototypical Mixing and Retrieval-based Refinement for Label Noise-resistant Image Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.188, + 0.215, + 0.78, + 0.235 + ], + "angle": 0, + "content": "Xinlong Yang\\(^{1*}\\), Haixin Wang\\(^{1*}\\), Jinan Sun\\(^{1}\\), Shikun Zhang\\(^{1}\\), Chong Chen\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.364, + 0.246, + 0.605, + 0.265 + ], + "angle": 0, + "content": "Xian-Sheng Hua², Xiao Luo³†" + }, + { + "type": "text", + "bbox": [ + 0.105, + 0.276, + 0.865, + 0.331 + ], + "angle": 0, + "content": "\\(^{1}\\) Peking University \\(^{2}\\) Terminus Group \\(^{3}\\) University of California, Los Angeles \\(\\{\\mathrm{xinlong.yang, wang.hx}\\} @\\)stu.pku.edu.cn, \\(\\{\\mathrm{sjn, zhangsk}\\} @\\)pu.edu.cn, cheung1990@126.com, huaxiansheng@gmail.com, xiaoluo@cs.ucla.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.375, + 0.314, + 0.392 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.409, + 0.473, + 0.756 + ], + "angle": 0, + "content": "Label noise is pervasive in real-world applications, which influences the optimization of neural network models. This paper investigates a realistic but understudied problem of image retrieval under label noise, which could lead to severe overfitting or memorization of noisy samples during optimization. Moreover, identifying noisy samples correctly is still a challenging problem for retrieval models. In this paper, we propose a novel approach called Prototypical Mixing and Retrieval-based Refinement (TITAN) for label noise-resistant image retrieval, which corrects label noise and mitigates the effects of the memorization simultaneously. Specifically, we first characterize numerous prototypes with Gaussian distributions in the hidden space, which would direct the Mixing procedure in providing synthesized samples. These samples are fed into a similarity learning framework with varying emphasis based on the prototypical structure to learn semantics with reduced overfitting. In addition, we retrieve comparable samples for each prototype from simple to complex, which refine noisy samples in an accurate and class-balanced manner. Comprehensive experiments on five benchmark datasets demonstrate the superiority of our proposed TITAN compared with various competing baselines." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.787, + 0.21, + 0.803 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.814, + 0.47, + 0.875 + ], + "angle": 0, + "content": "Content-based image retrieval has been an essential research area in computer vision [7], with various applications in search engineering [49, 13] and medical image analysis [19]. Content-based image retrieval can be divided" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.377, + 0.892, + 0.468 + ], + "angle": 0, + "content": "into instance-level retrieval [1, 62] and category-level retrieval [45, 43, 53]. The former focuses on capturing the same instance in different environments. In recent years, category-level retrieval has gained popularity by delivering samples from a massive database with results grouped by the same category as the query [36]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.893, + 0.685 + ], + "angle": 0, + "content": "The core of successful category-level retrieval is to map instances to data points in the feature space while preserving similarity connections. The majority of current approaches focus on similarity learning [46, 35], which use pairwise [30] and triplet [16, 50] objectives to maintain semantics in the embedding space. These approaches promote the proximity of semantically similar samples in the embedding space and the separation of semantically different samples. An alternative strategy is to utilize proxies [53, 36, 21, 14]. These methods map each class into the deep feature space to guide semantics learning in a pointwise manner. A few of studies use binary descriptors to improve efficiency [44, 56], which results in a candidate set followed by further refinement for precise image retrieval." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Despite their considerable success, these retrieval systems often presume that the semantic labels in the training set are accurate. In real-world applications, this assumption could be invalidated by the possibility of annotation mistakes and inadequate automated collecting tactics [47, 54]. For instance, web-based sources often include tags and captions, which are usually utilized to provide label information for convenience. These approaches could generate extensive label noise to collected datasets. To address this issue, this work studies a practical topic named image retrieval with label noise. Although there are extensive papers to study the problem of robust learning in classification tasks [29, 12, 25], retrieval models under label noise are still underexplored with unsatisfactory performance in practice." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.334, + 0.901 + ], + "angle": 0, + "content": "*Equal contribution. †Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11239" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.095, + 0.452, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.265, + 0.47, + 0.295 + ], + "angle": 0, + "content": "Figure 1. Two Mixing mechanisms are demonstrated including the standard Mixup (top) and our prototypical Mixing (bottom)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.311, + 0.47, + 0.552 + ], + "angle": 0, + "content": "However, developing a label-noise resistant retrieval model is challenging due to two reasons: (1) Erroneous supervision. Extensive label noise could result in erroneous supervision information, resulting in a significant decline in retrieval performance. In literature, a few works propose to refine noisy samples for effective image retrieval [28, 18]. For example, PRISM [28] estimates the probability of an example being clean with the help of a memory bank. However, they are prone to result in biased and overconfident refinement due to their point-wise calculation [60]. (2) Serious Memorization. Although deep neural networks tend to learn generalized patterns at the beginning stage, the overfitting or memorization of noisy data would compromise the optimization process gradually [57]. As a consequence, a robust optimization objective is anticipated to improve the retrieval performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In this study, we propose a novel retrieval method named Prototypical Mixing and Retrieval-based Refinement (TITAN) for label noise-resistant image retrieval. The essence of our TITAN is to measure the distributions of different prototypes in the hidden space. Note that Mixup [58] can generate synthesis samples, which follows the Vicinal Risk Minimization (VRM) [5] principle with high generalization capability. Here, synthetic samples are generated by merging the original data with samples from the respective prototypical distributions, hence avoiding the possible overfitting of noisy samples. Compared with standard Mixup [58], our prototypical Mixing considers more about the hidden structure and does not require mixing different labels. Afterward, we build a similarity learning framework that optimizes the similarity between samples with the same label against using different emphases inferred from prototypical distributions. In addition, to filter potential noisy data, we retrieve comparable samples for each prototype [55]. The identical retrieval number for different prototypes with curriculum learning [2] promises accurate and class-balanced label refinement. Finally, we involve in learning to cluster to enhance the discriminability for effective image retrieval. Comprehensive experiments on a variety of datasets verify" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "the superiority of our TITAN by comparing it to a number of benchmarks. The contribution of this paper can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.147, + 0.892, + 0.194 + ], + "angle": 0, + "content": "- This paper studies a less-explored but practical problem named label noise-resistant image retrieval and proposes a novel method named TITAN for this problem." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.204, + 0.894, + 0.295 + ], + "angle": 0, + "content": "- On the one hand, TITAN measures the distributions of different prototypes and then generates synthesis data to prevent the memorization of noisy samples. On the other hand, TITAN retrieves comparable samples for each prototype from easy to hard, promising accurate and class-balanced label refinement." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.306, + 0.892, + 0.352 + ], + "angle": 0, + "content": "- Extensive experiments on five benchmark datasets demonstrate the superiority of our TITAN compared with various baseline methods in different settings." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.147, + 0.894, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.366, + 0.642, + 0.381 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.39, + 0.776, + 0.407 + ], + "angle": 0, + "content": "2.1. Context-based Image Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.414, + 0.892, + 0.732 + ], + "angle": 0, + "content": "As a basic research topic in computer vision and multimedia communities, context-based image retrieval can be separated into instance-level retrieval [1, 62] and category-level retrieval [45, 43, 53]. Recent years have seen an increasing interest in category-level retrieval, which can be further divided into similarity-based [46, 35] and proxy-based approaches [53, 36, 21, 14]. Similarity-based approaches utilize similarity relationships to generate positive and negative pairs, which are then combined with pairwise [30] and triplet [16, 50] losses to optimize deep neural networks. For instance, GSS [27] tries to distinguish the pairwise similarity in the whole dataset in an unsupervised manner. In contrast, proxy-based approaches map labels into the embedding space before minimizing the distance between deep features and their respective proxies. Hashing-based search engines are also in great demand due to their high efficiency [44, 56]. Nevertheless, these approaches do not often account for label noise in real-world datasets. In contrast, we investigate the issue of label noise-resistant image retrieval and develop a novel framework named TITAN to address it." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.741, + 0.741, + 0.758 + ], + "angle": 0, + "content": "2.2. Learning with Label Noise" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Learning with label noise has been intensive in a variety of tasks including image segmentation [32], saliency detection [59], and network analysis [9]. A range of works proposes robust losses to potential label noise [11, 10]. For example, RINCE [8] modifies the formula for contrastive learning, which achieves robust performance under noisy augmented views. Another line of this topic is to choose samples with noisy labels and clean them [15, 48, 31, 24, 61, 37, 20]. Early attempts usually put forward a threshold," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11240" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.09, + 0.891, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.395, + 0.893, + 0.437 + ], + "angle": 0, + "content": "Figure 2. An overview of the proposed TITAN. TITAN first estimates the distributions of prototypes for each class, from which we sample features for Mixing to generate virtual features. Moreover, TITAN retrieves different samples for every prototype to refine noisy samples. The final losses are composed of both similarity learning and clustering losses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.451, + 0.473, + 0.664 + ], + "angle": 0, + "content": "and samples with losses above the threshold are deemed noisy. Co-teaching [15] optimizes two networks concurrently by utilizing small-loss examples from one network to optimize the other network. A few of works attempt to extend robust learning into image retrieval by identifying noisy samples based on similarity [28, 18]. However, these works still neglect the overfitting of noisy samples, and refinement procedures of label noise remain to be biased and overconfident, especially when the amount of noisy data increases. In this paper, we incorporate prototypical Mixing into a similarity learning framework to ease the overfitting of noisy data. To ensure that the labels are assigned correctly and balance class sizes, we also filter noisy samples according to the retrieval process." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.692, + 0.204, + 0.71 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.722, + 0.26, + 0.737 + ], + "angle": 0, + "content": "3.1. Problem Definition" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We start by giving the problem definition. Denote the training set as \\(\\mathcal{D} = \\{(x_i, y_i)\\}_{i=1}^n\\) where \\(x_i\\) is the \\(i\\)-th sample and \\(y_i\\) is its observe labels. \\(n\\) represents the data size. We aim to learn a mapping to project data points into an embedding space where similar image pairs should be mapped into similar deep features and vice versa. In our settings, we assume that the observed labels could be wrong, which increases the difficulty of discriminative feature learning. To evaluate our model, we would retrieve similar examples in the database for the given query sample." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.45, + 0.611, + 0.466 + ], + "angle": 0, + "content": "3.2. Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.895, + 0.732 + ], + "angle": 0, + "content": "Learning effective image representations under label noise requires us to reduce the extreme overfitting of noisy samples and clean up noisy labels in the dataset. Here, we propose a novel method named TITAN for this problem. Following previous works [18, 28], our TITAN modifies a popular classification network (e.g., VGG-F and ResNet50) by adding an MLP layer in place of its head to provide deep features, i.e., \\( \\pmb{h} = H(F(\\pmb{x})) \\) where \\( F(\\cdot) \\) is the feature extractor and \\( H(\\cdot) \\) is the MLP head. As illustrated in Figure 2, our model consists of two essential components: (1) Prototypical Mixing, which characterizes prototypes using Gaussian distributions and then generates virtual samples by incorporating prototype information to relieve the memorization of noisy samples; (2) Retrieval-based Refinement, which retrieves similar samples for every prototype to further refine noisy samples in a balanced way. Then, we elaborate on the details of our TITAN." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.741, + 0.892, + 0.773 + ], + "angle": 0, + "content": "3.3. Prototypical Mixing for Robust Representation Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.886 + ], + "angle": 0, + "content": "The overfitting of neural networks is a major challenge in deep representation learning [57]. As a consequence, we must enhance the generalization capacity of the model. Here, we first characterize the prototypes of various classes using different Gaussian distributions before developing a Mixing technique that blends hidden features with samples derived from these prototypes." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In detail, we characterize the distribution of each class in" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11241" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "the prototype as a latent Gaussian distribution \\(N(\\pmb{\\mu}_c, \\pmb{\\Sigma}_c)\\), and every related hidden feature can be thought of as a sample from the Gaussian distribution [26]. Note that even if these samples could be noisy, the centroid measurement of the distribution is still reliable since all the samples are considered together with potential label noise neutralized. In particular, we measure the centroid and the corresponding covariance matrix based on these samples. In formulation, denote the hidden feature of \\(\\pmb{x}_i\\) as \\(\\pmb{z}_i\\), we have the estimated mean vector \\(\\pmb{\\mu}_c\\) and the covariance matrix \\(\\pmb{\\Sigma}_c\\) of the \\(c\\)-th class in the formulation of:" + }, + { + "type": "equation", + "bbox": [ + 0.199, + 0.269, + 0.47, + 0.309 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\mu} _ {c} = \\frac {\\sum_ {i = 1} ^ {N} \\mathbf {1} _ {y _ {i} = c} \\boldsymbol {z} _ {i}}{\\sum_ {i = 1} ^ {N} \\mathbf {1} _ {y _ {i} = c}}, \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.314, + 0.47, + 0.356 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Sigma} _ {c} = \\frac {\\sum_ {i = 1} ^ {N} \\mathbf {1} _ {y _ {i} = c} (\\boldsymbol {z} _ {i} - \\boldsymbol {\\mu} _ {c}) (\\boldsymbol {z} _ {i} - \\boldsymbol {\\mu} _ {c}) ^ {T}}{\\sum_ {i = 1} ^ {N} \\mathbf {1} _ {y _ {i} = c}}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.359, + 0.47, + 0.42 + ], + "angle": 0, + "content": "Then, we generate a virtual sample from the distribution, which would be combined with the original sample. In formulation, we first select the prototype with the maximal probability for each sample, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.43, + 0.47, + 0.466 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {i} = \\arg \\max _ {c} \\frac {1}{\\sqrt {(2 \\pi) ^ {d} | \\boldsymbol {\\Sigma} _ {c} |}} \\mathrm {e} ^ {- \\frac {1}{2} (\\boldsymbol {z} _ {i} - \\boldsymbol {\\mu} _ {c}) ^ {\\mathrm {T}} \\boldsymbol {\\Sigma} _ {c} ^ {- 1} (\\boldsymbol {z} _ {i} - \\boldsymbol {\\mu} _ {c})}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.475, + 0.47, + 0.504 + ], + "angle": 0, + "content": "where \\(d\\) denotes the hidden dimension. The mixed hidden feature can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.516, + 0.47, + 0.535 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {z} _ {i} ^ {+} = \\lambda \\boldsymbol {z} _ {i} + (1 - \\lambda) \\boldsymbol {z} _ {i} ^ {\\prime}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.545, + 0.47, + 0.605 + ], + "angle": 0, + "content": "where \\( \\boldsymbol{z}_i' \\) is randomly generated from \\( N(\\boldsymbol{\\mu}_{\\hat{y}_i}, \\boldsymbol{\\Sigma}_{\\hat{y}_i}) \\), \\( \\boldsymbol{z}_i = F(\\boldsymbol{x}_i) \\) and \\( \\boldsymbol{x}_i \\) denotes the original image sample. \\( \\lambda \\) is a coefficient selected from a Beta distribution following previous works:" + }, + { + "type": "equation", + "bbox": [ + 0.217, + 0.606, + 0.47, + 0.623 + ], + "angle": 0, + "content": "\\[\n\\lambda \\sim B e t a (\\alpha , \\beta) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.469, + 0.674 + ], + "angle": 0, + "content": "where \\(\\alpha\\) and \\(\\beta\\) are two parameters both set to 2 empirically. To simplify the calculation, we adopt a diagonal \\(\\Sigma_{c}\\) for each distribution with the neglection of the covariance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.469, + 0.854 + ], + "angle": 0, + "content": "Advantages of Prototypical Mixing. Similarly to standard Mixup, our prototypical Mixing also generates synthetic samples, extending the Empirical Risk Minimization (ERM) principle [41] to the Vicinal Risk Minimization (VRM) principle [5]. In this way, our TITAN has a strong capacity for generalization and is resistant to the memorization of noisy examples. Moreover, our prototypical Mixing does not need to combine labels to generate synthetic labels, which could be biased since the label space contains distinct relationships. Lastly, our TITAN adequately explores prototypical structures in the hidden space, which can serve as implicit label correction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.9 + ], + "angle": 0, + "content": "Next, we include the mixed samples into a framework for deep representation learning that maintains similarity. Here, we concatenate the hidden feature with the mixed feature" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.171 + ], + "angle": 0, + "content": "into a mini-batch and maximize the similarity between deep features of positive pairs compared with negative pairs. The positives for \\( z_{i}^{+} \\) are mini-batch samples sharing the same label, i.e., \\( z_{j}^{+} \\) with \\( y_{i} = y_{j} \\). In formulation, given the minibatch \\( \\mathcal{B} \\), the index of positives for \\( z_{i}^{+} \\) is written as:" + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.182, + 0.892, + 0.2 + ], + "angle": 0, + "content": "\\[\n\\Pi (i) = \\{j | \\boldsymbol {x} _ {j} \\in \\mathcal {B}, y _ {i} = y _ {j} \\}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.21, + 0.892, + 0.256 + ], + "angle": 0, + "content": "Following previous works [38, 6], the negatives are all the other samples in a mini-batch, then the similarity learning objective is constructed as:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.266, + 0.896, + 0.324 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {S L} = - \\sum_ {\\boldsymbol {x} _ {i} \\in \\mathcal {B}} \\frac {1}{| \\Pi (i) |} \\sum_ {j \\in \\Pi (i)} \\log \\frac {\\exp \\left(\\boldsymbol {h} _ {i} ^ {+} \\cdot \\boldsymbol {h} _ {j} ^ {+} / \\tau\\right)}{\\sum_ {\\boldsymbol {x} _ {j ^ {\\prime}} \\in \\mathcal {B}} \\exp \\left(\\boldsymbol {h} _ {i} ^ {+} \\cdot \\boldsymbol {h} _ {j ^ {\\prime}} ^ {+} / \\tau\\right)} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.324, + 0.892, + 0.483 + ], + "angle": 0, + "content": "where \\( \\pmb{h}_i^+ = H(\\pmb{z}_i^+) \\) maps the hidden feature into the target space and \\( \\tau \\) is a temperature parameter preset to 0.5 as in [38]. Moreover, we also incorporate the probabilities in Eqn. 3 as the confidence scores, which gives more emphasis on samples with high confidence. Consequently, we alleviate the effect of unreliable mixed data and enlarge the range of sample weights. In other words, sample weights are assigned more heavily to reliable samples. Let \\( \\pmb{w}_i = \\frac{1}{\\sqrt{(2\\pi)^d|\\pmb{\\Sigma}_{\\hat{y}_i}|}}\\mathrm{e}^{-\\frac{1}{2} (\\pmb{z}_i - \\pmb{\\mu}_{\\hat{y}_i})^\\mathrm{T}\\pmb{\\Sigma}_c^{-1}(\\pmb{z}_i - \\pmb{\\mu}_{\\hat{y}_i})} \\) denote the confidence score, and we rewrite Eqn. 7 as:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.493, + 0.903, + 0.55 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {S L} = - \\sum_ {\\boldsymbol {x} _ {i} \\in \\mathcal {B}} \\frac {\\boldsymbol {w} _ {i}}{| \\Pi (i) |} \\sum_ {j \\in \\Pi (i)} \\log \\frac {\\exp \\left(\\boldsymbol {h} _ {i} ^ {+} \\cdot \\boldsymbol {h} _ {j} ^ {+} / \\tau\\right)}{\\sum_ {\\boldsymbol {x} _ {j ^ {\\prime}} \\in \\mathcal {B}} \\exp \\left(\\boldsymbol {h} _ {i} ^ {+} \\cdot \\boldsymbol {h} _ {j ^ {\\prime}} ^ {+} / \\tau\\right)}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.551, + 0.892, + 0.673 + ], + "angle": 0, + "content": "Compared with proxy-based methods [53, 36, 21, 14], our similarity learning-based objective makes use of pairwise labels, which can be more accurate due to the following reason. Even if two labels in a positive pair are both incorrect, there is still a chance that they share the same semantics [51]. Our Mixing strategy further relieves the memorization of noisy samples, producing label noise-resistant and similarity-preserving deep features." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.681, + 0.892, + 0.713 + ], + "angle": 0, + "content": "3.4. Retrieval-based Refinement with Curriculum Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We need to identify and refine those noisy samples to thoroughly get rid of label noise for better performances [53, 36, 21, 14]. Traditional classification techniques consider samples with small training losses to be clean samples [15], and they often introduce a threshold to distinguish between clean and noisy data. Nevertheless, we are unable to directly obtain losses for various samples in the similarity learning framework. Even worse, a low threshold could exclude too many noisy samples resulting in potential underfitting, while a high threshold may have a limited capacity to filter noisy data. These point-wise methods could also be biased to refine noisy samples into easy" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11242" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.152 + ], + "angle": 0, + "content": "classes with small losses [33]. To address the problems, we provide a retrieval-based refinement module, which retrieves comparable samples for each prototype with curriculum learning [2] for precise and balanced refinement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.153, + 0.471, + 0.243 + ], + "angle": 0, + "content": "In particular, we view the centroid of each prototype as a query and retrieve \\( K \\) samples in the dataset based on the Euclidean distance. For these retrieved samples, we regard them as clean if their labels are not consistent with their queries, otherwise refine their labels. In formulation, the refined datasets can be written as below:" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.252, + 0.47, + 0.293 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\mathcal {D}} = \\cup_ {c = 1} ^ {C} \\left\\{\\left(\\boldsymbol {x} _ {i}, c\\right) \\mid \\boldsymbol {z} _ {i} \\in N N \\left(\\boldsymbol {\\mu} _ {c}\\right) \\right\\} \\tag {9} \\\\ \\cup \\left\\{\\left(\\boldsymbol {x} _ {i}, y _ {i}\\right) \\mid \\boldsymbol {z} _ {i} \\notin \\cup_ {c = 1} ^ {C} N N \\left(\\boldsymbol {\\mu} _ {c}\\right) \\right\\}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.471, + 0.441 + ], + "angle": 0, + "content": "where \\( NN(\\cdot) \\) denotes the set of top \\( K \\) nearest samples in the datasets. Here we set the same \\( K \\) for every prototype, which generates an accurate and balanced dataset after refinement. In comparison, clean sample selection based on losses could lean toward selecting clean samples from easy classes. Moreover, we propose to increase the retrieval number \\( K \\) gradually following the principle of curriculum learning, which refines noisy samples from easy to hard. To be specific, we have different \\( K_{t} \\) at the \\( t \\)-th cycle:" + }, + { + "type": "equation", + "bbox": [ + 0.22, + 0.452, + 0.47, + 0.481 + ], + "angle": 0, + "content": "\\[\nK _ {t} = \\frac {t}{T} K _ {\\max }, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.47, + 0.552 + ], + "angle": 0, + "content": "where \\( T \\) denotes the total number of cycles and \\( K_{max} \\) denotes the maximal retrieval number. To increase framework efficiency, we would conduct retrieval-based refinement at the beginning of each cycle." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.563, + 0.192, + 0.579 + ], + "angle": 0, + "content": "3.5. Summary" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.47, + 0.692 + ], + "angle": 0, + "content": "Learn to Cluster. Finally, we enhance the discriminability of hidden features by learning to cluster [40]. This is accomplished by enforcing the accumulation of hidden features around their corresponding centroids. Here, we maximize the similarity between hidden features and their corresponding prototypes compared with the other prototypes by proposing the following objective:" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.703, + 0.469, + 0.742 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {C} = - \\sum_ {\\boldsymbol {x} _ {i} \\in \\mathcal {B}} \\log \\frac {\\exp \\left(\\boldsymbol {z} _ {i} \\cdot \\boldsymbol {\\mu} _ {y _ {i}} / \\tau\\right)}{\\sum_ {c = 1} ^ {C} \\exp \\left(\\boldsymbol {z} _ {i} \\cdot \\boldsymbol {\\mu} _ {c} / \\tau\\right)}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.753, + 0.47, + 0.782 + ], + "angle": 0, + "content": "Then the final objective is summarized by combining both two losses as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.212, + 0.797, + 0.469, + 0.813 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {S L} + \\eta \\mathcal {L} _ {C}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.901 + ], + "angle": 0, + "content": "where \\(\\eta\\) is a parameter to balance two losses. In practice, we would first warm up the neural network without conducting Mixing and then perform prototypical Mixing and retrieval-based refinement gradually. We would demonstrate the whole algorithm in Algorithm 1." + }, + { + "type": "code_caption", + "bbox": [ + 0.501, + 0.091, + 0.792, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 Training Algorithm of TITAN" + }, + { + "type": "algorithm", + "bbox": [ + 0.501, + 0.109, + 0.892, + 0.367 + ], + "angle": 0, + "content": "Require: Dataset \\(\\mathcal{D}\\) ; Iteration number \\(T\\) Max retrieval number \\(K_{max}\\) \nEnsure: The composited projector \\(H(F(\\cdot))\\) . \n1:Warm up the projector; \n2:repeat \n3: Update the retrieval number \\(K_{t}\\) using Eqn. 10 \n4: Estimate the distribution for every prototype using Eqn. 1 and Eqn. 2; \n5:Refine the dataset using Eqn.9; \n6:for \\(k = 1,2,\\dots ,k_{max}\\) do \n7: Sample \\(\\mathcal{B}\\subset \\hat{\\mathcal{D}}\\) to construct a mini-batch; \n8: Generate synthetic samples using Eqn. 4; \n9: Calculate the loss objective by Eqn. 12; \n10: Update the network parameters by backpropagata tion; \n11: end for \n12: until convergence" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.396, + 0.625, + 0.414 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.422, + 0.598, + 0.438 + ], + "angle": 0, + "content": "4.1. Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.892, + 0.686 + ], + "angle": 0, + "content": "Datasets. In order to evaluate the TITAN, we utilize four widely used datasets with various levels of granularity and size and one real-world noisy dataset. The concrete experimental setting is depicted in the Appendix. CIFAR10 [23] contains a total of 60k colorful images in 10 categories. CUB200-2011 [42] is the most common dataset utilized for fine-grained visual classification tasks and contains 11,788 images of 200 subcategories related to bird species. CARS196 [22] includes 16,185 samples of 196 distinct categories of car models. FLICKR25K [17] contains more coarsely grained categories and is more generalized. Cars98N [28] is a real-world noisy benchmark, it's built by collecting 9,558 examples for 98 car models from Pinterest. Normally the noisy examples in Cars98N usually consist of the car parts, the interior of the car, or pictures of other car models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.809 + ], + "angle": 0, + "content": "To investigate the noise-resistant ability, we firstly synthesize two kinds of artificial noise labels, Symmetric and Pairflip, added to the training set of the none real-world noise dataset. Following [28], we vary the noise ratio with three degrees: \\(10\\%\\), \\(20\\%\\), and \\(50\\%\\) respectively. Symmetric noise [34] simply flips labels between classes uniformly while Pairflip noise [34] similarly assigns the corrupted label to each nearby class." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Baselines. We compare our TITAN with eight baselines that have excellent performances in their corresponding field. Concretely, three of these methods are standard retrieval approaches (i.e., Fast-AP [4], Smooth-AP [3] and Proxy-Anor [21]), two are robust noise-resistant approaches (i.e., REL [52] and Jo-SRC [54]), one is noise" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11243" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.892, + 0.115 + ], + "angle": 0, + "content": "Table 1. The MAP@R scores implemented on 512-dimensional feature vectors for retrieval on CIFAR10, CUB, CARS, and FlickR25K with three degrees of symmetric label noise." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.116, + 0.892, + 0.314 + ], + "angle": 0, + "content": "
MethodCIFAR10CUB200CARS196FLICKR25K
0.10.20.50.10.20.50.10.20.50.10.20.5
FastAP85.0783.4065.9213.8512.818.6310.789.286.4788.9588.5987.50
SmoothAP84.4881.3870.1112.7111.789.789.708.826.1986.3785.2082.30
Proxy-Anchor87.2078.0469.2316.7015.8610.1112.2111.115.3389.1288.6987.79
Jo-SRC87.5885.5572.8615.9714.9112.9112.7411.097.1091.0190.2289.43
REL86.8184.7671.9015.7815.6713.8614.0213.337.9691.5991.4490.60
HEART85.3683.1571.6517.1015.7912.0015.3013.598.6492.1191.8191.01
T-SINT87.3886.2672.8717.9017.3614.3414.4113.019.8990.7990.4587.65
PRISM87.6586.2373.0518.1217.7915.2916.9915.8810.0292.4292.1291.23
TITAN (Ours)89.0188.0175.8619.1118.6916.9017.6416.3611.3794.3393.8993.07
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.325, + 0.892, + 0.352 + ], + "angle": 0, + "content": "Table 2. The MAP@R scores implemented on 512-dimensional feature vectors for retrieval on CIFAR10, CUB, CARS, and FLICKR25K with three degrees of pairflip label noise." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.353, + 0.892, + 0.538 + ], + "angle": 0, + "content": "
MethodCIFAR10CUB200CARS196FLICKR25K
0.10.20.50.10.20.50.10.20.50.10.20.5
FastAP77.4276.5256.2714.0612.4211.0610.608.536.3687.5387.1685.22
SmoothAP76.1574.5555.8612.1211.4210.5610.629.556.8485.3085.1885.02
Proxy-Anor75.5573.8257.6516.0815.1112.1613.5211.458.6190.1989.2688.23
Jo-SRC78.5276.2457.7715.9214.5513.4514.4813.439.2091.6391.6090.11
REL75.8375.1258.7215.7614.7813.0512.5011.729.0991.4690.7889.19
HEART77.8276.1158.5516.2615.3313.0713.5813.368.7791.7691.7290.99
T-SINT79.1977.9455.3916.5116.1414.2614.4513.699.0791.6290.7489.71
PRISM80.4380.3262.0517.1315.8313.1315.4615.159.3892.4492.2790.91
TITAN (Ours)83.8982.9967.8818.2917.3615.7316.9815.8210.1494.0593.9093.18
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.564, + 0.47, + 0.61 + ], + "angle": 0, + "content": "robust hash retrieval method (i.e., HEART [38]), two are noise-robust retrieval methods (i.e., T-SINT [18] and PRISM [28])." + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.622, + 0.47, + 0.649 + ], + "angle": 0, + "content": "Table 3. The MAP@R scores implemented on 512-dimensional feature vectors for retrieval on Cars98N." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.65, + 0.471, + 0.687 + ], + "angle": 0, + "content": "
MethodTITAN(Ours)T-SINTPRISMHEARTRELFastAP
Cars98N7.036.536.255.545.385.06
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.469, + 0.839 + ], + "angle": 0, + "content": "Evaluation Criterion. Following [28, 18], we mainly employ Mean Average Precision@R (MAP@R) as our criterion for evaluation. MAP@R metric is a widely used measure of average accuracy for multiple queries and is a common metric for evaluating the quality of retrieval systems. Note that the value of R is not a fixed value for all benchmarks, it is equal to the largest number of samples among all categories in the corresponding retrieved set of the benchmark." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Implementation Details. We implement our method using PyTorch with an NVIDIA 3090 GPU. We adopt mini-batch Adam for our model training. The mini-batch size is set to 64 and the learning rate for our model is fixed at \\(5 \\times 10^{-5}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.564, + 0.892, + 0.701 + ], + "angle": 0, + "content": "All the images are resized to \\(224 \\times 224\\), and the training images have a \\(50\\%\\) chance of being randomly flipped horizontally. In all experiments, we use ResNet18 as the feature extractor with the feature dimension being 512, and following [28] we use L2 normalization to make the output of the neural network be on the unit hypersphere for brief distance measurement. In particular, we also choose ResNet18 instead of CLIP as the teacher model when reimplementing T-SINT for a fair comparison." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.711, + 0.702, + 0.727 + ], + "angle": 0, + "content": "4.2. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Quantitative Comparison. Table 1 and Table 2 display the MAP@R results on CIFAR10, CARS, CUB, and FLICKR25K under Symmetric/Pairflip label noise specifically with noise rate being 0.1, 0.2, and 0.5. From these experimental results we can make the following observations: (1) The AP-based retrieval methods (i.e., FastAP and SmoothAP) often fail to perform as well as proxy-based retrieval methods in most cases. This may be due to the proxy-based approach's use of the feature centers of each class to protect metric learning from label noise. (2) The noise-resistant classification methods (i.e., Jo-SRC" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11244" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.095, + 0.27, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.094, + 0.47, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.23, + 0.27, + 0.364 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.23, + 0.47, + 0.364 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.367, + 0.27, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.367, + 0.47, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.536 + ], + "angle": 0, + "content": "Figure 3. The P-R curves are plotted in the left column and Top-N precision curves are in the right column." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.552, + 0.471, + 0.884 + ], + "angle": 0, + "content": "and REL) achieve limited performance increases compared with standard retrieval methods, which illustrates that point-based classification approaches are not suitable for retrieval tasks under label noise and special techniques need to be designed to solve the problem. (3) Our proposed TITAN achieves the best scores on all the benchmarks with different settings. For CUB200, our TITAN obtain an improvement of \\(5.46\\%\\), \\(5.05\\%\\), and \\(9.52\\%\\) over the best baseline PRISM under symmetric label noise with noise rate being 0.1, 0.2, 0.5 respectively. For CARS and FLICKR25K, our TITAN outperforms competitive baseline T-SINT by \\(21.04\\%\\) and \\(4.66\\%\\) in terms of average MAP@R scores under symmetric noise with different noise degrees. And the same tendency can also be observed on CIFAR10 under both noise label settings. The exceptional performance of our TITAN can be attributed to two primary factors. On the one hand, we improve the accuracy of noisy sample refinement by using retrieval-based refinement with curriculum learning instead of point-wise refinement. Our model, on the other hand, is enhanced by prototypical mixing technology that prevents it from memorizing noisy data, which facilitates semantic learning." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Table 3 displays the performance on Cars98N with real" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.094, + 0.703, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.093, + 0.897, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.236, + 0.702, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.236, + 0.897, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.38, + 0.702, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.38, + 0.897, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.526, + 0.892, + 0.568 + ], + "angle": 0, + "content": "Figure 4. The MAP@R scores w.r.t. different noise rates. Results with Symmetric noise are plotted in the left column while results with Pairflip noise are plotted in the right column." + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.574, + 0.698, + 0.716 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.574, + 0.9, + 0.716 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.721, + 0.892, + 0.761 + ], + "angle": 0, + "content": "Figure 5. The MAP@R scores of TITAN and PRISM implemented on CUB and Fickr25k with varying hidden dimensions while the noise rate is set to \\(10\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.778, + 0.892, + 0.839 + ], + "angle": 0, + "content": "world label noise. From these results, we can observe that TITAN also achieves significantly better performance in real-world settings, which demonstrates the generalizability and superiority of our approach." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Qualitative Comparison. Additionally, we plot the P-R curves and TopN-precision curves of the proposed TITAN and other compared methods with 512-dimensional feature vectors on three benchmarks in Figure 3. In the P-R curve," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "11245" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.47, + 0.114 + ], + "angle": 0, + "content": "Table 4. Ablation results on CIFAR10, CUB, CARS, and FLICKR25K with noise rate being 0.1." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.115, + 0.472, + 0.213 + ], + "angle": 0, + "content": "
MethodCIFAR10CUB200CARS196FLICKR25K
TITAN w/o LSL85.0417.0515.8291.98
TITAN w/o LC84.3316.6715.2491.23
TITAN w/o M87.5618.2516.1392.65
TITAN w/o R87.7818.0516.0892.11
TITAN w/o w88.5418.7717.2493.97
TITAN (full)89.0119.1117.6494.33
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.23, + 0.47, + 0.381 + ], + "angle": 0, + "content": "the area enclosed by the curve corresponding to our method is significantly larger than the remaining three baselines, which indicates that our method has better retrieval performance. In the curve of topN-precision, our method keeps the highest accuracy rate as the number of retrieved samples increases, especially when the number of returned samples is around 100. Overall, we have the conclusion based on these visualization results that when coming to actual image retrieval, Titan can achieve promising retrieval performances." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.382, + 0.47, + 0.593 + ], + "angle": 0, + "content": "Noise Degree Analysis. We plot the performance trends under two different types of noise variation, especially for the high noise rate in Figure 4. This result indicates that the performance of PRISM decreases rapidly with an increase in noise, as PRISM is unable to construct a clean memory bank at the beginning if the noise ratio is too high. Even with a high noise ratio, our proposed TITAN is still able to deliver the best performance. Due to curriculum learning and blending the semantic information of the prototype with the sample features, we gradually construct a relatively accurate prototype for semantic learning. In general, our TITAN achieves great performance under various noise ratios, demonstrating the robustness and superiority of our proposed TITAN." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.594, + 0.47, + 0.759 + ], + "angle": 0, + "content": "Feature Dimension Analysis. Figure 5 shows the MAP@R results of TITAN and PRISM methods implemented on CUB and FLICKR25k with feature dimensions varying from 128 to 2048. It can be found that the MAP@R value has a small decrease in both 128 and 2048 dimensions for TITAN, while for PRISM there is no obvious pattern of change. In general, probably because of the L2 normalization, the MAP@R value does not change much with the increase of hidden dimension. Note that our method outperforms the PRISM for all the cases, which proves the robustness of our method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.231, + 0.789 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We present an ablation study to investigate the effectiveness of the important inner module in our proposed TITAN and the experiment results are shown in Table 4. Specifically, we design the following model variants as: (1) TITAN w/o \\(\\mathcal{L}_{SL}\\) removes similarity learning loss for denoising in Eqn. 7. (2) TITAN w/o \\(\\mathcal{L}_C\\) removes cluster learning loss for retrieval in Eqn. 11. (3) TITAN w/o M removes" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.895, + 0.426 + ], + "angle": 0, + "content": "the sampled virtual feature in Eqn. 4. (4) TITAN w/o R removes the retrieval-based refinement procedure. (5) TITAN w/o \\( \\mathbf{w} \\) removes confidence scores in Eqn. 8. From these results, we can draw some observations as follows: First, TITAN w/o \\( \\mathcal{L}_C \\) has lower MAP@R scores than TITAN w/o \\( \\mathcal{L}_{SL} \\), perhaps because in the case of a large number of sample categories in the training set, using a small batch size will lead to few positive sample pairs in the mini-batch, which will affect the learning of similarity. Second, TITAN w/o M performs worse than TITAN, which indicates that our use of prototypical mixing is effective, it makes the feature representation more robust and alleviates the overfitting of the model to dirty data to some extent. Third, MAP@R values corresponding to TITAN w/o R drop by about the same amount as TITAN w/o M, which proves that Retrieval-based refinement is an important and influential module in our proposed TITAN, it provides an effective way to refine noisy samples for pairwise similarity learning framework in retrieval tasks. Finally, the slightly lower performance of TITAN w/o \\( \\mathbf{w} \\) compared to TITAN suggests that confidence scores can improve performance by attenuating the impact of unreliable mixed samples." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.44, + 0.698, + 0.58 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.44, + 0.892, + 0.581 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.586, + 0.878, + 0.601 + ], + "angle": 0, + "content": "Figure 6. Sensitivity analysis of two hyper-parameters on CUB." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.62, + 0.688, + 0.637 + ], + "angle": 0, + "content": "4.4. Sensitivity Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We investigate the effect of hyper-parameters \\(\\eta\\) and \\(K_{max}\\) on model retrieval performance on CUB with different noise rates. The loss balance coefficient \\(\\eta\\) controls the weight between different losses, firstly we vary \\(\\eta\\) in [0.1,0.3,0.5,0.8,1.0] with other parameters fixed, Figure 6 illustrates the experimental results, we can find that performance of our method is not sensitive to \\(\\eta\\) when it varies from 0.5 to 1.0, which demonstrates that the convergence of our proposed algorithm is stable. Moreover, we fix all other parameters and change \\(K_{max}\\) in [5,10,15,20,25,30], which controls the max retrieval number of each prototype, as shown in Figure 6, the MAP@R results decrease when \\(K_{max}\\) is set in [25,30], the potential reason is that a high \\(K_{max}\\) will cause more samples to change their labels, but our constructed prototype is not completely reliable at the early stage of training, this leads to refinement which may in turn increase the noise rate. From the analysis, we set \\(\\eta\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "11246" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.121 + ], + "angle": 0, + "content": "as 0.8 and \\( K_{max} \\) as 20 respectively for the proposed TITAN as default." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.134, + 0.201, + 0.151 + ], + "angle": 0, + "content": "4.5. Case Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.159, + 0.473, + 0.296 + ], + "angle": 0, + "content": "We present the top ten images retrieved by PRISM and the proposed TITAN on FLICKR25K. As depicted in Figure 7, the examples enclosed in green boxes represent accurate results, whereas those enclosed in red boxes are wrong results. Additionally, we have labeled the category of each image below it. It is evident that the proposed approach yields significantly more relevant and precise retrieval outcomes for the given queries, demonstrating the superiority of our methodology in handling realistic scenarios." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.313, + 0.487, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.457, + 0.47, + 0.485 + ], + "angle": 0, + "content": "Figure 7. Example of the Top10 returned images with 512-dimensional feature on FLICKR25K." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.508, + 0.285, + 0.525 + ], + "angle": 0, + "content": "4.6. Visulaization Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.533, + 0.473, + 0.759 + ], + "angle": 0, + "content": "T-SNE Visualization. We adopt T-Distributed Stochastic Neighbor Embedding (T-SNE) [39] to compress the dense feature vectors into the two-dimensional plane to visualize the correlations between the features embedded and their one-hot labels, which come from the feature space and the label space respectively. Figure 8 illustrates the visualization of dense vectors generated by our method and the competitive baselines, i.e., PRISM and Jo-SRC. Compared with the two baselines, our method can generate actually compact clusters and can separate each category more clearly while at the same time bringing feature vectors with similar semantic information closer together. This visualization shows that our method can generate dense features that are more discriminative, which could facilitate better image retrieval." + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.775, + 0.482, + 0.867 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.873, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Figure 8. The t-SNE visualization of 512-dimensional feature vectors on CIFAR10." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.62, + 0.107 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.117, + 0.895, + 0.329 + ], + "angle": 0, + "content": "This paper studies a practical but less-explored problem of label noise-resistant image retrieval and proposes a novel method TITAN, which simultaneously corrects label noise and mitigates the impacts of memorization to solve the problem. We describe different prototypes with Gaussian distributions in the hidden space, which directs Mixing to generate synthetic samples. In addition, we collect similar samples for each prototype ranging from easy to hard during optimization, which refines noisy samples in a precise and class-balanced way. Extensive experiments on five benchmark datasets reveal that our proposed TITAN can outperform various state-of-the-art methods. In future works, we would extend our TITAN to more scenarios such as learning to hash and cross-modal retrieval." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.348, + 0.597, + 0.364 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.374, + 0.892, + 0.415 + ], + "angle": 0, + "content": "[1] Artem Babenko and Victor Lempitsky. Aggregating local deep features for image retrieval. 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IEEE Transactions on Pattern Analysis and Machine Intelligence, 40(5):1224-1244, 2017. 1, 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "11249" + } + ] +] \ No newline at end of file diff --git a/2023/Prototypical Mixing and Retrieval-Based Refinement for Label Noise-Resistant Image Retrieval/ec71d51a-9735-4817-bbda-a4f4fe8a6bfa_origin.pdf b/2023/Prototypical Mixing and Retrieval-Based Refinement for Label Noise-Resistant Image Retrieval/ec71d51a-9735-4817-bbda-a4f4fe8a6bfa_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c9bc9e4ac872fa00a45b50f629c90fc8d324ca29 --- /dev/null +++ b/2023/Prototypical Mixing and Retrieval-Based Refinement for Label Noise-Resistant Image Retrieval/ec71d51a-9735-4817-bbda-a4f4fe8a6bfa_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7c7540d81288c0f11e648422e3f23fa3a607f7b4445209acb45864f213f4827b +size 4874845 diff --git a/2023/Prototypical Mixing and Retrieval-Based Refinement for Label Noise-Resistant Image Retrieval/full.md b/2023/Prototypical Mixing and Retrieval-Based Refinement for Label Noise-Resistant Image Retrieval/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ff13be46eb18747abfd784c6eb36800ba045f7d1 --- /dev/null +++ b/2023/Prototypical Mixing and Retrieval-Based Refinement for Label Noise-Resistant Image Retrieval/full.md @@ -0,0 +1,359 @@ +# Prototypical Mixing and Retrieval-based Refinement for Label Noise-resistant Image Retrieval + +Xinlong Yang $^{1*}$ , Haixin Wang $^{1*}$ , Jinan Sun $^{1}$ , Shikun Zhang $^{1}$ , Chong Chen $^{1}$ + +Xian-Sheng Hua², Xiao Luo³† + +$^{1}$ Peking University $^{2}$ Terminus Group $^{3}$ University of California, Los Angeles $\{\mathrm{xinlong.yang, wang.hx}\} @$ stu.pku.edu.cn, $\{\mathrm{sjn, zhangsk}\} @$ pu.edu.cn, cheung1990@126.com, huaxiansheng@gmail.com, xiaoluo@cs.ucla.edu + +# Abstract + +Label noise is pervasive in real-world applications, which influences the optimization of neural network models. This paper investigates a realistic but understudied problem of image retrieval under label noise, which could lead to severe overfitting or memorization of noisy samples during optimization. Moreover, identifying noisy samples correctly is still a challenging problem for retrieval models. In this paper, we propose a novel approach called Prototypical Mixing and Retrieval-based Refinement (TITAN) for label noise-resistant image retrieval, which corrects label noise and mitigates the effects of the memorization simultaneously. Specifically, we first characterize numerous prototypes with Gaussian distributions in the hidden space, which would direct the Mixing procedure in providing synthesized samples. These samples are fed into a similarity learning framework with varying emphasis based on the prototypical structure to learn semantics with reduced overfitting. In addition, we retrieve comparable samples for each prototype from simple to complex, which refine noisy samples in an accurate and class-balanced manner. Comprehensive experiments on five benchmark datasets demonstrate the superiority of our proposed TITAN compared with various competing baselines. + +# 1. Introduction + +Content-based image retrieval has been an essential research area in computer vision [7], with various applications in search engineering [49, 13] and medical image analysis [19]. Content-based image retrieval can be divided + +into instance-level retrieval [1, 62] and category-level retrieval [45, 43, 53]. The former focuses on capturing the same instance in different environments. In recent years, category-level retrieval has gained popularity by delivering samples from a massive database with results grouped by the same category as the query [36]. + +The core of successful category-level retrieval is to map instances to data points in the feature space while preserving similarity connections. The majority of current approaches focus on similarity learning [46, 35], which use pairwise [30] and triplet [16, 50] objectives to maintain semantics in the embedding space. These approaches promote the proximity of semantically similar samples in the embedding space and the separation of semantically different samples. An alternative strategy is to utilize proxies [53, 36, 21, 14]. These methods map each class into the deep feature space to guide semantics learning in a pointwise manner. A few of studies use binary descriptors to improve efficiency [44, 56], which results in a candidate set followed by further refinement for precise image retrieval. + +Despite their considerable success, these retrieval systems often presume that the semantic labels in the training set are accurate. In real-world applications, this assumption could be invalidated by the possibility of annotation mistakes and inadequate automated collecting tactics [47, 54]. For instance, web-based sources often include tags and captions, which are usually utilized to provide label information for convenience. These approaches could generate extensive label noise to collected datasets. To address this issue, this work studies a practical topic named image retrieval with label noise. Although there are extensive papers to study the problem of robust learning in classification tasks [29, 12, 25], retrieval models under label noise are still underexplored with unsatisfactory performance in practice. + +![](images/eaf01e6295403911afaebb022aec3f31d702e991ad3c779fc6a123ee6f8b86f7.jpg) +Figure 1. Two Mixing mechanisms are demonstrated including the standard Mixup (top) and our prototypical Mixing (bottom). + +However, developing a label-noise resistant retrieval model is challenging due to two reasons: (1) Erroneous supervision. Extensive label noise could result in erroneous supervision information, resulting in a significant decline in retrieval performance. In literature, a few works propose to refine noisy samples for effective image retrieval [28, 18]. For example, PRISM [28] estimates the probability of an example being clean with the help of a memory bank. However, they are prone to result in biased and overconfident refinement due to their point-wise calculation [60]. (2) Serious Memorization. Although deep neural networks tend to learn generalized patterns at the beginning stage, the overfitting or memorization of noisy data would compromise the optimization process gradually [57]. As a consequence, a robust optimization objective is anticipated to improve the retrieval performance. + +In this study, we propose a novel retrieval method named Prototypical Mixing and Retrieval-based Refinement (TITAN) for label noise-resistant image retrieval. The essence of our TITAN is to measure the distributions of different prototypes in the hidden space. Note that Mixup [58] can generate synthesis samples, which follows the Vicinal Risk Minimization (VRM) [5] principle with high generalization capability. Here, synthetic samples are generated by merging the original data with samples from the respective prototypical distributions, hence avoiding the possible overfitting of noisy samples. Compared with standard Mixup [58], our prototypical Mixing considers more about the hidden structure and does not require mixing different labels. Afterward, we build a similarity learning framework that optimizes the similarity between samples with the same label against using different emphases inferred from prototypical distributions. In addition, to filter potential noisy data, we retrieve comparable samples for each prototype [55]. The identical retrieval number for different prototypes with curriculum learning [2] promises accurate and class-balanced label refinement. Finally, we involve in learning to cluster to enhance the discriminability for effective image retrieval. Comprehensive experiments on a variety of datasets verify + +the superiority of our TITAN by comparing it to a number of benchmarks. The contribution of this paper can be summarized as follows: + +- This paper studies a less-explored but practical problem named label noise-resistant image retrieval and proposes a novel method named TITAN for this problem. +- On the one hand, TITAN measures the distributions of different prototypes and then generates synthesis data to prevent the memorization of noisy samples. On the other hand, TITAN retrieves comparable samples for each prototype from easy to hard, promising accurate and class-balanced label refinement. +- Extensive experiments on five benchmark datasets demonstrate the superiority of our TITAN compared with various baseline methods in different settings. + +# 2. Related Work + +# 2.1. Context-based Image Retrieval + +As a basic research topic in computer vision and multimedia communities, context-based image retrieval can be separated into instance-level retrieval [1, 62] and category-level retrieval [45, 43, 53]. Recent years have seen an increasing interest in category-level retrieval, which can be further divided into similarity-based [46, 35] and proxy-based approaches [53, 36, 21, 14]. Similarity-based approaches utilize similarity relationships to generate positive and negative pairs, which are then combined with pairwise [30] and triplet [16, 50] losses to optimize deep neural networks. For instance, GSS [27] tries to distinguish the pairwise similarity in the whole dataset in an unsupervised manner. In contrast, proxy-based approaches map labels into the embedding space before minimizing the distance between deep features and their respective proxies. Hashing-based search engines are also in great demand due to their high efficiency [44, 56]. Nevertheless, these approaches do not often account for label noise in real-world datasets. In contrast, we investigate the issue of label noise-resistant image retrieval and develop a novel framework named TITAN to address it. + +# 2.2. Learning with Label Noise + +Learning with label noise has been intensive in a variety of tasks including image segmentation [32], saliency detection [59], and network analysis [9]. A range of works proposes robust losses to potential label noise [11, 10]. For example, RINCE [8] modifies the formula for contrastive learning, which achieves robust performance under noisy augmented views. Another line of this topic is to choose samples with noisy labels and clean them [15, 48, 31, 24, 61, 37, 20]. Early attempts usually put forward a threshold, + +![](images/e100f3b38080bd47c77126ed46e275b12d8810736c9869e9d06ab5844fa9406c.jpg) +Figure 2. An overview of the proposed TITAN. TITAN first estimates the distributions of prototypes for each class, from which we sample features for Mixing to generate virtual features. Moreover, TITAN retrieves different samples for every prototype to refine noisy samples. The final losses are composed of both similarity learning and clustering losses. + +and samples with losses above the threshold are deemed noisy. Co-teaching [15] optimizes two networks concurrently by utilizing small-loss examples from one network to optimize the other network. A few of works attempt to extend robust learning into image retrieval by identifying noisy samples based on similarity [28, 18]. However, these works still neglect the overfitting of noisy samples, and refinement procedures of label noise remain to be biased and overconfident, especially when the amount of noisy data increases. In this paper, we incorporate prototypical Mixing into a similarity learning framework to ease the overfitting of noisy data. To ensure that the labels are assigned correctly and balance class sizes, we also filter noisy samples according to the retrieval process. + +# 3. Methodology + +# 3.1. Problem Definition + +We start by giving the problem definition. Denote the training set as $\mathcal{D} = \{(x_i, y_i)\}_{i=1}^n$ where $x_i$ is the $i$ -th sample and $y_i$ is its observe labels. $n$ represents the data size. We aim to learn a mapping to project data points into an embedding space where similar image pairs should be mapped into similar deep features and vice versa. In our settings, we assume that the observed labels could be wrong, which increases the difficulty of discriminative feature learning. To evaluate our model, we would retrieve similar examples in the database for the given query sample. + +# 3.2. Overview + +Learning effective image representations under label noise requires us to reduce the extreme overfitting of noisy samples and clean up noisy labels in the dataset. Here, we propose a novel method named TITAN for this problem. Following previous works [18, 28], our TITAN modifies a popular classification network (e.g., VGG-F and ResNet50) by adding an MLP layer in place of its head to provide deep features, i.e., $\pmb{h} = H(F(\pmb{x}))$ where $F(\cdot)$ is the feature extractor and $H(\cdot)$ is the MLP head. As illustrated in Figure 2, our model consists of two essential components: (1) Prototypical Mixing, which characterizes prototypes using Gaussian distributions and then generates virtual samples by incorporating prototype information to relieve the memorization of noisy samples; (2) Retrieval-based Refinement, which retrieves similar samples for every prototype to further refine noisy samples in a balanced way. Then, we elaborate on the details of our TITAN. + +# 3.3. Prototypical Mixing for Robust Representation Learning + +The overfitting of neural networks is a major challenge in deep representation learning [57]. As a consequence, we must enhance the generalization capacity of the model. Here, we first characterize the prototypes of various classes using different Gaussian distributions before developing a Mixing technique that blends hidden features with samples derived from these prototypes. + +In detail, we characterize the distribution of each class in + +the prototype as a latent Gaussian distribution $N(\pmb{\mu}_c, \pmb{\Sigma}_c)$ , and every related hidden feature can be thought of as a sample from the Gaussian distribution [26]. Note that even if these samples could be noisy, the centroid measurement of the distribution is still reliable since all the samples are considered together with potential label noise neutralized. In particular, we measure the centroid and the corresponding covariance matrix based on these samples. In formulation, denote the hidden feature of $\pmb{x}_i$ as $\pmb{z}_i$ , we have the estimated mean vector $\pmb{\mu}_c$ and the covariance matrix $\pmb{\Sigma}_c$ of the $c$ -th class in the formulation of: + +$$ +\boldsymbol {\mu} _ {c} = \frac {\sum_ {i = 1} ^ {N} \mathbf {1} _ {y _ {i} = c} \boldsymbol {z} _ {i}}{\sum_ {i = 1} ^ {N} \mathbf {1} _ {y _ {i} = c}}, \tag {1} +$$ + +$$ +\boldsymbol {\Sigma} _ {c} = \frac {\sum_ {i = 1} ^ {N} \mathbf {1} _ {y _ {i} = c} (\boldsymbol {z} _ {i} - \boldsymbol {\mu} _ {c}) (\boldsymbol {z} _ {i} - \boldsymbol {\mu} _ {c}) ^ {T}}{\sum_ {i = 1} ^ {N} \mathbf {1} _ {y _ {i} = c}}. \tag {2} +$$ + +Then, we generate a virtual sample from the distribution, which would be combined with the original sample. In formulation, we first select the prototype with the maximal probability for each sample, i.e., + +$$ +\hat {y} _ {i} = \arg \max _ {c} \frac {1}{\sqrt {(2 \pi) ^ {d} | \boldsymbol {\Sigma} _ {c} |}} \mathrm {e} ^ {- \frac {1}{2} (\boldsymbol {z} _ {i} - \boldsymbol {\mu} _ {c}) ^ {\mathrm {T}} \boldsymbol {\Sigma} _ {c} ^ {- 1} (\boldsymbol {z} _ {i} - \boldsymbol {\mu} _ {c})}, \tag {3} +$$ + +where $d$ denotes the hidden dimension. The mixed hidden feature can be written as: + +$$ +\boldsymbol {z} _ {i} ^ {+} = \lambda \boldsymbol {z} _ {i} + (1 - \lambda) \boldsymbol {z} _ {i} ^ {\prime}, \tag {4} +$$ + +where $\boldsymbol{z}_i'$ is randomly generated from $N(\boldsymbol{\mu}_{\hat{y}_i}, \boldsymbol{\Sigma}_{\hat{y}_i})$ , $\boldsymbol{z}_i = F(\boldsymbol{x}_i)$ and $\boldsymbol{x}_i$ denotes the original image sample. $\lambda$ is a coefficient selected from a Beta distribution following previous works: + +$$ +\lambda \sim B e t a (\alpha , \beta) \tag {5} +$$ + +where $\alpha$ and $\beta$ are two parameters both set to 2 empirically. To simplify the calculation, we adopt a diagonal $\Sigma_{c}$ for each distribution with the neglection of the covariance. + +Advantages of Prototypical Mixing. Similarly to standard Mixup, our prototypical Mixing also generates synthetic samples, extending the Empirical Risk Minimization (ERM) principle [41] to the Vicinal Risk Minimization (VRM) principle [5]. In this way, our TITAN has a strong capacity for generalization and is resistant to the memorization of noisy examples. Moreover, our prototypical Mixing does not need to combine labels to generate synthetic labels, which could be biased since the label space contains distinct relationships. Lastly, our TITAN adequately explores prototypical structures in the hidden space, which can serve as implicit label correction. + +Next, we include the mixed samples into a framework for deep representation learning that maintains similarity. Here, we concatenate the hidden feature with the mixed feature + +into a mini-batch and maximize the similarity between deep features of positive pairs compared with negative pairs. The positives for $z_{i}^{+}$ are mini-batch samples sharing the same label, i.e., $z_{j}^{+}$ with $y_{i} = y_{j}$ . In formulation, given the minibatch $\mathcal{B}$ , the index of positives for $z_{i}^{+}$ is written as: + +$$ +\Pi (i) = \{j | \boldsymbol {x} _ {j} \in \mathcal {B}, y _ {i} = y _ {j} \}. \tag {6} +$$ + +Following previous works [38, 6], the negatives are all the other samples in a mini-batch, then the similarity learning objective is constructed as: + +$$ +\mathcal {L} _ {S L} = - \sum_ {\boldsymbol {x} _ {i} \in \mathcal {B}} \frac {1}{| \Pi (i) |} \sum_ {j \in \Pi (i)} \log \frac {\exp \left(\boldsymbol {h} _ {i} ^ {+} \cdot \boldsymbol {h} _ {j} ^ {+} / \tau\right)}{\sum_ {\boldsymbol {x} _ {j ^ {\prime}} \in \mathcal {B}} \exp \left(\boldsymbol {h} _ {i} ^ {+} \cdot \boldsymbol {h} _ {j ^ {\prime}} ^ {+} / \tau\right)} \tag {7} +$$ + +where $\pmb{h}_i^+ = H(\pmb{z}_i^+)$ maps the hidden feature into the target space and $\tau$ is a temperature parameter preset to 0.5 as in [38]. Moreover, we also incorporate the probabilities in Eqn. 3 as the confidence scores, which gives more emphasis on samples with high confidence. Consequently, we alleviate the effect of unreliable mixed data and enlarge the range of sample weights. In other words, sample weights are assigned more heavily to reliable samples. Let $\pmb{w}_i = \frac{1}{\sqrt{(2\pi)^d|\pmb{\Sigma}_{\hat{y}_i}|}}\mathrm{e}^{-\frac{1}{2} (\pmb{z}_i - \pmb{\mu}_{\hat{y}_i})^\mathrm{T}\pmb{\Sigma}_c^{-1}(\pmb{z}_i - \pmb{\mu}_{\hat{y}_i})}$ denote the confidence score, and we rewrite Eqn. 7 as: + +$$ +\mathcal {L} _ {S L} = - \sum_ {\boldsymbol {x} _ {i} \in \mathcal {B}} \frac {\boldsymbol {w} _ {i}}{| \Pi (i) |} \sum_ {j \in \Pi (i)} \log \frac {\exp \left(\boldsymbol {h} _ {i} ^ {+} \cdot \boldsymbol {h} _ {j} ^ {+} / \tau\right)}{\sum_ {\boldsymbol {x} _ {j ^ {\prime}} \in \mathcal {B}} \exp \left(\boldsymbol {h} _ {i} ^ {+} \cdot \boldsymbol {h} _ {j ^ {\prime}} ^ {+} / \tau\right)}. \tag {8} +$$ + +Compared with proxy-based methods [53, 36, 21, 14], our similarity learning-based objective makes use of pairwise labels, which can be more accurate due to the following reason. Even if two labels in a positive pair are both incorrect, there is still a chance that they share the same semantics [51]. Our Mixing strategy further relieves the memorization of noisy samples, producing label noise-resistant and similarity-preserving deep features. + +# 3.4. Retrieval-based Refinement with Curriculum Learning + +We need to identify and refine those noisy samples to thoroughly get rid of label noise for better performances [53, 36, 21, 14]. Traditional classification techniques consider samples with small training losses to be clean samples [15], and they often introduce a threshold to distinguish between clean and noisy data. Nevertheless, we are unable to directly obtain losses for various samples in the similarity learning framework. Even worse, a low threshold could exclude too many noisy samples resulting in potential underfitting, while a high threshold may have a limited capacity to filter noisy data. These point-wise methods could also be biased to refine noisy samples into easy + +classes with small losses [33]. To address the problems, we provide a retrieval-based refinement module, which retrieves comparable samples for each prototype with curriculum learning [2] for precise and balanced refinement. + +In particular, we view the centroid of each prototype as a query and retrieve $K$ samples in the dataset based on the Euclidean distance. For these retrieved samples, we regard them as clean if their labels are not consistent with their queries, otherwise refine their labels. In formulation, the refined datasets can be written as below: + +$$ +\begin{array}{l} \hat {\mathcal {D}} = \cup_ {c = 1} ^ {C} \left\{\left(\boldsymbol {x} _ {i}, c\right) \mid \boldsymbol {z} _ {i} \in N N \left(\boldsymbol {\mu} _ {c}\right) \right\} \tag {9} \\ \cup \left\{\left(\boldsymbol {x} _ {i}, y _ {i}\right) \mid \boldsymbol {z} _ {i} \notin \cup_ {c = 1} ^ {C} N N \left(\boldsymbol {\mu} _ {c}\right) \right\}, \\ \end{array} +$$ + +where $NN(\cdot)$ denotes the set of top $K$ nearest samples in the datasets. Here we set the same $K$ for every prototype, which generates an accurate and balanced dataset after refinement. In comparison, clean sample selection based on losses could lean toward selecting clean samples from easy classes. Moreover, we propose to increase the retrieval number $K$ gradually following the principle of curriculum learning, which refines noisy samples from easy to hard. To be specific, we have different $K_{t}$ at the $t$ -th cycle: + +$$ +K _ {t} = \frac {t}{T} K _ {\max }, \tag {10} +$$ + +where $T$ denotes the total number of cycles and $K_{max}$ denotes the maximal retrieval number. To increase framework efficiency, we would conduct retrieval-based refinement at the beginning of each cycle. + +# 3.5. Summary + +Learn to Cluster. Finally, we enhance the discriminability of hidden features by learning to cluster [40]. This is accomplished by enforcing the accumulation of hidden features around their corresponding centroids. Here, we maximize the similarity between hidden features and their corresponding prototypes compared with the other prototypes by proposing the following objective: + +$$ +\mathcal {L} _ {C} = - \sum_ {\boldsymbol {x} _ {i} \in \mathcal {B}} \log \frac {\exp \left(\boldsymbol {z} _ {i} \cdot \boldsymbol {\mu} _ {y _ {i}} / \tau\right)}{\sum_ {c = 1} ^ {C} \exp \left(\boldsymbol {z} _ {i} \cdot \boldsymbol {\mu} _ {c} / \tau\right)}, \tag {11} +$$ + +Then the final objective is summarized by combining both two losses as follows: + +$$ +\mathcal {L} = \mathcal {L} _ {S L} + \eta \mathcal {L} _ {C}, \tag {12} +$$ + +where $\eta$ is a parameter to balance two losses. In practice, we would first warm up the neural network without conducting Mixing and then perform prototypical Mixing and retrieval-based refinement gradually. We would demonstrate the whole algorithm in Algorithm 1. + +Algorithm 1 Training Algorithm of TITAN +Require: Dataset $\mathcal{D}$ ; Iteration number $T$ Max retrieval number $K_{max}$ +Ensure: The composited projector $H(F(\cdot))$ . +1:Warm up the projector; +2:repeat +3: Update the retrieval number $K_{t}$ using Eqn. 10 +4: Estimate the distribution for every prototype using Eqn. 1 and Eqn. 2; +5:Refine the dataset using Eqn.9; +6:for $k = 1,2,\dots ,k_{max}$ do +7: Sample $\mathcal{B}\subset \hat{\mathcal{D}}$ to construct a mini-batch; +8: Generate synthetic samples using Eqn. 4; +9: Calculate the loss objective by Eqn. 12; +10: Update the network parameters by backpropagata tion; +11: end for +12: until convergence + +# 4. Experiment + +# 4.1. Settings + +Datasets. In order to evaluate the TITAN, we utilize four widely used datasets with various levels of granularity and size and one real-world noisy dataset. The concrete experimental setting is depicted in the Appendix. CIFAR10 [23] contains a total of 60k colorful images in 10 categories. CUB200-2011 [42] is the most common dataset utilized for fine-grained visual classification tasks and contains 11,788 images of 200 subcategories related to bird species. CARS196 [22] includes 16,185 samples of 196 distinct categories of car models. FLICKR25K [17] contains more coarsely grained categories and is more generalized. Cars98N [28] is a real-world noisy benchmark, it's built by collecting 9,558 examples for 98 car models from Pinterest. Normally the noisy examples in Cars98N usually consist of the car parts, the interior of the car, or pictures of other car models. + +To investigate the noise-resistant ability, we firstly synthesize two kinds of artificial noise labels, Symmetric and Pairflip, added to the training set of the none real-world noise dataset. Following [28], we vary the noise ratio with three degrees: $10\%$ , $20\%$ , and $50\%$ respectively. Symmetric noise [34] simply flips labels between classes uniformly while Pairflip noise [34] similarly assigns the corrupted label to each nearby class. + +Baselines. We compare our TITAN with eight baselines that have excellent performances in their corresponding field. Concretely, three of these methods are standard retrieval approaches (i.e., Fast-AP [4], Smooth-AP [3] and Proxy-Anor [21]), two are robust noise-resistant approaches (i.e., REL [52] and Jo-SRC [54]), one is noise + +Table 1. The MAP@R scores implemented on 512-dimensional feature vectors for retrieval on CIFAR10, CUB, CARS, and FlickR25K with three degrees of symmetric label noise. + +
MethodCIFAR10CUB200CARS196FLICKR25K
0.10.20.50.10.20.50.10.20.50.10.20.5
FastAP85.0783.4065.9213.8512.818.6310.789.286.4788.9588.5987.50
SmoothAP84.4881.3870.1112.7111.789.789.708.826.1986.3785.2082.30
Proxy-Anchor87.2078.0469.2316.7015.8610.1112.2111.115.3389.1288.6987.79
Jo-SRC87.5885.5572.8615.9714.9112.9112.7411.097.1091.0190.2289.43
REL86.8184.7671.9015.7815.6713.8614.0213.337.9691.5991.4490.60
HEART85.3683.1571.6517.1015.7912.0015.3013.598.6492.1191.8191.01
T-SINT87.3886.2672.8717.9017.3614.3414.4113.019.8990.7990.4587.65
PRISM87.6586.2373.0518.1217.7915.2916.9915.8810.0292.4292.1291.23
TITAN (Ours)89.0188.0175.8619.1118.6916.9017.6416.3611.3794.3393.8993.07
+ +Table 2. The MAP@R scores implemented on 512-dimensional feature vectors for retrieval on CIFAR10, CUB, CARS, and FLICKR25K with three degrees of pairflip label noise. + +
MethodCIFAR10CUB200CARS196FLICKR25K
0.10.20.50.10.20.50.10.20.50.10.20.5
FastAP77.4276.5256.2714.0612.4211.0610.608.536.3687.5387.1685.22
SmoothAP76.1574.5555.8612.1211.4210.5610.629.556.8485.3085.1885.02
Proxy-Anor75.5573.8257.6516.0815.1112.1613.5211.458.6190.1989.2688.23
Jo-SRC78.5276.2457.7715.9214.5513.4514.4813.439.2091.6391.6090.11
REL75.8375.1258.7215.7614.7813.0512.5011.729.0991.4690.7889.19
HEART77.8276.1158.5516.2615.3313.0713.5813.368.7791.7691.7290.99
T-SINT79.1977.9455.3916.5116.1414.2614.4513.699.0791.6290.7489.71
PRISM80.4380.3262.0517.1315.8313.1315.4615.159.3892.4492.2790.91
TITAN (Ours)83.8982.9967.8818.2917.3615.7316.9815.8210.1494.0593.9093.18
+ +robust hash retrieval method (i.e., HEART [38]), two are noise-robust retrieval methods (i.e., T-SINT [18] and PRISM [28]). + +Table 3. The MAP@R scores implemented on 512-dimensional feature vectors for retrieval on Cars98N. + +
MethodTITAN(Ours)T-SINTPRISMHEARTRELFastAP
Cars98N7.036.536.255.545.385.06
+ +Evaluation Criterion. Following [28, 18], we mainly employ Mean Average Precision@R (MAP@R) as our criterion for evaluation. MAP@R metric is a widely used measure of average accuracy for multiple queries and is a common metric for evaluating the quality of retrieval systems. Note that the value of R is not a fixed value for all benchmarks, it is equal to the largest number of samples among all categories in the corresponding retrieved set of the benchmark. + +Implementation Details. We implement our method using PyTorch with an NVIDIA 3090 GPU. We adopt mini-batch Adam for our model training. The mini-batch size is set to 64 and the learning rate for our model is fixed at $5 \times 10^{-5}$ . + +All the images are resized to $224 \times 224$ , and the training images have a $50\%$ chance of being randomly flipped horizontally. In all experiments, we use ResNet18 as the feature extractor with the feature dimension being 512, and following [28] we use L2 normalization to make the output of the neural network be on the unit hypersphere for brief distance measurement. In particular, we also choose ResNet18 instead of CLIP as the teacher model when reimplementing T-SINT for a fair comparison. + +# 4.2. Experimental Results + +Quantitative Comparison. Table 1 and Table 2 display the MAP@R results on CIFAR10, CARS, CUB, and FLICKR25K under Symmetric/Pairflip label noise specifically with noise rate being 0.1, 0.2, and 0.5. From these experimental results we can make the following observations: (1) The AP-based retrieval methods (i.e., FastAP and SmoothAP) often fail to perform as well as proxy-based retrieval methods in most cases. This may be due to the proxy-based approach's use of the feature centers of each class to protect metric learning from label noise. (2) The noise-resistant classification methods (i.e., Jo-SRC + +![](images/f670e3916558421739ffc6e10147c4d0acbbf7a94af76a89f107e863f75fc25d.jpg) + +![](images/5a71086040b4ec1b0ef3b6c358ad54599f07d958dc35041c665ba9ad81d7de43.jpg) + +![](images/4e51d28052af5336e455600b53fcecaf9dd5a44a95b8eb0a353fd0d986581ef2.jpg) + +![](images/eb68eb881a9910bf06312cc8825c89a82829fca3fd2874a17417c9813563e61e.jpg) + +![](images/deb5a0a7b924e90c4f4b71c6fd5264a129cd112a4756171aab1223374c073308.jpg) +Figure 3. The P-R curves are plotted in the left column and Top-N precision curves are in the right column. + +![](images/5e1f7d7c355770915aec9deaba5b5f930e4413bafc6979b9e3443244a4cf22e9.jpg) + +and REL) achieve limited performance increases compared with standard retrieval methods, which illustrates that point-based classification approaches are not suitable for retrieval tasks under label noise and special techniques need to be designed to solve the problem. (3) Our proposed TITAN achieves the best scores on all the benchmarks with different settings. For CUB200, our TITAN obtain an improvement of $5.46\%$ , $5.05\%$ , and $9.52\%$ over the best baseline PRISM under symmetric label noise with noise rate being 0.1, 0.2, 0.5 respectively. For CARS and FLICKR25K, our TITAN outperforms competitive baseline T-SINT by $21.04\%$ and $4.66\%$ in terms of average MAP@R scores under symmetric noise with different noise degrees. And the same tendency can also be observed on CIFAR10 under both noise label settings. The exceptional performance of our TITAN can be attributed to two primary factors. On the one hand, we improve the accuracy of noisy sample refinement by using retrieval-based refinement with curriculum learning instead of point-wise refinement. Our model, on the other hand, is enhanced by prototypical mixing technology that prevents it from memorizing noisy data, which facilitates semantic learning. + +Table 3 displays the performance on Cars98N with real + +![](images/094a3ca1d3f9dec8f20d4fa542300bb8aaa4623f311ae75a5ddead5345abb2b8.jpg) + +![](images/6e78dd18fbc5938dbe61b3a5ecc6db6f901447df9d65db0fa86e0e2cdb777e7c.jpg) + +![](images/f85ea0a949bdaaa831c8095dbc499aa584e1a7423d03a72d43bf6d6077c8c97a.jpg) + +![](images/617f6b80a287fcfccaf9964521f41ff9892a99aec2142f6f9caed9e2e0f692f1.jpg) + +![](images/e53fb4323937cd3844ce3c7c221a2e412727ffa4089e82c8e2d8dde78a805831.jpg) +Figure 4. The MAP@R scores w.r.t. different noise rates. Results with Symmetric noise are plotted in the left column while results with Pairflip noise are plotted in the right column. + +![](images/6b526fbb852aa6bd06a6834e2e9604c4fe4b4443e38f4df20ffc973943883e4b.jpg) + +![](images/79a7edeb86175b56f787a74a3227979bb2a18a19918d2b4854c653a4b918f85c.jpg) +Figure 5. The MAP@R scores of TITAN and PRISM implemented on CUB and Fickr25k with varying hidden dimensions while the noise rate is set to $10\%$ . + +![](images/09cd0f7b4dc71929ecadec5c6250b6837084b64eacd744b452561377308c0635.jpg) + +world label noise. From these results, we can observe that TITAN also achieves significantly better performance in real-world settings, which demonstrates the generalizability and superiority of our approach. + +Qualitative Comparison. Additionally, we plot the P-R curves and TopN-precision curves of the proposed TITAN and other compared methods with 512-dimensional feature vectors on three benchmarks in Figure 3. In the P-R curve, + +Table 4. Ablation results on CIFAR10, CUB, CARS, and FLICKR25K with noise rate being 0.1. + +
MethodCIFAR10CUB200CARS196FLICKR25K
TITAN w/o LSL85.0417.0515.8291.98
TITAN w/o LC84.3316.6715.2491.23
TITAN w/o M87.5618.2516.1392.65
TITAN w/o R87.7818.0516.0892.11
TITAN w/o w88.5418.7717.2493.97
TITAN (full)89.0119.1117.6494.33
+ +the area enclosed by the curve corresponding to our method is significantly larger than the remaining three baselines, which indicates that our method has better retrieval performance. In the curve of topN-precision, our method keeps the highest accuracy rate as the number of retrieved samples increases, especially when the number of returned samples is around 100. Overall, we have the conclusion based on these visualization results that when coming to actual image retrieval, Titan can achieve promising retrieval performances. + +Noise Degree Analysis. We plot the performance trends under two different types of noise variation, especially for the high noise rate in Figure 4. This result indicates that the performance of PRISM decreases rapidly with an increase in noise, as PRISM is unable to construct a clean memory bank at the beginning if the noise ratio is too high. Even with a high noise ratio, our proposed TITAN is still able to deliver the best performance. Due to curriculum learning and blending the semantic information of the prototype with the sample features, we gradually construct a relatively accurate prototype for semantic learning. In general, our TITAN achieves great performance under various noise ratios, demonstrating the robustness and superiority of our proposed TITAN. + +Feature Dimension Analysis. Figure 5 shows the MAP@R results of TITAN and PRISM methods implemented on CUB and FLICKR25k with feature dimensions varying from 128 to 2048. It can be found that the MAP@R value has a small decrease in both 128 and 2048 dimensions for TITAN, while for PRISM there is no obvious pattern of change. In general, probably because of the L2 normalization, the MAP@R value does not change much with the increase of hidden dimension. Note that our method outperforms the PRISM for all the cases, which proves the robustness of our method. + +# 4.3. Ablation Study + +We present an ablation study to investigate the effectiveness of the important inner module in our proposed TITAN and the experiment results are shown in Table 4. Specifically, we design the following model variants as: (1) TITAN w/o $\mathcal{L}_{SL}$ removes similarity learning loss for denoising in Eqn. 7. (2) TITAN w/o $\mathcal{L}_C$ removes cluster learning loss for retrieval in Eqn. 11. (3) TITAN w/o M removes + +the sampled virtual feature in Eqn. 4. (4) TITAN w/o R removes the retrieval-based refinement procedure. (5) TITAN w/o $\mathbf{w}$ removes confidence scores in Eqn. 8. From these results, we can draw some observations as follows: First, TITAN w/o $\mathcal{L}_C$ has lower MAP@R scores than TITAN w/o $\mathcal{L}_{SL}$ , perhaps because in the case of a large number of sample categories in the training set, using a small batch size will lead to few positive sample pairs in the mini-batch, which will affect the learning of similarity. Second, TITAN w/o M performs worse than TITAN, which indicates that our use of prototypical mixing is effective, it makes the feature representation more robust and alleviates the overfitting of the model to dirty data to some extent. Third, MAP@R values corresponding to TITAN w/o R drop by about the same amount as TITAN w/o M, which proves that Retrieval-based refinement is an important and influential module in our proposed TITAN, it provides an effective way to refine noisy samples for pairwise similarity learning framework in retrieval tasks. Finally, the slightly lower performance of TITAN w/o $\mathbf{w}$ compared to TITAN suggests that confidence scores can improve performance by attenuating the impact of unreliable mixed samples. + +![](images/451947d65c4c6e0303dc65d3bd7e96cef23cf453290d3b755ed32ac616b1762d.jpg) +Figure 6. Sensitivity analysis of two hyper-parameters on CUB. + +![](images/548ea1d1cd875c9bd223b0773cd444759b0773a594c94cde6ee681cd5aa3d4f5.jpg) + +# 4.4. Sensitivity Analysis + +We investigate the effect of hyper-parameters $\eta$ and $K_{max}$ on model retrieval performance on CUB with different noise rates. The loss balance coefficient $\eta$ controls the weight between different losses, firstly we vary $\eta$ in [0.1,0.3,0.5,0.8,1.0] with other parameters fixed, Figure 6 illustrates the experimental results, we can find that performance of our method is not sensitive to $\eta$ when it varies from 0.5 to 1.0, which demonstrates that the convergence of our proposed algorithm is stable. Moreover, we fix all other parameters and change $K_{max}$ in [5,10,15,20,25,30], which controls the max retrieval number of each prototype, as shown in Figure 6, the MAP@R results decrease when $K_{max}$ is set in [25,30], the potential reason is that a high $K_{max}$ will cause more samples to change their labels, but our constructed prototype is not completely reliable at the early stage of training, this leads to refinement which may in turn increase the noise rate. From the analysis, we set $\eta$ + +as 0.8 and $K_{max}$ as 20 respectively for the proposed TITAN as default. + +# 4.5. Case Study + +We present the top ten images retrieved by PRISM and the proposed TITAN on FLICKR25K. As depicted in Figure 7, the examples enclosed in green boxes represent accurate results, whereas those enclosed in red boxes are wrong results. Additionally, we have labeled the category of each image below it. It is evident that the proposed approach yields significantly more relevant and precise retrieval outcomes for the given queries, demonstrating the superiority of our methodology in handling realistic scenarios. + +![](images/364d2a5f0bd538b22d636f63482a897032a959ad9abcbf91b6b966fc6dd4742c.jpg) +Figure 7. Example of the Top10 returned images with 512-dimensional feature on FLICKR25K. + +# 4.6. Visulaization Analysis + +T-SNE Visualization. We adopt T-Distributed Stochastic Neighbor Embedding (T-SNE) [39] to compress the dense feature vectors into the two-dimensional plane to visualize the correlations between the features embedded and their one-hot labels, which come from the feature space and the label space respectively. Figure 8 illustrates the visualization of dense vectors generated by our method and the competitive baselines, i.e., PRISM and Jo-SRC. Compared with the two baselines, our method can generate actually compact clusters and can separate each category more clearly while at the same time bringing feature vectors with similar semantic information closer together. This visualization shows that our method can generate dense features that are more discriminative, which could facilitate better image retrieval. + +![](images/0bf1f41a97bebe19f6f8cb974e95c906a0a2d0a76aff20200cfa192f8879cfbe.jpg) +Figure 8. The t-SNE visualization of 512-dimensional feature vectors on CIFAR10. + +# 5. Conclusion + +This paper studies a practical but less-explored problem of label noise-resistant image retrieval and proposes a novel method TITAN, which simultaneously corrects label noise and mitigates the impacts of memorization to solve the problem. We describe different prototypes with Gaussian distributions in the hidden space, which directs Mixing to generate synthetic samples. 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IEEE Transactions on Pattern Analysis and Machine Intelligence, 40(5):1224-1244, 2017. 1, 2 \ No newline at end of file diff --git a/2023/Prototypical Mixing and Retrieval-Based Refinement for Label Noise-Resistant Image Retrieval/images.zip b/2023/Prototypical Mixing and Retrieval-Based Refinement for Label Noise-Resistant Image Retrieval/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..5dcfcad4d151a49b957a7d825646c9d760c11ecd --- /dev/null +++ b/2023/Prototypical Mixing and Retrieval-Based Refinement for Label Noise-Resistant Image Retrieval/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1431a6a176532be949734d55392b2761a9ab29e6c20f6b1f20e1a281615bc26a +size 670388 diff --git a/2023/Prototypical Mixing and Retrieval-Based Refinement for Label Noise-Resistant Image Retrieval/layout.json b/2023/Prototypical Mixing and Retrieval-Based Refinement for Label Noise-Resistant Image Retrieval/layout.json new file mode 100644 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is pervasive in real-world applications, which influences the optimization of neural network models. This paper investigates a realistic but understudied problem of image retrieval under label noise, which could lead to severe overfitting or memorization of noisy samples during optimization. Moreover, identifying noisy samples correctly is still a challenging problem for retrieval models. In this paper, we propose a novel approach called Prototypical Mixing and Retrieval-based Refinement (TITAN) for label noise-resistant image retrieval, which corrects label noise and mitigates the effects of the memorization simultaneously. Specifically, we first characterize numerous prototypes with Gaussian distributions in the hidden space, which would direct the Mixing procedure in providing synthesized samples. These samples are fed into a similarity learning framework with varying emphasis based on the prototypical structure to learn semantics with reduced overfitting. In addition, we retrieve comparable samples for each prototype from simple to complex, which refine noisy samples in an accurate and class-balanced manner. Comprehensive experiments on five benchmark datasets demonstrate the superiority of our proposed TITAN compared with various competing baselines." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 623, + 128, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 128, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 128, + 635 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "type": "text", + "content": "Content-based image retrieval has been an essential research area in computer vision [7], with various applications in search engineering [49, 13] and medical image analysis [19]. Content-based image retrieval can be divided" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 298, + 545, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 298, + 545, + 370 + ], + "spans": [ + { + "bbox": [ + 306, + 298, + 545, + 370 + ], + "type": "text", + "content": "into instance-level retrieval [1, 62] and category-level retrieval [45, 43, 53]. The former focuses on capturing the same instance in different environments. In recent years, category-level retrieval has gained popularity by delivering samples from a massive database with results grouped by the same category as the query [36]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 374, + 546, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 546, + 542 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 546, + 542 + ], + "type": "text", + "content": "The core of successful category-level retrieval is to map instances to data points in the feature space while preserving similarity connections. The majority of current approaches focus on similarity learning [46, 35], which use pairwise [30] and triplet [16, 50] objectives to maintain semantics in the embedding space. These approaches promote the proximity of semantically similar samples in the embedding space and the separation of semantically different samples. An alternative strategy is to utilize proxies [53, 36, 21, 14]. These methods map each class into the deep feature space to guide semantics learning in a pointwise manner. A few of studies use binary descriptors to improve efficiency [44, 56], which results in a candidate set followed by further refinement for precise image retrieval." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 546, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 547, + 714 + ], + "type": "text", + "content": "Despite their considerable success, these retrieval systems often presume that the semantic labels in the training set are accurate. In real-world applications, this assumption could be invalidated by the possibility of annotation mistakes and inadequate automated collecting tactics [47, 54]. For instance, web-based sources often include tags and captions, which are usually utilized to provide label information for convenience. These approaches could generate extensive label noise to collected datasets. To address this issue, this work studies a practical topic named image retrieval with label noise. Although there are extensive papers to study the problem of robust learning in classification tasks [29, 12, 25], retrieval models under label noise are still underexplored with unsatisfactory performance in practice." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 204, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 204, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 204, + 713 + ], + "type": "text", + "content": "*Equal contribution. †Corresponding author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "11239" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 75, + 276, + 205 + ], + "blocks": [ + { + "bbox": [ + 59, + 75, + 276, + 205 + ], + "lines": [ + { + "bbox": [ + 59, + 75, + 276, + 205 + ], + "spans": [ + { + "bbox": [ + 59, + 75, + 276, + 205 + ], + "type": "image", + "image_path": "eaf01e6295403911afaebb022aec3f31d702e991ad3c779fc6a123ee6f8b86f7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 209, + 287, + 233 + ], + "lines": [ + { + "bbox": [ + 47, + 209, + 287, + 233 + ], + "spans": [ + { + "bbox": [ + 47, + 209, + 287, + 233 + ], + "type": "text", + "content": "Figure 1. Two Mixing mechanisms are demonstrated including the standard Mixup (top) and our prototypical Mixing (bottom)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 246, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 246, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 246, + 287, + 437 + ], + "type": "text", + "content": "However, developing a label-noise resistant retrieval model is challenging due to two reasons: (1) Erroneous supervision. Extensive label noise could result in erroneous supervision information, resulting in a significant decline in retrieval performance. In literature, a few works propose to refine noisy samples for effective image retrieval [28, 18]. For example, PRISM [28] estimates the probability of an example being clean with the help of a memory bank. However, they are prone to result in biased and overconfident refinement due to their point-wise calculation [60]. (2) Serious Memorization. Although deep neural networks tend to learn generalized patterns at the beginning stage, the overfitting or memorization of noisy data would compromise the optimization process gradually [57]. As a consequence, a robust optimization objective is anticipated to improve the retrieval performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 288, + 715 + ], + "type": "text", + "content": "In this study, we propose a novel retrieval method named Prototypical Mixing and Retrieval-based Refinement (TITAN) for label noise-resistant image retrieval. The essence of our TITAN is to measure the distributions of different prototypes in the hidden space. Note that Mixup [58] can generate synthesis samples, which follows the Vicinal Risk Minimization (VRM) [5] principle with high generalization capability. Here, synthetic samples are generated by merging the original data with samples from the respective prototypical distributions, hence avoiding the possible overfitting of noisy samples. Compared with standard Mixup [58], our prototypical Mixing considers more about the hidden structure and does not require mixing different labels. Afterward, we build a similarity learning framework that optimizes the similarity between samples with the same label against using different emphases inferred from prototypical distributions. In addition, to filter potential noisy data, we retrieve comparable samples for each prototype [55]. The identical retrieval number for different prototypes with curriculum learning [2] promises accurate and class-balanced label refinement. Finally, we involve in learning to cluster to enhance the discriminability for effective image retrieval. Comprehensive experiments on a variety of datasets verify" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "content": "the superiority of our TITAN by comparing it to a number of benchmarks. The contribution of this paper can be summarized as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 116, + 547, + 278 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 306, + 116, + 545, + 153 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 116, + 545, + 153 + ], + "spans": [ + { + "bbox": [ + 306, + 116, + 545, + 153 + ], + "type": "text", + "content": "- This paper studies a less-explored but practical problem named label noise-resistant image retrieval and proposes a novel method named TITAN for this problem." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 161, + 547, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 161, + 547, + 233 + ], + "spans": [ + { + "bbox": [ + 306, + 161, + 547, + 233 + ], + "type": "text", + "content": "- On the one hand, TITAN measures the distributions of different prototypes and then generates synthesis data to prevent the memorization of noisy samples. On the other hand, TITAN retrieves comparable samples for each prototype from easy to hard, promising accurate and class-balanced label refinement." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 242, + 545, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 242, + 545, + 278 + ], + "spans": [ + { + "bbox": [ + 306, + 242, + 545, + 278 + ], + "type": "text", + "content": "- Extensive experiments on five benchmark datasets demonstrate the superiority of our TITAN compared with various baseline methods in different settings." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 289, + 392, + 301 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 289, + 392, + 301 + ], + "spans": [ + { + "bbox": [ + 306, + 289, + 392, + 301 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 308, + 474, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 308, + 474, + 322 + ], + "spans": [ + { + "bbox": [ + 306, + 308, + 474, + 322 + ], + "type": "text", + "content": "2.1. Context-based Image Retrieval" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 327, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 545, + 579 + ], + "type": "text", + "content": "As a basic research topic in computer vision and multimedia communities, context-based image retrieval can be separated into instance-level retrieval [1, 62] and category-level retrieval [45, 43, 53]. Recent years have seen an increasing interest in category-level retrieval, which can be further divided into similarity-based [46, 35] and proxy-based approaches [53, 36, 21, 14]. Similarity-based approaches utilize similarity relationships to generate positive and negative pairs, which are then combined with pairwise [30] and triplet [16, 50] losses to optimize deep neural networks. For instance, GSS [27] tries to distinguish the pairwise similarity in the whole dataset in an unsupervised manner. In contrast, proxy-based approaches map labels into the embedding space before minimizing the distance between deep features and their respective proxies. Hashing-based search engines are also in great demand due to their high efficiency [44, 56]. Nevertheless, these approaches do not often account for label noise in real-world datasets. In contrast, we investigate the issue of label noise-resistant image retrieval and develop a novel framework named TITAN to address it." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 586, + 453, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 453, + 600 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 453, + 600 + ], + "type": "text", + "content": "2.2. Learning with Label Noise" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "content": "Learning with label noise has been intensive in a variety of tasks including image segmentation [32], saliency detection [59], and network analysis [9]. A range of works proposes robust losses to potential label noise [11, 10]. For example, RINCE [8] modifies the formula for contrastive learning, which achieves robust performance under noisy augmented views. Another line of this topic is to choose samples with noisy labels and clean them [15, 48, 31, 24, 61, 37, 20]. Early attempts usually put forward a threshold," + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11240" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 71, + 545, + 308 + ], + "blocks": [ + { + "bbox": [ + 53, + 71, + 545, + 308 + ], + "lines": [ + { + "bbox": [ + 53, + 71, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 53, + 71, + 545, + 308 + ], + "type": "image", + "image_path": "e100f3b38080bd47c77126ed46e275b12d8810736c9869e9d06ab5844fa9406c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 312, + 546, + 346 + ], + "lines": [ + { + "bbox": [ + 46, + 312, + 546, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 546, + 346 + ], + "type": "text", + "content": "Figure 2. An overview of the proposed TITAN. TITAN first estimates the distributions of prototypes for each class, from which we sample features for Mixing to generate virtual features. Moreover, TITAN retrieves different samples for every prototype to refine noisy samples. The final losses are composed of both similarity learning and clustering losses." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 357, + 289, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 289, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 289, + 525 + ], + "type": "text", + "content": "and samples with losses above the threshold are deemed noisy. Co-teaching [15] optimizes two networks concurrently by utilizing small-loss examples from one network to optimize the other network. A few of works attempt to extend robust learning into image retrieval by identifying noisy samples based on similarity [28, 18]. However, these works still neglect the overfitting of noisy samples, and refinement procedures of label noise remain to be biased and overconfident, especially when the amount of noisy data increases. In this paper, we incorporate prototypical Mixing into a similarity learning framework to ease the overfitting of noisy data. To ensure that the labels are assigned correctly and balance class sizes, we also filter noisy samples according to the retrieval process." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 548, + 124, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 124, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 124, + 562 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 571, + 159, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 159, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 159, + 583 + ], + "type": "text", + "content": "3.1. Problem Definition" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "We start by giving the problem definition. Denote the training set as " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(x_i, y_i)\\}_{i=1}^n" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "-th sample and " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "y_i" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " is its observe labels. " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " represents the data size. We aim to learn a mapping to project data points into an embedding space where similar image pairs should be mapped into similar deep features and vice versa. In our settings, we assume that the observed labels could be wrong, which increases the difficulty of discriminative feature learning. To evaluate our model, we would retrieve similar examples in the database for the given query sample." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 356, + 373, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 356, + 373, + 369 + ], + "spans": [ + { + "bbox": [ + 306, + 356, + 373, + 369 + ], + "type": "text", + "content": "3.2. Overview" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 375, + 547, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 547, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 547, + 579 + ], + "type": "text", + "content": "Learning effective image representations under label noise requires us to reduce the extreme overfitting of noisy samples and clean up noisy labels in the dataset. Here, we propose a novel method named TITAN for this problem. Following previous works [18, 28], our TITAN modifies a popular classification network (e.g., VGG-F and ResNet50) by adding an MLP layer in place of its head to provide deep features, i.e., " + }, + { + "bbox": [ + 304, + 375, + 547, + 579 + ], + "type": "inline_equation", + "content": "\\pmb{h} = H(F(\\pmb{x}))" + }, + { + "bbox": [ + 304, + 375, + 547, + 579 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 375, + 547, + 579 + ], + "type": "inline_equation", + "content": "F(\\cdot)" + }, + { + "bbox": [ + 304, + 375, + 547, + 579 + ], + "type": "text", + "content": " is the feature extractor and " + }, + { + "bbox": [ + 304, + 375, + 547, + 579 + ], + "type": "inline_equation", + "content": "H(\\cdot)" + }, + { + "bbox": [ + 304, + 375, + 547, + 579 + ], + "type": "text", + "content": " is the MLP head. As illustrated in Figure 2, our model consists of two essential components: (1) Prototypical Mixing, which characterizes prototypes using Gaussian distributions and then generates virtual samples by incorporating prototype information to relieve the memorization of noisy samples; (2) Retrieval-based Refinement, which retrieves similar samples for every prototype to further refine noisy samples in a balanced way. Then, we elaborate on the details of our TITAN." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 586, + 545, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 586, + 545, + 612 + ], + "spans": [ + { + "bbox": [ + 305, + 586, + 545, + 612 + ], + "type": "text", + "content": "3.3. Prototypical Mixing for Robust Representation Learning" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 617, + 545, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 701 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 701 + ], + "type": "text", + "content": "The overfitting of neural networks is a major challenge in deep representation learning [57]. As a consequence, we must enhance the generalization capacity of the model. Here, we first characterize the prototypes of various classes using different Gaussian distributions before developing a Mixing technique that blends hidden features with samples derived from these prototypes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": "In detail, we characterize the distribution of each class in" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11241" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "the prototype as a latent Gaussian distribution " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "N(\\pmb{\\mu}_c, \\pmb{\\Sigma}_c)" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ", and every related hidden feature can be thought of as a sample from the Gaussian distribution [26]. Note that even if these samples could be noisy, the centroid measurement of the distribution is still reliable since all the samples are considered together with potential label noise neutralized. In particular, we measure the centroid and the corresponding covariance matrix based on these samples. In formulation, denote the hidden feature of " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\pmb{z}_i" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ", we have the estimated mean vector " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_c" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " and the covariance matrix " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\pmb{\\Sigma}_c" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "-th class in the formulation of:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 121, + 213, + 287, + 244 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 213, + 287, + 244 + ], + "spans": [ + { + "bbox": [ + 121, + 213, + 287, + 244 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\mu} _ {c} = \\frac {\\sum_ {i = 1} ^ {N} \\mathbf {1} _ {y _ {i} = c} \\boldsymbol {z} _ {i}}{\\sum_ {i = 1} ^ {N} \\mathbf {1} _ {y _ {i} = c}}, \\tag {1}", + "image_path": "069043c56b520c27462cb9138d72edfb846f022ab86d75e52c84516e3d0e3379.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 81, + 248, + 287, + 281 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 248, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 81, + 248, + 287, + 281 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\Sigma} _ {c} = \\frac {\\sum_ {i = 1} ^ {N} \\mathbf {1} _ {y _ {i} = c} (\\boldsymbol {z} _ {i} - \\boldsymbol {\\mu} _ {c}) (\\boldsymbol {z} _ {i} - \\boldsymbol {\\mu} _ {c}) ^ {T}}{\\sum_ {i = 1} ^ {N} \\mathbf {1} _ {y _ {i} = c}}. \\tag {2}", + "image_path": "36f594a94a0ee1c601d11a73e92e22034cb0495acb5eb510c65f41d82404579d.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 284, + 287, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 284, + 287, + 332 + ], + "spans": [ + { + "bbox": [ + 47, + 284, + 287, + 332 + ], + "type": "text", + "content": "Then, we generate a virtual sample from the distribution, which would be combined with the original sample. In formulation, we first select the prototype with the maximal probability for each sample, i.e.," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 340, + 287, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 340, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 53, + 340, + 287, + 369 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {i} = \\arg \\max _ {c} \\frac {1}{\\sqrt {(2 \\pi) ^ {d} | \\boldsymbol {\\Sigma} _ {c} |}} \\mathrm {e} ^ {- \\frac {1}{2} (\\boldsymbol {z} _ {i} - \\boldsymbol {\\mu} _ {c}) ^ {\\mathrm {T}} \\boldsymbol {\\Sigma} _ {c} ^ {- 1} (\\boldsymbol {z} _ {i} - \\boldsymbol {\\mu} _ {c})}, \\tag {3}", + "image_path": "434d273f58c63a84952c377d46673e4b23d60be7ff66556a1a2bf61b9765c6be.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 376, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 287, + 399 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 376, + 287, + 399 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 47, + 376, + 287, + 399 + ], + "type": "text", + "content": " denotes the hidden dimension. The mixed hidden feature can be written as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 117, + 408, + 287, + 423 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 408, + 287, + 423 + ], + "spans": [ + { + "bbox": [ + 117, + 408, + 287, + 423 + ], + "type": "interline_equation", + "content": "\\boldsymbol {z} _ {i} ^ {+} = \\lambda \\boldsymbol {z} _ {i} + (1 - \\lambda) \\boldsymbol {z} _ {i} ^ {\\prime}, \\tag {4}", + "image_path": "ecf42e3bf331531ec3cec8be5c417dbeb1fca0b07ab3d04ff6e16205252a7222.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 431, + 287, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 431, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 431, + 287, + 479 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 431, + 287, + 479 + ], + "type": "inline_equation", + "content": "\\boldsymbol{z}_i'" + }, + { + "bbox": [ + 47, + 431, + 287, + 479 + ], + "type": "text", + "content": " is randomly generated from " + }, + { + "bbox": [ + 47, + 431, + 287, + 479 + ], + "type": "inline_equation", + "content": "N(\\boldsymbol{\\mu}_{\\hat{y}_i}, \\boldsymbol{\\Sigma}_{\\hat{y}_i})" + }, + { + "bbox": [ + 47, + 431, + 287, + 479 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 431, + 287, + 479 + ], + "type": "inline_equation", + "content": "\\boldsymbol{z}_i = F(\\boldsymbol{x}_i)" + }, + { + "bbox": [ + 47, + 431, + 287, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 431, + 287, + 479 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_i" + }, + { + "bbox": [ + 47, + 431, + 287, + 479 + ], + "type": "text", + "content": " denotes the original image sample. " + }, + { + "bbox": [ + 47, + 431, + 287, + 479 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 431, + 287, + 479 + ], + "type": "text", + "content": " is a coefficient selected from a Beta distribution following previous works:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 132, + 479, + 287, + 493 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 479, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 132, + 479, + 287, + 493 + ], + "type": "interline_equation", + "content": "\\lambda \\sim B e t a (\\alpha , \\beta) \\tag {5}", + "image_path": "d11f56c1aca6399a70154e4cecc08120825f58a72f00f74d4680b45dfbeb564c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "type": "text", + "content": " are two parameters both set to 2 empirically. To simplify the calculation, we adopt a diagonal " + }, + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "type": "inline_equation", + "content": "\\Sigma_{c}" + }, + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "type": "text", + "content": " for each distribution with the neglection of the covariance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 534, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 287, + 676 + ], + "type": "text", + "content": "Advantages of Prototypical Mixing. Similarly to standard Mixup, our prototypical Mixing also generates synthetic samples, extending the Empirical Risk Minimization (ERM) principle [41] to the Vicinal Risk Minimization (VRM) principle [5]. In this way, our TITAN has a strong capacity for generalization and is resistant to the memorization of noisy examples. Moreover, our prototypical Mixing does not need to combine labels to generate synthetic labels, which could be biased since the label space contains distinct relationships. Lastly, our TITAN adequately explores prototypical structures in the hidden space, which can serve as implicit label correction." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "text", + "content": "Next, we include the mixed samples into a framework for deep representation learning that maintains similarity. Here, we concatenate the hidden feature with the mixed feature" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 135 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 135 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 135 + ], + "type": "text", + "content": "into a mini-batch and maximize the similarity between deep features of positive pairs compared with negative pairs. The positives for " + }, + { + "bbox": [ + 304, + 72, + 545, + 135 + ], + "type": "inline_equation", + "content": "z_{i}^{+}" + }, + { + "bbox": [ + 304, + 72, + 545, + 135 + ], + "type": "text", + "content": " are mini-batch samples sharing the same label, i.e., " + }, + { + "bbox": [ + 304, + 72, + 545, + 135 + ], + "type": "inline_equation", + "content": "z_{j}^{+}" + }, + { + "bbox": [ + 304, + 72, + 545, + 135 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 72, + 545, + 135 + ], + "type": "inline_equation", + "content": "y_{i} = y_{j}" + }, + { + "bbox": [ + 304, + 72, + 545, + 135 + ], + "type": "text", + "content": ". In formulation, given the minibatch " + }, + { + "bbox": [ + 304, + 72, + 545, + 135 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 304, + 72, + 545, + 135 + ], + "type": "text", + "content": ", the index of positives for " + }, + { + "bbox": [ + 304, + 72, + 545, + 135 + ], + "type": "inline_equation", + "content": "z_{i}^{+}" + }, + { + "bbox": [ + 304, + 72, + 545, + 135 + ], + "type": "text", + "content": " is written as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 365, + 144, + 545, + 158 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 144, + 545, + 158 + ], + "spans": [ + { + "bbox": [ + 365, + 144, + 545, + 158 + ], + "type": "interline_equation", + "content": "\\Pi (i) = \\{j | \\boldsymbol {x} _ {j} \\in \\mathcal {B}, y _ {i} = y _ {j} \\}. \\tag {6}", + "image_path": "bfcbfb3a821b2253db6196fb5a2c8fcb0065a6a268c66b7de78d1600f9939337.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 166, + 545, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 166, + 545, + 202 + ], + "spans": [ + { + "bbox": [ + 304, + 166, + 545, + 202 + ], + "type": "text", + "content": "Following previous works [38, 6], the negatives are all the other samples in a mini-batch, then the similarity learning objective is constructed as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 210, + 548, + 256 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 210, + 548, + 256 + ], + "spans": [ + { + "bbox": [ + 306, + 210, + 548, + 256 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {S L} = - \\sum_ {\\boldsymbol {x} _ {i} \\in \\mathcal {B}} \\frac {1}{| \\Pi (i) |} \\sum_ {j \\in \\Pi (i)} \\log \\frac {\\exp \\left(\\boldsymbol {h} _ {i} ^ {+} \\cdot \\boldsymbol {h} _ {j} ^ {+} / \\tau\\right)}{\\sum_ {\\boldsymbol {x} _ {j ^ {\\prime}} \\in \\mathcal {B}} \\exp \\left(\\boldsymbol {h} _ {i} ^ {+} \\cdot \\boldsymbol {h} _ {j ^ {\\prime}} ^ {+} / \\tau\\right)} \\tag {7}", + "image_path": "97eb4f2c482a66b52f32f8a7d370dbbd64fcc561422dde32bca8ae524cccf85b.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 256, + 545, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 256, + 545, + 382 + ], + "spans": [ + { + "bbox": [ + 304, + 256, + 545, + 382 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 256, + 545, + 382 + ], + "type": "inline_equation", + "content": "\\pmb{h}_i^+ = H(\\pmb{z}_i^+)" + }, + { + "bbox": [ + 304, + 256, + 545, + 382 + ], + "type": "text", + "content": " maps the hidden feature into the target space and " + }, + { + "bbox": [ + 304, + 256, + 545, + 382 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 256, + 545, + 382 + ], + "type": "text", + "content": " is a temperature parameter preset to 0.5 as in [38]. Moreover, we also incorporate the probabilities in Eqn. 3 as the confidence scores, which gives more emphasis on samples with high confidence. Consequently, we alleviate the effect of unreliable mixed data and enlarge the range of sample weights. In other words, sample weights are assigned more heavily to reliable samples. Let " + }, + { + "bbox": [ + 304, + 256, + 545, + 382 + ], + "type": "inline_equation", + "content": "\\pmb{w}_i = \\frac{1}{\\sqrt{(2\\pi)^d|\\pmb{\\Sigma}_{\\hat{y}_i}|}}\\mathrm{e}^{-\\frac{1}{2} (\\pmb{z}_i - \\pmb{\\mu}_{\\hat{y}_i})^\\mathrm{T}\\pmb{\\Sigma}_c^{-1}(\\pmb{z}_i - \\pmb{\\mu}_{\\hat{y}_i})}" + }, + { + "bbox": [ + 304, + 256, + 545, + 382 + ], + "type": "text", + "content": " denote the confidence score, and we rewrite Eqn. 7 as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 390, + 552, + 435 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 390, + 552, + 435 + ], + "spans": [ + { + "bbox": [ + 306, + 390, + 552, + 435 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {S L} = - \\sum_ {\\boldsymbol {x} _ {i} \\in \\mathcal {B}} \\frac {\\boldsymbol {w} _ {i}}{| \\Pi (i) |} \\sum_ {j \\in \\Pi (i)} \\log \\frac {\\exp \\left(\\boldsymbol {h} _ {i} ^ {+} \\cdot \\boldsymbol {h} _ {j} ^ {+} / \\tau\\right)}{\\sum_ {\\boldsymbol {x} _ {j ^ {\\prime}} \\in \\mathcal {B}} \\exp \\left(\\boldsymbol {h} _ {i} ^ {+} \\cdot \\boldsymbol {h} _ {j ^ {\\prime}} ^ {+} / \\tau\\right)}. \\tag {8}", + "image_path": "73f1a774476f88346b7dc752ce9fda90bb8efb1db3b57b8283a5f122ce2fa032.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 436, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 436, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 436, + 545, + 533 + ], + "type": "text", + "content": "Compared with proxy-based methods [53, 36, 21, 14], our similarity learning-based objective makes use of pairwise labels, which can be more accurate due to the following reason. Even if two labels in a positive pair are both incorrect, there is still a chance that they share the same semantics [51]. Our Mixing strategy further relieves the memorization of noisy samples, producing label noise-resistant and similarity-preserving deep features." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 539, + 545, + 564 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 539, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 306, + 539, + 545, + 564 + ], + "type": "text", + "content": "3.4. Retrieval-based Refinement with Curriculum Learning" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "We need to identify and refine those noisy samples to thoroughly get rid of label noise for better performances [53, 36, 21, 14]. Traditional classification techniques consider samples with small training losses to be clean samples [15], and they often introduce a threshold to distinguish between clean and noisy data. Nevertheless, we are unable to directly obtain losses for various samples in the similarity learning framework. Even worse, a low threshold could exclude too many noisy samples resulting in potential underfitting, while a high threshold may have a limited capacity to filter noisy data. These point-wise methods could also be biased to refine noisy samples into easy" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "11242" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "classes with small losses [33]. To address the problems, we provide a retrieval-based refinement module, which retrieves comparable samples for each prototype with curriculum learning [2] for precise and balanced refinement." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 121, + 288, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 288, + 192 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 288, + 192 + ], + "type": "text", + "content": "In particular, we view the centroid of each prototype as a query and retrieve " + }, + { + "bbox": [ + 46, + 121, + 288, + 192 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 121, + 288, + 192 + ], + "type": "text", + "content": " samples in the dataset based on the Euclidean distance. For these retrieved samples, we regard them as clean if their labels are not consistent with their queries, otherwise refine their labels. In formulation, the refined datasets can be written as below:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 87, + 199, + 287, + 232 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 199, + 287, + 232 + ], + "spans": [ + { + "bbox": [ + 87, + 199, + 287, + 232 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\mathcal {D}} = \\cup_ {c = 1} ^ {C} \\left\\{\\left(\\boldsymbol {x} _ {i}, c\\right) \\mid \\boldsymbol {z} _ {i} \\in N N \\left(\\boldsymbol {\\mu} _ {c}\\right) \\right\\} \\tag {9} \\\\ \\cup \\left\\{\\left(\\boldsymbol {x} _ {i}, y _ {i}\\right) \\mid \\boldsymbol {z} _ {i} \\notin \\cup_ {c = 1} ^ {C} N N \\left(\\boldsymbol {\\mu} _ {c}\\right) \\right\\}, \\\\ \\end{array}", + "image_path": "5090fe6ebc2c8aa6c0852ef550956d68812be7ff28451a73b4a5d47fab42b1e2.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 240, + 288, + 349 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 240, + 288, + 349 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 288, + 349 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 240, + 288, + 349 + ], + "type": "inline_equation", + "content": "NN(\\cdot)" + }, + { + "bbox": [ + 46, + 240, + 288, + 349 + ], + "type": "text", + "content": " denotes the set of top " + }, + { + "bbox": [ + 46, + 240, + 288, + 349 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 240, + 288, + 349 + ], + "type": "text", + "content": " nearest samples in the datasets. Here we set the same " + }, + { + "bbox": [ + 46, + 240, + 288, + 349 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 240, + 288, + 349 + ], + "type": "text", + "content": " for every prototype, which generates an accurate and balanced dataset after refinement. In comparison, clean sample selection based on losses could lean toward selecting clean samples from easy classes. Moreover, we propose to increase the retrieval number " + }, + { + "bbox": [ + 46, + 240, + 288, + 349 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 240, + 288, + 349 + ], + "type": "text", + "content": " gradually following the principle of curriculum learning, which refines noisy samples from easy to hard. To be specific, we have different " + }, + { + "bbox": [ + 46, + 240, + 288, + 349 + ], + "type": "inline_equation", + "content": "K_{t}" + }, + { + "bbox": [ + 46, + 240, + 288, + 349 + ], + "type": "text", + "content": " at the " + }, + { + "bbox": [ + 46, + 240, + 288, + 349 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 240, + 288, + 349 + ], + "type": "text", + "content": "-th cycle:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 134, + 357, + 287, + 380 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 357, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 134, + 357, + 287, + 380 + ], + "type": "interline_equation", + "content": "K _ {t} = \\frac {t}{T} K _ {\\max }, \\tag {10}", + "image_path": "02ff5b9c6d9dd29b8b48138dd41cac647b0f23016f4866d55a2c9a3f37276074.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "type": "text", + "content": " denotes the total number of cycles and " + }, + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "type": "inline_equation", + "content": "K_{max}" + }, + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "type": "text", + "content": " denotes the maximal retrieval number. To increase framework efficiency, we would conduct retrieval-based refinement at the beginning of each cycle." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 445, + 117, + 458 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 445, + 117, + 458 + ], + "spans": [ + { + "bbox": [ + 47, + 445, + 117, + 458 + ], + "type": "text", + "content": "3.5. Summary" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 464, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 548 + ], + "type": "text", + "content": "Learn to Cluster. Finally, we enhance the discriminability of hidden features by learning to cluster [40]. This is accomplished by enforcing the accumulation of hidden features around their corresponding centroids. Here, we maximize the similarity between hidden features and their corresponding prototypes compared with the other prototypes by proposing the following objective:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 82, + 556, + 287, + 587 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 556, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 82, + 556, + 287, + 587 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {C} = - \\sum_ {\\boldsymbol {x} _ {i} \\in \\mathcal {B}} \\log \\frac {\\exp \\left(\\boldsymbol {z} _ {i} \\cdot \\boldsymbol {\\mu} _ {y _ {i}} / \\tau\\right)}{\\sum_ {c = 1} ^ {C} \\exp \\left(\\boldsymbol {z} _ {i} \\cdot \\boldsymbol {\\mu} _ {c} / \\tau\\right)}, \\tag {11}", + "image_path": "8da9c0b378df330bbecdc177aa63bb05541e2fb4b497d731038152ff5869de89.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 596, + 287, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 596, + 287, + 619 + ], + "spans": [ + { + "bbox": [ + 46, + 596, + 287, + 619 + ], + "type": "text", + "content": "Then the final objective is summarized by combining both two losses as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 129, + 631, + 287, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 631, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 129, + 631, + 287, + 643 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {S L} + \\eta \\mathcal {L} _ {C}, \\tag {12}", + "image_path": "6f528df385ced42accb945d87e0c38db51dab417e4838596607c7dc5f509af8a.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": " is a parameter to balance two losses. In practice, we would first warm up the neural network without conducting Mixing and then perform prototypical Mixing and retrieval-based refinement gradually. We would demonstrate the whole algorithm in Algorithm 1." + } + ] + } + ], + "index": 11 + }, + { + "type": "code", + "bbox": [ + 306, + 86, + 545, + 290 + ], + "blocks": [ + { + "bbox": [ + 306, + 72, + 484, + 84 + ], + "lines": [ + { + "bbox": [ + 306, + 72, + 484, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 484, + 84 + ], + "type": "text", + "content": "Algorithm 1 Training Algorithm of TITAN" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 306, + 86, + 545, + 290 + ], + "lines": [ + { + "bbox": [ + 306, + 86, + 545, + 290 + ], + "spans": [ + { + "bbox": [ + 306, + 86, + 545, + 290 + ], + "type": "text", + "content": "Require: Dataset " + }, + { + "bbox": [ + 306, + 86, + 545, + 290 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 306, + 86, + 545, + 290 + ], + "type": "text", + "content": " ; Iteration number " + }, + { + "bbox": [ + 306, + 86, + 545, + 290 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 306, + 86, + 545, + 290 + ], + "type": "text", + "content": " Max retrieval number " + }, + { + "bbox": [ + 306, + 86, + 545, + 290 + ], + "type": "inline_equation", + "content": "K_{max}" + }, + { + "bbox": [ + 306, + 86, + 545, + 290 + ], + "type": "text", + "content": " \nEnsure: The composited projector " + }, + { + "bbox": [ + 306, + 86, + 545, + 290 + ], + "type": "inline_equation", + "content": "H(F(\\cdot))" + }, + { + "bbox": [ + 306, + 86, + 545, + 290 + ], + "type": "text", + "content": " . \n1:Warm up the projector; \n2:repeat \n3: Update the retrieval number " + }, + { + "bbox": [ + 306, + 86, + 545, + 290 + ], + "type": "inline_equation", + "content": "K_{t}" + }, + { + "bbox": [ + 306, + 86, + 545, + 290 + ], + "type": "text", + "content": " using Eqn. 10 \n4: Estimate the distribution for every prototype using Eqn. 1 and Eqn. 2; \n5:Refine the dataset using Eqn.9; \n6:for " + }, + { + "bbox": [ + 306, + 86, + 545, + 290 + ], + "type": "inline_equation", + "content": "k = 1,2,\\dots ,k_{max}" + }, + { + "bbox": [ + 306, + 86, + 545, + 290 + ], + "type": "text", + "content": " do \n7: Sample " + }, + { + "bbox": [ + 306, + 86, + 545, + 290 + ], + "type": "inline_equation", + "content": "\\mathcal{B}\\subset \\hat{\\mathcal{D}}" + }, + { + "bbox": [ + 306, + 86, + 545, + 290 + ], + "type": "text", + "content": " to construct a mini-batch; \n8: Generate synthetic samples using Eqn. 4; \n9: Calculate the loss objective by Eqn. 12; \n10: Update the network parameters by backpropagata tion; \n11: end for \n12: until convergence" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "code_body" + } + ], + "index": 13, + "sub_type": "algorithm" + }, + { + "bbox": [ + 306, + 313, + 382, + 327 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 313, + 382, + 327 + ], + "spans": [ + { + "bbox": [ + 306, + 313, + 382, + 327 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 334, + 365, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 334, + 365, + 346 + ], + "spans": [ + { + "bbox": [ + 306, + 334, + 365, + 346 + ], + "type": "text", + "content": "4.1. Settings" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 353, + 545, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 545, + 543 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 545, + 543 + ], + "type": "text", + "content": "Datasets. In order to evaluate the TITAN, we utilize four widely used datasets with various levels of granularity and size and one real-world noisy dataset. The concrete experimental setting is depicted in the Appendix. CIFAR10 [23] contains a total of 60k colorful images in 10 categories. CUB200-2011 [42] is the most common dataset utilized for fine-grained visual classification tasks and contains 11,788 images of 200 subcategories related to bird species. CARS196 [22] includes 16,185 samples of 196 distinct categories of car models. FLICKR25K [17] contains more coarsely grained categories and is more generalized. Cars98N [28] is a real-world noisy benchmark, it's built by collecting 9,558 examples for 98 car models from Pinterest. Normally the noisy examples in Cars98N usually consist of the car parts, the interior of the car, or pictures of other car models." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 545, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 640 + ], + "type": "text", + "content": "To investigate the noise-resistant ability, we firstly synthesize two kinds of artificial noise labels, Symmetric and Pairflip, added to the training set of the none real-world noise dataset. Following [28], we vary the noise ratio with three degrees: " + }, + { + "bbox": [ + 304, + 545, + 545, + 640 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 545, + 545, + 640 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 545, + 545, + 640 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 545, + 545, + 640 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 545, + 545, + 640 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 545, + 545, + 640 + ], + "type": "text", + "content": " respectively. Symmetric noise [34] simply flips labels between classes uniformly while Pairflip noise [34] similarly assigns the corrupted label to each nearby class." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Baselines. We compare our TITAN with eight baselines that have excellent performances in their corresponding field. Concretely, three of these methods are standard retrieval approaches (i.e., Fast-AP [4], Smooth-AP [3] and Proxy-Anor [21]), two are robust noise-resistant approaches (i.e., REL [52] and Jo-SRC [54]), one is noise" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11243" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 91, + 545, + 248 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "type": "text", + "content": "Table 1. The MAP@R scores implemented on 512-dimensional feature vectors for retrieval on CIFAR10, CUB, CARS, and FlickR25K with three degrees of symmetric label noise." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 91, + 545, + 248 + ], + "lines": [ + { + "bbox": [ + 50, + 91, + 545, + 248 + ], + "spans": [ + { + "bbox": [ + 50, + 91, + 545, + 248 + ], + "type": "table", + "html": "
MethodCIFAR10CUB200CARS196FLICKR25K
0.10.20.50.10.20.50.10.20.50.10.20.5
FastAP85.0783.4065.9213.8512.818.6310.789.286.4788.9588.5987.50
SmoothAP84.4881.3870.1112.7111.789.789.708.826.1986.3785.2082.30
Proxy-Anchor87.2078.0469.2316.7015.8610.1112.2111.115.3389.1288.6987.79
Jo-SRC87.5885.5572.8615.9714.9112.9112.7411.097.1091.0190.2289.43
REL86.8184.7671.9015.7815.6713.8614.0213.337.9691.5991.4490.60
HEART85.3683.1571.6517.1015.7912.0015.3013.598.6492.1191.8191.01
T-SINT87.3886.2672.8717.9017.3614.3414.4113.019.8990.7990.4587.65
PRISM87.6586.2373.0518.1217.7915.2916.9915.8810.0292.4292.1291.23
TITAN (Ours)89.0188.0175.8619.1118.6916.9017.6416.3611.3794.3393.8993.07
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MethodCIFAR10CUB200CARS196FLICKR25K
0.10.20.50.10.20.50.10.20.50.10.20.5
FastAP77.4276.5256.2714.0612.4211.0610.608.536.3687.5387.1685.22
SmoothAP76.1574.5555.8612.1211.4210.5610.629.556.8485.3085.1885.02
Proxy-Anor75.5573.8257.6516.0815.1112.1613.5211.458.6190.1989.2688.23
Jo-SRC78.5276.2457.7715.9214.5513.4514.4813.439.2091.6391.6090.11
REL75.8375.1258.7215.7614.7813.0512.5011.729.0991.4690.7889.19
HEART77.8276.1158.5516.2615.3313.0713.5813.368.7791.7691.7290.99
T-SINT79.1977.9455.3916.5116.1414.2614.4513.699.0791.6290.7489.71
PRISM80.4380.3262.0517.1315.8313.1315.4615.159.3892.4492.2790.91
TITAN (Ours)83.8982.9967.8818.2917.3615.7316.9815.8210.1494.0593.9093.18
", + "image_path": "476035a0cdd7af85e6570a36a67c6c1b15e0ae7883dd152e78d0968bd4974c06.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 446, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 446, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 47, + 446, + 287, + 483 + ], + "type": "text", + "content": "robust hash retrieval method (i.e., HEART [38]), two are noise-robust retrieval methods (i.e., T-SINT [18] and PRISM [28])." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 50, + 514, + 288, + 544 + ], + "blocks": [ + { + "bbox": [ + 47, + 492, + 287, + 514 + ], + "lines": [ + { + "bbox": [ + 47, + 492, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 492, + 287, + 514 + ], + "type": "text", + "content": "Table 3. The MAP@R scores implemented on 512-dimensional feature vectors for retrieval on Cars98N." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 514, + 288, + 544 + ], + "lines": [ + { + "bbox": [ + 50, + 514, + 288, + 544 + ], + "spans": [ + { + "bbox": [ + 50, + 514, + 288, + 544 + ], + "type": "table", + "html": "
MethodTITAN(Ours)T-SINTPRISMHEARTRELFastAP
Cars98N7.036.536.255.545.385.06
", + "image_path": "1caba4feb601873668e0bd4a3bb3a91a0d4a12a8baa9a7ca2f97ff399f73ce81.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 556, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 287, + 664 + ], + "type": "text", + "content": "Evaluation Criterion. Following [28, 18], we mainly employ Mean Average Precision@R (MAP@R) as our criterion for evaluation. MAP@R metric is a widely used measure of average accuracy for multiple queries and is a common metric for evaluating the quality of retrieval systems. Note that the value of R is not a fixed value for all benchmarks, it is equal to the largest number of samples among all categories in the corresponding retrieved set of the benchmark." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "Implementation Details. We implement our method using PyTorch with an NVIDIA 3090 GPU. We adopt mini-batch Adam for our model training. The mini-batch size is set to 64 and the learning rate for our model is fixed at " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-5}" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 446, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 446, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 446, + 545, + 555 + ], + "type": "text", + "content": "All the images are resized to " + }, + { + "bbox": [ + 304, + 446, + 545, + 555 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 446, + 545, + 555 + ], + "type": "text", + "content": ", and the training images have a " + }, + { + "bbox": [ + 304, + 446, + 545, + 555 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 446, + 545, + 555 + ], + "type": "text", + "content": " chance of being randomly flipped horizontally. In all experiments, we use ResNet18 as the feature extractor with the feature dimension being 512, and following [28] we use L2 normalization to make the output of the neural network be on the unit hypersphere for brief distance measurement. In particular, we also choose ResNet18 instead of CLIP as the teacher model when reimplementing T-SINT for a fair comparison." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 563, + 429, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 429, + 575 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 429, + 575 + ], + "type": "text", + "content": "4.2. Experimental Results" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Quantitative Comparison. Table 1 and Table 2 display the MAP@R results on CIFAR10, CARS, CUB, and FLICKR25K under Symmetric/Pairflip label noise specifically with noise rate being 0.1, 0.2, and 0.5. From these experimental results we can make the following observations: (1) The AP-based retrieval methods (i.e., FastAP and SmoothAP) often fail to perform as well as proxy-based retrieval methods in most cases. This may be due to the proxy-based approach's use of the feature centers of each class to protect metric learning from label noise. (2) The noise-resistant classification methods (i.e., Jo-SRC" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11244" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 75, + 165, + 178 + ], + "blocks": [ + { + "bbox": [ + 53, + 75, + 165, + 178 + ], + "lines": [ + { + "bbox": [ + 53, + 75, + 165, + 178 + ], + "spans": [ + { + "bbox": [ + 53, + 75, + 165, + 178 + ], + "type": "image", + "image_path": "f670e3916558421739ffc6e10147c4d0acbbf7a94af76a89f107e863f75fc25d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 168, + 74, + 287, + 180 + ], + "blocks": [ + { + "bbox": [ + 168, + 74, + 287, + 180 + ], + "lines": [ + { + "bbox": [ + 168, + 74, + 287, + 180 + ], + "spans": [ + { + "bbox": [ + 168, + 74, + 287, + 180 + ], + "type": "image", + "image_path": "5a71086040b4ec1b0ef3b6c358ad54599f07d958dc35041c665ba9ad81d7de43.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 53, + 182, + 165, + 288 + ], + "blocks": [ + { + "bbox": [ + 53, + 182, + 165, + 288 + ], + "lines": [ + { + "bbox": [ + 53, + 182, + 165, + 288 + ], + "spans": [ + { + "bbox": [ + 53, + 182, + 165, + 288 + ], + "type": "image", + "image_path": "4e51d28052af5336e455600b53fcecaf9dd5a44a95b8eb0a353fd0d986581ef2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 168, + 182, + 287, + 288 + ], + "blocks": [ + { + "bbox": [ + 168, + 182, + 287, + 288 + ], + "lines": [ + { + "bbox": [ + 168, + 182, + 287, + 288 + ], + "spans": [ + { + "bbox": [ + 168, + 182, + 287, + 288 + ], + "type": "image", + "image_path": "eb68eb881a9910bf06312cc8825c89a82829fca3fd2874a17417c9813563e61e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 53, + 290, + 165, + 396 + ], + "blocks": [ + { + "bbox": [ + 53, + 290, + 165, + 396 + ], + "lines": [ + { + "bbox": [ + 53, + 290, + 165, + 396 + ], + "spans": [ + { + "bbox": [ + 53, + 290, + 165, + 396 + ], + "type": "image", + "image_path": "deb5a0a7b924e90c4f4b71c6fd5264a129cd112a4756171aab1223374c073308.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 402, + 287, + 424 + ], + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 424 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 424 + ], + "type": "text", + "content": "Figure 3. The P-R curves are plotted in the left column and Top-N precision curves are in the right column." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 168, + 290, + 287, + 396 + ], + "blocks": [ + { + "bbox": [ + 168, + 290, + 287, + 396 + ], + "lines": [ + { + "bbox": [ + 168, + 290, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 168, + 290, + 287, + 396 + ], + "type": "image", + "image_path": "5e1f7d7c355770915aec9deaba5b5f930e4413bafc6979b9e3443244a4cf22e9.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 437, + 288, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 288, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 288, + 700 + ], + "type": "text", + "content": "and REL) achieve limited performance increases compared with standard retrieval methods, which illustrates that point-based classification approaches are not suitable for retrieval tasks under label noise and special techniques need to be designed to solve the problem. (3) Our proposed TITAN achieves the best scores on all the benchmarks with different settings. For CUB200, our TITAN obtain an improvement of " + }, + { + "bbox": [ + 46, + 437, + 288, + 700 + ], + "type": "inline_equation", + "content": "5.46\\%" + }, + { + "bbox": [ + 46, + 437, + 288, + 700 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 437, + 288, + 700 + ], + "type": "inline_equation", + "content": "5.05\\%" + }, + { + "bbox": [ + 46, + 437, + 288, + 700 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 437, + 288, + 700 + ], + "type": "inline_equation", + "content": "9.52\\%" + }, + { + "bbox": [ + 46, + 437, + 288, + 700 + ], + "type": "text", + "content": " over the best baseline PRISM under symmetric label noise with noise rate being 0.1, 0.2, 0.5 respectively. For CARS and FLICKR25K, our TITAN outperforms competitive baseline T-SINT by " + }, + { + "bbox": [ + 46, + 437, + 288, + 700 + ], + "type": "inline_equation", + "content": "21.04\\%" + }, + { + "bbox": [ + 46, + 437, + 288, + 700 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 437, + 288, + 700 + ], + "type": "inline_equation", + "content": "4.66\\%" + }, + { + "bbox": [ + 46, + 437, + 288, + 700 + ], + "type": "text", + "content": " in terms of average MAP@R scores under symmetric noise with different noise degrees. And the same tendency can also be observed on CIFAR10 under both noise label settings. The exceptional performance of our TITAN can be attributed to two primary factors. On the one hand, we improve the accuracy of noisy sample refinement by using retrieval-based refinement with curriculum learning instead of point-wise refinement. Our model, on the other hand, is enhanced by prototypical mixing technology that prevents it from memorizing noisy data, which facilitates semantic learning." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "content": "Table 3 displays the performance on Cars98N with real" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 312, + 74, + 430, + 184 + ], + "blocks": [ + { + "bbox": [ + 312, + 74, + 430, + 184 + ], + "lines": [ + { + "bbox": [ + 312, + 74, + 430, + 184 + ], + "spans": [ + { + "bbox": [ + 312, + 74, + 430, + 184 + ], + "type": "image", + "image_path": "094a3ca1d3f9dec8f20d4fa542300bb8aaa4623f311ae75a5ddead5345abb2b8.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 432, + 73, + 548, + 184 + ], + "blocks": [ + { + "bbox": [ + 432, + 73, + 548, + 184 + ], + "lines": [ + { + "bbox": [ + 432, + 73, + 548, + 184 + ], + "spans": [ + { + "bbox": [ + 432, + 73, + 548, + 184 + ], + "type": "image", + "image_path": "6e78dd18fbc5938dbe61b3a5ecc6db6f901447df9d65db0fa86e0e2cdb777e7c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 312, + 186, + 429, + 297 + ], + "blocks": [ + { + "bbox": [ + 312, + 186, + 429, + 297 + ], + "lines": [ + { + "bbox": [ + 312, + 186, + 429, + 297 + ], + "spans": [ + { + "bbox": [ + 312, + 186, + 429, + 297 + ], + "type": "image", + "image_path": "f85ea0a949bdaaa831c8095dbc499aa584e1a7423d03a72d43bf6d6077c8c97a.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 432, + 186, + 548, + 297 + ], + "blocks": [ + { + "bbox": [ + 432, + 186, + 548, + 297 + ], + "lines": [ + { + "bbox": [ + 432, + 186, + 548, + 297 + ], + "spans": [ + { + "bbox": [ + 432, + 186, + 548, + 297 + ], + "type": "image", + "image_path": "617f6b80a287fcfccaf9964521f41ff9892a99aec2142f6f9caed9e2e0f692f1.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 312, + 300, + 429, + 411 + ], + "blocks": [ + { + "bbox": [ + 312, + 300, + 429, + 411 + ], + "lines": [ + { + "bbox": [ + 312, + 300, + 429, + 411 + ], + "spans": [ + { + "bbox": [ + 312, + 300, + 429, + 411 + ], + "type": "image", + "image_path": "e53fb4323937cd3844ce3c7c221a2e412727ffa4089e82c8e2d8dde78a805831.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 416, + 545, + 449 + ], + "lines": [ + { + "bbox": [ + 305, + 416, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 416, + 545, + 449 + ], + "type": "text", + "content": "Figure 4. The MAP@R scores w.r.t. different noise rates. Results with Symmetric noise are plotted in the left column while results with Pairflip noise are plotted in the right column." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 432, + 300, + 548, + 411 + ], + "blocks": [ + { + "bbox": [ + 432, + 300, + 548, + 411 + ], + "lines": [ + { + "bbox": [ + 432, + 300, + 548, + 411 + ], + "spans": [ + { + "bbox": [ + 432, + 300, + 548, + 411 + ], + "type": "image", + "image_path": "6b526fbb852aa6bd06a6834e2e9604c4fe4b4443e38f4df20ffc973943883e4b.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 307, + 454, + 427, + 567 + ], + "blocks": [ + { + "bbox": [ + 307, + 454, + 427, + 567 + ], + "lines": [ + { + "bbox": [ + 307, + 454, + 427, + 567 + ], + "spans": [ + { + "bbox": [ + 307, + 454, + 427, + 567 + ], + "type": "image", + "image_path": "79a7edeb86175b56f787a74a3227979bb2a18a19918d2b4854c653a4b918f85c.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 571, + 545, + 602 + ], + "lines": [ + { + "bbox": [ + 305, + 571, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 305, + 571, + 545, + 602 + ], + "type": "text", + "content": "Figure 5. The MAP@R scores of TITAN and PRISM implemented on CUB and Fickr25k with varying hidden dimensions while the noise rate is set to " + }, + { + "bbox": [ + 305, + 571, + 545, + 602 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 305, + 571, + 545, + 602 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 430, + 454, + 550, + 567 + ], + "blocks": [ + { + "bbox": [ + 430, + 454, + 550, + 567 + ], + "lines": [ + { + "bbox": [ + 430, + 454, + 550, + 567 + ], + "spans": [ + { + "bbox": [ + 430, + 454, + 550, + 567 + ], + "type": "image", + "image_path": "09cd0f7b4dc71929ecadec5c6250b6837084b64eacd744b452561377308c0635.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 616, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 616, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 616, + 545, + 664 + ], + "type": "text", + "content": "world label noise. From these results, we can observe that TITAN also achieves significantly better performance in real-world settings, which demonstrates the generalizability and superiority of our approach." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Qualitative Comparison. Additionally, we plot the P-R curves and TopN-precision curves of the proposed TITAN and other compared methods with 512-dimensional feature vectors on three benchmarks in Figure 3. In the P-R curve," + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11245" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 91, + 288, + 168 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 287, + 90 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 287, + 90 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 287, + 90 + ], + "type": "text", + "content": "Table 4. Ablation results on CIFAR10, CUB, CARS, and FLICKR25K with noise rate being 0.1." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 91, + 288, + 168 + ], + "lines": [ + { + "bbox": [ + 49, + 91, + 288, + 168 + ], + "spans": [ + { + "bbox": [ + 49, + 91, + 288, + 168 + ], + "type": "table", + "html": "
MethodCIFAR10CUB200CARS196FLICKR25K
TITAN w/o LSL85.0417.0515.8291.98
TITAN w/o LC84.3316.6715.2491.23
TITAN w/o M87.5618.2516.1392.65
TITAN w/o R87.7818.0516.0892.11
TITAN w/o w88.5418.7717.2493.97
TITAN (full)89.0119.1117.6494.33
", + "image_path": "cb04dac45b766c785c81e13a15543428e606df929cf4c2f2869fdf9b0c5d188f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 182, + 287, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 287, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 287, + 301 + ], + "type": "text", + "content": "the area enclosed by the curve corresponding to our method is significantly larger than the remaining three baselines, which indicates that our method has better retrieval performance. In the curve of topN-precision, our method keeps the highest accuracy rate as the number of retrieved samples increases, especially when the number of returned samples is around 100. Overall, we have the conclusion based on these visualization results that when coming to actual image retrieval, Titan can achieve promising retrieval performances." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 302, + 287, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 302, + 287, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 302, + 287, + 469 + ], + "type": "text", + "content": "Noise Degree Analysis. We plot the performance trends under two different types of noise variation, especially for the high noise rate in Figure 4. This result indicates that the performance of PRISM decreases rapidly with an increase in noise, as PRISM is unable to construct a clean memory bank at the beginning if the noise ratio is too high. Even with a high noise ratio, our proposed TITAN is still able to deliver the best performance. Due to curriculum learning and blending the semantic information of the prototype with the sample features, we gradually construct a relatively accurate prototype for semantic learning. In general, our TITAN achieves great performance under various noise ratios, demonstrating the robustness and superiority of our proposed TITAN." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "text", + "content": "Feature Dimension Analysis. Figure 5 shows the MAP@R results of TITAN and PRISM methods implemented on CUB and FLICKR25k with feature dimensions varying from 128 to 2048. It can be found that the MAP@R value has a small decrease in both 128 and 2048 dimensions for TITAN, while for PRISM there is no obvious pattern of change. In general, probably because of the L2 normalization, the MAP@R value does not change much with the increase of hidden dimension. Note that our method outperforms the PRISM for all the cases, which proves the robustness of our method." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 610, + 141, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 141, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 141, + 624 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "We present an ablation study to investigate the effectiveness of the important inner module in our proposed TITAN and the experiment results are shown in Table 4. Specifically, we design the following model variants as: (1) TITAN w/o " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{SL}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " removes similarity learning loss for denoising in Eqn. 7. (2) TITAN w/o " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_C" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " removes cluster learning loss for retrieval in Eqn. 11. (3) TITAN w/o M removes" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 337 + ], + "type": "text", + "content": "the sampled virtual feature in Eqn. 4. (4) TITAN w/o R removes the retrieval-based refinement procedure. (5) TITAN w/o " + }, + { + "bbox": [ + 304, + 72, + 547, + 337 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 304, + 72, + 547, + 337 + ], + "type": "text", + "content": " removes confidence scores in Eqn. 8. From these results, we can draw some observations as follows: First, TITAN w/o " + }, + { + "bbox": [ + 304, + 72, + 547, + 337 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_C" + }, + { + "bbox": [ + 304, + 72, + 547, + 337 + ], + "type": "text", + "content": " has lower MAP@R scores than TITAN w/o " + }, + { + "bbox": [ + 304, + 72, + 547, + 337 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{SL}" + }, + { + "bbox": [ + 304, + 72, + 547, + 337 + ], + "type": "text", + "content": ", perhaps because in the case of a large number of sample categories in the training set, using a small batch size will lead to few positive sample pairs in the mini-batch, which will affect the learning of similarity. Second, TITAN w/o M performs worse than TITAN, which indicates that our use of prototypical mixing is effective, it makes the feature representation more robust and alleviates the overfitting of the model to dirty data to some extent. Third, MAP@R values corresponding to TITAN w/o R drop by about the same amount as TITAN w/o M, which proves that Retrieval-based refinement is an important and influential module in our proposed TITAN, it provides an effective way to refine noisy samples for pairwise similarity learning framework in retrieval tasks. Finally, the slightly lower performance of TITAN w/o " + }, + { + "bbox": [ + 304, + 72, + 547, + 337 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 304, + 72, + 547, + 337 + ], + "type": "text", + "content": " compared to TITAN suggests that confidence scores can improve performance by attenuating the impact of unreliable mixed samples." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 348, + 427, + 459 + ], + "blocks": [ + { + "bbox": [ + 307, + 348, + 427, + 459 + ], + "lines": [ + { + "bbox": [ + 307, + 348, + 427, + 459 + ], + "spans": [ + { + "bbox": [ + 307, + 348, + 427, + 459 + ], + "type": "image", + "image_path": "451947d65c4c6e0303dc65d3bd7e96cef23cf453290d3b755ed32ac616b1762d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 464, + 537, + 475 + ], + "lines": [ + { + "bbox": [ + 306, + 464, + 537, + 475 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 537, + 475 + ], + "type": "text", + "content": "Figure 6. Sensitivity analysis of two hyper-parameters on CUB." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 427, + 348, + 545, + 460 + ], + "blocks": [ + { + "bbox": [ + 427, + 348, + 545, + 460 + ], + "lines": [ + { + "bbox": [ + 427, + 348, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 427, + 348, + 545, + 460 + ], + "type": "image", + "image_path": "548ea1d1cd875c9bd223b0773cd444759b0773a594c94cde6ee681cd5aa3d4f5.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 491, + 421, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 421, + 504 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 421, + 504 + ], + "type": "text", + "content": "4.4. Sensitivity Analysis" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": "We investigate the effect of hyper-parameters " + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "inline_equation", + "content": "K_{max}" + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": " on model retrieval performance on CUB with different noise rates. The loss balance coefficient " + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": " controls the weight between different losses, firstly we vary " + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": " in [0.1,0.3,0.5,0.8,1.0] with other parameters fixed, Figure 6 illustrates the experimental results, we can find that performance of our method is not sensitive to " + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": " when it varies from 0.5 to 1.0, which demonstrates that the convergence of our proposed algorithm is stable. Moreover, we fix all other parameters and change " + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "inline_equation", + "content": "K_{max}" + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": " in [5,10,15,20,25,30], which controls the max retrieval number of each prototype, as shown in Figure 6, the MAP@R results decrease when " + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "inline_equation", + "content": "K_{max}" + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": " is set in [25,30], the potential reason is that a high " + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "inline_equation", + "content": "K_{max}" + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": " will cause more samples to change their labels, but our constructed prototype is not completely reliable at the early stage of training, this leads to refinement which may in turn increase the noise rate. From the analysis, we set " + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\eta" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11246" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "as 0.8 and " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "K_{max}" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": " as 20 respectively for the proposed TITAN as default." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 106, + 123, + 119 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 106, + 123, + 119 + ], + "spans": [ + { + "bbox": [ + 47, + 106, + 123, + 119 + ], + "type": "text", + "content": "4.5. Case Study" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 125, + 289, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 125, + 289, + 234 + ], + "spans": [ + { + "bbox": [ + 46, + 125, + 289, + 234 + ], + "type": "text", + "content": "We present the top ten images retrieved by PRISM and the proposed TITAN on FLICKR25K. As depicted in Figure 7, the examples enclosed in green boxes represent accurate results, whereas those enclosed in red boxes are wrong results. Additionally, we have labeled the category of each image below it. It is evident that the proposed approach yields significantly more relevant and precise retrieval outcomes for the given queries, demonstrating the superiority of our methodology in handling realistic scenarios." + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 50, + 247, + 298, + 358 + ], + "blocks": [ + { + "bbox": [ + 50, + 247, + 298, + 358 + ], + "lines": [ + { + "bbox": [ + 50, + 247, + 298, + 358 + ], + "spans": [ + { + "bbox": [ + 50, + 247, + 298, + 358 + ], + "type": "image", + "image_path": "364d2a5f0bd538b22d636f63482a897032a959ad9abcbf91b6b966fc6dd4742c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 361, + 287, + 384 + ], + "lines": [ + { + "bbox": [ + 46, + 361, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 287, + 384 + ], + "type": "text", + "content": "Figure 7. Example of the Top10 returned images with 512-dimensional feature on FLICKR25K." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 402, + 174, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 402, + 174, + 415 + ], + "spans": [ + { + "bbox": [ + 47, + 402, + 174, + 415 + ], + "type": "text", + "content": "4.6. Visulaization Analysis" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 422, + 289, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 422, + 289, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 289, + 601 + ], + "type": "text", + "content": "T-SNE Visualization. We adopt T-Distributed Stochastic Neighbor Embedding (T-SNE) [39] to compress the dense feature vectors into the two-dimensional plane to visualize the correlations between the features embedded and their one-hot labels, which come from the feature space and the label space respectively. Figure 8 illustrates the visualization of dense vectors generated by our method and the competitive baselines, i.e., PRISM and Jo-SRC. Compared with the two baselines, our method can generate actually compact clusters and can separate each category more clearly while at the same time bringing feature vectors with similar semantic information closer together. This visualization shows that our method can generate dense features that are more discriminative, which could facilitate better image retrieval." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 52, + 613, + 294, + 686 + ], + "blocks": [ + { + "bbox": [ + 52, + 613, + 294, + 686 + ], + "lines": [ + { + "bbox": [ + 52, + 613, + 294, + 686 + ], + "spans": [ + { + "bbox": [ + 52, + 613, + 294, + 686 + ], + "type": "image", + "image_path": "0bf1f41a97bebe19f6f8cb974e95c906a0a2d0a76aff20200cfa192f8879cfbe.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 691, + 286, + 712 + ], + "lines": [ + { + "bbox": [ + 46, + 691, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 691, + 286, + 712 + ], + "type": "text", + "content": "Figure 8. The t-SNE visualization of 512-dimensional feature vectors on CIFAR10." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 71, + 379, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 379, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 379, + 84 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 92, + 547, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 92, + 547, + 260 + ], + "spans": [ + { + "bbox": [ + 304, + 92, + 547, + 260 + ], + "type": "text", + "content": "This paper studies a practical but less-explored problem of label noise-resistant image retrieval and proposes a novel method TITAN, which simultaneously corrects label noise and mitigates the impacts of memorization to solve the problem. We describe different prototypes with Gaussian distributions in the hidden space, which directs Mixing to generate synthetic samples. In addition, we collect similar samples for each prototype ranging from easy to hard during optimization, which refines noisy samples in a precise and class-balanced way. Extensive experiments on five benchmark datasets reveal that our proposed TITAN can outperform various state-of-the-art methods. In future works, we would extend our TITAN to more scenarios such as learning to hash and cross-modal retrieval." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 275, + 365, + 288 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 275, + 365, + 288 + ], + "spans": [ + { + "bbox": [ + 306, + 275, + 365, + 288 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 307, + 296, + 547, + 712 + ], + "type": "list", + "angle": 0, + "index": 22, + "blocks": [ + { + "bbox": [ + 310, + 296, + 545, + 328 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 296, + 545, + 328 + ], + "spans": [ + { + "bbox": [ + 310, + 296, + 545, + 328 + ], + "type": "text", + "content": "[1] Artem Babenko and Victor Lempitsky. Aggregating local deep features for image retrieval. 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However, discovering novel categories in an incremental learning scenario remains a challenging problem due to the lack of prior knowledge about the number and nature of new categories. Existing methods for novel category discovery are limited by their reliance on labeled datasets and prior knowledge about the number of novel categories and the proportion of novel samples in the batch. To address the limitations and more accurately reflect real-world scenarios, in this paper, we propose a novel unsupervised class incremental learning approach for discovering novel categories on unlabeled sets without prior knowledge. The proposed method fine-tunes the feature extractor and proxy anchors on labeled sets, then splits samples into old and novel categories and clusters on the unlabeled dataset. Furthermore, the proxy anchors-based exemplar generates representative category vectors to mitigate catastrophic forgetting. Experimental results demonstrate that our proposed approach outperforms the state-of-the-art methods on fine-grained datasets under real-world scenarios.", + "bbox": [ + 75, + 411, + 472, + 729 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 739, + 209, + 753 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep neural networks have achieved remarkable performance in various computer vision tasks. However, current systems are still subject to constraints that are manually supervised and do not consider continual incremental categories. For extending to real-world environments, there are still gaps to catch up by overcoming the constraints and improving their abilities in fundamental tasks. Specifically, humans still perform better than machines in object cognitive and grouping skills (e.g. recognizing new products", + "bbox": [ + 75, + 763, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "or clothing on shopping and categorizing undefined moving objects while driving).", + "bbox": [ + 498, + 380, + 890, + 411 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Various methods have been proposed to address the limitations of the tasks by considering real-world circumstances, as presented in Figure 1 and Table 1. In detail, Novel Category Discovery (NCD) [10, 11, 43] and Generalized Category Discovery (GCD) [36, 6] aim to recognize not only pre-trained categories but also discover novel categories using a given dataset. NCD considers a disjoint dataset where labeled and unlabeled novel samples have no intersection with each other. In contrast, GCD exploits the joint set with intersected categories, making GCD a more complicated task than NCD. However, these approaches do not consider the class incremental scheme. Class incremental NCD (class-iNCD) [33, 15] has been proposed to adopt the incremental categories on NCD task, but they still focus on improving novel category discovery performance using the disjoint set, which is an unrealistic constraint. To address this issue, Grow and Merge (GM) [42] proposes a scenario that exploits the joint unlabeled dataset in the incremental novel category discovery task, which is called Continuous Category Discovery Mixed Incremental (CCDMI). However, most existing methods require prior knowledge, such as the number of unlabeled classes for NCD and class-iNCD, or the proportion of the novel samples in the batch for CCD-MI. Such prior knowledge requirements are not enough to mimic the real-world, as we lack information about the unlabeled sets.", + "bbox": [ + 496, + 412, + 892, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To overcome these constraints, we propose a novel scenario that better represents real-world circumstances by removing constraints on the available data. We assume that the given datasets are unlabeled joint sets without providing prior knowledge about the data. Employing the scenario, we propose a novel unsupervised class incremental", + "bbox": [ + 496, + 810, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16688", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e74bfc7940bf6fc68a927150b0cb0a20940110fbd699c2978315a89fef3671bc.jpg", + "image_caption": [ + "(a) NCD" + ], + "image_footnote": [], + "bbox": [ + 96, + 95, + 228, + 188 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/4b3f796cb879f5b29d9c07dc2df5d27278a8de5a50b9c8127fe24c13a0f14fa8.jpg", + "image_caption": [ + "(b) GCD", + "Figure 1. Comparison of existing and proposed scenarios for novel category discovery. The solid and dash-lined circles indicate labeled and unlabeled samples, respectively, with sample color depicting the class label. The circle with $i$ denotes the number of novel classes (pink) and the proportion of novel class samples in a batch (dark blue)." + ], + "image_footnote": [], + "bbox": [ + 259, + 92, + 387, + 188 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/0992e772d538ba724ff6181212baa5e4243ba48792eb4ee1d7917bad9a08202e.jpg", + "image_caption": [ + "(c) class-iNCD" + ], + "image_footnote": [], + "bbox": [ + 413, + 97, + 563, + 188 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/212d61951bd00c70cafbd4bb767be28804a9d52702ceb8dd9a0ee688d0740f66.jpg", + "image_caption": [ + "(d) CCD-MI" + ], + "image_footnote": [], + "bbox": [ + 570, + 93, + 725, + 188 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/13633ca7a3170b07c7e124d3089f2cdb970018dc2ff148a82f735fe01e92639d.jpg", + "image_caption": [ + "(e) CGCD" + ], + "image_footnote": [], + "bbox": [ + 733, + 95, + 880, + 188 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/298c9d2d1e4046a2fc33e573f894f0607b1407e1181bd22e2bd1b149a051fe54.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TaskMethodConstraints
Continual learningAssumption: yl∩yu=∅Number of novel classesProportion of new class data
NCDRankStat [10, 11], DRNCD [43]Not consideredRequiredRequiredNot required
GCDGCD [36], XCon [6]Not consideredNot requiredNot requiredNot required
class-iNCDFroST [33], NCDwF [15]ConsideredRequiredRequiredNot required
CCD-MIGM [42]ConsideredNot requiredNot requiredRequired
CGCDOursConsideredNot requiredNot requiredNot required
", + "bbox": [ + 86, + 258, + 883, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Table 1. Comparison of existing and proposed novel category discovery settings and the constraints", + "bbox": [ + 189, + 412, + 777, + 426 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "learning approach to simultaneously address the problems of discovering incremental novel categories and alleviating catastrophic forgetting. In addition, we focus on recognizing fine-grained objects, which is a more realistic use case for various applications in real-world applications.", + "bbox": [ + 75, + 441, + 468, + 517 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The proposed method exploits a deep metric learning scheme, proxy anchor (PA) [18] that presents fast and reliable convergence and robustness against noise samples, and also considers the relations between samples. Then, we divide the unlabeled data into old and novel categories using PAs, which inherit discriminative features of old categories. The cosine similarity is measured between the PAs and the samples, and then initially separated datasets are acquired on a criterion. For further splitting, we adopt a noisy label learning scheme, and then assign the predictions of the previous model and the clustering results by a nonparametric approach to old and novel categorized samples, respectively. To mitigate the forgetting, we use a PA-based exemplar, which inherits more representative features. In the experimental results, we demonstrate that the proposed method outperforms the existing state-of-the-art in discovering novel categories and forgetting alleviation on various fine-grained datasets. Specifically, the proposed method does not require any prior knowledge and considers continual learning on unlabeled joint datasets, making it a more realistic and practical solution for real-world scenarios.", + "bbox": [ + 75, + 517, + 468, + 834 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of the proposed method can be summarized as follows.", + "bbox": [ + 76, + 834, + 468, + 863 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We introduce a novel scenario, called Continuous Generalized novel Category Discovery (CGCD), which", + "bbox": [ + 94, + 869, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "is well-suited to tackle the challenges of discovering novel categories in real-world scenarios by removing the constraint that unlabeled data belong to only novel categories.", + "bbox": [ + 529, + 441, + 890, + 502 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel unsupervised learning approach for incremental novel category discovery that does not require prior knowledge of the number of novel categories or the proportion of new class data.", + "- We present a noisy label learning approach and deep metric learning to split unlabeled data into old and novel categories, and also show mitigation of catastrophic forgetting using a deep metric-based exemplar.", + "- The proposed method outperforms the state-of-the-art methods in novel category discovery and forgetting mitigation on various fine-grained datasets." + ], + "bbox": [ + 517, + 510, + 890, + 693 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Problem Definition", + "text_level": 1, + "bbox": [ + 500, + 700, + 684, + 715 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Continuous Generalized Category Discovery", + "text_level": 1, + "bbox": [ + 500, + 726, + 875, + 742 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As presented in Figure 1 and Table 1, various environmental schemes have been proposed to mimic real-world circumstances. Notable approaches include NCD [10, 11, 43], GCD [36], class-iNCD [33, 15], and CCD [42]. NCD considers disjoint datasets between labeled and unlabeled sets (i.e. $\\mathcal{Y}_l \\cap \\mathcal{Y}_u = \\emptyset$ ) and requires prior knowledge of the number of unlabeled categories $|\\mathcal{Y}_u|$ . In contrast, GCD exploits the joint set (i.e. $\\mathcal{Y}_l \\cap \\mathcal{Y}_u \\neq \\emptyset$ ). Although GCD is a more challenging task than NCD, it still does not consider continuous incremental category discovery.", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16689", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7d08a14bd02a454c1f8d6d9ffef4cc92107dd0ad0e21c2e290e4ae966d7fc290.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed CGCD framework. The framework comprises three steps. The first step is that the network model is fine-tuned on the target dataset using the labeled dataset. In the second step, the discovery of novel categories is performed on the joint and unlabeled dataset, which is split into unseen and seen sets using the initial and fine split methods. Pseudo-labels are assigned to the unlabeled dataset using the previous model's predictions (seen case) and non-parametric clustering results (unseen case). In the last step, a new model is trained on the fine split dataset, which incorporates new proxy anchors based on clustering results." + ], + "image_footnote": [], + "bbox": [ + 99, + 89, + 883, + 330 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Class-iNCD is an extension of NCD to the continual learning scheme. However, the method trains on the disjoint dataset under class incremental stages and has a requirement for $|\\mathcal{V}_u|$ . CCD also trains on discovering novel classes under the continual learning scheme with the joint dataset. Although CCD does not require $|\\mathcal{V}_u|$ , it still needs the proportion of the novel class data in a batch as prior knowledge, which is used to filter out the data.", + "bbox": [ + 75, + 417, + 470, + 539 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To address these limitations, we propose a more challenging problem, named Continuous Generalized novel Category Discovery (CGCD), that is closer to real-world circumstances. In CGCD, we exploit the unlabeled joint dataset in incremental steps without providing any prior knowledge and aim to discover novel classes. This formulation is more representative of real-world scenarios, where we are not aware of the number of unlabeled categories and the characteristics of the dataset.", + "bbox": [ + 75, + 541, + 468, + 676 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Setting of Continuous Generalized Category Discovery", + "text_level": 1, + "bbox": [ + 76, + 691, + 468, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fine-grained datasets consist of similar objects, such as canines [16], indoor scenes [30], vehicles [25], and birds [37], in constrained circumstances. Compared to coarse datasets such as CIFAR [19] and ImageNet [20], fine-grained datasets are closer to real-world scenarios. Therefore, we focus on training and discovering novel classes with fine-grained datasets to mimic real-world circumstances better.", + "bbox": [ + 75, + 732, + 468, + 852 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "CGCD employs the joint unlabeled dataset in incremental steps, and Table 2 describes the dataset partitioning used in the one-time incremental category discovery. First, the", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/080bfbe27e9627e113f4a61e90afe878c222d711a314b81a58b818bb22c23328.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetAll classesInitial stepCategory incremental step
Old classOld classNew class
CUB-200200160 (0.8)160 (0.2)40 (1.0)
MIT676753 (0.8)53 (0.2)14 (1.0)
Stanford Dogs12096 (0.8)96 (0.2)24 (1.0)
FGVC Aircraft10080 (0.8)80 (0.2)20 (1.0)
", + "bbox": [ + 501, + 415, + 890, + 525 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 2. Dataset configurations for one-time incremental category scenarios. The number of classes and the proportion of data from each class in parentheses are presented. Note that the ratios in parentheses are hidden information that is not revealed to the learning methods.", + "bbox": [ + 496, + 534, + 893, + 604 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "set of classes is partitioned into old classes and new classes at a certain rate, for example, 8: 2. The initial step utilizes labeled dataset $\\mathcal{D}^0$ consisting of old classes only. Then the following incremental step utilizes unlabeled dataset $\\mathcal{D}^1$ consisting of both old classes and new classes, which reflect more realistic and challenging real-world scenarios. The key element of the proposed method is to decide whether the unlabeled data point belongs to the old classes (seen) or new classes (unseen). The samples belonging to the old classes are assigned to labeled dataset $\\mathcal{D}^0$ and unlabeled dataset $\\mathcal{D}^1$ , and the rest of all the new class samples are assigned to $\\mathcal{D}^1$ . Here the choice of 8: 2 is an arbitrary example, and it is important to note that this ratio is just for data generation purposes and is not revealed to the learning methods.", + "bbox": [ + 496, + 613, + 893, + 828 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 843, + 591, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As described in Figure 2, our proposed method consists of three steps: the initial step, the novel category discovery and the final step.", + "bbox": [ + 498, + 869, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16690", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ery step, and the category incremental step. In the initial step, we fine-tune a pre-trained model on the labeled dataset $\\mathcal{D}^0 = \\{(x,y)\\in \\mathcal{X}_l\\times \\mathcal{Y}_l\\}$ , and obtain the embedding vector $z$ using the model $f(\\cdot)$ , denoted as $z = f^{0}(x)$ . We then use these vectors to train PAs [18] of each category, represented as $p = g^0 (z)$ , and also construct well-representative exemplars. In the following novel category discovery step, the given unlabeled joint datasets are denoted as $\\mathcal{D}^1 = \\{x|x\\in \\mathcal{X}_u\\}$ . We first separate them into old and novel categories through the initial and the fine splits. Since the separated sets are unlabeled, we pseudo-label for old and novel classes using the previous model prediction and non-parametric clustering results, respectively.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the category incremental step, the acquired set is trained to improve the performance of discovering novel categories. To avoid catastrophic forgetting, we exploit generated features by the exemplar and feature distillation between earlier and new models. The proposed model does not require any prior knowledge, such as $|\\mathcal{Y}_u|$ and the ratio of novel class samples in a batch. We evaluate the performance of the proposed method using the validation dataset, which includes all categories.", + "bbox": [ + 75, + 287, + 472, + 424 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Initial Step: Fine Tune", + "text_level": 1, + "bbox": [ + 76, + 435, + 289, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Existing NCD methods do not account for noisy categories, such as those categorized from old to novel or from novel to old, which can impair novel discovery performance and accumulate errors in the continuous procedure. To address these limitations, in this work, we propose a novel approach that leverages the benefits of PA to complement and improve the existing approaches. PA is a metric learning method that combines proxy- and pair-based methods to achieve rapid and reliable convergence, and robustness against noisy samples, and considers relations between data to extract meaningful semantic information.", + "bbox": [ + 75, + 459, + 472, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following the method, the embedding vector $z$ from the initial model $f^0$ is trained to map to each proxy anchor $p = g^0 (z)$ . Let the set of all proxy anchors as $P^0$ in the labeled data $\\mathcal{D}^0$ . In this manner, the number of proxy anchors of $\\mathcal{D}^0$ is the number of classes of the labeled set (i.e. $|P^0| = |\\mathcal{Y}_l|$ ) in the initial step. We train the model and proxy anchors using the following loss function defined in [18]:", + "bbox": [ + 75, + 626, + 470, + 733 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {p a} ^ {0} \\left(Z ^ {0}\\right) = \\frac {1}{| P ^ {0 +} |} \\sum_ {p \\in P ^ {0 +}} \\log \\left(1 + \\sum_ {z \\in Z _ {p} ^ {0 +}} e ^ {- \\alpha (s (z, p) - \\delta)}\\right) \\tag {1} \\\\ + \\frac {1}{| P ^ {0} |} \\sum_ {p \\in P ^ {0}} \\log \\left(1 + \\sum_ {z \\in Z _ {p} ^ {0 -}} e ^ {\\alpha (s (z, p) + \\delta)}\\right) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 742, + 468, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\delta > 0$ is a margin and $\\alpha > 0$ is a scaling factor. The function $s(\\cdot, \\cdot)$ indicates the cosine similarity score. $P^{0+}$ represents same class PAs(e.gpositive) in the batch. Each proxy $p$ divides the set of embedding vector $Z^0$ as $Z_p^{0+}$ and", + "bbox": [ + 75, + 835, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0547a841a326d4a2d01d2bc871f87059a9fc50c37947dd43ac2b98f991b2770b.jpg", + "image_caption": [ + "(a) Initial Split" + ], + "image_footnote": [], + "bbox": [ + 506, + 89, + 696, + 193 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0bc54aeb7531789ecc22dfe3ec46c62fbcf37e5d2e44e749fc552aff483090b6.jpg", + "image_caption": [ + "(b) Fine Split", + "Figure 3. Separation results on joint unlabeled datasets" + ], + "image_footnote": [], + "bbox": [ + 700, + 89, + 887, + 193 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$Z_{p}^{0^{-}} = Z^{0} - Z_{p}^{0^{+}}$ . $Z_{p}^{0^{+}}$ denotes the same class embedding points with the proxy anchor $p$ . The first term aims to pull $p$ and its dissimilar but hard positive data together, while the last term is to push $p$ and its similar but hard negatives apart.", + "bbox": [ + 496, + 226, + 893, + 290 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Discovering Novel Categories Step", + "text_level": 1, + "bbox": [ + 498, + 299, + 799, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Separation: In this procedure, we aim to split the given joint dataset $\\mathcal{D}^1$ into the novel and old categories without any prior knowledge. We conduct this task in two stages: initial split and fine split. In the initial split, we compute the cosine similarity between $p$ and each embedding vector $z_i \\in Z^1$ , where $z_i = f^0(x_i)$ and $x_i \\in D^1$ . Because the set of proxy anchors $P^0$ represents the old categories, we classify a sample to the old class if the maximum similarity score of $z_i$ is larger than a threshold $\\epsilon$ . We set $\\epsilon = 0$ since it is the median of the score ranges. The initial split is defined as:", + "bbox": [ + 496, + 323, + 890, + 487 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {y} _ {i} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} \\max _ {p \\in P ^ {0}} (s \\left(z _ {i}, p\\right)) \\geq \\epsilon = 0 \\\\ 1, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 486, + 890, + 534 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To acquire a cleaner novel and old dataset, we propose a noisy labeling scheme, fine split, which involves an iterative training of a simple multilayer perceptron (MLP) based classifier $m(\\cdot)$ on the binarized dataset. The initial split results in noisy and inaccurate separation, as shown in Figure 3 (a). Among them, only the data on both ends of the spectrum are assumed the clean and utilized to train the classifier. The loss of split network $m(\\cdot)$ is defined as follows:", + "bbox": [ + 496, + 541, + 890, + 675 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s p} = - \\mathbb {E} _ {z _ {c} \\in Z _ {c} ^ {1}} \\left[ \\tilde {y} _ {c} \\log \\left(m \\left(z _ {c}\\right)\\right) + \\left(1 - \\tilde {y} _ {c}\\right) \\log \\left(1 - m \\left(z _ {c}\\right)\\right) \\right] \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 689, + 890, + 707 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $z_{c}$ denotes clean embedding vectors, and $Z_{c}^{1}$ represents the set of clean vectors. $\\tilde{y}_{c}$ indicates the pseudo label of the clean data. After the warm-up training, the classifier is trained with re-assigned pseudo labels and the more cleaned data, which is divided with the Gaussian mixture model (GMM). Consequently, the Figure 3 (b) shows the cleaner separated results.", + "bbox": [ + 496, + 718, + 890, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Pseudo-labeling: After the separation, both the old $\\mathcal{D}_{old}^{1}$ and the novel categories $\\mathcal{D}_{new}^{1}$ are still unlabeled. Thus, we use pseudo-labels to assign labels to each sample. For $\\mathcal{D}_{old}^{1}$ , we use the predictions of the previous model and proxy anchors to assign pseudo-labels. In contrast, we use a", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16691", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "non-parametric clustering approach named Affinity propagation [8] to assign pseudo-labels to $\\mathcal{D}_{new}^{1}$ . In this manner, our proposed approach does not require any prior knowledge. Finally, from the clustering results, we obtain an estimate of the number of novel categories, denoted as $|\\hat{\\mathcal{Y}}_n|$ .", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Category Incremental Step", + "text_level": 1, + "bbox": [ + 76, + 180, + 320, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training modified model and PAs: To improve the performance of discovering novel categories, we modify the model since the previous model has PAs only for $|\\mathcal{Y}_l|$ classes and cannot categorize novel classes. We add new $p$ for $|\\hat{\\mathcal{Y}}_n|$ classes, increasing the total number of PAs like $|P^1| = |\\mathcal{Y}_l| + |\\hat{\\mathcal{Y}}_n|$ . The loss function to train the modified model $f^1$ and PA $p = g^1(z)$ is reformulated as follows:", + "bbox": [ + 75, + 204, + 468, + 310 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {p a} ^ {1} (Z ^ {1}) = \\frac {1}{| P ^ {1 +} |} \\sum_ {p \\in P ^ {1 +}} \\log \\left(1 + \\sum_ {z \\in Z _ {p} ^ {1 +}} e ^ {- \\alpha (s (z, p) - \\delta)}\\right) \\tag {4} \\\\ + \\frac {1}{| P ^ {1} |} \\sum_ {p \\in P ^ {1}} \\log \\left(1 + \\sum_ {z \\in Z _ {p} ^ {1 -}} e ^ {\\alpha (s (z, p) + \\delta)}\\right) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 325, + 467, + 404 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Avoiding forgetting: In the continual learning scheme, it is essential to alleviate catastrophic forgetting. We adopt feature replay, which leverages the PA information belonging to old categories. Each well-trained $p$ inherits the representation power for each category. We employ each $p$ to generate features by following the Gaussian distribution $\\mathcal{N}(p^0,\\sigma^2), p^0 \\in P^0$ . The number of generated features is determined based on data balancing, for example, the number of newly categorized samples in a batch. The generated features are concatenated into a batch, and the model and PAs are trained using the following loss function:", + "bbox": [ + 75, + 420, + 468, + 585 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {e x} ^ {1} (\\tilde {Z}) = \\mathcal {L} _ {p a} ^ {1} (\\tilde {Z}), \\quad \\tilde {Z} = \\left\\{\\tilde {z} \\sim \\mathcal {N} \\left(p ^ {0}, \\sigma^ {2}\\right) \\right\\} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 599, + 467, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Also, we utilize the distillation of the extracted embedding vectors from the present $f^1$ and the previous model $f^0$ . The distillation loss $\\mathcal{L}_{kd}$ is described as follows:", + "bbox": [ + 75, + 633, + 467, + 678 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {k d} ^ {1} \\left(z _ {o}\\right) = - \\mathbb {E} _ {z _ {o} \\in Z _ {o l d} ^ {1}} \\| z _ {o} ^ {0} - z _ {o} \\| _ {2} \\tag {6} \\\\ = - \\mathbb {E} _ {x _ {o} \\in D _ {o l d} ^ {1}} \\| f ^ {0} (x _ {o}) - f ^ {1} (x _ {o}) \\| _ {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 693, + 467, + 732 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $z^0$ represents the embedding vector for fixed previous feature network $f^0$ . $Z_{old}^{1}$ denotes seen data from $Z^{1} = \\{Z_{old}^{1}\\cup Z_{new}^{1}\\}$ .", + "bbox": [ + 76, + 747, + 468, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In conclusion, the loss consists of three different losses in the continuous category discovery step. One loss is for training the PAs and the model on $\\mathcal{D}^1$ , the others are to avoid forgetting by using generated features and knowledge distillation. $\\mathcal{L}^1$ is described as follows:", + "bbox": [ + 75, + 795, + 468, + 868 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} ^ {1} = \\mathcal {L} _ {p a} ^ {1} (Z ^ {1}) + \\mathcal {L} _ {e x} ^ {1} (\\tilde {Z}) + \\mathcal {L} _ {k d} ^ {1} \\left(z _ {o}\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 883, + 467, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental Results", + "text_level": 1, + "bbox": [ + 500, + 90, + 704, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 114, + 715, + 130 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We utilized the widely used augmentation techniques, including random crop after padding and random horizontal flip. All the experiments were trained for 60 epochs using AdamW optimizer with weight decay set to 0.0001. The initial learning rate was set to 0.0001 for the model $f(\\cdot)$ , while for the PAs, it was set to 0.01. The learning rate was decayed by a factor of 0.5 every five epochs. We used the threshold $\\epsilon$ only once for the initial split to divide the set into old and novel categories, and we set it to 0 for all the datasets and networks. For fine split, we used an MLP-based network architecture that consists of two dense layers with a batch normalization layer. The model was trained for three epochs using AdamW with a learning rate of 0.0001. The hyperparameters for PAs, $\\alpha$ and $\\delta$ , were set to 32 and 0.1, respectively.", + "bbox": [ + 498, + 137, + 890, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For fair comparisons of various methods, such as NCD, class-iNCD, and CCD, we follow the hyperparameters and the network architectures of the original implementations, referring to the papers for details. All the reported performances are average results over three runs.", + "bbox": [ + 498, + 364, + 890, + 439 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Evaluation Metrics", + "text_level": 1, + "bbox": [ + 500, + 449, + 683, + 463 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate the methods using metrics based on the cluster accuracy measurement, called Hungarian assignment algorithm [21]. The evaluation metric is defined as follows:", + "bbox": [ + 498, + 472, + 890, + 517 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {M} ^ {t} = \\frac {1}{| \\mathcal {D} |} \\sum_ {i = 1} ^ {| \\mathcal {D} |} \\mathbb {I} \\left(y _ {i} = h ^ {*} \\left(y _ {i} ^ {*}\\right)\\right) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 529, + 888, + 570 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $|\\mathcal{D}|$ is the size of the validation dataset $\\mathcal{D}$ and $h^*$ is the optimal assignment. So, $\\mathcal{M}^t$ measures the cluster accuracy at step $t$ on the $\\mathcal{D}$ . In this manner, $\\mathcal{M}_{all}$ and $\\mathcal{M}_o$ indicate the cluster accuracy metrics of the whole and old categories using $\\mathcal{M}^t$ , respectively. Furthermore, we employ two more metrics that, $\\mathcal{M}_f$ and $\\mathcal{M}_d$ , which are proposed on GM [42] and described as follows:", + "bbox": [ + 498, + 577, + 890, + 681 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {M} _ {f} = \\max _ {t} \\left\\{\\mathcal {M} _ {o} ^ {0} - \\mathcal {M} _ {o} ^ {t} \\right\\}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 691, + 888, + 712 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {M} _ {d} = \\frac {1}{| T |} \\sum_ {i = T} \\mathcal {M} _ {n} ^ {i}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 732, + 888, + 767 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{M}_o^0$ and $\\mathcal{M}_o^t$ are the old class cluster accuracy at the initial step and category incremental $t$ step, respectively. So $\\mathcal{M}_f$ measures the maximum forgetting values for old categories in the entire step and should be sufficiently low; if not, the method is not valuable in practical applications. In Equation (10), $|T|$ is the number of increased steps, and $\\mathcal{M}_d$ evaluates the averaged performance of novel category discovery in unlabeled joint datasets in each step. It means", + "bbox": [ + 498, + 779, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16692", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/7682ef9b8b7cad35aafb82ac77e7b2a476fb68d5548d1034df3ce75e8823069e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodCUB-200MIT67Stanford DogsFGVC aircraft
\\( {\\mathcal{M}}_{all} \\)↑\\( {\\mathcal{M}}_{o} \\)↑\\( {\\mathcal{M}}_{f} \\)↓\\( {\\mathcal{M}}_{d} \\)↑\\( {\\mathcal{M}}_{all} \\)↑\\( {\\mathcal{M}}_{o} \\)↑\\( {\\mathcal{M}}_{f} \\)↓\\( {\\mathcal{M}}_{d} \\)↑\\( {\\mathcal{M}}_{all} \\)↑\\( {\\mathcal{M}}_{o} \\)↑\\( {\\mathcal{M}}_{f} \\)↓\\(\\mathcal{M}_{d}\\uparrow\\)\\( {\\mathcal{M}}_{all} \\)↑\\( {\\mathcal{M}}_{o} \\)↑\\( {\\mathcal{M}}_{f} \\)↓\\( {\\mathcal{M}}_{d} \\)↑
Supervised61.6945.8323.3216.6355.5640.9019.5218.3464.2647.5725.4317.0164.6248.1726.2418.12
DRNCD [43]9.8010.4758.5134.2426.9927.6749.0738.9116.3910.3465.8363.3618.7319.5057.0545.63
FRoST [33]18.1917.3412.1817.2023.2123.5515.9624.7422.6222.2314.2926.0632.6133.5315.1927.69
GM [42]6.436.5739.825.9216.5216.7742.2615.505.995.9850.365.9812.0011.6353.3513.46
Ours54.7558.8015.4740.9054.4564.2310.6418.5866.2576.156.7730.0437.2841.6014.6620.04
", + "bbox": [ + 78, + 89, + 898, + 218 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Comparison results under continuous generalized categorized discovery scenario. The results present the mean over three runs.", + "bbox": [ + 76, + 224, + 875, + 238 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f8d1bd7dfc0d4d59e06cb26ce5c99dbc300c2781c479a50dce5f04f5c69be2c3.jpg", + "image_caption": [ + "Figure 4. Qualitative evaluation results of the proposed method using the CUB-200 dataset on ResNet-18. The first five columns with blue boxes denote well-clustered examples. The last two columns represent failed prediction results, including example images with purple boxes denoting hard negatives and those with red boxes indicating incorrect categorization." + ], + "image_footnote": [], + "bbox": [ + 81, + 243, + 890, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the higher method, the more appropriate method in real-world applications.", + "bbox": [ + 75, + 564, + 468, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison with State-of-the-arts Methods", + "text_level": 1, + "bbox": [ + 76, + 604, + 447, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conducted a series of experiments to compare the cluster accuracy performance of our proposed method with state-of-the-art approaches, as presented in Table 1. In the experiments, we excluded the GCD task, including XCon, as it focuses on discovering novel categories blended with labeled and unlabeled datasets and evaluates unknown discovery performance on only train datasets, not validation datasets, in their papers. Therefore, we compared our proposed method with other approaches, including Dual rank NCD (DRNCD) [43], FRoST [33], and GM, which are the representative methods that record the state-of-the-art results of each task.", + "bbox": [ + 75, + 628, + 468, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first evaluated the one-step incremental category setting and reported the comparison results in Table 3. The supervised method is the setting of a supervised continual learning manner, literally. We observed catastrophic forgetting in supervised learning. DRNCD is one of the NCD approaches and recorded the outstanding performances of", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$\\mathcal{M}_d$ on MIT67, Stanford Dogs, and FGVC aircraft. However, the method requires prior knowledge of the number of novel categories and does not identify specific classes, but only knows whether the samples are included in the novel category or not. Thus, the results are not regarded as outperforming. Instead, the method shows the highest results of $\\mathcal{M}_f$ , which means that the method focuses on learning novel categories without considering the prevention of forgetting previous categorical knowledge. In this regard, NCD is not sufficient to extend novel class incremental learning schemes. FRoST showed competitive results of discovering novel classes and decreased forgetting results $\\mathcal{M}_f$ on all datasets compared to DRNCD. Nevertheless, considering the required knowledge, the other metrics results, $\\mathcal{M}_{all}$ and $\\mathcal{M}_o$ were not competitive. GM proposed the CCD setting, which is the most similar to CGCD, in the perspective of the unknown number of novel categories and discovering novel and old categories on new unlabeled datasets. However, the method requires a crucial parameter, which is the ratio of novel category samples on the new dataset. Without considering the ratio, GM recorded the lowest results of $\\mathcal{M}_{all}$ , $\\mathcal{M}_o$ , and $\\mathcal{M}_d$ .", + "bbox": [ + 496, + 564, + 890, + 897 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16693", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d57f0f7fd163c035ad8deaed4eb858b99ba4becdf56a7bfd5ecefb822c8e00f5.jpg", + "image_caption": [ + "(a) Novel category discovery $M_{d}$ (b) Catastrophic forgetting $M_{f}$ Figure 5. Performances of novel category discovery and forgetting on two-step incremental novel categories experiment" + ], + "image_footnote": [], + "bbox": [ + 86, + 90, + 272, + 191 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d101bb3a145ac9a57fc21c05c7e766c19ab5748af5a0b47878d7bf0ed081d381.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 90, + 460, + 191 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The proposed method showed outstanding performance on the various datasets without requiring any prior information about new incoming unlabeled datasets. Our method recorded the second-best $\\mathcal{M}_f$ on the CUB-200 dataset and the best $\\mathcal{M}_f$ on the other datasets, such as MIT67, Dogs, and FGVC aircraft, by the effects of PA-based exemplar. On $\\mathcal{M}_d$ , the method was also competitive and compared to the GM, which has the most similar setting to our method.", + "bbox": [ + 75, + 242, + 467, + 363 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To evaluate the proposed method qualitatively, we clustered the evaluation dataset using the CUB-200 dataset. In Figure 4, our method well-discovered novel categories and clustered them correctly. Each row is clustered into the same category, and the classes are novel categories on the evaluation dataset. The left five columns are well-clustered, while the last two are not. The sixth-column images are still reasonable, but the last-columns are the worst cases.", + "bbox": [ + 75, + 364, + 467, + 484 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Two-step Novel Category Discovery", + "text_level": 1, + "bbox": [ + 76, + 492, + 383, + 508 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We present a two-step incremental category discovery experiment on the CUB-200 dataset using ResNet-18. The dataset configurations are more complicated as the datasets are joint sets in incremental steps. The initial step, the first incremental step, and the second incremental step have novel classes in each step, at a rate of $8:1:1$ , respectively. Each step has its dataset and is indicated as $\\mathcal{D}^0$ , $\\mathcal{D}^1$ , and $\\mathcal{D}^2$ . The samples belonging to novel labeled classes in the initial step are assigned to $\\mathcal{D}^0$ , $\\mathcal{D}^1$ , and $\\mathcal{D}^2$ at a rate of $8:1:1$ . Similarly, the samples belonging to novel classes in the first incremental step are assigned to $\\mathcal{D}^1$ , and $\\mathcal{D}^2$ at a rate of $8:2$ . Finally, the rest of the samples are assigned to $\\mathcal{D}^2$ .", + "bbox": [ + 75, + 517, + 467, + 698 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 5 describes the performance of the experiments. Since each incremental step is trained for 60 epochs, there are deep drops at the $60th$ epoch when new PAs are added. In addition, the cluster accuracy of the old categories, which belong to the $\\mathcal{D}^0$ , decreases by about $20\\%$ . The reason is that the number of old categories in the second incremental step is increased compared to the first step. The exemplar cannot focus on only generating the features of $\\mathcal{D}^0$ . However, the performance of $\\mathcal{M}_d$ increased steadily.", + "bbox": [ + 75, + 699, + 467, + 834 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 845, + 228, + 862 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of separations: We conducted an ablation study to show the effectiveness of our proposed splitter,", + "bbox": [ + 75, + 869, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/36b084e67cd4bf29d2e84390ff685b6f534e730efd018940691bbf00ca37348b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
NetworkFine SplitMetric
Mall ↑Mo ↑Mf ↓Md ↑
ResNet-18without53.3257.6316.5636.47
with54.7558.8015.4740.90
ResNet-50without66.5371.079.1248.76
with68.0971.758.4453.79
ViT-B-16without70.2273.0210.7559.24
with72.5174.289.4965.60
", + "bbox": [ + 500, + 90, + 890, + 239 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ed18a63397b5cf2a14b262e18bef9abce50bb6f55ca12fd6c8691743dee4eb2f.jpg", + "table_caption": [ + "Table 4. Ablation study for the proposed fine split on the CUB-200 using three different network architectures, including ResNet-18 and ResNet-50 pre-trained on ImageNet, and ViT-B-16 pre-trained on DINO-ImageNet. The results present the mean over three runs." + ], + "table_footnote": [], + "table_body": "
NetworkExemplarMetric
Mall ↑Mo ↑Mf ↓Md ↑
ResNet-18without38.2437.3136.8841.89
Data mean and std.40.2340.5633.6337.22
Proxy anchors54.7558.8015.4740.90
", + "bbox": [ + 501, + 303, + 890, + 398 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Effectiveness of the proposed PA-based exemplar on the CUB-200 dataset using ResNet-18 pre-trained on ImageNet", + "bbox": [ + 498, + 405, + 890, + 433 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "which consists of a combination of two different methods: the cosine similarity score and a binary splitter using the noise label approach. The ablation experiments were designed such that one used only the cosine similarity score, and another used both methods. As shown in Table 4, the approach using both methods presents improvements in both old and novel discovery performances. The results reveal the effectiveness of noise labeling for data separation.", + "bbox": [ + 496, + 443, + 890, + 565 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Proxy anchor exemplar: To mitigate catastrophic forgetting, various approaches, such as replay [2], prototype [31, 33], and pseudo-latents [15], have been proposed. Most of these methods exploit the computed average of feature embedding vectors or input data-driven values. However, we propose a novel PA-based exemplar approach and evaluate its efficiency. As shown in Table 5, the method without the exemplar recorded the highest novel discovery performances but also showed the highest forgetting. Adopting a general exemplar approach using mean and standard deviation values from the former dataset, $\\mathcal{M}_f$ slightly decreased, but $\\mathcal{M}_d$ is the lowest. However, our proposed method with the PA-based exemplar recorded the best $\\mathcal{M}_f$ and competitive $\\mathcal{M}_d$ . We analyze that the PAs have representatives of each cluster since PA inherits the relation between data to data and then representative figures of each class. Hence, our PA-based method leads to mitigating forgetting, and we confirm that it is a proper approach.", + "bbox": [ + 496, + 566, + 890, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Robustness of class and sample blending ratio variants: In general, the capability to recognize novel categories largely depends on a powerful and well-trained initial model with the target datasets. The more classes and", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16694", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/28bf902f71b7ceb7dc7e8c0e16d01d8cbfae5581b9c55f853f7e9aa9066cade2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
RatioMetric
Yold: YnewMall ↑Mo ↑Mf ↓Md ↑
9:161.3463.2211.8344.73
8:254.7558.8015.4740.90
7:352.6658.4214.6739.50
6:448.7857.9015.1635.53
5:545.2862.4111.3028.55
", + "bbox": [ + 81, + 88, + 464, + 210 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Qualitative evaluation by changing the ratio of classes and samples on the CUB-200 using ResNet18 pre-trained on ImageNet", + "bbox": [ + 80, + 217, + 467, + 246 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "samples are included in the initial training dataset $\\mathcal{D}^0$ , the better the model learns representative features to fit the sets. To evaluate the robustness of the proposed model, we conducted experiments with variants of the number of samples and classes in $\\mathcal{D}^0$ . As described in Table 6, decreasing the number of classes and data in the labeled set decreased the discovery of novel classes and clustering accuracies as the number of unlabeled novel data increased. On the other hand, catastrophic forgetting could increase since the number of novel data increases. However, forgetting was maintained within a reasonable boundary, indicating the effectiveness of our PA-based exemplar. The results suggest that our method has the robustness of the variants.", + "bbox": [ + 80, + 251, + 467, + 446 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Related work", + "text_level": 1, + "bbox": [ + 80, + 458, + 210, + 472 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.1. Novel Category Discovery", + "text_level": 1, + "bbox": [ + 80, + 482, + 308, + 498 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "NCD techniques have been proposed to classify data with various constraints on unlabeled data. One category of the methods presented pre-training the model on the labeled set and fine-tuning it on the unlabeled set using unsupervised clustering losses [41, 13, 12, 23, 24]. Another category assumed the availability of both the labeled and unlabeled data, and trained networks jointly with a labeled novel class loss within the semi-supervised scheme [10, 44, 45, 14, 7, 43]. Han et al. [11] proposed transferring knowledge from labeled to unlabeled data using ranking statistics in the joint learning stage. Recently, GCD [36] and XCon [6] tackled the more realistic scenario of joint datasets and distinguished known and unknown classes using prior knowledge. However, these approaches did not consider the continual learning scheme. To address the limitation, FRoST [33] and NCDwF [15] froze feature extractors and added the second head for each novel class, as much as the given number of novel categories. However, the methods employed disjoint sets. GM [42] proposed to consider novel category discovery on the joint datasets, but still require prior knowledge, such as the proportion of novel samples.", + "bbox": [ + 80, + 506, + 467, + 837 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2. Image Retrieval", + "text_level": 1, + "bbox": [ + 80, + 847, + 233, + 862 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Most of the image retrieval methods have utilized metric learning and can be categorized into two approaches.", + "bbox": [ + 80, + 869, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Pair-based methods exploited contrastive loss [3, 5, 9] and triplet loss [34, 38], that pull together data pairs in the same class and push apart those in different classes. Multiple data-based [35, 28] methods proposed considering the relations between multiple data. Entire data-based approaches [40, 39] presented considering all data in a batch, leveraging fine-grained semantic relations between them while requiring high computation costs and slow convergence. In contrast, proxy-based methods [26, 29, 1] employed fewer proxies than the training set, reducing training complexity. While these methods improved training convergence, they did not consider data-to-data relations, as each data was associated with its proxy. PA [18] inherited the strength of pair- and proxy-based methods, achieving fast and reliable convergence, robustness opposing noisy data, and leveraging rich data-to-data relations.", + "bbox": [ + 501, + 90, + 888, + 330 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Noise Label", + "text_level": 1, + "bbox": [ + 503, + 348, + 624, + 362 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Recently proposed methods for learning with noisy labels have highlighted the importance of discriminating between clean and noise-labeled data to improve performance. DivideMix [22] used GMM to distinguish between clean and noisy labeled data and treated the latter as unlabeled for semi-supervised learning. AugDesc [27] employed data augmentation to enhance the differentiation between clean and noisy labeled data, while INCV [4] introduced cross-validation to separate clean data from noisy training data. SplitNet [17] leveraged a compact network to perceive the difference between clean and noisy labels, improving model performance by more accurately differentiating noise.", + "bbox": [ + 501, + 375, + 888, + 554 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 503, + 564, + 614, + 579 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we presented a novel continual learning scenario, considered NCD on the unlabeled joint datasets without any prior knowledge of the dataset. Our framework utilized PAs to split known and novel categories, resulting in well-clustered and well-pseudo-labeled categories that mitigate catastrophic forgetting. We further refined the splitting of the dataset by adopting a noise labeling scheme. Our proposed approach outperformed existing state-of-the-art methods regarding novel category discovery and forgetting. While DeepDPM [32] has recently shown outstanding performance on non-parametric clustering tasks, we believe that our proposed method can achieve even better performance by adopting better clustering manners. In future work, we plan to evaluate our method by adopting a better clustering manner.", + "bbox": [ + 501, + 592, + 888, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 503, + 828, + 663, + 843 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was funded by Samsung Electro-Mechanics and was partially supported by Carl-Zeiss Stiftung under the Sustainable Embedded AI project (P2021-02-009).", + "bbox": [ + 503, + 854, + 888, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16695", + "bbox": [ + 480, + 946, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Nicolas Aziere and Sinisa Todorovic. Ensemble deep manifold similarity learning using hard proxies. 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In CVPR, 2021." + ], + "bbox": [ + 501, + 92, + 890, + 335 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "16697", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Proxy Anchor-based Unsupervised Learning for Continuous Generalized Category Discovery/82f1fc34-be8f-46cf-8cc9-6e1e6fe0df48_model.json b/2023/Proxy Anchor-based Unsupervised Learning for Continuous Generalized Category Discovery/82f1fc34-be8f-46cf-8cc9-6e1e6fe0df48_model.json new file mode 100644 index 0000000000000000000000000000000000000000..908e41209811bf8346339450e28928938e394f11 --- /dev/null +++ b/2023/Proxy Anchor-based Unsupervised Learning for Continuous Generalized Category Discovery/82f1fc34-be8f-46cf-8cc9-6e1e6fe0df48_model.json @@ -0,0 +1,2200 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.119, + 0.13, + 0.852, + 0.176 + ], + "angle": 0, + "content": "Proxy Anchor-based Unsupervised Learning for Continuous Generalized Category Discovery" + }, + { + "type": "text", + "bbox": [ + 0.104, + 0.202, + 0.868, + 0.237 + ], + "angle": 0, + "content": "Hyungmin \\(\\mathrm{Kim}^{1,2}\\) Sungho \\(\\mathrm{Suh}^{3,4}\\) Daehwan \\(\\mathrm{Kim}^{2}\\) Daun Jeong\\(^{2}\\) Hansang \\(\\mathrm{Cho}^{2}\\) Junmo \\(\\mathrm{Kim}^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.182, + 0.239, + 0.79, + 0.256 + ], + "angle": 0, + "content": "\\(^{1}\\)Korea Advanced Institute of Science and Technology, Daejeon, South Korea" + }, + { + "type": "text", + "bbox": [ + 0.282, + 0.257, + 0.689, + 0.274 + ], + "angle": 0, + "content": "\\(^{2}\\)Samsung Electro-Mechanics, Suwon, South Korea" + }, + { + "type": "text", + "bbox": [ + 0.148, + 0.275, + 0.824, + 0.292 + ], + "angle": 0, + "content": "\\(^{3}\\)German Research Center for Artificial Intelligence (DFKI), Kaiserslautern, Germany" + }, + { + "type": "text", + "bbox": [ + 0.126, + 0.293, + 0.845, + 0.311 + ], + "angle": 0, + "content": "\\(^{4}\\)Department of Computer Science, RPTU Kaiserslautern-Landau, Kaiserslautern, Germany" + }, + { + "type": "text", + "bbox": [ + 0.243, + 0.313, + 0.727, + 0.327 + ], + "angle": 0, + "content": "{hyungmin83, junmo.kim}@kaist.ac.kr, sungho.suh@dfki.de" + }, + { + "type": "text", + "bbox": [ + 0.258, + 0.33, + 0.715, + 0.345 + ], + "angle": 0, + "content": "{daehwan85.kim, du33.jeong, hansang.cho}@samsung.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.38, + 0.313, + 0.396 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.412, + 0.473, + 0.73 + ], + "angle": 0, + "content": "Recent advances in deep learning have significantly improved the performance of various computer vision applications. However, discovering novel categories in an incremental learning scenario remains a challenging problem due to the lack of prior knowledge about the number and nature of new categories. Existing methods for novel category discovery are limited by their reliance on labeled datasets and prior knowledge about the number of novel categories and the proportion of novel samples in the batch. To address the limitations and more accurately reflect real-world scenarios, in this paper, we propose a novel unsupervised class incremental learning approach for discovering novel categories on unlabeled sets without prior knowledge. The proposed method fine-tunes the feature extractor and proxy anchors on labeled sets, then splits samples into old and novel categories and clusters on the unlabeled dataset. Furthermore, the proxy anchors-based exemplar generates representative category vectors to mitigate catastrophic forgetting. Experimental results demonstrate that our proposed approach outperforms the state-of-the-art methods on fine-grained datasets under real-world scenarios." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.74, + 0.21, + 0.755 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Deep neural networks have achieved remarkable performance in various computer vision tasks. However, current systems are still subject to constraints that are manually supervised and do not consider continual incremental categories. For extending to real-world environments, there are still gaps to catch up by overcoming the constraints and improving their abilities in fundamental tasks. Specifically, humans still perform better than machines in object cognitive and grouping skills (e.g. recognizing new products" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.381, + 0.892, + 0.412 + ], + "angle": 0, + "content": "or clothing on shopping and categorizing undefined moving objects while driving)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.414, + 0.893, + 0.807 + ], + "angle": 0, + "content": "Various methods have been proposed to address the limitations of the tasks by considering real-world circumstances, as presented in Figure 1 and Table 1. In detail, Novel Category Discovery (NCD) [10, 11, 43] and Generalized Category Discovery (GCD) [36, 6] aim to recognize not only pre-trained categories but also discover novel categories using a given dataset. NCD considers a disjoint dataset where labeled and unlabeled novel samples have no intersection with each other. In contrast, GCD exploits the joint set with intersected categories, making GCD a more complicated task than NCD. However, these approaches do not consider the class incremental scheme. Class incremental NCD (class-iNCD) [33, 15] has been proposed to adopt the incremental categories on NCD task, but they still focus on improving novel category discovery performance using the disjoint set, which is an unrealistic constraint. To address this issue, Grow and Merge (GM) [42] proposes a scenario that exploits the joint unlabeled dataset in the incremental novel category discovery task, which is called Continuous Category Discovery Mixed Incremental (CCDMI). However, most existing methods require prior knowledge, such as the number of unlabeled classes for NCD and class-iNCD, or the proportion of the novel samples in the batch for CCD-MI. Such prior knowledge requirements are not enough to mimic the real-world, as we lack information about the unlabeled sets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.902 + ], + "angle": 0, + "content": "To overcome these constraints, we propose a novel scenario that better represents real-world circumstances by removing constraints on the available data. We assume that the given datasets are unlabeled joint sets without providing prior knowledge about the data. Employing the scenario, we propose a novel unsupervised class incremental" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16688" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.097, + 0.23, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.138, + 0.19, + 0.188, + 0.201 + ], + "angle": 0, + "content": "(a) NCD" + }, + { + "type": "image", + "bbox": [ + 0.261, + 0.093, + 0.388, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.299, + 0.19, + 0.35, + 0.201 + ], + "angle": 0, + "content": "(b) GCD" + }, + { + "type": "image", + "bbox": [ + 0.414, + 0.098, + 0.565, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.443, + 0.19, + 0.529, + 0.201 + ], + "angle": 0, + "content": "(c) class-iNCD" + }, + { + "type": "image", + "bbox": [ + 0.571, + 0.094, + 0.726, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.612, + 0.19, + 0.684, + 0.201 + ], + "angle": 0, + "content": "(d) CCD-MI" + }, + { + "type": "image", + "bbox": [ + 0.734, + 0.096, + 0.882, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.78, + 0.19, + 0.838, + 0.201 + ], + "angle": 0, + "content": "(e) CGCD" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.209, + 0.894, + 0.252 + ], + "angle": 0, + "content": "Figure 1. Comparison of existing and proposed scenarios for novel category discovery. The solid and dash-lined circles indicate labeled and unlabeled samples, respectively, with sample color depicting the class label. The circle with \\( i \\) denotes the number of novel classes (pink) and the proportion of novel class samples in a batch (dark blue)." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.259, + 0.885, + 0.409 + ], + "angle": 0, + "content": "
TaskMethodConstraints
Continual learningAssumption: yl∩yu=∅Number of novel classesProportion of new class data
NCDRankStat [10, 11], DRNCD [43]Not consideredRequiredRequiredNot required
GCDGCD [36], XCon [6]Not consideredNot requiredNot requiredNot required
class-iNCDFroST [33], NCDwF [15]ConsideredRequiredRequiredNot required
CCD-MIGM [42]ConsideredNot requiredNot requiredRequired
CGCDOursConsideredNot requiredNot requiredNot required
" + }, + { + "type": "table_caption", + "bbox": [ + 0.191, + 0.414, + 0.778, + 0.428 + ], + "angle": 0, + "content": "Table 1. Comparison of existing and proposed novel category discovery settings and the constraints" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.443, + 0.469, + 0.518 + ], + "angle": 0, + "content": "learning approach to simultaneously address the problems of discovering incremental novel categories and alleviating catastrophic forgetting. In addition, we focus on recognizing fine-grained objects, which is a more realistic use case for various applications in real-world applications." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.518, + 0.469, + 0.835 + ], + "angle": 0, + "content": "The proposed method exploits a deep metric learning scheme, proxy anchor (PA) [18] that presents fast and reliable convergence and robustness against noise samples, and also considers the relations between samples. Then, we divide the unlabeled data into old and novel categories using PAs, which inherit discriminative features of old categories. The cosine similarity is measured between the PAs and the samples, and then initially separated datasets are acquired on a criterion. For further splitting, we adopt a noisy label learning scheme, and then assign the predictions of the previous model and the clustering results by a nonparametric approach to old and novel categorized samples, respectively. To mitigate the forgetting, we use a PA-based exemplar, which inherits more representative features. In the experimental results, we demonstrate that the proposed method outperforms the existing state-of-the-art in discovering novel categories and forgetting alleviation on various fine-grained datasets. Specifically, the proposed method does not require any prior knowledge and considers continual learning on unlabeled joint datasets, making it a more realistic and practical solution for real-world scenarios." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.835, + 0.469, + 0.864 + ], + "angle": 0, + "content": "The main contributions of the proposed method can be summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "- We introduce a novel scenario, called Continuous Generalized novel Category Discovery (CGCD), which" + }, + { + "type": "text", + "bbox": [ + 0.53, + 0.443, + 0.892, + 0.503 + ], + "angle": 0, + "content": "is well-suited to tackle the challenges of discovering novel categories in real-world scenarios by removing the constraint that unlabeled data belong to only novel categories." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.511, + 0.892, + 0.572 + ], + "angle": 0, + "content": "- We propose a novel unsupervised learning approach for incremental novel category discovery that does not require prior knowledge of the number of novel categories or the proportion of new class data." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.58, + 0.892, + 0.641 + ], + "angle": 0, + "content": "- We present a noisy label learning approach and deep metric learning to split unlabeled data into old and novel categories, and also show mitigation of catastrophic forgetting using a deep metric-based exemplar." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.649, + 0.892, + 0.694 + ], + "angle": 0, + "content": "- The proposed method outperforms the state-of-the-art methods in novel category discovery and forgetting mitigation on various fine-grained datasets." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.511, + 0.892, + 0.694 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.702, + 0.685, + 0.717 + ], + "angle": 0, + "content": "2. Problem Definition" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.877, + 0.743 + ], + "angle": 0, + "content": "2.1. Continuous Generalized Category Discovery" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As presented in Figure 1 and Table 1, various environmental schemes have been proposed to mimic real-world circumstances. Notable approaches include NCD [10, 11, 43], GCD [36], class-iNCD [33, 15], and CCD [42]. NCD considers disjoint datasets between labeled and unlabeled sets (i.e. \\(\\mathcal{Y}_l \\cap \\mathcal{Y}_u = \\emptyset\\)) and requires prior knowledge of the number of unlabeled categories \\(|\\mathcal{Y}_u|\\). In contrast, GCD exploits the joint set (i.e. \\(\\mathcal{Y}_l \\cap \\mathcal{Y}_u \\neq \\emptyset\\)). Although GCD is a more challenging task than NCD, it still does not consider continuous incremental category discovery." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16689" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.09, + 0.885, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.339, + 0.895, + 0.41 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed CGCD framework. The framework comprises three steps. The first step is that the network model is fine-tuned on the target dataset using the labeled dataset. In the second step, the discovery of novel categories is performed on the joint and unlabeled dataset, which is split into unseen and seen sets using the initial and fine split methods. Pseudo-labels are assigned to the unlabeled dataset using the previous model's predictions (seen case) and non-parametric clustering results (unseen case). In the last step, a new model is trained on the fine split dataset, which incorporates new proxy anchors based on clustering results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.419, + 0.471, + 0.54 + ], + "angle": 0, + "content": "Class-iNCD is an extension of NCD to the continual learning scheme. However, the method trains on the disjoint dataset under class incremental stages and has a requirement for \\( |\\mathcal{V}_u| \\). CCD also trains on discovering novel classes under the continual learning scheme with the joint dataset. Although CCD does not require \\( |\\mathcal{V}_u| \\), it still needs the proportion of the novel class data in a batch as prior knowledge, which is used to filter out the data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.542, + 0.47, + 0.678 + ], + "angle": 0, + "content": "To address these limitations, we propose a more challenging problem, named Continuous Generalized novel Category Discovery (CGCD), that is closer to real-world circumstances. In CGCD, we exploit the unlabeled joint dataset in incremental steps without providing any prior knowledge and aim to discover novel classes. This formulation is more representative of real-world scenarios, where we are not aware of the number of unlabeled categories and the characteristics of the dataset." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.692, + 0.47, + 0.725 + ], + "angle": 0, + "content": "2.2. Setting of Continuous Generalized Category Discovery" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.47, + 0.853 + ], + "angle": 0, + "content": "Fine-grained datasets consist of similar objects, such as canines [16], indoor scenes [30], vehicles [25], and birds [37], in constrained circumstances. Compared to coarse datasets such as CIFAR [19] and ImageNet [20], fine-grained datasets are closer to real-world scenarios. Therefore, we focus on training and discovering novel classes with fine-grained datasets to mimic real-world circumstances better." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "CGCD employs the joint unlabeled dataset in incremental steps, and Table 2 describes the dataset partitioning used in the one-time incremental category discovery. First, the" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.416, + 0.892, + 0.526 + ], + "angle": 0, + "content": "
DatasetAll classesInitial stepCategory incremental step
Old classOld classNew class
CUB-200200160 (0.8)160 (0.2)40 (1.0)
MIT676753 (0.8)53 (0.2)14 (1.0)
Stanford Dogs12096 (0.8)96 (0.2)24 (1.0)
FGVC Aircraft10080 (0.8)80 (0.2)20 (1.0)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.535, + 0.894, + 0.605 + ], + "angle": 0, + "content": "Table 2. Dataset configurations for one-time incremental category scenarios. The number of classes and the proportion of data from each class in parentheses are presented. Note that the ratios in parentheses are hidden information that is not revealed to the learning methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.829 + ], + "angle": 0, + "content": "set of classes is partitioned into old classes and new classes at a certain rate, for example, 8: 2. The initial step utilizes labeled dataset \\(\\mathcal{D}^0\\) consisting of old classes only. Then the following incremental step utilizes unlabeled dataset \\(\\mathcal{D}^1\\) consisting of both old classes and new classes, which reflect more realistic and challenging real-world scenarios. The key element of the proposed method is to decide whether the unlabeled data point belongs to the old classes (seen) or new classes (unseen). The samples belonging to the old classes are assigned to labeled dataset \\(\\mathcal{D}^0\\) and unlabeled dataset \\(\\mathcal{D}^1\\), and the rest of all the new class samples are assigned to \\(\\mathcal{D}^1\\). Here the choice of 8: 2 is an arbitrary example, and it is important to note that this ratio is just for data generation purposes and is not revealed to the learning methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.844, + 0.593, + 0.86 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.903 + ], + "angle": 0, + "content": "As described in Figure 2, our proposed method consists of three steps: the initial step, the novel category discovery and the final step." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16690" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "ery step, and the category incremental step. In the initial step, we fine-tune a pre-trained model on the labeled dataset \\(\\mathcal{D}^0 = \\{(x,y)\\in \\mathcal{X}_l\\times \\mathcal{Y}_l\\}\\), and obtain the embedding vector \\(z\\) using the model \\(f(\\cdot)\\), denoted as \\(z = f^{0}(x)\\). We then use these vectors to train PAs [18] of each category, represented as \\(p = g^0 (z)\\), and also construct well-representative exemplars. In the following novel category discovery step, the given unlabeled joint datasets are denoted as \\(\\mathcal{D}^1 = \\{x|x\\in \\mathcal{X}_u\\}\\). We first separate them into old and novel categories through the initial and the fine splits. Since the separated sets are unlabeled, we pseudo-label for old and novel classes using the previous model prediction and non-parametric clustering results, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.289, + 0.473, + 0.425 + ], + "angle": 0, + "content": "In the category incremental step, the acquired set is trained to improve the performance of discovering novel categories. To avoid catastrophic forgetting, we exploit generated features by the exemplar and feature distillation between earlier and new models. The proposed model does not require any prior knowledge, such as \\(|\\mathcal{Y}_u|\\) and the ratio of novel class samples in a batch. We evaluate the performance of the proposed method using the validation dataset, which includes all categories." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.436, + 0.29, + 0.451 + ], + "angle": 0, + "content": "3.1. Initial Step: Fine Tune" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.473, + 0.625 + ], + "angle": 0, + "content": "Existing NCD methods do not account for noisy categories, such as those categorized from old to novel or from novel to old, which can impair novel discovery performance and accumulate errors in the continuous procedure. To address these limitations, in this work, we propose a novel approach that leverages the benefits of PA to complement and improve the existing approaches. PA is a metric learning method that combines proxy- and pair-based methods to achieve rapid and reliable convergence, and robustness against noisy samples, and considers relations between data to extract meaningful semantic information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.472, + 0.734 + ], + "angle": 0, + "content": "Following the method, the embedding vector \\(z\\) from the initial model \\(f^0\\) is trained to map to each proxy anchor \\(p = g^0 (z)\\). Let the set of all proxy anchors as \\(P^0\\) in the labeled data \\(\\mathcal{D}^0\\). In this manner, the number of proxy anchors of \\(\\mathcal{D}^0\\) is the number of classes of the labeled set (i.e. \\(|P^0| = |\\mathcal{Y}_l|\\)) in the initial step. We train the model and proxy anchors using the following loss function defined in [18]:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.743, + 0.47, + 0.824 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {p a} ^ {0} \\left(Z ^ {0}\\right) = \\frac {1}{| P ^ {0 +} |} \\sum_ {p \\in P ^ {0 +}} \\log \\left(1 + \\sum_ {z \\in Z _ {p} ^ {0 +}} e ^ {- \\alpha (s (z, p) - \\delta)}\\right) \\tag {1} \\\\ + \\frac {1}{| P ^ {0} |} \\sum_ {p \\in P ^ {0}} \\log \\left(1 + \\sum_ {z \\in Z _ {p} ^ {0 -}} e ^ {\\alpha (s (z, p) + \\delta)}\\right) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.837, + 0.473, + 0.904 + ], + "angle": 0, + "content": "where \\(\\delta > 0\\) is a margin and \\(\\alpha > 0\\) is a scaling factor. The function \\(s(\\cdot, \\cdot)\\) indicates the cosine similarity score. \\(P^{0+}\\) represents same class PAs(e.gpositive) in the batch. Each proxy \\(p\\) divides the set of embedding vector \\(Z^0\\) as \\(Z_p^{0+}\\) and" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.09, + 0.697, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.562, + 0.197, + 0.645, + 0.209 + ], + "angle": 0, + "content": "(a) Initial Split" + }, + { + "type": "image", + "bbox": [ + 0.701, + 0.09, + 0.888, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.756, + 0.197, + 0.832, + 0.209 + ], + "angle": 0, + "content": "(b) Fine Split" + }, + { + "type": "image_caption", + "bbox": [ + 0.532, + 0.208, + 0.859, + 0.221 + ], + "angle": 0, + "content": "Figure 3. Separation results on joint unlabeled datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.227, + 0.894, + 0.291 + ], + "angle": 0, + "content": "\\(Z_{p}^{0^{-}} = Z^{0} - Z_{p}^{0^{+}}\\). \\(Z_{p}^{0^{+}}\\) denotes the same class embedding points with the proxy anchor \\(p\\). The first term aims to pull \\(p\\) and its dissimilar but hard positive data together, while the last term is to push \\(p\\) and its similar but hard negatives apart." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.3, + 0.8, + 0.317 + ], + "angle": 0, + "content": "3.2. Discovering Novel Categories Step" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.324, + 0.892, + 0.488 + ], + "angle": 0, + "content": "Separation: In this procedure, we aim to split the given joint dataset \\(\\mathcal{D}^1\\) into the novel and old categories without any prior knowledge. We conduct this task in two stages: initial split and fine split. In the initial split, we compute the cosine similarity between \\(p\\) and each embedding vector \\(z_i \\in Z^1\\), where \\(z_i = f^0(x_i)\\) and \\(x_i \\in D^1\\). Because the set of proxy anchors \\(P^0\\) represents the old categories, we classify a sample to the old class if the maximum similarity score of \\(z_i\\) is larger than a threshold \\(\\epsilon\\). We set \\(\\epsilon = 0\\) since it is the median of the score ranges. The initial split is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.569, + 0.487, + 0.891, + 0.535 + ], + "angle": 0, + "content": "\\[\n\\tilde {y} _ {i} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} \\max _ {p \\in P ^ {0}} (s \\left(z _ {i}, p\\right)) \\geq \\epsilon = 0 \\\\ 1, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.542, + 0.892, + 0.676 + ], + "angle": 0, + "content": "To acquire a cleaner novel and old dataset, we propose a noisy labeling scheme, fine split, which involves an iterative training of a simple multilayer perceptron (MLP) based classifier \\( m(\\cdot) \\) on the binarized dataset. The initial split results in noisy and inaccurate separation, as shown in Figure 3 (a). Among them, only the data on both ends of the spectrum are assumed the clean and utilized to train the classifier. The loss of split network \\( m(\\cdot) \\) is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.69, + 0.891, + 0.708 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s p} = - \\mathbb {E} _ {z _ {c} \\in Z _ {c} ^ {1}} \\left[ \\tilde {y} _ {c} \\log \\left(m \\left(z _ {c}\\right)\\right) + \\left(1 - \\tilde {y} _ {c}\\right) \\log \\left(1 - m \\left(z _ {c}\\right)\\right) \\right] \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.892, + 0.825 + ], + "angle": 0, + "content": "where \\( z_{c} \\) denotes clean embedding vectors, and \\( Z_{c}^{1} \\) represents the set of clean vectors. \\( \\tilde{y}_{c} \\) indicates the pseudo label of the clean data. After the warm-up training, the classifier is trained with re-assigned pseudo labels and the more cleaned data, which is divided with the Gaussian mixture model (GMM). Consequently, the Figure 3 (b) shows the cleaner separated results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Pseudo-labeling: After the separation, both the old \\(\\mathcal{D}_{old}^{1}\\) and the novel categories \\(\\mathcal{D}_{new}^{1}\\) are still unlabeled. Thus, we use pseudo-labels to assign labels to each sample. For \\(\\mathcal{D}_{old}^{1}\\), we use the predictions of the previous model and proxy anchors to assign pseudo-labels. In contrast, we use a" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16691" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "non-parametric clustering approach named Affinity propagation [8] to assign pseudo-labels to \\(\\mathcal{D}_{new}^{1}\\). In this manner, our proposed approach does not require any prior knowledge. Finally, from the clustering results, we obtain an estimate of the number of novel categories, denoted as \\(|\\hat{\\mathcal{Y}}_n|\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.181, + 0.321, + 0.198 + ], + "angle": 0, + "content": "3.3. Category Incremental Step" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.205, + 0.469, + 0.311 + ], + "angle": 0, + "content": "Training modified model and PAs: To improve the performance of discovering novel categories, we modify the model since the previous model has PAs only for \\(|\\mathcal{Y}_l|\\) classes and cannot categorize novel classes. We add new \\(p\\) for \\(|\\hat{\\mathcal{Y}}_n|\\) classes, increasing the total number of PAs like \\(|P^1| = |\\mathcal{Y}_l| + |\\hat{\\mathcal{Y}}_n|\\). The loss function to train the modified model \\(f^1\\) and PA \\(p = g^1(z)\\) is reformulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.327, + 0.468, + 0.405 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {p a} ^ {1} (Z ^ {1}) = \\frac {1}{| P ^ {1 +} |} \\sum_ {p \\in P ^ {1 +}} \\log \\left(1 + \\sum_ {z \\in Z _ {p} ^ {1 +}} e ^ {- \\alpha (s (z, p) - \\delta)}\\right) \\tag {4} \\\\ + \\frac {1}{| P ^ {1} |} \\sum_ {p \\in P ^ {1}} \\log \\left(1 + \\sum_ {z \\in Z _ {p} ^ {1 -}} e ^ {\\alpha (s (z, p) + \\delta)}\\right) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.421, + 0.469, + 0.587 + ], + "angle": 0, + "content": "Avoiding forgetting: In the continual learning scheme, it is essential to alleviate catastrophic forgetting. We adopt feature replay, which leverages the PA information belonging to old categories. Each well-trained \\( p \\) inherits the representation power for each category. We employ each \\( p \\) to generate features by following the Gaussian distribution \\( \\mathcal{N}(p^0,\\sigma^2), p^0 \\in P^0 \\). The number of generated features is determined based on data balancing, for example, the number of newly categorized samples in a batch. The generated features are concatenated into a batch, and the model and PAs are trained using the following loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.109, + 0.601, + 0.468, + 0.62 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {e x} ^ {1} (\\tilde {Z}) = \\mathcal {L} _ {p a} ^ {1} (\\tilde {Z}), \\quad \\tilde {Z} = \\left\\{\\tilde {z} \\sim \\mathcal {N} \\left(p ^ {0}, \\sigma^ {2}\\right) \\right\\} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.635, + 0.468, + 0.679 + ], + "angle": 0, + "content": "Also, we utilize the distillation of the extracted embedding vectors from the present \\( f^1 \\) and the previous model \\( f^0 \\). The distillation loss \\( \\mathcal{L}_{kd} \\) is described as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.694, + 0.468, + 0.733 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {k d} ^ {1} \\left(z _ {o}\\right) = - \\mathbb {E} _ {z _ {o} \\in Z _ {o l d} ^ {1}} \\| z _ {o} ^ {0} - z _ {o} \\| _ {2} \\tag {6} \\\\ = - \\mathbb {E} _ {x _ {o} \\in D _ {o l d} ^ {1}} \\| f ^ {0} (x _ {o}) - f ^ {1} (x _ {o}) \\| _ {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.748, + 0.469, + 0.794 + ], + "angle": 0, + "content": "where \\(z^0\\) represents the embedding vector for fixed previous feature network \\(f^0\\). \\(Z_{old}^{1}\\) denotes seen data from \\(Z^{1} = \\{Z_{old}^{1}\\cup Z_{new}^{1}\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.869 + ], + "angle": 0, + "content": "In conclusion, the loss consists of three different losses in the continuous category discovery step. One loss is for training the PAs and the model on \\(\\mathcal{D}^1\\), the others are to avoid forgetting by using generated features and knowledge distillation. \\(\\mathcal{L}^1\\) is described as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.885, + 0.468, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} ^ {1} = \\mathcal {L} _ {p a} ^ {1} (Z ^ {1}) + \\mathcal {L} _ {e x} ^ {1} (\\tilde {Z}) + \\mathcal {L} _ {k d} ^ {1} \\left(z _ {o}\\right) \\tag {7}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.705, + 0.107 + ], + "angle": 0, + "content": "4. Experimental Results" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.115, + 0.716, + 0.131 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.138, + 0.892, + 0.365 + ], + "angle": 0, + "content": "We utilized the widely used augmentation techniques, including random crop after padding and random horizontal flip. All the experiments were trained for 60 epochs using AdamW optimizer with weight decay set to 0.0001. The initial learning rate was set to 0.0001 for the model \\( f(\\cdot) \\), while for the PAs, it was set to 0.01. The learning rate was decayed by a factor of 0.5 every five epochs. We used the threshold \\( \\epsilon \\) only once for the initial split to divide the set into old and novel categories, and we set it to 0 for all the datasets and networks. For fine split, we used an MLP-based network architecture that consists of two dense layers with a batch normalization layer. The model was trained for three epochs using AdamW with a learning rate of 0.0001. The hyperparameters for PAs, \\( \\alpha \\) and \\( \\delta \\), were set to 32 and 0.1, respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.365, + 0.892, + 0.44 + ], + "angle": 0, + "content": "For fair comparisons of various methods, such as NCD, class-iNCD, and CCD, we follow the hyperparameters and the network architectures of the original implementations, referring to the papers for details. All the reported performances are average results over three runs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.45, + 0.684, + 0.464 + ], + "angle": 0, + "content": "4.2. Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.473, + 0.891, + 0.518 + ], + "angle": 0, + "content": "We evaluate the methods using metrics based on the cluster accuracy measurement, called Hungarian assignment algorithm [21]. The evaluation metric is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.53, + 0.89, + 0.571 + ], + "angle": 0, + "content": "\\[\n\\mathcal {M} ^ {t} = \\frac {1}{| \\mathcal {D} |} \\sum_ {i = 1} ^ {| \\mathcal {D} |} \\mathbb {I} \\left(y _ {i} = h ^ {*} \\left(y _ {i} ^ {*}\\right)\\right) \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.578, + 0.891, + 0.682 + ], + "angle": 0, + "content": "where \\(|\\mathcal{D}|\\) is the size of the validation dataset \\(\\mathcal{D}\\) and \\(h^*\\) is the optimal assignment. So, \\(\\mathcal{M}^t\\) measures the cluster accuracy at step \\(t\\) on the \\(\\mathcal{D}\\). In this manner, \\(\\mathcal{M}_{all}\\) and \\(\\mathcal{M}_o\\) indicate the cluster accuracy metrics of the whole and old categories using \\(\\mathcal{M}^t\\), respectively. Furthermore, we employ two more metrics that, \\(\\mathcal{M}_f\\) and \\(\\mathcal{M}_d\\), which are proposed on GM [42] and described as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.61, + 0.693, + 0.89, + 0.713 + ], + "angle": 0, + "content": "\\[\n\\mathcal {M} _ {f} = \\max _ {t} \\left\\{\\mathcal {M} _ {o} ^ {0} - \\mathcal {M} _ {o} ^ {t} \\right\\}, \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.629, + 0.733, + 0.89, + 0.768 + ], + "angle": 0, + "content": "\\[\n\\mathcal {M} _ {d} = \\frac {1}{| T |} \\sum_ {i = T} \\mathcal {M} _ {n} ^ {i}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathcal{M}_o^0\\) and \\(\\mathcal{M}_o^t\\) are the old class cluster accuracy at the initial step and category incremental \\(t\\) step, respectively. So \\(\\mathcal{M}_f\\) measures the maximum forgetting values for old categories in the entire step and should be sufficiently low; if not, the method is not valuable in practical applications. In Equation (10), \\(|T|\\) is the number of increased steps, and \\(\\mathcal{M}_d\\) evaluates the averaged performance of novel category discovery in unlabeled joint datasets in each step. It means" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16692" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.09, + 0.9, + 0.219 + ], + "angle": 0, + "content": "
MethodCUB-200MIT67Stanford DogsFGVC aircraft
\\( {\\mathcal{M}}_{all} \\)↑\\( {\\mathcal{M}}_{o} \\)↑\\( {\\mathcal{M}}_{f} \\)↓\\( {\\mathcal{M}}_{d} \\)↑\\( {\\mathcal{M}}_{all} \\)↑\\( {\\mathcal{M}}_{o} \\)↑\\( {\\mathcal{M}}_{f} \\)↓\\( {\\mathcal{M}}_{d} \\)↑\\( {\\mathcal{M}}_{all} \\)↑\\( {\\mathcal{M}}_{o} \\)↑\\( {\\mathcal{M}}_{f} \\)↓\\(\\mathcal{M}_{d}\\uparrow\\)\\( {\\mathcal{M}}_{all} \\)↑\\( {\\mathcal{M}}_{o} \\)↑\\( {\\mathcal{M}}_{f} \\)↓\\( {\\mathcal{M}}_{d} \\)↑
Supervised61.6945.8323.3216.6355.5640.9019.5218.3464.2647.5725.4317.0164.6248.1726.2418.12
DRNCD [43]9.8010.4758.5134.2426.9927.6749.0738.9116.3910.3465.8363.3618.7319.5057.0545.63
FRoST [33]18.1917.3412.1817.2023.2123.5515.9624.7422.6222.2314.2926.0632.6133.5315.1927.69
GM [42]6.436.5739.825.9216.5216.7742.2615.505.995.9850.365.9812.0011.6353.3513.46
Ours54.7558.8015.4740.9054.4564.2310.6418.5866.2576.156.7730.0437.2841.6014.6620.04
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.225, + 0.877, + 0.239 + ], + "angle": 0, + "content": "Table 3. Comparison results under continuous generalized categorized discovery scenario. The results present the mean over three runs." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.244, + 0.891, + 0.509 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.51, + 0.893, + 0.551 + ], + "angle": 0, + "content": "Figure 4. Qualitative evaluation results of the proposed method using the CUB-200 dataset on ResNet-18. The first five columns with blue boxes denote well-clustered examples. The last two columns represent failed prediction results, including example images with purple boxes denoting hard negatives and those with red boxes indicating incorrect categorization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.47, + 0.597 + ], + "angle": 0, + "content": "the higher method, the more appropriate method in real-world applications." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.606, + 0.449, + 0.621 + ], + "angle": 0, + "content": "4.3. Comparison with State-of-the-arts Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.47, + 0.809 + ], + "angle": 0, + "content": "We conducted a series of experiments to compare the cluster accuracy performance of our proposed method with state-of-the-art approaches, as presented in Table 1. In the experiments, we excluded the GCD task, including XCon, as it focuses on discovering novel categories blended with labeled and unlabeled datasets and evaluates unknown discovery performance on only train datasets, not validation datasets, in their papers. Therefore, we compared our proposed method with other approaches, including Dual rank NCD (DRNCD) [43], FRoST [33], and GM, which are the representative methods that record the state-of-the-art results of each task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We first evaluated the one-step incremental category setting and reported the comparison results in Table 3. The supervised method is the setting of a supervised continual learning manner, literally. We observed catastrophic forgetting in supervised learning. DRNCD is one of the NCD approaches and recorded the outstanding performances of" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.892, + 0.898 + ], + "angle": 0, + "content": "\\(\\mathcal{M}_d\\) on MIT67, Stanford Dogs, and FGVC aircraft. However, the method requires prior knowledge of the number of novel categories and does not identify specific classes, but only knows whether the samples are included in the novel category or not. Thus, the results are not regarded as outperforming. Instead, the method shows the highest results of \\(\\mathcal{M}_f\\), which means that the method focuses on learning novel categories without considering the prevention of forgetting previous categorical knowledge. In this regard, NCD is not sufficient to extend novel class incremental learning schemes. FRoST showed competitive results of discovering novel classes and decreased forgetting results \\(\\mathcal{M}_f\\) on all datasets compared to DRNCD. Nevertheless, considering the required knowledge, the other metrics results, \\(\\mathcal{M}_{all}\\) and \\(\\mathcal{M}_o\\) were not competitive. GM proposed the CCD setting, which is the most similar to CGCD, in the perspective of the unknown number of novel categories and discovering novel and old categories on new unlabeled datasets. However, the method requires a crucial parameter, which is the ratio of novel category samples on the new dataset. Without considering the ratio, GM recorded the lowest results of \\(\\mathcal{M}_{all}\\), \\(\\mathcal{M}_o\\), and \\(\\mathcal{M}_d\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16693" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.091, + 0.273, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.278, + 0.091, + 0.462, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.196, + 0.468, + 0.235 + ], + "angle": 0, + "content": "(a) Novel category discovery \\( M_{d} \\) (b) Catastrophic forgetting \\( M_{f} \\) Figure 5. Performances of novel category discovery and forgetting on two-step incremental novel categories experiment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.468, + 0.364 + ], + "angle": 0, + "content": "The proposed method showed outstanding performance on the various datasets without requiring any prior information about new incoming unlabeled datasets. Our method recorded the second-best \\(\\mathcal{M}_f\\) on the CUB-200 dataset and the best \\(\\mathcal{M}_f\\) on the other datasets, such as MIT67, Dogs, and FGVC aircraft, by the effects of PA-based exemplar. On \\(\\mathcal{M}_d\\), the method was also competitive and compared to the GM, which has the most similar setting to our method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.468, + 0.485 + ], + "angle": 0, + "content": "To evaluate the proposed method qualitatively, we clustered the evaluation dataset using the CUB-200 dataset. In Figure 4, our method well-discovered novel categories and clustered them correctly. Each row is clustered into the same category, and the classes are novel categories on the evaluation dataset. The left five columns are well-clustered, while the last two are not. The sixth-column images are still reasonable, but the last-columns are the worst cases." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.493, + 0.385, + 0.51 + ], + "angle": 0, + "content": "4.4. Two-step Novel Category Discovery" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.518, + 0.468, + 0.699 + ], + "angle": 0, + "content": "We present a two-step incremental category discovery experiment on the CUB-200 dataset using ResNet-18. The dataset configurations are more complicated as the datasets are joint sets in incremental steps. The initial step, the first incremental step, and the second incremental step have novel classes in each step, at a rate of \\( 8:1:1 \\), respectively. Each step has its dataset and is indicated as \\( \\mathcal{D}^0 \\), \\( \\mathcal{D}^1 \\), and \\( \\mathcal{D}^2 \\). The samples belonging to novel labeled classes in the initial step are assigned to \\( \\mathcal{D}^0 \\), \\( \\mathcal{D}^1 \\), and \\( \\mathcal{D}^2 \\) at a rate of \\( 8:1:1 \\). Similarly, the samples belonging to novel classes in the first incremental step are assigned to \\( \\mathcal{D}^1 \\), and \\( \\mathcal{D}^2 \\) at a rate of \\( 8:2 \\). Finally, the rest of the samples are assigned to \\( \\mathcal{D}^2 \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.7, + 0.468, + 0.835 + ], + "angle": 0, + "content": "Figure 5 describes the performance of the experiments. Since each incremental step is trained for 60 epochs, there are deep drops at the \\(60th\\) epoch when new PAs are added. In addition, the cluster accuracy of the old categories, which belong to the \\(\\mathcal{D}^0\\), decreases by about \\(20\\%\\). The reason is that the number of old categories in the second incremental step is increased compared to the first step. The exemplar cannot focus on only generating the features of \\(\\mathcal{D}^0\\). However, the performance of \\(\\mathcal{M}_d\\) increased steadily." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.229, + 0.863 + ], + "angle": 0, + "content": "4.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of separations: We conducted an ablation study to show the effectiveness of our proposed splitter," + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.091, + 0.892, + 0.24 + ], + "angle": 0, + "content": "
NetworkFine SplitMetric
Mall ↑Mo ↑Mf ↓Md ↑
ResNet-18without53.3257.6316.5636.47
with54.7558.8015.4740.90
ResNet-50without66.5371.079.1248.76
with68.0971.758.4453.79
ViT-B-16without70.2273.0210.7559.24
with72.5174.289.4965.60
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.242, + 0.892, + 0.299 + ], + "angle": 0, + "content": "Table 4. Ablation study for the proposed fine split on the CUB-200 using three different network architectures, including ResNet-18 and ResNet-50 pre-trained on ImageNet, and ViT-B-16 pre-trained on DINO-ImageNet. The results present the mean over three runs." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.304, + 0.892, + 0.4 + ], + "angle": 0, + "content": "
NetworkExemplarMetric
Mall ↑Mo ↑Mf ↓Md ↑
ResNet-18without38.2437.3136.8841.89
Data mean and std.40.2340.5633.6337.22
Proxy anchors54.7558.8015.4740.90
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.406, + 0.892, + 0.434 + ], + "angle": 0, + "content": "Table 5. Effectiveness of the proposed PA-based exemplar on the CUB-200 dataset using ResNet-18 pre-trained on ImageNet" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.444, + 0.892, + 0.566 + ], + "angle": 0, + "content": "which consists of a combination of two different methods: the cosine similarity score and a binary splitter using the noise label approach. The ablation experiments were designed such that one used only the cosine similarity score, and another used both methods. As shown in Table 4, the approach using both methods presents improvements in both old and novel discovery performances. The results reveal the effectiveness of noise labeling for data separation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.892, + 0.839 + ], + "angle": 0, + "content": "Effectiveness of Proxy anchor exemplar: To mitigate catastrophic forgetting, various approaches, such as replay [2], prototype [31, 33], and pseudo-latents [15], have been proposed. Most of these methods exploit the computed average of feature embedding vectors or input data-driven values. However, we propose a novel PA-based exemplar approach and evaluate its efficiency. As shown in Table 5, the method without the exemplar recorded the highest novel discovery performances but also showed the highest forgetting. Adopting a general exemplar approach using mean and standard deviation values from the former dataset, \\(\\mathcal{M}_f\\) slightly decreased, but \\(\\mathcal{M}_d\\) is the lowest. However, our proposed method with the PA-based exemplar recorded the best \\(\\mathcal{M}_f\\) and competitive \\(\\mathcal{M}_d\\). We analyze that the PAs have representatives of each cluster since PA inherits the relation between data to data and then representative figures of each class. Hence, our PA-based method leads to mitigating forgetting, and we confirm that it is a proper approach." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Robustness of class and sample blending ratio variants: In general, the capability to recognize novel categories largely depends on a powerful and well-trained initial model with the target datasets. The more classes and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16694" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.465, + 0.211 + ], + "angle": 0, + "content": "
RatioMetric
Yold: YnewMall ↑Mo ↑Mf ↓Md ↑
9:161.3463.2211.8344.73
8:254.7558.8015.4740.90
7:352.6658.4214.6739.50
6:448.7857.9015.1635.53
5:545.2862.4111.3028.55
" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.218, + 0.468, + 0.247 + ], + "angle": 0, + "content": "Table 6. Qualitative evaluation by changing the ratio of classes and samples on the CUB-200 using ResNet18 pre-trained on ImageNet" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.252, + 0.468, + 0.448 + ], + "angle": 0, + "content": "samples are included in the initial training dataset \\(\\mathcal{D}^0\\), the better the model learns representative features to fit the sets. To evaluate the robustness of the proposed model, we conducted experiments with variants of the number of samples and classes in \\(\\mathcal{D}^0\\). As described in Table 6, decreasing the number of classes and data in the labeled set decreased the discovery of novel classes and clustering accuracies as the number of unlabeled novel data increased. On the other hand, catastrophic forgetting could increase since the number of novel data increases. However, forgetting was maintained within a reasonable boundary, indicating the effectiveness of our PA-based exemplar. The results suggest that our method has the robustness of the variants." + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.459, + 0.212, + 0.473 + ], + "angle": 0, + "content": "5. Related work" + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.483, + 0.31, + 0.499 + ], + "angle": 0, + "content": "5.1. Novel Category Discovery" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.507, + 0.468, + 0.838 + ], + "angle": 0, + "content": "NCD techniques have been proposed to classify data with various constraints on unlabeled data. One category of the methods presented pre-training the model on the labeled set and fine-tuning it on the unlabeled set using unsupervised clustering losses [41, 13, 12, 23, 24]. Another category assumed the availability of both the labeled and unlabeled data, and trained networks jointly with a labeled novel class loss within the semi-supervised scheme [10, 44, 45, 14, 7, 43]. Han et al. [11] proposed transferring knowledge from labeled to unlabeled data using ranking statistics in the joint learning stage. Recently, GCD [36] and XCon [6] tackled the more realistic scenario of joint datasets and distinguished known and unknown classes using prior knowledge. However, these approaches did not consider the continual learning scheme. To address the limitation, FRoST [33] and NCDwF [15] froze feature extractors and added the second head for each novel class, as much as the given number of novel categories. However, the methods employed disjoint sets. GM [42] proposed to consider novel category discovery on the joint datasets, but still require prior knowledge, such as the proportion of novel samples." + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.848, + 0.235, + 0.863 + ], + "angle": 0, + "content": "5.2. Image Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Most of the image retrieval methods have utilized metric learning and can be categorized into two approaches." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.092, + 0.89, + 0.332 + ], + "angle": 0, + "content": "Pair-based methods exploited contrastive loss [3, 5, 9] and triplet loss [34, 38], that pull together data pairs in the same class and push apart those in different classes. Multiple data-based [35, 28] methods proposed considering the relations between multiple data. Entire data-based approaches [40, 39] presented considering all data in a batch, leveraging fine-grained semantic relations between them while requiring high computation costs and slow convergence. In contrast, proxy-based methods [26, 29, 1] employed fewer proxies than the training set, reducing training complexity. While these methods improved training convergence, they did not consider data-to-data relations, as each data was associated with its proxy. PA [18] inherited the strength of pair- and proxy-based methods, achieving fast and reliable convergence, robustness opposing noisy data, and leveraging rich data-to-data relations." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.349, + 0.625, + 0.363 + ], + "angle": 0, + "content": "5.3. Noise Label" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.375, + 0.89, + 0.555 + ], + "angle": 0, + "content": "Recently proposed methods for learning with noisy labels have highlighted the importance of discriminating between clean and noise-labeled data to improve performance. DivideMix [22] used GMM to distinguish between clean and noisy labeled data and treated the latter as unlabeled for semi-supervised learning. AugDesc [27] employed data augmentation to enhance the differentiation between clean and noisy labeled data, while INCV [4] introduced cross-validation to separate clean data from noisy training data. SplitNet [17] leveraged a compact network to perceive the difference between clean and noisy labels, improving model performance by more accurately differentiating noise." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.565, + 0.616, + 0.58 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.593, + 0.89, + 0.818 + ], + "angle": 0, + "content": "In this paper, we presented a novel continual learning scenario, considered NCD on the unlabeled joint datasets without any prior knowledge of the dataset. Our framework utilized PAs to split known and novel categories, resulting in well-clustered and well-pseudo-labeled categories that mitigate catastrophic forgetting. We further refined the splitting of the dataset by adopting a noise labeling scheme. Our proposed approach outperformed existing state-of-the-art methods regarding novel category discovery and forgetting. While DeepDPM [32] has recently shown outstanding performance on non-parametric clustering tasks, we believe that our proposed method can achieve even better performance by adopting better clustering manners. In future work, we plan to evaluate our method by adopting a better clustering manner." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.829, + 0.665, + 0.844 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.856, + 0.89, + 0.901 + ], + "angle": 0, + "content": "This work was funded by Samsung Electro-Mechanics and was partially supported by Carl-Zeiss Stiftung under the Sustainable Embedded AI project (P2021-02-009)." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.947, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16695" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] Nicolas Aziere and Sinisa Todorovic. Ensemble deep manifold similarity learning using hard proxies. 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In CVPR, 2021." + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "16697" + } + ] +] \ No newline at end of file diff --git a/2023/Proxy Anchor-based Unsupervised Learning for Continuous Generalized Category Discovery/82f1fc34-be8f-46cf-8cc9-6e1e6fe0df48_origin.pdf b/2023/Proxy Anchor-based Unsupervised Learning for Continuous Generalized Category Discovery/82f1fc34-be8f-46cf-8cc9-6e1e6fe0df48_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..cbd4bcda2a89fecb2b02e91547175b6244774ab2 --- /dev/null +++ b/2023/Proxy Anchor-based Unsupervised Learning for Continuous Generalized Category Discovery/82f1fc34-be8f-46cf-8cc9-6e1e6fe0df48_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:85ca686f9ef3db86618db6710be5d505f62caafe1ead19ec07561ded4059815b +size 791286 diff --git a/2023/Proxy Anchor-based Unsupervised Learning for Continuous Generalized Category Discovery/full.md b/2023/Proxy Anchor-based Unsupervised Learning for Continuous Generalized Category Discovery/full.md new file mode 100644 index 0000000000000000000000000000000000000000..37267eea2a779264a37dfb37ec2d20bee890976b --- /dev/null +++ b/2023/Proxy Anchor-based Unsupervised Learning for Continuous Generalized Category Discovery/full.md @@ -0,0 +1,325 @@ +# Proxy Anchor-based Unsupervised Learning for Continuous Generalized Category Discovery + +Hyungmin $\mathrm{Kim}^{1,2}$ Sungho $\mathrm{Suh}^{3,4}$ Daehwan $\mathrm{Kim}^{2}$ Daun Jeong $^{2}$ Hansang $\mathrm{Cho}^{2}$ Junmo $\mathrm{Kim}^{1}$ + +$^{1}$ Korea Advanced Institute of Science and Technology, Daejeon, South Korea + +$^{2}$ Samsung Electro-Mechanics, Suwon, South Korea + +$^{3}$ German Research Center for Artificial Intelligence (DFKI), Kaiserslautern, Germany + +$^{4}$ Department of Computer Science, RPTU Kaiserslautern-Landau, Kaiserslautern, Germany + +{hyungmin83, junmo.kim}@kaist.ac.kr, sungho.suh@dfki.de + +{daehwan85.kim, du33.jeong, hansang.cho}@samsung.com + +# Abstract + +Recent advances in deep learning have significantly improved the performance of various computer vision applications. However, discovering novel categories in an incremental learning scenario remains a challenging problem due to the lack of prior knowledge about the number and nature of new categories. Existing methods for novel category discovery are limited by their reliance on labeled datasets and prior knowledge about the number of novel categories and the proportion of novel samples in the batch. To address the limitations and more accurately reflect real-world scenarios, in this paper, we propose a novel unsupervised class incremental learning approach for discovering novel categories on unlabeled sets without prior knowledge. The proposed method fine-tunes the feature extractor and proxy anchors on labeled sets, then splits samples into old and novel categories and clusters on the unlabeled dataset. Furthermore, the proxy anchors-based exemplar generates representative category vectors to mitigate catastrophic forgetting. Experimental results demonstrate that our proposed approach outperforms the state-of-the-art methods on fine-grained datasets under real-world scenarios. + +# 1. Introduction + +Deep neural networks have achieved remarkable performance in various computer vision tasks. However, current systems are still subject to constraints that are manually supervised and do not consider continual incremental categories. For extending to real-world environments, there are still gaps to catch up by overcoming the constraints and improving their abilities in fundamental tasks. Specifically, humans still perform better than machines in object cognitive and grouping skills (e.g. recognizing new products + +or clothing on shopping and categorizing undefined moving objects while driving). + +Various methods have been proposed to address the limitations of the tasks by considering real-world circumstances, as presented in Figure 1 and Table 1. In detail, Novel Category Discovery (NCD) [10, 11, 43] and Generalized Category Discovery (GCD) [36, 6] aim to recognize not only pre-trained categories but also discover novel categories using a given dataset. NCD considers a disjoint dataset where labeled and unlabeled novel samples have no intersection with each other. In contrast, GCD exploits the joint set with intersected categories, making GCD a more complicated task than NCD. However, these approaches do not consider the class incremental scheme. Class incremental NCD (class-iNCD) [33, 15] has been proposed to adopt the incremental categories on NCD task, but they still focus on improving novel category discovery performance using the disjoint set, which is an unrealistic constraint. To address this issue, Grow and Merge (GM) [42] proposes a scenario that exploits the joint unlabeled dataset in the incremental novel category discovery task, which is called Continuous Category Discovery Mixed Incremental (CCDMI). However, most existing methods require prior knowledge, such as the number of unlabeled classes for NCD and class-iNCD, or the proportion of the novel samples in the batch for CCD-MI. Such prior knowledge requirements are not enough to mimic the real-world, as we lack information about the unlabeled sets. + +To overcome these constraints, we propose a novel scenario that better represents real-world circumstances by removing constraints on the available data. We assume that the given datasets are unlabeled joint sets without providing prior knowledge about the data. Employing the scenario, we propose a novel unsupervised class incremental + +![](images/e74bfc7940bf6fc68a927150b0cb0a20940110fbd699c2978315a89fef3671bc.jpg) +(a) NCD + +![](images/4b3f796cb879f5b29d9c07dc2df5d27278a8de5a50b9c8127fe24c13a0f14fa8.jpg) +(b) GCD +Figure 1. Comparison of existing and proposed scenarios for novel category discovery. The solid and dash-lined circles indicate labeled and unlabeled samples, respectively, with sample color depicting the class label. The circle with $i$ denotes the number of novel classes (pink) and the proportion of novel class samples in a batch (dark blue). + +![](images/0992e772d538ba724ff6181212baa5e4243ba48792eb4ee1d7917bad9a08202e.jpg) +(c) class-iNCD + +![](images/212d61951bd00c70cafbd4bb767be28804a9d52702ceb8dd9a0ee688d0740f66.jpg) +(d) CCD-MI + +![](images/13633ca7a3170b07c7e124d3089f2cdb970018dc2ff148a82f735fe01e92639d.jpg) +(e) CGCD + +
TaskMethodConstraints
Continual learningAssumption: yl∩yu=∅Number of novel classesProportion of new class data
NCDRankStat [10, 11], DRNCD [43]Not consideredRequiredRequiredNot required
GCDGCD [36], XCon [6]Not consideredNot requiredNot requiredNot required
class-iNCDFroST [33], NCDwF [15]ConsideredRequiredRequiredNot required
CCD-MIGM [42]ConsideredNot requiredNot requiredRequired
CGCDOursConsideredNot requiredNot requiredNot required
+ +Table 1. Comparison of existing and proposed novel category discovery settings and the constraints + +learning approach to simultaneously address the problems of discovering incremental novel categories and alleviating catastrophic forgetting. In addition, we focus on recognizing fine-grained objects, which is a more realistic use case for various applications in real-world applications. + +The proposed method exploits a deep metric learning scheme, proxy anchor (PA) [18] that presents fast and reliable convergence and robustness against noise samples, and also considers the relations between samples. Then, we divide the unlabeled data into old and novel categories using PAs, which inherit discriminative features of old categories. The cosine similarity is measured between the PAs and the samples, and then initially separated datasets are acquired on a criterion. For further splitting, we adopt a noisy label learning scheme, and then assign the predictions of the previous model and the clustering results by a nonparametric approach to old and novel categorized samples, respectively. To mitigate the forgetting, we use a PA-based exemplar, which inherits more representative features. In the experimental results, we demonstrate that the proposed method outperforms the existing state-of-the-art in discovering novel categories and forgetting alleviation on various fine-grained datasets. Specifically, the proposed method does not require any prior knowledge and considers continual learning on unlabeled joint datasets, making it a more realistic and practical solution for real-world scenarios. + +The main contributions of the proposed method can be summarized as follows. + +- We introduce a novel scenario, called Continuous Generalized novel Category Discovery (CGCD), which + +is well-suited to tackle the challenges of discovering novel categories in real-world scenarios by removing the constraint that unlabeled data belong to only novel categories. + +- We propose a novel unsupervised learning approach for incremental novel category discovery that does not require prior knowledge of the number of novel categories or the proportion of new class data. +- We present a noisy label learning approach and deep metric learning to split unlabeled data into old and novel categories, and also show mitigation of catastrophic forgetting using a deep metric-based exemplar. +- The proposed method outperforms the state-of-the-art methods in novel category discovery and forgetting mitigation on various fine-grained datasets. + +# 2. Problem Definition + +# 2.1. Continuous Generalized Category Discovery + +As presented in Figure 1 and Table 1, various environmental schemes have been proposed to mimic real-world circumstances. Notable approaches include NCD [10, 11, 43], GCD [36], class-iNCD [33, 15], and CCD [42]. NCD considers disjoint datasets between labeled and unlabeled sets (i.e. $\mathcal{Y}_l \cap \mathcal{Y}_u = \emptyset$ ) and requires prior knowledge of the number of unlabeled categories $|\mathcal{Y}_u|$ . In contrast, GCD exploits the joint set (i.e. $\mathcal{Y}_l \cap \mathcal{Y}_u \neq \emptyset$ ). Although GCD is a more challenging task than NCD, it still does not consider continuous incremental category discovery. + +![](images/7d08a14bd02a454c1f8d6d9ffef4cc92107dd0ad0e21c2e290e4ae966d7fc290.jpg) +Figure 2. Overview of the proposed CGCD framework. The framework comprises three steps. The first step is that the network model is fine-tuned on the target dataset using the labeled dataset. In the second step, the discovery of novel categories is performed on the joint and unlabeled dataset, which is split into unseen and seen sets using the initial and fine split methods. Pseudo-labels are assigned to the unlabeled dataset using the previous model's predictions (seen case) and non-parametric clustering results (unseen case). In the last step, a new model is trained on the fine split dataset, which incorporates new proxy anchors based on clustering results. + +Class-iNCD is an extension of NCD to the continual learning scheme. However, the method trains on the disjoint dataset under class incremental stages and has a requirement for $|\mathcal{V}_u|$ . CCD also trains on discovering novel classes under the continual learning scheme with the joint dataset. Although CCD does not require $|\mathcal{V}_u|$ , it still needs the proportion of the novel class data in a batch as prior knowledge, which is used to filter out the data. + +To address these limitations, we propose a more challenging problem, named Continuous Generalized novel Category Discovery (CGCD), that is closer to real-world circumstances. In CGCD, we exploit the unlabeled joint dataset in incremental steps without providing any prior knowledge and aim to discover novel classes. This formulation is more representative of real-world scenarios, where we are not aware of the number of unlabeled categories and the characteristics of the dataset. + +# 2.2. Setting of Continuous Generalized Category Discovery + +Fine-grained datasets consist of similar objects, such as canines [16], indoor scenes [30], vehicles [25], and birds [37], in constrained circumstances. Compared to coarse datasets such as CIFAR [19] and ImageNet [20], fine-grained datasets are closer to real-world scenarios. Therefore, we focus on training and discovering novel classes with fine-grained datasets to mimic real-world circumstances better. + +CGCD employs the joint unlabeled dataset in incremental steps, and Table 2 describes the dataset partitioning used in the one-time incremental category discovery. First, the + +
DatasetAll classesInitial stepCategory incremental step
Old classOld classNew class
CUB-200200160 (0.8)160 (0.2)40 (1.0)
MIT676753 (0.8)53 (0.2)14 (1.0)
Stanford Dogs12096 (0.8)96 (0.2)24 (1.0)
FGVC Aircraft10080 (0.8)80 (0.2)20 (1.0)
+ +Table 2. Dataset configurations for one-time incremental category scenarios. The number of classes and the proportion of data from each class in parentheses are presented. Note that the ratios in parentheses are hidden information that is not revealed to the learning methods. + +set of classes is partitioned into old classes and new classes at a certain rate, for example, 8: 2. The initial step utilizes labeled dataset $\mathcal{D}^0$ consisting of old classes only. Then the following incremental step utilizes unlabeled dataset $\mathcal{D}^1$ consisting of both old classes and new classes, which reflect more realistic and challenging real-world scenarios. The key element of the proposed method is to decide whether the unlabeled data point belongs to the old classes (seen) or new classes (unseen). The samples belonging to the old classes are assigned to labeled dataset $\mathcal{D}^0$ and unlabeled dataset $\mathcal{D}^1$ , and the rest of all the new class samples are assigned to $\mathcal{D}^1$ . Here the choice of 8: 2 is an arbitrary example, and it is important to note that this ratio is just for data generation purposes and is not revealed to the learning methods. + +# 3. Method + +As described in Figure 2, our proposed method consists of three steps: the initial step, the novel category discovery and the final step. + +ery step, and the category incremental step. In the initial step, we fine-tune a pre-trained model on the labeled dataset $\mathcal{D}^0 = \{(x,y)\in \mathcal{X}_l\times \mathcal{Y}_l\}$ , and obtain the embedding vector $z$ using the model $f(\cdot)$ , denoted as $z = f^{0}(x)$ . We then use these vectors to train PAs [18] of each category, represented as $p = g^0 (z)$ , and also construct well-representative exemplars. In the following novel category discovery step, the given unlabeled joint datasets are denoted as $\mathcal{D}^1 = \{x|x\in \mathcal{X}_u\}$ . We first separate them into old and novel categories through the initial and the fine splits. Since the separated sets are unlabeled, we pseudo-label for old and novel classes using the previous model prediction and non-parametric clustering results, respectively. + +In the category incremental step, the acquired set is trained to improve the performance of discovering novel categories. To avoid catastrophic forgetting, we exploit generated features by the exemplar and feature distillation between earlier and new models. The proposed model does not require any prior knowledge, such as $|\mathcal{Y}_u|$ and the ratio of novel class samples in a batch. We evaluate the performance of the proposed method using the validation dataset, which includes all categories. + +# 3.1. Initial Step: Fine Tune + +Existing NCD methods do not account for noisy categories, such as those categorized from old to novel or from novel to old, which can impair novel discovery performance and accumulate errors in the continuous procedure. To address these limitations, in this work, we propose a novel approach that leverages the benefits of PA to complement and improve the existing approaches. PA is a metric learning method that combines proxy- and pair-based methods to achieve rapid and reliable convergence, and robustness against noisy samples, and considers relations between data to extract meaningful semantic information. + +Following the method, the embedding vector $z$ from the initial model $f^0$ is trained to map to each proxy anchor $p = g^0 (z)$ . Let the set of all proxy anchors as $P^0$ in the labeled data $\mathcal{D}^0$ . In this manner, the number of proxy anchors of $\mathcal{D}^0$ is the number of classes of the labeled set (i.e. $|P^0| = |\mathcal{Y}_l|$ ) in the initial step. We train the model and proxy anchors using the following loss function defined in [18]: + +$$ +\begin{array}{l} \mathcal {L} _ {p a} ^ {0} \left(Z ^ {0}\right) = \frac {1}{| P ^ {0 +} |} \sum_ {p \in P ^ {0 +}} \log \left(1 + \sum_ {z \in Z _ {p} ^ {0 +}} e ^ {- \alpha (s (z, p) - \delta)}\right) \tag {1} \\ + \frac {1}{| P ^ {0} |} \sum_ {p \in P ^ {0}} \log \left(1 + \sum_ {z \in Z _ {p} ^ {0 -}} e ^ {\alpha (s (z, p) + \delta)}\right) \\ \end{array} +$$ + +where $\delta > 0$ is a margin and $\alpha > 0$ is a scaling factor. The function $s(\cdot, \cdot)$ indicates the cosine similarity score. $P^{0+}$ represents same class PAs(e.gpositive) in the batch. Each proxy $p$ divides the set of embedding vector $Z^0$ as $Z_p^{0+}$ and + +![](images/0547a841a326d4a2d01d2bc871f87059a9fc50c37947dd43ac2b98f991b2770b.jpg) +(a) Initial Split + +![](images/0bc54aeb7531789ecc22dfe3ec46c62fbcf37e5d2e44e749fc552aff483090b6.jpg) +(b) Fine Split +Figure 3. Separation results on joint unlabeled datasets + +$Z_{p}^{0^{-}} = Z^{0} - Z_{p}^{0^{+}}$ . $Z_{p}^{0^{+}}$ denotes the same class embedding points with the proxy anchor $p$ . The first term aims to pull $p$ and its dissimilar but hard positive data together, while the last term is to push $p$ and its similar but hard negatives apart. + +# 3.2. Discovering Novel Categories Step + +Separation: In this procedure, we aim to split the given joint dataset $\mathcal{D}^1$ into the novel and old categories without any prior knowledge. We conduct this task in two stages: initial split and fine split. In the initial split, we compute the cosine similarity between $p$ and each embedding vector $z_i \in Z^1$ , where $z_i = f^0(x_i)$ and $x_i \in D^1$ . Because the set of proxy anchors $P^0$ represents the old categories, we classify a sample to the old class if the maximum similarity score of $z_i$ is larger than a threshold $\epsilon$ . We set $\epsilon = 0$ since it is the median of the score ranges. The initial split is defined as: + +$$ +\tilde {y} _ {i} = \left\{ \begin{array}{l l} 0, & \text {i f} \max _ {p \in P ^ {0}} (s \left(z _ {i}, p\right)) \geq \epsilon = 0 \\ 1, & \text {o t h e r w i s e} \end{array} \right. \tag {2} +$$ + +To acquire a cleaner novel and old dataset, we propose a noisy labeling scheme, fine split, which involves an iterative training of a simple multilayer perceptron (MLP) based classifier $m(\cdot)$ on the binarized dataset. The initial split results in noisy and inaccurate separation, as shown in Figure 3 (a). Among them, only the data on both ends of the spectrum are assumed the clean and utilized to train the classifier. The loss of split network $m(\cdot)$ is defined as follows: + +$$ +\mathcal {L} _ {s p} = - \mathbb {E} _ {z _ {c} \in Z _ {c} ^ {1}} \left[ \tilde {y} _ {c} \log \left(m \left(z _ {c}\right)\right) + \left(1 - \tilde {y} _ {c}\right) \log \left(1 - m \left(z _ {c}\right)\right) \right] \tag {3} +$$ + +where $z_{c}$ denotes clean embedding vectors, and $Z_{c}^{1}$ represents the set of clean vectors. $\tilde{y}_{c}$ indicates the pseudo label of the clean data. After the warm-up training, the classifier is trained with re-assigned pseudo labels and the more cleaned data, which is divided with the Gaussian mixture model (GMM). Consequently, the Figure 3 (b) shows the cleaner separated results. + +Pseudo-labeling: After the separation, both the old $\mathcal{D}_{old}^{1}$ and the novel categories $\mathcal{D}_{new}^{1}$ are still unlabeled. Thus, we use pseudo-labels to assign labels to each sample. For $\mathcal{D}_{old}^{1}$ , we use the predictions of the previous model and proxy anchors to assign pseudo-labels. In contrast, we use a + +non-parametric clustering approach named Affinity propagation [8] to assign pseudo-labels to $\mathcal{D}_{new}^{1}$ . In this manner, our proposed approach does not require any prior knowledge. Finally, from the clustering results, we obtain an estimate of the number of novel categories, denoted as $|\hat{\mathcal{Y}}_n|$ . + +# 3.3. Category Incremental Step + +Training modified model and PAs: To improve the performance of discovering novel categories, we modify the model since the previous model has PAs only for $|\mathcal{Y}_l|$ classes and cannot categorize novel classes. We add new $p$ for $|\hat{\mathcal{Y}}_n|$ classes, increasing the total number of PAs like $|P^1| = |\mathcal{Y}_l| + |\hat{\mathcal{Y}}_n|$ . The loss function to train the modified model $f^1$ and PA $p = g^1(z)$ is reformulated as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {p a} ^ {1} (Z ^ {1}) = \frac {1}{| P ^ {1 +} |} \sum_ {p \in P ^ {1 +}} \log \left(1 + \sum_ {z \in Z _ {p} ^ {1 +}} e ^ {- \alpha (s (z, p) - \delta)}\right) \tag {4} \\ + \frac {1}{| P ^ {1} |} \sum_ {p \in P ^ {1}} \log \left(1 + \sum_ {z \in Z _ {p} ^ {1 -}} e ^ {\alpha (s (z, p) + \delta)}\right) \\ \end{array} +$$ + +Avoiding forgetting: In the continual learning scheme, it is essential to alleviate catastrophic forgetting. We adopt feature replay, which leverages the PA information belonging to old categories. Each well-trained $p$ inherits the representation power for each category. We employ each $p$ to generate features by following the Gaussian distribution $\mathcal{N}(p^0,\sigma^2), p^0 \in P^0$ . The number of generated features is determined based on data balancing, for example, the number of newly categorized samples in a batch. The generated features are concatenated into a batch, and the model and PAs are trained using the following loss function: + +$$ +\mathcal {L} _ {e x} ^ {1} (\tilde {Z}) = \mathcal {L} _ {p a} ^ {1} (\tilde {Z}), \quad \tilde {Z} = \left\{\tilde {z} \sim \mathcal {N} \left(p ^ {0}, \sigma^ {2}\right) \right\} \tag {5} +$$ + +Also, we utilize the distillation of the extracted embedding vectors from the present $f^1$ and the previous model $f^0$ . The distillation loss $\mathcal{L}_{kd}$ is described as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {k d} ^ {1} \left(z _ {o}\right) = - \mathbb {E} _ {z _ {o} \in Z _ {o l d} ^ {1}} \| z _ {o} ^ {0} - z _ {o} \| _ {2} \tag {6} \\ = - \mathbb {E} _ {x _ {o} \in D _ {o l d} ^ {1}} \| f ^ {0} (x _ {o}) - f ^ {1} (x _ {o}) \| _ {2} \\ \end{array} +$$ + +where $z^0$ represents the embedding vector for fixed previous feature network $f^0$ . $Z_{old}^{1}$ denotes seen data from $Z^{1} = \{Z_{old}^{1}\cup Z_{new}^{1}\}$ . + +In conclusion, the loss consists of three different losses in the continuous category discovery step. One loss is for training the PAs and the model on $\mathcal{D}^1$ , the others are to avoid forgetting by using generated features and knowledge distillation. $\mathcal{L}^1$ is described as follows: + +$$ +\mathcal {L} ^ {1} = \mathcal {L} _ {p a} ^ {1} (Z ^ {1}) + \mathcal {L} _ {e x} ^ {1} (\tilde {Z}) + \mathcal {L} _ {k d} ^ {1} \left(z _ {o}\right) \tag {7} +$$ + +# 4. Experimental Results + +# 4.1. Implementation Details + +We utilized the widely used augmentation techniques, including random crop after padding and random horizontal flip. All the experiments were trained for 60 epochs using AdamW optimizer with weight decay set to 0.0001. The initial learning rate was set to 0.0001 for the model $f(\cdot)$ , while for the PAs, it was set to 0.01. The learning rate was decayed by a factor of 0.5 every five epochs. We used the threshold $\epsilon$ only once for the initial split to divide the set into old and novel categories, and we set it to 0 for all the datasets and networks. For fine split, we used an MLP-based network architecture that consists of two dense layers with a batch normalization layer. The model was trained for three epochs using AdamW with a learning rate of 0.0001. The hyperparameters for PAs, $\alpha$ and $\delta$ , were set to 32 and 0.1, respectively. + +For fair comparisons of various methods, such as NCD, class-iNCD, and CCD, we follow the hyperparameters and the network architectures of the original implementations, referring to the papers for details. All the reported performances are average results over three runs. + +# 4.2. Evaluation Metrics + +We evaluate the methods using metrics based on the cluster accuracy measurement, called Hungarian assignment algorithm [21]. The evaluation metric is defined as follows: + +$$ +\mathcal {M} ^ {t} = \frac {1}{| \mathcal {D} |} \sum_ {i = 1} ^ {| \mathcal {D} |} \mathbb {I} \left(y _ {i} = h ^ {*} \left(y _ {i} ^ {*}\right)\right) \tag {8} +$$ + +where $|\mathcal{D}|$ is the size of the validation dataset $\mathcal{D}$ and $h^*$ is the optimal assignment. So, $\mathcal{M}^t$ measures the cluster accuracy at step $t$ on the $\mathcal{D}$ . In this manner, $\mathcal{M}_{all}$ and $\mathcal{M}_o$ indicate the cluster accuracy metrics of the whole and old categories using $\mathcal{M}^t$ , respectively. Furthermore, we employ two more metrics that, $\mathcal{M}_f$ and $\mathcal{M}_d$ , which are proposed on GM [42] and described as follows: + +$$ +\mathcal {M} _ {f} = \max _ {t} \left\{\mathcal {M} _ {o} ^ {0} - \mathcal {M} _ {o} ^ {t} \right\}, \tag {9} +$$ + +$$ +\mathcal {M} _ {d} = \frac {1}{| T |} \sum_ {i = T} \mathcal {M} _ {n} ^ {i}. \tag {10} +$$ + +where $\mathcal{M}_o^0$ and $\mathcal{M}_o^t$ are the old class cluster accuracy at the initial step and category incremental $t$ step, respectively. So $\mathcal{M}_f$ measures the maximum forgetting values for old categories in the entire step and should be sufficiently low; if not, the method is not valuable in practical applications. In Equation (10), $|T|$ is the number of increased steps, and $\mathcal{M}_d$ evaluates the averaged performance of novel category discovery in unlabeled joint datasets in each step. It means + +
MethodCUB-200MIT67Stanford DogsFGVC aircraft
\( {\mathcal{M}}_{all} \)↑\( {\mathcal{M}}_{o} \)↑\( {\mathcal{M}}_{f} \)↓\( {\mathcal{M}}_{d} \)↑\( {\mathcal{M}}_{all} \)↑\( {\mathcal{M}}_{o} \)↑\( {\mathcal{M}}_{f} \)↓\( {\mathcal{M}}_{d} \)↑\( {\mathcal{M}}_{all} \)↑\( {\mathcal{M}}_{o} \)↑\( {\mathcal{M}}_{f} \)↓\(\mathcal{M}_{d}\uparrow\)\( {\mathcal{M}}_{all} \)↑\( {\mathcal{M}}_{o} \)↑\( {\mathcal{M}}_{f} \)↓\( {\mathcal{M}}_{d} \)↑
Supervised61.6945.8323.3216.6355.5640.9019.5218.3464.2647.5725.4317.0164.6248.1726.2418.12
DRNCD [43]9.8010.4758.5134.2426.9927.6749.0738.9116.3910.3465.8363.3618.7319.5057.0545.63
FRoST [33]18.1917.3412.1817.2023.2123.5515.9624.7422.6222.2314.2926.0632.6133.5315.1927.69
GM [42]6.436.5739.825.9216.5216.7742.2615.505.995.9850.365.9812.0011.6353.3513.46
Ours54.7558.8015.4740.9054.4564.2310.6418.5866.2576.156.7730.0437.2841.6014.6620.04
+ +Table 3. Comparison results under continuous generalized categorized discovery scenario. The results present the mean over three runs. + +![](images/f8d1bd7dfc0d4d59e06cb26ce5c99dbc300c2781c479a50dce5f04f5c69be2c3.jpg) +Figure 4. Qualitative evaluation results of the proposed method using the CUB-200 dataset on ResNet-18. The first five columns with blue boxes denote well-clustered examples. The last two columns represent failed prediction results, including example images with purple boxes denoting hard negatives and those with red boxes indicating incorrect categorization. + +the higher method, the more appropriate method in real-world applications. + +# 4.3. Comparison with State-of-the-arts Methods + +We conducted a series of experiments to compare the cluster accuracy performance of our proposed method with state-of-the-art approaches, as presented in Table 1. In the experiments, we excluded the GCD task, including XCon, as it focuses on discovering novel categories blended with labeled and unlabeled datasets and evaluates unknown discovery performance on only train datasets, not validation datasets, in their papers. Therefore, we compared our proposed method with other approaches, including Dual rank NCD (DRNCD) [43], FRoST [33], and GM, which are the representative methods that record the state-of-the-art results of each task. + +We first evaluated the one-step incremental category setting and reported the comparison results in Table 3. The supervised method is the setting of a supervised continual learning manner, literally. We observed catastrophic forgetting in supervised learning. DRNCD is one of the NCD approaches and recorded the outstanding performances of + +$\mathcal{M}_d$ on MIT67, Stanford Dogs, and FGVC aircraft. However, the method requires prior knowledge of the number of novel categories and does not identify specific classes, but only knows whether the samples are included in the novel category or not. Thus, the results are not regarded as outperforming. Instead, the method shows the highest results of $\mathcal{M}_f$ , which means that the method focuses on learning novel categories without considering the prevention of forgetting previous categorical knowledge. In this regard, NCD is not sufficient to extend novel class incremental learning schemes. FRoST showed competitive results of discovering novel classes and decreased forgetting results $\mathcal{M}_f$ on all datasets compared to DRNCD. Nevertheless, considering the required knowledge, the other metrics results, $\mathcal{M}_{all}$ and $\mathcal{M}_o$ were not competitive. GM proposed the CCD setting, which is the most similar to CGCD, in the perspective of the unknown number of novel categories and discovering novel and old categories on new unlabeled datasets. However, the method requires a crucial parameter, which is the ratio of novel category samples on the new dataset. Without considering the ratio, GM recorded the lowest results of $\mathcal{M}_{all}$ , $\mathcal{M}_o$ , and $\mathcal{M}_d$ . + +![](images/d57f0f7fd163c035ad8deaed4eb858b99ba4becdf56a7bfd5ecefb822c8e00f5.jpg) +(a) Novel category discovery $M_{d}$ (b) Catastrophic forgetting $M_{f}$ Figure 5. Performances of novel category discovery and forgetting on two-step incremental novel categories experiment + +![](images/d101bb3a145ac9a57fc21c05c7e766c19ab5748af5a0b47878d7bf0ed081d381.jpg) + +The proposed method showed outstanding performance on the various datasets without requiring any prior information about new incoming unlabeled datasets. Our method recorded the second-best $\mathcal{M}_f$ on the CUB-200 dataset and the best $\mathcal{M}_f$ on the other datasets, such as MIT67, Dogs, and FGVC aircraft, by the effects of PA-based exemplar. On $\mathcal{M}_d$ , the method was also competitive and compared to the GM, which has the most similar setting to our method. + +To evaluate the proposed method qualitatively, we clustered the evaluation dataset using the CUB-200 dataset. In Figure 4, our method well-discovered novel categories and clustered them correctly. Each row is clustered into the same category, and the classes are novel categories on the evaluation dataset. The left five columns are well-clustered, while the last two are not. The sixth-column images are still reasonable, but the last-columns are the worst cases. + +# 4.4. Two-step Novel Category Discovery + +We present a two-step incremental category discovery experiment on the CUB-200 dataset using ResNet-18. The dataset configurations are more complicated as the datasets are joint sets in incremental steps. The initial step, the first incremental step, and the second incremental step have novel classes in each step, at a rate of $8:1:1$ , respectively. Each step has its dataset and is indicated as $\mathcal{D}^0$ , $\mathcal{D}^1$ , and $\mathcal{D}^2$ . The samples belonging to novel labeled classes in the initial step are assigned to $\mathcal{D}^0$ , $\mathcal{D}^1$ , and $\mathcal{D}^2$ at a rate of $8:1:1$ . Similarly, the samples belonging to novel classes in the first incremental step are assigned to $\mathcal{D}^1$ , and $\mathcal{D}^2$ at a rate of $8:2$ . Finally, the rest of the samples are assigned to $\mathcal{D}^2$ . + +Figure 5 describes the performance of the experiments. Since each incremental step is trained for 60 epochs, there are deep drops at the $60th$ epoch when new PAs are added. In addition, the cluster accuracy of the old categories, which belong to the $\mathcal{D}^0$ , decreases by about $20\%$ . The reason is that the number of old categories in the second incremental step is increased compared to the first step. The exemplar cannot focus on only generating the features of $\mathcal{D}^0$ . However, the performance of $\mathcal{M}_d$ increased steadily. + +# 4.5. Ablation Study + +Effectiveness of separations: We conducted an ablation study to show the effectiveness of our proposed splitter, + +
NetworkFine SplitMetric
Mall ↑Mo ↑Mf ↓Md ↑
ResNet-18without53.3257.6316.5636.47
with54.7558.8015.4740.90
ResNet-50without66.5371.079.1248.76
with68.0971.758.4453.79
ViT-B-16without70.2273.0210.7559.24
with72.5174.289.4965.60
+ +Table 4. Ablation study for the proposed fine split on the CUB-200 using three different network architectures, including ResNet-18 and ResNet-50 pre-trained on ImageNet, and ViT-B-16 pre-trained on DINO-ImageNet. The results present the mean over three runs. + +
NetworkExemplarMetric
Mall ↑Mo ↑Mf ↓Md ↑
ResNet-18without38.2437.3136.8841.89
Data mean and std.40.2340.5633.6337.22
Proxy anchors54.7558.8015.4740.90
+ +Table 5. Effectiveness of the proposed PA-based exemplar on the CUB-200 dataset using ResNet-18 pre-trained on ImageNet + +which consists of a combination of two different methods: the cosine similarity score and a binary splitter using the noise label approach. The ablation experiments were designed such that one used only the cosine similarity score, and another used both methods. As shown in Table 4, the approach using both methods presents improvements in both old and novel discovery performances. The results reveal the effectiveness of noise labeling for data separation. + +Effectiveness of Proxy anchor exemplar: To mitigate catastrophic forgetting, various approaches, such as replay [2], prototype [31, 33], and pseudo-latents [15], have been proposed. Most of these methods exploit the computed average of feature embedding vectors or input data-driven values. However, we propose a novel PA-based exemplar approach and evaluate its efficiency. As shown in Table 5, the method without the exemplar recorded the highest novel discovery performances but also showed the highest forgetting. Adopting a general exemplar approach using mean and standard deviation values from the former dataset, $\mathcal{M}_f$ slightly decreased, but $\mathcal{M}_d$ is the lowest. However, our proposed method with the PA-based exemplar recorded the best $\mathcal{M}_f$ and competitive $\mathcal{M}_d$ . We analyze that the PAs have representatives of each cluster since PA inherits the relation between data to data and then representative figures of each class. Hence, our PA-based method leads to mitigating forgetting, and we confirm that it is a proper approach. + +Robustness of class and sample blending ratio variants: In general, the capability to recognize novel categories largely depends on a powerful and well-trained initial model with the target datasets. The more classes and + +
RatioMetric
Yold: YnewMall ↑Mo ↑Mf ↓Md ↑
9:161.3463.2211.8344.73
8:254.7558.8015.4740.90
7:352.6658.4214.6739.50
6:448.7857.9015.1635.53
5:545.2862.4111.3028.55
+ +Table 6. Qualitative evaluation by changing the ratio of classes and samples on the CUB-200 using ResNet18 pre-trained on ImageNet + +samples are included in the initial training dataset $\mathcal{D}^0$ , the better the model learns representative features to fit the sets. To evaluate the robustness of the proposed model, we conducted experiments with variants of the number of samples and classes in $\mathcal{D}^0$ . As described in Table 6, decreasing the number of classes and data in the labeled set decreased the discovery of novel classes and clustering accuracies as the number of unlabeled novel data increased. On the other hand, catastrophic forgetting could increase since the number of novel data increases. However, forgetting was maintained within a reasonable boundary, indicating the effectiveness of our PA-based exemplar. The results suggest that our method has the robustness of the variants. + +# 5. Related work + +# 5.1. Novel Category Discovery + +NCD techniques have been proposed to classify data with various constraints on unlabeled data. One category of the methods presented pre-training the model on the labeled set and fine-tuning it on the unlabeled set using unsupervised clustering losses [41, 13, 12, 23, 24]. Another category assumed the availability of both the labeled and unlabeled data, and trained networks jointly with a labeled novel class loss within the semi-supervised scheme [10, 44, 45, 14, 7, 43]. Han et al. [11] proposed transferring knowledge from labeled to unlabeled data using ranking statistics in the joint learning stage. Recently, GCD [36] and XCon [6] tackled the more realistic scenario of joint datasets and distinguished known and unknown classes using prior knowledge. However, these approaches did not consider the continual learning scheme. To address the limitation, FRoST [33] and NCDwF [15] froze feature extractors and added the second head for each novel class, as much as the given number of novel categories. However, the methods employed disjoint sets. GM [42] proposed to consider novel category discovery on the joint datasets, but still require prior knowledge, such as the proportion of novel samples. + +# 5.2. Image Retrieval + +Most of the image retrieval methods have utilized metric learning and can be categorized into two approaches. + +Pair-based methods exploited contrastive loss [3, 5, 9] and triplet loss [34, 38], that pull together data pairs in the same class and push apart those in different classes. Multiple data-based [35, 28] methods proposed considering the relations between multiple data. Entire data-based approaches [40, 39] presented considering all data in a batch, leveraging fine-grained semantic relations between them while requiring high computation costs and slow convergence. In contrast, proxy-based methods [26, 29, 1] employed fewer proxies than the training set, reducing training complexity. While these methods improved training convergence, they did not consider data-to-data relations, as each data was associated with its proxy. PA [18] inherited the strength of pair- and proxy-based methods, achieving fast and reliable convergence, robustness opposing noisy data, and leveraging rich data-to-data relations. + +# 5.3. Noise Label + +Recently proposed methods for learning with noisy labels have highlighted the importance of discriminating between clean and noise-labeled data to improve performance. DivideMix [22] used GMM to distinguish between clean and noisy labeled data and treated the latter as unlabeled for semi-supervised learning. AugDesc [27] employed data augmentation to enhance the differentiation between clean and noisy labeled data, while INCV [4] introduced cross-validation to separate clean data from noisy training data. SplitNet [17] leveraged a compact network to perceive the difference between clean and noisy labels, improving model performance by more accurately differentiating noise. + +# 6. Conclusion + +In this paper, we presented a novel continual learning scenario, considered NCD on the unlabeled joint datasets without any prior knowledge of the dataset. Our framework utilized PAs to split known and novel categories, resulting in well-clustered and well-pseudo-labeled categories that mitigate catastrophic forgetting. We further refined the splitting of the dataset by adopting a noise labeling scheme. Our proposed approach outperformed existing state-of-the-art methods regarding novel category discovery and forgetting. While DeepDPM [32] has recently shown outstanding performance on non-parametric clustering tasks, we believe that our proposed method can achieve even better performance by adopting better clustering manners. In future work, we plan to evaluate our method by adopting a better clustering manner. + +# Acknowledgements + +This work was funded by Samsung Electro-Mechanics and was partially supported by Carl-Zeiss Stiftung under the Sustainable Embedded AI project (P2021-02-009). + +# References + +[1] Nicolas Aziere and Sinisa Todorovic. Ensemble deep manifold similarity learning using hard proxies. In CVPR, pages 7299-7307, 2019. +[2] Jihwan Bang, Heesu Kim, YoungJoon Yoo, Jung-Woo Ha, and Jonghyun Choi. Rainbow memory: Continual learning with a memory of diverse samples. In CVPR, pages 8218-8227, June 2021. +[3] Jane Bromley, Isabelle Guyon, Yann LeCun, Eduard Säckinger, and Roopak Shah. Signature verification using a siamese time delay neural network. In NeurIPS, volume 6, 1993. +[4] Pengfei Chen, Ben Ben Liao, Guangyong Chen, and Shengyu Zhang. Understanding and utilizing deep neural networks trained with noisy labels. In ICML, pages 1062-1070, 2019. +[5] S. Chopra, R. Hadsell, and Y. 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However, discovering novel categories in an incremental learning scenario remains a challenging problem due to the lack of prior knowledge about the number and nature of new categories. Existing methods for novel category discovery are limited by their reliance on labeled datasets and prior knowledge about the number of novel categories and the proportion of novel samples in the batch. To address the limitations and more accurately reflect real-world scenarios, in this paper, we propose a novel unsupervised class incremental learning approach for discovering novel categories on unlabeled sets without prior knowledge. The proposed method fine-tunes the feature extractor and proxy anchors on labeled sets, then splits samples into old and novel categories and clusters on the unlabeled dataset. Furthermore, the proxy anchors-based exemplar generates representative category vectors to mitigate catastrophic forgetting. Experimental results demonstrate that our proposed approach outperforms the state-of-the-art methods on fine-grained datasets under real-world scenarios." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 586, + 128, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 128, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 128, + 597 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": "Deep neural networks have achieved remarkable performance in various computer vision tasks. However, current systems are still subject to constraints that are manually supervised and do not consider continual incremental categories. For extending to real-world environments, there are still gaps to catch up by overcoming the constraints and improving their abilities in fundamental tasks. Specifically, humans still perform better than machines in object cognitive and grouping skills (e.g. recognizing new products" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 301, + 545, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 301, + 545, + 326 + ], + "spans": [ + { + "bbox": [ + 305, + 301, + 545, + 326 + ], + "type": "text", + "content": "or clothing on shopping and categorizing undefined moving objects while driving)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 327, + 546, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 546, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 546, + 639 + ], + "type": "text", + "content": "Various methods have been proposed to address the limitations of the tasks by considering real-world circumstances, as presented in Figure 1 and Table 1. In detail, Novel Category Discovery (NCD) [10, 11, 43] and Generalized Category Discovery (GCD) [36, 6] aim to recognize not only pre-trained categories but also discover novel categories using a given dataset. NCD considers a disjoint dataset where labeled and unlabeled novel samples have no intersection with each other. In contrast, GCD exploits the joint set with intersected categories, making GCD a more complicated task than NCD. However, these approaches do not consider the class incremental scheme. Class incremental NCD (class-iNCD) [33, 15] has been proposed to adopt the incremental categories on NCD task, but they still focus on improving novel category discovery performance using the disjoint set, which is an unrealistic constraint. To address this issue, Grow and Merge (GM) [42] proposes a scenario that exploits the joint unlabeled dataset in the incremental novel category discovery task, which is called Continuous Category Discovery Mixed Incremental (CCDMI). However, most existing methods require prior knowledge, such as the number of unlabeled classes for NCD and class-iNCD, or the proportion of the novel samples in the batch for CCD-MI. Such prior knowledge requirements are not enough to mimic the real-world, as we lack information about the unlabeled sets." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": "To overcome these constraints, we propose a novel scenario that better represents real-world circumstances by removing constraints on the available data. We assume that the given datasets are unlabeled joint sets without providing prior knowledge about the data. Employing the scenario, we propose a novel unsupervised class incremental" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16688" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 76, + 140, + 149 + ], + "blocks": [ + { + "bbox": [ + 59, + 76, + 140, + 149 + ], + "lines": [ + { + "bbox": [ + 59, + 76, + 140, + 149 + ], + "spans": [ + { + "bbox": [ + 59, + 76, + 140, + 149 + ], + "type": "image", + "image_path": "e74bfc7940bf6fc68a927150b0cb0a20940110fbd699c2978315a89fef3671bc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 84, + 150, + 115, + 159 + ], + "lines": [ + { + "bbox": [ + 84, + 150, + 115, + 159 + ], + "spans": [ + { + "bbox": [ + 84, + 150, + 115, + 159 + ], + "type": "text", + "content": "(a) NCD" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 159, + 73, + 237, + 149 + ], + "blocks": [ + { + "bbox": [ + 159, + 73, + 237, + 149 + ], + "lines": [ + { + "bbox": [ + 159, + 73, + 237, + 149 + ], + "spans": [ + { + "bbox": [ + 159, + 73, + 237, + 149 + ], + "type": "image", + "image_path": "4b3f796cb879f5b29d9c07dc2df5d27278a8de5a50b9c8127fe24c13a0f14fa8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 182, + 150, + 214, + 159 + ], + "lines": [ + { + "bbox": [ + 182, + 150, + 214, + 159 + ], + "spans": [ + { + "bbox": [ + 182, + 150, + 214, + 159 + ], + "type": "text", + "content": "(b) GCD" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 165, + 547, + 199 + ], + "lines": [ + { + "bbox": [ + 46, + 165, + 547, + 199 + ], + "spans": [ + { + "bbox": [ + 46, + 165, + 547, + 199 + ], + "type": "text", + "content": "Figure 1. Comparison of existing and proposed scenarios for novel category discovery. The solid and dash-lined circles indicate labeled and unlabeled samples, respectively, with sample color depicting the class label. The circle with " + }, + { + "bbox": [ + 46, + 165, + 547, + 199 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 165, + 547, + 199 + ], + "type": "text", + "content": " denotes the number of novel classes (pink) and the proportion of novel class samples in a batch (dark blue)." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 253, + 77, + 345, + 149 + ], + "blocks": [ + { + "bbox": [ + 253, + 77, + 345, + 149 + ], + "lines": [ + { + "bbox": [ + 253, + 77, + 345, + 149 + ], + "spans": [ + { + "bbox": [ + 253, + 77, + 345, + 149 + ], + "type": "image", + "image_path": "0992e772d538ba724ff6181212baa5e4243ba48792eb4ee1d7917bad9a08202e.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 271, + 150, + 323, + 159 + ], + "lines": [ + { + "bbox": [ + 271, + 150, + 323, + 159 + ], + "spans": [ + { + "bbox": [ + 271, + 150, + 323, + 159 + ], + "type": "text", + "content": "(c) class-iNCD" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 349, + 74, + 444, + 149 + ], + "blocks": [ + { + "bbox": [ + 349, + 74, + 444, + 149 + ], + "lines": [ + { + "bbox": [ + 349, + 74, + 444, + 149 + ], + "spans": [ + { + "bbox": [ + 349, + 74, + 444, + 149 + ], + "type": "image", + "image_path": "212d61951bd00c70cafbd4bb767be28804a9d52702ceb8dd9a0ee688d0740f66.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 374, + 150, + 418, + 159 + ], + "lines": [ + { + "bbox": [ + 374, + 150, + 418, + 159 + ], + "spans": [ + { + "bbox": [ + 374, + 150, + 418, + 159 + ], + "type": "text", + "content": "(d) CCD-MI" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 449, + 76, + 539, + 149 + ], + "blocks": [ + { + "bbox": [ + 449, + 76, + 539, + 149 + ], + "lines": [ + { + "bbox": [ + 449, + 76, + 539, + 149 + ], + "spans": [ + { + "bbox": [ + 449, + 76, + 539, + 149 + ], + "type": "image", + "image_path": "13633ca7a3170b07c7e124d3089f2cdb970018dc2ff148a82f735fe01e92639d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 477, + 150, + 512, + 159 + ], + "lines": [ + { + "bbox": [ + 477, + 150, + 512, + 159 + ], + "spans": [ + { + "bbox": [ + 477, + 150, + 512, + 159 + ], + "type": "text", + "content": "(e) CGCD" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 53, + 205, + 541, + 323 + ], + "blocks": [ + { + "bbox": [ + 53, + 205, + 541, + 323 + ], + "lines": [ + { + "bbox": [ + 53, + 205, + 541, + 323 + ], + "spans": [ + { + "bbox": [ + 53, + 205, + 541, + 323 + ], + "type": "table", + "html": "
TaskMethodConstraints
Continual learningAssumption: yl∩yu=∅Number of novel classesProportion of new class data
NCDRankStat [10, 11], DRNCD [43]Not consideredRequiredRequiredNot required
GCDGCD [36], XCon [6]Not consideredNot requiredNot requiredNot required
class-iNCDFroST [33], NCDwF [15]ConsideredRequiredRequiredNot required
CCD-MIGM [42]ConsideredNot requiredNot requiredRequired
CGCDOursConsideredNot requiredNot requiredNot required
", + "image_path": "298c9d2d1e4046a2fc33e573f894f0607b1407e1181bd22e2bd1b149a051fe54.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 116, + 327, + 476, + 338 + ], + "lines": [ + { + "bbox": [ + 116, + 327, + 476, + 338 + ], + "spans": [ + { + "bbox": [ + 116, + 327, + 476, + 338 + ], + "type": "text", + "content": "Table 1. Comparison of existing and proposed novel category discovery settings and the constraints" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 350, + 287, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 410 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 410 + ], + "type": "text", + "content": "learning approach to simultaneously address the problems of discovering incremental novel categories and alleviating catastrophic forgetting. In addition, we focus on recognizing fine-grained objects, which is a more realistic use case for various applications in real-world applications." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 410, + 287, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 410, + 287, + 661 + ], + "spans": [ + { + "bbox": [ + 46, + 410, + 287, + 661 + ], + "type": "text", + "content": "The proposed method exploits a deep metric learning scheme, proxy anchor (PA) [18] that presents fast and reliable convergence and robustness against noise samples, and also considers the relations between samples. Then, we divide the unlabeled data into old and novel categories using PAs, which inherit discriminative features of old categories. The cosine similarity is measured between the PAs and the samples, and then initially separated datasets are acquired on a criterion. For further splitting, we adopt a noisy label learning scheme, and then assign the predictions of the previous model and the clustering results by a nonparametric approach to old and novel categorized samples, respectively. To mitigate the forgetting, we use a PA-based exemplar, which inherits more representative features. In the experimental results, we demonstrate that the proposed method outperforms the existing state-of-the-art in discovering novel categories and forgetting alleviation on various fine-grained datasets. Specifically, the proposed method does not require any prior knowledge and considers continual learning on unlabeled joint datasets, making it a more realistic and practical solution for real-world scenarios." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 661, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 661, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 661, + 287, + 684 + ], + "type": "text", + "content": "The main contributions of the proposed method can be summarized as follows." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 58, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 689, + 287, + 713 + ], + "type": "text", + "content": "- We introduce a novel scenario, called Continuous Generalized novel Category Discovery (CGCD), which" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 324, + 350, + 545, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 350, + 545, + 398 + ], + "spans": [ + { + "bbox": [ + 324, + 350, + 545, + 398 + ], + "type": "text", + "content": "is well-suited to tackle the challenges of discovering novel categories in real-world scenarios by removing the constraint that unlabeled data belong to only novel categories." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 317, + 404, + 545, + 549 + ], + "type": "list", + "angle": 0, + "index": 21, + "blocks": [ + { + "bbox": [ + 317, + 404, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 404, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 317, + 404, + 545, + 453 + ], + "type": "text", + "content": "- We propose a novel unsupervised learning approach for incremental novel category discovery that does not require prior knowledge of the number of novel categories or the proportion of new class data." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 317, + 459, + 545, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 459, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 317, + 459, + 545, + 507 + ], + "type": "text", + "content": "- We present a noisy label learning approach and deep metric learning to split unlabeled data into old and novel categories, and also show mitigation of catastrophic forgetting using a deep metric-based exemplar." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 317, + 514, + 545, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 514, + 545, + 549 + ], + "spans": [ + { + "bbox": [ + 317, + 514, + 545, + 549 + ], + "type": "text", + "content": "- The proposed method outperforms the state-of-the-art methods in novel category discovery and forgetting mitigation on various fine-grained datasets." + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 555, + 419, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 555, + 419, + 567 + ], + "spans": [ + { + "bbox": [ + 306, + 555, + 419, + 567 + ], + "type": "text", + "content": "2. Problem Definition" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 575, + 536, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 536, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 536, + 588 + ], + "type": "text", + "content": "2.1. Continuous Generalized Category Discovery" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "As presented in Figure 1 and Table 1, various environmental schemes have been proposed to mimic real-world circumstances. Notable approaches include NCD [10, 11, 43], GCD [36], class-iNCD [33, 15], and CCD [42]. NCD considers disjoint datasets between labeled and unlabeled sets (i.e. " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}_l \\cap \\mathcal{Y}_u = \\emptyset" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ") and requires prior knowledge of the number of unlabeled categories " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "|\\mathcal{Y}_u|" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ". In contrast, GCD exploits the joint set (i.e. " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}_l \\cap \\mathcal{Y}_u \\neq \\emptyset" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "). Although GCD is a more challenging task than NCD, it still does not consider continuous incremental category discovery." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16689" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 71, + 541, + 262 + ], + "blocks": [ + { + "bbox": [ + 61, + 71, + 541, + 262 + ], + "lines": [ + { + "bbox": [ + 61, + 71, + 541, + 262 + ], + "spans": [ + { + "bbox": [ + 61, + 71, + 541, + 262 + ], + "type": "image", + "image_path": "7d08a14bd02a454c1f8d6d9ffef4cc92107dd0ad0e21c2e290e4ae966d7fc290.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 268, + 547, + 324 + ], + "lines": [ + { + "bbox": [ + 46, + 268, + 547, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 268, + 547, + 324 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed CGCD framework. The framework comprises three steps. The first step is that the network model is fine-tuned on the target dataset using the labeled dataset. In the second step, the discovery of novel categories is performed on the joint and unlabeled dataset, which is split into unseen and seen sets using the initial and fine split methods. Pseudo-labels are assigned to the unlabeled dataset using the previous model's predictions (seen case) and non-parametric clustering results (unseen case). In the last step, a new model is trained on the fine split dataset, which incorporates new proxy anchors based on clustering results." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 331, + 288, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 288, + 427 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 288, + 427 + ], + "type": "text", + "content": "Class-iNCD is an extension of NCD to the continual learning scheme. However, the method trains on the disjoint dataset under class incremental stages and has a requirement for " + }, + { + "bbox": [ + 46, + 331, + 288, + 427 + ], + "type": "inline_equation", + "content": "|\\mathcal{V}_u|" + }, + { + "bbox": [ + 46, + 331, + 288, + 427 + ], + "type": "text", + "content": ". CCD also trains on discovering novel classes under the continual learning scheme with the joint dataset. Although CCD does not require " + }, + { + "bbox": [ + 46, + 331, + 288, + 427 + ], + "type": "inline_equation", + "content": "|\\mathcal{V}_u|" + }, + { + "bbox": [ + 46, + 331, + 288, + 427 + ], + "type": "text", + "content": ", it still needs the proportion of the novel class data in a batch as prior knowledge, which is used to filter out the data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 429, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 429, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 429, + 287, + 536 + ], + "type": "text", + "content": "To address these limitations, we propose a more challenging problem, named Continuous Generalized novel Category Discovery (CGCD), that is closer to real-world circumstances. In CGCD, we exploit the unlabeled joint dataset in incremental steps without providing any prior knowledge and aim to discover novel classes. This formulation is more representative of real-world scenarios, where we are not aware of the number of unlabeled categories and the characteristics of the dataset." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 548, + 287, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 287, + 574 + ], + "type": "text", + "content": "2.2. Setting of Continuous Generalized Category Discovery" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 580, + 287, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 287, + 675 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 287, + 675 + ], + "type": "text", + "content": "Fine-grained datasets consist of similar objects, such as canines [16], indoor scenes [30], vehicles [25], and birds [37], in constrained circumstances. Compared to coarse datasets such as CIFAR [19] and ImageNet [20], fine-grained datasets are closer to real-world scenarios. Therefore, we focus on training and discovering novel classes with fine-grained datasets to mimic real-world circumstances better." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "CGCD employs the joint unlabeled dataset in incremental steps, and Table 2 describes the dataset partitioning used in the one-time incremental category discovery. First, the" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 329, + 545, + 416 + ], + "blocks": [ + { + "bbox": [ + 307, + 329, + 545, + 416 + ], + "lines": [ + { + "bbox": [ + 307, + 329, + 545, + 416 + ], + "spans": [ + { + "bbox": [ + 307, + 329, + 545, + 416 + ], + "type": "table", + "html": "
DatasetAll classesInitial stepCategory incremental step
Old classOld classNew class
CUB-200200160 (0.8)160 (0.2)40 (1.0)
MIT676753 (0.8)53 (0.2)14 (1.0)
Stanford Dogs12096 (0.8)96 (0.2)24 (1.0)
FGVC Aircraft10080 (0.8)80 (0.2)20 (1.0)
", + "image_path": "080bfbe27e9627e113f4a61e90afe878c222d711a314b81a58b818bb22c23328.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 423, + 547, + 479 + ], + "lines": [ + { + "bbox": [ + 304, + 423, + 547, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 547, + 479 + ], + "type": "text", + "content": "Table 2. Dataset configurations for one-time incremental category scenarios. The number of classes and the proportion of data from each class in parentheses are presented. Note that the ratios in parentheses are hidden information that is not revealed to the learning methods." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 486, + 547, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 656 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 656 + ], + "type": "text", + "content": "set of classes is partitioned into old classes and new classes at a certain rate, for example, 8: 2. The initial step utilizes labeled dataset " + }, + { + "bbox": [ + 304, + 486, + 547, + 656 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^0" + }, + { + "bbox": [ + 304, + 486, + 547, + 656 + ], + "type": "text", + "content": " consisting of old classes only. Then the following incremental step utilizes unlabeled dataset " + }, + { + "bbox": [ + 304, + 486, + 547, + 656 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^1" + }, + { + "bbox": [ + 304, + 486, + 547, + 656 + ], + "type": "text", + "content": " consisting of both old classes and new classes, which reflect more realistic and challenging real-world scenarios. The key element of the proposed method is to decide whether the unlabeled data point belongs to the old classes (seen) or new classes (unseen). The samples belonging to the old classes are assigned to labeled dataset " + }, + { + "bbox": [ + 304, + 486, + 547, + 656 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^0" + }, + { + "bbox": [ + 304, + 486, + 547, + 656 + ], + "type": "text", + "content": " and unlabeled dataset " + }, + { + "bbox": [ + 304, + 486, + 547, + 656 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^1" + }, + { + "bbox": [ + 304, + 486, + 547, + 656 + ], + "type": "text", + "content": ", and the rest of all the new class samples are assigned to " + }, + { + "bbox": [ + 304, + 486, + 547, + 656 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^1" + }, + { + "bbox": [ + 304, + 486, + 547, + 656 + ], + "type": "text", + "content": ". Here the choice of 8: 2 is an arbitrary example, and it is important to note that this ratio is just for data generation purposes and is not revealed to the learning methods." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 668, + 362, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 668, + 362, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 668, + 362, + 681 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "content": "As described in Figure 2, our proposed method consists of three steps: the initial step, the novel category discovery and the final step." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16690" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "ery step, and the category incremental step. In the initial step, we fine-tune a pre-trained model on the labeled dataset " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^0 = \\{(x,y)\\in \\mathcal{X}_l\\times \\mathcal{Y}_l\\}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": ", and obtain the embedding vector " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " using the model " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": ", denoted as " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "z = f^{0}(x)" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": ". We then use these vectors to train PAs [18] of each category, represented as " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "p = g^0 (z)" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": ", and also construct well-representative exemplars. In the following novel category discovery step, the given unlabeled joint datasets are denoted as " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^1 = \\{x|x\\in \\mathcal{X}_u\\}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": ". We first separate them into old and novel categories through the initial and the fine splits. Since the separated sets are unlabeled, we pseudo-label for old and novel classes using the previous model prediction and non-parametric clustering results, respectively." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 289, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 336 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 336 + ], + "type": "text", + "content": "In the category incremental step, the acquired set is trained to improve the performance of discovering novel categories. To avoid catastrophic forgetting, we exploit generated features by the exemplar and feature distillation between earlier and new models. The proposed model does not require any prior knowledge, such as " + }, + { + "bbox": [ + 46, + 228, + 289, + 336 + ], + "type": "inline_equation", + "content": "|\\mathcal{Y}_u|" + }, + { + "bbox": [ + 46, + 228, + 289, + 336 + ], + "type": "text", + "content": " and the ratio of novel class samples in a batch. We evaluate the performance of the proposed method using the validation dataset, which includes all categories." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 345, + 177, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 345, + 177, + 357 + ], + "spans": [ + { + "bbox": [ + 47, + 345, + 177, + 357 + ], + "type": "text", + "content": "3.1. Initial Step: Fine Tune" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 364, + 289, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 289, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 289, + 495 + ], + "type": "text", + "content": "Existing NCD methods do not account for noisy categories, such as those categorized from old to novel or from novel to old, which can impair novel discovery performance and accumulate errors in the continuous procedure. To address these limitations, in this work, we propose a novel approach that leverages the benefits of PA to complement and improve the existing approaches. PA is a metric learning method that combines proxy- and pair-based methods to achieve rapid and reliable convergence, and robustness against noisy samples, and considers relations between data to extract meaningful semantic information." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 496, + 288, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 288, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 288, + 581 + ], + "type": "text", + "content": "Following the method, the embedding vector " + }, + { + "bbox": [ + 46, + 496, + 288, + 581 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 496, + 288, + 581 + ], + "type": "text", + "content": " from the initial model " + }, + { + "bbox": [ + 46, + 496, + 288, + 581 + ], + "type": "inline_equation", + "content": "f^0" + }, + { + "bbox": [ + 46, + 496, + 288, + 581 + ], + "type": "text", + "content": " is trained to map to each proxy anchor " + }, + { + "bbox": [ + 46, + 496, + 288, + 581 + ], + "type": "inline_equation", + "content": "p = g^0 (z)" + }, + { + "bbox": [ + 46, + 496, + 288, + 581 + ], + "type": "text", + "content": ". Let the set of all proxy anchors as " + }, + { + "bbox": [ + 46, + 496, + 288, + 581 + ], + "type": "inline_equation", + "content": "P^0" + }, + { + "bbox": [ + 46, + 496, + 288, + 581 + ], + "type": "text", + "content": " in the labeled data " + }, + { + "bbox": [ + 46, + 496, + 288, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^0" + }, + { + "bbox": [ + 46, + 496, + 288, + 581 + ], + "type": "text", + "content": ". In this manner, the number of proxy anchors of " + }, + { + "bbox": [ + 46, + 496, + 288, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^0" + }, + { + "bbox": [ + 46, + 496, + 288, + 581 + ], + "type": "text", + "content": " is the number of classes of the labeled set (i.e. " + }, + { + "bbox": [ + 46, + 496, + 288, + 581 + ], + "type": "inline_equation", + "content": "|P^0| = |\\mathcal{Y}_l|" + }, + { + "bbox": [ + 46, + 496, + 288, + 581 + ], + "type": "text", + "content": ") in the initial step. We train the model and proxy anchors using the following loss function defined in [18]:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 588, + 287, + 652 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 588, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 55, + 588, + 287, + 652 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {p a} ^ {0} \\left(Z ^ {0}\\right) = \\frac {1}{| P ^ {0 +} |} \\sum_ {p \\in P ^ {0 +}} \\log \\left(1 + \\sum_ {z \\in Z _ {p} ^ {0 +}} e ^ {- \\alpha (s (z, p) - \\delta)}\\right) \\tag {1} \\\\ + \\frac {1}{| P ^ {0} |} \\sum_ {p \\in P ^ {0}} \\log \\left(1 + \\sum_ {z \\in Z _ {p} ^ {0 -}} e ^ {\\alpha (s (z, p) + \\delta)}\\right) \\\\ \\end{array}", + "image_path": "d00aead86411d63df9ff85373a216af8c17b41f4d3f8065021510af86968f4ac.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 662, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 662, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 662, + 289, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 662, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\delta > 0" + }, + { + "bbox": [ + 46, + 662, + 289, + 715 + ], + "type": "text", + "content": " is a margin and " + }, + { + "bbox": [ + 46, + 662, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\alpha > 0" + }, + { + "bbox": [ + 46, + 662, + 289, + 715 + ], + "type": "text", + "content": " is a scaling factor. The function " + }, + { + "bbox": [ + 46, + 662, + 289, + 715 + ], + "type": "inline_equation", + "content": "s(\\cdot, \\cdot)" + }, + { + "bbox": [ + 46, + 662, + 289, + 715 + ], + "type": "text", + "content": " indicates the cosine similarity score. " + }, + { + "bbox": [ + 46, + 662, + 289, + 715 + ], + "type": "inline_equation", + "content": "P^{0+}" + }, + { + "bbox": [ + 46, + 662, + 289, + 715 + ], + "type": "text", + "content": " represents same class PAs(e.gpositive) in the batch. Each proxy " + }, + { + "bbox": [ + 46, + 662, + 289, + 715 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 662, + 289, + 715 + ], + "type": "text", + "content": " divides the set of embedding vector " + }, + { + "bbox": [ + 46, + 662, + 289, + 715 + ], + "type": "inline_equation", + "content": "Z^0" + }, + { + "bbox": [ + 46, + 662, + 289, + 715 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 662, + 289, + 715 + ], + "type": "inline_equation", + "content": "Z_p^{0+}" + }, + { + "bbox": [ + 46, + 662, + 289, + 715 + ], + "type": "text", + "content": " and" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 310, + 71, + 426, + 153 + ], + "blocks": [ + { + "bbox": [ + 310, + 71, + 426, + 153 + ], + "lines": [ + { + "bbox": [ + 310, + 71, + 426, + 153 + ], + "spans": [ + { + "bbox": [ + 310, + 71, + 426, + 153 + ], + "type": "image", + "image_path": "0547a841a326d4a2d01d2bc871f87059a9fc50c37947dd43ac2b98f991b2770b.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 343, + 156, + 394, + 165 + ], + "lines": [ + { + "bbox": [ + 343, + 156, + 394, + 165 + ], + "spans": [ + { + "bbox": [ + 343, + 156, + 394, + 165 + ], + "type": "text", + "content": "(a) Initial Split" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 429, + 71, + 543, + 153 + ], + "blocks": [ + { + "bbox": [ + 429, + 71, + 543, + 153 + ], + "lines": [ + { + "bbox": [ + 429, + 71, + 543, + 153 + ], + "spans": [ + { + "bbox": [ + 429, + 71, + 543, + 153 + ], + "type": "image", + "image_path": "0bc54aeb7531789ecc22dfe3ec46c62fbcf37e5d2e44e749fc552aff483090b6.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 462, + 156, + 509, + 165 + ], + "lines": [ + { + "bbox": [ + 462, + 156, + 509, + 165 + ], + "spans": [ + { + "bbox": [ + 462, + 156, + 509, + 165 + ], + "type": "text", + "content": "(b) Fine Split" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 325, + 164, + 525, + 175 + ], + "lines": [ + { + "bbox": [ + 325, + 164, + 525, + 175 + ], + "spans": [ + { + "bbox": [ + 325, + 164, + 525, + 175 + ], + "type": "text", + "content": "Figure 3. Separation results on joint unlabeled datasets" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 179, + 547, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 179, + 547, + 230 + ], + "spans": [ + { + "bbox": [ + 304, + 179, + 547, + 230 + ], + "type": "inline_equation", + "content": "Z_{p}^{0^{-}} = Z^{0} - Z_{p}^{0^{+}}" + }, + { + "bbox": [ + 304, + 179, + 547, + 230 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 179, + 547, + 230 + ], + "type": "inline_equation", + "content": "Z_{p}^{0^{+}}" + }, + { + "bbox": [ + 304, + 179, + 547, + 230 + ], + "type": "text", + "content": " denotes the same class embedding points with the proxy anchor " + }, + { + "bbox": [ + 304, + 179, + 547, + 230 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 179, + 547, + 230 + ], + "type": "text", + "content": ". The first term aims to pull " + }, + { + "bbox": [ + 304, + 179, + 547, + 230 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 179, + 547, + 230 + ], + "type": "text", + "content": " and its dissimilar but hard positive data together, while the last term is to push " + }, + { + "bbox": [ + 304, + 179, + 547, + 230 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 179, + 547, + 230 + ], + "type": "text", + "content": " and its similar but hard negatives apart." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 237, + 489, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 237, + 489, + 251 + ], + "spans": [ + { + "bbox": [ + 305, + 237, + 489, + 251 + ], + "type": "text", + "content": "3.2. Discovering Novel Categories Step" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "spans": [ + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "text", + "content": "Separation: In this procedure, we aim to split the given joint dataset " + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^1" + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "text", + "content": " into the novel and old categories without any prior knowledge. We conduct this task in two stages: initial split and fine split. In the initial split, we compute the cosine similarity between " + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "text", + "content": " and each embedding vector " + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "inline_equation", + "content": "z_i \\in Z^1" + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "inline_equation", + "content": "z_i = f^0(x_i)" + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "inline_equation", + "content": "x_i \\in D^1" + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "text", + "content": ". Because the set of proxy anchors " + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "inline_equation", + "content": "P^0" + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "text", + "content": " represents the old categories, we classify a sample to the old class if the maximum similarity score of " + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "inline_equation", + "content": "z_i" + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "text", + "content": " is larger than a threshold " + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "text", + "content": ". We set " + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "inline_equation", + "content": "\\epsilon = 0" + }, + { + "bbox": [ + 304, + 256, + 545, + 386 + ], + "type": "text", + "content": " since it is the median of the score ranges. The initial split is defined as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 348, + 385, + 545, + 423 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 385, + 545, + 423 + ], + "spans": [ + { + "bbox": [ + 348, + 385, + 545, + 423 + ], + "type": "interline_equation", + "content": "\\tilde {y} _ {i} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} \\max _ {p \\in P ^ {0}} (s \\left(z _ {i}, p\\right)) \\geq \\epsilon = 0 \\\\ 1, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {2}", + "image_path": "f8ab636c0449823db20cffc768e36564e677c629ee3dc93ecb8369a7b0c7b9a9.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 429, + 545, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 429, + 545, + 535 + ], + "spans": [ + { + "bbox": [ + 304, + 429, + 545, + 535 + ], + "type": "text", + "content": "To acquire a cleaner novel and old dataset, we propose a noisy labeling scheme, fine split, which involves an iterative training of a simple multilayer perceptron (MLP) based classifier " + }, + { + "bbox": [ + 304, + 429, + 545, + 535 + ], + "type": "inline_equation", + "content": "m(\\cdot)" + }, + { + "bbox": [ + 304, + 429, + 545, + 535 + ], + "type": "text", + "content": " on the binarized dataset. The initial split results in noisy and inaccurate separation, as shown in Figure 3 (a). Among them, only the data on both ends of the spectrum are assumed the clean and utilized to train the classifier. The loss of split network " + }, + { + "bbox": [ + 304, + 429, + 545, + 535 + ], + "type": "inline_equation", + "content": "m(\\cdot)" + }, + { + "bbox": [ + 304, + 429, + 545, + 535 + ], + "type": "text", + "content": " is defined as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 314, + 546, + 545, + 560 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 546, + 545, + 560 + ], + "spans": [ + { + "bbox": [ + 314, + 546, + 545, + 560 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s p} = - \\mathbb {E} _ {z _ {c} \\in Z _ {c} ^ {1}} \\left[ \\tilde {y} _ {c} \\log \\left(m \\left(z _ {c}\\right)\\right) + \\left(1 - \\tilde {y} _ {c}\\right) \\log \\left(1 - m \\left(z _ {c}\\right)\\right) \\right] \\tag {3}", + "image_path": "73b791eed97050c589756dc04fc605f6e397fc5067fdd1addc4c48a0944f71d0.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 569, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 545, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 569, + 545, + 653 + ], + "type": "inline_equation", + "content": "z_{c}" + }, + { + "bbox": [ + 304, + 569, + 545, + 653 + ], + "type": "text", + "content": " denotes clean embedding vectors, and " + }, + { + "bbox": [ + 304, + 569, + 545, + 653 + ], + "type": "inline_equation", + "content": "Z_{c}^{1}" + }, + { + "bbox": [ + 304, + 569, + 545, + 653 + ], + "type": "text", + "content": " represents the set of clean vectors. " + }, + { + "bbox": [ + 304, + 569, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\tilde{y}_{c}" + }, + { + "bbox": [ + 304, + 569, + 545, + 653 + ], + "type": "text", + "content": " indicates the pseudo label of the clean data. After the warm-up training, the classifier is trained with re-assigned pseudo labels and the more cleaned data, which is divided with the Gaussian mixture model (GMM). Consequently, the Figure 3 (b) shows the cleaner separated results." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Pseudo-labeling: After the separation, both the old " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{old}^{1}" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " and the novel categories " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{new}^{1}" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " are still unlabeled. Thus, we use pseudo-labels to assign labels to each sample. For " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{old}^{1}" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": ", we use the predictions of the previous model and proxy anchors to assign pseudo-labels. In contrast, we use a" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16691" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "non-parametric clustering approach named Affinity propagation [8] to assign pseudo-labels to " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{new}^{1}" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": ". In this manner, our proposed approach does not require any prior knowledge. Finally, from the clustering results, we obtain an estimate of the number of novel categories, denoted as " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "|\\hat{\\mathcal{Y}}_n|" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 143, + 196, + 156 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 143, + 196, + 156 + ], + "spans": [ + { + "bbox": [ + 47, + 143, + 196, + 156 + ], + "type": "text", + "content": "3.3. Category Incremental Step" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 162, + 287, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 162, + 287, + 246 + ], + "spans": [ + { + "bbox": [ + 46, + 162, + 287, + 246 + ], + "type": "text", + "content": "Training modified model and PAs: To improve the performance of discovering novel categories, we modify the model since the previous model has PAs only for " + }, + { + "bbox": [ + 46, + 162, + 287, + 246 + ], + "type": "inline_equation", + "content": "|\\mathcal{Y}_l|" + }, + { + "bbox": [ + 46, + 162, + 287, + 246 + ], + "type": "text", + "content": " classes and cannot categorize novel classes. We add new " + }, + { + "bbox": [ + 46, + 162, + 287, + 246 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 162, + 287, + 246 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 162, + 287, + 246 + ], + "type": "inline_equation", + "content": "|\\hat{\\mathcal{Y}}_n|" + }, + { + "bbox": [ + 46, + 162, + 287, + 246 + ], + "type": "text", + "content": " classes, increasing the total number of PAs like " + }, + { + "bbox": [ + 46, + 162, + 287, + 246 + ], + "type": "inline_equation", + "content": "|P^1| = |\\mathcal{Y}_l| + |\\hat{\\mathcal{Y}}_n|" + }, + { + "bbox": [ + 46, + 162, + 287, + 246 + ], + "type": "text", + "content": ". The loss function to train the modified model " + }, + { + "bbox": [ + 46, + 162, + 287, + 246 + ], + "type": "inline_equation", + "content": "f^1" + }, + { + "bbox": [ + 46, + 162, + 287, + 246 + ], + "type": "text", + "content": " and PA " + }, + { + "bbox": [ + 46, + 162, + 287, + 246 + ], + "type": "inline_equation", + "content": "p = g^1(z)" + }, + { + "bbox": [ + 46, + 162, + 287, + 246 + ], + "type": "text", + "content": " is reformulated as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 258, + 286, + 320 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 258, + 286, + 320 + ], + "spans": [ + { + "bbox": [ + 58, + 258, + 286, + 320 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {p a} ^ {1} (Z ^ {1}) = \\frac {1}{| P ^ {1 +} |} \\sum_ {p \\in P ^ {1 +}} \\log \\left(1 + \\sum_ {z \\in Z _ {p} ^ {1 +}} e ^ {- \\alpha (s (z, p) - \\delta)}\\right) \\tag {4} \\\\ + \\frac {1}{| P ^ {1} |} \\sum_ {p \\in P ^ {1}} \\log \\left(1 + \\sum_ {z \\in Z _ {p} ^ {1 -}} e ^ {\\alpha (s (z, p) + \\delta)}\\right) \\\\ \\end{array}", + "image_path": "0604f06827a1a05d9bec74737e68963f7c27043d18fed1a514015b96f4026216.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 333, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 333, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 333, + 287, + 464 + ], + "type": "text", + "content": "Avoiding forgetting: In the continual learning scheme, it is essential to alleviate catastrophic forgetting. We adopt feature replay, which leverages the PA information belonging to old categories. Each well-trained " + }, + { + "bbox": [ + 46, + 333, + 287, + 464 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 333, + 287, + 464 + ], + "type": "text", + "content": " inherits the representation power for each category. We employ each " + }, + { + "bbox": [ + 46, + 333, + 287, + 464 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 333, + 287, + 464 + ], + "type": "text", + "content": " to generate features by following the Gaussian distribution " + }, + { + "bbox": [ + 46, + 333, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(p^0,\\sigma^2), p^0 \\in P^0" + }, + { + "bbox": [ + 46, + 333, + 287, + 464 + ], + "type": "text", + "content": ". The number of generated features is determined based on data balancing, for example, the number of newly categorized samples in a batch. The generated features are concatenated into a batch, and the model and PAs are trained using the following loss function:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 66, + 475, + 286, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 475, + 286, + 491 + ], + "spans": [ + { + "bbox": [ + 66, + 475, + 286, + 491 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {e x} ^ {1} (\\tilde {Z}) = \\mathcal {L} _ {p a} ^ {1} (\\tilde {Z}), \\quad \\tilde {Z} = \\left\\{\\tilde {z} \\sim \\mathcal {N} \\left(p ^ {0}, \\sigma^ {2}\\right) \\right\\} \\tag {5}", + "image_path": "6eed34d021af142444da487717c133325f6ff5dd1ef8ffbf4d6f9d5d72464d56.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 502, + 286, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 502, + 286, + 537 + ], + "spans": [ + { + "bbox": [ + 46, + 502, + 286, + 537 + ], + "type": "text", + "content": "Also, we utilize the distillation of the extracted embedding vectors from the present " + }, + { + "bbox": [ + 46, + 502, + 286, + 537 + ], + "type": "inline_equation", + "content": "f^1" + }, + { + "bbox": [ + 46, + 502, + 286, + 537 + ], + "type": "text", + "content": " and the previous model " + }, + { + "bbox": [ + 46, + 502, + 286, + 537 + ], + "type": "inline_equation", + "content": "f^0" + }, + { + "bbox": [ + 46, + 502, + 286, + 537 + ], + "type": "text", + "content": ". The distillation loss " + }, + { + "bbox": [ + 46, + 502, + 286, + 537 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{kd}" + }, + { + "bbox": [ + 46, + 502, + 286, + 537 + ], + "type": "text", + "content": " is described as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 80, + 549, + 286, + 580 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 549, + 286, + 580 + ], + "spans": [ + { + "bbox": [ + 80, + 549, + 286, + 580 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {k d} ^ {1} \\left(z _ {o}\\right) = - \\mathbb {E} _ {z _ {o} \\in Z _ {o l d} ^ {1}} \\| z _ {o} ^ {0} - z _ {o} \\| _ {2} \\tag {6} \\\\ = - \\mathbb {E} _ {x _ {o} \\in D _ {o l d} ^ {1}} \\| f ^ {0} (x _ {o}) - f ^ {1} (x _ {o}) \\| _ {2} \\\\ \\end{array}", + "image_path": "d6359f6b149279b91ad411eacaf29c5f8c3bc47b37f3d18fe3551e8d4595a5f7.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 592, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 592, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 592, + 287, + 628 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 592, + 287, + 628 + ], + "type": "inline_equation", + "content": "z^0" + }, + { + "bbox": [ + 47, + 592, + 287, + 628 + ], + "type": "text", + "content": " represents the embedding vector for fixed previous feature network " + }, + { + "bbox": [ + 47, + 592, + 287, + 628 + ], + "type": "inline_equation", + "content": "f^0" + }, + { + "bbox": [ + 47, + 592, + 287, + 628 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 592, + 287, + 628 + ], + "type": "inline_equation", + "content": "Z_{old}^{1}" + }, + { + "bbox": [ + 47, + 592, + 287, + 628 + ], + "type": "text", + "content": " denotes seen data from " + }, + { + "bbox": [ + 47, + 592, + 287, + 628 + ], + "type": "inline_equation", + "content": "Z^{1} = \\{Z_{old}^{1}\\cup Z_{new}^{1}\\}" + }, + { + "bbox": [ + 47, + 592, + 287, + 628 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 630, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 688 + ], + "type": "text", + "content": "In conclusion, the loss consists of three different losses in the continuous category discovery step. One loss is for training the PAs and the model on " + }, + { + "bbox": [ + 46, + 630, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^1" + }, + { + "bbox": [ + 46, + 630, + 287, + 688 + ], + "type": "text", + "content": ", the others are to avoid forgetting by using generated features and knowledge distillation. " + }, + { + "bbox": [ + 46, + 630, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^1" + }, + { + "bbox": [ + 46, + 630, + 287, + 688 + ], + "type": "text", + "content": " is described as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 93, + 700, + 286, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 700, + 286, + 715 + ], + "spans": [ + { + "bbox": [ + 93, + 700, + 286, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} ^ {1} = \\mathcal {L} _ {p a} ^ {1} (Z ^ {1}) + \\mathcal {L} _ {e x} ^ {1} (\\tilde {Z}) + \\mathcal {L} _ {k d} ^ {1} \\left(z _ {o}\\right) \\tag {7}", + "image_path": "3a75e0573f8f654ef4b15a51ce7bf2b6c149d2415fe4ca133400bf45b658b034.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 72, + 431, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 431, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 431, + 84 + ], + "type": "text", + "content": "4. Experimental Results" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 91, + 438, + 103 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 91, + 438, + 103 + ], + "spans": [ + { + "bbox": [ + 306, + 91, + 438, + 103 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 109, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 109, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 305, + 109, + 545, + 289 + ], + "type": "text", + "content": "We utilized the widely used augmentation techniques, including random crop after padding and random horizontal flip. All the experiments were trained for 60 epochs using AdamW optimizer with weight decay set to 0.0001. The initial learning rate was set to 0.0001 for the model " + }, + { + "bbox": [ + 305, + 109, + 545, + 289 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 305, + 109, + 545, + 289 + ], + "type": "text", + "content": ", while for the PAs, it was set to 0.01. The learning rate was decayed by a factor of 0.5 every five epochs. We used the threshold " + }, + { + "bbox": [ + 305, + 109, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 305, + 109, + 545, + 289 + ], + "type": "text", + "content": " only once for the initial split to divide the set into old and novel categories, and we set it to 0 for all the datasets and networks. For fine split, we used an MLP-based network architecture that consists of two dense layers with a batch normalization layer. The model was trained for three epochs using AdamW with a learning rate of 0.0001. The hyperparameters for PAs, " + }, + { + "bbox": [ + 305, + 109, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 109, + 545, + 289 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 109, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 305, + 109, + 545, + 289 + ], + "type": "text", + "content": ", were set to 32 and 0.1, respectively." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 289, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 289, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 305, + 289, + 545, + 348 + ], + "type": "text", + "content": "For fair comparisons of various methods, such as NCD, class-iNCD, and CCD, we follow the hyperparameters and the network architectures of the original implementations, referring to the papers for details. All the reported performances are average results over three runs." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 356, + 418, + 367 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 356, + 418, + 367 + ], + "spans": [ + { + "bbox": [ + 306, + 356, + 418, + 367 + ], + "type": "text", + "content": "4.2. Evaluation Metrics" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 374, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 374, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 305, + 374, + 545, + 410 + ], + "type": "text", + "content": "We evaluate the methods using metrics based on the cluster accuracy measurement, called Hungarian assignment algorithm [21]. The evaluation metric is defined as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 364, + 419, + 544, + 452 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 419, + 544, + 452 + ], + "spans": [ + { + "bbox": [ + 364, + 419, + 544, + 452 + ], + "type": "interline_equation", + "content": "\\mathcal {M} ^ {t} = \\frac {1}{| \\mathcal {D} |} \\sum_ {i = 1} ^ {| \\mathcal {D} |} \\mathbb {I} \\left(y _ {i} = h ^ {*} \\left(y _ {i} ^ {*}\\right)\\right) \\tag {8}", + "image_path": "70a131f55c5f3c053748f20603e5f2c15d31743a392e3626c53f2eb077b9b3a0.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "inline_equation", + "content": "|\\mathcal{D}|" + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "text", + "content": " is the size of the validation dataset " + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "inline_equation", + "content": "h^*" + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "text", + "content": " is the optimal assignment. So, " + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^t" + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "text", + "content": " measures the cluster accuracy at step " + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "text", + "content": " on the " + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "text", + "content": ". In this manner, " + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{all}" + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_o" + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "text", + "content": " indicate the cluster accuracy metrics of the whole and old categories using " + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^t" + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "text", + "content": ", respectively. Furthermore, we employ two more metrics that, " + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_f" + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_d" + }, + { + "bbox": [ + 305, + 457, + 545, + 540 + ], + "type": "text", + "content": ", which are proposed on GM [42] and described as follows:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 373, + 548, + 544, + 564 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 548, + 544, + 564 + ], + "spans": [ + { + "bbox": [ + 373, + 548, + 544, + 564 + ], + "type": "interline_equation", + "content": "\\mathcal {M} _ {f} = \\max _ {t} \\left\\{\\mathcal {M} _ {o} ^ {0} - \\mathcal {M} _ {o} ^ {t} \\right\\}, \\tag {9}", + "image_path": "c825273d177f8904e09c1ac9c3ea184b27f5369c972fb9a65101fbaab3e73956.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 384, + 580, + 544, + 608 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 580, + 544, + 608 + ], + "spans": [ + { + "bbox": [ + 384, + 580, + 544, + 608 + ], + "type": "interline_equation", + "content": "\\mathcal {M} _ {d} = \\frac {1}{| T |} \\sum_ {i = T} \\mathcal {M} _ {n} ^ {i}. \\tag {10}", + "image_path": "76ce80c26f520c3ab7549c5b9a396b616fb95038f1cac9cfce7f8077fef735a5.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_o^0" + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_o^t" + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "text", + "content": " are the old class cluster accuracy at the initial step and category incremental " + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "text", + "content": " step, respectively. So " + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_f" + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "text", + "content": " measures the maximum forgetting values for old categories in the entire step and should be sufficiently low; if not, the method is not valuable in practical applications. In Equation (10), " + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "|T|" + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "text", + "content": " is the number of increased steps, and " + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_d" + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "text", + "content": " evaluates the averaged performance of novel category discovery in unlabeled joint datasets in each step. It means" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "16692" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 71, + 550, + 173 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 550, + 173 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 550, + 173 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 550, + 173 + ], + "type": "table", + "html": "
MethodCUB-200MIT67Stanford DogsFGVC aircraft
\\( {\\mathcal{M}}_{all} \\)↑\\( {\\mathcal{M}}_{o} \\)↑\\( {\\mathcal{M}}_{f} \\)↓\\( {\\mathcal{M}}_{d} \\)↑\\( {\\mathcal{M}}_{all} \\)↑\\( {\\mathcal{M}}_{o} \\)↑\\( {\\mathcal{M}}_{f} \\)↓\\( {\\mathcal{M}}_{d} \\)↑\\( {\\mathcal{M}}_{all} \\)↑\\( {\\mathcal{M}}_{o} \\)↑\\( {\\mathcal{M}}_{f} \\)↓\\(\\mathcal{M}_{d}\\uparrow\\)\\( {\\mathcal{M}}_{all} \\)↑\\( {\\mathcal{M}}_{o} \\)↑\\( {\\mathcal{M}}_{f} \\)↓\\( {\\mathcal{M}}_{d} \\)↑
Supervised61.6945.8323.3216.6355.5640.9019.5218.3464.2647.5725.4317.0164.6248.1726.2418.12
DRNCD [43]9.8010.4758.5134.2426.9927.6749.0738.9116.3910.3465.8363.3618.7319.5057.0545.63
FRoST [33]18.1917.3412.1817.2023.2123.5515.9624.7422.6222.2314.2926.0632.6133.5315.1927.69
GM [42]6.436.5739.825.9216.5216.7742.2615.505.995.9850.365.9812.0011.6353.3513.46
Ours54.7558.8015.4740.9054.4564.2310.6418.5866.2576.156.7730.0437.2841.6014.6620.04
", + "image_path": "7682ef9b8b7cad35aafb82ac77e7b2a476fb68d5548d1034df3ce75e8823069e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 178, + 536, + 189 + ], + "lines": [ + { + "bbox": [ + 47, + 178, + 536, + 189 + ], + "spans": [ + { + "bbox": [ + 47, + 178, + 536, + 189 + ], + "type": "text", + "content": "Table 3. Comparison results under continuous generalized categorized discovery scenario. The results present the mean over three runs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 50, + 193, + 545, + 403 + ], + "blocks": [ + { + "bbox": [ + 50, + 193, + 545, + 403 + ], + "lines": [ + { + "bbox": [ + 50, + 193, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 50, + 193, + 545, + 403 + ], + "type": "image", + "image_path": "f8d1bd7dfc0d4d59e06cb26ce5c99dbc300c2781c479a50dce5f04f5c69be2c3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 403, + 546, + 436 + ], + "lines": [ + { + "bbox": [ + 46, + 403, + 546, + 436 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 546, + 436 + ], + "type": "text", + "content": "Figure 4. Qualitative evaluation results of the proposed method using the CUB-200 dataset on ResNet-18. The first five columns with blue boxes denote well-clustered examples. The last two columns represent failed prediction results, including example images with purple boxes denoting hard negatives and those with red boxes indicating incorrect categorization." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 447, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 287, + 472 + ], + "type": "text", + "content": "the higher method, the more appropriate method in real-world applications." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 479, + 274, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 274, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 274, + 491 + ], + "type": "text", + "content": "4.3. Comparison with State-of-the-arts Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 498, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 640 + ], + "type": "text", + "content": "We conducted a series of experiments to compare the cluster accuracy performance of our proposed method with state-of-the-art approaches, as presented in Table 1. In the experiments, we excluded the GCD task, including XCon, as it focuses on discovering novel categories blended with labeled and unlabeled datasets and evaluates unknown discovery performance on only train datasets, not validation datasets, in their papers. Therefore, we compared our proposed method with other approaches, including Dual rank NCD (DRNCD) [43], FRoST [33], and GM, which are the representative methods that record the state-of-the-art results of each task." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "We first evaluated the one-step incremental category setting and reported the comparison results in Table 3. The supervised method is the setting of a supervised continual learning manner, literally. We observed catastrophic forgetting in supervised learning. DRNCD is one of the NCD approaches and recorded the outstanding performances of" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 447, + 545, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 545, + 711 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_d" + }, + { + "bbox": [ + 304, + 447, + 545, + 711 + ], + "type": "text", + "content": " on MIT67, Stanford Dogs, and FGVC aircraft. However, the method requires prior knowledge of the number of novel categories and does not identify specific classes, but only knows whether the samples are included in the novel category or not. Thus, the results are not regarded as outperforming. Instead, the method shows the highest results of " + }, + { + "bbox": [ + 304, + 447, + 545, + 711 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_f" + }, + { + "bbox": [ + 304, + 447, + 545, + 711 + ], + "type": "text", + "content": ", which means that the method focuses on learning novel categories without considering the prevention of forgetting previous categorical knowledge. In this regard, NCD is not sufficient to extend novel class incremental learning schemes. FRoST showed competitive results of discovering novel classes and decreased forgetting results " + }, + { + "bbox": [ + 304, + 447, + 545, + 711 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_f" + }, + { + "bbox": [ + 304, + 447, + 545, + 711 + ], + "type": "text", + "content": " on all datasets compared to DRNCD. Nevertheless, considering the required knowledge, the other metrics results, " + }, + { + "bbox": [ + 304, + 447, + 545, + 711 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{all}" + }, + { + "bbox": [ + 304, + 447, + 545, + 711 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 447, + 545, + 711 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_o" + }, + { + "bbox": [ + 304, + 447, + 545, + 711 + ], + "type": "text", + "content": " were not competitive. GM proposed the CCD setting, which is the most similar to CGCD, in the perspective of the unknown number of novel categories and discovering novel and old categories on new unlabeled datasets. However, the method requires a crucial parameter, which is the ratio of novel category samples on the new dataset. Without considering the ratio, GM recorded the lowest results of " + }, + { + "bbox": [ + 304, + 447, + 545, + 711 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{all}" + }, + { + "bbox": [ + 304, + 447, + 545, + 711 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 447, + 545, + 711 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_o" + }, + { + "bbox": [ + 304, + 447, + 545, + 711 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 447, + 545, + 711 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_d" + }, + { + "bbox": [ + 304, + 447, + 545, + 711 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16693" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 72, + 167, + 152 + ], + "blocks": [ + { + "bbox": [ + 53, + 72, + 167, + 152 + ], + "lines": [ + { + "bbox": [ + 53, + 72, + 167, + 152 + ], + "spans": [ + { + "bbox": [ + 53, + 72, + 167, + 152 + ], + "type": "image", + "image_path": "d57f0f7fd163c035ad8deaed4eb858b99ba4becdf56a7bfd5ecefb822c8e00f5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 155, + 286, + 186 + ], + "lines": [ + { + "bbox": [ + 47, + 155, + 286, + 186 + ], + "spans": [ + { + "bbox": [ + 47, + 155, + 286, + 186 + ], + "type": "text", + "content": "(a) Novel category discovery " + }, + { + "bbox": [ + 47, + 155, + 286, + 186 + ], + "type": "inline_equation", + "content": "M_{d}" + }, + { + "bbox": [ + 47, + 155, + 286, + 186 + ], + "type": "text", + "content": " (b) Catastrophic forgetting " + }, + { + "bbox": [ + 47, + 155, + 286, + 186 + ], + "type": "inline_equation", + "content": "M_{f}" + }, + { + "bbox": [ + 47, + 155, + 286, + 186 + ], + "type": "text", + "content": " Figure 5. Performances of novel category discovery and forgetting on two-step incremental novel categories experiment" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 170, + 72, + 282, + 152 + ], + "blocks": [ + { + "bbox": [ + 170, + 72, + 282, + 152 + ], + "lines": [ + { + "bbox": [ + 170, + 72, + 282, + 152 + ], + "spans": [ + { + "bbox": [ + 170, + 72, + 282, + 152 + ], + "type": "image", + "image_path": "d101bb3a145ac9a57fc21c05c7e766c19ab5748af5a0b47878d7bf0ed081d381.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 192, + 286, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 286, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 286, + 288 + ], + "type": "text", + "content": "The proposed method showed outstanding performance on the various datasets without requiring any prior information about new incoming unlabeled datasets. Our method recorded the second-best " + }, + { + "bbox": [ + 46, + 192, + 286, + 288 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_f" + }, + { + "bbox": [ + 46, + 192, + 286, + 288 + ], + "type": "text", + "content": " on the CUB-200 dataset and the best " + }, + { + "bbox": [ + 46, + 192, + 286, + 288 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_f" + }, + { + "bbox": [ + 46, + 192, + 286, + 288 + ], + "type": "text", + "content": " on the other datasets, such as MIT67, Dogs, and FGVC aircraft, by the effects of PA-based exemplar. On " + }, + { + "bbox": [ + 46, + 192, + 286, + 288 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_d" + }, + { + "bbox": [ + 46, + 192, + 286, + 288 + ], + "type": "text", + "content": ", the method was also competitive and compared to the GM, which has the most similar setting to our method." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 289, + 286, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 286, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 286, + 384 + ], + "type": "text", + "content": "To evaluate the proposed method qualitatively, we clustered the evaluation dataset using the CUB-200 dataset. In Figure 4, our method well-discovered novel categories and clustered them correctly. Each row is clustered into the same category, and the classes are novel categories on the evaluation dataset. The left five columns are well-clustered, while the last two are not. The sixth-column images are still reasonable, but the last-columns are the worst cases." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 390, + 235, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 390, + 235, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 390, + 235, + 403 + ], + "type": "text", + "content": "4.4. Two-step Novel Category Discovery" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "text", + "content": "We present a two-step incremental category discovery experiment on the CUB-200 dataset using ResNet-18. The dataset configurations are more complicated as the datasets are joint sets in incremental steps. The initial step, the first incremental step, and the second incremental step have novel classes in each step, at a rate of " + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "inline_equation", + "content": "8:1:1" + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "text", + "content": ", respectively. Each step has its dataset and is indicated as " + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^0" + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^1" + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^2" + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "text", + "content": ". The samples belonging to novel labeled classes in the initial step are assigned to " + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^0" + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^1" + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^2" + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "text", + "content": " at a rate of " + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "inline_equation", + "content": "8:1:1" + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "text", + "content": ". Similarly, the samples belonging to novel classes in the first incremental step are assigned to " + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^1" + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^2" + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "text", + "content": " at a rate of " + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "inline_equation", + "content": "8:2" + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "text", + "content": ". Finally, the rest of the samples are assigned to " + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^2" + }, + { + "bbox": [ + 46, + 410, + 286, + 553 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 554, + 286, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 554, + 286, + 661 + ], + "spans": [ + { + "bbox": [ + 46, + 554, + 286, + 661 + ], + "type": "text", + "content": "Figure 5 describes the performance of the experiments. Since each incremental step is trained for 60 epochs, there are deep drops at the " + }, + { + "bbox": [ + 46, + 554, + 286, + 661 + ], + "type": "inline_equation", + "content": "60th" + }, + { + "bbox": [ + 46, + 554, + 286, + 661 + ], + "type": "text", + "content": " epoch when new PAs are added. In addition, the cluster accuracy of the old categories, which belong to the " + }, + { + "bbox": [ + 46, + 554, + 286, + 661 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^0" + }, + { + "bbox": [ + 46, + 554, + 286, + 661 + ], + "type": "text", + "content": ", decreases by about " + }, + { + "bbox": [ + 46, + 554, + 286, + 661 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 554, + 286, + 661 + ], + "type": "text", + "content": ". The reason is that the number of old categories in the second incremental step is increased compared to the first step. The exemplar cannot focus on only generating the features of " + }, + { + "bbox": [ + 46, + 554, + 286, + 661 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^0" + }, + { + "bbox": [ + 46, + 554, + 286, + 661 + ], + "type": "text", + "content": ". However, the performance of " + }, + { + "bbox": [ + 46, + 554, + 286, + 661 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_d" + }, + { + "bbox": [ + 46, + 554, + 286, + 661 + ], + "type": "text", + "content": " increased steadily." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 670, + 140, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 140, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 140, + 683 + ], + "type": "text", + "content": "4.5. Ablation Study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "content": "Effectiveness of separations: We conducted an ablation study to show the effectiveness of our proposed splitter," + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 306, + 72, + 545, + 190 + ], + "blocks": [ + { + "bbox": [ + 306, + 72, + 545, + 190 + ], + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 190 + ], + "type": "table", + "html": "
NetworkFine SplitMetric
Mall ↑Mo ↑Mf ↓Md ↑
ResNet-18without53.3257.6316.5636.47
with54.7558.8015.4740.90
ResNet-50without66.5371.079.1248.76
with68.0971.758.4453.79
ViT-B-16without70.2273.0210.7559.24
with72.5174.289.4965.60
", + "image_path": "36b084e67cd4bf29d2e84390ff685b6f534e730efd018940691bbf00ca37348b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 307, + 240, + 545, + 316 + ], + "blocks": [ + { + "bbox": [ + 305, + 191, + 545, + 236 + ], + "lines": [ + { + "bbox": [ + 305, + 191, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 305, + 191, + 545, + 236 + ], + "type": "text", + "content": "Table 4. Ablation study for the proposed fine split on the CUB-200 using three different network architectures, including ResNet-18 and ResNet-50 pre-trained on ImageNet, and ViT-B-16 pre-trained on DINO-ImageNet. The results present the mean over three runs." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 240, + 545, + 316 + ], + "lines": [ + { + "bbox": [ + 307, + 240, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 307, + 240, + 545, + 316 + ], + "type": "table", + "html": "
NetworkExemplarMetric
Mall ↑Mo ↑Mf ↓Md ↑
ResNet-18without38.2437.3136.8841.89
Data mean and std.40.2340.5633.6337.22
Proxy anchors54.7558.8015.4740.90
", + "image_path": "ed18a63397b5cf2a14b262e18bef9abce50bb6f55ca12fd6c8691743dee4eb2f.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 321, + 545, + 343 + ], + "lines": [ + { + "bbox": [ + 305, + 321, + 545, + 343 + ], + "spans": [ + { + "bbox": [ + 305, + 321, + 545, + 343 + ], + "type": "text", + "content": "Table 5. Effectiveness of the proposed PA-based exemplar on the CUB-200 dataset using ResNet-18 pre-trained on ImageNet" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 351, + 545, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 351, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 545, + 448 + ], + "type": "text", + "content": "which consists of a combination of two different methods: the cosine similarity score and a binary splitter using the noise label approach. The ablation experiments were designed such that one used only the cosine similarity score, and another used both methods. As shown in Table 4, the approach using both methods presents improvements in both old and novel discovery performances. The results reveal the effectiveness of noise labeling for data separation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 449, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 664 + ], + "type": "text", + "content": "Effectiveness of Proxy anchor exemplar: To mitigate catastrophic forgetting, various approaches, such as replay [2], prototype [31, 33], and pseudo-latents [15], have been proposed. Most of these methods exploit the computed average of feature embedding vectors or input data-driven values. However, we propose a novel PA-based exemplar approach and evaluate its efficiency. As shown in Table 5, the method without the exemplar recorded the highest novel discovery performances but also showed the highest forgetting. Adopting a general exemplar approach using mean and standard deviation values from the former dataset, " + }, + { + "bbox": [ + 304, + 449, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_f" + }, + { + "bbox": [ + 304, + 449, + 545, + 664 + ], + "type": "text", + "content": " slightly decreased, but " + }, + { + "bbox": [ + 304, + 449, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_d" + }, + { + "bbox": [ + 304, + 449, + 545, + 664 + ], + "type": "text", + "content": " is the lowest. However, our proposed method with the PA-based exemplar recorded the best " + }, + { + "bbox": [ + 304, + 449, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_f" + }, + { + "bbox": [ + 304, + 449, + 545, + 664 + ], + "type": "text", + "content": " and competitive " + }, + { + "bbox": [ + 304, + 449, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_d" + }, + { + "bbox": [ + 304, + 449, + 545, + 664 + ], + "type": "text", + "content": ". We analyze that the PAs have representatives of each cluster since PA inherits the relation between data to data and then representative figures of each class. Hence, our PA-based method leads to mitigating forgetting, and we confirm that it is a proper approach." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Robustness of class and sample blending ratio variants: In general, the capability to recognize novel categories largely depends on a powerful and well-trained initial model with the target datasets. The more classes and" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16694" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 284, + 167 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 284, + 167 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 284, + 167 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 284, + 167 + ], + "type": "table", + "html": "
RatioMetric
Yold: YnewMall ↑Mo ↑Mf ↓Md ↑
9:161.3463.2211.8344.73
8:254.7558.8015.4740.90
7:352.6658.4214.6739.50
6:448.7857.9015.1635.53
5:545.2862.4111.3028.55
", + "image_path": "28bf902f71b7ceb7dc7e8c0e16d01d8cbfae5581b9c55f853f7e9aa9066cade2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 172, + 286, + 195 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 172, + 286, + 195 + ], + "spans": [ + { + "bbox": [ + 49, + 172, + 286, + 195 + ], + "type": "text", + "content": "Table 6. Qualitative evaluation by changing the ratio of classes and samples on the CUB-200 using ResNet18 pre-trained on ImageNet" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 199, + 286, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 199, + 286, + 354 + ], + "spans": [ + { + "bbox": [ + 49, + 199, + 286, + 354 + ], + "type": "text", + "content": "samples are included in the initial training dataset " + }, + { + "bbox": [ + 49, + 199, + 286, + 354 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^0" + }, + { + "bbox": [ + 49, + 199, + 286, + 354 + ], + "type": "text", + "content": ", the better the model learns representative features to fit the sets. To evaluate the robustness of the proposed model, we conducted experiments with variants of the number of samples and classes in " + }, + { + "bbox": [ + 49, + 199, + 286, + 354 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^0" + }, + { + "bbox": [ + 49, + 199, + 286, + 354 + ], + "type": "text", + "content": ". As described in Table 6, decreasing the number of classes and data in the labeled set decreased the discovery of novel classes and clustering accuracies as the number of unlabeled novel data increased. On the other hand, catastrophic forgetting could increase since the number of novel data increases. However, forgetting was maintained within a reasonable boundary, indicating the effectiveness of our PA-based exemplar. The results suggest that our method has the robustness of the variants." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 363, + 129, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 363, + 129, + 374 + ], + "spans": [ + { + "bbox": [ + 49, + 363, + 129, + 374 + ], + "type": "text", + "content": "5. Related work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 49, + 382, + 189, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 382, + 189, + 395 + ], + "spans": [ + { + "bbox": [ + 49, + 382, + 189, + 395 + ], + "type": "text", + "content": "5.1. Novel Category Discovery" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 49, + 401, + 286, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 401, + 286, + 663 + ], + "spans": [ + { + "bbox": [ + 49, + 401, + 286, + 663 + ], + "type": "text", + "content": "NCD techniques have been proposed to classify data with various constraints on unlabeled data. One category of the methods presented pre-training the model on the labeled set and fine-tuning it on the unlabeled set using unsupervised clustering losses [41, 13, 12, 23, 24]. Another category assumed the availability of both the labeled and unlabeled data, and trained networks jointly with a labeled novel class loss within the semi-supervised scheme [10, 44, 45, 14, 7, 43]. Han et al. [11] proposed transferring knowledge from labeled to unlabeled data using ranking statistics in the joint learning stage. Recently, GCD [36] and XCon [6] tackled the more realistic scenario of joint datasets and distinguished known and unknown classes using prior knowledge. However, these approaches did not consider the continual learning scheme. To address the limitation, FRoST [33] and NCDwF [15] froze feature extractors and added the second head for each novel class, as much as the given number of novel categories. However, the methods employed disjoint sets. GM [42] proposed to consider novel category discovery on the joint datasets, but still require prior knowledge, such as the proportion of novel samples." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 49, + 671, + 143, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 671, + 143, + 683 + ], + "spans": [ + { + "bbox": [ + 49, + 671, + 143, + 683 + ], + "type": "text", + "content": "5.2. Image Retrieval" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 49, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 49, + 689, + 286, + 713 + ], + "type": "text", + "content": "Most of the image retrieval methods have utilized metric learning and can be categorized into two approaches." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 307, + 72, + 544, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 72, + 544, + 262 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 544, + 262 + ], + "type": "text", + "content": "Pair-based methods exploited contrastive loss [3, 5, 9] and triplet loss [34, 38], that pull together data pairs in the same class and push apart those in different classes. Multiple data-based [35, 28] methods proposed considering the relations between multiple data. Entire data-based approaches [40, 39] presented considering all data in a batch, leveraging fine-grained semantic relations between them while requiring high computation costs and slow convergence. In contrast, proxy-based methods [26, 29, 1] employed fewer proxies than the training set, reducing training complexity. While these methods improved training convergence, they did not consider data-to-data relations, as each data was associated with its proxy. PA [18] inherited the strength of pair- and proxy-based methods, achieving fast and reliable convergence, robustness opposing noisy data, and leveraging rich data-to-data relations." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 308, + 276, + 382, + 287 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 276, + 382, + 287 + ], + "spans": [ + { + "bbox": [ + 308, + 276, + 382, + 287 + ], + "type": "text", + "content": "5.3. Noise Label" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 307, + 297, + 544, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 297, + 544, + 439 + ], + "spans": [ + { + "bbox": [ + 307, + 297, + 544, + 439 + ], + "type": "text", + "content": "Recently proposed methods for learning with noisy labels have highlighted the importance of discriminating between clean and noise-labeled data to improve performance. DivideMix [22] used GMM to distinguish between clean and noisy labeled data and treated the latter as unlabeled for semi-supervised learning. AugDesc [27] employed data augmentation to enhance the differentiation between clean and noisy labeled data, while INCV [4] introduced cross-validation to separate clean data from noisy training data. SplitNet [17] leveraged a compact network to perceive the difference between clean and noisy labels, improving model performance by more accurately differentiating noise." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 447, + 376, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 447, + 376, + 459 + ], + "spans": [ + { + "bbox": [ + 308, + 447, + 376, + 459 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 307, + 469, + 544, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 469, + 544, + 647 + ], + "spans": [ + { + "bbox": [ + 307, + 469, + 544, + 647 + ], + "type": "text", + "content": "In this paper, we presented a novel continual learning scenario, considered NCD on the unlabeled joint datasets without any prior knowledge of the dataset. Our framework utilized PAs to split known and novel categories, resulting in well-clustered and well-pseudo-labeled categories that mitigate catastrophic forgetting. We further refined the splitting of the dataset by adopting a noise labeling scheme. Our proposed approach outperformed existing state-of-the-art methods regarding novel category discovery and forgetting. While DeepDPM [32] has recently shown outstanding performance on non-parametric clustering tasks, we believe that our proposed method can achieve even better performance by adopting better clustering manners. In future work, we plan to evaluate our method by adopting a better clustering manner." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 308, + 656, + 406, + 668 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 656, + 406, + 668 + ], + "spans": [ + { + "bbox": [ + 308, + 656, + 406, + 668 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 308, + 677, + 544, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 677, + 544, + 713 + ], + "spans": [ + { + "bbox": [ + 308, + 677, + 544, + 713 + ], + "type": "text", + "content": "This work was funded by Samsung Electro-Mechanics and was partially supported by Carl-Zeiss Stiftung under the Sustainable Embedded AI project (P2021-02-009)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 750, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 750, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 750, + 317, + 757 + ], + "type": "text", + "content": "16695" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "text", + "content": "[1] Nicolas Aziere and Sinisa Todorovic. 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In CVPR, 2021." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "16697" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Prune Spatio-temporal Tokens by Semantic-aware Temporal Accumulation/6db1efd1-b765-4bc8-8a5a-d2a425ae5e95_content_list.json b/2023/Prune Spatio-temporal Tokens by Semantic-aware Temporal Accumulation/6db1efd1-b765-4bc8-8a5a-d2a425ae5e95_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..5c7df746d55f45dd5e503e74ddd9143670ca7171 --- /dev/null +++ b/2023/Prune Spatio-temporal Tokens by Semantic-aware Temporal Accumulation/6db1efd1-b765-4bc8-8a5a-d2a425ae5e95_content_list.json @@ -0,0 +1,1618 @@ +[ + { + "type": "text", + "text": "Prune Spatio-temporal Tokens by Semantic-aware Temporal Accumulation", + "text_level": 1, + "bbox": [ + 106, + 130, + 864, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shuangrui Ding $^{1,3*}$ Peisen Zhao $^{2}$ Xiaopeng Zhang $^{2}$ Rui Qian $^{3}$ Hongkai Xiong $^{1}$ Qi Tian $^{2\\dagger}$ $^{1}$ Shanghai Jiao Tong University $^{2}$ Huawei Cloud $^{3}$ The Chinese University of Hong Kong", + "bbox": [ + 91, + 178, + 883, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{dsr1212, xionghongkai}@sjtu.edu.cn qr021@ie.cuhk.edu.hk", + "bbox": [ + 236, + 218, + 732, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{pszhao93, zxphistory}@gmail.com tian.qil@huawei.com", + "bbox": [ + 254, + 234, + 714, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 285, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Transformers have become the primary backbone of the computer vision community due to their impressive performance. However, the unfriendly computation cost impedes their potential in the video recognition domain. To optimize the speed-accuracy trade-off, we propose Semantic-aware Temporal Accumulation score (STA) to prune spatiotemporal tokens integrally. STA score considers two critical factors: temporal redundancy and semantic importance. The former depicts a specific region based on whether it is a new occurrence or a seen entity by aggregating token-to-token similarity in consecutive frames while the latter evaluates each token based on its contribution to the overall prediction. As a result, tokens with higher scores of STA carry more temporal redundancy as well as lower semantics thus being pruned. Based on the STA score, we are able to progressively prune the tokens without introducing any additional parameters or requiring further re-training. We directly apply the STA module to off-the-shelf ViT and VideoSwin backbones, and the empirical results on Kinetics-400 and Something-Something V2 achieve over $30\\%$ computation reduction with a negligible $\\sim 0.2\\%$ accuracy drop. The code is released at https://github.com/Mark12Ding/STA.", + "bbox": [ + 76, + 318, + 473, + 667 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 698, + 209, + 714 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, there has been an unstoppable shift in the general backbone design from Convolutional Neural Networks (ConvNets) to Transformers, which are originally employed in natural language processing, and has shown promising potential for various vision tasks [8, 48, 47, 22, 1, 32, 5]. The key component of Transformers is the self-attention mechanism, which is apt to capture long-range dependencies and empowers ViT to perceive the global reception field. The seminal work, Vision Transformer (ViT) [8]", + "bbox": [ + 75, + 724, + 470, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4d0dbe1fa17b753a288d747b7f48d471730bc428d42be77b82058ee79f0ff0e6.jpg", + "image_caption": [ + "Figure 1: Kinectics-400 result for ViT and VideoSwin. The bubble's area is proportional to FLOPs of a variant in a model family. ViT/VideoSwin here takes $16 / 32 \\times 224^2$ video. The proposed STA saves over $30\\%$ FLOPs for all model variants with a negligible drop in performance." + ], + "image_footnote": [], + "bbox": [ + 501, + 284, + 890, + 497 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "closely follows the original Transformer architecture [38]. Equipped with a large-scale model and dataset, ViT outperforms ConvNets in image classification by a considerable margin. Inspired by this superior scaling behavior, Transformers have gained popularity as a backbone choice and are widely adopted for image recognition [22, 37], action recognition [1, 23], semantic segmentation [49, 6], action detection [43, 12], temporal perception [33, 34], etc.", + "bbox": [ + 496, + 612, + 893, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the promising potential of Transformers in spatio-temporal vision tasks, such as action recognition, the quadratic increase in complexity caused by the temporal dimension makes the video Transformers computationally unfriendly compared to images. For instance, earlier work TimeSformer [2], which applies Transformer backbone for video, required 7.14 Tera FLOPs to achieve $80.7\\%$ accuracy on the Kinetics-400 action recognition benchmark. The excessive computational cost makes it impractical for deployment in real-world scenarios. Therefore, there is an urgent need to explore ways to profit from the performance gains", + "bbox": [ + 496, + 734, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work done during an internship at Huawei Cloud.", + "bbox": [ + 94, + 875, + 367, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Corresponding author. Email: tian.qi1@huawei.com.", + "bbox": [ + 96, + 887, + 382, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16945", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "of Transformers while maintaining an affordable computation burden.", + "bbox": [ + 76, + 90, + 468, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fortunately, Transformers can handle a flexible number of tokens as input. Recent attempts [31, 30, 42], that dynamically prune tokens for images, have remarkably reduced computation overhead. These pruning approaches have inspired us to explore token pruning in the video domain, so as to balance accuracy and computation costs accordingly. However, performing frame-wise pruning alone seems to be not optimal since it ignores temporal context and disrupts the dynamic structure of the video. To address this issue, recent work STTS [40] decouples token pruning into temporal and spatial dimensions. Specifically, STTS first drops meaningless frames and then filters out detail-rich regions from the remained frames. However, this spatio-temporal decoupling strategy lacks contextual modeling of continuous temporal information, leading to limited performance.", + "bbox": [ + 75, + 125, + 470, + 366 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we argue that pruning spatio-temporal tokens integrally can lead to further computation reduction at an acceptable cost of accuracy degradation. To this end, we propose the Semantic-aware Temporal Accumulation (STA) score to depict the importance of each token. We take two factors into consideration, temporal redundancy and semantic importance. Our motivation is to discard tokens that have similar counterparts appearing earlier in the sequence while retaining only semantically significant tokens. As an example, static backgrounds across all timestamps contain highly repetitive information that is unnecessary to be included. Therefore, keeping only a few representative background patches is sufficient for reasoning. Specifically, we evaluate the temporal redundancy of a region by determining whether it is a novel or previously observed entity. In practice, we aggregate repetitive information on a per-frame basis and assign each token a score of temporal repetition degree. Nevertheless, there are cases where a repetitive region reveals a crucial action and should be retained. For example, if the sequence of tokens describes human-body motion, it is necessary to keep all the tokens for better understanding, even if there are only slight differences over time. Thus, we also take semantic importance into account during the pruning procedure. To depict each token's semantic contribution to video recognition, we take the summation of the feature activation map and then integrate this summation with the score of temporal aggregation to enhance the awareness of semantics. Based on the STA score, we progressively prune the tokens of the video Transformers three times. The whole pruning process does not introduce any tuning parameter and directly accelerates the off-the-shelf video Transformers without the need to retrain.", + "bbox": [ + 75, + 368, + 470, + 867 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We apply our pruning strategy to two mainstream video Transformers, ViT [8] and VideoSwin [23], and evalu", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ate 10 off-the-shelf backbones on two action recognition benchmarks, Kinetics-400 [14] and Something-Something V2 [11], to demonstrate the effectiveness of our method. As shown in Figure 1, we achieve significant computation reduction with a negligible accuracy drop on Kinetics-400. For instance, using ViT-H as the backbone, by hierarchically pruning $57\\%$ of the input tokens, STA reduces $49\\%$ FLOPs while the accuracy drop is only $0.2\\%$ . Besides, with STA, FLOPs of VideoSwin-B are decreased by $38\\%$ while maintaining $82.5\\%$ accuracy with only a minimal drop of $0.2\\%$ . A similar trend can also be observed in the Something-Something V2 dataset. Notably, we surpass STTS [40] by a $0.4\\%$ accuracy gain with $40\\%$ fewer FLOPs on Kinetics-400 and by a $0.5\\%$ accuracy increase with $20\\%$ fewer FLOPs on Something-Something V2 when using the same backbone.", + "bbox": [ + 496, + 90, + 890, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 349, + 640, + 366 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Video Transformers. Designing Transformer-based architectures for vision tasks has emerged as a general trend in the computer vision community, as evidenced by several recent works [8, 22, 50, 28, 49, 24, 39]. With an unprecedented number of parameters and millions of training data, Transformers significantly outperform prior arts spanning a variety of tasks, not only in image but also in video understanding tasks. Various variants of self-attention have been introduced in prior works [2, 26, 47, 1, 4, 28, 9, 23, 46, 19] to capture the spatiotemporal relationship. However, using pure patch-based Transformers incurs prohibitive costs on memory and computation when extracting global-range features from the whole video. To deal with it, Motionformer [28] introduces trajectory attention that focuses on implicitly determined motion paths and optimizes the quadratic calculation via efficient decomposition. MeMViT [43] proposes caching 'memory' of past frames and attending to the summarized prior context in an online manner. In this paper, we propose an orthogonal approach to make Transformers lighter by pruning the spatio-temporal tokens with high temporal redundancy.", + "bbox": [ + 496, + 376, + 890, + 694 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Token pruning for Transformers. Several works [31, 30, 42, 20, 25, 3, 17] have focused on reducing the number of tokens involved in the calculation to accelerate image Transformer models. In specific, DynamicViT [30] trains a lightweight decision module to rate the importance of each token and prune low-score tokens progressively. EViT [20] preserves the attentive tokens guided by the class token attention and fuses inattentive ones without the help of any extra parameter. ToMe [3] combines similar tokens to directly expedite off-the-shelf ViT without needing to train. While similar to ToMe [3], our method functions as a simple plug-in to enhance off-the-shelf video Transformers without", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16946", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a4f588521d1dbc54cc829f1019c5be2e410257e8ae3adfaeca69c3be15806f53.jpg", + "image_caption": [ + "(a) Conceptual pipeline of video Transformer with STA module." + ], + "image_footnote": [], + "bbox": [ + 84, + 90, + 488, + 284 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/82820ea25b69c62596464f9266540c024dea79086d8909aad815e59dc86110c1.jpg", + "image_caption": [ + "(b) Illustration of the proposed STA module.", + "Figure 2: An overview of our STA token-pruning algorithm for video Transformers. (a) STA module is a simple plug-in and can be inserted at the beginning or end of the Transformer block. In practice, we conduct a three-stage progressive strategy to prune the token with STA. (b) Our semantic-aware temporal accumulation algorithm. The wider arrows connecting two adjacent frames represent higher weight to transport the STA score." + ], + "image_footnote": [], + "bbox": [ + 503, + 90, + 880, + 282 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "requiring additional training. However, ToMe is an image-based pruning technique that does not model any temporal relations. In contrast, our method specifically devises a temporal aggregation mechanism tailored for video data. Although STTS [40] trains a score network to choose predefined anchors from filtered frames within a video, the empirical speed-accuracy trade-off remains limited. This is because decoupled anchor-level selection still retains unwanted spatial redundancy. On the contrary, we prune the video at the token level and eliminate the meaningless content by a large margin.", + "bbox": [ + 75, + 406, + 472, + 573 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Efficient video recognition. Due to the nature of the extra dimension, video understanding is computationally intensive. Thus, there have been attempts [51, 10, 36, 44, 15, 41, 7, 18, 16, 21, 13, 29] to design lightweight modules that enjoy both high efficiency and high accuracy. ECO [51] introduces a network architecture to sample a small subset of frames and learns the temporal context between these frames. Besides, AdaFocus [41] improves the computational efficiency by adopting a light-weighted ConvNet to localize the most salient spatiotemporal regions. While previous works have mainly concentrated on accelerating ConvNet models, efforts toward accelerating video Transformers have been relatively sparse and open to exploration. A recent approach [27] devises a novel token-based sampling using k-centered search before feeding tokens into video Transformers. Although we also select semantically meaningful tokens for video Transformers, our dynamic model processes whole tokens at the early stage and prunes them based on model-dependent features.", + "bbox": [ + 75, + 613, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 500, + 404, + 609, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The goal of this paper is to develop a principal token-pruning algorithm for video Transformers that achieves an optimal balance between cost, speed, and performance without requiring model re-training. We start by analyzing the video Transformers at hand and observe two interesting phenomena, detailed in Sec. 3.3. First, we find the high temporal redundancy when comparing the interframe similarity. Second, the area that contributes to the final prediction usually takes up a small portion. Motivated by these two findings, we carefully develop two principles to prune the tokens with high temporal redundancy and retain the meaningful tokens. The overall framework is shown in Figure 2(a). Our method is mainly built on the standard columnar Transformer [8], which we briefly go through in Sec. 3.1. Later, in Sec. 3.2, we elaborate on the proposed metric to help prune unnecessary tokens. Finally, Sec. 3.3 discusses why STA works in video Transformer.", + "bbox": [ + 496, + 430, + 893, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Revisit of Video Transformer", + "text_level": 1, + "bbox": [ + 498, + 696, + 759, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Video Transformers generally process video data as a 1D sequence of tokens and directly model the relationship between them. Initially, video Transformer linearly projects 3D data tubes into high-dimensional embeddings. Assuming the dimensions of video clips as $\\{T,H,W\\}$ and the size of 3D tubes as $\\{t,h,w\\}$ , then the number of token embeddings is $n = n_t\\times n_s = |\\frac{T}{t} | \\times |\\frac{HW}{hw} |$ . Additionally, positional embeddings are added to each token to break the permutation invariance. After the patch embedding layer, an $n$ -token sequence $\\mathbf{X}\\in \\mathbb{R}^{n\\times d}$ is passed into the selfattention layer, which computes a weighted sum of the values based on the affinity of other tokens. Mathematically,", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16947", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the self-attention is formulated as:", + "bbox": [ + 76, + 90, + 307, + 104 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A t t e n t i o n} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q} \\mathbf {K} ^ {T}}{\\sqrt {d}}\\right) \\mathbf {V}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 112, + 468, + 147 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{Q},\\mathbf{K},\\mathbf{V} = f_{Q}(\\mathbf{X}),f_{K}(\\mathbf{X}),f_{V}(\\mathbf{X})\\in \\mathbb{R}^{d}$ are typically linear transformations of $\\mathbf{X}$ . After spatial-temporal interaction, the tokens are sent into a feedforward network $f_{\\mathrm{FFN}}$ , which consists of a three-layer MLP to exchange inter-channel information.", + "bbox": [ + 76, + 156, + 468, + 232 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Semantic-aware Temporal Accumulative Score", + "text_level": 1, + "bbox": [ + 76, + 241, + 468, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our intuitive criterion is to drop a token if similar tokens exist before it while reserving semantically meaningful tokens. To this end, our approach considers two factors when determining whether to retain or discard a token in the Transformer. The first is its similarity to the other tokens along the temporal axis, and the second is its contribution to the class attribute. We discuss these two principles in order.", + "bbox": [ + 75, + 265, + 470, + 371 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Temporal redundancy. Intuitively, a token should be removed if similar tokens have already existed in previous frames. Therefore, we remove tokens frame-by-frame by comparing whether similar tokens have been retained. For simplicity, we reduce a constant number of tokens in each frame to ensure parallel computing. We introduce the accumulative temporal score $\\mathbf{A} \\in [0,1]^{n_t \\times n_s}$ to model the probability of dropping a token conditioned on the specific frame $t$ . Specifically, we define:", + "bbox": [ + 75, + 388, + 468, + 525 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} _ {t, s} := \\mathbb {P} _ {\\text {d r o p}} \\left(\\mathbf {X} _ {t, s}\\right) \\in [ 0, 1 ] \\quad \\text {s . t .} \\sum_ {s = 1} ^ {n _ {s}} \\mathbf {A} _ {t, s} = 1, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 534, + 468, + 573 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where tokens with higher temporal accumulative scores are more likely to be pruned because they carry a high degree of temporal redundancy. Next, we eliminate $r$ tokens with the highest scores from $\\mathbf{A}$ at $t$ -th frame and transfer the remaining probability distribution $\\mathbf{A}_t' \\in \\mathbb{R}^{(n_s - r) \\times 1}$ to the next frame via the transition probability $\\mathbb{P}_{\\mathrm{drop}}(\\mathbf{X}_t | \\mathbf{X}_{t-1}') \\in \\mathbb{R}^{n_s \\times (n_s - r)}$ . By excluding the dropped tokens of the last frame, we effectively restart the repetition aggregation. This prevents the high scores from being concentrated on specific tokens and allows for the global identification of redundancy. Mathematically,", + "bbox": [ + 75, + 582, + 468, + 750 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} _ {t + 1} := \\mathbb {P} _ {\\text {d r o p}} \\left(\\mathbf {X} _ {t + 1} \\mid \\mathbf {X} _ {t} ^ {\\prime}\\right) \\mathbf {A} _ {t} ^ {\\prime}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 758, + 468, + 786 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {P} _ {\\text {d r o p}} \\left(\\mathbf {X} _ {t + 1} \\mid \\mathbf {X} _ {t} ^ {\\prime}\\right) := \\operatorname {s o f t m a x} \\left(f \\left(\\mathbf {X} _ {t + 1}\\right) f \\left(\\mathbf {X} _ {t} ^ {\\prime}\\right) ^ {T}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 782, + 423, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $f$ is the projection head to measure the similarity, and we construct transition probability by softmax-based affinity matrix. Note that we do not need to train a new projection head $f$ because the self-attention provides the necessary functionality, and the key function $f_{K}$ extracts most relevant knowledge for affinity estimation, as shown", + "bbox": [ + 75, + 809, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Pseudocode of STA in a PyTorch-like style." + ], + "code_body": "# x: token embedding, n_t x n_s x d\n# I: image-based token pruning method\n# r: drop number per frame\n# sim: token-to-token affinity function\n# min-max norm, Eqn.(4)\naam = norm(x.abs().sum(-1)) # size: (n_t, n_s, 1)\n# token removal at 1-st frame\nx_0 = I(x[0]) # size: (n_s-r, d)\n# initialization\nx_list, x_old = [x_0], x_0\nfor t in range(1, n_t):\n # token-to-token affinity matrix\nA_t = sim(x[t], x_old) # size: (n_s, n_s-r)\n# accumulateative temporal score\ns_acc = mm(A_t, s_acc) # size: (n_s, 1)\n# class-aware accumulative temporal score, Eqn.(5)\ns = s_acc * (1-aam[t])\ns = s.squeeze(dim=-1) # size: (n_s)\n# keep tokens with the minimal score\ni_t = s.topk(k=N-r, largest=False) # size: (n_s-r)\nx_old = x[t, i_t] # size: (n_s-r, d)\nx_list = x_list.append(x_old)\n# cut off the dropped tokens' score\ns_acc = s_acc[i_t] # size: (n_s-r, 1)\n# first-order norm\ns_acc = s_acc / s_acc-sum()", + "bbox": [ + 500, + 114, + 879, + 420 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "in Table 6c. This formulation allows us to connect all temporally distinct tokens through a simple Markov chain and aggregate potential redundancy from the first frame to every subsequent frame.", + "bbox": [ + 496, + 465, + 890, + 527 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Semantic importance. Up until this point, our approach has focused on capturing temporally repetitive information. However, we have neglected the influence of semantic attributes. In other words, we have treated each token equally, regardless of its contribution to the semantics of the class. To integrate semantics importance with our approach, we use the activation-based attention map $\\mathcal{F}$ [45], which takes the feature matrix $\\mathbf{X} \\in \\mathbb{R}^{n_t \\times n_s \\times d}$ as input and produces a score for each token in the matrix. Specifically, we define the semantic score for token $\\mathbf{X}_{t,s}$ as:", + "bbox": [ + 496, + 547, + 890, + 700 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {F} \\left(\\mathbf {X} _ {t, s}\\right) = \\sum_ {i = 1} ^ {d} \\left| \\mathbf {X} _ {t, s, i} \\right| \\in \\mathbb {R} ^ {+}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 593, + 712, + 890, + 753 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Intuitively, through the summation of absolute activation values over channel dimension, a high absolute activation suggests a significant contribution to next layers. Moreover, we apply STA on off-the-shelf Transformers supervised by semantic labels, where high activation areas tend to represent discriminative category information. Thus, activation-based attention maps could effectively capture the importance or relevance of the token to the overall semantics. We then use this score to re-weigh the temporal accumulative", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16948", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "scores $\\mathbf{A}$ , giving tokens with high semantic contributions less weight in the pruning process. This ensures that tokens with high semantics are more likely to be retained, even if they have a high degree of temporal redundancy.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we compute the semantic-aware temporal accumulative score $\\widetilde{\\mathbf{A}}_{t,s}$ by integrating the semantic score $\\mathcal{F}(\\mathbf{X}_{t,s})$ with the accumulative temporal score $\\mathbf{A}$ , i.e.,", + "bbox": [ + 76, + 152, + 468, + 196 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\mathbf {A}} _ {t, s} = \\left(1 - \\mathcal {F} \\left(\\mathbf {X} _ {t, s}\\right)\\right) \\mathbf {A} _ {t, s}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 209, + 468, + 228 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{F}(\\mathbf{X}_{t,s})$ is min-max normalized to the range [0,1]. We utilize the semantic-aware accumulative temporal scores to guide token removal for all subsequent frames, except for the first frame. Thus, we adopt an image-based token pruning method on the first frame to kick off our algorithm. Once tokens are discarded through our strategy, they are never employed in subsequent layers, thus accelerating the inference of the Transformer.", + "bbox": [ + 75, + 234, + 468, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We summarize the pseudocode of STA in Alg. 1. The algorithm takes token embedding $\\mathbf{X} \\in \\mathbb{R}^{n_t \\times n_s \\times d}$ , an image-based token pruning method $I$ , the number of tokens to drop per frame $r$ , and a token-to-token affinity function as inputs. The algorithm calculates the STA score for each frame, selects the tokens with the minimal STA score, and retains them for the next frame. This process is repeated for all frames and returns the resulting token embedding matrix with the retained tokens $\\mathbf{X}' \\in \\mathbb{R}^{n_t \\times (n_s - r) \\times d}$ .", + "bbox": [ + 75, + 354, + 468, + 489 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Summary of the superiority of STA. Compared to the previous token-pruning methods, our approach, STA, offers three significant merits when applied to video data:", + "bbox": [ + 75, + 508, + 468, + 555 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- STA fully considers the potential repetition of tokens along the temporal axis and eliminates the genuine redundancy with insignificant semantics. The temporal aggregation design makes the scoring mechanism more motion-aware and suitable for video data;", + "- STA works as a plug-in module without the introduction of additional parameters and it does not require the retraining of the video Transformer;", + "- STA achieves a complexity of $O\\left(n_{t}n_{s}\\left(n_{s}-r\\right)\\right)$ , resulting in negligible additional FLOPs that only take up a small percentage of the total forward pass. Moreover, our algorithm allows for the bulk of computation to be done in parallel, making it friendly to modern GPU devices." + ], + "bbox": [ + 94, + 565, + 468, + 796 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Overall, our approach is efficient and easily deployable, making it an ideal solution for pruning video Transformers.", + "bbox": [ + 76, + 806, + 468, + 837 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Discussion", + "text_level": 1, + "bbox": [ + 76, + 847, + 194, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we present a two-part practical analysis to shed the light on the intuition behind STA.", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/0881e4f3c9f8ccfb93e240ae1f94c0e369428ac2d2ff41155a570fa4e1c5568a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelSmallBaseLargeHuge
ViT5.105.385.075.55
Rand-ViT5.005.324.955.46
STA-ViT4.434.744.284.78
", + "bbox": [ + 532, + 89, + 859, + 154 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1: Trajectory sum for ViT family on the Kinetics-400 validation set. Compared to random pruning, STA-ViT decreases the temporal redundancy significantly.", + "bbox": [ + 498, + 165, + 890, + 210 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3c897761d68f6c4aadf932d901bbd28b2c032cc451a9c65ec3745fc4f8bb35bc.jpg", + "image_caption": [ + "Figure 3: Gradient visualization for ViT-Large on the Kinetics-400 validation set. We stack original RGB frames, gradient norm heatmap, and our pruning result from top to bottom. Our pruning algorithm preserves the area of rich semantics well." + ], + "image_footnote": [], + "bbox": [ + 506, + 229, + 890, + 385 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Does STA effectively reduce the temporal redundancy? To answer this question, we first define temporal redundancy as the frequency with which similar tokens appear at different timestamps. We then assess this phenomenon in a video by probing the last frame, denoted as $\\mathbf{X}_{-1} \\in \\mathbb{R}^{n_s \\times d}$ , and aggregating the cosine similarity between each token and the most similar tokens in previous frames. We term this aggregation as trajectory sum $S \\in \\mathbb{R}$ . Mathematically,", + "bbox": [ + 498, + 497, + 890, + 619 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS = \\frac {1}{n _ {s}} \\sum_ {i = 1} ^ {n _ {s}} \\sum_ {t = 1} ^ {n _ {t} - 1} \\max _ {j \\in \\{1, \\dots , n _ {s} \\}} \\cos - \\operatorname {s i m} \\left(\\mathbf {X} _ {- 1}, \\mathbf {X} _ {t}\\right) _ {i j}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 628, + 890, + 670 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\cos -\\sin (\\mathbf{X},\\mathbf{Y})_{ij} = \\frac{\\mathbf{X}_i\\cdot\\mathbf{Y}_j}{|\\mathbf{X}_i||\\mathbf{Y}_j|}$ . A higher trajectory sum indicates greater temporal redundancy and lower diversity along the temporal axis. When all the frames are the same, the score would reach its theoretical maximum, which is $N_{t} - 1$ . Then, we compare our method with the standard Transformer and random-prune counterparts in terms of the proposed trajectory sum. Table 1 shows that the video Transformer exhibits heavy temporal redundancy and random pruning fails to alleviate them considerably. In contrast, STA achieves a far lower trajectory sum, indicating that it effectively eliminates temporal redundancy.", + "bbox": [ + 498, + 681, + 890, + 852 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Does STA retain semantics-rich tokens? To manifest it, we calculate the gradient norm for each token when back-", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16949", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "propagating the training loss $\\mathcal{L}$ . We then aggregated the first-order gradient norm of $\\mathbf{X}^l$ at each layer $l$ to obtain the GradNorm, which reflects the contribution of each token to the final prediction. Mathematically,", + "bbox": [ + 75, + 90, + 470, + 151 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {G r a d N o r m} (\\mathbf {X}) = \\sum_ {l = 1} ^ {L} \\sum_ {i = 1} ^ {d} \\left| \\frac {\\partial \\mathcal {L}}{\\partial \\mathbf {X} _ {.. , i} ^ {l}} \\right| \\in \\mathbb {R} ^ {n _ {t} \\times n _ {s}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 166, + 468, + 209 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $L$ is the total number of the Transformer block, e.g., $L = 24$ for ViT-Large. Figure 3 shows the GradNorm distribution in the form of a heatmap. The heatmap reveals sparse patterns across the board, indicating that most tokens do not contribute significantly to the final prediction. Instead, the key regions responsible for the final prediction are usually motion-centric entities. This agrees with our intuition of highlighting semantically meaningful regions. With the help of activation-based attention map $\\mathcal{F}$ in Eqn. (4), STA retains almost all areas of high-activation GradNorm as is evidenced in the last row of Figure 3.", + "bbox": [ + 75, + 222, + 470, + 388 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 409, + 209, + 425 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 435, + 266, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets and backbones. We evaluate our algorithm on two standard video action recognition datasets. Kinetics-400 [14] (K400) and Something-Something V2 [11] (SSV2). Kinetics-400 is a large-scale action recognition dataset sourced from YouTube, which consists of around 10-second clips with 400 human action classes. The training and validation set has approximately $240\\mathrm{K}$ and $20\\mathrm{K}$ videos, respectively. Something-Something V2 is a motion-heavy benchmark with 174 labels, where the object and background are shared across the different action categories. Around $170\\mathrm{K}$ and $25\\mathrm{K}$ videos exist in the training and validation set of SSV2, respectively. We implement our STA strategy with two mainstream Transformer-based backbones, namely ViT [8] and VideoSwin [23]. For ViT, we sample 16 frames with $224^2$ pixels as input and the size of 3D tube is $\\{2,16,16\\}$ . Therefore, the number of tokens for all layers is $n = \\frac{16}{2} \\times \\frac{224^2}{16^2} = 8 \\times 14^2$ . We load the open-sourced checkpoints from VideoMAE [35] due to its superior performance. For VideoSwin, the input resolution is $32 \\times 224^2$ and the size of 3D tube is $\\{2,4,4\\}$ . The number of tokens at four hierarchical stages would be $\\{16 \\times 56^2, 16 \\times 28^2, 16 \\times 14^2, 16 \\times 7^2\\}$ . Though our algorithm is not intended for window-based Transformers that require structural integrity, we still find a simple solution. We compensate for the discarded token with the nearest kept tokens when computing the window attention and speed up the rest of the process, such as the linear projection. In total, we test 10 off-the-shelf backbones with different pre-trained weights on two benchmarks.", + "bbox": [ + 75, + 460, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. To progressively remove inattentive tokens, we apply our STA module three times. For ViT, we insert our STA module at the end of the $1^{st}$ , $(1 + L/3)^{th}$ , $(1 + 2L/3)^{th}$ block, where $L$ is the total number of Transformer blocks. For VideoSwin, there are four hierarchical stages with varied resolutions and the STA module is located at the end of the first three stages. We denote different variants of STA as $\\mathrm{STA}^{r_1}$ -Model, where $r_1$ is the number of spatial tokens dropped per frame at the first stage. We adopt a decreasing schedule, which reduces the dropped number by half at each stage. For instance, $\\mathrm{STA}^{64}$ -ViT-L indicates pruning $\\{8 \\times 64, 8 \\times 32, 8 \\times 16\\}$ tokens on ViT-Large. We weigh the computation via two metrics, FLOPs (floating-point operations) and throughput. FLOPs are reported with the help of fvcore library1 and throughput (clips/s) is measured at a batch size of 32 on a single 32G Tesla V100. Besides, we closely follow the inference metric for ViT and VideoSwin in [35, 23].", + "bbox": [ + 496, + 90, + 890, + 363 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- ViT [35]: To evaluate on K400, we sample $5 \\times 3$ views by uniformly selecting 5 16-frame clips from a full-length video in the temporal dimension with the frame stride of 4. For each clip, we resize the shorter spatial side to 224 pixels and extract 3 crops of $224 \\times 224$ resolution that cover the longer spatial axis. The final score is the average score computed over all views. For SSV2, we follow a similar procedure by sampling 2 clips $\\times 3$ crops and the frames stride is 2.", + "- VideoSwin [23]: For K400, we extract 4 32-frame clips from each full-length video using a temporal stride of 2 and a spatial size of $224 \\times 224$ . Similarly, for SSV2, we extract 1 set of clips using a spatial size of $224 \\times 224$ and 3 spatial crops, with a frame stride of 2. Besides, we prune VideoSwin three times as $\\{r_1, 1.5r_1/4, 2r_1/16\\}$ . For instance, $\\mathrm{STA}^{256}$ -VideoSwin-S indicates pruning $\\{16 \\times 256, 16 \\times 96, 16 \\times 32\\}$ on VideoSwin-S." + ], + "bbox": [ + 517, + 369, + 890, + 652 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Main Results", + "text_level": 1, + "bbox": [ + 500, + 659, + 638, + 674 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct a thorough investigation of two off-the-shelf model families, ViT [8] and VideoSwin [23], on the Kinetics-400 and Something-Something V2 datasets. The results presented in Table 2 demonstrate that our proposed method can significantly reduce the computational costs of ViT models by $25\\% \\sim 49\\%$ , with negligible impacts on performance $(-0.2\\% \\sim -1.0\\%)$ . It is worth noting our method shows a favorable trade-off between complexity and performance for larger models. For instance, our method reduces the FLOPs of ViT-Huge by half to just 611 GFLOPs, with only a $0.2\\%$ drop in accuracy.", + "bbox": [ + 496, + 681, + 890, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To demonstrate the potential of our method to generalize well on various transformer backbones, we are conducting", + "bbox": [ + 500, + 848, + 890, + 878 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "", + "bbox": [ + 517, + 887, + 857, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16950", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c6c8634ad72c0b464a017222ff0e867b72b0ccdee1460a469febb8b22bc5f28a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Base ModelMetricsDrop Number r1
0324864
ViT-SK400 Acc. (%)78.878.8 (-0.0)78.6 (-0.2)78.1 (-0.7)
SSV2 Acc. (%)66.866.6 (-0.2)66.4 (-0.4)65.8 (-1.0)
GFLOPs5742 (-26%)35 (-39%)29 (-49%)
ViT-BK400 Acc. (%)81.281.2 (-0.0)81.1 (-0.1)80.8 (-0.4)
SSV2 Acc. (%)70.670.4 (-0.2)70.3 (-0.3)69.9 (-0.7)
GFLOPs180136 (-24%)116 (-36%)96 (-47%)
ViT-LK400 Acc. (%)85.185.2 (+0.1)85.1 (-0.0)85.0 (-0.1)
GFLOPs597446 (-25%)376 (-37%)308 (-48%)
ViT-HK400 Acc. (%)86.386.3 (-0.0)86.2 (-0.1)86.1 (-0.2)
GFLOPs1192890 (-25%)748 (-37%)611 (-49%)
", + "bbox": [ + 122, + 88, + 848, + 287 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c4befaa4a0459d0d1f9940eaf24caa3923664776b8c9bd6706e9115421295e98.jpg", + "table_caption": [ + "Table 2: Main Results for STA-ViT family on Kinetics-400 [14] (K400) and Something-Something V2 [11] (SSV2). All input resolution is ${16} \\times {224}^{2}$ ." + ], + "table_footnote": [], + "table_body": "
Base ModelMetricsDrop Number r1
0192256320
VideoSwin-TK400 Acc. (%)78.878.7 (-0.1)78.7 (-0.1)78.6 (-0.2)
GFLOPs8868 (-23%)61 (-31%)54 (-39%)
VideoSwin-SK400 Acc. (%)80.580.3 (-0.2)80.2 (-0.3)80.1 (-0.4)
GFLOPs166121 (-27%)106 (-36%)91 (-45%)
VideoSwin-BK400 Acc. (%)82.782.5 (-0.2)82.5 (-0.2)82.3 (-0.4)
K400 GFLOPs282202 (-28%)176 (-38%)149 (-47%)
SSV2 Acc. (%)69.669.6 (-0.0)69.5 (-0.1)69.2 (-0.4)
SSV2 GFLOPs321241 (-25%)215 (-33%)188 (-41%)
", + "bbox": [ + 122, + 342, + 848, + 512 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3: Main Results for STA-VideoSwin family on Kinetics-400 [14] (K400) and Something-Something V2 [11] (SSV2). All input resolution is $32 \\times 224^2$ . VideoSwin-B employs varying window sizes for K400 and SSV2, leading to a discrepancy in FLOPs.", + "bbox": [ + 75, + 522, + 892, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "further experiments on VideoSwin [23], a modern architecture that uses a window shuffling operation to interchange information. As VideoSwin is naturally unsuitable for unstructured tokens, we are filling the dropped locations during the window attention operation with the nearest tokens and then discarding the replicated tokens after the attention operation. Empirical results in Table 3 indicate that the performance of VideoSwin holds until FLOPs fall by roughly $40\\%$ . This observation verifies that both columnar ViT and hierarchical VideoSwin have heavy and unnecessary computations that can be significantly optimized.", + "bbox": [ + 75, + 595, + 472, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with the state of the art. Firstly, we tabulate a comparison of our proposed method on K400 in Table 4. Our model performs favorably in terms of both accuracy and computation cost. For example, ViT-L equipped with our STA achieves the same accuracy as MViTv2-L [19] but with less than a quarter of the computational cost. Moreover, STTS [40] proposes a scorer network to conduct dynamic token selection separately in space and time, re", + "bbox": [ + 75, + 779, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "quiring to be trained in an end-to-end fashion. Our result surpasses STTS by $0.4\\%$ accuracy using the same backbone VideoSwin-B but with only $60\\%$ GFLOPs. This result verifies that leveraging the model itself to weigh the redundancy of tokens is sufficient to reduce complexity. We also report the result on SSV2 in Table 5. The superior performance of our proposed method verifies that STA prunes the inconsequential tokens via temporal cues, as it is known that understanding SSV2 mainly relies on temporal information. Specifically, ViT-B equipped with our STA surpasses most of the prior arts with a considerably minor complexity of 116 GFLOPs. For VideoSwin, our strategy outperforms STTS-VideoSwin by $0.5\\%$ accuracy with $80\\%$ of the computation cost.", + "bbox": [ + 496, + 595, + 893, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visualization of STA. Figure 4 shows image patches corresponding to kept tokens after three stages. The results align with our objective of resisting temporal redundancy and retaining informative tokens. In a tennis sequence, STA preserves the most meaningful patches, including a human", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16951", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5ae05975b7b09580bca91c98a7a0fadfae6b0d362bbd101833aba60c03352377.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelGFLOPs×viewsTop-1
TimeSformer-L [2]8353 × 1 × 380.7
Motionformer-L [28]1185 × 10 × 380.2
ViViT [1]3981 × 4 × 384.9
Swin-L [23]2107 × 10 × 584.9
MViTv2-L [19]2828 × 5 × 386.1
ViT-H [35]1192 × 5 × 386.3
STTS-VideoSwin-B [40]253 × 4 × 381.9
ToMe-ViT-L [3]281 × 10 × 184.5
STA320-VideoSwin-B (ours)149 × 4 × 382.3
STA64-ViT-L (ours)308 × 5 × 385.0
STA64-ViT-H (ours)611 × 5 × 386.1
", + "bbox": [ + 83, + 88, + 464, + 265 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e369bd42deace75edce0ccb0b28cec4e8006a58a1508ee3af983ab38ba97b8c0.jpg", + "table_caption": [ + "Table 4: Comparisons with the-state-of-the-arts method on Kinetics-400. We report the computational cost with a single view (temporal clip with spatial crop) $\\times$ the number of views (FLOPs $\\times$ view_time $\\times$ view_space). Gray represents that this method leverages the dynamic token pooling to optimize existing backbones." + ], + "table_footnote": [], + "table_body": "
ModelGFLOPs×viewsTop-1
TimeSformer-L [2]5549 × 1 × 362.4
Motionformer-L [28]1185 × 1 × 368.1
MViTv2-B [19]225 × 1 × 370.5
VideoSwin-B [23]321 × 1 × 369.6
ViT-B [35]180 × 2 × 370.6
STTS-VideoSwin-B [40]237 × 1 × 368.7
STA320-VideoSwin-B (ours)188 × 1 × 369.2
STA48-ViT-B (ours)116 × 2 × 370.3
", + "bbox": [ + 83, + 382, + 464, + 517 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5: Comparisons with the-state-of-the-arts method on Something-Something V2. We report the computational cost with a single view (temporal clip with spatial crop) $\\times$ the number of views (FLOPs $\\times$ view_time $\\times$ view_space). Gray represents that this method leverages the dynamic token pooling to optimize existing backbones.", + "bbox": [ + 75, + 527, + 468, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "at the far end of the court, and filters out dull backgrounds like the blue ground. The temporal aggregation design ensures that the kept tokens are not just the most salient ones but also a variety of regions, preserving diversity within videos for better reasoning.", + "bbox": [ + 75, + 646, + 468, + 723 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 734, + 230, + 750 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To find the optimal strategy, we conduct a series of ablation studies. We evaluate off-the-shelf ViT-Large on K400 by default and report accuracy, FLOPs, and throughput for reference unless otherwise stated.", + "bbox": [ + 75, + 757, + 468, + 818 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Token removal at the first frame. To investigate how the first-frame removal affects performance, we conduct experiments on three candidates. (1) Random Prune: we randomly select $r$ tokens to discard. (2) Grid Prune: we split", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c401b239dc7f3c940ac06a72286fd4519fad726731758551bbf5838e1f2dc50e.jpg", + "image_caption": [ + "Figure 4: Visualization of the proposed STA strategy. We masked out the discarded tokens with white boxes. STA not only retains informative tokens but also ensures diverse regions for improved video reasoning." + ], + "image_footnote": [], + "bbox": [ + 506, + 92, + 893, + 300 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the first frame into $\\sqrt{r} \\times \\sqrt{r}$ grids spatially and drop one random token per grid. (3) ToMe Prune: inspired by recent image pruning method ToMe [3], we get rid of the most similar tokens by the simple bipartite soft matching. The difference here is that we just drop tokens rather than 'merge' tokens. Note that all three pruning ways are negligible in the terms of computation and lead to similar speedup. It actually echoes the main insight of STA, leveraging temporal aggregation to reduce spatio-temporal redundancy. Even given a random initialization state, the sequential STA strategy could still decrease the total temporal redundancy and optimize the video Transformers effectively.", + "bbox": [ + 496, + 396, + 890, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Pruning schedule. We explore how to assign the number of dropping tokens among three stages. When maintaining a similar throughput, we devise three types of schedules:", + "bbox": [ + 496, + 595, + 890, + 643 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Constant Schedule: $\\{8\\times 48,8\\times 48,8\\times 48\\}$", + "bbox": [ + 547, + 666, + 849, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Decreasing Schedule: $\\{8\\times 64,8\\times 32,8\\times 16\\}$", + "bbox": [ + 535, + 685, + 849, + 700 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Increasing Schedule: $\\{8\\times 27,8\\times 54,8\\times 108\\}$", + "bbox": [ + 539, + 704, + 854, + 720 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Table 6d, the decreasing schedule owns the least accuracy reduction with similar throughput. It verifies that standard video Transformers process a great number of uninformative tokens that can be dropped at the beginning.", + "bbox": [ + 496, + 729, + 893, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Temporal accumulation order. Besides starting the accumulation flow from the beginning of the input video, we could also kick off at the ending frames. In Table 6b, we empirically find alternating order at different dropping stages outperforms the consistent counterparts. We speculate that the same accumulation direction would amplify", + "bbox": [ + 496, + 809, + 890, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16952", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9cf4e27c70537d6aadbdfb7a1ba980e8c5e5e6b80be13bb5e697c590a6d9af6b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodTop-1Top-5
Random84.7896.46
Grid84.8596.50
ToMe84.9696.50
", + "bbox": [ + 138, + 101, + 349, + 172 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/39fbe1d843eebe4f343900ffca84e93aed1cade817f91e63ec9e5b7a5be6c326.jpg", + "table_caption": [], + "table_footnote": [ + "(a) Ablation on token removal meth- (b) Ablation on temporal accumula- (c) Ablation on different similarity ods at the first frame. tion order. function $f$" + ], + "table_body": "
OrderTop-1Top-5
F-B-F84.9696.50
B-F-B84.9796.43
F-F-F84.2696.41
B-B-B84.3596.37
", + "bbox": [ + 385, + 101, + 584, + 186 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/abb5240217cae4690cb6d5a1c3055daa36a143b2032dd2e20a6302f6bceee9ff.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SimilarityTop-1Top-5
fQ84.8396.52
fK84.9696.50
fV84.8496.50
fFFN84.9496.50
", + "bbox": [ + 614, + 101, + 834, + 186 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/c6e76c93019191063fce8cfeedc5049ff38cff14a56764cc3d8b7eecd0947678.jpg", + "table_caption": [], + "table_footnote": [ + "(d) Ablation on dropping schedule among three stages." + ], + "table_body": "
ScheduleTop-1Top-5clips/s
constant84.6896.3647
decreasing84.9696.5047
increasing77.6893.7244
", + "bbox": [ + 147, + 232, + 437, + 301 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/ee089e3934323f197a0f892c7ccf4b4e791cd03ea1ef239432233f137f06028d.jpg", + "table_caption": [], + "table_footnote": [ + "(e) Ablation on scoring mechanism. Top-1 is reported." + ], + "table_body": "
ScoreViT-SViT-BViT-L
1 - F(Xt,s)77.3380.5284.87
At,s77.7880.4384.69
(1 - F(Xt,s))At,s78.1280.8284.96
", + "bbox": [ + 514, + 232, + 839, + 301 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 6: Results of STA ablation experiments. F and B in (b) mean forward and backward order, respectively. The baseline ViT-L without STA obtains $85.05\\%$ Top-1 and $96.55\\%$ Top-5 accuracy on K400 at 19.5 clips/s. Gray is our default setting.", + "bbox": [ + 75, + 330, + 890, + 363 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "intrinsic propagation error but alternating the order counteracts it, leading to more reasonable pruning.", + "bbox": [ + 75, + 390, + 468, + 421 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Similarity function choice. We ablate four similarity project heads $\\{f_{Q}, f_{V}, f_{K}, f_{\\mathrm{FFN}}\\}$ . Table 6c shows that key function $f_{k}$ captures the most correct affinity with minimal noise. The observation coincides with previous work [3].", + "bbox": [ + 75, + 440, + 468, + 502 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Scoring mechanism. To explore how accumulation score and semantic identification boost each other, we conduct the experiment with different scoring formulas. Table 6e demonstrates that considering both temporal redundancy and semantics helps in discovering informative tokens. The results on ViT-S show that temporal aggregation modeled by the Markov Chain plays an important role in the pruning process, while semantic importance functions effectively for ViT-B and ViT-L.", + "bbox": [ + 75, + 521, + 468, + 657 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Performance vs. prune number $r$ . To seek the sweet spot of our algorithm, we vary the prune number $r$ at the first stage ranging from [16, 96] and evaluate the Top-1 accuracy. In addition, we compare our STA with the Random pruning baseline. As displayed in Figure. 5, STA behaves fairly robust to the token reduction and consistently surpasses the result of the random pruning. Specifically, $r = 64$ doubles the throughput but just drops $0.1\\%$ accuracy. This confirms that our algorithm retains the semantics-rich tokens with the lowest redundancy.", + "bbox": [ + 75, + 678, + 468, + 830 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 844, + 194, + 859 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In conclusion, we propose a new token pruning strategy, Semantic-aware Temporal Accumulation (STA), for", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/cd7ee016dbe8da99d81d462383b9944042512bf9dd7dc65cfd3993fb9557fcab.jpg", + "image_caption": [ + "Figure 5: Top-1 accuracy and throughput under two pruning methods with various prune numbers $r$ ." + ], + "image_footnote": [], + "bbox": [ + 513, + 390, + 874, + 597 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "video Transformers that can significantly reduce computation overhead with a subtle accuracy drop. Specifically, we consider temporal redundancy and semantic importance when deciding to keep or drop the token. Our approach does not introduce any parameter and can directly accelerate the off-the-shelf video Transformers without training. The extensive experiments demonstrate that our method empowers video Transformers to obtain a competitive speed-accuracy trade-off compared to the prior arts.", + "bbox": [ + 496, + 650, + 890, + 787 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 800, + 660, + 816 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported in part by the National Natural Science Foundation of China under Grant 62250055, Grant 61932022, Grant 62120106007, and in part by the Program of Shanghai Science and Technology Innovation Project under Grant 20511100100.", + "bbox": [ + 496, + 824, + 890, + 898 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "16953", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. 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In Proceedings of the European conference on computer vision (ECCV), pages 695-712, 2018. 3" + ], + "bbox": [ + 78, + 90, + 468, + 357 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "16956", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Prune Spatio-temporal Tokens by Semantic-aware Temporal Accumulation/6db1efd1-b765-4bc8-8a5a-d2a425ae5e95_model.json b/2023/Prune Spatio-temporal Tokens by Semantic-aware Temporal Accumulation/6db1efd1-b765-4bc8-8a5a-d2a425ae5e95_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2aafe0289ba4fa6e0736f256aa8da3b38aa5a7a6 --- /dev/null +++ b/2023/Prune Spatio-temporal Tokens by Semantic-aware Temporal Accumulation/6db1efd1-b765-4bc8-8a5a-d2a425ae5e95_model.json @@ -0,0 +1,2270 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.107, + 0.131, + 0.865, + 0.154 + ], + "angle": 0, + "content": "Prune Spatio-temporal Tokens by Semantic-aware Temporal Accumulation" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.179, + 0.884, + 0.218 + ], + "angle": 0, + "content": "Shuangrui Ding\\(^{1,3*}\\) Peisen Zhao\\(^{2}\\) Xiaopeng Zhang\\(^{2}\\) Rui Qian\\(^{3}\\) Hongkai Xiong\\(^{1}\\) Qi Tian\\(^{2\\dagger}\\) \n\\(^{1}\\)Shanghai Jiao Tong University \\(^{2}\\)Huawei Cloud \\(^{3}\\)The Chinese University of Hong Kong" + }, + { + "type": "text", + "bbox": [ + 0.238, + 0.219, + 0.733, + 0.235 + ], + "angle": 0, + "content": "{dsr1212, xionghongkai}@sjtu.edu.cn qr021@ie.cuhk.edu.hk" + }, + { + "type": "text", + "bbox": [ + 0.255, + 0.236, + 0.715, + 0.252 + ], + "angle": 0, + "content": "{pszhao93, zxphistory}@gmail.com tian.qil@huawei.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.286, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.319, + 0.474, + 0.668 + ], + "angle": 0, + "content": "Transformers have become the primary backbone of the computer vision community due to their impressive performance. However, the unfriendly computation cost impedes their potential in the video recognition domain. To optimize the speed-accuracy trade-off, we propose Semantic-aware Temporal Accumulation score (STA) to prune spatiotemporal tokens integrally. STA score considers two critical factors: temporal redundancy and semantic importance. The former depicts a specific region based on whether it is a new occurrence or a seen entity by aggregating token-to-token similarity in consecutive frames while the latter evaluates each token based on its contribution to the overall prediction. As a result, tokens with higher scores of STA carry more temporal redundancy as well as lower semantics thus being pruned. Based on the STA score, we are able to progressively prune the tokens without introducing any additional parameters or requiring further re-training. We directly apply the STA module to off-the-shelf ViT and VideoSwin backbones, and the empirical results on Kinetics-400 and Something-Something V2 achieve over \\(30\\%\\) computation reduction with a negligible \\(\\sim 0.2\\%\\) accuracy drop. The code is released at https://github.com/Mark12Ding/STA." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.699, + 0.21, + 0.715 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.726, + 0.471, + 0.864 + ], + "angle": 0, + "content": "Recently, there has been an unstoppable shift in the general backbone design from Convolutional Neural Networks (ConvNets) to Transformers, which are originally employed in natural language processing, and has shown promising potential for various vision tasks [8, 48, 47, 22, 1, 32, 5]. The key component of Transformers is the self-attention mechanism, which is apt to capture long-range dependencies and empowers ViT to perceive the global reception field. The seminal work, Vision Transformer (ViT) [8]" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.285, + 0.891, + 0.498 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.507, + 0.895, + 0.584 + ], + "angle": 0, + "content": "Figure 1: Kinectics-400 result for ViT and VideoSwin. The bubble's area is proportional to FLOPs of a variant in a model family. ViT/VideoSwin here takes \\(16 / 32 \\times 224^2\\) video. The proposed STA saves over \\(30\\%\\) FLOPs for all model variants with a negligible drop in performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.895, + 0.734 + ], + "angle": 0, + "content": "closely follows the original Transformer architecture [38]. Equipped with a large-scale model and dataset, ViT outperforms ConvNets in image classification by a considerable margin. Inspired by this superior scaling behavior, Transformers have gained popularity as a backbone choice and are widely adopted for image recognition [22, 37], action recognition [1, 23], semantic segmentation [49, 6], action detection [43, 12], temporal perception [33, 34], etc." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Despite the promising potential of Transformers in spatio-temporal vision tasks, such as action recognition, the quadratic increase in complexity caused by the temporal dimension makes the video Transformers computationally unfriendly compared to images. For instance, earlier work TimeSformer [2], which applies Transformer backbone for video, required 7.14 Tera FLOPs to achieve \\(80.7\\%\\) accuracy on the Kinetics-400 action recognition benchmark. The excessive computational cost makes it impractical for deployment in real-world scenarios. Therefore, there is an urgent need to explore ways to profit from the performance gains" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.369, + 0.888 + ], + "angle": 0, + "content": "*Work done during an internship at Huawei Cloud." + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.383, + 0.9 + ], + "angle": 0, + "content": "†Corresponding author. Email: tian.qi1@huawei.com." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.383, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16945" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "of Transformers while maintaining an affordable computation burden." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.125, + 0.471, + 0.367 + ], + "angle": 0, + "content": "Fortunately, Transformers can handle a flexible number of tokens as input. Recent attempts [31, 30, 42], that dynamically prune tokens for images, have remarkably reduced computation overhead. These pruning approaches have inspired us to explore token pruning in the video domain, so as to balance accuracy and computation costs accordingly. However, performing frame-wise pruning alone seems to be not optimal since it ignores temporal context and disrupts the dynamic structure of the video. To address this issue, recent work STTS [40] decouples token pruning into temporal and spatial dimensions. Specifically, STTS first drops meaningless frames and then filters out detail-rich regions from the remained frames. However, this spatio-temporal decoupling strategy lacks contextual modeling of continuous temporal information, leading to limited performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.369, + 0.471, + 0.868 + ], + "angle": 0, + "content": "In this paper, we argue that pruning spatio-temporal tokens integrally can lead to further computation reduction at an acceptable cost of accuracy degradation. To this end, we propose the Semantic-aware Temporal Accumulation (STA) score to depict the importance of each token. We take two factors into consideration, temporal redundancy and semantic importance. Our motivation is to discard tokens that have similar counterparts appearing earlier in the sequence while retaining only semantically significant tokens. As an example, static backgrounds across all timestamps contain highly repetitive information that is unnecessary to be included. Therefore, keeping only a few representative background patches is sufficient for reasoning. Specifically, we evaluate the temporal redundancy of a region by determining whether it is a novel or previously observed entity. In practice, we aggregate repetitive information on a per-frame basis and assign each token a score of temporal repetition degree. Nevertheless, there are cases where a repetitive region reveals a crucial action and should be retained. For example, if the sequence of tokens describes human-body motion, it is necessary to keep all the tokens for better understanding, even if there are only slight differences over time. Thus, we also take semantic importance into account during the pruning procedure. To depict each token's semantic contribution to video recognition, we take the summation of the feature activation map and then integrate this summation with the score of temporal aggregation to enhance the awareness of semantics. Based on the STA score, we progressively prune the tokens of the video Transformers three times. The whole pruning process does not introduce any tuning parameter and directly accelerates the off-the-shelf video Transformers without the need to retrain." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We apply our pruning strategy to two mainstream video Transformers, ViT [8] and VideoSwin [23], and evalu" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.332 + ], + "angle": 0, + "content": "ate 10 off-the-shelf backbones on two action recognition benchmarks, Kinetics-400 [14] and Something-Something V2 [11], to demonstrate the effectiveness of our method. As shown in Figure 1, we achieve significant computation reduction with a negligible accuracy drop on Kinetics-400. For instance, using ViT-H as the backbone, by hierarchically pruning \\(57\\%\\) of the input tokens, STA reduces \\(49\\%\\) FLOPs while the accuracy drop is only \\(0.2\\%\\). Besides, with STA, FLOPs of VideoSwin-B are decreased by \\(38\\%\\) while maintaining \\(82.5\\%\\) accuracy with only a minimal drop of \\(0.2\\%\\). A similar trend can also be observed in the Something-Something V2 dataset. Notably, we surpass STTS [40] by a \\(0.4\\%\\) accuracy gain with \\(40\\%\\) fewer FLOPs on Kinetics-400 and by a \\(0.5\\%\\) accuracy increase with \\(20\\%\\) fewer FLOPs on Something-Something V2 when using the same backbone." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.351, + 0.642, + 0.367 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.377, + 0.892, + 0.695 + ], + "angle": 0, + "content": "Video Transformers. Designing Transformer-based architectures for vision tasks has emerged as a general trend in the computer vision community, as evidenced by several recent works [8, 22, 50, 28, 49, 24, 39]. With an unprecedented number of parameters and millions of training data, Transformers significantly outperform prior arts spanning a variety of tasks, not only in image but also in video understanding tasks. Various variants of self-attention have been introduced in prior works [2, 26, 47, 1, 4, 28, 9, 23, 46, 19] to capture the spatiotemporal relationship. However, using pure patch-based Transformers incurs prohibitive costs on memory and computation when extracting global-range features from the whole video. To deal with it, Motionformer [28] introduces trajectory attention that focuses on implicitly determined motion paths and optimizes the quadratic calculation via efficient decomposition. MeMViT [43] proposes caching 'memory' of past frames and attending to the summarized prior context in an online manner. In this paper, we propose an orthogonal approach to make Transformers lighter by pruning the spatio-temporal tokens with high temporal redundancy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Token pruning for Transformers. Several works [31, 30, 42, 20, 25, 3, 17] have focused on reducing the number of tokens involved in the calculation to accelerate image Transformer models. In specific, DynamicViT [30] trains a lightweight decision module to rate the importance of each token and prune low-score tokens progressively. EViT [20] preserves the attentive tokens guided by the class token attention and fuses inattentive ones without the help of any extra parameter. ToMe [3] combines similar tokens to directly expedite off-the-shelf ViT without needing to train. While similar to ToMe [3], our method functions as a simple plug-in to enhance off-the-shelf video Transformers without" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16946" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.092, + 0.49, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.287, + 0.503, + 0.302 + ], + "angle": 0, + "content": "(a) Conceptual pipeline of video Transformer with STA module." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.092, + 0.882, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.552, + 0.288, + 0.825, + 0.302 + ], + "angle": 0, + "content": "(b) Illustration of the proposed STA module." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.319, + 0.895, + 0.381 + ], + "angle": 0, + "content": "Figure 2: An overview of our STA token-pruning algorithm for video Transformers. (a) STA module is a simple plug-in and can be inserted at the beginning or end of the Transformer block. In practice, we conduct a three-stage progressive strategy to prune the token with STA. (b) Our semantic-aware temporal accumulation algorithm. The wider arrows connecting two adjacent frames represent higher weight to transport the STA score." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.407, + 0.473, + 0.574 + ], + "angle": 0, + "content": "requiring additional training. However, ToMe is an image-based pruning technique that does not model any temporal relations. In contrast, our method specifically devises a temporal aggregation mechanism tailored for video data. Although STTS [40] trains a score network to choose predefined anchors from filtered frames within a video, the empirical speed-accuracy trade-off remains limited. This is because decoupled anchor-level selection still retains unwanted spatial redundancy. On the contrary, we prune the video at the token level and eliminate the meaningless content by a large margin." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Efficient video recognition. Due to the nature of the extra dimension, video understanding is computationally intensive. Thus, there have been attempts [51, 10, 36, 44, 15, 41, 7, 18, 16, 21, 13, 29] to design lightweight modules that enjoy both high efficiency and high accuracy. ECO [51] introduces a network architecture to sample a small subset of frames and learns the temporal context between these frames. Besides, AdaFocus [41] improves the computational efficiency by adopting a light-weighted ConvNet to localize the most salient spatiotemporal regions. While previous works have mainly concentrated on accelerating ConvNet models, efforts toward accelerating video Transformers have been relatively sparse and open to exploration. A recent approach [27] devises a novel token-based sampling using k-centered search before feeding tokens into video Transformers. Although we also select semantically meaningful tokens for video Transformers, our dynamic model processes whole tokens at the early stage and prunes them based on model-dependent features." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.405, + 0.61, + 0.423 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.431, + 0.895, + 0.688 + ], + "angle": 0, + "content": "The goal of this paper is to develop a principal token-pruning algorithm for video Transformers that achieves an optimal balance between cost, speed, and performance without requiring model re-training. We start by analyzing the video Transformers at hand and observe two interesting phenomena, detailed in Sec. 3.3. First, we find the high temporal redundancy when comparing the interframe similarity. Second, the area that contributes to the final prediction usually takes up a small portion. Motivated by these two findings, we carefully develop two principles to prune the tokens with high temporal redundancy and retain the meaningful tokens. The overall framework is shown in Figure 2(a). Our method is mainly built on the standard columnar Transformer [8], which we briefly go through in Sec. 3.1. Later, in Sec. 3.2, we elaborate on the proposed metric to help prune unnecessary tokens. Finally, Sec. 3.3 discusses why STA works in video Transformer." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.697, + 0.761, + 0.712 + ], + "angle": 0, + "content": "3.1. Revisit of Video Transformer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Video Transformers generally process video data as a 1D sequence of tokens and directly model the relationship between them. Initially, video Transformer linearly projects 3D data tubes into high-dimensional embeddings. Assuming the dimensions of video clips as \\(\\{T,H,W\\}\\) and the size of 3D tubes as \\(\\{t,h,w\\}\\), then the number of token embeddings is \\(n = n_t\\times n_s = |\\frac{T}{t} | \\times |\\frac{HW}{hw} |\\). Additionally, positional embeddings are added to each token to break the permutation invariance. After the patch embedding layer, an \\(n\\) -token sequence \\(\\mathbf{X}\\in \\mathbb{R}^{n\\times d}\\) is passed into the selfattention layer, which computes a weighted sum of the values based on the affinity of other tokens. Mathematically," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16947" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.308, + 0.106 + ], + "angle": 0, + "content": "the self-attention is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.113, + 0.47, + 0.148 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A t t e n t i o n} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q} \\mathbf {K} ^ {T}}{\\sqrt {d}}\\right) \\mathbf {V}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.157, + 0.47, + 0.233 + ], + "angle": 0, + "content": "where \\(\\mathbf{Q},\\mathbf{K},\\mathbf{V} = f_{Q}(\\mathbf{X}),f_{K}(\\mathbf{X}),f_{V}(\\mathbf{X})\\in \\mathbb{R}^{d}\\) are typically linear transformations of \\(\\mathbf{X}\\). After spatial-temporal interaction, the tokens are sent into a feedforward network \\(f_{\\mathrm{FFN}}\\), which consists of a three-layer MLP to exchange inter-channel information." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.242, + 0.47, + 0.259 + ], + "angle": 0, + "content": "3.2. Semantic-aware Temporal Accumulative Score" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.266, + 0.471, + 0.372 + ], + "angle": 0, + "content": "Our intuitive criterion is to drop a token if similar tokens exist before it while reserving semantically meaningful tokens. To this end, our approach considers two factors when determining whether to retain or discard a token in the Transformer. The first is its similarity to the other tokens along the temporal axis, and the second is its contribution to the class attribute. We discuss these two principles in order." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.389, + 0.47, + 0.526 + ], + "angle": 0, + "content": "Temporal redundancy. Intuitively, a token should be removed if similar tokens have already existed in previous frames. Therefore, we remove tokens frame-by-frame by comparing whether similar tokens have been retained. For simplicity, we reduce a constant number of tokens in each frame to ensure parallel computing. We introduce the accumulative temporal score \\(\\mathbf{A} \\in [0,1]^{n_t \\times n_s}\\) to model the probability of dropping a token conditioned on the specific frame \\(t\\). Specifically, we define:" + }, + { + "type": "equation", + "bbox": [ + 0.103, + 0.535, + 0.47, + 0.574 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} _ {t, s} := \\mathbb {P} _ {\\text {d r o p}} \\left(\\mathbf {X} _ {t, s}\\right) \\in [ 0, 1 ] \\quad \\text {s . t .} \\sum_ {s = 1} ^ {n _ {s}} \\mathbf {A} _ {t, s} = 1, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.47, + 0.751 + ], + "angle": 0, + "content": "where tokens with higher temporal accumulative scores are more likely to be pruned because they carry a high degree of temporal redundancy. Next, we eliminate \\( r \\) tokens with the highest scores from \\( \\mathbf{A} \\) at \\( t \\)-th frame and transfer the remaining probability distribution \\( \\mathbf{A}_t' \\in \\mathbb{R}^{(n_s - r) \\times 1} \\) to the next frame via the transition probability \\( \\mathbb{P}_{\\mathrm{drop}}(\\mathbf{X}_t | \\mathbf{X}_{t-1}') \\in \\mathbb{R}^{n_s \\times (n_s - r)} \\). By excluding the dropped tokens of the last frame, we effectively restart the repetition aggregation. This prevents the high scores from being concentrated on specific tokens and allows for the global identification of redundancy. Mathematically," + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.76, + 0.47, + 0.787 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} _ {t + 1} := \\mathbb {P} _ {\\text {d r o p}} \\left(\\mathbf {X} _ {t + 1} \\mid \\mathbf {X} _ {t} ^ {\\prime}\\right) \\mathbf {A} _ {t} ^ {\\prime}, \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.784, + 0.424, + 0.802 + ], + "angle": 0, + "content": "\\[\n\\mathrm {P} _ {\\text {d r o p}} \\left(\\mathbf {X} _ {t + 1} \\mid \\mathbf {X} _ {t} ^ {\\prime}\\right) := \\operatorname {s o f t m a x} \\left(f \\left(\\mathbf {X} _ {t + 1}\\right) f \\left(\\mathbf {X} _ {t} ^ {\\prime}\\right) ^ {T}\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.901 + ], + "angle": 0, + "content": "where \\( f \\) is the projection head to measure the similarity, and we construct transition probability by softmax-based affinity matrix. Note that we do not need to train a new projection head \\( f \\) because the self-attention provides the necessary functionality, and the key function \\( f_{K} \\) extracts most relevant knowledge for affinity estimation, as shown" + }, + { + "type": "code_caption", + "bbox": [ + 0.501, + 0.092, + 0.88, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 Pseudocode of STA in a PyTorch-like style." + }, + { + "type": "algorithm", + "bbox": [ + 0.501, + 0.116, + 0.88, + 0.421 + ], + "angle": 0, + "content": "```c\n# x: token embedding, n_t x n_s x d\n# I: image-based token pruning method\n# r: drop number per frame\n# sim: token-to-token affinity function\n# min-max norm, Eqn.(4)\naam = norm(x.abs().sum(-1)) # size: (n_t, n_s, 1)\n# token removal at 1-st frame\nx_0 = I(x[0]) # size: (n_s-r, d)\n# initialization\nx_list, x_old = [x_0], x_0\nfor t in range(1, n_t):\n # token-to-token affinity matrix\nA_t = sim(x[t], x_old) # size: (n_s, n_s-r)\n# accumulateative temporal score\ns_acc = mm(A_t, s_acc) # size: (n_s, 1)\n# class-aware accumulative temporal score, Eqn.(5)\ns = s_acc * (1-aam[t])\ns = s.squeeze(dim=-1) # size: (n_s)\n# keep tokens with the minimal score\ni_t = s.topk(k=N-r, largest=False) # size: (n_s-r)\nx_old = x[t, i_t] # size: (n_s-r, d)\nx_list = x_list.append(x_old)\n# cut off the dropped tokens' score\ns_acc = s_acc[i_t] # size: (n_s-r, 1)\n# first-order norm\ns_acc = s_acc / s_acc-sum()" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.467, + 0.892, + 0.528 + ], + "angle": 0, + "content": "in Table 6c. This formulation allows us to connect all temporally distinct tokens through a simple Markov chain and aggregate potential redundancy from the first frame to every subsequent frame." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.892, + 0.701 + ], + "angle": 0, + "content": "Semantic importance. Up until this point, our approach has focused on capturing temporally repetitive information. However, we have neglected the influence of semantic attributes. In other words, we have treated each token equally, regardless of its contribution to the semantics of the class. To integrate semantics importance with our approach, we use the activation-based attention map \\(\\mathcal{F}\\) [45], which takes the feature matrix \\(\\mathbf{X} \\in \\mathbb{R}^{n_t \\times n_s \\times d}\\) as input and produces a score for each token in the matrix. Specifically, we define the semantic score for token \\(\\mathbf{X}_{t,s}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.594, + 0.713, + 0.892, + 0.754 + ], + "angle": 0, + "content": "\\[\n\\mathcal {F} \\left(\\mathbf {X} _ {t, s}\\right) = \\sum_ {i = 1} ^ {d} \\left| \\mathbf {X} _ {t, s, i} \\right| \\in \\mathbb {R} ^ {+}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Intuitively, through the summation of absolute activation values over channel dimension, a high absolute activation suggests a significant contribution to next layers. Moreover, we apply STA on off-the-shelf Transformers supervised by semantic labels, where high activation areas tend to represent discriminative category information. Thus, activation-based attention maps could effectively capture the importance or relevance of the token to the overall semantics. We then use this score to re-weigh the temporal accumulative" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16948" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "scores \\(\\mathbf{A}\\), giving tokens with high semantic contributions less weight in the pruning process. This ensures that tokens with high semantics are more likely to be retained, even if they have a high degree of temporal redundancy." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.153, + 0.469, + 0.198 + ], + "angle": 0, + "content": "Finally, we compute the semantic-aware temporal accumulative score \\(\\widetilde{\\mathbf{A}}_{t,s}\\) by integrating the semantic score \\(\\mathcal{F}(\\mathbf{X}_{t,s})\\) with the accumulative temporal score \\(\\mathbf{A}\\), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.21, + 0.469, + 0.229 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\mathbf {A}} _ {t, s} = \\left(1 - \\mathcal {F} \\left(\\mathbf {X} _ {t, s}\\right)\\right) \\mathbf {A} _ {t, s}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.235, + 0.469, + 0.355 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}(\\mathbf{X}_{t,s})\\) is min-max normalized to the range [0,1]. We utilize the semantic-aware accumulative temporal scores to guide token removal for all subsequent frames, except for the first frame. Thus, we adopt an image-based token pruning method on the first frame to kick off our algorithm. Once tokens are discarded through our strategy, they are never employed in subsequent layers, thus accelerating the inference of the Transformer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.356, + 0.469, + 0.491 + ], + "angle": 0, + "content": "We summarize the pseudocode of STA in Alg. 1. The algorithm takes token embedding \\(\\mathbf{X} \\in \\mathbb{R}^{n_t \\times n_s \\times d}\\), an image-based token pruning method \\(I\\), the number of tokens to drop per frame \\(r\\), and a token-to-token affinity function as inputs. The algorithm calculates the STA score for each frame, selects the tokens with the minimal STA score, and retains them for the next frame. This process is repeated for all frames and returns the resulting token embedding matrix with the retained tokens \\(\\mathbf{X}' \\in \\mathbb{R}^{n_t \\times (n_s - r) \\times d}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.51, + 0.469, + 0.556 + ], + "angle": 0, + "content": "Summary of the superiority of STA. Compared to the previous token-pruning methods, our approach, STA, offers three significant merits when applied to video data:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.566, + 0.469, + 0.641 + ], + "angle": 0, + "content": "- STA fully considers the potential repetition of tokens along the temporal axis and eliminates the genuine redundancy with insignificant semantics. The temporal aggregation design makes the scoring mechanism more motion-aware and suitable for video data;" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.652, + 0.469, + 0.697 + ], + "angle": 0, + "content": "- STA works as a plug-in module without the introduction of additional parameters and it does not require the retraining of the video Transformer;" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.707, + 0.469, + 0.797 + ], + "angle": 0, + "content": "- STA achieves a complexity of \\( O\\left(n_{t}n_{s}\\left(n_{s}-r\\right)\\right) \\), resulting in negligible additional FLOPs that only take up a small percentage of the total forward pass. Moreover, our algorithm allows for the bulk of computation to be done in parallel, making it friendly to modern GPU devices." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.566, + 0.469, + 0.797 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.808, + 0.469, + 0.838 + ], + "angle": 0, + "content": "Overall, our approach is efficient and easily deployable, making it an ideal solution for pruning video Transformers." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.848, + 0.195, + 0.862 + ], + "angle": 0, + "content": "3.3. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "In this section, we present a two-part practical analysis to shed the light on the intuition behind STA." + }, + { + "type": "table", + "bbox": [ + 0.533, + 0.09, + 0.86, + 0.155 + ], + "angle": 0, + "content": "
ModelSmallBaseLargeHuge
ViT5.105.385.075.55
Rand-ViT5.005.324.955.46
STA-ViT4.434.744.284.78
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.166, + 0.892, + 0.211 + ], + "angle": 0, + "content": "Table 1: Trajectory sum for ViT family on the Kinetics-400 validation set. Compared to random pruning, STA-ViT decreases the temporal redundancy significantly." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.23, + 0.892, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.395, + 0.892, + 0.469 + ], + "angle": 0, + "content": "Figure 3: Gradient visualization for ViT-Large on the Kinetics-400 validation set. We stack original RGB frames, gradient norm heatmap, and our pruning result from top to bottom. Our pruning algorithm preserves the area of rich semantics well." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.498, + 0.892, + 0.62 + ], + "angle": 0, + "content": "Does STA effectively reduce the temporal redundancy? To answer this question, we first define temporal redundancy as the frequency with which similar tokens appear at different timestamps. We then assess this phenomenon in a video by probing the last frame, denoted as \\(\\mathbf{X}_{-1} \\in \\mathbb{R}^{n_s \\times d}\\), and aggregating the cosine similarity between each token and the most similar tokens in previous frames. We term this aggregation as trajectory sum \\(S \\in \\mathbb{R}\\). Mathematically," + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.63, + 0.892, + 0.671 + ], + "angle": 0, + "content": "\\[\nS = \\frac {1}{n _ {s}} \\sum_ {i = 1} ^ {n _ {s}} \\sum_ {t = 1} ^ {n _ {t} - 1} \\max _ {j \\in \\{1, \\dots , n _ {s} \\}} \\cos - \\operatorname {s i m} \\left(\\mathbf {X} _ {- 1}, \\mathbf {X} _ {t}\\right) _ {i j}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.683, + 0.892, + 0.853 + ], + "angle": 0, + "content": "where \\(\\cos -\\sin (\\mathbf{X},\\mathbf{Y})_{ij} = \\frac{\\mathbf{X}_i\\cdot\\mathbf{Y}_j}{|\\mathbf{X}_i||\\mathbf{Y}_j|}\\). A higher trajectory sum indicates greater temporal redundancy and lower diversity along the temporal axis. When all the frames are the same, the score would reach its theoretical maximum, which is \\(N_{t} - 1\\). Then, we compare our method with the standard Transformer and random-prune counterparts in terms of the proposed trajectory sum. Table 1 shows that the video Transformer exhibits heavy temporal redundancy and random pruning fails to alleviate them considerably. In contrast, STA achieves a far lower trajectory sum, indicating that it effectively eliminates temporal redundancy." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Does STA retain semantics-rich tokens? To manifest it, we calculate the gradient norm for each token when back-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16949" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.152 + ], + "angle": 0, + "content": "propagating the training loss \\(\\mathcal{L}\\). We then aggregated the first-order gradient norm of \\(\\mathbf{X}^l\\) at each layer \\(l\\) to obtain the GradNorm, which reflects the contribution of each token to the final prediction. Mathematically," + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.167, + 0.47, + 0.21 + ], + "angle": 0, + "content": "\\[\n\\operatorname {G r a d N o r m} (\\mathbf {X}) = \\sum_ {l = 1} ^ {L} \\sum_ {i = 1} ^ {d} \\left| \\frac {\\partial \\mathcal {L}}{\\partial \\mathbf {X} _ {.. , i} ^ {l}} \\right| \\in \\mathbb {R} ^ {n _ {t} \\times n _ {s}}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.223, + 0.471, + 0.39 + ], + "angle": 0, + "content": "where \\( L \\) is the total number of the Transformer block, e.g., \\( L = 24 \\) for ViT-Large. Figure 3 shows the GradNorm distribution in the form of a heatmap. The heatmap reveals sparse patterns across the board, indicating that most tokens do not contribute significantly to the final prediction. Instead, the key regions responsible for the final prediction are usually motion-centric entities. This agrees with our intuition of highlighting semantically meaningful regions. With the help of activation-based attention map \\( \\mathcal{F} \\) in Eqn. (4), STA retains almost all areas of high-activation GradNorm as is evidenced in the last row of Figure 3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.41, + 0.21, + 0.426 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.436, + 0.267, + 0.452 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Datasets and backbones. We evaluate our algorithm on two standard video action recognition datasets. Kinetics-400 [14] (K400) and Something-Something V2 [11] (SSV2). Kinetics-400 is a large-scale action recognition dataset sourced from YouTube, which consists of around 10-second clips with 400 human action classes. The training and validation set has approximately \\(240\\mathrm{K}\\) and \\(20\\mathrm{K}\\) videos, respectively. Something-Something V2 is a motion-heavy benchmark with 174 labels, where the object and background are shared across the different action categories. Around \\(170\\mathrm{K}\\) and \\(25\\mathrm{K}\\) videos exist in the training and validation set of SSV2, respectively. We implement our STA strategy with two mainstream Transformer-based backbones, namely ViT [8] and VideoSwin [23]. For ViT, we sample 16 frames with \\(224^2\\) pixels as input and the size of 3D tube is \\(\\{2,16,16\\}\\). Therefore, the number of tokens for all layers is \\(n = \\frac{16}{2} \\times \\frac{224^2}{16^2} = 8 \\times 14^2\\). We load the open-sourced checkpoints from VideoMAE [35] due to its superior performance. For VideoSwin, the input resolution is \\(32 \\times 224^2\\) and the size of 3D tube is \\(\\{2,4,4\\}\\). The number of tokens at four hierarchical stages would be \\(\\{16 \\times 56^2, 16 \\times 28^2, 16 \\times 14^2, 16 \\times 7^2\\}\\). Though our algorithm is not intended for window-based Transformers that require structural integrity, we still find a simple solution. We compensate for the discarded token with the nearest kept tokens when computing the window attention and speed up the rest of the process, such as the linear projection. In total, we test 10 off-the-shelf backbones with different pre-trained weights on two benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.364 + ], + "angle": 0, + "content": "Implementation details. To progressively remove inattentive tokens, we apply our STA module three times. For ViT, we insert our STA module at the end of the \\(1^{st}\\), \\((1 + L/3)^{th}\\), \\((1 + 2L/3)^{th}\\) block, where \\(L\\) is the total number of Transformer blocks. For VideoSwin, there are four hierarchical stages with varied resolutions and the STA module is located at the end of the first three stages. We denote different variants of STA as \\(\\mathrm{STA}^{r_1}\\)-Model, where \\(r_1\\) is the number of spatial tokens dropped per frame at the first stage. We adopt a decreasing schedule, which reduces the dropped number by half at each stage. For instance, \\(\\mathrm{STA}^{64}\\)-ViT-L indicates pruning \\(\\{8 \\times 64, 8 \\times 32, 8 \\times 16\\}\\) tokens on ViT-Large. We weigh the computation via two metrics, FLOPs (floating-point operations) and throughput. FLOPs are reported with the help of fvcore library1 and throughput (clips/s) is measured at a batch size of 32 on a single 32G Tesla V100. Besides, we closely follow the inference metric for ViT and VideoSwin in [35, 23]." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.371, + 0.892, + 0.508 + ], + "angle": 0, + "content": "- ViT [35]: To evaluate on K400, we sample \\( 5 \\times 3 \\) views by uniformly selecting 5 16-frame clips from a full-length video in the temporal dimension with the frame stride of 4. For each clip, we resize the shorter spatial side to 224 pixels and extract 3 crops of \\( 224 \\times 224 \\) resolution that cover the longer spatial axis. The final score is the average score computed over all views. For SSV2, we follow a similar procedure by sampling 2 clips \\( \\times 3 \\) crops and the frames stride is 2." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.516, + 0.892, + 0.653 + ], + "angle": 0, + "content": "- VideoSwin [23]: For K400, we extract 4 32-frame clips from each full-length video using a temporal stride of 2 and a spatial size of \\(224 \\times 224\\). Similarly, for SSV2, we extract 1 set of clips using a spatial size of \\(224 \\times 224\\) and 3 spatial crops, with a frame stride of 2. Besides, we prune VideoSwin three times as \\(\\{r_1, 1.5r_1/4, 2r_1/16\\}\\). For instance, \\(\\mathrm{STA}^{256}\\)-VideoSwin-S indicates pruning \\(\\{16 \\times 256, 16 \\times 96, 16 \\times 32\\}\\) on VideoSwin-S." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.371, + 0.892, + 0.653 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.66, + 0.64, + 0.675 + ], + "angle": 0, + "content": "4.2. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.683, + 0.892, + 0.848 + ], + "angle": 0, + "content": "We conduct a thorough investigation of two off-the-shelf model families, ViT [8] and VideoSwin [23], on the Kinetics-400 and Something-Something V2 datasets. The results presented in Table 2 demonstrate that our proposed method can significantly reduce the computational costs of ViT models by \\(25\\% \\sim 49\\%\\), with negligible impacts on performance \\((-0.2\\% \\sim -1.0\\%)\\). It is worth noting our method shows a favorable trade-off between complexity and performance for larger models. For instance, our method reduces the FLOPs of ViT-Huge by half to just 611 GFLOPs, with only a \\(0.2\\%\\) drop in accuracy." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.849, + 0.892, + 0.88 + ], + "angle": 0, + "content": "To demonstrate the potential of our method to generalize well on various transformer backbones, we are conducting" + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.888, + 0.858, + 0.9 + ], + "angle": 0, + "content": "" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16950" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.123, + 0.089, + 0.849, + 0.289 + ], + "angle": 0, + "content": "
Base ModelMetricsDrop Number r1
0324864
ViT-SK400 Acc. (%)78.878.8 (-0.0)78.6 (-0.2)78.1 (-0.7)
SSV2 Acc. (%)66.866.6 (-0.2)66.4 (-0.4)65.8 (-1.0)
GFLOPs5742 (-26%)35 (-39%)29 (-49%)
ViT-BK400 Acc. (%)81.281.2 (-0.0)81.1 (-0.1)80.8 (-0.4)
SSV2 Acc. (%)70.670.4 (-0.2)70.3 (-0.3)69.9 (-0.7)
GFLOPs180136 (-24%)116 (-36%)96 (-47%)
ViT-LK400 Acc. (%)85.185.2 (+0.1)85.1 (-0.0)85.0 (-0.1)
GFLOPs597446 (-25%)376 (-37%)308 (-48%)
ViT-HK400 Acc. (%)86.386.3 (-0.0)86.2 (-0.1)86.1 (-0.2)
GFLOPs1192890 (-25%)748 (-37%)611 (-49%)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.299, + 0.893, + 0.33 + ], + "angle": 0, + "content": "Table 2: Main Results for STA-ViT family on Kinetics-400 [14] (K400) and Something-Something V2 [11] (SSV2). All input resolution is \\( {16} \\times {224}^{2} \\) ." + }, + { + "type": "table", + "bbox": [ + 0.123, + 0.343, + 0.849, + 0.513 + ], + "angle": 0, + "content": "
Base ModelMetricsDrop Number r1
0192256320
VideoSwin-TK400 Acc. (%)78.878.7 (-0.1)78.7 (-0.1)78.6 (-0.2)
GFLOPs8868 (-23%)61 (-31%)54 (-39%)
VideoSwin-SK400 Acc. (%)80.580.3 (-0.2)80.2 (-0.3)80.1 (-0.4)
GFLOPs166121 (-27%)106 (-36%)91 (-45%)
VideoSwin-BK400 Acc. (%)82.782.5 (-0.2)82.5 (-0.2)82.3 (-0.4)
K400 GFLOPs282202 (-28%)176 (-38%)149 (-47%)
SSV2 Acc. (%)69.669.6 (-0.0)69.5 (-0.1)69.2 (-0.4)
SSV2 GFLOPs321241 (-25%)215 (-33%)188 (-41%)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.523, + 0.893, + 0.568 + ], + "angle": 0, + "content": "Table 3: Main Results for STA-VideoSwin family on Kinetics-400 [14] (K400) and Something-Something V2 [11] (SSV2). All input resolution is \\(32 \\times 224^2\\). VideoSwin-B employs varying window sizes for K400 and SSV2, leading to a discrepancy in FLOPs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.596, + 0.473, + 0.763 + ], + "angle": 0, + "content": "further experiments on VideoSwin [23], a modern architecture that uses a window shuffling operation to interchange information. As VideoSwin is naturally unsuitable for unstructured tokens, we are filling the dropped locations during the window attention operation with the nearest tokens and then discarding the replicated tokens after the attention operation. Empirical results in Table 3 indicate that the performance of VideoSwin holds until FLOPs fall by roughly \\(40\\%\\). This observation verifies that both columnar ViT and hierarchical VideoSwin have heavy and unnecessary computations that can be significantly optimized." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Comparison with the state of the art. Firstly, we tabulate a comparison of our proposed method on K400 in Table 4. Our model performs favorably in terms of both accuracy and computation cost. For example, ViT-L equipped with our STA achieves the same accuracy as MViTv2-L [19] but with less than a quarter of the computational cost. Moreover, STTS [40] proposes a scorer network to conduct dynamic token selection separately in space and time, re" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.895, + 0.807 + ], + "angle": 0, + "content": "quiring to be trained in an end-to-end fashion. Our result surpasses STTS by \\(0.4\\%\\) accuracy using the same backbone VideoSwin-B but with only \\(60\\%\\) GFLOPs. This result verifies that leveraging the model itself to weigh the redundancy of tokens is sufficient to reduce complexity. We also report the result on SSV2 in Table 5. The superior performance of our proposed method verifies that STA prunes the inconsequential tokens via temporal cues, as it is known that understanding SSV2 mainly relies on temporal information. Specifically, ViT-B equipped with our STA surpasses most of the prior arts with a considerably minor complexity of 116 GFLOPs. For VideoSwin, our strategy outperforms STTS-VideoSwin by \\(0.5\\%\\) accuracy with \\(80\\%\\) of the computation cost." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Visualization of STA. Figure 4 shows image patches corresponding to kept tokens after three stages. The results align with our objective of resisting temporal redundancy and retaining informative tokens. In a tennis sequence, STA preserves the most meaningful patches, including a human" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16951" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.084, + 0.089, + 0.465, + 0.266 + ], + "angle": 0, + "content": "
ModelGFLOPs×viewsTop-1
TimeSformer-L [2]8353 × 1 × 380.7
Motionformer-L [28]1185 × 10 × 380.2
ViViT [1]3981 × 4 × 384.9
Swin-L [23]2107 × 10 × 584.9
MViTv2-L [19]2828 × 5 × 386.1
ViT-H [35]1192 × 5 × 386.3
STTS-VideoSwin-B [40]253 × 4 × 381.9
ToMe-ViT-L [3]281 × 10 × 184.5
STA320-VideoSwin-B (ours)149 × 4 × 382.3
STA64-ViT-L (ours)308 × 5 × 385.0
STA64-ViT-H (ours)611 × 5 × 386.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.277, + 0.472, + 0.368 + ], + "angle": 0, + "content": "Table 4: Comparisons with the-state-of-the-arts method on Kinetics-400. We report the computational cost with a single view (temporal clip with spatial crop) \\(\\times\\) the number of views (FLOPs \\(\\times\\) view_time \\(\\times\\) view_space). Gray represents that this method leverages the dynamic token pooling to optimize existing backbones." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.383, + 0.465, + 0.518 + ], + "angle": 0, + "content": "
ModelGFLOPs×viewsTop-1
TimeSformer-L [2]5549 × 1 × 362.4
Motionformer-L [28]1185 × 1 × 368.1
MViTv2-B [19]225 × 1 × 370.5
VideoSwin-B [23]321 × 1 × 369.6
ViT-B [35]180 × 2 × 370.6
STTS-VideoSwin-B [40]237 × 1 × 368.7
STA320-VideoSwin-B (ours)188 × 1 × 369.2
STA48-ViT-B (ours)116 × 2 × 370.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.528, + 0.47, + 0.62 + ], + "angle": 0, + "content": "Table 5: Comparisons with the-state-of-the-arts method on Something-Something V2. We report the computational cost with a single view (temporal clip with spatial crop) \\(\\times\\) the number of views (FLOPs \\(\\times\\) view_time \\(\\times\\) view_space). Gray represents that this method leverages the dynamic token pooling to optimize existing backbones." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.647, + 0.47, + 0.724 + ], + "angle": 0, + "content": "at the far end of the court, and filters out dull backgrounds like the blue ground. The temporal aggregation design ensures that the kept tokens are not just the most salient ones but also a variety of regions, preserving diversity within videos for better reasoning." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.735, + 0.231, + 0.751 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.758, + 0.47, + 0.819 + ], + "angle": 0, + "content": "To find the optimal strategy, we conduct a series of ablation studies. We evaluate off-the-shelf ViT-Large on K400 by default and report accuracy, FLOPs, and throughput for reference unless otherwise stated." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Token removal at the first frame. To investigate how the first-frame removal affects performance, we conduct experiments on three candidates. (1) Random Prune: we randomly select \\( r \\) tokens to discard. (2) Grid Prune: we split" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.093, + 0.895, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.31, + 0.895, + 0.371 + ], + "angle": 0, + "content": "Figure 4: Visualization of the proposed STA strategy. We masked out the discarded tokens with white boxes. STA not only retains informative tokens but also ensures diverse regions for improved video reasoning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.397, + 0.892, + 0.581 + ], + "angle": 0, + "content": "the first frame into \\(\\sqrt{r} \\times \\sqrt{r}\\) grids spatially and drop one random token per grid. (3) ToMe Prune: inspired by recent image pruning method ToMe [3], we get rid of the most similar tokens by the simple bipartite soft matching. The difference here is that we just drop tokens rather than 'merge' tokens. Note that all three pruning ways are negligible in the terms of computation and lead to similar speedup. It actually echoes the main insight of STA, leveraging temporal aggregation to reduce spatio-temporal redundancy. Even given a random initialization state, the sequential STA strategy could still decrease the total temporal redundancy and optimize the video Transformers effectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.597, + 0.892, + 0.644 + ], + "angle": 0, + "content": "Pruning schedule. We explore how to assign the number of dropping tokens among three stages. When maintaining a similar throughput, we devise three types of schedules:" + }, + { + "type": "text", + "bbox": [ + 0.549, + 0.667, + 0.851, + 0.683 + ], + "angle": 0, + "content": "Constant Schedule: \\(\\{8\\times 48,8\\times 48,8\\times 48\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.536, + 0.686, + 0.85, + 0.702 + ], + "angle": 0, + "content": "Decreasing Schedule: \\(\\{8\\times 64,8\\times 32,8\\times 16\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.54, + 0.705, + 0.856, + 0.721 + ], + "angle": 0, + "content": "Increasing Schedule: \\(\\{8\\times 27,8\\times 54,8\\times 108\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.731, + 0.894, + 0.793 + ], + "angle": 0, + "content": "As shown in Table 6d, the decreasing schedule owns the least accuracy reduction with similar throughput. It verifies that standard video Transformers process a great number of uninformative tokens that can be dropped at the beginning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Temporal accumulation order. Besides starting the accumulation flow from the beginning of the input video, we could also kick off at the ending frames. In Table 6b, we empirically find alternating order at different dropping stages outperforms the consistent counterparts. We speculate that the same accumulation direction would amplify" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16952" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.14, + 0.102, + 0.35, + 0.173 + ], + "angle": 0, + "content": "
MethodTop-1Top-5
Random84.7896.46
Grid84.8596.50
ToMe84.9696.50
" + }, + { + "type": "table", + "bbox": [ + 0.386, + 0.102, + 0.585, + 0.187 + ], + "angle": 0, + "content": "
OrderTop-1Top-5
F-B-F84.9696.50
B-F-B84.9796.43
F-F-F84.2696.41
B-B-B84.3596.37
" + }, + { + "type": "table", + "bbox": [ + 0.615, + 0.102, + 0.835, + 0.187 + ], + "angle": 0, + "content": "
SimilarityTop-1Top-5
fQ84.8396.52
fK84.9696.50
fV84.8496.50
fFFN84.9496.50
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.123, + 0.189, + 0.844, + 0.22 + ], + "angle": 0, + "content": "(a) Ablation on token removal meth- (b) Ablation on temporal accumula- (c) Ablation on different similarity ods at the first frame. tion order. function \\(f\\)" + }, + { + "type": "table", + "bbox": [ + 0.148, + 0.233, + 0.438, + 0.303 + ], + "angle": 0, + "content": "
ScheduleTop-1Top-5clips/s
constant84.6896.3647
decreasing84.9696.5047
increasing77.6893.7244
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.11, + 0.305, + 0.468, + 0.32 + ], + "angle": 0, + "content": "(d) Ablation on dropping schedule among three stages." + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.233, + 0.84, + 0.303 + ], + "angle": 0, + "content": "
ScoreViT-SViT-BViT-L
1 - F(Xt,s)77.3380.5284.87
At,s77.7880.4384.69
(1 - F(Xt,s))At,s78.1280.8284.96
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.496, + 0.305, + 0.852, + 0.32 + ], + "angle": 0, + "content": "(e) Ablation on scoring mechanism. Top-1 is reported." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.332, + 0.892, + 0.364 + ], + "angle": 0, + "content": "Table 6: Results of STA ablation experiments. F and B in (b) mean forward and backward order, respectively. The baseline ViT-L without STA obtains \\(85.05\\%\\) Top-1 and \\(96.55\\%\\) Top-5 accuracy on K400 at 19.5 clips/s. Gray is our default setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.391, + 0.469, + 0.422 + ], + "angle": 0, + "content": "intrinsic propagation error but alternating the order counteracts it, leading to more reasonable pruning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.441, + 0.469, + 0.503 + ], + "angle": 0, + "content": "Similarity function choice. We ablate four similarity project heads \\(\\{f_{Q}, f_{V}, f_{K}, f_{\\mathrm{FFN}}\\}\\). Table 6c shows that key function \\(f_{k}\\) captures the most correct affinity with minimal noise. The observation coincides with previous work [3]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.469, + 0.658 + ], + "angle": 0, + "content": "Scoring mechanism. To explore how accumulation score and semantic identification boost each other, we conduct the experiment with different scoring formulas. Table 6e demonstrates that considering both temporal redundancy and semantics helps in discovering informative tokens. The results on ViT-S show that temporal aggregation modeled by the Markov Chain plays an important role in the pruning process, while semantic importance functions effectively for ViT-B and ViT-L." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.679, + 0.469, + 0.831 + ], + "angle": 0, + "content": "Performance vs. prune number \\( r \\). To seek the sweet spot of our algorithm, we vary the prune number \\( r \\) at the first stage ranging from [16, 96] and evaluate the Top-1 accuracy. In addition, we compare our STA with the Random pruning baseline. As displayed in Figure. 5, STA behaves fairly robust to the token reduction and consistently surpasses the result of the random pruning. Specifically, \\( r = 64 \\) doubles the throughput but just drops \\( 0.1\\% \\) accuracy. This confirms that our algorithm retains the semantics-rich tokens with the lowest redundancy." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.195, + 0.86 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "In conclusion, we propose a new token pruning strategy, Semantic-aware Temporal Accumulation (STA), for" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.391, + 0.875, + 0.598 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.607, + 0.892, + 0.639 + ], + "angle": 0, + "content": "Figure 5: Top-1 accuracy and throughput under two pruning methods with various prune numbers \\( r \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.651, + 0.892, + 0.788 + ], + "angle": 0, + "content": "video Transformers that can significantly reduce computation overhead with a subtle accuracy drop. Specifically, we consider temporal redundancy and semantic importance when deciding to keep or drop the token. Our approach does not introduce any parameter and can directly accelerate the off-the-shelf video Transformers without training. The extensive experiments demonstrate that our method empowers video Transformers to obtain a competitive speed-accuracy trade-off compared to the prior arts." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.801, + 0.661, + 0.817 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This work was supported in part by the National Natural Science Foundation of China under Grant 62250055, Grant 61932022, Grant 62120106007, and in part by the Program of Shanghai Science and Technology Innovation Project under Grant 20511100100." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16953" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. 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In Proceedings of the European conference on computer vision (ECCV), pages 695-712, 2018. 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "16956" + } + ] +] \ No newline at end of file diff --git a/2023/Prune Spatio-temporal Tokens by Semantic-aware Temporal Accumulation/6db1efd1-b765-4bc8-8a5a-d2a425ae5e95_origin.pdf b/2023/Prune Spatio-temporal Tokens by Semantic-aware Temporal Accumulation/6db1efd1-b765-4bc8-8a5a-d2a425ae5e95_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a3f5443caa3d34fec138686cade83ed19cf4dc73 --- /dev/null +++ b/2023/Prune Spatio-temporal Tokens by Semantic-aware Temporal Accumulation/6db1efd1-b765-4bc8-8a5a-d2a425ae5e95_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6069b970ec13704eb11413df0a7b8dba97cf2a46af5489f7e1655024c8f46bb5 +size 1542499 diff --git a/2023/Prune Spatio-temporal Tokens by Semantic-aware Temporal Accumulation/full.md b/2023/Prune Spatio-temporal Tokens by Semantic-aware Temporal Accumulation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d8fa15a6879d1c6dafce00b3685995478240c9d4 --- /dev/null +++ b/2023/Prune Spatio-temporal Tokens by Semantic-aware Temporal Accumulation/full.md @@ -0,0 +1,339 @@ +# Prune Spatio-temporal Tokens by Semantic-aware Temporal Accumulation + +Shuangrui Ding $^{1,3*}$ Peisen Zhao $^{2}$ Xiaopeng Zhang $^{2}$ Rui Qian $^{3}$ Hongkai Xiong $^{1}$ Qi Tian $^{2\dagger}$ $^{1}$ Shanghai Jiao Tong University $^{2}$ Huawei Cloud $^{3}$ The Chinese University of Hong Kong + +{dsr1212, xionghongkai}@sjtu.edu.cn qr021@ie.cuhk.edu.hk + +{pszhao93, zxphistory}@gmail.com tian.qil@huawei.com + +# Abstract + +Transformers have become the primary backbone of the computer vision community due to their impressive performance. However, the unfriendly computation cost impedes their potential in the video recognition domain. To optimize the speed-accuracy trade-off, we propose Semantic-aware Temporal Accumulation score (STA) to prune spatiotemporal tokens integrally. STA score considers two critical factors: temporal redundancy and semantic importance. The former depicts a specific region based on whether it is a new occurrence or a seen entity by aggregating token-to-token similarity in consecutive frames while the latter evaluates each token based on its contribution to the overall prediction. As a result, tokens with higher scores of STA carry more temporal redundancy as well as lower semantics thus being pruned. Based on the STA score, we are able to progressively prune the tokens without introducing any additional parameters or requiring further re-training. We directly apply the STA module to off-the-shelf ViT and VideoSwin backbones, and the empirical results on Kinetics-400 and Something-Something V2 achieve over $30\%$ computation reduction with a negligible $\sim 0.2\%$ accuracy drop. The code is released at https://github.com/Mark12Ding/STA. + +# 1. Introduction + +Recently, there has been an unstoppable shift in the general backbone design from Convolutional Neural Networks (ConvNets) to Transformers, which are originally employed in natural language processing, and has shown promising potential for various vision tasks [8, 48, 47, 22, 1, 32, 5]. The key component of Transformers is the self-attention mechanism, which is apt to capture long-range dependencies and empowers ViT to perceive the global reception field. The seminal work, Vision Transformer (ViT) [8] + +![](images/4d0dbe1fa17b753a288d747b7f48d471730bc428d42be77b82058ee79f0ff0e6.jpg) +Figure 1: Kinectics-400 result for ViT and VideoSwin. The bubble's area is proportional to FLOPs of a variant in a model family. ViT/VideoSwin here takes $16 / 32 \times 224^2$ video. The proposed STA saves over $30\%$ FLOPs for all model variants with a negligible drop in performance. + +closely follows the original Transformer architecture [38]. Equipped with a large-scale model and dataset, ViT outperforms ConvNets in image classification by a considerable margin. Inspired by this superior scaling behavior, Transformers have gained popularity as a backbone choice and are widely adopted for image recognition [22, 37], action recognition [1, 23], semantic segmentation [49, 6], action detection [43, 12], temporal perception [33, 34], etc. + +Despite the promising potential of Transformers in spatio-temporal vision tasks, such as action recognition, the quadratic increase in complexity caused by the temporal dimension makes the video Transformers computationally unfriendly compared to images. For instance, earlier work TimeSformer [2], which applies Transformer backbone for video, required 7.14 Tera FLOPs to achieve $80.7\%$ accuracy on the Kinetics-400 action recognition benchmark. The excessive computational cost makes it impractical for deployment in real-world scenarios. Therefore, there is an urgent need to explore ways to profit from the performance gains + +of Transformers while maintaining an affordable computation burden. + +Fortunately, Transformers can handle a flexible number of tokens as input. Recent attempts [31, 30, 42], that dynamically prune tokens for images, have remarkably reduced computation overhead. These pruning approaches have inspired us to explore token pruning in the video domain, so as to balance accuracy and computation costs accordingly. However, performing frame-wise pruning alone seems to be not optimal since it ignores temporal context and disrupts the dynamic structure of the video. To address this issue, recent work STTS [40] decouples token pruning into temporal and spatial dimensions. Specifically, STTS first drops meaningless frames and then filters out detail-rich regions from the remained frames. However, this spatio-temporal decoupling strategy lacks contextual modeling of continuous temporal information, leading to limited performance. + +In this paper, we argue that pruning spatio-temporal tokens integrally can lead to further computation reduction at an acceptable cost of accuracy degradation. To this end, we propose the Semantic-aware Temporal Accumulation (STA) score to depict the importance of each token. We take two factors into consideration, temporal redundancy and semantic importance. Our motivation is to discard tokens that have similar counterparts appearing earlier in the sequence while retaining only semantically significant tokens. As an example, static backgrounds across all timestamps contain highly repetitive information that is unnecessary to be included. Therefore, keeping only a few representative background patches is sufficient for reasoning. Specifically, we evaluate the temporal redundancy of a region by determining whether it is a novel or previously observed entity. In practice, we aggregate repetitive information on a per-frame basis and assign each token a score of temporal repetition degree. Nevertheless, there are cases where a repetitive region reveals a crucial action and should be retained. For example, if the sequence of tokens describes human-body motion, it is necessary to keep all the tokens for better understanding, even if there are only slight differences over time. Thus, we also take semantic importance into account during the pruning procedure. To depict each token's semantic contribution to video recognition, we take the summation of the feature activation map and then integrate this summation with the score of temporal aggregation to enhance the awareness of semantics. Based on the STA score, we progressively prune the tokens of the video Transformers three times. The whole pruning process does not introduce any tuning parameter and directly accelerates the off-the-shelf video Transformers without the need to retrain. + +We apply our pruning strategy to two mainstream video Transformers, ViT [8] and VideoSwin [23], and evalu + +ate 10 off-the-shelf backbones on two action recognition benchmarks, Kinetics-400 [14] and Something-Something V2 [11], to demonstrate the effectiveness of our method. As shown in Figure 1, we achieve significant computation reduction with a negligible accuracy drop on Kinetics-400. For instance, using ViT-H as the backbone, by hierarchically pruning $57\%$ of the input tokens, STA reduces $49\%$ FLOPs while the accuracy drop is only $0.2\%$ . Besides, with STA, FLOPs of VideoSwin-B are decreased by $38\%$ while maintaining $82.5\%$ accuracy with only a minimal drop of $0.2\%$ . A similar trend can also be observed in the Something-Something V2 dataset. Notably, we surpass STTS [40] by a $0.4\%$ accuracy gain with $40\%$ fewer FLOPs on Kinetics-400 and by a $0.5\%$ accuracy increase with $20\%$ fewer FLOPs on Something-Something V2 when using the same backbone. + +# 2. Related Work + +Video Transformers. Designing Transformer-based architectures for vision tasks has emerged as a general trend in the computer vision community, as evidenced by several recent works [8, 22, 50, 28, 49, 24, 39]. With an unprecedented number of parameters and millions of training data, Transformers significantly outperform prior arts spanning a variety of tasks, not only in image but also in video understanding tasks. Various variants of self-attention have been introduced in prior works [2, 26, 47, 1, 4, 28, 9, 23, 46, 19] to capture the spatiotemporal relationship. However, using pure patch-based Transformers incurs prohibitive costs on memory and computation when extracting global-range features from the whole video. To deal with it, Motionformer [28] introduces trajectory attention that focuses on implicitly determined motion paths and optimizes the quadratic calculation via efficient decomposition. MeMViT [43] proposes caching 'memory' of past frames and attending to the summarized prior context in an online manner. In this paper, we propose an orthogonal approach to make Transformers lighter by pruning the spatio-temporal tokens with high temporal redundancy. + +Token pruning for Transformers. Several works [31, 30, 42, 20, 25, 3, 17] have focused on reducing the number of tokens involved in the calculation to accelerate image Transformer models. In specific, DynamicViT [30] trains a lightweight decision module to rate the importance of each token and prune low-score tokens progressively. EViT [20] preserves the attentive tokens guided by the class token attention and fuses inattentive ones without the help of any extra parameter. ToMe [3] combines similar tokens to directly expedite off-the-shelf ViT without needing to train. While similar to ToMe [3], our method functions as a simple plug-in to enhance off-the-shelf video Transformers without + +![](images/a4f588521d1dbc54cc829f1019c5be2e410257e8ae3adfaeca69c3be15806f53.jpg) +(a) Conceptual pipeline of video Transformer with STA module. + +![](images/82820ea25b69c62596464f9266540c024dea79086d8909aad815e59dc86110c1.jpg) +(b) Illustration of the proposed STA module. +Figure 2: An overview of our STA token-pruning algorithm for video Transformers. (a) STA module is a simple plug-in and can be inserted at the beginning or end of the Transformer block. In practice, we conduct a three-stage progressive strategy to prune the token with STA. (b) Our semantic-aware temporal accumulation algorithm. The wider arrows connecting two adjacent frames represent higher weight to transport the STA score. + +requiring additional training. However, ToMe is an image-based pruning technique that does not model any temporal relations. In contrast, our method specifically devises a temporal aggregation mechanism tailored for video data. Although STTS [40] trains a score network to choose predefined anchors from filtered frames within a video, the empirical speed-accuracy trade-off remains limited. This is because decoupled anchor-level selection still retains unwanted spatial redundancy. On the contrary, we prune the video at the token level and eliminate the meaningless content by a large margin. + +Efficient video recognition. Due to the nature of the extra dimension, video understanding is computationally intensive. Thus, there have been attempts [51, 10, 36, 44, 15, 41, 7, 18, 16, 21, 13, 29] to design lightweight modules that enjoy both high efficiency and high accuracy. ECO [51] introduces a network architecture to sample a small subset of frames and learns the temporal context between these frames. Besides, AdaFocus [41] improves the computational efficiency by adopting a light-weighted ConvNet to localize the most salient spatiotemporal regions. While previous works have mainly concentrated on accelerating ConvNet models, efforts toward accelerating video Transformers have been relatively sparse and open to exploration. A recent approach [27] devises a novel token-based sampling using k-centered search before feeding tokens into video Transformers. Although we also select semantically meaningful tokens for video Transformers, our dynamic model processes whole tokens at the early stage and prunes them based on model-dependent features. + +# 3. Approach + +The goal of this paper is to develop a principal token-pruning algorithm for video Transformers that achieves an optimal balance between cost, speed, and performance without requiring model re-training. We start by analyzing the video Transformers at hand and observe two interesting phenomena, detailed in Sec. 3.3. First, we find the high temporal redundancy when comparing the interframe similarity. Second, the area that contributes to the final prediction usually takes up a small portion. Motivated by these two findings, we carefully develop two principles to prune the tokens with high temporal redundancy and retain the meaningful tokens. The overall framework is shown in Figure 2(a). Our method is mainly built on the standard columnar Transformer [8], which we briefly go through in Sec. 3.1. Later, in Sec. 3.2, we elaborate on the proposed metric to help prune unnecessary tokens. Finally, Sec. 3.3 discusses why STA works in video Transformer. + +# 3.1. Revisit of Video Transformer + +Video Transformers generally process video data as a 1D sequence of tokens and directly model the relationship between them. Initially, video Transformer linearly projects 3D data tubes into high-dimensional embeddings. Assuming the dimensions of video clips as $\{T,H,W\}$ and the size of 3D tubes as $\{t,h,w\}$ , then the number of token embeddings is $n = n_t\times n_s = |\frac{T}{t} | \times |\frac{HW}{hw} |$ . Additionally, positional embeddings are added to each token to break the permutation invariance. After the patch embedding layer, an $n$ -token sequence $\mathbf{X}\in \mathbb{R}^{n\times d}$ is passed into the selfattention layer, which computes a weighted sum of the values based on the affinity of other tokens. Mathematically, + +the self-attention is formulated as: + +$$ +\operatorname {A t t e n t i o n} (\mathbf {Q}, \mathbf {K}, \mathbf {V}) = \operatorname {s o f t m a x} \left(\frac {\mathbf {Q} \mathbf {K} ^ {T}}{\sqrt {d}}\right) \mathbf {V}, \tag {1} +$$ + +where $\mathbf{Q},\mathbf{K},\mathbf{V} = f_{Q}(\mathbf{X}),f_{K}(\mathbf{X}),f_{V}(\mathbf{X})\in \mathbb{R}^{d}$ are typically linear transformations of $\mathbf{X}$ . After spatial-temporal interaction, the tokens are sent into a feedforward network $f_{\mathrm{FFN}}$ , which consists of a three-layer MLP to exchange inter-channel information. + +# 3.2. Semantic-aware Temporal Accumulative Score + +Our intuitive criterion is to drop a token if similar tokens exist before it while reserving semantically meaningful tokens. To this end, our approach considers two factors when determining whether to retain or discard a token in the Transformer. The first is its similarity to the other tokens along the temporal axis, and the second is its contribution to the class attribute. We discuss these two principles in order. + +Temporal redundancy. Intuitively, a token should be removed if similar tokens have already existed in previous frames. Therefore, we remove tokens frame-by-frame by comparing whether similar tokens have been retained. For simplicity, we reduce a constant number of tokens in each frame to ensure parallel computing. We introduce the accumulative temporal score $\mathbf{A} \in [0,1]^{n_t \times n_s}$ to model the probability of dropping a token conditioned on the specific frame $t$ . Specifically, we define: + +$$ +\mathbf {A} _ {t, s} := \mathbb {P} _ {\text {d r o p}} \left(\mathbf {X} _ {t, s}\right) \in [ 0, 1 ] \quad \text {s . t .} \sum_ {s = 1} ^ {n _ {s}} \mathbf {A} _ {t, s} = 1, \tag {2} +$$ + +where tokens with higher temporal accumulative scores are more likely to be pruned because they carry a high degree of temporal redundancy. Next, we eliminate $r$ tokens with the highest scores from $\mathbf{A}$ at $t$ -th frame and transfer the remaining probability distribution $\mathbf{A}_t' \in \mathbb{R}^{(n_s - r) \times 1}$ to the next frame via the transition probability $\mathbb{P}_{\mathrm{drop}}(\mathbf{X}_t | \mathbf{X}_{t-1}') \in \mathbb{R}^{n_s \times (n_s - r)}$ . By excluding the dropped tokens of the last frame, we effectively restart the repetition aggregation. This prevents the high scores from being concentrated on specific tokens and allows for the global identification of redundancy. Mathematically, + +$$ +\mathbf {A} _ {t + 1} := \mathbb {P} _ {\text {d r o p}} \left(\mathbf {X} _ {t + 1} \mid \mathbf {X} _ {t} ^ {\prime}\right) \mathbf {A} _ {t} ^ {\prime}, \tag {3} +$$ + +$$ +\mathrm {P} _ {\text {d r o p}} \left(\mathbf {X} _ {t + 1} \mid \mathbf {X} _ {t} ^ {\prime}\right) := \operatorname {s o f t m a x} \left(f \left(\mathbf {X} _ {t + 1}\right) f \left(\mathbf {X} _ {t} ^ {\prime}\right) ^ {T}\right), +$$ + +where $f$ is the projection head to measure the similarity, and we construct transition probability by softmax-based affinity matrix. Note that we do not need to train a new projection head $f$ because the self-attention provides the necessary functionality, and the key function $f_{K}$ extracts most relevant knowledge for affinity estimation, as shown + +Algorithm 1 Pseudocode of STA in a PyTorch-like style. +# x: token embedding, n_t x n_s x d +# I: image-based token pruning method +# r: drop number per frame +# sim: token-to-token affinity function +# min-max norm, Eqn.(4) +aam = norm(x.abs().sum(-1)) # size: (n_t, n_s, 1) +# token removal at 1-st frame +x_0 = I(x[0]) # size: (n_s-r, d) +# initialization +x_list, x_old = [x_0], x_0 +for t in range(1, n_t): + # token-to-token affinity matrix +A_t = sim(x[t], x_old) # size: (n_s, n_s-r) +# accumulateative temporal score +s_acc = mm(A_t, s_acc) # size: (n_s, 1) +# class-aware accumulative temporal score, Eqn.(5) +s = s_acc * (1-aam[t]) +s = s.squeeze(dim=-1) # size: (n_s) +# keep tokens with the minimal score +i_t = s.topk(k=N-r, largest=False) # size: (n_s-r) +x_old = x[t, i_t] # size: (n_s-r, d) +x_list = x_list.append(x_old) +# cut off the dropped tokens' score +s_acc = s_acc[i_t] # size: (n_s-r, 1) +# first-order norm +s_acc = s_acc / s_acc-sum() + +in Table 6c. This formulation allows us to connect all temporally distinct tokens through a simple Markov chain and aggregate potential redundancy from the first frame to every subsequent frame. + +Semantic importance. Up until this point, our approach has focused on capturing temporally repetitive information. However, we have neglected the influence of semantic attributes. In other words, we have treated each token equally, regardless of its contribution to the semantics of the class. To integrate semantics importance with our approach, we use the activation-based attention map $\mathcal{F}$ [45], which takes the feature matrix $\mathbf{X} \in \mathbb{R}^{n_t \times n_s \times d}$ as input and produces a score for each token in the matrix. Specifically, we define the semantic score for token $\mathbf{X}_{t,s}$ as: + +$$ +\mathcal {F} \left(\mathbf {X} _ {t, s}\right) = \sum_ {i = 1} ^ {d} \left| \mathbf {X} _ {t, s, i} \right| \in \mathbb {R} ^ {+}. \tag {4} +$$ + +Intuitively, through the summation of absolute activation values over channel dimension, a high absolute activation suggests a significant contribution to next layers. Moreover, we apply STA on off-the-shelf Transformers supervised by semantic labels, where high activation areas tend to represent discriminative category information. Thus, activation-based attention maps could effectively capture the importance or relevance of the token to the overall semantics. We then use this score to re-weigh the temporal accumulative + +scores $\mathbf{A}$ , giving tokens with high semantic contributions less weight in the pruning process. This ensures that tokens with high semantics are more likely to be retained, even if they have a high degree of temporal redundancy. + +Finally, we compute the semantic-aware temporal accumulative score $\widetilde{\mathbf{A}}_{t,s}$ by integrating the semantic score $\mathcal{F}(\mathbf{X}_{t,s})$ with the accumulative temporal score $\mathbf{A}$ , i.e., + +$$ +\widetilde {\mathbf {A}} _ {t, s} = \left(1 - \mathcal {F} \left(\mathbf {X} _ {t, s}\right)\right) \mathbf {A} _ {t, s}, \tag {5} +$$ + +where $\mathcal{F}(\mathbf{X}_{t,s})$ is min-max normalized to the range [0,1]. We utilize the semantic-aware accumulative temporal scores to guide token removal for all subsequent frames, except for the first frame. Thus, we adopt an image-based token pruning method on the first frame to kick off our algorithm. Once tokens are discarded through our strategy, they are never employed in subsequent layers, thus accelerating the inference of the Transformer. + +We summarize the pseudocode of STA in Alg. 1. The algorithm takes token embedding $\mathbf{X} \in \mathbb{R}^{n_t \times n_s \times d}$ , an image-based token pruning method $I$ , the number of tokens to drop per frame $r$ , and a token-to-token affinity function as inputs. The algorithm calculates the STA score for each frame, selects the tokens with the minimal STA score, and retains them for the next frame. This process is repeated for all frames and returns the resulting token embedding matrix with the retained tokens $\mathbf{X}' \in \mathbb{R}^{n_t \times (n_s - r) \times d}$ . + +Summary of the superiority of STA. Compared to the previous token-pruning methods, our approach, STA, offers three significant merits when applied to video data: + +- STA fully considers the potential repetition of tokens along the temporal axis and eliminates the genuine redundancy with insignificant semantics. The temporal aggregation design makes the scoring mechanism more motion-aware and suitable for video data; +- STA works as a plug-in module without the introduction of additional parameters and it does not require the retraining of the video Transformer; +- STA achieves a complexity of $O\left(n_{t}n_{s}\left(n_{s}-r\right)\right)$ , resulting in negligible additional FLOPs that only take up a small percentage of the total forward pass. Moreover, our algorithm allows for the bulk of computation to be done in parallel, making it friendly to modern GPU devices. + +Overall, our approach is efficient and easily deployable, making it an ideal solution for pruning video Transformers. + +# 3.3. Discussion + +In this section, we present a two-part practical analysis to shed the light on the intuition behind STA. + +
ModelSmallBaseLargeHuge
ViT5.105.385.075.55
Rand-ViT5.005.324.955.46
STA-ViT4.434.744.284.78
+ +Table 1: Trajectory sum for ViT family on the Kinetics-400 validation set. Compared to random pruning, STA-ViT decreases the temporal redundancy significantly. + +![](images/3c897761d68f6c4aadf932d901bbd28b2c032cc451a9c65ec3745fc4f8bb35bc.jpg) +Figure 3: Gradient visualization for ViT-Large on the Kinetics-400 validation set. We stack original RGB frames, gradient norm heatmap, and our pruning result from top to bottom. Our pruning algorithm preserves the area of rich semantics well. + +Does STA effectively reduce the temporal redundancy? To answer this question, we first define temporal redundancy as the frequency with which similar tokens appear at different timestamps. We then assess this phenomenon in a video by probing the last frame, denoted as $\mathbf{X}_{-1} \in \mathbb{R}^{n_s \times d}$ , and aggregating the cosine similarity between each token and the most similar tokens in previous frames. We term this aggregation as trajectory sum $S \in \mathbb{R}$ . Mathematically, + +$$ +S = \frac {1}{n _ {s}} \sum_ {i = 1} ^ {n _ {s}} \sum_ {t = 1} ^ {n _ {t} - 1} \max _ {j \in \{1, \dots , n _ {s} \}} \cos - \operatorname {s i m} \left(\mathbf {X} _ {- 1}, \mathbf {X} _ {t}\right) _ {i j}, \tag {6} +$$ + +where $\cos -\sin (\mathbf{X},\mathbf{Y})_{ij} = \frac{\mathbf{X}_i\cdot\mathbf{Y}_j}{|\mathbf{X}_i||\mathbf{Y}_j|}$ . A higher trajectory sum indicates greater temporal redundancy and lower diversity along the temporal axis. When all the frames are the same, the score would reach its theoretical maximum, which is $N_{t} - 1$ . Then, we compare our method with the standard Transformer and random-prune counterparts in terms of the proposed trajectory sum. Table 1 shows that the video Transformer exhibits heavy temporal redundancy and random pruning fails to alleviate them considerably. In contrast, STA achieves a far lower trajectory sum, indicating that it effectively eliminates temporal redundancy. + +Does STA retain semantics-rich tokens? To manifest it, we calculate the gradient norm for each token when back- + +propagating the training loss $\mathcal{L}$ . We then aggregated the first-order gradient norm of $\mathbf{X}^l$ at each layer $l$ to obtain the GradNorm, which reflects the contribution of each token to the final prediction. Mathematically, + +$$ +\operatorname {G r a d N o r m} (\mathbf {X}) = \sum_ {l = 1} ^ {L} \sum_ {i = 1} ^ {d} \left| \frac {\partial \mathcal {L}}{\partial \mathbf {X} _ {.. , i} ^ {l}} \right| \in \mathbb {R} ^ {n _ {t} \times n _ {s}}, \tag {7} +$$ + +where $L$ is the total number of the Transformer block, e.g., $L = 24$ for ViT-Large. Figure 3 shows the GradNorm distribution in the form of a heatmap. The heatmap reveals sparse patterns across the board, indicating that most tokens do not contribute significantly to the final prediction. Instead, the key regions responsible for the final prediction are usually motion-centric entities. This agrees with our intuition of highlighting semantically meaningful regions. With the help of activation-based attention map $\mathcal{F}$ in Eqn. (4), STA retains almost all areas of high-activation GradNorm as is evidenced in the last row of Figure 3. + +# 4. Experiments + +# 4.1. Experimental Setup + +Datasets and backbones. We evaluate our algorithm on two standard video action recognition datasets. Kinetics-400 [14] (K400) and Something-Something V2 [11] (SSV2). Kinetics-400 is a large-scale action recognition dataset sourced from YouTube, which consists of around 10-second clips with 400 human action classes. The training and validation set has approximately $240\mathrm{K}$ and $20\mathrm{K}$ videos, respectively. Something-Something V2 is a motion-heavy benchmark with 174 labels, where the object and background are shared across the different action categories. Around $170\mathrm{K}$ and $25\mathrm{K}$ videos exist in the training and validation set of SSV2, respectively. We implement our STA strategy with two mainstream Transformer-based backbones, namely ViT [8] and VideoSwin [23]. For ViT, we sample 16 frames with $224^2$ pixels as input and the size of 3D tube is $\{2,16,16\}$ . Therefore, the number of tokens for all layers is $n = \frac{16}{2} \times \frac{224^2}{16^2} = 8 \times 14^2$ . We load the open-sourced checkpoints from VideoMAE [35] due to its superior performance. For VideoSwin, the input resolution is $32 \times 224^2$ and the size of 3D tube is $\{2,4,4\}$ . The number of tokens at four hierarchical stages would be $\{16 \times 56^2, 16 \times 28^2, 16 \times 14^2, 16 \times 7^2\}$ . Though our algorithm is not intended for window-based Transformers that require structural integrity, we still find a simple solution. We compensate for the discarded token with the nearest kept tokens when computing the window attention and speed up the rest of the process, such as the linear projection. In total, we test 10 off-the-shelf backbones with different pre-trained weights on two benchmarks. + +Implementation details. To progressively remove inattentive tokens, we apply our STA module three times. For ViT, we insert our STA module at the end of the $1^{st}$ , $(1 + L/3)^{th}$ , $(1 + 2L/3)^{th}$ block, where $L$ is the total number of Transformer blocks. For VideoSwin, there are four hierarchical stages with varied resolutions and the STA module is located at the end of the first three stages. We denote different variants of STA as $\mathrm{STA}^{r_1}$ -Model, where $r_1$ is the number of spatial tokens dropped per frame at the first stage. We adopt a decreasing schedule, which reduces the dropped number by half at each stage. For instance, $\mathrm{STA}^{64}$ -ViT-L indicates pruning $\{8 \times 64, 8 \times 32, 8 \times 16\}$ tokens on ViT-Large. We weigh the computation via two metrics, FLOPs (floating-point operations) and throughput. FLOPs are reported with the help of fvcore library1 and throughput (clips/s) is measured at a batch size of 32 on a single 32G Tesla V100. Besides, we closely follow the inference metric for ViT and VideoSwin in [35, 23]. + +- ViT [35]: To evaluate on K400, we sample $5 \times 3$ views by uniformly selecting 5 16-frame clips from a full-length video in the temporal dimension with the frame stride of 4. For each clip, we resize the shorter spatial side to 224 pixels and extract 3 crops of $224 \times 224$ resolution that cover the longer spatial axis. The final score is the average score computed over all views. For SSV2, we follow a similar procedure by sampling 2 clips $\times 3$ crops and the frames stride is 2. +- VideoSwin [23]: For K400, we extract 4 32-frame clips from each full-length video using a temporal stride of 2 and a spatial size of $224 \times 224$ . Similarly, for SSV2, we extract 1 set of clips using a spatial size of $224 \times 224$ and 3 spatial crops, with a frame stride of 2. Besides, we prune VideoSwin three times as $\{r_1, 1.5r_1/4, 2r_1/16\}$ . For instance, $\mathrm{STA}^{256}$ -VideoSwin-S indicates pruning $\{16 \times 256, 16 \times 96, 16 \times 32\}$ on VideoSwin-S. + +# 4.2. Main Results + +We conduct a thorough investigation of two off-the-shelf model families, ViT [8] and VideoSwin [23], on the Kinetics-400 and Something-Something V2 datasets. The results presented in Table 2 demonstrate that our proposed method can significantly reduce the computational costs of ViT models by $25\% \sim 49\%$ , with negligible impacts on performance $(-0.2\% \sim -1.0\%)$ . It is worth noting our method shows a favorable trade-off between complexity and performance for larger models. For instance, our method reduces the FLOPs of ViT-Huge by half to just 611 GFLOPs, with only a $0.2\%$ drop in accuracy. + +To demonstrate the potential of our method to generalize well on various transformer backbones, we are conducting + +
Base ModelMetricsDrop Number r1
0324864
ViT-SK400 Acc. (%)78.878.8 (-0.0)78.6 (-0.2)78.1 (-0.7)
SSV2 Acc. (%)66.866.6 (-0.2)66.4 (-0.4)65.8 (-1.0)
GFLOPs5742 (-26%)35 (-39%)29 (-49%)
ViT-BK400 Acc. (%)81.281.2 (-0.0)81.1 (-0.1)80.8 (-0.4)
SSV2 Acc. (%)70.670.4 (-0.2)70.3 (-0.3)69.9 (-0.7)
GFLOPs180136 (-24%)116 (-36%)96 (-47%)
ViT-LK400 Acc. (%)85.185.2 (+0.1)85.1 (-0.0)85.0 (-0.1)
GFLOPs597446 (-25%)376 (-37%)308 (-48%)
ViT-HK400 Acc. (%)86.386.3 (-0.0)86.2 (-0.1)86.1 (-0.2)
GFLOPs1192890 (-25%)748 (-37%)611 (-49%)
+ +Table 2: Main Results for STA-ViT family on Kinetics-400 [14] (K400) and Something-Something V2 [11] (SSV2). All input resolution is ${16} \times {224}^{2}$ . + +
Base ModelMetricsDrop Number r1
0192256320
VideoSwin-TK400 Acc. (%)78.878.7 (-0.1)78.7 (-0.1)78.6 (-0.2)
GFLOPs8868 (-23%)61 (-31%)54 (-39%)
VideoSwin-SK400 Acc. (%)80.580.3 (-0.2)80.2 (-0.3)80.1 (-0.4)
GFLOPs166121 (-27%)106 (-36%)91 (-45%)
VideoSwin-BK400 Acc. (%)82.782.5 (-0.2)82.5 (-0.2)82.3 (-0.4)
K400 GFLOPs282202 (-28%)176 (-38%)149 (-47%)
SSV2 Acc. (%)69.669.6 (-0.0)69.5 (-0.1)69.2 (-0.4)
SSV2 GFLOPs321241 (-25%)215 (-33%)188 (-41%)
+ +Table 3: Main Results for STA-VideoSwin family on Kinetics-400 [14] (K400) and Something-Something V2 [11] (SSV2). All input resolution is $32 \times 224^2$ . VideoSwin-B employs varying window sizes for K400 and SSV2, leading to a discrepancy in FLOPs. + +further experiments on VideoSwin [23], a modern architecture that uses a window shuffling operation to interchange information. As VideoSwin is naturally unsuitable for unstructured tokens, we are filling the dropped locations during the window attention operation with the nearest tokens and then discarding the replicated tokens after the attention operation. Empirical results in Table 3 indicate that the performance of VideoSwin holds until FLOPs fall by roughly $40\%$ . This observation verifies that both columnar ViT and hierarchical VideoSwin have heavy and unnecessary computations that can be significantly optimized. + +Comparison with the state of the art. Firstly, we tabulate a comparison of our proposed method on K400 in Table 4. Our model performs favorably in terms of both accuracy and computation cost. For example, ViT-L equipped with our STA achieves the same accuracy as MViTv2-L [19] but with less than a quarter of the computational cost. Moreover, STTS [40] proposes a scorer network to conduct dynamic token selection separately in space and time, re + +quiring to be trained in an end-to-end fashion. Our result surpasses STTS by $0.4\%$ accuracy using the same backbone VideoSwin-B but with only $60\%$ GFLOPs. This result verifies that leveraging the model itself to weigh the redundancy of tokens is sufficient to reduce complexity. We also report the result on SSV2 in Table 5. The superior performance of our proposed method verifies that STA prunes the inconsequential tokens via temporal cues, as it is known that understanding SSV2 mainly relies on temporal information. Specifically, ViT-B equipped with our STA surpasses most of the prior arts with a considerably minor complexity of 116 GFLOPs. For VideoSwin, our strategy outperforms STTS-VideoSwin by $0.5\%$ accuracy with $80\%$ of the computation cost. + +Visualization of STA. Figure 4 shows image patches corresponding to kept tokens after three stages. The results align with our objective of resisting temporal redundancy and retaining informative tokens. In a tennis sequence, STA preserves the most meaningful patches, including a human + +
ModelGFLOPs×viewsTop-1
TimeSformer-L [2]8353 × 1 × 380.7
Motionformer-L [28]1185 × 10 × 380.2
ViViT [1]3981 × 4 × 384.9
Swin-L [23]2107 × 10 × 584.9
MViTv2-L [19]2828 × 5 × 386.1
ViT-H [35]1192 × 5 × 386.3
STTS-VideoSwin-B [40]253 × 4 × 381.9
ToMe-ViT-L [3]281 × 10 × 184.5
STA320-VideoSwin-B (ours)149 × 4 × 382.3
STA64-ViT-L (ours)308 × 5 × 385.0
STA64-ViT-H (ours)611 × 5 × 386.1
+ +Table 4: Comparisons with the-state-of-the-arts method on Kinetics-400. We report the computational cost with a single view (temporal clip with spatial crop) $\times$ the number of views (FLOPs $\times$ view_time $\times$ view_space). Gray represents that this method leverages the dynamic token pooling to optimize existing backbones. + +
ModelGFLOPs×viewsTop-1
TimeSformer-L [2]5549 × 1 × 362.4
Motionformer-L [28]1185 × 1 × 368.1
MViTv2-B [19]225 × 1 × 370.5
VideoSwin-B [23]321 × 1 × 369.6
ViT-B [35]180 × 2 × 370.6
STTS-VideoSwin-B [40]237 × 1 × 368.7
STA320-VideoSwin-B (ours)188 × 1 × 369.2
STA48-ViT-B (ours)116 × 2 × 370.3
+ +Table 5: Comparisons with the-state-of-the-arts method on Something-Something V2. We report the computational cost with a single view (temporal clip with spatial crop) $\times$ the number of views (FLOPs $\times$ view_time $\times$ view_space). Gray represents that this method leverages the dynamic token pooling to optimize existing backbones. + +at the far end of the court, and filters out dull backgrounds like the blue ground. The temporal aggregation design ensures that the kept tokens are not just the most salient ones but also a variety of regions, preserving diversity within videos for better reasoning. + +# 4.3. Ablation Study + +To find the optimal strategy, we conduct a series of ablation studies. We evaluate off-the-shelf ViT-Large on K400 by default and report accuracy, FLOPs, and throughput for reference unless otherwise stated. + +Token removal at the first frame. To investigate how the first-frame removal affects performance, we conduct experiments on three candidates. (1) Random Prune: we randomly select $r$ tokens to discard. (2) Grid Prune: we split + +![](images/c401b239dc7f3c940ac06a72286fd4519fad726731758551bbf5838e1f2dc50e.jpg) +Figure 4: Visualization of the proposed STA strategy. We masked out the discarded tokens with white boxes. STA not only retains informative tokens but also ensures diverse regions for improved video reasoning. + +the first frame into $\sqrt{r} \times \sqrt{r}$ grids spatially and drop one random token per grid. (3) ToMe Prune: inspired by recent image pruning method ToMe [3], we get rid of the most similar tokens by the simple bipartite soft matching. The difference here is that we just drop tokens rather than 'merge' tokens. Note that all three pruning ways are negligible in the terms of computation and lead to similar speedup. It actually echoes the main insight of STA, leveraging temporal aggregation to reduce spatio-temporal redundancy. Even given a random initialization state, the sequential STA strategy could still decrease the total temporal redundancy and optimize the video Transformers effectively. + +Pruning schedule. We explore how to assign the number of dropping tokens among three stages. When maintaining a similar throughput, we devise three types of schedules: + +Constant Schedule: $\{8\times 48,8\times 48,8\times 48\}$ + +Decreasing Schedule: $\{8\times 64,8\times 32,8\times 16\}$ + +Increasing Schedule: $\{8\times 27,8\times 54,8\times 108\}$ + +As shown in Table 6d, the decreasing schedule owns the least accuracy reduction with similar throughput. It verifies that standard video Transformers process a great number of uninformative tokens that can be dropped at the beginning. + +Temporal accumulation order. Besides starting the accumulation flow from the beginning of the input video, we could also kick off at the ending frames. In Table 6b, we empirically find alternating order at different dropping stages outperforms the consistent counterparts. We speculate that the same accumulation direction would amplify + +
MethodTop-1Top-5
Random84.7896.46
Grid84.8596.50
ToMe84.9696.50
+ +
OrderTop-1Top-5
F-B-F84.9696.50
B-F-B84.9796.43
F-F-F84.2696.41
B-B-B84.3596.37
+ +(a) Ablation on token removal meth- (b) Ablation on temporal accumula- (c) Ablation on different similarity ods at the first frame. tion order. function $f$ + +
SimilarityTop-1Top-5
fQ84.8396.52
fK84.9696.50
fV84.8496.50
fFFN84.9496.50
+ +
ScheduleTop-1Top-5clips/s
constant84.6896.3647
decreasing84.9696.5047
increasing77.6893.7244
+ +(d) Ablation on dropping schedule among three stages. + +
ScoreViT-SViT-BViT-L
1 - F(Xt,s)77.3380.5284.87
At,s77.7880.4384.69
(1 - F(Xt,s))At,s78.1280.8284.96
+ +(e) Ablation on scoring mechanism. Top-1 is reported. + +Table 6: Results of STA ablation experiments. F and B in (b) mean forward and backward order, respectively. The baseline ViT-L without STA obtains $85.05\%$ Top-1 and $96.55\%$ Top-5 accuracy on K400 at 19.5 clips/s. Gray is our default setting. + +intrinsic propagation error but alternating the order counteracts it, leading to more reasonable pruning. + +Similarity function choice. We ablate four similarity project heads $\{f_{Q}, f_{V}, f_{K}, f_{\mathrm{FFN}}\}$ . Table 6c shows that key function $f_{k}$ captures the most correct affinity with minimal noise. The observation coincides with previous work [3]. + +Scoring mechanism. To explore how accumulation score and semantic identification boost each other, we conduct the experiment with different scoring formulas. Table 6e demonstrates that considering both temporal redundancy and semantics helps in discovering informative tokens. The results on ViT-S show that temporal aggregation modeled by the Markov Chain plays an important role in the pruning process, while semantic importance functions effectively for ViT-B and ViT-L. + +Performance vs. prune number $r$ . To seek the sweet spot of our algorithm, we vary the prune number $r$ at the first stage ranging from [16, 96] and evaluate the Top-1 accuracy. In addition, we compare our STA with the Random pruning baseline. As displayed in Figure. 5, STA behaves fairly robust to the token reduction and consistently surpasses the result of the random pruning. Specifically, $r = 64$ doubles the throughput but just drops $0.1\%$ accuracy. This confirms that our algorithm retains the semantics-rich tokens with the lowest redundancy. + +# 5. Conclusion + +In conclusion, we propose a new token pruning strategy, Semantic-aware Temporal Accumulation (STA), for + +![](images/cd7ee016dbe8da99d81d462383b9944042512bf9dd7dc65cfd3993fb9557fcab.jpg) +Figure 5: Top-1 accuracy and throughput under two pruning methods with various prune numbers $r$ . + +video Transformers that can significantly reduce computation overhead with a subtle accuracy drop. Specifically, we consider temporal redundancy and semantic importance when deciding to keep or drop the token. Our approach does not introduce any parameter and can directly accelerate the off-the-shelf video Transformers without training. The extensive experiments demonstrate that our method empowers video Transformers to obtain a competitive speed-accuracy trade-off compared to the prior arts. + +# Acknowledgement + +This work was supported in part by the National Natural Science Foundation of China under Grant 62250055, Grant 61932022, Grant 62120106007, and in part by the Program of Shanghai Science and Technology Innovation Project under Grant 20511100100. + +# References + +[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. Vivit: A video vision transformer. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 6836-6846, October 2021. 1, 2, 8 +[2] Gedas Bertasius, Heng Wang, and Lorenzo Torresani. Is space-time attention all you need for video understanding? In ICML, volume 2, page 4, 2021. 1, 2, 8 +[3] Daniel Bolya, Cheng-Yang Fu, Xiaoliang Dai, Peizhao Zhang, Christoph Feichtenhofer, and Judy Hoffman. 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In Proceedings of the IEEE/CVF international conference on computer vision, pages 13577-13587, 2021. 1, 2 + +[48] Hengshuang Zhao, Li Jiang, Jiaya Jia, Philip HS Torr, and Vladlen Koltun. Point transformer. In Proceedings of the IEEE/CVF international conference on computer vision, pages 16259-16268, 2021. 1 +[49] Sixiao Zheng, Jiachen Lu, Hengshuang Zhao, Xiatian Zhu, Zekun Luo, Yabiao Wang, Yanwei Fu, Jianfeng Feng, Tao Xiang, Philip HS Torr, et al. Rethinking semantic segmentation from a sequence-to-sequence perspective with transformers. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 6881-6890, 2021. 1, 2 +[50] Xizhou Zhu, Weijie Su, Lewei Lu, Bin Li, Xiaogang Wang, and Jifeng Dai. Deformable $\{\mathrm{detr}\}$ : Deformable transformers for end-to-end object detection. In International Conference on Learning Representations, 2021. 2 +[51] Mohammadreza Zolfaghari, Kamaljeet Singh, and Thomas Brox. Eco: Efficient convolutional network for online video understanding. 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However, the unfriendly computation cost impedes their potential in the video recognition domain. To optimize the speed-accuracy trade-off, we propose Semantic-aware Temporal Accumulation score (STA) to prune spatiotemporal tokens integrally. STA score considers two critical factors: temporal redundancy and semantic importance. The former depicts a specific region based on whether it is a new occurrence or a seen entity by aggregating token-to-token similarity in consecutive frames while the latter evaluates each token based on its contribution to the overall prediction. As a result, tokens with higher scores of STA carry more temporal redundancy as well as lower semantics thus being pruned. Based on the STA score, we are able to progressively prune the tokens without introducing any additional parameters or requiring further re-training. 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Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 574, + 288, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 288, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 288, + 684 + ], + "type": "text", + "content": "Recently, there has been an unstoppable shift in the general backbone design from Convolutional Neural Networks (ConvNets) to Transformers, which are originally employed in natural language processing, and has shown promising potential for various vision tasks [8, 48, 47, 22, 1, 32, 5]. The key component of Transformers is the self-attention mechanism, which is apt to capture long-range dependencies and empowers ViT to perceive the global reception field. The seminal work, Vision Transformer (ViT) [8]" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 225, + 545, + 394 + ], + "blocks": [ + { + "bbox": [ + 307, + 225, + 545, + 394 + ], + "lines": [ + { + "bbox": [ + 307, + 225, + 545, + 394 + ], + "spans": [ + { + "bbox": [ + 307, + 225, + 545, + 394 + ], + "type": "image", + "image_path": "4d0dbe1fa17b753a288d747b7f48d471730bc428d42be77b82058ee79f0ff0e6.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 401, + 547, + 462 + ], + "lines": [ + { + "bbox": [ + 304, + 401, + 547, + 462 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 547, + 462 + ], + "type": "text", + "content": "Figure 1: Kinectics-400 result for ViT and VideoSwin. The bubble's area is proportional to FLOPs of a variant in a model family. ViT/VideoSwin here takes " + }, + { + "bbox": [ + 304, + 401, + 547, + 462 + ], + "type": "inline_equation", + "content": "16 / 32 \\times 224^2" + }, + { + "bbox": [ + 304, + 401, + 547, + 462 + ], + "type": "text", + "content": " video. The proposed STA saves over " + }, + { + "bbox": [ + 304, + 401, + 547, + 462 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 304, + 401, + 547, + 462 + ], + "type": "text", + "content": " FLOPs for all model variants with a negligible drop in performance." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 485, + 547, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 547, + 581 + ], + "type": "text", + "content": "closely follows the original Transformer architecture [38]. Equipped with a large-scale model and dataset, ViT outperforms ConvNets in image classification by a considerable margin. Inspired by this superior scaling behavior, Transformers have gained popularity as a backbone choice and are widely adopted for image recognition [22, 37], action recognition [1, 23], semantic segmentation [49, 6], action detection [43, 12], temporal perception [33, 34], etc." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": "Despite the promising potential of Transformers in spatio-temporal vision tasks, such as action recognition, the quadratic increase in complexity caused by the temporal dimension makes the video Transformers computationally unfriendly compared to images. For instance, earlier work TimeSformer [2], which applies Transformer backbone for video, required 7.14 Tera FLOPs to achieve " + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "inline_equation", + "content": "80.7\\%" + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": " accuracy on the Kinetics-400 action recognition benchmark. The excessive computational cost makes it impractical for deployment in real-world scenarios. Therefore, there is an urgent need to explore ways to profit from the performance gains" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 225, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 225, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 225, + 703 + ], + "type": "text", + "content": "*Work done during an internship at Huawei Cloud." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 59, + 703, + 234, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 234, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 234, + 712 + ], + "type": "text", + "content": "†Corresponding author. Email: tian.qi1@huawei.com." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16945" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "content": "of Transformers while maintaining an affordable computation burden." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 99, + 288, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 99, + 288, + 290 + ], + "spans": [ + { + "bbox": [ + 46, + 99, + 288, + 290 + ], + "type": "text", + "content": "Fortunately, Transformers can handle a flexible number of tokens as input. Recent attempts [31, 30, 42], that dynamically prune tokens for images, have remarkably reduced computation overhead. These pruning approaches have inspired us to explore token pruning in the video domain, so as to balance accuracy and computation costs accordingly. However, performing frame-wise pruning alone seems to be not optimal since it ignores temporal context and disrupts the dynamic structure of the video. To address this issue, recent work STTS [40] decouples token pruning into temporal and spatial dimensions. Specifically, STTS first drops meaningless frames and then filters out detail-rich regions from the remained frames. However, this spatio-temporal decoupling strategy lacks contextual modeling of continuous temporal information, leading to limited performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 292, + 288, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 292, + 288, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 288, + 687 + ], + "type": "text", + "content": "In this paper, we argue that pruning spatio-temporal tokens integrally can lead to further computation reduction at an acceptable cost of accuracy degradation. To this end, we propose the Semantic-aware Temporal Accumulation (STA) score to depict the importance of each token. We take two factors into consideration, temporal redundancy and semantic importance. Our motivation is to discard tokens that have similar counterparts appearing earlier in the sequence while retaining only semantically significant tokens. As an example, static backgrounds across all timestamps contain highly repetitive information that is unnecessary to be included. Therefore, keeping only a few representative background patches is sufficient for reasoning. Specifically, we evaluate the temporal redundancy of a region by determining whether it is a novel or previously observed entity. In practice, we aggregate repetitive information on a per-frame basis and assign each token a score of temporal repetition degree. Nevertheless, there are cases where a repetitive region reveals a crucial action and should be retained. For example, if the sequence of tokens describes human-body motion, it is necessary to keep all the tokens for better understanding, even if there are only slight differences over time. Thus, we also take semantic importance into account during the pruning procedure. To depict each token's semantic contribution to video recognition, we take the summation of the feature activation map and then integrate this summation with the score of temporal aggregation to enhance the awareness of semantics. Based on the STA score, we progressively prune the tokens of the video Transformers three times. The whole pruning process does not introduce any tuning parameter and directly accelerates the off-the-shelf video Transformers without the need to retrain." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "We apply our pruning strategy to two mainstream video Transformers, ViT [8] and VideoSwin [23], and evalu" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "content": "ate 10 off-the-shelf backbones on two action recognition benchmarks, Kinetics-400 [14] and Something-Something V2 [11], to demonstrate the effectiveness of our method. As shown in Figure 1, we achieve significant computation reduction with a negligible accuracy drop on Kinetics-400. For instance, using ViT-H as the backbone, by hierarchically pruning " + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "inline_equation", + "content": "57\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "content": " of the input tokens, STA reduces " + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "inline_equation", + "content": "49\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "content": " FLOPs while the accuracy drop is only " + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "inline_equation", + "content": "0.2\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "content": ". Besides, with STA, FLOPs of VideoSwin-B are decreased by " + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "inline_equation", + "content": "38\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "content": " while maintaining " + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "inline_equation", + "content": "82.5\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "content": " accuracy with only a minimal drop of " + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "inline_equation", + "content": "0.2\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "content": ". A similar trend can also be observed in the Something-Something V2 dataset. Notably, we surpass STTS [40] by a " + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "inline_equation", + "content": "0.4\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "content": " accuracy gain with " + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "content": " fewer FLOPs on Kinetics-400 and by a " + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "content": " accuracy increase with " + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "content": " fewer FLOPs on Something-Something V2 when using the same backbone." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 277, + 392, + 290 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 277, + 392, + 290 + ], + "spans": [ + { + "bbox": [ + 306, + 277, + 392, + 290 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 298, + 545, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 298, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 298, + 545, + 550 + ], + "type": "text", + "content": "Video Transformers. Designing Transformer-based architectures for vision tasks has emerged as a general trend in the computer vision community, as evidenced by several recent works [8, 22, 50, 28, 49, 24, 39]. With an unprecedented number of parameters and millions of training data, Transformers significantly outperform prior arts spanning a variety of tasks, not only in image but also in video understanding tasks. Various variants of self-attention have been introduced in prior works [2, 26, 47, 1, 4, 28, 9, 23, 46, 19] to capture the spatiotemporal relationship. However, using pure patch-based Transformers incurs prohibitive costs on memory and computation when extracting global-range features from the whole video. To deal with it, Motionformer [28] introduces trajectory attention that focuses on implicitly determined motion paths and optimizes the quadratic calculation via efficient decomposition. MeMViT [43] proposes caching 'memory' of past frames and attending to the summarized prior context in an online manner. In this paper, we propose an orthogonal approach to make Transformers lighter by pruning the spatio-temporal tokens with high temporal redundancy." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Token pruning for Transformers. Several works [31, 30, 42, 20, 25, 3, 17] have focused on reducing the number of tokens involved in the calculation to accelerate image Transformer models. In specific, DynamicViT [30] trains a lightweight decision module to rate the importance of each token and prune low-score tokens progressively. EViT [20] preserves the attentive tokens guided by the class token attention and fuses inattentive ones without the help of any extra parameter. ToMe [3] combines similar tokens to directly expedite off-the-shelf ViT without needing to train. While similar to ToMe [3], our method functions as a simple plug-in to enhance off-the-shelf video Transformers without" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "16946" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 72, + 299, + 225 + ], + "blocks": [ + { + "bbox": [ + 52, + 72, + 299, + 225 + ], + "lines": [ + { + "bbox": [ + 52, + 72, + 299, + 225 + ], + "spans": [ + { + "bbox": [ + 52, + 72, + 299, + 225 + ], + "type": "image", + "image_path": "a4f588521d1dbc54cc829f1019c5be2e410257e8ae3adfaeca69c3be15806f53.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 69, + 227, + 307, + 239 + ], + "lines": [ + { + "bbox": [ + 69, + 227, + 307, + 239 + ], + "spans": [ + { + "bbox": [ + 69, + 227, + 307, + 239 + ], + "type": "text", + "content": "(a) Conceptual pipeline of video Transformer with STA module." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 308, + 72, + 539, + 224 + ], + "blocks": [ + { + "bbox": [ + 308, + 72, + 539, + 224 + ], + "lines": [ + { + "bbox": [ + 308, + 72, + 539, + 224 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 539, + 224 + ], + "type": "image", + "image_path": "82820ea25b69c62596464f9266540c024dea79086d8909aad815e59dc86110c1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 337, + 228, + 504, + 239 + ], + "lines": [ + { + "bbox": [ + 337, + 228, + 504, + 239 + ], + "spans": [ + { + "bbox": [ + 337, + 228, + 504, + 239 + ], + "type": "text", + "content": "(b) Illustration of the proposed STA module." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 252, + 547, + 301 + ], + "lines": [ + { + "bbox": [ + 46, + 252, + 547, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 547, + 301 + ], + "type": "text", + "content": "Figure 2: An overview of our STA token-pruning algorithm for video Transformers. (a) STA module is a simple plug-in and can be inserted at the beginning or end of the Transformer block. In practice, we conduct a three-stage progressive strategy to prune the token with STA. (b) Our semantic-aware temporal accumulation algorithm. The wider arrows connecting two adjacent frames represent higher weight to transport the STA score." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 322, + 289, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 322, + 289, + 454 + ], + "spans": [ + { + "bbox": [ + 46, + 322, + 289, + 454 + ], + "type": "text", + "content": "requiring additional training. However, ToMe is an image-based pruning technique that does not model any temporal relations. In contrast, our method specifically devises a temporal aggregation mechanism tailored for video data. Although STTS [40] trains a score network to choose predefined anchors from filtered frames within a video, the empirical speed-accuracy trade-off remains limited. This is because decoupled anchor-level selection still retains unwanted spatial redundancy. On the contrary, we prune the video at the token level and eliminate the meaningless content by a large margin." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 486, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 289, + 714 + ], + "type": "text", + "content": "Efficient video recognition. Due to the nature of the extra dimension, video understanding is computationally intensive. Thus, there have been attempts [51, 10, 36, 44, 15, 41, 7, 18, 16, 21, 13, 29] to design lightweight modules that enjoy both high efficiency and high accuracy. ECO [51] introduces a network architecture to sample a small subset of frames and learns the temporal context between these frames. Besides, AdaFocus [41] improves the computational efficiency by adopting a light-weighted ConvNet to localize the most salient spatiotemporal regions. While previous works have mainly concentrated on accelerating ConvNet models, efforts toward accelerating video Transformers have been relatively sparse and open to exploration. A recent approach [27] devises a novel token-based sampling using k-centered search before feeding tokens into video Transformers. Although we also select semantically meaningful tokens for video Transformers, our dynamic model processes whole tokens at the early stage and prunes them based on model-dependent features." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 320, + 373, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 320, + 373, + 335 + ], + "spans": [ + { + "bbox": [ + 306, + 320, + 373, + 335 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 341, + 547, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 341, + 547, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 341, + 547, + 544 + ], + "type": "text", + "content": "The goal of this paper is to develop a principal token-pruning algorithm for video Transformers that achieves an optimal balance between cost, speed, and performance without requiring model re-training. We start by analyzing the video Transformers at hand and observe two interesting phenomena, detailed in Sec. 3.3. First, we find the high temporal redundancy when comparing the interframe similarity. Second, the area that contributes to the final prediction usually takes up a small portion. Motivated by these two findings, we carefully develop two principles to prune the tokens with high temporal redundancy and retain the meaningful tokens. The overall framework is shown in Figure 2(a). Our method is mainly built on the standard columnar Transformer [8], which we briefly go through in Sec. 3.1. Later, in Sec. 3.2, we elaborate on the proposed metric to help prune unnecessary tokens. Finally, Sec. 3.3 discusses why STA works in video Transformer." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 552, + 465, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 552, + 465, + 563 + ], + "spans": [ + { + "bbox": [ + 305, + 552, + 465, + 563 + ], + "type": "text", + "content": "3.1. Revisit of Video Transformer" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "Video Transformers generally process video data as a 1D sequence of tokens and directly model the relationship between them. Initially, video Transformer linearly projects 3D data tubes into high-dimensional embeddings. Assuming the dimensions of video clips as " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\{T,H,W\\}" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " and the size of 3D tubes as " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\{t,h,w\\}" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": ", then the number of token embeddings is " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "n = n_t\\times n_s = |\\frac{T}{t} | \\times |\\frac{HW}{hw} |" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": ". Additionally, positional embeddings are added to each token to break the permutation invariance. After the patch embedding layer, an " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " -token sequence " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{X}\\in \\mathbb{R}^{n\\times d}" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " is passed into the selfattention layer, which computes a weighted sum of the values based on the affinity of other tokens. Mathematically," + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16947" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 188, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 188, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 188, + 83 + ], + "type": "text", + "content": "the self-attention is formulated as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 79, + 89, + 287, + 117 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 89, + 287, + 117 + ], + "spans": [ + { + "bbox": [ + 79, + 89, + 287, + 117 + ], + "type": "interline_equation", + "content": "\\operatorname {A t t e n t i o n} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q} \\mathbf {K} ^ {T}}{\\sqrt {d}}\\right) \\mathbf {V}, \\tag {1}", + "image_path": "297bf1fdac49894b222864d32d74f1904e2e9393e320f89f5c715ad9abe638c0.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 124, + 287, + 184 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 124, + 287, + 184 + ], + "spans": [ + { + "bbox": [ + 47, + 124, + 287, + 184 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 124, + 287, + 184 + ], + "type": "inline_equation", + "content": "\\mathbf{Q},\\mathbf{K},\\mathbf{V} = f_{Q}(\\mathbf{X}),f_{K}(\\mathbf{X}),f_{V}(\\mathbf{X})\\in \\mathbb{R}^{d}" + }, + { + "bbox": [ + 47, + 124, + 287, + 184 + ], + "type": "text", + "content": " are typically linear transformations of " + }, + { + "bbox": [ + 47, + 124, + 287, + 184 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 47, + 124, + 287, + 184 + ], + "type": "text", + "content": ". After spatial-temporal interaction, the tokens are sent into a feedforward network " + }, + { + "bbox": [ + 47, + 124, + 287, + 184 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{FFN}}" + }, + { + "bbox": [ + 47, + 124, + 287, + 184 + ], + "type": "text", + "content": ", which consists of a three-layer MLP to exchange inter-channel information." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 191, + 287, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 191, + 287, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 191, + 287, + 205 + ], + "type": "text", + "content": "3.2. Semantic-aware Temporal Accumulative Score" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 210, + 288, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 210, + 288, + 294 + ], + "spans": [ + { + "bbox": [ + 46, + 210, + 288, + 294 + ], + "type": "text", + "content": "Our intuitive criterion is to drop a token if similar tokens exist before it while reserving semantically meaningful tokens. To this end, our approach considers two factors when determining whether to retain or discard a token in the Transformer. The first is its similarity to the other tokens along the temporal axis, and the second is its contribution to the class attribute. We discuss these two principles in order." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 308, + 287, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 287, + 416 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 287, + 416 + ], + "type": "text", + "content": "Temporal redundancy. Intuitively, a token should be removed if similar tokens have already existed in previous frames. Therefore, we remove tokens frame-by-frame by comparing whether similar tokens have been retained. For simplicity, we reduce a constant number of tokens in each frame to ensure parallel computing. We introduce the accumulative temporal score " + }, + { + "bbox": [ + 46, + 308, + 287, + 416 + ], + "type": "inline_equation", + "content": "\\mathbf{A} \\in [0,1]^{n_t \\times n_s}" + }, + { + "bbox": [ + 46, + 308, + 287, + 416 + ], + "type": "text", + "content": " to model the probability of dropping a token conditioned on the specific frame " + }, + { + "bbox": [ + 46, + 308, + 287, + 416 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 308, + 287, + 416 + ], + "type": "text", + "content": ". Specifically, we define:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 63, + 423, + 287, + 454 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 423, + 287, + 454 + ], + "spans": [ + { + "bbox": [ + 63, + 423, + 287, + 454 + ], + "type": "interline_equation", + "content": "\\mathbf {A} _ {t, s} := \\mathbb {P} _ {\\text {d r o p}} \\left(\\mathbf {X} _ {t, s}\\right) \\in [ 0, 1 ] \\quad \\text {s . t .} \\sum_ {s = 1} ^ {n _ {s}} \\mathbf {A} _ {t, s} = 1, \\tag {2}", + "image_path": "74fae3399e3532cdffc23d2fca6dda0cfefd14ea3a6ae444a6c46968a115353b.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "text", + "content": "where tokens with higher temporal accumulative scores are more likely to be pruned because they carry a high degree of temporal redundancy. Next, we eliminate " + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "text", + "content": " tokens with the highest scores from " + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "text", + "content": "-th frame and transfer the remaining probability distribution " + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_t' \\in \\mathbb{R}^{(n_s - r) \\times 1}" + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "text", + "content": " to the next frame via the transition probability " + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathbb{P}_{\\mathrm{drop}}(\\mathbf{X}_t | \\mathbf{X}_{t-1}') \\in \\mathbb{R}^{n_s \\times (n_s - r)}" + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "text", + "content": ". By excluding the dropped tokens of the last frame, we effectively restart the repetition aggregation. This prevents the high scores from being concentrated on specific tokens and allows for the global identification of redundancy. Mathematically," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 63, + 601, + 287, + 623 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 601, + 287, + 623 + ], + "spans": [ + { + "bbox": [ + 63, + 601, + 287, + 623 + ], + "type": "interline_equation", + "content": "\\mathbf {A} _ {t + 1} := \\mathbb {P} _ {\\text {d r o p}} \\left(\\mathbf {X} _ {t + 1} \\mid \\mathbf {X} _ {t} ^ {\\prime}\\right) \\mathbf {A} _ {t} ^ {\\prime}, \\tag {3}", + "image_path": "ccef4315385272e661f26505e0a57ae8dffe1f27f65a980b6cdb31d4e9f8bf54.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 63, + 620, + 259, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 620, + 259, + 635 + ], + "spans": [ + { + "bbox": [ + 63, + 620, + 259, + 635 + ], + "type": "interline_equation", + "content": "\\mathrm {P} _ {\\text {d r o p}} \\left(\\mathbf {X} _ {t + 1} \\mid \\mathbf {X} _ {t} ^ {\\prime}\\right) := \\operatorname {s o f t m a x} \\left(f \\left(\\mathbf {X} _ {t + 1}\\right) f \\left(\\mathbf {X} _ {t} ^ {\\prime}\\right) ^ {T}\\right),", + "image_path": "caf52381fb70f85af091b8f352be3415f290612bbee974c324a6ff019d4c1fb5.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "content": " is the projection head to measure the similarity, and we construct transition probability by softmax-based affinity matrix. Note that we do not need to train a new projection head " + }, + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "content": " because the self-attention provides the necessary functionality, and the key function " + }, + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "inline_equation", + "content": "f_{K}" + }, + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "content": " extracts most relevant knowledge for affinity estimation, as shown" + } + ] + } + ], + "index": 10 + }, + { + "type": "code", + "bbox": [ + 306, + 91, + 538, + 333 + ], + "blocks": [ + { + "bbox": [ + 306, + 72, + 538, + 84 + ], + "lines": [ + { + "bbox": [ + 306, + 72, + 538, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 538, + 84 + ], + "type": "text", + "content": "Algorithm 1 Pseudocode of STA in a PyTorch-like style." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 306, + 91, + 538, + 333 + ], + "lines": [ + { + "bbox": [ + 306, + 91, + 538, + 333 + ], + "spans": [ + { + "bbox": [ + 306, + 91, + 538, + 333 + ], + "type": "text", + "content": "# x: token embedding, n_t x n_s x d\n# I: image-based token pruning method\n# r: drop number per frame\n# sim: token-to-token affinity function\n# min-max norm, Eqn.(4)\naam = norm(x.abs().sum(-1)) # size: (n_t, n_s, 1)\n# token removal at 1-st frame\nx_0 = I(x[0]) # size: (n_s-r, d)\n# initialization\nx_list, x_old = [x_0], x_0\nfor t in range(1, n_t):\n # token-to-token affinity matrix\nA_t = sim(x[t], x_old) # size: (n_s, n_s-r)\n# accumulateative temporal score\ns_acc = mm(A_t, s_acc) # size: (n_s, 1)\n# class-aware accumulative temporal score, Eqn.(5)\ns = s_acc * (1-aam[t])\ns = s.squeeze(dim=-1) # size: (n_s)\n# keep tokens with the minimal score\ni_t = s.topk(k=N-r, largest=False) # size: (n_s-r)\nx_old = x[t, i_t] # size: (n_s-r, d)\nx_list = x_list.append(x_old)\n# cut off the dropped tokens' score\ns_acc = s_acc[i_t] # size: (n_s-r, 1)\n# first-order norm\ns_acc = s_acc / s_acc-sum()" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "code_body" + } + ], + "index": 12, + "sub_type": "algorithm" + }, + { + "bbox": [ + 304, + 369, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 545, + 418 + ], + "type": "text", + "content": "in Table 6c. This formulation allows us to connect all temporally distinct tokens through a simple Markov chain and aggregate potential redundancy from the first frame to every subsequent frame." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "text", + "content": "Semantic importance. Up until this point, our approach has focused on capturing temporally repetitive information. However, we have neglected the influence of semantic attributes. In other words, we have treated each token equally, regardless of its contribution to the semantics of the class. To integrate semantics importance with our approach, we use the activation-based attention map " + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "text", + "content": " [45], which takes the feature matrix " + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{n_t \\times n_s \\times d}" + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "text", + "content": " as input and produces a score for each token in the matrix. Specifically, we define the semantic score for token " + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{t,s}" + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 363, + 564, + 545, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 363, + 564, + 545, + 597 + ], + "spans": [ + { + "bbox": [ + 363, + 564, + 545, + 597 + ], + "type": "interline_equation", + "content": "\\mathcal {F} \\left(\\mathbf {X} _ {t, s}\\right) = \\sum_ {i = 1} ^ {d} \\left| \\mathbf {X} _ {t, s, i} \\right| \\in \\mathbb {R} ^ {+}. \\tag {4}", + "image_path": "186ab74c5cc2001178e26139795debc5a6ebe142fa049bba501519639848ba41.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Intuitively, through the summation of absolute activation values over channel dimension, a high absolute activation suggests a significant contribution to next layers. Moreover, we apply STA on off-the-shelf Transformers supervised by semantic labels, where high activation areas tend to represent discriminative category information. Thus, activation-based attention maps could effectively capture the importance or relevance of the token to the overall semantics. We then use this score to re-weigh the temporal accumulative" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16948" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "scores " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": ", giving tokens with high semantic contributions less weight in the pruning process. This ensures that tokens with high semantics are more likely to be retained, even if they have a high degree of temporal redundancy." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 121, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 121, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 47, + 121, + 287, + 156 + ], + "type": "text", + "content": "Finally, we compute the semantic-aware temporal accumulative score " + }, + { + "bbox": [ + 47, + 121, + 287, + 156 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{A}}_{t,s}" + }, + { + "bbox": [ + 47, + 121, + 287, + 156 + ], + "type": "text", + "content": " by integrating the semantic score " + }, + { + "bbox": [ + 47, + 121, + 287, + 156 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(\\mathbf{X}_{t,s})" + }, + { + "bbox": [ + 47, + 121, + 287, + 156 + ], + "type": "text", + "content": " with the accumulative temporal score " + }, + { + "bbox": [ + 47, + 121, + 287, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 47, + 121, + 287, + 156 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 110, + 166, + 287, + 181 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 166, + 287, + 181 + ], + "spans": [ + { + "bbox": [ + 110, + 166, + 287, + 181 + ], + "type": "interline_equation", + "content": "\\widetilde {\\mathbf {A}} _ {t, s} = \\left(1 - \\mathcal {F} \\left(\\mathbf {X} _ {t, s}\\right)\\right) \\mathbf {A} _ {t, s}, \\tag {5}", + "image_path": "254f470cf4b9d0333538941d9581c219ff301ab08f72c4a167f46a66c108487e.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 186, + 287, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 186, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 287, + 281 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 186, + 287, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(\\mathbf{X}_{t,s})" + }, + { + "bbox": [ + 46, + 186, + 287, + 281 + ], + "type": "text", + "content": " is min-max normalized to the range [0,1]. We utilize the semantic-aware accumulative temporal scores to guide token removal for all subsequent frames, except for the first frame. Thus, we adopt an image-based token pruning method on the first frame to kick off our algorithm. Once tokens are discarded through our strategy, they are never employed in subsequent layers, thus accelerating the inference of the Transformer." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "text", + "content": "We summarize the pseudocode of STA in Alg. 1. The algorithm takes token embedding " + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{n_t \\times n_s \\times d}" + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "text", + "content": ", an image-based token pruning method " + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "text", + "content": ", the number of tokens to drop per frame " + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "text", + "content": ", and a token-to-token affinity function as inputs. The algorithm calculates the STA score for each frame, selects the tokens with the minimal STA score, and retains them for the next frame. This process is repeated for all frames and returns the resulting token embedding matrix with the retained tokens " + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "inline_equation", + "content": "\\mathbf{X}' \\in \\mathbb{R}^{n_t \\times (n_s - r) \\times d}" + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 403, + 287, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 440 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 440 + ], + "type": "text", + "content": "Summary of the superiority of STA. Compared to the previous token-pruning methods, our approach, STA, offers three significant merits when applied to video data:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 448, + 287, + 631 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 58, + 448, + 287, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 448, + 287, + 507 + ], + "spans": [ + { + "bbox": [ + 58, + 448, + 287, + 507 + ], + "type": "text", + "content": "- STA fully considers the potential repetition of tokens along the temporal axis and eliminates the genuine redundancy with insignificant semantics. The temporal aggregation design makes the scoring mechanism more motion-aware and suitable for video data;" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 516, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 516, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 58, + 516, + 287, + 552 + ], + "type": "text", + "content": "- STA works as a plug-in module without the introduction of additional parameters and it does not require the retraining of the video Transformer;" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 58, + 559, + 287, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 559, + 287, + 631 + ], + "spans": [ + { + "bbox": [ + 58, + 559, + 287, + 631 + ], + "type": "text", + "content": "- STA achieves a complexity of " + }, + { + "bbox": [ + 58, + 559, + 287, + 631 + ], + "type": "inline_equation", + "content": "O\\left(n_{t}n_{s}\\left(n_{s}-r\\right)\\right)" + }, + { + "bbox": [ + 58, + 559, + 287, + 631 + ], + "type": "text", + "content": ", resulting in negligible additional FLOPs that only take up a small percentage of the total forward pass. Moreover, our algorithm allows for the bulk of computation to be done in parallel, making it friendly to modern GPU devices." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 639, + 287, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 639, + 287, + 663 + ], + "spans": [ + { + "bbox": [ + 47, + 639, + 287, + 663 + ], + "type": "text", + "content": "Overall, our approach is efficient and easily deployable, making it an ideal solution for pruning video Transformers." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 671, + 119, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 119, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 119, + 682 + ], + "type": "text", + "content": "3.3. Discussion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "In this section, we present a two-part practical analysis to shed the light on the intuition behind STA." + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 326, + 71, + 526, + 122 + ], + "blocks": [ + { + "bbox": [ + 326, + 71, + 526, + 122 + ], + "lines": [ + { + "bbox": [ + 326, + 71, + 526, + 122 + ], + "spans": [ + { + "bbox": [ + 326, + 71, + 526, + 122 + ], + "type": "table", + "html": "
ModelSmallBaseLargeHuge
ViT5.105.385.075.55
Rand-ViT5.005.324.955.46
STA-ViT4.434.744.284.78
", + "image_path": "0881e4f3c9f8ccfb93e240ae1f94c0e369428ac2d2ff41155a570fa4e1c5568a.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 131, + 545, + 167 + ], + "lines": [ + { + "bbox": [ + 305, + 131, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 305, + 131, + 545, + 167 + ], + "type": "text", + "content": "Table 1: Trajectory sum for ViT family on the Kinetics-400 validation set. Compared to random pruning, STA-ViT decreases the temporal redundancy significantly." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 310, + 182, + 545, + 305 + ], + "blocks": [ + { + "bbox": [ + 310, + 182, + 545, + 305 + ], + "lines": [ + { + "bbox": [ + 310, + 182, + 545, + 305 + ], + "spans": [ + { + "bbox": [ + 310, + 182, + 545, + 305 + ], + "type": "image", + "image_path": "3c897761d68f6c4aadf932d901bbd28b2c032cc451a9c65ec3745fc4f8bb35bc.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 312, + 545, + 371 + ], + "lines": [ + { + "bbox": [ + 305, + 312, + 545, + 371 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 545, + 371 + ], + "type": "text", + "content": "Figure 3: Gradient visualization for ViT-Large on the Kinetics-400 validation set. We stack original RGB frames, gradient norm heatmap, and our pruning result from top to bottom. Our pruning algorithm preserves the area of rich semantics well." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 394, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 394, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 305, + 394, + 545, + 491 + ], + "type": "text", + "content": "Does STA effectively reduce the temporal redundancy? To answer this question, we first define temporal redundancy as the frequency with which similar tokens appear at different timestamps. We then assess this phenomenon in a video by probing the last frame, denoted as " + }, + { + "bbox": [ + 305, + 394, + 545, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{-1} \\in \\mathbb{R}^{n_s \\times d}" + }, + { + "bbox": [ + 305, + 394, + 545, + 491 + ], + "type": "text", + "content": ", and aggregating the cosine similarity between each token and the most similar tokens in previous frames. We term this aggregation as trajectory sum " + }, + { + "bbox": [ + 305, + 394, + 545, + 491 + ], + "type": "inline_equation", + "content": "S \\in \\mathbb{R}" + }, + { + "bbox": [ + 305, + 394, + 545, + 491 + ], + "type": "text", + "content": ". Mathematically," + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 318, + 498, + 545, + 531 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 498, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 318, + 498, + 545, + 531 + ], + "type": "interline_equation", + "content": "S = \\frac {1}{n _ {s}} \\sum_ {i = 1} ^ {n _ {s}} \\sum_ {t = 1} ^ {n _ {t} - 1} \\max _ {j \\in \\{1, \\dots , n _ {s} \\}} \\cos - \\operatorname {s i m} \\left(\\mathbf {X} _ {- 1}, \\mathbf {X} _ {t}\\right) _ {i j}, \\tag {6}", + "image_path": "178cee97d5406c2fea515e604faef23f6b858e97fbf0f48a1395463fd2e8abb0.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 540, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 540, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 305, + 540, + 545, + 675 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 540, + 545, + 675 + ], + "type": "inline_equation", + "content": "\\cos -\\sin (\\mathbf{X},\\mathbf{Y})_{ij} = \\frac{\\mathbf{X}_i\\cdot\\mathbf{Y}_j}{|\\mathbf{X}_i||\\mathbf{Y}_j|}" + }, + { + "bbox": [ + 305, + 540, + 545, + 675 + ], + "type": "text", + "content": ". A higher trajectory sum indicates greater temporal redundancy and lower diversity along the temporal axis. When all the frames are the same, the score would reach its theoretical maximum, which is " + }, + { + "bbox": [ + 305, + 540, + 545, + 675 + ], + "type": "inline_equation", + "content": "N_{t} - 1" + }, + { + "bbox": [ + 305, + 540, + 545, + 675 + ], + "type": "text", + "content": ". Then, we compare our method with the standard Transformer and random-prune counterparts in terms of the proposed trajectory sum. Table 1 shows that the video Transformer exhibits heavy temporal redundancy and random pruning fails to alleviate them considerably. In contrast, STA achieves a far lower trajectory sum, indicating that it effectively eliminates temporal redundancy." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Does STA retain semantics-rich tokens? To manifest it, we calculate the gradient norm for each token when back-" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16949" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": "propagating the training loss " + }, + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": ". We then aggregated the first-order gradient norm of " + }, + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^l" + }, + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": " at each layer " + }, + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": " to obtain the GradNorm, which reflects the contribution of each token to the final prediction. Mathematically," + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 71, + 132, + 287, + 166 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 132, + 287, + 166 + ], + "spans": [ + { + "bbox": [ + 71, + 132, + 287, + 166 + ], + "type": "interline_equation", + "content": "\\operatorname {G r a d N o r m} (\\mathbf {X}) = \\sum_ {l = 1} ^ {L} \\sum_ {i = 1} ^ {d} \\left| \\frac {\\partial \\mathcal {L}}{\\partial \\mathbf {X} _ {.. , i} ^ {l}} \\right| \\in \\mathbb {R} ^ {n _ {t} \\times n _ {s}}, \\tag {7}", + "image_path": "c27f4fb0c5bd5f7d7de55f838c19c367a832e43bfe86a79f996fca860531a9fb.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 176, + 288, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 176, + 288, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 176, + 288, + 308 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 176, + 288, + 308 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 176, + 288, + 308 + ], + "type": "text", + "content": " is the total number of the Transformer block, e.g., " + }, + { + "bbox": [ + 46, + 176, + 288, + 308 + ], + "type": "inline_equation", + "content": "L = 24" + }, + { + "bbox": [ + 46, + 176, + 288, + 308 + ], + "type": "text", + "content": " for ViT-Large. Figure 3 shows the GradNorm distribution in the form of a heatmap. The heatmap reveals sparse patterns across the board, indicating that most tokens do not contribute significantly to the final prediction. Instead, the key regions responsible for the final prediction are usually motion-centric entities. This agrees with our intuition of highlighting semantically meaningful regions. With the help of activation-based attention map " + }, + { + "bbox": [ + 46, + 176, + 288, + 308 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 176, + 288, + 308 + ], + "type": "text", + "content": " in Eqn. (4), STA retains almost all areas of high-activation GradNorm as is evidenced in the last row of Figure 3." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 324, + 128, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 324, + 128, + 337 + ], + "spans": [ + { + "bbox": [ + 47, + 324, + 128, + 337 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 345, + 163, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 345, + 163, + 357 + ], + "spans": [ + { + "bbox": [ + 47, + 345, + 163, + 357 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "text", + "content": "Datasets and backbones. We evaluate our algorithm on two standard video action recognition datasets. Kinetics-400 [14] (K400) and Something-Something V2 [11] (SSV2). Kinetics-400 is a large-scale action recognition dataset sourced from YouTube, which consists of around 10-second clips with 400 human action classes. The training and validation set has approximately " + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "inline_equation", + "content": "240\\mathrm{K}" + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "inline_equation", + "content": "20\\mathrm{K}" + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "text", + "content": " videos, respectively. Something-Something V2 is a motion-heavy benchmark with 174 labels, where the object and background are shared across the different action categories. Around " + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "inline_equation", + "content": "170\\mathrm{K}" + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "inline_equation", + "content": "25\\mathrm{K}" + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "text", + "content": " videos exist in the training and validation set of SSV2, respectively. We implement our STA strategy with two mainstream Transformer-based backbones, namely ViT [8] and VideoSwin [23]. For ViT, we sample 16 frames with " + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "inline_equation", + "content": "224^2" + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "text", + "content": " pixels as input and the size of 3D tube is " + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\{2,16,16\\}" + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "text", + "content": ". Therefore, the number of tokens for all layers is " + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "inline_equation", + "content": "n = \\frac{16}{2} \\times \\frac{224^2}{16^2} = 8 \\times 14^2" + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "text", + "content": ". We load the open-sourced checkpoints from VideoMAE [35] due to its superior performance. For VideoSwin, the input resolution is " + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "inline_equation", + "content": "32 \\times 224^2" + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "text", + "content": " and the size of 3D tube is " + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\{2,4,4\\}" + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "text", + "content": ". The number of tokens at four hierarchical stages would be " + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\{16 \\times 56^2, 16 \\times 28^2, 16 \\times 14^2, 16 \\times 7^2\\}" + }, + { + "bbox": [ + 46, + 365, + 288, + 713 + ], + "type": "text", + "content": ". Though our algorithm is not intended for window-based Transformers that require structural integrity, we still find a simple solution. We compensate for the discarded token with the nearest kept tokens when computing the window attention and speed up the rest of the process, such as the linear projection. In total, we test 10 off-the-shelf backbones with different pre-trained weights on two benchmarks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "text", + "content": "Implementation details. To progressively remove inattentive tokens, we apply our STA module three times. For ViT, we insert our STA module at the end of the " + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "inline_equation", + "content": "1^{st}" + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "inline_equation", + "content": "(1 + L/3)^{th}" + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "inline_equation", + "content": "(1 + 2L/3)^{th}" + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "text", + "content": " block, where " + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "text", + "content": " is the total number of Transformer blocks. For VideoSwin, there are four hierarchical stages with varied resolutions and the STA module is located at the end of the first three stages. We denote different variants of STA as " + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "inline_equation", + "content": "\\mathrm{STA}^{r_1}" + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "text", + "content": "-Model, where " + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "inline_equation", + "content": "r_1" + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "text", + "content": " is the number of spatial tokens dropped per frame at the first stage. We adopt a decreasing schedule, which reduces the dropped number by half at each stage. For instance, " + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "inline_equation", + "content": "\\mathrm{STA}^{64}" + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "text", + "content": "-ViT-L indicates pruning " + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "inline_equation", + "content": "\\{8 \\times 64, 8 \\times 32, 8 \\times 16\\}" + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "text", + "content": " tokens on ViT-Large. We weigh the computation via two metrics, FLOPs (floating-point operations) and throughput. FLOPs are reported with the help of fvcore library1 and throughput (clips/s) is measured at a batch size of 32 on a single 32G Tesla V100. Besides, we closely follow the inference metric for ViT and VideoSwin in [35, 23]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 293, + 545, + 517 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 317, + 293, + 545, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 293, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 317, + 293, + 545, + 402 + ], + "type": "text", + "content": "- ViT [35]: To evaluate on K400, we sample " + }, + { + "bbox": [ + 317, + 293, + 545, + 402 + ], + "type": "inline_equation", + "content": "5 \\times 3" + }, + { + "bbox": [ + 317, + 293, + 545, + 402 + ], + "type": "text", + "content": " views by uniformly selecting 5 16-frame clips from a full-length video in the temporal dimension with the frame stride of 4. For each clip, we resize the shorter spatial side to 224 pixels and extract 3 crops of " + }, + { + "bbox": [ + 317, + 293, + 545, + 402 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 317, + 293, + 545, + 402 + ], + "type": "text", + "content": " resolution that cover the longer spatial axis. The final score is the average score computed over all views. For SSV2, we follow a similar procedure by sampling 2 clips " + }, + { + "bbox": [ + 317, + 293, + 545, + 402 + ], + "type": "inline_equation", + "content": "\\times 3" + }, + { + "bbox": [ + 317, + 293, + 545, + 402 + ], + "type": "text", + "content": " crops and the frames stride is 2." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 408, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 408, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 317, + 408, + 545, + 517 + ], + "type": "text", + "content": "- VideoSwin [23]: For K400, we extract 4 32-frame clips from each full-length video using a temporal stride of 2 and a spatial size of " + }, + { + "bbox": [ + 317, + 408, + 545, + 517 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 317, + 408, + 545, + 517 + ], + "type": "text", + "content": ". Similarly, for SSV2, we extract 1 set of clips using a spatial size of " + }, + { + "bbox": [ + 317, + 408, + 545, + 517 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 317, + 408, + 545, + 517 + ], + "type": "text", + "content": " and 3 spatial crops, with a frame stride of 2. Besides, we prune VideoSwin three times as " + }, + { + "bbox": [ + 317, + 408, + 545, + 517 + ], + "type": "inline_equation", + "content": "\\{r_1, 1.5r_1/4, 2r_1/16\\}" + }, + { + "bbox": [ + 317, + 408, + 545, + 517 + ], + "type": "text", + "content": ". For instance, " + }, + { + "bbox": [ + 317, + 408, + 545, + 517 + ], + "type": "inline_equation", + "content": "\\mathrm{STA}^{256}" + }, + { + "bbox": [ + 317, + 408, + 545, + 517 + ], + "type": "text", + "content": "-VideoSwin-S indicates pruning " + }, + { + "bbox": [ + 317, + 408, + 545, + 517 + ], + "type": "inline_equation", + "content": "\\{16 \\times 256, 16 \\times 96, 16 \\times 32\\}" + }, + { + "bbox": [ + 317, + 408, + 545, + 517 + ], + "type": "text", + "content": " on VideoSwin-S." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 522, + 391, + 534 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 522, + 391, + 534 + ], + "spans": [ + { + "bbox": [ + 306, + 522, + 391, + 534 + ], + "type": "text", + "content": "4.2. Main Results" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 540, + 545, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 540, + 545, + 671 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 545, + 671 + ], + "type": "text", + "content": "We conduct a thorough investigation of two off-the-shelf model families, ViT [8] and VideoSwin [23], on the Kinetics-400 and Something-Something V2 datasets. The results presented in Table 2 demonstrate that our proposed method can significantly reduce the computational costs of ViT models by " + }, + { + "bbox": [ + 304, + 540, + 545, + 671 + ], + "type": "inline_equation", + "content": "25\\% \\sim 49\\%" + }, + { + "bbox": [ + 304, + 540, + 545, + 671 + ], + "type": "text", + "content": ", with negligible impacts on performance " + }, + { + "bbox": [ + 304, + 540, + 545, + 671 + ], + "type": "inline_equation", + "content": "(-0.2\\% \\sim -1.0\\%)" + }, + { + "bbox": [ + 304, + 540, + 545, + 671 + ], + "type": "text", + "content": ". It is worth noting our method shows a favorable trade-off between complexity and performance for larger models. For instance, our method reduces the FLOPs of ViT-Huge by half to just 611 GFLOPs, with only a " + }, + { + "bbox": [ + 304, + 540, + 545, + 671 + ], + "type": "inline_equation", + "content": "0.2\\%" + }, + { + "bbox": [ + 304, + 540, + 545, + 671 + ], + "type": "text", + "content": " drop in accuracy." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 672, + 545, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 672, + 545, + 696 + ], + "spans": [ + { + "bbox": [ + 306, + 672, + 545, + 696 + ], + "type": "text", + "content": "To demonstrate the potential of our method to generalize well on various transformer backbones, we are conducting" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 317, + 703, + 525, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 703, + 525, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 703, + 525, + 712 + ], + "type": "text", + "content": "" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16950" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 75, + 70, + 519, + 228 + ], + "blocks": [ + { + "bbox": [ + 75, + 70, + 519, + 228 + ], + "lines": [ + { + "bbox": [ + 75, + 70, + 519, + 228 + ], + "spans": [ + { + "bbox": [ + 75, + 70, + 519, + 228 + ], + "type": "table", + "html": "
Base ModelMetricsDrop Number r1
0324864
ViT-SK400 Acc. (%)78.878.8 (-0.0)78.6 (-0.2)78.1 (-0.7)
SSV2 Acc. (%)66.866.6 (-0.2)66.4 (-0.4)65.8 (-1.0)
GFLOPs5742 (-26%)35 (-39%)29 (-49%)
ViT-BK400 Acc. (%)81.281.2 (-0.0)81.1 (-0.1)80.8 (-0.4)
SSV2 Acc. (%)70.670.4 (-0.2)70.3 (-0.3)69.9 (-0.7)
GFLOPs180136 (-24%)116 (-36%)96 (-47%)
ViT-LK400 Acc. (%)85.185.2 (+0.1)85.1 (-0.0)85.0 (-0.1)
GFLOPs597446 (-25%)376 (-37%)308 (-48%)
ViT-HK400 Acc. (%)86.386.3 (-0.0)86.2 (-0.1)86.1 (-0.2)
GFLOPs1192890 (-25%)748 (-37%)611 (-49%)
", + "image_path": "c6c8634ad72c0b464a017222ff0e867b72b0ccdee1460a469febb8b22bc5f28a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 75, + 271, + 519, + 406 + ], + "blocks": [ + { + "bbox": [ + 46, + 236, + 546, + 261 + ], + "lines": [ + { + "bbox": [ + 46, + 236, + 546, + 261 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 546, + 261 + ], + "type": "text", + "content": "Table 2: Main Results for STA-ViT family on Kinetics-400 [14] (K400) and Something-Something V2 [11] (SSV2). All input resolution is " + }, + { + "bbox": [ + 46, + 236, + 546, + 261 + ], + "type": "inline_equation", + "content": "{16} \\times {224}^{2}" + }, + { + "bbox": [ + 46, + 236, + 546, + 261 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 75, + 271, + 519, + 406 + ], + "lines": [ + { + "bbox": [ + 75, + 271, + 519, + 406 + ], + "spans": [ + { + "bbox": [ + 75, + 271, + 519, + 406 + ], + "type": "table", + "html": "
Base ModelMetricsDrop Number r1
0192256320
VideoSwin-TK400 Acc. (%)78.878.7 (-0.1)78.7 (-0.1)78.6 (-0.2)
GFLOPs8868 (-23%)61 (-31%)54 (-39%)
VideoSwin-SK400 Acc. (%)80.580.3 (-0.2)80.2 (-0.3)80.1 (-0.4)
GFLOPs166121 (-27%)106 (-36%)91 (-45%)
VideoSwin-BK400 Acc. (%)82.782.5 (-0.2)82.5 (-0.2)82.3 (-0.4)
K400 GFLOPs282202 (-28%)176 (-38%)149 (-47%)
SSV2 Acc. (%)69.669.6 (-0.0)69.5 (-0.1)69.2 (-0.4)
SSV2 GFLOPs321241 (-25%)215 (-33%)188 (-41%)
", + "image_path": "c4befaa4a0459d0d1f9940eaf24caa3923664776b8c9bd6706e9115421295e98.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 414, + 546, + 449 + ], + "lines": [ + { + "bbox": [ + 46, + 414, + 546, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 546, + 449 + ], + "type": "text", + "content": "Table 3: Main Results for STA-VideoSwin family on Kinetics-400 [14] (K400) and Something-Something V2 [11] (SSV2). All input resolution is " + }, + { + "bbox": [ + 46, + 414, + 546, + 449 + ], + "type": "inline_equation", + "content": "32 \\times 224^2" + }, + { + "bbox": [ + 46, + 414, + 546, + 449 + ], + "type": "text", + "content": ". VideoSwin-B employs varying window sizes for K400 and SSV2, leading to a discrepancy in FLOPs." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 472, + 289, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 289, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 289, + 604 + ], + "type": "text", + "content": "further experiments on VideoSwin [23], a modern architecture that uses a window shuffling operation to interchange information. As VideoSwin is naturally unsuitable for unstructured tokens, we are filling the dropped locations during the window attention operation with the nearest tokens and then discarding the replicated tokens after the attention operation. Empirical results in Table 3 indicate that the performance of VideoSwin holds until FLOPs fall by roughly " + }, + { + "bbox": [ + 46, + 472, + 289, + 604 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 46, + 472, + 289, + 604 + ], + "type": "text", + "content": ". This observation verifies that both columnar ViT and hierarchical VideoSwin have heavy and unnecessary computations that can be significantly optimized." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": "Comparison with the state of the art. Firstly, we tabulate a comparison of our proposed method on K400 in Table 4. Our model performs favorably in terms of both accuracy and computation cost. For example, ViT-L equipped with our STA achieves the same accuracy as MViTv2-L [19] but with less than a quarter of the computational cost. Moreover, STTS [40] proposes a scorer network to conduct dynamic token selection separately in space and time, re" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 472, + 547, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 547, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 547, + 639 + ], + "type": "text", + "content": "quiring to be trained in an end-to-end fashion. Our result surpasses STTS by " + }, + { + "bbox": [ + 304, + 472, + 547, + 639 + ], + "type": "inline_equation", + "content": "0.4\\%" + }, + { + "bbox": [ + 304, + 472, + 547, + 639 + ], + "type": "text", + "content": " accuracy using the same backbone VideoSwin-B but with only " + }, + { + "bbox": [ + 304, + 472, + 547, + 639 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 304, + 472, + 547, + 639 + ], + "type": "text", + "content": " GFLOPs. This result verifies that leveraging the model itself to weigh the redundancy of tokens is sufficient to reduce complexity. We also report the result on SSV2 in Table 5. The superior performance of our proposed method verifies that STA prunes the inconsequential tokens via temporal cues, as it is known that understanding SSV2 mainly relies on temporal information. Specifically, ViT-B equipped with our STA surpasses most of the prior arts with a considerably minor complexity of 116 GFLOPs. For VideoSwin, our strategy outperforms STTS-VideoSwin by " + }, + { + "bbox": [ + 304, + 472, + 547, + 639 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 304, + 472, + 547, + 639 + ], + "type": "text", + "content": " accuracy with " + }, + { + "bbox": [ + 304, + 472, + 547, + 639 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 304, + 472, + 547, + 639 + ], + "type": "text", + "content": " of the computation cost." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "Visualization of STA. Figure 4 shows image patches corresponding to kept tokens after three stages. The results align with our objective of resisting temporal redundancy and retaining informative tokens. In a tennis sequence, STA preserves the most meaningful patches, including a human" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16951" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 70, + 284, + 210 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 284, + 210 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 284, + 210 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 284, + 210 + ], + "type": "table", + "html": "
ModelGFLOPs×viewsTop-1
TimeSformer-L [2]8353 × 1 × 380.7
Motionformer-L [28]1185 × 10 × 380.2
ViViT [1]3981 × 4 × 384.9
Swin-L [23]2107 × 10 × 584.9
MViTv2-L [19]2828 × 5 × 386.1
ViT-H [35]1192 × 5 × 386.3
STTS-VideoSwin-B [40]253 × 4 × 381.9
ToMe-ViT-L [3]281 × 10 × 184.5
STA320-VideoSwin-B (ours)149 × 4 × 382.3
STA64-ViT-L (ours)308 × 5 × 385.0
STA64-ViT-H (ours)611 × 5 × 386.1
", + "image_path": "5ae05975b7b09580bca91c98a7a0fadfae6b0d362bbd101833aba60c03352377.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 51, + 303, + 284, + 410 + ], + "blocks": [ + { + "bbox": [ + 46, + 219, + 288, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 219, + 288, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 288, + 291 + ], + "type": "text", + "content": "Table 4: Comparisons with the-state-of-the-arts method on Kinetics-400. We report the computational cost with a single view (temporal clip with spatial crop) " + }, + { + "bbox": [ + 46, + 219, + 288, + 291 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 46, + 219, + 288, + 291 + ], + "type": "text", + "content": " the number of views (FLOPs " + }, + { + "bbox": [ + 46, + 219, + 288, + 291 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 46, + 219, + 288, + 291 + ], + "type": "text", + "content": " view_time " + }, + { + "bbox": [ + 46, + 219, + 288, + 291 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 46, + 219, + 288, + 291 + ], + "type": "text", + "content": " view_space). Gray represents that this method leverages the dynamic token pooling to optimize existing backbones." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 303, + 284, + 410 + ], + "lines": [ + { + "bbox": [ + 51, + 303, + 284, + 410 + ], + "spans": [ + { + "bbox": [ + 51, + 303, + 284, + 410 + ], + "type": "table", + "html": "
ModelGFLOPs×viewsTop-1
TimeSformer-L [2]5549 × 1 × 362.4
Motionformer-L [28]1185 × 1 × 368.1
MViTv2-B [19]225 × 1 × 370.5
VideoSwin-B [23]321 × 1 × 369.6
ViT-B [35]180 × 2 × 370.6
STTS-VideoSwin-B [40]237 × 1 × 368.7
STA320-VideoSwin-B (ours)188 × 1 × 369.2
STA48-ViT-B (ours)116 × 2 × 370.3
", + "image_path": "e369bd42deace75edce0ccb0b28cec4e8006a58a1508ee3af983ab38ba97b8c0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 418, + 287, + 491 + ], + "lines": [ + { + "bbox": [ + 46, + 418, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 287, + 491 + ], + "type": "text", + "content": "Table 5: Comparisons with the-state-of-the-arts method on Something-Something V2. We report the computational cost with a single view (temporal clip with spatial crop) " + }, + { + "bbox": [ + 46, + 418, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 46, + 418, + 287, + 491 + ], + "type": "text", + "content": " the number of views (FLOPs " + }, + { + "bbox": [ + 46, + 418, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 46, + 418, + 287, + 491 + ], + "type": "text", + "content": " view_time " + }, + { + "bbox": [ + 46, + 418, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 46, + 418, + 287, + 491 + ], + "type": "text", + "content": " view_space). Gray represents that this method leverages the dynamic token pooling to optimize existing backbones." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 512, + 287, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 512, + 287, + 573 + ], + "spans": [ + { + "bbox": [ + 46, + 512, + 287, + 573 + ], + "type": "text", + "content": "at the far end of the court, and filters out dull backgrounds like the blue ground. The temporal aggregation design ensures that the kept tokens are not just the most salient ones but also a variety of regions, preserving diversity within videos for better reasoning." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 582, + 141, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 141, + 594 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 141, + 594 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 600, + 287, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 600, + 287, + 648 + ], + "spans": [ + { + "bbox": [ + 46, + 600, + 287, + 648 + ], + "type": "text", + "content": "To find the optimal strategy, we conduct a series of ablation studies. We evaluate off-the-shelf ViT-Large on K400 by default and report accuracy, FLOPs, and throughput for reference unless otherwise stated." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Token removal at the first frame. To investigate how the first-frame removal affects performance, we conduct experiments on three candidates. (1) Random Prune: we randomly select " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " tokens to discard. (2) Grid Prune: we split" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 73, + 547, + 238 + ], + "blocks": [ + { + "bbox": [ + 310, + 73, + 547, + 238 + ], + "lines": [ + { + "bbox": [ + 310, + 73, + 547, + 238 + ], + "spans": [ + { + "bbox": [ + 310, + 73, + 547, + 238 + ], + "type": "image", + "image_path": "c401b239dc7f3c940ac06a72286fd4519fad726731758551bbf5838e1f2dc50e.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 245, + 547, + 293 + ], + "lines": [ + { + "bbox": [ + 304, + 245, + 547, + 293 + ], + "spans": [ + { + "bbox": [ + 304, + 245, + 547, + 293 + ], + "type": "text", + "content": "Figure 4: Visualization of the proposed STA strategy. We masked out the discarded tokens with white boxes. STA not only retains informative tokens but also ensures diverse regions for improved video reasoning." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 314, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 314, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 545, + 460 + ], + "type": "text", + "content": "the first frame into " + }, + { + "bbox": [ + 304, + 314, + 545, + 460 + ], + "type": "inline_equation", + "content": "\\sqrt{r} \\times \\sqrt{r}" + }, + { + "bbox": [ + 304, + 314, + 545, + 460 + ], + "type": "text", + "content": " grids spatially and drop one random token per grid. (3) ToMe Prune: inspired by recent image pruning method ToMe [3], we get rid of the most similar tokens by the simple bipartite soft matching. The difference here is that we just drop tokens rather than 'merge' tokens. Note that all three pruning ways are negligible in the terms of computation and lead to similar speedup. It actually echoes the main insight of STA, leveraging temporal aggregation to reduce spatio-temporal redundancy. Even given a random initialization state, the sequential STA strategy could still decrease the total temporal redundancy and optimize the video Transformers effectively." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 472, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 545, + 510 + ], + "type": "text", + "content": "Pruning schedule. We explore how to assign the number of dropping tokens among three stages. When maintaining a similar throughput, we devise three types of schedules:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 335, + 528, + 520, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 528, + 520, + 540 + ], + "spans": [ + { + "bbox": [ + 335, + 528, + 520, + 540 + ], + "type": "text", + "content": "Constant Schedule: " + }, + { + "bbox": [ + 335, + 528, + 520, + 540 + ], + "type": "inline_equation", + "content": "\\{8\\times 48,8\\times 48,8\\times 48\\}" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 328, + 543, + 520, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 543, + 520, + 555 + ], + "spans": [ + { + "bbox": [ + 328, + 543, + 520, + 555 + ], + "type": "text", + "content": "Decreasing Schedule: " + }, + { + "bbox": [ + 328, + 543, + 520, + 555 + ], + "type": "inline_equation", + "content": "\\{8\\times 64,8\\times 32,8\\times 16\\}" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 330, + 558, + 523, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 558, + 523, + 571 + ], + "spans": [ + { + "bbox": [ + 330, + 558, + 523, + 571 + ], + "type": "text", + "content": "Increasing Schedule: " + }, + { + "bbox": [ + 330, + 558, + 523, + 571 + ], + "type": "inline_equation", + "content": "\\{8\\times 27,8\\times 54,8\\times 108\\}" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 578, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 547, + 628 + ], + "type": "text", + "content": "As shown in Table 6d, the decreasing schedule owns the least accuracy reduction with similar throughput. It verifies that standard video Transformers process a great number of uninformative tokens that can be dropped at the beginning." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "type": "text", + "content": "Temporal accumulation order. Besides starting the accumulation flow from the beginning of the input video, we could also kick off at the ending frames. In Table 6b, we empirically find alternating order at different dropping stages outperforms the consistent counterparts. We speculate that the same accumulation direction would amplify" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16952" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 85, + 80, + 214, + 137 + ], + "blocks": [ + { + "bbox": [ + 85, + 80, + 214, + 137 + ], + "lines": [ + { + "bbox": [ + 85, + 80, + 214, + 137 + ], + "spans": [ + { + "bbox": [ + 85, + 80, + 214, + 137 + ], + "type": "table", + "html": "
MethodTop-1Top-5
Random84.7896.46
Grid84.8596.50
ToMe84.9696.50
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OrderTop-1Top-5
F-B-F84.9696.50
B-F-B84.9796.43
F-F-F84.2696.41
B-B-B84.3596.37
", + "image_path": "39fbe1d843eebe4f343900ffca84e93aed1cade817f91e63ec9e5b7a5be6c326.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 75, + 149, + 516, + 174 + ], + "lines": [ + { + "bbox": [ + 75, + 149, + 516, + 174 + ], + "spans": [ + { + "bbox": [ + 75, + 149, + 516, + 174 + ], + "type": "text", + "content": "(a) Ablation on token removal meth- (b) Ablation on temporal accumula- (c) Ablation on different similarity ods at the first frame. tion order. function " + }, + { + "bbox": [ + 75, + 149, + 516, + 174 + ], + "type": "inline_equation", + "content": "f" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 376, + 80, + 511, + 148 + ], + "blocks": [ + { + "bbox": [ + 376, + 80, + 511, + 148 + ], + "lines": [ + { + "bbox": [ + 376, + 80, + 511, + 148 + ], + "spans": [ + { + "bbox": [ + 376, + 80, + 511, + 148 + ], + "type": "table", + "html": "
SimilarityTop-1Top-5
fQ84.8396.52
fK84.9696.50
fV84.8496.50
fFFN84.9496.50
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ScheduleTop-1Top-5clips/s
constant84.6896.3647
decreasing84.9696.5047
increasing77.6893.7244
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ScoreViT-SViT-BViT-L
1 - F(Xt,s)77.3380.5284.87
At,s77.7880.4384.69
(1 - F(Xt,s))At,s78.1280.8284.96
", + "image_path": "ee089e3934323f197a0f892c7ccf4b4e791cd03ea1ef239432233f137f06028d.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 303, + 241, + 521, + 253 + ], + "lines": [ + { + "bbox": [ + 303, + 241, + 521, + 253 + ], + "spans": [ + { + "bbox": [ + 303, + 241, + 521, + 253 + ], + "type": "text", + "content": "(e) Ablation on scoring mechanism. Top-1 is reported." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 262, + 545, + 288 + ], + "lines": [ + { + "bbox": [ + 46, + 262, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 545, + 288 + ], + "type": "text", + "content": "Table 6: Results of STA ablation experiments. F and B in (b) mean forward and backward order, respectively. The baseline ViT-L without STA obtains " + }, + { + "bbox": [ + 46, + 262, + 545, + 288 + ], + "type": "inline_equation", + "content": "85.05\\%" + }, + { + "bbox": [ + 46, + 262, + 545, + 288 + ], + "type": "text", + "content": " Top-1 and " + }, + { + "bbox": [ + 46, + 262, + 545, + 288 + ], + "type": "inline_equation", + "content": "96.55\\%" + }, + { + "bbox": [ + 46, + 262, + 545, + 288 + ], + "type": "text", + "content": " Top-5 accuracy on K400 at 19.5 clips/s. Gray is our default setting." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 309, + 287, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 309, + 287, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 309, + 287, + 334 + ], + "type": "text", + "content": "intrinsic propagation error but alternating the order counteracts it, leading to more reasonable pruning." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 349, + 287, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 349, + 287, + 398 + ], + "spans": [ + { + "bbox": [ + 46, + 349, + 287, + 398 + ], + "type": "text", + "content": "Similarity function choice. We ablate four similarity project heads " + }, + { + "bbox": [ + 46, + 349, + 287, + 398 + ], + "type": "inline_equation", + "content": "\\{f_{Q}, f_{V}, f_{K}, f_{\\mathrm{FFN}}\\}" + }, + { + "bbox": [ + 46, + 349, + 287, + 398 + ], + "type": "text", + "content": ". Table 6c shows that key function " + }, + { + "bbox": [ + 46, + 349, + 287, + 398 + ], + "type": "inline_equation", + "content": "f_{k}" + }, + { + "bbox": [ + 46, + 349, + 287, + 398 + ], + "type": "text", + "content": " captures the most correct affinity with minimal noise. The observation coincides with previous work [3]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 521 + ], + "type": "text", + "content": "Scoring mechanism. To explore how accumulation score and semantic identification boost each other, we conduct the experiment with different scoring formulas. Table 6e demonstrates that considering both temporal redundancy and semantics helps in discovering informative tokens. The results on ViT-S show that temporal aggregation modeled by the Markov Chain plays an important role in the pruning process, while semantic importance functions effectively for ViT-B and ViT-L." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 537, + 287, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 537, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 46, + 537, + 287, + 658 + ], + "type": "text", + "content": "Performance vs. prune number " + }, + { + "bbox": [ + 46, + 537, + 287, + 658 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 537, + 287, + 658 + ], + "type": "text", + "content": ". To seek the sweet spot of our algorithm, we vary the prune number " + }, + { + "bbox": [ + 46, + 537, + 287, + 658 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 537, + 287, + 658 + ], + "type": "text", + "content": " at the first stage ranging from [16, 96] and evaluate the Top-1 accuracy. In addition, we compare our STA with the Random pruning baseline. As displayed in Figure. 5, STA behaves fairly robust to the token reduction and consistently surpasses the result of the random pruning. Specifically, " + }, + { + "bbox": [ + 46, + 537, + 287, + 658 + ], + "type": "inline_equation", + "content": "r = 64" + }, + { + "bbox": [ + 46, + 537, + 287, + 658 + ], + "type": "text", + "content": " doubles the throughput but just drops " + }, + { + "bbox": [ + 46, + 537, + 287, + 658 + ], + "type": "inline_equation", + "content": "0.1\\%" + }, + { + "bbox": [ + 46, + 537, + 287, + 658 + ], + "type": "text", + "content": " accuracy. This confirms that our algorithm retains the semantics-rich tokens with the lowest redundancy." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 669, + 119, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 119, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 119, + 681 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "In conclusion, we propose a new token pruning strategy, Semantic-aware Temporal Accumulation (STA), for" + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 314, + 309, + 535, + 473 + ], + "blocks": [ + { + "bbox": [ + 314, + 309, + 535, + 473 + ], + "lines": [ + { + "bbox": [ + 314, + 309, + 535, + 473 + ], + "spans": [ + { + "bbox": [ + 314, + 309, + 535, + 473 + ], + "type": "image", + "image_path": "cd7ee016dbe8da99d81d462383b9944042512bf9dd7dc65cfd3993fb9557fcab.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 480, + 545, + 506 + ], + "lines": [ + { + "bbox": [ + 305, + 480, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 305, + 480, + 545, + 506 + ], + "type": "text", + "content": "Figure 5: Top-1 accuracy and throughput under two pruning methods with various prune numbers " + }, + { + "bbox": [ + 305, + 480, + 545, + 506 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 305, + 480, + 545, + 506 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 515, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 515, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 515, + 545, + 624 + ], + "type": "text", + "content": "video Transformers that can significantly reduce computation overhead with a subtle accuracy drop. Specifically, we consider temporal redundancy and semantic importance when deciding to keep or drop the token. Our approach does not introduce any parameter and can directly accelerate the off-the-shelf video Transformers without training. The extensive experiments demonstrate that our method empowers video Transformers to obtain a competitive speed-accuracy trade-off compared to the prior arts." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 634, + 404, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 634, + 404, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 634, + 404, + 647 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "type": "text", + "content": "This work was supported in part by the National Natural Science Foundation of China under Grant 62250055, Grant 61932022, Grant 62120106007, and in part by the Program of Shanghai Science and Technology Innovation Project under Grant 20511100100." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16953" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. 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In this paper, we propose a 6D object pose estimation method that can be trained with pure RGB images without any auxiliary information. We first obtain a rough pose initialization from networks trained on synthetic images rendered from the target's 3D mesh. Then, we introduce a refinement strategy leveraging the geometry constraint in synthetic-to-real image pairs from multiple different views. We formulate this geometry constraint as pixel-level flow consistency between the training images with dynamically generated pseudo labels. We evaluate our method on three challenging datasets and demonstrate that it outperforms state-of-the-art self-supervised methods significantly, with neither 2D annotations nor additional depth images.", + "bbox": [ + 75, + 282, + 473, + 541 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 571, + 209, + 585 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The goal of 6D object pose estimation is to accurately estimate the 3D rotation and 3D translation of a rigid object with respect to the camera, which gives essential information about the world beyond classical 2D understanding and is a fundamental component in many applications, such as robotic manipulation [5], autonomous driving [36], and augmented reality [37].", + "bbox": [ + 75, + 597, + 468, + 703 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent progress in this field has significantly improved the robustness and accuracy of the model [49, 60, 21, 56, 7, 29, 19, 18]. Most of these approaches, however, rely on a large number of real images with accurate 6D pose annotations. But, compared to classical 2D annotation, these 6D annotations are either very hard to obtain [38, 34] or are prone to contain large labeling errors [16, 11, 58]. Some recent methods propose to use techniques based on image synthesis [15] or self-supervised learning [55, 54] to handle this problem. The main problem with synthetic images is the large domain gap to the real images, making the model's generalization ability suffers in practice [42, 60]. On the other hand, most self-supervised methods rely on additional", + "bbox": [ + 75, + 704, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4b7ffd272f1744892a326b98e70744154e011ea56985c248d1888df9a8ece5ae.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 511, + 250, + 883, + 329 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/105a4625e7d5b7f84c193bfc492aebcb855250a8edf751a20a7c86e66b3d1135.jpg", + "image_caption": [ + "(a) Existing self-supervised 6D object pose methods", + "(b) Our solution based on pseudo flow consistency", + "Figure 1. Comparison of self-supervised object pose methods. (a) Most existing self-supervised object pose methods rely on either the depth image [55, 54, 4, 31] or additional mask annotations [61, 46], limiting their application range. (b) By contrast, our method can be trained only with the guidance of flow consistency based on the intrinsic geometry constraint of multiple different views, and produces more accurate results than existing solutions, without relying on any auxiliary information." + ], + "image_footnote": [], + "bbox": [ + 511, + 347, + 880, + 426 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "information. Some can only work with additional depth images [55, 54, 31, 4] or others need pixel-level annotation of a segmentation mask [46, 61], which prevents the general applicability, as shown in Fig. 1.", + "bbox": [ + 498, + 594, + 893, + 655 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we propose a self-supervised framework for 6D object pose estimation, which relies on neither depth nor additional 2D annotations. We first generate a synthetic dataset based on rendered images from the target's 3D mesh and train networks only on this dataset to get a rough pose initialization. To close the domain gap between the synthetic and real data, we use a refinement strategy where we compare the rendered reference image according to the initial pose and the real input based on pseudo labels [47, 62]. Pseudo labeling is widely used in many computer vision tasks [52, 59, 12, 8]. However, the two fundamental problems of pseudo labeling are still open questions in 6D object pose estimation, including the generative strategy of creating pseudo labels and the selection strategy of extracting high-quality labels from the noisy candidates, as shown in Fig. 2.", + "bbox": [ + 496, + 657, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14075", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1b2296d9be61097060f865d68e5fb214667282f3b6cb058544b0b48ed8fc3ca9.jpg", + "image_caption": [ + "(a) The standard strategy for self-supervised classification" + ], + "image_footnote": [], + "bbox": [ + 106, + 92, + 434, + 242 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ee9b2bc277275393f40f553257af4df180ab27be9a74355fead2e2d9f8237ded.jpg", + "image_caption": [ + "(b) The proposed strategy for self-supervised object pose estimation", + "Figure 2. Self-supervised strategies in different fields. (a) Teacher-student learning scheme is a classical framework for self-supervised classification [52]. The key is how to determine the quality of pseudo labels from the noisy prediction of the teacher network. For image classification, one can obtain the prediction quality by the output distribution after the softmax operation easily, which is usually implemented by checking if the probability of any class is above a threshold [47, 62]. (b) However, there is no such easy way to determine the quality of an object pose prediction without the ground truth. We propose to formulate pseudo object pose labels as pixel-level optical flow supervision signals, and then use the flow consistency between multiple views based on their underlying geometry constraint." + ], + "image_footnote": [], + "bbox": [ + 478, + 88, + 875, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We propose to formulate the pseudo 6D pose labels as pixel-level flow supervision signals in a render-and compare framework [16, 26, 29, 60, 21, 32, 9]. Unlike the common render-and compare frameworks that need accurate pose annotations, we propose a geometry-guided learning framework without any annotations. We render multiple images near the initial pose, and compare them with the real input with the guidance of flow consistency, based on the geometry constraints between these image pairs from different views. We choose high-quality flow labels based on the proposed consistency on the fly, and supervise the network training with these dynamically generated labels in every training step.", + "bbox": [ + 75, + 380, + 468, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate our method on three challenging datasets LINEMOD [14], Occluded-LINEMOD [24], and YCBV [58], and show that it outperforms state-of-the-art self-supervised methods significantly, including those methods relied on depth image [55, 54] or auxiliary annotation information [61, 46].", + "bbox": [ + 75, + 575, + 468, + 666 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be summarized as the following. First, we investigate the problem of the standard teacher-student methods in selecting high-quality pseudo labels for self-supervised object pose estimation. Second, we propose a strategy based on flow consistency that embeds the geometry constraint from multiple views. Finally, we demonstrate its effectiveness by significantly outperforming state-of-the-art self-supervised object pose methods, without relying on any auxiliary information.", + "bbox": [ + 75, + 667, + 470, + 803 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 814, + 218, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Object pose estimation has shown significant progress recently, based on different techniques, such as direct pose regression [56, 7, 26], 2D reprojection regression [44, 42, 18, 19, 40], 3D keypoint prediction [30, 41, 49, 11], and", + "bbox": [ + 76, + 839, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "differentiable PnP solver [27, 17, 2, 3]. However, most of these methods rely on a large number of real images with accurate 6D pose annotation, which is usually hard to obtain in practice, especially in cluttered scenes with multiple object instances and occlusions [58, 16].", + "bbox": [ + 496, + 380, + 892, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Some recent methods tackle this problem by training on synthetic images rendered from the target's 3D mesh [11, 42, 1], but this strategy suffers from the domain gap between the synthetic and real image sets [6]. In contrast, some pose refinement methods have shown significant improvement in the generalization ability across different domains [29, 32, 26, 21, 60, 9] and especially [16], which produces comparable results as the state-of-the-art methods with only about one-tenth of the real images involved in training. Although having this promising progress, these pose refinement methods still need many annotated real images for training, and can not easily benefit from more real data without further annotations.", + "bbox": [ + 496, + 459, + 892, + 654 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To solve this problem, some recent self-supervised methods [55, 61, 46, 54] try to remove the cumbersome procedure of pose annotation completely. Most of them are based on a strategy that compares the synthetic image rendered from an initial pose with the real image, and backpropagate the gradient through a differentiable renderer [23, 33] to update the network's weights during training, expecting to align the rendered image with the real input without explicit annotations. This type of strategy, however, relies heavily on the performance of comparing the final rendered image and the real input, which suffers from the domain gap, making them often rely either on depth [55] or on additional pixel-level annotations of segmentation masks [61]. In contrast, we propose to compare multiple synthetic-to-real image pairs at the same time, and force networks to comply with the geometry constraint between those image", + "bbox": [ + 496, + 657, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14076", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3508920f3cf6c03dc1a1cafa23543b238ba724e63a29fa9a85e40bb6ea8b3db4.jpg", + "image_caption": [ + "Figure 3. Method overview. We first obtain the initial pose based on a pose estimation network trained only on synthetic images, and then train our refinement framework on real images without any annotations. Our proposed framework is based on a teacher-student learning scheme. Given a rough pose initialization, we render multiple synthetic images around this initial pose, and create multiple image pairs between the synthetic and real images. We dynamically produce pixel-level flow supervision signals for the student network during the training, by leveraging the geometry-guided flow consistency between those image pairs from different views. After getting 3D-to-2D correspondences based on the predicted flow, we use a PnP solver to get the final pose [16]." + ], + "image_footnote": [], + "bbox": [ + 84, + 89, + 883, + 247 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "pairs from different views, which suffers little from the domain problem. On the other hand, we formulate the geometry constraint as pixel-level consistency, which provides us dynamic valid label mask during training, without any 3D depth information or additional 2D mask annotations.", + "bbox": [ + 75, + 359, + 467, + 434 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Pseudo labeling is also one of the basic techniques used in recent self-supervised object pose methods [31, 4]. However, these approaches still rely on additional depth images to select valid pseudo labels. In addition, they only update the pseudo labels after finishing the previous training, which usually means the model needs to be trained multiple times to utilize the slowly updated pseudo labels. By contrast, our pseudo flow labels are generated dynamically in every training step, and our model only needs to be trained once.", + "bbox": [ + 75, + 436, + 467, + 571 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method is related to the recent teacher-student formulation of pseudo labeling [47, 62, 52, 59, 25, 64, 28, 63, 57, 43, 22], which works under the assumption that the generated high-quality pseudo label of the teacher can be used to supervise the student network when having the same input as the teacher but only different data augmentations. Although this simple general framework has been widely used in image classification [47, 62], object detection [59, 28, 64, 51], and semantic segmentation [25], it only can work with high-quality pseudo labels. However, there is still no easy way to generate high-quality pose labels in the context of 6D object pose estimation. To solve this problem, we propose to formulate pseudo 6D pose labels as pixel-level flow supervision signals and select high-quality pseudo flow labels based on flow consistency across multiple different views during training. Our experiments demonstrate the effectiveness of this method.", + "bbox": [ + 75, + 571, + 467, + 828 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 76, + 844, + 184, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a dataset of calibrated RGB images and the 3D mesh of the target, our goal is to train a self-supervised", + "bbox": [ + 76, + 869, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "model on this dataset to estimate the 6D object pose of the target, without relying on depth images or any auxiliary information, such as 6D pose and 2D mask annotations. We first create a synthetic dataset by rendering the 3D mesh of the target in different poses and train an existing pose estimation network [19, 26] on it to obtain a rough pose initialization [16, 29, 21]. The core component of our method is a self-supervised pose refinement framework, which we will discuss in detail in this section. We first show an overview of our self-supervised framework, and then present how we formulate the flow consistency based on the geometry constraint between different views. Finally, we show how we extend it to multiple image pairs to further increase the robustness. Fig. 3 shows the overview of our method.", + "bbox": [ + 496, + 359, + 890, + 570 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Framework Overview", + "text_level": 1, + "bbox": [ + 500, + 580, + 704, + 594 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use a teacher-student architecture [52] for our self-supervised framework. It contains two networks with identical network structures, but not shared weights, which are called the teacher and student, respectively. During training, when an image input of the teacher network can produce a prediction that can fulfill some criteria, we convert this prediction to a one-hot pseudo-label, and use it to supervise the student network with the same image input but only different data augmentations. After updating the weights of the student network by gradient backpropagation supervised by this pseudo label, we then update the weights of the teacher network by a simple exponential moving averaging (EMA) strategy from the student network:", + "bbox": [ + 496, + 604, + 890, + 800 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {W} _ {t} = \\alpha \\mathbf {W} _ {t} + (1 - \\alpha) \\mathbf {W} _ {s}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 811, + 890, + 828 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{W}_t$ and $\\mathbf{W}_s$ are the network weight parameters of the teacher and student network, respectively, and $\\alpha$ is the exponential factor, which is typically 0.999. The weight updating and pseudo label generation is conducted after each", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14077", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/84b10bb4abc55380b44793043a096b2d7c3737adc90c5631ee0bcbcf9d1182ee.jpg", + "image_caption": [ + "(a) Flow consistency across multiple views" + ], + "image_footnote": [], + "bbox": [ + 102, + 88, + 472, + 200 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e99c75afb7d3f32c2ca2fc7a3f63224c00a5becfaac02f0c273b2aa3cca80d30.jpg", + "image_caption": [ + "(b) Flow-guided photometric consistency", + "Figure 4. Illustration of geometry-guided consistency. We predict the flow between synthetic and real images. (a) The 2D flow of the same 3D point from different synthetic views to the real input should be consistent. (b) On the other hand, the target 2D locations of the same 3D point on different real inputs should have similar textures." + ], + "image_footnote": [], + "bbox": [ + 513, + 87, + 883, + 200 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "iteration during training, making it much more efficient than other pseudo-label-based object pose methods [4, 31], which can only produce pseudo labels after the whole training pipeline and need to train the model multiple times.", + "bbox": [ + 75, + 292, + 467, + 353 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our main problem is how to select high-quality pseudo label candidates from the noisy predictions of the teacher network. For the image classification task as in [52], one can obtain the label quality by the output distribution after the softmax operation easily, which is usually implemented by checking if the probability of any class is above a threshold [47, 62]. However, there is no such easy way to determine the quality of an object pose prediction without the ground truth. We discuss our solution in the following sections.", + "bbox": [ + 75, + 354, + 467, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Flow Consistency across Multiple Views", + "text_level": 1, + "bbox": [ + 76, + 516, + 419, + 532 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To solve the problem of difficulties in determining the quality of object pose predictions, we first formulate object pose estimation as a problem of estimating dense 2D-to-2D correspondence, or optical flow estimation, as in PFA [16], which, however, is a fully-supervised object pose method. To tackle the problem of no pose annotation for the computation of ground truth flow, we render multiple images around the initial pose, and predict the flow between each of them and the real input. In principle, since both the rendered images and real input image are 2D reprojections of the same 3D object, the flow prediction that aligns with the underlying geometry should have a higher probability of being of high quality. Fig. 4(a) illustrates such consistency assumption.", + "bbox": [ + 75, + 540, + 468, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "More formally, given an unannotated real image $\\mathbf{I}^t$ and the obtained initial pose $\\mathbf{P}_0$ from networks trained only on synthetic data, we randomly generate another $n - 1$ poses $\\{\\mathbf{P}_1,\\dots ,\\mathbf{P}_{n - 1}\\}$ , around the initial pose $\\mathbf{P}_0$ , and then create $n$ synthetic images by rendering the target under the corresponding poses, generating $n$ image pairs:", + "bbox": [ + 75, + 752, + 468, + 843 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\left(\\mathbf {I} _ {i} ^ {r}, \\mathbf {I} ^ {t}\\right) \\right\\}, \\quad 0 \\leq i \\leq n - 1, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 854, + 468, + 873 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{I}_i^r$ is the rendered image of the target under pose $\\mathbf{P}_i$ .", + "bbox": [ + 76, + 885, + 467, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For an object having $N$ 3D keypoints, the 2D reprojection of a 3D keypoint $\\mathbf{p}_j$ , $1 \\leq j \\leq N$ , under pose $\\mathbf{P}_i$ can be obtained by", + "bbox": [ + 498, + 292, + 890, + 339 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\lambda_ {i j} ^ {r} \\left[ \\begin{array}{c} \\mathbf {u} _ {i j} ^ {r} \\\\ 1 \\end{array} \\right] = \\mathbf {K} \\left(\\mathbf {R} _ {i} \\mathbf {p} _ {j} + \\mathbf {t} _ {i}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 345, + 890, + 380 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda_{ij}^{r}$ is a scale factor, $\\mathbf{u}_{ij}^{r}$ is the 2D image location, $\\mathbf{K}$ is the intrinsic camera matrix, and $\\mathbf{R}_i$ and $\\mathbf{t}_i$ are the rotation and translation of pose $\\mathbf{P}_i$ , respectively. We then establish 3D-to-2D correspondence $\\mathbf{p}_j \\leftrightarrow \\mathbf{u}_{ij}^r$ under pose $\\mathbf{P}_i$ . For the real image $\\mathbf{I}^t$ , although its true pose $\\mathbf{P}^t$ is unknown to us, the relation between the 3D keypoint $\\mathbf{p}_j$ and its 2D image location $\\mathbf{u}_j^t$ should follow the perspective principle of Eq. 3, implicitly generating the correspondence $\\mathbf{p}_j \\leftrightarrow \\mathbf{u}_j^t$ .", + "bbox": [ + 496, + 386, + 890, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We train a network to predict dense 2D-to-2D correspondence $\\mathbf{F}_i^{r\\rightarrow t}$ between the two images in each image pair of Eq. 2, such that", + "bbox": [ + 498, + 508, + 890, + 553 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {u} _ {i j} ^ {r} + \\mathbf {f} _ {i} ^ {r \\rightarrow t} = \\mathbf {u} _ {i j} ^ {t}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 561, + 890, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{f}_i^{r\\rightarrow t}$ is the corresponding 2D flow vector. Although $\\mathbf{u}_j^t$ is unknown during training, we have the geometry constraint that the 2D image locations $\\{\\mathbf{u}_{ij}^r +\\mathbf{f}_i^{r\\rightarrow t}\\}$ of the same 3D keypoint $\\mathbf{p}_j$ from different synthetic views $0\\leq i\\leq n - 1$ should be the same.", + "bbox": [ + 498, + 585, + 890, + 660 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We use the standard variance of the predicted $\\mathbf{u}_{ij}^{t}$ from different views to determine if the current pixel's flow prediction is a valid pseudo label", + "bbox": [ + 496, + 662, + 890, + 708 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {j} = \\operatorname {s t d} \\left(\\left\\{\\mathbf {u} _ {i j} ^ {r} + \\mathbf {f} _ {i} ^ {r \\rightarrow t} \\right\\}\\right) \\quad 0 \\leq i \\leq n - 1, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 715, + 890, + 734 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and select valid flow pseudo labels by a simple threshold $\\tau$ . Fig. 7 shows some visualizations of the variance $\\sigma$ .", + "bbox": [ + 496, + 741, + 890, + 770 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After obtaining the valid flow labels from the teacher network, we use them to supervise the student network by a loss function", + "bbox": [ + 496, + 771, + 890, + 815 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {f l o w} = \\sum_ {i = 0} ^ {n - 1} V _ {i} \\| \\left(g \\left(\\mathbf {I} _ {i} ^ {r}, \\mathbf {I} ^ {t}; \\mathbf {W} _ {t}\\right) - g \\left(\\mathbf {I} _ {i} ^ {r}, \\tilde {\\mathbf {I}} ^ {t}; \\mathbf {W} _ {s}\\right)\\right) \\|, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 821, + 890, + 862 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $g$ is the flow network with parameters $\\mathbf{W}_t$ and $\\mathbf{W}_s$ for the teacher and student network, respectively, and $\\tilde{\\mathbf{I}}^t$", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14078", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "is the same real image as $\\mathbf{I}^t$ but only with different data augmentations, and $V_{i}$ is the mask containing valid pixels where $\\sigma_{j} < \\tau$ . Note that, $V_{i}$ is generated dynamically from the consistency check between multiple image pairs in Eq. 2, and does not rely on any 2D mask annotations.", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Flow-Guided Photometric Consistency", + "text_level": 1, + "bbox": [ + 76, + 172, + 410, + 189 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The previous section only investigates the consistency between the synthetic views and the real input. We further explore the consistency between multiple real inputs. Our motivation is that the 2D image reprojections of the same 3D object keypoint on different real images should have similar textures. We formulate this texture assumption as a photometric consistency, as illustrated in Fig. 4(b).", + "bbox": [ + 75, + 196, + 468, + 301 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given the real image $\\mathbf{I}^t$ with the initial pose $\\mathbf{P}_0$ , as in the previous section, we randomly retrieve another $m$ real images whose initial pose is around $\\mathbf{P}_0$ , generating $m$ image pairs", + "bbox": [ + 75, + 301, + 468, + 361 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\left(\\mathbf {I} _ {0} ^ {r}, \\mathbf {I} _ {k} ^ {t}\\right) \\right\\}, \\quad 1 \\leq k \\leq m, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 362, + 468, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and after feeding the two images in each image pair to the teacher network, we have", + "bbox": [ + 75, + 382, + 468, + 411 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\mathbf {u}} _ {k} ^ {t} = \\mathbf {u} _ {0} ^ {r} + g \\left(\\mathbf {I} _ {0} ^ {r}, \\mathbf {I} _ {k} ^ {t}; \\mathbf {W} _ {t}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 417, + 468, + 435 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\bar{\\mathbf{u}}_k^t$ is the predicted 2D image location on image $\\mathbf{I}_k^t$ . We assume these predicted 2D image locations of the same 3D keypoint have similar texture properties, and we use a photometric loss to model this", + "bbox": [ + 75, + 440, + 468, + 500 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p h o t o}} = \\sum_ {k = 1} ^ {m} V _ {0} \\rho \\left(w \\left(\\mathbf {I} _ {k} ^ {t}, \\bar {\\mathbf {u}} _ {k} ^ {t}\\right), w \\left(\\mathbf {I} ^ {t}, \\bar {\\mathbf {u}} ^ {t}\\right)\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 506, + 468, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $w$ is an operation function that warps the image according to the new pixel locations, $\\rho$ is a generalized Charbonnier function to measure the photometric difference based on the Census transformation [39], and $\\bar{\\mathbf{u}}^t$ is inferred from the student's prediction, where", + "bbox": [ + 75, + 550, + 468, + 625 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\mathbf {u}} ^ {t} = \\mathbf {u} _ {0} ^ {r} + g \\left(\\mathbf {I} _ {0} ^ {r}, \\tilde {\\mathbf {I}} ^ {t}; \\mathbf {W} _ {s}\\right) \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 631, + 468, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We combine the flow consistency and photometric consistency into our final loss", + "bbox": [ + 75, + 654, + 468, + 683 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {f l o w}} + 0. 5 \\mathcal {L} _ {\\text {p h o t o}}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 691, + 468, + 708 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that, we only apply the loss to the student network since the gradient backprogataion only occurs for the student network, and the teacher network only gets its weight updated by EMA updating as discussed in Section 3.1.", + "bbox": [ + 75, + 713, + 468, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 784, + 207, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we first present the experiment setting of our method and then compare our method with state-of-the-art self-supervised methods. We finally conduct detailed ablation studies of our method in various settings. Our source code is publicly available at https://github.com/YangHai-1218/PseudoFlow.", + "bbox": [ + 75, + 810, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experiment Setup", + "text_level": 1, + "bbox": [ + 500, + 90, + 674, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We evaluate our method on three widely-used datasets for 6D object pose estimation: LINEMOD (\"LM\") [14], Occluded-LINEMOD (\"LM-O\") [24], and YCB-V [58]. LINEMOD dataset contains 13 objects, with a single sequence per object without occlusions. We follow [55, 16] to use $15\\%$ of the real images for training, resulting in a total of 2.4k images. Occluded-LINEMOD is an extension of LINEMOD, which annotates all the objects in one sequence in LINEMOD as the test set and shares the training set with LINEMOD. The recent YCB-V dataset consists of 130k real training images for 21 texture-less objects captured in cluttered scenes. Although all these three datasets contain manually labeled annotations, we train our models on them without accessing the ground truth, and report the final accuracy on their test set. We use the synthetic dataset used in the BOP challenge [6, 15, 50] to train WDR-Pose [19] for the pose initialization.", + "bbox": [ + 496, + 112, + 890, + 369 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics. We mainly use ADD-0.1d as our metric, which computes the average distance between the mesh vertices transformed by the predicted pose and the ground truth pose, and then only treat the prediction with an average 3D error below $10\\%$ of the mesh diameter as a correct pose estimate. We use its symmetric version for symmetric objects. Additionally, in some settings, we also use BOP metrics [15] for evaluation, including the Visible Surface Discrepancy (VSD), the Maximum Symmetry-aware Surface Distance (MSSD), the Maximum Symmetry-aware Projection Distance (MSPD), and their average AR. We refer the readers to [15] for their detailed definition.", + "bbox": [ + 496, + 369, + 890, + 550 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training details. We use RAFT [53] as our flow network for both the teacher and student network. We initialize the weights of both teacher and student network with the weights pretrained on synthetic data and train the model using AdamW optimizer [35] with a batch size of 16. We use One-cycle strategy [45] to anneal the learning rate from a starting point $4\\mathrm{e} - 4$ . We crop the target object from the original image according to the initial pose, and then resize the image patch to $256\\times 256$ . We do not use any data augmentation in the teacher network, and only use random color augmentation used in PFA [16] for the student network. We typically set $\\tau = 1$ , $m = 3$ , and $n = 4$ in our experiments. Unlike [55, 54, 31, 20] that train a separate model for each object, which is cumbersome to train, we train a single model for all objects in the same dataset.", + "bbox": [ + 496, + 551, + 890, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Comparison against State of the Art", + "text_level": 1, + "bbox": [ + 500, + 786, + 813, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first compare our method against the state-of-the-art self-supervised pose estimation methods on LINEMOD and Occluded-LINEMOD. Since most of them report numbers only in ADD-0.1d, we follow the same for a fair comparison. Table. 1 and 2 summarize the result. Our method outperforms the state-of-the-art methods significantly. Espe", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14079", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/d1afcca9ef092753a855e5a7d4a0a5f9256b067801ab7c3238da412c93b3e58e.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Comparison with self-supervised methods on LINEMOD. “*” denotes symmetric objects. We use the latest version of Self6D++ [54], and we only denote it as “Self6D” for simplicity. “Self6D‡” is the version with supervision from additional depth images. Our method outperforms “Self6D‡” with only RGB images." + ], + "table_body": "
MethodDSC [61]Sock et al. [46]Lin et al. [31]Self6D [54]Self6D‡ [54]Ours
Ape31.237.667.576.075.481.9
Bench.83.078.699.991.694.995.0
Cam49.665.687.497.197.094.2
Can56.565.699.299.899.596.8
Cat57.952.594.385.686.695.4
Driller73.748.897.698.898.994.8
Duck31.335.167.256.568.383.5
Eggbox*96.089.298.991.099.093.9
Glue*63.464.596.292.296.196.5
Holep.38.841.549.935.441.984.5
Iron61.980.999.599.599.494.9
Lamp64.770.799.897.498.994.8
Phone54.460.591.591.894.394.1
Avg.58.660.688.485.688.592.2
", + "bbox": [ + 78, + 88, + 472, + 351 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/69d0fc5dc8187caf80a8e59051598d96ecf52059d79ea38ca04a85f0f645ed2e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodDSC [61]Sock et al. [46]Lin et al. [31]Self6D [54]Self6D‡ [54]Ours
Ape9.112.040.357.759.460.1
Can21.127.575.295.096.594.2
Cat26.012.035.052.660.856.5
Driller33.520.568.590.592.089.7
Duck12.223.025.726.730.630.9
Eggbox*39.425.144.745.051.158.1
Glue*37.027.060.787.188.688.9
Holep.20.435.028.023.538.544.2
Avg.24.822.847.359.864.765.4
", + "bbox": [ + 78, + 449, + 472, + 637 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "cially, our method, which requires only RGB images, even outperforms Self6D‡ [54] by $3.7\\%$ on LINEMOD, which is a method that relies on additional depth images. We show some qualitative results in Fig. 5.", + "bbox": [ + 75, + 678, + 468, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 741, + 232, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation of different components. Table. 3 summarizes the results of our method with different components. The first row is the results of the standard teacher-student structure used in [47]. Although it has the standard EMA updating strategy, its performance is limited, mainly caused by the lacking of high-quality pseudo pose labels. After adding our flow loss and photometric loss, the performance increases significantly, which demonstrates the effectiveness of the proposed components.", + "bbox": [ + 75, + 763, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5fc95f28ee0c72e3cc61bd41f062837301b1a6e8a2fbbc3a7449a651ea592abe.jpg", + "table_caption": [ + "Table 2. Comparison on Occluded-LINEMOD." + ], + "table_footnote": [ + "Table 3. Evaluation of different components on YCB-V. $\\mathcal{L}_{flow}$ is the key component of our framework, and $\\mathcal{L}_{photo}$ improves the performance further." + ], + "table_body": "
\\( \\mathcal{L}_{flow} \\)\\( \\mathcal{L}_{photo} \\)MSPDMSSDVSDADD
--0.7590.5890.51930.9
-✓0.7650.6310.57837.5
✓-0.7800.7110.65864.2
✓✓0.7850.7490.66467.4
", + "bbox": [ + 509, + 88, + 875, + 178 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7d0f67cafdd27a8b062b5d048ede1dac9f8b4215bcccbdf8ac54a35b162b4da2.jpg", + "table_caption": [], + "table_footnote": [ + "Table 4. Performance with different initialization and additional annotations on YCB-V. We evaluate three versions of pose initialization with different accuracy, including the results obtained by the original WDR-Pose (\"Initialization v1\"), and also two other versions with pre-cropping the detected regions of interest, based on Mask RCNN and RADet, respectively (\"v2\" and \"v3\"). Our self-supervised refinement (\"SSL\") boosts the initialization accuracy significantly and achieves similar performance as versions trained with fully-annotated real images (\"Real\")." + ], + "table_body": "
MethodMSPDMSSDVSDADD
Initialization v10.6320.4910.42027.4
+ Ours (Real)0.7800.7310.67364.6
+ Ours (SSL)0.7590.7220.65063.2
Initialization v20.6730.5800.50836.0
+ Ours (Real)0.7750.7220.66065.3
+ Ours (SSL)0.7640.7240.64364.2
Initialization v30.6940.5980.52238.6
+ Ours (Real)0.8030.7520.68669.2
+ Ours (SSL)0.7850.7490.66467.4
", + "bbox": [ + 517, + 239, + 867, + 409 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training analysis on YCB-V. We evaluate our method in three different settings during the training, as shown in Fig. 6. The baseline is the original teacher-student structure [52], and the other two are the proposed components of our method. The baseline model struggles to learn from the unannotated data without explicit quality measurement of pseudo labels. Our flow loss introduces a constraint based on flow consistency derived from multiview geometry, and tackles this problem effectively, and the proposed photometric loss increases performance further, as shown in Fig. 7.", + "bbox": [ + 496, + 565, + 890, + 731 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation of hyper-parameters. We evaluate the hyperparameters used in our framework in Fig. 8. We first evaluate the impact of the number of different views. More views generally increase the performance, since it adds more information to the geometry constraint. However, too many views, such as those larger than 4, has negative impacts on the performance. We believe it is caused by the noise introduced by too many views with large viewpoint differences, which usually makes the network harder to learn. We then evaluate the threshold $\\tau$ used in our framework, which is used to determine the reliability of pseudo flow labels. It", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14080", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/238d3189b2da1f3a7ddcd2f7adfc35debfe99f93169ddf9e6a1545f7ccccdc7c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 89, + 222, + 190 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bbfceb6ab438271b1176c5385a02abde500bd5eac5762f8581a38ede79b39b7b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 225, + 90, + 352, + 190 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b3b1f28b97f70ebb90a4b7fe5e1575991488882783c16312e4be86d14372059a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 90, + 483, + 190 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/50d02b4d8241385269f6983c1f7fe3f60f466728c2f2caf24fa2871ffe535335.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 90, + 614, + 190 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/13f68cbe7bbb214072ebde75a6523f20b84ccb94ae03b70f0550b3d58accb991.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 616, + 90, + 743, + 190 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1244496934013899e89d31644bfd5a3d17f7888143ffe9372a1c6c44cab142ee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 746, + 90, + 875, + 190 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b35d6fd848da520aaaf2c69448a3b0f138a2f9451606faba663dd89b3abdb089.jpg", + "image_caption": [ + "Figure 5. Qualitative results. We show the initialization results trained only on synthetic data at the top, and the refinement results after using our self-supervised strategy at the bottom. Our method significantly improves the baseline in various conditions, such as occluded, weak-textured, and symmetry objects." + ], + "image_footnote": [], + "bbox": [ + 94, + 191, + 223, + 290 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/009c12b9bf6915498a5b81aa3ff12556f79e698a6c1d051346db6891f69a4326.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 223, + 191, + 352, + 290 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d42a2d4d1eac0d91a0e828326ccfb7b1e8818f555c7d37a25d0b14f582c90cc1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 191, + 483, + 290 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d947efc8bf414e03ad4b7c46d4a2f97a8aaf9eadb43fd05db700db5b1dbe8262.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 191, + 614, + 290 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/324d9354da2ad253866e4056b2cff274056ae53124324708842131ffe8e520f7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 616, + 191, + 743, + 290 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/07c00dbf4d117592fa613d9faa734f4eb92d7b0e67b92ac3c4c185d2bf370ea0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 746, + 191, + 875, + 290 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/66f899017d5f07b8dff60af2b7d34ad65d4a0b482e9117b9a5026e73315d3c3b.jpg", + "image_caption": [ + "Figure 6. Training analysis on YCB-V. We report the results in three different settings during training. The baseline is the original teacher-student structure [52], and the other two are the proposed components of our method. The baseline model struggles to learn from unannotated data. By contrast, our flow loss tackles this problem effectively, and our photometric loss increases the performance further." + ], + "image_footnote": [], + "bbox": [ + 86, + 364, + 352, + 536 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7715e8debcbfb81890c4b1600209c31477c838d315f6fbd850dafd36ef73c0ab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 357, + 364, + 612, + 536 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b1b0a5431d21207de9202c274dad76bb0144918ea83c17ce54503522627fa370.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 364, + 885, + 536 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "works well between 1 and 4.", + "bbox": [ + 76, + 608, + 269, + 622 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation with limited real data. We evaluate our method on YCB-V with different amounts of real data used in training, as shown in Fig. 8(b). Our method increases the performance by about $20.2\\%$ (from $41.7\\%$ to $61.9\\%$ ) in ADD-0.1d by only using $1\\%$ of all the real data. $99\\%$ more real data can only increase the performance by $5.5\\%$ further, which demonstrates the effectiveness of our method in data-limited scenarios.", + "bbox": [ + 75, + 625, + 468, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation with different initialization and additional annotations. In principle, our method can be trained with ground truth pose annotations easily, which is basically training the student network in a standard fully-supervised way. We evaluate our self-supervised method with the version trained with real pose annotations. At the same time, to evaluate the robustness of our framework to different pose initialization, we evaluate three versions of pose initialization with different initialization accuracy, including the results obtained by the original WDR-Pose, and two other", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "versions with pre-cropping the detected regions of interest, based on Mask RCNN [13] and RADet [10], respectively. Table 4 summarizes the results. Although the initial poses have different accuracy, our self-supervised refinement framework boosts their performance significantly, and even achieves similar performance as that trained on fully-annotated real images.", + "bbox": [ + 496, + 608, + 892, + 714 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison against standard optical flow methods. In principle, one can use a self-supervised optical flow method to directly establish dense 2D-to-2D correspondence between the rendered image and the real image input, without any real pose annotations. However, we find that this strategy hardly can work, mainly due to the large domain gap between the rendered and real images, in which case the standard component of photometric comparison in self-supervised flow methods suffers. We evaluate a typical self-supervised optical flow method SMURF [48], and report the results on YCB-V in Table 5. Our self-supervised strategy suffers little from this domain gap problem and produces", + "bbox": [ + 496, + 719, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14081", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e69c194f28c8c9ffab9ae43e93ceefb749e90e70af8533acc75a17b766e380c6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 87, + 197, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c163975db63e9037fbbbd41b6d90284ed5b2acdd013755dfbd4a300307c79d38.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 197, + 88, + 310, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/140ecb44655b1c22663ca4f1c390fcd2fdcfa1e62396550c15e99afb47ecf87b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 310, + 88, + 421, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d5045c1be424f03cbe7d4cccd02fbada5a2eae3e084a7ff3e5985ed4be4a2f31.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 421, + 88, + 535, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a2a5dc0b23ea4a890d41a3031a031a082995c6a5661f0a0b70a421c9e1153ffb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 535, + 88, + 647, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d9dc5d5f188d66dcf21805954d733cb3d3fff809d93fd059ee0ec52a9e142439.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 647, + 88, + 759, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/55681e440731cd25dfb0227f46b3e6e624e31e6c92779d73cb69dcbd474ea55b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 88, + 875, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/18129befcfd1d35751fc574daed9ae84f063cb44662948fe69eda7ea3d3f5776.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 83, + 176, + 197, + 265 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/707e4847049a460942f3aa05ce98b46dfd4cbf145fac97e1b2c4e2e6fe84e790.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 197, + 176, + 308, + 265 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bcb1ec01e8166563a65c07b69107b27d19c70bbdf59d18dabf6e500cfba8e2c6.jpg", + "image_caption": [ + "Variance $\\sigma$" + ], + "image_footnote": [], + "bbox": [ + 310, + 176, + 423, + 265 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/530a4dce36477275c257384c24f77413977de9a687940b6b1ffe10c3a9a46c34.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 423, + 176, + 535, + 265 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/182f1cee8860cf2ff6db40ffc00f5dd3ad095df146122eff1c856dbb080ff4c5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 535, + 176, + 648, + 265 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1ca2ab75b56583321ad12a91fc2e36312d371f8251b38d822fdd49c3b03b7cbf.jpg", + "image_caption": [ + "Flow error" + ], + "image_footnote": [], + "bbox": [ + 648, + 176, + 763, + 265 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/99690228786ae4d52c3db6b3f881eca60563a7c799113c097ac7fd11f94811b4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 763, + 176, + 875, + 265 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5ed044dce8997c355fc2e3556925dc1c0878276c138b8728863e9cc69b26697a.jpg", + "image_caption": [ + "(a) Ablation study in ADD-0.1d and AR" + ], + "image_footnote": [], + "bbox": [ + 101, + 356, + 346, + 526 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c76ec96d73ac70866fb54241ba1353aa99d5a001aee53f52fc1e8cdfa5cae4bb.jpg", + "image_caption": [ + "Figure 7. Visualization with increasing training iterations. We show the normalized visualization of variance $\\sigma$ and flow error at training steps $40\\mathrm{k}$ , $70\\mathrm{k}$ , and $100\\mathrm{k}$ from left to right, respectively. The top row shows the baseline method [52], and the bottom row is ours. The baseline method struggles to produce valid flow labels and reliable optical flow, regardless of the training steps. By contrast, our method produces more and more valid flow labels with small variance $\\sigma$ during training, also with progressively better flow predictions." + ], + "image_footnote": [], + "bbox": [ + 356, + 354, + 609, + 526 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3ee43916c75df898cff9dd6be3c7f34118cc9ceb4e7868d5362b80821d074cb8.jpg", + "image_caption": [ + "(b) Different amount of real training data", + "Figure 8. Ablation study of hyper-parameters and training data on YCB-V. (a) $m$ and $n$ are the number of views used for $\\mathcal{L}_{\\text{photo}}$ and $\\mathcal{L}_{\\text{flow}}$ , respectively, and $\\tau$ is the threshold for determining the validity of flow labels for $\\mathcal{L}_{\\text{flow}}$ . Our method is robust to the choices of different hyper parameters. (b) Our method produces acceptable results with accessing only $1\\%$ of all the real data." + ], + "image_footnote": [], + "bbox": [ + 622, + 371, + 861, + 526 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3c61e5a51cfd891af6da42a925b01ed8d20c63d7eda0e2e64a497a5605ee070f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodMSPDMSSDVSDADD
SMURF [48]0.7510.5650.48828.7
Ours0.7850.7490.66467.4
", + "bbox": [ + 94, + 609, + 444, + 671 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Comparison against standard optical flow methods on YCB-V. The typical self-supervised optical flow method SMURF [48] suffers in producing 6D object poses without pose annotations.", + "bbox": [ + 75, + 672, + 468, + 727 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "much more accurate pose results than SMURF.", + "bbox": [ + 76, + 758, + 390, + 775 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Symmetry handling. We use the same strategy as in [16, 44] for symmetric objects in obtaining pose initialization, which restricts the range of poses used in training depending on the objects' symmetry type. We do not explicitly handle the symmetry for the refinement, where we build multiple views around the initial pose and use the consistency constraint between them to find the best flow to align different views within a small pose range. Fig. 9 shows two", + "bbox": [ + 75, + 780, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a5e91e3a7a6953c74ec0063f8116106290a314cfa0c4065a2fdb9728c4b01f08.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 609, + 602, + 681 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/576870821efcbdb55710affa701841cf7fea58420f2f2bd6a754027ddf908878.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 604, + 609, + 696, + 681 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3f6aabf3ad2c7e698062c2453616b9602493e0c98fdda6859b6e6b297e4578f2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 609, + 787, + 681 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/629b2cf04439c824aa5a59c96e2807da2052c8fe4b826260b1955d48f5f6407a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 787, + 609, + 880, + 681 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a2f8ad5867971146cf8e6b3154ec954be3b87b5f89268135042fd53fa8a7b74d.jpg", + "image_caption": [ + "Symmetry objects", + "Figure 9. Symmetric objects handling. Our refinement results align the target mesh with the images well in appearance." + ], + "image_footnote": [], + "bbox": [ + 509, + 683, + 601, + 753 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/46d7ea7b5606bae8e368f382642783f000f6112080987fa0a6ab94bb3e02bfe2.jpg", + "image_caption": [ + "Ground truth" + ], + "image_footnote": [], + "bbox": [ + 602, + 681, + 696, + 753 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f1ea717b87dda0d8e5627c45d3c4bc23dd6cd0069c935c7d5f48e6d6db861fd6.jpg", + "image_caption": [ + "Initialization" + ], + "image_footnote": [], + "bbox": [ + 696, + 681, + 787, + 753 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/90d4216933a115ced1bc4b72beccc952d46d4415ff9df42a388206cfafe6b44d.jpg", + "image_caption": [ + "Refinement" + ], + "image_footnote": [], + "bbox": [ + 789, + 681, + 880, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "examples with reflectional symmetry and rotational symmetry, respectively. Note how the predicted poses have different 3D axis from the ground truth pose but align the target mesh with the images well in appearance.", + "bbox": [ + 498, + 839, + 892, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14082", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Time analysis. We conduct all our experiments on a workstation with an NVIDIA RTX-3090 GPU and an Intel-Xeon CPU with 12 cores running at $2.1\\mathrm{GHz}$ . The training of our self-supervised framework is only about $20\\%$ slower than its fully-supervised version, consuming about 30 and 24 hours in the typical setting on YCB-V, respectively, which is much more efficient than methods relying on multiple times of retraining [31, 4]. For the inference time, our method is the same as its fully-supervised version and takes only $23\\mathrm{ms}$ for a single object, including the optical flow estimation $17\\mathrm{ms}$ and the PnP solver $6\\mathrm{ms}$ .", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 268, + 194, + 286 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We have introduced a simple self-supervised 6D object pose method. After obtaining the rough pose initialization based on a network training on synthetic images, we refine the pose with a teacher-student pseudo labeling framework. To solve the problem of identifying high-quality labels in the context of object pose estimation, we first formulate pseudo object pose labels as pixel-level optical flow supervision signals. Then, we introduce a flow consistency based on the underlying geometry constraint between multiple different views. Our experiments show that the proposed method significantly outperforms existing solutions in both accuracy and efficiency, without relying on any 2D annotations or additional depth images.", + "bbox": [ + 75, + 294, + 472, + 491 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgments. This work was supported by the Natural Science Foundation of China, the Youth Innovation Team of Shaanxi Universities, the Fundamental Research Funds for the Central Universities under Grant JBF220101, and the 111 Project of China under Grant B08038. We thank Thomas Probst, Daniel Koguciuk, Juan-Ting Lin, and Lin Sun for helpful discussions.", + "bbox": [ + 75, + 494, + 472, + 585 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 595, + 174, + 612 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Dingding Cai, Janne Heikkilä, and Esa Rahtu. 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In European Conference on Computer Vision, 2022. 3" + ], + "bbox": [ + 501, + 92, + 890, + 513 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "14085", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Pseudo Flow Consistency for Self-Supervised 6D Object Pose Estimation/cf29abfd-328a-4679-9b7c-7340065b4fa2_model.json b/2023/Pseudo Flow Consistency for Self-Supervised 6D Object Pose Estimation/cf29abfd-328a-4679-9b7c-7340065b4fa2_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d895e847a501283bd8c96d0eaf5e004d17207f56 --- /dev/null +++ b/2023/Pseudo Flow Consistency for Self-Supervised 6D Object Pose Estimation/cf29abfd-328a-4679-9b7c-7340065b4fa2_model.json @@ -0,0 +1,2807 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.121, + 0.131, + 0.851, + 0.154 + ], + "angle": 0, + "content": "Pseudo Flow Consistency for Self-Supervised 6D Object Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.19, + 0.18, + 0.781, + 0.2 + ], + "angle": 0, + "content": "Yang Hai 1, Rui Song 1, Jiaojiao Li 1, David Ferstl 2, Yinlin Hu 2" + }, + { + "type": "text", + "bbox": [ + 0.288, + 0.201, + 0.682, + 0.217 + ], + "angle": 0, + "content": "\\(^{1}\\) State Key Laboratory of ISN, Xidian University, \\(^{2}\\) MagicLeap" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.252, + 0.314, + 0.267 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.284, + 0.474, + 0.542 + ], + "angle": 0, + "content": "Most self-supervised 6D object pose estimation methods can only work with additional depth information or rely on the accurate annotation of 2D segmentation masks, limiting their application range. In this paper, we propose a 6D object pose estimation method that can be trained with pure RGB images without any auxiliary information. We first obtain a rough pose initialization from networks trained on synthetic images rendered from the target's 3D mesh. Then, we introduce a refinement strategy leveraging the geometry constraint in synthetic-to-real image pairs from multiple different views. We formulate this geometry constraint as pixel-level flow consistency between the training images with dynamically generated pseudo labels. We evaluate our method on three challenging datasets and demonstrate that it outperforms state-of-the-art self-supervised methods significantly, with neither 2D annotations nor additional depth images." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.572, + 0.21, + 0.587 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.47, + 0.704 + ], + "angle": 0, + "content": "The goal of 6D object pose estimation is to accurately estimate the 3D rotation and 3D translation of a rigid object with respect to the camera, which gives essential information about the world beyond classical 2D understanding and is a fundamental component in many applications, such as robotic manipulation [5], autonomous driving [36], and augmented reality [37]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Recent progress in this field has significantly improved the robustness and accuracy of the model [49, 60, 21, 56, 7, 29, 19, 18]. Most of these approaches, however, rely on a large number of real images with accurate 6D pose annotations. But, compared to classical 2D annotation, these 6D annotations are either very hard to obtain [38, 34] or are prone to contain large labeling errors [16, 11, 58]. Some recent methods propose to use techniques based on image synthesis [15] or self-supervised learning [55, 54] to handle this problem. The main problem with synthetic images is the large domain gap to the real images, making the model's generalization ability suffers in practice [42, 60]. On the other hand, most self-supervised methods rely on additional" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.25, + 0.885, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.541, + 0.334, + 0.853, + 0.347 + ], + "angle": 0, + "content": "(a) Existing self-supervised 6D object pose methods" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.348, + 0.882, + 0.428 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.546, + 0.432, + 0.847, + 0.446 + ], + "angle": 0, + "content": "(b) Our solution based on pseudo flow consistency" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.451, + 0.892, + 0.563 + ], + "angle": 0, + "content": "Figure 1. Comparison of self-supervised object pose methods. (a) Most existing self-supervised object pose methods rely on either the depth image [55, 54, 4, 31] or additional mask annotations [61, 46], limiting their application range. (b) By contrast, our method can be trained only with the guidance of flow consistency based on the intrinsic geometry constraint of multiple different views, and produces more accurate results than existing solutions, without relying on any auxiliary information." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.595, + 0.894, + 0.656 + ], + "angle": 0, + "content": "information. Some can only work with additional depth images [55, 54, 31, 4] or others need pixel-level annotation of a segmentation mask [46, 61], which prevents the general applicability, as shown in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.895, + 0.902 + ], + "angle": 0, + "content": "In this work, we propose a self-supervised framework for 6D object pose estimation, which relies on neither depth nor additional 2D annotations. We first generate a synthetic dataset based on rendered images from the target's 3D mesh and train networks only on this dataset to get a rough pose initialization. To close the domain gap between the synthetic and real data, we use a refinement strategy where we compare the rendered reference image according to the initial pose and the real input based on pseudo labels [47, 62]. Pseudo labeling is widely used in many computer vision tasks [52, 59, 12, 8]. However, the two fundamental problems of pseudo labeling are still open questions in 6D object pose estimation, including the generative strategy of creating pseudo labels and the selection strategy of extracting high-quality labels from the noisy candidates, as shown in Fig. 2." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14075" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.093, + 0.435, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.098, + 0.246, + 0.443, + 0.261 + ], + "angle": 0, + "content": "(a) The standard strategy for self-supervised classification" + }, + { + "type": "image", + "bbox": [ + 0.479, + 0.089, + 0.877, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.477, + 0.246, + 0.88, + 0.262 + ], + "angle": 0, + "content": "(b) The proposed strategy for self-supervised object pose estimation" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.272, + 0.895, + 0.357 + ], + "angle": 0, + "content": "Figure 2. Self-supervised strategies in different fields. (a) Teacher-student learning scheme is a classical framework for self-supervised classification [52]. The key is how to determine the quality of pseudo labels from the noisy prediction of the teacher network. For image classification, one can obtain the prediction quality by the output distribution after the softmax operation easily, which is usually implemented by checking if the probability of any class is above a threshold [47, 62]. (b) However, there is no such easy way to determine the quality of an object pose prediction without the ground truth. We propose to formulate pseudo object pose labels as pixel-level optical flow supervision signals, and then use the flow consistency between multiple views based on their underlying geometry constraint." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.47, + 0.577 + ], + "angle": 0, + "content": "We propose to formulate the pseudo 6D pose labels as pixel-level flow supervision signals in a render-and compare framework [16, 26, 29, 60, 21, 32, 9]. Unlike the common render-and compare frameworks that need accurate pose annotations, we propose a geometry-guided learning framework without any annotations. We render multiple images near the initial pose, and compare them with the real input with the guidance of flow consistency, based on the geometry constraints between these image pairs from different views. We choose high-quality flow labels based on the proposed consistency on the fly, and supervise the network training with these dynamically generated labels in every training step." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.577, + 0.47, + 0.667 + ], + "angle": 0, + "content": "We evaluate our method on three challenging datasets LINEMOD [14], Occluded-LINEMOD [24], and YCBV [58], and show that it outperforms state-of-the-art self-supervised methods significantly, including those methods relied on depth image [55, 54] or auxiliary annotation information [61, 46]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.668, + 0.471, + 0.804 + ], + "angle": 0, + "content": "Our contributions can be summarized as the following. First, we investigate the problem of the standard teacher-student methods in selecting high-quality pseudo labels for self-supervised object pose estimation. Second, we propose a strategy based on flow consistency that embeds the geometry constraint from multiple views. Finally, we demonstrate its effectiveness by significantly outperforming state-of-the-art self-supervised object pose methods, without relying on any auxiliary information." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.815, + 0.22, + 0.831 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Object pose estimation has shown significant progress recently, based on different techniques, such as direct pose regression [56, 7, 26], 2D reprojection regression [44, 42, 18, 19, 40], 3D keypoint prediction [30, 41, 49, 11], and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.893, + 0.457 + ], + "angle": 0, + "content": "differentiable PnP solver [27, 17, 2, 3]. However, most of these methods rely on a large number of real images with accurate 6D pose annotation, which is usually hard to obtain in practice, especially in cluttered scenes with multiple object instances and occlusions [58, 16]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.893, + 0.655 + ], + "angle": 0, + "content": "Some recent methods tackle this problem by training on synthetic images rendered from the target's 3D mesh [11, 42, 1], but this strategy suffers from the domain gap between the synthetic and real image sets [6]. In contrast, some pose refinement methods have shown significant improvement in the generalization ability across different domains [29, 32, 26, 21, 60, 9] and especially [16], which produces comparable results as the state-of-the-art methods with only about one-tenth of the real images involved in training. Although having this promising progress, these pose refinement methods still need many annotated real images for training, and can not easily benefit from more real data without further annotations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.895, + 0.902 + ], + "angle": 0, + "content": "To solve this problem, some recent self-supervised methods [55, 61, 46, 54] try to remove the cumbersome procedure of pose annotation completely. Most of them are based on a strategy that compares the synthetic image rendered from an initial pose with the real image, and backpropagate the gradient through a differentiable renderer [23, 33] to update the network's weights during training, expecting to align the rendered image with the real input without explicit annotations. This type of strategy, however, relies heavily on the performance of comparing the final rendered image and the real input, which suffers from the domain gap, making them often rely either on depth [55] or on additional pixel-level annotations of segmentation masks [61]. In contrast, we propose to compare multiple synthetic-to-real image pairs at the same time, and force networks to comply with the geometry constraint between those image" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14076" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.09, + 0.885, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.252, + 0.893, + 0.336 + ], + "angle": 0, + "content": "Figure 3. Method overview. We first obtain the initial pose based on a pose estimation network trained only on synthetic images, and then train our refinement framework on real images without any annotations. Our proposed framework is based on a teacher-student learning scheme. Given a rough pose initialization, we render multiple synthetic images around this initial pose, and create multiple image pairs between the synthetic and real images. We dynamically produce pixel-level flow supervision signals for the student network during the training, by leveraging the geometry-guided flow consistency between those image pairs from different views. After getting 3D-to-2D correspondences based on the predicted flow, we use a PnP solver to get the final pose [16]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.361, + 0.468, + 0.435 + ], + "angle": 0, + "content": "pairs from different views, which suffers little from the domain problem. On the other hand, we formulate the geometry constraint as pixel-level consistency, which provides us dynamic valid label mask during training, without any 3D depth information or additional 2D mask annotations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.437, + 0.468, + 0.572 + ], + "angle": 0, + "content": "Pseudo labeling is also one of the basic techniques used in recent self-supervised object pose methods [31, 4]. However, these approaches still rely on additional depth images to select valid pseudo labels. In addition, they only update the pseudo labels after finishing the previous training, which usually means the model needs to be trained multiple times to utilize the slowly updated pseudo labels. By contrast, our pseudo flow labels are generated dynamically in every training step, and our model only needs to be trained once." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.573, + 0.468, + 0.829 + ], + "angle": 0, + "content": "Our method is related to the recent teacher-student formulation of pseudo labeling [47, 62, 52, 59, 25, 64, 28, 63, 57, 43, 22], which works under the assumption that the generated high-quality pseudo label of the teacher can be used to supervise the student network when having the same input as the teacher but only different data augmentations. Although this simple general framework has been widely used in image classification [47, 62], object detection [59, 28, 64, 51], and semantic segmentation [25], it only can work with high-quality pseudo labels. However, there is still no easy way to generate high-quality pose labels in the context of 6D object pose estimation. To solve this problem, we propose to formulate pseudo 6D pose labels as pixel-level flow supervision signals and select high-quality pseudo flow labels based on flow consistency across multiple different views during training. Our experiments demonstrate the effectiveness of this method." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.845, + 0.185, + 0.862 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Given a dataset of calibrated RGB images and the 3D mesh of the target, our goal is to train a self-supervised" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.361, + 0.892, + 0.571 + ], + "angle": 0, + "content": "model on this dataset to estimate the 6D object pose of the target, without relying on depth images or any auxiliary information, such as 6D pose and 2D mask annotations. We first create a synthetic dataset by rendering the 3D mesh of the target in different poses and train an existing pose estimation network [19, 26] on it to obtain a rough pose initialization [16, 29, 21]. The core component of our method is a self-supervised pose refinement framework, which we will discuss in detail in this section. We first show an overview of our self-supervised framework, and then present how we formulate the flow consistency based on the geometry constraint between different views. Finally, we show how we extend it to multiple image pairs to further increase the robustness. Fig. 3 shows the overview of our method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.581, + 0.705, + 0.595 + ], + "angle": 0, + "content": "3.1. Framework Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.605, + 0.892, + 0.801 + ], + "angle": 0, + "content": "We use a teacher-student architecture [52] for our self-supervised framework. It contains two networks with identical network structures, but not shared weights, which are called the teacher and student, respectively. During training, when an image input of the teacher network can produce a prediction that can fulfill some criteria, we convert this prediction to a one-hot pseudo-label, and use it to supervise the student network with the same image input but only different data augmentations. After updating the weights of the student network by gradient backpropagation supervised by this pseudo label, we then update the weights of the teacher network by a simple exponential moving averaging (EMA) strategy from the student network:" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.813, + 0.891, + 0.829 + ], + "angle": 0, + "content": "\\[\n\\mathbf {W} _ {t} = \\alpha \\mathbf {W} _ {t} + (1 - \\alpha) \\mathbf {W} _ {s}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathbf{W}_t\\) and \\(\\mathbf{W}_s\\) are the network weight parameters of the teacher and student network, respectively, and \\(\\alpha\\) is the exponential factor, which is typically 0.999. The weight updating and pseudo label generation is conducted after each" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "14077" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.089, + 0.473, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.159, + 0.205, + 0.416, + 0.22 + ], + "angle": 0, + "content": "(a) Flow consistency across multiple views" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.088, + 0.885, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.577, + 0.205, + 0.822, + 0.22 + ], + "angle": 0, + "content": "(b) Flow-guided photometric consistency" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.227, + 0.894, + 0.27 + ], + "angle": 0, + "content": "Figure 4. Illustration of geometry-guided consistency. We predict the flow between synthetic and real images. (a) The 2D flow of the same 3D point from different synthetic views to the real input should be consistent. (b) On the other hand, the target 2D locations of the same 3D point on different real inputs should have similar textures." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.294, + 0.468, + 0.354 + ], + "angle": 0, + "content": "iteration during training, making it much more efficient than other pseudo-label-based object pose methods [4, 31], which can only produce pseudo labels after the whole training pipeline and need to train the model multiple times." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.468, + 0.504 + ], + "angle": 0, + "content": "Our main problem is how to select high-quality pseudo label candidates from the noisy predictions of the teacher network. For the image classification task as in [52], one can obtain the label quality by the output distribution after the softmax operation easily, which is usually implemented by checking if the probability of any class is above a threshold [47, 62]. However, there is no such easy way to determine the quality of an object pose prediction without the ground truth. We discuss our solution in the following sections." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.517, + 0.42, + 0.533 + ], + "angle": 0, + "content": "3.2. Flow Consistency across Multiple Views" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.541, + 0.469, + 0.751 + ], + "angle": 0, + "content": "To solve the problem of difficulties in determining the quality of object pose predictions, we first formulate object pose estimation as a problem of estimating dense 2D-to-2D correspondence, or optical flow estimation, as in PFA [16], which, however, is a fully-supervised object pose method. To tackle the problem of no pose annotation for the computation of ground truth flow, we render multiple images around the initial pose, and predict the flow between each of them and the real input. In principle, since both the rendered images and real input image are 2D reprojections of the same 3D object, the flow prediction that aligns with the underlying geometry should have a higher probability of being of high quality. Fig. 4(a) illustrates such consistency assumption." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.753, + 0.469, + 0.844 + ], + "angle": 0, + "content": "More formally, given an unannotated real image \\(\\mathbf{I}^t\\) and the obtained initial pose \\(\\mathbf{P}_0\\) from networks trained only on synthetic data, we randomly generate another \\(n - 1\\) poses \\(\\{\\mathbf{P}_1,\\dots ,\\mathbf{P}_{n - 1}\\}\\), around the initial pose \\(\\mathbf{P}_0\\), and then create \\(n\\) synthetic images by rendering the target under the corresponding poses, generating \\(n\\) image pairs:" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.856, + 0.469, + 0.874 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\left(\\mathbf {I} _ {i} ^ {r}, \\mathbf {I} ^ {t}\\right) \\right\\}, \\quad 0 \\leq i \\leq n - 1, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.468, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathbf{I}_i^r\\) is the rendered image of the target under pose \\(\\mathbf{P}_i\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.294, + 0.892, + 0.34 + ], + "angle": 0, + "content": "For an object having \\(N\\) 3D keypoints, the 2D reprojection of a 3D keypoint \\(\\mathbf{p}_j\\), \\(1 \\leq j \\leq N\\), under pose \\(\\mathbf{P}_i\\) can be obtained by" + }, + { + "type": "equation", + "bbox": [ + 0.6, + 0.347, + 0.892, + 0.381 + ], + "angle": 0, + "content": "\\[\n\\lambda_ {i j} ^ {r} \\left[ \\begin{array}{c} \\mathbf {u} _ {i j} ^ {r} \\\\ 1 \\end{array} \\right] = \\mathbf {K} \\left(\\mathbf {R} _ {i} \\mathbf {p} _ {j} + \\mathbf {t} _ {i}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.892, + 0.51 + ], + "angle": 0, + "content": "where \\(\\lambda_{ij}^{r}\\) is a scale factor, \\(\\mathbf{u}_{ij}^{r}\\) is the 2D image location, \\(\\mathbf{K}\\) is the intrinsic camera matrix, and \\(\\mathbf{R}_i\\) and \\(\\mathbf{t}_i\\) are the rotation and translation of pose \\(\\mathbf{P}_i\\), respectively. We then establish 3D-to-2D correspondence \\(\\mathbf{p}_j \\leftrightarrow \\mathbf{u}_{ij}^r\\) under pose \\(\\mathbf{P}_i\\). For the real image \\(\\mathbf{I}^t\\), although its true pose \\(\\mathbf{P}^t\\) is unknown to us, the relation between the 3D keypoint \\(\\mathbf{p}_j\\) and its 2D image location \\(\\mathbf{u}_j^t\\) should follow the perspective principle of Eq. 3, implicitly generating the correspondence \\(\\mathbf{p}_j \\leftrightarrow \\mathbf{u}_j^t\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.51, + 0.892, + 0.554 + ], + "angle": 0, + "content": "We train a network to predict dense 2D-to-2D correspondence \\(\\mathbf{F}_i^{r\\rightarrow t}\\) between the two images in each image pair of Eq. 2, such that" + }, + { + "type": "equation", + "bbox": [ + 0.629, + 0.562, + 0.891, + 0.581 + ], + "angle": 0, + "content": "\\[\n\\mathbf {u} _ {i j} ^ {r} + \\mathbf {f} _ {i} ^ {r \\rightarrow t} = \\mathbf {u} _ {i j} ^ {t}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.587, + 0.892, + 0.661 + ], + "angle": 0, + "content": "where \\(\\mathbf{f}_i^{r\\rightarrow t}\\) is the corresponding 2D flow vector. Although \\(\\mathbf{u}_j^t\\) is unknown during training, we have the geometry constraint that the 2D image locations \\(\\{\\mathbf{u}_{ij}^r +\\mathbf{f}_i^{r\\rightarrow t}\\}\\) of the same 3D keypoint \\(\\mathbf{p}_j\\) from different synthetic views \\(0\\leq i\\leq n - 1\\) should be the same." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.663, + 0.892, + 0.709 + ], + "angle": 0, + "content": "We use the standard variance of the predicted \\(\\mathbf{u}_{ij}^{t}\\) from different views to determine if the current pixel's flow prediction is a valid pseudo label" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.716, + 0.891, + 0.735 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {j} = \\operatorname {s t d} \\left(\\left\\{\\mathbf {u} _ {i j} ^ {r} + \\mathbf {f} _ {i} ^ {r \\rightarrow t} \\right\\}\\right) \\quad 0 \\leq i \\leq n - 1, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.742, + 0.891, + 0.771 + ], + "angle": 0, + "content": "and select valid flow pseudo labels by a simple threshold \\(\\tau\\). Fig. 7 shows some visualizations of the variance \\(\\sigma\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.772, + 0.892, + 0.816 + ], + "angle": 0, + "content": "After obtaining the valid flow labels from the teacher network, we use them to supervise the student network by a loss function" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.823, + 0.892, + 0.863 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {f l o w} = \\sum_ {i = 0} ^ {n - 1} V _ {i} \\| \\left(g \\left(\\mathbf {I} _ {i} ^ {r}, \\mathbf {I} ^ {t}; \\mathbf {W} _ {t}\\right) - g \\left(\\mathbf {I} _ {i} ^ {r}, \\tilde {\\mathbf {I}} ^ {t}; \\mathbf {W} _ {s}\\right)\\right) \\|, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(g\\) is the flow network with parameters \\(\\mathbf{W}_t\\) and \\(\\mathbf{W}_s\\) for the teacher and student network, respectively, and \\(\\tilde{\\mathbf{I}}^t\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "14078" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "is the same real image as \\(\\mathbf{I}^t\\) but only with different data augmentations, and \\(V_{i}\\) is the mask containing valid pixels where \\(\\sigma_{j} < \\tau\\). Note that, \\(V_{i}\\) is generated dynamically from the consistency check between multiple image pairs in Eq. 2, and does not rely on any 2D mask annotations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.174, + 0.411, + 0.19 + ], + "angle": 0, + "content": "3.3. Flow-Guided Photometric Consistency" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.197, + 0.469, + 0.303 + ], + "angle": 0, + "content": "The previous section only investigates the consistency between the synthetic views and the real input. We further explore the consistency between multiple real inputs. Our motivation is that the 2D image reprojections of the same 3D object keypoint on different real images should have similar textures. We formulate this texture assumption as a photometric consistency, as illustrated in Fig. 4(b)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.469, + 0.362 + ], + "angle": 0, + "content": "Given the real image \\(\\mathbf{I}^t\\) with the initial pose \\(\\mathbf{P}_0\\), as in the previous section, we randomly retrieve another \\(m\\) real images whose initial pose is around \\(\\mathbf{P}_0\\), generating \\(m\\) image pairs" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.363, + 0.469, + 0.38 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\left(\\mathbf {I} _ {0} ^ {r}, \\mathbf {I} _ {k} ^ {t}\\right) \\right\\}, \\quad 1 \\leq k \\leq m, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.383, + 0.469, + 0.412 + ], + "angle": 0, + "content": "and after feeding the two images in each image pair to the teacher network, we have" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.419, + 0.469, + 0.436 + ], + "angle": 0, + "content": "\\[\n\\bar {\\mathbf {u}} _ {k} ^ {t} = \\mathbf {u} _ {0} ^ {r} + g \\left(\\mathbf {I} _ {0} ^ {r}, \\mathbf {I} _ {k} ^ {t}; \\mathbf {W} _ {t}\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.441, + 0.469, + 0.501 + ], + "angle": 0, + "content": "where \\(\\bar{\\mathbf{u}}_k^t\\) is the predicted 2D image location on image \\(\\mathbf{I}_k^t\\). We assume these predicted 2D image locations of the same 3D keypoint have similar texture properties, and we use a photometric loss to model this" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.507, + 0.469, + 0.547 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p h o t o}} = \\sum_ {k = 1} ^ {m} V _ {0} \\rho \\left(w \\left(\\mathbf {I} _ {k} ^ {t}, \\bar {\\mathbf {u}} _ {k} ^ {t}\\right), w \\left(\\mathbf {I} ^ {t}, \\bar {\\mathbf {u}} ^ {t}\\right)\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.469, + 0.626 + ], + "angle": 0, + "content": "where \\( w \\) is an operation function that warps the image according to the new pixel locations, \\( \\rho \\) is a generalized Charbonnier function to measure the photometric difference based on the Census transformation [39], and \\( \\bar{\\mathbf{u}}^t \\) is inferred from the student's prediction, where" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.632, + 0.469, + 0.65 + ], + "angle": 0, + "content": "\\[\n\\bar {\\mathbf {u}} ^ {t} = \\mathbf {u} _ {0} ^ {r} + g \\left(\\mathbf {I} _ {0} ^ {r}, \\tilde {\\mathbf {I}} ^ {t}; \\mathbf {W} _ {s}\\right) \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.469, + 0.684 + ], + "angle": 0, + "content": "We combine the flow consistency and photometric consistency into our final loss" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.692, + 0.469, + 0.709 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {f l o w}} + 0. 5 \\mathcal {L} _ {\\text {p h o t o}}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.714, + 0.469, + 0.773 + ], + "angle": 0, + "content": "Note that, we only apply the loss to the student network since the gradient backprogataion only occurs for the student network, and the teacher network only gets its weight updated by EMA updating as discussed in Section 3.1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.785, + 0.209, + 0.802 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.9 + ], + "angle": 0, + "content": "In this section, we first present the experiment setting of our method and then compare our method with state-of-the-art self-supervised methods. We finally conduct detailed ablation studies of our method in various settings. Our source code is publicly available at https://github.com/YangHai-1218/PseudoFlow." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.092, + 0.676, + 0.107 + ], + "angle": 0, + "content": "4.1. Experiment Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.113, + 0.892, + 0.37 + ], + "angle": 0, + "content": "Datasets. We evaluate our method on three widely-used datasets for 6D object pose estimation: LINEMOD (\"LM\") [14], Occluded-LINEMOD (\"LM-O\") [24], and YCB-V [58]. LINEMOD dataset contains 13 objects, with a single sequence per object without occlusions. We follow [55, 16] to use \\(15\\%\\) of the real images for training, resulting in a total of 2.4k images. Occluded-LINEMOD is an extension of LINEMOD, which annotates all the objects in one sequence in LINEMOD as the test set and shares the training set with LINEMOD. The recent YCB-V dataset consists of 130k real training images for 21 texture-less objects captured in cluttered scenes. Although all these three datasets contain manually labeled annotations, we train our models on them without accessing the ground truth, and report the final accuracy on their test set. We use the synthetic dataset used in the BOP challenge [6, 15, 50] to train WDR-Pose [19] for the pose initialization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.371, + 0.892, + 0.551 + ], + "angle": 0, + "content": "Evaluation Metrics. We mainly use ADD-0.1d as our metric, which computes the average distance between the mesh vertices transformed by the predicted pose and the ground truth pose, and then only treat the prediction with an average 3D error below \\(10\\%\\) of the mesh diameter as a correct pose estimate. We use its symmetric version for symmetric objects. Additionally, in some settings, we also use BOP metrics [15] for evaluation, including the Visible Surface Discrepancy (VSD), the Maximum Symmetry-aware Surface Distance (MSSD), the Maximum Symmetry-aware Projection Distance (MSPD), and their average AR. We refer the readers to [15] for their detailed definition." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.892, + 0.779 + ], + "angle": 0, + "content": "Training details. We use RAFT [53] as our flow network for both the teacher and student network. We initialize the weights of both teacher and student network with the weights pretrained on synthetic data and train the model using AdamW optimizer [35] with a batch size of 16. We use One-cycle strategy [45] to anneal the learning rate from a starting point \\(4\\mathrm{e} - 4\\). We crop the target object from the original image according to the initial pose, and then resize the image patch to \\(256\\times 256\\). We do not use any data augmentation in the teacher network, and only use random color augmentation used in PFA [16] for the student network. We typically set \\(\\tau = 1\\), \\(m = 3\\), and \\(n = 4\\) in our experiments. Unlike [55, 54, 31, 20] that train a separate model for each object, which is cumbersome to train, we train a single model for all objects in the same dataset." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.815, + 0.803 + ], + "angle": 0, + "content": "4.2. Comparison against State of the Art" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We first compare our method against the state-of-the-art self-supervised pose estimation methods on LINEMOD and Occluded-LINEMOD. Since most of them report numbers only in ADD-0.1d, we follow the same for a fair comparison. Table. 1 and 2 summarize the result. Our method outperforms the state-of-the-art methods significantly. Espe" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14079" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.473, + 0.352 + ], + "angle": 0, + "content": "
MethodDSC [61]Sock et al. [46]Lin et al. [31]Self6D [54]Self6D‡ [54]Ours
Ape31.237.667.576.075.481.9
Bench.83.078.699.991.694.995.0
Cam49.665.687.497.197.094.2
Can56.565.699.299.899.596.8
Cat57.952.594.385.686.695.4
Driller73.748.897.698.898.994.8
Duck31.335.167.256.568.383.5
Eggbox*96.089.298.991.099.093.9
Glue*63.464.596.292.296.196.5
Holep.38.841.549.935.441.984.5
Iron61.980.999.599.599.494.9
Lamp64.770.799.897.498.994.8
Phone54.460.591.591.894.394.1
Avg.58.660.688.485.688.592.2
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.354, + 0.472, + 0.439 + ], + "angle": 0, + "content": "Table 1. Comparison with self-supervised methods on LINEMOD. “*” denotes symmetric objects. We use the latest version of Self6D++ [54], and we only denote it as “Self6D” for simplicity. “Self6D‡” is the version with supervision from additional depth images. Our method outperforms “Self6D‡” with only RGB images." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.45, + 0.473, + 0.638 + ], + "angle": 0, + "content": "
MethodDSC [61]Sock et al. [46]Lin et al. [31]Self6D [54]Self6D‡ [54]Ours
Ape9.112.040.357.759.460.1
Can21.127.575.295.096.594.2
Cat26.012.035.052.660.856.5
Driller33.520.568.590.592.089.7
Duck12.223.025.726.730.630.9
Eggbox*39.425.144.745.051.158.1
Glue*37.027.060.787.188.688.9
Holep.20.435.028.023.538.544.2
Avg.24.822.847.359.864.765.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.126, + 0.641, + 0.422, + 0.655 + ], + "angle": 0, + "content": "Table 2. Comparison on Occluded-LINEMOD." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.679, + 0.47, + 0.74 + ], + "angle": 0, + "content": "cially, our method, which requires only RGB images, even outperforms Self6D‡ [54] by \\(3.7\\%\\) on LINEMOD, which is a method that relies on additional depth images. We show some qualitative results in Fig. 5." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.233, + 0.759 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Evaluation of different components. Table. 3 summarizes the results of our method with different components. The first row is the results of the standard teacher-student structure used in [47]. Although it has the standard EMA updating strategy, its performance is limited, mainly caused by the lacking of high-quality pseudo pose labels. After adding our flow loss and photometric loss, the performance increases significantly, which demonstrates the effectiveness of the proposed components." + }, + { + "type": "table", + "bbox": [ + 0.511, + 0.089, + 0.877, + 0.179 + ], + "angle": 0, + "content": "
\\( \\mathcal{L}_{flow} \\)\\( \\mathcal{L}_{photo} \\)MSPDMSSDVSDADD
--0.7590.5890.51930.9
-✓0.7650.6310.57837.5
✓-0.7800.7110.65864.2
✓✓0.7850.7490.66467.4
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.499, + 0.181, + 0.892, + 0.223 + ], + "angle": 0, + "content": "Table 3. Evaluation of different components on YCB-V. \\(\\mathcal{L}_{flow}\\) is the key component of our framework, and \\(\\mathcal{L}_{photo}\\) improves the performance further." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.24, + 0.869, + 0.41 + ], + "angle": 0, + "content": "
MethodMSPDMSSDVSDADD
Initialization v10.6320.4910.42027.4
+ Ours (Real)0.7800.7310.67364.6
+ Ours (SSL)0.7590.7220.65063.2
Initialization v20.6730.5800.50836.0
+ Ours (Real)0.7750.7220.66065.3
+ Ours (SSL)0.7640.7240.64364.2
Initialization v30.6940.5980.52238.6
+ Ours (Real)0.8030.7520.68669.2
+ Ours (SSL)0.7850.7490.66467.4
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.499, + 0.411, + 0.895, + 0.538 + ], + "angle": 0, + "content": "Table 4. Performance with different initialization and additional annotations on YCB-V. We evaluate three versions of pose initialization with different accuracy, including the results obtained by the original WDR-Pose (\"Initialization v1\"), and also two other versions with pre-cropping the detected regions of interest, based on Mask RCNN and RADet, respectively (\"v2\" and \"v3\"). Our self-supervised refinement (\"SSL\") boosts the initialization accuracy significantly and achieves similar performance as versions trained with fully-annotated real images (\"Real\")." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.892, + 0.732 + ], + "angle": 0, + "content": "Training analysis on YCB-V. We evaluate our method in three different settings during the training, as shown in Fig. 6. The baseline is the original teacher-student structure [52], and the other two are the proposed components of our method. The baseline model struggles to learn from the unannotated data without explicit quality measurement of pseudo labels. Our flow loss introduces a constraint based on flow consistency derived from multiview geometry, and tackles this problem effectively, and the proposed photometric loss increases performance further, as shown in Fig. 7." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Evaluation of hyper-parameters. We evaluate the hyperparameters used in our framework in Fig. 8. We first evaluate the impact of the number of different views. More views generally increase the performance, since it adds more information to the geometry constraint. However, too many views, such as those larger than 4, has negative impacts on the performance. We believe it is caused by the noise introduced by too many views with large viewpoint differences, which usually makes the network harder to learn. We then evaluate the threshold \\(\\tau\\) used in our framework, which is used to determine the reliability of pseudo flow labels. It" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14080" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.096, + 0.09, + 0.223, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.226, + 0.091, + 0.354, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.355, + 0.091, + 0.484, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.091, + 0.615, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.091, + 0.745, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.747, + 0.091, + 0.876, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.192, + 0.224, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.225, + 0.192, + 0.354, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.355, + 0.192, + 0.484, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.192, + 0.615, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.192, + 0.744, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.747, + 0.192, + 0.876, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.308, + 0.895, + 0.351 + ], + "angle": 0, + "content": "Figure 5. Qualitative results. We show the initialization results trained only on synthetic data at the top, and the refinement results after using our self-supervised strategy at the bottom. Our method significantly improves the baseline in various conditions, such as occluded, weak-textured, and symmetry objects." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.365, + 0.353, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.359, + 0.365, + 0.614, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.622, + 0.365, + 0.887, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.542, + 0.893, + 0.585 + ], + "angle": 0, + "content": "Figure 6. Training analysis on YCB-V. We report the results in three different settings during training. The baseline is the original teacher-student structure [52], and the other two are the proposed components of our method. The baseline model struggles to learn from unannotated data. By contrast, our flow loss tackles this problem effectively, and our photometric loss increases the performance further." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.609, + 0.27, + 0.623 + ], + "angle": 0, + "content": "works well between 1 and 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.47, + 0.746 + ], + "angle": 0, + "content": "Evaluation with limited real data. We evaluate our method on YCB-V with different amounts of real data used in training, as shown in Fig. 8(b). Our method increases the performance by about \\(20.2\\%\\) (from \\(41.7\\%\\) to \\(61.9\\%\\)) in ADD-0.1d by only using \\(1\\%\\) of all the real data. \\(99\\%\\) more real data can only increase the performance by \\(5.5\\%\\) further, which demonstrates the effectiveness of our method in data-limited scenarios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Evaluation with different initialization and additional annotations. In principle, our method can be trained with ground truth pose annotations easily, which is basically training the student network in a standard fully-supervised way. We evaluate our self-supervised method with the version trained with real pose annotations. At the same time, to evaluate the robustness of our framework to different pose initialization, we evaluate three versions of pose initialization with different initialization accuracy, including the results obtained by the original WDR-Pose, and two other" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.893, + 0.715 + ], + "angle": 0, + "content": "versions with pre-cropping the detected regions of interest, based on Mask RCNN [13] and RADet [10], respectively. Table 4 summarizes the results. Although the initial poses have different accuracy, our self-supervised refinement framework boosts their performance significantly, and even achieves similar performance as that trained on fully-annotated real images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Comparison against standard optical flow methods. In principle, one can use a self-supervised optical flow method to directly establish dense 2D-to-2D correspondence between the rendered image and the real image input, without any real pose annotations. However, we find that this strategy hardly can work, mainly due to the large domain gap between the rendered and real images, in which case the standard component of photometric comparison in self-supervised flow methods suffers. We evaluate a typical self-supervised optical flow method SMURF [48], and report the results on YCB-V in Table 5. Our self-supervised strategy suffers little from this domain gap problem and produces" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14081" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.088, + 0.199, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.199, + 0.089, + 0.311, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.311, + 0.089, + 0.423, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.423, + 0.089, + 0.536, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.089, + 0.648, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.648, + 0.089, + 0.761, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.089, + 0.877, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.178, + 0.198, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.198, + 0.178, + 0.31, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.311, + 0.178, + 0.424, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.424, + 0.178, + 0.537, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.537, + 0.178, + 0.649, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.649, + 0.178, + 0.764, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.178, + 0.877, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.125, + 0.269, + 0.159, + 0.283 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.337, + 0.269, + 0.402, + 0.282 + ], + "angle": 0, + "content": "Variance \\(\\sigma\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.676, + 0.269, + 0.741, + 0.281 + ], + "angle": 0, + "content": "Flow error" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.288, + 0.895, + 0.346 + ], + "angle": 0, + "content": "Figure 7. Visualization with increasing training iterations. We show the normalized visualization of variance \\(\\sigma\\) and flow error at training steps \\(40\\mathrm{k}\\), \\(70\\mathrm{k}\\), and \\(100\\mathrm{k}\\) from left to right, respectively. The top row shows the baseline method [52], and the bottom row is ours. The baseline method struggles to produce valid flow labels and reliable optical flow, regardless of the training steps. By contrast, our method produces more and more valid flow labels with small variance \\(\\sigma\\) during training, also with progressively better flow predictions." + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.357, + 0.348, + 0.527 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.236, + 0.531, + 0.477, + 0.544 + ], + "angle": 0, + "content": "(a) Ablation study in ADD-0.1d and AR" + }, + { + "type": "image", + "bbox": [ + 0.357, + 0.356, + 0.611, + 0.527 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.372, + 0.862, + 0.527 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.621, + 0.531, + 0.865, + 0.545 + ], + "angle": 0, + "content": "(b) Different amount of real training data" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.547, + 0.895, + 0.59 + ], + "angle": 0, + "content": "Figure 8. Ablation study of hyper-parameters and training data on YCB-V. (a) \\( m \\) and \\( n \\) are the number of views used for \\( \\mathcal{L}_{\\text{photo}} \\) and \\( \\mathcal{L}_{\\text{flow}} \\), respectively, and \\( \\tau \\) is the threshold for determining the validity of flow labels for \\( \\mathcal{L}_{\\text{flow}} \\). Our method is robust to the choices of different hyper parameters. (b) Our method produces acceptable results with accessing only \\( 1\\% \\) of all the real data." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.61, + 0.446, + 0.672 + ], + "angle": 0, + "content": "
MethodMSPDMSSDVSDADD
SMURF [48]0.7510.5650.48828.7
Ours0.7850.7490.66467.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.673, + 0.47, + 0.728 + ], + "angle": 0, + "content": "Table 5. Comparison against standard optical flow methods on YCB-V. The typical self-supervised optical flow method SMURF [48] suffers in producing 6D object poses without pose annotations." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.76, + 0.391, + 0.776 + ], + "angle": 0, + "content": "much more accurate pose results than SMURF." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Symmetry handling. We use the same strategy as in [16, 44] for symmetric objects in obtaining pose initialization, which restricts the range of poses used in training depending on the objects' symmetry type. We do not explicitly handle the symmetry for the refinement, where we build multiple views around the initial pose and use the consistency constraint between them to find the best flow to align different views within a small pose range. Fig. 9 shows two" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.61, + 0.603, + 0.683 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.605, + 0.61, + 0.697, + 0.682 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.61, + 0.788, + 0.682 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.789, + 0.61, + 0.882, + 0.682 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.684, + 0.602, + 0.754 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.683, + 0.697, + 0.754 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.683, + 0.789, + 0.754 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.79, + 0.683, + 0.882, + 0.754 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.508, + 0.756, + 0.605, + 0.769 + ], + "angle": 0, + "content": "Symmetry objects" + }, + { + "type": "image_caption", + "bbox": [ + 0.606, + 0.756, + 0.686, + 0.768 + ], + "angle": 0, + "content": "Ground truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.709, + 0.756, + 0.779, + 0.768 + ], + "angle": 0, + "content": "Initialization" + }, + { + "type": "image_caption", + "bbox": [ + 0.804, + 0.756, + 0.867, + 0.768 + ], + "angle": 0, + "content": "Refinement" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.774, + 0.892, + 0.803 + ], + "angle": 0, + "content": "Figure 9. Symmetric objects handling. Our refinement results align the target mesh with the images well in appearance." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.893, + 0.903 + ], + "angle": 0, + "content": "examples with reflectional symmetry and rotational symmetry, respectively. Note how the predicted poses have different 3D axis from the ground truth pose but align the target mesh with the images well in appearance." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14082" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "Time analysis. We conduct all our experiments on a workstation with an NVIDIA RTX-3090 GPU and an Intel-Xeon CPU with 12 cores running at \\(2.1\\mathrm{GHz}\\). The training of our self-supervised framework is only about \\(20\\%\\) slower than its fully-supervised version, consuming about 30 and 24 hours in the typical setting on YCB-V, respectively, which is much more efficient than methods relying on multiple times of retraining [31, 4]. For the inference time, our method is the same as its fully-supervised version and takes only \\(23\\mathrm{ms}\\) for a single object, including the optical flow estimation \\(17\\mathrm{ms}\\) and the PnP solver \\(6\\mathrm{ms}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.27, + 0.196, + 0.287 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.295, + 0.473, + 0.492 + ], + "angle": 0, + "content": "We have introduced a simple self-supervised 6D object pose method. After obtaining the rough pose initialization based on a network training on synthetic images, we refine the pose with a teacher-student pseudo labeling framework. To solve the problem of identifying high-quality labels in the context of object pose estimation, we first formulate pseudo object pose labels as pixel-level optical flow supervision signals. Then, we introduce a flow consistency based on the underlying geometry constraint between multiple different views. Our experiments show that the proposed method significantly outperforms existing solutions in both accuracy and efficiency, without relying on any 2D annotations or additional depth images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.495, + 0.473, + 0.587 + ], + "angle": 0, + "content": "Acknowledgments. This work was supported by the Natural Science Foundation of China, the Youth Innovation Team of Shaanxi Universities, the Fundamental Research Funds for the Central Universities under Grant JBF220101, and the 111 Project of China under Grant B08038. We thank Thomas Probst, Daniel Koguciuk, Juan-Ting Lin, and Lin Sun for helpful discussions." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.597, + 0.175, + 0.613 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.085, + 0.621, + 0.47, + 0.675 + ], + "angle": 0, + "content": "[1] Dingding Cai, Janne Heikkilä, and Esa Rahtu. SC6D: Symmetry-agnostic and Correspondence-free 6D Object Pose Estimation. In International Conference on 3D Vision, 2022. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.678, + 0.47, + 0.734 + ], + "angle": 0, + "content": "[2] Bo Chen, Alvaro Parra, Jiewei Cao, Nan Li, and Tat-Jun Chin. End-to-End Learnable Geometric Vision by Backpropagating PnP Optimization. In Conference on Computer Vision and Pattern Recognition, 2020. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.735, + 0.47, + 0.803 + ], + "angle": 0, + "content": "[3] Hansheng Chen, Pichao Wang, Fan Wang, Wei Tian, Lu Xiong, and Hao Li. 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In this paper, we propose a 6D object pose estimation method that can be trained with pure RGB images without any auxiliary information. We first obtain a rough pose initialization from networks trained on synthetic images rendered from the target's 3D mesh. Then, we introduce a refinement strategy leveraging the geometry constraint in synthetic-to-real image pairs from multiple different views. We formulate this geometry constraint as pixel-level flow consistency between the training images with dynamically generated pseudo labels. We evaluate our method on three challenging datasets and demonstrate that it outperforms state-of-the-art self-supervised methods significantly, with neither 2D annotations nor additional depth images. + +# 1. Introduction + +The goal of 6D object pose estimation is to accurately estimate the 3D rotation and 3D translation of a rigid object with respect to the camera, which gives essential information about the world beyond classical 2D understanding and is a fundamental component in many applications, such as robotic manipulation [5], autonomous driving [36], and augmented reality [37]. + +Recent progress in this field has significantly improved the robustness and accuracy of the model [49, 60, 21, 56, 7, 29, 19, 18]. Most of these approaches, however, rely on a large number of real images with accurate 6D pose annotations. But, compared to classical 2D annotation, these 6D annotations are either very hard to obtain [38, 34] or are prone to contain large labeling errors [16, 11, 58]. Some recent methods propose to use techniques based on image synthesis [15] or self-supervised learning [55, 54] to handle this problem. The main problem with synthetic images is the large domain gap to the real images, making the model's generalization ability suffers in practice [42, 60]. On the other hand, most self-supervised methods rely on additional + +![](images/4b7ffd272f1744892a326b98e70744154e011ea56985c248d1888df9a8ece5ae.jpg) + +![](images/105a4625e7d5b7f84c193bfc492aebcb855250a8edf751a20a7c86e66b3d1135.jpg) +(a) Existing self-supervised 6D object pose methods +(b) Our solution based on pseudo flow consistency +Figure 1. Comparison of self-supervised object pose methods. (a) Most existing self-supervised object pose methods rely on either the depth image [55, 54, 4, 31] or additional mask annotations [61, 46], limiting their application range. (b) By contrast, our method can be trained only with the guidance of flow consistency based on the intrinsic geometry constraint of multiple different views, and produces more accurate results than existing solutions, without relying on any auxiliary information. + +information. Some can only work with additional depth images [55, 54, 31, 4] or others need pixel-level annotation of a segmentation mask [46, 61], which prevents the general applicability, as shown in Fig. 1. + +In this work, we propose a self-supervised framework for 6D object pose estimation, which relies on neither depth nor additional 2D annotations. We first generate a synthetic dataset based on rendered images from the target's 3D mesh and train networks only on this dataset to get a rough pose initialization. To close the domain gap between the synthetic and real data, we use a refinement strategy where we compare the rendered reference image according to the initial pose and the real input based on pseudo labels [47, 62]. Pseudo labeling is widely used in many computer vision tasks [52, 59, 12, 8]. However, the two fundamental problems of pseudo labeling are still open questions in 6D object pose estimation, including the generative strategy of creating pseudo labels and the selection strategy of extracting high-quality labels from the noisy candidates, as shown in Fig. 2. + +![](images/1b2296d9be61097060f865d68e5fb214667282f3b6cb058544b0b48ed8fc3ca9.jpg) +(a) The standard strategy for self-supervised classification + +![](images/ee9b2bc277275393f40f553257af4df180ab27be9a74355fead2e2d9f8237ded.jpg) +(b) The proposed strategy for self-supervised object pose estimation +Figure 2. Self-supervised strategies in different fields. (a) Teacher-student learning scheme is a classical framework for self-supervised classification [52]. The key is how to determine the quality of pseudo labels from the noisy prediction of the teacher network. For image classification, one can obtain the prediction quality by the output distribution after the softmax operation easily, which is usually implemented by checking if the probability of any class is above a threshold [47, 62]. (b) However, there is no such easy way to determine the quality of an object pose prediction without the ground truth. We propose to formulate pseudo object pose labels as pixel-level optical flow supervision signals, and then use the flow consistency between multiple views based on their underlying geometry constraint. + +We propose to formulate the pseudo 6D pose labels as pixel-level flow supervision signals in a render-and compare framework [16, 26, 29, 60, 21, 32, 9]. Unlike the common render-and compare frameworks that need accurate pose annotations, we propose a geometry-guided learning framework without any annotations. We render multiple images near the initial pose, and compare them with the real input with the guidance of flow consistency, based on the geometry constraints between these image pairs from different views. We choose high-quality flow labels based on the proposed consistency on the fly, and supervise the network training with these dynamically generated labels in every training step. + +We evaluate our method on three challenging datasets LINEMOD [14], Occluded-LINEMOD [24], and YCBV [58], and show that it outperforms state-of-the-art self-supervised methods significantly, including those methods relied on depth image [55, 54] or auxiliary annotation information [61, 46]. + +Our contributions can be summarized as the following. First, we investigate the problem of the standard teacher-student methods in selecting high-quality pseudo labels for self-supervised object pose estimation. Second, we propose a strategy based on flow consistency that embeds the geometry constraint from multiple views. Finally, we demonstrate its effectiveness by significantly outperforming state-of-the-art self-supervised object pose methods, without relying on any auxiliary information. + +# 2. Related Work + +Object pose estimation has shown significant progress recently, based on different techniques, such as direct pose regression [56, 7, 26], 2D reprojection regression [44, 42, 18, 19, 40], 3D keypoint prediction [30, 41, 49, 11], and + +differentiable PnP solver [27, 17, 2, 3]. However, most of these methods rely on a large number of real images with accurate 6D pose annotation, which is usually hard to obtain in practice, especially in cluttered scenes with multiple object instances and occlusions [58, 16]. + +Some recent methods tackle this problem by training on synthetic images rendered from the target's 3D mesh [11, 42, 1], but this strategy suffers from the domain gap between the synthetic and real image sets [6]. In contrast, some pose refinement methods have shown significant improvement in the generalization ability across different domains [29, 32, 26, 21, 60, 9] and especially [16], which produces comparable results as the state-of-the-art methods with only about one-tenth of the real images involved in training. Although having this promising progress, these pose refinement methods still need many annotated real images for training, and can not easily benefit from more real data without further annotations. + +To solve this problem, some recent self-supervised methods [55, 61, 46, 54] try to remove the cumbersome procedure of pose annotation completely. Most of them are based on a strategy that compares the synthetic image rendered from an initial pose with the real image, and backpropagate the gradient through a differentiable renderer [23, 33] to update the network's weights during training, expecting to align the rendered image with the real input without explicit annotations. This type of strategy, however, relies heavily on the performance of comparing the final rendered image and the real input, which suffers from the domain gap, making them often rely either on depth [55] or on additional pixel-level annotations of segmentation masks [61]. In contrast, we propose to compare multiple synthetic-to-real image pairs at the same time, and force networks to comply with the geometry constraint between those image + +![](images/3508920f3cf6c03dc1a1cafa23543b238ba724e63a29fa9a85e40bb6ea8b3db4.jpg) +Figure 3. Method overview. We first obtain the initial pose based on a pose estimation network trained only on synthetic images, and then train our refinement framework on real images without any annotations. Our proposed framework is based on a teacher-student learning scheme. Given a rough pose initialization, we render multiple synthetic images around this initial pose, and create multiple image pairs between the synthetic and real images. We dynamically produce pixel-level flow supervision signals for the student network during the training, by leveraging the geometry-guided flow consistency between those image pairs from different views. After getting 3D-to-2D correspondences based on the predicted flow, we use a PnP solver to get the final pose [16]. + +pairs from different views, which suffers little from the domain problem. On the other hand, we formulate the geometry constraint as pixel-level consistency, which provides us dynamic valid label mask during training, without any 3D depth information or additional 2D mask annotations. + +Pseudo labeling is also one of the basic techniques used in recent self-supervised object pose methods [31, 4]. However, these approaches still rely on additional depth images to select valid pseudo labels. In addition, they only update the pseudo labels after finishing the previous training, which usually means the model needs to be trained multiple times to utilize the slowly updated pseudo labels. By contrast, our pseudo flow labels are generated dynamically in every training step, and our model only needs to be trained once. + +Our method is related to the recent teacher-student formulation of pseudo labeling [47, 62, 52, 59, 25, 64, 28, 63, 57, 43, 22], which works under the assumption that the generated high-quality pseudo label of the teacher can be used to supervise the student network when having the same input as the teacher but only different data augmentations. Although this simple general framework has been widely used in image classification [47, 62], object detection [59, 28, 64, 51], and semantic segmentation [25], it only can work with high-quality pseudo labels. However, there is still no easy way to generate high-quality pose labels in the context of 6D object pose estimation. To solve this problem, we propose to formulate pseudo 6D pose labels as pixel-level flow supervision signals and select high-quality pseudo flow labels based on flow consistency across multiple different views during training. Our experiments demonstrate the effectiveness of this method. + +# 3. Approach + +Given a dataset of calibrated RGB images and the 3D mesh of the target, our goal is to train a self-supervised + +model on this dataset to estimate the 6D object pose of the target, without relying on depth images or any auxiliary information, such as 6D pose and 2D mask annotations. We first create a synthetic dataset by rendering the 3D mesh of the target in different poses and train an existing pose estimation network [19, 26] on it to obtain a rough pose initialization [16, 29, 21]. The core component of our method is a self-supervised pose refinement framework, which we will discuss in detail in this section. We first show an overview of our self-supervised framework, and then present how we formulate the flow consistency based on the geometry constraint between different views. Finally, we show how we extend it to multiple image pairs to further increase the robustness. Fig. 3 shows the overview of our method. + +# 3.1. Framework Overview + +We use a teacher-student architecture [52] for our self-supervised framework. It contains two networks with identical network structures, but not shared weights, which are called the teacher and student, respectively. During training, when an image input of the teacher network can produce a prediction that can fulfill some criteria, we convert this prediction to a one-hot pseudo-label, and use it to supervise the student network with the same image input but only different data augmentations. After updating the weights of the student network by gradient backpropagation supervised by this pseudo label, we then update the weights of the teacher network by a simple exponential moving averaging (EMA) strategy from the student network: + +$$ +\mathbf {W} _ {t} = \alpha \mathbf {W} _ {t} + (1 - \alpha) \mathbf {W} _ {s}, \tag {1} +$$ + +where $\mathbf{W}_t$ and $\mathbf{W}_s$ are the network weight parameters of the teacher and student network, respectively, and $\alpha$ is the exponential factor, which is typically 0.999. The weight updating and pseudo label generation is conducted after each + +![](images/84b10bb4abc55380b44793043a096b2d7c3737adc90c5631ee0bcbcf9d1182ee.jpg) +(a) Flow consistency across multiple views + +![](images/e99c75afb7d3f32c2ca2fc7a3f63224c00a5becfaac02f0c273b2aa3cca80d30.jpg) +(b) Flow-guided photometric consistency +Figure 4. Illustration of geometry-guided consistency. We predict the flow between synthetic and real images. (a) The 2D flow of the same 3D point from different synthetic views to the real input should be consistent. (b) On the other hand, the target 2D locations of the same 3D point on different real inputs should have similar textures. + +iteration during training, making it much more efficient than other pseudo-label-based object pose methods [4, 31], which can only produce pseudo labels after the whole training pipeline and need to train the model multiple times. + +Our main problem is how to select high-quality pseudo label candidates from the noisy predictions of the teacher network. For the image classification task as in [52], one can obtain the label quality by the output distribution after the softmax operation easily, which is usually implemented by checking if the probability of any class is above a threshold [47, 62]. However, there is no such easy way to determine the quality of an object pose prediction without the ground truth. We discuss our solution in the following sections. + +# 3.2. Flow Consistency across Multiple Views + +To solve the problem of difficulties in determining the quality of object pose predictions, we first formulate object pose estimation as a problem of estimating dense 2D-to-2D correspondence, or optical flow estimation, as in PFA [16], which, however, is a fully-supervised object pose method. To tackle the problem of no pose annotation for the computation of ground truth flow, we render multiple images around the initial pose, and predict the flow between each of them and the real input. In principle, since both the rendered images and real input image are 2D reprojections of the same 3D object, the flow prediction that aligns with the underlying geometry should have a higher probability of being of high quality. Fig. 4(a) illustrates such consistency assumption. + +More formally, given an unannotated real image $\mathbf{I}^t$ and the obtained initial pose $\mathbf{P}_0$ from networks trained only on synthetic data, we randomly generate another $n - 1$ poses $\{\mathbf{P}_1,\dots ,\mathbf{P}_{n - 1}\}$ , around the initial pose $\mathbf{P}_0$ , and then create $n$ synthetic images by rendering the target under the corresponding poses, generating $n$ image pairs: + +$$ +\left\{\left(\mathbf {I} _ {i} ^ {r}, \mathbf {I} ^ {t}\right) \right\}, \quad 0 \leq i \leq n - 1, \tag {2} +$$ + +where $\mathbf{I}_i^r$ is the rendered image of the target under pose $\mathbf{P}_i$ . + +For an object having $N$ 3D keypoints, the 2D reprojection of a 3D keypoint $\mathbf{p}_j$ , $1 \leq j \leq N$ , under pose $\mathbf{P}_i$ can be obtained by + +$$ +\lambda_ {i j} ^ {r} \left[ \begin{array}{c} \mathbf {u} _ {i j} ^ {r} \\ 1 \end{array} \right] = \mathbf {K} \left(\mathbf {R} _ {i} \mathbf {p} _ {j} + \mathbf {t} _ {i}\right), \tag {3} +$$ + +where $\lambda_{ij}^{r}$ is a scale factor, $\mathbf{u}_{ij}^{r}$ is the 2D image location, $\mathbf{K}$ is the intrinsic camera matrix, and $\mathbf{R}_i$ and $\mathbf{t}_i$ are the rotation and translation of pose $\mathbf{P}_i$ , respectively. We then establish 3D-to-2D correspondence $\mathbf{p}_j \leftrightarrow \mathbf{u}_{ij}^r$ under pose $\mathbf{P}_i$ . For the real image $\mathbf{I}^t$ , although its true pose $\mathbf{P}^t$ is unknown to us, the relation between the 3D keypoint $\mathbf{p}_j$ and its 2D image location $\mathbf{u}_j^t$ should follow the perspective principle of Eq. 3, implicitly generating the correspondence $\mathbf{p}_j \leftrightarrow \mathbf{u}_j^t$ . + +We train a network to predict dense 2D-to-2D correspondence $\mathbf{F}_i^{r\rightarrow t}$ between the two images in each image pair of Eq. 2, such that + +$$ +\mathbf {u} _ {i j} ^ {r} + \mathbf {f} _ {i} ^ {r \rightarrow t} = \mathbf {u} _ {i j} ^ {t}, \tag {4} +$$ + +where $\mathbf{f}_i^{r\rightarrow t}$ is the corresponding 2D flow vector. Although $\mathbf{u}_j^t$ is unknown during training, we have the geometry constraint that the 2D image locations $\{\mathbf{u}_{ij}^r +\mathbf{f}_i^{r\rightarrow t}\}$ of the same 3D keypoint $\mathbf{p}_j$ from different synthetic views $0\leq i\leq n - 1$ should be the same. + +We use the standard variance of the predicted $\mathbf{u}_{ij}^{t}$ from different views to determine if the current pixel's flow prediction is a valid pseudo label + +$$ +\sigma_ {j} = \operatorname {s t d} \left(\left\{\mathbf {u} _ {i j} ^ {r} + \mathbf {f} _ {i} ^ {r \rightarrow t} \right\}\right) \quad 0 \leq i \leq n - 1, \tag {5} +$$ + +and select valid flow pseudo labels by a simple threshold $\tau$ . Fig. 7 shows some visualizations of the variance $\sigma$ . + +After obtaining the valid flow labels from the teacher network, we use them to supervise the student network by a loss function + +$$ +\mathcal {L} _ {f l o w} = \sum_ {i = 0} ^ {n - 1} V _ {i} \| \left(g \left(\mathbf {I} _ {i} ^ {r}, \mathbf {I} ^ {t}; \mathbf {W} _ {t}\right) - g \left(\mathbf {I} _ {i} ^ {r}, \tilde {\mathbf {I}} ^ {t}; \mathbf {W} _ {s}\right)\right) \|, \tag {6} +$$ + +where $g$ is the flow network with parameters $\mathbf{W}_t$ and $\mathbf{W}_s$ for the teacher and student network, respectively, and $\tilde{\mathbf{I}}^t$ + +is the same real image as $\mathbf{I}^t$ but only with different data augmentations, and $V_{i}$ is the mask containing valid pixels where $\sigma_{j} < \tau$ . Note that, $V_{i}$ is generated dynamically from the consistency check between multiple image pairs in Eq. 2, and does not rely on any 2D mask annotations. + +# 3.3. Flow-Guided Photometric Consistency + +The previous section only investigates the consistency between the synthetic views and the real input. We further explore the consistency between multiple real inputs. Our motivation is that the 2D image reprojections of the same 3D object keypoint on different real images should have similar textures. We formulate this texture assumption as a photometric consistency, as illustrated in Fig. 4(b). + +Given the real image $\mathbf{I}^t$ with the initial pose $\mathbf{P}_0$ , as in the previous section, we randomly retrieve another $m$ real images whose initial pose is around $\mathbf{P}_0$ , generating $m$ image pairs + +$$ +\left\{\left(\mathbf {I} _ {0} ^ {r}, \mathbf {I} _ {k} ^ {t}\right) \right\}, \quad 1 \leq k \leq m, \tag {7} +$$ + +and after feeding the two images in each image pair to the teacher network, we have + +$$ +\bar {\mathbf {u}} _ {k} ^ {t} = \mathbf {u} _ {0} ^ {r} + g \left(\mathbf {I} _ {0} ^ {r}, \mathbf {I} _ {k} ^ {t}; \mathbf {W} _ {t}\right), \tag {8} +$$ + +where $\bar{\mathbf{u}}_k^t$ is the predicted 2D image location on image $\mathbf{I}_k^t$ . We assume these predicted 2D image locations of the same 3D keypoint have similar texture properties, and we use a photometric loss to model this + +$$ +\mathcal {L} _ {\text {p h o t o}} = \sum_ {k = 1} ^ {m} V _ {0} \rho \left(w \left(\mathbf {I} _ {k} ^ {t}, \bar {\mathbf {u}} _ {k} ^ {t}\right), w \left(\mathbf {I} ^ {t}, \bar {\mathbf {u}} ^ {t}\right)\right), \tag {9} +$$ + +where $w$ is an operation function that warps the image according to the new pixel locations, $\rho$ is a generalized Charbonnier function to measure the photometric difference based on the Census transformation [39], and $\bar{\mathbf{u}}^t$ is inferred from the student's prediction, where + +$$ +\bar {\mathbf {u}} ^ {t} = \mathbf {u} _ {0} ^ {r} + g \left(\mathbf {I} _ {0} ^ {r}, \tilde {\mathbf {I}} ^ {t}; \mathbf {W} _ {s}\right) \tag {10} +$$ + +We combine the flow consistency and photometric consistency into our final loss + +$$ +\mathcal {L} = \mathcal {L} _ {\text {f l o w}} + 0. 5 \mathcal {L} _ {\text {p h o t o}}. \tag {11} +$$ + +Note that, we only apply the loss to the student network since the gradient backprogataion only occurs for the student network, and the teacher network only gets its weight updated by EMA updating as discussed in Section 3.1. + +# 4. Experiments + +In this section, we first present the experiment setting of our method and then compare our method with state-of-the-art self-supervised methods. We finally conduct detailed ablation studies of our method in various settings. Our source code is publicly available at https://github.com/YangHai-1218/PseudoFlow. + +# 4.1. Experiment Setup + +Datasets. We evaluate our method on three widely-used datasets for 6D object pose estimation: LINEMOD ("LM") [14], Occluded-LINEMOD ("LM-O") [24], and YCB-V [58]. LINEMOD dataset contains 13 objects, with a single sequence per object without occlusions. We follow [55, 16] to use $15\%$ of the real images for training, resulting in a total of 2.4k images. Occluded-LINEMOD is an extension of LINEMOD, which annotates all the objects in one sequence in LINEMOD as the test set and shares the training set with LINEMOD. The recent YCB-V dataset consists of 130k real training images for 21 texture-less objects captured in cluttered scenes. Although all these three datasets contain manually labeled annotations, we train our models on them without accessing the ground truth, and report the final accuracy on their test set. We use the synthetic dataset used in the BOP challenge [6, 15, 50] to train WDR-Pose [19] for the pose initialization. + +Evaluation Metrics. We mainly use ADD-0.1d as our metric, which computes the average distance between the mesh vertices transformed by the predicted pose and the ground truth pose, and then only treat the prediction with an average 3D error below $10\%$ of the mesh diameter as a correct pose estimate. We use its symmetric version for symmetric objects. Additionally, in some settings, we also use BOP metrics [15] for evaluation, including the Visible Surface Discrepancy (VSD), the Maximum Symmetry-aware Surface Distance (MSSD), the Maximum Symmetry-aware Projection Distance (MSPD), and their average AR. We refer the readers to [15] for their detailed definition. + +Training details. We use RAFT [53] as our flow network for both the teacher and student network. We initialize the weights of both teacher and student network with the weights pretrained on synthetic data and train the model using AdamW optimizer [35] with a batch size of 16. We use One-cycle strategy [45] to anneal the learning rate from a starting point $4\mathrm{e} - 4$ . We crop the target object from the original image according to the initial pose, and then resize the image patch to $256\times 256$ . We do not use any data augmentation in the teacher network, and only use random color augmentation used in PFA [16] for the student network. We typically set $\tau = 1$ , $m = 3$ , and $n = 4$ in our experiments. Unlike [55, 54, 31, 20] that train a separate model for each object, which is cumbersome to train, we train a single model for all objects in the same dataset. + +# 4.2. Comparison against State of the Art + +We first compare our method against the state-of-the-art self-supervised pose estimation methods on LINEMOD and Occluded-LINEMOD. Since most of them report numbers only in ADD-0.1d, we follow the same for a fair comparison. Table. 1 and 2 summarize the result. Our method outperforms the state-of-the-art methods significantly. Espe + +
MethodDSC [61]Sock et al. [46]Lin et al. [31]Self6D [54]Self6D‡ [54]Ours
Ape31.237.667.576.075.481.9
Bench.83.078.699.991.694.995.0
Cam49.665.687.497.197.094.2
Can56.565.699.299.899.596.8
Cat57.952.594.385.686.695.4
Driller73.748.897.698.898.994.8
Duck31.335.167.256.568.383.5
Eggbox*96.089.298.991.099.093.9
Glue*63.464.596.292.296.196.5
Holep.38.841.549.935.441.984.5
Iron61.980.999.599.599.494.9
Lamp64.770.799.897.498.994.8
Phone54.460.591.591.894.394.1
Avg.58.660.688.485.688.592.2
+ +Table 1. Comparison with self-supervised methods on LINEMOD. “*” denotes symmetric objects. We use the latest version of Self6D++ [54], and we only denote it as “Self6D” for simplicity. “Self6D‡” is the version with supervision from additional depth images. Our method outperforms “Self6D‡” with only RGB images. + +
MethodDSC [61]Sock et al. [46]Lin et al. [31]Self6D [54]Self6D‡ [54]Ours
Ape9.112.040.357.759.460.1
Can21.127.575.295.096.594.2
Cat26.012.035.052.660.856.5
Driller33.520.568.590.592.089.7
Duck12.223.025.726.730.630.9
Eggbox*39.425.144.745.051.158.1
Glue*37.027.060.787.188.688.9
Holep.20.435.028.023.538.544.2
Avg.24.822.847.359.864.765.4
+ +cially, our method, which requires only RGB images, even outperforms Self6D‡ [54] by $3.7\%$ on LINEMOD, which is a method that relies on additional depth images. We show some qualitative results in Fig. 5. + +# 4.3. Ablation Study + +Evaluation of different components. Table. 3 summarizes the results of our method with different components. The first row is the results of the standard teacher-student structure used in [47]. Although it has the standard EMA updating strategy, its performance is limited, mainly caused by the lacking of high-quality pseudo pose labels. After adding our flow loss and photometric loss, the performance increases significantly, which demonstrates the effectiveness of the proposed components. + +Table 2. Comparison on Occluded-LINEMOD. + +
\( \mathcal{L}_{flow} \)\( \mathcal{L}_{photo} \)MSPDMSSDVSDADD
--0.7590.5890.51930.9
-✓0.7650.6310.57837.5
✓-0.7800.7110.65864.2
✓✓0.7850.7490.66467.4
+ +Table 3. Evaluation of different components on YCB-V. $\mathcal{L}_{flow}$ is the key component of our framework, and $\mathcal{L}_{photo}$ improves the performance further. + +
MethodMSPDMSSDVSDADD
Initialization v10.6320.4910.42027.4
+ Ours (Real)0.7800.7310.67364.6
+ Ours (SSL)0.7590.7220.65063.2
Initialization v20.6730.5800.50836.0
+ Ours (Real)0.7750.7220.66065.3
+ Ours (SSL)0.7640.7240.64364.2
Initialization v30.6940.5980.52238.6
+ Ours (Real)0.8030.7520.68669.2
+ Ours (SSL)0.7850.7490.66467.4
+ +Table 4. Performance with different initialization and additional annotations on YCB-V. We evaluate three versions of pose initialization with different accuracy, including the results obtained by the original WDR-Pose ("Initialization v1"), and also two other versions with pre-cropping the detected regions of interest, based on Mask RCNN and RADet, respectively ("v2" and "v3"). Our self-supervised refinement ("SSL") boosts the initialization accuracy significantly and achieves similar performance as versions trained with fully-annotated real images ("Real"). + +Training analysis on YCB-V. We evaluate our method in three different settings during the training, as shown in Fig. 6. The baseline is the original teacher-student structure [52], and the other two are the proposed components of our method. The baseline model struggles to learn from the unannotated data without explicit quality measurement of pseudo labels. Our flow loss introduces a constraint based on flow consistency derived from multiview geometry, and tackles this problem effectively, and the proposed photometric loss increases performance further, as shown in Fig. 7. + +Evaluation of hyper-parameters. We evaluate the hyperparameters used in our framework in Fig. 8. We first evaluate the impact of the number of different views. More views generally increase the performance, since it adds more information to the geometry constraint. However, too many views, such as those larger than 4, has negative impacts on the performance. We believe it is caused by the noise introduced by too many views with large viewpoint differences, which usually makes the network harder to learn. We then evaluate the threshold $\tau$ used in our framework, which is used to determine the reliability of pseudo flow labels. It + +![](images/238d3189b2da1f3a7ddcd2f7adfc35debfe99f93169ddf9e6a1545f7ccccdc7c.jpg) + +![](images/bbfceb6ab438271b1176c5385a02abde500bd5eac5762f8581a38ede79b39b7b.jpg) + +![](images/b3b1f28b97f70ebb90a4b7fe5e1575991488882783c16312e4be86d14372059a.jpg) + +![](images/50d02b4d8241385269f6983c1f7fe3f60f466728c2f2caf24fa2871ffe535335.jpg) + +![](images/13f68cbe7bbb214072ebde75a6523f20b84ccb94ae03b70f0550b3d58accb991.jpg) + +![](images/1244496934013899e89d31644bfd5a3d17f7888143ffe9372a1c6c44cab142ee.jpg) + +![](images/b35d6fd848da520aaaf2c69448a3b0f138a2f9451606faba663dd89b3abdb089.jpg) +Figure 5. Qualitative results. We show the initialization results trained only on synthetic data at the top, and the refinement results after using our self-supervised strategy at the bottom. Our method significantly improves the baseline in various conditions, such as occluded, weak-textured, and symmetry objects. + +![](images/009c12b9bf6915498a5b81aa3ff12556f79e698a6c1d051346db6891f69a4326.jpg) + +![](images/d42a2d4d1eac0d91a0e828326ccfb7b1e8818f555c7d37a25d0b14f582c90cc1.jpg) + +![](images/d947efc8bf414e03ad4b7c46d4a2f97a8aaf9eadb43fd05db700db5b1dbe8262.jpg) + +![](images/324d9354da2ad253866e4056b2cff274056ae53124324708842131ffe8e520f7.jpg) + +![](images/07c00dbf4d117592fa613d9faa734f4eb92d7b0e67b92ac3c4c185d2bf370ea0.jpg) + +![](images/66f899017d5f07b8dff60af2b7d34ad65d4a0b482e9117b9a5026e73315d3c3b.jpg) +Figure 6. Training analysis on YCB-V. We report the results in three different settings during training. The baseline is the original teacher-student structure [52], and the other two are the proposed components of our method. The baseline model struggles to learn from unannotated data. By contrast, our flow loss tackles this problem effectively, and our photometric loss increases the performance further. + +![](images/7715e8debcbfb81890c4b1600209c31477c838d315f6fbd850dafd36ef73c0ab.jpg) + +![](images/b1b0a5431d21207de9202c274dad76bb0144918ea83c17ce54503522627fa370.jpg) + +works well between 1 and 4. + +Evaluation with limited real data. We evaluate our method on YCB-V with different amounts of real data used in training, as shown in Fig. 8(b). Our method increases the performance by about $20.2\%$ (from $41.7\%$ to $61.9\%$ ) in ADD-0.1d by only using $1\%$ of all the real data. $99\%$ more real data can only increase the performance by $5.5\%$ further, which demonstrates the effectiveness of our method in data-limited scenarios. + +Evaluation with different initialization and additional annotations. In principle, our method can be trained with ground truth pose annotations easily, which is basically training the student network in a standard fully-supervised way. We evaluate our self-supervised method with the version trained with real pose annotations. At the same time, to evaluate the robustness of our framework to different pose initialization, we evaluate three versions of pose initialization with different initialization accuracy, including the results obtained by the original WDR-Pose, and two other + +versions with pre-cropping the detected regions of interest, based on Mask RCNN [13] and RADet [10], respectively. Table 4 summarizes the results. Although the initial poses have different accuracy, our self-supervised refinement framework boosts their performance significantly, and even achieves similar performance as that trained on fully-annotated real images. + +Comparison against standard optical flow methods. In principle, one can use a self-supervised optical flow method to directly establish dense 2D-to-2D correspondence between the rendered image and the real image input, without any real pose annotations. However, we find that this strategy hardly can work, mainly due to the large domain gap between the rendered and real images, in which case the standard component of photometric comparison in self-supervised flow methods suffers. We evaluate a typical self-supervised optical flow method SMURF [48], and report the results on YCB-V in Table 5. Our self-supervised strategy suffers little from this domain gap problem and produces + +![](images/e69c194f28c8c9ffab9ae43e93ceefb749e90e70af8533acc75a17b766e380c6.jpg) + +![](images/c163975db63e9037fbbbd41b6d90284ed5b2acdd013755dfbd4a300307c79d38.jpg) + +![](images/140ecb44655b1c22663ca4f1c390fcd2fdcfa1e62396550c15e99afb47ecf87b.jpg) + +![](images/d5045c1be424f03cbe7d4cccd02fbada5a2eae3e084a7ff3e5985ed4be4a2f31.jpg) + +![](images/a2a5dc0b23ea4a890d41a3031a031a082995c6a5661f0a0b70a421c9e1153ffb.jpg) + +![](images/d9dc5d5f188d66dcf21805954d733cb3d3fff809d93fd059ee0ec52a9e142439.jpg) + +![](images/55681e440731cd25dfb0227f46b3e6e624e31e6c92779d73cb69dcbd474ea55b.jpg) + +![](images/18129befcfd1d35751fc574daed9ae84f063cb44662948fe69eda7ea3d3f5776.jpg) +Input + +![](images/707e4847049a460942f3aa05ce98b46dfd4cbf145fac97e1b2c4e2e6fe84e790.jpg) + +![](images/bcb1ec01e8166563a65c07b69107b27d19c70bbdf59d18dabf6e500cfba8e2c6.jpg) +Variance $\sigma$ + +![](images/530a4dce36477275c257384c24f77413977de9a687940b6b1ffe10c3a9a46c34.jpg) + +![](images/182f1cee8860cf2ff6db40ffc00f5dd3ad095df146122eff1c856dbb080ff4c5.jpg) + +![](images/1ca2ab75b56583321ad12a91fc2e36312d371f8251b38d822fdd49c3b03b7cbf.jpg) +Flow error + +![](images/99690228786ae4d52c3db6b3f881eca60563a7c799113c097ac7fd11f94811b4.jpg) + +![](images/5ed044dce8997c355fc2e3556925dc1c0878276c138b8728863e9cc69b26697a.jpg) +(a) Ablation study in ADD-0.1d and AR + +![](images/c76ec96d73ac70866fb54241ba1353aa99d5a001aee53f52fc1e8cdfa5cae4bb.jpg) +Figure 7. Visualization with increasing training iterations. We show the normalized visualization of variance $\sigma$ and flow error at training steps $40\mathrm{k}$ , $70\mathrm{k}$ , and $100\mathrm{k}$ from left to right, respectively. The top row shows the baseline method [52], and the bottom row is ours. The baseline method struggles to produce valid flow labels and reliable optical flow, regardless of the training steps. By contrast, our method produces more and more valid flow labels with small variance $\sigma$ during training, also with progressively better flow predictions. + +![](images/3ee43916c75df898cff9dd6be3c7f34118cc9ceb4e7868d5362b80821d074cb8.jpg) +(b) Different amount of real training data +Figure 8. Ablation study of hyper-parameters and training data on YCB-V. (a) $m$ and $n$ are the number of views used for $\mathcal{L}_{\text{photo}}$ and $\mathcal{L}_{\text{flow}}$ , respectively, and $\tau$ is the threshold for determining the validity of flow labels for $\mathcal{L}_{\text{flow}}$ . Our method is robust to the choices of different hyper parameters. (b) Our method produces acceptable results with accessing only $1\%$ of all the real data. + +
MethodMSPDMSSDVSDADD
SMURF [48]0.7510.5650.48828.7
Ours0.7850.7490.66467.4
+ +Table 5. Comparison against standard optical flow methods on YCB-V. The typical self-supervised optical flow method SMURF [48] suffers in producing 6D object poses without pose annotations. + +much more accurate pose results than SMURF. + +Symmetry handling. We use the same strategy as in [16, 44] for symmetric objects in obtaining pose initialization, which restricts the range of poses used in training depending on the objects' symmetry type. We do not explicitly handle the symmetry for the refinement, where we build multiple views around the initial pose and use the consistency constraint between them to find the best flow to align different views within a small pose range. Fig. 9 shows two + +![](images/a5e91e3a7a6953c74ec0063f8116106290a314cfa0c4065a2fdb9728c4b01f08.jpg) + +![](images/576870821efcbdb55710affa701841cf7fea58420f2f2bd6a754027ddf908878.jpg) + +![](images/3f6aabf3ad2c7e698062c2453616b9602493e0c98fdda6859b6e6b297e4578f2.jpg) + +![](images/629b2cf04439c824aa5a59c96e2807da2052c8fe4b826260b1955d48f5f6407a.jpg) + +![](images/a2f8ad5867971146cf8e6b3154ec954be3b87b5f89268135042fd53fa8a7b74d.jpg) +Symmetry objects +Figure 9. Symmetric objects handling. Our refinement results align the target mesh with the images well in appearance. + +![](images/46d7ea7b5606bae8e368f382642783f000f6112080987fa0a6ab94bb3e02bfe2.jpg) +Ground truth + +![](images/f1ea717b87dda0d8e5627c45d3c4bc23dd6cd0069c935c7d5f48e6d6db861fd6.jpg) +Initialization + +![](images/90d4216933a115ced1bc4b72beccc952d46d4415ff9df42a388206cfafe6b44d.jpg) +Refinement + +examples with reflectional symmetry and rotational symmetry, respectively. Note how the predicted poses have different 3D axis from the ground truth pose but align the target mesh with the images well in appearance. + +Time analysis. We conduct all our experiments on a workstation with an NVIDIA RTX-3090 GPU and an Intel-Xeon CPU with 12 cores running at $2.1\mathrm{GHz}$ . The training of our self-supervised framework is only about $20\%$ slower than its fully-supervised version, consuming about 30 and 24 hours in the typical setting on YCB-V, respectively, which is much more efficient than methods relying on multiple times of retraining [31, 4]. For the inference time, our method is the same as its fully-supervised version and takes only $23\mathrm{ms}$ for a single object, including the optical flow estimation $17\mathrm{ms}$ and the PnP solver $6\mathrm{ms}$ . + +# 5. Conclusion + +We have introduced a simple self-supervised 6D object pose method. After obtaining the rough pose initialization based on a network training on synthetic images, we refine the pose with a teacher-student pseudo labeling framework. To solve the problem of identifying high-quality labels in the context of object pose estimation, we first formulate pseudo object pose labels as pixel-level optical flow supervision signals. Then, we introduce a flow consistency based on the underlying geometry constraint between multiple different views. Our experiments show that the proposed method significantly outperforms existing solutions in both accuracy and efficiency, without relying on any 2D annotations or additional depth images. + +Acknowledgments. This work was supported by the Natural Science Foundation of China, the Youth Innovation Team of Shaanxi Universities, the Fundamental Research Funds for the Central Universities under Grant JBF220101, and the 111 Project of China under Grant B08038. 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In this paper, we propose a 6D object pose estimation method that can be trained with pure RGB images without any auxiliary information. We first obtain a rough pose initialization from networks trained on synthetic images rendered from the target's 3D mesh. Then, we introduce a refinement strategy leveraging the geometry constraint in synthetic-to-real image pairs from multiple different views. We formulate this geometry constraint as pixel-level flow consistency between the training images with dynamically generated pseudo labels. We evaluate our method on three challenging datasets and demonstrate that it outperforms state-of-the-art self-supervised methods significantly, with neither 2D annotations nor additional depth images." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 453, + 128, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 128, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 128, + 464 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "text", + "content": "The goal of 6D object pose estimation is to accurately estimate the 3D rotation and 3D translation of a rigid object with respect to the camera, which gives essential information about the world beyond classical 2D understanding and is a fundamental component in many applications, such as robotic manipulation [5], autonomous driving [36], and augmented reality [37]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": "Recent progress in this field has significantly improved the robustness and accuracy of the model [49, 60, 21, 56, 7, 29, 19, 18]. Most of these approaches, however, rely on a large number of real images with accurate 6D pose annotations. But, compared to classical 2D annotation, these 6D annotations are either very hard to obtain [38, 34] or are prone to contain large labeling errors [16, 11, 58]. Some recent methods propose to use techniques based on image synthesis [15] or self-supervised learning [55, 54] to handle this problem. The main problem with synthetic images is the large domain gap to the real images, making the model's generalization ability suffers in practice [42, 60]. On the other hand, most self-supervised methods rely on additional" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 313, + 198, + 541, + 261 + ], + "blocks": [ + { + "bbox": [ + 313, + 198, + 541, + 261 + ], + "lines": [ + { + "bbox": [ + 313, + 198, + 541, + 261 + ], + "spans": [ + { + "bbox": [ + 313, + 198, + 541, + 261 + ], + "type": "image", + "image_path": "4b7ffd272f1744892a326b98e70744154e011ea56985c248d1888df9a8ece5ae.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 313, + 275, + 539, + 338 + ], + "blocks": [ + { + "bbox": [ + 331, + 264, + 522, + 274 + ], + "lines": [ + { + "bbox": [ + 331, + 264, + 522, + 274 + ], + "spans": [ + { + "bbox": [ + 331, + 264, + 522, + 274 + ], + "type": "text", + "content": "(a) Existing self-supervised 6D object pose methods" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 275, + 539, + 338 + ], + "lines": [ + { + "bbox": [ + 313, + 275, + 539, + 338 + ], + "spans": [ + { + "bbox": [ + 313, + 275, + 539, + 338 + ], + "type": "image", + "image_path": "105a4625e7d5b7f84c193bfc492aebcb855250a8edf751a20a7c86e66b3d1135.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 334, + 342, + 518, + 353 + ], + "lines": [ + { + "bbox": [ + 334, + 342, + 518, + 353 + ], + "spans": [ + { + "bbox": [ + 334, + 342, + 518, + 353 + ], + "type": "text", + "content": "(b) Our solution based on pseudo flow consistency" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 357, + 545, + 445 + ], + "lines": [ + { + "bbox": [ + 305, + 357, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 305, + 357, + 545, + 445 + ], + "type": "text", + "content": "Figure 1. Comparison of self-supervised object pose methods. (a) Most existing self-supervised object pose methods rely on either the depth image [55, 54, 4, 31] or additional mask annotations [61, 46], limiting their application range. (b) By contrast, our method can be trained only with the guidance of flow consistency based on the intrinsic geometry constraint of multiple different views, and produces more accurate results than existing solutions, without relying on any auxiliary information." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 471, + 547, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 471, + 547, + 519 + ], + "spans": [ + { + "bbox": [ + 305, + 471, + 547, + 519 + ], + "type": "text", + "content": "information. Some can only work with additional depth images [55, 54, 31, 4] or others need pixel-level annotation of a segmentation mask [46, 61], which prevents the general applicability, as shown in Fig. 1." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "text", + "content": "In this work, we propose a self-supervised framework for 6D object pose estimation, which relies on neither depth nor additional 2D annotations. We first generate a synthetic dataset based on rendered images from the target's 3D mesh and train networks only on this dataset to get a rough pose initialization. To close the domain gap between the synthetic and real data, we use a refinement strategy where we compare the rendered reference image according to the initial pose and the real input based on pseudo labels [47, 62]. Pseudo labeling is widely used in many computer vision tasks [52, 59, 12, 8]. However, the two fundamental problems of pseudo labeling are still open questions in 6D object pose estimation, including the generative strategy of creating pseudo labels and the selection strategy of extracting high-quality labels from the noisy candidates, as shown in Fig. 2." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14075" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 73, + 266, + 192 + ], + "blocks": [ + { + "bbox": [ + 65, + 73, + 266, + 192 + ], + "lines": [ + { + "bbox": [ + 65, + 73, + 266, + 192 + ], + "spans": [ + { + "bbox": [ + 65, + 73, + 266, + 192 + ], + "type": "image", + "image_path": "1b2296d9be61097060f865d68e5fb214667282f3b6cb058544b0b48ed8fc3ca9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 59, + 194, + 271, + 206 + ], + "lines": [ + { + "bbox": [ + 59, + 194, + 271, + 206 + ], + "spans": [ + { + "bbox": [ + 59, + 194, + 271, + 206 + ], + "type": "text", + "content": "(a) The standard strategy for self-supervised classification" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 293, + 70, + 536, + 192 + ], + "blocks": [ + { + "bbox": [ + 293, + 70, + 536, + 192 + ], + "lines": [ + { + "bbox": [ + 293, + 70, + 536, + 192 + ], + "spans": [ + { + "bbox": [ + 293, + 70, + 536, + 192 + ], + "type": "image", + "image_path": "ee9b2bc277275393f40f553257af4df180ab27be9a74355fead2e2d9f8237ded.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 291, + 194, + 538, + 207 + ], + "lines": [ + { + "bbox": [ + 291, + 194, + 538, + 207 + ], + "spans": [ + { + "bbox": [ + 291, + 194, + 538, + 207 + ], + "type": "text", + "content": "(b) The proposed strategy for self-supervised object pose estimation" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 215, + 547, + 282 + ], + "lines": [ + { + "bbox": [ + 46, + 215, + 547, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 547, + 282 + ], + "type": "text", + "content": "Figure 2. Self-supervised strategies in different fields. (a) Teacher-student learning scheme is a classical framework for self-supervised classification [52]. The key is how to determine the quality of pseudo labels from the noisy prediction of the teacher network. For image classification, one can obtain the prediction quality by the output distribution after the softmax operation easily, which is usually implemented by checking if the probability of any class is above a threshold [47, 62]. (b) However, there is no such easy way to determine the quality of an object pose prediction without the ground truth. We propose to formulate pseudo object pose labels as pixel-level optical flow supervision signals, and then use the flow consistency between multiple views based on their underlying geometry constraint." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 301, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 287, + 456 + ], + "type": "text", + "content": "We propose to formulate the pseudo 6D pose labels as pixel-level flow supervision signals in a render-and compare framework [16, 26, 29, 60, 21, 32, 9]. Unlike the common render-and compare frameworks that need accurate pose annotations, we propose a geometry-guided learning framework without any annotations. We render multiple images near the initial pose, and compare them with the real input with the guidance of flow consistency, based on the geometry constraints between these image pairs from different views. We choose high-quality flow labels based on the proposed consistency on the fly, and supervise the network training with these dynamically generated labels in every training step." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 456, + 287, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 528 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 528 + ], + "type": "text", + "content": "We evaluate our method on three challenging datasets LINEMOD [14], Occluded-LINEMOD [24], and YCBV [58], and show that it outperforms state-of-the-art self-supervised methods significantly, including those methods relied on depth image [55, 54] or auxiliary annotation information [61, 46]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 529, + 288, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 288, + 636 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 288, + 636 + ], + "type": "text", + "content": "Our contributions can be summarized as the following. First, we investigate the problem of the standard teacher-student methods in selecting high-quality pseudo labels for self-supervised object pose estimation. Second, we propose a strategy based on flow consistency that embeds the geometry constraint from multiple views. Finally, we demonstrate its effectiveness by significantly outperforming state-of-the-art self-supervised object pose methods, without relying on any auxiliary information." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 645, + 134, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 134, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 134, + 658 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": "Object pose estimation has shown significant progress recently, based on different techniques, such as direct pose regression [56, 7, 26], 2D reprojection regression [44, 42, 18, 19, 40], 3D keypoint prediction [30, 41, 49, 11], and" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 301, + 546, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 546, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 546, + 361 + ], + "type": "text", + "content": "differentiable PnP solver [27, 17, 2, 3]. However, most of these methods rely on a large number of real images with accurate 6D pose annotation, which is usually hard to obtain in practice, especially in cluttered scenes with multiple object instances and occlusions [58, 16]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 364, + 546, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 546, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 546, + 518 + ], + "type": "text", + "content": "Some recent methods tackle this problem by training on synthetic images rendered from the target's 3D mesh [11, 42, 1], but this strategy suffers from the domain gap between the synthetic and real image sets [6]. In contrast, some pose refinement methods have shown significant improvement in the generalization ability across different domains [29, 32, 26, 21, 60, 9] and especially [16], which produces comparable results as the state-of-the-art methods with only about one-tenth of the real images involved in training. Although having this promising progress, these pose refinement methods still need many annotated real images for training, and can not easily benefit from more real data without further annotations." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "text", + "content": "To solve this problem, some recent self-supervised methods [55, 61, 46, 54] try to remove the cumbersome procedure of pose annotation completely. Most of them are based on a strategy that compares the synthetic image rendered from an initial pose with the real image, and backpropagate the gradient through a differentiable renderer [23, 33] to update the network's weights during training, expecting to align the rendered image with the real input without explicit annotations. This type of strategy, however, relies heavily on the performance of comparing the final rendered image and the real input, which suffers from the domain gap, making them often rely either on depth [55] or on additional pixel-level annotations of segmentation masks [61]. In contrast, we propose to compare multiple synthetic-to-real image pairs at the same time, and force networks to comply with the geometry constraint between those image" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14076" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 71, + 541, + 196 + ], + "blocks": [ + { + "bbox": [ + 52, + 71, + 541, + 196 + ], + "lines": [ + { + "bbox": [ + 52, + 71, + 541, + 196 + ], + "spans": [ + { + "bbox": [ + 52, + 71, + 541, + 196 + ], + "type": "image", + "image_path": "3508920f3cf6c03dc1a1cafa23543b238ba724e63a29fa9a85e40bb6ea8b3db4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 199, + 546, + 266 + ], + "lines": [ + { + "bbox": [ + 46, + 199, + 546, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 199, + 546, + 266 + ], + "type": "text", + "content": "Figure 3. Method overview. We first obtain the initial pose based on a pose estimation network trained only on synthetic images, and then train our refinement framework on real images without any annotations. Our proposed framework is based on a teacher-student learning scheme. Given a rough pose initialization, we render multiple synthetic images around this initial pose, and create multiple image pairs between the synthetic and real images. We dynamically produce pixel-level flow supervision signals for the student network during the training, by leveraging the geometry-guided flow consistency between those image pairs from different views. After getting 3D-to-2D correspondences based on the predicted flow, we use a PnP solver to get the final pose [16]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 285, + 286, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 286, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 286, + 344 + ], + "type": "text", + "content": "pairs from different views, which suffers little from the domain problem. On the other hand, we formulate the geometry constraint as pixel-level consistency, which provides us dynamic valid label mask during training, without any 3D depth information or additional 2D mask annotations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 346, + 286, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 286, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 286, + 453 + ], + "type": "text", + "content": "Pseudo labeling is also one of the basic techniques used in recent self-supervised object pose methods [31, 4]. However, these approaches still rely on additional depth images to select valid pseudo labels. In addition, they only update the pseudo labels after finishing the previous training, which usually means the model needs to be trained multiple times to utilize the slowly updated pseudo labels. By contrast, our pseudo flow labels are generated dynamically in every training step, and our model only needs to be trained once." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 453, + 286, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 453, + 286, + 656 + ], + "spans": [ + { + "bbox": [ + 46, + 453, + 286, + 656 + ], + "type": "text", + "content": "Our method is related to the recent teacher-student formulation of pseudo labeling [47, 62, 52, 59, 25, 64, 28, 63, 57, 43, 22], which works under the assumption that the generated high-quality pseudo label of the teacher can be used to supervise the student network when having the same input as the teacher but only different data augmentations. Although this simple general framework has been widely used in image classification [47, 62], object detection [59, 28, 64, 51], and semantic segmentation [25], it only can work with high-quality pseudo labels. However, there is still no easy way to generate high-quality pose labels in the context of 6D object pose estimation. To solve this problem, we propose to formulate pseudo 6D pose labels as pixel-level flow supervision signals and select high-quality pseudo flow labels based on flow consistency across multiple different views during training. Our experiments demonstrate the effectiveness of this method." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 669, + 113, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 113, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 113, + 682 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": "Given a dataset of calibrated RGB images and the 3D mesh of the target, our goal is to train a self-supervised" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 285, + 545, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 545, + 452 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 545, + 452 + ], + "type": "text", + "content": "model on this dataset to estimate the 6D object pose of the target, without relying on depth images or any auxiliary information, such as 6D pose and 2D mask annotations. We first create a synthetic dataset by rendering the 3D mesh of the target in different poses and train an existing pose estimation network [19, 26] on it to obtain a rough pose initialization [16, 29, 21]. The core component of our method is a self-supervised pose refinement framework, which we will discuss in detail in this section. We first show an overview of our self-supervised framework, and then present how we formulate the flow consistency based on the geometry constraint between different views. Finally, we show how we extend it to multiple image pairs to further increase the robustness. Fig. 3 shows the overview of our method." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 460, + 431, + 471 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 460, + 431, + 471 + ], + "spans": [ + { + "bbox": [ + 306, + 460, + 431, + 471 + ], + "type": "text", + "content": "3.1. Framework Overview" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 479, + 545, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 634 + ], + "type": "text", + "content": "We use a teacher-student architecture [52] for our self-supervised framework. It contains two networks with identical network structures, but not shared weights, which are called the teacher and student, respectively. During training, when an image input of the teacher network can produce a prediction that can fulfill some criteria, we convert this prediction to a one-hot pseudo-label, and use it to supervise the student network with the same image input but only different data augmentations. After updating the weights of the student network by gradient backpropagation supervised by this pseudo label, we then update the weights of the teacher network by a simple exponential moving averaging (EMA) strategy from the student network:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 367, + 643, + 545, + 656 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 643, + 545, + 656 + ], + "spans": [ + { + "bbox": [ + 367, + 643, + 545, + 656 + ], + "type": "interline_equation", + "content": "\\mathbf {W} _ {t} = \\alpha \\mathbf {W} _ {t} + (1 - \\alpha) \\mathbf {W} _ {s}, \\tag {1}", + "image_path": "ef8b52d1290562cc5e00fc3cacf184782dbf16ef9e27b0f3687e1f68fc5ea7c2.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_t" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_s" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": " are the network weight parameters of the teacher and student network, respectively, and " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": " is the exponential factor, which is typically 0.999. The weight updating and pseudo label generation is conducted after each" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14077" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 70, + 289, + 159 + ], + "blocks": [ + { + "bbox": [ + 63, + 70, + 289, + 159 + ], + "lines": [ + { + "bbox": [ + 63, + 70, + 289, + 159 + ], + "spans": [ + { + "bbox": [ + 63, + 70, + 289, + 159 + ], + "type": "image", + "image_path": "84b10bb4abc55380b44793043a096b2d7c3737adc90c5631ee0bcbcf9d1182ee.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 97, + 162, + 254, + 174 + ], + "lines": [ + { + "bbox": [ + 97, + 162, + 254, + 174 + ], + "spans": [ + { + "bbox": [ + 97, + 162, + 254, + 174 + ], + "type": "text", + "content": "(a) Flow consistency across multiple views" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 314, + 69, + 541, + 159 + ], + "blocks": [ + { + "bbox": [ + 314, + 69, + 541, + 159 + ], + "lines": [ + { + "bbox": [ + 314, + 69, + 541, + 159 + ], + "spans": [ + { + "bbox": [ + 314, + 69, + 541, + 159 + ], + "type": "image", + "image_path": "e99c75afb7d3f32c2ca2fc7a3f63224c00a5becfaac02f0c273b2aa3cca80d30.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 353, + 162, + 503, + 174 + ], + "lines": [ + { + "bbox": [ + 353, + 162, + 503, + 174 + ], + "spans": [ + { + "bbox": [ + 353, + 162, + 503, + 174 + ], + "type": "text", + "content": "(b) Flow-guided photometric consistency" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 179, + 547, + 213 + ], + "lines": [ + { + "bbox": [ + 46, + 179, + 547, + 213 + ], + "spans": [ + { + "bbox": [ + 46, + 179, + 547, + 213 + ], + "type": "text", + "content": "Figure 4. Illustration of geometry-guided consistency. We predict the flow between synthetic and real images. (a) The 2D flow of the same 3D point from different synthetic views to the real input should be consistent. (b) On the other hand, the target 2D locations of the same 3D point on different real inputs should have similar textures." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 232, + 286, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 232, + 286, + 280 + ], + "spans": [ + { + "bbox": [ + 46, + 232, + 286, + 280 + ], + "type": "text", + "content": "iteration during training, making it much more efficient than other pseudo-label-based object pose methods [4, 31], which can only produce pseudo labels after the whole training pipeline and need to train the model multiple times." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 281, + 286, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 286, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 286, + 399 + ], + "type": "text", + "content": "Our main problem is how to select high-quality pseudo label candidates from the noisy predictions of the teacher network. For the image classification task as in [52], one can obtain the label quality by the output distribution after the softmax operation easily, which is usually implemented by checking if the probability of any class is above a threshold [47, 62]. However, there is no such easy way to determine the quality of an object pose prediction without the ground truth. We discuss our solution in the following sections." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 409, + 257, + 422 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 409, + 257, + 422 + ], + "spans": [ + { + "bbox": [ + 47, + 409, + 257, + 422 + ], + "type": "text", + "content": "3.2. Flow Consistency across Multiple Views" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 428, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 428, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 428, + 287, + 594 + ], + "type": "text", + "content": "To solve the problem of difficulties in determining the quality of object pose predictions, we first formulate object pose estimation as a problem of estimating dense 2D-to-2D correspondence, or optical flow estimation, as in PFA [16], which, however, is a fully-supervised object pose method. To tackle the problem of no pose annotation for the computation of ground truth flow, we render multiple images around the initial pose, and predict the flow between each of them and the real input. In principle, since both the rendered images and real input image are 2D reprojections of the same 3D object, the flow prediction that aligns with the underlying geometry should have a higher probability of being of high quality. Fig. 4(a) illustrates such consistency assumption." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 596, + 287, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 596, + 287, + 668 + ], + "spans": [ + { + "bbox": [ + 46, + 596, + 287, + 668 + ], + "type": "text", + "content": "More formally, given an unannotated real image " + }, + { + "bbox": [ + 46, + 596, + 287, + 668 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^t" + }, + { + "bbox": [ + 46, + 596, + 287, + 668 + ], + "type": "text", + "content": " and the obtained initial pose " + }, + { + "bbox": [ + 46, + 596, + 287, + 668 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_0" + }, + { + "bbox": [ + 46, + 596, + 287, + 668 + ], + "type": "text", + "content": " from networks trained only on synthetic data, we randomly generate another " + }, + { + "bbox": [ + 46, + 596, + 287, + 668 + ], + "type": "inline_equation", + "content": "n - 1" + }, + { + "bbox": [ + 46, + 596, + 287, + 668 + ], + "type": "text", + "content": " poses " + }, + { + "bbox": [ + 46, + 596, + 287, + 668 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{P}_1,\\dots ,\\mathbf{P}_{n - 1}\\}" + }, + { + "bbox": [ + 46, + 596, + 287, + 668 + ], + "type": "text", + "content": ", around the initial pose " + }, + { + "bbox": [ + 46, + 596, + 287, + 668 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_0" + }, + { + "bbox": [ + 46, + 596, + 287, + 668 + ], + "type": "text", + "content": ", and then create " + }, + { + "bbox": [ + 46, + 596, + 287, + 668 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 596, + 287, + 668 + ], + "type": "text", + "content": " synthetic images by rendering the target under the corresponding poses, generating " + }, + { + "bbox": [ + 46, + 596, + 287, + 668 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 596, + 287, + 668 + ], + "type": "text", + "content": " image pairs:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 108, + 677, + 287, + 692 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 677, + 287, + 692 + ], + "spans": [ + { + "bbox": [ + 108, + 677, + 287, + 692 + ], + "type": "interline_equation", + "content": "\\left\\{\\left(\\mathbf {I} _ {i} ^ {r}, \\mathbf {I} ^ {t}\\right) \\right\\}, \\quad 0 \\leq i \\leq n - 1, \\tag {2}", + "image_path": "e9ba9b800a3928514f89df44e297a36d7f1adb3aaa219580fb433b1a62375264.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 701, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 286, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 701, + 286, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_i^r" + }, + { + "bbox": [ + 47, + 701, + 286, + 714 + ], + "type": "text", + "content": " is the rendered image of the target under pose " + }, + { + "bbox": [ + 47, + 701, + 286, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i" + }, + { + "bbox": [ + 47, + 701, + 286, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 232, + 545, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 232, + 545, + 269 + ], + "spans": [ + { + "bbox": [ + 305, + 232, + 545, + 269 + ], + "type": "text", + "content": "For an object having " + }, + { + "bbox": [ + 305, + 232, + 545, + 269 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 232, + 545, + 269 + ], + "type": "text", + "content": " 3D keypoints, the 2D reprojection of a 3D keypoint " + }, + { + "bbox": [ + 305, + 232, + 545, + 269 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_j" + }, + { + "bbox": [ + 305, + 232, + 545, + 269 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 232, + 545, + 269 + ], + "type": "inline_equation", + "content": "1 \\leq j \\leq N" + }, + { + "bbox": [ + 305, + 232, + 545, + 269 + ], + "type": "text", + "content": ", under pose " + }, + { + "bbox": [ + 305, + 232, + 545, + 269 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i" + }, + { + "bbox": [ + 305, + 232, + 545, + 269 + ], + "type": "text", + "content": " can be obtained by" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 367, + 274, + 545, + 301 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 274, + 545, + 301 + ], + "spans": [ + { + "bbox": [ + 367, + 274, + 545, + 301 + ], + "type": "interline_equation", + "content": "\\lambda_ {i j} ^ {r} \\left[ \\begin{array}{c} \\mathbf {u} _ {i j} ^ {r} \\\\ 1 \\end{array} \\right] = \\mathbf {K} \\left(\\mathbf {R} _ {i} \\mathbf {p} _ {j} + \\mathbf {t} _ {i}\\right), \\tag {3}", + "image_path": "8eb7ac780124db687414d63a14dbde1c0cdb83b6f95e7712523c5dd9a04923d3.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\lambda_{ij}^{r}" + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "text", + "content": " is a scale factor, " + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{u}_{ij}^{r}" + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "text", + "content": " is the 2D image location, " + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "text", + "content": " is the intrinsic camera matrix, and " + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{R}_i" + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_i" + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "text", + "content": " are the rotation and translation of pose " + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i" + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "text", + "content": ", respectively. We then establish 3D-to-2D correspondence " + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_j \\leftrightarrow \\mathbf{u}_{ij}^r" + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "text", + "content": " under pose " + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i" + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "text", + "content": ". For the real image " + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^t" + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "text", + "content": ", although its true pose " + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^t" + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "text", + "content": " is unknown to us, the relation between the 3D keypoint " + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_j" + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "text", + "content": " and its 2D image location " + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{u}_j^t" + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "text", + "content": " should follow the perspective principle of Eq. 3, implicitly generating the correspondence " + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_j \\leftrightarrow \\mathbf{u}_j^t" + }, + { + "bbox": [ + 304, + 306, + 545, + 403 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 403, + 545, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 403, + 545, + 438 + ], + "spans": [ + { + "bbox": [ + 305, + 403, + 545, + 438 + ], + "type": "text", + "content": "We train a network to predict dense 2D-to-2D correspondence " + }, + { + "bbox": [ + 305, + 403, + 545, + 438 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_i^{r\\rightarrow t}" + }, + { + "bbox": [ + 305, + 403, + 545, + 438 + ], + "type": "text", + "content": " between the two images in each image pair of Eq. 2, such that" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 384, + 445, + 545, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 445, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 384, + 445, + 545, + 460 + ], + "type": "interline_equation", + "content": "\\mathbf {u} _ {i j} ^ {r} + \\mathbf {f} _ {i} ^ {r \\rightarrow t} = \\mathbf {u} _ {i j} ^ {t}, \\tag {4}", + "image_path": "094d255dfaade003f4a8578cfa0846a28fb3681bf0433f640824d3354662e646.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 464, + 545, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 464, + 545, + 523 + ], + "spans": [ + { + "bbox": [ + 305, + 464, + 545, + 523 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 464, + 545, + 523 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_i^{r\\rightarrow t}" + }, + { + "bbox": [ + 305, + 464, + 545, + 523 + ], + "type": "text", + "content": " is the corresponding 2D flow vector. Although " + }, + { + "bbox": [ + 305, + 464, + 545, + 523 + ], + "type": "inline_equation", + "content": "\\mathbf{u}_j^t" + }, + { + "bbox": [ + 305, + 464, + 545, + 523 + ], + "type": "text", + "content": " is unknown during training, we have the geometry constraint that the 2D image locations " + }, + { + "bbox": [ + 305, + 464, + 545, + 523 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{u}_{ij}^r +\\mathbf{f}_i^{r\\rightarrow t}\\}" + }, + { + "bbox": [ + 305, + 464, + 545, + 523 + ], + "type": "text", + "content": " of the same 3D keypoint " + }, + { + "bbox": [ + 305, + 464, + 545, + 523 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_j" + }, + { + "bbox": [ + 305, + 464, + 545, + 523 + ], + "type": "text", + "content": " from different synthetic views " + }, + { + "bbox": [ + 305, + 464, + 545, + 523 + ], + "type": "inline_equation", + "content": "0\\leq i\\leq n - 1" + }, + { + "bbox": [ + 305, + 464, + 545, + 523 + ], + "type": "text", + "content": " should be the same." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 525, + 545, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 525, + 545, + 561 + ], + "spans": [ + { + "bbox": [ + 304, + 525, + 545, + 561 + ], + "type": "text", + "content": "We use the standard variance of the predicted " + }, + { + "bbox": [ + 304, + 525, + 545, + 561 + ], + "type": "inline_equation", + "content": "\\mathbf{u}_{ij}^{t}" + }, + { + "bbox": [ + 304, + 525, + 545, + 561 + ], + "type": "text", + "content": " from different views to determine if the current pixel's flow prediction is a valid pseudo label" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 336, + 567, + 545, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 567, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 336, + 567, + 545, + 582 + ], + "type": "interline_equation", + "content": "\\sigma_ {j} = \\operatorname {s t d} \\left(\\left\\{\\mathbf {u} _ {i j} ^ {r} + \\mathbf {f} _ {i} ^ {r \\rightarrow t} \\right\\}\\right) \\quad 0 \\leq i \\leq n - 1, \\tag {5}", + "image_path": "dade52b4ddaa755ef990cd09b4f292090e9126f9b302a0ac56c5ef581b70508d.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 587, + 545, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 587, + 545, + 610 + ], + "spans": [ + { + "bbox": [ + 304, + 587, + 545, + 610 + ], + "type": "text", + "content": "and select valid flow pseudo labels by a simple threshold " + }, + { + "bbox": [ + 304, + 587, + 545, + 610 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 587, + 545, + 610 + ], + "type": "text", + "content": ". Fig. 7 shows some visualizations of the variance " + }, + { + "bbox": [ + 304, + 587, + 545, + 610 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 587, + 545, + 610 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 611, + 545, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 611, + 545, + 646 + ], + "spans": [ + { + "bbox": [ + 304, + 611, + 545, + 646 + ], + "type": "text", + "content": "After obtaining the valid flow labels from the teacher network, we use them to supervise the student network by a loss function" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 314, + 651, + 545, + 683 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 651, + 545, + 683 + ], + "spans": [ + { + "bbox": [ + 314, + 651, + 545, + 683 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {f l o w} = \\sum_ {i = 0} ^ {n - 1} V _ {i} \\| \\left(g \\left(\\mathbf {I} _ {i} ^ {r}, \\mathbf {I} ^ {t}; \\mathbf {W} _ {t}\\right) - g \\left(\\mathbf {I} _ {i} ^ {r}, \\tilde {\\mathbf {I}} ^ {t}; \\mathbf {W} _ {s}\\right)\\right) \\|, \\tag {6}", + "image_path": "9519845bbb3522de7f5f3d93dfd269a55a48d58468fe7e45efb93fb07857d58b.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " is the flow network with parameters " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_t" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_s" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " for the teacher and student network, respectively, and " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{I}}^t" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14078" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "is the same real image as " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^t" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": " but only with different data augmentations, and " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "V_{i}" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": " is the mask containing valid pixels where " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "\\sigma_{j} < \\tau" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": ". Note that, " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "V_{i}" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": " is generated dynamically from the consistency check between multiple image pairs in Eq. 2, and does not rely on any 2D mask annotations." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 137, + 251, + 150 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 137, + 251, + 150 + ], + "spans": [ + { + "bbox": [ + 47, + 137, + 251, + 150 + ], + "type": "text", + "content": "3.3. Flow-Guided Photometric Consistency" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 156, + 287, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 156, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 287, + 239 + ], + "type": "text", + "content": "The previous section only investigates the consistency between the synthetic views and the real input. We further explore the consistency between multiple real inputs. Our motivation is that the 2D image reprojections of the same 3D object keypoint on different real images should have similar textures. We formulate this texture assumption as a photometric consistency, as illustrated in Fig. 4(b)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 239, + 287, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 287, + 286 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 287, + 286 + ], + "type": "text", + "content": "Given the real image " + }, + { + "bbox": [ + 46, + 239, + 287, + 286 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^t" + }, + { + "bbox": [ + 46, + 239, + 287, + 286 + ], + "type": "text", + "content": " with the initial pose " + }, + { + "bbox": [ + 46, + 239, + 287, + 286 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_0" + }, + { + "bbox": [ + 46, + 239, + 287, + 286 + ], + "type": "text", + "content": ", as in the previous section, we randomly retrieve another " + }, + { + "bbox": [ + 46, + 239, + 287, + 286 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 239, + 287, + 286 + ], + "type": "text", + "content": " real images whose initial pose is around " + }, + { + "bbox": [ + 46, + 239, + 287, + 286 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_0" + }, + { + "bbox": [ + 46, + 239, + 287, + 286 + ], + "type": "text", + "content": ", generating " + }, + { + "bbox": [ + 46, + 239, + 287, + 286 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 239, + 287, + 286 + ], + "type": "text", + "content": " image pairs" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 115, + 287, + 287, + 300 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 287, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 115, + 287, + 287, + 300 + ], + "type": "interline_equation", + "content": "\\left\\{\\left(\\mathbf {I} _ {0} ^ {r}, \\mathbf {I} _ {k} ^ {t}\\right) \\right\\}, \\quad 1 \\leq k \\leq m, \\tag {7}", + "image_path": "3253efef3d513db3598f932beaaeca83d2412444e9cb6fac43bde4729c73d37f.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 303, + 287, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 303, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 287, + 326 + ], + "type": "text", + "content": "and after feeding the two images in each image pair to the teacher network, we have" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 111, + 331, + 287, + 345 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 331, + 287, + 345 + ], + "spans": [ + { + "bbox": [ + 111, + 331, + 287, + 345 + ], + "type": "interline_equation", + "content": "\\bar {\\mathbf {u}} _ {k} ^ {t} = \\mathbf {u} _ {0} ^ {r} + g \\left(\\mathbf {I} _ {0} ^ {r}, \\mathbf {I} _ {k} ^ {t}; \\mathbf {W} _ {t}\\right), \\tag {8}", + "image_path": "5c36c01cb01da2fe652b9db310712934c51c7692f1209c082996c682b2699a77.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 349, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 349, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 349, + 287, + 396 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 349, + 287, + 396 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{u}}_k^t" + }, + { + "bbox": [ + 46, + 349, + 287, + 396 + ], + "type": "text", + "content": " is the predicted 2D image location on image " + }, + { + "bbox": [ + 46, + 349, + 287, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_k^t" + }, + { + "bbox": [ + 46, + 349, + 287, + 396 + ], + "type": "text", + "content": ". We assume these predicted 2D image locations of the same 3D keypoint have similar texture properties, and we use a photometric loss to model this" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 82, + 401, + 287, + 433 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 401, + 287, + 433 + ], + "spans": [ + { + "bbox": [ + 82, + 401, + 287, + 433 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p h o t o}} = \\sum_ {k = 1} ^ {m} V _ {0} \\rho \\left(w \\left(\\mathbf {I} _ {k} ^ {t}, \\bar {\\mathbf {u}} _ {k} ^ {t}\\right), w \\left(\\mathbf {I} ^ {t}, \\bar {\\mathbf {u}} ^ {t}\\right)\\right), \\tag {9}", + "image_path": "b999fec85b78ec1c16674440387ea417eceab292ed043129ce3e746fafa7b3e2.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 436, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 287, + 495 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 436, + 287, + 495 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 436, + 287, + 495 + ], + "type": "text", + "content": " is an operation function that warps the image according to the new pixel locations, " + }, + { + "bbox": [ + 46, + 436, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 436, + 287, + 495 + ], + "type": "text", + "content": " is a generalized Charbonnier function to measure the photometric difference based on the Census transformation [39], and " + }, + { + "bbox": [ + 46, + 436, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{u}}^t" + }, + { + "bbox": [ + 46, + 436, + 287, + 495 + ], + "type": "text", + "content": " is inferred from the student's prediction, where" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 115, + 500, + 287, + 514 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 500, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 115, + 500, + 287, + 514 + ], + "type": "interline_equation", + "content": "\\bar {\\mathbf {u}} ^ {t} = \\mathbf {u} _ {0} ^ {r} + g \\left(\\mathbf {I} _ {0} ^ {r}, \\tilde {\\mathbf {I}} ^ {t}; \\mathbf {W} _ {s}\\right) \\tag {10}", + "image_path": "df06205605fd30f54ce2f4996f10b2ad5f64accd6d08cc8a91d73af64eee87db.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 518, + 287, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 518, + 287, + 541 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 287, + 541 + ], + "type": "text", + "content": "We combine the flow consistency and photometric consistency into our final loss" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 116, + 548, + 287, + 561 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 548, + 287, + 561 + ], + "spans": [ + { + "bbox": [ + 116, + 548, + 287, + 561 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {f l o w}} + 0. 5 \\mathcal {L} _ {\\text {p h o t o}}. \\tag {11}", + "image_path": "4cadf83076f32185b9b96c1425670d4472dd8a7a56e17019fb9966246b7802c5.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 565, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 565, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 565, + 287, + 612 + ], + "type": "text", + "content": "Note that, we only apply the loss to the student network since the gradient backprogataion only occurs for the student network, and the teacher network only gets its weight updated by EMA updating as discussed in Section 3.1." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 621, + 127, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 127, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 127, + 635 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "text", + "content": "In this section, we first present the experiment setting of our method and then compare our method with state-of-the-art self-supervised methods. We finally conduct detailed ablation studies of our method in various settings. Our source code is publicly available at https://github.com/YangHai-1218/PseudoFlow." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 72, + 413, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 413, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 413, + 84 + ], + "type": "text", + "content": "4.1. Experiment Setup" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 89, + 545, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 89, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 304, + 89, + 545, + 293 + ], + "type": "text", + "content": "Datasets. We evaluate our method on three widely-used datasets for 6D object pose estimation: LINEMOD (\"LM\") [14], Occluded-LINEMOD (\"LM-O\") [24], and YCB-V [58]. LINEMOD dataset contains 13 objects, with a single sequence per object without occlusions. We follow [55, 16] to use " + }, + { + "bbox": [ + 304, + 89, + 545, + 293 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 304, + 89, + 545, + 293 + ], + "type": "text", + "content": " of the real images for training, resulting in a total of 2.4k images. Occluded-LINEMOD is an extension of LINEMOD, which annotates all the objects in one sequence in LINEMOD as the test set and shares the training set with LINEMOD. The recent YCB-V dataset consists of 130k real training images for 21 texture-less objects captured in cluttered scenes. Although all these three datasets contain manually labeled annotations, we train our models on them without accessing the ground truth, and report the final accuracy on their test set. We use the synthetic dataset used in the BOP challenge [6, 15, 50] to train WDR-Pose [19] for the pose initialization." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 293, + 545, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 545, + 436 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 545, + 436 + ], + "type": "text", + "content": "Evaluation Metrics. We mainly use ADD-0.1d as our metric, which computes the average distance between the mesh vertices transformed by the predicted pose and the ground truth pose, and then only treat the prediction with an average 3D error below " + }, + { + "bbox": [ + 304, + 293, + 545, + 436 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 293, + 545, + 436 + ], + "type": "text", + "content": " of the mesh diameter as a correct pose estimate. We use its symmetric version for symmetric objects. Additionally, in some settings, we also use BOP metrics [15] for evaluation, including the Visible Surface Discrepancy (VSD), the Maximum Symmetry-aware Surface Distance (MSSD), the Maximum Symmetry-aware Projection Distance (MSPD), and their average AR. We refer the readers to [15] for their detailed definition." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 437, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 616 + ], + "type": "text", + "content": "Training details. We use RAFT [53] as our flow network for both the teacher and student network. We initialize the weights of both teacher and student network with the weights pretrained on synthetic data and train the model using AdamW optimizer [35] with a batch size of 16. We use One-cycle strategy [45] to anneal the learning rate from a starting point " + }, + { + "bbox": [ + 304, + 437, + 545, + 616 + ], + "type": "inline_equation", + "content": "4\\mathrm{e} - 4" + }, + { + "bbox": [ + 304, + 437, + 545, + 616 + ], + "type": "text", + "content": ". We crop the target object from the original image according to the initial pose, and then resize the image patch to " + }, + { + "bbox": [ + 304, + 437, + 545, + 616 + ], + "type": "inline_equation", + "content": "256\\times 256" + }, + { + "bbox": [ + 304, + 437, + 545, + 616 + ], + "type": "text", + "content": ". We do not use any data augmentation in the teacher network, and only use random color augmentation used in PFA [16] for the student network. We typically set " + }, + { + "bbox": [ + 304, + 437, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\tau = 1" + }, + { + "bbox": [ + 304, + 437, + 545, + 616 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 437, + 545, + 616 + ], + "type": "inline_equation", + "content": "m = 3" + }, + { + "bbox": [ + 304, + 437, + 545, + 616 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 437, + 545, + 616 + ], + "type": "inline_equation", + "content": "n = 4" + }, + { + "bbox": [ + 304, + 437, + 545, + 616 + ], + "type": "text", + "content": " in our experiments. Unlike [55, 54, 31, 20] that train a separate model for each object, which is cumbersome to train, we train a single model for all objects in the same dataset." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 623, + 498, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 498, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 498, + 635 + ], + "type": "text", + "content": "4.2. Comparison against State of the Art" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "We first compare our method against the state-of-the-art self-supervised pose estimation methods on LINEMOD and Occluded-LINEMOD. Since most of them report numbers only in ADD-0.1d, we follow the same for a fair comparison. Table. 1 and 2 summarize the result. Our method outperforms the state-of-the-art methods significantly. Espe" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14079" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 289, + 278 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 289, + 278 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 289, + 278 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 289, + 278 + ], + "type": "table", + "html": "
MethodDSC [61]Sock et al. [46]Lin et al. [31]Self6D [54]Self6D‡ [54]Ours
Ape31.237.667.576.075.481.9
Bench.83.078.699.991.694.995.0
Cam49.665.687.497.197.094.2
Can56.565.699.299.899.596.8
Cat57.952.594.385.686.695.4
Driller73.748.897.698.898.994.8
Duck31.335.167.256.568.383.5
Eggbox*96.089.298.991.099.093.9
Glue*63.464.596.292.296.196.5
Holep.38.841.549.935.441.984.5
Iron61.980.999.599.599.494.9
Lamp64.770.799.897.498.994.8
Phone54.460.591.591.894.394.1
Avg.58.660.688.485.688.592.2
", + "image_path": "d1afcca9ef092753a855e5a7d4a0a5f9256b067801ab7c3238da412c93b3e58e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 280, + 288, + 347 + ], + "lines": [ + { + "bbox": [ + 46, + 280, + 288, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 280, + 288, + 347 + ], + "type": "text", + "content": "Table 1. Comparison with self-supervised methods on LINEMOD. “*” denotes symmetric objects. We use the latest version of Self6D++ [54], and we only denote it as “Self6D” for simplicity. “Self6D‡” is the version with supervision from additional depth images. Our method outperforms “Self6D‡” with only RGB images." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 356, + 289, + 505 + ], + "blocks": [ + { + "bbox": [ + 48, + 356, + 289, + 505 + ], + "lines": [ + { + "bbox": [ + 48, + 356, + 289, + 505 + ], + "spans": [ + { + "bbox": [ + 48, + 356, + 289, + 505 + ], + "type": "table", + "html": "
MethodDSC [61]Sock et al. [46]Lin et al. [31]Self6D [54]Self6D‡ [54]Ours
Ape9.112.040.357.759.460.1
Can21.127.575.295.096.594.2
Cat26.012.035.052.660.856.5
Driller33.520.568.590.592.089.7
Duck12.223.025.726.730.630.9
Eggbox*39.425.144.745.051.158.1
Glue*37.027.060.787.188.688.9
Holep.20.435.028.023.538.544.2
Avg.24.822.847.359.864.765.4
", + "image_path": "69d0fc5dc8187caf80a8e59051598d96ecf52059d79ea38ca04a85f0f645ed2e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 537, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 537, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 537, + 287, + 586 + ], + "type": "text", + "content": "cially, our method, which requires only RGB images, even outperforms Self6D‡ [54] by " + }, + { + "bbox": [ + 46, + 537, + 287, + 586 + ], + "type": "inline_equation", + "content": "3.7\\%" + }, + { + "bbox": [ + 46, + 537, + 287, + 586 + ], + "type": "text", + "content": " on LINEMOD, which is a method that relies on additional depth images. We show some qualitative results in Fig. 5." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 587, + 142, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 142, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 142, + 601 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": "Evaluation of different components. Table. 3 summarizes the results of our method with different components. The first row is the results of the standard teacher-student structure used in [47]. Although it has the standard EMA updating strategy, its performance is limited, mainly caused by the lacking of high-quality pseudo pose labels. After adding our flow loss and photometric loss, the performance increases significantly, which demonstrates the effectiveness of the proposed components." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 312, + 70, + 536, + 141 + ], + "blocks": [ + { + "bbox": [ + 77, + 507, + 258, + 518 + ], + "lines": [ + { + "bbox": [ + 77, + 507, + 258, + 518 + ], + "spans": [ + { + "bbox": [ + 77, + 507, + 258, + 518 + ], + "type": "text", + "content": "Table 2. Comparison on Occluded-LINEMOD." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 312, + 70, + 536, + 141 + ], + "lines": [ + { + "bbox": [ + 312, + 70, + 536, + 141 + ], + "spans": [ + { + "bbox": [ + 312, + 70, + 536, + 141 + ], + "type": "table", + "html": "
\\( \\mathcal{L}_{flow} \\)\\( \\mathcal{L}_{photo} \\)MSPDMSSDVSDADD
--0.7590.5890.51930.9
-✓0.7650.6310.57837.5
✓-0.7800.7110.65864.2
✓✓0.7850.7490.66467.4
", + "image_path": "5fc95f28ee0c72e3cc61bd41f062837301b1a6e8a2fbbc3a7449a651ea592abe.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 305, + 143, + 545, + 176 + ], + "lines": [ + { + "bbox": [ + 305, + 143, + 545, + 176 + ], + "spans": [ + { + "bbox": [ + 305, + 143, + 545, + 176 + ], + "type": "text", + "content": "Table 3. Evaluation of different components on YCB-V. " + }, + { + "bbox": [ + 305, + 143, + 545, + 176 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{flow}" + }, + { + "bbox": [ + 305, + 143, + 545, + 176 + ], + "type": "text", + "content": " is the key component of our framework, and " + }, + { + "bbox": [ + 305, + 143, + 545, + 176 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{photo}" + }, + { + "bbox": [ + 305, + 143, + 545, + 176 + ], + "type": "text", + "content": " improves the performance further." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 317, + 190, + 531, + 324 + ], + "blocks": [ + { + "bbox": [ + 317, + 190, + 531, + 324 + ], + "lines": [ + { + "bbox": [ + 317, + 190, + 531, + 324 + ], + "spans": [ + { + "bbox": [ + 317, + 190, + 531, + 324 + ], + "type": "table", + "html": "
MethodMSPDMSSDVSDADD
Initialization v10.6320.4910.42027.4
+ Ours (Real)0.7800.7310.67364.6
+ Ours (SSL)0.7590.7220.65063.2
Initialization v20.6730.5800.50836.0
+ Ours (Real)0.7750.7220.66065.3
+ Ours (SSL)0.7640.7240.64364.2
Initialization v30.6940.5980.52238.6
+ Ours (Real)0.8030.7520.68669.2
+ Ours (SSL)0.7850.7490.66467.4
", + "image_path": "7d0f67cafdd27a8b062b5d048ede1dac9f8b4215bcccbdf8ac54a35b162b4da2.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 305, + 325, + 547, + 426 + ], + "lines": [ + { + "bbox": [ + 305, + 325, + 547, + 426 + ], + "spans": [ + { + "bbox": [ + 305, + 325, + 547, + 426 + ], + "type": "text", + "content": "Table 4. Performance with different initialization and additional annotations on YCB-V. We evaluate three versions of pose initialization with different accuracy, including the results obtained by the original WDR-Pose (\"Initialization v1\"), and also two other versions with pre-cropping the detected regions of interest, based on Mask RCNN and RADet, respectively (\"v2\" and \"v3\"). Our self-supervised refinement (\"SSL\") boosts the initialization accuracy significantly and achieves similar performance as versions trained with fully-annotated real images (\"Real\")." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 448, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 545, + 579 + ], + "type": "text", + "content": "Training analysis on YCB-V. We evaluate our method in three different settings during the training, as shown in Fig. 6. The baseline is the original teacher-student structure [52], and the other two are the proposed components of our method. The baseline model struggles to learn from the unannotated data without explicit quality measurement of pseudo labels. Our flow loss introduces a constraint based on flow consistency derived from multiview geometry, and tackles this problem effectively, and the proposed photometric loss increases performance further, as shown in Fig. 7." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "Evaluation of hyper-parameters. We evaluate the hyperparameters used in our framework in Fig. 8. We first evaluate the impact of the number of different views. More views generally increase the performance, since it adds more information to the geometry constraint. However, too many views, such as those larger than 4, has negative impacts on the performance. We believe it is caused by the noise introduced by too many views with large viewpoint differences, which usually makes the network harder to learn. We then evaluate the threshold " + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": " used in our framework, which is used to determine the reliability of pseudo flow labels. 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Qualitative results. We show the initialization results trained only on synthetic data at the top, and the refinement results after using our self-supervised strategy at the bottom. Our method significantly improves the baseline in various conditions, such as occluded, weak-textured, and symmetry objects." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 137, + 152, + 216, + 230 + ], + "blocks": [ + { + "bbox": [ + 137, + 152, + 216, + 230 + ], + "lines": [ + { + "bbox": [ + 137, + 152, + 216, + 230 + ], + "spans": [ + { + "bbox": [ + 137, + 152, + 216, + 230 + ], + "type": "image", + "image_path": "009c12b9bf6915498a5b81aa3ff12556f79e698a6c1d051346db6891f69a4326.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 217, + 152, + 296, + 230 + ], + "blocks": [ + { + "bbox": [ + 217, + 152, + 296, + 230 + ], + "lines": [ + { + "bbox": [ + 217, + 152, + 296, + 230 + ], + "spans": [ + { + "bbox": [ + 217, + 152, + 296, + 230 + ], + "type": "image", + "image_path": "d42a2d4d1eac0d91a0e828326ccfb7b1e8818f555c7d37a25d0b14f582c90cc1.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 296, + 152, + 376, + 230 + ], + "blocks": [ + { + "bbox": [ + 296, + 152, + 376, + 230 + ], + "lines": [ + { + "bbox": [ + 296, + 152, + 376, + 230 + ], + "spans": [ + { + "bbox": [ + 296, + 152, + 376, + 230 + ], + "type": "image", + "image_path": "d947efc8bf414e03ad4b7c46d4a2f97a8aaf9eadb43fd05db700db5b1dbe8262.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 377, + 152, + 455, + 230 + ], + "blocks": [ + { + "bbox": [ + 377, + 152, + 455, + 230 + ], + "lines": [ + { + "bbox": [ + 377, + 152, + 455, + 230 + ], + "spans": [ + { + "bbox": [ + 377, + 152, + 455, + 230 + ], + "type": "image", + "image_path": "324d9354da2ad253866e4056b2cff274056ae53124324708842131ffe8e520f7.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 457, + 152, + 536, + 230 + ], + "blocks": [ + { + "bbox": [ + 457, + 152, + 536, + 230 + ], + "lines": [ + { + "bbox": [ + 457, + 152, + 536, + 230 + ], + "spans": [ + { + "bbox": [ + 457, + 152, + 536, + 230 + ], + "type": "image", + "image_path": "07c00dbf4d117592fa613d9faa734f4eb92d7b0e67b92ac3c4c185d2bf370ea0.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 53, + 289, + 216, + 425 + ], + "blocks": [ + { + "bbox": [ + 53, + 289, + 216, + 425 + ], + "lines": [ + { + "bbox": [ + 53, + 289, + 216, + 425 + ], + "spans": [ + { + "bbox": [ + 53, + 289, + 216, + 425 + ], + "type": "image", + "image_path": "66f899017d5f07b8dff60af2b7d34ad65d4a0b482e9117b9a5026e73315d3c3b.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 429, + 546, + 463 + ], + "lines": [ + { + "bbox": [ + 46, + 429, + 546, + 463 + ], + "spans": [ + { + "bbox": [ + 46, + 429, + 546, + 463 + ], + "type": "text", + "content": "Figure 6. Training analysis on YCB-V. We report the results in three different settings during training. The baseline is the original teacher-student structure [52], and the other two are the proposed components of our method. The baseline model struggles to learn from unannotated data. By contrast, our flow loss tackles this problem effectively, and our photometric loss increases the performance further." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 219, + 289, + 375, + 425 + ], + "blocks": [ + { + "bbox": [ + 219, + 289, + 375, + 425 + ], + "lines": [ + { + "bbox": [ + 219, + 289, + 375, + 425 + ], + "spans": [ + { + "bbox": [ + 219, + 289, + 375, + 425 + ], + "type": "image", + "image_path": "7715e8debcbfb81890c4b1600209c31477c838d315f6fbd850dafd36ef73c0ab.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 380, + 289, + 542, + 425 + ], + "blocks": [ + { + "bbox": [ + 380, + 289, + 542, + 425 + ], + "lines": [ + { + "bbox": [ + 380, + 289, + 542, + 425 + ], + "spans": [ + { + "bbox": [ + 380, + 289, + 542, + 425 + ], + "type": "image", + "image_path": "b1b0a5431d21207de9202c274dad76bb0144918ea83c17ce54503522627fa370.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 482, + 165, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 482, + 165, + 493 + ], + "spans": [ + { + "bbox": [ + 47, + 482, + 165, + 493 + ], + "type": "text", + "content": "works well between 1 and 4." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 495, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 287, + 590 + ], + "type": "text", + "content": "Evaluation with limited real data. We evaluate our method on YCB-V with different amounts of real data used in training, as shown in Fig. 8(b). Our method increases the performance by about " + }, + { + "bbox": [ + 46, + 495, + 287, + 590 + ], + "type": "inline_equation", + "content": "20.2\\%" + }, + { + "bbox": [ + 46, + 495, + 287, + 590 + ], + "type": "text", + "content": " (from " + }, + { + "bbox": [ + 46, + 495, + 287, + 590 + ], + "type": "inline_equation", + "content": "41.7\\%" + }, + { + "bbox": [ + 46, + 495, + 287, + 590 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 495, + 287, + 590 + ], + "type": "inline_equation", + "content": "61.9\\%" + }, + { + "bbox": [ + 46, + 495, + 287, + 590 + ], + "type": "text", + "content": ") in ADD-0.1d by only using " + }, + { + "bbox": [ + 46, + 495, + 287, + 590 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 495, + 287, + 590 + ], + "type": "text", + "content": " of all the real data. " + }, + { + "bbox": [ + 46, + 495, + 287, + 590 + ], + "type": "inline_equation", + "content": "99\\%" + }, + { + "bbox": [ + 46, + 495, + 287, + 590 + ], + "type": "text", + "content": " more real data can only increase the performance by " + }, + { + "bbox": [ + 46, + 495, + 287, + 590 + ], + "type": "inline_equation", + "content": "5.5\\%" + }, + { + "bbox": [ + 46, + 495, + 287, + 590 + ], + "type": "text", + "content": " further, which demonstrates the effectiveness of our method in data-limited scenarios." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "Evaluation with different initialization and additional annotations. In principle, our method can be trained with ground truth pose annotations easily, which is basically training the student network in a standard fully-supervised way. We evaluate our self-supervised method with the version trained with real pose annotations. At the same time, to evaluate the robustness of our framework to different pose initialization, we evaluate three versions of pose initialization with different initialization accuracy, including the results obtained by the original WDR-Pose, and two other" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 482, + 546, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 546, + 566 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 546, + 566 + ], + "type": "text", + "content": "versions with pre-cropping the detected regions of interest, based on Mask RCNN [13] and RADet [10], respectively. Table 4 summarizes the results. Although the initial poses have different accuracy, our self-supervised refinement framework boosts their performance significantly, and even achieves similar performance as that trained on fully-annotated real images." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "content": "Comparison against standard optical flow methods. In principle, one can use a self-supervised optical flow method to directly establish dense 2D-to-2D correspondence between the rendered image and the real image input, without any real pose annotations. However, we find that this strategy hardly can work, mainly due to the large domain gap between the rendered and real images, in which case the standard component of photometric comparison in self-supervised flow methods suffers. 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Visualization with increasing training iterations. We show the normalized visualization of variance " + }, + { + "bbox": [ + 46, + 228, + 547, + 274 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 228, + 547, + 274 + ], + "type": "text", + "content": " and flow error at training steps " + }, + { + "bbox": [ + 46, + 228, + 547, + 274 + ], + "type": "inline_equation", + "content": "40\\mathrm{k}" + }, + { + "bbox": [ + 46, + 228, + 547, + 274 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 228, + 547, + 274 + ], + "type": "inline_equation", + "content": "70\\mathrm{k}" + }, + { + "bbox": [ + 46, + 228, + 547, + 274 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 228, + 547, + 274 + ], + "type": "inline_equation", + "content": "100\\mathrm{k}" + }, + { + "bbox": [ + 46, + 228, + 547, + 274 + ], + "type": "text", + "content": " from left to right, respectively. The top row shows the baseline method [52], and the bottom row is ours. The baseline method struggles to produce valid flow labels and reliable optical flow, regardless of the training steps. By contrast, our method produces more and more valid flow labels with small variance " + }, + { + "bbox": [ + 46, + 228, + 547, + 274 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 228, + 547, + 274 + ], + "type": "text", + "content": " during training, also with progressively better flow predictions." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 218, + 281, + 373, + 417 + ], + "lines": [ + { + "bbox": [ + 218, + 281, + 373, + 417 + ], + "spans": [ + { + "bbox": [ + 218, + 281, + 373, + 417 + ], + "type": "image", + "image_path": "c76ec96d73ac70866fb54241ba1353aa99d5a001aee53f52fc1e8cdfa5cae4bb.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 381, + 294, + 527, + 417 + ], + "blocks": [ + { + "bbox": [ + 381, + 294, + 527, + 417 + ], + "lines": [ + { + "bbox": [ + 381, + 294, + 527, + 417 + ], + "spans": [ + { + "bbox": [ + 381, + 294, + 527, + 417 + ], + "type": "image", + "image_path": "3ee43916c75df898cff9dd6be3c7f34118cc9ceb4e7868d5362b80821d074cb8.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 380, + 420, + 529, + 431 + ], + "lines": [ + { + "bbox": [ + 380, + 420, + 529, + 431 + ], + "spans": [ + { + "bbox": [ + 380, + 420, + 529, + 431 + ], + "type": "text", + "content": "(b) Different amount of real training data" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 433, + 547, + 467 + ], + "lines": [ + { + "bbox": [ + 46, + 433, + 547, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 433, + 547, + 467 + ], + "type": "text", + "content": "Figure 8. Ablation study of hyper-parameters and training data on YCB-V. (a) " + }, + { + "bbox": [ + 46, + 433, + 547, + 467 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 433, + 547, + 467 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 433, + 547, + 467 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 433, + 547, + 467 + ], + "type": "text", + "content": " are the number of views used for " + }, + { + "bbox": [ + 46, + 433, + 547, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{photo}}" + }, + { + "bbox": [ + 46, + 433, + 547, + 467 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 433, + 547, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{flow}}" + }, + { + "bbox": [ + 46, + 433, + 547, + 467 + ], + "type": "text", + "content": ", respectively, and " + }, + { + "bbox": [ + 46, + 433, + 547, + 467 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 433, + 547, + 467 + ], + "type": "text", + "content": " is the threshold for determining the validity of flow labels for " + }, + { + "bbox": [ + 46, + 433, + 547, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{flow}}" + }, + { + "bbox": [ + 46, + 433, + 547, + 467 + ], + "type": "text", + "content": ". Our method is robust to the choices of different hyper parameters. (b) Our method produces acceptable results with accessing only " + }, + { + "bbox": [ + 46, + 433, + 547, + 467 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 433, + 547, + 467 + ], + "type": "text", + "content": " of all the real data." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "table", + "bbox": [ + 58, + 483, + 272, + 532 + ], + "blocks": [ + { + "bbox": [ + 58, + 483, + 272, + 532 + ], + "lines": [ + { + "bbox": [ + 58, + 483, + 272, + 532 + ], + "spans": [ + { + "bbox": [ + 58, + 483, + 272, + 532 + ], + "type": "table", + "html": "
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SMURF [48]0.7510.5650.48828.7
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Note how the predicted poses have different 3D axis from the ground truth pose but align the target mesh with the images well in appearance." + } + ] + } + ], + "index": 41 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14082" + } + ] + } + ], + "index": 42 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "Time analysis. We conduct all our experiments on a workstation with an NVIDIA RTX-3090 GPU and an Intel-Xeon CPU with 12 cores running at " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "2.1\\mathrm{GHz}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ". The training of our self-supervised framework is only about " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " slower than its fully-supervised version, consuming about 30 and 24 hours in the typical setting on YCB-V, respectively, which is much more efficient than methods relying on multiple times of retraining [31, 4]. For the inference time, our method is the same as its fully-supervised version and takes only " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "23\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " for a single object, including the optical flow estimation " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "17\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " and the PnP solver " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "6\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 213, + 119, + 227 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 213, + 119, + 227 + ], + "spans": [ + { + "bbox": [ + 47, + 213, + 119, + 227 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 233, + 289, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 233, + 289, + 389 + ], + "spans": [ + { + "bbox": [ + 46, + 233, + 289, + 389 + ], + "type": "text", + "content": "We have introduced a simple self-supervised 6D object pose method. After obtaining the rough pose initialization based on a network training on synthetic images, we refine the pose with a teacher-student pseudo labeling framework. To solve the problem of identifying high-quality labels in the context of object pose estimation, we first formulate pseudo object pose labels as pixel-level optical flow supervision signals. Then, we introduce a flow consistency based on the underlying geometry constraint between multiple different views. Our experiments show that the proposed method significantly outperforms existing solutions in both accuracy and efficiency, without relying on any 2D annotations or additional depth images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 392, + 289, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 289, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 289, + 464 + ], + "type": "text", + "content": "Acknowledgments. This work was supported by the Natural Science Foundation of China, the Youth Innovation Team of Shaanxi Universities, the Fundamental Research Funds for the Central Universities under Grant JBF220101, and the 111 Project of China under Grant B08038. 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Limited", + "bbox": [ + 181, + 215, + 787, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 304, + 313, + 320 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Pseudo-labeling is significant for semi-supervised instance segmentation, which generates instance masks and classes from unannotated images for subsequent training. However, in existing pipelines, pseudo-labels that contain valuable information may be directly filtered out due to mismatches in class and mask quality. To address this issue, we propose a novel framework, called pseudo-label aligning instance segmentation (PAIS), in this paper. In PAIS, we devise a dynamic aligning loss (DALoss) that adjusts the weights of semi-supervised loss terms with varying class and mask score pairs. Through extensive experiments conducted on the COCO and Cityscapes datasets, we demonstrate that PAIS is a promising framework for semi-supervised instance segmentation, particularly in cases where labeled data is severely limited. Notably, with just $1\\%$ labeled data, PAIS achieves 21.2 mAP (based on Mask-RCNN) and 19.9 mAP (based on K-Net) on the COCO dataset, outperforming the current state-of-the-art model, i.e., NoisyBoundary with 7.7 mAP, by a margin of over 12 points. Code is available at: https://github.com/hujiecpp/PAIS.", + "bbox": [ + 75, + 335, + 473, + 654 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 683, + 209, + 698 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semi-supervised instance segmentation aims to alleviate the significant burden of human labeling by utilizing a small amount of labeled data in conjunction with abundant unlabeled data [35, 47, 50]. Existing semi-supervised instance segmentation pipelines typically generate pseudolabels from unlabeled images, which are then used to train the models together with labeled images. Therefore, pseudo-labels play a crucial role in semi-supervised instance segmentation. The generation of pseudo-masks, pseudo-classes, and pseudo-boxes from unlabeled images improves the model training. However, current semi", + "bbox": [ + 75, + 709, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "supervised instance segmentation frameworks do not fully leverage the potential of such pseudo-labels. Specifically, pseudo-labels with mismatched class and mask scores are often filtered out by fixed thresholds, leading to the exclusion of valuable information that could aid the model training. For instance, pseudo-labels with high-quality masks but low class scores would be filtered out by a class threshold, resulting in the loss of the pixel-level information.", + "bbox": [ + 500, + 305, + 890, + 426 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we present a new semi-supervised framework, termed pseudo-label aligning for instance segmentation (PAIS), aiming to improve the utilization of filtered pseudo-labels. As illustrated in Fig. 1, the main challenge of PAIS lies in the mismatched scores between pseudoclasses and pseudo-masks. The classification score and mask intersection over union (IoU) are misaligned in assessing the quality of pseudo-labels. As a result, masks with high IoUs would be filtered out due to low classification scores, and vice versa. In the mean time, lowering the threshold of both scores introduces incorrect classes or low-quality masks into the semi-supervised training. To overcome this dilemma, we propose a dynamic aligning loss (DALoss) that softly re-weights the classification and the segmentation losses based on the quality of different pseudo-labels. Specifically, DALoss penalizes low-score pseudo-labels rather than filtering them and promotes high-score ones, to adjust their contribution to the final loss function. Our experiments on the COCO and Cityscape datasets demonstrate the effectiveness of the proposed PAIS framework. Specifically, with only $1\\%$ labeled data, PAIS achieves $21.2\\mathrm{mAP}$ and $19.9\\mathrm{mAP}$ on the COCO dataset using Mask-RCNN [13] and K-Net [53], respectively. This outperforms the current state-of-the-art model, NoisyBoundary [47], by more than 12 points.", + "bbox": [ + 496, + 428, + 892, + 804 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Our contributions can be summarized as follows:", + "bbox": [ + 517, + 805, + 844, + 819 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "- We propose a novel pseudo-label aligning framework for semi-supervised instance segmentation, called PAIS, which unleashes the potential of utilizing pixel-level pseudo-labels in semi-supervised instance segmentation. Furthermore, to the best of our knowledge,", + "bbox": [ + 517, + 825, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 805, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author. † Equal contribution.", + "bbox": [ + 94, + 886, + 331, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16337", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/57279d70f6f037dbc92abada7946a2ba11569434ccb7fc015435590f03ebfa0c.jpg", + "image_caption": [ + "Figure 1. Pseudo-label wasting in semi-supervised instance segmentation. To illustrate this issue, we employed the K-Net model [53] trained on $10\\%$ labeled images and randomly sampled 5k unlabeled images, from the COCO train2017 dataset, to plot the figures. In (a), we present the predicted classification score w.r.t. the ground truth mask intersection over union (IoU), revealing that the predicted classification score is inadequate in evaluating mask quality. In (b), we added a mask IoU prediction branch to the model and plotted the predicted mask IoU w.r.t. the ground truth mask IoU, demonstrating that the predicted mask IoU can represent the mask quality. However, as shown in (c), a significant number of pseudo-labels with high-quality masks, i.e., mask IoU $>0.7$ , will be filtered out with high classification thresholds. Additionally, (d) shows that pseudo-labels with high-quality masks can also have correspondingly low classification scores. Therefore, the misalignment between the mask and class scores leads to a significant number of valuable pseudolabels being excluded during semi-supervised training." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 285, + 209 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/42a4e8b5f29d78ea0d22dd22a4db1e48cdb6bba23e30fbfd95ce52b4d602e21b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 88, + 488, + 210 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3c10d05e561321ec21bee95d6cabffe3c5500fa95b6f02b55840e7bc9085e569.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 88, + 686, + 210 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ae4734b7932dd715437e5be9a7f5245d76e3c6468b822cc041dfb850b012f2bb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 89, + 885, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "PAIS is the first framework that can be adapted to box-free instance segmentation models.", + "bbox": [ + 107, + 362, + 467, + 391 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a new loss function, named dynamic aligning loss (DALoss), which incorporates pseudolabels with diverse class and mask qualities into the semi-supervised training process. DALoss consistently enhances the performance of box-free and box-dependent instance segmentation frameworks.", + "- We conduct comprehensive experiments on the COCO and Cityscapes datasets to evaluate PAIS. In particular, PAIS achieves state-of-the-art results on the COCO dataset, i.e., 19.9, 27.6, and $31.1\\mathrm{mAP}$ for the box-free pipeline K-Net [53], and 21.2, 29.3, and $31.1\\mathrm{mAP}$ for the box-dependent pipeline Mask-RCNN [13], with $1\\%$ , $5\\%$ , and $10\\%$ labeled data, respectively." + ], + "bbox": [ + 96, + 398, + 467, + 603 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 632, + 218, + 647 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semi-supervised Image Classification. In image classification, semi-supervised learning has been extensively explored, and the methods can be classified into two categories: pseudo-label-based and consistency-regularization-based methods. Specifically, pseudo-label-based methods [40, 21] leverage pre-trained models to generate annotations for the unlabeled images to train the model. In contrast, consistency-regularization-based methods [1, 36, 20, 39, 48, 2, 7, 32, 31, 23] incorporate various data augmentation techniques such as random regularization [10] and adversarial perturbation [33] to generate different inputs for one image and enforce consistency between these inputs during training. FixMatch [41] combines the consistency-regularization-based techniques with a pseudo-label-based framework by applying a strong-weak data augmentation pipeline to input images and enforcing consistency between", + "bbox": [ + 75, + 657, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the augmented images. In this work, we follow the pseudolabel-based methods and also use strong-weak data augmentation during training in PAIS.", + "bbox": [ + 496, + 362, + 890, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semi-supervised Object Detection. From the very beginning, STAC [42] proposed the use of pseudo-labels and consistency training for semi-supervised object detection. However, the effectiveness of the method was limited by the two-stage training pipeline similar to that of Noisy Student [49], where the pseudo-labels were generated from pre-trained models and were not updated along with the model training. After STAC, several studies [50, 54, 43, 51, 28] incorporated the idea of exponential moving average (EMA) from MeanTeacher [44]. The teacher model and pseudo-labels are updated after each training iteration to generate instant pseudo-labels, making the entire pipeline end-to-end trainable. Additionally, Unbiased Teacher [28] utilized Focal loss [24] instead of traditional cross-entropy loss to alleviate the problem of unbalanced pseudo-labels. In this paper, we also follow the idea of incorporating EMA into the proposed PAIS framework, with a focus on integrating pixel-level annotations into the training process.", + "bbox": [ + 496, + 411, + 892, + 684 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fully-supervised Instance Segmentation. Instance segmentation aims to provide pixel-level predictions for each object instance in an image. Existing methods can be classified into three categories: top-down (or box-dependent) methods, bottom-up methods, and direct segmentation (or box-free) methods. Top-down methods [15, 27, 38, 37, 29] such as Mask R-CNN [13], YOLACT [3], and CenterMask [22] generate bounding boxes first and then segment the objects within the boxes. Bottom-up methods [52, 8, 26, 11, 16], regard instance segmentation as a label-then-cluster problem, which classify each pixel first and then group the pixels into an arbitrary number of object instances. Direct segmentation or box-free methods such as SOLO [45, 46], K-Net [53], MaskFormer [5, 4] and", + "bbox": [ + 496, + 689, + 892, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16338", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3b9d6905c6b74d715ed2754589e2d829608658ee580747da9a65ecee6404d16a.jpg", + "image_caption": [ + "Figure 2. Framework of pseudo-label aligning for semi-supervised instance segmentation (PAIS). The focus of PAIS is to explore the utility of pixel-level pseudo-labels for instance segmentation. To this end, we propose a novel approach called dynamic aligning loss (DALoss), which enables the incorporation of pseudo-labels with varying quality during training. This is particularly significant when the number of labeled images is limited. With DALoss, a significant number of predictions from the teacher model can be leveraged in the semi-supervised training process, rather than being discarded. Specifically, we consider three types of pseudo-masks with varying quality: (a) pseudo-masks with incorrect classes but high-quality masks, i.e., low classification scores but high mask IoUs; (b) pseudo-masks with accurate classes but low-quality masks, i.e., high classification scores but low mask IoUs; and (c) pseudo-masks with medium qualities." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 637, + 292 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/694187f758c656bdb92868e2fef6222eb5cba33765bd5a524c96798479b56dca.jpg", + "image_caption": [ + "(a) Score↓, IoU↑" + ], + "image_footnote": [], + "bbox": [ + 656, + 90, + 764, + 172 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c825972816ff2779d7824731dd640c7d705401762cd99bd8cb2dd2fd0d4b25ec.jpg", + "image_caption": [ + "(c) Score-, IoU-" + ], + "image_footnote": [], + "bbox": [ + 658, + 189, + 763, + 268 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ae1d9651c84de716480e1f4dc2c927d6bb64d321da5b7571aa8dba9357e3d08f.jpg", + "image_caption": [ + "(b) Score↑, IoU↓" + ], + "image_footnote": [], + "bbox": [ + 774, + 90, + 880, + 172 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/cd661cf983cb9e65df58db3acbe7f975396705014ca95dcbe4c289507a09f045.jpg", + "image_caption": [ + "(d) Score↑, IoU↑" + ], + "image_footnote": [], + "bbox": [ + 774, + 191, + 880, + 268 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SOTR [12] deal with instance segmentation without bounding box detection. Any of the aforementioned instance segmentation methods can be implemented into PAIS, and in this work, we present two examples, one from the box-dependent category, Mask R-CNN, and another from the box-free category, K-Net.", + "bbox": [ + 75, + 416, + 467, + 507 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Semi-supervised Instance Segmentation. Semi-supervised instance segmentation is commonly considered to be a sub-task of semi-supervised object detection [50, 28]. Consequently, existing frameworks rely heavily on bounding boxes, in which segmentation performance is strongly dependent on detection performance. Among them, NoisyBoundary [47] was the first to formally propose the semi-supervised instance segmentation task. Recent efforts have been made to construct box-free pipelines for fully-supervised instance segmentation [45, 46, 53, 5]. In this paper, we investigate PAIS in both box-free and box-dependent instance segmentation, revealing the potential of fully utilizing pixel-level annotations. In contrast to the recently-proposed PoliteTeacher [9], which filters out pseudo-labels with low confidence, the proposed PAIS leverages them. It is a novel and effective way of utilizing noisy pseudo-labels for semi-supervised learning.", + "bbox": [ + 75, + 507, + 467, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 777, + 166, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Task Formulation", + "text_level": 1, + "bbox": [ + 76, + 801, + 250, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The goal of PAIS is to better leverage unlabeled images with a limited number of pixel-labeled images to boost the performance of semi-supervised instance segmentation. The PAIS framework consists of three key steps: (1) pseudo-label generation, (2) dynamic pseudo", + "bbox": [ + 75, + 824, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "label alignment, and (3) end-to-end model training. In the pseudo-label generation step, we introduce a mask scoring branch [17] that predicts mask IoUs as an additional metric along with classification scores to assess the quality of pseudo-labels. In the dynamic aligning step, we re-weight the loss terms based on the quality of different pseudolabels. Finally, the teacher and student models are trained using exponential moving average (EMA) [44]. The overall framework of PAIS is illustrated in Fig. 2, and we introduce the key steps in detail as follows. It is important to note that the PAIS framework can be applied to any box-dependent or box-free framework for enhanced exploitation of pseudo-labels in semi-supervised instance segmentation. We instantiate two examples by Mask-RCNN [13] and K-Net [53] in this paper, but do not restrict to them.", + "bbox": [ + 496, + 416, + 890, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Pseudo Label Generation", + "text_level": 1, + "bbox": [ + 500, + 650, + 732, + 666 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the pseudo-label generation, we apply weak data augmentation to the unlabeled images and input them into a teacher model. The weak data augmentation includes scaling, horizontal flipping, and other augmentation operations that do not alter the image's content. The teacher model produces a set of pseudo-labels, including masks, boxes, and classification scores for each input image. In box-free pipelines, the box predictions are optional.", + "bbox": [ + 496, + 674, + 890, + 795 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As depicted in Fig. 1(a)(c), using the classification score alone is inadequate to measure the quality of predicted masks. To address this, we incorporate a mask scoring branch into the pipeline to predict mask Intersection over Union (IoU) for evaluating mask quality. As shown in Fig. 1(b), the predicted mask IoUs can be used to measure mask quality effectively, which has also been verified", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16339", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Algorithm 1 Pseudo-label Alignment", + "text_level": 1, + "bbox": [ + 80, + 90, + 328, + 104 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Initialize teacher and student models randomly.", + "2:Repeat", + "3: Apply weak augmentation to unlabeled images.", + "4: Obtain pseudo-labels $\\{\\pmb{m}_i, \\pmb{b}_i, \\pmb{c}_i, s_i | i = 1, \\dots, N\\}$ from teacher model via thresholds $\\tau_{cls}, \\tau_{iou}$ .", + "5: Apply strong augmentation to unlabeled images.", + "6: Obtain predictions $\\widetilde{m}, b, \\widetilde{c}$ for unlabeled images.", + "7: Calculate $\\mathcal{L}_u$ for unlabeled images by Eq. 5.", + "8: Inference labeled images by student model.", + "9: Calculate $\\mathcal{L}_l$ for labeled images.", + "10: Train student model with the loss $\\mathcal{L}_{semi}$ in Eq. 1.", + "11: Update teacher model via EMA.", + "12: Until scheduled epochs." + ], + "bbox": [ + 94, + 108, + 467, + 305 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "in MS-RCNN [17]. After generating pseudo-labels in the previous step, the predictions are filtered using two thresholds: a classification threshold $\\tau_{cls}$ and a mask IoU threshold $\\tau_{iou}$ . The resulting set of pseudo-labels includes $N$ elements, each containing a mask $m_i \\in \\mathbb{R}^{H \\times W}$ , a bounding box $b_i \\in \\mathbb{R}^4$ , a classification score $c_i \\in \\mathbb{R}^L$ (with an additional background category), and a mask IoU score $s_i \\in \\mathbb{R}$ . Note that $H, W$ denote the mask resolution, and $L$ is the number of classes.", + "bbox": [ + 75, + 339, + 468, + 474 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Dynamic Aligning Loss", + "text_level": 1, + "bbox": [ + 76, + 489, + 290, + 506 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although good pseudo-labels can be obtained by setting high thresholds for classification scores and mask IoUs, a large number of predictions with misaligned mask and classification qualities are discarded (as illustrated in Fig.1(c)(d)). These misaligned predictions can be useful since the amount of labeled data is limited in the semi-supervised setting. Fig.2 shows examples of pseudo-labels that can be included in the training process. If the misaligned pseudo-labels are directly used in semi-supervised learning, the incorrect predictions on classes or masks can introduce significant noise. To reduce the noise, we propose a dynamic aligning loss (DALoss).", + "bbox": [ + 75, + 515, + 468, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Vanilla Loss for PAIS. In semi-supervised instance segmentation, the loss function can be decomposed into two terms for labeled and unlabeled images, as:", + "bbox": [ + 75, + 698, + 468, + 744 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s e m i}} = \\lambda_ {l} \\mathcal {L} _ {l} + \\lambda_ {u} \\mathcal {L} _ {u}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 761, + 468, + 777 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda_{l}$ and $\\lambda_{u}$ are the hyper-parameters for balancing the loss terms. The loss for labeled images can be defined using the functions commonly employed in instance segmentation, augmented with an additional binary cross-entropy term for regressing mask IoUs. Given the pseudo-labels from the teacher model and the predictions from the student model, we formulate the loss for unlabeled images as:", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {u} = \\frac {1}{N _ {p o s}} \\sum_ {i = 1} ^ {N _ {p o s}} \\left(\\lambda_ {b} \\mathcal {L} _ {b} \\left(\\widetilde {\\boldsymbol {b}} _ {\\nu (i)}, \\boldsymbol {b} _ {\\mu (i)}\\right) \\right. \\\\ \\left. + \\lambda_ {c} \\mathcal {L} _ {c} \\left(\\widetilde {\\boldsymbol {c}} _ {\\nu (i)}, \\boldsymbol {c} _ {\\mu (i)} ^ {o}\\right) + \\lambda_ {m} \\mathcal {L} _ {m} \\left(\\widetilde {\\boldsymbol {m}} _ {\\nu (i)}, \\boldsymbol {m} _ {\\mu (i)} ^ {b}\\right)\\right) \\tag {2} \\\\ + \\frac {1}{N _ {n e g}} \\sum_ {i = 1} ^ {N _ {n e g}} \\left(\\lambda_ {c} \\mathcal {L} _ {c} (\\widetilde {\\boldsymbol {c}} _ {i}, \\boldsymbol {c} _ {n e g} ^ {o})\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 113, + 890, + 222 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_b$ includes the box IoU loss and the L1 loss, $\\mathcal{L}_c$ denotes the cross-entropy loss, $\\mathcal{L}_m$ is the dice loss. In Eq. 2, $\\widetilde{c}_i,\\widetilde{b}_i,\\widetilde{m}_i$ represent predictions from the student model. The pseudo-scores $c_{\\mu (i)}$ for classification are converted to one-hot vectors $c_{\\mu (i)}^o$ for the category with the highest score. The pseudo-masks $m_{\\mu (i)}$ are activated by sigmoid function and discretized into binary value as $m_{\\mu (i)}^{b}$ . The one-hot vector for the background class is denoted by $c_{neg}^o$ . The label indexing functions, $\\nu (i)$ and $\\mu (i)$ , match predictions with pseudo-labels for training, which are defined in terms of different pseudo-label assigning strategies. In our implementations, the one-to-many assignment defines the label indexing functions $\\nu (i) = i$ and $\\mu (i)$ as:", + "bbox": [ + 496, + 229, + 890, + 429 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mu (i) = \\underset {t \\in [ 1, N ]} {\\arg \\min } \\left(\\mathcal {L} _ {b} \\left(\\widetilde {\\boldsymbol {b}} _ {i}, \\boldsymbol {b} _ {t}\\right)\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 436, + 890, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Instead, the one-to-one assignment defines the label indicting functions $\\mu (i) = i$ , and finds the optimal $\\nu^{*}(\\cdot)$ via:", + "bbox": [ + 498, + 474, + 888, + 505 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\nu^ {*} = \\arg \\min _ {\\nu} \\sum_ {i = 1} ^ {t} \\left(\\lambda_ {b} \\mathcal {L} _ {b} \\left(\\widetilde {\\boldsymbol {b}} _ {\\nu (i)}, \\boldsymbol {b} _ {i}\\right) + \\lambda_ {c} \\mathcal {L} _ {c} \\left(\\widetilde {\\boldsymbol {c}} _ {\\nu (i)}, \\boldsymbol {c} _ {i} ^ {o}\\right) \\right. \\tag {4} \\\\ + \\lambda_ {m} \\mathcal {L} _ {m} (\\widetilde {\\boldsymbol {m}} _ {\\nu (i)}, \\boldsymbol {m} _ {i} ^ {b}) - s _ {i}). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 513, + 890, + 575 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that the loss terms for regressing boxes are optional in box-free instance segmentation frameworks.", + "bbox": [ + 498, + 582, + 888, + 612 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Dynamic Aligning Loss for PAIS. To optimize the model using pixel-level pseudo-labels, we propose to replace Eq. 2 with DALoss. Since the teacher model provides ideal metrics for measuring the quality of classification scores and mask IoUs, we propose to adjust the weight of loss terms based on the quality of the pseudo-labels. This is achieved by using the following equation:", + "bbox": [ + 496, + 613, + 890, + 718 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {u} ^ {D A} = \\frac {1}{N _ {p o s}} \\sum_ {i = 1} ^ {N _ {p o s}} \\left(\\lambda_ {b} \\mathcal {L} _ {b} (\\widetilde {\\boldsymbol {b}} _ {\\nu (i)}, \\boldsymbol {b} _ {\\mu (i)}) \\right. \\\\ + \\lambda_ {c} \\left(c _ {\\mu (i)} ^ {h}\\right) ^ {\\alpha} \\mathcal {L} _ {c} \\left(\\widetilde {c} _ {\\nu (i)}, c _ {\\mu (i)} ^ {o}\\right) \\tag {5} \\\\ \\left. + \\lambda_ {m} \\left(s _ {\\mu (i)}\\right) ^ {\\beta} \\mathcal {L} _ {m} \\left(\\widetilde {\\boldsymbol {m}} _ {\\nu (i)}, \\boldsymbol {m} _ {\\mu (i)} ^ {b}\\right)\\right) \\\\ + \\frac {1}{N _ {n e g}} \\sum_ {i = 1} ^ {N _ {n e g}} \\left(\\lambda_ {c} \\mathcal {L} _ {c} (\\widetilde {\\boldsymbol {c}} _ {i}, \\boldsymbol {c} _ {n e g} ^ {o})\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 727, + 890, + 858 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $c_{\\mu(i)}^{h}$ denotes the highest classification score, and $s_{\\mu(i)}$ denotes the mask IoU from the $\\mu(i)$ -th pseudo-label,", + "bbox": [ + 500, + 867, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16340", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/398f99a62d9590fdc07e504547e594352a5fea951836070cf16989cee996e4b9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method1%5%10%100%
Mask-RCNN [13], supervised*3.517.322.034.5
Mask-RCNN† [13], supervised*3.517.421.937.1
DD [35]3.820.424.235.7
Noisy Boundaries [47]7.724.929.238.6
PAIS, on Mask-RCNN, ours21.229.331.139.5
", + "bbox": [ + 80, + 89, + 462, + 174 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/89f3c34337ad2be00ad3959a5763925f9589869cfa1bb595c51f76506c9ba453.jpg", + "table_caption": [ + "Table 1. Comparison to state-of-the-art semi-supervised instance segmentation methods on the COCO val2017.† denotes using the same data augmentation as semi-supervised training. * denotes data from NoisyBoundary [47]." + ], + "table_footnote": [], + "table_body": "
Method5%10%20%30%
Mask-RCNN [13], supervised*11.816.822.326.3
Mask-RCNN† [13], supervised*11.316.422.626.6
DD [35]13.719.224.627.4
STAC [42]11.918.222.929.0
CSD [18]14.117.924.627.5
CCT [34]15.218.624.726.5
Dual-branch [30]13.918.924.028.9
Ubteacher [28]16.020.027.128.0
Noisy Boundaries [47]17.122.129.032.4
PAIS, on Mask-RCNN, ours18.022.929.232.8
", + "bbox": [ + 78, + 247, + 462, + 400 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2. Comparison to state-of-the-art semi-supervised instance segmentation methods on the Cityscapes validation set. $\\dagger$ denotes using the same data augmentation as semi-supervised training. \\* denotes data from NoisyBoundary [47].", + "bbox": [ + 76, + 404, + 467, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\alpha, \\beta$ are the hyper-parameters. Specifically, Eq. 5 adjusts the weights for the pseudo-labels conditioned on their qualities, i.e., dynamically dependent on the input images. For instance, for a pseudo-label with a low classification score and high mask IoU, DALoss encourages the segmentation loss while constraining the classification loss.", + "bbox": [ + 75, + 486, + 467, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. End-to-End Model Training", + "text_level": 1, + "bbox": [ + 76, + 587, + 328, + 603 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspired by [44], we employ EMA with the strong-weak data augmentation for PAIS. Specifically, unlabeled images undergo both strong and weak data augmentations and are then fed into the student and teacher models, respectively. The student model is trained to produce consistent results with the pseudo-labels, and the teacher model is updated by EMA. The training pipeline for PAIS is presented in Alg. 1.", + "bbox": [ + 75, + 609, + 467, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 746, + 207, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and Evaluation Metrics", + "text_level": 1, + "bbox": [ + 76, + 770, + 362, + 785 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conducted extensive experiments on the COCO [25] and Cityscapes [6] datasets to study the proposed PAIS. The COCO dataset consists of 118k images with 80-class instance labels, as well as 123k unlabeled images. The Cityscapes dataset contains urban street-view scenes and has 8 instance categories in 2.9k training images and 0.5k validation images. For the COCO dataset, we ran-", + "bbox": [ + 75, + 794, + 467, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "domly sampled $1\\%$ , $5\\%$ , and $10\\%$ of the images from the train2017 split as labeled data and treated the rest as unlabeled data following common settings. In addition, we also used the full COCO train2017 as labeled data and incorporated the 123k unlabeled data from COCO unlabel2017 to train the PAIS models. For the Cityscapes dataset, we randomly sampled $5\\%$ , $10\\%$ , $20\\%$ , and $30\\%$ of the images from the training set as labeled data and treated the remaining as unlabeled data following the common settings. We evaluated the PAIS models on the validation sets of the COCO and Cityscapes datasets, and reported standard COCO metrics including AP, AP50, AP75 (averaged over IoU thresholds), and $\\mathrm{AP}_S$ , $\\mathrm{AP}_M$ , $\\mathrm{AP}_L$ (AP for instances of different scales).", + "bbox": [ + 496, + 90, + 890, + 301 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 313, + 715, + 329 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We provide two examples of implementing PAIS with K-Net [53] and Mask-RCNN [13]. The models are trained using AdamW with a learning rate of 0.0001 for K-Net, and SGD with a learning rate of 0.01 for Mask-RCNN. The hyper-parameters $\\lambda_{l}$ and $\\lambda_{u}$ , which balance the loss terms for labeled and unlabeled images, are set to 1.0 and 0.3 for K-Net, and 1.0 and 1.5 for Mask-RCNN. We set the thresholds $\\tau_{cls}$ and $\\tau_{iou}$ experimentally as 0.35 and 0.30, respectively. For bipartite matching loss, we use the same hyperparameters as in [53]. The loss balancing parameters for box, class, and mask are set as $\\lambda_{b} = 2.0$ , $\\lambda_{c} = 4.0$ , and $\\lambda_{m} = 1.0$ respectively. We train the models on 4 GPUs with 4 images per GPU (1 labeled and 3 unlabeled images) for 220k iterations, unless otherwise specified. The teacher model is updated via EMA with a momentum of 0.999. We use ResNet50 [14] as the backbone for these models.", + "bbox": [ + 496, + 335, + 890, + 578 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Main Results", + "text_level": 1, + "bbox": [ + 500, + 589, + 637, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Comparison to state-of-the-art semi-supervised instance segmentation frameworks. In Tab. 1, we compare the performance of models trained with PAIS to the state-of-the-art semi-supervised instance segmentation frameworks on the COCO dataset. The results demonstrate that both K-Net and Mask-RCNN trained with PAIS surpass the previous methods DD [35] and Noisy Boundaries [47] by a large margin, especially when the number of labeled data is very limited (with only $1\\%$ or $5\\%$ labeled images). Specifically, when using $1\\%$ labeled COCO images, PAIS with K-Net achieves 19.9 mask mAP, which is 12.2 points higher than Noisy Boundaries. Interestingly, the proposed PAIS brings about better performance for Mask-RCNN when the percentage of labeled data is $1\\%$ or $5\\%$ , even though it originally has a inferior performance in fully-supervised instance segmentation compared to K-Net. To explain, the bounding boxes may provide better optimization for Mask-RCNN models when the labeled data is limited. Finally, when using $10\\%$ and $100\\%$ labeled images, PAIS with K-Net out", + "bbox": [ + 496, + 613, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16341", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/10e38b663711e6ab8d56789b5e69eaf3136100b744f539085d229b8997768f71.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method1% COCO5% COCO10% COCO
APAP0.5AP0.75APAP0.5AP0.75APAP0.5AP0.75
", + "bbox": [ + 76, + 88, + 890, + 119 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/94b16c121f377def13ba0ca497794c9387cee02028c9cd80bf130cc3e8f81312.jpg", + "table_caption": [ + "Box-free Instance Segmentation" + ], + "table_footnote": [], + "table_body": "
K-Net [53], supervised8.03±0.2516.33±0.317.00±0.2517.4±0.2230.08±0.2816.83±0.2121.63±0.2137.43±0.3821.8±0.20
K-Net†[53], supervised11.63±0.0522.30±0.0810.95±0.1022.28±0.0538.54±0.0922.7±0.0726.53±0.1244.87±0.1527.20±0.17
K-Net, PAIS w/o DALoss17.77±0.0632.17±0.1517.53±0.1225.40±0.0843.12±0.0526.05±0.1329.30±0.0748.64±0.0530.53±0.13
K-Net, PAIS19.78±0.1035.48±0.1519.65±0.0627.53±0.0645.63±0.0628.70±0.1031.04±0.0650.50±0.0732.34±0.05
", + "bbox": [ + 76, + 131, + 888, + 188 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7456750a5a2bae2ff606f421ac0d56b3d549f20405cb6f3e991160eea665bc80.jpg", + "table_caption": [ + "Box-dependent Instance Segmentation" + ], + "table_footnote": [], + "table_body": "
Mask-RCNN [13], supervised*3.5--17.3--22.0--
Mask-RCNN† [13], supervised11.54±0.0919.86±0.1111.64±0.0922.35±0.0637.98±0.1023.14±0.1127.07±0.0645.10±0.1028.67±0.06
Mask-RCNN, PAIS w/o DALoss20.13±0.0633.23±0.1521.27±0.0627.36±0.0644.10±0.1029.27±0.0629.77±0.0647.70±0.1031.97±0.06
Mask-RCNN, PAIS21.12±0.0536.03±0.0522.75±0.1029.28±0.1347.25±0.1331.20±0.2231.03±0.0649.83±0.1233.23±0.06
", + "bbox": [ + 76, + 200, + 888, + 258 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a98bb783c51b6e1cc6a3b23a0c917a5c221ebef35735633ba98c600aa8aa21fb.jpg", + "table_caption": [ + "Table 3. Results of PAIS with extremely limited number of labeled images. We randomly sampled $1\\%$ , $5\\%$ , and $10\\%$ of the labeled images from the COCO train2017 dataset, and repeated each experiment three times. The average values with standard deviation are reported. $\\dagger$ denotes using the same data augmentation as semi-supervised training. * denotes data from NoisyBoundary [47]. We can see that PAIS achieves good performance on both box-free and box-independent instance segmentation frameworks." + ], + "table_footnote": [], + "table_body": "
MethodAPAP0.5AP0.75APSAPMAPL
Box-free Instance Segmentation
K-Net [53], supervised37.860.339.916.941.257.5
K-Net†[53], supervised38.461.440.317.641.858.0
K-Net, PAIS w/o DALoss39.462.241.618.542.859.2
K-Net, PAIS40.863.543.319.244.461.4
Box-dependent Instance Segmentation
Mask-RCNN [13], supervised37.158.539.718.739.653.9
Mask-RCNN†[13], supervised37.558.940.418.640.253.8
Mask-RCNN, PAIS w/o DALoss38.459.741.519.441.155.0
Mask-RCNN, PAIS39.560.643.019.942.456.6
", + "bbox": [ + 78, + 339, + 467, + 498 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 4. Results of PAIS with abundant labeled images. We utilize all the labeled images in the COCO train2017 dataset, and supplement them with the unlabeled images in the COCO unlabel2017 dataset for semi-supervised training. $\\dagger$ denotes using the same data augmentation as semi-supervised training.", + "bbox": [ + 75, + 500, + 468, + 570 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "performs PAIS with Mask-RCNN. In Tab. 2, we compare PAIS with state-of-the-art methods on the Cityscape dataset, in which PAIS also achieves better performance than the predominant models. Specifically, we report NoisyBoundaries [47] w/o FocalLoss in Tab. 2, as we do not apply FocalLoss in PAIS. This ensures a fair and consistent comparison. Furthermore, we also add FocalLoss to PAIS on $10\\%$ Cityscapes, which achieves $25.1\\%$ , surpassing $23.7\\%$ of NoisyBoundaries w/ FocalLoss.", + "bbox": [ + 75, + 595, + 468, + 731 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The more significant performance improvement on the COCO dataset validates the effectiveness of our method for solving the noisy pseudo-label problem. The COCO dataset has 80 instance categories, while the Cityspaces dataset only has 8 instance categories. This implies that the COCO dataset can provide more diverse and informative pseudo-labels, which matches our goal to utilize noisy pseudo-labels for semi-supervised learning.", + "bbox": [ + 75, + 733, + 468, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results with an extremely limited number of labeled images. To demonstrate the effectiveness of PAIS, we conduct experiments with extremely limited numbers of labeled", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "images, as shown in Table 3. Specifically, we compare the performance of various models trained with randomly sampled $1\\%$ , $5\\%$ , and $10\\%$ labeled images. First, we train supervised models, K-Net (supervised) and Mask-RCNN (supervised), with the limited labeled images. Second, we train the same supervised models with the same data augmentation used in the semi-supervised setting, denoted as $\\mathrm{K - }$ $\\mathrm{Net}^{\\dagger}$ (supervised) and $\\mathrm{Mask - RCNN}^{\\dagger}$ (supervised). Third, we train PAIS models without DALoss, denoted as PAIS w/o DALoss on K-Net and Mask-RCNN. Lastly, we train the PAIS models with DALoss, denoted as PAIS on K-Net and Mask-RCNN. All models are trained three times, and the reported results are averaged.", + "bbox": [ + 496, + 342, + 890, + 539 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Based on the results of K-Net (supervised) and Mask-RCNN (supervised), it can be observed that fully-supervised models perform poorly when the number of labeled images is limited. The results of $\\mathrm{K - Net}^{\\dagger}$ (supervised) and $\\mathrm{Mask - RCNN}^{\\dagger}$ (supervised) show slight improvement with weak data augmentation from the semi-supervised setting. Interestingly, while K-Net outperforms Mask-RCNN in the fully-supervised setting, their performance is similar when the number of labeled images is limited, as indicated in the table. Comparing the performance of K-Net (PAIS w/o DALoss) and Mask-RCNN (PAIS w/o DALoss) with that of the supervised setting reveals significant improvement. By introducing the dynamically re-weighting process via DALoss, the performance is further improved. For instance, with only $1\\%$ labeled images, the mAP of K-Net and Mask-RCNN improved from 11.63 and 11.54 to 19.78 and 21.12, respectively, resulting in approximately +8.15 and +9.58 points improvement to the performance. Additionally, the improvement over $\\mathrm{AP}_{0.5}$ and $\\mathrm{AP}_{0.75}$ suggests that DALoss considers masks with moderate quality during training, which further benefits semi-supervised learning.", + "bbox": [ + 496, + 546, + 892, + 864 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results with abundant labeled images. In Tab. 4, we investigate the performance of semi-supervised learning", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16342", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4379d2ef93e27ef69870e7a18fe09a438e7280bb5614092b785d5e0556f24928.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Cls.IoU.Mask.APAP0.5AP0.75APSAPMAPL
29.348.730.511.331.445.5
✓29.749.031.011.431.846.3
✓29.448.930.611.731.546.0
✓✓30.450.131.911.932.847.6
✓✓✓31.150.632.412.333.348.3
", + "bbox": [ + 78, + 88, + 467, + 175 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b29780b7d98d290c892845a6db03ea6a1ccfa910a3dfbecbb8cf012405a78dc7.jpg", + "table_caption": [ + "Table 5. Effectiveness of different loss terms in DALoss. Cls. denotes the terms of dynamic aligned classification scores. IoU. denotes adding the mask IoU branch to the model. Mask. denotes using the terms of dynamic aligned mask scores." + ], + "table_footnote": [], + "table_body": "
α,βAPAP0.5AP0.75APSAPMAPL
129.949.131.010.932.147.0
230.249.531.111.132.247.1
330.550.131.711.632.947.6
431.150.632.412.333.348.3
", + "bbox": [ + 78, + 248, + 465, + 321 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "when abundant labeled data is available. Specifically, we use the entire COCO train2017 dataset as labeled data and COCO unlabeled2017 dataset as unlabeled data to train the models. The results show that the semi-supervised learning approach also leads to a performance gain. For instance, K-Net (PAIS) achieves a performance gain of approximately 1.0 point on mAP from semi-supervised learning. Additionally, the proposed DALoss consistently improves the performance of both box-dependent and box-free instance segmentation frameworks.", + "bbox": [ + 75, + 393, + 470, + 546 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 558, + 230, + 574 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In our ablation study, we investigate several aspects that can impact the performance of PAIS, including the utilization of various loss terms, the setting of hyper-parameters, the threshold values, the varying ratios of labeled and unlabeled images, and the convergence times. We perform the ablation studies on the COCO dataset using K-Net and Mask-RCNN, which are trained via PAIS under the setting of $10\\%$ labeled images.", + "bbox": [ + 75, + 582, + 468, + 703 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of different terms in DALoss. Tab. 5 shows the efficacy of the different components in DALoss, which suggests that: (1) DALoss yields an improvement of 1.8 points to the model. Specifically, the mAP increases from 45.5 to 48.3 on $\\mathrm{AP}_L$ , indicating a significant improvement for large objects. (2) The aligning weights for classification loss alone can also provide a marginal performance gain for the model. (3) Simply adding a mask IoU branch to the model does not enhance the overall performance. However, when incorporating the aligning weights for the segmentation loss, the mAP is increased. (4) Interestingly, the mask IoU branch can help improve the AP for objects of different scales. This is due to the mask IoU branch helping", + "bbox": [ + 75, + 704, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/536dd521bdf18cc3ec4e0ba2c793d977b5824f8ae0827ba9cef0168552e3e0d4.jpg", + "image_caption": [ + "Figure 3. Visualization of the loss alignment with different hyper-parameters. When changing the hyper-parameter from 1 to 5, the input classification score or mask IoU will be more properly adjusted by their quality, i.e., the difference between high- & low-quality mask or class will be enlarged." + ], + "image_footnote": [], + "bbox": [ + 516, + 90, + 740, + 218 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/daaba6a64b2f15c352a7132e07eb7fb2a9665d5218d6d9e35b66b6238365900f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 741, + 89, + 877, + 215 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/55574d924ee90354fc41484b9b5f3d504a458ce3c6a6309cee67e288a79c0f65.jpg", + "image_caption": [ + "Figure 4. Model convergence speed. DALoss leads to faster model convergence for training." + ], + "image_footnote": [], + "bbox": [ + 501, + 305, + 700, + 416 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b6e3d7e98296784ddf2f59c71b048d2f023689de8a054893b103da0664c26c01.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 306, + 888, + 416 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ad67513be520d1ef6c10ab5575d530c7ddb0781cadf20eb8f615a14e513a2736.jpg", + "table_caption": [ + "Table 6. Hyper-parameters in DALoss. Considering that the classification and segmentation are both important, we simply set $\\alpha = \\beta$ to investigate the influence of hyper-parameters." + ], + "table_footnote": [], + "table_body": "
τclsAPAP0.5AP0.75APSAPMAPL
0.3531.150.632.412.333.348.3
0.5030.650.031.911.232.647.8
0.6529.949.131.310.132.147.4
", + "bbox": [ + 503, + 459, + 885, + 518 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/01509da6c6e7caa8b92d191ae76a0f7b433befe16de8e24df2d27c060c5d7222.jpg", + "table_caption": [ + "Table 7. Results of different classification score threshold $\\tau_{cls}$ . The mask IoU threshold $\\tau_{iou}$ is set to 0.3." + ], + "table_footnote": [], + "table_body": "
τiouAPAP0.5AP0.75APSAPMAPL
0.331.150.632.412.333.348.3
0.530.850.331.912.032.947.9
0.730.650.031.211.632.347.1
", + "bbox": [ + 501, + 561, + 887, + 621 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/864e80fa58c4ca5fcbcb2d8bf86a76301e0e07609fded1231033779650fcb135.jpg", + "table_caption": [ + "Table 8. Results of different mask IoU threshold ${\\tau }_{iou}$ . The classification score threshold ${\\tau }_{cls}$ is set to 0.35 ." + ], + "table_footnote": [], + "table_body": "
RatioAPAP0.5AP0.75APSAPMAPL
1:129.047.731.011.031.645.5
1:230.148.832.211.532.447.1
1:331.150.632.412.333.348.3
1:431.350.932.612.433.548.7
", + "bbox": [ + 501, + 664, + 885, + 737 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 9. Different ratio of labeled images and unlabeled images in a batch. The performance saturates when the ratio of labeled and unlabeled images is set to 1:4.", + "bbox": [ + 498, + 739, + 890, + 782 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "to select good pseudo-labels for training.", + "bbox": [ + 500, + 810, + 769, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Hyper-parameters in DALoss. We investigated the effect of hyper-parameters, $\\alpha$ and $\\beta$ , used in DALoss. To give equal weight to both classification and segmentation, we set $\\alpha = \\beta$ . The results are shown in Tab. 6, indicating that larger values of $\\alpha$ and $\\beta$ lead to better performance. We", + "bbox": [ + 498, + 825, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16343", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a53b4672b3db38fa7af71eb47f2d0910516b31d42a65a4b52663254fc18d29ce.jpg", + "image_caption": [ + "Figure 5. Visualization of the predictions from different models. From the examples, we can clearly show the benefits introduced by pixel-level information from PAIS and DALoss." + ], + "image_footnote": [], + "bbox": [ + 84, + 88, + 480, + 422 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b2190e881133f61f417536d01e78914f9ceb9369d54711811a17bd6806c86150.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 88, + 883, + 422 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/93b24cc5c1a7dc367c7d27575b6afbb70f17639f86ba82cf023260cb9319327e.jpg", + "image_caption": [ + "Figure 6. Influence of imbalanced classes to semi-supervised training. The models are trained under $10\\%$ labeled images for the results. We randomly sampled 10k images from the rest of COCO train2017 to draw these figures. As the training progresses, the predictions from the teacher model are gradually fitted to the distribution of the number of labels." + ], + "image_footnote": [], + "bbox": [ + 78, + 465, + 282, + 579 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/80aa0ab8bd1a0a31e69976c013d9d9a1c2a9a9a0d90e1b25124ced40d262d486.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 467, + 483, + 579 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dc028c8877d4d5bb16d95071f9737cf56410e50a00acdf1b70f60c25c6222aec.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 467, + 686, + 579 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4eca97750f8f0fec46d87206b6eb23ecb923304a2fbbadcdd5a92b7d22ea8d0e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 467, + 888, + 579 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "also analyzed the functions of different hyper-parameters used to adjust the input score, as shown in Fig. 3. The figures illustrate that increasing the hyper-parameter enlarges the difference between high- and low-quality masks or classes, adjusting the input score more appropriately based on their quality. However, when the hyper-parameter is set too large, the low-quality masks or classes are significantly constrained, potentially affecting the generalization of the model as noise is removed entirely during training.", + "bbox": [ + 75, + 648, + 468, + 785 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Model convergence speed. In Fig. 4, we analyze the convergence speed of the models. The results demonstrate that DALoss can expedite the model training in terms of convergence rate. For instance, Mask-RCNN (PAIS) achieves a convergence speed that is approximately 2 times faster than that of Mask-RCNN (PAIS w/o DALoss). Moreover, by comparing the results between Mask-RCNN", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(PAIS) and K-Net (PAIS), we observe that DALoss may be particularly effective for box-dependent instance segmentation frameworks, which facilitates rapid convergence.", + "bbox": [ + 496, + 648, + 890, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Different thresholds for classification scores and mask IoUs. We observed from Tab. 7 and Tab. 8 that increasing the thresholds for classification score and mask IoU leads to a decrease in performance. This suggests that DALoss is able to make use of misaligned pseudo-labels instead of simply filtering them out. By allowing the model to learn from these potentially noisy labels, it is able to better handle situations where the alignment between labeled and unlabeled data is not perfect. This may result in improved generalization to new, unseen data, as the model has learned to adapt to the presence of noisy labels.", + "bbox": [ + 496, + 699, + 892, + 864 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Different ratios of labeled and unlabeled images per batch. Tab. 9 shows that increasing the ratio of unlabeled", + "bbox": [ + 498, + 869, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16344", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/fa5629d1e4a53e5e28593b293a09bc98c1d125df8882ac1dbc5eab47b7244129.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
τcls, τiou0.35, 0.30.50, 0.30.65, 0.30.35, 0.50.35, 0.7
w/o DALoss29.329.025.329.329.0
w/ DALoss31.130.629.930.830.6
", + "bbox": [ + 78, + 89, + 468, + 133 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/73356a67d82ac414342d23f8b84c5dbd95b44adac9404cbe9d8c29bb36a2802f.jpg", + "table_caption": [ + "Table 10. DALoss w.r.t. thresholds tuning. DALoss consistently outperforms threshold tuning in all settings." + ], + "table_footnote": [], + "table_body": "
Method1%5%10%100%
K-Net, supervise11.622.326.538.4
EMA w/o DALoss17.8(+6.2)25.4(+3.1)29.3(+2.8)39.4(+1.0)
EMA w/ DALoss19.8(+8.2)27.5(+5.2)31.0(+4.5)40.8(+2.4)
Performance gain+2.0+2.1+1.7+1.4
M-RCNN, supervise11.522.427.137.5
EMA w/o DALoss20.1(+8.6)27.4(+5.0)29.8(+2.7)38.4(+0.9)
EMA w/ DALoss21.1(+9.6)29.3(+6.9)31.0(+3.9)39.5(+2.0)
Performance gain+1.0+1.9+1.2+1.1
", + "bbox": [ + 78, + 178, + 467, + 304 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 11. Comparison of EMA with DALoss. The performance improvements are not mainly attributed to EMA.", + "bbox": [ + 76, + 308, + 467, + 335 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "images in a batch can improve the model's performance. The results indicate that performance saturates when the ratio is set to 1:4, suggesting that adding too many unlabeled images may lead to diminishing returns.", + "bbox": [ + 75, + 362, + 467, + 421 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Visualizations. We visualize the outputs of different models, including K-Net (supervised), K-Net (PAIS w/o DALoss), K-Net (PAIS), Mask-RCNN (supervised), Mask-RCNN (PAIS w/o DALoss), and Mask-RCNN (PAIS), in Fig. 5. The results show that: (1) PAIS can improve the recall for most instances in the supervised model, but the quality of the predictions is not guaranteed. (2) The use of DALoss in PAIS helps to improve the quality of predictions in terms of mask and classification.", + "bbox": [ + 75, + 422, + 467, + 556 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Influence of imbalanced classes. In Fig. 6, we investigate the effect of imbalanced classes on PAIS. We plot the number of labels obtained from the ground truth and the teacher models for Mask-RCNN and K-Net with PAIS at different iterations, namely $32\\mathrm{k}$ , $64\\mathrm{k}$ , $120\\mathrm{k}$ , and $180\\mathrm{k}$ . The results indicate that the predicted pseudo-labels gradually conform to the distribution of the imbalanced labels.", + "bbox": [ + 75, + 559, + 467, + 662 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Discussion", + "text_level": 1, + "bbox": [ + 76, + 678, + 191, + 694 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "DALoss w.r.t. Thresholds Tuning. As shown in Tab. 10, we conduct an ablation study by removing DALoss from our method in Tabs. 7 and 8. The results show that DALoss consistently outperforms threshold tuning in all settings, which validates that DALoss is indeed more effective than tuning the thresholds.", + "bbox": [ + 75, + 703, + 467, + 792 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Comparison of EMA with DALoss. We show that the performance improvements are not mainly attributed to EMA. First, we summarize the results of Tabs. 3 and 4 in Tab. 11. We can find that DALoss achieves a larger performance gain than EMA in $100\\%$ COCO $(+1.4, +1.1$ vs. $+1.0, +0.9)$ . Second, EMA alone cannot selectively utilize noisy pseudo-labels for better learning. DALoss solves this", + "bbox": [ + 75, + 795, + 467, + 900 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "problem and leads to further improvement over EMA.", + "bbox": [ + 498, + 90, + 854, + 104 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Discussion on Score Filtering. We have carefully chosen the values of $\\tau_{cls},\\tau_{iou}$ , based on Fig. 1(c)(d), which illustrates that decreasing the thresholds will generate more noisy but informative pseudo-labels. Therefore, we use low thresholds to obtain such pseudo-labels, which is different from previous methods that need to adjust thresholds to filter them out. This simplifies the tuning of the thresholds. We believe that the experiments in Tabs. 7, 8, and 10 are sufficient to show that lower thresholds are suitable for DALoss.", + "bbox": [ + 496, + 106, + 890, + 255 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Generality to Other Segmentation Tasks. DALoss can be applied to other semi-supervised segmentation tasks, as the noisy pseudo-labels are common in semi-supervised setting. To show the generality, we apply DALoss to panoptic segmentation, which is a more challenging task that requires both instance and semantic segmentation. We report a preliminary result under $10\\%$ COCO. The initial result shows that DALoss can improve the PQ performance from $36.8\\%$ PAIS w/o DALoss to $37.3\\%$ PAIS w/ DALoss. We remain more experiments in our future work.", + "bbox": [ + 496, + 257, + 890, + 407 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Discussion on Large Segment Everything Models. We envision that the future of image segmentation will not only aim to segment everything, but also to provide fine-grained text descriptions for the segmented regions. However, the recently proposed models such as SAM [19] and SEEM [55] either lack labeled semantic information or demand large amounts of labeled semantic data for training. Therefore, we believe that semi-supervised learning will be a crucial solution to leverage abundant unlabeled data and reduce the labeling burden.", + "bbox": [ + 496, + 409, + 890, + 559 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 574, + 617, + 589 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we presented a novel PAIS framework for semi-supervised instance segmentation. To address the misalignment between classification score and mask quality, we introduced a dynamic aligning loss (DALoss), which aligns the classification loss term and the segmentation loss term based on the quality of different pseudo-labels. Our experimental results demonstrate the effectiveness of the proposed PAIS framework. Specifically, when the amount of labeled data is extremely limited, our pipeline equipped with PAIS and DALoss achieves superior performance for instance segmentation. We believe that PAIS can serve as a strong baseline for future research on semi-supervised instance segmentation. We hope our work can inspire further exploration in this exciting research direction.", + "bbox": [ + 496, + 599, + 890, + 811 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported by National Key R&D Program of China (2022ZD0118202), National Science Fund for Distinguished Young Scholars (No.62025603), National Natural Science Foundation of China (No.U21B2037, No.U22B2051, No.62176222, No.62176223, No.62176226, No.62072386, No.62072387, No.62072389, No.62002305 and No.62272401), and Natural Science Foundation of Fujian Province of China (No.2021J01002, No.2022J06001).", + "bbox": [ + 496, + 814, + 890, + 898 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "16345", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Philip Bachman, Ouais Alsharif, and Doina Precup. Learning with pseudo-ensembles. 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Segment everything everywhere all at once. 9" + ], + "bbox": [ + 501, + 92, + 890, + 893 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "16347", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Pseudo-label Alignment for Semi-supervised Instance Segmentation/42aab451-44d8-431c-bd3b-859749553f79_model.json b/2023/Pseudo-label Alignment for Semi-supervised Instance Segmentation/42aab451-44d8-431c-bd3b-859749553f79_model.json new file mode 100644 index 0000000000000000000000000000000000000000..aa1b6f501ee87d9724f8db6fd0658ba0bff5daf6 --- /dev/null +++ b/2023/Pseudo-label Alignment for Semi-supervised Instance Segmentation/42aab451-44d8-431c-bd3b-859749553f79_model.json @@ -0,0 +1,2532 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.807, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.145, + 0.131, + 0.828, + 0.154 + ], + "angle": 0, + "content": "Pseudo-label Alignment for Semi-supervised Instance Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.197, + 0.18, + 0.771, + 0.217 + ], + "angle": 0, + "content": "Jie Hu\\(^{1\\dagger}\\), Chen Chen\\(^{1\\dagger}\\), Liujuan Cao\\(^{1*}\\), Shengchuan Zhang\\(^{1}\\), Annan Shu\\(^{2}\\), Guannan Jiang\\(^{2}\\), and Rongrong Ji\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.182, + 0.217, + 0.788, + 0.27 + ], + "angle": 0, + "content": "1Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University 2Contemporary Amperex Technology Co. Limited" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.314, + 0.321 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.474, + 0.655 + ], + "angle": 0, + "content": "Pseudo-labeling is significant for semi-supervised instance segmentation, which generates instance masks and classes from unannotated images for subsequent training. However, in existing pipelines, pseudo-labels that contain valuable information may be directly filtered out due to mismatches in class and mask quality. To address this issue, we propose a novel framework, called pseudo-label aligning instance segmentation (PAIS), in this paper. In PAIS, we devise a dynamic aligning loss (DALoss) that adjusts the weights of semi-supervised loss terms with varying class and mask score pairs. Through extensive experiments conducted on the COCO and Cityscapes datasets, we demonstrate that PAIS is a promising framework for semi-supervised instance segmentation, particularly in cases where labeled data is severely limited. Notably, with just \\(1\\%\\) labeled data, PAIS achieves 21.2 mAP (based on Mask-RCNN) and 19.9 mAP (based on K-Net) on the COCO dataset, outperforming the current state-of-the-art model, i.e., NoisyBoundary with 7.7 mAP, by a margin of over 12 points. Code is available at: https://github.com/hujiecpp/PAIS." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.684, + 0.21, + 0.699 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.71, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Semi-supervised instance segmentation aims to alleviate the significant burden of human labeling by utilizing a small amount of labeled data in conjunction with abundant unlabeled data [35, 47, 50]. Existing semi-supervised instance segmentation pipelines typically generate pseudolabels from unlabeled images, which are then used to train the models together with labeled images. Therefore, pseudo-labels play a crucial role in semi-supervised instance segmentation. The generation of pseudo-masks, pseudo-classes, and pseudo-boxes from unlabeled images improves the model training. However, current semi" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.306, + 0.892, + 0.427 + ], + "angle": 0, + "content": "supervised instance segmentation frameworks do not fully leverage the potential of such pseudo-labels. Specifically, pseudo-labels with mismatched class and mask scores are often filtered out by fixed thresholds, leading to the exclusion of valuable information that could aid the model training. For instance, pseudo-labels with high-quality masks but low class scores would be filtered out by a class threshold, resulting in the loss of the pixel-level information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.893, + 0.805 + ], + "angle": 0, + "content": "In this paper, we present a new semi-supervised framework, termed pseudo-label aligning for instance segmentation (PAIS), aiming to improve the utilization of filtered pseudo-labels. As illustrated in Fig. 1, the main challenge of PAIS lies in the mismatched scores between pseudoclasses and pseudo-masks. The classification score and mask intersection over union (IoU) are misaligned in assessing the quality of pseudo-labels. As a result, masks with high IoUs would be filtered out due to low classification scores, and vice versa. In the mean time, lowering the threshold of both scores introduces incorrect classes or low-quality masks into the semi-supervised training. To overcome this dilemma, we propose a dynamic aligning loss (DALoss) that softly re-weights the classification and the segmentation losses based on the quality of different pseudo-labels. Specifically, DALoss penalizes low-score pseudo-labels rather than filtering them and promotes high-score ones, to adjust their contribution to the final loss function. Our experiments on the COCO and Cityscape datasets demonstrate the effectiveness of the proposed PAIS framework. Specifically, with only \\(1\\%\\) labeled data, PAIS achieves \\(21.2\\mathrm{mAP}\\) and \\(19.9\\mathrm{mAP}\\) on the COCO dataset using Mask-RCNN [13] and K-Net [53], respectively. This outperforms the current state-of-the-art model, NoisyBoundary [47], by more than 12 points." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.806, + 0.845, + 0.82 + ], + "angle": 0, + "content": "Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.826, + 0.894, + 0.901 + ], + "angle": 0, + "content": "- We propose a novel pseudo-label aligning framework for semi-supervised instance segmentation, called PAIS, which unleashes the potential of utilizing pixel-level pseudo-labels in semi-supervised instance segmentation. Furthermore, to the best of our knowledge," + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.333, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author. † Equal contribution." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16337" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.287, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.089, + 0.489, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.089, + 0.687, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.688, + 0.09, + 0.887, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.213, + 0.894, + 0.337 + ], + "angle": 0, + "content": "Figure 1. Pseudo-label wasting in semi-supervised instance segmentation. To illustrate this issue, we employed the K-Net model [53] trained on \\(10\\%\\) labeled images and randomly sampled 5k unlabeled images, from the COCO train2017 dataset, to plot the figures. In (a), we present the predicted classification score w.r.t. the ground truth mask intersection over union (IoU), revealing that the predicted classification score is inadequate in evaluating mask quality. In (b), we added a mask IoU prediction branch to the model and plotted the predicted mask IoU w.r.t. the ground truth mask IoU, demonstrating that the predicted mask IoU can represent the mask quality. However, as shown in (c), a significant number of pseudo-labels with high-quality masks, i.e., mask IoU \\(>0.7\\), will be filtered out with high classification thresholds. Additionally, (d) shows that pseudo-labels with high-quality masks can also have correspondingly low classification scores. Therefore, the misalignment between the mask and class scores leads to a significant number of valuable pseudolabels being excluded during semi-supervised training." + }, + { + "type": "text", + "bbox": [ + 0.109, + 0.363, + 0.468, + 0.392 + ], + "angle": 0, + "content": "PAIS is the first framework that can be adapted to box-free instance segmentation models." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.4, + 0.468, + 0.49 + ], + "angle": 0, + "content": "- We introduce a new loss function, named dynamic aligning loss (DALoss), which incorporates pseudolabels with diverse class and mask qualities into the semi-supervised training process. DALoss consistently enhances the performance of box-free and box-dependent instance segmentation frameworks." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.498, + 0.468, + 0.604 + ], + "angle": 0, + "content": "- We conduct comprehensive experiments on the COCO and Cityscapes datasets to evaluate PAIS. In particular, PAIS achieves state-of-the-art results on the COCO dataset, i.e., 19.9, 27.6, and \\(31.1\\mathrm{mAP}\\) for the box-free pipeline K-Net [53], and 21.2, 29.3, and \\(31.1\\mathrm{mAP}\\) for the box-dependent pipeline Mask-RCNN [13], with \\(1\\%\\), \\(5\\%\\), and \\(10\\%\\) labeled data, respectively." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.4, + 0.468, + 0.604 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.633, + 0.219, + 0.648 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Semi-supervised Image Classification. In image classification, semi-supervised learning has been extensively explored, and the methods can be classified into two categories: pseudo-label-based and consistency-regularization-based methods. Specifically, pseudo-label-based methods [40, 21] leverage pre-trained models to generate annotations for the unlabeled images to train the model. In contrast, consistency-regularization-based methods [1, 36, 20, 39, 48, 2, 7, 32, 31, 23] incorporate various data augmentation techniques such as random regularization [10] and adversarial perturbation [33] to generate different inputs for one image and enforce consistency between these inputs during training. FixMatch [41] combines the consistency-regularization-based techniques with a pseudo-label-based framework by applying a strong-weak data augmentation pipeline to input images and enforcing consistency between" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.363, + 0.892, + 0.408 + ], + "angle": 0, + "content": "the augmented images. In this work, we follow the pseudolabel-based methods and also use strong-weak data augmentation during training in PAIS." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.412, + 0.893, + 0.685 + ], + "angle": 0, + "content": "Semi-supervised Object Detection. From the very beginning, STAC [42] proposed the use of pseudo-labels and consistency training for semi-supervised object detection. However, the effectiveness of the method was limited by the two-stage training pipeline similar to that of Noisy Student [49], where the pseudo-labels were generated from pre-trained models and were not updated along with the model training. After STAC, several studies [50, 54, 43, 51, 28] incorporated the idea of exponential moving average (EMA) from MeanTeacher [44]. The teacher model and pseudo-labels are updated after each training iteration to generate instant pseudo-labels, making the entire pipeline end-to-end trainable. Additionally, Unbiased Teacher [28] utilized Focal loss [24] instead of traditional cross-entropy loss to alleviate the problem of unbalanced pseudo-labels. In this paper, we also follow the idea of incorporating EMA into the proposed PAIS framework, with a focus on integrating pixel-level annotations into the training process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Fully-supervised Instance Segmentation. Instance segmentation aims to provide pixel-level predictions for each object instance in an image. Existing methods can be classified into three categories: top-down (or box-dependent) methods, bottom-up methods, and direct segmentation (or box-free) methods. Top-down methods [15, 27, 38, 37, 29] such as Mask R-CNN [13], YOLACT [3], and CenterMask [22] generate bounding boxes first and then segment the objects within the boxes. Bottom-up methods [52, 8, 26, 11, 16], regard instance segmentation as a label-then-cluster problem, which classify each pixel first and then group the pixels into an arbitrary number of object instances. Direct segmentation or box-free methods such as SOLO [45, 46], K-Net [53], MaskFormer [5, 4] and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16338" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.638, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.658, + 0.091, + 0.765, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.665, + 0.175, + 0.758, + 0.189 + ], + "angle": 0, + "content": "(a) Score↓, IoU↑" + }, + { + "type": "image", + "bbox": [ + 0.66, + 0.19, + 0.764, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.667, + 0.272, + 0.756, + 0.284 + ], + "angle": 0, + "content": "(c) Score-, IoU-" + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.092, + 0.882, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.781, + 0.176, + 0.874, + 0.19 + ], + "angle": 0, + "content": "(b) Score↑, IoU↓" + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.192, + 0.882, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.781, + 0.272, + 0.874, + 0.285 + ], + "angle": 0, + "content": "(d) Score↑, IoU↑" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.295, + 0.892, + 0.392 + ], + "angle": 0, + "content": "Figure 2. Framework of pseudo-label aligning for semi-supervised instance segmentation (PAIS). The focus of PAIS is to explore the utility of pixel-level pseudo-labels for instance segmentation. To this end, we propose a novel approach called dynamic aligning loss (DALoss), which enables the incorporation of pseudo-labels with varying quality during training. This is particularly significant when the number of labeled images is limited. With DALoss, a significant number of predictions from the teacher model can be leveraged in the semi-supervised training process, rather than being discarded. Specifically, we consider three types of pseudo-masks with varying quality: (a) pseudo-masks with incorrect classes but high-quality masks, i.e., low classification scores but high mask IoUs; (b) pseudo-masks with accurate classes but low-quality masks, i.e., high classification scores but low mask IoUs; and (c) pseudo-masks with medium qualities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.417, + 0.468, + 0.508 + ], + "angle": 0, + "content": "SOTR [12] deal with instance segmentation without bounding box detection. Any of the aforementioned instance segmentation methods can be implemented into PAIS, and in this work, we present two examples, one from the box-dependent category, Mask R-CNN, and another from the box-free category, K-Net." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.468, + 0.765 + ], + "angle": 0, + "content": "Semi-supervised Instance Segmentation. Semi-supervised instance segmentation is commonly considered to be a sub-task of semi-supervised object detection [50, 28]. Consequently, existing frameworks rely heavily on bounding boxes, in which segmentation performance is strongly dependent on detection performance. Among them, NoisyBoundary [47] was the first to formally propose the semi-supervised instance segmentation task. Recent efforts have been made to construct box-free pipelines for fully-supervised instance segmentation [45, 46, 53, 5]. In this paper, we investigate PAIS in both box-free and box-dependent instance segmentation, revealing the potential of fully utilizing pixel-level annotations. In contrast to the recently-proposed PoliteTeacher [9], which filters out pseudo-labels with low confidence, the proposed PAIS leverages them. It is a novel and effective way of utilizing noisy pseudo-labels for semi-supervised learning." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.778, + 0.168, + 0.793 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.251, + 0.817 + ], + "angle": 0, + "content": "3.1. Task Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.901 + ], + "angle": 0, + "content": "The goal of PAIS is to better leverage unlabeled images with a limited number of pixel-labeled images to boost the performance of semi-supervised instance segmentation. The PAIS framework consists of three key steps: (1) pseudo-label generation, (2) dynamic pseudo" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.417, + 0.892, + 0.644 + ], + "angle": 0, + "content": "label alignment, and (3) end-to-end model training. In the pseudo-label generation step, we introduce a mask scoring branch [17] that predicts mask IoUs as an additional metric along with classification scores to assess the quality of pseudo-labels. In the dynamic aligning step, we re-weight the loss terms based on the quality of different pseudolabels. Finally, the teacher and student models are trained using exponential moving average (EMA) [44]. The overall framework of PAIS is illustrated in Fig. 2, and we introduce the key steps in detail as follows. It is important to note that the PAIS framework can be applied to any box-dependent or box-free framework for enhanced exploitation of pseudo-labels in semi-supervised instance segmentation. We instantiate two examples by Mask-RCNN [13] and K-Net [53] in this paper, but do not restrict to them." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.733, + 0.667 + ], + "angle": 0, + "content": "3.2. Pseudo Label Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.796 + ], + "angle": 0, + "content": "In the pseudo-label generation, we apply weak data augmentation to the unlabeled images and input them into a teacher model. The weak data augmentation includes scaling, horizontal flipping, and other augmentation operations that do not alter the image's content. The teacher model produces a set of pseudo-labels, including masks, boxes, and classification scores for each input image. In box-free pipelines, the box predictions are optional." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As depicted in Fig. 1(a)(c), using the classification score alone is inadequate to measure the quality of predicted masks. To address this, we incorporate a mask scoring branch into the pipeline to predict mask Intersection over Union (IoU) for evaluating mask quality. As shown in Fig. 1(b), the predicted mask IoUs can be used to measure mask quality effectively, which has also been verified" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16339" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.081, + 0.092, + 0.329, + 0.106 + ], + "angle": 0, + "content": "Algorithm 1 Pseudo-label Alignment" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.109, + 0.425, + 0.123 + ], + "angle": 0, + "content": "1: Initialize teacher and student models randomly." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.125, + 0.166, + 0.138 + ], + "angle": 0, + "content": "2:Repeat" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.14, + 0.442, + 0.153 + ], + "angle": 0, + "content": "3: Apply weak augmentation to unlabeled images." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.154, + 0.468, + 0.184 + ], + "angle": 0, + "content": "4: Obtain pseudo-labels \\(\\{\\pmb{m}_i, \\pmb{b}_i, \\pmb{c}_i, s_i | i = 1, \\dots, N\\}\\) from teacher model via thresholds \\(\\tau_{cls}, \\tau_{iou}\\)." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.185, + 0.448, + 0.199 + ], + "angle": 0, + "content": "5: Apply strong augmentation to unlabeled images." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.201, + 0.449, + 0.215 + ], + "angle": 0, + "content": "6: Obtain predictions \\(\\widetilde{m}, b, \\widetilde{c}\\) for unlabeled images." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.216, + 0.425, + 0.23 + ], + "angle": 0, + "content": "7: Calculate \\(\\mathcal{L}_u\\) for unlabeled images by Eq. 5." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.231, + 0.42, + 0.245 + ], + "angle": 0, + "content": "8: Inference labeled images by student model." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.246, + 0.346, + 0.26 + ], + "angle": 0, + "content": "9: Calculate \\(\\mathcal{L}_l\\) for labeled images." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.261, + 0.457, + 0.276 + ], + "angle": 0, + "content": "10: Train student model with the loss \\(\\mathcal{L}_{semi}\\) in Eq. 1." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.277, + 0.347, + 0.29 + ], + "angle": 0, + "content": "11: Update teacher model via EMA." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.291, + 0.282, + 0.306 + ], + "angle": 0, + "content": "12: Until scheduled epochs." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.109, + 0.468, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.34, + 0.47, + 0.475 + ], + "angle": 0, + "content": "in MS-RCNN [17]. After generating pseudo-labels in the previous step, the predictions are filtered using two thresholds: a classification threshold \\(\\tau_{cls}\\) and a mask IoU threshold \\(\\tau_{iou}\\). The resulting set of pseudo-labels includes \\(N\\) elements, each containing a mask \\(m_i \\in \\mathbb{R}^{H \\times W}\\), a bounding box \\(b_i \\in \\mathbb{R}^4\\), a classification score \\(c_i \\in \\mathbb{R}^L\\) (with an additional background category), and a mask IoU score \\(s_i \\in \\mathbb{R}\\). Note that \\(H, W\\) denote the mask resolution, and \\(L\\) is the number of classes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.491, + 0.292, + 0.507 + ], + "angle": 0, + "content": "3.3. Dynamic Aligning Loss" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.516, + 0.469, + 0.697 + ], + "angle": 0, + "content": "Although good pseudo-labels can be obtained by setting high thresholds for classification scores and mask IoUs, a large number of predictions with misaligned mask and classification qualities are discarded (as illustrated in Fig.1(c)(d)). These misaligned predictions can be useful since the amount of labeled data is limited in the semi-supervised setting. Fig.2 shows examples of pseudo-labels that can be included in the training process. If the misaligned pseudo-labels are directly used in semi-supervised learning, the incorrect predictions on classes or masks can introduce significant noise. To reduce the noise, we propose a dynamic aligning loss (DALoss)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.699, + 0.469, + 0.745 + ], + "angle": 0, + "content": "Vanilla Loss for PAIS. In semi-supervised instance segmentation, the loss function can be decomposed into two terms for labeled and unlabeled images, as:" + }, + { + "type": "equation", + "bbox": [ + 0.193, + 0.762, + 0.469, + 0.778 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s e m i}} = \\lambda_ {l} \\mathcal {L} _ {l} + \\lambda_ {u} \\mathcal {L} _ {u}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.901 + ], + "angle": 0, + "content": "where \\(\\lambda_{l}\\) and \\(\\lambda_{u}\\) are the hyper-parameters for balancing the loss terms. The loss for labeled images can be defined using the functions commonly employed in instance segmentation, augmented with an additional binary cross-entropy term for regressing mask IoUs. Given the pseudo-labels from the teacher model and the predictions from the student model, we formulate the loss for unlabeled images as:" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.114, + 0.892, + 0.223 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {u} = \\frac {1}{N _ {p o s}} \\sum_ {i = 1} ^ {N _ {p o s}} \\left(\\lambda_ {b} \\mathcal {L} _ {b} \\left(\\widetilde {\\boldsymbol {b}} _ {\\nu (i)}, \\boldsymbol {b} _ {\\mu (i)}\\right) \\right. \\\\ \\left. + \\lambda_ {c} \\mathcal {L} _ {c} \\left(\\widetilde {\\boldsymbol {c}} _ {\\nu (i)}, \\boldsymbol {c} _ {\\mu (i)} ^ {o}\\right) + \\lambda_ {m} \\mathcal {L} _ {m} \\left(\\widetilde {\\boldsymbol {m}} _ {\\nu (i)}, \\boldsymbol {m} _ {\\mu (i)} ^ {b}\\right)\\right) \\tag {2} \\\\ + \\frac {1}{N _ {n e g}} \\sum_ {i = 1} ^ {N _ {n e g}} \\left(\\lambda_ {c} \\mathcal {L} _ {c} (\\widetilde {\\boldsymbol {c}} _ {i}, \\boldsymbol {c} _ {n e g} ^ {o})\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.23, + 0.892, + 0.43 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_b\\) includes the box IoU loss and the L1 loss, \\(\\mathcal{L}_c\\) denotes the cross-entropy loss, \\(\\mathcal{L}_m\\) is the dice loss. In Eq. 2, \\(\\widetilde{c}_i,\\widetilde{b}_i,\\widetilde{m}_i\\) represent predictions from the student model. The pseudo-scores \\(c_{\\mu (i)}\\) for classification are converted to one-hot vectors \\(c_{\\mu (i)}^o\\) for the category with the highest score. The pseudo-masks \\(m_{\\mu (i)}\\) are activated by sigmoid function and discretized into binary value as \\(m_{\\mu (i)}^{b}\\). The one-hot vector for the background class is denoted by \\(c_{neg}^o\\). The label indexing functions, \\(\\nu (i)\\) and \\(\\mu (i)\\), match predictions with pseudo-labels for training, which are defined in terms of different pseudo-label assigning strategies. In our implementations, the one-to-many assignment defines the label indexing functions \\(\\nu (i) = i\\) and \\(\\mu (i)\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.438, + 0.891, + 0.467 + ], + "angle": 0, + "content": "\\[\n\\mu (i) = \\underset {t \\in [ 1, N ]} {\\arg \\min } \\left(\\mathcal {L} _ {b} \\left(\\widetilde {\\boldsymbol {b}} _ {i}, \\boldsymbol {b} _ {t}\\right)\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.475, + 0.89, + 0.506 + ], + "angle": 0, + "content": "Instead, the one-to-one assignment defines the label indicting functions \\(\\mu (i) = i\\), and finds the optimal \\(\\nu^{*}(\\cdot)\\) via:" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.515, + 0.891, + 0.577 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\nu^ {*} = \\arg \\min _ {\\nu} \\sum_ {i = 1} ^ {t} \\left(\\lambda_ {b} \\mathcal {L} _ {b} \\left(\\widetilde {\\boldsymbol {b}} _ {\\nu (i)}, \\boldsymbol {b} _ {i}\\right) + \\lambda_ {c} \\mathcal {L} _ {c} \\left(\\widetilde {\\boldsymbol {c}} _ {\\nu (i)}, \\boldsymbol {c} _ {i} ^ {o}\\right) \\right. \\tag {4} \\\\ + \\lambda_ {m} \\mathcal {L} _ {m} (\\widetilde {\\boldsymbol {m}} _ {\\nu (i)}, \\boldsymbol {m} _ {i} ^ {b}) - s _ {i}). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.583, + 0.89, + 0.613 + ], + "angle": 0, + "content": "Note that the loss terms for regressing boxes are optional in box-free instance segmentation frameworks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.719 + ], + "angle": 0, + "content": "Dynamic Aligning Loss for PAIS. To optimize the model using pixel-level pseudo-labels, we propose to replace Eq. 2 with DALoss. Since the teacher model provides ideal metrics for measuring the quality of classification scores and mask IoUs, we propose to adjust the weight of loss terms based on the quality of the pseudo-labels. This is achieved by using the following equation:" + }, + { + "type": "equation", + "bbox": [ + 0.511, + 0.728, + 0.891, + 0.859 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {u} ^ {D A} = \\frac {1}{N _ {p o s}} \\sum_ {i = 1} ^ {N _ {p o s}} \\left(\\lambda_ {b} \\mathcal {L} _ {b} (\\widetilde {\\boldsymbol {b}} _ {\\nu (i)}, \\boldsymbol {b} _ {\\mu (i)}) \\right. \\\\ + \\lambda_ {c} \\left(c _ {\\mu (i)} ^ {h}\\right) ^ {\\alpha} \\mathcal {L} _ {c} \\left(\\widetilde {c} _ {\\nu (i)}, c _ {\\mu (i)} ^ {o}\\right) \\tag {5} \\\\ \\left. + \\lambda_ {m} \\left(s _ {\\mu (i)}\\right) ^ {\\beta} \\mathcal {L} _ {m} \\left(\\widetilde {\\boldsymbol {m}} _ {\\nu (i)}, \\boldsymbol {m} _ {\\mu (i)} ^ {b}\\right)\\right) \\\\ + \\frac {1}{N _ {n e g}} \\sum_ {i = 1} ^ {N _ {n e g}} \\left(\\lambda_ {c} \\mathcal {L} _ {c} (\\widetilde {\\boldsymbol {c}} _ {i}, \\boldsymbol {c} _ {n e g} ^ {o})\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.868, + 0.892, + 0.903 + ], + "angle": 0, + "content": "where \\(c_{\\mu(i)}^{h}\\) denotes the highest classification score, and \\(s_{\\mu(i)}\\) denotes the mask IoU from the \\(\\mu(i)\\)-th pseudo-label," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16340" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.09, + 0.464, + 0.175 + ], + "angle": 0, + "content": "
Method1%5%10%100%
Mask-RCNN [13], supervised*3.517.322.034.5
Mask-RCNN† [13], supervised*3.517.421.937.1
DD [35]3.820.424.235.7
Noisy Boundaries [47]7.724.929.238.6
PAIS, on Mask-RCNN, ours21.229.331.139.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.179, + 0.468, + 0.234 + ], + "angle": 0, + "content": "Table 1. Comparison to state-of-the-art semi-supervised instance segmentation methods on the COCO val2017.† denotes using the same data augmentation as semi-supervised training. * denotes data from NoisyBoundary [47]." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.248, + 0.464, + 0.401 + ], + "angle": 0, + "content": "
Method5%10%20%30%
Mask-RCNN [13], supervised*11.816.822.326.3
Mask-RCNN† [13], supervised*11.316.422.626.6
DD [35]13.719.224.627.4
STAC [42]11.918.222.929.0
CSD [18]14.117.924.627.5
CCT [34]15.218.624.726.5
Dual-branch [30]13.918.924.028.9
Ubteacher [28]16.020.027.128.0
Noisy Boundaries [47]17.122.129.032.4
PAIS, on Mask-RCNN, ours18.022.929.232.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.405, + 0.468, + 0.461 + ], + "angle": 0, + "content": "Table 2. Comparison to state-of-the-art semi-supervised instance segmentation methods on the Cityscapes validation set. \\(\\dagger\\) denotes using the same data augmentation as semi-supervised training. \\* denotes data from NoisyBoundary [47]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.487, + 0.468, + 0.577 + ], + "angle": 0, + "content": "\\(\\alpha, \\beta\\) are the hyper-parameters. Specifically, Eq. 5 adjusts the weights for the pseudo-labels conditioned on their qualities, i.e., dynamically dependent on the input images. For instance, for a pseudo-label with a low classification score and high mask IoU, DALoss encourages the segmentation loss while constraining the classification loss." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.588, + 0.33, + 0.604 + ], + "angle": 0, + "content": "3.4. End-to-End Model Training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.611, + 0.468, + 0.716 + ], + "angle": 0, + "content": "Inspired by [44], we employ EMA with the strong-weak data augmentation for PAIS. Specifically, unlabeled images undergo both strong and weak data augmentations and are then fed into the student and teacher models, respectively. The student model is trained to produce consistent results with the pseudo-labels, and the teacher model is updated by EMA. The training pipeline for PAIS is presented in Alg. 1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.747, + 0.208, + 0.763 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.363, + 0.786 + ], + "angle": 0, + "content": "4.1. Datasets and Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.468, + 0.9 + ], + "angle": 0, + "content": "We conducted extensive experiments on the COCO [25] and Cityscapes [6] datasets to study the proposed PAIS. The COCO dataset consists of 118k images with 80-class instance labels, as well as 123k unlabeled images. The Cityscapes dataset contains urban street-view scenes and has 8 instance categories in 2.9k training images and 0.5k validation images. For the COCO dataset, we ran-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.302 + ], + "angle": 0, + "content": "domly sampled \\(1\\%\\), \\(5\\%\\), and \\(10\\%\\) of the images from the train2017 split as labeled data and treated the rest as unlabeled data following common settings. In addition, we also used the full COCO train2017 as labeled data and incorporated the 123k unlabeled data from COCO unlabel2017 to train the PAIS models. For the Cityscapes dataset, we randomly sampled \\(5\\%\\), \\(10\\%\\), \\(20\\%\\), and \\(30\\%\\) of the images from the training set as labeled data and treated the remaining as unlabeled data following the common settings. We evaluated the PAIS models on the validation sets of the COCO and Cityscapes datasets, and reported standard COCO metrics including AP, AP50, AP75 (averaged over IoU thresholds), and \\(\\mathrm{AP}_S\\), \\(\\mathrm{AP}_M\\), \\(\\mathrm{AP}_L\\) (AP for instances of different scales)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.314, + 0.716, + 0.33 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.337, + 0.892, + 0.579 + ], + "angle": 0, + "content": "We provide two examples of implementing PAIS with K-Net [53] and Mask-RCNN [13]. The models are trained using AdamW with a learning rate of 0.0001 for K-Net, and SGD with a learning rate of 0.01 for Mask-RCNN. The hyper-parameters \\(\\lambda_{l}\\) and \\(\\lambda_{u}\\), which balance the loss terms for labeled and unlabeled images, are set to 1.0 and 0.3 for K-Net, and 1.0 and 1.5 for Mask-RCNN. We set the thresholds \\(\\tau_{cls}\\) and \\(\\tau_{iou}\\) experimentally as 0.35 and 0.30, respectively. For bipartite matching loss, we use the same hyperparameters as in [53]. The loss balancing parameters for box, class, and mask are set as \\(\\lambda_{b} = 2.0\\), \\(\\lambda_{c} = 4.0\\), and \\(\\lambda_{m} = 1.0\\) respectively. We train the models on 4 GPUs with 4 images per GPU (1 labeled and 3 unlabeled images) for 220k iterations, unless otherwise specified. The teacher model is updated via EMA with a momentum of 0.999. We use ResNet50 [14] as the backbone for these models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.59, + 0.638, + 0.605 + ], + "angle": 0, + "content": "4.3. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Comparison to state-of-the-art semi-supervised instance segmentation frameworks. In Tab. 1, we compare the performance of models trained with PAIS to the state-of-the-art semi-supervised instance segmentation frameworks on the COCO dataset. The results demonstrate that both K-Net and Mask-RCNN trained with PAIS surpass the previous methods DD [35] and Noisy Boundaries [47] by a large margin, especially when the number of labeled data is very limited (with only \\(1\\%\\) or \\(5\\%\\) labeled images). Specifically, when using \\(1\\%\\) labeled COCO images, PAIS with K-Net achieves 19.9 mask mAP, which is 12.2 points higher than Noisy Boundaries. Interestingly, the proposed PAIS brings about better performance for Mask-RCNN when the percentage of labeled data is \\(1\\%\\) or \\(5\\%\\), even though it originally has a inferior performance in fully-supervised instance segmentation compared to K-Net. To explain, the bounding boxes may provide better optimization for Mask-RCNN models when the labeled data is limited. Finally, when using \\(10\\%\\) and \\(100\\%\\) labeled images, PAIS with K-Net out" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16341" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.089, + 0.891, + 0.12 + ], + "angle": 0, + "content": "
Method1% COCO5% COCO10% COCO
APAP0.5AP0.75APAP0.5AP0.75APAP0.5AP0.75
" + }, + { + "type": "table_caption", + "bbox": [ + 0.399, + 0.12, + 0.568, + 0.132 + ], + "angle": 0, + "content": "Box-free Instance Segmentation" + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.132, + 0.89, + 0.189 + ], + "angle": 0, + "content": "
K-Net [53], supervised8.03±0.2516.33±0.317.00±0.2517.4±0.2230.08±0.2816.83±0.2121.63±0.2137.43±0.3821.8±0.20
K-Net†[53], supervised11.63±0.0522.30±0.0810.95±0.1022.28±0.0538.54±0.0922.7±0.0726.53±0.1244.87±0.1527.20±0.17
K-Net, PAIS w/o DALoss17.77±0.0632.17±0.1517.53±0.1225.40±0.0843.12±0.0526.05±0.1329.30±0.0748.64±0.0530.53±0.13
K-Net, PAIS19.78±0.1035.48±0.1519.65±0.0627.53±0.0645.63±0.0628.70±0.1031.04±0.0650.50±0.0732.34±0.05
" + }, + { + "type": "table_caption", + "bbox": [ + 0.382, + 0.19, + 0.585, + 0.201 + ], + "angle": 0, + "content": "Box-dependent Instance Segmentation" + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.202, + 0.89, + 0.259 + ], + "angle": 0, + "content": "
Mask-RCNN [13], supervised*3.5--17.3--22.0--
Mask-RCNN† [13], supervised11.54±0.0919.86±0.1111.64±0.0922.35±0.0637.98±0.1023.14±0.1127.07±0.0645.10±0.1028.67±0.06
Mask-RCNN, PAIS w/o DALoss20.13±0.0633.23±0.1521.27±0.0627.36±0.0644.10±0.1029.27±0.0629.77±0.0647.70±0.1031.97±0.06
Mask-RCNN, PAIS21.12±0.0536.03±0.0522.75±0.1029.28±0.1347.25±0.1331.20±0.2231.03±0.0649.83±0.1233.23±0.06
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.263, + 0.893, + 0.319 + ], + "angle": 0, + "content": "Table 3. Results of PAIS with extremely limited number of labeled images. We randomly sampled \\(1\\%\\), \\(5\\%\\), and \\(10\\%\\) of the labeled images from the COCO train2017 dataset, and repeated each experiment three times. The average values with standard deviation are reported. \\(\\dagger\\) denotes using the same data augmentation as semi-supervised training. * denotes data from NoisyBoundary [47]. We can see that PAIS achieves good performance on both box-free and box-independent instance segmentation frameworks." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.34, + 0.468, + 0.499 + ], + "angle": 0, + "content": "
MethodAPAP0.5AP0.75APSAPMAPL
Box-free Instance Segmentation
K-Net [53], supervised37.860.339.916.941.257.5
K-Net†[53], supervised38.461.440.317.641.858.0
K-Net, PAIS w/o DALoss39.462.241.618.542.859.2
K-Net, PAIS40.863.543.319.244.461.4
Box-dependent Instance Segmentation
Mask-RCNN [13], supervised37.158.539.718.739.653.9
Mask-RCNN†[13], supervised37.558.940.418.640.253.8
Mask-RCNN, PAIS w/o DALoss38.459.741.519.441.155.0
Mask-RCNN, PAIS39.560.643.019.942.456.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.501, + 0.47, + 0.571 + ], + "angle": 0, + "content": "Table 4. Results of PAIS with abundant labeled images. We utilize all the labeled images in the COCO train2017 dataset, and supplement them with the unlabeled images in the COCO unlabel2017 dataset for semi-supervised training. \\(\\dagger\\) denotes using the same data augmentation as semi-supervised training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.469, + 0.732 + ], + "angle": 0, + "content": "performs PAIS with Mask-RCNN. In Tab. 2, we compare PAIS with state-of-the-art methods on the Cityscape dataset, in which PAIS also achieves better performance than the predominant models. Specifically, we report NoisyBoundaries [47] w/o FocalLoss in Tab. 2, as we do not apply FocalLoss in PAIS. This ensures a fair and consistent comparison. Furthermore, we also add FocalLoss to PAIS on \\(10\\%\\) Cityscapes, which achieves \\(25.1\\%\\), surpassing \\(23.7\\%\\) of NoisyBoundaries w/ FocalLoss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.734, + 0.469, + 0.854 + ], + "angle": 0, + "content": "The more significant performance improvement on the COCO dataset validates the effectiveness of our method for solving the noisy pseudo-label problem. The COCO dataset has 80 instance categories, while the Cityspaces dataset only has 8 instance categories. This implies that the COCO dataset can provide more diverse and informative pseudo-labels, which matches our goal to utilize noisy pseudo-labels for semi-supervised learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Results with an extremely limited number of labeled images. To demonstrate the effectiveness of PAIS, we conduct experiments with extremely limited numbers of labeled" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.343, + 0.892, + 0.54 + ], + "angle": 0, + "content": "images, as shown in Table 3. Specifically, we compare the performance of various models trained with randomly sampled \\(1\\%\\), \\(5\\%\\), and \\(10\\%\\) labeled images. First, we train supervised models, K-Net (supervised) and Mask-RCNN (supervised), with the limited labeled images. Second, we train the same supervised models with the same data augmentation used in the semi-supervised setting, denoted as \\(\\mathrm{K - }\\) \\(\\mathrm{Net}^{\\dagger}\\) (supervised) and \\(\\mathrm{Mask - RCNN}^{\\dagger}\\) (supervised). Third, we train PAIS models without DALoss, denoted as PAIS w/o DALoss on K-Net and Mask-RCNN. Lastly, we train the PAIS models with DALoss, denoted as PAIS on K-Net and Mask-RCNN. All models are trained three times, and the reported results are averaged." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.893, + 0.865 + ], + "angle": 0, + "content": "Based on the results of K-Net (supervised) and Mask-RCNN (supervised), it can be observed that fully-supervised models perform poorly when the number of labeled images is limited. The results of \\(\\mathrm{K - Net}^{\\dagger}\\) (supervised) and \\(\\mathrm{Mask - RCNN}^{\\dagger}\\) (supervised) show slight improvement with weak data augmentation from the semi-supervised setting. Interestingly, while K-Net outperforms Mask-RCNN in the fully-supervised setting, their performance is similar when the number of labeled images is limited, as indicated in the table. Comparing the performance of K-Net (PAIS w/o DALoss) and Mask-RCNN (PAIS w/o DALoss) with that of the supervised setting reveals significant improvement. By introducing the dynamically re-weighting process via DALoss, the performance is further improved. For instance, with only \\(1\\%\\) labeled images, the mAP of K-Net and Mask-RCNN improved from 11.63 and 11.54 to 19.78 and 21.12, respectively, resulting in approximately +8.15 and +9.58 points improvement to the performance. Additionally, the improvement over \\(\\mathrm{AP}_{0.5}\\) and \\(\\mathrm{AP}_{0.75}\\) suggests that DALoss considers masks with moderate quality during training, which further benefits semi-supervised learning." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Results with abundant labeled images. In Tab. 4, we investigate the performance of semi-supervised learning" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16342" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.468, + 0.176 + ], + "angle": 0, + "content": "
Cls.IoU.Mask.APAP0.5AP0.75APSAPMAPL
29.348.730.511.331.445.5
✓29.749.031.011.431.846.3
✓29.448.930.611.731.546.0
✓✓30.450.131.911.932.847.6
✓✓✓31.150.632.412.333.348.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.179, + 0.47, + 0.237 + ], + "angle": 0, + "content": "Table 5. Effectiveness of different loss terms in DALoss. Cls. denotes the terms of dynamic aligned classification scores. IoU. denotes adding the mask IoU branch to the model. Mask. denotes using the terms of dynamic aligned mask scores." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.249, + 0.466, + 0.323 + ], + "angle": 0, + "content": "
α,βAPAP0.5AP0.75APSAPMAPL
129.949.131.010.932.147.0
230.249.531.111.132.247.1
330.550.131.711.632.947.6
431.150.632.412.333.348.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.325, + 0.47, + 0.368 + ], + "angle": 0, + "content": "Table 6. Hyper-parameters in DALoss. Considering that the classification and segmentation are both important, we simply set \\(\\alpha = \\beta\\) to investigate the influence of hyper-parameters." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.471, + 0.547 + ], + "angle": 0, + "content": "when abundant labeled data is available. Specifically, we use the entire COCO train2017 dataset as labeled data and COCO unlabeled2017 dataset as unlabeled data to train the models. The results show that the semi-supervised learning approach also leads to a performance gain. For instance, K-Net (PAIS) achieves a performance gain of approximately 1.0 point on mAP from semi-supervised learning. Additionally, the proposed DALoss consistently improves the performance of both box-dependent and box-free instance segmentation frameworks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.559, + 0.232, + 0.575 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.47, + 0.704 + ], + "angle": 0, + "content": "In our ablation study, we investigate several aspects that can impact the performance of PAIS, including the utilization of various loss terms, the setting of hyper-parameters, the threshold values, the varying ratios of labeled and unlabeled images, and the convergence times. We perform the ablation studies on the COCO dataset using K-Net and Mask-RCNN, which are trained via PAIS under the setting of \\(10\\%\\) labeled images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Effectiveness of different terms in DALoss. Tab. 5 shows the efficacy of the different components in DALoss, which suggests that: (1) DALoss yields an improvement of 1.8 points to the model. Specifically, the mAP increases from 45.5 to 48.3 on \\(\\mathrm{AP}_L\\), indicating a significant improvement for large objects. (2) The aligning weights for classification loss alone can also provide a marginal performance gain for the model. (3) Simply adding a mask IoU branch to the model does not enhance the overall performance. However, when incorporating the aligning weights for the segmentation loss, the mAP is increased. (4) Interestingly, the mask IoU branch can help improve the AP for objects of different scales. This is due to the mask IoU branch helping" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.092, + 0.741, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.743, + 0.09, + 0.878, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.222, + 0.892, + 0.292 + ], + "angle": 0, + "content": "Figure 3. Visualization of the loss alignment with different hyper-parameters. When changing the hyper-parameter from 1 to 5, the input classification score or mask IoU will be more properly adjusted by their quality, i.e., the difference between high- & low-quality mask or class will be enlarged." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.306, + 0.702, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.307, + 0.889, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.419, + 0.892, + 0.448 + ], + "angle": 0, + "content": "Figure 4. Model convergence speed. DALoss leads to faster model convergence for training." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.46, + 0.887, + 0.519 + ], + "angle": 0, + "content": "
τclsAPAP0.5AP0.75APSAPMAPL
0.3531.150.632.412.333.348.3
0.5030.650.031.911.232.647.8
0.6529.949.131.310.132.147.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.523, + 0.892, + 0.551 + ], + "angle": 0, + "content": "Table 7. Results of different classification score threshold \\( \\tau_{cls} \\). The mask IoU threshold \\( \\tau_{iou} \\) is set to 0.3." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.563, + 0.888, + 0.622 + ], + "angle": 0, + "content": "
τiouAPAP0.5AP0.75APSAPMAPL
0.331.150.632.412.333.348.3
0.530.850.331.912.032.947.9
0.730.650.031.211.632.347.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.625, + 0.892, + 0.654 + ], + "angle": 0, + "content": "Table 8. Results of different mask IoU threshold \\( {\\tau }_{iou} \\) . The classification score threshold \\( {\\tau }_{cls} \\) is set to 0.35 ." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.665, + 0.887, + 0.738 + ], + "angle": 0, + "content": "
RatioAPAP0.5AP0.75APSAPMAPL
1:129.047.731.011.031.645.5
1:230.148.832.211.532.447.1
1:331.150.632.412.333.348.3
1:431.350.932.612.433.548.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.741, + 0.892, + 0.784 + ], + "angle": 0, + "content": "Table 9. Different ratio of labeled images and unlabeled images in a batch. The performance saturates when the ratio of labeled and unlabeled images is set to 1:4." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.811, + 0.771, + 0.825 + ], + "angle": 0, + "content": "to select good pseudo-labels for training." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Hyper-parameters in DALoss. We investigated the effect of hyper-parameters, \\(\\alpha\\) and \\(\\beta\\), used in DALoss. To give equal weight to both classification and segmentation, we set \\(\\alpha = \\beta\\). The results are shown in Tab. 6, indicating that larger values of \\(\\alpha\\) and \\(\\beta\\) lead to better performance. We" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16343" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.089, + 0.481, + 0.423 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.089, + 0.885, + 0.423 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.426, + 0.893, + 0.454 + ], + "angle": 0, + "content": "Figure 5. Visualization of the predictions from different models. From the examples, we can clearly show the benefits introduced by pixel-level information from PAIS and DALoss." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.467, + 0.283, + 0.58 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.468, + 0.485, + 0.58 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.468, + 0.687, + 0.58 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.688, + 0.468, + 0.89, + 0.58 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.582, + 0.893, + 0.625 + ], + "angle": 0, + "content": "Figure 6. Influence of imbalanced classes to semi-supervised training. The models are trained under \\(10\\%\\) labeled images for the results. We randomly sampled 10k images from the rest of COCO train2017 to draw these figures. As the training progresses, the predictions from the teacher model are gradually fitted to the distribution of the number of labels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.649, + 0.47, + 0.786 + ], + "angle": 0, + "content": "also analyzed the functions of different hyper-parameters used to adjust the input score, as shown in Fig. 3. The figures illustrate that increasing the hyper-parameter enlarges the difference between high- and low-quality masks or classes, adjusting the input score more appropriately based on their quality. However, when the hyper-parameter is set too large, the low-quality masks or classes are significantly constrained, potentially affecting the generalization of the model as noise is removed entirely during training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Model convergence speed. In Fig. 4, we analyze the convergence speed of the models. The results demonstrate that DALoss can expedite the model training in terms of convergence rate. For instance, Mask-RCNN (PAIS) achieves a convergence speed that is approximately 2 times faster than that of Mask-RCNN (PAIS w/o DALoss). Moreover, by comparing the results between Mask-RCNN" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.649, + 0.892, + 0.695 + ], + "angle": 0, + "content": "(PAIS) and K-Net (PAIS), we observe that DALoss may be particularly effective for box-dependent instance segmentation frameworks, which facilitates rapid convergence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.893, + 0.866 + ], + "angle": 0, + "content": "Different thresholds for classification scores and mask IoUs. We observed from Tab. 7 and Tab. 8 that increasing the thresholds for classification score and mask IoU leads to a decrease in performance. This suggests that DALoss is able to make use of misaligned pseudo-labels instead of simply filtering them out. By allowing the model to learn from these potentially noisy labels, it is able to better handle situations where the alignment between labeled and unlabeled data is not perfect. This may result in improved generalization to new, unseen data, as the model has learned to adapt to the presence of noisy labels." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Different ratios of labeled and unlabeled images per batch. Tab. 9 shows that increasing the ratio of unlabeled" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16344" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.09, + 0.47, + 0.134 + ], + "angle": 0, + "content": "
τcls, τiou0.35, 0.30.50, 0.30.65, 0.30.35, 0.50.35, 0.7
w/o DALoss29.329.025.329.329.0
w/ DALoss31.130.629.930.830.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.137, + 0.468, + 0.166 + ], + "angle": 0, + "content": "Table 10. DALoss w.r.t. thresholds tuning. DALoss consistently outperforms threshold tuning in all settings." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.179, + 0.468, + 0.305 + ], + "angle": 0, + "content": "
Method1%5%10%100%
K-Net, supervise11.622.326.538.4
EMA w/o DALoss17.8(+6.2)25.4(+3.1)29.3(+2.8)39.4(+1.0)
EMA w/ DALoss19.8(+8.2)27.5(+5.2)31.0(+4.5)40.8(+2.4)
Performance gain+2.0+2.1+1.7+1.4
M-RCNN, supervise11.522.427.137.5
EMA w/o DALoss20.1(+8.6)27.4(+5.0)29.8(+2.7)38.4(+0.9)
EMA w/ DALoss21.1(+9.6)29.3(+6.9)31.0(+3.9)39.5(+2.0)
Performance gain+1.0+1.9+1.2+1.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.309, + 0.468, + 0.336 + ], + "angle": 0, + "content": "Table 11. Comparison of EMA with DALoss. The performance improvements are not mainly attributed to EMA." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.363, + 0.468, + 0.422 + ], + "angle": 0, + "content": "images in a batch can improve the model's performance. The results indicate that performance saturates when the ratio is set to 1:4, suggesting that adding too many unlabeled images may lead to diminishing returns." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.423, + 0.468, + 0.558 + ], + "angle": 0, + "content": "Visualizations. We visualize the outputs of different models, including K-Net (supervised), K-Net (PAIS w/o DALoss), K-Net (PAIS), Mask-RCNN (supervised), Mask-RCNN (PAIS w/o DALoss), and Mask-RCNN (PAIS), in Fig. 5. The results show that: (1) PAIS can improve the recall for most instances in the supervised model, but the quality of the predictions is not guaranteed. (2) The use of DALoss in PAIS helps to improve the quality of predictions in terms of mask and classification." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.56, + 0.468, + 0.664 + ], + "angle": 0, + "content": "Influence of imbalanced classes. In Fig. 6, we investigate the effect of imbalanced classes on PAIS. We plot the number of labels obtained from the ground truth and the teacher models for Mask-RCNN and K-Net with PAIS at different iterations, namely \\(32\\mathrm{k}\\), \\(64\\mathrm{k}\\), \\(120\\mathrm{k}\\), and \\(180\\mathrm{k}\\). The results indicate that the predicted pseudo-labels gradually conform to the distribution of the imbalanced labels." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.679, + 0.192, + 0.695 + ], + "angle": 0, + "content": "5. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.468, + 0.794 + ], + "angle": 0, + "content": "DALoss w.r.t. Thresholds Tuning. As shown in Tab. 10, we conduct an ablation study by removing DALoss from our method in Tabs. 7 and 8. The results show that DALoss consistently outperforms threshold tuning in all settings, which validates that DALoss is indeed more effective than tuning the thresholds." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Comparison of EMA with DALoss. We show that the performance improvements are not mainly attributed to EMA. First, we summarize the results of Tabs. 3 and 4 in Tab. 11. We can find that DALoss achieves a larger performance gain than EMA in \\(100\\%\\) COCO \\((+1.4, +1.1\\) vs. \\(+1.0, +0.9)\\). Second, EMA alone cannot selectively utilize noisy pseudo-labels for better learning. DALoss solves this" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.856, + 0.106 + ], + "angle": 0, + "content": "problem and leads to further improvement over EMA." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.107, + 0.892, + 0.256 + ], + "angle": 0, + "content": "Discussion on Score Filtering. We have carefully chosen the values of \\(\\tau_{cls},\\tau_{iou}\\), based on Fig. 1(c)(d), which illustrates that decreasing the thresholds will generate more noisy but informative pseudo-labels. Therefore, we use low thresholds to obtain such pseudo-labels, which is different from previous methods that need to adjust thresholds to filter them out. This simplifies the tuning of the thresholds. We believe that the experiments in Tabs. 7, 8, and 10 are sufficient to show that lower thresholds are suitable for DALoss." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.258, + 0.892, + 0.408 + ], + "angle": 0, + "content": "Generality to Other Segmentation Tasks. DALoss can be applied to other semi-supervised segmentation tasks, as the noisy pseudo-labels are common in semi-supervised setting. To show the generality, we apply DALoss to panoptic segmentation, which is a more challenging task that requires both instance and semantic segmentation. We report a preliminary result under \\(10\\%\\) COCO. The initial result shows that DALoss can improve the PQ performance from \\(36.8\\%\\) PAIS w/o DALoss to \\(37.3\\%\\) PAIS w/ DALoss. We remain more experiments in our future work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.892, + 0.56 + ], + "angle": 0, + "content": "Discussion on Large Segment Everything Models. We envision that the future of image segmentation will not only aim to segment everything, but also to provide fine-grained text descriptions for the segmented regions. However, the recently proposed models such as SAM [19] and SEEM [55] either lack labeled semantic information or demand large amounts of labeled semantic data for training. Therefore, we believe that semi-supervised learning will be a crucial solution to leverage abundant unlabeled data and reduce the labeling burden." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.575, + 0.619, + 0.59 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.601, + 0.892, + 0.812 + ], + "angle": 0, + "content": "In this paper, we presented a novel PAIS framework for semi-supervised instance segmentation. To address the misalignment between classification score and mask quality, we introduced a dynamic aligning loss (DALoss), which aligns the classification loss term and the segmentation loss term based on the quality of different pseudo-labels. Our experimental results demonstrate the effectiveness of the proposed PAIS framework. Specifically, when the amount of labeled data is extremely limited, our pipeline equipped with PAIS and DALoss achieves superior performance for instance segmentation. We believe that PAIS can serve as a strong baseline for future research on semi-supervised instance segmentation. We hope our work can inspire further exploration in this exciting research direction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.815, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported by National Key R&D Program of China (2022ZD0118202), National Science Fund for Distinguished Young Scholars (No.62025603), National Natural Science Foundation of China (No.U21B2037, No.U22B2051, No.62176222, No.62176223, No.62176226, No.62072386, No.62072387, No.62072389, No.62002305 and No.62272401), and Natural Science Foundation of Fujian Province of China (No.2021J01002, No.2022J06001)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16345" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.469, + 0.156 + ], + "angle": 0, + "content": "[1] Philip Bachman, Ouais Alsharif, and Doina Precup. Learning with pseudo-ensembles. 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Segment everything everywhere all at once. 9" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.895 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16347" + } + ] +] \ No newline at end of file diff --git a/2023/Pseudo-label Alignment for Semi-supervised Instance Segmentation/42aab451-44d8-431c-bd3b-859749553f79_origin.pdf b/2023/Pseudo-label Alignment for Semi-supervised Instance Segmentation/42aab451-44d8-431c-bd3b-859749553f79_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b37d3e4370d838d1e4be0de8d7cf08340b8efd9d --- /dev/null +++ b/2023/Pseudo-label Alignment for Semi-supervised Instance Segmentation/42aab451-44d8-431c-bd3b-859749553f79_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4281670f5124b8ececfe58cfa454508d052e28d9f36b181addf96adadd903d97 +size 3133013 diff --git a/2023/Pseudo-label Alignment for Semi-supervised Instance Segmentation/full.md b/2023/Pseudo-label Alignment for Semi-supervised Instance Segmentation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..8e9ffccfcaca78c7ab25d096f4c2006692f27479 --- /dev/null +++ b/2023/Pseudo-label Alignment for Semi-supervised Instance Segmentation/full.md @@ -0,0 +1,352 @@ +# Pseudo-label Alignment for Semi-supervised Instance Segmentation + +Jie Hu $^{1\dagger}$ , Chen Chen $^{1\dagger}$ , Liujuan Cao $^{1*}$ , Shengchuan Zhang $^{1}$ , Annan Shu $^{2}$ , Guannan Jiang $^{2}$ , and Rongrong Ji $^{1}$ + +1Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University 2Contemporary Amperex Technology Co. Limited + +# Abstract + +Pseudo-labeling is significant for semi-supervised instance segmentation, which generates instance masks and classes from unannotated images for subsequent training. However, in existing pipelines, pseudo-labels that contain valuable information may be directly filtered out due to mismatches in class and mask quality. To address this issue, we propose a novel framework, called pseudo-label aligning instance segmentation (PAIS), in this paper. In PAIS, we devise a dynamic aligning loss (DALoss) that adjusts the weights of semi-supervised loss terms with varying class and mask score pairs. Through extensive experiments conducted on the COCO and Cityscapes datasets, we demonstrate that PAIS is a promising framework for semi-supervised instance segmentation, particularly in cases where labeled data is severely limited. Notably, with just $1\%$ labeled data, PAIS achieves 21.2 mAP (based on Mask-RCNN) and 19.9 mAP (based on K-Net) on the COCO dataset, outperforming the current state-of-the-art model, i.e., NoisyBoundary with 7.7 mAP, by a margin of over 12 points. Code is available at: https://github.com/hujiecpp/PAIS. + +# 1. Introduction + +Semi-supervised instance segmentation aims to alleviate the significant burden of human labeling by utilizing a small amount of labeled data in conjunction with abundant unlabeled data [35, 47, 50]. Existing semi-supervised instance segmentation pipelines typically generate pseudolabels from unlabeled images, which are then used to train the models together with labeled images. Therefore, pseudo-labels play a crucial role in semi-supervised instance segmentation. The generation of pseudo-masks, pseudo-classes, and pseudo-boxes from unlabeled images improves the model training. However, current semi + +supervised instance segmentation frameworks do not fully leverage the potential of such pseudo-labels. Specifically, pseudo-labels with mismatched class and mask scores are often filtered out by fixed thresholds, leading to the exclusion of valuable information that could aid the model training. For instance, pseudo-labels with high-quality masks but low class scores would be filtered out by a class threshold, resulting in the loss of the pixel-level information. + +In this paper, we present a new semi-supervised framework, termed pseudo-label aligning for instance segmentation (PAIS), aiming to improve the utilization of filtered pseudo-labels. As illustrated in Fig. 1, the main challenge of PAIS lies in the mismatched scores between pseudoclasses and pseudo-masks. The classification score and mask intersection over union (IoU) are misaligned in assessing the quality of pseudo-labels. As a result, masks with high IoUs would be filtered out due to low classification scores, and vice versa. In the mean time, lowering the threshold of both scores introduces incorrect classes or low-quality masks into the semi-supervised training. To overcome this dilemma, we propose a dynamic aligning loss (DALoss) that softly re-weights the classification and the segmentation losses based on the quality of different pseudo-labels. Specifically, DALoss penalizes low-score pseudo-labels rather than filtering them and promotes high-score ones, to adjust their contribution to the final loss function. Our experiments on the COCO and Cityscape datasets demonstrate the effectiveness of the proposed PAIS framework. Specifically, with only $1\%$ labeled data, PAIS achieves $21.2\mathrm{mAP}$ and $19.9\mathrm{mAP}$ on the COCO dataset using Mask-RCNN [13] and K-Net [53], respectively. This outperforms the current state-of-the-art model, NoisyBoundary [47], by more than 12 points. + +Our contributions can be summarized as follows: + +- We propose a novel pseudo-label aligning framework for semi-supervised instance segmentation, called PAIS, which unleashes the potential of utilizing pixel-level pseudo-labels in semi-supervised instance segmentation. Furthermore, to the best of our knowledge, + +![](images/57279d70f6f037dbc92abada7946a2ba11569434ccb7fc015435590f03ebfa0c.jpg) +Figure 1. Pseudo-label wasting in semi-supervised instance segmentation. To illustrate this issue, we employed the K-Net model [53] trained on $10\%$ labeled images and randomly sampled 5k unlabeled images, from the COCO train2017 dataset, to plot the figures. In (a), we present the predicted classification score w.r.t. the ground truth mask intersection over union (IoU), revealing that the predicted classification score is inadequate in evaluating mask quality. In (b), we added a mask IoU prediction branch to the model and plotted the predicted mask IoU w.r.t. the ground truth mask IoU, demonstrating that the predicted mask IoU can represent the mask quality. However, as shown in (c), a significant number of pseudo-labels with high-quality masks, i.e., mask IoU $>0.7$ , will be filtered out with high classification thresholds. Additionally, (d) shows that pseudo-labels with high-quality masks can also have correspondingly low classification scores. Therefore, the misalignment between the mask and class scores leads to a significant number of valuable pseudolabels being excluded during semi-supervised training. + +![](images/42a4e8b5f29d78ea0d22dd22a4db1e48cdb6bba23e30fbfd95ce52b4d602e21b.jpg) + +![](images/3c10d05e561321ec21bee95d6cabffe3c5500fa95b6f02b55840e7bc9085e569.jpg) + +![](images/ae4734b7932dd715437e5be9a7f5245d76e3c6468b822cc041dfb850b012f2bb.jpg) + +PAIS is the first framework that can be adapted to box-free instance segmentation models. + +- We introduce a new loss function, named dynamic aligning loss (DALoss), which incorporates pseudolabels with diverse class and mask qualities into the semi-supervised training process. DALoss consistently enhances the performance of box-free and box-dependent instance segmentation frameworks. +- We conduct comprehensive experiments on the COCO and Cityscapes datasets to evaluate PAIS. In particular, PAIS achieves state-of-the-art results on the COCO dataset, i.e., 19.9, 27.6, and $31.1\mathrm{mAP}$ for the box-free pipeline K-Net [53], and 21.2, 29.3, and $31.1\mathrm{mAP}$ for the box-dependent pipeline Mask-RCNN [13], with $1\%$ , $5\%$ , and $10\%$ labeled data, respectively. + +# 2. Related Work + +Semi-supervised Image Classification. In image classification, semi-supervised learning has been extensively explored, and the methods can be classified into two categories: pseudo-label-based and consistency-regularization-based methods. Specifically, pseudo-label-based methods [40, 21] leverage pre-trained models to generate annotations for the unlabeled images to train the model. In contrast, consistency-regularization-based methods [1, 36, 20, 39, 48, 2, 7, 32, 31, 23] incorporate various data augmentation techniques such as random regularization [10] and adversarial perturbation [33] to generate different inputs for one image and enforce consistency between these inputs during training. FixMatch [41] combines the consistency-regularization-based techniques with a pseudo-label-based framework by applying a strong-weak data augmentation pipeline to input images and enforcing consistency between + +the augmented images. In this work, we follow the pseudolabel-based methods and also use strong-weak data augmentation during training in PAIS. + +Semi-supervised Object Detection. From the very beginning, STAC [42] proposed the use of pseudo-labels and consistency training for semi-supervised object detection. However, the effectiveness of the method was limited by the two-stage training pipeline similar to that of Noisy Student [49], where the pseudo-labels were generated from pre-trained models and were not updated along with the model training. After STAC, several studies [50, 54, 43, 51, 28] incorporated the idea of exponential moving average (EMA) from MeanTeacher [44]. The teacher model and pseudo-labels are updated after each training iteration to generate instant pseudo-labels, making the entire pipeline end-to-end trainable. Additionally, Unbiased Teacher [28] utilized Focal loss [24] instead of traditional cross-entropy loss to alleviate the problem of unbalanced pseudo-labels. In this paper, we also follow the idea of incorporating EMA into the proposed PAIS framework, with a focus on integrating pixel-level annotations into the training process. + +Fully-supervised Instance Segmentation. Instance segmentation aims to provide pixel-level predictions for each object instance in an image. Existing methods can be classified into three categories: top-down (or box-dependent) methods, bottom-up methods, and direct segmentation (or box-free) methods. Top-down methods [15, 27, 38, 37, 29] such as Mask R-CNN [13], YOLACT [3], and CenterMask [22] generate bounding boxes first and then segment the objects within the boxes. Bottom-up methods [52, 8, 26, 11, 16], regard instance segmentation as a label-then-cluster problem, which classify each pixel first and then group the pixels into an arbitrary number of object instances. Direct segmentation or box-free methods such as SOLO [45, 46], K-Net [53], MaskFormer [5, 4] and + +![](images/3b9d6905c6b74d715ed2754589e2d829608658ee580747da9a65ecee6404d16a.jpg) +Figure 2. Framework of pseudo-label aligning for semi-supervised instance segmentation (PAIS). The focus of PAIS is to explore the utility of pixel-level pseudo-labels for instance segmentation. To this end, we propose a novel approach called dynamic aligning loss (DALoss), which enables the incorporation of pseudo-labels with varying quality during training. This is particularly significant when the number of labeled images is limited. With DALoss, a significant number of predictions from the teacher model can be leveraged in the semi-supervised training process, rather than being discarded. Specifically, we consider three types of pseudo-masks with varying quality: (a) pseudo-masks with incorrect classes but high-quality masks, i.e., low classification scores but high mask IoUs; (b) pseudo-masks with accurate classes but low-quality masks, i.e., high classification scores but low mask IoUs; and (c) pseudo-masks with medium qualities. + +![](images/694187f758c656bdb92868e2fef6222eb5cba33765bd5a524c96798479b56dca.jpg) +(a) Score↓, IoU↑ + +![](images/c825972816ff2779d7824731dd640c7d705401762cd99bd8cb2dd2fd0d4b25ec.jpg) +(c) Score-, IoU- + +![](images/ae1d9651c84de716480e1f4dc2c927d6bb64d321da5b7571aa8dba9357e3d08f.jpg) +(b) Score↑, IoU↓ + +![](images/cd661cf983cb9e65df58db3acbe7f975396705014ca95dcbe4c289507a09f045.jpg) +(d) Score↑, IoU↑ + +SOTR [12] deal with instance segmentation without bounding box detection. Any of the aforementioned instance segmentation methods can be implemented into PAIS, and in this work, we present two examples, one from the box-dependent category, Mask R-CNN, and another from the box-free category, K-Net. + +Semi-supervised Instance Segmentation. Semi-supervised instance segmentation is commonly considered to be a sub-task of semi-supervised object detection [50, 28]. Consequently, existing frameworks rely heavily on bounding boxes, in which segmentation performance is strongly dependent on detection performance. Among them, NoisyBoundary [47] was the first to formally propose the semi-supervised instance segmentation task. Recent efforts have been made to construct box-free pipelines for fully-supervised instance segmentation [45, 46, 53, 5]. In this paper, we investigate PAIS in both box-free and box-dependent instance segmentation, revealing the potential of fully utilizing pixel-level annotations. In contrast to the recently-proposed PoliteTeacher [9], which filters out pseudo-labels with low confidence, the proposed PAIS leverages them. It is a novel and effective way of utilizing noisy pseudo-labels for semi-supervised learning. + +# 3. Method + +# 3.1. Task Formulation + +The goal of PAIS is to better leverage unlabeled images with a limited number of pixel-labeled images to boost the performance of semi-supervised instance segmentation. The PAIS framework consists of three key steps: (1) pseudo-label generation, (2) dynamic pseudo + +label alignment, and (3) end-to-end model training. In the pseudo-label generation step, we introduce a mask scoring branch [17] that predicts mask IoUs as an additional metric along with classification scores to assess the quality of pseudo-labels. In the dynamic aligning step, we re-weight the loss terms based on the quality of different pseudolabels. Finally, the teacher and student models are trained using exponential moving average (EMA) [44]. The overall framework of PAIS is illustrated in Fig. 2, and we introduce the key steps in detail as follows. It is important to note that the PAIS framework can be applied to any box-dependent or box-free framework for enhanced exploitation of pseudo-labels in semi-supervised instance segmentation. We instantiate two examples by Mask-RCNN [13] and K-Net [53] in this paper, but do not restrict to them. + +# 3.2. Pseudo Label Generation + +In the pseudo-label generation, we apply weak data augmentation to the unlabeled images and input them into a teacher model. The weak data augmentation includes scaling, horizontal flipping, and other augmentation operations that do not alter the image's content. The teacher model produces a set of pseudo-labels, including masks, boxes, and classification scores for each input image. In box-free pipelines, the box predictions are optional. + +As depicted in Fig. 1(a)(c), using the classification score alone is inadequate to measure the quality of predicted masks. To address this, we incorporate a mask scoring branch into the pipeline to predict mask Intersection over Union (IoU) for evaluating mask quality. As shown in Fig. 1(b), the predicted mask IoUs can be used to measure mask quality effectively, which has also been verified + +# Algorithm 1 Pseudo-label Alignment + +1: Initialize teacher and student models randomly. +2:Repeat +3: Apply weak augmentation to unlabeled images. +4: Obtain pseudo-labels $\{\pmb{m}_i, \pmb{b}_i, \pmb{c}_i, s_i | i = 1, \dots, N\}$ from teacher model via thresholds $\tau_{cls}, \tau_{iou}$ . +5: Apply strong augmentation to unlabeled images. +6: Obtain predictions $\widetilde{m}, b, \widetilde{c}$ for unlabeled images. +7: Calculate $\mathcal{L}_u$ for unlabeled images by Eq. 5. +8: Inference labeled images by student model. +9: Calculate $\mathcal{L}_l$ for labeled images. +10: Train student model with the loss $\mathcal{L}_{semi}$ in Eq. 1. +11: Update teacher model via EMA. +12: Until scheduled epochs. + +in MS-RCNN [17]. After generating pseudo-labels in the previous step, the predictions are filtered using two thresholds: a classification threshold $\tau_{cls}$ and a mask IoU threshold $\tau_{iou}$ . The resulting set of pseudo-labels includes $N$ elements, each containing a mask $m_i \in \mathbb{R}^{H \times W}$ , a bounding box $b_i \in \mathbb{R}^4$ , a classification score $c_i \in \mathbb{R}^L$ (with an additional background category), and a mask IoU score $s_i \in \mathbb{R}$ . Note that $H, W$ denote the mask resolution, and $L$ is the number of classes. + +# 3.3. Dynamic Aligning Loss + +Although good pseudo-labels can be obtained by setting high thresholds for classification scores and mask IoUs, a large number of predictions with misaligned mask and classification qualities are discarded (as illustrated in Fig.1(c)(d)). These misaligned predictions can be useful since the amount of labeled data is limited in the semi-supervised setting. Fig.2 shows examples of pseudo-labels that can be included in the training process. If the misaligned pseudo-labels are directly used in semi-supervised learning, the incorrect predictions on classes or masks can introduce significant noise. To reduce the noise, we propose a dynamic aligning loss (DALoss). + +Vanilla Loss for PAIS. In semi-supervised instance segmentation, the loss function can be decomposed into two terms for labeled and unlabeled images, as: + +$$ +\mathcal {L} _ {\text {s e m i}} = \lambda_ {l} \mathcal {L} _ {l} + \lambda_ {u} \mathcal {L} _ {u}, \tag {1} +$$ + +where $\lambda_{l}$ and $\lambda_{u}$ are the hyper-parameters for balancing the loss terms. The loss for labeled images can be defined using the functions commonly employed in instance segmentation, augmented with an additional binary cross-entropy term for regressing mask IoUs. Given the pseudo-labels from the teacher model and the predictions from the student model, we formulate the loss for unlabeled images as: + +$$ +\begin{array}{l} \mathcal {L} _ {u} = \frac {1}{N _ {p o s}} \sum_ {i = 1} ^ {N _ {p o s}} \left(\lambda_ {b} \mathcal {L} _ {b} \left(\widetilde {\boldsymbol {b}} _ {\nu (i)}, \boldsymbol {b} _ {\mu (i)}\right) \right. \\ \left. + \lambda_ {c} \mathcal {L} _ {c} \left(\widetilde {\boldsymbol {c}} _ {\nu (i)}, \boldsymbol {c} _ {\mu (i)} ^ {o}\right) + \lambda_ {m} \mathcal {L} _ {m} \left(\widetilde {\boldsymbol {m}} _ {\nu (i)}, \boldsymbol {m} _ {\mu (i)} ^ {b}\right)\right) \tag {2} \\ + \frac {1}{N _ {n e g}} \sum_ {i = 1} ^ {N _ {n e g}} \left(\lambda_ {c} \mathcal {L} _ {c} (\widetilde {\boldsymbol {c}} _ {i}, \boldsymbol {c} _ {n e g} ^ {o})\right), \\ \end{array} +$$ + +where $\mathcal{L}_b$ includes the box IoU loss and the L1 loss, $\mathcal{L}_c$ denotes the cross-entropy loss, $\mathcal{L}_m$ is the dice loss. In Eq. 2, $\widetilde{c}_i,\widetilde{b}_i,\widetilde{m}_i$ represent predictions from the student model. The pseudo-scores $c_{\mu (i)}$ for classification are converted to one-hot vectors $c_{\mu (i)}^o$ for the category with the highest score. The pseudo-masks $m_{\mu (i)}$ are activated by sigmoid function and discretized into binary value as $m_{\mu (i)}^{b}$ . The one-hot vector for the background class is denoted by $c_{neg}^o$ . The label indexing functions, $\nu (i)$ and $\mu (i)$ , match predictions with pseudo-labels for training, which are defined in terms of different pseudo-label assigning strategies. In our implementations, the one-to-many assignment defines the label indexing functions $\nu (i) = i$ and $\mu (i)$ as: + +$$ +\mu (i) = \underset {t \in [ 1, N ]} {\arg \min } \left(\mathcal {L} _ {b} \left(\widetilde {\boldsymbol {b}} _ {i}, \boldsymbol {b} _ {t}\right)\right). \tag {3} +$$ + +Instead, the one-to-one assignment defines the label indicting functions $\mu (i) = i$ , and finds the optimal $\nu^{*}(\cdot)$ via: + +$$ +\begin{array}{l} \nu^ {*} = \arg \min _ {\nu} \sum_ {i = 1} ^ {t} \left(\lambda_ {b} \mathcal {L} _ {b} \left(\widetilde {\boldsymbol {b}} _ {\nu (i)}, \boldsymbol {b} _ {i}\right) + \lambda_ {c} \mathcal {L} _ {c} \left(\widetilde {\boldsymbol {c}} _ {\nu (i)}, \boldsymbol {c} _ {i} ^ {o}\right) \right. \tag {4} \\ + \lambda_ {m} \mathcal {L} _ {m} (\widetilde {\boldsymbol {m}} _ {\nu (i)}, \boldsymbol {m} _ {i} ^ {b}) - s _ {i}). \\ \end{array} +$$ + +Note that the loss terms for regressing boxes are optional in box-free instance segmentation frameworks. + +Dynamic Aligning Loss for PAIS. To optimize the model using pixel-level pseudo-labels, we propose to replace Eq. 2 with DALoss. Since the teacher model provides ideal metrics for measuring the quality of classification scores and mask IoUs, we propose to adjust the weight of loss terms based on the quality of the pseudo-labels. This is achieved by using the following equation: + +$$ +\begin{array}{l} \mathcal {L} _ {u} ^ {D A} = \frac {1}{N _ {p o s}} \sum_ {i = 1} ^ {N _ {p o s}} \left(\lambda_ {b} \mathcal {L} _ {b} (\widetilde {\boldsymbol {b}} _ {\nu (i)}, \boldsymbol {b} _ {\mu (i)}) \right. \\ + \lambda_ {c} \left(c _ {\mu (i)} ^ {h}\right) ^ {\alpha} \mathcal {L} _ {c} \left(\widetilde {c} _ {\nu (i)}, c _ {\mu (i)} ^ {o}\right) \tag {5} \\ \left. + \lambda_ {m} \left(s _ {\mu (i)}\right) ^ {\beta} \mathcal {L} _ {m} \left(\widetilde {\boldsymbol {m}} _ {\nu (i)}, \boldsymbol {m} _ {\mu (i)} ^ {b}\right)\right) \\ + \frac {1}{N _ {n e g}} \sum_ {i = 1} ^ {N _ {n e g}} \left(\lambda_ {c} \mathcal {L} _ {c} (\widetilde {\boldsymbol {c}} _ {i}, \boldsymbol {c} _ {n e g} ^ {o})\right), \\ \end{array} +$$ + +where $c_{\mu(i)}^{h}$ denotes the highest classification score, and $s_{\mu(i)}$ denotes the mask IoU from the $\mu(i)$ -th pseudo-label, + +
Method1%5%10%100%
Mask-RCNN [13], supervised*3.517.322.034.5
Mask-RCNN† [13], supervised*3.517.421.937.1
DD [35]3.820.424.235.7
Noisy Boundaries [47]7.724.929.238.6
PAIS, on Mask-RCNN, ours21.229.331.139.5
+ +Table 1. Comparison to state-of-the-art semi-supervised instance segmentation methods on the COCO val2017.† denotes using the same data augmentation as semi-supervised training. * denotes data from NoisyBoundary [47]. + +
Method5%10%20%30%
Mask-RCNN [13], supervised*11.816.822.326.3
Mask-RCNN† [13], supervised*11.316.422.626.6
DD [35]13.719.224.627.4
STAC [42]11.918.222.929.0
CSD [18]14.117.924.627.5
CCT [34]15.218.624.726.5
Dual-branch [30]13.918.924.028.9
Ubteacher [28]16.020.027.128.0
Noisy Boundaries [47]17.122.129.032.4
PAIS, on Mask-RCNN, ours18.022.929.232.8
+ +Table 2. Comparison to state-of-the-art semi-supervised instance segmentation methods on the Cityscapes validation set. $\dagger$ denotes using the same data augmentation as semi-supervised training. \* denotes data from NoisyBoundary [47]. + +$\alpha, \beta$ are the hyper-parameters. Specifically, Eq. 5 adjusts the weights for the pseudo-labels conditioned on their qualities, i.e., dynamically dependent on the input images. For instance, for a pseudo-label with a low classification score and high mask IoU, DALoss encourages the segmentation loss while constraining the classification loss. + +# 3.4. End-to-End Model Training + +Inspired by [44], we employ EMA with the strong-weak data augmentation for PAIS. Specifically, unlabeled images undergo both strong and weak data augmentations and are then fed into the student and teacher models, respectively. The student model is trained to produce consistent results with the pseudo-labels, and the teacher model is updated by EMA. The training pipeline for PAIS is presented in Alg. 1. + +# 4. Experiments + +# 4.1. Datasets and Evaluation Metrics + +We conducted extensive experiments on the COCO [25] and Cityscapes [6] datasets to study the proposed PAIS. The COCO dataset consists of 118k images with 80-class instance labels, as well as 123k unlabeled images. The Cityscapes dataset contains urban street-view scenes and has 8 instance categories in 2.9k training images and 0.5k validation images. For the COCO dataset, we ran- + +domly sampled $1\%$ , $5\%$ , and $10\%$ of the images from the train2017 split as labeled data and treated the rest as unlabeled data following common settings. In addition, we also used the full COCO train2017 as labeled data and incorporated the 123k unlabeled data from COCO unlabel2017 to train the PAIS models. For the Cityscapes dataset, we randomly sampled $5\%$ , $10\%$ , $20\%$ , and $30\%$ of the images from the training set as labeled data and treated the remaining as unlabeled data following the common settings. We evaluated the PAIS models on the validation sets of the COCO and Cityscapes datasets, and reported standard COCO metrics including AP, AP50, AP75 (averaged over IoU thresholds), and $\mathrm{AP}_S$ , $\mathrm{AP}_M$ , $\mathrm{AP}_L$ (AP for instances of different scales). + +# 4.2. Implementation Details + +We provide two examples of implementing PAIS with K-Net [53] and Mask-RCNN [13]. The models are trained using AdamW with a learning rate of 0.0001 for K-Net, and SGD with a learning rate of 0.01 for Mask-RCNN. The hyper-parameters $\lambda_{l}$ and $\lambda_{u}$ , which balance the loss terms for labeled and unlabeled images, are set to 1.0 and 0.3 for K-Net, and 1.0 and 1.5 for Mask-RCNN. We set the thresholds $\tau_{cls}$ and $\tau_{iou}$ experimentally as 0.35 and 0.30, respectively. For bipartite matching loss, we use the same hyperparameters as in [53]. The loss balancing parameters for box, class, and mask are set as $\lambda_{b} = 2.0$ , $\lambda_{c} = 4.0$ , and $\lambda_{m} = 1.0$ respectively. We train the models on 4 GPUs with 4 images per GPU (1 labeled and 3 unlabeled images) for 220k iterations, unless otherwise specified. The teacher model is updated via EMA with a momentum of 0.999. We use ResNet50 [14] as the backbone for these models. + +# 4.3. Main Results + +Comparison to state-of-the-art semi-supervised instance segmentation frameworks. In Tab. 1, we compare the performance of models trained with PAIS to the state-of-the-art semi-supervised instance segmentation frameworks on the COCO dataset. The results demonstrate that both K-Net and Mask-RCNN trained with PAIS surpass the previous methods DD [35] and Noisy Boundaries [47] by a large margin, especially when the number of labeled data is very limited (with only $1\%$ or $5\%$ labeled images). Specifically, when using $1\%$ labeled COCO images, PAIS with K-Net achieves 19.9 mask mAP, which is 12.2 points higher than Noisy Boundaries. Interestingly, the proposed PAIS brings about better performance for Mask-RCNN when the percentage of labeled data is $1\%$ or $5\%$ , even though it originally has a inferior performance in fully-supervised instance segmentation compared to K-Net. To explain, the bounding boxes may provide better optimization for Mask-RCNN models when the labeled data is limited. Finally, when using $10\%$ and $100\%$ labeled images, PAIS with K-Net out + +
Method1% COCO5% COCO10% COCO
APAP0.5AP0.75APAP0.5AP0.75APAP0.5AP0.75
+ +Box-free Instance Segmentation + +
K-Net [53], supervised8.03±0.2516.33±0.317.00±0.2517.4±0.2230.08±0.2816.83±0.2121.63±0.2137.43±0.3821.8±0.20
K-Net†[53], supervised11.63±0.0522.30±0.0810.95±0.1022.28±0.0538.54±0.0922.7±0.0726.53±0.1244.87±0.1527.20±0.17
K-Net, PAIS w/o DALoss17.77±0.0632.17±0.1517.53±0.1225.40±0.0843.12±0.0526.05±0.1329.30±0.0748.64±0.0530.53±0.13
K-Net, PAIS19.78±0.1035.48±0.1519.65±0.0627.53±0.0645.63±0.0628.70±0.1031.04±0.0650.50±0.0732.34±0.05
+ +Box-dependent Instance Segmentation + +
Mask-RCNN [13], supervised*3.5--17.3--22.0--
Mask-RCNN† [13], supervised11.54±0.0919.86±0.1111.64±0.0922.35±0.0637.98±0.1023.14±0.1127.07±0.0645.10±0.1028.67±0.06
Mask-RCNN, PAIS w/o DALoss20.13±0.0633.23±0.1521.27±0.0627.36±0.0644.10±0.1029.27±0.0629.77±0.0647.70±0.1031.97±0.06
Mask-RCNN, PAIS21.12±0.0536.03±0.0522.75±0.1029.28±0.1347.25±0.1331.20±0.2231.03±0.0649.83±0.1233.23±0.06
+ +Table 3. Results of PAIS with extremely limited number of labeled images. We randomly sampled $1\%$ , $5\%$ , and $10\%$ of the labeled images from the COCO train2017 dataset, and repeated each experiment three times. The average values with standard deviation are reported. $\dagger$ denotes using the same data augmentation as semi-supervised training. * denotes data from NoisyBoundary [47]. We can see that PAIS achieves good performance on both box-free and box-independent instance segmentation frameworks. + +
MethodAPAP0.5AP0.75APSAPMAPL
Box-free Instance Segmentation
K-Net [53], supervised37.860.339.916.941.257.5
K-Net†[53], supervised38.461.440.317.641.858.0
K-Net, PAIS w/o DALoss39.462.241.618.542.859.2
K-Net, PAIS40.863.543.319.244.461.4
Box-dependent Instance Segmentation
Mask-RCNN [13], supervised37.158.539.718.739.653.9
Mask-RCNN†[13], supervised37.558.940.418.640.253.8
Mask-RCNN, PAIS w/o DALoss38.459.741.519.441.155.0
Mask-RCNN, PAIS39.560.643.019.942.456.6
+ +Table 4. Results of PAIS with abundant labeled images. We utilize all the labeled images in the COCO train2017 dataset, and supplement them with the unlabeled images in the COCO unlabel2017 dataset for semi-supervised training. $\dagger$ denotes using the same data augmentation as semi-supervised training. + +performs PAIS with Mask-RCNN. In Tab. 2, we compare PAIS with state-of-the-art methods on the Cityscape dataset, in which PAIS also achieves better performance than the predominant models. Specifically, we report NoisyBoundaries [47] w/o FocalLoss in Tab. 2, as we do not apply FocalLoss in PAIS. This ensures a fair and consistent comparison. Furthermore, we also add FocalLoss to PAIS on $10\%$ Cityscapes, which achieves $25.1\%$ , surpassing $23.7\%$ of NoisyBoundaries w/ FocalLoss. + +The more significant performance improvement on the COCO dataset validates the effectiveness of our method for solving the noisy pseudo-label problem. The COCO dataset has 80 instance categories, while the Cityspaces dataset only has 8 instance categories. This implies that the COCO dataset can provide more diverse and informative pseudo-labels, which matches our goal to utilize noisy pseudo-labels for semi-supervised learning. + +Results with an extremely limited number of labeled images. To demonstrate the effectiveness of PAIS, we conduct experiments with extremely limited numbers of labeled + +images, as shown in Table 3. Specifically, we compare the performance of various models trained with randomly sampled $1\%$ , $5\%$ , and $10\%$ labeled images. First, we train supervised models, K-Net (supervised) and Mask-RCNN (supervised), with the limited labeled images. Second, we train the same supervised models with the same data augmentation used in the semi-supervised setting, denoted as $\mathrm{K - }$ $\mathrm{Net}^{\dagger}$ (supervised) and $\mathrm{Mask - RCNN}^{\dagger}$ (supervised). Third, we train PAIS models without DALoss, denoted as PAIS w/o DALoss on K-Net and Mask-RCNN. Lastly, we train the PAIS models with DALoss, denoted as PAIS on K-Net and Mask-RCNN. All models are trained three times, and the reported results are averaged. + +Based on the results of K-Net (supervised) and Mask-RCNN (supervised), it can be observed that fully-supervised models perform poorly when the number of labeled images is limited. The results of $\mathrm{K - Net}^{\dagger}$ (supervised) and $\mathrm{Mask - RCNN}^{\dagger}$ (supervised) show slight improvement with weak data augmentation from the semi-supervised setting. Interestingly, while K-Net outperforms Mask-RCNN in the fully-supervised setting, their performance is similar when the number of labeled images is limited, as indicated in the table. Comparing the performance of K-Net (PAIS w/o DALoss) and Mask-RCNN (PAIS w/o DALoss) with that of the supervised setting reveals significant improvement. By introducing the dynamically re-weighting process via DALoss, the performance is further improved. For instance, with only $1\%$ labeled images, the mAP of K-Net and Mask-RCNN improved from 11.63 and 11.54 to 19.78 and 21.12, respectively, resulting in approximately +8.15 and +9.58 points improvement to the performance. Additionally, the improvement over $\mathrm{AP}_{0.5}$ and $\mathrm{AP}_{0.75}$ suggests that DALoss considers masks with moderate quality during training, which further benefits semi-supervised learning. + +Results with abundant labeled images. In Tab. 4, we investigate the performance of semi-supervised learning + +
Cls.IoU.Mask.APAP0.5AP0.75APSAPMAPL
29.348.730.511.331.445.5
✓29.749.031.011.431.846.3
✓29.448.930.611.731.546.0
✓✓30.450.131.911.932.847.6
✓✓✓31.150.632.412.333.348.3
+ +Table 5. Effectiveness of different loss terms in DALoss. Cls. denotes the terms of dynamic aligned classification scores. IoU. denotes adding the mask IoU branch to the model. Mask. denotes using the terms of dynamic aligned mask scores. + +
α,βAPAP0.5AP0.75APSAPMAPL
129.949.131.010.932.147.0
230.249.531.111.132.247.1
330.550.131.711.632.947.6
431.150.632.412.333.348.3
+ +when abundant labeled data is available. Specifically, we use the entire COCO train2017 dataset as labeled data and COCO unlabeled2017 dataset as unlabeled data to train the models. The results show that the semi-supervised learning approach also leads to a performance gain. For instance, K-Net (PAIS) achieves a performance gain of approximately 1.0 point on mAP from semi-supervised learning. Additionally, the proposed DALoss consistently improves the performance of both box-dependent and box-free instance segmentation frameworks. + +# 4.4. Ablation Study + +In our ablation study, we investigate several aspects that can impact the performance of PAIS, including the utilization of various loss terms, the setting of hyper-parameters, the threshold values, the varying ratios of labeled and unlabeled images, and the convergence times. We perform the ablation studies on the COCO dataset using K-Net and Mask-RCNN, which are trained via PAIS under the setting of $10\%$ labeled images. + +Effectiveness of different terms in DALoss. Tab. 5 shows the efficacy of the different components in DALoss, which suggests that: (1) DALoss yields an improvement of 1.8 points to the model. Specifically, the mAP increases from 45.5 to 48.3 on $\mathrm{AP}_L$ , indicating a significant improvement for large objects. (2) The aligning weights for classification loss alone can also provide a marginal performance gain for the model. (3) Simply adding a mask IoU branch to the model does not enhance the overall performance. However, when incorporating the aligning weights for the segmentation loss, the mAP is increased. (4) Interestingly, the mask IoU branch can help improve the AP for objects of different scales. This is due to the mask IoU branch helping + +![](images/536dd521bdf18cc3ec4e0ba2c793d977b5824f8ae0827ba9cef0168552e3e0d4.jpg) +Figure 3. Visualization of the loss alignment with different hyper-parameters. When changing the hyper-parameter from 1 to 5, the input classification score or mask IoU will be more properly adjusted by their quality, i.e., the difference between high- & low-quality mask or class will be enlarged. + +![](images/daaba6a64b2f15c352a7132e07eb7fb2a9665d5218d6d9e35b66b6238365900f.jpg) + +![](images/55574d924ee90354fc41484b9b5f3d504a458ce3c6a6309cee67e288a79c0f65.jpg) +Figure 4. Model convergence speed. DALoss leads to faster model convergence for training. + +![](images/b6e3d7e98296784ddf2f59c71b048d2f023689de8a054893b103da0664c26c01.jpg) + +Table 6. Hyper-parameters in DALoss. Considering that the classification and segmentation are both important, we simply set $\alpha = \beta$ to investigate the influence of hyper-parameters. + +
τclsAPAP0.5AP0.75APSAPMAPL
0.3531.150.632.412.333.348.3
0.5030.650.031.911.232.647.8
0.6529.949.131.310.132.147.4
+ +Table 7. Results of different classification score threshold $\tau_{cls}$ . The mask IoU threshold $\tau_{iou}$ is set to 0.3. + +
τiouAPAP0.5AP0.75APSAPMAPL
0.331.150.632.412.333.348.3
0.530.850.331.912.032.947.9
0.730.650.031.211.632.347.1
+ +Table 8. Results of different mask IoU threshold ${\tau }_{iou}$ . The classification score threshold ${\tau }_{cls}$ is set to 0.35 . + +
RatioAPAP0.5AP0.75APSAPMAPL
1:129.047.731.011.031.645.5
1:230.148.832.211.532.447.1
1:331.150.632.412.333.348.3
1:431.350.932.612.433.548.7
+ +Table 9. Different ratio of labeled images and unlabeled images in a batch. The performance saturates when the ratio of labeled and unlabeled images is set to 1:4. + +to select good pseudo-labels for training. + +Hyper-parameters in DALoss. We investigated the effect of hyper-parameters, $\alpha$ and $\beta$ , used in DALoss. To give equal weight to both classification and segmentation, we set $\alpha = \beta$ . The results are shown in Tab. 6, indicating that larger values of $\alpha$ and $\beta$ lead to better performance. We + +![](images/a53b4672b3db38fa7af71eb47f2d0910516b31d42a65a4b52663254fc18d29ce.jpg) +Figure 5. Visualization of the predictions from different models. From the examples, we can clearly show the benefits introduced by pixel-level information from PAIS and DALoss. + +![](images/b2190e881133f61f417536d01e78914f9ceb9369d54711811a17bd6806c86150.jpg) + +![](images/93b24cc5c1a7dc367c7d27575b6afbb70f17639f86ba82cf023260cb9319327e.jpg) +Figure 6. Influence of imbalanced classes to semi-supervised training. The models are trained under $10\%$ labeled images for the results. We randomly sampled 10k images from the rest of COCO train2017 to draw these figures. As the training progresses, the predictions from the teacher model are gradually fitted to the distribution of the number of labels. + +![](images/80aa0ab8bd1a0a31e69976c013d9d9a1c2a9a9a0d90e1b25124ced40d262d486.jpg) + +![](images/dc028c8877d4d5bb16d95071f9737cf56410e50a00acdf1b70f60c25c6222aec.jpg) + +![](images/4eca97750f8f0fec46d87206b6eb23ecb923304a2fbbadcdd5a92b7d22ea8d0e.jpg) + +also analyzed the functions of different hyper-parameters used to adjust the input score, as shown in Fig. 3. The figures illustrate that increasing the hyper-parameter enlarges the difference between high- and low-quality masks or classes, adjusting the input score more appropriately based on their quality. However, when the hyper-parameter is set too large, the low-quality masks or classes are significantly constrained, potentially affecting the generalization of the model as noise is removed entirely during training. + +Model convergence speed. In Fig. 4, we analyze the convergence speed of the models. The results demonstrate that DALoss can expedite the model training in terms of convergence rate. For instance, Mask-RCNN (PAIS) achieves a convergence speed that is approximately 2 times faster than that of Mask-RCNN (PAIS w/o DALoss). Moreover, by comparing the results between Mask-RCNN + +(PAIS) and K-Net (PAIS), we observe that DALoss may be particularly effective for box-dependent instance segmentation frameworks, which facilitates rapid convergence. + +Different thresholds for classification scores and mask IoUs. We observed from Tab. 7 and Tab. 8 that increasing the thresholds for classification score and mask IoU leads to a decrease in performance. This suggests that DALoss is able to make use of misaligned pseudo-labels instead of simply filtering them out. By allowing the model to learn from these potentially noisy labels, it is able to better handle situations where the alignment between labeled and unlabeled data is not perfect. This may result in improved generalization to new, unseen data, as the model has learned to adapt to the presence of noisy labels. + +Different ratios of labeled and unlabeled images per batch. Tab. 9 shows that increasing the ratio of unlabeled + +
τcls, τiou0.35, 0.30.50, 0.30.65, 0.30.35, 0.50.35, 0.7
w/o DALoss29.329.025.329.329.0
w/ DALoss31.130.629.930.830.6
+ +Table 10. DALoss w.r.t. thresholds tuning. DALoss consistently outperforms threshold tuning in all settings. + +
Method1%5%10%100%
K-Net, supervise11.622.326.538.4
EMA w/o DALoss17.8(+6.2)25.4(+3.1)29.3(+2.8)39.4(+1.0)
EMA w/ DALoss19.8(+8.2)27.5(+5.2)31.0(+4.5)40.8(+2.4)
Performance gain+2.0+2.1+1.7+1.4
M-RCNN, supervise11.522.427.137.5
EMA w/o DALoss20.1(+8.6)27.4(+5.0)29.8(+2.7)38.4(+0.9)
EMA w/ DALoss21.1(+9.6)29.3(+6.9)31.0(+3.9)39.5(+2.0)
Performance gain+1.0+1.9+1.2+1.1
+ +Table 11. Comparison of EMA with DALoss. The performance improvements are not mainly attributed to EMA. + +images in a batch can improve the model's performance. The results indicate that performance saturates when the ratio is set to 1:4, suggesting that adding too many unlabeled images may lead to diminishing returns. + +Visualizations. We visualize the outputs of different models, including K-Net (supervised), K-Net (PAIS w/o DALoss), K-Net (PAIS), Mask-RCNN (supervised), Mask-RCNN (PAIS w/o DALoss), and Mask-RCNN (PAIS), in Fig. 5. The results show that: (1) PAIS can improve the recall for most instances in the supervised model, but the quality of the predictions is not guaranteed. (2) The use of DALoss in PAIS helps to improve the quality of predictions in terms of mask and classification. + +Influence of imbalanced classes. In Fig. 6, we investigate the effect of imbalanced classes on PAIS. We plot the number of labels obtained from the ground truth and the teacher models for Mask-RCNN and K-Net with PAIS at different iterations, namely $32\mathrm{k}$ , $64\mathrm{k}$ , $120\mathrm{k}$ , and $180\mathrm{k}$ . The results indicate that the predicted pseudo-labels gradually conform to the distribution of the imbalanced labels. + +# 5. Discussion + +DALoss w.r.t. Thresholds Tuning. As shown in Tab. 10, we conduct an ablation study by removing DALoss from our method in Tabs. 7 and 8. The results show that DALoss consistently outperforms threshold tuning in all settings, which validates that DALoss is indeed more effective than tuning the thresholds. + +Comparison of EMA with DALoss. We show that the performance improvements are not mainly attributed to EMA. First, we summarize the results of Tabs. 3 and 4 in Tab. 11. We can find that DALoss achieves a larger performance gain than EMA in $100\%$ COCO $(+1.4, +1.1$ vs. $+1.0, +0.9)$ . Second, EMA alone cannot selectively utilize noisy pseudo-labels for better learning. DALoss solves this + +problem and leads to further improvement over EMA. + +Discussion on Score Filtering. We have carefully chosen the values of $\tau_{cls},\tau_{iou}$ , based on Fig. 1(c)(d), which illustrates that decreasing the thresholds will generate more noisy but informative pseudo-labels. Therefore, we use low thresholds to obtain such pseudo-labels, which is different from previous methods that need to adjust thresholds to filter them out. This simplifies the tuning of the thresholds. We believe that the experiments in Tabs. 7, 8, and 10 are sufficient to show that lower thresholds are suitable for DALoss. + +Generality to Other Segmentation Tasks. DALoss can be applied to other semi-supervised segmentation tasks, as the noisy pseudo-labels are common in semi-supervised setting. To show the generality, we apply DALoss to panoptic segmentation, which is a more challenging task that requires both instance and semantic segmentation. We report a preliminary result under $10\%$ COCO. The initial result shows that DALoss can improve the PQ performance from $36.8\%$ PAIS w/o DALoss to $37.3\%$ PAIS w/ DALoss. We remain more experiments in our future work. + +Discussion on Large Segment Everything Models. We envision that the future of image segmentation will not only aim to segment everything, but also to provide fine-grained text descriptions for the segmented regions. However, the recently proposed models such as SAM [19] and SEEM [55] either lack labeled semantic information or demand large amounts of labeled semantic data for training. Therefore, we believe that semi-supervised learning will be a crucial solution to leverage abundant unlabeled data and reduce the labeling burden. + +# 6. Conclusion + +In this paper, we presented a novel PAIS framework for semi-supervised instance segmentation. To address the misalignment between classification score and mask quality, we introduced a dynamic aligning loss (DALoss), which aligns the classification loss term and the segmentation loss term based on the quality of different pseudo-labels. Our experimental results demonstrate the effectiveness of the proposed PAIS framework. Specifically, when the amount of labeled data is extremely limited, our pipeline equipped with PAIS and DALoss achieves superior performance for instance segmentation. We believe that PAIS can serve as a strong baseline for future research on semi-supervised instance segmentation. We hope our work can inspire further exploration in this exciting research direction. + +Acknowledgements. This work was supported by National Key R&D Program of China (2022ZD0118202), National Science Fund for Distinguished Young Scholars (No.62025603), National Natural Science Foundation of China (No.U21B2037, No.U22B2051, No.62176222, No.62176223, No.62176226, No.62072386, No.62072387, No.62072389, No.62002305 and No.62272401), and Natural Science Foundation of Fujian Province of China (No.2021J01002, No.2022J06001). + +# References + +[1] Philip Bachman, Ouais Alsharif, and Doina Precup. Learning with pseudo-ensembles. Advances in Neural Information Processing Systems, 2014. 2 +[2] David Berthelot, Nicholas Carlini, Ekin D Cubuk, Alex Kurakin, Kihyuk Sohn, Han Zhang, and Colin Raffel. Remix-match: Semi-supervised learning with distribution alignment and augmentation anchoring. In International Conference on Learning Representations, 2020. 2 +[3] Daniel Bolya, Chong Zhou, Fanyi Xiao, and Yong Jae Lee. Yolact: Real-time instance segmentation. 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Limited" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 241, + 192, + 254 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 241, + 192, + 254 + ], + "spans": [ + { + "bbox": [ + 143, + 241, + 192, + 254 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 266, + 290, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 290, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 290, + 518 + ], + "type": "text", + "content": "Pseudo-labeling is significant for semi-supervised instance segmentation, which generates instance masks and classes from unannotated images for subsequent training. However, in existing pipelines, pseudo-labels that contain valuable information may be directly filtered out due to mismatches in class and mask quality. To address this issue, we propose a novel framework, called pseudo-label aligning instance segmentation (PAIS), in this paper. In PAIS, we devise a dynamic aligning loss (DALoss) that adjusts the weights of semi-supervised loss terms with varying class and mask score pairs. Through extensive experiments conducted on the COCO and Cityscapes datasets, we demonstrate that PAIS is a promising framework for semi-supervised instance segmentation, particularly in cases where labeled data is severely limited. Notably, with just " + }, + { + "bbox": [ + 46, + 266, + 290, + 518 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 266, + 290, + 518 + ], + "type": "text", + "content": " labeled data, PAIS achieves 21.2 mAP (based on Mask-RCNN) and 19.9 mAP (based on K-Net) on the COCO dataset, outperforming the current state-of-the-art model, i.e., NoisyBoundary with 7.7 mAP, by a margin of over 12 points. Code is available at: https://github.com/hujiecpp/PAIS." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 541, + 128, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 541, + 128, + 553 + ], + "spans": [ + { + "bbox": [ + 47, + 541, + 128, + 553 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 562, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 562, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 562, + 287, + 693 + ], + "type": "text", + "content": "Semi-supervised instance segmentation aims to alleviate the significant burden of human labeling by utilizing a small amount of labeled data in conjunction with abundant unlabeled data [35, 47, 50]. Existing semi-supervised instance segmentation pipelines typically generate pseudolabels from unlabeled images, which are then used to train the models together with labeled images. Therefore, pseudo-labels play a crucial role in semi-supervised instance segmentation. The generation of pseudo-masks, pseudo-classes, and pseudo-boxes from unlabeled images improves the model training. However, current semi" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 242, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 242, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 306, + 242, + 545, + 338 + ], + "type": "text", + "content": "supervised instance segmentation frameworks do not fully leverage the potential of such pseudo-labels. Specifically, pseudo-labels with mismatched class and mask scores are often filtered out by fixed thresholds, leading to the exclusion of valuable information that could aid the model training. For instance, pseudo-labels with high-quality masks but low class scores would be filtered out by a class threshold, resulting in the loss of the pixel-level information." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 339, + 546, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 546, + 637 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 546, + 637 + ], + "type": "text", + "content": "In this paper, we present a new semi-supervised framework, termed pseudo-label aligning for instance segmentation (PAIS), aiming to improve the utilization of filtered pseudo-labels. As illustrated in Fig. 1, the main challenge of PAIS lies in the mismatched scores between pseudoclasses and pseudo-masks. The classification score and mask intersection over union (IoU) are misaligned in assessing the quality of pseudo-labels. As a result, masks with high IoUs would be filtered out due to low classification scores, and vice versa. In the mean time, lowering the threshold of both scores introduces incorrect classes or low-quality masks into the semi-supervised training. To overcome this dilemma, we propose a dynamic aligning loss (DALoss) that softly re-weights the classification and the segmentation losses based on the quality of different pseudo-labels. Specifically, DALoss penalizes low-score pseudo-labels rather than filtering them and promotes high-score ones, to adjust their contribution to the final loss function. Our experiments on the COCO and Cityscape datasets demonstrate the effectiveness of the proposed PAIS framework. Specifically, with only " + }, + { + "bbox": [ + 304, + 339, + 546, + 637 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 339, + 546, + 637 + ], + "type": "text", + "content": " labeled data, PAIS achieves " + }, + { + "bbox": [ + 304, + 339, + 546, + 637 + ], + "type": "inline_equation", + "content": "21.2\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 339, + 546, + 637 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 339, + 546, + 637 + ], + "type": "inline_equation", + "content": "19.9\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 339, + 546, + 637 + ], + "type": "text", + "content": " on the COCO dataset using Mask-RCNN [13] and K-Net [53], respectively. This outperforms the current state-of-the-art model, NoisyBoundary [47], by more than 12 points." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 638, + 517, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 638, + 517, + 649 + ], + "spans": [ + { + "bbox": [ + 317, + 638, + 517, + 649 + ], + "type": "text", + "content": "Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 654, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 654, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 654, + 547, + 713 + ], + "type": "text", + "content": "- We propose a novel pseudo-label aligning framework for semi-supervised instance segmentation, called PAIS, which unleashes the potential of utilizing pixel-level pseudo-labels in semi-supervised instance segmentation. Furthermore, to the best of our knowledge," + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 203, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 203, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 203, + 713 + ], + "type": "text", + "content": "*Corresponding author. † Equal contribution." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16337" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 175, + 166 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 175, + 166 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 175, + 166 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 175, + 166 + ], + "type": "image", + "image_path": "57279d70f6f037dbc92abada7946a2ba11569434ccb7fc015435590f03ebfa0c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 168, + 547, + 266 + ], + "lines": [ + { + "bbox": [ + 46, + 168, + 547, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 547, + 266 + ], + "type": "text", + "content": "Figure 1. Pseudo-label wasting in semi-supervised instance segmentation. To illustrate this issue, we employed the K-Net model [53] trained on " + }, + { + "bbox": [ + 46, + 168, + 547, + 266 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 168, + 547, + 266 + ], + "type": "text", + "content": " labeled images and randomly sampled 5k unlabeled images, from the COCO train2017 dataset, to plot the figures. In (a), we present the predicted classification score w.r.t. the ground truth mask intersection over union (IoU), revealing that the predicted classification score is inadequate in evaluating mask quality. In (b), we added a mask IoU prediction branch to the model and plotted the predicted mask IoU w.r.t. the ground truth mask IoU, demonstrating that the predicted mask IoU can represent the mask quality. However, as shown in (c), a significant number of pseudo-labels with high-quality masks, i.e., mask IoU " + }, + { + "bbox": [ + 46, + 168, + 547, + 266 + ], + "type": "inline_equation", + "content": ">0.7" + }, + { + "bbox": [ + 46, + 168, + 547, + 266 + ], + "type": "text", + "content": ", will be filtered out with high classification thresholds. Additionally, (d) shows that pseudo-labels with high-quality masks can also have correspondingly low classification scores. Therefore, the misalignment between the mask and class scores leads to a significant number of valuable pseudolabels being excluded during semi-supervised training." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 175, + 70, + 299, + 167 + ], + "blocks": [ + { + "bbox": [ + 175, + 70, + 299, + 167 + ], + "lines": [ + { + "bbox": [ + 175, + 70, + 299, + 167 + ], + "spans": [ + { + "bbox": [ + 175, + 70, + 299, + 167 + ], + "type": "image", + "image_path": "42a4e8b5f29d78ea0d22dd22a4db1e48cdb6bba23e30fbfd95ce52b4d602e21b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 299, + 70, + 420, + 167 + ], + "blocks": [ + { + "bbox": [ + 299, + 70, + 420, + 167 + ], + "lines": [ + { + "bbox": [ + 299, + 70, + 420, + 167 + ], + "spans": [ + { + "bbox": [ + 299, + 70, + 420, + 167 + ], + "type": "image", + "image_path": "3c10d05e561321ec21bee95d6cabffe3c5500fa95b6f02b55840e7bc9085e569.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 421, + 71, + 542, + 167 + ], + "blocks": [ + { + "bbox": [ + 421, + 71, + 542, + 167 + ], + "lines": [ + { + "bbox": [ + 421, + 71, + 542, + 167 + ], + "spans": [ + { + "bbox": [ + 421, + 71, + 542, + 167 + ], + "type": "image", + "image_path": "ae4734b7932dd715437e5be9a7f5245d76e3c6468b822cc041dfb850b012f2bb.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 66, + 287, + 286, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 287, + 286, + 310 + ], + "spans": [ + { + "bbox": [ + 66, + 287, + 286, + 310 + ], + "type": "text", + "content": "PAIS is the first framework that can be adapted to box-free instance segmentation models." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 316, + 286, + 478 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 59, + 316, + 286, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 316, + 286, + 388 + ], + "spans": [ + { + "bbox": [ + 59, + 316, + 286, + 388 + ], + "type": "text", + "content": "- We introduce a new loss function, named dynamic aligning loss (DALoss), which incorporates pseudolabels with diverse class and mask qualities into the semi-supervised training process. DALoss consistently enhances the performance of box-free and box-dependent instance segmentation frameworks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 59, + 394, + 286, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 394, + 286, + 478 + ], + "spans": [ + { + "bbox": [ + 59, + 394, + 286, + 478 + ], + "type": "text", + "content": "- We conduct comprehensive experiments on the COCO and Cityscapes datasets to evaluate PAIS. In particular, PAIS achieves state-of-the-art results on the COCO dataset, i.e., 19.9, 27.6, and " + }, + { + "bbox": [ + 59, + 394, + 286, + 478 + ], + "type": "inline_equation", + "content": "31.1\\mathrm{mAP}" + }, + { + "bbox": [ + 59, + 394, + 286, + 478 + ], + "type": "text", + "content": " for the box-free pipeline K-Net [53], and 21.2, 29.3, and " + }, + { + "bbox": [ + 59, + 394, + 286, + 478 + ], + "type": "inline_equation", + "content": "31.1\\mathrm{mAP}" + }, + { + "bbox": [ + 59, + 394, + 286, + 478 + ], + "type": "text", + "content": " for the box-dependent pipeline Mask-RCNN [13], with " + }, + { + "bbox": [ + 59, + 394, + 286, + 478 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 59, + 394, + 286, + 478 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 59, + 394, + 286, + 478 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 59, + 394, + 286, + 478 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 59, + 394, + 286, + 478 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 59, + 394, + 286, + 478 + ], + "type": "text", + "content": " labeled data, respectively." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 501, + 134, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 501, + 134, + 513 + ], + "spans": [ + { + "bbox": [ + 47, + 501, + 134, + 513 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 521, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 713 + ], + "type": "text", + "content": "Semi-supervised Image Classification. In image classification, semi-supervised learning has been extensively explored, and the methods can be classified into two categories: pseudo-label-based and consistency-regularization-based methods. Specifically, pseudo-label-based methods [40, 21] leverage pre-trained models to generate annotations for the unlabeled images to train the model. In contrast, consistency-regularization-based methods [1, 36, 20, 39, 48, 2, 7, 32, 31, 23] incorporate various data augmentation techniques such as random regularization [10] and adversarial perturbation [33] to generate different inputs for one image and enforce consistency between these inputs during training. FixMatch [41] combines the consistency-regularization-based techniques with a pseudo-label-based framework by applying a strong-weak data augmentation pipeline to input images and enforcing consistency between" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 287, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 287, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 287, + 545, + 323 + ], + "type": "text", + "content": "the augmented images. In this work, we follow the pseudolabel-based methods and also use strong-weak data augmentation during training in PAIS." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 326, + 546, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 326, + 546, + 542 + ], + "spans": [ + { + "bbox": [ + 304, + 326, + 546, + 542 + ], + "type": "text", + "content": "Semi-supervised Object Detection. From the very beginning, STAC [42] proposed the use of pseudo-labels and consistency training for semi-supervised object detection. However, the effectiveness of the method was limited by the two-stage training pipeline similar to that of Noisy Student [49], where the pseudo-labels were generated from pre-trained models and were not updated along with the model training. After STAC, several studies [50, 54, 43, 51, 28] incorporated the idea of exponential moving average (EMA) from MeanTeacher [44]. The teacher model and pseudo-labels are updated after each training iteration to generate instant pseudo-labels, making the entire pipeline end-to-end trainable. Additionally, Unbiased Teacher [28] utilized Focal loss [24] instead of traditional cross-entropy loss to alleviate the problem of unbalanced pseudo-labels. In this paper, we also follow the idea of incorporating EMA into the proposed PAIS framework, with a focus on integrating pixel-level annotations into the training process." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": "Fully-supervised Instance Segmentation. Instance segmentation aims to provide pixel-level predictions for each object instance in an image. Existing methods can be classified into three categories: top-down (or box-dependent) methods, bottom-up methods, and direct segmentation (or box-free) methods. Top-down methods [15, 27, 38, 37, 29] such as Mask R-CNN [13], YOLACT [3], and CenterMask [22] generate bounding boxes first and then segment the objects within the boxes. Bottom-up methods [52, 8, 26, 11, 16], regard instance segmentation as a label-then-cluster problem, which classify each pixel first and then group the pixels into an arbitrary number of object instances. Direct segmentation or box-free methods such as SOLO [45, 46], K-Net [53], MaskFormer [5, 4] and" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16338" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 390, + 232 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 390, + 232 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 390, + 232 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 390, + 232 + ], + "type": "image", + "image_path": "3b9d6905c6b74d715ed2754589e2d829608658ee580747da9a65ecee6404d16a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 233, + 545, + 310 + ], + "lines": [ + { + "bbox": [ + 46, + 233, + 545, + 310 + ], + "spans": [ + { + "bbox": [ + 46, + 233, + 545, + 310 + ], + "type": "text", + "content": "Figure 2. Framework of pseudo-label aligning for semi-supervised instance segmentation (PAIS). The focus of PAIS is to explore the utility of pixel-level pseudo-labels for instance segmentation. To this end, we propose a novel approach called dynamic aligning loss (DALoss), which enables the incorporation of pseudo-labels with varying quality during training. This is particularly significant when the number of labeled images is limited. With DALoss, a significant number of predictions from the teacher model can be leveraged in the semi-supervised training process, rather than being discarded. Specifically, we consider three types of pseudo-masks with varying quality: (a) pseudo-masks with incorrect classes but high-quality masks, i.e., low classification scores but high mask IoUs; (b) pseudo-masks with accurate classes but low-quality masks, i.e., high classification scores but low mask IoUs; and (c) pseudo-masks with medium qualities." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 402, + 72, + 468, + 137 + ], + "blocks": [ + { + "bbox": [ + 402, + 72, + 468, + 137 + ], + "lines": [ + { + "bbox": [ + 402, + 72, + 468, + 137 + ], + "spans": [ + { + "bbox": [ + 402, + 72, + 468, + 137 + ], + "type": "image", + "image_path": "694187f758c656bdb92868e2fef6222eb5cba33765bd5a524c96798479b56dca.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 406, + 138, + 463, + 149 + ], + "lines": [ + { + "bbox": [ + 406, + 138, + 463, + 149 + ], + "spans": [ + { + "bbox": [ + 406, + 138, + 463, + 149 + ], + "type": "text", + "content": "(a) Score↓, IoU↑" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 403, + 150, + 467, + 213 + ], + "blocks": [ + { + "bbox": [ + 403, + 150, + 467, + 213 + ], + "lines": [ + { + "bbox": [ + 403, + 150, + 467, + 213 + ], + "spans": [ + { + "bbox": [ + 403, + 150, + 467, + 213 + ], + "type": "image", + "image_path": "c825972816ff2779d7824731dd640c7d705401762cd99bd8cb2dd2fd0d4b25ec.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 408, + 215, + 462, + 224 + ], + "lines": [ + { + "bbox": [ + 408, + 215, + 462, + 224 + ], + "spans": [ + { + "bbox": [ + 408, + 215, + 462, + 224 + ], + "type": "text", + "content": "(c) Score-, IoU-" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 474, + 72, + 539, + 137 + ], + "blocks": [ + { + "bbox": [ + 474, + 72, + 539, + 137 + ], + "lines": [ + { + "bbox": [ + 474, + 72, + 539, + 137 + ], + "spans": [ + { + "bbox": [ + 474, + 72, + 539, + 137 + ], + "type": "image", + "image_path": "ae1d9651c84de716480e1f4dc2c927d6bb64d321da5b7571aa8dba9357e3d08f.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 477, + 139, + 534, + 150 + ], + "lines": [ + { + "bbox": [ + 477, + 139, + 534, + 150 + ], + "spans": [ + { + "bbox": [ + 477, + 139, + 534, + 150 + ], + "type": "text", + "content": "(b) Score↑, IoU↓" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 474, + 152, + 539, + 213 + ], + "blocks": [ + { + "bbox": [ + 474, + 152, + 539, + 213 + ], + "lines": [ + { + "bbox": [ + 474, + 152, + 539, + 213 + ], + "spans": [ + { + "bbox": [ + 474, + 152, + 539, + 213 + ], + "type": "image", + "image_path": "cd661cf983cb9e65df58db3acbe7f975396705014ca95dcbe4c289507a09f045.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 477, + 215, + 534, + 225 + ], + "lines": [ + { + "bbox": [ + 477, + 215, + 534, + 225 + ], + "spans": [ + { + "bbox": [ + 477, + 215, + 534, + 225 + ], + "type": "text", + "content": "(d) Score↑, IoU↑" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 330, + 286, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 330, + 286, + 402 + ], + "spans": [ + { + "bbox": [ + 46, + 330, + 286, + 402 + ], + "type": "text", + "content": "SOTR [12] deal with instance segmentation without bounding box detection. Any of the aforementioned instance segmentation methods can be implemented into PAIS, and in this work, we present two examples, one from the box-dependent category, Mask R-CNN, and another from the box-free category, K-Net." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 402, + 286, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 286, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 286, + 605 + ], + "type": "text", + "content": "Semi-supervised Instance Segmentation. Semi-supervised instance segmentation is commonly considered to be a sub-task of semi-supervised object detection [50, 28]. Consequently, existing frameworks rely heavily on bounding boxes, in which segmentation performance is strongly dependent on detection performance. Among them, NoisyBoundary [47] was the first to formally propose the semi-supervised instance segmentation task. Recent efforts have been made to construct box-free pipelines for fully-supervised instance segmentation [45, 46, 53, 5]. In this paper, we investigate PAIS in both box-free and box-dependent instance segmentation, revealing the potential of fully utilizing pixel-level annotations. In contrast to the recently-proposed PoliteTeacher [9], which filters out pseudo-labels with low confidence, the proposed PAIS leverages them. It is a novel and effective way of utilizing noisy pseudo-labels for semi-supervised learning." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 616, + 102, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 616, + 102, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 616, + 102, + 628 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 635, + 153, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 153, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 153, + 647 + ], + "type": "text", + "content": "3.1. Task Formulation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "content": "The goal of PAIS is to better leverage unlabeled images with a limited number of pixel-labeled images to boost the performance of semi-supervised instance segmentation. The PAIS framework consists of three key steps: (1) pseudo-label generation, (2) dynamic pseudo" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 330, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 330, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 330, + 545, + 510 + ], + "type": "text", + "content": "label alignment, and (3) end-to-end model training. In the pseudo-label generation step, we introduce a mask scoring branch [17] that predicts mask IoUs as an additional metric along with classification scores to assess the quality of pseudo-labels. In the dynamic aligning step, we re-weight the loss terms based on the quality of different pseudolabels. Finally, the teacher and student models are trained using exponential moving average (EMA) [44]. The overall framework of PAIS is illustrated in Fig. 2, and we introduce the key steps in detail as follows. It is important to note that the PAIS framework can be applied to any box-dependent or box-free framework for enhanced exploitation of pseudo-labels in semi-supervised instance segmentation. We instantiate two examples by Mask-RCNN [13] and K-Net [53] in this paper, but do not restrict to them." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 515, + 448, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 448, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 448, + 528 + ], + "type": "text", + "content": "3.2. Pseudo Label Generation" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 534, + 545, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 630 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 630 + ], + "type": "text", + "content": "In the pseudo-label generation, we apply weak data augmentation to the unlabeled images and input them into a teacher model. The weak data augmentation includes scaling, horizontal flipping, and other augmentation operations that do not alter the image's content. The teacher model produces a set of pseudo-labels, including masks, boxes, and classification scores for each input image. In box-free pipelines, the box predictions are optional." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "As depicted in Fig. 1(a)(c), using the classification score alone is inadequate to measure the quality of predicted masks. To address this, we incorporate a mask scoring branch into the pipeline to predict mask Intersection over Union (IoU) for evaluating mask quality. As shown in Fig. 1(b), the predicted mask IoUs can be used to measure mask quality effectively, which has also been verified" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16339" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 72, + 201, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 72, + 201, + 83 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 201, + 83 + ], + "type": "text", + "content": "Algorithm 1 Pseudo-label Alignment" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 58, + 86, + 286, + 242 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 59, + 86, + 260, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 86, + 260, + 97 + ], + "spans": [ + { + "bbox": [ + 59, + 86, + 260, + 97 + ], + "type": "text", + "content": "1: Initialize teacher and student models randomly." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 99, + 101, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 99, + 101, + 109 + ], + "spans": [ + { + "bbox": [ + 59, + 99, + 101, + 109 + ], + "type": "text", + "content": "2:Repeat" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 110, + 270, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 110, + 270, + 121 + ], + "spans": [ + { + "bbox": [ + 59, + 110, + 270, + 121 + ], + "type": "text", + "content": "3: Apply weak augmentation to unlabeled images." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 121, + 286, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 121, + 286, + 145 + ], + "spans": [ + { + "bbox": [ + 58, + 121, + 286, + 145 + ], + "type": "text", + "content": "4: Obtain pseudo-labels " + }, + { + "bbox": [ + 58, + 121, + 286, + 145 + ], + "type": "inline_equation", + "content": "\\{\\pmb{m}_i, \\pmb{b}_i, \\pmb{c}_i, s_i | i = 1, \\dots, N\\}" + }, + { + "bbox": [ + 58, + 121, + 286, + 145 + ], + "type": "text", + "content": " from teacher model via thresholds " + }, + { + "bbox": [ + 58, + 121, + 286, + 145 + ], + "type": "inline_equation", + "content": "\\tau_{cls}, \\tau_{iou}" + }, + { + "bbox": [ + 58, + 121, + 286, + 145 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 146, + 274, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 146, + 274, + 157 + ], + "spans": [ + { + "bbox": [ + 58, + 146, + 274, + 157 + ], + "type": "text", + "content": "5: Apply strong augmentation to unlabeled images." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 159, + 274, + 170 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 159, + 274, + 170 + ], + "spans": [ + { + "bbox": [ + 58, + 159, + 274, + 170 + ], + "type": "text", + "content": "6: Obtain predictions " + }, + { + "bbox": [ + 58, + 159, + 274, + 170 + ], + "type": "inline_equation", + "content": "\\widetilde{m}, b, \\widetilde{c}" + }, + { + "bbox": [ + 58, + 159, + 274, + 170 + ], + "type": "text", + "content": " for unlabeled images." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 171, + 260, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 171, + 260, + 182 + ], + "spans": [ + { + "bbox": [ + 58, + 171, + 260, + 182 + ], + "type": "text", + "content": "7: Calculate " + }, + { + "bbox": [ + 58, + 171, + 260, + 182 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_u" + }, + { + "bbox": [ + 58, + 171, + 260, + 182 + ], + "type": "text", + "content": " for unlabeled images by Eq. 5." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 58, + 182, + 257, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 182, + 257, + 194 + ], + "spans": [ + { + "bbox": [ + 58, + 182, + 257, + 194 + ], + "type": "text", + "content": "8: Inference labeled images by student model." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 58, + 194, + 211, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 194, + 211, + 205 + ], + "spans": [ + { + "bbox": [ + 58, + 194, + 211, + 205 + ], + "type": "text", + "content": "9: Calculate " + }, + { + "bbox": [ + 58, + 194, + 211, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_l" + }, + { + "bbox": [ + 58, + 194, + 211, + 205 + ], + "type": "text", + "content": " for labeled images." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 58, + 206, + 279, + 218 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 206, + 279, + 218 + ], + "spans": [ + { + "bbox": [ + 58, + 206, + 279, + 218 + ], + "type": "text", + "content": "10: Train student model with the loss " + }, + { + "bbox": [ + 58, + 206, + 279, + 218 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{semi}" + }, + { + "bbox": [ + 58, + 206, + 279, + 218 + ], + "type": "text", + "content": " in Eq. 1." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 58, + 219, + 212, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 219, + 212, + 229 + ], + "spans": [ + { + "bbox": [ + 58, + 219, + 212, + 229 + ], + "type": "text", + "content": "11: Update teacher model via EMA." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 58, + 230, + 172, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 230, + 172, + 242 + ], + "spans": [ + { + "bbox": [ + 58, + 230, + 172, + 242 + ], + "type": "text", + "content": "12: Until scheduled epochs." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "text", + "content": "in MS-RCNN [17]. After generating pseudo-labels in the previous step, the predictions are filtered using two thresholds: a classification threshold " + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "inline_equation", + "content": "\\tau_{cls}" + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "text", + "content": " and a mask IoU threshold " + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "inline_equation", + "content": "\\tau_{iou}" + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "text", + "content": ". The resulting set of pseudo-labels includes " + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "text", + "content": " elements, each containing a mask " + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "inline_equation", + "content": "m_i \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "text", + "content": ", a bounding box " + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "inline_equation", + "content": "b_i \\in \\mathbb{R}^4" + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "text", + "content": ", a classification score " + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "inline_equation", + "content": "c_i \\in \\mathbb{R}^L" + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "text", + "content": " (with an additional background category), and a mask IoU score " + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "inline_equation", + "content": "s_i \\in \\mathbb{R}" + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "text", + "content": ". Note that " + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "inline_equation", + "content": "H, W" + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "text", + "content": " denote the mask resolution, and " + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 269, + 287, + 376 + ], + "type": "text", + "content": " is the number of classes." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 388, + 178, + 401 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 388, + 178, + 401 + ], + "spans": [ + { + "bbox": [ + 47, + 388, + 178, + 401 + ], + "type": "text", + "content": "3.3. Dynamic Aligning Loss" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 408, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 408, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 408, + 287, + 552 + ], + "type": "text", + "content": "Although good pseudo-labels can be obtained by setting high thresholds for classification scores and mask IoUs, a large number of predictions with misaligned mask and classification qualities are discarded (as illustrated in Fig.1(c)(d)). These misaligned predictions can be useful since the amount of labeled data is limited in the semi-supervised setting. Fig.2 shows examples of pseudo-labels that can be included in the training process. If the misaligned pseudo-labels are directly used in semi-supervised learning, the incorrect predictions on classes or masks can introduce significant noise. To reduce the noise, we propose a dynamic aligning loss (DALoss)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 553, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 553, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 553, + 287, + 590 + ], + "type": "text", + "content": "Vanilla Loss for PAIS. In semi-supervised instance segmentation, the loss function can be decomposed into two terms for labeled and unlabeled images, as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 118, + 603, + 287, + 616 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 603, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 118, + 603, + 287, + 616 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s e m i}} = \\lambda_ {l} \\mathcal {L} _ {l} + \\lambda_ {u} \\mathcal {L} _ {u}, \\tag {1}", + "image_path": "feb8c4c39dfca893c31f12919b24536bc69e100f9b89ee44fd2984d12b09d69d.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{l}" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{u}" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " are the hyper-parameters for balancing the loss terms. The loss for labeled images can be defined using the functions commonly employed in instance segmentation, augmented with an additional binary cross-entropy term for regressing mask IoUs. Given the pseudo-labels from the teacher model and the predictions from the student model, we formulate the loss for unlabeled images as:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 316, + 90, + 545, + 176 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 90, + 545, + 176 + ], + "spans": [ + { + "bbox": [ + 316, + 90, + 545, + 176 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {u} = \\frac {1}{N _ {p o s}} \\sum_ {i = 1} ^ {N _ {p o s}} \\left(\\lambda_ {b} \\mathcal {L} _ {b} \\left(\\widetilde {\\boldsymbol {b}} _ {\\nu (i)}, \\boldsymbol {b} _ {\\mu (i)}\\right) \\right. \\\\ \\left. + \\lambda_ {c} \\mathcal {L} _ {c} \\left(\\widetilde {\\boldsymbol {c}} _ {\\nu (i)}, \\boldsymbol {c} _ {\\mu (i)} ^ {o}\\right) + \\lambda_ {m} \\mathcal {L} _ {m} \\left(\\widetilde {\\boldsymbol {m}} _ {\\nu (i)}, \\boldsymbol {m} _ {\\mu (i)} ^ {b}\\right)\\right) \\tag {2} \\\\ + \\frac {1}{N _ {n e g}} \\sum_ {i = 1} ^ {N _ {n e g}} \\left(\\lambda_ {c} \\mathcal {L} _ {c} (\\widetilde {\\boldsymbol {c}} _ {i}, \\boldsymbol {c} _ {n e g} ^ {o})\\right), \\\\ \\end{array}", + "image_path": "33234cab68aaa2cdd5bd4c90e247d565245b9401627df48cc716d90b7a80f0bf.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_b" + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "text", + "content": " includes the box IoU loss and the L1 loss, " + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_c" + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "text", + "content": " denotes the cross-entropy loss, " + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_m" + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "text", + "content": " is the dice loss. In Eq. 2, " + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\widetilde{c}_i,\\widetilde{b}_i,\\widetilde{m}_i" + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "text", + "content": " represent predictions from the student model. The pseudo-scores " + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "inline_equation", + "content": "c_{\\mu (i)}" + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "text", + "content": " for classification are converted to one-hot vectors " + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "inline_equation", + "content": "c_{\\mu (i)}^o" + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "text", + "content": " for the category with the highest score. The pseudo-masks " + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "inline_equation", + "content": "m_{\\mu (i)}" + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "text", + "content": " are activated by sigmoid function and discretized into binary value as " + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "inline_equation", + "content": "m_{\\mu (i)}^{b}" + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "text", + "content": ". The one-hot vector for the background class is denoted by " + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "inline_equation", + "content": "c_{neg}^o" + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "text", + "content": ". The label indexing functions, " + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\nu (i)" + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\mu (i)" + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "text", + "content": ", match predictions with pseudo-labels for training, which are defined in terms of different pseudo-label assigning strategies. In our implementations, the one-to-many assignment defines the label indexing functions " + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\nu (i) = i" + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\mu (i)" + }, + { + "bbox": [ + 304, + 182, + 545, + 340 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 366, + 346, + 545, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 346, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 366, + 346, + 545, + 369 + ], + "type": "interline_equation", + "content": "\\mu (i) = \\underset {t \\in [ 1, N ]} {\\arg \\min } \\left(\\mathcal {L} _ {b} \\left(\\widetilde {\\boldsymbol {b}} _ {i}, \\boldsymbol {b} _ {t}\\right)\\right). \\tag {3}", + "image_path": "e59a7aa78c0f0f4b9b328fa38be5c6f7c76df3c5c7bf72781eda6f0132db8a88.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 376, + 544, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 376, + 544, + 400 + ], + "spans": [ + { + "bbox": [ + 305, + 376, + 544, + 400 + ], + "type": "text", + "content": "Instead, the one-to-one assignment defines the label indicting functions " + }, + { + "bbox": [ + 305, + 376, + 544, + 400 + ], + "type": "inline_equation", + "content": "\\mu (i) = i" + }, + { + "bbox": [ + 305, + 376, + 544, + 400 + ], + "type": "text", + "content": ", and finds the optimal " + }, + { + "bbox": [ + 305, + 376, + 544, + 400 + ], + "type": "inline_equation", + "content": "\\nu^{*}(\\cdot)" + }, + { + "bbox": [ + 305, + 376, + 544, + 400 + ], + "type": "text", + "content": " via:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 312, + 407, + 545, + 456 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 407, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 312, + 407, + 545, + 456 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\nu^ {*} = \\arg \\min _ {\\nu} \\sum_ {i = 1} ^ {t} \\left(\\lambda_ {b} \\mathcal {L} _ {b} \\left(\\widetilde {\\boldsymbol {b}} _ {\\nu (i)}, \\boldsymbol {b} _ {i}\\right) + \\lambda_ {c} \\mathcal {L} _ {c} \\left(\\widetilde {\\boldsymbol {c}} _ {\\nu (i)}, \\boldsymbol {c} _ {i} ^ {o}\\right) \\right. \\tag {4} \\\\ + \\lambda_ {m} \\mathcal {L} _ {m} (\\widetilde {\\boldsymbol {m}} _ {\\nu (i)}, \\boldsymbol {m} _ {i} ^ {b}) - s _ {i}). \\\\ \\end{array}", + "image_path": "ad6a50a6b236cc2b24f4571a8caecc62c7ec6f01b681616bcd276d45d19f8e5b.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 461, + 544, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 461, + 544, + 485 + ], + "spans": [ + { + "bbox": [ + 305, + 461, + 544, + 485 + ], + "type": "text", + "content": "Note that the loss terms for regressing boxes are optional in box-free instance segmentation frameworks." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 486, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 569 + ], + "type": "text", + "content": "Dynamic Aligning Loss for PAIS. To optimize the model using pixel-level pseudo-labels, we propose to replace Eq. 2 with DALoss. Since the teacher model provides ideal metrics for measuring the quality of classification scores and mask IoUs, we propose to adjust the weight of loss terms based on the quality of the pseudo-labels. This is achieved by using the following equation:" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 312, + 576, + 545, + 680 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 576, + 545, + 680 + ], + "spans": [ + { + "bbox": [ + 312, + 576, + 545, + 680 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {u} ^ {D A} = \\frac {1}{N _ {p o s}} \\sum_ {i = 1} ^ {N _ {p o s}} \\left(\\lambda_ {b} \\mathcal {L} _ {b} (\\widetilde {\\boldsymbol {b}} _ {\\nu (i)}, \\boldsymbol {b} _ {\\mu (i)}) \\right. \\\\ + \\lambda_ {c} \\left(c _ {\\mu (i)} ^ {h}\\right) ^ {\\alpha} \\mathcal {L} _ {c} \\left(\\widetilde {c} _ {\\nu (i)}, c _ {\\mu (i)} ^ {o}\\right) \\tag {5} \\\\ \\left. + \\lambda_ {m} \\left(s _ {\\mu (i)}\\right) ^ {\\beta} \\mathcal {L} _ {m} \\left(\\widetilde {\\boldsymbol {m}} _ {\\nu (i)}, \\boldsymbol {m} _ {\\mu (i)} ^ {b}\\right)\\right) \\\\ + \\frac {1}{N _ {n e g}} \\sum_ {i = 1} ^ {N _ {n e g}} \\left(\\lambda_ {c} \\mathcal {L} _ {c} (\\widetilde {\\boldsymbol {c}} _ {i}, \\boldsymbol {c} _ {n e g} ^ {o})\\right), \\\\ \\end{array}", + "image_path": "2e6aa156063f6d04082f66a62d5d3b579c04ee7375964932e275b8a8835eda18.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 687, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 687, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 687, + 545, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 687, + 545, + 715 + ], + "type": "inline_equation", + "content": "c_{\\mu(i)}^{h}" + }, + { + "bbox": [ + 306, + 687, + 545, + 715 + ], + "type": "text", + "content": " denotes the highest classification score, and " + }, + { + "bbox": [ + 306, + 687, + 545, + 715 + ], + "type": "inline_equation", + "content": "s_{\\mu(i)}" + }, + { + "bbox": [ + 306, + 687, + 545, + 715 + ], + "type": "text", + "content": " denotes the mask IoU from the " + }, + { + "bbox": [ + 306, + 687, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mu(i)" + }, + { + "bbox": [ + 306, + 687, + 545, + 715 + ], + "type": "text", + "content": "-th pseudo-label," + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16340" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 71, + 283, + 138 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 283, + 138 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 283, + 138 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 283, + 138 + ], + "type": "table", + "html": "
Method1%5%10%100%
Mask-RCNN [13], supervised*3.517.322.034.5
Mask-RCNN† [13], supervised*3.517.421.937.1
DD [35]3.820.424.235.7
Noisy Boundaries [47]7.724.929.238.6
PAIS, on Mask-RCNN, ours21.229.331.139.5
", + "image_path": "398f99a62d9590fdc07e504547e594352a5fea951836070cf16989cee996e4b9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 196, + 283, + 317 + ], + "blocks": [ + { + "bbox": [ + 47, + 141, + 286, + 185 + ], + "lines": [ + { + "bbox": [ + 47, + 141, + 286, + 185 + ], + "spans": [ + { + "bbox": [ + 47, + 141, + 286, + 185 + ], + "type": "text", + "content": "Table 1. Comparison to state-of-the-art semi-supervised instance segmentation methods on the COCO val2017.† denotes using the same data augmentation as semi-supervised training. * denotes data from NoisyBoundary [47]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 196, + 283, + 317 + ], + "lines": [ + { + "bbox": [ + 48, + 196, + 283, + 317 + ], + "spans": [ + { + "bbox": [ + 48, + 196, + 283, + 317 + ], + "type": "table", + "html": "
Method5%10%20%30%
Mask-RCNN [13], supervised*11.816.822.326.3
Mask-RCNN† [13], supervised*11.316.422.626.6
DD [35]13.719.224.627.4
STAC [42]11.918.222.929.0
CSD [18]14.117.924.627.5
CCT [34]15.218.624.726.5
Dual-branch [30]13.918.924.028.9
Ubteacher [28]16.020.027.128.0
Noisy Boundaries [47]17.122.129.032.4
PAIS, on Mask-RCNN, ours18.022.929.232.8
", + "image_path": "89f3c34337ad2be00ad3959a5763925f9589869cfa1bb595c51f76506c9ba453.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 320, + 286, + 365 + ], + "lines": [ + { + "bbox": [ + 47, + 320, + 286, + 365 + ], + "spans": [ + { + "bbox": [ + 47, + 320, + 286, + 365 + ], + "type": "text", + "content": "Table 2. Comparison to state-of-the-art semi-supervised instance segmentation methods on the Cityscapes validation set. " + }, + { + "bbox": [ + 47, + 320, + 286, + 365 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 47, + 320, + 286, + 365 + ], + "type": "text", + "content": " denotes using the same data augmentation as semi-supervised training. \\* denotes data from NoisyBoundary [47]." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 385, + 286, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 385, + 286, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 385, + 286, + 456 + ], + "type": "inline_equation", + "content": "\\alpha, \\beta" + }, + { + "bbox": [ + 46, + 385, + 286, + 456 + ], + "type": "text", + "content": " are the hyper-parameters. Specifically, Eq. 5 adjusts the weights for the pseudo-labels conditioned on their qualities, i.e., dynamically dependent on the input images. For instance, for a pseudo-label with a low classification score and high mask IoU, DALoss encourages the segmentation loss while constraining the classification loss." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 465, + 201, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 465, + 201, + 478 + ], + "spans": [ + { + "bbox": [ + 47, + 465, + 201, + 478 + ], + "type": "text", + "content": "3.4. End-to-End Model Training" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 483, + 286, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 286, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 286, + 567 + ], + "type": "text", + "content": "Inspired by [44], we employ EMA with the strong-weak data augmentation for PAIS. Specifically, unlabeled images undergo both strong and weak data augmentations and are then fed into the student and teacher models, respectively. The student model is trained to produce consistent results with the pseudo-labels, and the teacher model is updated by EMA. The training pipeline for PAIS is presented in Alg. 1." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 591, + 127, + 604 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 591, + 127, + 604 + ], + "spans": [ + { + "bbox": [ + 47, + 591, + 127, + 604 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 610, + 222, + 622 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 222, + 622 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 222, + 622 + ], + "type": "text", + "content": "4.1. Datasets and Evaluation Metrics" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 629, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 286, + 712 + ], + "type": "text", + "content": "We conducted extensive experiments on the COCO [25] and Cityscapes [6] datasets to study the proposed PAIS. The COCO dataset consists of 118k images with 80-class instance labels, as well as 123k unlabeled images. The Cityscapes dataset contains urban street-view scenes and has 8 instance categories in 2.9k training images and 0.5k validation images. For the COCO dataset, we ran-" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": "domly sampled " + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": " of the images from the train2017 split as labeled data and treated the rest as unlabeled data following common settings. In addition, we also used the full COCO train2017 as labeled data and incorporated the 123k unlabeled data from COCO unlabel2017 to train the PAIS models. For the Cityscapes dataset, we randomly sampled " + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": " of the images from the training set as labeled data and treated the remaining as unlabeled data following the common settings. We evaluated the PAIS models on the validation sets of the COCO and Cityscapes datasets, and reported standard COCO metrics including AP, AP50, AP75 (averaged over IoU thresholds), and " + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_S" + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_M" + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_L" + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": " (AP for instances of different scales)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 248, + 438, + 261 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 248, + 438, + 261 + ], + "spans": [ + { + "bbox": [ + 306, + 248, + 438, + 261 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "text", + "content": "We provide two examples of implementing PAIS with K-Net [53] and Mask-RCNN [13]. The models are trained using AdamW with a learning rate of 0.0001 for K-Net, and SGD with a learning rate of 0.01 for Mask-RCNN. The hyper-parameters " + }, + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "inline_equation", + "content": "\\lambda_{l}" + }, + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "inline_equation", + "content": "\\lambda_{u}" + }, + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "text", + "content": ", which balance the loss terms for labeled and unlabeled images, are set to 1.0 and 0.3 for K-Net, and 1.0 and 1.5 for Mask-RCNN. We set the thresholds " + }, + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "inline_equation", + "content": "\\tau_{cls}" + }, + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "inline_equation", + "content": "\\tau_{iou}" + }, + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "text", + "content": " experimentally as 0.35 and 0.30, respectively. For bipartite matching loss, we use the same hyperparameters as in [53]. The loss balancing parameters for box, class, and mask are set as " + }, + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "inline_equation", + "content": "\\lambda_{b} = 2.0" + }, + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "inline_equation", + "content": "\\lambda_{c} = 4.0" + }, + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "inline_equation", + "content": "\\lambda_{m} = 1.0" + }, + { + "bbox": [ + 304, + 266, + 545, + 458 + ], + "type": "text", + "content": " respectively. We train the models on 4 GPUs with 4 images per GPU (1 labeled and 3 unlabeled images) for 220k iterations, unless otherwise specified. The teacher model is updated via EMA with a momentum of 0.999. We use ResNet50 [14] as the backbone for these models." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 467, + 390, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 467, + 390, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 467, + 390, + 479 + ], + "type": "text", + "content": "4.3. Main Results" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "content": "Comparison to state-of-the-art semi-supervised instance segmentation frameworks. In Tab. 1, we compare the performance of models trained with PAIS to the state-of-the-art semi-supervised instance segmentation frameworks on the COCO dataset. The results demonstrate that both K-Net and Mask-RCNN trained with PAIS surpass the previous methods DD [35] and Noisy Boundaries [47] by a large margin, especially when the number of labeled data is very limited (with only " + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "content": " labeled images). Specifically, when using " + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "content": " labeled COCO images, PAIS with K-Net achieves 19.9 mask mAP, which is 12.2 points higher than Noisy Boundaries. Interestingly, the proposed PAIS brings about better performance for Mask-RCNN when the percentage of labeled data is " + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "content": ", even though it originally has a inferior performance in fully-supervised instance segmentation compared to K-Net. To explain, the bounding boxes may provide better optimization for Mask-RCNN models when the labeled data is limited. Finally, when using " + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 304, + 486, + 545, + 712 + ], + "type": "text", + "content": " labeled images, PAIS with K-Net out" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16341" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 70, + 545, + 95 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 95 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 95 + ], + "type": "table", + "html": "
Method1% COCO5% COCO10% COCO
APAP0.5AP0.75APAP0.5AP0.75APAP0.5AP0.75
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K-Net [53], supervised8.03±0.2516.33±0.317.00±0.2517.4±0.2230.08±0.2816.83±0.2121.63±0.2137.43±0.3821.8±0.20
K-Net†[53], supervised11.63±0.0522.30±0.0810.95±0.1022.28±0.0538.54±0.0922.7±0.0726.53±0.1244.87±0.1527.20±0.17
K-Net, PAIS w/o DALoss17.77±0.0632.17±0.1517.53±0.1225.40±0.0843.12±0.0526.05±0.1329.30±0.0748.64±0.0530.53±0.13
K-Net, PAIS19.78±0.1035.48±0.1519.65±0.0627.53±0.0645.63±0.0628.70±0.1031.04±0.0650.50±0.0732.34±0.05
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Mask-RCNN [13], supervised*3.5--17.3--22.0--
Mask-RCNN† [13], supervised11.54±0.0919.86±0.1111.64±0.0922.35±0.0637.98±0.1023.14±0.1127.07±0.0645.10±0.1028.67±0.06
Mask-RCNN, PAIS w/o DALoss20.13±0.0633.23±0.1521.27±0.0627.36±0.0644.10±0.1029.27±0.0629.77±0.0647.70±0.1031.97±0.06
Mask-RCNN, PAIS21.12±0.0536.03±0.0522.75±0.1029.28±0.1347.25±0.1331.20±0.2231.03±0.0649.83±0.1233.23±0.06
", + "image_path": "7456750a5a2bae2ff606f421ac0d56b3d549f20405cb6f3e991160eea665bc80.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 48, + 269, + 286, + 395 + ], + "blocks": [ + { + "bbox": [ + 46, + 208, + 546, + 252 + ], + "lines": [ + { + "bbox": [ + 46, + 208, + 546, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 208, + 546, + 252 + ], + "type": "text", + "content": "Table 3. Results of PAIS with extremely limited number of labeled images. We randomly sampled " + }, + { + "bbox": [ + 46, + 208, + 546, + 252 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 208, + 546, + 252 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 208, + 546, + 252 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 208, + 546, + 252 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 208, + 546, + 252 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 208, + 546, + 252 + ], + "type": "text", + "content": " of the labeled images from the COCO train2017 dataset, and repeated each experiment three times. The average values with standard deviation are reported. " + }, + { + "bbox": [ + 46, + 208, + 546, + 252 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 46, + 208, + 546, + 252 + ], + "type": "text", + "content": " denotes using the same data augmentation as semi-supervised training. * denotes data from NoisyBoundary [47]. We can see that PAIS achieves good performance on both box-free and box-independent instance segmentation frameworks." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 269, + 286, + 395 + ], + "lines": [ + { + "bbox": [ + 48, + 269, + 286, + 395 + ], + "spans": [ + { + "bbox": [ + 48, + 269, + 286, + 395 + ], + "type": "table", + "html": "
MethodAPAP0.5AP0.75APSAPMAPL
Box-free Instance Segmentation
K-Net [53], supervised37.860.339.916.941.257.5
K-Net†[53], supervised38.461.440.317.641.858.0
K-Net, PAIS w/o DALoss39.462.241.618.542.859.2
K-Net, PAIS40.863.543.319.244.461.4
Box-dependent Instance Segmentation
Mask-RCNN [13], supervised37.158.539.718.739.653.9
Mask-RCNN†[13], supervised37.558.940.418.640.253.8
Mask-RCNN, PAIS w/o DALoss38.459.741.519.441.155.0
Mask-RCNN, PAIS39.560.643.019.942.456.6
", + "image_path": "a98bb783c51b6e1cc6a3b23a0c917a5c221ebef35735633ba98c600aa8aa21fb.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 396, + 287, + 452 + ], + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 452 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 452 + ], + "type": "text", + "content": "Table 4. Results of PAIS with abundant labeled images. We utilize all the labeled images in the COCO train2017 dataset, and supplement them with the unlabeled images in the COCO unlabel2017 dataset for semi-supervised training. " + }, + { + "bbox": [ + 46, + 396, + 287, + 452 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 46, + 396, + 287, + 452 + ], + "type": "text", + "content": " denotes using the same data augmentation as semi-supervised training." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "text", + "content": "performs PAIS with Mask-RCNN. In Tab. 2, we compare PAIS with state-of-the-art methods on the Cityscape dataset, in which PAIS also achieves better performance than the predominant models. Specifically, we report NoisyBoundaries [47] w/o FocalLoss in Tab. 2, as we do not apply FocalLoss in PAIS. This ensures a fair and consistent comparison. Furthermore, we also add FocalLoss to PAIS on " + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "text", + "content": " Cityscapes, which achieves " + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "inline_equation", + "content": "25.1\\%" + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "text", + "content": ", surpassing " + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "inline_equation", + "content": "23.7\\%" + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "text", + "content": " of NoisyBoundaries w/ FocalLoss." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 581, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 581, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 581, + 287, + 676 + ], + "type": "text", + "content": "The more significant performance improvement on the COCO dataset validates the effectiveness of our method for solving the noisy pseudo-label problem. The COCO dataset has 80 instance categories, while the Cityspaces dataset only has 8 instance categories. This implies that the COCO dataset can provide more diverse and informative pseudo-labels, which matches our goal to utilize noisy pseudo-labels for semi-supervised learning." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Results with an extremely limited number of labeled images. To demonstrate the effectiveness of PAIS, we conduct experiments with extremely limited numbers of labeled" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "spans": [ + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "type": "text", + "content": "images, as shown in Table 3. Specifically, we compare the performance of various models trained with randomly sampled " + }, + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "type": "text", + "content": " labeled images. First, we train supervised models, K-Net (supervised) and Mask-RCNN (supervised), with the limited labeled images. Second, we train the same supervised models with the same data augmentation used in the semi-supervised setting, denoted as " + }, + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "type": "inline_equation", + "content": "\\mathrm{K - }" + }, + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "type": "inline_equation", + "content": "\\mathrm{Net}^{\\dagger}" + }, + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "type": "text", + "content": " (supervised) and " + }, + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "type": "inline_equation", + "content": "\\mathrm{Mask - RCNN}^{\\dagger}" + }, + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "type": "text", + "content": " (supervised). Third, we train PAIS models without DALoss, denoted as PAIS w/o DALoss on K-Net and Mask-RCNN. Lastly, we train the PAIS models with DALoss, denoted as PAIS on K-Net and Mask-RCNN. All models are trained three times, and the reported results are averaged." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 433, + 546, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 433, + 546, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 546, + 685 + ], + "type": "text", + "content": "Based on the results of K-Net (supervised) and Mask-RCNN (supervised), it can be observed that fully-supervised models perform poorly when the number of labeled images is limited. The results of " + }, + { + "bbox": [ + 304, + 433, + 546, + 685 + ], + "type": "inline_equation", + "content": "\\mathrm{K - Net}^{\\dagger}" + }, + { + "bbox": [ + 304, + 433, + 546, + 685 + ], + "type": "text", + "content": " (supervised) and " + }, + { + "bbox": [ + 304, + 433, + 546, + 685 + ], + "type": "inline_equation", + "content": "\\mathrm{Mask - RCNN}^{\\dagger}" + }, + { + "bbox": [ + 304, + 433, + 546, + 685 + ], + "type": "text", + "content": " (supervised) show slight improvement with weak data augmentation from the semi-supervised setting. Interestingly, while K-Net outperforms Mask-RCNN in the fully-supervised setting, their performance is similar when the number of labeled images is limited, as indicated in the table. Comparing the performance of K-Net (PAIS w/o DALoss) and Mask-RCNN (PAIS w/o DALoss) with that of the supervised setting reveals significant improvement. By introducing the dynamically re-weighting process via DALoss, the performance is further improved. For instance, with only " + }, + { + "bbox": [ + 304, + 433, + 546, + 685 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 433, + 546, + 685 + ], + "type": "text", + "content": " labeled images, the mAP of K-Net and Mask-RCNN improved from 11.63 and 11.54 to 19.78 and 21.12, respectively, resulting in approximately +8.15 and +9.58 points improvement to the performance. Additionally, the improvement over " + }, + { + "bbox": [ + 304, + 433, + 546, + 685 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{0.5}" + }, + { + "bbox": [ + 304, + 433, + 546, + 685 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 433, + 546, + 685 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{0.75}" + }, + { + "bbox": [ + 304, + 433, + 546, + 685 + ], + "type": "text", + "content": " suggests that DALoss considers masks with moderate quality during training, which further benefits semi-supervised learning." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Results with abundant labeled images. In Tab. 4, we investigate the performance of semi-supervised learning" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16342" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 286, + 139 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 286, + 139 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 286, + 139 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 286, + 139 + ], + "type": "table", + "html": "
Cls.IoU.Mask.APAP0.5AP0.75APSAPMAPL
29.348.730.511.331.445.5
✓29.749.031.011.431.846.3
✓29.448.930.611.731.546.0
✓✓30.450.131.911.932.847.6
✓✓✓31.150.632.412.333.348.3
", + "image_path": "4379d2ef93e27ef69870e7a18fe09a438e7280bb5614092b785d5e0556f24928.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 197, + 285, + 255 + ], + "blocks": [ + { + "bbox": [ + 47, + 141, + 287, + 187 + ], + "lines": [ + { + "bbox": [ + 47, + 141, + 287, + 187 + ], + "spans": [ + { + "bbox": [ + 47, + 141, + 287, + 187 + ], + "type": "text", + "content": "Table 5. Effectiveness of different loss terms in DALoss. Cls. denotes the terms of dynamic aligned classification scores. IoU. denotes adding the mask IoU branch to the model. Mask. denotes using the terms of dynamic aligned mask scores." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 197, + 285, + 255 + ], + "lines": [ + { + "bbox": [ + 48, + 197, + 285, + 255 + ], + "spans": [ + { + "bbox": [ + 48, + 197, + 285, + 255 + ], + "type": "table", + "html": "
α,βAPAP0.5AP0.75APSAPMAPL
129.949.131.010.932.147.0
230.249.531.111.132.247.1
330.550.131.711.632.947.6
431.150.632.412.333.348.3
", + "image_path": "b29780b7d98d290c892845a6db03ea6a1ccfa910a3dfbecbb8cf012405a78dc7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 312, + 288, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 288, + 433 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 288, + 433 + ], + "type": "text", + "content": "when abundant labeled data is available. Specifically, we use the entire COCO train2017 dataset as labeled data and COCO unlabeled2017 dataset as unlabeled data to train the models. The results show that the semi-supervised learning approach also leads to a performance gain. For instance, K-Net (PAIS) achieves a performance gain of approximately 1.0 point on mAP from semi-supervised learning. Additionally, the proposed DALoss consistently improves the performance of both box-dependent and box-free instance segmentation frameworks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 442, + 141, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 442, + 141, + 455 + ], + "spans": [ + { + "bbox": [ + 47, + 442, + 141, + 455 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 461, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 557 + ], + "type": "text", + "content": "In our ablation study, we investigate several aspects that can impact the performance of PAIS, including the utilization of various loss terms, the setting of hyper-parameters, the threshold values, the varying ratios of labeled and unlabeled images, and the convergence times. We perform the ablation studies on the COCO dataset using K-Net and Mask-RCNN, which are trained via PAIS under the setting of " + }, + { + "bbox": [ + 46, + 461, + 287, + 557 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 461, + 287, + 557 + ], + "type": "text", + "content": " labeled images." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": "Effectiveness of different terms in DALoss. Tab. 5 shows the efficacy of the different components in DALoss, which suggests that: (1) DALoss yields an improvement of 1.8 points to the model. Specifically, the mAP increases from 45.5 to 48.3 on " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_L" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": ", indicating a significant improvement for large objects. (2) The aligning weights for classification loss alone can also provide a marginal performance gain for the model. (3) Simply adding a mask IoU branch to the model does not enhance the overall performance. However, when incorporating the aligning weights for the segmentation loss, the mAP is increased. (4) Interestingly, the mask IoU branch can help improve the AP for objects of different scales. This is due to the mask IoU branch helping" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 316, + 72, + 453, + 173 + ], + "blocks": [ + { + "bbox": [ + 316, + 72, + 453, + 173 + ], + "lines": [ + { + "bbox": [ + 316, + 72, + 453, + 173 + ], + "spans": [ + { + "bbox": [ + 316, + 72, + 453, + 173 + ], + "type": "image", + "image_path": "536dd521bdf18cc3ec4e0ba2c793d977b5824f8ae0827ba9cef0168552e3e0d4.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 175, + 545, + 231 + ], + "lines": [ + { + "bbox": [ + 305, + 175, + 545, + 231 + ], + "spans": [ + { + "bbox": [ + 305, + 175, + 545, + 231 + ], + "type": "text", + "content": "Figure 3. Visualization of the loss alignment with different hyper-parameters. When changing the hyper-parameter from 1 to 5, the input classification score or mask IoU will be more properly adjusted by their quality, i.e., the difference between high- & low-quality mask or class will be enlarged." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 454, + 71, + 537, + 171 + ], + "blocks": [ + { + "bbox": [ + 454, + 71, + 537, + 171 + ], + "lines": [ + { + "bbox": [ + 454, + 71, + 537, + 171 + ], + "spans": [ + { + "bbox": [ + 454, + 71, + 537, + 171 + ], + "type": "image", + "image_path": "daaba6a64b2f15c352a7132e07eb7fb2a9665d5218d6d9e35b66b6238365900f.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 242, + 429, + 330 + ], + "blocks": [ + { + "bbox": [ + 307, + 242, + 429, + 330 + ], + "lines": [ + { + "bbox": [ + 307, + 242, + 429, + 330 + ], + "spans": [ + { + "bbox": [ + 307, + 242, + 429, + 330 + ], + "type": "image", + "image_path": "55574d924ee90354fc41484b9b5f3d504a458ce3c6a6309cee67e288a79c0f65.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 331, + 545, + 354 + ], + "lines": [ + { + "bbox": [ + 306, + 331, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 306, + 331, + 545, + 354 + ], + "type": "text", + "content": "Figure 4. Model convergence speed. DALoss leads to faster model convergence for training." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 430, + 243, + 544, + 330 + ], + "blocks": [ + { + "bbox": [ + 430, + 243, + 544, + 330 + ], + "lines": [ + { + "bbox": [ + 430, + 243, + 544, + 330 + ], + "spans": [ + { + "bbox": [ + 430, + 243, + 544, + 330 + ], + "type": "image", + "image_path": "b6e3d7e98296784ddf2f59c71b048d2f023689de8a054893b103da0664c26c01.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 308, + 364, + 542, + 411 + ], + "blocks": [ + { + "bbox": [ + 47, + 257, + 287, + 291 + ], + "lines": [ + { + "bbox": [ + 47, + 257, + 287, + 291 + ], + "spans": [ + { + "bbox": [ + 47, + 257, + 287, + 291 + ], + "type": "text", + "content": "Table 6. Hyper-parameters in DALoss. Considering that the classification and segmentation are both important, we simply set " + }, + { + "bbox": [ + 47, + 257, + 287, + 291 + ], + "type": "inline_equation", + "content": "\\alpha = \\beta" + }, + { + "bbox": [ + 47, + 257, + 287, + 291 + ], + "type": "text", + "content": " to investigate the influence of hyper-parameters." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 364, + 542, + 411 + ], + "lines": [ + { + "bbox": [ + 308, + 364, + 542, + 411 + ], + "spans": [ + { + "bbox": [ + 308, + 364, + 542, + 411 + ], + "type": "table", + "html": "
τclsAPAP0.5AP0.75APSAPMAPL
0.3531.150.632.412.333.348.3
0.5030.650.031.911.232.647.8
0.6529.949.131.310.132.147.4
", + "image_path": "ad67513be520d1ef6c10ab5575d530c7ddb0781cadf20eb8f615a14e513a2736.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 307, + 445, + 543, + 492 + ], + "blocks": [ + { + "bbox": [ + 306, + 414, + 545, + 436 + ], + "lines": [ + { + "bbox": [ + 306, + 414, + 545, + 436 + ], + "spans": [ + { + "bbox": [ + 306, + 414, + 545, + 436 + ], + "type": "text", + "content": "Table 7. Results of different classification score threshold " + }, + { + "bbox": [ + 306, + 414, + 545, + 436 + ], + "type": "inline_equation", + "content": "\\tau_{cls}" + }, + { + "bbox": [ + 306, + 414, + 545, + 436 + ], + "type": "text", + "content": ". The mask IoU threshold " + }, + { + "bbox": [ + 306, + 414, + 545, + 436 + ], + "type": "inline_equation", + "content": "\\tau_{iou}" + }, + { + "bbox": [ + 306, + 414, + 545, + 436 + ], + "type": "text", + "content": " is set to 0.3." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 445, + 543, + 492 + ], + "lines": [ + { + "bbox": [ + 307, + 445, + 543, + 492 + ], + "spans": [ + { + "bbox": [ + 307, + 445, + 543, + 492 + ], + "type": "table", + "html": "
τiouAPAP0.5AP0.75APSAPMAPL
0.331.150.632.412.333.348.3
0.530.850.331.912.032.947.9
0.730.650.031.211.632.347.1
", + "image_path": "01509da6c6e7caa8b92d191ae76a0f7b433befe16de8e24df2d27c060c5d7222.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 307, + 526, + 542, + 584 + ], + "blocks": [ + { + "bbox": [ + 306, + 495, + 545, + 517 + ], + "lines": [ + { + "bbox": [ + 306, + 495, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 545, + 517 + ], + "type": "text", + "content": "Table 8. Results of different mask IoU threshold " + }, + { + "bbox": [ + 306, + 495, + 545, + 517 + ], + "type": "inline_equation", + "content": "{\\tau }_{iou}" + }, + { + "bbox": [ + 306, + 495, + 545, + 517 + ], + "type": "text", + "content": " . The classification score threshold " + }, + { + "bbox": [ + 306, + 495, + 545, + 517 + ], + "type": "inline_equation", + "content": "{\\tau }_{cls}" + }, + { + "bbox": [ + 306, + 495, + 545, + 517 + ], + "type": "text", + "content": " is set to 0.35 ." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 526, + 542, + 584 + ], + "lines": [ + { + "bbox": [ + 307, + 526, + 542, + 584 + ], + "spans": [ + { + "bbox": [ + 307, + 526, + 542, + 584 + ], + "type": "table", + "html": "
RatioAPAP0.5AP0.75APSAPMAPL
1:129.047.731.011.031.645.5
1:230.148.832.211.532.447.1
1:331.150.632.412.333.348.3
1:431.350.932.612.433.548.7
", + "image_path": "864e80fa58c4ca5fcbcb2d8bf86a76301e0e07609fded1231033779650fcb135.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_body" + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 586, + 545, + 620 + ], + "lines": [ + { + "bbox": [ + 305, + 586, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 305, + 586, + 545, + 620 + ], + "type": "text", + "content": "Table 9. Different ratio of labeled images and unlabeled images in a batch. The performance saturates when the ratio of labeled and unlabeled images is set to 1:4." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 642, + 471, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 642, + 471, + 653 + ], + "spans": [ + { + "bbox": [ + 306, + 642, + 471, + 653 + ], + "type": "text", + "content": "to select good pseudo-labels for training." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "content": "Hyper-parameters in DALoss. We investigated the effect of hyper-parameters, " + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "content": ", used in DALoss. To give equal weight to both classification and segmentation, we set " + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\alpha = \\beta" + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "content": ". The results are shown in Tab. 6, indicating that larger values of " + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "content": " lead to better performance. We" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16343" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 70, + 294, + 335 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 294, + 335 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 294, + 335 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 294, + 335 + ], + "type": "image", + "image_path": "a53b4672b3db38fa7af71eb47f2d0910516b31d42a65a4b52663254fc18d29ce.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 337, + 546, + 359 + ], + "lines": [ + { + "bbox": [ + 46, + 337, + 546, + 359 + ], + "spans": [ + { + "bbox": [ + 46, + 337, + 546, + 359 + ], + "type": "text", + "content": "Figure 5. Visualization of the predictions from different models. From the examples, we can clearly show the benefits introduced by pixel-level information from PAIS and DALoss." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 299, + 70, + 541, + 335 + ], + "blocks": [ + { + "bbox": [ + 299, + 70, + 541, + 335 + ], + "lines": [ + { + "bbox": [ + 299, + 70, + 541, + 335 + ], + "spans": [ + { + "bbox": [ + 299, + 70, + 541, + 335 + ], + "type": "image", + "image_path": "b2190e881133f61f417536d01e78914f9ceb9369d54711811a17bd6806c86150.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 48, + 369, + 173, + 459 + ], + "blocks": [ + { + "bbox": [ + 48, + 369, + 173, + 459 + ], + "lines": [ + { + "bbox": [ + 48, + 369, + 173, + 459 + ], + "spans": [ + { + "bbox": [ + 48, + 369, + 173, + 459 + ], + "type": "image", + "image_path": "93b24cc5c1a7dc367c7d27575b6afbb70f17639f86ba82cf023260cb9319327e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 460, + 546, + 495 + ], + "lines": [ + { + "bbox": [ + 46, + 460, + 546, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 546, + 495 + ], + "type": "text", + "content": "Figure 6. Influence of imbalanced classes to semi-supervised training. The models are trained under " + }, + { + "bbox": [ + 46, + 460, + 546, + 495 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 460, + 546, + 495 + ], + "type": "text", + "content": " labeled images for the results. We randomly sampled 10k images from the rest of COCO train2017 to draw these figures. As the training progresses, the predictions from the teacher model are gradually fitted to the distribution of the number of labels." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 173, + 370, + 296, + 459 + ], + "blocks": [ + { + "bbox": [ + 173, + 370, + 296, + 459 + ], + "lines": [ + { + "bbox": [ + 173, + 370, + 296, + 459 + ], + "spans": [ + { + "bbox": [ + 173, + 370, + 296, + 459 + ], + "type": "image", + "image_path": "80aa0ab8bd1a0a31e69976c013d9d9a1c2a9a9a0d90e1b25124ced40d262d486.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 298, + 370, + 420, + 459 + ], + "blocks": [ + { + "bbox": [ + 298, + 370, + 420, + 459 + ], + "lines": [ + { + "bbox": [ + 298, + 370, + 420, + 459 + ], + "spans": [ + { + "bbox": [ + 298, + 370, + 420, + 459 + ], + "type": "image", + "image_path": "dc028c8877d4d5bb16d95071f9737cf56410e50a00acdf1b70f60c25c6222aec.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 421, + 370, + 544, + 459 + ], + "blocks": [ + { + "bbox": [ + 421, + 370, + 544, + 459 + ], + "lines": [ + { + "bbox": [ + 421, + 370, + 544, + 459 + ], + "spans": [ + { + "bbox": [ + 421, + 370, + 544, + 459 + ], + "type": "image", + "image_path": "4eca97750f8f0fec46d87206b6eb23ecb923304a2fbbadcdd5a92b7d22ea8d0e.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 514, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 514, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 514, + 287, + 622 + ], + "type": "text", + "content": "also analyzed the functions of different hyper-parameters used to adjust the input score, as shown in Fig. 3. The figures illustrate that increasing the hyper-parameter enlarges the difference between high- and low-quality masks or classes, adjusting the input score more appropriately based on their quality. However, when the hyper-parameter is set too large, the low-quality masks or classes are significantly constrained, potentially affecting the generalization of the model as noise is removed entirely during training." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "Model convergence speed. In Fig. 4, we analyze the convergence speed of the models. The results demonstrate that DALoss can expedite the model training in terms of convergence rate. For instance, Mask-RCNN (PAIS) achieves a convergence speed that is approximately 2 times faster than that of Mask-RCNN (PAIS w/o DALoss). Moreover, by comparing the results between Mask-RCNN" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 514, + 545, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 545, + 550 + ], + "type": "text", + "content": "(PAIS) and K-Net (PAIS), we observe that DALoss may be particularly effective for box-dependent instance segmentation frameworks, which facilitates rapid convergence." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 554, + 546, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 554, + 546, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 546, + 685 + ], + "type": "text", + "content": "Different thresholds for classification scores and mask IoUs. We observed from Tab. 7 and Tab. 8 that increasing the thresholds for classification score and mask IoU leads to a decrease in performance. This suggests that DALoss is able to make use of misaligned pseudo-labels instead of simply filtering them out. By allowing the model to learn from these potentially noisy labels, it is able to better handle situations where the alignment between labeled and unlabeled data is not perfect. This may result in improved generalization to new, unseen data, as the model has learned to adapt to the presence of noisy labels." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "content": "Different ratios of labeled and unlabeled images per batch. Tab. 9 shows that increasing the ratio of unlabeled" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16344" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 71, + 287, + 106 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 287, + 106 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 287, + 106 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 287, + 106 + ], + "type": "table", + "html": "
τcls, τiou0.35, 0.30.50, 0.30.65, 0.30.35, 0.50.35, 0.7
w/o DALoss29.329.025.329.329.0
w/ DALoss31.130.629.930.830.6
", + "image_path": "fa5629d1e4a53e5e28593b293a09bc98c1d125df8882ac1dbc5eab47b7244129.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 141, + 286, + 241 + ], + "blocks": [ + { + "bbox": [ + 47, + 108, + 286, + 131 + ], + "lines": [ + { + "bbox": [ + 47, + 108, + 286, + 131 + ], + "spans": [ + { + "bbox": [ + 47, + 108, + 286, + 131 + ], + "type": "text", + "content": "Table 10. DALoss w.r.t. thresholds tuning. DALoss consistently outperforms threshold tuning in all settings." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 141, + 286, + 241 + ], + "lines": [ + { + "bbox": [ + 48, + 141, + 286, + 241 + ], + "spans": [ + { + "bbox": [ + 48, + 141, + 286, + 241 + ], + "type": "table", + "html": "
Method1%5%10%100%
K-Net, supervise11.622.326.538.4
EMA w/o DALoss17.8(+6.2)25.4(+3.1)29.3(+2.8)39.4(+1.0)
EMA w/ DALoss19.8(+8.2)27.5(+5.2)31.0(+4.5)40.8(+2.4)
Performance gain+2.0+2.1+1.7+1.4
M-RCNN, supervise11.522.427.137.5
EMA w/o DALoss20.1(+8.6)27.4(+5.0)29.8(+2.7)38.4(+0.9)
EMA w/ DALoss21.1(+9.6)29.3(+6.9)31.0(+3.9)39.5(+2.0)
Performance gain+1.0+1.9+1.2+1.1
", + "image_path": "73356a67d82ac414342d23f8b84c5dbd95b44adac9404cbe9d8c29bb36a2802f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 244, + 286, + 266 + ], + "lines": [ + { + "bbox": [ + 47, + 244, + 286, + 266 + ], + "spans": [ + { + "bbox": [ + 47, + 244, + 286, + 266 + ], + "type": "text", + "content": "Table 11. Comparison of EMA with DALoss. The performance improvements are not mainly attributed to EMA." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 287, + 286, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 287, + 286, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 286, + 334 + ], + "type": "text", + "content": "images in a batch can improve the model's performance. The results indicate that performance saturates when the ratio is set to 1:4, suggesting that adding too many unlabeled images may lead to diminishing returns." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 335, + 286, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 286, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 286, + 441 + ], + "type": "text", + "content": "Visualizations. We visualize the outputs of different models, including K-Net (supervised), K-Net (PAIS w/o DALoss), K-Net (PAIS), Mask-RCNN (supervised), Mask-RCNN (PAIS w/o DALoss), and Mask-RCNN (PAIS), in Fig. 5. The results show that: (1) PAIS can improve the recall for most instances in the supervised model, but the quality of the predictions is not guaranteed. (2) The use of DALoss in PAIS helps to improve the quality of predictions in terms of mask and classification." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 443, + 286, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 443, + 286, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 443, + 286, + 525 + ], + "type": "text", + "content": "Influence of imbalanced classes. In Fig. 6, we investigate the effect of imbalanced classes on PAIS. We plot the number of labels obtained from the ground truth and the teacher models for Mask-RCNN and K-Net with PAIS at different iterations, namely " + }, + { + "bbox": [ + 46, + 443, + 286, + 525 + ], + "type": "inline_equation", + "content": "32\\mathrm{k}" + }, + { + "bbox": [ + 46, + 443, + 286, + 525 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 443, + 286, + 525 + ], + "type": "inline_equation", + "content": "64\\mathrm{k}" + }, + { + "bbox": [ + 46, + 443, + 286, + 525 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 443, + 286, + 525 + ], + "type": "inline_equation", + "content": "120\\mathrm{k}" + }, + { + "bbox": [ + 46, + 443, + 286, + 525 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 443, + 286, + 525 + ], + "type": "inline_equation", + "content": "180\\mathrm{k}" + }, + { + "bbox": [ + 46, + 443, + 286, + 525 + ], + "type": "text", + "content": ". The results indicate that the predicted pseudo-labels gradually conform to the distribution of the imbalanced labels." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 537, + 117, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 537, + 117, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 537, + 117, + 550 + ], + "type": "text", + "content": "5. Discussion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 557, + 286, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 286, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 286, + 628 + ], + "type": "text", + "content": "DALoss w.r.t. Thresholds Tuning. As shown in Tab. 10, we conduct an ablation study by removing DALoss from our method in Tabs. 7 and 8. The results show that DALoss consistently outperforms threshold tuning in all settings, which validates that DALoss is indeed more effective than tuning the thresholds." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": "Comparison of EMA with DALoss. We show that the performance improvements are not mainly attributed to EMA. First, we summarize the results of Tabs. 3 and 4 in Tab. 11. We can find that DALoss achieves a larger performance gain than EMA in " + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": " COCO " + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "inline_equation", + "content": "(+1.4, +1.1" + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": " vs. " + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "inline_equation", + "content": "+1.0, +0.9)" + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": ". Second, EMA alone cannot selectively utilize noisy pseudo-labels for better learning. DALoss solves this" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 523, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 523, + 83 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 523, + 83 + ], + "type": "text", + "content": "problem and leads to further improvement over EMA." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 84, + 545, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 84, + 545, + 202 + ], + "spans": [ + { + "bbox": [ + 304, + 84, + 545, + 202 + ], + "type": "text", + "content": "Discussion on Score Filtering. We have carefully chosen the values of " + }, + { + "bbox": [ + 304, + 84, + 545, + 202 + ], + "type": "inline_equation", + "content": "\\tau_{cls},\\tau_{iou}" + }, + { + "bbox": [ + 304, + 84, + 545, + 202 + ], + "type": "text", + "content": ", based on Fig. 1(c)(d), which illustrates that decreasing the thresholds will generate more noisy but informative pseudo-labels. Therefore, we use low thresholds to obtain such pseudo-labels, which is different from previous methods that need to adjust thresholds to filter them out. This simplifies the tuning of the thresholds. We believe that the experiments in Tabs. 7, 8, and 10 are sufficient to show that lower thresholds are suitable for DALoss." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 204, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 204, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 204, + 545, + 323 + ], + "type": "text", + "content": "Generality to Other Segmentation Tasks. DALoss can be applied to other semi-supervised segmentation tasks, as the noisy pseudo-labels are common in semi-supervised setting. To show the generality, we apply DALoss to panoptic segmentation, which is a more challenging task that requires both instance and semantic segmentation. We report a preliminary result under " + }, + { + "bbox": [ + 304, + 204, + 545, + 323 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 204, + 545, + 323 + ], + "type": "text", + "content": " COCO. The initial result shows that DALoss can improve the PQ performance from " + }, + { + "bbox": [ + 304, + 204, + 545, + 323 + ], + "type": "inline_equation", + "content": "36.8\\%" + }, + { + "bbox": [ + 304, + 204, + 545, + 323 + ], + "type": "text", + "content": " PAIS w/o DALoss to " + }, + { + "bbox": [ + 304, + 204, + 545, + 323 + ], + "type": "inline_equation", + "content": "37.3\\%" + }, + { + "bbox": [ + 304, + 204, + 545, + 323 + ], + "type": "text", + "content": " PAIS w/ DALoss. We remain more experiments in our future work." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 324, + 545, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 545, + 443 + ], + "type": "text", + "content": "Discussion on Large Segment Everything Models. We envision that the future of image segmentation will not only aim to segment everything, but also to provide fine-grained text descriptions for the segmented regions. However, the recently proposed models such as SAM [19] and SEEM [55] either lack labeled semantic information or demand large amounts of labeled semantic data for training. Therefore, we believe that semi-supervised learning will be a crucial solution to leverage abundant unlabeled data and reduce the labeling burden." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 455, + 378, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 455, + 378, + 467 + ], + "spans": [ + { + "bbox": [ + 306, + 455, + 378, + 467 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 475, + 545, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 545, + 643 + ], + "type": "text", + "content": "In this paper, we presented a novel PAIS framework for semi-supervised instance segmentation. To address the misalignment between classification score and mask quality, we introduced a dynamic aligning loss (DALoss), which aligns the classification loss term and the segmentation loss term based on the quality of different pseudo-labels. Our experimental results demonstrate the effectiveness of the proposed PAIS framework. Specifically, when the amount of labeled data is extremely limited, our pipeline equipped with PAIS and DALoss achieves superior performance for instance segmentation. We believe that PAIS can serve as a strong baseline for future research on semi-supervised instance segmentation. We hope our work can inspire further exploration in this exciting research direction." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 645, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 645, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 645, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgements. This work was supported by National Key R&D Program of China (2022ZD0118202), National Science Fund for Distinguished Young Scholars (No.62025603), National Natural Science Foundation of China (No.U21B2037, No.U22B2051, No.62176222, No.62176223, No.62176226, No.62072386, No.62072387, No.62072389, No.62002305 and No.62272401), and Natural Science Foundation of Fujian Province of China (No.2021J01002, No.2022J06001)." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16345" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Philip Bachman, Ouais Alsharif, and Doina Precup. 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Although the inborn connection with frequency domain, existing pan-sharpening research has almost investigated the potential solution upon frequency domain, thus limiting the model performance improvement. To this end, we first revisit the degradation process of pan-sharpening in Fourier space, and then devise a Pyramid Dual Domain Injection Pan-sharpening Network upon the above observation by fully exploring and exploiting the distinguished information in both the spatial and frequency domains. Specifically, the proposed network is organized with multi-scale U-shape manner and composed by two core parts: a spatial guidance pyramid sub-network for fusing local spatial information and a frequency guidance pyramid sub-network for fusing global frequency domain information, thus encouraging dual-domain complementary learning. In this way, the model can capture multi-scale dual-domain information to enable generating high-quality pan-sharpening results. Quantitative and qualitative experiments over multiple datasets demonstrate that our method performs the best against other state-of-the-art ones and comprises a strong generalization ability for real-world scenes.", + "bbox": [ + 76, + 335, + 473, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 743, + 209, + 758 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "There is often a high demand for high-resolution multispectral (HRMS) images in the domain of agricultural monitoring and mapping services. However, due to the limitations of satellite sensors, the existing approaches must instead separately capture high-resolution panchromatic (PAN) and multispectral low-resolution (LRMS) images and fuse them using a technique known as pan", + "bbox": [ + 76, + 768, + 468, + 876 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f9fa8c89a329af689097bc7ef6bf3738cecd23d65f8206523d51ee418b9dd366.jpg", + "image_caption": [ + "Figure 1. Frequency domain analysis of multi-scale PAN, MS, and Ground Truth images. The amplitude, denoted by A, is displayed for the original-scale image, the 2-times downsampled image, and the 4-times downsampled image, from top to bottom, respectively. The last two columns show the degradation of PAN and MS images relative to GT images." + ], + "image_footnote": [], + "bbox": [ + 504, + 304, + 890, + 477 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "harpening to get the desired HRMS images. Essentially, pan-sharpening is a super-resolution process that utilizes the richer details of PAN images to guide the reconstruction process of LRMS images. Pan-sharpening technology has expanded the use of remote sensing images in a wider range and gained considerable attention.", + "bbox": [ + 496, + 580, + 890, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Pan-sharpening has seen an increase in the use of deep learning-based techniques in recent years. The PNN [16], which started this trend, was motivated by the SRCNN [4] to introduce the convolutional neural network. The PNN presented a three-layer convolutional neural network that concatenated LRMS and PAN images as input and subsequently generated the output through the network. Since then, a flood of deep learning-based techniques has been developed to improve the model's representation capacity by employing deeper models or model-driven techniques [33, 29, 7, 32]. While significant progress has been made, there are still limitations need to be addressed. Prior approaches have primarily focused on spatial domain solutions, thereby neglecting the exploration of frequency domain solutions. Nevertheless, it has been established that CNNs in the spa", + "bbox": [ + 496, + 674, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Co-first authors contributed equally, † Corresponding author.", + "bbox": [ + 94, + 886, + 423, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12908", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tial domain exhibit a preference for low-frequency information and struggle to capture high-frequency information [1], resulting in insufficient texture in the generated images [14]. However, by incorporating frequency domain information, high-frequency features in low-dimensional manifolds can be efficiently captured [20]. Additionally, the LRMS images can be treated as degraded versions of HRMS images, which indicates that pan-sharpening is fundamentally an image restoration task. Image restoration are highly interrelated with frequency domain, as image degradation and content can be easily disentangled through the Fourier transform [9]. Thus, it is natural for us to investigate the feasibility of introducing frequency domain information into the pan-sharpening domain, as detailed in Figure 1 where the degradation effect of pan-sharpening is enlarged over multi-scale manner.", + "bbox": [ + 75, + 90, + 472, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivation. We conducted multi-scale Fourier analysis on LRMS, PAN, and HRMS images since the degradation mostly affects the amplitude of the image and the diversity scale of remote sensing landforms has an effect on the pan-sharpening process. The analysis results of image spectrum is shown in the Figure 1. We can draw two inspirations from the figure: 1) The difference in amplitudes between the PAN and HRMS images is primarily in the low frequency component, whereas the difference between the amplitudes of the HRMS and LRMS images is observed in both the high and low frequency components. 2) As the scale decreases, we can observe the missing information in the PAN image becomes more concentrated in the low-frequency component, while the degradation of the LRMS image becomes more concentrated in the high frequency component, and the degradation of images at various scales is not exactly the same. We may deduce from observation 1 that the frequency information in the PAN image can be used to fill in the missing information of the LRMS image. For observation 2, it is crucial to restore the information at several scales since the degradation is varied under multi-scale conditions. To encourage the learning of context information and multi-scale reconstruction, frequency domain information should be handled at various scales. Additionally, we can encourage the interaction of global and local, low-frequency and high-frequency features through multi-scale processing in the spatial and frequency domains in accordance with CNN's low-frequency preference in spatial domain and the global receptive field described by the spectral convolution theorem [6] in frequency domain to enhance the model's performance.", + "bbox": [ + 75, + 337, + 472, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In light of the aforementioned observation, we propose a brand new Pyramid Dual Domain Injection Network (PDDIN) to inject the multi-scale details of the PAN image into the LRMS image in both the spatial and frequency domains to aid in the restoration process. A Feature Extraction Pyramid, a Frequency Injection Pyramid, and a", + "bbox": [ + 75, + 810, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Spatial Injection Pyramid compensate the three major key components of the network. The Feature Extraction Pyramid is responsible for extracting multi-scale feature information from the PAN image. By using these features, the Frequency Injection Pyramid may inject global multi-scale features into the LRMS image, facilitating the recovery of global and high-frequency information in the spatial domain. To promote the reconstruction of local and spatial information, the spatial domain feature of PAN images is injected into the LRMS image in the Spatial Injection Pyramid. This approach effectively compensates for degradation at various scales, leading to a more thorough and precise reconstruction of the image. We conducted comprehensive experiments on multiple datasets to assess the effectiveness of our suggested network. The results show the efficacy of our method, by outperforming state-of-the-art techniques in both qualitative and quantitative evaluations.", + "bbox": [ + 496, + 90, + 893, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized below:", + "bbox": [ + 517, + 348, + 795, + 361 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- In this work, we revisit the degradation process of pan-sharpening in Fourier space, and then devise a Pyramid Dual Domain Injection Pan-sharpening Network, inspired by the above observation in both the spatial and frequency domains.", + "- To fully explore and exploit the distinguished information, we devised a frequency guidance pyramid sub-network and a spatial guidance pyramid sub-network. This design allows for the fusion of multi-scale information from both the frequency and spatial domains, lifting the learning capability of the model.", + "- Extensive experiments on multiple satellite datasets demonstrate our approach's quantitative and qualitative superiority to existing state-of-the-art pan-sharpening algorithms." + ], + "bbox": [ + 517, + 368, + 890, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 626, + 637, + 642 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Traditional pan-sharpening method", + "text_level": 1, + "bbox": [ + 500, + 650, + 808, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Three sorts of traditional techniques are widely adapted in the realm of pan-sharpening: component substitution (CS) method, MRA method, and VO-based method. The component substitution approach generates high-resolution images by substituting the LRMS image components with the spatial detail components from the PAN image. IHS algorithm [10], Brovey [8], PCA [12], and GS algorithm [11] are examples of CS methods. Due to the fact that spectral information is not fully considered in CS methods, the pan-sharpened images suffer from serious spectral distortion. In light of this, the MRA method reduces spectral distortion by fusing PAN and LRMS through multi-resolution decomposition. DWT [15] ATWT [17] HPF [19] and LP [22] algorithms are typical MRA algorithms. The VO-based methods, in contrast to the above two, treat pan-sharpening as", + "bbox": [ + 496, + 674, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12909", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/2e2fd26cd76184639ca8cadbcfe81784b2ba68544f3bcea0cc406eb114e74f76.jpg", + "image_caption": [ + "Figure 2. The framework of the Pyramid Dual Domain Injection Network. It consists of three key components: Feature Extraction Pyramid, Frequency Injection Pyramid and Spatial Injection Pyramid." + ], + "image_footnote": [], + "bbox": [ + 86, + 92, + 883, + 340 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "an optimization problem, design the loss function under a prior constraints, and then generate results by iterative solution and minimization of the loss function. The Bayesian technique [5] and the total variation algorithm [18] are common approaches in VO methods. The VO method can deliver decent results, but designing the optimization model and choosing the loss function is a significant challenge.", + "bbox": [ + 75, + 398, + 472, + 505 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. CNN-based pan-sharpening method", + "text_level": 1, + "bbox": [ + 76, + 525, + 390, + 542 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In recent years, the dominant approach in this area has been the CNN-based pan-sharpening method. PNN [16], which is inspired by SRCNN [4], is the pioneering work that introduced CNN to this field, giving rise to an unprecedented number of novel CNN-based techniques [27, 29, 7, 32, 33]. Despite having a clear and simple network structure, the results of PNN outperformed traditional techniques, demonstrating the promising potential of CNN techniques. Following that, Pannet [30] employs residual connection and high-frequency filtering to learn high-frequency features of images, while multi-scale convolution is taken into account in MsDCNN [31] to handle the varied remote sensing landforms. The model-driven models such as GPPNN [25], MMNet [28] and ARFNet [26] achieve interpretable models by utilizing deep unfolding techniques to construct the network structure. Additionally, SRPPNN [2] uses the progress super resolution method to enhance the performance of model and construct a profoundly deep network. Recently, MutNet [33] utilizes a mutual information mechanism to learn a more effective feature representation. The study of these techniques has also been expanded to include generative networks [13] and unsupervised pan-sharpening [21] technologies.", + "bbox": [ + 75, + 553, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 500, + 397, + 599, + 412 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this part, we first discuss the pertinent Fourier transform properties before delving into further details about our network shown in Figure 2, 3 and 4. It is organized into three parts: the Feature Extraction Pyramid, which extracts the multi-scale features from PAN images; the Frequency Injection Pyramid, which incorporates multi-scale frequency features from PAN into LRMS images for global and high-frequency information restoration; and the Spatial Injection Pyramid, which introduces the multi-scale spatial information from PAN into LRMS images to reconstruct local details. Finally, we will describe our loss function.", + "bbox": [ + 496, + 422, + 893, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Fourier transform of images", + "text_level": 1, + "bbox": [ + 500, + 598, + 754, + 614 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Due to its capacity to decompose signals into their frequency components, the Fourier transform is widely adapted in the image processing community. This transformation makes it possible to analyze the image from a different perspective and offers valuable insights into its features. The Fourier transform of an input image $x \\in R^{h \\times w}$ can be defined as follows:", + "bbox": [ + 496, + 621, + 890, + 726 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {F} (x) (u, v) = \\frac {1}{\\sqrt {H W}} \\sum_ {h = 0} ^ {H - 1} \\sum_ {w = 0} ^ {W - 1} x (h, w) e ^ {- j 2 \\pi \\left(\\frac {h}{H} u + \\frac {w}{W} v\\right)} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 734, + 890, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In our work, the Fourier transform is individually applied to each image channel. The amplitude and phase components can be described as follows:", + "bbox": [ + 496, + 789, + 893, + 833 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} (x) (u, v) = \\left[ R ^ {2} (x) (u, v) + I ^ {2} (x) (u, v) \\right] ^ {\\frac {1}{2}}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 843, + 892, + 864 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} (x) (u, v) = \\arctan \\left[ \\frac {I (x) (u , v)}{R (x) (u , v)} \\right] \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 864, + 890, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12910", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $I(x)$ and $R(x)$ indicate imaginary and real parts of the image's frequency representation $\\mathcal{F}(x)$ , correspondingly.", + "bbox": [ + 75, + 90, + 468, + 135 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The Fourier transform can be beneficial in the task of pan-sharpening by disentangling and analyzing image degradation in the amplitude component. We may obtain important insights into the level of degradation existing in the image by carefully evaluating the amplitude information, ultimately resulting in more effective restoration attempts. Figure 1 illustrates that whereas LRMS images degrade in both the high-frequency and low-frequency regions, while PAN images degrade mostly in the low-frequency region. Moreover, it is important to note that the frequency of image degradation can vary across different scales. Following frequency analysis, it is obvious that the frequency domain information from a PAN image can be effectively integrated into a LRMS image to assist with its restoration. This process can be further optimized by injecting the frequency domain information at multiple scales, allowing for a more comprehensive reconstruction of the image's contextual information.", + "bbox": [ + 75, + 136, + 470, + 409 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Network framework", + "text_level": 1, + "bbox": [ + 76, + 419, + 271, + 434 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Figure 2, given an input of a PAN and LRMS pair, we start by upsampling the LRMS image to the size of the PAN image. After that, a feature extraction pyramid is employed to process the PAN image, obtaining multi-scale features. Once the LRMS image is upsampled, the frequency injection pyramid injects multi-scale features into the LRMS image. The frequency injection pyramid is used to integrate the frequency domain features of various scales to further explore the frequency information. Then, we adopt spatial injection pyramid to reconstruct local details. Finally, the reconstruction image is obtained through a skip connection between network output and the upsampled LRMS image.", + "bbox": [ + 75, + 441, + 468, + 638 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. The key building components", + "text_level": 1, + "bbox": [ + 76, + 648, + 339, + 666 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Three essential elements make up the architecture of our network, and they are shown in Figures 2, 3, and 4. We go into great depth on each of these parts in the part that follows. Feature Extraction Pyramid. The Feature Extraction Pyramid is in charge of extracting multi-scale features from the PAN images, which can be utilized by other modules for further feature injection. To obtain the original size feature, the PAN image is first projected into the feature space using a convolution layer. After that, two sets of convolution and downsampling operations are carried out to generate features that are half as large and a quarter as large as the original. These features, namely $P_{1}, P_{2}$ , and $P_{3}$ , are then injected as supplemental information to the LRMS images to aid in the reconstruction process. The convolution operation with a stride of 2 is employed as a down-sampling", + "bbox": [ + 75, + 672, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/18a61e74edb06acb294204c6922cae3a764bbdd744f1d63a8c6cf6109b12a048.jpg", + "image_caption": [ + "Figure 3. Architecture of Frequency Injection Module (FIM). The phase and amplitude components of $P_{i}$ and $F_{i}$ are obtained using the Fourier transform. Feature fusion is performed in the frequency domain, and the resulting frequency domain feature map is combined with the spatial feature to facilitate frequency domain information recovery and dual-domain complementary learning." + ], + "image_footnote": [], + "bbox": [ + 529, + 87, + 875, + 229 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "operation in the pyramid. In the end, this module produces multi-scale feature maps for further information injection utilizing PAN image as input.", + "bbox": [ + 496, + 340, + 890, + 386 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Spatial Injection Pyramid. The Spatial Injection Pyramid is designed to inject the local, multi-scale spatial information from PAN into the LRMS image. This module may effectively concentrate on small objects by leveraging the locality of the convolution operation in the pixel domain. In this module, the spatial features of $P_{1}$ , $P_{2}$ , and $P_{3}$ are injected into LRMS images at various scales to aid in reconstruction. For instance, given the output of the frequency pyramid presented by $M s_{i}$ and the feature map $P_{i}$ at the original scale, further feature extraction is performed using a convolution layer to get $S_{i}$ , and then the features $P_{i}$ are injected into $S_{i}$ using the spatial injection module (SIM). Following injection, a down-sampling or up-sampling operation is applied to generate the feature map of a different size. Taking the down-sampling branch for example, the process can be described as follows:", + "bbox": [ + 496, + 387, + 892, + 628 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {i} = \\operatorname {c o n v} _ {3 \\times 3} (M s _ {i}) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 638, + 890, + 656 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF _ {s p a i n j} = S I M \\left(S _ {i}, P _ {i}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 657, + 890, + 675 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM s _ {i + 1} = \\operatorname {d o w n} \\left(F _ {\\text {s p a i n j}}\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 676, + 890, + 694 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The suggested spatial injection module, shown in the figure 4, uses the AFF [3] as a basis block and is built on attention mechanism to enable effective and consistent injection of spatial details. The module works by enabling interaction between the PAN and LRMS branches, which enhances detail injection and facilitates the acquisition of LRMS features with injected spatial details.", + "bbox": [ + 496, + 704, + 890, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Frequency Injection Pyramid. The purpose of the frequency injection pyramid is to provide LRMS features with high-frequency and global information from PAN image. By utilizing the multi-scale frequency injection, the restoration of LRMS image's frequency domain information is enhanced by leveraging the frequency information of PAN im", + "bbox": [ + 496, + 810, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12911", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f909e15196e26630003aed869af56528f8dfe8b28d0f715dc6e5b3b9fbb03ff4.jpg", + "image_caption": [ + "Figure 4. The proposed module for injecting spatial domain information, dubbed SIM, is based on attention mechanism and uses a basic module built on attentional fusion block." + ], + "image_footnote": [], + "bbox": [ + 81, + 85, + 472, + 219 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "age. Processing information in frequency domain enables the network to quickly capture high-frequency features that are challenging to acquire using pixel domain CNN, encourages dual-domain complementary learning, and generates clear texture features. Specifically, given the feature map of the LRMS image presented by $Mf_{i}$ and the feature map $P_{i}$ , first $M_{i}$ are fed to a convolution block to extract a further feature $F_{i}$ . Next, the frequency injection module (FIM) is used to inject the frequency domain features of $P_{i}$ into $F_{i}$ . The resulting feature map is then down-sampled or upsampled for the next scale of frequency domain information injection. Taking the up-sampling branch as an example, this process is summarized as follows:", + "bbox": [ + 75, + 289, + 472, + 484 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF _ {i} = \\operatorname {c o n v} _ {3 \\times 3} (M f _ {i}) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 496, + 468, + 512 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF _ {f r e i n j} = F I M \\left(F _ {i}, P _ {i}\\right) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 515, + 468, + 531 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nM f _ {i + 1} = u p \\left(F _ {f r e i n j}\\right) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 534, + 468, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $up$ is implemented by pixel-shuffle.", + "bbox": [ + 76, + 561, + 356, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the inputs $F_{i}$ and $P_{i}$ , the FIM shown in Figure 3 employs the Fourier transform to produce amplitude and phase components. Following that, the phase and amplitude information of $P_{i}$ is individually injected into $F_{i}$ to aid in the restoration of the LRMS image in the frequency domain.", + "bbox": [ + 75, + 575, + 468, + 665 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In particular, the following procedure is used to acquire the relevant amplitude and phase components:", + "bbox": [ + 76, + 667, + 468, + 696 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} \\left(F _ {i}\\right), \\mathcal {P} \\left(F _ {i}\\right) = \\mathcal {F} \\left(F _ {i}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 707, + 468, + 723 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} \\left(P _ {i}\\right), \\mathcal {P} \\left(P _ {i}\\right) = \\mathcal {F} \\left(P _ {i}\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 726, + 468, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the $\\mathcal{A}(F_i)$ , we use SFT [24] to inject frequency information from $\\mathcal{A}(P_i)$ , and use $Conv_{1\\times 1}$ to fuse phase components, for the difference between two modalities mainly lay in amplitude:", + "bbox": [ + 76, + 752, + 468, + 813 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha , \\beta = \\operatorname {C o n v} _ {3 \\times 3} (\\mathcal {A} (P _ {i})), \\operatorname {C o n v} _ {3 \\times 3} (\\mathcal {A} (P _ {i})), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 823, + 468, + 840 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} \\left(F _ {i}\\right) = \\mathcal {A} \\left(F _ {i}\\right) \\cdot \\alpha + \\beta , \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 842, + 468, + 858 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} (F) = \\operatorname {C o n v} _ {1 \\times 1} \\left(\\operatorname {C a t} \\left(\\left[ \\mathcal {A} \\left(P _ {i}\\right), \\mathcal {A} \\left(F _ {i}\\right) \\right]\\right)\\right), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 861, + 468, + 878 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} (F) = \\operatorname {C o n v} _ {1 \\times 1} \\left(\\operatorname {C a t} \\left(\\left[ \\mathcal {P} \\left(P _ {i}\\right), \\mathcal {P} \\left(F _ {i}\\right) \\right]\\right)\\right) \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 106, + 880, + 468, + 896 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The injected components are then transformed back to the pixel domain using the inverse transform, and are subsequently fused with spatial features to inject frequency features into spatial information and promote dual-domain complementary learning:", + "bbox": [ + 498, + 90, + 890, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF _ {f r e} = \\operatorname {C o n v} _ {1 \\times 1} \\left(\\mathcal {F} ^ {- 1} (\\mathcal {A} (F), \\mathcal {P} (F))\\right) \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 565, + 171, + 890, + 189 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF _ {s p a} = \\operatorname {C o n v} _ {3 \\times 3} \\left(F _ {i}\\right), \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 191, + 890, + 208 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF _ {f r e i n j} = F _ {f r e} + F _ {s p a} \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 210, + 890, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Loss Function", + "text_level": 1, + "bbox": [ + 500, + 231, + 643, + 244 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To improve the perception of high-frequency information, we propose a loss function that combines spatial and frequency domain losses in this study. Provided that $Y$ represents the model output, $Y_{f}$ represents the output of frequency injection pyramid and $H$ represents the ground truth, the $L_{1}$ distance between $Y$ and $H$ is employed to define the spatial domain loss:", + "bbox": [ + 496, + 253, + 890, + 359 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s} = \\left| \\left| Y - H \\right| \\right| _ {1}. \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 366, + 890, + 383 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The frequency domain loss, which aims to improve the perception of high-frequency information, is determined using the following formula:", + "bbox": [ + 496, + 388, + 890, + 433 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {f} = \\left| \\left| \\log \\left(\\mathcal {A} \\left(Y _ {f}\\right)\\right) - \\log \\left(\\mathcal {A} (H)\\right) \\right| \\right| _ {1} + \\left| \\left| \\mathcal {P} (Y) - \\mathcal {P} (H) \\right| \\right| _ {1}, \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 439, + 890, + 470 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the amplitude and phase components of the Fourier transform are denoted by $\\mathcal{A}$ and $\\mathcal{P}$ respectively. The complete loss function is a combination of the dual domain losses, and involves a hyper-parameter $\\lambda$ which is set to 0.1 based on empirical evidence.", + "bbox": [ + 496, + 476, + 890, + 551 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {s} + \\lambda \\mathcal {L} _ {f}. \\tag {21}\n$$\n", + "text_format": "latex", + "bbox": [ + 640, + 558, + 890, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 500, + 580, + 624, + 597 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and benchmark", + "text_level": 1, + "bbox": [ + 500, + 604, + 725, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Three datasets—WorldView-II (WV2), WorldView-III (WV3), and Gaofen2 (GF2) were used in our experiments. Due to the unavailability of real HRMS images, we utilized the Wald protocol [23] to generate the training and test data. In further detail, we extracted patches from the same location from the PAN and LRMS images, with the PAN patch being $r$ times larger than the LRMS patch. The original LRMS patch was utilized as the ground truth, and both the LRMS and PAN patches were downsampled by a factor of $r$ and used as input data. The selected patch sizes were 128x128 and 32x32, respectively.", + "bbox": [ + 496, + 628, + 890, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To evaluate the efficacy of our approach, we compared it with five traditional and six advanced CNN-based methods. Specifically, we included SFIM, Brovey [8], GS [11], IHS [10], and GFPCA [12] as traditional methods, and PANNET [30], MSDCNN [31], SRPPNN [2], GPPNN [25], MutNet [33] and INNformer [32] as advanced methods.", + "bbox": [ + 496, + 795, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12912", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/7e426b355e642e6e74a5755f9f26be64456f989aa7110ace2817361dd05d42d4.jpg", + "table_caption": [ + "Table 1. Quantitative comparison on three datasets. Best results are highlighted by red. $\\uparrow$ indicates that the larger the value, the better the performance, and $\\downarrow$ indicates that the smaller the value, the better the performance." + ], + "table_footnote": [], + "table_body": "
MethodWorldView-IIGaoFen2Worldview-III
PSNR↑SSIM↑SAM↓ERGAS↓PSNR↑SSIM↑SAM↓ERGAS↓PSNR↑SSIM↑SAM↓ERGAS↓
SFIM34.12970.89750.04392.344936.90600.88820.03181.739821.82120.54570.12088.9730
Brovey35.86460.92160.04031.823837.79740.90260.02181.372022.50600.54660.11598.2331
GS35.63760.91760.04231.877437.22600.90340.03091.673622.56080.54700.12178.2433
IHS35.29620.90270.04612.027838.17540.91000.02431.533622.55790.53540.12668.3616
GFPCA34.55810.90380.04882.141137.94430.92040.03141.560422.33440.48260.12948.3964
PANNET40.81760.96260.02571.055743.06590.96850.01780.857729.68400.90720.08513.4263
MSDCNN41.33550.96640.02420.994045.68470.98270.01350.638930.30380.91840.07823.1884
SRPPNN41.45380.96790.02330.989947.19980.98770.01060.558630.43460.92020.07703.1553
GPPNN41.16220.96840.02441.031544.21450.98150.01370.736130.17850.91750.07763.2593
MutNet41.67730.97050.02240.951947.30420.98920.01020.548130.49070.92230.07493.1125
INNformer41.69030.97040.02270.951447.35280.98930.01020.547930.53650.92250.07473.0997
Ours41.84730.97070.02220.935847.49390.98950.01000.536030.85020.92550.07262.9945
", + "bbox": [ + 76, + 114, + 903, + 393 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5d44b8d21dbfe664c770129a0eeca6b0bcf9050fa7c023502f641ca4748186ec.jpg", + "table_caption": [ + "Table 2. Evaluation of the proposed method on real-world full-resolution scenes from the GaoFen2 dataset." + ], + "table_footnote": [], + "table_body": "
MetricSFIMBroveyGSIHSGFPCAPANNETMSDCNNSRPPNNGPPNNMutNetINNformerOurs
Dλ↓0.08220.13780.06960.07700.09140.07370.07340.07670.07820.06940.06930.0682
DS↓0.10870.26050.24560.29850.16350.12240.11510.11620.12530.11180.11380.1101
QNR ↑0.82140.63900.07250.64850.76150.81430.82150.81730.80730.82470.82590.8307
", + "bbox": [ + 81, + 422, + 893, + 497 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation details", + "text_level": 1, + "bbox": [ + 76, + 522, + 290, + 537 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The experiment was conducted on an RTX 3060 GPU, using the PyTorch framework. The Adam optimizer was employed with an initial learning rate of $5 \\times 10^{-4}$ . To ensure stable training, the learning rate was decayed to $5 \\times 10^{-8}$ using the cosine annealing method after 500 epochs. Several commonly used evaluation metrics were chosen, including PSNR, SSIM, SAM, and ERGAS, as well as non-reference indices such as $D_{S}$ , $D_{\\lambda}$ , and QNR.", + "bbox": [ + 75, + 546, + 470, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison with state-of-the-art methods", + "text_level": 1, + "bbox": [ + 76, + 680, + 434, + 696 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation on Reduced-Resolution Scene. The evaluation results of our approach on three datasets are shown in Table 1. The results demonstrate that our model performs better than the state-of-the-art approaches in the majority of assessment measures, and the improvements are significant. To be specific, our method outperforms the cutting-edge method INNformer on most indicators, on the WV2 dataset, our model achieves a $0.16\\mathrm{~dB}$ improvement in PSNR compared to MIDN. Similarly, on the GF2 and WV3 datasets, our model achieves a $0.14\\mathrm{~dB}$ and $0.31\\mathrm{~dB}$ improvement in PSNR, respectively, demonstrating its excellent performance. Comparable improvements are also observed in other evaluation metrics.", + "bbox": [ + 75, + 704, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Additionally, for qualitative evaluation, we compared the results obtained from our method with those of the other nine methods on the WV2 and GF2 datasets. To evaluate the similarity between the generated results and the ground truth, a residual map was generated by computing their mean squared error. The brighter areas of residual map indicate the larger differences with the ground truth. Our approach produces images with the finest texture and most realistic spectrum, as shown in Figures 5 and 6. The residual maps exhibit the least amount of bright spots, indicating high congruence with the ground truth. These findings are further supported by the evaluation indicators presented in the Table 1.", + "bbox": [ + 496, + 523, + 890, + 719 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation on Full-Resolution Scene. To test the generalization ability of our model, we trained it on the GF2 dataset and evaluated full-resolution data from GF2 that was not downsampled, using the reserved portion of the dataset. Since there was no reference image available, we evaluated the dataset using no-reference indices. As shown in Table 2, our method achieved the best QNR index on this dataset, indicating its strong generalization ability compared to traditional and deep learning methods. This demonstrates that our approach can be applied to real-world scenes.", + "bbox": [ + 496, + 750, + 890, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12913", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/fbd9c9ef1a6e34e1723f9617b9405271627c12c75814cf4dcea64e82afa64919.jpg", + "table_caption": [ + "Table 3. The outcomes of the ablation experiments conducted on the WordView-II dataset are presented." + ], + "table_footnote": [], + "table_body": "
Config Multi-scale FIMWorldView-IIGaoFen2WorldView-III
PSNR↑SSIM↑SAM↓ERGAS↓PSNR↑SSIM↑SAM↓ERGAS↓PSNR↑SSIM↑SAM↓ERGAS↓
(I)×✓41.63610.97010.02250.958147.37880.98920.01020.546630.78490.92520.07173.0240
(II)✓×41.63990.96950.02270.960047.45880.98900.01010.540330.81400.92560.07183.0106
Ours✓✓41.84350.97110.02220.947847.49390.98950.01000.536030.86450.92580.07572.9851
", + "bbox": [ + 81, + 99, + 890, + 188 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e5aeee3728c797fdcabfaf89dc5c8238cb66282e081e94ee1b4ebb41eae31ffc.jpg", + "image_caption": [ + "LRMS" + ], + "image_footnote": [], + "bbox": [ + 78, + 200, + 207, + 299 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6d6e25d5dc801d55b04ef77b768090846c2cab877fc4f7a72c0e5063c36f91d9.jpg", + "image_caption": [ + "PAN" + ], + "image_footnote": [], + "bbox": [ + 214, + 200, + 341, + 299 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/548192da2c308dd62b58369b80378982141d0ec2bcfd153a82d84c08b4d6c543.jpg", + "image_caption": [ + "GFPCA" + ], + "image_footnote": [], + "bbox": [ + 346, + 200, + 475, + 299 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/35a16152a05d814399e2828c234572be061bff4d825e0cf3cecf35991fb535b1.jpg", + "image_caption": [ + "GS" + ], + "image_footnote": [], + "bbox": [ + 482, + 200, + 609, + 299 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ffdc3505761552e0144d5551c870e61c52f597a6816d673f95c9ede1ecdc1ed6.jpg", + "image_caption": [ + "SFIM" + ], + "image_footnote": [], + "bbox": [ + 617, + 200, + 746, + 299 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a540c01cf2e8b059eb24a03e3917c859a631de299c31bb002162c9facf482359.jpg", + "image_caption": [ + "PANNET" + ], + "image_footnote": [], + "bbox": [ + 751, + 200, + 880, + 299 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c1fe9dd71d5eff8597289101708539aa46a76cad19909104d4273002807b3d70.jpg", + "image_caption": [ + "MSDCNN" + ], + "image_footnote": [], + "bbox": [ + 80, + 314, + 207, + 412 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3d30be64af969bfa1c25e6b767a20b93c0607630915a887817f59b78bc52d8eb.jpg", + "image_caption": [ + "SRPPNN" + ], + "image_footnote": [], + "bbox": [ + 215, + 314, + 343, + 412 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dcc0dfe97b0396cb4e26fbf3625c83b9dcfd6c2195efad4d2dfd9cfbee1b36d7.jpg", + "image_caption": [ + "GPPNN" + ], + "image_footnote": [], + "bbox": [ + 348, + 314, + 475, + 412 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a90475dcc8e3fde28857fc58e80188ccd7c45ef99b6bc336bf8133d65924f894.jpg", + "image_caption": [ + "MutNet" + ], + "image_footnote": [], + "bbox": [ + 480, + 315, + 606, + 412 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8093429a22545ddd7ccfc7c5001f257fdd2233916109aac2866388ff5d32aabe.jpg", + "image_caption": [ + "INNformer" + ], + "image_footnote": [], + "bbox": [ + 617, + 315, + 743, + 412 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c8963b141e5aac2adbc8ce1b7eff5ab2964222a6dfb7a2dc0b1644959be95159.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 751, + 315, + 880, + 414 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c0d568334d674ea4293bc21ff200f1eac74b5ffbc6d668256134a7fbca6514a5.jpg", + "image_caption": [ + "GFPCA" + ], + "image_footnote": [], + "bbox": [ + 78, + 431, + 158, + 492 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3dab921ca5372464b0614bfd03be66295dd469609221e150678495e4f5588bf3.jpg", + "image_caption": [ + "GS" + ], + "image_footnote": [], + "bbox": [ + 158, + 431, + 236, + 491 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/519a7944f83bfd977a2e728ef3b7689a0ff505f9b705b3c33d7b16d7650d59f9.jpg", + "image_caption": [ + "SFIM" + ], + "image_footnote": [], + "bbox": [ + 238, + 433, + 316, + 492 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/786628240094241641522d052a4be43d48c59fc1d59f8432552ebe7772ceddb9.jpg", + "image_caption": [ + "PANNET" + ], + "image_footnote": [], + "bbox": [ + 316, + 433, + 395, + 492 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": 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The result of our approach was compared against nine other methods on WorldView-II dataset." + ], + "image_footnote": [], + "bbox": [ + 78, + 542, + 205, + 641 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1ae9cd95d1aecfa6398a1fd9e66b33539834da297afa45d80f3f7bd8fe7be560.jpg", + "image_caption": [ + "PAN" + ], + "image_footnote": [], + "bbox": [ + 215, + 542, + 341, + 641 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/84305f0f2d1fdf8ff1dc79b28c55cbea34b15f25cdff3683c072d853f7ad1f99.jpg", + "image_caption": [ + "GFPCA" + ], + "image_footnote": [], + "bbox": [ + 346, + 542, + 473, + 641 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3a64da425f2429a3e052c1fc62468238a59848f796c59f7e273f65d5d6a65c4a.jpg", + "image_caption": [ + "GS" + ], + "image_footnote": [], + "bbox": [ + 482, + 542, + 607, + 641 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d8f14abb291543a791186ba1583b9b21f566ccd638ff2cbd3bc0d3456334241e.jpg", + "image_caption": [ + "SFIM" + ], + "image_footnote": [], + "bbox": [ + 617, + 542, + 743, + 641 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/00bdeb75ec4e7bd95b81f29d9c1d64e6d2f89c79505243dfdd3b1eaa9d4fdd13.jpg", + "image_caption": [ + "PANNET" + ], + "image_footnote": [], + "bbox": [ + 751, + 542, + 879, + 641 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ff628b09ab32e29e24896454ac883b58c0a58477c06639f81c97288d0b5515f7.jpg", + "image_caption": [ + "LRMS" + ], + "image_footnote": [], + "bbox": [ + 80, + 655, + 205, + 753 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/45af43d3002359421dcb03293aae79350ec35d96d34e9d2d6974d67237889e65.jpg", + "image_caption": [ + "SRPPNN" + ], + "image_footnote": [], + "bbox": [ + 215, + 655, + 341, + 753 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/02de47e3c173ef6f221b6de9d231dcc8e565b1b68ee7652b0cc30da1fa229a65.jpg", + "image_caption": [ + "GPPNN" + ], + "image_footnote": [], + "bbox": [ + 346, + 655, + 473, + 753 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e8afdaeff36a24378aa2c390e48bf2d52403eaec5f957b7b81563a4126b6c8f8.jpg", + "image_caption": [ + "MutNet" + ], + "image_footnote": [], + "bbox": [ + 480, + 656, + 606, + 753 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/08ac0e41d756a880081efb4e6131a6078ca7c17316823e23f29cec192f486990.jpg", + "image_caption": [ + "INNformer" + ], + "image_footnote": [], + "bbox": [ + 617, + 657, + 741, + 753 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0a69a04bf4bc010a21046bad4bc00f5ef3230a7fb7269f70cced20cd6a0a8d8c.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 751, + 657, + 879, + 756 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f30e703fac6c4a197986abaccc98a142017eec8bca0494be6c7009e4859d52b1.jpg", + "image_caption": [ + "MSDCNN", + "GFPCA" + ], + "image_footnote": [], + "bbox": [ + 78, + 773, + 158, + 835 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3810b9fb286856a1c47c775de34bda4351dda85718ab60d42e212d563c096eb7.jpg", + "image_caption": [ + "GS", + "Figure 6. The result of our approach was compared against nine other methods on Gaofen2 dataset." + ], + "image_footnote": [], + "bbox": [ + 158, + 773, + 236, + 835 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bc5b9fdbccbcc9803a8b559717522e35633a10e782815f40b04f2991729083f5.jpg", + "image_caption": [ + "SFIM" + ], + "image_footnote": [], + "bbox": [ + 238, + 773, + 316, + 835 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f38701926997f836b9811daeae2a9a91b9650db5308af27b1b1cd2d055505126.jpg", + "image_caption": [ + "PANNET" + ], + "image_footnote": [], + "bbox": [ + 316, + 773, + 395, + 835 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/54b5a354014032201ac1bb8ce2235fd02a4c6c4b40bf3552069a8806f45e4d94.jpg", + "image_caption": [ + "MSDCNN" + ], + "image_footnote": [], + "bbox": [ + 395, + 773, + 473, + 835 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d4470ec0823b1e8fd9d4f71955a5b772ce04c0282a38a01a702b55affe7b23b0.jpg", + "image_caption": [ + "SRPPNN" + ], + "image_footnote": [], + "bbox": [ + 475, + 773, + 553, + 835 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/20bec2e6844ba2665bf59b2b0d3a7d2e69d789d14adc7e1bf3193e762c18f65d.jpg", + "image_caption": [ + "GPPNN" + ], + "image_footnote": [], + "bbox": [ + 553, + 773, + 630, + 835 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b1fc3c2833af4792191b67d858432a8cdc59da98979a866d389fba4a351964fe.jpg", + "image_caption": [ + "MutNet" + ], + "image_footnote": [], + "bbox": [ + 630, + 773, + 710, + 835 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/42bbc47ba0d76c638256a9c3475cf2ae8a02f2b577e9afd8c07c7e11cc7c4fae.jpg", + "image_caption": [ + "INNformer" + ], + "image_footnote": [], + "bbox": [ + 710, + 773, + 789, + 835 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b646a6e9effb975b2defdd60f3c8dcded30893cdda4273ebf059d58f29847659.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 790, + 773, + 870, + 835 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12914", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3fdc4360b46fd0f33e35c46c68577da8adb682d6d7c73d2bd81eefc8c978d94b.jpg", + "image_caption": [ + "Figure 7. The feature map display result reduces in size from the top to the bottom, corresponding to the output of the pyramid. It should be noted that the last two rows have been magnified for better visualization." + ], + "image_footnote": [], + "bbox": [ + 86, + 85, + 504, + 407 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/feee9e5bf5163b11f782d2a2ff2c748d405e00a20183dabf37ce9108f37fe458.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 513, + 88, + 892, + 409 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation experiments", + "text_level": 1, + "bbox": [ + 76, + 465, + 277, + 482 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conducted two sets of ablation experiments on three datasets to examine the effects of our suggested approach on model performance to further demonstrate the effectiveness of our method. Multi-scale information modeling and dual-domain information injection are the fundamental parts of our model, and we conducted ablation experiments by removing each part independently.", + "bbox": [ + 75, + 489, + 470, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Multi-scale feature extraction. The results of our model are shown in the first row of table 3 after the multi-scale feature extraction and reconstruction capabilities have been removed. We kept feature map size constant, eliminated all upsampling operations, and substituted the downsampling operation with standard convolution of stride 1 to conduct these trials. The results underscore the significance of multi-scale modeling for remote sensing images by showing that the model's performance declined after losing the capability of multi-scale modeling.", + "bbox": [ + 75, + 597, + 468, + 748 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Frequency Injection Pyramid. The impact of eliminating frequency domain information from the model is shown in the second row of table 3. In order to remove frequency domain information, we used SIM to replace FIM in the frequency injection pyramid and remove the frequency loss to conduct these studies. The importance of introducing frequency information into the pan-sharpening process is revealed by the observation that the different indicators deteriorated when the global frequency domain information was removed.", + "bbox": [ + 75, + 750, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Visualization of feature maps in different pyramids", + "text_level": 1, + "bbox": [ + 500, + 465, + 890, + 494 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To further demonstrate the multi-scale and dual-domain modeling capabilities of our model, we present $P$ , $M_{s}$ , $F_{spainj}$ , $M_{f}$ , $F_{fre}$ , and $F_{freinj}$ at different scales. These feature maps correspond to the output of the feature extraction pyramid, the features described in formula 6, and the features expressed in formulas 5, 9, 16, and 8, respectively. The Figure 7 illustrate that the features of different scales capture different regions of remote sensing images. The spatial pyramid features focus well on local information, while the frequency domain features effectively capture global and high-frequency features. The features after frequency domain injection combine the two types of information effectively.", + "bbox": [ + 496, + 508, + 892, + 705 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 734, + 617, + 750 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we investigate the amplitude degradation of LRMS and PAN images across various scales. Based on the results of our investigation, we suggest a pyramid dual-domain injection network that injects multi-scale frequency and spatial domain information from the PAN image into the LRMS image to aid in its restoration. Our rigorous experiments on a variety of datasets demonstrate that our suggested model surpasses SOTA methods, exhibits good generalization, and effectively handles real-world scenarios.", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12915", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment", + "text_level": 1, + "bbox": [ + 76, + 90, + 228, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was Supported by the HFIPS Director's Fund, Grant No.2023YZGH04.", + "bbox": [ + 76, + 114, + 468, + 143 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 160, + 174, + 176 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Devansh Arpit, Stanisław Jastrzebski, Nicolas Ballas, David Krueger, Emmanuel Bengio, Maxinder S Kanwal, Tegan Maharaj, Asja Fischer, Aaron Courville, Yoshua Bengio, et al. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1798-1808, 2022." + ], + "bbox": [ + 78, + 90, + 468, + 698 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "12917", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Pyramid Dual Domain Injection Network for Pan-sharpening/aa199a66-751b-4158-bd1f-1783173c94fd_model.json b/2023/Pyramid Dual Domain Injection Network for Pan-sharpening/aa199a66-751b-4158-bd1f-1783173c94fd_model.json new file mode 100644 index 0000000000000000000000000000000000000000..3d8f478c5404aa5ca8ce2e66c8abb4230cf49316 --- /dev/null +++ b/2023/Pyramid Dual Domain Injection Network for Pan-sharpening/aa199a66-751b-4158-bd1f-1783173c94fd_model.json @@ -0,0 +1,2783 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.175, + 0.131, + 0.797, + 0.154 + ], + "angle": 0, + "content": "Pyramid Dual Domain Injection Network for Pan-sharpening" + }, + { + "type": "text", + "bbox": [ + 0.134, + 0.179, + 0.836, + 0.2 + ], + "angle": 0, + "content": "Xuanhua \\(\\mathrm{He}^{1,2*}\\) Keyu Yan\\(^{1,2*}\\) Rui Li\\(^{2}\\) Chengjun Xie\\(^{1,2}\\) Jie Zhang\\(^{2\\dagger}\\) Man Zhou\\(^{3\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.267, + 0.199, + 0.705, + 0.217 + ], + "angle": 0, + "content": "1University of Science and Technology of China, China" + }, + { + "type": "text", + "bbox": [ + 0.192, + 0.217, + 0.778, + 0.234 + ], + "angle": 0, + "content": "\\(^{2}\\)Hefei Institute of Physical Science, Chinese Academy of Sciences, China" + }, + { + "type": "text", + "bbox": [ + 0.299, + 0.234, + 0.671, + 0.253 + ], + "angle": 0, + "content": "\\(^{3}\\)Nanyang Technological University, Singapore" + }, + { + "type": "text", + "bbox": [ + 0.098, + 0.255, + 0.871, + 0.27 + ], + "angle": 0, + "content": "{hexuanhua,keyu}@mail.ustc.edu.cn，{lirui,cjxie,zhangjie}@iim.ac.cn,manzhountu@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.313, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.337, + 0.474, + 0.716 + ], + "angle": 0, + "content": "Pan-sharpening, a panchromatic image guided low-spatial-resolution multi-spectral super-resolution task, aims to reconstruct the missing high-frequency information of high-resolution multi-spectral counterpart. Although the inborn connection with frequency domain, existing pan-sharpening research has almost investigated the potential solution upon frequency domain, thus limiting the model performance improvement. To this end, we first revisit the degradation process of pan-sharpening in Fourier space, and then devise a Pyramid Dual Domain Injection Pan-sharpening Network upon the above observation by fully exploring and exploiting the distinguished information in both the spatial and frequency domains. Specifically, the proposed network is organized with multi-scale U-shape manner and composed by two core parts: a spatial guidance pyramid sub-network for fusing local spatial information and a frequency guidance pyramid sub-network for fusing global frequency domain information, thus encouraging dual-domain complementary learning. In this way, the model can capture multi-scale dual-domain information to enable generating high-quality pan-sharpening results. Quantitative and qualitative experiments over multiple datasets demonstrate that our method performs the best against other state-of-the-art ones and comprises a strong generalization ability for real-world scenes." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.744, + 0.21, + 0.76 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.77, + 0.47, + 0.877 + ], + "angle": 0, + "content": "There is often a high demand for high-resolution multispectral (HRMS) images in the domain of agricultural monitoring and mapping services. However, due to the limitations of satellite sensors, the existing approaches must instead separately capture high-resolution panchromatic (PAN) and multispectral low-resolution (LRMS) images and fuse them using a technique known as pan" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.305, + 0.891, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.483, + 0.893, + 0.567 + ], + "angle": 0, + "content": "Figure 1. Frequency domain analysis of multi-scale PAN, MS, and Ground Truth images. The amplitude, denoted by A, is displayed for the original-scale image, the 2-times downsampled image, and the 4-times downsampled image, from top to bottom, respectively. The last two columns show the degradation of PAN and MS images relative to GT images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.892, + 0.673 + ], + "angle": 0, + "content": "harpening to get the desired HRMS images. Essentially, pan-sharpening is a super-resolution process that utilizes the richer details of PAN images to guide the reconstruction process of LRMS images. Pan-sharpening technology has expanded the use of remote sensing images in a wider range and gained considerable attention." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Pan-sharpening has seen an increase in the use of deep learning-based techniques in recent years. The PNN [16], which started this trend, was motivated by the SRCNN [4] to introduce the convolutional neural network. The PNN presented a three-layer convolutional neural network that concatenated LRMS and PAN images as input and subsequently generated the output through the network. Since then, a flood of deep learning-based techniques has been developed to improve the model's representation capacity by employing deeper models or model-driven techniques [33, 29, 7, 32]. While significant progress has been made, there are still limitations need to be addressed. Prior approaches have primarily focused on spatial domain solutions, thereby neglecting the exploration of frequency domain solutions. Nevertheless, it has been established that CNNs in the spa" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.424, + 0.901 + ], + "angle": 0, + "content": "*Co-first authors contributed equally, † Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12908" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.333 + ], + "angle": 0, + "content": "tial domain exhibit a preference for low-frequency information and struggle to capture high-frequency information [1], resulting in insufficient texture in the generated images [14]. However, by incorporating frequency domain information, high-frequency features in low-dimensional manifolds can be efficiently captured [20]. Additionally, the LRMS images can be treated as degraded versions of HRMS images, which indicates that pan-sharpening is fundamentally an image restoration task. Image restoration are highly interrelated with frequency domain, as image degradation and content can be easily disentangled through the Fourier transform [9]. Thus, it is natural for us to investigate the feasibility of introducing frequency domain information into the pan-sharpening domain, as detailed in Figure 1 where the degradation effect of pan-sharpening is enlarged over multi-scale manner." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.338, + 0.473, + 0.807 + ], + "angle": 0, + "content": "Motivation. We conducted multi-scale Fourier analysis on LRMS, PAN, and HRMS images since the degradation mostly affects the amplitude of the image and the diversity scale of remote sensing landforms has an effect on the pan-sharpening process. The analysis results of image spectrum is shown in the Figure 1. We can draw two inspirations from the figure: 1) The difference in amplitudes between the PAN and HRMS images is primarily in the low frequency component, whereas the difference between the amplitudes of the HRMS and LRMS images is observed in both the high and low frequency components. 2) As the scale decreases, we can observe the missing information in the PAN image becomes more concentrated in the low-frequency component, while the degradation of the LRMS image becomes more concentrated in the high frequency component, and the degradation of images at various scales is not exactly the same. We may deduce from observation 1 that the frequency information in the PAN image can be used to fill in the missing information of the LRMS image. For observation 2, it is crucial to restore the information at several scales since the degradation is varied under multi-scale conditions. To encourage the learning of context information and multi-scale reconstruction, frequency domain information should be handled at various scales. Additionally, we can encourage the interaction of global and local, low-frequency and high-frequency features through multi-scale processing in the spatial and frequency domains in accordance with CNN's low-frequency preference in spatial domain and the global receptive field described by the spectral convolution theorem [6] in frequency domain to enhance the model's performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In light of the aforementioned observation, we propose a brand new Pyramid Dual Domain Injection Network (PDDIN) to inject the multi-scale details of the PAN image into the LRMS image in both the spatial and frequency domains to aid in the restoration process. A Feature Extraction Pyramid, a Frequency Injection Pyramid, and a" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.348 + ], + "angle": 0, + "content": "Spatial Injection Pyramid compensate the three major key components of the network. The Feature Extraction Pyramid is responsible for extracting multi-scale feature information from the PAN image. By using these features, the Frequency Injection Pyramid may inject global multi-scale features into the LRMS image, facilitating the recovery of global and high-frequency information in the spatial domain. To promote the reconstruction of local and spatial information, the spatial domain feature of PAN images is injected into the LRMS image in the Spatial Injection Pyramid. This approach effectively compensates for degradation at various scales, leading to a more thorough and precise reconstruction of the image. We conducted comprehensive experiments on multiple datasets to assess the effectiveness of our suggested network. The results show the efficacy of our method, by outperforming state-of-the-art techniques in both qualitative and quantitative evaluations." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.349, + 0.796, + 0.362 + ], + "angle": 0, + "content": "Our contributions are summarized below:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.369, + 0.892, + 0.445 + ], + "angle": 0, + "content": "- In this work, we revisit the degradation process of pan-sharpening in Fourier space, and then devise a Pyramid Dual Domain Injection Pan-sharpening Network, inspired by the above observation in both the spatial and frequency domains." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.452, + 0.892, + 0.543 + ], + "angle": 0, + "content": "- To fully explore and exploit the distinguished information, we devised a frequency guidance pyramid sub-network and a spatial guidance pyramid sub-network. This design allows for the fusion of multi-scale information from both the frequency and spatial domains, lifting the learning capability of the model." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.55, + 0.892, + 0.61 + ], + "angle": 0, + "content": "- Extensive experiments on multiple satellite datasets demonstrate our approach's quantitative and qualitative superiority to existing state-of-the-art pan-sharpening algorithms." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.369, + 0.892, + 0.61 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.627, + 0.638, + 0.643 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.81, + 0.668 + ], + "angle": 0, + "content": "2.1. Traditional pan-sharpening method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Three sorts of traditional techniques are widely adapted in the realm of pan-sharpening: component substitution (CS) method, MRA method, and VO-based method. The component substitution approach generates high-resolution images by substituting the LRMS image components with the spatial detail components from the PAN image. IHS algorithm [10], Brovey [8], PCA [12], and GS algorithm [11] are examples of CS methods. Due to the fact that spectral information is not fully considered in CS methods, the pan-sharpened images suffer from serious spectral distortion. In light of this, the MRA method reduces spectral distortion by fusing PAN and LRMS through multi-resolution decomposition. DWT [15] ATWT [17] HPF [19] and LP [22] algorithms are typical MRA algorithms. The VO-based methods, in contrast to the above two, treat pan-sharpening as" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12909" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.093, + 0.885, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.346, + 0.893, + 0.377 + ], + "angle": 0, + "content": "Figure 2. The framework of the Pyramid Dual Domain Injection Network. It consists of three key components: Feature Extraction Pyramid, Frequency Injection Pyramid and Spatial Injection Pyramid." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.473, + 0.506 + ], + "angle": 0, + "content": "an optimization problem, design the loss function under a prior constraints, and then generate results by iterative solution and minimization of the loss function. The Bayesian technique [5] and the total variation algorithm [18] are common approaches in VO methods. The VO method can deliver decent results, but designing the optimization model and choosing the loss function is a significant challenge." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.526, + 0.391, + 0.543 + ], + "angle": 0, + "content": "2.2. CNN-based pan-sharpening method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.554, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In recent years, the dominant approach in this area has been the CNN-based pan-sharpening method. PNN [16], which is inspired by SRCNN [4], is the pioneering work that introduced CNN to this field, giving rise to an unprecedented number of novel CNN-based techniques [27, 29, 7, 32, 33]. Despite having a clear and simple network structure, the results of PNN outperformed traditional techniques, demonstrating the promising potential of CNN techniques. Following that, Pannet [30] employs residual connection and high-frequency filtering to learn high-frequency features of images, while multi-scale convolution is taken into account in MsDCNN [31] to handle the varied remote sensing landforms. The model-driven models such as GPPNN [25], MMNet [28] and ARFNet [26] achieve interpretable models by utilizing deep unfolding techniques to construct the network structure. Additionally, SRPPNN [2] uses the progress super resolution method to enhance the performance of model and construct a profoundly deep network. Recently, MutNet [33] utilizes a mutual information mechanism to learn a more effective feature representation. The study of these techniques has also been expanded to include generative networks [13] and unsupervised pan-sharpening [21] technologies." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.398, + 0.6, + 0.413 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.423, + 0.895, + 0.59 + ], + "angle": 0, + "content": "In this part, we first discuss the pertinent Fourier transform properties before delving into further details about our network shown in Figure 2, 3 and 4. It is organized into three parts: the Feature Extraction Pyramid, which extracts the multi-scale features from PAN images; the Frequency Injection Pyramid, which incorporates multi-scale frequency features from PAN into LRMS images for global and high-frequency information restoration; and the Spatial Injection Pyramid, which introduces the multi-scale spatial information from PAN into LRMS images to reconstruct local details. Finally, we will describe our loss function." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.599, + 0.755, + 0.615 + ], + "angle": 0, + "content": "3.1. Fourier transform of images" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.622, + 0.892, + 0.727 + ], + "angle": 0, + "content": "Due to its capacity to decompose signals into their frequency components, the Fourier transform is widely adapted in the image processing community. This transformation makes it possible to analyze the image from a different perspective and offers valuable insights into its features. The Fourier transform of an input image \\( x \\in R^{h \\times w} \\) can be defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.735, + 0.892, + 0.789 + ], + "angle": 0, + "content": "\\[\n\\mathcal {F} (x) (u, v) = \\frac {1}{\\sqrt {H W}} \\sum_ {h = 0} ^ {H - 1} \\sum_ {w = 0} ^ {W - 1} x (h, w) e ^ {- j 2 \\pi \\left(\\frac {h}{H} u + \\frac {w}{W} v\\right)} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.79, + 0.895, + 0.834 + ], + "angle": 0, + "content": "In our work, the Fourier transform is individually applied to each image channel. The amplitude and phase components can be described as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.546, + 0.844, + 0.893, + 0.865 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} (x) (u, v) = \\left[ R ^ {2} (x) (u, v) + I ^ {2} (x) (u, v) \\right] ^ {\\frac {1}{2}}, \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.866, + 0.892, + 0.899 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} (x) (u, v) = \\arctan \\left[ \\frac {I (x) (u , v)}{R (x) (u , v)} \\right] \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "12910" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.136 + ], + "angle": 0, + "content": "where \\(I(x)\\) and \\(R(x)\\) indicate imaginary and real parts of the image's frequency representation \\(\\mathcal{F}(x)\\), correspondingly." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.471, + 0.41 + ], + "angle": 0, + "content": "The Fourier transform can be beneficial in the task of pan-sharpening by disentangling and analyzing image degradation in the amplitude component. We may obtain important insights into the level of degradation existing in the image by carefully evaluating the amplitude information, ultimately resulting in more effective restoration attempts. Figure 1 illustrates that whereas LRMS images degrade in both the high-frequency and low-frequency regions, while PAN images degrade mostly in the low-frequency region. Moreover, it is important to note that the frequency of image degradation can vary across different scales. Following frequency analysis, it is obvious that the frequency domain information from a PAN image can be effectively integrated into a LRMS image to assist with its restoration. This process can be further optimized by injecting the frequency domain information at multiple scales, allowing for a more comprehensive reconstruction of the image's contextual information." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.42, + 0.272, + 0.435 + ], + "angle": 0, + "content": "3.2. Network framework" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.443, + 0.47, + 0.64 + ], + "angle": 0, + "content": "As shown in Figure 2, given an input of a PAN and LRMS pair, we start by upsampling the LRMS image to the size of the PAN image. After that, a feature extraction pyramid is employed to process the PAN image, obtaining multi-scale features. Once the LRMS image is upsampled, the frequency injection pyramid injects multi-scale features into the LRMS image. The frequency injection pyramid is used to integrate the frequency domain features of various scales to further explore the frequency information. Then, we adopt spatial injection pyramid to reconstruct local details. Finally, the reconstruction image is obtained through a skip connection between network output and the upsampled LRMS image." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.65, + 0.34, + 0.667 + ], + "angle": 0, + "content": "3.3. The key building components" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Three essential elements make up the architecture of our network, and they are shown in Figures 2, 3, and 4. We go into great depth on each of these parts in the part that follows. Feature Extraction Pyramid. The Feature Extraction Pyramid is in charge of extracting multi-scale features from the PAN images, which can be utilized by other modules for further feature injection. To obtain the original size feature, the PAN image is first projected into the feature space using a convolution layer. After that, two sets of convolution and downsampling operations are carried out to generate features that are half as large and a quarter as large as the original. These features, namely \\( P_{1}, P_{2} \\), and \\( P_{3} \\), are then injected as supplemental information to the LRMS images to aid in the reconstruction process. The convolution operation with a stride of 2 is employed as a down-sampling" + }, + { + "type": "image", + "bbox": [ + 0.53, + 0.088, + 0.877, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.235, + 0.894, + 0.32 + ], + "angle": 0, + "content": "Figure 3. Architecture of Frequency Injection Module (FIM). The phase and amplitude components of \\( P_{i} \\) and \\( F_{i} \\) are obtained using the Fourier transform. Feature fusion is performed in the frequency domain, and the resulting frequency domain feature map is combined with the spatial feature to facilitate frequency domain information recovery and dual-domain complementary learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.342, + 0.892, + 0.387 + ], + "angle": 0, + "content": "operation in the pyramid. In the end, this module produces multi-scale feature maps for further information injection utilizing PAN image as input." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.388, + 0.893, + 0.629 + ], + "angle": 0, + "content": "Spatial Injection Pyramid. The Spatial Injection Pyramid is designed to inject the local, multi-scale spatial information from PAN into the LRMS image. This module may effectively concentrate on small objects by leveraging the locality of the convolution operation in the pixel domain. In this module, the spatial features of \\( P_{1} \\), \\( P_{2} \\), and \\( P_{3} \\) are injected into LRMS images at various scales to aid in reconstruction. For instance, given the output of the frequency pyramid presented by \\( M s_{i} \\) and the feature map \\( P_{i} \\) at the original scale, further feature extraction is performed using a convolution layer to get \\( S_{i} \\), and then the features \\( P_{i} \\) are injected into \\( S_{i} \\) using the spatial injection module (SIM). Following injection, a down-sampling or up-sampling operation is applied to generate the feature map of a different size. Taking the down-sampling branch for example, the process can be described as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.64, + 0.891, + 0.657 + ], + "angle": 0, + "content": "\\[\nS _ {i} = \\operatorname {c o n v} _ {3 \\times 3} (M s _ {i}) \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.609, + 0.659, + 0.892, + 0.676 + ], + "angle": 0, + "content": "\\[\nF _ {s p a i n j} = S I M \\left(S _ {i}, P _ {i}\\right) \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.61, + 0.678, + 0.891, + 0.695 + ], + "angle": 0, + "content": "\\[\nM s _ {i + 1} = \\operatorname {d o w n} \\left(F _ {\\text {s p a i n j}}\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.81 + ], + "angle": 0, + "content": "The suggested spatial injection module, shown in the figure 4, uses the AFF [3] as a basis block and is built on attention mechanism to enable effective and consistent injection of spatial details. The module works by enabling interaction between the PAN and LRMS branches, which enhances detail injection and facilitates the acquisition of LRMS features with injected spatial details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Frequency Injection Pyramid. The purpose of the frequency injection pyramid is to provide LRMS features with high-frequency and global information from PAN image. By utilizing the multi-scale frequency injection, the restoration of LRMS image's frequency domain information is enhanced by leveraging the frequency information of PAN im" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12911" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.087, + 0.473, + 0.22 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.227, + 0.47, + 0.268 + ], + "angle": 0, + "content": "Figure 4. The proposed module for injecting spatial domain information, dubbed SIM, is based on attention mechanism and uses a basic module built on attentional fusion block." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.29, + 0.473, + 0.486 + ], + "angle": 0, + "content": "age. Processing information in frequency domain enables the network to quickly capture high-frequency features that are challenging to acquire using pixel domain CNN, encourages dual-domain complementary learning, and generates clear texture features. Specifically, given the feature map of the LRMS image presented by \\( Mf_{i} \\) and the feature map \\( P_{i} \\), first \\( M_{i} \\) are fed to a convolution block to extract a further feature \\( F_{i} \\). Next, the frequency injection module (FIM) is used to inject the frequency domain features of \\( P_{i} \\) into \\( F_{i} \\). The resulting feature map is then down-sampled or upsampled for the next scale of frequency domain information injection. Taking the up-sampling branch as an example, this process is summarized as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.497, + 0.469, + 0.513 + ], + "angle": 0, + "content": "\\[\nF _ {i} = \\operatorname {c o n v} _ {3 \\times 3} (M f _ {i}) \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.516, + 0.469, + 0.532 + ], + "angle": 0, + "content": "\\[\nF _ {f r e i n j} = F I M \\left(F _ {i}, P _ {i}\\right) \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.535, + 0.469, + 0.552 + ], + "angle": 0, + "content": "\\[\nM f _ {i + 1} = u p \\left(F _ {f r e i n j}\\right) \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.562, + 0.357, + 0.576 + ], + "angle": 0, + "content": "where \\(up\\) is implemented by pixel-shuffle." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.577, + 0.469, + 0.666 + ], + "angle": 0, + "content": "With the inputs \\(F_{i}\\) and \\(P_{i}\\), the FIM shown in Figure 3 employs the Fourier transform to produce amplitude and phase components. Following that, the phase and amplitude information of \\(P_{i}\\) is individually injected into \\(F_{i}\\) to aid in the restoration of the LRMS image in the frequency domain." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.668, + 0.469, + 0.698 + ], + "angle": 0, + "content": "In particular, the following procedure is used to acquire the relevant amplitude and phase components:" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.708, + 0.469, + 0.724 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} \\left(F _ {i}\\right), \\mathcal {P} \\left(F _ {i}\\right) = \\mathcal {F} \\left(F _ {i}\\right), \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.727, + 0.469, + 0.743 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} \\left(P _ {i}\\right), \\mathcal {P} \\left(P _ {i}\\right) = \\mathcal {F} \\left(P _ {i}\\right), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.753, + 0.469, + 0.814 + ], + "angle": 0, + "content": "For the \\(\\mathcal{A}(F_i)\\), we use SFT [24] to inject frequency information from \\(\\mathcal{A}(P_i)\\), and use \\(Conv_{1\\times 1}\\) to fuse phase components, for the difference between two modalities mainly lay in amplitude:" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.824, + 0.469, + 0.841 + ], + "angle": 0, + "content": "\\[\n\\alpha , \\beta = \\operatorname {C o n v} _ {3 \\times 3} (\\mathcal {A} (P _ {i})), \\operatorname {C o n v} _ {3 \\times 3} (\\mathcal {A} (P _ {i})), \\tag {12}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.843, + 0.469, + 0.859 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} \\left(F _ {i}\\right) = \\mathcal {A} \\left(F _ {i}\\right) \\cdot \\alpha + \\beta , \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.862, + 0.469, + 0.879 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} (F) = \\operatorname {C o n v} _ {1 \\times 1} \\left(\\operatorname {C a t} \\left(\\left[ \\mathcal {A} \\left(P _ {i}\\right), \\mathcal {A} \\left(F _ {i}\\right) \\right]\\right)\\right), \\tag {14}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.107, + 0.881, + 0.469, + 0.897 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} (F) = \\operatorname {C o n v} _ {1 \\times 1} \\left(\\operatorname {C a t} \\left(\\left[ \\mathcal {P} \\left(P _ {i}\\right), \\mathcal {P} \\left(F _ {i}\\right) \\right]\\right)\\right) \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "The injected components are then transformed back to the pixel domain using the inverse transform, and are subsequently fused with spatial features to inject frequency features into spatial information and promote dual-domain complementary learning:" + }, + { + "type": "equation", + "bbox": [ + 0.566, + 0.172, + 0.891, + 0.19 + ], + "angle": 0, + "content": "\\[\nF _ {f r e} = \\operatorname {C o n v} _ {1 \\times 1} \\left(\\mathcal {F} ^ {- 1} (\\mathcal {A} (F), \\mathcal {P} (F))\\right) \\tag {16}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.567, + 0.192, + 0.891, + 0.209 + ], + "angle": 0, + "content": "\\[\nF _ {s p a} = \\operatorname {C o n v} _ {3 \\times 3} \\left(F _ {i}\\right), \\tag {17}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.567, + 0.211, + 0.891, + 0.228 + ], + "angle": 0, + "content": "\\[\nF _ {f r e i n j} = F _ {f r e} + F _ {s p a} \\tag {18}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.232, + 0.645, + 0.246 + ], + "angle": 0, + "content": "3.4. Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.255, + 0.892, + 0.36 + ], + "angle": 0, + "content": "To improve the perception of high-frequency information, we propose a loss function that combines spatial and frequency domain losses in this study. Provided that \\( Y \\) represents the model output, \\( Y_{f} \\) represents the output of frequency injection pyramid and \\( H \\) represents the ground truth, the \\( L_{1} \\) distance between \\( Y \\) and \\( H \\) is employed to define the spatial domain loss:" + }, + { + "type": "equation", + "bbox": [ + 0.635, + 0.367, + 0.891, + 0.384 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s} = \\left| \\left| Y - H \\right| \\right| _ {1}. \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.389, + 0.891, + 0.434 + ], + "angle": 0, + "content": "The frequency domain loss, which aims to improve the perception of high-frequency information, is determined using the following formula:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.44, + 0.892, + 0.471 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {f} = \\left| \\left| \\log \\left(\\mathcal {A} \\left(Y _ {f}\\right)\\right) - \\log \\left(\\mathcal {A} (H)\\right) \\right| \\right| _ {1} + \\left| \\left| \\mathcal {P} (Y) - \\mathcal {P} (H) \\right| \\right| _ {1}, \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.892, + 0.553 + ], + "angle": 0, + "content": "where the amplitude and phase components of the Fourier transform are denoted by \\(\\mathcal{A}\\) and \\(\\mathcal{P}\\) respectively. The complete loss function is a combination of the dual domain losses, and involves a hyper-parameter \\(\\lambda\\) which is set to 0.1 based on empirical evidence." + }, + { + "type": "equation", + "bbox": [ + 0.641, + 0.559, + 0.891, + 0.575 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {s} + \\lambda \\mathcal {L} _ {f}. \\tag {21}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.581, + 0.625, + 0.598 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.606, + 0.727, + 0.621 + ], + "angle": 0, + "content": "4.1. Datasets and benchmark" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.795 + ], + "angle": 0, + "content": "Three datasets—WorldView-II (WV2), WorldView-III (WV3), and Gaofen2 (GF2) were used in our experiments. Due to the unavailability of real HRMS images, we utilized the Wald protocol [23] to generate the training and test data. In further detail, we extracted patches from the same location from the PAN and LRMS images, with the PAN patch being \\( r \\) times larger than the LRMS patch. The original LRMS patch was utilized as the ground truth, and both the LRMS and PAN patches were downsampled by a factor of \\( r \\) and used as input data. The selected patch sizes were 128x128 and 32x32, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.9 + ], + "angle": 0, + "content": "To evaluate the efficacy of our approach, we compared it with five traditional and six advanced CNN-based methods. Specifically, we included SFIM, Brovey [8], GS [11], IHS [10], and GFPCA [12] as traditional methods, and PANNET [30], MSDCNN [31], SRPPNN [2], GPPNN [25], MutNet [33] and INNformer [32] as advanced methods." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12912" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.892, + 0.116 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison on three datasets. Best results are highlighted by red. \\(\\uparrow\\) indicates that the larger the value, the better the performance, and \\(\\downarrow\\) indicates that the smaller the value, the better the performance." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.115, + 0.904, + 0.395 + ], + "angle": 0, + "content": "
MethodWorldView-IIGaoFen2Worldview-III
PSNR↑SSIM↑SAM↓ERGAS↓PSNR↑SSIM↑SAM↓ERGAS↓PSNR↑SSIM↑SAM↓ERGAS↓
SFIM34.12970.89750.04392.344936.90600.88820.03181.739821.82120.54570.12088.9730
Brovey35.86460.92160.04031.823837.79740.90260.02181.372022.50600.54660.11598.2331
GS35.63760.91760.04231.877437.22600.90340.03091.673622.56080.54700.12178.2433
IHS35.29620.90270.04612.027838.17540.91000.02431.533622.55790.53540.12668.3616
GFPCA34.55810.90380.04882.141137.94430.92040.03141.560422.33440.48260.12948.3964
PANNET40.81760.96260.02571.055743.06590.96850.01780.857729.68400.90720.08513.4263
MSDCNN41.33550.96640.02420.994045.68470.98270.01350.638930.30380.91840.07823.1884
SRPPNN41.45380.96790.02330.989947.19980.98770.01060.558630.43460.92020.07703.1553
GPPNN41.16220.96840.02441.031544.21450.98150.01370.736130.17850.91750.07763.2593
MutNet41.67730.97050.02240.951947.30420.98920.01020.548130.49070.92230.07493.1125
INNformer41.69030.97040.02270.951447.35280.98930.01020.547930.53650.92250.07473.0997
Ours41.84730.97070.02220.935847.49390.98950.01000.536030.85020.92550.07262.9945
" + }, + { + "type": "table_caption", + "bbox": [ + 0.168, + 0.411, + 0.8, + 0.424 + ], + "angle": 0, + "content": "Table 2. Evaluation of the proposed method on real-world full-resolution scenes from the GaoFen2 dataset." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.424, + 0.894, + 0.498 + ], + "angle": 0, + "content": "
MetricSFIMBroveyGSIHSGFPCAPANNETMSDCNNSRPPNNGPPNNMutNetINNformerOurs
Dλ↓0.08220.13780.06960.07700.09140.07370.07340.07670.07820.06940.06930.0682
DS↓0.10870.26050.24560.29850.16350.12240.11510.11620.12530.11180.11380.1101
QNR ↑0.82140.63900.07250.64850.76150.81430.82150.81730.80730.82470.82590.8307
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.523, + 0.291, + 0.539 + ], + "angle": 0, + "content": "4.2. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.547, + 0.471, + 0.669 + ], + "angle": 0, + "content": "The experiment was conducted on an RTX 3060 GPU, using the PyTorch framework. The Adam optimizer was employed with an initial learning rate of \\(5 \\times 10^{-4}\\). To ensure stable training, the learning rate was decayed to \\(5 \\times 10^{-8}\\) using the cosine annealing method after 500 epochs. Several commonly used evaluation metrics were chosen, including PSNR, SSIM, SAM, and ERGAS, as well as non-reference indices such as \\(D_{S}\\), \\(D_{\\lambda}\\), and QNR." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.681, + 0.436, + 0.697 + ], + "angle": 0, + "content": "4.3. Comparison with state-of-the-art methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Evaluation on Reduced-Resolution Scene. The evaluation results of our approach on three datasets are shown in Table 1. The results demonstrate that our model performs better than the state-of-the-art approaches in the majority of assessment measures, and the improvements are significant. To be specific, our method outperforms the cutting-edge method INNformer on most indicators, on the WV2 dataset, our model achieves a \\(0.16\\mathrm{~dB}\\) improvement in PSNR compared to MIDN. Similarly, on the GF2 and WV3 datasets, our model achieves a \\(0.14\\mathrm{~dB}\\) and \\(0.31\\mathrm{~dB}\\) improvement in PSNR, respectively, demonstrating its excellent performance. Comparable improvements are also observed in other evaluation metrics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.72 + ], + "angle": 0, + "content": "Additionally, for qualitative evaluation, we compared the results obtained from our method with those of the other nine methods on the WV2 and GF2 datasets. To evaluate the similarity between the generated results and the ground truth, a residual map was generated by computing their mean squared error. The brighter areas of residual map indicate the larger differences with the ground truth. Our approach produces images with the finest texture and most realistic spectrum, as shown in Figures 5 and 6. The residual maps exhibit the least amount of bright spots, indicating high congruence with the ground truth. These findings are further supported by the evaluation indicators presented in the Table 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Evaluation on Full-Resolution Scene. To test the generalization ability of our model, we trained it on the GF2 dataset and evaluated full-resolution data from GF2 that was not downsampled, using the reserved portion of the dataset. Since there was no reference image available, we evaluated the dataset using no-reference indices. As shown in Table 2, our method achieved the best QNR index on this dataset, indicating its strong generalization ability compared to traditional and deep learning methods. This demonstrates that our approach can be applied to real-world scenes." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "12913" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.176, + 0.088, + 0.791, + 0.101 + ], + "angle": 0, + "content": "Table 3. The outcomes of the ablation experiments conducted on the WordView-II dataset are presented." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.101, + 0.892, + 0.189 + ], + "angle": 0, + "content": "
Config Multi-scale FIMWorldView-IIGaoFen2WorldView-III
PSNR↑SSIM↑SAM↓ERGAS↓PSNR↑SSIM↑SAM↓ERGAS↓PSNR↑SSIM↑SAM↓ERGAS↓
(I)×✓41.63610.97010.02250.958147.37880.98920.01020.546630.78490.92520.07173.0240
(II)✓×41.63990.96950.02270.960047.45880.98900.01010.540330.81400.92560.07183.0106
Ours✓✓41.84350.97110.02220.947847.49390.98950.01000.536030.86450.92580.07572.9851
" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.202, + 0.209, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.121, + 0.303, + 0.165, + 0.314 + ], + "angle": 0, + "content": "LRMS" + }, + { + "type": "image", + "bbox": [ + 0.215, + 0.202, + 0.343, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.262, + 0.303, + 0.294, + 0.314 + ], + "angle": 0, + "content": "PAN" + }, + { + "type": "image", + "bbox": [ + 0.348, + 0.202, + 0.477, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.387, + 0.303, + 0.438, + 0.313 + ], + "angle": 0, + "content": "GFPCA" + }, + { + "type": "image", + "bbox": [ + 0.483, + 0.202, + 0.611, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.303, + 0.56, + 0.313 + ], + "angle": 0, + "content": "GS" + }, + { + "type": "image", + "bbox": [ + 0.619, + 0.202, + 0.747, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.666, + 0.303, + 0.704, + 0.313 + ], + "angle": 0, + "content": "SFIM" + }, + { + "type": "image", + "bbox": [ + 0.753, + 0.202, + 0.882, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.785, + 0.303, + 0.853, + 0.313 + ], + "angle": 0, + "content": "PANNET" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.315, + 0.208, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.416, + 0.18, + 0.428 + ], + "angle": 0, + "content": "MSDCNN" + }, + { + "type": "image", + "bbox": [ + 0.216, + 0.315, + 0.344, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.247, + 0.416, + 0.306, + 0.427 + ], + "angle": 0, + "content": "SRPPNN" + }, + { + "type": "image", + "bbox": [ + 0.349, + 0.315, + 0.477, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.383, + 0.416, + 0.434, + 0.428 + ], + "angle": 0, + "content": "GPPNN" + }, + { + "type": "image", + "bbox": [ + 0.482, + 0.316, + 0.607, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.519, + 0.416, + 0.568, + 0.427 + ], + "angle": 0, + "content": "MutNet" + }, + { + "type": "image", + "bbox": [ + 0.619, + 0.316, + 0.745, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.648, + 0.416, + 0.718, + 0.427 + ], + "angle": 0, + "content": "INNformer" + }, + { + "type": "image", + "bbox": [ + 0.753, + 0.316, + 0.882, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.8, + 0.417, + 0.832, + 0.428 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.433, + 0.159, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.099, + 0.498, + 0.138, + 0.507 + ], + "angle": 0, + "content": "GFPCA" + }, + { + "type": "image", + "bbox": [ + 0.16, + 0.433, + 0.238, + 0.492 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.191, + 0.498, + 0.209, + 0.506 + ], + "angle": 0, + "content": "GS" + }, + { + "type": "image", + "bbox": [ + 0.24, + 0.434, + 0.317, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.266, + 0.498, + 0.295, + 0.507 + ], + "angle": 0, + "content": "SFIM" + }, + { + "type": "image", + "bbox": [ + 0.318, + 0.434, + 0.396, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.336, + 0.498, + 0.381, + 0.507 + ], + "angle": 0, + "content": "PANNET" + }, + { + "type": "image", + "bbox": [ + 0.397, + 0.434, + 0.475, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.411, + 0.498, + 0.461, + 0.507 + ], + "angle": 0, + "content": "MSDCNN" + }, + { + "type": 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+ ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.821, + 0.498, + 0.846, + 0.507 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.175, + 0.517, + 0.793, + 0.531 + ], + "angle": 0, + "content": "Figure 5. The result of our approach was compared against nine other methods on WorldView-II dataset." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.544, + 0.207, + 0.642 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.121, + 0.645, + 0.165, + 0.655 + ], + "angle": 0, + "content": "LRMS" + }, + { + "type": "image", + "bbox": [ + 0.216, + 0.544, + 0.342, + 0.642 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.262, + 0.645, + 0.294, + 0.655 + ], + "angle": 0, + "content": "PAN" + }, + { + "type": "image", + "bbox": [ + 0.348, + 0.544, + 0.474, + 0.642 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.387, + 0.644, + 0.436, + 0.654 + ], + "angle": 0, + "content": "GFPCA" + }, + { + "type": "image", + "bbox": [ + 0.483, + 0.544, + 0.609, + 0.642 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.644, + 0.559, + 0.654 + ], + 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The result of our approach was compared against nine other methods on Gaofen2 dataset." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12914" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.087, + 0.506, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.089, + 0.893, + 0.41 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.413, + 0.893, + 0.443 + ], + "angle": 0, + "content": "Figure 7. The feature map display result reduces in size from the top to the bottom, corresponding to the output of the pyramid. It should be noted that the last two rows have been magnified for better visualization." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.466, + 0.279, + 0.483 + ], + "angle": 0, + "content": "4.4. Ablation experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.471, + 0.596 + ], + "angle": 0, + "content": "We conducted two sets of ablation experiments on three datasets to examine the effects of our suggested approach on model performance to further demonstrate the effectiveness of our method. Multi-scale information modeling and dual-domain information injection are the fundamental parts of our model, and we conducted ablation experiments by removing each part independently." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.47, + 0.749 + ], + "angle": 0, + "content": "Multi-scale feature extraction. The results of our model are shown in the first row of table 3 after the multi-scale feature extraction and reconstruction capabilities have been removed. We kept feature map size constant, eliminated all upsampling operations, and substituted the downsampling operation with standard convolution of stride 1 to conduct these trials. The results underscore the significance of multi-scale modeling for remote sensing images by showing that the model's performance declined after losing the capability of multi-scale modeling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Frequency Injection Pyramid. The impact of eliminating frequency domain information from the model is shown in the second row of table 3. In order to remove frequency domain information, we used SIM to replace FIM in the frequency injection pyramid and remove the frequency loss to conduct these studies. The importance of introducing frequency information into the pan-sharpening process is revealed by the observation that the different indicators deteriorated when the global frequency domain information was removed." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.466, + 0.892, + 0.496 + ], + "angle": 0, + "content": "4.5. Visualization of feature maps in different pyramids" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.893, + 0.707 + ], + "angle": 0, + "content": "To further demonstrate the multi-scale and dual-domain modeling capabilities of our model, we present \\( P \\), \\( M_{s} \\), \\( F_{spainj} \\), \\( M_{f} \\), \\( F_{fre} \\), and \\( F_{freinj} \\) at different scales. These feature maps correspond to the output of the feature extraction pyramid, the features described in formula 6, and the features expressed in formulas 5, 9, 16, and 8, respectively. The Figure 7 illustrate that the features of different scales capture different regions of remote sensing images. The spatial pyramid features focus well on local information, while the frequency domain features effectively capture global and high-frequency features. The features after frequency domain injection combine the two types of information effectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.735, + 0.619, + 0.751 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this paper, we investigate the amplitude degradation of LRMS and PAN images across various scales. Based on the results of our investigation, we suggest a pyramid dual-domain injection network that injects multi-scale frequency and spatial domain information from the PAN image into the LRMS image to aid in its restoration. Our rigorous experiments on a variety of datasets demonstrate that our suggested model surpasses SOTA methods, exhibits good generalization, and effectively handles real-world scenarios." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12915" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.229, + 0.108 + ], + "angle": 0, + "content": "Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.115, + 0.47, + 0.144 + ], + "angle": 0, + "content": "This work was Supported by the HFIPS Director's Fund, Grant No.2023YZGH04." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.161, + 0.175, + 0.177 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.187, + 0.47, + 0.269 + ], + "angle": 0, + "content": "[1] Devansh Arpit, Stanisław Jastrzebski, Nicolas Ballas, David Krueger, Emmanuel Bengio, Maxinder S Kanwal, Tegan Maharaj, Asja Fischer, Aaron Courville, Yoshua Bengio, et al. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1798-1808, 2022." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.469, + 0.699 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12917" + } + ] +] \ No newline at end of file diff --git a/2023/Pyramid Dual Domain Injection Network for Pan-sharpening/aa199a66-751b-4158-bd1f-1783173c94fd_origin.pdf b/2023/Pyramid Dual Domain Injection Network for Pan-sharpening/aa199a66-751b-4158-bd1f-1783173c94fd_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..80a2fa23f1b1b0df38e6951678f6c2a21ebc75b5 --- /dev/null +++ b/2023/Pyramid Dual Domain Injection Network for Pan-sharpening/aa199a66-751b-4158-bd1f-1783173c94fd_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2771d6c38aff14956c84332fc16b7df828f047937a11fe97a3ced322aae9259e +size 6726349 diff --git a/2023/Pyramid Dual Domain Injection Network for Pan-sharpening/full.md b/2023/Pyramid Dual Domain Injection Network for Pan-sharpening/full.md new file mode 100644 index 0000000000000000000000000000000000000000..5e11575b3e02e0822a6b4a3806d2a92e940cc1df --- /dev/null +++ b/2023/Pyramid Dual Domain Injection Network for Pan-sharpening/full.md @@ -0,0 +1,425 @@ +# Pyramid Dual Domain Injection Network for Pan-sharpening + +Xuanhua $\mathrm{He}^{1,2*}$ Keyu Yan $^{1,2*}$ Rui Li $^{2}$ Chengjun Xie $^{1,2}$ Jie Zhang $^{2\dagger}$ Man Zhou $^{3\dagger}$ + +1University of Science and Technology of China, China + +$^{2}$ Hefei Institute of Physical Science, Chinese Academy of Sciences, China + +$^{3}$ Nanyang Technological University, Singapore + +{hexuanhua,keyu}@mail.ustc.edu.cn，{lirui,cjxie,zhangjie}@iim.ac.cn,manzhountu@gmail.com + +# Abstract + +Pan-sharpening, a panchromatic image guided low-spatial-resolution multi-spectral super-resolution task, aims to reconstruct the missing high-frequency information of high-resolution multi-spectral counterpart. Although the inborn connection with frequency domain, existing pan-sharpening research has almost investigated the potential solution upon frequency domain, thus limiting the model performance improvement. To this end, we first revisit the degradation process of pan-sharpening in Fourier space, and then devise a Pyramid Dual Domain Injection Pan-sharpening Network upon the above observation by fully exploring and exploiting the distinguished information in both the spatial and frequency domains. Specifically, the proposed network is organized with multi-scale U-shape manner and composed by two core parts: a spatial guidance pyramid sub-network for fusing local spatial information and a frequency guidance pyramid sub-network for fusing global frequency domain information, thus encouraging dual-domain complementary learning. In this way, the model can capture multi-scale dual-domain information to enable generating high-quality pan-sharpening results. Quantitative and qualitative experiments over multiple datasets demonstrate that our method performs the best against other state-of-the-art ones and comprises a strong generalization ability for real-world scenes. + +# 1. Introduction + +There is often a high demand for high-resolution multispectral (HRMS) images in the domain of agricultural monitoring and mapping services. However, due to the limitations of satellite sensors, the existing approaches must instead separately capture high-resolution panchromatic (PAN) and multispectral low-resolution (LRMS) images and fuse them using a technique known as pan + +![](images/f9fa8c89a329af689097bc7ef6bf3738cecd23d65f8206523d51ee418b9dd366.jpg) +Figure 1. Frequency domain analysis of multi-scale PAN, MS, and Ground Truth images. The amplitude, denoted by A, is displayed for the original-scale image, the 2-times downsampled image, and the 4-times downsampled image, from top to bottom, respectively. The last two columns show the degradation of PAN and MS images relative to GT images. + +harpening to get the desired HRMS images. Essentially, pan-sharpening is a super-resolution process that utilizes the richer details of PAN images to guide the reconstruction process of LRMS images. Pan-sharpening technology has expanded the use of remote sensing images in a wider range and gained considerable attention. + +Pan-sharpening has seen an increase in the use of deep learning-based techniques in recent years. The PNN [16], which started this trend, was motivated by the SRCNN [4] to introduce the convolutional neural network. The PNN presented a three-layer convolutional neural network that concatenated LRMS and PAN images as input and subsequently generated the output through the network. Since then, a flood of deep learning-based techniques has been developed to improve the model's representation capacity by employing deeper models or model-driven techniques [33, 29, 7, 32]. While significant progress has been made, there are still limitations need to be addressed. Prior approaches have primarily focused on spatial domain solutions, thereby neglecting the exploration of frequency domain solutions. Nevertheless, it has been established that CNNs in the spa + +tial domain exhibit a preference for low-frequency information and struggle to capture high-frequency information [1], resulting in insufficient texture in the generated images [14]. However, by incorporating frequency domain information, high-frequency features in low-dimensional manifolds can be efficiently captured [20]. Additionally, the LRMS images can be treated as degraded versions of HRMS images, which indicates that pan-sharpening is fundamentally an image restoration task. Image restoration are highly interrelated with frequency domain, as image degradation and content can be easily disentangled through the Fourier transform [9]. Thus, it is natural for us to investigate the feasibility of introducing frequency domain information into the pan-sharpening domain, as detailed in Figure 1 where the degradation effect of pan-sharpening is enlarged over multi-scale manner. + +Motivation. We conducted multi-scale Fourier analysis on LRMS, PAN, and HRMS images since the degradation mostly affects the amplitude of the image and the diversity scale of remote sensing landforms has an effect on the pan-sharpening process. The analysis results of image spectrum is shown in the Figure 1. We can draw two inspirations from the figure: 1) The difference in amplitudes between the PAN and HRMS images is primarily in the low frequency component, whereas the difference between the amplitudes of the HRMS and LRMS images is observed in both the high and low frequency components. 2) As the scale decreases, we can observe the missing information in the PAN image becomes more concentrated in the low-frequency component, while the degradation of the LRMS image becomes more concentrated in the high frequency component, and the degradation of images at various scales is not exactly the same. We may deduce from observation 1 that the frequency information in the PAN image can be used to fill in the missing information of the LRMS image. For observation 2, it is crucial to restore the information at several scales since the degradation is varied under multi-scale conditions. To encourage the learning of context information and multi-scale reconstruction, frequency domain information should be handled at various scales. Additionally, we can encourage the interaction of global and local, low-frequency and high-frequency features through multi-scale processing in the spatial and frequency domains in accordance with CNN's low-frequency preference in spatial domain and the global receptive field described by the spectral convolution theorem [6] in frequency domain to enhance the model's performance. + +In light of the aforementioned observation, we propose a brand new Pyramid Dual Domain Injection Network (PDDIN) to inject the multi-scale details of the PAN image into the LRMS image in both the spatial and frequency domains to aid in the restoration process. A Feature Extraction Pyramid, a Frequency Injection Pyramid, and a + +Spatial Injection Pyramid compensate the three major key components of the network. The Feature Extraction Pyramid is responsible for extracting multi-scale feature information from the PAN image. By using these features, the Frequency Injection Pyramid may inject global multi-scale features into the LRMS image, facilitating the recovery of global and high-frequency information in the spatial domain. To promote the reconstruction of local and spatial information, the spatial domain feature of PAN images is injected into the LRMS image in the Spatial Injection Pyramid. This approach effectively compensates for degradation at various scales, leading to a more thorough and precise reconstruction of the image. We conducted comprehensive experiments on multiple datasets to assess the effectiveness of our suggested network. The results show the efficacy of our method, by outperforming state-of-the-art techniques in both qualitative and quantitative evaluations. + +Our contributions are summarized below: + +- In this work, we revisit the degradation process of pan-sharpening in Fourier space, and then devise a Pyramid Dual Domain Injection Pan-sharpening Network, inspired by the above observation in both the spatial and frequency domains. +- To fully explore and exploit the distinguished information, we devised a frequency guidance pyramid sub-network and a spatial guidance pyramid sub-network. This design allows for the fusion of multi-scale information from both the frequency and spatial domains, lifting the learning capability of the model. +- Extensive experiments on multiple satellite datasets demonstrate our approach's quantitative and qualitative superiority to existing state-of-the-art pan-sharpening algorithms. + +# 2. Related work + +# 2.1. Traditional pan-sharpening method + +Three sorts of traditional techniques are widely adapted in the realm of pan-sharpening: component substitution (CS) method, MRA method, and VO-based method. The component substitution approach generates high-resolution images by substituting the LRMS image components with the spatial detail components from the PAN image. IHS algorithm [10], Brovey [8], PCA [12], and GS algorithm [11] are examples of CS methods. Due to the fact that spectral information is not fully considered in CS methods, the pan-sharpened images suffer from serious spectral distortion. In light of this, the MRA method reduces spectral distortion by fusing PAN and LRMS through multi-resolution decomposition. DWT [15] ATWT [17] HPF [19] and LP [22] algorithms are typical MRA algorithms. The VO-based methods, in contrast to the above two, treat pan-sharpening as + +![](images/2e2fd26cd76184639ca8cadbcfe81784b2ba68544f3bcea0cc406eb114e74f76.jpg) +Figure 2. The framework of the Pyramid Dual Domain Injection Network. It consists of three key components: Feature Extraction Pyramid, Frequency Injection Pyramid and Spatial Injection Pyramid. + +an optimization problem, design the loss function under a prior constraints, and then generate results by iterative solution and minimization of the loss function. The Bayesian technique [5] and the total variation algorithm [18] are common approaches in VO methods. The VO method can deliver decent results, but designing the optimization model and choosing the loss function is a significant challenge. + +# 2.2. CNN-based pan-sharpening method + +In recent years, the dominant approach in this area has been the CNN-based pan-sharpening method. PNN [16], which is inspired by SRCNN [4], is the pioneering work that introduced CNN to this field, giving rise to an unprecedented number of novel CNN-based techniques [27, 29, 7, 32, 33]. Despite having a clear and simple network structure, the results of PNN outperformed traditional techniques, demonstrating the promising potential of CNN techniques. Following that, Pannet [30] employs residual connection and high-frequency filtering to learn high-frequency features of images, while multi-scale convolution is taken into account in MsDCNN [31] to handle the varied remote sensing landforms. The model-driven models such as GPPNN [25], MMNet [28] and ARFNet [26] achieve interpretable models by utilizing deep unfolding techniques to construct the network structure. Additionally, SRPPNN [2] uses the progress super resolution method to enhance the performance of model and construct a profoundly deep network. Recently, MutNet [33] utilizes a mutual information mechanism to learn a more effective feature representation. The study of these techniques has also been expanded to include generative networks [13] and unsupervised pan-sharpening [21] technologies. + +# 3. Methods + +In this part, we first discuss the pertinent Fourier transform properties before delving into further details about our network shown in Figure 2, 3 and 4. It is organized into three parts: the Feature Extraction Pyramid, which extracts the multi-scale features from PAN images; the Frequency Injection Pyramid, which incorporates multi-scale frequency features from PAN into LRMS images for global and high-frequency information restoration; and the Spatial Injection Pyramid, which introduces the multi-scale spatial information from PAN into LRMS images to reconstruct local details. Finally, we will describe our loss function. + +# 3.1. Fourier transform of images + +Due to its capacity to decompose signals into their frequency components, the Fourier transform is widely adapted in the image processing community. This transformation makes it possible to analyze the image from a different perspective and offers valuable insights into its features. The Fourier transform of an input image $x \in R^{h \times w}$ can be defined as follows: + +$$ +\mathcal {F} (x) (u, v) = \frac {1}{\sqrt {H W}} \sum_ {h = 0} ^ {H - 1} \sum_ {w = 0} ^ {W - 1} x (h, w) e ^ {- j 2 \pi \left(\frac {h}{H} u + \frac {w}{W} v\right)} \tag {1} +$$ + +In our work, the Fourier transform is individually applied to each image channel. The amplitude and phase components can be described as follows: + +$$ +\mathcal {A} (x) (u, v) = \left[ R ^ {2} (x) (u, v) + I ^ {2} (x) (u, v) \right] ^ {\frac {1}{2}}, \tag {2} +$$ + +$$ +\mathcal {P} (x) (u, v) = \arctan \left[ \frac {I (x) (u , v)}{R (x) (u , v)} \right] \tag {3} +$$ + +where $I(x)$ and $R(x)$ indicate imaginary and real parts of the image's frequency representation $\mathcal{F}(x)$ , correspondingly. + +The Fourier transform can be beneficial in the task of pan-sharpening by disentangling and analyzing image degradation in the amplitude component. We may obtain important insights into the level of degradation existing in the image by carefully evaluating the amplitude information, ultimately resulting in more effective restoration attempts. Figure 1 illustrates that whereas LRMS images degrade in both the high-frequency and low-frequency regions, while PAN images degrade mostly in the low-frequency region. Moreover, it is important to note that the frequency of image degradation can vary across different scales. Following frequency analysis, it is obvious that the frequency domain information from a PAN image can be effectively integrated into a LRMS image to assist with its restoration. This process can be further optimized by injecting the frequency domain information at multiple scales, allowing for a more comprehensive reconstruction of the image's contextual information. + +# 3.2. Network framework + +As shown in Figure 2, given an input of a PAN and LRMS pair, we start by upsampling the LRMS image to the size of the PAN image. After that, a feature extraction pyramid is employed to process the PAN image, obtaining multi-scale features. Once the LRMS image is upsampled, the frequency injection pyramid injects multi-scale features into the LRMS image. The frequency injection pyramid is used to integrate the frequency domain features of various scales to further explore the frequency information. Then, we adopt spatial injection pyramid to reconstruct local details. Finally, the reconstruction image is obtained through a skip connection between network output and the upsampled LRMS image. + +# 3.3. The key building components + +Three essential elements make up the architecture of our network, and they are shown in Figures 2, 3, and 4. We go into great depth on each of these parts in the part that follows. Feature Extraction Pyramid. The Feature Extraction Pyramid is in charge of extracting multi-scale features from the PAN images, which can be utilized by other modules for further feature injection. To obtain the original size feature, the PAN image is first projected into the feature space using a convolution layer. After that, two sets of convolution and downsampling operations are carried out to generate features that are half as large and a quarter as large as the original. These features, namely $P_{1}, P_{2}$ , and $P_{3}$ , are then injected as supplemental information to the LRMS images to aid in the reconstruction process. The convolution operation with a stride of 2 is employed as a down-sampling + +![](images/18a61e74edb06acb294204c6922cae3a764bbdd744f1d63a8c6cf6109b12a048.jpg) +Figure 3. Architecture of Frequency Injection Module (FIM). The phase and amplitude components of $P_{i}$ and $F_{i}$ are obtained using the Fourier transform. Feature fusion is performed in the frequency domain, and the resulting frequency domain feature map is combined with the spatial feature to facilitate frequency domain information recovery and dual-domain complementary learning. + +operation in the pyramid. In the end, this module produces multi-scale feature maps for further information injection utilizing PAN image as input. + +Spatial Injection Pyramid. The Spatial Injection Pyramid is designed to inject the local, multi-scale spatial information from PAN into the LRMS image. This module may effectively concentrate on small objects by leveraging the locality of the convolution operation in the pixel domain. In this module, the spatial features of $P_{1}$ , $P_{2}$ , and $P_{3}$ are injected into LRMS images at various scales to aid in reconstruction. For instance, given the output of the frequency pyramid presented by $M s_{i}$ and the feature map $P_{i}$ at the original scale, further feature extraction is performed using a convolution layer to get $S_{i}$ , and then the features $P_{i}$ are injected into $S_{i}$ using the spatial injection module (SIM). Following injection, a down-sampling or up-sampling operation is applied to generate the feature map of a different size. Taking the down-sampling branch for example, the process can be described as follows: + +$$ +S _ {i} = \operatorname {c o n v} _ {3 \times 3} (M s _ {i}) \tag {4} +$$ + +$$ +F _ {s p a i n j} = S I M \left(S _ {i}, P _ {i}\right) \tag {5} +$$ + +$$ +M s _ {i + 1} = \operatorname {d o w n} \left(F _ {\text {s p a i n j}}\right) \tag {6} +$$ + +The suggested spatial injection module, shown in the figure 4, uses the AFF [3] as a basis block and is built on attention mechanism to enable effective and consistent injection of spatial details. The module works by enabling interaction between the PAN and LRMS branches, which enhances detail injection and facilitates the acquisition of LRMS features with injected spatial details. + +Frequency Injection Pyramid. The purpose of the frequency injection pyramid is to provide LRMS features with high-frequency and global information from PAN image. By utilizing the multi-scale frequency injection, the restoration of LRMS image's frequency domain information is enhanced by leveraging the frequency information of PAN im + +![](images/f909e15196e26630003aed869af56528f8dfe8b28d0f715dc6e5b3b9fbb03ff4.jpg) +Figure 4. The proposed module for injecting spatial domain information, dubbed SIM, is based on attention mechanism and uses a basic module built on attentional fusion block. + +age. Processing information in frequency domain enables the network to quickly capture high-frequency features that are challenging to acquire using pixel domain CNN, encourages dual-domain complementary learning, and generates clear texture features. Specifically, given the feature map of the LRMS image presented by $Mf_{i}$ and the feature map $P_{i}$ , first $M_{i}$ are fed to a convolution block to extract a further feature $F_{i}$ . Next, the frequency injection module (FIM) is used to inject the frequency domain features of $P_{i}$ into $F_{i}$ . The resulting feature map is then down-sampled or upsampled for the next scale of frequency domain information injection. Taking the up-sampling branch as an example, this process is summarized as follows: + +$$ +F _ {i} = \operatorname {c o n v} _ {3 \times 3} (M f _ {i}) \tag {7} +$$ + +$$ +F _ {f r e i n j} = F I M \left(F _ {i}, P _ {i}\right) \tag {8} +$$ + +$$ +M f _ {i + 1} = u p \left(F _ {f r e i n j}\right) \tag {9} +$$ + +where $up$ is implemented by pixel-shuffle. + +With the inputs $F_{i}$ and $P_{i}$ , the FIM shown in Figure 3 employs the Fourier transform to produce amplitude and phase components. Following that, the phase and amplitude information of $P_{i}$ is individually injected into $F_{i}$ to aid in the restoration of the LRMS image in the frequency domain. + +In particular, the following procedure is used to acquire the relevant amplitude and phase components: + +$$ +\mathcal {A} \left(F _ {i}\right), \mathcal {P} \left(F _ {i}\right) = \mathcal {F} \left(F _ {i}\right), \tag {10} +$$ + +$$ +\mathcal {A} \left(P _ {i}\right), \mathcal {P} \left(P _ {i}\right) = \mathcal {F} \left(P _ {i}\right), \tag {11} +$$ + +For the $\mathcal{A}(F_i)$ , we use SFT [24] to inject frequency information from $\mathcal{A}(P_i)$ , and use $Conv_{1\times 1}$ to fuse phase components, for the difference between two modalities mainly lay in amplitude: + +$$ +\alpha , \beta = \operatorname {C o n v} _ {3 \times 3} (\mathcal {A} (P _ {i})), \operatorname {C o n v} _ {3 \times 3} (\mathcal {A} (P _ {i})), \tag {12} +$$ + +$$ +\mathcal {A} \left(F _ {i}\right) = \mathcal {A} \left(F _ {i}\right) \cdot \alpha + \beta , \tag {13} +$$ + +$$ +\mathcal {A} (F) = \operatorname {C o n v} _ {1 \times 1} \left(\operatorname {C a t} \left(\left[ \mathcal {A} \left(P _ {i}\right), \mathcal {A} \left(F _ {i}\right) \right]\right)\right), \tag {14} +$$ + +$$ +\mathcal {P} (F) = \operatorname {C o n v} _ {1 \times 1} \left(\operatorname {C a t} \left(\left[ \mathcal {P} \left(P _ {i}\right), \mathcal {P} \left(F _ {i}\right) \right]\right)\right) \tag {15} +$$ + +The injected components are then transformed back to the pixel domain using the inverse transform, and are subsequently fused with spatial features to inject frequency features into spatial information and promote dual-domain complementary learning: + +$$ +F _ {f r e} = \operatorname {C o n v} _ {1 \times 1} \left(\mathcal {F} ^ {- 1} (\mathcal {A} (F), \mathcal {P} (F))\right) \tag {16} +$$ + +$$ +F _ {s p a} = \operatorname {C o n v} _ {3 \times 3} \left(F _ {i}\right), \tag {17} +$$ + +$$ +F _ {f r e i n j} = F _ {f r e} + F _ {s p a} \tag {18} +$$ + +# 3.4. Loss Function + +To improve the perception of high-frequency information, we propose a loss function that combines spatial and frequency domain losses in this study. Provided that $Y$ represents the model output, $Y_{f}$ represents the output of frequency injection pyramid and $H$ represents the ground truth, the $L_{1}$ distance between $Y$ and $H$ is employed to define the spatial domain loss: + +$$ +\mathcal {L} _ {s} = \left| \left| Y - H \right| \right| _ {1}. \tag {19} +$$ + +The frequency domain loss, which aims to improve the perception of high-frequency information, is determined using the following formula: + +$$ +\mathcal {L} _ {f} = \left| \left| \log \left(\mathcal {A} \left(Y _ {f}\right)\right) - \log \left(\mathcal {A} (H)\right) \right| \right| _ {1} + \left| \left| \mathcal {P} (Y) - \mathcal {P} (H) \right| \right| _ {1}, \tag {20} +$$ + +where the amplitude and phase components of the Fourier transform are denoted by $\mathcal{A}$ and $\mathcal{P}$ respectively. The complete loss function is a combination of the dual domain losses, and involves a hyper-parameter $\lambda$ which is set to 0.1 based on empirical evidence. + +$$ +\mathcal {L} = \mathcal {L} _ {s} + \lambda \mathcal {L} _ {f}. \tag {21} +$$ + +# 4. Experiment + +# 4.1. Datasets and benchmark + +Three datasets—WorldView-II (WV2), WorldView-III (WV3), and Gaofen2 (GF2) were used in our experiments. Due to the unavailability of real HRMS images, we utilized the Wald protocol [23] to generate the training and test data. In further detail, we extracted patches from the same location from the PAN and LRMS images, with the PAN patch being $r$ times larger than the LRMS patch. The original LRMS patch was utilized as the ground truth, and both the LRMS and PAN patches were downsampled by a factor of $r$ and used as input data. The selected patch sizes were 128x128 and 32x32, respectively. + +To evaluate the efficacy of our approach, we compared it with five traditional and six advanced CNN-based methods. Specifically, we included SFIM, Brovey [8], GS [11], IHS [10], and GFPCA [12] as traditional methods, and PANNET [30], MSDCNN [31], SRPPNN [2], GPPNN [25], MutNet [33] and INNformer [32] as advanced methods. + +Table 1. Quantitative comparison on three datasets. Best results are highlighted by red. $\uparrow$ indicates that the larger the value, the better the performance, and $\downarrow$ indicates that the smaller the value, the better the performance. + +
MethodWorldView-IIGaoFen2Worldview-III
PSNR↑SSIM↑SAM↓ERGAS↓PSNR↑SSIM↑SAM↓ERGAS↓PSNR↑SSIM↑SAM↓ERGAS↓
SFIM34.12970.89750.04392.344936.90600.88820.03181.739821.82120.54570.12088.9730
Brovey35.86460.92160.04031.823837.79740.90260.02181.372022.50600.54660.11598.2331
GS35.63760.91760.04231.877437.22600.90340.03091.673622.56080.54700.12178.2433
IHS35.29620.90270.04612.027838.17540.91000.02431.533622.55790.53540.12668.3616
GFPCA34.55810.90380.04882.141137.94430.92040.03141.560422.33440.48260.12948.3964
PANNET40.81760.96260.02571.055743.06590.96850.01780.857729.68400.90720.08513.4263
MSDCNN41.33550.96640.02420.994045.68470.98270.01350.638930.30380.91840.07823.1884
SRPPNN41.45380.96790.02330.989947.19980.98770.01060.558630.43460.92020.07703.1553
GPPNN41.16220.96840.02441.031544.21450.98150.01370.736130.17850.91750.07763.2593
MutNet41.67730.97050.02240.951947.30420.98920.01020.548130.49070.92230.07493.1125
INNformer41.69030.97040.02270.951447.35280.98930.01020.547930.53650.92250.07473.0997
Ours41.84730.97070.02220.935847.49390.98950.01000.536030.85020.92550.07262.9945
+ +Table 2. Evaluation of the proposed method on real-world full-resolution scenes from the GaoFen2 dataset. + +
MetricSFIMBroveyGSIHSGFPCAPANNETMSDCNNSRPPNNGPPNNMutNetINNformerOurs
Dλ↓0.08220.13780.06960.07700.09140.07370.07340.07670.07820.06940.06930.0682
DS↓0.10870.26050.24560.29850.16350.12240.11510.11620.12530.11180.11380.1101
QNR ↑0.82140.63900.07250.64850.76150.81430.82150.81730.80730.82470.82590.8307
+ +# 4.2. Implementation details + +The experiment was conducted on an RTX 3060 GPU, using the PyTorch framework. The Adam optimizer was employed with an initial learning rate of $5 \times 10^{-4}$ . To ensure stable training, the learning rate was decayed to $5 \times 10^{-8}$ using the cosine annealing method after 500 epochs. Several commonly used evaluation metrics were chosen, including PSNR, SSIM, SAM, and ERGAS, as well as non-reference indices such as $D_{S}$ , $D_{\lambda}$ , and QNR. + +# 4.3. Comparison with state-of-the-art methods + +Evaluation on Reduced-Resolution Scene. The evaluation results of our approach on three datasets are shown in Table 1. The results demonstrate that our model performs better than the state-of-the-art approaches in the majority of assessment measures, and the improvements are significant. To be specific, our method outperforms the cutting-edge method INNformer on most indicators, on the WV2 dataset, our model achieves a $0.16\mathrm{~dB}$ improvement in PSNR compared to MIDN. Similarly, on the GF2 and WV3 datasets, our model achieves a $0.14\mathrm{~dB}$ and $0.31\mathrm{~dB}$ improvement in PSNR, respectively, demonstrating its excellent performance. Comparable improvements are also observed in other evaluation metrics. + +Additionally, for qualitative evaluation, we compared the results obtained from our method with those of the other nine methods on the WV2 and GF2 datasets. To evaluate the similarity between the generated results and the ground truth, a residual map was generated by computing their mean squared error. The brighter areas of residual map indicate the larger differences with the ground truth. Our approach produces images with the finest texture and most realistic spectrum, as shown in Figures 5 and 6. The residual maps exhibit the least amount of bright spots, indicating high congruence with the ground truth. These findings are further supported by the evaluation indicators presented in the Table 1. + +Evaluation on Full-Resolution Scene. To test the generalization ability of our model, we trained it on the GF2 dataset and evaluated full-resolution data from GF2 that was not downsampled, using the reserved portion of the dataset. Since there was no reference image available, we evaluated the dataset using no-reference indices. As shown in Table 2, our method achieved the best QNR index on this dataset, indicating its strong generalization ability compared to traditional and deep learning methods. This demonstrates that our approach can be applied to real-world scenes. + +Table 3. The outcomes of the ablation experiments conducted on the WordView-II dataset are presented. + +
Config Multi-scale FIMWorldView-IIGaoFen2WorldView-III
PSNR↑SSIM↑SAM↓ERGAS↓PSNR↑SSIM↑SAM↓ERGAS↓PSNR↑SSIM↑SAM↓ERGAS↓
(I)×✓41.63610.97010.02250.958147.37880.98920.01020.546630.78490.92520.07173.0240
(II)✓×41.63990.96950.02270.960047.45880.98900.01010.540330.81400.92560.07183.0106
Ours✓✓41.84350.97110.02220.947847.49390.98950.01000.536030.86450.92580.07572.9851
+ +![](images/e5aeee3728c797fdcabfaf89dc5c8238cb66282e081e94ee1b4ebb41eae31ffc.jpg) +LRMS + +![](images/6d6e25d5dc801d55b04ef77b768090846c2cab877fc4f7a72c0e5063c36f91d9.jpg) +PAN + +![](images/548192da2c308dd62b58369b80378982141d0ec2bcfd153a82d84c08b4d6c543.jpg) +GFPCA + +![](images/35a16152a05d814399e2828c234572be061bff4d825e0cf3cecf35991fb535b1.jpg) +GS + +![](images/ffdc3505761552e0144d5551c870e61c52f597a6816d673f95c9ede1ecdc1ed6.jpg) +SFIM + +![](images/a540c01cf2e8b059eb24a03e3917c859a631de299c31bb002162c9facf482359.jpg) +PANNET + +![](images/c1fe9dd71d5eff8597289101708539aa46a76cad19909104d4273002807b3d70.jpg) +MSDCNN + +![](images/3d30be64af969bfa1c25e6b767a20b93c0607630915a887817f59b78bc52d8eb.jpg) +SRPPNN + +![](images/dcc0dfe97b0396cb4e26fbf3625c83b9dcfd6c2195efad4d2dfd9cfbee1b36d7.jpg) +GPPNN + +![](images/a90475dcc8e3fde28857fc58e80188ccd7c45ef99b6bc336bf8133d65924f894.jpg) +MutNet + +![](images/8093429a22545ddd7ccfc7c5001f257fdd2233916109aac2866388ff5d32aabe.jpg) +INNformer + +![](images/c8963b141e5aac2adbc8ce1b7eff5ab2964222a6dfb7a2dc0b1644959be95159.jpg) +Ours + +![](images/c0d568334d674ea4293bc21ff200f1eac74b5ffbc6d668256134a7fbca6514a5.jpg) +GFPCA + +![](images/3dab921ca5372464b0614bfd03be66295dd469609221e150678495e4f5588bf3.jpg) +GS + +![](images/519a7944f83bfd977a2e728ef3b7689a0ff505f9b705b3c33d7b16d7650d59f9.jpg) +SFIM + +![](images/786628240094241641522d052a4be43d48c59fc1d59f8432552ebe7772ceddb9.jpg) +PANNET + +![](images/a130b8c13fcc90ac0807efc2105197332b806e1765c9335556ea9b27522d1e7e.jpg) +MSDCNN + +![](images/8d705da940276f92a69cb7329c0492f750e97257ecc07e6a5c118c5b4543da1b.jpg) +SRPPNN + +![](images/46996a6abe2aa16a98ae1168a0003110c3dda9a73645b9bbd49adbb5bc200f81.jpg) +GPPNN + +![](images/88b4a4b72a578ac6b8ecb0c78a39ad78d66696dfd00d82fcf35e2ecdc3f356d4.jpg) +MutNet + +![](images/6cec3321d19ccc88d880c12766e84d7136c6b6e8c65875c19371cb1f4f6dc3d1.jpg) +INNformer + +![](images/12b9ff22419ce01c09cfe4206e946d648cbe08dd2a2faa65b29b1910c68a12b1.jpg) +Ours + +![](images/1dd0299a34dbcb7606a209c227dc7b57cf44ed0bbe44be23d0ad691de9f24a34.jpg) +Figure 5. The result of our approach was compared against nine other methods on WorldView-II dataset. + +![](images/1ae9cd95d1aecfa6398a1fd9e66b33539834da297afa45d80f3f7bd8fe7be560.jpg) +PAN + +![](images/84305f0f2d1fdf8ff1dc79b28c55cbea34b15f25cdff3683c072d853f7ad1f99.jpg) +GFPCA + +![](images/3a64da425f2429a3e052c1fc62468238a59848f796c59f7e273f65d5d6a65c4a.jpg) +GS + +![](images/d8f14abb291543a791186ba1583b9b21f566ccd638ff2cbd3bc0d3456334241e.jpg) +SFIM + +![](images/00bdeb75ec4e7bd95b81f29d9c1d64e6d2f89c79505243dfdd3b1eaa9d4fdd13.jpg) +PANNET + +![](images/ff628b09ab32e29e24896454ac883b58c0a58477c06639f81c97288d0b5515f7.jpg) +LRMS + +![](images/45af43d3002359421dcb03293aae79350ec35d96d34e9d2d6974d67237889e65.jpg) +SRPPNN + +![](images/02de47e3c173ef6f221b6de9d231dcc8e565b1b68ee7652b0cc30da1fa229a65.jpg) +GPPNN + +![](images/e8afdaeff36a24378aa2c390e48bf2d52403eaec5f957b7b81563a4126b6c8f8.jpg) +MutNet + +![](images/08ac0e41d756a880081efb4e6131a6078ca7c17316823e23f29cec192f486990.jpg) +INNformer + +![](images/0a69a04bf4bc010a21046bad4bc00f5ef3230a7fb7269f70cced20cd6a0a8d8c.jpg) +Ours + +![](images/f30e703fac6c4a197986abaccc98a142017eec8bca0494be6c7009e4859d52b1.jpg) +MSDCNN +GFPCA + +![](images/3810b9fb286856a1c47c775de34bda4351dda85718ab60d42e212d563c096eb7.jpg) +GS +Figure 6. The result of our approach was compared against nine other methods on Gaofen2 dataset. + +![](images/bc5b9fdbccbcc9803a8b559717522e35633a10e782815f40b04f2991729083f5.jpg) +SFIM + +![](images/f38701926997f836b9811daeae2a9a91b9650db5308af27b1b1cd2d055505126.jpg) +PANNET + +![](images/54b5a354014032201ac1bb8ce2235fd02a4c6c4b40bf3552069a8806f45e4d94.jpg) +MSDCNN + +![](images/d4470ec0823b1e8fd9d4f71955a5b772ce04c0282a38a01a702b55affe7b23b0.jpg) +SRPPNN + +![](images/20bec2e6844ba2665bf59b2b0d3a7d2e69d789d14adc7e1bf3193e762c18f65d.jpg) +GPPNN + +![](images/b1fc3c2833af4792191b67d858432a8cdc59da98979a866d389fba4a351964fe.jpg) +MutNet + +![](images/42bbc47ba0d76c638256a9c3475cf2ae8a02f2b577e9afd8c07c7e11cc7c4fae.jpg) +INNformer + +![](images/b646a6e9effb975b2defdd60f3c8dcded30893cdda4273ebf059d58f29847659.jpg) +Ours + +![](images/3fdc4360b46fd0f33e35c46c68577da8adb682d6d7c73d2bd81eefc8c978d94b.jpg) +Figure 7. The feature map display result reduces in size from the top to the bottom, corresponding to the output of the pyramid. It should be noted that the last two rows have been magnified for better visualization. + +![](images/feee9e5bf5163b11f782d2a2ff2c748d405e00a20183dabf37ce9108f37fe458.jpg) + +# 4.4. Ablation experiments + +We conducted two sets of ablation experiments on three datasets to examine the effects of our suggested approach on model performance to further demonstrate the effectiveness of our method. Multi-scale information modeling and dual-domain information injection are the fundamental parts of our model, and we conducted ablation experiments by removing each part independently. + +Multi-scale feature extraction. The results of our model are shown in the first row of table 3 after the multi-scale feature extraction and reconstruction capabilities have been removed. We kept feature map size constant, eliminated all upsampling operations, and substituted the downsampling operation with standard convolution of stride 1 to conduct these trials. The results underscore the significance of multi-scale modeling for remote sensing images by showing that the model's performance declined after losing the capability of multi-scale modeling. + +Frequency Injection Pyramid. The impact of eliminating frequency domain information from the model is shown in the second row of table 3. In order to remove frequency domain information, we used SIM to replace FIM in the frequency injection pyramid and remove the frequency loss to conduct these studies. The importance of introducing frequency information into the pan-sharpening process is revealed by the observation that the different indicators deteriorated when the global frequency domain information was removed. + +# 4.5. Visualization of feature maps in different pyramids + +To further demonstrate the multi-scale and dual-domain modeling capabilities of our model, we present $P$ , $M_{s}$ , $F_{spainj}$ , $M_{f}$ , $F_{fre}$ , and $F_{freinj}$ at different scales. These feature maps correspond to the output of the feature extraction pyramid, the features described in formula 6, and the features expressed in formulas 5, 9, 16, and 8, respectively. The Figure 7 illustrate that the features of different scales capture different regions of remote sensing images. The spatial pyramid features focus well on local information, while the frequency domain features effectively capture global and high-frequency features. The features after frequency domain injection combine the two types of information effectively. + +# 5. Conclusion + +In this paper, we investigate the amplitude degradation of LRMS and PAN images across various scales. Based on the results of our investigation, we suggest a pyramid dual-domain injection network that injects multi-scale frequency and spatial domain information from the PAN image into the LRMS image to aid in its restoration. Our rigorous experiments on a variety of datasets demonstrate that our suggested model surpasses SOTA methods, exhibits good generalization, and effectively handles real-world scenarios. + +# Acknowledgment + +This work was Supported by the HFIPS Director's Fund, Grant No.2023YZGH04. + +# References + +[1] Devansh Arpit, Stanisław Jastrzebski, Nicolas Ballas, David Krueger, Emmanuel Bengio, Maxinder S Kanwal, Tegan Maharaj, Asja Fischer, Aaron Courville, Yoshua Bengio, et al. A closer look at memorization in deep networks. In International conference on machine learning, pages 233-242. PMLR, 2017. +[2] Jiajun Cai and Bo Huang. Super-resolution-guided progressive pansharpening based on a deep convolutional neural network. 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high-frequency information of high-resolution multi-spectral counterpart. Although the inborn connection with frequency domain, existing pan-sharpening research has almost investigated the potential solution upon frequency domain, thus limiting the model performance improvement. To this end, we first revisit the degradation process of pan-sharpening in Fourier space, and then devise a Pyramid Dual Domain Injection Pan-sharpening Network upon the above observation by fully exploring and exploiting the distinguished information in both the spatial and frequency domains. Specifically, the proposed network is organized with multi-scale U-shape manner and composed by two core parts: a spatial guidance pyramid sub-network for fusing local spatial information and a frequency guidance pyramid sub-network for fusing global frequency domain information, thus encouraging dual-domain complementary learning. In this way, the model can capture multi-scale dual-domain information to enable generating high-quality pan-sharpening results. Quantitative and qualitative experiments over multiple datasets demonstrate that our method performs the best against other state-of-the-art ones and comprises a strong generalization ability for real-world scenes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 589, + 128, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 589, + 128, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 589, + 128, + 601 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 609, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 287, + 694 + ], + "type": "text", + "content": "There is often a high demand for high-resolution multispectral (HRMS) images in the domain of agricultural monitoring and mapping services. However, due to the limitations of satellite sensors, the existing approaches must instead separately capture high-resolution panchromatic (PAN) and multispectral low-resolution (LRMS) images and fuse them using a technique known as pan" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 309, + 241, + 545, + 378 + ], + "blocks": [ + { + "bbox": [ + 309, + 241, + 545, + 378 + ], + "lines": [ + { + "bbox": [ + 309, + 241, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 309, + 241, + 545, + 378 + ], + "type": "image", + "image_path": "f9fa8c89a329af689097bc7ef6bf3738cecd23d65f8206523d51ee418b9dd366.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 382, + 546, + 449 + ], + "lines": [ + { + "bbox": [ + 305, + 382, + 546, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 382, + 546, + 449 + ], + "type": "text", + "content": "Figure 1. Frequency domain analysis of multi-scale PAN, MS, and Ground Truth images. The amplitude, denoted by A, is displayed for the original-scale image, the 2-times downsampled image, and the 4-times downsampled image, from top to bottom, respectively. The last two columns show the degradation of PAN and MS images relative to GT images." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 460, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 533 + ], + "type": "text", + "content": "harpening to get the desired HRMS images. Essentially, pan-sharpening is a super-resolution process that utilizes the richer details of PAN images to guide the reconstruction process of LRMS images. Pan-sharpening technology has expanded the use of remote sensing images in a wider range and gained considerable attention." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": "Pan-sharpening has seen an increase in the use of deep learning-based techniques in recent years. The PNN [16], which started this trend, was motivated by the SRCNN [4] to introduce the convolutional neural network. The PNN presented a three-layer convolutional neural network that concatenated LRMS and PAN images as input and subsequently generated the output through the network. Since then, a flood of deep learning-based techniques has been developed to improve the model's representation capacity by employing deeper models or model-driven techniques [33, 29, 7, 32]. While significant progress has been made, there are still limitations need to be addressed. Prior approaches have primarily focused on spatial domain solutions, thereby neglecting the exploration of frequency domain solutions. Nevertheless, it has been established that CNNs in the spa" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 259, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 259, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 259, + 713 + ], + "type": "text", + "content": "*Co-first authors contributed equally, † Corresponding author." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12908" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "content": "tial domain exhibit a preference for low-frequency information and struggle to capture high-frequency information [1], resulting in insufficient texture in the generated images [14]. However, by incorporating frequency domain information, high-frequency features in low-dimensional manifolds can be efficiently captured [20]. Additionally, the LRMS images can be treated as degraded versions of HRMS images, which indicates that pan-sharpening is fundamentally an image restoration task. Image restoration are highly interrelated with frequency domain, as image degradation and content can be easily disentangled through the Fourier transform [9]. Thus, it is natural for us to investigate the feasibility of introducing frequency domain information into the pan-sharpening domain, as detailed in Figure 1 where the degradation effect of pan-sharpening is enlarged over multi-scale manner." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 267, + 289, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 267, + 289, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 289, + 639 + ], + "type": "text", + "content": "Motivation. We conducted multi-scale Fourier analysis on LRMS, PAN, and HRMS images since the degradation mostly affects the amplitude of the image and the diversity scale of remote sensing landforms has an effect on the pan-sharpening process. The analysis results of image spectrum is shown in the Figure 1. We can draw two inspirations from the figure: 1) The difference in amplitudes between the PAN and HRMS images is primarily in the low frequency component, whereas the difference between the amplitudes of the HRMS and LRMS images is observed in both the high and low frequency components. 2) As the scale decreases, we can observe the missing information in the PAN image becomes more concentrated in the low-frequency component, while the degradation of the LRMS image becomes more concentrated in the high frequency component, and the degradation of images at various scales is not exactly the same. We may deduce from observation 1 that the frequency information in the PAN image can be used to fill in the missing information of the LRMS image. For observation 2, it is crucial to restore the information at several scales since the degradation is varied under multi-scale conditions. To encourage the learning of context information and multi-scale reconstruction, frequency domain information should be handled at various scales. Additionally, we can encourage the interaction of global and local, low-frequency and high-frequency features through multi-scale processing in the spatial and frequency domains in accordance with CNN's low-frequency preference in spatial domain and the global receptive field described by the spectral convolution theorem [6] in frequency domain to enhance the model's performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 642, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 289, + 715 + ], + "type": "text", + "content": "In light of the aforementioned observation, we propose a brand new Pyramid Dual Domain Injection Network (PDDIN) to inject the multi-scale details of the PAN image into the LRMS image in both the spatial and frequency domains to aid in the restoration process. A Feature Extraction Pyramid, a Frequency Injection Pyramid, and a" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "type": "text", + "content": "Spatial Injection Pyramid compensate the three major key components of the network. The Feature Extraction Pyramid is responsible for extracting multi-scale feature information from the PAN image. By using these features, the Frequency Injection Pyramid may inject global multi-scale features into the LRMS image, facilitating the recovery of global and high-frequency information in the spatial domain. To promote the reconstruction of local and spatial information, the spatial domain feature of PAN images is injected into the LRMS image in the Spatial Injection Pyramid. This approach effectively compensates for degradation at various scales, leading to a more thorough and precise reconstruction of the image. We conducted comprehensive experiments on multiple datasets to assess the effectiveness of our suggested network. The results show the efficacy of our method, by outperforming state-of-the-art techniques in both qualitative and quantitative evaluations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 317, + 276, + 487, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 276, + 487, + 286 + ], + "spans": [ + { + "bbox": [ + 317, + 276, + 487, + 286 + ], + "type": "text", + "content": "Our contributions are summarized below:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 292, + 545, + 483 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 317, + 292, + 545, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 292, + 545, + 352 + ], + "spans": [ + { + "bbox": [ + 317, + 292, + 545, + 352 + ], + "type": "text", + "content": "- In this work, we revisit the degradation process of pan-sharpening in Fourier space, and then devise a Pyramid Dual Domain Injection Pan-sharpening Network, inspired by the above observation in both the spatial and frequency domains." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 357, + 545, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 357, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 317, + 357, + 545, + 430 + ], + "type": "text", + "content": "- To fully explore and exploit the distinguished information, we devised a frequency guidance pyramid sub-network and a spatial guidance pyramid sub-network. This design allows for the fusion of multi-scale information from both the frequency and spatial domains, lifting the learning capability of the model." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 435, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 435, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 317, + 435, + 545, + 483 + ], + "type": "text", + "content": "- Extensive experiments on multiple satellite datasets demonstrate our approach's quantitative and qualitative superiority to existing state-of-the-art pan-sharpening algorithms." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 496, + 390, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 496, + 390, + 509 + ], + "spans": [ + { + "bbox": [ + 306, + 496, + 390, + 509 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 515, + 495, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 495, + 529 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 495, + 529 + ], + "type": "text", + "content": "2.1. Traditional pan-sharpening method" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 714 + ], + "type": "text", + "content": "Three sorts of traditional techniques are widely adapted in the realm of pan-sharpening: component substitution (CS) method, MRA method, and VO-based method. The component substitution approach generates high-resolution images by substituting the LRMS image components with the spatial detail components from the PAN image. IHS algorithm [10], Brovey [8], PCA [12], and GS algorithm [11] are examples of CS methods. Due to the fact that spectral information is not fully considered in CS methods, the pan-sharpened images suffer from serious spectral distortion. In light of this, the MRA method reduces spectral distortion by fusing PAN and LRMS through multi-resolution decomposition. DWT [15] ATWT [17] HPF [19] and LP [22] algorithms are typical MRA algorithms. The VO-based methods, in contrast to the above two, treat pan-sharpening as" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12909" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 73, + 541, + 270 + ], + "blocks": [ + { + "bbox": [ + 53, + 73, + 541, + 270 + ], + "lines": [ + { + "bbox": [ + 53, + 73, + 541, + 270 + ], + "spans": [ + { + "bbox": [ + 53, + 73, + 541, + 270 + ], + "type": "image", + "image_path": "2e2fd26cd76184639ca8cadbcfe81784b2ba68544f3bcea0cc406eb114e74f76.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 274, + 546, + 298 + ], + "lines": [ + { + "bbox": [ + 46, + 274, + 546, + 298 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 546, + 298 + ], + "type": "text", + "content": "Figure 2. The framework of the Pyramid Dual Domain Injection Network. It consists of three key components: Feature Extraction Pyramid, Frequency Injection Pyramid and Spatial Injection Pyramid." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 316, + 289, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 289, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 289, + 400 + ], + "type": "text", + "content": "an optimization problem, design the loss function under a prior constraints, and then generate results by iterative solution and minimization of the loss function. The Bayesian technique [5] and the total variation algorithm [18] are common approaches in VO methods. The VO method can deliver decent results, but designing the optimization model and choosing the loss function is a significant challenge." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 416, + 239, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 416, + 239, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 416, + 239, + 430 + ], + "type": "text", + "content": "2.2. CNN-based pan-sharpening method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "text", + "content": "In recent years, the dominant approach in this area has been the CNN-based pan-sharpening method. PNN [16], which is inspired by SRCNN [4], is the pioneering work that introduced CNN to this field, giving rise to an unprecedented number of novel CNN-based techniques [27, 29, 7, 32, 33]. Despite having a clear and simple network structure, the results of PNN outperformed traditional techniques, demonstrating the promising potential of CNN techniques. Following that, Pannet [30] employs residual connection and high-frequency filtering to learn high-frequency features of images, while multi-scale convolution is taken into account in MsDCNN [31] to handle the varied remote sensing landforms. The model-driven models such as GPPNN [25], MMNet [28] and ARFNet [26] achieve interpretable models by utilizing deep unfolding techniques to construct the network structure. Additionally, SRPPNN [2] uses the progress super resolution method to enhance the performance of model and construct a profoundly deep network. Recently, MutNet [33] utilizes a mutual information mechanism to learn a more effective feature representation. The study of these techniques has also been expanded to include generative networks [13] and unsupervised pan-sharpening [21] technologies." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 315, + 367, + 327 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 315, + 367, + 327 + ], + "spans": [ + { + "bbox": [ + 306, + 315, + 367, + 327 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 335, + 547, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 547, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 547, + 467 + ], + "type": "text", + "content": "In this part, we first discuss the pertinent Fourier transform properties before delving into further details about our network shown in Figure 2, 3 and 4. It is organized into three parts: the Feature Extraction Pyramid, which extracts the multi-scale features from PAN images; the Frequency Injection Pyramid, which incorporates multi-scale frequency features from PAN into LRMS images for global and high-frequency information restoration; and the Spatial Injection Pyramid, which introduces the multi-scale spatial information from PAN into LRMS images to reconstruct local details. Finally, we will describe our loss function." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 474, + 462, + 487 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 474, + 462, + 487 + ], + "spans": [ + { + "bbox": [ + 306, + 474, + 462, + 487 + ], + "type": "text", + "content": "3.1. Fourier transform of images" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 492, + 545, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 492, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 492, + 545, + 575 + ], + "type": "text", + "content": "Due to its capacity to decompose signals into their frequency components, the Fourier transform is widely adapted in the image processing community. This transformation makes it possible to analyze the image from a different perspective and offers valuable insights into its features. The Fourier transform of an input image " + }, + { + "bbox": [ + 304, + 492, + 545, + 575 + ], + "type": "inline_equation", + "content": "x \\in R^{h \\times w}" + }, + { + "bbox": [ + 304, + 492, + 545, + 575 + ], + "type": "text", + "content": " can be defined as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 312, + 582, + 545, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 582, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 312, + 582, + 545, + 624 + ], + "type": "interline_equation", + "content": "\\mathcal {F} (x) (u, v) = \\frac {1}{\\sqrt {H W}} \\sum_ {h = 0} ^ {H - 1} \\sum_ {w = 0} ^ {W - 1} x (h, w) e ^ {- j 2 \\pi \\left(\\frac {h}{H} u + \\frac {w}{W} v\\right)} \\tag {1}", + "image_path": "c56f9d1bdbb74c26665f397359a3360be621e2112e9540e27ee0f8ddecc2d5fa.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 625, + 547, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 625, + 547, + 660 + ], + "spans": [ + { + "bbox": [ + 304, + 625, + 547, + 660 + ], + "type": "text", + "content": "In our work, the Fourier transform is individually applied to each image channel. The amplitude and phase components can be described as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 334, + 668, + 546, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 668, + 546, + 685 + ], + "spans": [ + { + "bbox": [ + 334, + 668, + 546, + 685 + ], + "type": "interline_equation", + "content": "\\mathcal {A} (x) (u, v) = \\left[ R ^ {2} (x) (u, v) + I ^ {2} (x) (u, v) \\right] ^ {\\frac {1}{2}}, \\tag {2}", + "image_path": "fc38e82bb58ef6c677454cc06ed793bb128b28a751532590adb6e0527235920b.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 334, + 685, + 545, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 685, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 334, + 685, + 545, + 712 + ], + "type": "interline_equation", + "content": "\\mathcal {P} (x) (u, v) = \\arctan \\left[ \\frac {I (x) (u , v)}{R (x) (u , v)} \\right] \\tag {3}", + "image_path": "c671fcf528914da9b3900a5f5f664b28ff9d5133c92de6ad1a8c53e09a18a75b.jpg" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "12910" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "I(x)" + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "R(x)" + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": " indicate imaginary and real parts of the image's frequency representation " + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(x)" + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": ", correspondingly." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 288, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 288, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 288, + 324 + ], + "type": "text", + "content": "The Fourier transform can be beneficial in the task of pan-sharpening by disentangling and analyzing image degradation in the amplitude component. We may obtain important insights into the level of degradation existing in the image by carefully evaluating the amplitude information, ultimately resulting in more effective restoration attempts. Figure 1 illustrates that whereas LRMS images degrade in both the high-frequency and low-frequency regions, while PAN images degrade mostly in the low-frequency region. Moreover, it is important to note that the frequency of image degradation can vary across different scales. Following frequency analysis, it is obvious that the frequency domain information from a PAN image can be effectively integrated into a LRMS image to assist with its restoration. This process can be further optimized by injecting the frequency domain information at multiple scales, allowing for a more comprehensive reconstruction of the image's contextual information." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 332, + 166, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 332, + 166, + 344 + ], + "spans": [ + { + "bbox": [ + 47, + 332, + 166, + 344 + ], + "type": "text", + "content": "3.2. Network framework" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 350, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 506 + ], + "type": "text", + "content": "As shown in Figure 2, given an input of a PAN and LRMS pair, we start by upsampling the LRMS image to the size of the PAN image. After that, a feature extraction pyramid is employed to process the PAN image, obtaining multi-scale features. Once the LRMS image is upsampled, the frequency injection pyramid injects multi-scale features into the LRMS image. The frequency injection pyramid is used to integrate the frequency domain features of various scales to further explore the frequency information. Then, we adopt spatial injection pyramid to reconstruct local details. Finally, the reconstruction image is obtained through a skip connection between network output and the upsampled LRMS image." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 514, + 208, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 208, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 208, + 528 + ], + "type": "text", + "content": "3.3. The key building components" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "type": "text", + "content": "Three essential elements make up the architecture of our network, and they are shown in Figures 2, 3, and 4. We go into great depth on each of these parts in the part that follows. Feature Extraction Pyramid. The Feature Extraction Pyramid is in charge of extracting multi-scale features from the PAN images, which can be utilized by other modules for further feature injection. To obtain the original size feature, the PAN image is first projected into the feature space using a convolution layer. After that, two sets of convolution and downsampling operations are carried out to generate features that are half as large and a quarter as large as the original. These features, namely " + }, + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "type": "inline_equation", + "content": "P_{1}, P_{2}" + }, + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "type": "inline_equation", + "content": "P_{3}" + }, + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "type": "text", + "content": ", are then injected as supplemental information to the LRMS images to aid in the reconstruction process. The convolution operation with a stride of 2 is employed as a down-sampling" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 324, + 69, + 536, + 182 + ], + "blocks": [ + { + "bbox": [ + 324, + 69, + 536, + 182 + ], + "lines": [ + { + "bbox": [ + 324, + 69, + 536, + 182 + ], + "spans": [ + { + "bbox": [ + 324, + 69, + 536, + 182 + ], + "type": "image", + "image_path": "18a61e74edb06acb294204c6922cae3a764bbdd744f1d63a8c6cf6109b12a048.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 186, + 547, + 253 + ], + "lines": [ + { + "bbox": [ + 305, + 186, + 547, + 253 + ], + "spans": [ + { + "bbox": [ + 305, + 186, + 547, + 253 + ], + "type": "text", + "content": "Figure 3. Architecture of Frequency Injection Module (FIM). The phase and amplitude components of " + }, + { + "bbox": [ + 305, + 186, + 547, + 253 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 305, + 186, + 547, + 253 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 186, + 547, + 253 + ], + "type": "inline_equation", + "content": "F_{i}" + }, + { + "bbox": [ + 305, + 186, + 547, + 253 + ], + "type": "text", + "content": " are obtained using the Fourier transform. Feature fusion is performed in the frequency domain, and the resulting frequency domain feature map is combined with the spatial feature to facilitate frequency domain information recovery and dual-domain complementary learning." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 270, + 545, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 545, + 306 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 545, + 306 + ], + "type": "text", + "content": "operation in the pyramid. In the end, this module produces multi-scale feature maps for further information injection utilizing PAN image as input." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "type": "text", + "content": "Spatial Injection Pyramid. The Spatial Injection Pyramid is designed to inject the local, multi-scale spatial information from PAN into the LRMS image. This module may effectively concentrate on small objects by leveraging the locality of the convolution operation in the pixel domain. In this module, the spatial features of " + }, + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "type": "inline_equation", + "content": "P_{1}" + }, + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "type": "inline_equation", + "content": "P_{2}" + }, + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "type": "inline_equation", + "content": "P_{3}" + }, + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "type": "text", + "content": " are injected into LRMS images at various scales to aid in reconstruction. For instance, given the output of the frequency pyramid presented by " + }, + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "type": "inline_equation", + "content": "M s_{i}" + }, + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "type": "text", + "content": " and the feature map " + }, + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "type": "text", + "content": " at the original scale, further feature extraction is performed using a convolution layer to get " + }, + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "type": "text", + "content": ", and then the features " + }, + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "type": "text", + "content": " are injected into " + }, + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 304, + 307, + 546, + 498 + ], + "type": "text", + "content": " using the spatial injection module (SIM). Following injection, a down-sampling or up-sampling operation is applied to generate the feature map of a different size. Taking the down-sampling branch for example, the process can be described as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 372, + 506, + 545, + 520 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 506, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 372, + 506, + 545, + 520 + ], + "type": "interline_equation", + "content": "S _ {i} = \\operatorname {c o n v} _ {3 \\times 3} (M s _ {i}) \\tag {4}", + "image_path": "23beb785baacc915078a6753d3e057da9538ec4da9875f45f429d8dcfe572f3b.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 372, + 521, + 545, + 535 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 521, + 545, + 535 + ], + "spans": [ + { + "bbox": [ + 372, + 521, + 545, + 535 + ], + "type": "interline_equation", + "content": "F _ {s p a i n j} = S I M \\left(S _ {i}, P _ {i}\\right) \\tag {5}", + "image_path": "af43a1d5916a65aff3fd92ef8986b62ad082d9756e55699ddd8dc796dac3b505.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 373, + 536, + 545, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 536, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 373, + 536, + 545, + 550 + ], + "type": "interline_equation", + "content": "M s _ {i + 1} = \\operatorname {d o w n} \\left(F _ {\\text {s p a i n j}}\\right) \\tag {6}", + "image_path": "bf3a4fd1b927e842ea113cdc8b7530e62b9b562b75840857fb46428b958027cb.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 558, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 641 + ], + "type": "text", + "content": "The suggested spatial injection module, shown in the figure 4, uses the AFF [3] as a basis block and is built on attention mechanism to enable effective and consistent injection of spatial details. The module works by enabling interaction between the PAN and LRMS branches, which enhances detail injection and facilitates the acquisition of LRMS features with injected spatial details." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": "Frequency Injection Pyramid. The purpose of the frequency injection pyramid is to provide LRMS features with high-frequency and global information from PAN image. By utilizing the multi-scale frequency injection, the restoration of LRMS image's frequency domain information is enhanced by leveraging the frequency information of PAN im" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12911" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 68, + 289, + 174 + ], + "blocks": [ + { + "bbox": [ + 50, + 68, + 289, + 174 + ], + "lines": [ + { + "bbox": [ + 50, + 68, + 289, + 174 + ], + "spans": [ + { + "bbox": [ + 50, + 68, + 289, + 174 + ], + "type": "image", + "image_path": "f909e15196e26630003aed869af56528f8dfe8b28d0f715dc6e5b3b9fbb03ff4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 179, + 287, + 212 + ], + "lines": [ + { + "bbox": [ + 46, + 179, + 287, + 212 + ], + "spans": [ + { + "bbox": [ + 46, + 179, + 287, + 212 + ], + "type": "text", + "content": "Figure 4. The proposed module for injecting spatial domain information, dubbed SIM, is based on attention mechanism and uses a basic module built on attentional fusion block." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 229, + 289, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 229, + 289, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 229, + 289, + 384 + ], + "type": "text", + "content": "age. Processing information in frequency domain enables the network to quickly capture high-frequency features that are challenging to acquire using pixel domain CNN, encourages dual-domain complementary learning, and generates clear texture features. Specifically, given the feature map of the LRMS image presented by " + }, + { + "bbox": [ + 46, + 229, + 289, + 384 + ], + "type": "inline_equation", + "content": "Mf_{i}" + }, + { + "bbox": [ + 46, + 229, + 289, + 384 + ], + "type": "text", + "content": " and the feature map " + }, + { + "bbox": [ + 46, + 229, + 289, + 384 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 46, + 229, + 289, + 384 + ], + "type": "text", + "content": ", first " + }, + { + "bbox": [ + 46, + 229, + 289, + 384 + ], + "type": "inline_equation", + "content": "M_{i}" + }, + { + "bbox": [ + 46, + 229, + 289, + 384 + ], + "type": "text", + "content": " are fed to a convolution block to extract a further feature " + }, + { + "bbox": [ + 46, + 229, + 289, + 384 + ], + "type": "inline_equation", + "content": "F_{i}" + }, + { + "bbox": [ + 46, + 229, + 289, + 384 + ], + "type": "text", + "content": ". Next, the frequency injection module (FIM) is used to inject the frequency domain features of " + }, + { + "bbox": [ + 46, + 229, + 289, + 384 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 46, + 229, + 289, + 384 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 46, + 229, + 289, + 384 + ], + "type": "inline_equation", + "content": "F_{i}" + }, + { + "bbox": [ + 46, + 229, + 289, + 384 + ], + "type": "text", + "content": ". The resulting feature map is then down-sampled or upsampled for the next scale of frequency domain information injection. Taking the up-sampling branch as an example, this process is summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 116, + 393, + 287, + 406 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 393, + 287, + 406 + ], + "spans": [ + { + "bbox": [ + 116, + 393, + 287, + 406 + ], + "type": "interline_equation", + "content": "F _ {i} = \\operatorname {c o n v} _ {3 \\times 3} (M f _ {i}) \\tag {7}", + "image_path": "304adbb98013510a7ff457c831918b9662ed7ed75b627eed4e8fd1a3006bcbd0.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 116, + 408, + 287, + 421 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 408, + 287, + 421 + ], + "spans": [ + { + "bbox": [ + 116, + 408, + 287, + 421 + ], + "type": "interline_equation", + "content": "F _ {f r e i n j} = F I M \\left(F _ {i}, P _ {i}\\right) \\tag {8}", + "image_path": "fbfdc8c735a1d76e1b6aebc4498c20845a5ff1323f3317614b9af121424eab96.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 116, + 423, + 287, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 423, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 116, + 423, + 287, + 437 + ], + "type": "interline_equation", + "content": "M f _ {i + 1} = u p \\left(F _ {f r e i n j}\\right) \\tag {9}", + "image_path": "e5b02e160daf3be8e14338c9d9347856d4411d155d0631d39f2e114115d56d0d.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 445, + 218, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 445, + 218, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 445, + 218, + 456 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 445, + 218, + 456 + ], + "type": "inline_equation", + "content": "up" + }, + { + "bbox": [ + 47, + 445, + 218, + 456 + ], + "type": "text", + "content": " is implemented by pixel-shuffle." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 456, + 287, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 527 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 527 + ], + "type": "text", + "content": "With the inputs " + }, + { + "bbox": [ + 46, + 456, + 287, + 527 + ], + "type": "inline_equation", + "content": "F_{i}" + }, + { + "bbox": [ + 46, + 456, + 287, + 527 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 456, + 287, + 527 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 46, + 456, + 287, + 527 + ], + "type": "text", + "content": ", the FIM shown in Figure 3 employs the Fourier transform to produce amplitude and phase components. Following that, the phase and amplitude information of " + }, + { + "bbox": [ + 46, + 456, + 287, + 527 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 46, + 456, + 287, + 527 + ], + "type": "text", + "content": " is individually injected into " + }, + { + "bbox": [ + 46, + 456, + 287, + 527 + ], + "type": "inline_equation", + "content": "F_{i}" + }, + { + "bbox": [ + 46, + 456, + 287, + 527 + ], + "type": "text", + "content": " to aid in the restoration of the LRMS image in the frequency domain." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 529, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 529, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 529, + 287, + 552 + ], + "type": "text", + "content": "In particular, the following procedure is used to acquire the relevant amplitude and phase components:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 116, + 560, + 287, + 573 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 560, + 287, + 573 + ], + "spans": [ + { + "bbox": [ + 116, + 560, + 287, + 573 + ], + "type": "interline_equation", + "content": "\\mathcal {A} \\left(F _ {i}\\right), \\mathcal {P} \\left(F _ {i}\\right) = \\mathcal {F} \\left(F _ {i}\\right), \\tag {10}", + "image_path": "5bfde4864497627802b1afccf6289c113ba105d92e8f326b20c399a396521268.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 117, + 575, + 287, + 588 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 575, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 117, + 575, + 287, + 588 + ], + "type": "interline_equation", + "content": "\\mathcal {A} \\left(P _ {i}\\right), \\mathcal {P} \\left(P _ {i}\\right) = \\mathcal {F} \\left(P _ {i}\\right), \\tag {11}", + "image_path": "f6d22b77dd047eff6f3bc9c25d1b9d778aef4a948d439aa926ebd2135f2ff705.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 596, + 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}, + { + "bbox": [ + 70, + 652, + 287, + 666 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 652, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 70, + 652, + 287, + 666 + ], + "type": "interline_equation", + "content": "\\alpha , \\beta = \\operatorname {C o n v} _ {3 \\times 3} (\\mathcal {A} (P _ {i})), \\operatorname {C o n v} _ {3 \\times 3} (\\mathcal {A} (P _ {i})), \\tag {12}", + "image_path": "c7a785ae6c39d1f9f04dbeccd08a906b422db7a968868ae6d974eab2b7af7fc7.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 63, + 667, + 287, + 680 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 667, + 287, + 680 + ], + "spans": [ + { + "bbox": [ + 63, + 667, + 287, + 680 + ], + "type": "interline_equation", + "content": "\\mathcal {A} \\left(F _ {i}\\right) = \\mathcal {A} \\left(F _ {i}\\right) \\cdot \\alpha + \\beta , \\tag {13}", + "image_path": 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\\operatorname {C o n v} _ {1 \\times 1} \\left(\\operatorname {C a t} \\left(\\left[ \\mathcal {P} \\left(P _ {i}\\right), \\mathcal {P} \\left(F _ {i}\\right) \\right]\\right)\\right) \\tag {15}", + "image_path": "fec7883e566413d1daf1ca620b70f41c195a9dbdff9ce2bb62c5f08a3fb3bf40.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "content": "The injected components are then transformed back to the pixel domain using the inverse transform, and are subsequently fused with spatial features to inject frequency features into spatial information and promote dual-domain complementary learning:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 346, + 136, + 545, + 150 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 136, + 545, + 150 + ], + "spans": [ + { + "bbox": [ + 346, + 136, + 545, + 150 + ], + "type": "interline_equation", + "content": "F _ {f r e} = \\operatorname {C o n v} _ {1 \\times 1} \\left(\\mathcal {F} ^ {- 1} (\\mathcal {A} (F), \\mathcal {P} (F))\\right) \\tag {16}", + "image_path": "788602a4d0f6a3733744b7911c0b82a7b1b0f023127da10b627ff1f59670b275.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 347, + 152, + 545, + 165 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 152, + 545, + 165 + ], + "spans": [ + { + "bbox": [ + 347, + 152, + 545, + 165 + ], + "type": "interline_equation", + "content": "F _ {s p a} = \\operatorname {C o n v} _ {3 \\times 3} \\left(F _ {i}\\right), \\tag {17}", + "image_path": "fd78cd4919b5284b6a8b0cd6bc86b9483c75a94aa0b66050ad89b5dd6ac1e6a2.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 347, + 167, + 545, + 180 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 167, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 347, + 167, + 545, + 180 + ], + "type": "interline_equation", + "content": "F _ {f r e i n j} = F _ {f r e} + F _ {s p a} \\tag {18}", + "image_path": "107b8e0907f2c2892b821b98aa18bfe99ed1a7bf56e609fc640894048df29b06.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 183, + 394, + 194 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 183, + 394, + 194 + ], + "spans": [ + { + "bbox": [ + 306, + 183, + 394, + 194 + ], + "type": "text", + "content": "3.4. Loss Function" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 201, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 201, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 304, + 201, + 545, + 285 + ], + "type": "text", + "content": "To improve the perception of high-frequency information, we propose a loss function that combines spatial and frequency domain losses in this study. Provided that " + }, + { + "bbox": [ + 304, + 201, + 545, + 285 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 201, + 545, + 285 + ], + "type": "text", + "content": " represents the model output, " + }, + { + "bbox": [ + 304, + 201, + 545, + 285 + ], + "type": "inline_equation", + "content": "Y_{f}" + }, + { + "bbox": [ + 304, + 201, + 545, + 285 + ], + "type": "text", + "content": " represents the output of frequency injection pyramid and " + }, + { + "bbox": [ + 304, + 201, + 545, + 285 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 201, + 545, + 285 + ], + "type": "text", + "content": " represents the ground truth, the " + }, + { + "bbox": [ + 304, + 201, + 545, + 285 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 304, + 201, + 545, + 285 + ], + "type": "text", + "content": " distance between " + }, + { + "bbox": [ + 304, + 201, + 545, + 285 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 201, + 545, + 285 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 201, + 545, + 285 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 201, + 545, + 285 + ], + "type": "text", + "content": " is employed to define the spatial domain loss:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 388, + 290, + 545, + 304 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 290, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 388, + 290, + 545, + 304 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s} = \\left| \\left| Y - H \\right| \\right| _ {1}. \\tag {19}", + "image_path": "24b5d7501bde2f29a24a2a9da6f523ff5f31949e89ba36d77de1c988cbcf3bfc.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 308, + 545, + 343 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 545, + 343 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 545, + 343 + ], + "type": "text", + "content": "The frequency domain loss, which aims to improve the perception of high-frequency information, is determined using the following formula:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 348, + 545, + 373 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 348, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 306, + 348, + 545, + 373 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {f} = \\left| \\left| \\log \\left(\\mathcal {A} \\left(Y _ {f}\\right)\\right) - \\log \\left(\\mathcal {A} (H)\\right) \\right| \\right| _ {1} + \\left| \\left| \\mathcal {P} (Y) - \\mathcal {P} (H) \\right| \\right| _ {1}, \\tag {20}", + "image_path": "3324bd0d9defaf8ed48399cc88c132d185832887493cedc1f96cc14695abb3cb.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 377, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 545, + 437 + ], + "type": "text", + "content": "where the amplitude and phase components of the Fourier transform are denoted by " + }, + { + "bbox": [ + 304, + 377, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 304, + 377, + 545, + 437 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 377, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 377, + 545, + 437 + ], + "type": "text", + "content": " respectively. The complete loss function is a combination of the dual domain losses, and involves a hyper-parameter " + }, + { + "bbox": [ + 304, + 377, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 377, + 545, + 437 + ], + "type": "text", + "content": " which is set to 0.1 based on empirical evidence." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 392, + 442, + 545, + 455 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 392, + 442, + 545, + 455 + ], + "spans": [ + { + "bbox": [ + 392, + 442, + 545, + 455 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {s} + \\lambda \\mathcal {L} _ {f}. \\tag {21}", + "image_path": "247ab56931693d4dc7c99af20821baead9e50c18fece1e9e82533bf23f150512.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 460, + 382, + 473 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 460, + 382, + 473 + ], + "spans": [ + { + "bbox": [ + 306, + 460, + 382, + 473 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 479, + 444, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 444, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 444, + 491 + ], + "type": "text", + "content": "4.1. Datasets and benchmark" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 498, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 629 + ], + "type": "text", + "content": "Three datasets—WorldView-II (WV2), WorldView-III (WV3), and Gaofen2 (GF2) were used in our experiments. Due to the unavailability of real HRMS images, we utilized the Wald protocol [23] to generate the training and test data. In further detail, we extracted patches from the same location from the PAN and LRMS images, with the PAN patch being " + }, + { + "bbox": [ + 304, + 498, + 545, + 629 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 498, + 545, + 629 + ], + "type": "text", + "content": " times larger than the LRMS patch. The original LRMS patch was utilized as the ground truth, and both the LRMS and PAN patches were downsampled by a factor of " + }, + { + "bbox": [ + 304, + 498, + 545, + 629 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 498, + 545, + 629 + ], + "type": "text", + "content": " and used as input data. The selected patch sizes were 128x128 and 32x32, respectively." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "type": "text", + "content": "To evaluate the efficacy of our approach, we compared it with five traditional and six advanced CNN-based methods. Specifically, we included SFIM, Brovey [8], GS [11], IHS [10], and GFPCA [12] as traditional methods, and PANNET [30], MSDCNN [31], SRPPNN [2], GPPNN [25], MutNet [33] and INNformer [32] as advanced methods." + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "12912" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 91, + 553, + 312 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "type": "text", + "content": "Table 1. Quantitative comparison on three datasets. Best results are highlighted by red. " + }, + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "type": "text", + "content": " indicates that the larger the value, the better the performance, and " + }, + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "type": "text", + "content": " indicates that the smaller the value, the better the performance." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 91, + 553, + 312 + ], + "lines": [ + { + "bbox": [ + 47, + 91, + 553, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 553, + 312 + ], + "type": "table", + "html": "
MethodWorldView-IIGaoFen2Worldview-III
PSNR↑SSIM↑SAM↓ERGAS↓PSNR↑SSIM↑SAM↓ERGAS↓PSNR↑SSIM↑SAM↓ERGAS↓
SFIM34.12970.89750.04392.344936.90600.88820.03181.739821.82120.54570.12088.9730
Brovey35.86460.92160.04031.823837.79740.90260.02181.372022.50600.54660.11598.2331
GS35.63760.91760.04231.877437.22600.90340.03091.673622.56080.54700.12178.2433
IHS35.29620.90270.04612.027838.17540.91000.02431.533622.55790.53540.12668.3616
GFPCA34.55810.90380.04882.141137.94430.92040.03141.560422.33440.48260.12948.3964
PANNET40.81760.96260.02571.055743.06590.96850.01780.857729.68400.90720.08513.4263
MSDCNN41.33550.96640.02420.994045.68470.98270.01350.638930.30380.91840.07823.1884
SRPPNN41.45380.96790.02330.989947.19980.98770.01060.558630.43460.92020.07703.1553
GPPNN41.16220.96840.02441.031544.21450.98150.01370.736130.17850.91750.07763.2593
MutNet41.67730.97050.02240.951947.30420.98920.01020.548130.49070.92230.07493.1125
INNformer41.69030.97040.02270.951447.35280.98930.01020.547930.53650.92250.07473.0997
Ours41.84730.97070.02220.935847.49390.98950.01000.536030.85020.92550.07262.9945
", + "image_path": "7e426b355e642e6e74a5755f9f26be64456f989aa7110ace2817361dd05d42d4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 335, + 547, + 394 + ], + "blocks": [ + { + "bbox": [ + 102, + 325, + 489, + 335 + ], + "lines": [ + { + "bbox": [ + 102, + 325, + 489, + 335 + ], + "spans": [ + { + "bbox": [ + 102, + 325, + 489, + 335 + ], + "type": "text", + "content": "Table 2. Evaluation of the proposed method on real-world full-resolution scenes from the GaoFen2 dataset." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 335, + 547, + 394 + ], + "lines": [ + { + "bbox": [ + 50, + 335, + 547, + 394 + ], + "spans": [ + { + "bbox": [ + 50, + 335, + 547, + 394 + ], + "type": "table", + "html": "
MetricSFIMBroveyGSIHSGFPCAPANNETMSDCNNSRPPNNGPPNNMutNetINNformerOurs
Dλ↓0.08220.13780.06960.07700.09140.07370.07340.07670.07820.06940.06930.0682
DS↓0.10870.26050.24560.29850.16350.12240.11510.11620.12530.11180.11380.1101
QNR ↑0.82140.63900.07250.64850.76150.81430.82150.81730.80730.82470.82590.8307
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The Adam optimizer was employed with an initial learning rate of " + }, + { + "bbox": [ + 46, + 433, + 288, + 529 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-4}" + }, + { + "bbox": [ + 46, + 433, + 288, + 529 + ], + "type": "text", + "content": ". To ensure stable training, the learning rate was decayed to " + }, + { + "bbox": [ + 46, + 433, + 288, + 529 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-8}" + }, + { + "bbox": [ + 46, + 433, + 288, + 529 + ], + "type": "text", + "content": " using the cosine annealing method after 500 epochs. Several commonly used evaluation metrics were chosen, including PSNR, SSIM, SAM, and ERGAS, as well as non-reference indices such as " + }, + { + "bbox": [ + 46, + 433, + 288, + 529 + ], + "type": "inline_equation", + "content": "D_{S}" + }, + { + "bbox": [ + 46, + 433, + 288, + 529 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 433, + 288, + 529 + ], + "type": "inline_equation", + "content": "D_{\\lambda}" + }, + { + "bbox": [ + 46, + 433, + 288, + 529 + ], + "type": "text", + "content": ", and QNR." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 539, + 266, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 539, + 266, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 539, + 266, + 552 + ], + "type": "text", + "content": "4.3. Comparison with state-of-the-art methods" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": "Evaluation on Reduced-Resolution Scene. The evaluation results of our approach on three datasets are shown in Table 1. The results demonstrate that our model performs better than the state-of-the-art approaches in the majority of assessment measures, and the improvements are significant. To be specific, our method outperforms the cutting-edge method INNformer on most indicators, on the WV2 dataset, our model achieves a " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "0.16\\mathrm{~dB}" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " improvement in PSNR compared to MIDN. Similarly, on the GF2 and WV3 datasets, our model achieves a " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "0.14\\mathrm{~dB}" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "0.31\\mathrm{~dB}" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " improvement in PSNR, respectively, demonstrating its excellent performance. Comparable improvements are also observed in other evaluation metrics." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 415, + 545, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 570 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 570 + ], + "type": "text", + "content": "Additionally, for qualitative evaluation, we compared the results obtained from our method with those of the other nine methods on the WV2 and GF2 datasets. To evaluate the similarity between the generated results and the ground truth, a residual map was generated by computing their mean squared error. The brighter areas of residual map indicate the larger differences with the ground truth. Our approach produces images with the finest texture and most realistic spectrum, as shown in Figures 5 and 6. The residual maps exhibit the least amount of bright spots, indicating high congruence with the ground truth. These findings are further supported by the evaluation indicators presented in the Table 1." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "content": "Evaluation on Full-Resolution Scene. To test the generalization ability of our model, we trained it on the GF2 dataset and evaluated full-resolution data from GF2 that was not downsampled, using the reserved portion of the dataset. Since there was no reference image available, we evaluated the dataset using no-reference indices. As shown in Table 2, our method achieved the best QNR index on this dataset, indicating its strong generalization ability compared to traditional and deep learning methods. This demonstrates that our approach can be applied to real-world scenes." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "12913" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 79, + 545, + 149 + ], + "blocks": [ + { + "bbox": [ + 107, + 69, + 484, + 79 + ], + "lines": [ + { + "bbox": [ + 107, + 69, + 484, + 79 + ], + "spans": [ + { + "bbox": [ + 107, + 69, + 484, + 79 + ], + "type": "text", + "content": "Table 3. The outcomes of the ablation experiments conducted on the WordView-II dataset are presented." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 79, + 545, + 149 + ], + "lines": [ + { + "bbox": [ + 50, + 79, + 545, + 149 + ], + "spans": [ + { + "bbox": [ + 50, + 79, + 545, + 149 + ], + "type": "table", + "html": "
Config Multi-scale FIMWorldView-IIGaoFen2WorldView-III
PSNR↑SSIM↑SAM↓ERGAS↓PSNR↑SSIM↑SAM↓ERGAS↓PSNR↑SSIM↑SAM↓ERGAS↓
(I)×✓41.63610.97010.02250.958147.37880.98920.01020.546630.78490.92520.07173.0240
(II)✓×41.63990.96950.02270.960047.45880.98900.01010.540330.81400.92560.07183.0106
Ours✓✓41.84350.97110.02220.947847.49390.98950.01000.536030.86450.92580.07572.9851
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The feature map display result reduces in size from the top to the bottom, corresponding to the output of the pyramid. It should be noted that the last two rows have been magnified for better visualization." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 314, + 70, + 546, + 324 + ], + "blocks": [ + { + "bbox": [ + 314, + 70, + 546, + 324 + ], + "lines": [ + { + "bbox": [ + 314, + 70, + 546, + 324 + ], + "spans": [ + { + "bbox": [ + 314, + 70, + 546, + 324 + ], + "type": "image", + "image_path": "feee9e5bf5163b11f782d2a2ff2c748d405e00a20183dabf37ce9108f37fe458.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 369, + 170, + 382 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 369, + 170, + 382 + ], + "spans": [ + { + "bbox": [ + 47, + 369, + 170, + 382 + ], + "type": "text", + "content": "4.4. Ablation experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 388, + 288, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 288, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 288, + 472 + ], + "type": "text", + "content": "We conducted two sets of ablation experiments on three datasets to examine the effects of our suggested approach on model performance to further demonstrate the effectiveness of our method. Multi-scale information modeling and dual-domain information injection are the fundamental parts of our model, and we conducted ablation experiments by removing each part independently." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 473, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 287, + 593 + ], + "type": "text", + "content": "Multi-scale feature extraction. The results of our model are shown in the first row of table 3 after the multi-scale feature extraction and reconstruction capabilities have been removed. We kept feature map size constant, eliminated all upsampling operations, and substituted the downsampling operation with standard convolution of stride 1 to conduct these trials. The results underscore the significance of multi-scale modeling for remote sensing images by showing that the model's performance declined after losing the capability of multi-scale modeling." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": "Frequency Injection Pyramid. The impact of eliminating frequency domain information from the model is shown in the second row of table 3. In order to remove frequency domain information, we used SIM to replace FIM in the frequency injection pyramid and remove the frequency loss to conduct these studies. The importance of introducing frequency information into the pan-sharpening process is revealed by the observation that the different indicators deteriorated when the global frequency domain information was removed." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 369, + 545, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 369, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 369, + 545, + 392 + ], + "type": "text", + "content": "4.5. Visualization of feature maps in different pyramids" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 403, + 546, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 546, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 546, + 559 + ], + "type": "text", + "content": "To further demonstrate the multi-scale and dual-domain modeling capabilities of our model, we present " + }, + { + "bbox": [ + 304, + 403, + 546, + 559 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 403, + 546, + 559 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 403, + 546, + 559 + ], + "type": "inline_equation", + "content": "M_{s}" + }, + { + "bbox": [ + 304, + 403, + 546, + 559 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 403, + 546, + 559 + ], + "type": "inline_equation", + "content": "F_{spainj}" + }, + { + "bbox": [ + 304, + 403, + 546, + 559 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 403, + 546, + 559 + ], + "type": "inline_equation", + "content": "M_{f}" + }, + { + "bbox": [ + 304, + 403, + 546, + 559 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 403, + 546, + 559 + ], + "type": "inline_equation", + "content": "F_{fre}" + }, + { + "bbox": [ + 304, + 403, + 546, + 559 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 403, + 546, + 559 + ], + "type": "inline_equation", + "content": "F_{freinj}" + }, + { + "bbox": [ + 304, + 403, + 546, + 559 + ], + "type": "text", + "content": " at different scales. These feature maps correspond to the output of the feature extraction pyramid, the features described in formula 6, and the features expressed in formulas 5, 9, 16, and 8, respectively. The Figure 7 illustrate that the features of different scales capture different regions of remote sensing images. The spatial pyramid features focus well on local information, while the frequency domain features effectively capture global and high-frequency features. The features after frequency domain injection combine the two types of information effectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 582, + 378, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 582, + 378, + 594 + ], + "spans": [ + { + "bbox": [ + 306, + 582, + 378, + 594 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "In this paper, we investigate the amplitude degradation of LRMS and PAN images across various scales. Based on the results of our investigation, we suggest a pyramid dual-domain injection network that injects multi-scale frequency and spatial domain information from the PAN image into the LRMS image to aid in its restoration. Our rigorous experiments on a variety of datasets demonstrate that our suggested model surpasses SOTA methods, exhibits good generalization, and effectively handles real-world scenarios." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12915" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 140, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 140, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 140, + 85 + ], + "type": "text", + "content": "Acknowledgment" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 287, + 114 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 287, + 114 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 287, + 114 + ], + "type": "text", + "content": "This work was Supported by the HFIPS Director's Fund, Grant No.2023YZGH04." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 127, + 107, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 127, + 107, + 140 + ], + "spans": [ + { + "bbox": [ + 48, + 127, + 107, + 140 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 148, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 148, + 287, + 213 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 148, + 287, + 213 + ], + "spans": [ + { + "bbox": [ + 53, + 148, + 287, + 213 + ], + "type": "text", + "content": "[1] Devansh Arpit, Stanisław Jastrzebski, Nicolas Ballas, David Krueger, Emmanuel Bengio, Maxinder S Kanwal, Tegan Maharaj, Asja Fischer, Aaron Courville, Yoshua Bengio, et al. 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However, the slow inference, high memory consumption, and computation intensity of the noise estimation model hinder the efficient adoption of diffusion models. Although post-training quantization (PTQ) is considered a go-to compression method for other tasks, it does not work out-of-the-box on diffusion models. We propose a novel PTQ method specifically tailored towards the unique multistep pipeline and model architecture of the diffusion models, which compresses the noise estimation network to accelerate the generation process. We identify the key difficulty of diffusion model quantization as the changing output distributions of noise estimation networks over multiple time steps and the bimodal activation distribution of the shortcut layers within the noise estimation network. We tackle these challenges with timestep-aware calibration and split shortcut quantization in this work. Experimental results show that our proposed method is able to quantize full-precision unconditional diffusion models into 4-bit while maintaining comparable performance (small FID change of at most 2.34 compared to $>100$ for traditional PTQ) in a training-free manner. Our approach can also be applied to text-guided image generation, where we can run stable diffusion in 4-bit weights with high generation quality for the first time.", + "bbox": [ + 75, + 300, + 473, + 680 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 694, + 209, + 709 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diffusion models have shown great success in generating images with both high diversity and high fidelity [43, 13, 44, 42, 6, 33, 36, 34]. Recent work [16, 15] has demonstrated superior performance than state-of-the-art GAN models, which suffer from unstable training. As a class of flexible generative models, diffusion models demonstrate their power in various applications such as image super-resolution [37, 18], inpainting [44], shape generation [3], graph generation [31], image-to-image translation [40], and molecular conformation generation [47].", + "bbox": [ + 75, + 719, + 470, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, the generation process for diffusion models can be slow due to the need for an iterative noise estimation of 50", + "bbox": [ + 75, + 869, + 470, + 898 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "to 1,000 time steps [13, 42] using complex neural networks. While previous state-of-the-art approaches (e.g., GANs) are able to generate multiple images in under 1 second, it normally takes several seconds for a diffusion model to sample a single image. Consequently, speeding up the image generation process becomes an important step toward broadening the applications of diffusion models. Previous work has been solving this problem by finding shorter, more effective sampling trajectories [42, 30, 39, 22, 1, 24], which reduces the number of steps in the denoising process. However, they have largely ignored another important factor: the noise estimation model used in each iteration itself is compute- and memory-intensive. This is an orthogonal factor to the repetitive sampling, which not only slows down the inference speed of diffusion models, but also poses crucial challenges in terms of high memory footprints.", + "bbox": [ + 496, + 268, + 895, + 512 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This work explores the quantization [50, 8, 49, 7, 29] of the noise estimation model used in the diffusion model to accelerate the denoising of all time steps. Specifically, we propose exploring post-training quantization (PTQ) on the diffusion model. PTQ has already been well studied in other learning domains like classification and object detection [4, 2, 20, 11, 23], and has been considered a go-to compression method given its minimal requirement for training data and the straightforward deployment on real hardware devices. However, the iterative computation process of the diffusion model and the model architecture of the noise estimation network brings unique challenges to the PTQ of diffusion models. PTQ4DM [41] presents an inaugural application of PTQ to compress diffusion models down to 8-bit, but it primarily focuses on smaller datasets and lower resolutions.", + "bbox": [ + 496, + 516, + 895, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Our work, evolving concurrently with [41], offers a comprehensive analysis of the novel challenges of performing PTQ on diffusion models. Specifically, as visualized in Figure 1(a), we discover that the output distribution of the noise estimation network at each time step can be largely different, and naively applying previous PTQ calibration methods with an arbitrary time step leads to poor performance. Furthermore, as illustrated in Figure 1(b), the iterative inference of the noise estimation network leads to an accumulation of quantization error, which poses higher demands on design-", + "bbox": [ + 496, + 750, + 898, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17535", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/da7b51ccc505d7d59f7ae73ae25bedd841c663fb6b3714d2e40a47b40792b4c5.jpg", + "image_caption": [ + "Figure 1: Conventional PTQ scenarios and Q-Diffusion differ in (a) calibration dataset creation and (b) model inference workflow. Traditional PTQ approaches sample data randomly [11], synthesize with statistics in model layers [4], or draw from the training set to create calibration dataset [28, 20], which either contains inconsistency with real inputs during the inference time or are not data-free. In contrast, Q-Diffusion constructed calibration datasets with inputs that are an accurate reflection of data seen during the production in a data-free manner. Traditional PTQ inference only needs to go through the quantized model $\\theta_q$ one time, while Q-Diffusion needs to address the accumulated quantization errors in the multi-time step inference." + ], + "image_footnote": [], + "bbox": [ + 120, + 83, + 500, + 313 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ff529693cfe2a2c7b812150f166da8dfb5e460a764ab61715fc8b389baf421e9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 80, + 843, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ing novel quantization schemes and calibration objectives for the noise estimation network.", + "bbox": [ + 75, + 434, + 467, + 463 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these challenges, we propose Q-Diffusion, a PTQ solution to compress the cumbersome noise estimation network in diffusion models in a data-free manner, while maintaining comparable performance to the full precision counterparts. We propose a time step-aware calibration data sampling mechanism from the pretrained diffusion model, which represents the activation distribution of all time steps. We further tailor the design of the calibration objective and the weight and activation quantizer to the commonly used noise estimation model architecture to reduce quantization error. We perform thorough ablation studies to verify our design choices, and demonstrate good generation results with diffusion models quantized to only 4 bits.", + "bbox": [ + 75, + 464, + 468, + 660 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are:", + "bbox": [ + 96, + 661, + 326, + 674 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We propose Q-Diffusion, a data-free PTQ solution for the noise estimation network in diffusion models.", + "2. We identify the novel challenge of performing PTQ on diffusion models as the activation distribution diversity and the quantization error accumulation across time steps via a thorough analysis.", + "3. We propose time step-aware calibration data sampling to improve calibration quality, and propose a specialized quantizer for the noise estimation network.", + "4. Extensive results show Q-Diffusion enables W4A8 PTQ for both pixel-space and latent-space unconditional diffusion models with an FID increment of only" + ], + "bbox": [ + 88, + 686, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "0.39-2.34 over full precision models. It can also produce qualitatively comparable images when plugged into Stable Diffusion [34] for text-guided synthesis.", + "bbox": [ + 529, + 434, + 893, + 479 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 494, + 637, + 508 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion Models. Diffusion models generate images through a Markov chain, as illustrated in Figure 2. A forward diffusion process adds Gaussian noise to data $\\mathbf{x}_0 \\sim q(\\mathbf{x})$ for $T$ times, resulting in noisy samples $\\mathbf{x}_1, \\dots, \\mathbf{x}_T$ :", + "bbox": [ + 498, + 520, + 892, + 580 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 593, + 890, + 612 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\beta_{t} \\in (0,1)$ is the variance schedule that controls the strength of the Gaussian noise in each step. When $T \\to \\infty$ , $\\mathbf{x}_T$ approaches an isotropic Gaussian distribution.", + "bbox": [ + 498, + 625, + 893, + 669 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The reverse process removes noise from a sample from the Gaussian noise input $\\mathbf{x}_T\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ to gradually generate high-fidelity images. However, since the real reverse conditional distribution $q(\\mathbf{x}_{t - 1}|\\mathbf{x}_t)$ is unavailable, diffusion models sample from a learned conditional distribution:", + "bbox": [ + 496, + 670, + 893, + 746 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\tilde {\\boldsymbol {\\mu}} _ {\\theta , t} \\left(\\mathbf {x} _ {t}\\right), \\tilde {\\boldsymbol {\\beta}} _ {t} \\mathbf {I}\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 758, + 890, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With the reparameterization trick in [13], the mean $\\tilde{\\mu}_{\\theta ,t}(\\mathbf{x}_t)$ and variance $\\tilde{\\beta}_t$ could be derived as follows:", + "bbox": [ + 498, + 789, + 890, + 821 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\boldsymbol {\\mu}} _ {\\theta , t} \\left(\\mathbf {x} _ {t}\\right) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {x} _ {t} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\boldsymbol {\\epsilon} _ {\\theta , t}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 832, + 890, + 864 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\beta} _ {t} = \\frac {1 - \\bar {\\alpha} _ {t - 1}}{1 - \\bar {\\alpha} _ {t}} \\cdot \\beta_ {t} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 867, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17536", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5224a88d6432bf1fef55014a279f934533509072d14b15c9f646c3084f323f40.jpg", + "image_caption": [ + "(a) Forward diffusion process" + ], + "image_footnote": [], + "bbox": [ + 81, + 87, + 467, + 130 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ca9fad0fc7232a4b06ecf2d676caf71b1f8339914e11ff8d6464a4c0804ec580.jpg", + "image_caption": [ + "(b) Reverse diffusion process", + "Figure 2: The forward diffusion process (a) repeatedly adds Gaussian noise. The reverse diffusion process (b) uses a trained network to denoise from a standard Gaussian noise image in order to generate an image." + ], + "image_footnote": [], + "bbox": [ + 81, + 142, + 465, + 185 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\alpha_{t} = 1 - \\beta_{t}$ , $\\bar{\\alpha}_{t} = \\prod_{i=1}^{t} \\alpha_{i}$ . We refer readers to [26] for a more detailed introduction.", + "bbox": [ + 75, + 280, + 468, + 311 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In practice, the noise at each time step $t$ are computed from $\\mathbf{x}_t$ by a noise estimation model, with the same weights for all time steps. The UNet [35] dominates the design of the noise estimation model in diffusion models [42, 34, 33, 36], with some recent exploration on Transformer [32]. This work designs the PTQ method for the acceleration of the noise estimation model, especially for the common UNet.", + "bbox": [ + 75, + 311, + 468, + 417 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Accelerated diffusion process. Related methods include simulating the diffusion process in fewer steps by generalizing it to a non-Markovian process [42], adjusting the variance schedule [30], and the use of high-order solvers to approximate diffusion generation [22, 1, 24, 25]. Others have employed the technique of caching and reusing feature maps [19]. Efforts to distill the diffusion model into fewer time steps have also been undertaken [39, 27], which have achieved notable success but involve an extremely expensive retraining process. Our work focuses on accelerating the noise estimation model inference in each step, with a training-free PTQ process.", + "bbox": [ + 75, + 417, + 470, + 598 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Post-training Quantization. Post-training quantization (PTQ) compresses deep neural networks by rounding elements $w$ to a discrete set of values [10], where the quantization and de-quantization can be formulated as:", + "bbox": [ + 75, + 599, + 470, + 659 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {w} = \\mathrm {s} \\cdot \\operatorname {c l i p} \\left(\\operatorname {r o u n d} \\left(\\frac {w}{s}\\right), c _ {\\min }, c _ {\\max }\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 667, + 468, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $s$ denotes the quantization scale parameters, $c_{\\mathrm{min}}$ and $c_{\\mathrm{max}}$ are the lower and upper bounds for the clipping function $\\mathrm{clip}(\\cdot)$ . These parameters can be calibrated with the weight and activation distribution estimated in the PTQ process. The operator round(\\cdot) represents rounding, which can be either rounding-to-nearest [46, 4] or adaptive rounding [20].", + "bbox": [ + 75, + 704, + 468, + 795 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Previous PTQ research in classification and detection tasks focused on the calibration objective and the acquisition of calibration data. For example, EasyQuant [46] determines appropriate $c_{\\mathrm{min}}$ and $c_{\\mathrm{max}}$ based on training data, and BRECQ [20] introduces Fisher information into the objective. ZeroQ [4] employs a distillation technique to generate proxy input images for PTQ, and SQuant [11] uses", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "random samples with objectives based on sensitivity determined through the Hessian spectrum. For diffusion model quantization, a training dataset is not needed as the calibration data can be constructed by sampling the full-precision model with random inputs. However, the multi-time step inference of the noise estimation model brings new challenges in modeling the activation distribution. In parallel to our work, PTQ4DM [41] introduces the method of Normally Distributed Time-step Calibration, generating calibration data across all time steps with a specific distribution. Nevertheless, their explorations remain confined to lower resolutions, 8-bit precision, floating-point attention activation-to-activation matmuls, and with limited ablation study on other calibration schemes. This results in worse applicability of their method to lower precisions (see Appendix). Our work delves into the implications of calibration dataset creation in a holistic manner, establishing an efficient calibration objective for diffusion models. We fully quantize act-to-act matmuls, validated by experiments involving both pixel-space and latent-space diffusion models on large-scale datasets up to resolutions of $512 \\times 512$ .", + "bbox": [ + 496, + 90, + 893, + 409 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 422, + 589, + 436 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We present our method for post-training quantization of diffusion models in this section. Different from conventionally studied deep learning models and tasks such as CNNs and VITs for classification and detection, diffusion models are trained and evaluated in a distinctive multi-step manner with a unique UNet architecture. This presents notable challenges to the PTQ process. We analyze the challenges brought by the multi-step inference process and the UNet architecture in Section 3.1 and 3.2 respectively and describe the full Q-Diffusion PTQ pipeline in Section 3.3.", + "bbox": [ + 496, + 448, + 893, + 599 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Challenges under the Multi-step Denoising", + "text_level": 1, + "bbox": [ + 500, + 609, + 862, + 626 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We identify two major challenges in quantizing models that employ multi-step inference process. Namely, we investigate the accumulation of quantization error across time steps and the difficulty of sampling a small calibration dataset to reduce the quantization error at each time step.", + "bbox": [ + 496, + 633, + 893, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Challenge 1: Quantization errors accumulate across time steps. Performing quantization on a neural network model introduces noise on the weight and activation of the well-trained model, leading to quantization errors in each layer's output. Previous research has identified that quantization errors are likely to accumulate across layers [5], making deeper neural networks harder to quantize. In the case of diffusion models, at any time step $t$ , the input of the denoising model (denoted as $\\mathbf{x}_t$ ) is derived by $\\mathbf{x}_{t+1}$ , the output of the model at the previous time step $t+1$ (as depicted by Equation 2). This process effectively multiplies the number of layers involved in the computation by the number of de", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17537", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7a13bcbf9683434d92db803b95d4b212fe5f7010a07730acab221dbe9d42ad1a.jpg", + "image_caption": [ + "Figure 3: MSE between FP32 outputs and weight-quantized outputs of different precisions with Linear Quantization and our approach across time steps. Here the data is obtained by passing a batch with 64 samples through a model trained on CIFAR-10 [17] with DDIM sampling steps 100." + ], + "image_footnote": [], + "bbox": [ + 99, + 90, + 444, + 234 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c0a7e41022b3249801c9b6f5996acd95845572a359b129e9702032dc588f4832.jpg", + "image_caption": [ + "Figure 4: Effects of time steps in calibration dataset creation on 4-bit weights quantization results with DDIM on CIFAR-10. First $n$ , Mid $n$ , Last $n$ denotes that 5120 samples are selected uniformly from the first, middle, last $n$ time steps." + ], + "image_footnote": [], + "bbox": [ + 99, + 338, + 434, + 498 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "noising steps for the input $\\mathbf{x}_t$ at time step $t$ , leading to an accumulation of quantization errors towards later steps in the denoising process.", + "bbox": [ + 75, + 587, + 468, + 632 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We run the denoising process of DDIM [42] on CIFAR-10 [17] with a sampling batch size of 64, and compare the MSE differences between the full-precision model and the model quantized to INT8, INT5, and INT4 at each time step. As shown in Figure 3, there is a dramatic increase in the quantization errors when the model is quantized to 4-bit, and the errors accumulate quickly through iterative denoising. This brings difficulty in preserving the performance after quantizing the model down to low precision, which requires the reduction of quantization errors at all time steps as much as possible.", + "bbox": [ + 75, + 633, + 468, + 799 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Challenge 2: Activation distributions vary across time steps. To reduce the quantization errors at each time step, previous PTQ research [28, 20] calibrates the clipping range and scaling factors of the quantized model with a small set of calibration data. The calibration data should be sampled to resemble the true input distribution so that the activation dis", + "bbox": [ + 75, + 809, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The distribution of the model can be estimated correctly for proper calibration. Given that the Diffusion model uses the same noise estimation network to take inputs from all time steps, determining the data sampling policy across different time steps becomes an outstanding challenge. Here we start by analyzing the output activation distribution of the UNet model across different time steps. We conduct the same CIFAR-10 experiment using DDIM with 100 denoising steps, and draw the activations ranges of 1000 random samples among all time steps. As Figure 5 shows, the activation distributions gradually change, with neighboring time steps being similar and distant ones being distinctive. This is also echoed by the visualized $\\mathbf{x}_t$ in Figure 2.", + "bbox": [ + 496, + 90, + 890, + 286 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The fact that the output activations distribution varies across time steps further brings challenges to quantization. Calibrating the noise estimation model using only a few time steps that do not reflect the full range of activations seen among all time steps by the noise estimation model during the denoising process can cause overfitting to the activation distribution described by those specific time steps, while not generalizing to other time steps, which hurts the overall performance. For instance, here we try to calibrate the quantized DDIM on the CIFAR-10 dataset with data sampled from different parts of the denoising process. As shown in Figure 4, if we simply take 5120 samples from time steps that fall into a certain stage of the denoising process, significant performance drops will be induced under 4-bit weights quantization. Note that the case with samples taken from the middle 50 time steps caused smaller drops compared to cases with samples taken from either the first or the last $n$ time steps, and with $n$ increases, the drops are also alleviated. These results illustrate the gradual \"denoising\" process as depicted in Figure 5: the activations distribution changes gradually throughout time steps, with the middle part capturing the full range to some degree, while parts of the distant endpoints differing the most. To recover the performance of the quantized diffusion models, we need to select calibration data in a way that comprehensively takes into account the distributions of the output of different time steps.", + "bbox": [ + 496, + 287, + 892, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Challenges on Noise Estimation Model Quantization", + "text_level": 1, + "bbox": [ + 500, + 694, + 888, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Most diffusion models (Imagen [36], Stable Diffusion [34], VDMs [14]) adopt UNets as denoising backbones that downsample and upsample latent features. Although recent studies show that transformer architectures are also capable of serving as the noise estimation backbone [32], convolutional UNets are still the de facto choice of architecture today. UNets utilize shortcut layers to merge concatenated deep and shallow features and transmit them to subsequent layers. Through our analysis presented in Figure 6, we observe that input activations in shortcut layers exhibit abnormal value ranges in comparison to other layers.", + "bbox": [ + 496, + 734, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17538", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/924496e879da1b129aa92becbafb5799fc5bcc820a975764e330ae14ace14da0.jpg", + "image_caption": [ + "Figure 5: Activation ranges of $x_{t}$ across all 100 time steps of FP32 DDIM model on CIFAR-10." + ], + "image_footnote": [], + "bbox": [ + 140, + 84, + 831, + 200 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Notably, the input activations in DDIM's shortcut layers can be up to 200 times larger than other neighboring layers.", + "bbox": [ + 75, + 255, + 468, + 286 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To analyze the reason for this, we visualize the weight and activation tensor of a DDIM shortcut layer. As demonstrated in the dashed box in Figure 6, the ranges of activations from the deep feature channels $(X_{1})$ and shallow feature channels $(X_{2})$ being concatenated together vary significantly, which also resulted in a bimodal weight distribution in the corresponding channels (see also Figure 7). Naively quantizing the entire weight and activation distribution with the same quantizer will inevitably lead to large quantization errors.", + "bbox": [ + 75, + 286, + 472, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Post-Training Quantization of Diffusion Model", + "text_level": 1, + "bbox": [ + 76, + 434, + 468, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We propose two techniques: time step-aware calibration data sampling and shortcut-splitting quantization to tackle the challenges identified in the previous sections respectively.", + "bbox": [ + 75, + 458, + 472, + 505 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.1 Time step-aware calibration", + "text_level": 1, + "bbox": [ + 76, + 527, + 326, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since the output distributions of consecutive time steps are often very similar, we propose to randomly sample intermediate inputs uniformly in a fixed interval across all time steps to generate a small calibration set. This effectively balances the size of the calibration set and its representation ability of the distribution across all time steps. Empirically, we have found that the sampled calibration data can recover most of the INT4 quantized models' performance after the calibration, making it an effective sampling scheme for calibration data collection for quantization error correction.", + "bbox": [ + 75, + 551, + 468, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To calibrate the quantized model, we divide the model into several reconstruction blocks [20], and iteratively reconstruct outputs and tune the clipping range and scaling factors of weight quantizers in each block with adaptive rounding [28] to minimize the mean squared errors between the quantized and full precision outputs. We define a core component that contains residual connections in the diffusion model UNet as a block, such as a Residual Bottleneck Block or a Transformer Block. Other parts of the model that do not satisfy this condition are calibrated in a per-layer manner. This technique has been shown to improve the performance compared to fully layer-by-layer calibration since it addresses the inter-layer dependencies and generalization", + "bbox": [ + 75, + 704, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "better [20]. For activation quantization, since activations are constantly changing during inference, doing adaptive rounding is infeasible. Therefore, we only adjust the step sizes of activation quantizers according to [9]. The overall calibration workflow is described in Alg. 1.", + "bbox": [ + 496, + 255, + 893, + 332 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 Q-Diffusion Calibration", + "text_level": 1, + "bbox": [ + 500, + 354, + 750, + 369 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Require: Pretrained full precision diffusion model and the quantized diffusion model $[W_{\\theta},\\hat{W}_{\\theta}]$", + "bbox": [ + 500, + 371, + 890, + 402 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Require: Empty calibration dataset $\\mathcal{D}$", + "bbox": [ + 500, + 402, + 754, + 417 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Require: Number of denoising sampling steps $T$", + "bbox": [ + 500, + 417, + 826, + 431 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Require: Calibration sampling interval $c$ , amount of calibration data per sampling step $n$", + "bbox": [ + 500, + 431, + 893, + 463 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for $t = 1,\\dots ,T$ time step do", + "bbox": [ + 516, + 465, + 715, + 479 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "if $t\\% c = 0$ then", + "bbox": [ + 532, + 481, + 645, + 493 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sample $n$ intermediate inputs $\\mathbf{x}_t^{(1)},\\ldots ,\\mathbf{x}_t^{(n)}$ randomly at $t$ from $W_{\\theta}$ and add them to $\\mathcal{D}$", + "bbox": [ + 549, + 493, + 893, + 525 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "end if", + "bbox": [ + 532, + 526, + 578, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "end for", + "bbox": [ + 517, + 542, + 571, + 554 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for all $i = 1,\\dots ,N$ blocks do", + "bbox": [ + 517, + 556, + 720, + 570 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Update the weight quantizers of the $i$ -th block in $\\hat{W}_{\\theta}$ with $\\mathcal{D}$ and $W_{\\theta}$", + "bbox": [ + 535, + 570, + 890, + 599 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "end for", + "bbox": [ + 517, + 602, + 570, + 613 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "if do activation quantization then", + "bbox": [ + 517, + 616, + 738, + 630 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for all $i = 1,\\dots ,N$ blocks do", + "bbox": [ + 534, + 631, + 736, + 645 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Update the activation quantizers step sizes of the $i$ -th block with $\\hat{W}_{\\theta}, W_{\\theta}, \\mathcal{D}$ .", + "bbox": [ + 550, + 647, + 890, + 675 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "end for", + "bbox": [ + 534, + 676, + 586, + 689 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "end if", + "bbox": [ + 517, + 691, + 560, + 705 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.2 Shortcut-splitting quantization", + "text_level": 1, + "bbox": [ + 500, + 777, + 769, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To address the abnormal activation and weight distributions in shortcut layers, we propose a \"split\" quantization technique that performs quantization prior to concatenation, requiring negligible additional memory or computational resources. This strategy can be employed for both activation and weight quantization in shortcut layers, and is expressed", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17539", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f2ddb74b585e59e0ea7588a8eafc4ba0826022341d3fe39069bc97d6907cac29.jpg", + "image_caption": [ + "Figure 6: Activation ranges of DDIM's FP32 outputs across layers averaging among all time steps. We point out three shortcuts with the largest input activation ranges compared to other neighboring layers. Figures in the dashed box illustrate concatenation along channels. $\\oplus$ denotes the concatenation operation." + ], + "image_footnote": [], + "bbox": [ + 166, + 90, + 790, + 265 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2cf5c7374ed6b8ceab495098f25210476c2794e3b86bdd0d8da8a53d0ce4bbf2.jpg", + "image_caption": [ + "Figure 7: (Left) The typical UNet architecture with shortcut layers that concatenate features from the deep and shallow layers. (Right) The ranges of activations from the deep $(X_{1})$ and shallow $(X_{2})$ feature channels vary significantly, which also results in a bimodal weight distribution in the corresponding channels." + ], + "image_footnote": [], + "bbox": [ + 84, + 321, + 885, + 470 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "mathematically as follows:", + "bbox": [ + 76, + 553, + 256, + 568 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {Q} _ {X} (X) = \\mathcal {Q} _ {X _ {1}} (X _ {1}) \\oplus \\mathcal {Q} _ {X _ {2}} (X _ {2}) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 577, + 468, + 594 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {Q} _ {W} (W) = \\mathcal {Q} _ {W _ {1}} \\left(W _ {1}\\right) \\oplus \\mathcal {Q} _ {W _ {2}} \\left(W _ {2}\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 595, + 470, + 614 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {Q} _ {X} (X) \\mathcal {Q} _ {W} (W) = \\mathcal {Q} _ {X _ {1}} \\left(X _ {1}\\right) \\mathcal {Q} _ {W _ {1}} \\left(W _ {1}\\right) \\\\ + \\mathcal {Q} _ {X _ {2}} (X _ {2}) \\mathcal {Q} _ {W _ {2}} (W _ {2}) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 643, + 468, + 679 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $X \\in \\mathbb{R}^{w \\times h \\times c_{in}}$ and $W \\in \\mathbb{R}^{c_{in} \\times c_{out}}$ are the input activation and layer weight, which can be naturally split into $X_1 \\in \\mathbb{R}^{w \\times h \\times c_1}$ , $X_2 \\in \\mathbb{R}^{w \\times h \\times c_2}$ , $W_1 \\in \\mathbb{R}^{c_1 \\times c_{out}}$ , and $W_2 \\in \\mathbb{R}^{c_2 \\times c_{out}}$ , respectively. $c_1$ and $c_2$ are determined by the concatenation operation. $\\mathcal{Q}(\\cdot)$ denotes the quantization operator and $\\oplus$ denotes the concatenation operator.", + "bbox": [ + 76, + 688, + 468, + 780 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 792, + 209, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experiments Setup", + "text_level": 1, + "bbox": [ + 76, + 816, + 259, + 834 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we evaluate the proposed Q-Diffusion framework on pixel-space diffusion model DDPM [13] and latent-space diffusion model Latent Diffusion [34] for unconditional image generation. We also visualize the images", + "bbox": [ + 76, + 839, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "generated by Q-Diffusion on Stable Diffusion. To the best of our knowledge, there is currently no published work done on diffusion model quantization. Therefore, we report the basic channel-wise round-to-nearest Linear Quantization (i.e., Equation 5) as a baseline. We also re-implement the state-of-the-art data-free PTQ method SQuant [11] and include the results for comparison. Furthermore, we apply our approach to text-guided image synthesis with Stable Diffusion [34]. Experiments show that our approach can achieve competitive generation quality to the full-precision scenario on all tasks, even under INT4 quantization for weights.", + "bbox": [ + 496, + 553, + 893, + 720 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Unconditional Generation", + "text_level": 1, + "bbox": [ + 500, + 738, + 736, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conducted evaluations using the $32 \\times 32$ CIFAR-10 [17], $256 \\times 256$ LSUN Bedrooms, and $256 \\times 256$ LSUN Church-Outdoor [48]. We use the pretrained DDIM sampler [42] with 100 denoising time steps for CIFAR-10 experiments and Latent Diffusion (LDM) [34] for the higher resolution LSUN experiments. We evaluated the performance in terms of Frechet Inception Distance (FID) [12] and additionally evaluated the Inception Score (IS) [38] for CIFAR-10 results, since IS is not an accurate reference for datasets that", + "bbox": [ + 496, + 763, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17540", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1b402ef003af78d7a417a34d3dc6331f80d1295899bec2d31a162d535d687f55.jpg", + "image_caption": [ + "Bedroom Q-Diffusion (W4A8)", + "Figure 8: $256 \\times 256$ unconditional image generation results using Q-Diffusion and Linear Quantization under W4A8 precision." + ], + "image_footnote": [], + "bbox": [ + 80, + 114, + 274, + 265 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ec5ae5a0f63de2d42b58a65d5d1133b2726cd31ee8ebda6954975d7527fa0057.jpg", + "image_caption": [ + "Bedroom Linear Quantization (W4A8)" + ], + "image_footnote": [], + "bbox": [ + 282, + 114, + 478, + 265 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/763cef04e103078f997a271e1b021cc8b798e75172a0060f55cc24346334d4d3.jpg", + "image_caption": [ + "Church Q-Diffusion (W4A8)" + ], + "image_footnote": [], + "bbox": [ + 486, + 114, + 681, + 263 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d4f7b28b947f2ef355871aacf488353384493bac45c66cfa1ab3ef44d3ba9307.jpg", + "image_caption": [ + "Church Linear Quantization (W4A8)" + ], + "image_footnote": [], + "bbox": [ + 691, + 114, + 885, + 265 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/59a284ecfe3374b971d467e171ecc89095e1ff8912dd9cc13eab4d3ace0fec2b.jpg", + "table_caption": [ + "Table 1: Quantization results for unconditional image generation with DDIM on CIFAR-10 $(32\\times 32)$" + ], + "table_footnote": [], + "table_body": "
MethodBits (W/A)Size (Mb)GBopsFID↓IS↑
Full Precision32/32143.265974.229.12
Linear Quant8/3235.822944.718.93
SQuant8/3235.822944.618.99
Q-Diffusion8/3235.822944.279.15
Linear Quant4/3217.91147141.474.20
SQuant4/3217.91147160.402.91
Q-Diffusion4/3217.911475.098.78
Linear Quant8/835.8798118.265.23
SQuant8/835.8798464.691.17
Q-Diffusion8/835.87983.759.48
Linear Quant4/817.9399188.112.45
SQuant4/817.9399456.211.16
Q-Diffusion4/817.93994.939.12
", + "bbox": [ + 99, + 351, + 444, + 554 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "differ significantly from ImageNet's domain and categories. The results are reported in Table 1-3 and Figure 8, where Bops is calculated for one denoising step without considering the decoder compute cost for latent diffusion.", + "bbox": [ + 75, + 561, + 470, + 622 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The experiments show that Q-Diffusion significantly preserves the image generation quality and outperforms Linear Quantization by a large margin for all resolutions and types of diffusion models tested when the number of bits is low. Although 8-bit weight quantization has almost no performance loss compared to FP32 for both Linear Quantization and our approach, the generation quality with Linear Quantization drops drastically under 4-bit weight quantization. In contrast, Q-Diffusion still preserves most of the perceptual quality with at most 2.34 increase in FID and imperceptible distortions in produced samples.", + "bbox": [ + 75, + 623, + 468, + 789 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Text-guided Image Generation", + "text_level": 1, + "bbox": [ + 76, + 800, + 348, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate Q-Diffusion on Stable Diffusion pretrained on subsets of $512 \\times 512$ LAION-5B for text-guided image generation. Following [34], we sample text prompts from the MS-COCO [21] dataset to generate a calibration dataset with texts condition using Algorithm 1. In this work, we fix", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e381e8c150b12f1abf7541bcdf72605464b4ad51db72ba82e924fed807088df8.jpg", + "table_caption": [ + "Table 2: Quantization results for unconditional image generation with LDM-4 on LSUN-Bedrooms (256 × 256). The downsampling factor for the latent space is 4." + ], + "table_footnote": [], + "table_body": "
MethodBits (W/A)Size (Mb)TBopsFID↓
Full Precision32/321096.2107.172.98
Linear Quant8/32274.137.283.02
SQuant8/32274.137.282.94
Q-Diffusion8/32274.137.282.97
Linear Quant4/32137.018.6482.69
SQuant4/32137.018.64149.97
Q-Diffusion4/32137.018.644.86
Linear Quant8/8274.112.976.69
SQuant8/8274.112.974.92
Q-Diffusion8/8274.112.974.40
Linear Quant4/8137.06.4824.86
SQuant4/8137.06.4895.92
Q-Diffusion4/8137.06.485.32
", + "bbox": [ + 521, + 364, + 867, + 580 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2af77586da4eb43874266b62ce77f9fa2142c058ec640f4606e8982e7c1877a9.jpg", + "table_caption": [ + "Table 3: Quantization results for unconditional image generation with LDM-8 on LSUN-Churches (256 × 256). The downsampling factor for the latent space is 8." + ], + "table_footnote": [], + "table_body": "
MethodBits (W/A)Size (Mb)TBopsFID↓
Full Precision32/321179.922.174.06
Linear Quant8/32295.010.733.84
SQuant8/32295.010.734.01
Q-Diffusion8/32295.010.734.03
Linear Quant4/32147.55.3632.54
SQuant4/32147.55.3633.77
Q-Diffusion4/32147.55.364.45
Linear Quant8/8295.02.6814.62
SQuant8/8295.02.6854.15
Q-Diffusion8/8295.02.683.65
Linear Quant4/8147.51.3414.92
SQuant4/8147.51.3424.50
Q-Diffusion4/8147.51.344.12
", + "bbox": [ + 524, + 640, + 869, + 861 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17541", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5a6f4994244a30f440329693a9bf059b313aec831f8a244c379ed5c5ade1a3de.jpg", + "image_caption": [ + "Full Precision" + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 341, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/feb59c49aa55f53418a8447d760732aea2d764ab64a875cc87ba00f4cbb2d026.jpg", + "image_caption": [ + "Q-Diffusion (W4A8)", + "Figure 9: Stable Diffusion $512 \\times 512$ text-guided image synthesis results using Q-Diffusion and Linear Quantization under W4A8 precision with prompt A puppy wearing a hat." + ], + "image_footnote": [], + "bbox": [ + 352, + 89, + 612, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/92f3b447050a79097f5b3e15dabe5e32e2386b4d6628994a60700136a56e0fb3.jpg", + "image_caption": [ + "Linear Quantization (W4A8)" + ], + "image_footnote": [], + "bbox": [ + 625, + 89, + 885, + 191 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the guidance strength to the default 7.5 in Stable Diffusion as the trade-off between sample quality and diversity. Qualitative results are shown in Figure 9. Compared to Linear Quantization, our Q-Diffusion provides higher-quality images with more realistic details and better demonstration of the semantic information. Similar performance gain is also observed in other random samples showcased in Appendix, and quantitatively reported in Appendix. The output of the W4A8 Q-Diffusion model largely resembles the output of the full precision model. Interestingly, we find some diversity in the lower-level semantics between the Q-Diffusion model and the FP models, like the heading of the horse or the shape of the hat. We leave it to future work to understand how quantization contributes to the diversity.", + "bbox": [ + 75, + 276, + 473, + 488 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 494, + 230, + 512 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/593c5f505b31604228ddd1190e7c4a8922a8317656e31922b8105199c8206420.jpg", + "image_caption": [ + "Figure 10: Uniform sampling strategies which cover all time steps are better than strategies that cover only a part of the time steps, as in Fig. 4. Furthermore, adjusting the sampling techniques within uniform sampling, such as tuning the sampling interval and the number of samples, has a marginal effect on the performance of the quantized model." + ], + "image_footnote": [], + "bbox": [ + 94, + 527, + 437, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effects of Sampling Strategies To analyze the effects of different sampling strategies for calibration in detail, we implemented multiple variants of our method using different sampling strategies. We then evaluated the quality of the models quantized by each variant. We experimented", + "bbox": [ + 75, + 824, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "with varying numbers of time steps used for sampling and samples used for calibration. In addition to calibration sets from uniform timestep intervals, we also employed sampling at the first 50 and last 50 steps. As in Figure 10, uniform sampling that spans all time steps results in superior performance compared to sampling from only partial time steps. Furthermore, adjusting the sampling hyperparams, including using more calibration samples, does not significantly improve the performance. Therefore, we simply choose to sample uniformly every 20 steps for a total of 5,120 samples for calibration, resulting in a high-quality quantized model with low computational costs during quantization.", + "bbox": [ + 496, + 276, + 893, + 457 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also conduct ablation experiments to explore the effectiveness of several non-uniform calibration data sampling schemes, such as using Unsupervised Selecting Labeling (USL) [45] to select both representative and diverse calibration samples. We present the results in Appendix.", + "bbox": [ + 496, + 458, + 893, + 534 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effects of Split Previous linear quantization approaches suffer from severe performance degradation as shown in Figure 11, where 4-bit weight quantization achieves a high FID of 141.47 in DDIM CIFAR-10 generation. Employing additional 8-bit activation quantization further degrades the performance (FID: 188.11). By splitting shortcuts in quantization, we significantly improve the generation performance, achieving an FID of 4.93 on W4A8 quantization.", + "bbox": [ + 496, + 555, + 893, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 681, + 619, + 698 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work studies the use of quantization to accelerate and reduce the memory usage of diffusion models. We propose Q-Diffusion, a novel post-training quantization scheme that conducts calibration with multiple time steps in the denoising process and achieves significant improvements in the performance of the quantized model. Q-Diffusion models under 4-bit quantization achieve comparable results to the full precision models.", + "bbox": [ + 496, + 707, + 893, + 829 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 844, + 660, + 861 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We thank Berkeley Deep Drive, Intel Corporation, Panasonic, and NVIDIA for supporting this research. We also", + "bbox": [ + 500, + 869, + 893, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17542", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/631055b526ddb7e6675fc1fa0384bef5edc5cf21f88baae8df31d6d8526322d8.jpg", + "image_caption": [ + "Linear Quantization + Calibration + Split shortcuts", + "Figure 11: Splitting the shortcut convolution is crucial for both weight and activation quantization. Comparisons on CIFAR-10 show that Q-Diffusion could achieve comparable image generation quality to the model with full precision (dashed line) with shortcut splitting." + ], + "image_footnote": [], + "bbox": [ + 83, + 119, + 444, + 282 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/b9d3d8ab6937eebf5cb985780a79b64637537267fb8d97047327327a47523e9a.jpg", + "image_caption": [ + "Figure 12: Examples of text-to-image generation with a quantized Stable Diffusion model. Naive linear quantization degrades the appearance of teeth, which gets fixed by shortcut splitting. Q-Diffusion further improves the semantic consistency of eyes through calibration." + ], + "image_footnote": [], + "bbox": [ + 84, + 377, + 460, + 526 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "would like to thank Sehoon Kim, Muyang Li, and Minkai Xu for their valuable feedback.", + "bbox": [ + 75, + 632, + 468, + 662 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 676, + 174, + 694 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Fan Bao, Chongxuan Li, Jun Zhu, and Bo Zhang. Analytic-dpm: an analytic estimate of the optimal reverse variance in diffusion probabilistic models. ArXiv, abs/2201.06503, 2022. 1, 3", + "[2] Yash Bhalgat, Jinwon Lee, Markus Nagel, Tijmen Blankevoort, and Nojun Kwak. 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Geodiff: a geometric diffusion model for" + ], + "bbox": [ + 501, + 92, + 893, + 900 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "17544", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "molecular conformation generation. ArXiv, abs/2203.02923, 2022.1", + "[48] Fisher Yu, Ari Seff, Yinda Zhang, Shuran Song, Thomas Funkhouser, and Jianxiong Xiao. Lsun: Construction of a large-scale image dataset using deep learning with humans in the loop. arXiv preprint arXiv:1506.03365, 2015. 6", + "[49] Ritchie Zhao, Yuwei Hu, Jordan Dotzel, Chris De Sa, and Zhiru Zhang. Improving neural network quantization without retraining using outlier channel splitting. In International conference on machine learning, pages 7543-7552. PMLR, 2019. 1", + "[50] Aojun Zhou, Anbang Yao, Yiwen Guo, Lin Xu, and Yurong Chen. Incremental network quantization: Towards lossless cnns with low-precision weights. arXiv preprint arXiv:1702.03044, 2017. 1" + ], + "bbox": [ + 78, + 90, + 468, + 301 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "17545", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Q-Diffusion_ Quantizing Diffusion Models/64ad5dff-59b7-42a2-a4ac-ca7c9541d350_model.json b/2023/Q-Diffusion_ Quantizing Diffusion Models/64ad5dff-59b7-42a2-a4ac-ca7c9541d350_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7a53b8cf095c6c1789f413e8ae07c43471001d20 --- /dev/null +++ b/2023/Q-Diffusion_ Quantizing Diffusion Models/64ad5dff-59b7-42a2-a4ac-ca7c9541d350_model.json @@ -0,0 +1,2444 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.271, + 0.131, + 0.7, + 0.154 + ], + "angle": 0, + "content": "Q-Diffusion: Quantizing Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.195, + 0.18, + 0.773, + 0.218 + ], + "angle": 0, + "content": "Xiuyu Li\\(^{1}\\) Yijiang Liu\\(^{2}\\) Long Lian\\(^{1}\\) Huanrui Yang\\(^{1}\\) Zhen Dong\\(^{1}\\) Daniel Kang\\(^{3}\\) Shanghang Zhang\\(^{4}\\) Kurt Keutzer\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.197, + 0.219, + 0.773, + 0.235 + ], + "angle": 0, + "content": "1UC Berkeley 2Nanjing University 3University of Illinois Urbana-Champaign 4Peking University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.286 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.681 + ], + "angle": 0, + "content": "Diffusion models have achieved great success in image synthesis through iterative noise estimation using deep neural networks. However, the slow inference, high memory consumption, and computation intensity of the noise estimation model hinder the efficient adoption of diffusion models. Although post-training quantization (PTQ) is considered a go-to compression method for other tasks, it does not work out-of-the-box on diffusion models. We propose a novel PTQ method specifically tailored towards the unique multistep pipeline and model architecture of the diffusion models, which compresses the noise estimation network to accelerate the generation process. We identify the key difficulty of diffusion model quantization as the changing output distributions of noise estimation networks over multiple time steps and the bimodal activation distribution of the shortcut layers within the noise estimation network. We tackle these challenges with timestep-aware calibration and split shortcut quantization in this work. Experimental results show that our proposed method is able to quantize full-precision unconditional diffusion models into 4-bit while maintaining comparable performance (small FID change of at most 2.34 compared to \\(>100\\) for traditional PTQ) in a training-free manner. Our approach can also be applied to text-guided image generation, where we can run stable diffusion in 4-bit weights with high generation quality for the first time." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.695, + 0.21, + 0.71 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.472, + 0.87 + ], + "angle": 0, + "content": "Diffusion models have shown great success in generating images with both high diversity and high fidelity [43, 13, 44, 42, 6, 33, 36, 34]. Recent work [16, 15] has demonstrated superior performance than state-of-the-art GAN models, which suffer from unstable training. As a class of flexible generative models, diffusion models demonstrate their power in various applications such as image super-resolution [37, 18], inpainting [44], shape generation [3], graph generation [31], image-to-image translation [40], and molecular conformation generation [47]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.9 + ], + "angle": 0, + "content": "However, the generation process for diffusion models can be slow due to the need for an iterative noise estimation of 50" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.27, + 0.896, + 0.513 + ], + "angle": 0, + "content": "to 1,000 time steps [13, 42] using complex neural networks. While previous state-of-the-art approaches (e.g., GANs) are able to generate multiple images in under 1 second, it normally takes several seconds for a diffusion model to sample a single image. Consequently, speeding up the image generation process becomes an important step toward broadening the applications of diffusion models. Previous work has been solving this problem by finding shorter, more effective sampling trajectories [42, 30, 39, 22, 1, 24], which reduces the number of steps in the denoising process. However, they have largely ignored another important factor: the noise estimation model used in each iteration itself is compute- and memory-intensive. This is an orthogonal factor to the repetitive sampling, which not only slows down the inference speed of diffusion models, but also poses crucial challenges in terms of high memory footprints." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.517, + 0.897, + 0.746 + ], + "angle": 0, + "content": "This work explores the quantization [50, 8, 49, 7, 29] of the noise estimation model used in the diffusion model to accelerate the denoising of all time steps. Specifically, we propose exploring post-training quantization (PTQ) on the diffusion model. PTQ has already been well studied in other learning domains like classification and object detection [4, 2, 20, 11, 23], and has been considered a go-to compression method given its minimal requirement for training data and the straightforward deployment on real hardware devices. However, the iterative computation process of the diffusion model and the model architecture of the noise estimation network brings unique challenges to the PTQ of diffusion models. PTQ4DM [41] presents an inaugural application of PTQ to compress diffusion models down to 8-bit, but it primarily focuses on smaller datasets and lower resolutions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.899, + 0.903 + ], + "angle": 0, + "content": "Our work, evolving concurrently with [41], offers a comprehensive analysis of the novel challenges of performing PTQ on diffusion models. Specifically, as visualized in Figure 1(a), we discover that the output distribution of the noise estimation network at each time step can be largely different, and naively applying previous PTQ calibration methods with an arbitrary time step leads to poor performance. Furthermore, as illustrated in Figure 1(b), the iterative inference of the noise estimation network leads to an accumulation of quantization error, which poses higher demands on design-" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "17535" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.122, + 0.084, + 0.501, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.081, + 0.844, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.328, + 0.892, + 0.42 + ], + "angle": 0, + "content": "Figure 1: Conventional PTQ scenarios and Q-Diffusion differ in (a) calibration dataset creation and (b) model inference workflow. Traditional PTQ approaches sample data randomly [11], synthesize with statistics in model layers [4], or draw from the training set to create calibration dataset [28, 20], which either contains inconsistency with real inputs during the inference time or are not data-free. In contrast, Q-Diffusion constructed calibration datasets with inputs that are an accurate reflection of data seen during the production in a data-free manner. Traditional PTQ inference only needs to go through the quantized model \\(\\theta_q\\) one time, while Q-Diffusion needs to address the accumulated quantization errors in the multi-time step inference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.435, + 0.468, + 0.464 + ], + "angle": 0, + "content": "ing novel quantization schemes and calibration objectives for the noise estimation network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.465, + 0.469, + 0.661 + ], + "angle": 0, + "content": "To address these challenges, we propose Q-Diffusion, a PTQ solution to compress the cumbersome noise estimation network in diffusion models in a data-free manner, while maintaining comparable performance to the full precision counterparts. We propose a time step-aware calibration data sampling mechanism from the pretrained diffusion model, which represents the activation distribution of all time steps. We further tailor the design of the calibration objective and the weight and activation quantizer to the commonly used noise estimation model architecture to reduce quantization error. We perform thorough ablation studies to verify our design choices, and demonstrate good generation results with diffusion models quantized to only 4 bits." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.662, + 0.327, + 0.675 + ], + "angle": 0, + "content": "In summary, our contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.687, + 0.47, + 0.717 + ], + "angle": 0, + "content": "1. We propose Q-Diffusion, a data-free PTQ solution for the noise estimation network in diffusion models." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.728, + 0.47, + 0.789 + ], + "angle": 0, + "content": "2. We identify the novel challenge of performing PTQ on diffusion models as the activation distribution diversity and the quantization error accumulation across time steps via a thorough analysis." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.8, + 0.471, + 0.844 + ], + "angle": 0, + "content": "3. We propose time step-aware calibration data sampling to improve calibration quality, and propose a specialized quantizer for the noise estimation network." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "4. Extensive results show Q-Diffusion enables W4A8 PTQ for both pixel-space and latent-space unconditional diffusion models with an FID increment of only" + }, + { + "type": "list", + "bbox": [ + 0.089, + 0.687, + 0.471, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.435, + 0.894, + 0.481 + ], + "angle": 0, + "content": "0.39-2.34 over full precision models. It can also produce qualitatively comparable images when plugged into Stable Diffusion [34] for text-guided synthesis." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.495, + 0.638, + 0.51 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.521, + 0.893, + 0.582 + ], + "angle": 0, + "content": "Diffusion Models. Diffusion models generate images through a Markov chain, as illustrated in Figure 2. A forward diffusion process adds Gaussian noise to data \\(\\mathbf{x}_0 \\sim q(\\mathbf{x})\\) for \\(T\\) times, resulting in noisy samples \\(\\mathbf{x}_1, \\dots, \\mathbf{x}_T\\):" + }, + { + "type": "equation", + "bbox": [ + 0.559, + 0.594, + 0.892, + 0.613 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.625, + 0.894, + 0.67 + ], + "angle": 0, + "content": "where \\(\\beta_{t} \\in (0,1)\\) is the variance schedule that controls the strength of the Gaussian noise in each step. When \\(T \\to \\infty\\), \\(\\mathbf{x}_T\\) approaches an isotropic Gaussian distribution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.894, + 0.747 + ], + "angle": 0, + "content": "The reverse process removes noise from a sample from the Gaussian noise input \\(\\mathbf{x}_T\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) to gradually generate high-fidelity images. However, since the real reverse conditional distribution \\(q(\\mathbf{x}_{t - 1}|\\mathbf{x}_t)\\) is unavailable, diffusion models sample from a learned conditional distribution:" + }, + { + "type": "equation", + "bbox": [ + 0.562, + 0.759, + 0.892, + 0.778 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\tilde {\\boldsymbol {\\mu}} _ {\\theta , t} \\left(\\mathbf {x} _ {t}\\right), \\tilde {\\boldsymbol {\\beta}} _ {t} \\mathbf {I}\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.79, + 0.892, + 0.822 + ], + "angle": 0, + "content": "With the reparameterization trick in [13], the mean \\(\\tilde{\\mu}_{\\theta ,t}(\\mathbf{x}_t)\\) and variance \\(\\tilde{\\beta}_t\\) could be derived as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.833, + 0.892, + 0.866 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\boldsymbol {\\mu}} _ {\\theta , t} \\left(\\mathbf {x} _ {t}\\right) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {x} _ {t} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\boldsymbol {\\epsilon} _ {\\theta , t}\\right) \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.868, + 0.892, + 0.899 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\beta} _ {t} = \\frac {1 - \\bar {\\alpha} _ {t - 1}}{1 - \\bar {\\alpha} _ {t}} \\cdot \\beta_ {t} \\tag {4}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17536" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.088, + 0.468, + 0.131 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.239, + 0.132, + 0.351, + 0.14 + ], + "angle": 0, + "content": "(a) Forward diffusion process" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.143, + 0.466, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.24, + 0.187, + 0.351, + 0.197 + ], + "angle": 0, + "content": "(b) Reverse diffusion process" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.208, + 0.471, + 0.269 + ], + "angle": 0, + "content": "Figure 2: The forward diffusion process (a) repeatedly adds Gaussian noise. The reverse diffusion process (b) uses a trained network to denoise from a standard Gaussian noise image in order to generate an image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.281, + 0.469, + 0.312 + ], + "angle": 0, + "content": "where \\(\\alpha_{t} = 1 - \\beta_{t}\\), \\(\\bar{\\alpha}_{t} = \\prod_{i=1}^{t} \\alpha_{i}\\). We refer readers to [26] for a more detailed introduction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.313, + 0.47, + 0.418 + ], + "angle": 0, + "content": "In practice, the noise at each time step \\( t \\) are computed from \\( \\mathbf{x}_t \\) by a noise estimation model, with the same weights for all time steps. The UNet [35] dominates the design of the noise estimation model in diffusion models [42, 34, 33, 36], with some recent exploration on Transformer [32]. This work designs the PTQ method for the acceleration of the noise estimation model, especially for the common UNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.471, + 0.599 + ], + "angle": 0, + "content": "Accelerated diffusion process. Related methods include simulating the diffusion process in fewer steps by generalizing it to a non-Markovian process [42], adjusting the variance schedule [30], and the use of high-order solvers to approximate diffusion generation [22, 1, 24, 25]. Others have employed the technique of caching and reusing feature maps [19]. Efforts to distill the diffusion model into fewer time steps have also been undertaken [39, 27], which have achieved notable success but involve an extremely expensive retraining process. Our work focuses on accelerating the noise estimation model inference in each step, with a training-free PTQ process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.6, + 0.471, + 0.66 + ], + "angle": 0, + "content": "Post-training Quantization. Post-training quantization (PTQ) compresses deep neural networks by rounding elements \\( w \\) to a discrete set of values [10], where the quantization and de-quantization can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.669, + 0.47, + 0.697 + ], + "angle": 0, + "content": "\\[\n\\hat {w} = \\mathrm {s} \\cdot \\operatorname {c l i p} \\left(\\operatorname {r o u n d} \\left(\\frac {w}{s}\\right), c _ {\\min }, c _ {\\max }\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.796 + ], + "angle": 0, + "content": "where \\(s\\) denotes the quantization scale parameters, \\(c_{\\mathrm{min}}\\) and \\(c_{\\mathrm{max}}\\) are the lower and upper bounds for the clipping function \\(\\mathrm{clip}(\\cdot)\\). These parameters can be calibrated with the weight and activation distribution estimated in the PTQ process. The operator round(\\cdot) represents rounding, which can be either rounding-to-nearest [46, 4] or adaptive rounding [20]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Previous PTQ research in classification and detection tasks focused on the calibration objective and the acquisition of calibration data. For example, EasyQuant [46] determines appropriate \\( c_{\\mathrm{min}} \\) and \\( c_{\\mathrm{max}} \\) based on training data, and BRECQ [20] introduces Fisher information into the objective. ZeroQ [4] employs a distillation technique to generate proxy input images for PTQ, and SQuant [11] uses" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.41 + ], + "angle": 0, + "content": "random samples with objectives based on sensitivity determined through the Hessian spectrum. For diffusion model quantization, a training dataset is not needed as the calibration data can be constructed by sampling the full-precision model with random inputs. However, the multi-time step inference of the noise estimation model brings new challenges in modeling the activation distribution. In parallel to our work, PTQ4DM [41] introduces the method of Normally Distributed Time-step Calibration, generating calibration data across all time steps with a specific distribution. Nevertheless, their explorations remain confined to lower resolutions, 8-bit precision, floating-point attention activation-to-activation matmuls, and with limited ablation study on other calibration schemes. This results in worse applicability of their method to lower precisions (see Appendix). Our work delves into the implications of calibration dataset creation in a holistic manner, establishing an efficient calibration objective for diffusion models. We fully quantize act-to-act matmuls, validated by experiments involving both pixel-space and latent-space diffusion models on large-scale datasets up to resolutions of \\(512 \\times 512\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.424, + 0.591, + 0.438 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.895, + 0.601 + ], + "angle": 0, + "content": "We present our method for post-training quantization of diffusion models in this section. Different from conventionally studied deep learning models and tasks such as CNNs and VITs for classification and detection, diffusion models are trained and evaluated in a distinctive multi-step manner with a unique UNet architecture. This presents notable challenges to the PTQ process. We analyze the challenges brought by the multi-step inference process and the UNet architecture in Section 3.1 and 3.2 respectively and describe the full Q-Diffusion PTQ pipeline in Section 3.3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.611, + 0.864, + 0.627 + ], + "angle": 0, + "content": "3.1. Challenges under the Multi-step Denoising" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.635, + 0.894, + 0.711 + ], + "angle": 0, + "content": "We identify two major challenges in quantizing models that employ multi-step inference process. Namely, we investigate the accumulation of quantization error across time steps and the difficulty of sampling a small calibration dataset to reduce the quantization error at each time step." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Challenge 1: Quantization errors accumulate across time steps. Performing quantization on a neural network model introduces noise on the weight and activation of the well-trained model, leading to quantization errors in each layer's output. Previous research has identified that quantization errors are likely to accumulate across layers [5], making deeper neural networks harder to quantize. In the case of diffusion models, at any time step \\( t \\), the input of the denoising model (denoted as \\( \\mathbf{x}_t \\)) is derived by \\( \\mathbf{x}_{t+1} \\), the output of the model at the previous time step \\( t+1 \\) (as depicted by Equation 2). This process effectively multiplies the number of layers involved in the computation by the number of de" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17537" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.091, + 0.445, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.251, + 0.47, + 0.327 + ], + "angle": 0, + "content": "Figure 3: MSE between FP32 outputs and weight-quantized outputs of different precisions with Linear Quantization and our approach across time steps. Here the data is obtained by passing a batch with 64 samples through a model trained on CIFAR-10 [17] with DDIM sampling steps 100." + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.339, + 0.436, + 0.499 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.517, + 0.47, + 0.579 + ], + "angle": 0, + "content": "Figure 4: Effects of time steps in calibration dataset creation on 4-bit weights quantization results with DDIM on CIFAR-10. First \\( n \\), Mid \\( n \\), Last \\( n \\) denotes that 5120 samples are selected uniformly from the first, middle, last \\( n \\) time steps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.588, + 0.469, + 0.633 + ], + "angle": 0, + "content": "noising steps for the input \\(\\mathbf{x}_t\\) at time step \\(t\\), leading to an accumulation of quantization errors towards later steps in the denoising process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.634, + 0.47, + 0.8 + ], + "angle": 0, + "content": "We run the denoising process of DDIM [42] on CIFAR-10 [17] with a sampling batch size of 64, and compare the MSE differences between the full-precision model and the model quantized to INT8, INT5, and INT4 at each time step. As shown in Figure 3, there is a dramatic increase in the quantization errors when the model is quantized to 4-bit, and the errors accumulate quickly through iterative denoising. This brings difficulty in preserving the performance after quantizing the model down to low precision, which requires the reduction of quantization errors at all time steps as much as possible." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Challenge 2: Activation distributions vary across time steps. To reduce the quantization errors at each time step, previous PTQ research [28, 20] calibrates the clipping range and scaling factors of the quantized model with a small set of calibration data. The calibration data should be sampled to resemble the true input distribution so that the activation dis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.287 + ], + "angle": 0, + "content": "The distribution of the model can be estimated correctly for proper calibration. Given that the Diffusion model uses the same noise estimation network to take inputs from all time steps, determining the data sampling policy across different time steps becomes an outstanding challenge. Here we start by analyzing the output activation distribution of the UNet model across different time steps. We conduct the same CIFAR-10 experiment using DDIM with 100 denoising steps, and draw the activations ranges of 1000 random samples among all time steps. As Figure 5 shows, the activation distributions gradually change, with neighboring time steps being similar and distant ones being distinctive. This is also echoed by the visualized \\(\\mathbf{x}_t\\) in Figure 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.893, + 0.682 + ], + "angle": 0, + "content": "The fact that the output activations distribution varies across time steps further brings challenges to quantization. Calibrating the noise estimation model using only a few time steps that do not reflect the full range of activations seen among all time steps by the noise estimation model during the denoising process can cause overfitting to the activation distribution described by those specific time steps, while not generalizing to other time steps, which hurts the overall performance. For instance, here we try to calibrate the quantized DDIM on the CIFAR-10 dataset with data sampled from different parts of the denoising process. As shown in Figure 4, if we simply take 5120 samples from time steps that fall into a certain stage of the denoising process, significant performance drops will be induced under 4-bit weights quantization. Note that the case with samples taken from the middle 50 time steps caused smaller drops compared to cases with samples taken from either the first or the last \\( n \\) time steps, and with \\( n \\) increases, the drops are also alleviated. These results illustrate the gradual \"denoising\" process as depicted in Figure 5: the activations distribution changes gradually throughout time steps, with the middle part capturing the full range to some degree, while parts of the distant endpoints differing the most. To recover the performance of the quantized diffusion models, we need to select calibration data in a way that comprehensively takes into account the distributions of the output of different time steps." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.695, + 0.89, + 0.725 + ], + "angle": 0, + "content": "3.2. Challenges on Noise Estimation Model Quantization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Most diffusion models (Imagen [36], Stable Diffusion [34], VDMs [14]) adopt UNets as denoising backbones that downsample and upsample latent features. Although recent studies show that transformer architectures are also capable of serving as the noise estimation backbone [32], convolutional UNets are still the de facto choice of architecture today. UNets utilize shortcut layers to merge concatenated deep and shallow features and transmit them to subsequent layers. Through our analysis presented in Figure 6, we observe that input activations in shortcut layers exhibit abnormal value ranges in comparison to other layers." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "17538" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.141, + 0.085, + 0.833, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.169, + 0.214, + 0.8, + 0.23 + ], + "angle": 0, + "content": "Figure 5: Activation ranges of \\( x_{t} \\) across all 100 time steps of FP32 DDIM model on CIFAR-10." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.256, + 0.47, + 0.287 + ], + "angle": 0, + "content": "Notably, the input activations in DDIM's shortcut layers can be up to 200 times larger than other neighboring layers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.287, + 0.473, + 0.424 + ], + "angle": 0, + "content": "To analyze the reason for this, we visualize the weight and activation tensor of a DDIM shortcut layer. As demonstrated in the dashed box in Figure 6, the ranges of activations from the deep feature channels \\((X_{1})\\) and shallow feature channels \\((X_{2})\\) being concatenated together vary significantly, which also resulted in a bimodal weight distribution in the corresponding channels (see also Figure 7). Naively quantizing the entire weight and activation distribution with the same quantizer will inevitably lead to large quantization errors." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.435, + 0.47, + 0.451 + ], + "angle": 0, + "content": "3.3. Post-Training Quantization of Diffusion Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.473, + 0.506 + ], + "angle": 0, + "content": "We propose two techniques: time step-aware calibration data sampling and shortcut-splitting quantization to tackle the challenges identified in the previous sections respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.528, + 0.328, + 0.543 + ], + "angle": 0, + "content": "3.3.1 Time step-aware calibration" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.47, + 0.704 + ], + "angle": 0, + "content": "Since the output distributions of consecutive time steps are often very similar, we propose to randomly sample intermediate inputs uniformly in a fixed interval across all time steps to generate a small calibration set. This effectively balances the size of the calibration set and its representation ability of the distribution across all time steps. Empirically, we have found that the sampled calibration data can recover most of the INT4 quantized models' performance after the calibration, making it an effective sampling scheme for calibration data collection for quantization error correction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.902 + ], + "angle": 0, + "content": "To calibrate the quantized model, we divide the model into several reconstruction blocks [20], and iteratively reconstruct outputs and tune the clipping range and scaling factors of weight quantizers in each block with adaptive rounding [28] to minimize the mean squared errors between the quantized and full precision outputs. We define a core component that contains residual connections in the diffusion model UNet as a block, such as a Residual Bottleneck Block or a Transformer Block. Other parts of the model that do not satisfy this condition are calibrated in a per-layer manner. This technique has been shown to improve the performance compared to fully layer-by-layer calibration since it addresses the inter-layer dependencies and generalization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.256, + 0.895, + 0.333 + ], + "angle": 0, + "content": "better [20]. For activation quantization, since activations are constantly changing during inference, doing adaptive rounding is infeasible. Therefore, we only adjust the step sizes of activation quantizers according to [9]. The overall calibration workflow is described in Alg. 1." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.355, + 0.751, + 0.371 + ], + "angle": 0, + "content": "Algorithm 1 Q-Diffusion Calibration" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.372, + 0.892, + 0.403 + ], + "angle": 0, + "content": "Require: Pretrained full precision diffusion model and the quantized diffusion model \\([W_{\\theta},\\hat{W}_{\\theta}]\\)" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.403, + 0.756, + 0.418 + ], + "angle": 0, + "content": "Require: Empty calibration dataset \\(\\mathcal{D}\\)" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.418, + 0.827, + 0.433 + ], + "angle": 0, + "content": "Require: Number of denoising sampling steps \\( T \\)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.433, + 0.894, + 0.464 + ], + "angle": 0, + "content": "Require: Calibration sampling interval \\( c \\), amount of calibration data per sampling step \\( n \\)" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.466, + 0.716, + 0.481 + ], + "angle": 0, + "content": "for \\(t = 1,\\dots ,T\\) time step do" + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.482, + 0.646, + 0.494 + ], + "angle": 0, + "content": "if \\(t\\% c = 0\\) then" + }, + { + "type": "text", + "bbox": [ + 0.55, + 0.494, + 0.894, + 0.526 + ], + "angle": 0, + "content": "Sample \\(n\\) intermediate inputs \\(\\mathbf{x}_t^{(1)},\\ldots ,\\mathbf{x}_t^{(n)}\\) randomly at \\(t\\) from \\(W_{\\theta}\\) and add them to \\(\\mathcal{D}\\)" + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.527, + 0.579, + 0.539 + ], + "angle": 0, + "content": "end if" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.543, + 0.572, + 0.555 + ], + "angle": 0, + "content": "end for" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.557, + 0.722, + 0.571 + ], + "angle": 0, + "content": "for all \\(i = 1,\\dots ,N\\) blocks do" + }, + { + "type": "text", + "bbox": [ + 0.536, + 0.571, + 0.891, + 0.601 + ], + "angle": 0, + "content": "Update the weight quantizers of the \\(i\\)-th block in \\(\\hat{W}_{\\theta}\\) with \\(\\mathcal{D}\\) and \\(W_{\\theta}\\)" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.603, + 0.571, + 0.614 + ], + "angle": 0, + "content": "end for" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.617, + 0.739, + 0.631 + ], + "angle": 0, + "content": "if do activation quantization then" + }, + { + "type": "text", + "bbox": [ + 0.535, + 0.632, + 0.737, + 0.646 + ], + "angle": 0, + "content": "for all \\(i = 1,\\dots ,N\\) blocks do" + }, + { + "type": "text", + "bbox": [ + 0.551, + 0.648, + 0.891, + 0.676 + ], + "angle": 0, + "content": "Update the activation quantizers step sizes of the \\(i\\)-th block with \\(\\hat{W}_{\\theta}, W_{\\theta}, \\mathcal{D}\\)." + }, + { + "type": "text", + "bbox": [ + 0.535, + 0.678, + 0.588, + 0.69 + ], + "angle": 0, + "content": "end for" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.693, + 0.562, + 0.706 + ], + "angle": 0, + "content": "end if" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.778, + 0.771, + 0.794 + ], + "angle": 0, + "content": "3.3.2 Shortcut-splitting quantization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.903 + ], + "angle": 0, + "content": "To address the abnormal activation and weight distributions in shortcut layers, we propose a \"split\" quantization technique that performs quantization prior to concatenation, requiring negligible additional memory or computational resources. This strategy can be employed for both activation and weight quantization in shortcut layers, and is expressed" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17539" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.167, + 0.091, + 0.791, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.266, + 0.895, + 0.311 + ], + "angle": 0, + "content": "Figure 6: Activation ranges of DDIM's FP32 outputs across layers averaging among all time steps. We point out three shortcuts with the largest input activation ranges compared to other neighboring layers. Figures in the dashed box illustrate concatenation along channels. \\(\\oplus\\) denotes the concatenation operation." + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.323, + 0.887, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.488, + 0.893, + 0.534 + ], + "angle": 0, + "content": "Figure 7: (Left) The typical UNet architecture with shortcut layers that concatenate features from the deep and shallow layers. (Right) The ranges of activations from the deep \\((X_{1})\\) and shallow \\((X_{2})\\) feature channels vary significantly, which also results in a bimodal weight distribution in the corresponding channels." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.554, + 0.258, + 0.569 + ], + "angle": 0, + "content": "mathematically as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.578, + 0.47, + 0.595 + ], + "angle": 0, + "content": "\\[\n\\mathcal {Q} _ {X} (X) = \\mathcal {Q} _ {X _ {1}} (X _ {1}) \\oplus \\mathcal {Q} _ {X _ {2}} (X _ {2}) \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.597, + 0.471, + 0.615 + ], + "angle": 0, + "content": "\\[\n\\mathcal {Q} _ {W} (W) = \\mathcal {Q} _ {W _ {1}} \\left(W _ {1}\\right) \\oplus \\mathcal {Q} _ {W _ {2}} \\left(W _ {2}\\right) \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.644, + 0.47, + 0.68 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {Q} _ {X} (X) \\mathcal {Q} _ {W} (W) = \\mathcal {Q} _ {X _ {1}} \\left(X _ {1}\\right) \\mathcal {Q} _ {W _ {1}} \\left(W _ {1}\\right) \\\\ + \\mathcal {Q} _ {X _ {2}} (X _ {2}) \\mathcal {Q} _ {W _ {2}} (W _ {2}) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.689, + 0.47, + 0.781 + ], + "angle": 0, + "content": "where \\(X \\in \\mathbb{R}^{w \\times h \\times c_{in}}\\) and \\(W \\in \\mathbb{R}^{c_{in} \\times c_{out}}\\) are the input activation and layer weight, which can be naturally split into \\(X_1 \\in \\mathbb{R}^{w \\times h \\times c_1}\\), \\(X_2 \\in \\mathbb{R}^{w \\times h \\times c_2}\\), \\(W_1 \\in \\mathbb{R}^{c_1 \\times c_{out}}\\), and \\(W_2 \\in \\mathbb{R}^{c_2 \\times c_{out}}\\), respectively. \\(c_1\\) and \\(c_2\\) are determined by the concatenation operation. \\(\\mathcal{Q}(\\cdot)\\) denotes the quantization operator and \\(\\oplus\\) denotes the concatenation operator." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.793, + 0.21, + 0.809 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.818, + 0.26, + 0.835 + ], + "angle": 0, + "content": "4.1. Experiments Setup" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In this section, we evaluate the proposed Q-Diffusion framework on pixel-space diffusion model DDPM [13] and latent-space diffusion model Latent Diffusion [34] for unconditional image generation. We also visualize the images" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.895, + 0.721 + ], + "angle": 0, + "content": "generated by Q-Diffusion on Stable Diffusion. To the best of our knowledge, there is currently no published work done on diffusion model quantization. Therefore, we report the basic channel-wise round-to-nearest Linear Quantization (i.e., Equation 5) as a baseline. We also re-implement the state-of-the-art data-free PTQ method SQuant [11] and include the results for comparison. Furthermore, we apply our approach to text-guided image synthesis with Stable Diffusion [34]. Experiments show that our approach can achieve competitive generation quality to the full-precision scenario on all tasks, even under INT4 quantization for weights." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.739, + 0.738, + 0.754 + ], + "angle": 0, + "content": "4.2. Unconditional Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.901 + ], + "angle": 0, + "content": "We conducted evaluations using the \\(32 \\times 32\\) CIFAR-10 [17], \\(256 \\times 256\\) LSUN Bedrooms, and \\(256 \\times 256\\) LSUN Church-Outdoor [48]. We use the pretrained DDIM sampler [42] with 100 denoising time steps for CIFAR-10 experiments and Latent Diffusion (LDM) [34] for the higher resolution LSUN experiments. We evaluated the performance in terms of Frechet Inception Distance (FID) [12] and additionally evaluated the Inception Score (IS) [38] for CIFAR-10 results, since IS is not an accurate reference for datasets that" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17540" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.119, + 0.089, + 0.237, + 0.111 + ], + "angle": 0, + "content": "Bedroom Q-Diffusion (W4A8)" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.115, + 0.276, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.303, + 0.089, + 0.461, + 0.111 + ], + "angle": 0, + "content": "Bedroom Linear Quantization (W4A8)" + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.115, + 0.48, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.531, + 0.089, + 0.639, + 0.111 + ], + "angle": 0, + "content": "Church Q-Diffusion (W4A8)" + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.115, + 0.683, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.715, + 0.089, + 0.863, + 0.111 + ], + "angle": 0, + "content": "Church Linear Quantization (W4A8)" + }, + { + "type": "image", + "bbox": [ + 0.692, + 0.115, + 0.886, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.269, + 0.892, + 0.285 + ], + "angle": 0, + "content": "Figure 8: \\(256 \\times 256\\) unconditional image generation results using Q-Diffusion and Linear Quantization under W4A8 precision." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.316, + 0.471, + 0.346 + ], + "angle": 0, + "content": "Table 1: Quantization results for unconditional image generation with DDIM on CIFAR-10 \\((32\\times 32)\\)" + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.352, + 0.445, + 0.555 + ], + "angle": 0, + "content": "
MethodBits (W/A)Size (Mb)GBopsFID↓IS↑
Full Precision32/32143.265974.229.12
Linear Quant8/3235.822944.718.93
SQuant8/3235.822944.618.99
Q-Diffusion8/3235.822944.279.15
Linear Quant4/3217.91147141.474.20
SQuant4/3217.91147160.402.91
Q-Diffusion4/3217.911475.098.78
Linear Quant8/835.8798118.265.23
SQuant8/835.8798464.691.17
Q-Diffusion8/835.87983.759.48
Linear Quant4/817.9399188.112.45
SQuant4/817.9399456.211.16
Q-Diffusion4/817.93994.939.12
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.563, + 0.471, + 0.623 + ], + "angle": 0, + "content": "differ significantly from ImageNet's domain and categories. The results are reported in Table 1-3 and Figure 8, where Bops is calculated for one denoising step without considering the decoder compute cost for latent diffusion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.47, + 0.79 + ], + "angle": 0, + "content": "The experiments show that Q-Diffusion significantly preserves the image generation quality and outperforms Linear Quantization by a large margin for all resolutions and types of diffusion models tested when the number of bits is low. Although 8-bit weight quantization has almost no performance loss compared to FP32 for both Linear Quantization and our approach, the generation quality with Linear Quantization drops drastically under 4-bit weight quantization. In contrast, Q-Diffusion still preserves most of the perceptual quality with at most 2.34 increase in FID and imperceptible distortions in produced samples." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.801, + 0.349, + 0.818 + ], + "angle": 0, + "content": "4.3. Text-guided Image Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We evaluate Q-Diffusion on Stable Diffusion pretrained on subsets of \\(512 \\times 512\\) LAION-5B for text-guided image generation. Following [34], we sample text prompts from the MS-COCO [21] dataset to generate a calibration dataset with texts condition using Algorithm 1. In this work, we fix" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.316, + 0.895, + 0.361 + ], + "angle": 0, + "content": "Table 2: Quantization results for unconditional image generation with LDM-4 on LSUN-Bedrooms (256 × 256). The downsampling factor for the latent space is 4." + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.366, + 0.868, + 0.582 + ], + "angle": 0, + "content": "
MethodBits (W/A)Size (Mb)TBopsFID↓
Full Precision32/321096.2107.172.98
Linear Quant8/32274.137.283.02
SQuant8/32274.137.282.94
Q-Diffusion8/32274.137.282.97
Linear Quant4/32137.018.6482.69
SQuant4/32137.018.64149.97
Q-Diffusion4/32137.018.644.86
Linear Quant8/8274.112.976.69
SQuant8/8274.112.974.92
Q-Diffusion8/8274.112.974.40
Linear Quant4/8137.06.4824.86
SQuant4/8137.06.4895.92
Q-Diffusion4/8137.06.485.32
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.59, + 0.894, + 0.635 + ], + "angle": 0, + "content": "Table 3: Quantization results for unconditional image generation with LDM-8 on LSUN-Churches (256 × 256). The downsampling factor for the latent space is 8." + }, + { + "type": "table", + "bbox": [ + 0.525, + 0.641, + 0.87, + 0.862 + ], + "angle": 0, + "content": "
MethodBits (W/A)Size (Mb)TBopsFID↓
Full Precision32/321179.922.174.06
Linear Quant8/32295.010.733.84
SQuant8/32295.010.734.01
Q-Diffusion8/32295.010.734.03
Linear Quant4/32147.55.3632.54
SQuant4/32147.55.3633.77
Q-Diffusion4/32147.55.364.45
Linear Quant8/8295.02.6814.62
SQuant8/8295.02.6854.15
Q-Diffusion8/8295.02.683.65
Linear Quant4/8147.51.3414.92
SQuant4/8147.51.3424.50
Q-Diffusion4/8147.51.344.12
" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17541" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.172, + 0.076, + 0.249, + 0.087 + ], + "angle": 0, + "content": "Full Precision" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.342, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.427, + 0.075, + 0.542, + 0.088 + ], + "angle": 0, + "content": "Q-Diffusion (W4A8)" + }, + { + "type": "image", + "bbox": [ + 0.354, + 0.09, + 0.613, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.678, + 0.075, + 0.835, + 0.088 + ], + "angle": 0, + "content": "Linear Quantization (W4A8)" + }, + { + "type": "image", + "bbox": [ + 0.627, + 0.09, + 0.887, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.208, + 0.895, + 0.24 + ], + "angle": 0, + "content": "Figure 9: Stable Diffusion \\(512 \\times 512\\) text-guided image synthesis results using Q-Diffusion and Linear Quantization under W4A8 precision with prompt A puppy wearing a hat." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.277, + 0.474, + 0.489 + ], + "angle": 0, + "content": "the guidance strength to the default 7.5 in Stable Diffusion as the trade-off between sample quality and diversity. Qualitative results are shown in Figure 9. Compared to Linear Quantization, our Q-Diffusion provides higher-quality images with more realistic details and better demonstration of the semantic information. Similar performance gain is also observed in other random samples showcased in Appendix, and quantitatively reported in Appendix. The output of the W4A8 Q-Diffusion model largely resembles the output of the full precision model. Interestingly, we find some diversity in the lower-level semantics between the Q-Diffusion model and the FP models, like the heading of the horse or the shape of the hat. We leave it to future work to understand how quantization contributes to the diversity." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.496, + 0.232, + 0.513 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.528, + 0.439, + 0.726 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.727, + 0.471, + 0.817 + ], + "angle": 0, + "content": "Figure 10: Uniform sampling strategies which cover all time steps are better than strategies that cover only a part of the time steps, as in Fig. 4. Furthermore, adjusting the sampling techniques within uniform sampling, such as tuning the sampling interval and the number of samples, has a marginal effect on the performance of the quantized model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Effects of Sampling Strategies To analyze the effects of different sampling strategies for calibration in detail, we implemented multiple variants of our method using different sampling strategies. We then evaluated the quality of the models quantized by each variant. We experimented" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.277, + 0.895, + 0.458 + ], + "angle": 0, + "content": "with varying numbers of time steps used for sampling and samples used for calibration. In addition to calibration sets from uniform timestep intervals, we also employed sampling at the first 50 and last 50 steps. As in Figure 10, uniform sampling that spans all time steps results in superior performance compared to sampling from only partial time steps. Furthermore, adjusting the sampling hyperparams, including using more calibration samples, does not significantly improve the performance. Therefore, we simply choose to sample uniformly every 20 steps for a total of 5,120 samples for calibration, resulting in a high-quality quantized model with low computational costs during quantization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.895, + 0.535 + ], + "angle": 0, + "content": "We also conduct ablation experiments to explore the effectiveness of several non-uniform calibration data sampling schemes, such as using Unsupervised Selecting Labeling (USL) [45] to select both representative and diverse calibration samples. We present the results in Appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.556, + 0.895, + 0.678 + ], + "angle": 0, + "content": "Effects of Split Previous linear quantization approaches suffer from severe performance degradation as shown in Figure 11, where 4-bit weight quantization achieves a high FID of 141.47 in DDIM CIFAR-10 generation. Employing additional 8-bit activation quantization further degrades the performance (FID: 188.11). By splitting shortcuts in quantization, we significantly improve the generation performance, achieving an FID of 4.93 on W4A8 quantization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.682, + 0.62, + 0.699 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.708, + 0.895, + 0.83 + ], + "angle": 0, + "content": "This work studies the use of quantization to accelerate and reduce the memory usage of diffusion models. We propose Q-Diffusion, a novel post-training quantization scheme that conducts calibration with multiple time steps in the denoising process and achieves significant improvements in the performance of the quantized model. Q-Diffusion models under 4-bit quantization achieve comparable results to the full precision models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.845, + 0.661, + 0.862 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.895, + 0.902 + ], + "angle": 0, + "content": "We thank Berkeley Deep Drive, Intel Corporation, Panasonic, and NVIDIA for supporting this research. We also" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17542" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.135, + 0.094, + 0.454, + 0.106 + ], + "angle": 0, + "content": "Linear Quantization + Calibration + Split shortcuts" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.121, + 0.446, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.296, + 0.471, + 0.372 + ], + "angle": 0, + "content": "Figure 11: Splitting the shortcut convolution is crucial for both weight and activation quantization. Comparisons on CIFAR-10 show that Q-Diffusion could achieve comparable image generation quality to the model with full precision (dashed line) with shortcut splitting." + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.378, + 0.462, + 0.527 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.536, + 0.471, + 0.613 + ], + "angle": 0, + "content": "Figure 12: Examples of text-to-image generation with a quantized Stable Diffusion model. Naive linear quantization degrades the appearance of teeth, which gets fixed by shortcut splitting. Q-Diffusion further improves the semantic consistency of eyes through calibration." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.633, + 0.47, + 0.663 + ], + "angle": 0, + "content": "would like to thank Sehoon Kim, Muyang Li, and Minkai Xu for their valuable feedback." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.678, + 0.175, + 0.695 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.085, + 0.703, + 0.472, + 0.758 + ], + "angle": 0, + "content": "[1] Fan Bao, Chongxuan Li, Jun Zhu, and Bo Zhang. Analytic-dpm: an analytic estimate of the optimal reverse variance in diffusion probabilistic models. ArXiv, abs/2201.06503, 2022. 1, 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.086, + 0.761, + 0.472, + 0.843 + ], + "angle": 0, + "content": "[2] Yash Bhalgat, Jinwon Lee, Markus Nagel, Tijmen Blankevoort, and Nojun Kwak. 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However, the slow inference, high memory consumption, and computation intensity of the noise estimation model hinder the efficient adoption of diffusion models. Although post-training quantization (PTQ) is considered a go-to compression method for other tasks, it does not work out-of-the-box on diffusion models. We propose a novel PTQ method specifically tailored towards the unique multistep pipeline and model architecture of the diffusion models, which compresses the noise estimation network to accelerate the generation process. We identify the key difficulty of diffusion model quantization as the changing output distributions of noise estimation networks over multiple time steps and the bimodal activation distribution of the shortcut layers within the noise estimation network. We tackle these challenges with timestep-aware calibration and split shortcut quantization in this work. Experimental results show that our proposed method is able to quantize full-precision unconditional diffusion models into 4-bit while maintaining comparable performance (small FID change of at most 2.34 compared to $>100$ for traditional PTQ) in a training-free manner. Our approach can also be applied to text-guided image generation, where we can run stable diffusion in 4-bit weights with high generation quality for the first time. + +# 1. Introduction + +Diffusion models have shown great success in generating images with both high diversity and high fidelity [43, 13, 44, 42, 6, 33, 36, 34]. Recent work [16, 15] has demonstrated superior performance than state-of-the-art GAN models, which suffer from unstable training. As a class of flexible generative models, diffusion models demonstrate their power in various applications such as image super-resolution [37, 18], inpainting [44], shape generation [3], graph generation [31], image-to-image translation [40], and molecular conformation generation [47]. + +However, the generation process for diffusion models can be slow due to the need for an iterative noise estimation of 50 + +to 1,000 time steps [13, 42] using complex neural networks. While previous state-of-the-art approaches (e.g., GANs) are able to generate multiple images in under 1 second, it normally takes several seconds for a diffusion model to sample a single image. Consequently, speeding up the image generation process becomes an important step toward broadening the applications of diffusion models. Previous work has been solving this problem by finding shorter, more effective sampling trajectories [42, 30, 39, 22, 1, 24], which reduces the number of steps in the denoising process. However, they have largely ignored another important factor: the noise estimation model used in each iteration itself is compute- and memory-intensive. This is an orthogonal factor to the repetitive sampling, which not only slows down the inference speed of diffusion models, but also poses crucial challenges in terms of high memory footprints. + +This work explores the quantization [50, 8, 49, 7, 29] of the noise estimation model used in the diffusion model to accelerate the denoising of all time steps. Specifically, we propose exploring post-training quantization (PTQ) on the diffusion model. PTQ has already been well studied in other learning domains like classification and object detection [4, 2, 20, 11, 23], and has been considered a go-to compression method given its minimal requirement for training data and the straightforward deployment on real hardware devices. However, the iterative computation process of the diffusion model and the model architecture of the noise estimation network brings unique challenges to the PTQ of diffusion models. PTQ4DM [41] presents an inaugural application of PTQ to compress diffusion models down to 8-bit, but it primarily focuses on smaller datasets and lower resolutions. + +Our work, evolving concurrently with [41], offers a comprehensive analysis of the novel challenges of performing PTQ on diffusion models. Specifically, as visualized in Figure 1(a), we discover that the output distribution of the noise estimation network at each time step can be largely different, and naively applying previous PTQ calibration methods with an arbitrary time step leads to poor performance. Furthermore, as illustrated in Figure 1(b), the iterative inference of the noise estimation network leads to an accumulation of quantization error, which poses higher demands on design- + +![](images/da7b51ccc505d7d59f7ae73ae25bedd841c663fb6b3714d2e40a47b40792b4c5.jpg) +Figure 1: Conventional PTQ scenarios and Q-Diffusion differ in (a) calibration dataset creation and (b) model inference workflow. Traditional PTQ approaches sample data randomly [11], synthesize with statistics in model layers [4], or draw from the training set to create calibration dataset [28, 20], which either contains inconsistency with real inputs during the inference time or are not data-free. In contrast, Q-Diffusion constructed calibration datasets with inputs that are an accurate reflection of data seen during the production in a data-free manner. Traditional PTQ inference only needs to go through the quantized model $\theta_q$ one time, while Q-Diffusion needs to address the accumulated quantization errors in the multi-time step inference. + +![](images/ff529693cfe2a2c7b812150f166da8dfb5e460a764ab61715fc8b389baf421e9.jpg) + +ing novel quantization schemes and calibration objectives for the noise estimation network. + +To address these challenges, we propose Q-Diffusion, a PTQ solution to compress the cumbersome noise estimation network in diffusion models in a data-free manner, while maintaining comparable performance to the full precision counterparts. We propose a time step-aware calibration data sampling mechanism from the pretrained diffusion model, which represents the activation distribution of all time steps. We further tailor the design of the calibration objective and the weight and activation quantizer to the commonly used noise estimation model architecture to reduce quantization error. We perform thorough ablation studies to verify our design choices, and demonstrate good generation results with diffusion models quantized to only 4 bits. + +In summary, our contributions are: + +1. We propose Q-Diffusion, a data-free PTQ solution for the noise estimation network in diffusion models. +2. We identify the novel challenge of performing PTQ on diffusion models as the activation distribution diversity and the quantization error accumulation across time steps via a thorough analysis. +3. We propose time step-aware calibration data sampling to improve calibration quality, and propose a specialized quantizer for the noise estimation network. +4. Extensive results show Q-Diffusion enables W4A8 PTQ for both pixel-space and latent-space unconditional diffusion models with an FID increment of only + +0.39-2.34 over full precision models. It can also produce qualitatively comparable images when plugged into Stable Diffusion [34] for text-guided synthesis. + +# 2. Related work + +Diffusion Models. Diffusion models generate images through a Markov chain, as illustrated in Figure 2. A forward diffusion process adds Gaussian noise to data $\mathbf{x}_0 \sim q(\mathbf{x})$ for $T$ times, resulting in noisy samples $\mathbf{x}_1, \dots, \mathbf{x}_T$ : + +$$ +q \left(\mathbf {x} _ {t} \mid \mathbf {x} _ {t - 1}\right) = \mathcal {N} \left(\mathbf {x} _ {t}; \sqrt {1 - \beta_ {t}} \mathbf {x} _ {t - 1}, \beta_ {t} \mathbf {I}\right) \tag {1} +$$ + +where $\beta_{t} \in (0,1)$ is the variance schedule that controls the strength of the Gaussian noise in each step. When $T \to \infty$ , $\mathbf{x}_T$ approaches an isotropic Gaussian distribution. + +The reverse process removes noise from a sample from the Gaussian noise input $\mathbf{x}_T\sim \mathcal{N}(\mathbf{0},\mathbf{I})$ to gradually generate high-fidelity images. However, since the real reverse conditional distribution $q(\mathbf{x}_{t - 1}|\mathbf{x}_t)$ is unavailable, diffusion models sample from a learned conditional distribution: + +$$ +p _ {\theta} \left(\mathbf {x} _ {t - 1} \mid \mathbf {x} _ {t}\right) = \mathcal {N} \left(\mathbf {x} _ {t - 1}; \tilde {\boldsymbol {\mu}} _ {\theta , t} \left(\mathbf {x} _ {t}\right), \tilde {\boldsymbol {\beta}} _ {t} \mathbf {I}\right). \tag {2} +$$ + +With the reparameterization trick in [13], the mean $\tilde{\mu}_{\theta ,t}(\mathbf{x}_t)$ and variance $\tilde{\beta}_t$ could be derived as follows: + +$$ +\tilde {\boldsymbol {\mu}} _ {\theta , t} \left(\mathbf {x} _ {t}\right) = \frac {1}{\sqrt {\alpha_ {t}}} \left(\mathbf {x} _ {t} - \frac {1 - \alpha_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \boldsymbol {\epsilon} _ {\theta , t}\right) \tag {3} +$$ + +$$ +\tilde {\beta} _ {t} = \frac {1 - \bar {\alpha} _ {t - 1}}{1 - \bar {\alpha} _ {t}} \cdot \beta_ {t} \tag {4} +$$ + +![](images/5224a88d6432bf1fef55014a279f934533509072d14b15c9f646c3084f323f40.jpg) +(a) Forward diffusion process + +![](images/ca9fad0fc7232a4b06ecf2d676caf71b1f8339914e11ff8d6464a4c0804ec580.jpg) +(b) Reverse diffusion process +Figure 2: The forward diffusion process (a) repeatedly adds Gaussian noise. The reverse diffusion process (b) uses a trained network to denoise from a standard Gaussian noise image in order to generate an image. + +where $\alpha_{t} = 1 - \beta_{t}$ , $\bar{\alpha}_{t} = \prod_{i=1}^{t} \alpha_{i}$ . We refer readers to [26] for a more detailed introduction. + +In practice, the noise at each time step $t$ are computed from $\mathbf{x}_t$ by a noise estimation model, with the same weights for all time steps. The UNet [35] dominates the design of the noise estimation model in diffusion models [42, 34, 33, 36], with some recent exploration on Transformer [32]. This work designs the PTQ method for the acceleration of the noise estimation model, especially for the common UNet. + +Accelerated diffusion process. Related methods include simulating the diffusion process in fewer steps by generalizing it to a non-Markovian process [42], adjusting the variance schedule [30], and the use of high-order solvers to approximate diffusion generation [22, 1, 24, 25]. Others have employed the technique of caching and reusing feature maps [19]. Efforts to distill the diffusion model into fewer time steps have also been undertaken [39, 27], which have achieved notable success but involve an extremely expensive retraining process. Our work focuses on accelerating the noise estimation model inference in each step, with a training-free PTQ process. + +Post-training Quantization. Post-training quantization (PTQ) compresses deep neural networks by rounding elements $w$ to a discrete set of values [10], where the quantization and de-quantization can be formulated as: + +$$ +\hat {w} = \mathrm {s} \cdot \operatorname {c l i p} \left(\operatorname {r o u n d} \left(\frac {w}{s}\right), c _ {\min }, c _ {\max }\right), \tag {5} +$$ + +where $s$ denotes the quantization scale parameters, $c_{\mathrm{min}}$ and $c_{\mathrm{max}}$ are the lower and upper bounds for the clipping function $\mathrm{clip}(\cdot)$ . These parameters can be calibrated with the weight and activation distribution estimated in the PTQ process. The operator round(\cdot) represents rounding, which can be either rounding-to-nearest [46, 4] or adaptive rounding [20]. + +Previous PTQ research in classification and detection tasks focused on the calibration objective and the acquisition of calibration data. For example, EasyQuant [46] determines appropriate $c_{\mathrm{min}}$ and $c_{\mathrm{max}}$ based on training data, and BRECQ [20] introduces Fisher information into the objective. ZeroQ [4] employs a distillation technique to generate proxy input images for PTQ, and SQuant [11] uses + +random samples with objectives based on sensitivity determined through the Hessian spectrum. For diffusion model quantization, a training dataset is not needed as the calibration data can be constructed by sampling the full-precision model with random inputs. However, the multi-time step inference of the noise estimation model brings new challenges in modeling the activation distribution. In parallel to our work, PTQ4DM [41] introduces the method of Normally Distributed Time-step Calibration, generating calibration data across all time steps with a specific distribution. Nevertheless, their explorations remain confined to lower resolutions, 8-bit precision, floating-point attention activation-to-activation matmuls, and with limited ablation study on other calibration schemes. This results in worse applicability of their method to lower precisions (see Appendix). Our work delves into the implications of calibration dataset creation in a holistic manner, establishing an efficient calibration objective for diffusion models. We fully quantize act-to-act matmuls, validated by experiments involving both pixel-space and latent-space diffusion models on large-scale datasets up to resolutions of $512 \times 512$ . + +# 3. Method + +We present our method for post-training quantization of diffusion models in this section. Different from conventionally studied deep learning models and tasks such as CNNs and VITs for classification and detection, diffusion models are trained and evaluated in a distinctive multi-step manner with a unique UNet architecture. This presents notable challenges to the PTQ process. We analyze the challenges brought by the multi-step inference process and the UNet architecture in Section 3.1 and 3.2 respectively and describe the full Q-Diffusion PTQ pipeline in Section 3.3. + +# 3.1. Challenges under the Multi-step Denoising + +We identify two major challenges in quantizing models that employ multi-step inference process. Namely, we investigate the accumulation of quantization error across time steps and the difficulty of sampling a small calibration dataset to reduce the quantization error at each time step. + +Challenge 1: Quantization errors accumulate across time steps. Performing quantization on a neural network model introduces noise on the weight and activation of the well-trained model, leading to quantization errors in each layer's output. Previous research has identified that quantization errors are likely to accumulate across layers [5], making deeper neural networks harder to quantize. In the case of diffusion models, at any time step $t$ , the input of the denoising model (denoted as $\mathbf{x}_t$ ) is derived by $\mathbf{x}_{t+1}$ , the output of the model at the previous time step $t+1$ (as depicted by Equation 2). This process effectively multiplies the number of layers involved in the computation by the number of de + +![](images/7a13bcbf9683434d92db803b95d4b212fe5f7010a07730acab221dbe9d42ad1a.jpg) +Figure 3: MSE between FP32 outputs and weight-quantized outputs of different precisions with Linear Quantization and our approach across time steps. Here the data is obtained by passing a batch with 64 samples through a model trained on CIFAR-10 [17] with DDIM sampling steps 100. + +![](images/c0a7e41022b3249801c9b6f5996acd95845572a359b129e9702032dc588f4832.jpg) +Figure 4: Effects of time steps in calibration dataset creation on 4-bit weights quantization results with DDIM on CIFAR-10. First $n$ , Mid $n$ , Last $n$ denotes that 5120 samples are selected uniformly from the first, middle, last $n$ time steps. + +noising steps for the input $\mathbf{x}_t$ at time step $t$ , leading to an accumulation of quantization errors towards later steps in the denoising process. + +We run the denoising process of DDIM [42] on CIFAR-10 [17] with a sampling batch size of 64, and compare the MSE differences between the full-precision model and the model quantized to INT8, INT5, and INT4 at each time step. As shown in Figure 3, there is a dramatic increase in the quantization errors when the model is quantized to 4-bit, and the errors accumulate quickly through iterative denoising. This brings difficulty in preserving the performance after quantizing the model down to low precision, which requires the reduction of quantization errors at all time steps as much as possible. + +Challenge 2: Activation distributions vary across time steps. To reduce the quantization errors at each time step, previous PTQ research [28, 20] calibrates the clipping range and scaling factors of the quantized model with a small set of calibration data. The calibration data should be sampled to resemble the true input distribution so that the activation dis + +The distribution of the model can be estimated correctly for proper calibration. Given that the Diffusion model uses the same noise estimation network to take inputs from all time steps, determining the data sampling policy across different time steps becomes an outstanding challenge. Here we start by analyzing the output activation distribution of the UNet model across different time steps. We conduct the same CIFAR-10 experiment using DDIM with 100 denoising steps, and draw the activations ranges of 1000 random samples among all time steps. As Figure 5 shows, the activation distributions gradually change, with neighboring time steps being similar and distant ones being distinctive. This is also echoed by the visualized $\mathbf{x}_t$ in Figure 2. + +The fact that the output activations distribution varies across time steps further brings challenges to quantization. Calibrating the noise estimation model using only a few time steps that do not reflect the full range of activations seen among all time steps by the noise estimation model during the denoising process can cause overfitting to the activation distribution described by those specific time steps, while not generalizing to other time steps, which hurts the overall performance. For instance, here we try to calibrate the quantized DDIM on the CIFAR-10 dataset with data sampled from different parts of the denoising process. As shown in Figure 4, if we simply take 5120 samples from time steps that fall into a certain stage of the denoising process, significant performance drops will be induced under 4-bit weights quantization. Note that the case with samples taken from the middle 50 time steps caused smaller drops compared to cases with samples taken from either the first or the last $n$ time steps, and with $n$ increases, the drops are also alleviated. These results illustrate the gradual "denoising" process as depicted in Figure 5: the activations distribution changes gradually throughout time steps, with the middle part capturing the full range to some degree, while parts of the distant endpoints differing the most. To recover the performance of the quantized diffusion models, we need to select calibration data in a way that comprehensively takes into account the distributions of the output of different time steps. + +# 3.2. Challenges on Noise Estimation Model Quantization + +Most diffusion models (Imagen [36], Stable Diffusion [34], VDMs [14]) adopt UNets as denoising backbones that downsample and upsample latent features. Although recent studies show that transformer architectures are also capable of serving as the noise estimation backbone [32], convolutional UNets are still the de facto choice of architecture today. UNets utilize shortcut layers to merge concatenated deep and shallow features and transmit them to subsequent layers. Through our analysis presented in Figure 6, we observe that input activations in shortcut layers exhibit abnormal value ranges in comparison to other layers. + +![](images/924496e879da1b129aa92becbafb5799fc5bcc820a975764e330ae14ace14da0.jpg) +Figure 5: Activation ranges of $x_{t}$ across all 100 time steps of FP32 DDIM model on CIFAR-10. + +Notably, the input activations in DDIM's shortcut layers can be up to 200 times larger than other neighboring layers. + +To analyze the reason for this, we visualize the weight and activation tensor of a DDIM shortcut layer. As demonstrated in the dashed box in Figure 6, the ranges of activations from the deep feature channels $(X_{1})$ and shallow feature channels $(X_{2})$ being concatenated together vary significantly, which also resulted in a bimodal weight distribution in the corresponding channels (see also Figure 7). Naively quantizing the entire weight and activation distribution with the same quantizer will inevitably lead to large quantization errors. + +# 3.3. Post-Training Quantization of Diffusion Model + +We propose two techniques: time step-aware calibration data sampling and shortcut-splitting quantization to tackle the challenges identified in the previous sections respectively. + +# 3.3.1 Time step-aware calibration + +Since the output distributions of consecutive time steps are often very similar, we propose to randomly sample intermediate inputs uniformly in a fixed interval across all time steps to generate a small calibration set. This effectively balances the size of the calibration set and its representation ability of the distribution across all time steps. Empirically, we have found that the sampled calibration data can recover most of the INT4 quantized models' performance after the calibration, making it an effective sampling scheme for calibration data collection for quantization error correction. + +To calibrate the quantized model, we divide the model into several reconstruction blocks [20], and iteratively reconstruct outputs and tune the clipping range and scaling factors of weight quantizers in each block with adaptive rounding [28] to minimize the mean squared errors between the quantized and full precision outputs. We define a core component that contains residual connections in the diffusion model UNet as a block, such as a Residual Bottleneck Block or a Transformer Block. Other parts of the model that do not satisfy this condition are calibrated in a per-layer manner. This technique has been shown to improve the performance compared to fully layer-by-layer calibration since it addresses the inter-layer dependencies and generalization + +better [20]. For activation quantization, since activations are constantly changing during inference, doing adaptive rounding is infeasible. Therefore, we only adjust the step sizes of activation quantizers according to [9]. The overall calibration workflow is described in Alg. 1. + +# Algorithm 1 Q-Diffusion Calibration + +Require: Pretrained full precision diffusion model and the quantized diffusion model $[W_{\theta},\hat{W}_{\theta}]$ + +Require: Empty calibration dataset $\mathcal{D}$ + +Require: Number of denoising sampling steps $T$ + +Require: Calibration sampling interval $c$ , amount of calibration data per sampling step $n$ + +for $t = 1,\dots ,T$ time step do + +if $t\% c = 0$ then + +Sample $n$ intermediate inputs $\mathbf{x}_t^{(1)},\ldots ,\mathbf{x}_t^{(n)}$ randomly at $t$ from $W_{\theta}$ and add them to $\mathcal{D}$ + +end if + +end for + +for all $i = 1,\dots ,N$ blocks do + +Update the weight quantizers of the $i$ -th block in $\hat{W}_{\theta}$ with $\mathcal{D}$ and $W_{\theta}$ + +end for + +if do activation quantization then + +for all $i = 1,\dots ,N$ blocks do + +Update the activation quantizers step sizes of the $i$ -th block with $\hat{W}_{\theta}, W_{\theta}, \mathcal{D}$ . + +end for + +end if + +# 3.3.2 Shortcut-splitting quantization + +To address the abnormal activation and weight distributions in shortcut layers, we propose a "split" quantization technique that performs quantization prior to concatenation, requiring negligible additional memory or computational resources. This strategy can be employed for both activation and weight quantization in shortcut layers, and is expressed + +![](images/f2ddb74b585e59e0ea7588a8eafc4ba0826022341d3fe39069bc97d6907cac29.jpg) +Figure 6: Activation ranges of DDIM's FP32 outputs across layers averaging among all time steps. We point out three shortcuts with the largest input activation ranges compared to other neighboring layers. Figures in the dashed box illustrate concatenation along channels. $\oplus$ denotes the concatenation operation. + +![](images/2cf5c7374ed6b8ceab495098f25210476c2794e3b86bdd0d8da8a53d0ce4bbf2.jpg) +Figure 7: (Left) The typical UNet architecture with shortcut layers that concatenate features from the deep and shallow layers. (Right) The ranges of activations from the deep $(X_{1})$ and shallow $(X_{2})$ feature channels vary significantly, which also results in a bimodal weight distribution in the corresponding channels. + +mathematically as follows: + +$$ +\mathcal {Q} _ {X} (X) = \mathcal {Q} _ {X _ {1}} (X _ {1}) \oplus \mathcal {Q} _ {X _ {2}} (X _ {2}) \tag {6} +$$ + +$$ +\mathcal {Q} _ {W} (W) = \mathcal {Q} _ {W _ {1}} \left(W _ {1}\right) \oplus \mathcal {Q} _ {W _ {2}} \left(W _ {2}\right) \tag {7} +$$ + +$$ +\begin{array}{l} \mathcal {Q} _ {X} (X) \mathcal {Q} _ {W} (W) = \mathcal {Q} _ {X _ {1}} \left(X _ {1}\right) \mathcal {Q} _ {W _ {1}} \left(W _ {1}\right) \\ + \mathcal {Q} _ {X _ {2}} (X _ {2}) \mathcal {Q} _ {W _ {2}} (W _ {2}) \\ \end{array} +$$ + +where $X \in \mathbb{R}^{w \times h \times c_{in}}$ and $W \in \mathbb{R}^{c_{in} \times c_{out}}$ are the input activation and layer weight, which can be naturally split into $X_1 \in \mathbb{R}^{w \times h \times c_1}$ , $X_2 \in \mathbb{R}^{w \times h \times c_2}$ , $W_1 \in \mathbb{R}^{c_1 \times c_{out}}$ , and $W_2 \in \mathbb{R}^{c_2 \times c_{out}}$ , respectively. $c_1$ and $c_2$ are determined by the concatenation operation. $\mathcal{Q}(\cdot)$ denotes the quantization operator and $\oplus$ denotes the concatenation operator. + +# 4. Experiments + +# 4.1. Experiments Setup + +In this section, we evaluate the proposed Q-Diffusion framework on pixel-space diffusion model DDPM [13] and latent-space diffusion model Latent Diffusion [34] for unconditional image generation. We also visualize the images + +generated by Q-Diffusion on Stable Diffusion. To the best of our knowledge, there is currently no published work done on diffusion model quantization. Therefore, we report the basic channel-wise round-to-nearest Linear Quantization (i.e., Equation 5) as a baseline. We also re-implement the state-of-the-art data-free PTQ method SQuant [11] and include the results for comparison. Furthermore, we apply our approach to text-guided image synthesis with Stable Diffusion [34]. Experiments show that our approach can achieve competitive generation quality to the full-precision scenario on all tasks, even under INT4 quantization for weights. + +# 4.2. Unconditional Generation + +We conducted evaluations using the $32 \times 32$ CIFAR-10 [17], $256 \times 256$ LSUN Bedrooms, and $256 \times 256$ LSUN Church-Outdoor [48]. We use the pretrained DDIM sampler [42] with 100 denoising time steps for CIFAR-10 experiments and Latent Diffusion (LDM) [34] for the higher resolution LSUN experiments. We evaluated the performance in terms of Frechet Inception Distance (FID) [12] and additionally evaluated the Inception Score (IS) [38] for CIFAR-10 results, since IS is not an accurate reference for datasets that + +![](images/1b402ef003af78d7a417a34d3dc6331f80d1295899bec2d31a162d535d687f55.jpg) +Bedroom Q-Diffusion (W4A8) +Figure 8: $256 \times 256$ unconditional image generation results using Q-Diffusion and Linear Quantization under W4A8 precision. + +![](images/ec5ae5a0f63de2d42b58a65d5d1133b2726cd31ee8ebda6954975d7527fa0057.jpg) +Bedroom Linear Quantization (W4A8) + +![](images/763cef04e103078f997a271e1b021cc8b798e75172a0060f55cc24346334d4d3.jpg) +Church Q-Diffusion (W4A8) + +![](images/d4f7b28b947f2ef355871aacf488353384493bac45c66cfa1ab3ef44d3ba9307.jpg) +Church Linear Quantization (W4A8) + +Table 1: Quantization results for unconditional image generation with DDIM on CIFAR-10 $(32\times 32)$ + +
MethodBits (W/A)Size (Mb)GBopsFID↓IS↑
Full Precision32/32143.265974.229.12
Linear Quant8/3235.822944.718.93
SQuant8/3235.822944.618.99
Q-Diffusion8/3235.822944.279.15
Linear Quant4/3217.91147141.474.20
SQuant4/3217.91147160.402.91
Q-Diffusion4/3217.911475.098.78
Linear Quant8/835.8798118.265.23
SQuant8/835.8798464.691.17
Q-Diffusion8/835.87983.759.48
Linear Quant4/817.9399188.112.45
SQuant4/817.9399456.211.16
Q-Diffusion4/817.93994.939.12
+ +differ significantly from ImageNet's domain and categories. The results are reported in Table 1-3 and Figure 8, where Bops is calculated for one denoising step without considering the decoder compute cost for latent diffusion. + +The experiments show that Q-Diffusion significantly preserves the image generation quality and outperforms Linear Quantization by a large margin for all resolutions and types of diffusion models tested when the number of bits is low. Although 8-bit weight quantization has almost no performance loss compared to FP32 for both Linear Quantization and our approach, the generation quality with Linear Quantization drops drastically under 4-bit weight quantization. In contrast, Q-Diffusion still preserves most of the perceptual quality with at most 2.34 increase in FID and imperceptible distortions in produced samples. + +# 4.3. Text-guided Image Generation + +We evaluate Q-Diffusion on Stable Diffusion pretrained on subsets of $512 \times 512$ LAION-5B for text-guided image generation. Following [34], we sample text prompts from the MS-COCO [21] dataset to generate a calibration dataset with texts condition using Algorithm 1. In this work, we fix + +Table 2: Quantization results for unconditional image generation with LDM-4 on LSUN-Bedrooms (256 × 256). The downsampling factor for the latent space is 4. + +
MethodBits (W/A)Size (Mb)TBopsFID↓
Full Precision32/321096.2107.172.98
Linear Quant8/32274.137.283.02
SQuant8/32274.137.282.94
Q-Diffusion8/32274.137.282.97
Linear Quant4/32137.018.6482.69
SQuant4/32137.018.64149.97
Q-Diffusion4/32137.018.644.86
Linear Quant8/8274.112.976.69
SQuant8/8274.112.974.92
Q-Diffusion8/8274.112.974.40
Linear Quant4/8137.06.4824.86
SQuant4/8137.06.4895.92
Q-Diffusion4/8137.06.485.32
+ +Table 3: Quantization results for unconditional image generation with LDM-8 on LSUN-Churches (256 × 256). The downsampling factor for the latent space is 8. + +
MethodBits (W/A)Size (Mb)TBopsFID↓
Full Precision32/321179.922.174.06
Linear Quant8/32295.010.733.84
SQuant8/32295.010.734.01
Q-Diffusion8/32295.010.734.03
Linear Quant4/32147.55.3632.54
SQuant4/32147.55.3633.77
Q-Diffusion4/32147.55.364.45
Linear Quant8/8295.02.6814.62
SQuant8/8295.02.6854.15
Q-Diffusion8/8295.02.683.65
Linear Quant4/8147.51.3414.92
SQuant4/8147.51.3424.50
Q-Diffusion4/8147.51.344.12
+ +![](images/5a6f4994244a30f440329693a9bf059b313aec831f8a244c379ed5c5ade1a3de.jpg) +Full Precision + +![](images/feb59c49aa55f53418a8447d760732aea2d764ab64a875cc87ba00f4cbb2d026.jpg) +Q-Diffusion (W4A8) +Figure 9: Stable Diffusion $512 \times 512$ text-guided image synthesis results using Q-Diffusion and Linear Quantization under W4A8 precision with prompt A puppy wearing a hat. + +![](images/92f3b447050a79097f5b3e15dabe5e32e2386b4d6628994a60700136a56e0fb3.jpg) +Linear Quantization (W4A8) + +the guidance strength to the default 7.5 in Stable Diffusion as the trade-off between sample quality and diversity. Qualitative results are shown in Figure 9. Compared to Linear Quantization, our Q-Diffusion provides higher-quality images with more realistic details and better demonstration of the semantic information. Similar performance gain is also observed in other random samples showcased in Appendix, and quantitatively reported in Appendix. The output of the W4A8 Q-Diffusion model largely resembles the output of the full precision model. Interestingly, we find some diversity in the lower-level semantics between the Q-Diffusion model and the FP models, like the heading of the horse or the shape of the hat. We leave it to future work to understand how quantization contributes to the diversity. + +# 4.4. Ablation Study + +![](images/593c5f505b31604228ddd1190e7c4a8922a8317656e31922b8105199c8206420.jpg) +Figure 10: Uniform sampling strategies which cover all time steps are better than strategies that cover only a part of the time steps, as in Fig. 4. Furthermore, adjusting the sampling techniques within uniform sampling, such as tuning the sampling interval and the number of samples, has a marginal effect on the performance of the quantized model. + +Effects of Sampling Strategies To analyze the effects of different sampling strategies for calibration in detail, we implemented multiple variants of our method using different sampling strategies. We then evaluated the quality of the models quantized by each variant. We experimented + +with varying numbers of time steps used for sampling and samples used for calibration. In addition to calibration sets from uniform timestep intervals, we also employed sampling at the first 50 and last 50 steps. As in Figure 10, uniform sampling that spans all time steps results in superior performance compared to sampling from only partial time steps. Furthermore, adjusting the sampling hyperparams, including using more calibration samples, does not significantly improve the performance. Therefore, we simply choose to sample uniformly every 20 steps for a total of 5,120 samples for calibration, resulting in a high-quality quantized model with low computational costs during quantization. + +We also conduct ablation experiments to explore the effectiveness of several non-uniform calibration data sampling schemes, such as using Unsupervised Selecting Labeling (USL) [45] to select both representative and diverse calibration samples. We present the results in Appendix. + +Effects of Split Previous linear quantization approaches suffer from severe performance degradation as shown in Figure 11, where 4-bit weight quantization achieves a high FID of 141.47 in DDIM CIFAR-10 generation. Employing additional 8-bit activation quantization further degrades the performance (FID: 188.11). By splitting shortcuts in quantization, we significantly improve the generation performance, achieving an FID of 4.93 on W4A8 quantization. + +# 5. Conclusion + +This work studies the use of quantization to accelerate and reduce the memory usage of diffusion models. We propose Q-Diffusion, a novel post-training quantization scheme that conducts calibration with multiple time steps in the denoising process and achieves significant improvements in the performance of the quantized model. Q-Diffusion models under 4-bit quantization achieve comparable results to the full precision models. + +# Acknowledgement + +We thank Berkeley Deep Drive, Intel Corporation, Panasonic, and NVIDIA for supporting this research. We also + +![](images/631055b526ddb7e6675fc1fa0384bef5edc5cf21f88baae8df31d6d8526322d8.jpg) +Linear Quantization + Calibration + Split shortcuts +Figure 11: Splitting the shortcut convolution is crucial for both weight and activation quantization. Comparisons on CIFAR-10 show that Q-Diffusion could achieve comparable image generation quality to the model with full precision (dashed line) with shortcut splitting. + +![](images/b9d3d8ab6937eebf5cb985780a79b64637537267fb8d97047327327a47523e9a.jpg) +Figure 12: Examples of text-to-image generation with a quantized Stable Diffusion model. Naive linear quantization degrades the appearance of teeth, which gets fixed by shortcut splitting. Q-Diffusion further improves the semantic consistency of eyes through calibration. + +would like to thank Sehoon Kim, Muyang Li, and Minkai Xu for their valuable feedback. + +# References + +[1] Fan Bao, Chongxuan Li, Jun Zhu, and Bo Zhang. Analytic-dpm: an analytic estimate of the optimal reverse variance in diffusion probabilistic models. ArXiv, abs/2201.06503, 2022. 1, 3 +[2] Yash Bhalgat, Jinwon Lee, Markus Nagel, Tijmen Blankevoort, and Nojun Kwak. 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However, the slow inference, high memory consumption, and computation intensity of the noise estimation model hinder the efficient adoption of diffusion models. Although post-training quantization (PTQ) is considered a go-to compression method for other tasks, it does not work out-of-the-box on diffusion models. We propose a novel PTQ method specifically tailored towards the unique multistep pipeline and model architecture of the diffusion models, which compresses the noise estimation network to accelerate the generation process. We identify the key difficulty of diffusion model quantization as the changing output distributions of noise estimation networks over multiple time steps and the bimodal activation distribution of the shortcut layers within the noise estimation network. We tackle these challenges with timestep-aware calibration and split shortcut quantization in this work. Experimental results show that our proposed method is able to quantize full-precision unconditional diffusion models into 4-bit while maintaining comparable performance (small FID change of at most 2.34 compared to " + }, + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "inline_equation", + "content": ">100" + }, + { + "bbox": [ + 46, + 238, + 290, + 539 + ], + "type": "text", + "content": " for traditional PTQ) in a training-free manner. Our approach can also be applied to text-guided image generation, where we can run stable diffusion in 4-bit weights with high generation quality for the first time." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 550, + 128, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 550, + 128, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 550, + 128, + 562 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 570, + 288, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 689 + ], + "type": "text", + "content": "Diffusion models have shown great success in generating images with both high diversity and high fidelity [43, 13, 44, 42, 6, 33, 36, 34]. Recent work [16, 15] has demonstrated superior performance than state-of-the-art GAN models, which suffer from unstable training. As a class of flexible generative models, diffusion models demonstrate their power in various applications such as image super-resolution [37, 18], inpainting [44], shape generation [3], graph generation [31], image-to-image translation [40], and molecular conformation generation [47]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 288, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 712 + ], + "type": "text", + "content": "However, the generation process for diffusion models can be slow due to the need for an iterative noise estimation of 50" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 213, + 548, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 213, + 548, + 406 + ], + "spans": [ + { + "bbox": [ + 304, + 213, + 548, + 406 + ], + "type": "text", + "content": "to 1,000 time steps [13, 42] using complex neural networks. While previous state-of-the-art approaches (e.g., GANs) are able to generate multiple images in under 1 second, it normally takes several seconds for a diffusion model to sample a single image. Consequently, speeding up the image generation process becomes an important step toward broadening the applications of diffusion models. Previous work has been solving this problem by finding shorter, more effective sampling trajectories [42, 30, 39, 22, 1, 24], which reduces the number of steps in the denoising process. However, they have largely ignored another important factor: the noise estimation model used in each iteration itself is compute- and memory-intensive. This is an orthogonal factor to the repetitive sampling, which not only slows down the inference speed of diffusion models, but also poses crucial challenges in terms of high memory footprints." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 409, + 548, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 409, + 548, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 409, + 548, + 590 + ], + "type": "text", + "content": "This work explores the quantization [50, 8, 49, 7, 29] of the noise estimation model used in the diffusion model to accelerate the denoising of all time steps. Specifically, we propose exploring post-training quantization (PTQ) on the diffusion model. PTQ has already been well studied in other learning domains like classification and object detection [4, 2, 20, 11, 23], and has been considered a go-to compression method given its minimal requirement for training data and the straightforward deployment on real hardware devices. However, the iterative computation process of the diffusion model and the model architecture of the noise estimation network brings unique challenges to the PTQ of diffusion models. PTQ4DM [41] presents an inaugural application of PTQ to compress diffusion models down to 8-bit, but it primarily focuses on smaller datasets and lower resolutions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 550, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 550, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 550, + 715 + ], + "type": "text", + "content": "Our work, evolving concurrently with [41], offers a comprehensive analysis of the novel challenges of performing PTQ on diffusion models. Specifically, as visualized in Figure 1(a), we discover that the output distribution of the noise estimation network at each time step can be largely different, and naively applying previous PTQ calibration methods with an arbitrary time step leads to poor performance. Furthermore, as illustrated in Figure 1(b), the iterative inference of the noise estimation network leads to an accumulation of quantization error, which poses higher demands on design-" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "17535" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 74, + 66, + 306, + 248 + ], + "blocks": [ + { + "bbox": [ + 74, + 66, + 306, + 248 + ], + "lines": [ + { + "bbox": [ + 74, + 66, + 306, + 248 + ], + "spans": [ + { + "bbox": [ + 74, + 66, + 306, + 248 + ], + "type": "image", + "image_path": "da7b51ccc505d7d59f7ae73ae25bedd841c663fb6b3714d2e40a47b40792b4c5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 259, + 545, + 332 + ], + "lines": [ + { + "bbox": [ + 46, + 259, + 545, + 332 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 545, + 332 + ], + "type": "text", + "content": "Figure 1: Conventional PTQ scenarios and Q-Diffusion differ in (a) calibration dataset creation and (b) model inference workflow. Traditional PTQ approaches sample data randomly [11], synthesize with statistics in model layers [4], or draw from the training set to create calibration dataset [28, 20], which either contains inconsistency with real inputs during the inference time or are not data-free. In contrast, Q-Diffusion constructed calibration datasets with inputs that are an accurate reflection of data seen during the production in a data-free manner. Traditional PTQ inference only needs to go through the quantized model " + }, + { + "bbox": [ + 46, + 259, + 545, + 332 + ], + "type": "inline_equation", + "content": "\\theta_q" + }, + { + "bbox": [ + 46, + 259, + 545, + 332 + ], + "type": "text", + "content": " one time, while Q-Diffusion needs to address the accumulated quantization errors in the multi-time step inference." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 319, + 64, + 516, + 251 + ], + "blocks": [ + { + "bbox": [ + 319, + 64, + 516, + 251 + ], + "lines": [ + { + "bbox": [ + 319, + 64, + 516, + 251 + ], + "spans": [ + { + "bbox": [ + 319, + 64, + 516, + 251 + ], + "type": "image", + "image_path": "ff529693cfe2a2c7b812150f166da8dfb5e460a764ab61715fc8b389baf421e9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 344, + 286, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 344, + 286, + 367 + ], + "spans": [ + { + "bbox": [ + 46, + 344, + 286, + 367 + ], + "type": "text", + "content": "ing novel quantization schemes and calibration objectives for the noise estimation network." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 368, + 287, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 368, + 287, + 523 + ], + "spans": [ + { + "bbox": [ + 46, + 368, + 287, + 523 + ], + "type": "text", + "content": "To address these challenges, we propose Q-Diffusion, a PTQ solution to compress the cumbersome noise estimation network in diffusion models in a data-free manner, while maintaining comparable performance to the full precision counterparts. We propose a time step-aware calibration data sampling mechanism from the pretrained diffusion model, which represents the activation distribution of all time steps. We further tailor the design of the calibration objective and the weight and activation quantizer to the commonly used noise estimation model architecture to reduce quantization error. We perform thorough ablation studies to verify our design choices, and demonstrate good generation results with diffusion models quantized to only 4 bits." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 524, + 200, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 524, + 200, + 534 + ], + "spans": [ + { + "bbox": [ + 59, + 524, + 200, + 534 + ], + "type": "text", + "content": "In summary, our contributions are:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 544, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 55, + 544, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 544, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 55, + 544, + 287, + 567 + ], + "type": "text", + "content": "1. We propose Q-Diffusion, a data-free PTQ solution for the noise estimation network in diffusion models." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 576, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 576, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 55, + 576, + 287, + 624 + ], + "type": "text", + "content": "2. We identify the novel challenge of performing PTQ on diffusion models as the activation distribution diversity and the quantization error accumulation across time steps via a thorough analysis." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 633, + 288, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 633, + 288, + 668 + ], + "spans": [ + { + "bbox": [ + 55, + 633, + 288, + 668 + ], + "type": "text", + "content": "3. We propose time step-aware calibration data sampling to improve calibration quality, and propose a specialized quantizer for the noise estimation network." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 54, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 54, + 677, + 288, + 713 + ], + "type": "text", + "content": "4. Extensive results show Q-Diffusion enables W4A8 PTQ for both pixel-space and latent-space unconditional diffusion models with an FID increment of only" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 324, + 344, + 547, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 344, + 547, + 380 + ], + "spans": [ + { + "bbox": [ + 324, + 344, + 547, + 380 + ], + "type": "text", + "content": "0.39-2.34 over full precision models. It can also produce qualitatively comparable images when plugged into Stable Diffusion [34] for text-guided synthesis." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 392, + 390, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 392, + 390, + 403 + ], + "spans": [ + { + "bbox": [ + 306, + 392, + 390, + 403 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 412, + 546, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 412, + 546, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 412, + 546, + 460 + ], + "type": "text", + "content": "Diffusion Models. Diffusion models generate images through a Markov chain, as illustrated in Figure 2. A forward diffusion process adds Gaussian noise to data " + }, + { + "bbox": [ + 305, + 412, + 546, + 460 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0 \\sim q(\\mathbf{x})" + }, + { + "bbox": [ + 305, + 412, + 546, + 460 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 305, + 412, + 546, + 460 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 305, + 412, + 546, + 460 + ], + "type": "text", + "content": " times, resulting in noisy samples " + }, + { + "bbox": [ + 305, + 412, + 546, + 460 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_1, \\dots, \\mathbf{x}_T" + }, + { + "bbox": [ + 305, + 412, + 546, + 460 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 342, + 470, + 545, + 485 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 470, + 545, + 485 + ], + "spans": [ + { + "bbox": [ + 342, + 470, + 545, + 485 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right) \\tag {1}", + "image_path": "6f1bd55e6e1af5416ba8aa9489a665c5badbbaca66ff6faef01c2d4dc27dbce8.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 495, + 547, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 495, + 547, + 530 + ], + "spans": [ + { + "bbox": [ + 305, + 495, + 547, + 530 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 495, + 547, + 530 + ], + "type": "inline_equation", + "content": "\\beta_{t} \\in (0,1)" + }, + { + "bbox": [ + 305, + 495, + 547, + 530 + ], + "type": "text", + "content": " is the variance schedule that controls the strength of the Gaussian noise in each step. When " + }, + { + "bbox": [ + 305, + 495, + 547, + 530 + ], + "type": "inline_equation", + "content": "T \\to \\infty" + }, + { + "bbox": [ + 305, + 495, + 547, + 530 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 495, + 547, + 530 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T" + }, + { + "bbox": [ + 305, + 495, + 547, + 530 + ], + "type": "text", + "content": " approaches an isotropic Gaussian distribution." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 531, + 547, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 547, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 547, + 591 + ], + "type": "text", + "content": "The reverse process removes noise from a sample from the Gaussian noise input " + }, + { + "bbox": [ + 304, + 531, + 547, + 591 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 304, + 531, + 547, + 591 + ], + "type": "text", + "content": " to gradually generate high-fidelity images. However, since the real reverse conditional distribution " + }, + { + "bbox": [ + 304, + 531, + 547, + 591 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_{t - 1}|\\mathbf{x}_t)" + }, + { + "bbox": [ + 304, + 531, + 547, + 591 + ], + "type": "text", + "content": " is unavailable, diffusion models sample from a learned conditional distribution:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 343, + 601, + 545, + 616 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 601, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 343, + 601, + 545, + 616 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\tilde {\\boldsymbol {\\mu}} _ {\\theta , t} \\left(\\mathbf {x} _ {t}\\right), \\tilde {\\boldsymbol {\\beta}} _ {t} \\mathbf {I}\\right). \\tag {2}", + "image_path": "0114eba03616e5a8e556ebebc6b316b47a1975d54cc5e13901e84ff284f3df8b.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 625, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 625, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 305, + 625, + 545, + 651 + ], + "type": "text", + "content": "With the reparameterization trick in [13], the mean " + }, + { + "bbox": [ + 305, + 625, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\tilde{\\mu}_{\\theta ,t}(\\mathbf{x}_t)" + }, + { + "bbox": [ + 305, + 625, + 545, + 651 + ], + "type": "text", + "content": " and variance " + }, + { + "bbox": [ + 305, + 625, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\tilde{\\beta}_t" + }, + { + "bbox": [ + 305, + 625, + 545, + 651 + ], + "type": "text", + "content": " could be derived as follows:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 348, + 659, + 545, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 659, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 348, + 659, + 545, + 685 + ], + "type": "interline_equation", + "content": "\\tilde {\\boldsymbol {\\mu}} _ {\\theta , t} \\left(\\mathbf {x} _ {t}\\right) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\mathbf {x} _ {t} - \\frac {1 - \\alpha_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\boldsymbol {\\epsilon} _ {\\theta , t}\\right) \\tag {3}", + "image_path": "25c197993299e36fcc8382c94e37b97e34fbb7b3f37b79fcd606cd76223afc3c.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 374, + 687, + 545, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 687, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 374, + 687, + 545, + 712 + ], + "type": "interline_equation", + "content": "\\tilde {\\beta} _ {t} = \\frac {1 - \\bar {\\alpha} _ {t - 1}}{1 - \\bar {\\alpha} _ {t}} \\cdot \\beta_ {t} \\tag {4}", + "image_path": "936e5696d59391778b540b9642ea6f7b7a223f0692b8ecd4e4c9171f1e88c843.jpg" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "17536" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 69, + 286, + 103 + ], + "blocks": [ + { + "bbox": [ + 50, + 69, + 286, + 103 + ], + "lines": [ + { + "bbox": [ + 50, + 69, + 286, + 103 + ], + "spans": [ + { + "bbox": [ + 50, + 69, + 286, + 103 + ], + "type": "image", + "image_path": "5224a88d6432bf1fef55014a279f934533509072d14b15c9f646c3084f323f40.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 146, + 104, + 214, + 110 + ], + "lines": [ + { + "bbox": [ + 146, + 104, + 214, + 110 + ], + "spans": [ + { + "bbox": [ + 146, + 104, + 214, + 110 + ], + "type": "text", + "content": "(a) Forward diffusion process" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 113, + 285, + 147 + ], + "blocks": [ + { + "bbox": [ + 50, + 113, + 285, + 147 + ], + "lines": [ + { + "bbox": [ + 50, + 113, + 285, + 147 + ], + "spans": [ + { + "bbox": [ + 50, + 113, + 285, + 147 + ], + "type": "image", + "image_path": "ca9fad0fc7232a4b06ecf2d676caf71b1f8339914e11ff8d6464a4c0804ec580.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 146, + 148, + 214, + 156 + ], + "lines": [ + { + "bbox": [ + 146, + 148, + 214, + 156 + ], + "spans": [ + { + "bbox": [ + 146, + 148, + 214, + 156 + ], + "type": "text", + "content": "(b) Reverse diffusion process" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 164, + 288, + 213 + ], + "lines": [ + { + "bbox": [ + 46, + 164, + 288, + 213 + ], + "spans": [ + { + "bbox": [ + 46, + 164, + 288, + 213 + ], + "type": "text", + "content": "Figure 2: The forward diffusion process (a) repeatedly adds Gaussian noise. The reverse diffusion process (b) uses a trained network to denoise from a standard Gaussian noise image in order to generate an image." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 222, + 287, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 222, + 287, + 247 + ], + "spans": [ + { + "bbox": [ + 46, + 222, + 287, + 247 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 222, + 287, + 247 + ], + "type": "inline_equation", + "content": "\\alpha_{t} = 1 - \\beta_{t}" + }, + { + "bbox": [ + 46, + 222, + 287, + 247 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 222, + 287, + 247 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_{t} = \\prod_{i=1}^{t} \\alpha_{i}" + }, + { + "bbox": [ + 46, + 222, + 287, + 247 + ], + "type": "text", + "content": ". We refer readers to [26] for a more detailed introduction." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 247, + 287, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 287, + 331 + ], + "type": "text", + "content": "In practice, the noise at each time step " + }, + { + "bbox": [ + 46, + 247, + 287, + 331 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 247, + 287, + 331 + ], + "type": "text", + "content": " are computed from " + }, + { + "bbox": [ + 46, + 247, + 287, + 331 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 46, + 247, + 287, + 331 + ], + "type": "text", + "content": " by a noise estimation model, with the same weights for all time steps. The UNet [35] dominates the design of the noise estimation model in diffusion models [42, 34, 33, 36], with some recent exploration on Transformer [32]. This work designs the PTQ method for the acceleration of the noise estimation model, especially for the common UNet." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 331, + 288, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 288, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 288, + 474 + ], + "type": "text", + "content": "Accelerated diffusion process. Related methods include simulating the diffusion process in fewer steps by generalizing it to a non-Markovian process [42], adjusting the variance schedule [30], and the use of high-order solvers to approximate diffusion generation [22, 1, 24, 25]. Others have employed the technique of caching and reusing feature maps [19]. Efforts to distill the diffusion model into fewer time steps have also been undertaken [39, 27], which have achieved notable success but involve an extremely expensive retraining process. Our work focuses on accelerating the noise estimation model inference in each step, with a training-free PTQ process." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 475, + 288, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 288, + 522 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 288, + 522 + ], + "type": "text", + "content": "Post-training Quantization. Post-training quantization (PTQ) compresses deep neural networks by rounding elements " + }, + { + "bbox": [ + 46, + 475, + 288, + 522 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 475, + 288, + 522 + ], + "type": "text", + "content": " to a discrete set of values [10], where the quantization and de-quantization can be formulated as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 94, + 529, + 287, + 552 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 529, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 94, + 529, + 287, + 552 + ], + "type": "interline_equation", + "content": "\\hat {w} = \\mathrm {s} \\cdot \\operatorname {c l i p} \\left(\\operatorname {r o u n d} \\left(\\frac {w}{s}\\right), c _ {\\min }, c _ {\\max }\\right), \\tag {5}", + "image_path": "8479c26aa3e3fb83fdea195be7666fa309c22272d844228270c53606d889e8db.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 558, + 287, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 630 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 630 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 558, + 287, + 630 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 558, + 287, + 630 + ], + "type": "text", + "content": " denotes the quantization scale parameters, " + }, + { + "bbox": [ + 46, + 558, + 287, + 630 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{min}}" + }, + { + "bbox": [ + 46, + 558, + 287, + 630 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 558, + 287, + 630 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{max}}" + }, + { + "bbox": [ + 46, + 558, + 287, + 630 + ], + "type": "text", + "content": " are the lower and upper bounds for the clipping function " + }, + { + "bbox": [ + 46, + 558, + 287, + 630 + ], + "type": "inline_equation", + "content": "\\mathrm{clip}(\\cdot)" + }, + { + "bbox": [ + 46, + 558, + 287, + 630 + ], + "type": "text", + "content": ". These parameters can be calibrated with the weight and activation distribution estimated in the PTQ process. The operator round(\\cdot) represents rounding, which can be either rounding-to-nearest [46, 4] or adaptive rounding [20]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "Previous PTQ research in classification and detection tasks focused on the calibration objective and the acquisition of calibration data. For example, EasyQuant [46] determines appropriate " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{min}}" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{max}}" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": " based on training data, and BRECQ [20] introduces Fisher information into the objective. ZeroQ [4] employs a distillation technique to generate proxy input images for PTQ, and SQuant [11] uses" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": "random samples with objectives based on sensitivity determined through the Hessian spectrum. For diffusion model quantization, a training dataset is not needed as the calibration data can be constructed by sampling the full-precision model with random inputs. However, the multi-time step inference of the noise estimation model brings new challenges in modeling the activation distribution. In parallel to our work, PTQ4DM [41] introduces the method of Normally Distributed Time-step Calibration, generating calibration data across all time steps with a specific distribution. Nevertheless, their explorations remain confined to lower resolutions, 8-bit precision, floating-point attention activation-to-activation matmuls, and with limited ablation study on other calibration schemes. This results in worse applicability of their method to lower precisions (see Appendix). Our work delves into the implications of calibration dataset creation in a holistic manner, establishing an efficient calibration objective for diffusion models. We fully quantize act-to-act matmuls, validated by experiments involving both pixel-space and latent-space diffusion models on large-scale datasets up to resolutions of " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 335, + 361, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 335, + 361, + 346 + ], + "spans": [ + { + "bbox": [ + 306, + 335, + 361, + 346 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 355, + 547, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 355, + 547, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 547, + 475 + ], + "type": "text", + "content": "We present our method for post-training quantization of diffusion models in this section. Different from conventionally studied deep learning models and tasks such as CNNs and VITs for classification and detection, diffusion models are trained and evaluated in a distinctive multi-step manner with a unique UNet architecture. This presents notable challenges to the PTQ process. We analyze the challenges brought by the multi-step inference process and the UNet architecture in Section 3.1 and 3.2 respectively and describe the full Q-Diffusion PTQ pipeline in Section 3.3." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 483, + 528, + 496 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 483, + 528, + 496 + ], + "spans": [ + { + "bbox": [ + 306, + 483, + 528, + 496 + ], + "type": "text", + "content": "3.1. Challenges under the Multi-step Denoising" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 502, + 547, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 547, + 563 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 547, + 563 + ], + "type": "text", + "content": "We identify two major challenges in quantizing models that employ multi-step inference process. Namely, we investigate the accumulation of quantization error across time steps and the difficulty of sampling a small calibration dataset to reduce the quantization error at each time step." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "Challenge 1: Quantization errors accumulate across time steps. Performing quantization on a neural network model introduces noise on the weight and activation of the well-trained model, leading to quantization errors in each layer's output. Previous research has identified that quantization errors are likely to accumulate across layers [5], making deeper neural networks harder to quantize. In the case of diffusion models, at any time step " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": ", the input of the denoising model (denoted as " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": ") is derived by " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{t+1}" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": ", the output of the model at the previous time step " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "t+1" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " (as depicted by Equation 2). This process effectively multiplies the number of layers involved in the computation by the number of de" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17537" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 72, + 272, + 186 + ], + "blocks": [ + { + "bbox": [ + 61, + 72, + 272, + 186 + ], + "lines": [ + { + "bbox": [ + 61, + 72, + 272, + 186 + ], + "spans": [ + { + "bbox": [ + 61, + 72, + 272, + 186 + ], + "type": "image", + "image_path": "7a13bcbf9683434d92db803b95d4b212fe5f7010a07730acab221dbe9d42ad1a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 198, + 287, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 198, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 287, + 258 + ], + "type": "text", + "content": "Figure 3: MSE between FP32 outputs and weight-quantized outputs of different precisions with Linear Quantization and our approach across time steps. Here the data is obtained by passing a batch with 64 samples through a model trained on CIFAR-10 [17] with DDIM sampling steps 100." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 61, + 268, + 266, + 395 + ], + "blocks": [ + { + "bbox": [ + 61, + 268, + 266, + 395 + ], + "lines": [ + { + "bbox": [ + 61, + 268, + 266, + 395 + ], + "spans": [ + { + "bbox": [ + 61, + 268, + 266, + 395 + ], + "type": "image", + "image_path": "c0a7e41022b3249801c9b6f5996acd95845572a359b129e9702032dc588f4832.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 409, + 287, + 458 + ], + "lines": [ + { + "bbox": [ + 46, + 409, + 287, + 458 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 287, + 458 + ], + "type": "text", + "content": "Figure 4: Effects of time steps in calibration dataset creation on 4-bit weights quantization results with DDIM on CIFAR-10. First " + }, + { + "bbox": [ + 46, + 409, + 287, + 458 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 409, + 287, + 458 + ], + "type": "text", + "content": ", Mid " + }, + { + "bbox": [ + 46, + 409, + 287, + 458 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 409, + 287, + 458 + ], + "type": "text", + "content": ", Last " + }, + { + "bbox": [ + 46, + 409, + 287, + 458 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 409, + 287, + 458 + ], + "type": "text", + "content": " denotes that 5120 samples are selected uniformly from the first, middle, last " + }, + { + "bbox": [ + 46, + 409, + 287, + 458 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 409, + 287, + 458 + ], + "type": "text", + "content": " time steps." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 465, + 287, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 465, + 287, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 465, + 287, + 501 + ], + "type": "text", + "content": "noising steps for the input " + }, + { + "bbox": [ + 46, + 465, + 287, + 501 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 46, + 465, + 287, + 501 + ], + "type": "text", + "content": " at time step " + }, + { + "bbox": [ + 46, + 465, + 287, + 501 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 465, + 287, + 501 + ], + "type": "text", + "content": ", leading to an accumulation of quantization errors towards later steps in the denoising process." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 502, + 287, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 502, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 46, + 502, + 287, + 633 + ], + "type": "text", + "content": "We run the denoising process of DDIM [42] on CIFAR-10 [17] with a sampling batch size of 64, and compare the MSE differences between the full-precision model and the model quantized to INT8, INT5, and INT4 at each time step. As shown in Figure 3, there is a dramatic increase in the quantization errors when the model is quantized to 4-bit, and the errors accumulate quickly through iterative denoising. This brings difficulty in preserving the performance after quantizing the model down to low precision, which requires the reduction of quantization errors at all time steps as much as possible." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": "Challenge 2: Activation distributions vary across time steps. To reduce the quantization errors at each time step, previous PTQ research [28, 20] calibrates the clipping range and scaling factors of the quantized model with a small set of calibration data. The calibration data should be sampled to resemble the true input distribution so that the activation dis" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "content": "The distribution of the model can be estimated correctly for proper calibration. Given that the Diffusion model uses the same noise estimation network to take inputs from all time steps, determining the data sampling policy across different time steps becomes an outstanding challenge. Here we start by analyzing the output activation distribution of the UNet model across different time steps. We conduct the same CIFAR-10 experiment using DDIM with 100 denoising steps, and draw the activations ranges of 1000 random samples among all time steps. As Figure 5 shows, the activation distributions gradually change, with neighboring time steps being similar and distant ones being distinctive. This is also echoed by the visualized " + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "content": " in Figure 2." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 228, + 546, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 546, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 546, + 540 + ], + "type": "text", + "content": "The fact that the output activations distribution varies across time steps further brings challenges to quantization. Calibrating the noise estimation model using only a few time steps that do not reflect the full range of activations seen among all time steps by the noise estimation model during the denoising process can cause overfitting to the activation distribution described by those specific time steps, while not generalizing to other time steps, which hurts the overall performance. For instance, here we try to calibrate the quantized DDIM on the CIFAR-10 dataset with data sampled from different parts of the denoising process. As shown in Figure 4, if we simply take 5120 samples from time steps that fall into a certain stage of the denoising process, significant performance drops will be induced under 4-bit weights quantization. Note that the case with samples taken from the middle 50 time steps caused smaller drops compared to cases with samples taken from either the first or the last " + }, + { + "bbox": [ + 304, + 228, + 546, + 540 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 228, + 546, + 540 + ], + "type": "text", + "content": " time steps, and with " + }, + { + "bbox": [ + 304, + 228, + 546, + 540 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 228, + 546, + 540 + ], + "type": "text", + "content": " increases, the drops are also alleviated. These results illustrate the gradual \"denoising\" process as depicted in Figure 5: the activations distribution changes gradually throughout time steps, with the middle part capturing the full range to some degree, while parts of the distant endpoints differing the most. To recover the performance of the quantized diffusion models, we need to select calibration data in a way that comprehensively takes into account the distributions of the output of different time steps." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 550, + 544, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 550, + 544, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 550, + 544, + 574 + ], + "type": "text", + "content": "3.2. Challenges on Noise Estimation Model Quantization" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": "Most diffusion models (Imagen [36], Stable Diffusion [34], VDMs [14]) adopt UNets as denoising backbones that downsample and upsample latent features. Although recent studies show that transformer architectures are also capable of serving as the noise estimation backbone [32], convolutional UNets are still the de facto choice of architecture today. UNets utilize shortcut layers to merge concatenated deep and shallow features and transmit them to subsequent layers. Through our analysis presented in Figure 6, we observe that input activations in shortcut layers exhibit abnormal value ranges in comparison to other layers." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17538" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 86, + 67, + 509, + 159 + ], + "blocks": [ + { + "bbox": [ + 86, + 67, + 509, + 159 + ], + "lines": [ + { + "bbox": [ + 86, + 67, + 509, + 159 + ], + "spans": [ + { + "bbox": [ + 86, + 67, + 509, + 159 + ], + "type": "image", + "image_path": "924496e879da1b129aa92becbafb5799fc5bcc820a975764e330ae14ace14da0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 103, + 169, + 489, + 182 + ], + "lines": [ + { + "bbox": [ + 103, + 169, + 489, + 182 + ], + "spans": [ + { + "bbox": [ + 103, + 169, + 489, + 182 + ], + "type": "text", + "content": "Figure 5: Activation ranges of " + }, + { + "bbox": [ + 103, + 169, + 489, + 182 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 103, + 169, + 489, + 182 + ], + "type": "text", + "content": " across all 100 time steps of FP32 DDIM model on CIFAR-10." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 202, + 287, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 202, + 287, + 227 + ], + "spans": [ + { + "bbox": [ + 46, + 202, + 287, + 227 + ], + "type": "text", + "content": "Notably, the input activations in DDIM's shortcut layers can be up to 200 times larger than other neighboring layers." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 227, + 289, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 227, + 289, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 227, + 289, + 335 + ], + "type": "text", + "content": "To analyze the reason for this, we visualize the weight and activation tensor of a DDIM shortcut layer. As demonstrated in the dashed box in Figure 6, the ranges of activations from the deep feature channels " + }, + { + "bbox": [ + 46, + 227, + 289, + 335 + ], + "type": "inline_equation", + "content": "(X_{1})" + }, + { + "bbox": [ + 46, + 227, + 289, + 335 + ], + "type": "text", + "content": " and shallow feature channels " + }, + { + "bbox": [ + 46, + 227, + 289, + 335 + ], + "type": "inline_equation", + "content": "(X_{2})" + }, + { + "bbox": [ + 46, + 227, + 289, + 335 + ], + "type": "text", + "content": " being concatenated together vary significantly, which also resulted in a bimodal weight distribution in the corresponding channels (see also Figure 7). Naively quantizing the entire weight and activation distribution with the same quantizer will inevitably lead to large quantization errors." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 344, + 287, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 344, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 47, + 344, + 287, + 357 + ], + "type": "text", + "content": "3.3. Post-Training Quantization of Diffusion Model" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 363, + 289, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 289, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 289, + 400 + ], + "type": "text", + "content": "We propose two techniques: time step-aware calibration data sampling and shortcut-splitting quantization to tackle the challenges identified in the previous sections respectively." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 418, + 200, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 418, + 200, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 418, + 200, + 430 + ], + "type": "text", + "content": "3.3.1 Time step-aware calibration" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 437, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 557 + ], + "type": "text", + "content": "Since the output distributions of consecutive time steps are often very similar, we propose to randomly sample intermediate inputs uniformly in a fixed interval across all time steps to generate a small calibration set. This effectively balances the size of the calibration set and its representation ability of the distribution across all time steps. Empirically, we have found that the sampled calibration data can recover most of the INT4 quantized models' performance after the calibration, making it an effective sampling scheme for calibration data collection for quantization error correction." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": "To calibrate the quantized model, we divide the model into several reconstruction blocks [20], and iteratively reconstruct outputs and tune the clipping range and scaling factors of weight quantizers in each block with adaptive rounding [28] to minimize the mean squared errors between the quantized and full precision outputs. We define a core component that contains residual connections in the diffusion model UNet as a block, such as a Residual Bottleneck Block or a Transformer Block. Other parts of the model that do not satisfy this condition are calibrated in a per-layer manner. This technique has been shown to improve the performance compared to fully layer-by-layer calibration since it addresses the inter-layer dependencies and generalization" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 202, + 547, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 202, + 547, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 202, + 547, + 263 + ], + "type": "text", + "content": "better [20]. For activation quantization, since activations are constantly changing during inference, doing adaptive rounding is infeasible. Therefore, we only adjust the step sizes of activation quantizers according to [9]. 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" + }, + { + "bbox": [ + 47, + 545, + 287, + 618 + ], + "type": "inline_equation", + "content": "c_1" + }, + { + "bbox": [ + 47, + 545, + 287, + 618 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 545, + 287, + 618 + ], + "type": "inline_equation", + "content": "c_2" + }, + { + "bbox": [ + 47, + 545, + 287, + 618 + ], + "type": "text", + "content": " are determined by the concatenation operation. " + }, + { + "bbox": [ + 47, + 545, + 287, + 618 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}(\\cdot)" + }, + { + "bbox": [ + 47, + 545, + 287, + 618 + ], + "type": "text", + "content": " denotes the quantization operator and " + }, + { + "bbox": [ + 47, + 545, + 287, + 618 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 47, + 545, + 287, + 618 + ], + "type": "text", + "content": " denotes the concatenation operator." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 628, + 128, + 640 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 628, + 128, + 640 + ], + "spans": [ + { + "bbox": [ + 47, + 628, + 128, + 640 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 647, + 159, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 159, + 661 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 159, + 661 + ], + "type": "text", + "content": "4.1. Experiments Setup" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": "In this section, we evaluate the proposed Q-Diffusion framework on pixel-space diffusion model DDPM [13] and latent-space diffusion model Latent Diffusion [34] for unconditional image generation. We also visualize the images" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 438, + 547, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 547, + 571 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 547, + 571 + ], + "type": "text", + "content": "generated by Q-Diffusion on Stable Diffusion. To the best of our knowledge, there is currently no published work done on diffusion model quantization. Therefore, we report the basic channel-wise round-to-nearest Linear Quantization (i.e., Equation 5) as a baseline. We also re-implement the state-of-the-art data-free PTQ method SQuant [11] and include the results for comparison. Furthermore, we apply our approach to text-guided image synthesis with Stable Diffusion [34]. Experiments show that our approach can achieve competitive generation quality to the full-precision scenario on all tasks, even under INT4 quantization for weights." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 585, + 451, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 585, + 451, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 585, + 451, + 597 + ], + "type": "text", + "content": "4.2. Unconditional Generation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": "We conducted evaluations using the " + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": " CIFAR-10 [17], " + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": " LSUN Bedrooms, and " + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": " LSUN Church-Outdoor [48]. We use the pretrained DDIM sampler [42] with 100 denoising time steps for CIFAR-10 experiments and Latent Diffusion (LDM) [34] for the higher resolution LSUN experiments. We evaluated the performance in terms of Frechet Inception Distance (FID) [12] and additionally evaluated the Inception Score (IS) [38] for CIFAR-10 results, since IS is not an accurate reference for datasets that" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "17540" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 91, + 168, + 210 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 145, + 87 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 145, + 87 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 145, + 87 + ], + "type": "text", + "content": "Bedroom Q-Diffusion (W4A8)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 49, + 91, + 168, + 210 + ], + "lines": [ + { + "bbox": [ + 49, + 91, + 168, + 210 + ], + "spans": [ + { + "bbox": [ + 49, + 91, + 168, + 210 + ], + "type": "image", + "image_path": "1b402ef003af78d7a417a34d3dc6331f80d1295899bec2d31a162d535d687f55.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 213, + 545, + 225 + ], + "lines": [ + { + "bbox": [ + 47, + 213, + 545, + 225 + ], + "spans": [ + { + "bbox": [ + 47, + 213, + 545, + 225 + ], + "type": "text", + "content": "Figure 8: " + }, + { + "bbox": [ + 47, + 213, + 545, + 225 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 47, + 213, + 545, + 225 + ], + "type": "text", + "content": " unconditional image generation results using Q-Diffusion and Linear Quantization under W4A8 precision." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 173, + 91, + 293, + 210 + ], + "blocks": [ + { + "bbox": [ + 185, + 70, + 282, + 87 + ], + "lines": [ + { + "bbox": [ + 185, + 70, + 282, + 87 + ], + "spans": [ + { + "bbox": [ + 185, + 70, + 282, + 87 + ], + "type": "text", + "content": "Bedroom Linear Quantization (W4A8)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 173, + 91, + 293, + 210 + ], + "lines": [ + { + "bbox": [ + 173, + 91, + 293, + 210 + ], + "spans": [ + { + "bbox": [ + 173, + 91, + 293, + 210 + ], + "type": "image", + "image_path": "ec5ae5a0f63de2d42b58a65d5d1133b2726cd31ee8ebda6954975d7527fa0057.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 298, + 91, + 417, + 209 + ], + "blocks": [ + { + "bbox": [ + 324, + 70, + 391, + 87 + ], + "lines": [ + { + "bbox": [ + 324, + 70, + 391, + 87 + ], + "spans": [ + { + "bbox": [ + 324, + 70, + 391, + 87 + ], + "type": "text", + "content": "Church Q-Diffusion (W4A8)" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 298, + 91, + 417, + 209 + ], + "lines": [ + { + "bbox": [ + 298, + 91, + 417, + 209 + ], + "spans": [ + { + "bbox": [ + 298, + 91, + 417, + 209 + ], + "type": "image", + "image_path": "763cef04e103078f997a271e1b021cc8b798e75172a0060f55cc24346334d4d3.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 423, + 91, + 542, + 210 + ], + "blocks": [ + { + "bbox": [ + 437, + 70, + 528, + 87 + ], + "lines": [ + { + "bbox": [ + 437, + 70, + 528, + 87 + ], + "spans": [ + { + "bbox": [ + 437, + 70, + 528, + 87 + ], + "type": "text", + "content": "Church Linear Quantization (W4A8)" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 423, + 91, + 542, + 210 + ], + "lines": [ + { + "bbox": [ + 423, + 91, + 542, + 210 + ], + "spans": [ + { + "bbox": [ + 423, + 91, + 542, + 210 + ], + "type": "image", + "image_path": "d4f7b28b947f2ef355871aacf488353384493bac45c66cfa1ab3ef44d3ba9307.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 61, + 278, + 272, + 439 + ], + "blocks": [ + { + "bbox": [ + 47, + 250, + 288, + 274 + ], + "lines": [ + { + "bbox": [ + 47, + 250, + 288, + 274 + ], + "spans": [ + { + "bbox": [ + 47, + 250, + 288, + 274 + ], + "type": "text", + "content": "Table 1: Quantization results for unconditional image generation with DDIM on CIFAR-10 " + }, + { + "bbox": [ + 47, + 250, + 288, + 274 + ], + "type": "inline_equation", + "content": "(32\\times 32)" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 278, + 272, + 439 + ], + "lines": [ + { + "bbox": [ + 61, + 278, + 272, + 439 + ], + "spans": [ + { + "bbox": [ + 61, + 278, + 272, + 439 + ], + "type": "table", + "html": "
MethodBits (W/A)Size (Mb)GBopsFID↓IS↑
Full Precision32/32143.265974.229.12
Linear Quant8/3235.822944.718.93
SQuant8/3235.822944.618.99
Q-Diffusion8/3235.822944.279.15
Linear Quant4/3217.91147141.474.20
SQuant4/3217.91147160.402.91
Q-Diffusion4/3217.911475.098.78
Linear Quant8/835.8798118.265.23
SQuant8/835.8798464.691.17
Q-Diffusion8/835.87983.759.48
Linear Quant4/817.9399188.112.45
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Q-Diffusion4/817.93994.939.12
", + "image_path": "59a284ecfe3374b971d467e171ecc89095e1ff8912dd9cc13eab4d3ace0fec2b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 445, + 288, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 288, + 493 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 288, + 493 + ], + "type": "text", + "content": "differ significantly from ImageNet's domain and categories. The results are reported in Table 1-3 and Figure 8, where Bops is calculated for one denoising step without considering the decoder compute cost for latent diffusion." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 494, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 287, + 625 + ], + "type": "text", + "content": "The experiments show that Q-Diffusion significantly preserves the image generation quality and outperforms Linear Quantization by a large margin for all resolutions and types of diffusion models tested when the number of bits is low. Although 8-bit weight quantization has almost no performance loss compared to FP32 for both Linear Quantization and our approach, the generation quality with Linear Quantization drops drastically under 4-bit weight quantization. In contrast, Q-Diffusion still preserves most of the perceptual quality with at most 2.34 increase in FID and imperceptible distortions in produced samples." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 634, + 213, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 213, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 213, + 647 + ], + "type": "text", + "content": "4.3. Text-guided Image Generation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "We evaluate Q-Diffusion on Stable Diffusion pretrained on subsets of " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": " LAION-5B for text-guided image generation. Following [34], we sample text prompts from the MS-COCO [21] dataset to generate a calibration dataset with texts condition using Algorithm 1. In this work, we fix" + } + ] + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 319, + 289, + 531, + 460 + ], + "blocks": [ + { + "bbox": [ + 305, + 250, + 547, + 285 + ], + "lines": [ + { + "bbox": [ + 305, + 250, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 305, + 250, + 547, + 285 + ], + "type": "text", + "content": "Table 2: Quantization results for unconditional image generation with LDM-4 on LSUN-Bedrooms (256 × 256). The downsampling factor for the latent space is 4." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 319, + 289, + 531, + 460 + ], + "lines": [ + { + "bbox": [ + 319, + 289, + 531, + 460 + ], + "spans": [ + { + "bbox": [ + 319, + 289, + 531, + 460 + ], + "type": "table", + "html": "
MethodBits (W/A)Size (Mb)TBopsFID↓
Full Precision32/321096.2107.172.98
Linear Quant8/32274.137.283.02
SQuant8/32274.137.282.94
Q-Diffusion8/32274.137.282.97
Linear Quant4/32137.018.6482.69
SQuant4/32137.018.64149.97
Q-Diffusion4/32137.018.644.86
Linear Quant8/8274.112.976.69
SQuant8/8274.112.974.92
Q-Diffusion8/8274.112.974.40
Linear Quant4/8137.06.4824.86
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Q-Diffusion4/8137.06.485.32
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MethodBits (W/A)Size (Mb)TBopsFID↓
Full Precision32/321179.922.174.06
Linear Quant8/32295.010.733.84
SQuant8/32295.010.734.01
Q-Diffusion8/32295.010.734.03
Linear Quant4/32147.55.3632.54
SQuant4/32147.55.3633.77
Q-Diffusion4/32147.55.364.45
Linear Quant8/8295.02.6814.62
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Q-Diffusion8/8295.02.683.65
Linear Quant4/8147.51.3414.92
SQuant4/8147.51.3424.50
Q-Diffusion4/8147.51.344.12
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Qualitative results are shown in Figure 9. Compared to Linear Quantization, our Q-Diffusion provides higher-quality images with more realistic details and better demonstration of the semantic information. Similar performance gain is also observed in other random samples showcased in Appendix, and quantitatively reported in Appendix. The output of the W4A8 Q-Diffusion model largely resembles the output of the full precision model. Interestingly, we find some diversity in the lower-level semantics between the Q-Diffusion model and the FP models, like the heading of the horse or the shape of the hat. We leave it to future work to understand how quantization contributes to the diversity." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 392, + 141, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 392, + 141, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 141, + 406 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 58, + 418, + 268, + 574 + ], + "blocks": [ + { + "bbox": [ + 58, + 418, + 268, + 574 + ], + "lines": [ + { + "bbox": [ + 58, + 418, + 268, + 574 + ], + "spans": [ + { + "bbox": [ + 58, + 418, + 268, + 574 + ], + "type": "image", + "image_path": "593c5f505b31604228ddd1190e7c4a8922a8317656e31922b8105199c8206420.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 575, + 288, + 647 + ], + "lines": [ + { + "bbox": [ + 46, + 575, + 288, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 575, + 288, + 647 + ], + "type": "text", + "content": "Figure 10: Uniform sampling strategies which cover all time steps are better than strategies that cover only a part of the time steps, as in Fig. 4. Furthermore, adjusting the sampling techniques within uniform sampling, such as tuning the sampling interval and the number of samples, has a marginal effect on the performance of the quantized model." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "content": "Effects of Sampling Strategies To analyze the effects of different sampling strategies for calibration in detail, we implemented multiple variants of our method using different sampling strategies. We then evaluated the quality of the models quantized by each variant. We experimented" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 219, + 547, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 219, + 547, + 362 + ], + "spans": [ + { + "bbox": [ + 304, + 219, + 547, + 362 + ], + "type": "text", + "content": "with varying numbers of time steps used for sampling and samples used for calibration. In addition to calibration sets from uniform timestep intervals, we also employed sampling at the first 50 and last 50 steps. As in Figure 10, uniform sampling that spans all time steps results in superior performance compared to sampling from only partial time steps. Furthermore, adjusting the sampling hyperparams, including using more calibration samples, does not significantly improve the performance. Therefore, we simply choose to sample uniformly every 20 steps for a total of 5,120 samples for calibration, resulting in a high-quality quantized model with low computational costs during quantization." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 363, + 547, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 547, + 423 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 547, + 423 + ], + "type": "text", + "content": "We also conduct ablation experiments to explore the effectiveness of several non-uniform calibration data sampling schemes, such as using Unsupervised Selecting Labeling (USL) [45] to select both representative and diverse calibration samples. We present the results in Appendix." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 440, + 547, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 440, + 547, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 440, + 547, + 536 + ], + "type": "text", + "content": "Effects of Split Previous linear quantization approaches suffer from severe performance degradation as shown in Figure 11, where 4-bit weight quantization achieves a high FID of 141.47 in DDIM CIFAR-10 generation. Employing additional 8-bit activation quantization further degrades the performance (FID: 188.11). By splitting shortcuts in quantization, we significantly improve the generation performance, achieving an FID of 4.93 on W4A8 quantization." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 540, + 379, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 379, + 553 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 379, + 553 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 560, + 547, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 560, + 547, + 657 + ], + "spans": [ + { + "bbox": [ + 304, + 560, + 547, + 657 + ], + "type": "text", + "content": "This work studies the use of quantization to accelerate and reduce the memory usage of diffusion models. We propose Q-Diffusion, a novel post-training quantization scheme that conducts calibration with multiple time steps in the denoising process and achieves significant improvements in the performance of the quantized model. Q-Diffusion models under 4-bit quantization achieve comparable results to the full precision models." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 669, + 404, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 404, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 404, + 682 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "content": "We thank Berkeley Deep Drive, Intel Corporation, Panasonic, and NVIDIA for supporting this research. We also" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17542" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 95, + 272, + 224 + ], + "blocks": [ + { + "bbox": [ + 82, + 74, + 277, + 83 + ], + "lines": [ + { + "bbox": [ + 82, + 74, + 277, + 83 + ], + "spans": [ + { + "bbox": [ + 82, + 74, + 277, + 83 + ], + "type": "text", + "content": "Linear Quantization + Calibration + Split shortcuts" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 51, + 95, + 272, + 224 + ], + "lines": [ + { + "bbox": [ + 51, + 95, + 272, + 224 + ], + "spans": [ + { + "bbox": [ + 51, + 95, + 272, + 224 + ], + "type": "image", + "image_path": "631055b526ddb7e6675fc1fa0384bef5edc5cf21f88baae8df31d6d8526322d8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 234, + 288, + 294 + ], + "lines": [ + { + "bbox": [ + 46, + 234, + 288, + 294 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 288, + 294 + ], + "type": "text", + "content": "Figure 11: Splitting the shortcut convolution is crucial for both weight and activation quantization. Comparisons on CIFAR-10 show that Q-Diffusion could achieve comparable image generation quality to the model with full precision (dashed line) with shortcut splitting." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 52, + 299, + 282, + 417 + ], + "blocks": [ + { + "bbox": [ + 52, + 299, + 282, + 417 + ], + "lines": [ + { + "bbox": [ + 52, + 299, + 282, + 417 + ], + "spans": [ + { + "bbox": [ + 52, + 299, + 282, + 417 + ], + "type": "image", + "image_path": "b9d3d8ab6937eebf5cb985780a79b64637537267fb8d97047327327a47523e9a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 424, + 288, + 485 + ], + "lines": [ + { + "bbox": [ + 46, + 424, + 288, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 288, + 485 + ], + "type": "text", + "content": "Figure 12: Examples of text-to-image generation with a quantized Stable Diffusion model. Naive linear quantization degrades the appearance of teeth, which gets fixed by shortcut splitting. 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However, the huge memory consumption of state-of-the-art models makes it hard to deploy them on vehicles, and the nontrivial latency will affect the real-time perception of streaming applications. Despite the wide application of quantization to lighten models, we show in our paper that directly applying quantization in BEV tasks will 1) make the training unstable, and 2) lead to intolerable performance degradation. To solve these issues, our method QD-BEV enables a novel view-guided distillation (VGD) objective, which can stabilize the quantization-aware training (QAT) while enhancing the model performance by leveraging both image features and BEV features. Our experiments show that QD-BEV achieves similar or even better accuracy than previous methods with significant efficiency gains. On the nuScenes datasets, the 4-bit weight and 6-bit activation quantized QD-BEV-Tiny model achieves $37.2\\%$ NDS with only 15.8 MB model size, outperforming BevFormer-Tiny by $1.8\\%$ with an $8\\times$ model compression. On the Small and Base variants, QD-BEV models also perform superbly and achieve $47.9\\%$ NDS (28.2 MB) and $50.9\\%$ NDS (32.9 MB), respectively.", + "bbox": [ + 76, + 375, + 473, + 723 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 753, + 209, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Given its potential in enabling autopilot, multi-view 3D detection based on BEV (bird-eye-view) has become", + "bbox": [ + 76, + 780, + 468, + 810 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/65d7190e406100619b395886dc2249444c87c520c510fd95b7a95bf50905d247.jpg", + "image_caption": [ + "(a) mAP curve." + ], + "image_footnote": [], + "bbox": [ + 504, + 340, + 699, + 464 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4ee11694ecc32e832afc5494f2c72da14a4d2cee7ceec0ff6b448b184ccd8b63.jpg", + "image_caption": [ + "(b) NDS curve.", + "Figure 1: Training curves of QD-BEV (with VGD) versus progressive QAT on W4A6 quantization of BEVFormer-Tiny. Note that standard QAT works even worse compared to progressive QAT and it falls out of the targeted accuracy range in the figures." + ], + "image_footnote": [], + "bbox": [ + 700, + 340, + 895, + 464 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "an important research direction for autonomous driving. Based on input sensors, previous work can be divided into LiDAR-based methods [18, 47] and camera-only methods [23, 38, 14, 13, 24, 25]. Compared to the LiDAR-based methods, camera-only methods have the merits of lower deployment cost, closer to human eyes, and easier access to visual information in the driving environment. However, even if using the camera-only methods, the computational and memory costs of running state-of-the-art BEV models are still formidable, making it difficult to deploy them onto vehicles. For example, BEVFormer-Base has a $540~\\mathrm{ms}$ inference latency (corresponds to 1.85 fps) on one NVIDIA V100 GPU, which is infeasible for real-time applications that generally require 30 fps. Since a non-trivial latency will harm the streaming perception, it is particularly crucial to explore and devise lightweight models for camera-only 3D object detection based on BEV.", + "bbox": [ + 496, + 609, + 893, + 866 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Quantization [16, 11, 42, 10] can reduce the bitwidth used to represent weights and activations in deep neural net-", + "bbox": [ + 500, + 869, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal contribution : \nzhang_yifan@smail.nju.edu.cn, zhendong@berkeley.edu \n† Corresponding authors : \nldu@nju.edu.cn, shanghang@oku.edu.cn", + "bbox": [ + 76, + 837, + 413, + 895 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3825", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3200c2b36546e2c17d6813a1aba9553b45604f481f77e137d547f51bab561213.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 89, + 92, + 883, + 324 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/93b69a2e2268f57f7d74f78e42b517b74a4533b8181533203ae624f083e1aec7.jpg", + "image_caption": [ + "Figure 2: Illustration of QD-BEV. (a) In our pipeline, multi-camera images are input into the floating-point teacher network and the quantized student network in order to compute the KL divergence in an element-wise manner. The KL divergence is used as distillation loss in the image feature and the BEV feature, respectively. Then we conduct view-guided distillation using the BEV mask obtained from the external parameters of the camera. Please refer to Sec.3.1 for more details. (b) The lower flow chart shows the computation process of the view-guided distillation loss. Specific details are in Sec. 3.3." + ], + "image_footnote": [], + "bbox": [ + 89, + 325, + 883, + 488 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "works, which can greatly save the model size and computational costs while improving the speed of model reasoning. However, directly applying quantization would lead to significant performance degradation. Compared to image classification and 2D object detection tasks where the standard quantization methods shine, multi-camera 3D detection tasks are much more complicated and difficult due to the existence of multiple views and information from multiple dimensions (for example, the temporal information and spatial information used in BEVFormer [23]). Consequently, the structure of BEV networks tends to become more complex, with a deeper convolutional neural network backbone to extract image information from multiple views, and with transformers to encode and decode the features of the BEV domain. The presence of different neural architectures, multiple objectives, and knowledge from different modalities greatly challenges the standard quantization methods, decreasing their stability and accuracy, and even making the whole training process diverge. In Figure 1, we", + "bbox": [ + 75, + 602, + 472, + 891 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "show the training curves when applying W4A6 quantization on a BEVFormer-Tiny model. As can be seen, the performance of quantization-aware training (QAT) fluctuates significantly in different epochs, while the performance of our proposed method QD-BEV shows a stable rising trend. We perform more experiments to validate the effectiveness of QD-BEV in Sec 5.", + "bbox": [ + 496, + 602, + 893, + 708 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To solve the problems of standard QAT, in this work, we first conduct systematic experiments and analyses on quantizing BEV networks. Then we devise a quantization-aware view-guided distillation method (referred to as QD-BEV) that can decently solve the stability issue while improving the final performance of compact BEV models. Our proposed view-guided distillation (VGD) can better leverage information from both the image and the BEV domains for multi-view 3D object detection. This can significantly outperform previous distillation methods that cannot jointly handle the different types of losses in BEV networks. Specifically, as shown in Figure 2, we first take", + "bbox": [ + 496, + 719, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3826", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the FP (floating-point) model as the teacher model and the quantized model as the student model, then we calculate the KL divergence on the image feature and the BEV feature, respectively. Finally, we leverage the mapping relationship and realize VGD by organically combining the image feature and the BEV feature through the camera's external parameters. Note that in QD-BEV, neither additional training data nor larger powerful teacher networks are used to tune the accuracy, but QD-BEV models are still able to outperform previous baselines while having significantly smaller model sizes and computational requirements. Our contributions are as follows:", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We conduct systematic experiments on quantizing BEV models, unveiling major issues hampering standard quantization-aware training methods on BEV.", + "- We specially design view-guided distillation (VGD) for BEV models, which jointly leverages both image domain and BEV domain information. VGD boosts the final performance while solving the stability issue of standard QAT.", + "- Our W4A6 quantized QD-BEV-Tiny has $37.2\\%$ NDS with only 15.8 MB model size, which outperforms the $8 \\times$ larger BevFormer-Tiny model by $1.8\\%$ ." + ], + "bbox": [ + 96, + 289, + 468, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 76, + 515, + 225, + 531 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Camera-only 3D object detection", + "text_level": 1, + "bbox": [ + 76, + 542, + 366, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In camera-only 3D object detection tasks, many excellent methods have emerged based on BEV (bird-eye-view). Previous works, LSS [31] and BEVDet [14], project image features to the BEV space in a bottom-up manner. Based on DETR [5] and Deformable DETR [48], DETR3D [38] extends the 2D object detection to the 3D space through the architecture of Backbone + FPN + Decoder. In addition, PETR [24] introduces 3D position coding based on DETR3D [38]. In BEVFormer [23], the authors use dense BEV queries to exchange information in the BEV space with the multi-view image space. More stable BEV features are obtained by extracting temporal and spatial information through the transformer structure with temporal self-attention and spacial cross-attention. Based on the temporal interaction in BEVFormer, further improvements have been made in recent works, PETRv2 [25] and BEVDet4D [13]. Besides the aforementioned works, BEVDepth [21] and BEVstereo [20] are two state-of-the-art approaches for monocular depth estimation and stereo vision in the birdeye-view (BEV) domain, respectively, which leverage the unique characteristics of BEV representations to achieve high accuracy and efficiency.", + "bbox": [ + 75, + 568, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Quantization", + "text_level": 1, + "bbox": [ + 500, + 90, + 637, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To reduce the model size, quantization [45, 36, 15, 26] uses low bitwidth to represent weights and activations in neural networks. With the use of low-precision matrix multiplication or convolution, quantization can also make the inference process faster and more efficient. Given a pretrained model, directly performing quantization without any fine-tuning is referred to as post-training quantization (PTQ) [4, 29, 37, 17]. Despite the merits, PTQ with low bitwidth still results in significant accuracy degradation. As such, Quantization-aware training (QAT) is proposed to train the model to better adapt to quantization. QAT methods [9, 7, 40] are more costly compared to PTQ, but can potentially obtain higher accuracy. Furthermore, in the cases with ultra-low quantization bitwidth (for example, 4-bit), even QAT cannot close the accuracy gap. A promising direction to solve this is to use mixed-precision quantization [46, 36, 39], where some sensitive layers are kept at higher precision to recover the accuracy. Though effective, the support for mixed-precision quantization on general-purpose machines (CPUs and GPUs) is currently immature and may lead to extra latency overhead.", + "bbox": [ + 496, + 119, + 893, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Although standard quantization methods have shown great results on convolutional neural networks, recent works [27, 44] mention that it may suffer in other neural architectures such as transformers. The presence of both convolutional blocks and transformers in BEV networks makes them challenging to the traditional quantization methods.", + "bbox": [ + 496, + 446, + 893, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Distillation", + "text_level": 1, + "bbox": [ + 500, + 566, + 620, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Model distillation [12, 28, 22, 32, 1] generally uses a large model as the teacher to train a compact student model. Instead of using class labels during the training of the student model, the key idea is to leverage the soft probabilities produced by the teacher to guide the student's training. Previous methods of distillation explore different knowledge sources (for example, [12, 22, 30] use logits, aka the soft probabilities). The choices of teacher models are also studied, where [41, 34] use multiple teacher models, while [8, 43] apply self-distillation without an extra teacher model. Other previous efforts apply distillation with different settings on different applications. Regarding BEV networks, previous work [6] tries to teach LiDAR information to camera-based networks through distillation, but the additional requirement for LiDAR data makes it infeasible in our pure camera-based setting. Besides, the existence of different types of losses in BEV networks makes standard distillation methods invalid. An arbitrary or sub-optimal combination of knowledge sources would also make the training unstable, perform badly, or even diverge.", + "bbox": [ + 496, + 598, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3827", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 89, + 169, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Overview of QD-BEV pipeline", + "text_level": 1, + "bbox": [ + 76, + 114, + 346, + 131 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This work aims to improve the efficiency of state-of-the-art BEV models. Starting with the widely used BEV-Former [23], we apply a progressive quantization-aware training procedure in a stage-by-stage manner (details are introduced in Sec. 3.2). We further boost its stability and performance through a novel view-guided distillation process, which is highlighted in Figure 2, where we use a floating-point teacher model to facilitate the learning of our quantized QD-BEV student model. Specifically, the input multi-camera image is entered into the teacher and the student, respectively, and then the Image Backbone and Image Neck parts of the network are used to extract the multicamera image feature. After the transformer part of the network, the BEV features are extracted, and the two parts of the teacher model and the student model are used to calculate image distill loss and BEV distill loss, respectively. The two distillation losses are then fused through the external parameters of the camera to achieve our unique view-guided distillation mechanism. We provide a detailed formulation of the view-guided distillation process in Sec. 3.3.", + "bbox": [ + 75, + 138, + 472, + 441 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Quantization-aware training", + "text_level": 1, + "bbox": [ + 76, + 450, + 334, + 467 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In symmetric linear quantization, the quantizer maps weights and activations into integers with a scale factor $S$ . Uniformly quantizing to k bit can be expressed as:", + "bbox": [ + 76, + 474, + 468, + 517 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS = \\frac {2 \\left| r _ {\\max } \\right|}{2 ^ {k} - 1}, q = \\operatorname {r o u n d} \\left(\\frac {r}{S}\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 526, + 468, + 555 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $r$ is the floating-point number being quantized, $|r_{\\mathrm{max}}|$ is the largest absolute value in $r$ , and $q$ is the quantized integer. In this work, we conduct systematic experiments to analyze the performance of quantization on BEV networks. For PTQ, we apply the above quantization directly to the pre-trained models during the inference stage. For QAT, we utilize the straight-through estimator (STE) [2] to define the forward and backward processes for the above quantization operations, and then we train the model to better adapt to quantization. As previously mentioned in Sec. 1 and Sec. 2, considering that standard QAT may lead to divergence due to the characteristics of BEV models, we apply a stage-wise progressive QAT where we gradually reduce the weight precision in four stages (backbone, neck, encoder, and decoder) based on the design of BEV-Former [23]. The performance of this progressive QAT is illustrated in Figure 3. And we compare the effectiveness of the progressive QAT with standard QAT in Sec. 4.2.2.", + "bbox": [ + 75, + 564, + 472, + 837 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. View-guided distillation", + "text_level": 1, + "bbox": [ + 76, + 845, + 295, + 862 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Compared to traditional single-domain distillation methods, our approach exploits the complementary nature of", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "both BEV and image domains, which provides different perspectives and capture different aspects of the scene. The BEV domain offers a top-down view, enabling accurate perception and recognition of the surrounding environment, such as the structure of the road, the location of vehicles, and lane markings. On the other hand, the image domain provides more realistic visual information, capturing rich scene details and color information. In the following sections, we present details of VGD: the computation of the image feature distillation in Sec. 3.3.1, the BEV feature distillation in Sec. 3.3.2, and the view-guided distillation combining the previous two distillation losses in Sec. 3.3.3.", + "bbox": [ + 496, + 90, + 893, + 272 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.1 Image feature distillation", + "text_level": 1, + "bbox": [ + 498, + 290, + 730, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a pair of aligned teacher and student models, We first compute element-wise distillation loss on image features. We extract the image neck output as the image features to be distilled. To improve the smoothness of the distillation loss, we follow previous attempts [33] to use a KL divergence-based distillation loss. Specifically, we consider the flattened image features of the student and the teacher model as logits, which we convert into probability distribution via a softmax function with temperature $\\phi_{\\tau}$ , as defined in Eq. (2).", + "bbox": [ + 496, + 311, + 890, + 439 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\phi_ {\\tau} \\left(x _ {i}\\right) = \\frac {e ^ {x _ {i} / \\tau}}{\\sum_ {j} e ^ {x _ {j} / \\tau}} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 630, + 448, + 890, + 482 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then we calculate the KL divergence of each camera's output separately to obtain the image feature distillation loss, as in Eq. (3).", + "bbox": [ + 496, + 484, + 890, + 527 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i m g} = \\frac {\\tau^ {2}}{B \\cdot W \\cdot H \\cdot C} \\times \\mathcal {D} _ {K L} \\left(\\phi_ {\\tau} \\left(F _ {i m g} ^ {T}\\right), \\phi_ {\\tau} \\left(F _ {i m g} ^ {S}\\right)\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 535, + 890, + 564 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where B stands for the batch size, W, H, C mean the width, height, and number of channels of the image features, respectively. $F_{img}^{T}$ and $F_{img}^{S}$ denote the image features of the teacher model and the student model.", + "bbox": [ + 496, + 569, + 890, + 630 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.2 BEV feature distillation", + "text_level": 1, + "bbox": [ + 500, + 648, + 718, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first convert the BEV features of the student and teacher into probability distributions, following the same procedure as for image features. Then we compute the KL divergence for each point on the BEV features, as shown in Eq. (4).", + "bbox": [ + 496, + 671, + 890, + 729 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {b e v} = \\frac {\\tau^ {2}}{B \\cdot C} \\times \\mathcal {D} _ {\\mathrm {K L}} \\left(\\phi_ {\\tau} \\left(F _ {b e v} ^ {T}\\right), \\phi_ {\\tau} \\left(F _ {b e v} ^ {S}\\right)\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 734, + 890, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where B stands for the batch size, C means the number of channels of BEV features. $F_{bev}^{T}$ and $F_{bev}^{S}$ denote the BEV features of the teacher model and student model, respectively. We will get a loss with the shape of $[H_{bev} \\times W_{bev}, 1]$ .", + "bbox": [ + 496, + 770, + 893, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.3 View-guided distillation objective", + "text_level": 1, + "bbox": [ + 500, + 848, + 785, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the first two sections, we obtained the loss of each camera on the image feature and the corresponding loss of each", + "bbox": [ + 496, + 871, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3828", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Progressive Quantization-Aware VGD" + ], + "code_body": "Input: Training data; Pre-trained FP weights for teacher model $T_{fp}$ Student model $S$ Numbers of epochs for each phase $N_{1},\\ldots ,N_{4};P_{2}$ Quantization bit for weight and activation $B_{w};B_{a}$ \nOutput: Trained low-bit student model $S_{q}$ Phase 1: Progressive Quantization-Aware Training Init $S_0$ with $T_{fp}$ Divide model into 4 Parts: {Backbone,Neck,Encoder,Decoder}; for i, module in Parts do module $\\equiv$ quantize (module; $B_w,B_a)$ Init $S_{i}$ with $S_{i - 1}$ for Epoch $\\equiv N_{i - 1}$ ..., $N_{i}$ do Update $S_{q_i}$ by minimizing QAT loss", + "bbox": [ + 76, + 109, + 468, + 323 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Phase 2: View-Guided Distillation" + ], + "code_body": "Init $S$ with $S_{4}$ \nfor Epoch $\\mathbf{\\Phi} = 1,\\dots ,P_2$ do Update $S$ by minimizing QAT loss and $\\mathcal{L}_{vgd}$ in Eq. (6)", + "bbox": [ + 93, + 339, + 468, + 401 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "point on the BEV feature. On the nuScenes dataset, the camera external parameters are known, so we can obtain the distribution range of each camera corresponding to the BEV feature. Then we generate the BEV mask of views $M_{bev}$ that can be applied to the image feature, which is the same as defined in BEVFormer [23]. $M_{bev}$ is a tensor with four dimensions: number of cameras, batch size, BEV size $(H_{bev} \\times W_{bev})$ , and 3D Height, with binary values in each element. By calculating the average along the last dimension (3D Height), we can flatten the BEV mask $M_{bev}$ on the 2d plane with the BEV size $(H_{bev} \\times W_{bev})$ . Then the $\\mathcal{L}_{img}$ calculated for each camera can be extended to the corresponding loss for each point on the BEV feature, which we refer to as $\\widehat{\\mathcal{L}}_{img}$ :", + "bbox": [ + 75, + 431, + 472, + 630 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {\\mathcal {L}} _ {i m g} = \\mathcal {L} _ {i m g} \\odot M _ {b e v} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 638, + 468, + 656 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\odot$ denotes the hadamard product.", + "bbox": [ + 76, + 669, + 344, + 684 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we use $\\widehat{\\mathcal{L}}_{img}$ to get the view-guided distillation objective in Eq. (6):", + "bbox": [ + 75, + 685, + 468, + 715 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {v g d} = \\sum_ {i = 1} ^ {N \\cdot H \\cdot W} \\widehat {\\mathcal {L}} _ {i m g} \\odot \\mathcal {L} _ {b e v} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 723, + 468, + 761 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall process of view-guided distillation is shown in Algorithm 1.", + "bbox": [ + 76, + 770, + 468, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 814, + 209, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we first elaborate on the experimental settings, then we evaluate both PTQ and QAT methods on the BEV networks. Based on the analysis of these results, we propose QD-BEV to overcome shortcomings in standard", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "PTQ and QAT, and we dedicatedly compare our results with previous works under different settings and constraints.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental settings", + "text_level": 1, + "bbox": [ + 500, + 131, + 702, + 147 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.1 Dataset", + "text_level": 1, + "bbox": [ + 500, + 154, + 607, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluated our proposed method on a challenging 3D detection task using the nuScenes dataset [3], which is a large-scale public dataset for autopilot developed by the team at Motional (formerly nuTonomy). This dataset contains 1000 manually selected 20-second driving scenarios collected in Boston and Singapore, with 750 scenarios for training, 100 for validation, and 150 for testing. The images in the dataset were captured from 6 cameras with known internal and external parameters.", + "bbox": [ + 496, + 178, + 893, + 315 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.2 Evaluation metrics", + "text_level": 1, + "bbox": [ + 500, + 334, + 686, + 347 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The main measurement indicators on the nuScenes 3D test dataset are the mean Average Precision (mAP), and the unique evaluation index nuScenes detection score (NDS). NDS is a comprehensive evaluation index containing many aspects of information. The other indicators are mean Average Translation Error (mATE), mean Average Scale Error (mASE), mean Average Orientation Error (mAOE), mean Average Velocity Error (mAVE) and mean Average Attribute Error (mAAE). To evaluate the efficiency of the BEV networks, we use model size and BOPS as the metrics. Model size is the memory required to store a specific network, which is determined by the total amount of parameters in the model as well as the quantization bitwidth to store those parameters. BOPS measures the total Bit Operations of one network inference [35]. It is a common metric for evaluating the computation of quantized neural networks. For a model with $L$ layers, defining $b_{w_i}$ and $b_{a_i}$ to be the bitwidth used for weights and activations of the $i$ -th layer, then we have:", + "bbox": [ + 496, + 356, + 890, + 619 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nB O P S = \\sum_ {i = 1} ^ {L} b _ {w _ {i}} b _ {a _ {i}} M A C _ {i} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 628, + 890, + 652 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{MAC}_i$ is the total Multiply-Accumulate operations for computing the $i$ -th layer. To better demonstrate the advantages of our QD-BEV model over the floating-point model, we introduce sAP [19] (streaming average precision) as one of the evaluation metrics for our model performance. sAP is a dynamic metric that will be updated as new data arrive, making it ideal for evaluating models in real-time scenarios.", + "bbox": [ + 496, + 660, + 890, + 781 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.3 Baselines & Implementation Details", + "text_level": 1, + "bbox": [ + 498, + 801, + 803, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We mainly compare with floating-point baseline models proposed by BEVFormer [23] with different input image resolutions (specifically, BEVFormer-Tiny, BEVFormer-Small, and BEVFormer-Base). For quantization baselines, we apply the previous PTQ method DFQ [29] as well as", + "bbox": [ + 496, + 824, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3829", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/810ae290c2285b7097526c615fa2280ecc226c7f73ac277b3c0a149215e4a320.jpg", + "table_caption": [ + "Table 1: Results with PTQ separately applied on each part in BEVFormer." + ], + "table_footnote": [], + "table_body": "
Quantized ModuleBEVFormer-TinyBEVFormer-SmallBEVFormer-Base
BackboneNeckEncoderDecodermAP↑NDS↑mAP↑NDS↑mAP↑NDS↑
××××0.2520.3540.3700.4790.4160.517
✓×××0.2120.3100.2880.4170.3090.440
×✓××0.2520.3530.3700.4780.4160.516
××✓×0.1810.2950.2980.4210.1600.303
×××✓0.2510.3530.3690.4770.4160.517
✓✓✓✓0.1450.2460.2280.3690.0750.224
", + "bbox": [ + 81, + 116, + 893, + 301 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "QAT method PACT [7] and HAWQv3 [40] to quantize BEVFormer models and compare with QD-BEV.", + "bbox": [ + 75, + 325, + 468, + 356 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For floating-point models, we use the open-sourced repository of BEVFormer with two different backbones: ResNet50 and ResNet101-DCN. We use symmetrical linear quantization in a channel-wise manner for weights, and layer-wise quantization for activations, which are the standard settings for previous quantization methods. Since there is little related work in our settings for reference, we make our training adopt the same scheme as the original training strategy of BEVFormer, which is to train 24 epochs in each step, and to use optimizer of AdamW, a starting lr as 2e-4, a linear warmup of 500 iters, and cosine annealing.", + "bbox": [ + 75, + 363, + 470, + 531 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a87b56f03186a6d56c59d7ebd648999bbc1ab2176bffe08df6706da3b6261c74.jpg", + "table_caption": [ + "Table 2: PTQ results with different quantization bitwidth." + ], + "table_footnote": [], + "table_body": "
W-bit/A-bitModelNDS↑NDS DropmAP↑
32/32Tiny0.354-0.252
Small0.479-0.370
Base0.517-0.416
8/8Tiny0.3510.8%0.248
Small0.4770.4%0.366
Base0.4875.8%0.384
6/6Tiny0.31211.9%0.203
Small0.43010.2%0.306
Base0.40222.2%0.262
4/6Tiny0.24630.5%0.146
Small0.36923.0%0.228
Base0.22656.3%0.076
4/4Tiny0.03490.4%0.001
Small0.03492.9%0.001
Base0.02395.6%0.000
", + "bbox": [ + 81, + 585, + 470, + 875 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b34854435612c10b808bd9b109bf44e665f4303e45845036d8cc87543279eeb8.jpg", + "table_caption": [ + "Table 3: Comparison between progressive and standard QAT with W4A6. Please refer to Table 2 for baseline FP accuracy (W32A32)." + ], + "table_footnote": [], + "table_body": "
MethodModelNDS↑NDS DropmAP↑
Standard QATTiny0.3267.9%0.216
Small0.42112.1%0.303
base0.22456.7%0.071
Progressive QATTiny0.3481.7%0.234
Small0.4672.5%0.356
base0.4856.2%0.376
", + "bbox": [ + 504, + 378, + 893, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Analysis on BEV Quantization", + "text_level": 1, + "bbox": [ + 500, + 550, + 769, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.1 PTQ results", + "text_level": 1, + "bbox": [ + 500, + 585, + 638, + 601 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first analyze the sensitivity of different modules to quantization in Table 1. It can be seen that the backbone and the encoder parts of the network are more sensitive, while quantization of the neck and the decoder parts only brings a slight disturbance to the accuracy. We want to note that, based on the sensitivity analysis, it is possible to apply mixed-precision quantization to better preserve the sensitive modules, but we leave this as future work since it is beyond the scope of this paper.", + "bbox": [ + 496, + 631, + 893, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We then analyze the influence of different quantization bitwidth on the final performance. In Table 2, directly applying PTQ with less than 8-bit precision will lead to a significant accuracy drop, especially when quantized to W4A4 the results become pure noise with around $0\\mathrm{mAP}$ . As can be observed from Table 2, performing QAT is necessary in order to preserve the accuracy while achieving ultra-low bit quantization.", + "bbox": [ + 496, + 779, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3830", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1be7d15231491689c9a486b3813e02db553d6aab8685f6092a6d3f2ab7f6d914.jpg", + "table_caption": [ + "Table 4: QD-BEV results compared to previous methods or baselines." + ], + "table_footnote": [], + "table_body": "
Input SizeModelModel Size(MB)BOPS(Tera)NDS↑mAP↑mATE↓mASE↓mAOE↓mAVE↓mAAE↓
450×800BEVFormer-T[23]126.862.330.3540.2530.8990.2940.6550.6570.216
BEVFormer-T-DFQ[29]31.73.900.3400.2360.9490.2960.6510.6710.217
BEVFormer-T-HAWQv3[40]15.91.460.3480.2340.9490.3040.5680.6610.209
BEVFormer-T-PACT[7]15.91.460.3470.2340.9190.2890.6040.6710.216
QD-BEV-T (Ours)15.91.460.3720.2550.8820.3210.5430.5990.214
720×1280BEVFormer-S[23]225.6236.130.4790.3700.7220.2790.4070.4380.220
BEVFormer-S-DFQ[29]56.414.760.4670.3560.7510.2830.4050.4510.222
BEVFormer-S-HAWQv3[40]28.25.530.4670.3560.7510.2870.4190.4490.208
BEVFormer-S-PACT[7]28.25.530.4610.3510.7500.2750.4220.5070.196
QD-BEV-S (Ours)28.25.530.4790.3740.7160.2900.3890.4740.210
900×1600BEVFormer-B[23]262.9667.390.5170.4160.6720.2730.3700.3930.197
BEVFormer-B-DFQ[29]65.741.710.4860.3840.7710.2740.3780.4270.206
BEVFormer-B-HAWQv3[40]32.915.640.4850.3760.7270.2880.3810.4340.202
BEVFormer-B-PACT[7]32.915.640.4800.3740.7350.2910.3920.4580.201
QD-BEV-B (Ours)32.915.640.5090.4060.6910.2850.3600.4100.190
", + "bbox": [ + 84, + 116, + 890, + 452 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5ee206ceecc8b73755d7f7355f0fd93aa2d0c4c1e03044e3713b092f3fcbac4a.jpg", + "image_caption": [ + "Figure 3: The training process of QD-BEV. Progressive QAT with 4 stages is performed in the first 60 epochs, then the view-guided distillation is conducted together with QAT to steadily enhance the performance. The pink line in the figure represents the baseline NDS. Note that swapping VGD with pure QAT or other distillation methods (for example, CWD [33]) will lead to undesirable results, as we show in the last 20 epochs in this figure, compared with Figure 1 and Figure 5." + ], + "image_footnote": [], + "bbox": [ + 84, + 470, + 885, + 627 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2.2 QAT results", + "text_level": 1, + "bbox": [ + 76, + 726, + 215, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To address the severe accuracy degradation of PTQ, we apply QAT to better adapt the models towards 4-bit quantization. In all our experiments, the standard QAT method which directly quantizes the whole network to the target bitwidth will lead to unstable QAT processes, causing gradient explosion or a rapid decrease in accuracy in large models (for example, the W4A6 BEVFormer-Base has only $0.07\\mathrm{mAP}$ ). Based on this observation, we hypothesize that the quantization perturbation introduced in standard QAT", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "is too large to be recovered. As such, we apply progressive QAT to constrain the quantization perturbation along the training process. A comparison of the performance between progressive QAT and standard QAT with the same number of training epochs is presented in Table 3. We can see that progressive QAT consistently outperforms standard QAT by a large margin (up to $5\\%$ mAP) in BEVFormer-Tiny and BEVFormer-Small, and achieves an even larger performance gain on BEVFormer-Base. To better validate our analyses, we plot the training curve of progressive QAT as the first 60 epochs in Figure 3, where W4A6 quantization", + "bbox": [ + 496, + 726, + 890, + 893 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3831", + "bbox": [ + 482, + 945, + 513, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4eb9d2746fd83a132f8ff22ee1361fe68b04899a5f78f1bc026e47429af6adac.jpg", + "table_caption": [ + "Table 5: QD-BEV results on BEVDepth[21] and PETR[24]." + ], + "table_footnote": [], + "table_body": "
WAModelmAP↑NDS↑
3232BEVDepth-T[21]0.3300.435
88BEVDepth-T-DFQ[29]0.2810.377
46BEVDepth-T-HAWQ[40]0.1360.206
46BEVDepth-T-PACT[7]0.2700.362
46QD-BEVDepth-T (Ours)0.3010.394
3232PETR-r50dcn[24]0.3170.366
88PETR-r50dcn-DFQ[29]0.2900.343
46PETR-r50dcn-HAWQ[40]0.1620.216
46PETR-r50dcn-PACT[7]0.2680.320
46QD-PETR-r50dcn (Ours)0.2880.334
", + "bbox": [ + 81, + 114, + 465, + 415 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "is conducted on BEVFormer-Tiny. We separate the progressive QAT into 4 stages and iteratively quantize a new module in each stage. As can be seen, there is an NDS drop at beginning of each stage, corresponding to the quantization perturbation introduced by quantizing each new module.", + "bbox": [ + 75, + 429, + 468, + 505 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Despite the merits of progressive QAT, we want to note that it still suffers from unstable training and performance degradation. As illustrated in Figure 1 which corresponds to the last 20 epochs in Figure 3, progressive QAT keeps going up and down after reaching a plateau, while training curves of VGD show a rising trend with much better stability.", + "bbox": [ + 75, + 505, + 468, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Main Results of QD-BEV", + "text_level": 1, + "bbox": [ + 76, + 604, + 307, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In order to obtain better accuracy and stability, we apply view-guided distillation with the floating-point model as the teacher and the quantized model as the student. The effect of VGD on W4A6 quantization of BEVFormer-Tiny is shown in Figure 3. Note that we separate VGD from progressive QAT in the first 60 epochs for a clearer comparison and illustration, and VGD is actually a plug-and-play function that can always be jointly applied with QAT, as we do in the last 20 epochs. Benefiting from knowledge in both the image domain and the BEV domain, QD-BEV networks are able to fully recover the quantization degradation, and even outperform the floating-point baselines. As shown in Table 4, the NDS and mAP of the model outperform previous floating-point baselines as well as quantized networks. Since there are no existing results for compact BEV networks, we implement standard quantization methods DFQ [29], HAWQv3 [40] and PACT [7] on BEVFormer as a comparison. We apply W8A8 quantization for DFQ", + "bbox": [ + 75, + 628, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4db8ddb4e11ac53a04447dc1c484f6d061f6c6be18b19f81ae305ba73a8b460c.jpg", + "image_caption": [ + "Figure 4: Visualization of QD-BEV results and the comparison with results obtained by BEVFormer." + ], + "image_footnote": [], + "bbox": [ + 504, + 90, + 887, + 338 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(DFQ is a PTQ method, lower bitwidth will lead to intolerable accuracy degradation) and W4A6 for QAT methods and QD-BEV models. As a comparison, QD-BEV can achieve 0.509 NDS with only 32.9 MB model size, which is similar to the size of BEVFormer-T-DFQ (0.340 NDS) and much smaller than BEVFormer-Tiny (126.8 MB, 0.354 NDS).", + "bbox": [ + 496, + 407, + 890, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Preliminary tests were run on PETR [24] and BEVDepth [21] models using our method in figure 5. Performance did not match BEVFormer, but still surpassed conventional quantization methods, highlighting the method's potential despite varying results.", + "bbox": [ + 496, + 500, + 890, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Figure 4, we show the visualization results of the QDBEV-Base model on the nuScenes val dataset, and compare them with the results of BEVFormer-Tiny and the ground truth. As can be seen, more objects are detected by QDBEV-Base, and the 3D boxes predictions are more accurate than BEVFormer-Tiny. More visualizations are provided in the supplementary material.", + "bbox": [ + 496, + 575, + 890, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Streaming perception result", + "text_level": 1, + "bbox": [ + 500, + 695, + 750, + 710 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In the context of autonomous driving, streaming perception [19] is critical for enabling models to make rapid and precise decisions in real time. High latency will degrade the streaming perception because it will cause a delay between the sensory data and the neural network output. To enhance streaming perception, quantization is a necessary technique that compresses the model size, reduces computational load, and accelerates the inference process. In Table 6, we demonstrate the significant impact of quantization on the sAP metric in autonomous driving scenarios. As we can see, QD-BEV models show consistent improvements in sAP compared to the floating-point counterparts and the", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3832", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3ff40c9549d8c8b26f4716f6604600e3921ef3ac39cdf835dbf139878d05929c.jpg", + "table_caption": [ + "Table 6: sAP of QD-BEV models compared to baselines." + ], + "table_footnote": [], + "table_body": "
Input SizeModelWAmAP↑sAP↑
450×800BEVFormer-T[23]32320.2530.228
BEVFormer-T-DFQ[29]880.2360.230
QD-BEV-T (Ours)460.2550.251
720×1280BEVFormer-S[23]32320.3700.249
BEVFormer-S-DFQ[29]880.3560.322
QD-BEV-S (Ours)460.3740.350
900×1600BEVFormer-B[23]32320.4160.136
BEVFormer-B-DFQ[29]880.3840.290
QD-BEV-B (Ours)460.4060.337
", + "bbox": [ + 84, + 116, + 467, + 338 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/88fb07d0ced050705f677c3229af9d8d3f6b8b7ddebad0fc090775f1731c9fe8.jpg", + "image_caption": [ + "(a) mAP curve." + ], + "image_footnote": [], + "bbox": [ + 81, + 353, + 277, + 474 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/9f56193136f1a01ad3b9f2ba7585414cb59593f501af2744b361dbbd088daf9c.jpg", + "image_caption": [ + "(b) NDS curve.", + "Figure 5: The training curve of VGD versus CWD [33]. CWD uses only one type of features, referred to as cwd-image (image feature) and cwd-bev (bev feature), respectively." + ], + "image_footnote": [], + "bbox": [ + 279, + 353, + 473, + 474 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "quantized baselines.", + "bbox": [ + 76, + 580, + 212, + 595 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Ablation study", + "text_level": 1, + "bbox": [ + 76, + 609, + 225, + 627 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In Figure 5, we conduct an ablation study where we compare view-guided distillation with the cases using only distillation on the image feature, and only on the BEV feature, respectively. The method is referred to as CWD [33]. For a fair comparison, we apply the same pre-training weights and hyperparameters such as the temperature and the learning rate. From the figure, it can be found that view-guided distillation has a clear advantage over the CWD methods. In both the mAP and NDS curves, VGD has a more obvious and stable upward trend, and achieves better final results.", + "bbox": [ + 75, + 635, + 468, + 787 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 800, + 194, + 815 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this work, we systematically study both PTQ and QAT on BEV networks and showcase the major problems they are facing. Based on our analyses, we propose a view-guided distillation (VGD) method that can stabilize the QAT process and enhance the final performance by lever", + "bbox": [ + 75, + 824, + 467, + 902 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "aging information from both the image domain and the BEV domain. With VGD as a plug-and-play function that can be jointly applied when quantizing BEV models, QD-BEV can close the accuracy gap or even outperforms the floating-point baselines. On the nuScenes datasets, the 4-bit weight and 6-bit activation quantized QD-BEV-Tiny model achieves $37.2\\%$ NDS with only $15.8\\mathrm{MB}$ model size, outperforming BevFormer-Tiny by $1.8\\%$ with an $8\\times$ model compression.", + "bbox": [ + 496, + 90, + 890, + 227 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "7. Acknowledgement", + "text_level": 1, + "bbox": [ + 498, + 242, + 679, + 260 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported by the National Key R&D Program of China (2022ZD0116305). The authors would also like to express their gratitude to the CCF-Baidu Open Fund Project, Berkeley Deep Drive, and Intel Corporation for their support and assistance throughout this research. Special thanks to Yandong Guo from $\\mathrm{Al}^2$ Robotics (YAN-DONG.guo@live.com) for his valuable contributions to this work.", + "bbox": [ + 496, + 268, + 890, + 388 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 405, + 596, + 421 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sungsoo Ahn, Shell Xu Hu, Andreas Damianou, Neil D Lawrence, and Zhenwen Dai. Variational information distillation for knowledge transfer. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9163-9171, 2019.", + "[2] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. 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Be your own teacher: Improve the performance of convolutional neural networks via self distillation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 3713-3722, 2019.", + "[44] Lingran Zhao, Zhen Dong, and Kurt Keutzer. Analysis of quantization on mlp-based vision models. arXiv preprint arXiv:2209.06383, 2022.", + "[45] Aojun Zhou, Anbang Yao, Yiwen Guo, Lin Xu, and Yurong Chen. Incremental network quantization: Towards lossless cnns with low-precision weights. arXiv preprint arXiv:1702.03044, 2017.", + "[46] Yiren Zhou, Seyed-Mohsen Moosavi-Dezfooli, Ngai-Man Cheung, and Pascal Frossard. Adaptive quantization for deep neural network. arXiv preprint arXiv:1712.01048, 2017.", + "[47] Yin Zhou and Oncel Tuzel. Voxelnet: End-to-end learning for point cloud based 3d object detection. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 4490-4499, 2018.", + "[48] Xizhou Zhu, Weijie Su, Lewei Lu, Bin Li, Xiaogang Wang, and Jifeng Dai. Deformable detr: Deformable transformers for end-to-end object detection. arXiv preprint arXiv:2010.04159, 2020." + ], + "bbox": [ + 78, + 92, + 467, + 868 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "3835", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/QD-BEV _ Quantization-aware View-guided Distillation for Multi-view 3D Object Detection/ce2686ce-9d14-4ea8-b9f7-4395d3561b65_model.json b/2023/QD-BEV _ Quantization-aware View-guided Distillation for Multi-view 3D Object Detection/ce2686ce-9d14-4ea8-b9f7-4395d3561b65_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ece250333d48d29d7709c6a6b6cc1dafcea17eb2 --- /dev/null +++ b/2023/QD-BEV _ Quantization-aware View-guided Distillation for Multi-view 3D Object Detection/ce2686ce-9d14-4ea8-b9f7-4395d3561b65_model.json @@ -0,0 +1,2158 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.128, + 0.13, + 0.843, + 0.176 + ], + "angle": 0, + "content": "QD-BEV : Quantization-aware View-guided Distillation for Multi-view 3D Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.202, + 0.871, + 0.274 + ], + "angle": 0, + "content": "Yifan Zhang\\(^{1*}\\), Zhen Dong\\(^{2*}\\), Huanrui Yang\\(^{2}\\), Ming Lu\\(^{3}\\), Cheng-Ching Tseng\\(^{3}\\), Yuan Du\\(^{1}\\), Kurt Keutzer\\(^{2}\\), Li Du\\(^{1\\dagger}\\), Shanghang Zhang\\(^{3\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.316, + 0.275, + 0.654, + 0.289 + ], + "angle": 0, + "content": "\\(^{1}\\)Nanjing University, \\(^{2}\\)University of California, Berkeley," + }, + { + "type": "text", + "bbox": [ + 0.143, + 0.291, + 0.826, + 0.307 + ], + "angle": 0, + "content": "\\(^{3}\\)National Key Laboratory for Multimedia Information Processing, School of Computer Science, Peking University," + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.342, + 0.314, + 0.358 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.375, + 0.474, + 0.724 + ], + "angle": 0, + "content": "Multi-view 3D detection based on BEV (bird-eye-view) has recently achieved significant improvements. However, the huge memory consumption of state-of-the-art models makes it hard to deploy them on vehicles, and the nontrivial latency will affect the real-time perception of streaming applications. Despite the wide application of quantization to lighten models, we show in our paper that directly applying quantization in BEV tasks will 1) make the training unstable, and 2) lead to intolerable performance degradation. To solve these issues, our method QD-BEV enables a novel view-guided distillation (VGD) objective, which can stabilize the quantization-aware training (QAT) while enhancing the model performance by leveraging both image features and BEV features. Our experiments show that QD-BEV achieves similar or even better accuracy than previous methods with significant efficiency gains. On the nuScenes datasets, the 4-bit weight and 6-bit activation quantized QD-BEV-Tiny model achieves \\(37.2\\%\\) NDS with only 15.8 MB model size, outperforming BevFormer-Tiny by \\(1.8\\%\\) with an \\(8\\times\\) model compression. On the Small and Base variants, QD-BEV models also perform superbly and achieve \\(47.9\\%\\) NDS (28.2 MB) and \\(50.9\\%\\) NDS (32.9 MB), respectively." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.754, + 0.21, + 0.77 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.781, + 0.47, + 0.811 + ], + "angle": 0, + "content": "Given its potential in enabling autopilot, multi-view 3D detection based on BEV (bird-eye-view) has become" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.342, + 0.7, + 0.465 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.551, + 0.473, + 0.645, + 0.486 + ], + "angle": 0, + "content": "(a) mAP curve." + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.341, + 0.897, + 0.465 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.749, + 0.473, + 0.842, + 0.486 + ], + "angle": 0, + "content": "(b) NDS curve." + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.498, + 0.895, + 0.575 + ], + "angle": 0, + "content": "Figure 1: Training curves of QD-BEV (with VGD) versus progressive QAT on W4A6 quantization of BEVFormer-Tiny. Note that standard QAT works even worse compared to progressive QAT and it falls out of the targeted accuracy range in the figures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.61, + 0.895, + 0.867 + ], + "angle": 0, + "content": "an important research direction for autonomous driving. Based on input sensors, previous work can be divided into LiDAR-based methods [18, 47] and camera-only methods [23, 38, 14, 13, 24, 25]. Compared to the LiDAR-based methods, camera-only methods have the merits of lower deployment cost, closer to human eyes, and easier access to visual information in the driving environment. However, even if using the camera-only methods, the computational and memory costs of running state-of-the-art BEV models are still formidable, making it difficult to deploy them onto vehicles. For example, BEVFormer-Base has a \\(540~\\mathrm{ms}\\) inference latency (corresponds to 1.85 fps) on one NVIDIA V100 GPU, which is infeasible for real-time applications that generally require 30 fps. Since a non-trivial latency will harm the streaming perception, it is particularly crucial to explore and devise lightweight models for camera-only 3D object detection based on BEV." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Quantization [16, 11, 42, 10] can reduce the bitwidth used to represent weights and activations in deep neural net-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.838, + 0.415, + 0.896 + ], + "angle": 0, + "content": "* Equal contribution : \nzhang_yifan@smail.nju.edu.cn, zhendong@berkeley.edu \n† Corresponding authors : \nldu@nju.edu.cn, shanghang@oku.edu.cn" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3825" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.093, + 0.885, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.327, + 0.885, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.5, + 0.893, + 0.579 + ], + "angle": 0, + "content": "Figure 2: Illustration of QD-BEV. (a) In our pipeline, multi-camera images are input into the floating-point teacher network and the quantized student network in order to compute the KL divergence in an element-wise manner. The KL divergence is used as distillation loss in the image feature and the BEV feature, respectively. Then we conduct view-guided distillation using the BEV mask obtained from the external parameters of the camera. Please refer to Sec.3.1 for more details. (b) The lower flow chart shows the computation process of the view-guided distillation loss. Specific details are in Sec. 3.3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.603, + 0.473, + 0.892 + ], + "angle": 0, + "content": "works, which can greatly save the model size and computational costs while improving the speed of model reasoning. However, directly applying quantization would lead to significant performance degradation. Compared to image classification and 2D object detection tasks where the standard quantization methods shine, multi-camera 3D detection tasks are much more complicated and difficult due to the existence of multiple views and information from multiple dimensions (for example, the temporal information and spatial information used in BEVFormer [23]). Consequently, the structure of BEV networks tends to become more complex, with a deeper convolutional neural network backbone to extract image information from multiple views, and with transformers to encode and decode the features of the BEV domain. The presence of different neural architectures, multiple objectives, and knowledge from different modalities greatly challenges the standard quantization methods, decreasing their stability and accuracy, and even making the whole training process diverge. In Figure 1, we" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.603, + 0.895, + 0.709 + ], + "angle": 0, + "content": "show the training curves when applying W4A6 quantization on a BEVFormer-Tiny model. As can be seen, the performance of quantization-aware training (QAT) fluctuates significantly in different epochs, while the performance of our proposed method QD-BEV shows a stable rising trend. We perform more experiments to validate the effectiveness of QD-BEV in Sec 5." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.896, + 0.903 + ], + "angle": 0, + "content": "To solve the problems of standard QAT, in this work, we first conduct systematic experiments and analyses on quantizing BEV networks. Then we devise a quantization-aware view-guided distillation method (referred to as QD-BEV) that can decently solve the stability issue while improving the final performance of compact BEV models. Our proposed view-guided distillation (VGD) can better leverage information from both the image and the BEV domains for multi-view 3D object detection. This can significantly outperform previous distillation methods that cannot jointly handle the different types of losses in BEV networks. Specifically, as shown in Figure 2, we first take" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "3826" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "the FP (floating-point) model as the teacher model and the quantized model as the student model, then we calculate the KL divergence on the image feature and the BEV feature, respectively. Finally, we leverage the mapping relationship and realize VGD by organically combining the image feature and the BEV feature through the camera's external parameters. Note that in QD-BEV, neither additional training data nor larger powerful teacher networks are used to tune the accuracy, but QD-BEV models are still able to outperform previous baselines while having significantly smaller model sizes and computational requirements. Our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.29, + 0.47, + 0.337 + ], + "angle": 0, + "content": "- We conduct systematic experiments on quantizing BEV models, unveiling major issues hampering standard quantization-aware training methods on BEV." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.355, + 0.47, + 0.431 + ], + "angle": 0, + "content": "- We specially design view-guided distillation (VGD) for BEV models, which jointly leverages both image domain and BEV domain information. VGD boosts the final performance while solving the stability issue of standard QAT." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.45, + 0.469, + 0.496 + ], + "angle": 0, + "content": "- Our W4A6 quantized QD-BEV-Tiny has \\(37.2\\%\\) NDS with only 15.8 MB model size, which outperforms the \\(8 \\times\\) larger BevFormer-Tiny model by \\(1.8\\%\\)." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.29, + 0.47, + 0.496 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.516, + 0.227, + 0.532 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.543, + 0.367, + 0.56 + ], + "angle": 0, + "content": "2.1. Camera-only 3D object detection" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In camera-only 3D object detection tasks, many excellent methods have emerged based on BEV (bird-eye-view). Previous works, LSS [31] and BEVDet [14], project image features to the BEV space in a bottom-up manner. Based on DETR [5] and Deformable DETR [48], DETR3D [38] extends the 2D object detection to the 3D space through the architecture of Backbone + FPN + Decoder. In addition, PETR [24] introduces 3D position coding based on DETR3D [38]. In BEVFormer [23], the authors use dense BEV queries to exchange information in the BEV space with the multi-view image space. More stable BEV features are obtained by extracting temporal and spatial information through the transformer structure with temporal self-attention and spacial cross-attention. Based on the temporal interaction in BEVFormer, further improvements have been made in recent works, PETRv2 [25] and BEVDet4D [13]. Besides the aforementioned works, BEVDepth [21] and BEVstereo [20] are two state-of-the-art approaches for monocular depth estimation and stereo vision in the birdeye-view (BEV) domain, respectively, which leverage the unique characteristics of BEV representations to achieve high accuracy and efficiency." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.638, + 0.108 + ], + "angle": 0, + "content": "2.2. Quantization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.121, + 0.895, + 0.44 + ], + "angle": 0, + "content": "To reduce the model size, quantization [45, 36, 15, 26] uses low bitwidth to represent weights and activations in neural networks. With the use of low-precision matrix multiplication or convolution, quantization can also make the inference process faster and more efficient. Given a pretrained model, directly performing quantization without any fine-tuning is referred to as post-training quantization (PTQ) [4, 29, 37, 17]. Despite the merits, PTQ with low bitwidth still results in significant accuracy degradation. As such, Quantization-aware training (QAT) is proposed to train the model to better adapt to quantization. QAT methods [9, 7, 40] are more costly compared to PTQ, but can potentially obtain higher accuracy. Furthermore, in the cases with ultra-low quantization bitwidth (for example, 4-bit), even QAT cannot close the accuracy gap. A promising direction to solve this is to use mixed-precision quantization [46, 36, 39], where some sensitive layers are kept at higher precision to recover the accuracy. Though effective, the support for mixed-precision quantization on general-purpose machines (CPUs and GPUs) is currently immature and may lead to extra latency overhead." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.447, + 0.895, + 0.538 + ], + "angle": 0, + "content": "Although standard quantization methods have shown great results on convolutional neural networks, recent works [27, 44] mention that it may suffer in other neural architectures such as transformers. The presence of both convolutional blocks and transformers in BEV networks makes them challenging to the traditional quantization methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.568, + 0.622, + 0.584 + ], + "angle": 0, + "content": "2.3. Distillation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Model distillation [12, 28, 22, 32, 1] generally uses a large model as the teacher to train a compact student model. Instead of using class labels during the training of the student model, the key idea is to leverage the soft probabilities produced by the teacher to guide the student's training. Previous methods of distillation explore different knowledge sources (for example, [12, 22, 30] use logits, aka the soft probabilities). The choices of teacher models are also studied, where [41, 34] use multiple teacher models, while [8, 43] apply self-distillation without an extra teacher model. Other previous efforts apply distillation with different settings on different applications. Regarding BEV networks, previous work [6] tries to teach LiDAR information to camera-based networks through distillation, but the additional requirement for LiDAR data makes it infeasible in our pure camera-based setting. Besides, the existence of different types of losses in BEV networks makes standard distillation methods invalid. An arbitrary or sub-optimal combination of knowledge sources would also make the training unstable, perform badly, or even diverge." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3827" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.17, + 0.105 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.115, + 0.347, + 0.132 + ], + "angle": 0, + "content": "3.1. Overview of QD-BEV pipeline" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.139, + 0.473, + 0.442 + ], + "angle": 0, + "content": "This work aims to improve the efficiency of state-of-the-art BEV models. Starting with the widely used BEV-Former [23], we apply a progressive quantization-aware training procedure in a stage-by-stage manner (details are introduced in Sec. 3.2). We further boost its stability and performance through a novel view-guided distillation process, which is highlighted in Figure 2, where we use a floating-point teacher model to facilitate the learning of our quantized QD-BEV student model. Specifically, the input multi-camera image is entered into the teacher and the student, respectively, and then the Image Backbone and Image Neck parts of the network are used to extract the multicamera image feature. After the transformer part of the network, the BEV features are extracted, and the two parts of the teacher model and the student model are used to calculate image distill loss and BEV distill loss, respectively. The two distillation losses are then fused through the external parameters of the camera to achieve our unique view-guided distillation mechanism. We provide a detailed formulation of the view-guided distillation process in Sec. 3.3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.452, + 0.336, + 0.468 + ], + "angle": 0, + "content": "3.2. Quantization-aware training" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.475, + 0.47, + 0.518 + ], + "angle": 0, + "content": "In symmetric linear quantization, the quantizer maps weights and activations into integers with a scale factor \\( S \\). Uniformly quantizing to k bit can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.527, + 0.47, + 0.556 + ], + "angle": 0, + "content": "\\[\nS = \\frac {2 \\left| r _ {\\max } \\right|}{2 ^ {k} - 1}, q = \\operatorname {r o u n d} \\left(\\frac {r}{S}\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.473, + 0.838 + ], + "angle": 0, + "content": "where \\( r \\) is the floating-point number being quantized, \\( |r_{\\mathrm{max}}| \\) is the largest absolute value in \\( r \\), and \\( q \\) is the quantized integer. In this work, we conduct systematic experiments to analyze the performance of quantization on BEV networks. For PTQ, we apply the above quantization directly to the pre-trained models during the inference stage. For QAT, we utilize the straight-through estimator (STE) [2] to define the forward and backward processes for the above quantization operations, and then we train the model to better adapt to quantization. As previously mentioned in Sec. 1 and Sec. 2, considering that standard QAT may lead to divergence due to the characteristics of BEV models, we apply a stage-wise progressive QAT where we gradually reduce the weight precision in four stages (backbone, neck, encoder, and decoder) based on the design of BEV-Former [23]. The performance of this progressive QAT is illustrated in Figure 3. And we compare the effectiveness of the progressive QAT with standard QAT in Sec. 4.2.2." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.847, + 0.297, + 0.863 + ], + "angle": 0, + "content": "3.3. View-guided distillation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Compared to traditional single-domain distillation methods, our approach exploits the complementary nature of" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.273 + ], + "angle": 0, + "content": "both BEV and image domains, which provides different perspectives and capture different aspects of the scene. The BEV domain offers a top-down view, enabling accurate perception and recognition of the surrounding environment, such as the structure of the road, the location of vehicles, and lane markings. On the other hand, the image domain provides more realistic visual information, capturing rich scene details and color information. In the following sections, we present details of VGD: the computation of the image feature distillation in Sec. 3.3.1, the BEV feature distillation in Sec. 3.3.2, and the view-guided distillation combining the previous two distillation losses in Sec. 3.3.3." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.291, + 0.731, + 0.307 + ], + "angle": 0, + "content": "3.3.1 Image feature distillation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.313, + 0.892, + 0.44 + ], + "angle": 0, + "content": "Given a pair of aligned teacher and student models, We first compute element-wise distillation loss on image features. We extract the image neck output as the image features to be distilled. To improve the smoothness of the distillation loss, we follow previous attempts [33] to use a KL divergence-based distillation loss. Specifically, we consider the flattened image features of the student and the teacher model as logits, which we convert into probability distribution via a softmax function with temperature \\(\\phi_{\\tau}\\), as defined in Eq. (2)." + }, + { + "type": "equation", + "bbox": [ + 0.631, + 0.449, + 0.892, + 0.483 + ], + "angle": 0, + "content": "\\[\n\\phi_ {\\tau} \\left(x _ {i}\\right) = \\frac {e ^ {x _ {i} / \\tau}}{\\sum_ {j} e ^ {x _ {j} / \\tau}} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.485, + 0.892, + 0.528 + ], + "angle": 0, + "content": "Then we calculate the KL divergence of each camera's output separately to obtain the image feature distillation loss, as in Eq. (3)." + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.536, + 0.892, + 0.565 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i m g} = \\frac {\\tau^ {2}}{B \\cdot W \\cdot H \\cdot C} \\times \\mathcal {D} _ {K L} \\left(\\phi_ {\\tau} \\left(F _ {i m g} ^ {T}\\right), \\phi_ {\\tau} \\left(F _ {i m g} ^ {S}\\right)\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.57, + 0.892, + 0.631 + ], + "angle": 0, + "content": "where B stands for the batch size, W, H, C mean the width, height, and number of channels of the image features, respectively. \\(F_{img}^{T}\\) and \\(F_{img}^{S}\\) denote the image features of the teacher model and the student model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.649, + 0.72, + 0.663 + ], + "angle": 0, + "content": "3.3.2 BEV feature distillation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.892, + 0.73 + ], + "angle": 0, + "content": "We first convert the BEV features of the student and teacher into probability distributions, following the same procedure as for image features. Then we compute the KL divergence for each point on the BEV features, as shown in Eq. (4)." + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.736, + 0.892, + 0.765 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {b e v} = \\frac {\\tau^ {2}}{B \\cdot C} \\times \\mathcal {D} _ {\\mathrm {K L}} \\left(\\phi_ {\\tau} \\left(F _ {b e v} ^ {T}\\right), \\phi_ {\\tau} \\left(F _ {b e v} ^ {S}\\right)\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.771, + 0.894, + 0.833 + ], + "angle": 0, + "content": "where B stands for the batch size, C means the number of channels of BEV features. \\(F_{bev}^{T}\\) and \\(F_{bev}^{S}\\) denote the BEV features of the teacher model and student model, respectively. We will get a loss with the shape of \\([H_{bev} \\times W_{bev}, 1]\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.849, + 0.787, + 0.865 + ], + "angle": 0, + "content": "3.3.3 View-guided distillation objective" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.872, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In the first two sections, we obtained the loss of each camera on the image feature and the corresponding loss of each" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3828" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.078, + 0.09, + 0.423, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 Progressive Quantization-Aware VGD" + }, + { + "type": "algorithm", + "bbox": [ + 0.078, + 0.111, + 0.47, + 0.324 + ], + "angle": 0, + "content": "Input: Training data; Pre-trained FP weights for teacher model \\(T_{fp}\\) Student model \\(S\\) Numbers of epochs for each phase \\(N_{1},\\ldots ,N_{4};P_{2}\\) Quantization bit for weight and activation \\(B_{w};B_{a}\\) \nOutput: Trained low-bit student model \\(S_{q}\\) Phase 1: Progressive Quantization-Aware Training Init \\(S_0\\) with \\(T_{fp}\\) Divide model into 4 Parts: {Backbone,Neck,Encoder,Decoder}; for i, module in Parts do module \\(\\equiv\\) quantize (module; \\(B_w,B_a)\\) Init \\(S_{i}\\) with \\(S_{i - 1}\\) for Epoch \\(\\equiv N_{i - 1}\\) ..., \\(N_{i}\\) do Update \\(S_{q_i}\\) by minimizing QAT loss" + }, + { + "type": "code_caption", + "bbox": [ + 0.095, + 0.326, + 0.336, + 0.339 + ], + "angle": 0, + "content": "Phase 2: View-Guided Distillation" + }, + { + "type": "algorithm", + "bbox": [ + 0.094, + 0.34, + 0.47, + 0.402 + ], + "angle": 0, + "content": "Init \\(S\\) with \\(S_{4}\\) \nfor Epoch \\(\\mathbf{\\Phi} = 1,\\dots ,P_2\\) do Update \\(S\\) by minimizing QAT loss and \\(\\mathcal{L}_{vgd}\\) in Eq. (6)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.432, + 0.473, + 0.631 + ], + "angle": 0, + "content": "point on the BEV feature. On the nuScenes dataset, the camera external parameters are known, so we can obtain the distribution range of each camera corresponding to the BEV feature. Then we generate the BEV mask of views \\( M_{bev} \\) that can be applied to the image feature, which is the same as defined in BEVFormer [23]. \\( M_{bev} \\) is a tensor with four dimensions: number of cameras, batch size, BEV size \\( (H_{bev} \\times W_{bev}) \\), and 3D Height, with binary values in each element. By calculating the average along the last dimension (3D Height), we can flatten the BEV mask \\( M_{bev} \\) on the 2d plane with the BEV size \\( (H_{bev} \\times W_{bev}) \\). Then the \\( \\mathcal{L}_{img} \\) calculated for each camera can be extended to the corresponding loss for each point on the BEV feature, which we refer to as \\( \\widehat{\\mathcal{L}}_{img} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.64, + 0.47, + 0.657 + ], + "angle": 0, + "content": "\\[\n\\widehat {\\mathcal {L}} _ {i m g} = \\mathcal {L} _ {i m g} \\odot M _ {b e v} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.67, + 0.345, + 0.685 + ], + "angle": 0, + "content": "where \\(\\odot\\) denotes the hadamard product." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.686, + 0.469, + 0.716 + ], + "angle": 0, + "content": "Finally, we use \\(\\widehat{\\mathcal{L}}_{img}\\) to get the view-guided distillation objective in Eq. (6):" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.724, + 0.47, + 0.762 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {v g d} = \\sum_ {i = 1} ^ {N \\cdot H \\cdot W} \\widehat {\\mathcal {L}} _ {i m g} \\odot \\mathcal {L} _ {b e v} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.771, + 0.47, + 0.802 + ], + "angle": 0, + "content": "The overall process of view-guided distillation is shown in Algorithm 1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.815, + 0.21, + 0.833 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In this section, we first elaborate on the experimental settings, then we evaluate both PTQ and QAT methods on the BEV networks. Based on the analysis of these results, we propose QD-BEV to overcome shortcomings in standard" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "PTQ and QAT, and we dedicatedly compare our results with previous works under different settings and constraints." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.132, + 0.704, + 0.148 + ], + "angle": 0, + "content": "4.1. Experimental settings" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.155, + 0.608, + 0.169 + ], + "angle": 0, + "content": "4.1.1 Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.179, + 0.894, + 0.316 + ], + "angle": 0, + "content": "We evaluated our proposed method on a challenging 3D detection task using the nuScenes dataset [3], which is a large-scale public dataset for autopilot developed by the team at Motional (formerly nuTonomy). This dataset contains 1000 manually selected 20-second driving scenarios collected in Boston and Singapore, with 750 scenarios for training, 100 for validation, and 150 for testing. The images in the dataset were captured from 6 cameras with known internal and external parameters." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.335, + 0.687, + 0.348 + ], + "angle": 0, + "content": "4.1.2 Evaluation metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.892, + 0.621 + ], + "angle": 0, + "content": "The main measurement indicators on the nuScenes 3D test dataset are the mean Average Precision (mAP), and the unique evaluation index nuScenes detection score (NDS). NDS is a comprehensive evaluation index containing many aspects of information. The other indicators are mean Average Translation Error (mATE), mean Average Scale Error (mASE), mean Average Orientation Error (mAOE), mean Average Velocity Error (mAVE) and mean Average Attribute Error (mAAE). To evaluate the efficiency of the BEV networks, we use model size and BOPS as the metrics. Model size is the memory required to store a specific network, which is determined by the total amount of parameters in the model as well as the quantization bitwidth to store those parameters. BOPS measures the total Bit Operations of one network inference [35]. It is a common metric for evaluating the computation of quantized neural networks. For a model with \\( L \\) layers, defining \\( b_{w_i} \\) and \\( b_{a_i} \\) to be the bitwidth used for weights and activations of the \\( i \\)-th layer, then we have:" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.629, + 0.892, + 0.654 + ], + "angle": 0, + "content": "\\[\nB O P S = \\sum_ {i = 1} ^ {L} b _ {w _ {i}} b _ {a _ {i}} M A C _ {i} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.661, + 0.892, + 0.782 + ], + "angle": 0, + "content": "where \\(\\mathrm{MAC}_i\\) is the total Multiply-Accumulate operations for computing the \\(i\\)-th layer. To better demonstrate the advantages of our QD-BEV model over the floating-point model, we introduce sAP [19] (streaming average precision) as one of the evaluation metrics for our model performance. sAP is a dynamic metric that will be updated as new data arrive, making it ideal for evaluating models in real-time scenarios." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.802, + 0.805, + 0.817 + ], + "angle": 0, + "content": "4.1.3 Baselines & Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.902 + ], + "angle": 0, + "content": "We mainly compare with floating-point baseline models proposed by BEVFormer [23] with different input image resolutions (specifically, BEVFormer-Tiny, BEVFormer-Small, and BEVFormer-Base). For quantization baselines, we apply the previous PTQ method DFQ [29] as well as" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3829" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.24, + 0.089, + 0.729, + 0.107 + ], + "angle": 0, + "content": "Table 1: Results with PTQ separately applied on each part in BEVFormer." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.117, + 0.895, + 0.303 + ], + "angle": 0, + "content": "
Quantized ModuleBEVFormer-TinyBEVFormer-SmallBEVFormer-Base
BackboneNeckEncoderDecodermAP↑NDS↑mAP↑NDS↑mAP↑NDS↑
××××0.2520.3540.3700.4790.4160.517
✓×××0.2120.3100.2880.4170.3090.440
×✓××0.2520.3530.3700.4780.4160.516
××✓×0.1810.2950.2980.4210.1600.303
×××✓0.2510.3530.3690.4770.4160.517
✓✓✓✓0.1450.2460.2280.3690.0750.224
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.47, + 0.357 + ], + "angle": 0, + "content": "QAT method PACT [7] and HAWQv3 [40] to quantize BEVFormer models and compare with QD-BEV." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.471, + 0.532 + ], + "angle": 0, + "content": "For floating-point models, we use the open-sourced repository of BEVFormer with two different backbones: ResNet50 and ResNet101-DCN. We use symmetrical linear quantization in a channel-wise manner for weights, and layer-wise quantization for activations, which are the standard settings for previous quantization methods. Since there is little related work in our settings for reference, we make our training adopt the same scheme as the original training strategy of BEVFormer, which is to train 24 epochs in each step, and to use optimizer of AdamW, a starting lr as 2e-4, a linear warmup of 500 iters, and cosine annealing." + }, + { + "type": "table_caption", + "bbox": [ + 0.083, + 0.561, + 0.462, + 0.577 + ], + "angle": 0, + "content": "Table 2: PTQ results with different quantization bitwidth." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.587, + 0.472, + 0.876 + ], + "angle": 0, + "content": "
W-bit/A-bitModelNDS↑NDS DropmAP↑
32/32Tiny0.354-0.252
Small0.479-0.370
Base0.517-0.416
8/8Tiny0.3510.8%0.248
Small0.4770.4%0.366
Base0.4875.8%0.384
6/6Tiny0.31211.9%0.203
Small0.43010.2%0.306
Base0.40222.2%0.262
4/6Tiny0.24630.5%0.146
Small0.36923.0%0.228
Base0.22656.3%0.076
4/4Tiny0.03490.4%0.001
Small0.03492.9%0.001
Base0.02395.6%0.000
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.324, + 0.895, + 0.37 + ], + "angle": 0, + "content": "Table 3: Comparison between progressive and standard QAT with W4A6. Please refer to Table 2 for baseline FP accuracy (W32A32)." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.38, + 0.895, + 0.505 + ], + "angle": 0, + "content": "
MethodModelNDS↑NDS DropmAP↑
Standard QATTiny0.3267.9%0.216
Small0.42112.1%0.303
base0.22456.7%0.071
Progressive QATTiny0.3481.7%0.234
Small0.4672.5%0.356
base0.4856.2%0.376
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.551, + 0.771, + 0.568 + ], + "angle": 0, + "content": "4.2. Analysis on BEV Quantization" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.586, + 0.64, + 0.602 + ], + "angle": 0, + "content": "4.2.1 PTQ results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.632, + 0.894, + 0.77 + ], + "angle": 0, + "content": "We first analyze the sensitivity of different modules to quantization in Table 1. It can be seen that the backbone and the encoder parts of the network are more sensitive, while quantization of the neck and the decoder parts only brings a slight disturbance to the accuracy. We want to note that, based on the sensitivity analysis, it is possible to apply mixed-precision quantization to better preserve the sensitive modules, but we leave this as future work since it is beyond the scope of this paper." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We then analyze the influence of different quantization bitwidth on the final performance. In Table 2, directly applying PTQ with less than 8-bit precision will lead to a significant accuracy drop, especially when quantized to W4A4 the results become pure noise with around \\(0\\mathrm{mAP}\\). As can be observed from Table 2, performing QAT is necessary in order to preserve the accuracy while achieving ultra-low bit quantization." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "3830" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.254, + 0.09, + 0.715, + 0.105 + ], + "angle": 0, + "content": "Table 4: QD-BEV results compared to previous methods or baselines." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.117, + 0.891, + 0.453 + ], + "angle": 0, + "content": "
Input SizeModelModel Size(MB)BOPS(Tera)NDS↑mAP↑mATE↓mASE↓mAOE↓mAVE↓mAAE↓
450×800BEVFormer-T[23]126.862.330.3540.2530.8990.2940.6550.6570.216
BEVFormer-T-DFQ[29]31.73.900.3400.2360.9490.2960.6510.6710.217
BEVFormer-T-HAWQv3[40]15.91.460.3480.2340.9490.3040.5680.6610.209
BEVFormer-T-PACT[7]15.91.460.3470.2340.9190.2890.6040.6710.216
QD-BEV-T (Ours)15.91.460.3720.2550.8820.3210.5430.5990.214
720×1280BEVFormer-S[23]225.6236.130.4790.3700.7220.2790.4070.4380.220
BEVFormer-S-DFQ[29]56.414.760.4670.3560.7510.2830.4050.4510.222
BEVFormer-S-HAWQv3[40]28.25.530.4670.3560.7510.2870.4190.4490.208
BEVFormer-S-PACT[7]28.25.530.4610.3510.7500.2750.4220.5070.196
QD-BEV-S (Ours)28.25.530.4790.3740.7160.2900.3890.4740.210
900×1600BEVFormer-B[23]262.9667.390.5170.4160.6720.2730.3700.3930.197
BEVFormer-B-DFQ[29]65.741.710.4860.3840.7710.2740.3780.4270.206
BEVFormer-B-HAWQv3[40]32.915.640.4850.3760.7270.2880.3810.4340.202
BEVFormer-B-PACT[7]32.915.640.4800.3740.7350.2910.3920.4580.201
QD-BEV-B (Ours)32.915.640.5090.4060.6910.2850.3600.4100.190
" + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.472, + 0.887, + 0.628 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.639, + 0.895, + 0.701 + ], + "angle": 0, + "content": "Figure 3: The training process of QD-BEV. Progressive QAT with 4 stages is performed in the first 60 epochs, then the view-guided distillation is conducted together with QAT to steadily enhance the performance. The pink line in the figure represents the baseline NDS. Note that swapping VGD with pure QAT or other distillation methods (for example, CWD [33]) will lead to undesirable results, as we show in the last 20 epochs in this figure, compared with Figure 1 and Figure 5." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.727, + 0.216, + 0.743 + ], + "angle": 0, + "content": "4.2.2 QAT results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To address the severe accuracy degradation of PTQ, we apply QAT to better adapt the models towards 4-bit quantization. In all our experiments, the standard QAT method which directly quantizes the whole network to the target bitwidth will lead to unstable QAT processes, causing gradient explosion or a rapid decrease in accuracy in large models (for example, the W4A6 BEVFormer-Base has only \\(0.07\\mathrm{mAP}\\)). Based on this observation, we hypothesize that the quantization perturbation introduced in standard QAT" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.727, + 0.892, + 0.894 + ], + "angle": 0, + "content": "is too large to be recovered. As such, we apply progressive QAT to constrain the quantization perturbation along the training process. A comparison of the performance between progressive QAT and standard QAT with the same number of training epochs is presented in Table 3. We can see that progressive QAT consistently outperforms standard QAT by a large margin (up to \\(5\\%\\) mAP) in BEVFormer-Tiny and BEVFormer-Small, and achieves an even larger performance gain on BEVFormer-Base. To better validate our analyses, we plot the training curve of progressive QAT as the first 60 epochs in Figure 3, where W4A6 quantization" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.514, + 0.957 + ], + "angle": 0, + "content": "3831" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.09, + 0.454, + 0.105 + ], + "angle": 0, + "content": "Table 5: QD-BEV results on BEVDepth[21] and PETR[24]." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.116, + 0.467, + 0.416 + ], + "angle": 0, + "content": "
WAModelmAP↑NDS↑
3232BEVDepth-T[21]0.3300.435
88BEVDepth-T-DFQ[29]0.2810.377
46BEVDepth-T-HAWQ[40]0.1360.206
46BEVDepth-T-PACT[7]0.2700.362
46QD-BEVDepth-T (Ours)0.3010.394
3232PETR-r50dcn[24]0.3170.366
88PETR-r50dcn-DFQ[29]0.2900.343
46PETR-r50dcn-HAWQ[40]0.1620.216
46PETR-r50dcn-PACT[7]0.2680.320
46QD-PETR-r50dcn (Ours)0.2880.334
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.469, + 0.506 + ], + "angle": 0, + "content": "is conducted on BEVFormer-Tiny. We separate the progressive QAT into 4 stages and iteratively quantize a new module in each stage. As can be seen, there is an NDS drop at beginning of each stage, corresponding to the quantization perturbation introduced by quantizing each new module." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.469, + 0.597 + ], + "angle": 0, + "content": "Despite the merits of progressive QAT, we want to note that it still suffers from unstable training and performance degradation. As illustrated in Figure 1 which corresponds to the last 20 epochs in Figure 3, progressive QAT keeps going up and down after reaching a plateau, while training curves of VGD show a rising trend with much better stability." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.606, + 0.308, + 0.621 + ], + "angle": 0, + "content": "4.3. Main Results of QD-BEV" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In order to obtain better accuracy and stability, we apply view-guided distillation with the floating-point model as the teacher and the quantized model as the student. The effect of VGD on W4A6 quantization of BEVFormer-Tiny is shown in Figure 3. Note that we separate VGD from progressive QAT in the first 60 epochs for a clearer comparison and illustration, and VGD is actually a plug-and-play function that can always be jointly applied with QAT, as we do in the last 20 epochs. Benefiting from knowledge in both the image domain and the BEV domain, QD-BEV networks are able to fully recover the quantization degradation, and even outperform the floating-point baselines. As shown in Table 4, the NDS and mAP of the model outperform previous floating-point baselines as well as quantized networks. Since there are no existing results for compact BEV networks, we implement standard quantization methods DFQ [29], HAWQv3 [40] and PACT [7] on BEVFormer as a comparison. We apply W8A8 quantization for DFQ" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.091, + 0.888, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.35, + 0.892, + 0.381 + ], + "angle": 0, + "content": "Figure 4: Visualization of QD-BEV results and the comparison with results obtained by BEVFormer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.409, + 0.892, + 0.5 + ], + "angle": 0, + "content": "(DFQ is a PTQ method, lower bitwidth will lead to intolerable accuracy degradation) and W4A6 for QAT methods and QD-BEV models. As a comparison, QD-BEV can achieve 0.509 NDS with only 32.9 MB model size, which is similar to the size of BEVFormer-T-DFQ (0.340 NDS) and much smaller than BEVFormer-Tiny (126.8 MB, 0.354 NDS)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.501, + 0.892, + 0.577 + ], + "angle": 0, + "content": "Preliminary tests were run on PETR [24] and BEVDepth [21] models using our method in figure 5. Performance did not match BEVFormer, but still surpassed conventional quantization methods, highlighting the method's potential despite varying results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.683 + ], + "angle": 0, + "content": "In Figure 4, we show the visualization results of the QDBEV-Base model on the nuScenes val dataset, and compare them with the results of BEVFormer-Tiny and the ground truth. As can be seen, more objects are detected by QDBEV-Base, and the 3D boxes predictions are more accurate than BEVFormer-Tiny. More visualizations are provided in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.696, + 0.75, + 0.712 + ], + "angle": 0, + "content": "4.4. Streaming perception result" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In the context of autonomous driving, streaming perception [19] is critical for enabling models to make rapid and precise decisions in real time. High latency will degrade the streaming perception because it will cause a delay between the sensory data and the neural network output. To enhance streaming perception, quantization is a necessary technique that compresses the model size, reduces computational load, and accelerates the inference process. In Table 6, we demonstrate the significant impact of quantization on the sAP metric in autonomous driving scenarios. As we can see, QD-BEV models show consistent improvements in sAP compared to the floating-point counterparts and the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3832" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.085, + 0.089, + 0.462, + 0.105 + ], + "angle": 0, + "content": "Table 6: sAP of QD-BEV models compared to baselines." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.117, + 0.468, + 0.339 + ], + "angle": 0, + "content": "
Input SizeModelWAmAP↑sAP↑
450×800BEVFormer-T[23]32320.2530.228
BEVFormer-T-DFQ[29]880.2360.230
QD-BEV-T (Ours)460.2550.251
720×1280BEVFormer-S[23]32320.3700.249
BEVFormer-S-DFQ[29]880.3560.322
QD-BEV-S (Ours)460.3740.350
900×1600BEVFormer-B[23]32320.4160.136
BEVFormer-B-DFQ[29]880.3840.290
QD-BEV-B (Ours)460.4060.337
" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.354, + 0.278, + 0.476 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.13, + 0.484, + 0.222, + 0.496 + ], + "angle": 0, + "content": "(a) mAP curve." + }, + { + "type": "image", + "bbox": [ + 0.28, + 0.354, + 0.474, + 0.476 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.326, + 0.484, + 0.418, + 0.496 + ], + "angle": 0, + "content": "(b) NDS curve." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.509, + 0.47, + 0.556 + ], + "angle": 0, + "content": "Figure 5: The training curve of VGD versus CWD [33]. CWD uses only one type of features, referred to as cwd-image (image feature) and cwd-bev (bev feature), respectively." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.582, + 0.214, + 0.597 + ], + "angle": 0, + "content": "quantized baselines." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.61, + 0.226, + 0.628 + ], + "angle": 0, + "content": "5. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.636, + 0.47, + 0.788 + ], + "angle": 0, + "content": "In Figure 5, we conduct an ablation study where we compare view-guided distillation with the cases using only distillation on the image feature, and only on the BEV feature, respectively. The method is referred to as CWD [33]. For a fair comparison, we apply the same pre-training weights and hyperparameters such as the temperature and the learning rate. From the figure, it can be found that view-guided distillation has a clear advantage over the CWD methods. In both the mAP and NDS curves, VGD has a more obvious and stable upward trend, and achieves better final results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.801, + 0.196, + 0.816 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.903 + ], + "angle": 0, + "content": "In this work, we systematically study both PTQ and QAT on BEV networks and showcase the major problems they are facing. Based on our analyses, we propose a view-guided distillation (VGD) method that can stabilize the QAT process and enhance the final performance by lever" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.228 + ], + "angle": 0, + "content": "aging information from both the image domain and the BEV domain. With VGD as a plug-and-play function that can be jointly applied when quantizing BEV models, QD-BEV can close the accuracy gap or even outperforms the floating-point baselines. On the nuScenes datasets, the 4-bit weight and 6-bit activation quantized QD-BEV-Tiny model achieves \\(37.2\\%\\) NDS with only \\(15.8\\mathrm{MB}\\) model size, outperforming BevFormer-Tiny by \\(1.8\\%\\) with an \\(8\\times\\) model compression." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.243, + 0.681, + 0.261 + ], + "angle": 0, + "content": "7. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.269, + 0.892, + 0.389 + ], + "angle": 0, + "content": "This work was supported by the National Key R&D Program of China (2022ZD0116305). The authors would also like to express their gratitude to the CCF-Baidu Open Fund Project, Berkeley Deep Drive, and Intel Corporation for their support and assistance throughout this research. Special thanks to Yandong Guo from \\(\\mathrm{Al}^2\\) Robotics (YAN-DONG.guo@live.com) for his valuable contributions to this work." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.406, + 0.597, + 0.422 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.431, + 0.892, + 0.501 + ], + "angle": 0, + "content": "[1] Sungsoo Ahn, Shell Xu Hu, Andreas Damianou, Neil D Lawrence, and Zhenwen Dai. Variational information distillation for knowledge transfer. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9163-9171, 2019." + }, + { + "type": "ref_text", + "bbox": [ + 0.509, + 0.503, + 0.894, + 0.558 + ], + "angle": 0, + "content": "[2] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. 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Deformable detr: Deformable transformers for end-to-end object detection. arXiv preprint arXiv:2010.04159, 2020." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.093, + 0.468, + 0.869 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.515, + 0.956 + ], + "angle": 0, + "content": "3835" + } + ] +] \ No newline at end of file diff --git a/2023/QD-BEV _ Quantization-aware View-guided Distillation for Multi-view 3D Object Detection/ce2686ce-9d14-4ea8-b9f7-4395d3561b65_origin.pdf b/2023/QD-BEV _ Quantization-aware View-guided Distillation for Multi-view 3D Object Detection/ce2686ce-9d14-4ea8-b9f7-4395d3561b65_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..53776e59b24b944d81e07d78d536e9ece5ccd66e --- /dev/null +++ b/2023/QD-BEV _ Quantization-aware View-guided Distillation for Multi-view 3D Object Detection/ce2686ce-9d14-4ea8-b9f7-4395d3561b65_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ec77e5216c28cb1ebdde23464edc6e007a5a2e335a9f13b34d3dc880239129d3 +size 2637789 diff --git a/2023/QD-BEV _ Quantization-aware View-guided Distillation for Multi-view 3D Object Detection/full.md b/2023/QD-BEV _ Quantization-aware View-guided Distillation for Multi-view 3D Object Detection/full.md new file mode 100644 index 0000000000000000000000000000000000000000..fbea7e6062126e1c3d5ccf69dad405e0fcdbf72b --- /dev/null +++ b/2023/QD-BEV _ Quantization-aware View-guided Distillation for Multi-view 3D Object Detection/full.md @@ -0,0 +1,306 @@ +# QD-BEV : Quantization-aware View-guided Distillation for Multi-view 3D Object Detection + +Yifan Zhang $^{1*}$ , Zhen Dong $^{2*}$ , Huanrui Yang $^{2}$ , Ming Lu $^{3}$ , Cheng-Ching Tseng $^{3}$ , Yuan Du $^{1}$ , Kurt Keutzer $^{2}$ , Li Du $^{1\dagger}$ , Shanghang Zhang $^{3\dagger}$ + +$^{1}$ Nanjing University, $^{2}$ University of California, Berkeley, + +$^{3}$ National Key Laboratory for Multimedia Information Processing, School of Computer Science, Peking University, + +# Abstract + +Multi-view 3D detection based on BEV (bird-eye-view) has recently achieved significant improvements. However, the huge memory consumption of state-of-the-art models makes it hard to deploy them on vehicles, and the nontrivial latency will affect the real-time perception of streaming applications. Despite the wide application of quantization to lighten models, we show in our paper that directly applying quantization in BEV tasks will 1) make the training unstable, and 2) lead to intolerable performance degradation. To solve these issues, our method QD-BEV enables a novel view-guided distillation (VGD) objective, which can stabilize the quantization-aware training (QAT) while enhancing the model performance by leveraging both image features and BEV features. Our experiments show that QD-BEV achieves similar or even better accuracy than previous methods with significant efficiency gains. On the nuScenes datasets, the 4-bit weight and 6-bit activation quantized QD-BEV-Tiny model achieves $37.2\%$ NDS with only 15.8 MB model size, outperforming BevFormer-Tiny by $1.8\%$ with an $8\times$ model compression. On the Small and Base variants, QD-BEV models also perform superbly and achieve $47.9\%$ NDS (28.2 MB) and $50.9\%$ NDS (32.9 MB), respectively. + +# 1. Introduction + +Given its potential in enabling autopilot, multi-view 3D detection based on BEV (bird-eye-view) has become + +![](images/65d7190e406100619b395886dc2249444c87c520c510fd95b7a95bf50905d247.jpg) +(a) mAP curve. + +![](images/4ee11694ecc32e832afc5494f2c72da14a4d2cee7ceec0ff6b448b184ccd8b63.jpg) +(b) NDS curve. +Figure 1: Training curves of QD-BEV (with VGD) versus progressive QAT on W4A6 quantization of BEVFormer-Tiny. Note that standard QAT works even worse compared to progressive QAT and it falls out of the targeted accuracy range in the figures. + +an important research direction for autonomous driving. Based on input sensors, previous work can be divided into LiDAR-based methods [18, 47] and camera-only methods [23, 38, 14, 13, 24, 25]. Compared to the LiDAR-based methods, camera-only methods have the merits of lower deployment cost, closer to human eyes, and easier access to visual information in the driving environment. However, even if using the camera-only methods, the computational and memory costs of running state-of-the-art BEV models are still formidable, making it difficult to deploy them onto vehicles. For example, BEVFormer-Base has a $540~\mathrm{ms}$ inference latency (corresponds to 1.85 fps) on one NVIDIA V100 GPU, which is infeasible for real-time applications that generally require 30 fps. Since a non-trivial latency will harm the streaming perception, it is particularly crucial to explore and devise lightweight models for camera-only 3D object detection based on BEV. + +Quantization [16, 11, 42, 10] can reduce the bitwidth used to represent weights and activations in deep neural net- + +![](images/3200c2b36546e2c17d6813a1aba9553b45604f481f77e137d547f51bab561213.jpg) + +![](images/93b69a2e2268f57f7d74f78e42b517b74a4533b8181533203ae624f083e1aec7.jpg) +Figure 2: Illustration of QD-BEV. (a) In our pipeline, multi-camera images are input into the floating-point teacher network and the quantized student network in order to compute the KL divergence in an element-wise manner. The KL divergence is used as distillation loss in the image feature and the BEV feature, respectively. Then we conduct view-guided distillation using the BEV mask obtained from the external parameters of the camera. Please refer to Sec.3.1 for more details. (b) The lower flow chart shows the computation process of the view-guided distillation loss. Specific details are in Sec. 3.3. + +works, which can greatly save the model size and computational costs while improving the speed of model reasoning. However, directly applying quantization would lead to significant performance degradation. Compared to image classification and 2D object detection tasks where the standard quantization methods shine, multi-camera 3D detection tasks are much more complicated and difficult due to the existence of multiple views and information from multiple dimensions (for example, the temporal information and spatial information used in BEVFormer [23]). Consequently, the structure of BEV networks tends to become more complex, with a deeper convolutional neural network backbone to extract image information from multiple views, and with transformers to encode and decode the features of the BEV domain. The presence of different neural architectures, multiple objectives, and knowledge from different modalities greatly challenges the standard quantization methods, decreasing their stability and accuracy, and even making the whole training process diverge. In Figure 1, we + +show the training curves when applying W4A6 quantization on a BEVFormer-Tiny model. As can be seen, the performance of quantization-aware training (QAT) fluctuates significantly in different epochs, while the performance of our proposed method QD-BEV shows a stable rising trend. We perform more experiments to validate the effectiveness of QD-BEV in Sec 5. + +To solve the problems of standard QAT, in this work, we first conduct systematic experiments and analyses on quantizing BEV networks. Then we devise a quantization-aware view-guided distillation method (referred to as QD-BEV) that can decently solve the stability issue while improving the final performance of compact BEV models. Our proposed view-guided distillation (VGD) can better leverage information from both the image and the BEV domains for multi-view 3D object detection. This can significantly outperform previous distillation methods that cannot jointly handle the different types of losses in BEV networks. Specifically, as shown in Figure 2, we first take + +the FP (floating-point) model as the teacher model and the quantized model as the student model, then we calculate the KL divergence on the image feature and the BEV feature, respectively. Finally, we leverage the mapping relationship and realize VGD by organically combining the image feature and the BEV feature through the camera's external parameters. Note that in QD-BEV, neither additional training data nor larger powerful teacher networks are used to tune the accuracy, but QD-BEV models are still able to outperform previous baselines while having significantly smaller model sizes and computational requirements. Our contributions are as follows: + +- We conduct systematic experiments on quantizing BEV models, unveiling major issues hampering standard quantization-aware training methods on BEV. +- We specially design view-guided distillation (VGD) for BEV models, which jointly leverages both image domain and BEV domain information. VGD boosts the final performance while solving the stability issue of standard QAT. +- Our W4A6 quantized QD-BEV-Tiny has $37.2\%$ NDS with only 15.8 MB model size, which outperforms the $8 \times$ larger BevFormer-Tiny model by $1.8\%$ . + +# 2. Related Works + +# 2.1. Camera-only 3D object detection + +In camera-only 3D object detection tasks, many excellent methods have emerged based on BEV (bird-eye-view). Previous works, LSS [31] and BEVDet [14], project image features to the BEV space in a bottom-up manner. Based on DETR [5] and Deformable DETR [48], DETR3D [38] extends the 2D object detection to the 3D space through the architecture of Backbone + FPN + Decoder. In addition, PETR [24] introduces 3D position coding based on DETR3D [38]. In BEVFormer [23], the authors use dense BEV queries to exchange information in the BEV space with the multi-view image space. More stable BEV features are obtained by extracting temporal and spatial information through the transformer structure with temporal self-attention and spacial cross-attention. Based on the temporal interaction in BEVFormer, further improvements have been made in recent works, PETRv2 [25] and BEVDet4D [13]. Besides the aforementioned works, BEVDepth [21] and BEVstereo [20] are two state-of-the-art approaches for monocular depth estimation and stereo vision in the birdeye-view (BEV) domain, respectively, which leverage the unique characteristics of BEV representations to achieve high accuracy and efficiency. + +# 2.2. Quantization + +To reduce the model size, quantization [45, 36, 15, 26] uses low bitwidth to represent weights and activations in neural networks. With the use of low-precision matrix multiplication or convolution, quantization can also make the inference process faster and more efficient. Given a pretrained model, directly performing quantization without any fine-tuning is referred to as post-training quantization (PTQ) [4, 29, 37, 17]. Despite the merits, PTQ with low bitwidth still results in significant accuracy degradation. As such, Quantization-aware training (QAT) is proposed to train the model to better adapt to quantization. QAT methods [9, 7, 40] are more costly compared to PTQ, but can potentially obtain higher accuracy. Furthermore, in the cases with ultra-low quantization bitwidth (for example, 4-bit), even QAT cannot close the accuracy gap. A promising direction to solve this is to use mixed-precision quantization [46, 36, 39], where some sensitive layers are kept at higher precision to recover the accuracy. Though effective, the support for mixed-precision quantization on general-purpose machines (CPUs and GPUs) is currently immature and may lead to extra latency overhead. + +Although standard quantization methods have shown great results on convolutional neural networks, recent works [27, 44] mention that it may suffer in other neural architectures such as transformers. The presence of both convolutional blocks and transformers in BEV networks makes them challenging to the traditional quantization methods. + +# 2.3. Distillation + +Model distillation [12, 28, 22, 32, 1] generally uses a large model as the teacher to train a compact student model. Instead of using class labels during the training of the student model, the key idea is to leverage the soft probabilities produced by the teacher to guide the student's training. Previous methods of distillation explore different knowledge sources (for example, [12, 22, 30] use logits, aka the soft probabilities). The choices of teacher models are also studied, where [41, 34] use multiple teacher models, while [8, 43] apply self-distillation without an extra teacher model. Other previous efforts apply distillation with different settings on different applications. Regarding BEV networks, previous work [6] tries to teach LiDAR information to camera-based networks through distillation, but the additional requirement for LiDAR data makes it infeasible in our pure camera-based setting. Besides, the existence of different types of losses in BEV networks makes standard distillation methods invalid. An arbitrary or sub-optimal combination of knowledge sources would also make the training unstable, perform badly, or even diverge. + +# 3. Method + +# 3.1. Overview of QD-BEV pipeline + +This work aims to improve the efficiency of state-of-the-art BEV models. Starting with the widely used BEV-Former [23], we apply a progressive quantization-aware training procedure in a stage-by-stage manner (details are introduced in Sec. 3.2). We further boost its stability and performance through a novel view-guided distillation process, which is highlighted in Figure 2, where we use a floating-point teacher model to facilitate the learning of our quantized QD-BEV student model. Specifically, the input multi-camera image is entered into the teacher and the student, respectively, and then the Image Backbone and Image Neck parts of the network are used to extract the multicamera image feature. After the transformer part of the network, the BEV features are extracted, and the two parts of the teacher model and the student model are used to calculate image distill loss and BEV distill loss, respectively. The two distillation losses are then fused through the external parameters of the camera to achieve our unique view-guided distillation mechanism. We provide a detailed formulation of the view-guided distillation process in Sec. 3.3. + +# 3.2. Quantization-aware training + +In symmetric linear quantization, the quantizer maps weights and activations into integers with a scale factor $S$ . Uniformly quantizing to k bit can be expressed as: + +$$ +S = \frac {2 \left| r _ {\max } \right|}{2 ^ {k} - 1}, q = \operatorname {r o u n d} \left(\frac {r}{S}\right) \tag {1} +$$ + +where $r$ is the floating-point number being quantized, $|r_{\mathrm{max}}|$ is the largest absolute value in $r$ , and $q$ is the quantized integer. In this work, we conduct systematic experiments to analyze the performance of quantization on BEV networks. For PTQ, we apply the above quantization directly to the pre-trained models during the inference stage. For QAT, we utilize the straight-through estimator (STE) [2] to define the forward and backward processes for the above quantization operations, and then we train the model to better adapt to quantization. As previously mentioned in Sec. 1 and Sec. 2, considering that standard QAT may lead to divergence due to the characteristics of BEV models, we apply a stage-wise progressive QAT where we gradually reduce the weight precision in four stages (backbone, neck, encoder, and decoder) based on the design of BEV-Former [23]. The performance of this progressive QAT is illustrated in Figure 3. And we compare the effectiveness of the progressive QAT with standard QAT in Sec. 4.2.2. + +# 3.3. View-guided distillation + +Compared to traditional single-domain distillation methods, our approach exploits the complementary nature of + +both BEV and image domains, which provides different perspectives and capture different aspects of the scene. The BEV domain offers a top-down view, enabling accurate perception and recognition of the surrounding environment, such as the structure of the road, the location of vehicles, and lane markings. On the other hand, the image domain provides more realistic visual information, capturing rich scene details and color information. In the following sections, we present details of VGD: the computation of the image feature distillation in Sec. 3.3.1, the BEV feature distillation in Sec. 3.3.2, and the view-guided distillation combining the previous two distillation losses in Sec. 3.3.3. + +# 3.3.1 Image feature distillation + +Given a pair of aligned teacher and student models, We first compute element-wise distillation loss on image features. We extract the image neck output as the image features to be distilled. To improve the smoothness of the distillation loss, we follow previous attempts [33] to use a KL divergence-based distillation loss. Specifically, we consider the flattened image features of the student and the teacher model as logits, which we convert into probability distribution via a softmax function with temperature $\phi_{\tau}$ , as defined in Eq. (2). + +$$ +\phi_ {\tau} \left(x _ {i}\right) = \frac {e ^ {x _ {i} / \tau}}{\sum_ {j} e ^ {x _ {j} / \tau}} \tag {2} +$$ + +Then we calculate the KL divergence of each camera's output separately to obtain the image feature distillation loss, as in Eq. (3). + +$$ +\mathcal {L} _ {i m g} = \frac {\tau^ {2}}{B \cdot W \cdot H \cdot C} \times \mathcal {D} _ {K L} \left(\phi_ {\tau} \left(F _ {i m g} ^ {T}\right), \phi_ {\tau} \left(F _ {i m g} ^ {S}\right)\right) \tag {3} +$$ + +where B stands for the batch size, W, H, C mean the width, height, and number of channels of the image features, respectively. $F_{img}^{T}$ and $F_{img}^{S}$ denote the image features of the teacher model and the student model. + +# 3.3.2 BEV feature distillation + +We first convert the BEV features of the student and teacher into probability distributions, following the same procedure as for image features. Then we compute the KL divergence for each point on the BEV features, as shown in Eq. (4). + +$$ +\mathcal {L} _ {b e v} = \frac {\tau^ {2}}{B \cdot C} \times \mathcal {D} _ {\mathrm {K L}} \left(\phi_ {\tau} \left(F _ {b e v} ^ {T}\right), \phi_ {\tau} \left(F _ {b e v} ^ {S}\right)\right) \tag {4} +$$ + +where B stands for the batch size, C means the number of channels of BEV features. $F_{bev}^{T}$ and $F_{bev}^{S}$ denote the BEV features of the teacher model and student model, respectively. We will get a loss with the shape of $[H_{bev} \times W_{bev}, 1]$ . + +# 3.3.3 View-guided distillation objective + +In the first two sections, we obtained the loss of each camera on the image feature and the corresponding loss of each + +Algorithm 1 Progressive Quantization-Aware VGD +Input: Training data; Pre-trained FP weights for teacher model $T_{fp}$ Student model $S$ Numbers of epochs for each phase $N_{1},\ldots ,N_{4};P_{2}$ Quantization bit for weight and activation $B_{w};B_{a}$ +Output: Trained low-bit student model $S_{q}$ Phase 1: Progressive Quantization-Aware Training Init $S_0$ with $T_{fp}$ Divide model into 4 Parts: {Backbone,Neck,Encoder,Decoder}; for i, module in Parts do module $\equiv$ quantize (module; $B_w,B_a)$ Init $S_{i}$ with $S_{i - 1}$ for Epoch $\equiv N_{i - 1}$ ..., $N_{i}$ do Update $S_{q_i}$ by minimizing QAT loss + +Phase 2: View-Guided Distillation +Init $S$ with $S_{4}$ +for Epoch $\mathbf{\Phi} = 1,\dots ,P_2$ do Update $S$ by minimizing QAT loss and $\mathcal{L}_{vgd}$ in Eq. (6) + +point on the BEV feature. On the nuScenes dataset, the camera external parameters are known, so we can obtain the distribution range of each camera corresponding to the BEV feature. Then we generate the BEV mask of views $M_{bev}$ that can be applied to the image feature, which is the same as defined in BEVFormer [23]. $M_{bev}$ is a tensor with four dimensions: number of cameras, batch size, BEV size $(H_{bev} \times W_{bev})$ , and 3D Height, with binary values in each element. By calculating the average along the last dimension (3D Height), we can flatten the BEV mask $M_{bev}$ on the 2d plane with the BEV size $(H_{bev} \times W_{bev})$ . Then the $\mathcal{L}_{img}$ calculated for each camera can be extended to the corresponding loss for each point on the BEV feature, which we refer to as $\widehat{\mathcal{L}}_{img}$ : + +$$ +\widehat {\mathcal {L}} _ {i m g} = \mathcal {L} _ {i m g} \odot M _ {b e v} \tag {5} +$$ + +where $\odot$ denotes the hadamard product. + +Finally, we use $\widehat{\mathcal{L}}_{img}$ to get the view-guided distillation objective in Eq. (6): + +$$ +\mathcal {L} _ {v g d} = \sum_ {i = 1} ^ {N \cdot H \cdot W} \widehat {\mathcal {L}} _ {i m g} \odot \mathcal {L} _ {b e v} \tag {6} +$$ + +The overall process of view-guided distillation is shown in Algorithm 1. + +# 4. Experiments + +In this section, we first elaborate on the experimental settings, then we evaluate both PTQ and QAT methods on the BEV networks. Based on the analysis of these results, we propose QD-BEV to overcome shortcomings in standard + +PTQ and QAT, and we dedicatedly compare our results with previous works under different settings and constraints. + +# 4.1. Experimental settings + +# 4.1.1 Dataset + +We evaluated our proposed method on a challenging 3D detection task using the nuScenes dataset [3], which is a large-scale public dataset for autopilot developed by the team at Motional (formerly nuTonomy). This dataset contains 1000 manually selected 20-second driving scenarios collected in Boston and Singapore, with 750 scenarios for training, 100 for validation, and 150 for testing. The images in the dataset were captured from 6 cameras with known internal and external parameters. + +# 4.1.2 Evaluation metrics + +The main measurement indicators on the nuScenes 3D test dataset are the mean Average Precision (mAP), and the unique evaluation index nuScenes detection score (NDS). NDS is a comprehensive evaluation index containing many aspects of information. The other indicators are mean Average Translation Error (mATE), mean Average Scale Error (mASE), mean Average Orientation Error (mAOE), mean Average Velocity Error (mAVE) and mean Average Attribute Error (mAAE). To evaluate the efficiency of the BEV networks, we use model size and BOPS as the metrics. Model size is the memory required to store a specific network, which is determined by the total amount of parameters in the model as well as the quantization bitwidth to store those parameters. BOPS measures the total Bit Operations of one network inference [35]. It is a common metric for evaluating the computation of quantized neural networks. For a model with $L$ layers, defining $b_{w_i}$ and $b_{a_i}$ to be the bitwidth used for weights and activations of the $i$ -th layer, then we have: + +$$ +B O P S = \sum_ {i = 1} ^ {L} b _ {w _ {i}} b _ {a _ {i}} M A C _ {i} \tag {7} +$$ + +where $\mathrm{MAC}_i$ is the total Multiply-Accumulate operations for computing the $i$ -th layer. To better demonstrate the advantages of our QD-BEV model over the floating-point model, we introduce sAP [19] (streaming average precision) as one of the evaluation metrics for our model performance. sAP is a dynamic metric that will be updated as new data arrive, making it ideal for evaluating models in real-time scenarios. + +# 4.1.3 Baselines & Implementation Details + +We mainly compare with floating-point baseline models proposed by BEVFormer [23] with different input image resolutions (specifically, BEVFormer-Tiny, BEVFormer-Small, and BEVFormer-Base). For quantization baselines, we apply the previous PTQ method DFQ [29] as well as + +Table 1: Results with PTQ separately applied on each part in BEVFormer. + +
Quantized ModuleBEVFormer-TinyBEVFormer-SmallBEVFormer-Base
BackboneNeckEncoderDecodermAP↑NDS↑mAP↑NDS↑mAP↑NDS↑
××××0.2520.3540.3700.4790.4160.517
✓×××0.2120.3100.2880.4170.3090.440
×✓××0.2520.3530.3700.4780.4160.516
××✓×0.1810.2950.2980.4210.1600.303
×××✓0.2510.3530.3690.4770.4160.517
✓✓✓✓0.1450.2460.2280.3690.0750.224
+ +QAT method PACT [7] and HAWQv3 [40] to quantize BEVFormer models and compare with QD-BEV. + +For floating-point models, we use the open-sourced repository of BEVFormer with two different backbones: ResNet50 and ResNet101-DCN. We use symmetrical linear quantization in a channel-wise manner for weights, and layer-wise quantization for activations, which are the standard settings for previous quantization methods. Since there is little related work in our settings for reference, we make our training adopt the same scheme as the original training strategy of BEVFormer, which is to train 24 epochs in each step, and to use optimizer of AdamW, a starting lr as 2e-4, a linear warmup of 500 iters, and cosine annealing. + +Table 2: PTQ results with different quantization bitwidth. + +
W-bit/A-bitModelNDS↑NDS DropmAP↑
32/32Tiny0.354-0.252
Small0.479-0.370
Base0.517-0.416
8/8Tiny0.3510.8%0.248
Small0.4770.4%0.366
Base0.4875.8%0.384
6/6Tiny0.31211.9%0.203
Small0.43010.2%0.306
Base0.40222.2%0.262
4/6Tiny0.24630.5%0.146
Small0.36923.0%0.228
Base0.22656.3%0.076
4/4Tiny0.03490.4%0.001
Small0.03492.9%0.001
Base0.02395.6%0.000
+ +Table 3: Comparison between progressive and standard QAT with W4A6. Please refer to Table 2 for baseline FP accuracy (W32A32). + +
MethodModelNDS↑NDS DropmAP↑
Standard QATTiny0.3267.9%0.216
Small0.42112.1%0.303
base0.22456.7%0.071
Progressive QATTiny0.3481.7%0.234
Small0.4672.5%0.356
base0.4856.2%0.376
+ +# 4.2. Analysis on BEV Quantization + +# 4.2.1 PTQ results + +We first analyze the sensitivity of different modules to quantization in Table 1. It can be seen that the backbone and the encoder parts of the network are more sensitive, while quantization of the neck and the decoder parts only brings a slight disturbance to the accuracy. We want to note that, based on the sensitivity analysis, it is possible to apply mixed-precision quantization to better preserve the sensitive modules, but we leave this as future work since it is beyond the scope of this paper. + +We then analyze the influence of different quantization bitwidth on the final performance. In Table 2, directly applying PTQ with less than 8-bit precision will lead to a significant accuracy drop, especially when quantized to W4A4 the results become pure noise with around $0\mathrm{mAP}$ . As can be observed from Table 2, performing QAT is necessary in order to preserve the accuracy while achieving ultra-low bit quantization. + +Table 4: QD-BEV results compared to previous methods or baselines. + +
Input SizeModelModel Size(MB)BOPS(Tera)NDS↑mAP↑mATE↓mASE↓mAOE↓mAVE↓mAAE↓
450×800BEVFormer-T[23]126.862.330.3540.2530.8990.2940.6550.6570.216
BEVFormer-T-DFQ[29]31.73.900.3400.2360.9490.2960.6510.6710.217
BEVFormer-T-HAWQv3[40]15.91.460.3480.2340.9490.3040.5680.6610.209
BEVFormer-T-PACT[7]15.91.460.3470.2340.9190.2890.6040.6710.216
QD-BEV-T (Ours)15.91.460.3720.2550.8820.3210.5430.5990.214
720×1280BEVFormer-S[23]225.6236.130.4790.3700.7220.2790.4070.4380.220
BEVFormer-S-DFQ[29]56.414.760.4670.3560.7510.2830.4050.4510.222
BEVFormer-S-HAWQv3[40]28.25.530.4670.3560.7510.2870.4190.4490.208
BEVFormer-S-PACT[7]28.25.530.4610.3510.7500.2750.4220.5070.196
QD-BEV-S (Ours)28.25.530.4790.3740.7160.2900.3890.4740.210
900×1600BEVFormer-B[23]262.9667.390.5170.4160.6720.2730.3700.3930.197
BEVFormer-B-DFQ[29]65.741.710.4860.3840.7710.2740.3780.4270.206
BEVFormer-B-HAWQv3[40]32.915.640.4850.3760.7270.2880.3810.4340.202
BEVFormer-B-PACT[7]32.915.640.4800.3740.7350.2910.3920.4580.201
QD-BEV-B (Ours)32.915.640.5090.4060.6910.2850.3600.4100.190
+ +![](images/5ee206ceecc8b73755d7f7355f0fd93aa2d0c4c1e03044e3713b092f3fcbac4a.jpg) +Figure 3: The training process of QD-BEV. Progressive QAT with 4 stages is performed in the first 60 epochs, then the view-guided distillation is conducted together with QAT to steadily enhance the performance. The pink line in the figure represents the baseline NDS. Note that swapping VGD with pure QAT or other distillation methods (for example, CWD [33]) will lead to undesirable results, as we show in the last 20 epochs in this figure, compared with Figure 1 and Figure 5. + +# 4.2.2 QAT results + +To address the severe accuracy degradation of PTQ, we apply QAT to better adapt the models towards 4-bit quantization. In all our experiments, the standard QAT method which directly quantizes the whole network to the target bitwidth will lead to unstable QAT processes, causing gradient explosion or a rapid decrease in accuracy in large models (for example, the W4A6 BEVFormer-Base has only $0.07\mathrm{mAP}$ ). Based on this observation, we hypothesize that the quantization perturbation introduced in standard QAT + +is too large to be recovered. As such, we apply progressive QAT to constrain the quantization perturbation along the training process. A comparison of the performance between progressive QAT and standard QAT with the same number of training epochs is presented in Table 3. We can see that progressive QAT consistently outperforms standard QAT by a large margin (up to $5\%$ mAP) in BEVFormer-Tiny and BEVFormer-Small, and achieves an even larger performance gain on BEVFormer-Base. To better validate our analyses, we plot the training curve of progressive QAT as the first 60 epochs in Figure 3, where W4A6 quantization + +Table 5: QD-BEV results on BEVDepth[21] and PETR[24]. + +
WAModelmAP↑NDS↑
3232BEVDepth-T[21]0.3300.435
88BEVDepth-T-DFQ[29]0.2810.377
46BEVDepth-T-HAWQ[40]0.1360.206
46BEVDepth-T-PACT[7]0.2700.362
46QD-BEVDepth-T (Ours)0.3010.394
3232PETR-r50dcn[24]0.3170.366
88PETR-r50dcn-DFQ[29]0.2900.343
46PETR-r50dcn-HAWQ[40]0.1620.216
46PETR-r50dcn-PACT[7]0.2680.320
46QD-PETR-r50dcn (Ours)0.2880.334
+ +is conducted on BEVFormer-Tiny. We separate the progressive QAT into 4 stages and iteratively quantize a new module in each stage. As can be seen, there is an NDS drop at beginning of each stage, corresponding to the quantization perturbation introduced by quantizing each new module. + +Despite the merits of progressive QAT, we want to note that it still suffers from unstable training and performance degradation. As illustrated in Figure 1 which corresponds to the last 20 epochs in Figure 3, progressive QAT keeps going up and down after reaching a plateau, while training curves of VGD show a rising trend with much better stability. + +# 4.3. Main Results of QD-BEV + +In order to obtain better accuracy and stability, we apply view-guided distillation with the floating-point model as the teacher and the quantized model as the student. The effect of VGD on W4A6 quantization of BEVFormer-Tiny is shown in Figure 3. Note that we separate VGD from progressive QAT in the first 60 epochs for a clearer comparison and illustration, and VGD is actually a plug-and-play function that can always be jointly applied with QAT, as we do in the last 20 epochs. Benefiting from knowledge in both the image domain and the BEV domain, QD-BEV networks are able to fully recover the quantization degradation, and even outperform the floating-point baselines. As shown in Table 4, the NDS and mAP of the model outperform previous floating-point baselines as well as quantized networks. Since there are no existing results for compact BEV networks, we implement standard quantization methods DFQ [29], HAWQv3 [40] and PACT [7] on BEVFormer as a comparison. We apply W8A8 quantization for DFQ + +![](images/4db8ddb4e11ac53a04447dc1c484f6d061f6c6be18b19f81ae305ba73a8b460c.jpg) +Figure 4: Visualization of QD-BEV results and the comparison with results obtained by BEVFormer. + +(DFQ is a PTQ method, lower bitwidth will lead to intolerable accuracy degradation) and W4A6 for QAT methods and QD-BEV models. As a comparison, QD-BEV can achieve 0.509 NDS with only 32.9 MB model size, which is similar to the size of BEVFormer-T-DFQ (0.340 NDS) and much smaller than BEVFormer-Tiny (126.8 MB, 0.354 NDS). + +Preliminary tests were run on PETR [24] and BEVDepth [21] models using our method in figure 5. Performance did not match BEVFormer, but still surpassed conventional quantization methods, highlighting the method's potential despite varying results. + +In Figure 4, we show the visualization results of the QDBEV-Base model on the nuScenes val dataset, and compare them with the results of BEVFormer-Tiny and the ground truth. As can be seen, more objects are detected by QDBEV-Base, and the 3D boxes predictions are more accurate than BEVFormer-Tiny. More visualizations are provided in the supplementary material. + +# 4.4. Streaming perception result + +In the context of autonomous driving, streaming perception [19] is critical for enabling models to make rapid and precise decisions in real time. High latency will degrade the streaming perception because it will cause a delay between the sensory data and the neural network output. To enhance streaming perception, quantization is a necessary technique that compresses the model size, reduces computational load, and accelerates the inference process. In Table 6, we demonstrate the significant impact of quantization on the sAP metric in autonomous driving scenarios. As we can see, QD-BEV models show consistent improvements in sAP compared to the floating-point counterparts and the + +Table 6: sAP of QD-BEV models compared to baselines. + +
Input SizeModelWAmAP↑sAP↑
450×800BEVFormer-T[23]32320.2530.228
BEVFormer-T-DFQ[29]880.2360.230
QD-BEV-T (Ours)460.2550.251
720×1280BEVFormer-S[23]32320.3700.249
BEVFormer-S-DFQ[29]880.3560.322
QD-BEV-S (Ours)460.3740.350
900×1600BEVFormer-B[23]32320.4160.136
BEVFormer-B-DFQ[29]880.3840.290
QD-BEV-B (Ours)460.4060.337
+ +![](images/88fb07d0ced050705f677c3229af9d8d3f6b8b7ddebad0fc090775f1731c9fe8.jpg) +(a) mAP curve. + +![](images/9f56193136f1a01ad3b9f2ba7585414cb59593f501af2744b361dbbd088daf9c.jpg) +(b) NDS curve. +Figure 5: The training curve of VGD versus CWD [33]. CWD uses only one type of features, referred to as cwd-image (image feature) and cwd-bev (bev feature), respectively. + +quantized baselines. + +# 5. Ablation study + +In Figure 5, we conduct an ablation study where we compare view-guided distillation with the cases using only distillation on the image feature, and only on the BEV feature, respectively. The method is referred to as CWD [33]. For a fair comparison, we apply the same pre-training weights and hyperparameters such as the temperature and the learning rate. From the figure, it can be found that view-guided distillation has a clear advantage over the CWD methods. In both the mAP and NDS curves, VGD has a more obvious and stable upward trend, and achieves better final results. + +# 6. Conclusion + +In this work, we systematically study both PTQ and QAT on BEV networks and showcase the major problems they are facing. Based on our analyses, we propose a view-guided distillation (VGD) method that can stabilize the QAT process and enhance the final performance by lever + +aging information from both the image domain and the BEV domain. With VGD as a plug-and-play function that can be jointly applied when quantizing BEV models, QD-BEV can close the accuracy gap or even outperforms the floating-point baselines. On the nuScenes datasets, the 4-bit weight and 6-bit activation quantized QD-BEV-Tiny model achieves $37.2\%$ NDS with only $15.8\mathrm{MB}$ model size, outperforming BevFormer-Tiny by $1.8\%$ with an $8\times$ model compression. + +# 7. Acknowledgement + +This work was supported by the National Key R&D Program of China (2022ZD0116305). The authors would also like to express their gratitude to the CCF-Baidu Open Fund Project, Berkeley Deep Drive, and Intel Corporation for their support and assistance throughout this research. Special thanks to Yandong Guo from $\mathrm{Al}^2$ Robotics (YAN-DONG.guo@live.com) for his valuable contributions to this work. + +# References + +[1] Sungsoo Ahn, Shell Xu Hu, Andreas Damianou, Neil D Lawrence, and Zhenwen Dai. Variational information distillation for knowledge transfer. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9163-9171, 2019. +[2] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. Estimating or propagating gradients through stochastic neurons for conditional computation. arXiv preprint arXiv:1308.3432, 2013. +[3] Holger Caesar, Varun Bankiti, Alex H Lang, Sourabh Vora, Venice Erin Liong, Qiang Xu, Anush Krishnan, Yu Pan, Giancarlo Baldan, and Oscar Beijbom. nuscenes: A multimodal dataset for autonomous driving. 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+ "bbox": [ + 47, + 297, + 290, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 297, + 290, + 573 + ], + "spans": [ + { + "bbox": [ + 47, + 297, + 290, + 573 + ], + "type": "text", + "content": "Multi-view 3D detection based on BEV (bird-eye-view) has recently achieved significant improvements. However, the huge memory consumption of state-of-the-art models makes it hard to deploy them on vehicles, and the nontrivial latency will affect the real-time perception of streaming applications. Despite the wide application of quantization to lighten models, we show in our paper that directly applying quantization in BEV tasks will 1) make the training unstable, and 2) lead to intolerable performance degradation. To solve these issues, our method QD-BEV enables a novel view-guided distillation (VGD) objective, which can stabilize the quantization-aware training (QAT) while enhancing the model performance by leveraging both image features and BEV features. Our experiments show that QD-BEV achieves similar or even better accuracy than previous methods with significant efficiency gains. On the nuScenes datasets, the 4-bit weight and 6-bit activation quantized QD-BEV-Tiny model achieves " + }, + { + "bbox": [ + 47, + 297, + 290, + 573 + ], + "type": "inline_equation", + "content": "37.2\\%" + }, + { + "bbox": [ + 47, + 297, + 290, + 573 + ], + "type": "text", + "content": " NDS with only 15.8 MB model size, outperforming BevFormer-Tiny by " + }, + { + "bbox": [ + 47, + 297, + 290, + 573 + ], + "type": "inline_equation", + "content": "1.8\\%" + }, + { + "bbox": [ + 47, + 297, + 290, + 573 + ], + "type": "text", + "content": " with an " + }, + { + "bbox": [ + 47, + 297, + 290, + 573 + ], + "type": "inline_equation", + "content": "8\\times" + }, + { + "bbox": [ + 47, + 297, + 290, + 573 + ], + "type": "text", + "content": " model compression. On the Small and Base variants, QD-BEV models also perform superbly and achieve " + }, + { + "bbox": [ + 47, + 297, + 290, + 573 + ], + "type": "inline_equation", + "content": "47.9\\%" + }, + { + "bbox": [ + 47, + 297, + 290, + 573 + ], + "type": "text", + "content": " NDS (28.2 MB) and " + }, + { + "bbox": [ + 47, + 297, + 290, + 573 + ], + "type": "inline_equation", + "content": "50.9\\%" + }, + { + "bbox": [ + 47, + 297, + 290, + 573 + ], + "type": "text", + "content": " NDS (32.9 MB), respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 618, + 287, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 618, + 287, + 642 + ], + "spans": [ + { + "bbox": [ + 47, + 618, + 287, + 642 + ], + "type": "text", + "content": "Given its potential in enabling autopilot, multi-view 3D detection based on BEV (bird-eye-view) has become" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 309, + 270, + 428, + 368 + ], + "blocks": [ + { + "bbox": [ + 309, + 270, + 428, + 368 + ], + "lines": [ + { + "bbox": [ + 309, + 270, + 428, + 368 + ], + "spans": [ + { + "bbox": [ + 309, + 270, + 428, + 368 + ], + "type": "image", + "image_path": "65d7190e406100619b395886dc2249444c87c520c510fd95b7a95bf50905d247.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 337, + 374, + 394, + 384 + ], + "lines": [ + { + "bbox": [ + 337, + 374, + 394, + 384 + ], + "spans": [ + { + "bbox": [ + 337, + 374, + 394, + 384 + ], + "type": "text", + "content": "(a) mAP curve." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 429, + 270, + 548, + 368 + ], + "blocks": [ + { + "bbox": [ + 429, + 270, + 548, + 368 + ], + "lines": [ + { + "bbox": [ + 429, + 270, + 548, + 368 + ], + "spans": [ + { + "bbox": [ + 429, + 270, + 548, + 368 + ], + "type": "image", + "image_path": "4ee11694ecc32e832afc5494f2c72da14a4d2cee7ceec0ff6b448b184ccd8b63.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 458, + 374, + 515, + 384 + ], + "lines": [ + { + "bbox": [ + 458, + 374, + 515, + 384 + ], + "spans": [ + { + "bbox": [ + 458, + 374, + 515, + 384 + ], + "type": "text", + "content": "(b) NDS curve." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 394, + 547, + 455 + ], + "lines": [ + { + "bbox": [ + 304, + 394, + 547, + 455 + ], + "spans": [ + { + "bbox": [ + 304, + 394, + 547, + 455 + ], + "type": "text", + "content": "Figure 1: Training curves of QD-BEV (with VGD) versus progressive QAT on W4A6 quantization of BEVFormer-Tiny. Note that standard QAT works even worse compared to progressive QAT and it falls out of the targeted accuracy range in the figures." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 483, + 547, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 547, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 547, + 686 + ], + "type": "text", + "content": "an important research direction for autonomous driving. Based on input sensors, previous work can be divided into LiDAR-based methods [18, 47] and camera-only methods [23, 38, 14, 13, 24, 25]. Compared to the LiDAR-based methods, camera-only methods have the merits of lower deployment cost, closer to human eyes, and easier access to visual information in the driving environment. However, even if using the camera-only methods, the computational and memory costs of running state-of-the-art BEV models are still formidable, making it difficult to deploy them onto vehicles. For example, BEVFormer-Base has a " + }, + { + "bbox": [ + 304, + 483, + 547, + 686 + ], + "type": "inline_equation", + "content": "540~\\mathrm{ms}" + }, + { + "bbox": [ + 304, + 483, + 547, + 686 + ], + "type": "text", + "content": " inference latency (corresponds to 1.85 fps) on one NVIDIA V100 GPU, which is infeasible for real-time applications that generally require 30 fps. Since a non-trivial latency will harm the streaming perception, it is particularly crucial to explore and devise lightweight models for camera-only 3D object detection based on BEV." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "content": "Quantization [16, 11, 42, 10] can reduce the bitwidth used to represent weights and activations in deep neural net-" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 663, + 253, + 709 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 663, + 253, + 709 + ], + "spans": [ + { + "bbox": [ + 47, + 663, + 253, + 709 + ], + "type": "text", + "content": "* Equal contribution : \nzhang_yifan@smail.nju.edu.cn, zhendong@berkeley.edu \n† Corresponding authors : \nldu@nju.edu.cn, shanghang@oku.edu.cn" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3825" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 73, + 541, + 257 + ], + "blocks": [ + { + "bbox": [ + 55, + 73, + 541, + 257 + ], + "lines": [ + { + "bbox": [ + 55, + 73, + 541, + 257 + ], + "spans": [ + { + "bbox": [ + 55, + 73, + 541, + 257 + ], + "type": "image", + "image_path": "3200c2b36546e2c17d6813a1aba9553b45604f481f77e137d547f51bab561213.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 55, + 258, + 541, + 387 + ], + "blocks": [ + { + "bbox": [ + 55, + 258, + 541, + 387 + ], + "lines": [ + { + "bbox": [ + 55, + 258, + 541, + 387 + ], + "spans": [ + { + "bbox": [ + 55, + 258, + 541, + 387 + ], + "type": "image", + "image_path": "93b69a2e2268f57f7d74f78e42b517b74a4533b8181533203ae624f083e1aec7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 396, + 546, + 458 + ], + "lines": [ + { + "bbox": [ + 46, + 396, + 546, + 458 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 546, + 458 + ], + "type": "text", + "content": "Figure 2: Illustration of QD-BEV. (a) In our pipeline, multi-camera images are input into the floating-point teacher network and the quantized student network in order to compute the KL divergence in an element-wise manner. The KL divergence is used as distillation loss in the image feature and the BEV feature, respectively. Then we conduct view-guided distillation using the BEV mask obtained from the external parameters of the camera. Please refer to Sec.3.1 for more details. (b) The lower flow chart shows the computation process of the view-guided distillation loss. Specific details are in Sec. 3.3." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 477, + 289, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 477, + 289, + 706 + ], + "spans": [ + { + "bbox": [ + 46, + 477, + 289, + 706 + ], + "type": "text", + "content": "works, which can greatly save the model size and computational costs while improving the speed of model reasoning. However, directly applying quantization would lead to significant performance degradation. Compared to image classification and 2D object detection tasks where the standard quantization methods shine, multi-camera 3D detection tasks are much more complicated and difficult due to the existence of multiple views and information from multiple dimensions (for example, the temporal information and spatial information used in BEVFormer [23]). Consequently, the structure of BEV networks tends to become more complex, with a deeper convolutional neural network backbone to extract image information from multiple views, and with transformers to encode and decode the features of the BEV domain. The presence of different neural architectures, multiple objectives, and knowledge from different modalities greatly challenges the standard quantization methods, decreasing their stability and accuracy, and even making the whole training process diverge. In Figure 1, we" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 477, + 547, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 477, + 547, + 561 + ], + "spans": [ + { + "bbox": [ + 304, + 477, + 547, + 561 + ], + "type": "text", + "content": "show the training curves when applying W4A6 quantization on a BEVFormer-Tiny model. As can be seen, the performance of quantization-aware training (QAT) fluctuates significantly in different epochs, while the performance of our proposed method QD-BEV shows a stable rising trend. We perform more experiments to validate the effectiveness of QD-BEV in Sec 5." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": "To solve the problems of standard QAT, in this work, we first conduct systematic experiments and analyses on quantizing BEV networks. Then we devise a quantization-aware view-guided distillation method (referred to as QD-BEV) that can decently solve the stability issue while improving the final performance of compact BEV models. Our proposed view-guided distillation (VGD) can better leverage information from both the image and the BEV domains for multi-view 3D object detection. This can significantly outperform previous distillation methods that cannot jointly handle the different types of losses in BEV networks. Specifically, as shown in Figure 2, we first take" + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "3826" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "the FP (floating-point) model as the teacher model and the quantized model as the student model, then we calculate the KL divergence on the image feature and the BEV feature, respectively. Finally, we leverage the mapping relationship and realize VGD by organically combining the image feature and the BEV feature through the camera's external parameters. Note that in QD-BEV, neither additional training data nor larger powerful teacher networks are used to tune the accuracy, but QD-BEV models are still able to outperform previous baselines while having significantly smaller model sizes and computational requirements. Our contributions are as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 229, + 287, + 392 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 59, + 229, + 287, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 229, + 287, + 266 + ], + "spans": [ + { + "bbox": [ + 59, + 229, + 287, + 266 + ], + "type": "text", + "content": "- We conduct systematic experiments on quantizing BEV models, unveiling major issues hampering standard quantization-aware training methods on BEV." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 281, + 287, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 281, + 287, + 341 + ], + "spans": [ + { + "bbox": [ + 59, + 281, + 287, + 341 + ], + "type": "text", + "content": "- We specially design view-guided distillation (VGD) for BEV models, which jointly leverages both image domain and BEV domain information. VGD boosts the final performance while solving the stability issue of standard QAT." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 356, + 287, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 356, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 59, + 356, + 287, + 392 + ], + "type": "text", + "content": "- Our W4A6 quantized QD-BEV-Tiny has " + }, + { + "bbox": [ + 59, + 356, + 287, + 392 + ], + "type": "inline_equation", + "content": "37.2\\%" + }, + { + "bbox": [ + 59, + 356, + 287, + 392 + ], + "type": "text", + "content": " NDS with only 15.8 MB model size, which outperforms the " + }, + { + "bbox": [ + 59, + 356, + 287, + 392 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 59, + 356, + 287, + 392 + ], + "type": "text", + "content": " larger BevFormer-Tiny model by " + }, + { + "bbox": [ + 59, + 356, + 287, + 392 + ], + "type": "inline_equation", + "content": "1.8\\%" + }, + { + "bbox": [ + 59, + 356, + 287, + 392 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 408, + 138, + 421 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 408, + 138, + 421 + ], + "spans": [ + { + "bbox": [ + 47, + 408, + 138, + 421 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 430, + 224, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 224, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 224, + 443 + ], + "type": "text", + "content": "2.1. Camera-only 3D object detection" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": "In camera-only 3D object detection tasks, many excellent methods have emerged based on BEV (bird-eye-view). Previous works, LSS [31] and BEVDet [14], project image features to the BEV space in a bottom-up manner. Based on DETR [5] and Deformable DETR [48], DETR3D [38] extends the 2D object detection to the 3D space through the architecture of Backbone + FPN + Decoder. In addition, PETR [24] introduces 3D position coding based on DETR3D [38]. In BEVFormer [23], the authors use dense BEV queries to exchange information in the BEV space with the multi-view image space. More stable BEV features are obtained by extracting temporal and spatial information through the transformer structure with temporal self-attention and spacial cross-attention. Based on the temporal interaction in BEVFormer, further improvements have been made in recent works, PETRv2 [25] and BEVDet4D [13]. Besides the aforementioned works, BEVDepth [21] and BEVstereo [20] are two state-of-the-art approaches for monocular depth estimation and stereo vision in the birdeye-view (BEV) domain, respectively, which leverage the unique characteristics of BEV representations to achieve high accuracy and efficiency." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 72, + 390, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 390, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 390, + 85 + ], + "type": "text", + "content": "2.2. Quantization" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 95, + 547, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 95, + 547, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 95, + 547, + 348 + ], + "type": "text", + "content": "To reduce the model size, quantization [45, 36, 15, 26] uses low bitwidth to represent weights and activations in neural networks. With the use of low-precision matrix multiplication or convolution, quantization can also make the inference process faster and more efficient. Given a pretrained model, directly performing quantization without any fine-tuning is referred to as post-training quantization (PTQ) [4, 29, 37, 17]. Despite the merits, PTQ with low bitwidth still results in significant accuracy degradation. As such, Quantization-aware training (QAT) is proposed to train the model to better adapt to quantization. QAT methods [9, 7, 40] are more costly compared to PTQ, but can potentially obtain higher accuracy. Furthermore, in the cases with ultra-low quantization bitwidth (for example, 4-bit), even QAT cannot close the accuracy gap. A promising direction to solve this is to use mixed-precision quantization [46, 36, 39], where some sensitive layers are kept at higher precision to recover the accuracy. Though effective, the support for mixed-precision quantization on general-purpose machines (CPUs and GPUs) is currently immature and may lead to extra latency overhead." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 354, + 547, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 547, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 547, + 426 + ], + "type": "text", + "content": "Although standard quantization methods have shown great results on convolutional neural networks, recent works [27, 44] mention that it may suffer in other neural architectures such as transformers. The presence of both convolutional blocks and transformers in BEV networks makes them challenging to the traditional quantization methods." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 449, + 380, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 449, + 380, + 462 + ], + "spans": [ + { + "bbox": [ + 306, + 449, + 380, + 462 + ], + "type": "text", + "content": "2.3. Distillation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 547, + 715 + ], + "type": "text", + "content": "Model distillation [12, 28, 22, 32, 1] generally uses a large model as the teacher to train a compact student model. Instead of using class labels during the training of the student model, the key idea is to leverage the soft probabilities produced by the teacher to guide the student's training. Previous methods of distillation explore different knowledge sources (for example, [12, 22, 30] use logits, aka the soft probabilities). The choices of teacher models are also studied, where [41, 34] use multiple teacher models, while [8, 43] apply self-distillation without an extra teacher model. Other previous efforts apply distillation with different settings on different applications. Regarding BEV networks, previous work [6] tries to teach LiDAR information to camera-based networks through distillation, but the additional requirement for LiDAR data makes it infeasible in our pure camera-based setting. Besides, the existence of different types of losses in BEV networks makes standard distillation methods invalid. An arbitrary or sub-optimal combination of knowledge sources would also make the training unstable, perform badly, or even diverge." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3827" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 104, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 104, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 104, + 83 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 212, + 104 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 212, + 104 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 212, + 104 + ], + "type": "text", + "content": "3.1. Overview of QD-BEV pipeline" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 110, + 289, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 110, + 289, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 110, + 289, + 350 + ], + "type": "text", + "content": "This work aims to improve the efficiency of state-of-the-art BEV models. Starting with the widely used BEV-Former [23], we apply a progressive quantization-aware training procedure in a stage-by-stage manner (details are introduced in Sec. 3.2). We further boost its stability and performance through a novel view-guided distillation process, which is highlighted in Figure 2, where we use a floating-point teacher model to facilitate the learning of our quantized QD-BEV student model. Specifically, the input multi-camera image is entered into the teacher and the student, respectively, and then the Image Backbone and Image Neck parts of the network are used to extract the multicamera image feature. After the transformer part of the network, the BEV features are extracted, and the two parts of the teacher model and the student model are used to calculate image distill loss and BEV distill loss, respectively. The two distillation losses are then fused through the external parameters of the camera to achieve our unique view-guided distillation mechanism. We provide a detailed formulation of the view-guided distillation process in Sec. 3.3." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 357, + 205, + 370 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 357, + 205, + 370 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 205, + 370 + ], + "type": "text", + "content": "3.2. Quantization-aware training" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 376, + 287, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 287, + 410 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 287, + 410 + ], + "type": "text", + "content": "In symmetric linear quantization, the quantizer maps weights and activations into integers with a scale factor " + }, + { + "bbox": [ + 47, + 376, + 287, + 410 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 376, + 287, + 410 + ], + "type": "text", + "content": ". Uniformly quantizing to k bit can be expressed as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 108, + 417, + 287, + 440 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 417, + 287, + 440 + ], + "spans": [ + { + "bbox": [ + 108, + 417, + 287, + 440 + ], + "type": "interline_equation", + "content": "S = \\frac {2 \\left| r _ {\\max } \\right|}{2 ^ {k} - 1}, q = \\operatorname {r o u n d} \\left(\\frac {r}{S}\\right) \\tag {1}", + "image_path": "05227fd940f0d1022f8127283a01ca548d40808c52b0ea93764466568faa2d31.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 447, + 289, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 289, + 663 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 289, + 663 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 447, + 289, + 663 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 447, + 289, + 663 + ], + "type": "text", + "content": " is the floating-point number being quantized, " + }, + { + "bbox": [ + 46, + 447, + 289, + 663 + ], + "type": "inline_equation", + "content": "|r_{\\mathrm{max}}|" + }, + { + "bbox": [ + 46, + 447, + 289, + 663 + ], + "type": "text", + "content": " is the largest absolute value in " + }, + { + "bbox": [ + 46, + 447, + 289, + 663 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 447, + 289, + 663 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 447, + 289, + 663 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 447, + 289, + 663 + ], + "type": "text", + "content": " is the quantized integer. In this work, we conduct systematic experiments to analyze the performance of quantization on BEV networks. For PTQ, we apply the above quantization directly to the pre-trained models during the inference stage. For QAT, we utilize the straight-through estimator (STE) [2] to define the forward and backward processes for the above quantization operations, and then we train the model to better adapt to quantization. As previously mentioned in Sec. 1 and Sec. 2, considering that standard QAT may lead to divergence due to the characteristics of BEV models, we apply a stage-wise progressive QAT where we gradually reduce the weight precision in four stages (backbone, neck, encoder, and decoder) based on the design of BEV-Former [23]. The performance of this progressive QAT is illustrated in Figure 3. And we compare the effectiveness of the progressive QAT with standard QAT in Sec. 4.2.2." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 670, + 181, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 181, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 181, + 683 + ], + "type": "text", + "content": "3.3. View-guided distillation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "Compared to traditional single-domain distillation methods, our approach exploits the complementary nature of" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "content": "both BEV and image domains, which provides different perspectives and capture different aspects of the scene. The BEV domain offers a top-down view, enabling accurate perception and recognition of the surrounding environment, such as the structure of the road, the location of vehicles, and lane markings. On the other hand, the image domain provides more realistic visual information, capturing rich scene details and color information. In the following sections, we present details of VGD: the computation of the image feature distillation in Sec. 3.3.1, the BEV feature distillation in Sec. 3.3.2, and the view-guided distillation combining the previous two distillation losses in Sec. 3.3.3." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 230, + 447, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 230, + 447, + 243 + ], + "spans": [ + { + "bbox": [ + 305, + 230, + 447, + 243 + ], + "type": "text", + "content": "3.3.1 Image feature distillation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 247, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 545, + 348 + ], + "type": "text", + "content": "Given a pair of aligned teacher and student models, We first compute element-wise distillation loss on image features. We extract the image neck output as the image features to be distilled. To improve the smoothness of the distillation loss, we follow previous attempts [33] to use a KL divergence-based distillation loss. Specifically, we consider the flattened image features of the student and the teacher model as logits, which we convert into probability distribution via a softmax function with temperature " + }, + { + "bbox": [ + 304, + 247, + 545, + 348 + ], + "type": "inline_equation", + "content": "\\phi_{\\tau}" + }, + { + "bbox": [ + 304, + 247, + 545, + 348 + ], + "type": "text", + "content": ", as defined in Eq. (2)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 386, + 355, + 545, + 382 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 386, + 355, + 545, + 382 + ], + "spans": [ + { + "bbox": [ + 386, + 355, + 545, + 382 + ], + "type": "interline_equation", + "content": "\\phi_ {\\tau} \\left(x _ {i}\\right) = \\frac {e ^ {x _ {i} / \\tau}}{\\sum_ {j} e ^ {x _ {j} / \\tau}} \\tag {2}", + "image_path": "489b1ce3ea0852bf67751efc550512fa7550d0edb47e9a02799df058b5a785ef.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 384, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 418 + ], + "type": "text", + "content": "Then we calculate the KL divergence of each camera's output separately to obtain the image feature distillation loss, as in Eq. (3)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 315, + 424, + 545, + 447 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 424, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 315, + 424, + 545, + 447 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i m g} = \\frac {\\tau^ {2}}{B \\cdot W \\cdot H \\cdot C} \\times \\mathcal {D} _ {K L} \\left(\\phi_ {\\tau} \\left(F _ {i m g} ^ {T}\\right), \\phi_ {\\tau} \\left(F _ {i m g} ^ {S}\\right)\\right) \\tag {3}", + "image_path": "c1652a2dadd900d5007867a39e6437bfebef21150a973dcf39fbdec4c5e5b400.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 451, + 545, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 451, + 545, + 499 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 545, + 499 + ], + "type": "text", + "content": "where B stands for the batch size, W, H, C mean the width, height, and number of channels of the image features, respectively. " + }, + { + "bbox": [ + 304, + 451, + 545, + 499 + ], + "type": "inline_equation", + "content": "F_{img}^{T}" + }, + { + "bbox": [ + 304, + 451, + 545, + 499 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 451, + 545, + 499 + ], + "type": "inline_equation", + "content": "F_{img}^{S}" + }, + { + "bbox": [ + 304, + 451, + 545, + 499 + ], + "type": "text", + "content": " denote the image features of the teacher model and the student model." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 514, + 440, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 440, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 440, + 525 + ], + "type": "text", + "content": "3.3.2 BEV feature distillation" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 532, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 545, + 578 + ], + "type": "text", + "content": "We first convert the BEV features of the student and teacher into probability distributions, following the same procedure as for image features. Then we compute the KL divergence for each point on the BEV features, as shown in Eq. (4)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 339, + 582, + 545, + 605 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 582, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 339, + 582, + 545, + 605 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {b e v} = \\frac {\\tau^ {2}}{B \\cdot C} \\times \\mathcal {D} _ {\\mathrm {K L}} \\left(\\phi_ {\\tau} \\left(F _ {b e v} ^ {T}\\right), \\phi_ {\\tau} \\left(F _ {b e v} ^ {S}\\right)\\right) \\tag {4}", + "image_path": "efab513977b9bb76cbb54710580da56b481c78ce5160d42b677f1ee978e90450.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 610, + 547, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 610, + 547, + 659 + ], + "spans": [ + { + "bbox": [ + 304, + 610, + 547, + 659 + ], + "type": "text", + "content": "where B stands for the batch size, C means the number of channels of BEV features. " + }, + { + "bbox": [ + 304, + 610, + 547, + 659 + ], + "type": "inline_equation", + "content": "F_{bev}^{T}" + }, + { + "bbox": [ + 304, + 610, + 547, + 659 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 610, + 547, + 659 + ], + "type": "inline_equation", + "content": "F_{bev}^{S}" + }, + { + "bbox": [ + 304, + 610, + 547, + 659 + ], + "type": "text", + "content": " denote the BEV features of the teacher model and student model, respectively. We will get a loss with the shape of " + }, + { + "bbox": [ + 304, + 610, + 547, + 659 + ], + "type": "inline_equation", + "content": "[H_{bev} \\times W_{bev}, 1]" + }, + { + "bbox": [ + 304, + 610, + 547, + 659 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 672, + 481, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 672, + 481, + 685 + ], + "spans": [ + { + "bbox": [ + 306, + 672, + 481, + 685 + ], + "type": "text", + "content": "3.3.3 View-guided distillation objective" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 690, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 690, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 690, + 545, + 713 + ], + "type": "text", + "content": "In the first two sections, we obtained the loss of each camera on the image feature and the corresponding loss of each" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3828" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 47, + 87, + 287, + 256 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 258, + 84 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 258, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 258, + 84 + ], + "type": "text", + "content": "Algorithm 1 Progressive Quantization-Aware VGD" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 47, + 87, + 287, + 256 + ], + "lines": [ + { + "bbox": [ + 47, + 87, + 287, + 256 + ], + "spans": [ + { + "bbox": [ + 47, + 87, + 287, + 256 + ], + "type": "text", + "content": "Input: Training data; Pre-trained FP weights for teacher model " + }, + { + "bbox": [ + 47, + 87, + 287, + 256 + ], + "type": "inline_equation", + "content": "T_{fp}" + }, + { + "bbox": [ + 47, + 87, + 287, + 256 + ], + "type": "text", + "content": " Student model " + }, + { + "bbox": [ + 47, + 87, + 287, + 256 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 87, + 287, + 256 + ], + "type": "text", + "content": " Numbers of epochs for each phase " + }, + { + "bbox": [ + 47, + 87, + 287, + 256 + ], + "type": "inline_equation", + "content": "N_{1},\\ldots ,N_{4};P_{2}" + }, + { + "bbox": [ + 47, + 87, + 287, + 256 + ], + "type": "text", + "content": " Quantization bit for weight and activation " + }, + { + "bbox": [ + 47, + 87, + 287, + 256 + ], + "type": "inline_equation", + "content": "B_{w};B_{a}" + }, + { + "bbox": [ + 47, + 87, + 287, + 256 + ], + "type": "text", + "content": " \nOutput: Trained low-bit student model " + }, + { + "bbox": [ + 47, + 87, + 287, + 256 + ], + "type": "inline_equation", + "content": "S_{q}" + }, + { + "bbox": [ + 47, + 87, + 287, + 256 + ], + "type": "text", + "content": " Phase 1: Progressive Quantization-Aware Training Init " + }, + { + "bbox": [ + 47, + 87, + 287, + 256 + ], + "type": "inline_equation", + "content": "S_0" + }, + { + "bbox": [ + 47, + 87, + 287, + 256 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 47, + 87, + 287, + 256 + ], + "type": "inline_equation", + "content": "T_{fp}" + }, + { + "bbox": [ + 47, + 87, + 287, + 256 + ], + "type": "text", + "content": " Divide model into 4 Parts: {Backbone,Neck,Encoder,Decoder}; 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(6)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "code_body" + } + ], + "index": 3, + "sub_type": "algorithm" + }, + { + "bbox": [ + 46, + 342, + 289, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 289, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 289, + 499 + ], + "type": "text", + "content": "point on the BEV feature. On the nuScenes dataset, the camera external parameters are known, so we can obtain the distribution range of each camera corresponding to the BEV feature. Then we generate the BEV mask of views " + }, + { + "bbox": [ + 46, + 342, + 289, + 499 + ], + "type": "inline_equation", + "content": "M_{bev}" + }, + { + "bbox": [ + 46, + 342, + 289, + 499 + ], + "type": "text", + "content": " that can be applied to the image feature, which is the same as defined in BEVFormer [23]. " + }, + { + "bbox": [ + 46, + 342, + 289, + 499 + ], + "type": "inline_equation", + "content": "M_{bev}" + }, + { + "bbox": [ + 46, + 342, + 289, + 499 + ], + "type": "text", + "content": " is a tensor with four dimensions: number of cameras, batch size, BEV size " + }, + { + "bbox": [ + 46, + 342, + 289, + 499 + ], + "type": "inline_equation", + "content": "(H_{bev} \\times W_{bev})" + }, + { + "bbox": [ + 46, + 342, + 289, + 499 + ], + "type": "text", + "content": ", and 3D Height, with binary values in each element. By calculating the average along the last dimension (3D Height), we can flatten the BEV mask " + }, + { + "bbox": [ + 46, + 342, + 289, + 499 + ], + "type": "inline_equation", + "content": "M_{bev}" + }, + { + "bbox": [ + 46, + 342, + 289, + 499 + ], + "type": "text", + "content": " on the 2d plane with the BEV size " + }, + { + "bbox": [ + 46, + 342, + 289, + 499 + ], + "type": "inline_equation", + "content": "(H_{bev} \\times W_{bev})" + }, + { + "bbox": [ + 46, + 342, + 289, + 499 + ], + "type": "text", + "content": ". Then the " + }, + { + "bbox": [ + 46, + 342, + 289, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{img}" + }, + { + "bbox": [ + 46, + 342, + 289, + 499 + ], + "type": "text", + "content": " calculated for each camera can be extended to the corresponding loss for each point on the BEV feature, which we refer to as " + }, + { + "bbox": [ + 46, + 342, + 289, + 499 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{L}}_{img}" + }, + { + "bbox": [ + 46, + 342, + 289, + 499 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 123, + 506, + 287, + 520 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 506, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 123, + 506, + 287, + 520 + ], + "type": "interline_equation", + "content": "\\widehat {\\mathcal {L}} _ {i m g} = \\mathcal {L} _ {i m g} \\odot M _ {b e v} \\tag {5}", + "image_path": "f39f2f3a9fbfac2ed2e081775302d3c489e4996c8460fc97c751f34fc23e4f6e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 530, + 211, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 530, + 211, + 542 + ], + "spans": [ + { + "bbox": [ + 47, + 530, + 211, + 542 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 530, + 211, + 542 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 47, + 530, + 211, + 542 + ], + "type": "text", + "content": " denotes the hadamard product." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 543, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 543, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 543, + 287, + 567 + ], + "type": "text", + "content": "Finally, we use " + }, + { + "bbox": [ + 46, + 543, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{L}}_{img}" + }, + { + "bbox": [ + 46, + 543, + 287, + 567 + ], + "type": "text", + "content": " to get the view-guided distillation objective in Eq. (6):" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 113, + 573, + 287, + 603 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 573, + 287, + 603 + ], + "spans": [ + { + "bbox": [ + 113, + 573, + 287, + 603 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {v g d} = \\sum_ {i = 1} ^ {N \\cdot H \\cdot W} \\widehat {\\mathcal {L}} _ {i m g} \\odot \\mathcal {L} _ {b e v} \\tag {6}", + "image_path": "e9b58236df1320b31015902989d544a8c17da895a61104e8fff073f8865c9680.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 610, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 287, + 635 + ], + "type": "text", + "content": "The overall process of view-guided distillation is shown in Algorithm 1." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 645, + 128, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 128, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 128, + 659 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "In this section, we first elaborate on the experimental settings, then we evaluate both PTQ and QAT methods on the BEV networks. Based on the analysis of these results, we propose QD-BEV to overcome shortcomings in standard" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "PTQ and QAT, and we dedicatedly compare our results with previous works under different settings and constraints." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 104, + 430, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 104, + 430, + 117 + ], + "spans": [ + { + "bbox": [ + 306, + 104, + 430, + 117 + ], + "type": "text", + "content": "4.1. Experimental settings" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 122, + 372, + 133 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 122, + 372, + 133 + ], + "spans": [ + { + "bbox": [ + 306, + 122, + 372, + 133 + ], + "type": "text", + "content": "4.1.1 Dataset" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 141, + 547, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 141, + 547, + 250 + ], + "spans": [ + { + "bbox": [ + 304, + 141, + 547, + 250 + ], + "type": "text", + "content": "We evaluated our proposed method on a challenging 3D detection task using the nuScenes dataset [3], which is a large-scale public dataset for autopilot developed by the team at Motional (formerly nuTonomy). This dataset contains 1000 manually selected 20-second driving scenarios collected in Boston and Singapore, with 750 scenarios for training, 100 for validation, and 150 for testing. The images in the dataset were captured from 6 cameras with known internal and external parameters." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 265, + 420, + 275 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 265, + 420, + 275 + ], + "spans": [ + { + "bbox": [ + 306, + 265, + 420, + 275 + ], + "type": "text", + "content": "4.1.2 Evaluation metrics" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 282, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 545, + 491 + ], + "type": "text", + "content": "The main measurement indicators on the nuScenes 3D test dataset are the mean Average Precision (mAP), and the unique evaluation index nuScenes detection score (NDS). NDS is a comprehensive evaluation index containing many aspects of information. The other indicators are mean Average Translation Error (mATE), mean Average Scale Error (mASE), mean Average Orientation Error (mAOE), mean Average Velocity Error (mAVE) and mean Average Attribute Error (mAAE). To evaluate the efficiency of the BEV networks, we use model size and BOPS as the metrics. Model size is the memory required to store a specific network, which is determined by the total amount of parameters in the model as well as the quantization bitwidth to store those parameters. BOPS measures the total Bit Operations of one network inference [35]. It is a common metric for evaluating the computation of quantized neural networks. For a model with " + }, + { + "bbox": [ + 304, + 282, + 545, + 491 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 282, + 545, + 491 + ], + "type": "text", + "content": " layers, defining " + }, + { + "bbox": [ + 304, + 282, + 545, + 491 + ], + "type": "inline_equation", + "content": "b_{w_i}" + }, + { + "bbox": [ + 304, + 282, + 545, + 491 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 282, + 545, + 491 + ], + "type": "inline_equation", + "content": "b_{a_i}" + }, + { + "bbox": [ + 304, + 282, + 545, + 491 + ], + "type": "text", + "content": " to be the bitwidth used for weights and activations of the " + }, + { + "bbox": [ + 304, + 282, + 545, + 491 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 282, + 545, + 491 + ], + "type": "text", + "content": "-th layer, then we have:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 369, + 498, + 545, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 498, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 369, + 498, + 545, + 517 + ], + "type": "interline_equation", + "content": "B O P S = \\sum_ {i = 1} ^ {L} b _ {w _ {i}} b _ {a _ {i}} M A C _ {i} \\tag {7}", + "image_path": "e59fbab0684f58a2c991c30b82e77f9c1c27e007cbba299e1b1ab49bcdbd4155.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 523, + 545, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 523, + 545, + 619 + ], + "spans": [ + { + "bbox": [ + 304, + 523, + 545, + 619 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 523, + 545, + 619 + ], + "type": "inline_equation", + "content": "\\mathrm{MAC}_i" + }, + { + "bbox": [ + 304, + 523, + 545, + 619 + ], + "type": "text", + "content": " is the total Multiply-Accumulate operations for computing the " + }, + { + "bbox": [ + 304, + 523, + 545, + 619 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 523, + 545, + 619 + ], + "type": "text", + "content": "-th layer. To better demonstrate the advantages of our QD-BEV model over the floating-point model, we introduce sAP [19] (streaming average precision) as one of the evaluation metrics for our model performance. sAP is a dynamic metric that will be updated as new data arrive, making it ideal for evaluating models in real-time scenarios." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 635, + 492, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 635, + 492, + 647 + ], + "spans": [ + { + "bbox": [ + 305, + 635, + 492, + 647 + ], + "type": "text", + "content": "4.1.3 Baselines & Implementation Details" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": "We mainly compare with floating-point baseline models proposed by BEVFormer [23] with different input image resolutions (specifically, BEVFormer-Tiny, BEVFormer-Small, and BEVFormer-Base). For quantization baselines, we apply the previous PTQ method DFQ [29] as well as" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3829" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 92, + 547, + 239 + ], + "blocks": [ + { + "bbox": [ + 146, + 70, + 446, + 84 + ], + "lines": [ + { + "bbox": [ + 146, + 70, + 446, + 84 + ], + "spans": [ + { + "bbox": [ + 146, + 70, + 446, + 84 + ], + "type": "text", + "content": "Table 1: Results with PTQ separately applied on each part in BEVFormer." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 92, + 547, + 239 + ], + "lines": [ + { + "bbox": [ + 50, + 92, + 547, + 239 + ], + "spans": [ + { + "bbox": [ + 50, + 92, + 547, + 239 + ], + "type": "table", + "html": "
Quantized ModuleBEVFormer-TinyBEVFormer-SmallBEVFormer-Base
BackboneNeckEncoderDecodermAP↑NDS↑mAP↑NDS↑mAP↑NDS↑
××××0.2520.3540.3700.4790.4160.517
✓×××0.2120.3100.2880.4170.3090.440
×✓××0.2520.3530.3700.4780.4160.516
××✓×0.1810.2950.2980.4210.1600.303
×××✓0.2510.3530.3690.4770.4160.517
✓✓✓✓0.1450.2460.2280.3690.0750.224
", + "image_path": "810ae290c2285b7097526c615fa2280ecc226c7f73ac277b3c0a149215e4a320.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 258, + 287, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 287, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 287, + 282 + ], + "type": "text", + "content": "QAT method PACT [7] and HAWQv3 [40] to quantize BEVFormer models and compare with QD-BEV." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 288, + 288, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 288, + 421 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 288, + 421 + ], + "type": "text", + "content": "For floating-point models, we use the open-sourced repository of BEVFormer with two different backbones: ResNet50 and ResNet101-DCN. We use symmetrical linear quantization in a channel-wise manner for weights, and layer-wise quantization for activations, which are the standard settings for previous quantization methods. Since there is little related work in our settings for reference, we make our training adopt the same scheme as the original training strategy of BEVFormer, which is to train 24 epochs in each step, and to use optimizer of AdamW, a starting lr as 2e-4, a linear warmup of 500 iters, and cosine annealing." + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 50, + 464, + 288, + 693 + ], + "blocks": [ + { + "bbox": [ + 50, + 444, + 282, + 456 + ], + "lines": [ + { + "bbox": [ + 50, + 444, + 282, + 456 + ], + "spans": [ + { + "bbox": [ + 50, + 444, + 282, + 456 + ], + "type": "text", + "content": "Table 2: PTQ results with different quantization bitwidth." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 464, + 288, + 693 + ], + "lines": [ + { + "bbox": [ + 50, + 464, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 50, + 464, + 288, + 693 + ], + "type": "table", + "html": "
W-bit/A-bitModelNDS↑NDS DropmAP↑
32/32Tiny0.354-0.252
Small0.479-0.370
Base0.517-0.416
8/8Tiny0.3510.8%0.248
Small0.4770.4%0.366
Base0.4875.8%0.384
6/6Tiny0.31211.9%0.203
Small0.43010.2%0.306
Base0.40222.2%0.262
4/6Tiny0.24630.5%0.146
Small0.36923.0%0.228
Base0.22656.3%0.076
4/4Tiny0.03490.4%0.001
Small0.03492.9%0.001
Base0.02395.6%0.000
", + "image_path": "a87b56f03186a6d56c59d7ebd648999bbc1ab2176bffe08df6706da3b6261c74.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 309, + 300, + 547, + 399 + ], + "blocks": [ + { + "bbox": [ + 305, + 256, + 547, + 293 + ], + "lines": [ + { + "bbox": [ + 305, + 256, + 547, + 293 + ], + "spans": [ + { + "bbox": [ + 305, + 256, + 547, + 293 + ], + "type": "text", + "content": "Table 3: Comparison between progressive and standard QAT with W4A6. Please refer to Table 2 for baseline FP accuracy (W32A32)." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 300, + 547, + 399 + ], + "lines": [ + { + "bbox": [ + 309, + 300, + 547, + 399 + ], + "spans": [ + { + "bbox": [ + 309, + 300, + 547, + 399 + ], + "type": "table", + "html": "
MethodModelNDS↑NDS DropmAP↑
Standard QATTiny0.3267.9%0.216
Small0.42112.1%0.303
base0.22456.7%0.071
Progressive QATTiny0.3481.7%0.234
Small0.4672.5%0.356
base0.4856.2%0.376
", + "image_path": "b34854435612c10b808bd9b109bf44e665f4303e45845036d8cc87543279eeb8.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 436, + 471, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 436, + 471, + 449 + ], + "spans": [ + { + "bbox": [ + 306, + 436, + 471, + 449 + ], + "type": "text", + "content": "4.2. Analysis on BEV Quantization" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 464, + 391, + 476 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 464, + 391, + 476 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 391, + 476 + ], + "type": "text", + "content": "4.2.1 PTQ results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 500, + 547, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 500, + 547, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 500, + 547, + 609 + ], + "type": "text", + "content": "We first analyze the sensitivity of different modules to quantization in Table 1. It can be seen that the backbone and the encoder parts of the network are more sensitive, while quantization of the neck and the decoder parts only brings a slight disturbance to the accuracy. We want to note that, based on the sensitivity analysis, it is possible to apply mixed-precision quantization to better preserve the sensitive modules, but we leave this as future work since it is beyond the scope of this paper." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": "We then analyze the influence of different quantization bitwidth on the final performance. In Table 2, directly applying PTQ with less than 8-bit precision will lead to a significant accuracy drop, especially when quantized to W4A4 the results become pure noise with around " + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "inline_equation", + "content": "0\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": ". As can be observed from Table 2, performing QAT is necessary in order to preserve the accuracy while achieving ultra-low bit quantization." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "3830" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 92, + 545, + 358 + ], + "blocks": [ + { + "bbox": [ + 155, + 71, + 437, + 83 + ], + "lines": [ + { + "bbox": [ + 155, + 71, + 437, + 83 + ], + "spans": [ + { + "bbox": [ + 155, + 71, + 437, + 83 + ], + "type": "text", + "content": "Table 4: QD-BEV results compared to previous methods or baselines." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 92, + 545, + 358 + ], + "lines": [ + { + "bbox": [ + 52, + 92, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 52, + 92, + 545, + 358 + ], + "type": "table", + "html": "
Input SizeModelModel Size(MB)BOPS(Tera)NDS↑mAP↑mATE↓mASE↓mAOE↓mAVE↓mAAE↓
450×800BEVFormer-T[23]126.862.330.3540.2530.8990.2940.6550.6570.216
BEVFormer-T-DFQ[29]31.73.900.3400.2360.9490.2960.6510.6710.217
BEVFormer-T-HAWQv3[40]15.91.460.3480.2340.9490.3040.5680.6610.209
BEVFormer-T-PACT[7]15.91.460.3470.2340.9190.2890.6040.6710.216
QD-BEV-T (Ours)15.91.460.3720.2550.8820.3210.5430.5990.214
720×1280BEVFormer-S[23]225.6236.130.4790.3700.7220.2790.4070.4380.220
BEVFormer-S-DFQ[29]56.414.760.4670.3560.7510.2830.4050.4510.222
BEVFormer-S-HAWQv3[40]28.25.530.4670.3560.7510.2870.4190.4490.208
BEVFormer-S-PACT[7]28.25.530.4610.3510.7500.2750.4220.5070.196
QD-BEV-S (Ours)28.25.530.4790.3740.7160.2900.3890.4740.210
900×1600BEVFormer-B[23]262.9667.390.5170.4160.6720.2730.3700.3930.197
BEVFormer-B-DFQ[29]65.741.710.4860.3840.7710.2740.3780.4270.206
BEVFormer-B-HAWQv3[40]32.915.640.4850.3760.7270.2880.3810.4340.202
BEVFormer-B-PACT[7]32.915.640.4800.3740.7350.2910.3920.4580.201
QD-BEV-B (Ours)32.915.640.5090.4060.6910.2850.3600.4100.190
", + "image_path": "1be7d15231491689c9a486b3813e02db553d6aab8685f6092a6d3f2ab7f6d914.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 52, + 373, + 542, + 497 + ], + "blocks": [ + { + "bbox": [ + 52, + 373, + 542, + 497 + ], + "lines": [ + { + "bbox": [ + 52, + 373, + 542, + 497 + ], + "spans": [ + { + "bbox": [ + 52, + 373, + 542, + 497 + ], + "type": "image", + "image_path": "5ee206ceecc8b73755d7f7355f0fd93aa2d0c4c1e03044e3713b092f3fcbac4a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 506, + 547, + 555 + ], + "lines": [ + { + "bbox": [ + 46, + 506, + 547, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 506, + 547, + 555 + ], + "type": "text", + "content": "Figure 3: The training process of QD-BEV. Progressive QAT with 4 stages is performed in the first 60 epochs, then the view-guided distillation is conducted together with QAT to steadily enhance the performance. The pink line in the figure represents the baseline NDS. Note that swapping VGD with pure QAT or other distillation methods (for example, CWD [33]) will lead to undesirable results, as we show in the last 20 epochs in this figure, compared with Figure 1 and Figure 5." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 575, + 132, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 132, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 132, + 588 + ], + "type": "text", + "content": "4.2.2 QAT results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "To address the severe accuracy degradation of PTQ, we apply QAT to better adapt the models towards 4-bit quantization. In all our experiments, the standard QAT method which directly quantizes the whole network to the target bitwidth will lead to unstable QAT processes, causing gradient explosion or a rapid decrease in accuracy in large models (for example, the W4A6 BEVFormer-Base has only " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "0.07\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "). Based on this observation, we hypothesize that the quantization perturbation introduced in standard QAT" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 575, + 545, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 575, + 545, + 708 + ], + "spans": [ + { + "bbox": [ + 304, + 575, + 545, + 708 + ], + "type": "text", + "content": "is too large to be recovered. As such, we apply progressive QAT to constrain the quantization perturbation along the training process. A comparison of the performance between progressive QAT and standard QAT with the same number of training epochs is presented in Table 3. We can see that progressive QAT consistently outperforms standard QAT by a large margin (up to " + }, + { + "bbox": [ + 304, + 575, + 545, + 708 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 575, + 545, + 708 + ], + "type": "text", + "content": " mAP) in BEVFormer-Tiny and BEVFormer-Small, and achieves an even larger performance gain on BEVFormer-Base. To better validate our analyses, we plot the training curve of progressive QAT as the first 60 epochs in Figure 3, where W4A6 quantization" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "text", + "content": "3831" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 91, + 285, + 329 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 277, + 83 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 277, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 277, + 83 + ], + "type": "text", + "content": "Table 5: QD-BEV results on BEVDepth[21] and PETR[24]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 91, + 285, + 329 + ], + "lines": [ + { + "bbox": [ + 50, + 91, + 285, + 329 + ], + "spans": [ + { + "bbox": [ + 50, + 91, + 285, + 329 + ], + "type": "table", + "html": "
WAModelmAP↑NDS↑
3232BEVDepth-T[21]0.3300.435
88BEVDepth-T-DFQ[29]0.2810.377
46BEVDepth-T-HAWQ[40]0.1360.206
46BEVDepth-T-PACT[7]0.2700.362
46QD-BEVDepth-T (Ours)0.3010.394
3232PETR-r50dcn[24]0.3170.366
88PETR-r50dcn-DFQ[29]0.2900.343
46PETR-r50dcn-HAWQ[40]0.1620.216
46PETR-r50dcn-PACT[7]0.2680.320
46QD-PETR-r50dcn (Ours)0.2880.334
", + "image_path": "4eb9d2746fd83a132f8ff22ee1361fe68b04899a5f78f1bc026e47429af6adac.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 340, + 287, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 287, + 400 + ], + "type": "text", + "content": "is conducted on BEVFormer-Tiny. We separate the progressive QAT into 4 stages and iteratively quantize a new module in each stage. As can be seen, there is an NDS drop at beginning of each stage, corresponding to the quantization perturbation introduced by quantizing each new module." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 400, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 287, + 472 + ], + "type": "text", + "content": "Despite the merits of progressive QAT, we want to note that it still suffers from unstable training and performance degradation. As illustrated in Figure 1 which corresponds to the last 20 epochs in Figure 3, progressive QAT keeps going up and down after reaching a plateau, while training curves of VGD show a rising trend with much better stability." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 479, + 188, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 188, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 188, + 491 + ], + "type": "text", + "content": "4.3. Main Results of QD-BEV" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 498, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 714 + ], + "type": "text", + "content": "In order to obtain better accuracy and stability, we apply view-guided distillation with the floating-point model as the teacher and the quantized model as the student. The effect of VGD on W4A6 quantization of BEVFormer-Tiny is shown in Figure 3. Note that we separate VGD from progressive QAT in the first 60 epochs for a clearer comparison and illustration, and VGD is actually a plug-and-play function that can always be jointly applied with QAT, as we do in the last 20 epochs. Benefiting from knowledge in both the image domain and the BEV domain, QD-BEV networks are able to fully recover the quantization degradation, and even outperform the floating-point baselines. As shown in Table 4, the NDS and mAP of the model outperform previous floating-point baselines as well as quantized networks. Since there are no existing results for compact BEV networks, we implement standard quantization methods DFQ [29], HAWQv3 [40] and PACT [7] on BEVFormer as a comparison. We apply W8A8 quantization for DFQ" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 309, + 72, + 543, + 268 + ], + "blocks": [ + { + "bbox": [ + 309, + 72, + 543, + 268 + ], + "lines": [ + { + "bbox": [ + 309, + 72, + 543, + 268 + ], + "spans": [ + { + "bbox": [ + 309, + 72, + 543, + 268 + ], + "type": "image", + "image_path": "4db8ddb4e11ac53a04447dc1c484f6d061f6c6be18b19f81ae305ba73a8b460c.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 277, + 545, + 301 + ], + "lines": [ + { + "bbox": [ + 305, + 277, + 545, + 301 + ], + "spans": [ + { + "bbox": [ + 305, + 277, + 545, + 301 + ], + "type": "text", + "content": "Figure 4: Visualization of QD-BEV results and the comparison with results obtained by BEVFormer." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 323, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 323, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 545, + 396 + ], + "type": "text", + "content": "(DFQ is a PTQ method, lower bitwidth will lead to intolerable accuracy degradation) and W4A6 for QAT methods and QD-BEV models. As a comparison, QD-BEV can achieve 0.509 NDS with only 32.9 MB model size, which is similar to the size of BEVFormer-T-DFQ (0.340 NDS) and much smaller than BEVFormer-Tiny (126.8 MB, 0.354 NDS)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 396, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 545, + 456 + ], + "type": "text", + "content": "Preliminary tests were run on PETR [24] and BEVDepth [21] models using our method in figure 5. Performance did not match BEVFormer, but still surpassed conventional quantization methods, highlighting the method's potential despite varying results." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 456, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 540 + ], + "type": "text", + "content": "In Figure 4, we show the visualization results of the QDBEV-Base model on the nuScenes val dataset, and compare them with the results of BEVFormer-Tiny and the ground truth. As can be seen, more objects are detected by QDBEV-Base, and the 3D boxes predictions are more accurate than BEVFormer-Tiny. More visualizations are provided in the supplementary material." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 551, + 459, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 551, + 459, + 563 + ], + "spans": [ + { + "bbox": [ + 306, + 551, + 459, + 563 + ], + "type": "text", + "content": "4.4. Streaming perception result" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "In the context of autonomous driving, streaming perception [19] is critical for enabling models to make rapid and precise decisions in real time. High latency will degrade the streaming perception because it will cause a delay between the sensory data and the neural network output. To enhance streaming perception, quantization is a necessary technique that compresses the model size, reduces computational load, and accelerates the inference process. In Table 6, we demonstrate the significant impact of quantization on the sAP metric in autonomous driving scenarios. As we can see, QD-BEV models show consistent improvements in sAP compared to the floating-point counterparts and the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3832" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 92, + 286, + 268 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 282, + 83 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 282, + 83 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 282, + 83 + ], + "type": "text", + "content": "Table 6: sAP of QD-BEV models compared to baselines." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 92, + 286, + 268 + ], + "lines": [ + { + "bbox": [ + 52, + 92, + 286, + 268 + ], + "spans": [ + { + "bbox": [ + 52, + 92, + 286, + 268 + ], + "type": "table", + "html": "
Input SizeModelWAmAP↑sAP↑
450×800BEVFormer-T[23]32320.2530.228
BEVFormer-T-DFQ[29]880.2360.230
QD-BEV-T (Ours)460.2550.251
720×1280BEVFormer-S[23]32320.3700.249
BEVFormer-S-DFQ[29]880.3560.322
QD-BEV-S (Ours)460.3740.350
900×1600BEVFormer-B[23]32320.4160.136
BEVFormer-B-DFQ[29]880.3840.290
QD-BEV-B (Ours)460.4060.337
", + "image_path": "3ff40c9549d8c8b26f4716f6604600e3921ef3ac39cdf835dbf139878d05929c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 50, + 280, + 170, + 376 + ], + "blocks": [ + { + "bbox": [ + 50, + 280, + 170, + 376 + ], + "lines": [ + { + "bbox": [ + 50, + 280, + 170, + 376 + ], + "spans": [ + { + "bbox": [ + 50, + 280, + 170, + 376 + ], + "type": "image", + "image_path": "88fb07d0ced050705f677c3229af9d8d3f6b8b7ddebad0fc090775f1731c9fe8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 79, + 383, + 135, + 392 + ], + "lines": [ + { + "bbox": [ + 79, + 383, + 135, + 392 + ], + "spans": [ + { + "bbox": [ + 79, + 383, + 135, + 392 + ], + "type": "text", + "content": "(a) mAP curve." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 171, + 280, + 290, + 376 + ], + "blocks": [ + { + "bbox": [ + 171, + 280, + 290, + 376 + ], + "lines": [ + { + "bbox": [ + 171, + 280, + 290, + 376 + ], + "spans": [ + { + "bbox": [ + 171, + 280, + 290, + 376 + ], + "type": "image", + "image_path": "9f56193136f1a01ad3b9f2ba7585414cb59593f501af2744b361dbbd088daf9c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 199, + 383, + 255, + 392 + ], + "lines": [ + { + "bbox": [ + 199, + 383, + 255, + 392 + ], + "spans": [ + { + "bbox": [ + 199, + 383, + 255, + 392 + ], + "type": "text", + "content": "(b) NDS curve." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 403, + 287, + 440 + ], + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 440 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 440 + ], + "type": "text", + "content": "Figure 5: The training curve of VGD versus CWD [33]. CWD uses only one type of features, referred to as cwd-image (image feature) and cwd-bev (bev feature), respectively." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 460, + 130, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 460, + 130, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 130, + 472 + ], + "type": "text", + "content": "quantized baselines." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 483, + 138, + 497 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 483, + 138, + 497 + ], + "spans": [ + { + "bbox": [ + 47, + 483, + 138, + 497 + ], + "type": "text", + "content": "5. Ablation study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 503, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 503, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 503, + 287, + 624 + ], + "type": "text", + "content": "In Figure 5, we conduct an ablation study where we compare view-guided distillation with the cases using only distillation on the image feature, and only on the BEV feature, respectively. The method is referred to as CWD [33]. For a fair comparison, we apply the same pre-training weights and hyperparameters such as the temperature and the learning rate. From the figure, it can be found that view-guided distillation has a clear advantage over the CWD methods. In both the mAP and NDS curves, VGD has a more obvious and stable upward trend, and achieves better final results." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 634, + 119, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 119, + 646 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 119, + 646 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 653, + 286, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 715 + ], + "type": "text", + "content": "In this work, we systematically study both PTQ and QAT on BEV networks and showcase the major problems they are facing. Based on our analyses, we propose a view-guided distillation (VGD) method that can stabilize the QAT process and enhance the final performance by lever" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": "aging information from both the image domain and the BEV domain. With VGD as a plug-and-play function that can be jointly applied when quantizing BEV models, QD-BEV can close the accuracy gap or even outperforms the floating-point baselines. On the nuScenes datasets, the 4-bit weight and 6-bit activation quantized QD-BEV-Tiny model achieves " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "37.2\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " NDS with only " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "15.8\\mathrm{MB}" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " model size, outperforming BevFormer-Tiny by " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "1.8\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " with an " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "8\\times" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " model compression." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 192, + 416, + 206 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 192, + 416, + 206 + ], + "spans": [ + { + "bbox": [ + 305, + 192, + 416, + 206 + ], + "type": "text", + "content": "7. Acknowledgement" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 213, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 213, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 213, + 545, + 308 + ], + "type": "text", + "content": "This work was supported by the National Key R&D Program of China (2022ZD0116305). The authors would also like to express their gratitude to the CCF-Baidu Open Fund Project, Berkeley Deep Drive, and Intel Corporation for their support and assistance throughout this research. Special thanks to Yandong Guo from " + }, + { + "bbox": [ + 304, + 213, + 545, + 308 + ], + "type": "inline_equation", + "content": "\\mathrm{Al}^2" + }, + { + "bbox": [ + 304, + 213, + 545, + 308 + ], + "type": "text", + "content": " Robotics (YAN-DONG.guo@live.com) for his valuable contributions to this work." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 321, + 365, + 334 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 321, + 365, + 334 + ], + "spans": [ + { + "bbox": [ + 306, + 321, + 365, + 334 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 310, + 341, + 547, + 713 + ], + "type": "list", + "angle": 0, + "index": 23, + "blocks": [ + { + "bbox": [ + 310, + 341, + 545, + 396 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 341, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 310, + 341, + 545, + 396 + ], + "type": "text", + "content": "[1] Sungsoo Ahn, Shell Xu Hu, Andreas Damianou, Neil D Lawrence, and Zhenwen Dai. 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However, emerging evidence suggests that any single pre-trained feature will not perform well on diverse downstream tasks. Each pre-training strategy encodes a certain inductive bias, which may suit some downstream tasks but not others. Notably, the augmentations used in both supervised and self-supervised training lead to features with high invariance to spatial and appearance transformations. This renders them sub-optimal for tasks that demand sensitivity to these factors. In this paper we develop a feature that better supports diverse downstream tasks by providing a diverse set of sensitivities and invariances. In particular, we are inspired by Quality-Diversity in evolution, to define a pre-training objective that requires high quality yet diverse features — where diversity is defined in terms of transformation (in)variances. Our framework plugs in to both supervised and self-supervised pre-training, and produces a small ensemble of features. We further show how downstream tasks can easily and efficiently select their preferred (in)variances. Both empirical and theoretical analysis show the efficacy of our representation and transfer learning approach for diverse downstream tasks. Code available at https://github.com/ruchikachavhan/quality-diversity-pretraining.git", + "bbox": [ + 90, + 344, + 473, + 706 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 92, + 734, + 218, + 749 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Pre-training neural networks on large-scale datasets such as ImageNet followed by representation transfer is a dominant paradigm in applied deep learning [58]. Supervised pre-training [34] is long established, with self-supervised [14, 30, 15, 11, 69] pre-training rapidly gaining popularity. Such pre-training algorithms often aspire to providing a universal representation which is effective for diverse down-", + "bbox": [ + 90, + 758, + 470, + 852 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ead222294ef1e4f91683b4679bbd30afe9d64e96e5782ae387e5f6e6ceed6ecf.jpg", + "image_caption": [ + "Figure 1. Illustration of the quality and behavior space of QD4V feature representations. Each point in this space is a potential feature extractor. The $x$ and $y$ axes correspond sensitivity-invariance axes for spatial and appearance transformations, and define the behaviour space for features. The $z$ axis shows the quality of the features (eg: ImageNet accuracy). The shaded zones schematically show the range of feature encodings that might be preferred by different types of downstream tasks. Conventional pre-training learns a single solution (denoted with +) that is high-quality ( $z$ axis near 1) but by default occupies the green zone of high invariance to spatial and appearance transforms. In contrast, QD4V aims to learn a set of solutions (marked by $\\Delta$ ) that better span the (in)variance axes, while being also being high quality. These lead to better performance for diverse downstream tasks. Note that in practice the invariance space has many more dimensions than the two illustrated here." + ], + "image_footnote": [], + "bbox": [ + 524, + 317, + 855, + 483 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "stream tasks across computer vision, with evaluation studies showing promising results [34, 24]. Nevertheless, emerging evidence suggests that any single pre-trained feature will not be optimal for diverse downstream tasks [25, 68, 13]. This is because, any given pre-training strategy encodes a certain inductive bias in the learned representation, which will better suite some downstream tasks more than others.", + "bbox": [ + 497, + 705, + 875, + 797 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This issue is evident with regards to transformation invariance. By way of example, downstream object recognition benefits from strong affine invariance in a feature since pose is a distractor for object recognition. In con", + "bbox": [ + 497, + 799, + 875, + 852 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 95, + 8, + 171, + 45 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 231, + 5, + 815, + 47 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5384", + "bbox": [ + 468, + 879, + 500, + 891 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "trast, downstream pose estimation depends heavily on affine sensitivity in a feature. However, supervised pre-training tends to promote affine-invariance due to the nature of the task and the popular augmentations used. Meanwhile self-supervised pre-training produces feature with even stronger affine-invariance due to optimising for augmentation invariance. So neither may be optimal for downstream pose estimation. More generally, there are a diverse set of potential transformations, each of which may be nuisance factors for some tasks and crucial for others – and any given representation exhibits different degrees of (in)sensitivity to each each possible transformation. Thus, despite the power of mainstream supervised and self-supervised pretraining, since any single feature induces a particular set of (in)variance strengths, it will be sub-optimal for those downstream tasks with different (in)variance preferences.", + "bbox": [ + 90, + 140, + 472, + 353 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Within the self-supervised learning community, a few studies have attempted to address these issues by learning features with multiple (in)variances. This often achieved by an ensemble of different models [25], pre-training multi-headed networks with contrastive learning for different augmentations in each head [68], or with different heads dedicated to (invariance promoting) contrastive learning and (sensitivity promoting) transformation prediction [38]. However, these initial attempts suffer important limitations. Firstly, given that there are many transformations for which invariance or sensitivity may be preferred, it's unclear how to build a compact enough ensemble. For example, if $N$ models are used to encode $N$ distinct strengths of sensitivity to a particular transformation, and there are $K$ possible transformations, this naively leads to an ensemble of size $N^K$ to cover the possible invariance preferences of downstream tasks. Secondly, it's unclear how to optimally select or fuse these different features for downstream tasks with apriori unknown (in)variance preferences.", + "bbox": [ + 95, + 357, + 472, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we address the first of these challenges through the lens of Quality Diversity (QD) [12, 51, 27] a strategy in evolutionary computation that has seen great success in robotics [20]. QD strategies aim to more robustly solve problems by searching for a set of solutions rather than a single solution, and - crucially - requiring that the set of solutions are diverse in some meaningful behavioural metric. We introduce the notion of Quality Diversity Optimisation for Vision (QD4V), where, in a computer vision context, we interpret the idea of behaviour space for diversity measurement as degree of (in)variances to different data augmentations. When applied to supervised ImageNet pretraining, this corresponds to optimising for a small set of ImageNet models that are highly performant, yet use as different cues as possible for recognition. This is qualitatively illustrated in Fig. 1. Each downstream task is then presented with a meaningfully diverse set of high-quality features from which a feature meeting the (in)variance prefer", + "bbox": [ + 90, + 613, + 472, + 853 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ences of the task is more likely to be found.", + "bbox": [ + 499, + 140, + 778, + 152 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our second contribution addresses how to fuse this small ensemble of features for the downstream task. The limited existing work on learning multiple (in)variances relies on ad-hoc heuristics, such as simply concatenating features prior to linear readout [25, 68]. We argue that a better solution is train a per feature linear readout on the downstream train set, and then learn a fusion weight on the downstream val set, i.e., stacking [66]. We show both empirically and theoretically that this approach to transfer learning outperforms the standard approach.", + "bbox": [ + 497, + 153, + 877, + 285 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, we present a framework for learning a compact and high-quality yet meaningfully diverse set of features. We present a simple approach for transferring them to downstream tasks with strong theoretical backing. Finally, we show empirically that our framework improves on average compared to standard pre-trained features when evaluated on a diverse range of downstream tasks.", + "bbox": [ + 497, + 286, + 877, + 379 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 499, + 391, + 636, + 404 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Invariance learning in vision: Invariances for in-domain image classification have been learned using data augmentation [9] via MAP [6] and marginal likelihood [32] learning. However, these methods do not focus on transferability to downstream target tasks. On the other hand, the success of representation transfer in contrastive self-supervised learning has been attributed to augmentation-based training engendering invariances [25, 63, 52] which act as strong inductive biases for downstream tasks. The field aspires to provide a single general-purpose feature suited for all downstream tasks [8], however, this goal is not straightforward to achieve. Recent studies have shown that features with invariances to different augmentations are suited for different downstream tasks, with no single feature being optimal for all tasks [25, 68] and performance suffers if inappropriate invariances are provided. In contrastive learning, this leads to the laborious need to produce and combine an ensemble of features [68, 25], to disentangle invariance and transformation prediction [38], costly task-specific self-supervised pre-training [54, 61], or amortising invariances [13]. We introduce a framework for learning diverse invariances during either supervised or self-supervised pre-training, while maintaining the quality of those features in terms of encoding image semantics. We also provide an efficient and theoretically supported approach to fuse the resulting features that improves on standard heuristics [25, 68].", + "bbox": [ + 497, + 413, + 878, + 758 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Quality Diversity: Quality Diversity (QD) optimisation [12, 51, 27] originated in evolutionary algorithms as a strategy for finding a meaningfully diverse set of high-performing solutions to a problem, rather than just one global optimum. Access to a suite of meaningfully diverse high-quality solutions often has substantial robustness benefits that are widely exploited in robotics community", + "bbox": [ + 497, + 759, + 877, + 852 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5385", + "bbox": [ + 468, + 879, + 500, + 891 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "[20]. In order to drive diversity, a QD algorithm requires an application-specific measure of behaviour as a feature between which two models' difference can be compared. We develop a novel behavioural measure for vision in terms of invariances. Mainstream QD optimisation algorithms such as MAP-Elites are not amenable to the differentiable gradient-based solutions required for application in vision. We develop a simple differentiable instantiation of QD that is amenable to easy integration as a loss within a typical deep learning for vision pipeline.", + "bbox": [ + 90, + 139, + 472, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Ensemble methods: QD is related to ensemble methods, which have a long history in vision and machine learning [22]. However, ensembles have mostly focused on single-task learning rather than pre-training for transfer learning. A key challenge in ensemble methods is obtaining meaningful inter-model diversity, with the standard approaches of random seeds, boosting, and bagging, providing comparatively weak diversity. Our novel strategy is to take QD's insight that diversity should be measured in a meaningful space, and identifying (in)variance axes as such a meaningful space for diversity measurement in visual pre-training. A second key issue for ensembles is fusing the ensemble prediction, which has been variously performed by unweighted prediction averaging [45] or parameter averaging [46], and feature concatenation in transfer learning [25, 68]. We show both empirically and theoretically the efficacy of learning a weighted combination of predictions.", + "bbox": [ + 90, + 273, + 473, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 92, + 508, + 221, + 524 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Background", + "text_level": 1, + "bbox": [ + 92, + 530, + 218, + 544 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Mainstream QD optimization [27, 51] searches for a diverse set of solutions $\\{\\theta_i\\}$ to an optimization problem $\\mathcal{L}_q$ by solving an objective like", + "bbox": [ + 90, + 550, + 470, + 590 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\{\\theta_ {i} \\}} \\sum_ {i} \\mathcal {L} _ {q} (\\theta_ {i}) s. t. D (\\{\\pi (\\theta_ {i}) \\}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 595, + 470, + 624 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\pi$ is a vector of application relevant observable properties of a given solution $\\theta_{i}$ that is called phenotype in the QD community. $D$ is a diversity constraint that enforces diversity among the solutions. It is often enforced by tessellation, or gridding, the space of $\\pi$ . Thus solution sets $\\{\\theta_i\\}$ have the maximum possible quality $(\\mathcal{L}_q)$ while also covering the space of measurable differences in behaviour [27, 51]. To make such QD problems more efficient to solve in a vision context, we will relax them to", + "bbox": [ + 90, + 627, + 472, + 747 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\{\\theta_ {i} \\}} \\sum_ {i} \\mathcal {L} _ {q} (\\theta_ {i}) - \\sum_ {i \\neq j} \\mathcal {L} _ {d i v} (\\pi (\\theta_ {i}), \\pi (\\theta_ {j}) \\}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 751, + 472, + 781 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{div}$ is a loss that measures pairwise distance.", + "bbox": [ + 92, + 785, + 428, + 799 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Visual Pre-training", + "text_level": 1, + "bbox": [ + 92, + 804, + 272, + 820 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We denote a large dataset for pre-training by $\\mathcal{D}_t\\subset$ $\\mathcal{X}\\times \\mathcal{Y}$ , where $\\mathcal{X}$ is some space of input images and the", + "bbox": [ + 92, + 825, + 472, + 853 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "space $\\mathcal{V}$ may be contain labels obtained from manual annotation or pre-text tasks from self-supervision. We introduce a population of $N$ feature extractors, represented as an ensemble, $\\mathcal{F} = \\{f_{\\theta_i}\\}_{i=1}^N$ , which aim to learn a diverse set of invariances while maintaining high quality. Each member of the ensemble is followed by a projection layer $g_{\\phi_i}$ which can be a classifier layer in case of supervised learning or a projection head in case of self-supervised learning [14, 30, 16]. We denote a set of $K$ augmentations considered for pre-training as $\\mathcal{T}$ . Let us also denote a sample $\\mathbf{x}$ transformed by augmentation $\\mathcal{T}_j \\in \\mathcal{T}$ as $\\tilde{\\mathbf{x}}^j$ .", + "bbox": [ + 497, + 139, + 878, + 288 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1 QD for Visual Pre-training: Diversity", + "text_level": 1, + "bbox": [ + 497, + 302, + 801, + 317 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To quantify the diversity of solutions during pre-training, we must first define a phenotype — an observable measurement of a feature extractor's behaviour. We define the behavior of a solution by the degree of invariance it shows to a set of augmentations $\\mathcal{T}$ . We borrow the definition of invariance from [25], where invariance of a model to a particular data augmentation is defined as the cosine similarity $S(f_{\\theta}(\\mathbf{x}),f_{\\theta}(\\tilde{\\mathbf{x}}^{j}))$ between augmented and unaugmented features. Thus, we define a phenotype of a solution $f_{\\theta_i}$ as a vector $\\pi (\\mathbf{x};\\theta_i)\\in \\mathbb{R}^K$ such that $j^{\\mathrm{th}}$ element of the phenotype vector indicates the invariance that the model exhibits to augmentation $\\mathcal{T}_j\\in \\mathcal{T}$ , as shown in Eq 3.", + "bbox": [ + 497, + 323, + 878, + 483 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\pi (\\mathbf {x}; \\theta_ {i}) = \\left(S \\left(f _ {\\theta_ {i}} (\\mathbf {x}), f _ {\\theta_ {i}} \\left(\\tilde {\\mathbf {x}} ^ {j}\\right)\\right) _ {j = 1} ^ {| \\mathcal {T} |} \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 493, + 875, + 521 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diversity Loss: Based on the above phenotype definition, we can encourage each model to exhibit a diverse combination of invariances to augmentations in $\\mathcal{T}$ . Specifically, we minimise the negative exponential distance between phenotype vector of each member as in Eq 4", + "bbox": [ + 497, + 530, + 878, + 598 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {d i v e r s i t y}} = \\sum_ {i \\neq j} ^ {N} \\exp (- | \\pi (\\mathbf {x}; \\theta_ {i}) - \\pi (\\mathbf {x}; \\theta_ {j}) |) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 606, + 875, + 644 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.2 QD for visual pre-training: Quality", + "text_level": 1, + "bbox": [ + 499, + 659, + 789, + 674 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Quality Loss: Depending on the pre-training paradigm employed, different loss functions can be used to promote high quality. In the case of supervised learning, the loss function denoted by $l_{q}$ can be cross-entropy, while self-supervised methods such as SimCLR/MoCo use contrastive loss [48]. The loss function for the entire ensemble for a sample $(\\mathbf{x},y)\\in \\mathcal{D}$ is given in Eq. 5", + "bbox": [ + 497, + 680, + 878, + 776 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {q u a l i t y}} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} l _ {q} \\left(g _ {\\phi_ {i}} \\left(f _ {\\theta_ {i}} (\\mathbf {x})\\right), y\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 574, + 783, + 875, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This objective reflects standard supervised or self-supervised learning of the upstream model. Empirically,", + "bbox": [ + 499, + 825, + 877, + 853 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5386", + "bbox": [ + 468, + 879, + 500, + 891 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a26cfa82aad76becfd979cfaa06ce11d9af9aaf2f9a1303150a0b36d0865fbe8.jpg", + "image_caption": [ + "Figure 2. Schematic illustration of Quality Diversity Pre-training, shown with only 2 augmentations for simplicity. $\\mathcal{L}_{\\mathrm{diversity}}$ maximises the difference between invariances that models exhibit to $\\mathcal{T}_1$ and $\\mathcal{T}_2$ , while $L_{\\mathrm{quality}} + \\lambda_{kl}\\mathcal{L}_{KL}$ maximises the quality of the ensemble by pushing it to the quality of a conventionally pre-trained model (denoted by Baseline)." + ], + "image_footnote": [], + "bbox": [ + 184, + 140, + 794, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "we found that purely using this quality objective it is hard for a diverse ensemble to match the quality of a baseline model trained solely for quality. To help the diverse ensemble match the quality of the baseline we introduce an additional loss term, which is the Kullback-Leibler (KL) divergence between the posteriors of the ensemble members and baseline model with parameters $\\phi_{b}$ and $\\theta_{b}$ . We denote the predictions of a model by $\\hat{y}_i = g_{\\phi_i}(f_{\\theta_i}(x))$ . The loss function is shown in Eq. 6. This term ensures that the members of the ensemble mimic the predictions of the baseline model, thus ensuring high quality with diverse invariances.", + "bbox": [ + 90, + 350, + 472, + 497 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {q u a l i t y - K L}} = \\sum_ {i = 1} ^ {N} \\frac {1}{m} \\sum_ {j = 1} ^ {m} \\mathrm {K L} \\left(\\sigma \\left(\\hat {y} _ {i}; \\tau\\right) \\| \\sigma \\left(\\hat {y} _ {b}; \\tau\\right)\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 519, + 470, + 558 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, $\\sigma$ denotes the softmax function and $\\tau$ denotes the temperature used to scale the logits within softmax.", + "bbox": [ + 92, + 567, + 470, + 594 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Summary Finally, to achieve our goal of diverse invariances and high quality in QD4V pre-training, we formulate a total loss function asin Eq. 7.", + "bbox": [ + 92, + 596, + 470, + 638 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {q d} = \\mathcal {L} _ {\\text {q u a l i t y}} + \\lambda_ {k l} \\mathcal {L} _ {\\text {q u a l i t y - K L}} + \\lambda_ {d} \\mathcal {L} _ {\\text {d i v e r s i t y}} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 663, + 470, + 678 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The diverse set of optimal solutions learned from the proposed QD pre-training stage denoted as $\\mathcal{F}^*$ is then transferred to a downstream task.", + "bbox": [ + 92, + 688, + 470, + 728 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Downstream task Learning", + "text_level": 1, + "bbox": [ + 92, + 738, + 331, + 753 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We next address how to construct models for downstream tasks given the diverse ensemble of features $\\mathcal{F}^*$ produced by pre-training in the previous section. Existing approaches have concatenated features prior to linear readout [68], or conducted unweighted averaging of ensemble features [45]. We propose to fuse the ensemble via a variant of stacking [66].", + "bbox": [ + 92, + 759, + 472, + 853 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Decoder Design For each feature extractor, $f_{\\theta_i} \\in \\mathcal{F}$ we follow the standard linear readout approach, and build a linear model, $h^{(i)}$ , parameterised by $U^{(i)} \\in \\mathbb{R}^{k \\times d}$ and $\\mathbf{b}^{(i)} \\in \\mathbb{R}^k$", + "bbox": [ + 497, + 350, + 877, + 403 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nh ^ {(i)} (\\mathbf {x}) = \\rho (U ^ {(i)} f _ {\\theta_ {i}} (\\mathbf {x}) + \\mathbf {b} ^ {(i)}),\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 407, + 793, + 425 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\rho$ is a transfer function for linear models (e.g., the softmax function or identity). To produce a final prediction we fuse the ensemble of classifiers $h^{(i)}(x)$ by learning a weight vector, $\\mathbf{w} \\in \\mathbb{R}^N$ that is used to make a linear combination of their predictions,", + "bbox": [ + 497, + 429, + 877, + 495 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nh (\\mathbf {x}) = \\sum_ {i = 1} ^ {N} w _ {i} h ^ {(i)} (\\mathbf {x}).\n$$\n", + "text_format": "latex", + "bbox": [ + 613, + 501, + 761, + 538 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Decoder Training Strategy For each downstream task have a collection of data, $\\mathcal{D}_{ds}$ , which we split into two nonoverlapping subsets, $\\mathcal{D}_{tr}$ and $\\mathcal{D}_{val}$ . The hyperparameters of the linear models are tuned using this train-validation split, and the best model parameters found during this tuning phase are denoted by $\\tilde{U}^{(i)}$ and $\\tilde{\\mathbf{b}}^{(i)}$ . Each model is retrained using the full $\\mathcal{D}_{ds}$ dataset using the best hyperparameters to obtain the final values for each $U^{(i)}$ and $\\mathbf{b}^{(i)}$ . The procedure used to fit the weights for linearly combining the models is carried out using the $\\tilde{U}^{(i)}$ and $\\tilde{\\mathbf{b}}^{(i)}$ parameters, and $\\mathbf{w}$ is fit on the $\\mathcal{D}_{val}$ set,", + "bbox": [ + 497, + 541, + 877, + 688 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {w} = \\underset {\\mathbf {v} \\in \\mathbb {R} ^ {N}} {\\arg \\min } \\mathbb {E} _ {\\mathcal {D} _ {v a l}} \\left[ \\left\\| \\sum_ {i = 1} ^ {N} v _ {i} \\rho \\left(\\tilde {U} ^ {(i)} f _ {\\theta_ {i}} (\\mathbf {x}) + \\tilde {\\mathbf {b}} ^ {(i)}\\right) - y \\right\\| _ {2} ^ {2} \\right] \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 499, + 692, + 875, + 745 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the following section, we provide theoretical justification for our proposed downstream architecture and training strategy by way of bounding the generalisation error for downstream tasks learned in this way.", + "bbox": [ + 497, + 746, + 877, + 799 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Theoretical Analysis", + "text_level": 1, + "bbox": [ + 499, + 804, + 687, + 820 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For ease of exposition, consider the case where $\\rho$ is the identity and the underlying problem is binary classification.", + "bbox": [ + 499, + 826, + 877, + 853 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5387", + "bbox": [ + 468, + 879, + 500, + 891 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this case, each $U^{(i)}$ can be written as a vector, $\\mathbf{u}^{(i)}$ . We can define the effective hypothesis class of our algorithm for learning on downstream tasks as", + "bbox": [ + 92, + 139, + 472, + 180 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {H} = \\left\\{\\mathbf {x} \\rightarrow \\sum_ {i = 1} ^ {N} w _ {i} \\langle \\mathbf {u} ^ {(i)}, f _ {\\theta_ {i}} (\\mathbf {x}) \\rangle : \\right. \\\\ \\left. \\left\\| \\mathbf {w} - \\mathbb {E} [ \\mathbf {w} ] \\right\\| _ {2} \\leq A, \\left\\| \\mathbf {u} ^ {(i)} - \\mathbb {E} [ \\mathbf {u} ^ {(i)} ] \\right\\| _ {F} \\leq B \\right\\}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 192, + 453, + 265 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we have absorbed the bias values into $\\mathbf{u}$ by assuming a 1 has been appended to each $\\mathbf{x}$ . Our goal is to bound the generalisation error of models from this class trained using our stacking procedure in Sec 3.3. The first step is to bound the empirical Rademacher complexity in terms of $A$ and $B$ (from the definition of $\\mathcal{H}$ ), the norm of the features, and the total amount of data available for the downstream task, $m = |\\mathcal{D}_{ds}|$ . We then show how the stacking procedure influences the values of $A$ and $B$ . We use $\\eta$ to indicate the fraction of data used for training, hence $\\eta m = |\\mathcal{D}_{tr}|$ and $(1 - \\eta)m = |\\mathcal{D}_{val}|$ . Our main result in given below.", + "bbox": [ + 92, + 275, + 472, + 423 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Theorem 1. For a model trained using our stacking procedure and the conditions outlined in the statements of Lemmas 1 and 2, we have with probability at least $1 - 2\\delta$", + "bbox": [ + 92, + 432, + 472, + 472 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbb {E} [ \\mathbf {1} [ \\operatorname {s g n} (h (\\mathbf {x})) \\neq y) ] \\leq \\hat {\\mathbb {E}} [ l (h (\\mathbf {x}), y) ] \\\\ + \\frac {1 2 X ^ {3} \\| \\tilde {V} \\| _ {2} \\sqrt {\\ln (4 / \\delta) \\ln (4 N / \\delta)}}{\\gamma_ {1} \\gamma_ {2} \\sqrt {1 - \\eta m ^ {3 / 2}}} \\\\ + \\frac {2 X ^ {2} \\sqrt {2 \\ln (4 N / \\delta)}}{\\gamma_ {1} m} \\\\ + \\frac {2 X ^ {2} \\| \\tilde {V} \\| _ {2} \\sqrt {2 \\ln (4 / \\delta)}}{\\gamma_ {2} \\sqrt {1 - \\eta m}} \\\\ + 3 \\sqrt {\\frac {\\ln (1 / \\delta)}{2 m}}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 483, + 455, + 627 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{\\mathbb{E}}[l(h(\\mathbf{x}), y)]$ is the mean ramp loss of the model $h$ , computed on the training data.", + "bbox": [ + 92, + 640, + 468, + 669 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Notably, this bound achieves the \"fast\" rate of convergence, $\\mathcal{O}(m^{-1})$ , in the complexity terms, with the first term even exhibiting a super-fast rate of $\\mathcal{O}(m^{-3/2})$ . This is in contrast to the standard $\\mathcal{O}(m^{-1/2})$ rate in existing bounds. The proof is in the supplemental material.", + "bbox": [ + 92, + 678, + 468, + 745 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Discussion This theorem depends on both the specific architecture and optimisation strategy outlined in Sec. 3.3, and thus provides justification for these design choices. It says that the generalisation gap between train error and expected (test) error rapidly goes to zero with the size of the downstream train set $m$ . Furthermore, because we have access to an ensemble of features, the train error $\\hat{e} r(h)$ can likely be reduced below that of a single feature.", + "bbox": [ + 92, + 746, + 470, + 853 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Implementation details", + "text_level": 1, + "bbox": [ + 499, + 137, + 709, + 154 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pre-training: We perform supervised training for ResNet50 and ConvNeXt [42] on ImageNet1K [21] and contrastive training for ResNet50 on both ImageNet1K and ImageNet100 [68]. To learn our feature ensemble, in a parameter efficient way for both architectures, we share the first three layers (layer1, layer2, layer3 according to [65]), after which different members of the ensemble branch out into their own sequence of layers having a separate layer4 and projection head. We initialise the entire ensemble with ImageNet pre-trained models in case of supervised pre-training and MoCo pre-trained models in case of contrastive learning.", + "bbox": [ + 497, + 160, + 877, + 319 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Augmentations: For supervised pre-training, most methods that rely on strong augmentation policies. Our approach applies the quality loss (Eq. 5) to unaugmented samples only as using augmented samples for quality maximisation would lead to typical strong invariance to all augmentations and prevent diversity. For contrastive learning, we apply very weak augmentations for instance discrimination.", + "bbox": [ + 497, + 319, + 877, + 413 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Learning rates and Optimisers: For supervised pretraining and contrastive learning experiments, we train the model for 20 epochs with SGD and AdamW optimizers respectively, along with learning rate warm-up for 5 epochs, followed by a cosine decay schedule. For supervised pretraining, we apply label smoothening and perform exponential moving average (EMA) on the model weights.", + "bbox": [ + 497, + 414, + 877, + 506 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Downstream tasks: Our suite of downstream tasks consists of object recognition, regression, and dense estimation. We provide more details about downstream tasks in the supplementary material.", + "bbox": [ + 497, + 506, + 877, + 558 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Classification: For classification, we evaluate on standard benchmarks CIFAR10/100 [36], Caltech101 [26], Oxford Flowers [47], Stanford Cars [35], Describable Textures Dataset (DTD) [17], Aircraft [43].", + "- Regression: We include a set of spatially sensitive tasks including facial landmark detection on 300W [1], CelebA [41], human pose estimation in LSP [33] and MPII [2], Animal Pose prediction [10], AROI object orientation prediction [29], and Causal3DIdent 6D pose and appearance attribute prediction [60].", + "- Dense estimation: We also evaluate the QD pretrained models on dense estimation tasks like Pascal VOC object detection using Faster R-CNN [55] with a Feature Pyramid Network backbone [39] and linear semantic segmentation similar to [4] on CityScapes and ADE20k [7] datasets." + ], + "bbox": [ + 517, + 570, + 877, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Downstream evaluation: For classification and regression tasks, we fit multinomial logistic regression and multi-output linear regression on the extracted features from each", + "bbox": [ + 497, + 812, + 877, + 853 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5388", + "bbox": [ + 468, + 879, + 500, + 891 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e4a8775b0e435dfecb73edc415b4ed4271ca73984c7216d3b5595ad6384be519.jpg", + "image_caption": [ + "Figure 3. Radar plot comparing invariance w.r.t. for 4 Spatial and 4 Appearance based transformations of baseline models (green) and QD ensemble (dots). The red and blue lines correspond to maximum and minimum invariances within QD ensemble. The blue shaded region corresponds to the range of invariances spanned by the QD ensemble, which encompasses the (in)variance of the baselines." + ], + "image_footnote": [], + "bbox": [ + 240, + 153, + 472, + 321 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/38133b78b2eacf8ba7ff6a5ef7e6ce946a1f36ae9de85fff83f4b5f555f0d5ca.jpg", + "image_caption": [], + "image_footnote": [ + "ax, invariance in, invariance aseline" + ], + "bbox": [ + 505, + 156, + 736, + 319 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f5c2efadd1b24454ad7c91be9fe0beee96dc753ab244e3c25bbddc9a980940a8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsCIFAR10CIFAR100FlowersCaltech 101DTDCarsAircraft300wLS PoseCelebAAnimal PoseMPIIALOICausal3DRank
IN1K (RN50)Sup.Baseline90.468.285.284.771.944.436.070.255.449.011.218.024.164.12.7
Multihead90.367.384.884.169.943.235.068.353.250.110.917.022.862.33.7
Div. Ens. [23]91.672.984.689.369.842.735.366.652.649.211.517.922.660.83.4
MeTTA [3]91.071.685.385.171.841.134.065.352.847.910.516.323.161.23.8
QD4V90.370.486.989.972.245.436.976.662.461.512.518.528.472.81.4
MoCoMoCo90.370.689.887.973.939.341.887.269.092.513.919.946.078.11.9
Fusionx[25]95.0-81.086.0---65.068.033.0-----
QD4V88.971.285.288.275.841.343.988.971.895.214.222.447.480.61.2
Sup.Baseline (CN-T)89.470.694.589.168.052.548.463.148.152.511.517.78.0269.41.8
QD4V (CN-T)91.572.996.589.969.851.550.082.269.960.712.518.59.371.91.1
IN100Sup.MoCo84.661.682.477.364.533.937.285.558.761.013.218.630.961.43.5
AugSelf* [38]85.363.985.778.966.237.439.577.363.977.012.919.535.261.62.4
AI+ [13]81.364.681.378.468.838.637.390.065.282.012.521.632.762.62.5
QD4V84.565.485.581.271.939.837.988.969.785.014.320.633.865.31.5
", + "bbox": [ + 95, + 379, + 878, + 511 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Downstream performance of ImageNet (IN1K) pretrained (1) Supervised ResNet50, (2) MoCo ResNet50 and ImageNet-100 (IN100) pretrained (3) Supervised ConvNeXt-Tiny (CN-T), (4) MoCo ResNet50. The first seven columns are classification tasks (accuracy, %); the last seven are regression (R2, %). + numbers from [13] where reported, * A mix of our runs and numbers from [13] where reported, x numbers from [25], rest are our runs.", + "bbox": [ + 90, + 516, + 875, + 565 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bd931b75b5c2cb2d33ac0599f4f84174c8a262e15c1dc9642153e1431bc61d45.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 154, + 576, + 327, + 690 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/01d25f18044af3245957d30a7e144a3bccb817a48ef62fbaf430fb431c3c6871.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 327, + 576, + 490, + 690 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/554f2d81bafbdde470aba1f2b7451404875c624d8878a3958cae359a28ee64dc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 490, + 576, + 652, + 690 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d3e5e413be75d85167d01028f89519ea5a876830fce657a1ad1a2fbc7ac85567.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 652, + 576, + 813, + 690 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7ad8e6555d1f36d8ff6eeb554656228b6026412445e818cf1afda406605b5fdf.jpg", + "image_caption": [ + "Figure 4. Correlation between our classifier fusion weights (Eq 8) and task for 4 Spatial and 4 Appearance based augmentations. The y-axis corresponds to Pearson's r correlation between w assigned to each member by a particular task and invariances exhibited by that member to specific augmentations. Tasks are grouped by classification and regression, which tend to show different invariance preferences." + ], + "image_footnote": [], + "bbox": [ + 157, + 692, + 327, + 806 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1b4bc6146307adb9e768040023f6a7fc69f778d1722b85b57360ef37bc306448.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 329, + 692, + 490, + 806 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ddead2bdabe21de978f52c6a0ab982b52304e3b1d43410b368d3469c51334a94.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 490, + 692, + 650, + 806 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c05a5d5e4025e538e4c038bbf14c40a522613d0ab678c1087c561cc43bcae4a2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 652, + 692, + 813, + 806 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5389", + "bbox": [ + 468, + 879, + 500, + 891 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/112337d6f9c5518349339568ddaa142c2b3f4fd3833597c6755172406cd7ded7.jpg", + "table_caption": [], + "table_footnote": [ + "Table 2. Few-shot classification and regression accuracy (\\%, R2) of our QD ResNet50 ensemble for supervised (top), MoCo pre-trained on ImageNet (middle) and MoCo pre-trained on ImageNet-100 (bottom). Values are reported with $95\\%$ confidence intervals averaged over 2000 episodes on FC100, CUB200, and Plant Disease. (N, K) denotes N-way K-shot tasks. For regression tasks (300w, LS Pose, CelebA, Causal3D), we report downstream performance for different splits with train proportion given by $s$ ." + ], + "table_body": "
MethodsCUBFlowersFC 100Plant Disease300wLS PoseCelebACausal3DRank
(5,1)(5,5)(5,1)(5,5)(5,1)(5,5)(5,1)(5,5)s=0.05s=0.2s=0.05s=0.2s=0.05s=0.2s=0.05s=0.2
Baseline70.090.477.393.753.878.768.988.820.524.846.948.539.241.458.962.42.3
Multihead69.688.276.592.652.978.568.287.319.424.739.344.939.440.857.261.33.5
Div. Ensemble68.388.778.494.654.978.168.791.918.118.835.736.839.339.754.758.93.4
MeTTA68.488.977.692.354.472.868.787.518.320.336.837.537.237.949.358.64.1
Ours71.490.873.493.257.576.269.491.037.544.959.760.350.553.160.363.41.6
MoCo51.769.871.889.454.971.067.585.339.948.359.363.147.559.066.777.41.8
Ours49.974.170.493.450.972.962.389.657.360.462.665.664.264.770.379.41.3
MoCo41.056.969.676.431.743.965.785.039.050.154.260.340.252.352.557.03.7
AugSelf [38]44.257.476.085.635.048.871.887.842.051.853.860.153.266.354.461.82.7
LooC [38]--70.980.8-------------
AI [13]45.058.076.788.737.448.472.689.149.257.955.362.056.076.060.262.81.6
Ours41.356.667.888.939.553.765.988.151.157.558.364.850.257.761.863.91.9
", + "bbox": [ + 95, + 137, + 875, + 266 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of the ensemble and then learn a weighted combination of over all these predictions using linear regression. We sweep the regularisation parameters for all members for each downstream dataset based on its validation set. For dense tasks, we train a decoder head for each member of the ensemble using default hyperparameters in [67] for object detection and [18] for semantic segmentation.", + "bbox": [ + 95, + 336, + 468, + 429 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Few-shot downstream tasks: We also evaluate the pretrained networks on various few-shot learning benchmarks: FC100 [49], Caltech-UCSD Birds (CUB200), and Plant Disease [44]. We also show results for few-shot regression problems on 300w, Leeds Sports Pose, CelebA, and Causal3DIdent datasets, where we we repeatedly sampled $5\\%$ , and $20\\%$ to generate low-shot training sets. For few-shot classification, we perform logistic regression using the frozen ensemble and learn episode-wise fusion weights w the support set itself.", + "bbox": [ + 95, + 448, + 468, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Competitors: All methods are evaluated by readouts on fixed features. Supervised: Besides conventional supervised pre-training (denoted 'baseline'), we also train a conventional ensemble via a multi-head model ('multihead') that has the same architecture and number of parameters as our architecture but uses only $\\mathcal{L}_q$ loss. We also compare with another diverse ensemble strategy [23, 50] (denoted 'div ensemble'): to optimises for diversity in terms of KL between posterior probability of ensemble members. The idea being that differences in secondary probabilities are a good measure of diversity. We provide more details in the supplementary material. Finally, we compare with a test-time ensemble created by taking a single pretrained model and generating different invariances through test-time mean embeddings [3] (denoted 'MeTTA'). Contrastive: We compare our approach to two state of the art ensemble based alternatives AugSelf [68], LOOC [38] and amortised invariances (AI) [13]. Note that unlike other competitors, AI uses backprop to update the features.", + "bbox": [ + 95, + 600, + 468, + 851 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b3fd555bb33de95fa2231b518369ece530060de5abb75a797fea10e80d1d45ef.jpg", + "table_caption": [], + "table_footnote": [ + "Table 3. Downstream performance of (1) Frozen supervised (2) fine-tuned supervised, (3/4) MoCO trained on ImageNet1K/100 model evaluated on semantic segmentation for CityScapes and ADE20k datasets, and Pascal VOC object detection." + ], + "table_body": "
MethodsCityScapesADE20kPascal VOCRank
MIoUAcc.MIoUAcc.APAP50AP75
Sup.Baseline39.682.130.452.948.880.351.62.6
Multihead35.480.327.351.849.880.250.93.9
Div. Ensemble36.282.427.652.750.681.958.12.3
QD4V41.081.733.854.350.882.558.71.3
Baseline (FT)61.794.140.167.255.182.860.52.0
QD4V (FT)65.294.342.367.456.284.962.91.0
MoCo.Baseline46.387.435.250.454.281.859.91.7
QD4V49.288.939.054.653.382.259.91.1
Baseline34.583.426.740.641.271.442.93.0
AugSelf37.984.927.340.843.273.448.11.6
QD4V36.184.928.541.745.975.248.01.3
", + "bbox": [ + 504, + 332, + 875, + 450 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Results", + "text_level": 1, + "bbox": [ + 502, + 533, + 581, + 546 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Can we successfully learn diverse (in)variance strengths with QD pre-training? To answer this question, we use the definition of invariance in Eq. 3 and evaluate the invariances learned by both default models (i.e., supervised and MoCo) and members of our QD ensemble for four appearance augmentations (blur, brightness, grayscale, contrast) and four spatial augmentations (resized crop, horizontal flip, rotation, scale). We compare the invariance strengths learned by the models via the visualization shown in Figure 3. The results show that the standard models provide a fixed set of invariance strengths (green). The members of the QD ensemble (dots) span a diverse range of invariance strengths from low (blue) to high-invariance (red), which can be selected downstream by picking among ensemble members.", + "bbox": [ + 502, + 557, + 875, + 741 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Does QD4V benefit a set of downstream tasks with diverse invariance requirements? Our suite of downstream tasks is represent a diverse range of objectives with differing invariance-sensitivity requirements. The ability to exploit the appropriate (in)variance for each task is crucial to achieving high performance. As discussed earlier, off-the-shelf models tend towards high-invariance to multiple factors (Figure 3), which is often effective for object", + "bbox": [ + 502, + 746, + 875, + 851 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5390", + "bbox": [ + 470, + 881, + 500, + 891 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ab96768c0db1126e147295e41927adebc7c0eb797c3711eceb85c850e17063d9.jpg", + "table_caption": [], + "table_footnote": [ + "Table 4. Comparison of our proposed downstream task decoder with conventional approaches. Top: Supervised/ImageNet 1k pretrained. Middle/Bottom: Moco pre-training on ImageNet 1K/100. Our fusion strategy performs better than learning a classifier over concatenated features and averaging features of the ensemble." + ], + "table_body": "
DecoderAircraftFlowersDTDAnimal PoseALOICausal3DRank
Sup.Concat36.885.970.911.226.672.92.0
Average33.883.469.19.123.774.32.7
Ours36.986.972.212.528.472.81.3
MoCoConcat42.083.572.913.745.780.22.2
Average37.983.972.012.642.978.12.8
Ours43.985.275.814.247.480.61.0
MoCo.Concat35.984.968.613.828.265.12.0
Average33.377.864.612.125.365.03.0
Ours37.985.571.914.333.865.31.0
", + "bbox": [ + 110, + 136, + 448, + 217 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "recognition, but may not be effective for fine-grained tasks like CelebA facial attributes, or pose and lighting-prediction tasks like 300W and ALOI/Causal3D.", + "bbox": [ + 90, + 303, + 470, + 343 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To evaluate the ability of features to support diverse downstream tasks, we evaluate the competitors on a range of tasks likely to exhibit different invariance preferences in Table 1. Our approach achieves comparable or better performance than baselines on all tasks against both supervised and self-supervised baselines. It has particularly remarkable improvements in regression tasks such as CelebA and Causal3D where we see an improvement of $12.5\\%$ and $8.5\\%$ over supervised pre-training of ResNet50.", + "bbox": [ + 90, + 344, + 470, + 464 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To better understand the success of our method, we analyse the weights assigned to each member of the QD ensemble by different downstream tasks. Specifically, we employ Pearson's r correlation coefficient between $\\mathbf{w}$ and the invariances learned by the QD ensemble (in Fig 3) as a metric to measure the strength of the relationship between the two variables. The resulting correlations are shown in Figure 4 and grouped by classification vs regression tasks. The trend shows that the spatially sensitive regression tasks tend to assign lower or negative weights to spatially invariant models, whereas classification tasks prefer models with generally stronger invariances. This analysis illustrates how our framework achieves reliably high performance across the range of tasks evaluated quantitatively in Table 1 - by enabling task-specific invariance preference selection.", + "bbox": [ + 90, + 464, + 468, + 665 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Does QD4V benefit few-shot learning tasks? To answer this question we focused on MoCo-v2 CNN models trained on ImageNet1K and ImageNet100. For classification tasks, we followed [38, 68] in sampling C-way K-shot episodes from the target problem and training linear readouts and learning w for each episode. For regression tasks we repeatedly sampled $5\\%$ , and $20\\%$ to generate low-shot training sets. From the results in Table 2, QD pre-training usually performs better than all competitors, with substantial margins in several cases, especially for pose estimation tasks.", + "bbox": [ + 90, + 665, + 468, + 797 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Does QD4V benefit dense estimation tasks? We evaluate QD pre-training on semantic segmentation on Cityscapes [19] and ADE20k [7] datasets. We evaluate QD4V by (1) Freezing the entire backbone and solely train a linear seg", + "bbox": [ + 92, + 799, + 470, + 853 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "mentation head and (2) Finetuning the entire backbone. We report the Mean Intersection over Union (IoU) and average accuracy for segmentation. Similarly, we also examine the performance of QD pre-training on Pascal VOC object detection. The results for semantic segmentation and object detection for frozen features and finetuning in Table 3 show that QD pre-training generally provides performance gains.", + "bbox": [ + 497, + 139, + 877, + 234 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation study for decoders: Finally, we compare our proposed downstream task decoder (Section 3.3) with conventional approaches. The results in Table 4 show that learning fusion weights using Eq. 8 consistently performs better, especially for regression tasks than conventional concatenation and prediction averaging. Intuitively, this is because our stacked fusion decoder has the chance for explicit invariance weighting. More technically, this is explained by the fast convergence rate in Theorem 3.4 which shows that our generalisation gap (between train and test error) tends to zero much faster than standard linear models as a function of the amount of training data. (See Supplementary for further discussion).", + "bbox": [ + 497, + 235, + 877, + 407 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "How does QD4V compare to large scale pre-trained models? The seminal CLIP [53] model is highly effective at various downstream tasks. Table 9 (supplementary) compares CLIP/RN50 to ImageNet1K QD4V/RN50 in terms of invariances and performance on downstream pose sensitive tasks. The results show that QD4V substantially outperforms CLIP, despite being trained on orders of magnitude less data - which we attribute to CLIP having learned too strong spatial and appearance invariances. This shows that pre-training scale is not a substitute for providing the correct invariance for the downstream task at hand.", + "bbox": [ + 497, + 409, + 878, + 555 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 499, + 573, + 613, + 588 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We addressed the difficulty of pre-training a model to achieve high performance on diverse downstream tasks by introducing the notion of quality-diversity pre-training. By instantiating diversity optimisation in terms of the (in)variance properties of a feature extractor, we obtain a compact set of high-quality features with diverse (in)variance properties. Together with an efficient and effective fusion strategy, we show strong performance on a diverse range of downstream tasks including classification, pose estimation, semantic segmentation, and object detection. Our approach presents a step towards the vision of a universal feature representation capable of supporting multiple vision tasks. In future work we will explore other definitions of behavioural phenotypes in QD4V.", + "bbox": [ + 497, + 596, + 877, + 784 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements This research was partially supported by the Engineering and Physical Sciences Research Council (EPSRC) Grant number EP/S000631/1 and the MOD University Defence Research Collaboration (UDRC) in Signal Processing.", + "bbox": [ + 497, + 785, + 877, + 852 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5391", + "bbox": [ + 468, + 879, + 499, + 891 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 94, + 137, + 184, + 151 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] 300 faces in-the-wild challenge: database and results. 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Barlow twins: Self-supervised learning via redundancy reduction. In ICML, 2021. 1", + "bbox": [ + 94, + 140, + 470, + 177 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "5394", + "bbox": [ + 468, + 879, + 500, + 890 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Quality Diversity for Visual Pre-Training/3f69c090-f906-4d45-8423-292cfc679eb9_model.json b/2023/Quality Diversity for Visual Pre-Training/3f69c090-f906-4d45-8423-292cfc679eb9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7cbffc8b3e428bb5eafb6cadfe23ec4ab98089 --- /dev/null +++ b/2023/Quality Diversity for Visual Pre-Training/3f69c090-f906-4d45-8423-292cfc679eb9_model.json @@ -0,0 +1,2257 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.096, + 0.009, + 0.172, + 0.046 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.006, + 0.816, + 0.048 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.286, + 0.175, + 0.687, + 0.194 + ], + "angle": 0, + "content": "Quality Diversity for Visual Pre-Training" + }, + { + "type": "text", + "bbox": [ + 0.235, + 0.218, + 0.735, + 0.236 + ], + "angle": 0, + "content": "Ruchika Chavhan1, Henry Gouk1, Da Li2, Timothy Hospedales1,2" + }, + { + "type": "text", + "bbox": [ + 0.156, + 0.24, + 0.816, + 0.286 + ], + "angle": 0, + "content": "1The University of Edinburgh 2Samsung AI Center, Cambridge \nR.Chavhan@sms.ed.ac.uk, {henry.gouk, t.hospedales}@ed.ac.uk, \ndali.academic@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.245, + 0.317, + 0.32, + 0.331 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.346, + 0.474, + 0.707 + ], + "angle": 0, + "content": "Models pre-trained on large datasets such as ImageNet provide the de-facto standard for transfer learning, with both supervised and self-supervised approaches proving effective. However, emerging evidence suggests that any single pre-trained feature will not perform well on diverse downstream tasks. Each pre-training strategy encodes a certain inductive bias, which may suit some downstream tasks but not others. Notably, the augmentations used in both supervised and self-supervised training lead to features with high invariance to spatial and appearance transformations. This renders them sub-optimal for tasks that demand sensitivity to these factors. In this paper we develop a feature that better supports diverse downstream tasks by providing a diverse set of sensitivities and invariances. In particular, we are inspired by Quality-Diversity in evolution, to define a pre-training objective that requires high quality yet diverse features — where diversity is defined in terms of transformation (in)variances. Our framework plugs in to both supervised and self-supervised pre-training, and produces a small ensemble of features. We further show how downstream tasks can easily and efficiently select their preferred (in)variances. Both empirical and theoretical analysis show the efficacy of our representation and transfer learning approach for diverse downstream tasks. Code available at https://github.com/ruchikachavhan/quality-diversity-pretraining.git" + }, + { + "type": "title", + "bbox": [ + 0.094, + 0.736, + 0.22, + 0.75 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.759, + 0.471, + 0.853 + ], + "angle": 0, + "content": "Pre-training neural networks on large-scale datasets such as ImageNet followed by representation transfer is a dominant paradigm in applied deep learning [58]. Supervised pre-training [34] is long established, with self-supervised [14, 30, 15, 11, 69] pre-training rapidly gaining popularity. Such pre-training algorithms often aspire to providing a universal representation which is effective for diverse down-" + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.318, + 0.856, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.49, + 0.879, + 0.685 + ], + "angle": 0, + "content": "Figure 1. Illustration of the quality and behavior space of QD4V feature representations. Each point in this space is a potential feature extractor. The \\( x \\) and \\( y \\) axes correspond sensitivity-invariance axes for spatial and appearance transformations, and define the behaviour space for features. The \\( z \\) axis shows the quality of the features (eg: ImageNet accuracy). The shaded zones schematically show the range of feature encodings that might be preferred by different types of downstream tasks. Conventional pre-training learns a single solution (denoted with +) that is high-quality (\\( z \\) axis near 1) but by default occupies the green zone of high invariance to spatial and appearance transforms. In contrast, QD4V aims to learn a set of solutions (marked by \\( \\Delta \\)) that better span the (in)variance axes, while being also being high quality. These lead to better performance for diverse downstream tasks. Note that in practice the invariance space has many more dimensions than the two illustrated here." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.706, + 0.877, + 0.799 + ], + "angle": 0, + "content": "stream tasks across computer vision, with evaluation studies showing promising results [34, 24]. Nevertheless, emerging evidence suggests that any single pre-trained feature will not be optimal for diverse downstream tasks [25, 68, 13]. This is because, any given pre-training strategy encodes a certain inductive bias in the learned representation, which will better suite some downstream tasks more than others." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.8, + 0.877, + 0.853 + ], + "angle": 0, + "content": "This issue is evident with regards to transformation invariance. By way of example, downstream object recognition benefits from strong affine invariance in a feature since pose is a distractor for object recognition. In con" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.881, + 0.501, + 0.892 + ], + "angle": 0, + "content": "5384" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.092, + 0.141, + 0.473, + 0.354 + ], + "angle": 0, + "content": "trast, downstream pose estimation depends heavily on affine sensitivity in a feature. However, supervised pre-training tends to promote affine-invariance due to the nature of the task and the popular augmentations used. Meanwhile self-supervised pre-training produces feature with even stronger affine-invariance due to optimising for augmentation invariance. So neither may be optimal for downstream pose estimation. More generally, there are a diverse set of potential transformations, each of which may be nuisance factors for some tasks and crucial for others – and any given representation exhibits different degrees of (in)sensitivity to each each possible transformation. Thus, despite the power of mainstream supervised and self-supervised pretraining, since any single feature induces a particular set of (in)variance strengths, it will be sub-optimal for those downstream tasks with different (in)variance preferences." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.358, + 0.473, + 0.61 + ], + "angle": 0, + "content": "Within the self-supervised learning community, a few studies have attempted to address these issues by learning features with multiple (in)variances. This often achieved by an ensemble of different models [25], pre-training multi-headed networks with contrastive learning for different augmentations in each head [68], or with different heads dedicated to (invariance promoting) contrastive learning and (sensitivity promoting) transformation prediction [38]. However, these initial attempts suffer important limitations. Firstly, given that there are many transformations for which invariance or sensitivity may be preferred, it's unclear how to build a compact enough ensemble. For example, if \\(N\\) models are used to encode \\(N\\) distinct strengths of sensitivity to a particular transformation, and there are \\(K\\) possible transformations, this naively leads to an ensemble of size \\(N^K\\) to cover the possible invariance preferences of downstream tasks. Secondly, it's unclear how to optimally select or fuse these different features for downstream tasks with apriori unknown (in)variance preferences." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.614, + 0.473, + 0.854 + ], + "angle": 0, + "content": "In this paper, we address the first of these challenges through the lens of Quality Diversity (QD) [12, 51, 27] a strategy in evolutionary computation that has seen great success in robotics [20]. QD strategies aim to more robustly solve problems by searching for a set of solutions rather than a single solution, and - crucially - requiring that the set of solutions are diverse in some meaningful behavioural metric. We introduce the notion of Quality Diversity Optimisation for Vision (QD4V), where, in a computer vision context, we interpret the idea of behaviour space for diversity measurement as degree of (in)variances to different data augmentations. When applied to supervised ImageNet pretraining, this corresponds to optimising for a small set of ImageNet models that are highly performant, yet use as different cues as possible for recognition. This is qualitatively illustrated in Fig. 1. Each downstream task is then presented with a meaningfully diverse set of high-quality features from which a feature meeting the (in)variance prefer" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.141, + 0.779, + 0.153 + ], + "angle": 0, + "content": "ences of the task is more likely to be found." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.154, + 0.878, + 0.286 + ], + "angle": 0, + "content": "Our second contribution addresses how to fuse this small ensemble of features for the downstream task. The limited existing work on learning multiple (in)variances relies on ad-hoc heuristics, such as simply concatenating features prior to linear readout [25, 68]. We argue that a better solution is train a per feature linear readout on the downstream train set, and then learn a fusion weight on the downstream val set, i.e., stacking [66]. We show both empirically and theoretically that this approach to transfer learning outperforms the standard approach." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.287, + 0.878, + 0.38 + ], + "angle": 0, + "content": "In summary, we present a framework for learning a compact and high-quality yet meaningfully diverse set of features. We present a simple approach for transferring them to downstream tasks with strong theoretical backing. Finally, we show empirically that our framework improves on average compared to standard pre-trained features when evaluated on a diverse range of downstream tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.392, + 0.637, + 0.405 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.414, + 0.879, + 0.759 + ], + "angle": 0, + "content": "Invariance learning in vision: Invariances for in-domain image classification have been learned using data augmentation [9] via MAP [6] and marginal likelihood [32] learning. However, these methods do not focus on transferability to downstream target tasks. On the other hand, the success of representation transfer in contrastive self-supervised learning has been attributed to augmentation-based training engendering invariances [25, 63, 52] which act as strong inductive biases for downstream tasks. The field aspires to provide a single general-purpose feature suited for all downstream tasks [8], however, this goal is not straightforward to achieve. Recent studies have shown that features with invariances to different augmentations are suited for different downstream tasks, with no single feature being optimal for all tasks [25, 68] and performance suffers if inappropriate invariances are provided. In contrastive learning, this leads to the laborious need to produce and combine an ensemble of features [68, 25], to disentangle invariance and transformation prediction [38], costly task-specific self-supervised pre-training [54, 61], or amortising invariances [13]. We introduce a framework for learning diverse invariances during either supervised or self-supervised pre-training, while maintaining the quality of those features in terms of encoding image semantics. We also provide an efficient and theoretically supported approach to fuse the resulting features that improves on standard heuristics [25, 68]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.76, + 0.878, + 0.853 + ], + "angle": 0, + "content": "Quality Diversity: Quality Diversity (QD) optimisation [12, 51, 27] originated in evolutionary algorithms as a strategy for finding a meaningfully diverse set of high-performing solutions to a problem, rather than just one global optimum. Access to a suite of meaningfully diverse high-quality solutions often has substantial robustness benefits that are widely exploited in robotics community" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.881, + 0.501, + 0.892 + ], + "angle": 0, + "content": "5385" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.092, + 0.14, + 0.473, + 0.273 + ], + "angle": 0, + "content": "[20]. In order to drive diversity, a QD algorithm requires an application-specific measure of behaviour as a feature between which two models' difference can be compared. We develop a novel behavioural measure for vision in terms of invariances. Mainstream QD optimisation algorithms such as MAP-Elites are not amenable to the differentiable gradient-based solutions required for application in vision. We develop a simple differentiable instantiation of QD that is amenable to easy integration as a loss within a typical deep learning for vision pipeline." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.274, + 0.474, + 0.501 + ], + "angle": 0, + "content": "Ensemble methods: QD is related to ensemble methods, which have a long history in vision and machine learning [22]. However, ensembles have mostly focused on single-task learning rather than pre-training for transfer learning. A key challenge in ensemble methods is obtaining meaningful inter-model diversity, with the standard approaches of random seeds, boosting, and bagging, providing comparatively weak diversity. Our novel strategy is to take QD's insight that diversity should be measured in a meaningful space, and identifying (in)variance axes as such a meaningful space for diversity measurement in visual pre-training. A second key issue for ensembles is fusing the ensemble prediction, which has been variously performed by unweighted prediction averaging [45] or parameter averaging [46], and feature concatenation in transfer learning [25, 68]. We show both empirically and theoretically the efficacy of learning a weighted combination of predictions." + }, + { + "type": "title", + "bbox": [ + 0.094, + 0.51, + 0.223, + 0.525 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.094, + 0.531, + 0.22, + 0.545 + ], + "angle": 0, + "content": "3.1. Background" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.551, + 0.472, + 0.592 + ], + "angle": 0, + "content": "Mainstream QD optimization [27, 51] searches for a diverse set of solutions \\(\\{\\theta_i\\}\\) to an optimization problem \\(\\mathcal{L}_q\\) by solving an objective like" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.596, + 0.472, + 0.625 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\{\\theta_ {i} \\}} \\sum_ {i} \\mathcal {L} _ {q} (\\theta_ {i}) s. t. D (\\{\\pi (\\theta_ {i}) \\}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.629, + 0.473, + 0.749 + ], + "angle": 0, + "content": "where \\(\\pi\\) is a vector of application relevant observable properties of a given solution \\(\\theta_{i}\\) that is called phenotype in the QD community. \\(D\\) is a diversity constraint that enforces diversity among the solutions. It is often enforced by tessellation, or gridding, the space of \\(\\pi\\). Thus solution sets \\(\\{\\theta_i\\}\\) have the maximum possible quality \\((\\mathcal{L}_q)\\) while also covering the space of measurable differences in behaviour [27, 51]. To make such QD problems more efficient to solve in a vision context, we will relax them to" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.752, + 0.473, + 0.782 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\{\\theta_ {i} \\}} \\sum_ {i} \\mathcal {L} _ {q} (\\theta_ {i}) - \\sum_ {i \\neq j} \\mathcal {L} _ {d i v} (\\pi (\\theta_ {i}), \\pi (\\theta_ {j}) \\}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.786, + 0.43, + 0.8 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{div}\\) is a loss that measures pairwise distance." + }, + { + "type": "title", + "bbox": [ + 0.094, + 0.806, + 0.273, + 0.821 + ], + "angle": 0, + "content": "3.2. Visual Pre-training" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.826, + 0.473, + 0.854 + ], + "angle": 0, + "content": "We denote a large dataset for pre-training by \\(\\mathcal{D}_t\\subset\\) \\(\\mathcal{X}\\times \\mathcal{Y}\\) , where \\(\\mathcal{X}\\) is some space of input images and the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.14, + 0.88, + 0.289 + ], + "angle": 0, + "content": "space \\(\\mathcal{V}\\) may be contain labels obtained from manual annotation or pre-text tasks from self-supervision. We introduce a population of \\(N\\) feature extractors, represented as an ensemble, \\(\\mathcal{F} = \\{f_{\\theta_i}\\}_{i=1}^N\\), which aim to learn a diverse set of invariances while maintaining high quality. Each member of the ensemble is followed by a projection layer \\(g_{\\phi_i}\\) which can be a classifier layer in case of supervised learning or a projection head in case of self-supervised learning [14, 30, 16]. We denote a set of \\(K\\) augmentations considered for pre-training as \\(\\mathcal{T}\\). Let us also denote a sample \\(\\mathbf{x}\\) transformed by augmentation \\(\\mathcal{T}_j \\in \\mathcal{T}\\) as \\(\\tilde{\\mathbf{x}}^j\\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.303, + 0.803, + 0.318 + ], + "angle": 0, + "content": "3.2.1 QD for Visual Pre-training: Diversity" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.324, + 0.879, + 0.485 + ], + "angle": 0, + "content": "To quantify the diversity of solutions during pre-training, we must first define a phenotype — an observable measurement of a feature extractor's behaviour. We define the behavior of a solution by the degree of invariance it shows to a set of augmentations \\(\\mathcal{T}\\). We borrow the definition of invariance from [25], where invariance of a model to a particular data augmentation is defined as the cosine similarity \\(S(f_{\\theta}(\\mathbf{x}),f_{\\theta}(\\tilde{\\mathbf{x}}^{j}))\\) between augmented and unaugmented features. Thus, we define a phenotype of a solution \\(f_{\\theta_i}\\) as a vector \\(\\pi (\\mathbf{x};\\theta_i)\\in \\mathbb{R}^K\\) such that \\(j^{\\mathrm{th}}\\) element of the phenotype vector indicates the invariance that the model exhibits to augmentation \\(\\mathcal{T}_j\\in \\mathcal{T}\\), as shown in Eq 3." + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.494, + 0.877, + 0.523 + ], + "angle": 0, + "content": "\\[\n\\pi (\\mathbf {x}; \\theta_ {i}) = \\left(S \\left(f _ {\\theta_ {i}} (\\mathbf {x}), f _ {\\theta_ {i}} \\left(\\tilde {\\mathbf {x}} ^ {j}\\right)\\right) _ {j = 1} ^ {| \\mathcal {T} |} \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.879, + 0.599 + ], + "angle": 0, + "content": "Diversity Loss: Based on the above phenotype definition, we can encourage each model to exhibit a diverse combination of invariances to augmentations in \\(\\mathcal{T}\\). Specifically, we minimise the negative exponential distance between phenotype vector of each member as in Eq 4" + }, + { + "type": "equation", + "bbox": [ + 0.548, + 0.607, + 0.877, + 0.645 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {d i v e r s i t y}} = \\sum_ {i \\neq j} ^ {N} \\exp (- | \\pi (\\mathbf {x}; \\theta_ {i}) - \\pi (\\mathbf {x}; \\theta_ {j}) |) \\tag {4}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.66, + 0.791, + 0.675 + ], + "angle": 0, + "content": "3.2.2 QD for visual pre-training: Quality" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.681, + 0.879, + 0.777 + ], + "angle": 0, + "content": "Quality Loss: Depending on the pre-training paradigm employed, different loss functions can be used to promote high quality. In the case of supervised learning, the loss function denoted by \\( l_{q} \\) can be cross-entropy, while self-supervised methods such as SimCLR/MoCo use contrastive loss [48]. The loss function for the entire ensemble for a sample \\( (\\mathbf{x},y)\\in \\mathcal{D} \\) is given in Eq. 5" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.784, + 0.877, + 0.822 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {q u a l i t y}} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} l _ {q} \\left(g _ {\\phi_ {i}} \\left(f _ {\\theta_ {i}} (\\mathbf {x})\\right), y\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.826, + 0.878, + 0.854 + ], + "angle": 0, + "content": "This objective reflects standard supervised or self-supervised learning of the upstream model. Empirically," + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.881, + 0.502, + 0.892 + ], + "angle": 0, + "content": "5386" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.185, + 0.141, + 0.796, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.092, + 0.292, + 0.878, + 0.332 + ], + "angle": 0, + "content": "Figure 2. Schematic illustration of Quality Diversity Pre-training, shown with only 2 augmentations for simplicity. \\(\\mathcal{L}_{\\mathrm{diversity}}\\) maximises the difference between invariances that models exhibit to \\(\\mathcal{T}_1\\) and \\(\\mathcal{T}_2\\), while \\(L_{\\mathrm{quality}} + \\lambda_{kl}\\mathcal{L}_{KL}\\) maximises the quality of the ensemble by pushing it to the quality of a conventionally pre-trained model (denoted by Baseline)." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.351, + 0.473, + 0.498 + ], + "angle": 0, + "content": "we found that purely using this quality objective it is hard for a diverse ensemble to match the quality of a baseline model trained solely for quality. To help the diverse ensemble match the quality of the baseline we introduce an additional loss term, which is the Kullback-Leibler (KL) divergence between the posteriors of the ensemble members and baseline model with parameters \\(\\phi_{b}\\) and \\(\\theta_{b}\\). We denote the predictions of a model by \\(\\hat{y}_i = g_{\\phi_i}(f_{\\theta_i}(x))\\). The loss function is shown in Eq. 6. This term ensures that the members of the ensemble mimic the predictions of the baseline model, thus ensuring high quality with diverse invariances." + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.52, + 0.472, + 0.559 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {q u a l i t y - K L}} = \\sum_ {i = 1} ^ {N} \\frac {1}{m} \\sum_ {j = 1} ^ {m} \\mathrm {K L} \\left(\\sigma \\left(\\hat {y} _ {i}; \\tau\\right) \\| \\sigma \\left(\\hat {y} _ {b}; \\tau\\right)\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.568, + 0.471, + 0.595 + ], + "angle": 0, + "content": "Here, \\(\\sigma\\) denotes the softmax function and \\(\\tau\\) denotes the temperature used to scale the logits within softmax." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.598, + 0.472, + 0.639 + ], + "angle": 0, + "content": "Summary Finally, to achieve our goal of diverse invariances and high quality in QD4V pre-training, we formulate a total loss function asin Eq. 7." + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.664, + 0.471, + 0.68 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {q d} = \\mathcal {L} _ {\\text {q u a l i t y}} + \\lambda_ {k l} \\mathcal {L} _ {\\text {q u a l i t y - K L}} + \\lambda_ {d} \\mathcal {L} _ {\\text {d i v e r s i t y}} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.689, + 0.471, + 0.729 + ], + "angle": 0, + "content": "The diverse set of optimal solutions learned from the proposed QD pre-training stage denoted as \\(\\mathcal{F}^*\\) is then transferred to a downstream task." + }, + { + "type": "title", + "bbox": [ + 0.094, + 0.739, + 0.332, + 0.754 + ], + "angle": 0, + "content": "3.3. Downstream task Learning" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.76, + 0.473, + 0.854 + ], + "angle": 0, + "content": "We next address how to construct models for downstream tasks given the diverse ensemble of features \\(\\mathcal{F}^*\\) produced by pre-training in the previous section. Existing approaches have concatenated features prior to linear readout [68], or conducted unweighted averaging of ensemble features [45]. We propose to fuse the ensemble via a variant of stacking [66]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.351, + 0.878, + 0.404 + ], + "angle": 0, + "content": "Decoder Design For each feature extractor, \\(f_{\\theta_i} \\in \\mathcal{F}\\) we follow the standard linear readout approach, and build a linear model, \\(h^{(i)}\\), parameterised by \\(U^{(i)} \\in \\mathbb{R}^{k \\times d}\\) and \\(\\mathbf{b}^{(i)} \\in \\mathbb{R}^k\\)" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.408, + 0.794, + 0.426 + ], + "angle": 0, + "content": "\\[\nh ^ {(i)} (\\mathbf {x}) = \\rho (U ^ {(i)} f _ {\\theta_ {i}} (\\mathbf {x}) + \\mathbf {b} ^ {(i)}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.43, + 0.878, + 0.497 + ], + "angle": 0, + "content": "where \\(\\rho\\) is a transfer function for linear models (e.g., the softmax function or identity). To produce a final prediction we fuse the ensemble of classifiers \\(h^{(i)}(x)\\) by learning a weight vector, \\(\\mathbf{w} \\in \\mathbb{R}^N\\) that is used to make a linear combination of their predictions," + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.502, + 0.763, + 0.539 + ], + "angle": 0, + "content": "\\[\nh (\\mathbf {x}) = \\sum_ {i = 1} ^ {N} w _ {i} h ^ {(i)} (\\mathbf {x}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.542, + 0.878, + 0.689 + ], + "angle": 0, + "content": "Decoder Training Strategy For each downstream task have a collection of data, \\(\\mathcal{D}_{ds}\\), which we split into two nonoverlapping subsets, \\(\\mathcal{D}_{tr}\\) and \\(\\mathcal{D}_{val}\\). The hyperparameters of the linear models are tuned using this train-validation split, and the best model parameters found during this tuning phase are denoted by \\(\\tilde{U}^{(i)}\\) and \\(\\tilde{\\mathbf{b}}^{(i)}\\). Each model is retrained using the full \\(\\mathcal{D}_{ds}\\) dataset using the best hyperparameters to obtain the final values for each \\(U^{(i)}\\) and \\(\\mathbf{b}^{(i)}\\). The procedure used to fit the weights for linearly combining the models is carried out using the \\(\\tilde{U}^{(i)}\\) and \\(\\tilde{\\mathbf{b}}^{(i)}\\) parameters, and \\(\\mathbf{w}\\) is fit on the \\(\\mathcal{D}_{val}\\) set," + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.693, + 0.877, + 0.746 + ], + "angle": 0, + "content": "\\[\n\\mathbf {w} = \\underset {\\mathbf {v} \\in \\mathbb {R} ^ {N}} {\\arg \\min } \\mathbb {E} _ {\\mathcal {D} _ {v a l}} \\left[ \\left\\| \\sum_ {i = 1} ^ {N} v _ {i} \\rho \\left(\\tilde {U} ^ {(i)} f _ {\\theta_ {i}} (\\mathbf {x}) + \\tilde {\\mathbf {b}} ^ {(i)}\\right) - y \\right\\| _ {2} ^ {2} \\right] \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.747, + 0.878, + 0.8 + ], + "angle": 0, + "content": "In the following section, we provide theoretical justification for our proposed downstream architecture and training strategy by way of bounding the generalisation error for downstream tasks learned in this way." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.806, + 0.688, + 0.821 + ], + "angle": 0, + "content": "3.4. Theoretical Analysis" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.827, + 0.878, + 0.854 + ], + "angle": 0, + "content": "For ease of exposition, consider the case where \\(\\rho\\) is the identity and the underlying problem is binary classification." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.88, + 0.502, + 0.892 + ], + "angle": 0, + "content": "5387" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.093, + 0.14, + 0.473, + 0.181 + ], + "angle": 0, + "content": "In this case, each \\(U^{(i)}\\) can be written as a vector, \\(\\mathbf{u}^{(i)}\\). We can define the effective hypothesis class of our algorithm for learning on downstream tasks as" + }, + { + "type": "equation", + "bbox": [ + 0.113, + 0.193, + 0.454, + 0.266 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {H} = \\left\\{\\mathbf {x} \\rightarrow \\sum_ {i = 1} ^ {N} w _ {i} \\langle \\mathbf {u} ^ {(i)}, f _ {\\theta_ {i}} (\\mathbf {x}) \\rangle : \\right. \\\\ \\left. \\left\\| \\mathbf {w} - \\mathbb {E} [ \\mathbf {w} ] \\right\\| _ {2} \\leq A, \\left\\| \\mathbf {u} ^ {(i)} - \\mathbb {E} [ \\mathbf {u} ^ {(i)} ] \\right\\| _ {F} \\leq B \\right\\}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.276, + 0.473, + 0.424 + ], + "angle": 0, + "content": "where we have absorbed the bias values into \\(\\mathbf{u}\\) by assuming a 1 has been appended to each \\(\\mathbf{x}\\). Our goal is to bound the generalisation error of models from this class trained using our stacking procedure in Sec 3.3. The first step is to bound the empirical Rademacher complexity in terms of \\(A\\) and \\(B\\) (from the definition of \\(\\mathcal{H}\\)), the norm of the features, and the total amount of data available for the downstream task, \\(m = |\\mathcal{D}_{ds}|\\). We then show how the stacking procedure influences the values of \\(A\\) and \\(B\\). We use \\(\\eta\\) to indicate the fraction of data used for training, hence \\(\\eta m = |\\mathcal{D}_{tr}|\\) and \\((1 - \\eta)m = |\\mathcal{D}_{val}|\\). Our main result in given below." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.433, + 0.473, + 0.473 + ], + "angle": 0, + "content": "Theorem 1. For a model trained using our stacking procedure and the conditions outlined in the statements of Lemmas 1 and 2, we have with probability at least \\(1 - 2\\delta\\)" + }, + { + "type": "equation", + "bbox": [ + 0.108, + 0.485, + 0.457, + 0.629 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbb {E} [ \\mathbf {1} [ \\operatorname {s g n} (h (\\mathbf {x})) \\neq y) ] \\leq \\hat {\\mathbb {E}} [ l (h (\\mathbf {x}), y) ] \\\\ + \\frac {1 2 X ^ {3} \\| \\tilde {V} \\| _ {2} \\sqrt {\\ln (4 / \\delta) \\ln (4 N / \\delta)}}{\\gamma_ {1} \\gamma_ {2} \\sqrt {1 - \\eta m ^ {3 / 2}}} \\\\ + \\frac {2 X ^ {2} \\sqrt {2 \\ln (4 N / \\delta)}}{\\gamma_ {1} m} \\\\ + \\frac {2 X ^ {2} \\| \\tilde {V} \\| _ {2} \\sqrt {2 \\ln (4 / \\delta)}}{\\gamma_ {2} \\sqrt {1 - \\eta m}} \\\\ + 3 \\sqrt {\\frac {\\ln (1 / \\delta)}{2 m}}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.641, + 0.47, + 0.67 + ], + "angle": 0, + "content": "where \\(\\hat{\\mathbb{E}}[l(h(\\mathbf{x}), y)]\\) is the mean ramp loss of the model \\(h\\), computed on the training data." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.679, + 0.47, + 0.746 + ], + "angle": 0, + "content": "Notably, this bound achieves the \"fast\" rate of convergence, \\(\\mathcal{O}(m^{-1})\\), in the complexity terms, with the first term even exhibiting a super-fast rate of \\(\\mathcal{O}(m^{-3/2})\\). This is in contrast to the standard \\(\\mathcal{O}(m^{-1/2})\\) rate in existing bounds. The proof is in the supplemental material." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.747, + 0.471, + 0.854 + ], + "angle": 0, + "content": "Discussion This theorem depends on both the specific architecture and optimisation strategy outlined in Sec. 3.3, and thus provides justification for these design choices. It says that the generalisation gap between train error and expected (test) error rapidly goes to zero with the size of the downstream train set \\( m \\). Furthermore, because we have access to an ensemble of features, the train error \\( \\hat{e} r(h) \\) can likely be reduced below that of a single feature." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.139, + 0.71, + 0.155 + ], + "angle": 0, + "content": "4. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.161, + 0.878, + 0.32 + ], + "angle": 0, + "content": "Pre-training: We perform supervised training for ResNet50 and ConvNeXt [42] on ImageNet1K [21] and contrastive training for ResNet50 on both ImageNet1K and ImageNet100 [68]. To learn our feature ensemble, in a parameter efficient way for both architectures, we share the first three layers (layer1, layer2, layer3 according to [65]), after which different members of the ensemble branch out into their own sequence of layers having a separate layer4 and projection head. We initialise the entire ensemble with ImageNet pre-trained models in case of supervised pre-training and MoCo pre-trained models in case of contrastive learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.321, + 0.878, + 0.414 + ], + "angle": 0, + "content": "Augmentations: For supervised pre-training, most methods that rely on strong augmentation policies. Our approach applies the quality loss (Eq. 5) to unaugmented samples only as using augmented samples for quality maximisation would lead to typical strong invariance to all augmentations and prevent diversity. For contrastive learning, we apply very weak augmentations for instance discrimination." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.878, + 0.507 + ], + "angle": 0, + "content": "Learning rates and Optimisers: For supervised pretraining and contrastive learning experiments, we train the model for 20 epochs with SGD and AdamW optimizers respectively, along with learning rate warm-up for 5 epochs, followed by a cosine decay schedule. For supervised pretraining, we apply label smoothening and perform exponential moving average (EMA) on the model weights." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.878, + 0.56 + ], + "angle": 0, + "content": "Downstream tasks: Our suite of downstream tasks consists of object recognition, regression, and dense estimation. We provide more details about downstream tasks in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.571, + 0.878, + 0.626 + ], + "angle": 0, + "content": "- Classification: For classification, we evaluate on standard benchmarks CIFAR10/100 [36], Caltech101 [26], Oxford Flowers [47], Stanford Cars [35], Describable Textures Dataset (DTD) [17], Aircraft [43]." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.633, + 0.878, + 0.714 + ], + "angle": 0, + "content": "- Regression: We include a set of spatially sensitive tasks including facial landmark detection on 300W [1], CelebA [41], human pose estimation in LSP [33] and MPII [2], Animal Pose prediction [10], AROI object orientation prediction [29], and Causal3DIdent 6D pose and appearance attribute prediction [60]." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.722, + 0.878, + 0.802 + ], + "angle": 0, + "content": "- Dense estimation: We also evaluate the QD pretrained models on dense estimation tasks like Pascal VOC object detection using Faster R-CNN [55] with a Feature Pyramid Network backbone [39] and linear semantic segmentation similar to [4] on CityScapes and ADE20k [7] datasets." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.571, + 0.878, + 0.802 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.813, + 0.878, + 0.854 + ], + "angle": 0, + "content": "Downstream evaluation: For classification and regression tasks, we fit multinomial logistic regression and multi-output linear regression on the extracted features from each" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.881, + 0.502, + 0.892 + ], + "angle": 0, + "content": "5388" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.242, + 0.154, + 0.473, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.481, + 0.158, + 0.528, + 0.175 + ], + "angle": 0, + "content": "ax, invariance in, invariance aseline" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.158, + 0.737, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.092, + 0.334, + 0.877, + 0.371 + ], + "angle": 0, + "content": "Figure 3. Radar plot comparing invariance w.r.t. for 4 Spatial and 4 Appearance based transformations of baseline models (green) and QD ensemble (dots). The red and blue lines correspond to maximum and minimum invariances within QD ensemble. The blue shaded region corresponds to the range of invariances spanned by the QD ensemble, which encompasses the (in)variance of the baselines." + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.38, + 0.879, + 0.512 + ], + "angle": 0, + "content": "
MethodsCIFAR10CIFAR100FlowersCaltech 101DTDCarsAircraft300wLS PoseCelebAAnimal PoseMPIIALOICausal3DRank
IN1K (RN50)Sup.Baseline90.468.285.284.771.944.436.070.255.449.011.218.024.164.12.7
Multihead90.367.384.884.169.943.235.068.353.250.110.917.022.862.33.7
Div. Ens. [23]91.672.984.689.369.842.735.366.652.649.211.517.922.660.83.4
MeTTA [3]91.071.685.385.171.841.134.065.352.847.910.516.323.161.23.8
QD4V90.370.486.989.972.245.436.976.662.461.512.518.528.472.81.4
MoCoMoCo90.370.689.887.973.939.341.887.269.092.513.919.946.078.11.9
Fusionx[25]95.0-81.086.0---65.068.033.0-----
QD4V88.971.285.288.275.841.343.988.971.895.214.222.447.480.61.2
Sup.Baseline (CN-T)89.470.694.589.168.052.548.463.148.152.511.517.78.0269.41.8
QD4V (CN-T)91.572.996.589.969.851.550.082.269.960.712.518.59.371.91.1
IN100Sup.MoCo84.661.682.477.364.533.937.285.558.761.013.218.630.961.43.5
AugSelf* [38]85.363.985.778.966.237.439.577.363.977.012.919.535.261.62.4
AI+ [13]81.364.681.378.468.838.637.390.065.282.012.521.632.762.62.5
QD4V84.565.485.581.271.939.837.988.969.785.014.320.633.865.31.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.092, + 0.517, + 0.877, + 0.566 + ], + "angle": 0, + "content": "Table 1. Downstream performance of ImageNet (IN1K) pretrained (1) Supervised ResNet50, (2) MoCo ResNet50 and ImageNet-100 (IN100) pretrained (3) Supervised ConvNeXt-Tiny (CN-T), (4) MoCo ResNet50. The first seven columns are classification tasks (accuracy, %); the last seven are regression (R2, %). + numbers from [13] where reported, * A mix of our runs and numbers from [13] where reported, x numbers from [25], rest are our runs." + }, + { + "type": "image", + "bbox": [ + 0.156, + 0.577, + 0.328, + 0.692 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.329, + 0.577, + 0.491, + 0.692 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.577, + 0.653, + 0.692 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.653, + 0.577, + 0.815, + 0.692 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.158, + 0.693, + 0.329, + 0.807 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.33, + 0.693, + 0.491, + 0.807 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.693, + 0.652, + 0.807 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.653, + 0.693, + 0.815, + 0.807 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.092, + 0.813, + 0.877, + 0.851 + ], + "angle": 0, + "content": "Figure 4. Correlation between our classifier fusion weights (Eq 8) and task for 4 Spatial and 4 Appearance based augmentations. The y-axis corresponds to Pearson's r correlation between w assigned to each member by a particular task and invariances exhibited by that member to specific augmentations. Tasks are grouped by classification and regression, which tend to show different invariance preferences." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.881, + 0.501, + 0.892 + ], + "angle": 0, + "content": "5389" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.097, + 0.139, + 0.877, + 0.267 + ], + "angle": 0, + "content": "
MethodsCUBFlowersFC 100Plant Disease300wLS PoseCelebACausal3DRank
(5,1)(5,5)(5,1)(5,5)(5,1)(5,5)(5,1)(5,5)s=0.05s=0.2s=0.05s=0.2s=0.05s=0.2s=0.05s=0.2
Baseline70.090.477.393.753.878.768.988.820.524.846.948.539.241.458.962.42.3
Multihead69.688.276.592.652.978.568.287.319.424.739.344.939.440.857.261.33.5
Div. Ensemble68.388.778.494.654.978.168.791.918.118.835.736.839.339.754.758.93.4
MeTTA68.488.977.692.354.472.868.787.518.320.336.837.537.237.949.358.64.1
Ours71.490.873.493.257.576.269.491.037.544.959.760.350.553.160.363.41.6
MoCo51.769.871.889.454.971.067.585.339.948.359.363.147.559.066.777.41.8
Ours49.974.170.493.450.972.962.389.657.360.462.665.664.264.770.379.41.3
MoCo41.056.969.676.431.743.965.785.039.050.154.260.340.252.352.557.03.7
AugSelf [38]44.257.476.085.635.048.871.887.842.051.853.860.153.266.354.461.82.7
LooC [38]--70.980.8-------------
AI [13]45.058.076.788.737.448.472.689.149.257.955.362.056.076.060.262.81.6
Ours41.356.667.888.939.553.765.988.151.157.558.364.850.257.761.863.91.9
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.096, + 0.268, + 0.877, + 0.315 + ], + "angle": 0, + "content": "Table 2. Few-shot classification and regression accuracy (\\%, R2) of our QD ResNet50 ensemble for supervised (top), MoCo pre-trained on ImageNet (middle) and MoCo pre-trained on ImageNet-100 (bottom). Values are reported with \\(95\\%\\) confidence intervals averaged over 2000 episodes on FC100, CUB200, and Plant Disease. (N, K) denotes N-way K-shot tasks. For regression tasks (300w, LS Pose, CelebA, Causal3D), we report downstream performance for different splits with train proportion given by \\(s\\)." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.337, + 0.47, + 0.43 + ], + "angle": 0, + "content": "of the ensemble and then learn a weighted combination of over all these predictions using linear regression. We sweep the regularisation parameters for all members for each downstream dataset based on its validation set. For dense tasks, we train a decoder head for each member of the ensemble using default hyperparameters in [67] for object detection and [18] for semantic segmentation." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.449, + 0.47, + 0.581 + ], + "angle": 0, + "content": "Few-shot downstream tasks: We also evaluate the pretrained networks on various few-shot learning benchmarks: FC100 [49], Caltech-UCSD Birds (CUB200), and Plant Disease [44]. We also show results for few-shot regression problems on 300w, Leeds Sports Pose, CelebA, and Causal3DIdent datasets, where we we repeatedly sampled \\(5\\%\\), and \\(20\\%\\) to generate low-shot training sets. For few-shot classification, we perform logistic regression using the frozen ensemble and learn episode-wise fusion weights w the support set itself." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.601, + 0.47, + 0.852 + ], + "angle": 0, + "content": "Competitors: All methods are evaluated by readouts on fixed features. Supervised: Besides conventional supervised pre-training (denoted 'baseline'), we also train a conventional ensemble via a multi-head model ('multihead') that has the same architecture and number of parameters as our architecture but uses only \\(\\mathcal{L}_q\\) loss. We also compare with another diverse ensemble strategy [23, 50] (denoted 'div ensemble'): to optimises for diversity in terms of KL between posterior probability of ensemble members. The idea being that differences in secondary probabilities are a good measure of diversity. We provide more details in the supplementary material. Finally, we compare with a test-time ensemble created by taking a single pretrained model and generating different invariances through test-time mean embeddings [3] (denoted 'MeTTA'). Contrastive: We compare our approach to two state of the art ensemble based alternatives AugSelf [68], LOOC [38] and amortised invariances (AI) [13]. Note that unlike other competitors, AI uses backprop to update the features." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.334, + 0.876, + 0.451 + ], + "angle": 0, + "content": "
MethodsCityScapesADE20kPascal VOCRank
MIoUAcc.MIoUAcc.APAP50AP75
Sup.Baseline39.682.130.452.948.880.351.62.6
Multihead35.480.327.351.849.880.250.93.9
Div. Ensemble36.282.427.652.750.681.958.12.3
QD4V41.081.733.854.350.882.558.71.3
Baseline (FT)61.794.140.167.255.182.860.52.0
QD4V (FT)65.294.342.367.456.284.962.91.0
MoCo.Baseline46.387.435.250.454.281.859.91.7
QD4V49.288.939.054.653.382.259.91.1
Baseline34.583.426.740.641.271.442.93.0
AugSelf37.984.927.340.843.273.448.11.6
QD4V36.184.928.541.745.975.248.01.3
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.504, + 0.46, + 0.877, + 0.509 + ], + "angle": 0, + "content": "Table 3. Downstream performance of (1) Frozen supervised (2) fine-tuned supervised, (3/4) MoCO trained on ImageNet1K/100 model evaluated on semantic segmentation for CityScapes and ADE20k datasets, and Pascal VOC object detection." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.534, + 0.582, + 0.547 + ], + "angle": 0, + "content": "5. Results" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.558, + 0.877, + 0.743 + ], + "angle": 0, + "content": "Can we successfully learn diverse (in)variance strengths with QD pre-training? To answer this question, we use the definition of invariance in Eq. 3 and evaluate the invariances learned by both default models (i.e., supervised and MoCo) and members of our QD ensemble for four appearance augmentations (blur, brightness, grayscale, contrast) and four spatial augmentations (resized crop, horizontal flip, rotation, scale). We compare the invariance strengths learned by the models via the visualization shown in Figure 3. The results show that the standard models provide a fixed set of invariance strengths (green). The members of the QD ensemble (dots) span a diverse range of invariance strengths from low (blue) to high-invariance (red), which can be selected downstream by picking among ensemble members." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.747, + 0.877, + 0.852 + ], + "angle": 0, + "content": "Does QD4V benefit a set of downstream tasks with diverse invariance requirements? Our suite of downstream tasks is represent a diverse range of objectives with differing invariance-sensitivity requirements. The ability to exploit the appropriate (in)variance for each task is crucial to achieving high performance. As discussed earlier, off-the-shelf models tend towards high-invariance to multiple factors (Figure 3), which is often effective for object" + }, + { + "type": "page_number", + "bbox": [ + 0.471, + 0.882, + 0.501, + 0.892 + ], + "angle": 0, + "content": "5390" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.111, + 0.137, + 0.449, + 0.218 + ], + "angle": 0, + "content": "
DecoderAircraftFlowersDTDAnimal PoseALOICausal3DRank
Sup.Concat36.885.970.911.226.672.92.0
Average33.883.469.19.123.774.32.7
Ours36.986.972.212.528.472.81.3
MoCoConcat42.083.572.913.745.780.22.2
Average37.983.972.012.642.978.12.8
Ours43.985.275.814.247.480.61.0
MoCo.Concat35.984.968.613.828.265.12.0
Average33.377.864.612.125.365.03.0
Ours37.985.571.914.333.865.31.0
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.093, + 0.22, + 0.472, + 0.281 + ], + "angle": 0, + "content": "Table 4. Comparison of our proposed downstream task decoder with conventional approaches. Top: Supervised/ImageNet 1k pretrained. Middle/Bottom: Moco pre-training on ImageNet 1K/100. Our fusion strategy performs better than learning a classifier over concatenated features and averaging features of the ensemble." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.304, + 0.471, + 0.344 + ], + "angle": 0, + "content": "recognition, but may not be effective for fine-grained tasks like CelebA facial attributes, or pose and lighting-prediction tasks like 300W and ALOI/Causal3D." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.346, + 0.471, + 0.465 + ], + "angle": 0, + "content": "To evaluate the ability of features to support diverse downstream tasks, we evaluate the competitors on a range of tasks likely to exhibit different invariance preferences in Table 1. Our approach achieves comparable or better performance than baselines on all tasks against both supervised and self-supervised baselines. It has particularly remarkable improvements in regression tasks such as CelebA and Causal3D where we see an improvement of \\(12.5\\%\\) and \\(8.5\\%\\) over supervised pre-training of ResNet50." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.466, + 0.47, + 0.666 + ], + "angle": 0, + "content": "To better understand the success of our method, we analyse the weights assigned to each member of the QD ensemble by different downstream tasks. Specifically, we employ Pearson's r correlation coefficient between \\(\\mathbf{w}\\) and the invariances learned by the QD ensemble (in Fig 3) as a metric to measure the strength of the relationship between the two variables. The resulting correlations are shown in Figure 4 and grouped by classification vs regression tasks. The trend shows that the spatially sensitive regression tasks tend to assign lower or negative weights to spatially invariant models, whereas classification tasks prefer models with generally stronger invariances. This analysis illustrates how our framework achieves reliably high performance across the range of tasks evaluated quantitatively in Table 1 - by enabling task-specific invariance preference selection." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.666, + 0.47, + 0.799 + ], + "angle": 0, + "content": "Does QD4V benefit few-shot learning tasks? To answer this question we focused on MoCo-v2 CNN models trained on ImageNet1K and ImageNet100. For classification tasks, we followed [38, 68] in sampling C-way K-shot episodes from the target problem and training linear readouts and learning w for each episode. For regression tasks we repeatedly sampled \\(5\\%\\), and \\(20\\%\\) to generate low-shot training sets. From the results in Table 2, QD pre-training usually performs better than all competitors, with substantial margins in several cases, especially for pose estimation tasks." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.8, + 0.471, + 0.854 + ], + "angle": 0, + "content": "Does QD4V benefit dense estimation tasks? We evaluate QD pre-training on semantic segmentation on Cityscapes [19] and ADE20k [7] datasets. We evaluate QD4V by (1) Freezing the entire backbone and solely train a linear seg" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.14, + 0.878, + 0.235 + ], + "angle": 0, + "content": "mentation head and (2) Finetuning the entire backbone. We report the Mean Intersection over Union (IoU) and average accuracy for segmentation. Similarly, we also examine the performance of QD pre-training on Pascal VOC object detection. The results for semantic segmentation and object detection for frozen features and finetuning in Table 3 show that QD pre-training generally provides performance gains." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.236, + 0.878, + 0.408 + ], + "angle": 0, + "content": "Ablation study for decoders: Finally, we compare our proposed downstream task decoder (Section 3.3) with conventional approaches. The results in Table 4 show that learning fusion weights using Eq. 8 consistently performs better, especially for regression tasks than conventional concatenation and prediction averaging. Intuitively, this is because our stacked fusion decoder has the chance for explicit invariance weighting. More technically, this is explained by the fast convergence rate in Theorem 3.4 which shows that our generalisation gap (between train and test error) tends to zero much faster than standard linear models as a function of the amount of training data. (See Supplementary for further discussion)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.879, + 0.556 + ], + "angle": 0, + "content": "How does QD4V compare to large scale pre-trained models? The seminal CLIP [53] model is highly effective at various downstream tasks. Table 9 (supplementary) compares CLIP/RN50 to ImageNet1K QD4V/RN50 in terms of invariances and performance on downstream pose sensitive tasks. The results show that QD4V substantially outperforms CLIP, despite being trained on orders of magnitude less data - which we attribute to CLIP having learned too strong spatial and appearance invariances. This shows that pre-training scale is not a substitute for providing the correct invariance for the downstream task at hand." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.574, + 0.614, + 0.589 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.878, + 0.785 + ], + "angle": 0, + "content": "We addressed the difficulty of pre-training a model to achieve high performance on diverse downstream tasks by introducing the notion of quality-diversity pre-training. By instantiating diversity optimisation in terms of the (in)variance properties of a feature extractor, we obtain a compact set of high-quality features with diverse (in)variance properties. Together with an efficient and effective fusion strategy, we show strong performance on a diverse range of downstream tasks including classification, pose estimation, semantic segmentation, and object detection. Our approach presents a step towards the vision of a universal feature representation capable of supporting multiple vision tasks. In future work we will explore other definitions of behavioural phenotypes in QD4V." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.786, + 0.878, + 0.853 + ], + "angle": 0, + "content": "Acknowledgements This research was partially supported by the Engineering and Physical Sciences Research Council (EPSRC) Grant number EP/S000631/1 and the MOD University Defence Research Collaboration (UDRC) in Signal Processing." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.88, + 0.5, + 0.892 + ], + "angle": 0, + "content": "5391" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.095, + 0.139, + 0.186, + 0.152 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.103, + 0.162, + 0.47, + 0.198 + ], + "angle": 0, + "content": "[1] 300 faces in-the-wild challenge: database and results. 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However, emerging evidence suggests that any single pre-trained feature will not perform well on diverse downstream tasks. Each pre-training strategy encodes a certain inductive bias, which may suit some downstream tasks but not others. Notably, the augmentations used in both supervised and self-supervised training lead to features with high invariance to spatial and appearance transformations. This renders them sub-optimal for tasks that demand sensitivity to these factors. In this paper we develop a feature that better supports diverse downstream tasks by providing a diverse set of sensitivities and invariances. In particular, we are inspired by Quality-Diversity in evolution, to define a pre-training objective that requires high quality yet diverse features — where diversity is defined in terms of transformation (in)variances. Our framework plugs in to both supervised and self-supervised pre-training, and produces a small ensemble of features. We further show how downstream tasks can easily and efficiently select their preferred (in)variances. Both empirical and theoretical analysis show the efficacy of our representation and transfer learning approach for diverse downstream tasks. Code available at https://github.com/ruchikachavhan/quality-diversity-pretraining.git + +# 1. Introduction + +Pre-training neural networks on large-scale datasets such as ImageNet followed by representation transfer is a dominant paradigm in applied deep learning [58]. Supervised pre-training [34] is long established, with self-supervised [14, 30, 15, 11, 69] pre-training rapidly gaining popularity. Such pre-training algorithms often aspire to providing a universal representation which is effective for diverse down- + +![](images/ead222294ef1e4f91683b4679bbd30afe9d64e96e5782ae387e5f6e6ceed6ecf.jpg) +Figure 1. Illustration of the quality and behavior space of QD4V feature representations. Each point in this space is a potential feature extractor. The $x$ and $y$ axes correspond sensitivity-invariance axes for spatial and appearance transformations, and define the behaviour space for features. The $z$ axis shows the quality of the features (eg: ImageNet accuracy). The shaded zones schematically show the range of feature encodings that might be preferred by different types of downstream tasks. Conventional pre-training learns a single solution (denoted with +) that is high-quality ( $z$ axis near 1) but by default occupies the green zone of high invariance to spatial and appearance transforms. In contrast, QD4V aims to learn a set of solutions (marked by $\Delta$ ) that better span the (in)variance axes, while being also being high quality. These lead to better performance for diverse downstream tasks. Note that in practice the invariance space has many more dimensions than the two illustrated here. + +stream tasks across computer vision, with evaluation studies showing promising results [34, 24]. Nevertheless, emerging evidence suggests that any single pre-trained feature will not be optimal for diverse downstream tasks [25, 68, 13]. This is because, any given pre-training strategy encodes a certain inductive bias in the learned representation, which will better suite some downstream tasks more than others. + +This issue is evident with regards to transformation invariance. By way of example, downstream object recognition benefits from strong affine invariance in a feature since pose is a distractor for object recognition. In con + +trast, downstream pose estimation depends heavily on affine sensitivity in a feature. However, supervised pre-training tends to promote affine-invariance due to the nature of the task and the popular augmentations used. Meanwhile self-supervised pre-training produces feature with even stronger affine-invariance due to optimising for augmentation invariance. So neither may be optimal for downstream pose estimation. More generally, there are a diverse set of potential transformations, each of which may be nuisance factors for some tasks and crucial for others – and any given representation exhibits different degrees of (in)sensitivity to each each possible transformation. Thus, despite the power of mainstream supervised and self-supervised pretraining, since any single feature induces a particular set of (in)variance strengths, it will be sub-optimal for those downstream tasks with different (in)variance preferences. + +Within the self-supervised learning community, a few studies have attempted to address these issues by learning features with multiple (in)variances. This often achieved by an ensemble of different models [25], pre-training multi-headed networks with contrastive learning for different augmentations in each head [68], or with different heads dedicated to (invariance promoting) contrastive learning and (sensitivity promoting) transformation prediction [38]. However, these initial attempts suffer important limitations. Firstly, given that there are many transformations for which invariance or sensitivity may be preferred, it's unclear how to build a compact enough ensemble. For example, if $N$ models are used to encode $N$ distinct strengths of sensitivity to a particular transformation, and there are $K$ possible transformations, this naively leads to an ensemble of size $N^K$ to cover the possible invariance preferences of downstream tasks. Secondly, it's unclear how to optimally select or fuse these different features for downstream tasks with apriori unknown (in)variance preferences. + +In this paper, we address the first of these challenges through the lens of Quality Diversity (QD) [12, 51, 27] a strategy in evolutionary computation that has seen great success in robotics [20]. QD strategies aim to more robustly solve problems by searching for a set of solutions rather than a single solution, and - crucially - requiring that the set of solutions are diverse in some meaningful behavioural metric. We introduce the notion of Quality Diversity Optimisation for Vision (QD4V), where, in a computer vision context, we interpret the idea of behaviour space for diversity measurement as degree of (in)variances to different data augmentations. When applied to supervised ImageNet pretraining, this corresponds to optimising for a small set of ImageNet models that are highly performant, yet use as different cues as possible for recognition. This is qualitatively illustrated in Fig. 1. Each downstream task is then presented with a meaningfully diverse set of high-quality features from which a feature meeting the (in)variance prefer + +ences of the task is more likely to be found. + +Our second contribution addresses how to fuse this small ensemble of features for the downstream task. The limited existing work on learning multiple (in)variances relies on ad-hoc heuristics, such as simply concatenating features prior to linear readout [25, 68]. We argue that a better solution is train a per feature linear readout on the downstream train set, and then learn a fusion weight on the downstream val set, i.e., stacking [66]. We show both empirically and theoretically that this approach to transfer learning outperforms the standard approach. + +In summary, we present a framework for learning a compact and high-quality yet meaningfully diverse set of features. We present a simple approach for transferring them to downstream tasks with strong theoretical backing. Finally, we show empirically that our framework improves on average compared to standard pre-trained features when evaluated on a diverse range of downstream tasks. + +# 2. Related Work + +Invariance learning in vision: Invariances for in-domain image classification have been learned using data augmentation [9] via MAP [6] and marginal likelihood [32] learning. However, these methods do not focus on transferability to downstream target tasks. On the other hand, the success of representation transfer in contrastive self-supervised learning has been attributed to augmentation-based training engendering invariances [25, 63, 52] which act as strong inductive biases for downstream tasks. The field aspires to provide a single general-purpose feature suited for all downstream tasks [8], however, this goal is not straightforward to achieve. Recent studies have shown that features with invariances to different augmentations are suited for different downstream tasks, with no single feature being optimal for all tasks [25, 68] and performance suffers if inappropriate invariances are provided. In contrastive learning, this leads to the laborious need to produce and combine an ensemble of features [68, 25], to disentangle invariance and transformation prediction [38], costly task-specific self-supervised pre-training [54, 61], or amortising invariances [13]. We introduce a framework for learning diverse invariances during either supervised or self-supervised pre-training, while maintaining the quality of those features in terms of encoding image semantics. We also provide an efficient and theoretically supported approach to fuse the resulting features that improves on standard heuristics [25, 68]. + +Quality Diversity: Quality Diversity (QD) optimisation [12, 51, 27] originated in evolutionary algorithms as a strategy for finding a meaningfully diverse set of high-performing solutions to a problem, rather than just one global optimum. Access to a suite of meaningfully diverse high-quality solutions often has substantial robustness benefits that are widely exploited in robotics community + +[20]. In order to drive diversity, a QD algorithm requires an application-specific measure of behaviour as a feature between which two models' difference can be compared. We develop a novel behavioural measure for vision in terms of invariances. Mainstream QD optimisation algorithms such as MAP-Elites are not amenable to the differentiable gradient-based solutions required for application in vision. We develop a simple differentiable instantiation of QD that is amenable to easy integration as a loss within a typical deep learning for vision pipeline. + +Ensemble methods: QD is related to ensemble methods, which have a long history in vision and machine learning [22]. However, ensembles have mostly focused on single-task learning rather than pre-training for transfer learning. A key challenge in ensemble methods is obtaining meaningful inter-model diversity, with the standard approaches of random seeds, boosting, and bagging, providing comparatively weak diversity. Our novel strategy is to take QD's insight that diversity should be measured in a meaningful space, and identifying (in)variance axes as such a meaningful space for diversity measurement in visual pre-training. A second key issue for ensembles is fusing the ensemble prediction, which has been variously performed by unweighted prediction averaging [45] or parameter averaging [46], and feature concatenation in transfer learning [25, 68]. We show both empirically and theoretically the efficacy of learning a weighted combination of predictions. + +# 3. Methodology + +# 3.1. Background + +Mainstream QD optimization [27, 51] searches for a diverse set of solutions $\{\theta_i\}$ to an optimization problem $\mathcal{L}_q$ by solving an objective like + +$$ +\min _ {\{\theta_ {i} \}} \sum_ {i} \mathcal {L} _ {q} (\theta_ {i}) s. t. D (\{\pi (\theta_ {i}) \}), \tag {1} +$$ + +where $\pi$ is a vector of application relevant observable properties of a given solution $\theta_{i}$ that is called phenotype in the QD community. $D$ is a diversity constraint that enforces diversity among the solutions. It is often enforced by tessellation, or gridding, the space of $\pi$ . Thus solution sets $\{\theta_i\}$ have the maximum possible quality $(\mathcal{L}_q)$ while also covering the space of measurable differences in behaviour [27, 51]. To make such QD problems more efficient to solve in a vision context, we will relax them to + +$$ +\min _ {\{\theta_ {i} \}} \sum_ {i} \mathcal {L} _ {q} (\theta_ {i}) - \sum_ {i \neq j} \mathcal {L} _ {d i v} (\pi (\theta_ {i}), \pi (\theta_ {j}) \}), \tag {2} +$$ + +where $\mathcal{L}_{div}$ is a loss that measures pairwise distance. + +# 3.2. Visual Pre-training + +We denote a large dataset for pre-training by $\mathcal{D}_t\subset$ $\mathcal{X}\times \mathcal{Y}$ , where $\mathcal{X}$ is some space of input images and the + +space $\mathcal{V}$ may be contain labels obtained from manual annotation or pre-text tasks from self-supervision. We introduce a population of $N$ feature extractors, represented as an ensemble, $\mathcal{F} = \{f_{\theta_i}\}_{i=1}^N$ , which aim to learn a diverse set of invariances while maintaining high quality. Each member of the ensemble is followed by a projection layer $g_{\phi_i}$ which can be a classifier layer in case of supervised learning or a projection head in case of self-supervised learning [14, 30, 16]. We denote a set of $K$ augmentations considered for pre-training as $\mathcal{T}$ . Let us also denote a sample $\mathbf{x}$ transformed by augmentation $\mathcal{T}_j \in \mathcal{T}$ as $\tilde{\mathbf{x}}^j$ . + +# 3.2.1 QD for Visual Pre-training: Diversity + +To quantify the diversity of solutions during pre-training, we must first define a phenotype — an observable measurement of a feature extractor's behaviour. We define the behavior of a solution by the degree of invariance it shows to a set of augmentations $\mathcal{T}$ . We borrow the definition of invariance from [25], where invariance of a model to a particular data augmentation is defined as the cosine similarity $S(f_{\theta}(\mathbf{x}),f_{\theta}(\tilde{\mathbf{x}}^{j}))$ between augmented and unaugmented features. Thus, we define a phenotype of a solution $f_{\theta_i}$ as a vector $\pi (\mathbf{x};\theta_i)\in \mathbb{R}^K$ such that $j^{\mathrm{th}}$ element of the phenotype vector indicates the invariance that the model exhibits to augmentation $\mathcal{T}_j\in \mathcal{T}$ , as shown in Eq 3. + +$$ +\pi (\mathbf {x}; \theta_ {i}) = \left(S \left(f _ {\theta_ {i}} (\mathbf {x}), f _ {\theta_ {i}} \left(\tilde {\mathbf {x}} ^ {j}\right)\right) _ {j = 1} ^ {| \mathcal {T} |} \right. \tag {3} +$$ + +Diversity Loss: Based on the above phenotype definition, we can encourage each model to exhibit a diverse combination of invariances to augmentations in $\mathcal{T}$ . Specifically, we minimise the negative exponential distance between phenotype vector of each member as in Eq 4 + +$$ +\mathcal {L} _ {\text {d i v e r s i t y}} = \sum_ {i \neq j} ^ {N} \exp (- | \pi (\mathbf {x}; \theta_ {i}) - \pi (\mathbf {x}; \theta_ {j}) |) \tag {4} +$$ + +# 3.2.2 QD for visual pre-training: Quality + +Quality Loss: Depending on the pre-training paradigm employed, different loss functions can be used to promote high quality. In the case of supervised learning, the loss function denoted by $l_{q}$ can be cross-entropy, while self-supervised methods such as SimCLR/MoCo use contrastive loss [48]. The loss function for the entire ensemble for a sample $(\mathbf{x},y)\in \mathcal{D}$ is given in Eq. 5 + +$$ +\mathcal {L} _ {\text {q u a l i t y}} = \frac {1}{N} \sum_ {i = 1} ^ {N} l _ {q} \left(g _ {\phi_ {i}} \left(f _ {\theta_ {i}} (\mathbf {x})\right), y\right) \tag {5} +$$ + +This objective reflects standard supervised or self-supervised learning of the upstream model. Empirically, + +![](images/a26cfa82aad76becfd979cfaa06ce11d9af9aaf2f9a1303150a0b36d0865fbe8.jpg) +Figure 2. Schematic illustration of Quality Diversity Pre-training, shown with only 2 augmentations for simplicity. $\mathcal{L}_{\mathrm{diversity}}$ maximises the difference between invariances that models exhibit to $\mathcal{T}_1$ and $\mathcal{T}_2$ , while $L_{\mathrm{quality}} + \lambda_{kl}\mathcal{L}_{KL}$ maximises the quality of the ensemble by pushing it to the quality of a conventionally pre-trained model (denoted by Baseline). + +we found that purely using this quality objective it is hard for a diverse ensemble to match the quality of a baseline model trained solely for quality. To help the diverse ensemble match the quality of the baseline we introduce an additional loss term, which is the Kullback-Leibler (KL) divergence between the posteriors of the ensemble members and baseline model with parameters $\phi_{b}$ and $\theta_{b}$ . We denote the predictions of a model by $\hat{y}_i = g_{\phi_i}(f_{\theta_i}(x))$ . The loss function is shown in Eq. 6. This term ensures that the members of the ensemble mimic the predictions of the baseline model, thus ensuring high quality with diverse invariances. + +$$ +\mathcal {L} _ {\text {q u a l i t y - K L}} = \sum_ {i = 1} ^ {N} \frac {1}{m} \sum_ {j = 1} ^ {m} \mathrm {K L} \left(\sigma \left(\hat {y} _ {i}; \tau\right) \| \sigma \left(\hat {y} _ {b}; \tau\right)\right) \tag {6} +$$ + +Here, $\sigma$ denotes the softmax function and $\tau$ denotes the temperature used to scale the logits within softmax. + +Summary Finally, to achieve our goal of diverse invariances and high quality in QD4V pre-training, we formulate a total loss function asin Eq. 7. + +$$ +\mathcal {L} _ {q d} = \mathcal {L} _ {\text {q u a l i t y}} + \lambda_ {k l} \mathcal {L} _ {\text {q u a l i t y - K L}} + \lambda_ {d} \mathcal {L} _ {\text {d i v e r s i t y}} \tag {7} +$$ + +The diverse set of optimal solutions learned from the proposed QD pre-training stage denoted as $\mathcal{F}^*$ is then transferred to a downstream task. + +# 3.3. Downstream task Learning + +We next address how to construct models for downstream tasks given the diverse ensemble of features $\mathcal{F}^*$ produced by pre-training in the previous section. Existing approaches have concatenated features prior to linear readout [68], or conducted unweighted averaging of ensemble features [45]. We propose to fuse the ensemble via a variant of stacking [66]. + +Decoder Design For each feature extractor, $f_{\theta_i} \in \mathcal{F}$ we follow the standard linear readout approach, and build a linear model, $h^{(i)}$ , parameterised by $U^{(i)} \in \mathbb{R}^{k \times d}$ and $\mathbf{b}^{(i)} \in \mathbb{R}^k$ + +$$ +h ^ {(i)} (\mathbf {x}) = \rho (U ^ {(i)} f _ {\theta_ {i}} (\mathbf {x}) + \mathbf {b} ^ {(i)}), +$$ + +where $\rho$ is a transfer function for linear models (e.g., the softmax function or identity). To produce a final prediction we fuse the ensemble of classifiers $h^{(i)}(x)$ by learning a weight vector, $\mathbf{w} \in \mathbb{R}^N$ that is used to make a linear combination of their predictions, + +$$ +h (\mathbf {x}) = \sum_ {i = 1} ^ {N} w _ {i} h ^ {(i)} (\mathbf {x}). +$$ + +Decoder Training Strategy For each downstream task have a collection of data, $\mathcal{D}_{ds}$ , which we split into two nonoverlapping subsets, $\mathcal{D}_{tr}$ and $\mathcal{D}_{val}$ . The hyperparameters of the linear models are tuned using this train-validation split, and the best model parameters found during this tuning phase are denoted by $\tilde{U}^{(i)}$ and $\tilde{\mathbf{b}}^{(i)}$ . Each model is retrained using the full $\mathcal{D}_{ds}$ dataset using the best hyperparameters to obtain the final values for each $U^{(i)}$ and $\mathbf{b}^{(i)}$ . The procedure used to fit the weights for linearly combining the models is carried out using the $\tilde{U}^{(i)}$ and $\tilde{\mathbf{b}}^{(i)}$ parameters, and $\mathbf{w}$ is fit on the $\mathcal{D}_{val}$ set, + +$$ +\mathbf {w} = \underset {\mathbf {v} \in \mathbb {R} ^ {N}} {\arg \min } \mathbb {E} _ {\mathcal {D} _ {v a l}} \left[ \left\| \sum_ {i = 1} ^ {N} v _ {i} \rho \left(\tilde {U} ^ {(i)} f _ {\theta_ {i}} (\mathbf {x}) + \tilde {\mathbf {b}} ^ {(i)}\right) - y \right\| _ {2} ^ {2} \right] \tag {8} +$$ + +In the following section, we provide theoretical justification for our proposed downstream architecture and training strategy by way of bounding the generalisation error for downstream tasks learned in this way. + +# 3.4. Theoretical Analysis + +For ease of exposition, consider the case where $\rho$ is the identity and the underlying problem is binary classification. + +In this case, each $U^{(i)}$ can be written as a vector, $\mathbf{u}^{(i)}$ . We can define the effective hypothesis class of our algorithm for learning on downstream tasks as + +$$ +\begin{array}{l} \mathcal {H} = \left\{\mathbf {x} \rightarrow \sum_ {i = 1} ^ {N} w _ {i} \langle \mathbf {u} ^ {(i)}, f _ {\theta_ {i}} (\mathbf {x}) \rangle : \right. \\ \left. \left\| \mathbf {w} - \mathbb {E} [ \mathbf {w} ] \right\| _ {2} \leq A, \left\| \mathbf {u} ^ {(i)} - \mathbb {E} [ \mathbf {u} ^ {(i)} ] \right\| _ {F} \leq B \right\}, \\ \end{array} +$$ + +where we have absorbed the bias values into $\mathbf{u}$ by assuming a 1 has been appended to each $\mathbf{x}$ . Our goal is to bound the generalisation error of models from this class trained using our stacking procedure in Sec 3.3. The first step is to bound the empirical Rademacher complexity in terms of $A$ and $B$ (from the definition of $\mathcal{H}$ ), the norm of the features, and the total amount of data available for the downstream task, $m = |\mathcal{D}_{ds}|$ . We then show how the stacking procedure influences the values of $A$ and $B$ . We use $\eta$ to indicate the fraction of data used for training, hence $\eta m = |\mathcal{D}_{tr}|$ and $(1 - \eta)m = |\mathcal{D}_{val}|$ . Our main result in given below. + +Theorem 1. For a model trained using our stacking procedure and the conditions outlined in the statements of Lemmas 1 and 2, we have with probability at least $1 - 2\delta$ + +$$ +\begin{array}{l} \mathbb {E} [ \mathbf {1} [ \operatorname {s g n} (h (\mathbf {x})) \neq y) ] \leq \hat {\mathbb {E}} [ l (h (\mathbf {x}), y) ] \\ + \frac {1 2 X ^ {3} \| \tilde {V} \| _ {2} \sqrt {\ln (4 / \delta) \ln (4 N / \delta)}}{\gamma_ {1} \gamma_ {2} \sqrt {1 - \eta m ^ {3 / 2}}} \\ + \frac {2 X ^ {2} \sqrt {2 \ln (4 N / \delta)}}{\gamma_ {1} m} \\ + \frac {2 X ^ {2} \| \tilde {V} \| _ {2} \sqrt {2 \ln (4 / \delta)}}{\gamma_ {2} \sqrt {1 - \eta m}} \\ + 3 \sqrt {\frac {\ln (1 / \delta)}{2 m}}, \\ \end{array} +$$ + +where $\hat{\mathbb{E}}[l(h(\mathbf{x}), y)]$ is the mean ramp loss of the model $h$ , computed on the training data. + +Notably, this bound achieves the "fast" rate of convergence, $\mathcal{O}(m^{-1})$ , in the complexity terms, with the first term even exhibiting a super-fast rate of $\mathcal{O}(m^{-3/2})$ . This is in contrast to the standard $\mathcal{O}(m^{-1/2})$ rate in existing bounds. The proof is in the supplemental material. + +Discussion This theorem depends on both the specific architecture and optimisation strategy outlined in Sec. 3.3, and thus provides justification for these design choices. It says that the generalisation gap between train error and expected (test) error rapidly goes to zero with the size of the downstream train set $m$ . Furthermore, because we have access to an ensemble of features, the train error $\hat{e} r(h)$ can likely be reduced below that of a single feature. + +# 4. Implementation details + +Pre-training: We perform supervised training for ResNet50 and ConvNeXt [42] on ImageNet1K [21] and contrastive training for ResNet50 on both ImageNet1K and ImageNet100 [68]. To learn our feature ensemble, in a parameter efficient way for both architectures, we share the first three layers (layer1, layer2, layer3 according to [65]), after which different members of the ensemble branch out into their own sequence of layers having a separate layer4 and projection head. We initialise the entire ensemble with ImageNet pre-trained models in case of supervised pre-training and MoCo pre-trained models in case of contrastive learning. + +Augmentations: For supervised pre-training, most methods that rely on strong augmentation policies. Our approach applies the quality loss (Eq. 5) to unaugmented samples only as using augmented samples for quality maximisation would lead to typical strong invariance to all augmentations and prevent diversity. For contrastive learning, we apply very weak augmentations for instance discrimination. + +Learning rates and Optimisers: For supervised pretraining and contrastive learning experiments, we train the model for 20 epochs with SGD and AdamW optimizers respectively, along with learning rate warm-up for 5 epochs, followed by a cosine decay schedule. For supervised pretraining, we apply label smoothening and perform exponential moving average (EMA) on the model weights. + +Downstream tasks: Our suite of downstream tasks consists of object recognition, regression, and dense estimation. We provide more details about downstream tasks in the supplementary material. + +- Classification: For classification, we evaluate on standard benchmarks CIFAR10/100 [36], Caltech101 [26], Oxford Flowers [47], Stanford Cars [35], Describable Textures Dataset (DTD) [17], Aircraft [43]. +- Regression: We include a set of spatially sensitive tasks including facial landmark detection on 300W [1], CelebA [41], human pose estimation in LSP [33] and MPII [2], Animal Pose prediction [10], AROI object orientation prediction [29], and Causal3DIdent 6D pose and appearance attribute prediction [60]. +- Dense estimation: We also evaluate the QD pretrained models on dense estimation tasks like Pascal VOC object detection using Faster R-CNN [55] with a Feature Pyramid Network backbone [39] and linear semantic segmentation similar to [4] on CityScapes and ADE20k [7] datasets. + +Downstream evaluation: For classification and regression tasks, we fit multinomial logistic regression and multi-output linear regression on the extracted features from each + +![](images/e4a8775b0e435dfecb73edc415b4ed4271ca73984c7216d3b5595ad6384be519.jpg) +Figure 3. Radar plot comparing invariance w.r.t. for 4 Spatial and 4 Appearance based transformations of baseline models (green) and QD ensemble (dots). The red and blue lines correspond to maximum and minimum invariances within QD ensemble. The blue shaded region corresponds to the range of invariances spanned by the QD ensemble, which encompasses the (in)variance of the baselines. + +![](images/38133b78b2eacf8ba7ff6a5ef7e6ce946a1f36ae9de85fff83f4b5f555f0d5ca.jpg) +ax, invariance in, invariance aseline + +
MethodsCIFAR10CIFAR100FlowersCaltech 101DTDCarsAircraft300wLS PoseCelebAAnimal PoseMPIIALOICausal3DRank
IN1K (RN50)Sup.Baseline90.468.285.284.771.944.436.070.255.449.011.218.024.164.12.7
Multihead90.367.384.884.169.943.235.068.353.250.110.917.022.862.33.7
Div. Ens. [23]91.672.984.689.369.842.735.366.652.649.211.517.922.660.83.4
MeTTA [3]91.071.685.385.171.841.134.065.352.847.910.516.323.161.23.8
QD4V90.370.486.989.972.245.436.976.662.461.512.518.528.472.81.4
MoCoMoCo90.370.689.887.973.939.341.887.269.092.513.919.946.078.11.9
Fusionx[25]95.0-81.086.0---65.068.033.0-----
QD4V88.971.285.288.275.841.343.988.971.895.214.222.447.480.61.2
Sup.Baseline (CN-T)89.470.694.589.168.052.548.463.148.152.511.517.78.0269.41.8
QD4V (CN-T)91.572.996.589.969.851.550.082.269.960.712.518.59.371.91.1
IN100Sup.MoCo84.661.682.477.364.533.937.285.558.761.013.218.630.961.43.5
AugSelf* [38]85.363.985.778.966.237.439.577.363.977.012.919.535.261.62.4
AI+ [13]81.364.681.378.468.838.637.390.065.282.012.521.632.762.62.5
QD4V84.565.485.581.271.939.837.988.969.785.014.320.633.865.31.5
+ +Table 1. Downstream performance of ImageNet (IN1K) pretrained (1) Supervised ResNet50, (2) MoCo ResNet50 and ImageNet-100 (IN100) pretrained (3) Supervised ConvNeXt-Tiny (CN-T), (4) MoCo ResNet50. The first seven columns are classification tasks (accuracy, %); the last seven are regression (R2, %). + numbers from [13] where reported, * A mix of our runs and numbers from [13] where reported, x numbers from [25], rest are our runs. + +![](images/bd931b75b5c2cb2d33ac0599f4f84174c8a262e15c1dc9642153e1431bc61d45.jpg) + +![](images/01d25f18044af3245957d30a7e144a3bccb817a48ef62fbaf430fb431c3c6871.jpg) + +![](images/554f2d81bafbdde470aba1f2b7451404875c624d8878a3958cae359a28ee64dc.jpg) + +![](images/d3e5e413be75d85167d01028f89519ea5a876830fce657a1ad1a2fbc7ac85567.jpg) + +![](images/7ad8e6555d1f36d8ff6eeb554656228b6026412445e818cf1afda406605b5fdf.jpg) +Figure 4. Correlation between our classifier fusion weights (Eq 8) and task for 4 Spatial and 4 Appearance based augmentations. The y-axis corresponds to Pearson's r correlation between w assigned to each member by a particular task and invariances exhibited by that member to specific augmentations. Tasks are grouped by classification and regression, which tend to show different invariance preferences. + +![](images/1b4bc6146307adb9e768040023f6a7fc69f778d1722b85b57360ef37bc306448.jpg) + +![](images/ddead2bdabe21de978f52c6a0ab982b52304e3b1d43410b368d3469c51334a94.jpg) + +![](images/c05a5d5e4025e538e4c038bbf14c40a522613d0ab678c1087c561cc43bcae4a2.jpg) + +
MethodsCUBFlowersFC 100Plant Disease300wLS PoseCelebACausal3DRank
(5,1)(5,5)(5,1)(5,5)(5,1)(5,5)(5,1)(5,5)s=0.05s=0.2s=0.05s=0.2s=0.05s=0.2s=0.05s=0.2
Baseline70.090.477.393.753.878.768.988.820.524.846.948.539.241.458.962.42.3
Multihead69.688.276.592.652.978.568.287.319.424.739.344.939.440.857.261.33.5
Div. Ensemble68.388.778.494.654.978.168.791.918.118.835.736.839.339.754.758.93.4
MeTTA68.488.977.692.354.472.868.787.518.320.336.837.537.237.949.358.64.1
Ours71.490.873.493.257.576.269.491.037.544.959.760.350.553.160.363.41.6
MoCo51.769.871.889.454.971.067.585.339.948.359.363.147.559.066.777.41.8
Ours49.974.170.493.450.972.962.389.657.360.462.665.664.264.770.379.41.3
MoCo41.056.969.676.431.743.965.785.039.050.154.260.340.252.352.557.03.7
AugSelf [38]44.257.476.085.635.048.871.887.842.051.853.860.153.266.354.461.82.7
LooC [38]--70.980.8-------------
AI [13]45.058.076.788.737.448.472.689.149.257.955.362.056.076.060.262.81.6
Ours41.356.667.888.939.553.765.988.151.157.558.364.850.257.761.863.91.9
+ +Table 2. Few-shot classification and regression accuracy (\%, R2) of our QD ResNet50 ensemble for supervised (top), MoCo pre-trained on ImageNet (middle) and MoCo pre-trained on ImageNet-100 (bottom). Values are reported with $95\%$ confidence intervals averaged over 2000 episodes on FC100, CUB200, and Plant Disease. (N, K) denotes N-way K-shot tasks. For regression tasks (300w, LS Pose, CelebA, Causal3D), we report downstream performance for different splits with train proportion given by $s$ . + +of the ensemble and then learn a weighted combination of over all these predictions using linear regression. We sweep the regularisation parameters for all members for each downstream dataset based on its validation set. For dense tasks, we train a decoder head for each member of the ensemble using default hyperparameters in [67] for object detection and [18] for semantic segmentation. + +Few-shot downstream tasks: We also evaluate the pretrained networks on various few-shot learning benchmarks: FC100 [49], Caltech-UCSD Birds (CUB200), and Plant Disease [44]. We also show results for few-shot regression problems on 300w, Leeds Sports Pose, CelebA, and Causal3DIdent datasets, where we we repeatedly sampled $5\%$ , and $20\%$ to generate low-shot training sets. For few-shot classification, we perform logistic regression using the frozen ensemble and learn episode-wise fusion weights w the support set itself. + +Competitors: All methods are evaluated by readouts on fixed features. Supervised: Besides conventional supervised pre-training (denoted 'baseline'), we also train a conventional ensemble via a multi-head model ('multihead') that has the same architecture and number of parameters as our architecture but uses only $\mathcal{L}_q$ loss. We also compare with another diverse ensemble strategy [23, 50] (denoted 'div ensemble'): to optimises for diversity in terms of KL between posterior probability of ensemble members. The idea being that differences in secondary probabilities are a good measure of diversity. We provide more details in the supplementary material. Finally, we compare with a test-time ensemble created by taking a single pretrained model and generating different invariances through test-time mean embeddings [3] (denoted 'MeTTA'). Contrastive: We compare our approach to two state of the art ensemble based alternatives AugSelf [68], LOOC [38] and amortised invariances (AI) [13]. Note that unlike other competitors, AI uses backprop to update the features. + +
MethodsCityScapesADE20kPascal VOCRank
MIoUAcc.MIoUAcc.APAP50AP75
Sup.Baseline39.682.130.452.948.880.351.62.6
Multihead35.480.327.351.849.880.250.93.9
Div. Ensemble36.282.427.652.750.681.958.12.3
QD4V41.081.733.854.350.882.558.71.3
Baseline (FT)61.794.140.167.255.182.860.52.0
QD4V (FT)65.294.342.367.456.284.962.91.0
MoCo.Baseline46.387.435.250.454.281.859.91.7
QD4V49.288.939.054.653.382.259.91.1
Baseline34.583.426.740.641.271.442.93.0
AugSelf37.984.927.340.843.273.448.11.6
QD4V36.184.928.541.745.975.248.01.3
+ +Table 3. Downstream performance of (1) Frozen supervised (2) fine-tuned supervised, (3/4) MoCO trained on ImageNet1K/100 model evaluated on semantic segmentation for CityScapes and ADE20k datasets, and Pascal VOC object detection. + +# 5. Results + +Can we successfully learn diverse (in)variance strengths with QD pre-training? To answer this question, we use the definition of invariance in Eq. 3 and evaluate the invariances learned by both default models (i.e., supervised and MoCo) and members of our QD ensemble for four appearance augmentations (blur, brightness, grayscale, contrast) and four spatial augmentations (resized crop, horizontal flip, rotation, scale). We compare the invariance strengths learned by the models via the visualization shown in Figure 3. The results show that the standard models provide a fixed set of invariance strengths (green). The members of the QD ensemble (dots) span a diverse range of invariance strengths from low (blue) to high-invariance (red), which can be selected downstream by picking among ensemble members. + +Does QD4V benefit a set of downstream tasks with diverse invariance requirements? Our suite of downstream tasks is represent a diverse range of objectives with differing invariance-sensitivity requirements. The ability to exploit the appropriate (in)variance for each task is crucial to achieving high performance. As discussed earlier, off-the-shelf models tend towards high-invariance to multiple factors (Figure 3), which is often effective for object + +
DecoderAircraftFlowersDTDAnimal PoseALOICausal3DRank
Sup.Concat36.885.970.911.226.672.92.0
Average33.883.469.19.123.774.32.7
Ours36.986.972.212.528.472.81.3
MoCoConcat42.083.572.913.745.780.22.2
Average37.983.972.012.642.978.12.8
Ours43.985.275.814.247.480.61.0
MoCo.Concat35.984.968.613.828.265.12.0
Average33.377.864.612.125.365.03.0
Ours37.985.571.914.333.865.31.0
+ +Table 4. Comparison of our proposed downstream task decoder with conventional approaches. Top: Supervised/ImageNet 1k pretrained. Middle/Bottom: Moco pre-training on ImageNet 1K/100. Our fusion strategy performs better than learning a classifier over concatenated features and averaging features of the ensemble. + +recognition, but may not be effective for fine-grained tasks like CelebA facial attributes, or pose and lighting-prediction tasks like 300W and ALOI/Causal3D. + +To evaluate the ability of features to support diverse downstream tasks, we evaluate the competitors on a range of tasks likely to exhibit different invariance preferences in Table 1. Our approach achieves comparable or better performance than baselines on all tasks against both supervised and self-supervised baselines. It has particularly remarkable improvements in regression tasks such as CelebA and Causal3D where we see an improvement of $12.5\%$ and $8.5\%$ over supervised pre-training of ResNet50. + +To better understand the success of our method, we analyse the weights assigned to each member of the QD ensemble by different downstream tasks. Specifically, we employ Pearson's r correlation coefficient between $\mathbf{w}$ and the invariances learned by the QD ensemble (in Fig 3) as a metric to measure the strength of the relationship between the two variables. The resulting correlations are shown in Figure 4 and grouped by classification vs regression tasks. The trend shows that the spatially sensitive regression tasks tend to assign lower or negative weights to spatially invariant models, whereas classification tasks prefer models with generally stronger invariances. This analysis illustrates how our framework achieves reliably high performance across the range of tasks evaluated quantitatively in Table 1 - by enabling task-specific invariance preference selection. + +Does QD4V benefit few-shot learning tasks? To answer this question we focused on MoCo-v2 CNN models trained on ImageNet1K and ImageNet100. For classification tasks, we followed [38, 68] in sampling C-way K-shot episodes from the target problem and training linear readouts and learning w for each episode. For regression tasks we repeatedly sampled $5\%$ , and $20\%$ to generate low-shot training sets. From the results in Table 2, QD pre-training usually performs better than all competitors, with substantial margins in several cases, especially for pose estimation tasks. + +Does QD4V benefit dense estimation tasks? We evaluate QD pre-training on semantic segmentation on Cityscapes [19] and ADE20k [7] datasets. We evaluate QD4V by (1) Freezing the entire backbone and solely train a linear seg + +mentation head and (2) Finetuning the entire backbone. We report the Mean Intersection over Union (IoU) and average accuracy for segmentation. Similarly, we also examine the performance of QD pre-training on Pascal VOC object detection. The results for semantic segmentation and object detection for frozen features and finetuning in Table 3 show that QD pre-training generally provides performance gains. + +Ablation study for decoders: Finally, we compare our proposed downstream task decoder (Section 3.3) with conventional approaches. The results in Table 4 show that learning fusion weights using Eq. 8 consistently performs better, especially for regression tasks than conventional concatenation and prediction averaging. Intuitively, this is because our stacked fusion decoder has the chance for explicit invariance weighting. More technically, this is explained by the fast convergence rate in Theorem 3.4 which shows that our generalisation gap (between train and test error) tends to zero much faster than standard linear models as a function of the amount of training data. (See Supplementary for further discussion). + +How does QD4V compare to large scale pre-trained models? The seminal CLIP [53] model is highly effective at various downstream tasks. Table 9 (supplementary) compares CLIP/RN50 to ImageNet1K QD4V/RN50 in terms of invariances and performance on downstream pose sensitive tasks. The results show that QD4V substantially outperforms CLIP, despite being trained on orders of magnitude less data - which we attribute to CLIP having learned too strong spatial and appearance invariances. This shows that pre-training scale is not a substitute for providing the correct invariance for the downstream task at hand. + +# 6. Conclusion + +We addressed the difficulty of pre-training a model to achieve high performance on diverse downstream tasks by introducing the notion of quality-diversity pre-training. By instantiating diversity optimisation in terms of the (in)variance properties of a feature extractor, we obtain a compact set of high-quality features with diverse (in)variance properties. Together with an efficient and effective fusion strategy, we show strong performance on a diverse range of downstream tasks including classification, pose estimation, semantic segmentation, and object detection. Our approach presents a step towards the vision of a universal feature representation capable of supporting multiple vision tasks. In future work we will explore other definitions of behavioural phenotypes in QD4V. + +Acknowledgements This research was partially supported by the Engineering and Physical Sciences Research Council (EPSRC) Grant number EP/S000631/1 and the MOD University Defence Research Collaboration (UDRC) in Signal Processing. + +# References + +[1] 300 faces in-the-wild challenge: database and results. Image and Vision Computing, 2016. 300-W, the First Automatic Facial Landmark Detection in-the-Wild Challenge. 5, 13 +[2] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2d human pose estimation: New benchmark and state of the art analysis. In CVPR, 2014. 5, 13 +[3] Arsenii Ashukha, Andrei Atanov, and Dmitry Vetrov. Mean embeddings with test-time data augmentation for ensembling of representations. ICML Workshop on Uncertainty and Robustness in Deep Learning, 2021. 6, 7 +[4] Adrien Bardes, Jean Ponce, and Yann LeCun. 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In ICML, 2021. 1 \ No newline at end of file diff --git a/2023/Quality Diversity for Visual Pre-Training/images.zip b/2023/Quality Diversity for Visual Pre-Training/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..b98fef419d4c38a1557afcf099c8d6844dddde9b --- /dev/null +++ b/2023/Quality Diversity for Visual Pre-Training/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:82ec7bce07de0f401aa1b6591e31bd83c0fc44d816bc1f09bdb69e4e76521aaf +size 463650 diff --git a/2023/Quality Diversity for Visual Pre-Training/layout.json b/2023/Quality Diversity for Visual Pre-Training/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..49ff84a7aa4b0584c490c95ea805153aa185b5bc --- /dev/null +++ b/2023/Quality Diversity for Visual Pre-Training/layout.json @@ -0,0 +1,8929 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 170, + 147, + 408, + 163 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 170, + 147, + 408, + 163 + ], + "spans": [ + { + "bbox": [ + 170, + 147, + 408, + 163 + ], + "type": "text", + "content": "Quality Diversity for Visual Pre-Training" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 139, + 183, + 437, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 183, + 437, + 198 + ], + "spans": [ + { + "bbox": [ + 139, + 183, + 437, + 198 + ], + "type": "text", + "content": "Ruchika Chavhan1, Henry Gouk1, Da Li2, Timothy Hospedales1,2" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 92, + 201, + 485, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 201, + 485, + 240 + ], + "spans": [ + { + "bbox": [ + 92, + 201, + 485, + 240 + ], + "type": "text", + "content": "1The University of Edinburgh 2Samsung AI Center, Cambridge \nR.Chavhan@sms.ed.ac.uk, {henry.gouk, t.hospedales}@ed.ac.uk, \ndali.academic@gmail.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 145, + 266, + 190, + 278 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 266, + 190, + 278 + ], + "spans": [ + { + "bbox": [ + 145, + 266, + 190, + 278 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 290, + 282, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 290, + 282, + 594 + ], + "spans": [ + { + "bbox": [ + 54, + 290, + 282, + 594 + ], + "type": "text", + "content": "Models pre-trained on large datasets such as ImageNet provide the de-facto standard for transfer learning, with both supervised and self-supervised approaches proving effective. However, emerging evidence suggests that any single pre-trained feature will not perform well on diverse downstream tasks. Each pre-training strategy encodes a certain inductive bias, which may suit some downstream tasks but not others. Notably, the augmentations used in both supervised and self-supervised training lead to features with high invariance to spatial and appearance transformations. This renders them sub-optimal for tasks that demand sensitivity to these factors. In this paper we develop a feature that better supports diverse downstream tasks by providing a diverse set of sensitivities and invariances. In particular, we are inspired by Quality-Diversity in evolution, to define a pre-training objective that requires high quality yet diverse features — where diversity is defined in terms of transformation (in)variances. Our framework plugs in to both supervised and self-supervised pre-training, and produces a small ensemble of features. We further show how downstream tasks can easily and efficiently select their preferred (in)variances. Both empirical and theoretical analysis show the efficacy of our representation and transfer learning approach for diverse downstream tasks. Code available at https://github.com/ruchikachavhan/quality-diversity-pretraining.git" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 618, + 130, + 630 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 618, + 130, + 630 + ], + "spans": [ + { + "bbox": [ + 55, + 618, + 130, + 630 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 54, + 638, + 280, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 638, + 280, + 717 + ], + "spans": [ + { + "bbox": [ + 54, + 638, + 280, + 717 + ], + "type": "text", + "content": "Pre-training neural networks on large-scale datasets such as ImageNet followed by representation transfer is a dominant paradigm in applied deep learning [58]. Supervised pre-training [34] is long established, with self-supervised [14, 30, 15, 11, 69] pre-training rapidly gaining popularity. Such pre-training algorithms often aspire to providing a universal representation which is effective for diverse down-" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 312, + 267, + 509, + 407 + ], + "blocks": [ + { + "bbox": [ + 312, + 267, + 509, + 407 + ], + "lines": [ + { + "bbox": [ + 312, + 267, + 509, + 407 + ], + "spans": [ + { + "bbox": [ + 312, + 267, + 509, + 407 + ], + "type": "image", + "image_path": "ead222294ef1e4f91683b4679bbd30afe9d64e96e5782ae387e5f6e6ceed6ecf.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 412, + 523, + 576 + ], + "lines": [ + { + "bbox": [ + 296, + 412, + 523, + 576 + ], + "spans": [ + { + "bbox": [ + 296, + 412, + 523, + 576 + ], + "type": "text", + "content": "Figure 1. Illustration of the quality and behavior space of QD4V feature representations. Each point in this space is a potential feature extractor. The " + }, + { + "bbox": [ + 296, + 412, + 523, + 576 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 296, + 412, + 523, + 576 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 412, + 523, + 576 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 296, + 412, + 523, + 576 + ], + "type": "text", + "content": " axes correspond sensitivity-invariance axes for spatial and appearance transformations, and define the behaviour space for features. The " + }, + { + "bbox": [ + 296, + 412, + 523, + 576 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 296, + 412, + 523, + 576 + ], + "type": "text", + "content": " axis shows the quality of the features (eg: ImageNet accuracy). The shaded zones schematically show the range of feature encodings that might be preferred by different types of downstream tasks. Conventional pre-training learns a single solution (denoted with +) that is high-quality (" + }, + { + "bbox": [ + 296, + 412, + 523, + 576 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 296, + 412, + 523, + 576 + ], + "type": "text", + "content": " axis near 1) but by default occupies the green zone of high invariance to spatial and appearance transforms. In contrast, QD4V aims to learn a set of solutions (marked by " + }, + { + "bbox": [ + 296, + 412, + 523, + 576 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 296, + 412, + 523, + 576 + ], + "type": "text", + "content": ") that better span the (in)variance axes, while being also being high quality. These lead to better performance for diverse downstream tasks. Note that in practice the invariance space has many more dimensions than the two illustrated here." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 593, + 521, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 593, + 521, + 671 + ], + "spans": [ + { + "bbox": [ + 296, + 593, + 521, + 671 + ], + "type": "text", + "content": "stream tasks across computer vision, with evaluation studies showing promising results [34, 24]. Nevertheless, emerging evidence suggests that any single pre-trained feature will not be optimal for diverse downstream tasks [25, 68, 13]. This is because, any given pre-training strategy encodes a certain inductive bias in the learned representation, which will better suite some downstream tasks more than others." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 672, + 521, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 672, + 521, + 717 + ], + "spans": [ + { + "bbox": [ + 296, + 672, + 521, + 717 + ], + "type": "text", + "content": "This issue is evident with regards to transformation invariance. By way of example, downstream object recognition benefits from strong affine invariance in a feature since pose is a distractor for object recognition. In con" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 7, + 102, + 38 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 7, + 102, + 38 + ], + "spans": [ + { + "bbox": [ + 57, + 7, + 102, + 38 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 138, + 5, + 485, + 40 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 5, + 485, + 40 + ], + "spans": [ + { + "bbox": [ + 138, + 5, + 485, + 40 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 279, + 740, + 298, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 740, + 298, + 750 + ], + "spans": [ + { + "bbox": [ + 279, + 740, + 298, + 750 + ], + "type": "text", + "content": "5384" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 54, + 118, + 281, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 118, + 281, + 297 + ], + "spans": [ + { + "bbox": [ + 54, + 118, + 281, + 297 + ], + "type": "text", + "content": "trast, downstream pose estimation depends heavily on affine sensitivity in a feature. However, supervised pre-training tends to promote affine-invariance due to the nature of the task and the popular augmentations used. Meanwhile self-supervised pre-training produces feature with even stronger affine-invariance due to optimising for augmentation invariance. So neither may be optimal for downstream pose estimation. More generally, there are a diverse set of potential transformations, each of which may be nuisance factors for some tasks and crucial for others – and any given representation exhibits different degrees of (in)sensitivity to each each possible transformation. Thus, despite the power of mainstream supervised and self-supervised pretraining, since any single feature induces a particular set of (in)variance strengths, it will be sub-optimal for those downstream tasks with different (in)variance preferences." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 301, + 281, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 301, + 281, + 513 + ], + "spans": [ + { + "bbox": [ + 57, + 301, + 281, + 513 + ], + "type": "text", + "content": "Within the self-supervised learning community, a few studies have attempted to address these issues by learning features with multiple (in)variances. This often achieved by an ensemble of different models [25], pre-training multi-headed networks with contrastive learning for different augmentations in each head [68], or with different heads dedicated to (invariance promoting) contrastive learning and (sensitivity promoting) transformation prediction [38]. However, these initial attempts suffer important limitations. Firstly, given that there are many transformations for which invariance or sensitivity may be preferred, it's unclear how to build a compact enough ensemble. For example, if " + }, + { + "bbox": [ + 57, + 301, + 281, + 513 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 57, + 301, + 281, + 513 + ], + "type": "text", + "content": " models are used to encode " + }, + { + "bbox": [ + 57, + 301, + 281, + 513 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 57, + 301, + 281, + 513 + ], + "type": "text", + "content": " distinct strengths of sensitivity to a particular transformation, and there are " + }, + { + "bbox": [ + 57, + 301, + 281, + 513 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 57, + 301, + 281, + 513 + ], + "type": "text", + "content": " possible transformations, this naively leads to an ensemble of size " + }, + { + "bbox": [ + 57, + 301, + 281, + 513 + ], + "type": "inline_equation", + "content": "N^K" + }, + { + "bbox": [ + 57, + 301, + 281, + 513 + ], + "type": "text", + "content": " to cover the possible invariance preferences of downstream tasks. Secondly, it's unclear how to optimally select or fuse these different features for downstream tasks with apriori unknown (in)variance preferences." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 516, + 281, + 718 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 516, + 281, + 718 + ], + "spans": [ + { + "bbox": [ + 54, + 516, + 281, + 718 + ], + "type": "text", + "content": "In this paper, we address the first of these challenges through the lens of Quality Diversity (QD) [12, 51, 27] a strategy in evolutionary computation that has seen great success in robotics [20]. QD strategies aim to more robustly solve problems by searching for a set of solutions rather than a single solution, and - crucially - requiring that the set of solutions are diverse in some meaningful behavioural metric. We introduce the notion of Quality Diversity Optimisation for Vision (QD4V), where, in a computer vision context, we interpret the idea of behaviour space for diversity measurement as degree of (in)variances to different data augmentations. When applied to supervised ImageNet pretraining, this corresponds to optimising for a small set of ImageNet models that are highly performant, yet use as different cues as possible for recognition. This is qualitatively illustrated in Fig. 1. Each downstream task is then presented with a meaningfully diverse set of high-quality features from which a feature meeting the (in)variance prefer" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 297, + 118, + 463, + 128 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 118, + 463, + 128 + ], + "spans": [ + { + "bbox": [ + 297, + 118, + 463, + 128 + ], + "type": "text", + "content": "ences of the task is more likely to be found." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 296, + 129, + 522, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 129, + 522, + 240 + ], + "spans": [ + { + "bbox": [ + 296, + 129, + 522, + 240 + ], + "type": "text", + "content": "Our second contribution addresses how to fuse this small ensemble of features for the downstream task. The limited existing work on learning multiple (in)variances relies on ad-hoc heuristics, such as simply concatenating features prior to linear readout [25, 68]. We argue that a better solution is train a per feature linear readout on the downstream train set, and then learn a fusion weight on the downstream val set, i.e., stacking [66]. We show both empirically and theoretically that this approach to transfer learning outperforms the standard approach." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 296, + 241, + 522, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 241, + 522, + 319 + ], + "spans": [ + { + "bbox": [ + 296, + 241, + 522, + 319 + ], + "type": "text", + "content": "In summary, we present a framework for learning a compact and high-quality yet meaningfully diverse set of features. We present a simple approach for transferring them to downstream tasks with strong theoretical backing. Finally, we show empirically that our framework improves on average compared to standard pre-trained features when evaluated on a diverse range of downstream tasks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 297, + 329, + 379, + 340 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 329, + 379, + 340 + ], + "spans": [ + { + "bbox": [ + 297, + 329, + 379, + 340 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 348, + 523, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 348, + 523, + 638 + ], + "spans": [ + { + "bbox": [ + 296, + 348, + 523, + 638 + ], + "type": "text", + "content": "Invariance learning in vision: Invariances for in-domain image classification have been learned using data augmentation [9] via MAP [6] and marginal likelihood [32] learning. However, these methods do not focus on transferability to downstream target tasks. On the other hand, the success of representation transfer in contrastive self-supervised learning has been attributed to augmentation-based training engendering invariances [25, 63, 52] which act as strong inductive biases for downstream tasks. The field aspires to provide a single general-purpose feature suited for all downstream tasks [8], however, this goal is not straightforward to achieve. Recent studies have shown that features with invariances to different augmentations are suited for different downstream tasks, with no single feature being optimal for all tasks [25, 68] and performance suffers if inappropriate invariances are provided. In contrastive learning, this leads to the laborious need to produce and combine an ensemble of features [68, 25], to disentangle invariance and transformation prediction [38], costly task-specific self-supervised pre-training [54, 61], or amortising invariances [13]. We introduce a framework for learning diverse invariances during either supervised or self-supervised pre-training, while maintaining the quality of those features in terms of encoding image semantics. We also provide an efficient and theoretically supported approach to fuse the resulting features that improves on standard heuristics [25, 68]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 639, + 522, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 639, + 522, + 717 + ], + "spans": [ + { + "bbox": [ + 296, + 639, + 522, + 717 + ], + "type": "text", + "content": "Quality Diversity: Quality Diversity (QD) optimisation [12, 51, 27] originated in evolutionary algorithms as a strategy for finding a meaningfully diverse set of high-performing solutions to a problem, rather than just one global optimum. Access to a suite of meaningfully diverse high-quality solutions often has substantial robustness benefits that are widely exploited in robotics community" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 740, + 298, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 740, + 298, + 750 + ], + "spans": [ + { + "bbox": [ + 279, + 740, + 298, + 750 + ], + "type": "text", + "content": "5385" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 54, + 117, + 281, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 117, + 281, + 229 + ], + "spans": [ + { + "bbox": [ + 54, + 117, + 281, + 229 + ], + "type": "text", + "content": "[20]. In order to drive diversity, a QD algorithm requires an application-specific measure of behaviour as a feature between which two models' difference can be compared. We develop a novel behavioural measure for vision in terms of invariances. Mainstream QD optimisation algorithms such as MAP-Elites are not amenable to the differentiable gradient-based solutions required for application in vision. We develop a simple differentiable instantiation of QD that is amenable to easy integration as a loss within a typical deep learning for vision pipeline." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 230, + 282, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 230, + 282, + 421 + ], + "spans": [ + { + "bbox": [ + 54, + 230, + 282, + 421 + ], + "type": "text", + "content": "Ensemble methods: QD is related to ensemble methods, which have a long history in vision and machine learning [22]. However, ensembles have mostly focused on single-task learning rather than pre-training for transfer learning. A key challenge in ensemble methods is obtaining meaningful inter-model diversity, with the standard approaches of random seeds, boosting, and bagging, providing comparatively weak diversity. Our novel strategy is to take QD's insight that diversity should be measured in a meaningful space, and identifying (in)variance axes as such a meaningful space for diversity measurement in visual pre-training. A second key issue for ensembles is fusing the ensemble prediction, which has been variously performed by unweighted prediction averaging [45] or parameter averaging [46], and feature concatenation in transfer learning [25, 68]. We show both empirically and theoretically the efficacy of learning a weighted combination of predictions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 428, + 132, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 428, + 132, + 441 + ], + "spans": [ + { + "bbox": [ + 55, + 428, + 132, + 441 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 446, + 130, + 458 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 446, + 130, + 458 + ], + "spans": [ + { + "bbox": [ + 55, + 446, + 130, + 458 + ], + "type": "text", + "content": "3.1. Background" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 463, + 280, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 463, + 280, + 497 + ], + "spans": [ + { + "bbox": [ + 54, + 463, + 280, + 497 + ], + "type": "text", + "content": "Mainstream QD optimization [27, 51] searches for a diverse set of solutions " + }, + { + "bbox": [ + 54, + 463, + 280, + 497 + ], + "type": "inline_equation", + "content": "\\{\\theta_i\\}" + }, + { + "bbox": [ + 54, + 463, + 280, + 497 + ], + "type": "text", + "content": " to an optimization problem " + }, + { + "bbox": [ + 54, + 463, + 280, + 497 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_q" + }, + { + "bbox": [ + 54, + 463, + 280, + 497 + ], + "type": "text", + "content": " by solving an objective like" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 501, + 280, + 525 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 501, + 280, + 525 + ], + "spans": [ + { + "bbox": [ + 104, + 501, + 280, + 525 + ], + "type": "interline_equation", + "content": "\\min _ {\\{\\theta_ {i} \\}} \\sum_ {i} \\mathcal {L} _ {q} (\\theta_ {i}) s. t. D (\\{\\pi (\\theta_ {i}) \\}), \\tag {1}", + "image_path": "9c6c0302ac8d1355a36829fd15f4f61f9564fe574f5fbf47ad58cd93316bdf01.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 528, + 281, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 528, + 281, + 629 + ], + "spans": [ + { + "bbox": [ + 54, + 528, + 281, + 629 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 54, + 528, + 281, + 629 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 54, + 528, + 281, + 629 + ], + "type": "text", + "content": " is a vector of application relevant observable properties of a given solution " + }, + { + "bbox": [ + 54, + 528, + 281, + 629 + ], + "type": "inline_equation", + "content": "\\theta_{i}" + }, + { + "bbox": [ + 54, + 528, + 281, + 629 + ], + "type": "text", + "content": " that is called phenotype in the QD community. " + }, + { + "bbox": [ + 54, + 528, + 281, + 629 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 54, + 528, + 281, + 629 + ], + "type": "text", + "content": " is a diversity constraint that enforces diversity among the solutions. It is often enforced by tessellation, or gridding, the space of " + }, + { + "bbox": [ + 54, + 528, + 281, + 629 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 54, + 528, + 281, + 629 + ], + "type": "text", + "content": ". Thus solution sets " + }, + { + "bbox": [ + 54, + 528, + 281, + 629 + ], + "type": "inline_equation", + "content": "\\{\\theta_i\\}" + }, + { + "bbox": [ + 54, + 528, + 281, + 629 + ], + "type": "text", + "content": " have the maximum possible quality " + }, + { + "bbox": [ + 54, + 528, + 281, + 629 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_q)" + }, + { + "bbox": [ + 54, + 528, + 281, + 629 + ], + "type": "text", + "content": " while also covering the space of measurable differences in behaviour [27, 51]. To make such QD problems more efficient to solve in a vision context, we will relax them to" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 85, + 632, + 281, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 632, + 281, + 657 + ], + "spans": [ + { + "bbox": [ + 85, + 632, + 281, + 657 + ], + "type": "interline_equation", + "content": "\\min _ {\\{\\theta_ {i} \\}} \\sum_ {i} \\mathcal {L} _ {q} (\\theta_ {i}) - \\sum_ {i \\neq j} \\mathcal {L} _ {d i v} (\\pi (\\theta_ {i}), \\pi (\\theta_ {j}) \\}), \\tag {2}", + "image_path": "8ae38c4f31d6f04ce2d4b97e401d6c2bdcc4ce9c7425fb1931acbd5930cd1e8f.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 661, + 255, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 661, + 255, + 672 + ], + "spans": [ + { + "bbox": [ + 55, + 661, + 255, + 672 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 661, + 255, + 672 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{div}" + }, + { + "bbox": [ + 55, + 661, + 255, + 672 + ], + "type": "text", + "content": " is a loss that measures pairwise distance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 677, + 162, + 690 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 677, + 162, + 690 + ], + "spans": [ + { + "bbox": [ + 55, + 677, + 162, + 690 + ], + "type": "text", + "content": "3.2. Visual Pre-training" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 694, + 281, + 718 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 694, + 281, + 718 + ], + "spans": [ + { + "bbox": [ + 55, + 694, + 281, + 718 + ], + "type": "text", + "content": "We denote a large dataset for pre-training by " + }, + { + "bbox": [ + 55, + 694, + 281, + 718 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_t\\subset" + }, + { + "bbox": [ + 55, + 694, + 281, + 718 + ], + "type": "inline_equation", + "content": "\\mathcal{X}\\times \\mathcal{Y}" + }, + { + "bbox": [ + 55, + 694, + 281, + 718 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 55, + 694, + 281, + 718 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 55, + 694, + 281, + 718 + ], + "type": "text", + "content": " is some space of input images and the" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "spans": [ + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "text", + "content": "space " + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "text", + "content": " may be contain labels obtained from manual annotation or pre-text tasks from self-supervision. We introduce a population of " + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "text", + "content": " feature extractors, represented as an ensemble, " + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "inline_equation", + "content": "\\mathcal{F} = \\{f_{\\theta_i}\\}_{i=1}^N" + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "text", + "content": ", which aim to learn a diverse set of invariances while maintaining high quality. Each member of the ensemble is followed by a projection layer " + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "inline_equation", + "content": "g_{\\phi_i}" + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "text", + "content": " which can be a classifier layer in case of supervised learning or a projection head in case of self-supervised learning [14, 30, 16]. We denote a set of " + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "text", + "content": " augmentations considered for pre-training as " + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "text", + "content": ". Let us also denote a sample " + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "text", + "content": " transformed by augmentation " + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_j \\in \\mathcal{T}" + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{x}}^j" + }, + { + "bbox": [ + 296, + 117, + 523, + 243 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 254, + 477, + 267 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 254, + 477, + 267 + ], + "spans": [ + { + "bbox": [ + 296, + 254, + 477, + 267 + ], + "type": "text", + "content": "3.2.1 QD for Visual Pre-training: Diversity" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 272, + 523, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 272, + 523, + 407 + ], + "spans": [ + { + "bbox": [ + 296, + 272, + 523, + 407 + ], + "type": "text", + "content": "To quantify the diversity of solutions during pre-training, we must first define a phenotype — an observable measurement of a feature extractor's behaviour. We define the behavior of a solution by the degree of invariance it shows to a set of augmentations " + }, + { + "bbox": [ + 296, + 272, + 523, + 407 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 296, + 272, + 523, + 407 + ], + "type": "text", + "content": ". We borrow the definition of invariance from [25], where invariance of a model to a particular data augmentation is defined as the cosine similarity " + }, + { + "bbox": [ + 296, + 272, + 523, + 407 + ], + "type": "inline_equation", + "content": "S(f_{\\theta}(\\mathbf{x}),f_{\\theta}(\\tilde{\\mathbf{x}}^{j}))" + }, + { + "bbox": [ + 296, + 272, + 523, + 407 + ], + "type": "text", + "content": " between augmented and unaugmented features. Thus, we define a phenotype of a solution " + }, + { + "bbox": [ + 296, + 272, + 523, + 407 + ], + "type": "inline_equation", + "content": "f_{\\theta_i}" + }, + { + "bbox": [ + 296, + 272, + 523, + 407 + ], + "type": "text", + "content": " as a vector " + }, + { + "bbox": [ + 296, + 272, + 523, + 407 + ], + "type": "inline_equation", + "content": "\\pi (\\mathbf{x};\\theta_i)\\in \\mathbb{R}^K" + }, + { + "bbox": [ + 296, + 272, + 523, + 407 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 296, + 272, + 523, + 407 + ], + "type": "inline_equation", + "content": "j^{\\mathrm{th}}" + }, + { + "bbox": [ + 296, + 272, + 523, + 407 + ], + "type": "text", + "content": " element of the phenotype vector indicates the invariance that the model exhibits to augmentation " + }, + { + "bbox": [ + 296, + 272, + 523, + 407 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_j\\in \\mathcal{T}" + }, + { + "bbox": [ + 296, + 272, + 523, + 407 + ], + "type": "text", + "content": ", as shown in Eq 3." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 340, + 415, + 521, + 439 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 415, + 521, + 439 + ], + "spans": [ + { + "bbox": [ + 340, + 415, + 521, + 439 + ], + "type": "interline_equation", + "content": "\\pi (\\mathbf {x}; \\theta_ {i}) = \\left(S \\left(f _ {\\theta_ {i}} (\\mathbf {x}), f _ {\\theta_ {i}} \\left(\\tilde {\\mathbf {x}} ^ {j}\\right)\\right) _ {j = 1} ^ {| \\mathcal {T} |} \\right. \\tag {3}", + "image_path": "4fed6e50846cc62de72f3eb7a3e34c37fe1ec5ba633e180a99788e7336d8cbe0.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 446, + 523, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 446, + 523, + 503 + ], + "spans": [ + { + "bbox": [ + 296, + 446, + 523, + 503 + ], + "type": "text", + "content": "Diversity Loss: Based on the above phenotype definition, we can encourage each model to exhibit a diverse combination of invariances to augmentations in " + }, + { + "bbox": [ + 296, + 446, + 523, + 503 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 296, + 446, + 523, + 503 + ], + "type": "text", + "content": ". Specifically, we minimise the negative exponential distance between phenotype vector of each member as in Eq 4" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 326, + 510, + 521, + 542 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 510, + 521, + 542 + ], + "spans": [ + { + "bbox": [ + 326, + 510, + 521, + 542 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {d i v e r s i t y}} = \\sum_ {i \\neq j} ^ {N} \\exp (- | \\pi (\\mathbf {x}; \\theta_ {i}) - \\pi (\\mathbf {x}; \\theta_ {j}) |) \\tag {4}", + "image_path": "aa648ce49f694482432c995e29210b2b810a00c7cbca58432a4556da40021229.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 297, + 555, + 470, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 555, + 470, + 567 + ], + "spans": [ + { + "bbox": [ + 297, + 555, + 470, + 567 + ], + "type": "text", + "content": "3.2.2 QD for visual pre-training: Quality" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 572, + 523, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 572, + 523, + 653 + ], + "spans": [ + { + "bbox": [ + 296, + 572, + 523, + 653 + ], + "type": "text", + "content": "Quality Loss: Depending on the pre-training paradigm employed, different loss functions can be used to promote high quality. In the case of supervised learning, the loss function denoted by " + }, + { + "bbox": [ + 296, + 572, + 523, + 653 + ], + "type": "inline_equation", + "content": "l_{q}" + }, + { + "bbox": [ + 296, + 572, + 523, + 653 + ], + "type": "text", + "content": " can be cross-entropy, while self-supervised methods such as SimCLR/MoCo use contrastive loss [48]. The loss function for the entire ensemble for a sample " + }, + { + "bbox": [ + 296, + 572, + 523, + 653 + ], + "type": "inline_equation", + "content": "(\\mathbf{x},y)\\in \\mathcal{D}" + }, + { + "bbox": [ + 296, + 572, + 523, + 653 + ], + "type": "text", + "content": " is given in Eq. 5" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 342, + 659, + 521, + 691 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 659, + 521, + 691 + ], + "spans": [ + { + "bbox": [ + 342, + 659, + 521, + 691 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {q u a l i t y}} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} l _ {q} \\left(g _ {\\phi_ {i}} \\left(f _ {\\theta_ {i}} (\\mathbf {x})\\right), y\\right) \\tag {5}", + "image_path": "2a0a8ceb8e1024b466b1f0ebde5b1b8cec9bd68705da74bf1d0e5d15afef25e8.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 297, + 694, + 522, + 718 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 694, + 522, + 718 + ], + "spans": [ + { + "bbox": [ + 297, + 694, + 522, + 718 + ], + "type": "text", + "content": "This objective reflects standard supervised or self-supervised learning of the upstream model. Empirically," + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 740, + 298, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 740, + 298, + 750 + ], + "spans": [ + { + "bbox": [ + 279, + 740, + 298, + 750 + ], + "type": "text", + "content": "5386" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 110, + 118, + 473, + 242 + ], + "blocks": [ + { + "bbox": [ + 110, + 118, + 473, + 242 + ], + "lines": [ + { + "bbox": [ + 110, + 118, + 473, + 242 + ], + "spans": [ + { + "bbox": [ + 110, + 118, + 473, + 242 + ], + "type": "image", + "image_path": "a26cfa82aad76becfd979cfaa06ce11d9af9aaf2f9a1303150a0b36d0865fbe8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 245, + 522, + 279 + ], + "lines": [ + { + "bbox": [ + 54, + 245, + 522, + 279 + ], + "spans": [ + { + "bbox": [ + 54, + 245, + 522, + 279 + ], + "type": "text", + "content": "Figure 2. Schematic illustration of Quality Diversity Pre-training, shown with only 2 augmentations for simplicity. " + }, + { + "bbox": [ + 54, + 245, + 522, + 279 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{diversity}}" + }, + { + "bbox": [ + 54, + 245, + 522, + 279 + ], + "type": "text", + "content": " maximises the difference between invariances that models exhibit to " + }, + { + "bbox": [ + 54, + 245, + 522, + 279 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_1" + }, + { + "bbox": [ + 54, + 245, + 522, + 279 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 245, + 522, + 279 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_2" + }, + { + "bbox": [ + 54, + 245, + 522, + 279 + ], + "type": "text", + "content": ", while " + }, + { + "bbox": [ + 54, + 245, + 522, + 279 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{quality}} + \\lambda_{kl}\\mathcal{L}_{KL}" + }, + { + "bbox": [ + 54, + 245, + 522, + 279 + ], + "type": "text", + "content": " maximises the quality of the ensemble by pushing it to the quality of a conventionally pre-trained model (denoted by Baseline)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 295, + 281, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 295, + 281, + 418 + ], + "spans": [ + { + "bbox": [ + 54, + 295, + 281, + 418 + ], + "type": "text", + "content": "we found that purely using this quality objective it is hard for a diverse ensemble to match the quality of a baseline model trained solely for quality. To help the diverse ensemble match the quality of the baseline we introduce an additional loss term, which is the Kullback-Leibler (KL) divergence between the posteriors of the ensemble members and baseline model with parameters " + }, + { + "bbox": [ + 54, + 295, + 281, + 418 + ], + "type": "inline_equation", + "content": "\\phi_{b}" + }, + { + "bbox": [ + 54, + 295, + 281, + 418 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 295, + 281, + 418 + ], + "type": "inline_equation", + "content": "\\theta_{b}" + }, + { + "bbox": [ + 54, + 295, + 281, + 418 + ], + "type": "text", + "content": ". We denote the predictions of a model by " + }, + { + "bbox": [ + 54, + 295, + 281, + 418 + ], + "type": "inline_equation", + "content": "\\hat{y}_i = g_{\\phi_i}(f_{\\theta_i}(x))" + }, + { + "bbox": [ + 54, + 295, + 281, + 418 + ], + "type": "text", + "content": ". The loss function is shown in Eq. 6. This term ensures that the members of the ensemble mimic the predictions of the baseline model, thus ensuring high quality with diverse invariances." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 77, + 437, + 280, + 470 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 437, + 280, + 470 + ], + "spans": [ + { + "bbox": [ + 77, + 437, + 280, + 470 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {q u a l i t y - K L}} = \\sum_ {i = 1} ^ {N} \\frac {1}{m} \\sum_ {j = 1} ^ {m} \\mathrm {K L} \\left(\\sigma \\left(\\hat {y} _ {i}; \\tau\\right) \\| \\sigma \\left(\\hat {y} _ {b}; \\tau\\right)\\right) \\tag {6}", + "image_path": "1d7e71e44eecacf67ac0a0068dfd75f19d915a387199c02a7ea89dce64c89a2d.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 477, + 280, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 477, + 280, + 500 + ], + "spans": [ + { + "bbox": [ + 55, + 477, + 280, + 500 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 55, + 477, + 280, + 500 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 55, + 477, + 280, + 500 + ], + "type": "text", + "content": " denotes the softmax function and " + }, + { + "bbox": [ + 55, + 477, + 280, + 500 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 55, + 477, + 280, + 500 + ], + "type": "text", + "content": " denotes the temperature used to scale the logits within softmax." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 502, + 280, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 502, + 280, + 537 + ], + "spans": [ + { + "bbox": [ + 55, + 502, + 280, + 537 + ], + "type": "text", + "content": "Summary Finally, to achieve our goal of diverse invariances and high quality in QD4V pre-training, we formulate a total loss function asin Eq. 7." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 85, + 558, + 280, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 558, + 280, + 571 + ], + "spans": [ + { + "bbox": [ + 85, + 558, + 280, + 571 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {q d} = \\mathcal {L} _ {\\text {q u a l i t y}} + \\lambda_ {k l} \\mathcal {L} _ {\\text {q u a l i t y - K L}} + \\lambda_ {d} \\mathcal {L} _ {\\text {d i v e r s i t y}} \\tag {7}", + "image_path": "3db6f92c4e19f3e89db94147ed2988e3b77d5c0a2e5811e1fd369489b6b7855f.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 579, + 280, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 579, + 280, + 613 + ], + "spans": [ + { + "bbox": [ + 55, + 579, + 280, + 613 + ], + "type": "text", + "content": "The diverse set of optimal solutions learned from the proposed QD pre-training stage denoted as " + }, + { + "bbox": [ + 55, + 579, + 280, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^*" + }, + { + "bbox": [ + 55, + 579, + 280, + 613 + ], + "type": "text", + "content": " is then transferred to a downstream task." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 621, + 197, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 621, + 197, + 634 + ], + "spans": [ + { + "bbox": [ + 55, + 621, + 197, + 634 + ], + "type": "text", + "content": "3.3. Downstream task Learning" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 639, + 281, + 718 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 639, + 281, + 718 + ], + "spans": [ + { + "bbox": [ + 55, + 639, + 281, + 718 + ], + "type": "text", + "content": "We next address how to construct models for downstream tasks given the diverse ensemble of features " + }, + { + "bbox": [ + 55, + 639, + 281, + 718 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^*" + }, + { + "bbox": [ + 55, + 639, + 281, + 718 + ], + "type": "text", + "content": " produced by pre-training in the previous section. Existing approaches have concatenated features prior to linear readout [68], or conducted unweighted averaging of ensemble features [45]. We propose to fuse the ensemble via a variant of stacking [66]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 295, + 522, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 295, + 522, + 339 + ], + "spans": [ + { + "bbox": [ + 296, + 295, + 522, + 339 + ], + "type": "text", + "content": "Decoder Design For each feature extractor, " + }, + { + "bbox": [ + 296, + 295, + 522, + 339 + ], + "type": "inline_equation", + "content": "f_{\\theta_i} \\in \\mathcal{F}" + }, + { + "bbox": [ + 296, + 295, + 522, + 339 + ], + "type": "text", + "content": " we follow the standard linear readout approach, and build a linear model, " + }, + { + "bbox": [ + 296, + 295, + 522, + 339 + ], + "type": "inline_equation", + "content": "h^{(i)}" + }, + { + "bbox": [ + 296, + 295, + 522, + 339 + ], + "type": "text", + "content": ", parameterised by " + }, + { + "bbox": [ + 296, + 295, + 522, + 339 + ], + "type": "inline_equation", + "content": "U^{(i)} \\in \\mathbb{R}^{k \\times d}" + }, + { + "bbox": [ + 296, + 295, + 522, + 339 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 295, + 522, + 339 + ], + "type": "inline_equation", + "content": "\\mathbf{b}^{(i)} \\in \\mathbb{R}^k" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 347, + 343, + 472, + 358 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 343, + 472, + 358 + ], + "spans": [ + { + "bbox": [ + 347, + 343, + 472, + 358 + ], + "type": "interline_equation", + "content": "h ^ {(i)} (\\mathbf {x}) = \\rho (U ^ {(i)} f _ {\\theta_ {i}} (\\mathbf {x}) + \\mathbf {b} ^ {(i)}),", + "image_path": "98d9ae1e32dffb91aadae757299b63676e92adf81791c4e14a27a599c0da1669.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 361, + 522, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 361, + 522, + 417 + ], + "spans": [ + { + "bbox": [ + 296, + 361, + 522, + 417 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 361, + 522, + 417 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 296, + 361, + 522, + 417 + ], + "type": "text", + "content": " is a transfer function for linear models (e.g., the softmax function or identity). To produce a final prediction we fuse the ensemble of classifiers " + }, + { + "bbox": [ + 296, + 361, + 522, + 417 + ], + "type": "inline_equation", + "content": "h^{(i)}(x)" + }, + { + "bbox": [ + 296, + 361, + 522, + 417 + ], + "type": "text", + "content": " by learning a weight vector, " + }, + { + "bbox": [ + 296, + 361, + 522, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{w} \\in \\mathbb{R}^N" + }, + { + "bbox": [ + 296, + 361, + 522, + 417 + ], + "type": "text", + "content": " that is used to make a linear combination of their predictions," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 365, + 422, + 453, + 453 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 422, + 453, + 453 + ], + "spans": [ + { + "bbox": [ + 365, + 422, + 453, + 453 + ], + "type": "interline_equation", + "content": "h (\\mathbf {x}) = \\sum_ {i = 1} ^ {N} w _ {i} h ^ {(i)} (\\mathbf {x}).", + "image_path": "c027bfc7def994c8405328977c00618ade8bdb32c17555ed2310e91d56e37f25.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "spans": [ + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "text", + "content": "Decoder Training Strategy For each downstream task have a collection of data, " + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{ds}" + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "text", + "content": ", which we split into two nonoverlapping subsets, " + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{tr}" + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{val}" + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "text", + "content": ". The hyperparameters of the linear models are tuned using this train-validation split, and the best model parameters found during this tuning phase are denoted by " + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "inline_equation", + "content": "\\tilde{U}^{(i)}" + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{b}}^{(i)}" + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "text", + "content": ". Each model is retrained using the full " + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{ds}" + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "text", + "content": " dataset using the best hyperparameters to obtain the final values for each " + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "inline_equation", + "content": "U^{(i)}" + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "inline_equation", + "content": "\\mathbf{b}^{(i)}" + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "text", + "content": ". The procedure used to fit the weights for linearly combining the models is carried out using the " + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "inline_equation", + "content": "\\tilde{U}^{(i)}" + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{b}}^{(i)}" + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "text", + "content": " parameters, and " + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "text", + "content": " is fit on the " + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{val}" + }, + { + "bbox": [ + 296, + 455, + 522, + 579 + ], + "type": "text", + "content": " set," + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 297, + 582, + 521, + 627 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 582, + 521, + 627 + ], + "spans": [ + { + "bbox": [ + 297, + 582, + 521, + 627 + ], + "type": "interline_equation", + "content": "\\mathbf {w} = \\underset {\\mathbf {v} \\in \\mathbb {R} ^ {N}} {\\arg \\min } \\mathbb {E} _ {\\mathcal {D} _ {v a l}} \\left[ \\left\\| \\sum_ {i = 1} ^ {N} v _ {i} \\rho \\left(\\tilde {U} ^ {(i)} f _ {\\theta_ {i}} (\\mathbf {x}) + \\tilde {\\mathbf {b}} ^ {(i)}\\right) - y \\right\\| _ {2} ^ {2} \\right] \\tag {8}", + "image_path": "b09200ecc4efb8b08b5b9e6f26ec22566e059b7f1a8dc0326bc5e0075d918105.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 628, + 522, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 628, + 522, + 672 + ], + "spans": [ + { + "bbox": [ + 296, + 628, + 522, + 672 + ], + "type": "text", + "content": "In the following section, we provide theoretical justification for our proposed downstream architecture and training strategy by way of bounding the generalisation error for downstream tasks learned in this way." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 297, + 677, + 409, + 690 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 677, + 409, + 690 + ], + "spans": [ + { + "bbox": [ + 297, + 677, + 409, + 690 + ], + "type": "text", + "content": "3.4. Theoretical Analysis" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 297, + 695, + 522, + 718 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 695, + 522, + 718 + ], + "spans": [ + { + "bbox": [ + 297, + 695, + 522, + 718 + ], + "type": "text", + "content": "For ease of exposition, consider the case where " + }, + { + "bbox": [ + 297, + 695, + 522, + 718 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 297, + 695, + 522, + 718 + ], + "type": "text", + "content": " is the identity and the underlying problem is binary classification." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 740, + 298, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 740, + 298, + 750 + ], + "spans": [ + { + "bbox": [ + 279, + 740, + 298, + 750 + ], + "type": "text", + "content": "5387" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 117, + 281, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 117, + 281, + 152 + ], + "spans": [ + { + "bbox": [ + 55, + 117, + 281, + 152 + ], + "type": "text", + "content": "In this case, each " + }, + { + "bbox": [ + 55, + 117, + 281, + 152 + ], + "type": "inline_equation", + "content": "U^{(i)}" + }, + { + "bbox": [ + 55, + 117, + 281, + 152 + ], + "type": "text", + "content": " can be written as a vector, " + }, + { + "bbox": [ + 55, + 117, + 281, + 152 + ], + "type": "inline_equation", + "content": "\\mathbf{u}^{(i)}" + }, + { + "bbox": [ + 55, + 117, + 281, + 152 + ], + "type": "text", + "content": ". We can define the effective hypothesis class of our algorithm for learning on downstream tasks as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 67, + 162, + 270, + 223 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 162, + 270, + 223 + ], + "spans": [ + { + "bbox": [ + 67, + 162, + 270, + 223 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {H} = \\left\\{\\mathbf {x} \\rightarrow \\sum_ {i = 1} ^ {N} w _ {i} \\langle \\mathbf {u} ^ {(i)}, f _ {\\theta_ {i}} (\\mathbf {x}) \\rangle : \\right. \\\\ \\left. \\left\\| \\mathbf {w} - \\mathbb {E} [ \\mathbf {w} ] \\right\\| _ {2} \\leq A, \\left\\| \\mathbf {u} ^ {(i)} - \\mathbb {E} [ \\mathbf {u} ^ {(i)} ] \\right\\| _ {F} \\leq B \\right\\}, \\\\ \\end{array}", + "image_path": "74cf291429680b8ced0ee4b94f7ac30616561ac15676df17092781283179cec8.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "spans": [ + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "text", + "content": "where we have absorbed the bias values into " + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "inline_equation", + "content": "\\mathbf{u}" + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "text", + "content": " by assuming a 1 has been appended to each " + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "text", + "content": ". Our goal is to bound the generalisation error of models from this class trained using our stacking procedure in Sec 3.3. The first step is to bound the empirical Rademacher complexity in terms of " + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "text", + "content": " (from the definition of " + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "text", + "content": "), the norm of the features, and the total amount of data available for the downstream task, " + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "inline_equation", + "content": "m = |\\mathcal{D}_{ds}|" + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "text", + "content": ". We then show how the stacking procedure influences the values of " + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "text", + "content": ". We use " + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "text", + "content": " to indicate the fraction of data used for training, hence " + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "inline_equation", + "content": "\\eta m = |\\mathcal{D}_{tr}|" + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "inline_equation", + "content": "(1 - \\eta)m = |\\mathcal{D}_{val}|" + }, + { + "bbox": [ + 55, + 232, + 281, + 356 + ], + "type": "text", + "content": ". Our main result in given below." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 364, + 281, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 364, + 281, + 397 + ], + "spans": [ + { + "bbox": [ + 55, + 364, + 281, + 397 + ], + "type": "text", + "content": "Theorem 1. For a model trained using our stacking procedure and the conditions outlined in the statements of Lemmas 1 and 2, we have with probability at least " + }, + { + "bbox": [ + 55, + 364, + 281, + 397 + ], + "type": "inline_equation", + "content": "1 - 2\\delta" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 64, + 407, + 271, + 528 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 407, + 271, + 528 + ], + "spans": [ + { + "bbox": [ + 64, + 407, + 271, + 528 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbb {E} [ \\mathbf {1} [ \\operatorname {s g n} (h (\\mathbf {x})) \\neq y) ] \\leq \\hat {\\mathbb {E}} [ l (h (\\mathbf {x}), y) ] \\\\ + \\frac {1 2 X ^ {3} \\| \\tilde {V} \\| _ {2} \\sqrt {\\ln (4 / \\delta) \\ln (4 N / \\delta)}}{\\gamma_ {1} \\gamma_ {2} \\sqrt {1 - \\eta m ^ {3 / 2}}} \\\\ + \\frac {2 X ^ {2} \\sqrt {2 \\ln (4 N / \\delta)}}{\\gamma_ {1} m} \\\\ + \\frac {2 X ^ {2} \\| \\tilde {V} \\| _ {2} \\sqrt {2 \\ln (4 / \\delta)}}{\\gamma_ {2} \\sqrt {1 - \\eta m}} \\\\ + 3 \\sqrt {\\frac {\\ln (1 / \\delta)}{2 m}}, \\\\ \\end{array}", + "image_path": "60b8012cce119270a14656859df1844482adf071ed4b26f59f17265bca7c4d6c.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 539, + 279, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 539, + 279, + 563 + ], + "spans": [ + { + "bbox": [ + 55, + 539, + 279, + 563 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 55, + 539, + 279, + 563 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbb{E}}[l(h(\\mathbf{x}), y)]" + }, + { + "bbox": [ + 55, + 539, + 279, + 563 + ], + "type": "text", + "content": " is the mean ramp loss of the model " + }, + { + "bbox": [ + 55, + 539, + 279, + 563 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 55, + 539, + 279, + 563 + ], + "type": "text", + "content": ", computed on the training data." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 571, + 279, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 571, + 279, + 627 + ], + "spans": [ + { + "bbox": [ + 55, + 571, + 279, + 627 + ], + "type": "text", + "content": "Notably, this bound achieves the \"fast\" rate of convergence, " + }, + { + "bbox": [ + 55, + 571, + 279, + 627 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(m^{-1})" + }, + { + "bbox": [ + 55, + 571, + 279, + 627 + ], + "type": "text", + "content": ", in the complexity terms, with the first term even exhibiting a super-fast rate of " + }, + { + "bbox": [ + 55, + 571, + 279, + 627 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(m^{-3/2})" + }, + { + "bbox": [ + 55, + 571, + 279, + 627 + ], + "type": "text", + "content": ". This is in contrast to the standard " + }, + { + "bbox": [ + 55, + 571, + 279, + 627 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(m^{-1/2})" + }, + { + "bbox": [ + 55, + 571, + 279, + 627 + ], + "type": "text", + "content": " rate in existing bounds. The proof is in the supplemental material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 628, + 280, + 718 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 628, + 280, + 718 + ], + "spans": [ + { + "bbox": [ + 55, + 628, + 280, + 718 + ], + "type": "text", + "content": "Discussion This theorem depends on both the specific architecture and optimisation strategy outlined in Sec. 3.3, and thus provides justification for these design choices. It says that the generalisation gap between train error and expected (test) error rapidly goes to zero with the size of the downstream train set " + }, + { + "bbox": [ + 55, + 628, + 280, + 718 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 55, + 628, + 280, + 718 + ], + "type": "text", + "content": ". Furthermore, because we have access to an ensemble of features, the train error " + }, + { + "bbox": [ + 55, + 628, + 280, + 718 + ], + "type": "inline_equation", + "content": "\\hat{e} r(h)" + }, + { + "bbox": [ + 55, + 628, + 280, + 718 + ], + "type": "text", + "content": " can likely be reduced below that of a single feature." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 297, + 116, + 422, + 130 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 116, + 422, + 130 + ], + "spans": [ + { + "bbox": [ + 297, + 116, + 422, + 130 + ], + "type": "text", + "content": "4. Implementation details" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 135, + 522, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 135, + 522, + 269 + ], + "spans": [ + { + "bbox": [ + 296, + 135, + 522, + 269 + ], + "type": "text", + "content": "Pre-training: We perform supervised training for ResNet50 and ConvNeXt [42] on ImageNet1K [21] and contrastive training for ResNet50 on both ImageNet1K and ImageNet100 [68]. To learn our feature ensemble, in a parameter efficient way for both architectures, we share the first three layers (layer1, layer2, layer3 according to [65]), after which different members of the ensemble branch out into their own sequence of layers having a separate layer4 and projection head. We initialise the entire ensemble with ImageNet pre-trained models in case of supervised pre-training and MoCo pre-trained models in case of contrastive learning." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 269, + 522, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 269, + 522, + 348 + ], + "spans": [ + { + "bbox": [ + 296, + 269, + 522, + 348 + ], + "type": "text", + "content": "Augmentations: For supervised pre-training, most methods that rely on strong augmentation policies. Our approach applies the quality loss (Eq. 5) to unaugmented samples only as using augmented samples for quality maximisation would lead to typical strong invariance to all augmentations and prevent diversity. For contrastive learning, we apply very weak augmentations for instance discrimination." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 349, + 522, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 349, + 522, + 426 + ], + "spans": [ + { + "bbox": [ + 296, + 349, + 522, + 426 + ], + "type": "text", + "content": "Learning rates and Optimisers: For supervised pretraining and contrastive learning experiments, we train the model for 20 epochs with SGD and AdamW optimizers respectively, along with learning rate warm-up for 5 epochs, followed by a cosine decay schedule. For supervised pretraining, we apply label smoothening and perform exponential moving average (EMA) on the model weights." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 426, + 522, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 426, + 522, + 470 + ], + "spans": [ + { + "bbox": [ + 296, + 426, + 522, + 470 + ], + "type": "text", + "content": "Downstream tasks: Our suite of downstream tasks consists of object recognition, regression, and dense estimation. We provide more details about downstream tasks in the supplementary material." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 308, + 480, + 522, + 674 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 308, + 480, + 522, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 480, + 522, + 526 + ], + "spans": [ + { + "bbox": [ + 308, + 480, + 522, + 526 + ], + "type": "text", + "content": "- Classification: For classification, we evaluate on standard benchmarks CIFAR10/100 [36], Caltech101 [26], Oxford Flowers [47], Stanford Cars [35], Describable Textures Dataset (DTD) [17], Aircraft [43]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 308, + 532, + 522, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 532, + 522, + 600 + ], + "spans": [ + { + "bbox": [ + 308, + 532, + 522, + 600 + ], + "type": "text", + "content": "- Regression: We include a set of spatially sensitive tasks including facial landmark detection on 300W [1], CelebA [41], human pose estimation in LSP [33] and MPII [2], Animal Pose prediction [10], AROI object orientation prediction [29], and Causal3DIdent 6D pose and appearance attribute prediction [60]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 308, + 607, + 522, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 607, + 522, + 674 + ], + "spans": [ + { + "bbox": [ + 308, + 607, + 522, + 674 + ], + "type": "text", + "content": "- Dense estimation: We also evaluate the QD pretrained models on dense estimation tasks like Pascal VOC object detection using Faster R-CNN [55] with a Feature Pyramid Network backbone [39] and linear semantic segmentation similar to [4] on CityScapes and ADE20k [7] datasets." + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 296, + 683, + 522, + 718 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 683, + 522, + 718 + ], + "spans": [ + { + "bbox": [ + 296, + 683, + 522, + 718 + ], + "type": "text", + "content": "Downstream evaluation: For classification and regression tasks, we fit multinomial logistic regression and multi-output linear regression on the extracted features from each" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 740, + 298, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 740, + 298, + 750 + ], + "spans": [ + { + "bbox": [ + 279, + 740, + 298, + 750 + ], + "type": "text", + "content": "5388" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 143, + 129, + 281, + 270 + ], + "blocks": [ + { + "bbox": [ + 143, + 129, + 281, + 270 + ], + "lines": [ + { + "bbox": [ + 143, + 129, + 281, + 270 + ], + "spans": [ + { + "bbox": [ + 143, + 129, + 281, + 270 + ], + "type": "image", + "image_path": "e4a8775b0e435dfecb73edc415b4ed4271ca73984c7216d3b5595ad6384be519.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 280, + 521, + 312 + ], + "lines": [ + { + "bbox": [ + 54, + 280, + 521, + 312 + ], + "spans": [ + { + "bbox": [ + 54, + 280, + 521, + 312 + ], + "type": "text", + "content": "Figure 3. Radar plot comparing invariance w.r.t. for 4 Spatial and 4 Appearance based transformations of baseline models (green) and QD ensemble (dots). The red and blue lines correspond to maximum and minimum invariances within QD ensemble. The blue shaded region corresponds to the range of invariances spanned by the QD ensemble, which encompasses the (in)variance of the baselines." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 301, + 132, + 438, + 269 + ], + "blocks": [ + { + "bbox": [ + 286, + 132, + 314, + 147 + ], + "lines": [ + { + "bbox": [ + 286, + 132, + 314, + 147 + ], + "spans": [ + { + "bbox": [ + 286, + 132, + 314, + 147 + ], + "type": "text", + "content": "ax, invariance in, invariance aseline" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 301, + 132, + 438, + 269 + ], + "lines": [ + { + "bbox": [ + 301, + 132, + 438, + 269 + ], + "spans": [ + { + "bbox": [ + 301, + 132, + 438, + 269 + ], + "type": "image", + "image_path": "38133b78b2eacf8ba7ff6a5ef7e6ce946a1f36ae9de85fff83f4b5f555f0d5ca.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 57, + 319, + 523, + 430 + ], + "blocks": [ + { + "bbox": [ + 57, + 319, + 523, + 430 + ], + "lines": [ + { + "bbox": [ + 57, + 319, + 523, + 430 + ], + "spans": [ + { + "bbox": [ + 57, + 319, + 523, + 430 + ], + "type": "table", + "html": "
MethodsCIFAR10CIFAR100FlowersCaltech 101DTDCarsAircraft300wLS PoseCelebAAnimal PoseMPIIALOICausal3DRank
IN1K (RN50)Sup.Baseline90.468.285.284.771.944.436.070.255.449.011.218.024.164.12.7
Multihead90.367.384.884.169.943.235.068.353.250.110.917.022.862.33.7
Div. Ens. [23]91.672.984.689.369.842.735.366.652.649.211.517.922.660.83.4
MeTTA [3]91.071.685.385.171.841.134.065.352.847.910.516.323.161.23.8
QD4V90.370.486.989.972.245.436.976.662.461.512.518.528.472.81.4
MoCoMoCo90.370.689.887.973.939.341.887.269.092.513.919.946.078.11.9
Fusionx[25]95.0-81.086.0---65.068.033.0-----
QD4V88.971.285.288.275.841.343.988.971.895.214.222.447.480.61.2
Sup.Baseline (CN-T)89.470.694.589.168.052.548.463.148.152.511.517.78.0269.41.8
QD4V (CN-T)91.572.996.589.969.851.550.082.269.960.712.518.59.371.91.1
IN100Sup.MoCo84.661.682.477.364.533.937.285.558.761.013.218.630.961.43.5
AugSelf* [38]85.363.985.778.966.237.439.577.363.977.012.919.535.261.62.4
AI+ [13]81.364.681.378.468.838.637.390.065.282.012.521.632.762.62.5
QD4V84.565.485.581.271.939.837.988.969.785.014.320.633.865.31.5
", + "image_path": "f5c2efadd1b24454ad7c91be9fe0beee96dc753ab244e3c25bbddc9a980940a8.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 434, + 521, + 476 + ], + "lines": [ + { + "bbox": [ + 54, + 434, + 521, + 476 + ], + "spans": [ + { + "bbox": [ + 54, + 434, + 521, + 476 + ], + "type": "text", + "content": "Table 1. Downstream performance of ImageNet (IN1K) pretrained (1) Supervised ResNet50, (2) MoCo ResNet50 and ImageNet-100 (IN100) pretrained (3) Supervised ConvNeXt-Tiny (CN-T), (4) MoCo ResNet50. The first seven columns are classification tasks (accuracy, %); the last seven are regression (R2, %). + numbers from [13] where reported, * A mix of our runs and numbers from [13] where reported, x numbers from [25], rest are our runs." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 92, + 485, + 195, + 581 + ], + "blocks": [ + { + "bbox": [ + 92, + 485, + 195, + 581 + ], + "lines": [ + { + "bbox": [ + 92, + 485, + 195, + 581 + ], + "spans": [ + { + "bbox": [ + 92, + 485, + 195, + 581 + ], + "type": "image", + "image_path": "bd931b75b5c2cb2d33ac0599f4f84174c8a262e15c1dc9642153e1431bc61d45.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 195, + 485, + 292, + 581 + ], + "blocks": [ + { + "bbox": [ + 195, + 485, + 292, + 581 + ], + "lines": [ + { + "bbox": [ + 195, + 485, + 292, + 581 + ], + "spans": [ + { + "bbox": [ + 195, + 485, + 292, + 581 + ], + "type": "image", + "image_path": "01d25f18044af3245957d30a7e144a3bccb817a48ef62fbaf430fb431c3c6871.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 292, + 485, + 388, + 581 + ], + "blocks": [ + { + "bbox": [ + 292, + 485, + 388, + 581 + ], + "lines": [ + { + "bbox": [ + 292, + 485, + 388, + 581 + ], + "spans": [ + { + "bbox": [ + 292, + 485, + 388, + 581 + ], + "type": "image", + "image_path": "554f2d81bafbdde470aba1f2b7451404875c624d8878a3958cae359a28ee64dc.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 388, + 485, + 484, + 581 + ], + "blocks": [ + { + "bbox": [ + 388, + 485, + 484, + 581 + ], + "lines": [ + { + "bbox": [ + 388, + 485, + 484, + 581 + ], + "spans": [ + { + "bbox": [ + 388, + 485, + 484, + 581 + ], + "type": "image", + "image_path": "d3e5e413be75d85167d01028f89519ea5a876830fce657a1ad1a2fbc7ac85567.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 94, + 582, + 195, + 678 + ], + "blocks": [ + { + "bbox": [ + 94, + 582, + 195, + 678 + ], + "lines": [ + { + "bbox": [ + 94, + 582, + 195, + 678 + ], + "spans": [ + { + "bbox": [ + 94, + 582, + 195, + 678 + ], + "type": "image", + "image_path": "7ad8e6555d1f36d8ff6eeb554656228b6026412445e818cf1afda406605b5fdf.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 683, + 521, + 715 + ], + "lines": [ + { + "bbox": [ + 54, + 683, + 521, + 715 + ], + "spans": [ + { + "bbox": [ + 54, + 683, + 521, + 715 + ], + "type": "text", + "content": "Figure 4. Correlation between our classifier fusion weights (Eq 8) and task for 4 Spatial and 4 Appearance based augmentations. The y-axis corresponds to Pearson's r correlation between w assigned to each member by a particular task and invariances exhibited by that member to specific augmentations. Tasks are grouped by classification and regression, which tend to show different invariance preferences." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 196, + 582, + 292, + 678 + ], + "blocks": [ + { + "bbox": [ + 196, + 582, + 292, + 678 + ], + "lines": [ + { + "bbox": [ + 196, + 582, + 292, + 678 + ], + "spans": [ + { + "bbox": [ + 196, + 582, + 292, + 678 + ], + "type": "image", + "image_path": "1b4bc6146307adb9e768040023f6a7fc69f778d1722b85b57360ef37bc306448.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 292, + 582, + 387, + 678 + ], + "blocks": [ + { + "bbox": [ + 292, + 582, + 387, + 678 + ], + "lines": [ + { + "bbox": [ + 292, + 582, + 387, + 678 + ], + "spans": [ + { + "bbox": [ + 292, + 582, + 387, + 678 + ], + "type": "image", + "image_path": "ddead2bdabe21de978f52c6a0ab982b52304e3b1d43410b368d3469c51334a94.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 388, + 582, + 484, + 678 + ], + "blocks": [ + { + "bbox": [ + 388, + 582, + 484, + 678 + ], + "lines": [ + { + "bbox": [ + 388, + 582, + 484, + 678 + ], + "spans": [ + { + "bbox": [ + 388, + 582, + 484, + 678 + ], + "type": "image", + "image_path": "c05a5d5e4025e538e4c038bbf14c40a522613d0ab678c1087c561cc43bcae4a2.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 740, + 298, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 740, + 298, + 750 + ], + "spans": [ + { + "bbox": [ + 279, + 740, + 298, + 750 + ], + "type": "text", + "content": "5389" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 116, + 521, + 224 + ], + "blocks": [ + { + "bbox": [ + 57, + 116, + 521, + 224 + ], + "lines": [ + { + "bbox": [ + 57, + 116, + 521, + 224 + ], + "spans": [ + { + "bbox": [ + 57, + 116, + 521, + 224 + ], + "type": "table", + "html": "
MethodsCUBFlowersFC 100Plant Disease300wLS PoseCelebACausal3DRank
(5,1)(5,5)(5,1)(5,5)(5,1)(5,5)(5,1)(5,5)s=0.05s=0.2s=0.05s=0.2s=0.05s=0.2s=0.05s=0.2
Baseline70.090.477.393.753.878.768.988.820.524.846.948.539.241.458.962.42.3
Multihead69.688.276.592.652.978.568.287.319.424.739.344.939.440.857.261.33.5
Div. Ensemble68.388.778.494.654.978.168.791.918.118.835.736.839.339.754.758.93.4
MeTTA68.488.977.692.354.472.868.787.518.320.336.837.537.237.949.358.64.1
Ours71.490.873.493.257.576.269.491.037.544.959.760.350.553.160.363.41.6
MoCo51.769.871.889.454.971.067.585.339.948.359.363.147.559.066.777.41.8
Ours49.974.170.493.450.972.962.389.657.360.462.665.664.264.770.379.41.3
MoCo41.056.969.676.431.743.965.785.039.050.154.260.340.252.352.557.03.7
AugSelf [38]44.257.476.085.635.048.871.887.842.051.853.860.153.266.354.461.82.7
LooC [38]--70.980.8-------------
AI [13]45.058.076.788.737.448.472.689.149.257.955.362.056.076.060.262.81.6
Ours41.356.667.888.939.553.765.988.151.157.558.364.850.257.761.863.91.9
", + "image_path": "112337d6f9c5518349339568ddaa142c2b3f4fd3833597c6755172406cd7ded7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 57, + 225, + 521, + 264 + ], + "lines": [ + { + "bbox": [ + 57, + 225, + 521, + 264 + ], + "spans": [ + { + "bbox": [ + 57, + 225, + 521, + 264 + ], + "type": "text", + "content": "Table 2. Few-shot classification and regression accuracy (\\%, R2) of our QD ResNet50 ensemble for supervised (top), MoCo pre-trained on ImageNet (middle) and MoCo pre-trained on ImageNet-100 (bottom). Values are reported with " + }, + { + "bbox": [ + 57, + 225, + 521, + 264 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 57, + 225, + 521, + 264 + ], + "type": "text", + "content": " confidence intervals averaged over 2000 episodes on FC100, CUB200, and Plant Disease. (N, K) denotes N-way K-shot tasks. For regression tasks (300w, LS Pose, CelebA, Causal3D), we report downstream performance for different splits with train proportion given by " + }, + { + "bbox": [ + 57, + 225, + 521, + 264 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 57, + 225, + 521, + 264 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 283, + 279, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 283, + 279, + 361 + ], + "spans": [ + { + "bbox": [ + 57, + 283, + 279, + 361 + ], + "type": "text", + "content": "of the ensemble and then learn a weighted combination of over all these predictions using linear regression. We sweep the regularisation parameters for all members for each downstream dataset based on its validation set. For dense tasks, we train a decoder head for each member of the ensemble using default hyperparameters in [67] for object detection and [18] for semantic segmentation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 377, + 279, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 377, + 279, + 488 + ], + "spans": [ + { + "bbox": [ + 57, + 377, + 279, + 488 + ], + "type": "text", + "content": "Few-shot downstream tasks: We also evaluate the pretrained networks on various few-shot learning benchmarks: FC100 [49], Caltech-UCSD Birds (CUB200), and Plant Disease [44]. We also show results for few-shot regression problems on 300w, Leeds Sports Pose, CelebA, and Causal3DIdent datasets, where we we repeatedly sampled " + }, + { + "bbox": [ + 57, + 377, + 279, + 488 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 57, + 377, + 279, + 488 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 57, + 377, + 279, + 488 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 57, + 377, + 279, + 488 + ], + "type": "text", + "content": " to generate low-shot training sets. For few-shot classification, we perform logistic regression using the frozen ensemble and learn episode-wise fusion weights w the support set itself." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 57, + 505, + 279, + 716 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 505, + 279, + 716 + ], + "spans": [ + { + "bbox": [ + 57, + 505, + 279, + 716 + ], + "type": "text", + "content": "Competitors: All methods are evaluated by readouts on fixed features. Supervised: Besides conventional supervised pre-training (denoted 'baseline'), we also train a conventional ensemble via a multi-head model ('multihead') that has the same architecture and number of parameters as our architecture but uses only " + }, + { + "bbox": [ + 57, + 505, + 279, + 716 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_q" + }, + { + "bbox": [ + 57, + 505, + 279, + 716 + ], + "type": "text", + "content": " loss. We also compare with another diverse ensemble strategy [23, 50] (denoted 'div ensemble'): to optimises for diversity in terms of KL between posterior probability of ensemble members. The idea being that differences in secondary probabilities are a good measure of diversity. We provide more details in the supplementary material. Finally, we compare with a test-time ensemble created by taking a single pretrained model and generating different invariances through test-time mean embeddings [3] (denoted 'MeTTA'). Contrastive: We compare our approach to two state of the art ensemble based alternatives AugSelf [68], LOOC [38] and amortised invariances (AI) [13]. Note that unlike other competitors, AI uses backprop to update the features." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 300, + 280, + 521, + 379 + ], + "blocks": [ + { + "bbox": [ + 300, + 280, + 521, + 379 + ], + "lines": [ + { + "bbox": [ + 300, + 280, + 521, + 379 + ], + "spans": [ + { + "bbox": [ + 300, + 280, + 521, + 379 + ], + "type": "table", + "html": "
MethodsCityScapesADE20kPascal VOCRank
MIoUAcc.MIoUAcc.APAP50AP75
Sup.Baseline39.682.130.452.948.880.351.62.6
Multihead35.480.327.351.849.880.250.93.9
Div. Ensemble36.282.427.652.750.681.958.12.3
QD4V41.081.733.854.350.882.558.71.3
Baseline (FT)61.794.140.167.255.182.860.52.0
QD4V (FT)65.294.342.367.456.284.962.91.0
MoCo.Baseline46.387.435.250.454.281.859.91.7
QD4V49.288.939.054.653.382.259.91.1
Baseline34.583.426.740.641.271.442.93.0
AugSelf37.984.927.340.843.273.448.11.6
QD4V36.184.928.541.745.975.248.01.3
", + "image_path": "b3fd555bb33de95fa2231b518369ece530060de5abb75a797fea10e80d1d45ef.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 299, + 386, + 521, + 428 + ], + "lines": [ + { + "bbox": [ + 299, + 386, + 521, + 428 + ], + "spans": [ + { + "bbox": [ + 299, + 386, + 521, + 428 + ], + "type": "text", + "content": "Table 3. Downstream performance of (1) Frozen supervised (2) fine-tuned supervised, (3/4) MoCO trained on ImageNet1K/100 model evaluated on semantic segmentation for CityScapes and ADE20k datasets, and Pascal VOC object detection." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 5 + }, + { + "bbox": [ + 299, + 449, + 346, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 449, + 346, + 460 + ], + "spans": [ + { + "bbox": [ + 299, + 449, + 346, + 460 + ], + "type": "text", + "content": "5. Results" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 299, + 469, + 521, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 469, + 521, + 624 + ], + "spans": [ + { + "bbox": [ + 299, + 469, + 521, + 624 + ], + "type": "text", + "content": "Can we successfully learn diverse (in)variance strengths with QD pre-training? To answer this question, we use the definition of invariance in Eq. 3 and evaluate the invariances learned by both default models (i.e., supervised and MoCo) and members of our QD ensemble for four appearance augmentations (blur, brightness, grayscale, contrast) and four spatial augmentations (resized crop, horizontal flip, rotation, scale). We compare the invariance strengths learned by the models via the visualization shown in Figure 3. The results show that the standard models provide a fixed set of invariance strengths (green). The members of the QD ensemble (dots) span a diverse range of invariance strengths from low (blue) to high-invariance (red), which can be selected downstream by picking among ensemble members." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 299, + 628, + 521, + 716 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 628, + 521, + 716 + ], + "spans": [ + { + "bbox": [ + 299, + 628, + 521, + 716 + ], + "type": "text", + "content": "Does QD4V benefit a set of downstream tasks with diverse invariance requirements? Our suite of downstream tasks is represent a diverse range of objectives with differing invariance-sensitivity requirements. The ability to exploit the appropriate (in)variance for each task is crucial to achieving high performance. As discussed earlier, off-the-shelf models tend towards high-invariance to multiple factors (Figure 3), which is often effective for object" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 280, + 741, + 298, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 280, + 741, + 298, + 750 + ], + "spans": [ + { + "bbox": [ + 280, + 741, + 298, + 750 + ], + "type": "text", + "content": "5390" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 66, + 115, + 267, + 183 + ], + "blocks": [ + { + "bbox": [ + 66, + 115, + 267, + 183 + ], + "lines": [ + { + "bbox": [ + 66, + 115, + 267, + 183 + ], + "spans": [ + { + "bbox": [ + 66, + 115, + 267, + 183 + ], + "type": "table", + "html": "
DecoderAircraftFlowersDTDAnimal PoseALOICausal3DRank
Sup.Concat36.885.970.911.226.672.92.0
Average33.883.469.19.123.774.32.7
Ours36.986.972.212.528.472.81.3
MoCoConcat42.083.572.913.745.780.22.2
Average37.983.972.012.642.978.12.8
Ours43.985.275.814.247.480.61.0
MoCo.Concat35.984.968.613.828.265.12.0
Average33.377.864.612.125.365.03.0
Ours37.985.571.914.333.865.31.0
", + "image_path": "ab96768c0db1126e147295e41927adebc7c0eb797c3711eceb85c850e17063d9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 55, + 185, + 280, + 236 + ], + "lines": [ + { + "bbox": [ + 55, + 185, + 280, + 236 + ], + "spans": [ + { + "bbox": [ + 55, + 185, + 280, + 236 + ], + "type": "text", + "content": "Table 4. Comparison of our proposed downstream task decoder with conventional approaches. Top: Supervised/ImageNet 1k pretrained. Middle/Bottom: Moco pre-training on ImageNet 1K/100. Our fusion strategy performs better than learning a classifier over concatenated features and averaging features of the ensemble." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 54, + 255, + 280, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 255, + 280, + 289 + ], + "spans": [ + { + "bbox": [ + 54, + 255, + 280, + 289 + ], + "type": "text", + "content": "recognition, but may not be effective for fine-grained tasks like CelebA facial attributes, or pose and lighting-prediction tasks like 300W and ALOI/Causal3D." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 290, + 280, + 391 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 290, + 280, + 391 + ], + "spans": [ + { + "bbox": [ + 54, + 290, + 280, + 391 + ], + "type": "text", + "content": "To evaluate the ability of features to support diverse downstream tasks, we evaluate the competitors on a range of tasks likely to exhibit different invariance preferences in Table 1. Our approach achieves comparable or better performance than baselines on all tasks against both supervised and self-supervised baselines. It has particularly remarkable improvements in regression tasks such as CelebA and Causal3D where we see an improvement of " + }, + { + "bbox": [ + 54, + 290, + 280, + 391 + ], + "type": "inline_equation", + "content": "12.5\\%" + }, + { + "bbox": [ + 54, + 290, + 280, + 391 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 54, + 290, + 280, + 391 + ], + "type": "inline_equation", + "content": "8.5\\%" + }, + { + "bbox": [ + 54, + 290, + 280, + 391 + ], + "type": "text", + "content": " over supervised pre-training of ResNet50." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 391, + 279, + 560 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 391, + 279, + 560 + ], + "spans": [ + { + "bbox": [ + 54, + 391, + 279, + 560 + ], + "type": "text", + "content": "To better understand the success of our method, we analyse the weights assigned to each member of the QD ensemble by different downstream tasks. Specifically, we employ Pearson's r correlation coefficient between " + }, + { + "bbox": [ + 54, + 391, + 279, + 560 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 54, + 391, + 279, + 560 + ], + "type": "text", + "content": " and the invariances learned by the QD ensemble (in Fig 3) as a metric to measure the strength of the relationship between the two variables. The resulting correlations are shown in Figure 4 and grouped by classification vs regression tasks. The trend shows that the spatially sensitive regression tasks tend to assign lower or negative weights to spatially invariant models, whereas classification tasks prefer models with generally stronger invariances. This analysis illustrates how our framework achieves reliably high performance across the range of tasks evaluated quantitatively in Table 1 - by enabling task-specific invariance preference selection." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 560, + 279, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 560, + 279, + 671 + ], + "spans": [ + { + "bbox": [ + 54, + 560, + 279, + 671 + ], + "type": "text", + "content": "Does QD4V benefit few-shot learning tasks? To answer this question we focused on MoCo-v2 CNN models trained on ImageNet1K and ImageNet100. For classification tasks, we followed [38, 68] in sampling C-way K-shot episodes from the target problem and training linear readouts and learning w for each episode. For regression tasks we repeatedly sampled " + }, + { + "bbox": [ + 54, + 560, + 279, + 671 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 54, + 560, + 279, + 671 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 54, + 560, + 279, + 671 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 54, + 560, + 279, + 671 + ], + "type": "text", + "content": " to generate low-shot training sets. From the results in Table 2, QD pre-training usually performs better than all competitors, with substantial margins in several cases, especially for pose estimation tasks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 672, + 280, + 718 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 672, + 280, + 718 + ], + "spans": [ + { + "bbox": [ + 55, + 672, + 280, + 718 + ], + "type": "text", + "content": "Does QD4V benefit dense estimation tasks? We evaluate QD pre-training on semantic segmentation on Cityscapes [19] and ADE20k [7] datasets. We evaluate QD4V by (1) Freezing the entire backbone and solely train a linear seg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 117, + 522, + 197 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 117, + 522, + 197 + ], + "spans": [ + { + "bbox": [ + 296, + 117, + 522, + 197 + ], + "type": "text", + "content": "mentation head and (2) Finetuning the entire backbone. We report the Mean Intersection over Union (IoU) and average accuracy for segmentation. Similarly, we also examine the performance of QD pre-training on Pascal VOC object detection. The results for semantic segmentation and object detection for frozen features and finetuning in Table 3 show that QD pre-training generally provides performance gains." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 198, + 522, + 343 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 198, + 522, + 343 + ], + "spans": [ + { + "bbox": [ + 296, + 198, + 522, + 343 + ], + "type": "text", + "content": "Ablation study for decoders: Finally, we compare our proposed downstream task decoder (Section 3.3) with conventional approaches. The results in Table 4 show that learning fusion weights using Eq. 8 consistently performs better, especially for regression tasks than conventional concatenation and prediction averaging. Intuitively, this is because our stacked fusion decoder has the chance for explicit invariance weighting. More technically, this is explained by the fast convergence rate in Theorem 3.4 which shows that our generalisation gap (between train and test error) tends to zero much faster than standard linear models as a function of the amount of training data. (See Supplementary for further discussion)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 344, + 523, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 344, + 523, + 467 + ], + "spans": [ + { + "bbox": [ + 296, + 344, + 523, + 467 + ], + "type": "text", + "content": "How does QD4V compare to large scale pre-trained models? The seminal CLIP [53] model is highly effective at various downstream tasks. Table 9 (supplementary) compares CLIP/RN50 to ImageNet1K QD4V/RN50 in terms of invariances and performance on downstream pose sensitive tasks. The results show that QD4V substantially outperforms CLIP, despite being trained on orders of magnitude less data - which we attribute to CLIP having learned too strong spatial and appearance invariances. This shows that pre-training scale is not a substitute for providing the correct invariance for the downstream task at hand." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 297, + 482, + 365, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 482, + 365, + 495 + ], + "spans": [ + { + "bbox": [ + 297, + 482, + 365, + 495 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 502, + 522, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 502, + 522, + 660 + ], + "spans": [ + { + "bbox": [ + 296, + 502, + 522, + 660 + ], + "type": "text", + "content": "We addressed the difficulty of pre-training a model to achieve high performance on diverse downstream tasks by introducing the notion of quality-diversity pre-training. By instantiating diversity optimisation in terms of the (in)variance properties of a feature extractor, we obtain a compact set of high-quality features with diverse (in)variance properties. Together with an efficient and effective fusion strategy, we show strong performance on a diverse range of downstream tasks including classification, pose estimation, semantic segmentation, and object detection. Our approach presents a step towards the vision of a universal feature representation capable of supporting multiple vision tasks. In future work we will explore other definitions of behavioural phenotypes in QD4V." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 661, + 522, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 661, + 522, + 717 + ], + "spans": [ + { + "bbox": [ + 296, + 661, + 522, + 717 + ], + "type": "text", + "content": "Acknowledgements This research was partially supported by the Engineering and Physical Sciences Research Council (EPSRC) Grant number EP/S000631/1 and the MOD University Defence Research Collaboration (UDRC) in Signal Processing." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 740, + 297, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 740, + 297, + 750 + ], + "spans": [ + { + "bbox": [ + 279, + 740, + 297, + 750 + ], + "type": "text", + "content": "5391" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 56, + 116, + 110, + 127 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 116, + 110, + 127 + ], + "spans": [ + { + "bbox": [ + 56, + 116, + 110, + 127 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 57, + 136, + 280, + 716 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 61, + 136, + 279, + 166 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 136, + 279, + 166 + ], + "spans": [ + { + "bbox": [ + 61, + 136, + 279, + 166 + ], + "type": "text", + "content": "[1] 300 faces in-the-wild challenge: database and results. 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Le", + "bbox": [ + 246, + 166, + 343, + 181 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dept. of Computer Science & Engineering Sungkyunkwan University Suwon, South Korea", + "bbox": [ + 125, + 184, + 464, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "bmle@g.skku.edu", + "bbox": [ + 225, + 239, + 362, + 253 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Simon S. Woo*", + "bbox": [ + 614, + 166, + 740, + 181 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dept. of Computer Science & Engineering Sungkyunkwan University Suwon, South Korea", + "bbox": [ + 504, + 184, + 844, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "swoo@g.skku.edu", + "bbox": [ + 607, + 239, + 741, + 253 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deepfake has recently raised a plethora of societal concerns over its possible security threats and dissemination of fake information. Much research on deepfake detection has been undertaken. However, detecting low quality as well as simultaneously detecting different qualities of deepfakes still remains a grave challenge. Most SOTA approaches are limited by using a single specific model for detecting certain deepfake video quality type. When constructing multiple models with prior information about video quality, this kind of strategy incurs significant computational cost, as well as model and training data overhead. Further, it cannot be scalable and practical to deploy in real-world settings. In this work, we propose a universal intra-model collaborative learning framework to enable the effective and simultaneous detection of different quality of deepfakes. That is, our approach is the quality-agnostic deepfake detection method, dubbed QAD. In particular, by observing the upper bound of general error expectation, we maximize the dependency between intermediate representations of images from different quality levels via Hilbert-Schmidt Independence Criterion. In addition, an Adversarial Weight Perturbation module is carefully devised to enable the model to be more robust against image corruption while boosting the overall model's performance. Extensive experiments over seven popular deepfake datasets demonstrate the superiority of our QAD model over prior SOTA benchmarks.", + "bbox": [ + 75, + 319, + 472, + 710 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 742, + 209, + 758 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep learning approaches for facial manipulation, such as deepfakes, have recently received considerable attention [54, 31, 61, 25, 20, 23], because they can be abused for the malicious purposes such as fake news, pornography, etc. Due to the advancements made in Generative Adversarial Networks and other deep learning-based computer vision algorithms, deepfakes have also become more realistic and", + "bbox": [ + 75, + 768, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2850bc805620a8677c15bbeafa25e502019b051d85085dae8b9fa4b36bd12c41.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 285, + 640, + 393 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/65afc92280a6be32be55f5583227c5939604a993fa1fa835f53c59af7f61ff54.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 645, + 287, + 759, + 392 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/33f73aae8c97828d1ff97a420620e7aefe5b135aa72abb464aaf0ac7b8a76c89.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 287, + 897, + 392 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bd539fba419df6e44ea9f4cc21df917b11c06bccf640881686c247983cfc61fc.jpg", + "image_caption": [ + "Figure 1. A summary of our goal. Our approach stands out from previous works that detect deepfakes using separate models for different qualities (e.g. Baseline 2 [28]) or a single model without considering the interaction between qualities (e.g. Baseline 1 [43]). Instead, our method employs all quality levels and improves the performance of the model on each quality level, leading to overall enhanced performance." + ], + "image_footnote": [], + "bbox": [ + 508, + 393, + 614, + 474 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/35102a955e037dc10a358435db161a202fc1691ca6bf897196504784acbe7b83.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 617, + 393, + 751, + 474 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/093f479cbf013679a61674f473781dfcc0a6c15914b8601e0d3ea68bb38f641f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 754, + 393, + 893, + 474 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "natural, making it harder not only for humans, but also for classifiers to tell them apart. Moreover, it has been simpler than ever before to create convincing deepfakes using simple programs and apps without requiring advanced machine learning knowledge. Such easy-to-create and realistic fake images and videos can be maliciously exploited, raising significant security, privacy, and societal concerns such as fake news propagation [39], and stealing personal information via phishing and scams [10].", + "bbox": [ + 496, + 595, + 890, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To mitigate such problems caused by deepfakes, there has been a tremendous research effort put into constructing reliable detectors [32, 25, 8, 38, 61, 44]. Although they have achieved outstanding performance with high-quality deepfakes, most of them have failed to detect low-quality deepfakes effectively [8, 43]. While video compression steps do not significantly impact on visualization, it drastically drop deepfake detectors' performance on low-quality deepfakes (c40). A handful of research has been focused on detecting low-quality deepfakes such as ADD [28] and BZNet [29]. However, their methods can only detect low-quality com", + "bbox": [ + 496, + 734, + 892, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22378", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "pressed deepfakes. And, those prior approaches expose a critical problem, when deployed in practice since the prior video quality information of the input is unknown. Moreover, developing different models for each input quality induces significant computational overhead. Other works, such as LipForensics [16], also attempt to make their detectors robust against various corruptions and compression. Nevertheless, it is unable to detect image-based deepfakes with random lossy compression like JPEG.", + "bbox": [ + 75, + 90, + 472, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this research, we propose the novel deepfake detection method, QAD, which can simultaneously detect both high and low-quality (quality-agnostic) deepfakes in a single model, as illustrated in Fig. 1. Especially, we propose a universal intra-model collaborative learning framework to provide the effective detection of different quality deepfakes. We modulate the conventional model-based collaborative learning [47] to an instance-based intra-model collaborative learning framework in our training. During the training phase, our single model simultaneously learns the representations of one image, but with different qualities. By utilizing the collaborative learning framework, our QAD can align the distributions of high and low-quality image representations to be geometrically similar. Hence, it can avoid the overfitting caused by compressed images and the overconfidence caused by raw images, while boosting its overall performance.", + "bbox": [ + 75, + 229, + 472, + 486 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In particular, we perform a rigorous theoretical analysis, and show that the low-quality deepfake classification error can be bounded by two terms: classification loss and the distance between the representations of high and low-quality images. Instead of using a direct pairwise regularization to minimize the gaps between the high and low-quality image representations, we propose to apply Hilbert-Schmidt Independence Criterion (HSIC) to maximize the dependence between a mini-batch of high and low-quality images, thus maximizing the mutual information between them, and supporting the high-level representations and effective output predictions. Meanwhile, to enhance the model's robustness under heavy input compression, we propose Adversarial Weight Perturbation (AWP) [56, 3], which can further flatten the weight loss landscape of the model, bridging the gap in multiple quality learning for deepfake detection.", + "bbox": [ + 75, + 488, + 472, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Finally, we conduct extensive experiments to show the effectiveness of our QAD with seven different popular benchmark datasets. We first show that our method can outperform previous baselines when training with data from various video and image compression qualities. Furthermore, we show that our QAD exceeds the performance of the SOTA quality-aware models such as BZNet [29] by a significant margin, while requiring remarkably fewer computational parameters and no prior knowledge of the inputs. Our contributions are summarized as follows:", + "bbox": [ + 75, + 732, + 472, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1) We theoretically analyze and prove that the classifica", + "bbox": [ + 76, + 885, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tion error of low-quality deepfakes can be bounded by its classification loss and the representation distance with its corresponding high-quality images.", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "2) We propose a unified quality-agnostic deepfake detection framework (QAD), utilizing instance-based intramodel collaborative learning. We use the Hilbert-Schmidt Independence Criterion (HSIC) to maximize the geometrical similarity between intermediate representations of high and low-quality deepfakes, and Adversarial Weight Perturbation (AWP) to make our model robust under varying input compression.", + "3) We demonstrate that our approach outperforms well-known baselines, including the total of eight quality-agnostic and quality-aware SOTA methods with seven popular benchmark datasets." + ], + "bbox": [ + 496, + 136, + 893, + 318 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related works", + "text_level": 1, + "bbox": [ + 500, + 333, + 645, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Deepfake detection", + "text_level": 1, + "bbox": [ + 500, + 358, + 683, + 375 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, deepfakes have been of the utmost crucial because they can cause serious security and privacy threats. Theresfore, a large number of detection methods have been proposed to effectively identify such deepfakes [43, 31, 30, 22, 41, 54, 32, 25, 8, 61]. However, the majority of the aforementioned works focus on mining visual artifacts of deepfakes, such as the blending boundaries of generated faces [31], the irregularity of pupil shapes [14], the spatiotemporal inconsistency [6, 44], or exploring deep learning-based attention methods [61] to identify such artifacts. Meanwhile, several approaches also showed that exposing deepfakes in the frequency domain is effective. Such methods include analyzing the discrepancies of frequency spectrum [8, 27, 25], employing the checkerboard artifacts caused by the transposed convolutional operator [60, 11], or mining the statistical frequency features with dual deep learning models [38]. Nevertheless, such models' performance substantially decreases when encountering low-quality compressed images. To remedy the above shortcoming, recent studies proposed methods to detect the deepfake in highly compressed low-quality versions such as [28], which utilized a knowledge distillation. Also, [29] presented a supper-resolution-based network for enhancing the performance of low-quality deepfake detection. However, all of the aforementioned approaches are limited in developing a single model for each quality of deepfakes, which is impractical to deploy in real-world scenarios due to the requirement of prior knowledge of the input quality.", + "bbox": [ + 496, + 382, + 893, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Collaborative learning", + "text_level": 1, + "bbox": [ + 500, + 816, + 710, + 832 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Collaborative learning proposed by [47] is designed to achieve a global minimum of a deep neural network, while maintaining the same computational complexity at inference time as at training time. Collaborative learning inherits", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22379", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the advantages of auxiliary training [48], multi-task learning [58], and knowledge distillation [18]. Its applications cover supporting weakly-supervised learning [24], or integrating with online knowledge distillation [57, 15]. And, its training graph is divided into two or more sub-networks to ensure global minimum achievement [47]. Besides, [9] proposed an intra-model collaborative learning framework that shares a similar characteristic with self-knowledge distillation. However, all of the approaches are model-based collaborative learning, in which a single input generates multiple outputs (or views) through multiple classifier heads of one target network in both training and inference phase.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we distinguish ourselves by deploying the collaborative learning framework for simultaneously training deepfakes of various qualities with an undeviated single model, namely instance-based collaborative learning. Different from conventional mini-batch stochastic optimization, which independently samples random images from different qualities and optimizes the detector, our collaborative learning approach allows us to utilize the common features in the same image but from different qualities simultaneously. Thus, our deepfake detector circumvent the overfitting caused by compressed images or the overconfidence from raw images, enhancing its overall performance.", + "bbox": [ + 75, + 273, + 472, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Hilbert-Schmidt Independence Criterion", + "text_level": 1, + "bbox": [ + 76, + 468, + 426, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The Hilbert-Schmidt Independence Criterion (HSIC) [13] measures the statistical dependency between probability distributions. In fact, HSIC differs from the covariance, where $\\text{Cov}(X,Y) = 0$ does not imply that two random variables $X$ and $Y$ are independent [42], while HSIC shows its tractable computation and equivalency in terms of the independence property [13]. Moreover, HISC is easy to be estimated statistically and algorithmically. In practice, applications based on HSIC are found in a variety of practical domains, including maximizing the dependencies for self-supervised learning [33] and classification learning [34, 12], or defense against model inversion attacks [37]. In this paper, we utilize the HSIC to maximize the dependency between distributions of deepfake images of different qualities at intermediate layers. Therefore, we aim to constrain low-level representations of images not to be exactly the same, but to share a geometrical similarity of learning features that can support high-level output predictions.", + "bbox": [ + 75, + 493, + 472, + 765 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 76, + 782, + 174, + 797 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first theoretically examine the upper bound for our optimization problem by considering a DNN classifier of $K$ classes, and two modalities of input quality: raw (high-quality) and compressed (low-quality). Then, we discuss how to more efficiently collaborate on the representations of deepfake images of differing quality.", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary & our inspiration", + "text_level": 1, + "bbox": [ + 500, + 90, + 767, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a sample $x_r$ from a space $\\mathcal{X}$ and its compressed version at quantile $c$ , $x_c$ can be expressed as $x_c = x_r - \\delta_c$ , and we define the corresponding label $y \\in \\{0,1\\}$ (real and fake). Next, a family $\\mathcal{F}$ of learning functions $f: \\mathcal{X} \\to \\mathbb{R}^2$ returns a 2-tuple $f(x) = [f(x,j)]_{j=1}^2$ , whose $f(x,j)$ is proportional to the probability to assign $x$ to the $j$ -th class, and $f$ is defined by learning parameters $\\theta$ . Given a training data $\\mathcal{D} = \\{(x_i,y_i)\\}_{i=1}^n \\subset \\mathcal{X} \\times \\mathcal{Y}$ , our goal is to minimize the expectation of a loss function $\\mathcal{L}: \\mathbb{R}^2 \\times \\mathcal{Y} \\to \\mathbb{R}$ . Here, we consider $\\mathcal{L}(f(x),y) = 1 - \\sigma_T(f(x,y))$ , where $\\sigma_T$ is the softmax function with temperature $T > 0$ :", + "bbox": [ + 496, + 113, + 893, + 280 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {T} (f (x), y) = \\frac {\\exp (f (x , y) / T)}{\\sum_ {k = 1} ^ {2} \\exp (f (x , k) / T)}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 290, + 890, + 327 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Theorem 1. (Proof can be done similarly as [36] and [19] in Supp. Material) For any $f \\in \\mathcal{F}$ , and with probability $1 - \\delta$ over the draw of $\\mathcal{D}$ ,", + "bbox": [ + 496, + 337, + 893, + 383 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbb {E} \\left[ \\mathbb {I} \\left\\{\\hat {y} \\left(x _ {c}\\right) \\neq y \\right\\} \\right] \\leq 2 \\mathbb {E} _ {\\mathcal {D}} \\mathcal {L} \\left(f \\left(x _ {c}\\right), y\\right) \\\\ + \\frac {8}{T} \\mathbb {E} _ {\\mathcal {D}} \\mathcal {L} _ {i - c o l} (f (x _ {r}), f (x _ {c})) + 4 \\Re_ {\\mathcal {D}} (\\Phi_ {\\mathcal {W}}) \\\\ + \\frac {1 6}{n} + \\mathcal {O} \\left(\\sqrt {\\frac {\\log (2 / \\delta)}{2 n}}\\right), \\tag {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 393, + 900, + 486 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\Re_{\\mathcal{D}}$ is the Rademacher complexity, $\\Phi_{\\mathcal{W}} = \\{\\mathcal{L}(f(x_r),y),f\\in \\mathcal{F}\\}$ , and", + "bbox": [ + 500, + 496, + 890, + 527 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i - c o l} \\left(f \\left(x _ {r}\\right), f \\left(x _ {c}\\right)\\right) = \\| f \\left(x _ {r}\\right) - f \\left(x _ {c}\\right) \\| . \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 539, + 890, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Insight of Theorem 1. On the right-hand side of Eq. 2, our classifier $f$ depends on two terms, where the first term is the classification loss $\\mathcal{L}(f(x_c), y)$ applied to the prediction of the compressed image $x_c$ . And, the second term is the instance-based collaborative loss $\\mathcal{L}_{i-col}(f(x_r), f(x_c))$ that measures the pairwise difference between predictions of the raw image and its compressed version. Therefore, minimizing the expectation over training data $\\mathcal{D}$ of $2\\mathcal{L}(f(x_c), y) + 8\\mathcal{L}_{i-col}(f(x_r), f(x_c)) / T$ , can decrease the true error. Note that Eq. 2 is also general so that it can be applicable for raw images. Hence, in practice, the first term can be generalized to both raw and compressed images.", + "bbox": [ + 496, + 566, + 890, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In order to minimize the expectation of errors in both raw and compressed deepfake image predictions, our theoretical analysis shows that we can minimize both classification loss and collaborative loss at the output. However, as observed by [9] and in our experiments (see Tab. 4), this instance-based collaborative learning loss fails to achieve the best performance. Additionally, training solely with highly-compressed images makes the detector prone to overfitting, yielding a considerable gap between training and test performance [28]. As a result, the major research", + "bbox": [ + 496, + 750, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "footer", + "text": "22380", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1ba2b5ce79c5cd2ab2801b0cc1965138c0d49c13d0109e99e40daa0e4b2b4533.jpg", + "image_caption": [ + "Figure 2. Overview of our QAD framework. A mini-batch of images from different quality modalities (e.g., two in this diagram) is forwarded through a single universal model. Although it is one model, we pictorially split it into two branches for the reader's understanding. After training, we obtain one universal model that regulates different qualities. Top-right: The HSIC geometrically maximizes the dependency between images from various quality modalities at different resolutions, supporting high-level output predictions. Bottom-right: Through searching for the worst-case parameters' corruption and compensating for input corruption (compression), the AWP flattens the model's weight loss landscape, making the model robust under varying input compression." + ], + "image_footnote": [], + "bbox": [ + 99, + 85, + 500, + 377 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2dd487df5afb505779b16d1d4628972653870860bf4a46b3112dc43ba8203515.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 519, + 87, + 870, + 242 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/770e067dbdc8c4a88a06076e460843fdd8a49a2856cb624bdb85c318d0e6bffd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 522, + 250, + 870, + 375 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "challenge is how we can further lower the sensitivity of $f_{\\theta}$ to $x$ at various compression settings and push their representations close to each other.", + "bbox": [ + 75, + 487, + 468, + 532 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Classification loss. We can construct a robust model under input corruption by flattening the weight loss landscape. In particular, we apply the Adversarial Weight Perturbation [56] to search for the worst-case perturbations $\\phi^{*}$ of the model weights at every training step. Thereafter, optimizing the perturbed model via $\\mathcal{L}(f_{\\theta +\\phi^*},y)$ can enable it to be more robust under varying input image correlations/distortions, which represent the varying qualities of deepfake inputs (See Fig. 2—Bottom-right panel). Furthermore, the classification loss in Eq. 2 is upper bounded by this new loss function due to the worst-case perturbations.", + "bbox": [ + 75, + 536, + 468, + 702 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Collaborative loss. With respect to the collaborative learning loss, Eq. 3 shares similar characteristics with recent knowledge distillation research [18, 52]. However, our goal is to develop and train a single universal model, not having a teacher-student relationship. Nevertheless, we argue that the gap between raw and compressed image representations can be minimized more efficiently by regularizing their discrepancy at the low-level representations. Moreover, enforcing the similarity of the pairwise representations at the intermediate layers with an input difference of $|\\delta_c|$ can collapse layers' weights to zero or can lead a deep model to remember training data instead of learning discriminative features. Therefore, we relax this constraint by", + "bbox": [ + 75, + 704, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "maximizing the kernel dependency in a mini-batch of data between the raw and compressed image representations by the Hilbert-Schmidt Independence Criterion (HSIC). Using HSIC, we can instead enforce the geometrical structures of mini-batch of raw data and the compressed data to be similar, so that we can still effectively detect different-quality deepfakes in a single model. From a mutual information perspective, maximizing the kernel dependency can enforce the mutual information of the learned representations of different compression ratios, thus regularizing the detector to be more generalized (See Fig. 2—Top-right panel).", + "bbox": [ + 496, + 487, + 890, + 655 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Details of our methods", + "text_level": 1, + "bbox": [ + 500, + 664, + 709, + 679 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Weight loss landscape flattening", + "text_level": 1, + "bbox": [ + 500, + 688, + 774, + 704 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Recent studies [21, 55] suggest that searching for a flatter minima can improve the generalization ability of the model. To achieve this, we propose using Adversarial Weight Perturbation [56] to identify flat local minima of the empirical risk. The worst-case perturbations $\\phi^{*}$ of the model weights which increases the loss dramatically is formulated as:", + "bbox": [ + 496, + 712, + 890, + 803 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\phi^ {*} = \\underset {\\phi \\in \\mathcal {B} _ {p} (\\theta , \\gamma)} {\\arg \\max } \\mathcal {L} (f _ {\\theta + \\phi} (x), y), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 815, + 890, + 843 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{B}_p(\\theta, \\gamma) = \\{v \\in \\Theta : \\| \\theta - v \\|_p \\leq \\gamma\\}$ is the feasible region of any perturbation $\\phi$ . The AWP adds the worst-case perturbation to the model weight, so that $\\mathcal{L}(f_{\\theta + \\phi^*}(x), y)$", + "bbox": [ + 496, + 854, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22381", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "becomes the supremum value in $\\mathcal{B}_p(\\theta, \\gamma)$ . Therefore, optimizing $\\mathcal{L}(f_{\\theta + \\phi^*}(x), y)$ pushes $\\theta$ to adjust its values such that the loss landscape is more flatten with the same capability $\\mathcal{B}_p(\\theta, \\gamma)$ . As a result, $f$ becomes more stable under input image's changes.", + "bbox": [ + 75, + 90, + 468, + 166 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similar to adversarial example perturbation [35], $\\phi^{*}$ is generated by projected gradient method as follows:", + "bbox": [ + 75, + 166, + 468, + 198 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\phi^ {*} \\leftarrow \\Pi_ {\\theta} ^ {\\gamma} \\left(\\phi + \\eta \\frac {\\nabla \\mathcal {L} \\left(f _ {\\theta + \\phi} (x) , y\\right)}{\\| \\nabla \\mathcal {L} \\left(f _ {\\theta + \\phi} (x) , y\\right) \\|} \\| \\theta \\|\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 205, + 468, + 239 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\Pi_{\\theta}^{\\gamma}$ is an operator that projects its input into the feasible region $B_{p}(\\theta, \\gamma)$ , and $\\eta \\in \\mathbb{R}$ is the step size. In fact, we empirically find that using a one-step projection for $\\phi^{*}$ is sufficient for the model's robustness under the image corruptions formed by compression. By adding $\\phi^{*}$ in Eq. 5 to $\\theta$ , it is straightforward to bound $\\mathcal{L}(f(x_c), y)$ in Eq. 2.", + "bbox": [ + 75, + 247, + 468, + 339 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.2 Intra-model collaborative learning", + "text_level": 1, + "bbox": [ + 76, + 356, + 372, + 372 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Hilbert-Schmidt Independence Criterion (HSIC). Let $\\mathcal{T}$ and $\\mathcal{G}$ be two separable Reproducing Kernel Hilbert Spaces (RKHS) on metric spaces $\\mathcal{U}$ and $\\mathcal{V}$ , respectively. HSIC measures the dependency between two random variables $U$ and $V$ from a joint distribution on $\\mathcal{U}$ and $\\mathcal{V}$ , by evaluating the cross-covariance of the nonlinear transformations of the two random variables:", + "bbox": [ + 75, + 378, + 468, + 484 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nH S I C (U, V) = \\left\\| \\mathbb {E} [ \\zeta (U) \\psi (V) ^ {T} ] - \\mathbb {E} \\zeta (U) \\mathbb {E} \\psi (V) ^ {T} \\right\\| _ {H S} ^ {2}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 493, + 468, + 526 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\| \\cdot \\|_{HS}$ is the Hilbert-Schmidt norm, which becomes the Frobenius norm in finite dimensions. And, $\\zeta : \\mathcal{U} \\to \\mathcal{T}$ and $\\psi : \\mathcal{V} \\to \\mathcal{G}$ are nonlinear mapping functions. With appropriate transformation $\\zeta$ and $\\psi$ , HSIC is a dependence test, which can identify the nonlinear dependencies between $U$ and $V$ as follows: $HSIC(U,V) = 0 \\Leftrightarrow U \\perp V$ .", + "bbox": [ + 75, + 525, + 468, + 617 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Also, inner products in $\\mathcal{T}$ and $\\mathcal{G}$ are formed by positive definite kernel functions: $k(u,u^{\\prime}) = \\langle \\zeta (u),\\zeta (u^{\\prime})\\rangle_{\\mathcal{T}}$ and $l(v,v^{\\prime}) = \\langle \\psi (v),\\psi (v^{\\prime})\\rangle_{\\mathcal{G}}$ . And, let $(U^{\\prime},V^{\\prime})$ and $(U^{\\prime \\prime},V^{\\prime \\prime})$ be independent copies of $(U,V)$ , then Eq. 6 can be expressed as follows:", + "bbox": [ + 75, + 617, + 468, + 691 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} H S I C (U, V) = \\mathbb {E} [ k (U, U ^ {\\prime}) l (V, V ^ {\\prime}) ] \\\\ - 2 \\mathbb {E} [ k (U, U ^ {\\prime}) ] \\mathbb {E} [ l (V, V ^ {\\prime \\prime}) ] + \\mathbb {E} [ k (U, U ^ {\\prime}) ] \\mathbb {E} [ l (V, V ^ {\\prime}) ]. \\tag {7} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 700, + 468, + 752 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Estimation of HSIC. The empirical estimation of HSIC with an bias of $\\mathcal{O}(\\frac{1}{n})$ using $n$ samples i.i.d drawn $\\{(u_i,v_i)\\}_{i = 1}^n$ from the joint distribution $(U,V)$ is provided as follows [13]:", + "bbox": [ + 76, + 761, + 468, + 823 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {H S I C} (U, V) = \\frac {1}{(n - 1) ^ {2}} \\mathbf {t r} (K H L H), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 830, + 468, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $K_{i,j} = k(u_i, u_j)$ , and $L_{i,j} = l(v_i, v_j)$ are kernel matrices for the kernels $k$ , and $l$ , respectively, and $H_{i,j} =$", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 QAD: Quality-Agnostic Deepfake detection.", + "bbox": [ + 500, + 90, + 883, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Require: DNN $f$ parameterized by $\\theta$ , training dataset $\\mathcal{D}$ with M quality modalities $\\mathcal{T} = \\{r, c_1, \\dots, c_{M-1}\\}$ . Learning rate $\\alpha_l$ and mini-batch size of $B$ . Model weight perturbation size $\\gamma$ , step size $\\eta$ , and the number of steps $K$ . Layers of $f$ to apply HSIC $L$ .", + "bbox": [ + 500, + 107, + 890, + 183 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: while not converged do", + "2: for mini-batch $(X = [X_{\\tau}]_{\\tau \\in \\mathcal{T}}, Y) \\in \\mathcal{D}$ do", + "3: # One-step AWP", + "4: $\\mathcal{L}_1 = \\mathcal{L}(f_{\\theta +\\phi}(X),Y) / MB$", + "5: $\\phi \\gets \\Pi_{\\theta}^{\\gamma}\\left(\\phi +\\eta \\frac{\\nabla\\mathcal{L}_{1}}{\\|\\nabla\\mathcal{L}_{1}\\|}\\parallel \\theta \\parallel\\right)$", + "6: $\\theta \\gets \\theta +\\phi$", + "7: $\\mathcal{L}_1\\gets \\mathcal{L}(f_\\theta (X),Y) / MB$", + "8: # intermediate reps.", + "9: $[Z_l^\\tau ]_{l\\in L}^{\\tau \\in T}\\coloneqq f_\\theta (X)$", + "10: # HSIC: dependence maximization", + "11: $\\mathcal{L}_2\\gets \\sum_{\\tau ,\\rho \\in T}^{\\tau \\neq \\rho}\\mathcal{L}_{col}(\\tau ,\\rho)$", + "12: # Overall loss Eq. (10)", + "13: $\\mathcal{L}_{QAD} \\gets \\mathcal{L}_1 + \\alpha \\times \\mathcal{L}_2$", + "14: $\\theta \\gets \\theta -\\alpha_{l}\\cdot \\nabla_{\\theta}\\mathcal{L}_{QAD}$", + "15: $\\theta \\gets \\theta -\\phi$", + "16: end for", + "17: end while" + ], + "bbox": [ + 506, + 184, + 883, + 445 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\delta_{i,j} - \\frac{1}{n}$ is a centering matrix. Regarding the kernel functions, Theorem 4 in [13] suggested that an universal kernel, such as Laplace and Gaussian RBF kernel, can guarantee the HSIC to detect any dependency between $U$ and $V$ .", + "bbox": [ + 496, + 481, + 890, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "HSIC for maximizing the geometrical similarity. Let $\\tau$ and $\\rho$ be two different qualities of deepfakes, (e.g., raw vs. compressed). Consider the $l$ -th layer of the learning network $f$ , we denote the learning features of a mini-batch of $B$ images from $\\tau$ and $\\rho$ are $Z_{l}^{\\tau} = \\{u_{i}\\}_{B}$ , and $Z_{l}^{\\rho} = \\{v_{i}\\}_{B}$ respectively, where $u_{i}, v_{i} \\in \\mathbb{R}^{H \\times W \\times C}$ and $H, W$ and $C$ are the height, width, and channel number. Our regularization aims to maximize the dependency between $Z_{l}^{\\tau}$ and $Z_{l}^{\\rho}$ via a mini-batch of representations. In other words, we try to minimize the following loss:", + "bbox": [ + 496, + 545, + 892, + 696 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c o l} (\\tau , \\rho) = - \\sum_ {l \\in L} \\widehat {H S I C} \\left(Z _ {l} ^ {\\tau}, Z _ {l} ^ {\\rho}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 714, + 890, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $L$ is a predetermined collection of layers to apply the collaborative loss. And, the computational complexity for calculating Eq. 9 is $\\mathcal{O}(B^2 L)$ , which can be reduced to $\\mathcal{O}(BL)$ when applying random Fourier features [40].", + "bbox": [ + 496, + 763, + 890, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. End-to-end training loss", + "text_level": 1, + "bbox": [ + 500, + 844, + 720, + 859 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given a training mini-batch $B$ that include all $M$ quality modalities $\\mathcal{T} = \\{r,c_1,\\dots c_{M - 1}\\}$ , the overall collaborative", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22382", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/9b6b13e9f0de1f63c8dc95cabc972ba1910ebcb950d36b3dbc3c9d6787a175a8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelTest Set AUC (%)
NTDFF2FFSFSHCDFv2FFIW10KAvg
Video Compression (raw + c23 + c40 of test set)
MesoNet [1]◇70.2493.7294.1585.1796.0080.5294.5687.77
Rössler et al. [43]◇89.6499.0597.8998.8398.5097.4999.1797.22
F3Net [38]◇86.7998.7396.3297.8297.4595.0697.9495.73
MAT [61]◇86.7998.7396.3297.8297.4595.0697.9495.73
Fang & Lin [9]89.3098.9897.3398.4398.6696.5898.9496.89
SBIs [45]†78.3395.1979.7480.3780.48--82.82
BZNet [29]†80.1298.8194.1097.71---91.01
ADD [28]†86.2696.2390.6295.5795.94--92.92
QAD-R (ours)91.2599.5498.3499.0199.1298.3699.1097.82
QAD-E (ours)94.9299.5398.9499.2799.1298.3899.1698.47
", + "bbox": [ + 158, + 87, + 812, + 311 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3883650e15549b40e9da849f6f8071af0015c0a5bd889a8be70ad7ea9cc7c4b8.jpg", + "table_caption": [ + "Table 1. Classification performance in the quality-agnostic setting with video compression of test set. The methods are trained using one of three approaches: simultaneously with three modalities (raw + c23 + c40), individually with each of the three modalities, or with a mid-level of compression (c23) to prevent performance degradation resulting from lossy compression. In the inference phase, video compression is applied to the input. The best results are highlighted in bold. $\\dagger$ and $\\diamond$ indicate results were obtained from methods' pretrained weights and published code, respectively." + ], + "table_footnote": [], + "table_body": "
ModelTest Set AUC (%)
NTDFF2FFSFSHCDFv2FFIW10KAvg
Random Image Compression (JPEG on raw of test set)
MesoNet [1]◇70.2392.0288.3282.6091.8481.1291.8785.43
Rössler et al. [43]◇69.8998.6294.9796.6696.7696.9898.8193.24
F3Net [38]◇70.9597.8992.8396.3494.7295.4497.1992.19
MAT [61]◇69.5398.9695.5397.9996.9798.2198.9193.73
Fang & Lin [9]75.4998.3294.6397.6497.2896.6798.3994.06
SBIs [45]†77.7597.8382.0586.1085.42--85.83
BZNet [29]†79.0098.7795.2397.92---92.73
ADD [28]†75.8496.8392.2395.2496.00--91.23
QAD-R (ours)75.1898.8693.7298.5298.1898.5198.9694.56
QAD-E (ours)76.2799.2094.4498.6998.6098.5298.8694.94
", + "bbox": [ + 158, + 393, + 812, + 612 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Classification performance in the quality-agnostic setting with image compression of test set. The training approach resembles that of Table 1's setting, however, in the inference phase, random image compression is applied to the input.", + "bbox": [ + 75, + 613, + 892, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "learning loss in our QAD framework is formulated as:", + "bbox": [ + 75, + 656, + 436, + 672 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {Q A D} = \\frac {1}{M B} \\sum_ {\\tau \\in \\mathcal {T}, i \\in B} \\mathcal {L} _ {\\phi^ {*}} \\left(x _ {\\tau , i}, y _ {i}\\right) + \\alpha \\sum_ {\\tau , \\rho \\in \\mathcal {T}} ^ {\\tau \\neq \\rho} \\mathcal {L} _ {c o l} (\\tau , \\rho), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 75, + 681, + 472, + 741 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\alpha$ is a hyper-parameter to balance contribution of each loss. It is worth noting that our QAD training loss is parameter-free, and is not affected by the order of the modalities. Further, unlike other model-based collaborative learning [47], our QAD does not derive any sub-models. In other words, it can be integrated with any backbone, i.e., RESNET50, and introduces no extra computation at the inference time. Note that Theorem 1 still holds when replacing the classification loss $\\mathcal{L}(f(x),y)$ with any cross-entropy based loss, since $\\mathcal{L}(f(x),y)$ is bounded by the", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "cross-entropy loss. Finally, we present our end-to-end algorithm for optimizing Eq. 10 in Algorithm 1, and its pictorial illustration in Fig. 2.", + "bbox": [ + 496, + 656, + 892, + 702 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experimental Results", + "text_level": 1, + "bbox": [ + 498, + 715, + 705, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Dataset and pre-processing", + "text_level": 1, + "bbox": [ + 498, + 741, + 746, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For evaluating our proposed method, we experiment with seven different popular deepfake benchmark datasets: NeuralTextures (NT) [50], Deepfakes (DF) [4], Face2Face (F2F) [51], FaceSwap (FS) [5], FaceShifter (FSH) [30], CelebDFV2 (CDFv2) [59], and Face Forensics in the Wild (FFIW10K) [62]. Besides the raw version, these videos are also compressed into two types: medium (c23) and high (c40), utilizing the H.264 codec and constant rate quantization parameters of 23 and 40, respectively. These effectively", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22383", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f0a3326574ba8aed6088fea266388d7f04524643e82e99a5fb5f82a51052e0eb.jpg", + "table_caption": [], + "table_footnote": [ + "Table 3. Classification performance in the quality-aware setting with video compression of test set. Except for our model, each model is trained with three modalities: raw, c23, and c40, respectively (denoted $[ \\times 3 ]$ ). In the inference phase, while our QAD uses one single pre-trained model, other methods use their corresponding pre-trained model (e.g., pre-trained RESNET-50 on raw) to detect a given testing input (e.g., raw). Reported performances are averaged score of the three modalities." + ], + "table_body": "
Methodw/ prior infor.#paramsTest Set AUC (%)
NTDFF2FFSFSHCDFv2FFIW10KAvg
BZNet [29]†[×3]Y22M × 391.0199.3096.9098.82---96.51
ADD [28]†[×3]Y23.5M × 389.0899.2596.5398.2198.25--96.26
RESNET50 [×3]Y23.5M × 388.9699.2697.0498.6398.7197.0998.5896.90
QAD-R (ours)N23.5M × 188.8599.4297.7798.8398.9397.5698.9397.18
EFFICIENTNET-B1[×3]Y6.5M × 387.6399.0596.7298.1697.9596.7098.5496.39
QAD-E (ours)N6.5M × 192.2599.4698.3099.0898.9097.5099.0197.79
", + "bbox": [ + 109, + 87, + 859, + 255 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "result in different quality of deepfakes, and details of these datasets are provided in our Supp. Material.", + "bbox": [ + 75, + 334, + 468, + 364 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Experimental Settings", + "text_level": 1, + "bbox": [ + 76, + 375, + 284, + 391 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The models are trained with the Adam optimizer [26] with a learning rate of 2e-3, scheduled by one-cycle strategy [46] in 32 epochs. We use a mini-batch size of 64. In every training epoch, the model is evaluated ten times, and we save the best one based on the validation accuracy. Regarding the backbone network, we use the ResNET-50 [17] (QAD-R) and EfficientNet-B1 [49] (QAD-E) with their default input size of $224 \\times 224$ and $240 \\times 240$ , respectively. The backbone models utilize pre-trained weights from ImageNet dataset [7]. Our hyper-parameters settings $\\{\\sigma = 6, \\alpha = 0.004, \\gamma = 0.002\\}$ are obtained by fine-tuning on ResNet50 with NeuralTextures dataset and are kept the same throughout all datasets, whereas that of EfficientNet-B1 are $\\{\\sigma = 6, \\alpha = 0.002, \\gamma = 0.006\\}$ .", + "bbox": [ + 75, + 398, + 472, + 612 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Results", + "text_level": 1, + "bbox": [ + 76, + 621, + 171, + 636 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "This section reports the results of our QAD and other baselines under two scenarios: 1) quality-agnostic setting, which represents no model has prior knowledge of the input images' quality, and 2) quality-aware setting, which baselines are required to know inputs' quality information.", + "bbox": [ + 75, + 643, + 468, + 720 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3.1 Quality-agnostic models", + "text_level": 1, + "bbox": [ + 76, + 739, + 302, + 756 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We use the popular deepfake detection benchmark methods on our datasets: 1) MesoNet with Inception layer by [1], 2) Xception model proposed by [43], 3) $F^3$ Net [38], 4) MAT [61] - a multi-attention deepfake detector, 5) a deviation of the method proposed by [9] to the instance-based collaborative learning, SBIs [45] - a self-blended method using real image only during training, 7) ADD [28] - a knowledge distillation-based approach for detecting low-quality deepfakes, and 8) BZNet [29] - a super-resolution", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "approach for improving detection of low-quality deepfakes. Each method has a different training approach to defend against performance degradation caused by lossy compression. The first five methods are trained with a mixture of the three data quality types (raw + c23 + c40). SBIs is trained with the mid-level of video compression (c23), which is commonly adopted in many works. Meanwhile, ADD and BZNet models are trained on raw, c23, and c40, respectively; however, in the inference phase, they are blindly tested over the entire dataset without the prior knowledge of quality types, and we report their average performance. In the test set, we include both video compression and random JPEG image compression [2].", + "bbox": [ + 496, + 334, + 893, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The results for the video compression are presented in Table 1, where our QAD outperforms other SOTA baselines across multiple benchmark datasets. Notably, we achieve a significant improvement in AUC score of up to $5.28\\%$ for heavily compressed datasets, such as NeuralTextures (89.64% vs 94.92%). We also surpassed previous works on various deepfake datasets by $0.44\\%$ to $1.05\\%$ points, with the exception of Deepfakes and FFIW10K datasets, which are easy to detect even when compressed. Compared to the collaborative learning baseline by [9], which is a comparative benchmark, our QAD still gains a decent improvement on average, up to $0.93\\%$ and $1.54\\%$ points with QAD-R and QAD-E, respectively. Finally, our QAD-E models achieved the highest score on average, reaching $98.47\\%$ .", + "bbox": [ + 496, + 542, + 893, + 755 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Regarding the random image compression experiment, the results are provided in Table 2. Although BZNet is marginally outperform our model on face-reenactment deepfakes (NT and F2F), our method still achieves the best performance with the highest scores on five over seven datasets. On average, our enhancements show decent improvements, with margins of $0.5\\%$ and $0.88\\%$ of QAD-R and QAD-E, respectively, compared to the second-best competitor (Fang & Lin).", + "bbox": [ + 496, + 763, + 895, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22384", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4d88c5324fd3ae21bd400d2a928c8cb17f036a2582827f75ada9867e1336c59e.jpg", + "image_caption": [ + "Figure 3. Model's performance versus $\\alpha$ and $\\gamma$ on the NeuralTextures." + ], + "image_footnote": [], + "bbox": [ + 112, + 88, + 434, + 321 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7df64fcf0632e989cdf4376b26789b149461fd1a88e8511c2b5b9a234beb0aaa.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Model / lossRESNET-50
ACC (%)AUC (%)
Baseline78.888.2
Coll. lossSoft-label77.084.0
Pairwise loss79.789.1
Center loss79.888.9
HSIC80.390.1
Adv. lossAWP-KL80.989.4
AWP-XE81.790.7
QAD (ours)82.291.3
", + "bbox": [ + 117, + 363, + 429, + 507 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3.2 Quality-aware models", + "text_level": 1, + "bbox": [ + 76, + 559, + 284, + 574 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this experiment, we compare our models with quality-aware benchmark baselines. In particular, beside RESNET-50 and EFFICIENTNET-B1, for each of the raw, c23, and c40 datasets, we implement ADD [28] and BZNet [29] models. Since ADD and BZNet are the best performing methods, in which they utilized knowledge distillation and super-resolution approaches, respectively, for detecting deepfakes in different qualities. Hence, we only include them in this experiment. In the inference phase, the performance of these models is validated with the prior knowledge of the input image's quality, i.e., c40 images are evaluated by the same quality c40 pre-trained models. Meanwhile, our universal QAD is blindly evaluated without such prior knowledge. We integrate our QAD on RESNET50 and EFFICIENTNET-B1 and present their performance in Table 3. As we can observe, our QAD-E model performs slightly better or on par with RESNET-50, BZNet, and ADD models, despite having only one-third of the number of parameters and no prior knowledge of input image quality. Moreover, when integrating with EFFICIENTNET-B1, QAD-E achieves a new SOTA performance with an improvement", + "bbox": [ + 75, + 583, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/63abbc7324489a0e0050bd33ea30f5b3fdd853a088cc6c771b07054fc672101c.jpg", + "table_caption": [ + "Table 4. Performance (ACC & AUC) of RESNET50 integrated with different losses." + ], + "table_footnote": [], + "table_body": "
QADNTDFF2FFSFSHCDFv2FFIW10KAvg
ResNET18
X88.7398.9398.0598.0698.6797.0998.7296.89
✓91.3899.3298.3299.1998.9497.9799.1097.75
ResNET34
X88.2699.0197.9898.6798.8896.6198.9796.91
✓92.8799.3098.3799.1099.2198.4899.1498.07
EFFICIENTNET-B0
X86.1299.2997.9398.2198.4297.8198.8096.65
✓91.9999.3398.6699.1599.0098.3899.1297.95
", + "bbox": [ + 506, + 88, + 887, + 271 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Performance (AUC) of RESNET18, RESNET34, and EFFICIENTNET-B0 baseline and their integration with our QAD training framework.", + "bbox": [ + 500, + 272, + 890, + 314 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of up to $0.89\\%$ points (97.79% vs. 96.90%), with a modest number of parameters (6.5M).", + "bbox": [ + 498, + 339, + 890, + 371 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation studies", + "text_level": 1, + "bbox": [ + 500, + 381, + 661, + 396 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4.1 $\\alpha$ and $\\gamma$ of our loss", + "text_level": 1, + "bbox": [ + 500, + 405, + 684, + 420 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We investigate the sensitivities of our QAD with respect to $\\alpha$ and $\\gamma$ , and summarize the results of our analysis in Fig. 3. In this study, we experiment with ResNET50 on the NeuralTextures dataset, which is the hardest dataset to detect when compressed. And, we vary the values of the hyperparameters $\\alpha \\in \\{0.002, 0.004, 0.008\\}$ and $\\gamma \\in \\{0.001, 0.002, 0.003, 0.004\\}$ , where the value at $(\\alpha, \\gamma) = (0.0, 0.0)$ indicate the baseline. The results suggest that when $\\alpha$ is greater than 0.002, the performance of our model is high and stable, surpassing current SOTA with any $\\alpha$ greater than 0.002. Additionally, increasing $\\gamma$ generally improves performance. Note that, as we did not tune the hyper-parameters to optimize the test accuracy, Section 4.3's hyper-parameters are not the best, despite outperforming all current methods on the datasets.", + "bbox": [ + 498, + 430, + 890, + 656 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4.2 Selection of losses", + "text_level": 1, + "bbox": [ + 500, + 678, + 678, + 691 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We study different alternatives for the collaborative learning loss and the adversarial weight perturbation approach. In particular, for the collaborative learning loss, we apply the loss function that was introduced by [47], in which they aggregate the logits of different views, combining them with their true labels to generate the soft labels. Besides, we replace our HSIC regularization with intermediate pairwise loss (Eq. 3) and center loss. Regarding the adversarial weight perturbation, we further apply the KL divergence between the representations of raw and compressed images to perturb the model's weights.", + "bbox": [ + 496, + 703, + 890, + 869 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We report the results in Table 4, where we observe that the soft label loss fails to improve the baselines due to a", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22385", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/32d83f1ec0636614abc8f698b971e0c1801c175396f4ff0b9e87049c9fd85c29.jpg", + "image_caption": [ + "Figure 4. Performance (AUC) of our proposed method at different input resolutions with NeuralTextures dataset." + ], + "image_footnote": [], + "bbox": [ + 89, + 92, + 455, + 247 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/1525d5a32568c5d09592771c5826bee6aaec3d74bcc314d73b991d835f4d7afa.jpg", + "image_caption": [ + "Figure 5. t-SNE visualisation of baseline and our QAD." + ], + "image_footnote": [], + "bbox": [ + 89, + 294, + 272, + 439 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/9e26333e0f705ea9dfba454ec57d79e87e46db2db839caffa4172f54be435b39.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 295, + 457, + 439 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "lack of low-level representation agreement between different image qualities. While both pairwise and center loss slightly improve the baselines and are unstable with different model architecture, our HSIC consistently achieves the best performance by relaxing the instance-base constraint. Meanwhile, we can observe the model's performance drops in terms of both ACC and AUC, when replacing our AWP with cross-entropy loss with KL divergence. Generally, this experiment shows that using pairwise differences of various quality image representations at the output, such as soft label, pairwise constraint, or AWP-KL, for optimizing the model can hinder its convergence to the optimal parameters.", + "bbox": [ + 75, + 474, + 472, + 657 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.4.3 Experiment with different backbones", + "text_level": 1, + "bbox": [ + 76, + 678, + 390, + 693 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 5 shows the comparability of our QAD with three different backbone networks: RESNET18, RESNET34, and EFFICIENTNET-B0. The hyperparameter settings are kept the same for RESNET50 and EFFICIENTNET-B1. As shown in Table 5, our QAD consistently improves the baselines, from $0.86\\%$ to $1.3\\%$ points on average of seven deepfake datasets.", + "bbox": [ + 75, + 703, + 468, + 808 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.4.4 Performance at different input scales", + "text_level": 1, + "bbox": [ + 76, + 830, + 390, + 845 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Unlike other classification tasks, a notable factor that substantially affects the deepfake detection performance, which is omitted by most previous works [43, 38, 61], is", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "the input size of faces. We resize the input images from 56 to 336 and demonstrate how it impacts our QAD in comparison with ResNET50 baseline. The experiment is performed with the NeuralTextures dataset, and its results are reported in Fig. 4. We note that our proposed QAD and the baselines consistently improve their performance, when increasing the input size. Beside, our method also keep its staging improvement across the input resolutions compared to ResNET50 baseline.", + "bbox": [ + 496, + 90, + 893, + 227 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.4.5 Feature distribution visualization", + "text_level": 1, + "bbox": [ + 500, + 267, + 785, + 281 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "To verify the consistency of invariant representation upon the input quality, we draw the feature distribution of EFFICIENTNET-B1 and our QAD-EFFICIENTNET-B1 pretrained on NeuralTextures (with raw, c23, and c40 datasets) with t-SNE [53]. The results are shown in Fig. 5. As observed, our QAD model's representations are less dispersed both in terms of intra-class and inter-quality. This experiment demonstrates that traditional cross-entropy loss trained with multiple input quality are confused due to the low-level constraints, while our QAD enables the model to achieve more generalization regardless of input quality.", + "bbox": [ + 496, + 297, + 893, + 465 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 489, + 617, + 505 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Most deep learning-based deepfake detectors use a single model for each video quality, leaving an unsolved practical issue of their generalizability for detecting different quality of deepfakes. In this work, we propose a universal deepfake detection framework (QAD). Using intra-model collaborative learning, we minimize the geometrical differences of images in various qualities at different intermediate layers by the HSIC module. Moreover, our adversarial weight perturbation (AWP) module is directly applied to the model's parameters to provide its robustness against input image compression. Extensive experiments show that our QAD achieves competitive detection accuracy and marks the new SOTA results on various deepfake datasets without prior knowledge of input image quality.", + "bbox": [ + 496, + 518, + 893, + 731 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements. This work was partly supported by Institute for Information & communication Technology Planning & evaluation (IITP) grants funded by the Korean government MSIT: (No. 2022-0-01199, Graduate School of Convergence Security at Sungkyunkwan University), (No. 2022-0-01045, Self-directed Multi-Modal Intelligence for solving unknown, open domain problems), (No. 2022-0-00688, AI Platform to Fully Adapt and Reflect Privacy-Policy Changes), (No. 2021-0-02068, Artificial Intelligence Innovation Hub), (No. 2019-0-00421, AI Graduate School Support Program at Sungkyunkwan University), and (No. RS-2023-00230337, Advanced and Proactive AI Platform Research and Development Against Malicious deepfakes).", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "22386", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Darius Afchar, Vincent Nozick, Junichi Yamagishi, and Isao Echizen. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 5778-5788, June 2021. 6" + ], + "bbox": [ + 78, + 90, + 470, + 444 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "22389", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Quality-Agnostic Deepfake Detection with Intra-model Collaborative Learning/77142358-08da-4d47-9173-9c11400a028e_model.json b/2023/Quality-Agnostic Deepfake Detection with Intra-model Collaborative Learning/77142358-08da-4d47-9173-9c11400a028e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7efe451103f726c2ba8ccb1838e74480b6839100 --- /dev/null +++ b/2023/Quality-Agnostic Deepfake Detection with Intra-model Collaborative Learning/77142358-08da-4d47-9173-9c11400a028e_model.json @@ -0,0 +1,2666 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.088, + 0.131, + 0.882, + 0.153 + ], + "angle": 0, + "content": "Quality-Agnostic Deepfake Detection with Intra-model Collaborative Learning" + }, + { + "type": "text", + "bbox": [ + 0.247, + 0.167, + 0.344, + 0.183 + ], + "angle": 0, + "content": "Binh M. Le" + }, + { + "type": "text", + "bbox": [ + 0.126, + 0.185, + 0.465, + 0.236 + ], + "angle": 0, + "content": "Dept. of Computer Science & Engineering Sungkyunkwan University Suwon, South Korea" + }, + { + "type": "text", + "bbox": [ + 0.227, + 0.241, + 0.364, + 0.254 + ], + "angle": 0, + "content": "bmle@g.skku.edu" + }, + { + "type": "text", + "bbox": [ + 0.616, + 0.167, + 0.741, + 0.183 + ], + "angle": 0, + "content": "Simon S. Woo*" + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.185, + 0.845, + 0.236 + ], + "angle": 0, + "content": "Dept. of Computer Science & Engineering Sungkyunkwan University Suwon, South Korea" + }, + { + "type": "text", + "bbox": [ + 0.608, + 0.241, + 0.743, + 0.254 + ], + "angle": 0, + "content": "swoo@g.skku.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.473, + 0.712 + ], + "angle": 0, + "content": "Deepfake has recently raised a plethora of societal concerns over its possible security threats and dissemination of fake information. Much research on deepfake detection has been undertaken. However, detecting low quality as well as simultaneously detecting different qualities of deepfakes still remains a grave challenge. Most SOTA approaches are limited by using a single specific model for detecting certain deepfake video quality type. When constructing multiple models with prior information about video quality, this kind of strategy incurs significant computational cost, as well as model and training data overhead. Further, it cannot be scalable and practical to deploy in real-world settings. In this work, we propose a universal intra-model collaborative learning framework to enable the effective and simultaneous detection of different quality of deepfakes. That is, our approach is the quality-agnostic deepfake detection method, dubbed QAD. In particular, by observing the upper bound of general error expectation, we maximize the dependency between intermediate representations of images from different quality levels via Hilbert-Schmidt Independence Criterion. In addition, an Adversarial Weight Perturbation module is carefully devised to enable the model to be more robust against image corruption while boosting the overall model's performance. Extensive experiments over seven popular deepfake datasets demonstrate the superiority of our QAD model over prior SOTA benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.743, + 0.21, + 0.759 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.77, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Deep learning approaches for facial manipulation, such as deepfakes, have recently received considerable attention [54, 31, 61, 25, 20, 23], because they can be abused for the malicious purposes such as fake news, pornography, etc. Due to the advancements made in Generative Adversarial Networks and other deep learning-based computer vision algorithms, deepfakes have also become more realistic and" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.286, + 0.642, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.647, + 0.289, + 0.761, + 0.393 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.765, + 0.289, + 0.898, + 0.393 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.395, + 0.616, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.618, + 0.395, + 0.753, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.755, + 0.395, + 0.894, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.48, + 0.895, + 0.577 + ], + "angle": 0, + "content": "Figure 1. A summary of our goal. Our approach stands out from previous works that detect deepfakes using separate models for different qualities (e.g. Baseline 2 [28]) or a single model without considering the interaction between qualities (e.g. Baseline 1 [43]). Instead, our method employs all quality levels and improves the performance of the model on each quality level, leading to overall enhanced performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.597, + 0.892, + 0.734 + ], + "angle": 0, + "content": "natural, making it harder not only for humans, but also for classifiers to tell them apart. Moreover, it has been simpler than ever before to create convincing deepfakes using simple programs and apps without requiring advanced machine learning knowledge. Such easy-to-create and realistic fake images and videos can be maliciously exploited, raising significant security, privacy, and societal concerns such as fake news propagation [39], and stealing personal information via phishing and scams [10]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.893, + 0.902 + ], + "angle": 0, + "content": "To mitigate such problems caused by deepfakes, there has been a tremendous research effort put into constructing reliable detectors [32, 25, 8, 38, 61, 44]. Although they have achieved outstanding performance with high-quality deepfakes, most of them have failed to detect low-quality deepfakes effectively [8, 43]. While video compression steps do not significantly impact on visualization, it drastically drop deepfake detectors' performance on low-quality deepfakes (c40). A handful of research has been focused on detecting low-quality deepfakes such as ADD [28] and BZNet [29]. However, their methods can only detect low-quality com" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "22378" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.228 + ], + "angle": 0, + "content": "pressed deepfakes. And, those prior approaches expose a critical problem, when deployed in practice since the prior video quality information of the input is unknown. Moreover, developing different models for each input quality induces significant computational overhead. Other works, such as LipForensics [16], also attempt to make their detectors robust against various corruptions and compression. Nevertheless, it is unable to detect image-based deepfakes with random lossy compression like JPEG." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.23, + 0.473, + 0.487 + ], + "angle": 0, + "content": "In this research, we propose the novel deepfake detection method, QAD, which can simultaneously detect both high and low-quality (quality-agnostic) deepfakes in a single model, as illustrated in Fig. 1. Especially, we propose a universal intra-model collaborative learning framework to provide the effective detection of different quality deepfakes. We modulate the conventional model-based collaborative learning [47] to an instance-based intra-model collaborative learning framework in our training. During the training phase, our single model simultaneously learns the representations of one image, but with different qualities. By utilizing the collaborative learning framework, our QAD can align the distributions of high and low-quality image representations to be geometrically similar. Hence, it can avoid the overfitting caused by compressed images and the overconfidence caused by raw images, while boosting its overall performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.489, + 0.473, + 0.732 + ], + "angle": 0, + "content": "In particular, we perform a rigorous theoretical analysis, and show that the low-quality deepfake classification error can be bounded by two terms: classification loss and the distance between the representations of high and low-quality images. Instead of using a direct pairwise regularization to minimize the gaps between the high and low-quality image representations, we propose to apply Hilbert-Schmidt Independence Criterion (HSIC) to maximize the dependence between a mini-batch of high and low-quality images, thus maximizing the mutual information between them, and supporting the high-level representations and effective output predictions. Meanwhile, to enhance the model's robustness under heavy input compression, we propose Adversarial Weight Perturbation (AWP) [56, 3], which can further flatten the weight loss landscape of the model, bridging the gap in multiple quality learning for deepfake detection." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.473, + 0.884 + ], + "angle": 0, + "content": "Finally, we conduct extensive experiments to show the effectiveness of our QAD with seven different popular benchmark datasets. We first show that our method can outperform previous baselines when training with data from various video and image compression qualities. Furthermore, we show that our QAD exceeds the performance of the SOTA quality-aware models such as BZNet [29] by a significant margin, while requiring remarkably fewer computational parameters and no prior knowledge of the inputs. Our contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.886, + 0.472, + 0.902 + ], + "angle": 0, + "content": "1) We theoretically analyze and prove that the classifica" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "tion error of low-quality deepfakes can be bounded by its classification loss and the representation distance with its corresponding high-quality images." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.137, + 0.894, + 0.258 + ], + "angle": 0, + "content": "2) We propose a unified quality-agnostic deepfake detection framework (QAD), utilizing instance-based intramodel collaborative learning. We use the Hilbert-Schmidt Independence Criterion (HSIC) to maximize the geometrical similarity between intermediate representations of high and low-quality deepfakes, and Adversarial Weight Perturbation (AWP) to make our model robust under varying input compression." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.258, + 0.894, + 0.319 + ], + "angle": 0, + "content": "3) We demonstrate that our approach outperforms well-known baselines, including the total of eight quality-agnostic and quality-aware SOTA methods with seven popular benchmark datasets." + }, + { + "type": "list", + "bbox": [ + 0.497, + 0.137, + 0.894, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.334, + 0.646, + 0.35 + ], + "angle": 0, + "content": "2. Related works" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.359, + 0.684, + 0.375 + ], + "angle": 0, + "content": "2.1. Deepfake detection" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.383, + 0.895, + 0.807 + ], + "angle": 0, + "content": "Recently, deepfakes have been of the utmost crucial because they can cause serious security and privacy threats. Theresfore, a large number of detection methods have been proposed to effectively identify such deepfakes [43, 31, 30, 22, 41, 54, 32, 25, 8, 61]. However, the majority of the aforementioned works focus on mining visual artifacts of deepfakes, such as the blending boundaries of generated faces [31], the irregularity of pupil shapes [14], the spatiotemporal inconsistency [6, 44], or exploring deep learning-based attention methods [61] to identify such artifacts. Meanwhile, several approaches also showed that exposing deepfakes in the frequency domain is effective. Such methods include analyzing the discrepancies of frequency spectrum [8, 27, 25], employing the checkerboard artifacts caused by the transposed convolutional operator [60, 11], or mining the statistical frequency features with dual deep learning models [38]. Nevertheless, such models' performance substantially decreases when encountering low-quality compressed images. To remedy the above shortcoming, recent studies proposed methods to detect the deepfake in highly compressed low-quality versions such as [28], which utilized a knowledge distillation. Also, [29] presented a supper-resolution-based network for enhancing the performance of low-quality deepfake detection. However, all of the aforementioned approaches are limited in developing a single model for each quality of deepfakes, which is impractical to deploy in real-world scenarios due to the requirement of prior knowledge of the input quality." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.712, + 0.833 + ], + "angle": 0, + "content": "2.2. Collaborative learning" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Collaborative learning proposed by [47] is designed to achieve a global minimum of a deep neural network, while maintaining the same computational complexity at inference time as at training time. Collaborative learning inherits" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22379" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "the advantages of auxiliary training [48], multi-task learning [58], and knowledge distillation [18]. Its applications cover supporting weakly-supervised learning [24], or integrating with online knowledge distillation [57, 15]. And, its training graph is divided into two or more sub-networks to ensure global minimum achievement [47]. Besides, [9] proposed an intra-model collaborative learning framework that shares a similar characteristic with self-knowledge distillation. However, all of the approaches are model-based collaborative learning, in which a single input generates multiple outputs (or views) through multiple classifier heads of one target network in both training and inference phase." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.274, + 0.473, + 0.456 + ], + "angle": 0, + "content": "In this work, we distinguish ourselves by deploying the collaborative learning framework for simultaneously training deepfakes of various qualities with an undeviated single model, namely instance-based collaborative learning. Different from conventional mini-batch stochastic optimization, which independently samples random images from different qualities and optimizes the detector, our collaborative learning approach allows us to utilize the common features in the same image but from different qualities simultaneously. Thus, our deepfake detector circumvent the overfitting caused by compressed images or the overconfidence from raw images, enhancing its overall performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.469, + 0.427, + 0.485 + ], + "angle": 0, + "content": "2.3. Hilbert-Schmidt Independence Criterion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.494, + 0.473, + 0.766 + ], + "angle": 0, + "content": "The Hilbert-Schmidt Independence Criterion (HSIC) [13] measures the statistical dependency between probability distributions. In fact, HSIC differs from the covariance, where \\( \\text{Cov}(X,Y) = 0 \\) does not imply that two random variables \\( X \\) and \\( Y \\) are independent [42], while HSIC shows its tractable computation and equivalency in terms of the independence property [13]. Moreover, HISC is easy to be estimated statistically and algorithmically. In practice, applications based on HSIC are found in a variety of practical domains, including maximizing the dependencies for self-supervised learning [33] and classification learning [34, 12], or defense against model inversion attacks [37]. In this paper, we utilize the HSIC to maximize the dependency between distributions of deepfake images of different qualities at intermediate layers. Therefore, we aim to constrain low-level representations of images not to be exactly the same, but to share a geometrical similarity of learning features that can support high-level output predictions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.784, + 0.176, + 0.799 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In this section, we first theoretically examine the upper bound for our optimization problem by considering a DNN classifier of \\( K \\) classes, and two modalities of input quality: raw (high-quality) and compressed (low-quality). Then, we discuss how to more efficiently collaborate on the representations of deepfake images of differing quality." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.768, + 0.108 + ], + "angle": 0, + "content": "3.1. Preliminary & our inspiration" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.895, + 0.281 + ], + "angle": 0, + "content": "Given a sample \\( x_r \\) from a space \\( \\mathcal{X} \\) and its compressed version at quantile \\( c \\), \\( x_c \\) can be expressed as \\( x_c = x_r - \\delta_c \\), and we define the corresponding label \\( y \\in \\{0,1\\} \\) (real and fake). Next, a family \\( \\mathcal{F} \\) of learning functions \\( f: \\mathcal{X} \\to \\mathbb{R}^2 \\) returns a 2-tuple \\( f(x) = [f(x,j)]_{j=1}^2 \\), whose \\( f(x,j) \\) is proportional to the probability to assign \\( x \\) to the \\( j \\)-th class, and \\( f \\) is defined by learning parameters \\( \\theta \\). Given a training data \\( \\mathcal{D} = \\{(x_i,y_i)\\}_{i=1}^n \\subset \\mathcal{X} \\times \\mathcal{Y} \\), our goal is to minimize the expectation of a loss function \\( \\mathcal{L}: \\mathbb{R}^2 \\times \\mathcal{Y} \\to \\mathbb{R} \\). Here, we consider \\( \\mathcal{L}(f(x),y) = 1 - \\sigma_T(f(x,y)) \\), where \\( \\sigma_T \\) is the softmax function with temperature \\( T > 0 \\):" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.291, + 0.892, + 0.328 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {T} (f (x), y) = \\frac {\\exp (f (x , y) / T)}{\\sum_ {k = 1} ^ {2} \\exp (f (x , k) / T)}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.338, + 0.895, + 0.384 + ], + "angle": 0, + "content": "Theorem 1. (Proof can be done similarly as [36] and [19] in Supp. Material) For any \\( f \\in \\mathcal{F} \\), and with probability \\( 1 - \\delta \\) over the draw of \\( \\mathcal{D} \\)," + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.395, + 0.901, + 0.487 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbb {E} \\left[ \\mathbb {I} \\left\\{\\hat {y} \\left(x _ {c}\\right) \\neq y \\right\\} \\right] \\leq 2 \\mathbb {E} _ {\\mathcal {D}} \\mathcal {L} \\left(f \\left(x _ {c}\\right), y\\right) \\\\ + \\frac {8}{T} \\mathbb {E} _ {\\mathcal {D}} \\mathcal {L} _ {i - c o l} (f (x _ {r}), f (x _ {c})) + 4 \\Re_ {\\mathcal {D}} (\\Phi_ {\\mathcal {W}}) \\\\ + \\frac {1 6}{n} + \\mathcal {O} \\left(\\sqrt {\\frac {\\log (2 / \\delta)}{2 n}}\\right), \\tag {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.497, + 0.892, + 0.528 + ], + "angle": 0, + "content": "where \\(\\Re_{\\mathcal{D}}\\) is the Rademacher complexity, \\(\\Phi_{\\mathcal{W}} = \\{\\mathcal{L}(f(x_r),y),f\\in \\mathcal{F}\\}\\) , and" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.54, + 0.892, + 0.557 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i - c o l} \\left(f \\left(x _ {r}\\right), f \\left(x _ {c}\\right)\\right) = \\| f \\left(x _ {r}\\right) - f \\left(x _ {c}\\right) \\| . \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.749 + ], + "angle": 0, + "content": "Insight of Theorem 1. On the right-hand side of Eq. 2, our classifier \\( f \\) depends on two terms, where the first term is the classification loss \\( \\mathcal{L}(f(x_c), y) \\) applied to the prediction of the compressed image \\( x_c \\). And, the second term is the instance-based collaborative loss \\( \\mathcal{L}_{i-col}(f(x_r), f(x_c)) \\) that measures the pairwise difference between predictions of the raw image and its compressed version. Therefore, minimizing the expectation over training data \\( \\mathcal{D} \\) of \\( 2\\mathcal{L}(f(x_c), y) + 8\\mathcal{L}_{i-col}(f(x_r), f(x_c)) / T \\), can decrease the true error. Note that Eq. 2 is also general so that it can be applicable for raw images. Hence, in practice, the first term can be generalized to both raw and compressed images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.902 + ], + "angle": 0, + "content": "In order to minimize the expectation of errors in both raw and compressed deepfake image predictions, our theoretical analysis shows that we can minimize both classification loss and collaborative loss at the output. However, as observed by [9] and in our experiments (see Tab. 4), this instance-based collaborative learning loss fails to achieve the best performance. Additionally, training solely with highly-compressed images makes the detector prone to overfitting, yielding a considerable gap between training and test performance [28]. As a result, the major research" + }, + { + "type": "footer", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "22380" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.087, + 0.501, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.088, + 0.871, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.25, + 0.871, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.38, + 0.892, + 0.464 + ], + "angle": 0, + "content": "Figure 2. Overview of our QAD framework. A mini-batch of images from different quality modalities (e.g., two in this diagram) is forwarded through a single universal model. Although it is one model, we pictorially split it into two branches for the reader's understanding. After training, we obtain one universal model that regulates different qualities. Top-right: The HSIC geometrically maximizes the dependency between images from various quality modalities at different resolutions, supporting high-level output predictions. Bottom-right: Through searching for the worst-case parameters' corruption and compensating for input corruption (compression), the AWP flattens the model's weight loss landscape, making the model robust under varying input compression." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.488, + 0.469, + 0.533 + ], + "angle": 0, + "content": "challenge is how we can further lower the sensitivity of \\( f_{\\theta} \\) to \\( x \\) at various compression settings and push their representations close to each other." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.47, + 0.703 + ], + "angle": 0, + "content": "Classification loss. We can construct a robust model under input corruption by flattening the weight loss landscape. In particular, we apply the Adversarial Weight Perturbation [56] to search for the worst-case perturbations \\(\\phi^{*}\\) of the model weights at every training step. Thereafter, optimizing the perturbed model via \\(\\mathcal{L}(f_{\\theta +\\phi^*},y)\\) can enable it to be more robust under varying input image correlations/distortions, which represent the varying qualities of deepfake inputs (See Fig. 2—Bottom-right panel). Furthermore, the classification loss in Eq. 2 is upper bounded by this new loss function due to the worst-case perturbations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Collaborative loss. With respect to the collaborative learning loss, Eq. 3 shares similar characteristics with recent knowledge distillation research [18, 52]. However, our goal is to develop and train a single universal model, not having a teacher-student relationship. Nevertheless, we argue that the gap between raw and compressed image representations can be minimized more efficiently by regularizing their discrepancy at the low-level representations. Moreover, enforcing the similarity of the pairwise representations at the intermediate layers with an input difference of \\( |\\delta_c| \\) can collapse layers' weights to zero or can lead a deep model to remember training data instead of learning discriminative features. Therefore, we relax this constraint by" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.488, + 0.892, + 0.656 + ], + "angle": 0, + "content": "maximizing the kernel dependency in a mini-batch of data between the raw and compressed image representations by the Hilbert-Schmidt Independence Criterion (HSIC). Using HSIC, we can instead enforce the geometrical structures of mini-batch of raw data and the compressed data to be similar, so that we can still effectively detect different-quality deepfakes in a single model. From a mutual information perspective, maximizing the kernel dependency can enforce the mutual information of the learned representations of different compression ratios, thus regularizing the detector to be more generalized (See Fig. 2—Top-right panel)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.665, + 0.71, + 0.68 + ], + "angle": 0, + "content": "3.2. Details of our methods" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.689, + 0.776, + 0.705 + ], + "angle": 0, + "content": "3.2.1 Weight loss landscape flattening" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.713, + 0.892, + 0.804 + ], + "angle": 0, + "content": "Recent studies [21, 55] suggest that searching for a flatter minima can improve the generalization ability of the model. To achieve this, we propose using Adversarial Weight Perturbation [56] to identify flat local minima of the empirical risk. The worst-case perturbations \\(\\phi^{*}\\) of the model weights which increases the loss dramatically is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.816, + 0.892, + 0.844 + ], + "angle": 0, + "content": "\\[\n\\phi^ {*} = \\underset {\\phi \\in \\mathcal {B} _ {p} (\\theta , \\gamma)} {\\arg \\max } \\mathcal {L} (f _ {\\theta + \\phi} (x), y), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.855, + 0.892, + 0.903 + ], + "angle": 0, + "content": "where \\(\\mathcal{B}_p(\\theta, \\gamma) = \\{v \\in \\Theta : \\| \\theta - v \\|_p \\leq \\gamma\\}\\) is the feasible region of any perturbation \\(\\phi\\). The AWP adds the worst-case perturbation to the model weight, so that \\(\\mathcal{L}(f_{\\theta + \\phi^*}(x), y)\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22381" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.167 + ], + "angle": 0, + "content": "becomes the supremum value in \\(\\mathcal{B}_p(\\theta, \\gamma)\\). Therefore, optimizing \\(\\mathcal{L}(f_{\\theta + \\phi^*}(x), y)\\) pushes \\(\\theta\\) to adjust its values such that the loss landscape is more flatten with the same capability \\(\\mathcal{B}_p(\\theta, \\gamma)\\). As a result, \\(f\\) becomes more stable under input image's changes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.167, + 0.47, + 0.199 + ], + "angle": 0, + "content": "Similar to adversarial example perturbation [35], \\(\\phi^{*}\\) is generated by projected gradient method as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.206, + 0.47, + 0.241 + ], + "angle": 0, + "content": "\\[\n\\phi^ {*} \\leftarrow \\Pi_ {\\theta} ^ {\\gamma} \\left(\\phi + \\eta \\frac {\\nabla \\mathcal {L} \\left(f _ {\\theta + \\phi} (x) , y\\right)}{\\| \\nabla \\mathcal {L} \\left(f _ {\\theta + \\phi} (x) , y\\right) \\|} \\| \\theta \\|\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.248, + 0.47, + 0.34 + ], + "angle": 0, + "content": "where \\(\\Pi_{\\theta}^{\\gamma}\\) is an operator that projects its input into the feasible region \\(B_{p}(\\theta, \\gamma)\\), and \\(\\eta \\in \\mathbb{R}\\) is the step size. In fact, we empirically find that using a one-step projection for \\(\\phi^{*}\\) is sufficient for the model's robustness under the image corruptions formed by compression. By adding \\(\\phi^{*}\\) in Eq. 5 to \\(\\theta\\), it is straightforward to bound \\(\\mathcal{L}(f(x_c), y)\\) in Eq. 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.357, + 0.373, + 0.373 + ], + "angle": 0, + "content": "3.2.2 Intra-model collaborative learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.38, + 0.47, + 0.485 + ], + "angle": 0, + "content": "Hilbert-Schmidt Independence Criterion (HSIC). Let \\(\\mathcal{T}\\) and \\(\\mathcal{G}\\) be two separable Reproducing Kernel Hilbert Spaces (RKHS) on metric spaces \\(\\mathcal{U}\\) and \\(\\mathcal{V}\\), respectively. HSIC measures the dependency between two random variables \\(U\\) and \\(V\\) from a joint distribution on \\(\\mathcal{U}\\) and \\(\\mathcal{V}\\), by evaluating the cross-covariance of the nonlinear transformations of the two random variables:" + }, + { + "type": "equation", + "bbox": [ + 0.079, + 0.494, + 0.47, + 0.527 + ], + "angle": 0, + "content": "\\[\nH S I C (U, V) = \\left\\| \\mathbb {E} [ \\zeta (U) \\psi (V) ^ {T} ] - \\mathbb {E} \\zeta (U) \\mathbb {E} \\psi (V) ^ {T} \\right\\| _ {H S} ^ {2}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.526, + 0.47, + 0.618 + ], + "angle": 0, + "content": "where \\(\\| \\cdot \\|_{HS}\\) is the Hilbert-Schmidt norm, which becomes the Frobenius norm in finite dimensions. And, \\(\\zeta : \\mathcal{U} \\to \\mathcal{T}\\) and \\(\\psi : \\mathcal{V} \\to \\mathcal{G}\\) are nonlinear mapping functions. With appropriate transformation \\(\\zeta\\) and \\(\\psi\\), HSIC is a dependence test, which can identify the nonlinear dependencies between \\(U\\) and \\(V\\) as follows: \\(HSIC(U,V) = 0 \\Leftrightarrow U \\perp V\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.618, + 0.47, + 0.693 + ], + "angle": 0, + "content": "Also, inner products in \\(\\mathcal{T}\\) and \\(\\mathcal{G}\\) are formed by positive definite kernel functions: \\(k(u,u^{\\prime}) = \\langle \\zeta (u),\\zeta (u^{\\prime})\\rangle_{\\mathcal{T}}\\) and \\(l(v,v^{\\prime}) = \\langle \\psi (v),\\psi (v^{\\prime})\\rangle_{\\mathcal{G}}\\). And, let \\((U^{\\prime},V^{\\prime})\\) and \\((U^{\\prime \\prime},V^{\\prime \\prime})\\) be independent copies of \\((U,V)\\), then Eq. 6 can be expressed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.701, + 0.47, + 0.753 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} H S I C (U, V) = \\mathbb {E} [ k (U, U ^ {\\prime}) l (V, V ^ {\\prime}) ] \\\\ - 2 \\mathbb {E} [ k (U, U ^ {\\prime}) ] \\mathbb {E} [ l (V, V ^ {\\prime \\prime}) ] + \\mathbb {E} [ k (U, U ^ {\\prime}) ] \\mathbb {E} [ l (V, V ^ {\\prime}) ]. \\tag {7} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.762, + 0.47, + 0.824 + ], + "angle": 0, + "content": "Estimation of HSIC. The empirical estimation of HSIC with an bias of \\(\\mathcal{O}(\\frac{1}{n})\\) using \\(n\\) samples i.i.d drawn \\(\\{(u_i,v_i)\\}_{i = 1}^n\\) from the joint distribution \\((U,V)\\) is provided as follows [13]:" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.831, + 0.469, + 0.862 + ], + "angle": 0, + "content": "\\[\n\\widehat {H S I C} (U, V) = \\frac {1}{(n - 1) ^ {2}} \\mathbf {t r} (K H L H), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.87, + 0.47, + 0.903 + ], + "angle": 0, + "content": "where \\( K_{i,j} = k(u_i, u_j) \\), and \\( L_{i,j} = l(v_i, v_j) \\) are kernel matrices for the kernels \\( k \\), and \\( l \\), respectively, and \\( H_{i,j} = \\)" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.091, + 0.885, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 QAD: Quality-Agnostic Deepfake detection." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.108, + 0.892, + 0.184 + ], + "angle": 0, + "content": "Require: DNN \\(f\\) parameterized by \\(\\theta\\), training dataset \\(\\mathcal{D}\\) with M quality modalities \\(\\mathcal{T} = \\{r, c_1, \\dots, c_{M-1}\\}\\). Learning rate \\(\\alpha_l\\) and mini-batch size of \\(B\\). Model weight perturbation size \\(\\gamma\\), step size \\(\\eta\\), and the number of steps \\(K\\). Layers of \\(f\\) to apply HSIC \\(L\\)." + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.185, + 0.688, + 0.198 + ], + "angle": 0, + "content": "1: while not converged do" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.199, + 0.845, + 0.215 + ], + "angle": 0, + "content": "2: for mini-batch \\((X = [X_{\\tau}]_{\\tau \\in \\mathcal{T}}, Y) \\in \\mathcal{D}\\) do" + }, + { + "type": "text", + "bbox": [ + 0.51, + 0.216, + 0.719, + 0.228 + ], + "angle": 0, + "content": "3: # One-step AWP" + }, + { + "type": "text", + "bbox": [ + 0.51, + 0.229, + 0.765, + 0.244 + ], + "angle": 0, + "content": "4: \\(\\mathcal{L}_1 = \\mathcal{L}(f_{\\theta +\\phi}(X),Y) / MB\\)" + }, + { + "type": "text", + "bbox": [ + 0.51, + 0.245, + 0.777, + 0.269 + ], + "angle": 0, + "content": "5: \\(\\phi \\gets \\Pi_{\\theta}^{\\gamma}\\left(\\phi +\\eta \\frac{\\nabla\\mathcal{L}_{1}}{\\|\\nabla\\mathcal{L}_{1}\\|}\\parallel \\theta \\parallel\\right)\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.269, + 0.653, + 0.28 + ], + "angle": 0, + "content": "6: \\(\\theta \\gets \\theta +\\phi\\)" + }, + { + "type": "text", + "bbox": [ + 0.51, + 0.282, + 0.751, + 0.298 + ], + "angle": 0, + "content": "7: \\(\\mathcal{L}_1\\gets \\mathcal{L}(f_\\theta (X),Y) / MB\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.299, + 0.774, + 0.311 + ], + "angle": 0, + "content": "8: # intermediate reps." + }, + { + "type": "text", + "bbox": [ + 0.51, + 0.312, + 0.71, + 0.328 + ], + "angle": 0, + "content": "9: \\([Z_l^\\tau ]_{l\\in L}^{\\tau \\in T}\\coloneqq f_\\theta (X)\\)" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.329, + 0.884, + 0.34 + ], + "angle": 0, + "content": "10: # HSIC: dependence maximization" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.341, + 0.749, + 0.359 + ], + "angle": 0, + "content": "11: \\(\\mathcal{L}_2\\gets \\sum_{\\tau ,\\rho \\in T}^{\\tau \\neq \\rho}\\mathcal{L}_{col}(\\tau ,\\rho)\\)" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.359, + 0.812, + 0.372 + ], + "angle": 0, + "content": "12: # Overall loss Eq. (10)" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.373, + 0.737, + 0.387 + ], + "angle": 0, + "content": "13: \\(\\mathcal{L}_{QAD} \\gets \\mathcal{L}_1 + \\alpha \\times \\mathcal{L}_2\\)" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.388, + 0.733, + 0.402 + ], + "angle": 0, + "content": "14: \\(\\theta \\gets \\theta -\\alpha_{l}\\cdot \\nabla_{\\theta}\\mathcal{L}_{QAD}\\)" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.403, + 0.653, + 0.416 + ], + "angle": 0, + "content": "15: \\(\\theta \\gets \\theta -\\phi\\)" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.418, + 0.607, + 0.43 + ], + "angle": 0, + "content": "16: end for" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.433, + 0.6, + 0.446 + ], + "angle": 0, + "content": "17: end while" + }, + { + "type": "list", + "bbox": [ + 0.507, + 0.185, + 0.884, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.482, + 0.892, + 0.543 + ], + "angle": 0, + "content": "\\(\\delta_{i,j} - \\frac{1}{n}\\) is a centering matrix. Regarding the kernel functions, Theorem 4 in [13] suggested that an universal kernel, such as Laplace and Gaussian RBF kernel, can guarantee the HSIC to detect any dependency between \\(U\\) and \\(V\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.546, + 0.893, + 0.698 + ], + "angle": 0, + "content": "HSIC for maximizing the geometrical similarity. Let \\(\\tau\\) and \\(\\rho\\) be two different qualities of deepfakes, (e.g., raw vs. compressed). Consider the \\(l\\)-th layer of the learning network \\(f\\), we denote the learning features of a mini-batch of \\(B\\) images from \\(\\tau\\) and \\(\\rho\\) are \\(Z_{l}^{\\tau} = \\{u_{i}\\}_{B}\\), and \\(Z_{l}^{\\rho} = \\{v_{i}\\}_{B}\\) respectively, where \\(u_{i}, v_{i} \\in \\mathbb{R}^{H \\times W \\times C}\\) and \\(H, W\\) and \\(C\\) are the height, width, and channel number. Our regularization aims to maximize the dependency between \\(Z_{l}^{\\tau}\\) and \\(Z_{l}^{\\rho}\\) via a mini-batch of representations. In other words, we try to minimize the following loss:" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.715, + 0.892, + 0.75 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c o l} (\\tau , \\rho) = - \\sum_ {l \\in L} \\widehat {H S I C} \\left(Z _ {l} ^ {\\tau}, Z _ {l} ^ {\\rho}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.764, + 0.892, + 0.827 + ], + "angle": 0, + "content": "where \\( L \\) is a predetermined collection of layers to apply the collaborative loss. And, the computational complexity for calculating Eq. 9 is \\( \\mathcal{O}(B^2 L) \\), which can be reduced to \\( \\mathcal{O}(BL) \\) when applying random Fourier features [40]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.845, + 0.722, + 0.861 + ], + "angle": 0, + "content": "3.3. End-to-end training loss" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Given a training mini-batch \\(B\\) that include all \\(M\\) quality modalities \\(\\mathcal{T} = \\{r,c_1,\\dots c_{M - 1}\\}\\), the overall collaborative" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22382" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.159, + 0.088, + 0.813, + 0.313 + ], + "angle": 0, + "content": "
ModelTest Set AUC (%)
NTDFF2FFSFSHCDFv2FFIW10KAvg
Video Compression (raw + c23 + c40 of test set)
MesoNet [1]◇70.2493.7294.1585.1796.0080.5294.5687.77
Rössler et al. [43]◇89.6499.0597.8998.8398.5097.4999.1797.22
F3Net [38]◇86.7998.7396.3297.8297.4595.0697.9495.73
MAT [61]◇86.7998.7396.3297.8297.4595.0697.9495.73
Fang & Lin [9]89.3098.9897.3398.4398.6696.5898.9496.89
SBIs [45]†78.3395.1979.7480.3780.48--82.82
BZNet [29]†80.1298.8194.1097.71---91.01
ADD [28]†86.2696.2390.6295.5795.94--92.92
QAD-R (ours)91.2599.5498.3499.0199.1298.3699.1097.82
QAD-E (ours)94.9299.5398.9499.2799.1298.3899.1698.47
" + }, + { + "type": "table_caption", + "bbox": [ + 0.075, + 0.314, + 0.894, + 0.385 + ], + "angle": 0, + "content": "Table 1. Classification performance in the quality-agnostic setting with video compression of test set. The methods are trained using one of three approaches: simultaneously with three modalities (raw + c23 + c40), individually with each of the three modalities, or with a mid-level of compression (c23) to prevent performance degradation resulting from lossy compression. In the inference phase, video compression is applied to the input. The best results are highlighted in bold. \\(\\dagger\\) and \\(\\diamond\\) indicate results were obtained from methods' pretrained weights and published code, respectively." + }, + { + "type": "table", + "bbox": [ + 0.159, + 0.394, + 0.813, + 0.613 + ], + "angle": 0, + "content": "
ModelTest Set AUC (%)
NTDFF2FFSFSHCDFv2FFIW10KAvg
Random Image Compression (JPEG on raw of test set)
MesoNet [1]◇70.2392.0288.3282.6091.8481.1291.8785.43
Rössler et al. [43]◇69.8998.6294.9796.6696.7696.9898.8193.24
F3Net [38]◇70.9597.8992.8396.3494.7295.4497.1992.19
MAT [61]◇69.5398.9695.5397.9996.9798.2198.9193.73
Fang & Lin [9]75.4998.3294.6397.6497.2896.6798.3994.06
SBIs [45]†77.7597.8382.0586.1085.42--85.83
BZNet [29]†79.0098.7795.2397.92---92.73
ADD [28]†75.8496.8392.2395.2496.00--91.23
QAD-R (ours)75.1898.8693.7298.5298.1898.5198.9694.56
QAD-E (ours)76.2799.2094.4498.6998.6098.5298.8694.94
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.614, + 0.893, + 0.644 + ], + "angle": 0, + "content": "Table 2. Classification performance in the quality-agnostic setting with image compression of test set. The training approach resembles that of Table 1's setting, however, in the inference phase, random image compression is applied to the input." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.437, + 0.673 + ], + "angle": 0, + "content": "learning loss in our QAD framework is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.076, + 0.682, + 0.473, + 0.742 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {Q A D} = \\frac {1}{M B} \\sum_ {\\tau \\in \\mathcal {T}, i \\in B} \\mathcal {L} _ {\\phi^ {*}} \\left(x _ {\\tau , i}, y _ {i}\\right) + \\alpha \\sum_ {\\tau , \\rho \\in \\mathcal {T}} ^ {\\tau \\neq \\rho} \\mathcal {L} _ {c o l} (\\tau , \\rho), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is a hyper-parameter to balance contribution of each loss. It is worth noting that our QAD training loss is parameter-free, and is not affected by the order of the modalities. Further, unlike other model-based collaborative learning [47], our QAD does not derive any sub-models. In other words, it can be integrated with any backbone, i.e., RESNET50, and introduces no extra computation at the inference time. Note that Theorem 1 still holds when replacing the classification loss \\(\\mathcal{L}(f(x),y)\\) with any cross-entropy based loss, since \\(\\mathcal{L}(f(x),y)\\) is bounded by the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.893, + 0.703 + ], + "angle": 0, + "content": "cross-entropy loss. Finally, we present our end-to-end algorithm for optimizing Eq. 10 in Algorithm 1, and its pictorial illustration in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.717, + 0.707, + 0.734 + ], + "angle": 0, + "content": "4. Experimental Results" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.742, + 0.747, + 0.759 + ], + "angle": 0, + "content": "4.1. Dataset and pre-processing" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "For evaluating our proposed method, we experiment with seven different popular deepfake benchmark datasets: NeuralTextures (NT) [50], Deepfakes (DF) [4], Face2Face (F2F) [51], FaceSwap (FS) [5], FaceShifter (FSH) [30], CelebDFV2 (CDFv2) [59], and Face Forensics in the Wild (FFIW10K) [62]. Besides the raw version, these videos are also compressed into two types: medium (c23) and high (c40), utilizing the H.264 codec and constant rate quantization parameters of 23 and 40, respectively. These effectively" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22383" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.11, + 0.088, + 0.86, + 0.256 + ], + "angle": 0, + "content": "
Methodw/ prior infor.#paramsTest Set AUC (%)
NTDFF2FFSFSHCDFv2FFIW10KAvg
BZNet [29]†[×3]Y22M × 391.0199.3096.9098.82---96.51
ADD [28]†[×3]Y23.5M × 389.0899.2596.5398.2198.25--96.26
RESNET50 [×3]Y23.5M × 388.9699.2697.0498.6398.7197.0998.5896.90
QAD-R (ours)N23.5M × 188.8599.4297.7798.8398.9397.5698.9397.18
EFFICIENTNET-B1[×3]Y6.5M × 387.6399.0596.7298.1697.9596.7098.5496.39
QAD-E (ours)N6.5M × 192.2599.4698.3099.0898.9097.5099.0197.79
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.255, + 0.895, + 0.311 + ], + "angle": 0, + "content": "Table 3. Classification performance in the quality-aware setting with video compression of test set. Except for our model, each model is trained with three modalities: raw, c23, and c40, respectively (denoted \\([ \\times 3 ]\\)). In the inference phase, while our QAD uses one single pre-trained model, other methods use their corresponding pre-trained model (e.g., pre-trained RESNET-50 on raw) to detect a given testing input (e.g., raw). Reported performances are averaged score of the three modalities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.335, + 0.47, + 0.366 + ], + "angle": 0, + "content": "result in different quality of deepfakes, and details of these datasets are provided in our Supp. Material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.376, + 0.285, + 0.392 + ], + "angle": 0, + "content": "4.2. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.473, + 0.613 + ], + "angle": 0, + "content": "The models are trained with the Adam optimizer [26] with a learning rate of 2e-3, scheduled by one-cycle strategy [46] in 32 epochs. We use a mini-batch size of 64. In every training epoch, the model is evaluated ten times, and we save the best one based on the validation accuracy. Regarding the backbone network, we use the ResNET-50 [17] (QAD-R) and EfficientNet-B1 [49] (QAD-E) with their default input size of \\(224 \\times 224\\) and \\(240 \\times 240\\), respectively. The backbone models utilize pre-trained weights from ImageNet dataset [7]. Our hyper-parameters settings \\(\\{\\sigma = 6, \\alpha = 0.004, \\gamma = 0.002\\}\\) are obtained by fine-tuning on ResNet50 with NeuralTextures dataset and are kept the same throughout all datasets, whereas that of EfficientNet-B1 are \\(\\{\\sigma = 6, \\alpha = 0.002, \\gamma = 0.006\\}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.622, + 0.172, + 0.637 + ], + "angle": 0, + "content": "4.3. Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.47, + 0.722 + ], + "angle": 0, + "content": "This section reports the results of our QAD and other baselines under two scenarios: 1) quality-agnostic setting, which represents no model has prior knowledge of the input images' quality, and 2) quality-aware setting, which baselines are required to know inputs' quality information." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.741, + 0.303, + 0.757 + ], + "angle": 0, + "content": "4.3.1 Quality-agnostic models" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We use the popular deepfake detection benchmark methods on our datasets: 1) MesoNet with Inception layer by [1], 2) Xception model proposed by [43], 3) \\( F^3 \\)Net [38], 4) MAT [61] - a multi-attention deepfake detector, 5) a deviation of the method proposed by [9] to the instance-based collaborative learning, SBIs [45] - a self-blended method using real image only during training, 7) ADD [28] - a knowledge distillation-based approach for detecting low-quality deepfakes, and 8) BZNet [29] - a super-resolution" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.335, + 0.895, + 0.533 + ], + "angle": 0, + "content": "approach for improving detection of low-quality deepfakes. Each method has a different training approach to defend against performance degradation caused by lossy compression. The first five methods are trained with a mixture of the three data quality types (raw + c23 + c40). SBIs is trained with the mid-level of video compression (c23), which is commonly adopted in many works. Meanwhile, ADD and BZNet models are trained on raw, c23, and c40, respectively; however, in the inference phase, they are blindly tested over the entire dataset without the prior knowledge of quality types, and we report their average performance. In the test set, we include both video compression and random JPEG image compression [2]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.543, + 0.895, + 0.756 + ], + "angle": 0, + "content": "The results for the video compression are presented in Table 1, where our QAD outperforms other SOTA baselines across multiple benchmark datasets. Notably, we achieve a significant improvement in AUC score of up to \\(5.28\\%\\) for heavily compressed datasets, such as NeuralTextures (89.64% vs 94.92%). We also surpassed previous works on various deepfake datasets by \\(0.44\\%\\) to \\(1.05\\%\\) points, with the exception of Deepfakes and FFIW10K datasets, which are easy to detect even when compressed. Compared to the collaborative learning baseline by [9], which is a comparative benchmark, our QAD still gains a decent improvement on average, up to \\(0.93\\%\\) and \\(1.54\\%\\) points with QAD-R and QAD-E, respectively. Finally, our QAD-E models achieved the highest score on average, reaching \\(98.47\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Regarding the random image compression experiment, the results are provided in Table 2. Although BZNet is marginally outperform our model on face-reenactment deepfakes (NT and F2F), our method still achieves the best performance with the highest scores on five over seven datasets. On average, our enhancements show decent improvements, with margins of \\(0.5\\%\\) and \\(0.88\\%\\) of QAD-R and QAD-E, respectively, compared to the second-best competitor (Fang & Lin)." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22384" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.114, + 0.089, + 0.436, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.326, + 0.47, + 0.354 + ], + "angle": 0, + "content": "Figure 3. Model's performance versus \\(\\alpha\\) and \\(\\gamma\\) on the NeuralTextures." + }, + { + "type": "table", + "bbox": [ + 0.118, + 0.364, + 0.43, + 0.508 + ], + "angle": 0, + "content": "
Model / lossRESNET-50
ACC (%)AUC (%)
Baseline78.888.2
Coll. lossSoft-label77.084.0
Pairwise loss79.789.1
Center loss79.888.9
HSIC80.390.1
Adv. lossAWP-KL80.989.4
AWP-XE81.790.7
QAD (ours)82.291.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.508, + 0.47, + 0.535 + ], + "angle": 0, + "content": "Table 4. Performance (ACC & AUC) of RESNET50 integrated with different losses." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.56, + 0.285, + 0.575 + ], + "angle": 0, + "content": "4.3.2 Quality-aware models" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In this experiment, we compare our models with quality-aware benchmark baselines. In particular, beside RESNET-50 and EFFICIENTNET-B1, for each of the raw, c23, and c40 datasets, we implement ADD [28] and BZNet [29] models. Since ADD and BZNet are the best performing methods, in which they utilized knowledge distillation and super-resolution approaches, respectively, for detecting deepfakes in different qualities. Hence, we only include them in this experiment. In the inference phase, the performance of these models is validated with the prior knowledge of the input image's quality, i.e., c40 images are evaluated by the same quality c40 pre-trained models. Meanwhile, our universal QAD is blindly evaluated without such prior knowledge. We integrate our QAD on RESNET50 and EFFICIENTNET-B1 and present their performance in Table 3. As we can observe, our QAD-E model performs slightly better or on par with RESNET-50, BZNet, and ADD models, despite having only one-third of the number of parameters and no prior knowledge of input image quality. Moreover, when integrating with EFFICIENTNET-B1, QAD-E achieves a new SOTA performance with an improvement" + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.089, + 0.888, + 0.272 + ], + "angle": 0, + "content": "
QADNTDFF2FFSFSHCDFv2FFIW10KAvg
ResNET18
X88.7398.9398.0598.0698.6797.0998.7296.89
✓91.3899.3298.3299.1998.9497.9799.1097.75
ResNET34
X88.2699.0197.9898.6798.8896.6198.9796.91
✓92.8799.3098.3799.1099.2198.4899.1498.07
EFFICIENTNET-B0
X86.1299.2997.9398.2198.4297.8198.8096.65
✓91.9999.3398.6699.1599.0098.3899.1297.95
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.273, + 0.892, + 0.315 + ], + "angle": 0, + "content": "Table 5. Performance (AUC) of RESNET18, RESNET34, and EFFICIENTNET-B0 baseline and their integration with our QAD training framework." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.34, + 0.892, + 0.372 + ], + "angle": 0, + "content": "of up to \\(0.89\\%\\) points (97.79% vs. 96.90%), with a modest number of parameters (6.5M)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.382, + 0.662, + 0.397 + ], + "angle": 0, + "content": "4.4. Ablation studies" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.406, + 0.685, + 0.421 + ], + "angle": 0, + "content": "4.4.1 \\(\\alpha\\) and \\(\\gamma\\) of our loss" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.431, + 0.892, + 0.657 + ], + "angle": 0, + "content": "We investigate the sensitivities of our QAD with respect to \\(\\alpha\\) and \\(\\gamma\\), and summarize the results of our analysis in Fig. 3. In this study, we experiment with ResNET50 on the NeuralTextures dataset, which is the hardest dataset to detect when compressed. And, we vary the values of the hyperparameters \\(\\alpha \\in \\{0.002, 0.004, 0.008\\}\\) and \\(\\gamma \\in \\{0.001, 0.002, 0.003, 0.004\\}\\), where the value at \\((\\alpha, \\gamma) = (0.0, 0.0)\\) indicate the baseline. The results suggest that when \\(\\alpha\\) is greater than 0.002, the performance of our model is high and stable, surpassing current SOTA with any \\(\\alpha\\) greater than 0.002. Additionally, increasing \\(\\gamma\\) generally improves performance. Note that, as we did not tune the hyper-parameters to optimize the test accuracy, Section 4.3's hyper-parameters are not the best, despite outperforming all current methods on the datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.679, + 0.679, + 0.693 + ], + "angle": 0, + "content": "4.4.2 Selection of losses" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.87 + ], + "angle": 0, + "content": "We study different alternatives for the collaborative learning loss and the adversarial weight perturbation approach. In particular, for the collaborative learning loss, we apply the loss function that was introduced by [47], in which they aggregate the logits of different views, combining them with their true labels to generate the soft labels. Besides, we replace our HSIC regularization with intermediate pairwise loss (Eq. 3) and center loss. Regarding the adversarial weight perturbation, we further apply the KL divergence between the representations of raw and compressed images to perturb the model's weights." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We report the results in Table 4, where we observe that the soft label loss fails to improve the baselines due to a" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22385" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.093, + 0.457, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.254, + 0.47, + 0.283 + ], + "angle": 0, + "content": "Figure 4. Performance (AUC) of our proposed method at different input resolutions with NeuralTextures dataset." + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.295, + 0.273, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.296, + 0.458, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.105, + 0.445, + 0.441, + 0.46 + ], + "angle": 0, + "content": "Figure 5. t-SNE visualisation of baseline and our QAD." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.473, + 0.658 + ], + "angle": 0, + "content": "lack of low-level representation agreement between different image qualities. While both pairwise and center loss slightly improve the baselines and are unstable with different model architecture, our HSIC consistently achieves the best performance by relaxing the instance-base constraint. Meanwhile, we can observe the model's performance drops in terms of both ACC and AUC, when replacing our AWP with cross-entropy loss with KL divergence. Generally, this experiment shows that using pairwise differences of various quality image representations at the output, such as soft label, pairwise constraint, or AWP-KL, for optimizing the model can hinder its convergence to the optimal parameters." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.679, + 0.391, + 0.694 + ], + "angle": 0, + "content": "4.4.3 Experiment with different backbones" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.809 + ], + "angle": 0, + "content": "Table 5 shows the comparability of our QAD with three different backbone networks: RESNET18, RESNET34, and EFFICIENTNET-B0. The hyperparameter settings are kept the same for RESNET50 and EFFICIENTNET-B1. As shown in Table 5, our QAD consistently improves the baselines, from \\(0.86\\%\\) to \\(1.3\\%\\) points on average of seven deepfake datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.831, + 0.391, + 0.847 + ], + "angle": 0, + "content": "4.4.4 Performance at different input scales" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Unlike other classification tasks, a notable factor that substantially affects the deepfake detection performance, which is omitted by most previous works [43, 38, 61], is" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.228 + ], + "angle": 0, + "content": "the input size of faces. We resize the input images from 56 to 336 and demonstrate how it impacts our QAD in comparison with ResNET50 baseline. The experiment is performed with the NeuralTextures dataset, and its results are reported in Fig. 4. We note that our proposed QAD and the baselines consistently improve their performance, when increasing the input size. Beside, our method also keep its staging improvement across the input resolutions compared to ResNET50 baseline." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.268, + 0.787, + 0.282 + ], + "angle": 0, + "content": "4.4.5 Feature distribution visualization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.299, + 0.895, + 0.466 + ], + "angle": 0, + "content": "To verify the consistency of invariant representation upon the input quality, we draw the feature distribution of EFFICIENTNET-B1 and our QAD-EFFICIENTNET-B1 pretrained on NeuralTextures (with raw, c23, and c40 datasets) with t-SNE [53]. The results are shown in Fig. 5. As observed, our QAD model's representations are less dispersed both in terms of intra-class and inter-quality. This experiment demonstrates that traditional cross-entropy loss trained with multiple input quality are confused due to the low-level constraints, while our QAD enables the model to achieve more generalization regardless of input quality." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.49, + 0.619, + 0.506 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.894, + 0.732 + ], + "angle": 0, + "content": "Most deep learning-based deepfake detectors use a single model for each video quality, leaving an unsolved practical issue of their generalizability for detecting different quality of deepfakes. In this work, we propose a universal deepfake detection framework (QAD). Using intra-model collaborative learning, we minimize the geometrical differences of images in various qualities at different intermediate layers by the HSIC module. Moreover, our adversarial weight perturbation (AWP) module is directly applied to the model's parameters to provide its robustness against input image compression. Extensive experiments show that our QAD achieves competitive detection accuracy and marks the new SOTA results on various deepfake datasets without prior knowledge of input image quality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Acknowledgements. This work was partly supported by Institute for Information & communication Technology Planning & evaluation (IITP) grants funded by the Korean government MSIT: (No. 2022-0-01199, Graduate School of Convergence Security at Sungkyunkwan University), (No. 2022-0-01045, Self-directed Multi-Modal Intelligence for solving unknown, open domain problems), (No. 2022-0-00688, AI Platform to Fully Adapt and Reflect Privacy-Policy Changes), (No. 2021-0-02068, Artificial Intelligence Innovation Hub), (No. 2019-0-00421, AI Graduate School Support Program at Sungkyunkwan University), and (No. RS-2023-00230337, Advanced and Proactive AI Platform Research and Development Against Malicious deepfakes)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "22386" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.08, + 0.116, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Darius Afchar, Vincent Nozick, Junichi Yamagishi, and Isao Echizen. 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Le + +Dept. of Computer Science & Engineering Sungkyunkwan University Suwon, South Korea + +bmle@g.skku.edu + +Simon S. Woo* + +Dept. of Computer Science & Engineering Sungkyunkwan University Suwon, South Korea + +swoo@g.skku.edu + +# Abstract + +Deepfake has recently raised a plethora of societal concerns over its possible security threats and dissemination of fake information. Much research on deepfake detection has been undertaken. However, detecting low quality as well as simultaneously detecting different qualities of deepfakes still remains a grave challenge. Most SOTA approaches are limited by using a single specific model for detecting certain deepfake video quality type. When constructing multiple models with prior information about video quality, this kind of strategy incurs significant computational cost, as well as model and training data overhead. Further, it cannot be scalable and practical to deploy in real-world settings. In this work, we propose a universal intra-model collaborative learning framework to enable the effective and simultaneous detection of different quality of deepfakes. That is, our approach is the quality-agnostic deepfake detection method, dubbed QAD. In particular, by observing the upper bound of general error expectation, we maximize the dependency between intermediate representations of images from different quality levels via Hilbert-Schmidt Independence Criterion. In addition, an Adversarial Weight Perturbation module is carefully devised to enable the model to be more robust against image corruption while boosting the overall model's performance. Extensive experiments over seven popular deepfake datasets demonstrate the superiority of our QAD model over prior SOTA benchmarks. + +# 1. Introduction + +Deep learning approaches for facial manipulation, such as deepfakes, have recently received considerable attention [54, 31, 61, 25, 20, 23], because they can be abused for the malicious purposes such as fake news, pornography, etc. Due to the advancements made in Generative Adversarial Networks and other deep learning-based computer vision algorithms, deepfakes have also become more realistic and + +![](images/2850bc805620a8677c15bbeafa25e502019b051d85085dae8b9fa4b36bd12c41.jpg) + +![](images/65afc92280a6be32be55f5583227c5939604a993fa1fa835f53c59af7f61ff54.jpg) + +![](images/33f73aae8c97828d1ff97a420620e7aefe5b135aa72abb464aaf0ac7b8a76c89.jpg) + +![](images/bd539fba419df6e44ea9f4cc21df917b11c06bccf640881686c247983cfc61fc.jpg) +Figure 1. A summary of our goal. Our approach stands out from previous works that detect deepfakes using separate models for different qualities (e.g. Baseline 2 [28]) or a single model without considering the interaction between qualities (e.g. Baseline 1 [43]). Instead, our method employs all quality levels and improves the performance of the model on each quality level, leading to overall enhanced performance. + +![](images/35102a955e037dc10a358435db161a202fc1691ca6bf897196504784acbe7b83.jpg) + +![](images/093f479cbf013679a61674f473781dfcc0a6c15914b8601e0d3ea68bb38f641f.jpg) + +natural, making it harder not only for humans, but also for classifiers to tell them apart. Moreover, it has been simpler than ever before to create convincing deepfakes using simple programs and apps without requiring advanced machine learning knowledge. Such easy-to-create and realistic fake images and videos can be maliciously exploited, raising significant security, privacy, and societal concerns such as fake news propagation [39], and stealing personal information via phishing and scams [10]. + +To mitigate such problems caused by deepfakes, there has been a tremendous research effort put into constructing reliable detectors [32, 25, 8, 38, 61, 44]. Although they have achieved outstanding performance with high-quality deepfakes, most of them have failed to detect low-quality deepfakes effectively [8, 43]. While video compression steps do not significantly impact on visualization, it drastically drop deepfake detectors' performance on low-quality deepfakes (c40). A handful of research has been focused on detecting low-quality deepfakes such as ADD [28] and BZNet [29]. However, their methods can only detect low-quality com + +pressed deepfakes. And, those prior approaches expose a critical problem, when deployed in practice since the prior video quality information of the input is unknown. Moreover, developing different models for each input quality induces significant computational overhead. Other works, such as LipForensics [16], also attempt to make their detectors robust against various corruptions and compression. Nevertheless, it is unable to detect image-based deepfakes with random lossy compression like JPEG. + +In this research, we propose the novel deepfake detection method, QAD, which can simultaneously detect both high and low-quality (quality-agnostic) deepfakes in a single model, as illustrated in Fig. 1. Especially, we propose a universal intra-model collaborative learning framework to provide the effective detection of different quality deepfakes. We modulate the conventional model-based collaborative learning [47] to an instance-based intra-model collaborative learning framework in our training. During the training phase, our single model simultaneously learns the representations of one image, but with different qualities. By utilizing the collaborative learning framework, our QAD can align the distributions of high and low-quality image representations to be geometrically similar. Hence, it can avoid the overfitting caused by compressed images and the overconfidence caused by raw images, while boosting its overall performance. + +In particular, we perform a rigorous theoretical analysis, and show that the low-quality deepfake classification error can be bounded by two terms: classification loss and the distance between the representations of high and low-quality images. Instead of using a direct pairwise regularization to minimize the gaps between the high and low-quality image representations, we propose to apply Hilbert-Schmidt Independence Criterion (HSIC) to maximize the dependence between a mini-batch of high and low-quality images, thus maximizing the mutual information between them, and supporting the high-level representations and effective output predictions. Meanwhile, to enhance the model's robustness under heavy input compression, we propose Adversarial Weight Perturbation (AWP) [56, 3], which can further flatten the weight loss landscape of the model, bridging the gap in multiple quality learning for deepfake detection. + +Finally, we conduct extensive experiments to show the effectiveness of our QAD with seven different popular benchmark datasets. We first show that our method can outperform previous baselines when training with data from various video and image compression qualities. Furthermore, we show that our QAD exceeds the performance of the SOTA quality-aware models such as BZNet [29] by a significant margin, while requiring remarkably fewer computational parameters and no prior knowledge of the inputs. Our contributions are summarized as follows: + +1) We theoretically analyze and prove that the classifica + +tion error of low-quality deepfakes can be bounded by its classification loss and the representation distance with its corresponding high-quality images. + +2) We propose a unified quality-agnostic deepfake detection framework (QAD), utilizing instance-based intramodel collaborative learning. We use the Hilbert-Schmidt Independence Criterion (HSIC) to maximize the geometrical similarity between intermediate representations of high and low-quality deepfakes, and Adversarial Weight Perturbation (AWP) to make our model robust under varying input compression. +3) We demonstrate that our approach outperforms well-known baselines, including the total of eight quality-agnostic and quality-aware SOTA methods with seven popular benchmark datasets. + +# 2. Related works + +# 2.1. Deepfake detection + +Recently, deepfakes have been of the utmost crucial because they can cause serious security and privacy threats. Theresfore, a large number of detection methods have been proposed to effectively identify such deepfakes [43, 31, 30, 22, 41, 54, 32, 25, 8, 61]. However, the majority of the aforementioned works focus on mining visual artifacts of deepfakes, such as the blending boundaries of generated faces [31], the irregularity of pupil shapes [14], the spatiotemporal inconsistency [6, 44], or exploring deep learning-based attention methods [61] to identify such artifacts. Meanwhile, several approaches also showed that exposing deepfakes in the frequency domain is effective. Such methods include analyzing the discrepancies of frequency spectrum [8, 27, 25], employing the checkerboard artifacts caused by the transposed convolutional operator [60, 11], or mining the statistical frequency features with dual deep learning models [38]. Nevertheless, such models' performance substantially decreases when encountering low-quality compressed images. To remedy the above shortcoming, recent studies proposed methods to detect the deepfake in highly compressed low-quality versions such as [28], which utilized a knowledge distillation. Also, [29] presented a supper-resolution-based network for enhancing the performance of low-quality deepfake detection. However, all of the aforementioned approaches are limited in developing a single model for each quality of deepfakes, which is impractical to deploy in real-world scenarios due to the requirement of prior knowledge of the input quality. + +# 2.2. Collaborative learning + +Collaborative learning proposed by [47] is designed to achieve a global minimum of a deep neural network, while maintaining the same computational complexity at inference time as at training time. Collaborative learning inherits + +the advantages of auxiliary training [48], multi-task learning [58], and knowledge distillation [18]. Its applications cover supporting weakly-supervised learning [24], or integrating with online knowledge distillation [57, 15]. And, its training graph is divided into two or more sub-networks to ensure global minimum achievement [47]. Besides, [9] proposed an intra-model collaborative learning framework that shares a similar characteristic with self-knowledge distillation. However, all of the approaches are model-based collaborative learning, in which a single input generates multiple outputs (or views) through multiple classifier heads of one target network in both training and inference phase. + +In this work, we distinguish ourselves by deploying the collaborative learning framework for simultaneously training deepfakes of various qualities with an undeviated single model, namely instance-based collaborative learning. Different from conventional mini-batch stochastic optimization, which independently samples random images from different qualities and optimizes the detector, our collaborative learning approach allows us to utilize the common features in the same image but from different qualities simultaneously. Thus, our deepfake detector circumvent the overfitting caused by compressed images or the overconfidence from raw images, enhancing its overall performance. + +# 2.3. Hilbert-Schmidt Independence Criterion + +The Hilbert-Schmidt Independence Criterion (HSIC) [13] measures the statistical dependency between probability distributions. In fact, HSIC differs from the covariance, where $\text{Cov}(X,Y) = 0$ does not imply that two random variables $X$ and $Y$ are independent [42], while HSIC shows its tractable computation and equivalency in terms of the independence property [13]. Moreover, HISC is easy to be estimated statistically and algorithmically. In practice, applications based on HSIC are found in a variety of practical domains, including maximizing the dependencies for self-supervised learning [33] and classification learning [34, 12], or defense against model inversion attacks [37]. In this paper, we utilize the HSIC to maximize the dependency between distributions of deepfake images of different qualities at intermediate layers. Therefore, we aim to constrain low-level representations of images not to be exactly the same, but to share a geometrical similarity of learning features that can support high-level output predictions. + +# 3. Methods + +In this section, we first theoretically examine the upper bound for our optimization problem by considering a DNN classifier of $K$ classes, and two modalities of input quality: raw (high-quality) and compressed (low-quality). Then, we discuss how to more efficiently collaborate on the representations of deepfake images of differing quality. + +# 3.1. Preliminary & our inspiration + +Given a sample $x_r$ from a space $\mathcal{X}$ and its compressed version at quantile $c$ , $x_c$ can be expressed as $x_c = x_r - \delta_c$ , and we define the corresponding label $y \in \{0,1\}$ (real and fake). Next, a family $\mathcal{F}$ of learning functions $f: \mathcal{X} \to \mathbb{R}^2$ returns a 2-tuple $f(x) = [f(x,j)]_{j=1}^2$ , whose $f(x,j)$ is proportional to the probability to assign $x$ to the $j$ -th class, and $f$ is defined by learning parameters $\theta$ . Given a training data $\mathcal{D} = \{(x_i,y_i)\}_{i=1}^n \subset \mathcal{X} \times \mathcal{Y}$ , our goal is to minimize the expectation of a loss function $\mathcal{L}: \mathbb{R}^2 \times \mathcal{Y} \to \mathbb{R}$ . Here, we consider $\mathcal{L}(f(x),y) = 1 - \sigma_T(f(x,y))$ , where $\sigma_T$ is the softmax function with temperature $T > 0$ : + +$$ +\sigma_ {T} (f (x), y) = \frac {\exp (f (x , y) / T)}{\sum_ {k = 1} ^ {2} \exp (f (x , k) / T)}. \tag {1} +$$ + +Theorem 1. (Proof can be done similarly as [36] and [19] in Supp. Material) For any $f \in \mathcal{F}$ , and with probability $1 - \delta$ over the draw of $\mathcal{D}$ , + +$$ +\begin{array}{l} \mathbb {E} \left[ \mathbb {I} \left\{\hat {y} \left(x _ {c}\right) \neq y \right\} \right] \leq 2 \mathbb {E} _ {\mathcal {D}} \mathcal {L} \left(f \left(x _ {c}\right), y\right) \\ + \frac {8}{T} \mathbb {E} _ {\mathcal {D}} \mathcal {L} _ {i - c o l} (f (x _ {r}), f (x _ {c})) + 4 \Re_ {\mathcal {D}} (\Phi_ {\mathcal {W}}) \\ + \frac {1 6}{n} + \mathcal {O} \left(\sqrt {\frac {\log (2 / \delta)}{2 n}}\right), \tag {2} \\ \end{array} +$$ + +where $\Re_{\mathcal{D}}$ is the Rademacher complexity, $\Phi_{\mathcal{W}} = \{\mathcal{L}(f(x_r),y),f\in \mathcal{F}\}$ , and + +$$ +\mathcal {L} _ {i - c o l} \left(f \left(x _ {r}\right), f \left(x _ {c}\right)\right) = \| f \left(x _ {r}\right) - f \left(x _ {c}\right) \| . \tag {3} +$$ + +Insight of Theorem 1. On the right-hand side of Eq. 2, our classifier $f$ depends on two terms, where the first term is the classification loss $\mathcal{L}(f(x_c), y)$ applied to the prediction of the compressed image $x_c$ . And, the second term is the instance-based collaborative loss $\mathcal{L}_{i-col}(f(x_r), f(x_c))$ that measures the pairwise difference between predictions of the raw image and its compressed version. Therefore, minimizing the expectation over training data $\mathcal{D}$ of $2\mathcal{L}(f(x_c), y) + 8\mathcal{L}_{i-col}(f(x_r), f(x_c)) / T$ , can decrease the true error. Note that Eq. 2 is also general so that it can be applicable for raw images. Hence, in practice, the first term can be generalized to both raw and compressed images. + +In order to minimize the expectation of errors in both raw and compressed deepfake image predictions, our theoretical analysis shows that we can minimize both classification loss and collaborative loss at the output. However, as observed by [9] and in our experiments (see Tab. 4), this instance-based collaborative learning loss fails to achieve the best performance. Additionally, training solely with highly-compressed images makes the detector prone to overfitting, yielding a considerable gap between training and test performance [28]. As a result, the major research + +![](images/1ba2b5ce79c5cd2ab2801b0cc1965138c0d49c13d0109e99e40daa0e4b2b4533.jpg) +Figure 2. Overview of our QAD framework. A mini-batch of images from different quality modalities (e.g., two in this diagram) is forwarded through a single universal model. Although it is one model, we pictorially split it into two branches for the reader's understanding. After training, we obtain one universal model that regulates different qualities. Top-right: The HSIC geometrically maximizes the dependency between images from various quality modalities at different resolutions, supporting high-level output predictions. Bottom-right: Through searching for the worst-case parameters' corruption and compensating for input corruption (compression), the AWP flattens the model's weight loss landscape, making the model robust under varying input compression. + +![](images/2dd487df5afb505779b16d1d4628972653870860bf4a46b3112dc43ba8203515.jpg) + +![](images/770e067dbdc8c4a88a06076e460843fdd8a49a2856cb624bdb85c318d0e6bffd.jpg) + +challenge is how we can further lower the sensitivity of $f_{\theta}$ to $x$ at various compression settings and push their representations close to each other. + +Classification loss. We can construct a robust model under input corruption by flattening the weight loss landscape. In particular, we apply the Adversarial Weight Perturbation [56] to search for the worst-case perturbations $\phi^{*}$ of the model weights at every training step. Thereafter, optimizing the perturbed model via $\mathcal{L}(f_{\theta +\phi^*},y)$ can enable it to be more robust under varying input image correlations/distortions, which represent the varying qualities of deepfake inputs (See Fig. 2—Bottom-right panel). Furthermore, the classification loss in Eq. 2 is upper bounded by this new loss function due to the worst-case perturbations. + +Collaborative loss. With respect to the collaborative learning loss, Eq. 3 shares similar characteristics with recent knowledge distillation research [18, 52]. However, our goal is to develop and train a single universal model, not having a teacher-student relationship. Nevertheless, we argue that the gap between raw and compressed image representations can be minimized more efficiently by regularizing their discrepancy at the low-level representations. Moreover, enforcing the similarity of the pairwise representations at the intermediate layers with an input difference of $|\delta_c|$ can collapse layers' weights to zero or can lead a deep model to remember training data instead of learning discriminative features. Therefore, we relax this constraint by + +maximizing the kernel dependency in a mini-batch of data between the raw and compressed image representations by the Hilbert-Schmidt Independence Criterion (HSIC). Using HSIC, we can instead enforce the geometrical structures of mini-batch of raw data and the compressed data to be similar, so that we can still effectively detect different-quality deepfakes in a single model. From a mutual information perspective, maximizing the kernel dependency can enforce the mutual information of the learned representations of different compression ratios, thus regularizing the detector to be more generalized (See Fig. 2—Top-right panel). + +# 3.2. Details of our methods + +# 3.2.1 Weight loss landscape flattening + +Recent studies [21, 55] suggest that searching for a flatter minima can improve the generalization ability of the model. To achieve this, we propose using Adversarial Weight Perturbation [56] to identify flat local minima of the empirical risk. The worst-case perturbations $\phi^{*}$ of the model weights which increases the loss dramatically is formulated as: + +$$ +\phi^ {*} = \underset {\phi \in \mathcal {B} _ {p} (\theta , \gamma)} {\arg \max } \mathcal {L} (f _ {\theta + \phi} (x), y), \tag {4} +$$ + +where $\mathcal{B}_p(\theta, \gamma) = \{v \in \Theta : \| \theta - v \|_p \leq \gamma\}$ is the feasible region of any perturbation $\phi$ . The AWP adds the worst-case perturbation to the model weight, so that $\mathcal{L}(f_{\theta + \phi^*}(x), y)$ + +becomes the supremum value in $\mathcal{B}_p(\theta, \gamma)$ . Therefore, optimizing $\mathcal{L}(f_{\theta + \phi^*}(x), y)$ pushes $\theta$ to adjust its values such that the loss landscape is more flatten with the same capability $\mathcal{B}_p(\theta, \gamma)$ . As a result, $f$ becomes more stable under input image's changes. + +Similar to adversarial example perturbation [35], $\phi^{*}$ is generated by projected gradient method as follows: + +$$ +\phi^ {*} \leftarrow \Pi_ {\theta} ^ {\gamma} \left(\phi + \eta \frac {\nabla \mathcal {L} \left(f _ {\theta + \phi} (x) , y\right)}{\| \nabla \mathcal {L} \left(f _ {\theta + \phi} (x) , y\right) \|} \| \theta \|\right), \tag {5} +$$ + +where $\Pi_{\theta}^{\gamma}$ is an operator that projects its input into the feasible region $B_{p}(\theta, \gamma)$ , and $\eta \in \mathbb{R}$ is the step size. In fact, we empirically find that using a one-step projection for $\phi^{*}$ is sufficient for the model's robustness under the image corruptions formed by compression. By adding $\phi^{*}$ in Eq. 5 to $\theta$ , it is straightforward to bound $\mathcal{L}(f(x_c), y)$ in Eq. 2. + +# 3.2.2 Intra-model collaborative learning + +Hilbert-Schmidt Independence Criterion (HSIC). Let $\mathcal{T}$ and $\mathcal{G}$ be two separable Reproducing Kernel Hilbert Spaces (RKHS) on metric spaces $\mathcal{U}$ and $\mathcal{V}$ , respectively. HSIC measures the dependency between two random variables $U$ and $V$ from a joint distribution on $\mathcal{U}$ and $\mathcal{V}$ , by evaluating the cross-covariance of the nonlinear transformations of the two random variables: + +$$ +H S I C (U, V) = \left\| \mathbb {E} [ \zeta (U) \psi (V) ^ {T} ] - \mathbb {E} \zeta (U) \mathbb {E} \psi (V) ^ {T} \right\| _ {H S} ^ {2}, \tag {6} +$$ + +where $\| \cdot \|_{HS}$ is the Hilbert-Schmidt norm, which becomes the Frobenius norm in finite dimensions. And, $\zeta : \mathcal{U} \to \mathcal{T}$ and $\psi : \mathcal{V} \to \mathcal{G}$ are nonlinear mapping functions. With appropriate transformation $\zeta$ and $\psi$ , HSIC is a dependence test, which can identify the nonlinear dependencies between $U$ and $V$ as follows: $HSIC(U,V) = 0 \Leftrightarrow U \perp V$ . + +Also, inner products in $\mathcal{T}$ and $\mathcal{G}$ are formed by positive definite kernel functions: $k(u,u^{\prime}) = \langle \zeta (u),\zeta (u^{\prime})\rangle_{\mathcal{T}}$ and $l(v,v^{\prime}) = \langle \psi (v),\psi (v^{\prime})\rangle_{\mathcal{G}}$ . And, let $(U^{\prime},V^{\prime})$ and $(U^{\prime \prime},V^{\prime \prime})$ be independent copies of $(U,V)$ , then Eq. 6 can be expressed as follows: + +$$ +\begin{array}{l} H S I C (U, V) = \mathbb {E} [ k (U, U ^ {\prime}) l (V, V ^ {\prime}) ] \\ - 2 \mathbb {E} [ k (U, U ^ {\prime}) ] \mathbb {E} [ l (V, V ^ {\prime \prime}) ] + \mathbb {E} [ k (U, U ^ {\prime}) ] \mathbb {E} [ l (V, V ^ {\prime}) ]. \tag {7} \\ \end{array} +$$ + +Estimation of HSIC. The empirical estimation of HSIC with an bias of $\mathcal{O}(\frac{1}{n})$ using $n$ samples i.i.d drawn $\{(u_i,v_i)\}_{i = 1}^n$ from the joint distribution $(U,V)$ is provided as follows [13]: + +$$ +\widehat {H S I C} (U, V) = \frac {1}{(n - 1) ^ {2}} \mathbf {t r} (K H L H), \tag {8} +$$ + +where $K_{i,j} = k(u_i, u_j)$ , and $L_{i,j} = l(v_i, v_j)$ are kernel matrices for the kernels $k$ , and $l$ , respectively, and $H_{i,j} =$ + +Algorithm 1 QAD: Quality-Agnostic Deepfake detection. + +Require: DNN $f$ parameterized by $\theta$ , training dataset $\mathcal{D}$ with M quality modalities $\mathcal{T} = \{r, c_1, \dots, c_{M-1}\}$ . Learning rate $\alpha_l$ and mini-batch size of $B$ . Model weight perturbation size $\gamma$ , step size $\eta$ , and the number of steps $K$ . Layers of $f$ to apply HSIC $L$ . + +1: while not converged do +2: for mini-batch $(X = [X_{\tau}]_{\tau \in \mathcal{T}}, Y) \in \mathcal{D}$ do +3: # One-step AWP +4: $\mathcal{L}_1 = \mathcal{L}(f_{\theta +\phi}(X),Y) / MB$ +5: $\phi \gets \Pi_{\theta}^{\gamma}\left(\phi +\eta \frac{\nabla\mathcal{L}_{1}}{\|\nabla\mathcal{L}_{1}\|}\parallel \theta \parallel\right)$ +6: $\theta \gets \theta +\phi$ +7: $\mathcal{L}_1\gets \mathcal{L}(f_\theta (X),Y) / MB$ +8: # intermediate reps. +9: $[Z_l^\tau ]_{l\in L}^{\tau \in T}\coloneqq f_\theta (X)$ +10: # HSIC: dependence maximization +11: $\mathcal{L}_2\gets \sum_{\tau ,\rho \in T}^{\tau \neq \rho}\mathcal{L}_{col}(\tau ,\rho)$ +12: # Overall loss Eq. (10) +13: $\mathcal{L}_{QAD} \gets \mathcal{L}_1 + \alpha \times \mathcal{L}_2$ +14: $\theta \gets \theta -\alpha_{l}\cdot \nabla_{\theta}\mathcal{L}_{QAD}$ +15: $\theta \gets \theta -\phi$ +16: end for +17: end while + +$\delta_{i,j} - \frac{1}{n}$ is a centering matrix. Regarding the kernel functions, Theorem 4 in [13] suggested that an universal kernel, such as Laplace and Gaussian RBF kernel, can guarantee the HSIC to detect any dependency between $U$ and $V$ . + +HSIC for maximizing the geometrical similarity. Let $\tau$ and $\rho$ be two different qualities of deepfakes, (e.g., raw vs. compressed). Consider the $l$ -th layer of the learning network $f$ , we denote the learning features of a mini-batch of $B$ images from $\tau$ and $\rho$ are $Z_{l}^{\tau} = \{u_{i}\}_{B}$ , and $Z_{l}^{\rho} = \{v_{i}\}_{B}$ respectively, where $u_{i}, v_{i} \in \mathbb{R}^{H \times W \times C}$ and $H, W$ and $C$ are the height, width, and channel number. Our regularization aims to maximize the dependency between $Z_{l}^{\tau}$ and $Z_{l}^{\rho}$ via a mini-batch of representations. In other words, we try to minimize the following loss: + +$$ +\mathcal {L} _ {c o l} (\tau , \rho) = - \sum_ {l \in L} \widehat {H S I C} \left(Z _ {l} ^ {\tau}, Z _ {l} ^ {\rho}\right), \tag {9} +$$ + +where $L$ is a predetermined collection of layers to apply the collaborative loss. And, the computational complexity for calculating Eq. 9 is $\mathcal{O}(B^2 L)$ , which can be reduced to $\mathcal{O}(BL)$ when applying random Fourier features [40]. + +# 3.3. End-to-end training loss + +Given a training mini-batch $B$ that include all $M$ quality modalities $\mathcal{T} = \{r,c_1,\dots c_{M - 1}\}$ , the overall collaborative + +
ModelTest Set AUC (%)
NTDFF2FFSFSHCDFv2FFIW10KAvg
Video Compression (raw + c23 + c40 of test set)
MesoNet [1]◇70.2493.7294.1585.1796.0080.5294.5687.77
Rössler et al. [43]◇89.6499.0597.8998.8398.5097.4999.1797.22
F3Net [38]◇86.7998.7396.3297.8297.4595.0697.9495.73
MAT [61]◇86.7998.7396.3297.8297.4595.0697.9495.73
Fang & Lin [9]89.3098.9897.3398.4398.6696.5898.9496.89
SBIs [45]†78.3395.1979.7480.3780.48--82.82
BZNet [29]†80.1298.8194.1097.71---91.01
ADD [28]†86.2696.2390.6295.5795.94--92.92
QAD-R (ours)91.2599.5498.3499.0199.1298.3699.1097.82
QAD-E (ours)94.9299.5398.9499.2799.1298.3899.1698.47
+ +Table 1. Classification performance in the quality-agnostic setting with video compression of test set. The methods are trained using one of three approaches: simultaneously with three modalities (raw + c23 + c40), individually with each of the three modalities, or with a mid-level of compression (c23) to prevent performance degradation resulting from lossy compression. In the inference phase, video compression is applied to the input. The best results are highlighted in bold. $\dagger$ and $\diamond$ indicate results were obtained from methods' pretrained weights and published code, respectively. + +
ModelTest Set AUC (%)
NTDFF2FFSFSHCDFv2FFIW10KAvg
Random Image Compression (JPEG on raw of test set)
MesoNet [1]◇70.2392.0288.3282.6091.8481.1291.8785.43
Rössler et al. [43]◇69.8998.6294.9796.6696.7696.9898.8193.24
F3Net [38]◇70.9597.8992.8396.3494.7295.4497.1992.19
MAT [61]◇69.5398.9695.5397.9996.9798.2198.9193.73
Fang & Lin [9]75.4998.3294.6397.6497.2896.6798.3994.06
SBIs [45]†77.7597.8382.0586.1085.42--85.83
BZNet [29]†79.0098.7795.2397.92---92.73
ADD [28]†75.8496.8392.2395.2496.00--91.23
QAD-R (ours)75.1898.8693.7298.5298.1898.5198.9694.56
QAD-E (ours)76.2799.2094.4498.6998.6098.5298.8694.94
+ +Table 2. Classification performance in the quality-agnostic setting with image compression of test set. The training approach resembles that of Table 1's setting, however, in the inference phase, random image compression is applied to the input. + +learning loss in our QAD framework is formulated as: + +$$ +\mathcal {L} _ {Q A D} = \frac {1}{M B} \sum_ {\tau \in \mathcal {T}, i \in B} \mathcal {L} _ {\phi^ {*}} \left(x _ {\tau , i}, y _ {i}\right) + \alpha \sum_ {\tau , \rho \in \mathcal {T}} ^ {\tau \neq \rho} \mathcal {L} _ {c o l} (\tau , \rho), \tag {10} +$$ + +where $\alpha$ is a hyper-parameter to balance contribution of each loss. It is worth noting that our QAD training loss is parameter-free, and is not affected by the order of the modalities. Further, unlike other model-based collaborative learning [47], our QAD does not derive any sub-models. In other words, it can be integrated with any backbone, i.e., RESNET50, and introduces no extra computation at the inference time. Note that Theorem 1 still holds when replacing the classification loss $\mathcal{L}(f(x),y)$ with any cross-entropy based loss, since $\mathcal{L}(f(x),y)$ is bounded by the + +cross-entropy loss. Finally, we present our end-to-end algorithm for optimizing Eq. 10 in Algorithm 1, and its pictorial illustration in Fig. 2. + +# 4. Experimental Results + +# 4.1. Dataset and pre-processing + +For evaluating our proposed method, we experiment with seven different popular deepfake benchmark datasets: NeuralTextures (NT) [50], Deepfakes (DF) [4], Face2Face (F2F) [51], FaceSwap (FS) [5], FaceShifter (FSH) [30], CelebDFV2 (CDFv2) [59], and Face Forensics in the Wild (FFIW10K) [62]. Besides the raw version, these videos are also compressed into two types: medium (c23) and high (c40), utilizing the H.264 codec and constant rate quantization parameters of 23 and 40, respectively. These effectively + +
Methodw/ prior infor.#paramsTest Set AUC (%)
NTDFF2FFSFSHCDFv2FFIW10KAvg
BZNet [29]†[×3]Y22M × 391.0199.3096.9098.82---96.51
ADD [28]†[×3]Y23.5M × 389.0899.2596.5398.2198.25--96.26
RESNET50 [×3]Y23.5M × 388.9699.2697.0498.6398.7197.0998.5896.90
QAD-R (ours)N23.5M × 188.8599.4297.7798.8398.9397.5698.9397.18
EFFICIENTNET-B1[×3]Y6.5M × 387.6399.0596.7298.1697.9596.7098.5496.39
QAD-E (ours)N6.5M × 192.2599.4698.3099.0898.9097.5099.0197.79
+ +Table 3. Classification performance in the quality-aware setting with video compression of test set. Except for our model, each model is trained with three modalities: raw, c23, and c40, respectively (denoted $[ \times 3 ]$ ). In the inference phase, while our QAD uses one single pre-trained model, other methods use their corresponding pre-trained model (e.g., pre-trained RESNET-50 on raw) to detect a given testing input (e.g., raw). Reported performances are averaged score of the three modalities. + +result in different quality of deepfakes, and details of these datasets are provided in our Supp. Material. + +# 4.2. Experimental Settings + +The models are trained with the Adam optimizer [26] with a learning rate of 2e-3, scheduled by one-cycle strategy [46] in 32 epochs. We use a mini-batch size of 64. In every training epoch, the model is evaluated ten times, and we save the best one based on the validation accuracy. Regarding the backbone network, we use the ResNET-50 [17] (QAD-R) and EfficientNet-B1 [49] (QAD-E) with their default input size of $224 \times 224$ and $240 \times 240$ , respectively. The backbone models utilize pre-trained weights from ImageNet dataset [7]. Our hyper-parameters settings $\{\sigma = 6, \alpha = 0.004, \gamma = 0.002\}$ are obtained by fine-tuning on ResNet50 with NeuralTextures dataset and are kept the same throughout all datasets, whereas that of EfficientNet-B1 are $\{\sigma = 6, \alpha = 0.002, \gamma = 0.006\}$ . + +# 4.3. Results + +This section reports the results of our QAD and other baselines under two scenarios: 1) quality-agnostic setting, which represents no model has prior knowledge of the input images' quality, and 2) quality-aware setting, which baselines are required to know inputs' quality information. + +# 4.3.1 Quality-agnostic models + +We use the popular deepfake detection benchmark methods on our datasets: 1) MesoNet with Inception layer by [1], 2) Xception model proposed by [43], 3) $F^3$ Net [38], 4) MAT [61] - a multi-attention deepfake detector, 5) a deviation of the method proposed by [9] to the instance-based collaborative learning, SBIs [45] - a self-blended method using real image only during training, 7) ADD [28] - a knowledge distillation-based approach for detecting low-quality deepfakes, and 8) BZNet [29] - a super-resolution + +approach for improving detection of low-quality deepfakes. Each method has a different training approach to defend against performance degradation caused by lossy compression. The first five methods are trained with a mixture of the three data quality types (raw + c23 + c40). SBIs is trained with the mid-level of video compression (c23), which is commonly adopted in many works. Meanwhile, ADD and BZNet models are trained on raw, c23, and c40, respectively; however, in the inference phase, they are blindly tested over the entire dataset without the prior knowledge of quality types, and we report their average performance. In the test set, we include both video compression and random JPEG image compression [2]. + +The results for the video compression are presented in Table 1, where our QAD outperforms other SOTA baselines across multiple benchmark datasets. Notably, we achieve a significant improvement in AUC score of up to $5.28\%$ for heavily compressed datasets, such as NeuralTextures (89.64% vs 94.92%). We also surpassed previous works on various deepfake datasets by $0.44\%$ to $1.05\%$ points, with the exception of Deepfakes and FFIW10K datasets, which are easy to detect even when compressed. Compared to the collaborative learning baseline by [9], which is a comparative benchmark, our QAD still gains a decent improvement on average, up to $0.93\%$ and $1.54\%$ points with QAD-R and QAD-E, respectively. Finally, our QAD-E models achieved the highest score on average, reaching $98.47\%$ . + +Regarding the random image compression experiment, the results are provided in Table 2. Although BZNet is marginally outperform our model on face-reenactment deepfakes (NT and F2F), our method still achieves the best performance with the highest scores on five over seven datasets. On average, our enhancements show decent improvements, with margins of $0.5\%$ and $0.88\%$ of QAD-R and QAD-E, respectively, compared to the second-best competitor (Fang & Lin). + +![](images/4d88c5324fd3ae21bd400d2a928c8cb17f036a2582827f75ada9867e1336c59e.jpg) +Figure 3. Model's performance versus $\alpha$ and $\gamma$ on the NeuralTextures. + +
Model / lossRESNET-50
ACC (%)AUC (%)
Baseline78.888.2
Coll. lossSoft-label77.084.0
Pairwise loss79.789.1
Center loss79.888.9
HSIC80.390.1
Adv. lossAWP-KL80.989.4
AWP-XE81.790.7
QAD (ours)82.291.3
+ +# 4.3.2 Quality-aware models + +In this experiment, we compare our models with quality-aware benchmark baselines. In particular, beside RESNET-50 and EFFICIENTNET-B1, for each of the raw, c23, and c40 datasets, we implement ADD [28] and BZNet [29] models. Since ADD and BZNet are the best performing methods, in which they utilized knowledge distillation and super-resolution approaches, respectively, for detecting deepfakes in different qualities. Hence, we only include them in this experiment. In the inference phase, the performance of these models is validated with the prior knowledge of the input image's quality, i.e., c40 images are evaluated by the same quality c40 pre-trained models. Meanwhile, our universal QAD is blindly evaluated without such prior knowledge. We integrate our QAD on RESNET50 and EFFICIENTNET-B1 and present their performance in Table 3. As we can observe, our QAD-E model performs slightly better or on par with RESNET-50, BZNet, and ADD models, despite having only one-third of the number of parameters and no prior knowledge of input image quality. Moreover, when integrating with EFFICIENTNET-B1, QAD-E achieves a new SOTA performance with an improvement + +Table 4. Performance (ACC & AUC) of RESNET50 integrated with different losses. + +
QADNTDFF2FFSFSHCDFv2FFIW10KAvg
ResNET18
X88.7398.9398.0598.0698.6797.0998.7296.89
✓91.3899.3298.3299.1998.9497.9799.1097.75
ResNET34
X88.2699.0197.9898.6798.8896.6198.9796.91
✓92.8799.3098.3799.1099.2198.4899.1498.07
EFFICIENTNET-B0
X86.1299.2997.9398.2198.4297.8198.8096.65
✓91.9999.3398.6699.1599.0098.3899.1297.95
+ +Table 5. Performance (AUC) of RESNET18, RESNET34, and EFFICIENTNET-B0 baseline and their integration with our QAD training framework. + +of up to $0.89\%$ points (97.79% vs. 96.90%), with a modest number of parameters (6.5M). + +# 4.4. Ablation studies + +# 4.4.1 $\alpha$ and $\gamma$ of our loss + +We investigate the sensitivities of our QAD with respect to $\alpha$ and $\gamma$ , and summarize the results of our analysis in Fig. 3. In this study, we experiment with ResNET50 on the NeuralTextures dataset, which is the hardest dataset to detect when compressed. And, we vary the values of the hyperparameters $\alpha \in \{0.002, 0.004, 0.008\}$ and $\gamma \in \{0.001, 0.002, 0.003, 0.004\}$ , where the value at $(\alpha, \gamma) = (0.0, 0.0)$ indicate the baseline. The results suggest that when $\alpha$ is greater than 0.002, the performance of our model is high and stable, surpassing current SOTA with any $\alpha$ greater than 0.002. Additionally, increasing $\gamma$ generally improves performance. Note that, as we did not tune the hyper-parameters to optimize the test accuracy, Section 4.3's hyper-parameters are not the best, despite outperforming all current methods on the datasets. + +# 4.4.2 Selection of losses + +We study different alternatives for the collaborative learning loss and the adversarial weight perturbation approach. In particular, for the collaborative learning loss, we apply the loss function that was introduced by [47], in which they aggregate the logits of different views, combining them with their true labels to generate the soft labels. Besides, we replace our HSIC regularization with intermediate pairwise loss (Eq. 3) and center loss. Regarding the adversarial weight perturbation, we further apply the KL divergence between the representations of raw and compressed images to perturb the model's weights. + +We report the results in Table 4, where we observe that the soft label loss fails to improve the baselines due to a + +![](images/32d83f1ec0636614abc8f698b971e0c1801c175396f4ff0b9e87049c9fd85c29.jpg) +Figure 4. Performance (AUC) of our proposed method at different input resolutions with NeuralTextures dataset. + +![](images/1525d5a32568c5d09592771c5826bee6aaec3d74bcc314d73b991d835f4d7afa.jpg) +Figure 5. t-SNE visualisation of baseline and our QAD. + +![](images/9e26333e0f705ea9dfba454ec57d79e87e46db2db839caffa4172f54be435b39.jpg) + +lack of low-level representation agreement between different image qualities. While both pairwise and center loss slightly improve the baselines and are unstable with different model architecture, our HSIC consistently achieves the best performance by relaxing the instance-base constraint. Meanwhile, we can observe the model's performance drops in terms of both ACC and AUC, when replacing our AWP with cross-entropy loss with KL divergence. Generally, this experiment shows that using pairwise differences of various quality image representations at the output, such as soft label, pairwise constraint, or AWP-KL, for optimizing the model can hinder its convergence to the optimal parameters. + +# 4.4.3 Experiment with different backbones + +Table 5 shows the comparability of our QAD with three different backbone networks: RESNET18, RESNET34, and EFFICIENTNET-B0. The hyperparameter settings are kept the same for RESNET50 and EFFICIENTNET-B1. As shown in Table 5, our QAD consistently improves the baselines, from $0.86\%$ to $1.3\%$ points on average of seven deepfake datasets. + +# 4.4.4 Performance at different input scales + +Unlike other classification tasks, a notable factor that substantially affects the deepfake detection performance, which is omitted by most previous works [43, 38, 61], is + +the input size of faces. We resize the input images from 56 to 336 and demonstrate how it impacts our QAD in comparison with ResNET50 baseline. The experiment is performed with the NeuralTextures dataset, and its results are reported in Fig. 4. We note that our proposed QAD and the baselines consistently improve their performance, when increasing the input size. Beside, our method also keep its staging improvement across the input resolutions compared to ResNET50 baseline. + +# 4.4.5 Feature distribution visualization + +To verify the consistency of invariant representation upon the input quality, we draw the feature distribution of EFFICIENTNET-B1 and our QAD-EFFICIENTNET-B1 pretrained on NeuralTextures (with raw, c23, and c40 datasets) with t-SNE [53]. The results are shown in Fig. 5. As observed, our QAD model's representations are less dispersed both in terms of intra-class and inter-quality. This experiment demonstrates that traditional cross-entropy loss trained with multiple input quality are confused due to the low-level constraints, while our QAD enables the model to achieve more generalization regardless of input quality. + +# 5. Conclusion + +Most deep learning-based deepfake detectors use a single model for each video quality, leaving an unsolved practical issue of their generalizability for detecting different quality of deepfakes. In this work, we propose a universal deepfake detection framework (QAD). Using intra-model collaborative learning, we minimize the geometrical differences of images in various qualities at different intermediate layers by the HSIC module. Moreover, our adversarial weight perturbation (AWP) module is directly applied to the model's parameters to provide its robustness against input image compression. Extensive experiments show that our QAD achieves competitive detection accuracy and marks the new SOTA results on various deepfake datasets without prior knowledge of input image quality. + +Acknowledgements. This work was partly supported by Institute for Information & communication Technology Planning & evaluation (IITP) grants funded by the Korean government MSIT: (No. 2022-0-01199, Graduate School of Convergence Security at Sungkyunkwan University), (No. 2022-0-01045, Self-directed Multi-Modal Intelligence for solving unknown, open domain problems), (No. 2022-0-00688, AI Platform to Fully Adapt and Reflect Privacy-Policy Changes), (No. 2021-0-02068, Artificial Intelligence Innovation Hub), (No. 2019-0-00421, AI Graduate School Support Program at Sungkyunkwan University), and (No. RS-2023-00230337, Advanced and Proactive AI Platform Research and Development Against Malicious deepfakes). + +# References + +[1] Darius Afchar, Vincent Nozick, Junichi Yamagishi, and Isao Echizen. Mesonet: a compact facial video forgery detection network. In 2018 IEEE international workshop on information forensics and security (WIFS), pages 1-7. 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Much research on deepfake detection has been undertaken. However, detecting low quality as well as simultaneously detecting different qualities of deepfakes still remains a grave challenge. Most SOTA approaches are limited by using a single specific model for detecting certain deepfake video quality type. When constructing multiple models with prior information about video quality, this kind of strategy incurs significant computational cost, as well as model and training data overhead. Further, it cannot be scalable and practical to deploy in real-world settings. In this work, we propose a universal intra-model collaborative learning framework to enable the effective and simultaneous detection of different quality of deepfakes. That is, our approach is the quality-agnostic deepfake detection method, dubbed QAD. In particular, by observing the upper bound of general error expectation, we maximize the dependency between intermediate representations of images from different quality levels via Hilbert-Schmidt Independence Criterion. In addition, an Adversarial Weight Perturbation module is carefully devised to enable the model to be more robust against image corruption while boosting the overall model's performance. Extensive experiments over seven popular deepfake datasets demonstrate the superiority of our QAD model over prior SOTA benchmarks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 588, + 128, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 588, + 128, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 588, + 128, + 601 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "text", + "content": "Deep learning approaches for facial manipulation, such as deepfakes, have recently received considerable attention [54, 31, 61, 25, 20, 23], because they can be abused for the malicious purposes such as fake news, pornography, etc. Due to the advancements made in Generative Adversarial Networks and other deep learning-based computer vision algorithms, deepfakes have also become more realistic and" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 310, + 226, + 392, + 312 + ], + "blocks": [ + { + "bbox": [ + 310, + 226, + 392, + 312 + ], + "lines": [ + { + "bbox": [ + 310, + 226, + 392, + 312 + ], + "spans": [ + { + "bbox": [ + 310, + 226, + 392, + 312 + ], + "type": "image", + "image_path": "2850bc805620a8677c15bbeafa25e502019b051d85085dae8b9fa4b36bd12c41.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 395, + 228, + 465, + 311 + ], + "blocks": [ + { + "bbox": [ + 395, + 228, + 465, + 311 + ], + "lines": [ + { + "bbox": [ + 395, + 228, + 465, + 311 + ], + "spans": [ + { + "bbox": [ + 395, + 228, + 465, + 311 + ], + "type": "image", + "image_path": "65afc92280a6be32be55f5583227c5939604a993fa1fa835f53c59af7f61ff54.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 468, + 228, + 549, + 311 + ], + "blocks": [ + { + "bbox": [ + 468, + 228, + 549, + 311 + ], + "lines": [ + { + "bbox": [ + 468, + 228, + 549, + 311 + ], + "spans": [ + { + "bbox": [ + 468, + 228, + 549, + 311 + ], + "type": "image", + "image_path": "33f73aae8c97828d1ff97a420620e7aefe5b135aa72abb464aaf0ac7b8a76c89.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 311, + 312, + 376, + 376 + ], + "blocks": [ + { + "bbox": [ + 311, + 312, + 376, + 376 + ], + "lines": [ + { + "bbox": [ + 311, + 312, + 376, + 376 + ], + "spans": [ + { + "bbox": [ + 311, + 312, + 376, + 376 + ], + "type": "image", + "image_path": "bd539fba419df6e44ea9f4cc21df917b11c06bccf640881686c247983cfc61fc.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 380, + 547, + 456 + ], + "lines": [ + { + "bbox": [ + 305, + 380, + 547, + 456 + ], + "spans": [ + { + "bbox": [ + 305, + 380, + 547, + 456 + ], + "type": "text", + "content": "Figure 1. A summary of our goal. Our approach stands out from previous works that detect deepfakes using separate models for different qualities (e.g. Baseline 2 [28]) or a single model without considering the interaction between qualities (e.g. Baseline 1 [43]). Instead, our method employs all quality levels and improves the performance of the model on each quality level, leading to overall enhanced performance." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 378, + 312, + 460, + 376 + ], + "blocks": [ + { + "bbox": [ + 378, + 312, + 460, + 376 + ], + "lines": [ + { + "bbox": [ + 378, + 312, + 460, + 376 + ], + "spans": [ + { + "bbox": [ + 378, + 312, + 460, + 376 + ], + "type": "image", + "image_path": "35102a955e037dc10a358435db161a202fc1691ca6bf897196504784acbe7b83.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 462, + 312, + 547, + 376 + ], + "blocks": [ + { + "bbox": [ + 462, + 312, + 547, + 376 + ], + "lines": [ + { + "bbox": [ + 462, + 312, + 547, + 376 + ], + "spans": [ + { + "bbox": [ + 462, + 312, + 547, + 376 + ], + "type": "image", + "image_path": "093f479cbf013679a61674f473781dfcc0a6c15914b8601e0d3ea68bb38f641f.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 472, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 545, + 581 + ], + "type": "text", + "content": "natural, making it harder not only for humans, but also for classifiers to tell them apart. Moreover, it has been simpler than ever before to create convincing deepfakes using simple programs and apps without requiring advanced machine learning knowledge. Such easy-to-create and realistic fake images and videos can be maliciously exploited, raising significant security, privacy, and societal concerns such as fake news propagation [39], and stealing personal information via phishing and scams [10]." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 582, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 546, + 714 + ], + "type": "text", + "content": "To mitigate such problems caused by deepfakes, there has been a tremendous research effort put into constructing reliable detectors [32, 25, 8, 38, 61, 44]. Although they have achieved outstanding performance with high-quality deepfakes, most of them have failed to detect low-quality deepfakes effectively [8, 43]. While video compression steps do not significantly impact on visualization, it drastically drop deepfake detectors' performance on low-quality deepfakes (c40). A handful of research has been focused on detecting low-quality deepfakes such as ADD [28] and BZNet [29]. However, their methods can only detect low-quality com" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "22378" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": "pressed deepfakes. And, those prior approaches expose a critical problem, when deployed in practice since the prior video quality information of the input is unknown. Moreover, developing different models for each input quality induces significant computational overhead. Other works, such as LipForensics [16], also attempt to make their detectors robust against various corruptions and compression. Nevertheless, it is unable to detect image-based deepfakes with random lossy compression like JPEG." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 182, + 289, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 289, + 385 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 289, + 385 + ], + "type": "text", + "content": "In this research, we propose the novel deepfake detection method, QAD, which can simultaneously detect both high and low-quality (quality-agnostic) deepfakes in a single model, as illustrated in Fig. 1. Especially, we propose a universal intra-model collaborative learning framework to provide the effective detection of different quality deepfakes. We modulate the conventional model-based collaborative learning [47] to an instance-based intra-model collaborative learning framework in our training. During the training phase, our single model simultaneously learns the representations of one image, but with different qualities. By utilizing the collaborative learning framework, our QAD can align the distributions of high and low-quality image representations to be geometrically similar. Hence, it can avoid the overfitting caused by compressed images and the overconfidence caused by raw images, while boosting its overall performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 387, + 289, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 387, + 289, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 387, + 289, + 579 + ], + "type": "text", + "content": "In particular, we perform a rigorous theoretical analysis, and show that the low-quality deepfake classification error can be bounded by two terms: classification loss and the distance between the representations of high and low-quality images. Instead of using a direct pairwise regularization to minimize the gaps between the high and low-quality image representations, we propose to apply Hilbert-Schmidt Independence Criterion (HSIC) to maximize the dependence between a mini-batch of high and low-quality images, thus maximizing the mutual information between them, and supporting the high-level representations and effective output predictions. Meanwhile, to enhance the model's robustness under heavy input compression, we propose Adversarial Weight Perturbation (AWP) [56, 3], which can further flatten the weight loss landscape of the model, bridging the gap in multiple quality learning for deepfake detection." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 580, + 289, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 289, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 289, + 700 + ], + "type": "text", + "content": "Finally, we conduct extensive experiments to show the effectiveness of our QAD with seven different popular benchmark datasets. We first show that our method can outperform previous baselines when training with data from various video and image compression qualities. Furthermore, we show that our QAD exceeds the performance of the SOTA quality-aware models such as BZNet [29] by a significant margin, while requiring remarkably fewer computational parameters and no prior knowledge of the inputs. Our contributions are summarized as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 701, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 288, + 714 + ], + "type": "text", + "content": "1) We theoretically analyze and prove that the classifica" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "tion error of low-quality deepfakes can be bounded by its classification loss and the representation distance with its corresponding high-quality images." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 108, + 547, + 252 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 304, + 108, + 547, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 547, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 547, + 204 + ], + "type": "text", + "content": "2) We propose a unified quality-agnostic deepfake detection framework (QAD), utilizing instance-based intramodel collaborative learning. We use the Hilbert-Schmidt Independence Criterion (HSIC) to maximize the geometrical similarity between intermediate representations of high and low-quality deepfakes, and Adversarial Weight Perturbation (AWP) to make our model robust under varying input compression." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 204, + 547, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 204, + 547, + 252 + ], + "spans": [ + { + "bbox": [ + 304, + 204, + 547, + 252 + ], + "type": "text", + "content": "3) We demonstrate that our approach outperforms well-known baselines, including the total of eight quality-agnostic and quality-aware SOTA methods with seven popular benchmark datasets." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 264, + 395, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 264, + 395, + 277 + ], + "spans": [ + { + "bbox": [ + 306, + 264, + 395, + 277 + ], + "type": "text", + "content": "2. Related works" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 284, + 418, + 297 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 284, + 418, + 297 + ], + "spans": [ + { + "bbox": [ + 306, + 284, + 418, + 297 + ], + "type": "text", + "content": "2.1. Deepfake detection" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 303, + 547, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 303, + 547, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 303, + 547, + 639 + ], + "type": "text", + "content": "Recently, deepfakes have been of the utmost crucial because they can cause serious security and privacy threats. Theresfore, a large number of detection methods have been proposed to effectively identify such deepfakes [43, 31, 30, 22, 41, 54, 32, 25, 8, 61]. However, the majority of the aforementioned works focus on mining visual artifacts of deepfakes, such as the blending boundaries of generated faces [31], the irregularity of pupil shapes [14], the spatiotemporal inconsistency [6, 44], or exploring deep learning-based attention methods [61] to identify such artifacts. Meanwhile, several approaches also showed that exposing deepfakes in the frequency domain is effective. Such methods include analyzing the discrepancies of frequency spectrum [8, 27, 25], employing the checkerboard artifacts caused by the transposed convolutional operator [60, 11], or mining the statistical frequency features with dual deep learning models [38]. Nevertheless, such models' performance substantially decreases when encountering low-quality compressed images. To remedy the above shortcoming, recent studies proposed methods to detect the deepfake in highly compressed low-quality versions such as [28], which utilized a knowledge distillation. Also, [29] presented a supper-resolution-based network for enhancing the performance of low-quality deepfake detection. However, all of the aforementioned approaches are limited in developing a single model for each quality of deepfakes, which is impractical to deploy in real-world scenarios due to the requirement of prior knowledge of the input quality." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 647, + 435, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 435, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 435, + 659 + ], + "type": "text", + "content": "2.2. Collaborative learning" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Collaborative learning proposed by [47] is designed to achieve a global minimum of a deep neural network, while maintaining the same computational complexity at inference time as at training time. Collaborative learning inherits" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22379" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "the advantages of auxiliary training [48], multi-task learning [58], and knowledge distillation [18]. Its applications cover supporting weakly-supervised learning [24], or integrating with online knowledge distillation [57, 15]. And, its training graph is divided into two or more sub-networks to ensure global minimum achievement [47]. Besides, [9] proposed an intra-model collaborative learning framework that shares a similar characteristic with self-knowledge distillation. However, all of the approaches are model-based collaborative learning, in which a single input generates multiple outputs (or views) through multiple classifier heads of one target network in both training and inference phase." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 217, + 289, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 289, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 289, + 361 + ], + "type": "text", + "content": "In this work, we distinguish ourselves by deploying the collaborative learning framework for simultaneously training deepfakes of various qualities with an undeviated single model, namely instance-based collaborative learning. Different from conventional mini-batch stochastic optimization, which independently samples random images from different qualities and optimizes the detector, our collaborative learning approach allows us to utilize the common features in the same image but from different qualities simultaneously. Thus, our deepfake detector circumvent the overfitting caused by compressed images or the overconfidence from raw images, enhancing its overall performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 371, + 261, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 371, + 261, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 371, + 261, + 384 + ], + "type": "text", + "content": "2.3. Hilbert-Schmidt Independence Criterion" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 391, + 289, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 391, + 289, + 606 + ], + "spans": [ + { + "bbox": [ + 46, + 391, + 289, + 606 + ], + "type": "text", + "content": "The Hilbert-Schmidt Independence Criterion (HSIC) [13] measures the statistical dependency between probability distributions. In fact, HSIC differs from the covariance, where " + }, + { + "bbox": [ + 46, + 391, + 289, + 606 + ], + "type": "inline_equation", + "content": "\\text{Cov}(X,Y) = 0" + }, + { + "bbox": [ + 46, + 391, + 289, + 606 + ], + "type": "text", + "content": " does not imply that two random variables " + }, + { + "bbox": [ + 46, + 391, + 289, + 606 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 391, + 289, + 606 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 391, + 289, + 606 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 46, + 391, + 289, + 606 + ], + "type": "text", + "content": " are independent [42], while HSIC shows its tractable computation and equivalency in terms of the independence property [13]. Moreover, HISC is easy to be estimated statistically and algorithmically. In practice, applications based on HSIC are found in a variety of practical domains, including maximizing the dependencies for self-supervised learning [33] and classification learning [34, 12], or defense against model inversion attacks [37]. In this paper, we utilize the HSIC to maximize the dependency between distributions of deepfake images of different qualities at intermediate layers. Therefore, we aim to constrain low-level representations of images not to be exactly the same, but to share a geometrical similarity of learning features that can support high-level output predictions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 620, + 107, + 632 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 620, + 107, + 632 + ], + "spans": [ + { + "bbox": [ + 47, + 620, + 107, + 632 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "In this section, we first theoretically examine the upper bound for our optimization problem by considering a DNN classifier of " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " classes, and two modalities of input quality: raw (high-quality) and compressed (low-quality). Then, we discuss how to more efficiently collaborate on the representations of deepfake images of differing quality." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 470, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 470, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 470, + 85 + ], + "type": "text", + "content": "3.1. Preliminary & our inspiration" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": "Given a sample " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "x_r" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": " from a space " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": " and its compressed version at quantile " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "x_c" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": " can be expressed as " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "x_c = x_r - \\delta_c" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": ", and we define the corresponding label " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "y \\in \\{0,1\\}" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": " (real and fake). Next, a family " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": " of learning functions " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "f: \\mathcal{X} \\to \\mathbb{R}^2" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": " returns a 2-tuple " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "f(x) = [f(x,j)]_{j=1}^2" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": ", whose " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "f(x,j)" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": " is proportional to the probability to assign " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": " to the " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": "-th class, and " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": " is defined by learning parameters " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": ". Given a training data " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(x_i,y_i)\\}_{i=1}^n \\subset \\mathcal{X} \\times \\mathcal{Y}" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": ", our goal is to minimize the expectation of a loss function " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "\\mathcal{L}: \\mathbb{R}^2 \\times \\mathcal{Y} \\to \\mathbb{R}" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": ". Here, we consider " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(f(x),y) = 1 - \\sigma_T(f(x,y))" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "\\sigma_T" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": " is the softmax function with temperature " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "T > 0" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 344, + 230, + 545, + 259 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 230, + 545, + 259 + ], + "spans": [ + { + "bbox": [ + 344, + 230, + 545, + 259 + ], + "type": "interline_equation", + "content": "\\sigma_ {T} (f (x), y) = \\frac {\\exp (f (x , y) / T)}{\\sum_ {k = 1} ^ {2} \\exp (f (x , k) / T)}. \\tag {1}", + "image_path": "774e84a1c2aeb18be9419dc183bc11f139a2164f22223e31223bd0627ef06abe.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 267, + 547, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 267, + 547, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 267, + 547, + 304 + ], + "type": "text", + "content": "Theorem 1. (Proof can be done similarly as [36] and [19] in Supp. Material) For any " + }, + { + "bbox": [ + 304, + 267, + 547, + 304 + ], + "type": "inline_equation", + "content": "f \\in \\mathcal{F}" + }, + { + "bbox": [ + 304, + 267, + 547, + 304 + ], + "type": "text", + "content": ", and with probability " + }, + { + "bbox": [ + 304, + 267, + 547, + 304 + ], + "type": "inline_equation", + "content": "1 - \\delta" + }, + { + "bbox": [ + 304, + 267, + 547, + 304 + ], + "type": "text", + "content": " over the draw of " + }, + { + "bbox": [ + 304, + 267, + 547, + 304 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 267, + 547, + 304 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 312, + 551, + 385 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 312, + 551, + 385 + ], + "spans": [ + { + "bbox": [ + 306, + 312, + 551, + 385 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbb {E} \\left[ \\mathbb {I} \\left\\{\\hat {y} \\left(x _ {c}\\right) \\neq y \\right\\} \\right] \\leq 2 \\mathbb {E} _ {\\mathcal {D}} \\mathcal {L} \\left(f \\left(x _ {c}\\right), y\\right) \\\\ + \\frac {8}{T} \\mathbb {E} _ {\\mathcal {D}} \\mathcal {L} _ {i - c o l} (f (x _ {r}), f (x _ {c})) + 4 \\Re_ {\\mathcal {D}} (\\Phi_ {\\mathcal {W}}) \\\\ + \\frac {1 6}{n} + \\mathcal {O} \\left(\\sqrt {\\frac {\\log (2 / \\delta)}{2 n}}\\right), \\tag {2} \\\\ \\end{array}", + "image_path": "30ad00aee2212083506596180cb23f3b3cbac19a0b670b372004c537e83a5706.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 393, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 393, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 306, + 393, + 545, + 418 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 393, + 545, + 418 + ], + "type": "inline_equation", + "content": "\\Re_{\\mathcal{D}}" + }, + { + "bbox": [ + 306, + 393, + 545, + 418 + ], + "type": "text", + "content": " is the Rademacher complexity, " + }, + { + "bbox": [ + 306, + 393, + 545, + 418 + ], + "type": "inline_equation", + "content": "\\Phi_{\\mathcal{W}} = \\{\\mathcal{L}(f(x_r),y),f\\in \\mathcal{F}\\}" + }, + { + "bbox": [ + 306, + 393, + 545, + 418 + ], + "type": "text", + "content": " , and" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 336, + 427, + 545, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 427, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 336, + 427, + 545, + 441 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i - c o l} \\left(f \\left(x _ {r}\\right), f \\left(x _ {c}\\right)\\right) = \\| f \\left(x _ {r}\\right) - f \\left(x _ {c}\\right) \\| . \\tag {3}", + "image_path": "64c6ac289155fc09009f6ff814e0ddf0f5f964d4264ade7e4adeeb0668d8ef7e.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 449, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 593 + ], + "type": "text", + "content": "Insight of Theorem 1. On the right-hand side of Eq. 2, our classifier " + }, + { + "bbox": [ + 304, + 449, + 545, + 593 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 449, + 545, + 593 + ], + "type": "text", + "content": " depends on two terms, where the first term is the classification loss " + }, + { + "bbox": [ + 304, + 449, + 545, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(f(x_c), y)" + }, + { + "bbox": [ + 304, + 449, + 545, + 593 + ], + "type": "text", + "content": " applied to the prediction of the compressed image " + }, + { + "bbox": [ + 304, + 449, + 545, + 593 + ], + "type": "inline_equation", + "content": "x_c" + }, + { + "bbox": [ + 304, + 449, + 545, + 593 + ], + "type": "text", + "content": ". And, the second term is the instance-based collaborative loss " + }, + { + "bbox": [ + 304, + 449, + 545, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{i-col}(f(x_r), f(x_c))" + }, + { + "bbox": [ + 304, + 449, + 545, + 593 + ], + "type": "text", + "content": " that measures the pairwise difference between predictions of the raw image and its compressed version. Therefore, minimizing the expectation over training data " + }, + { + "bbox": [ + 304, + 449, + 545, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 449, + 545, + 593 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 449, + 545, + 593 + ], + "type": "inline_equation", + "content": "2\\mathcal{L}(f(x_c), y) + 8\\mathcal{L}_{i-col}(f(x_r), f(x_c)) / T" + }, + { + "bbox": [ + 304, + 449, + 545, + 593 + ], + "type": "text", + "content": ", can decrease the true error. Note that Eq. 2 is also general so that it can be applicable for raw images. Hence, in practice, the first term can be generalized to both raw and compressed images." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": "In order to minimize the expectation of errors in both raw and compressed deepfake image predictions, our theoretical analysis shows that we can minimize both classification loss and collaborative loss at the output. However, as observed by [9] and in our experiments (see Tab. 4), this instance-based collaborative learning loss fails to achieve the best performance. Additionally, training solely with highly-compressed images makes the detector prone to overfitting, yielding a considerable gap between training and test performance [28]. As a result, the major research" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "22380" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 68, + 306, + 299 + ], + "blocks": [ + { + "bbox": [ + 61, + 68, + 306, + 299 + ], + "lines": [ + { + "bbox": [ + 61, + 68, + 306, + 299 + ], + "spans": [ + { + "bbox": [ + 61, + 68, + 306, + 299 + ], + "type": "image", + "image_path": "1ba2b5ce79c5cd2ab2801b0cc1965138c0d49c13d0109e99e40daa0e4b2b4533.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 300, + 545, + 367 + ], + "lines": [ + { + "bbox": [ + 46, + 300, + 545, + 367 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 545, + 367 + ], + "type": "text", + "content": "Figure 2. Overview of our QAD framework. A mini-batch of images from different quality modalities (e.g., two in this diagram) is forwarded through a single universal model. Although it is one model, we pictorially split it into two branches for the reader's understanding. After training, we obtain one universal model that regulates different qualities. Top-right: The HSIC geometrically maximizes the dependency between images from various quality modalities at different resolutions, supporting high-level output predictions. Bottom-right: Through searching for the worst-case parameters' corruption and compensating for input corruption (compression), the AWP flattens the model's weight loss landscape, making the model robust under varying input compression." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 318, + 69, + 533, + 192 + ], + "blocks": [ + { + "bbox": [ + 318, + 69, + 533, + 192 + ], + "lines": [ + { + "bbox": [ + 318, + 69, + 533, + 192 + ], + "spans": [ + { + "bbox": [ + 318, + 69, + 533, + 192 + ], + "type": "image", + "image_path": "2dd487df5afb505779b16d1d4628972653870860bf4a46b3112dc43ba8203515.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 320, + 198, + 533, + 297 + ], + "blocks": [ + { + "bbox": [ + 320, + 198, + 533, + 297 + ], + "lines": [ + { + "bbox": [ + 320, + 198, + 533, + 297 + ], + "spans": [ + { + "bbox": [ + 320, + 198, + 533, + 297 + ], + "type": "image", + "image_path": "770e067dbdc8c4a88a06076e460843fdd8a49a2856cb624bdb85c318d0e6bffd.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 386, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 386, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 386, + 287, + 422 + ], + "type": "text", + "content": "challenge is how we can further lower the sensitivity of " + }, + { + "bbox": [ + 46, + 386, + 287, + 422 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 386, + 287, + 422 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 386, + 287, + 422 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 386, + 287, + 422 + ], + "type": "text", + "content": " at various compression settings and push their representations close to each other." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 425, + 287, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 287, + 556 + ], + "type": "text", + "content": "Classification loss. We can construct a robust model under input corruption by flattening the weight loss landscape. In particular, we apply the Adversarial Weight Perturbation [56] to search for the worst-case perturbations " + }, + { + "bbox": [ + 46, + 425, + 287, + 556 + ], + "type": "inline_equation", + "content": "\\phi^{*}" + }, + { + "bbox": [ + 46, + 425, + 287, + 556 + ], + "type": "text", + "content": " of the model weights at every training step. Thereafter, optimizing the perturbed model via " + }, + { + "bbox": [ + 46, + 425, + 287, + 556 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(f_{\\theta +\\phi^*},y)" + }, + { + "bbox": [ + 46, + 425, + 287, + 556 + ], + "type": "text", + "content": " can enable it to be more robust under varying input image correlations/distortions, which represent the varying qualities of deepfake inputs (See Fig. 2—Bottom-right panel). Furthermore, the classification loss in Eq. 2 is upper bounded by this new loss function due to the worst-case perturbations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": "Collaborative loss. With respect to the collaborative learning loss, Eq. 3 shares similar characteristics with recent knowledge distillation research [18, 52]. However, our goal is to develop and train a single universal model, not having a teacher-student relationship. Nevertheless, we argue that the gap between raw and compressed image representations can be minimized more efficiently by regularizing their discrepancy at the low-level representations. Moreover, enforcing the similarity of the pairwise representations at the intermediate layers with an input difference of " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "|\\delta_c|" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": " can collapse layers' weights to zero or can lead a deep model to remember training data instead of learning discriminative features. Therefore, we relax this constraint by" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 386, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 386, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 545, + 519 + ], + "type": "text", + "content": "maximizing the kernel dependency in a mini-batch of data between the raw and compressed image representations by the Hilbert-Schmidt Independence Criterion (HSIC). Using HSIC, we can instead enforce the geometrical structures of mini-batch of raw data and the compressed data to be similar, so that we can still effectively detect different-quality deepfakes in a single model. From a mutual information perspective, maximizing the kernel dependency can enforce the mutual information of the learned representations of different compression ratios, thus regularizing the detector to be more generalized (See Fig. 2—Top-right panel)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 526, + 434, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 526, + 434, + 538 + ], + "spans": [ + { + "bbox": [ + 306, + 526, + 434, + 538 + ], + "type": "text", + "content": "3.2. Details of our methods" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 545, + 474, + 558 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 545, + 474, + 558 + ], + "spans": [ + { + "bbox": [ + 306, + 545, + 474, + 558 + ], + "type": "text", + "content": "3.2.1 Weight loss landscape flattening" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 564, + 545, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 564, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 564, + 545, + 636 + ], + "type": "text", + "content": "Recent studies [21, 55] suggest that searching for a flatter minima can improve the generalization ability of the model. To achieve this, we propose using Adversarial Weight Perturbation [56] to identify flat local minima of the empirical risk. The worst-case perturbations " + }, + { + "bbox": [ + 304, + 564, + 545, + 636 + ], + "type": "inline_equation", + "content": "\\phi^{*}" + }, + { + "bbox": [ + 304, + 564, + 545, + 636 + ], + "type": "text", + "content": " of the model weights which increases the loss dramatically is formulated as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 362, + 646, + 545, + 668 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 646, + 545, + 668 + ], + "spans": [ + { + "bbox": [ + 362, + 646, + 545, + 668 + ], + "type": "interline_equation", + "content": "\\phi^ {*} = \\underset {\\phi \\in \\mathcal {B} _ {p} (\\theta , \\gamma)} {\\arg \\max } \\mathcal {L} (f _ {\\theta + \\phi} (x), y), \\tag {4}", + "image_path": "0db6ed5a3923b27ab4012114db24f9858375185a7a3912427a628c82fa3d6593.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_p(\\theta, \\gamma) = \\{v \\in \\Theta : \\| \\theta - v \\|_p \\leq \\gamma\\}" + }, + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "content": " is the feasible region of any perturbation " + }, + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "content": ". The AWP adds the worst-case perturbation to the model weight, so that " + }, + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(f_{\\theta + \\phi^*}(x), y)" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22381" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": "becomes the supremum value in " + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_p(\\theta, \\gamma)" + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": ". Therefore, optimizing " + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(f_{\\theta + \\phi^*}(x), y)" + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": " pushes " + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": " to adjust its values such that the loss landscape is more flatten with the same capability " + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_p(\\theta, \\gamma)" + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": ". As a result, " + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": " becomes more stable under input image's changes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 132, + 287, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 132, + 287, + 157 + ], + "spans": [ + { + "bbox": [ + 46, + 132, + 287, + 157 + ], + "type": "text", + "content": "Similar to adversarial example perturbation [35], " + }, + { + "bbox": [ + 46, + 132, + 287, + 157 + ], + "type": "inline_equation", + "content": "\\phi^{*}" + }, + { + "bbox": [ + 46, + 132, + 287, + 157 + ], + "type": "text", + "content": " is generated by projected gradient method as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 64, + 163, + 287, + 190 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 163, + 287, + 190 + ], + "spans": [ + { + "bbox": [ + 64, + 163, + 287, + 190 + ], + "type": "interline_equation", + "content": "\\phi^ {*} \\leftarrow \\Pi_ {\\theta} ^ {\\gamma} \\left(\\phi + \\eta \\frac {\\nabla \\mathcal {L} \\left(f _ {\\theta + \\phi} (x) , y\\right)}{\\| \\nabla \\mathcal {L} \\left(f _ {\\theta + \\phi} (x) , y\\right) \\|} \\| \\theta \\|\\right), \\tag {5}", + "image_path": "31fb35817016375bc3bbc359505288ff19b8e1461bc5353aca8b80c46cc664bd.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 196, + 287, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 196, + 287, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 287, + 269 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 196, + 287, + 269 + ], + "type": "inline_equation", + "content": "\\Pi_{\\theta}^{\\gamma}" + }, + { + "bbox": [ + 46, + 196, + 287, + 269 + ], + "type": "text", + "content": " is an operator that projects its input into the feasible region " + }, + { + "bbox": [ + 46, + 196, + 287, + 269 + ], + "type": "inline_equation", + "content": "B_{p}(\\theta, \\gamma)" + }, + { + "bbox": [ + 46, + 196, + 287, + 269 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 196, + 287, + 269 + ], + "type": "inline_equation", + "content": "\\eta \\in \\mathbb{R}" + }, + { + "bbox": [ + 46, + 196, + 287, + 269 + ], + "type": "text", + "content": " is the step size. In fact, we empirically find that using a one-step projection for " + }, + { + "bbox": [ + 46, + 196, + 287, + 269 + ], + "type": "inline_equation", + "content": "\\phi^{*}" + }, + { + "bbox": [ + 46, + 196, + 287, + 269 + ], + "type": "text", + "content": " is sufficient for the model's robustness under the image corruptions formed by compression. By adding " + }, + { + "bbox": [ + 46, + 196, + 287, + 269 + ], + "type": "inline_equation", + "content": "\\phi^{*}" + }, + { + "bbox": [ + 46, + 196, + 287, + 269 + ], + "type": "text", + "content": " in Eq. 5 to " + }, + { + "bbox": [ + 46, + 196, + 287, + 269 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 196, + 287, + 269 + ], + "type": "text", + "content": ", it is straightforward to bound " + }, + { + "bbox": [ + 46, + 196, + 287, + 269 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(f(x_c), y)" + }, + { + "bbox": [ + 46, + 196, + 287, + 269 + ], + "type": "text", + "content": " in Eq. 2." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 282, + 228, + 295 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 282, + 228, + 295 + ], + "spans": [ + { + "bbox": [ + 47, + 282, + 228, + 295 + ], + "type": "text", + "content": "3.2.2 Intra-model collaborative learning" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "type": "text", + "content": "Hilbert-Schmidt Independence Criterion (HSIC). Let " + }, + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "type": "text", + "content": " be two separable Reproducing Kernel Hilbert Spaces (RKHS) on metric spaces " + }, + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "type": "text", + "content": ", respectively. HSIC measures the dependency between two random variables " + }, + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "type": "text", + "content": " from a joint distribution on " + }, + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 300, + 287, + 384 + ], + "type": "text", + "content": ", by evaluating the cross-covariance of the nonlinear transformations of the two random variables:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 48, + 391, + 287, + 417 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 391, + 287, + 417 + ], + "spans": [ + { + "bbox": [ + 48, + 391, + 287, + 417 + ], + "type": "interline_equation", + "content": "H S I C (U, V) = \\left\\| \\mathbb {E} [ \\zeta (U) \\psi (V) ^ {T} ] - \\mathbb {E} \\zeta (U) \\mathbb {E} \\psi (V) ^ {T} \\right\\| _ {H S} ^ {2}, \\tag {6}", + "image_path": "e1a7993d0e6a805ed7c3c33c658a3333161ab9239fb5a76832e15f82f3bf95c2.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\|_{HS}" + }, + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "type": "text", + "content": " is the Hilbert-Schmidt norm, which becomes the Frobenius norm in finite dimensions. And, " + }, + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "type": "inline_equation", + "content": "\\zeta : \\mathcal{U} \\to \\mathcal{T}" + }, + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "type": "inline_equation", + "content": "\\psi : \\mathcal{V} \\to \\mathcal{G}" + }, + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "type": "text", + "content": " are nonlinear mapping functions. With appropriate transformation " + }, + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "type": "inline_equation", + "content": "\\zeta" + }, + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "type": "text", + "content": ", HSIC is a dependence test, which can identify the nonlinear dependencies between " + }, + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "type": "text", + "content": " as follows: " + }, + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "type": "inline_equation", + "content": "HSIC(U,V) = 0 \\Leftrightarrow U \\perp V" + }, + { + "bbox": [ + 46, + 416, + 287, + 489 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 489, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 489, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 489, + 287, + 548 + ], + "type": "text", + "content": "Also, inner products in " + }, + { + "bbox": [ + 46, + 489, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 489, + 287, + 548 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 489, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 489, + 287, + 548 + ], + "type": "text", + "content": " are formed by positive definite kernel functions: " + }, + { + "bbox": [ + 46, + 489, + 287, + 548 + ], + "type": "inline_equation", + "content": "k(u,u^{\\prime}) = \\langle \\zeta (u),\\zeta (u^{\\prime})\\rangle_{\\mathcal{T}}" + }, + { + "bbox": [ + 46, + 489, + 287, + 548 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 489, + 287, + 548 + ], + "type": "inline_equation", + "content": "l(v,v^{\\prime}) = \\langle \\psi (v),\\psi (v^{\\prime})\\rangle_{\\mathcal{G}}" + }, + { + "bbox": [ + 46, + 489, + 287, + 548 + ], + "type": "text", + "content": ". And, let " + }, + { + "bbox": [ + 46, + 489, + 287, + 548 + ], + "type": "inline_equation", + "content": "(U^{\\prime},V^{\\prime})" + }, + { + "bbox": [ + 46, + 489, + 287, + 548 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 489, + 287, + 548 + ], + "type": "inline_equation", + "content": "(U^{\\prime \\prime},V^{\\prime \\prime})" + }, + { + "bbox": [ + 46, + 489, + 287, + 548 + ], + "type": "text", + "content": " be independent copies of " + }, + { + "bbox": [ + 46, + 489, + 287, + 548 + ], + "type": "inline_equation", + "content": "(U,V)" + }, + { + "bbox": [ + 46, + 489, + 287, + 548 + ], + "type": "text", + "content": ", then Eq. 6 can be expressed as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 56, + 555, + 287, + 596 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 555, + 287, + 596 + ], + "spans": [ + { + "bbox": [ + 56, + 555, + 287, + 596 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} H S I C (U, V) = \\mathbb {E} [ k (U, U ^ {\\prime}) l (V, V ^ {\\prime}) ] \\\\ - 2 \\mathbb {E} [ k (U, U ^ {\\prime}) ] \\mathbb {E} [ l (V, V ^ {\\prime \\prime}) ] + \\mathbb {E} [ k (U, U ^ {\\prime}) ] \\mathbb {E} [ l (V, V ^ {\\prime}) ]. \\tag {7} \\\\ \\end{array}", + "image_path": "47e462d4d9f4c1e4c421eaf3f63634def9ecbd3bd3161e080e35a17e3a32fe41.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 603, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 603, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 47, + 603, + 287, + 652 + ], + "type": "text", + "content": "Estimation of HSIC. The empirical estimation of HSIC with an bias of " + }, + { + "bbox": [ + 47, + 603, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\frac{1}{n})" + }, + { + "bbox": [ + 47, + 603, + 287, + 652 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 47, + 603, + 287, + 652 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 47, + 603, + 287, + 652 + ], + "type": "text", + "content": " samples i.i.d drawn " + }, + { + "bbox": [ + 47, + 603, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\{(u_i,v_i)\\}_{i = 1}^n" + }, + { + "bbox": [ + 47, + 603, + 287, + 652 + ], + "type": "text", + "content": " from the joint distribution " + }, + { + "bbox": [ + 47, + 603, + 287, + 652 + ], + "type": "inline_equation", + "content": "(U,V)" + }, + { + "bbox": [ + 47, + 603, + 287, + 652 + ], + "type": "text", + "content": " is provided as follows [13]:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 85, + 658, + 287, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 658, + 287, + 682 + ], + "spans": [ + { + "bbox": [ + 85, + 658, + 287, + 682 + ], + "type": "interline_equation", + "content": "\\widehat {H S I C} (U, V) = \\frac {1}{(n - 1) ^ {2}} \\mathbf {t r} (K H L H), \\tag {8}", + "image_path": "6c308e7957eebef6198306bf04eee8ac771186cb76a8dc404c5a8727e4ab8f8f.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "K_{i,j} = k(u_i, u_j)" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "L_{i,j} = l(v_i, v_j)" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": " are kernel matrices for the kernels " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": ", respectively, and " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "H_{i,j} =" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 72, + 541, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 541, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 541, + 84 + ], + "type": "text", + "content": "Algorithm 1 QAD: Quality-Agnostic Deepfake detection." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 85, + 545, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 85, + 545, + 145 + ], + "spans": [ + { + "bbox": [ + 306, + 85, + 545, + 145 + ], + "type": "text", + "content": "Require: DNN " + }, + { + "bbox": [ + 306, + 85, + 545, + 145 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 306, + 85, + 545, + 145 + ], + "type": "text", + "content": " parameterized by " + }, + { + "bbox": [ + 306, + 85, + 545, + 145 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 306, + 85, + 545, + 145 + ], + "type": "text", + "content": ", training dataset " + }, + { + "bbox": [ + 306, + 85, + 545, + 145 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 306, + 85, + 545, + 145 + ], + "type": "text", + "content": " with M quality modalities " + }, + { + "bbox": [ + 306, + 85, + 545, + 145 + ], + "type": "inline_equation", + "content": "\\mathcal{T} = \\{r, c_1, \\dots, c_{M-1}\\}" + }, + { + "bbox": [ + 306, + 85, + 545, + 145 + ], + "type": "text", + "content": ". Learning rate " + }, + { + "bbox": [ + 306, + 85, + 545, + 145 + ], + "type": "inline_equation", + "content": "\\alpha_l" + }, + { + "bbox": [ + 306, + 85, + 545, + 145 + ], + "type": "text", + "content": " and mini-batch size of " + }, + { + "bbox": [ + 306, + 85, + 545, + 145 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 306, + 85, + 545, + 145 + ], + "type": "text", + "content": ". 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Let " + }, + { + "bbox": [ + 304, + 432, + 546, + 552 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 432, + 546, + 552 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 432, + 546, + 552 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 432, + 546, + 552 + ], + "type": "text", + "content": " be two different qualities of deepfakes, (e.g., raw vs. compressed). 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End-to-end training loss" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "Given a training mini-batch " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " that include all " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " quality modalities " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{T} = \\{r,c_1,\\dots c_{M - 1}\\}" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": ", the overall collaborative" + } + ] + } + ], + "index": 38 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22382" + } + ] + } + ], + "index": 39 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 97, + 69, + 497, + 247 + ], + "blocks": [ + { + "bbox": [ + 97, + 69, + 497, + 247 + ], + "lines": [ + { + "bbox": [ + 97, + 69, + 497, + 247 + ], + "spans": [ + { + "bbox": [ + 97, + 69, + 497, + 247 + ], + "type": "table", + "html": "
ModelTest Set AUC (%)
NTDFF2FFSFSHCDFv2FFIW10KAvg
Video Compression (raw + c23 + c40 of test set)
MesoNet [1]◇70.2493.7294.1585.1796.0080.5294.5687.77
Rössler et al. [43]◇89.6499.0597.8998.8398.5097.4999.1797.22
F3Net [38]◇86.7998.7396.3297.8297.4595.0697.9495.73
MAT [61]◇86.7998.7396.3297.8297.4595.0697.9495.73
Fang & Lin [9]89.3098.9897.3398.4398.6696.5898.9496.89
SBIs [45]†78.3395.1979.7480.3780.48--82.82
BZNet [29]†80.1298.8194.1097.71---91.01
ADD [28]†86.2696.2390.6295.5795.94--92.92
QAD-R (ours)91.2599.5498.3499.0199.1298.3699.1097.82
QAD-E (ours)94.9299.5398.9499.2799.1298.3899.1698.47
", + "image_path": "9b6b13e9f0de1f63c8dc95cabc972ba1910ebcb950d36b3dbc3c9d6787a175a8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 97, + 312, + 497, + 485 + ], + "blocks": [ + { + "bbox": [ + 45, + 248, + 547, + 304 + ], + "lines": [ + { + "bbox": [ + 45, + 248, + 547, + 304 + ], + "spans": [ + { + "bbox": [ + 45, + 248, + 547, + 304 + ], + "type": "text", + "content": "Table 1. Classification performance in the quality-agnostic setting with video compression of test set. The methods are trained using one of three approaches: simultaneously with three modalities (raw + c23 + c40), individually with each of the three modalities, or with a mid-level of compression (c23) to prevent performance degradation resulting from lossy compression. In the inference phase, video compression is applied to the input. The best results are highlighted in bold. " + }, + { + "bbox": [ + 45, + 248, + 547, + 304 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 45, + 248, + 547, + 304 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 248, + 547, + 304 + ], + "type": "inline_equation", + "content": "\\diamond" + }, + { + "bbox": [ + 45, + 248, + 547, + 304 + ], + "type": "text", + "content": " indicate results were obtained from methods' pretrained weights and published code, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 97, + 312, + 497, + 485 + ], + "lines": [ + { + "bbox": [ + 97, + 312, + 497, + 485 + ], + "spans": [ + { + "bbox": [ + 97, + 312, + 497, + 485 + ], + "type": "table", + "html": "
ModelTest Set AUC (%)
NTDFF2FFSFSHCDFv2FFIW10KAvg
Random Image Compression (JPEG on raw of test set)
MesoNet [1]◇70.2392.0288.3282.6091.8481.1291.8785.43
Rössler et al. [43]◇69.8998.6294.9796.6696.7696.9898.8193.24
F3Net [38]◇70.9597.8992.8396.3494.7295.4497.1992.19
MAT [61]◇69.5398.9695.5397.9996.9798.2198.9193.73
Fang & Lin [9]75.4998.3294.6397.6497.2896.6798.3994.06
SBIs [45]†77.7597.8382.0586.1085.42--85.83
BZNet [29]†79.0098.7795.2397.92---92.73
ADD [28]†75.8496.8392.2395.2496.00--91.23
QAD-R (ours)75.1898.8693.7298.5298.1898.5198.9694.56
QAD-E (ours)76.2799.2094.4498.6998.6098.5298.8694.94
", + "image_path": "3883650e15549b40e9da849f6f8071af0015c0a5bd889a8be70ad7ea9cc7c4b8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 486, + 546, + 510 + ], + "lines": [ + { + "bbox": [ + 46, + 486, + 546, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 546, + 510 + ], + "type": "text", + "content": "Table 2. Classification performance in the quality-agnostic setting with image compression of test set. The training approach resembles that of Table 1's setting, however, in the inference phase, random image compression is applied to the input." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 520, + 267, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 267, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 267, + 533 + ], + "type": "text", + "content": "learning loss in our QAD framework is formulated as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 540, + 289, + 587 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 289, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 289, + 587 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {Q A D} = \\frac {1}{M B} \\sum_ {\\tau \\in \\mathcal {T}, i \\in B} \\mathcal {L} _ {\\phi^ {*}} \\left(x _ {\\tau , i}, y _ {i}\\right) + \\alpha \\sum_ {\\tau , \\rho \\in \\mathcal {T}} ^ {\\tau \\neq \\rho} \\mathcal {L} _ {c o l} (\\tau , \\rho), \\tag {10}", + "image_path": "e7576ae67f31dd10422a91693bc1418c7ae01d10bdfacbe5aa537266c581ad04.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " is a hyper-parameter to balance contribution of each loss. It is worth noting that our QAD training loss is parameter-free, and is not affected by the order of the modalities. Further, unlike other model-based collaborative learning [47], our QAD does not derive any sub-models. In other words, it can be integrated with any backbone, i.e., RESNET50, and introduces no extra computation at the inference time. Note that Theorem 1 still holds when replacing the classification loss " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(f(x),y)" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " with any cross-entropy based loss, since " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(f(x),y)" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " is bounded by the" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 520, + 546, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 546, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 546, + 556 + ], + "type": "text", + "content": "cross-entropy loss. Finally, we present our end-to-end algorithm for optimizing Eq. 10 in Algorithm 1, and its pictorial illustration in Fig. 2." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 567, + 432, + 581 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 567, + 432, + 581 + ], + "spans": [ + { + "bbox": [ + 305, + 567, + 432, + 581 + ], + "type": "text", + "content": "4. Experimental Results" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 587, + 457, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 587, + 457, + 601 + ], + "spans": [ + { + "bbox": [ + 305, + 587, + 457, + 601 + ], + "type": "text", + "content": "4.1. Dataset and pre-processing" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "For evaluating our proposed method, we experiment with seven different popular deepfake benchmark datasets: NeuralTextures (NT) [50], Deepfakes (DF) [4], Face2Face (F2F) [51], FaceSwap (FS) [5], FaceShifter (FSH) [30], CelebDFV2 (CDFv2) [59], and Face Forensics in the Wild (FFIW10K) [62]. Besides the raw version, these videos are also compressed into two types: medium (c23) and high (c40), utilizing the H.264 codec and constant rate quantization parameters of 23 and 40, respectively. These effectively" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22383" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 69, + 526, + 202 + ], + "blocks": [ + { + "bbox": [ + 67, + 69, + 526, + 202 + ], + "lines": [ + { + "bbox": [ + 67, + 69, + 526, + 202 + ], + "spans": [ + { + "bbox": [ + 67, + 69, + 526, + 202 + ], + "type": "table", + "html": "
Methodw/ prior infor.#paramsTest Set AUC (%)
NTDFF2FFSFSHCDFv2FFIW10KAvg
BZNet [29]†[×3]Y22M × 391.0199.3096.9098.82---96.51
ADD [28]†[×3]Y23.5M × 389.0899.2596.5398.2198.25--96.26
RESNET50 [×3]Y23.5M × 388.9699.2697.0498.6398.7197.0998.5896.90
QAD-R (ours)N23.5M × 188.8599.4297.7798.8398.9397.5698.9397.18
EFFICIENTNET-B1[×3]Y6.5M × 387.6399.0596.7298.1697.9596.7098.5496.39
QAD-E (ours)N6.5M × 192.2599.4698.3099.0898.9097.5099.0197.79
", + "image_path": "f0a3326574ba8aed6088fea266388d7f04524643e82e99a5fb5f82a51052e0eb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 201, + 547, + 246 + ], + "lines": [ + { + "bbox": [ + 46, + 201, + 547, + 246 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 547, + 246 + ], + "type": "text", + "content": "Table 3. Classification performance in the quality-aware setting with video compression of test set. Except for our model, each model is trained with three modalities: raw, c23, and c40, respectively (denoted " + }, + { + "bbox": [ + 46, + 201, + 547, + 246 + ], + "type": "inline_equation", + "content": "[ \\times 3 ]" + }, + { + "bbox": [ + 46, + 201, + 547, + 246 + ], + "type": "text", + "content": "). In the inference phase, while our QAD uses one single pre-trained model, other methods use their corresponding pre-trained model (e.g., pre-trained RESNET-50 on raw) to detect a given testing input (e.g., raw). Reported performances are averaged score of the three modalities." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 265, + 287, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 265, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 265, + 287, + 289 + ], + "type": "text", + "content": "result in different quality of deepfakes, and details of these datasets are provided in our Supp. Material." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 297, + 174, + 310 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 297, + 174, + 310 + ], + "spans": [ + { + "bbox": [ + 47, + 297, + 174, + 310 + ], + "type": "text", + "content": "4.2. Experimental Settings" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 316, + 289, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 289, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 289, + 485 + ], + "type": "text", + "content": "The models are trained with the Adam optimizer [26] with a learning rate of 2e-3, scheduled by one-cycle strategy [46] in 32 epochs. We use a mini-batch size of 64. In every training epoch, the model is evaluated ten times, and we save the best one based on the validation accuracy. Regarding the backbone network, we use the ResNET-50 [17] (QAD-R) and EfficientNet-B1 [49] (QAD-E) with their default input size of " + }, + { + "bbox": [ + 46, + 316, + 289, + 485 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 316, + 289, + 485 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 316, + 289, + 485 + ], + "type": "inline_equation", + "content": "240 \\times 240" + }, + { + "bbox": [ + 46, + 316, + 289, + 485 + ], + "type": "text", + "content": ", respectively. The backbone models utilize pre-trained weights from ImageNet dataset [7]. Our hyper-parameters settings " + }, + { + "bbox": [ + 46, + 316, + 289, + 485 + ], + "type": "inline_equation", + "content": "\\{\\sigma = 6, \\alpha = 0.004, \\gamma = 0.002\\}" + }, + { + "bbox": [ + 46, + 316, + 289, + 485 + ], + "type": "text", + "content": " are obtained by fine-tuning on ResNet50 with NeuralTextures dataset and are kept the same throughout all datasets, whereas that of EfficientNet-B1 are " + }, + { + "bbox": [ + 46, + 316, + 289, + 485 + ], + "type": "inline_equation", + "content": "\\{\\sigma = 6, \\alpha = 0.002, \\gamma = 0.006\\}" + }, + { + "bbox": [ + 46, + 316, + 289, + 485 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 492, + 105, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 492, + 105, + 504 + ], + "spans": [ + { + "bbox": [ + 47, + 492, + 105, + 504 + ], + "type": "text", + "content": "4.3. Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 510, + 287, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 571 + ], + "type": "text", + "content": "This section reports the results of our QAD and other baselines under two scenarios: 1) quality-agnostic setting, which represents no model has prior knowledge of the input images' quality, and 2) quality-aware setting, which baselines are required to know inputs' quality information." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 586, + 185, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 185, + 599 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 185, + 599 + ], + "type": "text", + "content": "4.3.1 Quality-agnostic models" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "We use the popular deepfake detection benchmark methods on our datasets: 1) MesoNet with Inception layer by [1], 2) Xception model proposed by [43], 3) " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "F^3" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Net [38], 4) MAT [61] - a multi-attention deepfake detector, 5) a deviation of the method proposed by [9] to the instance-based collaborative learning, SBIs [45] - a self-blended method using real image only during training, 7) ADD [28] - a knowledge distillation-based approach for detecting low-quality deepfakes, and 8) BZNet [29] - a super-resolution" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 265, + 547, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 265, + 547, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 265, + 547, + 422 + ], + "type": "text", + "content": "approach for improving detection of low-quality deepfakes. Each method has a different training approach to defend against performance degradation caused by lossy compression. The first five methods are trained with a mixture of the three data quality types (raw + c23 + c40). SBIs is trained with the mid-level of video compression (c23), which is commonly adopted in many works. Meanwhile, ADD and BZNet models are trained on raw, c23, and c40, respectively; however, in the inference phase, they are blindly tested over the entire dataset without the prior knowledge of quality types, and we report their average performance. In the test set, we include both video compression and random JPEG image compression [2]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 430, + 547, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 430, + 547, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 430, + 547, + 598 + ], + "type": "text", + "content": "The results for the video compression are presented in Table 1, where our QAD outperforms other SOTA baselines across multiple benchmark datasets. Notably, we achieve a significant improvement in AUC score of up to " + }, + { + "bbox": [ + 304, + 430, + 547, + 598 + ], + "type": "inline_equation", + "content": "5.28\\%" + }, + { + "bbox": [ + 304, + 430, + 547, + 598 + ], + "type": "text", + "content": " for heavily compressed datasets, such as NeuralTextures (89.64% vs 94.92%). We also surpassed previous works on various deepfake datasets by " + }, + { + "bbox": [ + 304, + 430, + 547, + 598 + ], + "type": "inline_equation", + "content": "0.44\\%" + }, + { + "bbox": [ + 304, + 430, + 547, + 598 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 430, + 547, + 598 + ], + "type": "inline_equation", + "content": "1.05\\%" + }, + { + "bbox": [ + 304, + 430, + 547, + 598 + ], + "type": "text", + "content": " points, with the exception of Deepfakes and FFIW10K datasets, which are easy to detect even when compressed. Compared to the collaborative learning baseline by [9], which is a comparative benchmark, our QAD still gains a decent improvement on average, up to " + }, + { + "bbox": [ + 304, + 430, + 547, + 598 + ], + "type": "inline_equation", + "content": "0.93\\%" + }, + { + "bbox": [ + 304, + 430, + 547, + 598 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 430, + 547, + 598 + ], + "type": "inline_equation", + "content": "1.54\\%" + }, + { + "bbox": [ + 304, + 430, + 547, + 598 + ], + "type": "text", + "content": " points with QAD-R and QAD-E, respectively. Finally, our QAD-E models achieved the highest score on average, reaching " + }, + { + "bbox": [ + 304, + 430, + 547, + 598 + ], + "type": "inline_equation", + "content": "98.47\\%" + }, + { + "bbox": [ + 304, + 430, + 547, + 598 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "text", + "content": "Regarding the random image compression experiment, the results are provided in Table 2. Although BZNet is marginally outperform our model on face-reenactment deepfakes (NT and F2F), our method still achieves the best performance with the highest scores on five over seven datasets. On average, our enhancements show decent improvements, with margins of " + }, + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "inline_equation", + "content": "0.88\\%" + }, + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "text", + "content": " of QAD-R and QAD-E, respectively, compared to the second-best competitor (Fang & Lin)." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22384" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 70, + 266, + 255 + ], + "blocks": [ + { + "bbox": [ + 69, + 70, + 266, + 255 + ], + "lines": [ + { + "bbox": [ + 69, + 70, + 266, + 255 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 266, + 255 + ], + "type": "image", + "image_path": "4d88c5324fd3ae21bd400d2a928c8cb17f036a2582827f75ada9867e1336c59e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 258, + 287, + 280 + ], + "lines": [ + { + "bbox": [ + 47, + 258, + 287, + 280 + ], + "spans": [ + { + "bbox": [ + 47, + 258, + 287, + 280 + ], + "type": "text", + "content": "Figure 3. Model's performance versus " + }, + { + "bbox": [ + 47, + 258, + 287, + 280 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 258, + 287, + 280 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 258, + 287, + 280 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 47, + 258, + 287, + 280 + ], + "type": "text", + "content": " on the NeuralTextures." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 72, + 288, + 263, + 402 + ], + "blocks": [ + { + "bbox": [ + 72, + 288, + 263, + 402 + ], + "lines": [ + { + "bbox": [ + 72, + 288, + 263, + 402 + ], + "spans": [ + { + "bbox": [ + 72, + 288, + 263, + 402 + ], + "type": "table", + "html": "
Model / lossRESNET-50
ACC (%)AUC (%)
Baseline78.888.2
Coll. lossSoft-label77.084.0
Pairwise loss79.789.1
Center loss79.888.9
HSIC80.390.1
Adv. lossAWP-KL80.989.4
AWP-XE81.790.7
QAD (ours)82.291.3
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QADNTDFF2FFSFSHCDFv2FFIW10KAvg
ResNET18
X88.7398.9398.0598.0698.6797.0998.7296.89
✓91.3899.3298.3299.1998.9497.9799.1097.75
ResNET34
X88.2699.0197.9898.6798.8896.6198.9796.91
✓92.8799.3098.3799.1099.2198.4899.1498.07
EFFICIENTNET-B0
X86.1299.2997.9398.2198.4297.8198.8096.65
✓91.9999.3398.6699.1599.0098.3899.1297.95
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Performance (AUC) of RESNET18, RESNET34, and EFFICIENTNET-B0 baseline and their integration with our QAD training framework." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 269, + 545, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 269, + 545, + 294 + ], + "spans": [ + { + "bbox": [ + 305, + 269, + 545, + 294 + ], + "type": "text", + "content": "of up to " + }, + { + "bbox": [ + 305, + 269, + 545, + 294 + ], + "type": "inline_equation", + "content": "0.89\\%" + }, + { + "bbox": [ + 305, + 269, + 545, + 294 + ], + "type": "text", + "content": " points (97.79% vs. 96.90%), with a modest number of parameters (6.5M)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 302, + 405, + 314 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 302, + 405, + 314 + ], + "spans": [ + { + "bbox": [ + 306, + 302, + 405, + 314 + ], + "type": "text", + "content": "4.4. Ablation studies" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 321, + 419, + 333 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 321, + 419, + 333 + ], + "spans": [ + { + "bbox": [ + 306, + 321, + 419, + 333 + ], + "type": "text", + "content": "4.4.1 " + }, + { + "bbox": [ + 306, + 321, + 419, + 333 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 306, + 321, + 419, + 333 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 321, + 419, + 333 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 306, + 321, + 419, + 333 + ], + "type": "text", + "content": " of our loss" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "type": "text", + "content": "We investigate the sensitivities of our QAD with respect to " + }, + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "type": "text", + "content": ", and summarize the results of our analysis in Fig. 3. In this study, we experiment with ResNET50 on the NeuralTextures dataset, which is the hardest dataset to detect when compressed. And, we vary the values of the hyperparameters " + }, + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\alpha \\in \\{0.002, 0.004, 0.008\\}" + }, + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\gamma \\in \\{0.001, 0.002, 0.003, 0.004\\}" + }, + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "type": "text", + "content": ", where the value at " + }, + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "type": "inline_equation", + "content": "(\\alpha, \\gamma) = (0.0, 0.0)" + }, + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "type": "text", + "content": " indicate the baseline. The results suggest that when " + }, + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "type": "text", + "content": " is greater than 0.002, the performance of our model is high and stable, surpassing current SOTA with any " + }, + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "type": "text", + "content": " greater than 0.002. Additionally, increasing " + }, + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 305, + 341, + 545, + 520 + ], + "type": "text", + "content": " generally improves performance. Note that, as we did not tune the hyper-parameters to optimize the test accuracy, Section 4.3's hyper-parameters are not the best, despite outperforming all current methods on the datasets." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 537, + 415, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 537, + 415, + 548 + ], + "spans": [ + { + "bbox": [ + 306, + 537, + 415, + 548 + ], + "type": "text", + "content": "4.4.2 Selection of losses" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "text", + "content": "We study different alternatives for the collaborative learning loss and the adversarial weight perturbation approach. In particular, for the collaborative learning loss, we apply the loss function that was introduced by [47], in which they aggregate the logits of different views, combining them with their true labels to generate the soft labels. Besides, we replace our HSIC regularization with intermediate pairwise loss (Eq. 3) and center loss. Regarding the adversarial weight perturbation, we further apply the KL divergence between the representations of raw and compressed images to perturb the model's weights." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "We report the results in Table 4, where we observe that the soft label loss fails to improve the baselines due to a" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22385" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 73, + 279, + 196 + ], + "blocks": [ + { + "bbox": [ + 55, + 73, + 279, + 196 + ], + "lines": [ + { + "bbox": [ + 55, + 73, + 279, + 196 + ], + "spans": [ + { + "bbox": [ + 55, + 73, + 279, + 196 + ], + "type": "image", + "image_path": "32d83f1ec0636614abc8f698b971e0c1801c175396f4ff0b9e87049c9fd85c29.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 201, + 287, + 224 + ], + "lines": [ + { + "bbox": [ + 47, + 201, + 287, + 224 + ], + "spans": [ + { + "bbox": [ + 47, + 201, + 287, + 224 + ], + "type": "text", + "content": "Figure 4. Performance (AUC) of our proposed method at different input resolutions with NeuralTextures dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 55, + 233, + 167, + 348 + ], + "blocks": [ + { + "bbox": [ + 55, + 233, + 167, + 348 + ], + "lines": [ + { + "bbox": [ + 55, + 233, + 167, + 348 + ], + "spans": [ + { + "bbox": [ + 55, + 233, + 167, + 348 + ], + "type": "image", + "image_path": "1525d5a32568c5d09592771c5826bee6aaec3d74bcc314d73b991d835f4d7afa.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 64, + 352, + 269, + 364 + ], + "lines": [ + { + "bbox": [ + 64, + 352, + 269, + 364 + ], + "spans": [ + { + "bbox": [ + 64, + 352, + 269, + 364 + ], + "type": "text", + "content": "Figure 5. t-SNE visualisation of baseline and our QAD." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 168, + 234, + 280, + 348 + ], + "blocks": [ + { + "bbox": [ + 168, + 234, + 280, + 348 + ], + "lines": [ + { + "bbox": [ + 168, + 234, + 280, + 348 + ], + "spans": [ + { + "bbox": [ + 168, + 234, + 280, + 348 + ], + "type": "image", + "image_path": "9e26333e0f705ea9dfba454ec57d79e87e46db2db839caffa4172f54be435b39.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 376, + 289, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 289, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 289, + 521 + ], + "type": "text", + "content": "lack of low-level representation agreement between different image qualities. While both pairwise and center loss slightly improve the baselines and are unstable with different model architecture, our HSIC consistently achieves the best performance by relaxing the instance-base constraint. Meanwhile, we can observe the model's performance drops in terms of both ACC and AUC, when replacing our AWP with cross-entropy loss with KL divergence. Generally, this experiment shows that using pairwise differences of various quality image representations at the output, such as soft label, pairwise constraint, or AWP-KL, for optimizing the model can hinder its convergence to the optimal parameters." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 537, + 239, + 549 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 537, + 239, + 549 + ], + "spans": [ + { + "bbox": [ + 47, + 537, + 239, + 549 + ], + "type": "text", + "content": "4.4.3 Experiment with different backbones" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 557, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 640 + ], + "type": "text", + "content": "Table 5 shows the comparability of our QAD with three different backbone networks: RESNET18, RESNET34, and EFFICIENTNET-B0. The hyperparameter settings are kept the same for RESNET50 and EFFICIENTNET-B1. As shown in Table 5, our QAD consistently improves the baselines, from " + }, + { + "bbox": [ + 46, + 557, + 287, + 640 + ], + "type": "inline_equation", + "content": "0.86\\%" + }, + { + "bbox": [ + 46, + 557, + 287, + 640 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 557, + 287, + 640 + ], + "type": "inline_equation", + "content": "1.3\\%" + }, + { + "bbox": [ + 46, + 557, + 287, + 640 + ], + "type": "text", + "content": " points on average of seven deepfake datasets." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 658, + 239, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 239, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 239, + 670 + ], + "type": "text", + "content": "4.4.4 Performance at different input scales" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "Unlike other classification tasks, a notable factor that substantially affects the deepfake detection performance, which is omitted by most previous works [43, 38, 61], is" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": "the input size of faces. We resize the input images from 56 to 336 and demonstrate how it impacts our QAD in comparison with ResNET50 baseline. The experiment is performed with the NeuralTextures dataset, and its results are reported in Fig. 4. We note that our proposed QAD and the baselines consistently improve their performance, when increasing the input size. Beside, our method also keep its staging improvement across the input resolutions compared to ResNET50 baseline." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 212, + 481, + 223 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 212, + 481, + 223 + ], + "spans": [ + { + "bbox": [ + 306, + 212, + 481, + 223 + ], + "type": "text", + "content": "4.4.5 Feature distribution visualization" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 236, + 547, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 236, + 547, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 236, + 547, + 369 + ], + "type": "text", + "content": "To verify the consistency of invariant representation upon the input quality, we draw the feature distribution of EFFICIENTNET-B1 and our QAD-EFFICIENTNET-B1 pretrained on NeuralTextures (with raw, c23, and c40 datasets) with t-SNE [53]. The results are shown in Fig. 5. As observed, our QAD model's representations are less dispersed both in terms of intra-class and inter-quality. This experiment demonstrates that traditional cross-entropy loss trained with multiple input quality are confused due to the low-level constraints, while our QAD enables the model to achieve more generalization regardless of input quality." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 388, + 378, + 400 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 388, + 378, + 400 + ], + "spans": [ + { + "bbox": [ + 306, + 388, + 378, + 400 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 411, + 547, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 547, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 547, + 579 + ], + "type": "text", + "content": "Most deep learning-based deepfake detectors use a single model for each video quality, leaving an unsolved practical issue of their generalizability for detecting different quality of deepfakes. In this work, we propose a universal deepfake detection framework (QAD). Using intra-model collaborative learning, we minimize the geometrical differences of images in various qualities at different intermediate layers by the HSIC module. Moreover, our adversarial weight perturbation (AWP) module is directly applied to the model's parameters to provide its robustness against input image compression. Extensive experiments show that our QAD achieves competitive detection accuracy and marks the new SOTA results on various deepfake datasets without prior knowledge of input image quality." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "Acknowledgements. This work was partly supported by Institute for Information & communication Technology Planning & evaluation (IITP) grants funded by the Korean government MSIT: (No. 2022-0-01199, Graduate School of Convergence Security at Sungkyunkwan University), (No. 2022-0-01045, Self-directed Multi-Modal Intelligence for solving unknown, open domain problems), (No. 2022-0-00688, AI Platform to Fully Adapt and Reflect Privacy-Policy Changes), (No. 2021-0-02068, Artificial Intelligence Innovation Hub), (No. 2019-0-00421, AI Graduate School Support Program at Sungkyunkwan University), and (No. RS-2023-00230337, Advanced and Proactive AI Platform Research and Development Against Malicious deepfakes)." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "22386" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 48, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 48, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Darius Afchar, Vincent Nozick, Junichi Yamagishi, and Isao Echizen. 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However, object instances are diverse in shape and category, and point clouds are usually sparse, unordered, and irregular, which leads to a query sampling dilemma. Besides, noise background queries interfere with proper scene perception and accurate instance segmentation. To address the above issues, we propose the Query Refinement Transformer termed QueryFormer. The key to our approach is to exploit a query initialization module to optimize the initialization process for the query distribution with a high coverage and low repetition rate. Additionally, we design an affiliated transformer decoder that suppresses the interference of noise background queries and helps the foreground queries focus on instance discriminative parts to predict final segmentation results. Extensive experiments on ScanNetV2 and S3DIS datasets show that our QueryFormer can surpass state-of-the-art 3D instance segmentation methods.", + "bbox": [ + 75, + 300, + 473, + 590 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 607, + 209, + 625 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3D instance segmentation is a fundamental task for 3D scene understanding, which aims to predict the semantic labels and the binary foreground masks for every object in the scene simultaneously. With the popularity of AR/VR [31], 3D indoor scanning [21], and autonomous driving [46], 3D instance segmentation has become a key technology facilitating scene understanding. However, the complex layout of the scene and the variety of object categories pose severe challenges to 3D instance segmentation in segmenting similar objects and accurate point cloud masking.", + "bbox": [ + 75, + 633, + 468, + 785 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To overcome the above challenges, a series of 3D instance segmentation methods [11, 24, 4, 23, 39, 36] have been proposed. Generally, these methods can be divided into three categories: proposal-based [45, 11, 24], grouping-based [17, 4, 23, 39], and query-based [36]. Proposal-based methods [45, 11, 24] extract 3D bound-", + "bbox": [ + 75, + 785, + 470, + 877 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f784115a6bf0fb1578534d62324e52860c05bf405cdbcd1308271e39afef689d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 268, + 890, + 323 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0fff207730706ef70d9904a9c68b4cdfdb28f2ce72457bc0f6c2d88bf9037295.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 323, + 888, + 377 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c0088c33963a89e1eae9929452c6039e3c553ee7e059b4267f488aa36617ccb3.jpg", + "image_caption": [ + "Figure 1. The visualization of query distribution and segmentation results. A. The query initialization module samples a query on each of the two chairs to distinguish the two instances precisely. B. Repeated queries incorrectly split the complete board into two pieces. C. The denoising module removes many noise background queries and optimizes the final segmentation results." + ], + "image_footnote": [], + "bbox": [ + 504, + 377, + 888, + 443 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing boxes and utilize a mask learning branch to predict the object mask inside each box. Grouping-based methods [17, 4, 23, 39] rely on a bottom-up pipeline that generates predictions for each point (e.g., semantic categories and geometric offsets) and then groups the points into instances. However, proposal-based and grouping-based methods strongly rely on high-quality proposals and require manual selection of geometric properties and tuning of hyperparameters. These drawbacks and limitations prompt query-based methods to be proposed and receive extensive attention from researchers. Query-based methods are regarded as a class of transformer query-based methods [2, 5] in which each object instance is represented as an instance query. Query-based methods require a large number of queries spread throughout the scene to cover a large part of foreground objects in the scene so that there are one or even more queries on each covered object instance. Then a transformer decoder learns the instance queries by iteratively focusing on multi-level point cloud features. Eventually, the instance queries aggregate point cloud features to produce all instance masks in parallel.", + "bbox": [ + 496, + 535, + 893, + 852 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Based on the discussion of the above approaches, query-based methods show great promise for 3D instance segmentation tasks by offering superior performance while not re", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author", + "bbox": [ + 94, + 886, + 223, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18516", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0a1ec487998e39b5bc247ba83f08649fe9585d1bc0ee1a68aa8966bc47eb0805.jpg", + "image_caption": [ + "Query Distribution" + ], + "image_footnote": [], + "bbox": [ + 127, + 95, + 236, + 186 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a92cf0c2c1e69badd9b93024b9da710f88fc461ac4c1b40950db830e4bd0aa4b.jpg", + "image_caption": [ + "Mask3D", + "Ours" + ], + "image_footnote": [], + "bbox": [ + 248, + 95, + 354, + 186 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/4c3322a4c5de53260a2eddd057d2f24eab82f98238ba37986bb812dab0fda61c.jpg", + "image_caption": [ + "Foreground Query", + "Figure 2. Statistics on coverage rate&repetition rate and query distribution. For query distribution, our method has more foreground distribution and less noise background queries and FPS initialization exists many noise background queries. Besides, our method guarantees a high coverage rate of foreground object instances while maintaining a low repetition rate." + ], + "image_footnote": [], + "bbox": [ + 99, + 205, + 248, + 260 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3c337583894a707bd71ccfa11858b1c5fb26c90b4f3c7f226a4dac3ed40f351b.jpg", + "image_caption": [ + "Noise Background Query", + "Background Query", + "General Background Query" + ], + "image_footnote": [], + "bbox": [ + 279, + 207, + 444, + 260 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "quiring high-quality 3D proposals and reducing the need for extensive manual setup. By analyzing the query-based method, we summarize the following two core points of query-based 3D instance segmentation: 1) How to effectively initialize queries? For the query-based method, we conclude that coverage and repetition rates are two significant factors affecting query initialization. The coverage rate is defined as the proportion of foreground object instances with queries distributed to the total foreground object instances in the scene. As the statistical results in Figure 2, the coverage rate of FPS [35] is $74\\%$ (Ours is $89\\%$ ), and the lower coverage rate causes some objects to be missed. For example, as shown in Figure 1(A), the two chairs are incorrectly segmented into one whole object because one chair is not covered by queries. The repetition rate is defined as the proportion of queries that have other queries coexisting in the same foreground object instance to the total number of foreground queries. The higher repetition rate ( $64\\%$ vs our $47\\%$ ) results in low query utilization and unnecessary overlapping computation. Besides, repeated queries contradict one-to-one bipartite matching mechanism and will destroy the integrity of segmentation results. As shown in Figure 1(B), multiple queries split the board into two parts. In practice, a high coverage rate often leads to a high repetition rate, and a low repetition rate is accompanied by a low coverage rate, so it is necessary to design an initialization strategy that can guarantee a high coverage rate of foreground object instances while maintaining a low repetition rate. 2) How to suppress the interference of noise background queries on accurate segmentation? Query-based methods yield outstanding performance but sample more queries than object instances in the scene. For example, sampling results by the Mask3D [36] in Figure 2 show that $48\\%$ of the queries are distributed on foreground", + "bbox": [ + 75, + 387, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "objects, while $15\\%$ of the $52\\%$ of the background queries are distributed near the instances. The background queries distributed near the instances are called noise background queries because the closer the queries are to the instances, the more negatively they affect the accurate segmentation of the instances. As shown in Figure 1(C), the foreground queries(red) incorrectly segment a part of the background as a foreground instance due to the interference of the noise background queries(green). Therefore, in addition to ensuring that foreground queries accurately segment foreground instances, it is equally essential to suppress the interference of noise background queries on the segmentation task.", + "bbox": [ + 496, + 90, + 890, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inspired by the above discussion, we propose a Query Refinement Transformer for 3D Instance Segmentation, named QueryFormer, including a point encoder, a query initialization module, and an affiliated transformer decoder. We use a generic U-net point cloud representation network [7] as the point encoder of the method. In the query initialization module, we aggregate the superpoint features [20] and the multi-level features extracted by the point encoder to the seed points through the Aggregation Module. The Set Grouping module (SG) is designed to achieve a high coverage rate and low repetition rate distribution of seed points on instances. Specifically, the set grouping module shifts seed points to the centers of the objects to ensure a high coverage rate and filters out duplicate seed points to decrease the repetition rate and minimize the computational cost. The affiliated transformer decoder is dedicated to suppressing the impacts of noise background queries on the instance segmentation. Specifically, we generate some perturbed ground-truth centers around the instance centers during training. The perturbed centers are encoded in the same space as the query and input to the decoder for mapping to a consistent feature space. For each foreground instance, a unique query is matched by the Hungarian matching [18]. This query forms positive pairs with perturbed centers, while unmatched queries form several negative pairs with perturbed centers. We design a denoising module with contrastive loss [30] to drive the unmatched noise background queries away from the instance to reduce interference with the instance mask prediction.", + "bbox": [ + 496, + 276, + 890, + 715 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, the main contributions of this work are as follows: (i) We design a query initialization module to optimize the initialization process for a high coverage and low repetition rate query distribution, which further helps the proposed affiliated transformer decoder to achieve more accurate results. (ii) The proposed affiliated transformer decoder suppresses the interference of noise background queries and helps the foreground queries focus on discriminative parts for more accurate instance segmentation. (iii) Extensive experimental results on two standard benchmarks, ScanNetV2 [8] and S3DIS [1], demonstrate that the proposed model performs favorably against state-", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18517", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "of-the-art 3D instance segmentation methods.", + "bbox": [ + 76, + 90, + 379, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 119, + 217, + 135 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we briefly overview related works on 3D instance segmentation, including proposal-based methods, grouping-based methods, and instance segmentation with transformer.", + "bbox": [ + 76, + 145, + 467, + 205 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Proposal-based Methods. Existing proposal-based methods are greatly influenced by the success of Mask R-CNN [14] for 2D instance segmentation. GSPN [45] takes an analysis-by-synthesis strategy to generate high-quality 3D proposals, which are refined by a region-based PointNet [34]. 3D-BoNet [44] uses PointNet++ [35] to extract features from point clouds and applies Hungarian matching [18] to generate 3D bounding boxes. GICN [24] approximates the instance center of each object as a Gaussian distribution. 3D-MPA [11] predicts centers of instances and employs a graph-based convolutional network to cluster points near the centers to refine proposal features. The proposal-based methods have high expectations for the quality of proposals.", + "bbox": [ + 75, + 205, + 467, + 416 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Grouping-based Methods. Grouping-based methods produce per-point predictions, such as semantic categories and geometric offsets, and then group points into instances. To group points, MTML [19] uses a multi-task learning strategy. PointGroup [17] segments objects on the original and offset-shifted point clouds and uses the ScoreNet to predict scores for instances. HAIS [4] extends PointGroup by absorbing surrounding fragments of instances and then refining the instances based on intra-instance prediction. SSTNet [23] constructs a tree network from precomputed superpoints and splits non-similar nodes to get object instances. SoftGroup [39] groups on soft semantic scores instead of hard semantic prediction and processes each proposal to refine positive samples and suppress negative ones. Although the grouping-based approaches require many manual settings, they have dominated the field until recently.", + "bbox": [ + 75, + 417, + 467, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Instance Segmentation with Transformer. Transformer [38] introduces the self-attention mechanism to model long-range dependencies and has been widely applied in computer vision tasks such as image classification [10, 3], object detection [2, 9], and segmentation [48, 6, 5]. Recently, DETR [2] has been proposed as a new paradigm to use object queries for object detection in an image. Based on the set prediction mechanism proposed in DETR, MaskFormer [6] employs a transformer decoder to compute a set of pairs, each consisting of a class prediction and a mask embedding vector, to solve both semantic and instance segmentation tasks in a unified manner. Mask2Former [5] outperforms state-of-the-art specialized architectures on all considered datasets for 2D image semantic, instance, and panoptic segmentation. The success", + "bbox": [ + 75, + 674, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "of transformer has come to prominence in some 3D point cloud tasks such as 3D object detection [28, 25] and 3D semantic segmentation [47]. However, applications of transformer to 3D instance segmentation tasks have yet to be exploited profoundly. DyCo3D [15] uses a transformer at the bottleneck of the feature backbone to increase the receptive field size. Mask3D [36] proposes the first transformer framework for 3D instance segmentation and achieves the state-of-the-art performance. In Mask3D, each object instance is represented as an instance query, and a vanilla transformer decoder is applied to predict instance masks. In this paper, we design a novel query initialization module to effectively initialize queries and formulate a denoising module with contrastive loss to suppress the interference of noise background queries. Eventually, QueryFormer achieves superior results with better query refinement.", + "bbox": [ + 496, + 90, + 890, + 332 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 348, + 589, + 364 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This section provides the details of our proposed method. We first illustrate the overview of the proposed method in Section 3.1, and then introduce the proposed Query Initialization Module in Section 3.2. In Section 3.3, we explain how the Affiliated Transformer Decoder works to suppress the undesirable interference of noise background queries on isntance segmentation. Finally, we elaborate the model training and inference in Section 3.4.", + "bbox": [ + 496, + 375, + 890, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 500, + 507, + 609, + 522 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The goal of 3D instance segmentation is to determine the categories and binary masks of all foreground objects in the scene. Unlike the bounding boxes of 3D object detection, 3D instance segmentation requires further accurate delineation of the mask. The architecture of our method is illustrated in Figure 3(a). Assuming that the input point cloud has $N$ points, each point contains position $x, y, z$ and color $r, g, b$ information. First, we use a 3D-UNet based on sparse convolution for multi-level feature extraction $F_{0}, F_{1}, F_{2}$ . To select the query points with high coverage rate and low repetition rate from the scene, we input the seed points $P_{seed}$ sampled by Farthest Point Sampling (FPS) into the Query Initialization Module (QIM). Through feature fusion in the aggregation module and filtering in the set grouping, we get the high quality query points $Q_{1}$ . Finally, we input the obtained query points into the proposed Affiliated Transformer Decoder (ATD) to get the final predictions.", + "bbox": [ + 496, + 532, + 890, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Query Initialization Module", + "text_level": 1, + "bbox": [ + 500, + 800, + 751, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Before we introduce the module, we give the definition of two concepts (coverage rate and repetition rate of query points). The Coverage Rate (CR) of query points indicates the number $N_{p}$ of instances contained in the query points as a percentage of the total number $N_{ins}$ of instances in the", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18518", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/bce3256db7d0977cae770f3621d375d94c84a50a98dbafa1023690200bff132b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 102, + 77, + 867, + 246 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b26932b2561adba67230598c299d333cffda62b7464c1ff920fd20fb47bb96b6.jpg", + "image_caption": [ + "Figure 3. The overview of our query refinement transformer for 3D instance segmentation. As shown in (a), we first generate seed points $P_{seed}$ by sampling from the raw point cloud. Next, we design the Query Initialization Module to improve the coverage rate and reduce the repetition rate of seed points. Afterwards, we send the generated high-quality query points $Q_{1}$ to the Affiliated Transformer Decoder to generate the final instance masks. Meanwhile, we design the Denoising Module to alleviate the interference of noise background queries on instance mask prediction. The details of each module are shown in (b), (c), (d) and (e)." + ], + "image_footnote": [], + "bbox": [ + 102, + 250, + 433, + 465 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/607a8adfddcfa60332440869ed7c5b653ab2b0d83e4d94d3ca687a0ce9ee894c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 450, + 250, + 651, + 463 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6ac5a4678fd9f9f300e298e0224e14eafd009fe50322fcfa27b998f37faaf44c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 666, + 250, + 864, + 464 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "scene, which can be formulated as:", + "bbox": [ + 76, + 550, + 308, + 564 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nC R = N _ {p} / N _ {i n s}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 214, + 575, + 468, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The Repetition Rate (RR) of query points indicates the proportion of instances covered by repetition in the query points, which can be formulated as:", + "bbox": [ + 75, + 589, + 468, + 633 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nR R = \\left(N _ {f} - N _ {p}\\right) / N _ {f}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 638, + 468, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $N_{f}$ denotes the number of foreground points in the query points. The previous methods [36] usually use FPS to select query locations. However, FPS makes it challenging to balance the coverage and repetition rates. As shown in Figure 3(b), to solve this problem, we propose the Query Initialization Module, which contains two main submodules, the aggregation module and the set grouping module.", + "bbox": [ + 75, + 659, + 468, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Aggregation Module. In feature aggregation, we design a module that allows the point features in the same instance to fuse while reducing the interference of point features in other adjacent instances. As shown in Figure 3(c), the module contains three parts, cross-attention layer, correlation-based self-attention layer and feed-forward layer. First, we use the cross-attention mechanism to update the features of the seed points $P_{\\text{seed}}$ using the features of the superpoints in the scene. Here we initialize the seed point features by", + "bbox": [ + 75, + 765, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "encoding the coordinates of the seed points. After that, the seed point features are input to the correlation-based self-attention mechanism. Unlike the previous self-attention mechanism, we use the information cues from the correlation relations in the attention map for feature fusion, and this design promotes the appropriate correlations of relevant seed-seed pairs and suppress the erroneous correlations of irrelevant seed-seed pairs. Specifically, we first calculate the similarity matrix of seed point features, as follows:", + "bbox": [ + 496, + 550, + 890, + 686 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM = \\frac {Q K ^ {T}}{\\sqrt {C}} w _ {M} + P, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 686, + 890, + 720 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $w_{M}$ is a linear projection, $P$ represents the position embeddings of seed points. We use the similarity matrix of features as the new features to calculate the similarity, with the following formula:", + "bbox": [ + 496, + 720, + 890, + 780 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM ^ {c} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathrm {Q} _ {\\mathrm {M}} \\mathrm {K} _ {\\mathrm {M}} ^ {\\mathrm {T}}}{\\sqrt {\\mathrm {C} _ {\\mathrm {M}}}}\\right) \\mathrm {M}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 776, + 890, + 810 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then we calculate the updated features $F_{\\text{seed}}^c$ for each seed point based on the similarity matrix $M^c$ . Finally, we input $F_{\\text{seed}}^c$ into the feed-forward layer and then predict the mask, category and IoU scores by different MLP heads.", + "bbox": [ + 496, + 810, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Many-to-one Matching. Different from the one-to-one matching[18] used previously, we use many-to-one match", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18519", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ing in the aggregation module. Formally, we introduce a pairwise cost matrix $CM_{k}$ to evaluate the similarity of seed point $q$ and the k-th ground-truth. $CM_{k}$ is determined by classification probability, superpoint mask cost and distance cost. We will introduce how to obtain the cost matrix in the supplementary material. With the cost matrix, we assign corresponding instance to each seed point,", + "bbox": [ + 75, + 90, + 472, + 196 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nI n s _ {q} = \\left\\{ \\begin{array}{l} \\arg \\min _ {k} C M _ {k}, i f \\min _ {k} D _ {k} < \\tau , \\\\ - 1, e l s e, \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 200, + 468, + 242 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tau$ represents a threshold, $D_{k}$ represents the distance between the coordinate of seed point $q$ and the centerpoint of the k-th ground-truth, and -1 represents that no instance matches the seed point.", + "bbox": [ + 75, + 244, + 468, + 305 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Set Grouping Module. The set grouping module aims to improve coverage rate and reduce repetition rate, which contains shift and IoU-guided NMS [29] operations. The shift operation offsets seed points to the centers of the instances to ensure a high coverage rate so that most foreground instances can have a corresponding seed point. While the IoU-guided NMS operation filters out duplicate seed points to ensure that each foreground instance retains only one high-quality seed point thus reducing the repetition rate of seed points. Specifically, we first use a MLP to predict each seed point $q$ relative to its matching instance $Ins_{q}$ coordinate offset of the center point. After obtaining this coordinate offset, add it to the original coordinate $p$ :", + "bbox": [ + 75, + 306, + 470, + 501 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np = M L P (s) + p. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 506, + 468, + 522 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this way, we can not only shift some background points to the foreground, but also close the points on the same instance, which will promote these points to learn similar features and help NMS remove redundant seed points. Then we get the corresponding instance mask $M_{ins}$ of the seed point $q$ by calculating the dot product between superpoint features and seed point features. And we obtain the final mask through sigmoid and a threshold of 0.5, as follows:", + "bbox": [ + 75, + 526, + 468, + 647 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nM _ {b} = \\phi (M _ {i n s}) > 0. 5. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 652, + 468, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we adopt the IoU-guided NMS to filter out a large number of redundant seed points. Here, the confidence of NMS is the multiplication of class score and IoU score. In order to enable the network to operate in parallel, we add extra seed points to satisfy the same number. Specifically, we do a $\\bigcup$ operation on the mask $M_{b}$ of all seed points and then operate FPS on the complement $M^{-}$ of the whole scene to sample extra seed points.", + "bbox": [ + 75, + 672, + 470, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Affiliated Transformer Decoder", + "text_level": 1, + "bbox": [ + 76, + 801, + 356, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the Query Initialization Module, we have obtained queries with high coverage rate and low repetition rate through the Aggregation Module and Set Grouping Module. In this section, we describe how the Affiliated Transformer Decoder generates the final instance segmentation", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "results with these queries. As shown in Figure 3(d), the Affiliated Transformer Decoder mainly contains the Cluster-based Layer and the Denoising Module.", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Cluster-based Layer. Existing query-based methods [36] tend to compute similarities across the entire point cloud, which introduces large computational redundancy. Therefore, we propose the Cluster-based Layer. As shown in Figure 3(e), the method is based on the idea of clustering, assigning each point in the scene to its most similar query.", + "bbox": [ + 496, + 137, + 890, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, we first calculate the similarity of the backbone features and the query features. Next, we assign each backbone feature via arg max operation as following,", + "bbox": [ + 496, + 228, + 890, + 273 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nI d x _ {k} = \\arg \\max _ {i} M _ {i, k}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 282, + 890, + 303 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $M_{i,k}$ is a dot product of query $i$ and backbone feature $k$ . Therefore, we divide all backbone features into disjoint sets by clustering. Next, we do cross-attention for queries and their corresponding sets. By this way, we only need to calculate attention map on some similar backbone features for each query. Finally we input queries into the self-attention layer and the feed-forward layer.", + "bbox": [ + 496, + 308, + 890, + 414 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "One-to-one Matching. In this section, we use one-to-one matching to replace many-to-one matching in Section 3.2. Concretely, we obtain the cost matrix $CM$ the same as Aggregation Module but replace arg min with Hungarian matching[18] to obtain the query-GT pairs.", + "bbox": [ + 496, + 416, + 890, + 491 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Denoising Module. In section 3.2, we shift the background points around the foreground points to the center of the instance to improve the coverage rate. However, during the offset, not every point is well migrated to the center due to the different scales and classes of objects [40]. This leads to some background points that may affect the information aggregation of the foreground points. Therefore, we deal with the interference caused by background point offset in this module. We take the center of the instance from ground-truth and resample it, as follows:", + "bbox": [ + 496, + 491, + 890, + 642 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nQ _ {g t} \\sim N \\left(C _ {g t}, \\sigma^ {2}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 648, + 890, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $N$ means the Gaussian distribution and $\\sigma$ represents deviation. We encode the perturbed GT centers $Q_{gt}$ together with the query points $Q_{1}$ obtained in the query initialization module and feed them into the affiliated transformer decoder. Then, we match the query outputs with the ground-truth in the dataset. The query with the minimal matching cost forms several positive pairs with the ground-truth perturbed centers. We encourage the output features of the positive queries to be consistent with the output features of the corresponding center points and drive the unmatched noise background queries away from the instance to reduce interference with the instance mask prediction. Therefore, we use the contrastive loss. Suppose the number of queries is $K$ , the number of ground-truth is $N_{gt}$ , ground-truth $j$ generates $\\beta$ perturbed GT centers, query $i$ and the perturbed", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18520", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "GT centers of ground-truth $j$ are positive pairs,", + "bbox": [ + 76, + 90, + 388, + 107 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {c o n t}} = - \\frac {1}{| \\beta N _ {g t} |} \\sum_ {j = 1} ^ {N _ {g t}} \\sum_ {m = 1} ^ {\\beta} \\log \\left(\\frac {\\exp \\left(d \\left(q _ {i} , q _ {j , m} ^ {g t}\\right) / \\varepsilon\\right)}{\\sum_ {s = 1} ^ {K} \\exp \\left(d \\left(q _ {s} , q _ {j , m} ^ {g t}\\right) / \\varepsilon\\right)}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 117, + 472, + 172 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $d(.,.)$ is a distance measurement and $\\varepsilon$ is the temperature in contrastive learning.", + "bbox": [ + 76, + 174, + 468, + 205 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. Training and Inference", + "text_level": 1, + "bbox": [ + 76, + 214, + 290, + 229 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As to query initialization module, only the aggregation modules are supervised. We assign the unmatched queries with $N_{\\text{class}} + 1$ class label and compute the cross-entropy loss $L_{\\text{cls}}$ for each query. Then we compute the superpoint mask loss which consists of binary cross-entropy loss $L_{\\text{bce}}$ and dice loss $L_{\\text{dice}}$ [27] for each query-GT pair. Meanwhile, we compute the score loss $L_{\\text{sco}}$ using binary cross-entropy loss. Suppose that the Hungarian matching assigns the k-th ground-truth to the i-th query,", + "bbox": [ + 75, + 238, + 468, + 375 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL _ {s c o, i} = B C E \\left(o _ {i}, I o U _ {i, k}\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 386, + 468, + 402 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $o_i$ represents the IoU prediction of query $i$ . In addition, we add the offset loss $L_{off}$ which uses L1loss to close the distance between the coordinates of queries and the instance center points.", + "bbox": [ + 76, + 414, + 468, + 474 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL _ {o f f, i} = \\left| p _ {i} - p _ {k} ^ {G T} \\right| \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 484, + 468, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The overall loss is defined as:", + "bbox": [ + 76, + 515, + 274, + 529 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L = \\lambda_ {1} \\cdot L _ {d i c e} + \\lambda_ {2} \\cdot L _ {b c e} + \\lambda_ {3} \\cdot L _ {c l s} \\\\ + \\lambda_ {4} \\cdot L _ {\\text {o f f}} + \\lambda_ {5} \\cdot L _ {s c o}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 539, + 401, + 575 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To Affiliated Transformer Decoder, we also add losses after each Cluster-based Layer. Compared to $L$ , we add contrastive loss which is introduced in Section 3.3.", + "bbox": [ + 76, + 585, + 468, + 631 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL ^ {*} = L + \\lambda_ {6} \\cdot L _ {\\text {c o n t}} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 643, + 468, + 659 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Following DN-DETR[22], we use the same losses as query-GT pairs to supervise the perturbed GT centers. This can ensure the perturbed GT centers would not diverge.", + "bbox": [ + 76, + 671, + 468, + 717 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During inference, it should be noted that perturbed GT centers will not be generated, that is, we only infer queries generated by Query Initialization Module.", + "bbox": [ + 76, + 717, + 468, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 776, + 207, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 801, + 266, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset and Metrics. We conduct our experiments on ScanNetV2 [8] and S3DIS [1] datasets. ScanNetV2 includes 1,613 scenes with 18 instance categories. Among them, 1,201 scenes are used for training, 312 scenes are used for validation, and 100 scenes are used for test. S3DIS", + "bbox": [ + 76, + 824, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/af889b0c52885b4e9bfda50051e38059e6a85c076db19f84e81a7db1e8124ffe.jpg", + "table_caption": [ + "Table 1. Comparison on ScanNetV2 benchmark." + ], + "table_footnote": [], + "table_body": "
MethodScanNetV2
mAPAP@50AP@25Box AP@50Box AP@25
F-PointNet [33]///10.819.8
GSPN [45]/37.853.417.730.6
3D-SIS [16]/18.735.722.540.2
VoteNet [32]///33.558.6
3D-MPA [11]35.351.972.449.264.2
DyCo3D [15]40.661.0/45.358.9
PointGroup [17]34.856.971.348.961.5
MaskGroup [49]42.063.374.0//
OccuSeg [13]44.260.7///
HAIS [4]43.564.475.653.164.3
SSTNet [23]49.464.37452.762.5
SoftGroup [39]45.867.678.959.471.6
DKNet [43]50.866.976.959.067.4
Mask3D [36]55.273.782.956.671.0
Ours56.574.283.361.773.4
", + "bbox": [ + 501, + 108, + 893, + 327 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "is a large-scale indoor dataset collected from six different areas. It contains 272 scenes with 13 instance categories. Following previous works [39], we evaluate our approach: testing on Area 5 and 6-fold cross-validation. AP@25 and AP@50 represent the average precision scores with IoU thresholds $25\\%$ and $50\\%$ , and mAP represents the average of all the APs with IoU thresholds ranging from $50\\%$ to $95\\%$ with a step size of $5\\%$ . On ScanNetV2, we report mAP, AP@50 and AP@25. Moreover, we also report the Box AP@50 and AP@25 results following SoftGroup [39] and DKNet [43]. On S3DIS, we report mAP, AP@50, mean precision (mPrec), and mean recall (mRec).", + "bbox": [ + 496, + 354, + 890, + 535 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We train our model on a single RTX3090 with a batch size of 5 for 600 epochs. We use AdamW [26] and a one-cycle learning rate schedule [37] with a maximal learning rate of $10^{-4}$ . We voxelize the point clouds with the size of $0.02\\mathrm{m}$ . For a fair comparison, the point encoder is a Minkowski Res16UNet34C [7], which is the same as Mask3D [36]. For hyperparameters, we tune $\\tau, \\sigma, \\varepsilon, \\beta$ as 0.6, 0.05, 0.5, 3 respectively. $\\lambda_1, \\lambda_2, \\lambda_3, \\lambda_4, \\lambda_5$ in Equation 13 and 14 are set as 2, 5, 2, 3, 2. $\\lambda_6$ in Equation 14 is set as 2. More implementation details are stated in the supplementary material.", + "bbox": [ + 496, + 536, + 890, + 703 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with the state-of-the-art methods.", + "text_level": 1, + "bbox": [ + 500, + 710, + 888, + 727 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ScanNetV2. As shown in Table 1, we compare our approach with existing state-of-the-art methods on the ScanNetV2 validation set. Our approach attains relative $2.4\\%$ improvements on mAP and shows relative $3.9\\%$ and $2.5\\%$ improvements on Box AP@50 and Box AP@25, respectively. On these metrics, our proposed model achieves state-of-the-art results. From Figure 4, we can see visualization of instance segmentation results. Compared to Mask3D, our approach correctly segments each instance and produces finer segmentation results.", + "bbox": [ + 496, + 734, + 890, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "S3DIS. We evaluate our method on S3DIS using Area", + "bbox": [ + 517, + 885, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18521", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2c5c22e6201a74037b2f546c35d6e54fc7086cf2e3ab5d2ca095c37994eeb43c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 109, + 75, + 295, + 176 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9fc724c60d97cc3de796866dc62ac3816ece00cd8d51dca5f67259235c228a6e.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 109, + 183, + 295, + 271 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/96ae93c271b23a085f76a6c3e0f5de70498d0186c0c0c16212759d45517e1209.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 305, + 80, + 493, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e0429cc64cdf25949d30b473c6054a2b74837d9b45007501a5e1b77f868e7e7f.jpg", + "image_caption": [ + "Mask3D" + ], + "image_footnote": [], + "bbox": [ + 305, + 183, + 491, + 271 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b06a469790cca6724bcec516f8bb6ddd403fdbb962bd16607d57bd787517ea99.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 80, + 687, + 180 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cbfba701ee351df2060545f3153cbcfe6753ae1f007e0a4c88e922ea6f524dac.jpg", + "image_caption": [ + "Ours", + "Figure 4. Visualization of instance segmentation results on the ScanNetV2 validation set. The red boxes highlight the key regions." + ], + "image_footnote": [], + "bbox": [ + 500, + 181, + 687, + 271 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a2385f571c621b6a01671ec51325683b9bdd26d7006059020101365b269c43f0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 80, + 885, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f63bd2c503fa463d32a1bc609adb368e873acbd61661faa1705782e338882b81.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 700, + 185, + 877, + 268 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a20768098dc2dd4e3af97a0ab39633cb627815666c9f7ee2807e184786dc31b7.jpg", + "table_caption": [ + "Table 2. Comparison on S3DIS benchmark." + ], + "table_footnote": [], + "table_body": "
MethodS3DIS Area 5S3DIS 6-fold CV
mAPAP@50mPrecmRecmAPAP@50mPrecmRec
SGPN [41]//36.028.7//38.231.2
ASIS [42]//55.342.4//63.647.5
3D-Bonet [44]//57.540.2//65.647.6
OccuSeg [13]//////72.860.3
3D-MPA [11]//63.158.0//66.764.1
PointGroup [17]/57.861.962.1/64.069.669.2
DyCo3D [15]//64.364.2////
MaskGroup [49]/65.062.964.7/69.966.669.6
SSTNet [23]42.759.365.564.254.167.873.573.4
SoftGroup [39]51.666.173.666.654.468.975.369.8
DKNet [43]//70.865.3//75.371.1
Mask3D [36]56.569.368.770.760.772.070.572.5
Ours57.769.970.572.262.073.372.773.4
", + "bbox": [ + 78, + 329, + 468, + 525 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a1bb289999b5b225bf998c34ba9c4c4d526a008afed24e02c1027bf8e8dc4eaf.jpg", + "table_caption": [ + "Table 3. Comparison on ScanNet200 benchmark." + ], + "table_footnote": [], + "table_body": "
MethodmAPAP@50AP@25
Mask3D [36]27.437.042.3
Ours28.137.143.4
", + "bbox": [ + 140, + 551, + 403, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5 and 6-fold cross-validation respectively. For a fair comparison, Mask3D and our method are all supervised by instance labels at the superpoint level instead of the point level. As shown in Table 2, our superior results on some important metrics validate the effects and generalization of our method.", + "bbox": [ + 75, + 623, + 468, + 712 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ScanNet200. We also compare our approach with existing state-of-the-art method on the ScanNet200 validation set, which includes a magnitude more class categories than ScanNetV2. As shown in Table 3, the results demonstrate the remarkable generalization of our model.", + "bbox": [ + 75, + 714, + 468, + 789 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Effects of DBSCAN [12].", + "text_level": 1, + "bbox": [ + 76, + 800, + 303, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "DBSCAN is a time-consuming density-based clustering algorithm that can separate multiple instances which are incorrectly predicted as a whole. Some methods with low coverage rates can easily divide multiple instances into a whole, so these methods rely heavily on DBSCAN for post-", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e0f320766b91b9ae8861892996bdaac9d48c78e977c09dffff701e4594fbe256.jpg", + "table_caption": [ + "Table 4. Effects of DBSCAN. In this experiment, the number of queries in both methods is set to 100." + ], + "table_footnote": [], + "table_body": "
MethodDBSCANScanNetV2S3DIS Area 5
mAP AP@50 AP@25mAP AP@50 AP@25
Mask3D [36]X53.773.082.553.967.073.9
✓54.774.082.956.569.375.6
Improvements+1+1+0.4+2.6+2.3+1.7
OursX56.273.883.257.169.376.6
✓56.574.283.357.769.977.1
Improvements+0.3+0.4+0.1+0.6+0.6+0.5
", + "bbox": [ + 500, + 345, + 893, + 463 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "processing. As shown in Table 4, the high performance of Mask3D must be guaranteed by DBSCAN. However, profiting from our designed query initialization module and denoising module, our method can achieve an superior performance without support from DBSCAN. In order to show the effects of DBSCAN more explicitly, as shown in Figure 5, two chairs in Mask3D are not covered by queries, so the three chairs are jointly predicted. After the post-processing of DBSCAN, this problem has been alleviated. Although DBSCAN is effective, there are two problems. The first is that multiple hyperparameters need to be readjusted for different scenarios. The other is the time-consuming problem. For example, DBSCAN takes about 1 minute to process an indoor scenario. Therefore, our method can achieve superior performance at a low time cost.", + "bbox": [ + 496, + 488, + 890, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study.", + "text_level": 1, + "bbox": [ + 500, + 724, + 655, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Components Analysis. In this section, we perform extensive ablation studies on the ScanNetV2 dataset to evaluate the effects of each design. Table 5 demonstrates the performance of the model with different designs. Concretely, the second row demonstrates that the query initialization module improves by 1.6 on mAP with a high coverage rate and low repetition rate query distribution. The cluster-based layer is designed to reduce the complexity of calculations and therefore only makes a modest contribution to accuracy. In the fifth row, the denoising module", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18522", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b0a03e81a504e2aae28076f7286042f78977bf1ce43680a92e1ca3ab64904b62.jpg", + "image_caption": [ + "Figure 5. Visualization of query distribution and instance segmentation results on the ScanNetV2 validation set. The red points represent the position of queries, and the red boxes highlight the key regions." + ], + "image_footnote": [], + "bbox": [ + 96, + 70, + 225, + 172 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/894890354256e64f6fec33280944b3e5c504935702ce94e0882fb1a048ef122f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 227, + 70, + 359, + 172 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/62da2f039516712dd7525c11df3435792a40bf0e05a4e435f660cc763f393d04.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 361, + 71, + 491, + 172 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6172d7b3a7f87c941dfbe09a5ca4566ad9062d81429a383acb9fd2da5b6b4e26.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 493, + 71, + 625, + 172 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d3c1de3da99dd0836c943e5c37d196db7fdd2b4b29bf206ba1ff880c57fbd0d2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 627, + 71, + 756, + 172 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1aaccac30322c7a9dafcdd146e497d4c698bd1247c29e7601a50efa337213b43.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 71, + 890, + 172 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/edecb8a49d39b395aa32e3d4cb50ab431777672f14d54932cbbb7c3b58a919bc.jpg", + "table_caption": [ + "Table 5. Evaluation of the model with different designs on ScanNetV2. QIM represents the Query Initialization Module, CL represents the Cluster-based Layer, DM is the Denoising Module." + ], + "table_footnote": [], + "table_body": "
QIMCLDMDBSCANScanNetV2
mAPAP@50AP@25
XXXX53.773.082.5
✓XXX55.373.583.2
X✓XX54.073.082.7
✓✓XX55.473.683.2
✓✓✓X56.273.883.2
✓✓✓✓56.574.283.3
", + "bbox": [ + 99, + 258, + 444, + 371 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d90e2804f0a4e1f40828185177fa8cc32d69a686b5fe40d905f77c240f58a786.jpg", + "table_caption": [ + "Table 6. Effects of QIM. Here, the experiment is conducted on ScanNetV2 without DBSCAN. CR means the coverage rate, while RR refers to the repetition rate. Higher CR and lower RR reflect a better result." + ], + "table_footnote": [], + "table_body": "
MethodNumScanNetV2
CR↑RR↓mAPAP@50AP@25
Mask3D [36]500.540.4847.665.575.2
Mask3D1000.740.6453.773.082.5
Mask3D1500.830.7254.373.082.8
Mask3D5000.970.9952.870.679.9
Ours500.760.4354.072.982.5
Ours1000.890.4756.273.883.2
Ours1500.920.7055.372.583.0
", + "bbox": [ + 117, + 444, + 426, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "improves the performance by 0.8 on mAP through noise background query suppression. Since the query initialization module improves the sampling quality of the query, our method does not rely on DBSCAN post-processing. Therefore, after time-consuming DBSCAN post-processing, our results are only marginally improved.", + "bbox": [ + 75, + 595, + 468, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effects of QIM. As shown in Table 6, a large number of queries can not only bring a high coverage rate but also lead to a high repetition rate. Fewer queries always bring a lower repetition rate, but a lower coverage rate of the scene may follow. Therefore, we should balance the relationship between repetition and coverage rates when selecting the number of queries. The experimental results of Table 6 on ScanNetV2 also verify that higher experimental performance can be obtained by balancing the coverage and repetition rates. Thanks to the high-quality queries obtained in QIM, our method performs best when the number of queries is 100, while Mask3d performs best when the number of queries is 150. Therefore, our method achieves better performance with less computational overhead.", + "bbox": [ + 75, + 688, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/20ffb915ec989f4c90c48c85d219cdb445ecfa6b31b83e3e019b4b1afb5bfb50.jpg", + "image_caption": [ + "Figure 6. The visualization of segmentation results related to the denoising module in the affiliated transformer decoder. The red points represent the position of queries, the green points represent the position of noise background queries, and the red boxes highlight the key regions." + ], + "image_footnote": [], + "bbox": [ + 506, + 215, + 890, + 315 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b9f3673837c98f48a562676a7013c0f4b68010bfa403b0b65221ac3425c1aefe.jpg", + "table_caption": [ + "Table 7. Efficiency comparison on a single cluster-based layer." + ], + "table_footnote": [], + "table_body": "
MethodMemory(KB)FLOPs(G)Inference Time(ms)
Mask3D [36]48.82.31.1
Ours0.491.30.72
", + "bbox": [ + 540, + 412, + 849, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effects of ATD. The affiliated transformer decoder is conceived to suppress the interference of noise background queries and thus maintain a robust and desirable instance segmentation result. In order to vividly and dually validate the importance of suppressing this interference, relevant visualization experiments are carried out in Figure 6. The denoising module in the affiliated transformer decoder pulls away the noise background points (green) for the two scenes to suppress the interference with the foreground queries (red). Furthermore, the segmentation visualization in the third and fourth columns verifies the suppression beneficial for more accurate and robust segmentation results and validates the positive effects of our designed affiliated transformer decoder.", + "bbox": [ + 496, + 474, + 890, + 685 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Efficiency comparison. As shown in Table 7, we compare the efficiency of the cluster-based layer provided by our method and the normal layer used in Mask3D. It can be seen from the results that the cluster-based layer is superior to the normal layer in terms of memory, FLOPs and inference time.", + "bbox": [ + 496, + 686, + 890, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Parameter and Runtime Analysis.", + "text_level": 1, + "bbox": [ + 500, + 786, + 795, + 803 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8 reports the model parameter and the runtime per scan of different methods on the ScanNetV2 validation set. For a fair comparison, the reported runtime is measured on the same RTX 3090 GPU. Compared with Mask3D, our method achieves noticeable performance improvement with only a 2.7M parameter increment. As to the inference", + "bbox": [ + 496, + 810, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18523", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1dd8411d6916433d1b708ed0fb0748e004a2011d106c37da4a5e1da8dfdf5261.jpg", + "table_caption": [ + "Table 8. Parameter and runtime analysis of different methods on the ScanNetV2 validation set. The runtime is measured on the same RTX 3090 GPU." + ], + "table_footnote": [], + "table_body": "
MethodParameter(M)Runtime(ms)
HAIS [4]30.9578
SoftGroup [39]30.9588
SSTNet [23]/729
Mask3D [36]39.6578
Ours42.3487
", + "bbox": [ + 153, + 135, + 390, + 223 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "speed, our model is the fastest among all methods by reducing the decoder size. Concretely, Mask3D uses 12 layers of decoder, while our model only uses 8 layers. Although we add the Query Initialization Module, we adopt the superpoint features as the keys and values of cross attention, and down-sampling is done for each layer.", + "bbox": [ + 75, + 231, + 467, + 321 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 335, + 194, + 351 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we propose the Query Refinement Transformer for 3D instance segmentation. To solve the query sampling dilemma, we design a query initialization module to guarantee a high coverage rate of object instances while maintaining a low repetition rate. Furthermore, the well-designed affiliated transformer decoder suppresses the interference of noise background queries for better instance segmentation results. Extensive experiments conducted on two widely used 3D instance segmentation benchmarks demonstrate the superior performance of QueryFormer.", + "bbox": [ + 75, + 362, + 467, + 512 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Acknowledgements", + "text_level": 1, + "bbox": [ + 76, + 527, + 264, + 544 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was partially supported by the National Nature Science Foundation of China (Grant 62022078), National Defense Basic Scientific Research Program of China (Grant JCKY2021601B013) and the National Nature Science Foundation of China (Grant 62021001).", + "bbox": [ + 75, + 551, + 467, + 621 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 76, + 650, + 171, + 666 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Iro Armeni, Ozan Sener, Amir R Zamir, Helen Jiang, Ioannis Brilakis, Martin Fischer, and Silvio Savarese. 3d semantic parsing of large-scale indoor spaces. 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IEEE, 2022. 6, 7" + ], + "bbox": [ + 78, + 90, + 468, + 555 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "18526", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Query Refinement Transformer for 3D Instance Segmentation/8435ea40-79e7-4103-b1c6-be175c97058d_model.json b/2023/Query Refinement Transformer for 3D Instance Segmentation/8435ea40-79e7-4103-b1c6-be175c97058d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..77c698c4f4cc4526b0ff69123057e450b336cf33 --- /dev/null +++ b/2023/Query Refinement Transformer for 3D Instance Segmentation/8435ea40-79e7-4103-b1c6-be175c97058d_model.json @@ -0,0 +1,2543 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.131, + 0.8, + 0.154 + ], + "angle": 0, + "content": "Query Refinement Transformer for 3D Instance Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.176, + 0.18, + 0.794, + 0.2 + ], + "angle": 0, + "content": "Jiahao Lu1, Jiacheng Deng1, Chuxin Wang1, Jianfeng He1, Tianzhu Zhang1,2,†" + }, + { + "type": "text", + "bbox": [ + 0.248, + 0.201, + 0.722, + 0.217 + ], + "angle": 0, + "content": "1University of Science and Technology of China, 2Deep Space Exploration Lab" + }, + { + "type": "text", + "bbox": [ + 0.172, + 0.22, + 0.799, + 0.234 + ], + "angle": 0, + "content": "{lujiahao, dengjc, wcx0602, hejf}@mail.ustc.edu.cn, tzzhang@ustc.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.591 + ], + "angle": 0, + "content": "3D instance segmentation aims to predict a set of object instances in a scene and represent them as binary foreground masks with corresponding semantic labels. However, object instances are diverse in shape and category, and point clouds are usually sparse, unordered, and irregular, which leads to a query sampling dilemma. Besides, noise background queries interfere with proper scene perception and accurate instance segmentation. To address the above issues, we propose the Query Refinement Transformer termed QueryFormer. The key to our approach is to exploit a query initialization module to optimize the initialization process for the query distribution with a high coverage and low repetition rate. Additionally, we design an affiliated transformer decoder that suppresses the interference of noise background queries and helps the foreground queries focus on instance discriminative parts to predict final segmentation results. Extensive experiments on ScanNetV2 and S3DIS datasets show that our QueryFormer can surpass state-of-the-art 3D instance segmentation methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.608, + 0.21, + 0.625 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.634, + 0.47, + 0.786 + ], + "angle": 0, + "content": "3D instance segmentation is a fundamental task for 3D scene understanding, which aims to predict the semantic labels and the binary foreground masks for every object in the scene simultaneously. With the popularity of AR/VR [31], 3D indoor scanning [21], and autonomous driving [46], 3D instance segmentation has become a key technology facilitating scene understanding. However, the complex layout of the scene and the variety of object categories pose severe challenges to 3D instance segmentation in segmenting similar objects and accurate point cloud masking." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.786, + 0.471, + 0.878 + ], + "angle": 0, + "content": "To overcome the above challenges, a series of 3D instance segmentation methods [11, 24, 4, 23, 39, 36] have been proposed. Generally, these methods can be divided into three categories: proposal-based [45, 11, 24], grouping-based [17, 4, 23, 39], and query-based [36]. Proposal-based methods [45, 11, 24] extract 3D bound-" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.27, + 0.891, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.324, + 0.89, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.378, + 0.889, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.447, + 0.893, + 0.531 + ], + "angle": 0, + "content": "Figure 1. The visualization of query distribution and segmentation results. A. The query initialization module samples a query on each of the two chairs to distinguish the two instances precisely. B. Repeated queries incorrectly split the complete board into two pieces. C. The denoising module removes many noise background queries and optimizes the final segmentation results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.536, + 0.895, + 0.853 + ], + "angle": 0, + "content": "ing boxes and utilize a mask learning branch to predict the object mask inside each box. Grouping-based methods [17, 4, 23, 39] rely on a bottom-up pipeline that generates predictions for each point (e.g., semantic categories and geometric offsets) and then groups the points into instances. However, proposal-based and grouping-based methods strongly rely on high-quality proposals and require manual selection of geometric properties and tuning of hyperparameters. These drawbacks and limitations prompt query-based methods to be proposed and receive extensive attention from researchers. Query-based methods are regarded as a class of transformer query-based methods [2, 5] in which each object instance is represented as an instance query. Query-based methods require a large number of queries spread throughout the scene to cover a large part of foreground objects in the scene so that there are one or even more queries on each covered object instance. Then a transformer decoder learns the instance queries by iteratively focusing on multi-level point cloud features. Eventually, the instance queries aggregate point cloud features to produce all instance masks in parallel." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Based on the discussion of the above approaches, query-based methods show great promise for 3D instance segmentation tasks by offering superior performance while not re" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.225, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18516" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.129, + 0.096, + 0.237, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.249, + 0.096, + 0.356, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.382, + 0.103, + 0.431, + 0.113 + ], + "angle": 0, + "content": "Mask3D" + }, + { + "type": "image_caption", + "bbox": [ + 0.384, + 0.117, + 0.42, + 0.127 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.231, + 0.194, + 0.317, + 0.203 + ], + "angle": 0, + "content": "Query Distribution" + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.206, + 0.249, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.167, + 0.265, + 0.25, + 0.276 + ], + "angle": 0, + "content": "Foreground Query" + }, + { + "type": "image", + "bbox": [ + 0.281, + 0.208, + 0.446, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.167, + 0.281, + 0.274, + 0.291 + ], + "angle": 0, + "content": "Noise Background Query" + }, + { + "type": "image_caption", + "bbox": [ + 0.282, + 0.265, + 0.366, + 0.275 + ], + "angle": 0, + "content": "Background Query" + }, + { + "type": "image_caption", + "bbox": [ + 0.299, + 0.281, + 0.397, + 0.291 + ], + "angle": 0, + "content": "General Background Query" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.297, + 0.47, + 0.38 + ], + "angle": 0, + "content": "Figure 2. Statistics on coverage rate&repetition rate and query distribution. For query distribution, our method has more foreground distribution and less noise background queries and FPS initialization exists many noise background queries. Besides, our method guarantees a high coverage rate of foreground object instances while maintaining a low repetition rate." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.388, + 0.471, + 0.901 + ], + "angle": 0, + "content": "quiring high-quality 3D proposals and reducing the need for extensive manual setup. By analyzing the query-based method, we summarize the following two core points of query-based 3D instance segmentation: 1) How to effectively initialize queries? For the query-based method, we conclude that coverage and repetition rates are two significant factors affecting query initialization. The coverage rate is defined as the proportion of foreground object instances with queries distributed to the total foreground object instances in the scene. As the statistical results in Figure 2, the coverage rate of FPS [35] is \\(74\\%\\) (Ours is \\(89\\%\\)), and the lower coverage rate causes some objects to be missed. For example, as shown in Figure 1(A), the two chairs are incorrectly segmented into one whole object because one chair is not covered by queries. The repetition rate is defined as the proportion of queries that have other queries coexisting in the same foreground object instance to the total number of foreground queries. The higher repetition rate (\\(64\\%\\) vs our \\(47\\%\\)) results in low query utilization and unnecessary overlapping computation. Besides, repeated queries contradict one-to-one bipartite matching mechanism and will destroy the integrity of segmentation results. As shown in Figure 1(B), multiple queries split the board into two parts. In practice, a high coverage rate often leads to a high repetition rate, and a low repetition rate is accompanied by a low coverage rate, so it is necessary to design an initialization strategy that can guarantee a high coverage rate of foreground object instances while maintaining a low repetition rate. 2) How to suppress the interference of noise background queries on accurate segmentation? Query-based methods yield outstanding performance but sample more queries than object instances in the scene. For example, sampling results by the Mask3D [36] in Figure 2 show that \\(48\\%\\) of the queries are distributed on foreground" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.273 + ], + "angle": 0, + "content": "objects, while \\(15\\%\\) of the \\(52\\%\\) of the background queries are distributed near the instances. The background queries distributed near the instances are called noise background queries because the closer the queries are to the instances, the more negatively they affect the accurate segmentation of the instances. As shown in Figure 1(C), the foreground queries(red) incorrectly segment a part of the background as a foreground instance due to the interference of the noise background queries(green). Therefore, in addition to ensuring that foreground queries accurately segment foreground instances, it is equally essential to suppress the interference of noise background queries on the segmentation task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.277, + 0.892, + 0.716 + ], + "angle": 0, + "content": "Inspired by the above discussion, we propose a Query Refinement Transformer for 3D Instance Segmentation, named QueryFormer, including a point encoder, a query initialization module, and an affiliated transformer decoder. We use a generic U-net point cloud representation network [7] as the point encoder of the method. In the query initialization module, we aggregate the superpoint features [20] and the multi-level features extracted by the point encoder to the seed points through the Aggregation Module. The Set Grouping module (SG) is designed to achieve a high coverage rate and low repetition rate distribution of seed points on instances. Specifically, the set grouping module shifts seed points to the centers of the objects to ensure a high coverage rate and filters out duplicate seed points to decrease the repetition rate and minimize the computational cost. The affiliated transformer decoder is dedicated to suppressing the impacts of noise background queries on the instance segmentation. Specifically, we generate some perturbed ground-truth centers around the instance centers during training. The perturbed centers are encoded in the same space as the query and input to the decoder for mapping to a consistent feature space. For each foreground instance, a unique query is matched by the Hungarian matching [18]. This query forms positive pairs with perturbed centers, while unmatched queries form several negative pairs with perturbed centers. We design a denoising module with contrastive loss [30] to drive the unmatched noise background queries away from the instance to reduce interference with the instance mask prediction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In summary, the main contributions of this work are as follows: (i) We design a query initialization module to optimize the initialization process for a high coverage and low repetition rate query distribution, which further helps the proposed affiliated transformer decoder to achieve more accurate results. (ii) The proposed affiliated transformer decoder suppresses the interference of noise background queries and helps the foreground queries focus on discriminative parts for more accurate instance segmentation. (iii) Extensive experimental results on two standard benchmarks, ScanNetV2 [8] and S3DIS [1], demonstrate that the proposed model performs favorably against state-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18517" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.38, + 0.106 + ], + "angle": 0, + "content": "of-the-art 3D instance segmentation methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.121, + 0.218, + 0.136 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.146, + 0.468, + 0.206 + ], + "angle": 0, + "content": "In this section, we briefly overview related works on 3D instance segmentation, including proposal-based methods, grouping-based methods, and instance segmentation with transformer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.207, + 0.468, + 0.417 + ], + "angle": 0, + "content": "Proposal-based Methods. Existing proposal-based methods are greatly influenced by the success of Mask R-CNN [14] for 2D instance segmentation. GSPN [45] takes an analysis-by-synthesis strategy to generate high-quality 3D proposals, which are refined by a region-based PointNet [34]. 3D-BoNet [44] uses PointNet++ [35] to extract features from point clouds and applies Hungarian matching [18] to generate 3D bounding boxes. GICN [24] approximates the instance center of each object as a Gaussian distribution. 3D-MPA [11] predicts centers of instances and employs a graph-based convolutional network to cluster points near the centers to refine proposal features. The proposal-based methods have high expectations for the quality of proposals." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.468, + 0.674 + ], + "angle": 0, + "content": "Grouping-based Methods. Grouping-based methods produce per-point predictions, such as semantic categories and geometric offsets, and then group points into instances. To group points, MTML [19] uses a multi-task learning strategy. PointGroup [17] segments objects on the original and offset-shifted point clouds and uses the ScoreNet to predict scores for instances. HAIS [4] extends PointGroup by absorbing surrounding fragments of instances and then refining the instances based on intra-instance prediction. SSTNet [23] constructs a tree network from precomputed superpoints and splits non-similar nodes to get object instances. SoftGroup [39] groups on soft semantic scores instead of hard semantic prediction and processes each proposal to refine positive samples and suppress negative ones. Although the grouping-based approaches require many manual settings, they have dominated the field until recently." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Instance Segmentation with Transformer. Transformer [38] introduces the self-attention mechanism to model long-range dependencies and has been widely applied in computer vision tasks such as image classification [10, 3], object detection [2, 9], and segmentation [48, 6, 5]. Recently, DETR [2] has been proposed as a new paradigm to use object queries for object detection in an image. Based on the set prediction mechanism proposed in DETR, MaskFormer [6] employs a transformer decoder to compute a set of pairs, each consisting of a class prediction and a mask embedding vector, to solve both semantic and instance segmentation tasks in a unified manner. Mask2Former [5] outperforms state-of-the-art specialized architectures on all considered datasets for 2D image semantic, instance, and panoptic segmentation. The success" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.333 + ], + "angle": 0, + "content": "of transformer has come to prominence in some 3D point cloud tasks such as 3D object detection [28, 25] and 3D semantic segmentation [47]. However, applications of transformer to 3D instance segmentation tasks have yet to be exploited profoundly. DyCo3D [15] uses a transformer at the bottleneck of the feature backbone to increase the receptive field size. Mask3D [36] proposes the first transformer framework for 3D instance segmentation and achieves the state-of-the-art performance. In Mask3D, each object instance is represented as an instance query, and a vanilla transformer decoder is applied to predict instance masks. In this paper, we design a novel query initialization module to effectively initialize queries and formulate a denoising module with contrastive loss to suppress the interference of noise background queries. Eventually, QueryFormer achieves superior results with better query refinement." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.349, + 0.59, + 0.365 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.376, + 0.892, + 0.496 + ], + "angle": 0, + "content": "This section provides the details of our proposed method. We first illustrate the overview of the proposed method in Section 3.1, and then introduce the proposed Query Initialization Module in Section 3.2. In Section 3.3, we explain how the Affiliated Transformer Decoder works to suppress the undesirable interference of noise background queries on isntance segmentation. Finally, we elaborate the model training and inference in Section 3.4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.508, + 0.61, + 0.523 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.533, + 0.892, + 0.789 + ], + "angle": 0, + "content": "The goal of 3D instance segmentation is to determine the categories and binary masks of all foreground objects in the scene. Unlike the bounding boxes of 3D object detection, 3D instance segmentation requires further accurate delineation of the mask. The architecture of our method is illustrated in Figure 3(a). Assuming that the input point cloud has \\( N \\) points, each point contains position \\( x, y, z \\) and color \\( r, g, b \\) information. First, we use a 3D-UNet based on sparse convolution for multi-level feature extraction \\( F_{0}, F_{1}, F_{2} \\). To select the query points with high coverage rate and low repetition rate from the scene, we input the seed points \\( P_{seed} \\) sampled by Farthest Point Sampling (FPS) into the Query Initialization Module (QIM). Through feature fusion in the aggregation module and filtering in the set grouping, we get the high quality query points \\( Q_{1} \\). Finally, we input the obtained query points into the proposed Affiliated Transformer Decoder (ATD) to get the final predictions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.801, + 0.753, + 0.817 + ], + "angle": 0, + "content": "3.2. Query Initialization Module" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Before we introduce the module, we give the definition of two concepts (coverage rate and repetition rate of query points). The Coverage Rate (CR) of query points indicates the number \\( N_{p} \\) of instances contained in the query points as a percentage of the total number \\( N_{ins} \\) of instances in the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18518" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.078, + 0.868, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.25, + 0.434, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.451, + 0.25, + 0.653, + 0.464 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.668, + 0.251, + 0.865, + 0.465 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.469, + 0.892, + 0.539 + ], + "angle": 0, + "content": "Figure 3. The overview of our query refinement transformer for 3D instance segmentation. As shown in (a), we first generate seed points \\( P_{seed} \\) by sampling from the raw point cloud. Next, we design the Query Initialization Module to improve the coverage rate and reduce the repetition rate of seed points. Afterwards, we send the generated high-quality query points \\( Q_{1} \\) to the Affiliated Transformer Decoder to generate the final instance masks. Meanwhile, we design the Denoising Module to alleviate the interference of noise background queries on instance mask prediction. The details of each module are shown in (b), (c), (d) and (e)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.551, + 0.31, + 0.565 + ], + "angle": 0, + "content": "scene, which can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.215, + 0.577, + 0.469, + 0.592 + ], + "angle": 0, + "content": "\\[\nC R = N _ {p} / N _ {i n s}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.59, + 0.469, + 0.635 + ], + "angle": 0, + "content": "The Repetition Rate (RR) of query points indicates the proportion of instances covered by repetition in the query points, which can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.64, + 0.469, + 0.657 + ], + "angle": 0, + "content": "\\[\nR R = \\left(N _ {f} - N _ {p}\\right) / N _ {f}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.469, + 0.765 + ], + "angle": 0, + "content": "where \\( N_{f} \\) denotes the number of foreground points in the query points. The previous methods [36] usually use FPS to select query locations. However, FPS makes it challenging to balance the coverage and repetition rates. As shown in Figure 3(b), to solve this problem, we propose the Query Initialization Module, which contains two main submodules, the aggregation module and the set grouping module." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.766, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Aggregation Module. In feature aggregation, we design a module that allows the point features in the same instance to fuse while reducing the interference of point features in other adjacent instances. As shown in Figure 3(c), the module contains three parts, cross-attention layer, correlation-based self-attention layer and feed-forward layer. First, we use the cross-attention mechanism to update the features of the seed points \\( P_{\\text{seed}} \\) using the features of the superpoints in the scene. Here we initialize the seed point features by" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.551, + 0.892, + 0.687 + ], + "angle": 0, + "content": "encoding the coordinates of the seed points. After that, the seed point features are input to the correlation-based self-attention mechanism. Unlike the previous self-attention mechanism, we use the information cues from the correlation relations in the attention map for feature fusion, and this design promotes the appropriate correlations of relevant seed-seed pairs and suppress the erroneous correlations of irrelevant seed-seed pairs. Specifically, we first calculate the similarity matrix of seed point features, as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.621, + 0.688, + 0.892, + 0.722 + ], + "angle": 0, + "content": "\\[\nM = \\frac {Q K ^ {T}}{\\sqrt {C}} w _ {M} + P, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.722, + 0.892, + 0.781 + ], + "angle": 0, + "content": "where \\(w_{M}\\) is a linear projection, \\(P\\) represents the position embeddings of seed points. We use the similarity matrix of features as the new features to calculate the similarity, with the following formula:" + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.777, + 0.891, + 0.811 + ], + "angle": 0, + "content": "\\[\nM ^ {c} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathrm {Q} _ {\\mathrm {M}} \\mathrm {K} _ {\\mathrm {M}} ^ {\\mathrm {T}}}{\\sqrt {\\mathrm {C} _ {\\mathrm {M}}}}\\right) \\mathrm {M}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Then we calculate the updated features \\( F_{\\text{seed}}^c \\) for each seed point based on the similarity matrix \\( M^c \\). Finally, we input \\( F_{\\text{seed}}^c \\) into the feed-forward layer and then predict the mask, category and IoU scores by different MLP heads." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Many-to-one Matching. Different from the one-to-one matching[18] used previously, we use many-to-one match" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18519" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.198 + ], + "angle": 0, + "content": "ing in the aggregation module. Formally, we introduce a pairwise cost matrix \\( CM_{k} \\) to evaluate the similarity of seed point \\( q \\) and the k-th ground-truth. \\( CM_{k} \\) is determined by classification probability, superpoint mask cost and distance cost. We will introduce how to obtain the cost matrix in the supplementary material. With the cost matrix, we assign corresponding instance to each seed point," + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.201, + 0.47, + 0.243 + ], + "angle": 0, + "content": "\\[\nI n s _ {q} = \\left\\{ \\begin{array}{l} \\arg \\min _ {k} C M _ {k}, i f \\min _ {k} D _ {k} < \\tau , \\\\ - 1, e l s e, \\end{array} \\right. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.246, + 0.47, + 0.306 + ], + "angle": 0, + "content": "where \\(\\tau\\) represents a threshold, \\(D_{k}\\) represents the distance between the coordinate of seed point \\(q\\) and the centerpoint of the k-th ground-truth, and -1 represents that no instance matches the seed point." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.307, + 0.471, + 0.502 + ], + "angle": 0, + "content": "Set Grouping Module. The set grouping module aims to improve coverage rate and reduce repetition rate, which contains shift and IoU-guided NMS [29] operations. The shift operation offsets seed points to the centers of the instances to ensure a high coverage rate so that most foreground instances can have a corresponding seed point. While the IoU-guided NMS operation filters out duplicate seed points to ensure that each foreground instance retains only one high-quality seed point thus reducing the repetition rate of seed points. Specifically, we first use a MLP to predict each seed point \\( q \\) relative to its matching instance \\( Ins_{q} \\) coordinate offset of the center point. After obtaining this coordinate offset, add it to the original coordinate \\( p \\):" + }, + { + "type": "equation", + "bbox": [ + 0.207, + 0.507, + 0.469, + 0.523 + ], + "angle": 0, + "content": "\\[\np = M L P (s) + p. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.527, + 0.47, + 0.648 + ], + "angle": 0, + "content": "In this way, we can not only shift some background points to the foreground, but also close the points on the same instance, which will promote these points to learn similar features and help NMS remove redundant seed points. Then we get the corresponding instance mask \\( M_{ins} \\) of the seed point \\( q \\) by calculating the dot product between superpoint features and seed point features. And we obtain the final mask through sigmoid and a threshold of 0.5, as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.653, + 0.469, + 0.668 + ], + "angle": 0, + "content": "\\[\nM _ {b} = \\phi (M _ {i n s}) > 0. 5. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.471, + 0.794 + ], + "angle": 0, + "content": "Finally, we adopt the IoU-guided NMS to filter out a large number of redundant seed points. Here, the confidence of NMS is the multiplication of class score and IoU score. In order to enable the network to operate in parallel, we add extra seed points to satisfy the same number. Specifically, we do a \\(\\bigcup\\) operation on the mask \\(M_{b}\\) of all seed points and then operate FPS on the complement \\(M^{-}\\) of the whole scene to sample extra seed points." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.357, + 0.817 + ], + "angle": 0, + "content": "3.3. Affiliated Transformer Decoder" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In the Query Initialization Module, we have obtained queries with high coverage rate and low repetition rate through the Aggregation Module and Set Grouping Module. In this section, we describe how the Affiliated Transformer Decoder generates the final instance segmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "results with these queries. As shown in Figure 3(d), the Affiliated Transformer Decoder mainly contains the Cluster-based Layer and the Denoising Module." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.138, + 0.892, + 0.228 + ], + "angle": 0, + "content": "Cluster-based Layer. Existing query-based methods [36] tend to compute similarities across the entire point cloud, which introduces large computational redundancy. Therefore, we propose the Cluster-based Layer. As shown in Figure 3(e), the method is based on the idea of clustering, assigning each point in the scene to its most similar query." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.229, + 0.892, + 0.275 + ], + "angle": 0, + "content": "Specifically, we first calculate the similarity of the backbone features and the query features. Next, we assign each backbone feature via arg max operation as following," + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.283, + 0.892, + 0.304 + ], + "angle": 0, + "content": "\\[\nI d x _ {k} = \\arg \\max _ {i} M _ {i, k}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.309, + 0.892, + 0.415 + ], + "angle": 0, + "content": "where \\( M_{i,k} \\) is a dot product of query \\( i \\) and backbone feature \\( k \\). Therefore, we divide all backbone features into disjoint sets by clustering. Next, we do cross-attention for queries and their corresponding sets. By this way, we only need to calculate attention map on some similar backbone features for each query. Finally we input queries into the self-attention layer and the feed-forward layer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.417, + 0.892, + 0.492 + ], + "angle": 0, + "content": "One-to-one Matching. In this section, we use one-to-one matching to replace many-to-one matching in Section 3.2. Concretely, we obtain the cost matrix \\( CM \\) the same as Aggregation Module but replace arg min with Hungarian matching[18] to obtain the query-GT pairs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.892, + 0.643 + ], + "angle": 0, + "content": "Denoising Module. In section 3.2, we shift the background points around the foreground points to the center of the instance to improve the coverage rate. However, during the offset, not every point is well migrated to the center due to the different scales and classes of objects [40]. This leads to some background points that may affect the information aggregation of the foreground points. Therefore, we deal with the interference caused by background point offset in this module. We take the center of the instance from ground-truth and resample it, as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.629, + 0.65, + 0.892, + 0.668 + ], + "angle": 0, + "content": "\\[\nQ _ {g t} \\sim N \\left(C _ {g t}, \\sigma^ {2}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(N\\) means the Gaussian distribution and \\(\\sigma\\) represents deviation. We encode the perturbed GT centers \\(Q_{gt}\\) together with the query points \\(Q_{1}\\) obtained in the query initialization module and feed them into the affiliated transformer decoder. Then, we match the query outputs with the ground-truth in the dataset. The query with the minimal matching cost forms several positive pairs with the ground-truth perturbed centers. We encourage the output features of the positive queries to be consistent with the output features of the corresponding center points and drive the unmatched noise background queries away from the instance to reduce interference with the instance mask prediction. Therefore, we use the contrastive loss. Suppose the number of queries is \\(K\\), the number of ground-truth is \\(N_{gt}\\), ground-truth \\(j\\) generates \\(\\beta\\) perturbed GT centers, query \\(i\\) and the perturbed" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18520" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.39, + 0.108 + ], + "angle": 0, + "content": "GT centers of ground-truth \\(j\\) are positive pairs," + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.118, + 0.473, + 0.174 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {c o n t}} = - \\frac {1}{| \\beta N _ {g t} |} \\sum_ {j = 1} ^ {N _ {g t}} \\sum_ {m = 1} ^ {\\beta} \\log \\left(\\frac {\\exp \\left(d \\left(q _ {i} , q _ {j , m} ^ {g t}\\right) / \\varepsilon\\right)}{\\sum_ {s = 1} ^ {K} \\exp \\left(d \\left(q _ {s} , q _ {j , m} ^ {g t}\\right) / \\varepsilon\\right)}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.175, + 0.469, + 0.207 + ], + "angle": 0, + "content": "where \\( d(.,.) \\) is a distance measurement and \\( \\varepsilon \\) is the temperature in contrastive learning." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.215, + 0.292, + 0.231 + ], + "angle": 0, + "content": "3.4. Training and Inference" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.239, + 0.47, + 0.375 + ], + "angle": 0, + "content": "As to query initialization module, only the aggregation modules are supervised. We assign the unmatched queries with \\( N_{\\text{class}} + 1 \\) class label and compute the cross-entropy loss \\( L_{\\text{cls}} \\) for each query. Then we compute the superpoint mask loss which consists of binary cross-entropy loss \\( L_{\\text{bce}} \\) and dice loss \\( L_{\\text{dice}} \\) [27] for each query-GT pair. Meanwhile, we compute the score loss \\( L_{\\text{sco}} \\) using binary cross-entropy loss. Suppose that the Hungarian matching assigns the k-th ground-truth to the i-th query," + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.387, + 0.469, + 0.404 + ], + "angle": 0, + "content": "\\[\nL _ {s c o, i} = B C E \\left(o _ {i}, I o U _ {i, k}\\right), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.415, + 0.469, + 0.476 + ], + "angle": 0, + "content": "where \\(o_i\\) represents the IoU prediction of query \\(i\\). In addition, we add the offset loss \\(L_{off}\\) which uses L1loss to close the distance between the coordinates of queries and the instance center points." + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.486, + 0.469, + 0.505 + ], + "angle": 0, + "content": "\\[\nL _ {o f f, i} = \\left| p _ {i} - p _ {k} ^ {G T} \\right| \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.516, + 0.275, + 0.53 + ], + "angle": 0, + "content": "The overall loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.54, + 0.402, + 0.576 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L = \\lambda_ {1} \\cdot L _ {d i c e} + \\lambda_ {2} \\cdot L _ {b c e} + \\lambda_ {3} \\cdot L _ {c l s} \\\\ + \\lambda_ {4} \\cdot L _ {\\text {o f f}} + \\lambda_ {5} \\cdot L _ {s c o}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.587, + 0.469, + 0.632 + ], + "angle": 0, + "content": "To Affiliated Transformer Decoder, we also add losses after each Cluster-based Layer. Compared to \\( L \\), we add contrastive loss which is introduced in Section 3.3." + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.645, + 0.469, + 0.66 + ], + "angle": 0, + "content": "\\[\nL ^ {*} = L + \\lambda_ {6} \\cdot L _ {\\text {c o n t}} \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.672, + 0.469, + 0.718 + ], + "angle": 0, + "content": "Following DN-DETR[22], we use the same losses as query-GT pairs to supervise the perturbed GT centers. This can ensure the perturbed GT centers would not diverge." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.718, + 0.469, + 0.763 + ], + "angle": 0, + "content": "During inference, it should be noted that perturbed GT centers will not be generated, that is, we only infer queries generated by Query Initialization Module." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.777, + 0.209, + 0.794 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.802, + 0.267, + 0.818 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Dataset and Metrics. We conduct our experiments on ScanNetV2 [8] and S3DIS [1] datasets. ScanNetV2 includes 1,613 scenes with 18 instance categories. Among them, 1,201 scenes are used for training, 312 scenes are used for validation, and 100 scenes are used for test. S3DIS" + }, + { + "type": "table_caption", + "bbox": [ + 0.544, + 0.088, + 0.848, + 0.102 + ], + "angle": 0, + "content": "Table 1. Comparison on ScanNetV2 benchmark." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.109, + 0.895, + 0.328 + ], + "angle": 0, + "content": "
MethodScanNetV2
mAPAP@50AP@25Box AP@50Box AP@25
F-PointNet [33]///10.819.8
GSPN [45]/37.853.417.730.6
3D-SIS [16]/18.735.722.540.2
VoteNet [32]///33.558.6
3D-MPA [11]35.351.972.449.264.2
DyCo3D [15]40.661.0/45.358.9
PointGroup [17]34.856.971.348.961.5
MaskGroup [49]42.063.374.0//
OccuSeg [13]44.260.7///
HAIS [4]43.564.475.653.164.3
SSTNet [23]49.464.37452.762.5
SoftGroup [39]45.867.678.959.471.6
DKNet [43]50.866.976.959.067.4
Mask3D [36]55.273.782.956.671.0
Ours56.574.283.361.773.4
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.355, + 0.892, + 0.536 + ], + "angle": 0, + "content": "is a large-scale indoor dataset collected from six different areas. It contains 272 scenes with 13 instance categories. Following previous works [39], we evaluate our approach: testing on Area 5 and 6-fold cross-validation. AP@25 and AP@50 represent the average precision scores with IoU thresholds \\(25\\%\\) and \\(50\\%\\), and mAP represents the average of all the APs with IoU thresholds ranging from \\(50\\%\\) to \\(95\\%\\) with a step size of \\(5\\%\\). On ScanNetV2, we report mAP, AP@50 and AP@25. Moreover, we also report the Box AP@50 and AP@25 results following SoftGroup [39] and DKNet [43]. On S3DIS, we report mAP, AP@50, mean precision (mPrec), and mean recall (mRec)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.892, + 0.704 + ], + "angle": 0, + "content": "Implementation Details. We train our model on a single RTX3090 with a batch size of 5 for 600 epochs. We use AdamW [26] and a one-cycle learning rate schedule [37] with a maximal learning rate of \\(10^{-4}\\). We voxelize the point clouds with the size of \\(0.02\\mathrm{m}\\). For a fair comparison, the point encoder is a Minkowski Res16UNet34C [7], which is the same as Mask3D [36]. For hyperparameters, we tune \\(\\tau, \\sigma, \\varepsilon, \\beta\\) as 0.6, 0.05, 0.5, 3 respectively. \\(\\lambda_1, \\lambda_2, \\lambda_3, \\lambda_4, \\lambda_5\\) in Equation 13 and 14 are set as 2, 5, 2, 3, 2. \\(\\lambda_6\\) in Equation 14 is set as 2. More implementation details are stated in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.712, + 0.89, + 0.728 + ], + "angle": 0, + "content": "4.2. Comparison with the state-of-the-art methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.884 + ], + "angle": 0, + "content": "ScanNetV2. As shown in Table 1, we compare our approach with existing state-of-the-art methods on the ScanNetV2 validation set. Our approach attains relative \\(2.4\\%\\) improvements on mAP and shows relative \\(3.9\\%\\) and \\(2.5\\%\\) improvements on Box AP@50 and Box AP@25, respectively. On these metrics, our proposed model achieves state-of-the-art results. From Figure 4, we can see visualization of instance segmentation results. Compared to Mask3D, our approach correctly segments each instance and produces finer segmentation results." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "S3DIS. We evaluate our method on S3DIS using Area" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18521" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.111, + 0.077, + 0.296, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.111, + 0.184, + 0.296, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.184, + 0.273, + 0.221, + 0.285 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.306, + 0.081, + 0.495, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.306, + 0.184, + 0.493, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.383, + 0.273, + 0.437, + 0.284 + ], + "angle": 0, + "content": "Mask3D" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.082, + 0.688, + 0.181 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.182, + 0.689, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.593, + 0.273, + 0.626, + 0.284 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.082, + 0.886, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.186, + 0.879, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.788, + 0.273, + 0.807, + 0.283 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.287, + 0.868, + 0.302 + ], + "angle": 0, + "content": "Figure 4. Visualization of instance segmentation results on the ScanNetV2 validation set. The red boxes highlight the key regions." + }, + { + "type": "table_caption", + "bbox": [ + 0.136, + 0.309, + 0.411, + 0.324 + ], + "angle": 0, + "content": "Table 2. Comparison on S3DIS benchmark." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.33, + 0.47, + 0.526 + ], + "angle": 0, + "content": "
MethodS3DIS Area 5S3DIS 6-fold CV
mAPAP@50mPrecmRecmAPAP@50mPrecmRec
SGPN [41]//36.028.7//38.231.2
ASIS [42]//55.342.4//63.647.5
3D-Bonet [44]//57.540.2//65.647.6
OccuSeg [13]//////72.860.3
3D-MPA [11]//63.158.0//66.764.1
PointGroup [17]/57.861.962.1/64.069.669.2
DyCo3D [15]//64.364.2////
MaskGroup [49]/65.062.964.7/69.966.669.6
SSTNet [23]42.759.365.564.254.167.873.573.4
SoftGroup [39]51.666.173.666.654.468.975.369.8
DKNet [43]//70.865.3//75.371.1
Mask3D [36]56.569.368.770.760.772.070.572.5
Ours57.769.970.572.262.073.372.773.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.119, + 0.533, + 0.427, + 0.546 + ], + "angle": 0, + "content": "Table 3. Comparison on ScanNet200 benchmark." + }, + { + "type": "table", + "bbox": [ + 0.141, + 0.553, + 0.404, + 0.606 + ], + "angle": 0, + "content": "
MethodmAPAP@50AP@25
Mask3D [36]27.437.042.3
Ours28.137.143.4
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.47, + 0.713 + ], + "angle": 0, + "content": "5 and 6-fold cross-validation respectively. For a fair comparison, Mask3D and our method are all supervised by instance labels at the superpoint level instead of the point level. As shown in Table 2, our superior results on some important metrics validate the effects and generalization of our method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.715, + 0.469, + 0.79 + ], + "angle": 0, + "content": "ScanNet200. We also compare our approach with existing state-of-the-art method on the ScanNet200 validation set, which includes a magnitude more class categories than ScanNetV2. As shown in Table 3, the results demonstrate the remarkable generalization of our model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.801, + 0.304, + 0.817 + ], + "angle": 0, + "content": "4.3. Effects of DBSCAN [12]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.901 + ], + "angle": 0, + "content": "DBSCAN is a time-consuming density-based clustering algorithm that can separate multiple instances which are incorrectly predicted as a whole. Some methods with low coverage rates can easily divide multiple instances into a whole, so these methods rely heavily on DBSCAN for post-" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.309, + 0.894, + 0.337 + ], + "angle": 0, + "content": "Table 4. Effects of DBSCAN. In this experiment, the number of queries in both methods is set to 100." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.346, + 0.895, + 0.464 + ], + "angle": 0, + "content": "
MethodDBSCANScanNetV2S3DIS Area 5
mAP AP@50 AP@25mAP AP@50 AP@25
Mask3D [36]X53.773.082.553.967.073.9
✓54.774.082.956.569.375.6
Improvements+1+1+0.4+2.6+2.3+1.7
OursX56.273.883.257.169.376.6
✓56.574.283.357.769.977.1
Improvements+0.3+0.4+0.1+0.6+0.6+0.5
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.489, + 0.892, + 0.716 + ], + "angle": 0, + "content": "processing. As shown in Table 4, the high performance of Mask3D must be guaranteed by DBSCAN. However, profiting from our designed query initialization module and denoising module, our method can achieve an superior performance without support from DBSCAN. In order to show the effects of DBSCAN more explicitly, as shown in Figure 5, two chairs in Mask3D are not covered by queries, so the three chairs are jointly predicted. After the post-processing of DBSCAN, this problem has been alleviated. Although DBSCAN is effective, there are two problems. The first is that multiple hyperparameters need to be readjusted for different scenarios. The other is the time-consuming problem. For example, DBSCAN takes about 1 minute to process an indoor scenario. Therefore, our method can achieve superior performance at a low time cost." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.726, + 0.656, + 0.743 + ], + "angle": 0, + "content": "4.4. Ablation Study." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Components Analysis. In this section, we perform extensive ablation studies on the ScanNetV2 dataset to evaluate the effects of each design. Table 5 demonstrates the performance of the model with different designs. Concretely, the second row demonstrates that the query initialization module improves by 1.6 on mAP with a high coverage rate and low repetition rate query distribution. The cluster-based layer is designed to reduce the complexity of calculations and therefore only makes a modest contribution to accuracy. In the fifth row, the denoising module" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18522" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.071, + 0.227, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.228, + 0.071, + 0.36, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.362, + 0.072, + 0.493, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.072, + 0.627, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.629, + 0.072, + 0.758, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.072, + 0.892, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.177, + 0.894, + 0.207 + ], + "angle": 0, + "content": "Figure 5. Visualization of query distribution and instance segmentation results on the ScanNetV2 validation set. The red points represent the position of queries, and the red boxes highlight the key regions." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.214, + 0.47, + 0.256 + ], + "angle": 0, + "content": "Table 5. Evaluation of the model with different designs on ScanNetV2. QIM represents the Query Initialization Module, CL represents the Cluster-based Layer, DM is the Denoising Module." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.26, + 0.446, + 0.372 + ], + "angle": 0, + "content": "
QIMCLDMDBSCANScanNetV2
mAPAP@50AP@25
XXXX53.773.082.5
✓XXX55.373.583.2
X✓XX54.073.082.7
✓✓XX55.473.683.2
✓✓✓X56.273.883.2
✓✓✓✓56.574.283.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.383, + 0.471, + 0.438 + ], + "angle": 0, + "content": "Table 6. Effects of QIM. Here, the experiment is conducted on ScanNetV2 without DBSCAN. CR means the coverage rate, while RR refers to the repetition rate. Higher CR and lower RR reflect a better result." + }, + { + "type": "table", + "bbox": [ + 0.119, + 0.445, + 0.428, + 0.576 + ], + "angle": 0, + "content": "
MethodNumScanNetV2
CR↑RR↓mAPAP@50AP@25
Mask3D [36]500.540.4847.665.575.2
Mask3D1000.740.6453.773.082.5
Mask3D1500.830.7254.373.082.8
Mask3D5000.970.9952.870.679.9
Ours500.760.4354.072.982.5
Ours1000.890.4756.273.883.2
Ours1500.920.7055.372.583.0
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.47, + 0.688 + ], + "angle": 0, + "content": "improves the performance by 0.8 on mAP through noise background query suppression. Since the query initialization module improves the sampling quality of the query, our method does not rely on DBSCAN post-processing. Therefore, after time-consuming DBSCAN post-processing, our results are only marginally improved." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Effects of QIM. As shown in Table 6, a large number of queries can not only bring a high coverage rate but also lead to a high repetition rate. Fewer queries always bring a lower repetition rate, but a lower coverage rate of the scene may follow. Therefore, we should balance the relationship between repetition and coverage rates when selecting the number of queries. The experimental results of Table 6 on ScanNetV2 also verify that higher experimental performance can be obtained by balancing the coverage and repetition rates. Thanks to the high-quality queries obtained in QIM, our method performs best when the number of queries is 100, while Mask3d performs best when the number of queries is 150. Therefore, our method achieves better performance with less computational overhead." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.216, + 0.892, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.32, + 0.894, + 0.39 + ], + "angle": 0, + "content": "Figure 6. The visualization of segmentation results related to the denoising module in the affiliated transformer decoder. The red points represent the position of queries, the green points represent the position of noise background queries, and the red boxes highlight the key regions." + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.395, + 0.889, + 0.41 + ], + "angle": 0, + "content": "Table 7. Efficiency comparison on a single cluster-based layer." + }, + { + "type": "table", + "bbox": [ + 0.541, + 0.414, + 0.85, + 0.457 + ], + "angle": 0, + "content": "
MethodMemory(KB)FLOPs(G)Inference Time(ms)
Mask3D [36]48.82.31.1
Ours0.491.30.72
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.892, + 0.686 + ], + "angle": 0, + "content": "Effects of ATD. The affiliated transformer decoder is conceived to suppress the interference of noise background queries and thus maintain a robust and desirable instance segmentation result. In order to vividly and dually validate the importance of suppressing this interference, relevant visualization experiments are carried out in Figure 6. The denoising module in the affiliated transformer decoder pulls away the noise background points (green) for the two scenes to suppress the interference with the foreground queries (red). Furthermore, the segmentation visualization in the third and fourth columns verifies the suppression beneficial for more accurate and robust segmentation results and validates the positive effects of our designed affiliated transformer decoder." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.779 + ], + "angle": 0, + "content": "Efficiency comparison. As shown in Table 7, we compare the efficiency of the cluster-based layer provided by our method and the normal layer used in Mask3D. It can be seen from the results that the cluster-based layer is superior to the normal layer in terms of memory, FLOPs and inference time." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.797, + 0.804 + ], + "angle": 0, + "content": "4.5. Parameter and Runtime Analysis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Table 8 reports the model parameter and the runtime per scan of different methods on the ScanNetV2 validation set. For a fair comparison, the reported runtime is measured on the same RTX 3090 GPU. Compared with Mask3D, our method achieves noticeable performance improvement with only a 2.7M parameter increment. As to the inference" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18523" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.47, + 0.128 + ], + "angle": 0, + "content": "Table 8. Parameter and runtime analysis of different methods on the ScanNetV2 validation set. The runtime is measured on the same RTX 3090 GPU." + }, + { + "type": "table", + "bbox": [ + 0.155, + 0.136, + 0.391, + 0.224 + ], + "angle": 0, + "content": "
MethodParameter(M)Runtime(ms)
HAIS [4]30.9578
SoftGroup [39]30.9588
SSTNet [23]/729
Mask3D [36]39.6578
Ours42.3487
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.232, + 0.468, + 0.323 + ], + "angle": 0, + "content": "speed, our model is the fastest among all methods by reducing the decoder size. Concretely, Mask3D uses 12 layers of decoder, while our model only uses 8 layers. Although we add the Query Initialization Module, we adopt the superpoint features as the keys and values of cross attention, and down-sampling is done for each layer." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.337, + 0.196, + 0.352 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.363, + 0.468, + 0.513 + ], + "angle": 0, + "content": "In this paper, we propose the Query Refinement Transformer for 3D instance segmentation. To solve the query sampling dilemma, we design a query initialization module to guarantee a high coverage rate of object instances while maintaining a low repetition rate. Furthermore, the well-designed affiliated transformer decoder suppresses the interference of noise background queries for better instance segmentation results. Extensive experiments conducted on two widely used 3D instance segmentation benchmarks demonstrate the superior performance of QueryFormer." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.528, + 0.265, + 0.545 + ], + "angle": 0, + "content": "6. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.552, + 0.468, + 0.622 + ], + "angle": 0, + "content": "This work was partially supported by the National Nature Science Foundation of China (Grant 62022078), National Defense Basic Scientific Research Program of China (Grant JCKY2021601B013) and the National Nature Science Foundation of China (Grant 62021001)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.651, + 0.173, + 0.667 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.085, + 0.677, + 0.47, + 0.745 + ], + "angle": 0, + "content": "[1] Iro Armeni, Ozan Sener, Amir R Zamir, Helen Jiang, Ioannis Brilakis, Martin Fischer, and Silvio Savarese. 3d semantic parsing of large-scale indoor spaces. 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IEEE, 2022. 6, 7" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.469, + 0.556 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18526" + } + ] +] \ No newline at end of file diff --git a/2023/Query Refinement Transformer for 3D Instance Segmentation/8435ea40-79e7-4103-b1c6-be175c97058d_origin.pdf b/2023/Query Refinement Transformer for 3D Instance Segmentation/8435ea40-79e7-4103-b1c6-be175c97058d_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..413595c58b915a1f29b177dc0ea3bee4845111cf --- /dev/null +++ b/2023/Query Refinement Transformer for 3D Instance Segmentation/8435ea40-79e7-4103-b1c6-be175c97058d_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f73e75de7542d5e6277670b0565faaa3a65cfc4879c7b3899ebb46fac1699f06 +size 3493342 diff --git a/2023/Query Refinement Transformer for 3D Instance Segmentation/full.md b/2023/Query Refinement Transformer for 3D Instance Segmentation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..638405b5513fdb02d9d64cbd9b333fd8a16a7e56 --- /dev/null +++ b/2023/Query Refinement Transformer for 3D Instance Segmentation/full.md @@ -0,0 +1,384 @@ +# Query Refinement Transformer for 3D Instance Segmentation + +Jiahao Lu1, Jiacheng Deng1, Chuxin Wang1, Jianfeng He1, Tianzhu Zhang1,2,† + +1University of Science and Technology of China, 2Deep Space Exploration Lab + +{lujiahao, dengjc, wcx0602, hejf}@mail.ustc.edu.cn, tzzhang@ustc.edu.cn + +# Abstract + +3D instance segmentation aims to predict a set of object instances in a scene and represent them as binary foreground masks with corresponding semantic labels. However, object instances are diverse in shape and category, and point clouds are usually sparse, unordered, and irregular, which leads to a query sampling dilemma. Besides, noise background queries interfere with proper scene perception and accurate instance segmentation. To address the above issues, we propose the Query Refinement Transformer termed QueryFormer. The key to our approach is to exploit a query initialization module to optimize the initialization process for the query distribution with a high coverage and low repetition rate. Additionally, we design an affiliated transformer decoder that suppresses the interference of noise background queries and helps the foreground queries focus on instance discriminative parts to predict final segmentation results. Extensive experiments on ScanNetV2 and S3DIS datasets show that our QueryFormer can surpass state-of-the-art 3D instance segmentation methods. + +# 1. Introduction + +3D instance segmentation is a fundamental task for 3D scene understanding, which aims to predict the semantic labels and the binary foreground masks for every object in the scene simultaneously. With the popularity of AR/VR [31], 3D indoor scanning [21], and autonomous driving [46], 3D instance segmentation has become a key technology facilitating scene understanding. However, the complex layout of the scene and the variety of object categories pose severe challenges to 3D instance segmentation in segmenting similar objects and accurate point cloud masking. + +To overcome the above challenges, a series of 3D instance segmentation methods [11, 24, 4, 23, 39, 36] have been proposed. Generally, these methods can be divided into three categories: proposal-based [45, 11, 24], grouping-based [17, 4, 23, 39], and query-based [36]. Proposal-based methods [45, 11, 24] extract 3D bound- + +![](images/f784115a6bf0fb1578534d62324e52860c05bf405cdbcd1308271e39afef689d.jpg) + +![](images/0fff207730706ef70d9904a9c68b4cdfdb28f2ce72457bc0f6c2d88bf9037295.jpg) + +![](images/c0088c33963a89e1eae9929452c6039e3c553ee7e059b4267f488aa36617ccb3.jpg) +Figure 1. The visualization of query distribution and segmentation results. A. The query initialization module samples a query on each of the two chairs to distinguish the two instances precisely. B. Repeated queries incorrectly split the complete board into two pieces. C. The denoising module removes many noise background queries and optimizes the final segmentation results. + +ing boxes and utilize a mask learning branch to predict the object mask inside each box. Grouping-based methods [17, 4, 23, 39] rely on a bottom-up pipeline that generates predictions for each point (e.g., semantic categories and geometric offsets) and then groups the points into instances. However, proposal-based and grouping-based methods strongly rely on high-quality proposals and require manual selection of geometric properties and tuning of hyperparameters. These drawbacks and limitations prompt query-based methods to be proposed and receive extensive attention from researchers. Query-based methods are regarded as a class of transformer query-based methods [2, 5] in which each object instance is represented as an instance query. Query-based methods require a large number of queries spread throughout the scene to cover a large part of foreground objects in the scene so that there are one or even more queries on each covered object instance. Then a transformer decoder learns the instance queries by iteratively focusing on multi-level point cloud features. Eventually, the instance queries aggregate point cloud features to produce all instance masks in parallel. + +Based on the discussion of the above approaches, query-based methods show great promise for 3D instance segmentation tasks by offering superior performance while not re + +![](images/0a1ec487998e39b5bc247ba83f08649fe9585d1bc0ee1a68aa8966bc47eb0805.jpg) +Query Distribution + +![](images/a92cf0c2c1e69badd9b93024b9da710f88fc461ac4c1b40950db830e4bd0aa4b.jpg) +Mask3D +Ours + +![](images/4c3322a4c5de53260a2eddd057d2f24eab82f98238ba37986bb812dab0fda61c.jpg) +Foreground Query +Figure 2. Statistics on coverage rate&repetition rate and query distribution. For query distribution, our method has more foreground distribution and less noise background queries and FPS initialization exists many noise background queries. Besides, our method guarantees a high coverage rate of foreground object instances while maintaining a low repetition rate. + +![](images/3c337583894a707bd71ccfa11858b1c5fb26c90b4f3c7f226a4dac3ed40f351b.jpg) +Noise Background Query +Background Query +General Background Query + +quiring high-quality 3D proposals and reducing the need for extensive manual setup. By analyzing the query-based method, we summarize the following two core points of query-based 3D instance segmentation: 1) How to effectively initialize queries? For the query-based method, we conclude that coverage and repetition rates are two significant factors affecting query initialization. The coverage rate is defined as the proportion of foreground object instances with queries distributed to the total foreground object instances in the scene. As the statistical results in Figure 2, the coverage rate of FPS [35] is $74\%$ (Ours is $89\%$ ), and the lower coverage rate causes some objects to be missed. For example, as shown in Figure 1(A), the two chairs are incorrectly segmented into one whole object because one chair is not covered by queries. The repetition rate is defined as the proportion of queries that have other queries coexisting in the same foreground object instance to the total number of foreground queries. The higher repetition rate ( $64\%$ vs our $47\%$ ) results in low query utilization and unnecessary overlapping computation. Besides, repeated queries contradict one-to-one bipartite matching mechanism and will destroy the integrity of segmentation results. As shown in Figure 1(B), multiple queries split the board into two parts. In practice, a high coverage rate often leads to a high repetition rate, and a low repetition rate is accompanied by a low coverage rate, so it is necessary to design an initialization strategy that can guarantee a high coverage rate of foreground object instances while maintaining a low repetition rate. 2) How to suppress the interference of noise background queries on accurate segmentation? Query-based methods yield outstanding performance but sample more queries than object instances in the scene. For example, sampling results by the Mask3D [36] in Figure 2 show that $48\%$ of the queries are distributed on foreground + +objects, while $15\%$ of the $52\%$ of the background queries are distributed near the instances. The background queries distributed near the instances are called noise background queries because the closer the queries are to the instances, the more negatively they affect the accurate segmentation of the instances. As shown in Figure 1(C), the foreground queries(red) incorrectly segment a part of the background as a foreground instance due to the interference of the noise background queries(green). Therefore, in addition to ensuring that foreground queries accurately segment foreground instances, it is equally essential to suppress the interference of noise background queries on the segmentation task. + +Inspired by the above discussion, we propose a Query Refinement Transformer for 3D Instance Segmentation, named QueryFormer, including a point encoder, a query initialization module, and an affiliated transformer decoder. We use a generic U-net point cloud representation network [7] as the point encoder of the method. In the query initialization module, we aggregate the superpoint features [20] and the multi-level features extracted by the point encoder to the seed points through the Aggregation Module. The Set Grouping module (SG) is designed to achieve a high coverage rate and low repetition rate distribution of seed points on instances. Specifically, the set grouping module shifts seed points to the centers of the objects to ensure a high coverage rate and filters out duplicate seed points to decrease the repetition rate and minimize the computational cost. The affiliated transformer decoder is dedicated to suppressing the impacts of noise background queries on the instance segmentation. Specifically, we generate some perturbed ground-truth centers around the instance centers during training. The perturbed centers are encoded in the same space as the query and input to the decoder for mapping to a consistent feature space. For each foreground instance, a unique query is matched by the Hungarian matching [18]. This query forms positive pairs with perturbed centers, while unmatched queries form several negative pairs with perturbed centers. We design a denoising module with contrastive loss [30] to drive the unmatched noise background queries away from the instance to reduce interference with the instance mask prediction. + +In summary, the main contributions of this work are as follows: (i) We design a query initialization module to optimize the initialization process for a high coverage and low repetition rate query distribution, which further helps the proposed affiliated transformer decoder to achieve more accurate results. (ii) The proposed affiliated transformer decoder suppresses the interference of noise background queries and helps the foreground queries focus on discriminative parts for more accurate instance segmentation. (iii) Extensive experimental results on two standard benchmarks, ScanNetV2 [8] and S3DIS [1], demonstrate that the proposed model performs favorably against state- + +of-the-art 3D instance segmentation methods. + +# 2. Related Work + +In this section, we briefly overview related works on 3D instance segmentation, including proposal-based methods, grouping-based methods, and instance segmentation with transformer. + +Proposal-based Methods. Existing proposal-based methods are greatly influenced by the success of Mask R-CNN [14] for 2D instance segmentation. GSPN [45] takes an analysis-by-synthesis strategy to generate high-quality 3D proposals, which are refined by a region-based PointNet [34]. 3D-BoNet [44] uses PointNet++ [35] to extract features from point clouds and applies Hungarian matching [18] to generate 3D bounding boxes. GICN [24] approximates the instance center of each object as a Gaussian distribution. 3D-MPA [11] predicts centers of instances and employs a graph-based convolutional network to cluster points near the centers to refine proposal features. The proposal-based methods have high expectations for the quality of proposals. + +Grouping-based Methods. Grouping-based methods produce per-point predictions, such as semantic categories and geometric offsets, and then group points into instances. To group points, MTML [19] uses a multi-task learning strategy. PointGroup [17] segments objects on the original and offset-shifted point clouds and uses the ScoreNet to predict scores for instances. HAIS [4] extends PointGroup by absorbing surrounding fragments of instances and then refining the instances based on intra-instance prediction. SSTNet [23] constructs a tree network from precomputed superpoints and splits non-similar nodes to get object instances. SoftGroup [39] groups on soft semantic scores instead of hard semantic prediction and processes each proposal to refine positive samples and suppress negative ones. Although the grouping-based approaches require many manual settings, they have dominated the field until recently. + +Instance Segmentation with Transformer. Transformer [38] introduces the self-attention mechanism to model long-range dependencies and has been widely applied in computer vision tasks such as image classification [10, 3], object detection [2, 9], and segmentation [48, 6, 5]. Recently, DETR [2] has been proposed as a new paradigm to use object queries for object detection in an image. Based on the set prediction mechanism proposed in DETR, MaskFormer [6] employs a transformer decoder to compute a set of pairs, each consisting of a class prediction and a mask embedding vector, to solve both semantic and instance segmentation tasks in a unified manner. Mask2Former [5] outperforms state-of-the-art specialized architectures on all considered datasets for 2D image semantic, instance, and panoptic segmentation. The success + +of transformer has come to prominence in some 3D point cloud tasks such as 3D object detection [28, 25] and 3D semantic segmentation [47]. However, applications of transformer to 3D instance segmentation tasks have yet to be exploited profoundly. DyCo3D [15] uses a transformer at the bottleneck of the feature backbone to increase the receptive field size. Mask3D [36] proposes the first transformer framework for 3D instance segmentation and achieves the state-of-the-art performance. In Mask3D, each object instance is represented as an instance query, and a vanilla transformer decoder is applied to predict instance masks. In this paper, we design a novel query initialization module to effectively initialize queries and formulate a denoising module with contrastive loss to suppress the interference of noise background queries. Eventually, QueryFormer achieves superior results with better query refinement. + +# 3. Method + +This section provides the details of our proposed method. We first illustrate the overview of the proposed method in Section 3.1, and then introduce the proposed Query Initialization Module in Section 3.2. In Section 3.3, we explain how the Affiliated Transformer Decoder works to suppress the undesirable interference of noise background queries on isntance segmentation. Finally, we elaborate the model training and inference in Section 3.4. + +# 3.1. Overview + +The goal of 3D instance segmentation is to determine the categories and binary masks of all foreground objects in the scene. Unlike the bounding boxes of 3D object detection, 3D instance segmentation requires further accurate delineation of the mask. The architecture of our method is illustrated in Figure 3(a). Assuming that the input point cloud has $N$ points, each point contains position $x, y, z$ and color $r, g, b$ information. First, we use a 3D-UNet based on sparse convolution for multi-level feature extraction $F_{0}, F_{1}, F_{2}$ . To select the query points with high coverage rate and low repetition rate from the scene, we input the seed points $P_{seed}$ sampled by Farthest Point Sampling (FPS) into the Query Initialization Module (QIM). Through feature fusion in the aggregation module and filtering in the set grouping, we get the high quality query points $Q_{1}$ . Finally, we input the obtained query points into the proposed Affiliated Transformer Decoder (ATD) to get the final predictions. + +# 3.2. Query Initialization Module + +Before we introduce the module, we give the definition of two concepts (coverage rate and repetition rate of query points). The Coverage Rate (CR) of query points indicates the number $N_{p}$ of instances contained in the query points as a percentage of the total number $N_{ins}$ of instances in the + +![](images/bce3256db7d0977cae770f3621d375d94c84a50a98dbafa1023690200bff132b.jpg) + +![](images/b26932b2561adba67230598c299d333cffda62b7464c1ff920fd20fb47bb96b6.jpg) +Figure 3. The overview of our query refinement transformer for 3D instance segmentation. As shown in (a), we first generate seed points $P_{seed}$ by sampling from the raw point cloud. Next, we design the Query Initialization Module to improve the coverage rate and reduce the repetition rate of seed points. Afterwards, we send the generated high-quality query points $Q_{1}$ to the Affiliated Transformer Decoder to generate the final instance masks. Meanwhile, we design the Denoising Module to alleviate the interference of noise background queries on instance mask prediction. The details of each module are shown in (b), (c), (d) and (e). + +![](images/607a8adfddcfa60332440869ed7c5b653ab2b0d83e4d94d3ca687a0ce9ee894c.jpg) + +![](images/6ac5a4678fd9f9f300e298e0224e14eafd009fe50322fcfa27b998f37faaf44c.jpg) + +scene, which can be formulated as: + +$$ +C R = N _ {p} / N _ {i n s}. \tag {1} +$$ + +The Repetition Rate (RR) of query points indicates the proportion of instances covered by repetition in the query points, which can be formulated as: + +$$ +R R = \left(N _ {f} - N _ {p}\right) / N _ {f}, \tag {2} +$$ + +where $N_{f}$ denotes the number of foreground points in the query points. The previous methods [36] usually use FPS to select query locations. However, FPS makes it challenging to balance the coverage and repetition rates. As shown in Figure 3(b), to solve this problem, we propose the Query Initialization Module, which contains two main submodules, the aggregation module and the set grouping module. + +Aggregation Module. In feature aggregation, we design a module that allows the point features in the same instance to fuse while reducing the interference of point features in other adjacent instances. As shown in Figure 3(c), the module contains three parts, cross-attention layer, correlation-based self-attention layer and feed-forward layer. First, we use the cross-attention mechanism to update the features of the seed points $P_{\text{seed}}$ using the features of the superpoints in the scene. Here we initialize the seed point features by + +encoding the coordinates of the seed points. After that, the seed point features are input to the correlation-based self-attention mechanism. Unlike the previous self-attention mechanism, we use the information cues from the correlation relations in the attention map for feature fusion, and this design promotes the appropriate correlations of relevant seed-seed pairs and suppress the erroneous correlations of irrelevant seed-seed pairs. Specifically, we first calculate the similarity matrix of seed point features, as follows: + +$$ +M = \frac {Q K ^ {T}}{\sqrt {C}} w _ {M} + P, \tag {3} +$$ + +where $w_{M}$ is a linear projection, $P$ represents the position embeddings of seed points. We use the similarity matrix of features as the new features to calculate the similarity, with the following formula: + +$$ +M ^ {c} = \operatorname {S o f t m a x} \left(\frac {\mathrm {Q} _ {\mathrm {M}} \mathrm {K} _ {\mathrm {M}} ^ {\mathrm {T}}}{\sqrt {\mathrm {C} _ {\mathrm {M}}}}\right) \mathrm {M}. \tag {4} +$$ + +Then we calculate the updated features $F_{\text{seed}}^c$ for each seed point based on the similarity matrix $M^c$ . Finally, we input $F_{\text{seed}}^c$ into the feed-forward layer and then predict the mask, category and IoU scores by different MLP heads. + +Many-to-one Matching. Different from the one-to-one matching[18] used previously, we use many-to-one match + +ing in the aggregation module. Formally, we introduce a pairwise cost matrix $CM_{k}$ to evaluate the similarity of seed point $q$ and the k-th ground-truth. $CM_{k}$ is determined by classification probability, superpoint mask cost and distance cost. We will introduce how to obtain the cost matrix in the supplementary material. With the cost matrix, we assign corresponding instance to each seed point, + +$$ +I n s _ {q} = \left\{ \begin{array}{l} \arg \min _ {k} C M _ {k}, i f \min _ {k} D _ {k} < \tau , \\ - 1, e l s e, \end{array} \right. \tag {5} +$$ + +where $\tau$ represents a threshold, $D_{k}$ represents the distance between the coordinate of seed point $q$ and the centerpoint of the k-th ground-truth, and -1 represents that no instance matches the seed point. + +Set Grouping Module. The set grouping module aims to improve coverage rate and reduce repetition rate, which contains shift and IoU-guided NMS [29] operations. The shift operation offsets seed points to the centers of the instances to ensure a high coverage rate so that most foreground instances can have a corresponding seed point. While the IoU-guided NMS operation filters out duplicate seed points to ensure that each foreground instance retains only one high-quality seed point thus reducing the repetition rate of seed points. Specifically, we first use a MLP to predict each seed point $q$ relative to its matching instance $Ins_{q}$ coordinate offset of the center point. After obtaining this coordinate offset, add it to the original coordinate $p$ : + +$$ +p = M L P (s) + p. \tag {6} +$$ + +In this way, we can not only shift some background points to the foreground, but also close the points on the same instance, which will promote these points to learn similar features and help NMS remove redundant seed points. Then we get the corresponding instance mask $M_{ins}$ of the seed point $q$ by calculating the dot product between superpoint features and seed point features. And we obtain the final mask through sigmoid and a threshold of 0.5, as follows: + +$$ +M _ {b} = \phi (M _ {i n s}) > 0. 5. \tag {7} +$$ + +Finally, we adopt the IoU-guided NMS to filter out a large number of redundant seed points. Here, the confidence of NMS is the multiplication of class score and IoU score. In order to enable the network to operate in parallel, we add extra seed points to satisfy the same number. Specifically, we do a $\bigcup$ operation on the mask $M_{b}$ of all seed points and then operate FPS on the complement $M^{-}$ of the whole scene to sample extra seed points. + +# 3.3. Affiliated Transformer Decoder + +In the Query Initialization Module, we have obtained queries with high coverage rate and low repetition rate through the Aggregation Module and Set Grouping Module. In this section, we describe how the Affiliated Transformer Decoder generates the final instance segmentation + +results with these queries. As shown in Figure 3(d), the Affiliated Transformer Decoder mainly contains the Cluster-based Layer and the Denoising Module. + +Cluster-based Layer. Existing query-based methods [36] tend to compute similarities across the entire point cloud, which introduces large computational redundancy. Therefore, we propose the Cluster-based Layer. As shown in Figure 3(e), the method is based on the idea of clustering, assigning each point in the scene to its most similar query. + +Specifically, we first calculate the similarity of the backbone features and the query features. Next, we assign each backbone feature via arg max operation as following, + +$$ +I d x _ {k} = \arg \max _ {i} M _ {i, k}, \tag {8} +$$ + +where $M_{i,k}$ is a dot product of query $i$ and backbone feature $k$ . Therefore, we divide all backbone features into disjoint sets by clustering. Next, we do cross-attention for queries and their corresponding sets. By this way, we only need to calculate attention map on some similar backbone features for each query. Finally we input queries into the self-attention layer and the feed-forward layer. + +One-to-one Matching. In this section, we use one-to-one matching to replace many-to-one matching in Section 3.2. Concretely, we obtain the cost matrix $CM$ the same as Aggregation Module but replace arg min with Hungarian matching[18] to obtain the query-GT pairs. + +Denoising Module. In section 3.2, we shift the background points around the foreground points to the center of the instance to improve the coverage rate. However, during the offset, not every point is well migrated to the center due to the different scales and classes of objects [40]. This leads to some background points that may affect the information aggregation of the foreground points. Therefore, we deal with the interference caused by background point offset in this module. We take the center of the instance from ground-truth and resample it, as follows: + +$$ +Q _ {g t} \sim N \left(C _ {g t}, \sigma^ {2}\right), \tag {9} +$$ + +where $N$ means the Gaussian distribution and $\sigma$ represents deviation. We encode the perturbed GT centers $Q_{gt}$ together with the query points $Q_{1}$ obtained in the query initialization module and feed them into the affiliated transformer decoder. Then, we match the query outputs with the ground-truth in the dataset. The query with the minimal matching cost forms several positive pairs with the ground-truth perturbed centers. We encourage the output features of the positive queries to be consistent with the output features of the corresponding center points and drive the unmatched noise background queries away from the instance to reduce interference with the instance mask prediction. Therefore, we use the contrastive loss. Suppose the number of queries is $K$ , the number of ground-truth is $N_{gt}$ , ground-truth $j$ generates $\beta$ perturbed GT centers, query $i$ and the perturbed + +GT centers of ground-truth $j$ are positive pairs, + +$$ +L _ {\text {c o n t}} = - \frac {1}{| \beta N _ {g t} |} \sum_ {j = 1} ^ {N _ {g t}} \sum_ {m = 1} ^ {\beta} \log \left(\frac {\exp \left(d \left(q _ {i} , q _ {j , m} ^ {g t}\right) / \varepsilon\right)}{\sum_ {s = 1} ^ {K} \exp \left(d \left(q _ {s} , q _ {j , m} ^ {g t}\right) / \varepsilon\right)}\right), \tag {10} +$$ + +where $d(.,.)$ is a distance measurement and $\varepsilon$ is the temperature in contrastive learning. + +# 3.4. Training and Inference + +As to query initialization module, only the aggregation modules are supervised. We assign the unmatched queries with $N_{\text{class}} + 1$ class label and compute the cross-entropy loss $L_{\text{cls}}$ for each query. Then we compute the superpoint mask loss which consists of binary cross-entropy loss $L_{\text{bce}}$ and dice loss $L_{\text{dice}}$ [27] for each query-GT pair. Meanwhile, we compute the score loss $L_{\text{sco}}$ using binary cross-entropy loss. Suppose that the Hungarian matching assigns the k-th ground-truth to the i-th query, + +$$ +L _ {s c o, i} = B C E \left(o _ {i}, I o U _ {i, k}\right), \tag {11} +$$ + +where $o_i$ represents the IoU prediction of query $i$ . In addition, we add the offset loss $L_{off}$ which uses L1loss to close the distance between the coordinates of queries and the instance center points. + +$$ +L _ {o f f, i} = \left| p _ {i} - p _ {k} ^ {G T} \right| \tag {12} +$$ + +The overall loss is defined as: + +$$ +\begin{array}{l} L = \lambda_ {1} \cdot L _ {d i c e} + \lambda_ {2} \cdot L _ {b c e} + \lambda_ {3} \cdot L _ {c l s} \\ + \lambda_ {4} \cdot L _ {\text {o f f}} + \lambda_ {5} \cdot L _ {s c o}. \\ \end{array} +$$ + +To Affiliated Transformer Decoder, we also add losses after each Cluster-based Layer. Compared to $L$ , we add contrastive loss which is introduced in Section 3.3. + +$$ +L ^ {*} = L + \lambda_ {6} \cdot L _ {\text {c o n t}} \tag {14} +$$ + +Following DN-DETR[22], we use the same losses as query-GT pairs to supervise the perturbed GT centers. This can ensure the perturbed GT centers would not diverge. + +During inference, it should be noted that perturbed GT centers will not be generated, that is, we only infer queries generated by Query Initialization Module. + +# 4. Experiments + +# 4.1. Experimental Setup + +Dataset and Metrics. We conduct our experiments on ScanNetV2 [8] and S3DIS [1] datasets. ScanNetV2 includes 1,613 scenes with 18 instance categories. Among them, 1,201 scenes are used for training, 312 scenes are used for validation, and 100 scenes are used for test. S3DIS + +Table 1. Comparison on ScanNetV2 benchmark. + +
MethodScanNetV2
mAPAP@50AP@25Box AP@50Box AP@25
F-PointNet [33]///10.819.8
GSPN [45]/37.853.417.730.6
3D-SIS [16]/18.735.722.540.2
VoteNet [32]///33.558.6
3D-MPA [11]35.351.972.449.264.2
DyCo3D [15]40.661.0/45.358.9
PointGroup [17]34.856.971.348.961.5
MaskGroup [49]42.063.374.0//
OccuSeg [13]44.260.7///
HAIS [4]43.564.475.653.164.3
SSTNet [23]49.464.37452.762.5
SoftGroup [39]45.867.678.959.471.6
DKNet [43]50.866.976.959.067.4
Mask3D [36]55.273.782.956.671.0
Ours56.574.283.361.773.4
+ +is a large-scale indoor dataset collected from six different areas. It contains 272 scenes with 13 instance categories. Following previous works [39], we evaluate our approach: testing on Area 5 and 6-fold cross-validation. AP@25 and AP@50 represent the average precision scores with IoU thresholds $25\%$ and $50\%$ , and mAP represents the average of all the APs with IoU thresholds ranging from $50\%$ to $95\%$ with a step size of $5\%$ . On ScanNetV2, we report mAP, AP@50 and AP@25. Moreover, we also report the Box AP@50 and AP@25 results following SoftGroup [39] and DKNet [43]. On S3DIS, we report mAP, AP@50, mean precision (mPrec), and mean recall (mRec). + +Implementation Details. We train our model on a single RTX3090 with a batch size of 5 for 600 epochs. We use AdamW [26] and a one-cycle learning rate schedule [37] with a maximal learning rate of $10^{-4}$ . We voxelize the point clouds with the size of $0.02\mathrm{m}$ . For a fair comparison, the point encoder is a Minkowski Res16UNet34C [7], which is the same as Mask3D [36]. For hyperparameters, we tune $\tau, \sigma, \varepsilon, \beta$ as 0.6, 0.05, 0.5, 3 respectively. $\lambda_1, \lambda_2, \lambda_3, \lambda_4, \lambda_5$ in Equation 13 and 14 are set as 2, 5, 2, 3, 2. $\lambda_6$ in Equation 14 is set as 2. More implementation details are stated in the supplementary material. + +# 4.2. Comparison with the state-of-the-art methods. + +ScanNetV2. As shown in Table 1, we compare our approach with existing state-of-the-art methods on the ScanNetV2 validation set. Our approach attains relative $2.4\%$ improvements on mAP and shows relative $3.9\%$ and $2.5\%$ improvements on Box AP@50 and Box AP@25, respectively. On these metrics, our proposed model achieves state-of-the-art results. From Figure 4, we can see visualization of instance segmentation results. Compared to Mask3D, our approach correctly segments each instance and produces finer segmentation results. + +S3DIS. We evaluate our method on S3DIS using Area + +![](images/2c5c22e6201a74037b2f546c35d6e54fc7086cf2e3ab5d2ca095c37994eeb43c.jpg) + +![](images/9fc724c60d97cc3de796866dc62ac3816ece00cd8d51dca5f67259235c228a6e.jpg) +Input + +![](images/96ae93c271b23a085f76a6c3e0f5de70498d0186c0c0c16212759d45517e1209.jpg) + +![](images/e0429cc64cdf25949d30b473c6054a2b74837d9b45007501a5e1b77f868e7e7f.jpg) +Mask3D + +![](images/b06a469790cca6724bcec516f8bb6ddd403fdbb962bd16607d57bd787517ea99.jpg) + +![](images/cbfba701ee351df2060545f3153cbcfe6753ae1f007e0a4c88e922ea6f524dac.jpg) +Ours +Figure 4. Visualization of instance segmentation results on the ScanNetV2 validation set. The red boxes highlight the key regions. + +![](images/a2385f571c621b6a01671ec51325683b9bdd26d7006059020101365b269c43f0.jpg) + +![](images/f63bd2c503fa463d32a1bc609adb368e873acbd61661faa1705782e338882b81.jpg) +GT + +Table 2. Comparison on S3DIS benchmark. + +
MethodS3DIS Area 5S3DIS 6-fold CV
mAPAP@50mPrecmRecmAPAP@50mPrecmRec
SGPN [41]//36.028.7//38.231.2
ASIS [42]//55.342.4//63.647.5
3D-Bonet [44]//57.540.2//65.647.6
OccuSeg [13]//////72.860.3
3D-MPA [11]//63.158.0//66.764.1
PointGroup [17]/57.861.962.1/64.069.669.2
DyCo3D [15]//64.364.2////
MaskGroup [49]/65.062.964.7/69.966.669.6
SSTNet [23]42.759.365.564.254.167.873.573.4
SoftGroup [39]51.666.173.666.654.468.975.369.8
DKNet [43]//70.865.3//75.371.1
Mask3D [36]56.569.368.770.760.772.070.572.5
Ours57.769.970.572.262.073.372.773.4
+ +Table 3. Comparison on ScanNet200 benchmark. + +
MethodmAPAP@50AP@25
Mask3D [36]27.437.042.3
Ours28.137.143.4
+ +5 and 6-fold cross-validation respectively. For a fair comparison, Mask3D and our method are all supervised by instance labels at the superpoint level instead of the point level. As shown in Table 2, our superior results on some important metrics validate the effects and generalization of our method. + +ScanNet200. We also compare our approach with existing state-of-the-art method on the ScanNet200 validation set, which includes a magnitude more class categories than ScanNetV2. As shown in Table 3, the results demonstrate the remarkable generalization of our model. + +# 4.3. Effects of DBSCAN [12]. + +DBSCAN is a time-consuming density-based clustering algorithm that can separate multiple instances which are incorrectly predicted as a whole. Some methods with low coverage rates can easily divide multiple instances into a whole, so these methods rely heavily on DBSCAN for post- + +Table 4. Effects of DBSCAN. In this experiment, the number of queries in both methods is set to 100. + +
MethodDBSCANScanNetV2S3DIS Area 5
mAP AP@50 AP@25mAP AP@50 AP@25
Mask3D [36]X53.773.082.553.967.073.9
✓54.774.082.956.569.375.6
Improvements+1+1+0.4+2.6+2.3+1.7
OursX56.273.883.257.169.376.6
✓56.574.283.357.769.977.1
Improvements+0.3+0.4+0.1+0.6+0.6+0.5
+ +processing. As shown in Table 4, the high performance of Mask3D must be guaranteed by DBSCAN. However, profiting from our designed query initialization module and denoising module, our method can achieve an superior performance without support from DBSCAN. In order to show the effects of DBSCAN more explicitly, as shown in Figure 5, two chairs in Mask3D are not covered by queries, so the three chairs are jointly predicted. After the post-processing of DBSCAN, this problem has been alleviated. Although DBSCAN is effective, there are two problems. The first is that multiple hyperparameters need to be readjusted for different scenarios. The other is the time-consuming problem. For example, DBSCAN takes about 1 minute to process an indoor scenario. Therefore, our method can achieve superior performance at a low time cost. + +# 4.4. Ablation Study. + +Components Analysis. In this section, we perform extensive ablation studies on the ScanNetV2 dataset to evaluate the effects of each design. Table 5 demonstrates the performance of the model with different designs. Concretely, the second row demonstrates that the query initialization module improves by 1.6 on mAP with a high coverage rate and low repetition rate query distribution. The cluster-based layer is designed to reduce the complexity of calculations and therefore only makes a modest contribution to accuracy. In the fifth row, the denoising module + +![](images/b0a03e81a504e2aae28076f7286042f78977bf1ce43680a92e1ca3ab64904b62.jpg) +Figure 5. Visualization of query distribution and instance segmentation results on the ScanNetV2 validation set. The red points represent the position of queries, and the red boxes highlight the key regions. + +![](images/894890354256e64f6fec33280944b3e5c504935702ce94e0882fb1a048ef122f.jpg) + +![](images/62da2f039516712dd7525c11df3435792a40bf0e05a4e435f660cc763f393d04.jpg) + +![](images/6172d7b3a7f87c941dfbe09a5ca4566ad9062d81429a383acb9fd2da5b6b4e26.jpg) + +![](images/d3c1de3da99dd0836c943e5c37d196db7fdd2b4b29bf206ba1ff880c57fbd0d2.jpg) + +![](images/1aaccac30322c7a9dafcdd146e497d4c698bd1247c29e7601a50efa337213b43.jpg) + +Table 5. Evaluation of the model with different designs on ScanNetV2. QIM represents the Query Initialization Module, CL represents the Cluster-based Layer, DM is the Denoising Module. + +
QIMCLDMDBSCANScanNetV2
mAPAP@50AP@25
XXXX53.773.082.5
✓XXX55.373.583.2
X✓XX54.073.082.7
✓✓XX55.473.683.2
✓✓✓X56.273.883.2
✓✓✓✓56.574.283.3
+ +Table 6. Effects of QIM. Here, the experiment is conducted on ScanNetV2 without DBSCAN. CR means the coverage rate, while RR refers to the repetition rate. Higher CR and lower RR reflect a better result. + +
MethodNumScanNetV2
CR↑RR↓mAPAP@50AP@25
Mask3D [36]500.540.4847.665.575.2
Mask3D1000.740.6453.773.082.5
Mask3D1500.830.7254.373.082.8
Mask3D5000.970.9952.870.679.9
Ours500.760.4354.072.982.5
Ours1000.890.4756.273.883.2
Ours1500.920.7055.372.583.0
+ +improves the performance by 0.8 on mAP through noise background query suppression. Since the query initialization module improves the sampling quality of the query, our method does not rely on DBSCAN post-processing. Therefore, after time-consuming DBSCAN post-processing, our results are only marginally improved. + +Effects of QIM. As shown in Table 6, a large number of queries can not only bring a high coverage rate but also lead to a high repetition rate. Fewer queries always bring a lower repetition rate, but a lower coverage rate of the scene may follow. Therefore, we should balance the relationship between repetition and coverage rates when selecting the number of queries. The experimental results of Table 6 on ScanNetV2 also verify that higher experimental performance can be obtained by balancing the coverage and repetition rates. Thanks to the high-quality queries obtained in QIM, our method performs best when the number of queries is 100, while Mask3d performs best when the number of queries is 150. Therefore, our method achieves better performance with less computational overhead. + +![](images/20ffb915ec989f4c90c48c85d219cdb445ecfa6b31b83e3e019b4b1afb5bfb50.jpg) +Figure 6. The visualization of segmentation results related to the denoising module in the affiliated transformer decoder. The red points represent the position of queries, the green points represent the position of noise background queries, and the red boxes highlight the key regions. + +Table 7. Efficiency comparison on a single cluster-based layer. + +
MethodMemory(KB)FLOPs(G)Inference Time(ms)
Mask3D [36]48.82.31.1
Ours0.491.30.72
+ +Effects of ATD. The affiliated transformer decoder is conceived to suppress the interference of noise background queries and thus maintain a robust and desirable instance segmentation result. In order to vividly and dually validate the importance of suppressing this interference, relevant visualization experiments are carried out in Figure 6. The denoising module in the affiliated transformer decoder pulls away the noise background points (green) for the two scenes to suppress the interference with the foreground queries (red). Furthermore, the segmentation visualization in the third and fourth columns verifies the suppression beneficial for more accurate and robust segmentation results and validates the positive effects of our designed affiliated transformer decoder. + +Efficiency comparison. As shown in Table 7, we compare the efficiency of the cluster-based layer provided by our method and the normal layer used in Mask3D. It can be seen from the results that the cluster-based layer is superior to the normal layer in terms of memory, FLOPs and inference time. + +# 4.5. Parameter and Runtime Analysis. + +Table 8 reports the model parameter and the runtime per scan of different methods on the ScanNetV2 validation set. For a fair comparison, the reported runtime is measured on the same RTX 3090 GPU. Compared with Mask3D, our method achieves noticeable performance improvement with only a 2.7M parameter increment. As to the inference + +Table 8. Parameter and runtime analysis of different methods on the ScanNetV2 validation set. The runtime is measured on the same RTX 3090 GPU. + +
MethodParameter(M)Runtime(ms)
HAIS [4]30.9578
SoftGroup [39]30.9588
SSTNet [23]/729
Mask3D [36]39.6578
Ours42.3487
+ +speed, our model is the fastest among all methods by reducing the decoder size. Concretely, Mask3D uses 12 layers of decoder, while our model only uses 8 layers. Although we add the Query Initialization Module, we adopt the superpoint features as the keys and values of cross attention, and down-sampling is done for each layer. + +# 5. Conclusion + +In this paper, we propose the Query Refinement Transformer for 3D instance segmentation. To solve the query sampling dilemma, we design a query initialization module to guarantee a high coverage rate of object instances while maintaining a low repetition rate. Furthermore, the well-designed affiliated transformer decoder suppresses the interference of noise background queries for better instance segmentation results. Extensive experiments conducted on two widely used 3D instance segmentation benchmarks demonstrate the superior performance of QueryFormer. + +# 6. Acknowledgements + +This work was partially supported by the National Nature Science Foundation of China (Grant 62022078), National Defense Basic Scientific Research Program of China (Grant JCKY2021601B013) and the National Nature Science Foundation of China (Grant 62021001). + +# References + +[1] Iro Armeni, Ozan Sener, Amir R Zamir, Helen Jiang, Ioannis Brilakis, Martin Fischer, and Silvio Savarese. 3d semantic parsing of large-scale indoor spaces. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1534-1543, 2016. 2, 6 +[2] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part I 16, pages 213-229. Springer, 2020. 1, 3 +[3] Chun-Fu Richard Chen, Quanfu Fan, and Rameswar Panda. 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However, object instances are diverse in shape and category, and point clouds are usually sparse, unordered, and irregular, which leads to a query sampling dilemma. Besides, noise background queries interfere with proper scene perception and accurate instance segmentation. To address the above issues, we propose the Query Refinement Transformer termed QueryFormer. The key to our approach is to exploit a query initialization module to optimize the initialization process for the query distribution with a high coverage and low repetition rate. Additionally, we design an affiliated transformer decoder that suppresses the interference of noise background queries and helps the foreground queries focus on instance discriminative parts to predict final segmentation results. 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With the popularity of AR/VR [31], 3D indoor scanning [21], and autonomous driving [46], 3D instance segmentation has become a key technology facilitating scene understanding. However, the complex layout of the scene and the variety of object categories pose severe challenges to 3D instance segmentation in segmenting similar objects and accurate point cloud masking." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 622, + 288, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 622, + 288, + 695 + ], + "spans": [ + { + "bbox": [ + 46, + 622, + 288, + 695 + ], + "type": "text", + "content": "To overcome the above challenges, a series of 3D instance segmentation methods [11, 24, 4, 23, 39, 36] have been proposed. Generally, these methods can be divided into three categories: proposal-based [45, 11, 24], grouping-based [17, 4, 23, 39], and query-based [36]. 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The visualization of query distribution and segmentation results. A. The query initialization module samples a query on each of the two chairs to distinguish the two instances precisely. B. Repeated queries incorrectly split the complete board into two pieces. C. The denoising module removes many noise background queries and optimizes the final segmentation results." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 424, + 547, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 424, + 547, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 424, + 547, + 675 + ], + "type": "text", + "content": "ing boxes and utilize a mask learning branch to predict the object mask inside each box. Grouping-based methods [17, 4, 23, 39] rely on a bottom-up pipeline that generates predictions for each point (e.g., semantic categories and geometric offsets) and then groups the points into instances. However, proposal-based and grouping-based methods strongly rely on high-quality proposals and require manual selection of geometric properties and tuning of hyperparameters. These drawbacks and limitations prompt query-based methods to be proposed and receive extensive attention from researchers. Query-based methods are regarded as a class of transformer query-based methods [2, 5] in which each object instance is represented as an instance query. Query-based methods require a large number of queries spread throughout the scene to cover a large part of foreground objects in the scene so that there are one or even more queries on each covered object instance. Then a transformer decoder learns the instance queries by iteratively focusing on multi-level point cloud features. Eventually, the instance queries aggregate point cloud features to produce all instance masks in parallel." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "Based on the discussion of the above approaches, query-based methods show great promise for 3D instance segmentation tasks by offering superior performance while not re" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "text", + "content": "*Corresponding Author" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18516" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 78, + 76, + 145, + 148 + ], + "blocks": [ + { + "bbox": [ + 78, + 76, + 145, + 148 + ], + "lines": [ + { + "bbox": [ + 78, + 76, + 145, + 148 + ], + "spans": [ + { + "bbox": [ + 78, + 76, + 145, + 148 + ], + "type": "image", + "image_path": "0a1ec487998e39b5bc247ba83f08649fe9585d1bc0ee1a68aa8966bc47eb0805.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 141, + 153, + 194, + 160 + ], + "lines": [ + { + "bbox": [ + 141, + 153, + 194, + 160 + ], + "spans": [ + { + "bbox": [ + 141, + 153, + 194, + 160 + ], + "type": "text", + "content": "Query Distribution" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 152, + 76, + 217, + 148 + ], + "blocks": [ + { + "bbox": [ + 152, + 76, + 217, + 148 + ], + "lines": [ + { + "bbox": [ + 152, + 76, + 217, + 148 + ], + "spans": [ + { + "bbox": [ + 152, + 76, + 217, + 148 + ], + "type": "image", + "image_path": "a92cf0c2c1e69badd9b93024b9da710f88fc461ac4c1b40950db830e4bd0aa4b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 233, + 81, + 263, + 89 + ], + "lines": [ + { + "bbox": [ + 233, + 81, + 263, + 89 + ], + "spans": [ + { + "bbox": [ + 233, + 81, + 263, + 89 + ], + "type": "text", + "content": "Mask3D" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 235, + 92, + 257, + 100 + ], + "lines": [ + { + "bbox": [ + 235, + 92, + 257, + 100 + ], + "spans": [ + { + "bbox": [ + 235, + 92, + 257, + 100 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 61, + 163, + 152, + 206 + ], + "blocks": [ + { + "bbox": [ + 61, + 163, + 152, + 206 + ], + "lines": [ + { + "bbox": [ + 61, + 163, + 152, + 206 + ], + "spans": [ + { + "bbox": [ + 61, + 163, + 152, + 206 + ], + "type": "image", + "image_path": "4c3322a4c5de53260a2eddd057d2f24eab82f98238ba37986bb812dab0fda61c.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 102, + 209, + 153, + 218 + ], + "lines": [ + { + "bbox": [ + 102, + 209, + 153, + 218 + ], + "spans": [ + { + "bbox": [ + 102, + 209, + 153, + 218 + ], + "type": "text", + "content": "Foreground Query" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 235, + 287, + 300 + ], + "lines": [ + { + "bbox": [ + 46, + 235, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 287, + 300 + ], + "type": "text", + "content": "Figure 2. Statistics on coverage rate&repetition rate and query distribution. For query distribution, our method has more foreground distribution and less noise background queries and FPS initialization exists many noise background queries. Besides, our method guarantees a high coverage rate of foreground object instances while maintaining a low repetition rate." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 171, + 164, + 272, + 206 + ], + "blocks": [ + { + "bbox": [ + 171, + 164, + 272, + 206 + ], + "lines": [ + { + "bbox": [ + 171, + 164, + 272, + 206 + ], + "spans": [ + { + "bbox": [ + 171, + 164, + 272, + 206 + ], + "type": "image", + "image_path": "3c337583894a707bd71ccfa11858b1c5fb26c90b4f3c7f226a4dac3ed40f351b.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 102, + 222, + 167, + 230 + ], + "lines": [ + { + "bbox": [ + 102, + 222, + 167, + 230 + ], + "spans": [ + { + "bbox": [ + 102, + 222, + 167, + 230 + ], + "type": "text", + "content": "Noise Background Query" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 172, + 209, + 223, + 217 + ], + "lines": [ + { + "bbox": [ + 172, + 209, + 223, + 217 + ], + "spans": [ + { + "bbox": [ + 172, + 209, + 223, + 217 + ], + "type": "text", + "content": "Background Query" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 182, + 222, + 242, + 230 + ], + "lines": [ + { + "bbox": [ + 182, + 222, + 242, + 230 + ], + "spans": [ + { + "bbox": [ + 182, + 222, + 242, + 230 + ], + "type": "text", + "content": "General Background Query" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 307, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 307, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 307, + 288, + 713 + ], + "type": "text", + "content": "quiring high-quality 3D proposals and reducing the need for extensive manual setup. By analyzing the query-based method, we summarize the following two core points of query-based 3D instance segmentation: 1) How to effectively initialize queries? For the query-based method, we conclude that coverage and repetition rates are two significant factors affecting query initialization. The coverage rate is defined as the proportion of foreground object instances with queries distributed to the total foreground object instances in the scene. As the statistical results in Figure 2, the coverage rate of FPS [35] is " + }, + { + "bbox": [ + 46, + 307, + 288, + 713 + ], + "type": "inline_equation", + "content": "74\\%" + }, + { + "bbox": [ + 46, + 307, + 288, + 713 + ], + "type": "text", + "content": " (Ours is " + }, + { + "bbox": [ + 46, + 307, + 288, + 713 + ], + "type": "inline_equation", + "content": "89\\%" + }, + { + "bbox": [ + 46, + 307, + 288, + 713 + ], + "type": "text", + "content": "), and the lower coverage rate causes some objects to be missed. For example, as shown in Figure 1(A), the two chairs are incorrectly segmented into one whole object because one chair is not covered by queries. The repetition rate is defined as the proportion of queries that have other queries coexisting in the same foreground object instance to the total number of foreground queries. The higher repetition rate (" + }, + { + "bbox": [ + 46, + 307, + 288, + 713 + ], + "type": "inline_equation", + "content": "64\\%" + }, + { + "bbox": [ + 46, + 307, + 288, + 713 + ], + "type": "text", + "content": " vs our " + }, + { + "bbox": [ + 46, + 307, + 288, + 713 + ], + "type": "inline_equation", + "content": "47\\%" + }, + { + "bbox": [ + 46, + 307, + 288, + 713 + ], + "type": "text", + "content": ") results in low query utilization and unnecessary overlapping computation. Besides, repeated queries contradict one-to-one bipartite matching mechanism and will destroy the integrity of segmentation results. As shown in Figure 1(B), multiple queries split the board into two parts. In practice, a high coverage rate often leads to a high repetition rate, and a low repetition rate is accompanied by a low coverage rate, so it is necessary to design an initialization strategy that can guarantee a high coverage rate of foreground object instances while maintaining a low repetition rate. 2) How to suppress the interference of noise background queries on accurate segmentation? Query-based methods yield outstanding performance but sample more queries than object instances in the scene. For example, sampling results by the Mask3D [36] in Figure 2 show that " + }, + { + "bbox": [ + 46, + 307, + 288, + 713 + ], + "type": "inline_equation", + "content": "48\\%" + }, + { + "bbox": [ + 46, + 307, + 288, + 713 + ], + "type": "text", + "content": " of the queries are distributed on foreground" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "content": "objects, while " + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "inline_equation", + "content": "52\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "content": " of the background queries are distributed near the instances. The background queries distributed near the instances are called noise background queries because the closer the queries are to the instances, the more negatively they affect the accurate segmentation of the instances. As shown in Figure 1(C), the foreground queries(red) incorrectly segment a part of the background as a foreground instance due to the interference of the noise background queries(green). Therefore, in addition to ensuring that foreground queries accurately segment foreground instances, it is equally essential to suppress the interference of noise background queries on the segmentation task." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 219, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 219, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 219, + 545, + 567 + ], + "type": "text", + "content": "Inspired by the above discussion, we propose a Query Refinement Transformer for 3D Instance Segmentation, named QueryFormer, including a point encoder, a query initialization module, and an affiliated transformer decoder. We use a generic U-net point cloud representation network [7] as the point encoder of the method. In the query initialization module, we aggregate the superpoint features [20] and the multi-level features extracted by the point encoder to the seed points through the Aggregation Module. The Set Grouping module (SG) is designed to achieve a high coverage rate and low repetition rate distribution of seed points on instances. Specifically, the set grouping module shifts seed points to the centers of the objects to ensure a high coverage rate and filters out duplicate seed points to decrease the repetition rate and minimize the computational cost. The affiliated transformer decoder is dedicated to suppressing the impacts of noise background queries on the instance segmentation. Specifically, we generate some perturbed ground-truth centers around the instance centers during training. The perturbed centers are encoded in the same space as the query and input to the decoder for mapping to a consistent feature space. For each foreground instance, a unique query is matched by the Hungarian matching [18]. This query forms positive pairs with perturbed centers, while unmatched queries form several negative pairs with perturbed centers. We design a denoising module with contrastive loss [30] to drive the unmatched noise background queries away from the instance to reduce interference with the instance mask prediction." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "In summary, the main contributions of this work are as follows: (i) We design a query initialization module to optimize the initialization process for a high coverage and low repetition rate query distribution, which further helps the proposed affiliated transformer decoder to achieve more accurate results. (ii) The proposed affiliated transformer decoder suppresses the interference of noise background queries and helps the foreground queries focus on discriminative parts for more accurate instance segmentation. (iii) Extensive experimental results on two standard benchmarks, ScanNetV2 [8] and S3DIS [1], demonstrate that the proposed model performs favorably against state-" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18517" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 232, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 232, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 232, + 83 + ], + "type": "text", + "content": "of-the-art 3D instance segmentation methods." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 95, + 133, + 107 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 95, + 133, + 107 + ], + "spans": [ + { + "bbox": [ + 47, + 95, + 133, + 107 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 115, + 286, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 115, + 286, + 163 + ], + "spans": [ + { + "bbox": [ + 47, + 115, + 286, + 163 + ], + "type": "text", + "content": "In this section, we briefly overview related works on 3D instance segmentation, including proposal-based methods, grouping-based methods, and instance segmentation with transformer." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 163, + 286, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 163, + 286, + 330 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 286, + 330 + ], + "type": "text", + "content": "Proposal-based Methods. Existing proposal-based methods are greatly influenced by the success of Mask R-CNN [14] for 2D instance segmentation. GSPN [45] takes an analysis-by-synthesis strategy to generate high-quality 3D proposals, which are refined by a region-based PointNet [34]. 3D-BoNet [44] uses PointNet++ [35] to extract features from point clouds and applies Hungarian matching [18] to generate 3D bounding boxes. GICN [24] approximates the instance center of each object as a Gaussian distribution. 3D-MPA [11] predicts centers of instances and employs a graph-based convolutional network to cluster points near the centers to refine proposal features. The proposal-based methods have high expectations for the quality of proposals." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 331, + 286, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 286, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 286, + 533 + ], + "type": "text", + "content": "Grouping-based Methods. Grouping-based methods produce per-point predictions, such as semantic categories and geometric offsets, and then group points into instances. To group points, MTML [19] uses a multi-task learning strategy. PointGroup [17] segments objects on the original and offset-shifted point clouds and uses the ScoreNet to predict scores for instances. HAIS [4] extends PointGroup by absorbing surrounding fragments of instances and then refining the instances based on intra-instance prediction. SSTNet [23] constructs a tree network from precomputed superpoints and splits non-similar nodes to get object instances. SoftGroup [39] groups on soft semantic scores instead of hard semantic prediction and processes each proposal to refine positive samples and suppress negative ones. Although the grouping-based approaches require many manual settings, they have dominated the field until recently." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 534, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 286, + 713 + ], + "type": "text", + "content": "Instance Segmentation with Transformer. Transformer [38] introduces the self-attention mechanism to model long-range dependencies and has been widely applied in computer vision tasks such as image classification [10, 3], object detection [2, 9], and segmentation [48, 6, 5]. Recently, DETR [2] has been proposed as a new paradigm to use object queries for object detection in an image. Based on the set prediction mechanism proposed in DETR, MaskFormer [6] employs a transformer decoder to compute a set of pairs, each consisting of a class prediction and a mask embedding vector, to solve both semantic and instance segmentation tasks in a unified manner. Mask2Former [5] outperforms state-of-the-art specialized architectures on all considered datasets for 2D image semantic, instance, and panoptic segmentation. The success" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": "of transformer has come to prominence in some 3D point cloud tasks such as 3D object detection [28, 25] and 3D semantic segmentation [47]. However, applications of transformer to 3D instance segmentation tasks have yet to be exploited profoundly. DyCo3D [15] uses a transformer at the bottleneck of the feature backbone to increase the receptive field size. Mask3D [36] proposes the first transformer framework for 3D instance segmentation and achieves the state-of-the-art performance. In Mask3D, each object instance is represented as an instance query, and a vanilla transformer decoder is applied to predict instance masks. In this paper, we design a novel query initialization module to effectively initialize queries and formulate a denoising module with contrastive loss to suppress the interference of noise background queries. Eventually, QueryFormer achieves superior results with better query refinement." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 276, + 361, + 289 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 276, + 361, + 289 + ], + "spans": [ + { + "bbox": [ + 306, + 276, + 361, + 289 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 297, + 545, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 545, + 392 + ], + "type": "text", + "content": "This section provides the details of our proposed method. We first illustrate the overview of the proposed method in Section 3.1, and then introduce the proposed Query Initialization Module in Section 3.2. In Section 3.3, we explain how the Affiliated Transformer Decoder works to suppress the undesirable interference of noise background queries on isntance segmentation. Finally, we elaborate the model training and inference in Section 3.4." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 402, + 373, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 402, + 373, + 414 + ], + "spans": [ + { + "bbox": [ + 306, + 402, + 373, + 414 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 422, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 545, + 624 + ], + "type": "text", + "content": "The goal of 3D instance segmentation is to determine the categories and binary masks of all foreground objects in the scene. Unlike the bounding boxes of 3D object detection, 3D instance segmentation requires further accurate delineation of the mask. The architecture of our method is illustrated in Figure 3(a). Assuming that the input point cloud has " + }, + { + "bbox": [ + 304, + 422, + 545, + 624 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 422, + 545, + 624 + ], + "type": "text", + "content": " points, each point contains position " + }, + { + "bbox": [ + 304, + 422, + 545, + 624 + ], + "type": "inline_equation", + "content": "x, y, z" + }, + { + "bbox": [ + 304, + 422, + 545, + 624 + ], + "type": "text", + "content": " and color " + }, + { + "bbox": [ + 304, + 422, + 545, + 624 + ], + "type": "inline_equation", + "content": "r, g, b" + }, + { + "bbox": [ + 304, + 422, + 545, + 624 + ], + "type": "text", + "content": " information. First, we use a 3D-UNet based on sparse convolution for multi-level feature extraction " + }, + { + "bbox": [ + 304, + 422, + 545, + 624 + ], + "type": "inline_equation", + "content": "F_{0}, F_{1}, F_{2}" + }, + { + "bbox": [ + 304, + 422, + 545, + 624 + ], + "type": "text", + "content": ". To select the query points with high coverage rate and low repetition rate from the scene, we input the seed points " + }, + { + "bbox": [ + 304, + 422, + 545, + 624 + ], + "type": "inline_equation", + "content": "P_{seed}" + }, + { + "bbox": [ + 304, + 422, + 545, + 624 + ], + "type": "text", + "content": " sampled by Farthest Point Sampling (FPS) into the Query Initialization Module (QIM). Through feature fusion in the aggregation module and filtering in the set grouping, we get the high quality query points " + }, + { + "bbox": [ + 304, + 422, + 545, + 624 + ], + "type": "inline_equation", + "content": "Q_{1}" + }, + { + "bbox": [ + 304, + 422, + 545, + 624 + ], + "type": "text", + "content": ". Finally, we input the obtained query points into the proposed Affiliated Transformer Decoder (ATD) to get the final predictions." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 634, + 460, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 634, + 460, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 634, + 460, + 647 + ], + "type": "text", + "content": "3.2. Query Initialization Module" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Before we introduce the module, we give the definition of two concepts (coverage rate and repetition rate of query points). The Coverage Rate (CR) of query points indicates the number " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " of instances contained in the query points as a percentage of the total number " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "N_{ins}" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " of instances in the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18518" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 61, + 531, + 195 + ], + "blocks": [ + { + "bbox": [ + 63, + 61, + 531, + 195 + ], + "lines": [ + { + "bbox": [ + 63, + 61, + 531, + 195 + ], + "spans": [ + { + "bbox": [ + 63, + 61, + 531, + 195 + ], + "type": "image", + "image_path": "bce3256db7d0977cae770f3621d375d94c84a50a98dbafa1023690200bff132b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 63, + 198, + 265, + 369 + ], + "blocks": [ + { + "bbox": [ + 63, + 198, + 265, + 369 + ], + "lines": [ + { + "bbox": [ + 63, + 198, + 265, + 369 + ], + "spans": [ + { + "bbox": [ + 63, + 198, + 265, + 369 + ], + "type": "image", + "image_path": "b26932b2561adba67230598c299d333cffda62b7464c1ff920fd20fb47bb96b6.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 371, + 545, + 426 + ], + "lines": [ + { + "bbox": [ + 46, + 371, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 545, + 426 + ], + "type": "text", + "content": "Figure 3. The overview of our query refinement transformer for 3D instance segmentation. As shown in (a), we first generate seed points " + }, + { + "bbox": [ + 46, + 371, + 545, + 426 + ], + "type": "inline_equation", + "content": "P_{seed}" + }, + { + "bbox": [ + 46, + 371, + 545, + 426 + ], + "type": "text", + "content": " by sampling from the raw point cloud. Next, we design the Query Initialization Module to improve the coverage rate and reduce the repetition rate of seed points. Afterwards, we send the generated high-quality query points " + }, + { + "bbox": [ + 46, + 371, + 545, + 426 + ], + "type": "inline_equation", + "content": "Q_{1}" + }, + { + "bbox": [ + 46, + 371, + 545, + 426 + ], + "type": "text", + "content": " to the Affiliated Transformer Decoder to generate the final instance masks. Meanwhile, we design the Denoising Module to alleviate the interference of noise background queries on instance mask prediction. The details of each module are shown in (b), (c), (d) and (e)." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 276, + 198, + 399, + 367 + ], + "blocks": [ + { + "bbox": [ + 276, + 198, + 399, + 367 + ], + "lines": [ + { + "bbox": [ + 276, + 198, + 399, + 367 + ], + "spans": [ + { + "bbox": [ + 276, + 198, + 399, + 367 + ], + "type": "image", + "image_path": "607a8adfddcfa60332440869ed7c5b653ab2b0d83e4d94d3ca687a0ce9ee894c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 408, + 198, + 529, + 368 + ], + "blocks": [ + { + "bbox": [ + 408, + 198, + 529, + 368 + ], + "lines": [ + { + "bbox": [ + 408, + 198, + 529, + 368 + ], + "spans": [ + { + "bbox": [ + 408, + 198, + 529, + 368 + ], + "type": "image", + "image_path": "6ac5a4678fd9f9f300e298e0224e14eafd009fe50322fcfa27b998f37faaf44c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 436, + 189, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 436, + 189, + 447 + ], + "spans": [ + { + "bbox": [ + 47, + 436, + 189, + 447 + ], + "type": "text", + "content": "scene, which can be formulated as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 131, + 456, + 287, + 468 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 131, + 456, + 287, + 468 + ], + "spans": [ + { + "bbox": [ + 131, + 456, + 287, + 468 + ], + "type": "interline_equation", + "content": "C R = N _ {p} / N _ {i n s}. \\tag {1}", + "image_path": "affea4a201bf42e4b5eab73a087ad362c64213df85452fe72ec7e62470f430a2.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 467, + 287, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 467, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 467, + 287, + 502 + ], + "type": "text", + "content": "The Repetition Rate (RR) of query points indicates the proportion of instances covered by repetition in the query points, which can be formulated as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 118, + 506, + 287, + 520 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 506, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 118, + 506, + 287, + 520 + ], + "type": "interline_equation", + "content": "R R = \\left(N _ {f} - N _ {p}\\right) / N _ {f}, \\tag {2}", + "image_path": "b8acba8259f50a9f6988a4856fe93d70a844e4891d929fb8536f9656660e68f7.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 522, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 605 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 522, + 287, + 605 + ], + "type": "inline_equation", + "content": "N_{f}" + }, + { + "bbox": [ + 46, + 522, + 287, + 605 + ], + "type": "text", + "content": " denotes the number of foreground points in the query points. The previous methods [36] usually use FPS to select query locations. However, FPS makes it challenging to balance the coverage and repetition rates. As shown in Figure 3(b), to solve this problem, we propose the Query Initialization Module, which contains two main submodules, the aggregation module and the set grouping module." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 606, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 606, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 606, + 287, + 713 + ], + "type": "text", + "content": "Aggregation Module. In feature aggregation, we design a module that allows the point features in the same instance to fuse while reducing the interference of point features in other adjacent instances. As shown in Figure 3(c), the module contains three parts, cross-attention layer, correlation-based self-attention layer and feed-forward layer. First, we use the cross-attention mechanism to update the features of the seed points " + }, + { + "bbox": [ + 46, + 606, + 287, + 713 + ], + "type": "inline_equation", + "content": "P_{\\text{seed}}" + }, + { + "bbox": [ + 46, + 606, + 287, + 713 + ], + "type": "text", + "content": " using the features of the superpoints in the scene. Here we initialize the seed point features by" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 436, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 436, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 436, + 545, + 544 + ], + "type": "text", + "content": "encoding the coordinates of the seed points. After that, the seed point features are input to the correlation-based self-attention mechanism. Unlike the previous self-attention mechanism, we use the information cues from the correlation relations in the attention map for feature fusion, and this design promotes the appropriate correlations of relevant seed-seed pairs and suppress the erroneous correlations of irrelevant seed-seed pairs. Specifically, we first calculate the similarity matrix of seed point features, as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 380, + 544, + 545, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 544, + 545, + 571 + ], + "spans": [ + { + "bbox": [ + 380, + 544, + 545, + 571 + ], + "type": "interline_equation", + "content": "M = \\frac {Q K ^ {T}}{\\sqrt {C}} w _ {M} + P, \\tag {3}", + "image_path": "b02477e76dc8ae95897b121160f4b1359f6bf52621fb11bd637fd0df34f4240d.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 571, + 545, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 571, + 545, + 618 + ], + "spans": [ + { + "bbox": [ + 304, + 571, + 545, + 618 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 571, + 545, + 618 + ], + "type": "inline_equation", + "content": "w_{M}" + }, + { + "bbox": [ + 304, + 571, + 545, + 618 + ], + "type": "text", + "content": " is a linear projection, " + }, + { + "bbox": [ + 304, + 571, + 545, + 618 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 571, + 545, + 618 + ], + "type": "text", + "content": " represents the position embeddings of seed points. We use the similarity matrix of features as the new features to calculate the similarity, with the following formula:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 365, + 615, + 545, + 642 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 615, + 545, + 642 + ], + "spans": [ + { + "bbox": [ + 365, + 615, + 545, + 642 + ], + "type": "interline_equation", + "content": "M ^ {c} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathrm {Q} _ {\\mathrm {M}} \\mathrm {K} _ {\\mathrm {M}} ^ {\\mathrm {T}}}{\\sqrt {\\mathrm {C} _ {\\mathrm {M}}}}\\right) \\mathrm {M}. \\tag {4}", + "image_path": "5df2db3a156126caa2e1fc04465313bbfdfec96768440973b931ecfcdaecb73b.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": "Then we calculate the updated features " + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "inline_equation", + "content": "F_{\\text{seed}}^c" + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": " for each seed point based on the similarity matrix " + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "inline_equation", + "content": "M^c" + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": ". Finally, we input " + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "inline_equation", + "content": "F_{\\text{seed}}^c" + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": " into the feed-forward layer and then predict the mask, category and IoU scores by different MLP heads." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Many-to-one Matching. Different from the one-to-one matching[18] used previously, we use many-to-one match" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18519" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": "ing in the aggregation module. Formally, we introduce a pairwise cost matrix " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "CM_{k}" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " to evaluate the similarity of seed point " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " and the k-th ground-truth. " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "CM_{k}" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " is determined by classification probability, superpoint mask cost and distance cost. We will introduce how to obtain the cost matrix in the supplementary material. With the cost matrix, we assign corresponding instance to each seed point," + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 80, + 159, + 287, + 192 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 159, + 287, + 192 + ], + "spans": [ + { + "bbox": [ + 80, + 159, + 287, + 192 + ], + "type": "interline_equation", + "content": "I n s _ {q} = \\left\\{ \\begin{array}{l} \\arg \\min _ {k} C M _ {k}, i f \\min _ {k} D _ {k} < \\tau , \\\\ - 1, e l s e, \\end{array} \\right. \\tag {5}", + "image_path": "93dcf49c164c97ce2fcba06f66cab84c8d7a5b8d01cc3424c3ecb26327bdf3f2.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 194, + 287, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 287, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 287, + 242 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 194, + 287, + 242 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 194, + 287, + 242 + ], + "type": "text", + "content": " represents a threshold, " + }, + { + "bbox": [ + 46, + 194, + 287, + 242 + ], + "type": "inline_equation", + "content": "D_{k}" + }, + { + "bbox": [ + 46, + 194, + 287, + 242 + ], + "type": "text", + "content": " represents the distance between the coordinate of seed point " + }, + { + "bbox": [ + 46, + 194, + 287, + 242 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 194, + 287, + 242 + ], + "type": "text", + "content": " and the centerpoint of the k-th ground-truth, and -1 represents that no instance matches the seed point." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 243, + 288, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 288, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 288, + 397 + ], + "type": "text", + "content": "Set Grouping Module. The set grouping module aims to improve coverage rate and reduce repetition rate, which contains shift and IoU-guided NMS [29] operations. The shift operation offsets seed points to the centers of the instances to ensure a high coverage rate so that most foreground instances can have a corresponding seed point. While the IoU-guided NMS operation filters out duplicate seed points to ensure that each foreground instance retains only one high-quality seed point thus reducing the repetition rate of seed points. Specifically, we first use a MLP to predict each seed point " + }, + { + "bbox": [ + 46, + 243, + 288, + 397 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 243, + 288, + 397 + ], + "type": "text", + "content": " relative to its matching instance " + }, + { + "bbox": [ + 46, + 243, + 288, + 397 + ], + "type": "inline_equation", + "content": "Ins_{q}" + }, + { + "bbox": [ + 46, + 243, + 288, + 397 + ], + "type": "text", + "content": " coordinate offset of the center point. After obtaining this coordinate offset, add it to the original coordinate " + }, + { + "bbox": [ + 46, + 243, + 288, + 397 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 243, + 288, + 397 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 126, + 401, + 287, + 414 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 401, + 287, + 414 + ], + "spans": [ + { + "bbox": [ + 126, + 401, + 287, + 414 + ], + "type": "interline_equation", + "content": "p = M L P (s) + p. \\tag {6}", + "image_path": "b18fba42965647b8feae3c329251249d370cb4679196432b53008279ebd2dbb8.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "text", + "content": "In this way, we can not only shift some background points to the foreground, but also close the points on the same instance, which will promote these points to learn similar features and help NMS remove redundant seed points. Then we get the corresponding instance mask " + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "inline_equation", + "content": "M_{ins}" + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "text", + "content": " of the seed point " + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "text", + "content": " by calculating the dot product between superpoint features and seed point features. And we obtain the final mask through sigmoid and a threshold of 0.5, as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 120, + 517, + 287, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 517, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 120, + 517, + 287, + 529 + ], + "type": "interline_equation", + "content": "M _ {b} = \\phi (M _ {i n s}) > 0. 5. \\tag {7}", + "image_path": "fc41d52dffbdc34c7821295c6c286d1b64676ee5453c7378e5c72b5e4b620fab.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 533, + 288, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 288, + 628 + ], + "type": "text", + "content": "Finally, we adopt the IoU-guided NMS to filter out a large number of redundant seed points. Here, the confidence of NMS is the multiplication of class score and IoU score. In order to enable the network to operate in parallel, we add extra seed points to satisfy the same number. Specifically, we do a " + }, + { + "bbox": [ + 46, + 533, + 288, + 628 + ], + "type": "inline_equation", + "content": "\\bigcup" + }, + { + "bbox": [ + 46, + 533, + 288, + 628 + ], + "type": "text", + "content": " operation on the mask " + }, + { + "bbox": [ + 46, + 533, + 288, + 628 + ], + "type": "inline_equation", + "content": "M_{b}" + }, + { + "bbox": [ + 46, + 533, + 288, + 628 + ], + "type": "text", + "content": " of all seed points and then operate FPS on the complement " + }, + { + "bbox": [ + 46, + 533, + 288, + 628 + ], + "type": "inline_equation", + "content": "M^{-}" + }, + { + "bbox": [ + 46, + 533, + 288, + 628 + ], + "type": "text", + "content": " of the whole scene to sample extra seed points." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 635, + 218, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 218, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 218, + 647 + ], + "type": "text", + "content": "3.3. Affiliated Transformer Decoder" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "In the Query Initialization Module, we have obtained queries with high coverage rate and low repetition rate through the Aggregation Module and Set Grouping Module. In this section, we describe how the Affiliated Transformer Decoder generates the final instance segmentation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "results with these queries. As shown in Figure 3(d), the Affiliated Transformer Decoder mainly contains the Cluster-based Layer and the Denoising Module." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 109, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 109, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 109, + 545, + 180 + ], + "type": "text", + "content": "Cluster-based Layer. Existing query-based methods [36] tend to compute similarities across the entire point cloud, which introduces large computational redundancy. Therefore, we propose the Cluster-based Layer. As shown in Figure 3(e), the method is based on the idea of clustering, assigning each point in the scene to its most similar query." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 181, + 545, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 181, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 304, + 181, + 545, + 217 + ], + "type": "text", + "content": "Specifically, we first calculate the similarity of the backbone features and the query features. Next, we assign each backbone feature via arg max operation as following," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 378, + 224, + 545, + 240 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 224, + 545, + 240 + ], + "spans": [ + { + "bbox": [ + 378, + 224, + 545, + 240 + ], + "type": "interline_equation", + "content": "I d x _ {k} = \\arg \\max _ {i} M _ {i, k}, \\tag {8}", + "image_path": "f5d673ff1b4c59039d21fa9bfc1de86e5951e1f3313fc1cec6076535b459b14b.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 244, + 545, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 244, + 545, + 328 + ], + "spans": [ + { + "bbox": [ + 304, + 244, + 545, + 328 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 244, + 545, + 328 + ], + "type": "inline_equation", + "content": "M_{i,k}" + }, + { + "bbox": [ + 304, + 244, + 545, + 328 + ], + "type": "text", + "content": " is a dot product of query " + }, + { + "bbox": [ + 304, + 244, + 545, + 328 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 244, + 545, + 328 + ], + "type": "text", + "content": " and backbone feature " + }, + { + "bbox": [ + 304, + 244, + 545, + 328 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 244, + 545, + 328 + ], + "type": "text", + "content": ". Therefore, we divide all backbone features into disjoint sets by clustering. Next, we do cross-attention for queries and their corresponding sets. By this way, we only need to calculate attention map on some similar backbone features for each query. Finally we input queries into the self-attention layer and the feed-forward layer." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 330, + 545, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 330, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 304, + 330, + 545, + 389 + ], + "type": "text", + "content": "One-to-one Matching. In this section, we use one-to-one matching to replace many-to-one matching in Section 3.2. Concretely, we obtain the cost matrix " + }, + { + "bbox": [ + 304, + 330, + 545, + 389 + ], + "type": "inline_equation", + "content": "CM" + }, + { + "bbox": [ + 304, + 330, + 545, + 389 + ], + "type": "text", + "content": " the same as Aggregation Module but replace arg min with Hungarian matching[18] to obtain the query-GT pairs." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 389, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 545, + 509 + ], + "type": "text", + "content": "Denoising Module. In section 3.2, we shift the background points around the foreground points to the center of the instance to improve the coverage rate. However, during the offset, not every point is well migrated to the center due to the different scales and classes of objects [40]. This leads to some background points that may affect the information aggregation of the foreground points. Therefore, we deal with the interference caused by background point offset in this module. We take the center of the instance from ground-truth and resample it, as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 384, + 514, + 545, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 514, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 384, + 514, + 545, + 529 + ], + "type": "interline_equation", + "content": "Q _ {g t} \\sim N \\left(C _ {g t}, \\sigma^ {2}\\right), \\tag {9}", + "image_path": "ba6ef76988a3137fd421758deb437c924e731d8507fa9b627e7a98f5f8341a80.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " means the Gaussian distribution and " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " represents deviation. We encode the perturbed GT centers " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "Q_{gt}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " together with the query points " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "Q_{1}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " obtained in the query initialization module and feed them into the affiliated transformer decoder. Then, we match the query outputs with the ground-truth in the dataset. The query with the minimal matching cost forms several positive pairs with the ground-truth perturbed centers. We encourage the output features of the positive queries to be consistent with the output features of the corresponding center points and drive the unmatched noise background queries away from the instance to reduce interference with the instance mask prediction. Therefore, we use the contrastive loss. Suppose the number of queries is " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ", the number of ground-truth is " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "N_{gt}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ", ground-truth " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " generates " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " perturbed GT centers, query " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " and the perturbed" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18520" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 238, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 238, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 238, + 85 + ], + "type": "text", + "content": "GT centers of ground-truth " + }, + { + "bbox": [ + 47, + 72, + 238, + 85 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 72, + 238, + 85 + ], + "type": "text", + "content": " are positive pairs," + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 93, + 289, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 93, + 289, + 137 + ], + "spans": [ + { + "bbox": [ + 47, + 93, + 289, + 137 + ], + "type": "interline_equation", + "content": "L _ {\\text {c o n t}} = - \\frac {1}{| \\beta N _ {g t} |} \\sum_ {j = 1} ^ {N _ {g t}} \\sum_ {m = 1} ^ {\\beta} \\log \\left(\\frac {\\exp \\left(d \\left(q _ {i} , q _ {j , m} ^ {g t}\\right) / \\varepsilon\\right)}{\\sum_ {s = 1} ^ {K} \\exp \\left(d \\left(q _ {s} , q _ {j , m} ^ {g t}\\right) / \\varepsilon\\right)}\\right), \\tag {10}", + "image_path": "3e6a85a429475b0d1a228e7c23fbf5e87b55046016ed1b0bcf11dab0555f2500.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 138, + 287, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 138, + 287, + 163 + ], + "spans": [ + { + "bbox": [ + 47, + 138, + 287, + 163 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 138, + 287, + 163 + ], + "type": "inline_equation", + "content": "d(.,.)" + }, + { + "bbox": [ + 47, + 138, + 287, + 163 + ], + "type": "text", + "content": " is a distance measurement and " + }, + { + "bbox": [ + 47, + 138, + 287, + 163 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 47, + 138, + 287, + 163 + ], + "type": "text", + "content": " is the temperature in contrastive learning." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 170, + 178, + 182 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 170, + 178, + 182 + ], + "spans": [ + { + "bbox": [ + 47, + 170, + 178, + 182 + ], + "type": "text", + "content": "3.4. Training and Inference" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 189, + 287, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 189, + 287, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 189, + 287, + 297 + ], + "type": "text", + "content": "As to query initialization module, only the aggregation modules are supervised. We assign the unmatched queries with " + }, + { + "bbox": [ + 46, + 189, + 287, + 297 + ], + "type": "inline_equation", + "content": "N_{\\text{class}} + 1" + }, + { + "bbox": [ + 46, + 189, + 287, + 297 + ], + "type": "text", + "content": " class label and compute the cross-entropy loss " + }, + { + "bbox": [ + 46, + 189, + 287, + 297 + ], + "type": "inline_equation", + "content": "L_{\\text{cls}}" + }, + { + "bbox": [ + 46, + 189, + 287, + 297 + ], + "type": "text", + "content": " for each query. Then we compute the superpoint mask loss which consists of binary cross-entropy loss " + }, + { + "bbox": [ + 46, + 189, + 287, + 297 + ], + "type": "inline_equation", + "content": "L_{\\text{bce}}" + }, + { + "bbox": [ + 46, + 189, + 287, + 297 + ], + "type": "text", + "content": " and dice loss " + }, + { + "bbox": [ + 46, + 189, + 287, + 297 + ], + "type": "inline_equation", + "content": "L_{\\text{dice}}" + }, + { + "bbox": [ + 46, + 189, + 287, + 297 + ], + "type": "text", + "content": " [27] for each query-GT pair. Meanwhile, we compute the score loss " + }, + { + "bbox": [ + 46, + 189, + 287, + 297 + ], + "type": "inline_equation", + "content": "L_{\\text{sco}}" + }, + { + "bbox": [ + 46, + 189, + 287, + 297 + ], + "type": "text", + "content": " using binary cross-entropy loss. Suppose that the Hungarian matching assigns the k-th ground-truth to the i-th query," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 110, + 306, + 287, + 319 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 306, + 287, + 319 + ], + "spans": [ + { + "bbox": [ + 110, + 306, + 287, + 319 + ], + "type": "interline_equation", + "content": "L _ {s c o, i} = B C E \\left(o _ {i}, I o U _ {i, k}\\right), \\tag {11}", + "image_path": "29a54b887f86c63288ec986f1668cead80b71f51252150d9ddf05ee05a71a1c8.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 328, + 287, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 328, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 47, + 328, + 287, + 376 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 328, + 287, + 376 + ], + "type": "inline_equation", + "content": "o_i" + }, + { + "bbox": [ + 47, + 328, + 287, + 376 + ], + "type": "text", + "content": " represents the IoU prediction of query " + }, + { + "bbox": [ + 47, + 328, + 287, + 376 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 328, + 287, + 376 + ], + "type": "text", + "content": ". In addition, we add the offset loss " + }, + { + "bbox": [ + 47, + 328, + 287, + 376 + ], + "type": "inline_equation", + "content": "L_{off}" + }, + { + "bbox": [ + 47, + 328, + 287, + 376 + ], + "type": "text", + "content": " which uses L1loss to close the distance between the coordinates of queries and the instance center points." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 123, + 384, + 287, + 399 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 384, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 123, + 384, + 287, + 399 + ], + "type": "interline_equation", + "content": "L _ {o f f, i} = \\left| p _ {i} - p _ {k} ^ {G T} \\right| \\tag {12}", + "image_path": "9190899da583b1019b7d66ee37c179df5eea2f2a87d96009697d0f16235d98ba.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 408, + 168, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 408, + 168, + 419 + ], + "spans": [ + { + "bbox": [ + 47, + 408, + 168, + 419 + ], + "type": "text", + "content": "The overall loss is defined as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 88, + 427, + 246, + 456 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 427, + 246, + 456 + ], + "spans": [ + { + "bbox": [ + 88, + 427, + 246, + 456 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L = \\lambda_ {1} \\cdot L _ {d i c e} + \\lambda_ {2} \\cdot L _ {b c e} + \\lambda_ {3} \\cdot L _ {c l s} \\\\ + \\lambda_ {4} \\cdot L _ {\\text {o f f}} + \\lambda_ {5} \\cdot L _ {s c o}. \\\\ \\end{array}", + "image_path": "31eeee82659d6f930932f176e5a74b9e0a75c061a64016aa1cf5745033231864.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 464, + 287, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 287, + 500 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 287, + 500 + ], + "type": "text", + "content": "To Affiliated Transformer Decoder, we also add losses after each Cluster-based Layer. Compared to " + }, + { + "bbox": [ + 47, + 464, + 287, + 500 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 47, + 464, + 287, + 500 + ], + "type": "text", + "content": ", we add contrastive loss which is introduced in Section 3.3." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 123, + 510, + 287, + 522 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 510, + 287, + 522 + ], + "spans": [ + { + "bbox": [ + 123, + 510, + 287, + 522 + ], + "type": "interline_equation", + "content": "L ^ {*} = L + \\lambda_ {6} \\cdot L _ {\\text {c o n t}} \\tag {14}", + "image_path": "775d9c902a1446a94fd6215c5f19e0a27d0b29cabd917497c8a747c03ea5e0bd.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 532, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 532, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 47, + 532, + 287, + 568 + ], + "type": "text", + "content": "Following DN-DETR[22], we use the same losses as query-GT pairs to supervise the perturbed GT centers. This can ensure the perturbed GT centers would not diverge." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 568, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 568, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 47, + 568, + 287, + 604 + ], + "type": "text", + "content": "During inference, it should be noted that perturbed GT centers will not be generated, that is, we only infer queries generated by Query Initialization Module." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 615, + 127, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 615, + 127, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 615, + 127, + 628 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 635, + 163, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 163, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 163, + 647 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 653, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 287, + 712 + ], + "type": "text", + "content": "Dataset and Metrics. We conduct our experiments on ScanNetV2 [8] and S3DIS [1] datasets. ScanNetV2 includes 1,613 scenes with 18 instance categories. Among them, 1,201 scenes are used for training, 312 scenes are used for validation, and 100 scenes are used for test. S3DIS" + } + ] + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 307, + 86, + 547, + 259 + ], + "blocks": [ + { + "bbox": [ + 332, + 69, + 518, + 80 + ], + "lines": [ + { + "bbox": [ + 332, + 69, + 518, + 80 + ], + "spans": [ + { + "bbox": [ + 332, + 69, + 518, + 80 + ], + "type": "text", + "content": "Table 1. Comparison on ScanNetV2 benchmark." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 86, + 547, + 259 + ], + "lines": [ + { + "bbox": [ + 307, + 86, + 547, + 259 + ], + "spans": [ + { + "bbox": [ + 307, + 86, + 547, + 259 + ], + "type": "table", + "html": "
MethodScanNetV2
mAPAP@50AP@25Box AP@50Box AP@25
F-PointNet [33]///10.819.8
GSPN [45]/37.853.417.730.6
3D-SIS [16]/18.735.722.540.2
VoteNet [32]///33.558.6
3D-MPA [11]35.351.972.449.264.2
DyCo3D [15]40.661.0/45.358.9
PointGroup [17]34.856.971.348.961.5
MaskGroup [49]42.063.374.0//
OccuSeg [13]44.260.7///
HAIS [4]43.564.475.653.164.3
SSTNet [23]49.464.37452.762.5
SoftGroup [39]45.867.678.959.471.6
DKNet [43]50.866.976.959.067.4
Mask3D [36]55.273.782.956.671.0
Ours56.574.283.361.773.4
", + "image_path": "af889b0c52885b4e9bfda50051e38059e6a85c076db19f84e81a7db1e8124ffe.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_body" + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 281, + 545, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 545, + 424 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 545, + 424 + ], + "type": "text", + "content": "is a large-scale indoor dataset collected from six different areas. It contains 272 scenes with 13 instance categories. Following previous works [39], we evaluate our approach: testing on Area 5 and 6-fold cross-validation. AP@25 and AP@50 represent the average precision scores with IoU thresholds " + }, + { + "bbox": [ + 304, + 281, + 545, + 424 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 304, + 281, + 545, + 424 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 281, + 545, + 424 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 281, + 545, + 424 + ], + "type": "text", + "content": ", and mAP represents the average of all the APs with IoU thresholds ranging from " + }, + { + "bbox": [ + 304, + 281, + 545, + 424 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 281, + 545, + 424 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 281, + 545, + 424 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 304, + 281, + 545, + 424 + ], + "type": "text", + "content": " with a step size of " + }, + { + "bbox": [ + 304, + 281, + 545, + 424 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 281, + 545, + 424 + ], + "type": "text", + "content": ". On ScanNetV2, we report mAP, AP@50 and AP@25. Moreover, we also report the Box AP@50 and AP@25 results following SoftGroup [39] and DKNet [43]. On S3DIS, we report mAP, AP@50, mean precision (mPrec), and mean recall (mRec)." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "type": "text", + "content": "Implementation Details. We train our model on a single RTX3090 with a batch size of 5 for 600 epochs. We use AdamW [26] and a one-cycle learning rate schedule [37] with a maximal learning rate of " + }, + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "type": "text", + "content": ". We voxelize the point clouds with the size of " + }, + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "type": "inline_equation", + "content": "0.02\\mathrm{m}" + }, + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "type": "text", + "content": ". For a fair comparison, the point encoder is a Minkowski Res16UNet34C [7], which is the same as Mask3D [36]. For hyperparameters, we tune " + }, + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\tau, \\sigma, \\varepsilon, \\beta" + }, + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "type": "text", + "content": " as 0.6, 0.05, 0.5, 3 respectively. " + }, + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\lambda_1, \\lambda_2, \\lambda_3, \\lambda_4, \\lambda_5" + }, + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "type": "text", + "content": " in Equation 13 and 14 are set as 2, 5, 2, 3, 2. " + }, + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\lambda_6" + }, + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "type": "text", + "content": " in Equation 14 is set as 2. More implementation details are stated in the supplementary material." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 563, + 544, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 544, + 576 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 544, + 576 + ], + "type": "text", + "content": "4.2. Comparison with the state-of-the-art methods." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "text", + "content": "ScanNetV2. As shown in Table 1, we compare our approach with existing state-of-the-art methods on the ScanNetV2 validation set. Our approach attains relative " + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "inline_equation", + "content": "2.4\\%" + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "text", + "content": " improvements on mAP and shows relative " + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "inline_equation", + "content": "3.9\\%" + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "inline_equation", + "content": "2.5\\%" + }, + { + "bbox": [ + 304, + 582, + 545, + 700 + ], + "type": "text", + "content": " improvements on Box AP@50 and Box AP@25, respectively. On these metrics, our proposed model achieves state-of-the-art results. From Figure 4, we can see visualization of instance segmentation results. Compared to Mask3D, our approach correctly segments each instance and produces finer segmentation results." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": "S3DIS. 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The red boxes highlight the key regions." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 425, + 64, + 542, + 144 + ], + "blocks": [ + { + "bbox": [ + 425, + 64, + 542, + 144 + ], + "lines": [ + { + "bbox": [ + 425, + 64, + 542, + 144 + ], + "spans": [ + { + "bbox": [ + 425, + 64, + 542, + 144 + ], + "type": "image", + "image_path": "a2385f571c621b6a01671ec51325683b9bdd26d7006059020101365b269c43f0.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 429, + 147, + 537, + 213 + ], + "blocks": [ + { + "bbox": [ + 429, + 147, + 537, + 213 + ], + "lines": [ + { + "bbox": [ + 429, + 147, + 537, + 213 + ], + "spans": [ + { + "bbox": [ + 429, + 147, + 537, + 213 + ], + "type": "image", + "image_path": "f63bd2c503fa463d32a1bc609adb368e873acbd61661faa1705782e338882b81.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 482, + 216, + 493, + 224 + ], + "lines": [ + { + "bbox": [ + 482, + 216, + 493, + 224 + ], + "spans": [ + { + "bbox": [ + 482, + 216, + 493, + 224 + ], + "type": "text", + "content": "GT" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 48, + 261, + 287, + 416 + ], + "blocks": [ + { + "bbox": [ + 83, + 244, + 251, + 256 + ], + "lines": [ + { + "bbox": [ + 83, + 244, + 251, + 256 + ], + "spans": [ + { + "bbox": [ + 83, + 244, + 251, + 256 + ], + "type": "text", + "content": "Table 2. Comparison on S3DIS benchmark." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 261, + 287, + 416 + ], + "lines": [ + { + "bbox": [ + 48, + 261, + 287, + 416 + ], + "spans": [ + { + "bbox": [ + 48, + 261, + 287, + 416 + ], + "type": "table", + "html": "
MethodS3DIS Area 5S3DIS 6-fold CV
mAPAP@50mPrecmRecmAPAP@50mPrecmRec
SGPN [41]//36.028.7//38.231.2
ASIS [42]//55.342.4//63.647.5
3D-Bonet [44]//57.540.2//65.647.6
OccuSeg [13]//////72.860.3
3D-MPA [11]//63.158.0//66.764.1
PointGroup [17]/57.861.962.1/64.069.669.2
DyCo3D [15]//64.364.2////
MaskGroup [49]/65.062.964.7/69.966.669.6
SSTNet [23]42.759.365.564.254.167.873.573.4
SoftGroup [39]51.666.173.666.654.468.975.369.8
DKNet [43]//70.865.3//75.371.1
Mask3D [36]56.569.368.770.760.772.070.572.5
Ours57.769.970.572.262.073.372.773.4
", + "image_path": "a20768098dc2dd4e3af97a0ab39633cb627815666c9f7ee2807e184786dc31b7.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 86, + 437, + 247, + 479 + ], + "blocks": [ + { + "bbox": [ + 72, + 422, + 261, + 432 + ], + "lines": [ + { + "bbox": [ + 72, + 422, + 261, + 432 + ], + "spans": [ + { + "bbox": [ + 72, + 422, + 261, + 432 + ], + "type": "text", + "content": "Table 3. Comparison on ScanNet200 benchmark." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 86, + 437, + 247, + 479 + ], + "lines": [ + { + "bbox": [ + 86, + 437, + 247, + 479 + ], + "spans": [ + { + "bbox": [ + 86, + 437, + 247, + 479 + ], + "type": "table", + "html": "
MethodmAPAP@50AP@25
Mask3D [36]27.437.042.3
Ours28.137.143.4
", + "image_path": "a1bb289999b5b225bf998c34ba9c4c4d526a008afed24e02c1027bf8e8dc4eaf.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 494, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 287, + 564 + ], + "type": "text", + "content": "5 and 6-fold cross-validation respectively. For a fair comparison, Mask3D and our method are all supervised by instance labels at the superpoint level instead of the point level. As shown in Table 2, our superior results on some important metrics validate the effects and generalization of our method." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 566, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 566, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 566, + 287, + 625 + ], + "type": "text", + "content": "ScanNet200. We also compare our approach with existing state-of-the-art method on the ScanNet200 validation set, which includes a magnitude more class categories than ScanNetV2. As shown in Table 3, the results demonstrate the remarkable generalization of our model." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 47, + 634, + 186, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 186, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 186, + 647 + ], + "type": "text", + "content": "4.3. Effects of DBSCAN [12]." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "DBSCAN is a time-consuming density-based clustering algorithm that can separate multiple instances which are incorrectly predicted as a whole. Some methods with low coverage rates can easily divide multiple instances into a whole, so these methods rely heavily on DBSCAN for post-" + } + ] + } + ], + "index": 20 + }, + { + "type": "table", + "bbox": [ + 306, + 274, + 547, + 367 + ], + "blocks": [ + { + "bbox": [ + 305, + 244, + 547, + 266 + ], + "lines": [ + { + "bbox": [ + 305, + 244, + 547, + 266 + ], + "spans": [ + { + "bbox": [ + 305, + 244, + 547, + 266 + ], + "type": "text", + "content": "Table 4. Effects of DBSCAN. In this experiment, the number of queries in both methods is set to 100." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 274, + 547, + 367 + ], + "lines": [ + { + "bbox": [ + 306, + 274, + 547, + 367 + ], + "spans": [ + { + "bbox": [ + 306, + 274, + 547, + 367 + ], + "type": "table", + "html": "
MethodDBSCANScanNetV2S3DIS Area 5
mAP AP@50 AP@25mAP AP@50 AP@25
Mask3D [36]X53.773.082.553.967.073.9
✓54.774.082.956.569.375.6
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", + "image_path": "e0f320766b91b9ae8861892996bdaac9d48c78e977c09dffff701e4594fbe256.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "table_body" + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 387, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 387, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 545, + 567 + ], + "type": "text", + "content": "processing. As shown in Table 4, the high performance of Mask3D must be guaranteed by DBSCAN. However, profiting from our designed query initialization module and denoising module, our method can achieve an superior performance without support from DBSCAN. In order to show the effects of DBSCAN more explicitly, as shown in Figure 5, two chairs in Mask3D are not covered by queries, so the three chairs are jointly predicted. After the post-processing of DBSCAN, this problem has been alleviated. Although DBSCAN is effective, there are two problems. The first is that multiple hyperparameters need to be readjusted for different scenarios. The other is the time-consuming problem. For example, DBSCAN takes about 1 minute to process an indoor scenario. Therefore, our method can achieve superior performance at a low time cost." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 574, + 401, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 401, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 401, + 588 + ], + "type": "text", + "content": "4.4. Ablation Study." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Components Analysis. In this section, we perform extensive ablation studies on the ScanNetV2 dataset to evaluate the effects of each design. Table 5 demonstrates the performance of the model with different designs. Concretely, the second row demonstrates that the query initialization module improves by 1.6 on mAP with a high coverage rate and low repetition rate query distribution. The cluster-based layer is designed to reduce the complexity of calculations and therefore only makes a modest contribution to accuracy. In the fifth row, the denoising module" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18522" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 56, + 138, + 137 + ], + "blocks": [ + { + "bbox": [ + 59, + 56, + 138, + 137 + ], + "lines": [ + { + "bbox": [ + 59, + 56, + 138, + 137 + ], + "spans": [ + { + "bbox": [ + 59, + 56, + 138, + 137 + ], + "type": "image", + "image_path": "b0a03e81a504e2aae28076f7286042f78977bf1ce43680a92e1ca3ab64904b62.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 140, + 547, + 163 + ], + "lines": [ + { + "bbox": [ + 46, + 140, + 547, + 163 + ], + "spans": [ + { + "bbox": [ + 46, + 140, + 547, + 163 + ], + "type": "text", + "content": "Figure 5. Visualization of query distribution and instance segmentation results on the ScanNetV2 validation set. 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Evaluation of the model with different designs on ScanNetV2. QIM represents the Query Initialization Module, CL represents the Cluster-based Layer, DM is the Denoising Module." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 205, + 272, + 294 + ], + "lines": [ + { + "bbox": [ + 61, + 205, + 272, + 294 + ], + "spans": [ + { + "bbox": [ + 61, + 205, + 272, + 294 + ], + "type": "table", + "html": "
QIMCLDMDBSCANScanNetV2
mAPAP@50AP@25
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", + "image_path": "edecb8a49d39b395aa32e3d4cb50ab431777672f14d54932cbbb7c3b58a919bc.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 72, + 352, + 261, + 456 + ], + "blocks": [ + { + "bbox": [ + 46, + 303, + 288, + 346 + ], + "lines": [ + { + "bbox": [ + 46, + 303, + 288, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 288, + 346 + ], + "type": "text", + "content": "Table 6. Effects of QIM. Here, the experiment is conducted on ScanNetV2 without DBSCAN. CR means the coverage rate, while RR refers to the repetition rate. Higher CR and lower RR reflect a better result." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 72, + 352, + 261, + 456 + ], + "lines": [ + { + "bbox": [ + 72, + 352, + 261, + 456 + ], + "spans": [ + { + "bbox": [ + 72, + 352, + 261, + 456 + ], + "type": "table", + "html": "
MethodNumScanNetV2
CR↑RR↓mAPAP@50AP@25
Mask3D [36]500.540.4847.665.575.2
Mask3D1000.740.6453.773.082.5
Mask3D1500.830.7254.373.082.8
Mask3D5000.970.9952.870.679.9
Ours500.760.4354.072.982.5
Ours1000.890.4756.273.883.2
Ours1500.920.7055.372.583.0
", + "image_path": "d90e2804f0a4e1f40828185177fa8cc32d69a686b5fe40d905f77c240f58a786.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "text", + "content": "improves the performance by 0.8 on mAP through noise background query suppression. Since the query initialization module improves the sampling quality of the query, our method does not rely on DBSCAN post-processing. Therefore, after time-consuming DBSCAN post-processing, our results are only marginally improved." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": "Effects of QIM. As shown in Table 6, a large number of queries can not only bring a high coverage rate but also lead to a high repetition rate. Fewer queries always bring a lower repetition rate, but a lower coverage rate of the scene may follow. Therefore, we should balance the relationship between repetition and coverage rates when selecting the number of queries. The experimental results of Table 6 on ScanNetV2 also verify that higher experimental performance can be obtained by balancing the coverage and repetition rates. Thanks to the high-quality queries obtained in QIM, our method performs best when the number of queries is 100, while Mask3d performs best when the number of queries is 150. Therefore, our method achieves better performance with less computational overhead." + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 310, + 171, + 545, + 250 + ], + "blocks": [ + { + "bbox": [ + 310, + 171, + 545, + 250 + ], + "lines": [ + { + "bbox": [ + 310, + 171, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 310, + 171, + 545, + 250 + ], + "type": "image", + "image_path": "20ffb915ec989f4c90c48c85d219cdb445ecfa6b31b83e3e019b4b1afb5bfb50.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 253, + 547, + 308 + ], + "lines": [ + { + "bbox": [ + 305, + 253, + 547, + 308 + ], + "spans": [ + { + "bbox": [ + 305, + 253, + 547, + 308 + ], + "type": "text", + "content": "Figure 6. The visualization of segmentation results related to the denoising module in the affiliated transformer decoder. The red points represent the position of queries, the green points represent the position of noise background queries, and the red boxes highlight the key regions." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 331, + 327, + 520, + 361 + ], + "blocks": [ + { + "bbox": [ + 306, + 312, + 544, + 324 + ], + "lines": [ + { + "bbox": [ + 306, + 312, + 544, + 324 + ], + "spans": [ + { + "bbox": [ + 306, + 312, + 544, + 324 + ], + "type": "text", + "content": "Table 7. Efficiency comparison on a single cluster-based layer." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 331, + 327, + 520, + 361 + ], + "lines": [ + { + "bbox": [ + 331, + 327, + 520, + 361 + ], + "spans": [ + { + "bbox": [ + 331, + 327, + 520, + 361 + ], + "type": "table", + "html": "
MethodMemory(KB)FLOPs(G)Inference Time(ms)
Mask3D [36]48.82.31.1
Ours0.491.30.72
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MethodParameter(M)Runtime(ms)
HAIS [4]30.9578
SoftGroup [39]30.9588
SSTNet [23]/729
Mask3D [36]39.6578
Ours42.3487
", + "image_path": "1dd8411d6916433d1b708ed0fb0748e004a2011d106c37da4a5e1da8dfdf5261.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 183, + 286, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 183, + 286, + 255 + ], + "spans": [ + { + "bbox": [ + 46, + 183, + 286, + 255 + ], + "type": "text", + "content": "speed, our model is the fastest among all methods by reducing the decoder size. Concretely, Mask3D uses 12 layers of decoder, while our model only uses 8 layers. Although we add the Query Initialization Module, we adopt the superpoint features as the keys and values of cross attention, and down-sampling is done for each layer." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 266, + 119, + 278 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 266, + 119, + 278 + ], + "spans": [ + { + "bbox": [ + 47, + 266, + 119, + 278 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 287, + 286, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 287, + 286, + 406 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 286, + 406 + ], + "type": "text", + "content": "In this paper, we propose the Query Refinement Transformer for 3D instance segmentation. To solve the query sampling dilemma, we design a query initialization module to guarantee a high coverage rate of object instances while maintaining a low repetition rate. Furthermore, the well-designed affiliated transformer decoder suppresses the interference of noise background queries for better instance segmentation results. Extensive experiments conducted on two widely used 3D instance segmentation benchmarks demonstrate the superior performance of QueryFormer." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 418, + 162, + 431 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 418, + 162, + 431 + ], + "spans": [ + { + "bbox": [ + 47, + 418, + 162, + 431 + ], + "type": "text", + "content": "6. Acknowledgements" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 437, + 286, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 286, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 286, + 492 + ], + "type": "text", + "content": "This work was partially supported by the National Nature Science Foundation of China (Grant 62022078), National Defense Basic Scientific Research Program of China (Grant JCKY2021601B013) and the National Nature Science Foundation of China (Grant 62021001)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 515, + 105, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 515, + 105, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 515, + 105, + 528 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 52, + 536, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 52, + 536, + 287, + 590 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 536, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 52, + 536, + 287, + 590 + ], + "type": "text", + "content": "[1] Iro Armeni, Ozan Sener, Amir R Zamir, Helen Jiang, Ioannis Brilakis, Martin Fischer, and Silvio Savarese. 3d semantic parsing of large-scale indoor spaces. 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IEEE, 2022. 6, 7" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "18526" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Query6DoF_ Learning Sparse Queries as Implicit Shape Prior for Category-Level 6DoF Pose Estimation/4d1aafad-a31c-4773-aac8-62fd2260bfdc_content_list.json b/2023/Query6DoF_ Learning Sparse Queries as Implicit Shape Prior for Category-Level 6DoF Pose Estimation/4d1aafad-a31c-4773-aac8-62fd2260bfdc_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..6dee6a2f6b15b73faf24e38ee05706d18eaf3fd4 --- /dev/null +++ b/2023/Query6DoF_ Learning Sparse Queries as Implicit Shape Prior for Category-Level 6DoF Pose Estimation/4d1aafad-a31c-4773-aac8-62fd2260bfdc_content_list.json @@ -0,0 +1,1597 @@ +[ + { + "type": "text", + "text": "Query6DoF: Learning Sparse Queries as Implicit Shape Prior for Category-Level 6DoF Pose Estimation", + "text_level": 1, + "bbox": [ + 153, + 130, + 818, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ruiqi Wang $^{1}$ , Xinggang Wang $^{1}$ , Te Li $^{\\dagger,2,3}$ , Rong Yang $^{2,3}$ , Minhong Wan $^{\\dagger,2,3}$ , Wenyu Liu $^{\\dagger,1}$", + "bbox": [ + 135, + 214, + 833, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Hubei Key Laboratory of Smart Internet Technology, School of Electronic Information and Communications, Huazhong University of Science and Technology", + "bbox": [ + 84, + 252, + 885, + 282 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Research Center for Intelligent Robotics, Research Institute of Interdisciplinary Innovation, Zhejiang Lab, China $^{3}$ Zhejiang Engineering Research Center for Intelligent Robotics, China", + "bbox": [ + 147, + 282, + 820, + 310 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 354, + 313, + 372 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Category-level 6DoF object pose estimation intends to estimate the rotation, translation, and size of unseen objects. Many previous works use point clouds as a prelearned shape prior to overcome intra-category variability. The shape prior is deformed to reconstruct instances' point clouds in canonical space and to build dense 3D-3D correspondences between the observed and reconstructed point clouds. However, the pre-learned shape prior is not jointly optimized with estimation networks, and they are trained with a surrogate objective. We propose a novel 6D pose estimation network, named Query6DoF, based on a series of category-specific sparse queries that represent the prior shape. Each query represents a shape component, and these queries are learnable embeddings that can be optimized together with the estimation network according to the point cloud reconstruction loss, the normalized object coordinate loss, and the 6d pose estimation loss. Query6DoF adopts a deformation-and-matching paradigm with attention, where the queries dynamically extract features from regions of interest using the attention mechanism and then directly regress results. Furthermore, Query6DoF reduces computation overhead through the sparseness of the queries and the incorporation of a lightweight global information injection block. With the aforementioned design, Query6DoF achieves state-of-the-art (SOTA) pose estimation performance on the NOCS datasets. The source code and models are available at https://github.com/hustvl/Query6DoF.", + "bbox": [ + 73, + 393, + 473, + 816 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e34ba91f291e408c6a57e410f6633b07e3ac9fc2096063fbcb267123ba295735.jpg", + "image_caption": [ + "Figure 1: Comparisons with conventional works. a) Conventional methods adopt pre-learned shape prior and have a two-stage pipeline, i.e., deforming the prior and building correspondences between points. b) Our method uses sparse learnable queries as the shape prior and conducts query/feature-based deformation and matching." + ], + "image_footnote": [], + "bbox": [ + 503, + 354, + 893, + 527 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 657, + 633, + 674 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Category-level object pose estimation is aimed at estimating an object's rotation, translation, and size from an RGB-D scene within a given set of categories. This task has attracted increasing attention due to its vital role in robotics [5], 3D understanding [4, 22], and augmented reality [29]. Compared with instance-level object pose estimation, category-level object pose estimation doesn't require obtaining the object's CAD model in advance, making it more generally applicable.", + "bbox": [ + 496, + 686, + 893, + 823 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Many existing methods [2, 7, 16, 30, 41, 38, 20, 35] solve this problem as shown in Figure 1(a). First, they attempt to reconstruct the input object point cloud in the Normalized Object Coordinate Space [34] (NOCS). Then they estimate the 3D-3D correspondences between the input ob", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Corresponding authors: Wenyu Liu (liuwy@hust.edu.cn), Te Li (lite@zhejianglab.com) and Minhong Wan (wanmh@ zhejianglab.com).", + "bbox": [ + 75, + 862, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14055", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "served point cloud and the reconstructed object point cloud. Finally, they determine object poses and sizes by applying the Umeyama algorithm [31] to these correspondences. To handle intra-category variability, a shape prior, which represents a basic shape for objects in the same category, is introduced in [30] to this task. This shape prior is a set of point clouds pre-learned in NOCS for each category. Objects are reconstructed by deforming the shape prior. However, this approach has its drawbacks: 1) the shape prior is a dense representation of objects in a specific category, which is not only redundant but also makes the network computationally expensive. 2) the shape prior is pre-learned in advance and remains static during model training. Additionally, these methods are trained to predict the deformation field $D$ and a correspondence matrix $A$ , which is a surrogate task. 3) Conventional model architectures [30, 3, 2] typically rely on either pooling operations in the PointNet [26] style or 3D graph convolution (3DGC) [19] to explore geometry features. However, the pooling operation can result in the loss of local geometry features, and these operations are not adaptive to extract the feature information.", + "bbox": [ + 76, + 90, + 472, + 409 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these issues, we propose a novel method called Query6DoF (illustrated in Figure 1(b)). Instead of relying on dense and static point clouds as the shape prior, we introduce a series of sparse and learnable category-specific queries. Each query in this series is designed to encode a specific component of an object's shape with implicitly shared semantics and is optimized concurrently with the whole model parameters. Due to intra-category variability, the queries only need to capture the most representative components of objects and disregard unrepresentative shape details. Consequently, the queries can be sparse. Moreover, due to the sparseness of queries, the sparseness of the queries reduces computational overhead. Therefore, there is no need to use techniques such as Low-Rank transformer [36] mentioned in SGPA [2]. To eliminate the need for surrogate training objectives, we employ a direct prediction framework. However, unlike previous direct regression methods, e.g., [3, 20], we choose to perform the core deformation-and-matching paradigm in feature space. The deformation process is accomplished based on an attention mechanism, which adaptively extracts information from instance features to queries. This transforms queries from category-specific into instance-specific shape representations. Then, correspondences between instance features and deformed queries are established by computing their similarity. Using these correspondences, the instance features are paired with deformed queries. Finally, these pairs are used to determine the pose and size through a neural network. Since the shape prior already consists of implicit queries, it is reasonable to also execute the entire pipeline implicitly in the feature space to better leverage these queries. Without pre-learned prior and surrogate train", + "bbox": [ + 76, + 417, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ing objectives, our model is trained entirely and directly. As a result, the prior can be more suitable for the model, enabling us to achieve state-of-the-art performance on the task.", + "bbox": [ + 496, + 90, + 890, + 150 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Conventionally, the self-attention mechanism is used in transformers to inject global information. Unfortunately, adding self-attention layers significantly increases computational load. Therefore, we propose an efficient global enhancement layer to balance efficiency and performance.", + "bbox": [ + 496, + 152, + 893, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of this work can be summarized as:", + "bbox": [ + 500, + 227, + 893, + 255 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose to use sparse and learnable queries as shape prior rather than dense and static point clouds. In this way, the queries are optimized at the same time as the whole model to discover the optimal set of priors, and the sparseness design reduces the computation overhead.", + "- We adapt existing architectures to fit the novel shape prior representation with the help of attention mechanisms. We design a lightweight self-attention module in this to balance accuracy and speed.", + "- The overall 6DoF pose estimation accuracy of our method is better than previous state-of-the-art methods on the CAMERA25 and REAL275 datasets, especially, on the strict $5^{\\circ}2cm$ metric our results are significantly better than previous methods." + ], + "bbox": [ + 517, + 263, + 890, + 507 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 518, + 640, + 535 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Instance-Level 6D Object Pose Estimation", + "text_level": 1, + "bbox": [ + 500, + 544, + 857, + 560 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based on the input data format, existing methods can be divided into two categories: RGB-based [15, 28, 25, 22, 37, 23] and RGB-D-based [14, 32, 10, 13] approaches. A common approach for using RGB as input to accomplish this task is to detect the object's keypoints in the image and match them to the CAD model. With the 2D-3D correspondences, the PnP algorithm is then implemented to obtain the object's pose. Additionally, some methods [12, 33, 6, 1, 39, 11] do not use PnP algorithm but instead employ neural networks to directly output object's pose.", + "bbox": [ + 496, + 566, + 890, + 719 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Category-level 6D Object Pose and Size Estimation", + "text_level": 1, + "bbox": [ + 498, + 726, + 890, + 756 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "[34] first introduced Normalized Object Coordinate Space to represent all the possible object instances in a unified space. DualPoseNet [18] introduced a network stacking an implicit decoder to impose complementary supervision on pose encoder. We absorb this practice and provide extra implicit supervision. To handle the intra-class shape variation, SPD [30] proposes a deep network to reconstruct the 3D object model by explicitly modeling the deformation from a pre-learning categorical shape prior. However,", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14056", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9fe692b59118b343603427486909eb6d560095d79be679544893fda2087bc513.jpg", + "image_caption": [ + "Figure 2: Entire schematic illustration of our proposed method. The target point cloud $P_{obj}$ is fed to PointNet++ [27] as a backbone to extract the object's geometry features $F_{obj}$ . A set of queries $Q_{cat}$ is prepared to serve as the shape prior. Each of the queries represents a component of object shape. The queries pass through the queries deformation estimator to gain instance shape information from $F_{obj}$ using an attention mechanism to adaptively select instance features, and then they are deformed to the specific representation of the target observed object $Q_{obj}$ . Next, in the query-point correspondence estimator, the correspondence between $Q_{obj}$ and $F_{obj}$ is built. In the end, the poses and sizes estimator makes use of the previous output. This block simply adopts global average pooling to aggregate all the input features and output resulting poses and sizes through three parallel MLPs." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 890, + 275 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "this prior is not flexible enough because it is obtained in advance and remains unchanged during training. Therefore, we propose to transform it into the learnable queries. DPDN [17] makes efforts to overcoming synthetic-to-real domain gap using self-supervised learning. We further develop its paradigm of deforming and matching in feature space with the attention mechanism to make it much more effective. SGPA [2] further leverages the advantage of category prior. It uses the transformer architecture and in order to reduce computational complexity SGPA utilized the low-rank transformer [36]. But in our work, our proposed queries do not require to this technique for its sparseness.", + "bbox": [ + 75, + 433, + 472, + 614 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 633, + 168, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 76, + 661, + 187, + 676 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given an RGB-D image, the goal of the category-level object pose and size estimation is to predict the 6D object pose and size represented by rotation $R \\in SO(3)$ , translation $t \\in \\mathbb{R}^3$ , and size $s \\in \\mathbb{R}^3$ . We segment objects from the RGB image using an off-the-shelf object segmentation technique e.g., Mask R-CNN [9]. The segmented object's depth data is transferred to a 3D point cloud. Then the 3D point cloud is uniformly sampled into a fixed number. The same as [3], noting that objects' appearance varies much more than their shape even in the same category, our method only uses point cloud data as input instead of together with RGB data.", + "bbox": [ + 75, + 686, + 468, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let's denote the observed target point cloud as $P_{obj} \\in \\mathbb{R}^{N_{obj} \\times 3}$ . Our method uses a feature extraction module to", + "bbox": [ + 76, + 869, + 468, + 898 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "extract object geometry feature $F_{obj} \\in \\mathbb{R}^{N_{obj} \\times d}$ from $P_{obj}$ . Unlike conventional methods that use an extra set of point clouds as explicit shape priors, we prepare a set of queries $Q_{cat} \\in \\mathbb{R}^{N_{cat} \\times d}$ for each category as implicit shape prior. Each query expresses a semantic component of the object and they are the general category-specific representation. The number of queries $N_{cat}$ can be significantly fewer than the number of points in the input point cloud $N_{obj}$ . Besides, the queries are learnable, which means that there is no pre-defined prior and the full model is trained entirely and directly.", + "bbox": [ + 496, + 431, + 890, + 599 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A traditional approach to obtaining the final poses and sizes with shape prior can be summarized as follows. First, deform the prior point cloud to reconstruct the object shape. Then, the correspondence between the reconstructed point cloud and the observed object point cloud is estimated. Afterward, poses and sizes can be solved via Umayama [31].", + "bbox": [ + 496, + 609, + 890, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The entire schematic illustration of our proposed method is shown in Figure 2. We implement this process in feature space with an attention mechanism. Specifically, our method consists of three parts: queries deformation estimator, query-point correspondence estimator, and poses and sizes estimator. Furthermore, we propose a global enhancement block to reinforce the features with global information.", + "bbox": [ + 496, + 709, + 890, + 829 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Queries deformation estimator is used to deform the queries $Q_{cat}$ from the general category-specific representation to an object-specific one for the observed input object using the input instance geometry feature $F_{obj}$ , which can", + "bbox": [ + 496, + 839, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14057", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "be formulated as:", + "bbox": [ + 76, + 90, + 197, + 104 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nQ _ {o b j} = Q D E \\left(Q _ {c a t}, F _ {o b j}\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 117, + 468, + 135 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $Q_{obj} \\in \\mathbb{R}^{N_{cat} \\times d}$ denotes the deformed queries. $QDE$ denotes the queries deformation estimator. In this process, we adopt the attention mechanism to extract the information of regions of interest from $F_{obj}$ adaptively. After deforming the queries, the canonical point cloud can be decoded from $Q_{obj}$ denoted as:", + "bbox": [ + 76, + 143, + 468, + 236 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP _ {i} = \\Phi_ {1} (Q _ {o b j}) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 244, + 468, + 263 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $P_{i} \\in \\mathbb{R}^{N_{\\text{cat}} \\times 3}$ denotes the object's canonical sparse point cloud. $\\Phi_{1}$ denotes the decoder implemented by an MLP (multi-layer perceptron). Supervision is applied to $P_{i}$ to help better guide the learning of $Q_{obj}$ via the loss function $L_{rec}$ . Query-point correspondence estimator is used to estimate the correspondences between deformed queries $Q_{obj}$ and object feature $F_{obj}$ . The correspondence then is used to combine $Q_{obj}$ with $F_{obj}$ as matching feature pairs. These pairs are fed forward an MLP and a global enhancement block. The result is denoted as $F_{nocs}$ . The corresponding NOCS coordinates of the observed object point cloud are obtained from $F_{nocs}$ using an MLP.", + "bbox": [ + 75, + 271, + 470, + 454 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP _ {r} = \\Phi_ {2} \\left(F _ {\\text {n o c s}}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 464, + 468, + 481 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $P_r \\in \\mathbb{R}^{N_{obj} \\times 3}$ denotes the corresponding NOCS coordinates. $\\Phi_2$ is an MLP. $P_r$ does not take part in the calculation of objects' poses and sizes but only participates in the calculation of the loss function $L_{nocs}$ . This loss function is an auxiliary loss function, which is used to apply supervision on $P_r$ in order to guide the learning of $F_{nocs}$ .", + "bbox": [ + 75, + 489, + 468, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The pose and size estimator takes the previous output and gives the object's pose and size with three parallel MLPs.", + "bbox": [ + 75, + 580, + 468, + 612 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Queries Deformation Estimator", + "text_level": 1, + "bbox": [ + 76, + 619, + 357, + 636 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the queries deformation estimator, we aim to deform the queries $Q_{cat}$ to a representation of the observed target object. This goal can be achieved by injecting the object geometry feature $F_{obj}$ into $Q_{cat}$ . Due to the unordered property of the point cloud, the PointNet [26] style operation, which is mainly composed of pooling, is adopted by many methods such as [30, 38]. However, this operation loses the detailed geometry structure and cannot adaptively pay attention to features of interest. Therefore, we use the cross-attention mechanism. Thanks to the permutation-invariance of the attention mechanism, it is feasible to implement it for point cloud processing. Moreover, we enhance the feature using the proposed global enhancement block.", + "bbox": [ + 75, + 643, + 468, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The detailed structure of the queries deformation estimator is illustrated in Figure 2. Cross-attention is computed to determine which feature in $F_{obj}$ is necessary to extract into $Q_{cat}$ . Specifically, we take the $Q_{cat}$ as the query and", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/32166ef3d8cbbed306cf4a315450d3ef0651147a91514d9de9c4e81dfbc0f7e4.jpg", + "image_caption": [ + "Figure 3: Overview of the global enhancement block. The input feature $f$ pass through a global average pooling operation and a fully-connected layer to create a global feature $g$ . Then, the input feature $f$ serves as the query, and the global feature $g$ serves as both key and value. A self-attention mechanism is then applied to them." + ], + "image_footnote": [], + "bbox": [ + 501, + 99, + 893, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the $F_{obj}$ as key and value of the multi-head cross-attention module. The computation of attention map can be formulated as:", + "bbox": [ + 496, + 321, + 892, + 367 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA ^ {(m)} = \\operatorname {N o r m} \\left(\\Psi_ {1} \\left(Q _ {c a t}\\right) \\left(F _ {o b j}\\right) ^ {T}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 377, + 890, + 397 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $A^{(m)}\\in \\mathbb{R}^{N_{cat}\\times N_{obj}}$ is the attention map in the mth head. Norm is the normalization function. Instead of using learnable linear projections, we use $\\Psi_{1}$ , an MLP, applied to $Q_{cat}$ in order to reduce the gap between $Q_{cat}$ and $F_{obj}$ and it experimentally works better. Vanilla attention uses softmax to normalize the attention map, which can be formulated as norm = $\\frac{f(x_i)}{\\sum_k f(x_k)}$ where $f(x) = e^x$ for softmax. Different from that, we use:", + "bbox": [ + 496, + 406, + 892, + 531 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf (x) = \\frac {\\alpha}{1 + e ^ {- x}} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 637, + 540, + 890, + 568 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha$ is a learnable parameter. This is a sigmoid function with a learnable parameter. This function's output is limited between 0 and $\\alpha$ , so there is no need to scale the dot-product result between query and key by dividing by $\\sqrt{d}$ . This function tends to saturate and thus activate larger regions than softmax does, and the learnable parameter allows the model to choose the range. Since each query corresponds to a certain semantic part of the object in a specific category, the attention map indicates which component of the observed object has the same semantics as the query by calculating the similarity between the queries $Q_{cat}$ and the object feature $F_{obj}$ .", + "bbox": [ + 496, + 578, + 892, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, the multi-head cross-attention can be formulated as:", + "bbox": [ + 496, + 758, + 893, + 787 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nD = \\left[ A ^ {(1)} F _ {o b j}; \\dots ; A ^ {(m)} F _ {o b j} \\right] W _ {v} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 787, + 890, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $D \\in \\mathbb{R}^{N_{cat} \\times d}$ is the multi-head cross-attention result and $W_v$ is the learnable parameter. In this way, the related object feature is extracted from the $F_{obj}$ . Then $D$ can be used to deform $Q_{cat}$ by adding it to $Q_{cat}$ :", + "bbox": [ + 496, + 811, + 892, + 873 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nQ _ {o b j} = Q _ {c a t} + D \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 885, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14058", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $Q_{obj} \\in \\mathbb{R}^{N_{cat} \\times d}$ is deformed queries.", + "bbox": [ + 76, + 90, + 372, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$Q_{obj}$ is expected to embed the object's canonical point cloud. It can be decoded into 3D points using a simple MLP.", + "bbox": [ + 76, + 106, + 468, + 137 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP _ {i} = \\operatorname {S i g m o i d} \\left(M L P \\left(Q _ {o b j}\\right)\\right) - 0. 5 \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 151, + 468, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $P_{i} \\in \\mathbb{R}^{N_{\\text{cat}} \\times 3}$ . A Sigmoid function is used to limit it to $(-0.5, 0.5)$ , so the output points are in canonical space. We apply supervision to $P_{i}$ which could guide the learning of $Q_{obj}$ . Therefore, loss function $L_{rec}$ is applied to $P_{i}$ to provide supervision to it.", + "bbox": [ + 76, + 172, + 468, + 248 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Global enhancement block tends to enhance features by fusing their global feature. Normally, this can be achieved via the self-attention mechanism. However, to make the entire model lightweight, a more efficient block is needed. For this reason, we propose a global enhancement block.", + "bbox": [ + 76, + 250, + 468, + 338 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The global enhancement block is illustrated in Figure 3. Suppose the global enhancement block takes feature $f \\in \\mathbb{R}^{N \\times d}$ as input. We adopt the result of the global average pooling as the global feature and pass it through a fully connected layer. The outcome is denoted as $g$ :", + "bbox": [ + 76, + 339, + 468, + 415 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ng = F C \\left(A v g P o o l (f)\\right) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 426, + 468, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $FC$ is a fully connected layer. Instead of simply concatenating it to $f$ and then feeding it to an MLP, we borrow the idea from self-attention as shown in Figure 3. We use $f$ as query and $g$ as key and value to carry out self-attention, which can be denoted as:", + "bbox": [ + 76, + 452, + 468, + 527 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf ^ {\\prime} = f + \\operatorname {N o r m} \\left(f g ^ {T}\\right) g \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 537, + 468, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After that, $f'$ is fed into an MLP with residual. In this way, global information is injected into the feature. This block, unlike vanilla self-attention, reduces the complexity of the computation. Compared with the computation complexity of vanilla self-attention, $O(N^2 \\times d)$ , our efficient global enhancement block has a computation complexity of $O(N \\times d)$ .", + "bbox": [ + 76, + 566, + 468, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Query-Point Correspondence Estimator", + "text_level": 1, + "bbox": [ + 76, + 681, + 419, + 696 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We obtain the deformed queries $Q_{obj}$ by adaptively selecting feature from the observed object feature $F_{obj}$ . In previous works, a correspondence matrix $A \\in \\mathbb{R}^{N_{obj} \\times N_{cat}}$ is estimated, which models correspondences between points in observed point cloud $P_{obj}$ and reconstructed point cloud $P_i$ . This matrix then samples the points from $P_i$ to be paired with $P_{obj}$ , and it can be formulated as $P = A \\times P_i$ , where $P$ denotes the sampled points. Finally, solving of Umeyama algorithm [31] to align the sample points with $P_i$ gives out the target pose and size. Instead of using this conventional way, we move this process to the feature space. In the query-point correspondence estimator, the correspondences between $F_{obj}$ and $Q_{obj}$ are built as illustrated in Figure 2.", + "bbox": [ + 76, + 704, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In detail, the correspondences are built by computing the similarity between $F_{obj}$ and $Q_{obj}$ using dot-product, which can be formulated as:", + "bbox": [ + 498, + 90, + 890, + 135 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nA ^ {\\prime} = \\operatorname {N o r m} \\left(\\Psi_ {2} \\left(F _ {o b j}\\right) \\left(Q _ {o b j}\\right) ^ {T}\\right) \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 143, + 890, + 161 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $A' \\in \\mathbb{R}^{N_{obj} \\times N_{cat}}$ denotes the correspondence matrix between $F_{obj}$ and $Q_{obj}$ . Norm is the same as that used in queries deformation estimator. $\\Psi_2$ is an MLP. $A'$ represents the soft matching between $F_{obj}$ and $Q_{obj}$ . Then we multiply $A'$ by $Q_{obj}$ to obtain the sampled features. Essentially, we find that this process is similar to cross-attention. For this reason, we add $F_{obj}$ to the result for implementing a residual structure similar to attention mechanism. Also, we implement multi-head technique to the computation. Next, we need to pair the object feature with the sampled feature. Experimentally, it is better to use a more direct feature as the object feature here instead of the deep object feature $F_{obj}$ . Thereby, we do not use $F_{obj}$ but simply feed object point cloud $P_{obj}$ forward an MLP. The output of the MLP is concatenated to the sampled feature. To further enhance the feature, we use an MLP and a global enhancement block after that. The result is denoted as $F_{nocs}$ . To apply supervision on $F_{nocs}$ and better guide its learning, we use a simple MLP to transform $F_{nocs}$ into NOCS coordinates denoted as $P_r \\in \\mathbb{R}^{N_{obj} \\times 3}$ . $P_r$ is not used to solve the Umeyama algorithm to obtain target pose and size, but only used to compute loss function $L_{nocs}$ .", + "bbox": [ + 496, + 167, + 890, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Poses and Sizes Estimator", + "text_level": 1, + "bbox": [ + 500, + 508, + 735, + 522 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The rest of the work is to obtain the final object's pose and size, which is accomplished in the pose and size estimator. The pose and size estimator applies global average pooling operation to $F_{nocs}$ , which can be formulated as:", + "bbox": [ + 498, + 532, + 890, + 592 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\text {p o s e}} = \\operatorname {A v g P o o l} \\left(F _ {\\text {n o c s}}\\right) \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 599, + 890, + 616 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $f_{\\text{pose}} \\in \\mathbb{R}^{1 \\times d}$ . Then after it, three parallel MLPs predict the rotation $R$ , translation $t$ , and size $s$ respectively.", + "bbox": [ + 498, + 623, + 890, + 655 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nR, t, s = M L P \\left(f _ {p o s e}\\right), M L P \\left(f _ {p o s e}\\right), M L P \\left(f _ {p o s e}\\right) \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 676, + 890, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The representation of $R$ here is the Continuity of Rotation Representations [40]. For $s$ , we follow [3] to estimate the residual between object's size and the mean category size. Similarly, for $t$ , we predict the residual between the translation ground truth and the mean value of the point cloud.", + "bbox": [ + 498, + 700, + 890, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Overall Loss Function", + "text_level": 1, + "bbox": [ + 500, + 784, + 707, + 799 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall loss function is as follows:", + "bbox": [ + 517, + 808, + 774, + 821 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL = \\lambda_ {1} L _ {\\text {p o s e}} + \\lambda_ {2} L _ {\\text {r e c}} + \\lambda_ {3} L _ {\\text {n o c s}} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 830, + 890, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$L_{\\text{pose}}$ is used to compute loss on predicted $R, t$ and $s$ . We simply use smooth L1 loss [8] for all of them with threshold of $1 \\times 10^{-3}, 5 \\times 10^{-3}, 5 \\times 10^{-3}$ respectively. $L_{\\text{rec}}$ and", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14059", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$L_{nocs}$ are the auxiliary losses function for $P_{i}$ and $P_{r}$ respectively. $L_{rec}$ is applied to $P_{i}$ to encourage it to reconstruct the instance point cloud in the NOCS space. Therefore, for $L_{rec}$ , we use Chamfer distance between $P_{i}$ and $M_{gt}$ where $M_{gt} \\in \\mathbb{R}^{N_{obj} \\times 3}$ represents the instance point cloud model in the NOCS space. $L_{rec}$ can be formulated as follows:", + "bbox": [ + 76, + 90, + 468, + 181 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {r e c} = \\frac {1}{N _ {c a t}} \\sum_ {x _ {i} \\in P _ {r}} \\min _ {y _ {j} \\in M _ {g t}} \\| x _ {i} - y _ {j} \\| _ {2} ^ {2} + \\\\ \\frac {1}{N _ {o b j}} \\sum_ {y _ {i} \\in M _ {g t}} \\min _ {x _ {i} \\in P _ {r}} \\| x _ {i} - y _ {j} \\| _ {2} ^ {2} \\tag {15} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 189, + 468, + 266 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$L_{nocs}$ is applied on $P_r$ to encourage it in predicting the corresponding coordinates of $P_{obj}$ in Normalized Object Coordinate Space. For $L_{nocs}$ , we also use a smooth L1 loss [8] with a threshold of 0.1.", + "bbox": [ + 76, + 273, + 468, + 334 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 345, + 209, + 363 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We conduct experiments using the benchmark CAMERA25 and REAL275 [34] datasets for category-level 6D object pose and size estimation which consists of six object categories. The CAMERA25 dataset is generated by rendering and compositing synthetic object instances under different views. The CAMERA25 dataset contains 300K synthetic images of 1,085 object instances, among which 25,000 images of 184 instances are used for evaluation. The REAL275 dataset is complementary to the CAMERA25 dataset. It includes 4,300 real-world images of 6 scenes with 3 unseen instances per category; its training set contains 4,300 images of 7 scenes, and the test set contains 2,750 images of 6 scenes. We train our model with a combined use of the two datasets, as done in [18].", + "bbox": [ + 75, + 372, + 468, + 583 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implement Details. We employ a Mask R-CNN [9] to obtain instance masks the same as [30]. The instances are then cropped based on the segmentation result. After that, the depth is converted to the instance point cloud using the camera's intrinsic parameters. 1024 points are randomly sampled from that, so $N_{obj}$ is set to 1024. To extract instance geometry features, we choose PointNet++ [27] with four abstraction levels. The number of prior queries $N_{cat}$ is set to 64. In this case, $N_{cat} \\ll N_{obj}$ . A detailed study on the parameter $N_{cat}$ is given in our ablation study. The queries are initialized randomly at the beginning of training. The dimension of features and queries is set to 256. The crossattention in queries deformation estimator and query-point correspondence estimator has four heads each. In the loss function, we set $\\lambda_1, \\lambda_2, \\lambda_3$ to 1.0, 3.0, 1.0, respectively. We use AdamW [21] to train this model with an initial learning rate of $1 \\times 10^{-4}$ and weight decay $1 \\times 10^{-4}$ . All models are trained 42k iterations with batch size of 60 and cosine learning rate decay is conducted. We employ several strategies for depth augmentation, such as adding Gaussian noise, random scaling, random rotation, adding random points as well", + "bbox": [ + 75, + 584, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "as linear shape augmentation proposed in [3] and non-linear shape augmentation proposed in [38]. All FPS(Frames Per Second) data of our method is evaluated on a single RTX 2080Ti, an Intel(R) Xeon(R) CPU E5-2650 v4 @ 2.20GHz, PyTorch [24] 1.10, CUDA version 11.1.", + "bbox": [ + 496, + 90, + 890, + 165 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. For category-level pose estimation, we follow [34] and use two metrics to evaluate the quality.", + "bbox": [ + 496, + 167, + 890, + 212 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- 3D IoU. The overlap of two 3D bounding boxes under the predicted pose and the ground truth pose is computed. The overlap ratios larger than the threshold are regarded as accepted. The mean Average Precision (mAP) of the overlapping is reported.", + "- $n^{\\circ}m$ cm. The rotation and translation errors between the predicted pose and the ground truth pose are computed. The errors smaller than an angle threshold $n^{\\circ}$ and a translation threshold $m$ cm are accepted." + ], + "bbox": [ + 517, + 220, + 890, + 367 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Comparisons with Existing Methods", + "text_level": 1, + "bbox": [ + 498, + 376, + 815, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "NOCS-REAL275 In Table 1 we compare our method with the existing ones for category-level 6D object pose and size estimation. We divide these methods into two groups: those with and without shape prior. As it is shown in Table 1, our method outperforms other existing methods. In detail, we outperform NOCS [34] by 46.0 in $IoU_{75}$ , 41.8 in $5^{\\circ}2cm$ , 48.9 in $5^{\\circ}5cm$ . Moreover, we achieve a better result than existing methods that using prior information. Specifically, we outperform SPD [30] by 22.9 in $IoU_{75}$ , 29.7 in $5^{\\circ}2cm$ , 37.5 in $5^{\\circ}5cm$ and 14.2, 13.1, and 19.3 higher than SGPA [2] which is a representative method based on attention. This outcome demonstrates that our sparse shape prior is superior to the traditional shape prior.", + "bbox": [ + 496, + 398, + 890, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "NOCS-CAMERA25 The results for CAMERA25 are shown Table 1. Our method outperforms others at least 4.9, 4.3 in the items of $5^{\\circ}2cm$ , $5^{\\circ}5cm$ , and it is on par with the best methods for $IoU_{75}$ . Figure 4 presents a more detailed error evaluation result on two datasets.", + "bbox": [ + 496, + 595, + 890, + 671 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 681, + 663, + 695 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect of the design in Query6DoF. We verify the efficacy of each component in Query6DoF in Table 2. By replacing queries with point cloud proposed in [30] and adding an extra PointNet++ [27] after the prior point cloud as a feature extractor, $5^{\\circ}2cm$ drops from 49.0 to 47.2, and computation increases. Removing the global enhancement block results in a 4.8 drop in $5^{\\circ}2cm$ . Removing the queries deformation estimator results in a 2.5 drop in $5^{\\circ}2cm$ . If the query-point correspondence estimator is detached, it renders the usage of queries and queries deformation estimator senseless. Therefore, without using them together, our method experiences a 13.6 drop in $5^{\\circ}2cm$ . Moreover, we remove the poses and sizes estimator but use $P_r$ and $P_i$", + "bbox": [ + 496, + 703, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14060", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/fb6b78ed09c3c8bc6a6276248020499dcca4e77daf1f72e3e16eacc3a1501520.jpg", + "table_caption": [ + "Table 1: Comparison with state-of-the-art methods on the CAMERA25 dataset and REAL275 dataset. * denotes results without linear shape augmentation and non-linear shape augmentation. The best results shown in bold." + ], + "table_footnote": [], + "table_body": "
MethodpriorCAMERA25REAL275
IoU50IoU755°2cm5°5cm10°2cm10°5cmIoU50IoU755°2cm5°5cm10°2cm10°5cm
NOCS [34]83.969.532.340.948.264.678.030.17.210.013.825.2
DualPoseNet [18]92.486.464.770.777.284.779.862.229.335.950.066.8
GPV-Pose [7]93.488.372.179.1-89.083.064.432.042.9-73.3
SPD [30]✓93.283.154.359.073.381.577.353.219.321.443.254.1
CR-Net [35]✓93.888.072.076.481.087.779.355.927.834.347.260.8
SAR-Net [16]✓86.879.066.770.975.680.379.362.431.642.350.368.3
SGPA [2]✓93.288.170.774.582.788.480.161.935.939.661.370.7
RBP-Pose [38]✓93.189.073.579.682.189.5-67.838.248.163.179.2
Self-DPDN [17]✓------83.676.046.050.770.478.4
Ours*✓92.388.678.483.984.090.582.976.046.854.767.981.6
Ours✓91.988.178.083.183.990.082.576.149.058.968.783.0
", + "bbox": [ + 116, + 130, + 849, + 282 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5f99da3aa03e50c8f4a7fa4a7b43b1367cc974b7d8711c3a17864caaf759bb46.jpg", + "table_caption": [ + "Table 2: Effect of the design on Query6DoF, evaluated on the REAL275 dataset. GlobEnhance denotes the global enhancement block, QueryDeform denotes the queries deformation estimator, Query2Point denotes the query-point correspondence estimator, and PoseSize denotes the poses and sizes estimator" + ], + "table_footnote": [], + "table_body": "
QueriesGlobEnhanceQueryDeformQuery2PointPoseSizeI0U50I0U755°2cm5°5cm10°2cm10°5cm
1-✓✓✓✓82.175.447.256.267.381.2
2✓-✓✓✓82.675.744.253.365.881.1
3✓✓-✓✓83.075.346.556.665.981.3
4-✓--✓82.170.935.448.759.580.2
5✓✓✓✓-82.270.040.046.365.176.5
6✓✓✓✓✓82.576.149.058.968.783.0
", + "bbox": [ + 116, + 352, + 849, + 446 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/81378a0a73ad900342c1f3204776795ae7b16a1b00afcd1bd50d65253f125872.jpg", + "image_caption": [ + "Figure 4: Mean Average Precision (mAP) in different thresholds. REAL275 (top rows) and CAMERA25 (bottom rows)" + ], + "image_footnote": [], + "bbox": [ + 104, + 470, + 447, + 698 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "to obtain poses and sizes via Umeyama [31]. As a result, $5^{\\circ}2cm$ falls by 9.0 points.", + "bbox": [ + 75, + 791, + 468, + 821 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of the number of prior queries. In our method, we use sparse queries to represent the shape prior. In this experiment, we investigate the effect of the number of prior queries $N_{cat}$ on the results of REAL275. Table 3 presents the result of the ablation of the effect of the number of prior", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/468e897265f30796ec121b10c3af584c4d346e8bda5bcd095400964a383f06d3.jpg", + "table_caption": [ + "Table 3: Effect of the number of queries on REAL275" + ], + "table_footnote": [], + "table_body": "
NcatIoU50IoU755°2cm5°5cm10°2cm10°5cm
1682.574.646.055.466.681.0
3282.574.946.755.967.281.5
6482.676.149.058.968.783.0
12882.876.946.155.968.882.8
25682.876.647.657.367.881.6
51282.675.646.856.266.981.4
102483.176.748.756.870.482.4
", + "bbox": [ + 521, + 494, + 867, + 594 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/573ea9b808860cf44132d5190cf118b42f913d5ccb5bc2e0804fd7b806d60b3c.jpg", + "table_caption": [ + "Table 4: Effect of different attention normalization evaluated on REAL275." + ], + "table_footnote": [], + "table_body": "
NormI0U50I0U755°2cm5°5cm10°2cm10°5cm
Softmax82.174.748.657.268.682.4
Ours82.576.149.058.968.783.0
", + "bbox": [ + 504, + 648, + 888, + 693 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "queries. The results show that reducing the number of prior queries does not significantly affect the performance of our method. This fact means that it is not necessary to use excessive points to express the object's shape prior. A small number of queries can effectively represent the object's shape. Specifically, when $N_{cat} = 64$ , our method achieves the best performance in the $5^{\\circ}2cm$ , $5^{\\circ}5cm$ , $10^{\\circ}5cm$ metrics and when $N_{cat} = 1024$ , our method achieves the best performance in the $IoU_{50}$ metric. However, the smaller $N_{cat}$ results in less computational overhead. Therefore, we adopt $N_{cat} = 64$ as the default setting in all other experiments.", + "bbox": [ + 496, + 719, + 890, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of different attention normalization. While", + "bbox": [ + 517, + 885, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14061", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0273c03d260c05a4cf076de92d803aa8a86585ed57a302284834f7f0e2e588a9.jpg", + "image_caption": [ + "Figure 5: Qualitative results of our method (red line) and SGPA [2] (green line)." + ], + "image_footnote": [], + "bbox": [ + 119, + 90, + 848, + 170 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/914d399b303d132dce74e281b74a19a93d889b61ea347c92d86b1fc3e5b549b5.jpg", + "image_caption": [ + "Figure 6: Sparse point cloud reconstruction in the REAL275 dataset. The yellow points represent the reconstruction points $P_{i}$ , while the blue points are the observed point cloud." + ], + "image_footnote": [], + "bbox": [ + 119, + 210, + 849, + 385 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a512da0abffa399f4ccb28ca6d713177264f9e26ba02e4363bbcb487b3b48573.jpg", + "table_caption": [ + "Table 5: Model complexity and FPS w/o Mask R-CNN [9], evaluated on REAL275. GEB denotes the global enhancement block." + ], + "table_footnote": [], + "table_body": "
MethodParams(M)FPS w/o Mask R-CNN [9]5°2cm
Ncat = 64 (Default)19.5334.949.0
Ncat = 102421.1823.348.7
w/o GEB18.7136.844.2
w/o Queries22.2424.047.2
", + "bbox": [ + 81, + 508, + 465, + 573 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "common attention mechanisms adopt softmax to normalize the attention map, in our method, we use a different normalization approach, namely sigmoid with a learnable parameter mentioned earlier. In this experiment, we compare two different settings shown in Table 4. We conduct the evaluation on the REAL275 dataset. Using softmax to normalize results in a 1.4 drop in $IoU_{75}$ and a 0.4 drop in $5^{\\circ}2cm$ .", + "bbox": [ + 75, + 602, + 468, + 723 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Runtime Analysis", + "text_level": 1, + "bbox": [ + 76, + 739, + 250, + 755 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Table 5, our method, in the default setting, has 19.43M parameters and runs at 34.9 FPS without Mask R-CNN [9]. Increasing $N_{cat}$ to 1024 brings no gain but the FPS drops to 23.3, which shows that sparse queries are sufficient to represent the shape prior. Adding the global enhancement block results in a 4.8 improvement in $5^{\\circ}2cm$ with only a 1.9 FPS drop, demonstrating its efficiency. W/o Queries means that we replace the queries with the prelearned shape prior proposed in [30] and use PointNet++", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "[27] as a feature extractor. In this way, due to the extra PointNet++ [27], the speed drops to 24.0FPS, but there is no gain in $5^{\\circ}2cm$ . Therefore, the usage of queries is more efficient than using point cloud both in terms of accuracy and speed.", + "bbox": [ + 496, + 453, + 890, + 530 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Visualization", + "text_level": 1, + "bbox": [ + 500, + 537, + 637, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative Results. Figure 5 shows the qualitative results of our method, demonstrating that our method can accurately estimate the objects' poses and sizes.", + "bbox": [ + 496, + 560, + 890, + 606 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Sparse point cloud reconstruction. Our method outputs $P_{i}$ as the sparse point cloud reconstruction in NOCS space. We align $P_{i}$ to the object's location in RGB images for better comparison with the object's actual shape, as shown in Figure 6. $P_{i}$ is the yellow points in it. The blue points in it represent the observed point cloud for comparison. It shows that our sparse point cloud can accurately cover different objects' shapes. This effect can be attributed to our queries deformation estimator, where category-specific queries transformed into instance-specific ones. Through this process, the queries are able to reconstruct the objects.", + "bbox": [ + 496, + 607, + 892, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 800, + 617, + 814 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In conclusion, we present a novel network for category-level 6D object pose and size estimation, namely Query6DoF. In particular, we propose to use a series of sparse and learnable queries serving as a shape prior, which is a set of tokens that implicitly represent objects in a cer", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14062", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tain category. Furthermore, we transform the traditional deformation-and-matching paradigm to the feature space using attention. Specifically, the queries are deformed by a process where we dynamically use the attention mechanism to select object features and incorporate them into queries. This step transforms the queries into a representation of a certain target object. Next, we establish the correspondences between deformed queries and object features. Finally, the poses and sizes are regressed using the correspondences. Thanks to learnable queries and direct output results, the queries are trained directly alongside the entire network. This method achieves state-of-the-art performance compared to other existing methods and holds promise for applications in robotics and augmented reality.", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgement This work was supported by the Key Research Project of Zhejiang Lab (No. G2021NB0AL03) and Modern Agriculture Major-core Technology Innovation Project of Jiangsu Province (No. cx(22)2031).", + "bbox": [ + 76, + 303, + 468, + 364 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 378, + 174, + 393 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Tuo Cao, Fei Luo, Yanping Fu, Wenxiao Zhang, Shengjie Zheng, and Chunxia Xiao. Dgecn: A depth-guided edge convolutional network for end-to-end 6d pose estimation. 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IEEE Transactions on Image Processing, 31:6907-6921, 2022." + ], + "bbox": [ + 501, + 92, + 890, + 753 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "14064", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Query6DoF_ Learning Sparse Queries as Implicit Shape Prior for Category-Level 6DoF Pose Estimation/4d1aafad-a31c-4773-aac8-62fd2260bfdc_model.json b/2023/Query6DoF_ Learning Sparse Queries as Implicit Shape Prior for Category-Level 6DoF Pose Estimation/4d1aafad-a31c-4773-aac8-62fd2260bfdc_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ea804c8f0d408b597589b8d1f2c7053ddc6caf64 --- /dev/null +++ b/2023/Query6DoF_ Learning Sparse Queries as Implicit Shape Prior for Category-Level 6DoF Pose Estimation/4d1aafad-a31c-4773-aac8-62fd2260bfdc_model.json @@ -0,0 +1,2123 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.155, + 0.131, + 0.819, + 0.177 + ], + "angle": 0, + "content": "Query6DoF: Learning Sparse Queries as Implicit Shape Prior for Category-Level 6DoF Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.136, + 0.215, + 0.834, + 0.236 + ], + "angle": 0, + "content": "Ruiqi Wang\\(^{1}\\), Xinggang Wang\\(^{1}\\), Te Li\\(^{\\dagger,2,3}\\), Rong Yang\\(^{2,3}\\), Minhong Wan\\(^{\\dagger,2,3}\\), Wenyu Liu\\(^{\\dagger,1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.253, + 0.887, + 0.283 + ], + "angle": 0, + "content": "1Hubei Key Laboratory of Smart Internet Technology, School of Electronic Information and Communications, Huazhong University of Science and Technology" + }, + { + "type": "text", + "bbox": [ + 0.148, + 0.283, + 0.821, + 0.311 + ], + "angle": 0, + "content": "\\(^{2}\\)Research Center for Intelligent Robotics, Research Institute of Interdisciplinary Innovation, Zhejiang Lab, China \\(^{3}\\)Zhejiang Engineering Research Center for Intelligent Robotics, China" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.356, + 0.314, + 0.373 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.394, + 0.474, + 0.818 + ], + "angle": 0, + "content": "Category-level 6DoF object pose estimation intends to estimate the rotation, translation, and size of unseen objects. Many previous works use point clouds as a prelearned shape prior to overcome intra-category variability. The shape prior is deformed to reconstruct instances' point clouds in canonical space and to build dense 3D-3D correspondences between the observed and reconstructed point clouds. However, the pre-learned shape prior is not jointly optimized with estimation networks, and they are trained with a surrogate objective. We propose a novel 6D pose estimation network, named Query6DoF, based on a series of category-specific sparse queries that represent the prior shape. Each query represents a shape component, and these queries are learnable embeddings that can be optimized together with the estimation network according to the point cloud reconstruction loss, the normalized object coordinate loss, and the 6d pose estimation loss. Query6DoF adopts a deformation-and-matching paradigm with attention, where the queries dynamically extract features from regions of interest using the attention mechanism and then directly regress results. Furthermore, Query6DoF reduces computation overhead through the sparseness of the queries and the incorporation of a lightweight global information injection block. With the aforementioned design, Query6DoF achieves state-of-the-art (SOTA) pose estimation performance on the NOCS datasets. The source code and models are available at https://github.com/hustvl/Query6DoF." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.356, + 0.895, + 0.528 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.537, + 0.895, + 0.63 + ], + "angle": 0, + "content": "Figure 1: Comparisons with conventional works. a) Conventional methods adopt pre-learned shape prior and have a two-stage pipeline, i.e., deforming the prior and building correspondences between points. b) Our method uses sparse learnable queries as the shape prior and conducts query/feature-based deformation and matching." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.659, + 0.634, + 0.675 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.895, + 0.824 + ], + "angle": 0, + "content": "Category-level object pose estimation is aimed at estimating an object's rotation, translation, and size from an RGB-D scene within a given set of categories. This task has attracted increasing attention due to its vital role in robotics [5], 3D understanding [4, 22], and augmented reality [29]. Compared with instance-level object pose estimation, category-level object pose estimation doesn't require obtaining the object's CAD model in advance, making it more generally applicable." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Many existing methods [2, 7, 16, 30, 41, 38, 20, 35] solve this problem as shown in Figure 1(a). First, they attempt to reconstruct the input object point cloud in the Normalized Object Coordinate Space [34] (NOCS). Then they estimate the 3D-3D correspondences between the input ob" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.863, + 0.47, + 0.901 + ], + "angle": 0, + "content": "†Corresponding authors: Wenyu Liu (liuwy@hust.edu.cn), Te Li (lite@zhejianglab.com) and Minhong Wan (wanmh@ zhejianglab.com)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "14055" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.41 + ], + "angle": 0, + "content": "served point cloud and the reconstructed object point cloud. Finally, they determine object poses and sizes by applying the Umeyama algorithm [31] to these correspondences. To handle intra-category variability, a shape prior, which represents a basic shape for objects in the same category, is introduced in [30] to this task. This shape prior is a set of point clouds pre-learned in NOCS for each category. Objects are reconstructed by deforming the shape prior. However, this approach has its drawbacks: 1) the shape prior is a dense representation of objects in a specific category, which is not only redundant but also makes the network computationally expensive. 2) the shape prior is pre-learned in advance and remains static during model training. Additionally, these methods are trained to predict the deformation field \\( D \\) and a correspondence matrix \\( A \\), which is a surrogate task. 3) Conventional model architectures [30, 3, 2] typically rely on either pooling operations in the PointNet [26] style or 3D graph convolution (3DGC) [19] to explore geometry features. However, the pooling operation can result in the loss of local geometry features, and these operations are not adaptive to extract the feature information." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.418, + 0.473, + 0.904 + ], + "angle": 0, + "content": "To address these issues, we propose a novel method called Query6DoF (illustrated in Figure 1(b)). Instead of relying on dense and static point clouds as the shape prior, we introduce a series of sparse and learnable category-specific queries. Each query in this series is designed to encode a specific component of an object's shape with implicitly shared semantics and is optimized concurrently with the whole model parameters. Due to intra-category variability, the queries only need to capture the most representative components of objects and disregard unrepresentative shape details. Consequently, the queries can be sparse. Moreover, due to the sparseness of queries, the sparseness of the queries reduces computational overhead. Therefore, there is no need to use techniques such as Low-Rank transformer [36] mentioned in SGPA [2]. To eliminate the need for surrogate training objectives, we employ a direct prediction framework. However, unlike previous direct regression methods, e.g., [3, 20], we choose to perform the core deformation-and-matching paradigm in feature space. The deformation process is accomplished based on an attention mechanism, which adaptively extracts information from instance features to queries. This transforms queries from category-specific into instance-specific shape representations. Then, correspondences between instance features and deformed queries are established by computing their similarity. Using these correspondences, the instance features are paired with deformed queries. Finally, these pairs are used to determine the pose and size through a neural network. Since the shape prior already consists of implicit queries, it is reasonable to also execute the entire pipeline implicitly in the feature space to better leverage these queries. Without pre-learned prior and surrogate train" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.151 + ], + "angle": 0, + "content": "ing objectives, our model is trained entirely and directly. As a result, the prior can be more suitable for the model, enabling us to achieve state-of-the-art performance on the task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.153, + 0.894, + 0.228 + ], + "angle": 0, + "content": "Conventionally, the self-attention mechanism is used in transformers to inject global information. Unfortunately, adding self-attention layers significantly increases computational load. Therefore, we propose an efficient global enhancement layer to balance efficiency and performance." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.228, + 0.894, + 0.256 + ], + "angle": 0, + "content": "The main contributions of this work can be summarized as:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.265, + 0.892, + 0.354 + ], + "angle": 0, + "content": "- We propose to use sparse and learnable queries as shape prior rather than dense and static point clouds. In this way, the queries are optimized at the same time as the whole model to discover the optimal set of priors, and the sparseness design reduces the computation overhead." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.364, + 0.892, + 0.424 + ], + "angle": 0, + "content": "- We adapt existing architectures to fit the novel shape prior representation with the help of attention mechanisms. We design a lightweight self-attention module in this to balance accuracy and speed." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.432, + 0.892, + 0.508 + ], + "angle": 0, + "content": "- The overall 6DoF pose estimation accuracy of our method is better than previous state-of-the-art methods on the CAMERA25 and REAL275 datasets, especially, on the strict \\(5^{\\circ}2cm\\) metric our results are significantly better than previous methods." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.265, + 0.892, + 0.508 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.52, + 0.642, + 0.536 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.545, + 0.859, + 0.561 + ], + "angle": 0, + "content": "2.1. Instance-Level 6D Object Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.72 + ], + "angle": 0, + "content": "Based on the input data format, existing methods can be divided into two categories: RGB-based [15, 28, 25, 22, 37, 23] and RGB-D-based [14, 32, 10, 13] approaches. A common approach for using RGB as input to accomplish this task is to detect the object's keypoints in the image and match them to the CAD model. With the 2D-3D correspondences, the PnP algorithm is then implemented to obtain the object's pose. Additionally, some methods [12, 33, 6, 1, 39, 11] do not use PnP algorithm but instead employ neural networks to directly output object's pose." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.727, + 0.892, + 0.757 + ], + "angle": 0, + "content": "2.2. Category-level 6D Object Pose and Size Estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.894, + 0.903 + ], + "angle": 0, + "content": "[34] first introduced Normalized Object Coordinate Space to represent all the possible object instances in a unified space. DualPoseNet [18] introduced a network stacking an implicit decoder to impose complementary supervision on pose encoder. We absorb this practice and provide extra implicit supervision. To handle the intra-class shape variation, SPD [30] proposes a deep network to reconstruct the 3D object model by explicitly modeling the deformation from a pre-learning categorical shape prior. However," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14056" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.891, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.286, + 0.893, + 0.409 + ], + "angle": 0, + "content": "Figure 2: Entire schematic illustration of our proposed method. The target point cloud \\( P_{obj} \\) is fed to PointNet++ [27] as a backbone to extract the object's geometry features \\( F_{obj} \\). A set of queries \\( Q_{cat} \\) is prepared to serve as the shape prior. Each of the queries represents a component of object shape. The queries pass through the queries deformation estimator to gain instance shape information from \\( F_{obj} \\) using an attention mechanism to adaptively select instance features, and then they are deformed to the specific representation of the target observed object \\( Q_{obj} \\). Next, in the query-point correspondence estimator, the correspondence between \\( Q_{obj} \\) and \\( F_{obj} \\) is built. In the end, the poses and sizes estimator makes use of the previous output. This block simply adopts global average pooling to aggregate all the input features and output resulting poses and sizes through three parallel MLPs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.434, + 0.473, + 0.616 + ], + "angle": 0, + "content": "this prior is not flexible enough because it is obtained in advance and remains unchanged during training. Therefore, we propose to transform it into the learnable queries. DPDN [17] makes efforts to overcoming synthetic-to-real domain gap using self-supervised learning. We further develop its paradigm of deforming and matching in feature space with the attention mechanism to make it much more effective. SGPA [2] further leverages the advantage of category prior. It uses the transformer architecture and in order to reduce computational complexity SGPA utilized the low-rank transformer [36]. But in our work, our proposed queries do not require to this technique for its sparseness." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.635, + 0.169, + 0.65 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.662, + 0.188, + 0.677 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.47, + 0.867 + ], + "angle": 0, + "content": "Given an RGB-D image, the goal of the category-level object pose and size estimation is to predict the 6D object pose and size represented by rotation \\( R \\in SO(3) \\), translation \\( t \\in \\mathbb{R}^3 \\), and size \\( s \\in \\mathbb{R}^3 \\). We segment objects from the RGB image using an off-the-shelf object segmentation technique e.g., Mask R-CNN [9]. The segmented object's depth data is transferred to a 3D point cloud. Then the 3D point cloud is uniformly sampled into a fixed number. The same as [3], noting that objects' appearance varies much more than their shape even in the same category, our method only uses point cloud data as input instead of together with RGB data." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.9 + ], + "angle": 0, + "content": "Let's denote the observed target point cloud as \\( P_{obj} \\in \\mathbb{R}^{N_{obj} \\times 3} \\). Our method uses a feature extraction module to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.433, + 0.892, + 0.601 + ], + "angle": 0, + "content": "extract object geometry feature \\(F_{obj} \\in \\mathbb{R}^{N_{obj} \\times d}\\) from \\(P_{obj}\\). Unlike conventional methods that use an extra set of point clouds as explicit shape priors, we prepare a set of queries \\(Q_{cat} \\in \\mathbb{R}^{N_{cat} \\times d}\\) for each category as implicit shape prior. Each query expresses a semantic component of the object and they are the general category-specific representation. The number of queries \\(N_{cat}\\) can be significantly fewer than the number of points in the input point cloud \\(N_{obj}\\). Besides, the queries are learnable, which means that there is no pre-defined prior and the full model is trained entirely and directly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.61, + 0.892, + 0.701 + ], + "angle": 0, + "content": "A traditional approach to obtaining the final poses and sizes with shape prior can be summarized as follows. First, deform the prior point cloud to reconstruct the object shape. Then, the correspondence between the reconstructed point cloud and the observed object point cloud is estimated. Afterward, poses and sizes can be solved via Umayama [31]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.71, + 0.892, + 0.83 + ], + "angle": 0, + "content": "The entire schematic illustration of our proposed method is shown in Figure 2. We implement this process in feature space with an attention mechanism. Specifically, our method consists of three parts: queries deformation estimator, query-point correspondence estimator, and poses and sizes estimator. Furthermore, we propose a global enhancement block to reinforce the features with global information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Queries deformation estimator is used to deform the queries \\( Q_{cat} \\) from the general category-specific representation to an object-specific one for the observed input object using the input instance geometry feature \\( F_{obj} \\), which can" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14057" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.198, + 0.106 + ], + "angle": 0, + "content": "be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.118, + 0.47, + 0.136 + ], + "angle": 0, + "content": "\\[\nQ _ {o b j} = Q D E \\left(Q _ {c a t}, F _ {o b j}\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.144, + 0.47, + 0.237 + ], + "angle": 0, + "content": "where \\( Q_{obj} \\in \\mathbb{R}^{N_{cat} \\times d} \\) denotes the deformed queries. \\( QDE \\) denotes the queries deformation estimator. In this process, we adopt the attention mechanism to extract the information of regions of interest from \\( F_{obj} \\) adaptively. After deforming the queries, the canonical point cloud can be decoded from \\( Q_{obj} \\) denoted as:" + }, + { + "type": "equation", + "bbox": [ + 0.22, + 0.246, + 0.47, + 0.265 + ], + "angle": 0, + "content": "\\[\nP _ {i} = \\Phi_ {1} (Q _ {o b j}) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.272, + 0.471, + 0.455 + ], + "angle": 0, + "content": "where \\( P_{i} \\in \\mathbb{R}^{N_{\\text{cat}} \\times 3} \\) denotes the object's canonical sparse point cloud. \\( \\Phi_{1} \\) denotes the decoder implemented by an MLP (multi-layer perceptron). Supervision is applied to \\( P_{i} \\) to help better guide the learning of \\( Q_{obj} \\) via the loss function \\( L_{rec} \\). Query-point correspondence estimator is used to estimate the correspondences between deformed queries \\( Q_{obj} \\) and object feature \\( F_{obj} \\). The correspondence then is used to combine \\( Q_{obj} \\) with \\( F_{obj} \\) as matching feature pairs. These pairs are fed forward an MLP and a global enhancement block. The result is denoted as \\( F_{nocs} \\). The corresponding NOCS coordinates of the observed object point cloud are obtained from \\( F_{nocs} \\) using an MLP." + }, + { + "type": "equation", + "bbox": [ + 0.217, + 0.465, + 0.47, + 0.482 + ], + "angle": 0, + "content": "\\[\nP _ {r} = \\Phi_ {2} \\left(F _ {\\text {n o c s}}\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.47, + 0.581 + ], + "angle": 0, + "content": "where \\( P_r \\in \\mathbb{R}^{N_{obj} \\times 3} \\) denotes the corresponding NOCS coordinates. \\( \\Phi_2 \\) is an MLP. \\( P_r \\) does not take part in the calculation of objects' poses and sizes but only participates in the calculation of the loss function \\( L_{nocs} \\). This loss function is an auxiliary loss function, which is used to apply supervision on \\( P_r \\) in order to guide the learning of \\( F_{nocs} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.582, + 0.47, + 0.613 + ], + "angle": 0, + "content": "The pose and size estimator takes the previous output and gives the object's pose and size with three parallel MLPs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.621, + 0.358, + 0.637 + ], + "angle": 0, + "content": "3.2. Queries Deformation Estimator" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.47, + 0.84 + ], + "angle": 0, + "content": "In the queries deformation estimator, we aim to deform the queries \\( Q_{cat} \\) to a representation of the observed target object. This goal can be achieved by injecting the object geometry feature \\( F_{obj} \\) into \\( Q_{cat} \\). Due to the unordered property of the point cloud, the PointNet [26] style operation, which is mainly composed of pooling, is adopted by many methods such as [30, 38]. However, this operation loses the detailed geometry structure and cannot adaptively pay attention to features of interest. Therefore, we use the cross-attention mechanism. Thanks to the permutation-invariance of the attention mechanism, it is feasible to implement it for point cloud processing. Moreover, we enhance the feature using the proposed global enhancement block." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "The detailed structure of the queries deformation estimator is illustrated in Figure 2. Cross-attention is computed to determine which feature in \\( F_{obj} \\) is necessary to extract into \\( Q_{cat} \\). Specifically, we take the \\( Q_{cat} \\) as the query and" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.1, + 0.895, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.204, + 0.894, + 0.296 + ], + "angle": 0, + "content": "Figure 3: Overview of the global enhancement block. The input feature \\( f \\) pass through a global average pooling operation and a fully-connected layer to create a global feature \\( g \\). Then, the input feature \\( f \\) serves as the query, and the global feature \\( g \\) serves as both key and value. A self-attention mechanism is then applied to them." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.322, + 0.893, + 0.368 + ], + "angle": 0, + "content": "the \\(F_{obj}\\) as key and value of the multi-head cross-attention module. The computation of attention map can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.378, + 0.892, + 0.398 + ], + "angle": 0, + "content": "\\[\nA ^ {(m)} = \\operatorname {N o r m} \\left(\\Psi_ {1} \\left(Q _ {c a t}\\right) \\left(F _ {o b j}\\right) ^ {T}\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.407, + 0.893, + 0.532 + ], + "angle": 0, + "content": "where \\(A^{(m)}\\in \\mathbb{R}^{N_{cat}\\times N_{obj}}\\) is the attention map in the mth head. Norm is the normalization function. Instead of using learnable linear projections, we use \\(\\Psi_{1}\\), an MLP, applied to \\(Q_{cat}\\) in order to reduce the gap between \\(Q_{cat}\\) and \\(F_{obj}\\) and it experimentally works better. Vanilla attention uses softmax to normalize the attention map, which can be formulated as norm = \\(\\frac{f(x_i)}{\\sum_k f(x_k)}\\) where \\(f(x) = e^x\\) for softmax. Different from that, we use:" + }, + { + "type": "equation", + "bbox": [ + 0.638, + 0.541, + 0.892, + 0.569 + ], + "angle": 0, + "content": "\\[\nf (x) = \\frac {\\alpha}{1 + e ^ {- x}} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.579, + 0.893, + 0.759 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is a learnable parameter. This is a sigmoid function with a learnable parameter. This function's output is limited between 0 and \\(\\alpha\\), so there is no need to scale the dot-product result between query and key by dividing by \\(\\sqrt{d}\\). This function tends to saturate and thus activate larger regions than softmax does, and the learnable parameter allows the model to choose the range. Since each query corresponds to a certain semantic part of the object in a specific category, the attention map indicates which component of the observed object has the same semantics as the query by calculating the similarity between the queries \\(Q_{cat}\\) and the object feature \\(F_{obj}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.76, + 0.894, + 0.788 + ], + "angle": 0, + "content": "Then, the multi-head cross-attention can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.789, + 0.892, + 0.808 + ], + "angle": 0, + "content": "\\[\nD = \\left[ A ^ {(1)} F _ {o b j}; \\dots ; A ^ {(m)} F _ {o b j} \\right] W _ {v} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.812, + 0.893, + 0.874 + ], + "angle": 0, + "content": "where \\(D \\in \\mathbb{R}^{N_{cat} \\times d}\\) is the multi-head cross-attention result and \\(W_v\\) is the learnable parameter. In this way, the related object feature is extracted from the \\(F_{obj}\\). Then \\(D\\) can be used to deform \\(Q_{cat}\\) by adding it to \\(Q_{cat}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.886, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\nQ _ {o b j} = Q _ {c a t} + D \\tag {7}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14058" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.373, + 0.107 + ], + "angle": 0, + "content": "where \\(Q_{obj} \\in \\mathbb{R}^{N_{cat} \\times d}\\) is deformed queries." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.107, + 0.47, + 0.138 + ], + "angle": 0, + "content": "\\(Q_{obj}\\) is expected to embed the object's canonical point cloud. It can be decoded into 3D points using a simple MLP." + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.152, + 0.469, + 0.168 + ], + "angle": 0, + "content": "\\[\nP _ {i} = \\operatorname {S i g m o i d} \\left(M L P \\left(Q _ {o b j}\\right)\\right) - 0. 5 \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.173, + 0.469, + 0.249 + ], + "angle": 0, + "content": "where \\( P_{i} \\in \\mathbb{R}^{N_{\\text{cat}} \\times 3} \\). A Sigmoid function is used to limit it to \\((-0.5, 0.5)\\), so the output points are in canonical space. We apply supervision to \\( P_{i} \\) which could guide the learning of \\( Q_{obj} \\). Therefore, loss function \\( L_{rec} \\) is applied to \\( P_{i} \\) to provide supervision to it." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.25, + 0.469, + 0.339 + ], + "angle": 0, + "content": "Global enhancement block tends to enhance features by fusing their global feature. Normally, this can be achieved via the self-attention mechanism. However, to make the entire model lightweight, a more efficient block is needed. For this reason, we propose a global enhancement block." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.34, + 0.469, + 0.416 + ], + "angle": 0, + "content": "The global enhancement block is illustrated in Figure 3. Suppose the global enhancement block takes feature \\( f \\in \\mathbb{R}^{N \\times d} \\) as input. We adopt the result of the global average pooling as the global feature and pass it through a fully connected layer. The outcome is denoted as \\( g \\):" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.427, + 0.469, + 0.443 + ], + "angle": 0, + "content": "\\[\ng = F C \\left(A v g P o o l (f)\\right) \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.453, + 0.469, + 0.528 + ], + "angle": 0, + "content": "where \\(FC\\) is a fully connected layer. Instead of simply concatenating it to \\(f\\) and then feeding it to an MLP, we borrow the idea from self-attention as shown in Figure 3. We use \\(f\\) as query and \\(g\\) as key and value to carry out self-attention, which can be denoted as:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.539, + 0.469, + 0.557 + ], + "angle": 0, + "content": "\\[\nf ^ {\\prime} = f + \\operatorname {N o r m} \\left(f g ^ {T}\\right) g \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.567, + 0.469, + 0.673 + ], + "angle": 0, + "content": "After that, \\( f' \\) is fed into an MLP with residual. In this way, global information is injected into the feature. This block, unlike vanilla self-attention, reduces the complexity of the computation. Compared with the computation complexity of vanilla self-attention, \\( O(N^2 \\times d) \\), our efficient global enhancement block has a computation complexity of \\( O(N \\times d) \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.682, + 0.421, + 0.698 + ], + "angle": 0, + "content": "3.3. Query-Point Correspondence Estimator" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.705, + 0.47, + 0.902 + ], + "angle": 0, + "content": "We obtain the deformed queries \\( Q_{obj} \\) by adaptively selecting feature from the observed object feature \\( F_{obj} \\). In previous works, a correspondence matrix \\( A \\in \\mathbb{R}^{N_{obj} \\times N_{cat}} \\) is estimated, which models correspondences between points in observed point cloud \\( P_{obj} \\) and reconstructed point cloud \\( P_i \\). This matrix then samples the points from \\( P_i \\) to be paired with \\( P_{obj} \\), and it can be formulated as \\( P = A \\times P_i \\), where \\( P \\) denotes the sampled points. Finally, solving of Umeyama algorithm [31] to align the sample points with \\( P_i \\) gives out the target pose and size. Instead of using this conventional way, we move this process to the feature space. In the query-point correspondence estimator, the correspondences between \\( F_{obj} \\) and \\( Q_{obj} \\) are built as illustrated in Figure 2." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "In detail, the correspondences are built by computing the similarity between \\( F_{obj} \\) and \\( Q_{obj} \\) using dot-product, which can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.144, + 0.892, + 0.162 + ], + "angle": 0, + "content": "\\[\nA ^ {\\prime} = \\operatorname {N o r m} \\left(\\Psi_ {2} \\left(F _ {o b j}\\right) \\left(Q _ {o b j}\\right) ^ {T}\\right) \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.892, + 0.501 + ], + "angle": 0, + "content": "where \\( A' \\in \\mathbb{R}^{N_{obj} \\times N_{cat}} \\) denotes the correspondence matrix between \\( F_{obj} \\) and \\( Q_{obj} \\). Norm is the same as that used in queries deformation estimator. \\( \\Psi_2 \\) is an MLP. \\( A' \\) represents the soft matching between \\( F_{obj} \\) and \\( Q_{obj} \\). Then we multiply \\( A' \\) by \\( Q_{obj} \\) to obtain the sampled features. Essentially, we find that this process is similar to cross-attention. For this reason, we add \\( F_{obj} \\) to the result for implementing a residual structure similar to attention mechanism. Also, we implement multi-head technique to the computation. Next, we need to pair the object feature with the sampled feature. Experimentally, it is better to use a more direct feature as the object feature here instead of the deep object feature \\( F_{obj} \\). Thereby, we do not use \\( F_{obj} \\) but simply feed object point cloud \\( P_{obj} \\) forward an MLP. The output of the MLP is concatenated to the sampled feature. To further enhance the feature, we use an MLP and a global enhancement block after that. The result is denoted as \\( F_{nocs} \\). To apply supervision on \\( F_{nocs} \\) and better guide its learning, we use a simple MLP to transform \\( F_{nocs} \\) into NOCS coordinates denoted as \\( P_r \\in \\mathbb{R}^{N_{obj} \\times 3} \\). \\( P_r \\) is not used to solve the Umeyama algorithm to obtain target pose and size, but only used to compute loss function \\( L_{nocs} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.509, + 0.736, + 0.523 + ], + "angle": 0, + "content": "3.4. Poses and Sizes Estimator" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.533, + 0.892, + 0.593 + ], + "angle": 0, + "content": "The rest of the work is to obtain the final object's pose and size, which is accomplished in the pose and size estimator. The pose and size estimator applies global average pooling operation to \\( F_{nocs} \\), which can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.601, + 0.891, + 0.617 + ], + "angle": 0, + "content": "\\[\nf _ {\\text {p o s e}} = \\operatorname {A v g P o o l} \\left(F _ {\\text {n o c s}}\\right) \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.624, + 0.892, + 0.656 + ], + "angle": 0, + "content": "where \\(f_{\\text{pose}} \\in \\mathbb{R}^{1 \\times d}\\). Then after it, three parallel MLPs predict the rotation \\(R\\), translation \\(t\\), and size \\(s\\) respectively." + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.678, + 0.891, + 0.695 + ], + "angle": 0, + "content": "\\[\nR, t, s = M L P \\left(f _ {p o s e}\\right), M L P \\left(f _ {p o s e}\\right), M L P \\left(f _ {p o s e}\\right) \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.702, + 0.892, + 0.778 + ], + "angle": 0, + "content": "The representation of \\( R \\) here is the Continuity of Rotation Representations [40]. For \\( s \\), we follow [3] to estimate the residual between object's size and the mean category size. Similarly, for \\( t \\), we predict the residual between the translation ground truth and the mean value of the point cloud." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.785, + 0.708, + 0.8 + ], + "angle": 0, + "content": "3.5. Overall Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.809, + 0.776, + 0.823 + ], + "angle": 0, + "content": "The overall loss function is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.832, + 0.892, + 0.849 + ], + "angle": 0, + "content": "\\[\nL = \\lambda_ {1} L _ {\\text {p o s e}} + \\lambda_ {2} L _ {\\text {r e c}} + \\lambda_ {3} L _ {\\text {n o c s}} \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\(L_{\\text{pose}}\\) is used to compute loss on predicted \\(R, t\\) and \\(s\\). We simply use smooth L1 loss [8] for all of them with threshold of \\(1 \\times 10^{-3}, 5 \\times 10^{-3}, 5 \\times 10^{-3}\\) respectively. \\(L_{\\text{rec}}\\) and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14059" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.182 + ], + "angle": 0, + "content": "\\(L_{nocs}\\) are the auxiliary losses function for \\(P_{i}\\) and \\(P_{r}\\) respectively. \\(L_{rec}\\) is applied to \\(P_{i}\\) to encourage it to reconstruct the instance point cloud in the NOCS space. Therefore, for \\(L_{rec}\\), we use Chamfer distance between \\(P_{i}\\) and \\(M_{gt}\\) where \\(M_{gt} \\in \\mathbb{R}^{N_{obj} \\times 3}\\) represents the instance point cloud model in the NOCS space. \\(L_{rec}\\) can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.19, + 0.469, + 0.267 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {r e c} = \\frac {1}{N _ {c a t}} \\sum_ {x _ {i} \\in P _ {r}} \\min _ {y _ {j} \\in M _ {g t}} \\| x _ {i} - y _ {j} \\| _ {2} ^ {2} + \\\\ \\frac {1}{N _ {o b j}} \\sum_ {y _ {i} \\in M _ {g t}} \\min _ {x _ {i} \\in P _ {r}} \\| x _ {i} - y _ {j} \\| _ {2} ^ {2} \\tag {15} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.275, + 0.469, + 0.335 + ], + "angle": 0, + "content": "\\(L_{nocs}\\) is applied on \\(P_r\\) to encourage it in predicting the corresponding coordinates of \\(P_{obj}\\) in Normalized Object Coordinate Space. For \\(L_{nocs}\\), we also use a smooth L1 loss [8] with a threshold of 0.1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.347, + 0.21, + 0.364 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.373, + 0.469, + 0.584 + ], + "angle": 0, + "content": "Datasets. We conduct experiments using the benchmark CAMERA25 and REAL275 [34] datasets for category-level 6D object pose and size estimation which consists of six object categories. The CAMERA25 dataset is generated by rendering and compositing synthetic object instances under different views. The CAMERA25 dataset contains 300K synthetic images of 1,085 object instances, among which 25,000 images of 184 instances are used for evaluation. The REAL275 dataset is complementary to the CAMERA25 dataset. It includes 4,300 real-world images of 6 scenes with 3 unseen instances per category; its training set contains 4,300 images of 7 scenes, and the test set contains 2,750 images of 6 scenes. We train our model with a combined use of the two datasets, as done in [18]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.585, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Implement Details. We employ a Mask R-CNN [9] to obtain instance masks the same as [30]. The instances are then cropped based on the segmentation result. After that, the depth is converted to the instance point cloud using the camera's intrinsic parameters. 1024 points are randomly sampled from that, so \\( N_{obj} \\) is set to 1024. To extract instance geometry features, we choose PointNet++ [27] with four abstraction levels. The number of prior queries \\( N_{cat} \\) is set to 64. In this case, \\( N_{cat} \\ll N_{obj} \\). A detailed study on the parameter \\( N_{cat} \\) is given in our ablation study. The queries are initialized randomly at the beginning of training. The dimension of features and queries is set to 256. The crossattention in queries deformation estimator and query-point correspondence estimator has four heads each. In the loss function, we set \\( \\lambda_1, \\lambda_2, \\lambda_3 \\) to 1.0, 3.0, 1.0, respectively. We use AdamW [21] to train this model with an initial learning rate of \\( 1 \\times 10^{-4} \\) and weight decay \\( 1 \\times 10^{-4} \\). All models are trained 42k iterations with batch size of 60 and cosine learning rate decay is conducted. We employ several strategies for depth augmentation, such as adding Gaussian noise, random scaling, random rotation, adding random points as well" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.166 + ], + "angle": 0, + "content": "as linear shape augmentation proposed in [3] and non-linear shape augmentation proposed in [38]. All FPS(Frames Per Second) data of our method is evaluated on a single RTX 2080Ti, an Intel(R) Xeon(R) CPU E5-2650 v4 @ 2.20GHz, PyTorch [24] 1.10, CUDA version 11.1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.892, + 0.213 + ], + "angle": 0, + "content": "Evaluation Metrics. For category-level pose estimation, we follow [34] and use two metrics to evaluate the quality." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.222, + 0.892, + 0.298 + ], + "angle": 0, + "content": "- 3D IoU. The overlap of two 3D bounding boxes under the predicted pose and the ground truth pose is computed. The overlap ratios larger than the threshold are regarded as accepted. The mean Average Precision (mAP) of the overlapping is reported." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.308, + 0.892, + 0.368 + ], + "angle": 0, + "content": "- \\(n^{\\circ}m\\) cm. The rotation and translation errors between the predicted pose and the ground truth pose are computed. The errors smaller than an angle threshold \\(n^{\\circ}\\) and a translation threshold \\(m\\) cm are accepted." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.222, + 0.892, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.377, + 0.816, + 0.394 + ], + "angle": 0, + "content": "4.1. Comparisons with Existing Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.4, + 0.892, + 0.597 + ], + "angle": 0, + "content": "NOCS-REAL275 In Table 1 we compare our method with the existing ones for category-level 6D object pose and size estimation. We divide these methods into two groups: those with and without shape prior. As it is shown in Table 1, our method outperforms other existing methods. In detail, we outperform NOCS [34] by 46.0 in \\( IoU_{75} \\), 41.8 in \\( 5^{\\circ}2cm \\), 48.9 in \\( 5^{\\circ}5cm \\). Moreover, we achieve a better result than existing methods that using prior information. Specifically, we outperform SPD [30] by 22.9 in \\( IoU_{75} \\), 29.7 in \\( 5^{\\circ}2cm \\), 37.5 in \\( 5^{\\circ}5cm \\) and 14.2, 13.1, and 19.3 higher than SGPA [2] which is a representative method based on attention. This outcome demonstrates that our sparse shape prior is superior to the traditional shape prior." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.597, + 0.892, + 0.672 + ], + "angle": 0, + "content": "NOCS-CAMERA25 The results for CAMERA25 are shown Table 1. Our method outperforms others at least 4.9, 4.3 in the items of \\(5^{\\circ}2cm\\), \\(5^{\\circ}5cm\\), and it is on par with the best methods for \\(IoU_{75}\\). Figure 4 presents a more detailed error evaluation result on two datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.682, + 0.665, + 0.696 + ], + "angle": 0, + "content": "4.2. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effect of the design in Query6DoF. We verify the efficacy of each component in Query6DoF in Table 2. By replacing queries with point cloud proposed in [30] and adding an extra PointNet++ [27] after the prior point cloud as a feature extractor, \\(5^{\\circ}2cm\\) drops from 49.0 to 47.2, and computation increases. Removing the global enhancement block results in a 4.8 drop in \\(5^{\\circ}2cm\\). Removing the queries deformation estimator results in a 2.5 drop in \\(5^{\\circ}2cm\\). If the query-point correspondence estimator is detached, it renders the usage of queries and queries deformation estimator senseless. Therefore, without using them together, our method experiences a 13.6 drop in \\(5^{\\circ}2cm\\). Moreover, we remove the poses and sizes estimator but use \\(P_r\\) and \\(P_i\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14060" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.121 + ], + "angle": 0, + "content": "Table 1: Comparison with state-of-the-art methods on the CAMERA25 dataset and REAL275 dataset. * denotes results without linear shape augmentation and non-linear shape augmentation. The best results shown in bold." + }, + { + "type": "table", + "bbox": [ + 0.117, + 0.131, + 0.851, + 0.284 + ], + "angle": 0, + "content": "
MethodpriorCAMERA25REAL275
IoU50IoU755°2cm5°5cm10°2cm10°5cmIoU50IoU755°2cm5°5cm10°2cm10°5cm
NOCS [34]83.969.532.340.948.264.678.030.17.210.013.825.2
DualPoseNet [18]92.486.464.770.777.284.779.862.229.335.950.066.8
GPV-Pose [7]93.488.372.179.1-89.083.064.432.042.9-73.3
SPD [30]✓93.283.154.359.073.381.577.353.219.321.443.254.1
CR-Net [35]✓93.888.072.076.481.087.779.355.927.834.347.260.8
SAR-Net [16]✓86.879.066.770.975.680.379.362.431.642.350.368.3
SGPA [2]✓93.288.170.774.582.788.480.161.935.939.661.370.7
RBP-Pose [38]✓93.189.073.579.682.189.5-67.838.248.163.179.2
Self-DPDN [17]✓------83.676.046.050.770.478.4
Ours*✓92.388.678.483.984.090.582.976.046.854.767.981.6
Ours✓91.988.178.083.183.990.082.576.149.058.968.783.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.296, + 0.895, + 0.342 + ], + "angle": 0, + "content": "Table 2: Effect of the design on Query6DoF, evaluated on the REAL275 dataset. GlobEnhance denotes the global enhancement block, QueryDeform denotes the queries deformation estimator, Query2Point denotes the query-point correspondence estimator, and PoseSize denotes the poses and sizes estimator" + }, + { + "type": "table", + "bbox": [ + 0.117, + 0.353, + 0.851, + 0.448 + ], + "angle": 0, + "content": "
QueriesGlobEnhanceQueryDeformQuery2PointPoseSizeI0U50I0U755°2cm5°5cm10°2cm10°5cm
1-✓✓✓✓82.175.447.256.267.381.2
2✓-✓✓✓82.675.744.253.365.881.1
3✓✓-✓✓83.075.346.556.665.981.3
4-✓--✓82.170.935.448.759.580.2
5✓✓✓✓-82.270.040.046.365.176.5
6✓✓✓✓✓82.576.149.058.968.783.0
" + }, + { + "type": "image", + "bbox": [ + 0.105, + 0.471, + 0.449, + 0.699 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.714, + 0.47, + 0.759 + ], + "angle": 0, + "content": "Figure 4: Mean Average Precision (mAP) in different thresholds. REAL275 (top rows) and CAMERA25 (bottom rows)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.792, + 0.469, + 0.822 + ], + "angle": 0, + "content": "to obtain poses and sizes via Umeyama [31]. As a result, \\(5^{\\circ}2cm\\) falls by 9.0 points." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Effect of the number of prior queries. In our method, we use sparse queries to represent the shape prior. In this experiment, we investigate the effect of the number of prior queries \\( N_{cat} \\) on the results of REAL275. Table 3 presents the result of the ablation of the effect of the number of prior" + }, + { + "type": "table_caption", + "bbox": [ + 0.517, + 0.469, + 0.875, + 0.485 + ], + "angle": 0, + "content": "Table 3: Effect of the number of queries on REAL275" + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.495, + 0.868, + 0.595 + ], + "angle": 0, + "content": "
NcatIoU50IoU755°2cm5°5cm10°2cm10°5cm
1682.574.646.055.466.681.0
3282.574.946.755.967.281.5
6482.676.149.058.968.783.0
12882.876.946.155.968.882.8
25682.876.647.657.367.881.6
51282.675.646.856.266.981.4
102483.176.748.756.870.482.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.608, + 0.892, + 0.638 + ], + "angle": 0, + "content": "Table 4: Effect of different attention normalization evaluated on REAL275." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.649, + 0.889, + 0.694 + ], + "angle": 0, + "content": "
NormI0U50I0U755°2cm5°5cm10°2cm10°5cm
Softmax82.174.748.657.268.682.4
Ours82.576.149.058.968.783.0
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.885 + ], + "angle": 0, + "content": "queries. The results show that reducing the number of prior queries does not significantly affect the performance of our method. This fact means that it is not necessary to use excessive points to express the object's shape prior. A small number of queries can effectively represent the object's shape. Specifically, when \\( N_{cat} = 64 \\), our method achieves the best performance in the \\( 5^{\\circ}2cm \\), \\( 5^{\\circ}5cm \\), \\( 10^{\\circ}5cm \\) metrics and when \\( N_{cat} = 1024 \\), our method achieves the best performance in the \\( IoU_{50} \\) metric. However, the smaller \\( N_{cat} \\) results in less computational overhead. Therefore, we adopt \\( N_{cat} = 64 \\) as the default setting in all other experiments." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.886, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Effect of different attention normalization. While" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14061" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.091, + 0.849, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.22, + 0.181, + 0.75, + 0.198 + ], + "angle": 0, + "content": "Figure 5: Qualitative results of our method (red line) and SGPA [2] (green line)." + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.212, + 0.85, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.397, + 0.895, + 0.429 + ], + "angle": 0, + "content": "Figure 6: Sparse point cloud reconstruction in the REAL275 dataset. The yellow points represent the reconstruction points \\( P_{i} \\), while the blue points are the observed point cloud." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.452, + 0.471, + 0.498 + ], + "angle": 0, + "content": "Table 5: Model complexity and FPS w/o Mask R-CNN [9], evaluated on REAL275. GEB denotes the global enhancement block." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.509, + 0.467, + 0.574 + ], + "angle": 0, + "content": "
MethodParams(M)FPS w/o Mask R-CNN [9]5°2cm
Ncat = 64 (Default)19.5334.949.0
Ncat = 102421.1823.348.7
w/o GEB18.7136.844.2
w/o Queries22.2424.047.2
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.603, + 0.47, + 0.724 + ], + "angle": 0, + "content": "common attention mechanisms adopt softmax to normalize the attention map, in our method, we use a different normalization approach, namely sigmoid with a learnable parameter mentioned earlier. In this experiment, we compare two different settings shown in Table 4. We conduct the evaluation on the REAL275 dataset. Using softmax to normalize results in a 1.4 drop in \\( IoU_{75} \\) and a 0.4 drop in \\( 5^{\\circ}2cm \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.74, + 0.251, + 0.756 + ], + "angle": 0, + "content": "4.3. Runtime Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "As shown in Table 5, our method, in the default setting, has 19.43M parameters and runs at 34.9 FPS without Mask R-CNN [9]. Increasing \\( N_{cat} \\) to 1024 brings no gain but the FPS drops to 23.3, which shows that sparse queries are sufficient to represent the shape prior. Adding the global enhancement block results in a 4.8 improvement in \\( 5^{\\circ}2cm \\) with only a 1.9 FPS drop, demonstrating its efficiency. W/o Queries means that we replace the queries with the prelearned shape prior proposed in [30] and use PointNet++" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.454, + 0.892, + 0.531 + ], + "angle": 0, + "content": "[27] as a feature extractor. In this way, due to the extra PointNet++ [27], the speed drops to 24.0FPS, but there is no gain in \\(5^{\\circ}2cm\\). Therefore, the usage of queries is more efficient than using point cloud both in terms of accuracy and speed." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.538, + 0.638, + 0.552 + ], + "angle": 0, + "content": "4.4. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.607 + ], + "angle": 0, + "content": "Qualitative Results. Figure 5 shows the qualitative results of our method, demonstrating that our method can accurately estimate the objects' poses and sizes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.608, + 0.893, + 0.789 + ], + "angle": 0, + "content": "Sparse point cloud reconstruction. Our method outputs \\( P_{i} \\) as the sparse point cloud reconstruction in NOCS space. We align \\( P_{i} \\) to the object's location in RGB images for better comparison with the object's actual shape, as shown in Figure 6. \\( P_{i} \\) is the yellow points in it. The blue points in it represent the observed point cloud for comparison. It shows that our sparse point cloud can accurately cover different objects' shapes. This effect can be attributed to our queries deformation estimator, where category-specific queries transformed into instance-specific ones. Through this process, the queries are able to reconstruct the objects." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.801, + 0.619, + 0.815 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.903 + ], + "angle": 0, + "content": "In conclusion, we present a novel network for category-level 6D object pose and size estimation, namely Query6DoF. In particular, we propose to use a series of sparse and learnable queries serving as a shape prior, which is a set of tokens that implicitly represent objects in a cer" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14062" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.304 + ], + "angle": 0, + "content": "tain category. Furthermore, we transform the traditional deformation-and-matching paradigm to the feature space using attention. Specifically, the queries are deformed by a process where we dynamically use the attention mechanism to select object features and incorporate them into queries. This step transforms the queries into a representation of a certain target object. Next, we establish the correspondences between deformed queries and object features. Finally, the poses and sizes are regressed using the correspondences. Thanks to learnable queries and direct output results, the queries are trained directly alongside the entire network. This method achieves state-of-the-art performance compared to other existing methods and holds promise for applications in robotics and augmented reality." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.304, + 0.47, + 0.365 + ], + "angle": 0, + "content": "Acknowledgement This work was supported by the Key Research Project of Zhejiang Lab (No. G2021NB0AL03) and Modern Agriculture Major-core Technology Innovation Project of Jiangsu Province (No. cx(22)2031)." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.379, + 0.175, + 0.395 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.405, + 0.47, + 0.475 + ], + "angle": 0, + "content": "[1] Tuo Cao, Fei Luo, Yanping Fu, Wenxiao Zhang, Shengjie Zheng, and Chunxia Xiao. Dgecn: A depth-guided edge convolutional network for end-to-end 6d pose estimation. 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IEEE Transactions on Image Processing, 31:6907-6921, 2022." + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.755 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14064" + } + ] +] \ No newline at end of file diff --git a/2023/Query6DoF_ Learning Sparse Queries as Implicit Shape Prior for Category-Level 6DoF Pose Estimation/4d1aafad-a31c-4773-aac8-62fd2260bfdc_origin.pdf b/2023/Query6DoF_ Learning Sparse Queries as Implicit Shape Prior for Category-Level 6DoF Pose Estimation/4d1aafad-a31c-4773-aac8-62fd2260bfdc_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1fdeb61fcfd4b7615ecb9ef3ba005dee750f5e59 --- /dev/null +++ b/2023/Query6DoF_ Learning Sparse Queries as Implicit Shape Prior for Category-Level 6DoF Pose Estimation/4d1aafad-a31c-4773-aac8-62fd2260bfdc_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:22f5ee5a92084f55e0f8e9784e0a282b37a2ecb53a439531f5ce03b112476779 +size 2018226 diff --git a/2023/Query6DoF_ Learning Sparse Queries as Implicit Shape Prior for Category-Level 6DoF Pose Estimation/full.md b/2023/Query6DoF_ Learning Sparse Queries as Implicit Shape Prior for Category-Level 6DoF Pose Estimation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ad8c3b92f2f3138f88fb4e473c97f882b46a2974 --- /dev/null +++ b/2023/Query6DoF_ Learning Sparse Queries as Implicit Shape Prior for Category-Level 6DoF Pose Estimation/full.md @@ -0,0 +1,325 @@ +# Query6DoF: Learning Sparse Queries as Implicit Shape Prior for Category-Level 6DoF Pose Estimation + +Ruiqi Wang $^{1}$ , Xinggang Wang $^{1}$ , Te Li $^{\dagger,2,3}$ , Rong Yang $^{2,3}$ , Minhong Wan $^{\dagger,2,3}$ , Wenyu Liu $^{\dagger,1}$ + +1Hubei Key Laboratory of Smart Internet Technology, School of Electronic Information and Communications, Huazhong University of Science and Technology + +$^{2}$ Research Center for Intelligent Robotics, Research Institute of Interdisciplinary Innovation, Zhejiang Lab, China $^{3}$ Zhejiang Engineering Research Center for Intelligent Robotics, China + +# Abstract + +Category-level 6DoF object pose estimation intends to estimate the rotation, translation, and size of unseen objects. Many previous works use point clouds as a prelearned shape prior to overcome intra-category variability. The shape prior is deformed to reconstruct instances' point clouds in canonical space and to build dense 3D-3D correspondences between the observed and reconstructed point clouds. However, the pre-learned shape prior is not jointly optimized with estimation networks, and they are trained with a surrogate objective. We propose a novel 6D pose estimation network, named Query6DoF, based on a series of category-specific sparse queries that represent the prior shape. Each query represents a shape component, and these queries are learnable embeddings that can be optimized together with the estimation network according to the point cloud reconstruction loss, the normalized object coordinate loss, and the 6d pose estimation loss. Query6DoF adopts a deformation-and-matching paradigm with attention, where the queries dynamically extract features from regions of interest using the attention mechanism and then directly regress results. Furthermore, Query6DoF reduces computation overhead through the sparseness of the queries and the incorporation of a lightweight global information injection block. With the aforementioned design, Query6DoF achieves state-of-the-art (SOTA) pose estimation performance on the NOCS datasets. The source code and models are available at https://github.com/hustvl/Query6DoF. + +![](images/e34ba91f291e408c6a57e410f6633b07e3ac9fc2096063fbcb267123ba295735.jpg) +Figure 1: Comparisons with conventional works. a) Conventional methods adopt pre-learned shape prior and have a two-stage pipeline, i.e., deforming the prior and building correspondences between points. b) Our method uses sparse learnable queries as the shape prior and conducts query/feature-based deformation and matching. + +# 1. Introduction + +Category-level object pose estimation is aimed at estimating an object's rotation, translation, and size from an RGB-D scene within a given set of categories. This task has attracted increasing attention due to its vital role in robotics [5], 3D understanding [4, 22], and augmented reality [29]. Compared with instance-level object pose estimation, category-level object pose estimation doesn't require obtaining the object's CAD model in advance, making it more generally applicable. + +Many existing methods [2, 7, 16, 30, 41, 38, 20, 35] solve this problem as shown in Figure 1(a). First, they attempt to reconstruct the input object point cloud in the Normalized Object Coordinate Space [34] (NOCS). Then they estimate the 3D-3D correspondences between the input ob + +served point cloud and the reconstructed object point cloud. Finally, they determine object poses and sizes by applying the Umeyama algorithm [31] to these correspondences. To handle intra-category variability, a shape prior, which represents a basic shape for objects in the same category, is introduced in [30] to this task. This shape prior is a set of point clouds pre-learned in NOCS for each category. Objects are reconstructed by deforming the shape prior. However, this approach has its drawbacks: 1) the shape prior is a dense representation of objects in a specific category, which is not only redundant but also makes the network computationally expensive. 2) the shape prior is pre-learned in advance and remains static during model training. Additionally, these methods are trained to predict the deformation field $D$ and a correspondence matrix $A$ , which is a surrogate task. 3) Conventional model architectures [30, 3, 2] typically rely on either pooling operations in the PointNet [26] style or 3D graph convolution (3DGC) [19] to explore geometry features. However, the pooling operation can result in the loss of local geometry features, and these operations are not adaptive to extract the feature information. + +To address these issues, we propose a novel method called Query6DoF (illustrated in Figure 1(b)). Instead of relying on dense and static point clouds as the shape prior, we introduce a series of sparse and learnable category-specific queries. Each query in this series is designed to encode a specific component of an object's shape with implicitly shared semantics and is optimized concurrently with the whole model parameters. Due to intra-category variability, the queries only need to capture the most representative components of objects and disregard unrepresentative shape details. Consequently, the queries can be sparse. Moreover, due to the sparseness of queries, the sparseness of the queries reduces computational overhead. Therefore, there is no need to use techniques such as Low-Rank transformer [36] mentioned in SGPA [2]. To eliminate the need for surrogate training objectives, we employ a direct prediction framework. However, unlike previous direct regression methods, e.g., [3, 20], we choose to perform the core deformation-and-matching paradigm in feature space. The deformation process is accomplished based on an attention mechanism, which adaptively extracts information from instance features to queries. This transforms queries from category-specific into instance-specific shape representations. Then, correspondences between instance features and deformed queries are established by computing their similarity. Using these correspondences, the instance features are paired with deformed queries. Finally, these pairs are used to determine the pose and size through a neural network. Since the shape prior already consists of implicit queries, it is reasonable to also execute the entire pipeline implicitly in the feature space to better leverage these queries. Without pre-learned prior and surrogate train + +ing objectives, our model is trained entirely and directly. As a result, the prior can be more suitable for the model, enabling us to achieve state-of-the-art performance on the task. + +Conventionally, the self-attention mechanism is used in transformers to inject global information. Unfortunately, adding self-attention layers significantly increases computational load. Therefore, we propose an efficient global enhancement layer to balance efficiency and performance. + +The main contributions of this work can be summarized as: + +- We propose to use sparse and learnable queries as shape prior rather than dense and static point clouds. In this way, the queries are optimized at the same time as the whole model to discover the optimal set of priors, and the sparseness design reduces the computation overhead. +- We adapt existing architectures to fit the novel shape prior representation with the help of attention mechanisms. We design a lightweight self-attention module in this to balance accuracy and speed. +- The overall 6DoF pose estimation accuracy of our method is better than previous state-of-the-art methods on the CAMERA25 and REAL275 datasets, especially, on the strict $5^{\circ}2cm$ metric our results are significantly better than previous methods. + +# 2. Related Work + +# 2.1. Instance-Level 6D Object Pose Estimation + +Based on the input data format, existing methods can be divided into two categories: RGB-based [15, 28, 25, 22, 37, 23] and RGB-D-based [14, 32, 10, 13] approaches. A common approach for using RGB as input to accomplish this task is to detect the object's keypoints in the image and match them to the CAD model. With the 2D-3D correspondences, the PnP algorithm is then implemented to obtain the object's pose. Additionally, some methods [12, 33, 6, 1, 39, 11] do not use PnP algorithm but instead employ neural networks to directly output object's pose. + +# 2.2. Category-level 6D Object Pose and Size Estimation + +[34] first introduced Normalized Object Coordinate Space to represent all the possible object instances in a unified space. DualPoseNet [18] introduced a network stacking an implicit decoder to impose complementary supervision on pose encoder. We absorb this practice and provide extra implicit supervision. To handle the intra-class shape variation, SPD [30] proposes a deep network to reconstruct the 3D object model by explicitly modeling the deformation from a pre-learning categorical shape prior. However, + +![](images/9fe692b59118b343603427486909eb6d560095d79be679544893fda2087bc513.jpg) +Figure 2: Entire schematic illustration of our proposed method. The target point cloud $P_{obj}$ is fed to PointNet++ [27] as a backbone to extract the object's geometry features $F_{obj}$ . A set of queries $Q_{cat}$ is prepared to serve as the shape prior. Each of the queries represents a component of object shape. The queries pass through the queries deformation estimator to gain instance shape information from $F_{obj}$ using an attention mechanism to adaptively select instance features, and then they are deformed to the specific representation of the target observed object $Q_{obj}$ . Next, in the query-point correspondence estimator, the correspondence between $Q_{obj}$ and $F_{obj}$ is built. In the end, the poses and sizes estimator makes use of the previous output. This block simply adopts global average pooling to aggregate all the input features and output resulting poses and sizes through three parallel MLPs. + +this prior is not flexible enough because it is obtained in advance and remains unchanged during training. Therefore, we propose to transform it into the learnable queries. DPDN [17] makes efforts to overcoming synthetic-to-real domain gap using self-supervised learning. We further develop its paradigm of deforming and matching in feature space with the attention mechanism to make it much more effective. SGPA [2] further leverages the advantage of category prior. It uses the transformer architecture and in order to reduce computational complexity SGPA utilized the low-rank transformer [36]. But in our work, our proposed queries do not require to this technique for its sparseness. + +# 3. Method + +# 3.1. Overview + +Given an RGB-D image, the goal of the category-level object pose and size estimation is to predict the 6D object pose and size represented by rotation $R \in SO(3)$ , translation $t \in \mathbb{R}^3$ , and size $s \in \mathbb{R}^3$ . We segment objects from the RGB image using an off-the-shelf object segmentation technique e.g., Mask R-CNN [9]. The segmented object's depth data is transferred to a 3D point cloud. Then the 3D point cloud is uniformly sampled into a fixed number. The same as [3], noting that objects' appearance varies much more than their shape even in the same category, our method only uses point cloud data as input instead of together with RGB data. + +Let's denote the observed target point cloud as $P_{obj} \in \mathbb{R}^{N_{obj} \times 3}$ . Our method uses a feature extraction module to + +extract object geometry feature $F_{obj} \in \mathbb{R}^{N_{obj} \times d}$ from $P_{obj}$ . Unlike conventional methods that use an extra set of point clouds as explicit shape priors, we prepare a set of queries $Q_{cat} \in \mathbb{R}^{N_{cat} \times d}$ for each category as implicit shape prior. Each query expresses a semantic component of the object and they are the general category-specific representation. The number of queries $N_{cat}$ can be significantly fewer than the number of points in the input point cloud $N_{obj}$ . Besides, the queries are learnable, which means that there is no pre-defined prior and the full model is trained entirely and directly. + +A traditional approach to obtaining the final poses and sizes with shape prior can be summarized as follows. First, deform the prior point cloud to reconstruct the object shape. Then, the correspondence between the reconstructed point cloud and the observed object point cloud is estimated. Afterward, poses and sizes can be solved via Umayama [31]. + +The entire schematic illustration of our proposed method is shown in Figure 2. We implement this process in feature space with an attention mechanism. Specifically, our method consists of three parts: queries deformation estimator, query-point correspondence estimator, and poses and sizes estimator. Furthermore, we propose a global enhancement block to reinforce the features with global information. + +Queries deformation estimator is used to deform the queries $Q_{cat}$ from the general category-specific representation to an object-specific one for the observed input object using the input instance geometry feature $F_{obj}$ , which can + +be formulated as: + +$$ +Q _ {o b j} = Q D E \left(Q _ {c a t}, F _ {o b j}\right) \tag {1} +$$ + +where $Q_{obj} \in \mathbb{R}^{N_{cat} \times d}$ denotes the deformed queries. $QDE$ denotes the queries deformation estimator. In this process, we adopt the attention mechanism to extract the information of regions of interest from $F_{obj}$ adaptively. After deforming the queries, the canonical point cloud can be decoded from $Q_{obj}$ denoted as: + +$$ +P _ {i} = \Phi_ {1} (Q _ {o b j}) \tag {2} +$$ + +where $P_{i} \in \mathbb{R}^{N_{\text{cat}} \times 3}$ denotes the object's canonical sparse point cloud. $\Phi_{1}$ denotes the decoder implemented by an MLP (multi-layer perceptron). Supervision is applied to $P_{i}$ to help better guide the learning of $Q_{obj}$ via the loss function $L_{rec}$ . Query-point correspondence estimator is used to estimate the correspondences between deformed queries $Q_{obj}$ and object feature $F_{obj}$ . The correspondence then is used to combine $Q_{obj}$ with $F_{obj}$ as matching feature pairs. These pairs are fed forward an MLP and a global enhancement block. The result is denoted as $F_{nocs}$ . The corresponding NOCS coordinates of the observed object point cloud are obtained from $F_{nocs}$ using an MLP. + +$$ +P _ {r} = \Phi_ {2} \left(F _ {\text {n o c s}}\right) \tag {3} +$$ + +where $P_r \in \mathbb{R}^{N_{obj} \times 3}$ denotes the corresponding NOCS coordinates. $\Phi_2$ is an MLP. $P_r$ does not take part in the calculation of objects' poses and sizes but only participates in the calculation of the loss function $L_{nocs}$ . This loss function is an auxiliary loss function, which is used to apply supervision on $P_r$ in order to guide the learning of $F_{nocs}$ . + +The pose and size estimator takes the previous output and gives the object's pose and size with three parallel MLPs. + +# 3.2. Queries Deformation Estimator + +In the queries deformation estimator, we aim to deform the queries $Q_{cat}$ to a representation of the observed target object. This goal can be achieved by injecting the object geometry feature $F_{obj}$ into $Q_{cat}$ . Due to the unordered property of the point cloud, the PointNet [26] style operation, which is mainly composed of pooling, is adopted by many methods such as [30, 38]. However, this operation loses the detailed geometry structure and cannot adaptively pay attention to features of interest. Therefore, we use the cross-attention mechanism. Thanks to the permutation-invariance of the attention mechanism, it is feasible to implement it for point cloud processing. Moreover, we enhance the feature using the proposed global enhancement block. + +The detailed structure of the queries deformation estimator is illustrated in Figure 2. Cross-attention is computed to determine which feature in $F_{obj}$ is necessary to extract into $Q_{cat}$ . Specifically, we take the $Q_{cat}$ as the query and + +![](images/32166ef3d8cbbed306cf4a315450d3ef0651147a91514d9de9c4e81dfbc0f7e4.jpg) +Figure 3: Overview of the global enhancement block. The input feature $f$ pass through a global average pooling operation and a fully-connected layer to create a global feature $g$ . Then, the input feature $f$ serves as the query, and the global feature $g$ serves as both key and value. A self-attention mechanism is then applied to them. + +the $F_{obj}$ as key and value of the multi-head cross-attention module. The computation of attention map can be formulated as: + +$$ +A ^ {(m)} = \operatorname {N o r m} \left(\Psi_ {1} \left(Q _ {c a t}\right) \left(F _ {o b j}\right) ^ {T}\right) \tag {4} +$$ + +where $A^{(m)}\in \mathbb{R}^{N_{cat}\times N_{obj}}$ is the attention map in the mth head. Norm is the normalization function. Instead of using learnable linear projections, we use $\Psi_{1}$ , an MLP, applied to $Q_{cat}$ in order to reduce the gap between $Q_{cat}$ and $F_{obj}$ and it experimentally works better. Vanilla attention uses softmax to normalize the attention map, which can be formulated as norm = $\frac{f(x_i)}{\sum_k f(x_k)}$ where $f(x) = e^x$ for softmax. Different from that, we use: + +$$ +f (x) = \frac {\alpha}{1 + e ^ {- x}} \tag {5} +$$ + +where $\alpha$ is a learnable parameter. This is a sigmoid function with a learnable parameter. This function's output is limited between 0 and $\alpha$ , so there is no need to scale the dot-product result between query and key by dividing by $\sqrt{d}$ . This function tends to saturate and thus activate larger regions than softmax does, and the learnable parameter allows the model to choose the range. Since each query corresponds to a certain semantic part of the object in a specific category, the attention map indicates which component of the observed object has the same semantics as the query by calculating the similarity between the queries $Q_{cat}$ and the object feature $F_{obj}$ . + +Then, the multi-head cross-attention can be formulated as: + +$$ +D = \left[ A ^ {(1)} F _ {o b j}; \dots ; A ^ {(m)} F _ {o b j} \right] W _ {v} \tag {6} +$$ + +where $D \in \mathbb{R}^{N_{cat} \times d}$ is the multi-head cross-attention result and $W_v$ is the learnable parameter. In this way, the related object feature is extracted from the $F_{obj}$ . Then $D$ can be used to deform $Q_{cat}$ by adding it to $Q_{cat}$ : + +$$ +Q _ {o b j} = Q _ {c a t} + D \tag {7} +$$ + +where $Q_{obj} \in \mathbb{R}^{N_{cat} \times d}$ is deformed queries. + +$Q_{obj}$ is expected to embed the object's canonical point cloud. It can be decoded into 3D points using a simple MLP. + +$$ +P _ {i} = \operatorname {S i g m o i d} \left(M L P \left(Q _ {o b j}\right)\right) - 0. 5 \tag {8} +$$ + +where $P_{i} \in \mathbb{R}^{N_{\text{cat}} \times 3}$ . A Sigmoid function is used to limit it to $(-0.5, 0.5)$ , so the output points are in canonical space. We apply supervision to $P_{i}$ which could guide the learning of $Q_{obj}$ . Therefore, loss function $L_{rec}$ is applied to $P_{i}$ to provide supervision to it. + +Global enhancement block tends to enhance features by fusing their global feature. Normally, this can be achieved via the self-attention mechanism. However, to make the entire model lightweight, a more efficient block is needed. For this reason, we propose a global enhancement block. + +The global enhancement block is illustrated in Figure 3. Suppose the global enhancement block takes feature $f \in \mathbb{R}^{N \times d}$ as input. We adopt the result of the global average pooling as the global feature and pass it through a fully connected layer. The outcome is denoted as $g$ : + +$$ +g = F C \left(A v g P o o l (f)\right) \tag {9} +$$ + +where $FC$ is a fully connected layer. Instead of simply concatenating it to $f$ and then feeding it to an MLP, we borrow the idea from self-attention as shown in Figure 3. We use $f$ as query and $g$ as key and value to carry out self-attention, which can be denoted as: + +$$ +f ^ {\prime} = f + \operatorname {N o r m} \left(f g ^ {T}\right) g \tag {10} +$$ + +After that, $f'$ is fed into an MLP with residual. In this way, global information is injected into the feature. This block, unlike vanilla self-attention, reduces the complexity of the computation. Compared with the computation complexity of vanilla self-attention, $O(N^2 \times d)$ , our efficient global enhancement block has a computation complexity of $O(N \times d)$ . + +# 3.3. Query-Point Correspondence Estimator + +We obtain the deformed queries $Q_{obj}$ by adaptively selecting feature from the observed object feature $F_{obj}$ . In previous works, a correspondence matrix $A \in \mathbb{R}^{N_{obj} \times N_{cat}}$ is estimated, which models correspondences between points in observed point cloud $P_{obj}$ and reconstructed point cloud $P_i$ . This matrix then samples the points from $P_i$ to be paired with $P_{obj}$ , and it can be formulated as $P = A \times P_i$ , where $P$ denotes the sampled points. Finally, solving of Umeyama algorithm [31] to align the sample points with $P_i$ gives out the target pose and size. Instead of using this conventional way, we move this process to the feature space. In the query-point correspondence estimator, the correspondences between $F_{obj}$ and $Q_{obj}$ are built as illustrated in Figure 2. + +In detail, the correspondences are built by computing the similarity between $F_{obj}$ and $Q_{obj}$ using dot-product, which can be formulated as: + +$$ +A ^ {\prime} = \operatorname {N o r m} \left(\Psi_ {2} \left(F _ {o b j}\right) \left(Q _ {o b j}\right) ^ {T}\right) \tag {11} +$$ + +where $A' \in \mathbb{R}^{N_{obj} \times N_{cat}}$ denotes the correspondence matrix between $F_{obj}$ and $Q_{obj}$ . Norm is the same as that used in queries deformation estimator. $\Psi_2$ is an MLP. $A'$ represents the soft matching between $F_{obj}$ and $Q_{obj}$ . Then we multiply $A'$ by $Q_{obj}$ to obtain the sampled features. Essentially, we find that this process is similar to cross-attention. For this reason, we add $F_{obj}$ to the result for implementing a residual structure similar to attention mechanism. Also, we implement multi-head technique to the computation. Next, we need to pair the object feature with the sampled feature. Experimentally, it is better to use a more direct feature as the object feature here instead of the deep object feature $F_{obj}$ . Thereby, we do not use $F_{obj}$ but simply feed object point cloud $P_{obj}$ forward an MLP. The output of the MLP is concatenated to the sampled feature. To further enhance the feature, we use an MLP and a global enhancement block after that. The result is denoted as $F_{nocs}$ . To apply supervision on $F_{nocs}$ and better guide its learning, we use a simple MLP to transform $F_{nocs}$ into NOCS coordinates denoted as $P_r \in \mathbb{R}^{N_{obj} \times 3}$ . $P_r$ is not used to solve the Umeyama algorithm to obtain target pose and size, but only used to compute loss function $L_{nocs}$ . + +# 3.4. Poses and Sizes Estimator + +The rest of the work is to obtain the final object's pose and size, which is accomplished in the pose and size estimator. The pose and size estimator applies global average pooling operation to $F_{nocs}$ , which can be formulated as: + +$$ +f _ {\text {p o s e}} = \operatorname {A v g P o o l} \left(F _ {\text {n o c s}}\right) \tag {12} +$$ + +where $f_{\text{pose}} \in \mathbb{R}^{1 \times d}$ . Then after it, three parallel MLPs predict the rotation $R$ , translation $t$ , and size $s$ respectively. + +$$ +R, t, s = M L P \left(f _ {p o s e}\right), M L P \left(f _ {p o s e}\right), M L P \left(f _ {p o s e}\right) \tag {13} +$$ + +The representation of $R$ here is the Continuity of Rotation Representations [40]. For $s$ , we follow [3] to estimate the residual between object's size and the mean category size. Similarly, for $t$ , we predict the residual between the translation ground truth and the mean value of the point cloud. + +# 3.5. Overall Loss Function + +The overall loss function is as follows: + +$$ +L = \lambda_ {1} L _ {\text {p o s e}} + \lambda_ {2} L _ {\text {r e c}} + \lambda_ {3} L _ {\text {n o c s}} \tag {14} +$$ + +$L_{\text{pose}}$ is used to compute loss on predicted $R, t$ and $s$ . We simply use smooth L1 loss [8] for all of them with threshold of $1 \times 10^{-3}, 5 \times 10^{-3}, 5 \times 10^{-3}$ respectively. $L_{\text{rec}}$ and + +$L_{nocs}$ are the auxiliary losses function for $P_{i}$ and $P_{r}$ respectively. $L_{rec}$ is applied to $P_{i}$ to encourage it to reconstruct the instance point cloud in the NOCS space. Therefore, for $L_{rec}$ , we use Chamfer distance between $P_{i}$ and $M_{gt}$ where $M_{gt} \in \mathbb{R}^{N_{obj} \times 3}$ represents the instance point cloud model in the NOCS space. $L_{rec}$ can be formulated as follows: + +$$ +\begin{array}{l} L _ {r e c} = \frac {1}{N _ {c a t}} \sum_ {x _ {i} \in P _ {r}} \min _ {y _ {j} \in M _ {g t}} \| x _ {i} - y _ {j} \| _ {2} ^ {2} + \\ \frac {1}{N _ {o b j}} \sum_ {y _ {i} \in M _ {g t}} \min _ {x _ {i} \in P _ {r}} \| x _ {i} - y _ {j} \| _ {2} ^ {2} \tag {15} \\ \end{array} +$$ + +$L_{nocs}$ is applied on $P_r$ to encourage it in predicting the corresponding coordinates of $P_{obj}$ in Normalized Object Coordinate Space. For $L_{nocs}$ , we also use a smooth L1 loss [8] with a threshold of 0.1. + +# 4. Experiments + +Datasets. We conduct experiments using the benchmark CAMERA25 and REAL275 [34] datasets for category-level 6D object pose and size estimation which consists of six object categories. The CAMERA25 dataset is generated by rendering and compositing synthetic object instances under different views. The CAMERA25 dataset contains 300K synthetic images of 1,085 object instances, among which 25,000 images of 184 instances are used for evaluation. The REAL275 dataset is complementary to the CAMERA25 dataset. It includes 4,300 real-world images of 6 scenes with 3 unseen instances per category; its training set contains 4,300 images of 7 scenes, and the test set contains 2,750 images of 6 scenes. We train our model with a combined use of the two datasets, as done in [18]. + +Implement Details. We employ a Mask R-CNN [9] to obtain instance masks the same as [30]. The instances are then cropped based on the segmentation result. After that, the depth is converted to the instance point cloud using the camera's intrinsic parameters. 1024 points are randomly sampled from that, so $N_{obj}$ is set to 1024. To extract instance geometry features, we choose PointNet++ [27] with four abstraction levels. The number of prior queries $N_{cat}$ is set to 64. In this case, $N_{cat} \ll N_{obj}$ . A detailed study on the parameter $N_{cat}$ is given in our ablation study. The queries are initialized randomly at the beginning of training. The dimension of features and queries is set to 256. The crossattention in queries deformation estimator and query-point correspondence estimator has four heads each. In the loss function, we set $\lambda_1, \lambda_2, \lambda_3$ to 1.0, 3.0, 1.0, respectively. We use AdamW [21] to train this model with an initial learning rate of $1 \times 10^{-4}$ and weight decay $1 \times 10^{-4}$ . All models are trained 42k iterations with batch size of 60 and cosine learning rate decay is conducted. We employ several strategies for depth augmentation, such as adding Gaussian noise, random scaling, random rotation, adding random points as well + +as linear shape augmentation proposed in [3] and non-linear shape augmentation proposed in [38]. All FPS(Frames Per Second) data of our method is evaluated on a single RTX 2080Ti, an Intel(R) Xeon(R) CPU E5-2650 v4 @ 2.20GHz, PyTorch [24] 1.10, CUDA version 11.1. + +Evaluation Metrics. For category-level pose estimation, we follow [34] and use two metrics to evaluate the quality. + +- 3D IoU. The overlap of two 3D bounding boxes under the predicted pose and the ground truth pose is computed. The overlap ratios larger than the threshold are regarded as accepted. The mean Average Precision (mAP) of the overlapping is reported. +- $n^{\circ}m$ cm. The rotation and translation errors between the predicted pose and the ground truth pose are computed. The errors smaller than an angle threshold $n^{\circ}$ and a translation threshold $m$ cm are accepted. + +# 4.1. Comparisons with Existing Methods + +NOCS-REAL275 In Table 1 we compare our method with the existing ones for category-level 6D object pose and size estimation. We divide these methods into two groups: those with and without shape prior. As it is shown in Table 1, our method outperforms other existing methods. In detail, we outperform NOCS [34] by 46.0 in $IoU_{75}$ , 41.8 in $5^{\circ}2cm$ , 48.9 in $5^{\circ}5cm$ . Moreover, we achieve a better result than existing methods that using prior information. Specifically, we outperform SPD [30] by 22.9 in $IoU_{75}$ , 29.7 in $5^{\circ}2cm$ , 37.5 in $5^{\circ}5cm$ and 14.2, 13.1, and 19.3 higher than SGPA [2] which is a representative method based on attention. This outcome demonstrates that our sparse shape prior is superior to the traditional shape prior. + +NOCS-CAMERA25 The results for CAMERA25 are shown Table 1. Our method outperforms others at least 4.9, 4.3 in the items of $5^{\circ}2cm$ , $5^{\circ}5cm$ , and it is on par with the best methods for $IoU_{75}$ . Figure 4 presents a more detailed error evaluation result on two datasets. + +# 4.2. Ablation Studies + +Effect of the design in Query6DoF. We verify the efficacy of each component in Query6DoF in Table 2. By replacing queries with point cloud proposed in [30] and adding an extra PointNet++ [27] after the prior point cloud as a feature extractor, $5^{\circ}2cm$ drops from 49.0 to 47.2, and computation increases. Removing the global enhancement block results in a 4.8 drop in $5^{\circ}2cm$ . Removing the queries deformation estimator results in a 2.5 drop in $5^{\circ}2cm$ . If the query-point correspondence estimator is detached, it renders the usage of queries and queries deformation estimator senseless. Therefore, without using them together, our method experiences a 13.6 drop in $5^{\circ}2cm$ . Moreover, we remove the poses and sizes estimator but use $P_r$ and $P_i$ + +Table 1: Comparison with state-of-the-art methods on the CAMERA25 dataset and REAL275 dataset. * denotes results without linear shape augmentation and non-linear shape augmentation. The best results shown in bold. + +
MethodpriorCAMERA25REAL275
IoU50IoU755°2cm5°5cm10°2cm10°5cmIoU50IoU755°2cm5°5cm10°2cm10°5cm
NOCS [34]83.969.532.340.948.264.678.030.17.210.013.825.2
DualPoseNet [18]92.486.464.770.777.284.779.862.229.335.950.066.8
GPV-Pose [7]93.488.372.179.1-89.083.064.432.042.9-73.3
SPD [30]✓93.283.154.359.073.381.577.353.219.321.443.254.1
CR-Net [35]✓93.888.072.076.481.087.779.355.927.834.347.260.8
SAR-Net [16]✓86.879.066.770.975.680.379.362.431.642.350.368.3
SGPA [2]✓93.288.170.774.582.788.480.161.935.939.661.370.7
RBP-Pose [38]✓93.189.073.579.682.189.5-67.838.248.163.179.2
Self-DPDN [17]✓------83.676.046.050.770.478.4
Ours*✓92.388.678.483.984.090.582.976.046.854.767.981.6
Ours✓91.988.178.083.183.990.082.576.149.058.968.783.0
+ +Table 2: Effect of the design on Query6DoF, evaluated on the REAL275 dataset. GlobEnhance denotes the global enhancement block, QueryDeform denotes the queries deformation estimator, Query2Point denotes the query-point correspondence estimator, and PoseSize denotes the poses and sizes estimator + +
QueriesGlobEnhanceQueryDeformQuery2PointPoseSizeI0U50I0U755°2cm5°5cm10°2cm10°5cm
1-✓✓✓✓82.175.447.256.267.381.2
2✓-✓✓✓82.675.744.253.365.881.1
3✓✓-✓✓83.075.346.556.665.981.3
4-✓--✓82.170.935.448.759.580.2
5✓✓✓✓-82.270.040.046.365.176.5
6✓✓✓✓✓82.576.149.058.968.783.0
+ +![](images/81378a0a73ad900342c1f3204776795ae7b16a1b00afcd1bd50d65253f125872.jpg) +Figure 4: Mean Average Precision (mAP) in different thresholds. REAL275 (top rows) and CAMERA25 (bottom rows) + +to obtain poses and sizes via Umeyama [31]. As a result, $5^{\circ}2cm$ falls by 9.0 points. + +Effect of the number of prior queries. In our method, we use sparse queries to represent the shape prior. In this experiment, we investigate the effect of the number of prior queries $N_{cat}$ on the results of REAL275. Table 3 presents the result of the ablation of the effect of the number of prior + +Table 3: Effect of the number of queries on REAL275 + +
NcatIoU50IoU755°2cm5°5cm10°2cm10°5cm
1682.574.646.055.466.681.0
3282.574.946.755.967.281.5
6482.676.149.058.968.783.0
12882.876.946.155.968.882.8
25682.876.647.657.367.881.6
51282.675.646.856.266.981.4
102483.176.748.756.870.482.4
+ +Table 4: Effect of different attention normalization evaluated on REAL275. + +
NormI0U50I0U755°2cm5°5cm10°2cm10°5cm
Softmax82.174.748.657.268.682.4
Ours82.576.149.058.968.783.0
+ +queries. The results show that reducing the number of prior queries does not significantly affect the performance of our method. This fact means that it is not necessary to use excessive points to express the object's shape prior. A small number of queries can effectively represent the object's shape. Specifically, when $N_{cat} = 64$ , our method achieves the best performance in the $5^{\circ}2cm$ , $5^{\circ}5cm$ , $10^{\circ}5cm$ metrics and when $N_{cat} = 1024$ , our method achieves the best performance in the $IoU_{50}$ metric. However, the smaller $N_{cat}$ results in less computational overhead. Therefore, we adopt $N_{cat} = 64$ as the default setting in all other experiments. + +Effect of different attention normalization. While + +![](images/0273c03d260c05a4cf076de92d803aa8a86585ed57a302284834f7f0e2e588a9.jpg) +Figure 5: Qualitative results of our method (red line) and SGPA [2] (green line). + +![](images/914d399b303d132dce74e281b74a19a93d889b61ea347c92d86b1fc3e5b549b5.jpg) +Figure 6: Sparse point cloud reconstruction in the REAL275 dataset. The yellow points represent the reconstruction points $P_{i}$ , while the blue points are the observed point cloud. + +Table 5: Model complexity and FPS w/o Mask R-CNN [9], evaluated on REAL275. GEB denotes the global enhancement block. + +
MethodParams(M)FPS w/o Mask R-CNN [9]5°2cm
Ncat = 64 (Default)19.5334.949.0
Ncat = 102421.1823.348.7
w/o GEB18.7136.844.2
w/o Queries22.2424.047.2
+ +common attention mechanisms adopt softmax to normalize the attention map, in our method, we use a different normalization approach, namely sigmoid with a learnable parameter mentioned earlier. In this experiment, we compare two different settings shown in Table 4. We conduct the evaluation on the REAL275 dataset. Using softmax to normalize results in a 1.4 drop in $IoU_{75}$ and a 0.4 drop in $5^{\circ}2cm$ . + +# 4.3. Runtime Analysis + +As shown in Table 5, our method, in the default setting, has 19.43M parameters and runs at 34.9 FPS without Mask R-CNN [9]. Increasing $N_{cat}$ to 1024 brings no gain but the FPS drops to 23.3, which shows that sparse queries are sufficient to represent the shape prior. Adding the global enhancement block results in a 4.8 improvement in $5^{\circ}2cm$ with only a 1.9 FPS drop, demonstrating its efficiency. W/o Queries means that we replace the queries with the prelearned shape prior proposed in [30] and use PointNet++ + +[27] as a feature extractor. In this way, due to the extra PointNet++ [27], the speed drops to 24.0FPS, but there is no gain in $5^{\circ}2cm$ . Therefore, the usage of queries is more efficient than using point cloud both in terms of accuracy and speed. + +# 4.4. Visualization + +Qualitative Results. Figure 5 shows the qualitative results of our method, demonstrating that our method can accurately estimate the objects' poses and sizes. + +Sparse point cloud reconstruction. Our method outputs $P_{i}$ as the sparse point cloud reconstruction in NOCS space. We align $P_{i}$ to the object's location in RGB images for better comparison with the object's actual shape, as shown in Figure 6. $P_{i}$ is the yellow points in it. The blue points in it represent the observed point cloud for comparison. It shows that our sparse point cloud can accurately cover different objects' shapes. This effect can be attributed to our queries deformation estimator, where category-specific queries transformed into instance-specific ones. Through this process, the queries are able to reconstruct the objects. + +# 5. Conclusion + +In conclusion, we present a novel network for category-level 6D object pose and size estimation, namely Query6DoF. In particular, we propose to use a series of sparse and learnable queries serving as a shape prior, which is a set of tokens that implicitly represent objects in a cer + +tain category. Furthermore, we transform the traditional deformation-and-matching paradigm to the feature space using attention. Specifically, the queries are deformed by a process where we dynamically use the attention mechanism to select object features and incorporate them into queries. This step transforms the queries into a representation of a certain target object. Next, we establish the correspondences between deformed queries and object features. Finally, the poses and sizes are regressed using the correspondences. Thanks to learnable queries and direct output results, the queries are trained directly alongside the entire network. This method achieves state-of-the-art performance compared to other existing methods and holds promise for applications in robotics and augmented reality. + +Acknowledgement This work was supported by the Key Research Project of Zhejiang Lab (No. G2021NB0AL03) and Modern Agriculture Major-core Technology Innovation Project of Jiangsu Province (No. cx(22)2031). + +# References + +[1] Tuo Cao, Fei Luo, Yanping Fu, Wenxiao Zhang, Shengjie Zheng, and Chunxia Xiao. Dgecn: A depth-guided edge convolutional network for end-to-end 6d pose estimation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3783-3792, 2022. +[2] Kai Chen and Qi Dou. 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Many previous works use point clouds as a prelearned shape prior to overcome intra-category variability. The shape prior is deformed to reconstruct instances' point clouds in canonical space and to build dense 3D-3D correspondences between the observed and reconstructed point clouds. However, the pre-learned shape prior is not jointly optimized with estimation networks, and they are trained with a surrogate objective. We propose a novel 6D pose estimation network, named Query6DoF, based on a series of category-specific sparse queries that represent the prior shape. Each query represents a shape component, and these queries are learnable embeddings that can be optimized together with the estimation network according to the point cloud reconstruction loss, the normalized object coordinate loss, and the 6d pose estimation loss. Query6DoF adopts a deformation-and-matching paradigm with attention, where the queries dynamically extract features from regions of interest using the attention mechanism and then directly regress results. Furthermore, Query6DoF reduces computation overhead through the sparseness of the queries and the incorporation of a lightweight global information injection block. With the aforementioned design, Query6DoF achieves state-of-the-art (SOTA) pose estimation performance on the NOCS datasets. The source code and models are available at https://github.com/hustvl/Query6DoF." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 308, + 281, + 547, + 418 + ], + "blocks": [ + { + "bbox": [ + 308, + 281, + 547, + 418 + ], + "lines": [ + { + "bbox": [ + 308, + 281, + 547, + 418 + ], + "spans": [ + { + "bbox": [ + 308, + 281, + 547, + 418 + ], + "type": "image", + "image_path": "e34ba91f291e408c6a57e410f6633b07e3ac9fc2096063fbcb267123ba295735.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 425, + 547, + 498 + ], + "lines": [ + { + "bbox": [ + 304, + 425, + 547, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 547, + 498 + ], + "type": "text", + "content": "Figure 1: Comparisons with conventional works. a) Conventional methods adopt pre-learned shape prior and have a two-stage pipeline, i.e., deforming the prior and building correspondences between points. b) Our method uses sparse learnable queries as the shape prior and conducts query/feature-based deformation and matching." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 521, + 388, + 534 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 521, + 388, + 534 + ], + "spans": [ + { + "bbox": [ + 306, + 521, + 388, + 534 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 544, + 547, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 547, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 547, + 652 + ], + "type": "text", + "content": "Category-level object pose estimation is aimed at estimating an object's rotation, translation, and size from an RGB-D scene within a given set of categories. This task has attracted increasing attention due to its vital role in robotics [5], 3D understanding [4, 22], and augmented reality [29]. Compared with instance-level object pose estimation, category-level object pose estimation doesn't require obtaining the object's CAD model in advance, making it more generally applicable." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "Many existing methods [2, 7, 16, 30, 41, 38, 20, 35] solve this problem as shown in Figure 1(a). First, they attempt to reconstruct the input object point cloud in the Normalized Object Coordinate Space [34] (NOCS). Then they estimate the 3D-3D correspondences between the input ob" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "text", + "content": "†Corresponding authors: Wenyu Liu (liuwy@hust.edu.cn), Te Li (lite@zhejianglab.com) and Minhong Wan (wanmh@ zhejianglab.com)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "14055" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 324 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 324 + ], + "type": "text", + "content": "served point cloud and the reconstructed object point cloud. Finally, they determine object poses and sizes by applying the Umeyama algorithm [31] to these correspondences. To handle intra-category variability, a shape prior, which represents a basic shape for objects in the same category, is introduced in [30] to this task. This shape prior is a set of point clouds pre-learned in NOCS for each category. Objects are reconstructed by deforming the shape prior. However, this approach has its drawbacks: 1) the shape prior is a dense representation of objects in a specific category, which is not only redundant but also makes the network computationally expensive. 2) the shape prior is pre-learned in advance and remains static during model training. Additionally, these methods are trained to predict the deformation field " + }, + { + "bbox": [ + 47, + 72, + 289, + 324 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 72, + 289, + 324 + ], + "type": "text", + "content": " and a correspondence matrix " + }, + { + "bbox": [ + 47, + 72, + 289, + 324 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 47, + 72, + 289, + 324 + ], + "type": "text", + "content": ", which is a surrogate task. 3) Conventional model architectures [30, 3, 2] typically rely on either pooling operations in the PointNet [26] style or 3D graph convolution (3DGC) [19] to explore geometry features. However, the pooling operation can result in the loss of local geometry features, and these operations are not adaptive to extract the feature information." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 331, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 331, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 331, + 289, + 715 + ], + "type": "text", + "content": "To address these issues, we propose a novel method called Query6DoF (illustrated in Figure 1(b)). Instead of relying on dense and static point clouds as the shape prior, we introduce a series of sparse and learnable category-specific queries. Each query in this series is designed to encode a specific component of an object's shape with implicitly shared semantics and is optimized concurrently with the whole model parameters. Due to intra-category variability, the queries only need to capture the most representative components of objects and disregard unrepresentative shape details. Consequently, the queries can be sparse. Moreover, due to the sparseness of queries, the sparseness of the queries reduces computational overhead. Therefore, there is no need to use techniques such as Low-Rank transformer [36] mentioned in SGPA [2]. To eliminate the need for surrogate training objectives, we employ a direct prediction framework. However, unlike previous direct regression methods, e.g., [3, 20], we choose to perform the core deformation-and-matching paradigm in feature space. The deformation process is accomplished based on an attention mechanism, which adaptively extracts information from instance features to queries. This transforms queries from category-specific into instance-specific shape representations. Then, correspondences between instance features and deformed queries are established by computing their similarity. Using these correspondences, the instance features are paired with deformed queries. Finally, these pairs are used to determine the pose and size through a neural network. Since the shape prior already consists of implicit queries, it is reasonable to also execute the entire pipeline implicitly in the feature space to better leverage these queries. Without pre-learned prior and surrogate train" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "type": "text", + "content": "ing objectives, our model is trained entirely and directly. As a result, the prior can be more suitable for the model, enabling us to achieve state-of-the-art performance on the task." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 121, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 121, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 121, + 547, + 180 + ], + "type": "text", + "content": "Conventionally, the self-attention mechanism is used in transformers to inject global information. Unfortunately, adding self-attention layers significantly increases computational load. Therefore, we propose an efficient global enhancement layer to balance efficiency and performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 180, + 547, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 180, + 547, + 202 + ], + "spans": [ + { + "bbox": [ + 306, + 180, + 547, + 202 + ], + "type": "text", + "content": "The main contributions of this work can be summarized as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 209, + 545, + 402 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 317, + 209, + 545, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 209, + 545, + 280 + ], + "spans": [ + { + "bbox": [ + 317, + 209, + 545, + 280 + ], + "type": "text", + "content": "- We propose to use sparse and learnable queries as shape prior rather than dense and static point clouds. In this way, the queries are optimized at the same time as the whole model to discover the optimal set of priors, and the sparseness design reduces the computation overhead." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 288, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 288, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 317, + 288, + 545, + 335 + ], + "type": "text", + "content": "- We adapt existing architectures to fit the novel shape prior representation with the help of attention mechanisms. We design a lightweight self-attention module in this to balance accuracy and speed." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 342, + 545, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 342, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 317, + 342, + 545, + 402 + ], + "type": "text", + "content": "- The overall 6DoF pose estimation accuracy of our method is better than previous state-of-the-art methods on the CAMERA25 and REAL275 datasets, especially, on the strict " + }, + { + "bbox": [ + 317, + 342, + 545, + 402 + ], + "type": "inline_equation", + "content": "5^{\\circ}2cm" + }, + { + "bbox": [ + 317, + 342, + 545, + 402 + ], + "type": "text", + "content": " metric our results are significantly better than previous methods." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 411, + 392, + 424 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 411, + 392, + 424 + ], + "spans": [ + { + "bbox": [ + 306, + 411, + 392, + 424 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 431, + 525, + 444 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 431, + 525, + 444 + ], + "spans": [ + { + "bbox": [ + 306, + 431, + 525, + 444 + ], + "type": "text", + "content": "2.1. Instance-Level 6D Object Pose Estimation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 449, + 545, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 570 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 570 + ], + "type": "text", + "content": "Based on the input data format, existing methods can be divided into two categories: RGB-based [15, 28, 25, 22, 37, 23] and RGB-D-based [14, 32, 10, 13] approaches. A common approach for using RGB as input to accomplish this task is to detect the object's keypoints in the image and match them to the CAD model. With the 2D-3D correspondences, the PnP algorithm is then implemented to obtain the object's pose. Additionally, some methods [12, 33, 6, 1, 39, 11] do not use PnP algorithm but instead employ neural networks to directly output object's pose." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 575, + 545, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 575, + 545, + 599 + ], + "spans": [ + { + "bbox": [ + 305, + 575, + 545, + 599 + ], + "type": "text", + "content": "2.2. Category-level 6D Object Pose and Size Estimation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "[34] first introduced Normalized Object Coordinate Space to represent all the possible object instances in a unified space. DualPoseNet [18] introduced a network stacking an implicit decoder to impose complementary supervision on pose encoder. We absorb this practice and provide extra implicit supervision. To handle the intra-class shape variation, SPD [30] proposes a deep network to reconstruct the 3D object model by explicitly modeling the deformation from a pre-learning categorical shape prior. However," + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14056" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 545, + 218 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 545, + 218 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 545, + 218 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 545, + 218 + ], + "type": "image", + "image_path": "9fe692b59118b343603427486909eb6d560095d79be679544893fda2087bc513.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 226, + 546, + 323 + ], + "lines": [ + { + "bbox": [ + 46, + 226, + 546, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 226, + 546, + 323 + ], + "type": "text", + "content": "Figure 2: Entire schematic illustration of our proposed method. The target point cloud " + }, + { + "bbox": [ + 46, + 226, + 546, + 323 + ], + "type": "inline_equation", + "content": "P_{obj}" + }, + { + "bbox": [ + 46, + 226, + 546, + 323 + ], + "type": "text", + "content": " is fed to PointNet++ [27] as a backbone to extract the object's geometry features " + }, + { + "bbox": [ + 46, + 226, + 546, + 323 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 46, + 226, + 546, + 323 + ], + "type": "text", + "content": ". A set of queries " + }, + { + "bbox": [ + 46, + 226, + 546, + 323 + ], + "type": "inline_equation", + "content": "Q_{cat}" + }, + { + "bbox": [ + 46, + 226, + 546, + 323 + ], + "type": "text", + "content": " is prepared to serve as the shape prior. Each of the queries represents a component of object shape. The queries pass through the queries deformation estimator to gain instance shape information from " + }, + { + "bbox": [ + 46, + 226, + 546, + 323 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 46, + 226, + 546, + 323 + ], + "type": "text", + "content": " using an attention mechanism to adaptively select instance features, and then they are deformed to the specific representation of the target observed object " + }, + { + "bbox": [ + 46, + 226, + 546, + 323 + ], + "type": "inline_equation", + "content": "Q_{obj}" + }, + { + "bbox": [ + 46, + 226, + 546, + 323 + ], + "type": "text", + "content": ". Next, in the query-point correspondence estimator, the correspondence between " + }, + { + "bbox": [ + 46, + 226, + 546, + 323 + ], + "type": "inline_equation", + "content": "Q_{obj}" + }, + { + "bbox": [ + 46, + 226, + 546, + 323 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 226, + 546, + 323 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 46, + 226, + 546, + 323 + ], + "type": "text", + "content": " is built. In the end, the poses and sizes estimator makes use of the previous output. This block simply adopts global average pooling to aggregate all the input features and output resulting poses and sizes through three parallel MLPs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 343, + 289, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 343, + 289, + 487 + ], + "spans": [ + { + "bbox": [ + 46, + 343, + 289, + 487 + ], + "type": "text", + "content": "this prior is not flexible enough because it is obtained in advance and remains unchanged during training. Therefore, we propose to transform it into the learnable queries. DPDN [17] makes efforts to overcoming synthetic-to-real domain gap using self-supervised learning. We further develop its paradigm of deforming and matching in feature space with the attention mechanism to make it much more effective. SGPA [2] further leverages the advantage of category prior. It uses the transformer architecture and in order to reduce computational complexity SGPA utilized the low-rank transformer [36]. But in our work, our proposed queries do not require to this technique for its sparseness." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 502, + 103, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 103, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 103, + 514 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 524, + 115, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 524, + 115, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 524, + 115, + 536 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 544, + 287, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 686 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 686 + ], + "type": "text", + "content": "Given an RGB-D image, the goal of the category-level object pose and size estimation is to predict the 6D object pose and size represented by rotation " + }, + { + "bbox": [ + 46, + 544, + 287, + 686 + ], + "type": "inline_equation", + "content": "R \\in SO(3)" + }, + { + "bbox": [ + 46, + 544, + 287, + 686 + ], + "type": "text", + "content": ", translation " + }, + { + "bbox": [ + 46, + 544, + 287, + 686 + ], + "type": "inline_equation", + "content": "t \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 544, + 287, + 686 + ], + "type": "text", + "content": ", and size " + }, + { + "bbox": [ + 46, + 544, + 287, + 686 + ], + "type": "inline_equation", + "content": "s \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 544, + 287, + 686 + ], + "type": "text", + "content": ". We segment objects from the RGB image using an off-the-shelf object segmentation technique e.g., Mask R-CNN [9]. The segmented object's depth data is transferred to a 3D point cloud. Then the 3D point cloud is uniformly sampled into a fixed number. The same as [3], noting that objects' appearance varies much more than their shape even in the same category, our method only uses point cloud data as input instead of together with RGB data." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 712 + ], + "type": "text", + "content": "Let's denote the observed target point cloud as " + }, + { + "bbox": [ + 47, + 689, + 287, + 712 + ], + "type": "inline_equation", + "content": "P_{obj} \\in \\mathbb{R}^{N_{obj} \\times 3}" + }, + { + "bbox": [ + 47, + 689, + 287, + 712 + ], + "type": "text", + "content": ". Our method uses a feature extraction module to" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 342, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 545, + 475 + ], + "type": "text", + "content": "extract object geometry feature " + }, + { + "bbox": [ + 304, + 342, + 545, + 475 + ], + "type": "inline_equation", + "content": "F_{obj} \\in \\mathbb{R}^{N_{obj} \\times d}" + }, + { + "bbox": [ + 304, + 342, + 545, + 475 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 342, + 545, + 475 + ], + "type": "inline_equation", + "content": "P_{obj}" + }, + { + "bbox": [ + 304, + 342, + 545, + 475 + ], + "type": "text", + "content": ". Unlike conventional methods that use an extra set of point clouds as explicit shape priors, we prepare a set of queries " + }, + { + "bbox": [ + 304, + 342, + 545, + 475 + ], + "type": "inline_equation", + "content": "Q_{cat} \\in \\mathbb{R}^{N_{cat} \\times d}" + }, + { + "bbox": [ + 304, + 342, + 545, + 475 + ], + "type": "text", + "content": " for each category as implicit shape prior. Each query expresses a semantic component of the object and they are the general category-specific representation. The number of queries " + }, + { + "bbox": [ + 304, + 342, + 545, + 475 + ], + "type": "inline_equation", + "content": "N_{cat}" + }, + { + "bbox": [ + 304, + 342, + 545, + 475 + ], + "type": "text", + "content": " can be significantly fewer than the number of points in the input point cloud " + }, + { + "bbox": [ + 304, + 342, + 545, + 475 + ], + "type": "inline_equation", + "content": "N_{obj}" + }, + { + "bbox": [ + 304, + 342, + 545, + 475 + ], + "type": "text", + "content": ". Besides, the queries are learnable, which means that there is no pre-defined prior and the full model is trained entirely and directly." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 483, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 555 + ], + "type": "text", + "content": "A traditional approach to obtaining the final poses and sizes with shape prior can be summarized as follows. First, deform the prior point cloud to reconstruct the object shape. Then, the correspondence between the reconstructed point cloud and the observed object point cloud is estimated. Afterward, poses and sizes can be solved via Umayama [31]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 562, + 545, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 562, + 545, + 657 + ], + "spans": [ + { + "bbox": [ + 304, + 562, + 545, + 657 + ], + "type": "text", + "content": "The entire schematic illustration of our proposed method is shown in Figure 2. We implement this process in feature space with an attention mechanism. Specifically, our method consists of three parts: queries deformation estimator, query-point correspondence estimator, and poses and sizes estimator. Furthermore, we propose a global enhancement block to reinforce the features with global information." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "content": "Queries deformation estimator is used to deform the queries " + }, + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "inline_equation", + "content": "Q_{cat}" + }, + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "content": " from the general category-specific representation to an object-specific one for the observed input object using the input instance geometry feature " + }, + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "content": ", which can" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14057" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 121, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 121, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 121, + 83 + ], + "type": "text", + "content": "be formulated as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 111, + 93, + 287, + 107 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 93, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 111, + 93, + 287, + 107 + ], + "type": "interline_equation", + "content": "Q _ {o b j} = Q D E \\left(Q _ {c a t}, F _ {o b j}\\right) \\tag {1}", + "image_path": "b7559408e0b928ea91ffeab0dd36d2a597f9a3088cf2fa4a9e44cf5029d6bbc0.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 114, + 287, + 187 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 114, + 287, + 187 + ], + "spans": [ + { + "bbox": [ + 47, + 114, + 287, + 187 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 114, + 287, + 187 + ], + "type": "inline_equation", + "content": "Q_{obj} \\in \\mathbb{R}^{N_{cat} \\times d}" + }, + { + "bbox": [ + 47, + 114, + 287, + 187 + ], + "type": "text", + "content": " denotes the deformed queries. " + }, + { + "bbox": [ + 47, + 114, + 287, + 187 + ], + "type": "inline_equation", + "content": "QDE" + }, + { + "bbox": [ + 47, + 114, + 287, + 187 + ], + "type": "text", + "content": " denotes the queries deformation estimator. In this process, we adopt the attention mechanism to extract the information of regions of interest from " + }, + { + "bbox": [ + 47, + 114, + 287, + 187 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 47, + 114, + 287, + 187 + ], + "type": "text", + "content": " adaptively. After deforming the queries, the canonical point cloud can be decoded from " + }, + { + "bbox": [ + 47, + 114, + 287, + 187 + ], + "type": "inline_equation", + "content": "Q_{obj}" + }, + { + "bbox": [ + 47, + 114, + 287, + 187 + ], + "type": "text", + "content": " denoted as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 134, + 194, + 287, + 209 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 194, + 287, + 209 + ], + "spans": [ + { + "bbox": [ + 134, + 194, + 287, + 209 + ], + "type": "interline_equation", + "content": "P _ {i} = \\Phi_ {1} (Q _ {o b j}) \\tag {2}", + "image_path": "d54b2c818ee10a5947b6bbb83e50fd0e23906a09b2af3985637e769c8598b3b9.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "inline_equation", + "content": "P_{i} \\in \\mathbb{R}^{N_{\\text{cat}} \\times 3}" + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "text", + "content": " denotes the object's canonical sparse point cloud. " + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "inline_equation", + "content": "\\Phi_{1}" + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "text", + "content": " denotes the decoder implemented by an MLP (multi-layer perceptron). Supervision is applied to " + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "text", + "content": " to help better guide the learning of " + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "inline_equation", + "content": "Q_{obj}" + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "text", + "content": " via the loss function " + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "inline_equation", + "content": "L_{rec}" + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "text", + "content": ". Query-point correspondence estimator is used to estimate the correspondences between deformed queries " + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "inline_equation", + "content": "Q_{obj}" + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "text", + "content": " and object feature " + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "text", + "content": ". The correspondence then is used to combine " + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "inline_equation", + "content": "Q_{obj}" + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "text", + "content": " as matching feature pairs. These pairs are fed forward an MLP and a global enhancement block. The result is denoted as " + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "inline_equation", + "content": "F_{nocs}" + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "text", + "content": ". The corresponding NOCS coordinates of the observed object point cloud are obtained from " + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "inline_equation", + "content": "F_{nocs}" + }, + { + "bbox": [ + 46, + 215, + 288, + 360 + ], + "type": "text", + "content": " using an MLP." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 132, + 368, + 287, + 381 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 368, + 287, + 381 + ], + "spans": [ + { + "bbox": [ + 132, + 368, + 287, + 381 + ], + "type": "interline_equation", + "content": "P _ {r} = \\Phi_ {2} \\left(F _ {\\text {n o c s}}\\right) \\tag {3}", + "image_path": "a27397b754ee420c9497dd4ca7827a733275217d3201961dbb0f7477020ebadc.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "inline_equation", + "content": "P_r \\in \\mathbb{R}^{N_{obj} \\times 3}" + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "content": " denotes the corresponding NOCS coordinates. " + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\Phi_2" + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "content": " is an MLP. " + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "inline_equation", + "content": "P_r" + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "content": " does not take part in the calculation of objects' poses and sizes but only participates in the calculation of the loss function " + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "inline_equation", + "content": "L_{nocs}" + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "content": ". This loss function is an auxiliary loss function, which is used to apply supervision on " + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "inline_equation", + "content": "P_r" + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "content": " in order to guide the learning of " + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "inline_equation", + "content": "F_{nocs}" + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 460, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 485 + ], + "type": "text", + "content": "The pose and size estimator takes the previous output and gives the object's pose and size with three parallel MLPs." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 491, + 219, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 219, + 504 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 219, + 504 + ], + "type": "text", + "content": "3.2. Queries Deformation Estimator" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 510, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 665 + ], + "type": "text", + "content": "In the queries deformation estimator, we aim to deform the queries " + }, + { + "bbox": [ + 46, + 510, + 287, + 665 + ], + "type": "inline_equation", + "content": "Q_{cat}" + }, + { + "bbox": [ + 46, + 510, + 287, + 665 + ], + "type": "text", + "content": " to a representation of the observed target object. This goal can be achieved by injecting the object geometry feature " + }, + { + "bbox": [ + 46, + 510, + 287, + 665 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 46, + 510, + 287, + 665 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 46, + 510, + 287, + 665 + ], + "type": "inline_equation", + "content": "Q_{cat}" + }, + { + "bbox": [ + 46, + 510, + 287, + 665 + ], + "type": "text", + "content": ". Due to the unordered property of the point cloud, the PointNet [26] style operation, which is mainly composed of pooling, is adopted by many methods such as [30, 38]. However, this operation loses the detailed geometry structure and cannot adaptively pay attention to features of interest. Therefore, we use the cross-attention mechanism. Thanks to the permutation-invariance of the attention mechanism, it is feasible to implement it for point cloud processing. Moreover, we enhance the feature using the proposed global enhancement block." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "The detailed structure of the queries deformation estimator is illustrated in Figure 2. Cross-attention is computed to determine which feature in " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": " is necessary to extract into " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "Q_{cat}" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": ". Specifically, we take the " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "Q_{cat}" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": " as the query and" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 79, + 547, + 148 + ], + "blocks": [ + { + "bbox": [ + 307, + 79, + 547, + 148 + ], + "lines": [ + { + "bbox": [ + 307, + 79, + 547, + 148 + ], + "spans": [ + { + "bbox": [ + 307, + 79, + 547, + 148 + ], + "type": "image", + "image_path": "32166ef3d8cbbed306cf4a315450d3ef0651147a91514d9de9c4e81dfbc0f7e4.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 161, + 547, + 234 + ], + "lines": [ + { + "bbox": [ + 304, + 161, + 547, + 234 + ], + "spans": [ + { + "bbox": [ + 304, + 161, + 547, + 234 + ], + "type": "text", + "content": "Figure 3: Overview of the global enhancement block. The input feature " + }, + { + "bbox": [ + 304, + 161, + 547, + 234 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 161, + 547, + 234 + ], + "type": "text", + "content": " pass through a global average pooling operation and a fully-connected layer to create a global feature " + }, + { + "bbox": [ + 304, + 161, + 547, + 234 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 161, + 547, + 234 + ], + "type": "text", + "content": ". Then, the input feature " + }, + { + "bbox": [ + 304, + 161, + 547, + 234 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 161, + 547, + 234 + ], + "type": "text", + "content": " serves as the query, and the global feature " + }, + { + "bbox": [ + 304, + 161, + 547, + 234 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 161, + 547, + 234 + ], + "type": "text", + "content": " serves as both key and value. A self-attention mechanism is then applied to them." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 255, + 546, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 255, + 546, + 291 + ], + "spans": [ + { + "bbox": [ + 304, + 255, + 546, + 291 + ], + "type": "text", + "content": "the " + }, + { + "bbox": [ + 304, + 255, + 546, + 291 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 304, + 255, + 546, + 291 + ], + "type": "text", + "content": " as key and value of the multi-head cross-attention module. The computation of attention map can be formulated as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 353, + 299, + 545, + 315 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 299, + 545, + 315 + ], + "spans": [ + { + "bbox": [ + 353, + 299, + 545, + 315 + ], + "type": "interline_equation", + "content": "A ^ {(m)} = \\operatorname {N o r m} \\left(\\Psi_ {1} \\left(Q _ {c a t}\\right) \\left(F _ {o b j}\\right) ^ {T}\\right) \\tag {4}", + "image_path": "5da5981a91b4ef717904ed119cc8c06e884fc2ef48a3343c8d8537b0fcf70d1c.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 322, + 546, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 322, + 546, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 322, + 546, + 421 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 322, + 546, + 421 + ], + "type": "inline_equation", + "content": "A^{(m)}\\in \\mathbb{R}^{N_{cat}\\times N_{obj}}" + }, + { + "bbox": [ + 304, + 322, + 546, + 421 + ], + "type": "text", + "content": " is the attention map in the mth head. Norm is the normalization function. Instead of using learnable linear projections, we use " + }, + { + "bbox": [ + 304, + 322, + 546, + 421 + ], + "type": "inline_equation", + "content": "\\Psi_{1}" + }, + { + "bbox": [ + 304, + 322, + 546, + 421 + ], + "type": "text", + "content": ", an MLP, applied to " + }, + { + "bbox": [ + 304, + 322, + 546, + 421 + ], + "type": "inline_equation", + "content": "Q_{cat}" + }, + { + "bbox": [ + 304, + 322, + 546, + 421 + ], + "type": "text", + "content": " in order to reduce the gap between " + }, + { + "bbox": [ + 304, + 322, + 546, + 421 + ], + "type": "inline_equation", + "content": "Q_{cat}" + }, + { + "bbox": [ + 304, + 322, + 546, + 421 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 322, + 546, + 421 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 304, + 322, + 546, + 421 + ], + "type": "text", + "content": " and it experimentally works better. Vanilla attention uses softmax to normalize the attention map, which can be formulated as norm = " + }, + { + "bbox": [ + 304, + 322, + 546, + 421 + ], + "type": "inline_equation", + "content": "\\frac{f(x_i)}{\\sum_k f(x_k)}" + }, + { + "bbox": [ + 304, + 322, + 546, + 421 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 322, + 546, + 421 + ], + "type": "inline_equation", + "content": "f(x) = e^x" + }, + { + "bbox": [ + 304, + 322, + 546, + 421 + ], + "type": "text", + "content": " for softmax. Different from that, we use:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 390, + 428, + 545, + 450 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 390, + 428, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 390, + 428, + 545, + 450 + ], + "type": "interline_equation", + "content": "f (x) = \\frac {\\alpha}{1 + e ^ {- x}} \\tag {5}", + "image_path": "fd948cfb5759b047d071481475fa5a7a5f5f3b0fa1ac7e820e7594f1bff566b8.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 458, + 546, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 458, + 546, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 458, + 546, + 601 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 458, + 546, + 601 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 458, + 546, + 601 + ], + "type": "text", + "content": " is a learnable parameter. This is a sigmoid function with a learnable parameter. This function's output is limited between 0 and " + }, + { + "bbox": [ + 304, + 458, + 546, + 601 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 458, + 546, + 601 + ], + "type": "text", + "content": ", so there is no need to scale the dot-product result between query and key by dividing by " + }, + { + "bbox": [ + 304, + 458, + 546, + 601 + ], + "type": "inline_equation", + "content": "\\sqrt{d}" + }, + { + "bbox": [ + 304, + 458, + 546, + 601 + ], + "type": "text", + "content": ". This function tends to saturate and thus activate larger regions than softmax does, and the learnable parameter allows the model to choose the range. Since each query corresponds to a certain semantic part of the object in a specific category, the attention map indicates which component of the observed object has the same semantics as the query by calculating the similarity between the queries " + }, + { + "bbox": [ + 304, + 458, + 546, + 601 + ], + "type": "inline_equation", + "content": "Q_{cat}" + }, + { + "bbox": [ + 304, + 458, + 546, + 601 + ], + "type": "text", + "content": " and the object feature " + }, + { + "bbox": [ + 304, + 458, + 546, + 601 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 304, + 458, + 546, + 601 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 601, + 547, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 601, + 547, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 601, + 547, + 624 + ], + "type": "text", + "content": "Then, the multi-head cross-attention can be formulated as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 357, + 624, + 545, + 639 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 624, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 357, + 624, + 545, + 639 + ], + "type": "interline_equation", + "content": "D = \\left[ A ^ {(1)} F _ {o b j}; \\dots ; A ^ {(m)} F _ {o b j} \\right] W _ {v} \\tag {6}", + "image_path": "8c8cb461b6b6cba6b90bd6775961d60f533de50acc507c1bf1721d4dc4e38ed5.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 643, + 546, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 643, + 546, + 692 + ], + "spans": [ + { + "bbox": [ + 304, + 643, + 546, + 692 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 643, + 546, + 692 + ], + "type": "inline_equation", + "content": "D \\in \\mathbb{R}^{N_{cat} \\times d}" + }, + { + "bbox": [ + 304, + 643, + 546, + 692 + ], + "type": "text", + "content": " is the multi-head cross-attention result and " + }, + { + "bbox": [ + 304, + 643, + 546, + 692 + ], + "type": "inline_equation", + "content": "W_v" + }, + { + "bbox": [ + 304, + 643, + 546, + 692 + ], + "type": "text", + "content": " is the learnable parameter. In this way, the related object feature is extracted from the " + }, + { + "bbox": [ + 304, + 643, + 546, + 692 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 304, + 643, + 546, + 692 + ], + "type": "text", + "content": ". Then " + }, + { + "bbox": [ + 304, + 643, + 546, + 692 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 643, + 546, + 692 + ], + "type": "text", + "content": " can be used to deform " + }, + { + "bbox": [ + 304, + 643, + 546, + 692 + ], + "type": "inline_equation", + "content": "Q_{cat}" + }, + { + "bbox": [ + 304, + 643, + 546, + 692 + ], + "type": "text", + "content": " by adding it to " + }, + { + "bbox": [ + 304, + 643, + 546, + 692 + ], + "type": "inline_equation", + "content": "Q_{cat}" + }, + { + "bbox": [ + 304, + 643, + 546, + 692 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 387, + 701, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 701, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 387, + 701, + 545, + 715 + ], + "type": "interline_equation", + "content": "Q _ {o b j} = Q _ {c a t} + D \\tag {7}", + "image_path": "9149a2ce82b5ea96e6fe5b725b4b4366367144aa18f63ce76a0eaa23662e7b46.jpg" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14058" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 228, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 228, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 228, + 84 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 72, + 228, + 84 + ], + "type": "inline_equation", + "content": "Q_{obj} \\in \\mathbb{R}^{N_{cat} \\times d}" + }, + { + "bbox": [ + 47, + 72, + 228, + 84 + ], + "type": "text", + "content": " is deformed queries." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 84, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 84, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 47, + 84, + 287, + 109 + ], + "type": "inline_equation", + "content": "Q_{obj}" + }, + { + "bbox": [ + 47, + 84, + 287, + 109 + ], + "type": "text", + "content": " is expected to embed the object's canonical point cloud. It can be decoded into 3D points using a simple MLP." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 93, + 120, + 287, + 133 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 120, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 93, + 120, + 287, + 133 + ], + "type": "interline_equation", + "content": "P _ {i} = \\operatorname {S i g m o i d} \\left(M L P \\left(Q _ {o b j}\\right)\\right) - 0. 5 \\tag {8}", + "image_path": "0e8a151c7ee02bb47e621d16038691bbcefe6f92a966f1e0ea62a120fc825a9c.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 137, + 287, + 197 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 137, + 287, + 197 + ], + "spans": [ + { + "bbox": [ + 47, + 137, + 287, + 197 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 137, + 287, + 197 + ], + "type": "inline_equation", + "content": "P_{i} \\in \\mathbb{R}^{N_{\\text{cat}} \\times 3}" + }, + { + "bbox": [ + 47, + 137, + 287, + 197 + ], + "type": "text", + "content": ". A Sigmoid function is used to limit it to " + }, + { + "bbox": [ + 47, + 137, + 287, + 197 + ], + "type": "inline_equation", + "content": "(-0.5, 0.5)" + }, + { + "bbox": [ + 47, + 137, + 287, + 197 + ], + "type": "text", + "content": ", so the output points are in canonical space. We apply supervision to " + }, + { + "bbox": [ + 47, + 137, + 287, + 197 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 47, + 137, + 287, + 197 + ], + "type": "text", + "content": " which could guide the learning of " + }, + { + "bbox": [ + 47, + 137, + 287, + 197 + ], + "type": "inline_equation", + "content": "Q_{obj}" + }, + { + "bbox": [ + 47, + 137, + 287, + 197 + ], + "type": "text", + "content": ". Therefore, loss function " + }, + { + "bbox": [ + 47, + 137, + 287, + 197 + ], + "type": "inline_equation", + "content": "L_{rec}" + }, + { + "bbox": [ + 47, + 137, + 287, + 197 + ], + "type": "text", + "content": " is applied to " + }, + { + "bbox": [ + 47, + 137, + 287, + 197 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 47, + 137, + 287, + 197 + ], + "type": "text", + "content": " to provide supervision to it." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 198, + 287, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 198, + 287, + 268 + ], + "spans": [ + { + "bbox": [ + 47, + 198, + 287, + 268 + ], + "type": "text", + "content": "Global enhancement block tends to enhance features by fusing their global feature. Normally, this can be achieved via the self-attention mechanism. However, to make the entire model lightweight, a more efficient block is needed. For this reason, we propose a global enhancement block." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 269, + 287, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 269, + 287, + 329 + ], + "spans": [ + { + "bbox": [ + 47, + 269, + 287, + 329 + ], + "type": "text", + "content": "The global enhancement block is illustrated in Figure 3. Suppose the global enhancement block takes feature " + }, + { + "bbox": [ + 47, + 269, + 287, + 329 + ], + "type": "inline_equation", + "content": "f \\in \\mathbb{R}^{N \\times d}" + }, + { + "bbox": [ + 47, + 269, + 287, + 329 + ], + "type": "text", + "content": " as input. We adopt the result of the global average pooling as the global feature and pass it through a fully connected layer. The outcome is denoted as " + }, + { + "bbox": [ + 47, + 269, + 287, + 329 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 47, + 269, + 287, + 329 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 117, + 338, + 287, + 350 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 338, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 117, + 338, + 287, + 350 + ], + "type": "interline_equation", + "content": "g = F C \\left(A v g P o o l (f)\\right) \\tag {9}", + "image_path": "1b92134dca69d9c24764122464c8fd85cb3f307bea3c8bd40060a49c639473cd.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 358, + 287, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 358, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 358, + 287, + 418 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 358, + 287, + 418 + ], + "type": "inline_equation", + "content": "FC" + }, + { + "bbox": [ + 47, + 358, + 287, + 418 + ], + "type": "text", + "content": " is a fully connected layer. Instead of simply concatenating it to " + }, + { + "bbox": [ + 47, + 358, + 287, + 418 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 358, + 287, + 418 + ], + "type": "text", + "content": " and then feeding it to an MLP, we borrow the idea from self-attention as shown in Figure 3. We use " + }, + { + "bbox": [ + 47, + 358, + 287, + 418 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 358, + 287, + 418 + ], + "type": "text", + "content": " as query and " + }, + { + "bbox": [ + 47, + 358, + 287, + 418 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 47, + 358, + 287, + 418 + ], + "type": "text", + "content": " as key and value to carry out self-attention, which can be denoted as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 116, + 426, + 287, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 426, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 116, + 426, + 287, + 441 + ], + "type": "interline_equation", + "content": "f ^ {\\prime} = f + \\operatorname {N o r m} \\left(f g ^ {T}\\right) g \\tag {10}", + "image_path": "8f0e95a28a5cb07b3c1867ec2f0405fb08c94a757dd572a896bd7470e56f123f.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 449, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 449, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 47, + 449, + 287, + 533 + ], + "type": "text", + "content": "After that, " + }, + { + "bbox": [ + 47, + 449, + 287, + 533 + ], + "type": "inline_equation", + "content": "f'" + }, + { + "bbox": [ + 47, + 449, + 287, + 533 + ], + "type": "text", + "content": " is fed into an MLP with residual. In this way, global information is injected into the feature. This block, unlike vanilla self-attention, reduces the complexity of the computation. Compared with the computation complexity of vanilla self-attention, " + }, + { + "bbox": [ + 47, + 449, + 287, + 533 + ], + "type": "inline_equation", + "content": "O(N^2 \\times d)" + }, + { + "bbox": [ + 47, + 449, + 287, + 533 + ], + "type": "text", + "content": ", our efficient global enhancement block has a computation complexity of " + }, + { + "bbox": [ + 47, + 449, + 287, + 533 + ], + "type": "inline_equation", + "content": "O(N \\times d)" + }, + { + "bbox": [ + 47, + 449, + 287, + 533 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 540, + 257, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 257, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 257, + 552 + ], + "type": "text", + "content": "3.3. Query-Point Correspondence Estimator" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "text", + "content": "We obtain the deformed queries " + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "inline_equation", + "content": "Q_{obj}" + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "text", + "content": " by adaptively selecting feature from the observed object feature " + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "text", + "content": ". In previous works, a correspondence matrix " + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "inline_equation", + "content": "A \\in \\mathbb{R}^{N_{obj} \\times N_{cat}}" + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "text", + "content": " is estimated, which models correspondences between points in observed point cloud " + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "inline_equation", + "content": "P_{obj}" + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "text", + "content": " and reconstructed point cloud " + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "inline_equation", + "content": "P_i" + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "text", + "content": ". This matrix then samples the points from " + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "inline_equation", + "content": "P_i" + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "text", + "content": " to be paired with " + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "inline_equation", + "content": "P_{obj}" + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "text", + "content": ", and it can be formulated as " + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "inline_equation", + "content": "P = A \\times P_i" + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "text", + "content": " denotes the sampled points. Finally, solving of Umeyama algorithm [31] to align the sample points with " + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "inline_equation", + "content": "P_i" + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "text", + "content": " gives out the target pose and size. Instead of using this conventional way, we move this process to the feature space. In the query-point correspondence estimator, the correspondences between " + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "inline_equation", + "content": "Q_{obj}" + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "text", + "content": " are built as illustrated in Figure 2." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": "In detail, the correspondences are built by computing the similarity between " + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "inline_equation", + "content": "Q_{obj}" + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": " using dot-product, which can be formulated as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 359, + 114, + 545, + 128 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 114, + 545, + 128 + ], + "spans": [ + { + "bbox": [ + 359, + 114, + 545, + 128 + ], + "type": "interline_equation", + "content": "A ^ {\\prime} = \\operatorname {N o r m} \\left(\\Psi_ {2} \\left(F _ {o b j}\\right) \\left(Q _ {o b j}\\right) ^ {T}\\right) \\tag {11}", + "image_path": "7321ec846ad314f96abdac267336dd9920c0732685f33dfd3caaa496e0e3e576.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "A' \\in \\mathbb{R}^{N_{obj} \\times N_{cat}}" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": " denotes the correspondence matrix between " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "Q_{obj}" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": ". Norm is the same as that used in queries deformation estimator. " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\Psi_2" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": " is an MLP. " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": " represents the soft matching between " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "Q_{obj}" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": ". Then we multiply " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "Q_{obj}" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": " to obtain the sampled features. Essentially, we find that this process is similar to cross-attention. For this reason, we add " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": " to the result for implementing a residual structure similar to attention mechanism. Also, we implement multi-head technique to the computation. Next, we need to pair the object feature with the sampled feature. Experimentally, it is better to use a more direct feature as the object feature here instead of the deep object feature " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": ". Thereby, we do not use " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "F_{obj}" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": " but simply feed object point cloud " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "P_{obj}" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": " forward an MLP. The output of the MLP is concatenated to the sampled feature. To further enhance the feature, we use an MLP and a global enhancement block after that. The result is denoted as " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "F_{nocs}" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": ". To apply supervision on " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "F_{nocs}" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": " and better guide its learning, we use a simple MLP to transform " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "F_{nocs}" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": " into NOCS coordinates denoted as " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "P_r \\in \\mathbb{R}^{N_{obj} \\times 3}" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "P_r" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": " is not used to solve the Umeyama algorithm to obtain target pose and size, but only used to compute loss function " + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "inline_equation", + "content": "L_{nocs}" + }, + { + "bbox": [ + 304, + 133, + 545, + 396 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 403, + 450, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 403, + 450, + 414 + ], + "spans": [ + { + "bbox": [ + 306, + 403, + 450, + 414 + ], + "type": "text", + "content": "3.4. Poses and Sizes Estimator" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 422, + 545, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 422, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 305, + 422, + 545, + 469 + ], + "type": "text", + "content": "The rest of the work is to obtain the final object's pose and size, which is accomplished in the pose and size estimator. The pose and size estimator applies global average pooling operation to " + }, + { + "bbox": [ + 305, + 422, + 545, + 469 + ], + "type": "inline_equation", + "content": "F_{nocs}" + }, + { + "bbox": [ + 305, + 422, + 545, + 469 + ], + "type": "text", + "content": ", which can be formulated as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 372, + 475, + 545, + 488 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 475, + 545, + 488 + ], + "spans": [ + { + "bbox": [ + 372, + 475, + 545, + 488 + ], + "type": "interline_equation", + "content": "f _ {\\text {p o s e}} = \\operatorname {A v g P o o l} \\left(F _ {\\text {n o c s}}\\right) \\tag {12}", + "image_path": "90f6fd176eea943673ad5ae39ce8f16b1b3f06a2cb6e96b9f0008f2a3ec88a0a.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 494, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 494, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 305, + 494, + 545, + 519 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 494, + 545, + 519 + ], + "type": "inline_equation", + "content": "f_{\\text{pose}} \\in \\mathbb{R}^{1 \\times d}" + }, + { + "bbox": [ + 305, + 494, + 545, + 519 + ], + "type": "text", + "content": ". Then after it, three parallel MLPs predict the rotation " + }, + { + "bbox": [ + 305, + 494, + 545, + 519 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 305, + 494, + 545, + 519 + ], + "type": "text", + "content": ", translation " + }, + { + "bbox": [ + 305, + 494, + 545, + 519 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 494, + 545, + 519 + ], + "type": "text", + "content": ", and size " + }, + { + "bbox": [ + 305, + 494, + 545, + 519 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 494, + 545, + 519 + ], + "type": "text", + "content": " respectively." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 311, + 536, + 545, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 536, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 311, + 536, + 545, + 550 + ], + "type": "interline_equation", + "content": "R, t, s = M L P \\left(f _ {p o s e}\\right), M L P \\left(f _ {p o s e}\\right), M L P \\left(f _ {p o s e}\\right) \\tag {13}", + "image_path": "f267437c1821bc1fcebcbeb82ddda58e9f847e2900c780bc1a2366308b1ef76b.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 555, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 555, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 305, + 555, + 545, + 616 + ], + "type": "text", + "content": "The representation of " + }, + { + "bbox": [ + 305, + 555, + 545, + 616 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 305, + 555, + 545, + 616 + ], + "type": "text", + "content": " here is the Continuity of Rotation Representations [40]. For " + }, + { + "bbox": [ + 305, + 555, + 545, + 616 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 555, + 545, + 616 + ], + "type": "text", + "content": ", we follow [3] to estimate the residual between object's size and the mean category size. Similarly, for " + }, + { + "bbox": [ + 305, + 555, + 545, + 616 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 555, + 545, + 616 + ], + "type": "text", + "content": ", we predict the residual between the translation ground truth and the mean value of the point cloud." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 621, + 433, + 633 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 433, + 633 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 433, + 633 + ], + "type": "text", + "content": "3.5. Overall Loss Function" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 317, + 640, + 474, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 640, + 474, + 651 + ], + "spans": [ + { + "bbox": [ + 317, + 640, + 474, + 651 + ], + "type": "text", + "content": "The overall loss function is as follows:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 354, + 658, + 545, + 672 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 658, + 545, + 672 + ], + "spans": [ + { + "bbox": [ + 354, + 658, + 545, + 672 + ], + "type": "interline_equation", + "content": "L = \\lambda_ {1} L _ {\\text {p o s e}} + \\lambda_ {2} L _ {\\text {r e c}} + \\lambda_ {3} L _ {\\text {n o c s}} \\tag {14}", + "image_path": "cb854e69ccf06d815580cff616d4676086cfd43ecbe99a34aee741dd4fee2b1a.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "L_{\\text{pose}}" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": " is used to compute loss on predicted " + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "R, t" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": ". We simply use smooth L1 loss [8] for all of them with threshold of " + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-3}, 5 \\times 10^{-3}, 5 \\times 10^{-3}" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": " respectively. " + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "L_{\\text{rec}}" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": " and" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14059" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "L_{nocs}" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": " are the auxiliary losses function for " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "P_{r}" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": " respectively. " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "L_{rec}" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": " is applied to " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": " to encourage it to reconstruct the instance point cloud in the NOCS space. Therefore, for " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "L_{rec}" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": ", we use Chamfer distance between " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "M_{gt}" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "M_{gt} \\in \\mathbb{R}^{N_{obj} \\times 3}" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": " represents the instance point cloud model in the NOCS space. " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "L_{rec}" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": " can be formulated as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 85, + 150, + 287, + 211 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 150, + 287, + 211 + ], + "spans": [ + { + "bbox": [ + 85, + 150, + 287, + 211 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {r e c} = \\frac {1}{N _ {c a t}} \\sum_ {x _ {i} \\in P _ {r}} \\min _ {y _ {j} \\in M _ {g t}} \\| x _ {i} - y _ {j} \\| _ {2} ^ {2} + \\\\ \\frac {1}{N _ {o b j}} \\sum_ {y _ {i} \\in M _ {g t}} \\min _ {x _ {i} \\in P _ {r}} \\| x _ {i} - y _ {j} \\| _ {2} ^ {2} \\tag {15} \\\\ \\end{array}", + "image_path": "450b8c1a645d8faf0bbbd49a532d905a5c86bcdf5da6d2efb4f28c27763fa9ec.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 217, + 287, + 265 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 217, + 287, + 265 + ], + "spans": [ + { + "bbox": [ + 47, + 217, + 287, + 265 + ], + "type": "inline_equation", + "content": "L_{nocs}" + }, + { + "bbox": [ + 47, + 217, + 287, + 265 + ], + "type": "text", + "content": " is applied on " + }, + { + "bbox": [ + 47, + 217, + 287, + 265 + ], + "type": "inline_equation", + "content": "P_r" + }, + { + "bbox": [ + 47, + 217, + 287, + 265 + ], + "type": "text", + "content": " to encourage it in predicting the corresponding coordinates of " + }, + { + "bbox": [ + 47, + 217, + 287, + 265 + ], + "type": "inline_equation", + "content": "P_{obj}" + }, + { + "bbox": [ + 47, + 217, + 287, + 265 + ], + "type": "text", + "content": " in Normalized Object Coordinate Space. For " + }, + { + "bbox": [ + 47, + 217, + 287, + 265 + ], + "type": "inline_equation", + "content": "L_{nocs}" + }, + { + "bbox": [ + 47, + 217, + 287, + 265 + ], + "type": "text", + "content": ", we also use a smooth L1 loss [8] with a threshold of 0.1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 274, + 128, + 288 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 274, + 128, + 288 + ], + "spans": [ + { + "bbox": [ + 47, + 274, + 128, + 288 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 295, + 287, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 295, + 287, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 295, + 287, + 462 + ], + "type": "text", + "content": "Datasets. We conduct experiments using the benchmark CAMERA25 and REAL275 [34] datasets for category-level 6D object pose and size estimation which consists of six object categories. The CAMERA25 dataset is generated by rendering and compositing synthetic object instances under different views. The CAMERA25 dataset contains 300K synthetic images of 1,085 object instances, among which 25,000 images of 184 instances are used for evaluation. The REAL275 dataset is complementary to the CAMERA25 dataset. It includes 4,300 real-world images of 6 scenes with 3 unseen instances per category; its training set contains 4,300 images of 7 scenes, and the test set contains 2,750 images of 6 scenes. We train our model with a combined use of the two datasets, as done in [18]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 463, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 463, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 463, + 287, + 713 + ], + "type": "text", + "content": "Implement Details. We employ a Mask R-CNN [9] to obtain instance masks the same as [30]. The instances are then cropped based on the segmentation result. After that, the depth is converted to the instance point cloud using the camera's intrinsic parameters. 1024 points are randomly sampled from that, so " + }, + { + "bbox": [ + 46, + 463, + 287, + 713 + ], + "type": "inline_equation", + "content": "N_{obj}" + }, + { + "bbox": [ + 46, + 463, + 287, + 713 + ], + "type": "text", + "content": " is set to 1024. To extract instance geometry features, we choose PointNet++ [27] with four abstraction levels. The number of prior queries " + }, + { + "bbox": [ + 46, + 463, + 287, + 713 + ], + "type": "inline_equation", + "content": "N_{cat}" + }, + { + "bbox": [ + 46, + 463, + 287, + 713 + ], + "type": "text", + "content": " is set to 64. In this case, " + }, + { + "bbox": [ + 46, + 463, + 287, + 713 + ], + "type": "inline_equation", + "content": "N_{cat} \\ll N_{obj}" + }, + { + "bbox": [ + 46, + 463, + 287, + 713 + ], + "type": "text", + "content": ". A detailed study on the parameter " + }, + { + "bbox": [ + 46, + 463, + 287, + 713 + ], + "type": "inline_equation", + "content": "N_{cat}" + }, + { + "bbox": [ + 46, + 463, + 287, + 713 + ], + "type": "text", + "content": " is given in our ablation study. The queries are initialized randomly at the beginning of training. The dimension of features and queries is set to 256. The crossattention in queries deformation estimator and query-point correspondence estimator has four heads each. In the loss function, we set " + }, + { + "bbox": [ + 46, + 463, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_1, \\lambda_2, \\lambda_3" + }, + { + "bbox": [ + 46, + 463, + 287, + 713 + ], + "type": "text", + "content": " to 1.0, 3.0, 1.0, respectively. We use AdamW [21] to train this model with an initial learning rate of " + }, + { + "bbox": [ + 46, + 463, + 287, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 46, + 463, + 287, + 713 + ], + "type": "text", + "content": " and weight decay " + }, + { + "bbox": [ + 46, + 463, + 287, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 46, + 463, + 287, + 713 + ], + "type": "text", + "content": ". All models are trained 42k iterations with batch size of 60 and cosine learning rate decay is conducted. We employ several strategies for depth augmentation, such as adding Gaussian noise, random scaling, random rotation, adding random points as well" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "content": "as linear shape augmentation proposed in [3] and non-linear shape augmentation proposed in [38]. All FPS(Frames Per Second) data of our method is evaluated on a single RTX 2080Ti, an Intel(R) Xeon(R) CPU E5-2650 v4 @ 2.20GHz, PyTorch [24] 1.10, CUDA version 11.1." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 133, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 545, + 168 + ], + "type": "text", + "content": "Evaluation Metrics. For category-level pose estimation, we follow [34] and use two metrics to evaluate the quality." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 175, + 545, + 291 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 317, + 175, + 545, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 175, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 317, + 175, + 545, + 236 + ], + "type": "text", + "content": "- 3D IoU. The overlap of two 3D bounding boxes under the predicted pose and the ground truth pose is computed. The overlap ratios larger than the threshold are regarded as accepted. The mean Average Precision (mAP) of the overlapping is reported." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 243, + 545, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 243, + 545, + 291 + ], + "spans": [ + { + "bbox": [ + 317, + 243, + 545, + 291 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 317, + 243, + 545, + 291 + ], + "type": "inline_equation", + "content": "n^{\\circ}m" + }, + { + "bbox": [ + 317, + 243, + 545, + 291 + ], + "type": "text", + "content": " cm. The rotation and translation errors between the predicted pose and the ground truth pose are computed. The errors smaller than an angle threshold " + }, + { + "bbox": [ + 317, + 243, + 545, + 291 + ], + "type": "inline_equation", + "content": "n^{\\circ}" + }, + { + "bbox": [ + 317, + 243, + 545, + 291 + ], + "type": "text", + "content": " and a translation threshold " + }, + { + "bbox": [ + 317, + 243, + 545, + 291 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 317, + 243, + 545, + 291 + ], + "type": "text", + "content": " cm are accepted." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 298, + 499, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 298, + 499, + 312 + ], + "spans": [ + { + "bbox": [ + 305, + 298, + 499, + 312 + ], + "type": "text", + "content": "4.1. Comparisons with Existing Methods" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "content": "NOCS-REAL275 In Table 1 we compare our method with the existing ones for category-level 6D object pose and size estimation. We divide these methods into two groups: those with and without shape prior. As it is shown in Table 1, our method outperforms other existing methods. In detail, we outperform NOCS [34] by 46.0 in " + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "inline_equation", + "content": "IoU_{75}" + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "content": ", 41.8 in " + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "inline_equation", + "content": "5^{\\circ}2cm" + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "content": ", 48.9 in " + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "inline_equation", + "content": "5^{\\circ}5cm" + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "content": ". Moreover, we achieve a better result than existing methods that using prior information. Specifically, we outperform SPD [30] by 22.9 in " + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "inline_equation", + "content": "IoU_{75}" + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "content": ", 29.7 in " + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "inline_equation", + "content": "5^{\\circ}2cm" + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "content": ", 37.5 in " + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "inline_equation", + "content": "5^{\\circ}5cm" + }, + { + "bbox": [ + 304, + 316, + 545, + 472 + ], + "type": "text", + "content": " and 14.2, 13.1, and 19.3 higher than SGPA [2] which is a representative method based on attention. This outcome demonstrates that our sparse shape prior is superior to the traditional shape prior." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 472, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 545, + 532 + ], + "type": "text", + "content": "NOCS-CAMERA25 The results for CAMERA25 are shown Table 1. Our method outperforms others at least 4.9, 4.3 in the items of " + }, + { + "bbox": [ + 304, + 472, + 545, + 532 + ], + "type": "inline_equation", + "content": "5^{\\circ}2cm" + }, + { + "bbox": [ + 304, + 472, + 545, + 532 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 472, + 545, + 532 + ], + "type": "inline_equation", + "content": "5^{\\circ}5cm" + }, + { + "bbox": [ + 304, + 472, + 545, + 532 + ], + "type": "text", + "content": ", and it is on par with the best methods for " + }, + { + "bbox": [ + 304, + 472, + 545, + 532 + ], + "type": "inline_equation", + "content": "IoU_{75}" + }, + { + "bbox": [ + 304, + 472, + 545, + 532 + ], + "type": "text", + "content": ". Figure 4 presents a more detailed error evaluation result on two datasets." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 540, + 406, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 406, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 406, + 551 + ], + "type": "text", + "content": "4.2. Ablation Studies" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": "Effect of the design in Query6DoF. We verify the efficacy of each component in Query6DoF in Table 2. By replacing queries with point cloud proposed in [30] and adding an extra PointNet++ [27] after the prior point cloud as a feature extractor, " + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "inline_equation", + "content": "5^{\\circ}2cm" + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": " drops from 49.0 to 47.2, and computation increases. Removing the global enhancement block results in a 4.8 drop in " + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "inline_equation", + "content": "5^{\\circ}2cm" + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": ". Removing the queries deformation estimator results in a 2.5 drop in " + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "inline_equation", + "content": "5^{\\circ}2cm" + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": ". If the query-point correspondence estimator is detached, it renders the usage of queries and queries deformation estimator senseless. Therefore, without using them together, our method experiences a 13.6 drop in " + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "inline_equation", + "content": "5^{\\circ}2cm" + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": ". Moreover, we remove the poses and sizes estimator but use " + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "inline_equation", + "content": "P_r" + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "inline_equation", + "content": "P_i" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14060" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 71, + 103, + 520, + 224 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "type": "text", + "content": "Table 1: Comparison with state-of-the-art methods on the CAMERA25 dataset and REAL275 dataset. * denotes results without linear shape augmentation and non-linear shape augmentation. The best results shown in bold." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 71, + 103, + 520, + 224 + ], + "lines": [ + { + "bbox": [ + 71, + 103, + 520, + 224 + ], + "spans": [ + { + "bbox": [ + 71, + 103, + 520, + 224 + ], + "type": "table", + "html": "
MethodpriorCAMERA25REAL275
IoU50IoU755°2cm5°5cm10°2cm10°5cmIoU50IoU755°2cm5°5cm10°2cm10°5cm
NOCS [34]83.969.532.340.948.264.678.030.17.210.013.825.2
DualPoseNet [18]92.486.464.770.777.284.779.862.229.335.950.066.8
GPV-Pose [7]93.488.372.179.1-89.083.064.432.042.9-73.3
SPD [30]✓93.283.154.359.073.381.577.353.219.321.443.254.1
CR-Net [35]✓93.888.072.076.481.087.779.355.927.834.347.260.8
SAR-Net [16]✓86.879.066.770.975.680.379.362.431.642.350.368.3
SGPA [2]✓93.288.170.774.582.788.480.161.935.939.661.370.7
RBP-Pose [38]✓93.189.073.579.682.189.5-67.838.248.163.179.2
Self-DPDN [17]✓------83.676.046.050.770.478.4
Ours*✓92.388.678.483.984.090.582.976.046.854.767.981.6
Ours✓91.988.178.083.183.990.082.576.149.058.968.783.0
", + "image_path": "fb6b78ed09c3c8bc6a6276248020499dcca4e77daf1f72e3e16eacc3a1501520.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 71, + 279, + 520, + 354 + ], + "blocks": [ + { + "bbox": [ + 46, + 234, + 547, + 270 + ], + "lines": [ + { + "bbox": [ + 46, + 234, + 547, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 547, + 270 + ], + "type": "text", + "content": "Table 2: Effect of the design on Query6DoF, evaluated on the REAL275 dataset. GlobEnhance denotes the global enhancement block, QueryDeform denotes the queries deformation estimator, Query2Point denotes the query-point correspondence estimator, and PoseSize denotes the poses and sizes estimator" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 71, + 279, + 520, + 354 + ], + "lines": [ + { + "bbox": [ + 71, + 279, + 520, + 354 + ], + "spans": [ + { + "bbox": [ + 71, + 279, + 520, + 354 + ], + "type": "table", + "html": "
QueriesGlobEnhanceQueryDeformQuery2PointPoseSizeI0U50I0U755°2cm5°5cm10°2cm10°5cm
1-✓✓✓✓82.175.447.256.267.381.2
2✓-✓✓✓82.675.744.253.365.881.1
3✓✓-✓✓83.075.346.556.665.981.3
4-✓--✓82.170.935.448.759.580.2
5✓✓✓✓-82.270.040.046.365.176.5
6✓✓✓✓✓82.576.149.058.968.783.0
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NcatIoU50IoU755°2cm5°5cm10°2cm10°5cm
1682.574.646.055.466.681.0
3282.574.946.755.967.281.5
6482.676.149.058.968.783.0
12882.876.946.155.968.882.8
25682.876.647.657.367.881.6
51282.675.646.856.266.981.4
102483.176.748.756.870.482.4
", + "image_path": "468e897265f30796ec121b10c3af584c4d346e8bda5bcd095400964a383f06d3.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 309, + 514, + 544, + 549 + ], + "blocks": [ + { + "bbox": [ + 306, + 481, + 545, + 505 + ], + "lines": [ + { + "bbox": [ + 306, + 481, + 545, + 505 + ], + "spans": [ + { + "bbox": [ + 306, + 481, + 545, + 505 + ], + "type": "text", + "content": "Table 4: Effect of different attention normalization evaluated on REAL275." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 514, + 544, + 549 + ], + "lines": [ + { + "bbox": [ + 309, + 514, + 544, + 549 + ], + "spans": [ + { + "bbox": [ + 309, + 514, + 544, + 549 + ], + "type": "table", + "html": "
NormI0U50I0U755°2cm5°5cm10°2cm10°5cm
Softmax82.174.748.657.268.682.4
Ours82.576.149.058.968.783.0
", + "image_path": "573ea9b808860cf44132d5190cf118b42f913d5ccb5bc2e0804fd7b806d60b3c.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "text", + "content": "queries. The results show that reducing the number of prior queries does not significantly affect the performance of our method. This fact means that it is not necessary to use excessive points to express the object's shape prior. A small number of queries can effectively represent the object's shape. Specifically, when " + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "inline_equation", + "content": "N_{cat} = 64" + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "text", + "content": ", our method achieves the best performance in the " + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "inline_equation", + "content": "5^{\\circ}2cm" + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "inline_equation", + "content": "5^{\\circ}5cm" + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "inline_equation", + "content": "10^{\\circ}5cm" + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "text", + "content": " metrics and when " + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "inline_equation", + "content": "N_{cat} = 1024" + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "text", + "content": ", our method achieves the best performance in the " + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "inline_equation", + "content": "IoU_{50}" + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "text", + "content": " metric. However, the smaller " + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "inline_equation", + "content": "N_{cat}" + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "text", + "content": " results in less computational overhead. Therefore, we adopt " + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "inline_equation", + "content": "N_{cat} = 64" + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "text", + "content": " as the default setting in all other experiments." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 701, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 712 + ], + "type": "text", + "content": "Effect of different attention normalization. While" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14061" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 73, + 72, + 519, + 135 + ], + "blocks": [ + { + "bbox": [ + 73, + 72, + 519, + 135 + ], + "lines": [ + { + "bbox": [ + 73, + 72, + 519, + 135 + ], + "spans": [ + { + "bbox": [ + 73, + 72, + 519, + 135 + ], + "type": "image", + "image_path": "0273c03d260c05a4cf076de92d803aa8a86585ed57a302284834f7f0e2e588a9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 134, + 143, + 459, + 156 + ], + "lines": [ + { + "bbox": [ + 134, + 143, + 459, + 156 + ], + "spans": [ + { + "bbox": [ + 134, + 143, + 459, + 156 + ], + "type": "text", + "content": "Figure 5: Qualitative results of our method (red line) and SGPA [2] (green line)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 73, + 167, + 520, + 305 + ], + "blocks": [ + { + "bbox": [ + 73, + 167, + 520, + 305 + ], + "lines": [ + { + "bbox": [ + 73, + 167, + 520, + 305 + ], + "spans": [ + { + "bbox": [ + 73, + 167, + 520, + 305 + ], + "type": "image", + "image_path": "914d399b303d132dce74e281b74a19a93d889b61ea347c92d86b1fc3e5b549b5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 314, + 547, + 339 + ], + "lines": [ + { + "bbox": [ + 47, + 314, + 547, + 339 + ], + "spans": [ + { + "bbox": [ + 47, + 314, + 547, + 339 + ], + "type": "text", + "content": "Figure 6: Sparse point cloud reconstruction in the REAL275 dataset. The yellow points represent the reconstruction points " + }, + { + "bbox": [ + 47, + 314, + 547, + 339 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 47, + 314, + 547, + 339 + ], + "type": "text", + "content": ", while the blue points are the observed point cloud." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 50, + 403, + 285, + 454 + ], + "blocks": [ + { + "bbox": [ + 47, + 357, + 288, + 394 + ], + "lines": [ + { + "bbox": [ + 47, + 357, + 288, + 394 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 288, + 394 + ], + "type": "text", + "content": "Table 5: Model complexity and FPS w/o Mask R-CNN [9], evaluated on REAL275. GEB denotes the global enhancement block." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 403, + 285, + 454 + ], + "lines": [ + { + "bbox": [ + 50, + 403, + 285, + 454 + ], + "spans": [ + { + "bbox": [ + 50, + 403, + 285, + 454 + ], + "type": "table", + "html": "
MethodParams(M)FPS w/o Mask R-CNN [9]5°2cm
Ncat = 64 (Default)19.5334.949.0
Ncat = 102421.1823.348.7
w/o GEB18.7136.844.2
w/o Queries22.2424.047.2
", + "image_path": "a512da0abffa399f4ccb28ca6d713177264f9e26ba02e4363bbcb487b3b48573.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 477, + 287, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 477, + 287, + 573 + ], + "spans": [ + { + "bbox": [ + 46, + 477, + 287, + 573 + ], + "type": "text", + "content": "common attention mechanisms adopt softmax to normalize the attention map, in our method, we use a different normalization approach, namely sigmoid with a learnable parameter mentioned earlier. In this experiment, we compare two different settings shown in Table 4. We conduct the evaluation on the REAL275 dataset. Using softmax to normalize results in a 1.4 drop in " + }, + { + "bbox": [ + 46, + 477, + 287, + 573 + ], + "type": "inline_equation", + "content": "IoU_{75}" + }, + { + "bbox": [ + 46, + 477, + 287, + 573 + ], + "type": "text", + "content": " and a 0.4 drop in " + }, + { + "bbox": [ + 46, + 477, + 287, + 573 + ], + "type": "inline_equation", + "content": "5^{\\circ}2cm" + }, + { + "bbox": [ + 46, + 477, + 287, + 573 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 586, + 153, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 153, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 153, + 598 + ], + "type": "text", + "content": "4.3. Runtime Analysis" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "As shown in Table 5, our method, in the default setting, has 19.43M parameters and runs at 34.9 FPS without Mask R-CNN [9]. Increasing " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "N_{cat}" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " to 1024 brings no gain but the FPS drops to 23.3, which shows that sparse queries are sufficient to represent the shape prior. Adding the global enhancement block results in a 4.8 improvement in " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "5^{\\circ}2cm" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " with only a 1.9 FPS drop, demonstrating its efficiency. W/o Queries means that we replace the queries with the prelearned shape prior proposed in [30] and use PointNet++" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 359, + 545, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 359, + 545, + 420 + ], + "spans": [ + { + "bbox": [ + 304, + 359, + 545, + 420 + ], + "type": "text", + "content": "[27] as a feature extractor. In this way, due to the extra PointNet++ [27], the speed drops to 24.0FPS, but there is no gain in " + }, + { + "bbox": [ + 304, + 359, + 545, + 420 + ], + "type": "inline_equation", + "content": "5^{\\circ}2cm" + }, + { + "bbox": [ + 304, + 359, + 545, + 420 + ], + "type": "text", + "content": ". Therefore, the usage of queries is more efficient than using point cloud both in terms of accuracy and speed." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 426, + 390, + 437 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 426, + 390, + 437 + ], + "spans": [ + { + "bbox": [ + 306, + 426, + 390, + 437 + ], + "type": "text", + "content": "4.4. Visualization" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 444, + 545, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 545, + 480 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 545, + 480 + ], + "type": "text", + "content": "Qualitative Results. Figure 5 shows the qualitative results of our method, demonstrating that our method can accurately estimate the objects' poses and sizes." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 481, + 546, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 481, + 546, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 481, + 546, + 624 + ], + "type": "text", + "content": "Sparse point cloud reconstruction. Our method outputs " + }, + { + "bbox": [ + 304, + 481, + 546, + 624 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 304, + 481, + 546, + 624 + ], + "type": "text", + "content": " as the sparse point cloud reconstruction in NOCS space. We align " + }, + { + "bbox": [ + 304, + 481, + 546, + 624 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 304, + 481, + 546, + 624 + ], + "type": "text", + "content": " to the object's location in RGB images for better comparison with the object's actual shape, as shown in Figure 6. " + }, + { + "bbox": [ + 304, + 481, + 546, + 624 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 304, + 481, + 546, + 624 + ], + "type": "text", + "content": " is the yellow points in it. The blue points in it represent the observed point cloud for comparison. It shows that our sparse point cloud can accurately cover different objects' shapes. This effect can be attributed to our queries deformation estimator, where category-specific queries transformed into instance-specific ones. Through this process, the queries are able to reconstruct the objects." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 634, + 378, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 634, + 378, + 645 + ], + "spans": [ + { + "bbox": [ + 306, + 634, + 378, + 645 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "In conclusion, we present a novel network for category-level 6D object pose and size estimation, namely Query6DoF. In particular, we propose to use a series of sparse and learnable queries serving as a shape prior, which is a set of tokens that implicitly represent objects in a cer" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14062" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "tain category. Furthermore, we transform the traditional deformation-and-matching paradigm to the feature space using attention. Specifically, the queries are deformed by a process where we dynamically use the attention mechanism to select object features and incorporate them into queries. This step transforms the queries into a representation of a certain target object. Next, we establish the correspondences between deformed queries and object features. Finally, the poses and sizes are regressed using the correspondences. Thanks to learnable queries and direct output results, the queries are trained directly alongside the entire network. This method achieves state-of-the-art performance compared to other existing methods and holds promise for applications in robotics and augmented reality." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 240, + 287, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 240, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 47, + 240, + 287, + 289 + ], + "type": "text", + "content": "Acknowledgement This work was supported by the Key Research Project of Zhejiang Lab (No. G2021NB0AL03) and Modern Agriculture Major-core Technology Innovation Project of Jiangsu Province (No. cx(22)2031)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 300, + 107, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 300, + 107, + 312 + ], + "spans": [ + { + "bbox": [ + 48, + 300, + 107, + 312 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 320, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 53, + 320, + 287, + 376 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 320, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 53, + 320, + 287, + 376 + ], + "type": "text", + "content": "[1] Tuo Cao, Fei Luo, Yanping Fu, Wenxiao Zhang, Shengjie Zheng, and Chunxia Xiao. 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IEEE Transactions on Image Processing, 31:6907-6921, 2022." + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "14064" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/R-Pred_ Two-Stage Motion Prediction Via Tube-Query Attention-Based Trajectory Refinement/cbd955af-2686-4f7c-843a-a3576e04bc6e_content_list.json b/2023/R-Pred_ Two-Stage Motion Prediction Via Tube-Query Attention-Based Trajectory Refinement/cbd955af-2686-4f7c-843a-a3576e04bc6e_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..6a8bb85575832e011384741aa801061c88945ace --- /dev/null +++ b/2023/R-Pred_ Two-Stage Motion Prediction Via Tube-Query Attention-Based Trajectory Refinement/cbd955af-2686-4f7c-843a-a3576e04bc6e_content_list.json @@ -0,0 +1,1627 @@ +[ + { + "type": "text", + "text": "R-Pred: Two-Stage Motion Prediction Via Tube-Query Attention-Based Trajectory Refinement", + "text_level": 1, + "bbox": [ + 158, + 122, + 841, + 165 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sehwan Choi $^{1}$ Jungho Kim $^{1}$ Junyong Yun $^{1}$ Jun Won Choi $^{1,2*}$ $^{1}$ Hanyang University and $^{2}$ Qualcomm", + "bbox": [ + 218, + 189, + 784, + 224 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1{sehwanchoi, junghokim, jyyun}@spa.hanyang.ac.kr 1,2 junwchoi@hanyang.ac.kr", + "bbox": [ + 173, + 233, + 823, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 263, + 281, + 336, + 296 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Predicting the future motion of dynamic agents is of paramount importance to ensuring safety and assessing risks in motion planning for autonomous robots. In this study, we propose a two-stage motion prediction method, called R-Pred, designed to effectively utilize both scene and interaction context using a cascade of the initial trajectory proposal and trajectory refinement networks. The initial trajectory proposal network produces $M$ trajectory proposals corresponding to the $M$ modes of the future trajectory distribution. The trajectory refinement network enhances each of the $M$ proposals using 1) tube-query scene attention (TQSA) and 2) proposal-level interaction attention (PIA) mechanisms. TQSA uses tube-queries to aggregate local scene context features pooled from proximity around trajectory proposals of interest. PIA further enhances the trajectory proposals by modeling inter-agent interactions using a group of trajectory proposals selected by their distances from neighboring agents. Our experiments conducted on Argoverse and nuScenes datasets demonstrate that the proposed refinement network provides significant performance improvements compared to the single-stage baseline and that R-Pred achieves state-of-the-art performance in some categories of the benchmarks.", + "bbox": [ + 112, + 311, + 486, + 638 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 114, + 669, + 238, + 684 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In autonomous vehicles and robotics applications, dynamic objects move in complex environments while avoiding collisions with other agents. Each dynamic agent plans its motion by predicting the future motion and behavior of other agents around it. Motion prediction refers to the task of predicting the future trajectory of dynamic agents based on their historical trajectories and information on the surrounding environment. The task of predicting motion is challenging because the trajectory of an agent is affected", + "bbox": [ + 112, + 694, + 486, + 823 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b4828ccbee500981864552b324cc20ecc63e308a08c5f7b7dd7b0052fd4ebb48.jpg", + "image_caption": [ + "Figure 1. Key concept of R-Pred. R-Pred performs two stages of trajectory prediction. ITPNet produces $M$ trajectory proposals with the corresponding proposal features and TRNet refines each trajectory proposal using separate networks. ITPNet uses a scene context acquired from a relatively large area, whereas TRNet uses a local scene context that exists in a tube-shaped area. TRNet also refines the trajectory proposal using an inter-agent interaction context represented at a proposal level." + ], + "image_footnote": [], + "bbox": [ + 521, + 280, + 874, + 505 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "by a variety of contextual factors, which must be taken into account when modeling motion. In the context of autonomous vehicles, examples of such factors include permissible roads, lanes, traffic signals, blinker states, interactions with other agents, and so forth. The difficulty of predicting future motion also arises from the fact that the distribution of future trajectories tends to be multi-modal. In a given scene, a target agent can choose one of several distinct maneuvers such as changing lanes, turning left, turning right, or continuing straight ahead. Accordingly, prediction models should be able to generate one or more plausible future trajectories with probabilities.", + "bbox": [ + 509, + 646, + 883, + 816 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, deep neural networks have been developed as a new paradigm in trajectory prediction, and have achieved", + "bbox": [ + 511, + 819, + 883, + 848 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 138, + 45, + 207, + 80 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 259, + 42, + 781, + 84 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author: Jun Won Choi.", + "bbox": [ + 132, + 834, + 328, + 847 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "8525", + "bbox": [ + 483, + 882, + 513, + 893 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "considerable improvements in performance compared to traditional prediction models through data-driven modeling of trajectory data. Sequence modeling networks such as long short term memory (LSTM) [23] or gated recurrent unit (GRU) [6] architectures have been shown to be effective in representing sequential trajectory data [25, 26]. Trajectory prediction task has been successfully performed using encoder-decoder architectures [35, 53, 29, 30, 16, 19, 45, 55, 43, 32, 26, 15, 17, 10, 8, 20, 24, 40, 28, 36]. Recently, the accuracy of trajectory prediction has been rapidly improved by utilizing various sources of contextual information available for prediction. Numerous methods have jointly modeled the trajectories of multiple neighboring agents to account for their interactions, including socialLSTM [1], soft hardwired attention [12], social GAN [20], MATLAB [54], Trajectron [24, 40], DESIRE [28], DATF [36], and SoPhie [39]. Static scene information around the target agent was also used to generate more physically plausible trajectories. A scene was represented by a two-dimensional raster image that describes the scene [11, 4, 7, 32, 37, 52]. A vector representation of the scene was also proposed for scene encoding [13, 29, 53, 19, 55, 26, 16, 34, 30, 10, 45, 47, 48]. Recently, Transformer models [44] have been used to model the scene and interaction context using the attention mechanism [30, 34, 55, 33, 45, 50].", + "bbox": [ + 114, + 85, + 485, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a new two-stage motion prediction framework, referred to as $R$ -Pred. As shown in Fig. 1, the proposed R-Pred architecture consists of two-stage networks: an initial trajectory proposal network (ITPNet) and a trajectory refinement network (TRNet). The ITPNet produces $M$ initial trajectory proposals corresponding to the $M$ modes of the trajectory distribution for a target agent. TRNet then refines each trajectory proposal using the contexts customized for each proposal. Using the initial trajectory proposals as a priori information, TRNet can utilize the scene and interaction contexts in more selective and effective ways.", + "bbox": [ + 114, + 445, + 486, + 617 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "TRNet employs the following two refinement submodules. First, we present tube-query scene attention (TQSA) to utilize the local scene context effectively. Unlike ITPNet, which uses a global scene context, TQSA extracts local scene context features within a tube-shaped region around each trajectory proposal. (See Fig. 1 for illustration). Then, the extracted scene context features are used to enhance the corresponding trajectory proposal through cross-attention mechanism. TQSA allows the important scene context to be used to improve each $M$ trajectory proposal. Second, we propose the proposal-level interaction attention (PIA) mechanism. PIA models inter-agent interactions using the trajectory proposals produced for multiple neighboring agents by ITPNet. PIA selects a group of trajectory proposals that have the highest influence on the trajectory proposal of interest using the distance-wise proposal", + "bbox": [ + 114, + 619, + 486, + 849 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "grouping strategy. The proposal group is used to refine the trajectory of interest through cross-attention.", + "bbox": [ + 511, + 85, + 880, + 113 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In fact, our per-proposal refinement strategy is motivated by two-stage object detectors (e.g., Faster RCNN [38]), where the initial object proposals are first obtained from the entire convolutional neural network (CNN) features and then local features in the region of interest (RoI) are pooled to refine each object proposal [18, 38, 21]. Similarly, RPred generates the context features based on the initial trajectory proposals produced by ITPNet and uses them to refine each proposal.", + "bbox": [ + 511, + 116, + 883, + 243 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "By combining these two sub-modules, R-Pred can generate refined trajectory outputs. We evaluated the proposed approach using the widely adopted Argoverse [5] and nuScenes [3] datasets. The results demonstrate that the proposed refinement network significantly improved the accuracy of ITPNet baseline. The results also show that R-Pred achieves the state-of-the-art performance in some categories of official Argoverse and nuScenes leaderboards.", + "bbox": [ + 511, + 246, + 883, + 359 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions are summarized as follows:", + "bbox": [ + 531, + 362, + 851, + 376 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel trajectory refinement network that refines each of $M$ trajectory proposals using the local scene context and the proposal-level inter-agent interactions. The per-proposal refinement strategy effectively improves the trajectory predictions obtained by the first-stage network.", + "- We introduce the concept of global-to-local hierarchical attention to effectively utilize the scene context. Our refinement network uses a tube-query to gather the scene context from the local region around the proposal trajectory. The proposed global-to-local hierarchical attention mechanism is contrasted with factorized attention [34, 33], which iterates attention over different sources of context.", + "- We use trajectory proposals of neighboring agents to model interactions between agents. Using the trajectory proposal features reflecting particular intentions of other agents, PIA can better model inter-agent interactions than the conventional interaction modeling that uses the past trajectory features only.", + "- R-Pred can use any off-the-shelf single-stage trajectory prediction network as the initial trajectory proposal network. That is, the proposed refinement framework can also be readily applied to any trajectory prediction network available.", + "- The source code used in this work will be released publicly." + ], + "bbox": [ + 531, + 392, + 883, + 847 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "8526", + "bbox": [ + 483, + 882, + 514, + 893 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 114, + 84, + 254, + 98 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Context-Aware Trajectory Prediction", + "text_level": 1, + "bbox": [ + 114, + 108, + 416, + 123 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Numerous methods have improved the performance of trajectory prediction by leveraging the contextual information available for prediction. For example, information on the static scene around a target agent has been utilized as scene context. Raster-based scene encoding uses 2D raster images to summarize scene information and extract semantic features using convolutional neural networks [32, 4, 37, 14, 40, 9, 46]. The advantage of this approach is that different types of scene components can be easily accommodated in a raster image. However, the performance of these methods is limited owing to quantization errors and a lack of receptive fields in the encoding architectures. Vector-based scene encoding represents scene components using vectors, and encodes their relationships using graph structures or attention models [29, 10, 40, 20, 24, 27, 13]. VectorNet [13] introduced a hierarchical graph neural network that exploited the spatial locality of road components by vectorized representation. Similarly, LaneGCN [29] was proposed as an effective graph convolutional network to represent complicated topology and long-range dependency. Trajectory++ [40] employed a directed spatiotemporal graph to represent scene context vectors while incorporating agent dynamics and heterogeneous data.", + "bbox": [ + 117, + 130, + 485, + 457 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The performance of trajectory prediction has also been improved by taking into account interactions with surrounding dynamic agents and static environment information. Social pooling methods pooled the trajectory features of other agents for interaction modeling [1, 28, 20, 39, 8]. Recently, attention mechanisms have been proposed to exploit the meaningful relationships between dynamic agents and lane segments [26, 41, 55, 10, 19, 51, 29, 13, 16, 32, 45, 29].", + "bbox": [ + 112, + 458, + 483, + 573 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Transformer-based Trajectory Prediction", + "text_level": 1, + "bbox": [ + 114, + 583, + 447, + 598 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Transformer architectures offer an effective method for training attention mechanisms capable of capturing long-range dependencies within sequence data. Recently, Transformers have been adopted for trajectory prediction to model spatio-temporal context as well as interactions between agents [50, 45, 55, 30, 33, 34]. mmTransformer [30] employed an efficient stacked Transformer that applied cross-attention on multi-agent and scene contexts one by one. HiVT [55] summarized the spatio-temporal features of agents using translation-invariant agent-centric local scene structure. In SceneTransformer [34], a simple varying form of self-attention was exploited to integrate various features, generating scene-level consistent predictions for all agents jointly. Along these lines, Wayformer [33] was proposed as a general multi-dimensional attention architecture designed to jointly encode multiple agent trajectories and map data in time, space, and agent dimensions.", + "bbox": [ + 112, + 606, + 485, + 848 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Problem Setup", + "text_level": 1, + "bbox": [ + 513, + 84, + 653, + 99 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Suppose that the historical trajectory states of $N$ dynamic agents are obtained from the multi-object tracker, where $N$ can vary depending on the scenario. The agent requiring prediction of its future trajectory is denoted as the target agent, while the other agents are termed neighbor agents. The past trajectory states over $T$ time steps for the $i$ -th agent are denoted as $\\mathbf{x}_i = [x_i(t - T + 1), x_i(t - T + 2), \\dots, x_i(t)]$ , where $t$ denotes the current time step and $x_i(t - s)$ is the state of the $i$ -th agent at the time step $(t - s)$ . The trajectory state is of the form $(x, y, \\varepsilon)$ consisting of the $(x, y)$ position and the agent's semantic property $\\varepsilon$ . The $(x, y)$ coordinates are represented in the agent-centric reference frame, where the current position of a target agent is the origin and its heading angle is aligned with the positive x-axis. Similarly, the future trajectory states over $F$ time steps for the $i$ -th agent are given by $\\mathbf{y}_i = [y_i(t + 1), y_i(t + 2), \\dots, y_i(t + F)]$ . We assume that the vector representation of a scene is available along with the trajectory data. For instance, a lane is represented by a set of points on its centerline, where the $(x, y)$ coordinates of each point are expressed in an agent-centric frame. We accommodate different types of scene components by appending an attribute index $\\epsilon_l$ to the $(x, y)$ coordinate as $(x, y, \\epsilon_l)$ . The set of scene components around the target agent at the time $t$ is expressed as the vector $\\xi = [\\xi_1, \\dots, \\xi_L]$ , where the dimension $L$ varies depending on the scene complexity and the region of interest on the map.", + "bbox": [ + 511, + 108, + 883, + 505 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Without loss of generality, let $\\mathbf{x}_1$ be the trajectory of the target agent and $\\mathbf{x}_2,\\dots,\\mathbf{x}_N$ be the trajectories of neighboring agents. Finally, the goal of the motion prediction task is to estimate the future trajectory of the target agent $\\mathbf{y}_1$ given the past trajectories of $N$ agents $\\mathbf{x}_1,\\dots,\\mathbf{x}_N$ and the scene information $\\xi$ .", + "bbox": [ + 511, + 507, + 883, + 592 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Proposed Trajectory Prediction Network", + "text_level": 1, + "bbox": [ + 511, + 606, + 857, + 622 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we present the details of the proposed motion prediction method, R-Pred.", + "bbox": [ + 511, + 630, + 880, + 659 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Overall Framework", + "text_level": 1, + "bbox": [ + 511, + 667, + 691, + 683 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An overview of the proposed R-Pred framework is presented in Fig. 2. Our proposed architecture produces $M$ multi-modal trajectory predictions for a target agent over two stages. First, ITPNet produces $M$ trajectory proposals for all $N$ agents present in the scene. Along with the trajectory proposals, ITPNet returns $M$ intermediate features used to produce the trajectory proposals. These features are called proposal features. ITPNet follows traditional trajectory prediction methods for scene and interaction encoding; that is, it utilizes the global scene context features extracted from a fixed region around the current position of the agent.", + "bbox": [ + 511, + 691, + 883, + 848 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "8527", + "bbox": [ + 483, + 882, + 513, + 893 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2785089d938485a030f3e888f6d36ff24ca53764386752f92288f13a43b5a711.jpg", + "image_caption": [ + "Figure 2. Overall structure of R-Pred. Given the past trajectories of the dynamic agents and the global scene information, ITPNet generates $M$ trajectory proposals for each agent. TRNet refines each of the $M$ trajectory proposals of the target agent through TQSA and PIA. TQSA utilizes local scene context features obtained by tubular region pooling. PIA captures interaction context using the proposal group found by the distance-wise proposal grouping. Finally, the prediction header produces the refined future trajectories based on the joint trajectory features obtained by concatenation of the attention values from TQSA and PIA." + ], + "image_footnote": [], + "bbox": [ + 169, + 84, + 823, + 356 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In addition, the ITPNet exploits the interaction context derived from the past trajectories of $N$ agents. Second, TRNet refines each of the $M$ trajectory proposals of the target agent based on the prior trajectory information generated by the ITPNet. TRNet employs TQSA and PIA to generate the context features customized for each proposal. TQSA extracts the local scene context features cropped from a tube-shaped region around the target trajectory proposal. PIA generates the inter-agent interaction context features using a group of selected proposal trajectories of $N$ agents. The context features generated by TQSA and PIA enhance the proposal features through cross-attention. The final joint trajectory features are obtained by concatenating two attention values from TQSA and PIA. Finally, the prediction head produces $M$ future trajectory predictions and their confidence scores for each target agent.", + "bbox": [ + 112, + 454, + 483, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Initial Trajectory Proposal Network", + "text_level": 1, + "bbox": [ + 114, + 696, + 408, + 710 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given the past trajectories $\\mathbf{x}_1,\\dots,\\mathbf{x}_N$ of the $N$ agents present in the scene and the scene information $\\xi$ , ITP-Net produces $M$ trajectory proposals and their confidence scores for each agent. $M$ intermediate features, known as proposal features, are also extracted for the subsequent refinement phase. The trajectory proposals, their confidence scores, and the proposal features for the $i$ -th agent are denoted as $\\hat{\\mathbf{y}}_i = [\\hat{\\mathbf{y}}_1^1,\\dots,\\hat{\\mathbf{y}}_i^M]$ , $\\hat{\\mathbf{c}}_i = [\\hat{\\mathbf{c}}_i^1,\\dots,\\hat{\\mathbf{c}}_i^M]$ , and $\\mathbf{f}_i = [\\mathbf{f}_i^1,\\dots,\\mathbf{f}_i^M]$ , respectively.", + "bbox": [ + 112, + 719, + 483, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1 Tubular Region Pooling", + "text_level": 1, + "bbox": [ + 514, + 454, + 750, + 468 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Input: Trajectory proposal $\\hat{\\mathbf{y}}_1^m$ , scene context vectors $\\xi$ , scene embedding features $\\Psi$ , and thresholding radius $\\tau$ .", + "bbox": [ + 514, + 470, + 880, + 513 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Output: Local scene context features $\\Psi_1^m$ .", + "bbox": [ + 514, + 513, + 782, + 527 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: $\\Psi_1^m = set()$", + "2: for $f \\gets t + 1$ to $t + F$ do", + "3: for each $\\xi_l \\in \\xi$ do", + "4: $dist = \\| \\hat{y}_1^m (f) - \\xi_l\\| _2$", + "5: if dist $< \\tau$ then", + "5: $\\Psi_1^m$ .add $(\\psi_l)$", + "6:", + "7: return $\\Psi_1^m$" + ], + "bbox": [ + 524, + 529, + 712, + 642 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Trajectory Refinement Network", + "text_level": 1, + "bbox": [ + 513, + 676, + 777, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "TRNet refines each of trajectory proposals $\\hat{\\mathbf{y}}_1$ of the target agent through TQSA and PIA.", + "bbox": [ + 511, + 702, + 880, + 731 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Tube-Query Scene Attention. We construct the set of scene embedding features $\\Psi = \\{\\psi_1,\\dots,\\psi_L\\}$ by encoding each element of $\\xi$ via a linear projection, i.e., $\\psi_l =$ linear\\_proj $(\\xi_{l})$ .TQSA pools the scene embedding features in a tubular region around the trajectory proposal on the map from $\\Psi$ .We denote the set of scene embedding features prepared for the $m$ th trajectory proposal $\\hat{\\mathbf{y}}_1^m$ of the target agent as $\\Psi_1^m$ . Tubular region pooling is efficiently per", + "bbox": [ + 511, + 734, + 880, + 849 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "8528", + "bbox": [ + 483, + 882, + 513, + 893 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 2 Distance-Wise Proposal Grouping", + "text_level": 1, + "bbox": [ + 116, + 85, + 413, + 99 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Input: Trajectory proposals $\\hat{\\mathbf{y}}_1,\\dots ,\\hat{\\mathbf{y}}_N$ proposal confidence scores $\\hat{\\mathbf{c}}_1,\\dots ,\\hat{\\mathbf{c}}_N$ proposal features $\\mathbf{f}_1,\\dots ,\\mathbf{f}_N$ distance threshold $\\mathcal{D}$ and confidence threshold $\\mathcal{T}$", + "bbox": [ + 116, + 101, + 483, + 143 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Output: Proposal group set $\\mathcal{G}(\\hat{\\mathbf{y}}_1^m)$", + "bbox": [ + 114, + 143, + 344, + 159 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: for $i \\gets 2$ to $N$ do", + "2: for $m^{\\prime}\\gets 1$ to $M$ do", + "3: if $\\hat{\\mathbf{c}}_j^{m'} > \\mathcal{T}$ then", + "4: $dist = \\min_{f\\in [t + 1,t + F]}\\| \\hat{y}_1^m (f) - \\hat{y}_i^{m'}(f)\\| _2$", + "5: if $dist < \\mathcal{D}$ then", + "6: $\\mathcal{G}(\\hat{\\mathbf{y}}_1^m)$ .append $(\\mathbf{f}_i^{m'})$", + "7:", + "8: return $\\mathcal{G}(\\hat{\\mathbf{y}}_1^m)$" + ], + "bbox": [ + 125, + 160, + 434, + 280 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "formed to aggregate scene embedding features within the search radius $\\tau$ around each waypoint of the trajectory proposal $\\hat{\\mathbf{y}}_1^m$ . Note that a collection of search disks centered at all waypoints on the trajectory forms an approximately tubular polygon. See Algorithm 1 for further details.", + "bbox": [ + 112, + 308, + 483, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "TQSA decodes the proposal features $\\mathbf{f}_1^m$ (associated with $\\hat{\\mathbf{y}}_1^m$ ) of the target agent by performing cross-attention on the local scene context $\\Psi_1^m$ . Specifically, we use the proposal features $\\mathbf{f}_1^m$ as the query and the local scene context features $\\Psi_1^m$ as the key and value, i.e.,", + "bbox": [ + 114, + 378, + 483, + 450 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nQ = \\mathbf {f} _ {1} ^ {m} W ^ {Q _ {T Q S A}} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 459, + 483, + 476 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nK = \\Psi_ {1} ^ {m} W ^ {K _ {T Q S A}} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 479, + 483, + 496 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nV = \\Psi_ {1} ^ {m} W ^ {V _ {T Q S A}} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 498, + 483, + 515 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} _ {1} ^ {m} = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {\\top}}{\\sqrt {d _ {k}}}\\right) V, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 518, + 483, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $W^{Q_{TQSA}}$ , $W^{K_{TQSA}}$ , and $W^{V_{TQSA}}$ are learnable weight matrices and $d_k$ is the dimension of the embedding vectors. We combine the attention value $\\mathcal{A}_1^m$ and the proposal features $\\mathbf{f}_1^m$ using the gating function introduced in [55]", + "bbox": [ + 112, + 559, + 483, + 632 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\lambda = \\sigma \\left(\\mathrm {f} _ {1} ^ {m} W ^ {\\text {i n p u t}} + \\mathcal {A} _ {1} ^ {m} W ^ {\\text {h i d d e n}}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 640, + 483, + 657 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {t} _ {1} ^ {m} = \\lambda \\odot \\mathbf {f} _ {1} ^ {m} W ^ {\\text {g a t e}} + (1 - \\lambda) \\odot \\mathcal {A} _ {1} ^ {m} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 660, + 483, + 676 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {t} _ {1} ^ {m} = \\mathbf {f} _ {1} ^ {m} + \\phi \\left(\\mathbf {t} _ {1} ^ {m}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 679, + 483, + 695 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $W^{input}$ , $W^{hidden}$ , and $W^{gate}$ are learnable matrices, $\\odot$ indicates element-wise product, $\\sigma$ indicates the sigmoid function and $\\phi(\\cdot)$ denotes a multi-layer perceptron (MLP). We add layer normalization [2], Dropout [42], and residual connection [22] in the middle of the attention process.", + "bbox": [ + 114, + 704, + 483, + 775 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that the aforementioned local scene attention process to produce the output of TQSA $\\mathbf{t}_1^m$ is performed for each trajectory proposal (for each $m$ value) in parallel.", + "bbox": [ + 112, + 777, + 483, + 819 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proposal-level Interaction Attention. PIA uses a distance-wise proposal grouping algorithm to find a group", + "bbox": [ + 112, + 819, + 483, + 849 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "of the trajectory proposals for the nearby agents to model their inter-agent interactions. First, among $MN$ trajectory proposals from $N$ agents, those with a confidence score below the threshold $\\mathcal{T}$ are discarded because they are unlikely to occur. Subsequently, for a given $m$ -th trajectory proposal $\\hat{\\mathbf{y}}_1^m$ of the target agent, the algorithm selects the trajectory proposals of the nearby agents, whose distance from $\\hat{\\mathbf{y}}_1^m$ is closer than the distance threshold $\\mathcal{D}$ . These are considered the most influential trajectory proposals to use for interaction modeling. A distance between two trajectories $\\mathbf{y}_1^\\star$ and $\\mathbf{y}_2^\\star$ is defined by", + "bbox": [ + 511, + 85, + 882, + 242 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {d i s t} \\left(\\mathbf {y} _ {1} ^ {\\star}, \\mathbf {y} _ {2} ^ {\\star}\\right) = \\min _ {f \\in [ t + 1, t + F ]} \\| \\mathbf {y} _ {1} ^ {\\star} (f) - \\mathbf {y} _ {2} ^ {\\star} (f) \\| _ {2}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 248, + 880, + 271 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the selected trajectory proposals, the algorithm groups the corresponding proposal features into the proposal feature group $\\mathcal{G}(\\hat{\\mathbf{y}}_1^m)$ . The distance-wise proposal grouping algorithm is summarized in Algorithm 2.", + "bbox": [ + 511, + 276, + 880, + 333 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proposal feature group is used to decode the proposal features $\\mathbf{f}_1^m$ through cross-attention. Using $\\mathbf{f}_1^m$ as query and $\\mathcal{G}(\\mathbf{y}_1^m)$ as key and value, the cross-attention module produces the attention value $\\mathbf{p}_1^m$ similarly to Eq. (1) - (7).", + "bbox": [ + 511, + 333, + 880, + 402 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Multi-modal Prediction Head. TRNet constructs the final joint trajectory feature $\\mathbf{j}_1^m$ by concatenating the attention output $\\mathbf{t}_1^m$ from TQSA and the attention output $\\mathbf{p}_1^m$ from PIA. The prediction head is then applied to $\\mathbf{j}_1^m$ to produce the refined trajectories and the confidence scores. The prediction head consists of the regression branch and a classification branch. First, by modeling the trajectory points as multi-variate random vectors with independent Laplace distribution, the regression branch applies an MLP to $\\mathbf{j}_1^m$ to predict the mean and covariance of $\\mathbf{y}_1$ . The predicted mean is denoted as $\\tilde{\\mathbf{y}}_1^m = [\\tilde{y}_1^m (t + 1),\\dots,\\tilde{y}_1^m (t + F)]$ and the predicted variance is denoted as $\\mathbf{b}_1^m = [\\tilde{b}_1^m (t + 1),\\dots,\\tilde{b}_1^m (t + F)]$ . The regression branch is applied separately for each mode $m$ . Next, the classification branch applies another MLP to the concatenation of $\\mathbf{j}_1^1,\\dots,\\mathbf{j}_1^M$ to produce the confidence scores $\\check{\\mathbf{c}}_1^1,\\dots,\\check{\\mathbf{c}}_1^M$ for all modes.", + "bbox": [ + 511, + 404, + 880, + 632 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Training Details", + "text_level": 1, + "bbox": [ + 513, + 638, + 663, + 652 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The total loss function $L_{total}$ used to train the entire network is given by", + "bbox": [ + 511, + 660, + 880, + 689 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {t o t a l} = \\alpha L _ {r e g. p r o} + \\beta L _ {c l s. p r o} + \\gamma L _ {r e g. r e f} + \\delta L _ {c l s. r e f},\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 695, + 875, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $L_{reg-pro}$ and $L_{reg-ref}$ are the regression loss functions for ITPNet, and TRNet and $L_{cls-pro}$ and $L_{cls-ref}$ are the classification loss functions for ITPNet, and TRNet. We used $\\alpha = \\beta = \\gamma = \\delta = 1$ in our setup. The negative log-likelihood function for the Laplace distribution is used for $L_{reg-ref}$ as follows,", + "bbox": [ + 511, + 715, + 880, + 801 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {r e g - r e f} = - \\frac {1}{N F} \\sum_ {n = 1} ^ {N} \\sum_ {f = t + 1} ^ {t + F} \\log \\mathbb {P} \\left(y _ {n} (f) \\mid \\check {y} _ {n} ^ {m ^ {*}} (f), \\check {\\mathbf {b}} _ {n} ^ {m ^ {*}} (f)\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 806, + 890, + 849 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "8529", + "bbox": [ + 483, + 882, + 513, + 893 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/e57630678c6480e95fb95f513eea89dc853ac63064728a238157d413b55a069b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodminADE1minFDE1minADE6minFDE6brierFDE6MR6%
LaneRCNN[51]1.693.690.901.452.1512.3
LaPred[26]1.934.330.911.502.1318.0
TNT[53]2.174.960.911.452.1416.6
PRIME[41]1.913.821.221.562.1011.5
HOME[14]1.723.730.921.36-11.3
LaneGCN[29]1.703.760.871.362.0516.2
mmTransformer[30]1.774.000.841.342.0315.4
DenseTNT[19]1.683.630.881.281.9812.6
THOMAS[16]1.673.590.941.441.9710.3
SceneTransformer[34]1.813.620.801.231.8912.5
LTP[45]1.623.550.831.301.8614.7
HOME+GOHOME[15]1.703.680.891.291.868.5
TPCN[49]1.663.690.871.38-15.8
HiVT[55]1.603.520.771.171.8412.7
MultiPath++[43]1.623.610.791.211.7913.2
Wayformer[33]1.643.670.771.161.7411.9
ITPNet baseline1.623.570.791.211.8613.1
R-Pred1.583.470.761.121.7711.6
", + "bbox": [ + 181, + 84, + 816, + 367 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbb{P}(\\cdot |\\cdot)$ is the probability density function of Laplace distribution. $L_{reg - pro}$ is defined similarly. When evaluating the loss function during training, we adopt a winner-takes-all strategy [7] in which the mode $m^{*}$ of the trajectory output that yields the smallest average displacement error is used, i.e., $m^{*} = \\underset {m\\in [1,M]}{\\mathrm{argmin}}\\sum_{f = t + 1}^{t + F}\\| y_n(f) - \\tilde{y}_n^m (f)\\| _2.$", + "bbox": [ + 114, + 444, + 483, + 539 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We used the cross entropy loss for the classification losses $L_{cls-pro}$ and $L_{cls-ref}$ . We trained the entire network end-to-end with random initialization.", + "bbox": [ + 114, + 539, + 483, + 580 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/75d28369d9cbdb7b560e46d12d777aabc9f67f7363bbc86f73a5d5985ce1cfa2.jpg", + "table_caption": [ + "Table 1. Performance comparison on Argoverse test set in the official leaderboard. The best performed metrics are shown in bold. The \"-\" symbol means the corresponding metric is unknown, either because the authors have not disclosed it or it was not specified in the leaderboard. Our model achieves the state-of-the-art performance in terms of the $\\text{minADE}_1$ , $\\text{minFDE}_1$ , $\\text{minADE}_6$ and $\\text{minFDE}_6$ metrics." + ], + "table_footnote": [], + "table_body": "
Method\\( mADE_5 \\)\\( mFDE_5 \\)\\( mADE_{10} \\)\\( mFDE_{10} \\)
MTP[7]2.224.831.743.54
CoverNet[37]1.96-1.48-
Trajectory++[40]1.88-1.51-
MHA-JAM[32]1.813.721.242.21
MultiPath[4]1.783.621.552.93
CXX[31]1.63-1.29-
LaPred[26]1.533.371.122.39
P2T[9]1.45-1.16-
THOMAS[16]1.33-1.04-
PGP[10]1.272.470.941.55
ITPNet baseline1.292.580.971.60
R-Pred1.192.280.941.50
", + "bbox": [ + 117, + 599, + 485, + 767 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Performance comparison on nuScenes validation set in the official leaderboard. The \"-\" symbol means the corresponding metric unknown. Our model achieves state-of-the-art performance on all metrics.", + "bbox": [ + 112, + 776, + 485, + 829 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 513, + 443, + 637, + 459 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we describe the experimental setup used to evaluate the performance of the proposed R-Pred, and present both quantitative and qualitative analyses of the behavior of the model.", + "bbox": [ + 511, + 470, + 883, + 526 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. Both Argoverse [5] and nuScenes [3] datasets provide dynamic agent trajectories and HD-map in real-world driving scenarios. The Argoverse dataset was collected from two US cities, including Miami and Pittsburgh. Each sample contains 5 seconds trajectories of tracked vehicles sampled at $10\\mathrm{Hz}$ . Argoverse dataset provides HD-map with detailed lane information. The prediction task is to predict future trajectories for 3 seconds given past trajectories of 2 seconds. The dataset contains 205,942 training, 39,272 validation, and 78,143 test samples.", + "bbox": [ + 511, + 529, + 883, + 672 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The nuScenes dataset was collected in Boston and Singapore. The collected trajectories are 6 seconds long and are sampled at $2\\mathrm{Hz}$ . The prediction task is defined as that of predicting future trajectories for 6 seconds given past trajectories of 2 seconds. HD-map is also provided along with the trajectory data. The dataset is split into 32, 186 training, 8,560 validation, and 9,041 test samples.", + "bbox": [ + 511, + 674, + 880, + 773 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. For the performance evaluation, we adopt widely used performance metrics including average displacement error (ADE), final displacement error (FDE), and miss rate (MR). ADE refers to the mean square error compared to the ground truth over the entire time steps, and FDE is", + "bbox": [ + 511, + 776, + 883, + 848 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "8530", + "bbox": [ + 483, + 882, + 513, + 893 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/397dbd67b850d1794c6a5b24d2d378251ec0621a35a4dbd005305e2dd846cb24.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 181, + 88, + 334, + 209 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d3db5eb23a31014b0d5feee0ebc2fcceee3ac003e79d99139615b7506c951530.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 338, + 89, + 491, + 209 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0e0242d1f23d0e23b28c59de90f6ef36c2406efe8595881b659421bb94e00da1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 495, + 89, + 648, + 209 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/53364e555fd46ce8f6755ed56e1afb260f6811e1fec9d8c7fb0e3d5129af6b85.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 651, + 90, + 816, + 209 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7daae0af989f1544d25790833dfb0ae5ad9899bb632e4f55e23d0ae389c5de66.jpg", + "image_caption": [ + "Figure 3. Qualitative results of R-Pred on Argoverse validation set. Yellow, green, blue, and red lines represent the history, ground truth, the initial trajectory proposal with the highest score, and the final (refined) trajectory, respectively. The sky blue region denotes tubular regions used for TQSA. These figures present different vehicle motion scenarios such as continuing straight ahead, turning left, slowing down, changing lanes, etc." + ], + "image_footnote": [], + "bbox": [ + 181, + 212, + 334, + 330 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ab605dc8d31eb3288a15c2c9d5748a1bbb6eaf89109e012a195e717bacef7255.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 338, + 212, + 491, + 330 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5b56582c0e867255c05a66d5d92cda37b929f7a38b7aeffca768b7d3b2b2aadf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 495, + 212, + 648, + 330 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/272bd5f915a53bd85fc7ae021652bef873c919c02b777b99d20e6d8bdcdcfcb2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 651, + 212, + 815, + 330 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate the prediction accuracy with $M > 1$ trajectory predictions using minADEM and minFDEM, which are the minimum ADE and FDE over $M$ predicted trajectories, respectively. $MR_{M}$ measures the ratio within 2 meters of the endpoint of the best-predicted trajectory and ground truth. We also use brier minimum FDE (brierFDEM), which measures the value of minFDEM + (1 - p)², where $p$ is corresponding trajectory probability. This imposes a penalty when the probability of the best trajectory is low. Implementation Details. We set the threshold $\\mathcal{D}$ and $\\mathcal{T}$ of PIA to 0.1 and 10 meters and $\\tau$ of TQSA to 20 meters. The embedding size of all features is set to 128 for comparative performance analysis. We used existing prediction architectures for the ITPNet. We chose the structure of [55] on Argoverse and that of [10] on nuScenes. These models achieved excellent performance on both benchmarks. They are considered ITPNet baselines and are used to measure the performance gain achieved by our refinement network. We trained the proposed model on TiTAN RTX GPU for 64 epochs with 32 batch sizes. The data are batched randomly. For all experiments, we trained the model using AdamW optimizer with an initial learning rate of 5e-4. We used cosine annealing to decay the learning rate and applied dropout with a 0.1 ratio. Data augmentation was not used.", + "bbox": [ + 112, + 416, + 485, + 773 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1.Quantitative Results", + "text_level": 1, + "bbox": [ + 114, + 782, + 297, + 797 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1 presents the performance of R-Pred evaluated on Argoverse test set. We compare the performance of R-Pred with that of several top ranked models [51, 53, 41, 29, 14,", + "bbox": [ + 112, + 805, + 485, + 848 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1ab67d4e03f17836a3e8dc4abd54accfe7572f05b245c6da4cfc0e29d01eb5f4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ITPNetPIATQSAminADE6minFDE6MR6%
✓0.6941.05710.63
✓✓0.6770.9929.64
✓✓✓0.6570.9458.69
", + "bbox": [ + 517, + 415, + 883, + 479 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Contributions of the main components evaluated on the Argoverse validation set.", + "bbox": [ + 511, + 488, + 883, + 516 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "30, 19, 16, 34, 45, 15, 49, 43, 33, 55]. R-Pred achieves the best prediction accuracy in terms of the $\\text{minADE}_1$ , $\\text{minFDE}_1$ , $\\text{minADE}_6$ and $\\text{minFDE}_6$ metrics and competitive performance in terms of $\\text{brierFDE}_6$ and $\\text{MR}_6$ . R-Pred sets a new state-of-the-art performance surpassing the current best methods, Wayformer [33] and Multi-Path++ [43]. Compared to the ITPNet baseline, the proposed method offers performance improvements of $3.80\\%$ and $7.43\\%$ in terms of $\\text{minADE}_6$ , and $\\text{minFDE}_6$ , respectively. This indicates that our trajectory refinement strategy can effectively improve the reliability and robustness of the initial prediction using ITPNet.", + "bbox": [ + 511, + 545, + 883, + 717 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2 presents the performance of several motion prediction methods on nuScenes validation set. We compare R-Pred with the top ranked methods [37, 40, 32, 4, 31, 26, 9, 16, 10] on the nuScenes leaderboard. R-Pred achieves significant performance gains compared with other prediction methods. R-Pred exhibits the performance gain of $7.75\\%$ and $11.62\\%$ in $\\min ADE_5$ and $\\min FDE_5$ compared to the ITPNet baseline. These results demonstrate that the proposed two refinement modules have high-quality learning", + "bbox": [ + 511, + 719, + 883, + 849 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "8531", + "bbox": [ + 483, + 882, + 511, + 893 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "capabilities.", + "bbox": [ + 114, + 85, + 192, + 99 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/53cd954d37e19c0a88ca950084f290132e1195075394bc4c6fa3248c68d8e3c6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
τminADE6minFDE6MR6%
50.6590.9578.927
100.6580.9528.840
200.6570.9458.698
300.6570.9468.714
500.6590.9548.878
", + "bbox": [ + 168, + 112, + 426, + 209 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7249afb154c539a7a93f579fbd7ee494bc90234c86a10f617066aa829d11433e.jpg", + "table_caption": [ + "Table 4. Performance versus $\\tau$ parameter of TQSA evaluated on the Argoverse validation set." + ], + "table_footnote": [], + "table_body": "
DminADE6minFDE6MR6%
50.6590.9488.802
100.6570.9458.698
200.6580.9478.730
300.6590.9498.811
400.6590.9508.821
", + "bbox": [ + 168, + 265, + 426, + 362 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2. Ablation Study", + "text_level": 1, + "bbox": [ + 114, + 412, + 259, + 429 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conducted several ablation studies on the Argoverse validation set. We reduced the training time required to conduct the ablation study by decreasing the feature size from 128 to 64 and increasing the batch size from 32 to 64. The trained model was evaluated on the entire validation set.", + "bbox": [ + 114, + 435, + 483, + 505 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Contribution of Each Module. Table 3 shows the contributions of each module to overall performance achieved by R-Pred. We evaluated performance as we added each component one by one. We consider the following three modules of R-Pred: 1) ITPNet baseline, 2) PIA, and 3) TQSA. When the PIA is added to ITPNet baseline, the $\\text{minFDE}_6$ improves by $6.15\\%$ and $MR_6$ improves by $9.31\\%$ . This indicates the effectiveness of inter-agent interaction modeling by PIA. When TQSA is added, it achieves the performance gains of $4.74\\%$ and $9.85\\%$ in $\\text{minFDE}_6$ and $MR_6$ . We observe that proposal refinement using local scene context improves the performance significantly. Finally, the combination of PIA and TQSA has improved the performance of ITPNet baseline by $10.6\\%$ and $18.25\\%$ , in $\\text{minFDE}_6$ and $MR_6$ , respectively.", + "bbox": [ + 114, + 506, + 483, + 719 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Performance Versus $\\tau$ and $\\mathcal{D}$ . We investigated the impact of the parameters $\\tau$ and $\\mathcal{D}$ on the performance. Recall that $\\tau$ and $\\mathcal{D}$ are the distance thresholds used in TQSA and PIA, respectively. Table 4 presents the performance of R-Pred evaluated for several values of $\\tau = \\{5,10,20,30,50\\}$ . R-Pred performs best at $\\tau = 20,30$ , and degrades as $\\tau$ becomes larger or smaller than these values. This is likely due to the fact that when the threshold gets too large, a lot of irrelevant scene context can be used for cross-attrbution.", + "bbox": [ + 114, + 719, + 483, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5 presents the performance of R-Pred for several values of $\\mathcal{D} = \\{5,10,20,30,40\\}$ . R-Pred achieves the best performance with $\\mathcal{D} = 10$ . Note that increasing the threshold $\\mathcal{D}$ above 10 does not improve performance.", + "bbox": [ + 511, + 85, + 880, + 142 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of Per-proposal Scene Context Strategy. One of our key innovations is to use the tube-query for pooling the customized scene context for each proposal. We investigated the benefit of our per-proposal feature pooling method. We compare R-Pred with the baseline that shares the global scene context features for all proposals in the refinement step. Table 6 shows that our strategy offers $1.76\\%$ and $3.24\\%$ performance gains in $minFDE_{6}$ and $MR_{6}$ over the baseline, which confirms the advantage of the proposed per-proposal feature pooling method.", + "bbox": [ + 511, + 142, + 880, + 285 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c98028865f1c32ca58143f34df91ceb7f39356f3437f43b7d744b84c4f1e33f2.jpg", + "table_caption": [ + "Table 5. Performance versus $\\mathcal{D}$ parameter of PIA evaluated on the Argoverse validation set." + ], + "table_footnote": [], + "table_body": "
Per-proposal scene contextShared scene contextminADE6minFDE6MR6%
✓0.6620.9628.981
✓0.6570.9458.69
", + "bbox": [ + 517, + 297, + 879, + 357 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Comparison of per-proposal scene context versus shared scene context evaluated on the Argoverse validation set.", + "bbox": [ + 511, + 364, + 880, + 393 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Qualitative Results", + "text_level": 1, + "bbox": [ + 511, + 417, + 684, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fig. 3 shows a visualization of the actual predicted trajectory samples generated by R-Pred using Argoverse validation set. We visualize the final trajectory with the best score produced by R-Pred (red line) and the corresponding trajectory proposal from ITPNet (blue line). We also include the ground truth trajectory (green line). We added the tubular area used for TQSA to the figure (sky blue region). We observe that our refinement network reduced the prediction error in the trajectories generated by ITPNet. Note that in the third column, our refinement stage modifies the initial trajectory proposal off-road to the trajectory within the road. More qualitative results are provided in Supplementary Material.", + "bbox": [ + 511, + 439, + 880, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusions", + "text_level": 1, + "bbox": [ + 511, + 638, + 633, + 652 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have proposed a two-stage trajectory prediction method, referred to as R-Pred. We have introduced a novel per proposal trajectory refinement strategy in which each trajectory proposal generated in the first-stage network is refined using contextual information tailored to the proposal. TRNet utilized the local scene context captured by pooling scene component features in a tubular region around the trajectory proposal. TRNet also uses the inter-agent interaction context inferred from a group of influential trajectory proposals of neighboring agents. The results of an experimental evaluation conducted on Argoverse and nuScenes benchmark datasets confirmed that R-Pred significantly outperforms existing methods and achieves", + "bbox": [ + 511, + 662, + 880, + 848 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8532", + "bbox": [ + 483, + 882, + 513, + 893 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "state-of-the-art performance in terms of some evaluation metrics.", + "bbox": [ + 114, + 85, + 485, + 112 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 220, + 127, + 380, + 143 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was partly supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No.2020-0-01373, Artificial Intelligence Graduate School Program(Hanyang University)) and National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.2020R1A2C2012146).", + "bbox": [ + 114, + 151, + 485, + 251 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 116, + 265, + 205, + 279 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Alexandre Alahi, Kratarth Goel, Vignesh Ramanathan, Alexandre Robicquet, Li Fei-Fei, and Silvio Savarese. 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Hivt: Hierarchical vector transformer for multiagent motion prediction. In In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 8823-8833, 2022. 2, 3, 5, 6, 7" + ], + "bbox": [ + 116, + 85, + 485, + 763 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "8535", + "bbox": [ + 483, + 882, + 513, + 893 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/R-Pred_ Two-Stage Motion Prediction Via Tube-Query Attention-Based Trajectory Refinement/cbd955af-2686-4f7c-843a-a3576e04bc6e_model.json b/2023/R-Pred_ Two-Stage Motion Prediction Via Tube-Query Attention-Based Trajectory Refinement/cbd955af-2686-4f7c-843a-a3576e04bc6e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5dffc81f62f9c91bbf3409cba34530ef12e17af3 --- /dev/null +++ b/2023/R-Pred_ Two-Stage Motion Prediction Via Tube-Query Attention-Based Trajectory Refinement/cbd955af-2686-4f7c-843a-a3576e04bc6e_model.json @@ -0,0 +1,2378 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.14, + 0.046, + 0.209, + 0.082 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.261, + 0.043, + 0.782, + 0.085 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.16, + 0.123, + 0.842, + 0.166 + ], + "angle": 0, + "content": "R-Pred: Two-Stage Motion Prediction Via Tube-Query Attention-Based Trajectory Refinement" + }, + { + "type": "text", + "bbox": [ + 0.219, + 0.19, + 0.785, + 0.226 + ], + "angle": 0, + "content": "Sehwan Choi\\(^{1}\\) Jungho Kim\\(^{1}\\) Junyong Yun\\(^{1}\\) Jun Won Choi\\(^{1,2*}\\) \n\\(^{1}\\)Hanyang University and \\(^{2}\\)Qualcomm" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.234, + 0.825, + 0.25 + ], + "angle": 0, + "content": "1{sehwanchoi, junghokim, jyyun}@spa.hanyang.ac.kr 1,2 junwchoi@hanyang.ac.kr" + }, + { + "type": "title", + "bbox": [ + 0.264, + 0.282, + 0.338, + 0.297 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.313, + 0.487, + 0.64 + ], + "angle": 0, + "content": "Predicting the future motion of dynamic agents is of paramount importance to ensuring safety and assessing risks in motion planning for autonomous robots. In this study, we propose a two-stage motion prediction method, called R-Pred, designed to effectively utilize both scene and interaction context using a cascade of the initial trajectory proposal and trajectory refinement networks. The initial trajectory proposal network produces \\( M \\) trajectory proposals corresponding to the \\( M \\) modes of the future trajectory distribution. The trajectory refinement network enhances each of the \\( M \\) proposals using 1) tube-query scene attention (TQSA) and 2) proposal-level interaction attention (PIA) mechanisms. TQSA uses tube-queries to aggregate local scene context features pooled from proximity around trajectory proposals of interest. PIA further enhances the trajectory proposals by modeling inter-agent interactions using a group of trajectory proposals selected by their distances from neighboring agents. Our experiments conducted on Argoverse and nuScenes datasets demonstrate that the proposed refinement network provides significant performance improvements compared to the single-stage baseline and that R-Pred achieves state-of-the-art performance in some categories of the benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.116, + 0.67, + 0.24, + 0.685 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.695, + 0.487, + 0.824 + ], + "angle": 0, + "content": "In autonomous vehicles and robotics applications, dynamic objects move in complex environments while avoiding collisions with other agents. Each dynamic agent plans its motion by predicting the future motion and behavior of other agents around it. Motion prediction refers to the task of predicting the future trajectory of dynamic agents based on their historical trajectories and information on the surrounding environment. The task of predicting motion is challenging because the trajectory of an agent is affected" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.281, + 0.875, + 0.506 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.513, + 0.884, + 0.619 + ], + "angle": 0, + "content": "Figure 1. Key concept of R-Pred. R-Pred performs two stages of trajectory prediction. ITPNet produces \\(M\\) trajectory proposals with the corresponding proposal features and TRNet refines each trajectory proposal using separate networks. ITPNet uses a scene context acquired from a relatively large area, whereas TRNet uses a local scene context that exists in a tube-shaped area. TRNet also refines the trajectory proposal using an inter-agent interaction context represented at a proposal level." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.647, + 0.884, + 0.817 + ], + "angle": 0, + "content": "by a variety of contextual factors, which must be taken into account when modeling motion. In the context of autonomous vehicles, examples of such factors include permissible roads, lanes, traffic signals, blinker states, interactions with other agents, and so forth. The difficulty of predicting future motion also arises from the fact that the distribution of future trajectories tends to be multi-modal. In a given scene, a target agent can choose one of several distinct maneuvers such as changing lanes, turning left, turning right, or continuing straight ahead. Accordingly, prediction models should be able to generate one or more plausible future trajectories with probabilities." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.82, + 0.884, + 0.849 + ], + "angle": 0, + "content": "Recently, deep neural networks have been developed as a new paradigm in trajectory prediction, and have achieved" + }, + { + "type": "page_footnote", + "bbox": [ + 0.133, + 0.835, + 0.33, + 0.848 + ], + "angle": 0, + "content": "*Corresponding author: Jun Won Choi." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.883, + 0.514, + 0.894 + ], + "angle": 0, + "content": "8525" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.115, + 0.087, + 0.486, + 0.442 + ], + "angle": 0, + "content": "considerable improvements in performance compared to traditional prediction models through data-driven modeling of trajectory data. Sequence modeling networks such as long short term memory (LSTM) [23] or gated recurrent unit (GRU) [6] architectures have been shown to be effective in representing sequential trajectory data [25, 26]. Trajectory prediction task has been successfully performed using encoder-decoder architectures [35, 53, 29, 30, 16, 19, 45, 55, 43, 32, 26, 15, 17, 10, 8, 20, 24, 40, 28, 36]. Recently, the accuracy of trajectory prediction has been rapidly improved by utilizing various sources of contextual information available for prediction. Numerous methods have jointly modeled the trajectories of multiple neighboring agents to account for their interactions, including socialLSTM [1], soft hardwired attention [12], social GAN [20], MATLAB [54], Trajectron [24, 40], DESIRE [28], DATF [36], and SoPhie [39]. Static scene information around the target agent was also used to generate more physically plausible trajectories. A scene was represented by a two-dimensional raster image that describes the scene [11, 4, 7, 32, 37, 52]. A vector representation of the scene was also proposed for scene encoding [13, 29, 53, 19, 55, 26, 16, 34, 30, 10, 45, 47, 48]. Recently, Transformer models [44] have been used to model the scene and interaction context using the attention mechanism [30, 34, 55, 33, 45, 50]." + }, + { + "type": "text", + "bbox": [ + 0.115, + 0.446, + 0.487, + 0.618 + ], + "angle": 0, + "content": "In this paper, we propose a new two-stage motion prediction framework, referred to as \\( R \\)-Pred. As shown in Fig. 1, the proposed R-Pred architecture consists of two-stage networks: an initial trajectory proposal network (ITPNet) and a trajectory refinement network (TRNet). The ITPNet produces \\( M \\) initial trajectory proposals corresponding to the \\( M \\) modes of the trajectory distribution for a target agent. TRNet then refines each trajectory proposal using the contexts customized for each proposal. Using the initial trajectory proposals as a priori information, TRNet can utilize the scene and interaction contexts in more selective and effective ways." + }, + { + "type": "text", + "bbox": [ + 0.115, + 0.621, + 0.487, + 0.851 + ], + "angle": 0, + "content": "TRNet employs the following two refinement submodules. First, we present tube-query scene attention (TQSA) to utilize the local scene context effectively. Unlike ITPNet, which uses a global scene context, TQSA extracts local scene context features within a tube-shaped region around each trajectory proposal. (See Fig. 1 for illustration). Then, the extracted scene context features are used to enhance the corresponding trajectory proposal through cross-attention mechanism. TQSA allows the important scene context to be used to improve each \\(M\\) trajectory proposal. Second, we propose the proposal-level interaction attention (PIA) mechanism. PIA models inter-agent interactions using the trajectory proposals produced for multiple neighboring agents by ITPNet. PIA selects a group of trajectory proposals that have the highest influence on the trajectory proposal of interest using the distance-wise proposal" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.086, + 0.882, + 0.114 + ], + "angle": 0, + "content": "grouping strategy. The proposal group is used to refine the trajectory of interest through cross-attention." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.117, + 0.884, + 0.244 + ], + "angle": 0, + "content": "In fact, our per-proposal refinement strategy is motivated by two-stage object detectors (e.g., Faster RCNN [38]), where the initial object proposals are first obtained from the entire convolutional neural network (CNN) features and then local features in the region of interest (RoI) are pooled to refine each object proposal [18, 38, 21]. Similarly, RPred generates the context features based on the initial trajectory proposals produced by ITPNet and uses them to refine each proposal." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.247, + 0.885, + 0.361 + ], + "angle": 0, + "content": "By combining these two sub-modules, R-Pred can generate refined trajectory outputs. We evaluated the proposed approach using the widely adopted Argoverse [5] and nuScenes [3] datasets. The results demonstrate that the proposed refinement network significantly improved the accuracy of ITPNet baseline. The results also show that R-Pred achieves the state-of-the-art performance in some categories of official Argoverse and nuScenes leaderboards." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.363, + 0.852, + 0.377 + ], + "angle": 0, + "content": "The main contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.393, + 0.884, + 0.478 + ], + "angle": 0, + "content": "- We propose a novel trajectory refinement network that refines each of \\( M \\) trajectory proposals using the local scene context and the proposal-level inter-agent interactions. The per-proposal refinement strategy effectively improves the trajectory predictions obtained by the first-stage network." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.496, + 0.885, + 0.61 + ], + "angle": 0, + "content": "- We introduce the concept of global-to-local hierarchical attention to effectively utilize the scene context. Our refinement network uses a tube-query to gather the scene context from the local region around the proposal trajectory. The proposed global-to-local hierarchical attention mechanism is contrasted with factorized attention [34, 33], which iterates attention over different sources of context." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.628, + 0.884, + 0.713 + ], + "angle": 0, + "content": "- We use trajectory proposals of neighboring agents to model interactions between agents. Using the trajectory proposal features reflecting particular intentions of other agents, PIA can better model inter-agent interactions than the conventional interaction modeling that uses the past trajectory features only." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.731, + 0.882, + 0.801 + ], + "angle": 0, + "content": "- R-Pred can use any off-the-shelf single-stage trajectory prediction network as the initial trajectory proposal network. That is, the proposed refinement framework can also be readily applied to any trajectory prediction network available." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.82, + 0.882, + 0.848 + ], + "angle": 0, + "content": "- The source code used in this work will be released publicly." + }, + { + "type": "list", + "bbox": [ + 0.532, + 0.393, + 0.885, + 0.848 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.883, + 0.515, + 0.894 + ], + "angle": 0, + "content": "8526" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.116, + 0.085, + 0.255, + 0.099 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.116, + 0.109, + 0.418, + 0.124 + ], + "angle": 0, + "content": "2.1. Context-Aware Trajectory Prediction" + }, + { + "type": "text", + "bbox": [ + 0.118, + 0.131, + 0.486, + 0.458 + ], + "angle": 0, + "content": "Numerous methods have improved the performance of trajectory prediction by leveraging the contextual information available for prediction. For example, information on the static scene around a target agent has been utilized as scene context. Raster-based scene encoding uses 2D raster images to summarize scene information and extract semantic features using convolutional neural networks [32, 4, 37, 14, 40, 9, 46]. The advantage of this approach is that different types of scene components can be easily accommodated in a raster image. However, the performance of these methods is limited owing to quantization errors and a lack of receptive fields in the encoding architectures. Vector-based scene encoding represents scene components using vectors, and encodes their relationships using graph structures or attention models [29, 10, 40, 20, 24, 27, 13]. VectorNet [13] introduced a hierarchical graph neural network that exploited the spatial locality of road components by vectorized representation. Similarly, LaneGCN [29] was proposed as an effective graph convolutional network to represent complicated topology and long-range dependency. Trajectory++ [40] employed a directed spatiotemporal graph to represent scene context vectors while incorporating agent dynamics and heterogeneous data." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.459, + 0.484, + 0.574 + ], + "angle": 0, + "content": "The performance of trajectory prediction has also been improved by taking into account interactions with surrounding dynamic agents and static environment information. Social pooling methods pooled the trajectory features of other agents for interaction modeling [1, 28, 20, 39, 8]. Recently, attention mechanisms have been proposed to exploit the meaningful relationships between dynamic agents and lane segments [26, 41, 55, 10, 19, 51, 29, 13, 16, 32, 45, 29]." + }, + { + "type": "title", + "bbox": [ + 0.116, + 0.584, + 0.449, + 0.599 + ], + "angle": 0, + "content": "2.2. Transformer-based Trajectory Prediction" + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.607, + 0.486, + 0.849 + ], + "angle": 0, + "content": "Transformer architectures offer an effective method for training attention mechanisms capable of capturing long-range dependencies within sequence data. Recently, Transformers have been adopted for trajectory prediction to model spatio-temporal context as well as interactions between agents [50, 45, 55, 30, 33, 34]. mmTransformer [30] employed an efficient stacked Transformer that applied cross-attention on multi-agent and scene contexts one by one. HiVT [55] summarized the spatio-temporal features of agents using translation-invariant agent-centric local scene structure. In SceneTransformer [34], a simple varying form of self-attention was exploited to integrate various features, generating scene-level consistent predictions for all agents jointly. Along these lines, Wayformer [33] was proposed as a general multi-dimensional attention architecture designed to jointly encode multiple agent trajectories and map data in time, space, and agent dimensions." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.085, + 0.655, + 0.101 + ], + "angle": 0, + "content": "3. Problem Setup" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.109, + 0.884, + 0.506 + ], + "angle": 0, + "content": "Suppose that the historical trajectory states of \\(N\\) dynamic agents are obtained from the multi-object tracker, where \\(N\\) can vary depending on the scenario. The agent requiring prediction of its future trajectory is denoted as the target agent, while the other agents are termed neighbor agents. The past trajectory states over \\(T\\) time steps for the \\(i\\)-th agent are denoted as \\(\\mathbf{x}_i = [x_i(t - T + 1), x_i(t - T + 2), \\dots, x_i(t)]\\), where \\(t\\) denotes the current time step and \\(x_i(t - s)\\) is the state of the \\(i\\)-th agent at the time step \\((t - s)\\). The trajectory state is of the form \\((x, y, \\varepsilon)\\) consisting of the \\((x, y)\\) position and the agent's semantic property \\(\\varepsilon\\). The \\((x, y)\\) coordinates are represented in the agent-centric reference frame, where the current position of a target agent is the origin and its heading angle is aligned with the positive x-axis. Similarly, the future trajectory states over \\(F\\) time steps for the \\(i\\)-th agent are given by \\(\\mathbf{y}_i = [y_i(t + 1), y_i(t + 2), \\dots, y_i(t + F)]\\). We assume that the vector representation of a scene is available along with the trajectory data. For instance, a lane is represented by a set of points on its centerline, where the \\((x, y)\\) coordinates of each point are expressed in an agent-centric frame. We accommodate different types of scene components by appending an attribute index \\(\\epsilon_l\\) to the \\((x, y)\\) coordinate as \\((x, y, \\epsilon_l)\\). The set of scene components around the target agent at the time \\(t\\) is expressed as the vector \\(\\xi = [\\xi_1, \\dots, \\xi_L]\\), where the dimension \\(L\\) varies depending on the scene complexity and the region of interest on the map." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.508, + 0.884, + 0.593 + ], + "angle": 0, + "content": "Without loss of generality, let \\(\\mathbf{x}_1\\) be the trajectory of the target agent and \\(\\mathbf{x}_2,\\dots,\\mathbf{x}_N\\) be the trajectories of neighboring agents. Finally, the goal of the motion prediction task is to estimate the future trajectory of the target agent \\(\\mathbf{y}_1\\) given the past trajectories of \\(N\\) agents \\(\\mathbf{x}_1,\\dots,\\mathbf{x}_N\\) and the scene information \\(\\xi\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.607, + 0.858, + 0.623 + ], + "angle": 0, + "content": "4. Proposed Trajectory Prediction Network" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.631, + 0.882, + 0.66 + ], + "angle": 0, + "content": "In this section, we present the details of the proposed motion prediction method, R-Pred." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.669, + 0.692, + 0.684 + ], + "angle": 0, + "content": "4.1. Overall Framework" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.692, + 0.884, + 0.849 + ], + "angle": 0, + "content": "An overview of the proposed R-Pred framework is presented in Fig. 2. Our proposed architecture produces \\(M\\) multi-modal trajectory predictions for a target agent over two stages. First, ITPNet produces \\(M\\) trajectory proposals for all \\(N\\) agents present in the scene. Along with the trajectory proposals, ITPNet returns \\(M\\) intermediate features used to produce the trajectory proposals. These features are called proposal features. ITPNet follows traditional trajectory prediction methods for scene and interaction encoding; that is, it utilizes the global scene context features extracted from a fixed region around the current position of the agent." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.883, + 0.514, + 0.894 + ], + "angle": 0, + "content": "8527" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.171, + 0.085, + 0.825, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.366, + 0.884, + 0.434 + ], + "angle": 0, + "content": "Figure 2. Overall structure of R-Pred. Given the past trajectories of the dynamic agents and the global scene information, ITPNet generates \\(M\\) trajectory proposals for each agent. TRNet refines each of the \\(M\\) trajectory proposals of the target agent through TQSA and PIA. TQSA utilizes local scene context features obtained by tubular region pooling. PIA captures interaction context using the proposal group found by the distance-wise proposal grouping. Finally, the prediction header produces the refined future trajectories based on the joint trajectory features obtained by concatenation of the attention values from TQSA and PIA." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.455, + 0.484, + 0.683 + ], + "angle": 0, + "content": "In addition, the ITPNet exploits the interaction context derived from the past trajectories of \\(N\\) agents. Second, TRNet refines each of the \\(M\\) trajectory proposals of the target agent based on the prior trajectory information generated by the ITPNet. TRNet employs TQSA and PIA to generate the context features customized for each proposal. TQSA extracts the local scene context features cropped from a tube-shaped region around the target trajectory proposal. PIA generates the inter-agent interaction context features using a group of selected proposal trajectories of \\(N\\) agents. The context features generated by TQSA and PIA enhance the proposal features through cross-attention. The final joint trajectory features are obtained by concatenating two attention values from TQSA and PIA. Finally, the prediction head produces \\(M\\) future trajectory predictions and their confidence scores for each target agent." + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.697, + 0.41, + 0.712 + ], + "angle": 0, + "content": "4.2. Initial Trajectory Proposal Network" + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.72, + 0.484, + 0.849 + ], + "angle": 0, + "content": "Given the past trajectories \\(\\mathbf{x}_1,\\dots,\\mathbf{x}_N\\) of the \\(N\\) agents present in the scene and the scene information \\(\\xi\\), ITP-Net produces \\(M\\) trajectory proposals and their confidence scores for each agent. \\(M\\) intermediate features, known as proposal features, are also extracted for the subsequent refinement phase. The trajectory proposals, their confidence scores, and the proposal features for the \\(i\\)-th agent are denoted as \\(\\hat{\\mathbf{y}}_i = [\\hat{\\mathbf{y}}_1^1,\\dots,\\hat{\\mathbf{y}}_i^M]\\), \\(\\hat{\\mathbf{c}}_i = [\\hat{\\mathbf{c}}_i^1,\\dots,\\hat{\\mathbf{c}}_i^M]\\), and \\(\\mathbf{f}_i = [\\mathbf{f}_i^1,\\dots,\\mathbf{f}_i^M]\\), respectively." + }, + { + "type": "title", + "bbox": [ + 0.516, + 0.455, + 0.75, + 0.469 + ], + "angle": 0, + "content": "Algorithm 1 Tubular Region Pooling" + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.472, + 0.882, + 0.514 + ], + "angle": 0, + "content": "Input: Trajectory proposal \\(\\hat{\\mathbf{y}}_1^m\\), scene context vectors \\(\\xi\\), scene embedding features \\(\\Psi\\), and thresholding radius \\(\\tau\\)." + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.515, + 0.783, + 0.529 + ], + "angle": 0, + "content": "Output: Local scene context features \\(\\Psi_1^m\\)." + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.53, + 0.62, + 0.544 + ], + "angle": 0, + "content": "1: \\(\\Psi_1^m = set()\\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.545, + 0.708, + 0.557 + ], + "angle": 0, + "content": "2: for \\( f \\gets t + 1 \\) to \\( t + F \\) do" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.559, + 0.672, + 0.571 + ], + "angle": 0, + "content": "3: for each \\(\\xi_l \\in \\xi\\) do" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.572, + 0.714, + 0.587 + ], + "angle": 0, + "content": "4: \\(dist = \\| \\hat{y}_1^m (f) - \\xi_l\\| _2\\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.588, + 0.676, + 0.599 + ], + "angle": 0, + "content": "5: if dist \\(< \\tau\\) then" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.601, + 0.664, + 0.615 + ], + "angle": 0, + "content": "5: \\(\\Psi_1^m\\).add \\((\\psi_l)\\)" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.617, + 0.538, + 0.626 + ], + "angle": 0, + "content": "6:" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.63, + 0.615, + 0.643 + ], + "angle": 0, + "content": "7: return \\(\\Psi_1^m\\)" + }, + { + "type": "list", + "bbox": [ + 0.526, + 0.53, + 0.714, + 0.643 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.678, + 0.778, + 0.693 + ], + "angle": 0, + "content": "4.3. Trajectory Refinement Network" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.703, + 0.882, + 0.732 + ], + "angle": 0, + "content": "TRNet refines each of trajectory proposals \\(\\hat{\\mathbf{y}}_1\\) of the target agent through TQSA and PIA." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.735, + 0.882, + 0.85 + ], + "angle": 0, + "content": "Tube-Query Scene Attention. We construct the set of scene embedding features \\(\\Psi = \\{\\psi_1,\\dots,\\psi_L\\}\\) by encoding each element of \\(\\xi\\) via a linear projection, i.e., \\(\\psi_l =\\) linear\\_proj \\((\\xi_{l})\\) .TQSA pools the scene embedding features in a tubular region around the trajectory proposal on the map from \\(\\Psi\\) .We denote the set of scene embedding features prepared for the \\(m\\) th trajectory proposal \\(\\hat{\\mathbf{y}}_1^m\\) of the target agent as \\(\\Psi_1^m\\) . Tubular region pooling is efficiently per" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.883, + 0.514, + 0.894 + ], + "angle": 0, + "content": "8528" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.117, + 0.086, + 0.414, + 0.1 + ], + "angle": 0, + "content": "Algorithm 2 Distance-Wise Proposal Grouping" + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.102, + 0.484, + 0.144 + ], + "angle": 0, + "content": "Input: Trajectory proposals \\(\\hat{\\mathbf{y}}_1,\\dots ,\\hat{\\mathbf{y}}_N\\) proposal confidence scores \\(\\hat{\\mathbf{c}}_1,\\dots ,\\hat{\\mathbf{c}}_N\\) proposal features \\(\\mathbf{f}_1,\\dots ,\\mathbf{f}_N\\) distance threshold \\(\\mathcal{D}\\) and confidence threshold \\(\\mathcal{T}\\)" + }, + { + "type": "text", + "bbox": [ + 0.116, + 0.145, + 0.346, + 0.16 + ], + "angle": 0, + "content": "Output: Proposal group set \\(\\mathcal{G}(\\hat{\\mathbf{y}}_1^m)\\)" + }, + { + "type": "text", + "bbox": [ + 0.127, + 0.161, + 0.26, + 0.172 + ], + "angle": 0, + "content": "1: for \\( i \\gets 2 \\) to \\( N \\) do" + }, + { + "type": "text", + "bbox": [ + 0.126, + 0.174, + 0.291, + 0.187 + ], + "angle": 0, + "content": "2: for \\(m^{\\prime}\\gets 1\\) to \\(M\\) do" + }, + { + "type": "text", + "bbox": [ + 0.126, + 0.188, + 0.279, + 0.201 + ], + "angle": 0, + "content": "3: if \\(\\hat{\\mathbf{c}}_j^{m'} > \\mathcal{T}\\) then" + }, + { + "type": "text", + "bbox": [ + 0.126, + 0.203, + 0.435, + 0.224 + ], + "angle": 0, + "content": "4: \\(dist = \\min_{f\\in [t + 1,t + F]}\\| \\hat{y}_1^m (f) - \\hat{y}_i^{m'}(f)\\| _2\\)" + }, + { + "type": "text", + "bbox": [ + 0.126, + 0.225, + 0.298, + 0.236 + ], + "angle": 0, + "content": "5: if \\(dist < \\mathcal{D}\\) then" + }, + { + "type": "text", + "bbox": [ + 0.126, + 0.237, + 0.332, + 0.253 + ], + "angle": 0, + "content": "6: \\(\\mathcal{G}(\\hat{\\mathbf{y}}_1^m)\\) .append \\((\\mathbf{f}_i^{m'})\\)" + }, + { + "type": "text", + "bbox": [ + 0.126, + 0.255, + 0.138, + 0.263 + ], + "angle": 0, + "content": "7:" + }, + { + "type": "text", + "bbox": [ + 0.126, + 0.267, + 0.238, + 0.281 + ], + "angle": 0, + "content": "8: return \\(\\mathcal{G}(\\hat{\\mathbf{y}}_1^m)\\)" + }, + { + "type": "list", + "bbox": [ + 0.126, + 0.161, + 0.435, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.309, + 0.485, + 0.379 + ], + "angle": 0, + "content": "formed to aggregate scene embedding features within the search radius \\(\\tau\\) around each waypoint of the trajectory proposal \\(\\hat{\\mathbf{y}}_1^m\\). Note that a collection of search disks centered at all waypoints on the trajectory forms an approximately tubular polygon. See Algorithm 1 for further details." + }, + { + "type": "text", + "bbox": [ + 0.115, + 0.38, + 0.484, + 0.451 + ], + "angle": 0, + "content": "TQSA decodes the proposal features \\(\\mathbf{f}_1^m\\) (associated with \\(\\hat{\\mathbf{y}}_1^m\\)) of the target agent by performing cross-attention on the local scene context \\(\\Psi_1^m\\). Specifically, we use the proposal features \\(\\mathbf{f}_1^m\\) as the query and the local scene context features \\(\\Psi_1^m\\) as the key and value, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.204, + 0.46, + 0.484, + 0.477 + ], + "angle": 0, + "content": "\\[\nQ = \\mathbf {f} _ {1} ^ {m} W ^ {Q _ {T Q S A}} \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.48, + 0.484, + 0.497 + ], + "angle": 0, + "content": "\\[\nK = \\Psi_ {1} ^ {m} W ^ {K _ {T Q S A}} \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.499, + 0.484, + 0.516 + ], + "angle": 0, + "content": "\\[\nV = \\Psi_ {1} ^ {m} W ^ {V _ {T Q S A}} \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.204, + 0.519, + 0.484, + 0.553 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} _ {1} ^ {m} = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {\\top}}{\\sqrt {d _ {k}}}\\right) V, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.56, + 0.485, + 0.633 + ], + "angle": 0, + "content": "where \\(W^{Q_{TQSA}}\\), \\(W^{K_{TQSA}}\\), and \\(W^{V_{TQSA}}\\) are learnable weight matrices and \\(d_k\\) is the dimension of the embedding vectors. We combine the attention value \\(\\mathcal{A}_1^m\\) and the proposal features \\(\\mathbf{f}_1^m\\) using the gating function introduced in [55]" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.641, + 0.484, + 0.658 + ], + "angle": 0, + "content": "\\[\n\\lambda = \\sigma \\left(\\mathrm {f} _ {1} ^ {m} W ^ {\\text {i n p u t}} + \\mathcal {A} _ {1} ^ {m} W ^ {\\text {h i d d e n}}\\right) \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.661, + 0.484, + 0.677 + ], + "angle": 0, + "content": "\\[\n\\mathbf {t} _ {1} ^ {m} = \\lambda \\odot \\mathbf {f} _ {1} ^ {m} W ^ {\\text {g a t e}} + (1 - \\lambda) \\odot \\mathcal {A} _ {1} ^ {m} \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.68, + 0.484, + 0.696 + ], + "angle": 0, + "content": "\\[\n\\mathbf {t} _ {1} ^ {m} = \\mathbf {f} _ {1} ^ {m} + \\phi \\left(\\mathbf {t} _ {1} ^ {m}\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.115, + 0.705, + 0.485, + 0.776 + ], + "angle": 0, + "content": "where \\(W^{input}\\), \\(W^{hidden}\\), and \\(W^{gate}\\) are learnable matrices, \\(\\odot\\) indicates element-wise product, \\(\\sigma\\) indicates the sigmoid function and \\(\\phi(\\cdot)\\) denotes a multi-layer perceptron (MLP). We add layer normalization [2], Dropout [42], and residual connection [22] in the middle of the attention process." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.778, + 0.484, + 0.82 + ], + "angle": 0, + "content": "Note that the aforementioned local scene attention process to produce the output of TQSA \\(\\mathbf{t}_1^m\\) is performed for each trajectory proposal (for each \\(m\\) value) in parallel." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.82, + 0.484, + 0.85 + ], + "angle": 0, + "content": "Proposal-level Interaction Attention. PIA uses a distance-wise proposal grouping algorithm to find a group" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.086, + 0.883, + 0.243 + ], + "angle": 0, + "content": "of the trajectory proposals for the nearby agents to model their inter-agent interactions. First, among \\(MN\\) trajectory proposals from \\(N\\) agents, those with a confidence score below the threshold \\(\\mathcal{T}\\) are discarded because they are unlikely to occur. Subsequently, for a given \\(m\\)-th trajectory proposal \\(\\hat{\\mathbf{y}}_1^m\\) of the target agent, the algorithm selects the trajectory proposals of the nearby agents, whose distance from \\(\\hat{\\mathbf{y}}_1^m\\) is closer than the distance threshold \\(\\mathcal{D}\\). These are considered the most influential trajectory proposals to use for interaction modeling. A distance between two trajectories \\(\\mathbf{y}_1^\\star\\) and \\(\\mathbf{y}_2^\\star\\) is defined by" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.249, + 0.882, + 0.272 + ], + "angle": 0, + "content": "\\[\n\\operatorname {d i s t} \\left(\\mathbf {y} _ {1} ^ {\\star}, \\mathbf {y} _ {2} ^ {\\star}\\right) = \\min _ {f \\in [ t + 1, t + F ]} \\| \\mathbf {y} _ {1} ^ {\\star} (f) - \\mathbf {y} _ {2} ^ {\\star} (f) \\| _ {2}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.277, + 0.882, + 0.334 + ], + "angle": 0, + "content": "For the selected trajectory proposals, the algorithm groups the corresponding proposal features into the proposal feature group \\(\\mathcal{G}(\\hat{\\mathbf{y}}_1^m)\\). The distance-wise proposal grouping algorithm is summarized in Algorithm 2." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.334, + 0.882, + 0.404 + ], + "angle": 0, + "content": "The proposal feature group is used to decode the proposal features \\(\\mathbf{f}_1^m\\) through cross-attention. Using \\(\\mathbf{f}_1^m\\) as query and \\(\\mathcal{G}(\\mathbf{y}_1^m)\\) as key and value, the cross-attention module produces the attention value \\(\\mathbf{p}_1^m\\) similarly to Eq. (1) - (7)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.405, + 0.882, + 0.633 + ], + "angle": 0, + "content": "Multi-modal Prediction Head. TRNet constructs the final joint trajectory feature \\(\\mathbf{j}_1^m\\) by concatenating the attention output \\(\\mathbf{t}_1^m\\) from TQSA and the attention output \\(\\mathbf{p}_1^m\\) from PIA. The prediction head is then applied to \\(\\mathbf{j}_1^m\\) to produce the refined trajectories and the confidence scores. The prediction head consists of the regression branch and a classification branch. First, by modeling the trajectory points as multi-variate random vectors with independent Laplace distribution, the regression branch applies an MLP to \\(\\mathbf{j}_1^m\\) to predict the mean and covariance of \\(\\mathbf{y}_1\\). The predicted mean is denoted as \\(\\tilde{\\mathbf{y}}_1^m = [\\tilde{y}_1^m (t + 1),\\dots,\\tilde{y}_1^m (t + F)]\\) and the predicted variance is denoted as \\(\\mathbf{b}_1^m = [\\tilde{b}_1^m (t + 1),\\dots,\\tilde{b}_1^m (t + F)]\\). The regression branch is applied separately for each mode \\(m\\). Next, the classification branch applies another MLP to the concatenation of \\(\\mathbf{j}_1^1,\\dots,\\mathbf{j}_1^M\\) to produce the confidence scores \\(\\check{\\mathbf{c}}_1^1,\\dots,\\check{\\mathbf{c}}_1^M\\) for all modes." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.639, + 0.665, + 0.654 + ], + "angle": 0, + "content": "4.4. Training Details" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.661, + 0.882, + 0.69 + ], + "angle": 0, + "content": "The total loss function \\( L_{total} \\) used to train the entire network is given by" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.696, + 0.876, + 0.712 + ], + "angle": 0, + "content": "\\[\nL _ {t o t a l} = \\alpha L _ {r e g. p r o} + \\beta L _ {c l s. p r o} + \\gamma L _ {r e g. r e f} + \\delta L _ {c l s. r e f},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.717, + 0.882, + 0.803 + ], + "angle": 0, + "content": "where \\( L_{reg-pro} \\) and \\( L_{reg-ref} \\) are the regression loss functions for ITPNet, and TRNet and \\( L_{cls-pro} \\) and \\( L_{cls-ref} \\) are the classification loss functions for ITPNet, and TRNet. We used \\( \\alpha = \\beta = \\gamma = \\delta = 1 \\) in our setup. The negative log-likelihood function for the Laplace distribution is used for \\( L_{reg-ref} \\) as follows," + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.808, + 0.892, + 0.85 + ], + "angle": 0, + "content": "\\[\nL _ {r e g - r e f} = - \\frac {1}{N F} \\sum_ {n = 1} ^ {N} \\sum_ {f = t + 1} ^ {t + F} \\log \\mathbb {P} \\left(y _ {n} (f) \\mid \\check {y} _ {n} ^ {m ^ {*}} (f), \\check {\\mathbf {b}} _ {n} ^ {m ^ {*}} (f)\\right),\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.883, + 0.514, + 0.894 + ], + "angle": 0, + "content": "8529" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.182, + 0.085, + 0.817, + 0.368 + ], + "angle": 0, + "content": "
MethodminADE1minFDE1minADE6minFDE6brierFDE6MR6%
LaneRCNN[51]1.693.690.901.452.1512.3
LaPred[26]1.934.330.911.502.1318.0
TNT[53]2.174.960.911.452.1416.6
PRIME[41]1.913.821.221.562.1011.5
HOME[14]1.723.730.921.36-11.3
LaneGCN[29]1.703.760.871.362.0516.2
mmTransformer[30]1.774.000.841.342.0315.4
DenseTNT[19]1.683.630.881.281.9812.6
THOMAS[16]1.673.590.941.441.9710.3
SceneTransformer[34]1.813.620.801.231.8912.5
LTP[45]1.623.550.831.301.8614.7
HOME+GOHOME[15]1.703.680.891.291.868.5
TPCN[49]1.663.690.871.38-15.8
HiVT[55]1.603.520.771.171.8412.7
MultiPath++[43]1.623.610.791.211.7913.2
Wayformer[33]1.643.670.771.161.7411.9
ITPNet baseline1.623.570.791.211.8613.1
R-Pred1.583.470.761.121.7711.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.114, + 0.371, + 0.884, + 0.424 + ], + "angle": 0, + "content": "Table 1. Performance comparison on Argoverse test set in the official leaderboard. The best performed metrics are shown in bold. The \"-\" symbol means the corresponding metric is unknown, either because the authors have not disclosed it or it was not specified in the leaderboard. Our model achieves the state-of-the-art performance in terms of the \\( \\text{minADE}_1 \\), \\( \\text{minFDE}_1 \\), \\( \\text{minADE}_6 \\) and \\( \\text{minFDE}_6 \\) metrics." + }, + { + "type": "text", + "bbox": [ + 0.115, + 0.445, + 0.484, + 0.54 + ], + "angle": 0, + "content": "where \\(\\mathbb{P}(\\cdot |\\cdot)\\) is the probability density function of Laplace distribution. \\(L_{reg - pro}\\) is defined similarly. When evaluating the loss function during training, we adopt a winner-takes-all strategy [7] in which the mode \\(m^{*}\\) of the trajectory output that yields the smallest average displacement error is used, i.e., \\(m^{*} = \\underset {m\\in [1,M]}{\\mathrm{argmin}}\\sum_{f = t + 1}^{t + F}\\| y_n(f) - \\tilde{y}_n^m (f)\\| _2.\\)" + }, + { + "type": "text", + "bbox": [ + 0.116, + 0.54, + 0.484, + 0.581 + ], + "angle": 0, + "content": "We used the cross entropy loss for the classification losses \\( L_{cls-pro} \\) and \\( L_{cls-ref} \\). We trained the entire network end-to-end with random initialization." + }, + { + "type": "table", + "bbox": [ + 0.119, + 0.6, + 0.486, + 0.768 + ], + "angle": 0, + "content": "
Method\\( mADE_5 \\)\\( mFDE_5 \\)\\( mADE_{10} \\)\\( mFDE_{10} \\)
MTP[7]2.224.831.743.54
CoverNet[37]1.96-1.48-
Trajectory++[40]1.88-1.51-
MHA-JAM[32]1.813.721.242.21
MultiPath[4]1.783.621.552.93
CXX[31]1.63-1.29-
LaPred[26]1.533.371.122.39
P2T[9]1.45-1.16-
THOMAS[16]1.33-1.04-
PGP[10]1.272.470.941.55
ITPNet baseline1.292.580.971.60
R-Pred1.192.280.941.50
" + }, + { + "type": "table_caption", + "bbox": [ + 0.114, + 0.777, + 0.486, + 0.83 + ], + "angle": 0, + "content": "Table 2. Performance comparison on nuScenes validation set in the official leaderboard. The \"-\" symbol means the corresponding metric unknown. Our model achieves state-of-the-art performance on all metrics." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.444, + 0.638, + 0.46 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.471, + 0.884, + 0.527 + ], + "angle": 0, + "content": "In this section, we describe the experimental setup used to evaluate the performance of the proposed R-Pred, and present both quantitative and qualitative analyses of the behavior of the model." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.53, + 0.884, + 0.673 + ], + "angle": 0, + "content": "Datasets. Both Argoverse [5] and nuScenes [3] datasets provide dynamic agent trajectories and HD-map in real-world driving scenarios. The Argoverse dataset was collected from two US cities, including Miami and Pittsburgh. Each sample contains 5 seconds trajectories of tracked vehicles sampled at \\(10\\mathrm{Hz}\\). Argoverse dataset provides HD-map with detailed lane information. The prediction task is to predict future trajectories for 3 seconds given past trajectories of 2 seconds. The dataset contains 205,942 training, 39,272 validation, and 78,143 test samples." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.675, + 0.882, + 0.775 + ], + "angle": 0, + "content": "The nuScenes dataset was collected in Boston and Singapore. The collected trajectories are 6 seconds long and are sampled at \\(2\\mathrm{Hz}\\). The prediction task is defined as that of predicting future trajectories for 6 seconds given past trajectories of 2 seconds. HD-map is also provided along with the trajectory data. The dataset is split into 32, 186 training, 8,560 validation, and 9,041 test samples." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.777, + 0.884, + 0.849 + ], + "angle": 0, + "content": "Metrics. For the performance evaluation, we adopt widely used performance metrics including average displacement error (ADE), final displacement error (FDE), and miss rate (MR). ADE refers to the mean square error compared to the ground truth over the entire time steps, and FDE is" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.883, + 0.514, + 0.894 + ], + "angle": 0, + "content": "8530" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.182, + 0.089, + 0.335, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.339, + 0.09, + 0.493, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.496, + 0.09, + 0.65, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.653, + 0.091, + 0.817, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.213, + 0.335, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.339, + 0.213, + 0.493, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.496, + 0.213, + 0.65, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.653, + 0.213, + 0.816, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.341, + 0.885, + 0.395 + ], + "angle": 0, + "content": "Figure 3. Qualitative results of R-Pred on Argoverse validation set. Yellow, green, blue, and red lines represent the history, ground truth, the initial trajectory proposal with the highest score, and the final (refined) trajectory, respectively. The sky blue region denotes tubular regions used for TQSA. These figures present different vehicle motion scenarios such as continuing straight ahead, turning left, slowing down, changing lanes, etc." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.417, + 0.486, + 0.775 + ], + "angle": 0, + "content": "We evaluate the prediction accuracy with \\(M > 1\\) trajectory predictions using minADEM and minFDEM, which are the minimum ADE and FDE over \\(M\\) predicted trajectories, respectively. \\(MR_{M}\\) measures the ratio within 2 meters of the endpoint of the best-predicted trajectory and ground truth. We also use brier minimum FDE (brierFDEM), which measures the value of minFDEM + (1 - p)², where \\(p\\) is corresponding trajectory probability. This imposes a penalty when the probability of the best trajectory is low. Implementation Details. We set the threshold \\(\\mathcal{D}\\) and \\(\\mathcal{T}\\) of PIA to 0.1 and 10 meters and \\(\\tau\\) of TQSA to 20 meters. The embedding size of all features is set to 128 for comparative performance analysis. We used existing prediction architectures for the ITPNet. We chose the structure of [55] on Argoverse and that of [10] on nuScenes. These models achieved excellent performance on both benchmarks. They are considered ITPNet baselines and are used to measure the performance gain achieved by our refinement network. We trained the proposed model on TiTAN RTX GPU for 64 epochs with 32 batch sizes. The data are batched randomly. For all experiments, we trained the model using AdamW optimizer with an initial learning rate of 5e-4. We used cosine annealing to decay the learning rate and applied dropout with a 0.1 ratio. Data augmentation was not used." + }, + { + "type": "title", + "bbox": [ + 0.116, + 0.783, + 0.299, + 0.799 + ], + "angle": 0, + "content": "5.1.Quantitative Results" + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.806, + 0.486, + 0.849 + ], + "angle": 0, + "content": "Table 1 presents the performance of R-Pred evaluated on Argoverse test set. We compare the performance of R-Pred with that of several top ranked models [51, 53, 41, 29, 14," + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.416, + 0.885, + 0.48 + ], + "angle": 0, + "content": "
ITPNetPIATQSAminADE6minFDE6MR6%
✓0.6941.05710.63
✓✓0.6770.9929.64
✓✓✓0.6570.9458.69
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.489, + 0.884, + 0.517 + ], + "angle": 0, + "content": "Table 3. Contributions of the main components evaluated on the Argoverse validation set." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.546, + 0.884, + 0.718 + ], + "angle": 0, + "content": "30, 19, 16, 34, 45, 15, 49, 43, 33, 55]. R-Pred achieves the best prediction accuracy in terms of the \\( \\text{minADE}_1 \\), \\( \\text{minFDE}_1 \\), \\( \\text{minADE}_6 \\) and \\( \\text{minFDE}_6 \\) metrics and competitive performance in terms of \\( \\text{brierFDE}_6 \\) and \\( \\text{MR}_6 \\). R-Pred sets a new state-of-the-art performance surpassing the current best methods, Wayformer [33] and Multi-Path++ [43]. Compared to the ITPNet baseline, the proposed method offers performance improvements of \\( 3.80\\% \\) and \\( 7.43\\% \\) in terms of \\( \\text{minADE}_6 \\), and \\( \\text{minFDE}_6 \\), respectively. This indicates that our trajectory refinement strategy can effectively improve the reliability and robustness of the initial prediction using ITPNet." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.885, + 0.851 + ], + "angle": 0, + "content": "Table 2 presents the performance of several motion prediction methods on nuScenes validation set. We compare R-Pred with the top ranked methods [37, 40, 32, 4, 31, 26, 9, 16, 10] on the nuScenes leaderboard. R-Pred achieves significant performance gains compared with other prediction methods. R-Pred exhibits the performance gain of \\(7.75\\%\\) and \\(11.62\\%\\) in \\(\\min ADE_5\\) and \\(\\min FDE_5\\) compared to the ITPNet baseline. These results demonstrate that the proposed two refinement modules have high-quality learning" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.883, + 0.513, + 0.894 + ], + "angle": 0, + "content": "8531" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.116, + 0.086, + 0.194, + 0.1 + ], + "angle": 0, + "content": "capabilities." + }, + { + "type": "table", + "bbox": [ + 0.169, + 0.113, + 0.428, + 0.21 + ], + "angle": 0, + "content": "
τminADE6minFDE6MR6%
50.6590.9578.927
100.6580.9528.840
200.6570.9458.698
300.6570.9468.714
500.6590.9548.878
" + }, + { + "type": "table_caption", + "bbox": [ + 0.115, + 0.213, + 0.486, + 0.24 + ], + "angle": 0, + "content": "Table 4. Performance versus \\( \\tau \\) parameter of TQSA evaluated on the Argoverse validation set." + }, + { + "type": "table", + "bbox": [ + 0.169, + 0.266, + 0.428, + 0.363 + ], + "angle": 0, + "content": "
DminADE6minFDE6MR6%
50.6590.9488.802
100.6570.9458.698
200.6580.9478.730
300.6590.9498.811
400.6590.9508.821
" + }, + { + "type": "table_caption", + "bbox": [ + 0.115, + 0.366, + 0.485, + 0.392 + ], + "angle": 0, + "content": "Table 5. Performance versus \\( \\mathcal{D} \\) parameter of PIA evaluated on the Argoverse validation set." + }, + { + "type": "title", + "bbox": [ + 0.116, + 0.414, + 0.26, + 0.43 + ], + "angle": 0, + "content": "5.2. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.115, + 0.436, + 0.484, + 0.506 + ], + "angle": 0, + "content": "We conducted several ablation studies on the Argoverse validation set. We reduced the training time required to conduct the ablation study by decreasing the feature size from 128 to 64 and increasing the batch size from 32 to 64. The trained model was evaluated on the entire validation set." + }, + { + "type": "text", + "bbox": [ + 0.115, + 0.507, + 0.484, + 0.72 + ], + "angle": 0, + "content": "Contribution of Each Module. Table 3 shows the contributions of each module to overall performance achieved by R-Pred. We evaluated performance as we added each component one by one. We consider the following three modules of R-Pred: 1) ITPNet baseline, 2) PIA, and 3) TQSA. When the PIA is added to ITPNet baseline, the \\( \\text{minFDE}_6 \\) improves by \\( 6.15\\% \\) and \\( MR_6 \\) improves by \\( 9.31\\% \\). This indicates the effectiveness of inter-agent interaction modeling by PIA. When TQSA is added, it achieves the performance gains of \\( 4.74\\% \\) and \\( 9.85\\% \\) in \\( \\text{minFDE}_6 \\) and \\( MR_6 \\). We observe that proposal refinement using local scene context improves the performance significantly. Finally, the combination of PIA and TQSA has improved the performance of ITPNet baseline by \\( 10.6\\% \\) and \\( 18.25\\% \\), in \\( \\text{minFDE}_6 \\) and \\( MR_6 \\), respectively." + }, + { + "type": "text", + "bbox": [ + 0.115, + 0.72, + 0.484, + 0.848 + ], + "angle": 0, + "content": "Performance Versus \\(\\tau\\) and \\(\\mathcal{D}\\). We investigated the impact of the parameters \\(\\tau\\) and \\(\\mathcal{D}\\) on the performance. Recall that \\(\\tau\\) and \\(\\mathcal{D}\\) are the distance thresholds used in TQSA and PIA, respectively. Table 4 presents the performance of R-Pred evaluated for several values of \\(\\tau = \\{5,10,20,30,50\\}\\). R-Pred performs best at \\(\\tau = 20,30\\), and degrades as \\(\\tau\\) becomes larger or smaller than these values. This is likely due to the fact that when the threshold gets too large, a lot of irrelevant scene context can be used for cross-attrbution." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.086, + 0.882, + 0.143 + ], + "angle": 0, + "content": "Table 5 presents the performance of R-Pred for several values of \\(\\mathcal{D} = \\{5,10,20,30,40\\}\\). R-Pred achieves the best performance with \\(\\mathcal{D} = 10\\). Note that increasing the threshold \\(\\mathcal{D}\\) above 10 does not improve performance." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.143, + 0.882, + 0.286 + ], + "angle": 0, + "content": "Effect of Per-proposal Scene Context Strategy. One of our key innovations is to use the tube-query for pooling the customized scene context for each proposal. We investigated the benefit of our per-proposal feature pooling method. We compare R-Pred with the baseline that shares the global scene context features for all proposals in the refinement step. Table 6 shows that our strategy offers \\(1.76\\%\\) and \\(3.24\\%\\) performance gains in \\(minFDE_{6}\\) and \\(MR_{6}\\) over the baseline, which confirms the advantage of the proposed per-proposal feature pooling method." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.299, + 0.88, + 0.358 + ], + "angle": 0, + "content": "
Per-proposal scene contextShared scene contextminADE6minFDE6MR6%
✓0.6620.9628.981
✓0.6570.9458.69
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.366, + 0.882, + 0.394 + ], + "angle": 0, + "content": "Table 6. Comparison of per-proposal scene context versus shared scene context evaluated on the Argoverse validation set." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.418, + 0.686, + 0.433 + ], + "angle": 0, + "content": "5.3. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.44, + 0.882, + 0.625 + ], + "angle": 0, + "content": "Fig. 3 shows a visualization of the actual predicted trajectory samples generated by R-Pred using Argoverse validation set. We visualize the final trajectory with the best score produced by R-Pred (red line) and the corresponding trajectory proposal from ITPNet (blue line). We also include the ground truth trajectory (green line). We added the tubular area used for TQSA to the figure (sky blue region). We observe that our refinement network reduced the prediction error in the trajectories generated by ITPNet. Note that in the third column, our refinement stage modifies the initial trajectory proposal off-road to the trajectory within the road. More qualitative results are provided in Supplementary Material." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.639, + 0.634, + 0.654 + ], + "angle": 0, + "content": "6. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.664, + 0.882, + 0.849 + ], + "angle": 0, + "content": "In this paper, we have proposed a two-stage trajectory prediction method, referred to as R-Pred. We have introduced a novel per proposal trajectory refinement strategy in which each trajectory proposal generated in the first-stage network is refined using contextual information tailored to the proposal. TRNet utilized the local scene context captured by pooling scene component features in a tubular region around the trajectory proposal. TRNet also uses the inter-agent interaction context inferred from a group of influential trajectory proposals of neighboring agents. The results of an experimental evaluation conducted on Argoverse and nuScenes benchmark datasets confirmed that R-Pred significantly outperforms existing methods and achieves" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.883, + 0.514, + 0.894 + ], + "angle": 0, + "content": "8532" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.115, + 0.086, + 0.486, + 0.113 + ], + "angle": 0, + "content": "state-of-the-art performance in terms of some evaluation metrics." + }, + { + "type": "title", + "bbox": [ + 0.222, + 0.128, + 0.381, + 0.144 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.115, + 0.152, + 0.486, + 0.252 + ], + "angle": 0, + "content": "This work was partly supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No.2020-0-01373, Artificial Intelligence Graduate School Program(Hanyang University)) and National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.2020R1A2C2012146)." + }, + { + "type": "title", + "bbox": [ + 0.117, + 0.266, + 0.207, + 0.28 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.123, + 0.289, + 0.484, + 0.354 + ], + "angle": 0, + "content": "[1] Alexandre Alahi, Kratarth Goel, Vignesh Ramanathan, Alexandre Robicquet, Li Fei-Fei, and Silvio Savarese. 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In In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 8823-8833, 2022. 2, 3, 5, 6, 7" + }, + { + "type": "list", + "bbox": [ + 0.117, + 0.087, + 0.486, + 0.764 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.485, + 0.883, + 0.514, + 0.894 + ], + "angle": 0, + "content": "8535" + } + ] +] \ No newline at end of file diff --git a/2023/R-Pred_ Two-Stage Motion Prediction Via Tube-Query Attention-Based Trajectory Refinement/cbd955af-2686-4f7c-843a-a3576e04bc6e_origin.pdf b/2023/R-Pred_ Two-Stage Motion Prediction Via Tube-Query Attention-Based Trajectory Refinement/cbd955af-2686-4f7c-843a-a3576e04bc6e_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..06f880efcf19cd69fc47ecb42bf29b4f4773d5b4 --- /dev/null +++ b/2023/R-Pred_ Two-Stage Motion Prediction Via Tube-Query Attention-Based Trajectory Refinement/cbd955af-2686-4f7c-843a-a3576e04bc6e_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8b452137bed113743bbc3edd9dcda63b6015fd2cabc9c20abce9ecd46d9c28ab +size 5644058 diff --git a/2023/R-Pred_ Two-Stage Motion Prediction Via Tube-Query Attention-Based Trajectory Refinement/full.md b/2023/R-Pred_ Two-Stage Motion Prediction Via Tube-Query Attention-Based Trajectory Refinement/full.md new file mode 100644 index 0000000000000000000000000000000000000000..b695572368632d774beac40015bb0374bb82967f --- /dev/null +++ b/2023/R-Pred_ Two-Stage Motion Prediction Via Tube-Query Attention-Based Trajectory Refinement/full.md @@ -0,0 +1,332 @@ +# R-Pred: Two-Stage Motion Prediction Via Tube-Query Attention-Based Trajectory Refinement + +Sehwan Choi $^{1}$ Jungho Kim $^{1}$ Junyong Yun $^{1}$ Jun Won Choi $^{1,2*}$ $^{1}$ Hanyang University and $^{2}$ Qualcomm + +1{sehwanchoi, junghokim, jyyun}@spa.hanyang.ac.kr 1,2 junwchoi@hanyang.ac.kr + +# Abstract + +Predicting the future motion of dynamic agents is of paramount importance to ensuring safety and assessing risks in motion planning for autonomous robots. In this study, we propose a two-stage motion prediction method, called R-Pred, designed to effectively utilize both scene and interaction context using a cascade of the initial trajectory proposal and trajectory refinement networks. The initial trajectory proposal network produces $M$ trajectory proposals corresponding to the $M$ modes of the future trajectory distribution. The trajectory refinement network enhances each of the $M$ proposals using 1) tube-query scene attention (TQSA) and 2) proposal-level interaction attention (PIA) mechanisms. TQSA uses tube-queries to aggregate local scene context features pooled from proximity around trajectory proposals of interest. PIA further enhances the trajectory proposals by modeling inter-agent interactions using a group of trajectory proposals selected by their distances from neighboring agents. Our experiments conducted on Argoverse and nuScenes datasets demonstrate that the proposed refinement network provides significant performance improvements compared to the single-stage baseline and that R-Pred achieves state-of-the-art performance in some categories of the benchmarks. + +# 1. Introduction + +In autonomous vehicles and robotics applications, dynamic objects move in complex environments while avoiding collisions with other agents. Each dynamic agent plans its motion by predicting the future motion and behavior of other agents around it. Motion prediction refers to the task of predicting the future trajectory of dynamic agents based on their historical trajectories and information on the surrounding environment. The task of predicting motion is challenging because the trajectory of an agent is affected + +![](images/b4828ccbee500981864552b324cc20ecc63e308a08c5f7b7dd7b0052fd4ebb48.jpg) +Figure 1. Key concept of R-Pred. R-Pred performs two stages of trajectory prediction. ITPNet produces $M$ trajectory proposals with the corresponding proposal features and TRNet refines each trajectory proposal using separate networks. ITPNet uses a scene context acquired from a relatively large area, whereas TRNet uses a local scene context that exists in a tube-shaped area. TRNet also refines the trajectory proposal using an inter-agent interaction context represented at a proposal level. + +by a variety of contextual factors, which must be taken into account when modeling motion. In the context of autonomous vehicles, examples of such factors include permissible roads, lanes, traffic signals, blinker states, interactions with other agents, and so forth. The difficulty of predicting future motion also arises from the fact that the distribution of future trajectories tends to be multi-modal. In a given scene, a target agent can choose one of several distinct maneuvers such as changing lanes, turning left, turning right, or continuing straight ahead. Accordingly, prediction models should be able to generate one or more plausible future trajectories with probabilities. + +Recently, deep neural networks have been developed as a new paradigm in trajectory prediction, and have achieved + +considerable improvements in performance compared to traditional prediction models through data-driven modeling of trajectory data. Sequence modeling networks such as long short term memory (LSTM) [23] or gated recurrent unit (GRU) [6] architectures have been shown to be effective in representing sequential trajectory data [25, 26]. Trajectory prediction task has been successfully performed using encoder-decoder architectures [35, 53, 29, 30, 16, 19, 45, 55, 43, 32, 26, 15, 17, 10, 8, 20, 24, 40, 28, 36]. Recently, the accuracy of trajectory prediction has been rapidly improved by utilizing various sources of contextual information available for prediction. Numerous methods have jointly modeled the trajectories of multiple neighboring agents to account for their interactions, including socialLSTM [1], soft hardwired attention [12], social GAN [20], MATLAB [54], Trajectron [24, 40], DESIRE [28], DATF [36], and SoPhie [39]. Static scene information around the target agent was also used to generate more physically plausible trajectories. A scene was represented by a two-dimensional raster image that describes the scene [11, 4, 7, 32, 37, 52]. A vector representation of the scene was also proposed for scene encoding [13, 29, 53, 19, 55, 26, 16, 34, 30, 10, 45, 47, 48]. Recently, Transformer models [44] have been used to model the scene and interaction context using the attention mechanism [30, 34, 55, 33, 45, 50]. + +In this paper, we propose a new two-stage motion prediction framework, referred to as $R$ -Pred. As shown in Fig. 1, the proposed R-Pred architecture consists of two-stage networks: an initial trajectory proposal network (ITPNet) and a trajectory refinement network (TRNet). The ITPNet produces $M$ initial trajectory proposals corresponding to the $M$ modes of the trajectory distribution for a target agent. TRNet then refines each trajectory proposal using the contexts customized for each proposal. Using the initial trajectory proposals as a priori information, TRNet can utilize the scene and interaction contexts in more selective and effective ways. + +TRNet employs the following two refinement submodules. First, we present tube-query scene attention (TQSA) to utilize the local scene context effectively. Unlike ITPNet, which uses a global scene context, TQSA extracts local scene context features within a tube-shaped region around each trajectory proposal. (See Fig. 1 for illustration). Then, the extracted scene context features are used to enhance the corresponding trajectory proposal through cross-attention mechanism. TQSA allows the important scene context to be used to improve each $M$ trajectory proposal. Second, we propose the proposal-level interaction attention (PIA) mechanism. PIA models inter-agent interactions using the trajectory proposals produced for multiple neighboring agents by ITPNet. PIA selects a group of trajectory proposals that have the highest influence on the trajectory proposal of interest using the distance-wise proposal + +grouping strategy. The proposal group is used to refine the trajectory of interest through cross-attention. + +In fact, our per-proposal refinement strategy is motivated by two-stage object detectors (e.g., Faster RCNN [38]), where the initial object proposals are first obtained from the entire convolutional neural network (CNN) features and then local features in the region of interest (RoI) are pooled to refine each object proposal [18, 38, 21]. Similarly, RPred generates the context features based on the initial trajectory proposals produced by ITPNet and uses them to refine each proposal. + +By combining these two sub-modules, R-Pred can generate refined trajectory outputs. We evaluated the proposed approach using the widely adopted Argoverse [5] and nuScenes [3] datasets. The results demonstrate that the proposed refinement network significantly improved the accuracy of ITPNet baseline. The results also show that R-Pred achieves the state-of-the-art performance in some categories of official Argoverse and nuScenes leaderboards. + +The main contributions are summarized as follows: + +- We propose a novel trajectory refinement network that refines each of $M$ trajectory proposals using the local scene context and the proposal-level inter-agent interactions. The per-proposal refinement strategy effectively improves the trajectory predictions obtained by the first-stage network. +- We introduce the concept of global-to-local hierarchical attention to effectively utilize the scene context. Our refinement network uses a tube-query to gather the scene context from the local region around the proposal trajectory. The proposed global-to-local hierarchical attention mechanism is contrasted with factorized attention [34, 33], which iterates attention over different sources of context. +- We use trajectory proposals of neighboring agents to model interactions between agents. Using the trajectory proposal features reflecting particular intentions of other agents, PIA can better model inter-agent interactions than the conventional interaction modeling that uses the past trajectory features only. +- R-Pred can use any off-the-shelf single-stage trajectory prediction network as the initial trajectory proposal network. That is, the proposed refinement framework can also be readily applied to any trajectory prediction network available. +- The source code used in this work will be released publicly. + +# 2. Related Works + +# 2.1. Context-Aware Trajectory Prediction + +Numerous methods have improved the performance of trajectory prediction by leveraging the contextual information available for prediction. For example, information on the static scene around a target agent has been utilized as scene context. Raster-based scene encoding uses 2D raster images to summarize scene information and extract semantic features using convolutional neural networks [32, 4, 37, 14, 40, 9, 46]. The advantage of this approach is that different types of scene components can be easily accommodated in a raster image. However, the performance of these methods is limited owing to quantization errors and a lack of receptive fields in the encoding architectures. Vector-based scene encoding represents scene components using vectors, and encodes their relationships using graph structures or attention models [29, 10, 40, 20, 24, 27, 13]. VectorNet [13] introduced a hierarchical graph neural network that exploited the spatial locality of road components by vectorized representation. Similarly, LaneGCN [29] was proposed as an effective graph convolutional network to represent complicated topology and long-range dependency. Trajectory++ [40] employed a directed spatiotemporal graph to represent scene context vectors while incorporating agent dynamics and heterogeneous data. + +The performance of trajectory prediction has also been improved by taking into account interactions with surrounding dynamic agents and static environment information. Social pooling methods pooled the trajectory features of other agents for interaction modeling [1, 28, 20, 39, 8]. Recently, attention mechanisms have been proposed to exploit the meaningful relationships between dynamic agents and lane segments [26, 41, 55, 10, 19, 51, 29, 13, 16, 32, 45, 29]. + +# 2.2. Transformer-based Trajectory Prediction + +Transformer architectures offer an effective method for training attention mechanisms capable of capturing long-range dependencies within sequence data. Recently, Transformers have been adopted for trajectory prediction to model spatio-temporal context as well as interactions between agents [50, 45, 55, 30, 33, 34]. mmTransformer [30] employed an efficient stacked Transformer that applied cross-attention on multi-agent and scene contexts one by one. HiVT [55] summarized the spatio-temporal features of agents using translation-invariant agent-centric local scene structure. In SceneTransformer [34], a simple varying form of self-attention was exploited to integrate various features, generating scene-level consistent predictions for all agents jointly. Along these lines, Wayformer [33] was proposed as a general multi-dimensional attention architecture designed to jointly encode multiple agent trajectories and map data in time, space, and agent dimensions. + +# 3. Problem Setup + +Suppose that the historical trajectory states of $N$ dynamic agents are obtained from the multi-object tracker, where $N$ can vary depending on the scenario. The agent requiring prediction of its future trajectory is denoted as the target agent, while the other agents are termed neighbor agents. The past trajectory states over $T$ time steps for the $i$ -th agent are denoted as $\mathbf{x}_i = [x_i(t - T + 1), x_i(t - T + 2), \dots, x_i(t)]$ , where $t$ denotes the current time step and $x_i(t - s)$ is the state of the $i$ -th agent at the time step $(t - s)$ . The trajectory state is of the form $(x, y, \varepsilon)$ consisting of the $(x, y)$ position and the agent's semantic property $\varepsilon$ . The $(x, y)$ coordinates are represented in the agent-centric reference frame, where the current position of a target agent is the origin and its heading angle is aligned with the positive x-axis. Similarly, the future trajectory states over $F$ time steps for the $i$ -th agent are given by $\mathbf{y}_i = [y_i(t + 1), y_i(t + 2), \dots, y_i(t + F)]$ . We assume that the vector representation of a scene is available along with the trajectory data. For instance, a lane is represented by a set of points on its centerline, where the $(x, y)$ coordinates of each point are expressed in an agent-centric frame. We accommodate different types of scene components by appending an attribute index $\epsilon_l$ to the $(x, y)$ coordinate as $(x, y, \epsilon_l)$ . The set of scene components around the target agent at the time $t$ is expressed as the vector $\xi = [\xi_1, \dots, \xi_L]$ , where the dimension $L$ varies depending on the scene complexity and the region of interest on the map. + +Without loss of generality, let $\mathbf{x}_1$ be the trajectory of the target agent and $\mathbf{x}_2,\dots,\mathbf{x}_N$ be the trajectories of neighboring agents. Finally, the goal of the motion prediction task is to estimate the future trajectory of the target agent $\mathbf{y}_1$ given the past trajectories of $N$ agents $\mathbf{x}_1,\dots,\mathbf{x}_N$ and the scene information $\xi$ . + +# 4. Proposed Trajectory Prediction Network + +In this section, we present the details of the proposed motion prediction method, R-Pred. + +# 4.1. Overall Framework + +An overview of the proposed R-Pred framework is presented in Fig. 2. Our proposed architecture produces $M$ multi-modal trajectory predictions for a target agent over two stages. First, ITPNet produces $M$ trajectory proposals for all $N$ agents present in the scene. Along with the trajectory proposals, ITPNet returns $M$ intermediate features used to produce the trajectory proposals. These features are called proposal features. ITPNet follows traditional trajectory prediction methods for scene and interaction encoding; that is, it utilizes the global scene context features extracted from a fixed region around the current position of the agent. + +![](images/2785089d938485a030f3e888f6d36ff24ca53764386752f92288f13a43b5a711.jpg) +Figure 2. Overall structure of R-Pred. Given the past trajectories of the dynamic agents and the global scene information, ITPNet generates $M$ trajectory proposals for each agent. TRNet refines each of the $M$ trajectory proposals of the target agent through TQSA and PIA. TQSA utilizes local scene context features obtained by tubular region pooling. PIA captures interaction context using the proposal group found by the distance-wise proposal grouping. Finally, the prediction header produces the refined future trajectories based on the joint trajectory features obtained by concatenation of the attention values from TQSA and PIA. + +In addition, the ITPNet exploits the interaction context derived from the past trajectories of $N$ agents. Second, TRNet refines each of the $M$ trajectory proposals of the target agent based on the prior trajectory information generated by the ITPNet. TRNet employs TQSA and PIA to generate the context features customized for each proposal. TQSA extracts the local scene context features cropped from a tube-shaped region around the target trajectory proposal. PIA generates the inter-agent interaction context features using a group of selected proposal trajectories of $N$ agents. The context features generated by TQSA and PIA enhance the proposal features through cross-attention. The final joint trajectory features are obtained by concatenating two attention values from TQSA and PIA. Finally, the prediction head produces $M$ future trajectory predictions and their confidence scores for each target agent. + +# 4.2. Initial Trajectory Proposal Network + +Given the past trajectories $\mathbf{x}_1,\dots,\mathbf{x}_N$ of the $N$ agents present in the scene and the scene information $\xi$ , ITP-Net produces $M$ trajectory proposals and their confidence scores for each agent. $M$ intermediate features, known as proposal features, are also extracted for the subsequent refinement phase. The trajectory proposals, their confidence scores, and the proposal features for the $i$ -th agent are denoted as $\hat{\mathbf{y}}_i = [\hat{\mathbf{y}}_1^1,\dots,\hat{\mathbf{y}}_i^M]$ , $\hat{\mathbf{c}}_i = [\hat{\mathbf{c}}_i^1,\dots,\hat{\mathbf{c}}_i^M]$ , and $\mathbf{f}_i = [\mathbf{f}_i^1,\dots,\mathbf{f}_i^M]$ , respectively. + +# Algorithm 1 Tubular Region Pooling + +Input: Trajectory proposal $\hat{\mathbf{y}}_1^m$ , scene context vectors $\xi$ , scene embedding features $\Psi$ , and thresholding radius $\tau$ . + +Output: Local scene context features $\Psi_1^m$ . + +1: $\Psi_1^m = set()$ +2: for $f \gets t + 1$ to $t + F$ do +3: for each $\xi_l \in \xi$ do +4: $dist = \| \hat{y}_1^m (f) - \xi_l\| _2$ +5: if dist $< \tau$ then +5: $\Psi_1^m$ .add $(\psi_l)$ +6: +7: return $\Psi_1^m$ + +# 4.3. Trajectory Refinement Network + +TRNet refines each of trajectory proposals $\hat{\mathbf{y}}_1$ of the target agent through TQSA and PIA. + +Tube-Query Scene Attention. We construct the set of scene embedding features $\Psi = \{\psi_1,\dots,\psi_L\}$ by encoding each element of $\xi$ via a linear projection, i.e., $\psi_l =$ linear\_proj $(\xi_{l})$ .TQSA pools the scene embedding features in a tubular region around the trajectory proposal on the map from $\Psi$ .We denote the set of scene embedding features prepared for the $m$ th trajectory proposal $\hat{\mathbf{y}}_1^m$ of the target agent as $\Psi_1^m$ . Tubular region pooling is efficiently per + +# Algorithm 2 Distance-Wise Proposal Grouping + +Input: Trajectory proposals $\hat{\mathbf{y}}_1,\dots ,\hat{\mathbf{y}}_N$ proposal confidence scores $\hat{\mathbf{c}}_1,\dots ,\hat{\mathbf{c}}_N$ proposal features $\mathbf{f}_1,\dots ,\mathbf{f}_N$ distance threshold $\mathcal{D}$ and confidence threshold $\mathcal{T}$ + +Output: Proposal group set $\mathcal{G}(\hat{\mathbf{y}}_1^m)$ + +1: for $i \gets 2$ to $N$ do +2: for $m^{\prime}\gets 1$ to $M$ do +3: if $\hat{\mathbf{c}}_j^{m'} > \mathcal{T}$ then +4: $dist = \min_{f\in [t + 1,t + F]}\| \hat{y}_1^m (f) - \hat{y}_i^{m'}(f)\| _2$ +5: if $dist < \mathcal{D}$ then +6: $\mathcal{G}(\hat{\mathbf{y}}_1^m)$ .append $(\mathbf{f}_i^{m'})$ +7: +8: return $\mathcal{G}(\hat{\mathbf{y}}_1^m)$ + +formed to aggregate scene embedding features within the search radius $\tau$ around each waypoint of the trajectory proposal $\hat{\mathbf{y}}_1^m$ . Note that a collection of search disks centered at all waypoints on the trajectory forms an approximately tubular polygon. See Algorithm 1 for further details. + +TQSA decodes the proposal features $\mathbf{f}_1^m$ (associated with $\hat{\mathbf{y}}_1^m$ ) of the target agent by performing cross-attention on the local scene context $\Psi_1^m$ . Specifically, we use the proposal features $\mathbf{f}_1^m$ as the query and the local scene context features $\Psi_1^m$ as the key and value, i.e., + +$$ +Q = \mathbf {f} _ {1} ^ {m} W ^ {Q _ {T Q S A}} \tag {1} +$$ + +$$ +K = \Psi_ {1} ^ {m} W ^ {K _ {T Q S A}} \tag {2} +$$ + +$$ +V = \Psi_ {1} ^ {m} W ^ {V _ {T Q S A}} \tag {3} +$$ + +$$ +\mathcal {A} _ {1} ^ {m} = \operatorname {s o f t m a x} \left(\frac {Q K ^ {\top}}{\sqrt {d _ {k}}}\right) V, \tag {4} +$$ + +where $W^{Q_{TQSA}}$ , $W^{K_{TQSA}}$ , and $W^{V_{TQSA}}$ are learnable weight matrices and $d_k$ is the dimension of the embedding vectors. We combine the attention value $\mathcal{A}_1^m$ and the proposal features $\mathbf{f}_1^m$ using the gating function introduced in [55] + +$$ +\lambda = \sigma \left(\mathrm {f} _ {1} ^ {m} W ^ {\text {i n p u t}} + \mathcal {A} _ {1} ^ {m} W ^ {\text {h i d d e n}}\right) \tag {5} +$$ + +$$ +\mathbf {t} _ {1} ^ {m} = \lambda \odot \mathbf {f} _ {1} ^ {m} W ^ {\text {g a t e}} + (1 - \lambda) \odot \mathcal {A} _ {1} ^ {m} \tag {6} +$$ + +$$ +\mathbf {t} _ {1} ^ {m} = \mathbf {f} _ {1} ^ {m} + \phi \left(\mathbf {t} _ {1} ^ {m}\right), \tag {7} +$$ + +where $W^{input}$ , $W^{hidden}$ , and $W^{gate}$ are learnable matrices, $\odot$ indicates element-wise product, $\sigma$ indicates the sigmoid function and $\phi(\cdot)$ denotes a multi-layer perceptron (MLP). We add layer normalization [2], Dropout [42], and residual connection [22] in the middle of the attention process. + +Note that the aforementioned local scene attention process to produce the output of TQSA $\mathbf{t}_1^m$ is performed for each trajectory proposal (for each $m$ value) in parallel. + +Proposal-level Interaction Attention. PIA uses a distance-wise proposal grouping algorithm to find a group + +of the trajectory proposals for the nearby agents to model their inter-agent interactions. First, among $MN$ trajectory proposals from $N$ agents, those with a confidence score below the threshold $\mathcal{T}$ are discarded because they are unlikely to occur. Subsequently, for a given $m$ -th trajectory proposal $\hat{\mathbf{y}}_1^m$ of the target agent, the algorithm selects the trajectory proposals of the nearby agents, whose distance from $\hat{\mathbf{y}}_1^m$ is closer than the distance threshold $\mathcal{D}$ . These are considered the most influential trajectory proposals to use for interaction modeling. A distance between two trajectories $\mathbf{y}_1^\star$ and $\mathbf{y}_2^\star$ is defined by + +$$ +\operatorname {d i s t} \left(\mathbf {y} _ {1} ^ {\star}, \mathbf {y} _ {2} ^ {\star}\right) = \min _ {f \in [ t + 1, t + F ]} \| \mathbf {y} _ {1} ^ {\star} (f) - \mathbf {y} _ {2} ^ {\star} (f) \| _ {2}. \tag {8} +$$ + +For the selected trajectory proposals, the algorithm groups the corresponding proposal features into the proposal feature group $\mathcal{G}(\hat{\mathbf{y}}_1^m)$ . The distance-wise proposal grouping algorithm is summarized in Algorithm 2. + +The proposal feature group is used to decode the proposal features $\mathbf{f}_1^m$ through cross-attention. Using $\mathbf{f}_1^m$ as query and $\mathcal{G}(\mathbf{y}_1^m)$ as key and value, the cross-attention module produces the attention value $\mathbf{p}_1^m$ similarly to Eq. (1) - (7). + +Multi-modal Prediction Head. TRNet constructs the final joint trajectory feature $\mathbf{j}_1^m$ by concatenating the attention output $\mathbf{t}_1^m$ from TQSA and the attention output $\mathbf{p}_1^m$ from PIA. The prediction head is then applied to $\mathbf{j}_1^m$ to produce the refined trajectories and the confidence scores. The prediction head consists of the regression branch and a classification branch. First, by modeling the trajectory points as multi-variate random vectors with independent Laplace distribution, the regression branch applies an MLP to $\mathbf{j}_1^m$ to predict the mean and covariance of $\mathbf{y}_1$ . The predicted mean is denoted as $\tilde{\mathbf{y}}_1^m = [\tilde{y}_1^m (t + 1),\dots,\tilde{y}_1^m (t + F)]$ and the predicted variance is denoted as $\mathbf{b}_1^m = [\tilde{b}_1^m (t + 1),\dots,\tilde{b}_1^m (t + F)]$ . The regression branch is applied separately for each mode $m$ . Next, the classification branch applies another MLP to the concatenation of $\mathbf{j}_1^1,\dots,\mathbf{j}_1^M$ to produce the confidence scores $\check{\mathbf{c}}_1^1,\dots,\check{\mathbf{c}}_1^M$ for all modes. + +# 4.4. Training Details + +The total loss function $L_{total}$ used to train the entire network is given by + +$$ +L _ {t o t a l} = \alpha L _ {r e g. p r o} + \beta L _ {c l s. p r o} + \gamma L _ {r e g. r e f} + \delta L _ {c l s. r e f}, +$$ + +where $L_{reg-pro}$ and $L_{reg-ref}$ are the regression loss functions for ITPNet, and TRNet and $L_{cls-pro}$ and $L_{cls-ref}$ are the classification loss functions for ITPNet, and TRNet. We used $\alpha = \beta = \gamma = \delta = 1$ in our setup. The negative log-likelihood function for the Laplace distribution is used for $L_{reg-ref}$ as follows, + +$$ +L _ {r e g - r e f} = - \frac {1}{N F} \sum_ {n = 1} ^ {N} \sum_ {f = t + 1} ^ {t + F} \log \mathbb {P} \left(y _ {n} (f) \mid \check {y} _ {n} ^ {m ^ {*}} (f), \check {\mathbf {b}} _ {n} ^ {m ^ {*}} (f)\right), +$$ + +
MethodminADE1minFDE1minADE6minFDE6brierFDE6MR6%
LaneRCNN[51]1.693.690.901.452.1512.3
LaPred[26]1.934.330.911.502.1318.0
TNT[53]2.174.960.911.452.1416.6
PRIME[41]1.913.821.221.562.1011.5
HOME[14]1.723.730.921.36-11.3
LaneGCN[29]1.703.760.871.362.0516.2
mmTransformer[30]1.774.000.841.342.0315.4
DenseTNT[19]1.683.630.881.281.9812.6
THOMAS[16]1.673.590.941.441.9710.3
SceneTransformer[34]1.813.620.801.231.8912.5
LTP[45]1.623.550.831.301.8614.7
HOME+GOHOME[15]1.703.680.891.291.868.5
TPCN[49]1.663.690.871.38-15.8
HiVT[55]1.603.520.771.171.8412.7
MultiPath++[43]1.623.610.791.211.7913.2
Wayformer[33]1.643.670.771.161.7411.9
ITPNet baseline1.623.570.791.211.8613.1
R-Pred1.583.470.761.121.7711.6
+ +where $\mathbb{P}(\cdot |\cdot)$ is the probability density function of Laplace distribution. $L_{reg - pro}$ is defined similarly. When evaluating the loss function during training, we adopt a winner-takes-all strategy [7] in which the mode $m^{*}$ of the trajectory output that yields the smallest average displacement error is used, i.e., $m^{*} = \underset {m\in [1,M]}{\mathrm{argmin}}\sum_{f = t + 1}^{t + F}\| y_n(f) - \tilde{y}_n^m (f)\| _2.$ + +We used the cross entropy loss for the classification losses $L_{cls-pro}$ and $L_{cls-ref}$ . We trained the entire network end-to-end with random initialization. + +Table 1. Performance comparison on Argoverse test set in the official leaderboard. The best performed metrics are shown in bold. The "-" symbol means the corresponding metric is unknown, either because the authors have not disclosed it or it was not specified in the leaderboard. Our model achieves the state-of-the-art performance in terms of the $\text{minADE}_1$ , $\text{minFDE}_1$ , $\text{minADE}_6$ and $\text{minFDE}_6$ metrics. + +
Method\( mADE_5 \)\( mFDE_5 \)\( mADE_{10} \)\( mFDE_{10} \)
MTP[7]2.224.831.743.54
CoverNet[37]1.96-1.48-
Trajectory++[40]1.88-1.51-
MHA-JAM[32]1.813.721.242.21
MultiPath[4]1.783.621.552.93
CXX[31]1.63-1.29-
LaPred[26]1.533.371.122.39
P2T[9]1.45-1.16-
THOMAS[16]1.33-1.04-
PGP[10]1.272.470.941.55
ITPNet baseline1.292.580.971.60
R-Pred1.192.280.941.50
+ +Table 2. Performance comparison on nuScenes validation set in the official leaderboard. The "-" symbol means the corresponding metric unknown. Our model achieves state-of-the-art performance on all metrics. + +# 5. Experiments + +In this section, we describe the experimental setup used to evaluate the performance of the proposed R-Pred, and present both quantitative and qualitative analyses of the behavior of the model. + +Datasets. Both Argoverse [5] and nuScenes [3] datasets provide dynamic agent trajectories and HD-map in real-world driving scenarios. The Argoverse dataset was collected from two US cities, including Miami and Pittsburgh. Each sample contains 5 seconds trajectories of tracked vehicles sampled at $10\mathrm{Hz}$ . Argoverse dataset provides HD-map with detailed lane information. The prediction task is to predict future trajectories for 3 seconds given past trajectories of 2 seconds. The dataset contains 205,942 training, 39,272 validation, and 78,143 test samples. + +The nuScenes dataset was collected in Boston and Singapore. The collected trajectories are 6 seconds long and are sampled at $2\mathrm{Hz}$ . The prediction task is defined as that of predicting future trajectories for 6 seconds given past trajectories of 2 seconds. HD-map is also provided along with the trajectory data. The dataset is split into 32, 186 training, 8,560 validation, and 9,041 test samples. + +Metrics. For the performance evaluation, we adopt widely used performance metrics including average displacement error (ADE), final displacement error (FDE), and miss rate (MR). ADE refers to the mean square error compared to the ground truth over the entire time steps, and FDE is + +![](images/397dbd67b850d1794c6a5b24d2d378251ec0621a35a4dbd005305e2dd846cb24.jpg) + +![](images/d3db5eb23a31014b0d5feee0ebc2fcceee3ac003e79d99139615b7506c951530.jpg) + +![](images/0e0242d1f23d0e23b28c59de90f6ef36c2406efe8595881b659421bb94e00da1.jpg) + +![](images/53364e555fd46ce8f6755ed56e1afb260f6811e1fec9d8c7fb0e3d5129af6b85.jpg) + +![](images/7daae0af989f1544d25790833dfb0ae5ad9899bb632e4f55e23d0ae389c5de66.jpg) +Figure 3. Qualitative results of R-Pred on Argoverse validation set. Yellow, green, blue, and red lines represent the history, ground truth, the initial trajectory proposal with the highest score, and the final (refined) trajectory, respectively. The sky blue region denotes tubular regions used for TQSA. These figures present different vehicle motion scenarios such as continuing straight ahead, turning left, slowing down, changing lanes, etc. + +![](images/ab605dc8d31eb3288a15c2c9d5748a1bbb6eaf89109e012a195e717bacef7255.jpg) + +![](images/5b56582c0e867255c05a66d5d92cda37b929f7a38b7aeffca768b7d3b2b2aadf.jpg) + +![](images/272bd5f915a53bd85fc7ae021652bef873c919c02b777b99d20e6d8bdcdcfcb2.jpg) + +We evaluate the prediction accuracy with $M > 1$ trajectory predictions using minADEM and minFDEM, which are the minimum ADE and FDE over $M$ predicted trajectories, respectively. $MR_{M}$ measures the ratio within 2 meters of the endpoint of the best-predicted trajectory and ground truth. We also use brier minimum FDE (brierFDEM), which measures the value of minFDEM + (1 - p)², where $p$ is corresponding trajectory probability. This imposes a penalty when the probability of the best trajectory is low. Implementation Details. We set the threshold $\mathcal{D}$ and $\mathcal{T}$ of PIA to 0.1 and 10 meters and $\tau$ of TQSA to 20 meters. The embedding size of all features is set to 128 for comparative performance analysis. We used existing prediction architectures for the ITPNet. We chose the structure of [55] on Argoverse and that of [10] on nuScenes. These models achieved excellent performance on both benchmarks. They are considered ITPNet baselines and are used to measure the performance gain achieved by our refinement network. We trained the proposed model on TiTAN RTX GPU for 64 epochs with 32 batch sizes. The data are batched randomly. For all experiments, we trained the model using AdamW optimizer with an initial learning rate of 5e-4. We used cosine annealing to decay the learning rate and applied dropout with a 0.1 ratio. Data augmentation was not used. + +# 5.1.Quantitative Results + +Table 1 presents the performance of R-Pred evaluated on Argoverse test set. We compare the performance of R-Pred with that of several top ranked models [51, 53, 41, 29, 14, + +
ITPNetPIATQSAminADE6minFDE6MR6%
✓0.6941.05710.63
✓✓0.6770.9929.64
✓✓✓0.6570.9458.69
+ +Table 3. Contributions of the main components evaluated on the Argoverse validation set. + +30, 19, 16, 34, 45, 15, 49, 43, 33, 55]. R-Pred achieves the best prediction accuracy in terms of the $\text{minADE}_1$ , $\text{minFDE}_1$ , $\text{minADE}_6$ and $\text{minFDE}_6$ metrics and competitive performance in terms of $\text{brierFDE}_6$ and $\text{MR}_6$ . R-Pred sets a new state-of-the-art performance surpassing the current best methods, Wayformer [33] and Multi-Path++ [43]. Compared to the ITPNet baseline, the proposed method offers performance improvements of $3.80\%$ and $7.43\%$ in terms of $\text{minADE}_6$ , and $\text{minFDE}_6$ , respectively. This indicates that our trajectory refinement strategy can effectively improve the reliability and robustness of the initial prediction using ITPNet. + +Table 2 presents the performance of several motion prediction methods on nuScenes validation set. We compare R-Pred with the top ranked methods [37, 40, 32, 4, 31, 26, 9, 16, 10] on the nuScenes leaderboard. R-Pred achieves significant performance gains compared with other prediction methods. R-Pred exhibits the performance gain of $7.75\%$ and $11.62\%$ in $\min ADE_5$ and $\min FDE_5$ compared to the ITPNet baseline. These results demonstrate that the proposed two refinement modules have high-quality learning + +capabilities. + +
τminADE6minFDE6MR6%
50.6590.9578.927
100.6580.9528.840
200.6570.9458.698
300.6570.9468.714
500.6590.9548.878
+ +Table 4. Performance versus $\tau$ parameter of TQSA evaluated on the Argoverse validation set. + +
DminADE6minFDE6MR6%
50.6590.9488.802
100.6570.9458.698
200.6580.9478.730
300.6590.9498.811
400.6590.9508.821
+ +# 5.2. Ablation Study + +We conducted several ablation studies on the Argoverse validation set. We reduced the training time required to conduct the ablation study by decreasing the feature size from 128 to 64 and increasing the batch size from 32 to 64. The trained model was evaluated on the entire validation set. + +Contribution of Each Module. Table 3 shows the contributions of each module to overall performance achieved by R-Pred. We evaluated performance as we added each component one by one. We consider the following three modules of R-Pred: 1) ITPNet baseline, 2) PIA, and 3) TQSA. When the PIA is added to ITPNet baseline, the $\text{minFDE}_6$ improves by $6.15\%$ and $MR_6$ improves by $9.31\%$ . This indicates the effectiveness of inter-agent interaction modeling by PIA. When TQSA is added, it achieves the performance gains of $4.74\%$ and $9.85\%$ in $\text{minFDE}_6$ and $MR_6$ . We observe that proposal refinement using local scene context improves the performance significantly. Finally, the combination of PIA and TQSA has improved the performance of ITPNet baseline by $10.6\%$ and $18.25\%$ , in $\text{minFDE}_6$ and $MR_6$ , respectively. + +Performance Versus $\tau$ and $\mathcal{D}$ . We investigated the impact of the parameters $\tau$ and $\mathcal{D}$ on the performance. Recall that $\tau$ and $\mathcal{D}$ are the distance thresholds used in TQSA and PIA, respectively. Table 4 presents the performance of R-Pred evaluated for several values of $\tau = \{5,10,20,30,50\}$ . R-Pred performs best at $\tau = 20,30$ , and degrades as $\tau$ becomes larger or smaller than these values. This is likely due to the fact that when the threshold gets too large, a lot of irrelevant scene context can be used for cross-attrbution. + +Table 5 presents the performance of R-Pred for several values of $\mathcal{D} = \{5,10,20,30,40\}$ . R-Pred achieves the best performance with $\mathcal{D} = 10$ . Note that increasing the threshold $\mathcal{D}$ above 10 does not improve performance. + +Effect of Per-proposal Scene Context Strategy. One of our key innovations is to use the tube-query for pooling the customized scene context for each proposal. We investigated the benefit of our per-proposal feature pooling method. We compare R-Pred with the baseline that shares the global scene context features for all proposals in the refinement step. Table 6 shows that our strategy offers $1.76\%$ and $3.24\%$ performance gains in $minFDE_{6}$ and $MR_{6}$ over the baseline, which confirms the advantage of the proposed per-proposal feature pooling method. + +Table 5. Performance versus $\mathcal{D}$ parameter of PIA evaluated on the Argoverse validation set. + +
Per-proposal scene contextShared scene contextminADE6minFDE6MR6%
✓0.6620.9628.981
✓0.6570.9458.69
+ +Table 6. Comparison of per-proposal scene context versus shared scene context evaluated on the Argoverse validation set. + +# 5.3. Qualitative Results + +Fig. 3 shows a visualization of the actual predicted trajectory samples generated by R-Pred using Argoverse validation set. We visualize the final trajectory with the best score produced by R-Pred (red line) and the corresponding trajectory proposal from ITPNet (blue line). We also include the ground truth trajectory (green line). We added the tubular area used for TQSA to the figure (sky blue region). We observe that our refinement network reduced the prediction error in the trajectories generated by ITPNet. Note that in the third column, our refinement stage modifies the initial trajectory proposal off-road to the trajectory within the road. More qualitative results are provided in Supplementary Material. + +# 6. Conclusions + +In this paper, we have proposed a two-stage trajectory prediction method, referred to as R-Pred. We have introduced a novel per proposal trajectory refinement strategy in which each trajectory proposal generated in the first-stage network is refined using contextual information tailored to the proposal. TRNet utilized the local scene context captured by pooling scene component features in a tubular region around the trajectory proposal. TRNet also uses the inter-agent interaction context inferred from a group of influential trajectory proposals of neighboring agents. The results of an experimental evaluation conducted on Argoverse and nuScenes benchmark datasets confirmed that R-Pred significantly outperforms existing methods and achieves + +state-of-the-art performance in terms of some evaluation metrics. + +# Acknowledgements + +This work was partly supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No.2020-0-01373, Artificial Intelligence Graduate School Program(Hanyang University)) and National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.2020R1A2C2012146). + +# References + +[1] Alexandre Alahi, Kratarth Goel, Vignesh Ramanathan, Alexandre Robicquet, Li Fei-Fei, and Silvio Savarese. Social lstm: Human trajectory prediction in crowded spaces. In In Proceedings of the IEEE conference on computer vision and pattern recognition (CVPR), pages 961-971, 2016. 2, 3 +[2] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. 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In this study, we propose a two-stage motion prediction method, called R-Pred, designed to effectively utilize both scene and interaction context using a cascade of the initial trajectory proposal and trajectory refinement networks. The initial trajectory proposal network produces " + }, + { + "bbox": [ + 69, + 247, + 298, + 506 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 69, + 247, + 298, + 506 + ], + "type": "text", + "content": " trajectory proposals corresponding to the " + }, + { + "bbox": [ + 69, + 247, + 298, + 506 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 69, + 247, + 298, + 506 + ], + "type": "text", + "content": " modes of the future trajectory distribution. 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Our experiments conducted on Argoverse and nuScenes datasets demonstrate that the proposed refinement network provides significant performance improvements compared to the single-stage baseline and that R-Pred achieves state-of-the-art performance in some categories of the benchmarks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 70, + 530, + 146, + 542 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 530, + 146, + 542 + ], + "spans": [ + { + "bbox": [ + 70, + 530, + 146, + 542 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 69, + 550, + 298, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 550, + 298, + 652 + ], + "spans": [ + { + "bbox": [ + 69, + 550, + 298, + 652 + ], + "type": "text", + "content": "In autonomous vehicles and robotics applications, dynamic objects move in complex environments while avoiding collisions with other agents. Each dynamic agent plans its motion by predicting the future motion and behavior of other agents around it. Motion prediction refers to the task of predicting the future trajectory of dynamic agents based on their historical trajectories and information on the surrounding environment. The task of predicting motion is challenging because the trajectory of an agent is affected" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 319, + 222, + 535, + 400 + ], + "blocks": [ + { + "bbox": [ + 319, + 222, + 535, + 400 + ], + "lines": [ + { + "bbox": [ + 319, + 222, + 535, + 400 + ], + "spans": [ + { + "bbox": [ + 319, + 222, + 535, + 400 + ], + "type": "image", + "image_path": "b4828ccbee500981864552b324cc20ecc63e308a08c5f7b7dd7b0052fd4ebb48.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 406, + 541, + 490 + ], + "lines": [ + { + "bbox": [ + 313, + 406, + 541, + 490 + ], + "spans": [ + { + "bbox": [ + 313, + 406, + 541, + 490 + ], + "type": "text", + "content": "Figure 1. Key concept of R-Pred. R-Pred performs two stages of trajectory prediction. ITPNet produces " + }, + { + "bbox": [ + 313, + 406, + 541, + 490 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 406, + 541, + 490 + ], + "type": "text", + "content": " trajectory proposals with the corresponding proposal features and TRNet refines each trajectory proposal using separate networks. ITPNet uses a scene context acquired from a relatively large area, whereas TRNet uses a local scene context that exists in a tube-shaped area. TRNet also refines the trajectory proposal using an inter-agent interaction context represented at a proposal level." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 312, + 512, + 541, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 512, + 541, + 647 + ], + "spans": [ + { + "bbox": [ + 312, + 512, + 541, + 647 + ], + "type": "text", + "content": "by a variety of contextual factors, which must be taken into account when modeling motion. In the context of autonomous vehicles, examples of such factors include permissible roads, lanes, traffic signals, blinker states, interactions with other agents, and so forth. The difficulty of predicting future motion also arises from the fact that the distribution of future trajectories tends to be multi-modal. In a given scene, a target agent can choose one of several distinct maneuvers such as changing lanes, turning left, turning right, or continuing straight ahead. Accordingly, prediction models should be able to generate one or more plausible future trajectories with probabilities." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 649, + 541, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 649, + 541, + 672 + ], + "spans": [ + { + "bbox": [ + 313, + 649, + 541, + 672 + ], + "type": "text", + "content": "Recently, deep neural networks have been developed as a new paradigm in trajectory prediction, and have achieved" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 85, + 36, + 127, + 64 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 36, + 127, + 64 + ], + "spans": [ + { + "bbox": [ + 85, + 36, + 127, + 64 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 159, + 34, + 478, + 67 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 159, + 34, + 478, + 67 + ], + "spans": [ + { + "bbox": [ + 159, + 34, + 478, + 67 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 81, + 661, + 201, + 671 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 661, + 201, + 671 + ], + "spans": [ + { + "bbox": [ + 81, + 661, + 201, + 671 + ], + "type": "text", + "content": "*Corresponding author: Jun Won Choi." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 699, + 314, + 708 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 699, + 314, + 708 + ], + "spans": [ + { + "bbox": [ + 296, + 699, + 314, + 708 + ], + "type": "text", + "content": "8525" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 70, + 68, + 297, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 68, + 297, + 350 + ], + "spans": [ + { + "bbox": [ + 70, + 68, + 297, + 350 + ], + "type": "text", + "content": "considerable improvements in performance compared to traditional prediction models through data-driven modeling of trajectory data. Sequence modeling networks such as long short term memory (LSTM) [23] or gated recurrent unit (GRU) [6] architectures have been shown to be effective in representing sequential trajectory data [25, 26]. Trajectory prediction task has been successfully performed using encoder-decoder architectures [35, 53, 29, 30, 16, 19, 45, 55, 43, 32, 26, 15, 17, 10, 8, 20, 24, 40, 28, 36]. Recently, the accuracy of trajectory prediction has been rapidly improved by utilizing various sources of contextual information available for prediction. Numerous methods have jointly modeled the trajectories of multiple neighboring agents to account for their interactions, including socialLSTM [1], soft hardwired attention [12], social GAN [20], MATLAB [54], Trajectron [24, 40], DESIRE [28], DATF [36], and SoPhie [39]. Static scene information around the target agent was also used to generate more physically plausible trajectories. A scene was represented by a two-dimensional raster image that describes the scene [11, 4, 7, 32, 37, 52]. A vector representation of the scene was also proposed for scene encoding [13, 29, 53, 19, 55, 26, 16, 34, 30, 10, 45, 47, 48]. Recently, Transformer models [44] have been used to model the scene and interaction context using the attention mechanism [30, 34, 55, 33, 45, 50]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 70, + 353, + 298, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 353, + 298, + 489 + ], + "spans": [ + { + "bbox": [ + 70, + 353, + 298, + 489 + ], + "type": "text", + "content": "In this paper, we propose a new two-stage motion prediction framework, referred to as " + }, + { + "bbox": [ + 70, + 353, + 298, + 489 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 70, + 353, + 298, + 489 + ], + "type": "text", + "content": "-Pred. As shown in Fig. 1, the proposed R-Pred architecture consists of two-stage networks: an initial trajectory proposal network (ITPNet) and a trajectory refinement network (TRNet). The ITPNet produces " + }, + { + "bbox": [ + 70, + 353, + 298, + 489 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 70, + 353, + 298, + 489 + ], + "type": "text", + "content": " initial trajectory proposals corresponding to the " + }, + { + "bbox": [ + 70, + 353, + 298, + 489 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 70, + 353, + 298, + 489 + ], + "type": "text", + "content": " modes of the trajectory distribution for a target agent. TRNet then refines each trajectory proposal using the contexts customized for each proposal. Using the initial trajectory proposals as a priori information, TRNet can utilize the scene and interaction contexts in more selective and effective ways." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 70, + 491, + 298, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 491, + 298, + 673 + ], + "spans": [ + { + "bbox": [ + 70, + 491, + 298, + 673 + ], + "type": "text", + "content": "TRNet employs the following two refinement submodules. First, we present tube-query scene attention (TQSA) to utilize the local scene context effectively. Unlike ITPNet, which uses a global scene context, TQSA extracts local scene context features within a tube-shaped region around each trajectory proposal. (See Fig. 1 for illustration). Then, the extracted scene context features are used to enhance the corresponding trajectory proposal through cross-attention mechanism. TQSA allows the important scene context to be used to improve each " + }, + { + "bbox": [ + 70, + 491, + 298, + 673 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 70, + 491, + 298, + 673 + ], + "type": "text", + "content": " trajectory proposal. Second, we propose the proposal-level interaction attention (PIA) mechanism. PIA models inter-agent interactions using the trajectory proposals produced for multiple neighboring agents by ITPNet. PIA selects a group of trajectory proposals that have the highest influence on the trajectory proposal of interest using the distance-wise proposal" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 313, + 68, + 539, + 90 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 68, + 539, + 90 + ], + "spans": [ + { + "bbox": [ + 313, + 68, + 539, + 90 + ], + "type": "text", + "content": "grouping strategy. The proposal group is used to refine the trajectory of interest through cross-attention." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 313, + 92, + 541, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 92, + 541, + 193 + ], + "spans": [ + { + "bbox": [ + 313, + 92, + 541, + 193 + ], + "type": "text", + "content": "In fact, our per-proposal refinement strategy is motivated by two-stage object detectors (e.g., Faster RCNN [38]), where the initial object proposals are first obtained from the entire convolutional neural network (CNN) features and then local features in the region of interest (RoI) are pooled to refine each object proposal [18, 38, 21]. Similarly, RPred generates the context features based on the initial trajectory proposals produced by ITPNet and uses them to refine each proposal." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 195, + 541, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 195, + 541, + 285 + ], + "spans": [ + { + "bbox": [ + 313, + 195, + 541, + 285 + ], + "type": "text", + "content": "By combining these two sub-modules, R-Pred can generate refined trajectory outputs. We evaluated the proposed approach using the widely adopted Argoverse [5] and nuScenes [3] datasets. The results demonstrate that the proposed refinement network significantly improved the accuracy of ITPNet baseline. The results also show that R-Pred achieves the state-of-the-art performance in some categories of official Argoverse and nuScenes leaderboards." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 325, + 287, + 521, + 298 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 287, + 521, + 298 + ], + "spans": [ + { + "bbox": [ + 325, + 287, + 521, + 298 + ], + "type": "text", + "content": "The main contributions are summarized as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 325, + 311, + 541, + 671 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 325, + 311, + 541, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 311, + 541, + 378 + ], + "spans": [ + { + "bbox": [ + 325, + 311, + 541, + 378 + ], + "type": "text", + "content": "- We propose a novel trajectory refinement network that refines each of " + }, + { + "bbox": [ + 325, + 311, + 541, + 378 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 325, + 311, + 541, + 378 + ], + "type": "text", + "content": " trajectory proposals using the local scene context and the proposal-level inter-agent interactions. The per-proposal refinement strategy effectively improves the trajectory predictions obtained by the first-stage network." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 325, + 392, + 541, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 392, + 541, + 483 + ], + "spans": [ + { + "bbox": [ + 325, + 392, + 541, + 483 + ], + "type": "text", + "content": "- We introduce the concept of global-to-local hierarchical attention to effectively utilize the scene context. Our refinement network uses a tube-query to gather the scene context from the local region around the proposal trajectory. The proposed global-to-local hierarchical attention mechanism is contrasted with factorized attention [34, 33], which iterates attention over different sources of context." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 325, + 497, + 541, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 497, + 541, + 564 + ], + "spans": [ + { + "bbox": [ + 325, + 497, + 541, + 564 + ], + "type": "text", + "content": "- We use trajectory proposals of neighboring agents to model interactions between agents. Using the trajectory proposal features reflecting particular intentions of other agents, PIA can better model inter-agent interactions than the conventional interaction modeling that uses the past trajectory features only." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 325, + 578, + 539, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 578, + 539, + 634 + ], + "spans": [ + { + "bbox": [ + 325, + 578, + 539, + 634 + ], + "type": "text", + "content": "- R-Pred can use any off-the-shelf single-stage trajectory prediction network as the initial trajectory proposal network. That is, the proposed refinement framework can also be readily applied to any trajectory prediction network available." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 325, + 649, + 539, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 649, + 539, + 671 + ], + "spans": [ + { + "bbox": [ + 325, + 649, + 539, + 671 + ], + "type": "text", + "content": "- The source code used in this work will be released publicly." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 699, + 315, + 708 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 699, + 315, + 708 + ], + "spans": [ + { + "bbox": [ + 296, + 699, + 315, + 708 + ], + "type": "text", + "content": "8526" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 70, + 67, + 156, + 78 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 67, + 156, + 78 + ], + "spans": [ + { + "bbox": [ + 70, + 67, + 156, + 78 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 70, + 86, + 255, + 98 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 86, + 255, + 98 + ], + "spans": [ + { + "bbox": [ + 70, + 86, + 255, + 98 + ], + "type": "text", + "content": "2.1. Context-Aware Trajectory Prediction" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 72, + 103, + 297, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 103, + 297, + 362 + ], + "spans": [ + { + "bbox": [ + 72, + 103, + 297, + 362 + ], + "type": "text", + "content": "Numerous methods have improved the performance of trajectory prediction by leveraging the contextual information available for prediction. For example, information on the static scene around a target agent has been utilized as scene context. Raster-based scene encoding uses 2D raster images to summarize scene information and extract semantic features using convolutional neural networks [32, 4, 37, 14, 40, 9, 46]. The advantage of this approach is that different types of scene components can be easily accommodated in a raster image. However, the performance of these methods is limited owing to quantization errors and a lack of receptive fields in the encoding architectures. Vector-based scene encoding represents scene components using vectors, and encodes their relationships using graph structures or attention models [29, 10, 40, 20, 24, 27, 13]. VectorNet [13] introduced a hierarchical graph neural network that exploited the spatial locality of road components by vectorized representation. Similarly, LaneGCN [29] was proposed as an effective graph convolutional network to represent complicated topology and long-range dependency. Trajectory++ [40] employed a directed spatiotemporal graph to represent scene context vectors while incorporating agent dynamics and heterogeneous data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 363, + 296, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 363, + 296, + 454 + ], + "spans": [ + { + "bbox": [ + 69, + 363, + 296, + 454 + ], + "type": "text", + "content": "The performance of trajectory prediction has also been improved by taking into account interactions with surrounding dynamic agents and static environment information. Social pooling methods pooled the trajectory features of other agents for interaction modeling [1, 28, 20, 39, 8]. Recently, attention mechanisms have been proposed to exploit the meaningful relationships between dynamic agents and lane segments [26, 41, 55, 10, 19, 51, 29, 13, 16, 32, 45, 29]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 70, + 462, + 274, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 462, + 274, + 474 + ], + "spans": [ + { + "bbox": [ + 70, + 462, + 274, + 474 + ], + "type": "text", + "content": "2.2. Transformer-based Trajectory Prediction" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 69, + 480, + 297, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 480, + 297, + 672 + ], + "spans": [ + { + "bbox": [ + 69, + 480, + 297, + 672 + ], + "type": "text", + "content": "Transformer architectures offer an effective method for training attention mechanisms capable of capturing long-range dependencies within sequence data. Recently, Transformers have been adopted for trajectory prediction to model spatio-temporal context as well as interactions between agents [50, 45, 55, 30, 33, 34]. mmTransformer [30] employed an efficient stacked Transformer that applied cross-attention on multi-agent and scene contexts one by one. HiVT [55] summarized the spatio-temporal features of agents using translation-invariant agent-centric local scene structure. In SceneTransformer [34], a simple varying form of self-attention was exploited to integrate various features, generating scene-level consistent predictions for all agents jointly. Along these lines, Wayformer [33] was proposed as a general multi-dimensional attention architecture designed to jointly encode multiple agent trajectories and map data in time, space, and agent dimensions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 314, + 67, + 400, + 79 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 67, + 400, + 79 + ], + "spans": [ + { + "bbox": [ + 314, + 67, + 400, + 79 + ], + "type": "text", + "content": "3. Problem Setup" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "spans": [ + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": "Suppose that the historical trajectory states of " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": " dynamic agents are obtained from the multi-object tracker, where " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": " can vary depending on the scenario. The agent requiring prediction of its future trajectory is denoted as the target agent, while the other agents are termed neighbor agents. The past trajectory states over " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": " time steps for the " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": "-th agent are denoted as " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i = [x_i(t - T + 1), x_i(t - T + 2), \\dots, x_i(t)]" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": " denotes the current time step and " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "x_i(t - s)" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": " is the state of the " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": "-th agent at the time step " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "(t - s)" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": ". The trajectory state is of the form " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "(x, y, \\varepsilon)" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": " consisting of the " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "(x, y)" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": " position and the agent's semantic property " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "(x, y)" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": " coordinates are represented in the agent-centric reference frame, where the current position of a target agent is the origin and its heading angle is aligned with the positive x-axis. Similarly, the future trajectory states over " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": " time steps for the " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": "-th agent are given by " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i = [y_i(t + 1), y_i(t + 2), \\dots, y_i(t + F)]" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": ". We assume that the vector representation of a scene is available along with the trajectory data. For instance, a lane is represented by a set of points on its centerline, where the " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "(x, y)" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": " coordinates of each point are expressed in an agent-centric frame. We accommodate different types of scene components by appending an attribute index " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "\\epsilon_l" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": " to the " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "(x, y)" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": " coordinate as " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "(x, y, \\epsilon_l)" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": ". The set of scene components around the target agent at the time " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": " is expressed as the vector " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "\\xi = [\\xi_1, \\dots, \\xi_L]" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": ", where the dimension " + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 313, + 86, + 541, + 400 + ], + "type": "text", + "content": " varies depending on the scene complexity and the region of interest on the map." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 402, + 541, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 402, + 541, + 469 + ], + "spans": [ + { + "bbox": [ + 313, + 402, + 541, + 469 + ], + "type": "text", + "content": "Without loss of generality, let " + }, + { + "bbox": [ + 313, + 402, + 541, + 469 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_1" + }, + { + "bbox": [ + 313, + 402, + 541, + 469 + ], + "type": "text", + "content": " be the trajectory of the target agent and " + }, + { + "bbox": [ + 313, + 402, + 541, + 469 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_2,\\dots,\\mathbf{x}_N" + }, + { + "bbox": [ + 313, + 402, + 541, + 469 + ], + "type": "text", + "content": " be the trajectories of neighboring agents. Finally, the goal of the motion prediction task is to estimate the future trajectory of the target agent " + }, + { + "bbox": [ + 313, + 402, + 541, + 469 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_1" + }, + { + "bbox": [ + 313, + 402, + 541, + 469 + ], + "type": "text", + "content": " given the past trajectories of " + }, + { + "bbox": [ + 313, + 402, + 541, + 469 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 402, + 541, + 469 + ], + "type": "text", + "content": " agents " + }, + { + "bbox": [ + 313, + 402, + 541, + 469 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_1,\\dots,\\mathbf{x}_N" + }, + { + "bbox": [ + 313, + 402, + 541, + 469 + ], + "type": "text", + "content": " and the scene information " + }, + { + "bbox": [ + 313, + 402, + 541, + 469 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 313, + 402, + 541, + 469 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 480, + 525, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 480, + 525, + 493 + ], + "spans": [ + { + "bbox": [ + 313, + 480, + 525, + 493 + ], + "type": "text", + "content": "4. Proposed Trajectory Prediction Network" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 499, + 539, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 499, + 539, + 522 + ], + "spans": [ + { + "bbox": [ + 313, + 499, + 539, + 522 + ], + "type": "text", + "content": "In this section, we present the details of the proposed motion prediction method, R-Pred." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 529, + 423, + 541 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 529, + 423, + 541 + ], + "spans": [ + { + "bbox": [ + 313, + 529, + 423, + 541 + ], + "type": "text", + "content": "4.1. Overall Framework" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 548, + 541, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 548, + 541, + 672 + ], + "spans": [ + { + "bbox": [ + 313, + 548, + 541, + 672 + ], + "type": "text", + "content": "An overview of the proposed R-Pred framework is presented in Fig. 2. Our proposed architecture produces " + }, + { + "bbox": [ + 313, + 548, + 541, + 672 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 548, + 541, + 672 + ], + "type": "text", + "content": " multi-modal trajectory predictions for a target agent over two stages. First, ITPNet produces " + }, + { + "bbox": [ + 313, + 548, + 541, + 672 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 548, + 541, + 672 + ], + "type": "text", + "content": " trajectory proposals for all " + }, + { + "bbox": [ + 313, + 548, + 541, + 672 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 548, + 541, + 672 + ], + "type": "text", + "content": " agents present in the scene. Along with the trajectory proposals, ITPNet returns " + }, + { + "bbox": [ + 313, + 548, + 541, + 672 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 313, + 548, + 541, + 672 + ], + "type": "text", + "content": " intermediate features used to produce the trajectory proposals. These features are called proposal features. 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Overall structure of R-Pred. Given the past trajectories of the dynamic agents and the global scene information, ITPNet generates " + }, + { + "bbox": [ + 69, + 289, + 541, + 343 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 69, + 289, + 541, + 343 + ], + "type": "text", + "content": " trajectory proposals for each agent. TRNet refines each of the " + }, + { + "bbox": [ + 69, + 289, + 541, + 343 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 69, + 289, + 541, + 343 + ], + "type": "text", + "content": " trajectory proposals of the target agent through TQSA and PIA. TQSA utilizes local scene context features obtained by tubular region pooling. PIA captures interaction context using the proposal group found by the distance-wise proposal grouping. 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Second, TRNet refines each of the " + }, + { + "bbox": [ + 69, + 360, + 296, + 540 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 69, + 360, + 296, + 540 + ], + "type": "text", + "content": " trajectory proposals of the target agent based on the prior trajectory information generated by the ITPNet. TRNet employs TQSA and PIA to generate the context features customized for each proposal. TQSA extracts the local scene context features cropped from a tube-shaped region around the target trajectory proposal. PIA generates the inter-agent interaction context features using a group of selected proposal trajectories of " + }, + { + "bbox": [ + 69, + 360, + 296, + 540 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 69, + 360, + 296, + 540 + ], + "type": "text", + "content": " agents. The context features generated by TQSA and PIA enhance the proposal features through cross-attention. 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Tubular region pooling is efficiently per" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 699, + 314, + 708 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 699, + 314, + 708 + ], + "spans": [ + { + "bbox": [ + 296, + 699, + 314, + 708 + ], + "type": "text", + "content": "8528" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 71, + 68, + 253, + 79 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 68, + 253, + 79 + ], + "spans": [ + { + "bbox": [ + 71, + 68, + 253, + 79 + ], + "type": "text", + "content": "Algorithm 2 Distance-Wise Proposal Grouping" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 71, + 80, + 296, + 114 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 80, + 296, + 114 + ], + "spans": [ + { + "bbox": [ + 71, + 80, + 296, + 114 + ], + "type": "text", + "content": "Input: Trajectory proposals " + }, + { + "bbox": [ + 71, + 80, + 296, + 114 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}_1,\\dots ,\\hat{\\mathbf{y}}_N" + }, + { + "bbox": [ + 71, + 80, + 296, + 114 + ], + "type": "text", + "content": " proposal confidence scores " + }, + { + "bbox": [ + 71, + 80, + 296, + 114 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}_1,\\dots ,\\hat{\\mathbf{c}}_N" + }, + { + "bbox": [ + 71, + 80, + 296, + 114 + ], + "type": "text", + "content": " proposal features " + }, + { + "bbox": [ + 71, + 80, + 296, + 114 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_1,\\dots ,\\mathbf{f}_N" + }, + { + "bbox": [ + 71, + 80, + 296, + 114 + ], + "type": "text", + "content": " distance threshold " + }, + { + "bbox": [ + 71, + 80, + 296, + 114 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 71, + 80, + 296, + 114 + ], + "type": "text", + "content": " and confidence threshold " + }, + { + "bbox": [ + 71, + 80, + 296, + 114 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 70, + 114, + 211, + 126 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 114, + 211, + 126 + ], + "spans": [ + { + "bbox": [ + 70, + 114, + 211, + 126 + ], + "type": "text", + "content": "Output: Proposal group set " + }, + { + "bbox": [ + 70, + 114, + 211, + 126 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(\\hat{\\mathbf{y}}_1^m)" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 77, + 127, + 266, + 222 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 77, + 127, + 159, + 136 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 127, + 159, + 136 + ], + "spans": [ + { + "bbox": [ + 77, + 127, + 159, + 136 + ], + "type": "text", + "content": "1: for " + }, + { + "bbox": [ + 77, + 127, + 159, + 136 + ], + "type": "inline_equation", + "content": "i \\gets 2" + }, + { + "bbox": [ + 77, + 127, + 159, + 136 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 77, + 127, + 159, + 136 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 77, + 127, + 159, + 136 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 77, + 137, + 178, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 137, + 178, + 148 + ], + "spans": [ + { + "bbox": [ + 77, + 137, + 178, + 148 + ], + "type": "text", + "content": "2: for " + }, + { + "bbox": [ + 77, + 137, + 178, + 148 + ], + "type": "inline_equation", + "content": "m^{\\prime}\\gets 1" + }, + { + "bbox": [ + 77, + 137, + 178, + 148 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 77, + 137, + 178, + 148 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 77, + 137, + 178, + 148 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 77, + 148, + 170, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 148, + 170, + 159 + ], + "spans": [ + { + "bbox": [ + 77, + 148, + 170, + 159 + ], + "type": "text", + "content": "3: if " + }, + { + "bbox": [ + 77, + 148, + 170, + 159 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}_j^{m'} > \\mathcal{T}" + }, + { + "bbox": [ + 77, + 148, + 170, + 159 + ], + "type": "text", + "content": " then" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 77, + 160, + 266, + 177 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 160, + 266, + 177 + ], + "spans": [ + { + "bbox": [ + 77, + 160, + 266, + 177 + ], + "type": "text", + "content": "4: " + }, + { + "bbox": [ + 77, + 160, + 266, + 177 + ], + "type": "inline_equation", + "content": "dist = \\min_{f\\in [t + 1,t + F]}\\| \\hat{y}_1^m (f) - \\hat{y}_i^{m'}(f)\\| _2" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 77, + 178, + 182, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 178, + 182, + 186 + ], + "spans": [ + { + "bbox": [ + 77, + 178, + 182, + 186 + ], + "type": "text", + "content": "5: if " + }, + { + "bbox": [ + 77, + 178, + 182, + 186 + ], + "type": "inline_equation", + "content": "dist < \\mathcal{D}" + }, + { + "bbox": [ + 77, + 178, + 182, + 186 + ], + "type": "text", + "content": " then" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 77, + 187, + 203, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 187, + 203, + 200 + ], + "spans": [ + { + "bbox": [ + 77, + 187, + 203, + 200 + ], + "type": "text", + "content": "6: " + }, + { + "bbox": [ + 77, + 187, + 203, + 200 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(\\hat{\\mathbf{y}}_1^m)" + }, + { + "bbox": [ + 77, + 187, + 203, + 200 + ], + "type": "text", + "content": " .append " + }, + { + "bbox": [ + 77, + 187, + 203, + 200 + ], + "type": "inline_equation", + "content": "(\\mathbf{f}_i^{m'})" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 77, + 201, + 84, + 208 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 201, + 84, + 208 + ], + "spans": [ + { + "bbox": [ + 77, + 201, + 84, + 208 + ], + "type": "text", + "content": "7:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 77, + 211, + 145, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 211, + 145, + 222 + ], + "spans": [ + { + "bbox": [ + 77, + 211, + 145, + 222 + ], + "type": "text", + "content": "8: return " + }, + { + "bbox": [ + 77, + 211, + 145, + 222 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(\\hat{\\mathbf{y}}_1^m)" + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 69, + 244, + 296, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 244, + 296, + 300 + ], + "spans": [ + { + "bbox": [ + 69, + 244, + 296, + 300 + ], + "type": "text", + "content": "formed to aggregate scene embedding features within the search radius " + }, + { + "bbox": [ + 69, + 244, + 296, + 300 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 69, + 244, + 296, + 300 + ], + "type": "text", + "content": " around each waypoint of the trajectory proposal " + }, + { + "bbox": [ + 69, + 244, + 296, + 300 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}_1^m" + }, + { + "bbox": [ + 69, + 244, + 296, + 300 + ], + "type": "text", + "content": ". Note that a collection of search disks centered at all waypoints on the trajectory forms an approximately tubular polygon. See Algorithm 1 for further details." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 70, + 300, + 296, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 300, + 296, + 357 + ], + "spans": [ + { + "bbox": [ + 70, + 300, + 296, + 357 + ], + "type": "text", + "content": "TQSA decodes the proposal features " + }, + { + "bbox": [ + 70, + 300, + 296, + 357 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_1^m" + }, + { + "bbox": [ + 70, + 300, + 296, + 357 + ], + "type": "text", + "content": " (associated with " + }, + { + "bbox": [ + 70, + 300, + 296, + 357 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}_1^m" + }, + { + "bbox": [ + 70, + 300, + 296, + 357 + ], + "type": "text", + "content": ") of the target agent by performing cross-attention on the local scene context " + }, + { + "bbox": [ + 70, + 300, + 296, + 357 + ], + "type": "inline_equation", + "content": "\\Psi_1^m" + }, + { + "bbox": [ + 70, + 300, + 296, + 357 + ], + "type": "text", + "content": ". Specifically, we use the proposal features " + }, + { + "bbox": [ + 70, + 300, + 296, + 357 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_1^m" + }, + { + "bbox": [ + 70, + 300, + 296, + 357 + ], + "type": "text", + "content": " as the query and the local scene context features " + }, + { + "bbox": [ + 70, + 300, + 296, + 357 + ], + "type": "inline_equation", + "content": "\\Psi_1^m" + }, + { + "bbox": [ + 70, + 300, + 296, + 357 + ], + "type": "text", + "content": " as the key and value, i.e.," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 124, + 364, + 296, + 377 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 364, + 296, + 377 + ], + "spans": [ + { + "bbox": [ + 124, + 364, + 296, + 377 + ], + "type": "interline_equation", + "content": "Q = \\mathbf {f} _ {1} ^ {m} W ^ {Q _ {T Q S A}} \\tag {1}", + "image_path": "821bef6a0762b7a30bcb938ecdf0f22d6b16152b64a518f55d8e825a2f65ff23.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 125, + 380, + 296, + 393 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 380, + 296, + 393 + ], + "spans": [ + { + "bbox": [ + 125, + 380, + 296, + 393 + ], + "type": "interline_equation", + "content": "K = \\Psi_ {1} ^ {m} W ^ {K _ {T Q S A}} \\tag {2}", + "image_path": "e223ade8a9917d103c8b9ba9498818f262fba4e12fedd4e38920f31a35aaaa81.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 125, + 395, + 296, + 408 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 395, + 296, + 408 + ], + "spans": [ + { + "bbox": [ + 125, + 395, + 296, + 408 + ], + "type": "interline_equation", + "content": "V = \\Psi_ {1} ^ {m} W ^ {V _ {T Q S A}} \\tag {3}", + "image_path": "4023afcfdba56743c7335fdbd623902fd62f54abe09a4197de03586d5726d091.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 124, + 411, + 296, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 411, + 296, + 437 + ], + "spans": [ + { + "bbox": [ + 124, + 411, + 296, + 437 + ], + "type": "interline_equation", + "content": "\\mathcal {A} _ {1} ^ {m} = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {\\top}}{\\sqrt {d _ {k}}}\\right) V, \\tag {4}", + "image_path": "2e2ea765dd7e1a860d13b4e6c1c4b42e241e3a3ff8b01e3eaf402477792cc3b3.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 69, + 443, + 296, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 443, + 296, + 501 + ], + "spans": [ + { + "bbox": [ + 69, + 443, + 296, + 501 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 69, + 443, + 296, + 501 + ], + "type": "inline_equation", + "content": "W^{Q_{TQSA}}" + }, + { + "bbox": [ + 69, + 443, + 296, + 501 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 69, + 443, + 296, + 501 + ], + "type": "inline_equation", + "content": "W^{K_{TQSA}}" + }, + { + "bbox": [ + 69, + 443, + 296, + 501 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 69, + 443, + 296, + 501 + ], + "type": "inline_equation", + "content": "W^{V_{TQSA}}" + }, + { + "bbox": [ + 69, + 443, + 296, + 501 + ], + "type": "text", + "content": " are learnable weight matrices and " + }, + { + "bbox": [ + 69, + 443, + 296, + 501 + ], + "type": "inline_equation", + "content": "d_k" + }, + { + "bbox": [ + 69, + 443, + 296, + 501 + ], + "type": "text", + "content": " is the dimension of the embedding vectors. We combine the attention value " + }, + { + "bbox": [ + 69, + 443, + 296, + 501 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_1^m" + }, + { + "bbox": [ + 69, + 443, + 296, + 501 + ], + "type": "text", + "content": " and the proposal features " + }, + { + "bbox": [ + 69, + 443, + 296, + 501 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_1^m" + }, + { + "bbox": [ + 69, + 443, + 296, + 501 + ], + "type": "text", + "content": " using the gating function introduced in [55]" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 110, + 507, + 296, + 521 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 507, + 296, + 521 + ], + "spans": [ + { + "bbox": [ + 110, + 507, + 296, + 521 + ], + "type": "interline_equation", + "content": "\\lambda = \\sigma \\left(\\mathrm {f} _ {1} ^ {m} W ^ {\\text {i n p u t}} + \\mathcal {A} _ {1} ^ {m} W ^ {\\text {h i d d e n}}\\right) \\tag {5}", + "image_path": "016783448e51475cd7c26f1f183531cc3e9b709d6d86e6e3ab73e50bd1382f40.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 110, + 523, + 296, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 523, + 296, + 536 + ], + "spans": [ + { + "bbox": [ + 110, + 523, + 296, + 536 + ], + "type": "interline_equation", + "content": "\\mathbf {t} _ {1} ^ {m} = \\lambda \\odot \\mathbf {f} _ {1} ^ {m} W ^ {\\text {g a t e}} + (1 - \\lambda) \\odot \\mathcal {A} _ {1} ^ {m} \\tag {6}", + "image_path": "097c48ac2feb97ba0433d6b5e3f2298828774f49e612effd2ac9885d6581efe9.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 110, + 538, + 296, + 551 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 538, + 296, + 551 + ], + "spans": [ + { + "bbox": [ + 110, + 538, + 296, + 551 + ], + "type": "interline_equation", + "content": "\\mathbf {t} _ {1} ^ {m} = \\mathbf {f} _ {1} ^ {m} + \\phi \\left(\\mathbf {t} _ {1} ^ {m}\\right), \\tag {7}", + "image_path": "96dcb67a15af6dca4205970f01ac8f8c49de738326d9c024c875fd44e1e7df48.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 70, + 558, + 296, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 558, + 296, + 614 + ], + "spans": [ + { + "bbox": [ + 70, + 558, + 296, + 614 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 70, + 558, + 296, + 614 + ], + "type": "inline_equation", + "content": "W^{input}" + }, + { + "bbox": [ + 70, + 558, + 296, + 614 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 70, + 558, + 296, + 614 + ], + "type": "inline_equation", + "content": "W^{hidden}" + }, + { + "bbox": [ + 70, + 558, + 296, + 614 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 70, + 558, + 296, + 614 + ], + "type": "inline_equation", + "content": "W^{gate}" + }, + { + "bbox": [ + 70, + 558, + 296, + 614 + ], + "type": "text", + "content": " are learnable matrices, " + }, + { + "bbox": [ + 70, + 558, + 296, + 614 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 70, + 558, + 296, + 614 + ], + "type": "text", + "content": " indicates element-wise product, " + }, + { + "bbox": [ + 70, + 558, + 296, + 614 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 70, + 558, + 296, + 614 + ], + "type": "text", + "content": " indicates the sigmoid function and " + }, + { + "bbox": [ + 70, + 558, + 296, + 614 + ], + "type": "inline_equation", + "content": "\\phi(\\cdot)" + }, + { + "bbox": [ + 70, + 558, + 296, + 614 + ], + "type": "text", + "content": " denotes a multi-layer perceptron (MLP). We add layer normalization [2], Dropout [42], and residual connection [22] in the middle of the attention process." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 69, + 616, + 296, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 616, + 296, + 649 + ], + "spans": [ + { + "bbox": [ + 69, + 616, + 296, + 649 + ], + "type": "text", + "content": "Note that the aforementioned local scene attention process to produce the output of TQSA " + }, + { + "bbox": [ + 69, + 616, + 296, + 649 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_1^m" + }, + { + "bbox": [ + 69, + 616, + 296, + 649 + ], + "type": "text", + "content": " is performed for each trajectory proposal (for each " + }, + { + "bbox": [ + 69, + 616, + 296, + 649 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 69, + 616, + 296, + 649 + ], + "type": "text", + "content": " value) in parallel." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 69, + 649, + 296, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 649, + 296, + 673 + ], + "spans": [ + { + "bbox": [ + 69, + 649, + 296, + 673 + ], + "type": "text", + "content": "Proposal-level Interaction Attention. PIA uses a distance-wise proposal grouping algorithm to find a group" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "spans": [ + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "text", + "content": "of the trajectory proposals for the nearby agents to model their inter-agent interactions. First, among " + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "inline_equation", + "content": "MN" + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "text", + "content": " trajectory proposals from " + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "text", + "content": " agents, those with a confidence score below the threshold " + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "text", + "content": " are discarded because they are unlikely to occur. Subsequently, for a given " + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "text", + "content": "-th trajectory proposal " + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}_1^m" + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "text", + "content": " of the target agent, the algorithm selects the trajectory proposals of the nearby agents, whose distance from " + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}_1^m" + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "text", + "content": " is closer than the distance threshold " + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "text", + "content": ". These are considered the most influential trajectory proposals to use for interaction modeling. A distance between two trajectories " + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_1^\\star" + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_2^\\star" + }, + { + "bbox": [ + 313, + 68, + 540, + 192 + ], + "type": "text", + "content": " is defined by" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 336, + 197, + 539, + 215 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 197, + 539, + 215 + ], + "spans": [ + { + "bbox": [ + 336, + 197, + 539, + 215 + ], + "type": "interline_equation", + "content": "\\operatorname {d i s t} \\left(\\mathbf {y} _ {1} ^ {\\star}, \\mathbf {y} _ {2} ^ {\\star}\\right) = \\min _ {f \\in [ t + 1, t + F ]} \\| \\mathbf {y} _ {1} ^ {\\star} (f) - \\mathbf {y} _ {2} ^ {\\star} (f) \\| _ {2}. \\tag {8}", + "image_path": "791fa751897043759c630024408c7cbcfae4680174c93b5cddaab617fc2d01ec.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 313, + 219, + 539, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 219, + 539, + 264 + ], + "spans": [ + { + "bbox": [ + 313, + 219, + 539, + 264 + ], + "type": "text", + "content": "For the selected trajectory proposals, the algorithm groups the corresponding proposal features into the proposal feature group " + }, + { + "bbox": [ + 313, + 219, + 539, + 264 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(\\hat{\\mathbf{y}}_1^m)" + }, + { + "bbox": [ + 313, + 219, + 539, + 264 + ], + "type": "text", + "content": ". The distance-wise proposal grouping algorithm is summarized in Algorithm 2." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 313, + 264, + 539, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 264, + 539, + 319 + ], + "spans": [ + { + "bbox": [ + 313, + 264, + 539, + 319 + ], + "type": "text", + "content": "The proposal feature group is used to decode the proposal features " + }, + { + "bbox": [ + 313, + 264, + 539, + 319 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_1^m" + }, + { + "bbox": [ + 313, + 264, + 539, + 319 + ], + "type": "text", + "content": " through cross-attention. Using " + }, + { + "bbox": [ + 313, + 264, + 539, + 319 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_1^m" + }, + { + "bbox": [ + 313, + 264, + 539, + 319 + ], + "type": "text", + "content": " as query and " + }, + { + "bbox": [ + 313, + 264, + 539, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(\\mathbf{y}_1^m)" + }, + { + "bbox": [ + 313, + 264, + 539, + 319 + ], + "type": "text", + "content": " as key and value, the cross-attention module produces the attention value " + }, + { + "bbox": [ + 313, + 264, + 539, + 319 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_1^m" + }, + { + "bbox": [ + 313, + 264, + 539, + 319 + ], + "type": "text", + "content": " similarly to Eq. (1) - (7)." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "spans": [ + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "text", + "content": "Multi-modal Prediction Head. TRNet constructs the final joint trajectory feature " + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "inline_equation", + "content": "\\mathbf{j}_1^m" + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "text", + "content": " by concatenating the attention output " + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_1^m" + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "text", + "content": " from TQSA and the attention output " + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_1^m" + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "text", + "content": " from PIA. The prediction head is then applied to " + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "inline_equation", + "content": "\\mathbf{j}_1^m" + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "text", + "content": " to produce the refined trajectories and the confidence scores. The prediction head consists of the regression branch and a classification branch. First, by modeling the trajectory points as multi-variate random vectors with independent Laplace distribution, the regression branch applies an MLP to " + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "inline_equation", + "content": "\\mathbf{j}_1^m" + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "text", + "content": " to predict the mean and covariance of " + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_1" + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "text", + "content": ". The predicted mean is denoted as " + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{y}}_1^m = [\\tilde{y}_1^m (t + 1),\\dots,\\tilde{y}_1^m (t + F)]" + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "text", + "content": " and the predicted variance is denoted as " + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "inline_equation", + "content": "\\mathbf{b}_1^m = [\\tilde{b}_1^m (t + 1),\\dots,\\tilde{b}_1^m (t + F)]" + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "text", + "content": ". The regression branch is applied separately for each mode " + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "text", + "content": ". Next, the classification branch applies another MLP to the concatenation of " + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "inline_equation", + "content": "\\mathbf{j}_1^1,\\dots,\\mathbf{j}_1^M" + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "text", + "content": " to produce the confidence scores " + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "inline_equation", + "content": "\\check{\\mathbf{c}}_1^1,\\dots,\\check{\\mathbf{c}}_1^M" + }, + { + "bbox": [ + 313, + 320, + 539, + 501 + ], + "type": "text", + "content": " for all modes." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 314, + 506, + 406, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 506, + 406, + 517 + ], + "spans": [ + { + "bbox": [ + 314, + 506, + 406, + 517 + ], + "type": "text", + "content": "4.4. Training Details" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 313, + 523, + 539, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 523, + 539, + 546 + ], + "spans": [ + { + "bbox": [ + 313, + 523, + 539, + 546 + ], + "type": "text", + "content": "The total loss function " + }, + { + "bbox": [ + 313, + 523, + 539, + 546 + ], + "type": "inline_equation", + "content": "L_{total}" + }, + { + "bbox": [ + 313, + 523, + 539, + 546 + ], + "type": "text", + "content": " used to train the entire network is given by" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 318, + 551, + 536, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 551, + 536, + 563 + ], + "spans": [ + { + "bbox": [ + 318, + 551, + 536, + 563 + ], + "type": "interline_equation", + "content": "L _ {t o t a l} = \\alpha L _ {r e g. p r o} + \\beta L _ {c l s. p r o} + \\gamma L _ {r e g. r e f} + \\delta L _ {c l s. r e f},", + "image_path": "9c9d849e841ca2a66ef6f4811e92513808e9c309526414d202a1ff32bbe876bb.jpg" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 313, + 567, + 539, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 567, + 539, + 635 + ], + "spans": [ + { + "bbox": [ + 313, + 567, + 539, + 635 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 567, + 539, + 635 + ], + "type": "inline_equation", + "content": "L_{reg-pro}" + }, + { + "bbox": [ + 313, + 567, + 539, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 567, + 539, + 635 + ], + "type": "inline_equation", + "content": "L_{reg-ref}" + }, + { + "bbox": [ + 313, + 567, + 539, + 635 + ], + "type": "text", + "content": " are the regression loss functions for ITPNet, and TRNet and " + }, + { + "bbox": [ + 313, + 567, + 539, + 635 + ], + "type": "inline_equation", + "content": "L_{cls-pro}" + }, + { + "bbox": [ + 313, + 567, + 539, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 567, + 539, + 635 + ], + "type": "inline_equation", + "content": "L_{cls-ref}" + }, + { + "bbox": [ + 313, + 567, + 539, + 635 + ], + "type": "text", + "content": " are the classification loss functions for ITPNet, and TRNet. We used " + }, + { + "bbox": [ + 313, + 567, + 539, + 635 + ], + "type": "inline_equation", + "content": "\\alpha = \\beta = \\gamma = \\delta = 1" + }, + { + "bbox": [ + 313, + 567, + 539, + 635 + ], + "type": "text", + "content": " in our setup. The negative log-likelihood function for the Laplace distribution is used for " + }, + { + "bbox": [ + 313, + 567, + 539, + 635 + ], + "type": "inline_equation", + "content": "L_{reg-ref}" + }, + { + "bbox": [ + 313, + 567, + 539, + 635 + ], + "type": "text", + "content": " as follows," + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 314, + 639, + 545, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 639, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 314, + 639, + 545, + 673 + ], + "type": "interline_equation", + "content": "L _ {r e g - r e f} = - \\frac {1}{N F} \\sum_ {n = 1} ^ {N} \\sum_ {f = t + 1} ^ {t + F} \\log \\mathbb {P} \\left(y _ {n} (f) \\mid \\check {y} _ {n} ^ {m ^ {*}} (f), \\check {\\mathbf {b}} _ {n} ^ {m ^ {*}} (f)\\right),", + "image_path": "ec3eaa374fb124c4554dbf0c23f6733baa970003668f772d5f79866bcaac2d09.jpg" + } + ] + } + ], + "index": 34 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 699, + 314, + 708 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 699, + 314, + 708 + ], + "spans": [ + { + "bbox": [ + 296, + 699, + 314, + 708 + ], + "type": "text", + "content": "8529" + } + ] + } + ], + "index": 35 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 111, + 67, + 500, + 291 + ], + "blocks": [ + { + "bbox": [ + 111, + 67, + 500, + 291 + ], + "lines": [ + { + "bbox": [ + 111, + 67, + 500, + 291 + ], + "spans": [ + { + "bbox": [ + 111, + 67, + 500, + 291 + ], + "type": "table", + "html": "
MethodminADE1minFDE1minADE6minFDE6brierFDE6MR6%
LaneRCNN[51]1.693.690.901.452.1512.3
LaPred[26]1.934.330.911.502.1318.0
TNT[53]2.174.960.911.452.1416.6
PRIME[41]1.913.821.221.562.1011.5
HOME[14]1.723.730.921.36-11.3
LaneGCN[29]1.703.760.871.362.0516.2
mmTransformer[30]1.774.000.841.342.0315.4
DenseTNT[19]1.683.630.881.281.9812.6
THOMAS[16]1.673.590.941.441.9710.3
SceneTransformer[34]1.813.620.801.231.8912.5
LTP[45]1.623.550.831.301.8614.7
HOME+GOHOME[15]1.703.680.891.291.868.5
TPCN[49]1.663.690.871.38-15.8
HiVT[55]1.603.520.771.171.8412.7
MultiPath++[43]1.623.610.791.211.7913.2
Wayformer[33]1.643.670.771.161.7411.9
ITPNet baseline1.623.570.791.211.8613.1
R-Pred1.583.470.761.121.7711.6
", + "image_path": "e57630678c6480e95fb95f513eea89dc853ac63064728a238157d413b55a069b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 70, + 352, + 296, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 352, + 296, + 427 + ], + "spans": [ + { + "bbox": [ + 70, + 352, + 296, + 427 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 70, + 352, + 296, + 427 + ], + "type": "inline_equation", + "content": "\\mathbb{P}(\\cdot |\\cdot)" + }, + { + "bbox": [ + 70, + 352, + 296, + 427 + ], + "type": "text", + "content": " is the probability density function of Laplace distribution. " + }, + { + "bbox": [ + 70, + 352, + 296, + 427 + ], + "type": "inline_equation", + "content": "L_{reg - pro}" + }, + { + "bbox": [ + 70, + 352, + 296, + 427 + ], + "type": "text", + "content": " is defined similarly. When evaluating the loss function during training, we adopt a winner-takes-all strategy [7] in which the mode " + }, + { + "bbox": [ + 70, + 352, + 296, + 427 + ], + "type": "inline_equation", + "content": "m^{*}" + }, + { + "bbox": [ + 70, + 352, + 296, + 427 + ], + "type": "text", + "content": " of the trajectory output that yields the smallest average displacement error is used, i.e., " + }, + { + "bbox": [ + 70, + 352, + 296, + 427 + ], + "type": "inline_equation", + "content": "m^{*} = \\underset {m\\in [1,M]}{\\mathrm{argmin}}\\sum_{f = t + 1}^{t + F}\\| y_n(f) - \\tilde{y}_n^m (f)\\| _2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 70, + 427, + 296, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 427, + 296, + 460 + ], + "spans": [ + { + "bbox": [ + 70, + 427, + 296, + 460 + ], + "type": "text", + "content": "We used the cross entropy loss for the classification losses " + }, + { + "bbox": [ + 70, + 427, + 296, + 460 + ], + "type": "inline_equation", + "content": "L_{cls-pro}" + }, + { + "bbox": [ + 70, + 427, + 296, + 460 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 70, + 427, + 296, + 460 + ], + "type": "inline_equation", + "content": "L_{cls-ref}" + }, + { + "bbox": [ + 70, + 427, + 296, + 460 + ], + "type": "text", + "content": ". We trained the entire network end-to-end with random initialization." + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 72, + 475, + 297, + 608 + ], + "blocks": [ + { + "bbox": [ + 69, + 293, + 541, + 335 + ], + "lines": [ + { + "bbox": [ + 69, + 293, + 541, + 335 + ], + "spans": [ + { + "bbox": [ + 69, + 293, + 541, + 335 + ], + "type": "text", + "content": "Table 1. Performance comparison on Argoverse test set in the official leaderboard. The best performed metrics are shown in bold. The \"-\" symbol means the corresponding metric is unknown, either because the authors have not disclosed it or it was not specified in the leaderboard. Our model achieves the state-of-the-art performance in terms of the " + }, + { + "bbox": [ + 69, + 293, + 541, + 335 + ], + "type": "inline_equation", + "content": "\\text{minADE}_1" + }, + { + "bbox": [ + 69, + 293, + 541, + 335 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 69, + 293, + 541, + 335 + ], + "type": "inline_equation", + "content": "\\text{minFDE}_1" + }, + { + "bbox": [ + 69, + 293, + 541, + 335 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 69, + 293, + 541, + 335 + ], + "type": "inline_equation", + "content": "\\text{minADE}_6" + }, + { + "bbox": [ + 69, + 293, + 541, + 335 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 69, + 293, + 541, + 335 + ], + "type": "inline_equation", + "content": "\\text{minFDE}_6" + }, + { + "bbox": [ + 69, + 293, + 541, + 335 + ], + "type": "text", + "content": " metrics." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 72, + 475, + 297, + 608 + ], + "lines": [ + { + "bbox": [ + 72, + 475, + 297, + 608 + ], + "spans": [ + { + "bbox": [ + 72, + 475, + 297, + 608 + ], + "type": "table", + "html": "
Method\\( mADE_5 \\)\\( mFDE_5 \\)\\( mADE_{10} \\)\\( mFDE_{10} \\)
MTP[7]2.224.831.743.54
CoverNet[37]1.96-1.48-
Trajectory++[40]1.88-1.51-
MHA-JAM[32]1.813.721.242.21
MultiPath[4]1.783.621.552.93
CXX[31]1.63-1.29-
LaPred[26]1.533.371.122.39
P2T[9]1.45-1.16-
THOMAS[16]1.33-1.04-
PGP[10]1.272.470.941.55
ITPNet baseline1.292.580.971.60
R-Pred1.192.280.941.50
", + "image_path": "75d28369d9cbdb7b560e46d12d777aabc9f67f7363bbc86f73a5d5985ce1cfa2.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 69, + 615, + 297, + 657 + ], + "lines": [ + { + "bbox": [ + 69, + 615, + 297, + 657 + ], + "spans": [ + { + "bbox": [ + 69, + 615, + 297, + 657 + ], + "type": "text", + "content": "Table 2. Performance comparison on nuScenes validation set in the official leaderboard. The \"-\" symbol means the corresponding metric unknown. Our model achieves state-of-the-art performance on all metrics." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 314, + 351, + 390, + 364 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 351, + 390, + 364 + ], + "spans": [ + { + "bbox": [ + 314, + 351, + 390, + 364 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 373, + 541, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 373, + 541, + 417 + ], + "spans": [ + { + "bbox": [ + 313, + 373, + 541, + 417 + ], + "type": "text", + "content": "In this section, we describe the experimental setup used to evaluate the performance of the proposed R-Pred, and present both quantitative and qualitative analyses of the behavior of the model." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 419, + 541, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 419, + 541, + 533 + ], + "spans": [ + { + "bbox": [ + 313, + 419, + 541, + 533 + ], + "type": "text", + "content": "Datasets. Both Argoverse [5] and nuScenes [3] datasets provide dynamic agent trajectories and HD-map in real-world driving scenarios. The Argoverse dataset was collected from two US cities, including Miami and Pittsburgh. Each sample contains 5 seconds trajectories of tracked vehicles sampled at " + }, + { + "bbox": [ + 313, + 419, + 541, + 533 + ], + "type": "inline_equation", + "content": "10\\mathrm{Hz}" + }, + { + "bbox": [ + 313, + 419, + 541, + 533 + ], + "type": "text", + "content": ". Argoverse dataset provides HD-map with detailed lane information. The prediction task is to predict future trajectories for 3 seconds given past trajectories of 2 seconds. The dataset contains 205,942 training, 39,272 validation, and 78,143 test samples." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 534, + 539, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 534, + 539, + 613 + ], + "spans": [ + { + "bbox": [ + 313, + 534, + 539, + 613 + ], + "type": "text", + "content": "The nuScenes dataset was collected in Boston and Singapore. The collected trajectories are 6 seconds long and are sampled at " + }, + { + "bbox": [ + 313, + 534, + 539, + 613 + ], + "type": "inline_equation", + "content": "2\\mathrm{Hz}" + }, + { + "bbox": [ + 313, + 534, + 539, + 613 + ], + "type": "text", + "content": ". The prediction task is defined as that of predicting future trajectories for 6 seconds given past trajectories of 2 seconds. HD-map is also provided along with the trajectory data. The dataset is split into 32, 186 training, 8,560 validation, and 9,041 test samples." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 615, + 541, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 615, + 541, + 672 + ], + "spans": [ + { + "bbox": [ + 313, + 615, + 541, + 672 + ], + "type": "text", + "content": "Metrics. For the performance evaluation, we adopt widely used performance metrics including average displacement error (ADE), final displacement error (FDE), and miss rate (MR). ADE refers to the mean square error compared to the ground truth over the entire time steps, and FDE is" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 699, + 314, + 708 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 699, + 314, + 708 + ], + "spans": [ + { + "bbox": [ + 296, + 699, + 314, + 708 + ], + "type": "text", + "content": "8530" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 111, + 70, + 205, + 166 + ], + "blocks": [ + { + "bbox": [ + 111, + 70, + 205, + 166 + ], + "lines": [ + { + "bbox": [ + 111, + 70, + 205, + 166 + ], + "spans": [ + { + "bbox": [ + 111, + 70, + 205, + 166 + ], + "type": "image", + "image_path": "397dbd67b850d1794c6a5b24d2d378251ec0621a35a4dbd005305e2dd846cb24.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 207, + 71, + 301, + 166 + ], + "blocks": [ + { + "bbox": [ + 207, + 71, + 301, + 166 + ], + "lines": [ + { + "bbox": [ + 207, + 71, + 301, + 166 + ], + "spans": [ + { + "bbox": [ + 207, + 71, + 301, + 166 + ], + "type": "image", + "image_path": "d3db5eb23a31014b0d5feee0ebc2fcceee3ac003e79d99139615b7506c951530.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 303, + 71, + 397, + 166 + ], + "blocks": [ + { + "bbox": [ + 303, + 71, + 397, + 166 + ], + "lines": [ + { + "bbox": [ + 303, + 71, + 397, + 166 + ], + "spans": [ + { + "bbox": [ + 303, + 71, + 397, + 166 + ], + "type": "image", + "image_path": "0e0242d1f23d0e23b28c59de90f6ef36c2406efe8595881b659421bb94e00da1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 399, + 72, + 500, + 166 + ], + "blocks": [ + { + "bbox": [ + 399, + 72, + 500, + 166 + ], + "lines": [ + { + "bbox": [ + 399, + 72, + 500, + 166 + ], + "spans": [ + { + "bbox": [ + 399, + 72, + 500, + 166 + ], + "type": "image", + "image_path": "53364e555fd46ce8f6755ed56e1afb260f6811e1fec9d8c7fb0e3d5129af6b85.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 111, + 168, + 205, + 262 + ], + "blocks": [ + { + "bbox": [ + 111, + 168, + 205, + 262 + ], + "lines": [ + { + "bbox": [ + 111, + 168, + 205, + 262 + ], + "spans": [ + { + "bbox": [ + 111, + 168, + 205, + 262 + ], + "type": "image", + "image_path": "7daae0af989f1544d25790833dfb0ae5ad9899bb632e4f55e23d0ae389c5de66.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 69, + 270, + 541, + 312 + ], + "lines": [ + { + "bbox": [ + 69, + 270, + 541, + 312 + ], + "spans": [ + { + "bbox": [ + 69, + 270, + 541, + 312 + ], + "type": "text", + "content": "Figure 3. Qualitative results of R-Pred on Argoverse validation set. Yellow, green, blue, and red lines represent the history, ground truth, the initial trajectory proposal with the highest score, and the final (refined) trajectory, respectively. The sky blue region denotes tubular regions used for TQSA. These figures present different vehicle motion scenarios such as continuing straight ahead, turning left, slowing down, changing lanes, etc." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 207, + 168, + 301, + 262 + ], + "blocks": [ + { + "bbox": [ + 207, + 168, + 301, + 262 + ], + "lines": [ + { + "bbox": [ + 207, + 168, + 301, + 262 + ], + "spans": [ + { + "bbox": [ + 207, + 168, + 301, + 262 + ], + "type": "image", + "image_path": "ab605dc8d31eb3288a15c2c9d5748a1bbb6eaf89109e012a195e717bacef7255.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 303, + 168, + 397, + 262 + ], + "blocks": [ + { + "bbox": [ + 303, + 168, + 397, + 262 + ], + "lines": [ + { + "bbox": [ + 303, + 168, + 397, + 262 + ], + "spans": [ + { + "bbox": [ + 303, + 168, + 397, + 262 + ], + "type": "image", + "image_path": "5b56582c0e867255c05a66d5d92cda37b929f7a38b7aeffca768b7d3b2b2aadf.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 399, + 168, + 499, + 262 + ], + "blocks": [ + { + "bbox": [ + 399, + 168, + 499, + 262 + ], + "lines": [ + { + "bbox": [ + 399, + 168, + 499, + 262 + ], + "spans": [ + { + "bbox": [ + 399, + 168, + 499, + 262 + ], + "type": "image", + "image_path": "272bd5f915a53bd85fc7ae021652bef873c919c02b777b99d20e6d8bdcdcfcb2.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 69, + 330, + 297, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 330, + 297, + 613 + ], + "spans": [ + { + "bbox": [ + 69, + 330, + 297, + 613 + ], + "type": "text", + "content": "We evaluate the prediction accuracy with " + }, + { + "bbox": [ + 69, + 330, + 297, + 613 + ], + "type": "inline_equation", + "content": "M > 1" + }, + { + "bbox": [ + 69, + 330, + 297, + 613 + ], + "type": "text", + "content": " trajectory predictions using minADEM and minFDEM, which are the minimum ADE and FDE over " + }, + { + "bbox": [ + 69, + 330, + 297, + 613 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 69, + 330, + 297, + 613 + ], + "type": "text", + "content": " predicted trajectories, respectively. " + }, + { + "bbox": [ + 69, + 330, + 297, + 613 + ], + "type": "inline_equation", + "content": "MR_{M}" + }, + { + "bbox": [ + 69, + 330, + 297, + 613 + ], + "type": "text", + "content": " measures the ratio within 2 meters of the endpoint of the best-predicted trajectory and ground truth. We also use brier minimum FDE (brierFDEM), which measures the value of minFDEM + (1 - p)², where " + }, + { + "bbox": [ + 69, + 330, + 297, + 613 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 69, + 330, + 297, + 613 + ], + "type": "text", + "content": " is corresponding trajectory probability. This imposes a penalty when the probability of the best trajectory is low. Implementation Details. We set the threshold " + }, + { + "bbox": [ + 69, + 330, + 297, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 69, + 330, + 297, + 613 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 69, + 330, + 297, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 69, + 330, + 297, + 613 + ], + "type": "text", + "content": " of PIA to 0.1 and 10 meters and " + }, + { + "bbox": [ + 69, + 330, + 297, + 613 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 69, + 330, + 297, + 613 + ], + "type": "text", + "content": " of TQSA to 20 meters. The embedding size of all features is set to 128 for comparative performance analysis. We used existing prediction architectures for the ITPNet. We chose the structure of [55] on Argoverse and that of [10] on nuScenes. These models achieved excellent performance on both benchmarks. They are considered ITPNet baselines and are used to measure the performance gain achieved by our refinement network. We trained the proposed model on TiTAN RTX GPU for 64 epochs with 32 batch sizes. The data are batched randomly. For all experiments, we trained the model using AdamW optimizer with an initial learning rate of 5e-4. We used cosine annealing to decay the learning rate and applied dropout with a 0.1 ratio. Data augmentation was not used." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 70, + 620, + 182, + 632 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 620, + 182, + 632 + ], + "spans": [ + { + "bbox": [ + 70, + 620, + 182, + 632 + ], + "type": "text", + "content": "5.1.Quantitative Results" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 69, + 638, + 297, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 638, + 297, + 672 + ], + "spans": [ + { + "bbox": [ + 69, + 638, + 297, + 672 + ], + "type": "text", + "content": "Table 1 presents the performance of R-Pred evaluated on Argoverse test set. We compare the performance of R-Pred with that of several top ranked models [51, 53, 41, 29, 14," + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 317, + 329, + 541, + 380 + ], + "blocks": [ + { + "bbox": [ + 317, + 329, + 541, + 380 + ], + "lines": [ + { + "bbox": [ + 317, + 329, + 541, + 380 + ], + "spans": [ + { + "bbox": [ + 317, + 329, + 541, + 380 + ], + "type": "table", + "html": "
ITPNetPIATQSAminADE6minFDE6MR6%
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", + "image_path": "1ab67d4e03f17836a3e8dc4abd54accfe7572f05b245c6da4cfc0e29d01eb5f4.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 387, + 541, + 409 + ], + "lines": [ + { + "bbox": [ + 313, + 387, + 541, + 409 + ], + "spans": [ + { + "bbox": [ + 313, + 387, + 541, + 409 + ], + "type": "text", + "content": "Table 3. Contributions of the main components evaluated on the Argoverse validation set." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "spans": [ + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "text", + "content": "30, 19, 16, 34, 45, 15, 49, 43, 33, 55]. R-Pred achieves the best prediction accuracy in terms of the " + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "inline_equation", + "content": "\\text{minADE}_1" + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "inline_equation", + "content": "\\text{minFDE}_1" + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "inline_equation", + "content": "\\text{minADE}_6" + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "inline_equation", + "content": "\\text{minFDE}_6" + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "text", + "content": " metrics and competitive performance in terms of " + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "inline_equation", + "content": "\\text{brierFDE}_6" + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "inline_equation", + "content": "\\text{MR}_6" + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "text", + "content": ". R-Pred sets a new state-of-the-art performance surpassing the current best methods, Wayformer [33] and Multi-Path++ [43]. Compared to the ITPNet baseline, the proposed method offers performance improvements of " + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "inline_equation", + "content": "3.80\\%" + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "inline_equation", + "content": "7.43\\%" + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "text", + "content": " in terms of " + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "inline_equation", + "content": "\\text{minADE}_6" + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "inline_equation", + "content": "\\text{minFDE}_6" + }, + { + "bbox": [ + 313, + 432, + 541, + 568 + ], + "type": "text", + "content": ", respectively. This indicates that our trajectory refinement strategy can effectively improve the reliability and robustness of the initial prediction using ITPNet." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 570, + 541, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 541, + 673 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 541, + 673 + ], + "type": "text", + "content": "Table 2 presents the performance of several motion prediction methods on nuScenes validation set. We compare R-Pred with the top ranked methods [37, 40, 32, 4, 31, 26, 9, 16, 10] on the nuScenes leaderboard. R-Pred achieves significant performance gains compared with other prediction methods. R-Pred exhibits the performance gain of " + }, + { + "bbox": [ + 313, + 570, + 541, + 673 + ], + "type": "inline_equation", + "content": "7.75\\%" + }, + { + "bbox": [ + 313, + 570, + 541, + 673 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 570, + 541, + 673 + ], + "type": "inline_equation", + "content": "11.62\\%" + }, + { + "bbox": [ + 313, + 570, + 541, + 673 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 313, + 570, + 541, + 673 + ], + "type": "inline_equation", + "content": "\\min ADE_5" + }, + { + "bbox": [ + 313, + 570, + 541, + 673 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 570, + 541, + 673 + ], + "type": "inline_equation", + "content": "\\min FDE_5" + }, + { + "bbox": [ + 313, + 570, + 541, + 673 + ], + "type": "text", + "content": " compared to the ITPNet baseline. These results demonstrate that the proposed two refinement modules have high-quality learning" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 699, + 313, + 708 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 699, + 313, + 708 + ], + "spans": [ + { + "bbox": [ + 296, + 699, + 313, + 708 + ], + "type": "text", + "content": "8531" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 70, + 68, + 118, + 79 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 68, + 118, + 79 + ], + "spans": [ + { + "bbox": [ + 70, + 68, + 118, + 79 + ], + "type": "text", + "content": "capabilities." + } + ] + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 103, + 89, + 261, + 166 + ], + "blocks": [ + { + "bbox": [ + 103, + 89, + 261, + 166 + ], + "lines": [ + { + "bbox": [ + 103, + 89, + 261, + 166 + ], + "spans": [ + { + "bbox": [ + 103, + 89, + 261, + 166 + ], + "type": "table", + "html": "
τminADE6minFDE6MR6%
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", + "image_path": "53cd954d37e19c0a88ca950084f290132e1195075394bc4c6fa3248c68d8e3c6.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 103, + 210, + 261, + 287 + ], + "blocks": [ + { + "bbox": [ + 70, + 168, + 297, + 190 + ], + "lines": [ + { + "bbox": [ + 70, + 168, + 297, + 190 + ], + "spans": [ + { + "bbox": [ + 70, + 168, + 297, + 190 + ], + "type": "text", + "content": "Table 4. Performance versus " + }, + { + "bbox": [ + 70, + 168, + 297, + 190 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 70, + 168, + 297, + 190 + ], + "type": "text", + "content": " parameter of TQSA evaluated on the Argoverse validation set." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 103, + 210, + 261, + 287 + ], + "lines": [ + { + "bbox": [ + 103, + 210, + 261, + 287 + ], + "spans": [ + { + "bbox": [ + 103, + 210, + 261, + 287 + ], + "type": "table", + "html": "
DminADE6minFDE6MR6%
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", + "image_path": "7249afb154c539a7a93f579fbd7ee494bc90234c86a10f617066aa829d11433e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 70, + 327, + 159, + 340 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 327, + 159, + 340 + ], + "spans": [ + { + "bbox": [ + 70, + 327, + 159, + 340 + ], + "type": "text", + "content": "5.2. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 70, + 345, + 296, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 345, + 296, + 400 + ], + "spans": [ + { + "bbox": [ + 70, + 345, + 296, + 400 + ], + "type": "text", + "content": "We conducted several ablation studies on the Argoverse validation set. We reduced the training time required to conduct the ablation study by decreasing the feature size from 128 to 64 and increasing the batch size from 32 to 64. The trained model was evaluated on the entire validation set." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "spans": [ + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "text", + "content": "Contribution of Each Module. Table 3 shows the contributions of each module to overall performance achieved by R-Pred. We evaluated performance as we added each component one by one. We consider the following three modules of R-Pred: 1) ITPNet baseline, 2) PIA, and 3) TQSA. When the PIA is added to ITPNet baseline, the " + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "inline_equation", + "content": "\\text{minFDE}_6" + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "text", + "content": " improves by " + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "inline_equation", + "content": "6.15\\%" + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "inline_equation", + "content": "MR_6" + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "text", + "content": " improves by " + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "inline_equation", + "content": "9.31\\%" + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "text", + "content": ". This indicates the effectiveness of inter-agent interaction modeling by PIA. When TQSA is added, it achieves the performance gains of " + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "inline_equation", + "content": "4.74\\%" + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "inline_equation", + "content": "9.85\\%" + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "inline_equation", + "content": "\\text{minFDE}_6" + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "inline_equation", + "content": "MR_6" + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "text", + "content": ". We observe that proposal refinement using local scene context improves the performance significantly. Finally, the combination of PIA and TQSA has improved the performance of ITPNet baseline by " + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "inline_equation", + "content": "10.6\\%" + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "inline_equation", + "content": "18.25\\%" + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "text", + "content": ", in " + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "inline_equation", + "content": "\\text{minFDE}_6" + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "inline_equation", + "content": "MR_6" + }, + { + "bbox": [ + 70, + 401, + 296, + 570 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "spans": [ + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "text", + "content": "Performance Versus " + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "text", + "content": ". We investigated the impact of the parameters " + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "text", + "content": " on the performance. Recall that " + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "text", + "content": " are the distance thresholds used in TQSA and PIA, respectively. Table 4 presents the performance of R-Pred evaluated for several values of " + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "inline_equation", + "content": "\\tau = \\{5,10,20,30,50\\}" + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "text", + "content": ". R-Pred performs best at " + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "inline_equation", + "content": "\\tau = 20,30" + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "text", + "content": ", and degrades as " + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 70, + 570, + 296, + 671 + ], + "type": "text", + "content": " becomes larger or smaller than these values. This is likely due to the fact that when the threshold gets too large, a lot of irrelevant scene context can be used for cross-attrbution." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 68, + 539, + 113 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 68, + 539, + 113 + ], + "spans": [ + { + "bbox": [ + 313, + 68, + 539, + 113 + ], + "type": "text", + "content": "Table 5 presents the performance of R-Pred for several values of " + }, + { + "bbox": [ + 313, + 68, + 539, + 113 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{5,10,20,30,40\\}" + }, + { + "bbox": [ + 313, + 68, + 539, + 113 + ], + "type": "text", + "content": ". R-Pred achieves the best performance with " + }, + { + "bbox": [ + 313, + 68, + 539, + 113 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = 10" + }, + { + "bbox": [ + 313, + 68, + 539, + 113 + ], + "type": "text", + "content": ". Note that increasing the threshold " + }, + { + "bbox": [ + 313, + 68, + 539, + 113 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 313, + 68, + 539, + 113 + ], + "type": "text", + "content": " above 10 does not improve performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 113, + 539, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 113, + 539, + 226 + ], + "spans": [ + { + "bbox": [ + 313, + 113, + 539, + 226 + ], + "type": "text", + "content": "Effect of Per-proposal Scene Context Strategy. One of our key innovations is to use the tube-query for pooling the customized scene context for each proposal. We investigated the benefit of our per-proposal feature pooling method. We compare R-Pred with the baseline that shares the global scene context features for all proposals in the refinement step. Table 6 shows that our strategy offers " + }, + { + "bbox": [ + 313, + 113, + 539, + 226 + ], + "type": "inline_equation", + "content": "1.76\\%" + }, + { + "bbox": [ + 313, + 113, + 539, + 226 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 113, + 539, + 226 + ], + "type": "inline_equation", + "content": "3.24\\%" + }, + { + "bbox": [ + 313, + 113, + 539, + 226 + ], + "type": "text", + "content": " performance gains in " + }, + { + "bbox": [ + 313, + 113, + 539, + 226 + ], + "type": "inline_equation", + "content": "minFDE_{6}" + }, + { + "bbox": [ + 313, + 113, + 539, + 226 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 113, + 539, + 226 + ], + "type": "inline_equation", + "content": "MR_{6}" + }, + { + "bbox": [ + 313, + 113, + 539, + 226 + ], + "type": "text", + "content": " over the baseline, which confirms the advantage of the proposed per-proposal feature pooling method." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 317, + 236, + 538, + 283 + ], + "blocks": [ + { + "bbox": [ + 70, + 289, + 296, + 310 + ], + "lines": [ + { + "bbox": [ + 70, + 289, + 296, + 310 + ], + "spans": [ + { + "bbox": [ + 70, + 289, + 296, + 310 + ], + "type": "text", + "content": "Table 5. Performance versus " + }, + { + "bbox": [ + 70, + 289, + 296, + 310 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 70, + 289, + 296, + 310 + ], + "type": "text", + "content": " parameter of PIA evaluated on the Argoverse validation set." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 236, + 538, + 283 + ], + "lines": [ + { + "bbox": [ + 317, + 236, + 538, + 283 + ], + "spans": [ + { + "bbox": [ + 317, + 236, + 538, + 283 + ], + "type": "table", + "html": "
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", + "image_path": "c98028865f1c32ca58143f34df91ceb7f39356f3437f43b7d744b84c4f1e33f2.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 289, + 539, + 312 + ], + "lines": [ + { + "bbox": [ + 313, + 289, + 539, + 312 + ], + "spans": [ + { + "bbox": [ + 313, + 289, + 539, + 312 + ], + "type": "text", + "content": "Table 6. Comparison of per-proposal scene context versus shared scene context evaluated on the Argoverse validation set." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 331, + 419, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 331, + 419, + 342 + ], + "spans": [ + { + "bbox": [ + 313, + 331, + 419, + 342 + ], + "type": "text", + "content": "5.3. Qualitative Results" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 348, + 539, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 348, + 539, + 495 + ], + "spans": [ + { + "bbox": [ + 313, + 348, + 539, + 495 + ], + "type": "text", + "content": "Fig. 3 shows a visualization of the actual predicted trajectory samples generated by R-Pred using Argoverse validation set. We visualize the final trajectory with the best score produced by R-Pred (red line) and the corresponding trajectory proposal from ITPNet (blue line). We also include the ground truth trajectory (green line). We added the tubular area used for TQSA to the figure (sky blue region). We observe that our refinement network reduced the prediction error in the trajectories generated by ITPNet. Note that in the third column, our refinement stage modifies the initial trajectory proposal off-road to the trajectory within the road. More qualitative results are provided in Supplementary Material." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 506, + 388, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 506, + 388, + 517 + ], + "spans": [ + { + "bbox": [ + 313, + 506, + 388, + 517 + ], + "type": "text", + "content": "6. Conclusions" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 525, + 539, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 525, + 539, + 672 + ], + "spans": [ + { + "bbox": [ + 313, + 525, + 539, + 672 + ], + "type": "text", + "content": "In this paper, we have proposed a two-stage trajectory prediction method, referred to as R-Pred. We have introduced a novel per proposal trajectory refinement strategy in which each trajectory proposal generated in the first-stage network is refined using contextual information tailored to the proposal. TRNet utilized the local scene context captured by pooling scene component features in a tubular region around the trajectory proposal. TRNet also uses the inter-agent interaction context inferred from a group of influential trajectory proposals of neighboring agents. The results of an experimental evaluation conducted on Argoverse and nuScenes benchmark datasets confirmed that R-Pred significantly outperforms existing methods and achieves" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 699, + 314, + 708 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 699, + 314, + 708 + ], + "spans": [ + { + "bbox": [ + 296, + 699, + 314, + 708 + ], + "type": "text", + "content": "8532" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 70, + 68, + 297, + 89 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 68, + 297, + 89 + ], + "spans": [ + { + "bbox": [ + 70, + 68, + 297, + 89 + ], + "type": "text", + "content": "state-of-the-art performance in terms of some evaluation metrics." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 135, + 101, + 233, + 114 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 135, + 101, + 233, + 114 + ], + "spans": [ + { + "bbox": [ + 135, + 101, + 233, + 114 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 70, + 120, + 297, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 120, + 297, + 199 + ], + "spans": [ + { + "bbox": [ + 70, + 120, + 297, + 199 + ], + "type": "text", + "content": "This work was partly supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No.2020-0-01373, Artificial Intelligence Graduate School Program(Hanyang University)) and National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.2020R1A2C2012146)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 71, + 210, + 126, + 221 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 210, + 126, + 221 + ], + "spans": [ + { + "bbox": [ + 71, + 210, + 126, + 221 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 75, + 228, + 296, + 671 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 75, + 228, + 296, + 280 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 228, + 296, + 280 + ], + "spans": [ + { + "bbox": [ + 75, + 228, + 296, + 280 + ], + "type": "text", + "content": "[1] Alexandre Alahi, Kratarth Goel, Vignesh Ramanathan, Alexandre Robicquet, Li Fei-Fei, and Silvio Savarese. 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In In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 8823-8833, 2022. 2, 3, 5, 6, 7" + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 699, + 314, + 708 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 699, + 314, + 708 + ], + "spans": [ + { + "bbox": [ + 296, + 699, + 314, + 708 + ], + "type": "text", + "content": "8535" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/R3D3_ Dense 3D Reconstruction of Dynamic Scenes from Multiple Cameras/df3f55bd-3906-48f7-856c-09ad31d9f51b_content_list.json b/2023/R3D3_ Dense 3D Reconstruction of Dynamic Scenes from Multiple Cameras/df3f55bd-3906-48f7-856c-09ad31d9f51b_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..7be0bc63b3e87d91ad250bf63eb81b3cb5858a25 --- /dev/null +++ b/2023/R3D3_ Dense 3D Reconstruction of Dynamic Scenes from Multiple Cameras/df3f55bd-3906-48f7-856c-09ad31d9f51b_content_list.json @@ -0,0 +1,1747 @@ +[ + { + "type": "text", + "text": "R3D3: Dense 3D Reconstruction of Dynamic Scenes from Multiple Cameras", + "text_level": 1, + "bbox": [ + 101, + 130, + 869, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Aron Schmied1*", + "bbox": [ + 89, + 179, + 220, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tobias Fischer $^{1*}$ Martin Danelljan $^{1}$ Marc Pollefeys $^{1,2}$ ETH Zürich 2 Microsoft", + "bbox": [ + 254, + 179, + 746, + 219 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://www.vis.xyz/pub/r3d3/", + "bbox": [ + 310, + 220, + 656, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Fisher $\\mathrm{Yu}^1$", + "bbox": [ + 787, + 180, + 872, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 272, + 313, + 287 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dense 3D reconstruction and ego-motion estimation are key challenges in autonomous driving and robotics. Compared to the complex, multi-modal systems deployed today, multi-camera systems provide a simpler, low-cost alternative. However, camera-based 3D reconstruction of complex dynamic scenes has proven extremely difficult, as existing solutions often produce incomplete or incoherent results. We propose R3D3, a multi-camera system for dense 3D reconstruction and ego-motion estimation. Our approach iterates between geometric estimation that exploits spatial-temporal information from multiple cameras, and monocular depth refinement. We integrate multi-camera feature correlation and dense bundle adjustment operators that yield robust geometric depth and pose estimates. To improve reconstruction where geometric depth is unreliable, e.g. for moving objects or low-textured regions, we introduce learnable scene priors via a depth refinement network. We show that this design enables a dense, consistent 3D reconstruction of challenging, dynamic outdoor environments. Consequently, we achieve state-of-the-art dense depth prediction on the DDAD and NuScenes benchmarks.", + "bbox": [ + 75, + 304, + 473, + 621 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 642, + 209, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Translating sensory inputs into a dense 3D reconstruction of the environment and tracking the position of the observer is a cornerstone of robotics and fundamental to the development of autonomous vehicles (AVs). Contemporary systems rely on fusing many sensor modalities like camera, LiDAR, RADAR, IMU and more, making hardware and software stacks complex and expensive. In contrast, multi-camera systems provide a simpler, low-cost alternative already widely available in modern consumer vehicles. However, image-based dense 3D reconstruction and egomotion estimation of large-scale, dynamic scenes is an open research problem as moving objects, uniform and repetitive textures, and optical degradations pose significant algorithmic challenges.", + "bbox": [ + 75, + 667, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f6e13b1b26d5aa583f195fb5d1a80779a70bb0c3626c9f6d51c837c0a4faedf2.jpg", + "image_caption": [ + "Figure 1. Many methods use temporal context but neglect inter-camera information, leading to incomplete results (top). Other works focus on exploiting inter-camera context but neglect temporal information, yielding incoherent predictions (middle). In contrast, our method achieves a consistent, dense 3D reconstruction by iteratively integrating geometric depth estimation from multiple cameras with monocular depth refinement (bottom)." + ], + "image_footnote": [], + "bbox": [ + 506, + 268, + 888, + 590 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing works approaching the aforementioned task can be divided into two lines of research. Many methods have focused on recovering 3D scene structure via structure-from-motion (SfM). In particular, simultaneous localization and mapping (SLAM) methods focus on accurate egomotion estimation and usually only recover sparse 3D structure [9, 29, 34, 12, 11]. They typically treat dynamic objects or uniformly textured regions as outliers yielding an incomplete 3D reconstruction result, which makes them less suitable for AVs and robotics. In addition, only a few works have focused on multi-camera setups [24, 8, 33, 30, 26]. In contrast, multi-view stereo (MVS) methods [31, 32, 41, 28,", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution.", + "bbox": [ + 94, + 887, + 205, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3216", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "57, 27, 17] aim to estimate dense 3D geometry but focus on static scenes and highly overlapping sets of images with known poses.", + "bbox": [ + 78, + 90, + 467, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The second line of research focuses on dense depth prediction from monocular cues, such as perspective object appearance and scene context [65, 15, 16, 59, 49, 61, 19]. However, due to the injective property of projecting 3D structures onto a 2D plane, reconstructing depth from a single image is an ill-posed problem, which limits the accuracy and generalization of these methods. Recent methods [51, 18, 21], inspired by MVS literature, combine monocular cues with temporal context but are focused on front-facing, single-camera setups. A handful of recent works extend monocular depth estimation to multi-camera setups [22, 52, 54]. These methods utilize the spatial context to improve accuracy and realize absolute scale depth learning. However, those works neglect the temporal domain which provides useful cues for depth estimation.", + "bbox": [ + 80, + 138, + 467, + 364 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivated by this observation, we introduce R3D3, a system for dense 3D reconstruction and ego-motion estimation from multiple cameras of dynamic outdoor environments. Our approach combines monocular cues with geometric depth estimates from both spatial inter-camera context as well as inter- and intra-camera temporal context. We compute accurate geometric depth and pose estimates via iterative dense correspondence on frames in a co-visibility graph. For this, we extend the dense bundle adjustment (DBA) operator in [48] to multi-camera setups, increasing robustness and recovering absolute scene scale. To determine co-visible frames across cameras, we propose a simple yet effective multi-camera algorithm that balances performance and efficiency. A depth refinement network takes geometric depth and uncertainty as input and produces a refined depth that improves the reconstruction of, e.g., moving objects and uniformly textured areas. We train this network on real-world driving data without requiring any LiDAR ground-truth. Finally, the refined depth estimates serve as the basis for the next iterations of geometric estimation, thus closing the loop between incremental geometric reconstruction and monocular depth estimation.", + "bbox": [ + 80, + 368, + 467, + 698 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We summarize our contributions as follows. 1) we propose R3D3, a system for dense 3D reconstruction and egomotion estimation in dynamic scenes, 2) we estimate geometric depth and poses with a novel multi-camera DBA formulation and a multi-camera co-visibility graph, 3) we integrate prior geometric depth and uncertainty with monocular cues via a depth refinement network.", + "bbox": [ + 80, + 702, + 467, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As a result, we achieve state-of-the-art performance across two widely used multi-camera depth estimation benchmarks, namely DDAD [19] and NuScenes [3]. Further, we show that our system exhibits superior accuracy and robustness compared to monocular SLAM methods [48, 5].", + "bbox": [ + 80, + 810, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 504, + 90, + 638, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-view stereo. MVS methods aim to recover dense 3D scene structure from a set of images with known poses. While earlier works focused on classical optimization [31, 41, 4, 13, 14, 62, 32], more recent works capitalize on the success of convolutional neural networks (CNNs). They use CNNs to estimate features that are matched across multiple depth-hypothesis planes in a 3D cost volume [28, 57, 64, 27, 17, 58, 60]. While early approaches adopt multiple cost volumes across image pairs [64], recent approaches use a single cost volume across the whole image set [57]. These works assume a controlled setting with many, highly overlapping images and known poses to create a 3D cost volume. Instead, we aim to achieve robust, dense 3D reconstruction from an arbitrary multi-camera setup on a moving platform with an unknown trajectory.", + "bbox": [ + 503, + 114, + 888, + 340 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual SLAM. Visual SLAM approaches focus on jointly mapping the environment and tracking the trajectory of the observer from visual inputs, i.e. one or multiple RGB cameras. Traditional SLAM systems are often split into different stages, where first images are processed into keypoint matches, which subsequently are used to estimate the 3D scene geometry and camera trajectory [9, 10, 6, 34, 35, 5, 39]. Another line of work focuses on directly optimizing 3D geometry and camera trajectory based on pixel intensities [12, 11, 56, 55]. A handful of works have focused on multi-camera SLAM systems [24, 8, 33, 30, 26]. Recent methods integrate CNN-based depth and pose predictions [45, 56, 55] into the SLAM pipeline. The common challenge these methods face is outliers in the pixel correspondences caused by the presence of low-textured areas, dynamic objects, or optical degradations. Hence, robust estimation techniques are used to filter these outliers, yielding an incomplete, sparse 3D reconstruction result.", + "bbox": [ + 503, + 340, + 888, + 612 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In contrast, dense 3D reconstruction and ego-motion estimation has proven to be more challenging. Early works utilize active depth sensors [36, 64] to alleviate the above-mentioned challenges. Recently, several works on dense visual SLAM from RGB input have emerged [1, 44, 7, 46, 48]. While these methods are able to produce high-quality depth maps and camera trajectories, they inherit the limitations of their traditional counterparts, i.e. their predictions are subject to noise when there are outliers in the pixel correspondences. This can lead to artifacts in the depth maps, inaccurate trajectories, or even a complete failure of the system. On the contrary, we achieve robust, dense 3D reconstruction and ego-motion estimates by jointly leveraging multi-camera constraints as well as monocular depth cues.", + "bbox": [ + 503, + 614, + 888, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Self-supervised depth estimation. The pioneering work of Zhou et al. [65] learns depth estimation as a proxy task while minimizing a view synthesis loss that uses geometric constraints to warp color information from a reference to a target view. Subsequent research has focused on improv-", + "bbox": [ + 503, + 825, + 888, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3217", + "bbox": [ + 483, + 946, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ing network architectures, loss regularization, and training schemes [15, 16, 20, 59, 49, 61, 19]. Recent methods draw inspiration from MVS and propose to use 3D cost volumes in order to incorporate temporal information [51, 18, 53, 21]. While these methods achieve promising results, they still focus on single-camera, front-facing scenarios that do not reflect the real-world sensor setups of AVs [3, 43, 19]. Another recent line of work focuses on exploiting spatial information across overlapping cameras in a multi-camera setup [22, 52, 54]. These works propose to use static feature matches across cameras at a given time to guide depth learning and estimation, and to recover absolute scale. Our work aims to exploit both spatial and temporal cues in order to achieve a robust, dense 3D reconstruction from multiple cameras in dynamic outdoor environments.", + "bbox": [ + 75, + 90, + 472, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 334, + 169, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Problem formulation. At each timestep $t \\in T$ we are given a set of images $\\{\\mathbf{I}_t^c\\}_{c=1}^C$ from $C$ cameras that are mounted on a moving platform with known camera intrinsics $\\mathbf{K}_c$ and extrinsics $\\mathbf{T}_c$ with respect to a common reference frame. We aim to estimate the depth maps $\\mathbf{d}_t^c \\in \\mathbb{R}_+^{H \\times W}$ and ego-pose $\\mathbf{P}_t \\in SE(3)$ at the current time step.", + "bbox": [ + 75, + 359, + 468, + 450 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Overview. Our system is composed of three stages. First, given a new set of images $\\{\\mathbf{I}_t^c\\}_{c = 1}^C$ , we extract deep features from each $\\mathbf{I}_t^c$ . We maintain a co-visibility graph $\\mathcal{G} = (\\mathcal{V},\\mathcal{E})$ where a frame $\\mathbf{I}_t^c$ represents a node $v\\in \\mathcal{V}$ and co-visible frames are connected with edges. For each edge $(i,j)\\in \\mathcal{E}$ in this graph, we compute the feature correlation $\\mathbf{C}_{ij}$ of the two adjacent frames. Second, given initial estimates of the depth $\\mathbf{d}_i$ and the relative pose $\\mathbf{G}_{ij} = \\left(\\mathbf{P}_{t_j}\\mathbf{T}_{c_j}\\right)^{-1}\\mathbf{P}_{t_i}\\mathbf{T}_{c_i}$ between the two frames, we compute the induced flow $\\mathbf{f}_{ij}^{*}$ . We correct the induced flow with a recurrent update operator using the feature correlations $\\mathbf{C}_{ij}$ . We then globally align the updated flow estimates at each edge $(i,j)$ with the current estimates of $\\mathbf{G}_{ij}$ and $\\mathbf{d}_i$ across the co-visibility graph $\\mathcal{G}$ with our proposed multi-camera DBA. Third, we introduce a depth refinement network that refines the geometric depth estimates with monocular depth cues to better handle scenarios that are challenging for geometric estimation methods. We illustrate our architecture in Fig. 2.", + "bbox": [ + 75, + 452, + 472, + 727 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Feature Extraction and Correlation", + "text_level": 1, + "bbox": [ + 76, + 738, + 387, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a new observation $\\{\\mathbf{I}_t^c\\}_{c = 1}^C$ , we first extract deep image features, update the co-visibility graph, and compute feature correlations. We describe these steps next.", + "bbox": [ + 75, + 761, + 468, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Feature extraction. We follow [47, 48] and extract both correlation and context features from each image individually via deep correlation and context encoders $g_{\\phi}$ and $g_{\\psi}$ .", + "bbox": [ + 75, + 809, + 468, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Co-visibility graph. We store correlation and context features in a graph $\\mathcal{G} = (\\mathcal{V},\\mathcal{E})$ . Each node corresponds to an image $\\mathbf{I}_t^c$ and an edge in the graph indicates that two", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "images are considered a pair in the feature correlation and bundle adjustment steps. Contrary to [48], we construct $\\mathcal{G}$ with three kinds of edges: temporal, spatial, and spatial-temporal. Since the number of possible edges is $|\\mathcal{V}|^2$ and the system runtime scales linearly with $|\\mathcal{E}|$ , the degree of sparsity in the co-visibility graph is crucial. We thus carefully design a simple yet effective co-visibility graph construction algorithm in multi-camera setups (see Fig. 3).", + "bbox": [ + 496, + 90, + 890, + 210 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For temporal edges (Fig. 3 in green), we examine the time window $t - \\Delta t_{\\mathrm{intra}}$ and connect all frames of the same camera that are less than $r_{\\mathrm{intra}}$ time steps apart. For spatial and spatial-temporal edges we exploit three priors. 1) we know camera adjacency from the given calibration, 2) we assume motion in the direction of the forward-facing camera and 3) the observer undergoes limited motion within the local time window. We establish spatial edges (Fig. 3 in red) between adjacent cameras within time step $t$ . We further establish spatial-temporal edges (Fig. 3 in orange) given the static camera adjacency within $t - \\Delta t_{\\mathrm{inter}}$ . In particular, we connect camera $c_i$ and $c_j$ from any $t'$ to $t' - r_{\\mathrm{inter}}$ , if $c_i$ and $c_j$ connect within $t$ and if $c_j$ is closer to the forward-facing camera than $c_i$ under forward motion assumption. Finally, we remove an edge $(i,j)$ if node $i$ or $j$ is outside the local time windows $t - \\Delta t_{\\mathrm{inter}}$ or $t - \\Delta t_{\\mathrm{intra}}$ . We remove unconnected nodes from the graph. We provide pseudo-code and additional discussion in the supplemental material.", + "bbox": [ + 496, + 212, + 892, + 483 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Feature correlation. For each edge $(i,j) \\in \\mathcal{E}$ we compute the 4D feature correlation volume via the dot-product", + "bbox": [ + 498, + 484, + 890, + 513 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {C} _ {i j} = \\left\\langle g _ {\\phi} (\\mathbf {I} _ {i}), g _ {\\phi} (\\mathbf {I} _ {j}) \\right\\rangle \\in \\mathbb {R} ^ {H \\times W \\times H \\times W}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 518, + 890, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As in [47, 48], we constrain the correlation search region to a radius $r$ with a lookup operator", + "bbox": [ + 498, + 542, + 890, + 571 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {r}: \\mathbb {R} ^ {H \\times W \\times H \\times W} \\times \\mathbb {R} ^ {H \\times W \\times 2} \\rightarrow \\mathbb {R} ^ {H \\times W \\times (r + 1) ^ {2}}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 577, + 890, + 597 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "that samples a $H \\times W$ grid of coordinates from the correlation volume using bilinear interpolation.", + "bbox": [ + 498, + 603, + 890, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Depth and Pose Estimation", + "text_level": 1, + "bbox": [ + 500, + 640, + 745, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given the correlation volume $\\mathbf{C}_{ij}$ , we here describe how to estimate the relative pose $\\mathbf{G}_{ij}$ and depth $\\mathbf{d}_i$ for each edge $(i,j)\\in \\mathcal{E}$ in the co-visibility graph.", + "bbox": [ + 498, + 662, + 890, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Flow correction. Given an initial estimate of $\\mathbf{G}_{ij}$ and $\\mathbf{d}_i$ , we first compute the induced flow $\\mathbf{f}_{ij}^*$ to sample the correlation volume $\\mathbf{C}_{ij}$ using (2). We then feed the sampled correlation features, the context features $g_{\\psi}(\\mathbf{I}_i)$ , and the induced flow $\\mathbf{f}_{ij}^*$ into a convolutional GRU. The GRU predicts a flow residual $\\mathbf{r}_{ij}$ and confidence weights $\\mathbf{w}_{ij} \\in \\mathbb{R}^{H \\times W \\times 2}$ as in [48]. A challenge of correspondence estimation in a multi-camera setup is that the flow magnitude varies greatly among edges in the co-visibility graph due to inter-camera edges with large relative rotation. To this end, we propose to subtract the rotational part of $\\mathbf{f}_{ij}^*$ in those edges via", + "bbox": [ + 496, + 709, + 890, + 878 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {i j} ^ {\\prime} = \\left(\\mathbf {x} _ {i} + \\mathbf {f} _ {i j} ^ {*}\\right) - \\Pi_ {c _ {j}} \\left(\\mathbf {R} _ {c _ {j}} ^ {- 1} \\mathbf {R} _ {c _ {i}} \\circ \\Pi_ {c _ {i}} ^ {- 1} (\\mathbf {1})\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 883, + 890, + 904 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3218", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3394cc6e27e1e5ae6b92a7c4290f3b4bf962e9fc7188f204c48fe8cc431e1d4f.jpg", + "image_caption": [ + "Figure 2. Method overview. First, frames $\\{\\mathbf{I}_t^c\\}_{c=1}^C$ from $C$ cameras at time $t$ are encoded and integrated into the co-visibility graph $\\mathcal{G} = (\\mathcal{V}, \\mathcal{E})$ with initial guesses of depth maps $\\mathbf{d}_t^c$ and ego-pose $\\mathbf{P}_t$ (Sec. 3.1). Second, for each edge $(i,j) \\in \\mathcal{E}$ , we compute the induced flow $\\mathbf{f}_{ij}^*$ from $\\mathbf{d}_i$ and relative camera pose $\\mathbf{G}_{ij}$ derived from ego-poses $\\mathbf{P}$ and camera extrinsics $\\mathbf{T}$ . Given $\\mathbf{f}_{ij}^*$ , we pool feature correlations from $\\mathbf{C}_{ij}$ with operator $L_r$ as input to a GRU that estimates flow update $\\mathbf{r}_{ij}$ and confidence $\\mathbf{w}_{ij}$ . We globally align depths $\\mathbf{d}$ and poses $\\mathbf{P}$ with the new flow estimates $\\mathbf{f}$ via our multi-camera DBA operator in $k$ iterations (Sec. 3.2). Finally, for each node $i \\in \\mathcal{V}$ , we refine the initial geometric estimate $\\mathbf{d}_i$ given the aggregated confidence $\\mathbf{w}_i$ via $\\mathcal{D}_{\\theta}$ (Sec. 3.3). We highlight our contributions in color." + ], + "image_footnote": [], + "bbox": [ + 83, + 95, + 872, + 306 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e3b07928cdfa93032e6481220250b593cdd47e060120998b8a615d949cd65742.jpg", + "image_caption": [ + "Figure 3. Co-visibility graph. We illustrate an example of the connectivity pattern of the co-visibility graph using our multi-camera graph construction algorithm. We use $\\Delta t_{\\mathrm{intra}} = 3$ , $\\Delta t_{\\mathrm{inter}} = 2$ , $r_{\\mathrm{intra}} = 2$ , $r_{\\mathrm{inter}} = 2$ with six cameras. We depict temporal, spatial, and spatial-temporal edges." + ], + "image_footnote": [], + "bbox": [ + 125, + 412, + 421, + 599 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{x}_i$ are pixel coordinates of frame $i$ , $\\Pi_c$ denotes the projection operator under camera $c$ and $\\mathbf{R}$ is the rotation of transformation $\\mathbf{T} = (\\mathbf{R} \\mathbf{t})$ . This aligns the flow magnitude with temporal, intra-camera edges. Note that, while we input $\\mathbf{f}_{ij}'$ instead of $\\mathbf{f}_{ij}^*$ to the GRU, we still sample the correlation volume $\\mathbf{C}_{ij}$ based on $\\mathbf{f}_{ij}^*$ .", + "bbox": [ + 75, + 690, + 468, + 781 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Pose and depth correction. We update our pose and depth estimates given the updated flow $\\mathbf{f}_{ij} = \\mathbf{f}_{ij}^{*} + \\mathbf{r}_{ij}$ by minimizing the re-projection error, defined as", + "bbox": [ + 75, + 781, + 468, + 825 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nE = \\sum_ {(i, j) \\in \\mathcal {E}} \\left\\| \\left(\\mathbf {x} _ {i} + \\mathbf {f} _ {i j}\\right) - \\Pi_ {c _ {j}} \\left(\\mathbf {G} _ {i j} \\circ \\Pi_ {c _ {i}} ^ {- 1} (\\mathbf {d} _ {i})\\right) \\right\\| _ {\\Sigma_ {i j}} ^ {2}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 838, + 468, + 873 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\| .\\|_{\\Sigma_{ij}}$ is the Mahalanobis norm and $\\Sigma_{ij} =$", + "bbox": [ + 76, + 885, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\operatorname{diag}(\\mathbf{w}_{ij})$ . Thus, only matched pixels where the confidence $\\mathbf{w}_{ij}$ is greater than zero contribute to the total cost. We extend the dense bundle adjustment (DBA) proposed in [48] to include the known extrinsics of the multi-camera setup. In particular, we decompose the relative poses between two frames $\\mathbf{G}_{ij}$ into the unknown, time-varying poses $\\mathbf{P}$ in the reference frame and the known static relative transformations $\\mathbf{T}$ between the cameras and the reference frame via", + "bbox": [ + 498, + 412, + 890, + 532 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {G} _ {i j} = \\left(\\mathbf {P} _ {t _ {j}} \\mathbf {T} _ {c _ {j}}\\right) ^ {- 1} \\mathbf {P} _ {t _ {i}} \\mathbf {T} _ {c _ {i}}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 539, + 890, + 560 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We linearize the residual of the energy function in Eq. 4 with a first-order Taylor expansion. We use Eq. 5 and treat $\\mathbf{T}_{c_j}$ and $\\mathbf{T}_{c_i}$ as constants when calculating the Jacobians, thus computing updates only for ego-pose $\\mathbf{P}$ . We apply the Gauss-Newton step to compute the updated $\\mathbf{P}^{(k)} = \\exp (\\delta \\xi^{(k - 1)})\\mathbf{P}^{(k - 1)}$ and depth $\\mathbf{d}^{(k)} = \\delta \\mathbf{d}^{(k - 1)} + \\mathbf{d}^{(k - 1)}$ with $\\delta \\xi^{(k - 1)}\\in \\mathfrak{se}(3)$ . We provide a detailed derivation in the supplementary material.", + "bbox": [ + 498, + 568, + 890, + 688 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our formulation has two advantages over DBA [48]. First, the optimization is more robust since $C$ frames are connected through a single ego-pose $\\mathbf{P}$ . If one or multiple frames have a high outlier ratio in feature matching, e.g. through lens-flare, low textured regions, or dynamic objects, we can still reliably estimate $\\mathbf{P}$ with at least one undisturbed camera. Second, if there are not only pixels matched across the temporal context but also pixels matched across the static, spatial context, we can recover the absolute scale of the scene. This is because for static, spatial matches the relative transformation $\\mathbf{G}_{ij} = \\mathbf{T}_{c_j}^{-1}\\mathbf{T}_{c_i}$ is known to scale so that $E$ is minimized if and only if $\\mathbf{d}$ is in absolute scale.", + "bbox": [ + 496, + 689, + 892, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training. We train the networks $g_{\\phi}$ and $g_{\\psi}$ as well as the flow correction GRU on dynamic scenes following the", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3219", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "procedure in [48]. As shown in [48], the geometric features learned from synthetic data can generalize to real-world scenes. We can therefore leverage existing synthetic driving datasets without relying on real-world ground-truth measurements from sensors like LiDAR or IMU to adjust our method to dynamic, multi-camera scenarios.", + "bbox": [ + 75, + 90, + 472, + 183 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Depth Refinement", + "text_level": 1, + "bbox": [ + 76, + 189, + 253, + 207 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "SfM relies on three assumptions: accurate pixel matches, sufficient camera movement, and a static scene. These assumptions do not always hold in the real world due to, e.g., low-textured areas, a static ego vehicle, or many dynamic agents. Still, we would like the system to produce reasonable scene geometry to ensure safe operation.", + "bbox": [ + 75, + 212, + 468, + 303 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "On the contrary, monocular depth cues are inherently not affected by these issues. However, they usually lack the accurate geometric detail of SfM methods. Hence, for each node $i \\in \\mathcal{V}$ , we complement the accurate, but sparse geometric depth estimates with monocular cues.", + "bbox": [ + 75, + 304, + 468, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Network design. We use a CNN $\\mathcal{D}_{\\theta}$ parameterized by $\\theta$ . We input the depth $\\mathbf{d}_i$ , confidence $\\mathbf{w}_i$ , and the corresponding image $\\mathbf{I}_i$ . The network predicts an improved, dense depth $\\mathbf{d}_i' = \\mathcal{D}_{\\theta}(\\mathbf{I}_i, \\mathbf{d}_i, \\mathbf{w}_i)$ . We obtain the per-frame depth confidence $\\mathbf{w}_i$ for frame $i$ by using the maximum across the per-edge confidence weights $\\mathbf{w}_{ij}$ . We compute $\\mathbf{w}_i = \\max_j \\frac{1}{2} (\\mathbf{w}_{ij}^x + \\mathbf{w}_{ij}^y)$ where $x$ and $y$ are the flow directions. We use $\\max(\\cdot)$ because we observe that depth triangulation will be accurate if at least one pixel is matched with high confidence. We sparsify input depth and confidence weights by setting regions with confidence $\\mathbf{w}_i < \\beta$ to zero. We concatenate these with the image $\\mathbf{I}_i$ . We further concatenate depth and confidence with features at $1/8^{\\text{th}}$ scale. As in [16], the output depth is predicted at four scales. To accommodate different focal lengths among cameras in the sensor setup, we do focal length scaling of the output [45]. Training. Contrary to geometric approaches, monocular depth estimators infer depth from semantic cues, which makes it hard for them to generalize across domains [23]. Hence, instead of relying on synthetic data, we train $\\mathcal{D}_{\\theta}$ on raw, real-world video in a self-supervised manner by minimizing a view synthesis loss [65]. We minimize the photometric error $\\mathrm{pe}(\\mathbf{I}_t^c, \\mathbf{I}_{t'}^{c' \\rightarrow c})$ between a target image $\\mathbf{I}_t^c$ and a reference image $\\mathbf{I}_{t'}^{c'}$ warped to the target viewpoint via", + "bbox": [ + 75, + 378, + 468, + 743 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I} _ {t ^ {\\prime} \\rightarrow t} ^ {c ^ {\\prime} \\rightarrow c} = \\Phi \\big (\\mathbf {I} _ {t ^ {\\prime}} ^ {c ^ {\\prime}}; \\Pi_ {c ^ {\\prime}} \\big (\\mathbf {G} _ {(t, c) (t ^ {\\prime}, c ^ {\\prime})} \\circ \\Pi_ {c} ^ {- 1} \\big (\\mathbf {d} _ {t} ^ {c} \\big) \\big) \\big), \\quad (6)\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 752, + 468, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with $\\Phi$ the bi-linear sampling function, $\\mathbf{d}_t^c$ the predicted depth, $c' = c \\pm 1$ and $t' = t \\pm 1$ . We compute photometric similarity with SSIM [50] and $L_1$ distances. We use $\\mathbf{G}_{(t,c)(t',c')} = (\\mathbf{P}_{t'}\\mathbf{T}_{c'})^{-1}\\mathbf{P}_t\\mathbf{T}_c$ generated by the first two stages of our system (see Sec. 3.2). Further, self-supervised depth estimation is well-studied, and we follow the common practice of applying regularization techniques to filter the photometric error [16, 63, 20]. First, we mask areas", + "bbox": [ + 75, + 779, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{M}^{\\mathrm{st}} = \\left[\\mathrm{pe}(\\mathbf{I}_t^c,\\mathbf{I}_{t'\\to t}^{c'\\to c}) < \\mathrm{pe}(\\mathbf{I}_t^c,\\mathbf{I}_{t'}^{c'})\\right]$ , i.e. we filter regions where assuming a stationary scene would induce a lower loss than re-projection. Second, we compute an induced flow consistency mask from $\\mathbf{f}^*$", + "bbox": [ + 496, + 89, + 893, + 151 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} ^ {\\mathrm {f c}} = \\left[ \\left\\| \\mathbf {f} _ {(t, c) \\left(t ^ {\\prime}, c ^ {\\prime}\\right)} ^ {*} + \\Phi \\left(\\mathbf {f} _ {\\left(t ^ {\\prime}, c ^ {\\prime}\\right) (t, c)} ^ {*}; \\mathbf {x} + \\mathbf {f} _ {(t, c) \\left(t ^ {\\prime}, c ^ {\\prime}\\right)} ^ {*}\\right) \\right\\| _ {2} < \\gamma \\right]. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 160, + 893, + 200 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This term warps pixel coordinates $\\mathbf{x}$ from target to reference view, looks up their value in $\\mathbf{f}_{(t',c')}(t,c)$ , and compares them to $\\mathbf{f}_{(t,c)(t',c')}^*$ . Therefore, pixels not following the epipolar constraint like dynamic objects are masked. Third, to handle the self-occlusion of the ego-vehicle, we manually draw a static mask $\\mathbf{M}^{\\mathrm{oc}}$ . We can use a single mask for all frames since the cameras are mounted rigidly. Further, to handle occlusions due to change in perspective, we take the minimum loss $\\min_{t',c'}\\mathrm{pe}(\\mathbf{I}_t^c,\\mathbf{I}_{t'\\to t}^{c'\\to c})$ across all reference views. The overall loss for $\\mathcal{D}_{\\theta}$ is thus", + "bbox": [ + 496, + 200, + 890, + 349 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\min _ {t ^ {\\prime}, c ^ {\\prime}} \\left(\\mathbf {M} ^ {\\mathrm {s t}} \\mathbf {M} ^ {\\mathrm {f c}} \\mathbf {M} ^ {\\mathrm {o c}} \\cdot \\operatorname {p e} \\left(\\mathbf {I} _ {t} ^ {c}, \\mathbf {I} _ {t ^ {\\prime} \\rightarrow t} ^ {c ^ {\\prime} \\rightarrow c}\\right)\\right) + \\lambda \\mathcal {L} _ {\\text {s m o o t h}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 361, + 890, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with $\\mathcal{L}_{\\mathrm{smooth}}$ a spatial smoothness regularization term [15].", + "bbox": [ + 500, + 398, + 885, + 414 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Inference Procedure", + "text_level": 1, + "bbox": [ + 500, + 422, + 692, + 436 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given an input stream of multi-camera image sets, we perform incremental 3D reconstruction in three phases.", + "bbox": [ + 496, + 446, + 890, + 476 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Warmup phase. First, we add frames to the co-visibility graph if a single GRU step of a reference camera yields a large enough mean optical flow until we reach $n_{\\mathrm{warmup}}$ frames. At this stage, we infer depth with our refinement network $\\mathbf{d}_t^c = \\mathcal{D}_{\\theta}(\\mathbf{I}_t^c,\\mathbf{0},\\mathbf{0})$ . We write the depth into the co-visibility graph so that it can be used during initialization.", + "bbox": [ + 496, + 477, + 890, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Initialization phase. We initialize the co-visibility graph with the available frames and run $n_{\\mathrm{itr - wm}}$ GRU and bundle adjustment iterations. For the first $n_{\\mathrm{itr - wm}} / 2$ iterations, we fix depths in the bundle adjustment and only optimize poses, which helps with inferring the absolute scale of the scene.", + "bbox": [ + 496, + 566, + 890, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Active phase. We now add each incoming frame to the co-visibility graph. We initialize the new frames with $\\mathbf{d}_t^c = \\mathrm{mean}(\\mathbf{d}_{t - 4:t - 1}^c)$ and $\\mathbf{P}_t = \\mathbf{P}_{t - 1}$ . Then, we perform $n_{\\mathrm{iter1}}$ GRU and bundle adjustment updates, and apply the refinement network to all updated frames. If the mean optical flow of the reference camera between $t$ and $t - 1$ is low, we remove all frames at $t - 1$ from the co-visibility graph. This helps to handle situations with little to no egomotion. In case no frame is removed, we do another $n_{\\mathrm{iter2}}$ iterations. Finally, we write the updated depths and poses into the co-visibility graph.", + "bbox": [ + 496, + 643, + 890, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 821, + 633, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 847, + 689, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We perform extensive experiments on large-scale driving datasets that contain recordings from vehicles equipped", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3220", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/f494cd25cd1c3fe8c1864f472d1ef1f53c991dff70509eee5553210bccd23e05.jpg", + "table_caption": [ + "Table 1. Method ablation. We ablate our method components on the DDAD [19] dataset. We examine the influence of each component given the geometric estimation as in [48] with naive DBA as the baseline. Further, we show the influence of VKITTI [2] fine-tuning on the geometric estimation. We enumerate each variant for better reference. * median scaled depth, ** scaled trajectory." + ], + "table_footnote": [], + "table_body": "
No.Geom. Est.VKITTIMulti-Cam DBARefinementAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑ATE [m] ↓ATE** [m] ↓
1a*✓✓0.43826.9719.1090.636-2.134
1b✓✓0.44236.3918.6640.7361.6720.435
1c✓✓✓0.32015.4516.3030.7272.3560.922
2a✓0.2113.80612.6680.715--
3a✓✓✓✓0.1623.01911.4080.8111.2350.433
", + "bbox": [ + 114, + 128, + 849, + 222 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1e55eaccbd754ed38cb86e91d1f96b3b96e363d40188146b4da469df9ea8fa23.jpg", + "table_caption": [ + "Table 2. Co-visibility graph ablation. We compare our co-visibility graph construction algorithm to the original algorithm in [48] on the DDAD [19] dataset. We observe that our algorithm improves the overall runtime by an order of magnitude while maintaining the same level of performance." + ], + "table_footnote": [], + "table_body": "
GraphAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑ATE [m] ↓tinf [s] ↓
Original0.1622.96811.1560.8160.9823.23
Ours0.1623.01911.4080.8111.2350.35
", + "bbox": [ + 84, + 306, + 459, + 353 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/13cfb64e2236369bd900976dc1e18713f1e968a3b2ab7a45e9e23afbd345e8e4.jpg", + "table_caption": [ + "Table 3. Refinement network ablation. We show on the DDAD [19] dataset that both adding confidence weights $\\mathbf{w}_i$ and sparsifying the depth input via $\\mathbf{w}_i < \\beta$ to filter outliers in the input of depth refinement network $\\mathcal{D}_{\\theta}$ is vital to depth accuracy." + ], + "table_footnote": [], + "table_body": "
wiwi<βAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
0.1814.07812.1080.789
✓0.1733.49711.9240.792
✓✓0.1623.01911.4080.811
", + "bbox": [ + 106, + 414, + 437, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "with multiple cameras, LiDARs, and other sensors. Note that we only use camera data for training and inference, and use LiDAR data only as ground-truth for evaluation. We evaluate our method in inference mode (cf. Sec. 3.4), i.e. we obtain predictions in a fully online (causal) manner to mimic real-world deployment.", + "bbox": [ + 75, + 492, + 468, + 582 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "DDAD. This dataset consists of 150 training and 50 validation scenes from urban areas. Each sequence has a length of 50 or 100 time steps at a frame rate of $10\\mathrm{Hz}$ . The sensor setup includes six cameras in a surround-view setup with up to $20\\%$ overlap. We follow [19] and evaluate depth up to $200\\mathrm{m}$ averaged across all cameras. We use self-occlusion masks from [52] to filter the ego-vehicle in the images. Images have a resolution of $1216\\times 1936$ and are downsampled to $384\\times 640$ in our experiments.", + "bbox": [ + 75, + 583, + 468, + 718 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "NuScenes. This dataset contains 700 training, 150 validation, and 150 testing sequences of urban scenes with challenging conditions such as nighttime and rain. Each scene is composed of 40 keyframes at $2\\mathrm{Hz}$ synchronized across sensors. The six cameras have a sampling rate of $12\\mathrm{Hz}$ and are arranged in a surround-view setup with up to $10\\%$ overlap. We follow [22] and evaluate depth averaged across all cameras on the validation set. We use a single self-occlusion mask for all scenes. While the raw images have a resolution of $900 \\times 1600$ , we use $768 \\times 448$ .", + "bbox": [ + 75, + 719, + 468, + 868 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. We implement our system in PyTorch [37]. Our multi-camera DBA is implemented in", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/df455e6662489f8ffabab06a4682c2ee2994ae6c2b6f807082be9e601ca3fd01.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 504, + 250, + 635, + 310 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0f3d17e6add867abf6235566e5f57d3c8f99632215273e840df03a58525cc11b.jpg", + "image_caption": [ + "Geom. Depth" + ], + "image_footnote": [], + "bbox": [ + 637, + 250, + 764, + 310 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/854459c2f6c83fd446b2d3b41b21f6bc2116e870ad253a9f390d19437ff69772.jpg", + "image_caption": [ + "Refined" + ], + "image_footnote": [], + "bbox": [ + 767, + 250, + 898, + 310 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c3fba9cbbd9e44db0532e9b65cadbb0c9bafb58cff347c82408351e0aca428d1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 311, + 633, + 375 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/65058b1936539c0c613c01b1acce8736f13be4318e37c9790785d4979f916471.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 637, + 311, + 764, + 375 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/036c9f240024360805fd3fc0529fff4f9e95d6e72d39ebafdd8c2011d29b10fd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 767, + 311, + 898, + 375 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1493ca10345502ffccbd606d8b06a98079489c9031715da8046bf7beaaab7f95.jpg", + "image_caption": [ + "Figure 4. Depth refinement. We plot images overlayed with confidence $\\mathbf{w}_i$ , the geometric depth estimate $\\mathbf{d}$ , and the refined depth $\\mathbf{d}'$ from $\\mathcal{D}_{\\theta}$ . We observe a smoother ground plane, corrected dynamic objects, and filtered outliers." + ], + "image_footnote": [], + "bbox": [ + 504, + 376, + 633, + 436 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7ab81b528b6f25eaad7c7954b3e7c0f867677f18bb9f14debc57b95f20729b73.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 637, + 376, + 764, + 436 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/190b36e7b2546ecc8f404e338e25c94909342a702db666c68ac3f5af845b1f07.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 767, + 376, + 898, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CUDA. We fine-tune $g_{\\phi}$ , $g_{\\psi}$ and the flow correction GRU on VIKITTI2 [2] for 10 epochs with a batch size of 1, sequence length of 7, and learning rate $10^{-4}$ with the pretrained model in [48]. For $\\mathcal{D}_{\\theta}$ , we use a U-Net [38] with ResNet18 [25] encoder and initialize it with ImageNet [40] pre-trained weights. We use $\\beta = 0.5$ , $\\gamma = 3$ and $\\lambda = 10^{-3}$ . We train for 20 epochs with batch size of 6 and the Adam optimizer with learning rate $10^{-4}$ , $\\beta_{1} = 0.9$ , and $\\beta_{2} = 0.999$ . We reduce the learning rate by a factor of 10 after 15 epochs. For inference, the runtime is measured for a set of six images on a single RTX3090 GPU. Each sequence is initialized with 3 warmup frames filtered at a mean flow threshold of 1.75. We build the co-visibility graph with $\\Delta t_{\\mathrm{intra}} = 3$ , $r_{\\mathrm{intra}} = 2$ , $\\Delta t_{\\mathrm{inter}} = 2$ and $r_{\\mathrm{inter}} = 2$ .", + "bbox": [ + 496, + 513, + 890, + 727 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 739, + 663, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Method ablation. We ablate our method components on the DDAD dataset in Tab. 1. The geometric estimation baseline (1a) consists of [48] with the naive DBA formulation applied to all cameras and the co-visibility graph as described in Sec. 3.1. It performs poorly in depth and pose estimation, with an Abs. Rel. score of 0.438 and an absolute trajectory error (ATE) [42] of $2.134\\mathrm{m}$ , even when adjusting for scale. Next, we add our multi-camera DBA (1b). We observe that, even without VKITTI fine-tuning, the pose esti", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3221", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0e4dbeede49c8541ef7b3f60700ebd01c515d36ac92053cb923131591dd807ae.jpg", + "table_caption": [ + "Table 4. Comparison to state-of-the-art on DDAD. We compare favorably to existing methods on both scale-aware and scale-invariant depth prediction. * median scaled depth." + ], + "table_footnote": [], + "table_body": "
MethodAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
FSM [22]0.201---
SurroundDepth [52]0.2083.37112.9770.693
Ours0.1623.01911.4080.811
FSM* [22]0.202---
SurroundDepth* [52]0.2003.39212.2700.740
MCDP* [54]0.1933.11112.2640.811
Ours*0.1693.04111.3720.809
", + "bbox": [ + 102, + 128, + 437, + 234 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8d5ffd8822b859ad9c40089f6e8dcad5edfa1dc692534a708eb7935a47ee737c.jpg", + "table_caption": [ + "Table 5. Per-camera evaluation on DDAD. We show a per-camera breakdown of previous works, our $\\mathcal{D}_{\\theta}$ only (cf. 2a in Tab. 1), and our full method. Our full method performs the best with a particularly significant improvement on the side-view cameras while $\\mathcal{D}_{\\theta}$ performs similarly to previous works." + ], + "table_footnote": [], + "table_body": "
MethodAbs Rel ↓
FrontF.LeftF-rightB.LeftB-rightBack
FSM [22]0.1300.2010.2240.2290.2400.186
SurroundDepth [52]0.1520.2070.2300.2200.2390.200
Dθ only0.1540.2130.2370.2310.2370.194
Ours0.1280.1600.1680.1720.1740.169
", + "bbox": [ + 76, + 310, + 470, + 402 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/03b9f5987f04225edb4ce20aa3ffbb651943db495e644671dc9dd576123336a6.jpg", + "table_caption": [ + "Table 6. Comparison to multi-frame methods on DDAD. We compare to methods that exploit temporal context from a single camera [51, 18]. We evaluate only the front camera since these methods were trained only on this camera." + ], + "table_footnote": [], + "table_body": "
MethodFront Camera
Abs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
ManyDepth [51]0.1463.25814.0980.822
DepthFormer [18]0.1352.95312.4770.836
Ours0.1283.16813.2140.868
", + "bbox": [ + 102, + 465, + 437, + 542 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0766c5aadf320b1e2f29a2edb3979849034769e4b6e09b8cbc5e9add958b7c5f.jpg", + "table_caption": [ + "Table 7. Pose evaluation on DDAD. We compare our method to state-of-the-art monocular SLAM methods for which we report the average ATE across the cameras that successfully tracked the camera path. ** scaled trajectory." + ], + "table_footnote": [], + "table_body": "
DROID-SLAM [48]ORB-SLAMv3 [5]Ours
ATE** [m] ↓7.5006.1790.433
", + "bbox": [ + 102, + 603, + 434, + 637 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "mation accuracy improves dramatically over the naive DBA baseline. The relative scale ATE drops from $2.134\\mathrm{m}$ to only $0.435\\mathrm{m}$ . The absolute scale ATE is only about $1.2\\mathrm{m}$ higher, indicating the scene scale is recovered accurately.", + "bbox": [ + 75, + 657, + 467, + 717 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Using VKITTI fine-tuning (1c), we achieve significant gains in depth accuracy, where Abs. Rel. drops to 0.32 and $\\delta_{1.25}$ increases to $72.7\\%$ . However, note that VKITTI fine-tuning does not affect the $\\delta_{1.25}$ score, i.e. it helps mostly with depth outliers. We attribute this to the absence of dynamic objects in the training data of [48] so that fine-tuning helps to adjust the confidence prediction to handle such outliers (cf. Sec. 3.2). We further test the depth refinement network (Sec. 3.3) without geometric estimation prior (2a). The depth obtained from $\\mathcal{D}_{\\theta}$ is less prone to outliers, as evidenced by its low Abs. Rel., Sq. Rel. and RMSE scores. However, note that its $\\delta_{1.25}$ is only $71.5\\%$ , i.e. its", + "bbox": [ + 75, + 719, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/eb4eceb587e81555ce56c84b82137c45e4c2b8b83925d21f488663cfdcc0b9a7.jpg", + "image_caption": [ + "Figure 5. Depth in $\\delta_{1.25^n}$ range for different thresholds on DDAD. We depict the ratio of depth estimates $d$ for which $\\delta(d) < 1.25^n$ where $\\delta(d) = \\max\\left(\\frac{d}{d^*}, \\frac{d^*}{d}\\right)$ and $d^*$ is ground-truth depth. Note that values at $n = 1, 2, 3$ represent $\\delta_{1.25}, \\delta_{1.25^2}, \\delta_{1.25^3}$ ." + ], + "image_footnote": [], + "bbox": [ + 526, + 92, + 867, + 290 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1006bf72ead2621a5ec995540021983a5fee1e057cad7c79cd06b38a5540604c.jpg", + "table_caption": [ + "Table 8. Comparison to state-of-the-art on NuScenes. Evaluated up to $80\\mathrm{m}$ for scale-aware depth as in [22, 52] and $60\\mathrm{m}$ for median-scaled depth (denoted with $*$ ) as in [54]." + ], + "table_footnote": [], + "table_body": "
MethodAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
FSM [22]0.297---
SurroundDepth [52]0.2804.4017.4670.661
Ours0.2534.7597.1500.729
PackNet*[19]0.3033.1547.0140.655
FSM* [22]0.2703.1856.8320.689
SurroundDepth* [52]0.2453.0676.8350.719
MCDP* [54]0.2373.0306.8220.719
Ours*0.2353.3326.0210.749
", + "bbox": [ + 526, + 397, + 861, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "depth accuracy compared to the geometric depth estimates is actually lower when disregarding outliers. Finally, we test our full system (3a). Compared to geometric estimation (1d), we observe a significant improvement in outlier sensitive metrics like RMSE, but also in outlier robust metrics like $\\delta_{1.25}$ . Additionally, the pose estimation accuracy is increased and the difference between scaled and non-scaled ATE is smaller. Compared to depth obtained from $\\mathcal{D}_{\\theta}(2\\mathrm{a})$ , the increase in outlier sensitive metrics is smaller but still significant, e.g. 1.26m in RMSE. Further, we observe a sizable gain in $\\delta_{1.25}$ of 9.6 percentage points.", + "bbox": [ + 496, + 535, + 890, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Further, in Fig. 5, we compare the $\\delta_{1.25^n}$ scores at different accuracy thresholds $n$ of our geometric depth estimation without refinement ('Ours (Geometric)'), our refinement network only ('Ours (Monocular)') and our full method ('Ours'). The results confirm our hypothesis that while geometric estimates are more accurate than monocular depth estimates, they are also noisier. Importantly, the results further illustrate that our full method can effectively combine the strengths of both approaches while not suffering from their weaknesses.", + "bbox": [ + 496, + 703, + 890, + 853 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Co-visibility graph construction. In Tab. 2, we compare our co-visibility graph construction algorithm (Sec. 3.1) to a multi-camera adaption of the algorithm in [48]. Ours", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3222", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d4ed7805dd5f915234f2ecc5675ba5b2575d43a5930b9062b3e46d4b5581b42a.jpg", + "table_caption": [ + "Table 9. Per-camera evaluation on NuScenes. We compare our method with previous works on scale-aware depth estimation. Evaluated up to $80\\mathrm{m}$ as in Tab. 8. We observe the same trend as on DDAD, i.e. our method performs best across all cameras, with a particularly high improvement on the side views." + ], + "table_footnote": [], + "table_body": "
MethodAbs Rel ↓
FrontF.LeftF-rightB.LeftB_rightBack
FSM [22]0.1860.2870.3750.2960.4180.221
SurroundDepth [52]0.1790.2600.3400.2820.4030.212
Ours0.1740.2300.3020.2490.3600.201
", + "bbox": [ + 83, + 156, + 459, + 233 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/77c761330b5834edeb108e744c4d6ed40a9c4a4a91383e2e1b587f6e61929549.jpg", + "table_caption": [ + "Table 10. Cross-dataset transfer. We use models trained on DDAD to evaluate scale-aware depth prediction on the NuScenes dataset. We compare to state-of-the-art methods [22, 52] and observe that our method exhibits better generalization ability (cf. Tab. 8)." + ], + "table_footnote": [], + "table_body": "
MethodAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
FSM [22]0.3495.0648.7850.499
SurroundDepth [52]0.3645.4768.4470.525
Ours0.2924.8007.6770.660
", + "bbox": [ + 104, + 313, + 437, + 371 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "yields similar performance in depth estimation, with the exact same Abs. Rel. score and only minor difference in other metrics. Further, the absolute scale ATE is only slightly $(25\\mathrm{cm})$ higher. In contrast, using our algorithm, we achieve a runtime reduction of nearly $10\\times$ on the full system.", + "bbox": [ + 75, + 383, + 467, + 458 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Depth refinement network. We verify the choice of our inputs to $\\mathcal{D}_{\\theta}$ in Tab. 3. If we do not input the confidence $\\mathbf{w}_i$ and do not sparsify the depth via $\\mathbf{w}_i < \\beta$ before feeding it to $\\mathcal{D}_{\\theta}$ , we observe the lowest performance. If we input the confidence $\\mathbf{w}_i$ but do not sparsify the depth, we see an improvement over not using them. We achieve the best performance with the inputs described in Sec. 3.3.", + "bbox": [ + 75, + 458, + 467, + 563 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Moreover, we show qualitative examples of our depth refinement in Fig. 4. The confidence $\\mathbf{w}_i$ (overlaid with the image) segments regions where geometric estimation is ambiguous, i.e. dynamic objects and uniformly textured areas like the sky and the road surface. The geometric depth maps exhibit severe artifacts in such regions. After refinement, these artifacts are corrected.", + "bbox": [ + 75, + 564, + 467, + 669 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Comparison to State-of-the-Art", + "text_level": 1, + "bbox": [ + 76, + 680, + 354, + 696 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "DDAD. In Tab. 4, we compare our method to existing self-supervised multi-camera depth estimation methods. We achieve significant improvements in scale-aware and scale-invariant depth prediction with only minor differences in absolute and relative scale results. In both settings, we achieve state-of-the-art results with the lowest Abs. Rel. scores of 0.162 and 0.169, respectively.", + "bbox": [ + 75, + 703, + 467, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Fig. 5 we compare the $\\delta_{1.25^n}$ scores of our method to the state-of-the-art approaches on DDAD at different $n$ . For small values of $n$ , we observe a particularly pronounced performance gain over existing methods. This shows the advantage of combining highly accurate geometric estimates with monocular cues. Further, our method consistently out", + "bbox": [ + 75, + 810, + 467, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "performs the baselines over all values of $n$ for $\\delta < 1.25^n$ .", + "bbox": [ + 498, + 90, + 877, + 104 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Fig. 6, we show a qualitative comparison to existing works. On the left side, we illustrate depth maps across three cameras. Compared to FSM [22] and Surround-Depth [52], we produce sharper depth boundaries. On the right side, we illustrate point clouds accumulated over time. We produce a more consistent reconstruction, as can be seen when focusing on the vehicles or the fences beside the road.", + "bbox": [ + 496, + 107, + 890, + 212 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tab. 5 shows the per-camera breakdown of the scale-aware depth prediction comparison. The advantage of our method is particularly pronounced on the side cameras. Other methods struggle with the side views because the static spatial context is limited and they do not exploit any temporal or spatial-temporal context. The temporal and spatial-temporal contexts are conducive in the side views since sideward motion leads to better triangulation angles than forward motion. This is also evidenced by the results of $\\mathcal{D}_{\\theta}$ without geometric estimation, which performs similarly to the baseline methods, struggling with the side views. In contrast, our full system performs well across all cameras.", + "bbox": [ + 496, + 215, + 890, + 396 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We further compare to self-supervised single-camera methods that leverage temporal information in Tab. 6. For a fair comparison, we evaluate only the front camera. We compare favorably to DepthFormer [18] and Many-Depth [51]. In particular, we substantially improve in the outlier robust metric $\\delta_{1.25}$ and perform competitively in all others. Our Abs. Rel. score is the lowest at 0.128.", + "bbox": [ + 496, + 398, + 890, + 503 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To evaluate ego-motion estimation, we compare our system to state-of-the-art monocular SLAM methods [48, 5] in Tab. 7. We run the baselines on each camera and report the average ATE across the cameras that successfully tracked the camera path. Note that, contrary to our approach, the competing methods frequently failed to produce a trajectory. We observe that state-of-the-art monocular SLAM methods exhibit a large error (ATE), while our method recovers accurate trajectories.", + "bbox": [ + 496, + 506, + 890, + 641 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "NuScenes. In Tab. 8, we compare our system to previous self-supervised multi-camera depth estimation methods. We outperform previous methods by a significant margin, corroborating our findings on DDAD. Notably, we observe substantial improvements in scale-aware depth estimation, while previous works usually struggle with recovering absolute scale on this dataset since the overlap between cameras is smaller than in DDAD [22]. Therefore, previous works like MCDP [54] report results on scale-invariant depth prediction. We outperform existing methods also in this setting, although the performance gap is smaller. Note that the gap between scale-aware and scale-invariant evaluation is only 2 percentage points in $\\delta_{1.25}$ for our method, while for SurroundDepth [52] the gap is much larger with 5.8 percentage points. We show a per-camera breakdown of the comparison to the state-of-the-art in scale-aware depth estimation in Tab. 9. The results corroborate our findings", + "bbox": [ + 496, + 643, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3223", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/95e55d4b7101af8d04192135547bb051457ef804e1133ce167ef313bfac449b4.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison on DDAD. We show depth maps and point clouds accumulated over time along with input images, ground-truth LiDAR 3D Reconstruction, and the ego-vehicle in red. Our depth maps are sharper and more accurate. Our accumulated point clouds yield a more consistent 3D reconstruction. Note that we use our pose predictions for [22, 52] since these do not predict pose." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 893, + 415 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "on DDAD, namely that our method outperforms previous works across all cameras with a particularly pronounced improvement on the side views.", + "bbox": [ + 75, + 476, + 470, + 521 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Cross-dataset transfer. We finally test the cross-dataset generalization of our method versus FSM [22] and SurroundDepth [52]. In Tab. 10, we show scale-aware depth estimation results of models trained on DDAD, evaluated on NuScenes. We observe that the gap in Abs. Rel. widens compared to Tab. 8, with our method outperforming SurroundDepth by 0.072 in Abs. Rel. and FSM by 0.057. Further, our method maintains much higher levels of $\\delta_{1.25}$ and Sq. Rel., while SurroundDepth drops significantly in both metrics. Note that we apply focal length scaling [45] to all methods to accommodate differences in camera intrinsics.", + "bbox": [ + 75, + 523, + 472, + 690 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 707, + 194, + 722 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We introduced R3D3, a multi-camera system for dense 3D reconstruction of dynamic outdoor environments. The key ideas we presented are a multi-camera DBA operator that greatly improves geometric depth and pose estimation, a multi-camera co-visibility graph construction algorithm that reduces the runtime of our system by nearly $10\\times$ without significant performance drop, and a depth refinement network that effectively fuses geometric depth estimates with monocular cues. We observe that our design choices enable dense 3D mapping in challenging scenes presenting many dynamic objects, uniform and repetitive textures, and", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "complicated camera phenomena like lens flare and autoexposure. We achieve state-of-the-art performance in dense depth prediction across two multi-camera benchmarks.", + "bbox": [ + 498, + 476, + 890, + 522 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 501, + 539, + 596, + 554 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Michael Bloesch, Jan Czarnowski, Ronald Clark, Stefan Leutenegger, and Andrew J Davison. Codeslam—learning a compact, optimisable representation for dense visual slam. In CVPR, 2018.", + "[2] Yohann Cabon, Naila Murray, and Martin Humenberger. Virtual KITTI 2. 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In CVPR, 2017." + ], + "bbox": [ + 501, + 90, + 888, + 161 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "3226", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/R3D3_ Dense 3D Reconstruction of Dynamic Scenes from Multiple Cameras/df3f55bd-3906-48f7-856c-09ad31d9f51b_model.json b/2023/R3D3_ Dense 3D Reconstruction of Dynamic Scenes from Multiple Cameras/df3f55bd-3906-48f7-856c-09ad31d9f51b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..bd8dee6415ee8365c882ed69c4b5e2eba225c72f --- /dev/null +++ b/2023/R3D3_ Dense 3D Reconstruction of Dynamic Scenes from Multiple Cameras/df3f55bd-3906-48f7-856c-09ad31d9f51b_model.json @@ -0,0 +1,2499 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.131, + 0.87, + 0.153 + ], + "angle": 0, + "content": "R3D3: Dense 3D Reconstruction of Dynamic Scenes from Multiple Cameras" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.18, + 0.222, + 0.198 + ], + "angle": 0, + "content": "Aron Schmied1*" + }, + { + "type": "text", + "bbox": [ + 0.255, + 0.18, + 0.748, + 0.22 + ], + "angle": 0, + "content": "Tobias Fischer\\(^{1*}\\) Martin Danelljan\\(^{1}\\) Marc Pollefeys\\(^{1,2}\\) ETH Zürich 2 Microsoft" + }, + { + "type": "text", + "bbox": [ + 0.312, + 0.221, + 0.658, + 0.239 + ], + "angle": 0, + "content": "https://www.vis.xyz/pub/r3d3/" + }, + { + "type": "text", + "bbox": [ + 0.788, + 0.181, + 0.874, + 0.198 + ], + "angle": 0, + "content": "Fisher \\(\\mathrm{Yu}^1\\)" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.273, + 0.314, + 0.289 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.305, + 0.474, + 0.622 + ], + "angle": 0, + "content": "Dense 3D reconstruction and ego-motion estimation are key challenges in autonomous driving and robotics. Compared to the complex, multi-modal systems deployed today, multi-camera systems provide a simpler, low-cost alternative. However, camera-based 3D reconstruction of complex dynamic scenes has proven extremely difficult, as existing solutions often produce incomplete or incoherent results. We propose R3D3, a multi-camera system for dense 3D reconstruction and ego-motion estimation. Our approach iterates between geometric estimation that exploits spatial-temporal information from multiple cameras, and monocular depth refinement. We integrate multi-camera feature correlation and dense bundle adjustment operators that yield robust geometric depth and pose estimates. To improve reconstruction where geometric depth is unreliable, e.g. for moving objects or low-textured regions, we introduce learnable scene priors via a depth refinement network. We show that this design enables a dense, consistent 3D reconstruction of challenging, dynamic outdoor environments. Consequently, we achieve state-of-the-art dense depth prediction on the DDAD and NuScenes benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.643, + 0.21, + 0.658 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.668, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Translating sensory inputs into a dense 3D reconstruction of the environment and tracking the position of the observer is a cornerstone of robotics and fundamental to the development of autonomous vehicles (AVs). Contemporary systems rely on fusing many sensor modalities like camera, LiDAR, RADAR, IMU and more, making hardware and software stacks complex and expensive. In contrast, multi-camera systems provide a simpler, low-cost alternative already widely available in modern consumer vehicles. However, image-based dense 3D reconstruction and egomotion estimation of large-scale, dynamic scenes is an open research problem as moving objects, uniform and repetitive textures, and optical degradations pose significant algorithmic challenges." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.27, + 0.889, + 0.591 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.597, + 0.895, + 0.695 + ], + "angle": 0, + "content": "Figure 1. Many methods use temporal context but neglect inter-camera information, leading to incomplete results (top). Other works focus on exploiting inter-camera context but neglect temporal information, yielding incoherent predictions (middle). In contrast, our method achieves a consistent, dense 3D reconstruction by iteratively integrating geometric depth estimation from multiple cameras with monocular depth refinement (bottom)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Existing works approaching the aforementioned task can be divided into two lines of research. Many methods have focused on recovering 3D scene structure via structure-from-motion (SfM). In particular, simultaneous localization and mapping (SLAM) methods focus on accurate egomotion estimation and usually only recover sparse 3D structure [9, 29, 34, 12, 11]. They typically treat dynamic objects or uniformly textured regions as outliers yielding an incomplete 3D reconstruction result, which makes them less suitable for AVs and robotics. In addition, only a few works have focused on multi-camera setups [24, 8, 33, 30, 26]. In contrast, multi-view stereo (MVS) methods [31, 32, 41, 28," + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.206, + 0.9 + ], + "angle": 0, + "content": "*Equal contribution." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3216" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.137 + ], + "angle": 0, + "content": "57, 27, 17] aim to estimate dense 3D geometry but focus on static scenes and highly overlapping sets of images with known poses." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.139, + 0.468, + 0.365 + ], + "angle": 0, + "content": "The second line of research focuses on dense depth prediction from monocular cues, such as perspective object appearance and scene context [65, 15, 16, 59, 49, 61, 19]. However, due to the injective property of projecting 3D structures onto a 2D plane, reconstructing depth from a single image is an ill-posed problem, which limits the accuracy and generalization of these methods. Recent methods [51, 18, 21], inspired by MVS literature, combine monocular cues with temporal context but are focused on front-facing, single-camera setups. A handful of recent works extend monocular depth estimation to multi-camera setups [22, 52, 54]. These methods utilize the spatial context to improve accuracy and realize absolute scale depth learning. However, those works neglect the temporal domain which provides useful cues for depth estimation." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.369, + 0.468, + 0.699 + ], + "angle": 0, + "content": "Motivated by this observation, we introduce R3D3, a system for dense 3D reconstruction and ego-motion estimation from multiple cameras of dynamic outdoor environments. Our approach combines monocular cues with geometric depth estimates from both spatial inter-camera context as well as inter- and intra-camera temporal context. We compute accurate geometric depth and pose estimates via iterative dense correspondence on frames in a co-visibility graph. For this, we extend the dense bundle adjustment (DBA) operator in [48] to multi-camera setups, increasing robustness and recovering absolute scene scale. To determine co-visible frames across cameras, we propose a simple yet effective multi-camera algorithm that balances performance and efficiency. A depth refinement network takes geometric depth and uncertainty as input and produces a refined depth that improves the reconstruction of, e.g., moving objects and uniformly textured areas. We train this network on real-world driving data without requiring any LiDAR ground-truth. Finally, the refined depth estimates serve as the basis for the next iterations of geometric estimation, thus closing the loop between incremental geometric reconstruction and monocular depth estimation." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.703, + 0.468, + 0.807 + ], + "angle": 0, + "content": "We summarize our contributions as follows. 1) we propose R3D3, a system for dense 3D reconstruction and egomotion estimation in dynamic scenes, 2) we estimate geometric depth and poses with a novel multi-camera DBA formulation and a multi-camera co-visibility graph, 3) we integrate prior geometric depth and uncertainty with monocular cues via a depth refinement network." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.811, + 0.468, + 0.9 + ], + "angle": 0, + "content": "As a result, we achieve state-of-the-art performance across two widely used multi-camera depth estimation benchmarks, namely DDAD [19] and NuScenes [3]. Further, we show that our system exhibits superior accuracy and robustness compared to monocular SLAM methods [48, 5]." + }, + { + "type": "title", + "bbox": [ + 0.505, + 0.091, + 0.64, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.116, + 0.89, + 0.341 + ], + "angle": 0, + "content": "Multi-view stereo. MVS methods aim to recover dense 3D scene structure from a set of images with known poses. While earlier works focused on classical optimization [31, 41, 4, 13, 14, 62, 32], more recent works capitalize on the success of convolutional neural networks (CNNs). They use CNNs to estimate features that are matched across multiple depth-hypothesis planes in a 3D cost volume [28, 57, 64, 27, 17, 58, 60]. While early approaches adopt multiple cost volumes across image pairs [64], recent approaches use a single cost volume across the whole image set [57]. These works assume a controlled setting with many, highly overlapping images and known poses to create a 3D cost volume. Instead, we aim to achieve robust, dense 3D reconstruction from an arbitrary multi-camera setup on a moving platform with an unknown trajectory." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.342, + 0.89, + 0.613 + ], + "angle": 0, + "content": "Visual SLAM. Visual SLAM approaches focus on jointly mapping the environment and tracking the trajectory of the observer from visual inputs, i.e. one or multiple RGB cameras. Traditional SLAM systems are often split into different stages, where first images are processed into keypoint matches, which subsequently are used to estimate the 3D scene geometry and camera trajectory [9, 10, 6, 34, 35, 5, 39]. Another line of work focuses on directly optimizing 3D geometry and camera trajectory based on pixel intensities [12, 11, 56, 55]. A handful of works have focused on multi-camera SLAM systems [24, 8, 33, 30, 26]. Recent methods integrate CNN-based depth and pose predictions [45, 56, 55] into the SLAM pipeline. The common challenge these methods face is outliers in the pixel correspondences caused by the presence of low-textured areas, dynamic objects, or optical degradations. Hence, robust estimation techniques are used to filter these outliers, yielding an incomplete, sparse 3D reconstruction result." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.615, + 0.89, + 0.824 + ], + "angle": 0, + "content": "In contrast, dense 3D reconstruction and ego-motion estimation has proven to be more challenging. Early works utilize active depth sensors [36, 64] to alleviate the above-mentioned challenges. Recently, several works on dense visual SLAM from RGB input have emerged [1, 44, 7, 46, 48]. While these methods are able to produce high-quality depth maps and camera trajectories, they inherit the limitations of their traditional counterparts, i.e. their predictions are subject to noise when there are outliers in the pixel correspondences. This can lead to artifacts in the depth maps, inaccurate trajectories, or even a complete failure of the system. On the contrary, we achieve robust, dense 3D reconstruction and ego-motion estimates by jointly leveraging multi-camera constraints as well as monocular depth cues." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.826, + 0.89, + 0.899 + ], + "angle": 0, + "content": "Self-supervised depth estimation. The pioneering work of Zhou et al. [65] learns depth estimation as a proxy task while minimizing a view synthesis loss that uses geometric constraints to warp color information from a reference to a target view. Subsequent research has focused on improv-" + }, + { + "type": "page_number", + "bbox": [ + 0.485, + 0.947, + 0.514, + 0.957 + ], + "angle": 0, + "content": "3217" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.318 + ], + "angle": 0, + "content": "ing network architectures, loss regularization, and training schemes [15, 16, 20, 59, 49, 61, 19]. Recent methods draw inspiration from MVS and propose to use 3D cost volumes in order to incorporate temporal information [51, 18, 53, 21]. While these methods achieve promising results, they still focus on single-camera, front-facing scenarios that do not reflect the real-world sensor setups of AVs [3, 43, 19]. Another recent line of work focuses on exploiting spatial information across overlapping cameras in a multi-camera setup [22, 52, 54]. These works propose to use static feature matches across cameras at a given time to guide depth learning and estimation, and to recover absolute scale. Our work aims to exploit both spatial and temporal cues in order to achieve a robust, dense 3D reconstruction from multiple cameras in dynamic outdoor environments." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.335, + 0.17, + 0.35 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.361, + 0.47, + 0.452 + ], + "angle": 0, + "content": "Problem formulation. At each timestep \\( t \\in T \\) we are given a set of images \\( \\{\\mathbf{I}_t^c\\}_{c=1}^C \\) from \\( C \\) cameras that are mounted on a moving platform with known camera intrinsics \\( \\mathbf{K}_c \\) and extrinsics \\( \\mathbf{T}_c \\) with respect to a common reference frame. We aim to estimate the depth maps \\( \\mathbf{d}_t^c \\in \\mathbb{R}_+^{H \\times W} \\) and ego-pose \\( \\mathbf{P}_t \\in SE(3) \\) at the current time step." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.453, + 0.473, + 0.728 + ], + "angle": 0, + "content": "Overview. Our system is composed of three stages. First, given a new set of images \\(\\{\\mathbf{I}_t^c\\}_{c = 1}^C\\), we extract deep features from each \\(\\mathbf{I}_t^c\\). We maintain a co-visibility graph \\(\\mathcal{G} = (\\mathcal{V},\\mathcal{E})\\) where a frame \\(\\mathbf{I}_t^c\\) represents a node \\(v\\in \\mathcal{V}\\) and co-visible frames are connected with edges. For each edge \\((i,j)\\in \\mathcal{E}\\) in this graph, we compute the feature correlation \\(\\mathbf{C}_{ij}\\) of the two adjacent frames. Second, given initial estimates of the depth \\(\\mathbf{d}_i\\) and the relative pose \\(\\mathbf{G}_{ij} = \\left(\\mathbf{P}_{t_j}\\mathbf{T}_{c_j}\\right)^{-1}\\mathbf{P}_{t_i}\\mathbf{T}_{c_i}\\) between the two frames, we compute the induced flow \\(\\mathbf{f}_{ij}^{*}\\). We correct the induced flow with a recurrent update operator using the feature correlations \\(\\mathbf{C}_{ij}\\). We then globally align the updated flow estimates at each edge \\((i,j)\\) with the current estimates of \\(\\mathbf{G}_{ij}\\) and \\(\\mathbf{d}_i\\) across the co-visibility graph \\(\\mathcal{G}\\) with our proposed multi-camera DBA. Third, we introduce a depth refinement network that refines the geometric depth estimates with monocular depth cues to better handle scenarios that are challenging for geometric estimation methods. We illustrate our architecture in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.739, + 0.388, + 0.755 + ], + "angle": 0, + "content": "3.1. Feature Extraction and Correlation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.762, + 0.47, + 0.809 + ], + "angle": 0, + "content": "Given a new observation \\(\\{\\mathbf{I}_t^c\\}_{c = 1}^C\\), we first extract deep image features, update the co-visibility graph, and compute feature correlations. We describe these steps next." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.856 + ], + "angle": 0, + "content": "Feature extraction. We follow [47, 48] and extract both correlation and context features from each image individually via deep correlation and context encoders \\( g_{\\phi} \\) and \\( g_{\\psi} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Co-visibility graph. We store correlation and context features in a graph \\(\\mathcal{G} = (\\mathcal{V},\\mathcal{E})\\). Each node corresponds to an image \\(\\mathbf{I}_t^c\\) and an edge in the graph indicates that two" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.212 + ], + "angle": 0, + "content": "images are considered a pair in the feature correlation and bundle adjustment steps. Contrary to [48], we construct \\(\\mathcal{G}\\) with three kinds of edges: temporal, spatial, and spatial-temporal. Since the number of possible edges is \\(|\\mathcal{V}|^2\\) and the system runtime scales linearly with \\(|\\mathcal{E}|\\), the degree of sparsity in the co-visibility graph is crucial. We thus carefully design a simple yet effective co-visibility graph construction algorithm in multi-camera setups (see Fig. 3)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.213, + 0.893, + 0.484 + ], + "angle": 0, + "content": "For temporal edges (Fig. 3 in green), we examine the time window \\( t - \\Delta t_{\\mathrm{intra}} \\) and connect all frames of the same camera that are less than \\( r_{\\mathrm{intra}} \\) time steps apart. For spatial and spatial-temporal edges we exploit three priors. 1) we know camera adjacency from the given calibration, 2) we assume motion in the direction of the forward-facing camera and 3) the observer undergoes limited motion within the local time window. We establish spatial edges (Fig. 3 in red) between adjacent cameras within time step \\( t \\). We further establish spatial-temporal edges (Fig. 3 in orange) given the static camera adjacency within \\( t - \\Delta t_{\\mathrm{inter}} \\). In particular, we connect camera \\( c_i \\) and \\( c_j \\) from any \\( t' \\) to \\( t' - r_{\\mathrm{inter}} \\), if \\( c_i \\) and \\( c_j \\) connect within \\( t \\) and if \\( c_j \\) is closer to the forward-facing camera than \\( c_i \\) under forward motion assumption. Finally, we remove an edge \\( (i,j) \\) if node \\( i \\) or \\( j \\) is outside the local time windows \\( t - \\Delta t_{\\mathrm{inter}} \\) or \\( t - \\Delta t_{\\mathrm{intra}} \\). We remove unconnected nodes from the graph. We provide pseudo-code and additional discussion in the supplemental material." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.485, + 0.892, + 0.515 + ], + "angle": 0, + "content": "Feature correlation. For each edge \\((i,j) \\in \\mathcal{E}\\) we compute the 4D feature correlation volume via the dot-product" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.519, + 0.892, + 0.539 + ], + "angle": 0, + "content": "\\[\n\\mathbf {C} _ {i j} = \\left\\langle g _ {\\phi} (\\mathbf {I} _ {i}), g _ {\\phi} (\\mathbf {I} _ {j}) \\right\\rangle \\in \\mathbb {R} ^ {H \\times W \\times H \\times W}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.543, + 0.892, + 0.573 + ], + "angle": 0, + "content": "As in [47, 48], we constrain the correlation search region to a radius \\( r \\) with a lookup operator" + }, + { + "type": "equation", + "bbox": [ + 0.513, + 0.578, + 0.892, + 0.598 + ], + "angle": 0, + "content": "\\[\nL _ {r}: \\mathbb {R} ^ {H \\times W \\times H \\times W} \\times \\mathbb {R} ^ {H \\times W \\times 2} \\rightarrow \\mathbb {R} ^ {H \\times W \\times (r + 1) ^ {2}}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.604, + 0.892, + 0.634 + ], + "angle": 0, + "content": "that samples a \\( H \\times W \\) grid of coordinates from the correlation volume using bilinear interpolation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.641, + 0.746, + 0.657 + ], + "angle": 0, + "content": "3.2. Depth and Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.664, + 0.892, + 0.71 + ], + "angle": 0, + "content": "Given the correlation volume \\(\\mathbf{C}_{ij}\\), we here describe how to estimate the relative pose \\(\\mathbf{G}_{ij}\\) and depth \\(\\mathbf{d}_i\\) for each edge \\((i,j)\\in \\mathcal{E}\\) in the co-visibility graph." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.71, + 0.892, + 0.879 + ], + "angle": 0, + "content": "Flow correction. Given an initial estimate of \\(\\mathbf{G}_{ij}\\) and \\(\\mathbf{d}_i\\), we first compute the induced flow \\(\\mathbf{f}_{ij}^*\\) to sample the correlation volume \\(\\mathbf{C}_{ij}\\) using (2). We then feed the sampled correlation features, the context features \\(g_{\\psi}(\\mathbf{I}_i)\\), and the induced flow \\(\\mathbf{f}_{ij}^*\\) into a convolutional GRU. The GRU predicts a flow residual \\(\\mathbf{r}_{ij}\\) and confidence weights \\(\\mathbf{w}_{ij} \\in \\mathbb{R}^{H \\times W \\times 2}\\) as in [48]. A challenge of correspondence estimation in a multi-camera setup is that the flow magnitude varies greatly among edges in the co-visibility graph due to inter-camera edges with large relative rotation. To this end, we propose to subtract the rotational part of \\(\\mathbf{f}_{ij}^*\\) in those edges via" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.884, + 0.892, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {i j} ^ {\\prime} = \\left(\\mathbf {x} _ {i} + \\mathbf {f} _ {i j} ^ {*}\\right) - \\Pi_ {c _ {j}} \\left(\\mathbf {R} _ {c _ {j}} ^ {- 1} \\mathbf {R} _ {c _ {i}} \\circ \\Pi_ {c _ {i}} ^ {- 1} (\\mathbf {1})\\right), \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3218" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.096, + 0.873, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.312, + 0.895, + 0.397 + ], + "angle": 0, + "content": "Figure 2. Method overview. First, frames \\(\\{\\mathbf{I}_t^c\\}_{c=1}^C\\) from \\(C\\) cameras at time \\(t\\) are encoded and integrated into the co-visibility graph \\(\\mathcal{G} = (\\mathcal{V}, \\mathcal{E})\\) with initial guesses of depth maps \\(\\mathbf{d}_t^c\\) and ego-pose \\(\\mathbf{P}_t\\) (Sec. 3.1). Second, for each edge \\((i,j) \\in \\mathcal{E}\\), we compute the induced flow \\(\\mathbf{f}_{ij}^*\\) from \\(\\mathbf{d}_i\\) and relative camera pose \\(\\mathbf{G}_{ij}\\) derived from ego-poses \\(\\mathbf{P}\\) and camera extrinsics \\(\\mathbf{T}\\). Given \\(\\mathbf{f}_{ij}^*\\), we pool feature correlations from \\(\\mathbf{C}_{ij}\\) with operator \\(L_r\\) as input to a GRU that estimates flow update \\(\\mathbf{r}_{ij}\\) and confidence \\(\\mathbf{w}_{ij}\\). We globally align depths \\(\\mathbf{d}\\) and poses \\(\\mathbf{P}\\) with the new flow estimates \\(\\mathbf{f}\\) via our multi-camera DBA operator in \\(k\\) iterations (Sec. 3.2). Finally, for each node \\(i \\in \\mathcal{V}\\), we refine the initial geometric estimate \\(\\mathbf{d}_i\\) given the aggregated confidence \\(\\mathbf{w}_i\\) via \\(\\mathcal{D}_{\\theta}\\) (Sec. 3.3). We highlight our contributions in color." + }, + { + "type": "image", + "bbox": [ + 0.127, + 0.414, + 0.422, + 0.6 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.603, + 0.471, + 0.675 + ], + "angle": 0, + "content": "Figure 3. Co-visibility graph. We illustrate an example of the connectivity pattern of the co-visibility graph using our multi-camera graph construction algorithm. We use \\(\\Delta t_{\\mathrm{intra}} = 3\\), \\(\\Delta t_{\\mathrm{inter}} = 2\\), \\(r_{\\mathrm{intra}} = 2\\), \\(r_{\\mathrm{inter}} = 2\\) with six cameras. We depict temporal, spatial, and spatial-temporal edges." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.691, + 0.469, + 0.782 + ], + "angle": 0, + "content": "where \\(\\mathbf{x}_i\\) are pixel coordinates of frame \\(i\\), \\(\\Pi_c\\) denotes the projection operator under camera \\(c\\) and \\(\\mathbf{R}\\) is the rotation of transformation \\(\\mathbf{T} = (\\mathbf{R} \\mathbf{t})\\). This aligns the flow magnitude with temporal, intra-camera edges. Note that, while we input \\(\\mathbf{f}_{ij}'\\) instead of \\(\\mathbf{f}_{ij}^*\\) to the GRU, we still sample the correlation volume \\(\\mathbf{C}_{ij}\\) based on \\(\\mathbf{f}_{ij}^*\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.782, + 0.469, + 0.827 + ], + "angle": 0, + "content": "Pose and depth correction. We update our pose and depth estimates given the updated flow \\(\\mathbf{f}_{ij} = \\mathbf{f}_{ij}^{*} + \\mathbf{r}_{ij}\\) by minimizing the re-projection error, defined as" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.839, + 0.469, + 0.874 + ], + "angle": 0, + "content": "\\[\nE = \\sum_ {(i, j) \\in \\mathcal {E}} \\left\\| \\left(\\mathbf {x} _ {i} + \\mathbf {f} _ {i j}\\right) - \\Pi_ {c _ {j}} \\left(\\mathbf {G} _ {i j} \\circ \\Pi_ {c _ {i}} ^ {- 1} (\\mathbf {d} _ {i})\\right) \\right\\| _ {\\Sigma_ {i j}} ^ {2}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.886, + 0.469, + 0.903 + ], + "angle": 0, + "content": "where \\(\\| .\\|_{\\Sigma_{ij}}\\) is the Mahalanobis norm and \\(\\Sigma_{ij} =\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.413, + 0.892, + 0.534 + ], + "angle": 0, + "content": "\\(\\operatorname{diag}(\\mathbf{w}_{ij})\\). Thus, only matched pixels where the confidence \\(\\mathbf{w}_{ij}\\) is greater than zero contribute to the total cost. We extend the dense bundle adjustment (DBA) proposed in [48] to include the known extrinsics of the multi-camera setup. In particular, we decompose the relative poses between two frames \\(\\mathbf{G}_{ij}\\) into the unknown, time-varying poses \\(\\mathbf{P}\\) in the reference frame and the known static relative transformations \\(\\mathbf{T}\\) between the cameras and the reference frame via" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.54, + 0.891, + 0.561 + ], + "angle": 0, + "content": "\\[\n\\mathbf {G} _ {i j} = \\left(\\mathbf {P} _ {t _ {j}} \\mathbf {T} _ {c _ {j}}\\right) ^ {- 1} \\mathbf {P} _ {t _ {i}} \\mathbf {T} _ {c _ {i}}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.569, + 0.892, + 0.689 + ], + "angle": 0, + "content": "We linearize the residual of the energy function in Eq. 4 with a first-order Taylor expansion. We use Eq. 5 and treat \\(\\mathbf{T}_{c_j}\\) and \\(\\mathbf{T}_{c_i}\\) as constants when calculating the Jacobians, thus computing updates only for ego-pose \\(\\mathbf{P}\\). We apply the Gauss-Newton step to compute the updated \\(\\mathbf{P}^{(k)} = \\exp (\\delta \\xi^{(k - 1)})\\mathbf{P}^{(k - 1)}\\) and depth \\(\\mathbf{d}^{(k)} = \\delta \\mathbf{d}^{(k - 1)} + \\mathbf{d}^{(k - 1)}\\) with \\(\\delta \\xi^{(k - 1)}\\in \\mathfrak{se}(3)\\). We provide a detailed derivation in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.893, + 0.87 + ], + "angle": 0, + "content": "Our formulation has two advantages over DBA [48]. First, the optimization is more robust since \\(C\\) frames are connected through a single ego-pose \\(\\mathbf{P}\\). If one or multiple frames have a high outlier ratio in feature matching, e.g. through lens-flare, low textured regions, or dynamic objects, we can still reliably estimate \\(\\mathbf{P}\\) with at least one undisturbed camera. Second, if there are not only pixels matched across the temporal context but also pixels matched across the static, spatial context, we can recover the absolute scale of the scene. This is because for static, spatial matches the relative transformation \\(\\mathbf{G}_{ij} = \\mathbf{T}_{c_j}^{-1}\\mathbf{T}_{c_i}\\) is known to scale so that \\(E\\) is minimized if and only if \\(\\mathbf{d}\\) is in absolute scale." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Training. We train the networks \\( g_{\\phi} \\) and \\( g_{\\psi} \\) as well as the flow correction GRU on dynamic scenes following the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3219" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.184 + ], + "angle": 0, + "content": "procedure in [48]. As shown in [48], the geometric features learned from synthetic data can generalize to real-world scenes. We can therefore leverage existing synthetic driving datasets without relying on real-world ground-truth measurements from sensors like LiDAR or IMU to adjust our method to dynamic, multi-camera scenarios." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.19, + 0.254, + 0.208 + ], + "angle": 0, + "content": "3.3. Depth Refinement" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.47, + 0.304 + ], + "angle": 0, + "content": "SfM relies on three assumptions: accurate pixel matches, sufficient camera movement, and a static scene. These assumptions do not always hold in the real world due to, e.g., low-textured areas, a static ego vehicle, or many dynamic agents. Still, we would like the system to produce reasonable scene geometry to ensure safe operation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.305, + 0.47, + 0.379 + ], + "angle": 0, + "content": "On the contrary, monocular depth cues are inherently not affected by these issues. However, they usually lack the accurate geometric detail of SfM methods. Hence, for each node \\(i \\in \\mathcal{V}\\), we complement the accurate, but sparse geometric depth estimates with monocular cues." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.38, + 0.47, + 0.744 + ], + "angle": 0, + "content": "Network design. We use a CNN \\(\\mathcal{D}_{\\theta}\\) parameterized by \\(\\theta\\). We input the depth \\(\\mathbf{d}_i\\), confidence \\(\\mathbf{w}_i\\), and the corresponding image \\(\\mathbf{I}_i\\). The network predicts an improved, dense depth \\(\\mathbf{d}_i' = \\mathcal{D}_{\\theta}(\\mathbf{I}_i, \\mathbf{d}_i, \\mathbf{w}_i)\\). We obtain the per-frame depth confidence \\(\\mathbf{w}_i\\) for frame \\(i\\) by using the maximum across the per-edge confidence weights \\(\\mathbf{w}_{ij}\\). We compute \\(\\mathbf{w}_i = \\max_j \\frac{1}{2} (\\mathbf{w}_{ij}^x + \\mathbf{w}_{ij}^y)\\) where \\(x\\) and \\(y\\) are the flow directions. We use \\(\\max(\\cdot)\\) because we observe that depth triangulation will be accurate if at least one pixel is matched with high confidence. We sparsify input depth and confidence weights by setting regions with confidence \\(\\mathbf{w}_i < \\beta\\) to zero. We concatenate these with the image \\(\\mathbf{I}_i\\). We further concatenate depth and confidence with features at \\(1/8^{\\text{th}}\\) scale. As in [16], the output depth is predicted at four scales. To accommodate different focal lengths among cameras in the sensor setup, we do focal length scaling of the output [45]. Training. Contrary to geometric approaches, monocular depth estimators infer depth from semantic cues, which makes it hard for them to generalize across domains [23]. Hence, instead of relying on synthetic data, we train \\(\\mathcal{D}_{\\theta}\\) on raw, real-world video in a self-supervised manner by minimizing a view synthesis loss [65]. We minimize the photometric error \\(\\mathrm{pe}(\\mathbf{I}_t^c, \\mathbf{I}_{t'}^{c' \\rightarrow c})\\) between a target image \\(\\mathbf{I}_t^c\\) and a reference image \\(\\mathbf{I}_{t'}^{c'}\\) warped to the target viewpoint via" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.753, + 0.47, + 0.773 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I} _ {t ^ {\\prime} \\rightarrow t} ^ {c ^ {\\prime} \\rightarrow c} = \\Phi \\big (\\mathbf {I} _ {t ^ {\\prime}} ^ {c ^ {\\prime}}; \\Pi_ {c ^ {\\prime}} \\big (\\mathbf {G} _ {(t, c) (t ^ {\\prime}, c ^ {\\prime})} \\circ \\Pi_ {c} ^ {- 1} \\big (\\mathbf {d} _ {t} ^ {c} \\big) \\big) \\big), \\quad (6)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.902 + ], + "angle": 0, + "content": "with \\(\\Phi\\) the bi-linear sampling function, \\(\\mathbf{d}_t^c\\) the predicted depth, \\(c' = c \\pm 1\\) and \\(t' = t \\pm 1\\). We compute photometric similarity with SSIM [50] and \\(L_1\\) distances. We use \\(\\mathbf{G}_{(t,c)(t',c')} = (\\mathbf{P}_{t'}\\mathbf{T}_{c'})^{-1}\\mathbf{P}_t\\mathbf{T}_c\\) generated by the first two stages of our system (see Sec. 3.2). Further, self-supervised depth estimation is well-studied, and we follow the common practice of applying regularization techniques to filter the photometric error [16, 63, 20]. First, we mask areas" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.09, + 0.894, + 0.152 + ], + "angle": 0, + "content": "where \\(\\mathbf{M}^{\\mathrm{st}} = \\left[\\mathrm{pe}(\\mathbf{I}_t^c,\\mathbf{I}_{t'\\to t}^{c'\\to c}) < \\mathrm{pe}(\\mathbf{I}_t^c,\\mathbf{I}_{t'}^{c'})\\right]\\) , i.e. we filter regions where assuming a stationary scene would induce a lower loss than re-projection. Second, we compute an induced flow consistency mask from \\(\\mathbf{f}^*\\)" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.161, + 0.895, + 0.201 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} ^ {\\mathrm {f c}} = \\left[ \\left\\| \\mathbf {f} _ {(t, c) \\left(t ^ {\\prime}, c ^ {\\prime}\\right)} ^ {*} + \\Phi \\left(\\mathbf {f} _ {\\left(t ^ {\\prime}, c ^ {\\prime}\\right) (t, c)} ^ {*}; \\mathbf {x} + \\mathbf {f} _ {(t, c) \\left(t ^ {\\prime}, c ^ {\\prime}\\right)} ^ {*}\\right) \\right\\| _ {2} < \\gamma \\right]. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.202, + 0.892, + 0.351 + ], + "angle": 0, + "content": "This term warps pixel coordinates \\(\\mathbf{x}\\) from target to reference view, looks up their value in \\(\\mathbf{f}_{(t',c')}(t,c)\\), and compares them to \\(\\mathbf{f}_{(t,c)(t',c')}^*\\). Therefore, pixels not following the epipolar constraint like dynamic objects are masked. Third, to handle the self-occlusion of the ego-vehicle, we manually draw a static mask \\(\\mathbf{M}^{\\mathrm{oc}}\\). We can use a single mask for all frames since the cameras are mounted rigidly. Further, to handle occlusions due to change in perspective, we take the minimum loss \\(\\min_{t',c'}\\mathrm{pe}(\\mathbf{I}_t^c,\\mathbf{I}_{t'\\to t}^{c'\\to c})\\) across all reference views. The overall loss for \\(\\mathcal{D}_{\\theta}\\) is thus" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.362, + 0.892, + 0.389 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\min _ {t ^ {\\prime}, c ^ {\\prime}} \\left(\\mathbf {M} ^ {\\mathrm {s t}} \\mathbf {M} ^ {\\mathrm {f c}} \\mathbf {M} ^ {\\mathrm {o c}} \\cdot \\operatorname {p e} \\left(\\mathbf {I} _ {t} ^ {c}, \\mathbf {I} _ {t ^ {\\prime} \\rightarrow t} ^ {c ^ {\\prime} \\rightarrow c}\\right)\\right) + \\lambda \\mathcal {L} _ {\\text {s m o o t h}}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.399, + 0.886, + 0.415 + ], + "angle": 0, + "content": "with \\(\\mathcal{L}_{\\mathrm{smooth}}\\) a spatial smoothness regularization term [15]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.424, + 0.693, + 0.438 + ], + "angle": 0, + "content": "3.4. Inference Procedure" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.892, + 0.477 + ], + "angle": 0, + "content": "Given an input stream of multi-camera image sets, we perform incremental 3D reconstruction in three phases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.892, + 0.568 + ], + "angle": 0, + "content": "Warmup phase. First, we add frames to the co-visibility graph if a single GRU step of a reference camera yields a large enough mean optical flow until we reach \\( n_{\\mathrm{warmup}} \\) frames. At this stage, we infer depth with our refinement network \\( \\mathbf{d}_t^c = \\mathcal{D}_{\\theta}(\\mathbf{I}_t^c,\\mathbf{0},\\mathbf{0}) \\). We write the depth into the co-visibility graph so that it can be used during initialization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.643 + ], + "angle": 0, + "content": "Initialization phase. We initialize the co-visibility graph with the available frames and run \\( n_{\\mathrm{itr - wm}} \\) GRU and bundle adjustment iterations. For the first \\( n_{\\mathrm{itr - wm}} / 2 \\) iterations, we fix depths in the bundle adjustment and only optimize poses, which helps with inferring the absolute scale of the scene." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Active phase. We now add each incoming frame to the co-visibility graph. We initialize the new frames with \\(\\mathbf{d}_t^c = \\mathrm{mean}(\\mathbf{d}_{t - 4:t - 1}^c)\\) and \\(\\mathbf{P}_t = \\mathbf{P}_{t - 1}\\). Then, we perform \\(n_{\\mathrm{iter1}}\\) GRU and bundle adjustment updates, and apply the refinement network to all updated frames. If the mean optical flow of the reference camera between \\(t\\) and \\(t - 1\\) is low, we remove all frames at \\(t - 1\\) from the co-visibility graph. This helps to handle situations with little to no egomotion. In case no frame is removed, we do another \\(n_{\\mathrm{iter2}}\\) iterations. Finally, we write the updated depths and poses into the co-visibility graph." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.822, + 0.634, + 0.839 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.691, + 0.864 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "We perform extensive experiments on large-scale driving datasets that contain recordings from vehicles equipped" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3220" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.088, + 0.895, + 0.129 + ], + "angle": 0, + "content": "Table 1. Method ablation. We ablate our method components on the DDAD [19] dataset. We examine the influence of each component given the geometric estimation as in [48] with naive DBA as the baseline. Further, we show the influence of VKITTI [2] fine-tuning on the geometric estimation. We enumerate each variant for better reference. * median scaled depth, ** scaled trajectory." + }, + { + "type": "table", + "bbox": [ + 0.116, + 0.13, + 0.85, + 0.223 + ], + "angle": 0, + "content": "
No.Geom. Est.VKITTIMulti-Cam DBARefinementAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑ATE [m] ↓ATE** [m] ↓
1a*✓✓0.43826.9719.1090.636-2.134
1b✓✓0.44236.3918.6640.7361.6720.435
1c✓✓✓0.32015.4516.3030.7272.3560.922
2a✓0.2113.80612.6680.715--
3a✓✓✓✓0.1623.01911.4080.8111.2350.433
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.237, + 0.47, + 0.306 + ], + "angle": 0, + "content": "Table 2. Co-visibility graph ablation. We compare our co-visibility graph construction algorithm to the original algorithm in [48] on the DDAD [19] dataset. We observe that our algorithm improves the overall runtime by an order of magnitude while maintaining the same level of performance." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.307, + 0.46, + 0.354 + ], + "angle": 0, + "content": "
GraphAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑ATE [m] ↓tinf [s] ↓
Original0.1622.96811.1560.8160.9823.23
Ours0.1623.01911.4080.8111.2350.35
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.359, + 0.469, + 0.414 + ], + "angle": 0, + "content": "Table 3. Refinement network ablation. We show on the DDAD [19] dataset that both adding confidence weights \\(\\mathbf{w}_i\\) and sparsifying the depth input via \\(\\mathbf{w}_i < \\beta\\) to filter outliers in the input of depth refinement network \\(\\mathcal{D}_{\\theta}\\) is vital to depth accuracy." + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.415, + 0.438, + 0.476 + ], + "angle": 0, + "content": "
wiwi<βAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
0.1814.07812.1080.789
✓0.1733.49711.9240.792
✓✓0.1623.01911.4080.811
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.493, + 0.469, + 0.583 + ], + "angle": 0, + "content": "with multiple cameras, LiDARs, and other sensors. Note that we only use camera data for training and inference, and use LiDAR data only as ground-truth for evaluation. We evaluate our method in inference mode (cf. Sec. 3.4), i.e. we obtain predictions in a fully online (causal) manner to mimic real-world deployment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.469, + 0.719 + ], + "angle": 0, + "content": "DDAD. This dataset consists of 150 training and 50 validation scenes from urban areas. Each sequence has a length of 50 or 100 time steps at a frame rate of \\(10\\mathrm{Hz}\\). The sensor setup includes six cameras in a surround-view setup with up to \\(20\\%\\) overlap. We follow [19] and evaluate depth up to \\(200\\mathrm{m}\\) averaged across all cameras. We use self-occlusion masks from [52] to filter the ego-vehicle in the images. Images have a resolution of \\(1216\\times 1936\\) and are downsampled to \\(384\\times 640\\) in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.469, + 0.869 + ], + "angle": 0, + "content": "NuScenes. This dataset contains 700 training, 150 validation, and 150 testing sequences of urban scenes with challenging conditions such as nighttime and rain. Each scene is composed of 40 keyframes at \\(2\\mathrm{Hz}\\) synchronized across sensors. The six cameras have a sampling rate of \\(12\\mathrm{Hz}\\) and are arranged in a surround-view setup with up to \\(10\\%\\) overlap. We follow [22] and evaluate depth averaged across all cameras on the validation set. We use a single self-occlusion mask for all scenes. While the raw images have a resolution of \\(900 \\times 1600\\), we use \\(768 \\times 448\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Implementation details. We implement our system in PyTorch [37]. Our multi-camera DBA is implemented in" + }, + { + "type": "image_caption", + "bbox": [ + 0.554, + 0.239, + 0.586, + 0.249 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.665, + 0.239, + 0.738, + 0.25 + ], + "angle": 0, + "content": "Geom. Depth" + }, + { + "type": "image_caption", + "bbox": [ + 0.812, + 0.239, + 0.855, + 0.249 + ], + "angle": 0, + "content": "Refined" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.251, + 0.636, + 0.311 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.251, + 0.766, + 0.311 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.768, + 0.251, + 0.9, + 0.311 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.313, + 0.635, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.313, + 0.766, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.768, + 0.313, + 0.9, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.377, + 0.635, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.377, + 0.766, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.768, + 0.377, + 0.9, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.44, + 0.892, + 0.495 + ], + "angle": 0, + "content": "Figure 4. Depth refinement. We plot images overlayed with confidence \\(\\mathbf{w}_i\\), the geometric depth estimate \\(\\mathbf{d}\\), and the refined depth \\(\\mathbf{d}'\\) from \\(\\mathcal{D}_{\\theta}\\). We observe a smoother ground plane, corrected dynamic objects, and filtered outliers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.892, + 0.728 + ], + "angle": 0, + "content": "CUDA. We fine-tune \\( g_{\\phi} \\), \\( g_{\\psi} \\) and the flow correction GRU on VIKITTI2 [2] for 10 epochs with a batch size of 1, sequence length of 7, and learning rate \\( 10^{-4} \\) with the pretrained model in [48]. For \\( \\mathcal{D}_{\\theta} \\), we use a U-Net [38] with ResNet18 [25] encoder and initialize it with ImageNet [40] pre-trained weights. We use \\( \\beta = 0.5 \\), \\( \\gamma = 3 \\) and \\( \\lambda = 10^{-3} \\). We train for 20 epochs with batch size of 6 and the Adam optimizer with learning rate \\( 10^{-4} \\), \\( \\beta_{1} = 0.9 \\), and \\( \\beta_{2} = 0.999 \\). We reduce the learning rate by a factor of 10 after 15 epochs. For inference, the runtime is measured for a set of six images on a single RTX3090 GPU. Each sequence is initialized with 3 warmup frames filtered at a mean flow threshold of 1.75. We build the co-visibility graph with \\( \\Delta t_{\\mathrm{intra}} = 3 \\), \\( r_{\\mathrm{intra}} = 2 \\), \\( \\Delta t_{\\mathrm{inter}} = 2 \\) and \\( r_{\\mathrm{inter}} = 2 \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.741, + 0.665, + 0.755 + ], + "angle": 0, + "content": "4.2. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Method ablation. We ablate our method components on the DDAD dataset in Tab. 1. The geometric estimation baseline (1a) consists of [48] with the naive DBA formulation applied to all cameras and the co-visibility graph as described in Sec. 3.1. It performs poorly in depth and pose estimation, with an Abs. Rel. score of 0.438 and an absolute trajectory error (ATE) [42] of \\(2.134\\mathrm{m}\\), even when adjusting for scale. Next, we add our multi-camera DBA (1b). We observe that, even without VKITTI fine-tuning, the pose esti" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "3221" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.47, + 0.129 + ], + "angle": 0, + "content": "Table 4. Comparison to state-of-the-art on DDAD. We compare favorably to existing methods on both scale-aware and scale-invariant depth prediction. * median scaled depth." + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.13, + 0.438, + 0.235 + ], + "angle": 0, + "content": "
MethodAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
FSM [22]0.201---
SurroundDepth [52]0.2083.37112.9770.693
Ours0.1623.01911.4080.811
FSM* [22]0.202---
SurroundDepth* [52]0.2003.39212.2700.740
MCDP* [54]0.1933.11112.2640.811
Ours*0.1693.04111.3720.809
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.242, + 0.47, + 0.311 + ], + "angle": 0, + "content": "Table 5. Per-camera evaluation on DDAD. We show a per-camera breakdown of previous works, our \\(\\mathcal{D}_{\\theta}\\) only (cf. 2a in Tab. 1), and our full method. Our full method performs the best with a particularly significant improvement on the side-view cameras while \\(\\mathcal{D}_{\\theta}\\) performs similarly to previous works." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.311, + 0.471, + 0.404 + ], + "angle": 0, + "content": "
MethodAbs Rel ↓
FrontF.LeftF-rightB.LeftB-rightBack
FSM [22]0.1300.2010.2240.2290.2400.186
SurroundDepth [52]0.1520.2070.2300.2200.2390.200
Dθ only0.1540.2130.2370.2310.2370.194
Ours0.1280.1600.1680.1720.1740.169
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.411, + 0.47, + 0.466 + ], + "angle": 0, + "content": "Table 6. Comparison to multi-frame methods on DDAD. We compare to methods that exploit temporal context from a single camera [51, 18]. We evaluate only the front camera since these methods were trained only on this camera." + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.467, + 0.438, + 0.543 + ], + "angle": 0, + "content": "
MethodFront Camera
Abs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
ManyDepth [51]0.1463.25814.0980.822
DepthFormer [18]0.1352.95312.4770.836
Ours0.1283.16813.2140.868
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.549, + 0.47, + 0.604 + ], + "angle": 0, + "content": "Table 7. Pose evaluation on DDAD. We compare our method to state-of-the-art monocular SLAM methods for which we report the average ATE across the cameras that successfully tracked the camera path. ** scaled trajectory." + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.604, + 0.436, + 0.638 + ], + "angle": 0, + "content": "
DROID-SLAM [48]ORB-SLAMv3 [5]Ours
ATE** [m] ↓7.5006.1790.433
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.468, + 0.718 + ], + "angle": 0, + "content": "mation accuracy improves dramatically over the naive DBA baseline. The relative scale ATE drops from \\(2.134\\mathrm{m}\\) to only \\(0.435\\mathrm{m}\\). The absolute scale ATE is only about \\(1.2\\mathrm{m}\\) higher, indicating the scene scale is recovered accurately." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Using VKITTI fine-tuning (1c), we achieve significant gains in depth accuracy, where Abs. Rel. drops to 0.32 and \\(\\delta_{1.25}\\) increases to \\(72.7\\%\\). However, note that VKITTI fine-tuning does not affect the \\(\\delta_{1.25}\\) score, i.e. it helps mostly with depth outliers. We attribute this to the absence of dynamic objects in the training data of [48] so that fine-tuning helps to adjust the confidence prediction to handle such outliers (cf. Sec. 3.2). We further test the depth refinement network (Sec. 3.3) without geometric estimation prior (2a). The depth obtained from \\(\\mathcal{D}_{\\theta}\\) is less prone to outliers, as evidenced by its low Abs. Rel., Sq. Rel. and RMSE scores. However, note that its \\(\\delta_{1.25}\\) is only \\(71.5\\%\\), i.e. its" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.093, + 0.868, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.293, + 0.892, + 0.351 + ], + "angle": 0, + "content": "Figure 5. Depth in \\(\\delta_{1.25^n}\\) range for different thresholds on DDAD. We depict the ratio of depth estimates \\(d\\) for which \\(\\delta(d) < 1.25^n\\) where \\(\\delta(d) = \\max\\left(\\frac{d}{d^*}, \\frac{d^*}{d}\\right)\\) and \\(d^*\\) is ground-truth depth. Note that values at \\(n = 1, 2, 3\\) represent \\(\\delta_{1.25}, \\delta_{1.25^2}, \\delta_{1.25^3}\\)." + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.356, + 0.892, + 0.397 + ], + "angle": 0, + "content": "Table 8. Comparison to state-of-the-art on NuScenes. Evaluated up to \\(80\\mathrm{m}\\) for scale-aware depth as in [22, 52] and \\(60\\mathrm{m}\\) for median-scaled depth (denoted with \\(*\\) ) as in [54]." + }, + { + "type": "table", + "bbox": [ + 0.527, + 0.398, + 0.862, + 0.515 + ], + "angle": 0, + "content": "
MethodAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
FSM [22]0.297---
SurroundDepth [52]0.2804.4017.4670.661
Ours0.2534.7597.1500.729
PackNet*[19]0.3033.1547.0140.655
FSM* [22]0.2703.1856.8320.689
SurroundDepth* [52]0.2453.0676.8350.719
MCDP* [54]0.2373.0306.8220.719
Ours*0.2353.3326.0210.749
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.536, + 0.892, + 0.702 + ], + "angle": 0, + "content": "depth accuracy compared to the geometric depth estimates is actually lower when disregarding outliers. Finally, we test our full system (3a). Compared to geometric estimation (1d), we observe a significant improvement in outlier sensitive metrics like RMSE, but also in outlier robust metrics like \\(\\delta_{1.25}\\). Additionally, the pose estimation accuracy is increased and the difference between scaled and non-scaled ATE is smaller. Compared to depth obtained from \\(\\mathcal{D}_{\\theta}(2\\mathrm{a})\\), the increase in outlier sensitive metrics is smaller but still significant, e.g. 1.26m in RMSE. Further, we observe a sizable gain in \\(\\delta_{1.25}\\) of 9.6 percentage points." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.854 + ], + "angle": 0, + "content": "Further, in Fig. 5, we compare the \\(\\delta_{1.25^n}\\) scores at different accuracy thresholds \\(n\\) of our geometric depth estimation without refinement ('Ours (Geometric)'), our refinement network only ('Ours (Monocular)') and our full method ('Ours'). The results confirm our hypothesis that while geometric estimates are more accurate than monocular depth estimates, they are also noisier. Importantly, the results further illustrate that our full method can effectively combine the strengths of both approaches while not suffering from their weaknesses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Co-visibility graph construction. In Tab. 2, we compare our co-visibility graph construction algorithm (Sec. 3.1) to a multi-camera adaption of the algorithm in [48]. Ours" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3222" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.47, + 0.156 + ], + "angle": 0, + "content": "Table 9. Per-camera evaluation on NuScenes. We compare our method with previous works on scale-aware depth estimation. Evaluated up to \\(80\\mathrm{m}\\) as in Tab. 8. We observe the same trend as on DDAD, i.e. our method performs best across all cameras, with a particularly high improvement on the side views." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.157, + 0.46, + 0.234 + ], + "angle": 0, + "content": "
MethodAbs Rel ↓
FrontF.LeftF-rightB.LeftB_rightBack
FSM [22]0.1860.2870.3750.2960.4180.221
SurroundDepth [52]0.1790.2600.3400.2820.4030.212
Ours0.1740.2300.3020.2490.3600.201
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.245, + 0.468, + 0.313 + ], + "angle": 0, + "content": "Table 10. Cross-dataset transfer. We use models trained on DDAD to evaluate scale-aware depth prediction on the NuScenes dataset. We compare to state-of-the-art methods [22, 52] and observe that our method exhibits better generalization ability (cf. Tab. 8)." + }, + { + "type": "table", + "bbox": [ + 0.105, + 0.314, + 0.438, + 0.372 + ], + "angle": 0, + "content": "
MethodAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
FSM [22]0.3495.0648.7850.499
SurroundDepth [52]0.3645.4768.4470.525
Ours0.2924.8007.6770.660
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.384, + 0.468, + 0.459 + ], + "angle": 0, + "content": "yields similar performance in depth estimation, with the exact same Abs. Rel. score and only minor difference in other metrics. Further, the absolute scale ATE is only slightly \\((25\\mathrm{cm})\\) higher. In contrast, using our algorithm, we achieve a runtime reduction of nearly \\(10\\times\\) on the full system." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.468, + 0.564 + ], + "angle": 0, + "content": "Depth refinement network. We verify the choice of our inputs to \\(\\mathcal{D}_{\\theta}\\) in Tab. 3. If we do not input the confidence \\(\\mathbf{w}_i\\) and do not sparsify the depth via \\(\\mathbf{w}_i < \\beta\\) before feeding it to \\(\\mathcal{D}_{\\theta}\\), we observe the lowest performance. If we input the confidence \\(\\mathbf{w}_i\\) but do not sparsify the depth, we see an improvement over not using them. We achieve the best performance with the inputs described in Sec. 3.3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.468, + 0.67 + ], + "angle": 0, + "content": "Moreover, we show qualitative examples of our depth refinement in Fig. 4. The confidence \\(\\mathbf{w}_i\\) (overlaid with the image) segments regions where geometric estimation is ambiguous, i.e. dynamic objects and uniformly textured areas like the sky and the road surface. The geometric depth maps exhibit severe artifacts in such regions. After refinement, these artifacts are corrected." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.681, + 0.355, + 0.697 + ], + "angle": 0, + "content": "4.3. Comparison to State-of-the-Art" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.468, + 0.809 + ], + "angle": 0, + "content": "DDAD. In Tab. 4, we compare our method to existing self-supervised multi-camera depth estimation methods. We achieve significant improvements in scale-aware and scale-invariant depth prediction with only minor differences in absolute and relative scale results. In both settings, we achieve state-of-the-art results with the lowest Abs. Rel. scores of 0.162 and 0.169, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.468, + 0.9 + ], + "angle": 0, + "content": "In Fig. 5 we compare the \\(\\delta_{1.25^n}\\) scores of our method to the state-of-the-art approaches on DDAD at different \\(n\\). For small values of \\(n\\), we observe a particularly pronounced performance gain over existing methods. This shows the advantage of combining highly accurate geometric estimates with monocular cues. Further, our method consistently out" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.879, + 0.106 + ], + "angle": 0, + "content": "performs the baselines over all values of \\(n\\) for \\(\\delta < 1.25^n\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.108, + 0.891, + 0.213 + ], + "angle": 0, + "content": "In Fig. 6, we show a qualitative comparison to existing works. On the left side, we illustrate depth maps across three cameras. Compared to FSM [22] and Surround-Depth [52], we produce sharper depth boundaries. On the right side, we illustrate point clouds accumulated over time. We produce a more consistent reconstruction, as can be seen when focusing on the vehicles or the fences beside the road." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.216, + 0.892, + 0.397 + ], + "angle": 0, + "content": "Tab. 5 shows the per-camera breakdown of the scale-aware depth prediction comparison. The advantage of our method is particularly pronounced on the side cameras. Other methods struggle with the side views because the static spatial context is limited and they do not exploit any temporal or spatial-temporal context. The temporal and spatial-temporal contexts are conducive in the side views since sideward motion leads to better triangulation angles than forward motion. This is also evidenced by the results of \\(\\mathcal{D}_{\\theta}\\) without geometric estimation, which performs similarly to the baseline methods, struggling with the side views. In contrast, our full system performs well across all cameras." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.399, + 0.892, + 0.504 + ], + "angle": 0, + "content": "We further compare to self-supervised single-camera methods that leverage temporal information in Tab. 6. For a fair comparison, we evaluate only the front camera. We compare favorably to DepthFormer [18] and Many-Depth [51]. In particular, we substantially improve in the outlier robust metric \\(\\delta_{1.25}\\) and perform competitively in all others. Our Abs. Rel. score is the lowest at 0.128." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.892, + 0.642 + ], + "angle": 0, + "content": "To evaluate ego-motion estimation, we compare our system to state-of-the-art monocular SLAM methods [48, 5] in Tab. 7. We run the baselines on each camera and report the average ATE across the cameras that successfully tracked the camera path. Note that, contrary to our approach, the competing methods frequently failed to produce a trajectory. We observe that state-of-the-art monocular SLAM methods exhibit a large error (ATE), while our method recovers accurate trajectories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.901 + ], + "angle": 0, + "content": "NuScenes. In Tab. 8, we compare our system to previous self-supervised multi-camera depth estimation methods. We outperform previous methods by a significant margin, corroborating our findings on DDAD. Notably, we observe substantial improvements in scale-aware depth estimation, while previous works usually struggle with recovering absolute scale on this dataset since the overlap between cameras is smaller than in DDAD [22]. Therefore, previous works like MCDP [54] report results on scale-invariant depth prediction. We outperform existing methods also in this setting, although the performance gap is smaller. Note that the gap between scale-aware and scale-invariant evaluation is only 2 percentage points in \\(\\delta_{1.25}\\) for our method, while for SurroundDepth [52] the gap is much larger with 5.8 percentage points. We show a per-camera breakdown of the comparison to the state-of-the-art in scale-aware depth estimation in Tab. 9. The results corroborate our findings" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3223" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.895, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.417, + 0.895, + 0.461 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison on DDAD. We show depth maps and point clouds accumulated over time along with input images, ground-truth LiDAR 3D Reconstruction, and the ego-vehicle in red. Our depth maps are sharper and more accurate. Our accumulated point clouds yield a more consistent 3D reconstruction. Note that we use our pose predictions for [22, 52] since these do not predict pose." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.471, + 0.522 + ], + "angle": 0, + "content": "on DDAD, namely that our method outperforms previous works across all cameras with a particularly pronounced improvement on the side views." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.473, + 0.691 + ], + "angle": 0, + "content": "Cross-dataset transfer. We finally test the cross-dataset generalization of our method versus FSM [22] and SurroundDepth [52]. In Tab. 10, we show scale-aware depth estimation results of models trained on DDAD, evaluated on NuScenes. We observe that the gap in Abs. Rel. widens compared to Tab. 8, with our method outperforming SurroundDepth by 0.072 in Abs. Rel. and FSM by 0.057. Further, our method maintains much higher levels of \\(\\delta_{1.25}\\) and Sq. Rel., while SurroundDepth drops significantly in both metrics. Note that we apply focal length scaling [45] to all methods to accommodate differences in camera intrinsics." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.708, + 0.196, + 0.723 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We introduced R3D3, a multi-camera system for dense 3D reconstruction of dynamic outdoor environments. The key ideas we presented are a multi-camera DBA operator that greatly improves geometric depth and pose estimation, a multi-camera co-visibility graph construction algorithm that reduces the runtime of our system by nearly \\(10\\times\\) without significant performance drop, and a depth refinement network that effectively fuses geometric depth estimates with monocular cues. We observe that our design choices enable dense 3D mapping in challenging scenes presenting many dynamic objects, uniform and repetitive textures, and" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.477, + 0.892, + 0.523 + ], + "angle": 0, + "content": "complicated camera phenomena like lens flare and autoexposure. We achieve state-of-the-art performance in dense depth prediction across two multi-camera benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.54, + 0.597, + 0.555 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.566, + 0.892, + 0.62 + ], + "angle": 0, + "content": "[1] Michael Bloesch, Jan Czarnowski, Ronald Clark, Stefan Leutenegger, and Andrew J Davison. Codeslam—learning a compact, optimisable representation for dense visual slam. 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In CVPR, 2017." + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.89, + 0.162 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.956 + ], + "angle": 0, + "content": "3226" + } + ] +] \ No newline at end of file diff --git a/2023/R3D3_ Dense 3D Reconstruction of Dynamic Scenes from Multiple Cameras/df3f55bd-3906-48f7-856c-09ad31d9f51b_origin.pdf b/2023/R3D3_ Dense 3D Reconstruction of Dynamic Scenes from Multiple Cameras/df3f55bd-3906-48f7-856c-09ad31d9f51b_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..89dfc1f24a7d0f7e75160443311e652cc80607a8 --- /dev/null +++ b/2023/R3D3_ Dense 3D Reconstruction of Dynamic Scenes from Multiple Cameras/df3f55bd-3906-48f7-856c-09ad31d9f51b_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:37b77b12e02ed37663fd364b8eec90c642afcb4f86f8cf81489e2e77dc60f3d9 +size 2232753 diff --git a/2023/R3D3_ Dense 3D Reconstruction of Dynamic Scenes from Multiple Cameras/full.md b/2023/R3D3_ Dense 3D Reconstruction of Dynamic Scenes from Multiple Cameras/full.md new file mode 100644 index 0000000000000000000000000000000000000000..7935c9c530289ff587b0f7d00e7012a5b18382a9 --- /dev/null +++ b/2023/R3D3_ Dense 3D Reconstruction of Dynamic Scenes from Multiple Cameras/full.md @@ -0,0 +1,358 @@ +# R3D3: Dense 3D Reconstruction of Dynamic Scenes from Multiple Cameras + +Aron Schmied1* + +Tobias Fischer $^{1*}$ Martin Danelljan $^{1}$ Marc Pollefeys $^{1,2}$ ETH Zürich 2 Microsoft + +https://www.vis.xyz/pub/r3d3/ + +Fisher $\mathrm{Yu}^1$ + +# Abstract + +Dense 3D reconstruction and ego-motion estimation are key challenges in autonomous driving and robotics. Compared to the complex, multi-modal systems deployed today, multi-camera systems provide a simpler, low-cost alternative. However, camera-based 3D reconstruction of complex dynamic scenes has proven extremely difficult, as existing solutions often produce incomplete or incoherent results. We propose R3D3, a multi-camera system for dense 3D reconstruction and ego-motion estimation. Our approach iterates between geometric estimation that exploits spatial-temporal information from multiple cameras, and monocular depth refinement. We integrate multi-camera feature correlation and dense bundle adjustment operators that yield robust geometric depth and pose estimates. To improve reconstruction where geometric depth is unreliable, e.g. for moving objects or low-textured regions, we introduce learnable scene priors via a depth refinement network. We show that this design enables a dense, consistent 3D reconstruction of challenging, dynamic outdoor environments. Consequently, we achieve state-of-the-art dense depth prediction on the DDAD and NuScenes benchmarks. + +# 1. Introduction + +Translating sensory inputs into a dense 3D reconstruction of the environment and tracking the position of the observer is a cornerstone of robotics and fundamental to the development of autonomous vehicles (AVs). Contemporary systems rely on fusing many sensor modalities like camera, LiDAR, RADAR, IMU and more, making hardware and software stacks complex and expensive. In contrast, multi-camera systems provide a simpler, low-cost alternative already widely available in modern consumer vehicles. However, image-based dense 3D reconstruction and egomotion estimation of large-scale, dynamic scenes is an open research problem as moving objects, uniform and repetitive textures, and optical degradations pose significant algorithmic challenges. + +![](images/f6e13b1b26d5aa583f195fb5d1a80779a70bb0c3626c9f6d51c837c0a4faedf2.jpg) +Figure 1. Many methods use temporal context but neglect inter-camera information, leading to incomplete results (top). Other works focus on exploiting inter-camera context but neglect temporal information, yielding incoherent predictions (middle). In contrast, our method achieves a consistent, dense 3D reconstruction by iteratively integrating geometric depth estimation from multiple cameras with monocular depth refinement (bottom). + +Existing works approaching the aforementioned task can be divided into two lines of research. Many methods have focused on recovering 3D scene structure via structure-from-motion (SfM). In particular, simultaneous localization and mapping (SLAM) methods focus on accurate egomotion estimation and usually only recover sparse 3D structure [9, 29, 34, 12, 11]. They typically treat dynamic objects or uniformly textured regions as outliers yielding an incomplete 3D reconstruction result, which makes them less suitable for AVs and robotics. In addition, only a few works have focused on multi-camera setups [24, 8, 33, 30, 26]. In contrast, multi-view stereo (MVS) methods [31, 32, 41, 28, + +57, 27, 17] aim to estimate dense 3D geometry but focus on static scenes and highly overlapping sets of images with known poses. + +The second line of research focuses on dense depth prediction from monocular cues, such as perspective object appearance and scene context [65, 15, 16, 59, 49, 61, 19]. However, due to the injective property of projecting 3D structures onto a 2D plane, reconstructing depth from a single image is an ill-posed problem, which limits the accuracy and generalization of these methods. Recent methods [51, 18, 21], inspired by MVS literature, combine monocular cues with temporal context but are focused on front-facing, single-camera setups. A handful of recent works extend monocular depth estimation to multi-camera setups [22, 52, 54]. These methods utilize the spatial context to improve accuracy and realize absolute scale depth learning. However, those works neglect the temporal domain which provides useful cues for depth estimation. + +Motivated by this observation, we introduce R3D3, a system for dense 3D reconstruction and ego-motion estimation from multiple cameras of dynamic outdoor environments. Our approach combines monocular cues with geometric depth estimates from both spatial inter-camera context as well as inter- and intra-camera temporal context. We compute accurate geometric depth and pose estimates via iterative dense correspondence on frames in a co-visibility graph. For this, we extend the dense bundle adjustment (DBA) operator in [48] to multi-camera setups, increasing robustness and recovering absolute scene scale. To determine co-visible frames across cameras, we propose a simple yet effective multi-camera algorithm that balances performance and efficiency. A depth refinement network takes geometric depth and uncertainty as input and produces a refined depth that improves the reconstruction of, e.g., moving objects and uniformly textured areas. We train this network on real-world driving data without requiring any LiDAR ground-truth. Finally, the refined depth estimates serve as the basis for the next iterations of geometric estimation, thus closing the loop between incremental geometric reconstruction and monocular depth estimation. + +We summarize our contributions as follows. 1) we propose R3D3, a system for dense 3D reconstruction and egomotion estimation in dynamic scenes, 2) we estimate geometric depth and poses with a novel multi-camera DBA formulation and a multi-camera co-visibility graph, 3) we integrate prior geometric depth and uncertainty with monocular cues via a depth refinement network. + +As a result, we achieve state-of-the-art performance across two widely used multi-camera depth estimation benchmarks, namely DDAD [19] and NuScenes [3]. Further, we show that our system exhibits superior accuracy and robustness compared to monocular SLAM methods [48, 5]. + +# 2. Related Work + +Multi-view stereo. MVS methods aim to recover dense 3D scene structure from a set of images with known poses. While earlier works focused on classical optimization [31, 41, 4, 13, 14, 62, 32], more recent works capitalize on the success of convolutional neural networks (CNNs). They use CNNs to estimate features that are matched across multiple depth-hypothesis planes in a 3D cost volume [28, 57, 64, 27, 17, 58, 60]. While early approaches adopt multiple cost volumes across image pairs [64], recent approaches use a single cost volume across the whole image set [57]. These works assume a controlled setting with many, highly overlapping images and known poses to create a 3D cost volume. Instead, we aim to achieve robust, dense 3D reconstruction from an arbitrary multi-camera setup on a moving platform with an unknown trajectory. + +Visual SLAM. Visual SLAM approaches focus on jointly mapping the environment and tracking the trajectory of the observer from visual inputs, i.e. one or multiple RGB cameras. Traditional SLAM systems are often split into different stages, where first images are processed into keypoint matches, which subsequently are used to estimate the 3D scene geometry and camera trajectory [9, 10, 6, 34, 35, 5, 39]. Another line of work focuses on directly optimizing 3D geometry and camera trajectory based on pixel intensities [12, 11, 56, 55]. A handful of works have focused on multi-camera SLAM systems [24, 8, 33, 30, 26]. Recent methods integrate CNN-based depth and pose predictions [45, 56, 55] into the SLAM pipeline. The common challenge these methods face is outliers in the pixel correspondences caused by the presence of low-textured areas, dynamic objects, or optical degradations. Hence, robust estimation techniques are used to filter these outliers, yielding an incomplete, sparse 3D reconstruction result. + +In contrast, dense 3D reconstruction and ego-motion estimation has proven to be more challenging. Early works utilize active depth sensors [36, 64] to alleviate the above-mentioned challenges. Recently, several works on dense visual SLAM from RGB input have emerged [1, 44, 7, 46, 48]. While these methods are able to produce high-quality depth maps and camera trajectories, they inherit the limitations of their traditional counterparts, i.e. their predictions are subject to noise when there are outliers in the pixel correspondences. This can lead to artifacts in the depth maps, inaccurate trajectories, or even a complete failure of the system. On the contrary, we achieve robust, dense 3D reconstruction and ego-motion estimates by jointly leveraging multi-camera constraints as well as monocular depth cues. + +Self-supervised depth estimation. The pioneering work of Zhou et al. [65] learns depth estimation as a proxy task while minimizing a view synthesis loss that uses geometric constraints to warp color information from a reference to a target view. Subsequent research has focused on improv- + +ing network architectures, loss regularization, and training schemes [15, 16, 20, 59, 49, 61, 19]. Recent methods draw inspiration from MVS and propose to use 3D cost volumes in order to incorporate temporal information [51, 18, 53, 21]. While these methods achieve promising results, they still focus on single-camera, front-facing scenarios that do not reflect the real-world sensor setups of AVs [3, 43, 19]. Another recent line of work focuses on exploiting spatial information across overlapping cameras in a multi-camera setup [22, 52, 54]. These works propose to use static feature matches across cameras at a given time to guide depth learning and estimation, and to recover absolute scale. Our work aims to exploit both spatial and temporal cues in order to achieve a robust, dense 3D reconstruction from multiple cameras in dynamic outdoor environments. + +# 3. Method + +Problem formulation. At each timestep $t \in T$ we are given a set of images $\{\mathbf{I}_t^c\}_{c=1}^C$ from $C$ cameras that are mounted on a moving platform with known camera intrinsics $\mathbf{K}_c$ and extrinsics $\mathbf{T}_c$ with respect to a common reference frame. We aim to estimate the depth maps $\mathbf{d}_t^c \in \mathbb{R}_+^{H \times W}$ and ego-pose $\mathbf{P}_t \in SE(3)$ at the current time step. + +Overview. Our system is composed of three stages. First, given a new set of images $\{\mathbf{I}_t^c\}_{c = 1}^C$ , we extract deep features from each $\mathbf{I}_t^c$ . We maintain a co-visibility graph $\mathcal{G} = (\mathcal{V},\mathcal{E})$ where a frame $\mathbf{I}_t^c$ represents a node $v\in \mathcal{V}$ and co-visible frames are connected with edges. For each edge $(i,j)\in \mathcal{E}$ in this graph, we compute the feature correlation $\mathbf{C}_{ij}$ of the two adjacent frames. Second, given initial estimates of the depth $\mathbf{d}_i$ and the relative pose $\mathbf{G}_{ij} = \left(\mathbf{P}_{t_j}\mathbf{T}_{c_j}\right)^{-1}\mathbf{P}_{t_i}\mathbf{T}_{c_i}$ between the two frames, we compute the induced flow $\mathbf{f}_{ij}^{*}$ . We correct the induced flow with a recurrent update operator using the feature correlations $\mathbf{C}_{ij}$ . We then globally align the updated flow estimates at each edge $(i,j)$ with the current estimates of $\mathbf{G}_{ij}$ and $\mathbf{d}_i$ across the co-visibility graph $\mathcal{G}$ with our proposed multi-camera DBA. Third, we introduce a depth refinement network that refines the geometric depth estimates with monocular depth cues to better handle scenarios that are challenging for geometric estimation methods. We illustrate our architecture in Fig. 2. + +# 3.1. Feature Extraction and Correlation + +Given a new observation $\{\mathbf{I}_t^c\}_{c = 1}^C$ , we first extract deep image features, update the co-visibility graph, and compute feature correlations. We describe these steps next. + +Feature extraction. We follow [47, 48] and extract both correlation and context features from each image individually via deep correlation and context encoders $g_{\phi}$ and $g_{\psi}$ . + +Co-visibility graph. We store correlation and context features in a graph $\mathcal{G} = (\mathcal{V},\mathcal{E})$ . Each node corresponds to an image $\mathbf{I}_t^c$ and an edge in the graph indicates that two + +images are considered a pair in the feature correlation and bundle adjustment steps. Contrary to [48], we construct $\mathcal{G}$ with three kinds of edges: temporal, spatial, and spatial-temporal. Since the number of possible edges is $|\mathcal{V}|^2$ and the system runtime scales linearly with $|\mathcal{E}|$ , the degree of sparsity in the co-visibility graph is crucial. We thus carefully design a simple yet effective co-visibility graph construction algorithm in multi-camera setups (see Fig. 3). + +For temporal edges (Fig. 3 in green), we examine the time window $t - \Delta t_{\mathrm{intra}}$ and connect all frames of the same camera that are less than $r_{\mathrm{intra}}$ time steps apart. For spatial and spatial-temporal edges we exploit three priors. 1) we know camera adjacency from the given calibration, 2) we assume motion in the direction of the forward-facing camera and 3) the observer undergoes limited motion within the local time window. We establish spatial edges (Fig. 3 in red) between adjacent cameras within time step $t$ . We further establish spatial-temporal edges (Fig. 3 in orange) given the static camera adjacency within $t - \Delta t_{\mathrm{inter}}$ . In particular, we connect camera $c_i$ and $c_j$ from any $t'$ to $t' - r_{\mathrm{inter}}$ , if $c_i$ and $c_j$ connect within $t$ and if $c_j$ is closer to the forward-facing camera than $c_i$ under forward motion assumption. Finally, we remove an edge $(i,j)$ if node $i$ or $j$ is outside the local time windows $t - \Delta t_{\mathrm{inter}}$ or $t - \Delta t_{\mathrm{intra}}$ . We remove unconnected nodes from the graph. We provide pseudo-code and additional discussion in the supplemental material. + +Feature correlation. For each edge $(i,j) \in \mathcal{E}$ we compute the 4D feature correlation volume via the dot-product + +$$ +\mathbf {C} _ {i j} = \left\langle g _ {\phi} (\mathbf {I} _ {i}), g _ {\phi} (\mathbf {I} _ {j}) \right\rangle \in \mathbb {R} ^ {H \times W \times H \times W}. \tag {1} +$$ + +As in [47, 48], we constrain the correlation search region to a radius $r$ with a lookup operator + +$$ +L _ {r}: \mathbb {R} ^ {H \times W \times H \times W} \times \mathbb {R} ^ {H \times W \times 2} \rightarrow \mathbb {R} ^ {H \times W \times (r + 1) ^ {2}}, \tag {2} +$$ + +that samples a $H \times W$ grid of coordinates from the correlation volume using bilinear interpolation. + +# 3.2. Depth and Pose Estimation + +Given the correlation volume $\mathbf{C}_{ij}$ , we here describe how to estimate the relative pose $\mathbf{G}_{ij}$ and depth $\mathbf{d}_i$ for each edge $(i,j)\in \mathcal{E}$ in the co-visibility graph. + +Flow correction. Given an initial estimate of $\mathbf{G}_{ij}$ and $\mathbf{d}_i$ , we first compute the induced flow $\mathbf{f}_{ij}^*$ to sample the correlation volume $\mathbf{C}_{ij}$ using (2). We then feed the sampled correlation features, the context features $g_{\psi}(\mathbf{I}_i)$ , and the induced flow $\mathbf{f}_{ij}^*$ into a convolutional GRU. The GRU predicts a flow residual $\mathbf{r}_{ij}$ and confidence weights $\mathbf{w}_{ij} \in \mathbb{R}^{H \times W \times 2}$ as in [48]. A challenge of correspondence estimation in a multi-camera setup is that the flow magnitude varies greatly among edges in the co-visibility graph due to inter-camera edges with large relative rotation. To this end, we propose to subtract the rotational part of $\mathbf{f}_{ij}^*$ in those edges via + +$$ +\mathbf {f} _ {i j} ^ {\prime} = \left(\mathbf {x} _ {i} + \mathbf {f} _ {i j} ^ {*}\right) - \Pi_ {c _ {j}} \left(\mathbf {R} _ {c _ {j}} ^ {- 1} \mathbf {R} _ {c _ {i}} \circ \Pi_ {c _ {i}} ^ {- 1} (\mathbf {1})\right), \tag {3} +$$ + +![](images/3394cc6e27e1e5ae6b92a7c4290f3b4bf962e9fc7188f204c48fe8cc431e1d4f.jpg) +Figure 2. Method overview. First, frames $\{\mathbf{I}_t^c\}_{c=1}^C$ from $C$ cameras at time $t$ are encoded and integrated into the co-visibility graph $\mathcal{G} = (\mathcal{V}, \mathcal{E})$ with initial guesses of depth maps $\mathbf{d}_t^c$ and ego-pose $\mathbf{P}_t$ (Sec. 3.1). Second, for each edge $(i,j) \in \mathcal{E}$ , we compute the induced flow $\mathbf{f}_{ij}^*$ from $\mathbf{d}_i$ and relative camera pose $\mathbf{G}_{ij}$ derived from ego-poses $\mathbf{P}$ and camera extrinsics $\mathbf{T}$ . Given $\mathbf{f}_{ij}^*$ , we pool feature correlations from $\mathbf{C}_{ij}$ with operator $L_r$ as input to a GRU that estimates flow update $\mathbf{r}_{ij}$ and confidence $\mathbf{w}_{ij}$ . We globally align depths $\mathbf{d}$ and poses $\mathbf{P}$ with the new flow estimates $\mathbf{f}$ via our multi-camera DBA operator in $k$ iterations (Sec. 3.2). Finally, for each node $i \in \mathcal{V}$ , we refine the initial geometric estimate $\mathbf{d}_i$ given the aggregated confidence $\mathbf{w}_i$ via $\mathcal{D}_{\theta}$ (Sec. 3.3). We highlight our contributions in color. + +![](images/e3b07928cdfa93032e6481220250b593cdd47e060120998b8a615d949cd65742.jpg) +Figure 3. Co-visibility graph. We illustrate an example of the connectivity pattern of the co-visibility graph using our multi-camera graph construction algorithm. We use $\Delta t_{\mathrm{intra}} = 3$ , $\Delta t_{\mathrm{inter}} = 2$ , $r_{\mathrm{intra}} = 2$ , $r_{\mathrm{inter}} = 2$ with six cameras. We depict temporal, spatial, and spatial-temporal edges. + +where $\mathbf{x}_i$ are pixel coordinates of frame $i$ , $\Pi_c$ denotes the projection operator under camera $c$ and $\mathbf{R}$ is the rotation of transformation $\mathbf{T} = (\mathbf{R} \mathbf{t})$ . This aligns the flow magnitude with temporal, intra-camera edges. Note that, while we input $\mathbf{f}_{ij}'$ instead of $\mathbf{f}_{ij}^*$ to the GRU, we still sample the correlation volume $\mathbf{C}_{ij}$ based on $\mathbf{f}_{ij}^*$ . + +Pose and depth correction. We update our pose and depth estimates given the updated flow $\mathbf{f}_{ij} = \mathbf{f}_{ij}^{*} + \mathbf{r}_{ij}$ by minimizing the re-projection error, defined as + +$$ +E = \sum_ {(i, j) \in \mathcal {E}} \left\| \left(\mathbf {x} _ {i} + \mathbf {f} _ {i j}\right) - \Pi_ {c _ {j}} \left(\mathbf {G} _ {i j} \circ \Pi_ {c _ {i}} ^ {- 1} (\mathbf {d} _ {i})\right) \right\| _ {\Sigma_ {i j}} ^ {2}, \tag {4} +$$ + +where $\| .\|_{\Sigma_{ij}}$ is the Mahalanobis norm and $\Sigma_{ij} =$ + +$\operatorname{diag}(\mathbf{w}_{ij})$ . Thus, only matched pixels where the confidence $\mathbf{w}_{ij}$ is greater than zero contribute to the total cost. We extend the dense bundle adjustment (DBA) proposed in [48] to include the known extrinsics of the multi-camera setup. In particular, we decompose the relative poses between two frames $\mathbf{G}_{ij}$ into the unknown, time-varying poses $\mathbf{P}$ in the reference frame and the known static relative transformations $\mathbf{T}$ between the cameras and the reference frame via + +$$ +\mathbf {G} _ {i j} = \left(\mathbf {P} _ {t _ {j}} \mathbf {T} _ {c _ {j}}\right) ^ {- 1} \mathbf {P} _ {t _ {i}} \mathbf {T} _ {c _ {i}}. \tag {5} +$$ + +We linearize the residual of the energy function in Eq. 4 with a first-order Taylor expansion. We use Eq. 5 and treat $\mathbf{T}_{c_j}$ and $\mathbf{T}_{c_i}$ as constants when calculating the Jacobians, thus computing updates only for ego-pose $\mathbf{P}$ . We apply the Gauss-Newton step to compute the updated $\mathbf{P}^{(k)} = \exp (\delta \xi^{(k - 1)})\mathbf{P}^{(k - 1)}$ and depth $\mathbf{d}^{(k)} = \delta \mathbf{d}^{(k - 1)} + \mathbf{d}^{(k - 1)}$ with $\delta \xi^{(k - 1)}\in \mathfrak{se}(3)$ . We provide a detailed derivation in the supplementary material. + +Our formulation has two advantages over DBA [48]. First, the optimization is more robust since $C$ frames are connected through a single ego-pose $\mathbf{P}$ . If one or multiple frames have a high outlier ratio in feature matching, e.g. through lens-flare, low textured regions, or dynamic objects, we can still reliably estimate $\mathbf{P}$ with at least one undisturbed camera. Second, if there are not only pixels matched across the temporal context but also pixels matched across the static, spatial context, we can recover the absolute scale of the scene. This is because for static, spatial matches the relative transformation $\mathbf{G}_{ij} = \mathbf{T}_{c_j}^{-1}\mathbf{T}_{c_i}$ is known to scale so that $E$ is minimized if and only if $\mathbf{d}$ is in absolute scale. + +Training. We train the networks $g_{\phi}$ and $g_{\psi}$ as well as the flow correction GRU on dynamic scenes following the + +procedure in [48]. As shown in [48], the geometric features learned from synthetic data can generalize to real-world scenes. We can therefore leverage existing synthetic driving datasets without relying on real-world ground-truth measurements from sensors like LiDAR or IMU to adjust our method to dynamic, multi-camera scenarios. + +# 3.3. Depth Refinement + +SfM relies on three assumptions: accurate pixel matches, sufficient camera movement, and a static scene. These assumptions do not always hold in the real world due to, e.g., low-textured areas, a static ego vehicle, or many dynamic agents. Still, we would like the system to produce reasonable scene geometry to ensure safe operation. + +On the contrary, monocular depth cues are inherently not affected by these issues. However, they usually lack the accurate geometric detail of SfM methods. Hence, for each node $i \in \mathcal{V}$ , we complement the accurate, but sparse geometric depth estimates with monocular cues. + +Network design. We use a CNN $\mathcal{D}_{\theta}$ parameterized by $\theta$ . We input the depth $\mathbf{d}_i$ , confidence $\mathbf{w}_i$ , and the corresponding image $\mathbf{I}_i$ . The network predicts an improved, dense depth $\mathbf{d}_i' = \mathcal{D}_{\theta}(\mathbf{I}_i, \mathbf{d}_i, \mathbf{w}_i)$ . We obtain the per-frame depth confidence $\mathbf{w}_i$ for frame $i$ by using the maximum across the per-edge confidence weights $\mathbf{w}_{ij}$ . We compute $\mathbf{w}_i = \max_j \frac{1}{2} (\mathbf{w}_{ij}^x + \mathbf{w}_{ij}^y)$ where $x$ and $y$ are the flow directions. We use $\max(\cdot)$ because we observe that depth triangulation will be accurate if at least one pixel is matched with high confidence. We sparsify input depth and confidence weights by setting regions with confidence $\mathbf{w}_i < \beta$ to zero. We concatenate these with the image $\mathbf{I}_i$ . We further concatenate depth and confidence with features at $1/8^{\text{th}}$ scale. As in [16], the output depth is predicted at four scales. To accommodate different focal lengths among cameras in the sensor setup, we do focal length scaling of the output [45]. Training. Contrary to geometric approaches, monocular depth estimators infer depth from semantic cues, which makes it hard for them to generalize across domains [23]. Hence, instead of relying on synthetic data, we train $\mathcal{D}_{\theta}$ on raw, real-world video in a self-supervised manner by minimizing a view synthesis loss [65]. We minimize the photometric error $\mathrm{pe}(\mathbf{I}_t^c, \mathbf{I}_{t'}^{c' \rightarrow c})$ between a target image $\mathbf{I}_t^c$ and a reference image $\mathbf{I}_{t'}^{c'}$ warped to the target viewpoint via + +$$ +\mathbf {I} _ {t ^ {\prime} \rightarrow t} ^ {c ^ {\prime} \rightarrow c} = \Phi \big (\mathbf {I} _ {t ^ {\prime}} ^ {c ^ {\prime}}; \Pi_ {c ^ {\prime}} \big (\mathbf {G} _ {(t, c) (t ^ {\prime}, c ^ {\prime})} \circ \Pi_ {c} ^ {- 1} \big (\mathbf {d} _ {t} ^ {c} \big) \big) \big), \quad (6) +$$ + +with $\Phi$ the bi-linear sampling function, $\mathbf{d}_t^c$ the predicted depth, $c' = c \pm 1$ and $t' = t \pm 1$ . We compute photometric similarity with SSIM [50] and $L_1$ distances. We use $\mathbf{G}_{(t,c)(t',c')} = (\mathbf{P}_{t'}\mathbf{T}_{c'})^{-1}\mathbf{P}_t\mathbf{T}_c$ generated by the first two stages of our system (see Sec. 3.2). Further, self-supervised depth estimation is well-studied, and we follow the common practice of applying regularization techniques to filter the photometric error [16, 63, 20]. First, we mask areas + +where $\mathbf{M}^{\mathrm{st}} = \left[\mathrm{pe}(\mathbf{I}_t^c,\mathbf{I}_{t'\to t}^{c'\to c}) < \mathrm{pe}(\mathbf{I}_t^c,\mathbf{I}_{t'}^{c'})\right]$ , i.e. we filter regions where assuming a stationary scene would induce a lower loss than re-projection. Second, we compute an induced flow consistency mask from $\mathbf{f}^*$ + +$$ +\mathbf {M} ^ {\mathrm {f c}} = \left[ \left\| \mathbf {f} _ {(t, c) \left(t ^ {\prime}, c ^ {\prime}\right)} ^ {*} + \Phi \left(\mathbf {f} _ {\left(t ^ {\prime}, c ^ {\prime}\right) (t, c)} ^ {*}; \mathbf {x} + \mathbf {f} _ {(t, c) \left(t ^ {\prime}, c ^ {\prime}\right)} ^ {*}\right) \right\| _ {2} < \gamma \right]. \tag {7} +$$ + +This term warps pixel coordinates $\mathbf{x}$ from target to reference view, looks up their value in $\mathbf{f}_{(t',c')}(t,c)$ , and compares them to $\mathbf{f}_{(t,c)(t',c')}^*$ . Therefore, pixels not following the epipolar constraint like dynamic objects are masked. Third, to handle the self-occlusion of the ego-vehicle, we manually draw a static mask $\mathbf{M}^{\mathrm{oc}}$ . We can use a single mask for all frames since the cameras are mounted rigidly. Further, to handle occlusions due to change in perspective, we take the minimum loss $\min_{t',c'}\mathrm{pe}(\mathbf{I}_t^c,\mathbf{I}_{t'\to t}^{c'\to c})$ across all reference views. The overall loss for $\mathcal{D}_{\theta}$ is thus + +$$ +\mathcal {L} = \min _ {t ^ {\prime}, c ^ {\prime}} \left(\mathbf {M} ^ {\mathrm {s t}} \mathbf {M} ^ {\mathrm {f c}} \mathbf {M} ^ {\mathrm {o c}} \cdot \operatorname {p e} \left(\mathbf {I} _ {t} ^ {c}, \mathbf {I} _ {t ^ {\prime} \rightarrow t} ^ {c ^ {\prime} \rightarrow c}\right)\right) + \lambda \mathcal {L} _ {\text {s m o o t h}}, \tag {8} +$$ + +with $\mathcal{L}_{\mathrm{smooth}}$ a spatial smoothness regularization term [15]. + +# 3.4. Inference Procedure + +Given an input stream of multi-camera image sets, we perform incremental 3D reconstruction in three phases. + +Warmup phase. First, we add frames to the co-visibility graph if a single GRU step of a reference camera yields a large enough mean optical flow until we reach $n_{\mathrm{warmup}}$ frames. At this stage, we infer depth with our refinement network $\mathbf{d}_t^c = \mathcal{D}_{\theta}(\mathbf{I}_t^c,\mathbf{0},\mathbf{0})$ . We write the depth into the co-visibility graph so that it can be used during initialization. + +Initialization phase. We initialize the co-visibility graph with the available frames and run $n_{\mathrm{itr - wm}}$ GRU and bundle adjustment iterations. For the first $n_{\mathrm{itr - wm}} / 2$ iterations, we fix depths in the bundle adjustment and only optimize poses, which helps with inferring the absolute scale of the scene. + +Active phase. We now add each incoming frame to the co-visibility graph. We initialize the new frames with $\mathbf{d}_t^c = \mathrm{mean}(\mathbf{d}_{t - 4:t - 1}^c)$ and $\mathbf{P}_t = \mathbf{P}_{t - 1}$ . Then, we perform $n_{\mathrm{iter1}}$ GRU and bundle adjustment updates, and apply the refinement network to all updated frames. If the mean optical flow of the reference camera between $t$ and $t - 1$ is low, we remove all frames at $t - 1$ from the co-visibility graph. This helps to handle situations with little to no egomotion. In case no frame is removed, we do another $n_{\mathrm{iter2}}$ iterations. Finally, we write the updated depths and poses into the co-visibility graph. + +# 4. Experiments + +# 4.1. Experimental Setup + +We perform extensive experiments on large-scale driving datasets that contain recordings from vehicles equipped + +Table 1. Method ablation. We ablate our method components on the DDAD [19] dataset. We examine the influence of each component given the geometric estimation as in [48] with naive DBA as the baseline. Further, we show the influence of VKITTI [2] fine-tuning on the geometric estimation. We enumerate each variant for better reference. * median scaled depth, ** scaled trajectory. + +
No.Geom. Est.VKITTIMulti-Cam DBARefinementAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑ATE [m] ↓ATE** [m] ↓
1a*✓✓0.43826.9719.1090.636-2.134
1b✓✓0.44236.3918.6640.7361.6720.435
1c✓✓✓0.32015.4516.3030.7272.3560.922
2a✓0.2113.80612.6680.715--
3a✓✓✓✓0.1623.01911.4080.8111.2350.433
+ +Table 2. Co-visibility graph ablation. We compare our co-visibility graph construction algorithm to the original algorithm in [48] on the DDAD [19] dataset. We observe that our algorithm improves the overall runtime by an order of magnitude while maintaining the same level of performance. + +
GraphAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑ATE [m] ↓tinf [s] ↓
Original0.1622.96811.1560.8160.9823.23
Ours0.1623.01911.4080.8111.2350.35
+ +Table 3. Refinement network ablation. We show on the DDAD [19] dataset that both adding confidence weights $\mathbf{w}_i$ and sparsifying the depth input via $\mathbf{w}_i < \beta$ to filter outliers in the input of depth refinement network $\mathcal{D}_{\theta}$ is vital to depth accuracy. + +
wiwi<βAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
0.1814.07812.1080.789
✓0.1733.49711.9240.792
✓✓0.1623.01911.4080.811
+ +with multiple cameras, LiDARs, and other sensors. Note that we only use camera data for training and inference, and use LiDAR data only as ground-truth for evaluation. We evaluate our method in inference mode (cf. Sec. 3.4), i.e. we obtain predictions in a fully online (causal) manner to mimic real-world deployment. + +DDAD. This dataset consists of 150 training and 50 validation scenes from urban areas. Each sequence has a length of 50 or 100 time steps at a frame rate of $10\mathrm{Hz}$ . The sensor setup includes six cameras in a surround-view setup with up to $20\%$ overlap. We follow [19] and evaluate depth up to $200\mathrm{m}$ averaged across all cameras. We use self-occlusion masks from [52] to filter the ego-vehicle in the images. Images have a resolution of $1216\times 1936$ and are downsampled to $384\times 640$ in our experiments. + +NuScenes. This dataset contains 700 training, 150 validation, and 150 testing sequences of urban scenes with challenging conditions such as nighttime and rain. Each scene is composed of 40 keyframes at $2\mathrm{Hz}$ synchronized across sensors. The six cameras have a sampling rate of $12\mathrm{Hz}$ and are arranged in a surround-view setup with up to $10\%$ overlap. We follow [22] and evaluate depth averaged across all cameras on the validation set. We use a single self-occlusion mask for all scenes. While the raw images have a resolution of $900 \times 1600$ , we use $768 \times 448$ . + +Implementation details. We implement our system in PyTorch [37]. Our multi-camera DBA is implemented in + +![](images/df455e6662489f8ffabab06a4682c2ee2994ae6c2b6f807082be9e601ca3fd01.jpg) +Input + +![](images/0f3d17e6add867abf6235566e5f57d3c8f99632215273e840df03a58525cc11b.jpg) +Geom. Depth + +![](images/854459c2f6c83fd446b2d3b41b21f6bc2116e870ad253a9f390d19437ff69772.jpg) +Refined + +![](images/c3fba9cbbd9e44db0532e9b65cadbb0c9bafb58cff347c82408351e0aca428d1.jpg) + +![](images/65058b1936539c0c613c01b1acce8736f13be4318e37c9790785d4979f916471.jpg) + +![](images/036c9f240024360805fd3fc0529fff4f9e95d6e72d39ebafdd8c2011d29b10fd.jpg) + +![](images/1493ca10345502ffccbd606d8b06a98079489c9031715da8046bf7beaaab7f95.jpg) +Figure 4. Depth refinement. We plot images overlayed with confidence $\mathbf{w}_i$ , the geometric depth estimate $\mathbf{d}$ , and the refined depth $\mathbf{d}'$ from $\mathcal{D}_{\theta}$ . We observe a smoother ground plane, corrected dynamic objects, and filtered outliers. + +![](images/7ab81b528b6f25eaad7c7954b3e7c0f867677f18bb9f14debc57b95f20729b73.jpg) + +![](images/190b36e7b2546ecc8f404e338e25c94909342a702db666c68ac3f5af845b1f07.jpg) + +CUDA. We fine-tune $g_{\phi}$ , $g_{\psi}$ and the flow correction GRU on VIKITTI2 [2] for 10 epochs with a batch size of 1, sequence length of 7, and learning rate $10^{-4}$ with the pretrained model in [48]. For $\mathcal{D}_{\theta}$ , we use a U-Net [38] with ResNet18 [25] encoder and initialize it with ImageNet [40] pre-trained weights. We use $\beta = 0.5$ , $\gamma = 3$ and $\lambda = 10^{-3}$ . We train for 20 epochs with batch size of 6 and the Adam optimizer with learning rate $10^{-4}$ , $\beta_{1} = 0.9$ , and $\beta_{2} = 0.999$ . We reduce the learning rate by a factor of 10 after 15 epochs. For inference, the runtime is measured for a set of six images on a single RTX3090 GPU. Each sequence is initialized with 3 warmup frames filtered at a mean flow threshold of 1.75. We build the co-visibility graph with $\Delta t_{\mathrm{intra}} = 3$ , $r_{\mathrm{intra}} = 2$ , $\Delta t_{\mathrm{inter}} = 2$ and $r_{\mathrm{inter}} = 2$ . + +# 4.2. Ablation Studies + +Method ablation. We ablate our method components on the DDAD dataset in Tab. 1. The geometric estimation baseline (1a) consists of [48] with the naive DBA formulation applied to all cameras and the co-visibility graph as described in Sec. 3.1. It performs poorly in depth and pose estimation, with an Abs. Rel. score of 0.438 and an absolute trajectory error (ATE) [42] of $2.134\mathrm{m}$ , even when adjusting for scale. Next, we add our multi-camera DBA (1b). We observe that, even without VKITTI fine-tuning, the pose esti + +Table 4. Comparison to state-of-the-art on DDAD. We compare favorably to existing methods on both scale-aware and scale-invariant depth prediction. * median scaled depth. + +
MethodAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
FSM [22]0.201---
SurroundDepth [52]0.2083.37112.9770.693
Ours0.1623.01911.4080.811
FSM* [22]0.202---
SurroundDepth* [52]0.2003.39212.2700.740
MCDP* [54]0.1933.11112.2640.811
Ours*0.1693.04111.3720.809
+ +Table 5. Per-camera evaluation on DDAD. We show a per-camera breakdown of previous works, our $\mathcal{D}_{\theta}$ only (cf. 2a in Tab. 1), and our full method. Our full method performs the best with a particularly significant improvement on the side-view cameras while $\mathcal{D}_{\theta}$ performs similarly to previous works. + +
MethodAbs Rel ↓
FrontF.LeftF-rightB.LeftB-rightBack
FSM [22]0.1300.2010.2240.2290.2400.186
SurroundDepth [52]0.1520.2070.2300.2200.2390.200
Dθ only0.1540.2130.2370.2310.2370.194
Ours0.1280.1600.1680.1720.1740.169
+ +Table 6. Comparison to multi-frame methods on DDAD. We compare to methods that exploit temporal context from a single camera [51, 18]. We evaluate only the front camera since these methods were trained only on this camera. + +
MethodFront Camera
Abs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
ManyDepth [51]0.1463.25814.0980.822
DepthFormer [18]0.1352.95312.4770.836
Ours0.1283.16813.2140.868
+ +Table 7. Pose evaluation on DDAD. We compare our method to state-of-the-art monocular SLAM methods for which we report the average ATE across the cameras that successfully tracked the camera path. ** scaled trajectory. + +
DROID-SLAM [48]ORB-SLAMv3 [5]Ours
ATE** [m] ↓7.5006.1790.433
+ +mation accuracy improves dramatically over the naive DBA baseline. The relative scale ATE drops from $2.134\mathrm{m}$ to only $0.435\mathrm{m}$ . The absolute scale ATE is only about $1.2\mathrm{m}$ higher, indicating the scene scale is recovered accurately. + +Using VKITTI fine-tuning (1c), we achieve significant gains in depth accuracy, where Abs. Rel. drops to 0.32 and $\delta_{1.25}$ increases to $72.7\%$ . However, note that VKITTI fine-tuning does not affect the $\delta_{1.25}$ score, i.e. it helps mostly with depth outliers. We attribute this to the absence of dynamic objects in the training data of [48] so that fine-tuning helps to adjust the confidence prediction to handle such outliers (cf. Sec. 3.2). We further test the depth refinement network (Sec. 3.3) without geometric estimation prior (2a). The depth obtained from $\mathcal{D}_{\theta}$ is less prone to outliers, as evidenced by its low Abs. Rel., Sq. Rel. and RMSE scores. However, note that its $\delta_{1.25}$ is only $71.5\%$ , i.e. its + +![](images/eb4eceb587e81555ce56c84b82137c45e4c2b8b83925d21f488663cfdcc0b9a7.jpg) +Figure 5. Depth in $\delta_{1.25^n}$ range for different thresholds on DDAD. We depict the ratio of depth estimates $d$ for which $\delta(d) < 1.25^n$ where $\delta(d) = \max\left(\frac{d}{d^*}, \frac{d^*}{d}\right)$ and $d^*$ is ground-truth depth. Note that values at $n = 1, 2, 3$ represent $\delta_{1.25}, \delta_{1.25^2}, \delta_{1.25^3}$ . + +Table 8. Comparison to state-of-the-art on NuScenes. Evaluated up to $80\mathrm{m}$ for scale-aware depth as in [22, 52] and $60\mathrm{m}$ for median-scaled depth (denoted with $*$ ) as in [54]. + +
MethodAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
FSM [22]0.297---
SurroundDepth [52]0.2804.4017.4670.661
Ours0.2534.7597.1500.729
PackNet*[19]0.3033.1547.0140.655
FSM* [22]0.2703.1856.8320.689
SurroundDepth* [52]0.2453.0676.8350.719
MCDP* [54]0.2373.0306.8220.719
Ours*0.2353.3326.0210.749
+ +depth accuracy compared to the geometric depth estimates is actually lower when disregarding outliers. Finally, we test our full system (3a). Compared to geometric estimation (1d), we observe a significant improvement in outlier sensitive metrics like RMSE, but also in outlier robust metrics like $\delta_{1.25}$ . Additionally, the pose estimation accuracy is increased and the difference between scaled and non-scaled ATE is smaller. Compared to depth obtained from $\mathcal{D}_{\theta}(2\mathrm{a})$ , the increase in outlier sensitive metrics is smaller but still significant, e.g. 1.26m in RMSE. Further, we observe a sizable gain in $\delta_{1.25}$ of 9.6 percentage points. + +Further, in Fig. 5, we compare the $\delta_{1.25^n}$ scores at different accuracy thresholds $n$ of our geometric depth estimation without refinement ('Ours (Geometric)'), our refinement network only ('Ours (Monocular)') and our full method ('Ours'). The results confirm our hypothesis that while geometric estimates are more accurate than monocular depth estimates, they are also noisier. Importantly, the results further illustrate that our full method can effectively combine the strengths of both approaches while not suffering from their weaknesses. + +Co-visibility graph construction. In Tab. 2, we compare our co-visibility graph construction algorithm (Sec. 3.1) to a multi-camera adaption of the algorithm in [48]. Ours + +Table 9. Per-camera evaluation on NuScenes. We compare our method with previous works on scale-aware depth estimation. Evaluated up to $80\mathrm{m}$ as in Tab. 8. We observe the same trend as on DDAD, i.e. our method performs best across all cameras, with a particularly high improvement on the side views. + +
MethodAbs Rel ↓
FrontF.LeftF-rightB.LeftB_rightBack
FSM [22]0.1860.2870.3750.2960.4180.221
SurroundDepth [52]0.1790.2600.3400.2820.4030.212
Ours0.1740.2300.3020.2490.3600.201
+ +Table 10. Cross-dataset transfer. We use models trained on DDAD to evaluate scale-aware depth prediction on the NuScenes dataset. We compare to state-of-the-art methods [22, 52] and observe that our method exhibits better generalization ability (cf. Tab. 8). + +
MethodAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
FSM [22]0.3495.0648.7850.499
SurroundDepth [52]0.3645.4768.4470.525
Ours0.2924.8007.6770.660
+ +yields similar performance in depth estimation, with the exact same Abs. Rel. score and only minor difference in other metrics. Further, the absolute scale ATE is only slightly $(25\mathrm{cm})$ higher. In contrast, using our algorithm, we achieve a runtime reduction of nearly $10\times$ on the full system. + +Depth refinement network. We verify the choice of our inputs to $\mathcal{D}_{\theta}$ in Tab. 3. If we do not input the confidence $\mathbf{w}_i$ and do not sparsify the depth via $\mathbf{w}_i < \beta$ before feeding it to $\mathcal{D}_{\theta}$ , we observe the lowest performance. If we input the confidence $\mathbf{w}_i$ but do not sparsify the depth, we see an improvement over not using them. We achieve the best performance with the inputs described in Sec. 3.3. + +Moreover, we show qualitative examples of our depth refinement in Fig. 4. The confidence $\mathbf{w}_i$ (overlaid with the image) segments regions where geometric estimation is ambiguous, i.e. dynamic objects and uniformly textured areas like the sky and the road surface. The geometric depth maps exhibit severe artifacts in such regions. After refinement, these artifacts are corrected. + +# 4.3. Comparison to State-of-the-Art + +DDAD. In Tab. 4, we compare our method to existing self-supervised multi-camera depth estimation methods. We achieve significant improvements in scale-aware and scale-invariant depth prediction with only minor differences in absolute and relative scale results. In both settings, we achieve state-of-the-art results with the lowest Abs. Rel. scores of 0.162 and 0.169, respectively. + +In Fig. 5 we compare the $\delta_{1.25^n}$ scores of our method to the state-of-the-art approaches on DDAD at different $n$ . For small values of $n$ , we observe a particularly pronounced performance gain over existing methods. This shows the advantage of combining highly accurate geometric estimates with monocular cues. Further, our method consistently out + +performs the baselines over all values of $n$ for $\delta < 1.25^n$ . + +In Fig. 6, we show a qualitative comparison to existing works. On the left side, we illustrate depth maps across three cameras. Compared to FSM [22] and Surround-Depth [52], we produce sharper depth boundaries. On the right side, we illustrate point clouds accumulated over time. We produce a more consistent reconstruction, as can be seen when focusing on the vehicles or the fences beside the road. + +Tab. 5 shows the per-camera breakdown of the scale-aware depth prediction comparison. The advantage of our method is particularly pronounced on the side cameras. Other methods struggle with the side views because the static spatial context is limited and they do not exploit any temporal or spatial-temporal context. The temporal and spatial-temporal contexts are conducive in the side views since sideward motion leads to better triangulation angles than forward motion. This is also evidenced by the results of $\mathcal{D}_{\theta}$ without geometric estimation, which performs similarly to the baseline methods, struggling with the side views. In contrast, our full system performs well across all cameras. + +We further compare to self-supervised single-camera methods that leverage temporal information in Tab. 6. For a fair comparison, we evaluate only the front camera. We compare favorably to DepthFormer [18] and Many-Depth [51]. In particular, we substantially improve in the outlier robust metric $\delta_{1.25}$ and perform competitively in all others. Our Abs. Rel. score is the lowest at 0.128. + +To evaluate ego-motion estimation, we compare our system to state-of-the-art monocular SLAM methods [48, 5] in Tab. 7. We run the baselines on each camera and report the average ATE across the cameras that successfully tracked the camera path. Note that, contrary to our approach, the competing methods frequently failed to produce a trajectory. We observe that state-of-the-art monocular SLAM methods exhibit a large error (ATE), while our method recovers accurate trajectories. + +NuScenes. In Tab. 8, we compare our system to previous self-supervised multi-camera depth estimation methods. We outperform previous methods by a significant margin, corroborating our findings on DDAD. Notably, we observe substantial improvements in scale-aware depth estimation, while previous works usually struggle with recovering absolute scale on this dataset since the overlap between cameras is smaller than in DDAD [22]. Therefore, previous works like MCDP [54] report results on scale-invariant depth prediction. We outperform existing methods also in this setting, although the performance gap is smaller. Note that the gap between scale-aware and scale-invariant evaluation is only 2 percentage points in $\delta_{1.25}$ for our method, while for SurroundDepth [52] the gap is much larger with 5.8 percentage points. We show a per-camera breakdown of the comparison to the state-of-the-art in scale-aware depth estimation in Tab. 9. The results corroborate our findings + +![](images/95e55d4b7101af8d04192135547bb051457ef804e1133ce167ef313bfac449b4.jpg) +Figure 6. Qualitative comparison on DDAD. We show depth maps and point clouds accumulated over time along with input images, ground-truth LiDAR 3D Reconstruction, and the ego-vehicle in red. Our depth maps are sharper and more accurate. Our accumulated point clouds yield a more consistent 3D reconstruction. Note that we use our pose predictions for [22, 52] since these do not predict pose. + +on DDAD, namely that our method outperforms previous works across all cameras with a particularly pronounced improvement on the side views. + +Cross-dataset transfer. We finally test the cross-dataset generalization of our method versus FSM [22] and SurroundDepth [52]. In Tab. 10, we show scale-aware depth estimation results of models trained on DDAD, evaluated on NuScenes. We observe that the gap in Abs. Rel. widens compared to Tab. 8, with our method outperforming SurroundDepth by 0.072 in Abs. Rel. and FSM by 0.057. Further, our method maintains much higher levels of $\delta_{1.25}$ and Sq. Rel., while SurroundDepth drops significantly in both metrics. Note that we apply focal length scaling [45] to all methods to accommodate differences in camera intrinsics. + +# 5. Conclusion + +We introduced R3D3, a multi-camera system for dense 3D reconstruction of dynamic outdoor environments. 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Unsupervised learning of depth and ego-motion from video. 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Compared to the complex, multi-modal systems deployed today, multi-camera systems provide a simpler, low-cost alternative. However, camera-based 3D reconstruction of complex dynamic scenes has proven extremely difficult, as existing solutions often produce incomplete or incoherent results. We propose R3D3, a multi-camera system for dense 3D reconstruction and ego-motion estimation. Our approach iterates between geometric estimation that exploits spatial-temporal information from multiple cameras, and monocular depth refinement. We integrate multi-camera feature correlation and dense bundle adjustment operators that yield robust geometric depth and pose estimates. To improve reconstruction where geometric depth is unreliable, e.g. for moving objects or low-textured regions, we introduce learnable scene priors via a depth refinement network. We show that this design enables a dense, consistent 3D reconstruction of challenging, dynamic outdoor environments. Consequently, we achieve state-of-the-art dense depth prediction on the DDAD and NuScenes benchmarks." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 509, + 128, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 509, + 128, + 521 + ], + "spans": [ + { + "bbox": [ + 47, + 509, + 128, + 521 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 529, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 696 + ], + "type": "text", + "content": "Translating sensory inputs into a dense 3D reconstruction of the environment and tracking the position of the observer is a cornerstone of robotics and fundamental to the development of autonomous vehicles (AVs). Contemporary systems rely on fusing many sensor modalities like camera, LiDAR, RADAR, IMU and more, making hardware and software stacks complex and expensive. In contrast, multi-camera systems provide a simpler, low-cost alternative already widely available in modern consumer vehicles. However, image-based dense 3D reconstruction and egomotion estimation of large-scale, dynamic scenes is an open research problem as moving objects, uniform and repetitive textures, and optical degradations pose significant algorithmic challenges." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 310, + 213, + 544, + 468 + ], + "blocks": [ + { + "bbox": [ + 310, + 213, + 544, + 468 + ], + "lines": [ + { + "bbox": [ + 310, + 213, + 544, + 468 + ], + "spans": [ + { + "bbox": [ + 310, + 213, + 544, + 468 + ], + "type": "image", + "image_path": "f6e13b1b26d5aa583f195fb5d1a80779a70bb0c3626c9f6d51c837c0a4faedf2.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 472, + 547, + 550 + ], + "lines": [ + { + "bbox": [ + 304, + 472, + 547, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 547, + 550 + ], + "type": "text", + "content": "Figure 1. Many methods use temporal context but neglect inter-camera information, leading to incomplete results (top). Other works focus on exploiting inter-camera context but neglect temporal information, yielding incoherent predictions (middle). In contrast, our method achieves a consistent, dense 3D reconstruction by iteratively integrating geometric depth estimation from multiple cameras with monocular depth refinement (bottom)." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "Existing works approaching the aforementioned task can be divided into two lines of research. Many methods have focused on recovering 3D scene structure via structure-from-motion (SfM). In particular, simultaneous localization and mapping (SLAM) methods focus on accurate egomotion estimation and usually only recover sparse 3D structure [9, 29, 34, 12, 11]. They typically treat dynamic objects or uniformly textured regions as outliers yielding an incomplete 3D reconstruction result, which makes them less suitable for AVs and robotics. In addition, only a few works have focused on multi-camera setups [24, 8, 33, 30, 26]. In contrast, multi-view stereo (MVS) methods [31, 32, 41, 28," + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 126, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 126, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 126, + 712 + ], + "type": "text", + "content": "*Equal contribution." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3216" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 286, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 286, + 108 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 286, + 108 + ], + "type": "text", + "content": "57, 27, 17] aim to estimate dense 3D geometry but focus on static scenes and highly overlapping sets of images with known poses." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 110, + 286, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 110, + 286, + 289 + ], + "spans": [ + { + "bbox": [ + 49, + 110, + 286, + 289 + ], + "type": "text", + "content": "The second line of research focuses on dense depth prediction from monocular cues, such as perspective object appearance and scene context [65, 15, 16, 59, 49, 61, 19]. However, due to the injective property of projecting 3D structures onto a 2D plane, reconstructing depth from a single image is an ill-posed problem, which limits the accuracy and generalization of these methods. Recent methods [51, 18, 21], inspired by MVS literature, combine monocular cues with temporal context but are focused on front-facing, single-camera setups. A handful of recent works extend monocular depth estimation to multi-camera setups [22, 52, 54]. These methods utilize the spatial context to improve accuracy and realize absolute scale depth learning. However, those works neglect the temporal domain which provides useful cues for depth estimation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 292, + 286, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 292, + 286, + 553 + ], + "spans": [ + { + "bbox": [ + 49, + 292, + 286, + 553 + ], + "type": "text", + "content": "Motivated by this observation, we introduce R3D3, a system for dense 3D reconstruction and ego-motion estimation from multiple cameras of dynamic outdoor environments. Our approach combines monocular cues with geometric depth estimates from both spatial inter-camera context as well as inter- and intra-camera temporal context. We compute accurate geometric depth and pose estimates via iterative dense correspondence on frames in a co-visibility graph. For this, we extend the dense bundle adjustment (DBA) operator in [48] to multi-camera setups, increasing robustness and recovering absolute scene scale. To determine co-visible frames across cameras, we propose a simple yet effective multi-camera algorithm that balances performance and efficiency. A depth refinement network takes geometric depth and uncertainty as input and produces a refined depth that improves the reconstruction of, e.g., moving objects and uniformly textured areas. We train this network on real-world driving data without requiring any LiDAR ground-truth. Finally, the refined depth estimates serve as the basis for the next iterations of geometric estimation, thus closing the loop between incremental geometric reconstruction and monocular depth estimation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 556, + 286, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 556, + 286, + 639 + ], + "spans": [ + { + "bbox": [ + 49, + 556, + 286, + 639 + ], + "type": "text", + "content": "We summarize our contributions as follows. 1) we propose R3D3, a system for dense 3D reconstruction and egomotion estimation in dynamic scenes, 2) we estimate geometric depth and poses with a novel multi-camera DBA formulation and a multi-camera co-visibility graph, 3) we integrate prior geometric depth and uncertainty with monocular cues via a depth refinement network." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 49, + 642, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 642, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 49, + 642, + 286, + 712 + ], + "type": "text", + "content": "As a result, we achieve state-of-the-art performance across two widely used multi-camera depth estimation benchmarks, namely DDAD [19] and NuScenes [3]. Further, we show that our system exhibits superior accuracy and robustness compared to monocular SLAM methods [48, 5]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 309, + 72, + 391, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 72, + 391, + 83 + ], + "spans": [ + { + "bbox": [ + 309, + 72, + 391, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 91, + 544, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 91, + 544, + 270 + ], + "spans": [ + { + "bbox": [ + 308, + 91, + 544, + 270 + ], + "type": "text", + "content": "Multi-view stereo. MVS methods aim to recover dense 3D scene structure from a set of images with known poses. While earlier works focused on classical optimization [31, 41, 4, 13, 14, 62, 32], more recent works capitalize on the success of convolutional neural networks (CNNs). They use CNNs to estimate features that are matched across multiple depth-hypothesis planes in a 3D cost volume [28, 57, 64, 27, 17, 58, 60]. While early approaches adopt multiple cost volumes across image pairs [64], recent approaches use a single cost volume across the whole image set [57]. These works assume a controlled setting with many, highly overlapping images and known poses to create a 3D cost volume. Instead, we aim to achieve robust, dense 3D reconstruction from an arbitrary multi-camera setup on a moving platform with an unknown trajectory." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 308, + 270, + 544, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 270, + 544, + 485 + ], + "spans": [ + { + "bbox": [ + 308, + 270, + 544, + 485 + ], + "type": "text", + "content": "Visual SLAM. Visual SLAM approaches focus on jointly mapping the environment and tracking the trajectory of the observer from visual inputs, i.e. one or multiple RGB cameras. Traditional SLAM systems are often split into different stages, where first images are processed into keypoint matches, which subsequently are used to estimate the 3D scene geometry and camera trajectory [9, 10, 6, 34, 35, 5, 39]. Another line of work focuses on directly optimizing 3D geometry and camera trajectory based on pixel intensities [12, 11, 56, 55]. A handful of works have focused on multi-camera SLAM systems [24, 8, 33, 30, 26]. Recent methods integrate CNN-based depth and pose predictions [45, 56, 55] into the SLAM pipeline. The common challenge these methods face is outliers in the pixel correspondences caused by the presence of low-textured areas, dynamic objects, or optical degradations. Hence, robust estimation techniques are used to filter these outliers, yielding an incomplete, sparse 3D reconstruction result." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 487, + 544, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 487, + 544, + 652 + ], + "spans": [ + { + "bbox": [ + 308, + 487, + 544, + 652 + ], + "type": "text", + "content": "In contrast, dense 3D reconstruction and ego-motion estimation has proven to be more challenging. Early works utilize active depth sensors [36, 64] to alleviate the above-mentioned challenges. Recently, several works on dense visual SLAM from RGB input have emerged [1, 44, 7, 46, 48]. While these methods are able to produce high-quality depth maps and camera trajectories, they inherit the limitations of their traditional counterparts, i.e. their predictions are subject to noise when there are outliers in the pixel correspondences. This can lead to artifacts in the depth maps, inaccurate trajectories, or even a complete failure of the system. On the contrary, we achieve robust, dense 3D reconstruction and ego-motion estimates by jointly leveraging multi-camera constraints as well as monocular depth cues." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 308, + 654, + 544, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 654, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 654, + 544, + 712 + ], + "type": "text", + "content": "Self-supervised depth estimation. The pioneering work of Zhou et al. [65] learns depth estimation as a proxy task while minimizing a view synthesis loss that uses geometric constraints to warp color information from a reference to a target view. Subsequent research has focused on improv-" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "type": "text", + "content": "3217" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "ing network architectures, loss regularization, and training schemes [15, 16, 20, 59, 49, 61, 19]. Recent methods draw inspiration from MVS and propose to use 3D cost volumes in order to incorporate temporal information [51, 18, 53, 21]. While these methods achieve promising results, they still focus on single-camera, front-facing scenarios that do not reflect the real-world sensor setups of AVs [3, 43, 19]. Another recent line of work focuses on exploiting spatial information across overlapping cameras in a multi-camera setup [22, 52, 54]. These works propose to use static feature matches across cameras at a given time to guide depth learning and estimation, and to recover absolute scale. Our work aims to exploit both spatial and temporal cues in order to achieve a robust, dense 3D reconstruction from multiple cameras in dynamic outdoor environments." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 265, + 104, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 265, + 104, + 277 + ], + "spans": [ + { + "bbox": [ + 47, + 265, + 104, + 277 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "type": "text", + "content": "Problem formulation. At each timestep " + }, + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "type": "inline_equation", + "content": "t \\in T" + }, + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "type": "text", + "content": " we are given a set of images " + }, + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{I}_t^c\\}_{c=1}^C" + }, + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "type": "text", + "content": " cameras that are mounted on a moving platform with known camera intrinsics " + }, + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_c" + }, + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "type": "text", + "content": " and extrinsics " + }, + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_c" + }, + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "type": "text", + "content": " with respect to a common reference frame. We aim to estimate the depth maps " + }, + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_t^c \\in \\mathbb{R}_+^{H \\times W}" + }, + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "type": "text", + "content": " and ego-pose " + }, + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_t \\in SE(3)" + }, + { + "bbox": [ + 46, + 285, + 287, + 357 + ], + "type": "text", + "content": " at the current time step." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "text", + "content": "Overview. Our system is composed of three stages. First, given a new set of images " + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{I}_t^c\\}_{c = 1}^C" + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "text", + "content": ", we extract deep features from each " + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_t^c" + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "text", + "content": ". We maintain a co-visibility graph " + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "inline_equation", + "content": "\\mathcal{G} = (\\mathcal{V},\\mathcal{E})" + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "text", + "content": " where a frame " + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_t^c" + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "text", + "content": " represents a node " + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "inline_equation", + "content": "v\\in \\mathcal{V}" + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "text", + "content": " and co-visible frames are connected with edges. For each edge " + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "inline_equation", + "content": "(i,j)\\in \\mathcal{E}" + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "text", + "content": " in this graph, we compute the feature correlation " + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{ij}" + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "text", + "content": " of the two adjacent frames. Second, given initial estimates of the depth " + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_i" + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "text", + "content": " and the relative pose " + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_{ij} = \\left(\\mathbf{P}_{t_j}\\mathbf{T}_{c_j}\\right)^{-1}\\mathbf{P}_{t_i}\\mathbf{T}_{c_i}" + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "text", + "content": " between the two frames, we compute the induced flow " + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{ij}^{*}" + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "text", + "content": ". We correct the induced flow with a recurrent update operator using the feature correlations " + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{ij}" + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "text", + "content": ". We then globally align the updated flow estimates at each edge " + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "text", + "content": " with the current estimates of " + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_{ij}" + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_i" + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "text", + "content": " across the co-visibility graph " + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 358, + 289, + 576 + ], + "type": "text", + "content": " with our proposed multi-camera DBA. Third, we introduce a depth refinement network that refines the geometric depth estimates with monocular depth cues to better handle scenarios that are challenging for geometric estimation methods. We illustrate our architecture in Fig. 2." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 585, + 237, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 585, + 237, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 585, + 237, + 597 + ], + "type": "text", + "content": "3.1. Feature Extraction and Correlation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 603, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 603, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 603, + 287, + 640 + ], + "type": "text", + "content": "Given a new observation " + }, + { + "bbox": [ + 46, + 603, + 287, + 640 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{I}_t^c\\}_{c = 1}^C" + }, + { + "bbox": [ + 46, + 603, + 287, + 640 + ], + "type": "text", + "content": ", we first extract deep image features, update the co-visibility graph, and compute feature correlations. We describe these steps next." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 641, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 677 + ], + "type": "text", + "content": "Feature extraction. We follow [47, 48] and extract both correlation and context features from each image individually via deep correlation and context encoders " + }, + { + "bbox": [ + 46, + 641, + 287, + 677 + ], + "type": "inline_equation", + "content": "g_{\\phi}" + }, + { + "bbox": [ + 46, + 641, + 287, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 641, + 287, + 677 + ], + "type": "inline_equation", + "content": "g_{\\psi}" + }, + { + "bbox": [ + 46, + 641, + 287, + 677 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "Co-visibility graph. We store correlation and context features in a graph " + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{G} = (\\mathcal{V},\\mathcal{E})" + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": ". Each node corresponds to an image " + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_t^c" + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": " and an edge in the graph indicates that two" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": "images are considered a pair in the feature correlation and bundle adjustment steps. Contrary to [48], we construct " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": " with three kinds of edges: temporal, spatial, and spatial-temporal. Since the number of possible edges is " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "|\\mathcal{V}|^2" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": " and the system runtime scales linearly with " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "|\\mathcal{E}|" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": ", the degree of sparsity in the co-visibility graph is crucial. We thus carefully design a simple yet effective co-visibility graph construction algorithm in multi-camera setups (see Fig. 3)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": "For temporal edges (Fig. 3 in green), we examine the time window " + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "inline_equation", + "content": "t - \\Delta t_{\\mathrm{intra}}" + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": " and connect all frames of the same camera that are less than " + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "inline_equation", + "content": "r_{\\mathrm{intra}}" + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": " time steps apart. For spatial and spatial-temporal edges we exploit three priors. 1) we know camera adjacency from the given calibration, 2) we assume motion in the direction of the forward-facing camera and 3) the observer undergoes limited motion within the local time window. We establish spatial edges (Fig. 3 in red) between adjacent cameras within time step " + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": ". We further establish spatial-temporal edges (Fig. 3 in orange) given the static camera adjacency within " + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "inline_equation", + "content": "t - \\Delta t_{\\mathrm{inter}}" + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": ". In particular, we connect camera " + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "inline_equation", + "content": "c_i" + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "inline_equation", + "content": "c_j" + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": " from any " + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "inline_equation", + "content": "t'" + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "inline_equation", + "content": "t' - r_{\\mathrm{inter}}" + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": ", if " + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "inline_equation", + "content": "c_i" + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "inline_equation", + "content": "c_j" + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": " connect within " + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": " and if " + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "inline_equation", + "content": "c_j" + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": " is closer to the forward-facing camera than " + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "inline_equation", + "content": "c_i" + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": " under forward motion assumption. Finally, we remove an edge " + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": " if node " + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": " is outside the local time windows " + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "inline_equation", + "content": "t - \\Delta t_{\\mathrm{inter}}" + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "inline_equation", + "content": "t - \\Delta t_{\\mathrm{intra}}" + }, + { + "bbox": [ + 304, + 168, + 546, + 383 + ], + "type": "text", + "content": ". We remove unconnected nodes from the graph. We provide pseudo-code and additional discussion in the supplemental material." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 384, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 384, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 305, + 384, + 545, + 407 + ], + "type": "text", + "content": "Feature correlation. For each edge " + }, + { + "bbox": [ + 305, + 384, + 545, + 407 + ], + "type": "inline_equation", + "content": "(i,j) \\in \\mathcal{E}" + }, + { + "bbox": [ + 305, + 384, + 545, + 407 + ], + "type": "text", + "content": " we compute the 4D feature correlation volume via the dot-product" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 341, + 411, + 545, + 426 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 411, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 341, + 411, + 545, + 426 + ], + "type": "interline_equation", + "content": "\\mathbf {C} _ {i j} = \\left\\langle g _ {\\phi} (\\mathbf {I} _ {i}), g _ {\\phi} (\\mathbf {I} _ {j}) \\right\\rangle \\in \\mathbb {R} ^ {H \\times W \\times H \\times W}. \\tag {1}", + "image_path": "2f75fd57a3436857193fe732d675ea0338b6f117036a59678555206f8aebd743.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 430, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 430, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 305, + 430, + 545, + 453 + ], + "type": "text", + "content": "As in [47, 48], we constrain the correlation search region to a radius " + }, + { + "bbox": [ + 305, + 430, + 545, + 453 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 305, + 430, + 545, + 453 + ], + "type": "text", + "content": " with a lookup operator" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 457, + 545, + 473 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 457, + 545, + 473 + ], + "spans": [ + { + "bbox": [ + 313, + 457, + 545, + 473 + ], + "type": "interline_equation", + "content": "L _ {r}: \\mathbb {R} ^ {H \\times W \\times H \\times W} \\times \\mathbb {R} ^ {H \\times W \\times 2} \\rightarrow \\mathbb {R} ^ {H \\times W \\times (r + 1) ^ {2}}, \\tag {2}", + "image_path": "fd9382807b8ab3658a5c1eee6b03ef376422237aea8e94482f84b463436f417f.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 478, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 478, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 305, + 478, + 545, + 502 + ], + "type": "text", + "content": "that samples a " + }, + { + "bbox": [ + 305, + 478, + 545, + 502 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 305, + 478, + 545, + 502 + ], + "type": "text", + "content": " grid of coordinates from the correlation volume using bilinear interpolation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 507, + 456, + 520 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 507, + 456, + 520 + ], + "spans": [ + { + "bbox": [ + 306, + 507, + 456, + 520 + ], + "type": "text", + "content": "3.2. Depth and Pose Estimation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 525, + 545, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 525, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 305, + 525, + 545, + 562 + ], + "type": "text", + "content": "Given the correlation volume " + }, + { + "bbox": [ + 305, + 525, + 545, + 562 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{ij}" + }, + { + "bbox": [ + 305, + 525, + 545, + 562 + ], + "type": "text", + "content": ", we here describe how to estimate the relative pose " + }, + { + "bbox": [ + 305, + 525, + 545, + 562 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_{ij}" + }, + { + "bbox": [ + 305, + 525, + 545, + 562 + ], + "type": "text", + "content": " and depth " + }, + { + "bbox": [ + 305, + 525, + 545, + 562 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_i" + }, + { + "bbox": [ + 305, + 525, + 545, + 562 + ], + "type": "text", + "content": " for each edge " + }, + { + "bbox": [ + 305, + 525, + 545, + 562 + ], + "type": "inline_equation", + "content": "(i,j)\\in \\mathcal{E}" + }, + { + "bbox": [ + 305, + 525, + 545, + 562 + ], + "type": "text", + "content": " in the co-visibility graph." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "text", + "content": "Flow correction. Given an initial estimate of " + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_{ij}" + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_i" + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "text", + "content": ", we first compute the induced flow " + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{ij}^*" + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "text", + "content": " to sample the correlation volume " + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{ij}" + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "text", + "content": " using (2). We then feed the sampled correlation features, the context features " + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "inline_equation", + "content": "g_{\\psi}(\\mathbf{I}_i)" + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "text", + "content": ", and the induced flow " + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{ij}^*" + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "text", + "content": " into a convolutional GRU. The GRU predicts a flow residual " + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_{ij}" + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "text", + "content": " and confidence weights " + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_{ij} \\in \\mathbb{R}^{H \\times W \\times 2}" + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "text", + "content": " as in [48]. A challenge of correspondence estimation in a multi-camera setup is that the flow magnitude varies greatly among edges in the co-visibility graph due to inter-camera edges with large relative rotation. To this end, we propose to subtract the rotational part of " + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{ij}^*" + }, + { + "bbox": [ + 304, + 562, + 545, + 696 + ], + "type": "text", + "content": " in those edges via" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 333, + 700, + 545, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 700, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 333, + 700, + 545, + 716 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {i j} ^ {\\prime} = \\left(\\mathbf {x} _ {i} + \\mathbf {f} _ {i j} ^ {*}\\right) - \\Pi_ {c _ {j}} \\left(\\mathbf {R} _ {c _ {j}} ^ {- 1} \\mathbf {R} _ {c _ {i}} \\circ \\Pi_ {c _ {i}} ^ {- 1} (\\mathbf {1})\\right), \\tag {3}", + "image_path": "2d9a31121d5e4d42ffff253130e27a34210afccfee9f1edcd74fe43a65c232b3.jpg" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3218" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 76, + 534, + 243 + ], + "blocks": [ + { + "bbox": [ + 51, + 76, + 534, + 243 + ], + "lines": [ + { + "bbox": [ + 51, + 76, + 534, + 243 + ], + "spans": [ + { + "bbox": [ + 51, + 76, + 534, + 243 + ], + "type": "image", + "image_path": "3394cc6e27e1e5ae6b92a7c4290f3b4bf962e9fc7188f204c48fe8cc431e1d4f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "lines": [ + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": "Figure 2. Method overview. First, frames " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{I}_t^c\\}_{c=1}^C" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " cameras at time " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " are encoded and integrated into the co-visibility graph " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\mathcal{G} = (\\mathcal{V}, \\mathcal{E})" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " with initial guesses of depth maps " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_t^c" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " and ego-pose " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_t" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " (Sec. 3.1). Second, for each edge " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "(i,j) \\in \\mathcal{E}" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": ", we compute the induced flow " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{ij}^*" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_i" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " and relative camera pose " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_{ij}" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " derived from ego-poses " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " and camera extrinsics " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": ". Given " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{ij}^*" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": ", we pool feature correlations from " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{ij}" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " with operator " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "L_r" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " as input to a GRU that estimates flow update " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_{ij}" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " and confidence " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_{ij}" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": ". We globally align depths " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " and poses " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " with the new flow estimates " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " via our multi-camera DBA operator in " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " iterations (Sec. 3.2). Finally, for each node " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "i \\in \\mathcal{V}" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": ", we refine the initial geometric estimate " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_i" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " given the aggregated confidence " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " via " + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": " (Sec. 3.3). We highlight our contributions in color." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 77, + 327, + 258, + 475 + ], + "blocks": [ + { + "bbox": [ + 77, + 327, + 258, + 475 + ], + "lines": [ + { + "bbox": [ + 77, + 327, + 258, + 475 + ], + "spans": [ + { + "bbox": [ + 77, + 327, + 258, + 475 + ], + "type": "image", + "image_path": "e3b07928cdfa93032e6481220250b593cdd47e060120998b8a615d949cd65742.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 477, + 288, + 534 + ], + "lines": [ + { + "bbox": [ + 46, + 477, + 288, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 477, + 288, + 534 + ], + "type": "text", + "content": "Figure 3. Co-visibility graph. We illustrate an example of the connectivity pattern of the co-visibility graph using our multi-camera graph construction algorithm. We use " + }, + { + "bbox": [ + 46, + 477, + 288, + 534 + ], + "type": "inline_equation", + "content": "\\Delta t_{\\mathrm{intra}} = 3" + }, + { + "bbox": [ + 46, + 477, + 288, + 534 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 477, + 288, + 534 + ], + "type": "inline_equation", + "content": "\\Delta t_{\\mathrm{inter}} = 2" + }, + { + "bbox": [ + 46, + 477, + 288, + 534 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 477, + 288, + 534 + ], + "type": "inline_equation", + "content": "r_{\\mathrm{intra}} = 2" + }, + { + "bbox": [ + 46, + 477, + 288, + 534 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 477, + 288, + 534 + ], + "type": "inline_equation", + "content": "r_{\\mathrm{inter}} = 2" + }, + { + "bbox": [ + 46, + 477, + 288, + 534 + ], + "type": "text", + "content": " with six cameras. We depict temporal, spatial, and spatial-temporal edges." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "spans": [ + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "text", + "content": " are pixel coordinates of frame " + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "inline_equation", + "content": "\\Pi_c" + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "text", + "content": " denotes the projection operator under camera " + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "text", + "content": " is the rotation of transformation " + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "inline_equation", + "content": "\\mathbf{T} = (\\mathbf{R} \\mathbf{t})" + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "text", + "content": ". This aligns the flow magnitude with temporal, intra-camera edges. Note that, while we input " + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{ij}'" + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "text", + "content": " instead of " + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{ij}^*" + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "text", + "content": " to the GRU, we still sample the correlation volume " + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{ij}" + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "text", + "content": " based on " + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{ij}^*" + }, + { + "bbox": [ + 46, + 547, + 287, + 619 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 619, + 287, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 619, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 619, + 287, + 654 + ], + "type": "text", + "content": "Pose and depth correction. We update our pose and depth estimates given the updated flow " + }, + { + "bbox": [ + 46, + 619, + 287, + 654 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{ij} = \\mathbf{f}_{ij}^{*} + \\mathbf{r}_{ij}" + }, + { + "bbox": [ + 46, + 619, + 287, + 654 + ], + "type": "text", + "content": " by minimizing the re-projection error, defined as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 664, + 287, + 692 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 664, + 287, + 692 + ], + "spans": [ + { + "bbox": [ + 52, + 664, + 287, + 692 + ], + "type": "interline_equation", + "content": "E = \\sum_ {(i, j) \\in \\mathcal {E}} \\left\\| \\left(\\mathbf {x} _ {i} + \\mathbf {f} _ {i j}\\right) - \\Pi_ {c _ {j}} \\left(\\mathbf {G} _ {i j} \\circ \\Pi_ {c _ {i}} ^ {- 1} (\\mathbf {d} _ {i})\\right) \\right\\| _ {\\Sigma_ {i j}} ^ {2}, \\tag {4}", + "image_path": "c46acdb9dea1d5eade19b6e89e1caa628db6b14352369b42d58502885989ab27.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 701, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 701, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\| .\\|_{\\Sigma_{ij}}" + }, + { + "bbox": [ + 47, + 701, + 287, + 715 + ], + "type": "text", + "content": " is the Mahalanobis norm and " + }, + { + "bbox": [ + 47, + 701, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\Sigma_{ij} =" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 327, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 327, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 327, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\operatorname{diag}(\\mathbf{w}_{ij})" + }, + { + "bbox": [ + 305, + 327, + 545, + 422 + ], + "type": "text", + "content": ". Thus, only matched pixels where the confidence " + }, + { + "bbox": [ + 305, + 327, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_{ij}" + }, + { + "bbox": [ + 305, + 327, + 545, + 422 + ], + "type": "text", + "content": " is greater than zero contribute to the total cost. We extend the dense bundle adjustment (DBA) proposed in [48] to include the known extrinsics of the multi-camera setup. In particular, we decompose the relative poses between two frames " + }, + { + "bbox": [ + 305, + 327, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_{ij}" + }, + { + "bbox": [ + 305, + 327, + 545, + 422 + ], + "type": "text", + "content": " into the unknown, time-varying poses " + }, + { + "bbox": [ + 305, + 327, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 305, + 327, + 545, + 422 + ], + "type": "text", + "content": " in the reference frame and the known static relative transformations " + }, + { + "bbox": [ + 305, + 327, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 305, + 327, + 545, + 422 + ], + "type": "text", + "content": " between the cameras and the reference frame via" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 366, + 427, + 545, + 444 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 427, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 366, + 427, + 545, + 444 + ], + "type": "interline_equation", + "content": "\\mathbf {G} _ {i j} = \\left(\\mathbf {P} _ {t _ {j}} \\mathbf {T} _ {c _ {j}}\\right) ^ {- 1} \\mathbf {P} _ {t _ {i}} \\mathbf {T} _ {c _ {i}}. \\tag {5}", + "image_path": "ba40cb90074119ce11c94270ec1bb43a7eeec5b4646d726592c6fef1a314b7c0.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 450, + 545, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 450, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 305, + 450, + 545, + 545 + ], + "type": "text", + "content": "We linearize the residual of the energy function in Eq. 4 with a first-order Taylor expansion. We use Eq. 5 and treat " + }, + { + "bbox": [ + 305, + 450, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{c_j}" + }, + { + "bbox": [ + 305, + 450, + 545, + 545 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 450, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_{c_i}" + }, + { + "bbox": [ + 305, + 450, + 545, + 545 + ], + "type": "text", + "content": " as constants when calculating the Jacobians, thus computing updates only for ego-pose " + }, + { + "bbox": [ + 305, + 450, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 305, + 450, + 545, + 545 + ], + "type": "text", + "content": ". We apply the Gauss-Newton step to compute the updated " + }, + { + "bbox": [ + 305, + 450, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^{(k)} = \\exp (\\delta \\xi^{(k - 1)})\\mathbf{P}^{(k - 1)}" + }, + { + "bbox": [ + 305, + 450, + 545, + 545 + ], + "type": "text", + "content": " and depth " + }, + { + "bbox": [ + 305, + 450, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{d}^{(k)} = \\delta \\mathbf{d}^{(k - 1)} + \\mathbf{d}^{(k - 1)}" + }, + { + "bbox": [ + 305, + 450, + 545, + 545 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 305, + 450, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\delta \\xi^{(k - 1)}\\in \\mathfrak{se}(3)" + }, + { + "bbox": [ + 305, + 450, + 545, + 545 + ], + "type": "text", + "content": ". We provide a detailed derivation in the supplementary material." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 546, + 546, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 546, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 546, + 689 + ], + "type": "text", + "content": "Our formulation has two advantages over DBA [48]. First, the optimization is more robust since " + }, + { + "bbox": [ + 304, + 546, + 546, + 689 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 546, + 546, + 689 + ], + "type": "text", + "content": " frames are connected through a single ego-pose " + }, + { + "bbox": [ + 304, + 546, + 546, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 304, + 546, + 546, + 689 + ], + "type": "text", + "content": ". If one or multiple frames have a high outlier ratio in feature matching, e.g. through lens-flare, low textured regions, or dynamic objects, we can still reliably estimate " + }, + { + "bbox": [ + 304, + 546, + 546, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 304, + 546, + 546, + 689 + ], + "type": "text", + "content": " with at least one undisturbed camera. Second, if there are not only pixels matched across the temporal context but also pixels matched across the static, spatial context, we can recover the absolute scale of the scene. This is because for static, spatial matches the relative transformation " + }, + { + "bbox": [ + 304, + 546, + 546, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_{ij} = \\mathbf{T}_{c_j}^{-1}\\mathbf{T}_{c_i}" + }, + { + "bbox": [ + 304, + 546, + 546, + 689 + ], + "type": "text", + "content": " is known to scale so that " + }, + { + "bbox": [ + 304, + 546, + 546, + 689 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 546, + 546, + 689 + ], + "type": "text", + "content": " is minimized if and only if " + }, + { + "bbox": [ + 304, + 546, + 546, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 304, + 546, + 546, + 689 + ], + "type": "text", + "content": " is in absolute scale." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Training. We train the networks " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "g_{\\phi}" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "g_{\\psi}" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " as well as the flow correction GRU on dynamic scenes following the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3219" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": "procedure in [48]. As shown in [48], the geometric features learned from synthetic data can generalize to real-world scenes. We can therefore leverage existing synthetic driving datasets without relying on real-world ground-truth measurements from sensors like LiDAR or IMU to adjust our method to dynamic, multi-camera scenarios." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 150, + 155, + 164 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 150, + 155, + 164 + ], + "spans": [ + { + "bbox": [ + 47, + 150, + 155, + 164 + ], + "type": "text", + "content": "3.3. Depth Refinement" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 168, + 287, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 287, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 287, + 240 + ], + "type": "text", + "content": "SfM relies on three assumptions: accurate pixel matches, sufficient camera movement, and a static scene. These assumptions do not always hold in the real world due to, e.g., low-textured areas, a static ego vehicle, or many dynamic agents. Still, we would like the system to produce reasonable scene geometry to ensure safe operation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 241, + 287, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 241, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 287, + 300 + ], + "type": "text", + "content": "On the contrary, monocular depth cues are inherently not affected by these issues. However, they usually lack the accurate geometric detail of SfM methods. Hence, for each node " + }, + { + "bbox": [ + 46, + 241, + 287, + 300 + ], + "type": "inline_equation", + "content": "i \\in \\mathcal{V}" + }, + { + "bbox": [ + 46, + 241, + 287, + 300 + ], + "type": "text", + "content": ", we complement the accurate, but sparse geometric depth estimates with monocular cues." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": "Network design. We use a CNN " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": " parameterized by " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": ". We input the depth " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_i" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": ", confidence " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": ", and the corresponding image " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_i" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": ". The network predicts an improved, dense depth " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_i' = \\mathcal{D}_{\\theta}(\\mathbf{I}_i, \\mathbf{d}_i, \\mathbf{w}_i)" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": ". We obtain the per-frame depth confidence " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": " for frame " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": " by using the maximum across the per-edge confidence weights " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_{ij}" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": ". We compute " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i = \\max_j \\frac{1}{2} (\\mathbf{w}_{ij}^x + \\mathbf{w}_{ij}^y)" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": " are the flow directions. We use " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\max(\\cdot)" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": " because we observe that depth triangulation will be accurate if at least one pixel is matched with high confidence. We sparsify input depth and confidence weights by setting regions with confidence " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i < \\beta" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": " to zero. We concatenate these with the image " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_i" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": ". We further concatenate depth and confidence with features at " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "1/8^{\\text{th}}" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": " scale. As in [16], the output depth is predicted at four scales. To accommodate different focal lengths among cameras in the sensor setup, we do focal length scaling of the output [45]. Training. Contrary to geometric approaches, monocular depth estimators infer depth from semantic cues, which makes it hard for them to generalize across domains [23]. Hence, instead of relying on synthetic data, we train " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": " on raw, real-world video in a self-supervised manner by minimizing a view synthesis loss [65]. We minimize the photometric error " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\mathrm{pe}(\\mathbf{I}_t^c, \\mathbf{I}_{t'}^{c' \\rightarrow c})" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": " between a target image " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_t^c" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": " and a reference image " + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{t'}^{c'}" + }, + { + "bbox": [ + 46, + 300, + 287, + 589 + ], + "type": "text", + "content": " warped to the target viewpoint via" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 73, + 596, + 287, + 612 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 596, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 73, + 596, + 287, + 612 + ], + "type": "interline_equation", + "content": "\\mathbf {I} _ {t ^ {\\prime} \\rightarrow t} ^ {c ^ {\\prime} \\rightarrow c} = \\Phi \\big (\\mathbf {I} _ {t ^ {\\prime}} ^ {c ^ {\\prime}}; \\Pi_ {c ^ {\\prime}} \\big (\\mathbf {G} _ {(t, c) (t ^ {\\prime}, c ^ {\\prime})} \\circ \\Pi_ {c} ^ {- 1} \\big (\\mathbf {d} _ {t} ^ {c} \\big) \\big) \\big), \\quad (6)", + "image_path": "5b403e182ec0e0d99d34ffae6eaa6c814621f4e9eece4f1e190802e7d728e118.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " the bi-linear sampling function, " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_t^c" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " the predicted depth, " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "c' = c \\pm 1" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "t' = t \\pm 1" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": ". We compute photometric similarity with SSIM [50] and " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "L_1" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " distances. We use " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_{(t,c)(t',c')} = (\\mathbf{P}_{t'}\\mathbf{T}_{c'})^{-1}\\mathbf{P}_t\\mathbf{T}_c" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " generated by the first two stages of our system (see Sec. 3.2). Further, self-supervised depth estimation is well-studied, and we follow the common practice of applying regularization techniques to filter the photometric error [16, 63, 20]. First, we mask areas" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 71, + 547, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 71, + 547, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 71, + 547, + 120 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 71, + 547, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^{\\mathrm{st}} = \\left[\\mathrm{pe}(\\mathbf{I}_t^c,\\mathbf{I}_{t'\\to t}^{c'\\to c}) < \\mathrm{pe}(\\mathbf{I}_t^c,\\mathbf{I}_{t'}^{c'})\\right]" + }, + { + "bbox": [ + 304, + 71, + 547, + 120 + ], + "type": "text", + "content": " , i.e. we filter regions where assuming a stationary scene would induce a lower loss than re-projection. Second, we compute an induced flow consistency mask from " + }, + { + "bbox": [ + 304, + 71, + 547, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{f}^*" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 127, + 547, + 159 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 127, + 547, + 159 + ], + "spans": [ + { + "bbox": [ + 306, + 127, + 547, + 159 + ], + "type": "interline_equation", + "content": "\\mathbf {M} ^ {\\mathrm {f c}} = \\left[ \\left\\| \\mathbf {f} _ {(t, c) \\left(t ^ {\\prime}, c ^ {\\prime}\\right)} ^ {*} + \\Phi \\left(\\mathbf {f} _ {\\left(t ^ {\\prime}, c ^ {\\prime}\\right) (t, c)} ^ {*}; \\mathbf {x} + \\mathbf {f} _ {(t, c) \\left(t ^ {\\prime}, c ^ {\\prime}\\right)} ^ {*}\\right) \\right\\| _ {2} < \\gamma \\right]. \\tag {7}", + "image_path": "23c4ccaf825f4d93b905b479e57f4aa73b77bd9bcc8c321defae7fb6eab3cb6d.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 159, + 545, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 159, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 159, + 545, + 277 + ], + "type": "text", + "content": "This term warps pixel coordinates " + }, + { + "bbox": [ + 304, + 159, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 159, + 545, + 277 + ], + "type": "text", + "content": " from target to reference view, looks up their value in " + }, + { + "bbox": [ + 304, + 159, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{(t',c')}(t,c)" + }, + { + "bbox": [ + 304, + 159, + 545, + 277 + ], + "type": "text", + "content": ", and compares them to " + }, + { + "bbox": [ + 304, + 159, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{(t,c)(t',c')}^*" + }, + { + "bbox": [ + 304, + 159, + 545, + 277 + ], + "type": "text", + "content": ". Therefore, pixels not following the epipolar constraint like dynamic objects are masked. Third, to handle the self-occlusion of the ego-vehicle, we manually draw a static mask " + }, + { + "bbox": [ + 304, + 159, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^{\\mathrm{oc}}" + }, + { + "bbox": [ + 304, + 159, + 545, + 277 + ], + "type": "text", + "content": ". We can use a single mask for all frames since the cameras are mounted rigidly. Further, to handle occlusions due to change in perspective, we take the minimum loss " + }, + { + "bbox": [ + 304, + 159, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\min_{t',c'}\\mathrm{pe}(\\mathbf{I}_t^c,\\mathbf{I}_{t'\\to t}^{c'\\to c})" + }, + { + "bbox": [ + 304, + 159, + 545, + 277 + ], + "type": "text", + "content": " across all reference views. The overall loss for " + }, + { + "bbox": [ + 304, + 159, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 304, + 159, + 545, + 277 + ], + "type": "text", + "content": " is thus" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 312, + 286, + 545, + 308 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 286, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 312, + 286, + 545, + 308 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\min _ {t ^ {\\prime}, c ^ {\\prime}} \\left(\\mathbf {M} ^ {\\mathrm {s t}} \\mathbf {M} ^ {\\mathrm {f c}} \\mathbf {M} ^ {\\mathrm {o c}} \\cdot \\operatorname {p e} \\left(\\mathbf {I} _ {t} ^ {c}, \\mathbf {I} _ {t ^ {\\prime} \\rightarrow t} ^ {c ^ {\\prime} \\rightarrow c}\\right)\\right) + \\lambda \\mathcal {L} _ {\\text {s m o o t h}}, \\tag {8}", + "image_path": "15aa9fe26a92dd90839d462af1a601a313a0dbe5f11af32d63c3012282e5db30.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 316, + 542, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 316, + 542, + 328 + ], + "spans": [ + { + "bbox": [ + 306, + 316, + 542, + 328 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 306, + 316, + 542, + 328 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{smooth}}" + }, + { + "bbox": [ + 306, + 316, + 542, + 328 + ], + "type": "text", + "content": " a spatial smoothness regularization term [15]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 335, + 424, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 335, + 424, + 346 + ], + "spans": [ + { + "bbox": [ + 306, + 335, + 424, + 346 + ], + "type": "text", + "content": "3.4. Inference Procedure" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 354, + 545, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 377 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 377 + ], + "type": "text", + "content": "Given an input stream of multi-camera image sets, we perform incremental 3D reconstruction in three phases." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 378, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 545, + 449 + ], + "type": "text", + "content": "Warmup phase. First, we add frames to the co-visibility graph if a single GRU step of a reference camera yields a large enough mean optical flow until we reach " + }, + { + "bbox": [ + 304, + 378, + 545, + 449 + ], + "type": "inline_equation", + "content": "n_{\\mathrm{warmup}}" + }, + { + "bbox": [ + 304, + 378, + 545, + 449 + ], + "type": "text", + "content": " frames. At this stage, we infer depth with our refinement network " + }, + { + "bbox": [ + 304, + 378, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_t^c = \\mathcal{D}_{\\theta}(\\mathbf{I}_t^c,\\mathbf{0},\\mathbf{0})" + }, + { + "bbox": [ + 304, + 378, + 545, + 449 + ], + "type": "text", + "content": ". We write the depth into the co-visibility graph so that it can be used during initialization." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 449, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 509 + ], + "type": "text", + "content": "Initialization phase. We initialize the co-visibility graph with the available frames and run " + }, + { + "bbox": [ + 304, + 449, + 545, + 509 + ], + "type": "inline_equation", + "content": "n_{\\mathrm{itr - wm}}" + }, + { + "bbox": [ + 304, + 449, + 545, + 509 + ], + "type": "text", + "content": " GRU and bundle adjustment iterations. For the first " + }, + { + "bbox": [ + 304, + 449, + 545, + 509 + ], + "type": "inline_equation", + "content": "n_{\\mathrm{itr - wm}} / 2" + }, + { + "bbox": [ + 304, + 449, + 545, + 509 + ], + "type": "text", + "content": " iterations, we fix depths in the bundle adjustment and only optimize poses, which helps with inferring the absolute scale of the scene." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "type": "text", + "content": "Active phase. We now add each incoming frame to the co-visibility graph. We initialize the new frames with " + }, + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_t^c = \\mathrm{mean}(\\mathbf{d}_{t - 4:t - 1}^c)" + }, + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_t = \\mathbf{P}_{t - 1}" + }, + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "type": "text", + "content": ". Then, we perform " + }, + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "type": "inline_equation", + "content": "n_{\\mathrm{iter1}}" + }, + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "type": "text", + "content": " GRU and bundle adjustment updates, and apply the refinement network to all updated frames. If the mean optical flow of the reference camera between " + }, + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "type": "inline_equation", + "content": "t - 1" + }, + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "type": "text", + "content": " is low, we remove all frames at " + }, + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "type": "inline_equation", + "content": "t - 1" + }, + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "type": "text", + "content": " from the co-visibility graph. This helps to handle situations with little to no egomotion. In case no frame is removed, we do another " + }, + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "type": "inline_equation", + "content": "n_{\\mathrm{iter2}}" + }, + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "type": "text", + "content": " iterations. Finally, we write the updated depths and poses into the co-visibility graph." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 651, + 388, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 651, + 388, + 664 + ], + "spans": [ + { + "bbox": [ + 306, + 651, + 388, + 664 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 671, + 422, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 422, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 422, + 684 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "We perform extensive experiments on large-scale driving datasets that contain recordings from vehicles equipped" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3220" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 102, + 520, + 176 + ], + "blocks": [ + { + "bbox": [ + 46, + 69, + 547, + 102 + ], + "lines": [ + { + "bbox": [ + 46, + 69, + 547, + 102 + ], + "spans": [ + { + "bbox": [ + 46, + 69, + 547, + 102 + ], + "type": "text", + "content": "Table 1. Method ablation. We ablate our method components on the DDAD [19] dataset. We examine the influence of each component given the geometric estimation as in [48] with naive DBA as the baseline. Further, we show the influence of VKITTI [2] fine-tuning on the geometric estimation. We enumerate each variant for better reference. * median scaled depth, ** scaled trajectory." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 70, + 102, + 520, + 176 + ], + "lines": [ + { + "bbox": [ + 70, + 102, + 520, + 176 + ], + "spans": [ + { + "bbox": [ + 70, + 102, + 520, + 176 + ], + "type": "table", + "html": "
No.Geom. Est.VKITTIMulti-Cam DBARefinementAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑ATE [m] ↓ATE** [m] ↓
1a*✓✓0.43826.9719.1090.636-2.134
1b✓✓0.44236.3918.6640.7361.6720.435
1c✓✓✓0.32015.4516.3030.7272.3560.922
2a✓0.2113.80612.6680.715--
3a✓✓✓✓0.1623.01911.4080.8111.2350.433
", + "image_path": "f494cd25cd1c3fe8c1864f472d1ef1f53c991dff70509eee5553210bccd23e05.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 52, + 243, + 281, + 280 + ], + "blocks": [ + { + "bbox": [ + 46, + 187, + 287, + 242 + ], + "lines": [ + { + "bbox": [ + 46, + 187, + 287, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 187, + 287, + 242 + ], + "type": "text", + "content": "Table 2. Co-visibility graph ablation. We compare our co-visibility graph construction algorithm to the original algorithm in [48] on the DDAD [19] dataset. We observe that our algorithm improves the overall runtime by an order of magnitude while maintaining the same level of performance." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 243, + 281, + 280 + ], + "lines": [ + { + "bbox": [ + 52, + 243, + 281, + 280 + ], + "spans": [ + { + "bbox": [ + 52, + 243, + 281, + 280 + ], + "type": "table", + "html": "
GraphAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑ATE [m] ↓tinf [s] ↓
Original0.1622.96811.1560.8160.9823.23
Ours0.1623.01911.4080.8111.2350.35
", + "image_path": "1e55eaccbd754ed38cb86e91d1f96b3b96e363d40188146b4da469df9ea8fa23.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 65, + 328, + 268, + 376 + ], + "blocks": [ + { + "bbox": [ + 46, + 284, + 287, + 327 + ], + "lines": [ + { + "bbox": [ + 46, + 284, + 287, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 287, + 327 + ], + "type": "text", + "content": "Table 3. Refinement network ablation. We show on the DDAD [19] dataset that both adding confidence weights " + }, + { + "bbox": [ + 46, + 284, + 287, + 327 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i" + }, + { + "bbox": [ + 46, + 284, + 287, + 327 + ], + "type": "text", + "content": " and sparsifying the depth input via " + }, + { + "bbox": [ + 46, + 284, + 287, + 327 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i < \\beta" + }, + { + "bbox": [ + 46, + 284, + 287, + 327 + ], + "type": "text", + "content": " to filter outliers in the input of depth refinement network " + }, + { + "bbox": [ + 46, + 284, + 287, + 327 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 46, + 284, + 287, + 327 + ], + "type": "text", + "content": " is vital to depth accuracy." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 65, + 328, + 268, + 376 + ], + "lines": [ + { + "bbox": [ + 65, + 328, + 268, + 376 + ], + "spans": [ + { + "bbox": [ + 65, + 328, + 268, + 376 + ], + "type": "table", + "html": "
wiwi<βAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
0.1814.07812.1080.789
✓0.1733.49711.9240.792
✓✓0.1623.01911.4080.811
", + "image_path": "13cfb64e2236369bd900976dc1e18713f1e968a3b2ab7a45e9e23afbd345e8e4.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 390, + 287, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 390, + 287, + 461 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 287, + 461 + ], + "type": "text", + "content": "with multiple cameras, LiDARs, and other sensors. Note that we only use camera data for training and inference, and use LiDAR data only as ground-truth for evaluation. We evaluate our method in inference mode (cf. Sec. 3.4), i.e. we obtain predictions in a fully online (causal) manner to mimic real-world deployment." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 462, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 287, + 569 + ], + "type": "text", + "content": "DDAD. This dataset consists of 150 training and 50 validation scenes from urban areas. Each sequence has a length of 50 or 100 time steps at a frame rate of " + }, + { + "bbox": [ + 46, + 462, + 287, + 569 + ], + "type": "inline_equation", + "content": "10\\mathrm{Hz}" + }, + { + "bbox": [ + 46, + 462, + 287, + 569 + ], + "type": "text", + "content": ". The sensor setup includes six cameras in a surround-view setup with up to " + }, + { + "bbox": [ + 46, + 462, + 287, + 569 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 462, + 287, + 569 + ], + "type": "text", + "content": " overlap. We follow [19] and evaluate depth up to " + }, + { + "bbox": [ + 46, + 462, + 287, + 569 + ], + "type": "inline_equation", + "content": "200\\mathrm{m}" + }, + { + "bbox": [ + 46, + 462, + 287, + 569 + ], + "type": "text", + "content": " averaged across all cameras. We use self-occlusion masks from [52] to filter the ego-vehicle in the images. Images have a resolution of " + }, + { + "bbox": [ + 46, + 462, + 287, + 569 + ], + "type": "inline_equation", + "content": "1216\\times 1936" + }, + { + "bbox": [ + 46, + 462, + 287, + 569 + ], + "type": "text", + "content": " and are downsampled to " + }, + { + "bbox": [ + 46, + 462, + 287, + 569 + ], + "type": "inline_equation", + "content": "384\\times 640" + }, + { + "bbox": [ + 46, + 462, + 287, + 569 + ], + "type": "text", + "content": " in our experiments." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 570, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 688 + ], + "type": "text", + "content": "NuScenes. This dataset contains 700 training, 150 validation, and 150 testing sequences of urban scenes with challenging conditions such as nighttime and rain. Each scene is composed of 40 keyframes at " + }, + { + "bbox": [ + 46, + 570, + 287, + 688 + ], + "type": "inline_equation", + "content": "2\\mathrm{Hz}" + }, + { + "bbox": [ + 46, + 570, + 287, + 688 + ], + "type": "text", + "content": " synchronized across sensors. The six cameras have a sampling rate of " + }, + { + "bbox": [ + 46, + 570, + 287, + 688 + ], + "type": "inline_equation", + "content": "12\\mathrm{Hz}" + }, + { + "bbox": [ + 46, + 570, + 287, + 688 + ], + "type": "text", + "content": " and are arranged in a surround-view setup with up to " + }, + { + "bbox": [ + 46, + 570, + 287, + 688 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 570, + 287, + 688 + ], + "type": "text", + "content": " overlap. We follow [22] and evaluate depth averaged across all cameras on the validation set. We use a single self-occlusion mask for all scenes. While the raw images have a resolution of " + }, + { + "bbox": [ + 46, + 570, + 287, + 688 + ], + "type": "inline_equation", + "content": "900 \\times 1600" + }, + { + "bbox": [ + 46, + 570, + 287, + 688 + ], + "type": "text", + "content": ", we use " + }, + { + "bbox": [ + 46, + 570, + 287, + 688 + ], + "type": "inline_equation", + "content": "768 \\times 448" + }, + { + "bbox": [ + 46, + 570, + 287, + 688 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Implementation details. We implement our system in PyTorch [37]. Our multi-camera DBA is implemented in" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 309, + 198, + 389, + 246 + ], + "blocks": [ + { + "bbox": [ + 339, + 189, + 358, + 197 + ], + "lines": [ + { + "bbox": [ + 339, + 189, + 358, + 197 + ], + "spans": [ + { + "bbox": [ + 339, + 189, + 358, + 197 + ], + "type": "text", + "content": "Input" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 309, + 198, + 389, + 246 + ], + "lines": [ + { + "bbox": [ + 309, + 198, + 389, + 246 + ], + "spans": [ + { + "bbox": [ + 309, + 198, + 389, + 246 + ], + "type": "image", + "image_path": "df455e6662489f8ffabab06a4682c2ee2994ae6c2b6f807082be9e601ca3fd01.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 390, + 198, + 468, + 246 + ], + "blocks": [ + { + "bbox": [ + 406, + 189, + 451, + 198 + ], + "lines": [ + { + "bbox": [ + 406, + 189, + 451, + 198 + ], + "spans": [ + { + "bbox": [ + 406, + 189, + 451, + 198 + ], + "type": "text", + "content": "Geom. Depth" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 390, + 198, + 468, + 246 + ], + "lines": [ + { + "bbox": [ + 390, + 198, + 468, + 246 + ], + "spans": [ + { + "bbox": [ + 390, + 198, + 468, + 246 + ], + "type": "image", + "image_path": "0f3d17e6add867abf6235566e5f57d3c8f99632215273e840df03a58525cc11b.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 470, + 198, + 550, + 246 + ], + "blocks": [ + { + "bbox": [ + 496, + 189, + 523, + 197 + ], + "lines": [ + { + "bbox": [ + 496, + 189, + 523, + 197 + ], + "spans": [ + { + "bbox": [ + 496, + 189, + 523, + 197 + ], + "type": "text", + "content": "Refined" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 470, + 198, + 550, + 246 + ], + "lines": [ + { + "bbox": [ + 470, + 198, + 550, + 246 + ], + "spans": [ + { + "bbox": [ + 470, + 198, + 550, + 246 + ], + "type": "image", + "image_path": "854459c2f6c83fd446b2d3b41b21f6bc2116e870ad253a9f390d19437ff69772.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 309, + 247, + 388, + 297 + ], + "blocks": [ + { + "bbox": [ + 309, + 247, + 388, + 297 + ], + "lines": [ + { + "bbox": [ + 309, + 247, + 388, + 297 + ], + "spans": [ + { + "bbox": [ + 309, + 247, + 388, + 297 + ], + "type": "image", + "image_path": "c3fba9cbbd9e44db0532e9b65cadbb0c9bafb58cff347c82408351e0aca428d1.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 390, + 247, + 468, + 297 + ], + "blocks": [ + { + "bbox": [ + 390, + 247, + 468, + 297 + ], + "lines": [ + { + "bbox": [ + 390, + 247, + 468, + 297 + ], + "spans": [ + { + "bbox": [ + 390, + 247, + 468, + 297 + ], + "type": "image", + "image_path": "65058b1936539c0c613c01b1acce8736f13be4318e37c9790785d4979f916471.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 470, + 247, + 550, + 297 + ], + "blocks": [ + { + "bbox": [ + 470, + 247, + 550, + 297 + ], + "lines": [ + { + "bbox": [ + 470, + 247, + 550, + 297 + ], + "spans": [ + { + "bbox": [ + 470, + 247, + 550, + 297 + ], + "type": "image", + "image_path": "036c9f240024360805fd3fc0529fff4f9e95d6e72d39ebafdd8c2011d29b10fd.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 309, + 298, + 388, + 346 + ], + "blocks": [ + { + "bbox": [ + 309, + 298, + 388, + 346 + ], + "lines": [ + { + "bbox": [ + 309, + 298, + 388, + 346 + ], + "spans": [ + { + "bbox": [ + 309, + 298, + 388, + 346 + ], + "type": "image", + "image_path": "1493ca10345502ffccbd606d8b06a98079489c9031715da8046bf7beaaab7f95.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 348, + 545, + 392 + ], + "lines": [ + { + "bbox": [ + 306, + 348, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 348, + 545, + 392 + ], + "type": "text", + "content": "Figure 4. Depth refinement. We plot images overlayed with confidence " + }, + { + "bbox": [ + 306, + 348, + 545, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i" + }, + { + "bbox": [ + 306, + 348, + 545, + 392 + ], + "type": "text", + "content": ", the geometric depth estimate " + }, + { + "bbox": [ + 306, + 348, + 545, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 306, + 348, + 545, + 392 + ], + "type": "text", + "content": ", and the refined depth " + }, + { + "bbox": [ + 306, + 348, + 545, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{d}'" + }, + { + "bbox": [ + 306, + 348, + 545, + 392 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 306, + 348, + 545, + 392 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 306, + 348, + 545, + 392 + ], + "type": "text", + "content": ". We observe a smoother ground plane, corrected dynamic objects, and filtered outliers." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 390, + 298, + 468, + 346 + ], + "blocks": [ + { + "bbox": [ + 390, + 298, + 468, + 346 + ], + "lines": [ + { + "bbox": [ + 390, + 298, + 468, + 346 + ], + "spans": [ + { + "bbox": [ + 390, + 298, + 468, + 346 + ], + "type": "image", + "image_path": "7ab81b528b6f25eaad7c7954b3e7c0f867677f18bb9f14debc57b95f20729b73.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 470, + 298, + 550, + 346 + ], + "blocks": [ + { + "bbox": [ + 470, + 298, + 550, + 346 + ], + "lines": [ + { + "bbox": [ + 470, + 298, + 550, + 346 + ], + "spans": [ + { + "bbox": [ + 470, + 298, + 550, + 346 + ], + "type": "image", + "image_path": "190b36e7b2546ecc8f404e338e25c94909342a702db666c68ac3f5af845b1f07.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "text", + "content": "CUDA. We fine-tune " + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "inline_equation", + "content": "g_{\\phi}" + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "inline_equation", + "content": "g_{\\psi}" + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "text", + "content": " and the flow correction GRU on VIKITTI2 [2] for 10 epochs with a batch size of 1, sequence length of 7, and learning rate " + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "text", + "content": " with the pretrained model in [48]. For " + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "text", + "content": ", we use a U-Net [38] with ResNet18 [25] encoder and initialize it with ImageNet [40] pre-trained weights. We use " + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "inline_equation", + "content": "\\beta = 0.5" + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "inline_equation", + "content": "\\gamma = 3" + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "inline_equation", + "content": "\\lambda = 10^{-3}" + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "text", + "content": ". We train for 20 epochs with batch size of 6 and the Adam optimizer with learning rate " + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "text", + "content": ". We reduce the learning rate by a factor of 10 after 15 epochs. For inference, the runtime is measured for a set of six images on a single RTX3090 GPU. Each sequence is initialized with 3 warmup frames filtered at a mean flow threshold of 1.75. We build the co-visibility graph with " + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "inline_equation", + "content": "\\Delta t_{\\mathrm{intra}} = 3" + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "inline_equation", + "content": "r_{\\mathrm{intra}} = 2" + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "inline_equation", + "content": "\\Delta t_{\\mathrm{inter}} = 2" + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "inline_equation", + "content": "r_{\\mathrm{inter}} = 2" + }, + { + "bbox": [ + 304, + 407, + 545, + 576 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 586, + 406, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 406, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 406, + 597 + ], + "type": "text", + "content": "4.2. Ablation Studies" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Method ablation. We ablate our method components on the DDAD dataset in Tab. 1. The geometric estimation baseline (1a) consists of [48] with the naive DBA formulation applied to all cameras and the co-visibility graph as described in Sec. 3.1. It performs poorly in depth and pose estimation, with an Abs. Rel. score of 0.438 and an absolute trajectory error (ATE) [42] of " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "2.134\\mathrm{m}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ", even when adjusting for scale. Next, we add our multi-camera DBA (1b). We observe that, even without VKITTI fine-tuning, the pose esti" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "3221" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 63, + 102, + 268, + 186 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "type": "text", + "content": "Table 4. Comparison to state-of-the-art on DDAD. We compare favorably to existing methods on both scale-aware and scale-invariant depth prediction. * median scaled depth." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 63, + 102, + 268, + 186 + ], + "lines": [ + { + "bbox": [ + 63, + 102, + 268, + 186 + ], + "spans": [ + { + "bbox": [ + 63, + 102, + 268, + 186 + ], + "type": "table", + "html": "
MethodAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
FSM [22]0.201---
SurroundDepth [52]0.2083.37112.9770.693
Ours0.1623.01911.4080.811
FSM* [22]0.202---
SurroundDepth* [52]0.2003.39212.2700.740
MCDP* [54]0.1933.11112.2640.811
Ours*0.1693.04111.3720.809
", + "image_path": "0e4dbeede49c8541ef7b3f60700ebd01c515d36ac92053cb923131591dd807ae.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 47, + 246, + 288, + 319 + ], + "blocks": [ + { + "bbox": [ + 46, + 191, + 287, + 246 + ], + "lines": [ + { + "bbox": [ + 46, + 191, + 287, + 246 + ], + "spans": [ + { + "bbox": [ + 46, + 191, + 287, + 246 + ], + "type": "text", + "content": "Table 5. Per-camera evaluation on DDAD. We show a per-camera breakdown of previous works, our " + }, + { + "bbox": [ + 46, + 191, + 287, + 246 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 46, + 191, + 287, + 246 + ], + "type": "text", + "content": " only (cf. 2a in Tab. 1), and our full method. Our full method performs the best with a particularly significant improvement on the side-view cameras while " + }, + { + "bbox": [ + 46, + 191, + 287, + 246 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 46, + 191, + 287, + 246 + ], + "type": "text", + "content": " performs similarly to previous works." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 246, + 288, + 319 + ], + "lines": [ + { + "bbox": [ + 47, + 246, + 288, + 319 + ], + "spans": [ + { + "bbox": [ + 47, + 246, + 288, + 319 + ], + "type": "table", + "html": "
MethodAbs Rel ↓
FrontF.LeftF-rightB.LeftB-rightBack
FSM [22]0.1300.2010.2240.2290.2400.186
SurroundDepth [52]0.1520.2070.2300.2200.2390.200
Dθ only0.1540.2130.2370.2310.2370.194
Ours0.1280.1600.1680.1720.1740.169
", + "image_path": "8d5ffd8822b859ad9c40089f6e8dcad5edfa1dc692534a708eb7935a47ee737c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 63, + 369, + 268, + 430 + ], + "blocks": [ + { + "bbox": [ + 46, + 325, + 287, + 369 + ], + "lines": [ + { + "bbox": [ + 46, + 325, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 325, + 287, + 369 + ], + "type": "text", + "content": "Table 6. Comparison to multi-frame methods on DDAD. We compare to methods that exploit temporal context from a single camera [51, 18]. We evaluate only the front camera since these methods were trained only on this camera." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 63, + 369, + 268, + 430 + ], + "lines": [ + { + "bbox": [ + 63, + 369, + 268, + 430 + ], + "spans": [ + { + "bbox": [ + 63, + 369, + 268, + 430 + ], + "type": "table", + "html": "
MethodFront Camera
Abs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
ManyDepth [51]0.1463.25814.0980.822
DepthFormer [18]0.1352.95312.4770.836
Ours0.1283.16813.2140.868
", + "image_path": "03b9f5987f04225edb4ce20aa3ffbb651943db495e644671dc9dd576123336a6.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 63, + 478, + 266, + 505 + ], + "blocks": [ + { + "bbox": [ + 46, + 434, + 287, + 478 + ], + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 478 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 478 + ], + "type": "text", + "content": "Table 7. Pose evaluation on DDAD. We compare our method to state-of-the-art monocular SLAM methods for which we report the average ATE across the cameras that successfully tracked the camera path. ** scaled trajectory." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 63, + 478, + 266, + 505 + ], + "lines": [ + { + "bbox": [ + 63, + 478, + 266, + 505 + ], + "spans": [ + { + "bbox": [ + 63, + 478, + 266, + 505 + ], + "type": "table", + "html": "
DROID-SLAM [48]ORB-SLAMv3 [5]Ours
ATE** [m] ↓7.5006.1790.433
", + "image_path": "0766c5aadf320b1e2f29a2edb3979849034769e4b6e09b8cbc5e9add958b7c5f.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 521, + 286, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 286, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 286, + 568 + ], + "type": "text", + "content": "mation accuracy improves dramatically over the naive DBA baseline. The relative scale ATE drops from " + }, + { + "bbox": [ + 46, + 521, + 286, + 568 + ], + "type": "inline_equation", + "content": "2.134\\mathrm{m}" + }, + { + "bbox": [ + 46, + 521, + 286, + 568 + ], + "type": "text", + "content": " to only " + }, + { + "bbox": [ + 46, + 521, + 286, + 568 + ], + "type": "inline_equation", + "content": "0.435\\mathrm{m}" + }, + { + "bbox": [ + 46, + 521, + 286, + 568 + ], + "type": "text", + "content": ". The absolute scale ATE is only about " + }, + { + "bbox": [ + 46, + 521, + 286, + 568 + ], + "type": "inline_equation", + "content": "1.2\\mathrm{m}" + }, + { + "bbox": [ + 46, + 521, + 286, + 568 + ], + "type": "text", + "content": " higher, indicating the scene scale is recovered accurately." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "content": "Using VKITTI fine-tuning (1c), we achieve significant gains in depth accuracy, where Abs. Rel. drops to 0.32 and " + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\delta_{1.25}" + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "content": " increases to " + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "inline_equation", + "content": "72.7\\%" + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "content": ". However, note that VKITTI fine-tuning does not affect the " + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\delta_{1.25}" + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "content": " score, i.e. it helps mostly with depth outliers. We attribute this to the absence of dynamic objects in the training data of [48] so that fine-tuning helps to adjust the confidence prediction to handle such outliers (cf. Sec. 3.2). We further test the depth refinement network (Sec. 3.3) without geometric estimation prior (2a). The depth obtained from " + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "content": " is less prone to outliers, as evidenced by its low Abs. Rel., Sq. Rel. and RMSE scores. However, note that its " + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\delta_{1.25}" + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "content": " is only " + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "inline_equation", + "content": "71.5\\%" + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "content": ", i.e. its" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 322, + 73, + 531, + 230 + ], + "blocks": [ + { + "bbox": [ + 322, + 73, + 531, + 230 + ], + "lines": [ + { + "bbox": [ + 322, + 73, + 531, + 230 + ], + "spans": [ + { + "bbox": [ + 322, + 73, + 531, + 230 + ], + "type": "image", + "image_path": "eb4eceb587e81555ce56c84b82137c45e4c2b8b83925d21f488663cfdcc0b9a7.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 232, + 545, + 277 + ], + "lines": [ + { + "bbox": [ + 306, + 232, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 306, + 232, + 545, + 277 + ], + "type": "text", + "content": "Figure 5. Depth in " + }, + { + "bbox": [ + 306, + 232, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\delta_{1.25^n}" + }, + { + "bbox": [ + 306, + 232, + 545, + 277 + ], + "type": "text", + "content": " range for different thresholds on DDAD. We depict the ratio of depth estimates " + }, + { + "bbox": [ + 306, + 232, + 545, + 277 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 306, + 232, + 545, + 277 + ], + "type": "text", + "content": " for which " + }, + { + "bbox": [ + 306, + 232, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\delta(d) < 1.25^n" + }, + { + "bbox": [ + 306, + 232, + 545, + 277 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 306, + 232, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\delta(d) = \\max\\left(\\frac{d}{d^*}, \\frac{d^*}{d}\\right)" + }, + { + "bbox": [ + 306, + 232, + 545, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 232, + 545, + 277 + ], + "type": "inline_equation", + "content": "d^*" + }, + { + "bbox": [ + 306, + 232, + 545, + 277 + ], + "type": "text", + "content": " is ground-truth depth. Note that values at " + }, + { + "bbox": [ + 306, + 232, + 545, + 277 + ], + "type": "inline_equation", + "content": "n = 1, 2, 3" + }, + { + "bbox": [ + 306, + 232, + 545, + 277 + ], + "type": "text", + "content": " represent " + }, + { + "bbox": [ + 306, + 232, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\delta_{1.25}, \\delta_{1.25^2}, \\delta_{1.25^3}" + }, + { + "bbox": [ + 306, + 232, + 545, + 277 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 322, + 315, + 527, + 407 + ], + "blocks": [ + { + "bbox": [ + 306, + 281, + 545, + 314 + ], + "lines": [ + { + "bbox": [ + 306, + 281, + 545, + 314 + ], + "spans": [ + { + "bbox": [ + 306, + 281, + 545, + 314 + ], + "type": "text", + "content": "Table 8. Comparison to state-of-the-art on NuScenes. Evaluated up to " + }, + { + "bbox": [ + 306, + 281, + 545, + 314 + ], + "type": "inline_equation", + "content": "80\\mathrm{m}" + }, + { + "bbox": [ + 306, + 281, + 545, + 314 + ], + "type": "text", + "content": " for scale-aware depth as in [22, 52] and " + }, + { + "bbox": [ + 306, + 281, + 545, + 314 + ], + "type": "inline_equation", + "content": "60\\mathrm{m}" + }, + { + "bbox": [ + 306, + 281, + 545, + 314 + ], + "type": "text", + "content": " for median-scaled depth (denoted with " + }, + { + "bbox": [ + 306, + 281, + 545, + 314 + ], + "type": "inline_equation", + "content": "*" + }, + { + "bbox": [ + 306, + 281, + 545, + 314 + ], + "type": "text", + "content": " ) as in [54]." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 322, + 315, + 527, + 407 + ], + "lines": [ + { + "bbox": [ + 322, + 315, + 527, + 407 + ], + "spans": [ + { + "bbox": [ + 322, + 315, + 527, + 407 + ], + "type": "table", + "html": "
MethodAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
FSM [22]0.297---
SurroundDepth [52]0.2804.4017.4670.661
Ours0.2534.7597.1500.729
PackNet*[19]0.3033.1547.0140.655
FSM* [22]0.2703.1856.8320.689
SurroundDepth* [52]0.2453.0676.8350.719
MCDP* [54]0.2373.0306.8220.719
Ours*0.2353.3326.0210.749
", + "image_path": "1006bf72ead2621a5ec995540021983a5fee1e057cad7c79cd06b38a5540604c.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 424, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 424, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 424, + 545, + 555 + ], + "type": "text", + "content": "depth accuracy compared to the geometric depth estimates is actually lower when disregarding outliers. Finally, we test our full system (3a). Compared to geometric estimation (1d), we observe a significant improvement in outlier sensitive metrics like RMSE, but also in outlier robust metrics like " + }, + { + "bbox": [ + 304, + 424, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\delta_{1.25}" + }, + { + "bbox": [ + 304, + 424, + 545, + 555 + ], + "type": "text", + "content": ". Additionally, the pose estimation accuracy is increased and the difference between scaled and non-scaled ATE is smaller. Compared to depth obtained from " + }, + { + "bbox": [ + 304, + 424, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}(2\\mathrm{a})" + }, + { + "bbox": [ + 304, + 424, + 545, + 555 + ], + "type": "text", + "content": ", the increase in outlier sensitive metrics is smaller but still significant, e.g. 1.26m in RMSE. Further, we observe a sizable gain in " + }, + { + "bbox": [ + 304, + 424, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\delta_{1.25}" + }, + { + "bbox": [ + 304, + 424, + 545, + 555 + ], + "type": "text", + "content": " of 9.6 percentage points." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "text", + "content": "Further, in Fig. 5, we compare the " + }, + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "inline_equation", + "content": "\\delta_{1.25^n}" + }, + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "text", + "content": " scores at different accuracy thresholds " + }, + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "text", + "content": " of our geometric depth estimation without refinement ('Ours (Geometric)'), our refinement network only ('Ours (Monocular)') and our full method ('Ours'). The results confirm our hypothesis that while geometric estimates are more accurate than monocular depth estimates, they are also noisier. Importantly, the results further illustrate that our full method can effectively combine the strengths of both approaches while not suffering from their weaknesses." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Co-visibility graph construction. In Tab. 2, we compare our co-visibility graph construction algorithm (Sec. 3.1) to a multi-camera adaption of the algorithm in [48]. Ours" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3222" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 124, + 281, + 185 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 287, + 123 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 287, + 123 + ], + "type": "text", + "content": "Table 9. Per-camera evaluation on NuScenes. We compare our method with previous works on scale-aware depth estimation. Evaluated up to " + }, + { + "bbox": [ + 47, + 69, + 287, + 123 + ], + "type": "inline_equation", + "content": "80\\mathrm{m}" + }, + { + "bbox": [ + 47, + 69, + 287, + 123 + ], + "type": "text", + "content": " as in Tab. 8. We observe the same trend as on DDAD, i.e. our method performs best across all cameras, with a particularly high improvement on the side views." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 124, + 281, + 185 + ], + "lines": [ + { + "bbox": [ + 51, + 124, + 281, + 185 + ], + "spans": [ + { + "bbox": [ + 51, + 124, + 281, + 185 + ], + "type": "table", + "html": "
MethodAbs Rel ↓
FrontF.LeftF-rightB.LeftB_rightBack
FSM [22]0.1860.2870.3750.2960.4180.221
SurroundDepth [52]0.1790.2600.3400.2820.4030.212
Ours0.1740.2300.3020.2490.3600.201
", + "image_path": "d4ed7805dd5f915234f2ecc5675ba5b2575d43a5930b9062b3e46d4b5581b42a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 64, + 248, + 268, + 294 + ], + "blocks": [ + { + "bbox": [ + 47, + 194, + 286, + 247 + ], + "lines": [ + { + "bbox": [ + 47, + 194, + 286, + 247 + ], + "spans": [ + { + "bbox": [ + 47, + 194, + 286, + 247 + ], + "type": "text", + "content": "Table 10. Cross-dataset transfer. We use models trained on DDAD to evaluate scale-aware depth prediction on the NuScenes dataset. We compare to state-of-the-art methods [22, 52] and observe that our method exhibits better generalization ability (cf. Tab. 8)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 64, + 248, + 268, + 294 + ], + "lines": [ + { + "bbox": [ + 64, + 248, + 268, + 294 + ], + "spans": [ + { + "bbox": [ + 64, + 248, + 268, + 294 + ], + "type": "table", + "html": "
MethodAbs Rel ↓Sq Rel ↓RMSE ↓δ1.25 ↑
FSM [22]0.3495.0648.7850.499
SurroundDepth [52]0.3645.4768.4470.525
Ours0.2924.8007.6770.660
", + "image_path": "77c761330b5834edeb108e744c4d6ed40a9c4a4a91383e2e1b587f6e61929549.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 304, + 286, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 286, + 363 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 286, + 363 + ], + "type": "text", + "content": "yields similar performance in depth estimation, with the exact same Abs. Rel. score and only minor difference in other metrics. Further, the absolute scale ATE is only slightly " + }, + { + "bbox": [ + 46, + 304, + 286, + 363 + ], + "type": "inline_equation", + "content": "(25\\mathrm{cm})" + }, + { + "bbox": [ + 46, + 304, + 286, + 363 + ], + "type": "text", + "content": " higher. In contrast, using our algorithm, we achieve a runtime reduction of nearly " + }, + { + "bbox": [ + 46, + 304, + 286, + 363 + ], + "type": "inline_equation", + "content": "10\\times" + }, + { + "bbox": [ + 46, + 304, + 286, + 363 + ], + "type": "text", + "content": " on the full system." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 363, + 286, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 286, + 446 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 286, + 446 + ], + "type": "text", + "content": "Depth refinement network. We verify the choice of our inputs to " + }, + { + "bbox": [ + 46, + 363, + 286, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 46, + 363, + 286, + 446 + ], + "type": "text", + "content": " in Tab. 3. If we do not input the confidence " + }, + { + "bbox": [ + 46, + 363, + 286, + 446 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i" + }, + { + "bbox": [ + 46, + 363, + 286, + 446 + ], + "type": "text", + "content": " and do not sparsify the depth via " + }, + { + "bbox": [ + 46, + 363, + 286, + 446 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i < \\beta" + }, + { + "bbox": [ + 46, + 363, + 286, + 446 + ], + "type": "text", + "content": " before feeding it to " + }, + { + "bbox": [ + 46, + 363, + 286, + 446 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 46, + 363, + 286, + 446 + ], + "type": "text", + "content": ", we observe the lowest performance. If we input the confidence " + }, + { + "bbox": [ + 46, + 363, + 286, + 446 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i" + }, + { + "bbox": [ + 46, + 363, + 286, + 446 + ], + "type": "text", + "content": " but do not sparsify the depth, we see an improvement over not using them. We achieve the best performance with the inputs described in Sec. 3.3." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 447, + 286, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 286, + 530 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 286, + 530 + ], + "type": "text", + "content": "Moreover, we show qualitative examples of our depth refinement in Fig. 4. The confidence " + }, + { + "bbox": [ + 46, + 447, + 286, + 530 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i" + }, + { + "bbox": [ + 46, + 447, + 286, + 530 + ], + "type": "text", + "content": " (overlaid with the image) segments regions where geometric estimation is ambiguous, i.e. dynamic objects and uniformly textured areas like the sky and the road surface. The geometric depth maps exhibit severe artifacts in such regions. After refinement, these artifacts are corrected." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 539, + 217, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 539, + 217, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 539, + 217, + 552 + ], + "type": "text", + "content": "4.3. Comparison to State-of-the-Art" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 557, + 286, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 286, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 286, + 640 + ], + "type": "text", + "content": "DDAD. In Tab. 4, we compare our method to existing self-supervised multi-camera depth estimation methods. We achieve significant improvements in scale-aware and scale-invariant depth prediction with only minor differences in absolute and relative scale results. In both settings, we achieve state-of-the-art results with the lowest Abs. Rel. scores of 0.162 and 0.169, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 642, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 286, + 712 + ], + "type": "text", + "content": "In Fig. 5 we compare the " + }, + { + "bbox": [ + 46, + 642, + 286, + 712 + ], + "type": "inline_equation", + "content": "\\delta_{1.25^n}" + }, + { + "bbox": [ + 46, + 642, + 286, + 712 + ], + "type": "text", + "content": " scores of our method to the state-of-the-art approaches on DDAD at different " + }, + { + "bbox": [ + 46, + 642, + 286, + 712 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 642, + 286, + 712 + ], + "type": "text", + "content": ". For small values of " + }, + { + "bbox": [ + 46, + 642, + 286, + 712 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 642, + 286, + 712 + ], + "type": "text", + "content": ", we observe a particularly pronounced performance gain over existing methods. This shows the advantage of combining highly accurate geometric estimates with monocular cues. Further, our method consistently out" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 537, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 537, + 83 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 537, + 83 + ], + "type": "text", + "content": "performs the baselines over all values of " + }, + { + "bbox": [ + 305, + 72, + 537, + 83 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 72, + 537, + 83 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 305, + 72, + 537, + 83 + ], + "type": "inline_equation", + "content": "\\delta < 1.25^n" + }, + { + "bbox": [ + 305, + 72, + 537, + 83 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 85, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 85, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 85, + 545, + 168 + ], + "type": "text", + "content": "In Fig. 6, we show a qualitative comparison to existing works. On the left side, we illustrate depth maps across three cameras. Compared to FSM [22] and Surround-Depth [52], we produce sharper depth boundaries. On the right side, we illustrate point clouds accumulated over time. We produce a more consistent reconstruction, as can be seen when focusing on the vehicles or the fences beside the road." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 171, + 545, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 171, + 545, + 314 + ], + "spans": [ + { + "bbox": [ + 304, + 171, + 545, + 314 + ], + "type": "text", + "content": "Tab. 5 shows the per-camera breakdown of the scale-aware depth prediction comparison. The advantage of our method is particularly pronounced on the side cameras. Other methods struggle with the side views because the static spatial context is limited and they do not exploit any temporal or spatial-temporal context. The temporal and spatial-temporal contexts are conducive in the side views since sideward motion leads to better triangulation angles than forward motion. This is also evidenced by the results of " + }, + { + "bbox": [ + 304, + 171, + 545, + 314 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 304, + 171, + 545, + 314 + ], + "type": "text", + "content": " without geometric estimation, which performs similarly to the baseline methods, struggling with the side views. In contrast, our full system performs well across all cameras." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "text", + "content": "We further compare to self-supervised single-camera methods that leverage temporal information in Tab. 6. For a fair comparison, we evaluate only the front camera. We compare favorably to DepthFormer [18] and Many-Depth [51]. In particular, we substantially improve in the outlier robust metric " + }, + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\delta_{1.25}" + }, + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "text", + "content": " and perform competitively in all others. Our Abs. Rel. score is the lowest at 0.128." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 401, + 545, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 545, + 508 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 545, + 508 + ], + "type": "text", + "content": "To evaluate ego-motion estimation, we compare our system to state-of-the-art monocular SLAM methods [48, 5] in Tab. 7. We run the baselines on each camera and report the average ATE across the cameras that successfully tracked the camera path. Note that, contrary to our approach, the competing methods frequently failed to produce a trajectory. We observe that state-of-the-art monocular SLAM methods exhibit a large error (ATE), while our method recovers accurate trajectories." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": "NuScenes. In Tab. 8, we compare our system to previous self-supervised multi-camera depth estimation methods. We outperform previous methods by a significant margin, corroborating our findings on DDAD. Notably, we observe substantial improvements in scale-aware depth estimation, while previous works usually struggle with recovering absolute scale on this dataset since the overlap between cameras is smaller than in DDAD [22]. Therefore, previous works like MCDP [54] report results on scale-invariant depth prediction. We outperform existing methods also in this setting, although the performance gap is smaller. Note that the gap between scale-aware and scale-invariant evaluation is only 2 percentage points in " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\delta_{1.25}" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " for our method, while for SurroundDepth [52] the gap is much larger with 5.8 percentage points. We show a per-camera breakdown of the comparison to the state-of-the-art in scale-aware depth estimation in Tab. 9. The results corroborate our findings" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3223" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 547, + 329 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 329 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 329 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 329 + ], + "type": "image", + "image_path": "95e55d4b7101af8d04192135547bb051457ef804e1133ce167ef313bfac449b4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 330, + 547, + 365 + ], + "lines": [ + { + "bbox": [ + 46, + 330, + 547, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 330, + 547, + 365 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison on DDAD. We show depth maps and point clouds accumulated over time along with input images, ground-truth LiDAR 3D Reconstruction, and the ego-vehicle in red. Our depth maps are sharper and more accurate. Our accumulated point clouds yield a more consistent 3D reconstruction. Note that we use our pose predictions for [22, 52] since these do not predict pose." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 377, + 288, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 288, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 288, + 413 + ], + "type": "text", + "content": "on DDAD, namely that our method outperforms previous works across all cameras with a particularly pronounced improvement on the side views." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 415, + 289, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 289, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 289, + 547 + ], + "type": "text", + "content": "Cross-dataset transfer. We finally test the cross-dataset generalization of our method versus FSM [22] and SurroundDepth [52]. In Tab. 10, we show scale-aware depth estimation results of models trained on DDAD, evaluated on NuScenes. We observe that the gap in Abs. Rel. widens compared to Tab. 8, with our method outperforming SurroundDepth by 0.072 in Abs. Rel. and FSM by 0.057. Further, our method maintains much higher levels of " + }, + { + "bbox": [ + 46, + 415, + 289, + 547 + ], + "type": "inline_equation", + "content": "\\delta_{1.25}" + }, + { + "bbox": [ + 46, + 415, + 289, + 547 + ], + "type": "text", + "content": " and Sq. Rel., while SurroundDepth drops significantly in both metrics. Note that we apply focal length scaling [45] to all methods to accommodate differences in camera intrinsics." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 560, + 119, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 560, + 119, + 572 + ], + "spans": [ + { + "bbox": [ + 47, + 560, + 119, + 572 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "We introduced R3D3, a multi-camera system for dense 3D reconstruction of dynamic outdoor environments. The key ideas we presented are a multi-camera DBA operator that greatly improves geometric depth and pose estimation, a multi-camera co-visibility graph construction algorithm that reduces the runtime of our system by nearly " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "10\\times" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " without significant performance drop, and a depth refinement network that effectively fuses geometric depth estimates with monocular cues. We observe that our design choices enable dense 3D mapping in challenging scenes presenting many dynamic objects, uniform and repetitive textures, and" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 377, + 545, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 377, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 305, + 377, + 545, + 414 + ], + "type": "text", + "content": "complicated camera phenomena like lens flare and autoexposure. 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In CVPR, 2017." + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "3226" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/RANA_ Relightable Articulated Neural Avatars/ae3b789d-a192-4696-b97f-daa6528a52ba_content_list.json b/2023/RANA_ Relightable Articulated Neural Avatars/ae3b789d-a192-4696-b97f-daa6528a52ba_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..06545e620201aa338816d56d259eddbe0a3d716e --- /dev/null +++ b/2023/RANA_ Relightable Articulated Neural Avatars/ae3b789d-a192-4696-b97f-daa6528a52ba_content_list.json @@ -0,0 +1,1950 @@ +[ + { + "type": "text", + "text": "RANA: Relightable Articulated Neural Avatars", + "text_level": 1, + "bbox": [ + 243, + 111, + 725, + 133 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Umar Iqbal $^{1*}$ Akin Caliskan $^{2*}$ Koki Nagano $^{1}$ Sameh Khamis $^{1}$ Pavlo Molchanov $^{1}$ Jan Kautz $^{1}$ $^{1}$ NVIDIA ${}^{2}$ Flawless AI https://nvlabs.github.io/RANA/", + "bbox": [ + 86, + 152, + 908, + 209 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e51e8665b0fa8ba44cd9cb4531b5d310568e3c99c67db993af467bb00d478576.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 89, + 241, + 251, + 601 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0da1b718d7fb666d951fd2fbd4fe11117258f1efb7ecf1e3a6712db20bc3363c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 251, + 241, + 411, + 601 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6c34ba8841f7939950229c0b0a4ad39bc2fdf616014f8f3185b0c87f7b8be3d2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 413, + 241, + 573, + 601 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d1972ae8125f49caaa8effb5451982a60caf7efe896a9991a8ed21fabc042e23.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 573, + 241, + 733, + 601 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2402a115b8ba3b48f3127b7446c028b345784ba5e5169f68a295146e0e81e6d8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 733, + 241, + 893, + 601 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We present, RANA, an approach for learning dynamic and relightable full-body avatars from monocular RGB videos. A training frame of the person is shown in the first column. RANA can synthesize images of the person under novel poses, viewpoints, and lighting environments. In the insets, we show the synthesized albedo image, the normal map, and the target HDRI light map.", + "bbox": [ + 75, + 601, + 893, + 662 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 236, + 660, + 316, + 676 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We propose RANA, a relightable and articulated neural avatar for the synthesis of humans under arbitrary viewpoints, body poses, and lighting. We only require a short video clip of the person to create the avatar and assume no knowledge about the lighting environment. We present a novel framework to model humans while disentangling their geometry, texture, and lighting environment from monocular RGB videos. To simplify this otherwise ill-posed task we first estimate the coarse geometry and texture of the person via SMPL+D model fitting and then learn an articulated neural representation for higher quality image syn", + "bbox": [ + 75, + 693, + 470, + 861 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "thesis. RANA first generates the normal and albedo maps of the person in any given target body pose and then uses spherical harmonics lighting to generate the shaded image in the target lighting environment. We also propose to pre-train RANA using synthetic images and demonstrate that it leads to better disentanglement between geometry and texture while also improving robustness to novel body poses. Finally, we also present a new photo-realistic synthetic dataset, Relighting Human, to quantitatively evaluate the performance of the proposed approach.", + "bbox": [ + 496, + 662, + 893, + 815 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 844, + 632, + 859 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Articulated neural avatars of humans have numerous applications across telepresence, animation, and visual con", + "bbox": [ + 500, + 869, + 892, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*equal contribution. The work was partially done during AC's internship at NVIDIA.", + "bbox": [ + 75, + 875, + 468, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23142", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tent creation. To enable the widespread adoption of these neural avatars, they should be easy to generate and animate under novel poses and viewpoints, able to render in photorealistic image quality, and easy to relight in novel environments. Existing methods commonly aim to learn such neural avatars using monocular videos [47, 46, 45, 54, 66, 58, 31]. While this allows photo-realistic image quality and animation, the synthesized images are always limited to the lighting environment of the training video. Other works directly tackle relighting of human avatars but do not provide control over the body pose [23, 41]. Moreover, these approaches often require multiview images recorded in a Light Stage for training, which is limited to controlled settings only. Some recent methods aim to relight RGB videos of a dynamic human but do not provide control over body pose [16].", + "bbox": [ + 75, + 90, + 472, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we present the Relightable Articulated Neural Avatar (RANA) method, which allows animation of people under any novel body pose, viewpoint, and lighting environment. To create an avatar, we only require a short monocular video clip of the person in unconstrained environment, clothing, and arbitrary body pose. During inference, we only require the target body pose and target lighting information.", + "bbox": [ + 75, + 337, + 472, + 458 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learning relightable neural avatars of dynamics humans from monocular RGB videos recorded in unknown environments is a challenging problem. First, it requires modeling the complex human body articulations and geometry. Second, in order to allow relighting under novel environments, the texture, geometry, and illumination information have to be disentangled, which is an ill-posed problem to solve from RGB videos [8]. To address these challenges, we first extract canonical coarse geometry and texture information from the training frames using a statistical human shape model SMPL+D [40, 5, 36]. We then propose a novel convolutional neural network that is trained on synthetic data to remove the shading information from the coarse texture. We augment the coarse geometry and texture with learnable latent features and pass them to our proposed neural avatar framework, which generates refined normal and albedo maps of the person under the target body pose using two separate convolutional networks. Given the normal map, albedo map, and lighting information, we generate the final shaded image using spherical harmonics (SH) lighting [49]. During training, since the environment lighting is unknown, we jointly optimize it together with the person's appearance and propose novel regularization terms to prevent the leaking of lighting into the albedo texture. We also propose to pre-train the avatar using photo-realistic synthetic data with ground-truth albedo and normal maps. During pretraining, we train a single model for multiple subjects while having separate neural features for each subject. This not only improves the generalizability of the neural avatar", + "bbox": [ + 75, + 463, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "to novel body poses but also learns to decouple the texture and geometry information. For a new subject, we only learn a new set of neural features and fine-tune the avatar model to capture fine-grained person-specific details. In our experiments, the avatar for a novel subject can be learned within 15k training iterations.", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Since no dataset exists to evaluate the renderings of avatars in terms of both novel light and pose synthesis, we also propose a novel photo-realistic synthetic Relighting Human Dataset (RHD) with ground truth albedo, normals, and lighting information. We also perform a qualitative evaluation of RANA on the People Snapshot dataset [5] to compare with other baselines.", + "bbox": [ + 496, + 181, + 893, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be summarized as follows:", + "bbox": [ + 517, + 289, + 844, + 304 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present, RANA, a novel framework for learning relightable articulated neural avatars from short unconstrained monocular videos. The proposed approach is very easy to train and does not require any knowledge about the environment lighting of the training video.", + "- Our proposed approach can synthesize images of articulated humans under any arbitrary body pose, viewpoint, and lighting. It can also be used for relighting videos of dynamic humans.", + "- We present a new photo-realistic synthetic dataset for quantitative evaluation and to further the research in this direction." + ], + "bbox": [ + 517, + 316, + 890, + 510 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 527, + 637, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Mesh Based Human Avatars. These methods represent human avatars using a rigged mesh and an associated texture map. Earlier methods captured human avatars using multi-view cameras [12, 53] or with the help of depth sensors [9, 71]. However, their adoption remained limited due to the constrained hardware requirements. The recent works, therefore, focus on creating the avatars from monocular videos [5, 4, 31, 10], or images [36, 64, 27, 25, 6, 10, 11]. The methods [5, 4, 36] use body model fitting to capture the humans, while more recent methods use data-driven implicit functions combined with pixel-aligned features [50] for human reconstruction [71, 27, 64, 6]. Self-Recon [31] combines both explicit and implicit meshes to reconstruct the detailed geometry of the person from self-rotating videos, however, it requires manual human effort to make the avatar animatable. The main limitation of these methods, however, is that the shading information is baked into the texture. Hence, the avatars cannot be rendered with novel lights. The recent methods PHORUM [6] and S3F [17] are the only exceptions, however, they create avatar from a single image and rely on data-driven priors to hallucinate the occluded regions of the person. Hence, the generated images may not be the true representation of the", + "bbox": [ + 496, + 553, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23143", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c4046231706afa8751158ef0e51b64103a8046ca4f452eb46733aae3e19b3b3a.jpg", + "image_caption": [ + "Table 1. Comparison of some of the representative methods for neural human avatar creation. Ours (RANA) is the only method that allows novel view, pose and light synthesis." + ], + "image_footnote": [], + "bbox": [ + 91, + 89, + 452, + 219 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "person. In contrast, our approach uses video data to capture a detailed human representation, while also allowing the rendering of the person in novel lighting.", + "bbox": [ + 75, + 287, + 470, + 333 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Neural Human Avatars. More recent methods learn a neural representation of the person and use neural renderers [57] to directly generate photo-realistic images in the target body pose and viewpoints [7, 20, 13, 59, 26, 63]. These methods are generally classified into 2D or 3D neural rendering based methods [57]. The 3D neural rendering methods represent the person using neural radiance fields [42] and render the target images using volume rendering [46, 62, 32, 45, 14, 58, 24, 38]. The 2D neural rendering methods, on the other hand, use CNNs to render the images [47, 66, 22, 70]. One limitation of the 3D neural rendering methods is that the avatar has to be created from scratch for each person. Some methods learn generalizable avatars but require exemplar images of the person during inference [34, 48]. In contrast, the 2D based methods offer some generalizability by sharing the neural renderer across multiple subjects [47]. Our method falls into the 2D neural rendering paradigm as we use CNNs to generate the albedo and normal images of the person. In particular, we take inspiration from ANR [47] for designing our framework. Tab. 1 compares existing neural avatar creation methods. Ours is the only method that allows synthesis under novel poses, viewpoints, and lighting, while also being generalizable.", + "bbox": [ + 75, + 348, + 472, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Human Relighting. Relighting of human images has been studied extensively in the literature [18, 51, 33, 55, 72, 61, 56, 30, 37, 35, 69, 17]. However, these methods cannot render relighted images in novel body poses and viewpoints. Some recent methods allow relighting from novel views but provide no control over the body pose [23, 43, 16, 65]. The method TexMesh [71] also provides control over body pose but requires RGB-D videos for training and assumes that the environment map of the training video is known. Our approach, in contrast, provides full control over the body pose, viewpoint, and lighting, and learns the avatar from RGB videos with unknown lighting.", + "bbox": [ + 75, + 719, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 89, + 591, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to learn a relightable articulated neural avatar, RANA, that can synthesize high-quality images of the person under any target body pose, viewpoint, and lighting. To create the avatar, we use a small video sequence $\\mathbf{I} = \\{I_{\\mathrm{f}}\\}_{f = 1}^{F}$ with $F$ video frames and assume no knowledge about the lighting environment and body poses present in the video. We parameterize RANA using the SMPL [40] body model to control the animation and use Spherical Harmonics (SH) [49] lighting to model the lighting. During inference, we only need the target body pose and target lighting information in the form of SH coefficients and do not require any exemplar images for ground-truth. Learning RANA from a monocular video requires capturing the geometry and appearance of the dynamic human while also disentangling the shading information. In order to tackle this ill-posed problem, we first capture the coarse geometry using the SMPL+D fits (Sec. 3.1). We use the coarse geometry to extract a coarse texture map from the training images which is converted to an albedo texture map using a convolutional network (Sec. 3.2). We then propose RANA that generates the refined albedo and normal maps. The refined normal maps are used to obtain the shading map using SH lighting which is combined with the refined albedo map to obtain the final image in the target body pose and light (Sec. 3.3). An overview of our method can be seen in Fig. 1. In the following, we describe each of these modules in greater detail.", + "bbox": [ + 496, + 114, + 893, + 523 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Coarse Geometry Estimation", + "text_level": 1, + "bbox": [ + 498, + 535, + 761, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given the training frames, we first estimate the coarse geometry of the person including the clothing and hair details. For this, we employ the SMPL+D [4, 36] variant of the SMPL body model [40]. SMPL is a linear function $M(\\theta, \\beta)$ that takes the body pose $\\theta \\in \\mathbb{R}^{72}$ and shape parameters $\\beta \\in \\mathbb{R}^{10}$ as input and produces a triangulated mesh $\\mathbf{M} \\in \\mathbb{R}^{V \\times 3}$ with $V = 6890$ vertices. SMPL only captures the undressed shape of the body and ignores the clothing and hair details. For this, SMPL+D adds a set of 3D offsets $\\mathbf{D} \\in \\mathbf{R}^{V \\times 3}$ to SMPL to capture the additional geometric details, i.e., $M(\\theta, \\beta, \\mathbf{D}) \\in \\mathbb{R}^{V \\times 3}$ can also model clothed humans. We refer the readers to [36, 4] for a detailed description of SMPL+D.", + "bbox": [ + 496, + 559, + 893, + 755 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For fitting SMPL+D to training images, we first estimate the parameters of SMPL using an off-the-shelf method SMPLify3D [29]. Since the person in the video remains the same, we optimize a single $\\beta$ for the entire video. We then fix the pose $\\{\\theta\\}_{f=1}^{F}$ and shape $\\beta$ parameters and optimize for the offsets $\\mathbf{D}$ using the following objective:", + "bbox": [ + 496, + 756, + 893, + 848 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {D} = \\underset {\\mathbf {D} ^ {\\prime}} {\\operatorname {a r g m i n}} \\sum_ {f = 1} ^ {F} \\mathcal {L} \\left(M \\left(\\theta_ {f}, \\beta , \\mathbf {D} ^ {\\prime}\\right)\\right) = \\mathcal {L} _ {\\mathrm {S i l}} + \\mathcal {L} _ {\\mathrm {s m o o t h}}. (1)\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 859, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23144", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f5e3dfe34d81cf40decc56a0acad6123bed527971dbd71d544792d357353fc94.jpg", + "image_caption": [ + "(a) Training frames" + ], + "image_footnote": [], + "bbox": [ + 80, + 104, + 166, + 172 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2911cad416ef82dec6d857493bd546722bb10833084bf816c7b5d02a7b149fac.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 168, + 104, + 254, + 172 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4b215f111b0234e17ce58ebc358d94226657340ecd2c6b37e34ec00d5c4d238a.jpg", + "image_caption": [ + "(d) RANA: Relightable Articulated Neural Avatar (Sec 3.3)" + ], + "image_footnote": [], + "bbox": [ + 256, + 104, + 341, + 172 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a87ea00d0be44acab546b9e970f64d6929f8840b885e7b9a6e0f0a786893e0e6.jpg", + "image_caption": [ + "(b) Coarse Geometry Estimation (Sec. 3.1)" + ], + "image_footnote": [], + "bbox": [ + 359, + 104, + 447, + 172 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/91f868b5bb54ada2b6f97a3aef897b12f7e95bad91cc8433a5a92dbc5a094922.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 450, + 104, + 537, + 172 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/153c176951931e718aee668f9bd032e2036ab3ec3c7bd83cc668c3d884d65469.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 540, + 104, + 625, + 172 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/04e1a6c5427577653946a16c11d5ec009ac109e31a640a3c77e78b924a435b77.jpg", + "image_caption": [ + "(c) Coarse Texture Estimation (Sec 3.2)" + ], + "image_footnote": [], + "bbox": [ + 643, + 104, + 730, + 172 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7af2ae35432a13df7dbb0a89818574bb4b17a207ddf8ccf8703d34dd09d7307a.jpg", + "image_caption": [ + "TextureNet" + ], + "image_footnote": [], + "bbox": [ + 736, + 119, + 803, + 130 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a522a7d759fb06fe413b45bd3e1dfae8be83916ac5555d3d00cd244ab6d03b20.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 131, + 803, + 140 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7f70c6ae2ee66f8680509a4eb633017706e98659d34a5e97c636aa1b67b59044.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 785, + 141, + 803, + 151 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/db347b505deebb70109d8ced3478f61b1cc073e70db6cb144afabe7c44ffa58f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 805, + 132, + 834, + 141 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/025798a817c2bf58782eccfeaca0b032818c32eb243ea9b7f9fafbb31e9eefb4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 805, + 142, + 834, + 152 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2cb3776682018cd3753896e62809bb0c6773f94268bf0e12a28942c0cde1db59.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 805, + 152, + 834, + 160 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6b03d78654077fd5582acb77791fbe41ff402546690bb418a3fd8519a613a09d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 834, + 132, + 892, + 172 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/602a5eee04a5e8e65e83497225af907c850a6023bfe5f519aeb10f80e2fd7639.jpg", + "image_caption": [ + "Latent Neural Features", + "Figure 1. Overview of the proposed approach. (a) shows some training frames. (b) We estimate the coarse geometry of the person using the SMPL+D body model. (c) The SMPL+D fits are used to extract a UV texture map, which we process using TextureNet to obtain a coarse albedo texture map. (d) Given a target body pose, we rasterize person-specific neural features, coarse albedo, and coarse normals from SMPL+D to the target body pose and pass them to NormalNet and AlbedoNet to obtain refined normal and albedo maps, respectively. We then use the normal map and spherical harmonics lighting to obtain the shading image, which is multiplied with refined albedo to produce the shaded image. AlbedoNet also generates a binary mask, which we use to overlay the shaded image onto the background." + ], + "image_footnote": [], + "bbox": [ + 84, + 208, + 879, + 411 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here the term $\\mathcal{L}_{\\mathrm{Sil}}$ is the silhouette loss. We obtain the silhouette of SMPL+D vertices $S_{f}$ for frame $f$ using a differentiable renderer [39] while the target silhouette $\\hat{S}_t$ is obtained using a person segmentation model [15]. We define the $\\mathcal{L}_{\\mathrm{Sil}}$ loss as", + "bbox": [ + 75, + 523, + 468, + 602 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {S i l}} = \\frac {1}{F} \\sum_ {f = 1} ^ {F} \\left| S _ {f} - \\hat {S} _ {f} \\right|. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 608, + 468, + 651 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The term $\\mathcal{L}_{\\mathrm{smooth}}$ is a laplacian smoothing term to encourage the smooth surface of the mesh:", + "bbox": [ + 76, + 659, + 468, + 689 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s m o o t h}} = \\frac {1}{F} \\sum_ {f = 1} ^ {F} | | L \\mathbf {M} _ {f} | |, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 696, + 468, + 739 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $L$ is the mesh Laplacian operator. Note that we optimize a single set of $\\mathbf{D}$ for the entire video, hence it does not model any pose-dependent geometric deformations. Some examples of SMPL+D can be seen in Fig. 1b.", + "bbox": [ + 75, + 748, + 468, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Coarse Albedo Estimation", + "text_level": 1, + "bbox": [ + 76, + 816, + 316, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given the SMPL+D fits for the training frames, we estimate an albedo texture map $T_{A}$ of the person in the UV space of SMPL. We follow [5] and first extract a partial texture map for each frame by back-projecting the image colors", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of all visible vertices to the UV space. The final texture map $T_{I}$ is then generated by calculating the median color value of most orthogonal texels from all frames. Depending on the available body poses in the training video, the obtained texture map can be noisy, and still have missing regions, e.g., hand regions are often very noisy as no hand tracking is performed during SMPL fitting. Also, to ensure plausible relighting, the unknown shading from the texture map has to be removed, which is a challenging problem since decomposing shading and albedo is an ill-posed problem.", + "bbox": [ + 496, + 523, + 892, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To address these problems, we propose TextureNet, $G_{\\mathrm{Tex}}$ (Fig. 1c), which takes a noisy texture map $T_I$ with unknown lighting as input and produces a clean albedo texture map as output, i.e., $T_A = G_{\\mathrm{Tex}}(T_I)$ [36, 28]. One main challenge for training such a model is the availability of training pairs of noisy/shaded and albedo texture maps. We generate these pairs using 400 rigged characters from the RenderPeople dataset [2]. Since each character in RenderPeople has different UV coordinates, we follow [36] and register the characters with SMPL to obtain ground-truth UV maps in consistent SMPL UV coordinates. For noisy pairs, we generate images with random poses and lighting and extract texture maps like any other video mentioned", + "bbox": [ + 496, + 704, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23145", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "above. We train $G_{\\mathrm{Tex}}$ using the following losses:", + "bbox": [ + 76, + 90, + 403, + 107 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {T e x}} = \\mathcal {L} _ {\\text {p i x e l}} + \\mathcal {L} _ {\\mathrm {V G G}} + \\mathcal {L} _ {\\mathrm {G A N}}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 118, + 468, + 135 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here $\\mathcal{L}_{\\mathrm{pixel}}$ is the $L_{1}$ loss between the predicted and ground-truth albedo texture maps, $\\mathcal{L}_{\\mathrm{VGG}}$ is $L_{1}$ difference between their VGG features, and $\\mathcal{L}_{\\mathrm{GAN}}$ is the GAN loss [21, 44]. We use a vanilla U-Net architecture for TextureNet. It takes a noisy/shaded UV texture map with a resolution of $512\\times 512$ as input and produces the albedo texture with the same resolution as output. We also concatenate a 2D tensor of UV coordinates with the input texture map to provide part-specific information to the model. We train the network using Adam optimizer with a batch size of 8 and a learning rate of $1e^{-4}$ with cosine annealing and a minimum learning rate of $1e^{-5}$ . To avoid overfitting during training, we perform random noise augmentation to the input texture maps including coarse dropout, gaussian noise, random brightness, and MixUp ( $\\beta = 0.4$ ) [67]. Some examples of estimated albedo maps can be seen in Fig. 2.", + "bbox": [ + 75, + 147, + 472, + 390 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Relightable Articulated Neural Avatar", + "text_level": 1, + "bbox": [ + 76, + 398, + 408, + 414 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The coarse albedo texture and geometry obtained so far lack photo-realism and fine-grained details of the person. First, the topology of SMPL+D is fixed and cannot fully capture the fine geometric details, for example, loose clothing or long hairs. Second, the TextureNet can confuse the texture of the person with shading and may remove some texture details while estimating the albedo texture map. In this section, we present RANA which utilizes the coarse geometry and albedo map and generates higher quality images of the person. We parametrize RANA using the SMPL body model and SH lighting [5]. Specifically, RANA takes the target body pose $\\theta$ and the target lighting in the form of second-order spherical harmonics coefficients $E\\in \\mathbb{R}^{9\\times 3}$ as input and synthesizes the target image $I^{\\theta ,E}$ as:", + "bbox": [ + 75, + 421, + 472, + 633 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nI ^ {\\theta , E} = \\operatorname {R A N A} (\\theta , E, K), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 643, + 468, + 662 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $K$ corresponds to the intrinsic parameters of the target camera viewpoint. One main challenge in learning such a neural avatar from a short RGB video is to maintain the disentanglement of geometry, albedo, and lighting, as any learnable parameters can overfit the training frames disregarding plausible disentanglement. Hence, we design RANA such that a plausible disentanglement is encouraged during training. Specifically, RANA consists of two convolutional neural networks NormalNet, $G_{\\mathrm{N}}$ , and AlbedoNet, $G_{\\mathrm{A}}$ , each responsible for generating the normal map $I_N^\\theta \\in \\mathbb{R}^{h\\times w\\times 3}$ , and albedo map, $I_A^\\theta \\in \\mathbb{R}^{h\\times w\\times 3}$ , of the person in the body pose $\\theta$ , respectively. It also consists of a set of subject-specific latent neural features $Z \\in \\mathbb{R}^{256\\times 256\\times 16}$ in UV coordinates to augment the details available in the coarse albedo map and geometry.", + "bbox": [ + 75, + 674, + 472, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "More specifically, given the target body pose $\\theta$ , we first generate the SMPL+D mesh $\\mathbf{M}^{\\theta} = M(\\theta ,\\beta ,\\mathbf{D})$ , where the shape parameters $\\beta$ and clothing offsets $\\mathbf{D}$ are the ones obtained in Sec. 3.1. We then use $\\mathbf{M}^{\\theta}$ to differentiably rasterize [39] the latent features $Z$ and coarse albedo texture $T_{A}$ to obtain a features image $I_Z^\\theta$ and coarse albedo image $\\bar{I}_A^\\theta$ in the target body pose. We also rasterize a coarse normal image $\\bar{I}_N^\\theta$ and a UV image $I_{\\mathrm{uv}}^\\theta$ using the normals and UV coordinates of $M^{\\theta}$ , respectively. The refined normal image $I_N^\\theta$ and refined albedo image $I_A^\\theta$ are then obtained as", + "bbox": [ + 496, + 90, + 893, + 244 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nI _ {N} ^ {\\theta} = G _ {N} \\left(I _ {Z} ^ {\\theta}, \\bar {I} _ {N} ^ {\\theta}, \\gamma \\left(I _ {\\mathrm {u v}} ^ {\\theta}\\right)\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 253, + 890, + 272 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nI _ {A} ^ {\\theta}, S ^ {\\theta} = G _ {A} \\left(I _ {Z} ^ {\\theta}, \\bar {I} _ {A} ^ {\\theta}, \\gamma \\left(I _ {\\mathrm {u v}} ^ {\\theta}\\right)\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 273, + 890, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $S^{\\theta}$ is the person mask in the target pose and $\\gamma$ corresponds to the positional encoding of the UV coordinates [42]. Given the lighting $E$ , we obtain the shading image $I_S^{\\theta ,E}$ using the normal map $I_N^\\theta$ and SH lighting [49]. Under the usual assumptions of Lambertian material, distant lighting, and no cast shadows, the final shaded image $I^{\\theta ,E}$ is then obtained as", + "bbox": [ + 496, + 306, + 893, + 412 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nI ^ {\\theta , E} = I _ {A} ^ {\\theta} \\cdot I _ {S} ^ {\\theta , E}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 422, + 890, + 444 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "An overview of RANA can be seen in Fig. 1d. Since the lighting environment of the training video is unknown, we also optimize the second order SH coefficients $E \\in \\mathbb{R}^{9 \\times 3}$ [49] of the training video during training. Under the assumption of Lambertian surface, none of the learnable parameters in RANA depend on the lighting information. Hence, if the disentanglement of normals, albedo, and lighting during training is correct, we can simply replace $E$ during inference with any other novel lighting environment to obtain relit images. We train RANA with the following objective:", + "bbox": [ + 496, + 455, + 893, + 621 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\text {p i x e l}} + \\mathcal {L} _ {\\text {f a c e}} + \\mathcal {L} _ {\\text {m a s k}} + \\mathcal {L} _ {\\mathrm {V G G}} + \\mathcal {L} _ {\\mathrm {G A N}} (9) \\\\ + \\mathcal {L} _ {\\text {r e g}} ^ {\\text {a l b e d o}} + \\mathcal {L} _ {\\text {r e g}} ^ {\\text {n o r m a l}}. (10) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 635, + 890, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here $\\mathcal{L}_{\\mathrm{pixel}}$ is the $L_{1}$ difference between the generated image $I^{\\theta ,E}$ and the ground-truth training frame, $\\mathcal{L}_{\\mathrm{face}}$ is the $L_{1}$ difference between their face regions to assign a higher weight to face, and $\\mathcal{L}_{\\mathrm{mask}}$ is the binary-cross-entropy loss between the estimated mask $S^{\\theta}$ using $G_{A}$ and the pseudoground-truth mask obtained using a person segmentation model [15]. The term $\\mathcal{L}_{\\mathrm{VGG}}$ is the $L_{1}$ difference between the VGG features of generated and ground-truth images, and $\\mathcal{L}_{\\mathrm{GAN}}$ is the commonly used GAN loss [44, 21]. The term $\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}$ is the albedo regularization term that prevents the light information from leaking into the albedo image:", + "bbox": [ + 496, + 685, + 893, + 852 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e g}} ^ {\\text {a l b e d o}} = \\left\\| \\sigma \\left(I _ {A} ^ {\\theta}, k\\right) - \\sigma \\left(\\bar {I} _ {A} ^ {\\theta}, k\\right) \\right\\| ^ {2}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 877, + 890, + 897 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23146", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c2f24a0159874b9ae2a58729b566599659eb8b636a50522ac04db4b3401ffb65.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 88, + 220, + 193 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6e41b09266594a0b8b6b12638a7666f5dd6d3e00e3b0ff70473a95b211bee87d.jpg", + "image_caption": [ + "Noisy/Shaded Map", + "Figure 2. Examples of estimated albedo maps from noisy/shaded maps using our proposed TextureNet (Sec. 3.2). The first row shows some examples from the PeopleSnapshot dataset, while the second row shows examples from our proposed RelightingHuman dataset." + ], + "image_footnote": [], + "bbox": [ + 83, + 193, + 220, + 297 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/055247530e13fc6d0dc3d854374e36ded2aeaf7bccb65764af852d7946cfdf04.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 222, + 88, + 357, + 193 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/63d621b540f06b20fb35a89369ba5efd88746bdb622d86219067d791c667cb59.jpg", + "image_caption": [ + "Albedo Map" + ], + "image_footnote": [], + "bbox": [ + 222, + 193, + 357, + 297 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5119f216f8d9e8f43b0e81d0d1fda922db0a0a1c2e28c9fa9be4e1cd6353c3aa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 357, + 88, + 493, + 193 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bd7bd53f2f5775756af0125fa876f7b856fa42ea0e6260f0c22333c6e937daa9.jpg", + "image_caption": [ + "Noisy/Shaded Map" + ], + "image_footnote": [], + "bbox": [ + 357, + 193, + 493, + 297 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/15c4991232efedd962a0442cd52eebee90787652acc56af2835370bee6baa993.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 493, + 88, + 630, + 193 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9ccb0a5077ea2ffbe05f52a0a1ba053c2986292898fe11797b6a6ac7e36ad770.jpg", + "image_caption": [ + "Albedo Map" + ], + "image_footnote": [], + "bbox": [ + 495, + 193, + 630, + 297 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3c6112f873765621cf85e22fd18bc8028dff89ef19a5e5c525b5d375950bc742.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 88, + 767, + 193 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/82448cb60edc22eb190a97b23b41de96cee8906167a9df921f83e388f7ec5c39.jpg", + "image_caption": [ + "Noisy/Shaded Map" + ], + "image_footnote": [], + "bbox": [ + 630, + 193, + 767, + 297 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7805893d83b08097445ebad887c8d01ce9a0a76bc9904f4164fe40ddc8d15cfa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 767, + 88, + 903, + 193 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/31c8336c8bf966697e0a8f06df560be3284554ee628f2e37cd8140ed70172bfe.jpg", + "image_caption": [ + "Albedo Map" + ], + "image_footnote": [], + "bbox": [ + 767, + 193, + 903, + 297 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here $I_A^\\theta$ is the albedo image obtained using $G_{A}$ , $\\bar{I}_A^\\theta$ is the coarse albedo image, and $\\sigma$ is the Gaussian smoothing operator with a kernel size $k = 51$ . $\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}$ encourages the overall color information in $I_A^\\theta$ to be close to $\\bar{I}_A^\\theta$ while disregarding the texture information. Similarly, $\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{normal}}$ is the normal regularization loss which prevents the normal image $I_N^\\theta$ to move very far from the coarse normal image $\\bar{I}_N^\\theta$ :", + "bbox": [ + 75, + 358, + 468, + 470 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e g}} ^ {\\text {n o r m a l}} = \\left| S _ {\\text {s m p l}} ^ {\\theta} I _ {N} ^ {\\theta} - S _ {\\text {s m p l}} ^ {\\theta} \\bar {I} _ {N} ^ {\\theta} \\right|, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 479, + 468, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $S_{\\mathrm{mpl}}^{\\theta}$ is the rasterized mask of SMPL+D mesh. It ensures that the regularization is applied only on the pixels where SMPL+D normals are valid. Note that no ground-truth supervision is provided to $G_{A}$ and $G_{N}$ . They are mostly learned via the image reconstruction losses, while the disentanglement of normals and albedo is ensured via the novel design of RANA and regularization losses. For $\\mathcal{L}_{\\mathrm{face}}$ , we project the nose keypoint of SMPL body model on to the image and crop a $100 \\times 100$ patch around the face to compute the loss. All other losses are calculated on the $512 \\times 512$ generated images.", + "bbox": [ + 75, + 510, + 468, + 676 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3.1 Pre-training using synthetic data", + "text_level": 1, + "bbox": [ + 76, + 695, + 359, + 710 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "While we design RANA such that it generalizes well to novel body poses, the networks $G_{A}$ and $G_{N}$ may still overfit to the body poses available in the training video, in particular, when the coarse geometry and albedo are noisy. A significant advantage of RANA is that it can be trained simultaneously for multiple subjects, i.e., we use different neural features $Z$ for each subject while sharing the networks $G_{A}$ and $G_{N}$ . This not only allows the model to see diverse body poses during pre-training but also helps in learning to disentangle normals and albedo. Hence, we propose to pretrain $G_{A}$ and $G_{N}$ on synthetic data. For this, we use 400 rigged characters from the RenderPeople dataset. We", + "bbox": [ + 75, + 719, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "generated 150 albedo and normal images for each subject under random body poses and pretrain both networks using ground-truth albedo and normal images. We use the $L_{1}$ loss for both terms.", + "bbox": [ + 496, + 359, + 890, + 419 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3.2 Personalization.", + "text_level": 1, + "bbox": [ + 500, + 440, + 665, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "After pre-training, given the RGB video of a novel subject, we optimize the latent features $Z$ and lighting environment $E$ of the video from scratch and only fine-tune AlbedoNet $(G_{A})$ . During our experiments, we found that fine-tuning $G_{N}$ is not required if the model is pretrained (see Sec. 4.3). We keep $G_{A}$ fixed for the first 1000 iterations and only optimize $Z$ and $E$ . This allows optimization of the latent features $Z$ to be compatible with the pretrained $G_{A}$ and $G_{N}$ . We then optimize $G_{A}, Z$ , and $E$ jointly for a total of 15k iterations. Note that, while we do pre-training on synthetic data, RANA does not suffer from domain gap because the neural texture is learned from scratch and AlbedoNet is finetuned for every video. Similar to TextureNet, we use vanilla U-Net for AlbedoNet and NormalNet. For training, we use Adam optimizer with a batch size of 16 and learning rate of $1e^{-4}$ with cosine annealing and minimum learning rate of $1e^{-5}$ .", + "bbox": [ + 496, + 464, + 890, + 719 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 734, + 632, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we evaluate the performance of RANA using two different datasets. We perform an ablation study to validate our design choices and also compare our method with state-of-the-art and other baselines.", + "bbox": [ + 496, + 761, + 890, + 820 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 830, + 601, + 845 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Relighting Human Dataset. We propose a new photorealistic synthetic dataset to quantitatively evaluate the performance of our method. We use 49 rigged characters from the", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23147", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a93d65b5e46cb059b9b57906da1a63a85947d93d31be5eb2b24be2fe16d10eac.jpg", + "image_caption": [ + "(a) Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 86, + 87, + 220, + 255 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/acc6e5fce361c26d8efba36ea6f39ba9c3f6b9a6197ab86daa0d3158a45cc070.jpg", + "image_caption": [ + "(b) Full Model" + ], + "image_footnote": [], + "bbox": [ + 220, + 88, + 377, + 255 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fed8e3fab599ccb73be828533c295102384577335d17b418b79f04d2497e8d11.jpg", + "image_caption": [ + "(c) w/o $\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}$", + "Figure 3. Ablation Study. Impact of the different components of the proposed approach. Our full model yields the best results. Without the $\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}$ loss, the light information leaks into the albedo texture resulting in incorrect illumination. If we do not use coarse geometry and albedo texture, the resulting model does not generalize well to novel body poses. Similarly, training the model from scratch, without any pretraining on synthetic data, can result in an incorrect disentanglement of texture and geometry." + ], + "image_footnote": [], + "bbox": [ + 385, + 88, + 537, + 255 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7ab6f54d82aa64c4787ef3caa15351835dd55a660adc3be6a1444799372238a0.jpg", + "image_caption": [ + "(d) w/o coarse geo. & tex." + ], + "image_footnote": [], + "bbox": [ + 555, + 88, + 720, + 255 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4f9865814d21d22eb5bd232e27371d7f133e34add7d392fb958156ecd7eb4c14.jpg", + "image_caption": [ + "(e) w/o pre-training" + ], + "image_footnote": [], + "bbox": [ + 725, + 88, + 875, + 255 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/33eb1d1ae78a332b0dc4ffa2a8f0ec7a290a0baa2bc89d67b331f49ea4dda5cb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodImageNormal MapAlbedo Map
LPIPS ↓DISTS ↓SSIM ↑PSNR ↑Degree° ↓LPIPS ↓DISTS ↓SSIM ↑PSNR ↑
Full model0.2170.2040.75119.49864.3500.2190.2070.77921.832
w/o Lalbedo0.2490.2410.69715.19964.0640.2640.2570.71315.688
w/o coarse geo. & tex.0.2420.2220.73018.58065.8870.2600.2320.75120.778
w/o pre-training0.3010.2930.66913.79874.2150.3270.3070.69615.632
fine-tune GN0.2190.2050.74619.19864.2260.2210.2100.77821.577
", + "bbox": [ + 81, + 344, + 890, + 460 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Ablation study. We evaluate the impact of different components of the proposed method. See Fig. 3 for a qualitative comparison.", + "bbox": [ + 76, + 462, + 888, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "RenderPeople dataset [2] to generate photo-realistic images for each subject. We use HDRI maps from PolyHaven [1] to illuminate the characters and use the CMU motion capture dataset [3] to pose the characters. In contrast to our proposed method that uses image-based lighting, we use full Path Tracing to generate the dataset. Hence, it is the closest setting to an in-the-wild video, and any future work that uses a more sophisticated lighting model can be evaluated on this dataset. For a fair evaluation, we ensure that none of the characters is used during the training in Sec 3.2 and Sec 3.3. All testing images come with a ground-truth albedo map, a normal map, a segmentation mask, and light information. For our experiments, we evaluate on all 49 characters and train a separate RANA model for each subject. We develop three different protocols for evaluation:", + "bbox": [ + 75, + 500, + 467, + 724 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "a) Novel Pose and Light Synthesis This protocol evaluates the quality in terms of novel pose and light synthesis. We generate 100 training images for each subject rotating $360^{\\circ}$ with A-posed in front of the camera with fixed lighting. It mimics the self-rotating videos commonly used for training. For testing, we generate 150 frames for each subject with random body pose and light in each frame.", + "b) Arbitrary Pose Training To represent in-the-wild scenarios, we generate 100 training images for each subject with arbitrary poses in fixed lighting. For testing, we generate 50 frames for each subject with random unseen body" + ], + "bbox": [ + 75, + 726, + 467, + 892 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "pose and random light in each frame.", + "bbox": [ + 498, + 500, + 746, + 515 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "c) Novel Light Synthesis. This protocol evaluates the relighting ability of the methods. We generate 150 frames for train and test sets. The train set is generated with fixed lighting and random body poses. The body poses in the test set are exactly the same as the train sets, but each frame is generated using a different light source.", + "bbox": [ + 498, + 515, + 890, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "People Snapshot Dataset. [5]. This dataset consists of real videos of characters rotating in front of the camera. We use this dataset for qualitative evaluation.", + "bbox": [ + 498, + 606, + 890, + 651 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Metrics", + "text_level": 1, + "bbox": [ + 500, + 661, + 594, + 676 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We report several metrics to evaluate the quality of synthesized images as well as the disentanglement of normal and albedo images. For synthesized images and albedo maps, we use Learned Perceptual Patch Similarity (LPIPS $\\downarrow$ ) [68], Deep Image Structure and Texture Similarity (DISTS $\\downarrow$ ) [19], Structural Similarity Index (SSIM $\\uparrow$ ) [60] and Peak Signal-to-Noise Ratio (PSNR $\\uparrow$ ). For normals, we compute the error in degrees ( $^\\circ$ ).", + "bbox": [ + 496, + 685, + 890, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation study", + "text_level": 1, + "bbox": [ + 500, + 816, + 648, + 832 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate different design choices of RANA in Tab. 2 and Fig 3. We use protocol-a of the Relighting Human dataset for all experiments. We first report the results of the final model which includes all loss terms in (10)", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23148", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ebc4335a79f665668895000b173da109a8eaaabd9a2088aaf8262724e79e9d01.jpg", + "image_caption": [ + "Reference", + "RANA (Ours)", + "ANR[47]+RH[33]", + "SMPL+D", + "Relighting4D [16]", + "RANA (Ours)", + "Relighting4D [16]", + "Figure 4. Comparison with the baselines and state-of-the-art methods. Column 1 shows a reference frame with the target body pose and lighting in the insets. In the absence of true reference images, for the Snapshot dataset (rows 1-2), we show training frames for reference. Columns 2-5 compare different methods for protocol-a, while columns 6-7 provide a comparison for protocol-b." + ], + "image_footnote": [], + "bbox": [ + 89, + 85, + 890, + 452 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/134ecc9dfaebb4d7936095739ac5beb35bf565b6c09829a0ebf3a256e417b7c1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodImageNormal MapAlbedo Map
LPIPS ↓DISTS ↓SSIM ↑PSNR ↑Degree° ↓LPIPS ↓DISTS ↓SSIM ↑PSNR ↑
Protocol (a): Novel Pose and Light Synthesis
ANR [47] + RH [33]0.2750.4160.66417.495N.A.0.2660.4290.65614.804
Relightable SMPL+D0.2650.2250.75119.67864.1210.2160.1820.81122.623
RANA (Ours)0.2170.2040.75119.49864.3500.2190.2070.77921.832
Protocol (b): Arbitrary Pose Training
Relightable SMPL+D0.2590.2220.76119.98863.7560.2100.1800.82323.052
RANA (Ours)0.1930.1830.79320.69363.4090.2260.1940.82522.935
Protocol (c): Novel Light Synthesis
Relighting Humans [33]0.2260.3530.66821.205-----
Relighting4D [16]0.1920.3420.65421.08065.0990.2630.3740.59320.014
RANA (Ours)0.1730.1710.84222.33862.8230.2000.1790.86524.721
", + "bbox": [ + 81, + 518, + 890, + 743 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Comparison with the baselines and state-of-the-art methods. See Fig. 4 for qualitative comparison.", + "bbox": [ + 165, + 743, + 797, + 755 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and pretraining using synthetic data (Sec. 3.3.1). The full model achieves an LPIPS score of 0.217 for image synthesis and 0.219 for albedo map reconstruction. If we remove the loss term $\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}$ from (10), the LPIPS scores for image and albedo map reconstruction increase to 0.249 and 0.264, respectively. Note that the error for albedo maps increases significantly while the error for normal maps re", + "bbox": [ + 75, + 781, + 468, + 887 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "mains roughly the same. This indicates that without $\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}$ the light information leaks into the albedo image. An example of this behavior can also be seen in Fig 3c (w/o $\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}$ ).", + "bbox": [ + 498, + 780, + 890, + 829 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Next, we evaluate the impact of coarse geometry and albedo texture on RANA. If we do not use coarse geometry and albedo, LPIPS score increases to 0.242 as compared to 0.217 for the full model. The normal error also increases", + "bbox": [ + 498, + 840, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23149", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "to $65.9^{\\circ}$ from $64.3^{\\circ}$ . This is also evident from the qualitative results shown in Fig 3d, indicating that coarse geometry and albedo help in improved image synthesis quality, in particular when the target body pose is far from the training poses. Next, we evaluate the impact of pretraining on synthetic data. Without the pretraining, all error metrics increase significantly. Specifically, the LPIPS score for image reconstruction increases from 0.217 to 0.301, while the normal error increases from $64.3^{\\circ}$ to $74.2^{\\circ}$ . If we look at Fig 3e, we can see that shading information leaks into both the normals and albedo maps. Hence, pretraining the networks also helps with the plausible disentanglement of geometry, texture, and light. Thanks to the design of RANA, we can pretrain on as many subjects as available, which is not possible with most of the state-of-the-art methods for human synthesis [45, 46, 58, 31]. Finally, as discussed in Sec 3.3.1, we keep the network $G_{N}$ fixed during finetuning if RANA is pretrained on synthetic data. In the last row of Tab. 2, we evaluate the case when $G_{N}$ is also fine-tuned. We can see that it has a negligible impact on the results.", + "bbox": [ + 76, + 90, + 472, + 393 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.4. Comparison with other methods", + "text_level": 1, + "bbox": [ + 76, + 406, + 361, + 422 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Since ours is the first work that simultaneously evaluates novel light and pose synthesis, we ourselves build some baselines as follows:", + "bbox": [ + 76, + 431, + 468, + 474 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Relightable SMPL+D: We rasterize the SMPL+D mesh normals and albedo texture estimated using TextureNet in the target body pose and use SH lighting to generate the shaded images.", + "bbox": [ + 76, + 491, + 468, + 551 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "ANR [47]+RH[33]: We train an ANR [47] model which synthesizes images in the lighting of the training video. We then pass the generated images to the single-image human relighting method Relighting Humans (RH) [33] to obtain the relighted images for the target light. We use the publicly available source code and models of [33].", + "bbox": [ + 76, + 551, + 468, + 643 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Relighting4D [16] is a state-of-the-art human video relighting method. We use the publicly available source code and train it on our dataset.", + "bbox": [ + 76, + 642, + 468, + 686 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The results are summarized in Tab. 3 and Fig 4. We do not report results of Relighting4D [16] for protocol-a since it cannot handle novel body poses as can be seen in Fig 4 (column-5). For protocol-a, our method clearly outperforms other baselines for final image synthesis results. Surprisingly, the SMPL+D baseline yields better numbers for albedo reconstruction, even though it provides overly smooth albedo textures. This is because TextureNet is trained on synthetic data, hence albedo maps in SMPL+D baseline achieve the best result in this synthetic data benchmark. However, the SMPL+D baseline does not produce the best image quality. RANA, on the other hand, achieves significantly better image quality while staying close to the", + "bbox": [ + 76, + 704, + 468, + 901 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "unlit texture in SMPL+D.", + "bbox": [ + 500, + 90, + 671, + 104 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "For protocol-b, we only compare the best two methods from protocol-a as we found it unnecessary to retrain ANR based on the results of protocol-a. As we can see in Tab. 3, the results are consistent with protocol-a.", + "bbox": [ + 498, + 111, + 890, + 172 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "For protocol-c, we compare with a video-based relighting method Relighting4D [16] and the single-image-based relighting method Relighting Humans [33]. RANA outperforms both methods across all metrics. Some qualitative comparisons with Relighting4D [16] can be seen in Fig. 4 (columns 6-7), where RANA clearly yields better image relighting results. Note that each model for Relighting4D [16] requires $260\\mathrm{k}$ iterations for training whereas RANA models are trained only for $15\\mathrm{k}$ iterations, thanks to our novel design that allows pre-training on synthetic data, allowing quick fine-tuning for new subjects. In contrast, Relighting4D [16] by design cannot be pretrained easily on multiple subjects. On the other hand, the method [33] is trained for up-right frontal poses only and cannot handle arbitrary body poses, resulting in inferior relighting performance. This is also the main reason behind the inferior performance of the ANR $[47] + \\mathrm{RH}$ [33] baseline for protocol-a.", + "bbox": [ + 496, + 178, + 892, + 435 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Finally, we provide additional qualitative results of avatars animated with complex motions in the supp. video.", + "bbox": [ + 500, + 440, + 893, + 470 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion and Future Work", + "text_level": 1, + "bbox": [ + 500, + 501, + 769, + 517 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We presented RANA which is a novel framework for learning reconfigurable and articulated neural avatars of humans. We demonstrated that RANA can model humans from unconstrained RGB videos while also disentangling their geometry, albedo texture, and environmental lighting. We showed that it can generate high-quality images of people under any novel body pose, viewpoint, and lighting. RANA can be trained simultaneously for multiple people and we showed that pre-training it on multiple (400) synthetic characters significantly improves the image synthesis quality. We also proposed a new photo-realistic synthetic dataset (Relighting Human) to quantitatively evaluate the performance of our proposed method, and believe that it will prove to be very useful to further the research in this direction.", + "bbox": [ + 496, + 532, + 890, + 758 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The most pressing limitation of RANA is the assumption of Lambertian surface, no cast shadows, and image-based lighting. In the future, we hope to incorporate more sophisticated physically-based rendering in our framework which will hopefully result in better image quality, self-shadowing and normal maps with more details. Moreover, RANA does not explicitly model motion-dependent clothing deformations. 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Neu" + ], + "bbox": [ + 78, + 90, + 468, + 271 + ], + "page_idx": 11 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "ral light transport for relighting and view synthesis. SIGGRAPH, 2021. 3", + "[70] Hao Zhao, Jinsong Zhang, Yu-Kun Lai, Zerong Zheng, Yingdi Xie, Yebin Liu, and Kun Li. High-fidelity human avatars from a single rgb camera. In CVPR, 2022. 3", + "[71] Tiancheng Zhi, Christoph Lassner, Tony Tung, Carsten Stoll, Srinivasa G Narasimhan, and Minh Vo. Texmesh: Reconstructing detailed human texture and geometry from rgb-video. In ECCV, 2020. 2, 3", + "[72] Hao Zhou, Sunil Hadap, Kalyan Sunkavalli, and David W. Jacobs. Deep single portrait image relighting. In ICCV, 2019. 3" + ], + "bbox": [ + 501, + 92, + 890, + 260 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "23153", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/RANA_ Relightable Articulated Neural Avatars/ae3b789d-a192-4696-b97f-daa6528a52ba_model.json b/2023/RANA_ Relightable Articulated Neural Avatars/ae3b789d-a192-4696-b97f-daa6528a52ba_model.json new file mode 100644 index 0000000000000000000000000000000000000000..6b04a0a5b36bd76162fb46d8ed0b03c49a7b0465 --- /dev/null +++ b/2023/RANA_ Relightable Articulated Neural Avatars/ae3b789d-a192-4696-b97f-daa6528a52ba_model.json @@ -0,0 +1,2897 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.245, + 0.112, + 0.726, + 0.134 + ], + "angle": 0, + "content": "RANA: Relightable Articulated Neural Avatars" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.154, + 0.91, + 0.21 + ], + "angle": 0, + "content": "Umar Iqbal\\(^{1*}\\) Akin Caliskan\\(^{2*}\\) Koki Nagano\\(^{1}\\) Sameh Khamis\\(^{1}\\) Pavlo Molchanov\\(^{1}\\) Jan Kautz\\(^{1}\\) \n\\(^{1}\\)NVIDIA \\({}^{2}\\)Flawless AI https://nvlabs.github.io/RANA/" + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.242, + 0.252, + 0.602 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.253, + 0.242, + 0.413, + 0.602 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.414, + 0.242, + 0.574, + 0.602 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.574, + 0.242, + 0.734, + 0.602 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.734, + 0.242, + 0.895, + 0.602 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.602, + 0.895, + 0.663 + ], + "angle": 0, + "content": "We present, RANA, an approach for learning dynamic and relightable full-body avatars from monocular RGB videos. A training frame of the person is shown in the first column. RANA can synthesize images of the person under novel poses, viewpoints, and lighting environments. In the insets, we show the synthesized albedo image, the normal map, and the target HDRI light map." + }, + { + "type": "title", + "bbox": [ + 0.238, + 0.661, + 0.317, + 0.677 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.694, + 0.472, + 0.862 + ], + "angle": 0, + "content": "We propose RANA, a relightable and articulated neural avatar for the synthesis of humans under arbitrary viewpoints, body poses, and lighting. We only require a short video clip of the person to create the avatar and assume no knowledge about the lighting environment. We present a novel framework to model humans while disentangling their geometry, texture, and lighting environment from monocular RGB videos. To simplify this otherwise ill-posed task we first estimate the coarse geometry and texture of the person via SMPL+D model fitting and then learn an articulated neural representation for higher quality image syn" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.663, + 0.895, + 0.816 + ], + "angle": 0, + "content": "thesis. RANA first generates the normal and albedo maps of the person in any given target body pose and then uses spherical harmonics lighting to generate the shaded image in the target lighting environment. We also propose to pre-train RANA using synthetic images and demonstrate that it leads to better disentanglement between geometry and texture while also improving robustness to novel body poses. Finally, we also present a new photo-realistic synthetic dataset, Relighting Human, to quantitatively evaluate the performance of the proposed approach." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.845, + 0.633, + 0.86 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Articulated neural avatars of humans have numerous applications across telepresence, animation, and visual con" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.47, + 0.9 + ], + "angle": 0, + "content": "*equal contribution. The work was partially done during AC's internship at NVIDIA." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23142" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.333 + ], + "angle": 0, + "content": "tent creation. To enable the widespread adoption of these neural avatars, they should be easy to generate and animate under novel poses and viewpoints, able to render in photorealistic image quality, and easy to relight in novel environments. Existing methods commonly aim to learn such neural avatars using monocular videos [47, 46, 45, 54, 66, 58, 31]. While this allows photo-realistic image quality and animation, the synthesized images are always limited to the lighting environment of the training video. Other works directly tackle relighting of human avatars but do not provide control over the body pose [23, 41]. Moreover, these approaches often require multiview images recorded in a Light Stage for training, which is limited to controlled settings only. Some recent methods aim to relight RGB videos of a dynamic human but do not provide control over body pose [16]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.338, + 0.473, + 0.459 + ], + "angle": 0, + "content": "In this work, we present the Relightable Articulated Neural Avatar (RANA) method, which allows animation of people under any novel body pose, viewpoint, and lighting environment. To create an avatar, we only require a short monocular video clip of the person in unconstrained environment, clothing, and arbitrary body pose. During inference, we only require the target body pose and target lighting information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.464, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Learning relightable neural avatars of dynamics humans from monocular RGB videos recorded in unknown environments is a challenging problem. First, it requires modeling the complex human body articulations and geometry. Second, in order to allow relighting under novel environments, the texture, geometry, and illumination information have to be disentangled, which is an ill-posed problem to solve from RGB videos [8]. To address these challenges, we first extract canonical coarse geometry and texture information from the training frames using a statistical human shape model SMPL+D [40, 5, 36]. We then propose a novel convolutional neural network that is trained on synthetic data to remove the shading information from the coarse texture. We augment the coarse geometry and texture with learnable latent features and pass them to our proposed neural avatar framework, which generates refined normal and albedo maps of the person under the target body pose using two separate convolutional networks. Given the normal map, albedo map, and lighting information, we generate the final shaded image using spherical harmonics (SH) lighting [49]. During training, since the environment lighting is unknown, we jointly optimize it together with the person's appearance and propose novel regularization terms to prevent the leaking of lighting into the albedo texture. We also propose to pre-train the avatar using photo-realistic synthetic data with ground-truth albedo and normal maps. During pretraining, we train a single model for multiple subjects while having separate neural features for each subject. This not only improves the generalizability of the neural avatar" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "to novel body poses but also learns to decouple the texture and geometry information. For a new subject, we only learn a new set of neural features and fine-tune the avatar model to capture fine-grained person-specific details. In our experiments, the avatar for a novel subject can be learned within 15k training iterations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.183, + 0.895, + 0.288 + ], + "angle": 0, + "content": "Since no dataset exists to evaluate the renderings of avatars in terms of both novel light and pose synthesis, we also propose a novel photo-realistic synthetic Relighting Human Dataset (RHD) with ground truth albedo, normals, and lighting information. We also perform a qualitative evaluation of RANA on the People Snapshot dataset [5] to compare with other baselines." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.29, + 0.845, + 0.305 + ], + "angle": 0, + "content": "Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.317, + 0.892, + 0.393 + ], + "angle": 0, + "content": "- We present, RANA, a novel framework for learning relightable articulated neural avatars from short unconstrained monocular videos. The proposed approach is very easy to train and does not require any knowledge about the environment lighting of the training video." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.4, + 0.892, + 0.46 + ], + "angle": 0, + "content": "- Our proposed approach can synthesize images of articulated humans under any arbitrary body pose, viewpoint, and lighting. It can also be used for relighting videos of dynamic humans." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.467, + 0.892, + 0.511 + ], + "angle": 0, + "content": "- We present a new photo-realistic synthetic dataset for quantitative evaluation and to further the research in this direction." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.317, + 0.892, + 0.511 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.528, + 0.638, + 0.543 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Mesh Based Human Avatars. These methods represent human avatars using a rigged mesh and an associated texture map. Earlier methods captured human avatars using multi-view cameras [12, 53] or with the help of depth sensors [9, 71]. However, their adoption remained limited due to the constrained hardware requirements. The recent works, therefore, focus on creating the avatars from monocular videos [5, 4, 31, 10], or images [36, 64, 27, 25, 6, 10, 11]. The methods [5, 4, 36] use body model fitting to capture the humans, while more recent methods use data-driven implicit functions combined with pixel-aligned features [50] for human reconstruction [71, 27, 64, 6]. Self-Recon [31] combines both explicit and implicit meshes to reconstruct the detailed geometry of the person from self-rotating videos, however, it requires manual human effort to make the avatar animatable. The main limitation of these methods, however, is that the shading information is baked into the texture. Hence, the avatars cannot be rendered with novel lights. The recent methods PHORUM [6] and S3F [17] are the only exceptions, however, they create avatar from a single image and rely on data-driven priors to hallucinate the occluded regions of the person. Hence, the generated images may not be the true representation of the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23143" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.09, + 0.454, + 0.22 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.222, + 0.47, + 0.263 + ], + "angle": 0, + "content": "Table 1. Comparison of some of the representative methods for neural human avatar creation. Ours (RANA) is the only method that allows novel view, pose and light synthesis." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.288, + 0.471, + 0.334 + ], + "angle": 0, + "content": "person. In contrast, our approach uses video data to capture a detailed human representation, while also allowing the rendering of the person in novel lighting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.473, + 0.71 + ], + "angle": 0, + "content": "Neural Human Avatars. More recent methods learn a neural representation of the person and use neural renderers [57] to directly generate photo-realistic images in the target body pose and viewpoints [7, 20, 13, 59, 26, 63]. These methods are generally classified into 2D or 3D neural rendering based methods [57]. The 3D neural rendering methods represent the person using neural radiance fields [42] and render the target images using volume rendering [46, 62, 32, 45, 14, 58, 24, 38]. The 2D neural rendering methods, on the other hand, use CNNs to render the images [47, 66, 22, 70]. One limitation of the 3D neural rendering methods is that the avatar has to be created from scratch for each person. Some methods learn generalizable avatars but require exemplar images of the person during inference [34, 48]. In contrast, the 2D based methods offer some generalizability by sharing the neural renderer across multiple subjects [47]. Our method falls into the 2D neural rendering paradigm as we use CNNs to generate the albedo and normal images of the person. In particular, we take inspiration from ANR [47] for designing our framework. Tab. 1 compares existing neural avatar creation methods. Ours is the only method that allows synthesis under novel poses, viewpoints, and lighting, while also being generalizable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Human Relighting. Relighting of human images has been studied extensively in the literature [18, 51, 33, 55, 72, 61, 56, 30, 37, 35, 69, 17]. However, these methods cannot render relighted images in novel body poses and viewpoints. Some recent methods allow relighting from novel views but provide no control over the body pose [23, 43, 16, 65]. The method TexMesh [71] also provides control over body pose but requires RGB-D videos for training and assumes that the environment map of the training video is known. Our approach, in contrast, provides full control over the body pose, viewpoint, and lighting, and learns the avatar from RGB videos with unknown lighting." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.593, + 0.107 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.116, + 0.895, + 0.525 + ], + "angle": 0, + "content": "Our goal is to learn a relightable articulated neural avatar, RANA, that can synthesize high-quality images of the person under any target body pose, viewpoint, and lighting. To create the avatar, we use a small video sequence \\(\\mathbf{I} = \\{I_{\\mathrm{f}}\\}_{f = 1}^{F}\\) with \\(F\\) video frames and assume no knowledge about the lighting environment and body poses present in the video. We parameterize RANA using the SMPL [40] body model to control the animation and use Spherical Harmonics (SH) [49] lighting to model the lighting. During inference, we only need the target body pose and target lighting information in the form of SH coefficients and do not require any exemplar images for ground-truth. Learning RANA from a monocular video requires capturing the geometry and appearance of the dynamic human while also disentangling the shading information. In order to tackle this ill-posed problem, we first capture the coarse geometry using the SMPL+D fits (Sec. 3.1). We use the coarse geometry to extract a coarse texture map from the training images which is converted to an albedo texture map using a convolutional network (Sec. 3.2). We then propose RANA that generates the refined albedo and normal maps. The refined normal maps are used to obtain the shading map using SH lighting which is combined with the refined albedo map to obtain the final image in the target body pose and light (Sec. 3.3). An overview of our method can be seen in Fig. 1. In the following, we describe each of these modules in greater detail." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.536, + 0.762, + 0.552 + ], + "angle": 0, + "content": "3.1. Coarse Geometry Estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.56, + 0.895, + 0.756 + ], + "angle": 0, + "content": "Given the training frames, we first estimate the coarse geometry of the person including the clothing and hair details. For this, we employ the SMPL+D [4, 36] variant of the SMPL body model [40]. SMPL is a linear function \\( M(\\theta, \\beta) \\) that takes the body pose \\( \\theta \\in \\mathbb{R}^{72} \\) and shape parameters \\( \\beta \\in \\mathbb{R}^{10} \\) as input and produces a triangulated mesh \\( \\mathbf{M} \\in \\mathbb{R}^{V \\times 3} \\) with \\( V = 6890 \\) vertices. SMPL only captures the undressed shape of the body and ignores the clothing and hair details. For this, SMPL+D adds a set of 3D offsets \\( \\mathbf{D} \\in \\mathbf{R}^{V \\times 3} \\) to SMPL to capture the additional geometric details, i.e., \\( M(\\theta, \\beta, \\mathbf{D}) \\in \\mathbb{R}^{V \\times 3} \\) can also model clothed humans. We refer the readers to [36, 4] for a detailed description of SMPL+D." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.757, + 0.895, + 0.849 + ], + "angle": 0, + "content": "For fitting SMPL+D to training images, we first estimate the parameters of SMPL using an off-the-shelf method SMPLify3D [29]. Since the person in the video remains the same, we optimize a single \\(\\beta\\) for the entire video. We then fix the pose \\(\\{\\theta\\}_{f=1}^{F}\\) and shape \\(\\beta\\) parameters and optimize for the offsets \\(\\mathbf{D}\\) using the following objective:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.861, + 0.895, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathbf {D} = \\underset {\\mathbf {D} ^ {\\prime}} {\\operatorname {a r g m i n}} \\sum_ {f = 1} ^ {F} \\mathcal {L} \\left(M \\left(\\theta_ {f}, \\beta , \\mathbf {D} ^ {\\prime}\\right)\\right) = \\mathcal {L} _ {\\mathrm {S i l}} + \\mathcal {L} _ {\\mathrm {s m o o t h}}. (1)\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23144" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.156, + 0.089, + 0.269, + 0.102 + ], + "angle": 0, + "content": "(a) Training frames" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.106, + 0.167, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.169, + 0.106, + 0.255, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.257, + 0.106, + 0.343, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.361, + 0.089, + 0.616, + 0.102 + ], + "angle": 0, + "content": "(b) Coarse Geometry Estimation (Sec. 3.1)" + }, + { + "type": "image", + "bbox": [ + 0.361, + 0.106, + 0.448, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.452, + 0.106, + 0.538, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.106, + 0.627, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.662, + 0.089, + 0.882, + 0.102 + ], + "angle": 0, + "content": "(c) Coarse Texture Estimation (Sec 3.2)" + }, + { + "type": "image", + "bbox": [ + 0.645, + 0.106, + 0.732, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.738, + 0.108, + 0.801, + 0.12 + ], + "angle": 0, + "content": "TextureNet" + }, + { + "type": "image", + "bbox": [ + 0.738, + 0.121, + 0.805, + 0.131 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.132, + 0.805, + 0.141 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.142, + 0.805, + 0.152 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.807, + 0.133, + 0.836, + 0.142 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.807, + 0.143, + 0.836, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.807, + 0.153, + 0.836, + 0.161 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.836, + 0.133, + 0.893, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.32, + 0.185, + 0.654, + 0.199 + ], + "angle": 0, + "content": "(d) RANA: Relightable Articulated Neural Avatar (Sec 3.3)" + }, + { + "type": "image_caption", + "bbox": [ + 0.086, + 0.197, + 0.21, + 0.208 + ], + "angle": 0, + "content": "Latent Neural Features" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.209, + 0.88, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.416, + 0.894, + 0.501 + ], + "angle": 0, + "content": "Figure 1. Overview of the proposed approach. (a) shows some training frames. (b) We estimate the coarse geometry of the person using the SMPL+D body model. (c) The SMPL+D fits are used to extract a UV texture map, which we process using TextureNet to obtain a coarse albedo texture map. (d) Given a target body pose, we rasterize person-specific neural features, coarse albedo, and coarse normals from SMPL+D to the target body pose and pass them to NormalNet and AlbedoNet to obtain refined normal and albedo maps, respectively. We then use the normal map and spherical harmonics lighting to obtain the shading image, which is multiplied with refined albedo to produce the shaded image. AlbedoNet also generates a binary mask, which we use to overlay the shaded image onto the background." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.525, + 0.47, + 0.603 + ], + "angle": 0, + "content": "Here the term \\(\\mathcal{L}_{\\mathrm{Sil}}\\) is the silhouette loss. We obtain the silhouette of SMPL+D vertices \\(S_{f}\\) for frame \\(f\\) using a differentiable renderer [39] while the target silhouette \\(\\hat{S}_t\\) is obtained using a person segmentation model [15]. We define the \\(\\mathcal{L}_{\\mathrm{Sil}}\\) loss as" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.609, + 0.47, + 0.652 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {S i l}} = \\frac {1}{F} \\sum_ {f = 1} ^ {F} \\left| S _ {f} - \\hat {S} _ {f} \\right|. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.66, + 0.47, + 0.69 + ], + "angle": 0, + "content": "The term \\(\\mathcal{L}_{\\mathrm{smooth}}\\) is a laplacian smoothing term to encourage the smooth surface of the mesh:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.698, + 0.47, + 0.741 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s m o o t h}} = \\frac {1}{F} \\sum_ {f = 1} ^ {F} | | L \\mathbf {M} _ {f} | |, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.749, + 0.47, + 0.81 + ], + "angle": 0, + "content": "where \\( L \\) is the mesh Laplacian operator. Note that we optimize a single set of \\( \\mathbf{D} \\) for the entire video, hence it does not model any pose-dependent geometric deformations. Some examples of SMPL+D can be seen in Fig. 1b." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.818, + 0.317, + 0.833 + ], + "angle": 0, + "content": "3.2. Coarse Albedo Estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Given the SMPL+D fits for the training frames, we estimate an albedo texture map \\( T_{A} \\) of the person in the UV space of SMPL. We follow [5] and first extract a partial texture map for each frame by back-projecting the image colors" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.525, + 0.893, + 0.678 + ], + "angle": 0, + "content": "of all visible vertices to the UV space. The final texture map \\( T_{I} \\) is then generated by calculating the median color value of most orthogonal texels from all frames. Depending on the available body poses in the training video, the obtained texture map can be noisy, and still have missing regions, e.g., hand regions are often very noisy as no hand tracking is performed during SMPL fitting. Also, to ensure plausible relighting, the unknown shading from the texture map has to be removed, which is a challenging problem since decomposing shading and albedo is an ill-posed problem." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.902 + ], + "angle": 0, + "content": "To address these problems, we propose TextureNet, \\( G_{\\mathrm{Tex}} \\) (Fig. 1c), which takes a noisy texture map \\( T_I \\) with unknown lighting as input and produces a clean albedo texture map as output, i.e., \\( T_A = G_{\\mathrm{Tex}}(T_I) \\) [36, 28]. One main challenge for training such a model is the availability of training pairs of noisy/shaded and albedo texture maps. We generate these pairs using 400 rigged characters from the RenderPeople dataset [2]. Since each character in RenderPeople has different UV coordinates, we follow [36] and register the characters with SMPL to obtain ground-truth UV maps in consistent SMPL UV coordinates. For noisy pairs, we generate images with random poses and lighting and extract texture maps like any other video mentioned" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "23145" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.405, + 0.108 + ], + "angle": 0, + "content": "above. We train \\( G_{\\mathrm{Tex}} \\) using the following losses:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.119, + 0.47, + 0.136 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {T e x}} = \\mathcal {L} _ {\\text {p i x e l}} + \\mathcal {L} _ {\\mathrm {V G G}} + \\mathcal {L} _ {\\mathrm {G A N}}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.148, + 0.473, + 0.391 + ], + "angle": 0, + "content": "Here \\(\\mathcal{L}_{\\mathrm{pixel}}\\) is the \\(L_{1}\\) loss between the predicted and ground-truth albedo texture maps, \\(\\mathcal{L}_{\\mathrm{VGG}}\\) is \\(L_{1}\\) difference between their VGG features, and \\(\\mathcal{L}_{\\mathrm{GAN}}\\) is the GAN loss [21, 44]. We use a vanilla U-Net architecture for TextureNet. It takes a noisy/shaded UV texture map with a resolution of \\(512\\times 512\\) as input and produces the albedo texture with the same resolution as output. We also concatenate a 2D tensor of UV coordinates with the input texture map to provide part-specific information to the model. We train the network using Adam optimizer with a batch size of 8 and a learning rate of \\(1e^{-4}\\) with cosine annealing and a minimum learning rate of \\(1e^{-5}\\). To avoid overfitting during training, we perform random noise augmentation to the input texture maps including coarse dropout, gaussian noise, random brightness, and MixUp (\\(\\beta = 0.4\\)) [67]. Some examples of estimated albedo maps can be seen in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.399, + 0.409, + 0.415 + ], + "angle": 0, + "content": "3.3. Relightable Articulated Neural Avatar" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.422, + 0.473, + 0.635 + ], + "angle": 0, + "content": "The coarse albedo texture and geometry obtained so far lack photo-realism and fine-grained details of the person. First, the topology of SMPL+D is fixed and cannot fully capture the fine geometric details, for example, loose clothing or long hairs. Second, the TextureNet can confuse the texture of the person with shading and may remove some texture details while estimating the albedo texture map. In this section, we present RANA which utilizes the coarse geometry and albedo map and generates higher quality images of the person. We parametrize RANA using the SMPL body model and SH lighting [5]. Specifically, RANA takes the target body pose \\(\\theta\\) and the target lighting in the form of second-order spherical harmonics coefficients \\(E\\in \\mathbb{R}^{9\\times 3}\\) as input and synthesizes the target image \\(I^{\\theta ,E}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.644, + 0.47, + 0.663 + ], + "angle": 0, + "content": "\\[\nI ^ {\\theta , E} = \\operatorname {R A N A} (\\theta , E, K), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.473, + 0.902 + ], + "angle": 0, + "content": "where \\(K\\) corresponds to the intrinsic parameters of the target camera viewpoint. One main challenge in learning such a neural avatar from a short RGB video is to maintain the disentanglement of geometry, albedo, and lighting, as any learnable parameters can overfit the training frames disregarding plausible disentanglement. Hence, we design RANA such that a plausible disentanglement is encouraged during training. Specifically, RANA consists of two convolutional neural networks NormalNet, \\(G_{\\mathrm{N}}\\), and AlbedoNet, \\(G_{\\mathrm{A}}\\), each responsible for generating the normal map \\(I_N^\\theta \\in \\mathbb{R}^{h\\times w\\times 3}\\), and albedo map, \\(I_A^\\theta \\in \\mathbb{R}^{h\\times w\\times 3}\\), of the person in the body pose \\(\\theta\\), respectively. It also consists of a set of subject-specific latent neural features \\(Z \\in \\mathbb{R}^{256\\times 256\\times 16}\\) in UV coordinates to augment the details available in the coarse albedo map and geometry." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.245 + ], + "angle": 0, + "content": "More specifically, given the target body pose \\(\\theta\\), we first generate the SMPL+D mesh \\(\\mathbf{M}^{\\theta} = M(\\theta ,\\beta ,\\mathbf{D})\\), where the shape parameters \\(\\beta\\) and clothing offsets \\(\\mathbf{D}\\) are the ones obtained in Sec. 3.1. We then use \\(\\mathbf{M}^{\\theta}\\) to differentiably rasterize [39] the latent features \\(Z\\) and coarse albedo texture \\(T_{A}\\) to obtain a features image \\(I_Z^\\theta\\) and coarse albedo image \\(\\bar{I}_A^\\theta\\) in the target body pose. We also rasterize a coarse normal image \\(\\bar{I}_N^\\theta\\) and a UV image \\(I_{\\mathrm{uv}}^\\theta\\) using the normals and UV coordinates of \\(M^{\\theta}\\), respectively. The refined normal image \\(I_N^\\theta\\) and refined albedo image \\(I_A^\\theta\\) are then obtained as" + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.255, + 0.892, + 0.273 + ], + "angle": 0, + "content": "\\[\nI _ {N} ^ {\\theta} = G _ {N} \\left(I _ {Z} ^ {\\theta}, \\bar {I} _ {N} ^ {\\theta}, \\gamma \\left(I _ {\\mathrm {u v}} ^ {\\theta}\\right)\\right), \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.593, + 0.275, + 0.892, + 0.294 + ], + "angle": 0, + "content": "\\[\nI _ {A} ^ {\\theta}, S ^ {\\theta} = G _ {A} \\left(I _ {Z} ^ {\\theta}, \\bar {I} _ {A} ^ {\\theta}, \\gamma \\left(I _ {\\mathrm {u v}} ^ {\\theta}\\right)\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.307, + 0.895, + 0.413 + ], + "angle": 0, + "content": "where \\(S^{\\theta}\\) is the person mask in the target pose and \\(\\gamma\\) corresponds to the positional encoding of the UV coordinates [42]. Given the lighting \\(E\\), we obtain the shading image \\(I_S^{\\theta ,E}\\) using the normal map \\(I_N^\\theta\\) and SH lighting [49]. Under the usual assumptions of Lambertian material, distant lighting, and no cast shadows, the final shaded image \\(I^{\\theta ,E}\\) is then obtained as" + }, + { + "type": "equation", + "bbox": [ + 0.636, + 0.424, + 0.892, + 0.445 + ], + "angle": 0, + "content": "\\[\nI ^ {\\theta , E} = I _ {A} ^ {\\theta} \\cdot I _ {S} ^ {\\theta , E}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.456, + 0.895, + 0.622 + ], + "angle": 0, + "content": "An overview of RANA can be seen in Fig. 1d. Since the lighting environment of the training video is unknown, we also optimize the second order SH coefficients \\( E \\in \\mathbb{R}^{9 \\times 3} \\) [49] of the training video during training. Under the assumption of Lambertian surface, none of the learnable parameters in RANA depend on the lighting information. Hence, if the disentanglement of normals, albedo, and lighting during training is correct, we can simply replace \\( E \\) during inference with any other novel lighting environment to obtain relit images. We train RANA with the following objective:" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.636, + 0.892, + 0.674 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\text {p i x e l}} + \\mathcal {L} _ {\\text {f a c e}} + \\mathcal {L} _ {\\text {m a s k}} + \\mathcal {L} _ {\\mathrm {V G G}} + \\mathcal {L} _ {\\mathrm {G A N}} (9) \\\\ + \\mathcal {L} _ {\\text {r e g}} ^ {\\text {a l b e d o}} + \\mathcal {L} _ {\\text {r e g}} ^ {\\text {n o r m a l}}. (10) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.686, + 0.895, + 0.853 + ], + "angle": 0, + "content": "Here \\(\\mathcal{L}_{\\mathrm{pixel}}\\) is the \\(L_{1}\\) difference between the generated image \\(I^{\\theta ,E}\\) and the ground-truth training frame, \\(\\mathcal{L}_{\\mathrm{face}}\\) is the \\(L_{1}\\) difference between their face regions to assign a higher weight to face, and \\(\\mathcal{L}_{\\mathrm{mask}}\\) is the binary-cross-entropy loss between the estimated mask \\(S^{\\theta}\\) using \\(G_{A}\\) and the pseudoground-truth mask obtained using a person segmentation model [15]. The term \\(\\mathcal{L}_{\\mathrm{VGG}}\\) is the \\(L_{1}\\) difference between the VGG features of generated and ground-truth images, and \\(\\mathcal{L}_{\\mathrm{GAN}}\\) is the commonly used GAN loss [44, 21]. The term \\(\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}\\) is the albedo regularization term that prevents the light information from leaking into the albedo image:" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.878, + 0.892, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e g}} ^ {\\text {a l b e d o}} = \\left\\| \\sigma \\left(I _ {A} ^ {\\theta}, k\\right) - \\sigma \\left(\\bar {I} _ {A} ^ {\\theta}, k\\right) \\right\\| ^ {2}. \\tag {11}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23146" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.222, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.194, + 0.222, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.095, + 0.298, + 0.211, + 0.311 + ], + "angle": 0, + "content": "Noisy/Shaded Map" + }, + { + "type": "image", + "bbox": [ + 0.223, + 0.089, + 0.358, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.223, + 0.194, + 0.358, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.252, + 0.298, + 0.328, + 0.31 + ], + "angle": 0, + "content": "Albedo Map" + }, + { + "type": "image", + "bbox": [ + 0.358, + 0.089, + 0.495, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.358, + 0.194, + 0.495, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.368, + 0.298, + 0.485, + 0.31 + ], + "angle": 0, + "content": "Noisy/Shaded Map" + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.089, + 0.631, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.496, + 0.194, + 0.631, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.526, + 0.298, + 0.602, + 0.31 + ], + "angle": 0, + "content": "Albedo Map" + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.089, + 0.768, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.194, + 0.768, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.298, + 0.758, + 0.31 + ], + "angle": 0, + "content": "Noisy/Shaded Map" + }, + { + "type": "image", + "bbox": [ + 0.768, + 0.089, + 0.905, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.768, + 0.194, + 0.905, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.799, + 0.298, + 0.875, + 0.31 + ], + "angle": 0, + "content": "Albedo Map" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.31, + 0.892, + 0.336 + ], + "angle": 0, + "content": "Figure 2. Examples of estimated albedo maps from noisy/shaded maps using our proposed TextureNet (Sec. 3.2). The first row shows some examples from the PeopleSnapshot dataset, while the second row shows examples from our proposed RelightingHuman dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.359, + 0.47, + 0.472 + ], + "angle": 0, + "content": "Here \\( I_A^\\theta \\) is the albedo image obtained using \\( G_{A} \\), \\( \\bar{I}_A^\\theta \\) is the coarse albedo image, and \\( \\sigma \\) is the Gaussian smoothing operator with a kernel size \\( k = 51 \\). \\( \\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}} \\) encourages the overall color information in \\( I_A^\\theta \\) to be close to \\( \\bar{I}_A^\\theta \\) while disregarding the texture information. Similarly, \\( \\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{normal}} \\) is the normal regularization loss which prevents the normal image \\( I_N^\\theta \\) to move very far from the coarse normal image \\( \\bar{I}_N^\\theta \\):" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.48, + 0.469, + 0.5 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e g}} ^ {\\text {n o r m a l}} = \\left| S _ {\\text {s m p l}} ^ {\\theta} I _ {N} ^ {\\theta} - S _ {\\text {s m p l}} ^ {\\theta} \\bar {I} _ {N} ^ {\\theta} \\right|, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.511, + 0.47, + 0.678 + ], + "angle": 0, + "content": "where \\( S_{\\mathrm{mpl}}^{\\theta} \\) is the rasterized mask of SMPL+D mesh. It ensures that the regularization is applied only on the pixels where SMPL+D normals are valid. Note that no ground-truth supervision is provided to \\( G_{A} \\) and \\( G_{N} \\). They are mostly learned via the image reconstruction losses, while the disentanglement of normals and albedo is ensured via the novel design of RANA and regularization losses. For \\( \\mathcal{L}_{\\mathrm{face}} \\), we project the nose keypoint of SMPL body model on to the image and crop a \\( 100 \\times 100 \\) patch around the face to compute the loss. All other losses are calculated on the \\( 512 \\times 512 \\) generated images." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.696, + 0.36, + 0.712 + ], + "angle": 0, + "content": "3.3.1 Pre-training using synthetic data" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.901 + ], + "angle": 0, + "content": "While we design RANA such that it generalizes well to novel body poses, the networks \\( G_{A} \\) and \\( G_{N} \\) may still overfit to the body poses available in the training video, in particular, when the coarse geometry and albedo are noisy. A significant advantage of RANA is that it can be trained simultaneously for multiple subjects, i.e., we use different neural features \\( Z \\) for each subject while sharing the networks \\( G_{A} \\) and \\( G_{N} \\). This not only allows the model to see diverse body poses during pre-training but also helps in learning to disentangle normals and albedo. Hence, we propose to pretrain \\( G_{A} \\) and \\( G_{N} \\) on synthetic data. For this, we use 400 rigged characters from the RenderPeople dataset. We" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.361, + 0.892, + 0.42 + ], + "angle": 0, + "content": "generated 150 albedo and normal images for each subject under random body poses and pretrain both networks using ground-truth albedo and normal images. We use the \\( L_{1} \\) loss for both terms." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.441, + 0.666, + 0.456 + ], + "angle": 0, + "content": "3.3.2 Personalization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.465, + 0.892, + 0.72 + ], + "angle": 0, + "content": "After pre-training, given the RGB video of a novel subject, we optimize the latent features \\( Z \\) and lighting environment \\( E \\) of the video from scratch and only fine-tune AlbedoNet \\( (G_{A}) \\). During our experiments, we found that fine-tuning \\( G_{N} \\) is not required if the model is pretrained (see Sec. 4.3). We keep \\( G_{A} \\) fixed for the first 1000 iterations and only optimize \\( Z \\) and \\( E \\). This allows optimization of the latent features \\( Z \\) to be compatible with the pretrained \\( G_{A} \\) and \\( G_{N} \\). We then optimize \\( G_{A}, Z \\), and \\( E \\) jointly for a total of 15k iterations. Note that, while we do pre-training on synthetic data, RANA does not suffer from domain gap because the neural texture is learned from scratch and AlbedoNet is finetuned for every video. Similar to TextureNet, we use vanilla U-Net for AlbedoNet and NormalNet. For training, we use Adam optimizer with a batch size of 16 and learning rate of \\( 1e^{-4} \\) with cosine annealing and minimum learning rate of \\( 1e^{-5} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.736, + 0.633, + 0.754 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.762, + 0.892, + 0.821 + ], + "angle": 0, + "content": "In this section, we evaluate the performance of RANA using two different datasets. We perform an ablation study to validate our design choices and also compare our method with state-of-the-art and other baselines." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.602, + 0.847 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Relighting Human Dataset. We propose a new photorealistic synthetic dataset to quantitatively evaluate the performance of our method. We use 49 rigged characters from the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23147" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.088, + 0.221, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.258, + 0.2, + 0.27 + ], + "angle": 0, + "content": "(a) Ground Truth" + }, + { + "type": "image", + "bbox": [ + 0.221, + 0.089, + 0.379, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.235, + 0.258, + 0.324, + 0.27 + ], + "angle": 0, + "content": "(b) Full Model" + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.089, + 0.538, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.385, + 0.257, + 0.477, + 0.273 + ], + "angle": 0, + "content": "(c) w/o \\(\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}\\)" + }, + { + "type": "image", + "bbox": [ + 0.557, + 0.089, + 0.721, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.521, + 0.258, + 0.676, + 0.272 + ], + "angle": 0, + "content": "(d) w/o coarse geo. & tex." + }, + { + "type": "image", + "bbox": [ + 0.727, + 0.089, + 0.876, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.735, + 0.258, + 0.853, + 0.272 + ], + "angle": 0, + "content": "(e) w/o pre-training" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.272, + 0.894, + 0.327 + ], + "angle": 0, + "content": "Figure 3. Ablation Study. Impact of the different components of the proposed approach. Our full model yields the best results. Without the \\(\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}\\) loss, the light information leaks into the albedo texture resulting in incorrect illumination. If we do not use coarse geometry and albedo texture, the resulting model does not generalize well to novel body poses. Similarly, training the model from scratch, without any pretraining on synthetic data, can result in an incorrect disentanglement of texture and geometry." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.345, + 0.892, + 0.462 + ], + "angle": 0, + "content": "
MethodImageNormal MapAlbedo Map
LPIPS ↓DISTS ↓SSIM ↑PSNR ↑Degree° ↓LPIPS ↓DISTS ↓SSIM ↑PSNR ↑
Full model0.2170.2040.75119.49864.3500.2190.2070.77921.832
w/o Lalbedo0.2490.2410.69715.19964.0640.2640.2570.71315.688
w/o coarse geo. & tex.0.2420.2220.73018.58065.8870.2600.2320.75120.778
w/o pre-training0.3010.2930.66913.79874.2150.3270.3070.69615.632
fine-tune GN0.2190.2050.74619.19864.2260.2210.2100.77821.577
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.463, + 0.89, + 0.476 + ], + "angle": 0, + "content": "Table 2. Ablation study. We evaluate the impact of different components of the proposed method. See Fig. 3 for a qualitative comparison." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.468, + 0.726 + ], + "angle": 0, + "content": "RenderPeople dataset [2] to generate photo-realistic images for each subject. We use HDRI maps from PolyHaven [1] to illuminate the characters and use the CMU motion capture dataset [3] to pose the characters. In contrast to our proposed method that uses image-based lighting, we use full Path Tracing to generate the dataset. Hence, it is the closest setting to an in-the-wild video, and any future work that uses a more sophisticated lighting model can be evaluated on this dataset. For a fair evaluation, we ensure that none of the characters is used during the training in Sec 3.2 and Sec 3.3. All testing images come with a ground-truth albedo map, a normal map, a segmentation mask, and light information. For our experiments, we evaluate on all 49 characters and train a separate RANA model for each subject. We develop three different protocols for evaluation:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.727, + 0.468, + 0.833 + ], + "angle": 0, + "content": "a) Novel Pose and Light Synthesis This protocol evaluates the quality in terms of novel pose and light synthesis. We generate 100 training images for each subject rotating \\(360^{\\circ}\\) with A-posed in front of the camera with fixed lighting. It mimics the self-rotating videos commonly used for training. For testing, we generate 150 frames for each subject with random body pose and light in each frame." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.833, + 0.468, + 0.893 + ], + "angle": 0, + "content": "b) Arbitrary Pose Training To represent in-the-wild scenarios, we generate 100 training images for each subject with arbitrary poses in fixed lighting. For testing, we generate 50 frames for each subject with random unseen body" + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.727, + 0.468, + 0.893 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.501, + 0.747, + 0.516 + ], + "angle": 0, + "content": "pose and random light in each frame." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.516, + 0.892, + 0.606 + ], + "angle": 0, + "content": "c) Novel Light Synthesis. This protocol evaluates the relighting ability of the methods. We generate 150 frames for train and test sets. The train set is generated with fixed lighting and random body poses. The body poses in the test set are exactly the same as the train sets, but each frame is generated using a different light source." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.607, + 0.892, + 0.652 + ], + "angle": 0, + "content": "People Snapshot Dataset. [5]. This dataset consists of real videos of characters rotating in front of the camera. We use this dataset for qualitative evaluation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.662, + 0.596, + 0.677 + ], + "angle": 0, + "content": "4.2. Metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.686, + 0.892, + 0.807 + ], + "angle": 0, + "content": "We report several metrics to evaluate the quality of synthesized images as well as the disentanglement of normal and albedo images. For synthesized images and albedo maps, we use Learned Perceptual Patch Similarity (LPIPS \\(\\downarrow\\)) [68], Deep Image Structure and Texture Similarity (DISTS \\(\\downarrow\\)) [19], Structural Similarity Index (SSIM \\(\\uparrow\\)) [60] and Peak Signal-to-Noise Ratio (PSNR \\(\\uparrow\\)). For normals, we compute the error in degrees (\\(^\\circ\\))." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.65, + 0.833 + ], + "angle": 0, + "content": "4.3. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We evaluate different design choices of RANA in Tab. 2 and Fig 3. We use protocol-a of the Relighting Human dataset for all experiments. We first report the results of the final model which includes all loss terms in (10)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23148" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.087, + 0.892, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.119, + 0.454, + 0.179, + 0.464 + ], + "angle": 0, + "content": "Reference" + }, + { + "type": "image_caption", + "bbox": [ + 0.222, + 0.454, + 0.304, + 0.464 + ], + "angle": 0, + "content": "RANA (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.323, + 0.454, + 0.43, + 0.464 + ], + "angle": 0, + "content": "ANR[47]+RH[33]" + }, + { + "type": "image_caption", + "bbox": [ + 0.462, + 0.454, + 0.519, + 0.464 + ], + "angle": 0, + "content": "SMPL+D" + }, + { + "type": "image_caption", + "bbox": [ + 0.551, + 0.454, + 0.661, + 0.464 + ], + "angle": 0, + "content": "Relighting4D [16]" + }, + { + "type": "image_caption", + "bbox": [ + 0.678, + 0.454, + 0.761, + 0.464 + ], + "angle": 0, + "content": "RANA (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.78, + 0.454, + 0.887, + 0.464 + ], + "angle": 0, + "content": "Relighting4D [16]" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.465, + 0.891, + 0.505 + ], + "angle": 0, + "content": "Figure 4. Comparison with the baselines and state-of-the-art methods. Column 1 shows a reference frame with the target body pose and lighting in the insets. In the absence of true reference images, for the Snapshot dataset (rows 1-2), we show training frames for reference. Columns 2-5 compare different methods for protocol-a, while columns 6-7 provide a comparison for protocol-b." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.519, + 0.892, + 0.744 + ], + "angle": 0, + "content": "
MethodImageNormal MapAlbedo Map
LPIPS ↓DISTS ↓SSIM ↑PSNR ↑Degree° ↓LPIPS ↓DISTS ↓SSIM ↑PSNR ↑
Protocol (a): Novel Pose and Light Synthesis
ANR [47] + RH [33]0.2750.4160.66417.495N.A.0.2660.4290.65614.804
Relightable SMPL+D0.2650.2250.75119.67864.1210.2160.1820.81122.623
RANA (Ours)0.2170.2040.75119.49864.3500.2190.2070.77921.832
Protocol (b): Arbitrary Pose Training
Relightable SMPL+D0.2590.2220.76119.98863.7560.2100.1800.82323.052
RANA (Ours)0.1930.1830.79320.69363.4090.2260.1940.82522.935
Protocol (c): Novel Light Synthesis
Relighting Humans [33]0.2260.3530.66821.205-----
Relighting4D [16]0.1920.3420.65421.08065.0990.2630.3740.59320.014
RANA (Ours)0.1730.1710.84222.33862.8230.2000.1790.86524.721
" + }, + { + "type": "table_caption", + "bbox": [ + 0.166, + 0.744, + 0.798, + 0.756 + ], + "angle": 0, + "content": "Table 3. Comparison with the baselines and state-of-the-art methods. See Fig. 4 for qualitative comparison." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.782, + 0.47, + 0.888 + ], + "angle": 0, + "content": "and pretraining using synthetic data (Sec. 3.3.1). The full model achieves an LPIPS score of 0.217 for image synthesis and 0.219 for albedo map reconstruction. If we remove the loss term \\(\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}\\) from (10), the LPIPS scores for image and albedo map reconstruction increase to 0.249 and 0.264, respectively. Note that the error for albedo maps increases significantly while the error for normal maps re" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.781, + 0.892, + 0.83 + ], + "angle": 0, + "content": "mains roughly the same. This indicates that without \\(\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}\\) the light information leaks into the albedo image. An example of this behavior can also be seen in Fig 3c (w/o \\(\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}\\))." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.841, + 0.892, + 0.899 + ], + "angle": 0, + "content": "Next, we evaluate the impact of coarse geometry and albedo texture on RANA. If we do not use coarse geometry and albedo, LPIPS score increases to 0.242 as compared to 0.217 for the full model. The normal error also increases" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23149" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.473, + 0.395 + ], + "angle": 0, + "content": "to \\(65.9^{\\circ}\\) from \\(64.3^{\\circ}\\). This is also evident from the qualitative results shown in Fig 3d, indicating that coarse geometry and albedo help in improved image synthesis quality, in particular when the target body pose is far from the training poses. Next, we evaluate the impact of pretraining on synthetic data. Without the pretraining, all error metrics increase significantly. Specifically, the LPIPS score for image reconstruction increases from 0.217 to 0.301, while the normal error increases from \\(64.3^{\\circ}\\) to \\(74.2^{\\circ}\\). If we look at Fig 3e, we can see that shading information leaks into both the normals and albedo maps. Hence, pretraining the networks also helps with the plausible disentanglement of geometry, texture, and light. Thanks to the design of RANA, we can pretrain on as many subjects as available, which is not possible with most of the state-of-the-art methods for human synthesis [45, 46, 58, 31]. Finally, as discussed in Sec 3.3.1, we keep the network \\(G_{N}\\) fixed during finetuning if RANA is pretrained on synthetic data. In the last row of Tab. 2, we evaluate the case when \\(G_{N}\\) is also fine-tuned. We can see that it has a negligible impact on the results." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.407, + 0.362, + 0.423 + ], + "angle": 0, + "content": "4.4. Comparison with other methods" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.432, + 0.47, + 0.476 + ], + "angle": 0, + "content": "Since ours is the first work that simultaneously evaluates novel light and pose synthesis, we ourselves build some baselines as follows:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.492, + 0.469, + 0.553 + ], + "angle": 0, + "content": "Relightable SMPL+D: We rasterize the SMPL+D mesh normals and albedo texture estimated using TextureNet in the target body pose and use SH lighting to generate the shaded images." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.552, + 0.469, + 0.644 + ], + "angle": 0, + "content": "ANR [47]+RH[33]: We train an ANR [47] model which synthesizes images in the lighting of the training video. We then pass the generated images to the single-image human relighting method Relighting Humans (RH) [33] to obtain the relighted images for the target light. We use the publicly available source code and models of [33]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.643, + 0.469, + 0.688 + ], + "angle": 0, + "content": "Relighting4D [16] is a state-of-the-art human video relighting method. We use the publicly available source code and train it on our dataset." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.705, + 0.47, + 0.902 + ], + "angle": 0, + "content": "The results are summarized in Tab. 3 and Fig 4. We do not report results of Relighting4D [16] for protocol-a since it cannot handle novel body poses as can be seen in Fig 4 (column-5). For protocol-a, our method clearly outperforms other baselines for final image synthesis results. Surprisingly, the SMPL+D baseline yields better numbers for albedo reconstruction, even though it provides overly smooth albedo textures. This is because TextureNet is trained on synthetic data, hence albedo maps in SMPL+D baseline achieve the best result in this synthetic data benchmark. However, the SMPL+D baseline does not produce the best image quality. RANA, on the other hand, achieves significantly better image quality while staying close to the" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.673, + 0.106 + ], + "angle": 0, + "content": "unlit texture in SMPL+D." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.112, + 0.892, + 0.173 + ], + "angle": 0, + "content": "For protocol-b, we only compare the best two methods from protocol-a as we found it unnecessary to retrain ANR based on the results of protocol-a. As we can see in Tab. 3, the results are consistent with protocol-a." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.179, + 0.893, + 0.436 + ], + "angle": 0, + "content": "For protocol-c, we compare with a video-based relighting method Relighting4D [16] and the single-image-based relighting method Relighting Humans [33]. RANA outperforms both methods across all metrics. Some qualitative comparisons with Relighting4D [16] can be seen in Fig. 4 (columns 6-7), where RANA clearly yields better image relighting results. Note that each model for Relighting4D [16] requires \\(260\\mathrm{k}\\) iterations for training whereas RANA models are trained only for \\(15\\mathrm{k}\\) iterations, thanks to our novel design that allows pre-training on synthetic data, allowing quick fine-tuning for new subjects. In contrast, Relighting4D [16] by design cannot be pretrained easily on multiple subjects. On the other hand, the method [33] is trained for up-right frontal poses only and cannot handle arbitrary body poses, resulting in inferior relighting performance. This is also the main reason behind the inferior performance of the ANR \\([47] + \\mathrm{RH}\\) [33] baseline for protocol-a." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.441, + 0.894, + 0.471 + ], + "angle": 0, + "content": "Finally, we provide additional qualitative results of avatars animated with complex motions in the supp. video." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.502, + 0.771, + 0.518 + ], + "angle": 0, + "content": "5. Conclusion and Future Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.533, + 0.892, + 0.759 + ], + "angle": 0, + "content": "We presented RANA which is a novel framework for learning reconfigurable and articulated neural avatars of humans. We demonstrated that RANA can model humans from unconstrained RGB videos while also disentangling their geometry, albedo texture, and environmental lighting. We showed that it can generate high-quality images of people under any novel body pose, viewpoint, and lighting. RANA can be trained simultaneously for multiple people and we showed that pre-training it on multiple (400) synthetic characters significantly improves the image synthesis quality. We also proposed a new photo-realistic synthetic dataset (Relighting Human) to quantitatively evaluate the performance of our proposed method, and believe that it will prove to be very useful to further the research in this direction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The most pressing limitation of RANA is the assumption of Lambertian surface, no cast shadows, and image-based lighting. In the future, we hope to incorporate more sophisticated physically-based rendering in our framework which will hopefully result in better image quality, self-shadowing and normal maps with more details. Moreover, RANA does not explicitly model motion-dependent clothing deformations. Modeling and neural rendering clothing deformations from a short video clip would be interesting future work." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23150" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.431, + 0.129 + ], + "angle": 0, + "content": "[1] Poly Haven, 2020. https://hdrihaven.com. 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.131, + 0.468, + 0.157 + ], + "angle": 0, + "content": "[2] Render People, 2020. https://renderpeople.com/3d-people.4,7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.159, + 0.468, + 0.186 + ], + "angle": 0, + "content": "[3] Carnegie Mellon University Graphics Lab: Motion Capture Database. http://mocap.cs.cmu.edu, 2014.7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.188, + 0.468, + 0.227 + ], + "angle": 0, + "content": "[4] Thiemo Alldieck, Marcus Magnor, Weipeng Xu, Christian Theobalt, and Gerard Pons-Moll. 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In ICCV, 2019. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23153" + } + ] +] \ No newline at end of file diff --git a/2023/RANA_ Relightable Articulated Neural Avatars/ae3b789d-a192-4696-b97f-daa6528a52ba_origin.pdf b/2023/RANA_ Relightable Articulated Neural Avatars/ae3b789d-a192-4696-b97f-daa6528a52ba_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7949e78870eed60a8ccfd11408f0eb273cd7567b --- /dev/null +++ b/2023/RANA_ Relightable Articulated Neural Avatars/ae3b789d-a192-4696-b97f-daa6528a52ba_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0b73a23b4cfab62414f4026bd44ee9af897e32b1fc606170d17f03f70ed08f46 +size 7715962 diff --git a/2023/RANA_ Relightable Articulated Neural Avatars/full.md b/2023/RANA_ Relightable Articulated Neural Avatars/full.md new file mode 100644 index 0000000000000000000000000000000000000000..9ccb7672991396aabc5140aac1a1450b95e14b3b --- /dev/null +++ b/2023/RANA_ Relightable Articulated Neural Avatars/full.md @@ -0,0 +1,398 @@ +# RANA: Relightable Articulated Neural Avatars + +Umar Iqbal $^{1*}$ Akin Caliskan $^{2*}$ Koki Nagano $^{1}$ Sameh Khamis $^{1}$ Pavlo Molchanov $^{1}$ Jan Kautz $^{1}$ $^{1}$ NVIDIA ${}^{2}$ Flawless AI https://nvlabs.github.io/RANA/ + +![](images/e51e8665b0fa8ba44cd9cb4531b5d310568e3c99c67db993af467bb00d478576.jpg) + +![](images/0da1b718d7fb666d951fd2fbd4fe11117258f1efb7ecf1e3a6712db20bc3363c.jpg) + +![](images/6c34ba8841f7939950229c0b0a4ad39bc2fdf616014f8f3185b0c87f7b8be3d2.jpg) + +![](images/d1972ae8125f49caaa8effb5451982a60caf7efe896a9991a8ed21fabc042e23.jpg) + +![](images/2402a115b8ba3b48f3127b7446c028b345784ba5e5169f68a295146e0e81e6d8.jpg) + +We present, RANA, an approach for learning dynamic and relightable full-body avatars from monocular RGB videos. A training frame of the person is shown in the first column. RANA can synthesize images of the person under novel poses, viewpoints, and lighting environments. In the insets, we show the synthesized albedo image, the normal map, and the target HDRI light map. + +# Abstract + +We propose RANA, a relightable and articulated neural avatar for the synthesis of humans under arbitrary viewpoints, body poses, and lighting. We only require a short video clip of the person to create the avatar and assume no knowledge about the lighting environment. We present a novel framework to model humans while disentangling their geometry, texture, and lighting environment from monocular RGB videos. To simplify this otherwise ill-posed task we first estimate the coarse geometry and texture of the person via SMPL+D model fitting and then learn an articulated neural representation for higher quality image syn + +thesis. RANA first generates the normal and albedo maps of the person in any given target body pose and then uses spherical harmonics lighting to generate the shaded image in the target lighting environment. We also propose to pre-train RANA using synthetic images and demonstrate that it leads to better disentanglement between geometry and texture while also improving robustness to novel body poses. Finally, we also present a new photo-realistic synthetic dataset, Relighting Human, to quantitatively evaluate the performance of the proposed approach. + +# 1. Introduction + +Articulated neural avatars of humans have numerous applications across telepresence, animation, and visual con + +tent creation. To enable the widespread adoption of these neural avatars, they should be easy to generate and animate under novel poses and viewpoints, able to render in photorealistic image quality, and easy to relight in novel environments. Existing methods commonly aim to learn such neural avatars using monocular videos [47, 46, 45, 54, 66, 58, 31]. While this allows photo-realistic image quality and animation, the synthesized images are always limited to the lighting environment of the training video. Other works directly tackle relighting of human avatars but do not provide control over the body pose [23, 41]. Moreover, these approaches often require multiview images recorded in a Light Stage for training, which is limited to controlled settings only. Some recent methods aim to relight RGB videos of a dynamic human but do not provide control over body pose [16]. + +In this work, we present the Relightable Articulated Neural Avatar (RANA) method, which allows animation of people under any novel body pose, viewpoint, and lighting environment. To create an avatar, we only require a short monocular video clip of the person in unconstrained environment, clothing, and arbitrary body pose. During inference, we only require the target body pose and target lighting information. + +Learning relightable neural avatars of dynamics humans from monocular RGB videos recorded in unknown environments is a challenging problem. First, it requires modeling the complex human body articulations and geometry. Second, in order to allow relighting under novel environments, the texture, geometry, and illumination information have to be disentangled, which is an ill-posed problem to solve from RGB videos [8]. To address these challenges, we first extract canonical coarse geometry and texture information from the training frames using a statistical human shape model SMPL+D [40, 5, 36]. We then propose a novel convolutional neural network that is trained on synthetic data to remove the shading information from the coarse texture. We augment the coarse geometry and texture with learnable latent features and pass them to our proposed neural avatar framework, which generates refined normal and albedo maps of the person under the target body pose using two separate convolutional networks. Given the normal map, albedo map, and lighting information, we generate the final shaded image using spherical harmonics (SH) lighting [49]. During training, since the environment lighting is unknown, we jointly optimize it together with the person's appearance and propose novel regularization terms to prevent the leaking of lighting into the albedo texture. We also propose to pre-train the avatar using photo-realistic synthetic data with ground-truth albedo and normal maps. During pretraining, we train a single model for multiple subjects while having separate neural features for each subject. This not only improves the generalizability of the neural avatar + +to novel body poses but also learns to decouple the texture and geometry information. For a new subject, we only learn a new set of neural features and fine-tune the avatar model to capture fine-grained person-specific details. In our experiments, the avatar for a novel subject can be learned within 15k training iterations. + +Since no dataset exists to evaluate the renderings of avatars in terms of both novel light and pose synthesis, we also propose a novel photo-realistic synthetic Relighting Human Dataset (RHD) with ground truth albedo, normals, and lighting information. We also perform a qualitative evaluation of RANA on the People Snapshot dataset [5] to compare with other baselines. + +Our contributions can be summarized as follows: + +- We present, RANA, a novel framework for learning relightable articulated neural avatars from short unconstrained monocular videos. The proposed approach is very easy to train and does not require any knowledge about the environment lighting of the training video. +- Our proposed approach can synthesize images of articulated humans under any arbitrary body pose, viewpoint, and lighting. It can also be used for relighting videos of dynamic humans. +- We present a new photo-realistic synthetic dataset for quantitative evaluation and to further the research in this direction. + +# 2. Related work + +Mesh Based Human Avatars. These methods represent human avatars using a rigged mesh and an associated texture map. Earlier methods captured human avatars using multi-view cameras [12, 53] or with the help of depth sensors [9, 71]. However, their adoption remained limited due to the constrained hardware requirements. The recent works, therefore, focus on creating the avatars from monocular videos [5, 4, 31, 10], or images [36, 64, 27, 25, 6, 10, 11]. The methods [5, 4, 36] use body model fitting to capture the humans, while more recent methods use data-driven implicit functions combined with pixel-aligned features [50] for human reconstruction [71, 27, 64, 6]. Self-Recon [31] combines both explicit and implicit meshes to reconstruct the detailed geometry of the person from self-rotating videos, however, it requires manual human effort to make the avatar animatable. The main limitation of these methods, however, is that the shading information is baked into the texture. Hence, the avatars cannot be rendered with novel lights. The recent methods PHORUM [6] and S3F [17] are the only exceptions, however, they create avatar from a single image and rely on data-driven priors to hallucinate the occluded regions of the person. Hence, the generated images may not be the true representation of the + +![](images/c4046231706afa8751158ef0e51b64103a8046ca4f452eb46733aae3e19b3b3a.jpg) +Table 1. Comparison of some of the representative methods for neural human avatar creation. Ours (RANA) is the only method that allows novel view, pose and light synthesis. + +person. In contrast, our approach uses video data to capture a detailed human representation, while also allowing the rendering of the person in novel lighting. + +Neural Human Avatars. More recent methods learn a neural representation of the person and use neural renderers [57] to directly generate photo-realistic images in the target body pose and viewpoints [7, 20, 13, 59, 26, 63]. These methods are generally classified into 2D or 3D neural rendering based methods [57]. The 3D neural rendering methods represent the person using neural radiance fields [42] and render the target images using volume rendering [46, 62, 32, 45, 14, 58, 24, 38]. The 2D neural rendering methods, on the other hand, use CNNs to render the images [47, 66, 22, 70]. One limitation of the 3D neural rendering methods is that the avatar has to be created from scratch for each person. Some methods learn generalizable avatars but require exemplar images of the person during inference [34, 48]. In contrast, the 2D based methods offer some generalizability by sharing the neural renderer across multiple subjects [47]. Our method falls into the 2D neural rendering paradigm as we use CNNs to generate the albedo and normal images of the person. In particular, we take inspiration from ANR [47] for designing our framework. Tab. 1 compares existing neural avatar creation methods. Ours is the only method that allows synthesis under novel poses, viewpoints, and lighting, while also being generalizable. + +Human Relighting. Relighting of human images has been studied extensively in the literature [18, 51, 33, 55, 72, 61, 56, 30, 37, 35, 69, 17]. However, these methods cannot render relighted images in novel body poses and viewpoints. Some recent methods allow relighting from novel views but provide no control over the body pose [23, 43, 16, 65]. The method TexMesh [71] also provides control over body pose but requires RGB-D videos for training and assumes that the environment map of the training video is known. Our approach, in contrast, provides full control over the body pose, viewpoint, and lighting, and learns the avatar from RGB videos with unknown lighting. + +# 3. Method + +Our goal is to learn a relightable articulated neural avatar, RANA, that can synthesize high-quality images of the person under any target body pose, viewpoint, and lighting. To create the avatar, we use a small video sequence $\mathbf{I} = \{I_{\mathrm{f}}\}_{f = 1}^{F}$ with $F$ video frames and assume no knowledge about the lighting environment and body poses present in the video. We parameterize RANA using the SMPL [40] body model to control the animation and use Spherical Harmonics (SH) [49] lighting to model the lighting. During inference, we only need the target body pose and target lighting information in the form of SH coefficients and do not require any exemplar images for ground-truth. Learning RANA from a monocular video requires capturing the geometry and appearance of the dynamic human while also disentangling the shading information. In order to tackle this ill-posed problem, we first capture the coarse geometry using the SMPL+D fits (Sec. 3.1). We use the coarse geometry to extract a coarse texture map from the training images which is converted to an albedo texture map using a convolutional network (Sec. 3.2). We then propose RANA that generates the refined albedo and normal maps. The refined normal maps are used to obtain the shading map using SH lighting which is combined with the refined albedo map to obtain the final image in the target body pose and light (Sec. 3.3). An overview of our method can be seen in Fig. 1. In the following, we describe each of these modules in greater detail. + +# 3.1. Coarse Geometry Estimation + +Given the training frames, we first estimate the coarse geometry of the person including the clothing and hair details. For this, we employ the SMPL+D [4, 36] variant of the SMPL body model [40]. SMPL is a linear function $M(\theta, \beta)$ that takes the body pose $\theta \in \mathbb{R}^{72}$ and shape parameters $\beta \in \mathbb{R}^{10}$ as input and produces a triangulated mesh $\mathbf{M} \in \mathbb{R}^{V \times 3}$ with $V = 6890$ vertices. SMPL only captures the undressed shape of the body and ignores the clothing and hair details. For this, SMPL+D adds a set of 3D offsets $\mathbf{D} \in \mathbf{R}^{V \times 3}$ to SMPL to capture the additional geometric details, i.e., $M(\theta, \beta, \mathbf{D}) \in \mathbb{R}^{V \times 3}$ can also model clothed humans. We refer the readers to [36, 4] for a detailed description of SMPL+D. + +For fitting SMPL+D to training images, we first estimate the parameters of SMPL using an off-the-shelf method SMPLify3D [29]. Since the person in the video remains the same, we optimize a single $\beta$ for the entire video. We then fix the pose $\{\theta\}_{f=1}^{F}$ and shape $\beta$ parameters and optimize for the offsets $\mathbf{D}$ using the following objective: + +$$ +\mathbf {D} = \underset {\mathbf {D} ^ {\prime}} {\operatorname {a r g m i n}} \sum_ {f = 1} ^ {F} \mathcal {L} \left(M \left(\theta_ {f}, \beta , \mathbf {D} ^ {\prime}\right)\right) = \mathcal {L} _ {\mathrm {S i l}} + \mathcal {L} _ {\mathrm {s m o o t h}}. (1) +$$ + +![](images/f5e3dfe34d81cf40decc56a0acad6123bed527971dbd71d544792d357353fc94.jpg) +(a) Training frames + +![](images/2911cad416ef82dec6d857493bd546722bb10833084bf816c7b5d02a7b149fac.jpg) + +![](images/4b215f111b0234e17ce58ebc358d94226657340ecd2c6b37e34ec00d5c4d238a.jpg) +(d) RANA: Relightable Articulated Neural Avatar (Sec 3.3) + +![](images/a87ea00d0be44acab546b9e970f64d6929f8840b885e7b9a6e0f0a786893e0e6.jpg) +(b) Coarse Geometry Estimation (Sec. 3.1) + +![](images/91f868b5bb54ada2b6f97a3aef897b12f7e95bad91cc8433a5a92dbc5a094922.jpg) + +![](images/153c176951931e718aee668f9bd032e2036ab3ec3c7bd83cc668c3d884d65469.jpg) + +![](images/04e1a6c5427577653946a16c11d5ec009ac109e31a640a3c77e78b924a435b77.jpg) +(c) Coarse Texture Estimation (Sec 3.2) + +![](images/7af2ae35432a13df7dbb0a89818574bb4b17a207ddf8ccf8703d34dd09d7307a.jpg) +TextureNet + +![](images/a522a7d759fb06fe413b45bd3e1dfae8be83916ac5555d3d00cd244ab6d03b20.jpg) + +![](images/7f70c6ae2ee66f8680509a4eb633017706e98659d34a5e97c636aa1b67b59044.jpg) + +![](images/db347b505deebb70109d8ced3478f61b1cc073e70db6cb144afabe7c44ffa58f.jpg) + +![](images/025798a817c2bf58782eccfeaca0b032818c32eb243ea9b7f9fafbb31e9eefb4.jpg) + +![](images/2cb3776682018cd3753896e62809bb0c6773f94268bf0e12a28942c0cde1db59.jpg) + +![](images/6b03d78654077fd5582acb77791fbe41ff402546690bb418a3fd8519a613a09d.jpg) + +![](images/602a5eee04a5e8e65e83497225af907c850a6023bfe5f519aeb10f80e2fd7639.jpg) +Latent Neural Features +Figure 1. Overview of the proposed approach. (a) shows some training frames. (b) We estimate the coarse geometry of the person using the SMPL+D body model. (c) The SMPL+D fits are used to extract a UV texture map, which we process using TextureNet to obtain a coarse albedo texture map. (d) Given a target body pose, we rasterize person-specific neural features, coarse albedo, and coarse normals from SMPL+D to the target body pose and pass them to NormalNet and AlbedoNet to obtain refined normal and albedo maps, respectively. We then use the normal map and spherical harmonics lighting to obtain the shading image, which is multiplied with refined albedo to produce the shaded image. AlbedoNet also generates a binary mask, which we use to overlay the shaded image onto the background. + +Here the term $\mathcal{L}_{\mathrm{Sil}}$ is the silhouette loss. We obtain the silhouette of SMPL+D vertices $S_{f}$ for frame $f$ using a differentiable renderer [39] while the target silhouette $\hat{S}_t$ is obtained using a person segmentation model [15]. We define the $\mathcal{L}_{\mathrm{Sil}}$ loss as + +$$ +\mathcal {L} _ {\mathrm {S i l}} = \frac {1}{F} \sum_ {f = 1} ^ {F} \left| S _ {f} - \hat {S} _ {f} \right|. \tag {2} +$$ + +The term $\mathcal{L}_{\mathrm{smooth}}$ is a laplacian smoothing term to encourage the smooth surface of the mesh: + +$$ +\mathcal {L} _ {\text {s m o o t h}} = \frac {1}{F} \sum_ {f = 1} ^ {F} | | L \mathbf {M} _ {f} | |, \tag {3} +$$ + +where $L$ is the mesh Laplacian operator. Note that we optimize a single set of $\mathbf{D}$ for the entire video, hence it does not model any pose-dependent geometric deformations. Some examples of SMPL+D can be seen in Fig. 1b. + +# 3.2. Coarse Albedo Estimation + +Given the SMPL+D fits for the training frames, we estimate an albedo texture map $T_{A}$ of the person in the UV space of SMPL. We follow [5] and first extract a partial texture map for each frame by back-projecting the image colors + +of all visible vertices to the UV space. The final texture map $T_{I}$ is then generated by calculating the median color value of most orthogonal texels from all frames. Depending on the available body poses in the training video, the obtained texture map can be noisy, and still have missing regions, e.g., hand regions are often very noisy as no hand tracking is performed during SMPL fitting. Also, to ensure plausible relighting, the unknown shading from the texture map has to be removed, which is a challenging problem since decomposing shading and albedo is an ill-posed problem. + +To address these problems, we propose TextureNet, $G_{\mathrm{Tex}}$ (Fig. 1c), which takes a noisy texture map $T_I$ with unknown lighting as input and produces a clean albedo texture map as output, i.e., $T_A = G_{\mathrm{Tex}}(T_I)$ [36, 28]. One main challenge for training such a model is the availability of training pairs of noisy/shaded and albedo texture maps. We generate these pairs using 400 rigged characters from the RenderPeople dataset [2]. Since each character in RenderPeople has different UV coordinates, we follow [36] and register the characters with SMPL to obtain ground-truth UV maps in consistent SMPL UV coordinates. For noisy pairs, we generate images with random poses and lighting and extract texture maps like any other video mentioned + +above. We train $G_{\mathrm{Tex}}$ using the following losses: + +$$ +\mathcal {L} _ {\mathrm {T e x}} = \mathcal {L} _ {\text {p i x e l}} + \mathcal {L} _ {\mathrm {V G G}} + \mathcal {L} _ {\mathrm {G A N}}. \tag {4} +$$ + +Here $\mathcal{L}_{\mathrm{pixel}}$ is the $L_{1}$ loss between the predicted and ground-truth albedo texture maps, $\mathcal{L}_{\mathrm{VGG}}$ is $L_{1}$ difference between their VGG features, and $\mathcal{L}_{\mathrm{GAN}}$ is the GAN loss [21, 44]. We use a vanilla U-Net architecture for TextureNet. It takes a noisy/shaded UV texture map with a resolution of $512\times 512$ as input and produces the albedo texture with the same resolution as output. We also concatenate a 2D tensor of UV coordinates with the input texture map to provide part-specific information to the model. We train the network using Adam optimizer with a batch size of 8 and a learning rate of $1e^{-4}$ with cosine annealing and a minimum learning rate of $1e^{-5}$ . To avoid overfitting during training, we perform random noise augmentation to the input texture maps including coarse dropout, gaussian noise, random brightness, and MixUp ( $\beta = 0.4$ ) [67]. Some examples of estimated albedo maps can be seen in Fig. 2. + +# 3.3. Relightable Articulated Neural Avatar + +The coarse albedo texture and geometry obtained so far lack photo-realism and fine-grained details of the person. First, the topology of SMPL+D is fixed and cannot fully capture the fine geometric details, for example, loose clothing or long hairs. Second, the TextureNet can confuse the texture of the person with shading and may remove some texture details while estimating the albedo texture map. In this section, we present RANA which utilizes the coarse geometry and albedo map and generates higher quality images of the person. We parametrize RANA using the SMPL body model and SH lighting [5]. Specifically, RANA takes the target body pose $\theta$ and the target lighting in the form of second-order spherical harmonics coefficients $E\in \mathbb{R}^{9\times 3}$ as input and synthesizes the target image $I^{\theta ,E}$ as: + +$$ +I ^ {\theta , E} = \operatorname {R A N A} (\theta , E, K), \tag {5} +$$ + +where $K$ corresponds to the intrinsic parameters of the target camera viewpoint. One main challenge in learning such a neural avatar from a short RGB video is to maintain the disentanglement of geometry, albedo, and lighting, as any learnable parameters can overfit the training frames disregarding plausible disentanglement. Hence, we design RANA such that a plausible disentanglement is encouraged during training. Specifically, RANA consists of two convolutional neural networks NormalNet, $G_{\mathrm{N}}$ , and AlbedoNet, $G_{\mathrm{A}}$ , each responsible for generating the normal map $I_N^\theta \in \mathbb{R}^{h\times w\times 3}$ , and albedo map, $I_A^\theta \in \mathbb{R}^{h\times w\times 3}$ , of the person in the body pose $\theta$ , respectively. It also consists of a set of subject-specific latent neural features $Z \in \mathbb{R}^{256\times 256\times 16}$ in UV coordinates to augment the details available in the coarse albedo map and geometry. + +More specifically, given the target body pose $\theta$ , we first generate the SMPL+D mesh $\mathbf{M}^{\theta} = M(\theta ,\beta ,\mathbf{D})$ , where the shape parameters $\beta$ and clothing offsets $\mathbf{D}$ are the ones obtained in Sec. 3.1. We then use $\mathbf{M}^{\theta}$ to differentiably rasterize [39] the latent features $Z$ and coarse albedo texture $T_{A}$ to obtain a features image $I_Z^\theta$ and coarse albedo image $\bar{I}_A^\theta$ in the target body pose. We also rasterize a coarse normal image $\bar{I}_N^\theta$ and a UV image $I_{\mathrm{uv}}^\theta$ using the normals and UV coordinates of $M^{\theta}$ , respectively. The refined normal image $I_N^\theta$ and refined albedo image $I_A^\theta$ are then obtained as + +$$ +I _ {N} ^ {\theta} = G _ {N} \left(I _ {Z} ^ {\theta}, \bar {I} _ {N} ^ {\theta}, \gamma \left(I _ {\mathrm {u v}} ^ {\theta}\right)\right), \tag {6} +$$ + +$$ +I _ {A} ^ {\theta}, S ^ {\theta} = G _ {A} \left(I _ {Z} ^ {\theta}, \bar {I} _ {A} ^ {\theta}, \gamma \left(I _ {\mathrm {u v}} ^ {\theta}\right)\right), \tag {7} +$$ + +where $S^{\theta}$ is the person mask in the target pose and $\gamma$ corresponds to the positional encoding of the UV coordinates [42]. Given the lighting $E$ , we obtain the shading image $I_S^{\theta ,E}$ using the normal map $I_N^\theta$ and SH lighting [49]. Under the usual assumptions of Lambertian material, distant lighting, and no cast shadows, the final shaded image $I^{\theta ,E}$ is then obtained as + +$$ +I ^ {\theta , E} = I _ {A} ^ {\theta} \cdot I _ {S} ^ {\theta , E}. \tag {8} +$$ + +An overview of RANA can be seen in Fig. 1d. Since the lighting environment of the training video is unknown, we also optimize the second order SH coefficients $E \in \mathbb{R}^{9 \times 3}$ [49] of the training video during training. Under the assumption of Lambertian surface, none of the learnable parameters in RANA depend on the lighting information. Hence, if the disentanglement of normals, albedo, and lighting during training is correct, we can simply replace $E$ during inference with any other novel lighting environment to obtain relit images. We train RANA with the following objective: + +$$ +\begin{array}{l} \mathcal {L} = \mathcal {L} _ {\text {p i x e l}} + \mathcal {L} _ {\text {f a c e}} + \mathcal {L} _ {\text {m a s k}} + \mathcal {L} _ {\mathrm {V G G}} + \mathcal {L} _ {\mathrm {G A N}} (9) \\ + \mathcal {L} _ {\text {r e g}} ^ {\text {a l b e d o}} + \mathcal {L} _ {\text {r e g}} ^ {\text {n o r m a l}}. (10) \\ \end{array} +$$ + +Here $\mathcal{L}_{\mathrm{pixel}}$ is the $L_{1}$ difference between the generated image $I^{\theta ,E}$ and the ground-truth training frame, $\mathcal{L}_{\mathrm{face}}$ is the $L_{1}$ difference between their face regions to assign a higher weight to face, and $\mathcal{L}_{\mathrm{mask}}$ is the binary-cross-entropy loss between the estimated mask $S^{\theta}$ using $G_{A}$ and the pseudoground-truth mask obtained using a person segmentation model [15]. The term $\mathcal{L}_{\mathrm{VGG}}$ is the $L_{1}$ difference between the VGG features of generated and ground-truth images, and $\mathcal{L}_{\mathrm{GAN}}$ is the commonly used GAN loss [44, 21]. The term $\mathcal{L}_{\mathrm{reg}}^{\mathrm{albedo}}$ is the albedo regularization term that prevents the light information from leaking into the albedo image: + +$$ +\mathcal {L} _ {\text {r e g}} ^ {\text {a l b e d o}} = \left\| \sigma \left(I _ {A} ^ {\theta}, k\right) - \sigma \left(\bar {I} _ {A} ^ {\theta}, k\right) \right\| ^ {2}. \tag {11} +$$ + +![](images/c2f24a0159874b9ae2a58729b566599659eb8b636a50522ac04db4b3401ffb65.jpg) + +![](images/6e41b09266594a0b8b6b12638a7666f5dd6d3e00e3b0ff70473a95b211bee87d.jpg) +Noisy/Shaded Map +Figure 2. Examples of estimated albedo maps from noisy/shaded maps using our proposed TextureNet (Sec. 3.2). The first row shows some examples from the PeopleSnapshot dataset, while the second row shows examples from our proposed RelightingHuman dataset. + +![](images/055247530e13fc6d0dc3d854374e36ded2aeaf7bccb65764af852d7946cfdf04.jpg) + +![](images/63d621b540f06b20fb35a89369ba5efd88746bdb622d86219067d791c667cb59.jpg) +Albedo Map + +![](images/5119f216f8d9e8f43b0e81d0d1fda922db0a0a1c2e28c9fa9be4e1cd6353c3aa.jpg) + +![](images/bd7bd53f2f5775756af0125fa876f7b856fa42ea0e6260f0c22333c6e937daa9.jpg) +Noisy/Shaded Map + +![](images/15c4991232efedd962a0442cd52eebee90787652acc56af2835370bee6baa993.jpg) + +![](images/9ccb0a5077ea2ffbe05f52a0a1ba053c2986292898fe11797b6a6ac7e36ad770.jpg) +Albedo Map + +![](images/3c6112f873765621cf85e22fd18bc8028dff89ef19a5e5c525b5d375950bc742.jpg) + +![](images/82448cb60edc22eb190a97b23b41de96cee8906167a9df921f83e388f7ec5c39.jpg) +Noisy/Shaded Map + +![](images/7805893d83b08097445ebad887c8d01ce9a0a76bc9904f4164fe40ddc8d15cfa.jpg) + +![](images/31c8336c8bf966697e0a8f06df560be3284554ee628f2e37cd8140ed70172bfe.jpg) +Albedo Map + +Here $I_A^\theta$ is the albedo image obtained using $G_{A}$ , $\bar{I}_A^\theta$ is the coarse albedo image, and $\sigma$ is the Gaussian smoothing operator with a kernel size $k = 51$ . $\mathcal{L}_{\mathrm{reg}}^{\mathrm{albedo}}$ encourages the overall color information in $I_A^\theta$ to be close to $\bar{I}_A^\theta$ while disregarding the texture information. Similarly, $\mathcal{L}_{\mathrm{reg}}^{\mathrm{normal}}$ is the normal regularization loss which prevents the normal image $I_N^\theta$ to move very far from the coarse normal image $\bar{I}_N^\theta$ : + +$$ +\mathcal {L} _ {\text {r e g}} ^ {\text {n o r m a l}} = \left| S _ {\text {s m p l}} ^ {\theta} I _ {N} ^ {\theta} - S _ {\text {s m p l}} ^ {\theta} \bar {I} _ {N} ^ {\theta} \right|, \tag {12} +$$ + +where $S_{\mathrm{mpl}}^{\theta}$ is the rasterized mask of SMPL+D mesh. It ensures that the regularization is applied only on the pixels where SMPL+D normals are valid. Note that no ground-truth supervision is provided to $G_{A}$ and $G_{N}$ . They are mostly learned via the image reconstruction losses, while the disentanglement of normals and albedo is ensured via the novel design of RANA and regularization losses. For $\mathcal{L}_{\mathrm{face}}$ , we project the nose keypoint of SMPL body model on to the image and crop a $100 \times 100$ patch around the face to compute the loss. All other losses are calculated on the $512 \times 512$ generated images. + +# 3.3.1 Pre-training using synthetic data + +While we design RANA such that it generalizes well to novel body poses, the networks $G_{A}$ and $G_{N}$ may still overfit to the body poses available in the training video, in particular, when the coarse geometry and albedo are noisy. A significant advantage of RANA is that it can be trained simultaneously for multiple subjects, i.e., we use different neural features $Z$ for each subject while sharing the networks $G_{A}$ and $G_{N}$ . This not only allows the model to see diverse body poses during pre-training but also helps in learning to disentangle normals and albedo. Hence, we propose to pretrain $G_{A}$ and $G_{N}$ on synthetic data. For this, we use 400 rigged characters from the RenderPeople dataset. We + +generated 150 albedo and normal images for each subject under random body poses and pretrain both networks using ground-truth albedo and normal images. We use the $L_{1}$ loss for both terms. + +# 3.3.2 Personalization. + +After pre-training, given the RGB video of a novel subject, we optimize the latent features $Z$ and lighting environment $E$ of the video from scratch and only fine-tune AlbedoNet $(G_{A})$ . During our experiments, we found that fine-tuning $G_{N}$ is not required if the model is pretrained (see Sec. 4.3). We keep $G_{A}$ fixed for the first 1000 iterations and only optimize $Z$ and $E$ . This allows optimization of the latent features $Z$ to be compatible with the pretrained $G_{A}$ and $G_{N}$ . We then optimize $G_{A}, Z$ , and $E$ jointly for a total of 15k iterations. Note that, while we do pre-training on synthetic data, RANA does not suffer from domain gap because the neural texture is learned from scratch and AlbedoNet is finetuned for every video. Similar to TextureNet, we use vanilla U-Net for AlbedoNet and NormalNet. For training, we use Adam optimizer with a batch size of 16 and learning rate of $1e^{-4}$ with cosine annealing and minimum learning rate of $1e^{-5}$ . + +# 4. Experiments + +In this section, we evaluate the performance of RANA using two different datasets. We perform an ablation study to validate our design choices and also compare our method with state-of-the-art and other baselines. + +# 4.1. Datasets + +Relighting Human Dataset. We propose a new photorealistic synthetic dataset to quantitatively evaluate the performance of our method. We use 49 rigged characters from the + +![](images/a93d65b5e46cb059b9b57906da1a63a85947d93d31be5eb2b24be2fe16d10eac.jpg) +(a) Ground Truth + +![](images/acc6e5fce361c26d8efba36ea6f39ba9c3f6b9a6197ab86daa0d3158a45cc070.jpg) +(b) Full Model + +![](images/fed8e3fab599ccb73be828533c295102384577335d17b418b79f04d2497e8d11.jpg) +(c) w/o $\mathcal{L}_{\mathrm{reg}}^{\mathrm{albedo}}$ +Figure 3. Ablation Study. Impact of the different components of the proposed approach. Our full model yields the best results. Without the $\mathcal{L}_{\mathrm{reg}}^{\mathrm{albedo}}$ loss, the light information leaks into the albedo texture resulting in incorrect illumination. If we do not use coarse geometry and albedo texture, the resulting model does not generalize well to novel body poses. Similarly, training the model from scratch, without any pretraining on synthetic data, can result in an incorrect disentanglement of texture and geometry. + +![](images/7ab6f54d82aa64c4787ef3caa15351835dd55a660adc3be6a1444799372238a0.jpg) +(d) w/o coarse geo. & tex. + +![](images/4f9865814d21d22eb5bd232e27371d7f133e34add7d392fb958156ecd7eb4c14.jpg) +(e) w/o pre-training + +
MethodImageNormal MapAlbedo Map
LPIPS ↓DISTS ↓SSIM ↑PSNR ↑Degree° ↓LPIPS ↓DISTS ↓SSIM ↑PSNR ↑
Full model0.2170.2040.75119.49864.3500.2190.2070.77921.832
w/o Lalbedo0.2490.2410.69715.19964.0640.2640.2570.71315.688
w/o coarse geo. & tex.0.2420.2220.73018.58065.8870.2600.2320.75120.778
w/o pre-training0.3010.2930.66913.79874.2150.3270.3070.69615.632
fine-tune GN0.2190.2050.74619.19864.2260.2210.2100.77821.577
+ +Table 2. Ablation study. We evaluate the impact of different components of the proposed method. See Fig. 3 for a qualitative comparison. + +RenderPeople dataset [2] to generate photo-realistic images for each subject. We use HDRI maps from PolyHaven [1] to illuminate the characters and use the CMU motion capture dataset [3] to pose the characters. In contrast to our proposed method that uses image-based lighting, we use full Path Tracing to generate the dataset. Hence, it is the closest setting to an in-the-wild video, and any future work that uses a more sophisticated lighting model can be evaluated on this dataset. For a fair evaluation, we ensure that none of the characters is used during the training in Sec 3.2 and Sec 3.3. All testing images come with a ground-truth albedo map, a normal map, a segmentation mask, and light information. For our experiments, we evaluate on all 49 characters and train a separate RANA model for each subject. We develop three different protocols for evaluation: + +a) Novel Pose and Light Synthesis This protocol evaluates the quality in terms of novel pose and light synthesis. We generate 100 training images for each subject rotating $360^{\circ}$ with A-posed in front of the camera with fixed lighting. It mimics the self-rotating videos commonly used for training. For testing, we generate 150 frames for each subject with random body pose and light in each frame. +b) Arbitrary Pose Training To represent in-the-wild scenarios, we generate 100 training images for each subject with arbitrary poses in fixed lighting. For testing, we generate 50 frames for each subject with random unseen body + +pose and random light in each frame. + +c) Novel Light Synthesis. This protocol evaluates the relighting ability of the methods. We generate 150 frames for train and test sets. The train set is generated with fixed lighting and random body poses. The body poses in the test set are exactly the same as the train sets, but each frame is generated using a different light source. + +People Snapshot Dataset. [5]. This dataset consists of real videos of characters rotating in front of the camera. We use this dataset for qualitative evaluation. + +# 4.2. Metrics + +We report several metrics to evaluate the quality of synthesized images as well as the disentanglement of normal and albedo images. For synthesized images and albedo maps, we use Learned Perceptual Patch Similarity (LPIPS $\downarrow$ ) [68], Deep Image Structure and Texture Similarity (DISTS $\downarrow$ ) [19], Structural Similarity Index (SSIM $\uparrow$ ) [60] and Peak Signal-to-Noise Ratio (PSNR $\uparrow$ ). For normals, we compute the error in degrees ( $^\circ$ ). + +# 4.3. Ablation study + +We evaluate different design choices of RANA in Tab. 2 and Fig 3. We use protocol-a of the Relighting Human dataset for all experiments. We first report the results of the final model which includes all loss terms in (10) + +![](images/ebc4335a79f665668895000b173da109a8eaaabd9a2088aaf8262724e79e9d01.jpg) +Reference +RANA (Ours) +ANR[47]+RH[33] +SMPL+D +Relighting4D [16] +RANA (Ours) +Relighting4D [16] +Figure 4. Comparison with the baselines and state-of-the-art methods. Column 1 shows a reference frame with the target body pose and lighting in the insets. In the absence of true reference images, for the Snapshot dataset (rows 1-2), we show training frames for reference. Columns 2-5 compare different methods for protocol-a, while columns 6-7 provide a comparison for protocol-b. + +
MethodImageNormal MapAlbedo Map
LPIPS ↓DISTS ↓SSIM ↑PSNR ↑Degree° ↓LPIPS ↓DISTS ↓SSIM ↑PSNR ↑
Protocol (a): Novel Pose and Light Synthesis
ANR [47] + RH [33]0.2750.4160.66417.495N.A.0.2660.4290.65614.804
Relightable SMPL+D0.2650.2250.75119.67864.1210.2160.1820.81122.623
RANA (Ours)0.2170.2040.75119.49864.3500.2190.2070.77921.832
Protocol (b): Arbitrary Pose Training
Relightable SMPL+D0.2590.2220.76119.98863.7560.2100.1800.82323.052
RANA (Ours)0.1930.1830.79320.69363.4090.2260.1940.82522.935
Protocol (c): Novel Light Synthesis
Relighting Humans [33]0.2260.3530.66821.205-----
Relighting4D [16]0.1920.3420.65421.08065.0990.2630.3740.59320.014
RANA (Ours)0.1730.1710.84222.33862.8230.2000.1790.86524.721
+ +Table 3. Comparison with the baselines and state-of-the-art methods. See Fig. 4 for qualitative comparison. + +and pretraining using synthetic data (Sec. 3.3.1). The full model achieves an LPIPS score of 0.217 for image synthesis and 0.219 for albedo map reconstruction. If we remove the loss term $\mathcal{L}_{\mathrm{reg}}^{\mathrm{albedo}}$ from (10), the LPIPS scores for image and albedo map reconstruction increase to 0.249 and 0.264, respectively. Note that the error for albedo maps increases significantly while the error for normal maps re + +mains roughly the same. This indicates that without $\mathcal{L}_{\mathrm{reg}}^{\mathrm{albedo}}$ the light information leaks into the albedo image. An example of this behavior can also be seen in Fig 3c (w/o $\mathcal{L}_{\mathrm{reg}}^{\mathrm{albedo}}$ ). + +Next, we evaluate the impact of coarse geometry and albedo texture on RANA. If we do not use coarse geometry and albedo, LPIPS score increases to 0.242 as compared to 0.217 for the full model. The normal error also increases + +to $65.9^{\circ}$ from $64.3^{\circ}$ . This is also evident from the qualitative results shown in Fig 3d, indicating that coarse geometry and albedo help in improved image synthesis quality, in particular when the target body pose is far from the training poses. Next, we evaluate the impact of pretraining on synthetic data. Without the pretraining, all error metrics increase significantly. Specifically, the LPIPS score for image reconstruction increases from 0.217 to 0.301, while the normal error increases from $64.3^{\circ}$ to $74.2^{\circ}$ . If we look at Fig 3e, we can see that shading information leaks into both the normals and albedo maps. Hence, pretraining the networks also helps with the plausible disentanglement of geometry, texture, and light. Thanks to the design of RANA, we can pretrain on as many subjects as available, which is not possible with most of the state-of-the-art methods for human synthesis [45, 46, 58, 31]. Finally, as discussed in Sec 3.3.1, we keep the network $G_{N}$ fixed during finetuning if RANA is pretrained on synthetic data. In the last row of Tab. 2, we evaluate the case when $G_{N}$ is also fine-tuned. We can see that it has a negligible impact on the results. + +# 4.4. Comparison with other methods + +Since ours is the first work that simultaneously evaluates novel light and pose synthesis, we ourselves build some baselines as follows: + +Relightable SMPL+D: We rasterize the SMPL+D mesh normals and albedo texture estimated using TextureNet in the target body pose and use SH lighting to generate the shaded images. + +ANR [47]+RH[33]: We train an ANR [47] model which synthesizes images in the lighting of the training video. We then pass the generated images to the single-image human relighting method Relighting Humans (RH) [33] to obtain the relighted images for the target light. We use the publicly available source code and models of [33]. + +Relighting4D [16] is a state-of-the-art human video relighting method. We use the publicly available source code and train it on our dataset. + +The results are summarized in Tab. 3 and Fig 4. We do not report results of Relighting4D [16] for protocol-a since it cannot handle novel body poses as can be seen in Fig 4 (column-5). For protocol-a, our method clearly outperforms other baselines for final image synthesis results. Surprisingly, the SMPL+D baseline yields better numbers for albedo reconstruction, even though it provides overly smooth albedo textures. This is because TextureNet is trained on synthetic data, hence albedo maps in SMPL+D baseline achieve the best result in this synthetic data benchmark. However, the SMPL+D baseline does not produce the best image quality. RANA, on the other hand, achieves significantly better image quality while staying close to the + +unlit texture in SMPL+D. + +For protocol-b, we only compare the best two methods from protocol-a as we found it unnecessary to retrain ANR based on the results of protocol-a. As we can see in Tab. 3, the results are consistent with protocol-a. + +For protocol-c, we compare with a video-based relighting method Relighting4D [16] and the single-image-based relighting method Relighting Humans [33]. RANA outperforms both methods across all metrics. Some qualitative comparisons with Relighting4D [16] can be seen in Fig. 4 (columns 6-7), where RANA clearly yields better image relighting results. Note that each model for Relighting4D [16] requires $260\mathrm{k}$ iterations for training whereas RANA models are trained only for $15\mathrm{k}$ iterations, thanks to our novel design that allows pre-training on synthetic data, allowing quick fine-tuning for new subjects. In contrast, Relighting4D [16] by design cannot be pretrained easily on multiple subjects. On the other hand, the method [33] is trained for up-right frontal poses only and cannot handle arbitrary body poses, resulting in inferior relighting performance. This is also the main reason behind the inferior performance of the ANR $[47] + \mathrm{RH}$ [33] baseline for protocol-a. + +Finally, we provide additional qualitative results of avatars animated with complex motions in the supp. video. + +# 5. Conclusion and Future Work + +We presented RANA which is a novel framework for learning reconfigurable and articulated neural avatars of humans. We demonstrated that RANA can model humans from unconstrained RGB videos while also disentangling their geometry, albedo texture, and environmental lighting. We showed that it can generate high-quality images of people under any novel body pose, viewpoint, and lighting. RANA can be trained simultaneously for multiple people and we showed that pre-training it on multiple (400) synthetic characters significantly improves the image synthesis quality. We also proposed a new photo-realistic synthetic dataset (Relighting Human) to quantitatively evaluate the performance of our proposed method, and believe that it will prove to be very useful to further the research in this direction. + +The most pressing limitation of RANA is the assumption of Lambertian surface, no cast shadows, and image-based lighting. 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In TIP, 2021. 3 +[64] Ze Yang, Shenlong Wang, Sivabalan Manivasagam, Zeng Huang, Wei-Chiu Ma, Xinchen Yan, Ersin Yumer, and Raquel Urtasun. S3: Neural shape, skeleton, and skinning fields for 3d human modeling. In CVPR, 2021. 2 +[65] Yu-Ying Yeh, Koki Nagano, Sameh Khamis, Jan Kautz, Ming-Yu Liu, and Ting-Chun Wang. Learning to relight portrait images via a virtual light stage and synthetic-to-real adaptation. SIGGRAPH ASIA, 2022. 3 + +[66] Jae Shin Yoon, Duygu Ceylan, Tuanfeng Y. Wang, Jingwan Lu, Jimei Yang, Zhixin Shu, and Hyun Soo Park. Learning motion-dependent appearance for high-fidelity rendering of dynamic humans from a single camera. In CVPR, 2022. 2, 3 +[67] Hongyi Zhang, Moustapha Cisse, Yann N. Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. In ICLR, 2018. 5 +[68] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In CVPR, 2018. 7 +[69] Xiuming Zhang, Sean Fanello, Yun-Ta Tsai, Tiancheng Sun, Tianfan Xue, Rohit Pandey, Sergio Orts-Escalano, Philip Davidson, Christoph Rhemann, Paul Debevec, et al. Neu + +ral light transport for relighting and view synthesis. SIGGRAPH, 2021. 3 +[70] Hao Zhao, Jinsong Zhang, Yu-Kun Lai, Zerong Zheng, Yingdi Xie, Yebin Liu, and Kun Li. High-fidelity human avatars from a single rgb camera. In CVPR, 2022. 3 +[71] Tiancheng Zhi, Christoph Lassner, Tony Tung, Carsten Stoll, Srinivasa G Narasimhan, and Minh Vo. Texmesh: Reconstructing detailed human texture and geometry from rgb-video. In ECCV, 2020. 2, 3 +[72] Hao Zhou, Sunil Hadap, Kalyan Sunkavalli, and David W. Jacobs. Deep single portrait image relighting. 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We only require a short video clip of the person to create the avatar and assume no knowledge about the lighting environment. We present a novel framework to model humans while disentangling their geometry, texture, and lighting environment from monocular RGB videos. To simplify this otherwise ill-posed task we first estimate the coarse geometry and texture of the person via SMPL+D model fitting and then learn an articulated neural representation for higher quality image syn" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 525, + 547, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 525, + 547, + 646 + ], + "spans": [ + { + "bbox": [ + 304, + 525, + 547, + 646 + ], + "type": "text", + "content": "thesis. RANA first generates the normal and albedo maps of the person in any given target body pose and then uses spherical harmonics lighting to generate the shaded image in the target lighting environment. We also propose to pre-train RANA using synthetic images and demonstrate that it leads to better disentanglement between geometry and texture while also improving robustness to novel body poses. Finally, we also present a new photo-realistic synthetic dataset, Relighting Human, to quantitatively evaluate the performance of the proposed approach." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 669, + 387, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 387, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 387, + 681 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "text", + "content": "Articulated neural avatars of humans have numerous applications across telepresence, animation, and visual con" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 693, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 287, + 712 + ], + "type": "text", + "content": "*equal contribution. The work was partially done during AC's internship at NVIDIA." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23142" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "content": "tent creation. To enable the widespread adoption of these neural avatars, they should be easy to generate and animate under novel poses and viewpoints, able to render in photorealistic image quality, and easy to relight in novel environments. Existing methods commonly aim to learn such neural avatars using monocular videos [47, 46, 45, 54, 66, 58, 31]. While this allows photo-realistic image quality and animation, the synthesized images are always limited to the lighting environment of the training video. Other works directly tackle relighting of human avatars but do not provide control over the body pose [23, 41]. Moreover, these approaches often require multiview images recorded in a Light Stage for training, which is limited to controlled settings only. Some recent methods aim to relight RGB videos of a dynamic human but do not provide control over body pose [16]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 267, + 289, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 267, + 289, + 363 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 289, + 363 + ], + "type": "text", + "content": "In this work, we present the Relightable Articulated Neural Avatar (RANA) method, which allows animation of people under any novel body pose, viewpoint, and lighting environment. To create an avatar, we only require a short monocular video clip of the person in unconstrained environment, clothing, and arbitrary body pose. During inference, we only require the target body pose and target lighting information." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 367, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 367, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 367, + 289, + 715 + ], + "type": "text", + "content": "Learning relightable neural avatars of dynamics humans from monocular RGB videos recorded in unknown environments is a challenging problem. First, it requires modeling the complex human body articulations and geometry. Second, in order to allow relighting under novel environments, the texture, geometry, and illumination information have to be disentangled, which is an ill-posed problem to solve from RGB videos [8]. To address these challenges, we first extract canonical coarse geometry and texture information from the training frames using a statistical human shape model SMPL+D [40, 5, 36]. We then propose a novel convolutional neural network that is trained on synthetic data to remove the shading information from the coarse texture. We augment the coarse geometry and texture with learnable latent features and pass them to our proposed neural avatar framework, which generates refined normal and albedo maps of the person under the target body pose using two separate convolutional networks. Given the normal map, albedo map, and lighting information, we generate the final shaded image using spherical harmonics (SH) lighting [49]. During training, since the environment lighting is unknown, we jointly optimize it together with the person's appearance and propose novel regularization terms to prevent the leaking of lighting into the albedo texture. We also propose to pre-train the avatar using photo-realistic synthetic data with ground-truth albedo and normal maps. During pretraining, we train a single model for multiple subjects while having separate neural features for each subject. This not only improves the generalizability of the neural avatar" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "to novel body poses but also learns to decouple the texture and geometry information. For a new subject, we only learn a new set of neural features and fine-tune the avatar model to capture fine-grained person-specific details. In our experiments, the avatar for a novel subject can be learned within 15k training iterations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 144, + 547, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 547, + 228 + ], + "type": "text", + "content": "Since no dataset exists to evaluate the renderings of avatars in terms of both novel light and pose synthesis, we also propose a novel photo-realistic synthetic Relighting Human Dataset (RHD) with ground truth albedo, normals, and lighting information. We also perform a qualitative evaluation of RANA on the People Snapshot dataset [5] to compare with other baselines." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 229, + 517, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 229, + 517, + 241 + ], + "spans": [ + { + "bbox": [ + 317, + 229, + 517, + 241 + ], + "type": "text", + "content": "Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 251, + 545, + 404 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 317, + 251, + 545, + 311 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 251, + 545, + 311 + ], + "spans": [ + { + "bbox": [ + 317, + 251, + 545, + 311 + ], + "type": "text", + "content": "- We present, RANA, a novel framework for learning relightable articulated neural avatars from short unconstrained monocular videos. The proposed approach is very easy to train and does not require any knowledge about the environment lighting of the training video." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 316, + 545, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 316, + 545, + 364 + ], + "spans": [ + { + "bbox": [ + 317, + 316, + 545, + 364 + ], + "type": "text", + "content": "- Our proposed approach can synthesize images of articulated humans under any arbitrary body pose, viewpoint, and lighting. It can also be used for relighting videos of dynamic humans." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 369, + 545, + 404 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 369, + 545, + 404 + ], + "spans": [ + { + "bbox": [ + 317, + 369, + 545, + 404 + ], + "type": "text", + "content": "- We present a new photo-realistic synthetic dataset for quantitative evaluation and to further the research in this direction." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 418, + 390, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 418, + 390, + 430 + ], + "spans": [ + { + "bbox": [ + 306, + 418, + 390, + 430 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 438, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 547, + 715 + ], + "type": "text", + "content": "Mesh Based Human Avatars. These methods represent human avatars using a rigged mesh and an associated texture map. Earlier methods captured human avatars using multi-view cameras [12, 53] or with the help of depth sensors [9, 71]. However, their adoption remained limited due to the constrained hardware requirements. The recent works, therefore, focus on creating the avatars from monocular videos [5, 4, 31, 10], or images [36, 64, 27, 25, 6, 10, 11]. The methods [5, 4, 36] use body model fitting to capture the humans, while more recent methods use data-driven implicit functions combined with pixel-aligned features [50] for human reconstruction [71, 27, 64, 6]. Self-Recon [31] combines both explicit and implicit meshes to reconstruct the detailed geometry of the person from self-rotating videos, however, it requires manual human effort to make the avatar animatable. The main limitation of these methods, however, is that the shading information is baked into the texture. Hence, the avatars cannot be rendered with novel lights. The recent methods PHORUM [6] and S3F [17] are the only exceptions, however, they create avatar from a single image and rely on data-driven priors to hallucinate the occluded regions of the person. Hence, the generated images may not be the true representation of the" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23143" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 71, + 277, + 174 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 277, + 174 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 277, + 174 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 277, + 174 + ], + "type": "image", + "image_path": "c4046231706afa8751158ef0e51b64103a8046ca4f452eb46733aae3e19b3b3a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 175, + 287, + 208 + ], + "lines": [ + { + "bbox": [ + 47, + 175, + 287, + 208 + ], + "spans": [ + { + "bbox": [ + 47, + 175, + 287, + 208 + ], + "type": "text", + "content": "Table 1. Comparison of some of the representative methods for neural human avatar creation. Ours (RANA) is the only method that allows novel view, pose and light synthesis." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 288, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 288, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 288, + 264 + ], + "type": "text", + "content": "person. In contrast, our approach uses video data to capture a detailed human representation, while also allowing the rendering of the person in novel lighting." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 276, + 289, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 289, + 562 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 289, + 562 + ], + "type": "text", + "content": "Neural Human Avatars. More recent methods learn a neural representation of the person and use neural renderers [57] to directly generate photo-realistic images in the target body pose and viewpoints [7, 20, 13, 59, 26, 63]. These methods are generally classified into 2D or 3D neural rendering based methods [57]. The 3D neural rendering methods represent the person using neural radiance fields [42] and render the target images using volume rendering [46, 62, 32, 45, 14, 58, 24, 38]. The 2D neural rendering methods, on the other hand, use CNNs to render the images [47, 66, 22, 70]. One limitation of the 3D neural rendering methods is that the avatar has to be created from scratch for each person. Some methods learn generalizable avatars but require exemplar images of the person during inference [34, 48]. In contrast, the 2D based methods offer some generalizability by sharing the neural renderer across multiple subjects [47]. Our method falls into the 2D neural rendering paradigm as we use CNNs to generate the albedo and normal images of the person. In particular, we take inspiration from ANR [47] for designing our framework. Tab. 1 compares existing neural avatar creation methods. Ours is the only method that allows synthesis under novel poses, viewpoints, and lighting, while also being generalizable." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": "Human Relighting. Relighting of human images has been studied extensively in the literature [18, 51, 33, 55, 72, 61, 56, 30, 37, 35, 69, 17]. However, these methods cannot render relighted images in novel body poses and viewpoints. Some recent methods allow relighting from novel views but provide no control over the body pose [23, 43, 16, 65]. The method TexMesh [71] also provides control over body pose but requires RGB-D videos for training and assumes that the environment map of the training video is known. Our approach, in contrast, provides full control over the body pose, viewpoint, and lighting, and learns the avatar from RGB videos with unknown lighting." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 71, + 362, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 362, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 362, + 84 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 91, + 547, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 415 + ], + "type": "text", + "content": "Our goal is to learn a relightable articulated neural avatar, RANA, that can synthesize high-quality images of the person under any target body pose, viewpoint, and lighting. To create the avatar, we use a small video sequence " + }, + { + "bbox": [ + 304, + 91, + 547, + 415 + ], + "type": "inline_equation", + "content": "\\mathbf{I} = \\{I_{\\mathrm{f}}\\}_{f = 1}^{F}" + }, + { + "bbox": [ + 304, + 91, + 547, + 415 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 91, + 547, + 415 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 91, + 547, + 415 + ], + "type": "text", + "content": " video frames and assume no knowledge about the lighting environment and body poses present in the video. We parameterize RANA using the SMPL [40] body model to control the animation and use Spherical Harmonics (SH) [49] lighting to model the lighting. During inference, we only need the target body pose and target lighting information in the form of SH coefficients and do not require any exemplar images for ground-truth. Learning RANA from a monocular video requires capturing the geometry and appearance of the dynamic human while also disentangling the shading information. In order to tackle this ill-posed problem, we first capture the coarse geometry using the SMPL+D fits (Sec. 3.1). We use the coarse geometry to extract a coarse texture map from the training images which is converted to an albedo texture map using a convolutional network (Sec. 3.2). We then propose RANA that generates the refined albedo and normal maps. The refined normal maps are used to obtain the shading map using SH lighting which is combined with the refined albedo map to obtain the final image in the target body pose and light (Sec. 3.3). An overview of our method can be seen in Fig. 1. In the following, we describe each of these modules in greater detail." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 424, + 466, + 437 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 424, + 466, + 437 + ], + "spans": [ + { + "bbox": [ + 305, + 424, + 466, + 437 + ], + "type": "text", + "content": "3.1. Coarse Geometry Estimation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 443, + 547, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 443, + 547, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 443, + 547, + 598 + ], + "type": "text", + "content": "Given the training frames, we first estimate the coarse geometry of the person including the clothing and hair details. For this, we employ the SMPL+D [4, 36] variant of the SMPL body model [40]. SMPL is a linear function " + }, + { + "bbox": [ + 304, + 443, + 547, + 598 + ], + "type": "inline_equation", + "content": "M(\\theta, \\beta)" + }, + { + "bbox": [ + 304, + 443, + 547, + 598 + ], + "type": "text", + "content": " that takes the body pose " + }, + { + "bbox": [ + 304, + 443, + 547, + 598 + ], + "type": "inline_equation", + "content": "\\theta \\in \\mathbb{R}^{72}" + }, + { + "bbox": [ + 304, + 443, + 547, + 598 + ], + "type": "text", + "content": " and shape parameters " + }, + { + "bbox": [ + 304, + 443, + 547, + 598 + ], + "type": "inline_equation", + "content": "\\beta \\in \\mathbb{R}^{10}" + }, + { + "bbox": [ + 304, + 443, + 547, + 598 + ], + "type": "text", + "content": " as input and produces a triangulated mesh " + }, + { + "bbox": [ + 304, + 443, + 547, + 598 + ], + "type": "inline_equation", + "content": "\\mathbf{M} \\in \\mathbb{R}^{V \\times 3}" + }, + { + "bbox": [ + 304, + 443, + 547, + 598 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 443, + 547, + 598 + ], + "type": "inline_equation", + "content": "V = 6890" + }, + { + "bbox": [ + 304, + 443, + 547, + 598 + ], + "type": "text", + "content": " vertices. SMPL only captures the undressed shape of the body and ignores the clothing and hair details. For this, SMPL+D adds a set of 3D offsets " + }, + { + "bbox": [ + 304, + 443, + 547, + 598 + ], + "type": "inline_equation", + "content": "\\mathbf{D} \\in \\mathbf{R}^{V \\times 3}" + }, + { + "bbox": [ + 304, + 443, + 547, + 598 + ], + "type": "text", + "content": " to SMPL to capture the additional geometric details, i.e., " + }, + { + "bbox": [ + 304, + 443, + 547, + 598 + ], + "type": "inline_equation", + "content": "M(\\theta, \\beta, \\mathbf{D}) \\in \\mathbb{R}^{V \\times 3}" + }, + { + "bbox": [ + 304, + 443, + 547, + 598 + ], + "type": "text", + "content": " can also model clothed humans. We refer the readers to [36, 4] for a detailed description of SMPL+D." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 599, + 547, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 599, + 547, + 672 + ], + "spans": [ + { + "bbox": [ + 304, + 599, + 547, + 672 + ], + "type": "text", + "content": "For fitting SMPL+D to training images, we first estimate the parameters of SMPL using an off-the-shelf method SMPLify3D [29]. Since the person in the video remains the same, we optimize a single " + }, + { + "bbox": [ + 304, + 599, + 547, + 672 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 599, + 547, + 672 + ], + "type": "text", + "content": " for the entire video. We then fix the pose " + }, + { + "bbox": [ + 304, + 599, + 547, + 672 + ], + "type": "inline_equation", + "content": "\\{\\theta\\}_{f=1}^{F}" + }, + { + "bbox": [ + 304, + 599, + 547, + 672 + ], + "type": "text", + "content": " and shape " + }, + { + "bbox": [ + 304, + 599, + 547, + 672 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 599, + 547, + 672 + ], + "type": "text", + "content": " parameters and optimize for the offsets " + }, + { + "bbox": [ + 304, + 599, + 547, + 672 + ], + "type": "inline_equation", + "content": "\\mathbf{D}" + }, + { + "bbox": [ + 304, + 599, + 547, + 672 + ], + "type": "text", + "content": " using the following objective:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 310, + 681, + 547, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 681, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 310, + 681, + 547, + 715 + ], + "type": "interline_equation", + "content": "\\mathbf {D} = \\underset {\\mathbf {D} ^ {\\prime}} {\\operatorname {a r g m i n}} \\sum_ {f = 1} ^ {F} \\mathcal {L} \\left(M \\left(\\theta_ {f}, \\beta , \\mathbf {D} ^ {\\prime}\\right)\\right) = \\mathcal {L} _ {\\mathrm {S i l}} + \\mathcal {L} _ {\\mathrm {s m o o t h}}. 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Overview of the proposed approach. (a) shows some training frames. (b) We estimate the coarse geometry of the person using the SMPL+D body model. (c) The SMPL+D fits are used to extract a UV texture map, which we process using TextureNet to obtain a coarse albedo texture map. (d) Given a target body pose, we rasterize person-specific neural features, coarse albedo, and coarse normals from SMPL+D to the target body pose and pass them to NormalNet and AlbedoNet to obtain refined normal and albedo maps, respectively. We then use the normal map and spherical harmonics lighting to obtain the shading image, which is multiplied with refined albedo to produce the shaded image. AlbedoNet also generates a binary mask, which we use to overlay the shaded image onto the background." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 415, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 477 + ], + "type": "text", + "content": "Here the term " + }, + { + "bbox": [ + 46, + 415, + 287, + 477 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{Sil}}" + }, + { + "bbox": [ + 46, + 415, + 287, + 477 + ], + "type": "text", + "content": " is the silhouette loss. We obtain the silhouette of SMPL+D vertices " + }, + { + "bbox": [ + 46, + 415, + 287, + 477 + ], + "type": "inline_equation", + "content": "S_{f}" + }, + { + "bbox": [ + 46, + 415, + 287, + 477 + ], + "type": "text", + "content": " for frame " + }, + { + "bbox": [ + 46, + 415, + 287, + 477 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 415, + 287, + 477 + ], + "type": "text", + "content": " using a differentiable renderer [39] while the target silhouette " + }, + { + "bbox": [ + 46, + 415, + 287, + 477 + ], + "type": "inline_equation", + "content": "\\hat{S}_t" + }, + { + "bbox": [ + 46, + 415, + 287, + 477 + ], + "type": "text", + "content": " is obtained using a person segmentation model [15]. We define the " + }, + { + "bbox": [ + 46, + 415, + 287, + 477 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{Sil}}" + }, + { + "bbox": [ + 46, + 415, + 287, + 477 + ], + "type": "text", + "content": " loss as" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 115, + 482, + 287, + 516 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 482, + 287, + 516 + ], + "spans": [ + { + "bbox": [ + 115, + 482, + 287, + 516 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {S i l}} = \\frac {1}{F} \\sum_ {f = 1} ^ {F} \\left| S _ {f} - \\hat {S} _ {f} \\right|. \\tag {2}", + "image_path": "c6bf0f2bb6b25657085fd695d53c786a0cde2b5dfd380fa81a8f7b1e971405b4.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 47, + 522, + 287, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 522, + 287, + 546 + ], + "spans": [ + { + "bbox": [ + 47, + 522, + 287, + 546 + ], + "type": "text", + "content": "The term " + }, + { + "bbox": [ + 47, + 522, + 287, + 546 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{smooth}}" + }, + { + "bbox": [ + 47, + 522, + 287, + 546 + ], + "type": "text", + "content": " is a laplacian smoothing term to encourage the smooth surface of the mesh:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 110, + 552, + 287, + 586 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 552, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 110, + 552, + 287, + 586 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s m o o t h}} = \\frac {1}{F} \\sum_ {f = 1} ^ {F} | | L \\mathbf {M} _ {f} | |, \\tag {3}", + "image_path": "a071273cfb7f49dc7c8e5b22d6564163280ff262db95be64f4c5982087bdd61e.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 593, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 593, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 593, + 287, + 641 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 593, + 287, + 641 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 593, + 287, + 641 + ], + "type": "text", + "content": " is the mesh Laplacian operator. Note that we optimize a single set of " + }, + { + "bbox": [ + 46, + 593, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathbf{D}" + }, + { + "bbox": [ + 46, + 593, + 287, + 641 + ], + "type": "text", + "content": " for the entire video, hence it does not model any pose-dependent geometric deformations. Some examples of SMPL+D can be seen in Fig. 1b." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 47, + 647, + 194, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 194, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 194, + 659 + ], + "type": "text", + "content": "3.2. Coarse Albedo Estimation" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Given the SMPL+D fits for the training frames, we estimate an albedo texture map " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "T_{A}" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " of the person in the UV space of SMPL. We follow [5] and first extract a partial texture map for each frame by back-projecting the image colors" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 415, + 546, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 546, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 546, + 536 + ], + "type": "text", + "content": "of all visible vertices to the UV space. The final texture map " + }, + { + "bbox": [ + 304, + 415, + 546, + 536 + ], + "type": "inline_equation", + "content": "T_{I}" + }, + { + "bbox": [ + 304, + 415, + 546, + 536 + ], + "type": "text", + "content": " is then generated by calculating the median color value of most orthogonal texels from all frames. Depending on the available body poses in the training video, the obtained texture map can be noisy, and still have missing regions, e.g., hand regions are often very noisy as no hand tracking is performed during SMPL fitting. Also, to ensure plausible relighting, the unknown shading from the texture map has to be removed, which is a challenging problem since decomposing shading and albedo is an ill-posed problem." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "content": "To address these problems, we propose TextureNet, " + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{Tex}}" + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "content": " (Fig. 1c), which takes a noisy texture map " + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "inline_equation", + "content": "T_I" + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "content": " with unknown lighting as input and produces a clean albedo texture map as output, i.e., " + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "inline_equation", + "content": "T_A = G_{\\mathrm{Tex}}(T_I)" + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "content": " [36, 28]. One main challenge for training such a model is the availability of training pairs of noisy/shaded and albedo texture maps. We generate these pairs using 400 rigged characters from the RenderPeople dataset [2]. Since each character in RenderPeople has different UV coordinates, we follow [36] and register the characters with SMPL to obtain ground-truth UV maps in consistent SMPL UV coordinates. For noisy pairs, we generate images with random poses and lighting and extract texture maps like any other video mentioned" + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23145" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 247, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 247, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 247, + 85 + ], + "type": "text", + "content": "above. We train " + }, + { + "bbox": [ + 47, + 72, + 247, + 85 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{Tex}}" + }, + { + "bbox": [ + 47, + 72, + 247, + 85 + ], + "type": "text", + "content": " using the following losses:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 97, + 94, + 287, + 107 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 94, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 97, + 94, + 287, + 107 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {T e x}} = \\mathcal {L} _ {\\text {p i x e l}} + \\mathcal {L} _ {\\mathrm {V G G}} + \\mathcal {L} _ {\\mathrm {G A N}}. \\tag {4}", + "image_path": "303b02e930aaf5df2eeac2e21a80d8b5f840660eb3ec65dd99c046d674b1c59c.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{pixel}}" + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "text", + "content": " loss between the predicted and ground-truth albedo texture maps, " + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{VGG}}" + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "text", + "content": " difference between their VGG features, and " + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{GAN}}" + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "text", + "content": " is the GAN loss [21, 44]. We use a vanilla U-Net architecture for TextureNet. It takes a noisy/shaded UV texture map with a resolution of " + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "inline_equation", + "content": "512\\times 512" + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "text", + "content": " as input and produces the albedo texture with the same resolution as output. We also concatenate a 2D tensor of UV coordinates with the input texture map to provide part-specific information to the model. We train the network using Adam optimizer with a batch size of 8 and a learning rate of " + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "inline_equation", + "content": "1e^{-4}" + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "text", + "content": " with cosine annealing and a minimum learning rate of " + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "inline_equation", + "content": "1e^{-5}" + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "text", + "content": ". To avoid overfitting during training, we perform random noise augmentation to the input texture maps including coarse dropout, gaussian noise, random brightness, and MixUp (" + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "inline_equation", + "content": "\\beta = 0.4" + }, + { + "bbox": [ + 46, + 117, + 289, + 309 + ], + "type": "text", + "content": ") [67]. Some examples of estimated albedo maps can be seen in Fig. 2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 316, + 250, + 328 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 250, + 328 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 250, + 328 + ], + "type": "text", + "content": "3.3. Relightable Articulated Neural Avatar" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 334, + 289, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 334, + 289, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 334, + 289, + 502 + ], + "type": "text", + "content": "The coarse albedo texture and geometry obtained so far lack photo-realism and fine-grained details of the person. First, the topology of SMPL+D is fixed and cannot fully capture the fine geometric details, for example, loose clothing or long hairs. Second, the TextureNet can confuse the texture of the person with shading and may remove some texture details while estimating the albedo texture map. In this section, we present RANA which utilizes the coarse geometry and albedo map and generates higher quality images of the person. We parametrize RANA using the SMPL body model and SH lighting [5]. Specifically, RANA takes the target body pose " + }, + { + "bbox": [ + 46, + 334, + 289, + 502 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 334, + 289, + 502 + ], + "type": "text", + "content": " and the target lighting in the form of second-order spherical harmonics coefficients " + }, + { + "bbox": [ + 46, + 334, + 289, + 502 + ], + "type": "inline_equation", + "content": "E\\in \\mathbb{R}^{9\\times 3}" + }, + { + "bbox": [ + 46, + 334, + 289, + 502 + ], + "type": "text", + "content": " as input and synthesizes the target image " + }, + { + "bbox": [ + 46, + 334, + 289, + 502 + ], + "type": "inline_equation", + "content": "I^{\\theta ,E}" + }, + { + "bbox": [ + 46, + 334, + 289, + 502 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 117, + 510, + 287, + 525 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 510, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 117, + 510, + 287, + 525 + ], + "type": "interline_equation", + "content": "I ^ {\\theta , E} = \\operatorname {R A N A} (\\theta , E, K), \\tag {5}", + "image_path": "105171ac204a1319d076087139274fcdbc7a45a4ed79460f3983e09cda3fc8e2.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "content": " corresponds to the intrinsic parameters of the target camera viewpoint. One main challenge in learning such a neural avatar from a short RGB video is to maintain the disentanglement of geometry, albedo, and lighting, as any learnable parameters can overfit the training frames disregarding plausible disentanglement. Hence, we design RANA such that a plausible disentanglement is encouraged during training. Specifically, RANA consists of two convolutional neural networks NormalNet, " + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{N}}" + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "content": ", and AlbedoNet, " + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "inline_equation", + "content": "G_{\\mathrm{A}}" + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "content": ", each responsible for generating the normal map " + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "inline_equation", + "content": "I_N^\\theta \\in \\mathbb{R}^{h\\times w\\times 3}" + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "content": ", and albedo map, " + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "inline_equation", + "content": "I_A^\\theta \\in \\mathbb{R}^{h\\times w\\times 3}" + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "content": ", of the person in the body pose " + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "content": ", respectively. It also consists of a set of subject-specific latent neural features " + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "inline_equation", + "content": "Z \\in \\mathbb{R}^{256\\times 256\\times 16}" + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "content": " in UV coordinates to augment the details available in the coarse albedo map and geometry." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "text", + "content": "More specifically, given the target body pose " + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "text", + "content": ", we first generate the SMPL+D mesh " + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^{\\theta} = M(\\theta ,\\beta ,\\mathbf{D})" + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "text", + "content": ", where the shape parameters " + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "text", + "content": " and clothing offsets " + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "inline_equation", + "content": "\\mathbf{D}" + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "text", + "content": " are the ones obtained in Sec. 3.1. We then use " + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^{\\theta}" + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "text", + "content": " to differentiably rasterize [39] the latent features " + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "text", + "content": " and coarse albedo texture " + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "inline_equation", + "content": "T_{A}" + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "text", + "content": " to obtain a features image " + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "inline_equation", + "content": "I_Z^\\theta" + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "text", + "content": " and coarse albedo image " + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "inline_equation", + "content": "\\bar{I}_A^\\theta" + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "text", + "content": " in the target body pose. We also rasterize a coarse normal image " + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "inline_equation", + "content": "\\bar{I}_N^\\theta" + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "text", + "content": " and a UV image " + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{uv}}^\\theta" + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "text", + "content": " using the normals and UV coordinates of " + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "inline_equation", + "content": "M^{\\theta}" + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "text", + "content": ", respectively. The refined normal image " + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "inline_equation", + "content": "I_N^\\theta" + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "text", + "content": " and refined albedo image " + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "inline_equation", + "content": "I_A^\\theta" + }, + { + "bbox": [ + 304, + 72, + 547, + 194 + ], + "type": "text", + "content": " are then obtained as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 376, + 201, + 545, + 216 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 201, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 376, + 201, + 545, + 216 + ], + "type": "interline_equation", + "content": "I _ {N} ^ {\\theta} = G _ {N} \\left(I _ {Z} ^ {\\theta}, \\bar {I} _ {N} ^ {\\theta}, \\gamma \\left(I _ {\\mathrm {u v}} ^ {\\theta}\\right)\\right), \\tag {6}", + "image_path": "493f33bda7740cb84ed4b7bf231b0ad2af161840d19449c9f913a653064ac991.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 362, + 217, + 545, + 232 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 217, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 362, + 217, + 545, + 232 + ], + "type": "interline_equation", + "content": "I _ {A} ^ {\\theta}, S ^ {\\theta} = G _ {A} \\left(I _ {Z} ^ {\\theta}, \\bar {I} _ {A} ^ {\\theta}, \\gamma \\left(I _ {\\mathrm {u v}} ^ {\\theta}\\right)\\right), \\tag {7}", + "image_path": "9bd167cd1640c73d91b555f4e6f11c5989e0b17f0ddb383c806672ab8cfb156d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "type": "inline_equation", + "content": "S^{\\theta}" + }, + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "type": "text", + "content": " is the person mask in the target pose and " + }, + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "type": "text", + "content": " corresponds to the positional encoding of the UV coordinates [42]. Given the lighting " + }, + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "type": "text", + "content": ", we obtain the shading image " + }, + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "type": "inline_equation", + "content": "I_S^{\\theta ,E}" + }, + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "type": "text", + "content": " using the normal map " + }, + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "type": "inline_equation", + "content": "I_N^\\theta" + }, + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "type": "text", + "content": " and SH lighting [49]. Under the usual assumptions of Lambertian material, distant lighting, and no cast shadows, the final shaded image " + }, + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "type": "inline_equation", + "content": "I^{\\theta ,E}" + }, + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "type": "text", + "content": " is then obtained as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 389, + 335, + 545, + 352 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 335, + 545, + 352 + ], + "spans": [ + { + "bbox": [ + 389, + 335, + 545, + 352 + ], + "type": "interline_equation", + "content": "I ^ {\\theta , E} = I _ {A} ^ {\\theta} \\cdot I _ {S} ^ {\\theta , E}. \\tag {8}", + "image_path": "74f8cf2881dd59510e39a5025b57b5a23ca8cf7161425d31ea6b0d349adf9ba9.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 361, + 547, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 547, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 547, + 492 + ], + "type": "text", + "content": "An overview of RANA can be seen in Fig. 1d. Since the lighting environment of the training video is unknown, we also optimize the second order SH coefficients " + }, + { + "bbox": [ + 304, + 361, + 547, + 492 + ], + "type": "inline_equation", + "content": "E \\in \\mathbb{R}^{9 \\times 3}" + }, + { + "bbox": [ + 304, + 361, + 547, + 492 + ], + "type": "text", + "content": " [49] of the training video during training. Under the assumption of Lambertian surface, none of the learnable parameters in RANA depend on the lighting information. Hence, if the disentanglement of normals, albedo, and lighting during training is correct, we can simply replace " + }, + { + "bbox": [ + 304, + 361, + 547, + 492 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 361, + 547, + 492 + ], + "type": "text", + "content": " during inference with any other novel lighting environment to obtain relit images. We train RANA with the following objective:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 329, + 503, + 545, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 503, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 329, + 503, + 545, + 533 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\text {p i x e l}} + \\mathcal {L} _ {\\text {f a c e}} + \\mathcal {L} _ {\\text {m a s k}} + \\mathcal {L} _ {\\mathrm {V G G}} + \\mathcal {L} _ {\\mathrm {G A N}} (9) \\\\ + \\mathcal {L} _ {\\text {r e g}} ^ {\\text {a l b e d o}} + \\mathcal {L} _ {\\text {r e g}} ^ {\\text {n o r m a l}}. (10) \\\\ \\end{array}", + "image_path": "8a8cda275e978830881812b37759c338722d0dc3b273b426d35941b1a69aef79.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{pixel}}" + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "text", + "content": " difference between the generated image " + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "inline_equation", + "content": "I^{\\theta ,E}" + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "text", + "content": " and the ground-truth training frame, " + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{face}}" + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "text", + "content": " difference between their face regions to assign a higher weight to face, and " + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mask}}" + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "text", + "content": " is the binary-cross-entropy loss between the estimated mask " + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "inline_equation", + "content": "S^{\\theta}" + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "inline_equation", + "content": "G_{A}" + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "text", + "content": " and the pseudoground-truth mask obtained using a person segmentation model [15]. The term " + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{VGG}}" + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "text", + "content": " difference between the VGG features of generated and ground-truth images, and " + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{GAN}}" + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "text", + "content": " is the commonly used GAN loss [44, 21]. The term " + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}" + }, + { + "bbox": [ + 304, + 543, + 547, + 675 + ], + "type": "text", + "content": " is the albedo regularization term that prevents the light information from leaking into the albedo image:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 352, + 695, + 545, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 695, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 352, + 695, + 545, + 711 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e g}} ^ {\\text {a l b e d o}} = \\left\\| \\sigma \\left(I _ {A} ^ {\\theta}, k\\right) - \\sigma \\left(\\bar {I} _ {A} ^ {\\theta}, k\\right) \\right\\| ^ {2}. \\tag {11}", + "image_path": "64821343c3c9d7bca935fca8184da027bc817a81c5b1849b8e0a303a786f5507.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23146" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 135, + 153 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 135, + 153 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 135, + 153 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 135, + 153 + ], + "type": "image", + "image_path": "c2f24a0159874b9ae2a58729b566599659eb8b636a50522ac04db4b3401ffb65.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 51, + 153, + 135, + 236 + ], + "blocks": [ + { + "bbox": [ + 51, + 153, + 135, + 236 + ], + "lines": [ + { + "bbox": [ + 51, + 153, + 135, + 236 + ], + "spans": [ + { + "bbox": [ + 51, + 153, + 135, + 236 + ], + "type": "image", + "image_path": "6e41b09266594a0b8b6b12638a7666f5dd6d3e00e3b0ff70473a95b211bee87d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 58, + 236, + 129, + 246 + ], + "lines": [ + { + "bbox": [ + 58, + 236, + 129, + 246 + ], + "spans": [ + { + "bbox": [ + 58, + 236, + 129, + 246 + ], + "type": "text", + "content": "Noisy/Shaded Map" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 245, + 545, + 266 + ], + "lines": [ + { + "bbox": [ + 46, + 245, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 245, + 545, + 266 + ], + "type": "text", + "content": "Figure 2. Examples of estimated albedo maps from noisy/shaded maps using our proposed TextureNet (Sec. 3.2). The first row shows some examples from the PeopleSnapshot dataset, while the second row shows examples from our proposed RelightingHuman dataset." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 136, + 70, + 219, + 153 + ], + "blocks": [ + { + "bbox": [ + 136, + 70, + 219, + 153 + ], + "lines": [ + { + "bbox": [ + 136, + 70, + 219, + 153 + ], + "spans": [ + { + "bbox": [ + 136, + 70, + 219, + 153 + ], + "type": "image", + "image_path": "055247530e13fc6d0dc3d854374e36ded2aeaf7bccb65764af852d7946cfdf04.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 136, + 153, + 219, + 236 + ], + "blocks": [ + { + "bbox": [ + 136, + 153, + 219, + 236 + ], + "lines": [ + { + "bbox": [ + 136, + 153, + 219, + 236 + ], + "spans": [ + { + "bbox": [ + 136, + 153, + 219, + 236 + ], + "type": "image", + "image_path": 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It ensures that the regularization is applied only on the pixels where SMPL+D normals are valid. Note that no ground-truth supervision is provided to " + }, + { + "bbox": [ + 46, + 404, + 287, + 536 + ], + "type": "inline_equation", + "content": "G_{A}" + }, + { + "bbox": [ + 46, + 404, + 287, + 536 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 404, + 287, + 536 + ], + "type": "inline_equation", + "content": "G_{N}" + }, + { + "bbox": [ + 46, + 404, + 287, + 536 + ], + "type": "text", + "content": ". They are mostly learned via the image reconstruction losses, while the disentanglement of normals and albedo is ensured via the novel design of RANA and regularization losses. For " + }, + { + "bbox": [ + 46, + 404, + 287, + 536 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{face}}" + }, + { + "bbox": [ + 46, + 404, + 287, + 536 + ], + "type": "text", + "content": ", we project the nose keypoint of SMPL body model on to the image and crop a " + }, + { + "bbox": [ + 46, + 404, + 287, + 536 + ], + "type": "inline_equation", + "content": "100 \\times 100" + }, + { + "bbox": [ + 46, + 404, + 287, + 536 + ], + "type": "text", + "content": " patch around the face to compute the loss. All other losses are calculated on the " + }, + { + "bbox": [ + 46, + 404, + 287, + 536 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 404, + 287, + 536 + ], + "type": "text", + "content": " generated images." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 47, + 551, + 220, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 551, + 220, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 551, + 220, + 563 + ], + "type": "text", + "content": "3.3.1 Pre-training using synthetic data" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": "While we design RANA such that it generalizes well to novel body poses, the networks " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "G_{A}" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "G_{N}" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": " may still overfit to the body poses available in the training video, in particular, when the coarse geometry and albedo are noisy. A significant advantage of RANA is that it can be trained simultaneously for multiple subjects, i.e., we use different neural features " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": " for each subject while sharing the networks " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "G_{A}" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "G_{N}" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": ". This not only allows the model to see diverse body poses during pre-training but also helps in learning to disentangle normals and albedo. Hence, we propose to pretrain " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "G_{A}" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "G_{N}" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": " on synthetic data. For this, we use 400 rigged characters from the RenderPeople dataset. We" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 285, + 545, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 545, + 332 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 545, + 332 + ], + "type": "text", + "content": "generated 150 albedo and normal images for each subject under random body poses and pretrain both networks using ground-truth albedo and normal images. We use the " + }, + { + "bbox": [ + 304, + 285, + 545, + 332 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 304, + 285, + 545, + 332 + ], + "type": "text", + "content": " loss for both terms." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 349, + 407, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 349, + 407, + 361 + ], + "spans": [ + { + "bbox": [ + 306, + 349, + 407, + 361 + ], + "type": "text", + "content": "3.3.2 Personalization." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "spans": [ + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "text", + "content": "After pre-training, given the RGB video of a novel subject, we optimize the latent features " + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "text", + "content": " and lighting environment " + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "text", + "content": " of the video from scratch and only fine-tune AlbedoNet " + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "inline_equation", + "content": "(G_{A})" + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "text", + "content": ". During our experiments, we found that fine-tuning " + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "inline_equation", + "content": "G_{N}" + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "text", + "content": " is not required if the model is pretrained (see Sec. 4.3). We keep " + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "inline_equation", + "content": "G_{A}" + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "text", + "content": " fixed for the first 1000 iterations and only optimize " + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "text", + "content": ". This allows optimization of the latent features " + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "text", + "content": " to be compatible with the pretrained " + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "inline_equation", + "content": "G_{A}" + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "inline_equation", + "content": "G_{N}" + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "text", + "content": ". We then optimize " + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "inline_equation", + "content": "G_{A}, Z" + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "text", + "content": " jointly for a total of 15k iterations. Note that, while we do pre-training on synthetic data, RANA does not suffer from domain gap because the neural texture is learned from scratch and AlbedoNet is finetuned for every video. Similar to TextureNet, we use vanilla U-Net for AlbedoNet and NormalNet. For training, we use Adam optimizer with a batch size of 16 and learning rate of " + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "inline_equation", + "content": "1e^{-4}" + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "text", + "content": " with cosine annealing and minimum learning rate of " + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "inline_equation", + "content": "1e^{-5}" + }, + { + "bbox": [ + 304, + 368, + 545, + 570 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 582, + 387, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 582, + 387, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 582, + 387, + 597 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 603, + 545, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 603, + 545, + 650 + ], + "spans": [ + { + "bbox": [ + 304, + 603, + 545, + 650 + ], + "type": "text", + "content": "In this section, we evaluate the performance of RANA using two different datasets. We perform an ablation study to validate our design choices and also compare our method with state-of-the-art and other baselines." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 658, + 368, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 368, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 368, + 670 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Relighting Human Dataset. We propose a new photorealistic synthetic dataset to quantitatively evaluate the performance of our method. We use 49 rigged characters from the" + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23147" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 69, + 135, + 202 + ], + "blocks": [ + { + "bbox": [ + 53, + 69, + 135, + 202 + ], + "lines": [ + { + "bbox": [ + 53, + 69, + 135, + 202 + ], + "spans": [ + { + "bbox": [ + 53, + 69, + 135, + 202 + ], + "type": "image", + "image_path": "a93d65b5e46cb059b9b57906da1a63a85947d93d31be5eb2b24be2fe16d10eac.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 59, + 204, + 122, + 213 + ], + "lines": [ + { + "bbox": [ + 59, + 204, + 122, + 213 + ], + "spans": [ + { + "bbox": [ + 59, + 204, + 122, + 213 + ], + "type": "text", + "content": "(a) Ground Truth" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 135, + 70, + 231, + 202 + ], + "blocks": [ + { + "bbox": [ + 135, + 70, + 231, + 202 + ], + "lines": [ + { + "bbox": [ + 135, + 70, + 231, + 202 + ], + "spans": [ + { + "bbox": [ + 135, + 70, + 231, + 202 + ], + "type": "image", + "image_path": "acc6e5fce361c26d8efba36ea6f39ba9c3f6b9a6197ab86daa0d3158a45cc070.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 143, + 204, + 198, + 213 + ], + "lines": [ + { + "bbox": [ + 143, + 204, + 198, + 213 + ], + "spans": [ + { + "bbox": [ + 143, + 204, + 198, + 213 + ], + "type": "text", + "content": "(b) Full Model" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 236, + 70, + 329, + 202 + ], + "blocks": [ + { + "bbox": [ + 236, + 70, + 329, + 202 + ], + "lines": [ + { + "bbox": [ + 236, + 70, + 329, + 202 + ], + "spans": [ + { + "bbox": [ + 236, + 70, + 329, + 202 + ], + "type": "image", + "image_path": "fed8e3fab599ccb73be828533c295102384577335d17b418b79f04d2497e8d11.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 235, + 203, + 291, + 216 + ], + "lines": [ + { + "bbox": [ + 235, + 203, + 291, + 216 + ], + "spans": [ + { + "bbox": [ + 235, + 203, + 291, + 216 + ], + "type": "text", + "content": "(c) w/o " + }, + { + "bbox": [ + 235, + 203, + 291, + 216 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 215, + 547, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 215, + 547, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 547, + 258 + ], + "type": "text", + "content": "Figure 3. Ablation Study. Impact of the different components of the proposed approach. Our full model yields the best results. Without the " + }, + { + "bbox": [ + 46, + 215, + 547, + 258 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}" + }, + { + "bbox": [ + 46, + 215, + 547, + 258 + ], + "type": "text", + "content": " loss, the light information leaks into the albedo texture resulting in incorrect illumination. If we do not use coarse geometry and albedo texture, the resulting model does not generalize well to novel body poses. Similarly, training the model from scratch, without any pretraining on synthetic data, can result in an incorrect disentanglement of texture and geometry." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 340, + 70, + 441, + 202 + ], + "blocks": [ + { + "bbox": [ + 340, + 70, + 441, + 202 + ], + "lines": [ + { + "bbox": [ + 340, + 70, + 441, + 202 + ], + "spans": [ + { + "bbox": [ + 340, + 70, + 441, + 202 + ], + "type": "image", + "image_path": "7ab6f54d82aa64c4787ef3caa15351835dd55a660adc3be6a1444799372238a0.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 318, + 204, + 413, + 215 + ], + "lines": [ + { + "bbox": [ + 318, + 204, + 413, + 215 + ], + "spans": [ + { + "bbox": [ + 318, + 204, + 413, + 215 + ], + "type": "text", + "content": "(d) w/o coarse geo. & tex." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 444, + 70, + 536, + 202 + ], + "blocks": [ + { + "bbox": [ + 444, + 70, + 536, + 202 + ], + "lines": [ + { + "bbox": [ + 444, + 70, + 536, + 202 + ], + "spans": [ + { + "bbox": [ + 444, + 70, + 536, + 202 + ], + "type": "image", + "image_path": "4f9865814d21d22eb5bd232e27371d7f133e34add7d392fb958156ecd7eb4c14.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 449, + 204, + 522, + 215 + ], + "lines": [ + { + "bbox": [ + 449, + 204, + 522, + 215 + ], + "spans": [ + { + "bbox": [ + 449, + 204, + 522, + 215 + ], + "type": "text", + "content": "(e) w/o pre-training" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 50, + 273, + 545, + 365 + ], + "blocks": [ + { + "bbox": [ + 50, + 273, + 545, + 365 + ], + "lines": [ + { + "bbox": [ + 50, + 273, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 50, + 273, + 545, + 365 + ], + "type": "table", + "html": "
MethodImageNormal MapAlbedo Map
LPIPS ↓DISTS ↓SSIM ↑PSNR ↑Degree° ↓LPIPS ↓DISTS ↓SSIM ↑PSNR ↑
Full model0.2170.2040.75119.49864.3500.2190.2070.77921.832
w/o Lalbedo0.2490.2410.69715.19964.0640.2640.2570.71315.688
w/o coarse geo. & tex.0.2420.2220.73018.58065.8870.2600.2320.75120.778
w/o pre-training0.3010.2930.66913.79874.2150.3270.3070.69615.632
fine-tune GN0.2190.2050.74619.19864.2260.2210.2100.77821.577
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We use HDRI maps from PolyHaven [1] to illuminate the characters and use the CMU motion capture dataset [3] to pose the characters. In contrast to our proposed method that uses image-based lighting, we use full Path Tracing to generate the dataset. Hence, it is the closest setting to an in-the-wild video, and any future work that uses a more sophisticated lighting model can be evaluated on this dataset. For a fair evaluation, we ensure that none of the characters is used during the training in Sec 3.2 and Sec 3.3. All testing images come with a ground-truth albedo map, a normal map, a segmentation mask, and light information. For our experiments, we evaluate on all 49 characters and train a separate RANA model for each subject. We develop three different protocols for evaluation:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 575, + 286, + 707 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 46, + 575, + 286, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 575, + 286, + 659 + ], + "spans": [ + { + "bbox": [ + 46, + 575, + 286, + 659 + ], + "type": "text", + "content": "a) Novel Pose and Light Synthesis This protocol evaluates the quality in terms of novel pose and light synthesis. We generate 100 training images for each subject rotating " + }, + { + "bbox": [ + 46, + 575, + 286, + 659 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 575, + 286, + 659 + ], + "type": "text", + "content": " with A-posed in front of the camera with fixed lighting. It mimics the self-rotating videos commonly used for training. For testing, we generate 150 frames for each subject with random body pose and light in each frame." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 659, + 286, + 707 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 659, + 286, + 707 + ], + "spans": [ + { + "bbox": [ + 46, + 659, + 286, + 707 + ], + "type": "text", + "content": "b) Arbitrary Pose Training To represent in-the-wild scenarios, we generate 100 training images for each subject with arbitrary poses in fixed lighting. For testing, we generate 50 frames for each subject with random unseen body" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 396, + 457, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 396, + 457, + 408 + ], + "spans": [ + { + "bbox": [ + 305, + 396, + 457, + 408 + ], + "type": "text", + "content": "pose and random light in each frame." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 408, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 408, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 305, + 408, + 545, + 479 + ], + "type": "text", + "content": "c) Novel Light Synthesis. This protocol evaluates the relighting ability of the methods. We generate 150 frames for train and test sets. The train set is generated with fixed lighting and random body poses. The body poses in the test set are exactly the same as the train sets, but each frame is generated using a different light source." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 480, + 545, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 480, + 545, + 516 + ], + "spans": [ + { + "bbox": [ + 305, + 480, + 545, + 516 + ], + "type": "text", + "content": "People Snapshot Dataset. [5]. This dataset consists of real videos of characters rotating in front of the camera. We use this dataset for qualitative evaluation." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 524, + 364, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 524, + 364, + 536 + ], + "spans": [ + { + "bbox": [ + 306, + 524, + 364, + 536 + ], + "type": "text", + "content": "4.2. Metrics" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 543, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 543, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 543, + 545, + 639 + ], + "type": "text", + "content": "We report several metrics to evaluate the quality of synthesized images as well as the disentanglement of normal and albedo images. For synthesized images and albedo maps, we use Learned Perceptual Patch Similarity (LPIPS " + }, + { + "bbox": [ + 304, + 543, + 545, + 639 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 304, + 543, + 545, + 639 + ], + "type": "text", + "content": ") [68], Deep Image Structure and Texture Similarity (DISTS " + }, + { + "bbox": [ + 304, + 543, + 545, + 639 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 304, + 543, + 545, + 639 + ], + "type": "text", + "content": ") [19], Structural Similarity Index (SSIM " + }, + { + "bbox": [ + 304, + 543, + 545, + 639 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 304, + 543, + 545, + 639 + ], + "type": "text", + "content": ") [60] and Peak Signal-to-Noise Ratio (PSNR " + }, + { + "bbox": [ + 304, + 543, + 545, + 639 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 304, + 543, + 545, + 639 + ], + "type": "text", + "content": "). For normals, we compute the error in degrees (" + }, + { + "bbox": [ + 304, + 543, + 545, + 639 + ], + "type": "inline_equation", + "content": "^\\circ" + }, + { + "bbox": [ + 304, + 543, + 545, + 639 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 647, + 397, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 397, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 397, + 659 + ], + "type": "text", + "content": "4.3. Ablation study" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "We evaluate different design choices of RANA in Tab. 2 and Fig 3. We use protocol-a of the Relighting Human dataset for all experiments. We first report the results of the final model which includes all loss terms in (10)" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23148" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 68, + 545, + 358 + ], + "blocks": [ + { + "bbox": [ + 55, + 68, + 545, + 358 + ], + "lines": [ + { + "bbox": [ + 55, + 68, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 55, + 68, + 545, + 358 + ], + "type": "image", + "image_path": "ebc4335a79f665668895000b173da109a8eaaabd9a2088aaf8262724e79e9d01.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 72, + 359, + 109, + 367 + ], + "lines": [ + { + "bbox": [ + 72, + 359, + 109, + 367 + ], + "spans": [ + { + "bbox": [ + 72, + 359, + 109, + 367 + ], + "type": "text", + "content": "Reference" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 135, + 359, + 186, + 367 + ], + "lines": [ + { + "bbox": [ + 135, + 359, + 186, + 367 + ], + "spans": [ + { + "bbox": [ + 135, + 359, + 186, + 367 + ], + "type": "text", + "content": "RANA (Ours)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 197, + 359, + 263, + 367 + ], + "lines": [ + { + "bbox": [ + 197, + 359, + 263, + 367 + ], + "spans": [ + { + "bbox": [ + 197, + 359, + 263, + 367 + ], + "type": "text", + "content": "ANR[47]+RH[33]" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 282, + 359, + 317, + 367 + ], + "lines": [ + { + "bbox": [ + 282, + 359, + 317, + 367 + ], + "spans": [ + { + "bbox": [ + 282, + 359, + 317, + 367 + ], + "type": "text", + "content": "SMPL+D" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 337, + 359, + 404, + 367 + ], + "lines": [ + { + "bbox": [ + 337, + 359, + 404, + 367 + ], + "spans": [ + { + "bbox": [ + 337, + 359, + 404, + 367 + ], + "type": "text", + "content": "Relighting4D [16]" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 414, + 359, + 465, + 367 + ], + "lines": [ + { + "bbox": [ + 414, + 359, + 465, + 367 + ], + "spans": [ + { + "bbox": [ + 414, + 359, + 465, + 367 + ], + "type": "text", + "content": "RANA (Ours)" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 477, + 359, + 542, + 367 + ], + "lines": [ + { + "bbox": [ + 477, + 359, + 542, + 367 + ], + "spans": [ + { + "bbox": [ + 477, + 359, + 542, + 367 + ], + "type": "text", + "content": "Relighting4D [16]" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 368, + 545, + 399 + ], + "lines": [ + { + "bbox": [ + 46, + 368, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 368, + 545, + 399 + ], + "type": "text", + "content": "Figure 4. Comparison with the baselines and state-of-the-art methods. Column 1 shows a reference frame with the target body pose and lighting in the insets. In the absence of true reference images, for the Snapshot dataset (rows 1-2), we show training frames for reference. Columns 2-5 compare different methods for protocol-a, while columns 6-7 provide a comparison for protocol-b." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 411, + 545, + 589 + ], + "blocks": [ + { + "bbox": [ + 50, + 411, + 545, + 589 + ], + "lines": [ + { + "bbox": [ + 50, + 411, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 50, + 411, + 545, + 589 + ], + "type": "table", + "html": "
MethodImageNormal MapAlbedo Map
LPIPS ↓DISTS ↓SSIM ↑PSNR ↑Degree° ↓LPIPS ↓DISTS ↓SSIM ↑PSNR ↑
Protocol (a): Novel Pose and Light Synthesis
ANR [47] + RH [33]0.2750.4160.66417.495N.A.0.2660.4290.65614.804
Relightable SMPL+D0.2650.2250.75119.67864.1210.2160.1820.81122.623
RANA (Ours)0.2170.2040.75119.49864.3500.2190.2070.77921.832
Protocol (b): Arbitrary Pose Training
Relightable SMPL+D0.2590.2220.76119.98863.7560.2100.1800.82323.052
RANA (Ours)0.1930.1830.79320.69363.4090.2260.1940.82522.935
Protocol (c): Novel Light Synthesis
Relighting Humans [33]0.2260.3530.66821.205-----
Relighting4D [16]0.1920.3420.65421.08065.0990.2630.3740.59320.014
RANA (Ours)0.1730.1710.84222.33862.8230.2000.1790.86524.721
", + "image_path": "134ecc9dfaebb4d7936095739ac5beb35bf565b6c09829a0ebf3a256e417b7c1.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 101, + 589, + 488, + 598 + ], + "lines": [ + { + "bbox": [ + 101, + 589, + 488, + 598 + ], + "spans": [ + { + "bbox": [ + 101, + 589, + 488, + 598 + ], + "type": "text", + "content": "Table 3. Comparison with the baselines and state-of-the-art methods. See Fig. 4 for qualitative comparison." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 619, + 287, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 619, + 287, + 703 + ], + "spans": [ + { + "bbox": [ + 46, + 619, + 287, + 703 + ], + "type": "text", + "content": "and pretraining using synthetic data (Sec. 3.3.1). The full model achieves an LPIPS score of 0.217 for image synthesis and 0.219 for albedo map reconstruction. If we remove the loss term " + }, + { + "bbox": [ + 46, + 619, + 287, + 703 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}" + }, + { + "bbox": [ + 46, + 619, + 287, + 703 + ], + "type": "text", + "content": " from (10), the LPIPS scores for image and albedo map reconstruction increase to 0.249 and 0.264, respectively. Note that the error for albedo maps increases significantly while the error for normal maps re" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 618, + 545, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 618, + 545, + 657 + ], + "spans": [ + { + "bbox": [ + 305, + 618, + 545, + 657 + ], + "type": "text", + "content": "mains roughly the same. This indicates that without " + }, + { + "bbox": [ + 305, + 618, + 545, + 657 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}" + }, + { + "bbox": [ + 305, + 618, + 545, + 657 + ], + "type": "text", + "content": " the light information leaks into the albedo image. An example of this behavior can also be seen in Fig 3c (w/o " + }, + { + "bbox": [ + 305, + 618, + 545, + 657 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{albedo}}" + }, + { + "bbox": [ + 305, + 618, + 545, + 657 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 666, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 666, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 666, + 545, + 712 + ], + "type": "text", + "content": "Next, we evaluate the impact of coarse geometry and albedo texture on RANA. If we do not use coarse geometry and albedo, LPIPS score increases to 0.242 as compared to 0.217 for the full model. The normal error also increases" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "23149" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "text", + "content": "to " + }, + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "inline_equation", + "content": "65.9^{\\circ}" + }, + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "inline_equation", + "content": "64.3^{\\circ}" + }, + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "text", + "content": ". This is also evident from the qualitative results shown in Fig 3d, indicating that coarse geometry and albedo help in improved image synthesis quality, in particular when the target body pose is far from the training poses. Next, we evaluate the impact of pretraining on synthetic data. Without the pretraining, all error metrics increase significantly. Specifically, the LPIPS score for image reconstruction increases from 0.217 to 0.301, while the normal error increases from " + }, + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "inline_equation", + "content": "64.3^{\\circ}" + }, + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "inline_equation", + "content": "74.2^{\\circ}" + }, + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "text", + "content": ". If we look at Fig 3e, we can see that shading information leaks into both the normals and albedo maps. Hence, pretraining the networks also helps with the plausible disentanglement of geometry, texture, and light. Thanks to the design of RANA, we can pretrain on as many subjects as available, which is not possible with most of the state-of-the-art methods for human synthesis [45, 46, 58, 31]. Finally, as discussed in Sec 3.3.1, we keep the network " + }, + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "inline_equation", + "content": "G_{N}" + }, + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "text", + "content": " fixed during finetuning if RANA is pretrained on synthetic data. In the last row of Tab. 2, we evaluate the case when " + }, + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "inline_equation", + "content": "G_{N}" + }, + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "text", + "content": " is also fine-tuned. We can see that it has a negligible impact on the results." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 322, + 221, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 322, + 221, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 322, + 221, + 335 + ], + "type": "text", + "content": "4.4. Comparison with other methods" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 342, + 287, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 342, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 47, + 342, + 287, + 376 + ], + "type": "text", + "content": "Since ours is the first work that simultaneously evaluates novel light and pose synthesis, we ourselves build some baselines as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 389, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 389, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 47, + 389, + 287, + 437 + ], + "type": "text", + "content": "Relightable SMPL+D: We rasterize the SMPL+D mesh normals and albedo texture estimated using TextureNet in the target body pose and use SH lighting to generate the shaded images." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 437, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 437, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 47, + 437, + 287, + 510 + ], + "type": "text", + "content": "ANR [47]+RH[33]: We train an ANR [47] model which synthesizes images in the lighting of the training video. We then pass the generated images to the single-image human relighting method Relighting Humans (RH) [33] to obtain the relighted images for the target light. We use the publicly available source code and models of [33]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 509, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 509, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 509, + 287, + 544 + ], + "type": "text", + "content": "Relighting4D [16] is a state-of-the-art human video relighting method. We use the publicly available source code and train it on our dataset." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 558, + 287, + 714 + ], + "type": "text", + "content": "The results are summarized in Tab. 3 and Fig 4. We do not report results of Relighting4D [16] for protocol-a since it cannot handle novel body poses as can be seen in Fig 4 (column-5). For protocol-a, our method clearly outperforms other baselines for final image synthesis results. Surprisingly, the SMPL+D baseline yields better numbers for albedo reconstruction, even though it provides overly smooth albedo textures. This is because TextureNet is trained on synthetic data, hence albedo maps in SMPL+D baseline achieve the best result in this synthetic data benchmark. However, the SMPL+D baseline does not produce the best image quality. RANA, on the other hand, achieves significantly better image quality while staying close to the" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 411, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 411, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 411, + 83 + ], + "type": "text", + "content": "unlit texture in SMPL+D." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 88, + 545, + 137 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 88, + 545, + 137 + ], + "spans": [ + { + "bbox": [ + 305, + 88, + 545, + 137 + ], + "type": "text", + "content": "For protocol-b, we only compare the best two methods from protocol-a as we found it unnecessary to retrain ANR based on the results of protocol-a. As we can see in Tab. 3, the results are consistent with protocol-a." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 141, + 546, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 141, + 546, + 345 + ], + "spans": [ + { + "bbox": [ + 304, + 141, + 546, + 345 + ], + "type": "text", + "content": "For protocol-c, we compare with a video-based relighting method Relighting4D [16] and the single-image-based relighting method Relighting Humans [33]. RANA outperforms both methods across all metrics. Some qualitative comparisons with Relighting4D [16] can be seen in Fig. 4 (columns 6-7), where RANA clearly yields better image relighting results. Note that each model for Relighting4D [16] requires " + }, + { + "bbox": [ + 304, + 141, + 546, + 345 + ], + "type": "inline_equation", + "content": "260\\mathrm{k}" + }, + { + "bbox": [ + 304, + 141, + 546, + 345 + ], + "type": "text", + "content": " iterations for training whereas RANA models are trained only for " + }, + { + "bbox": [ + 304, + 141, + 546, + 345 + ], + "type": "inline_equation", + "content": "15\\mathrm{k}" + }, + { + "bbox": [ + 304, + 141, + 546, + 345 + ], + "type": "text", + "content": " iterations, thanks to our novel design that allows pre-training on synthetic data, allowing quick fine-tuning for new subjects. In contrast, Relighting4D [16] by design cannot be pretrained easily on multiple subjects. On the other hand, the method [33] is trained for up-right frontal poses only and cannot handle arbitrary body poses, resulting in inferior relighting performance. This is also the main reason behind the inferior performance of the ANR " + }, + { + "bbox": [ + 304, + 141, + 546, + 345 + ], + "type": "inline_equation", + "content": "[47] + \\mathrm{RH}" + }, + { + "bbox": [ + 304, + 141, + 546, + 345 + ], + "type": "text", + "content": " [33] baseline for protocol-a." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 349, + 547, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 349, + 547, + 373 + ], + "spans": [ + { + "bbox": [ + 306, + 349, + 547, + 373 + ], + "type": "text", + "content": "Finally, we provide additional qualitative results of avatars animated with complex motions in the supp. video." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 397, + 471, + 410 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 397, + 471, + 410 + ], + "spans": [ + { + "bbox": [ + 306, + 397, + 471, + 410 + ], + "type": "text", + "content": "5. Conclusion and Future Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 422, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 545, + 601 + ], + "type": "text", + "content": "We presented RANA which is a novel framework for learning reconfigurable and articulated neural avatars of humans. We demonstrated that RANA can model humans from unconstrained RGB videos while also disentangling their geometry, albedo texture, and environmental lighting. We showed that it can generate high-quality images of people under any novel body pose, viewpoint, and lighting. RANA can be trained simultaneously for multiple people and we showed that pre-training it on multiple (400) synthetic characters significantly improves the image synthesis quality. We also proposed a new photo-realistic synthetic dataset (Relighting Human) to quantitatively evaluate the performance of our proposed method, and believe that it will prove to be very useful to further the research in this direction." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "The most pressing limitation of RANA is the assumption of Lambertian surface, no cast shadows, and image-based lighting. In the future, we hope to incorporate more sophisticated physically-based rendering in our framework which will hopefully result in better image quality, self-shadowing and normal maps with more details. Moreover, RANA does not explicitly model motion-dependent clothing deformations. Modeling and neural rendering clothing deformations from a short video clip would be interesting future work." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23150" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 705 + ], + "type": "list", + "angle": 0, + "index": 20, + "blocks": [ + { + "bbox": [ + 53, + 91, + 263, + 102 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 263, + 102 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 263, + 102 + ], + "type": "text", + "content": "[1] Poly Haven, 2020. https://hdrihaven.com. 7" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 103, + 286, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 103, + 286, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 103, + 286, + 124 + ], + "type": "text", + "content": "[2] Render People, 2020. https://renderpeople.com/3d-people.4,7" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 125, + 286, + 147 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 125, + 286, + 147 + ], + "spans": [ + { + "bbox": [ + 53, + 125, + 286, + 147 + ], + "type": "text", + "content": "[3] Carnegie Mellon University Graphics Lab: Motion Capture Database. http://mocap.cs.cmu.edu, 2014.7" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 148, + 286, + 179 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 148, + 286, + 179 + ], + "spans": [ + { + "bbox": [ + 53, + 148, + 286, + 179 + ], + "type": "text", + "content": "[4] Thiemo Alldieck, Marcus Magnor, Weipeng Xu, Christian Theobalt, and Gerard Pons-Moll. 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Our approach maximizes compatibility between regions and object tags in a contrastive manner. To set up a proper contrastive learning objective, for each image, we augment tags by leveraging the relative nature of positive and negative pairs obtained from foundation models such as CLIP. We then use the rank of each augmented tag in a list as a relative relevance label to contrast each top-ranked tag with a set of lower-ranked tags. This learning objective encourages the top-ranked tags to be more compatible with their image and text context than lower-ranked tags, thus improving the discriminative ability of the learned multi-modality representation. We evaluate our approach on two datasets and show that our proposed RCA-NOC approach outperforms state-of-the-art methods by a large margin, demonstrating its effectiveness in improving vision-language representation for novel object captioning.", + "bbox": [ + 75, + 305, + 473, + 587 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 619, + 209, + 636 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Describing novel objects unseen in training data is a highly desired capability for a real-world image captioning model. Conventional image captioning models [4, 20, 28] often fail to describe novel objects because they only cover limited visual concepts and generalize poorly to images in the wild [26]. To overcome this limitation, approaches that rely on object detection as the external resource [7, 8, 13, 18, 20, 25, 27, 33, 35] have been widely explored and demonstrated breakthroughs in vision-language (VL) understanding.", + "bbox": [ + 75, + 646, + 468, + 796 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although object detection models (e.g., Faster RCNN [23]) have been improved to recognize a wide range of objects including novel ones like zero-shot object detection [14], using object detection in novel captioning models brings a new challenge. VIVO [13] leverages extra object tags to pre-train a visual vocabulary and help image captioning generalize to new categories. NOC-REK [29]", + "bbox": [ + 75, + 796, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/72c73d59bf1906ec193dadf5c0e214f3fbb2a69e9098b7b1361850154623373e.jpg", + "image_caption": [ + "(a) : Training" + ], + "image_footnote": [], + "bbox": [ + 506, + 273, + 637, + 333 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "NOC-REK: panda, animal, chunk, tree, branch. \nVIVO: panda, bear, chunk, tree, branch, animal, raccoon, hedge, food, raccoon.", + "bbox": [ + 655, + 277, + 852, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ours: panda, animal, tree, branch, chunk.../ hedge, raccoon, sky, advertisement, water...", + "bbox": [ + 656, + 310, + 869, + 328 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7d37de3d5f6ed670f7f2547fe4baa17e811399bc7e73c6af485b016b64769826.jpg", + "image_caption": [ + "(b): Inference" + ], + "image_footnote": [], + "bbox": [ + 508, + 342, + 637, + 401 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "NOC-REK: A raccoon sitting on top of a tree branch. (panda, tree, branch)", + "bbox": [ + 655, + 343, + 869, + 361 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "VIVO: A raccoon sitting on a tree branch. (panda, tree, branch)", + "bbox": [ + 656, + 363, + 877, + 381 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ours: A red panda sitting in a tree branch (panda, tree, branch)", + "bbox": [ + 656, + 383, + 877, + 401 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Figure 1. An illustrative example of our method to leverage relative semantic relevance to achieve modality alignment. Our method could give accurate captions \"A cute red panda sitting in a tree branch\" conditioned on the objects \"red panda\" while VINVL+VIVO generates a wrong caption \"A cute raccoon sitting in a tree branch\". This inference result shows that our method can differentiate some confusing objects and generate accurate captions for novel objects when the object detection is well aligned with other modalities.", + "bbox": [ + 496, + 420, + 893, + 544 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tries to augment object tags in the training stage based on the similarity between region and word. Such methods simply concatenate regions, object tags, and caption features as input to a Transformer-based model and use masked token reconstruction to implicitly learn an alignment between vision and language. Although such an alignment can help bring regions and words of the same concept closer, it lacks an effective mechanism to push away irrelevant concepts. As a result, it still makes mistakes on some confusing concepts, as shown in Figure 1.", + "bbox": [ + 496, + 559, + 893, + 708 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Different from previous methods, this study aims to learn visual and semantic alignment in a contrastive manner. Gupta et al. [10] showed that modality alignment could be achieved by maximizing the information lower bound between an image and its object tags. That is, given pairs of image and object tags, we can maximize the compatibility between tags and their attention-weighted region representations, compared to regions and non-corresponding tags. However, there are two critical problems that need to be further addressed: 1) how to effectively generate contrastive tags (augmented tags) that are closely relevant to an image, and 2) how to design a proper contrastive learning objective that allows the model to effectively leverage the contrastive", + "bbox": [ + 496, + 708, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15510", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tags to align vision and semantics.", + "bbox": [ + 76, + 90, + 307, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To tackle the first problem, we utilize CLIP [22] to create a list of contrastive tags which are closely linked to an image and contain global structural information and high-level concepts describing scenes. This approach aids in the discovery of useful tags that are essential for contrastive learning. To address the second problem, a proper contrastive learning objective needs to be explored. The major challenge here is that the augmented contrastive tags are inaccurate and inevitably noisy. We cannot simply treat one tag as positive and others as negative to perform contrastive learning, because the augmented tags might be highly correlated or similar to each other. To tackle this problem, we leverage the relative relevance, rather than the absolute relevance, of the augmented tags, which is more robust to data noise.", + "bbox": [ + 75, + 119, + 472, + 327 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, given an image, for each of its labeled object tags, we generate a ranked list of contrastive tags using CLIP. We regard the rank of each augmented tag as its relative semantic relevance with the image. In general, the top-ranked tags are assumed to be more relevant to the image than the lower-ranked tags. We divide the list into two parts: the (relatively) relevant part with higher rank and the (relatively) irrelevant part with lower rank (Figure 1 (a)). In our proposed objective, we treat each tag in the relevant part as positive and all tags in the irrelevant part as negative to perform contrastive learning. Note that we do not let tags both in the relevant part contrast with each other as they might be highly correlated concepts. In this way, our approach weakens the strict assumption of contrastive learning in previous works and exploits the relative ranking in a loose form to achieve modality alignment.", + "bbox": [ + 75, + 340, + 472, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conduct experiments on the Nocaps and Held-Out COCO datasets to demonstrate the effectiveness of RCA-NOC. Our contributions can be summarized as follows:", + "bbox": [ + 76, + 590, + 468, + 636 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose Relative Contrastive Alignment (RCA) to learn the relative semantic relevance in a loose form by maximizing the compatibility between regions and their relevant tags compared with regions and irrelevant tags to achieve vision and language alignment and improve the discriminative ability of the multi-modality representation.", + "- A method called Uncertainty-Aware Selection and Reweighting (UASR) is proposed to estimate and exploit the uncertainty of each contrastive sample to mitigate the negative effect brought by noisy tags. UASR can effectively prioritize highly reliable samples and demote false positives and false negatives.", + "- We validate the proposed method on the Nocaps and Held-Out COCO benchmarks, which outperforms other state-of-the-art methods by a large margin." + ], + "bbox": [ + 75, + 650, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 89, + 640, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Related work", + "text_level": 1, + "bbox": [ + 500, + 114, + 637, + 131 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Novel object captioning aims to describe images with objects that are unseen in the training stage (we define these objects as novel objects) where many methods. [7, 8, 13, 18, 20, 22, 27, 31, 33, 35] have been proposed. Early works such as Hendricks et al. [12] and Venugopalan et al. [27] utilize unpaired labeled image and sentence data to enhance semantically visual concepts. Recent studies propose to explicitly leverage the object detection results for NOC, Lu et al. [20], Wu et al. [33], and Demirel et al. [8] fill the generated template sentence with objects detected by object/novel object detectors. Chen et al. [7] combine object detector and human attention to identify novel objects. In addition, Li et al. are the first to utilize semantics in VLP tasks, which are further extended by Zhang et al. [35]. Hu et al. [13] built upon [35] and propose to leverage extra region-tag pairs to conduct pretraining. Duc et al. [29] tried to augment object tags in the training stage based on the similarity of regions and objects.", + "bbox": [ + 496, + 140, + 890, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, most aforementioned methods for NOC ignore the misalignment problem of object tags, thereby failing to fully exploit the semantic relationship between vision and language (Figure 1), which we argue is crucial to the quality of generated captions. In this paper, we propose a simple but effective contrastive learning objective to learn the relative semantic relevance in a loose form where the object tags could be explicitly aligned with their corresponding image feature representations in a semantic space.", + "bbox": [ + 496, + 407, + 890, + 541 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contrastive Learning aims to learn discriminative representations to distinguish an image from others. Many methods [6,10,11,16,17,22,32] have shown their effectiveness. For example, Chen et al. [6] proposed to learn visual representations by maximizing agreement between differently augmented views of the same image via a contrastive loss. He et al. [11] proposed Momentum Contrast (MoCo) for unsupervised visual representation learning. Wei et al. [32] utilized contrastive learning in the detection task. Li et al. [16] focused on the problem of contextual outpainting. Gupta et al. [10] proposed a method $\\mathrm{CPG}^{\\dagger}$ to find hard negative words by replacing a word in a caption.", + "bbox": [ + 496, + 541, + 890, + 718 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Other data-driven studies such as CLIP [22] and ALIGNN [17] focus on learning a corresponding relative relationship from massive web data. CLIP [22] predicts which text goes with which image and learns a relative imagetext corresponding relationship from broad web data with noisy supervision. ALIGNN [17] further scales up CLIP by leveraging a noisy dataset that covers more than one billion image-text pairs. These methods achieve remarkable results but require massive fully-annotated data, which are difficult to obtain.", + "bbox": [ + 496, + 719, + 890, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1For better illustration, we use the abbreviation CPG to denote the paper \"Contrastive Learning for Weakly Supervised Phrase Grounding\" [10]", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15511", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/0e1bcd376e8077ab743c09348aef0ffb6744d2905587fb59b5086b610a96c3e4.jpg", + "image_caption": [ + "\"A close up of a small animal on a tree branch\"" + ], + "image_footnote": [], + "bbox": [ + 125, + 104, + 326, + 210 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/31b4970adb0f96d988cbd6786871d81d94ee746f1c822ef51bcb8fdf539e1c73.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 352, + 95, + 883, + 252 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c79f9f754ee43660e6346b91b0738f19014abd31e133d789ea7e4a3ee71065ad.jpg", + "image_caption": [ + "(a) Training: learn discriminative feature", + "Result: \"A red panda sitting in a tree branch\"", + "(b) Inference: novel object captioning" + ], + "image_footnote": [], + "bbox": [ + 120, + 261, + 287, + 345 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Red panda", + "bbox": [ + 437, + 263, + 504, + 276 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multi-layer Transformer", + "bbox": [ + 511, + 297, + 709, + 313 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6e1b86125f9e32226a22ae22d886e231bad5139edbc5f71c84ce37eecbe93fcd.jpg", + "image_caption": [ + "Figure 2. The main pipeline of our proposed RCA-NOC, including training and inference: In addition to the normal caption loss $L_{G}$ in the training process, we also compute the cross-modality and inner-modality loss $L_{cross}$ and $L_{inner}$ in Eq. 22 and Eq. 23 by contrasting the positive tags against the negative tags. The corresponding relationship is denoted in green and red line separately. During training, the input is a concatenated sequence of words—ROI tags—ROIs and augmented contrastive tags. The training loss comprises caption loss (with [MASK] in words for reconstruction) and contrastive learning loss (with [MASK] in ROI tags token for indicating the specific positions where augmented tags are inserted). Augmented tags replace certain ROI tags and are encoded into contrastive tag feature embeddings for comparison with region and caption embeddings. During prediction, the input is a concatenated sequence of ROI tags—ROIs without additional retrieval steps." + ], + "image_footnote": [], + "bbox": [ + 359, + 325, + 880, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Proposed Methods", + "text_level": 1, + "bbox": [ + 76, + 515, + 256, + 531 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose to enhance the modality alignment by explicitly injecting visual semantics. These semantics are extracted for each image, obtained with existing foundation models such as CLIP.", + "bbox": [ + 75, + 541, + 468, + 599 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "There are two motivations behind our approach. First, by maximizing the compatibility between regions and their relevant tags compared with regions and irrelevant tags, we could not only learn vision-semantic alignment and improve the discriminative ability of the multi-modality representation. Second, we introduce a relative contrastive learning objective that considers the relative relationships between positive and negative examples, rather than using absolute prototype-contrastive learning methods. This approach is more generalized and can be easily integrated into any existing NOC method.", + "bbox": [ + 75, + 599, + 468, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Visual Semantics Extraction", + "text_level": 1, + "bbox": [ + 76, + 773, + 330, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Different from other approaches (e.g., [13, 18]) that extract object tags using pretrained object detectors, we use an off-the-shelf foundational model to extract more diverse, larger and semantically meaningful set of visual semantics. We show in section 6, that this approach helps to capture high level and global semantics describing the scenes, which are hard to obtain with other approaches (e.g. object", + "bbox": [ + 75, + 796, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "detectors).", + "bbox": [ + 500, + 517, + 571, + 531 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use a pretrained CLIP (ViT-B/16) model to obtain the embeddings of all the images and the extracted semantics. For each image, we compute its cosine similarity with all the embedded semantics and select the top M similar semantics as augmented tags $T = \\{t_l\\}_{l=1}^M$ . The augmented tags will be ranked using global (image-level) cosine similarity $p(t_l)$ . Then we utilize the rank of each augmented tag in $T$ as a relative relevance label. In general, the top-ranked tags are assumed to be more relevant to the image than the lower-ranked tags. We divide $T$ into positive and negative tags: positive tags being the (relatively) relevant tags with higher rank $T^P = \\{t_n^P\\}_{n=1}^K = \\{t_l\\}_{l=1}^K$ and negative tags being the (relatively) irrelevant tags with lower rank $T^N = \\{t_l^N\\}_{l=1}^K = \\{t_l\\}_{l=K+1}^{2K}$ ( $M = 2K$ ).", + "bbox": [ + 496, + 545, + 890, + 755 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here we propose a simple yet effective augmentation technique. Having a set of visual semantics extracted for each image, instead of considering all the visual semantics at once, we sample randomly a fraction of these augmented tags at each iteration step. Hence, we could not only prevent the model from overfitting on specific semantics and potentially disregard the image or other semantics during training, but also let the model see different combinations of visual semantics, which helps to have more diversity.", + "bbox": [ + 496, + 767, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15512", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.2. Relative Contrastive Alignment", + "text_level": 1, + "bbox": [ + 76, + 90, + 356, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "InfoNCE [21] is a typical type of contrastive loss function used for self-supervised learning that contrasts one positive sample against a set of negative samples. CPG [10] builds upon InfoNCE and proposes a compatibility function for regions and a caption word. Both InfoNCE and CPG utilize the absolute relevance to optimize the contrastive loss.", + "bbox": [ + 75, + 113, + 467, + 202 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, such a contrastive learning objective is hard to optimize for object tags since they may be highly correlated to each other. In RCA-NOC, we focus on the relative semantic relevance and utilize the attention-based compatibility function to measure the relativity information for regions and a set of object tags, which is more robust to data noise.", + "bbox": [ + 75, + 202, + 467, + 290 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, we first compute the dot product for a region-tag pair.", + "bbox": [ + 75, + 290, + 467, + 320 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ns _ {j k} = \\mathbf {w} _ {j} ^ {T} \\mathbf {v} _ {k} / \\sqrt {d}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 321, + 467, + 340 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{w}_j$ and $\\mathbf{v}_k$ refer to the corresponding embeddings for tag and region, and $d$ is the feature dimension. Here, $s_{jk}$ represents the similarity between the $j$ -th tag and the $k$ -th region. To find a contextualized region representation for the $j$ -th tag, we define $\\mathbf{a}_j^v$ as follows.", + "bbox": [ + 75, + 345, + 467, + 421 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {a} _ {j} ^ {v} = \\sum_ {k = 1} ^ {K} \\alpha_ {j k} \\mathbf {v} _ {k}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 422, + 467, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha_{jk} = \\frac{e^{s_{jk}}}{\\sum_{k' = 1}^{K}e^{s_{jk'}}},$ (3)", + "bbox": [ + 76, + 465, + 467, + 496 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To measure the compatibility between a tag $\\mathbf{w}_j$ and its contextualized region representation $\\mathbf{a}_j^v$ , we define", + "bbox": [ + 75, + 500, + 467, + 532 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\phi (\\mathbf {V}, \\mathbf {w} _ {j}) = \\mathbf {w} _ {j} ^ {T} \\mathbf {a} _ {j} ^ {v}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 542, + 467, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this way, we can derive our cross-modality contrastive loss function $L_{cross}$ .", + "bbox": [ + 75, + 566, + 467, + 595 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {c r o s s}} (\\mathbf {V}, \\mathbf {W} ^ {P}, \\mathbf {W} ^ {N}) = \\\\ - \\frac {1}{K} \\sum_ {n = 1} ^ {K} \\log \\left(\\frac {e ^ {\\phi (\\mathbf {V} , \\mathbf {w} _ {n} ^ {P})}}{e ^ {\\phi (\\mathbf {V} , \\mathbf {w} _ {n} ^ {P})} + \\sum_ {l = 1} ^ {K} e ^ {\\phi (\\mathbf {V} , \\mathbf {w} _ {l} ^ {N})}}\\right), \\tag {5} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 606, + 467, + 665 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{W}^P = \\{\\mathbf{w}_l^P\\}_{l=1}^K$ and $\\mathbf{W}^N = \\{\\mathbf{w}_n^N\\}_{n=1}^K$ are the word embeddings for positives/negatives $T^P$ and $T^N$ , extracted from CLIP. $\\phi()$ is the compatibility function defined in Eq. 11.", + "bbox": [ + 75, + 676, + 467, + 736 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This equation encourages each positive tag $\\mathbf{w}_n^P$ to be more compatible with image regions $\\mathbf{V}$ than all negative tags in $\\mathbf{W}^N$ . Essentially, if tag $t_j$ is not relevant to the image (negative), its representation $\\mathbf{w}_j$ should not be similar to its contextualized region representation $\\mathbf{a}_j^v$ since it would not be able to collect good information while computing $\\mathbf{a}_j^v$ . Note that we do not let two positive tags (top-ranked tags) contrast with each other as it is hard to tell which one is more relevant.", + "bbox": [ + 75, + 737, + 467, + 868 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inner modality Alignment. To further enhance modality alignment, we also compute the inner-modality contrastive", + "bbox": [ + 75, + 869, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "loss over tag-caption pairs. The formulation for inner-modality contrastive loss is similar to cross-modality contrastive loss but slightly different. We enforce contrastive learning not to be between tags and all caption words, but just between tags and noun caption words. This is because a caption may have many irrelevant tokens, such as \"the, a, is\", which will harm our alignment process and cause redundant computational costs.", + "bbox": [ + 496, + 90, + 890, + 208 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we can derive our inner-modality contrastive loss function $L_{inner}$ .", + "bbox": [ + 498, + 210, + 890, + 239 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\phi (\\mathbf {C}, \\mathbf {w} _ {l}) = \\mathbf {w} _ {l} ^ {T} \\mathbf {a} _ {l} ^ {c}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 247, + 890, + 266 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {i n n e r}} \\left(\\mathbf {C}, \\mathbf {W} ^ {P}, \\mathbf {W} ^ {N}\\right) = \\\\ - \\frac {1}{K} \\sum_ {n = 1} ^ {K} \\log \\left(\\frac {e ^ {\\phi (\\mathbf {C} , \\mathbf {w} _ {n} ^ {P})}}{e ^ {\\phi (\\mathbf {C} , \\mathbf {w} _ {n} ^ {P})} + \\sum_ {l = 1} ^ {K} e ^ {\\phi (\\mathbf {C} , \\mathbf {w} _ {l} ^ {N})}}\\right), \\tag {7} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 282, + 890, + 342 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where this time we take noun caption words $\\mathbf{C} = \\{\\mathbf{c}_i\\}_{i=1}^P$ in Eq. 13 as input. By further considering inner-modality alignment, we not only learn caption-tag semantics to connect relevant caption tokens, but also enable region-caption interactions.", + "bbox": [ + 496, + 352, + 890, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5. Proposed Methods", + "text_level": 1, + "bbox": [ + 500, + 441, + 679, + 458 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We propose to enhance the modality alignment by explicitly injecting visual semantics. These semantics are extracted for each image, obtained with existing foundation models such as CLIP.", + "bbox": [ + 496, + 465, + 890, + 525 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "There are two motivations behind our approach. First, by maximizing the compatibility between regions and their relevant tags compared with regions and irrelevant tags, we could not only learn vision-semantic alignment and improve the discriminative ability of the multi-modality representation. Second, we introduce a relative contrastive learning objective that considers the relative relationships between positive and negative examples, rather than using absolute prototype-contrastive learning methods. This approach is more generalized and can be easily integrated into any existing NOC method.", + "bbox": [ + 496, + 526, + 890, + 688 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5.1. Visual Semantics Extraction", + "text_level": 1, + "bbox": [ + 500, + 699, + 751, + 714 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Different from other approaches (e.g., [13, 18]) that extract object tags using pretrained object detectors, we use an off-the-shelf foundational model to extract more diverse, larger and semantically meaningful set of visual semantics. We show in section 6, that this approach helps to capture high level and global semantics describing the scenes, which are hard to obtain with other approaches (e.g. object detectors).", + "bbox": [ + 496, + 722, + 890, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We use a pretrained CLIP (ViT-B/16) model to obtain the embeddings of all the images and the extracted semantics. For each image, we compute its cosine similarity with all the embedded semantics and select the top M similar", + "bbox": [ + 496, + 840, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15513", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "semantics as augmented tags $T = \\{t_l\\}_{l=1}^M$ . The augmented tags will be ranked using global (image-level) cosine similarity $p(t_l)$ . Then we utilize the rank of each augmented tag in $T$ as a relative relevance label. In general, the top-ranked tags are assumed to be more relevant to the image than the lower-ranked tags. We divide $T$ into positive and negative tags: positive tags being the (relatively) relevant tags with higher rank $T^P = \\{t_n^P\\}_{n=1}^K = \\{t_l\\}_{l=1}^K$ and negative tags being the (relatively) irrelevant tags with lower rank $T^N = \\{t_l^N\\}_{l=1}^K = \\{t_l\\}_{l=K+1}^{2K}$ ( $M = 2K$ ).", + "bbox": [ + 75, + 90, + 472, + 239 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here we propose a simple yet effective augmentation technique. Having a set of visual semantics extracted for each image, instead of considering all the visual semantics at once, we sample randomly a fraction of these augmented tags at each iteration step. Hence, we could not only prevent the model from overfitting on specific semantics and potentially disregard the image or other semantics during training, but also let the model see different combinations of visual semantics, which helps to have more diversity.", + "bbox": [ + 75, + 239, + 472, + 375 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Relative Contrastive Alignment", + "text_level": 1, + "bbox": [ + 76, + 383, + 357, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "InfoNCE [21] is a typical type of contrastive loss function used for self-supervised learning that contrasts one positive sample against a set of negative samples. CPG [10] builds upon InfoNCE and proposes a compatibility function for regions and a caption word. Both InfoNCE and CPG utilize the absolute relevance to optimize the contrastive loss.", + "bbox": [ + 75, + 406, + 468, + 494 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, such a contrastive learning objective is hard to optimize for object tags since they may be highly correlated to each other. In RCA-NOC, we focus on the relative semantic relevance and utilize the attention-based compatibility function to measure the relativity information for regions and a set of object tags, which is more robust to data noise.", + "bbox": [ + 75, + 494, + 468, + 584 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, we first compute the dot product for a region-tag pair.", + "bbox": [ + 75, + 584, + 468, + 614 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ns _ {j k} = \\mathbf {w} _ {j} ^ {T} \\mathbf {v} _ {k} / \\sqrt {d}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 616, + 468, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{w}_j$ and $\\mathbf{v}_k$ refer to the corresponding embeddings for tag and region, and $d$ is the feature dimension. Here, $s_{jk}$ represents the similarity between the $j$ -th tag and the $k$ -th region. To find a contextualized region representation for the $j$ -th tag, we define $\\mathbf{a}_j^v$ as follows.", + "bbox": [ + 75, + 642, + 468, + 717 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {a} _ {j} ^ {v} = \\sum_ {k = 1} ^ {K} \\alpha_ {j k} \\mathbf {v} _ {k}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 719, + 468, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha_{jk} = \\frac{e^{s_{jk}}}{\\sum_{k'=1}^{K} e^{s_{jk'}}},$ (10)", + "bbox": [ + 76, + 760, + 468, + 796 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To measure the compatibility between a tag $\\mathbf{w}_j$ and its contextualized region representation $\\mathbf{a}_j^v$ , we define", + "bbox": [ + 76, + 801, + 468, + 832 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\phi (\\mathbf {V}, \\mathbf {w} _ {j}) = \\mathbf {w} _ {j} ^ {T} \\mathbf {a} _ {j} ^ {v}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 844, + 468, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this way, we can derive our cross-modality contrastive loss function $L_{cross}$ .", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {c r o s s}} (\\mathbf {V}, \\mathbf {W} ^ {P}, \\mathbf {W} ^ {N}) = \\\\ - \\frac {1}{K} \\sum_ {n = 1} ^ {K} \\log \\left(\\frac {e ^ {\\phi (\\mathbf {V} , \\mathbf {w} _ {n} ^ {P})}}{e ^ {\\phi (\\mathbf {V} , \\mathbf {w} _ {n} ^ {P})} + \\sum_ {l = 1} ^ {K} e ^ {\\phi (\\mathbf {V} , \\mathbf {w} _ {l} ^ {N})}}\\right), \\tag {12} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 114, + 890, + 174 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{W}^P = \\{\\mathbf{w}_l^P\\}_{l=1}^K$ and $\\mathbf{W}^N = \\{\\mathbf{w}_n^N\\}_{n=1}^K$ are the word embeddings for positives/negatives $T^P$ and $T^N$ , extracted from CLIP. $\\phi()$ is the compatibility function defined in Eq. 11.", + "bbox": [ + 496, + 186, + 890, + 244 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This equation encourages each positive tag $\\mathbf{w}_n^P$ to be more compatible with image regions $\\mathbf{V}$ than all negative tags in $\\mathbf{W}^N$ . Essentially, if tag $t_j$ is not relevant to the image (negative), its representation $\\mathbf{w}_j$ should not be similar to its contextualized region representation $\\mathbf{a}_j^v$ since it would not be able to collect good information while computing $\\mathbf{a}_j^v$ . Note that we do not let two positive tags (top-ranked tags) contrast with each other as it is hard to tell which one is more relevant.", + "bbox": [ + 496, + 246, + 890, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inner modality Alignment. To further enhance modality alignment, we also compute the inner-modality contrastive loss over tag-caption pairs. The formulation for inner-modality contrastive loss is similar to cross-modality contrastive loss but slightly different. We enforce contrastive learning not to be between tags and all caption words, but just between tags and noun caption words. This is because a caption may have many irrelevant tokens, such as \"the, a, is\", which will harm our alignment process and cause redundant computational costs.", + "bbox": [ + 496, + 380, + 890, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we can derive our inner-modality contrastive loss function $L_{inner}$ .", + "bbox": [ + 496, + 527, + 890, + 559 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\phi (\\mathbf {C}, \\mathbf {w} _ {l}) = \\mathbf {w} _ {l} ^ {T} \\mathbf {a} _ {l} ^ {c}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 566, + 890, + 585 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {i n n e r}} (\\mathbf {C}, \\mathbf {W} ^ {P}, \\mathbf {W} ^ {N}) = \\\\ - \\frac {1}{K} \\sum_ {n = 1} ^ {K} \\log \\left(\\frac {e ^ {\\phi (\\mathbf {C} , \\mathbf {w} _ {n} ^ {P})}}{e ^ {\\phi (\\mathbf {C} , \\mathbf {w} _ {n} ^ {P})} + \\sum_ {l = 1} ^ {K} e ^ {\\phi (\\mathbf {C} , \\mathbf {w} _ {l} ^ {N})}}\\right), \\tag {14} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 602, + 890, + 661 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where this time we take noun caption words $\\mathbf{C} = \\{\\mathbf{c}_i\\}_{i=1}^P$ in Eq. 13 as input. By further considering inner-modality alignment, we not only learn caption-tag semantics to connect relevant caption tokens, but also enable region-caption interactions.", + "bbox": [ + 496, + 671, + 890, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.3. Uncertainty-Aware Selection and Re-weighting", + "text_level": 1, + "bbox": [ + 500, + 756, + 890, + 773 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The augmented contrastive tags are often noisy and would harm the discriminative ability and robustness of the contrastive learning process. Therefore, we design a sample selection strategy to deal with noisy contrastive tags (e.g., false positives/negatives).", + "bbox": [ + 496, + 780, + 890, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Uncertainty-Aware Selection. Specifically, we first use the local cosine similarity to calculate the correlation between a region and a tag and filter false positives/negatives. The", + "bbox": [ + 496, + 856, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15514", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "stronger the correlation, the more reliable a positive tag is and the more uncertain a negative tag.", + "bbox": [ + 76, + 90, + 468, + 119 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {u} (\\mathbf {v}, \\mathbf {w}) = \\frac {\\mathbf {v} ^ {\\top} \\mathbf {w}}{\\| \\mathbf {v} \\| \\| \\mathbf {w} \\|}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 121, + 468, + 156 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Then we retrieve $L$ tags and their corresponding representations $\\mathbf{H} = \\{\\mathbf{w}_j\\}_{j=1}^L$ for the given $L$ region features $\\{\\mathbf{v}_i\\}_{i=1}^L$ . We use arg max to choose the most correlated tag $t_j$ for region $\\mathbf{v}_i$ .", + "bbox": [ + 76, + 165, + 468, + 227 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nj = \\underset {k} {\\arg \\max } \\left(\\mathrm {u} \\left(\\mathbf {v} _ {i}, \\mathbf {w} _ {k}\\right)\\right), \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 237, + 468, + 261 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "According to the score in Eq. 15, the corresponding top-L tags will be listed as confusion samples for negatives (actually positive), and these confusion samples will be removed from the original contrastive tags. Similarly, we will also choose the true positives based on these top- $L$ tags since tags with low-similarity scores should be regarded as outliers to the positives and they are too sparse to have a positive influence on the shape of embedding space. In this way, we can derive Eq. 17, where / is the removing set operation, $\\cap$ is the intersection set operation. $\\overline{\\mathbf{W}}^P = \\{\\bar{\\mathbf{w}}_l^P\\}_{l=1}^K$ and $\\overline{\\mathbf{W}}^N = \\{\\bar{\\mathbf{w}}_n^N\\}_{n=1}^K$ is the final positive/negative tags' embedding sets. Note that if the set length of $\\overline{\\mathbf{W}}^P / \\overline{\\mathbf{W}}^N$ is less than M, we will over-sample $\\overline{\\mathbf{W}}^P / \\overline{\\mathbf{W}}^N$ until the set length is equal to M.", + "bbox": [ + 75, + 272, + 470, + 479 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\overline {{\\mathbf {W}}} ^ {P} = \\mathbf {W} ^ {P} \\cap \\mathbf {H}, \\overline {{\\mathbf {W}}} ^ {N} = \\mathbf {W} ^ {N} / \\mathbf {H}, \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 484, + 468, + 502 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Uncertainty-Aware Re-weighting. To further mitigate the negative effect of noisy tags, we use the correlation function defined above to enhance reliable samples and reduce the influence of high-uncertainty samples. The information from more reliable samples should have a larger impact on the shape of the embedding and vice versa. Specifically, we first introduce the weight in Eq. 18.", + "bbox": [ + 75, + 507, + 468, + 611 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nq _ {1} \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right) = \\exp \\left(\\mathrm {u} \\left(\\mathbf {v} _ {k}, \\bar {\\mathbf {w}} _ {n} ^ {P}\\right)\\right), \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 619, + 468, + 638 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nj = \\underset {k} {\\arg \\max } \\left(\\mathrm {u} \\left(\\mathbf {v} _ {i}, \\bar {\\mathbf {w}} _ {k} ^ {P}\\right)\\right), \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 652, + 468, + 678 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nq _ {2} \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right) = p \\left(t _ {n}\\right), \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 214, + 685, + 468, + 704 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $q_{1}(\\bar{\\mathbf{w}}_{n}^{P})$ in Eq. 18 is the uncertainty score computed by the most relevant region with the corresponding tag. Moreover, we further consider how certain each tag is and combine the corresponding score $q_{2}(\\bar{\\mathbf{w}}_{n}^{P})$ in Eq. 20 with $q_{1}(\\bar{\\mathbf{w}}_{n}^{P})$ to derive the final uncertainty score $q(\\bar{\\mathbf{w}}_{n}^{P})$ in Eq. 21. Here $p(t_{n})$ in Eq. 20 is the global similarity mentioned in Section 5.1.", + "bbox": [ + 75, + 715, + 468, + 819 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right) = q _ {1} \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right) * q _ {2} \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right), \\tag {21}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 829, + 468, + 849 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Thus, our method could mitigate the negative effect of noisy contrastive tags by considering the similarity from both the local region features (region-tag) and the", + "bbox": [ + 75, + 858, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "global structural information (image-tag). Finally, we could rewrite our contrastive loss function in Eq. 22, Eq. 23.", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c r o s s}} \\left(\\mathbf {V}, \\overline {{\\mathbf {W}}} ^ {P}, \\overline {{\\mathbf {W}}} ^ {N}\\right) =\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 133, + 767, + 152 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n- \\frac {1}{K} \\sum_ {n = 1} ^ {K} - q \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right) \\log \\left(\\frac {e ^ {\\phi \\left(\\mathbf {V} , \\bar {\\mathbf {w}} _ {n} ^ {P}\\right)}}{e ^ {\\phi \\left(\\mathbf {V} , \\bar {\\mathbf {w}} _ {n} ^ {P}\\right)} + \\sum_ {l = 1} ^ {K} e ^ {\\phi \\left(\\mathbf {V} , \\bar {\\mathbf {w}} _ {l} ^ {N}\\right)}}\\right), \\tag {22}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 156, + 890, + 193 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {i n n e r}} \\left(\\mathbf {C}, \\overline {{\\mathbf {W}}} ^ {P}, \\overline {{\\mathbf {W}}} ^ {N}\\right) = \\\\ - \\frac {1}{K} \\sum_ {n = 1} ^ {K} - q \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right) \\log \\left(\\frac {e ^ {\\phi \\left(\\mathbf {C} , \\bar {\\mathbf {w}} _ {n} ^ {P}\\right)}}{e ^ {\\phi \\left(\\mathbf {C} , \\bar {\\mathbf {w}} _ {n} ^ {P}\\right)} + \\sum_ {l = 1} ^ {K} e ^ {\\phi \\left(\\mathbf {C} , \\bar {\\mathbf {w}} _ {l} ^ {N}\\right)}}\\right), \\tag {23} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 210, + 890, + 270 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6. Experiments", + "text_level": 1, + "bbox": [ + 500, + 273, + 630, + 290 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 297, + 689, + 314 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. Our main experiments and ablation studies are based on the Nocaps [2] dataset. Our method was built with PyTorch, and we used a pre-trained BERT-base model from Huggingfaces [1] for parameters initialization, and no ground-truth tags are used on the Nocaps validation and test sets. For the training stage, we use the COCO training set which consists of 118K images, each with 5 captions. We evaluate our model on the validation and test sets of the Nocaps dataset, which consist of 4.5K and 10.6K images from the Open Images validation and test sets, respectively. Additionally, we test the proposed method on the Held-Out COCO [12], which is a subset of MS COCO [19] where the following eight object categories are excluded from the training set: bottle, bus, couch, microwave, pizza, racket, suitcase, and zebra. We randomly split the COCO validation set and use half of it for validation and the other half for testing, each with 20,252 images. In addition, we empirically set $M = 50$ to generate augmented object tags for the best performance.", + "bbox": [ + 496, + 320, + 890, + 601 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. In the training stage, the model is trained for 30 epochs with a batch size of 512 and a learning rate of $10^{-4}$ , optimized using the cross-entropy loss and our contrastive loss. We set the maximum caption length to 40 and the maximum tag length to 30. To further boost the performance, we also perform the SCST optimization (Rennie et al. [24]) with a learning rate of $1.4 \\times 10^{-6}$ for 10 epochs. During inference, we use greedy decoding to generate image captions with a maximum length of 20. Our model is trained with 8 A100 GPUS and takes 1 day to train.", + "bbox": [ + 496, + 601, + 890, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.2. Quantitative evaluation.", + "text_level": 1, + "bbox": [ + 500, + 758, + 720, + 773 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on Nocaps dataset. In this section, we extensively compare our frameworks with previous methods on the Nocaps benchmark. The other compared state-of-art results are from NOC-REK [29]. Note that all the methods use the BERT-base [9] for a fair comparison. We compare our method with UpDown [2, 5], OSCAR [18], VinVL [35], VIVO [13], and NOC-REK [29], which hold the state-of-the-art result on the Nocaps benchmark. The training data", + "bbox": [ + 496, + 781, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15515", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/966ef07c5f0da061eeb024a8fec75d4ab2af99198894e5463d55827fae622d7e.jpg", + "table_caption": [ + "Table 1. Our evaluation results using SPICE and CIDEr on the Nocaps validation and test sets. We achieve the best scores for in-domain, near-domain, out-domain and Overall. Notably, the captions generated by our method are better than those by human in most cases. We note that our results on the test set are better than those by other methods which are publicly submitted to Nocaps leader-boardb. Higher score is better." + ], + "table_footnote": [], + "table_body": "
MethodValidation setTest set
in-domainnear-domainout-domainOverallin-domainnear-domainout-domainOverall
CIDErSPICECIDErSPICECIDErSPICECIDErSPICECIDErSPICECIDErSPICECIDErSPICECIDErSPICE
UpDown [4]78.111.657.710.331.38.355.310.176.011.874.211.566.79.773.111.2
Oscar [18]83.412.081.612.077.610.681.111.781.311.979.611.973.610.678.811.7
VIVO [13]92.212.987.812.687.511.588.312.489.012.987.812.680.111.186.612.4
VinVL [35]96.813.590.713.187.411.690.912.893.813.389.012.866.110.985.512.5
VinVL + VIVO [13,35]103.713.795.613.483.811.994.313.198.013.695.213.478.011.592.513.1
NOC-REK [29]104.714.8100.214.1100.713.0100.914.0100.014.195.713.677.411.693.013.4
RCA-NOC**95.013.691.313.193.212.192.213.087.713.388.112.977.911.486.312.7
RCA-NOC107.815.3104.014.6105.813.6107.114.6104.114.8101.214.688.512.9101.114.0
Δ3.1↑0.5↑4.2↑0.5↑5.1↑0.6↑6.2↑0.6↑4.1↑0.7↑5.5↑1.0↑11.1↑1.3↑8.1↑0.6↑
Human [2]84.414.385.014.395.714.087.114.280.615.084.614.791.614.285.314.6
", + "bbox": [ + 78, + 152, + 890, + 340 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/92c56a0bb4a719325d80a3b0186af70f78ecd1759b840cf966e5d1d1d44ca1a9.jpg", + "table_caption": [ + "Table 2. Comparison of F1-scores (in %) on object classes of Open Images, evaluated on the Nocaps validation set. There are 504 classes in total. 80 of them are in-domain, which are common classes from COCO. The remaining 424 classes are the out-of-domain objects." + ], + "table_footnote": [], + "table_body": "
modelin-domainout-of-domainentire
VIVO39.229.130.4
NOC-REK45.330.532.8
Ours58.639.243.1
", + "bbox": [ + 117, + 422, + 424, + 491 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "for the baselines is the COCO dataset. Following prior settings, we also report the results after the model is optimized using SCST [24]. Our generated captions also adopt Constrained Beam Search (CBS) following [3].", + "bbox": [ + 75, + 507, + 468, + 568 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Table 1, we present our results of SPICE and CIDEr scores on the Nocaps validation and test sets. We also show the results of our different training stages in the middle of the table, where RCA-NOC** denotes our first training stage result and RCA-NOC is our final result after CIDEr optimization. Note that we do not compare with the data-driven methods [17, 30, 34] which use massive out-of-domain image-caption pairs in the training and fail to follow the rule of Nocaps. By leveraging relative semantic relevance in contrastive learning, our method has achieved a significant improvement compared to all prior works. It is worth noting that our first stage training could generate a comparable result with [13, 18, 35]. After the CIDEr optimization process, our method could outperform the recent state-of-art method NOC-REK [29] with a large margin, which is 8.1 and 0.6 (CIDEr and SPICE) better than [29] on the Nocaps Test set. This suggests that our model is more capable of generating captions with novel objects.", + "bbox": [ + 75, + 570, + 468, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To quantitatively evaluate how well the model can describe novel objects, we also calculate the F1-score between our generated and the ground-truth tags on the validation set. Table 2 shows the comparison with VIVO and NOC-", + "bbox": [ + 75, + 840, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8759125f84a77c793b32f5368f25dbe919147e84b0db7c65cb191c9733b10172.jpg", + "table_caption": [ + "Table 3. Evaluation results on the Held-Out COCO test set. The best results are highlighted in red." + ], + "table_footnote": [], + "table_body": "
MethodAvg. F1-scoreSPICEMeteorCIDEr
NOC48.8-21.4-
NBT48.515.722.877.0
DNOC57.9-21.6-
ZSC29.814.221.9-
ANOC64.318.225.294.7
VinVL+VIVO71.824.530.6132.8
NOC-REK76.326.932.8138.4
RCA-NOc79.527.035.9142.8
", + "bbox": [ + 524, + 377, + 864, + 503 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "REK on the Nocaps validation set. We see that RCA-NOC improves NOC-REK and VIVO on F1-score substantially, especially for out-of-domain objects. This again verifies the effectiveness of RCA-NOC's discriminative ability to describe and distinguish novel objects.", + "bbox": [ + 496, + 517, + 890, + 590 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on the Held-Out COCO dataset. To further prove the generalization ability of our method, we also conduct experiments on the Held-Out COCO dataset. As we can see from Table 3, our method consistently beats the baseline VinVL+VIVO with a large margin. The improvements are 7.7, 2.5, 5.3, and 10.0 with BERT-base on the F1, SPICE, METEOR, and CIDEr metrics. Additionally, our method is superior to all other state-of-art methods. In particular, compared with the recent state-of-art method NOC-REK [29], the recent state-of-art on the Held-Out COCO dataset, RCA-NOC achieves a 4.4 improvement on CIDEr (from 138.4 to 142.8) and 3.1 improvement on METEOR (from 32.8 to 35.9). The 3.2 improvement on the F1 score also shows that RCA-NOC performs better in describing novel objects.", + "bbox": [ + 496, + 592, + 892, + 815 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.3. Ablation study.", + "text_level": 1, + "bbox": [ + 500, + 832, + 653, + 848 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this subsection, we will discuss every component's contribution to our framework. If not mentioned by purpose, all methods are conducted on the Nocaps validation", + "bbox": [ + 496, + 854, + 890, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15516", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c7e3ad6c617f794e7092864e788d959fe730270031202dd197fcdb1439726cbe.jpg", + "table_caption": [ + "Table 4. Effectiveness of the source of visual semantics." + ], + "table_footnote": [], + "table_body": "
Methodin-domainnear-domainout-of-domainOverall
CIDErSPICECIDErSPICECIDErSPICECIDErSPICE
N.A.103.614.7100.814.2100.913.2103.214.2
NOC-REK103.914.9101.614.3102.013.4103.414.3
VIVO105.215.1103.514.4103.613.4105.214.4
CLIP107.815.3104.014.6105.813.6107.114.6
", + "bbox": [ + 112, + 106, + 431, + 188 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/716ef64475395f24f20ff2845a984fd21762b234a0816ec579c11da7f66df4fa.jpg", + "table_caption": [ + "Table 5. Effectiveness of the UASR. UAR: Uncertainty-Aware Reweight, UAS: Uncertainty-Aware Selection, $UAS^{N}$ : Uncertainty-Aware Selection for Negatives), UASR: Uncertainty-Aware Selection and Re-weight." + ], + "table_footnote": [], + "table_body": "
Methodin-domainnear-domainout-of-domainOverall
CIDEr SPICECIDEr SPICECIDEr SPICECIDEr SPICE
N.A.103.614.7100.814.2100.913.2102.414.2
\\( UAS^N \\)105.214.8102.114.3102.413.3104.214.3
UAS105.915.0104.514.3103.913.4105.314.5
UAR104.314.8103.314.4104.713.3105.614.3
UASR107.815.3104.014.6105.813.6107.114.6
", + "bbox": [ + 109, + 257, + 433, + 348 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "set with BERT-base. (we cannot use the Nocaps test set because only 5 times submissions are allowed for the test set).", + "bbox": [ + 75, + 362, + 467, + 391 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of visual semantics. We enhance the modality alignment by incorporating visual semantics from foundational models, with a specific instantiation using CLIP. To evaluate the generalization ability of our approach, we modify the model to extract visual semantics and conduct further experiments to compare it with NOC-REK [29] and VIVO for generating visual semantics. Our baseline model is trained using a contrastive approach that ranks ROI tags extracted from Faster R-CNN based on their softmax values, distinguishing between relevant and irrelevant tags.", + "bbox": [ + 75, + 393, + 467, + 541 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our findings indicate that using NOC-REK to generate augmented tags provides only marginal improvement to our framework, resulting in a 0.8 and 0.1 (CIDEr and SPICE) increase compared to the baseline. We hypothesize that this limited improvement may be due to the restricted linguistic knowledge contained in BERT, which may not encompass a wide range of novel categories and lack higher-level and global concepts required to describe complex scenes. In contrast, utilizing a larger pool of noisy visual semantics (CLIP) extracted from captions leads to better results, with a 4.9 and 0.4 (CIDEr and SPICE) increase compared to the baseline. Using a smaller and cleaner pool of visual semantics extracted from the classes of various object detection datasets (VIVO) only results in a 2.0 and 0.2 (CIDEr and SPICE) increase compared to the baseline. This is likely due to the fact that the CLIP is pre-trained on vast amounts of training data, enabling it to extract a more diverse, extensive, and semantically meaningful set of high-level visual concepts compared to NOC-REK.", + "bbox": [ + 75, + 542, + 467, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of the UASR. We investigate the performance of our Uncertainty-Aware Selection and Reweighting (UASR) on the Nocaps validation set in this part. Table 5 shows that Uncertainty-Aware Reweighting (UAR) could effectively enhance the reliable contrastive samples", + "bbox": [ + 75, + 825, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/addfb202e14ab6d40796995f860c0f3fb2164cc29d56a2fc6fe14af3d478ae9d.jpg", + "table_caption": [ + "Table 6. Evaluation on COCO test set of Karpathy split [15]. All results are based on single model with cross-entropy optimization." + ], + "table_footnote": [], + "table_body": "
pre-trainingBLEU4MeteorCIDErSPICE
N.A33.828.1118.321.2
OSCAR + VIVO34.928.4119.821.7
RCA-NOC37.429.6128.423.1
", + "bbox": [ + 526, + 118, + 864, + 178 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/bf7b746039e23252c65bef820fd49115bbd4b9a1ddb3aaf26b4e9a56c7bc0bce.jpg", + "table_caption": [ + "Table 7. Ablation study on the effectiveness of different components, including (i) CA: Cross-modality Alignment, our prototype contrastive loss for region-tag pairs, (ii) IA: Inner-modality Alignment, (iii) CLIP: Without CLIP refers to extracting visual semantics with object detection, and (iv) UASR: Uncertainty-Aware Selection and Re-weighting." + ], + "table_footnote": [], + "table_body": "
CAIAUASRCLIPCIDERSPICE
90.912.8
✓96.513.5
✓✓98.713.8
✓✓✓103.214.2
✓✓✓✓107.114.6
", + "bbox": [ + 521, + 270, + 867, + 345 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and bring 3.2 and 0.1 boosts on CIDEr and SPICE. In addition, the false positives/negatives severely harm our training process. By further incorporating Uncertainty-Aware Selection for Negatives $(UAS^{N})$ into our method and filtering false negatives, our model's performance is boosted to 104.2 and 14.3 on CIDEr and SPICE. When filtering false positives/negatives simultaneously, we could reach 105.3 and 14.5 on CIDEr and SPICE with Uncertainty-Aware Selection (UAS). Finally, our method improves the performance by 4.7 and 0.4 (CIDEr and SPICE) by combining UAR and UAS, which illustrates the proposed UASR is a more powerful tool for tackling noisy contrastive samples in NOC.", + "bbox": [ + 496, + 347, + 890, + 539 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.4. Qualitative Results", + "text_level": 1, + "bbox": [ + 500, + 549, + 683, + 565 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Figure 3, we display some qualitative results on Held-Out COCO and Nocaps, and all the approaches are based on BERT-base. On Held-Out COCO, the result compared with GT shows that our proposed method could effectively generate accurate and precise captions with novel objects by leveraging relative semantic relevance into training. On Nocaps, VinVL+VIVO [13, 35] sometimes cannot include the desired novel objects in their captions (first and third examples) or generate wrong captions (second example). Our RCA-NOC, on the other hand, successfully generates correct and coherent captions via differentiating confusing classes and aligning object detection with other modalities. For better illustration, we show top-5 Positive and Negative Tag results extracted from CLIP.", + "bbox": [ + 496, + 571, + 890, + 779 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.5. General Image Captioning", + "text_level": 1, + "bbox": [ + 500, + 787, + 741, + 805 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Improving modality alignment is a shared objective of general image captioning tasks. As demonstrated in Table 6, our proposed method, RCL-NOC, improves the model's performance across all metrics assessed on the COCO test set, particularly in the CIDEr score. However, we have observed that the improvement on the COCO benchmark is", + "bbox": [ + 496, + 811, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15517", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2320bd51d2972b870148cb0114702ed70317dda8e6c4ba745e4464be385f9363.jpg", + "image_caption": [], + "image_footnote": [ + "GT: A boy in a tie holding a small suitcase.", + "RCA-NOC: A young boy wearing a tie holding a suitcase.", + "PT: Person, human, tie, suitcase, dress*... (Person, human, suitcase, tie...)", + "NT: Hair*, chair, soda, step, umbrella ... (Chair, soda, step, umbrella...)" + ], + "bbox": [ + 81, + 95, + 181, + 147 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/7967f96606f0b36458826f4222a6f89bfeecea206eab094854724b8898d2d6d4.jpg", + "image_caption": [], + "image_footnote": [ + "GT: 2 men sit on the couch, video game controllers in hands.", + "RCA-NOC: A couple of men sitting on a couch playing a video game with wheels.", + "PT: Couch, person, face, wheel, shirt... (person, wheel, couch, face, shirt...)", + "NT: Wheelchair, leg\\* tie, stone, coat... (Wheelchair, tie, stone, coat...)" + ], + "bbox": [ + 84, + 183, + 181, + 236 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/8b6619f61484916499feca8de3571c462e0c7677d3987634eb9e0be4f67b939a.jpg", + "image_caption": [ + "Figure 3. Examples of generated captions and contrastive tags by compared methods on Held-Out COCO (left) and Nocaps (right). We show the ground-truth captions (GT) on Held-Out COCO for reference. PT/NT denotes the positive/negative tags before and after Uncertainty-Aware Selection and Reweighting (UASR). Blue/Red text indicates novel objects in Held-Out COCO/Nocaps, and * indicates the false positives/negatives." + ], + "image_footnote": [ + "GT: Someone cutting a small pizza with a pizza cutter.", + "RCA-NOC: A person is cutting a pizza with a pizza cutter.", + "PT: Person, food, pizza, kitchen, bottle*... (Person, food, kitchen, pizza...)", + "NT: Microwave, design, hammer, wine, tie... (Microwave, design, hammer, wine, tie...)" + ], + "bbox": [ + 84, + 275, + 181, + 329 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/d9650dbf1a3fd5545f3f5ecfbab2eeea00491409f5d90ef39e11a3f04b9cec63.jpg", + "image_caption": [], + "image_footnote": [ + "VinVL + VIVO: A man with a jacket and a cowboy hat next to a bull.", + "RCA-NOC: A man with a blue shirt and a cowboy hat next to a bull.", + "PT: Hat, hay, bull, shirt, man... (Man, bull, shirt, hat, hay...)", + "NT: face*, tie, road, barn, jacket... (Tie, road, barn, jacket...)" + ], + "bbox": [ + 491, + 92, + 589, + 146 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/f78b65bf065079936bf36b85b3a844b09a478ae78c6bcef40a68067607961278.jpg", + "image_caption": [], + "image_footnote": [ + "VinVL + VIVO: A jaguar standing on top of a tree.", + "RCA-NOC: A jaguar standing behind a green fence.", + "PT: Jaguar, fence, dog*, carnivore, chest*... (Jaguar, fence, carnivore...)", + "NT: animal*, wall, coat, cage, sign... (wall, coat, cage, sign...)" + ], + "bbox": [ + 504, + 171, + 573, + 250 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/1b2e2989a0365e192e6c781b1a3aa5024383a607bd63aa2d6ec5f4469835c7f4.jpg", + "image_caption": [], + "image_footnote": [ + "VinVL + VIVO: A white plate of food with dessert and a tomato.", + "RCA-NOC: A white plate with two pieces of bread and a tomato.", + "PT: Tomato, bread, lunch, plate, vegetable* ... (Tomato, bread, plate, lunch...)", + "NT: Piece*, salad, cake, snack, table*... (Salad, cake, snack...)" + ], + "bbox": [ + 493, + 271, + 586, + 325 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "not as substantial as that on the nocaps benchmark. We hypothesize that this discrepancy is due to the COCO dataset having a limited number of visual concepts, thus reducing the benefits of learning visual semantics. Additionally, our method's use of tags is general and does not rely on fully annotated data. It's possible to utilize potentially unlimited amounts of images and different sources of tags, including those from Faster R-CNN, image tagging, or keywords extracted from captions. These possibilities will be explored in our future work..", + "bbox": [ + 75, + 422, + 470, + 571 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6.6. Data and Compute Efficiency", + "text_level": 1, + "bbox": [ + 76, + 583, + 339, + 599 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The way the visual semantics are extracted (using CLIP) is not central to our work, as for the gain coming from 400M pairs of CLIP. This is supported in section 6.3. Table 7 shows that other components contribute significantly. Notably, the gain achieved by our Contrastive Alignment (CA) component alone can surpass that of CLIP by a large margin. Importantly, our method achieves this without increasing the number of parameters during training and inference, with the same parameter count as NOC-REK and VINVL (110 M). The training time of NOC-REK is 49 hours, for NOC-REK the training time is much lower (23h). This is with the paper setup (8 GPUs A100). Compared with NOC-REK, which adopts test time augmentation during inference, our inference time is much lower (1 minute) while NOC-REK is 2 minutes.", + "bbox": [ + 75, + 606, + 470, + 829 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 844, + 194, + 859 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we present RCA-NOC, which achieves visual-semantic alignment via relative contrastive learning.", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Specifically, for each image, we first extract augmented tags obtained from foundation models such as CLIP. Then we utilize the rank of each augmented object tag in a list as a relative relevance label to contrast each top ranked tag with a set of lower ranked tags. We empirically find that such a learning objective is effective and easy to optimize by encouraging the top ranked tags to be more compatible with their image and text context than lower ranked tags, hence improving the discriminative ability of the learned multimodality representation. We prove the effectiveness of our paradigm in novel object caption, with the spotlight on Nocaps and Held-Out COCO benchmark.", + "bbox": [ + 496, + 422, + 890, + 599 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The effectiveness of object tags has already been proved in recent works. However, there are few studies to further explore why such tags could perform well and the problem of object tags' misalignment is often ignored. So how to further exploit use tags explicitly while having a deep understanding of their roles is meaningful in the future.", + "bbox": [ + 496, + 601, + 890, + 690 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "15518", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] https://huggingface.co/transformers/modeldoc/bert.html.6", + "[2] Harsh Agrawal, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, Stefan Lee, and Peter Anderson. nocaps: novel object captioning at scale. In ICCV, 2019. 6, 7", + "[3] Peter Anderson, Basura Fernando, Mark Johnson, and Stephen Gould. Guided open vocabulary image captioning with constrained beam search. 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Coca: Contrastive captioners are image-text foundation models. arXiv preprint arXiv:2205.01917, 2022. 7", + "[35] Pengchuan Zhang, Xiujun Li, Xiaowei Hu, Jianwei Yang, Lei Zhang, Lijuan Wang, Yejin Choi, and Jianfeng Gao. Vinvl: Revisiting visual representations in vision-language models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5579-5588, 2021. 1, 2, 6, 7, 8" + ], + "bbox": [ + 78, + 90, + 468, + 282 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "15520", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/RCA-NOC_ Relative Contrastive Alignment for Novel Object Captioning/cbdb5e43-66b1-4704-93d9-a919fc74c296_model.json b/2023/RCA-NOC_ Relative Contrastive Alignment for Novel Object Captioning/cbdb5e43-66b1-4704-93d9-a919fc74c296_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2170d250adfc3e7969b0eb93f9c43b6083b06536 --- /dev/null +++ b/2023/RCA-NOC_ Relative Contrastive Alignment for Novel Object Captioning/cbdb5e43-66b1-4704-93d9-a919fc74c296_model.json @@ -0,0 +1,2796 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.264, + 0.13, + 0.71, + 0.176 + ], + "angle": 0, + "content": "RCA-NOC: Relative Contrastive Alignment for Novel Object Captioning" + }, + { + "type": "text", + "bbox": [ + 0.155, + 0.202, + 0.812, + 0.24 + ], + "angle": 0, + "content": "Jiashuo Fan \\(^{2}\\) Yaoyuan Liang \\(^{2}\\) Leyao Liu \\(^{2}\\) Shaolun Huang \\(^{2}\\) Lei Zhang \\(^{1}\\) International Digital Economy Academy \\(^{2}\\)Tsinghua University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.273, + 0.314, + 0.289 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.474, + 0.588 + ], + "angle": 0, + "content": "In this paper, we introduce a novel approach to novel object captioning which employs relative contrastive learning to learn visual and semantic alignment. Our approach maximizes compatibility between regions and object tags in a contrastive manner. To set up a proper contrastive learning objective, for each image, we augment tags by leveraging the relative nature of positive and negative pairs obtained from foundation models such as CLIP. We then use the rank of each augmented tag in a list as a relative relevance label to contrast each top-ranked tag with a set of lower-ranked tags. This learning objective encourages the top-ranked tags to be more compatible with their image and text context than lower-ranked tags, thus improving the discriminative ability of the learned multi-modality representation. We evaluate our approach on two datasets and show that our proposed RCA-NOC approach outperforms state-of-the-art methods by a large margin, demonstrating its effectiveness in improving vision-language representation for novel object captioning." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.621, + 0.21, + 0.637 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.647, + 0.47, + 0.797 + ], + "angle": 0, + "content": "Describing novel objects unseen in training data is a highly desired capability for a real-world image captioning model. Conventional image captioning models [4, 20, 28] often fail to describe novel objects because they only cover limited visual concepts and generalize poorly to images in the wild [26]. To overcome this limitation, approaches that rely on object detection as the external resource [7, 8, 13, 18, 20, 25, 27, 33, 35] have been widely explored and demonstrated breakthroughs in vision-language (VL) understanding." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.797, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Although object detection models (e.g., Faster RCNN [23]) have been improved to recognize a wide range of objects including novel ones like zero-shot object detection [14], using object detection in novel captioning models brings a new challenge. VIVO [13] leverages extra object tags to pre-train a visual vocabulary and help image captioning generalize to new categories. NOC-REK [29]" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.274, + 0.638, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.334, + 0.598, + 0.343 + ], + "angle": 0, + "content": "(a) : Training" + }, + { + "type": "text", + "bbox": [ + 0.656, + 0.279, + 0.854, + 0.308 + ], + "angle": 0, + "content": "NOC-REK: panda, animal, chunk, tree, branch. \nVIVO: panda, bear, chunk, tree, branch, animal, raccoon, hedge, food, raccoon." + }, + { + "type": "text", + "bbox": [ + 0.657, + 0.311, + 0.87, + 0.329 + ], + "angle": 0, + "content": "Ours: panda, animal, tree, branch, chunk.../ hedge, raccoon, sky, advertisement, water..." + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.343, + 0.638, + 0.402 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.402, + 0.605, + 0.411 + ], + "angle": 0, + "content": "(b): Inference" + }, + { + "type": "text", + "bbox": [ + 0.656, + 0.344, + 0.87, + 0.362 + ], + "angle": 0, + "content": "NOC-REK: A raccoon sitting on top of a tree branch. (panda, tree, branch)" + }, + { + "type": "text", + "bbox": [ + 0.657, + 0.364, + 0.878, + 0.382 + ], + "angle": 0, + "content": "VIVO: A raccoon sitting on a tree branch. (panda, tree, branch)" + }, + { + "type": "text", + "bbox": [ + 0.657, + 0.384, + 0.878, + 0.402 + ], + "angle": 0, + "content": "Ours: A red panda sitting in a tree branch (panda, tree, branch)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.421, + 0.895, + 0.545 + ], + "angle": 0, + "content": "Figure 1. An illustrative example of our method to leverage relative semantic relevance to achieve modality alignment. Our method could give accurate captions \"A cute red panda sitting in a tree branch\" conditioned on the objects \"red panda\" while VINVL+VIVO generates a wrong caption \"A cute raccoon sitting in a tree branch\". This inference result shows that our method can differentiate some confusing objects and generate accurate captions for novel objects when the object detection is well aligned with other modalities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.56, + 0.895, + 0.709 + ], + "angle": 0, + "content": "tries to augment object tags in the training stage based on the similarity between region and word. Such methods simply concatenate regions, object tags, and caption features as input to a Transformer-based model and use masked token reconstruction to implicitly learn an alignment between vision and language. Although such an alignment can help bring regions and words of the same concept closer, it lacks an effective mechanism to push away irrelevant concepts. As a result, it still makes mistakes on some confusing concepts, as shown in Figure 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.709, + 0.896, + 0.902 + ], + "angle": 0, + "content": "Different from previous methods, this study aims to learn visual and semantic alignment in a contrastive manner. Gupta et al. [10] showed that modality alignment could be achieved by maximizing the information lower bound between an image and its object tags. That is, given pairs of image and object tags, we can maximize the compatibility between tags and their attention-weighted region representations, compared to regions and non-corresponding tags. However, there are two critical problems that need to be further addressed: 1) how to effectively generate contrastive tags (augmented tags) that are closely relevant to an image, and 2) how to design a proper contrastive learning objective that allows the model to effectively leverage the contrastive" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15510" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.308, + 0.106 + ], + "angle": 0, + "content": "tags to align vision and semantics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.12, + 0.473, + 0.328 + ], + "angle": 0, + "content": "To tackle the first problem, we utilize CLIP [22] to create a list of contrastive tags which are closely linked to an image and contain global structural information and high-level concepts describing scenes. This approach aids in the discovery of useful tags that are essential for contrastive learning. To address the second problem, a proper contrastive learning objective needs to be explored. The major challenge here is that the augmented contrastive tags are inaccurate and inevitably noisy. We cannot simply treat one tag as positive and others as negative to perform contrastive learning, because the augmented tags might be highly correlated or similar to each other. To tackle this problem, we leverage the relative relevance, rather than the absolute relevance, of the augmented tags, which is more robust to data noise." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.473, + 0.581 + ], + "angle": 0, + "content": "Specifically, given an image, for each of its labeled object tags, we generate a ranked list of contrastive tags using CLIP. We regard the rank of each augmented tag as its relative semantic relevance with the image. In general, the top-ranked tags are assumed to be more relevant to the image than the lower-ranked tags. We divide the list into two parts: the (relatively) relevant part with higher rank and the (relatively) irrelevant part with lower rank (Figure 1 (a)). In our proposed objective, we treat each tag in the relevant part as positive and all tags in the irrelevant part as negative to perform contrastive learning. Note that we do not let tags both in the relevant part contrast with each other as they might be highly correlated concepts. In this way, our approach weakens the strict assumption of contrastive learning in previous works and exploits the relative ranking in a loose form to achieve modality alignment." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.592, + 0.47, + 0.637 + ], + "angle": 0, + "content": "We conduct experiments on the Nocaps and Held-Out COCO datasets to demonstrate the effectiveness of RCA-NOC. Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.651, + 0.47, + 0.74 + ], + "angle": 0, + "content": "- We propose Relative Contrastive Alignment (RCA) to learn the relative semantic relevance in a loose form by maximizing the compatibility between regions and their relevant tags compared with regions and irrelevant tags to achieve vision and language alignment and improve the discriminative ability of the multi-modality representation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.754, + 0.47, + 0.844 + ], + "angle": 0, + "content": "- A method called Uncertainty-Aware Selection and Reweighting (UASR) is proposed to estimate and exploit the uncertainty of each contrastive sample to mitigate the negative effect brought by noisy tags. UASR can effectively prioritize highly reliable samples and demote false positives and false negatives." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.857, + 0.47, + 0.902 + ], + "angle": 0, + "content": "- We validate the proposed method on the Nocaps and Held-Out COCO benchmarks, which outperforms other state-of-the-art methods by a large margin." + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.651, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.642, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.116, + 0.638, + 0.132 + ], + "angle": 0, + "content": "3. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.141, + 0.892, + 0.408 + ], + "angle": 0, + "content": "Novel object captioning aims to describe images with objects that are unseen in the training stage (we define these objects as novel objects) where many methods. [7, 8, 13, 18, 20, 22, 27, 31, 33, 35] have been proposed. Early works such as Hendricks et al. [12] and Venugopalan et al. [27] utilize unpaired labeled image and sentence data to enhance semantically visual concepts. Recent studies propose to explicitly leverage the object detection results for NOC, Lu et al. [20], Wu et al. [33], and Demirel et al. [8] fill the generated template sentence with objects detected by object/novel object detectors. Chen et al. [7] combine object detector and human attention to identify novel objects. In addition, Li et al. are the first to utilize semantics in VLP tasks, which are further extended by Zhang et al. [35]. Hu et al. [13] built upon [35] and propose to leverage extra region-tag pairs to conduct pretraining. Duc et al. [29] tried to augment object tags in the training stage based on the similarity of regions and objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.408, + 0.892, + 0.542 + ], + "angle": 0, + "content": "However, most aforementioned methods for NOC ignore the misalignment problem of object tags, thereby failing to fully exploit the semantic relationship between vision and language (Figure 1), which we argue is crucial to the quality of generated captions. In this paper, we propose a simple but effective contrastive learning objective to learn the relative semantic relevance in a loose form where the object tags could be explicitly aligned with their corresponding image feature representations in a semantic space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.542, + 0.892, + 0.719 + ], + "angle": 0, + "content": "Contrastive Learning aims to learn discriminative representations to distinguish an image from others. Many methods [6,10,11,16,17,22,32] have shown their effectiveness. For example, Chen et al. [6] proposed to learn visual representations by maximizing agreement between differently augmented views of the same image via a contrastive loss. He et al. [11] proposed Momentum Contrast (MoCo) for unsupervised visual representation learning. Wei et al. [32] utilized contrastive learning in the detection task. Li et al. [16] focused on the problem of contextual outpainting. Gupta et al. [10] proposed a method \\(\\mathrm{CPG}^{\\dagger}\\) to find hard negative words by replacing a word in a caption." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Other data-driven studies such as CLIP [22] and ALIGNN [17] focus on learning a corresponding relative relationship from massive web data. CLIP [22] predicts which text goes with which image and learns a relative imagetext corresponding relationship from broad web data with noisy supervision. ALIGNN [17] further scales up CLIP by leveraging a noisy dataset that covers more than one billion image-text pairs. These methods achieve remarkable results but require massive fully-annotated data, which are difficult to obtain." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "1For better illustration, we use the abbreviation CPG to denote the paper \"Contrastive Learning for Weakly Supervised Phrase Grounding\" [10]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15511" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.126, + 0.106, + 0.327, + 0.211 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.088, + 0.213, + 0.345, + 0.226 + ], + "angle": 0, + "content": "\"A close up of a small animal on a tree branch\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.082, + 0.238, + 0.338, + 0.252 + ], + "angle": 0, + "content": "(a) Training: learn discriminative feature" + }, + { + "type": "image", + "bbox": [ + 0.354, + 0.096, + 0.884, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.121, + 0.262, + 0.288, + 0.347 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.082, + 0.349, + 0.345, + 0.362 + ], + "angle": 0, + "content": "Result: \"A red panda sitting in a tree branch\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.088, + 0.364, + 0.321, + 0.378 + ], + "angle": 0, + "content": "(b) Inference: novel object captioning" + }, + { + "type": "text", + "bbox": [ + 0.439, + 0.264, + 0.506, + 0.277 + ], + "angle": 0, + "content": "Red panda" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.298, + 0.71, + 0.314 + ], + "angle": 0, + "content": "Multi-layer Transformer" + }, + { + "type": "image", + "bbox": [ + 0.361, + 0.326, + 0.882, + 0.381 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.392, + 0.892, + 0.501 + ], + "angle": 0, + "content": "Figure 2. The main pipeline of our proposed RCA-NOC, including training and inference: In addition to the normal caption loss \\( L_{G} \\) in the training process, we also compute the cross-modality and inner-modality loss \\( L_{cross} \\) and \\( L_{inner} \\) in Eq. 22 and Eq. 23 by contrasting the positive tags against the negative tags. The corresponding relationship is denoted in green and red line separately. During training, the input is a concatenated sequence of words—ROI tags—ROIs and augmented contrastive tags. The training loss comprises caption loss (with [MASK] in words for reconstruction) and contrastive learning loss (with [MASK] in ROI tags token for indicating the specific positions where augmented tags are inserted). Augmented tags replace certain ROI tags and are encoded into contrastive tag feature embeddings for comparison with region and caption embeddings. During prediction, the input is a concatenated sequence of ROI tags—ROIs without additional retrieval steps." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.516, + 0.258, + 0.532 + ], + "angle": 0, + "content": "4. Proposed Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.542, + 0.469, + 0.6 + ], + "angle": 0, + "content": "We propose to enhance the modality alignment by explicitly injecting visual semantics. These semantics are extracted for each image, obtained with existing foundation models such as CLIP." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.601, + 0.469, + 0.764 + ], + "angle": 0, + "content": "There are two motivations behind our approach. First, by maximizing the compatibility between regions and their relevant tags compared with regions and irrelevant tags, we could not only learn vision-semantic alignment and improve the discriminative ability of the multi-modality representation. Second, we introduce a relative contrastive learning objective that considers the relative relationships between positive and negative examples, rather than using absolute prototype-contrastive learning methods. This approach is more generalized and can be easily integrated into any existing NOC method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.774, + 0.331, + 0.789 + ], + "angle": 0, + "content": "4.1. Visual Semantics Extraction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.797, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Different from other approaches (e.g., [13, 18]) that extract object tags using pretrained object detectors, we use an off-the-shelf foundational model to extract more diverse, larger and semantically meaningful set of visual semantics. We show in section 6, that this approach helps to capture high level and global semantics describing the scenes, which are hard to obtain with other approaches (e.g. object" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.518, + 0.573, + 0.532 + ], + "angle": 0, + "content": "detectors)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.546, + 0.892, + 0.756 + ], + "angle": 0, + "content": "We use a pretrained CLIP (ViT-B/16) model to obtain the embeddings of all the images and the extracted semantics. For each image, we compute its cosine similarity with all the embedded semantics and select the top M similar semantics as augmented tags \\( T = \\{t_l\\}_{l=1}^M \\). The augmented tags will be ranked using global (image-level) cosine similarity \\( p(t_l) \\). Then we utilize the rank of each augmented tag in \\( T \\) as a relative relevance label. In general, the top-ranked tags are assumed to be more relevant to the image than the lower-ranked tags. We divide \\( T \\) into positive and negative tags: positive tags being the (relatively) relevant tags with higher rank \\( T^P = \\{t_n^P\\}_{n=1}^K = \\{t_l\\}_{l=1}^K \\) and negative tags being the (relatively) irrelevant tags with lower rank \\( T^N = \\{t_l^N\\}_{l=1}^K = \\{t_l\\}_{l=K+1}^{2K} \\) (\\( M = 2K \\))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.768, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Here we propose a simple yet effective augmentation technique. Having a set of visual semantics extracted for each image, instead of considering all the visual semantics at once, we sample randomly a fraction of these augmented tags at each iteration step. Hence, we could not only prevent the model from overfitting on specific semantics and potentially disregard the image or other semantics during training, but also let the model see different combinations of visual semantics, which helps to have more diversity." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15512" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.357, + 0.108 + ], + "angle": 0, + "content": "4.2. Relative Contrastive Alignment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.468, + 0.203 + ], + "angle": 0, + "content": "InfoNCE [21] is a typical type of contrastive loss function used for self-supervised learning that contrasts one positive sample against a set of negative samples. CPG [10] builds upon InfoNCE and proposes a compatibility function for regions and a caption word. Both InfoNCE and CPG utilize the absolute relevance to optimize the contrastive loss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.203, + 0.468, + 0.291 + ], + "angle": 0, + "content": "However, such a contrastive learning objective is hard to optimize for object tags since they may be highly correlated to each other. In RCA-NOC, we focus on the relative semantic relevance and utilize the attention-based compatibility function to measure the relativity information for regions and a set of object tags, which is more robust to data noise." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.291, + 0.468, + 0.321 + ], + "angle": 0, + "content": "Specifically, we first compute the dot product for a region-tag pair." + }, + { + "type": "equation", + "bbox": [ + 0.212, + 0.323, + 0.468, + 0.342 + ], + "angle": 0, + "content": "\\[\ns _ {j k} = \\mathbf {w} _ {j} ^ {T} \\mathbf {v} _ {k} / \\sqrt {d}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.347, + 0.468, + 0.422 + ], + "angle": 0, + "content": "where \\(\\mathbf{w}_j\\) and \\(\\mathbf{v}_k\\) refer to the corresponding embeddings for tag and region, and \\(d\\) is the feature dimension. Here, \\(s_{jk}\\) represents the similarity between the \\(j\\)-th tag and the \\(k\\)-th region. To find a contextualized region representation for the \\(j\\)-th tag, we define \\(\\mathbf{a}_j^v\\) as follows." + }, + { + "type": "equation", + "bbox": [ + 0.216, + 0.423, + 0.468, + 0.462 + ], + "angle": 0, + "content": "\\[\n\\mathbf {a} _ {j} ^ {v} = \\sum_ {k = 1} ^ {K} \\alpha_ {j k} \\mathbf {v} _ {k}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.467, + 0.468, + 0.497 + ], + "angle": 0, + "content": "where \\(\\alpha_{jk} = \\frac{e^{s_{jk}}}{\\sum_{k' = 1}^{K}e^{s_{jk'}}},\\) (3)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.468, + 0.533 + ], + "angle": 0, + "content": "To measure the compatibility between a tag \\(\\mathbf{w}_j\\) and its contextualized region representation \\(\\mathbf{a}_j^v\\), we define" + }, + { + "type": "equation", + "bbox": [ + 0.208, + 0.543, + 0.468, + 0.563 + ], + "angle": 0, + "content": "\\[\n\\phi (\\mathbf {V}, \\mathbf {w} _ {j}) = \\mathbf {w} _ {j} ^ {T} \\mathbf {a} _ {j} ^ {v}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.468, + 0.597 + ], + "angle": 0, + "content": "In this way, we can derive our cross-modality contrastive loss function \\( L_{cross} \\)." + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.607, + 0.468, + 0.666 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {c r o s s}} (\\mathbf {V}, \\mathbf {W} ^ {P}, \\mathbf {W} ^ {N}) = \\\\ - \\frac {1}{K} \\sum_ {n = 1} ^ {K} \\log \\left(\\frac {e ^ {\\phi (\\mathbf {V} , \\mathbf {w} _ {n} ^ {P})}}{e ^ {\\phi (\\mathbf {V} , \\mathbf {w} _ {n} ^ {P})} + \\sum_ {l = 1} ^ {K} e ^ {\\phi (\\mathbf {V} , \\mathbf {w} _ {l} ^ {N})}}\\right), \\tag {5} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.678, + 0.468, + 0.737 + ], + "angle": 0, + "content": "where \\(\\mathbf{W}^P = \\{\\mathbf{w}_l^P\\}_{l=1}^K\\) and \\(\\mathbf{W}^N = \\{\\mathbf{w}_n^N\\}_{n=1}^K\\) are the word embeddings for positives/negatives \\(T^P\\) and \\(T^N\\), extracted from CLIP. \\(\\phi()\\) is the compatibility function defined in Eq. 11." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.738, + 0.468, + 0.869 + ], + "angle": 0, + "content": "This equation encourages each positive tag \\(\\mathbf{w}_n^P\\) to be more compatible with image regions \\(\\mathbf{V}\\) than all negative tags in \\(\\mathbf{W}^N\\). Essentially, if tag \\(t_j\\) is not relevant to the image (negative), its representation \\(\\mathbf{w}_j\\) should not be similar to its contextualized region representation \\(\\mathbf{a}_j^v\\) since it would not be able to collect good information while computing \\(\\mathbf{a}_j^v\\). Note that we do not let two positive tags (top-ranked tags) contrast with each other as it is hard to tell which one is more relevant." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Inner modality Alignment. To further enhance modality alignment, we also compute the inner-modality contrastive" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.209 + ], + "angle": 0, + "content": "loss over tag-caption pairs. The formulation for inner-modality contrastive loss is similar to cross-modality contrastive loss but slightly different. We enforce contrastive learning not to be between tags and all caption words, but just between tags and noun caption words. This is because a caption may have many irrelevant tokens, such as \"the, a, is\", which will harm our alignment process and cause redundant computational costs." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.211, + 0.892, + 0.24 + ], + "angle": 0, + "content": "Finally, we can derive our inner-modality contrastive loss function \\( L_{inner} \\)." + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.248, + 0.892, + 0.267 + ], + "angle": 0, + "content": "\\[\n\\phi (\\mathbf {C}, \\mathbf {w} _ {l}) = \\mathbf {w} _ {l} ^ {T} \\mathbf {a} _ {l} ^ {c}, \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.284, + 0.892, + 0.343 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {i n n e r}} \\left(\\mathbf {C}, \\mathbf {W} ^ {P}, \\mathbf {W} ^ {N}\\right) = \\\\ - \\frac {1}{K} \\sum_ {n = 1} ^ {K} \\log \\left(\\frac {e ^ {\\phi (\\mathbf {C} , \\mathbf {w} _ {n} ^ {P})}}{e ^ {\\phi (\\mathbf {C} , \\mathbf {w} _ {n} ^ {P})} + \\sum_ {l = 1} ^ {K} e ^ {\\phi (\\mathbf {C} , \\mathbf {w} _ {l} ^ {N})}}\\right), \\tag {7} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.353, + 0.892, + 0.427 + ], + "angle": 0, + "content": "where this time we take noun caption words \\(\\mathbf{C} = \\{\\mathbf{c}_i\\}_{i=1}^P\\) in Eq. 13 as input. By further considering inner-modality alignment, we not only learn caption-tag semantics to connect relevant caption tokens, but also enable region-caption interactions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.442, + 0.681, + 0.459 + ], + "angle": 0, + "content": "5. Proposed Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.467, + 0.892, + 0.526 + ], + "angle": 0, + "content": "We propose to enhance the modality alignment by explicitly injecting visual semantics. These semantics are extracted for each image, obtained with existing foundation models such as CLIP." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.527, + 0.892, + 0.689 + ], + "angle": 0, + "content": "There are two motivations behind our approach. First, by maximizing the compatibility between regions and their relevant tags compared with regions and irrelevant tags, we could not only learn vision-semantic alignment and improve the discriminative ability of the multi-modality representation. Second, we introduce a relative contrastive learning objective that considers the relative relationships between positive and negative examples, rather than using absolute prototype-contrastive learning methods. This approach is more generalized and can be easily integrated into any existing NOC method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.7, + 0.753, + 0.715 + ], + "angle": 0, + "content": "5.1. Visual Semantics Extraction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.723, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Different from other approaches (e.g., [13, 18]) that extract object tags using pretrained object detectors, we use an off-the-shelf foundational model to extract more diverse, larger and semantically meaningful set of visual semantics. We show in section 6, that this approach helps to capture high level and global semantics describing the scenes, which are hard to obtain with other approaches (e.g. object detectors)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We use a pretrained CLIP (ViT-B/16) model to obtain the embeddings of all the images and the extracted semantics. For each image, we compute its cosine similarity with all the embedded semantics and select the top M similar" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15513" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.24 + ], + "angle": 0, + "content": "semantics as augmented tags \\( T = \\{t_l\\}_{l=1}^M \\). The augmented tags will be ranked using global (image-level) cosine similarity \\( p(t_l) \\). Then we utilize the rank of each augmented tag in \\( T \\) as a relative relevance label. In general, the top-ranked tags are assumed to be more relevant to the image than the lower-ranked tags. We divide \\( T \\) into positive and negative tags: positive tags being the (relatively) relevant tags with higher rank \\( T^P = \\{t_n^P\\}_{n=1}^K = \\{t_l\\}_{l=1}^K \\) and negative tags being the (relatively) irrelevant tags with lower rank \\( T^N = \\{t_l^N\\}_{l=1}^K = \\{t_l\\}_{l=K+1}^{2K} \\) (\\( M = 2K \\))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.241, + 0.473, + 0.375 + ], + "angle": 0, + "content": "Here we propose a simple yet effective augmentation technique. Having a set of visual semantics extracted for each image, instead of considering all the visual semantics at once, we sample randomly a fraction of these augmented tags at each iteration step. Hence, we could not only prevent the model from overfitting on specific semantics and potentially disregard the image or other semantics during training, but also let the model see different combinations of visual semantics, which helps to have more diversity." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.384, + 0.358, + 0.4 + ], + "angle": 0, + "content": "5.2. Relative Contrastive Alignment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.407, + 0.47, + 0.496 + ], + "angle": 0, + "content": "InfoNCE [21] is a typical type of contrastive loss function used for self-supervised learning that contrasts one positive sample against a set of negative samples. CPG [10] builds upon InfoNCE and proposes a compatibility function for regions and a caption word. Both InfoNCE and CPG utilize the absolute relevance to optimize the contrastive loss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.496, + 0.47, + 0.585 + ], + "angle": 0, + "content": "However, such a contrastive learning objective is hard to optimize for object tags since they may be highly correlated to each other. In RCA-NOC, we focus on the relative semantic relevance and utilize the attention-based compatibility function to measure the relativity information for regions and a set of object tags, which is more robust to data noise." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.585, + 0.47, + 0.615 + ], + "angle": 0, + "content": "Specifically, we first compute the dot product for a region-tag pair." + }, + { + "type": "equation", + "bbox": [ + 0.212, + 0.617, + 0.47, + 0.639 + ], + "angle": 0, + "content": "\\[\ns _ {j k} = \\mathbf {w} _ {j} ^ {T} \\mathbf {v} _ {k} / \\sqrt {d}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.718 + ], + "angle": 0, + "content": "where \\(\\mathbf{w}_j\\) and \\(\\mathbf{v}_k\\) refer to the corresponding embeddings for tag and region, and \\(d\\) is the feature dimension. Here, \\(s_{jk}\\) represents the similarity between the \\(j\\)-th tag and the \\(k\\)-th region. To find a contextualized region representation for the \\(j\\)-th tag, we define \\(\\mathbf{a}_j^v\\) as follows." + }, + { + "type": "equation", + "bbox": [ + 0.216, + 0.72, + 0.469, + 0.76 + ], + "angle": 0, + "content": "\\[\n\\mathbf {a} _ {j} ^ {v} = \\sum_ {k = 1} ^ {K} \\alpha_ {j k} \\mathbf {v} _ {k}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.761, + 0.469, + 0.797 + ], + "angle": 0, + "content": "where \\(\\alpha_{jk} = \\frac{e^{s_{jk}}}{\\sum_{k'=1}^{K} e^{s_{jk'}}},\\) (10)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.802, + 0.47, + 0.833 + ], + "angle": 0, + "content": "To measure the compatibility between a tag \\(\\mathbf{w}_j\\) and its contextualized region representation \\(\\mathbf{a}_j^v\\), we define" + }, + { + "type": "equation", + "bbox": [ + 0.208, + 0.845, + 0.469, + 0.866 + ], + "angle": 0, + "content": "\\[\n\\phi (\\mathbf {V}, \\mathbf {w} _ {j}) = \\mathbf {w} _ {j} ^ {T} \\mathbf {a} _ {j} ^ {v}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In this way, we can derive our cross-modality contrastive loss function \\( L_{cross} \\)." + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.115, + 0.892, + 0.175 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {c r o s s}} (\\mathbf {V}, \\mathbf {W} ^ {P}, \\mathbf {W} ^ {N}) = \\\\ - \\frac {1}{K} \\sum_ {n = 1} ^ {K} \\log \\left(\\frac {e ^ {\\phi (\\mathbf {V} , \\mathbf {w} _ {n} ^ {P})}}{e ^ {\\phi (\\mathbf {V} , \\mathbf {w} _ {n} ^ {P})} + \\sum_ {l = 1} ^ {K} e ^ {\\phi (\\mathbf {V} , \\mathbf {w} _ {l} ^ {N})}}\\right), \\tag {12} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.187, + 0.892, + 0.246 + ], + "angle": 0, + "content": "where \\(\\mathbf{W}^P = \\{\\mathbf{w}_l^P\\}_{l=1}^K\\) and \\(\\mathbf{W}^N = \\{\\mathbf{w}_n^N\\}_{n=1}^K\\) are the word embeddings for positives/negatives \\(T^P\\) and \\(T^N\\), extracted from CLIP. \\(\\phi()\\) is the compatibility function defined in Eq. 11." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.247, + 0.892, + 0.379 + ], + "angle": 0, + "content": "This equation encourages each positive tag \\(\\mathbf{w}_n^P\\) to be more compatible with image regions \\(\\mathbf{V}\\) than all negative tags in \\(\\mathbf{W}^N\\). Essentially, if tag \\(t_j\\) is not relevant to the image (negative), its representation \\(\\mathbf{w}_j\\) should not be similar to its contextualized region representation \\(\\mathbf{a}_j^v\\) since it would not be able to collect good information while computing \\(\\mathbf{a}_j^v\\). Note that we do not let two positive tags (top-ranked tags) contrast with each other as it is hard to tell which one is more relevant." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.892, + 0.528 + ], + "angle": 0, + "content": "Inner modality Alignment. To further enhance modality alignment, we also compute the inner-modality contrastive loss over tag-caption pairs. The formulation for inner-modality contrastive loss is similar to cross-modality contrastive loss but slightly different. We enforce contrastive learning not to be between tags and all caption words, but just between tags and noun caption words. This is because a caption may have many irrelevant tokens, such as \"the, a, is\", which will harm our alignment process and cause redundant computational costs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.892, + 0.56 + ], + "angle": 0, + "content": "Finally, we can derive our inner-modality contrastive loss function \\( L_{inner} \\)." + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.567, + 0.892, + 0.587 + ], + "angle": 0, + "content": "\\[\n\\phi (\\mathbf {C}, \\mathbf {w} _ {l}) = \\mathbf {w} _ {l} ^ {T} \\mathbf {a} _ {l} ^ {c}, \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.603, + 0.892, + 0.662 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {i n n e r}} (\\mathbf {C}, \\mathbf {W} ^ {P}, \\mathbf {W} ^ {N}) = \\\\ - \\frac {1}{K} \\sum_ {n = 1} ^ {K} \\log \\left(\\frac {e ^ {\\phi (\\mathbf {C} , \\mathbf {w} _ {n} ^ {P})}}{e ^ {\\phi (\\mathbf {C} , \\mathbf {w} _ {n} ^ {P})} + \\sum_ {l = 1} ^ {K} e ^ {\\phi (\\mathbf {C} , \\mathbf {w} _ {l} ^ {N})}}\\right), \\tag {14} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.892, + 0.746 + ], + "angle": 0, + "content": "where this time we take noun caption words \\(\\mathbf{C} = \\{\\mathbf{c}_i\\}_{i=1}^P\\) in Eq. 13 as input. By further considering inner-modality alignment, we not only learn caption-tag semantics to connect relevant caption tokens, but also enable region-caption interactions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.892, + 0.774 + ], + "angle": 0, + "content": "5.3. Uncertainty-Aware Selection and Re-weighting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.855 + ], + "angle": 0, + "content": "The augmented contrastive tags are often noisy and would harm the discriminative ability and robustness of the contrastive learning process. Therefore, we design a sample selection strategy to deal with noisy contrastive tags (e.g., false positives/negatives)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.857, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Uncertainty-Aware Selection. Specifically, we first use the local cosine similarity to calculate the correlation between a region and a tag and filter false positives/negatives. The" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15514" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "stronger the correlation, the more reliable a positive tag is and the more uncertain a negative tag." + }, + { + "type": "equation", + "bbox": [ + 0.203, + 0.122, + 0.47, + 0.157 + ], + "angle": 0, + "content": "\\[\n\\mathrm {u} (\\mathbf {v}, \\mathbf {w}) = \\frac {\\mathbf {v} ^ {\\top} \\mathbf {w}}{\\| \\mathbf {v} \\| \\| \\mathbf {w} \\|}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.166, + 0.47, + 0.228 + ], + "angle": 0, + "content": "Then we retrieve \\(L\\) tags and their corresponding representations \\(\\mathbf{H} = \\{\\mathbf{w}_j\\}_{j=1}^L\\) for the given \\(L\\) region features \\(\\{\\mathbf{v}_i\\}_{i=1}^L\\). We use arg max to choose the most correlated tag \\(t_j\\) for region \\(\\mathbf{v}_i\\)." + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.238, + 0.469, + 0.262 + ], + "angle": 0, + "content": "\\[\nj = \\underset {k} {\\arg \\max } \\left(\\mathrm {u} \\left(\\mathbf {v} _ {i}, \\mathbf {w} _ {k}\\right)\\right), \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.471, + 0.48 + ], + "angle": 0, + "content": "According to the score in Eq. 15, the corresponding top-L tags will be listed as confusion samples for negatives (actually positive), and these confusion samples will be removed from the original contrastive tags. Similarly, we will also choose the true positives based on these top- \\(L\\) tags since tags with low-similarity scores should be regarded as outliers to the positives and they are too sparse to have a positive influence on the shape of embedding space. In this way, we can derive Eq. 17, where / is the removing set operation, \\(\\cap\\) is the intersection set operation. \\(\\overline{\\mathbf{W}}^P = \\{\\bar{\\mathbf{w}}_l^P\\}_{l=1}^K\\) and \\(\\overline{\\mathbf{W}}^N = \\{\\bar{\\mathbf{w}}_n^N\\}_{n=1}^K\\) is the final positive/negative tags' embedding sets. Note that if the set length of \\(\\overline{\\mathbf{W}}^P / \\overline{\\mathbf{W}}^N\\) is less than M, we will over-sample \\(\\overline{\\mathbf{W}}^P / \\overline{\\mathbf{W}}^N\\) until the set length is equal to M." + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.485, + 0.469, + 0.503 + ], + "angle": 0, + "content": "\\[\n\\overline {{\\mathbf {W}}} ^ {P} = \\mathbf {W} ^ {P} \\cap \\mathbf {H}, \\overline {{\\mathbf {W}}} ^ {N} = \\mathbf {W} ^ {N} / \\mathbf {H}, \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.612 + ], + "angle": 0, + "content": "Uncertainty-Aware Re-weighting. To further mitigate the negative effect of noisy tags, we use the correlation function defined above to enhance reliable samples and reduce the influence of high-uncertainty samples. The information from more reliable samples should have a larger impact on the shape of the embedding and vice versa. Specifically, we first introduce the weight in Eq. 18." + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.62, + 0.469, + 0.64 + ], + "angle": 0, + "content": "\\[\nq _ {1} \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right) = \\exp \\left(\\mathrm {u} \\left(\\mathbf {v} _ {k}, \\bar {\\mathbf {w}} _ {n} ^ {P}\\right)\\right), \\tag {18}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.186, + 0.654, + 0.469, + 0.679 + ], + "angle": 0, + "content": "\\[\nj = \\underset {k} {\\arg \\max } \\left(\\mathrm {u} \\left(\\mathbf {v} _ {i}, \\bar {\\mathbf {w}} _ {k} ^ {P}\\right)\\right), \\tag {19}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.215, + 0.686, + 0.469, + 0.705 + ], + "angle": 0, + "content": "\\[\nq _ {2} \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right) = p \\left(t _ {n}\\right), \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.717, + 0.47, + 0.82 + ], + "angle": 0, + "content": "where \\( q_{1}(\\bar{\\mathbf{w}}_{n}^{P}) \\) in Eq. 18 is the uncertainty score computed by the most relevant region with the corresponding tag. Moreover, we further consider how certain each tag is and combine the corresponding score \\( q_{2}(\\bar{\\mathbf{w}}_{n}^{P}) \\) in Eq. 20 with \\( q_{1}(\\bar{\\mathbf{w}}_{n}^{P}) \\) to derive the final uncertainty score \\( q(\\bar{\\mathbf{w}}_{n}^{P}) \\) in Eq. 21. Here \\( p(t_{n}) \\) in Eq. 20 is the global similarity mentioned in Section 5.1." + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.83, + 0.469, + 0.85 + ], + "angle": 0, + "content": "\\[\nq \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right) = q _ {1} \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right) * q _ {2} \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right), \\tag {21}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.859, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Thus, our method could mitigate the negative effect of noisy contrastive tags by considering the similarity from both the local region features (region-tag) and the" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "global structural information (image-tag). Finally, we could rewrite our contrastive loss function in Eq. 22, Eq. 23." + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.134, + 0.768, + 0.153 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c r o s s}} \\left(\\mathbf {V}, \\overline {{\\mathbf {W}}} ^ {P}, \\overline {{\\mathbf {W}}} ^ {N}\\right) =\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.157, + 0.892, + 0.194 + ], + "angle": 0, + "content": "\\[\n- \\frac {1}{K} \\sum_ {n = 1} ^ {K} - q \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right) \\log \\left(\\frac {e ^ {\\phi \\left(\\mathbf {V} , \\bar {\\mathbf {w}} _ {n} ^ {P}\\right)}}{e ^ {\\phi \\left(\\mathbf {V} , \\bar {\\mathbf {w}} _ {n} ^ {P}\\right)} + \\sum_ {l = 1} ^ {K} e ^ {\\phi \\left(\\mathbf {V} , \\bar {\\mathbf {w}} _ {l} ^ {N}\\right)}}\\right), \\tag {22}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.211, + 0.892, + 0.271 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {i n n e r}} \\left(\\mathbf {C}, \\overline {{\\mathbf {W}}} ^ {P}, \\overline {{\\mathbf {W}}} ^ {N}\\right) = \\\\ - \\frac {1}{K} \\sum_ {n = 1} ^ {K} - q \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right) \\log \\left(\\frac {e ^ {\\phi \\left(\\mathbf {C} , \\bar {\\mathbf {w}} _ {n} ^ {P}\\right)}}{e ^ {\\phi \\left(\\mathbf {C} , \\bar {\\mathbf {w}} _ {n} ^ {P}\\right)} + \\sum_ {l = 1} ^ {K} e ^ {\\phi \\left(\\mathbf {C} , \\bar {\\mathbf {w}} _ {l} ^ {N}\\right)}}\\right), \\tag {23} \\\\ \\end{array}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.275, + 0.632, + 0.291 + ], + "angle": 0, + "content": "6. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.299, + 0.691, + 0.315 + ], + "angle": 0, + "content": "6.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.321, + 0.892, + 0.602 + ], + "angle": 0, + "content": "Datasets. Our main experiments and ablation studies are based on the Nocaps [2] dataset. Our method was built with PyTorch, and we used a pre-trained BERT-base model from Huggingfaces [1] for parameters initialization, and no ground-truth tags are used on the Nocaps validation and test sets. For the training stage, we use the COCO training set which consists of 118K images, each with 5 captions. We evaluate our model on the validation and test sets of the Nocaps dataset, which consist of 4.5K and 10.6K images from the Open Images validation and test sets, respectively. Additionally, we test the proposed method on the Held-Out COCO [12], which is a subset of MS COCO [19] where the following eight object categories are excluded from the training set: bottle, bus, couch, microwave, pizza, racket, suitcase, and zebra. We randomly split the COCO validation set and use half of it for validation and the other half for testing, each with 20,252 images. In addition, we empirically set \\( M = 50 \\) to generate augmented object tags for the best performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.602, + 0.892, + 0.751 + ], + "angle": 0, + "content": "Implementation Details. In the training stage, the model is trained for 30 epochs with a batch size of 512 and a learning rate of \\(10^{-4}\\), optimized using the cross-entropy loss and our contrastive loss. We set the maximum caption length to 40 and the maximum tag length to 30. To further boost the performance, we also perform the SCST optimization (Rennie et al. [24]) with a learning rate of \\(1.4 \\times 10^{-6}\\) for 10 epochs. During inference, we use greedy decoding to generate image captions with a maximum length of 20. Our model is trained with 8 A100 GPUS and takes 1 day to train." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.76, + 0.721, + 0.775 + ], + "angle": 0, + "content": "6.2. Quantitative evaluation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.782, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Results on Nocaps dataset. In this section, we extensively compare our frameworks with previous methods on the Nocaps benchmark. The other compared state-of-art results are from NOC-REK [29]. Note that all the methods use the BERT-base [9] for a fair comparison. We compare our method with UpDown [2, 5], OSCAR [18], VinVL [35], VIVO [13], and NOC-REK [29], which hold the state-of-the-art result on the Nocaps benchmark. The training data" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15515" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.144 + ], + "angle": 0, + "content": "Table 1. Our evaluation results using SPICE and CIDEr on the Nocaps validation and test sets. We achieve the best scores for in-domain, near-domain, out-domain and Overall. Notably, the captions generated by our method are better than those by human in most cases. We note that our results on the test set are better than those by other methods which are publicly submitted to Nocaps leader-boardb. Higher score is better." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.153, + 0.891, + 0.342 + ], + "angle": 0, + "content": "
MethodValidation setTest set
in-domainnear-domainout-domainOverallin-domainnear-domainout-domainOverall
CIDErSPICECIDErSPICECIDErSPICECIDErSPICECIDErSPICECIDErSPICECIDErSPICECIDErSPICE
UpDown [4]78.111.657.710.331.38.355.310.176.011.874.211.566.79.773.111.2
Oscar [18]83.412.081.612.077.610.681.111.781.311.979.611.973.610.678.811.7
VIVO [13]92.212.987.812.687.511.588.312.489.012.987.812.680.111.186.612.4
VinVL [35]96.813.590.713.187.411.690.912.893.813.389.012.866.110.985.512.5
VinVL + VIVO [13,35]103.713.795.613.483.811.994.313.198.013.695.213.478.011.592.513.1
NOC-REK [29]104.714.8100.214.1100.713.0100.914.0100.014.195.713.677.411.693.013.4
RCA-NOC**95.013.691.313.193.212.192.213.087.713.388.112.977.911.486.312.7
RCA-NOC107.815.3104.014.6105.813.6107.114.6104.114.8101.214.688.512.9101.114.0
Δ3.1↑0.5↑4.2↑0.5↑5.1↑0.6↑6.2↑0.6↑4.1↑0.7↑5.5↑1.0↑11.1↑1.3↑8.1↑0.6↑
Human [2]84.414.385.014.395.714.087.114.280.615.084.614.791.614.285.314.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.348, + 0.472, + 0.417 + ], + "angle": 0, + "content": "Table 2. Comparison of F1-scores (in %) on object classes of Open Images, evaluated on the Nocaps validation set. There are 504 classes in total. 80 of them are in-domain, which are common classes from COCO. The remaining 424 classes are the out-of-domain objects." + }, + { + "type": "table", + "bbox": [ + 0.119, + 0.424, + 0.426, + 0.492 + ], + "angle": 0, + "content": "
modelin-domainout-of-domainentire
VIVO39.229.130.4
NOC-REK45.330.532.8
Ours58.639.243.1
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.569 + ], + "angle": 0, + "content": "for the baselines is the COCO dataset. Following prior settings, we also report the results after the model is optimized using SCST [24]. Our generated captions also adopt Constrained Beam Search (CBS) following [3]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.571, + 0.47, + 0.839 + ], + "angle": 0, + "content": "In Table 1, we present our results of SPICE and CIDEr scores on the Nocaps validation and test sets. We also show the results of our different training stages in the middle of the table, where RCA-NOC** denotes our first training stage result and RCA-NOC is our final result after CIDEr optimization. Note that we do not compare with the data-driven methods [17, 30, 34] which use massive out-of-domain image-caption pairs in the training and fail to follow the rule of Nocaps. By leveraging relative semantic relevance in contrastive learning, our method has achieved a significant improvement compared to all prior works. It is worth noting that our first stage training could generate a comparable result with [13, 18, 35]. After the CIDEr optimization process, our method could outperform the recent state-of-art method NOC-REK [29] with a large margin, which is 8.1 and 0.6 (CIDEr and SPICE) better than [29] on the Nocaps Test set. This suggests that our model is more capable of generating captions with novel objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.47, + 0.901 + ], + "angle": 0, + "content": "To quantitatively evaluate how well the model can describe novel objects, we also calculate the F1-score between our generated and the ground-truth tags on the validation set. Table 2 shows the comparison with VIVO and NOC-" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.348, + 0.892, + 0.375 + ], + "angle": 0, + "content": "Table 3. Evaluation results on the Held-Out COCO test set. The best results are highlighted in red." + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.378, + 0.865, + 0.505 + ], + "angle": 0, + "content": "
MethodAvg. F1-scoreSPICEMeteorCIDEr
NOC48.8-21.4-
NBT48.515.722.877.0
DNOC57.9-21.6-
ZSC29.814.221.9-
ANOC64.318.225.294.7
VinVL+VIVO71.824.530.6132.8
NOC-REK76.326.932.8138.4
RCA-NOc79.527.035.9142.8
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.892, + 0.592 + ], + "angle": 0, + "content": "REK on the Nocaps validation set. We see that RCA-NOC improves NOC-REK and VIVO on F1-score substantially, especially for out-of-domain objects. This again verifies the effectiveness of RCA-NOC's discriminative ability to describe and distinguish novel objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.593, + 0.893, + 0.816 + ], + "angle": 0, + "content": "Results on the Held-Out COCO dataset. To further prove the generalization ability of our method, we also conduct experiments on the Held-Out COCO dataset. As we can see from Table 3, our method consistently beats the baseline VinVL+VIVO with a large margin. The improvements are 7.7, 2.5, 5.3, and 10.0 with BERT-base on the F1, SPICE, METEOR, and CIDEr metrics. Additionally, our method is superior to all other state-of-art methods. In particular, compared with the recent state-of-art method NOC-REK [29], the recent state-of-art on the Held-Out COCO dataset, RCA-NOC achieves a 4.4 improvement on CIDEr (from 138.4 to 142.8) and 3.1 improvement on METEOR (from 32.8 to 35.9). The 3.2 improvement on the F1 score also shows that RCA-NOC performs better in describing novel objects." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.655, + 0.849 + ], + "angle": 0, + "content": "6.3. Ablation study." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.903 + ], + "angle": 0, + "content": "In this subsection, we will discuss every component's contribution to our framework. If not mentioned by purpose, all methods are conducted on the Nocaps validation" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15516" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.107, + 0.09, + 0.439, + 0.103 + ], + "angle": 0, + "content": "Table 4. Effectiveness of the source of visual semantics." + }, + { + "type": "table", + "bbox": [ + 0.113, + 0.107, + 0.432, + 0.189 + ], + "angle": 0, + "content": "
Methodin-domainnear-domainout-of-domainOverall
CIDErSPICECIDErSPICECIDErSPICECIDErSPICE
N.A.103.614.7100.814.2100.913.2103.214.2
NOC-REK103.914.9101.614.3102.013.4103.414.3
VIVO105.215.1103.514.4103.613.4105.214.4
CLIP107.815.3104.014.6105.813.6107.114.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.197, + 0.47, + 0.252 + ], + "angle": 0, + "content": "Table 5. Effectiveness of the UASR. UAR: Uncertainty-Aware Reweight, UAS: Uncertainty-Aware Selection, \\(UAS^{N}\\): Uncertainty-Aware Selection for Negatives), UASR: Uncertainty-Aware Selection and Re-weight." + }, + { + "type": "table", + "bbox": [ + 0.111, + 0.258, + 0.434, + 0.349 + ], + "angle": 0, + "content": "
Methodin-domainnear-domainout-of-domainOverall
CIDEr SPICECIDEr SPICECIDEr SPICECIDEr SPICE
N.A.103.614.7100.814.2100.913.2102.414.2
\\( UAS^N \\)105.214.8102.114.3102.413.3104.214.3
UAS105.915.0104.514.3103.913.4105.314.5
UAR104.314.8103.314.4104.713.3105.614.3
UASR107.815.3104.014.6105.813.6107.114.6
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.363, + 0.468, + 0.392 + ], + "angle": 0, + "content": "set with BERT-base. (we cannot use the Nocaps test set because only 5 times submissions are allowed for the test set)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.394, + 0.468, + 0.542 + ], + "angle": 0, + "content": "Effectiveness of visual semantics. We enhance the modality alignment by incorporating visual semantics from foundational models, with a specific instantiation using CLIP. To evaluate the generalization ability of our approach, we modify the model to extract visual semantics and conduct further experiments to compare it with NOC-REK [29] and VIVO for generating visual semantics. Our baseline model is trained using a contrastive approach that ranks ROI tags extracted from Faster R-CNN based on their softmax values, distinguishing between relevant and irrelevant tags." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.543, + 0.468, + 0.825 + ], + "angle": 0, + "content": "Our findings indicate that using NOC-REK to generate augmented tags provides only marginal improvement to our framework, resulting in a 0.8 and 0.1 (CIDEr and SPICE) increase compared to the baseline. We hypothesize that this limited improvement may be due to the restricted linguistic knowledge contained in BERT, which may not encompass a wide range of novel categories and lack higher-level and global concepts required to describe complex scenes. In contrast, utilizing a larger pool of noisy visual semantics (CLIP) extracted from captions leads to better results, with a 4.9 and 0.4 (CIDEr and SPICE) increase compared to the baseline. Using a smaller and cleaner pool of visual semantics extracted from the classes of various object detection datasets (VIVO) only results in a 2.0 and 0.2 (CIDEr and SPICE) increase compared to the baseline. This is likely due to the fact that the CLIP is pre-trained on vast amounts of training data, enabling it to extract a more diverse, extensive, and semantically meaningful set of high-level visual concepts compared to NOC-REK." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.827, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of the UASR. We investigate the performance of our Uncertainty-Aware Selection and Reweighting (UASR) on the Nocaps validation set in this part. Table 5 shows that Uncertainty-Aware Reweighting (UAR) could effectively enhance the reliable contrastive samples" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.09, + 0.892, + 0.117 + ], + "angle": 0, + "content": "Table 6. Evaluation on COCO test set of Karpathy split [15]. All results are based on single model with cross-entropy optimization." + }, + { + "type": "table", + "bbox": [ + 0.527, + 0.119, + 0.865, + 0.179 + ], + "angle": 0, + "content": "
pre-trainingBLEU4MeteorCIDErSPICE
N.A33.828.1118.321.2
OSCAR + VIVO34.928.4119.821.7
RCA-NOC37.429.6128.423.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.185, + 0.892, + 0.267 + ], + "angle": 0, + "content": "Table 7. Ablation study on the effectiveness of different components, including (i) CA: Cross-modality Alignment, our prototype contrastive loss for region-tag pairs, (ii) IA: Inner-modality Alignment, (iii) CLIP: Without CLIP refers to extracting visual semantics with object detection, and (iv) UASR: Uncertainty-Aware Selection and Re-weighting." + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.271, + 0.869, + 0.346 + ], + "angle": 0, + "content": "
CAIAUASRCLIPCIDERSPICE
90.912.8
✓96.513.5
✓✓98.713.8
✓✓✓103.214.2
✓✓✓✓107.114.6
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.348, + 0.892, + 0.54 + ], + "angle": 0, + "content": "and bring 3.2 and 0.1 boosts on CIDEr and SPICE. In addition, the false positives/negatives severely harm our training process. By further incorporating Uncertainty-Aware Selection for Negatives \\((UAS^{N})\\) into our method and filtering false negatives, our model's performance is boosted to 104.2 and 14.3 on CIDEr and SPICE. When filtering false positives/negatives simultaneously, we could reach 105.3 and 14.5 on CIDEr and SPICE with Uncertainty-Aware Selection (UAS). Finally, our method improves the performance by 4.7 and 0.4 (CIDEr and SPICE) by combining UAR and UAS, which illustrates the proposed UASR is a more powerful tool for tackling noisy contrastive samples in NOC." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.55, + 0.684, + 0.566 + ], + "angle": 0, + "content": "6.4. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.573, + 0.892, + 0.78 + ], + "angle": 0, + "content": "In Figure 3, we display some qualitative results on Held-Out COCO and Nocaps, and all the approaches are based on BERT-base. On Held-Out COCO, the result compared with GT shows that our proposed method could effectively generate accurate and precise captions with novel objects by leveraging relative semantic relevance into training. On Nocaps, VinVL+VIVO [13, 35] sometimes cannot include the desired novel objects in their captions (first and third examples) or generate wrong captions (second example). Our RCA-NOC, on the other hand, successfully generates correct and coherent captions via differentiating confusing classes and aligning object detection with other modalities. For better illustration, we show top-5 Positive and Negative Tag results extracted from CLIP." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.789, + 0.742, + 0.806 + ], + "angle": 0, + "content": "6.5. General Image Captioning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.812, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Improving modality alignment is a shared objective of general image captioning tasks. As demonstrated in Table 6, our proposed method, RCL-NOC, improves the model's performance across all metrics assessed on the COCO test set, particularly in the CIDEr score. However, we have observed that the improvement on the COCO benchmark is" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15517" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.083, + 0.096, + 0.182, + 0.148 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.183, + 0.095, + 0.358, + 0.106 + ], + "angle": 0, + "content": "GT: A boy in a tie holding a small suitcase." + }, + { + "type": "image_footnote", + "bbox": [ + 0.184, + 0.113, + 0.413, + 0.124 + ], + "angle": 0, + "content": "RCA-NOC: A young boy wearing a tie holding a suitcase." + }, + { + "type": "image_footnote", + "bbox": [ + 0.184, + 0.132, + 0.476, + 0.142 + ], + "angle": 0, + "content": "PT: Person, human, tie, suitcase, dress*... (Person, human, suitcase, tie...)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.184, + 0.15, + 0.466, + 0.161 + ], + "angle": 0, + "content": "NT: Hair*, chair, soda, step, umbrella ... (Chair, soda, step, umbrella...)" + }, + { + "type": "list", + "bbox": [ + 0.183, + 0.095, + 0.476, + 0.161 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.184, + 0.182, + 0.237 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.183, + 0.185, + 0.422, + 0.196 + ], + "angle": 0, + "content": "GT: 2 men sit on the couch, video game controllers in hands." + }, + { + "type": "image_footnote", + "bbox": [ + 0.183, + 0.204, + 0.476, + 0.223 + ], + "angle": 0, + "content": "RCA-NOC: A couple of men sitting on a couch playing a video game with wheels." + }, + { + "type": "image_footnote", + "bbox": [ + 0.184, + 0.232, + 0.486, + 0.242 + ], + "angle": 0, + "content": "PT: Couch, person, face, wheel, shirt... (person, wheel, couch, face, shirt...)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.183, + 0.25, + 0.46, + 0.26 + ], + "angle": 0, + "content": "NT: Wheelchair, leg\\* tie, stone, coat... (Wheelchair, tie, stone, coat...)" + }, + { + "type": "list", + "bbox": [ + 0.183, + 0.185, + 0.486, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.276, + 0.182, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.183, + 0.278, + 0.399, + 0.289 + ], + "angle": 0, + "content": "GT: Someone cutting a small pizza with a pizza cutter." + }, + { + "type": "image_footnote", + "bbox": [ + 0.183, + 0.296, + 0.414, + 0.307 + ], + "angle": 0, + "content": "RCA-NOC: A person is cutting a pizza with a pizza cutter." + }, + { + "type": "image_footnote", + "bbox": [ + 0.183, + 0.315, + 0.477, + 0.326 + ], + "angle": 0, + "content": "PT: Person, food, pizza, kitchen, bottle*... (Person, food, kitchen, pizza...)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.183, + 0.333, + 0.481, + 0.352 + ], + "angle": 0, + "content": "NT: Microwave, design, hammer, wine, tie... (Microwave, design, hammer, wine, tie...)" + }, + { + "type": "list", + "bbox": [ + 0.183, + 0.278, + 0.481, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.093, + 0.591, + 0.147 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.591, + 0.093, + 0.865, + 0.103 + ], + "angle": 0, + "content": "VinVL + VIVO: A man with a jacket and a cowboy hat next to a bull." + }, + { + "type": "image_footnote", + "bbox": [ + 0.592, + 0.111, + 0.862, + 0.122 + ], + "angle": 0, + "content": "RCA-NOC: A man with a blue shirt and a cowboy hat next to a bull." + }, + { + "type": "image_footnote", + "bbox": [ + 0.591, + 0.129, + 0.837, + 0.14 + ], + "angle": 0, + "content": "PT: Hat, hay, bull, shirt, man... (Man, bull, shirt, hat, hay...)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.591, + 0.148, + 0.833, + 0.158 + ], + "angle": 0, + "content": "NT: face*, tie, road, barn, jacket... (Tie, road, barn, jacket...)" + }, + { + "type": "list", + "bbox": [ + 0.591, + 0.093, + 0.865, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.172, + 0.575, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.591, + 0.184, + 0.795, + 0.195 + ], + "angle": 0, + "content": "VinVL + VIVO: A jaguar standing on top of a tree." + }, + { + "type": "image_footnote", + "bbox": [ + 0.591, + 0.203, + 0.799, + 0.214 + ], + "angle": 0, + "content": "RCA-NOC: A jaguar standing behind a green fence." + }, + { + "type": "image_footnote", + "bbox": [ + 0.591, + 0.221, + 0.832, + 0.24 + ], + "angle": 0, + "content": "PT: Jaguar, fence, dog*, carnivore, chest*... (Jaguar, fence, carnivore...)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.591, + 0.248, + 0.84, + 0.259 + ], + "angle": 0, + "content": "NT: animal*, wall, coat, cage, sign... (wall, coat, cage, sign...)" + }, + { + "type": "list", + "bbox": [ + 0.591, + 0.184, + 0.84, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.272, + 0.588, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.591, + 0.276, + 0.865, + 0.287 + ], + "angle": 0, + "content": "VinVL + VIVO: A white plate of food with dessert and a tomato." + }, + { + "type": "image_footnote", + "bbox": [ + 0.591, + 0.295, + 0.865, + 0.306 + ], + "angle": 0, + "content": "RCA-NOC: A white plate with two pieces of bread and a tomato." + }, + { + "type": "image_footnote", + "bbox": [ + 0.591, + 0.314, + 0.865, + 0.334 + ], + "angle": 0, + "content": "PT: Tomato, bread, lunch, plate, vegetable* ... (Tomato, bread, plate, lunch...)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.591, + 0.342, + 0.852, + 0.352 + ], + "angle": 0, + "content": "NT: Piece*, salad, cake, snack, table*... (Salad, cake, snack...)" + }, + { + "type": "list", + "bbox": [ + 0.591, + 0.276, + 0.865, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.364, + 0.894, + 0.42 + ], + "angle": 0, + "content": "Figure 3. Examples of generated captions and contrastive tags by compared methods on Held-Out COCO (left) and Nocaps (right). We show the ground-truth captions (GT) on Held-Out COCO for reference. PT/NT denotes the positive/negative tags before and after Uncertainty-Aware Selection and Reweighting (UASR). Blue/Red text indicates novel objects in Held-Out COCO/Nocaps, and * indicates the false positives/negatives." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.471, + 0.572 + ], + "angle": 0, + "content": "not as substantial as that on the nocaps benchmark. We hypothesize that this discrepancy is due to the COCO dataset having a limited number of visual concepts, thus reducing the benefits of learning visual semantics. Additionally, our method's use of tags is general and does not rely on fully annotated data. It's possible to utilize potentially unlimited amounts of images and different sources of tags, including those from Faster R-CNN, image tagging, or keywords extracted from captions. These possibilities will be explored in our future work.." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.584, + 0.34, + 0.601 + ], + "angle": 0, + "content": "6.6. Data and Compute Efficiency" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.607, + 0.471, + 0.83 + ], + "angle": 0, + "content": "The way the visual semantics are extracted (using CLIP) is not central to our work, as for the gain coming from 400M pairs of CLIP. This is supported in section 6.3. Table 7 shows that other components contribute significantly. Notably, the gain achieved by our Contrastive Alignment (CA) component alone can surpass that of CLIP by a large margin. Importantly, our method achieves this without increasing the number of parameters during training and inference, with the same parameter count as NOC-REK and VINVL (110 M). The training time of NOC-REK is 49 hours, for NOC-REK the training time is much lower (23h). This is with the paper setup (8 GPUs A100). Compared with NOC-REK, which adopts test time augmentation during inference, our inference time is much lower (1 minute) while NOC-REK is 2 minutes." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.845, + 0.196, + 0.861 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "In this paper, we present RCA-NOC, which achieves visual-semantic alignment via relative contrastive learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.424, + 0.892, + 0.601 + ], + "angle": 0, + "content": "Specifically, for each image, we first extract augmented tags obtained from foundation models such as CLIP. Then we utilize the rank of each augmented object tag in a list as a relative relevance label to contrast each top ranked tag with a set of lower ranked tags. We empirically find that such a learning objective is effective and easy to optimize by encouraging the top ranked tags to be more compatible with their image and text context than lower ranked tags, hence improving the discriminative ability of the learned multimodality representation. We prove the effectiveness of our paradigm in novel object caption, with the spotlight on Nocaps and Held-Out COCO benchmark." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.602, + 0.892, + 0.691 + ], + "angle": 0, + "content": "The effectiveness of object tags has already been proved in recent works. However, there are few studies to further explore why such tags could perform well and the problem of object tags' misalignment is often ignored. So how to further exploit use tags explicitly while having a deep understanding of their roles is meaningful in the future." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15518" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.468, + 0.142 + ], + "angle": 0, + "content": "[1] https://huggingface.co/transformers/modeldoc/bert.html.6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.145, + 0.468, + 0.199 + ], + "angle": 0, + "content": "[2] Harsh Agrawal, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, Stefan Lee, and Peter Anderson. nocaps: novel object captioning at scale. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5579-5588, 2021. 1, 2, 6, 7, 8" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15520" + } + ] +] \ No newline at end of file diff --git a/2023/RCA-NOC_ Relative Contrastive Alignment for Novel Object Captioning/cbdb5e43-66b1-4704-93d9-a919fc74c296_origin.pdf b/2023/RCA-NOC_ Relative Contrastive Alignment for Novel Object Captioning/cbdb5e43-66b1-4704-93d9-a919fc74c296_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b1751df82f79970bfd894397c8578b5e2da78e6b --- /dev/null +++ b/2023/RCA-NOC_ Relative Contrastive Alignment for Novel Object Captioning/cbdb5e43-66b1-4704-93d9-a919fc74c296_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5247b82ce9e124c32adfb0358e4f65e6bd26ca5ef122220dcf5315d6e364231b +size 1788140 diff --git a/2023/RCA-NOC_ Relative Contrastive Alignment for Novel Object Captioning/full.md b/2023/RCA-NOC_ Relative Contrastive Alignment for Novel Object Captioning/full.md new file mode 100644 index 0000000000000000000000000000000000000000..86906e321eb09acd030ce071a17156d0c07b68b7 --- /dev/null +++ b/2023/RCA-NOC_ Relative Contrastive Alignment for Novel Object Captioning/full.md @@ -0,0 +1,434 @@ +# RCA-NOC: Relative Contrastive Alignment for Novel Object Captioning + +Jiashuo Fan $^{2}$ Yaoyuan Liang $^{2}$ Leyao Liu $^{2}$ Shaolun Huang $^{2}$ Lei Zhang $^{1}$ International Digital Economy Academy $^{2}$ Tsinghua University + +# Abstract + +In this paper, we introduce a novel approach to novel object captioning which employs relative contrastive learning to learn visual and semantic alignment. Our approach maximizes compatibility between regions and object tags in a contrastive manner. To set up a proper contrastive learning objective, for each image, we augment tags by leveraging the relative nature of positive and negative pairs obtained from foundation models such as CLIP. We then use the rank of each augmented tag in a list as a relative relevance label to contrast each top-ranked tag with a set of lower-ranked tags. This learning objective encourages the top-ranked tags to be more compatible with their image and text context than lower-ranked tags, thus improving the discriminative ability of the learned multi-modality representation. We evaluate our approach on two datasets and show that our proposed RCA-NOC approach outperforms state-of-the-art methods by a large margin, demonstrating its effectiveness in improving vision-language representation for novel object captioning. + +# 1. Introduction + +Describing novel objects unseen in training data is a highly desired capability for a real-world image captioning model. Conventional image captioning models [4, 20, 28] often fail to describe novel objects because they only cover limited visual concepts and generalize poorly to images in the wild [26]. To overcome this limitation, approaches that rely on object detection as the external resource [7, 8, 13, 18, 20, 25, 27, 33, 35] have been widely explored and demonstrated breakthroughs in vision-language (VL) understanding. + +Although object detection models (e.g., Faster RCNN [23]) have been improved to recognize a wide range of objects including novel ones like zero-shot object detection [14], using object detection in novel captioning models brings a new challenge. VIVO [13] leverages extra object tags to pre-train a visual vocabulary and help image captioning generalize to new categories. NOC-REK [29] + +![](images/72c73d59bf1906ec193dadf5c0e214f3fbb2a69e9098b7b1361850154623373e.jpg) +(a) : Training + +NOC-REK: panda, animal, chunk, tree, branch. +VIVO: panda, bear, chunk, tree, branch, animal, raccoon, hedge, food, raccoon. + +Ours: panda, animal, tree, branch, chunk.../ hedge, raccoon, sky, advertisement, water... + +![](images/7d37de3d5f6ed670f7f2547fe4baa17e811399bc7e73c6af485b016b64769826.jpg) +(b): Inference + +NOC-REK: A raccoon sitting on top of a tree branch. (panda, tree, branch) + +VIVO: A raccoon sitting on a tree branch. (panda, tree, branch) + +Ours: A red panda sitting in a tree branch (panda, tree, branch) + +Figure 1. An illustrative example of our method to leverage relative semantic relevance to achieve modality alignment. Our method could give accurate captions "A cute red panda sitting in a tree branch" conditioned on the objects "red panda" while VINVL+VIVO generates a wrong caption "A cute raccoon sitting in a tree branch". This inference result shows that our method can differentiate some confusing objects and generate accurate captions for novel objects when the object detection is well aligned with other modalities. + +tries to augment object tags in the training stage based on the similarity between region and word. Such methods simply concatenate regions, object tags, and caption features as input to a Transformer-based model and use masked token reconstruction to implicitly learn an alignment between vision and language. Although such an alignment can help bring regions and words of the same concept closer, it lacks an effective mechanism to push away irrelevant concepts. As a result, it still makes mistakes on some confusing concepts, as shown in Figure 1. + +Different from previous methods, this study aims to learn visual and semantic alignment in a contrastive manner. Gupta et al. [10] showed that modality alignment could be achieved by maximizing the information lower bound between an image and its object tags. That is, given pairs of image and object tags, we can maximize the compatibility between tags and their attention-weighted region representations, compared to regions and non-corresponding tags. However, there are two critical problems that need to be further addressed: 1) how to effectively generate contrastive tags (augmented tags) that are closely relevant to an image, and 2) how to design a proper contrastive learning objective that allows the model to effectively leverage the contrastive + +tags to align vision and semantics. + +To tackle the first problem, we utilize CLIP [22] to create a list of contrastive tags which are closely linked to an image and contain global structural information and high-level concepts describing scenes. This approach aids in the discovery of useful tags that are essential for contrastive learning. To address the second problem, a proper contrastive learning objective needs to be explored. The major challenge here is that the augmented contrastive tags are inaccurate and inevitably noisy. We cannot simply treat one tag as positive and others as negative to perform contrastive learning, because the augmented tags might be highly correlated or similar to each other. To tackle this problem, we leverage the relative relevance, rather than the absolute relevance, of the augmented tags, which is more robust to data noise. + +Specifically, given an image, for each of its labeled object tags, we generate a ranked list of contrastive tags using CLIP. We regard the rank of each augmented tag as its relative semantic relevance with the image. In general, the top-ranked tags are assumed to be more relevant to the image than the lower-ranked tags. We divide the list into two parts: the (relatively) relevant part with higher rank and the (relatively) irrelevant part with lower rank (Figure 1 (a)). In our proposed objective, we treat each tag in the relevant part as positive and all tags in the irrelevant part as negative to perform contrastive learning. Note that we do not let tags both in the relevant part contrast with each other as they might be highly correlated concepts. In this way, our approach weakens the strict assumption of contrastive learning in previous works and exploits the relative ranking in a loose form to achieve modality alignment. + +We conduct experiments on the Nocaps and Held-Out COCO datasets to demonstrate the effectiveness of RCA-NOC. Our contributions can be summarized as follows: + +- We propose Relative Contrastive Alignment (RCA) to learn the relative semantic relevance in a loose form by maximizing the compatibility between regions and their relevant tags compared with regions and irrelevant tags to achieve vision and language alignment and improve the discriminative ability of the multi-modality representation. +- A method called Uncertainty-Aware Selection and Reweighting (UASR) is proposed to estimate and exploit the uncertainty of each contrastive sample to mitigate the negative effect brought by noisy tags. UASR can effectively prioritize highly reliable samples and demote false positives and false negatives. +- We validate the proposed method on the Nocaps and Held-Out COCO benchmarks, which outperforms other state-of-the-art methods by a large margin. + +# 2. Related Work + +# 3. Related work + +Novel object captioning aims to describe images with objects that are unseen in the training stage (we define these objects as novel objects) where many methods. [7, 8, 13, 18, 20, 22, 27, 31, 33, 35] have been proposed. Early works such as Hendricks et al. [12] and Venugopalan et al. [27] utilize unpaired labeled image and sentence data to enhance semantically visual concepts. Recent studies propose to explicitly leverage the object detection results for NOC, Lu et al. [20], Wu et al. [33], and Demirel et al. [8] fill the generated template sentence with objects detected by object/novel object detectors. Chen et al. [7] combine object detector and human attention to identify novel objects. In addition, Li et al. are the first to utilize semantics in VLP tasks, which are further extended by Zhang et al. [35]. Hu et al. [13] built upon [35] and propose to leverage extra region-tag pairs to conduct pretraining. Duc et al. [29] tried to augment object tags in the training stage based on the similarity of regions and objects. + +However, most aforementioned methods for NOC ignore the misalignment problem of object tags, thereby failing to fully exploit the semantic relationship between vision and language (Figure 1), which we argue is crucial to the quality of generated captions. In this paper, we propose a simple but effective contrastive learning objective to learn the relative semantic relevance in a loose form where the object tags could be explicitly aligned with their corresponding image feature representations in a semantic space. + +Contrastive Learning aims to learn discriminative representations to distinguish an image from others. Many methods [6,10,11,16,17,22,32] have shown their effectiveness. For example, Chen et al. [6] proposed to learn visual representations by maximizing agreement between differently augmented views of the same image via a contrastive loss. He et al. [11] proposed Momentum Contrast (MoCo) for unsupervised visual representation learning. Wei et al. [32] utilized contrastive learning in the detection task. Li et al. [16] focused on the problem of contextual outpainting. Gupta et al. [10] proposed a method $\mathrm{CPG}^{\dagger}$ to find hard negative words by replacing a word in a caption. + +Other data-driven studies such as CLIP [22] and ALIGNN [17] focus on learning a corresponding relative relationship from massive web data. CLIP [22] predicts which text goes with which image and learns a relative imagetext corresponding relationship from broad web data with noisy supervision. ALIGNN [17] further scales up CLIP by leveraging a noisy dataset that covers more than one billion image-text pairs. These methods achieve remarkable results but require massive fully-annotated data, which are difficult to obtain. + +![](images/0e1bcd376e8077ab743c09348aef0ffb6744d2905587fb59b5086b610a96c3e4.jpg) +"A close up of a small animal on a tree branch" + +![](images/31b4970adb0f96d988cbd6786871d81d94ee746f1c822ef51bcb8fdf539e1c73.jpg) + +![](images/c79f9f754ee43660e6346b91b0738f19014abd31e133d789ea7e4a3ee71065ad.jpg) +(a) Training: learn discriminative feature +Result: "A red panda sitting in a tree branch" +(b) Inference: novel object captioning + +Red panda + +Multi-layer Transformer + +![](images/6e1b86125f9e32226a22ae22d886e231bad5139edbc5f71c84ce37eecbe93fcd.jpg) +Figure 2. The main pipeline of our proposed RCA-NOC, including training and inference: In addition to the normal caption loss $L_{G}$ in the training process, we also compute the cross-modality and inner-modality loss $L_{cross}$ and $L_{inner}$ in Eq. 22 and Eq. 23 by contrasting the positive tags against the negative tags. The corresponding relationship is denoted in green and red line separately. During training, the input is a concatenated sequence of words—ROI tags—ROIs and augmented contrastive tags. The training loss comprises caption loss (with [MASK] in words for reconstruction) and contrastive learning loss (with [MASK] in ROI tags token for indicating the specific positions where augmented tags are inserted). Augmented tags replace certain ROI tags and are encoded into contrastive tag feature embeddings for comparison with region and caption embeddings. During prediction, the input is a concatenated sequence of ROI tags—ROIs without additional retrieval steps. + +# 4. Proposed Methods + +We propose to enhance the modality alignment by explicitly injecting visual semantics. These semantics are extracted for each image, obtained with existing foundation models such as CLIP. + +There are two motivations behind our approach. First, by maximizing the compatibility between regions and their relevant tags compared with regions and irrelevant tags, we could not only learn vision-semantic alignment and improve the discriminative ability of the multi-modality representation. Second, we introduce a relative contrastive learning objective that considers the relative relationships between positive and negative examples, rather than using absolute prototype-contrastive learning methods. This approach is more generalized and can be easily integrated into any existing NOC method. + +# 4.1. Visual Semantics Extraction + +Different from other approaches (e.g., [13, 18]) that extract object tags using pretrained object detectors, we use an off-the-shelf foundational model to extract more diverse, larger and semantically meaningful set of visual semantics. We show in section 6, that this approach helps to capture high level and global semantics describing the scenes, which are hard to obtain with other approaches (e.g. object + +detectors). + +We use a pretrained CLIP (ViT-B/16) model to obtain the embeddings of all the images and the extracted semantics. For each image, we compute its cosine similarity with all the embedded semantics and select the top M similar semantics as augmented tags $T = \{t_l\}_{l=1}^M$ . The augmented tags will be ranked using global (image-level) cosine similarity $p(t_l)$ . Then we utilize the rank of each augmented tag in $T$ as a relative relevance label. In general, the top-ranked tags are assumed to be more relevant to the image than the lower-ranked tags. We divide $T$ into positive and negative tags: positive tags being the (relatively) relevant tags with higher rank $T^P = \{t_n^P\}_{n=1}^K = \{t_l\}_{l=1}^K$ and negative tags being the (relatively) irrelevant tags with lower rank $T^N = \{t_l^N\}_{l=1}^K = \{t_l\}_{l=K+1}^{2K}$ ( $M = 2K$ ). + +Here we propose a simple yet effective augmentation technique. Having a set of visual semantics extracted for each image, instead of considering all the visual semantics at once, we sample randomly a fraction of these augmented tags at each iteration step. Hence, we could not only prevent the model from overfitting on specific semantics and potentially disregard the image or other semantics during training, but also let the model see different combinations of visual semantics, which helps to have more diversity. + +# 4.2. Relative Contrastive Alignment + +InfoNCE [21] is a typical type of contrastive loss function used for self-supervised learning that contrasts one positive sample against a set of negative samples. CPG [10] builds upon InfoNCE and proposes a compatibility function for regions and a caption word. Both InfoNCE and CPG utilize the absolute relevance to optimize the contrastive loss. + +However, such a contrastive learning objective is hard to optimize for object tags since they may be highly correlated to each other. In RCA-NOC, we focus on the relative semantic relevance and utilize the attention-based compatibility function to measure the relativity information for regions and a set of object tags, which is more robust to data noise. + +Specifically, we first compute the dot product for a region-tag pair. + +$$ +s _ {j k} = \mathbf {w} _ {j} ^ {T} \mathbf {v} _ {k} / \sqrt {d}, \tag {1} +$$ + +where $\mathbf{w}_j$ and $\mathbf{v}_k$ refer to the corresponding embeddings for tag and region, and $d$ is the feature dimension. Here, $s_{jk}$ represents the similarity between the $j$ -th tag and the $k$ -th region. To find a contextualized region representation for the $j$ -th tag, we define $\mathbf{a}_j^v$ as follows. + +$$ +\mathbf {a} _ {j} ^ {v} = \sum_ {k = 1} ^ {K} \alpha_ {j k} \mathbf {v} _ {k}, \tag {2} +$$ + +where $\alpha_{jk} = \frac{e^{s_{jk}}}{\sum_{k' = 1}^{K}e^{s_{jk'}}},$ (3) + +To measure the compatibility between a tag $\mathbf{w}_j$ and its contextualized region representation $\mathbf{a}_j^v$ , we define + +$$ +\phi (\mathbf {V}, \mathbf {w} _ {j}) = \mathbf {w} _ {j} ^ {T} \mathbf {a} _ {j} ^ {v}. \tag {4} +$$ + +In this way, we can derive our cross-modality contrastive loss function $L_{cross}$ . + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {c r o s s}} (\mathbf {V}, \mathbf {W} ^ {P}, \mathbf {W} ^ {N}) = \\ - \frac {1}{K} \sum_ {n = 1} ^ {K} \log \left(\frac {e ^ {\phi (\mathbf {V} , \mathbf {w} _ {n} ^ {P})}}{e ^ {\phi (\mathbf {V} , \mathbf {w} _ {n} ^ {P})} + \sum_ {l = 1} ^ {K} e ^ {\phi (\mathbf {V} , \mathbf {w} _ {l} ^ {N})}}\right), \tag {5} \\ \end{array} +$$ + +where $\mathbf{W}^P = \{\mathbf{w}_l^P\}_{l=1}^K$ and $\mathbf{W}^N = \{\mathbf{w}_n^N\}_{n=1}^K$ are the word embeddings for positives/negatives $T^P$ and $T^N$ , extracted from CLIP. $\phi()$ is the compatibility function defined in Eq. 11. + +This equation encourages each positive tag $\mathbf{w}_n^P$ to be more compatible with image regions $\mathbf{V}$ than all negative tags in $\mathbf{W}^N$ . Essentially, if tag $t_j$ is not relevant to the image (negative), its representation $\mathbf{w}_j$ should not be similar to its contextualized region representation $\mathbf{a}_j^v$ since it would not be able to collect good information while computing $\mathbf{a}_j^v$ . Note that we do not let two positive tags (top-ranked tags) contrast with each other as it is hard to tell which one is more relevant. + +Inner modality Alignment. To further enhance modality alignment, we also compute the inner-modality contrastive + +loss over tag-caption pairs. The formulation for inner-modality contrastive loss is similar to cross-modality contrastive loss but slightly different. We enforce contrastive learning not to be between tags and all caption words, but just between tags and noun caption words. This is because a caption may have many irrelevant tokens, such as "the, a, is", which will harm our alignment process and cause redundant computational costs. + +Finally, we can derive our inner-modality contrastive loss function $L_{inner}$ . + +$$ +\phi (\mathbf {C}, \mathbf {w} _ {l}) = \mathbf {w} _ {l} ^ {T} \mathbf {a} _ {l} ^ {c}, \tag {6} +$$ + +$$ +\begin{array}{l} \mathcal {L} _ {\text {i n n e r}} \left(\mathbf {C}, \mathbf {W} ^ {P}, \mathbf {W} ^ {N}\right) = \\ - \frac {1}{K} \sum_ {n = 1} ^ {K} \log \left(\frac {e ^ {\phi (\mathbf {C} , \mathbf {w} _ {n} ^ {P})}}{e ^ {\phi (\mathbf {C} , \mathbf {w} _ {n} ^ {P})} + \sum_ {l = 1} ^ {K} e ^ {\phi (\mathbf {C} , \mathbf {w} _ {l} ^ {N})}}\right), \tag {7} \\ \end{array} +$$ + +where this time we take noun caption words $\mathbf{C} = \{\mathbf{c}_i\}_{i=1}^P$ in Eq. 13 as input. By further considering inner-modality alignment, we not only learn caption-tag semantics to connect relevant caption tokens, but also enable region-caption interactions. + +# 5. Proposed Methods + +We propose to enhance the modality alignment by explicitly injecting visual semantics. These semantics are extracted for each image, obtained with existing foundation models such as CLIP. + +There are two motivations behind our approach. First, by maximizing the compatibility between regions and their relevant tags compared with regions and irrelevant tags, we could not only learn vision-semantic alignment and improve the discriminative ability of the multi-modality representation. Second, we introduce a relative contrastive learning objective that considers the relative relationships between positive and negative examples, rather than using absolute prototype-contrastive learning methods. This approach is more generalized and can be easily integrated into any existing NOC method. + +# 5.1. Visual Semantics Extraction + +Different from other approaches (e.g., [13, 18]) that extract object tags using pretrained object detectors, we use an off-the-shelf foundational model to extract more diverse, larger and semantically meaningful set of visual semantics. We show in section 6, that this approach helps to capture high level and global semantics describing the scenes, which are hard to obtain with other approaches (e.g. object detectors). + +We use a pretrained CLIP (ViT-B/16) model to obtain the embeddings of all the images and the extracted semantics. For each image, we compute its cosine similarity with all the embedded semantics and select the top M similar + +semantics as augmented tags $T = \{t_l\}_{l=1}^M$ . The augmented tags will be ranked using global (image-level) cosine similarity $p(t_l)$ . Then we utilize the rank of each augmented tag in $T$ as a relative relevance label. In general, the top-ranked tags are assumed to be more relevant to the image than the lower-ranked tags. We divide $T$ into positive and negative tags: positive tags being the (relatively) relevant tags with higher rank $T^P = \{t_n^P\}_{n=1}^K = \{t_l\}_{l=1}^K$ and negative tags being the (relatively) irrelevant tags with lower rank $T^N = \{t_l^N\}_{l=1}^K = \{t_l\}_{l=K+1}^{2K}$ ( $M = 2K$ ). + +Here we propose a simple yet effective augmentation technique. Having a set of visual semantics extracted for each image, instead of considering all the visual semantics at once, we sample randomly a fraction of these augmented tags at each iteration step. Hence, we could not only prevent the model from overfitting on specific semantics and potentially disregard the image or other semantics during training, but also let the model see different combinations of visual semantics, which helps to have more diversity. + +# 5.2. Relative Contrastive Alignment + +InfoNCE [21] is a typical type of contrastive loss function used for self-supervised learning that contrasts one positive sample against a set of negative samples. CPG [10] builds upon InfoNCE and proposes a compatibility function for regions and a caption word. Both InfoNCE and CPG utilize the absolute relevance to optimize the contrastive loss. + +However, such a contrastive learning objective is hard to optimize for object tags since they may be highly correlated to each other. In RCA-NOC, we focus on the relative semantic relevance and utilize the attention-based compatibility function to measure the relativity information for regions and a set of object tags, which is more robust to data noise. + +Specifically, we first compute the dot product for a region-tag pair. + +$$ +s _ {j k} = \mathbf {w} _ {j} ^ {T} \mathbf {v} _ {k} / \sqrt {d}, \tag {8} +$$ + +where $\mathbf{w}_j$ and $\mathbf{v}_k$ refer to the corresponding embeddings for tag and region, and $d$ is the feature dimension. Here, $s_{jk}$ represents the similarity between the $j$ -th tag and the $k$ -th region. To find a contextualized region representation for the $j$ -th tag, we define $\mathbf{a}_j^v$ as follows. + +$$ +\mathbf {a} _ {j} ^ {v} = \sum_ {k = 1} ^ {K} \alpha_ {j k} \mathbf {v} _ {k}, \tag {9} +$$ + +where $\alpha_{jk} = \frac{e^{s_{jk}}}{\sum_{k'=1}^{K} e^{s_{jk'}}},$ (10) + +To measure the compatibility between a tag $\mathbf{w}_j$ and its contextualized region representation $\mathbf{a}_j^v$ , we define + +$$ +\phi (\mathbf {V}, \mathbf {w} _ {j}) = \mathbf {w} _ {j} ^ {T} \mathbf {a} _ {j} ^ {v}. \tag {11} +$$ + +In this way, we can derive our cross-modality contrastive loss function $L_{cross}$ . + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {c r o s s}} (\mathbf {V}, \mathbf {W} ^ {P}, \mathbf {W} ^ {N}) = \\ - \frac {1}{K} \sum_ {n = 1} ^ {K} \log \left(\frac {e ^ {\phi (\mathbf {V} , \mathbf {w} _ {n} ^ {P})}}{e ^ {\phi (\mathbf {V} , \mathbf {w} _ {n} ^ {P})} + \sum_ {l = 1} ^ {K} e ^ {\phi (\mathbf {V} , \mathbf {w} _ {l} ^ {N})}}\right), \tag {12} \\ \end{array} +$$ + +where $\mathbf{W}^P = \{\mathbf{w}_l^P\}_{l=1}^K$ and $\mathbf{W}^N = \{\mathbf{w}_n^N\}_{n=1}^K$ are the word embeddings for positives/negatives $T^P$ and $T^N$ , extracted from CLIP. $\phi()$ is the compatibility function defined in Eq. 11. + +This equation encourages each positive tag $\mathbf{w}_n^P$ to be more compatible with image regions $\mathbf{V}$ than all negative tags in $\mathbf{W}^N$ . Essentially, if tag $t_j$ is not relevant to the image (negative), its representation $\mathbf{w}_j$ should not be similar to its contextualized region representation $\mathbf{a}_j^v$ since it would not be able to collect good information while computing $\mathbf{a}_j^v$ . Note that we do not let two positive tags (top-ranked tags) contrast with each other as it is hard to tell which one is more relevant. + +Inner modality Alignment. To further enhance modality alignment, we also compute the inner-modality contrastive loss over tag-caption pairs. The formulation for inner-modality contrastive loss is similar to cross-modality contrastive loss but slightly different. We enforce contrastive learning not to be between tags and all caption words, but just between tags and noun caption words. This is because a caption may have many irrelevant tokens, such as "the, a, is", which will harm our alignment process and cause redundant computational costs. + +Finally, we can derive our inner-modality contrastive loss function $L_{inner}$ . + +$$ +\phi (\mathbf {C}, \mathbf {w} _ {l}) = \mathbf {w} _ {l} ^ {T} \mathbf {a} _ {l} ^ {c}, \tag {13} +$$ + +$$ +\begin{array}{l} \mathcal {L} _ {\text {i n n e r}} (\mathbf {C}, \mathbf {W} ^ {P}, \mathbf {W} ^ {N}) = \\ - \frac {1}{K} \sum_ {n = 1} ^ {K} \log \left(\frac {e ^ {\phi (\mathbf {C} , \mathbf {w} _ {n} ^ {P})}}{e ^ {\phi (\mathbf {C} , \mathbf {w} _ {n} ^ {P})} + \sum_ {l = 1} ^ {K} e ^ {\phi (\mathbf {C} , \mathbf {w} _ {l} ^ {N})}}\right), \tag {14} \\ \end{array} +$$ + +where this time we take noun caption words $\mathbf{C} = \{\mathbf{c}_i\}_{i=1}^P$ in Eq. 13 as input. By further considering inner-modality alignment, we not only learn caption-tag semantics to connect relevant caption tokens, but also enable region-caption interactions. + +# 5.3. Uncertainty-Aware Selection and Re-weighting + +The augmented contrastive tags are often noisy and would harm the discriminative ability and robustness of the contrastive learning process. Therefore, we design a sample selection strategy to deal with noisy contrastive tags (e.g., false positives/negatives). + +Uncertainty-Aware Selection. Specifically, we first use the local cosine similarity to calculate the correlation between a region and a tag and filter false positives/negatives. The + +stronger the correlation, the more reliable a positive tag is and the more uncertain a negative tag. + +$$ +\mathrm {u} (\mathbf {v}, \mathbf {w}) = \frac {\mathbf {v} ^ {\top} \mathbf {w}}{\| \mathbf {v} \| \| \mathbf {w} \|}, \tag {15} +$$ + +Then we retrieve $L$ tags and their corresponding representations $\mathbf{H} = \{\mathbf{w}_j\}_{j=1}^L$ for the given $L$ region features $\{\mathbf{v}_i\}_{i=1}^L$ . We use arg max to choose the most correlated tag $t_j$ for region $\mathbf{v}_i$ . + +$$ +j = \underset {k} {\arg \max } \left(\mathrm {u} \left(\mathbf {v} _ {i}, \mathbf {w} _ {k}\right)\right), \tag {16} +$$ + +According to the score in Eq. 15, the corresponding top-L tags will be listed as confusion samples for negatives (actually positive), and these confusion samples will be removed from the original contrastive tags. Similarly, we will also choose the true positives based on these top- $L$ tags since tags with low-similarity scores should be regarded as outliers to the positives and they are too sparse to have a positive influence on the shape of embedding space. In this way, we can derive Eq. 17, where / is the removing set operation, $\cap$ is the intersection set operation. $\overline{\mathbf{W}}^P = \{\bar{\mathbf{w}}_l^P\}_{l=1}^K$ and $\overline{\mathbf{W}}^N = \{\bar{\mathbf{w}}_n^N\}_{n=1}^K$ is the final positive/negative tags' embedding sets. Note that if the set length of $\overline{\mathbf{W}}^P / \overline{\mathbf{W}}^N$ is less than M, we will over-sample $\overline{\mathbf{W}}^P / \overline{\mathbf{W}}^N$ until the set length is equal to M. + +$$ +\overline {{\mathbf {W}}} ^ {P} = \mathbf {W} ^ {P} \cap \mathbf {H}, \overline {{\mathbf {W}}} ^ {N} = \mathbf {W} ^ {N} / \mathbf {H}, \tag {17} +$$ + +Uncertainty-Aware Re-weighting. To further mitigate the negative effect of noisy tags, we use the correlation function defined above to enhance reliable samples and reduce the influence of high-uncertainty samples. The information from more reliable samples should have a larger impact on the shape of the embedding and vice versa. Specifically, we first introduce the weight in Eq. 18. + +$$ +q _ {1} \left(\bar {\mathbf {w}} _ {n} ^ {P}\right) = \exp \left(\mathrm {u} \left(\mathbf {v} _ {k}, \bar {\mathbf {w}} _ {n} ^ {P}\right)\right), \tag {18} +$$ + +$$ +j = \underset {k} {\arg \max } \left(\mathrm {u} \left(\mathbf {v} _ {i}, \bar {\mathbf {w}} _ {k} ^ {P}\right)\right), \tag {19} +$$ + +$$ +q _ {2} \left(\bar {\mathbf {w}} _ {n} ^ {P}\right) = p \left(t _ {n}\right), \tag {20} +$$ + +where $q_{1}(\bar{\mathbf{w}}_{n}^{P})$ in Eq. 18 is the uncertainty score computed by the most relevant region with the corresponding tag. Moreover, we further consider how certain each tag is and combine the corresponding score $q_{2}(\bar{\mathbf{w}}_{n}^{P})$ in Eq. 20 with $q_{1}(\bar{\mathbf{w}}_{n}^{P})$ to derive the final uncertainty score $q(\bar{\mathbf{w}}_{n}^{P})$ in Eq. 21. Here $p(t_{n})$ in Eq. 20 is the global similarity mentioned in Section 5.1. + +$$ +q \left(\bar {\mathbf {w}} _ {n} ^ {P}\right) = q _ {1} \left(\bar {\mathbf {w}} _ {n} ^ {P}\right) * q _ {2} \left(\bar {\mathbf {w}} _ {n} ^ {P}\right), \tag {21} +$$ + +Thus, our method could mitigate the negative effect of noisy contrastive tags by considering the similarity from both the local region features (region-tag) and the + +global structural information (image-tag). Finally, we could rewrite our contrastive loss function in Eq. 22, Eq. 23. + +$$ +\mathcal {L} _ {\text {c r o s s}} \left(\mathbf {V}, \overline {{\mathbf {W}}} ^ {P}, \overline {{\mathbf {W}}} ^ {N}\right) = +$$ + +$$ +- \frac {1}{K} \sum_ {n = 1} ^ {K} - q \left(\bar {\mathbf {w}} _ {n} ^ {P}\right) \log \left(\frac {e ^ {\phi \left(\mathbf {V} , \bar {\mathbf {w}} _ {n} ^ {P}\right)}}{e ^ {\phi \left(\mathbf {V} , \bar {\mathbf {w}} _ {n} ^ {P}\right)} + \sum_ {l = 1} ^ {K} e ^ {\phi \left(\mathbf {V} , \bar {\mathbf {w}} _ {l} ^ {N}\right)}}\right), \tag {22} +$$ + +$$ +\begin{array}{l} \mathcal {L} _ {\text {i n n e r}} \left(\mathbf {C}, \overline {{\mathbf {W}}} ^ {P}, \overline {{\mathbf {W}}} ^ {N}\right) = \\ - \frac {1}{K} \sum_ {n = 1} ^ {K} - q \left(\bar {\mathbf {w}} _ {n} ^ {P}\right) \log \left(\frac {e ^ {\phi \left(\mathbf {C} , \bar {\mathbf {w}} _ {n} ^ {P}\right)}}{e ^ {\phi \left(\mathbf {C} , \bar {\mathbf {w}} _ {n} ^ {P}\right)} + \sum_ {l = 1} ^ {K} e ^ {\phi \left(\mathbf {C} , \bar {\mathbf {w}} _ {l} ^ {N}\right)}}\right), \tag {23} \\ \end{array} +$$ + +# 6. Experiments + +# 6.1. Experimental Setup + +Datasets. Our main experiments and ablation studies are based on the Nocaps [2] dataset. Our method was built with PyTorch, and we used a pre-trained BERT-base model from Huggingfaces [1] for parameters initialization, and no ground-truth tags are used on the Nocaps validation and test sets. For the training stage, we use the COCO training set which consists of 118K images, each with 5 captions. We evaluate our model on the validation and test sets of the Nocaps dataset, which consist of 4.5K and 10.6K images from the Open Images validation and test sets, respectively. Additionally, we test the proposed method on the Held-Out COCO [12], which is a subset of MS COCO [19] where the following eight object categories are excluded from the training set: bottle, bus, couch, microwave, pizza, racket, suitcase, and zebra. We randomly split the COCO validation set and use half of it for validation and the other half for testing, each with 20,252 images. In addition, we empirically set $M = 50$ to generate augmented object tags for the best performance. + +Implementation Details. In the training stage, the model is trained for 30 epochs with a batch size of 512 and a learning rate of $10^{-4}$ , optimized using the cross-entropy loss and our contrastive loss. We set the maximum caption length to 40 and the maximum tag length to 30. To further boost the performance, we also perform the SCST optimization (Rennie et al. [24]) with a learning rate of $1.4 \times 10^{-6}$ for 10 epochs. During inference, we use greedy decoding to generate image captions with a maximum length of 20. Our model is trained with 8 A100 GPUS and takes 1 day to train. + +# 6.2. Quantitative evaluation. + +Results on Nocaps dataset. In this section, we extensively compare our frameworks with previous methods on the Nocaps benchmark. The other compared state-of-art results are from NOC-REK [29]. Note that all the methods use the BERT-base [9] for a fair comparison. We compare our method with UpDown [2, 5], OSCAR [18], VinVL [35], VIVO [13], and NOC-REK [29], which hold the state-of-the-art result on the Nocaps benchmark. The training data + +Table 1. Our evaluation results using SPICE and CIDEr on the Nocaps validation and test sets. We achieve the best scores for in-domain, near-domain, out-domain and Overall. Notably, the captions generated by our method are better than those by human in most cases. We note that our results on the test set are better than those by other methods which are publicly submitted to Nocaps leader-boardb. Higher score is better. + +
MethodValidation setTest set
in-domainnear-domainout-domainOverallin-domainnear-domainout-domainOverall
CIDErSPICECIDErSPICECIDErSPICECIDErSPICECIDErSPICECIDErSPICECIDErSPICECIDErSPICE
UpDown [4]78.111.657.710.331.38.355.310.176.011.874.211.566.79.773.111.2
Oscar [18]83.412.081.612.077.610.681.111.781.311.979.611.973.610.678.811.7
VIVO [13]92.212.987.812.687.511.588.312.489.012.987.812.680.111.186.612.4
VinVL [35]96.813.590.713.187.411.690.912.893.813.389.012.866.110.985.512.5
VinVL + VIVO [13,35]103.713.795.613.483.811.994.313.198.013.695.213.478.011.592.513.1
NOC-REK [29]104.714.8100.214.1100.713.0100.914.0100.014.195.713.677.411.693.013.4
RCA-NOC**95.013.691.313.193.212.192.213.087.713.388.112.977.911.486.312.7
RCA-NOC107.815.3104.014.6105.813.6107.114.6104.114.8101.214.688.512.9101.114.0
Δ3.1↑0.5↑4.2↑0.5↑5.1↑0.6↑6.2↑0.6↑4.1↑0.7↑5.5↑1.0↑11.1↑1.3↑8.1↑0.6↑
Human [2]84.414.385.014.395.714.087.114.280.615.084.614.791.614.285.314.6
+ +Table 2. Comparison of F1-scores (in %) on object classes of Open Images, evaluated on the Nocaps validation set. There are 504 classes in total. 80 of them are in-domain, which are common classes from COCO. The remaining 424 classes are the out-of-domain objects. + +
modelin-domainout-of-domainentire
VIVO39.229.130.4
NOC-REK45.330.532.8
Ours58.639.243.1
+ +for the baselines is the COCO dataset. Following prior settings, we also report the results after the model is optimized using SCST [24]. Our generated captions also adopt Constrained Beam Search (CBS) following [3]. + +In Table 1, we present our results of SPICE and CIDEr scores on the Nocaps validation and test sets. We also show the results of our different training stages in the middle of the table, where RCA-NOC** denotes our first training stage result and RCA-NOC is our final result after CIDEr optimization. Note that we do not compare with the data-driven methods [17, 30, 34] which use massive out-of-domain image-caption pairs in the training and fail to follow the rule of Nocaps. By leveraging relative semantic relevance in contrastive learning, our method has achieved a significant improvement compared to all prior works. It is worth noting that our first stage training could generate a comparable result with [13, 18, 35]. After the CIDEr optimization process, our method could outperform the recent state-of-art method NOC-REK [29] with a large margin, which is 8.1 and 0.6 (CIDEr and SPICE) better than [29] on the Nocaps Test set. This suggests that our model is more capable of generating captions with novel objects. + +To quantitatively evaluate how well the model can describe novel objects, we also calculate the F1-score between our generated and the ground-truth tags on the validation set. Table 2 shows the comparison with VIVO and NOC- + +Table 3. Evaluation results on the Held-Out COCO test set. The best results are highlighted in red. + +
MethodAvg. F1-scoreSPICEMeteorCIDEr
NOC48.8-21.4-
NBT48.515.722.877.0
DNOC57.9-21.6-
ZSC29.814.221.9-
ANOC64.318.225.294.7
VinVL+VIVO71.824.530.6132.8
NOC-REK76.326.932.8138.4
RCA-NOc79.527.035.9142.8
+ +REK on the Nocaps validation set. We see that RCA-NOC improves NOC-REK and VIVO on F1-score substantially, especially for out-of-domain objects. This again verifies the effectiveness of RCA-NOC's discriminative ability to describe and distinguish novel objects. + +Results on the Held-Out COCO dataset. To further prove the generalization ability of our method, we also conduct experiments on the Held-Out COCO dataset. As we can see from Table 3, our method consistently beats the baseline VinVL+VIVO with a large margin. The improvements are 7.7, 2.5, 5.3, and 10.0 with BERT-base on the F1, SPICE, METEOR, and CIDEr metrics. Additionally, our method is superior to all other state-of-art methods. In particular, compared with the recent state-of-art method NOC-REK [29], the recent state-of-art on the Held-Out COCO dataset, RCA-NOC achieves a 4.4 improvement on CIDEr (from 138.4 to 142.8) and 3.1 improvement on METEOR (from 32.8 to 35.9). The 3.2 improvement on the F1 score also shows that RCA-NOC performs better in describing novel objects. + +# 6.3. Ablation study. + +In this subsection, we will discuss every component's contribution to our framework. If not mentioned by purpose, all methods are conducted on the Nocaps validation + +Table 4. Effectiveness of the source of visual semantics. + +
Methodin-domainnear-domainout-of-domainOverall
CIDErSPICECIDErSPICECIDErSPICECIDErSPICE
N.A.103.614.7100.814.2100.913.2103.214.2
NOC-REK103.914.9101.614.3102.013.4103.414.3
VIVO105.215.1103.514.4103.613.4105.214.4
CLIP107.815.3104.014.6105.813.6107.114.6
+ +Table 5. Effectiveness of the UASR. UAR: Uncertainty-Aware Reweight, UAS: Uncertainty-Aware Selection, $UAS^{N}$ : Uncertainty-Aware Selection for Negatives), UASR: Uncertainty-Aware Selection and Re-weight. + +
Methodin-domainnear-domainout-of-domainOverall
CIDEr SPICECIDEr SPICECIDEr SPICECIDEr SPICE
N.A.103.614.7100.814.2100.913.2102.414.2
\( UAS^N \)105.214.8102.114.3102.413.3104.214.3
UAS105.915.0104.514.3103.913.4105.314.5
UAR104.314.8103.314.4104.713.3105.614.3
UASR107.815.3104.014.6105.813.6107.114.6
+ +set with BERT-base. (we cannot use the Nocaps test set because only 5 times submissions are allowed for the test set). + +Effectiveness of visual semantics. We enhance the modality alignment by incorporating visual semantics from foundational models, with a specific instantiation using CLIP. To evaluate the generalization ability of our approach, we modify the model to extract visual semantics and conduct further experiments to compare it with NOC-REK [29] and VIVO for generating visual semantics. Our baseline model is trained using a contrastive approach that ranks ROI tags extracted from Faster R-CNN based on their softmax values, distinguishing between relevant and irrelevant tags. + +Our findings indicate that using NOC-REK to generate augmented tags provides only marginal improvement to our framework, resulting in a 0.8 and 0.1 (CIDEr and SPICE) increase compared to the baseline. We hypothesize that this limited improvement may be due to the restricted linguistic knowledge contained in BERT, which may not encompass a wide range of novel categories and lack higher-level and global concepts required to describe complex scenes. In contrast, utilizing a larger pool of noisy visual semantics (CLIP) extracted from captions leads to better results, with a 4.9 and 0.4 (CIDEr and SPICE) increase compared to the baseline. Using a smaller and cleaner pool of visual semantics extracted from the classes of various object detection datasets (VIVO) only results in a 2.0 and 0.2 (CIDEr and SPICE) increase compared to the baseline. This is likely due to the fact that the CLIP is pre-trained on vast amounts of training data, enabling it to extract a more diverse, extensive, and semantically meaningful set of high-level visual concepts compared to NOC-REK. + +Effectiveness of the UASR. We investigate the performance of our Uncertainty-Aware Selection and Reweighting (UASR) on the Nocaps validation set in this part. Table 5 shows that Uncertainty-Aware Reweighting (UAR) could effectively enhance the reliable contrastive samples + +Table 6. Evaluation on COCO test set of Karpathy split [15]. All results are based on single model with cross-entropy optimization. + +
pre-trainingBLEU4MeteorCIDErSPICE
N.A33.828.1118.321.2
OSCAR + VIVO34.928.4119.821.7
RCA-NOC37.429.6128.423.1
+ +Table 7. Ablation study on the effectiveness of different components, including (i) CA: Cross-modality Alignment, our prototype contrastive loss for region-tag pairs, (ii) IA: Inner-modality Alignment, (iii) CLIP: Without CLIP refers to extracting visual semantics with object detection, and (iv) UASR: Uncertainty-Aware Selection and Re-weighting. + +
CAIAUASRCLIPCIDERSPICE
90.912.8
✓96.513.5
✓✓98.713.8
✓✓✓103.214.2
✓✓✓✓107.114.6
+ +and bring 3.2 and 0.1 boosts on CIDEr and SPICE. In addition, the false positives/negatives severely harm our training process. By further incorporating Uncertainty-Aware Selection for Negatives $(UAS^{N})$ into our method and filtering false negatives, our model's performance is boosted to 104.2 and 14.3 on CIDEr and SPICE. When filtering false positives/negatives simultaneously, we could reach 105.3 and 14.5 on CIDEr and SPICE with Uncertainty-Aware Selection (UAS). Finally, our method improves the performance by 4.7 and 0.4 (CIDEr and SPICE) by combining UAR and UAS, which illustrates the proposed UASR is a more powerful tool for tackling noisy contrastive samples in NOC. + +# 6.4. Qualitative Results + +In Figure 3, we display some qualitative results on Held-Out COCO and Nocaps, and all the approaches are based on BERT-base. On Held-Out COCO, the result compared with GT shows that our proposed method could effectively generate accurate and precise captions with novel objects by leveraging relative semantic relevance into training. On Nocaps, VinVL+VIVO [13, 35] sometimes cannot include the desired novel objects in their captions (first and third examples) or generate wrong captions (second example). Our RCA-NOC, on the other hand, successfully generates correct and coherent captions via differentiating confusing classes and aligning object detection with other modalities. For better illustration, we show top-5 Positive and Negative Tag results extracted from CLIP. + +# 6.5. General Image Captioning + +Improving modality alignment is a shared objective of general image captioning tasks. As demonstrated in Table 6, our proposed method, RCL-NOC, improves the model's performance across all metrics assessed on the COCO test set, particularly in the CIDEr score. However, we have observed that the improvement on the COCO benchmark is + +![](images/2320bd51d2972b870148cb0114702ed70317dda8e6c4ba745e4464be385f9363.jpg) +GT: A boy in a tie holding a small suitcase. +RCA-NOC: A young boy wearing a tie holding a suitcase. +PT: Person, human, tie, suitcase, dress*... (Person, human, suitcase, tie...) +NT: Hair*, chair, soda, step, umbrella ... (Chair, soda, step, umbrella...) + +![](images/7967f96606f0b36458826f4222a6f89bfeecea206eab094854724b8898d2d6d4.jpg) +GT: 2 men sit on the couch, video game controllers in hands. +RCA-NOC: A couple of men sitting on a couch playing a video game with wheels. +PT: Couch, person, face, wheel, shirt... (person, wheel, couch, face, shirt...) +NT: Wheelchair, leg\* tie, stone, coat... (Wheelchair, tie, stone, coat...) + +Figure 3. Examples of generated captions and contrastive tags by compared methods on Held-Out COCO (left) and Nocaps (right). We show the ground-truth captions (GT) on Held-Out COCO for reference. PT/NT denotes the positive/negative tags before and after Uncertainty-Aware Selection and Reweighting (UASR). Blue/Red text indicates novel objects in Held-Out COCO/Nocaps, and * indicates the false positives/negatives. +![](images/8b6619f61484916499feca8de3571c462e0c7677d3987634eb9e0be4f67b939a.jpg) +GT: Someone cutting a small pizza with a pizza cutter. +RCA-NOC: A person is cutting a pizza with a pizza cutter. +PT: Person, food, pizza, kitchen, bottle*... (Person, food, kitchen, pizza...) +NT: Microwave, design, hammer, wine, tie... (Microwave, design, hammer, wine, tie...) + +![](images/d9650dbf1a3fd5545f3f5ecfbab2eeea00491409f5d90ef39e11a3f04b9cec63.jpg) +VinVL + VIVO: A man with a jacket and a cowboy hat next to a bull. +RCA-NOC: A man with a blue shirt and a cowboy hat next to a bull. +PT: Hat, hay, bull, shirt, man... (Man, bull, shirt, hat, hay...) +NT: face*, tie, road, barn, jacket... (Tie, road, barn, jacket...) + +![](images/f78b65bf065079936bf36b85b3a844b09a478ae78c6bcef40a68067607961278.jpg) +VinVL + VIVO: A jaguar standing on top of a tree. +RCA-NOC: A jaguar standing behind a green fence. +PT: Jaguar, fence, dog*, carnivore, chest*... (Jaguar, fence, carnivore...) +NT: animal*, wall, coat, cage, sign... (wall, coat, cage, sign...) + +![](images/1b2e2989a0365e192e6c781b1a3aa5024383a607bd63aa2d6ec5f4469835c7f4.jpg) +VinVL + VIVO: A white plate of food with dessert and a tomato. +RCA-NOC: A white plate with two pieces of bread and a tomato. +PT: Tomato, bread, lunch, plate, vegetable* ... (Tomato, bread, plate, lunch...) +NT: Piece*, salad, cake, snack, table*... (Salad, cake, snack...) + +not as substantial as that on the nocaps benchmark. We hypothesize that this discrepancy is due to the COCO dataset having a limited number of visual concepts, thus reducing the benefits of learning visual semantics. Additionally, our method's use of tags is general and does not rely on fully annotated data. It's possible to utilize potentially unlimited amounts of images and different sources of tags, including those from Faster R-CNN, image tagging, or keywords extracted from captions. These possibilities will be explored in our future work.. + +# 6.6. Data and Compute Efficiency + +The way the visual semantics are extracted (using CLIP) is not central to our work, as for the gain coming from 400M pairs of CLIP. This is supported in section 6.3. Table 7 shows that other components contribute significantly. Notably, the gain achieved by our Contrastive Alignment (CA) component alone can surpass that of CLIP by a large margin. Importantly, our method achieves this without increasing the number of parameters during training and inference, with the same parameter count as NOC-REK and VINVL (110 M). The training time of NOC-REK is 49 hours, for NOC-REK the training time is much lower (23h). This is with the paper setup (8 GPUs A100). Compared with NOC-REK, which adopts test time augmentation during inference, our inference time is much lower (1 minute) while NOC-REK is 2 minutes. + +# 7. Conclusion + +In this paper, we present RCA-NOC, which achieves visual-semantic alignment via relative contrastive learning. + +Specifically, for each image, we first extract augmented tags obtained from foundation models such as CLIP. Then we utilize the rank of each augmented object tag in a list as a relative relevance label to contrast each top ranked tag with a set of lower ranked tags. We empirically find that such a learning objective is effective and easy to optimize by encouraging the top ranked tags to be more compatible with their image and text context than lower ranked tags, hence improving the discriminative ability of the learned multimodality representation. We prove the effectiveness of our paradigm in novel object caption, with the spotlight on Nocaps and Held-Out COCO benchmark. + +The effectiveness of object tags has already been proved in recent works. However, there are few studies to further explore why such tags could perform well and the problem of object tags' misalignment is often ignored. So how to further exploit use tags explicitly while having a deep understanding of their roles is meaningful in the future. + +# References + +[1] https://huggingface.co/transformers/modeldoc/bert.html.6 +[2] Harsh Agrawal, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, Stefan Lee, and Peter Anderson. nocaps: novel object captioning at scale. In ICCV, 2019. 6, 7 +[3] Peter Anderson, Basura Fernando, Mark Johnson, and Stephen Gould. Guided open vocabulary image captioning with constrained beam search. 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Faster r-cnn: Towards real-time object detection with region proposal networks. In NIPS, 2015. 1 +[24] Steven J Rennie, Etienne Marcheret, Youssef Mroueh, Jerret Ross, and Vaibhava Goel. Self-critical sequence training for image captioning. In CVPR, 2017. 6, 7 +[25] Mikihiro Tanaka and Tatsuya Harada. Captioning images with novel objects via online vocabulary expansion. In ECCV, 2020. 1 +[26] Kenneth Tran, Xiaodong He, Lei Zhang, Jian Sun, Cornelia Carapcea, Chris Thrasher, Chris Buehler, and Chris Sienkiewicz. Rich image captioning in the wild. In CVPR Workshop on DeepVision, 2016. 1 +[27] Subhashini Venugopalan, Lisa Anne Hendricks, Marcus Rohrbach, Raymond Mooney, Trevor Darrell, and Kate Saenko. Captioning images with diverse objects. In CVPR, 2017. 1, 2 +[28] Oriol Vinyals, Alexander Toshev, Samy Bengio, and Dumitru Erhan. Show and tell: A neural image caption generator. In CVPR, 2015. 1 +[29] Duc Minh Vo, Hong Chen, Akihiro Sugimoto, and Hideki Nakayama. Noc-rek: Novel object captioning with retrieved vocabulary from external knowledge, 2022. 1, 2, 6, 7, 8 +[30] Jianfeng Wang, Zhengyuan Yang, Xiaowei Hu, Linjie Li, Kevin Lin, Zhe Gan, Zicheng Liu, Ce Liu, and Lijuan Wang. Git: A generative image-to-text transformer for vision and language. arXiv preprint arXiv:2205.14100, 2022. 7 +[31] Zirui Wang, Jiahui Yu, Adams Wei Yu, Zihang Dai, Yulia Tsvetkov, and Yuan Cao. Simvlm: Simple visual language model pretraining with weak supervision. arXiv preprint arXiv:2108.10904, 2021. 2 +[32] Fangyun Wei, Yue Gao, Zhirong Wu, Han Hu, and Stephen Lin. Aligning pretraining for detection via object-level contrastive learning. Advances in Neural Information Processing Systems, 34:22682-22694, 2021. 2 + +[33] Yu Wu, Linchao Zhu, Lu Jiang, and Yi Yang. Decoupled novel object captioner. In Proceedings of the 26th ACM international conference on Multimedia, pages 1029-1037, 2018. 1, 2 +[34] Jiahui Yu, Zirui Wang, Vijay Vasudevan, Legg Yeung, Mojtaba Seyhedhosseini, and Yonghui Wu. Coca: Contrastive captioners are image-text foundation models. arXiv preprint arXiv:2205.01917, 2022. 7 +[35] Pengchuan Zhang, Xiujun Li, Xiaowei Hu, Jianwei Yang, Lei Zhang, Lijuan Wang, Yejin Choi, and Jianfeng Gao. Vinvl: Revisiting visual representations in vision-language models. 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Our approach maximizes compatibility between regions and object tags in a contrastive manner. To set up a proper contrastive learning objective, for each image, we augment tags by leveraging the relative nature of positive and negative pairs obtained from foundation models such as CLIP. We then use the rank of each augmented tag in a list as a relative relevance label to contrast each top-ranked tag with a set of lower-ranked tags. This learning objective encourages the top-ranked tags to be more compatible with their image and text context than lower-ranked tags, thus improving the discriminative ability of the learned multi-modality representation. We evaluate our approach on two datasets and show that our proposed RCA-NOC approach outperforms state-of-the-art methods by a large margin, demonstrating its effectiveness in improving vision-language representation for novel object captioning." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 491, + 128, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 128, + 504 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 128, + 504 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 512, + 287, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 512, + 287, + 631 + ], + "spans": [ + { + "bbox": [ + 46, + 512, + 287, + 631 + ], + "type": "text", + "content": "Describing novel objects unseen in training data is a highly desired capability for a real-world image captioning model. Conventional image captioning models [4, 20, 28] often fail to describe novel objects because they only cover limited visual concepts and generalize poorly to images in the wild [26]. To overcome this limitation, approaches that rely on object detection as the external resource [7, 8, 13, 18, 20, 25, 27, 33, 35] have been widely explored and demonstrated breakthroughs in vision-language (VL) understanding." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 631, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 631, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 631, + 288, + 714 + ], + "type": "text", + "content": "Although object detection models (e.g., Faster RCNN [23]) have been improved to recognize a wide range of objects including novel ones like zero-shot object detection [14], using object detection in novel captioning models brings a new challenge. VIVO [13] leverages extra object tags to pre-train a visual vocabulary and help image captioning generalize to new categories. NOC-REK [29]" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 217, + 390, + 264 + ], + "blocks": [ + { + "bbox": [ + 310, + 217, + 390, + 264 + ], + "lines": [ + { + "bbox": [ + 310, + 217, + 390, + 264 + ], + "spans": [ + { + "bbox": [ + 310, + 217, + 390, + 264 + ], + "type": "image", + "image_path": "72c73d59bf1906ec193dadf5c0e214f3fbb2a69e9098b7b1361850154623373e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 329, + 264, + 365, + 271 + ], + "lines": [ + { + "bbox": [ + 329, + 264, + 365, + 271 + ], + "spans": [ + { + "bbox": [ + 329, + 264, + 365, + 271 + ], + "type": "text", + "content": "(a) : Training" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 401, + 220, + 522, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 401, + 220, + 522, + 243 + ], + "spans": [ + { + "bbox": [ + 401, + 220, + 522, + 243 + ], + "type": "text", + "content": "NOC-REK: panda, animal, chunk, tree, branch. \nVIVO: panda, bear, chunk, tree, branch, animal, raccoon, hedge, food, raccoon." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 402, + 246, + 532, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 402, + 246, + 532, + 260 + ], + "spans": [ + { + "bbox": [ + 402, + 246, + 532, + 260 + ], + "type": "text", + "content": "Ours: panda, animal, tree, branch, chunk.../ hedge, raccoon, sky, advertisement, water..." + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 311, + 271, + 390, + 318 + ], + "blocks": [ + { + "bbox": [ + 311, + 271, + 390, + 318 + ], + "lines": [ + { + "bbox": [ + 311, + 271, + 390, + 318 + ], + "spans": [ + { + "bbox": [ + 311, + 271, + 390, + 318 + ], + "type": "image", + "image_path": "7d37de3d5f6ed670f7f2547fe4baa17e811399bc7e73c6af485b016b64769826.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 329, + 318, + 370, + 325 + ], + "lines": [ + { + "bbox": [ + 329, + 318, + 370, + 325 + ], + "spans": [ + { + "bbox": [ + 329, + 318, + 370, + 325 + ], + "type": "text", + "content": "(b): Inference" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 401, + 272, + 532, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 401, + 272, + 532, + 286 + ], + "spans": [ + { + "bbox": [ + 401, + 272, + 532, + 286 + ], + "type": "text", + "content": "NOC-REK: A raccoon sitting on top of a tree branch. (panda, tree, branch)" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 402, + 288, + 537, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 402, + 288, + 537, + 302 + ], + "spans": [ + { + "bbox": [ + 402, + 288, + 537, + 302 + ], + "type": "text", + "content": "VIVO: A raccoon sitting on a tree branch. (panda, tree, branch)" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 402, + 304, + 537, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 402, + 304, + 537, + 318 + ], + "spans": [ + { + "bbox": [ + 402, + 304, + 537, + 318 + ], + "type": "text", + "content": "Ours: A red panda sitting in a tree branch (panda, tree, branch)" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 333, + 547, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 333, + 547, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 333, + 547, + 431 + ], + "type": "text", + "content": "Figure 1. An illustrative example of our method to leverage relative semantic relevance to achieve modality alignment. Our method could give accurate captions \"A cute red panda sitting in a tree branch\" conditioned on the objects \"red panda\" while VINVL+VIVO generates a wrong caption \"A cute raccoon sitting in a tree branch\". This inference result shows that our method can differentiate some confusing objects and generate accurate captions for novel objects when the object detection is well aligned with other modalities." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 443, + 547, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 443, + 547, + 561 + ], + "spans": [ + { + "bbox": [ + 304, + 443, + 547, + 561 + ], + "type": "text", + "content": "tries to augment object tags in the training stage based on the similarity between region and word. Such methods simply concatenate regions, object tags, and caption features as input to a Transformer-based model and use masked token reconstruction to implicitly learn an alignment between vision and language. Although such an alignment can help bring regions and words of the same concept closer, it lacks an effective mechanism to push away irrelevant concepts. As a result, it still makes mistakes on some confusing concepts, as shown in Figure 1." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 561, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 561, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 561, + 548, + 714 + ], + "type": "text", + "content": "Different from previous methods, this study aims to learn visual and semantic alignment in a contrastive manner. Gupta et al. [10] showed that modality alignment could be achieved by maximizing the information lower bound between an image and its object tags. That is, given pairs of image and object tags, we can maximize the compatibility between tags and their attention-weighted region representations, compared to regions and non-corresponding tags. However, there are two critical problems that need to be further addressed: 1) how to effectively generate contrastive tags (augmented tags) that are closely relevant to an image, and 2) how to design a proper contrastive learning objective that allows the model to effectively leverage the contrastive" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15510" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 188, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 188, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 188, + 83 + ], + "type": "text", + "content": "tags to align vision and semantics." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 95, + 289, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 95, + 289, + 259 + ], + "spans": [ + { + "bbox": [ + 46, + 95, + 289, + 259 + ], + "type": "text", + "content": "To tackle the first problem, we utilize CLIP [22] to create a list of contrastive tags which are closely linked to an image and contain global structural information and high-level concepts describing scenes. This approach aids in the discovery of useful tags that are essential for contrastive learning. To address the second problem, a proper contrastive learning objective needs to be explored. The major challenge here is that the augmented contrastive tags are inaccurate and inevitably noisy. We cannot simply treat one tag as positive and others as negative to perform contrastive learning, because the augmented tags might be highly correlated or similar to each other. To tackle this problem, we leverage the relative relevance, rather than the absolute relevance, of the augmented tags, which is more robust to data noise." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 270, + 289, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 289, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 289, + 460 + ], + "type": "text", + "content": "Specifically, given an image, for each of its labeled object tags, we generate a ranked list of contrastive tags using CLIP. We regard the rank of each augmented tag as its relative semantic relevance with the image. In general, the top-ranked tags are assumed to be more relevant to the image than the lower-ranked tags. We divide the list into two parts: the (relatively) relevant part with higher rank and the (relatively) irrelevant part with lower rank (Figure 1 (a)). In our proposed objective, we treat each tag in the relevant part as positive and all tags in the irrelevant part as negative to perform contrastive learning. Note that we do not let tags both in the relevant part contrast with each other as they might be highly correlated concepts. In this way, our approach weakens the strict assumption of contrastive learning in previous works and exploits the relative ranking in a loose form to achieve modality alignment." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 468, + 287, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 468, + 287, + 504 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 287, + 504 + ], + "type": "text", + "content": "We conduct experiments on the Nocaps and Held-Out COCO datasets to demonstrate the effectiveness of RCA-NOC. Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 515, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 46, + 515, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 515, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 515, + 287, + 586 + ], + "type": "text", + "content": "- We propose Relative Contrastive Alignment (RCA) to learn the relative semantic relevance in a loose form by maximizing the compatibility between regions and their relevant tags compared with regions and irrelevant tags to achieve vision and language alignment and improve the discriminative ability of the multi-modality representation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 597, + 287, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 287, + 668 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 287, + 668 + ], + "type": "text", + "content": "- A method called Uncertainty-Aware Selection and Reweighting (UASR) is proposed to estimate and exploit the uncertainty of each contrastive sample to mitigate the negative effect brought by noisy tags. UASR can effectively prioritize highly reliable samples and demote false positives and false negatives." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 678, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 678, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 678, + 287, + 714 + ], + "type": "text", + "content": "- We validate the proposed method on the Nocaps and Held-Out COCO benchmarks, which outperforms other state-of-the-art methods by a large margin." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 91, + 390, + 104 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 91, + 390, + 104 + ], + "spans": [ + { + "bbox": [ + 306, + 91, + 390, + 104 + ], + "type": "text", + "content": "3. Related work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 111, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 111, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 111, + 545, + 323 + ], + "type": "text", + "content": "Novel object captioning aims to describe images with objects that are unseen in the training stage (we define these objects as novel objects) where many methods. [7, 8, 13, 18, 20, 22, 27, 31, 33, 35] have been proposed. Early works such as Hendricks et al. [12] and Venugopalan et al. [27] utilize unpaired labeled image and sentence data to enhance semantically visual concepts. Recent studies propose to explicitly leverage the object detection results for NOC, Lu et al. [20], Wu et al. [33], and Demirel et al. [8] fill the generated template sentence with objects detected by object/novel object detectors. Chen et al. [7] combine object detector and human attention to identify novel objects. In addition, Li et al. are the first to utilize semantics in VLP tasks, which are further extended by Zhang et al. [35]. Hu et al. [13] built upon [35] and propose to leverage extra region-tag pairs to conduct pretraining. Duc et al. [29] tried to augment object tags in the training stage based on the similarity of regions and objects." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 323, + 545, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 323, + 545, + 429 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 545, + 429 + ], + "type": "text", + "content": "However, most aforementioned methods for NOC ignore the misalignment problem of object tags, thereby failing to fully exploit the semantic relationship between vision and language (Figure 1), which we argue is crucial to the quality of generated captions. In this paper, we propose a simple but effective contrastive learning objective to learn the relative semantic relevance in a loose form where the object tags could be explicitly aligned with their corresponding image feature representations in a semantic space." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 429, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 429, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 429, + 545, + 569 + ], + "type": "text", + "content": "Contrastive Learning aims to learn discriminative representations to distinguish an image from others. Many methods [6,10,11,16,17,22,32] have shown their effectiveness. For example, Chen et al. [6] proposed to learn visual representations by maximizing agreement between differently augmented views of the same image via a contrastive loss. He et al. [11] proposed Momentum Contrast (MoCo) for unsupervised visual representation learning. Wei et al. [32] utilized contrastive learning in the detection task. Li et al. [16] focused on the problem of contextual outpainting. Gupta et al. [10] proposed a method " + }, + { + "bbox": [ + 304, + 429, + 545, + 569 + ], + "type": "inline_equation", + "content": "\\mathrm{CPG}^{\\dagger}" + }, + { + "bbox": [ + 304, + 429, + 545, + 569 + ], + "type": "text", + "content": " to find hard negative words by replacing a word in a caption." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 570, + 545, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 686 + ], + "type": "text", + "content": "Other data-driven studies such as CLIP [22] and ALIGNN [17] focus on learning a corresponding relative relationship from massive web data. CLIP [22] predicts which text goes with which image and learns a relative imagetext corresponding relationship from broad web data with noisy supervision. ALIGNN [17] further scales up CLIP by leveraging a noisy dataset that covers more than one billion image-text pairs. These methods achieve remarkable results but require massive fully-annotated data, which are difficult to obtain." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "1For better illustration, we use the abbreviation CPG to denote the paper \"Contrastive Learning for Weakly Supervised Phrase Grounding\" [10]" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15511" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 77, + 83, + 200, + 167 + ], + "blocks": [ + { + "bbox": [ + 77, + 83, + 200, + 167 + ], + "lines": [ + { + "bbox": [ + 77, + 83, + 200, + 167 + ], + "spans": [ + { + "bbox": [ + 77, + 83, + 200, + 167 + ], + "type": "image", + "image_path": "0e1bcd376e8077ab743c09348aef0ffb6744d2905587fb59b5086b610a96c3e4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 53, + 168, + 211, + 178 + ], + "lines": [ + { + "bbox": [ + 53, + 168, + 211, + 178 + ], + "spans": [ + { + "bbox": [ + 53, + 168, + 211, + 178 + ], + "type": "text", + "content": "\"A close up of a small animal on a tree branch\"" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 216, + 76, + 541, + 200 + ], + "blocks": [ + { + "bbox": [ + 216, + 76, + 541, + 200 + ], + "lines": [ + { + "bbox": [ + 216, + 76, + 541, + 200 + ], + "spans": [ + { + "bbox": [ + 216, + 76, + 541, + 200 + ], + "type": "image", + "image_path": "31b4970adb0f96d988cbd6786871d81d94ee746f1c822ef51bcb8fdf539e1c73.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 74, + 207, + 176, + 274 + ], + "blocks": [ + { + "bbox": [ + 50, + 188, + 206, + 199 + ], + "lines": [ + { + "bbox": [ + 50, + 188, + 206, + 199 + ], + "spans": [ + { + "bbox": [ + 50, + 188, + 206, + 199 + ], + "type": "text", + "content": "(a) Training: learn discriminative feature" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 74, + 207, + 176, + 274 + ], + "lines": [ + { + "bbox": [ + 74, + 207, + 176, + 274 + ], + "spans": [ + { + "bbox": [ + 74, + 207, + 176, + 274 + ], + "type": "image", + "image_path": "c79f9f754ee43660e6346b91b0738f19014abd31e133d789ea7e4a3ee71065ad.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 50, + 276, + 211, + 286 + ], + "lines": [ + { + "bbox": [ + 50, + 276, + 211, + 286 + ], + "spans": [ + { + "bbox": [ + 50, + 276, + 211, + 286 + ], + "type": "text", + "content": "Result: \"A red panda sitting in a tree branch\"" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 53, + 288, + 196, + 299 + ], + "lines": [ + { + "bbox": [ + 53, + 288, + 196, + 299 + ], + "spans": [ + { + "bbox": [ + 53, + 288, + 196, + 299 + ], + "type": "text", + "content": "(b) Inference: novel object captioning" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 268, + 209, + 309, + 219 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 268, + 209, + 309, + 219 + ], + "spans": [ + { + "bbox": [ + 268, + 209, + 309, + 219 + ], + "type": "text", + "content": "Red panda" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 236, + 434, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 236, + 434, + 248 + ], + "spans": [ + { + "bbox": [ + 313, + 236, + 434, + 248 + ], + "type": "text", + "content": "Multi-layer Transformer" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 220, + 258, + 539, + 301 + ], + "blocks": [ + { + "bbox": [ + 220, + 258, + 539, + 301 + ], + "lines": [ + { + "bbox": [ + 220, + 258, + 539, + 301 + ], + "spans": [ + { + "bbox": [ + 220, + 258, + 539, + 301 + ], + "type": "image", + "image_path": "6e1b86125f9e32226a22ae22d886e231bad5139edbc5f71c84ce37eecbe93fcd.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 310, + 545, + 396 + ], + "lines": [ + { + "bbox": [ + 46, + 310, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 545, + 396 + ], + "type": "text", + "content": "Figure 2. The main pipeline of our proposed RCA-NOC, including training and inference: In addition to the normal caption loss " + }, + { + "bbox": [ + 46, + 310, + 545, + 396 + ], + "type": "inline_equation", + "content": "L_{G}" + }, + { + "bbox": [ + 46, + 310, + 545, + 396 + ], + "type": "text", + "content": " in the training process, we also compute the cross-modality and inner-modality loss " + }, + { + "bbox": [ + 46, + 310, + 545, + 396 + ], + "type": "inline_equation", + "content": "L_{cross}" + }, + { + "bbox": [ + 46, + 310, + 545, + 396 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 310, + 545, + 396 + ], + "type": "inline_equation", + "content": "L_{inner}" + }, + { + "bbox": [ + 46, + 310, + 545, + 396 + ], + "type": "text", + "content": " in Eq. 22 and Eq. 23 by contrasting the positive tags against the negative tags. The corresponding relationship is denoted in green and red line separately. During training, the input is a concatenated sequence of words—ROI tags—ROIs and augmented contrastive tags. The training loss comprises caption loss (with [MASK] in words for reconstruction) and contrastive learning loss (with [MASK] in ROI tags token for indicating the specific positions where augmented tags are inserted). Augmented tags replace certain ROI tags and are encoded into contrastive tag feature embeddings for comparison with region and caption embeddings. During prediction, the input is a concatenated sequence of ROI tags—ROIs without additional retrieval steps." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 408, + 157, + 421 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 408, + 157, + 421 + ], + "spans": [ + { + "bbox": [ + 47, + 408, + 157, + 421 + ], + "type": "text", + "content": "4. Proposed Methods" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 429, + 287, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 429, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 46, + 429, + 287, + 475 + ], + "type": "text", + "content": "We propose to enhance the modality alignment by explicitly injecting visual semantics. These semantics are extracted for each image, obtained with existing foundation models such as CLIP." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 475, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 287, + 605 + ], + "type": "text", + "content": "There are two motivations behind our approach. First, by maximizing the compatibility between regions and their relevant tags compared with regions and irrelevant tags, we could not only learn vision-semantic alignment and improve the discriminative ability of the multi-modality representation. Second, we introduce a relative contrastive learning objective that considers the relative relationships between positive and negative examples, rather than using absolute prototype-contrastive learning methods. This approach is more generalized and can be easily integrated into any existing NOC method." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 613, + 202, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 202, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 202, + 624 + ], + "type": "text", + "content": "4.1. Visual Semantics Extraction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 631, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 631, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 631, + 287, + 713 + ], + "type": "text", + "content": "Different from other approaches (e.g., [13, 18]) that extract object tags using pretrained object detectors, we use an off-the-shelf foundational model to extract more diverse, larger and semantically meaningful set of visual semantics. We show in section 6, that this approach helps to capture high level and global semantics describing the scenes, which are hard to obtain with other approaches (e.g. object" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 410, + 350, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 410, + 350, + 421 + ], + "spans": [ + { + "bbox": [ + 306, + 410, + 350, + 421 + ], + "type": "text", + "content": "detectors)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 432, + 545, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 432, + 545, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 432, + 545, + 598 + ], + "type": "text", + "content": "We use a pretrained CLIP (ViT-B/16) model to obtain the embeddings of all the images and the extracted semantics. For each image, we compute its cosine similarity with all the embedded semantics and select the top M similar semantics as augmented tags " + }, + { + "bbox": [ + 304, + 432, + 545, + 598 + ], + "type": "inline_equation", + "content": "T = \\{t_l\\}_{l=1}^M" + }, + { + "bbox": [ + 304, + 432, + 545, + 598 + ], + "type": "text", + "content": ". The augmented tags will be ranked using global (image-level) cosine similarity " + }, + { + "bbox": [ + 304, + 432, + 545, + 598 + ], + "type": "inline_equation", + "content": "p(t_l)" + }, + { + "bbox": [ + 304, + 432, + 545, + 598 + ], + "type": "text", + "content": ". Then we utilize the rank of each augmented tag in " + }, + { + "bbox": [ + 304, + 432, + 545, + 598 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 432, + 545, + 598 + ], + "type": "text", + "content": " as a relative relevance label. In general, the top-ranked tags are assumed to be more relevant to the image than the lower-ranked tags. We divide " + }, + { + "bbox": [ + 304, + 432, + 545, + 598 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 432, + 545, + 598 + ], + "type": "text", + "content": " into positive and negative tags: positive tags being the (relatively) relevant tags with higher rank " + }, + { + "bbox": [ + 304, + 432, + 545, + 598 + ], + "type": "inline_equation", + "content": "T^P = \\{t_n^P\\}_{n=1}^K = \\{t_l\\}_{l=1}^K" + }, + { + "bbox": [ + 304, + 432, + 545, + 598 + ], + "type": "text", + "content": " and negative tags being the (relatively) irrelevant tags with lower rank " + }, + { + "bbox": [ + 304, + 432, + 545, + 598 + ], + "type": "inline_equation", + "content": "T^N = \\{t_l^N\\}_{l=1}^K = \\{t_l\\}_{l=K+1}^{2K}" + }, + { + "bbox": [ + 304, + 432, + 545, + 598 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 432, + 545, + 598 + ], + "type": "inline_equation", + "content": "M = 2K" + }, + { + "bbox": [ + 304, + 432, + 545, + 598 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 608, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 608, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 608, + 545, + 713 + ], + "type": "text", + "content": "Here we propose a simple yet effective augmentation technique. Having a set of visual semantics extracted for each image, instead of considering all the visual semantics at once, we sample randomly a fraction of these augmented tags at each iteration step. Hence, we could not only prevent the model from overfitting on specific semantics and potentially disregard the image or other semantics during training, but also let the model see different combinations of visual semantics, which helps to have more diversity." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15512" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 218, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 218, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 218, + 85 + ], + "type": "text", + "content": "4.2. Relative Contrastive Alignment" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 286, + 160 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 286, + 160 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 286, + 160 + ], + "type": "text", + "content": "InfoNCE [21] is a typical type of contrastive loss function used for self-supervised learning that contrasts one positive sample against a set of negative samples. CPG [10] builds upon InfoNCE and proposes a compatibility function for regions and a caption word. Both InfoNCE and CPG utilize the absolute relevance to optimize the contrastive loss." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 160, + 286, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 160, + 286, + 230 + ], + "spans": [ + { + "bbox": [ + 46, + 160, + 286, + 230 + ], + "type": "text", + "content": "However, such a contrastive learning objective is hard to optimize for object tags since they may be highly correlated to each other. In RCA-NOC, we focus on the relative semantic relevance and utilize the attention-based compatibility function to measure the relativity information for regions and a set of object tags, which is more robust to data noise." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 230, + 286, + 254 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 230, + 286, + 254 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 286, + 254 + ], + "type": "text", + "content": "Specifically, we first compute the dot product for a region-tag pair." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 129, + 255, + 286, + 270 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 255, + 286, + 270 + ], + "spans": [ + { + "bbox": [ + 129, + 255, + 286, + 270 + ], + "type": "interline_equation", + "content": "s _ {j k} = \\mathbf {w} _ {j} ^ {T} \\mathbf {v} _ {k} / \\sqrt {d}, \\tag {1}", + "image_path": "dac4c6c37309f13b3147403a4aca96dab0d57e40c5fe477ec76ee6415fb76bbb.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_j" + }, + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_k" + }, + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "type": "text", + "content": " refer to the corresponding embeddings for tag and region, and " + }, + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "type": "text", + "content": " is the feature dimension. Here, " + }, + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "type": "inline_equation", + "content": "s_{jk}" + }, + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "type": "text", + "content": " represents the similarity between the " + }, + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "type": "text", + "content": "-th tag and the " + }, + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "type": "text", + "content": "-th region. To find a contextualized region representation for the " + }, + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "type": "text", + "content": "-th tag, we define " + }, + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_j^v" + }, + { + "bbox": [ + 46, + 274, + 286, + 334 + ], + "type": "text", + "content": " as follows." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 132, + 335, + 286, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 335, + 286, + 365 + ], + "spans": [ + { + "bbox": [ + 132, + 335, + 286, + 365 + ], + "type": "interline_equation", + "content": "\\mathbf {a} _ {j} ^ {v} = \\sum_ {k = 1} ^ {K} \\alpha_ {j k} \\mathbf {v} _ {k}, \\tag {2}", + "image_path": "3b10171b551d3ab8966eee490dfec2cb9e9674aae00ed2bbcf3491040ee1c0c0.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 369, + 286, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 369, + 286, + 393 + ], + "spans": [ + { + "bbox": [ + 47, + 369, + 286, + 393 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 369, + 286, + 393 + ], + "type": "inline_equation", + "content": "\\alpha_{jk} = \\frac{e^{s_{jk}}}{\\sum_{k' = 1}^{K}e^{s_{jk'}}}," + }, + { + "bbox": [ + 47, + 369, + 286, + 393 + ], + "type": "text", + "content": " (3)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 396, + 286, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 286, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 286, + 422 + ], + "type": "text", + "content": "To measure the compatibility between a tag " + }, + { + "bbox": [ + 46, + 396, + 286, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_j" + }, + { + "bbox": [ + 46, + 396, + 286, + 422 + ], + "type": "text", + "content": " and its contextualized region representation " + }, + { + "bbox": [ + 46, + 396, + 286, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_j^v" + }, + { + "bbox": [ + 46, + 396, + 286, + 422 + ], + "type": "text", + "content": ", we define" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 127, + 430, + 286, + 445 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 430, + 286, + 445 + ], + "spans": [ + { + "bbox": [ + 127, + 430, + 286, + 445 + ], + "type": "interline_equation", + "content": "\\phi (\\mathbf {V}, \\mathbf {w} _ {j}) = \\mathbf {w} _ {j} ^ {T} \\mathbf {a} _ {j} ^ {v}. \\tag {4}", + "image_path": "1b903b75c1b70136af3875014176dd9c8b1f47c11d5458bf11f3c8a165defb5a.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 449, + 286, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 286, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 286, + 472 + ], + "type": "text", + "content": "In this way, we can derive our cross-modality contrastive loss function " + }, + { + "bbox": [ + 46, + 449, + 286, + 472 + ], + "type": "inline_equation", + "content": "L_{cross}" + }, + { + "bbox": [ + 46, + 449, + 286, + 472 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 83, + 480, + 286, + 527 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 480, + 286, + 527 + ], + "spans": [ + { + "bbox": [ + 83, + 480, + 286, + 527 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {c r o s s}} (\\mathbf {V}, \\mathbf {W} ^ {P}, \\mathbf {W} ^ {N}) = \\\\ - \\frac {1}{K} \\sum_ {n = 1} ^ {K} \\log \\left(\\frac {e ^ {\\phi (\\mathbf {V} , \\mathbf {w} _ {n} ^ {P})}}{e ^ {\\phi (\\mathbf {V} , \\mathbf {w} _ {n} ^ {P})} + \\sum_ {l = 1} ^ {K} e ^ {\\phi (\\mathbf {V} , \\mathbf {w} _ {l} ^ {N})}}\\right), \\tag {5} \\\\ \\end{array}", + "image_path": "2ad70d5532035111fa56fdaa72ad5d92262eca8214b408811414c47a4d3966ac.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 536, + 286, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 286, + 583 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 286, + 583 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 536, + 286, + 583 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^P = \\{\\mathbf{w}_l^P\\}_{l=1}^K" + }, + { + "bbox": [ + 46, + 536, + 286, + 583 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 536, + 286, + 583 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^N = \\{\\mathbf{w}_n^N\\}_{n=1}^K" + }, + { + "bbox": [ + 46, + 536, + 286, + 583 + ], + "type": "text", + "content": " are the word embeddings for positives/negatives " + }, + { + "bbox": [ + 46, + 536, + 286, + 583 + ], + "type": "inline_equation", + "content": "T^P" + }, + { + "bbox": [ + 46, + 536, + 286, + 583 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 536, + 286, + 583 + ], + "type": "inline_equation", + "content": "T^N" + }, + { + "bbox": [ + 46, + 536, + 286, + 583 + ], + "type": "text", + "content": ", extracted from CLIP. " + }, + { + "bbox": [ + 46, + 536, + 286, + 583 + ], + "type": "inline_equation", + "content": "\\phi()" + }, + { + "bbox": [ + 46, + 536, + 286, + 583 + ], + "type": "text", + "content": " is the compatibility function defined in Eq. 11." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 584, + 286, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 584, + 286, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 584, + 286, + 688 + ], + "type": "text", + "content": "This equation encourages each positive tag " + }, + { + "bbox": [ + 46, + 584, + 286, + 688 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_n^P" + }, + { + "bbox": [ + 46, + 584, + 286, + 688 + ], + "type": "text", + "content": " to be more compatible with image regions " + }, + { + "bbox": [ + 46, + 584, + 286, + 688 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 46, + 584, + 286, + 688 + ], + "type": "text", + "content": " than all negative tags in " + }, + { + "bbox": [ + 46, + 584, + 286, + 688 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^N" + }, + { + "bbox": [ + 46, + 584, + 286, + 688 + ], + "type": "text", + "content": ". Essentially, if tag " + }, + { + "bbox": [ + 46, + 584, + 286, + 688 + ], + "type": "inline_equation", + "content": "t_j" + }, + { + "bbox": [ + 46, + 584, + 286, + 688 + ], + "type": "text", + "content": " is not relevant to the image (negative), its representation " + }, + { + "bbox": [ + 46, + 584, + 286, + 688 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_j" + }, + { + "bbox": [ + 46, + 584, + 286, + 688 + ], + "type": "text", + "content": " should not be similar to its contextualized region representation " + }, + { + "bbox": [ + 46, + 584, + 286, + 688 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_j^v" + }, + { + "bbox": [ + 46, + 584, + 286, + 688 + ], + "type": "text", + "content": " since it would not be able to collect good information while computing " + }, + { + "bbox": [ + 46, + 584, + 286, + 688 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_j^v" + }, + { + "bbox": [ + 46, + 584, + 286, + 688 + ], + "type": "text", + "content": ". Note that we do not let two positive tags (top-ranked tags) contrast with each other as it is hard to tell which one is more relevant." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "content": "Inner modality Alignment. To further enhance modality alignment, we also compute the inner-modality contrastive" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 72, + 545, + 165 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 165 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 165 + ], + "type": "text", + "content": "loss over tag-caption pairs. The formulation for inner-modality contrastive loss is similar to cross-modality contrastive loss but slightly different. We enforce contrastive learning not to be between tags and all caption words, but just between tags and noun caption words. This is because a caption may have many irrelevant tokens, such as \"the, a, is\", which will harm our alignment process and cause redundant computational costs." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 167, + 545, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 167, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 305, + 167, + 545, + 190 + ], + "type": "text", + "content": "Finally, we can derive our inner-modality contrastive loss function " + }, + { + "bbox": [ + 305, + 167, + 545, + 190 + ], + "type": "inline_equation", + "content": "L_{inner}" + }, + { + "bbox": [ + 305, + 167, + 545, + 190 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 387, + 196, + 545, + 211 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 196, + 545, + 211 + ], + "spans": [ + { + "bbox": [ + 387, + 196, + 545, + 211 + ], + "type": "interline_equation", + "content": "\\phi (\\mathbf {C}, \\mathbf {w} _ {l}) = \\mathbf {w} _ {l} ^ {T} \\mathbf {a} _ {l} ^ {c}, \\tag {6}", + "image_path": "584e12803e02b02564cc7dc560c83bda3796023c2155a5b7065e87fad7c05b73.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 341, + 224, + 545, + 271 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 224, + 545, + 271 + ], + "spans": [ + { + "bbox": [ + 341, + 224, + 545, + 271 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {i n n e r}} \\left(\\mathbf {C}, \\mathbf {W} ^ {P}, \\mathbf {W} ^ {N}\\right) = \\\\ - \\frac {1}{K} \\sum_ {n = 1} ^ {K} \\log \\left(\\frac {e ^ {\\phi (\\mathbf {C} , \\mathbf {w} _ {n} ^ {P})}}{e ^ {\\phi (\\mathbf {C} , \\mathbf {w} _ {n} ^ {P})} + \\sum_ {l = 1} ^ {K} e ^ {\\phi (\\mathbf {C} , \\mathbf {w} _ {l} ^ {N})}}\\right), \\tag {7} \\\\ \\end{array}", + "image_path": "4436f2679450651a3459f95c19588d6022c987f0b1e4e1aeffa285aca8f7a4e5.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 279, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 279, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 304, + 279, + 545, + 338 + ], + "type": "text", + "content": "where this time we take noun caption words " + }, + { + "bbox": [ + 304, + 279, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{C} = \\{\\mathbf{c}_i\\}_{i=1}^P" + }, + { + "bbox": [ + 304, + 279, + 545, + 338 + ], + "type": "text", + "content": " in Eq. 13 as input. By further considering inner-modality alignment, we not only learn caption-tag semantics to connect relevant caption tokens, but also enable region-caption interactions." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 350, + 416, + 363 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 350, + 416, + 363 + ], + "spans": [ + { + "bbox": [ + 306, + 350, + 416, + 363 + ], + "type": "text", + "content": "5. Proposed Methods" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 369, + 545, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 545, + 416 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 545, + 416 + ], + "type": "text", + "content": "We propose to enhance the modality alignment by explicitly injecting visual semantics. These semantics are extracted for each image, obtained with existing foundation models such as CLIP." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 417, + 545, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 417, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 417, + 545, + 545 + ], + "type": "text", + "content": "There are two motivations behind our approach. First, by maximizing the compatibility between regions and their relevant tags compared with regions and irrelevant tags, we could not only learn vision-semantic alignment and improve the discriminative ability of the multi-modality representation. Second, we introduce a relative contrastive learning objective that considers the relative relationships between positive and negative examples, rather than using absolute prototype-contrastive learning methods. This approach is more generalized and can be easily integrated into any existing NOC method." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 554, + 460, + 566 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 554, + 460, + 566 + ], + "spans": [ + { + "bbox": [ + 306, + 554, + 460, + 566 + ], + "type": "text", + "content": "5.1. Visual Semantics Extraction" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 572, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 572, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 572, + 545, + 665 + ], + "type": "text", + "content": "Different from other approaches (e.g., [13, 18]) that extract object tags using pretrained object detectors, we use an off-the-shelf foundational model to extract more diverse, larger and semantically meaningful set of visual semantics. We show in section 6, that this approach helps to capture high level and global semantics describing the scenes, which are hard to obtain with other approaches (e.g. object detectors)." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": "We use a pretrained CLIP (ViT-B/16) model to obtain the embeddings of all the images and the extracted semantics. For each image, we compute its cosine similarity with all the embedded semantics and select the top M similar" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15513" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 190 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 190 + ], + "type": "text", + "content": "semantics as augmented tags " + }, + { + "bbox": [ + 46, + 72, + 289, + 190 + ], + "type": "inline_equation", + "content": "T = \\{t_l\\}_{l=1}^M" + }, + { + "bbox": [ + 46, + 72, + 289, + 190 + ], + "type": "text", + "content": ". The augmented tags will be ranked using global (image-level) cosine similarity " + }, + { + "bbox": [ + 46, + 72, + 289, + 190 + ], + "type": "inline_equation", + "content": "p(t_l)" + }, + { + "bbox": [ + 46, + 72, + 289, + 190 + ], + "type": "text", + "content": ". Then we utilize the rank of each augmented tag in " + }, + { + "bbox": [ + 46, + 72, + 289, + 190 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 72, + 289, + 190 + ], + "type": "text", + "content": " as a relative relevance label. In general, the top-ranked tags are assumed to be more relevant to the image than the lower-ranked tags. We divide " + }, + { + "bbox": [ + 46, + 72, + 289, + 190 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 72, + 289, + 190 + ], + "type": "text", + "content": " into positive and negative tags: positive tags being the (relatively) relevant tags with higher rank " + }, + { + "bbox": [ + 46, + 72, + 289, + 190 + ], + "type": "inline_equation", + "content": "T^P = \\{t_n^P\\}_{n=1}^K = \\{t_l\\}_{l=1}^K" + }, + { + "bbox": [ + 46, + 72, + 289, + 190 + ], + "type": "text", + "content": " and negative tags being the (relatively) irrelevant tags with lower rank " + }, + { + "bbox": [ + 46, + 72, + 289, + 190 + ], + "type": "inline_equation", + "content": "T^N = \\{t_l^N\\}_{l=1}^K = \\{t_l\\}_{l=K+1}^{2K}" + }, + { + "bbox": [ + 46, + 72, + 289, + 190 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 72, + 289, + 190 + ], + "type": "inline_equation", + "content": "M = 2K" + }, + { + "bbox": [ + 46, + 72, + 289, + 190 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 190, + 289, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 190, + 289, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 190, + 289, + 297 + ], + "type": "text", + "content": "Here we propose a simple yet effective augmentation technique. Having a set of visual semantics extracted for each image, instead of considering all the visual semantics at once, we sample randomly a fraction of these augmented tags at each iteration step. Hence, we could not only prevent the model from overfitting on specific semantics and potentially disregard the image or other semantics during training, but also let the model see different combinations of visual semantics, which helps to have more diversity." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 304, + 219, + 316 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 304, + 219, + 316 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 219, + 316 + ], + "type": "text", + "content": "5.2. Relative Contrastive Alignment" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 322, + 287, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 322, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 322, + 287, + 392 + ], + "type": "text", + "content": "InfoNCE [21] is a typical type of contrastive loss function used for self-supervised learning that contrasts one positive sample against a set of negative samples. CPG [10] builds upon InfoNCE and proposes a compatibility function for regions and a caption word. Both InfoNCE and CPG utilize the absolute relevance to optimize the contrastive loss." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 392, + 287, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 287, + 463 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 287, + 463 + ], + "type": "text", + "content": "However, such a contrastive learning objective is hard to optimize for object tags since they may be highly correlated to each other. In RCA-NOC, we focus on the relative semantic relevance and utilize the attention-based compatibility function to measure the relativity information for regions and a set of object tags, which is more robust to data noise." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 463, + 287, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 463, + 287, + 487 + ], + "spans": [ + { + "bbox": [ + 46, + 463, + 287, + 487 + ], + "type": "text", + "content": "Specifically, we first compute the dot product for a region-tag pair." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 129, + 488, + 287, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 488, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 129, + 488, + 287, + 506 + ], + "type": "interline_equation", + "content": "s _ {j k} = \\mathbf {w} _ {j} ^ {T} \\mathbf {v} _ {k} / \\sqrt {d}, \\tag {8}", + "image_path": "f2fbc81abe0a510ec28190ccd3abc1b36b8a1c0887c3ead834c5d65a1387e413.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_j" + }, + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_k" + }, + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "text", + "content": " refer to the corresponding embeddings for tag and region, and " + }, + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "text", + "content": " is the feature dimension. Here, " + }, + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "inline_equation", + "content": "s_{jk}" + }, + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "text", + "content": " represents the similarity between the " + }, + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "text", + "content": "-th tag and the " + }, + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "text", + "content": "-th region. To find a contextualized region representation for the " + }, + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "text", + "content": "-th tag, we define " + }, + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_j^v" + }, + { + "bbox": [ + 46, + 509, + 287, + 568 + ], + "type": "text", + "content": " as follows." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 132, + 570, + 287, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 570, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 132, + 570, + 287, + 601 + ], + "type": "interline_equation", + "content": "\\mathbf {a} _ {j} ^ {v} = \\sum_ {k = 1} ^ {K} \\alpha_ {j k} \\mathbf {v} _ {k}, \\tag {9}", + "image_path": "5aeab8b3efbe4965b6c72a15a82a143862943fb04babc4ea6d9ce781919629ee.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 602, + 287, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 602, + 287, + 631 + ], + "spans": [ + { + "bbox": [ + 47, + 602, + 287, + 631 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 602, + 287, + 631 + ], + "type": "inline_equation", + "content": "\\alpha_{jk} = \\frac{e^{s_{jk}}}{\\sum_{k'=1}^{K} e^{s_{jk'}}}," + }, + { + "bbox": [ + 47, + 602, + 287, + 631 + ], + "type": "text", + "content": " (10)" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 635, + 287, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 287, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 287, + 659 + ], + "type": "text", + "content": "To measure the compatibility between a tag " + }, + { + "bbox": [ + 47, + 635, + 287, + 659 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_j" + }, + { + "bbox": [ + 47, + 635, + 287, + 659 + ], + "type": "text", + "content": " and its contextualized region representation " + }, + { + "bbox": [ + 47, + 635, + 287, + 659 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_j^v" + }, + { + "bbox": [ + 47, + 635, + 287, + 659 + ], + "type": "text", + "content": ", we define" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 127, + 669, + 287, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 669, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 127, + 669, + 287, + 685 + ], + "type": "interline_equation", + "content": "\\phi (\\mathbf {V}, \\mathbf {w} _ {j}) = \\mathbf {w} _ {j} ^ {T} \\mathbf {a} _ {j} ^ {v}. \\tag {11}", + "image_path": "ef9ed33abba3f25598121e7d84253ba61dc9bc2acfd0f9bcf780c9bc10c5eb09.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "In this way, we can derive our cross-modality contrastive loss function " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "L_{cross}" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 341, + 91, + 545, + 138 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 91, + 545, + 138 + ], + "spans": [ + { + "bbox": [ + 341, + 91, + 545, + 138 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {c r o s s}} (\\mathbf {V}, \\mathbf {W} ^ {P}, \\mathbf {W} ^ {N}) = \\\\ - \\frac {1}{K} \\sum_ {n = 1} ^ {K} \\log \\left(\\frac {e ^ {\\phi (\\mathbf {V} , \\mathbf {w} _ {n} ^ {P})}}{e ^ {\\phi (\\mathbf {V} , \\mathbf {w} _ {n} ^ {P})} + \\sum_ {l = 1} ^ {K} e ^ {\\phi (\\mathbf {V} , \\mathbf {w} _ {l} ^ {N})}}\\right), \\tag {12} \\\\ \\end{array}", + "image_path": "0886b48353abd680a8fb3c30d61afc8e68ca2114133c06fb9e3767f836cc384e.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 148, + 545, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 148, + 545, + 194 + ], + "spans": [ + { + "bbox": [ + 304, + 148, + 545, + 194 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 148, + 545, + 194 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^P = \\{\\mathbf{w}_l^P\\}_{l=1}^K" + }, + { + "bbox": [ + 304, + 148, + 545, + 194 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 148, + 545, + 194 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^N = \\{\\mathbf{w}_n^N\\}_{n=1}^K" + }, + { + "bbox": [ + 304, + 148, + 545, + 194 + ], + "type": "text", + "content": " are the word embeddings for positives/negatives " + }, + { + "bbox": [ + 304, + 148, + 545, + 194 + ], + "type": "inline_equation", + "content": "T^P" + }, + { + "bbox": [ + 304, + 148, + 545, + 194 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 148, + 545, + 194 + ], + "type": "inline_equation", + "content": "T^N" + }, + { + "bbox": [ + 304, + 148, + 545, + 194 + ], + "type": "text", + "content": ", extracted from CLIP. " + }, + { + "bbox": [ + 304, + 148, + 545, + 194 + ], + "type": "inline_equation", + "content": "\\phi()" + }, + { + "bbox": [ + 304, + 148, + 545, + 194 + ], + "type": "text", + "content": " is the compatibility function defined in Eq. 11." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 195, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 195, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 195, + 545, + 300 + ], + "type": "text", + "content": "This equation encourages each positive tag " + }, + { + "bbox": [ + 304, + 195, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_n^P" + }, + { + "bbox": [ + 304, + 195, + 545, + 300 + ], + "type": "text", + "content": " to be more compatible with image regions " + }, + { + "bbox": [ + 304, + 195, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 304, + 195, + 545, + 300 + ], + "type": "text", + "content": " than all negative tags in " + }, + { + "bbox": [ + 304, + 195, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^N" + }, + { + "bbox": [ + 304, + 195, + 545, + 300 + ], + "type": "text", + "content": ". Essentially, if tag " + }, + { + "bbox": [ + 304, + 195, + 545, + 300 + ], + "type": "inline_equation", + "content": "t_j" + }, + { + "bbox": [ + 304, + 195, + 545, + 300 + ], + "type": "text", + "content": " is not relevant to the image (negative), its representation " + }, + { + "bbox": [ + 304, + 195, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_j" + }, + { + "bbox": [ + 304, + 195, + 545, + 300 + ], + "type": "text", + "content": " should not be similar to its contextualized region representation " + }, + { + "bbox": [ + 304, + 195, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_j^v" + }, + { + "bbox": [ + 304, + 195, + 545, + 300 + ], + "type": "text", + "content": " since it would not be able to collect good information while computing " + }, + { + "bbox": [ + 304, + 195, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_j^v" + }, + { + "bbox": [ + 304, + 195, + 545, + 300 + ], + "type": "text", + "content": ". Note that we do not let two positive tags (top-ranked tags) contrast with each other as it is hard to tell which one is more relevant." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 301, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 545, + 418 + ], + "type": "text", + "content": "Inner modality Alignment. To further enhance modality alignment, we also compute the inner-modality contrastive loss over tag-caption pairs. The formulation for inner-modality contrastive loss is similar to cross-modality contrastive loss but slightly different. We enforce contrastive learning not to be between tags and all caption words, but just between tags and noun caption words. This is because a caption may have many irrelevant tokens, such as \"the, a, is\", which will harm our alignment process and cause redundant computational costs." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 418, + 545, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 443 + ], + "type": "text", + "content": "Finally, we can derive our inner-modality contrastive loss function " + }, + { + "bbox": [ + 304, + 418, + 545, + 443 + ], + "type": "inline_equation", + "content": "L_{inner}" + }, + { + "bbox": [ + 304, + 418, + 545, + 443 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 387, + 449, + 545, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 449, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 387, + 449, + 545, + 464 + ], + "type": "interline_equation", + "content": "\\phi (\\mathbf {C}, \\mathbf {w} _ {l}) = \\mathbf {w} _ {l} ^ {T} \\mathbf {a} _ {l} ^ {c}, \\tag {13}", + "image_path": "badc2a7bc1923c8b70d42ee4c5265b14d8e5bf6400cfb12556a4905da609e067.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 341, + 477, + 545, + 524 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 477, + 545, + 524 + ], + "spans": [ + { + "bbox": [ + 341, + 477, + 545, + 524 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {i n n e r}} (\\mathbf {C}, \\mathbf {W} ^ {P}, \\mathbf {W} ^ {N}) = \\\\ - \\frac {1}{K} \\sum_ {n = 1} ^ {K} \\log \\left(\\frac {e ^ {\\phi (\\mathbf {C} , \\mathbf {w} _ {n} ^ {P})}}{e ^ {\\phi (\\mathbf {C} , \\mathbf {w} _ {n} ^ {P})} + \\sum_ {l = 1} ^ {K} e ^ {\\phi (\\mathbf {C} , \\mathbf {w} _ {l} ^ {N})}}\\right), \\tag {14} \\\\ \\end{array}", + "image_path": "45ac9cad2d1bd9f752e9360e051b51dee2c37efe7c7ce67f4dd13aa28aca182e.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 532, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 545, + 590 + ], + "type": "text", + "content": "where this time we take noun caption words " + }, + { + "bbox": [ + 304, + 532, + 545, + 590 + ], + "type": "inline_equation", + "content": "\\mathbf{C} = \\{\\mathbf{c}_i\\}_{i=1}^P" + }, + { + "bbox": [ + 304, + 532, + 545, + 590 + ], + "type": "text", + "content": " in Eq. 13 as input. By further considering inner-modality alignment, we not only learn caption-tag semantics to connect relevant caption tokens, but also enable region-caption interactions." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 599, + 545, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 545, + 613 + ], + "type": "text", + "content": "5.3. Uncertainty-Aware Selection and Re-weighting" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 618, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 677 + ], + "type": "text", + "content": "The augmented contrastive tags are often noisy and would harm the discriminative ability and robustness of the contrastive learning process. Therefore, we design a sample selection strategy to deal with noisy contrastive tags (e.g., false positives/negatives)." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 678, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 678, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 678, + 545, + 713 + ], + "type": "text", + "content": "Uncertainty-Aware Selection. Specifically, we first use the local cosine similarity to calculate the correlation between a region and a tag and filter false positives/negatives. The" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15514" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "content": "stronger the correlation, the more reliable a positive tag is and the more uncertain a negative tag." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 124, + 96, + 287, + 124 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 96, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 124, + 96, + 287, + 124 + ], + "type": "interline_equation", + "content": "\\mathrm {u} (\\mathbf {v}, \\mathbf {w}) = \\frac {\\mathbf {v} ^ {\\top} \\mathbf {w}}{\\| \\mathbf {v} \\| \\| \\mathbf {w} \\|}, \\tag {15}", + "image_path": "721f362a727bb29ab491730a409ca06d2f7c5c3438ee52d53ac8904810783edd.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 131, + 287, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 131, + 287, + 180 + ], + "spans": [ + { + "bbox": [ + 47, + 131, + 287, + 180 + ], + "type": "text", + "content": "Then we retrieve " + }, + { + "bbox": [ + 47, + 131, + 287, + 180 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 47, + 131, + 287, + 180 + ], + "type": "text", + "content": " tags and their corresponding representations " + }, + { + "bbox": [ + 47, + 131, + 287, + 180 + ], + "type": "inline_equation", + "content": "\\mathbf{H} = \\{\\mathbf{w}_j\\}_{j=1}^L" + }, + { + "bbox": [ + 47, + 131, + 287, + 180 + ], + "type": "text", + "content": " for the given " + }, + { + "bbox": [ + 47, + 131, + 287, + 180 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 47, + 131, + 287, + 180 + ], + "type": "text", + "content": " region features " + }, + { + "bbox": [ + 47, + 131, + 287, + 180 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{v}_i\\}_{i=1}^L" + }, + { + "bbox": [ + 47, + 131, + 287, + 180 + ], + "type": "text", + "content": ". We use arg max to choose the most correlated tag " + }, + { + "bbox": [ + 47, + 131, + 287, + 180 + ], + "type": "inline_equation", + "content": "t_j" + }, + { + "bbox": [ + 47, + 131, + 287, + 180 + ], + "type": "text", + "content": " for region " + }, + { + "bbox": [ + 47, + 131, + 287, + 180 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 47, + 131, + 287, + 180 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 115, + 188, + 287, + 207 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 188, + 287, + 207 + ], + "spans": [ + { + "bbox": [ + 115, + 188, + 287, + 207 + ], + "type": "interline_equation", + "content": "j = \\underset {k} {\\arg \\max } \\left(\\mathrm {u} \\left(\\mathbf {v} _ {i}, \\mathbf {w} _ {k}\\right)\\right), \\tag {16}", + "image_path": "b15c7dfcef3f9b59f5464e3667f5e6fb4c7f5ae88259d309db0088b99ce53843.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 216, + 288, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 288, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 288, + 380 + ], + "type": "text", + "content": "According to the score in Eq. 15, the corresponding top-L tags will be listed as confusion samples for negatives (actually positive), and these confusion samples will be removed from the original contrastive tags. Similarly, we will also choose the true positives based on these top- " + }, + { + "bbox": [ + 46, + 216, + 288, + 380 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 216, + 288, + 380 + ], + "type": "text", + "content": " tags since tags with low-similarity scores should be regarded as outliers to the positives and they are too sparse to have a positive influence on the shape of embedding space. In this way, we can derive Eq. 17, where / is the removing set operation, " + }, + { + "bbox": [ + 46, + 216, + 288, + 380 + ], + "type": "inline_equation", + "content": "\\cap" + }, + { + "bbox": [ + 46, + 216, + 288, + 380 + ], + "type": "text", + "content": " is the intersection set operation. " + }, + { + "bbox": [ + 46, + 216, + 288, + 380 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{W}}^P = \\{\\bar{\\mathbf{w}}_l^P\\}_{l=1}^K" + }, + { + "bbox": [ + 46, + 216, + 288, + 380 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 216, + 288, + 380 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{W}}^N = \\{\\bar{\\mathbf{w}}_n^N\\}_{n=1}^K" + }, + { + "bbox": [ + 46, + 216, + 288, + 380 + ], + "type": "text", + "content": " is the final positive/negative tags' embedding sets. Note that if the set length of " + }, + { + "bbox": [ + 46, + 216, + 288, + 380 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{W}}^P / \\overline{\\mathbf{W}}^N" + }, + { + "bbox": [ + 46, + 216, + 288, + 380 + ], + "type": "text", + "content": " is less than M, we will over-sample " + }, + { + "bbox": [ + 46, + 216, + 288, + 380 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{W}}^P / \\overline{\\mathbf{W}}^N" + }, + { + "bbox": [ + 46, + 216, + 288, + 380 + ], + "type": "text", + "content": " until the set length is equal to M." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 384, + 287, + 398 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 384, + 287, + 398 + ], + "spans": [ + { + "bbox": [ + 104, + 384, + 287, + 398 + ], + "type": "interline_equation", + "content": "\\overline {{\\mathbf {W}}} ^ {P} = \\mathbf {W} ^ {P} \\cap \\mathbf {H}, \\overline {{\\mathbf {W}}} ^ {N} = \\mathbf {W} ^ {N} / \\mathbf {H}, \\tag {17}", + "image_path": "fc60f8018a2cd616103554c910e8c5a1d3d995c1db442475f25e7ee9b1b289e2.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 402, + 287, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 484 + ], + "type": "text", + "content": "Uncertainty-Aware Re-weighting. To further mitigate the negative effect of noisy tags, we use the correlation function defined above to enhance reliable samples and reduce the influence of high-uncertainty samples. The information from more reliable samples should have a larger impact on the shape of the embedding and vice versa. Specifically, we first introduce the weight in Eq. 18." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 108, + 491, + 287, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 491, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 108, + 491, + 287, + 506 + ], + "type": "interline_equation", + "content": "q _ {1} \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right) = \\exp \\left(\\mathrm {u} \\left(\\mathbf {v} _ {k}, \\bar {\\mathbf {w}} _ {n} ^ {P}\\right)\\right), \\tag {18}", + "image_path": "03e23c52f0c425df5c712bda943902aa37c3b78bd6a610cb7c96aadb86d29021.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 113, + 517, + 287, + 537 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 517, + 287, + 537 + ], + "spans": [ + { + "bbox": [ + 113, + 517, + 287, + 537 + ], + "type": "interline_equation", + "content": "j = \\underset {k} {\\arg \\max } \\left(\\mathrm {u} \\left(\\mathbf {v} _ {i}, \\bar {\\mathbf {w}} _ {k} ^ {P}\\right)\\right), \\tag {19}", + "image_path": "b8f00e57998937f85c3569001fa23849153218880f1ec92e0fb8e669c90f82f6.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 131, + 543, + 287, + 558 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 131, + 543, + 287, + 558 + ], + "spans": [ + { + "bbox": [ + 131, + 543, + 287, + 558 + ], + "type": "interline_equation", + "content": "q _ {2} \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right) = p \\left(t _ {n}\\right), \\tag {20}", + "image_path": "9d65dd6dfc277798da5305a36ad1430d5650879fc683635b214aa34f2b5f4ff9.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 567, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 649 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 567, + 287, + 649 + ], + "type": "inline_equation", + "content": "q_{1}(\\bar{\\mathbf{w}}_{n}^{P})" + }, + { + "bbox": [ + 46, + 567, + 287, + 649 + ], + "type": "text", + "content": " in Eq. 18 is the uncertainty score computed by the most relevant region with the corresponding tag. Moreover, we further consider how certain each tag is and combine the corresponding score " + }, + { + "bbox": [ + 46, + 567, + 287, + 649 + ], + "type": "inline_equation", + "content": "q_{2}(\\bar{\\mathbf{w}}_{n}^{P})" + }, + { + "bbox": [ + 46, + 567, + 287, + 649 + ], + "type": "text", + "content": " in Eq. 20 with " + }, + { + "bbox": [ + 46, + 567, + 287, + 649 + ], + "type": "inline_equation", + "content": "q_{1}(\\bar{\\mathbf{w}}_{n}^{P})" + }, + { + "bbox": [ + 46, + 567, + 287, + 649 + ], + "type": "text", + "content": " to derive the final uncertainty score " + }, + { + "bbox": [ + 46, + 567, + 287, + 649 + ], + "type": "inline_equation", + "content": "q(\\bar{\\mathbf{w}}_{n}^{P})" + }, + { + "bbox": [ + 46, + 567, + 287, + 649 + ], + "type": "text", + "content": " in Eq. 21. Here " + }, + { + "bbox": [ + 46, + 567, + 287, + 649 + ], + "type": "inline_equation", + "content": "p(t_{n})" + }, + { + "bbox": [ + 46, + 567, + 287, + 649 + ], + "type": "text", + "content": " in Eq. 20 is the global similarity mentioned in Section 5.1." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 108, + 657, + 287, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 657, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 108, + 657, + 287, + 673 + ], + "type": "interline_equation", + "content": "q \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right) = q _ {1} \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right) * q _ {2} \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right), \\tag {21}", + "image_path": "8e4fbec2a1be43a3b9e1c5d821b5b53741765ec374386dd205c7ffc875938d79.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 680, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 680, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 680, + 287, + 714 + ], + "type": "text", + "content": "Thus, our method could mitigate the negative effect of noisy contrastive tags by considering the similarity from both the local region features (region-tag) and the" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "global structural information (image-tag). Finally, we could rewrite our contrastive loss function in Eq. 22, Eq. 23." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 382, + 106, + 470, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 106, + 470, + 121 + ], + "spans": [ + { + "bbox": [ + 382, + 106, + 470, + 121 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c r o s s}} \\left(\\mathbf {V}, \\overline {{\\mathbf {W}}} ^ {P}, \\overline {{\\mathbf {W}}} ^ {N}\\right) =", + "image_path": "964c2086a2b149f40879b562e2c19d57e2f8485d4cf5b7bce684e5cf0c65bf92.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 316, + 124, + 545, + 153 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 124, + 545, + 153 + ], + "spans": [ + { + "bbox": [ + 316, + 124, + 545, + 153 + ], + "type": "interline_equation", + "content": "- \\frac {1}{K} \\sum_ {n = 1} ^ {K} - q \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right) \\log \\left(\\frac {e ^ {\\phi \\left(\\mathbf {V} , \\bar {\\mathbf {w}} _ {n} ^ {P}\\right)}}{e ^ {\\phi \\left(\\mathbf {V} , \\bar {\\mathbf {w}} _ {n} ^ {P}\\right)} + \\sum_ {l = 1} ^ {K} e ^ {\\phi \\left(\\mathbf {V} , \\bar {\\mathbf {w}} _ {l} ^ {N}\\right)}}\\right), \\tag {22}", + "image_path": "f477d4fa4b651d4ad7bd37fb88f3c9112fa7ac074c63a78c162186b88bd20111.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 316, + 167, + 545, + 214 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 167, + 545, + 214 + ], + "spans": [ + { + "bbox": [ + 316, + 167, + 545, + 214 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {i n n e r}} \\left(\\mathbf {C}, \\overline {{\\mathbf {W}}} ^ {P}, \\overline {{\\mathbf {W}}} ^ {N}\\right) = \\\\ - \\frac {1}{K} \\sum_ {n = 1} ^ {K} - q \\left(\\bar {\\mathbf {w}} _ {n} ^ {P}\\right) \\log \\left(\\frac {e ^ {\\phi \\left(\\mathbf {C} , \\bar {\\mathbf {w}} _ {n} ^ {P}\\right)}}{e ^ {\\phi \\left(\\mathbf {C} , \\bar {\\mathbf {w}} _ {n} ^ {P}\\right)} + \\sum_ {l = 1} ^ {K} e ^ {\\phi \\left(\\mathbf {C} , \\bar {\\mathbf {w}} _ {l} ^ {N}\\right)}}\\right), \\tag {23} \\\\ \\end{array}", + "image_path": "3ed91bdb6549ea1298009196c7d8f3f5fc75e524a9740994dba99591e9d206c1.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 217, + 386, + 230 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 217, + 386, + 230 + ], + "spans": [ + { + "bbox": [ + 306, + 217, + 386, + 230 + ], + "type": "text", + "content": "6. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 236, + 422, + 249 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 236, + 422, + 249 + ], + "spans": [ + { + "bbox": [ + 306, + 236, + 422, + 249 + ], + "type": "text", + "content": "6.1. Experimental Setup" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 254, + 545, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 254, + 545, + 476 + ], + "spans": [ + { + "bbox": [ + 304, + 254, + 545, + 476 + ], + "type": "text", + "content": "Datasets. Our main experiments and ablation studies are based on the Nocaps [2] dataset. Our method was built with PyTorch, and we used a pre-trained BERT-base model from Huggingfaces [1] for parameters initialization, and no ground-truth tags are used on the Nocaps validation and test sets. For the training stage, we use the COCO training set which consists of 118K images, each with 5 captions. We evaluate our model on the validation and test sets of the Nocaps dataset, which consist of 4.5K and 10.6K images from the Open Images validation and test sets, respectively. Additionally, we test the proposed method on the Held-Out COCO [12], which is a subset of MS COCO [19] where the following eight object categories are excluded from the training set: bottle, bus, couch, microwave, pizza, racket, suitcase, and zebra. We randomly split the COCO validation set and use half of it for validation and the other half for testing, each with 20,252 images. In addition, we empirically set " + }, + { + "bbox": [ + 304, + 254, + 545, + 476 + ], + "type": "inline_equation", + "content": "M = 50" + }, + { + "bbox": [ + 304, + 254, + 545, + 476 + ], + "type": "text", + "content": " to generate augmented object tags for the best performance." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 476, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 476, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 476, + 545, + 594 + ], + "type": "text", + "content": "Implementation Details. In the training stage, the model is trained for 30 epochs with a batch size of 512 and a learning rate of " + }, + { + "bbox": [ + 304, + 476, + 545, + 594 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 304, + 476, + 545, + 594 + ], + "type": "text", + "content": ", optimized using the cross-entropy loss and our contrastive loss. We set the maximum caption length to 40 and the maximum tag length to 30. To further boost the performance, we also perform the SCST optimization (Rennie et al. [24]) with a learning rate of " + }, + { + "bbox": [ + 304, + 476, + 545, + 594 + ], + "type": "inline_equation", + "content": "1.4 \\times 10^{-6}" + }, + { + "bbox": [ + 304, + 476, + 545, + 594 + ], + "type": "text", + "content": " for 10 epochs. During inference, we use greedy decoding to generate image captions with a maximum length of 20. Our model is trained with 8 A100 GPUS and takes 1 day to train." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 601, + 441, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 601, + 441, + 613 + ], + "spans": [ + { + "bbox": [ + 306, + 601, + 441, + 613 + ], + "type": "text", + "content": "6.2. Quantitative evaluation." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 619, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 619, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 619, + 545, + 714 + ], + "type": "text", + "content": "Results on Nocaps dataset. In this section, we extensively compare our frameworks with previous methods on the Nocaps benchmark. The other compared state-of-art results are from NOC-REK [29]. Note that all the methods use the BERT-base [9] for a fair comparison. We compare our method with UpDown [2, 5], OSCAR [18], VinVL [35], VIVO [13], and NOC-REK [29], which hold the state-of-the-art result on the Nocaps benchmark. The training data" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15515" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 121, + 545, + 270 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 114 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 114 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 114 + ], + "type": "text", + "content": "Table 1. Our evaluation results using SPICE and CIDEr on the Nocaps validation and test sets. We achieve the best scores for in-domain, near-domain, out-domain and Overall. Notably, the captions generated by our method are better than those by human in most cases. We note that our results on the test set are better than those by other methods which are publicly submitted to Nocaps leader-boardb. Higher score is better." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 121, + 545, + 270 + ], + "lines": [ + { + "bbox": [ + 48, + 121, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 48, + 121, + 545, + 270 + ], + "type": "table", + "html": "
MethodValidation setTest set
in-domainnear-domainout-domainOverallin-domainnear-domainout-domainOverall
CIDErSPICECIDErSPICECIDErSPICECIDErSPICECIDErSPICECIDErSPICECIDErSPICECIDErSPICE
UpDown [4]78.111.657.710.331.38.355.310.176.011.874.211.566.79.773.111.2
Oscar [18]83.412.081.612.077.610.681.111.781.311.979.611.973.610.678.811.7
VIVO [13]92.212.987.812.687.511.588.312.489.012.987.812.680.111.186.612.4
VinVL [35]96.813.590.713.187.411.690.912.893.813.389.012.866.110.985.512.5
VinVL + VIVO [13,35]103.713.795.613.483.811.994.313.198.013.695.213.478.011.592.513.1
NOC-REK [29]104.714.8100.214.1100.713.0100.914.0100.014.195.713.677.411.693.013.4
RCA-NOC**95.013.691.313.193.212.192.213.087.713.388.112.977.911.486.312.7
RCA-NOC107.815.3104.014.6105.813.6107.114.6104.114.8101.214.688.512.9101.114.0
Δ3.1↑0.5↑4.2↑0.5↑5.1↑0.6↑6.2↑0.6↑4.1↑0.7↑5.5↑1.0↑11.1↑1.3↑8.1↑0.6↑
Human [2]84.414.385.014.395.714.087.114.280.615.084.614.791.614.285.314.6
", + "image_path": "966ef07c5f0da061eeb024a8fec75d4ab2af99198894e5463d55827fae622d7e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 72, + 335, + 260, + 389 + ], + "blocks": [ + { + "bbox": [ + 46, + 275, + 288, + 330 + ], + "lines": [ + { + "bbox": [ + 46, + 275, + 288, + 330 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 288, + 330 + ], + "type": "text", + "content": "Table 2. Comparison of F1-scores (in %) on object classes of Open Images, evaluated on the Nocaps validation set. There are 504 classes in total. 80 of them are in-domain, which are common classes from COCO. The remaining 424 classes are the out-of-domain objects." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 72, + 335, + 260, + 389 + ], + "lines": [ + { + "bbox": [ + 72, + 335, + 260, + 389 + ], + "spans": [ + { + "bbox": [ + 72, + 335, + 260, + 389 + ], + "type": "table", + "html": "
modelin-domainout-of-domainentire
VIVO39.229.130.4
NOC-REK45.330.532.8
Ours58.639.243.1
", + "image_path": "92c56a0bb4a719325d80a3b0186af70f78ecd1759b840cf966e5d1d1d44ca1a9.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 402, + 287, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 450 + ], + "type": "text", + "content": "for the baselines is the COCO dataset. Following prior settings, we also report the results after the model is optimized using SCST [24]. Our generated captions also adopt Constrained Beam Search (CBS) following [3]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 452, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 452, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 452, + 287, + 664 + ], + "type": "text", + "content": "In Table 1, we present our results of SPICE and CIDEr scores on the Nocaps validation and test sets. We also show the results of our different training stages in the middle of the table, where RCA-NOC** denotes our first training stage result and RCA-NOC is our final result after CIDEr optimization. Note that we do not compare with the data-driven methods [17, 30, 34] which use massive out-of-domain image-caption pairs in the training and fail to follow the rule of Nocaps. By leveraging relative semantic relevance in contrastive learning, our method has achieved a significant improvement compared to all prior works. It is worth noting that our first stage training could generate a comparable result with [13, 18, 35]. After the CIDEr optimization process, our method could outperform the recent state-of-art method NOC-REK [29] with a large margin, which is 8.1 and 0.6 (CIDEr and SPICE) better than [29] on the Nocaps Test set. This suggests that our model is more capable of generating captions with novel objects." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "content": "To quantitatively evaluate how well the model can describe novel objects, we also calculate the F1-score between our generated and the ground-truth tags on the validation set. Table 2 shows the comparison with VIVO and NOC-" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 321, + 299, + 529, + 399 + ], + "blocks": [ + { + "bbox": [ + 305, + 275, + 545, + 297 + ], + "lines": [ + { + "bbox": [ + 305, + 275, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 305, + 275, + 545, + 297 + ], + "type": "text", + "content": "Table 3. Evaluation results on the Held-Out COCO test set. The best results are highlighted in red." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 299, + 529, + 399 + ], + "lines": [ + { + "bbox": [ + 321, + 299, + 529, + 399 + ], + "spans": [ + { + "bbox": [ + 321, + 299, + 529, + 399 + ], + "type": "table", + "html": "
MethodAvg. F1-scoreSPICEMeteorCIDEr
NOC48.8-21.4-
NBT48.515.722.877.0
DNOC57.9-21.6-
ZSC29.814.221.9-
ANOC64.318.225.294.7
VinVL+VIVO71.824.530.6132.8
NOC-REK76.326.932.8138.4
RCA-NOc79.527.035.9142.8
", + "image_path": "8759125f84a77c793b32f5368f25dbe919147e84b0db7c65cb191c9733b10172.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 410, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 410, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 545, + 468 + ], + "type": "text", + "content": "REK on the Nocaps validation set. We see that RCA-NOC improves NOC-REK and VIVO on F1-score substantially, especially for out-of-domain objects. This again verifies the effectiveness of RCA-NOC's discriminative ability to describe and distinguish novel objects." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 469, + 546, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 469, + 546, + 646 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 546, + 646 + ], + "type": "text", + "content": "Results on the Held-Out COCO dataset. To further prove the generalization ability of our method, we also conduct experiments on the Held-Out COCO dataset. As we can see from Table 3, our method consistently beats the baseline VinVL+VIVO with a large margin. The improvements are 7.7, 2.5, 5.3, and 10.0 with BERT-base on the F1, SPICE, METEOR, and CIDEr metrics. Additionally, our method is superior to all other state-of-art methods. In particular, compared with the recent state-of-art method NOC-REK [29], the recent state-of-art on the Held-Out COCO dataset, RCA-NOC achieves a 4.4 improvement on CIDEr (from 138.4 to 142.8) and 3.1 improvement on METEOR (from 32.8 to 35.9). The 3.2 improvement on the F1 score also shows that RCA-NOC performs better in describing novel objects." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 659, + 400, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 400, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 400, + 672 + ], + "type": "text", + "content": "6.3. Ablation study." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "content": "In this subsection, we will discuss every component's contribution to our framework. If not mentioned by purpose, all methods are conducted on the Nocaps validation" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15516" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 69, + 84, + 264, + 149 + ], + "blocks": [ + { + "bbox": [ + 65, + 71, + 268, + 81 + ], + "lines": [ + { + "bbox": [ + 65, + 71, + 268, + 81 + ], + "spans": [ + { + "bbox": [ + 65, + 71, + 268, + 81 + ], + "type": "text", + "content": "Table 4. Effectiveness of the source of visual semantics." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 69, + 84, + 264, + 149 + ], + "lines": [ + { + "bbox": [ + 69, + 84, + 264, + 149 + ], + "spans": [ + { + "bbox": [ + 69, + 84, + 264, + 149 + ], + "type": "table", + "html": "
Methodin-domainnear-domainout-of-domainOverall
CIDErSPICECIDErSPICECIDErSPICECIDErSPICE
N.A.103.614.7100.814.2100.913.2103.214.2
NOC-REK103.914.9101.614.3102.013.4103.414.3
VIVO105.215.1103.514.4103.613.4105.214.4
CLIP107.815.3104.014.6105.813.6107.114.6
", + "image_path": "c7e3ad6c617f794e7092864e788d959fe730270031202dd197fcdb1439726cbe.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 67, + 204, + 265, + 276 + ], + "blocks": [ + { + "bbox": [ + 47, + 156, + 287, + 199 + ], + "lines": [ + { + "bbox": [ + 47, + 156, + 287, + 199 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 287, + 199 + ], + "type": "text", + "content": "Table 5. Effectiveness of the UASR. UAR: Uncertainty-Aware Reweight, UAS: Uncertainty-Aware Selection, " + }, + { + "bbox": [ + 47, + 156, + 287, + 199 + ], + "type": "inline_equation", + "content": "UAS^{N}" + }, + { + "bbox": [ + 47, + 156, + 287, + 199 + ], + "type": "text", + "content": ": Uncertainty-Aware Selection for Negatives), UASR: Uncertainty-Aware Selection and Re-weight." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 67, + 204, + 265, + 276 + ], + "lines": [ + { + "bbox": [ + 67, + 204, + 265, + 276 + ], + "spans": [ + { + "bbox": [ + 67, + 204, + 265, + 276 + ], + "type": "table", + "html": "
Methodin-domainnear-domainout-of-domainOverall
CIDEr SPICECIDEr SPICECIDEr SPICECIDEr SPICE
N.A.103.614.7100.814.2100.913.2102.414.2
\\( UAS^N \\)105.214.8102.114.3102.413.3104.214.3
UAS105.915.0104.514.3103.913.4105.314.5
UAR104.314.8103.314.4104.713.3105.614.3
UASR107.815.3104.014.6105.813.6107.114.6
", + "image_path": "716ef64475395f24f20ff2845a984fd21762b234a0816ec579c11da7f66df4fa.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 287, + 286, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 287, + 286, + 310 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 286, + 310 + ], + "type": "text", + "content": "set with BERT-base. (we cannot use the Nocaps test set because only 5 times submissions are allowed for the test set)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 312, + 286, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 286, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 286, + 429 + ], + "type": "text", + "content": "Effectiveness of visual semantics. We enhance the modality alignment by incorporating visual semantics from foundational models, with a specific instantiation using CLIP. To evaluate the generalization ability of our approach, we modify the model to extract visual semantics and conduct further experiments to compare it with NOC-REK [29] and VIVO for generating visual semantics. Our baseline model is trained using a contrastive approach that ranks ROI tags extracted from Faster R-CNN based on their softmax values, distinguishing between relevant and irrelevant tags." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 430, + 286, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 286, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 286, + 653 + ], + "type": "text", + "content": "Our findings indicate that using NOC-REK to generate augmented tags provides only marginal improvement to our framework, resulting in a 0.8 and 0.1 (CIDEr and SPICE) increase compared to the baseline. We hypothesize that this limited improvement may be due to the restricted linguistic knowledge contained in BERT, which may not encompass a wide range of novel categories and lack higher-level and global concepts required to describe complex scenes. In contrast, utilizing a larger pool of noisy visual semantics (CLIP) extracted from captions leads to better results, with a 4.9 and 0.4 (CIDEr and SPICE) increase compared to the baseline. Using a smaller and cleaner pool of visual semantics extracted from the classes of various object detection datasets (VIVO) only results in a 2.0 and 0.2 (CIDEr and SPICE) increase compared to the baseline. This is likely due to the fact that the CLIP is pre-trained on vast amounts of training data, enabling it to extract a more diverse, extensive, and semantically meaningful set of high-level visual concepts compared to NOC-REK." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "text", + "content": "Effectiveness of the UASR. We investigate the performance of our Uncertainty-Aware Selection and Reweighting (UASR) on the Nocaps validation set in this part. Table 5 shows that Uncertainty-Aware Reweighting (UAR) could effectively enhance the reliable contrastive samples" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 322, + 94, + 529, + 141 + ], + "blocks": [ + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "lines": [ + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "type": "text", + "content": "Table 6. Evaluation on COCO test set of Karpathy split [15]. All results are based on single model with cross-entropy optimization." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 322, + 94, + 529, + 141 + ], + "lines": [ + { + "bbox": [ + 322, + 94, + 529, + 141 + ], + "spans": [ + { + "bbox": [ + 322, + 94, + 529, + 141 + ], + "type": "table", + "html": "
pre-trainingBLEU4MeteorCIDErSPICE
N.A33.828.1118.321.2
OSCAR + VIVO34.928.4119.821.7
RCA-NOC37.429.6128.423.1
", + "image_path": "addfb202e14ab6d40796995f860c0f3fb2164cc29d56a2fc6fe14af3d478ae9d.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 319, + 214, + 531, + 274 + ], + "blocks": [ + { + "bbox": [ + 305, + 146, + 545, + 211 + ], + "lines": [ + { + "bbox": [ + 305, + 146, + 545, + 211 + ], + "spans": [ + { + "bbox": [ + 305, + 146, + 545, + 211 + ], + "type": "text", + "content": "Table 7. Ablation study on the effectiveness of different components, including (i) CA: Cross-modality Alignment, our prototype contrastive loss for region-tag pairs, (ii) IA: Inner-modality Alignment, (iii) CLIP: Without CLIP refers to extracting visual semantics with object detection, and (iv) UASR: Uncertainty-Aware Selection and Re-weighting." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 319, + 214, + 531, + 274 + ], + "lines": [ + { + "bbox": [ + 319, + 214, + 531, + 274 + ], + "spans": [ + { + "bbox": [ + 319, + 214, + 531, + 274 + ], + "type": "table", + "html": "
CAIAUASRCLIPCIDERSPICE
90.912.8
✓96.513.5
✓✓98.713.8
✓✓✓103.214.2
✓✓✓✓107.114.6
", + "image_path": "bf7b746039e23252c65bef820fd49115bbd4b9a1ddb3aaf26b4e9a56c7bc0bce.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 275, + 545, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 275, + 545, + 427 + ], + "spans": [ + { + "bbox": [ + 304, + 275, + 545, + 427 + ], + "type": "text", + "content": "and bring 3.2 and 0.1 boosts on CIDEr and SPICE. In addition, the false positives/negatives severely harm our training process. By further incorporating Uncertainty-Aware Selection for Negatives " + }, + { + "bbox": [ + 304, + 275, + 545, + 427 + ], + "type": "inline_equation", + "content": "(UAS^{N})" + }, + { + "bbox": [ + 304, + 275, + 545, + 427 + ], + "type": "text", + "content": " into our method and filtering false negatives, our model's performance is boosted to 104.2 and 14.3 on CIDEr and SPICE. When filtering false positives/negatives simultaneously, we could reach 105.3 and 14.5 on CIDEr and SPICE with Uncertainty-Aware Selection (UAS). Finally, our method improves the performance by 4.7 and 0.4 (CIDEr and SPICE) by combining UAR and UAS, which illustrates the proposed UASR is a more powerful tool for tackling noisy contrastive samples in NOC." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 435, + 418, + 448 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 435, + 418, + 448 + ], + "spans": [ + { + "bbox": [ + 306, + 435, + 418, + 448 + ], + "type": "text", + "content": "6.4. Qualitative Results" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 453, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 545, + 617 + ], + "type": "text", + "content": "In Figure 3, we display some qualitative results on Held-Out COCO and Nocaps, and all the approaches are based on BERT-base. On Held-Out COCO, the result compared with GT shows that our proposed method could effectively generate accurate and precise captions with novel objects by leveraging relative semantic relevance into training. On Nocaps, VinVL+VIVO [13, 35] sometimes cannot include the desired novel objects in their captions (first and third examples) or generate wrong captions (second example). Our RCA-NOC, on the other hand, successfully generates correct and coherent captions via differentiating confusing classes and aligning object detection with other modalities. For better illustration, we show top-5 Positive and Negative Tag results extracted from CLIP." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 624, + 454, + 638 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 624, + 454, + 638 + ], + "spans": [ + { + "bbox": [ + 306, + 624, + 454, + 638 + ], + "type": "text", + "content": "6.5. General Image Captioning" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 643, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 643, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 643, + 545, + 712 + ], + "type": "text", + "content": "Improving modality alignment is a shared objective of general image captioning tasks. As demonstrated in Table 6, our proposed method, RCL-NOC, improves the model's performance across all metrics assessed on the COCO test set, particularly in the CIDEr score. However, we have observed that the improvement on the COCO benchmark is" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15517" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 76, + 111, + 117 + ], + "blocks": [ + { + "bbox": [ + 50, + 76, + 111, + 117 + ], + "lines": [ + { + "bbox": [ + 50, + 76, + 111, + 117 + ], + "spans": [ + { + "bbox": [ + 50, + 76, + 111, + 117 + ], + "type": "image", + "image_path": "2320bd51d2972b870148cb0114702ed70317dda8e6c4ba745e4464be385f9363.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 111, + 75, + 219, + 83 + ], + "lines": [ + { + "bbox": [ + 111, + 75, + 219, + 83 + ], + "spans": [ + { + "bbox": [ + 111, + 75, + 219, + 83 + ], + "type": "text", + "content": "GT: A boy in a tie holding a small suitcase." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 112, + 89, + 252, + 98 + ], + "lines": [ + { + "bbox": [ + 112, + 89, + 252, + 98 + ], + "spans": [ + { + "bbox": [ + 112, + 89, + 252, + 98 + ], + "type": "text", + "content": "RCA-NOC: A young boy wearing a tie holding a suitcase." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 112, + 104, + 291, + 112 + ], + "lines": [ + { + "bbox": [ + 112, + 104, + 291, + 112 + ], + "spans": [ + { + "bbox": [ + 112, + 104, + 291, + 112 + ], + "type": "text", + "content": "PT: Person, human, tie, suitcase, dress*... (Person, human, suitcase, tie...)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 112, + 118, + 285, + 127 + ], + "lines": [ + { + "bbox": [ + 112, + 118, + 285, + 127 + ], + "spans": [ + { + "bbox": [ + 112, + 118, + 285, + 127 + ], + "type": "text", + "content": "NT: Hair*, chair, soda, step, umbrella ... (Chair, soda, step, umbrella...)" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 52, + 145, + 111, + 187 + ], + "blocks": [ + { + "bbox": [ + 52, + 145, + 111, + 187 + ], + "lines": [ + { + "bbox": [ + 52, + 145, + 111, + 187 + ], + "spans": [ + { + "bbox": [ + 52, + 145, + 111, + 187 + ], + "type": "image", + "image_path": "7967f96606f0b36458826f4222a6f89bfeecea206eab094854724b8898d2d6d4.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 111, + 146, + 258, + 155 + ], + "lines": [ + { + "bbox": [ + 111, + 146, + 258, + 155 + ], + "spans": [ + { + "bbox": [ + 111, + 146, + 258, + 155 + ], + "type": "text", + "content": "GT: 2 men sit on the couch, video game controllers in hands." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 111, + 161, + 291, + 176 + ], + "lines": [ + { + "bbox": [ + 111, + 161, + 291, + 176 + ], + "spans": [ + { + "bbox": [ + 111, + 161, + 291, + 176 + ], + "type": "text", + "content": "RCA-NOC: A couple of men sitting on a couch playing a video game with wheels." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 112, + 183, + 297, + 191 + ], + "lines": [ + { + "bbox": [ + 112, + 183, + 297, + 191 + ], + "spans": [ + { + "bbox": [ + 112, + 183, + 297, + 191 + ], + "type": "text", + "content": "PT: Couch, person, face, wheel, shirt... (person, wheel, couch, face, shirt...)" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 111, + 198, + 281, + 205 + ], + "lines": [ + { + "bbox": [ + 111, + 198, + 281, + 205 + ], + "spans": [ + { + "bbox": [ + 111, + 198, + 281, + 205 + ], + "type": "text", + "content": "NT: Wheelchair, leg\\* tie, stone, coat... (Wheelchair, tie, stone, coat...)" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 52, + 218, + 111, + 261 + ], + "blocks": [ + { + "bbox": [ + 52, + 218, + 111, + 261 + ], + "lines": [ + { + "bbox": [ + 52, + 218, + 111, + 261 + ], + "spans": [ + { + "bbox": [ + 52, + 218, + 111, + 261 + ], + "type": "image", + "image_path": "8b6619f61484916499feca8de3571c462e0c7677d3987634eb9e0be4f67b939a.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 111, + 220, + 244, + 228 + ], + "lines": [ + { + "bbox": [ + 111, + 220, + 244, + 228 + ], + "spans": [ + { + "bbox": [ + 111, + 220, + 244, + 228 + ], + "type": "text", + "content": "GT: Someone cutting a small pizza with a pizza cutter." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 111, + 234, + 253, + 243 + ], + "lines": [ + { + "bbox": [ + 111, + 234, + 253, + 243 + ], + "spans": [ + { + "bbox": [ + 111, + 234, + 253, + 243 + ], + "type": "text", + "content": "RCA-NOC: A person is cutting a pizza with a pizza cutter." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 111, + 249, + 291, + 258 + ], + "lines": [ + { + "bbox": [ + 111, + 249, + 291, + 258 + ], + "spans": [ + { + "bbox": [ + 111, + 249, + 291, + 258 + ], + "type": "text", + "content": "PT: Person, food, pizza, kitchen, bottle*... (Person, food, kitchen, pizza...)" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 111, + 263, + 294, + 278 + ], + "lines": [ + { + "bbox": [ + 111, + 263, + 294, + 278 + ], + "spans": [ + { + "bbox": [ + 111, + 263, + 294, + 278 + ], + "type": "text", + "content": "NT: Microwave, design, hammer, wine, tie... (Microwave, design, hammer, wine, tie...)" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 46, + 288, + 547, + 332 + ], + "lines": [ + { + "bbox": [ + 46, + 288, + 547, + 332 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 547, + 332 + ], + "type": "text", + "content": "Figure 3. Examples of generated captions and contrastive tags by compared methods on Held-Out COCO (left) and Nocaps (right). We show the ground-truth captions (GT) on Held-Out COCO for reference. PT/NT denotes the positive/negative tags before and after Uncertainty-Aware Selection and Reweighting (UASR). Blue/Red text indicates novel objects in Held-Out COCO/Nocaps, and * indicates the false positives/negatives." + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 301, + 73, + 361, + 116 + ], + "blocks": [ + { + "bbox": [ + 301, + 73, + 361, + 116 + ], + "lines": [ + { + "bbox": [ + 301, + 73, + 361, + 116 + ], + "spans": [ + { + "bbox": [ + 301, + 73, + 361, + 116 + ], + "type": "image", + "image_path": "d9650dbf1a3fd5545f3f5ecfbab2eeea00491409f5d90ef39e11a3f04b9cec63.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 361, + 73, + 529, + 81 + ], + "lines": [ + { + "bbox": [ + 361, + 73, + 529, + 81 + ], + "spans": [ + { + "bbox": [ + 361, + 73, + 529, + 81 + ], + "type": "text", + "content": "VinVL + VIVO: A man with a jacket and a cowboy hat next to a bull." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 362, + 87, + 527, + 96 + ], + "lines": [ + { + "bbox": [ + 362, + 87, + 527, + 96 + ], + "spans": [ + { + "bbox": [ + 362, + 87, + 527, + 96 + ], + "type": "text", + "content": "RCA-NOC: A man with a blue shirt and a cowboy hat next to a bull." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 361, + 102, + 512, + 110 + ], + "lines": [ + { + "bbox": [ + 361, + 102, + 512, + 110 + ], + "spans": [ + { + "bbox": [ + 361, + 102, + 512, + 110 + ], + "type": "text", + "content": "PT: Hat, hay, bull, shirt, man... (Man, bull, shirt, hat, hay...)" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 361, + 117, + 509, + 125 + ], + "lines": [ + { + "bbox": [ + 361, + 117, + 509, + 125 + ], + "spans": [ + { + "bbox": [ + 361, + 117, + 509, + 125 + ], + "type": "text", + "content": "NT: face*, tie, road, barn, jacket... (Tie, road, barn, jacket...)" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 309, + 136, + 351, + 198 + ], + "blocks": [ + { + "bbox": [ + 309, + 136, + 351, + 198 + ], + "lines": [ + { + "bbox": [ + 309, + 136, + 351, + 198 + ], + "spans": [ + { + "bbox": [ + 309, + 136, + 351, + 198 + ], + "type": "image", + "image_path": "f78b65bf065079936bf36b85b3a844b09a478ae78c6bcef40a68067607961278.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 361, + 145, + 486, + 154 + ], + "lines": [ + { + "bbox": [ + 361, + 145, + 486, + 154 + ], + "spans": [ + { + "bbox": [ + 361, + 145, + 486, + 154 + ], + "type": "text", + "content": "VinVL + VIVO: A jaguar standing on top of a tree." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 361, + 160, + 488, + 169 + ], + "lines": [ + { + "bbox": [ + 361, + 160, + 488, + 169 + ], + "spans": [ + { + "bbox": [ + 361, + 160, + 488, + 169 + ], + "type": "text", + "content": "RCA-NOC: A jaguar standing behind a green fence." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 361, + 175, + 509, + 190 + ], + "lines": [ + { + "bbox": [ + 361, + 175, + 509, + 190 + ], + "spans": [ + { + "bbox": [ + 361, + 175, + 509, + 190 + ], + "type": "text", + "content": "PT: Jaguar, fence, dog*, carnivore, chest*... (Jaguar, fence, carnivore...)" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 361, + 196, + 514, + 205 + ], + "lines": [ + { + "bbox": [ + 361, + 196, + 514, + 205 + ], + "spans": [ + { + "bbox": [ + 361, + 196, + 514, + 205 + ], + "type": "text", + "content": "NT: animal*, wall, coat, cage, sign... (wall, coat, cage, sign...)" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 302, + 215, + 359, + 258 + ], + "blocks": [ + { + "bbox": [ + 302, + 215, + 359, + 258 + ], + "lines": [ + { + "bbox": [ + 302, + 215, + 359, + 258 + ], + "spans": [ + { + "bbox": [ + 302, + 215, + 359, + 258 + ], + "type": "image", + "image_path": "1b2e2989a0365e192e6c781b1a3aa5024383a607bd63aa2d6ec5f4469835c7f4.jpg" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 361, + 218, + 529, + 227 + ], + "lines": [ + { + "bbox": [ + 361, + 218, + 529, + 227 + ], + "spans": [ + { + "bbox": [ + 361, + 218, + 529, + 227 + ], + "type": "text", + "content": "VinVL + VIVO: A white plate of food with dessert and a tomato." + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 361, + 233, + 529, + 242 + ], + "lines": [ + { + "bbox": [ + 361, + 233, + 529, + 242 + ], + "spans": [ + { + "bbox": [ + 361, + 233, + 529, + 242 + ], + "type": "text", + "content": "RCA-NOC: A white plate with two pieces of bread and a tomato." + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 361, + 248, + 529, + 264 + ], + "lines": [ + { + "bbox": [ + 361, + 248, + 529, + 264 + ], + "spans": [ + { + "bbox": [ + 361, + 248, + 529, + 264 + ], + "type": "text", + "content": "PT: Tomato, bread, lunch, plate, vegetable* ... (Tomato, bread, plate, lunch...)" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 361, + 270, + 521, + 278 + ], + "lines": [ + { + "bbox": [ + 361, + 270, + 521, + 278 + ], + "spans": [ + { + "bbox": [ + 361, + 270, + 521, + 278 + ], + "type": "text", + "content": "NT: Piece*, salad, cake, snack, table*... (Salad, cake, snack...)" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 30 + }, + { + "bbox": [ + 46, + 335, + 288, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 288, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 288, + 453 + ], + "type": "text", + "content": "not as substantial as that on the nocaps benchmark. We hypothesize that this discrepancy is due to the COCO dataset having a limited number of visual concepts, thus reducing the benefits of learning visual semantics. Additionally, our method's use of tags is general and does not rely on fully annotated data. It's possible to utilize potentially unlimited amounts of images and different sources of tags, including those from Faster R-CNN, image tagging, or keywords extracted from captions. These possibilities will be explored in our future work.." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 47, + 462, + 208, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 462, + 208, + 475 + ], + "spans": [ + { + "bbox": [ + 47, + 462, + 208, + 475 + ], + "type": "text", + "content": "6.6. Data and Compute Efficiency" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 46, + 480, + 288, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 480, + 288, + 657 + ], + "spans": [ + { + "bbox": [ + 46, + 480, + 288, + 657 + ], + "type": "text", + "content": "The way the visual semantics are extracted (using CLIP) is not central to our work, as for the gain coming from 400M pairs of CLIP. This is supported in section 6.3. Table 7 shows that other components contribute significantly. Notably, the gain achieved by our Contrastive Alignment (CA) component alone can surpass that of CLIP by a large margin. Importantly, our method achieves this without increasing the number of parameters during training and inference, with the same parameter count as NOC-REK and VINVL (110 M). The training time of NOC-REK is 49 hours, for NOC-REK the training time is much lower (23h). This is with the paper setup (8 GPUs A100). Compared with NOC-REK, which adopts test time augmentation during inference, our inference time is much lower (1 minute) while NOC-REK is 2 minutes." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 47, + 669, + 119, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 119, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 119, + 681 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "In this paper, we present RCA-NOC, which achieves visual-semantic alignment via relative contrastive learning." + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 304, + 335, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 545, + 475 + ], + "type": "text", + "content": "Specifically, for each image, we first extract augmented tags obtained from foundation models such as CLIP. Then we utilize the rank of each augmented object tag in a list as a relative relevance label to contrast each top ranked tag with a set of lower ranked tags. We empirically find that such a learning objective is effective and easy to optimize by encouraging the top ranked tags to be more compatible with their image and text context than lower ranked tags, hence improving the discriminative ability of the learned multimodality representation. We prove the effectiveness of our paradigm in novel object caption, with the spotlight on Nocaps and Held-Out COCO benchmark." + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 304, + 476, + 545, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 476, + 545, + 547 + ], + "spans": [ + { + "bbox": [ + 304, + 476, + 545, + 547 + ], + "type": "text", + "content": "The effectiveness of object tags has already been proved in recent works. However, there are few studies to further explore why such tags could perform well and the problem of object tags' misalignment is often ignored. So how to further exploit use tags explicitly while having a deep understanding of their roles is meaningful in the future." + } + ] + } + ], + "index": 43 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15518" + } + ] + } + ], + "index": 44 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "text", + "content": "[1] https://huggingface.co/transformers/modeldoc/bert.html.6" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 114, + 286, + 157 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 114, + 286, + 157 + ], + "spans": [ + { + "bbox": [ + 53, + 114, + 286, + 157 + ], + "type": "text", + "content": "[2] Harsh Agrawal, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, Stefan Lee, and Peter Anderson. nocaps: novel object captioning at scale. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5579-5588, 2021. 1, 2, 6, 7, 8" + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "15520" + } + ] + } + ], + "index": 4 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/REAP_ A Large-Scale Realistic Adversarial Patch Benchmark/451492ac-a33d-4658-b61d-707c2258ba9b_content_list.json b/2023/REAP_ A Large-Scale Realistic Adversarial Patch Benchmark/451492ac-a33d-4658-b61d-707c2258ba9b_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..742124b8f82c46774abb70b6c949377f5396a549 --- /dev/null +++ b/2023/REAP_ A Large-Scale Realistic Adversarial Patch Benchmark/451492ac-a33d-4658-b61d-707c2258ba9b_content_list.json @@ -0,0 +1,1831 @@ +[ + { + "type": "text", + "text": "REAP: A Large-Scale Realistic Adversarial Patch Benchmark", + "text_level": 1, + "bbox": [ + 171, + 130, + 799, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Nabeel Hingun*", + "bbox": [ + 196, + 180, + 325, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "UC Berkeley", + "bbox": [ + 209, + 199, + 313, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "nabeel126@berkeley.edu", + "bbox": [ + 161, + 220, + 359, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chawin Sitawarin*", + "bbox": [ + 421, + 180, + 571, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "UC Berkeley", + "bbox": [ + 444, + 199, + 550, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "chawins@berkeley.edu", + "bbox": [ + 408, + 220, + 586, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jerry Li", + "bbox": [ + 687, + 181, + 753, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Microsoft", + "bbox": [ + 681, + 199, + 761, + 214 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "jerrl@microsoft.com", + "bbox": [ + 637, + 220, + 807, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "David Wagner", + "bbox": [ + 426, + 242, + 542, + 258 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "UC Berkeley", + "bbox": [ + 433, + 260, + 537, + 277 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "daw@cs.berkeley.edu", + "bbox": [ + 400, + 280, + 570, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Adversarial Patch Evaluation in Previous Work", + "bbox": [ + 364, + 308, + 604, + 319 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/57bd9da3a4d0a12de70faffb2c73ece789cce48fa168e46db869660377bf6c41.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 150, + 321, + 287, + 426 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/78a482b3fadc9a3bf51c96ea9d769219171ed003b5319167aa0571dff3e1a84c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 321, + 426, + 426 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/42cdf61e6b73b786a0d3f8ea211b811de0250241429d065c652d8223a3a0a127.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 428, + 321, + 635, + 426 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/63beb20a49ddc9dcbb800c0a5bb9f58f9940abd6ba0d0fc7d06e3be7523cd094.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 637, + 321, + 821, + 426 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fd71a813da804e7d463a2a0547c616bf525ff9d6f91c2608fd2f800e7fef7a40.jpg", + "image_caption": [ + "Figure 1: When digitally evaluating patch attacks, past work (top row) ignores many real-world factors and thus may yield a misleading evaluation. We develop the REAP benchmark (bottom row) that more realistically simulates the effect of a real-world patch attack on road signs, accounting for the pose, the location, and the lighting condition." + ], + "image_footnote": [], + "bbox": [ + 147, + 446, + 338, + 558 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ceb7c4d6c2dc059358abfd0352900c6cf75279342625024bc26405231d6541c9.jpg", + "image_caption": [ + "Our REAP Benchmark" + ], + "image_footnote": [], + "bbox": [ + 339, + 446, + 482, + 556 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/da8228c891a07f64ede6a94fa32ff2543e34af256c313d3546d14a9a3dccc7d3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 446, + 678, + 558 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/eb38663fcaf638d02c4ede269f275dfcbefb6a43fffdf72505979d4c5ee00876.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 679, + 446, + 821, + 558 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 633, + 313, + 648 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Machine learning models are known to be susceptible to adversarial perturbation. One famous attack is the adversarial patch, a particularly crafted sticker that makes the model mispredict the object it is placed on. This attack presents a critical threat to cyber-physical systems that rely on cameras such as autonomous cars. Despite the significance of the problem, conducting research in this setting has been difficult; evaluating attacks and defenses in the real world is exceptionally costly while synthetic data are unrealistic. In this work, we propose the REAP (REalistic Adversarial Patch) benchmark, a digital benchmark that enables the evaluations on real images under real-world conditions. Built on top of the Mapillary Vistas dataset, our benchmark contains over 14,000 traffic signs. Each sign is augmented with geometric and lighting transformations for applying a digi", + "bbox": [ + 75, + 674, + 473, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tally generated patch realistically onto the sign. Using our benchmark, we perform the first large-scale assessments of adversarial patch attacks under realistic conditions. Our experiments suggest that patch attacks may present a smaller threat than previously believed and that the success rate of an attack on simpler digital simulations is not predictive of its actual effectiveness in practice. Our benchmark is released publicly at https://github.com/wagner-group/reap-benchmark.", + "bbox": [ + 496, + 635, + 895, + 771 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 779, + 632, + 794 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Research has shown that machine learning models lack robustness against adversarially chosen perturbations. Szegedy et al. [54] first demonstrated that one can engineer perturbations that are indiscernible to the human eye yet that cause neural networks to misclassify images with high confidence.", + "bbox": [ + 496, + 804, + 895, + 878 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution.", + "bbox": [ + 526, + 886, + 633, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4640", + "bbox": [ + 482, + 925, + 514, + 936 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Since then, there has been a large body of academic work on understanding the robustness of neural networks to such attacks [18, 39, 55, 8, 27, 57, 36, 7, 22].", + "bbox": [ + 76, + 90, + 468, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "One particularly concerning type of attack is the adversarial patch attack [6, 17, 24, 53, 10, 23, 33, 43, 52, 66, 21, 61]. These are real-world attacks, where the attacker's objective is to print out a patch, physically place it in a scene, and cause a vision network processing the scene to malfunction. These attacks are especially concerning because of the potential impact on autonomous vehicles. A malicious agent could, for instance, produce a sticker that, when placed on a stop sign, cause a self-driving car to believe it is (say) a speed limit sign, and fail to stop. Indeed, similar attacks have already been demonstrated both in academic settings [31, 16, 50] and on real-world autonomous vehicles [56].", + "bbox": [ + 75, + 138, + 470, + 318 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite this significant risk, research on these attacks has stalled to a certain extent because quantitatively evaluating the significance of this threat is challenging. The most accurate approach would be to conduct real-world experiments, but they are very expensive, and at present, not practical to do at a large scale. This leaves much to be desired compared to other branches of computer vision research, where the availability of benchmarks such as ImageNet have reduced the barriers to research and spurred tremendous innovation.", + "bbox": [ + 75, + 320, + 468, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Instead, researchers turn to one of two techniques: either, they physically create their attacks and try them out on a small number of real-world examples by physically attaching them to objects, or they digitally evaluate patch attacks using digital images containing simulated patches. Both approaches have major drawbacks. Although the former simulates more realistic conditions, the sample size is very small, and typically one cannot draw statistical conclusions from the results [6, 17, 53, 10, 66, 20, 21, 61]. Additionally, because of the ad-hoc nature of these evaluations, it is impossible to compare the results across different papers. Ultimately, such experiments only serve as a proof of concept for the proposed attacks and defenses, but not as a rigorous evaluation of their effectiveness.", + "bbox": [ + 75, + 457, + 470, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In contrast, a digital simulation of attacks/defenses allows quantitative evaluation [24, 33, 65, 46, 37, 62, 58, 44]. However, it is difficult to accurately capture all of the challenges that arise in the real world. Past work often made unrealistic assumptions, such as that the patch is square, axis-aligned, can be located anywhere on the image, fully under the control of the attacker, and ignore noise and variation in lighting and pose (see top row of Fig. 1). Consequently, it is unclear if these evaluations are actually reflective of what would happen in real-world scenarios.", + "bbox": [ + 75, + 669, + 470, + 820 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1.1. Our Contributions", + "text_level": 1, + "bbox": [ + 76, + 833, + 256, + 848 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The REAP Benchmark: We propose Realistic Adversarial Patch Benchmark (REAP), the first large-scale standardized benchmark for security against patch attacks. Motivated by", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the aforementioned shortcomings of prior evaluations, we design REAP with the following principles in mind:", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Large-scale evaluation: REAP consists of 14,651 images of road signs drawn from the Mapillary Vistas dataset. This allows us to draw quantitative conclusions about the effectiveness of attacks/defenses on the dataset.", + "2. Realistic patch rendering: REAP has tooling, which, for every road sign in the dataset, allows us to realistically render any digital patch onto the sign, matching factors such as where to place the patch, the camera angle, lighting conditions, etc. Importantly, this transformation is fast and differentiable so one can still perform backpropagation through the rendering process.", + "3. Realistic image distribution: REAP consists of images taken under realistic conditions, including variation in sizes and distances from the camera as well as various lighting conditions and degrees of occlusion." + ], + "bbox": [ + 500, + 125, + 893, + 351 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "**Evaluations with REAP:** With our new benchmark in hand, we also perform the first large-scale evaluations of existing attacks on object detectors. We evaluate existing attacks on three different object detection architectures: Faster R-CNN [48], YOLOF [9], and DINO [64]. We also implement and evaluate a baseline defense adapted from adversarial training [36] to defend against patch attacks on object detection. The conclusions we find are:", + "bbox": [ + 496, + 363, + 893, + 484 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Existing patch attacks are not that effective. Perhaps surprisingly, existing attacks do not succeed on a majority of images on our benchmark. This is in contrast to simpler attack models such as $\\ell_p$ -bounded perturbations or patch attacks on simpler benchmarks, where the attack success rate is near $100\\%$ . Moreover, adversarily trained models can almost completely stop the attacks with only a minor performance drop on benign data.", + "2. Performance on synthetic data is not reflective of performance on REAP. We find that the success rates of attacks on synthetic versions of our benchmark and the full REAP are only poorly correlated. We conclude that performance on simple synthetic benchmarks is not predictive of attack success rate in more realistic conditions.", + "3. Lighting and patch placement are particularly important. Finally, we investigate what transforms in the patch rendering are the most important, in terms of the effect on the attack success rate. We find that the most significant first-order effects are from the lighting transform, as well as the positioning of the patch. In contrast, the perspective transforms—while still important—seem to affect the attack success rate somewhat less." + ], + "bbox": [ + 500, + 488, + 893, + 819 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While we believe these conclusions are already quite interesting, they are only the tip of the iceberg of what can be done with REAP. We believe that REAP will help support future research in adversarial patches by enabling a more accurate evaluation of new attacks and defenses.", + "bbox": [ + 496, + 825, + 893, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4641", + "bbox": [ + 480, + 924, + 513, + 936 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 89, + 218, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Adversarial patch attacks. The literature on adversarial patches, and adversarial attacks more generally, is vast and a full review is beyond the scope of this paper. For conciseness, we only survey the most relevant works. Since their introduction in Brown et al. [6], Karmon et al. [24], Eykholt et al. [17], there have been a variety of adversarial patch attacks proposed [23, 33, 43, 52, 21, 61]. Of particular interest to us are the ones on object detection of road signs [17, 53, 10, 66].", + "bbox": [ + 75, + 112, + 470, + 234 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Small scale, real-world tests. A common methodology used to test the transferability of the adversarial patch to the physical world is to print it out, physically place it onto an object, and capture pictures or videos of the patch for evaluation [6, 17, 53, 10, 66, 20, 21, 61]. While this method provides the most realistic evaluation, it has a number of downsides. First, it is, by nature, very time-consuming and hence limits the number of images that can be used for testing. Consequently, one cannot extract quantitative conclusions from the results. Additionally, they are difficult to standardize across papers, making their result not directly comparable. For instance, the pictures of the adversarial patches are taken under different angles, lighting conditions, or from varying distances. Sometimes, the adversarial patches themselves are printed using different printers [10, 66].", + "bbox": [ + 75, + 239, + 473, + 467 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Completely simulated environment. Another line of work considers purely simulated environments for evaluating adversarial patches such as CARLA [14, 32, 45] and AttackScenes [21]. A huge advantage of this method is that it has the most precise and the most flexible control of the environment, e.g., cameras and objects can be placed anywhere. However, it is labor-intensive to build a diverse set of scenes digitally, and it compromises heavily on realism. Another example is 3DB [28], a photorealistic simulation for studying the reliability of computer vision systems. Nevertheless, it lacks the tooling necessary for evaluating adversarial patches and does not contain any driving scene, a setting to which adversarial patches are most applicable. Our benchmark utilizes images of real and diverse driving scenes and focuses on realistically simulating only the adversarial patches.", + "bbox": [ + 75, + 470, + 470, + 698 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Digital simulation. This third approach takes a middle road and simulates the effects of the adversarial patch by digitally inserting it into a real image. This has been done at scale and to varying degrees of sophistication. One of the most common, but also simplest, ways this is done is to apply the patch to the image at some random position, and with some simple transformations, for instance, those induced by expectation over transformation [6, 24, 33, 65, 46, 37, 62, 58, 44]. This approach violates all the physical constraints and hence, is far from being realistic.", + "bbox": [ + 75, + 703, + 470, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Arguably the benchmarks most similar to ours are the ones in Zhao et al. [66] and Braunegg et al. [5]. Zhao et al. [66] digitally insert synthetic stop signs with patches into", + "bbox": [ + 76, + 854, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "images with realistic camera angles. However, they do not account for lighting conditions, and the target object itself is synthetic. In contrast, all signs in our dataset are real, and we also produce a transformation to match lighting conditions. In Section 4.3, we find that these two factors affect the evaluation metrics to a large extent. APRICOT [5] contains images of real scenes with a printed adversarial patch. Compared to ours, APRICOT is smaller in size (1K vs 14K images) and is heavily inflexible as it comes with a pre-defined adversarial patch with a fixed size and location.", + "bbox": [ + 496, + 90, + 893, + 243 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Defenses. There have also been a slew of proposed defenses against patch attacks, e.g., [19, 41, 65, 62, 46, 37, 40, 11]. Most examine object classification. Only a handful consider object detection, which may be more relevant in practice [12, 63]. We choose to experiment with adversarial training [36] as a defense because, to the extent of our knowledge, it has not been applied in this setting (Rao et al. [46] study patch adversarial training on classifiers). It is also known to be a strong baseline and arguably the only effective defense across other $\\ell_p$ -norms [13]. Importantly, unlike the other defenses listed above, adversarial training does not make assumptions about the number or size of the patch.", + "bbox": [ + 496, + 246, + 895, + 429 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Adversarial Patch Benchmark", + "text_level": 1, + "bbox": [ + 498, + 443, + 779, + 459 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 500, + 465, + 609, + 481 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our dataset is a collection of images containing traffic signs, each of which comes with a segmentation mask and a class. So far, this is more or less standard. The main additional feature of our benchmark is that, for each sign, we also provide an associated rendering transformation.", + "bbox": [ + 496, + 487, + 893, + 563 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a digital patch, this transformation allows us to apply the patch on the sign in a way that respects the scaling, orientation, and lighting of the sign in the image. We emphasize that a separate transformation is inferred individually for each sign, in order to ensure that the transformation is accurate for every image. Moreover, the rendering transformation is fully differentiable, which allows our dataset to be used to generate patch attacks and to apply adversarial defenses along the line of adversarial training.", + "bbox": [ + 496, + 564, + 895, + 699 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Figs. 2 and 3 give an overview of the process to obtain the geometric (Section 3.4.1) and the relighting (Section 3.4.2) transformations, respectively. We use an algorithm to generate the candidate annotations automatically, visually inspect each of them, and then manually fix any wrong annotation. In total, we label 14,651 traffic signs across 8,433 images.", + "bbox": [ + 496, + 699, + 893, + 790 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Datasets", + "text_level": 1, + "bbox": [ + 500, + 801, + 602, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We build our benchmark using images from the Mapillary Vistas dataset [42]. It includes 20,000 street-level images from around the world, annotated with bounding boxes of 124 object categories, including traffic signs. A limitation of Vistas is that all traffic signs are grouped under one class.", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4642", + "bbox": [ + 480, + 924, + 514, + 936 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This creates a challenge for us, because our patch-rendering process depends on the size and shape of the sign. Without this information, the rendering is less realistic. We deal with this challenge by grouping the signs so that all signs in the same group can use the same geometric transform procedure. The grouping process is described in the next section.", + "bbox": [ + 75, + 90, + 472, + 183 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Traffic Sign Classification", + "text_level": 1, + "bbox": [ + 76, + 191, + 312, + 208 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Grouping traffic signs by their shape and size has two advantages. First, it allows more accurate geometric transforms as previously mentioned. Second, it allows us to study multiclass sign detection. Instead of labeling the Vistas signs by hand, we train a ResNet-18 on a similar dataset, Mapillary Traffic Sign (MTSD) [15], to classify them. MTSD contains granular labeling of over 300 traffic sign classes, but we cannot use it in place of Vistas as it lacks segmentation labels required to compute the geometric transforms.", + "bbox": [ + 75, + 215, + 470, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We created two versions of the benchmark: REAP and REAP-S. REAP is our main benchmark with the classes matching those of MTSD. However, most of the classes contain fewer than 10 samples so we only keep the 100 most common classes. We need a sufficient number of samples per class because (i) some will be further filtered out in the preprocessing and (ii) the samples will be split into a \"training\" (for the attacker to \"train\" the adversarial patch) and a test set (for evaluating the attack). Conversely, REAP-S groups the signs into 11 classes by shape and size, namely circle, triangle, upside-down triangle, diamond (S), diamond (L), square, rectangle (S), rectangle (M), rectangle (L), pentagon, and octagon. REAP-S serves as a simpler alternative to REAP and is also intuitively more \"defender-friendly.\" For both REAP and REAP-S, the remaining signs that do not belong to the classes are labeled as a background class or \"others\" which will be ignored when we compute the metrics.", + "bbox": [ + 75, + 351, + 472, + 607 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since Mapillary Vistas does not come with these labels, we first trained a ConvNeXt model [35] on MTSD, which achieves about $98\\%$ accuracy on the validation set, to generate the candidate class labels. The labels were then automatically corrected when we compute the parameters for the geometric transform in Section 3.4.1. For the remaining ones that cannot be automatically verified, we manually inspected and corrected them.", + "bbox": [ + 75, + 608, + 470, + 728 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our grouping of the signs in REAP-S has an extra benefit. Since each class is (approximately) associated with a standardized physical size, we can specify the patch size in real units (e.g., inches) instead of pixels. The real unit is arguably more useful for estimating the threat of adversarial patches than constraining the size by the number of pixels. One complication is that a single class of sign may come in different sizes, e.g., stop signs can be 24\", 36\", or 48\", depending on the kind of road they are located on, but usually one size is", + "bbox": [ + 75, + 729, + 470, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "more common. The Vistas dataset does not contain sufficient information to distinguish between these sizes so we pick one canonical size for each sign type. Specifically, we select the size specified for \"Expressway\" according to the official U.S. Department of Transportation's guideline. Appendix A describes our design decision in detail.", + "bbox": [ + 500, + 90, + 893, + 183 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Transformations", + "text_level": 1, + "bbox": [ + 500, + 196, + 666, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We render adversarial patches with two types of transformations: geometric and relighting. Since the traffic signs in our dataset vary in shape, size, and orientation, we first need to apply a geometric, specifically perspective or 3D, transform to the patch to simulate these variations. Next, we account for the fact that pictures of real-world traffic signs are taken under different lighting conditions by applying a relighting transform to the patch. The importance of these transformations is highlighted in Fig. 4.", + "bbox": [ + 498, + 222, + 893, + 359 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4.1 Geometric Transformation", + "text_level": 1, + "bbox": [ + 500, + 388, + 741, + 402 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To determine the parameters of the perspective transform, we need four keypoints for each sign. We infer the keypoints for a particular traffic sign using only its segmentation mask (which is provided in the Mapillary Vistas dataset) by following the four steps below (also visualized in Fig. 2):", + "bbox": [ + 498, + 415, + 893, + 491 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Find contour: First, we find the contour of the segmentation mask.", + "2. Compute convex hull: Then, we find the convex hull of the contour to correct annotation errors and occlusion. This does not affect correct masks, as they should already be convex.", + "3. Fit polygon and ellipse: We fit an ellipse to the convex hull, to find circular signs. If the fitted ellipse results in a larger error than a certain threshold, we know that the sign is not circular and therefore fit a polygon instead.", + "4. Cross verify: We verify that the shape obtained from the previous step matches with the ResNet's prediction. If not, the sign is flagged for manual inspection." + ], + "bbox": [ + 500, + 493, + 893, + 689 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The last step is finding the keypoints. For polygons, we first match the vertices to the canonical ones and then take the four predefined vertices as the keypoints. For circular signs, we use the ends of their major and minor axes as the four keypoints. These keypoints are used to infer a perspective transform appropriate for this sign. Triangular signs are a special case as we can only identify a maximum of three keypoints which means we can only infer a unique affine transform (six degrees of freedom). Note that this transform is linear and hence is fully differentiable. Lastly, we manually check all annotations and correct any errors.", + "bbox": [ + 498, + 691, + 893, + 858 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "Update August 18, 2023: In the previous version of the paper, we only present REAP-S which was called REAP.", + "bbox": [ + 75, + 875, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "https://mutcd.fhwa.dot.gov/htm/2003/part2/part2b1.htm", + "bbox": [ + 500, + 875, + 857, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4643", + "bbox": [ + 482, + 924, + 514, + 936 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/641e0e87f34571762b1f58e1e0fa5b355eb400399aa73e6f8a65814778825601.jpg", + "image_caption": [ + "Figure 2: The automated procedure we use to extract the keypoints from each traffic sign." + ], + "image_footnote": [], + "bbox": [ + 117, + 88, + 851, + 271 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7f17b8a34d38a397c6bdb1d0a651593de638302a759b8b269868f399214025dd.jpg", + "image_caption": [ + "Figure 3: Computing relighting parameters (top) and applying the transform (bottom)." + ], + "image_footnote": [], + "bbox": [ + 78, + 313, + 465, + 488 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4.2 Relighting Transformation", + "text_level": 1, + "bbox": [ + 76, + 550, + 316, + 565 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Each traffic sign in our dataset has two associated relighting parameters, $\\alpha, \\beta \\in \\mathbb{R}$ . Given a patch $\\mathbf{P}$ , its relighted version $\\mathbf{P}_{\\mathrm{relighted}} = \\alpha \\mathbf{P} + \\beta$ is rendered on the scene as depicted on the bottom row of Fig. 3. We infer $\\alpha, \\beta$ by matching the histogram of the original sign (e.g., the real stop sign on the upper-right of Fig. 3) to a canonical image (e.g., the synthetic stop sign on the upper-left): in particular, we set $\\beta$ as the $p$ -th percentile of all the pixel values (aggregated over all three RGB channels) on that sign and $\\alpha$ as the difference between the $p$ -th and $(1 - p)$ -th percentile. We call this the \"percentile\" method and explain why we chose it in Section 3.5. This method assumes that relighting can be approximated with a linear transform where $\\alpha$ and $\\beta$ represent contrast and brightness adjustments. Like before, since this transformation is linear, it is differentiable.", + "bbox": [ + 75, + 575, + 468, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Realism Test", + "text_level": 1, + "bbox": [ + 76, + 815, + 210, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we measure how realistic the patches are when rendered with different transform methods: three for geometric and eight for relighting. The geometric transforms include perspective (or homographic), affine, and translate", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/addfcb402de2f8f50bd6106136ce613fce22591ca4957f9027faa89de7158a0b.jpg", + "image_caption": [ + "Figure 4: Example ablation of the geometric and relighting transforms in our dataset. The rightmost stop sign has a patch rendered with a perspective and relighting transform which makes it more realistic. The first and second images have patches that are too bright whereas the first and third images have patches that do not respect the sign's orientation." + ], + "image_footnote": [], + "bbox": [ + 501, + 311, + 890, + 401 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/5d9125ac722df530887bac4d5458f7e5d145e763f690738f5458fed88abd1fd0.jpg", + "table_caption": [ + "Table 1: Comparison of different geometric and relighting transforms from our realism test (mean ± standard deviation of RMSE across 44 samples). The best results are in bold." + ], + "table_footnote": [], + "table_body": "
TransformsMethodsColorsRMSE (↓)
GeometricTranslate & Scalen/a1.72 ± 1.19
Affinen/a1.35 ± 0.49
Perspective (3D)n/a1.13 ± 0.41
RelightingPercentileRGB0.110 ± 0.034
HSV0.227 ± 0.118
LAB0.652 ± 0.112
PolynomialRGB0.113 ± 0.037
HSV0.118 ± 0.035
LAB0.161 ± 0.043
Color TransferHSV0.117 ± 0.035
LAB0.184 ± 0.062
", + "bbox": [ + 514, + 570, + 877, + 771 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "& scale transforms. For relighting, we experiment with three methods, each of which can be carried out on different color spaces (RGB, HSV, and LAB): the percentile method, described in Section 3.4.2; polynomial fitting, where we find the polynomial that best fits the pixel values on each real sign given the corresponding pixel values on the digital one; and Color Transfer [47], which tries to match the mean and", + "bbox": [ + 496, + 794, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4644", + "bbox": [ + 480, + 924, + 514, + 936 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/412f07cd059447c2ddb50f651d9386bb0afa2ec353866de8cbf356904e2b982f.jpg", + "image_caption": [ + "Figure 5: RMSE between the photographed and the rendered patches using the \"percentile\" method with different values of $p$ . The shaded region denotes the standard deviation across 44 samples. $p = 20$ yields the lowest RMSE." + ], + "image_footnote": [], + "bbox": [ + 117, + 88, + 428, + 263 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/619059a995c458ee908f741369f34f521544bd0bd8a7645552a161fda1fa25d1.jpg", + "image_caption": [ + "Figure 6: Random samples used in our realism experiments (left: real, right: rendered). Fig. 17 contains all samples." + ], + "image_footnote": [], + "bbox": [ + 81, + 363, + 464, + 414 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the standard deviation of the pixel values.", + "bbox": [ + 76, + 477, + 354, + 493 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We photograph 44 pairs of real traffic signs with and without an adversarial patch: 11 signs, one for each class, in four scenes and lighting conditions. For each sample, we hand-annotated the keypoints of both the signs and the patches. Then, given an image of the sign without the patch, we render the patch on it using the different transform methods. For geometric transforms, we measure the root mean square error (RMSE) between the rendered and the corresponding groundtruth corners of the patch. To compare the relighting methods, we compute the RMSE between the rendered and the corresponding groundtruth pixel values of the patch. We use the groundtruth geometric transform when computing the relighting parameters to disentangle the potential error from the geometric transform.", + "bbox": [ + 75, + 500, + 470, + 710 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1 reports the best RMSE achieved by each transform after a hyperparameter sweep ( $p$ , polynomial degrees, etc.). The perspective transform achieves the lowest RMSE as expected which emphasizes the importance of using the full 3D transform instead of simpler alternatives. For relighting, the percentile method with $p = 0.2$ performs as well as, or better than, any other at rendering the adversarial patches. Hence, these are the two transforms we use to construct the REAP benchmark and in all of the experiments in Section 4 unless stated otherwise. Fig. 6 visually compares the rendered patches with the groundtruth ones under these best transform methods. Appendix B contains more details.", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments on REAP Benchmark", + "text_level": 1, + "bbox": [ + 500, + 89, + 816, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our benchmark can be used to evaluate attacks and defenses under various threat models, e.g., making objects appear vs disappear, using a universal patch vs a targeted attack, etc. In this paper, we focus on the setting where the adversary tries to make a traffic sign disappear or be misclassified using the per-class attack, i.e., only one patch per class of objects, similar to Benz et al. [4]. We argue that this threat model is more realistic and more alarming as the attacker only needs to distribute several adversarial stickers that are effective across million of traffic signs. We assume the adversary has access to the target model (white-box).", + "bbox": [ + 496, + 114, + 893, + 282 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experiment Setup", + "text_level": 1, + "bbox": [ + 500, + 292, + 676, + 308 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Traffic sign detectors. We experiment with three object detection models, Faster R-CNN [48], YOLOF [9], and DINO [64], all trained on the MTSD dataset to predict bounding boxes for all 11 traffic sign classes plus the \"other\" class. We follow the training method and hyperparameters from Neuhold et al. [42]. As mentioned in Section 4.2, we report the false negative rate (FNR) in addition to mAP scores. For FNR, the score threshold is chosen as one that maximizes the F1 score on the validation set of MTSD.", + "bbox": [ + 496, + 315, + 893, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Attack algorithms. We use the RP2 attack [17] and the DPatch attack [33] to generate adversarial patches for all models. We assume that the adversary has access to 5 held-out images from our benchmark and use them to generate one adversarial patch per sign class. We note that this setting, referred to as per-class attack, is different from the usual white-box attack threat model where each sample is given a unique perturbation (we call it per-instance attack) and is more similar to the \"universal\" adversarial perturbation [38]. We argue that this threat model is more realistic and more alarming as the attacker only needs to distribute one adversarial sticker that are effective across million of traffic signs of the same type. Appendix D.5 discusses the threat models in more detail.", + "bbox": [ + 496, + 472, + 893, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Each of the classes has a specific set of these 5 images each of which contains at least one sign of that class. For REAP-S, we use 50 images since there are more samples per class. In practice, an adversary may benefit from using more than 5 (or 50) images to generate the patch, but we set our limit here to leave sufficient samples for the evaluation phase. We do not find a significant difference in the performance of the two attacks (Appendix D.1) so we report only the results of DPatch attack with PGD optimizer in the main paper.", + "bbox": [ + 496, + 683, + 893, + 820 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Defense algorithm. We use adversarial training with DPatch attack and five-step PGD as it performs the best empirically. The patches are generated per-instance at a random location to prevent overfitting to a specific one. To", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4645", + "bbox": [ + 480, + 924, + 514, + 936 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e33dcea175f7bb242ad4bfa2320ef23db032dc956cc430b107821f857524c558.jpg", + "table_caption": [ + "Table 2: Mean FNR and mAP of the adversarial patches on six traffic sign detectors on REAP. \"FRCNN\" refers to Faster R-CNN, \"Adv.\" indicates adversarially trained models. For defenders, lower FNR $(\\downarrow)$ and higher mAP $(\\uparrow)$ are better." + ], + "table_footnote": [], + "table_body": "
Patch SizeFRCNNYOLOFDINOAdv. FRCNNAdv. YOLOFAdv. DINO
FNRmAPFNRmAPFNRmAPFNRmAPFNRmAPFNRmAP
No patch4.372.918.554.814.168.23.173.321.055.09.474.2
Small (10”×10”)15.459.433.743.532.060.43.871.822.554.71.880.6
Medium (10”×20”)22.446.542.736.635.452.66.166.827.151.91.280.1
Large (two 10”×20”)50.018.272.819.462.839.513.956.357.734.13.677.8
", + "bbox": [ + 120, + 125, + 849, + 229 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "improve the effectiveness of adversarial training under a small number of steps, we cache patches generated in the previous epoch and use it as an initialization for the next one [67]. For more detailed setup and results, please see Appendix C.", + "bbox": [ + 75, + 255, + 472, + 333 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Synthetic Benchmark. We use canonical synthetic signs, one per class, as a baseline to compare our REAP-S benchmark to (we cannot find canonical synthetic signs for all 100 classes of REAP). Similarly to Eykholt et al. [17], the synthetic sign is placed at a random location on one of 50 random background images and randomly rotated between 0 and 15 degrees. We use the synthetic benchmark for both generating and testing the adversarial patch. For testing, we use 2,000 background images per class, randomly selected from our REAP-S benchmark to keep the distribution of the scenes similar.", + "bbox": [ + 75, + 349, + 470, + 515 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Evaluation Metrics", + "text_level": 1, + "bbox": [ + 76, + 523, + 261, + 539 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Here, we define a successful attack as a patch that makes the sign either (i) undetected or (ii) classified to a wrong class (i.e., any of the other classes, or the background class). Similarly to previous work, we measure the effectiveness of an attack by the attack success rate (ASR), defined as follows. Given a list of signs $\\{x_i\\}_{i=1}^N$ and the corresponding version with an adversarial patch applied to it, $\\{x_i'\\}_{i=1}^N$ ,", + "bbox": [ + 75, + 547, + 468, + 655 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {A S R} = \\frac {\\sum_ {i = 1} ^ {N} \\mathbf {1} _ {x _ {i} \\text {i s d e t e c t e d}} \\wedge \\mathbf {1} _ {x _ {i} ^ {\\prime} \\text {i s n o t d e t e c t e d}}}{\\sum_ {i = 1} ^ {N} \\mathbf {1} _ {x _ {i} \\text {i s d e t e c t e d}}}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 664, + 468, + 705 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ASR and FNR are easy to interpret but dependent on specific thresholds of both the confidence score and the IoU between the groundtruth and the detected boxes. Hence, we also report mAP which averages across these thresholds.", + "bbox": [ + 75, + 713, + 468, + 773 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Main Results", + "text_level": 1, + "bbox": [ + 76, + 782, + 215, + 797 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Experiments on our REAP benchmark illuminate several findings that were not previously observed due to the lack of scalability and reproducibility of real-world experiments:", + "bbox": [ + 75, + 806, + 470, + 853 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(1) Patch attacks against road signs are less effective than previously believed. From Table 2, a $10^{\\prime \\prime} \\times 10^{\\prime \\prime}$ adversarial", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "patch increases FNR by only 11-18 percentage points on the undefended models. For REAP-S (Table 3), the increase is 8-12 percentage points. For comparison, a class-wise adversarial perturbation under imperceptible $\\ell_{\\infty}$ norms achieves above $90\\%$ success rate [4]. More importantly, on adversarially trained models, FNR remains almost identical before and after applying the patch on Faster R-CNN andYOLOF. Surprisingly, adversarially trained DINO performs better on samples with adversarial patches than without. We hypothesize that this is a result of overfitting to some adversarial patches and not a clear sign of weak attacks or gradient obfuscation. We refer to Section 4.4 for additional detail.", + "bbox": [ + 496, + 255, + 893, + 436 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "This result implies that a well-known defense like adversarial training is effective and may be sufficient to protect against patch attacks in the real world. Adversarial attacks are most troubling when they are imperceptible; patches as large as $10^{\\prime \\prime} \\times 10^{\\prime \\prime}$ (or larger) are likely to draw attention, which may make them less of a threat in practice.", + "bbox": [ + 496, + 436, + 893, + 527 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our findings are also consistent with prior works that investigate physical-world attacks on stop signs. In these works, the attack is often clearly visible. For instance, Eykholt et al. [17] and Zhao et al. [66] use a patch that is close to our two $10^{\\prime \\prime} \\times 20^{\\prime \\prime}$ patches which is why they observe a high attack success rate similar to our results with the larger patch size. Nonetheless, a patch of this size surely breaches all notions of imperceptibility. Perhaps an interesting threat model to study in the future is to allow large patches but additionally constrain the perturbation with $\\ell_{\\infty}$ -norm.", + "bbox": [ + 496, + 529, + 893, + 681 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(2) ASR measured on synthetic data is not predictive of ASR measured on our realistic benchmark. We compare REAP-S to a synthetic benchmark intended to be representative of methodology often found in prior work: we take a single synthetic image of a road sign, then generate attacks against it (instead of a real image). Table 3 and Fig. 8 show that there is a large difference between metrics as measured on such a synthetic benchmark compared to our benchmark. The gap can be up to 50–60 percentage points on average.", + "bbox": [ + 496, + 703, + 893, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 8 and Table 9 in Appendix D compare ASR on the two benchmarks by class of the traffic signs. If the two ASRs were similar, all data points would have lied close to the diagonal dashed line. Instead, most of the data points", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4646", + "bbox": [ + 480, + 924, + 514, + 936 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/fed58c35cd655a768b319522e58b48cd0c861d7b013f931120cad976239a0249.jpg", + "table_caption": [ + "Table 3: Mean ASR and FNR of the adversarial patches on the six traffic sign detectors on REAP-S. For sign-specific metrics, see Table 9. It is clear that evaluating on the synthetic signs overestimates the attack's potency in every setting. For defenders, lower FNR $(\\downarrow)$ and ASR $(\\downarrow)$ are better." + ], + "table_footnote": [], + "table_body": "
Patch SizeBenchmarksFRCNNYOLOFDINOAdv. FRCNNAdv. YOLOFAdv. DINO
FNRASRFNRASRFNRASRFNRASRFNRASRFNRASR
No patchSynthetic19.8n/a17.0n/a12.7n/a15.7n/a19.0n/a5.8n/a
REAP-S (ours)20.2n/a17.1n/a12.8n/a17.4n/a19.2n/a6.1n/a
Small (10"×10")Synthetic76.973.189.888.658.856.950.043.976.873.424.122.6
REAP-S (ours)50.539.248.638.936.228.018.75.128.312.71.10.1
Medium (10"×20")Synthetic89.988.392.091.173.172.679.577.383.781.734.733.9
REAP-S (ours)64.456.160.552.845.538.433.823.546.534.71.30.1
Large (two 10"×20")Synthetic99.699.6100.0100.096.596.498.998.899.198.952.952.7
REAP-S (ours)85.282.088.286.185.183.559.353.669.964.35.14.3
", + "bbox": [ + 83, + 138, + 888, + 321 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d50b1ade17dd267eb78a9918829a6071ccea9a6469e26b062f24057ec3aa9a2d.jpg", + "image_caption": [ + "Figure 7: Examples of small $(10^{\\prime \\prime}\\times 10^{\\prime \\prime})$ , medium $(10^{\\prime \\prime}\\times 20^{\\prime \\prime})$ and large (two $10^{\\prime \\prime}\\times 20^{\\prime \\prime}$ ) patches applied to three of the signs from our benchmark. The large patch size is clearly visible and obscures the notion of imperceptibility. We still choose to experiment with it since it is approximately the same size used by prior work [17, 66]." + ], + "image_footnote": [], + "bbox": [ + 78, + 332, + 890, + 405 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1c52d0d73411f95ac37fa20e6fcd5dd5a5b54b172d49303917d04445e3b35046.jpg", + "image_caption": [ + "(a) Faster R-CNN" + ], + "image_footnote": [], + "bbox": [ + 78, + 481, + 261, + 614 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/743268b0e88296ef41c8513ec599a5b1793e9840b0be2825b71783393360e56f.jpg", + "image_caption": [ + "(b) DINO" + ], + "image_footnote": [], + "bbox": [ + 281, + 481, + 464, + 614 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "are below the line, suggesting that the synthetic benchmark consistently overestimates the ASR. Moreover, there is no clear relationship between the two measurements of ASR. If the rankings of the ASRs are well-correlated, we should expect ordering of the points to be similar in both horizontal and vertical directions, but this is not the case.", + "bbox": [ + 75, + 709, + 468, + 800 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(3) The lighting transform affects the attack's effectiveness more than the geometric transform. Fig. 9 shows how the transformations our benchmark applies to the patch affect its mAP scores. For all models, our realistic lighting transform has a much larger effect than the geometric trans", + "bbox": [ + 75, + 824, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/97c2a901f6e6a0ae5f5aa252da46905c5cb68724729a8c1cf5af45dd8a140b61.jpg", + "image_caption": [ + "Figure 8: ASRs on synthetic vs REAP-S benchmarks for Faster R-CNN (left) and DINO (right). The dashed line marks the points with an equal ASR on both datasets.", + "Figure 9: Effects of different geometric and relighting transform methods on the mAP of the YOLOF model under attack. The hatched bars are the default setting. When either geometric or relighting transform is varied, the other one is fixed to the default (perspective, $p = 0.2$ )." + ], + "image_footnote": [], + "bbox": [ + 509, + 483, + 879, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "form. Without the lighting transform, mAP decreases by 17 percentage points for YOLOF and 15 for Faster R-CNN (i.e., an increase of 23 and 14 points on the ASR). This observation explains why the synthetic benchmark as well as synthetic evaluations in previous works overestimate ASR.", + "bbox": [ + 496, + 760, + 893, + 835 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Extended Attack Evaluation", + "text_level": 1, + "bbox": [ + 500, + 845, + 754, + 861 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Because these results were so surprising, we investigated the possibility that our attack algorithms are not sufficiently", + "bbox": [ + 500, + 869, + 892, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4647", + "bbox": [ + 480, + 924, + 514, + 936 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/de3610598aabc2ee9ca480eac0e64aa267bca528bcff95ec7b2df29e1c4dc6e5.jpg", + "table_caption": [ + "Table 4: Robustness of the adversarially trained models under different attack threat models ( $10^{\\prime \\prime} \\times 10^{\\prime \\prime}$ patch size). The per-instance attack has the highest ASR and the lowest mAP as expected, and there is no sign of gradient obfuscation." + ], + "table_footnote": [], + "table_body": "
AttacksASR (↑)mAP (↓)
Adv. Faster R-CNN
No Attackn/a66.0
Per-Class Attack5.165.7
Per-Instance Attack16.059.3
Transfer from YOLOF3.267.8
Transfer from Adv. YOLOF7.063.6
Transfer from Synthetic2.769.1
Adv. YOLOF
No Attackn/a58.5
Per-Class Attack17.751.3
Per-Instance Attack28.246.5
Transfer from Faster R-CNN13.553.1
Transfer from Adv. Faster R-CNN7.955.4
Transfer from Synthetic12.254.3
Adv. DINO
No Attackn/a65.7
Per-Class Attack0.175.1
Per-Instance Attack2.763.7
Transfer from Adv. Faster R-CNN0.176.5
Transfer from Adv. YOLOF0.276.1
Transfer from DINO0.079.6
Transfer from Synthetic0.472.7
", + "bbox": [ + 99, + 154, + 447, + 520 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/38d1b99e986e8e78640a1c7c45240e7bb875c6ee8077d389b01478bb2c2e5ac2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
AugmentStrengthFRCNNAdv. YOLOFAdv. DINO
FNRmAPFNRmAPFNRmAP
Nonen/a15.459.422.554.71.280.1
0.116.158.823.154.71.280.1
Color-jitter0.216.058.523.654.61.280.0
0.315.559.023.354.71.380.1
0.115.758.923.054.81.280.4
Unif. noise0.215.458.822.654.71.480.1
0.315.658.622.954.71.480.2
", + "bbox": [ + 76, + 534, + 470, + 695 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 5: FNR and mAP with color-jitter or random noise applied during the attack EoS on REAP. We use the small patch for Faster R-CNN and Adv. YOLOF, and the medium size for Adv. DINO. None of the augmentations seems to affect the potency of the attack.", + "bbox": [ + 75, + 704, + 470, + 781 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "strong (e.g., gradient obfuscation [2]) or that the adversarially trained models \"catastrophically overfit\" [59, 25, 1], i.e., they memorize the attack patterns during training but are not actually robust. In particular, we evaluate the adversarially trained models against transfer and per-instance attacks.", + "bbox": [ + 75, + 809, + 470, + 883 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The per-instance attack generates one patch for each in-", + "bbox": [ + 96, + 885, + 470, + 900 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "stance of traffic signs, as opposed to our default per-class patch. The transfer attack generates per-class patches from either a different source model or the synthetic data. Table 4 shows that the per-instance attack always achieves a higher ASR (and lower mAP) than the per-class attack, and the transfer attack has the lowest ASR in most cases. This result is expected and does not indicate that the gradient obfuscation or the catastrophic overfitting phenomenon is happening.", + "bbox": [ + 496, + 90, + 893, + 227 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "To further improve the robustness of the adversarial patches (i.e., making the attack transfer to other instances in the same class), we also tried to generate the adversarial patches by applying random augmentations including color-jitter and uniform noise injection (similar to expectation over transformation [3]). Table 5 shows that the augmentations with varying strength levels do not significantly affect the ASR of the attack.", + "bbox": [ + 496, + 228, + 893, + 348 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Overall, the effectiveness of all the attacks remains limited against all the adversarially trained models. In particular, the ASR of the per-instance attack, which is an upper bound of ASR on all threat models, is only $3\\%$ on Adv. DINO on REAP-S. Based on these experiments (and others in Appendix D.6), we tentatively conclude that the adversarially trained classifiers truly do appear robust for the REAP detection task. Because this result is so surprising, further research is needed before we can have full confidence in this conclusion.", + "bbox": [ + 496, + 352, + 895, + 502 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion and Future Directions", + "text_level": 1, + "bbox": [ + 500, + 523, + 808, + 539 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We construct the first large-scale benchmark for evaluating adversarial patches. Our benchmark consists of over 14,000 signs from real driving scenes, and each sign is annotated with the transformations necessary to render an adversarial patch realistically onto it. Using this benchmark, we experiment with a broad range of models and attacks. We find that adversarial patches of a clearly visible size fool an undefended model on less than $28\\%$ of the signs and only $1\\%$ for a defended model. This is in contrast to adversarial examples with bounded $\\ell_p$ -norm, where attacks nearly always succeed. All in all, our experiments suggest that realistic constraints render patch attacks significantly less effective, and vanilla adversarial training is an effective defense against the current practical patch attacks.", + "bbox": [ + 496, + 551, + 893, + 762 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "One interesting direction for future research is to explore whether attacks against object detectors can be improved. Also, in our experiments, adversarial training achieved strong robustness at the cost of degrading mAP on clean images by about 5 percentage points. It would be interesting to explore new defenses that have less impact on clean performance. We hope that our benchmark will provide a foundation for more realistic evaluation of patch attacks and drive future research on defenses against them.", + "bbox": [ + 496, + 763, + 895, + 900 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "4648", + "bbox": [ + 482, + 924, + 514, + 936 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Maksym Andriushchenko and Nicolas Flammarion. Understanding and improving fast adversarial training. In Advances in Neural Information Processing Systems, volume 33, pages 16048-16059. Curran Associates, Inc., 2020. 9", + "[2] Anish Athalye, Nicholas Carlini, and David Wagner. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.131, + 0.8, + 0.152 + ], + "angle": 0, + "content": "REAP: A Large-Scale Realistic Adversarial Patch Benchmark" + }, + { + "type": "text", + "bbox": [ + 0.197, + 0.181, + 0.326, + 0.199 + ], + "angle": 0, + "content": "Nabeel Hingun*" + }, + { + "type": "text", + "bbox": [ + 0.21, + 0.2, + 0.315, + 0.218 + ], + "angle": 0, + "content": "UC Berkeley" + }, + { + "type": "text", + "bbox": [ + 0.163, + 0.221, + 0.361, + 0.234 + ], + "angle": 0, + "content": "nabeel126@berkeley.edu" + }, + { + "type": "text", + "bbox": [ + 0.422, + 0.181, + 0.573, + 0.199 + ], + "angle": 0, + "content": "Chawin Sitawarin*" + }, + { + "type": "text", + "bbox": [ + 0.446, + 0.2, + 0.551, + 0.218 + ], + "angle": 0, + "content": "UC Berkeley" + }, + { + "type": "text", + "bbox": [ + 0.41, + 0.221, + 0.588, + 0.234 + ], + "angle": 0, + "content": "chawins@berkeley.edu" + }, + { + "type": "text", + "bbox": [ + 0.688, + 0.182, + 0.754, + 0.199 + ], + "angle": 0, + "content": "Jerry Li" + }, + { + "type": "text", + "bbox": [ + 0.682, + 0.2, + 0.762, + 0.215 + ], + "angle": 0, + "content": "Microsoft" + }, + { + "type": "text", + "bbox": [ + 0.638, + 0.221, + 0.808, + 0.234 + ], + "angle": 0, + "content": "jerrl@microsoft.com" + }, + { + "type": "text", + "bbox": [ + 0.427, + 0.243, + 0.544, + 0.26 + ], + "angle": 0, + "content": "David Wagner" + }, + { + "type": "text", + "bbox": [ + 0.434, + 0.261, + 0.538, + 0.278 + ], + "angle": 0, + "content": "UC Berkeley" + }, + { + "type": "text", + "bbox": [ + 0.401, + 0.281, + 0.571, + 0.294 + ], + "angle": 0, + "content": "daw@cs.berkeley.edu" + }, + { + "type": "text", + "bbox": [ + 0.365, + 0.309, + 0.605, + 0.32 + ], + "angle": 0, + "content": "Adversarial Patch Evaluation in Previous Work" + }, + { + "type": "image", + "bbox": [ + 0.151, + 0.322, + 0.288, + 0.428 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.322, + 0.427, + 0.428 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.429, + 0.322, + 0.636, + 0.428 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.322, + 0.822, + 0.428 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.43, + 0.436, + 0.548, + 0.447 + ], + "angle": 0, + "content": "Our REAP Benchmark" + }, + { + "type": "image", + "bbox": [ + 0.148, + 0.447, + 0.339, + 0.559 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.341, + 0.447, + 0.483, + 0.558 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.448, + 0.679, + 0.559 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.68, + 0.448, + 0.823, + 0.559 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.576, + 0.895, + 0.622 + ], + "angle": 0, + "content": "Figure 1: When digitally evaluating patch attacks, past work (top row) ignores many real-world factors and thus may yield a misleading evaluation. We develop the REAP benchmark (bottom row) that more realistically simulates the effect of a real-world patch attack on road signs, accounting for the pose, the location, and the lighting condition." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.634, + 0.314, + 0.65 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.474, + 0.903 + ], + "angle": 0, + "content": "Machine learning models are known to be susceptible to adversarial perturbation. One famous attack is the adversarial patch, a particularly crafted sticker that makes the model mispredict the object it is placed on. This attack presents a critical threat to cyber-physical systems that rely on cameras such as autonomous cars. Despite the significance of the problem, conducting research in this setting has been difficult; evaluating attacks and defenses in the real world is exceptionally costly while synthetic data are unrealistic. In this work, we propose the REAP (REalistic Adversarial Patch) benchmark, a digital benchmark that enables the evaluations on real images under real-world conditions. Built on top of the Mapillary Vistas dataset, our benchmark contains over 14,000 traffic signs. Each sign is augmented with geometric and lighting transformations for applying a digi" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.636, + 0.896, + 0.772 + ], + "angle": 0, + "content": "tally generated patch realistically onto the sign. Using our benchmark, we perform the first large-scale assessments of adversarial patch attacks under realistic conditions. Our experiments suggest that patch attacks may present a smaller threat than previously believed and that the success rate of an attack on simpler digital simulations is not predictive of its actual effectiveness in practice. Our benchmark is released publicly at https://github.com/wagner-group/reap-benchmark." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.78, + 0.633, + 0.795 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.805, + 0.896, + 0.88 + ], + "angle": 0, + "content": "Research has shown that machine learning models lack robustness against adversarially chosen perturbations. Szegedy et al. [54] first demonstrated that one can engineer perturbations that are indiscernible to the human eye yet that cause neural networks to misclassify images with high confidence." + }, + { + "type": "page_footnote", + "bbox": [ + 0.527, + 0.887, + 0.635, + 0.9 + ], + "angle": 0, + "content": "*Equal contribution." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.926, + 0.516, + 0.937 + ], + "angle": 0, + "content": "4640" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "Since then, there has been a large body of academic work on understanding the robustness of neural networks to such attacks [18, 39, 55, 8, 27, 57, 36, 7, 22]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.139, + 0.471, + 0.319 + ], + "angle": 0, + "content": "One particularly concerning type of attack is the adversarial patch attack [6, 17, 24, 53, 10, 23, 33, 43, 52, 66, 21, 61]. These are real-world attacks, where the attacker's objective is to print out a patch, physically place it in a scene, and cause a vision network processing the scene to malfunction. These attacks are especially concerning because of the potential impact on autonomous vehicles. A malicious agent could, for instance, produce a sticker that, when placed on a stop sign, cause a self-driving car to believe it is (say) a speed limit sign, and fail to stop. Indeed, similar attacks have already been demonstrated both in academic settings [31, 16, 50] and on real-world autonomous vehicles [56]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.321, + 0.47, + 0.457 + ], + "angle": 0, + "content": "Despite this significant risk, research on these attacks has stalled to a certain extent because quantitatively evaluating the significance of this threat is challenging. The most accurate approach would be to conduct real-world experiments, but they are very expensive, and at present, not practical to do at a large scale. This leaves much to be desired compared to other branches of computer vision research, where the availability of benchmarks such as ImageNet have reduced the barriers to research and spurred tremendous innovation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.458, + 0.471, + 0.669 + ], + "angle": 0, + "content": "Instead, researchers turn to one of two techniques: either, they physically create their attacks and try them out on a small number of real-world examples by physically attaching them to objects, or they digitally evaluate patch attacks using digital images containing simulated patches. Both approaches have major drawbacks. Although the former simulates more realistic conditions, the sample size is very small, and typically one cannot draw statistical conclusions from the results [6, 17, 53, 10, 66, 20, 21, 61]. Additionally, because of the ad-hoc nature of these evaluations, it is impossible to compare the results across different papers. Ultimately, such experiments only serve as a proof of concept for the proposed attacks and defenses, but not as a rigorous evaluation of their effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.67, + 0.471, + 0.821 + ], + "angle": 0, + "content": "In contrast, a digital simulation of attacks/defenses allows quantitative evaluation [24, 33, 65, 46, 37, 62, 58, 44]. However, it is difficult to accurately capture all of the challenges that arise in the real world. Past work often made unrealistic assumptions, such as that the patch is square, axis-aligned, can be located anywhere on the image, fully under the control of the attacker, and ignore noise and variation in lighting and pose (see top row of Fig. 1). Consequently, it is unclear if these evaluations are actually reflective of what would happen in real-world scenarios." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.834, + 0.258, + 0.849 + ], + "angle": 0, + "content": "1.1. Our Contributions" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The REAP Benchmark: We propose Realistic Adversarial Patch Benchmark (REAP), the first large-scale standardized benchmark for security against patch attacks. Motivated by" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "the aforementioned shortcomings of prior evaluations, we design REAP with the following principles in mind:" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.126, + 0.894, + 0.186 + ], + "angle": 0, + "content": "1. Large-scale evaluation: REAP consists of 14,651 images of road signs drawn from the Mapillary Vistas dataset. This allows us to draw quantitative conclusions about the effectiveness of attacks/defenses on the dataset." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.187, + 0.895, + 0.292 + ], + "angle": 0, + "content": "2. Realistic patch rendering: REAP has tooling, which, for every road sign in the dataset, allows us to realistically render any digital patch onto the sign, matching factors such as where to place the patch, the camera angle, lighting conditions, etc. Importantly, this transformation is fast and differentiable so one can still perform backpropagation through the rendering process." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.292, + 0.894, + 0.352 + ], + "angle": 0, + "content": "3. Realistic image distribution: REAP consists of images taken under realistic conditions, including variation in sizes and distances from the camera as well as various lighting conditions and degrees of occlusion." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.126, + 0.895, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.364, + 0.895, + 0.485 + ], + "angle": 0, + "content": "**Evaluations with REAP:** With our new benchmark in hand, we also perform the first large-scale evaluations of existing attacks on object detectors. We evaluate existing attacks on three different object detection architectures: Faster R-CNN [48], YOLOF [9], and DINO [64]. We also implement and evaluate a baseline defense adapted from adversarial training [36] to defend against patch attacks on object detection. The conclusions we find are:" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.489, + 0.894, + 0.61 + ], + "angle": 0, + "content": "1. Existing patch attacks are not that effective. Perhaps surprisingly, existing attacks do not succeed on a majority of images on our benchmark. This is in contrast to simpler attack models such as \\(\\ell_p\\)-bounded perturbations or patch attacks on simpler benchmarks, where the attack success rate is near \\(100\\%\\). Moreover, adversarily trained models can almost completely stop the attacks with only a minor performance drop on benign data." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.611, + 0.895, + 0.699 + ], + "angle": 0, + "content": "2. Performance on synthetic data is not reflective of performance on REAP. We find that the success rates of attacks on synthetic versions of our benchmark and the full REAP are only poorly correlated. We conclude that performance on simple synthetic benchmarks is not predictive of attack success rate in more realistic conditions." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.701, + 0.895, + 0.82 + ], + "angle": 0, + "content": "3. Lighting and patch placement are particularly important. Finally, we investigate what transforms in the patch rendering are the most important, in terms of the effect on the attack success rate. We find that the most significant first-order effects are from the lighting transform, as well as the positioning of the patch. In contrast, the perspective transforms—while still important—seem to affect the attack success rate somewhat less." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.489, + 0.895, + 0.82 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.9 + ], + "angle": 0, + "content": "While we believe these conclusions are already quite interesting, they are only the tip of the iceberg of what can be done with REAP. We believe that REAP will help support future research in adversarial patches by enabling a more accurate evaluation of new attacks and defenses." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.925, + 0.514, + 0.937 + ], + "angle": 0, + "content": "4641" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.22, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.113, + 0.471, + 0.236 + ], + "angle": 0, + "content": "Adversarial patch attacks. The literature on adversarial patches, and adversarial attacks more generally, is vast and a full review is beyond the scope of this paper. For conciseness, we only survey the most relevant works. Since their introduction in Brown et al. [6], Karmon et al. [24], Eykholt et al. [17], there have been a variety of adversarial patch attacks proposed [23, 33, 43, 52, 21, 61]. Of particular interest to us are the ones on object detection of road signs [17, 53, 10, 66]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.24, + 0.474, + 0.468 + ], + "angle": 0, + "content": "Small scale, real-world tests. A common methodology used to test the transferability of the adversarial patch to the physical world is to print it out, physically place it onto an object, and capture pictures or videos of the patch for evaluation [6, 17, 53, 10, 66, 20, 21, 61]. While this method provides the most realistic evaluation, it has a number of downsides. First, it is, by nature, very time-consuming and hence limits the number of images that can be used for testing. Consequently, one cannot extract quantitative conclusions from the results. Additionally, they are difficult to standardize across papers, making their result not directly comparable. For instance, the pictures of the adversarial patches are taken under different angles, lighting conditions, or from varying distances. Sometimes, the adversarial patches themselves are printed using different printers [10, 66]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.471, + 0.472, + 0.699 + ], + "angle": 0, + "content": "Completely simulated environment. Another line of work considers purely simulated environments for evaluating adversarial patches such as CARLA [14, 32, 45] and AttackScenes [21]. A huge advantage of this method is that it has the most precise and the most flexible control of the environment, e.g., cameras and objects can be placed anywhere. However, it is labor-intensive to build a diverse set of scenes digitally, and it compromises heavily on realism. Another example is 3DB [28], a photorealistic simulation for studying the reliability of computer vision systems. Nevertheless, it lacks the tooling necessary for evaluating adversarial patches and does not contain any driving scene, a setting to which adversarial patches are most applicable. Our benchmark utilizes images of real and diverse driving scenes and focuses on realistically simulating only the adversarial patches." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.471, + 0.856 + ], + "angle": 0, + "content": "Digital simulation. This third approach takes a middle road and simulates the effects of the adversarial patch by digitally inserting it into a real image. This has been done at scale and to varying degrees of sophistication. One of the most common, but also simplest, ways this is done is to apply the patch to the image at some random position, and with some simple transformations, for instance, those induced by expectation over transformation [6, 24, 33, 65, 46, 37, 62, 58, 44]. This approach violates all the physical constraints and hence, is far from being realistic." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Arguably the benchmarks most similar to ours are the ones in Zhao et al. [66] and Braunegg et al. [5]. Zhao et al. [66] digitally insert synthetic stop signs with patches into" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.244 + ], + "angle": 0, + "content": "images with realistic camera angles. However, they do not account for lighting conditions, and the target object itself is synthetic. In contrast, all signs in our dataset are real, and we also produce a transformation to match lighting conditions. In Section 4.3, we find that these two factors affect the evaluation metrics to a large extent. APRICOT [5] contains images of real scenes with a printed adversarial patch. Compared to ours, APRICOT is smaller in size (1K vs 14K images) and is heavily inflexible as it comes with a pre-defined adversarial patch with a fixed size and location." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.247, + 0.897, + 0.43 + ], + "angle": 0, + "content": "Defenses. There have also been a slew of proposed defenses against patch attacks, e.g., [19, 41, 65, 62, 46, 37, 40, 11]. Most examine object classification. Only a handful consider object detection, which may be more relevant in practice [12, 63]. We choose to experiment with adversarial training [36] as a defense because, to the extent of our knowledge, it has not been applied in this setting (Rao et al. [46] study patch adversarial training on classifiers). It is also known to be a strong baseline and arguably the only effective defense across other \\(\\ell_p\\)-norms [13]. Importantly, unlike the other defenses listed above, adversarial training does not make assumptions about the number or size of the patch." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.444, + 0.78, + 0.46 + ], + "angle": 0, + "content": "3. Adversarial Patch Benchmark" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.467, + 0.611, + 0.482 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.488, + 0.895, + 0.564 + ], + "angle": 0, + "content": "Our dataset is a collection of images containing traffic signs, each of which comes with a segmentation mask and a class. So far, this is more or less standard. The main additional feature of our benchmark is that, for each sign, we also provide an associated rendering transformation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.896, + 0.7 + ], + "angle": 0, + "content": "Given a digital patch, this transformation allows us to apply the patch on the sign in a way that respects the scaling, orientation, and lighting of the sign in the image. We emphasize that a separate transformation is inferred individually for each sign, in order to ensure that the transformation is accurate for every image. Moreover, the rendering transformation is fully differentiable, which allows our dataset to be used to generate patch attacks and to apply adversarial defenses along the line of adversarial training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.895, + 0.791 + ], + "angle": 0, + "content": "Figs. 2 and 3 give an overview of the process to obtain the geometric (Section 3.4.1) and the relighting (Section 3.4.2) transformations, respectively. We use an algorithm to generate the candidate annotations automatically, visually inspect each of them, and then manually fix any wrong annotation. In total, we label 14,651 traffic signs across 8,433 images." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.603, + 0.817 + ], + "angle": 0, + "content": "3.2. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We build our benchmark using images from the Mapillary Vistas dataset [42]. It includes 20,000 street-level images from around the world, annotated with bounding boxes of 124 object categories, including traffic signs. A limitation of Vistas is that all traffic signs are grouped under one class." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "4642" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.184 + ], + "angle": 0, + "content": "This creates a challenge for us, because our patch-rendering process depends on the size and shape of the sign. Without this information, the rendering is less realistic. We deal with this challenge by grouping the signs so that all signs in the same group can use the same geometric transform procedure. The grouping process is described in the next section." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.192, + 0.313, + 0.209 + ], + "angle": 0, + "content": "3.3. Traffic Sign Classification" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.216, + 0.471, + 0.351 + ], + "angle": 0, + "content": "Grouping traffic signs by their shape and size has two advantages. First, it allows more accurate geometric transforms as previously mentioned. Second, it allows us to study multiclass sign detection. Instead of labeling the Vistas signs by hand, we train a ResNet-18 on a similar dataset, Mapillary Traffic Sign (MTSD) [15], to classify them. MTSD contains granular labeling of over 300 traffic sign classes, but we cannot use it in place of Vistas as it lacks segmentation labels required to compute the geometric transforms." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.352, + 0.473, + 0.608 + ], + "angle": 0, + "content": "We created two versions of the benchmark: REAP and REAP-S. REAP is our main benchmark with the classes matching those of MTSD. However, most of the classes contain fewer than 10 samples so we only keep the 100 most common classes. We need a sufficient number of samples per class because (i) some will be further filtered out in the preprocessing and (ii) the samples will be split into a \"training\" (for the attacker to \"train\" the adversarial patch) and a test set (for evaluating the attack). Conversely, REAP-S groups the signs into 11 classes by shape and size, namely circle, triangle, upside-down triangle, diamond (S), diamond (L), square, rectangle (S), rectangle (M), rectangle (L), pentagon, and octagon. REAP-S serves as a simpler alternative to REAP and is also intuitively more \"defender-friendly.\" For both REAP and REAP-S, the remaining signs that do not belong to the classes are labeled as a background class or \"others\" which will be ignored when we compute the metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.609, + 0.472, + 0.729 + ], + "angle": 0, + "content": "Since Mapillary Vistas does not come with these labels, we first trained a ConvNeXt model [35] on MTSD, which achieves about \\(98\\%\\) accuracy on the validation set, to generate the candidate class labels. The labels were then automatically corrected when we compute the parameters for the geometric transform in Section 3.4.1. For the remaining ones that cannot be automatically verified, we manually inspected and corrected them." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.73, + 0.472, + 0.866 + ], + "angle": 0, + "content": "Our grouping of the signs in REAP-S has an extra benefit. Since each class is (approximately) associated with a standardized physical size, we can specify the patch size in real units (e.g., inches) instead of pixels. The real unit is arguably more useful for estimating the threat of adversarial patches than constraining the size by the number of pixels. One complication is that a single class of sign may come in different sizes, e.g., stop signs can be 24\", 36\", or 48\", depending on the kind of road they are located on, but usually one size is" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.894, + 0.184 + ], + "angle": 0, + "content": "more common. The Vistas dataset does not contain sufficient information to distinguish between these sizes so we pick one canonical size for each sign type. Specifically, we select the size specified for \"Expressway\" according to the official U.S. Department of Transportation's guideline. Appendix A describes our design decision in detail." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.198, + 0.667, + 0.213 + ], + "angle": 0, + "content": "3.4. Transformations" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.223, + 0.895, + 0.36 + ], + "angle": 0, + "content": "We render adversarial patches with two types of transformations: geometric and relighting. Since the traffic signs in our dataset vary in shape, size, and orientation, we first need to apply a geometric, specifically perspective or 3D, transform to the patch to simulate these variations. Next, we account for the fact that pictures of real-world traffic signs are taken under different lighting conditions by applying a relighting transform to the patch. The importance of these transformations is highlighted in Fig. 4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.389, + 0.742, + 0.403 + ], + "angle": 0, + "content": "3.4.1 Geometric Transformation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.416, + 0.895, + 0.492 + ], + "angle": 0, + "content": "To determine the parameters of the perspective transform, we need four keypoints for each sign. We infer the keypoints for a particular traffic sign using only its segmentation mask (which is provided in the Mapillary Vistas dataset) by following the four steps below (also visualized in Fig. 2):" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.494, + 0.894, + 0.522 + ], + "angle": 0, + "content": "1. Find contour: First, we find the contour of the segmentation mask." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.524, + 0.894, + 0.583 + ], + "angle": 0, + "content": "2. Compute convex hull: Then, we find the convex hull of the contour to correct annotation errors and occlusion. This does not affect correct masks, as they should already be convex." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.585, + 0.894, + 0.645 + ], + "angle": 0, + "content": "3. Fit polygon and ellipse: We fit an ellipse to the convex hull, to find circular signs. If the fitted ellipse results in a larger error than a certain threshold, we know that the sign is not circular and therefore fit a polygon instead." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.645, + 0.894, + 0.69 + ], + "angle": 0, + "content": "4. Cross verify: We verify that the shape obtained from the previous step matches with the ResNet's prediction. If not, the sign is flagged for manual inspection." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.494, + 0.894, + 0.69 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.692, + 0.895, + 0.859 + ], + "angle": 0, + "content": "The last step is finding the keypoints. For polygons, we first match the vertices to the canonical ones and then take the four predefined vertices as the keypoints. For circular signs, we use the ends of their major and minor axes as the four keypoints. These keypoints are used to infer a perspective transform appropriate for this sign. Triangular signs are a special case as we can only identify a maximum of three keypoints which means we can only infer a unique affine transform (six degrees of freedom). Note that this transform is linear and hence is fully differentiable. Lastly, we manually check all annotations and correct any errors." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Update August 18, 2023: In the previous version of the paper, we only present REAP-S which was called REAP." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.858, + 0.901 + ], + "angle": 0, + "content": "https://mutcd.fhwa.dot.gov/htm/2003/part2/part2b1.htm" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "4643" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.089, + 0.852, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.19, + 0.274, + 0.778, + 0.29 + ], + "angle": 0, + "content": "Figure 2: The automated procedure we use to extract the keypoints from each traffic sign." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.314, + 0.466, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.491, + 0.472, + 0.522 + ], + "angle": 0, + "content": "Figure 3: Computing relighting parameters (top) and applying the transform (bottom)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.551, + 0.318, + 0.566 + ], + "angle": 0, + "content": "3.4.2 Relighting Transformation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.577, + 0.47, + 0.803 + ], + "angle": 0, + "content": "Each traffic sign in our dataset has two associated relighting parameters, \\(\\alpha, \\beta \\in \\mathbb{R}\\). Given a patch \\(\\mathbf{P}\\), its relighted version \\(\\mathbf{P}_{\\mathrm{relighted}} = \\alpha \\mathbf{P} + \\beta\\) is rendered on the scene as depicted on the bottom row of Fig. 3. We infer \\(\\alpha, \\beta\\) by matching the histogram of the original sign (e.g., the real stop sign on the upper-right of Fig. 3) to a canonical image (e.g., the synthetic stop sign on the upper-left): in particular, we set \\(\\beta\\) as the \\(p\\)-th percentile of all the pixel values (aggregated over all three RGB channels) on that sign and \\(\\alpha\\) as the difference between the \\(p\\)-th and \\((1 - p)\\)-th percentile. We call this the \"percentile\" method and explain why we chose it in Section 3.5. This method assumes that relighting can be approximated with a linear transform where \\(\\alpha\\) and \\(\\beta\\) represent contrast and brightness adjustments. Like before, since this transformation is linear, it is differentiable." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.816, + 0.212, + 0.831 + ], + "angle": 0, + "content": "3.5. Realism Test" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In this section, we measure how realistic the patches are when rendered with different transform methods: three for geometric and eight for relighting. The geometric transforms include perspective (or homographic), affine, and translate" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.313, + 0.892, + 0.402 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.409, + 0.892, + 0.5 + ], + "angle": 0, + "content": "Figure 4: Example ablation of the geometric and relighting transforms in our dataset. The rightmost stop sign has a patch rendered with a perspective and relighting transform which makes it more realistic. The first and second images have patches that are too bright whereas the first and third images have patches that do not respect the sign's orientation." + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.519, + 0.892, + 0.566 + ], + "angle": 0, + "content": "Table 1: Comparison of different geometric and relighting transforms from our realism test (mean ± standard deviation of RMSE across 44 samples). The best results are in bold." + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.571, + 0.878, + 0.772 + ], + "angle": 0, + "content": "
TransformsMethodsColorsRMSE (↓)
GeometricTranslate & Scalen/a1.72 ± 1.19
Affinen/a1.35 ± 0.49
Perspective (3D)n/a1.13 ± 0.41
RelightingPercentileRGB0.110 ± 0.034
HSV0.227 ± 0.118
LAB0.652 ± 0.112
PolynomialRGB0.113 ± 0.037
HSV0.118 ± 0.035
LAB0.161 ± 0.043
Color TransferHSV0.117 ± 0.035
LAB0.184 ± 0.062
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.903 + ], + "angle": 0, + "content": "& scale transforms. For relighting, we experiment with three methods, each of which can be carried out on different color spaces (RGB, HSV, and LAB): the percentile method, described in Section 3.4.2; polynomial fitting, where we find the polynomial that best fits the pixel values on each real sign given the corresponding pixel values on the digital one; and Color Transfer [47], which tries to match the mean and" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "4644" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.089, + 0.429, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.278, + 0.472, + 0.34 + ], + "angle": 0, + "content": "Figure 5: RMSE between the photographed and the rendered patches using the \"percentile\" method with different values of \\( p \\). The shaded region denotes the standard deviation across 44 samples. \\( p = 20 \\) yields the lowest RMSE." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.364, + 0.465, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.418, + 0.468, + 0.448 + ], + "angle": 0, + "content": "Figure 6: Random samples used in our realism experiments (left: real, right: rendered). Fig. 17 contains all samples." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.478, + 0.355, + 0.494 + ], + "angle": 0, + "content": "the standard deviation of the pixel values." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.471, + 0.712 + ], + "angle": 0, + "content": "We photograph 44 pairs of real traffic signs with and without an adversarial patch: 11 signs, one for each class, in four scenes and lighting conditions. For each sample, we hand-annotated the keypoints of both the signs and the patches. Then, given an image of the sign without the patch, we render the patch on it using the different transform methods. For geometric transforms, we measure the root mean square error (RMSE) between the rendered and the corresponding groundtruth corners of the patch. To compare the relighting methods, we compute the RMSE between the rendered and the corresponding groundtruth pixel values of the patch. We use the groundtruth geometric transform when computing the relighting parameters to disentangle the potential error from the geometric transform." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Table 1 reports the best RMSE achieved by each transform after a hyperparameter sweep (\\( p \\), polynomial degrees, etc.). The perspective transform achieves the lowest RMSE as expected which emphasizes the importance of using the full 3D transform instead of simpler alternatives. For relighting, the percentile method with \\( p = 0.2 \\) performs as well as, or better than, any other at rendering the adversarial patches. Hence, these are the two transforms we use to construct the REAP benchmark and in all of the experiments in Section 4 unless stated otherwise. Fig. 6 visually compares the rendered patches with the groundtruth ones under these best transform methods. Appendix B contains more details." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.818, + 0.108 + ], + "angle": 0, + "content": "4. Experiments on REAP Benchmark" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.116, + 0.895, + 0.283 + ], + "angle": 0, + "content": "Our benchmark can be used to evaluate attacks and defenses under various threat models, e.g., making objects appear vs disappear, using a universal patch vs a targeted attack, etc. In this paper, we focus on the setting where the adversary tries to make a traffic sign disappear or be misclassified using the per-class attack, i.e., only one patch per class of objects, similar to Benz et al. [4]. We argue that this threat model is more realistic and more alarming as the attacker only needs to distribute several adversarial stickers that are effective across million of traffic signs. We assume the adversary has access to the target model (white-box)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.293, + 0.677, + 0.309 + ], + "angle": 0, + "content": "4.1. Experiment Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.316, + 0.895, + 0.452 + ], + "angle": 0, + "content": "Traffic sign detectors. We experiment with three object detection models, Faster R-CNN [48], YOLOF [9], and DINO [64], all trained on the MTSD dataset to predict bounding boxes for all 11 traffic sign classes plus the \"other\" class. We follow the training method and hyperparameters from Neuhold et al. [42]. As mentioned in Section 4.2, we report the false negative rate (FNR) in addition to mAP scores. For FNR, the score threshold is chosen as one that maximizes the F1 score on the validation set of MTSD." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.895, + 0.682 + ], + "angle": 0, + "content": "Attack algorithms. We use the RP2 attack [17] and the DPatch attack [33] to generate adversarial patches for all models. We assume that the adversary has access to 5 held-out images from our benchmark and use them to generate one adversarial patch per sign class. We note that this setting, referred to as per-class attack, is different from the usual white-box attack threat model where each sample is given a unique perturbation (we call it per-instance attack) and is more similar to the \"universal\" adversarial perturbation [38]. We argue that this threat model is more realistic and more alarming as the attacker only needs to distribute one adversarial sticker that are effective across million of traffic signs of the same type. Appendix D.5 discusses the threat models in more detail." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.684, + 0.894, + 0.821 + ], + "angle": 0, + "content": "Each of the classes has a specific set of these 5 images each of which contains at least one sign of that class. For REAP-S, we use 50 images since there are more samples per class. In practice, an adversary may benefit from using more than 5 (or 50) images to generate the patch, but we set our limit here to leave sufficient samples for the evaluation phase. We do not find a significant difference in the performance of the two attacks (Appendix D.1) so we report only the results of DPatch attack with PGD optimizer in the main paper." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Defense algorithm. We use adversarial training with DPatch attack and five-step PGD as it performs the best empirically. The patches are generated per-instance at a random location to prevent overfitting to a specific one. To" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "4645" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.121 + ], + "angle": 0, + "content": "Table 2: Mean FNR and mAP of the adversarial patches on six traffic sign detectors on REAP. \"FRCNN\" refers to Faster R-CNN, \"Adv.\" indicates adversarially trained models. For defenders, lower FNR \\((\\downarrow)\\) and higher mAP \\((\\uparrow)\\) are better." + }, + { + "type": "table", + "bbox": [ + 0.122, + 0.125, + 0.85, + 0.231 + ], + "angle": 0, + "content": "
Patch SizeFRCNNYOLOFDINOAdv. FRCNNAdv. YOLOFAdv. DINO
FNRmAPFNRmAPFNRmAPFNRmAPFNRmAPFNRmAP
No patch4.372.918.554.814.168.23.173.321.055.09.474.2
Small (10”×10”)15.459.433.743.532.060.43.871.822.554.71.880.6
Medium (10”×20”)22.446.542.736.635.452.66.166.827.151.91.280.1
Large (two 10”×20”)50.018.272.819.462.839.513.956.357.734.13.677.8
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.256, + 0.473, + 0.334 + ], + "angle": 0, + "content": "improve the effectiveness of adversarial training under a small number of steps, we cache patches generated in the previous epoch and use it as an initialization for the next one [67]. For more detailed setup and results, please see Appendix C." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.472, + 0.516 + ], + "angle": 0, + "content": "Synthetic Benchmark. We use canonical synthetic signs, one per class, as a baseline to compare our REAP-S benchmark to (we cannot find canonical synthetic signs for all 100 classes of REAP). Similarly to Eykholt et al. [17], the synthetic sign is placed at a random location on one of 50 random background images and randomly rotated between 0 and 15 degrees. We use the synthetic benchmark for both generating and testing the adversarial patch. For testing, we use 2,000 background images per class, randomly selected from our REAP-S benchmark to keep the distribution of the scenes similar." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.525, + 0.263, + 0.54 + ], + "angle": 0, + "content": "4.2. Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.549, + 0.47, + 0.656 + ], + "angle": 0, + "content": "Here, we define a successful attack as a patch that makes the sign either (i) undetected or (ii) classified to a wrong class (i.e., any of the other classes, or the background class). Similarly to previous work, we measure the effectiveness of an attack by the attack success rate (ASR), defined as follows. Given a list of signs \\(\\{x_i\\}_{i=1}^N\\) and the corresponding version with an adversarial patch applied to it, \\(\\{x_i'\\}_{i=1}^N\\)," + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.665, + 0.47, + 0.707 + ], + "angle": 0, + "content": "\\[\n\\mathrm {A S R} = \\frac {\\sum_ {i = 1} ^ {N} \\mathbf {1} _ {x _ {i} \\text {i s d e t e c t e d}} \\wedge \\mathbf {1} _ {x _ {i} ^ {\\prime} \\text {i s n o t d e t e c t e d}}}{\\sum_ {i = 1} ^ {N} \\mathbf {1} _ {x _ {i} \\text {i s d e t e c t e d}}}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.714, + 0.47, + 0.775 + ], + "angle": 0, + "content": "ASR and FNR are easy to interpret but dependent on specific thresholds of both the confidence score and the IoU between the groundtruth and the detected boxes. Hence, we also report mAP which averages across these thresholds." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.784, + 0.216, + 0.799 + ], + "angle": 0, + "content": "4.3. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.807, + 0.471, + 0.854 + ], + "angle": 0, + "content": "Experiments on our REAP benchmark illuminate several findings that were not previously observed due to the lack of scalability and reproducibility of real-world experiments:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "(1) Patch attacks against road signs are less effective than previously believed. From Table 2, a \\(10^{\\prime \\prime} \\times 10^{\\prime \\prime}\\) adversarial" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.256, + 0.895, + 0.437 + ], + "angle": 0, + "content": "patch increases FNR by only 11-18 percentage points on the undefended models. For REAP-S (Table 3), the increase is 8-12 percentage points. For comparison, a class-wise adversarial perturbation under imperceptible \\(\\ell_{\\infty}\\) norms achieves above \\(90\\%\\) success rate [4]. More importantly, on adversarially trained models, FNR remains almost identical before and after applying the patch on Faster R-CNN andYOLOF. Surprisingly, adversarially trained DINO performs better on samples with adversarial patches than without. We hypothesize that this is a result of overfitting to some adversarial patches and not a clear sign of weak attacks or gradient obfuscation. We refer to Section 4.4 for additional detail." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.438, + 0.895, + 0.529 + ], + "angle": 0, + "content": "This result implies that a well-known defense like adversarial training is effective and may be sufficient to protect against patch attacks in the real world. Adversarial attacks are most troubling when they are imperceptible; patches as large as \\(10^{\\prime \\prime} \\times 10^{\\prime \\prime}\\) (or larger) are likely to draw attention, which may make them less of a threat in practice." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.53, + 0.894, + 0.682 + ], + "angle": 0, + "content": "Our findings are also consistent with prior works that investigate physical-world attacks on stop signs. In these works, the attack is often clearly visible. For instance, Eykholt et al. [17] and Zhao et al. [66] use a patch that is close to our two \\( 10^{\\prime \\prime} \\times 20^{\\prime \\prime} \\) patches which is why they observe a high attack success rate similar to our results with the larger patch size. Nonetheless, a patch of this size surely breaches all notions of imperceptibility. Perhaps an interesting threat model to study in the future is to allow large patches but additionally constrain the perturbation with \\( \\ell_{\\infty} \\)-norm." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.895, + 0.84 + ], + "angle": 0, + "content": "(2) ASR measured on synthetic data is not predictive of ASR measured on our realistic benchmark. We compare REAP-S to a synthetic benchmark intended to be representative of methodology often found in prior work: we take a single synthetic image of a road sign, then generate attacks against it (instead of a real image). Table 3 and Fig. 8 show that there is a large difference between metrics as measured on such a synthetic benchmark compared to our benchmark. The gap can be up to 50–60 percentage points on average." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Fig. 8 and Table 9 in Appendix D compare ASR on the two benchmarks by class of the traffic signs. If the two ASRs were similar, all data points would have lied close to the diagonal dashed line. Instead, most of the data points" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "4646" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.135 + ], + "angle": 0, + "content": "Table 3: Mean ASR and FNR of the adversarial patches on the six traffic sign detectors on REAP-S. For sign-specific metrics, see Table 9. It is clear that evaluating on the synthetic signs overestimates the attack's potency in every setting. For defenders, lower FNR \\((\\downarrow)\\) and ASR \\((\\downarrow)\\) are better." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.14, + 0.89, + 0.322 + ], + "angle": 0, + "content": "
Patch SizeBenchmarksFRCNNYOLOFDINOAdv. FRCNNAdv. YOLOFAdv. DINO
FNRASRFNRASRFNRASRFNRASRFNRASRFNRASR
No patchSynthetic19.8n/a17.0n/a12.7n/a15.7n/a19.0n/a5.8n/a
REAP-S (ours)20.2n/a17.1n/a12.8n/a17.4n/a19.2n/a6.1n/a
Small (10"×10")Synthetic76.973.189.888.658.856.950.043.976.873.424.122.6
REAP-S (ours)50.539.248.638.936.228.018.75.128.312.71.10.1
Medium (10"×20")Synthetic89.988.392.091.173.172.679.577.383.781.734.733.9
REAP-S (ours)64.456.160.552.845.538.433.823.546.534.71.30.1
Large (two 10"×20")Synthetic99.699.6100.0100.096.596.498.998.899.198.952.952.7
REAP-S (ours)85.282.088.286.185.183.559.353.669.964.35.14.3
" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.333, + 0.892, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.412, + 0.895, + 0.46 + ], + "angle": 0, + "content": "Figure 7: Examples of small \\((10^{\\prime \\prime}\\times 10^{\\prime \\prime})\\), medium \\((10^{\\prime \\prime}\\times 20^{\\prime \\prime})\\) and large (two \\(10^{\\prime \\prime}\\times 20^{\\prime \\prime}\\)) patches applied to three of the signs from our benchmark. The large patch size is clearly visible and obscures the notion of imperceptibility. We still choose to experiment with it since it is approximately the same size used by prior work [17, 66]." + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.482, + 0.262, + 0.616 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.116, + 0.622, + 0.224, + 0.635 + ], + "angle": 0, + "content": "(a) Faster R-CNN" + }, + { + "type": "image", + "bbox": [ + 0.282, + 0.482, + 0.465, + 0.615 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.344, + 0.622, + 0.404, + 0.634 + ], + "angle": 0, + "content": "(b) DINO" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.642, + 0.47, + 0.687 + ], + "angle": 0, + "content": "Figure 8: ASRs on synthetic vs REAP-S benchmarks for Faster R-CNN (left) and DINO (right). The dashed line marks the points with an equal ASR on both datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.71, + 0.47, + 0.801 + ], + "angle": 0, + "content": "are below the line, suggesting that the synthetic benchmark consistently overestimates the ASR. Moreover, there is no clear relationship between the two measurements of ASR. If the rankings of the ASRs are well-correlated, we should expect ordering of the points to be similar in both horizontal and vertical directions, but this is not the case." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.473, + 0.903 + ], + "angle": 0, + "content": "(3) The lighting transform affects the attack's effectiveness more than the geometric transform. Fig. 9 shows how the transformations our benchmark applies to the patch affect its mAP scores. For all models, our realistic lighting transform has a much larger effect than the geometric trans" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.484, + 0.88, + 0.658 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.664, + 0.895, + 0.741 + ], + "angle": 0, + "content": "Figure 9: Effects of different geometric and relighting transform methods on the mAP of the YOLOF model under attack. The hatched bars are the default setting. When either geometric or relighting transform is varied, the other one is fixed to the default (perspective, \\( p = 0.2 \\))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.761, + 0.894, + 0.837 + ], + "angle": 0, + "content": "form. Without the lighting transform, mAP decreases by 17 percentage points for YOLOF and 15 for Faster R-CNN (i.e., an increase of 23 and 14 points on the ASR). This observation explains why the synthetic benchmark as well as synthetic evaluations in previous works overestimate ASR." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.755, + 0.862 + ], + "angle": 0, + "content": "4.4. Extended Attack Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Because these results were so surprising, we investigated the possibility that our attack algorithms are not sufficiently" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "4647" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.472, + 0.151 + ], + "angle": 0, + "content": "Table 4: Robustness of the adversarially trained models under different attack threat models (\\(10^{\\prime \\prime} \\times 10^{\\prime \\prime}\\) patch size). The per-instance attack has the highest ASR and the lowest mAP as expected, and there is no sign of gradient obfuscation." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.155, + 0.449, + 0.521 + ], + "angle": 0, + "content": "
AttacksASR (↑)mAP (↓)
Adv. Faster R-CNN
No Attackn/a66.0
Per-Class Attack5.165.7
Per-Instance Attack16.059.3
Transfer from YOLOF3.267.8
Transfer from Adv. YOLOF7.063.6
Transfer from Synthetic2.769.1
Adv. YOLOF
No Attackn/a58.5
Per-Class Attack17.751.3
Per-Instance Attack28.246.5
Transfer from Faster R-CNN13.553.1
Transfer from Adv. Faster R-CNN7.955.4
Transfer from Synthetic12.254.3
Adv. DINO
No Attackn/a65.7
Per-Class Attack0.175.1
Per-Instance Attack2.763.7
Transfer from Adv. Faster R-CNN0.176.5
Transfer from Adv. YOLOF0.276.1
Transfer from DINO0.079.6
Transfer from Synthetic0.472.7
" + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.535, + 0.472, + 0.696 + ], + "angle": 0, + "content": "
AugmentStrengthFRCNNAdv. YOLOFAdv. DINO
FNRmAPFNRmAPFNRmAP
Nonen/a15.459.422.554.71.280.1
0.116.158.823.154.71.280.1
Color-jitter0.216.058.523.654.61.280.0
0.315.559.023.354.71.380.1
0.115.758.923.054.81.280.4
Unif. noise0.215.458.822.654.71.480.1
0.315.658.622.954.71.480.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.782 + ], + "angle": 0, + "content": "Table 5: FNR and mAP with color-jitter or random noise applied during the attack EoS on REAP. We use the small patch for Faster R-CNN and Adv. YOLOF, and the medium size for Adv. DINO. None of the augmentations seems to affect the potency of the attack." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.472, + 0.884 + ], + "angle": 0, + "content": "strong (e.g., gradient obfuscation [2]) or that the adversarially trained models \"catastrophically overfit\" [59, 25, 1], i.e., they memorize the attack patterns during training but are not actually robust. In particular, we evaluate the adversarially trained models against transfer and per-instance attacks." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.472, + 0.901 + ], + "angle": 0, + "content": "The per-instance attack generates one patch for each in-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.228 + ], + "angle": 0, + "content": "stance of traffic signs, as opposed to our default per-class patch. The transfer attack generates per-class patches from either a different source model or the synthetic data. Table 4 shows that the per-instance attack always achieves a higher ASR (and lower mAP) than the per-class attack, and the transfer attack has the lowest ASR in most cases. This result is expected and does not indicate that the gradient obfuscation or the catastrophic overfitting phenomenon is happening." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.229, + 0.895, + 0.349 + ], + "angle": 0, + "content": "To further improve the robustness of the adversarial patches (i.e., making the attack transfer to other instances in the same class), we also tried to generate the adversarial patches by applying random augmentations including color-jitter and uniform noise injection (similar to expectation over transformation [3]). Table 5 shows that the augmentations with varying strength levels do not significantly affect the ASR of the attack." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.353, + 0.897, + 0.503 + ], + "angle": 0, + "content": "Overall, the effectiveness of all the attacks remains limited against all the adversarially trained models. In particular, the ASR of the per-instance attack, which is an upper bound of ASR on all threat models, is only \\(3\\%\\) on Adv. DINO on REAP-S. Based on these experiments (and others in Appendix D.6), we tentatively conclude that the adversarially trained classifiers truly do appear robust for the REAP detection task. Because this result is so surprising, further research is needed before we can have full confidence in this conclusion." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.524, + 0.809, + 0.54 + ], + "angle": 0, + "content": "5. Conclusion and Future Directions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.895, + 0.763 + ], + "angle": 0, + "content": "We construct the first large-scale benchmark for evaluating adversarial patches. Our benchmark consists of over 14,000 signs from real driving scenes, and each sign is annotated with the transformations necessary to render an adversarial patch realistically onto it. Using this benchmark, we experiment with a broad range of models and attacks. We find that adversarial patches of a clearly visible size fool an undefended model on less than \\(28\\%\\) of the signs and only \\(1\\%\\) for a defended model. This is in contrast to adversarial examples with bounded \\(\\ell_p\\)-norm, where attacks nearly always succeed. All in all, our experiments suggest that realistic constraints render patch attacks significantly less effective, and vanilla adversarial training is an effective defense against the current practical patch attacks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.897, + 0.901 + ], + "angle": 0, + "content": "One interesting direction for future research is to explore whether attacks against object detectors can be improved. Also, in our experiments, adversarial training achieved strong robustness at the cost of degrading mAP on clean images by about 5 percentage points. It would be interesting to explore new defenses that have less impact on clean performance. We hope that our benchmark will provide a foundation for more realistic evaluation of patch attacks and drive future research on defenses against them." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "4648" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Maksym Andriushchenko and Nicolas Flammarion. Understanding and improving fast adversarial training. In Advances in Neural Information Processing Systems, volume 33, pages 16048-16059. Curran Associates, Inc., 2020. 9" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.17, + 0.472, + 0.265 + ], + "angle": 0, + "content": "[2] Anish Athalye, Nicholas Carlini, and David Wagner. 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IEEE. 7" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.894, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.926, + 0.514, + 0.937 + ], + "angle": 0, + "content": "4651" + } + ] +] \ No newline at end of file diff --git a/2023/REAP_ A Large-Scale Realistic Adversarial Patch Benchmark/451492ac-a33d-4658-b61d-707c2258ba9b_origin.pdf b/2023/REAP_ A Large-Scale Realistic Adversarial Patch Benchmark/451492ac-a33d-4658-b61d-707c2258ba9b_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8fdad0400e9cd580b20babc34e6ca1b3c19cc613 --- /dev/null +++ b/2023/REAP_ A Large-Scale Realistic Adversarial Patch Benchmark/451492ac-a33d-4658-b61d-707c2258ba9b_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:55e9e95bdaedc480bae1a8d09e8e324b35dd95e580028dade5efb011f3421c04 +size 3525101 diff --git a/2023/REAP_ A Large-Scale Realistic Adversarial Patch Benchmark/full.md b/2023/REAP_ A Large-Scale Realistic Adversarial Patch Benchmark/full.md new file mode 100644 index 0000000000000000000000000000000000000000..db7ab38acb4b63480a7c63351f9f280fcc165318 --- /dev/null +++ b/2023/REAP_ A Large-Scale Realistic Adversarial Patch Benchmark/full.md @@ -0,0 +1,356 @@ +# REAP: A Large-Scale Realistic Adversarial Patch Benchmark + +Nabeel Hingun* + +UC Berkeley + +nabeel126@berkeley.edu + +Chawin Sitawarin* + +UC Berkeley + +chawins@berkeley.edu + +Jerry Li + +Microsoft + +jerrl@microsoft.com + +David Wagner + +UC Berkeley + +daw@cs.berkeley.edu + +Adversarial Patch Evaluation in Previous Work + +![](images/57bd9da3a4d0a12de70faffb2c73ece789cce48fa168e46db869660377bf6c41.jpg) + +![](images/78a482b3fadc9a3bf51c96ea9d769219171ed003b5319167aa0571dff3e1a84c.jpg) + +![](images/42cdf61e6b73b786a0d3f8ea211b811de0250241429d065c652d8223a3a0a127.jpg) + +![](images/63beb20a49ddc9dcbb800c0a5bb9f58f9940abd6ba0d0fc7d06e3be7523cd094.jpg) + +![](images/fd71a813da804e7d463a2a0547c616bf525ff9d6f91c2608fd2f800e7fef7a40.jpg) +Figure 1: When digitally evaluating patch attacks, past work (top row) ignores many real-world factors and thus may yield a misleading evaluation. We develop the REAP benchmark (bottom row) that more realistically simulates the effect of a real-world patch attack on road signs, accounting for the pose, the location, and the lighting condition. + +![](images/ceb7c4d6c2dc059358abfd0352900c6cf75279342625024bc26405231d6541c9.jpg) +Our REAP Benchmark + +![](images/da8228c891a07f64ede6a94fa32ff2543e34af256c313d3546d14a9a3dccc7d3.jpg) + +![](images/eb38663fcaf638d02c4ede269f275dfcbefb6a43fffdf72505979d4c5ee00876.jpg) + +# Abstract + +Machine learning models are known to be susceptible to adversarial perturbation. One famous attack is the adversarial patch, a particularly crafted sticker that makes the model mispredict the object it is placed on. This attack presents a critical threat to cyber-physical systems that rely on cameras such as autonomous cars. Despite the significance of the problem, conducting research in this setting has been difficult; evaluating attacks and defenses in the real world is exceptionally costly while synthetic data are unrealistic. In this work, we propose the REAP (REalistic Adversarial Patch) benchmark, a digital benchmark that enables the evaluations on real images under real-world conditions. Built on top of the Mapillary Vistas dataset, our benchmark contains over 14,000 traffic signs. Each sign is augmented with geometric and lighting transformations for applying a digi + +tally generated patch realistically onto the sign. Using our benchmark, we perform the first large-scale assessments of adversarial patch attacks under realistic conditions. Our experiments suggest that patch attacks may present a smaller threat than previously believed and that the success rate of an attack on simpler digital simulations is not predictive of its actual effectiveness in practice. Our benchmark is released publicly at https://github.com/wagner-group/reap-benchmark. + +# 1. Introduction + +Research has shown that machine learning models lack robustness against adversarially chosen perturbations. Szegedy et al. [54] first demonstrated that one can engineer perturbations that are indiscernible to the human eye yet that cause neural networks to misclassify images with high confidence. + +Since then, there has been a large body of academic work on understanding the robustness of neural networks to such attacks [18, 39, 55, 8, 27, 57, 36, 7, 22]. + +One particularly concerning type of attack is the adversarial patch attack [6, 17, 24, 53, 10, 23, 33, 43, 52, 66, 21, 61]. These are real-world attacks, where the attacker's objective is to print out a patch, physically place it in a scene, and cause a vision network processing the scene to malfunction. These attacks are especially concerning because of the potential impact on autonomous vehicles. A malicious agent could, for instance, produce a sticker that, when placed on a stop sign, cause a self-driving car to believe it is (say) a speed limit sign, and fail to stop. Indeed, similar attacks have already been demonstrated both in academic settings [31, 16, 50] and on real-world autonomous vehicles [56]. + +Despite this significant risk, research on these attacks has stalled to a certain extent because quantitatively evaluating the significance of this threat is challenging. The most accurate approach would be to conduct real-world experiments, but they are very expensive, and at present, not practical to do at a large scale. This leaves much to be desired compared to other branches of computer vision research, where the availability of benchmarks such as ImageNet have reduced the barriers to research and spurred tremendous innovation. + +Instead, researchers turn to one of two techniques: either, they physically create their attacks and try them out on a small number of real-world examples by physically attaching them to objects, or they digitally evaluate patch attacks using digital images containing simulated patches. Both approaches have major drawbacks. Although the former simulates more realistic conditions, the sample size is very small, and typically one cannot draw statistical conclusions from the results [6, 17, 53, 10, 66, 20, 21, 61]. Additionally, because of the ad-hoc nature of these evaluations, it is impossible to compare the results across different papers. Ultimately, such experiments only serve as a proof of concept for the proposed attacks and defenses, but not as a rigorous evaluation of their effectiveness. + +In contrast, a digital simulation of attacks/defenses allows quantitative evaluation [24, 33, 65, 46, 37, 62, 58, 44]. However, it is difficult to accurately capture all of the challenges that arise in the real world. Past work often made unrealistic assumptions, such as that the patch is square, axis-aligned, can be located anywhere on the image, fully under the control of the attacker, and ignore noise and variation in lighting and pose (see top row of Fig. 1). Consequently, it is unclear if these evaluations are actually reflective of what would happen in real-world scenarios. + +# 1.1. Our Contributions + +The REAP Benchmark: We propose Realistic Adversarial Patch Benchmark (REAP), the first large-scale standardized benchmark for security against patch attacks. Motivated by + +the aforementioned shortcomings of prior evaluations, we design REAP with the following principles in mind: + +1. Large-scale evaluation: REAP consists of 14,651 images of road signs drawn from the Mapillary Vistas dataset. This allows us to draw quantitative conclusions about the effectiveness of attacks/defenses on the dataset. +2. Realistic patch rendering: REAP has tooling, which, for every road sign in the dataset, allows us to realistically render any digital patch onto the sign, matching factors such as where to place the patch, the camera angle, lighting conditions, etc. Importantly, this transformation is fast and differentiable so one can still perform backpropagation through the rendering process. +3. Realistic image distribution: REAP consists of images taken under realistic conditions, including variation in sizes and distances from the camera as well as various lighting conditions and degrees of occlusion. + +**Evaluations with REAP:** With our new benchmark in hand, we also perform the first large-scale evaluations of existing attacks on object detectors. We evaluate existing attacks on three different object detection architectures: Faster R-CNN [48], YOLOF [9], and DINO [64]. We also implement and evaluate a baseline defense adapted from adversarial training [36] to defend against patch attacks on object detection. The conclusions we find are: + +1. Existing patch attacks are not that effective. Perhaps surprisingly, existing attacks do not succeed on a majority of images on our benchmark. This is in contrast to simpler attack models such as $\ell_p$ -bounded perturbations or patch attacks on simpler benchmarks, where the attack success rate is near $100\%$ . Moreover, adversarily trained models can almost completely stop the attacks with only a minor performance drop on benign data. +2. Performance on synthetic data is not reflective of performance on REAP. We find that the success rates of attacks on synthetic versions of our benchmark and the full REAP are only poorly correlated. We conclude that performance on simple synthetic benchmarks is not predictive of attack success rate in more realistic conditions. +3. Lighting and patch placement are particularly important. Finally, we investigate what transforms in the patch rendering are the most important, in terms of the effect on the attack success rate. We find that the most significant first-order effects are from the lighting transform, as well as the positioning of the patch. In contrast, the perspective transforms—while still important—seem to affect the attack success rate somewhat less. + +While we believe these conclusions are already quite interesting, they are only the tip of the iceberg of what can be done with REAP. We believe that REAP will help support future research in adversarial patches by enabling a more accurate evaluation of new attacks and defenses. + +# 2. Related Work + +Adversarial patch attacks. The literature on adversarial patches, and adversarial attacks more generally, is vast and a full review is beyond the scope of this paper. For conciseness, we only survey the most relevant works. Since their introduction in Brown et al. [6], Karmon et al. [24], Eykholt et al. [17], there have been a variety of adversarial patch attacks proposed [23, 33, 43, 52, 21, 61]. Of particular interest to us are the ones on object detection of road signs [17, 53, 10, 66]. + +Small scale, real-world tests. A common methodology used to test the transferability of the adversarial patch to the physical world is to print it out, physically place it onto an object, and capture pictures or videos of the patch for evaluation [6, 17, 53, 10, 66, 20, 21, 61]. While this method provides the most realistic evaluation, it has a number of downsides. First, it is, by nature, very time-consuming and hence limits the number of images that can be used for testing. Consequently, one cannot extract quantitative conclusions from the results. Additionally, they are difficult to standardize across papers, making their result not directly comparable. For instance, the pictures of the adversarial patches are taken under different angles, lighting conditions, or from varying distances. Sometimes, the adversarial patches themselves are printed using different printers [10, 66]. + +Completely simulated environment. Another line of work considers purely simulated environments for evaluating adversarial patches such as CARLA [14, 32, 45] and AttackScenes [21]. A huge advantage of this method is that it has the most precise and the most flexible control of the environment, e.g., cameras and objects can be placed anywhere. However, it is labor-intensive to build a diverse set of scenes digitally, and it compromises heavily on realism. Another example is 3DB [28], a photorealistic simulation for studying the reliability of computer vision systems. Nevertheless, it lacks the tooling necessary for evaluating adversarial patches and does not contain any driving scene, a setting to which adversarial patches are most applicable. Our benchmark utilizes images of real and diverse driving scenes and focuses on realistically simulating only the adversarial patches. + +Digital simulation. This third approach takes a middle road and simulates the effects of the adversarial patch by digitally inserting it into a real image. This has been done at scale and to varying degrees of sophistication. One of the most common, but also simplest, ways this is done is to apply the patch to the image at some random position, and with some simple transformations, for instance, those induced by expectation over transformation [6, 24, 33, 65, 46, 37, 62, 58, 44]. This approach violates all the physical constraints and hence, is far from being realistic. + +Arguably the benchmarks most similar to ours are the ones in Zhao et al. [66] and Braunegg et al. [5]. Zhao et al. [66] digitally insert synthetic stop signs with patches into + +images with realistic camera angles. However, they do not account for lighting conditions, and the target object itself is synthetic. In contrast, all signs in our dataset are real, and we also produce a transformation to match lighting conditions. In Section 4.3, we find that these two factors affect the evaluation metrics to a large extent. APRICOT [5] contains images of real scenes with a printed adversarial patch. Compared to ours, APRICOT is smaller in size (1K vs 14K images) and is heavily inflexible as it comes with a pre-defined adversarial patch with a fixed size and location. + +Defenses. There have also been a slew of proposed defenses against patch attacks, e.g., [19, 41, 65, 62, 46, 37, 40, 11]. Most examine object classification. Only a handful consider object detection, which may be more relevant in practice [12, 63]. We choose to experiment with adversarial training [36] as a defense because, to the extent of our knowledge, it has not been applied in this setting (Rao et al. [46] study patch adversarial training on classifiers). It is also known to be a strong baseline and arguably the only effective defense across other $\ell_p$ -norms [13]. Importantly, unlike the other defenses listed above, adversarial training does not make assumptions about the number or size of the patch. + +# 3. Adversarial Patch Benchmark + +# 3.1. Overview + +Our dataset is a collection of images containing traffic signs, each of which comes with a segmentation mask and a class. So far, this is more or less standard. The main additional feature of our benchmark is that, for each sign, we also provide an associated rendering transformation. + +Given a digital patch, this transformation allows us to apply the patch on the sign in a way that respects the scaling, orientation, and lighting of the sign in the image. We emphasize that a separate transformation is inferred individually for each sign, in order to ensure that the transformation is accurate for every image. Moreover, the rendering transformation is fully differentiable, which allows our dataset to be used to generate patch attacks and to apply adversarial defenses along the line of adversarial training. + +Figs. 2 and 3 give an overview of the process to obtain the geometric (Section 3.4.1) and the relighting (Section 3.4.2) transformations, respectively. We use an algorithm to generate the candidate annotations automatically, visually inspect each of them, and then manually fix any wrong annotation. In total, we label 14,651 traffic signs across 8,433 images. + +# 3.2. Datasets + +We build our benchmark using images from the Mapillary Vistas dataset [42]. It includes 20,000 street-level images from around the world, annotated with bounding boxes of 124 object categories, including traffic signs. A limitation of Vistas is that all traffic signs are grouped under one class. + +This creates a challenge for us, because our patch-rendering process depends on the size and shape of the sign. Without this information, the rendering is less realistic. We deal with this challenge by grouping the signs so that all signs in the same group can use the same geometric transform procedure. The grouping process is described in the next section. + +# 3.3. Traffic Sign Classification + +Grouping traffic signs by their shape and size has two advantages. First, it allows more accurate geometric transforms as previously mentioned. Second, it allows us to study multiclass sign detection. Instead of labeling the Vistas signs by hand, we train a ResNet-18 on a similar dataset, Mapillary Traffic Sign (MTSD) [15], to classify them. MTSD contains granular labeling of over 300 traffic sign classes, but we cannot use it in place of Vistas as it lacks segmentation labels required to compute the geometric transforms. + +We created two versions of the benchmark: REAP and REAP-S. REAP is our main benchmark with the classes matching those of MTSD. However, most of the classes contain fewer than 10 samples so we only keep the 100 most common classes. We need a sufficient number of samples per class because (i) some will be further filtered out in the preprocessing and (ii) the samples will be split into a "training" (for the attacker to "train" the adversarial patch) and a test set (for evaluating the attack). Conversely, REAP-S groups the signs into 11 classes by shape and size, namely circle, triangle, upside-down triangle, diamond (S), diamond (L), square, rectangle (S), rectangle (M), rectangle (L), pentagon, and octagon. REAP-S serves as a simpler alternative to REAP and is also intuitively more "defender-friendly." For both REAP and REAP-S, the remaining signs that do not belong to the classes are labeled as a background class or "others" which will be ignored when we compute the metrics. + +Since Mapillary Vistas does not come with these labels, we first trained a ConvNeXt model [35] on MTSD, which achieves about $98\%$ accuracy on the validation set, to generate the candidate class labels. The labels were then automatically corrected when we compute the parameters for the geometric transform in Section 3.4.1. For the remaining ones that cannot be automatically verified, we manually inspected and corrected them. + +Our grouping of the signs in REAP-S has an extra benefit. Since each class is (approximately) associated with a standardized physical size, we can specify the patch size in real units (e.g., inches) instead of pixels. The real unit is arguably more useful for estimating the threat of adversarial patches than constraining the size by the number of pixels. One complication is that a single class of sign may come in different sizes, e.g., stop signs can be 24", 36", or 48", depending on the kind of road they are located on, but usually one size is + +more common. The Vistas dataset does not contain sufficient information to distinguish between these sizes so we pick one canonical size for each sign type. Specifically, we select the size specified for "Expressway" according to the official U.S. Department of Transportation's guideline. Appendix A describes our design decision in detail. + +# 3.4. Transformations + +We render adversarial patches with two types of transformations: geometric and relighting. Since the traffic signs in our dataset vary in shape, size, and orientation, we first need to apply a geometric, specifically perspective or 3D, transform to the patch to simulate these variations. Next, we account for the fact that pictures of real-world traffic signs are taken under different lighting conditions by applying a relighting transform to the patch. The importance of these transformations is highlighted in Fig. 4. + +# 3.4.1 Geometric Transformation + +To determine the parameters of the perspective transform, we need four keypoints for each sign. We infer the keypoints for a particular traffic sign using only its segmentation mask (which is provided in the Mapillary Vistas dataset) by following the four steps below (also visualized in Fig. 2): + +1. Find contour: First, we find the contour of the segmentation mask. +2. Compute convex hull: Then, we find the convex hull of the contour to correct annotation errors and occlusion. This does not affect correct masks, as they should already be convex. +3. Fit polygon and ellipse: We fit an ellipse to the convex hull, to find circular signs. If the fitted ellipse results in a larger error than a certain threshold, we know that the sign is not circular and therefore fit a polygon instead. +4. Cross verify: We verify that the shape obtained from the previous step matches with the ResNet's prediction. If not, the sign is flagged for manual inspection. + +The last step is finding the keypoints. For polygons, we first match the vertices to the canonical ones and then take the four predefined vertices as the keypoints. For circular signs, we use the ends of their major and minor axes as the four keypoints. These keypoints are used to infer a perspective transform appropriate for this sign. Triangular signs are a special case as we can only identify a maximum of three keypoints which means we can only infer a unique affine transform (six degrees of freedom). Note that this transform is linear and hence is fully differentiable. Lastly, we manually check all annotations and correct any errors. + +![](images/641e0e87f34571762b1f58e1e0fa5b355eb400399aa73e6f8a65814778825601.jpg) +Figure 2: The automated procedure we use to extract the keypoints from each traffic sign. + +![](images/7f17b8a34d38a397c6bdb1d0a651593de638302a759b8b269868f399214025dd.jpg) +Figure 3: Computing relighting parameters (top) and applying the transform (bottom). + +# 3.4.2 Relighting Transformation + +Each traffic sign in our dataset has two associated relighting parameters, $\alpha, \beta \in \mathbb{R}$ . Given a patch $\mathbf{P}$ , its relighted version $\mathbf{P}_{\mathrm{relighted}} = \alpha \mathbf{P} + \beta$ is rendered on the scene as depicted on the bottom row of Fig. 3. We infer $\alpha, \beta$ by matching the histogram of the original sign (e.g., the real stop sign on the upper-right of Fig. 3) to a canonical image (e.g., the synthetic stop sign on the upper-left): in particular, we set $\beta$ as the $p$ -th percentile of all the pixel values (aggregated over all three RGB channels) on that sign and $\alpha$ as the difference between the $p$ -th and $(1 - p)$ -th percentile. We call this the "percentile" method and explain why we chose it in Section 3.5. This method assumes that relighting can be approximated with a linear transform where $\alpha$ and $\beta$ represent contrast and brightness adjustments. Like before, since this transformation is linear, it is differentiable. + +# 3.5. Realism Test + +In this section, we measure how realistic the patches are when rendered with different transform methods: three for geometric and eight for relighting. The geometric transforms include perspective (or homographic), affine, and translate + +![](images/addfcb402de2f8f50bd6106136ce613fce22591ca4957f9027faa89de7158a0b.jpg) +Figure 4: Example ablation of the geometric and relighting transforms in our dataset. The rightmost stop sign has a patch rendered with a perspective and relighting transform which makes it more realistic. The first and second images have patches that are too bright whereas the first and third images have patches that do not respect the sign's orientation. + +Table 1: Comparison of different geometric and relighting transforms from our realism test (mean ± standard deviation of RMSE across 44 samples). The best results are in bold. + +
TransformsMethodsColorsRMSE (↓)
GeometricTranslate & Scalen/a1.72 ± 1.19
Affinen/a1.35 ± 0.49
Perspective (3D)n/a1.13 ± 0.41
RelightingPercentileRGB0.110 ± 0.034
HSV0.227 ± 0.118
LAB0.652 ± 0.112
PolynomialRGB0.113 ± 0.037
HSV0.118 ± 0.035
LAB0.161 ± 0.043
Color TransferHSV0.117 ± 0.035
LAB0.184 ± 0.062
+ +& scale transforms. For relighting, we experiment with three methods, each of which can be carried out on different color spaces (RGB, HSV, and LAB): the percentile method, described in Section 3.4.2; polynomial fitting, where we find the polynomial that best fits the pixel values on each real sign given the corresponding pixel values on the digital one; and Color Transfer [47], which tries to match the mean and + +![](images/412f07cd059447c2ddb50f651d9386bb0afa2ec353866de8cbf356904e2b982f.jpg) +Figure 5: RMSE between the photographed and the rendered patches using the "percentile" method with different values of $p$ . The shaded region denotes the standard deviation across 44 samples. $p = 20$ yields the lowest RMSE. + +![](images/619059a995c458ee908f741369f34f521544bd0bd8a7645552a161fda1fa25d1.jpg) +Figure 6: Random samples used in our realism experiments (left: real, right: rendered). Fig. 17 contains all samples. + +the standard deviation of the pixel values. + +We photograph 44 pairs of real traffic signs with and without an adversarial patch: 11 signs, one for each class, in four scenes and lighting conditions. For each sample, we hand-annotated the keypoints of both the signs and the patches. Then, given an image of the sign without the patch, we render the patch on it using the different transform methods. For geometric transforms, we measure the root mean square error (RMSE) between the rendered and the corresponding groundtruth corners of the patch. To compare the relighting methods, we compute the RMSE between the rendered and the corresponding groundtruth pixel values of the patch. We use the groundtruth geometric transform when computing the relighting parameters to disentangle the potential error from the geometric transform. + +Table 1 reports the best RMSE achieved by each transform after a hyperparameter sweep ( $p$ , polynomial degrees, etc.). The perspective transform achieves the lowest RMSE as expected which emphasizes the importance of using the full 3D transform instead of simpler alternatives. For relighting, the percentile method with $p = 0.2$ performs as well as, or better than, any other at rendering the adversarial patches. Hence, these are the two transforms we use to construct the REAP benchmark and in all of the experiments in Section 4 unless stated otherwise. Fig. 6 visually compares the rendered patches with the groundtruth ones under these best transform methods. Appendix B contains more details. + +# 4. Experiments on REAP Benchmark + +Our benchmark can be used to evaluate attacks and defenses under various threat models, e.g., making objects appear vs disappear, using a universal patch vs a targeted attack, etc. In this paper, we focus on the setting where the adversary tries to make a traffic sign disappear or be misclassified using the per-class attack, i.e., only one patch per class of objects, similar to Benz et al. [4]. We argue that this threat model is more realistic and more alarming as the attacker only needs to distribute several adversarial stickers that are effective across million of traffic signs. We assume the adversary has access to the target model (white-box). + +# 4.1. Experiment Setup + +Traffic sign detectors. We experiment with three object detection models, Faster R-CNN [48], YOLOF [9], and DINO [64], all trained on the MTSD dataset to predict bounding boxes for all 11 traffic sign classes plus the "other" class. We follow the training method and hyperparameters from Neuhold et al. [42]. As mentioned in Section 4.2, we report the false negative rate (FNR) in addition to mAP scores. For FNR, the score threshold is chosen as one that maximizes the F1 score on the validation set of MTSD. + +Attack algorithms. We use the RP2 attack [17] and the DPatch attack [33] to generate adversarial patches for all models. We assume that the adversary has access to 5 held-out images from our benchmark and use them to generate one adversarial patch per sign class. We note that this setting, referred to as per-class attack, is different from the usual white-box attack threat model where each sample is given a unique perturbation (we call it per-instance attack) and is more similar to the "universal" adversarial perturbation [38]. We argue that this threat model is more realistic and more alarming as the attacker only needs to distribute one adversarial sticker that are effective across million of traffic signs of the same type. Appendix D.5 discusses the threat models in more detail. + +Each of the classes has a specific set of these 5 images each of which contains at least one sign of that class. For REAP-S, we use 50 images since there are more samples per class. In practice, an adversary may benefit from using more than 5 (or 50) images to generate the patch, but we set our limit here to leave sufficient samples for the evaluation phase. We do not find a significant difference in the performance of the two attacks (Appendix D.1) so we report only the results of DPatch attack with PGD optimizer in the main paper. + +Defense algorithm. We use adversarial training with DPatch attack and five-step PGD as it performs the best empirically. The patches are generated per-instance at a random location to prevent overfitting to a specific one. To + +Table 2: Mean FNR and mAP of the adversarial patches on six traffic sign detectors on REAP. "FRCNN" refers to Faster R-CNN, "Adv." indicates adversarially trained models. For defenders, lower FNR $(\downarrow)$ and higher mAP $(\uparrow)$ are better. + +
Patch SizeFRCNNYOLOFDINOAdv. FRCNNAdv. YOLOFAdv. DINO
FNRmAPFNRmAPFNRmAPFNRmAPFNRmAPFNRmAP
No patch4.372.918.554.814.168.23.173.321.055.09.474.2
Small (10”×10”)15.459.433.743.532.060.43.871.822.554.71.880.6
Medium (10”×20”)22.446.542.736.635.452.66.166.827.151.91.280.1
Large (two 10”×20”)50.018.272.819.462.839.513.956.357.734.13.677.8
+ +improve the effectiveness of adversarial training under a small number of steps, we cache patches generated in the previous epoch and use it as an initialization for the next one [67]. For more detailed setup and results, please see Appendix C. + +Synthetic Benchmark. We use canonical synthetic signs, one per class, as a baseline to compare our REAP-S benchmark to (we cannot find canonical synthetic signs for all 100 classes of REAP). Similarly to Eykholt et al. [17], the synthetic sign is placed at a random location on one of 50 random background images and randomly rotated between 0 and 15 degrees. We use the synthetic benchmark for both generating and testing the adversarial patch. For testing, we use 2,000 background images per class, randomly selected from our REAP-S benchmark to keep the distribution of the scenes similar. + +# 4.2. Evaluation Metrics + +Here, we define a successful attack as a patch that makes the sign either (i) undetected or (ii) classified to a wrong class (i.e., any of the other classes, or the background class). Similarly to previous work, we measure the effectiveness of an attack by the attack success rate (ASR), defined as follows. Given a list of signs $\{x_i\}_{i=1}^N$ and the corresponding version with an adversarial patch applied to it, $\{x_i'\}_{i=1}^N$ , + +$$ +\mathrm {A S R} = \frac {\sum_ {i = 1} ^ {N} \mathbf {1} _ {x _ {i} \text {i s d e t e c t e d}} \wedge \mathbf {1} _ {x _ {i} ^ {\prime} \text {i s n o t d e t e c t e d}}}{\sum_ {i = 1} ^ {N} \mathbf {1} _ {x _ {i} \text {i s d e t e c t e d}}}. \tag {1} +$$ + +ASR and FNR are easy to interpret but dependent on specific thresholds of both the confidence score and the IoU between the groundtruth and the detected boxes. Hence, we also report mAP which averages across these thresholds. + +# 4.3. Main Results + +Experiments on our REAP benchmark illuminate several findings that were not previously observed due to the lack of scalability and reproducibility of real-world experiments: + +(1) Patch attacks against road signs are less effective than previously believed. From Table 2, a $10^{\prime \prime} \times 10^{\prime \prime}$ adversarial + +patch increases FNR by only 11-18 percentage points on the undefended models. For REAP-S (Table 3), the increase is 8-12 percentage points. For comparison, a class-wise adversarial perturbation under imperceptible $\ell_{\infty}$ norms achieves above $90\%$ success rate [4]. More importantly, on adversarially trained models, FNR remains almost identical before and after applying the patch on Faster R-CNN andYOLOF. Surprisingly, adversarially trained DINO performs better on samples with adversarial patches than without. We hypothesize that this is a result of overfitting to some adversarial patches and not a clear sign of weak attacks or gradient obfuscation. We refer to Section 4.4 for additional detail. + +This result implies that a well-known defense like adversarial training is effective and may be sufficient to protect against patch attacks in the real world. Adversarial attacks are most troubling when they are imperceptible; patches as large as $10^{\prime \prime} \times 10^{\prime \prime}$ (or larger) are likely to draw attention, which may make them less of a threat in practice. + +Our findings are also consistent with prior works that investigate physical-world attacks on stop signs. In these works, the attack is often clearly visible. For instance, Eykholt et al. [17] and Zhao et al. [66] use a patch that is close to our two $10^{\prime \prime} \times 20^{\prime \prime}$ patches which is why they observe a high attack success rate similar to our results with the larger patch size. Nonetheless, a patch of this size surely breaches all notions of imperceptibility. Perhaps an interesting threat model to study in the future is to allow large patches but additionally constrain the perturbation with $\ell_{\infty}$ -norm. + +(2) ASR measured on synthetic data is not predictive of ASR measured on our realistic benchmark. We compare REAP-S to a synthetic benchmark intended to be representative of methodology often found in prior work: we take a single synthetic image of a road sign, then generate attacks against it (instead of a real image). Table 3 and Fig. 8 show that there is a large difference between metrics as measured on such a synthetic benchmark compared to our benchmark. The gap can be up to 50–60 percentage points on average. + +Fig. 8 and Table 9 in Appendix D compare ASR on the two benchmarks by class of the traffic signs. If the two ASRs were similar, all data points would have lied close to the diagonal dashed line. Instead, most of the data points + +Table 3: Mean ASR and FNR of the adversarial patches on the six traffic sign detectors on REAP-S. For sign-specific metrics, see Table 9. It is clear that evaluating on the synthetic signs overestimates the attack's potency in every setting. For defenders, lower FNR $(\downarrow)$ and ASR $(\downarrow)$ are better. + +
Patch SizeBenchmarksFRCNNYOLOFDINOAdv. FRCNNAdv. YOLOFAdv. DINO
FNRASRFNRASRFNRASRFNRASRFNRASRFNRASR
No patchSynthetic19.8n/a17.0n/a12.7n/a15.7n/a19.0n/a5.8n/a
REAP-S (ours)20.2n/a17.1n/a12.8n/a17.4n/a19.2n/a6.1n/a
Small (10"×10")Synthetic76.973.189.888.658.856.950.043.976.873.424.122.6
REAP-S (ours)50.539.248.638.936.228.018.75.128.312.71.10.1
Medium (10"×20")Synthetic89.988.392.091.173.172.679.577.383.781.734.733.9
REAP-S (ours)64.456.160.552.845.538.433.823.546.534.71.30.1
Large (two 10"×20")Synthetic99.699.6100.0100.096.596.498.998.899.198.952.952.7
REAP-S (ours)85.282.088.286.185.183.559.353.669.964.35.14.3
+ +![](images/d50b1ade17dd267eb78a9918829a6071ccea9a6469e26b062f24057ec3aa9a2d.jpg) +Figure 7: Examples of small $(10^{\prime \prime}\times 10^{\prime \prime})$ , medium $(10^{\prime \prime}\times 20^{\prime \prime})$ and large (two $10^{\prime \prime}\times 20^{\prime \prime}$ ) patches applied to three of the signs from our benchmark. The large patch size is clearly visible and obscures the notion of imperceptibility. We still choose to experiment with it since it is approximately the same size used by prior work [17, 66]. + +![](images/1c52d0d73411f95ac37fa20e6fcd5dd5a5b54b172d49303917d04445e3b35046.jpg) +(a) Faster R-CNN + +![](images/743268b0e88296ef41c8513ec599a5b1793e9840b0be2825b71783393360e56f.jpg) +(b) DINO + +are below the line, suggesting that the synthetic benchmark consistently overestimates the ASR. Moreover, there is no clear relationship between the two measurements of ASR. If the rankings of the ASRs are well-correlated, we should expect ordering of the points to be similar in both horizontal and vertical directions, but this is not the case. + +(3) The lighting transform affects the attack's effectiveness more than the geometric transform. Fig. 9 shows how the transformations our benchmark applies to the patch affect its mAP scores. For all models, our realistic lighting transform has a much larger effect than the geometric trans + +![](images/97c2a901f6e6a0ae5f5aa252da46905c5cb68724729a8c1cf5af45dd8a140b61.jpg) +Figure 8: ASRs on synthetic vs REAP-S benchmarks for Faster R-CNN (left) and DINO (right). The dashed line marks the points with an equal ASR on both datasets. +Figure 9: Effects of different geometric and relighting transform methods on the mAP of the YOLOF model under attack. The hatched bars are the default setting. When either geometric or relighting transform is varied, the other one is fixed to the default (perspective, $p = 0.2$ ). + +form. Without the lighting transform, mAP decreases by 17 percentage points for YOLOF and 15 for Faster R-CNN (i.e., an increase of 23 and 14 points on the ASR). This observation explains why the synthetic benchmark as well as synthetic evaluations in previous works overestimate ASR. + +# 4.4. Extended Attack Evaluation + +Because these results were so surprising, we investigated the possibility that our attack algorithms are not sufficiently + +Table 4: Robustness of the adversarially trained models under different attack threat models ( $10^{\prime \prime} \times 10^{\prime \prime}$ patch size). The per-instance attack has the highest ASR and the lowest mAP as expected, and there is no sign of gradient obfuscation. + +
AttacksASR (↑)mAP (↓)
Adv. Faster R-CNN
No Attackn/a66.0
Per-Class Attack5.165.7
Per-Instance Attack16.059.3
Transfer from YOLOF3.267.8
Transfer from Adv. YOLOF7.063.6
Transfer from Synthetic2.769.1
Adv. YOLOF
No Attackn/a58.5
Per-Class Attack17.751.3
Per-Instance Attack28.246.5
Transfer from Faster R-CNN13.553.1
Transfer from Adv. Faster R-CNN7.955.4
Transfer from Synthetic12.254.3
Adv. DINO
No Attackn/a65.7
Per-Class Attack0.175.1
Per-Instance Attack2.763.7
Transfer from Adv. Faster R-CNN0.176.5
Transfer from Adv. YOLOF0.276.1
Transfer from DINO0.079.6
Transfer from Synthetic0.472.7
+ +
AugmentStrengthFRCNNAdv. YOLOFAdv. DINO
FNRmAPFNRmAPFNRmAP
Nonen/a15.459.422.554.71.280.1
0.116.158.823.154.71.280.1
Color-jitter0.216.058.523.654.61.280.0
0.315.559.023.354.71.380.1
0.115.758.923.054.81.280.4
Unif. noise0.215.458.822.654.71.480.1
0.315.658.622.954.71.480.2
+ +Table 5: FNR and mAP with color-jitter or random noise applied during the attack EoS on REAP. We use the small patch for Faster R-CNN and Adv. YOLOF, and the medium size for Adv. DINO. None of the augmentations seems to affect the potency of the attack. + +strong (e.g., gradient obfuscation [2]) or that the adversarially trained models "catastrophically overfit" [59, 25, 1], i.e., they memorize the attack patterns during training but are not actually robust. In particular, we evaluate the adversarially trained models against transfer and per-instance attacks. + +The per-instance attack generates one patch for each in- + +stance of traffic signs, as opposed to our default per-class patch. The transfer attack generates per-class patches from either a different source model or the synthetic data. Table 4 shows that the per-instance attack always achieves a higher ASR (and lower mAP) than the per-class attack, and the transfer attack has the lowest ASR in most cases. This result is expected and does not indicate that the gradient obfuscation or the catastrophic overfitting phenomenon is happening. + +To further improve the robustness of the adversarial patches (i.e., making the attack transfer to other instances in the same class), we also tried to generate the adversarial patches by applying random augmentations including color-jitter and uniform noise injection (similar to expectation over transformation [3]). Table 5 shows that the augmentations with varying strength levels do not significantly affect the ASR of the attack. + +Overall, the effectiveness of all the attacks remains limited against all the adversarially trained models. In particular, the ASR of the per-instance attack, which is an upper bound of ASR on all threat models, is only $3\%$ on Adv. DINO on REAP-S. Based on these experiments (and others in Appendix D.6), we tentatively conclude that the adversarially trained classifiers truly do appear robust for the REAP detection task. Because this result is so surprising, further research is needed before we can have full confidence in this conclusion. + +# 5. Conclusion and Future Directions + +We construct the first large-scale benchmark for evaluating adversarial patches. Our benchmark consists of over 14,000 signs from real driving scenes, and each sign is annotated with the transformations necessary to render an adversarial patch realistically onto it. Using this benchmark, we experiment with a broad range of models and attacks. We find that adversarial patches of a clearly visible size fool an undefended model on less than $28\%$ of the signs and only $1\%$ for a defended model. This is in contrast to adversarial examples with bounded $\ell_p$ -norm, where attacks nearly always succeed. 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One famous attack is the adversarial patch, a particularly crafted sticker that makes the model mispredict the object it is placed on. This attack presents a critical threat to cyber-physical systems that rely on cameras such as autonomous cars. Despite the significance of the problem, conducting research in this setting has been difficult; evaluating attacks and defenses in the real world is exceptionally costly while synthetic data are unrealistic. In this work, we propose the REAP (REalistic Adversarial Patch) benchmark, a digital benchmark that enables the evaluations on real images under real-world conditions. Built on top of the Mapillary Vistas dataset, our benchmark contains over 14,000 traffic signs. Each sign is augmented with geometric and lighting transformations for applying a digi" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 503, + 548, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 503, + 548, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 503, + 548, + 611 + ], + "type": "text", + "content": "tally generated patch realistically onto the sign. Using our benchmark, we perform the first large-scale assessments of adversarial patch attacks under realistic conditions. Our experiments suggest that patch attacks may present a smaller threat than previously believed and that the success rate of an attack on simpler digital simulations is not predictive of its actual effectiveness in practice. Our benchmark is released publicly at https://github.com/wagner-group/reap-benchmark." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 617, + 387, + 629 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 617, + 387, + 629 + ], + "spans": [ + { + "bbox": [ + 306, + 617, + 387, + 629 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 637, + 548, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 637, + 548, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 637, + 548, + 696 + ], + "type": "text", + "content": "Research has shown that machine learning models lack robustness against adversarially chosen perturbations. Szegedy et al. [54] first demonstrated that one can engineer perturbations that are indiscernible to the human eye yet that cause neural networks to misclassify images with high confidence." + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 322, + 702, + 388, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 702, + 388, + 712 + ], + "spans": [ + { + "bbox": [ + 322, + 702, + 388, + 712 + ], + "type": "text", + "content": "*Equal contribution." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 295, + 733, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 733, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 733, + 315, + 742 + ], + "type": "text", + "content": "4640" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 108 + ], + "type": "text", + "content": "Since then, there has been a large body of academic work on understanding the robustness of neural networks to such attacks [18, 39, 55, 8, 27, 57, 36, 7, 22]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 110, + 288, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 110, + 288, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 110, + 288, + 252 + ], + "type": "text", + "content": "One particularly concerning type of attack is the adversarial patch attack [6, 17, 24, 53, 10, 23, 33, 43, 52, 66, 21, 61]. These are real-world attacks, where the attacker's objective is to print out a patch, physically place it in a scene, and cause a vision network processing the scene to malfunction. These attacks are especially concerning because of the potential impact on autonomous vehicles. A malicious agent could, for instance, produce a sticker that, when placed on a stop sign, cause a self-driving car to believe it is (say) a speed limit sign, and fail to stop. Indeed, similar attacks have already been demonstrated both in academic settings [31, 16, 50] and on real-world autonomous vehicles [56]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 254, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 254, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 254, + 287, + 361 + ], + "type": "text", + "content": "Despite this significant risk, research on these attacks has stalled to a certain extent because quantitatively evaluating the significance of this threat is challenging. The most accurate approach would be to conduct real-world experiments, but they are very expensive, and at present, not practical to do at a large scale. This leaves much to be desired compared to other branches of computer vision research, where the availability of benchmarks such as ImageNet have reduced the barriers to research and spurred tremendous innovation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 362, + 288, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 362, + 288, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 362, + 288, + 529 + ], + "type": "text", + "content": "Instead, researchers turn to one of two techniques: either, they physically create their attacks and try them out on a small number of real-world examples by physically attaching them to objects, or they digitally evaluate patch attacks using digital images containing simulated patches. Both approaches have major drawbacks. Although the former simulates more realistic conditions, the sample size is very small, and typically one cannot draw statistical conclusions from the results [6, 17, 53, 10, 66, 20, 21, 61]. Additionally, because of the ad-hoc nature of these evaluations, it is impossible to compare the results across different papers. Ultimately, such experiments only serve as a proof of concept for the proposed attacks and defenses, but not as a rigorous evaluation of their effectiveness." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 530, + 288, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 530, + 288, + 650 + ], + "spans": [ + { + "bbox": [ + 46, + 530, + 288, + 650 + ], + "type": "text", + "content": "In contrast, a digital simulation of attacks/defenses allows quantitative evaluation [24, 33, 65, 46, 37, 62, 58, 44]. However, it is difficult to accurately capture all of the challenges that arise in the real world. Past work often made unrealistic assumptions, such as that the patch is square, axis-aligned, can be located anywhere on the image, fully under the control of the attacker, and ignore noise and variation in lighting and pose (see top row of Fig. 1). Consequently, it is unclear if these evaluations are actually reflective of what would happen in real-world scenarios." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 660, + 157, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 660, + 157, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 660, + 157, + 672 + ], + "type": "text", + "content": "1.1. Our Contributions" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "The REAP Benchmark: We propose Realistic Adversarial Patch Benchmark (REAP), the first large-scale standardized benchmark for security against patch attacks. Motivated by" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "the aforementioned shortcomings of prior evaluations, we design REAP with the following principles in mind:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 99, + 547, + 278 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 306, + 99, + 547, + 147 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 99, + 547, + 147 + ], + "spans": [ + { + "bbox": [ + 306, + 99, + 547, + 147 + ], + "type": "text", + "content": "1. Large-scale evaluation: REAP consists of 14,651 images of road signs drawn from the Mapillary Vistas dataset. This allows us to draw quantitative conclusions about the effectiveness of attacks/defenses on the dataset." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 148, + 547, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 148, + 547, + 231 + ], + "spans": [ + { + "bbox": [ + 306, + 148, + 547, + 231 + ], + "type": "text", + "content": "2. Realistic patch rendering: REAP has tooling, which, for every road sign in the dataset, allows us to realistically render any digital patch onto the sign, matching factors such as where to place the patch, the camera angle, lighting conditions, etc. Importantly, this transformation is fast and differentiable so one can still perform backpropagation through the rendering process." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 231, + 547, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 231, + 547, + 278 + ], + "spans": [ + { + "bbox": [ + 306, + 231, + 547, + 278 + ], + "type": "text", + "content": "3. Realistic image distribution: REAP consists of images taken under realistic conditions, including variation in sizes and distances from the camera as well as various lighting conditions and degrees of occlusion." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 288, + 547, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 288, + 547, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 288, + 547, + 384 + ], + "type": "text", + "content": "**Evaluations with REAP:** With our new benchmark in hand, we also perform the first large-scale evaluations of existing attacks on object detectors. We evaluate existing attacks on three different object detection architectures: Faster R-CNN [48], YOLOF [9], and DINO [64]. We also implement and evaluate a baseline defense adapted from adversarial training [36] to defend against patch attacks on object detection. The conclusions we find are:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 387, + 547, + 649 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 306, + 387, + 547, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 387, + 547, + 483 + ], + "spans": [ + { + "bbox": [ + 306, + 387, + 547, + 483 + ], + "type": "text", + "content": "1. Existing patch attacks are not that effective. Perhaps surprisingly, existing attacks do not succeed on a majority of images on our benchmark. This is in contrast to simpler attack models such as " + }, + { + "bbox": [ + 306, + 387, + 547, + 483 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 306, + 387, + 547, + 483 + ], + "type": "text", + "content": "-bounded perturbations or patch attacks on simpler benchmarks, where the attack success rate is near " + }, + { + "bbox": [ + 306, + 387, + 547, + 483 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 306, + 387, + 547, + 483 + ], + "type": "text", + "content": ". Moreover, adversarily trained models can almost completely stop the attacks with only a minor performance drop on benign data." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 483, + 547, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 483, + 547, + 553 + ], + "spans": [ + { + "bbox": [ + 306, + 483, + 547, + 553 + ], + "type": "text", + "content": "2. Performance on synthetic data is not reflective of performance on REAP. We find that the success rates of attacks on synthetic versions of our benchmark and the full REAP are only poorly correlated. We conclude that performance on simple synthetic benchmarks is not predictive of attack success rate in more realistic conditions." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 555, + 547, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 555, + 547, + 649 + ], + "spans": [ + { + "bbox": [ + 306, + 555, + 547, + 649 + ], + "type": "text", + "content": "3. Lighting and patch placement are particularly important. Finally, we investigate what transforms in the patch rendering are the most important, in terms of the effect on the attack success rate. We find that the most significant first-order effects are from the lighting transform, as well as the positioning of the patch. In contrast, the perspective transforms—while still important—seem to affect the attack success rate somewhat less." + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 654, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 712 + ], + "type": "text", + "content": "While we believe these conclusions are already quite interesting, they are only the tip of the iceberg of what can be done with REAP. We believe that REAP will help support future research in adversarial patches by enabling a more accurate evaluation of new attacks and defenses." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 314, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 314, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 314, + 742 + ], + "type": "text", + "content": "4641" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 89, + 288, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 89, + 288, + 186 + ], + "spans": [ + { + "bbox": [ + 46, + 89, + 288, + 186 + ], + "type": "text", + "content": "Adversarial patch attacks. The literature on adversarial patches, and adversarial attacks more generally, is vast and a full review is beyond the scope of this paper. For conciseness, we only survey the most relevant works. Since their introduction in Brown et al. [6], Karmon et al. [24], Eykholt et al. [17], there have been a variety of adversarial patch attacks proposed [23, 33, 43, 52, 21, 61]. Of particular interest to us are the ones on object detection of road signs [17, 53, 10, 66]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 190, + 290, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 190, + 290, + 370 + ], + "spans": [ + { + "bbox": [ + 46, + 190, + 290, + 370 + ], + "type": "text", + "content": "Small scale, real-world tests. A common methodology used to test the transferability of the adversarial patch to the physical world is to print it out, physically place it onto an object, and capture pictures or videos of the patch for evaluation [6, 17, 53, 10, 66, 20, 21, 61]. While this method provides the most realistic evaluation, it has a number of downsides. First, it is, by nature, very time-consuming and hence limits the number of images that can be used for testing. Consequently, one cannot extract quantitative conclusions from the results. Additionally, they are difficult to standardize across papers, making their result not directly comparable. For instance, the pictures of the adversarial patches are taken under different angles, lighting conditions, or from varying distances. Sometimes, the adversarial patches themselves are printed using different printers [10, 66]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 373, + 288, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 288, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 288, + 553 + ], + "type": "text", + "content": "Completely simulated environment. Another line of work considers purely simulated environments for evaluating adversarial patches such as CARLA [14, 32, 45] and AttackScenes [21]. A huge advantage of this method is that it has the most precise and the most flexible control of the environment, e.g., cameras and objects can be placed anywhere. However, it is labor-intensive to build a diverse set of scenes digitally, and it compromises heavily on realism. Another example is 3DB [28], a photorealistic simulation for studying the reliability of computer vision systems. Nevertheless, it lacks the tooling necessary for evaluating adversarial patches and does not contain any driving scene, a setting to which adversarial patches are most applicable. Our benchmark utilizes images of real and diverse driving scenes and focuses on realistically simulating only the adversarial patches." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 557, + 288, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 288, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 288, + 677 + ], + "type": "text", + "content": "Digital simulation. This third approach takes a middle road and simulates the effects of the adversarial patch by digitally inserting it into a real image. This has been done at scale and to varying degrees of sophistication. One of the most common, but also simplest, ways this is done is to apply the patch to the image at some random position, and with some simple transformations, for instance, those induced by expectation over transformation [6, 24, 33, 65, 46, 37, 62, 58, 44]. This approach violates all the physical constraints and hence, is far from being realistic." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "content": "Arguably the benchmarks most similar to ours are the ones in Zhao et al. [66] and Braunegg et al. [5]. Zhao et al. [66] digitally insert synthetic stop signs with patches into" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "content": "images with realistic camera angles. However, they do not account for lighting conditions, and the target object itself is synthetic. In contrast, all signs in our dataset are real, and we also produce a transformation to match lighting conditions. In Section 4.3, we find that these two factors affect the evaluation metrics to a large extent. APRICOT [5] contains images of real scenes with a printed adversarial patch. Compared to ours, APRICOT is smaller in size (1K vs 14K images) and is heavily inflexible as it comes with a pre-defined adversarial patch with a fixed size and location." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 195, + 548, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 195, + 548, + 340 + ], + "spans": [ + { + "bbox": [ + 304, + 195, + 548, + 340 + ], + "type": "text", + "content": "Defenses. There have also been a slew of proposed defenses against patch attacks, e.g., [19, 41, 65, 62, 46, 37, 40, 11]. Most examine object classification. Only a handful consider object detection, which may be more relevant in practice [12, 63]. We choose to experiment with adversarial training [36] as a defense because, to the extent of our knowledge, it has not been applied in this setting (Rao et al. [46] study patch adversarial training on classifiers). It is also known to be a strong baseline and arguably the only effective defense across other " + }, + { + "bbox": [ + 304, + 195, + 548, + 340 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 304, + 195, + 548, + 340 + ], + "type": "text", + "content": "-norms [13]. Importantly, unlike the other defenses listed above, adversarial training does not make assumptions about the number or size of the patch." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 351, + 477, + 364 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 351, + 477, + 364 + ], + "spans": [ + { + "bbox": [ + 305, + 351, + 477, + 364 + ], + "type": "text", + "content": "3. Adversarial Patch Benchmark" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 369, + 373, + 381 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 369, + 373, + 381 + ], + "spans": [ + { + "bbox": [ + 306, + 369, + 373, + 381 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 386, + 547, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 386, + 547, + 446 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 547, + 446 + ], + "type": "text", + "content": "Our dataset is a collection of images containing traffic signs, each of which comes with a segmentation mask and a class. So far, this is more or less standard. The main additional feature of our benchmark is that, for each sign, we also provide an associated rendering transformation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 447, + 548, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 548, + 554 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 548, + 554 + ], + "type": "text", + "content": "Given a digital patch, this transformation allows us to apply the patch on the sign in a way that respects the scaling, orientation, and lighting of the sign in the image. We emphasize that a separate transformation is inferred individually for each sign, in order to ensure that the transformation is accurate for every image. Moreover, the rendering transformation is fully differentiable, which allows our dataset to be used to generate patch attacks and to apply adversarial defenses along the line of adversarial training." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 554, + 547, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 554, + 547, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 547, + 626 + ], + "type": "text", + "content": "Figs. 2 and 3 give an overview of the process to obtain the geometric (Section 3.4.1) and the relighting (Section 3.4.2) transformations, respectively. We use an algorithm to generate the candidate annotations automatically, visually inspect each of them, and then manually fix any wrong annotation. In total, we label 14,651 traffic signs across 8,433 images." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 635, + 369, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 369, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 369, + 647 + ], + "type": "text", + "content": "3.2. Datasets" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "We build our benchmark using images from the Mapillary Vistas dataset [42]. It includes 20,000 street-level images from around the world, annotated with bounding boxes of 124 object categories, including traffic signs. A limitation of Vistas is that all traffic signs are grouped under one class." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "text", + "content": "4642" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": "This creates a challenge for us, because our patch-rendering process depends on the size and shape of the sign. Without this information, the rendering is less realistic. We deal with this challenge by grouping the signs so that all signs in the same group can use the same geometric transform procedure. The grouping process is described in the next section." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 152, + 191, + 165 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 152, + 191, + 165 + ], + "spans": [ + { + "bbox": [ + 47, + 152, + 191, + 165 + ], + "type": "text", + "content": "3.3. Traffic Sign Classification" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 171, + 288, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 171, + 288, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 288, + 277 + ], + "type": "text", + "content": "Grouping traffic signs by their shape and size has two advantages. First, it allows more accurate geometric transforms as previously mentioned. Second, it allows us to study multiclass sign detection. Instead of labeling the Vistas signs by hand, we train a ResNet-18 on a similar dataset, Mapillary Traffic Sign (MTSD) [15], to classify them. MTSD contains granular labeling of over 300 traffic sign classes, but we cannot use it in place of Vistas as it lacks segmentation labels required to compute the geometric transforms." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 278, + 289, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 278, + 289, + 481 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 289, + 481 + ], + "type": "text", + "content": "We created two versions of the benchmark: REAP and REAP-S. REAP is our main benchmark with the classes matching those of MTSD. However, most of the classes contain fewer than 10 samples so we only keep the 100 most common classes. We need a sufficient number of samples per class because (i) some will be further filtered out in the preprocessing and (ii) the samples will be split into a \"training\" (for the attacker to \"train\" the adversarial patch) and a test set (for evaluating the attack). Conversely, REAP-S groups the signs into 11 classes by shape and size, namely circle, triangle, upside-down triangle, diamond (S), diamond (L), square, rectangle (S), rectangle (M), rectangle (L), pentagon, and octagon. REAP-S serves as a simpler alternative to REAP and is also intuitively more \"defender-friendly.\" For both REAP and REAP-S, the remaining signs that do not belong to the classes are labeled as a background class or \"others\" which will be ignored when we compute the metrics." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 482, + 288, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 482, + 288, + 577 + ], + "spans": [ + { + "bbox": [ + 46, + 482, + 288, + 577 + ], + "type": "text", + "content": "Since Mapillary Vistas does not come with these labels, we first trained a ConvNeXt model [35] on MTSD, which achieves about " + }, + { + "bbox": [ + 46, + 482, + 288, + 577 + ], + "type": "inline_equation", + "content": "98\\%" + }, + { + "bbox": [ + 46, + 482, + 288, + 577 + ], + "type": "text", + "content": " accuracy on the validation set, to generate the candidate class labels. The labels were then automatically corrected when we compute the parameters for the geometric transform in Section 3.4.1. For the remaining ones that cannot be automatically verified, we manually inspected and corrected them." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 578, + 288, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 288, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 288, + 685 + ], + "type": "text", + "content": "Our grouping of the signs in REAP-S has an extra benefit. Since each class is (approximately) associated with a standardized physical size, we can specify the patch size in real units (e.g., inches) instead of pixels. The real unit is arguably more useful for estimating the threat of adversarial patches than constraining the size by the number of pixels. One complication is that a single class of sign may come in different sizes, e.g., stop signs can be 24\", 36\", or 48\", depending on the kind of road they are located on, but usually one size is" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 547, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 547, + 145 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 547, + 145 + ], + "type": "text", + "content": "more common. The Vistas dataset does not contain sufficient information to distinguish between these sizes so we pick one canonical size for each sign type. Specifically, we select the size specified for \"Expressway\" according to the official U.S. Department of Transportation's guideline. Appendix A describes our design decision in detail." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 156, + 408, + 168 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 156, + 408, + 168 + ], + "spans": [ + { + "bbox": [ + 306, + 156, + 408, + 168 + ], + "type": "text", + "content": "3.4. Transformations" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 176, + 547, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 176, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 305, + 176, + 547, + 285 + ], + "type": "text", + "content": "We render adversarial patches with two types of transformations: geometric and relighting. Since the traffic signs in our dataset vary in shape, size, and orientation, we first need to apply a geometric, specifically perspective or 3D, transform to the patch to simulate these variations. Next, we account for the fact that pictures of real-world traffic signs are taken under different lighting conditions by applying a relighting transform to the patch. The importance of these transformations is highlighted in Fig. 4." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 308, + 454, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 308, + 454, + 319 + ], + "spans": [ + { + "bbox": [ + 306, + 308, + 454, + 319 + ], + "type": "text", + "content": "3.4.1 Geometric Transformation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 329, + 547, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 329, + 547, + 389 + ], + "spans": [ + { + "bbox": [ + 305, + 329, + 547, + 389 + ], + "type": "text", + "content": "To determine the parameters of the perspective transform, we need four keypoints for each sign. We infer the keypoints for a particular traffic sign using only its segmentation mask (which is provided in the Mapillary Vistas dataset) by following the four steps below (also visualized in Fig. 2):" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 391, + 547, + 546 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 306, + 391, + 547, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 391, + 547, + 413 + ], + "spans": [ + { + "bbox": [ + 306, + 391, + 547, + 413 + ], + "type": "text", + "content": "1. Find contour: First, we find the contour of the segmentation mask." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 415, + 547, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 415, + 547, + 461 + ], + "spans": [ + { + "bbox": [ + 306, + 415, + 547, + 461 + ], + "type": "text", + "content": "2. Compute convex hull: Then, we find the convex hull of the contour to correct annotation errors and occlusion. This does not affect correct masks, as they should already be convex." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 463, + 547, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 463, + 547, + 510 + ], + "spans": [ + { + "bbox": [ + 306, + 463, + 547, + 510 + ], + "type": "text", + "content": "3. Fit polygon and ellipse: We fit an ellipse to the convex hull, to find circular signs. If the fitted ellipse results in a larger error than a certain threshold, we know that the sign is not circular and therefore fit a polygon instead." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 510, + 547, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 510, + 547, + 546 + ], + "spans": [ + { + "bbox": [ + 306, + 510, + 547, + 546 + ], + "type": "text", + "content": "4. Cross verify: We verify that the shape obtained from the previous step matches with the ResNet's prediction. If not, the sign is flagged for manual inspection." + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 548, + 547, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 548, + 547, + 680 + ], + "spans": [ + { + "bbox": [ + 305, + 548, + 547, + 680 + ], + "type": "text", + "content": "The last step is finding the keypoints. For polygons, we first match the vertices to the canonical ones and then take the four predefined vertices as the keypoints. For circular signs, we use the ends of their major and minor axes as the four keypoints. These keypoints are used to infer a perspective transform appropriate for this sign. Triangular signs are a special case as we can only identify a maximum of three keypoints which means we can only infer a unique affine transform (six degrees of freedom). Note that this transform is linear and hence is fully differentiable. Lastly, we manually check all annotations and correct any errors." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 693, + 288, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 288, + 713 + ], + "type": "text", + "content": "Update August 18, 2023: In the previous version of the paper, we only present REAP-S which was called REAP." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 693, + 525, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 525, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 525, + 713 + ], + "type": "text", + "content": "https://mutcd.fhwa.dot.gov/htm/2003/part2/part2b1.htm" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "type": "text", + "content": "4643" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 70, + 521, + 215 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 521, + 215 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 521, + 215 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 521, + 215 + ], + "type": "image", + "image_path": "641e0e87f34571762b1f58e1e0fa5b355eb400399aa73e6f8a65814778825601.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 116, + 217, + 476, + 229 + ], + "lines": [ + { + "bbox": [ + 116, + 217, + 476, + 229 + ], + "spans": [ + { + "bbox": [ + 116, + 217, + 476, + 229 + ], + "type": "text", + "content": "Figure 2: The automated procedure we use to extract the keypoints from each traffic sign." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 248, + 285, + 387 + ], + "blocks": [ + { + "bbox": [ + 48, + 248, + 285, + 387 + ], + "lines": [ + { + "bbox": [ + 48, + 248, + 285, + 387 + ], + "spans": [ + { + "bbox": [ + 48, + 248, + 285, + 387 + ], + "type": "image", + "image_path": "7f17b8a34d38a397c6bdb1d0a651593de638302a759b8b269868f399214025dd.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 388, + 288, + 413 + ], + "lines": [ + { + "bbox": [ + 46, + 388, + 288, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 288, + 413 + ], + "type": "text", + "content": "Figure 3: Computing relighting parameters (top) and applying the transform (bottom)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 436, + 194, + 448 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 436, + 194, + 448 + ], + "spans": [ + { + "bbox": [ + 47, + 436, + 194, + 448 + ], + "type": "text", + "content": "3.4.2 Relighting Transformation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "text", + "content": "Each traffic sign in our dataset has two associated relighting parameters, " + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\alpha, \\beta \\in \\mathbb{R}" + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "text", + "content": ". Given a patch " + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "text", + "content": ", its relighted version " + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{\\mathrm{relighted}} = \\alpha \\mathbf{P} + \\beta" + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "text", + "content": " is rendered on the scene as depicted on the bottom row of Fig. 3. We infer " + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\alpha, \\beta" + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "text", + "content": " by matching the histogram of the original sign (e.g., the real stop sign on the upper-right of Fig. 3) to a canonical image (e.g., the synthetic stop sign on the upper-left): in particular, we set " + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "text", + "content": " as the " + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "text", + "content": "-th percentile of all the pixel values (aggregated over all three RGB channels) on that sign and " + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "text", + "content": " as the difference between the " + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "text", + "content": "-th and " + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "inline_equation", + "content": "(1 - p)" + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "text", + "content": "-th percentile. We call this the \"percentile\" method and explain why we chose it in Section 3.5. This method assumes that relighting can be approximated with a linear transform where " + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 456, + 287, + 635 + ], + "type": "text", + "content": " represent contrast and brightness adjustments. Like before, since this transformation is linear, it is differentiable." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 646, + 129, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 646, + 129, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 646, + 129, + 658 + ], + "type": "text", + "content": "3.5. Realism Test" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "In this section, we measure how realistic the patches are when rendered with different transform methods: three for geometric and eight for relighting. The geometric transforms include perspective (or homographic), affine, and translate" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 247, + 545, + 318 + ], + "blocks": [ + { + "bbox": [ + 307, + 247, + 545, + 318 + ], + "lines": [ + { + "bbox": [ + 307, + 247, + 545, + 318 + ], + "spans": [ + { + "bbox": [ + 307, + 247, + 545, + 318 + ], + "type": "image", + "image_path": "addfcb402de2f8f50bd6106136ce613fce22591ca4957f9027faa89de7158a0b.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 323, + 545, + 396 + ], + "lines": [ + { + "bbox": [ + 304, + 323, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 545, + 396 + ], + "type": "text", + "content": "Figure 4: Example ablation of the geometric and relighting transforms in our dataset. The rightmost stop sign has a patch rendered with a perspective and relighting transform which makes it more realistic. The first and second images have patches that are too bright whereas the first and third images have patches that do not respect the sign's orientation." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 315, + 452, + 537, + 611 + ], + "blocks": [ + { + "bbox": [ + 304, + 411, + 545, + 448 + ], + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 448 + ], + "type": "text", + "content": "Table 1: Comparison of different geometric and relighting transforms from our realism test (mean ± standard deviation of RMSE across 44 samples). The best results are in bold." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 452, + 537, + 611 + ], + "lines": [ + { + "bbox": [ + 315, + 452, + 537, + 611 + ], + "spans": [ + { + "bbox": [ + 315, + 452, + 537, + 611 + ], + "type": "table", + "html": "
TransformsMethodsColorsRMSE (↓)
GeometricTranslate & Scalen/a1.72 ± 1.19
Affinen/a1.35 ± 0.49
Perspective (3D)n/a1.13 ± 0.41
RelightingPercentileRGB0.110 ± 0.034
HSV0.227 ± 0.118
LAB0.652 ± 0.112
PolynomialRGB0.113 ± 0.037
HSV0.118 ± 0.035
LAB0.161 ± 0.043
Color TransferHSV0.117 ± 0.035
LAB0.184 ± 0.062
", + "image_path": "5d9125ac722df530887bac4d5458f7e5d145e763f690738f5458fed88abd1fd0.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "& scale transforms. For relighting, we experiment with three methods, each of which can be carried out on different color spaces (RGB, HSV, and LAB): the percentile method, described in Section 3.4.2; polynomial fitting, where we find the polynomial that best fits the pixel values on each real sign given the corresponding pixel values on the digital one; and Color Transfer [47], which tries to match the mean and" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "text", + "content": "4644" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 70, + 262, + 209 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 262, + 209 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 262, + 209 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 262, + 209 + ], + "type": "image", + "image_path": "412f07cd059447c2ddb50f651d9386bb0afa2ec353866de8cbf356904e2b982f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 220, + 288, + 269 + ], + "lines": [ + { + "bbox": [ + 46, + 220, + 288, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 288, + 269 + ], + "type": "text", + "content": "Figure 5: RMSE between the photographed and the rendered patches using the \"percentile\" method with different values of " + }, + { + "bbox": [ + 46, + 220, + 288, + 269 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 220, + 288, + 269 + ], + "type": "text", + "content": ". The shaded region denotes the standard deviation across 44 samples. " + }, + { + "bbox": [ + 46, + 220, + 288, + 269 + ], + "type": "inline_equation", + "content": "p = 20" + }, + { + "bbox": [ + 46, + 220, + 288, + 269 + ], + "type": "text", + "content": " yields the lowest RMSE." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 288, + 284, + 328 + ], + "blocks": [ + { + "bbox": [ + 50, + 288, + 284, + 328 + ], + "lines": [ + { + "bbox": [ + 50, + 288, + 284, + 328 + ], + "spans": [ + { + "bbox": [ + 50, + 288, + 284, + 328 + ], + "type": "image", + "image_path": "619059a995c458ee908f741369f34f521544bd0bd8a7645552a161fda1fa25d1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 331, + 286, + 354 + ], + "lines": [ + { + "bbox": [ + 47, + 331, + 286, + 354 + ], + "spans": [ + { + "bbox": [ + 47, + 331, + 286, + 354 + ], + "type": "text", + "content": "Figure 6: Random samples used in our realism experiments (left: real, right: rendered). Fig. 17 contains all samples." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 378, + 217, + 391 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 378, + 217, + 391 + ], + "spans": [ + { + "bbox": [ + 47, + 378, + 217, + 391 + ], + "type": "text", + "content": "the standard deviation of the pixel values." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 396, + 288, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 288, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 288, + 563 + ], + "type": "text", + "content": "We photograph 44 pairs of real traffic signs with and without an adversarial patch: 11 signs, one for each class, in four scenes and lighting conditions. For each sample, we hand-annotated the keypoints of both the signs and the patches. Then, given an image of the sign without the patch, we render the patch on it using the different transform methods. For geometric transforms, we measure the root mean square error (RMSE) between the rendered and the corresponding groundtruth corners of the patch. To compare the relighting methods, we compute the RMSE between the rendered and the corresponding groundtruth pixel values of the patch. We use the groundtruth geometric transform when computing the relighting parameters to disentangle the potential error from the geometric transform." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "Table 1 reports the best RMSE achieved by each transform after a hyperparameter sweep (" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ", polynomial degrees, etc.). The perspective transform achieves the lowest RMSE as expected which emphasizes the importance of using the full 3D transform instead of simpler alternatives. For relighting, the percentile method with " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "p = 0.2" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " performs as well as, or better than, any other at rendering the adversarial patches. Hence, these are the two transforms we use to construct the REAP benchmark and in all of the experiments in Section 4 unless stated otherwise. Fig. 6 visually compares the rendered patches with the groundtruth ones under these best transform methods. Appendix B contains more details." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 71, + 500, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 500, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 500, + 85 + ], + "type": "text", + "content": "4. Experiments on REAP Benchmark" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 91, + 547, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 224 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 224 + ], + "type": "text", + "content": "Our benchmark can be used to evaluate attacks and defenses under various threat models, e.g., making objects appear vs disappear, using a universal patch vs a targeted attack, etc. In this paper, we focus on the setting where the adversary tries to make a traffic sign disappear or be misclassified using the per-class attack, i.e., only one patch per class of objects, similar to Benz et al. [4]. We argue that this threat model is more realistic and more alarming as the attacker only needs to distribute several adversarial stickers that are effective across million of traffic signs. We assume the adversary has access to the target model (white-box)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 232, + 414, + 244 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 232, + 414, + 244 + ], + "spans": [ + { + "bbox": [ + 306, + 232, + 414, + 244 + ], + "type": "text", + "content": "4.1. Experiment Setup" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 250, + 547, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 250, + 547, + 357 + ], + "spans": [ + { + "bbox": [ + 304, + 250, + 547, + 357 + ], + "type": "text", + "content": "Traffic sign detectors. We experiment with three object detection models, Faster R-CNN [48], YOLOF [9], and DINO [64], all trained on the MTSD dataset to predict bounding boxes for all 11 traffic sign classes plus the \"other\" class. We follow the training method and hyperparameters from Neuhold et al. [42]. As mentioned in Section 4.2, we report the false negative rate (FNR) in addition to mAP scores. For FNR, the score threshold is chosen as one that maximizes the F1 score on the validation set of MTSD." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 374, + 547, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 547, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 547, + 540 + ], + "type": "text", + "content": "Attack algorithms. We use the RP2 attack [17] and the DPatch attack [33] to generate adversarial patches for all models. We assume that the adversary has access to 5 held-out images from our benchmark and use them to generate one adversarial patch per sign class. We note that this setting, referred to as per-class attack, is different from the usual white-box attack threat model where each sample is given a unique perturbation (we call it per-instance attack) and is more similar to the \"universal\" adversarial perturbation [38]. We argue that this threat model is more realistic and more alarming as the attacker only needs to distribute one adversarial sticker that are effective across million of traffic signs of the same type. Appendix D.5 discusses the threat models in more detail." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 541, + 547, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 541, + 547, + 650 + ], + "spans": [ + { + "bbox": [ + 304, + 541, + 547, + 650 + ], + "type": "text", + "content": "Each of the classes has a specific set of these 5 images each of which contains at least one sign of that class. For REAP-S, we use 50 images since there are more samples per class. In practice, an adversary may benefit from using more than 5 (or 50) images to generate the patch, but we set our limit here to leave sufficient samples for the evaluation phase. We do not find a significant difference in the performance of the two attacks (Appendix D.1) so we report only the results of DPatch attack with PGD optimizer in the main paper." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Defense algorithm. We use adversarial training with DPatch attack and five-step PGD as it performs the best empirically. The patches are generated per-instance at a random location to prevent overfitting to a specific one. To" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "text", + "content": "4645" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 74, + 99, + 520, + 182 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "type": "text", + "content": "Table 2: Mean FNR and mAP of the adversarial patches on six traffic sign detectors on REAP. \"FRCNN\" refers to Faster R-CNN, \"Adv.\" indicates adversarially trained models. For defenders, lower FNR " + }, + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "type": "inline_equation", + "content": "(\\downarrow)" + }, + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "type": "text", + "content": " and higher mAP " + }, + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "type": "inline_equation", + "content": "(\\uparrow)" + }, + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "type": "text", + "content": " are better." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 74, + 99, + 520, + 182 + ], + "lines": [ + { + "bbox": [ + 74, + 99, + 520, + 182 + ], + "spans": [ + { + "bbox": [ + 74, + 99, + 520, + 182 + ], + "type": "table", + "html": "
Patch SizeFRCNNYOLOFDINOAdv. FRCNNAdv. YOLOFAdv. DINO
FNRmAPFNRmAPFNRmAPFNRmAPFNRmAPFNRmAP
No patch4.372.918.554.814.168.23.173.321.055.09.474.2
Small (10”×10”)15.459.433.743.532.060.43.871.822.554.71.880.6
Medium (10”×20”)22.446.542.736.635.452.66.166.827.151.91.280.1
Large (two 10”×20”)50.018.272.819.462.839.513.956.357.734.13.677.8
", + "image_path": "e33dcea175f7bb242ad4bfa2320ef23db032dc956cc430b107821f857524c558.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 202, + 289, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 202, + 289, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 202, + 289, + 264 + ], + "type": "text", + "content": "improve the effectiveness of adversarial training under a small number of steps, we cache patches generated in the previous epoch and use it as an initialization for the next one [67]. For more detailed setup and results, please see Appendix C." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 277, + 288, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 288, + 408 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 288, + 408 + ], + "type": "text", + "content": "Synthetic Benchmark. We use canonical synthetic signs, one per class, as a baseline to compare our REAP-S benchmark to (we cannot find canonical synthetic signs for all 100 classes of REAP). Similarly to Eykholt et al. [17], the synthetic sign is placed at a random location on one of 50 random background images and randomly rotated between 0 and 15 degrees. We use the synthetic benchmark for both generating and testing the adversarial patch. For testing, we use 2,000 background images per class, randomly selected from our REAP-S benchmark to keep the distribution of the scenes similar." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 415, + 160, + 427 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 415, + 160, + 427 + ], + "spans": [ + { + "bbox": [ + 47, + 415, + 160, + 427 + ], + "type": "text", + "content": "4.2. Evaluation Metrics" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 434, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 519 + ], + "type": "text", + "content": "Here, we define a successful attack as a patch that makes the sign either (i) undetected or (ii) classified to a wrong class (i.e., any of the other classes, or the background class). Similarly to previous work, we measure the effectiveness of an attack by the attack success rate (ASR), defined as follows. Given a list of signs " + }, + { + "bbox": [ + 46, + 434, + 287, + 519 + ], + "type": "inline_equation", + "content": "\\{x_i\\}_{i=1}^N" + }, + { + "bbox": [ + 46, + 434, + 287, + 519 + ], + "type": "text", + "content": " and the corresponding version with an adversarial patch applied to it, " + }, + { + "bbox": [ + 46, + 434, + 287, + 519 + ], + "type": "inline_equation", + "content": "\\{x_i'\\}_{i=1}^N" + }, + { + "bbox": [ + 46, + 434, + 287, + 519 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 61, + 526, + 287, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 526, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 61, + 526, + 287, + 559 + ], + "type": "interline_equation", + "content": "\\mathrm {A S R} = \\frac {\\sum_ {i = 1} ^ {N} \\mathbf {1} _ {x _ {i} \\text {i s d e t e c t e d}} \\wedge \\mathbf {1} _ {x _ {i} ^ {\\prime} \\text {i s n o t d e t e c t e d}}}{\\sum_ {i = 1} ^ {N} \\mathbf {1} _ {x _ {i} \\text {i s d e t e c t e d}}}. \\tag {1}", + "image_path": "4c79a703a55d4ef504a831e7ac0e845268d10beeefd52f25c176214ca2b082a7.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 565, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 565, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 565, + 287, + 613 + ], + "type": "text", + "content": "ASR and FNR are easy to interpret but dependent on specific thresholds of both the confidence score and the IoU between the groundtruth and the detected boxes. Hence, we also report mAP which averages across these thresholds." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 620, + 132, + 632 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 620, + 132, + 632 + ], + "spans": [ + { + "bbox": [ + 47, + 620, + 132, + 632 + ], + "type": "text", + "content": "4.3. Main Results" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 639, + 288, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 639, + 288, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 639, + 288, + 676 + ], + "type": "text", + "content": "Experiments on our REAP benchmark illuminate several findings that were not previously observed due to the lack of scalability and reproducibility of real-world experiments:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "(1) Patch attacks against road signs are less effective than previously believed. From Table 2, a " + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "inline_equation", + "content": "10^{\\prime \\prime} \\times 10^{\\prime \\prime}" + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": " adversarial" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 202, + 547, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 202, + 547, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 202, + 547, + 346 + ], + "type": "text", + "content": "patch increases FNR by only 11-18 percentage points on the undefended models. For REAP-S (Table 3), the increase is 8-12 percentage points. For comparison, a class-wise adversarial perturbation under imperceptible " + }, + { + "bbox": [ + 304, + 202, + 547, + 346 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 304, + 202, + 547, + 346 + ], + "type": "text", + "content": " norms achieves above " + }, + { + "bbox": [ + 304, + 202, + 547, + 346 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 304, + 202, + 547, + 346 + ], + "type": "text", + "content": " success rate [4]. More importantly, on adversarially trained models, FNR remains almost identical before and after applying the patch on Faster R-CNN andYOLOF. Surprisingly, adversarially trained DINO performs better on samples with adversarial patches than without. We hypothesize that this is a result of overfitting to some adversarial patches and not a clear sign of weak attacks or gradient obfuscation. We refer to Section 4.4 for additional detail." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 346, + 547, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 547, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 547, + 418 + ], + "type": "text", + "content": "This result implies that a well-known defense like adversarial training is effective and may be sufficient to protect against patch attacks in the real world. Adversarial attacks are most troubling when they are imperceptible; patches as large as " + }, + { + "bbox": [ + 304, + 346, + 547, + 418 + ], + "type": "inline_equation", + "content": "10^{\\prime \\prime} \\times 10^{\\prime \\prime}" + }, + { + "bbox": [ + 304, + 346, + 547, + 418 + ], + "type": "text", + "content": " (or larger) are likely to draw attention, which may make them less of a threat in practice." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 419, + 547, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 419, + 547, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 419, + 547, + 540 + ], + "type": "text", + "content": "Our findings are also consistent with prior works that investigate physical-world attacks on stop signs. In these works, the attack is often clearly visible. For instance, Eykholt et al. [17] and Zhao et al. [66] use a patch that is close to our two " + }, + { + "bbox": [ + 304, + 419, + 547, + 540 + ], + "type": "inline_equation", + "content": "10^{\\prime \\prime} \\times 20^{\\prime \\prime}" + }, + { + "bbox": [ + 304, + 419, + 547, + 540 + ], + "type": "text", + "content": " patches which is why they observe a high attack success rate similar to our results with the larger patch size. Nonetheless, a patch of this size surely breaches all notions of imperceptibility. Perhaps an interesting threat model to study in the future is to allow large patches but additionally constrain the perturbation with " + }, + { + "bbox": [ + 304, + 419, + 547, + 540 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 304, + 419, + 547, + 540 + ], + "type": "text", + "content": "-norm." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 557, + 547, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 665 + ], + "type": "text", + "content": "(2) ASR measured on synthetic data is not predictive of ASR measured on our realistic benchmark. We compare REAP-S to a synthetic benchmark intended to be representative of methodology often found in prior work: we take a single synthetic image of a road sign, then generate attacks against it (instead of a real image). Table 3 and Fig. 8 show that there is a large difference between metrics as measured on such a synthetic benchmark compared to our benchmark. The gap can be up to 50–60 percentage points on average." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Fig. 8 and Table 9 in Appendix D compare ASR on the two benchmarks by class of the traffic signs. If the two ASRs were similar, all data points would have lied close to the diagonal dashed line. Instead, most of the data points" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "text", + "content": "4646" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 110, + 544, + 255 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 106 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 106 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 106 + ], + "type": "text", + "content": "Table 3: Mean ASR and FNR of the adversarial patches on the six traffic sign detectors on REAP-S. For sign-specific metrics, see Table 9. It is clear that evaluating on the synthetic signs overestimates the attack's potency in every setting. For defenders, lower FNR " + }, + { + "bbox": [ + 46, + 70, + 547, + 106 + ], + "type": "inline_equation", + "content": "(\\downarrow)" + }, + { + "bbox": [ + 46, + 70, + 547, + 106 + ], + "type": "text", + "content": " and ASR " + }, + { + "bbox": [ + 46, + 70, + 547, + 106 + ], + "type": "inline_equation", + "content": "(\\downarrow)" + }, + { + "bbox": [ + 46, + 70, + 547, + 106 + ], + "type": "text", + "content": " are better." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 110, + 544, + 255 + ], + "lines": [ + { + "bbox": [ + 51, + 110, + 544, + 255 + ], + "spans": [ + { + "bbox": [ + 51, + 110, + 544, + 255 + ], + "type": "table", + "html": "
Patch SizeBenchmarksFRCNNYOLOFDINOAdv. FRCNNAdv. YOLOFAdv. DINO
FNRASRFNRASRFNRASRFNRASRFNRASRFNRASR
No patchSynthetic19.8n/a17.0n/a12.7n/a15.7n/a19.0n/a5.8n/a
REAP-S (ours)20.2n/a17.1n/a12.8n/a17.4n/a19.2n/a6.1n/a
Small (10"×10")Synthetic76.973.189.888.658.856.950.043.976.873.424.122.6
REAP-S (ours)50.539.248.638.936.228.018.75.128.312.71.10.1
Medium (10"×20")Synthetic89.988.392.091.173.172.679.577.383.781.734.733.9
REAP-S (ours)64.456.160.552.845.538.433.823.546.534.71.30.1
Large (two 10"×20")Synthetic99.699.6100.0100.096.596.498.998.899.198.952.952.7
REAP-S (ours)85.282.088.286.185.183.559.353.669.964.35.14.3
", + "image_path": "fed58c35cd655a768b319522e58b48cd0c861d7b013f931120cad976239a0249.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 48, + 263, + 545, + 321 + ], + "blocks": [ + { + "bbox": [ + 48, + 263, + 545, + 321 + ], + "lines": [ + { + "bbox": [ + 48, + 263, + 545, + 321 + ], + "spans": [ + { + "bbox": [ + 48, + 263, + 545, + 321 + ], + "type": "image", + "image_path": "d50b1ade17dd267eb78a9918829a6071ccea9a6469e26b062f24057ec3aa9a2d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 326, + 547, + 364 + ], + "lines": [ + { + "bbox": [ + 46, + 326, + 547, + 364 + ], + "spans": [ + { + "bbox": [ + 46, + 326, + 547, + 364 + ], + "type": "text", + "content": "Figure 7: Examples of small " + }, + { + "bbox": [ + 46, + 326, + 547, + 364 + ], + "type": "inline_equation", + "content": "(10^{\\prime \\prime}\\times 10^{\\prime \\prime})" + }, + { + "bbox": [ + 46, + 326, + 547, + 364 + ], + "type": "text", + "content": ", medium " + }, + { + "bbox": [ + 46, + 326, + 547, + 364 + ], + "type": "inline_equation", + "content": "(10^{\\prime \\prime}\\times 20^{\\prime \\prime})" + }, + { + "bbox": [ + 46, + 326, + 547, + 364 + ], + "type": "text", + "content": " and large (two " + }, + { + "bbox": [ + 46, + 326, + 547, + 364 + ], + "type": "inline_equation", + "content": "10^{\\prime \\prime}\\times 20^{\\prime \\prime}" + }, + { + "bbox": [ + 46, + 326, + 547, + 364 + ], + "type": "text", + "content": ") patches applied to three of the signs from our benchmark. The large patch size is clearly visible and obscures the notion of imperceptibility. We still choose to experiment with it since it is approximately the same size used by prior work [17, 66]." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 48, + 381, + 160, + 487 + ], + "blocks": [ + { + "bbox": [ + 48, + 381, + 160, + 487 + ], + "lines": [ + { + "bbox": [ + 48, + 381, + 160, + 487 + ], + "spans": [ + { + "bbox": [ + 48, + 381, + 160, + 487 + ], + "type": "image", + "image_path": "1c52d0d73411f95ac37fa20e6fcd5dd5a5b54b172d49303917d04445e3b35046.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 70, + 492, + 137, + 502 + ], + "lines": [ + { + "bbox": [ + 70, + 492, + 137, + 502 + ], + "spans": [ + { + "bbox": [ + 70, + 492, + 137, + 502 + ], + "type": "text", + "content": "(a) Faster R-CNN" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 172, + 381, + 284, + 487 + ], + "blocks": [ + { + "bbox": [ + 172, + 381, + 284, + 487 + ], + "lines": [ + { + "bbox": [ + 172, + 381, + 284, + 487 + ], + "spans": [ + { + "bbox": [ + 172, + 381, + 284, + 487 + ], + "type": "image", + "image_path": "743268b0e88296ef41c8513ec599a5b1793e9840b0be2825b71783393360e56f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 210, + 492, + 247, + 502 + ], + "lines": [ + { + "bbox": [ + 210, + 492, + 247, + 502 + ], + "spans": [ + { + "bbox": [ + 210, + 492, + 247, + 502 + ], + "type": "text", + "content": "(b) DINO" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 562, + 287, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 562, + 287, + 634 + ], + "spans": [ + { + "bbox": [ + 46, + 562, + 287, + 634 + ], + "type": "text", + "content": "are below the line, suggesting that the synthetic benchmark consistently overestimates the ASR. Moreover, there is no clear relationship between the two measurements of ASR. If the rankings of the ASRs are well-correlated, we should expect ordering of the points to be similar in both horizontal and vertical directions, but this is not the case." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "content": "(3) The lighting transform affects the attack's effectiveness more than the geometric transform. Fig. 9 shows how the transformations our benchmark applies to the patch affect its mAP scores. For all models, our realistic lighting transform has a much larger effect than the geometric trans" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 312, + 383, + 538, + 521 + ], + "blocks": [ + { + "bbox": [ + 46, + 508, + 287, + 544 + ], + "lines": [ + { + "bbox": [ + 46, + 508, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 287, + 544 + ], + "type": "text", + "content": "Figure 8: ASRs on synthetic vs REAP-S benchmarks for Faster R-CNN (left) and DINO (right). The dashed line marks the points with an equal ASR on both datasets." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 312, + 383, + 538, + 521 + ], + "lines": [ + { + "bbox": [ + 312, + 383, + 538, + 521 + ], + "spans": [ + { + "bbox": [ + 312, + 383, + 538, + 521 + ], + "type": "image", + "image_path": "97c2a901f6e6a0ae5f5aa252da46905c5cb68724729a8c1cf5af45dd8a140b61.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 525, + 547, + 586 + ], + "lines": [ + { + "bbox": [ + 304, + 525, + 547, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 525, + 547, + 586 + ], + "type": "text", + "content": "Figure 9: Effects of different geometric and relighting transform methods on the mAP of the YOLOF model under attack. The hatched bars are the default setting. When either geometric or relighting transform is varied, the other one is fixed to the default (perspective, " + }, + { + "bbox": [ + 304, + 525, + 547, + 586 + ], + "type": "inline_equation", + "content": "p = 0.2" + }, + { + "bbox": [ + 304, + 525, + 547, + 586 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 602, + 547, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 602, + 547, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 602, + 547, + 662 + ], + "type": "text", + "content": "form. Without the lighting transform, mAP decreases by 17 percentage points for YOLOF and 15 for Faster R-CNN (i.e., an increase of 23 and 14 points on the ASR). This observation explains why the synthetic benchmark as well as synthetic evaluations in previous works overestimate ASR." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 670, + 462, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 462, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 462, + 682 + ], + "type": "text", + "content": "4.4. Extended Attack Evaluation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "type": "text", + "content": "Because these results were so surprising, we investigated the possibility that our attack algorithms are not sufficiently" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "text", + "content": "4647" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 122, + 274, + 412 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 119 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 119 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 119 + ], + "type": "text", + "content": "Table 4: Robustness of the adversarially trained models under different attack threat models (" + }, + { + "bbox": [ + 47, + 70, + 288, + 119 + ], + "type": "inline_equation", + "content": "10^{\\prime \\prime} \\times 10^{\\prime \\prime}" + }, + { + "bbox": [ + 47, + 70, + 288, + 119 + ], + "type": "text", + "content": " patch size). The per-instance attack has the highest ASR and the lowest mAP as expected, and there is no sign of gradient obfuscation." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 122, + 274, + 412 + ], + "lines": [ + { + "bbox": [ + 61, + 122, + 274, + 412 + ], + "spans": [ + { + "bbox": [ + 61, + 122, + 274, + 412 + ], + "type": "table", + "html": "
AttacksASR (↑)mAP (↓)
Adv. Faster R-CNN
No Attackn/a66.0
Per-Class Attack5.165.7
Per-Instance Attack16.059.3
Transfer from YOLOF3.267.8
Transfer from Adv. YOLOF7.063.6
Transfer from Synthetic2.769.1
Adv. YOLOF
No Attackn/a58.5
Per-Class Attack17.751.3
Per-Instance Attack28.246.5
Transfer from Faster R-CNN13.553.1
Transfer from Adv. Faster R-CNN7.955.4
Transfer from Synthetic12.254.3
Adv. DINO
No Attackn/a65.7
Per-Class Attack0.175.1
Per-Instance Attack2.763.7
Transfer from Adv. Faster R-CNN0.176.5
Transfer from Adv. YOLOF0.276.1
Transfer from DINO0.079.6
Transfer from Synthetic0.472.7
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AugmentStrengthFRCNNAdv. YOLOFAdv. DINO
FNRmAPFNRmAPFNRmAP
Nonen/a15.459.422.554.71.280.1
0.116.158.823.154.71.280.1
Color-jitter0.216.058.523.654.61.280.0
0.315.559.023.354.71.380.1
0.115.758.923.054.81.280.4
Unif. noise0.215.458.822.654.71.480.1
0.315.658.622.954.71.480.2
", + "image_path": "38d1b99e986e8e78640a1c7c45240e7bb875c6ee8077d389b01478bb2c2e5ac2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 558, + 288, + 619 + ], + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 619 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 619 + ], + "type": "text", + "content": "Table 5: FNR and mAP with color-jitter or random noise applied during the attack EoS on REAP. We use the small patch for Faster R-CNN and Adv. YOLOF, and the medium size for Adv. DINO. None of the augmentations seems to affect the potency of the attack." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 641, + 288, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 700 + ], + "type": "text", + "content": "strong (e.g., gradient obfuscation [2]) or that the adversarially trained models \"catastrophically overfit\" [59, 25, 1], i.e., they memorize the attack patterns during training but are not actually robust. In particular, we evaluate the adversarially trained models against transfer and per-instance attacks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 701, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 288, + 713 + ], + "type": "text", + "content": "The per-instance attack generates one patch for each in-" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": "stance of traffic signs, as opposed to our default per-class patch. The transfer attack generates per-class patches from either a different source model or the synthetic data. Table 4 shows that the per-instance attack always achieves a higher ASR (and lower mAP) than the per-class attack, and the transfer attack has the lowest ASR in most cases. This result is expected and does not indicate that the gradient obfuscation or the catastrophic overfitting phenomenon is happening." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 181, + 547, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 181, + 547, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 181, + 547, + 276 + ], + "type": "text", + "content": "To further improve the robustness of the adversarial patches (i.e., making the attack transfer to other instances in the same class), we also tried to generate the adversarial patches by applying random augmentations including color-jitter and uniform noise injection (similar to expectation over transformation [3]). Table 5 shows that the augmentations with varying strength levels do not significantly affect the ASR of the attack." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 279, + 548, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 279, + 548, + 398 + ], + "spans": [ + { + "bbox": [ + 304, + 279, + 548, + 398 + ], + "type": "text", + "content": "Overall, the effectiveness of all the attacks remains limited against all the adversarially trained models. In particular, the ASR of the per-instance attack, which is an upper bound of ASR on all threat models, is only " + }, + { + "bbox": [ + 304, + 279, + 548, + 398 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 304, + 279, + 548, + 398 + ], + "type": "text", + "content": " on Adv. DINO on REAP-S. Based on these experiments (and others in Appendix D.6), we tentatively conclude that the adversarially trained classifiers truly do appear robust for the REAP detection task. Because this result is so surprising, further research is needed before we can have full confidence in this conclusion." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 415, + 495, + 427 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 415, + 495, + 427 + ], + "spans": [ + { + "bbox": [ + 306, + 415, + 495, + 427 + ], + "type": "text", + "content": "5. Conclusion and Future Directions" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 437, + 547, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 547, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 547, + 604 + ], + "type": "text", + "content": "We construct the first large-scale benchmark for evaluating adversarial patches. Our benchmark consists of over 14,000 signs from real driving scenes, and each sign is annotated with the transformations necessary to render an adversarial patch realistically onto it. Using this benchmark, we experiment with a broad range of models and attacks. We find that adversarial patches of a clearly visible size fool an undefended model on less than " + }, + { + "bbox": [ + 304, + 437, + 547, + 604 + ], + "type": "inline_equation", + "content": "28\\%" + }, + { + "bbox": [ + 304, + 437, + 547, + 604 + ], + "type": "text", + "content": " of the signs and only " + }, + { + "bbox": [ + 304, + 437, + 547, + 604 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 437, + 547, + 604 + ], + "type": "text", + "content": " for a defended model. This is in contrast to adversarial examples with bounded " + }, + { + "bbox": [ + 304, + 437, + 547, + 604 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 304, + 437, + 547, + 604 + ], + "type": "text", + "content": "-norm, where attacks nearly always succeed. All in all, our experiments suggest that realistic constraints render patch attacks significantly less effective, and vanilla adversarial training is an effective defense against the current practical patch attacks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 548, + 713 + ], + "type": "text", + "content": "One interesting direction for future research is to explore whether attacks against object detectors can be improved. Also, in our experiments, adversarial training achieved strong robustness at the cost of degrading mAP on clean images by about 5 percentage points. It would be interesting to explore new defenses that have less impact on clean performance. We hope that our benchmark will provide a foundation for more realistic evaluation of patch attacks and drive future research on defenses against them." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "type": "text", + "content": "4648" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 704 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] Maksym Andriushchenko and Nicolas Flammarion. 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Klasky2", + "bbox": [ + 413, + 203, + 547, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yoram Bresler", + "bbox": [ + 593, + 203, + 715, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "berki2@illinois.edu", + "bbox": [ + 230, + 223, + 385, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "mklasky@lanl.gov", + "bbox": [ + 410, + 224, + 537, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ybresler@illinois.edu", + "bbox": [ + 563, + 224, + 733, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1University of Illinois at Urbana-Champaign, USA 2Los Alamos National Laboratory, USA", + "bbox": [ + 200, + 236, + 767, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 271, + 312, + 286 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dynamic imaging involves the recovery of a time-varying 2D or 3D object at each time instant using its undersampled measurements. In particular, in dynamic tomography, only a single projection at a single view angle may be available at a time, making the problem severely ill-posed. In this work, we propose an approach, RED-PSM, which combines for the first time two powerful techniques to address this challenging imaging problem. The first, are partially separable models, which have been used to introduce a low-rank prior for the spatio-temporal object. The second is the recent Regularization by Denoising (RED), which provides a flexible framework to exploit the impressive performance of state-of-the-art image denoising algorithms, for various inverse problems. We propose a partially separable objective with RED and an optimization scheme with variable splitting and ADMM. Our objective is proved to converge to a value corresponding to a stationary point satisfying the first-order optimality conditions. Convergence is accelerated by a particular projection-domain-based initialization. We demonstrate the performance and computational improvements of our proposed RED-PSM with a learned image denoiser by comparing it to a recent deep-prior-based method TD-DIP. Although the emphasis is on dynamic tomography, we also demonstrate the performance advantages of RED-PSM in a dynamic cardiac MRI setting.", + "bbox": [ + 75, + 303, + 472, + 681 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 708, + 207, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Time-varying tomography is a challenging ill-posed inverse problem that involves reconstructing a dynamic object using its sequential projections at each time instant. Since the measurements are inconsistent due to the evolving object, traditional reconstruction algorithms lead to significant artifacts.", + "bbox": [ + 75, + 733, + 468, + 824 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The problem arises in micro-CT [1], myocardial perfusion imaging [2], thoracic CT [3], imaging of fluid flow processes [4, 5] and dynamic imaging of material samples undergoing compression [6, 7]. Also, it is closely related to the dynamic MRI (dMRI) problem, which typically arises", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "in cardiac imaging [8].", + "bbox": [ + 500, + 273, + 653, + 287 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Previous work [9, 10] treated the problem as time-sequential sampling of bandlimited signals and provided an optimal view angle sampling order and theoretical guarantees for unique and stable reconstruction. However, the approach is limited by its bandlimitedness assumptions.", + "bbox": [ + 496, + 290, + 890, + 366 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Several methods [11, 12] recover the underlying motion field from projections using the Radon transform properties. However, these methods require the object information a priori. Other algorithms [13, 14] alternate between estimating the motion field and the time-varying object. These methods assume the total density to be preserved for a given object at different times which may be a limiting assumption. For instance, imaging a fixed slice of a time-varying object under compression may violate this assumption due to perpendicularly evolving parts.", + "bbox": [ + 496, + 367, + 892, + 518 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In dynamic tomography and MRI, partially-separable models (PSM) have been used to represent the underlying object [15] and the time-sequential projections [16, 17]. The projection-domain PSM in [16, 17] carries the PSM to the projection domain using the harmonic representation of projections, and provides uniqueness and stability analysis for the problem. In spite of this advantage of the projection domain PSM over its object-domain counterparts, the performance of this approach is limited by the null space of the measurement operator.", + "bbox": [ + 496, + 520, + 892, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A different PSM-based method for dMRI [18] imposes the low-rank structure as a soft constraint. It uses a hybrid objective with the PSM model used in the data fidelity term and the object in a simple $l_{1}$ -norm penalty, with an additional penalty term to penalize the mismatch between the PSM and the object. The method does not use a guided initial guess for the object or for the PSM basis functions. A fast alternative low-rank (or PSM)-based method for dMRI [19] decomposes the object representation into three components: the mean signal, a low-rank PSM, and the residual, which is assumed to be sparse in the Fourier domain. Then, each component is estimated in order. Although on some of the data sets used for the comparison in [19] competing methods are either faster or more accurate, the method provides better results when averaged over all data sets.", + "bbox": [ + 496, + 672, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10595", + "bbox": [ + 480, + 924, + 517, + 936 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, object-domain deep image prior (DIP)-based algorithms [20,21] have been proposed for dMRI. Providing impressive results, DIP-based algorithms such as [20] suffer from overfitting and usually require handcrafted early stopping criteria during the optimization of generator network parameters. In an attempt to overcome the overfitting and the need for handcrafted early stopping, the authors of [21] regularize the problem by constraining the geodesic distances between generated objects in proportion to the distances between their latent representation. However, this requires the computation of the Jacobian of the generator network at each iteration of the update of the weights and significantly increases the computational load and run time.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A different approach [22] combines partially separable and generative models. It employs spatial and temporal regularization by penalizing the generator weights and a particular initialization scheme for the inputs to the generator networks. Although it combines the PSM with the recent DIP framework, this method has the following limitations, which are overcome by the proposed approach: (i) The spatial generator is an artifact removal network taking the full-sized spatial basis functions as input. Since this prevents a patch-based implementation, it may be difficult to scale to high-resolution 3D+temporal settings. (ii) The CNN prior for natural images may not be useful as a prior for the individual spatial basis functions, since the least-squares optimal spatial basis functions are the left singular vectors of the complete object, and as such may not have the structure of natural images. (iii) As with other DIP-based methods, if the additional penalty on the generator parameters is insufficient, this method can be prone to overfitting.", + "bbox": [ + 75, + 287, + 472, + 561 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contributions", + "text_level": 1, + "bbox": [ + 96, + 566, + 192, + 580 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. To the best of our knowledge, RED-PSM is the first PSM-based approach to dynamic imaging, that uses a pre-trained, learned (RED-based [23]) spatial prior.", + "2. A novel and effective ADMM algorithm for the resulting new minimization problem enforcing PSM as a hard constraint and incorporating the learned RED spatial regularizer is proposed.", + "3. The method is supported by theoretical analysis, with a convergence guarantee.", + "4. Compared to a recent DIP-based [20] algorithm, RED-PSM achieves better reconstruction accuracy with orders of magnitude faster run times.", + "5. A version of the approach with a patch-based regularizer is shown to provide almost equivalent reconstruction accuracy. This makes the proposed method conveniently scalable to high-resolution 3D or 4D settings." + ], + "bbox": [ + 88, + 595, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9e062c8cb60b485f4bcc5c1dbc0365ca5064edb7924296adc7dd2aea28d8060f.jpg", + "image_caption": [ + "Figure 1: Projection acquisition geometry for time-varying tomography of the object $f_{t}$ with single measurement $g_{t}$ at each time instant for $t \\in \\{0,1,2\\}$ ." + ], + "image_footnote": [], + "bbox": [ + 509, + 90, + 877, + 256 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Problem Statement", + "text_level": 1, + "bbox": [ + 500, + 314, + 687, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In a 2D setting, the goal in the ill-posed dynamic tomography problem is to reconstruct a time-varying object $f(\\mathbf{x},t)$ , $\\mathbf{x} \\in \\mathbb{R}^2$ vanishing outside a disc of diameter $L$ , from its projections", + "bbox": [ + 498, + 339, + 893, + 401 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\ng (\\cdot , \\theta , t) = \\mathcal {R} _ {\\theta} \\{f (\\mathbf {x}, t) \\}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 412, + 777, + 430 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "obtained using the Radon transform operator $\\mathcal{R}_{\\theta}$ at angle $\\theta$ . Considering time-sequential sampling, in which only one projection is acquired at each time instant, and sampling uniform in time, the acquired measurements are", + "bbox": [ + 498, + 441, + 892, + 502 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{g \\left(s, \\theta_ {p}, t _ {p}\\right) \\right\\} _ {p = 0} ^ {P - 1}, \\forall s, t _ {p} = p \\Delta_ {t}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 512, + 890, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $s$ is the offset of the line of integration from the origin (i.e., detector position), and $P$ is the total number of projections (and temporal samples) acquired. The sampling of the $s$ variable is assumed fine enough and is suppressed in the notation. The angular sampling scheme, the sequence $\\{\\theta_p\\}_{p=0}^{P-1}$ , with $\\theta_p \\in [0,2\\pi]$ , is considered as a free design parameter. Figure 1 shows a simplified time-sequential sampling scheme for a time-varying object.", + "bbox": [ + 498, + 542, + 893, + 664 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our objective in dynamic tomography, and in dynamic imaging in general, is to reconstruct the underlying object with temporal variation $\\{f(\\mathbf{x},t_p)\\}_{p = 0}^{P - 1}$ from the time-sequential measurements in (1). The challenge is that because each projection belongs to a different object, the projections in (1) are inconsistent. Therefore, a conventional, e.g., filtered backprojection (FBP) reconstruction as for a static object results in significant reconstruction artifacts.", + "bbox": [ + 496, + 664, + 893, + 785 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Partially Separable Models (PSM)", + "text_level": 1, + "bbox": [ + 498, + 799, + 812, + 816 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For spatio-temporal inverse problems such as dynamic MRI and tomography, the underlying object can be accurately represented using a partially-separable model (PSM), which effectively introduces a low-rank prior to the problem. For dynamic tomography, a PSM can represent the", + "bbox": [ + 496, + 825, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "footer", + "text": "10596", + "bbox": [ + 480, + 924, + 519, + 936 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "imagined object $f$ , or its full set of projections $g$ . In this paper we use an object-domain PSM.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The representation of a dynamic object $f(\\mathbf{x}, t)$ by a $K$ -th order PSM is the series expansion", + "bbox": [ + 75, + 119, + 468, + 151 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf (\\mathbf {x}, t) = \\sum_ {k = 0} ^ {K - 1} \\Lambda_ {k} (\\mathbf {x}) \\psi_ {k} (t). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 157, + 468, + 199 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The model helps with interpretability by separating the spatial structure from the temporal dynamics. This expansion is dense in $\\mathcal{L}_2$ [24], meaning that any finite energy object can be approximated arbitrarily well by such a model of sufficiently high order. Empirically, modest values of $K$ provide high accuracy in applications to MR cardiac imaging [15, 25, 26]. Theoretical analysis in [17] shows that for a spatially bandlimited object undergoing a time-varying affine transformation (i.e., combination of time-varying translation, scaling, and rotation) of bounded magnitude, a low order PSM provides a good approximation.", + "bbox": [ + 75, + 205, + 470, + 371 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The PSM using a $d$ -dimensional representation for the temporal functions leads to significant reduction of $\\approx PL^2$ representation parameters for an unstructured object of diameter $L$ with $P$ temporal samples to $\\approx KL^2 + Kd$ with $K \\ll P$ and $d \\ll P$ . Thus, it provides an effective parsimonious model for the spatio-temporal object $f$ .", + "bbox": [ + 75, + 371, + 468, + 462 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Also, by propagating the PSM object model to the projection domain, it enables quantitative analysis [17] of the choice of optimal sequential projection angular schedule.", + "bbox": [ + 75, + 462, + 468, + 508 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Proposed Method: RED-PSM", + "text_level": 1, + "bbox": [ + 76, + 518, + 352, + 536 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Variational Formulation", + "text_level": 1, + "bbox": [ + 76, + 544, + 302, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use a discretized version of the PSM (2) for the dynamic object, with the object $f(\\cdot ,t)$ at each time instant $t = 0,1,\\ldots ,P - 1$ , represented by a $J\\times J$ -pixel image. Vectorizing these images to vectors $f_{t}\\in \\mathbb{R}^{J^{2}}$ , the entire dynamic object is the $J^2\\times P$ matrix $f = [f_0\\dots f_{P - 1}] = \\Lambda \\Psi^T\\in \\mathbb{R}^{J^2\\times P}$ . Denoting the $t$ -th column of the $P\\times P$ identity matrix by $e_t$ , we have $f e_{t} = f_{t}$ for the $t$ -th individual time frame of $f$ . The columns $\\Lambda_{k}$ and $\\Psi_{k}$ of $\\Lambda \\in \\mathbb{R}^{J^2\\times K}$ and $\\Psi \\in \\mathbb{R}^{P\\times K}$ are the discretized spatial and temporal basis functions for the PSM representation, respectively.", + "bbox": [ + 75, + 566, + 468, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Assuming that the x-ray detector has $J$ bins, the projection of the object at time $t$ is $g_{t} = g(\\cdot ,\\theta_{t},t) = R_{\\theta_{t}}f_{t}\\in \\mathbb{R}^{J}$ , where the measurement matrix $R_{\\theta_t}\\in \\mathbb{R}^{J\\times J^2}$ computes the projection at view angle $\\theta_t$ .", + "bbox": [ + 75, + 736, + 468, + 797 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We formulate the recovery of $f$ as the solution $\\hat{f} = \\hat{\\Lambda}\\hat{\\Psi}^T$ to the following variational problem", + "bbox": [ + 75, + 797, + 468, + 829 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} (\\hat {\\Lambda}, \\hat {\\Psi}) = \\arg \\min _ {\\Lambda , \\Psi} \\sum_ {t = 0} ^ {P - 1} \\| R _ {\\theta_ {t}} \\Lambda \\Psi^ {T} e _ {t} - g _ {t} \\| _ {2} ^ {2} + \\lambda \\rho (\\Lambda \\Psi^ {T} e _ {t}) \\\\ + \\xi \\| \\Psi \\| _ {F} ^ {2} + \\xi \\| \\Lambda \\| _ {F} ^ {2} \\quad \\text {w h e r e} \\quad \\Psi = U Z. \\tag {3} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 81, + 835, + 468, + 897 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The first term is the data fidelity term measuring the fit between available undersampled measurements $g_{t}$ of the true object and the measurements obtained from the estimated object $f = \\Lambda \\Psi^{T} \\in \\mathbb{R}^{J^{2} \\times P}$ . The second term with weight $\\lambda > 0$ is a spatial regularizer injecting relevant spatial prior to the problem. The last two terms with weight $\\xi > 0$ prevent the bilinear factors $\\Lambda$ or $\\Psi$ from growing without limit.", + "bbox": [ + 496, + 90, + 890, + 198 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Finally, the constraint $\\Psi = UZ$ is an implicit temporal regularizer that restricts the temporal basis functions $\\Psi$ to a $d$ -dimensional subspace of $\\mathbb{R}^P$ spanned by a fixed basis $U \\in \\mathbb{R}^{P \\times d}$ . In practice, we incorporate this constraint by explicit substitution (reparametrization of $\\Psi$ in terms of the free variable $Z \\in \\mathbb{Z}^{d \\times K}$ ) into the objective, and the minimization in (3) over $\\Psi$ is thus replaced by minimization over $Z$ . This reduces the number of degrees of freedom in $\\Psi$ to a fixed number $dK$ , independent of the number $P$ of temporal sampling instants. For notational conciseness, We do not display this constraint/reparametrization in the sequel, but it is used throughout.", + "bbox": [ + 496, + 199, + 892, + 381 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.2. Incorporating Regularization by Denoising", + "text_level": 1, + "bbox": [ + 498, + 397, + 864, + 414 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For the spatial regularizer $\\rho(\\cdot)$ we consider \"Regularization by Denoising (RED)\" [23]. RED proposes a recovery method using a denoiser in an explicit regularizer of the form", + "bbox": [ + 496, + 422, + 890, + 482 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\rho \\left(f _ {t}\\right) = \\frac {1}{2} f _ {t} ^ {T} \\left(f _ {t} - D \\left(f _ {t}\\right)\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 496, + 890, + 525 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $D:\\mathbb{R}^{J^2}\\to \\mathbb{R}^{J^2}$ is the denoising operator. Recent works using RED provide impressive results for various static reconstruction tasks, including high-dimensional cases [27]. Providing significant flexibility for the type of denoisers that can be used, RED still requires $D$ to be differentiable and locally homogeneous, and to satisfy the passivity condition $\\| G(f)\\| \\leq \\| f\\|$ , for its theoretical analysis to apply.", + "bbox": [ + 496, + 541, + 890, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For the conventional variational formulation", + "bbox": [ + 517, + 666, + 813, + 679 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {f} _ {t} = \\arg \\min _ {f _ {t}} \\| R _ {\\theta_ {t}} f _ {t} - g _ {t} \\| _ {2} ^ {2} + \\lambda \\rho (f _ {t}),\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 696, + 825, + 720 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "an efficient choice are iterative algorithms [23] that use the standard \"early termination\" approach [29], and only require a single use of the denoiser per iteration.", + "bbox": [ + 496, + 736, + 890, + 781 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, the regularized PSM objective in (3) does not allow to propagate the RED updates on $f$ to the respective basis functions in an efficient manner. To overcome this difficulty, we perform a bilinear variable splitting $f = \\Lambda \\Psi^T$", + "bbox": [ + 496, + 784, + 890, + 844 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "1While many powerful denoisers satisfy these conditions [23], recent work [28] provides an alternative framework to explain the good performance of RED with denoisers not satisfying conditions in [23].", + "bbox": [ + 500, + 862, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10597", + "bbox": [ + 480, + 925, + 517, + 936 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and obtain our final formulation", + "bbox": [ + 76, + 90, + 292, + 104 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {f, \\Lambda , \\Psi} \\sum_ {t} \\| R _ {\\theta_ {t}} \\Lambda \\Psi_ {k} ^ {T} e _ {t} - g _ {t} \\| _ {2} ^ {2} + \\lambda \\rho (f e _ {t}) \\tag {5} \\\\ + \\xi \\| \\Psi \\| _ {F} ^ {2} + \\xi \\| \\Lambda \\| _ {F} ^ {2} \\quad \\mathrm {s . t .} \\quad f = \\Lambda \\Psi^ {T}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 112, + 468, + 165 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since the PSM is enforced as a hard constraint, the estimated object $f$ is constrained to have $\\mathrm{rank}(f) \\leq K$ . We propose an algorithm based on ADMM to solve (5).", + "bbox": [ + 76, + 172, + 468, + 217 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To cast the problem with the PSM constraint into the ADMM framework, we form the augmented Lagrangian in the scaled form, [30, 31]", + "bbox": [ + 76, + 217, + 468, + 262 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\beta} [ \\Lambda , \\Psi , f; \\gamma ] = \\sum_ {t} \\left\\| R _ {\\theta_ {t}} \\Lambda \\Psi^ {T} e _ {t} - g _ {t} \\right\\| _ {2} ^ {2} + \\lambda \\rho (f e _ {t}) \\\\ + \\xi \\| \\Psi \\| _ {F} ^ {2} + \\xi \\| \\Lambda \\| _ {F} ^ {2} - \\frac {\\beta}{2} \\| \\gamma \\| _ {F} ^ {2} + \\frac {\\beta}{2} \\| \\Lambda \\Psi^ {T} - f + \\gamma \\| _ {F} ^ {2}, \\tag {6} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 268, + 468, + 351 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\gamma \\in \\mathbb{R}^{P\\times J^2}$ represents the scaled dual variable and $\\beta >0$ is the penalty parameter.", + "bbox": [ + 76, + 361, + 468, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, ADMM can be used to solve (6) as in Algorithm 1.", + "bbox": [ + 96, + 393, + 468, + 409 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1 RED-PSM", + "text_level": 1, + "bbox": [ + 78, + 422, + 241, + 436 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "input: $\\Lambda^{(0)},\\Psi^{(0)},\\gamma^{(0)},f^{(0)} = \\Lambda^{(0)}\\Psi^{(0)T},\\beta >0,$ $\\lambda >0,\\xi >0$", + "bbox": [ + 76, + 440, + 468, + 472 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "1: for $i \\in \\{1, \\dots, I\\}$ do", + "bbox": [ + 88, + 474, + 251, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2: $\\Lambda^{(i)} = \\arg \\min_{\\Lambda}\\{\\sum_t\\| R_{\\theta_t}\\Lambda \\Psi^{(i - 1)T}e_t - g_t\\| _2^2$", + "bbox": [ + 88, + 489, + 431, + 506 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3: $\\Psi^{(i)} = \\arg \\min_{\\Psi}\\{\\sum_t\\| R_{\\theta_t}\\Lambda^{(i)}\\Psi^T e_t - g_t\\| _2^2$", + "bbox": [ + 88, + 526, + 418, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4: $\\forall t:f_t^{(i)} = \\arg \\min_{f_t}\\{\\lambda \\rho (f_t)\\}$", + "bbox": [ + 88, + 564, + 323, + 582 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5: $\\gamma^{(i)} = \\gamma^{(i - 1)} + \\Lambda^{(i)}\\Psi^{(i)T} - f^{(i)}$", + "bbox": [ + 88, + 602, + 341, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "6: end for", + "bbox": [ + 88, + 621, + 158, + 632 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} + \\frac {\\beta}{2} \\| \\Lambda \\Psi^ {(i - 1) T} - f ^ {(i - 1)} + \\gamma^ {(i - 1)} \\| _ {F} ^ {2} + \\xi \\| \\Lambda \\| _ {F} ^ {2} \\} \\\\ + \\frac {\\beta}{2} \\| \\Lambda^ {(i)} \\Psi^ {T} + \\gamma^ {(i - 1)} - f ^ {(i - 1)} \\| _ {F} ^ {2} + \\xi \\| \\Psi \\| _ {F} ^ {2} \\} \\\\ + \\frac {\\beta}{2} \\| (\\Lambda^ {(i)} \\Psi^ {(i) T} + \\gamma^ {(i - 1)}) e _ {t} - f _ {t} \\| _ {2} ^ {2} \\rbrace \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 88, + 474, + 439, + 632 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Line 4 in Algorithm 1 corresponds to the variational denoising of $(\\Lambda^{(i)}\\Psi^{(i)T} + \\gamma^{(i - 1)})e_t$ with regularization $\\lambda \\rho (f_t)$ . Algorithm 1 is reformulated into Algorithm 2 to use RED as in [23] and [28], where $D_{\\phi}$ is the denoiser for which we have the gradient rule", + "bbox": [ + 76, + 654, + 468, + 729 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla \\rho (f _ {t}) = f _ {t} - D _ {\\phi} (f _ {t}) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 738, + 468, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and each $f_{t}$ update in Step 4 is a single fixed-point iteration step using the approach of early stopping [29] (Sec. 4.3.2). In contrast to an iterative method to perform Line 4 in Algorithm 1, Step 4 in Algorithm 2 requires only single use of the denoiser per iteration of ADMM.", + "bbox": [ + 76, + 763, + 468, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Regularization Denoiser", + "text_level": 1, + "bbox": [ + 76, + 847, + 302, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The regularization denoiser $D_{\\phi}$ has a DnCNN [32] architecture and was trained in a supervised manner on a training", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 2 RED-PSM with efficient $f$ step", + "text_level": 1, + "bbox": [ + 500, + 90, + 799, + 106 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note: Inputs, and Lines 1-3 & 5-6 are the same as Algorithm 1.", + "bbox": [ + 500, + 107, + 890, + 133 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n4: \\forall t: f _ {t} ^ {(i)} = \\frac {\\lambda}{\\lambda + \\beta} D _ {\\phi} (f _ {t} ^ {(i - 1)}) + \\frac {\\beta}{\\lambda + \\beta} \\big (\\Lambda^ {(i)} \\Psi^ {(i) T} + \\gamma^ {(i - 1)} \\big) e _ {t}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 135, + 890, + 155 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "set of static 2D slices $f_{i} \\in \\mathbb{R}^{J^{2}}$ , $i = 1, \\dots, N$ assuming that such data will be available in the settings of interest. Thus, the RED steps are agnostic to the specific motion type. The training objective for the denoiser is", + "bbox": [ + 498, + 184, + 890, + 246 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\phi} \\sum_ {i} \\| f _ {i} - D _ {\\phi} (\\tilde {f} _ {i}) \\| _ {F} ^ {2} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 257, + 890, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tilde{f}_i = f_i + \\eta_i$ , and the injected noise $\\eta_{i}\\sim \\mathcal{N}(0,\\sigma_{i}^{2}I)$ has noise level $\\sigma_{i}\\sim U[0,\\sigma_{\\mathrm{max}}]$ spanning a range of values, so that the denoiser learns to denoise data with various noise levels.", + "bbox": [ + 498, + 301, + 890, + 362 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.4. Convergence Analysis", + "text_level": 1, + "bbox": [ + 500, + 375, + 705, + 390 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In [33](Section V.), we follow an approach along the lines of [34] to analyze convergence. We show that under mild technical conditions, the objective in Algorithm 1 is guaranteed to converge (with increasing number $I$ of iterations) to a value corresponding to a stationary point of the Lagrangian, that is, satisfying the necessary conditions for first order optimality. In practice, Algorithm 2 with the efficient $f$ step version, which we implemented and used in the experiments reported in Section 5 has better run times, and rapid empirical convergence. However, its analysis requires additional steps, which are not particularly illuminating. Thus, following the tradition in related analyses [29, 35], we focus on the analysis of the nominal Algorithm 1.", + "bbox": [ + 498, + 398, + 890, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 609, + 632, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 633, + 601, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Three categories of data sets are used in this work.", + "bbox": [ + 517, + 657, + 852, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Walnut Dataset: We use the CT reconstructions of two different (static) walnut objects from the publicly available 3D walnut CT dataset [36]. We create a dynamic test object by synthetically warping the central axial slice of one of the walnut objects using a sinusoidal piecewise-affine time-varying warp [37]. To be precise, the image is divided into a $J \\times J$ uniformly spaced rectangular grid, and the following vertical displacement is applied on each row separately to drive the temporally varying warp $\\Delta_{j,t} = -C(t)\\sin(3\\pi j / J)$ , $j \\in \\{0, \\dots, J-1\\}$ , where $C(t)$ is a linearly increasing function of $t$ and $C(0) = 0$ . Static axial, coronal, and sagittal slices of the other walnut object are used to train the denoiser $D_{\\phi}$ .", + "bbox": [ + 498, + 674, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Compressed Object Dataset: This data set is obtained from a materials science experiment [38] with a sequence", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10598", + "bbox": [ + 480, + 924, + 517, + 936 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of nine increasing compression steps applied to an object, with a full set of radiographic projections collected (using Carl Zeiss Xradia 520 Versa) and reconstructed by the instrument's software at each step. Using this quasi-static data set, a fixed axial slice is extracted from each reconstruction. Nine extracted slices are interpolated to $P$ time frames using a recent deep learning-based video interpolation algorithm [39]. The denoiser $D_{\\phi}$ for our experiments on this data set was trained using the axial slices of the static pre-compression and post-compression objects, which would be available in actual dynamic loading experiments.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We note that all algorithms compared in this paper are agnostic to both the synthetic warp applied on the static walnut slice and to the data-driven interpolation method used for the compressed object.", + "bbox": [ + 75, + 257, + 468, + 318 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Spatio-temporal projection data for each dataset is simulated by a parallel-beam projection with $J = 128$ detector bins of the dynamic phantoms, a single projection at each of the $P$ time instants. The sequence of projection angles $\\{\\theta_t\\}_{t=0}^{P-1}$ (a free experimental design parameter) was chosen to follow the bit-reversed view angle sampling scheme, which has been shown [16] to provide an especially favorable conditioning of the recovery problem. The simulated measurements are corrupted using AWGN with standard deviation $\\sigma = 5 \\cdot 10^{-3}$ . This noise level leads to the FBP (with Ram-Lak filter) of the full set of $P = 512$ projections at each time instant having a PSNR of approximately 46 dB. When, in the actual experiments with sequentially sampled data, only $1 / P$ of this data is used, the PSNR of the reconstruction may be expected to be lower.", + "bbox": [ + 75, + 318, + 473, + 545 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Ground-truth frames for $P = 4$ are shown in Figure 2.", + "bbox": [ + 96, + 546, + 455, + 560 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Cardiac dMRI Dataset: For a more direct comparison with the setting and data used in dMRI works, we also test RED-PSM on the \"retrospective\" cardiac dMRI data in [20]. The data includes 23 distinct time frames for one cardiac cycle. Details of the data and experiments are in Section 5.4.3.", + "bbox": [ + 75, + 561, + 468, + 650 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/167e7ee59929a2e09799f5eb620bee3fe2b5b7151ec889e57e91482f07e5ab23.jpg", + "image_caption": [ + "Figure 2: Ground-truth frames for the time-varying walnut (top) and compressed object (bottom) datasets, uniformly sampled in time, $t \\in \\{0, \\dots, P - 1\\}$ , for $P = 4$ ." + ], + "image_footnote": [], + "bbox": [ + 86, + 662, + 459, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Baseline Methods", + "text_level": 1, + "bbox": [ + 76, + 830, + 250, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "PSM-TV: Similar to the proposed approach, this algorithm also uses a partially separable model to represent the object with a different regularization type. For PSM-TV,", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "regularization penalizes the $\\ell_1$ -norm of the discrete 2D total variation of the temporal slices of $f$ at each time instant. To this end, the constraint $f = \\Lambda \\Psi^T$ is implemented by substitution into the objective in (5), and the definition of $\\rho$ is changed to $\\rho (\\Lambda \\Psi^T e_t) = \\mathrm{TV}(\\Lambda \\Psi^T e_t)$ , and the rest of the objective is kept the same. The unconstrained problem is then solved for $\\{\\hat{\\Lambda},\\hat{\\Psi}\\}$ (using, as a convenient implementation, the Adam optimizer in Pytorch). Finally, the estimated object is obtained as $\\hat{f} = \\hat{\\Lambda}\\hat{\\Psi}^{T}$ .", + "bbox": [ + 496, + 90, + 890, + 226 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "TD-DIP [20]: TD-DIP is a recent method based on the Deep Image Prior (DIP) approach. It uses a mapping network $M_{\\alpha}$ and a generative model $N_{\\beta}$ sequentially to obtain the estimated object at each time instant $f_{t}$ from fixed and handcrafted latent representations $\\chi_t$ . Because TD-DIP was originally proposed for dynamic MRI, we modified the objective minimally for dynamic tomography as", + "bbox": [ + 496, + 227, + 890, + 333 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\alpha , \\beta} \\sum_ {t} \\| g _ {t} - R _ {\\theta (t)} \\left(\\left(N _ {\\beta} \\circ M _ {\\alpha}\\right) (\\chi_ {t})\\right) \\| ^ {2}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 344, + 890, + 375 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the comparisons in this work, identical mapping network and generator architectures, latent representation dimensionality, optimizer, learning rate, and decay schemes are used as in the available online implementation [40]. The original work focuses on the beating heart problem and thus proposes a helix-shaped latent manifold for $\\chi_t$ with cycles equal to the number of heartbeats during measurement acquisition. Since we do not have a repetition assumption for the motion types included in this paper, we use a linear manifold as explained in the original paper [20]. Thus, the method is sometimes denoted as \"TD-DIP (L)\" in Section 5.4 for clarification.", + "bbox": [ + 496, + 386, + 892, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.3. Experimental Settings", + "text_level": 1, + "bbox": [ + 500, + 578, + 705, + 594 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "All methods are run on a workstation with an Intel(R) Xeon(R) Gold 5320 CPU and NVIDIA RTX A6000 GPU. In practice, we used a minor variation of Algorithm 2, where we combined the subproblems in $\\Lambda$ and $\\Psi$ , and minimized with respect to both basis functions simultaneously using gradient descent with Adam [41] optimizer.", + "bbox": [ + 496, + 602, + 890, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Denoiser training. The upper limit for noise level used in training the denoiser was set to $\\sigma_{\\mathrm{max}} = 5 \\cdot 10^{-2}$ . For the dynamic walnut object, the denoiser $D_{\\phi}$ is trained on the central 200 axial, 200 sagittal, and 200 coronal slices of another walnut CT reconstruction downsampled to size $128 \\times 128$ . For the compressed object, axial slices of precompression and post-compression static objects, containing 462 slices in total, are used to train $D_{\\phi}$ . For the cardiac MRI setting, the denoiser was trained on the static MRI", + "bbox": [ + 496, + 693, + 890, + 829 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "2It would be interesting to include yet another baseline method - the DIP-based PSM approach [22] (also developed for MRI). However we were unable to do so as an implementation of this method was not available, and because of potential issues with replicating its performance and adapting to our CT problem.", + "bbox": [ + 496, + 838, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10599", + "bbox": [ + 480, + 925, + 517, + 936 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e0541d9605d18db12e067518136d5ba9e4b6eb2c29d7eb6b551fa239663f906f.jpg", + "image_caption": [ + "Figure 3: Reconstruction PSNR, SSIM, MAE, and HFEN for the time-varying walnut object (top) and compressed material (bottom) vs. $P$ using different methods. For TD-DIP, accuracy statistics for the best PSNR reconstruction during optimization are reported assuming such an oracle is available. The minimum and maximum values are indicated with error bars and the mean values are connected by the dashed line for different $P$ for three different runs." + ], + "image_footnote": [], + "bbox": [ + 76, + 90, + 285, + 311 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9f646b60d1e06fdcbfa357f67ec74177b15273069d3abf96a20fa5aaaa1bd6ac.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 90, + 486, + 311 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6f97db83192577f02658f4ef1b4145ce0fa26e8dcc8b9ae4a2cdaebb931cee81.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 90, + 691, + 311 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/151dd039336443623d6b5a98dadac46eb6981e548f13e1e3a5192876a50d4d55.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 692, + 90, + 897, + 311 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/978668ae12f3598e4d34b50d8566c5318abed270d3f8ccef1a876144535b7cdf.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
(a) Walnut(b) Compressed Material
PMethodPSNR (dB)SSIMMAE (1e-3)HFENPSNR (dB)SSIMMAE (1e-2)HFEN
32PSM-TV (R)21.10.6782.91.0422.50.6972.911.6
TD-DIP (L)22.50.8822.10.8725.40.9091.58.1
RED-PSM (Pr)22.70.9141.50.7923.90.9161.29.9
64PSM-TV (R)24.00.8791.90.9425.60.8451.810.7
TD-DIP (L)25.60.9161.50.7429.00.9471.16.5
RED-PSM (Pr)26.40.9580.90.5729.30.9520.56.0
128PSM-TV (R)26.80.9121.40.7829.20.9071.19.6
TD-DIP (L)29.00.9531.00.5032.40.9530.85.1
RED-PSM (Pr)29.90.9780.60.4333.10.9720.44.7
256PSM-TV (R)30.10.9341.00.6331.90.9630.78.0
TD-DIP (L)31.70.9660.80.4534.70.9660.74.6
RED-PSM (Pr)33.80.9870.40.3235.90.9860.34.4
", + "bbox": [ + 78, + 375, + 470, + 553 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1: Reconstruction accuracies for different $P$ . Random (R) and ProSep (Pr) initialization for the PSM methods. For TD-DIP, the reported accuracies are for the best PSNR using a \"stopping oracle\", averaged over three runs with random initial conditions.", + "bbox": [ + 75, + 555, + 468, + 612 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "training slices of the ACDC dataset [42]. For all datasets, $D_{\\phi}$ is trained for 500 epochs using the Adam optimizer with a learning rate of $5 \\cdot 10^{-3}$ . Each convolutional layer is followed by a ReLU nonlinearity except for the final layer, which has a single-channel output. We test both direct and residual DnCNN denoisers where the former predicts the denoised image and the latter estimates the noise from the noisy input.", + "bbox": [ + 75, + 621, + 468, + 743 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Architectural details for denoisers used in our experiments are provided in Table 6 in Supplementary Material C. We use a fixed pre-trained denoiser for all $P$ for the same object type.", + "bbox": [ + 75, + 744, + 468, + 806 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Temporal Basis. In all experiments, we use a fixed basis $U$ as a cubic spline interpolator to interpolate the low-dimensional temporal representation $Z$ to $\\Psi$ .", + "bbox": [ + 75, + 808, + 468, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Initialization. Unless stated otherwise, spatial and temporal basis functions are initialized using the SVD truncated to order $K$ the rank of the dynamic object estimate pro", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "duced by a recent projection-domain PSM-based method \"ProSep\" [17]. If the ProSep estimate has rank smaller than $K$ , the remaining basis functions are initialized as 0. Otherwise, all spatial basis functions are initialized as 0 and the latent representations $z_{k}$ of the temporal basis functions are initialized randomly as $z_{k} \\sim \\mathcal{N}(0, I)$ .", + "bbox": [ + 496, + 377, + 890, + 467 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tomographic Acquisition Scheme. All methods mentioned in this paper use the bit-reversed angular sampling scheme, over the range $[0,\\pi ]$ .", + "bbox": [ + 496, + 468, + 890, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Run Times. For $P = 256$ and using the specified computational resources and parameter settings, To achieve the peak PSNR during optimization, RED-PSM with ProSep initialization requires $50 <$ iterations $< 150$ taking about 2 to 6 minutes whereas TD-DIP with batch size $P$ typically requires $> 30k$ steps, taking about 3.5 hours to complete. Hence, RED-PSM provides a speedup over TD-DIP by a factor of 35 to 105 to reach its peak performance. We note that based on the parameter configuration, the speedup factor may vary. However, the proposed method provides a significant run time reduction in all cases.", + "bbox": [ + 496, + 513, + 890, + 678 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. Four quantitative metrics were implemented for evaluating reconstruction accuracy (i) the peak signal-to-noise ratio (PSNR) in dB; (ii) the structural similarity index (SSIM) [43]; (iii) the mean absolute error (MAE); and (iv) the high-frequency error norm (HFEN) [44] defined as $\\mathrm{HFEN}(f, f_r) = \\| \\mathrm{LoG}(f) - \\mathrm{LoG}(f_r)\\|_2$ where LoG is a rotationally symmetric Laplacian of Gaussian filter with a standard deviation of 1.5 pixels.", + "bbox": [ + 496, + 679, + 890, + 800 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.4. Results", + "text_level": 1, + "bbox": [ + 500, + 808, + 591, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.4.1 Reconstruction accuracies for different $P$", + "text_level": 1, + "bbox": [ + 500, + 830, + 841, + 845 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Figure 3 and Table 1, the performance of RED-PSM is compared with PSM-TV and with TD-DIP that uses a linear latent representation for both objects. While Figure 3", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10600", + "bbox": [ + 480, + 926, + 517, + 936 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f25bcfea3f73944bbeba99e933c8adedc629c6e5457815e6e72036b47ad23ff2.jpg", + "image_caption": [ + "Figure 4: Comparison of reconstructed object frames at two time instants using different methods for $P = 256$ , and the corresponding normalized absolute reconstruction errors for (A) the time-varying walnut, and (B) compressed object." + ], + "image_footnote": [], + "bbox": [ + 94, + 87, + 864, + 385 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "facilitates the comparison of metrics for different $P$ for the various methods, since the range of metrics is very large for varying $P$ . Table 1 emphasizes important differences between methods for the same $P$ , and provides detail for a more precise quantitative comparison. As expected, the estimates improve with increasing $P$ for all methods. In terms of PSNR, the proposed algorithm performs on par with or better than the best PSNR TD-DIP estimate for various $P$ , with improvement for RED-PSM enhancing with the increase in $P$ . Moreover, in terms of SSIM, MAE, and HFEN, the improvements with RED-PSM are even more significant. Although these observations are valid for both objects, for the walnut, RED-PSM provides slightly greater improvement over TD-DIP.", + "bbox": [ + 75, + 426, + 472, + 636 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 4 compares the reconstructions for both objects at two different $t$ for $P = 256$ . As expected, providing blurry reconstructions lacking finer details for both objects, PSM-TV performs the worst among the compared methods. The TD-DIP reconstructions contain visible noise-like artifacts on the piecewise constant regions of the walnut object, which are alleviated by RED-PSM. This observation manifests itself also in the absolute difference figures, with error for TD-DIP distributed throughout the interior regions of the walnut. Furthermore, RED-PSM preserves sharp details around the shell of the walnut better. Throughout the compressed material object for the given time frames, compared to TD-DIP, RED-PSM has an almost consistently smaller absolute error. This difference is more prominent around the highly dynamic regions of the object, emphasizing the advantage of the proposed method.", + "bbox": [ + 75, + 641, + 472, + 882 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Figure 5, the reconstructed $x - t$ cross-sections of the", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "dynamic walnut are shown for different methods. The location of the cross-section is highlighted by a yellow line on the static $x - y$ frame at $t = 0$ . Consistent with the comparison in Figure 4, RED-PSM provides reduced absolute error values throughout the respective cross-section. Also, as more apparent in the error figures, TD-DIP produces higher background errors.", + "bbox": [ + 496, + 426, + 893, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4.2 Effect of Initialization", + "text_level": 1, + "bbox": [ + 498, + 554, + 707, + 569 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The initialization of $\\Lambda$ , $\\Psi$ , and $f$ plays an important role in the performance and convergence speed of RED-PSM. We observe significant speed-up when rather than a random initialization, we initialize the algorithm with ProSep [16] estimated reconstruction. Figure 7 shows PSNR vs. iterations comparison for different initialization techniques for the dynamic walnut object with $P = 256$ . The rest of the parameters were selected identically as indicated in Table 5 in Supplementary Material. This experiment highlights the advantages of initializing with ProSep estimated basis functions: eliminating the need for multiple runs for a best-case result; and speeding up convergence considerably.", + "bbox": [ + 496, + 580, + 893, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4.3 Cardiac dMRI data experiments", + "text_level": 1, + "bbox": [ + 498, + 784, + 782, + 800 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this setting, different to the previous experiments, we used $4k$ -space radial lines (\"spokes\") per frame at the bitreversed angles. We used 1.4 and 2.8 cardiac cycles, with $23 \\times 4 = 92$ spokes/cycle, for a total of $P = 128$ and $P = 256$ spokes. The problem is still severely undersampled compared to the experiment in [20] where 13 spokes are used", + "bbox": [ + 496, + 810, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10601", + "bbox": [ + 480, + 926, + 517, + 936 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b933e3c8c0dfc105bc8e7b8061f2343b10eea044acef736e2dfbca0b107ab5c4.jpg", + "image_caption": [ + "Figure 5: Comparison of reconstructed $x - t$ cross-sections using different methods for $P = 256$ (top), with corresponding normalized absolute error counterparts (bottom). The location of the cross-section is indicated with a yellow line on the static object at time $t = 0$ (left). The $x - y - t$ coordinates are indicated on the static object and bottom left absolute error figure in white text." + ], + "image_footnote": [], + "bbox": [ + 98, + 93, + 235, + 200 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/09d3208231d9d75f956e27c02d09e12340b28f2da42d61a0a394b6a44ee1f344.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 235, + 93, + 383, + 200 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4e2d324213887fee614a4ee031ae5c2b834b2f48514acae517041474796ec816.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 383, + 93, + 527, + 200 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/384f4706bf41f52296a3ca8b7a7e1a1c5b27979073f392095ed59fce9c1668d1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 527, + 93, + 673, + 200 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d974b72d97dc6fcba4f6cd5a0e071a5534fa77c08d9962816882c193d3ee48d3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 673, + 93, + 816, + 200 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/30a4e5748de863c9924f0b2bd603c64adeb56c3c50c06f8d172bc7cf2b2eb4f2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 818, + 93, + 864, + 200 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "per frame for 13 cycles, for a total of $13 \\times 23 \\times 13 = 3,887$ spokes. Since the data is periodic, we also tested the helix latent scheme (H) for TD-DIP.", + "bbox": [ + 75, + 253, + 467, + 297 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The metrics in Table 2 and the qualitative comparison in Figure 6 with zoomed-in reconstructions and absolute error maps, show that RED-PSM performs better than both versions of TD-DIP.", + "bbox": [ + 75, + 299, + 467, + 357 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c740dcf4dde0c91aa3c47502dc6ccc5c48d1690e962dc99a7e4f0cf0100b3b18.jpg", + "image_caption": [ + "Figure 6: Reconstructed frames for $P = 256$ for retrospective dMRI data [20] with zoomed-in frames (middle row), and absolute reconstruction errors (last row)." + ], + "image_footnote": [], + "bbox": [ + 84, + 369, + 454, + 583 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/21f04080e7e1edf1048618b3e87f02bbc9267efe4a152e6a3e4478b35b0c8644.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
PMethodPSNR (dB)SSIMMAE (1e-2)HFEN
128TD-DIP (L)34.60.9231.73.38
TD-DIP (H)34.60.9281.73.32
RED-PSM36.60.9391.42.73
256TD-DIP (L)36.20.9481.43.47
TD-DIP (H)36.40.9471.43.44
RED-PSM38.40.9621.12.99
", + "bbox": [ + 109, + 633, + 431, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2: Reconstruction accuracies for RED-PSM and TD-DIP for the retrospective dMRI data [20].", + "bbox": [ + 75, + 718, + 467, + 746 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5. PSNR vs. $t$ , and a Patch-Based Scheme", + "text_level": 1, + "bbox": [ + 76, + 755, + 411, + 771 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Supplementary Material A, we compare the PSNR of the reconstructed frames for each $t$ for all methods for the walnut object with $P = 256$ and show the consistently better performance of RED-PSM.", + "bbox": [ + 75, + 779, + 467, + 839 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Also, in Supplementary Material B, to improve scalability to high-resolution and high-dimensional settings, we propose and evaluate a patch-based version of RED-PSM with a patch-based denoiser $D_{\\phi}$ . In the experiments,", + "bbox": [ + 75, + 839, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the patch-based scheme provided reconstruction accuracies similar to those reported here for the original scheme.", + "bbox": [ + 498, + 253, + 888, + 284 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 299, + 625, + 314 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "RED-PSM is the first PSM-based approach to dynamic imaging using a pre-trained and learned (RED-based) spatial prior. The objective in the proposed variational formulation is optimized using a novel and effective bilinear ADMM algorithm, which enforces the PSM as a hard constraint. Unlike existing PSM-based techniques, RED-PSM is supported by theoretical analysis, with a convergence guarantee to a stationary point of the objective. The results of the numerical experiments show better reconstruction accuracy and considerably faster run times compared to a recent DIP-based algorithm. A patch-based regularizer version of RED-PSM provides almost equivalent performance with a massive reduction of storage requirements, indicating the potential of our framework for dynamic high-resolution 2D or 3D settings.", + "bbox": [ + 496, + 324, + 890, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Possible directions for future work include the application of RED-PSM to various imaging scenarios other than tomography and MRI, and robust denoiser training for the RED framework, since the deep denoisers encounter varying artifact distributions during optimization. This could also improve the generalizability of the framework to different input types.", + "bbox": [ + 496, + 551, + 890, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This research was supported in part by Los Alamos National Labs under Subcontract No. 599416/CW13995. We thank Dr. Brian M. Patterson for providing the data for the compressed material experiments.", + "bbox": [ + 496, + 659, + 890, + 719 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6e8a2d405e3c354bf6928f9c643f0eb52a0818eb616d9694215e3f2c3ebb2ec0.jpg", + "image_caption": [ + "Figure 7: PSNR vs. iteration comparison for RED-PSM as described in Section 5.4.2. The area between the best and the worst PSNR for each iteration is shown in blue to highlight the varying performances of five different runs with random initialization." + ], + "image_footnote": [], + "bbox": [ + 562, + 736, + 826, + 845 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10602", + "bbox": [ + 480, + 925, + 517, + 936 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] E. Maire, C. Le Bourlot, J. Adrien, A. Mortensen, and R. Mokso, “20 Hz X-ray tomography during an in situ tensile test,” International Journal of Fracture, vol. 200, no. 1, pp. 3–12, 2016.", + "[2] I. Danad, J. Szymonifka, J. Schulman-Marcus, and J. K. 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Bresler, \"MR image reconstruction from highly undersampled k-space data by dictionary learning,\" IEEE Transactions on Medical Imaging, vol. 30, no. 5, pp. 1028-1041, 2010.", + "bbox": [ + 501, + 90, + 890, + 148 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10604", + "bbox": [ + 480, + 926, + 519, + 936 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/RED-PSM_ Regularization by Denoising of Partially Separable Models for Dynamic Imaging/ffd9f980-64f4-43d0-a9f4-e03ede33c976_model.json b/2023/RED-PSM_ Regularization by Denoising of Partially Separable Models for Dynamic Imaging/ffd9f980-64f4-43d0-a9f4-e03ede33c976_model.json new file mode 100644 index 0000000000000000000000000000000000000000..174c5760e3c4cd3eefe61c799e381d76ea5e90d8 --- /dev/null +++ b/2023/RED-PSM_ Regularization by Denoising of Partially Separable Models for Dynamic Imaging/ffd9f980-64f4-43d0-a9f4-e03ede33c976_model.json @@ -0,0 +1,2486 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.13, + 0.13, + 0.842, + 0.177 + ], + "angle": 0, + "content": "RED-PSM: Regularization by Denoising of Partially Separable Models for Dynamic Imaging" + }, + { + "type": "text", + "bbox": [ + 0.252, + 0.204, + 0.372, + 0.221 + ], + "angle": 0, + "content": "Berk Iskender1" + }, + { + "type": "text", + "bbox": [ + 0.414, + 0.204, + 0.548, + 0.222 + ], + "angle": 0, + "content": "Marc L. Klasky2" + }, + { + "type": "text", + "bbox": [ + 0.594, + 0.204, + 0.716, + 0.222 + ], + "angle": 0, + "content": "Yoram Bresler" + }, + { + "type": "text", + "bbox": [ + 0.232, + 0.224, + 0.386, + 0.236 + ], + "angle": 0, + "content": "berki2@illinois.edu" + }, + { + "type": "text", + "bbox": [ + 0.411, + 0.225, + 0.539, + 0.236 + ], + "angle": 0, + "content": "mklasky@lanl.gov" + }, + { + "type": "text", + "bbox": [ + 0.565, + 0.225, + 0.734, + 0.236 + ], + "angle": 0, + "content": "ybresler@illinois.edu" + }, + { + "type": "text", + "bbox": [ + 0.202, + 0.237, + 0.768, + 0.251 + ], + "angle": 0, + "content": "1University of Illinois at Urbana-Champaign, USA 2Los Alamos National Laboratory, USA" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.272, + 0.313, + 0.287 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.473, + 0.683 + ], + "angle": 0, + "content": "Dynamic imaging involves the recovery of a time-varying 2D or 3D object at each time instant using its undersampled measurements. In particular, in dynamic tomography, only a single projection at a single view angle may be available at a time, making the problem severely ill-posed. In this work, we propose an approach, RED-PSM, which combines for the first time two powerful techniques to address this challenging imaging problem. The first, are partially separable models, which have been used to introduce a low-rank prior for the spatio-temporal object. The second is the recent Regularization by Denoising (RED), which provides a flexible framework to exploit the impressive performance of state-of-the-art image denoising algorithms, for various inverse problems. We propose a partially separable objective with RED and an optimization scheme with variable splitting and ADMM. Our objective is proved to converge to a value corresponding to a stationary point satisfying the first-order optimality conditions. Convergence is accelerated by a particular projection-domain-based initialization. We demonstrate the performance and computational improvements of our proposed RED-PSM with a learned image denoiser by comparing it to a recent deep-prior-based method TD-DIP. Although the emphasis is on dynamic tomography, we also demonstrate the performance advantages of RED-PSM in a dynamic cardiac MRI setting." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.709, + 0.208, + 0.725 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.734, + 0.47, + 0.825 + ], + "angle": 0, + "content": "Time-varying tomography is a challenging ill-posed inverse problem that involves reconstructing a dynamic object using its sequential projections at each time instant. Since the measurements are inconsistent due to the evolving object, traditional reconstruction algorithms lead to significant artifacts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "The problem arises in micro-CT [1], myocardial perfusion imaging [2], thoracic CT [3], imaging of fluid flow processes [4, 5] and dynamic imaging of material samples undergoing compression [6, 7]. Also, it is closely related to the dynamic MRI (dMRI) problem, which typically arises" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.274, + 0.655, + 0.289 + ], + "angle": 0, + "content": "in cardiac imaging [8]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.291, + 0.892, + 0.367 + ], + "angle": 0, + "content": "Previous work [9, 10] treated the problem as time-sequential sampling of bandlimited signals and provided an optimal view angle sampling order and theoretical guarantees for unique and stable reconstruction. However, the approach is limited by its bandlimitedness assumptions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.368, + 0.893, + 0.52 + ], + "angle": 0, + "content": "Several methods [11, 12] recover the underlying motion field from projections using the Radon transform properties. However, these methods require the object information a priori. Other algorithms [13, 14] alternate between estimating the motion field and the time-varying object. These methods assume the total density to be preserved for a given object at different times which may be a limiting assumption. For instance, imaging a fixed slice of a time-varying object under compression may violate this assumption due to perpendicularly evolving parts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.893, + 0.673 + ], + "angle": 0, + "content": "In dynamic tomography and MRI, partially-separable models (PSM) have been used to represent the underlying object [15] and the time-sequential projections [16, 17]. The projection-domain PSM in [16, 17] carries the PSM to the projection domain using the harmonic representation of projections, and provides uniqueness and stability analysis for the problem. In spite of this advantage of the projection domain PSM over its object-domain counterparts, the performance of this approach is limited by the null space of the measurement operator." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.895, + 0.901 + ], + "angle": 0, + "content": "A different PSM-based method for dMRI [18] imposes the low-rank structure as a soft constraint. It uses a hybrid objective with the PSM model used in the data fidelity term and the object in a simple \\( l_{1} \\)-norm penalty, with an additional penalty term to penalize the mismatch between the PSM and the object. The method does not use a guided initial guess for the object or for the PSM basis functions. A fast alternative low-rank (or PSM)-based method for dMRI [19] decomposes the object representation into three components: the mean signal, a low-rank PSM, and the residual, which is assumed to be sparse in the Fourier domain. Then, each component is estimated in order. Although on some of the data sets used for the comparison in [19] competing methods are either faster or more accurate, the method provides better results when averaged over all data sets." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "10595" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "Recently, object-domain deep image prior (DIP)-based algorithms [20,21] have been proposed for dMRI. Providing impressive results, DIP-based algorithms such as [20] suffer from overfitting and usually require handcrafted early stopping criteria during the optimization of generator network parameters. In an attempt to overcome the overfitting and the need for handcrafted early stopping, the authors of [21] regularize the problem by constraining the geodesic distances between generated objects in proportion to the distances between their latent representation. However, this requires the computation of the Jacobian of the generator network at each iteration of the update of the weights and significantly increases the computational load and run time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.289, + 0.473, + 0.562 + ], + "angle": 0, + "content": "A different approach [22] combines partially separable and generative models. It employs spatial and temporal regularization by penalizing the generator weights and a particular initialization scheme for the inputs to the generator networks. Although it combines the PSM with the recent DIP framework, this method has the following limitations, which are overcome by the proposed approach: (i) The spatial generator is an artifact removal network taking the full-sized spatial basis functions as input. Since this prevents a patch-based implementation, it may be difficult to scale to high-resolution 3D+temporal settings. (ii) The CNN prior for natural images may not be useful as a prior for the individual spatial basis functions, since the least-squares optimal spatial basis functions are the left singular vectors of the complete object, and as such may not have the structure of natural images. (iii) As with other DIP-based methods, if the additional penalty on the generator parameters is insufficient, this method can be prone to overfitting." + }, + { + "type": "title", + "bbox": [ + 0.098, + 0.568, + 0.194, + 0.582 + ], + "angle": 0, + "content": "Contributions" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.597, + 0.47, + 0.645 + ], + "angle": 0, + "content": "1. To the best of our knowledge, RED-PSM is the first PSM-based approach to dynamic imaging, that uses a pre-trained, learned (RED-based [23]) spatial prior." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.658, + 0.47, + 0.72 + ], + "angle": 0, + "content": "2. A novel and effective ADMM algorithm for the resulting new minimization problem enforcing PSM as a hard constraint and incorporating the learned RED spatial regularizer is proposed." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.733, + 0.47, + 0.765 + ], + "angle": 0, + "content": "3. The method is supported by theoretical analysis, with a convergence guarantee." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.78, + 0.47, + 0.825 + ], + "angle": 0, + "content": "4. Compared to a recent DIP-based [20] algorithm, RED-PSM achieves better reconstruction accuracy with orders of magnitude faster run times." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "5. A version of the approach with a patch-based regularizer is shown to provide almost equivalent reconstruction accuracy. This makes the proposed method conveniently scalable to high-resolution 3D or 4D settings." + }, + { + "type": "list", + "bbox": [ + 0.089, + 0.597, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.091, + 0.878, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.262, + 0.894, + 0.306 + ], + "angle": 0, + "content": "Figure 1: Projection acquisition geometry for time-varying tomography of the object \\( f_{t} \\) with single measurement \\( g_{t} \\) at each time instant for \\( t \\in \\{0,1,2\\} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.315, + 0.688, + 0.331 + ], + "angle": 0, + "content": "2. Problem Statement" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.34, + 0.894, + 0.402 + ], + "angle": 0, + "content": "In a 2D setting, the goal in the ill-posed dynamic tomography problem is to reconstruct a time-varying object \\( f(\\mathbf{x},t) \\), \\( \\mathbf{x} \\in \\mathbb{R}^2 \\) vanishing outside a disc of diameter \\( L \\), from its projections" + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.414, + 0.779, + 0.431 + ], + "angle": 0, + "content": "\\[\ng (\\cdot , \\theta , t) = \\mathcal {R} _ {\\theta} \\{f (\\mathbf {x}, t) \\}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.442, + 0.893, + 0.503 + ], + "angle": 0, + "content": "obtained using the Radon transform operator \\(\\mathcal{R}_{\\theta}\\) at angle \\(\\theta\\). Considering time-sequential sampling, in which only one projection is acquired at each time instant, and sampling uniform in time, the acquired measurements are" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.513, + 0.892, + 0.534 + ], + "angle": 0, + "content": "\\[\n\\left\\{g \\left(s, \\theta_ {p}, t _ {p}\\right) \\right\\} _ {p = 0} ^ {P - 1}, \\forall s, t _ {p} = p \\Delta_ {t}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.544, + 0.894, + 0.665 + ], + "angle": 0, + "content": "where \\( s \\) is the offset of the line of integration from the origin (i.e., detector position), and \\( P \\) is the total number of projections (and temporal samples) acquired. The sampling of the \\( s \\) variable is assumed fine enough and is suppressed in the notation. The angular sampling scheme, the sequence \\( \\{\\theta_p\\}_{p=0}^{P-1} \\), with \\( \\theta_p \\in [0,2\\pi] \\), is considered as a free design parameter. Figure 1 shows a simplified time-sequential sampling scheme for a time-varying object." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.665, + 0.894, + 0.786 + ], + "angle": 0, + "content": "Our objective in dynamic tomography, and in dynamic imaging in general, is to reconstruct the underlying object with temporal variation \\(\\{f(\\mathbf{x},t_p)\\}_{p = 0}^{P - 1}\\) from the time-sequential measurements in (1). The challenge is that because each projection belongs to a different object, the projections in (1) are inconsistent. Therefore, a conventional, e.g., filtered backprojection (FBP) reconstruction as for a static object results in significant reconstruction artifacts." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.8, + 0.813, + 0.818 + ], + "angle": 0, + "content": "3. Partially Separable Models (PSM)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.902 + ], + "angle": 0, + "content": "For spatio-temporal inverse problems such as dynamic MRI and tomography, the underlying object can be accurately represented using a partially-separable model (PSM), which effectively introduces a low-rank prior to the problem. For dynamic tomography, a PSM can represent the" + }, + { + "type": "footer", + "bbox": [ + 0.481, + 0.925, + 0.52, + 0.937 + ], + "angle": 0, + "content": "10596" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "imagined object \\( f \\), or its full set of projections \\( g \\). In this paper we use an object-domain PSM." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.121, + 0.47, + 0.152 + ], + "angle": 0, + "content": "The representation of a dynamic object \\( f(\\mathbf{x}, t) \\) by a \\( K \\)-th order PSM is the series expansion" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.159, + 0.47, + 0.2 + ], + "angle": 0, + "content": "\\[\nf (\\mathbf {x}, t) = \\sum_ {k = 0} ^ {K - 1} \\Lambda_ {k} (\\mathbf {x}) \\psi_ {k} (t). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.206, + 0.471, + 0.372 + ], + "angle": 0, + "content": "The model helps with interpretability by separating the spatial structure from the temporal dynamics. This expansion is dense in \\(\\mathcal{L}_2\\) [24], meaning that any finite energy object can be approximated arbitrarily well by such a model of sufficiently high order. Empirically, modest values of \\(K\\) provide high accuracy in applications to MR cardiac imaging [15, 25, 26]. Theoretical analysis in [17] shows that for a spatially bandlimited object undergoing a time-varying affine transformation (i.e., combination of time-varying translation, scaling, and rotation) of bounded magnitude, a low order PSM provides a good approximation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.372, + 0.47, + 0.463 + ], + "angle": 0, + "content": "The PSM using a \\(d\\)-dimensional representation for the temporal functions leads to significant reduction of \\(\\approx PL^2\\) representation parameters for an unstructured object of diameter \\(L\\) with \\(P\\) temporal samples to \\(\\approx KL^2 + Kd\\) with \\(K \\ll P\\) and \\(d \\ll P\\). Thus, it provides an effective parsimonious model for the spatio-temporal object \\(f\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.463, + 0.469, + 0.509 + ], + "angle": 0, + "content": "Also, by propagating the PSM object model to the projection domain, it enables quantitative analysis [17] of the choice of optimal sequential projection angular schedule." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.52, + 0.353, + 0.537 + ], + "angle": 0, + "content": "4. Proposed Method: RED-PSM" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.545, + 0.303, + 0.56 + ], + "angle": 0, + "content": "4.1. Variational Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.47, + 0.736 + ], + "angle": 0, + "content": "We use a discretized version of the PSM (2) for the dynamic object, with the object \\( f(\\cdot ,t) \\) at each time instant \\( t = 0,1,\\ldots ,P - 1 \\), represented by a \\( J\\times J \\)-pixel image. Vectorizing these images to vectors \\( f_{t}\\in \\mathbb{R}^{J^{2}} \\), the entire dynamic object is the \\( J^2\\times P \\) matrix \\( f = [f_0\\dots f_{P - 1}] = \\Lambda \\Psi^T\\in \\mathbb{R}^{J^2\\times P} \\). Denoting the \\( t \\)-th column of the \\( P\\times P \\) identity matrix by \\( e_t \\), we have \\( f e_{t} = f_{t} \\) for the \\( t \\)-th individual time frame of \\( f \\). The columns \\( \\Lambda_{k} \\) and \\( \\Psi_{k} \\) of \\( \\Lambda \\in \\mathbb{R}^{J^2\\times K} \\) and \\( \\Psi \\in \\mathbb{R}^{P\\times K} \\) are the discretized spatial and temporal basis functions for the PSM representation, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.737, + 0.469, + 0.799 + ], + "angle": 0, + "content": "Assuming that the x-ray detector has \\(J\\) bins, the projection of the object at time \\(t\\) is \\(g_{t} = g(\\cdot ,\\theta_{t},t) = R_{\\theta_{t}}f_{t}\\in \\mathbb{R}^{J}\\), where the measurement matrix \\(R_{\\theta_t}\\in \\mathbb{R}^{J\\times J^2}\\) computes the projection at view angle \\(\\theta_t\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.798, + 0.469, + 0.83 + ], + "angle": 0, + "content": "We formulate the recovery of \\( f \\) as the solution \\( \\hat{f} = \\hat{\\Lambda}\\hat{\\Psi}^T \\) to the following variational problem" + }, + { + "type": "equation", + "bbox": [ + 0.082, + 0.836, + 0.469, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} (\\hat {\\Lambda}, \\hat {\\Psi}) = \\arg \\min _ {\\Lambda , \\Psi} \\sum_ {t = 0} ^ {P - 1} \\| R _ {\\theta_ {t}} \\Lambda \\Psi^ {T} e _ {t} - g _ {t} \\| _ {2} ^ {2} + \\lambda \\rho (\\Lambda \\Psi^ {T} e _ {t}) \\\\ + \\xi \\| \\Psi \\| _ {F} ^ {2} + \\xi \\| \\Lambda \\| _ {F} ^ {2} \\quad \\text {w h e r e} \\quad \\Psi = U Z. \\tag {3} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.199 + ], + "angle": 0, + "content": "The first term is the data fidelity term measuring the fit between available undersampled measurements \\( g_{t} \\) of the true object and the measurements obtained from the estimated object \\( f = \\Lambda \\Psi^{T} \\in \\mathbb{R}^{J^{2} \\times P} \\). The second term with weight \\( \\lambda > 0 \\) is a spatial regularizer injecting relevant spatial prior to the problem. The last two terms with weight \\( \\xi > 0 \\) prevent the bilinear factors \\( \\Lambda \\) or \\( \\Psi \\) from growing without limit." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.2, + 0.893, + 0.382 + ], + "angle": 0, + "content": "Finally, the constraint \\(\\Psi = UZ\\) is an implicit temporal regularizer that restricts the temporal basis functions \\(\\Psi\\) to a \\(d\\)-dimensional subspace of \\(\\mathbb{R}^P\\) spanned by a fixed basis \\(U \\in \\mathbb{R}^{P \\times d}\\). In practice, we incorporate this constraint by explicit substitution (reparametrization of \\(\\Psi\\) in terms of the free variable \\(Z \\in \\mathbb{Z}^{d \\times K}\\)) into the objective, and the minimization in (3) over \\(\\Psi\\) is thus replaced by minimization over \\(Z\\). This reduces the number of degrees of freedom in \\(\\Psi\\) to a fixed number \\(dK\\), independent of the number \\(P\\) of temporal sampling instants. For notational conciseness, We do not display this constraint/reparametrization in the sequel, but it is used throughout." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.398, + 0.866, + 0.415 + ], + "angle": 0, + "content": "4.2. Incorporating Regularization by Denoising" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.424, + 0.892, + 0.483 + ], + "angle": 0, + "content": "For the spatial regularizer \\(\\rho(\\cdot)\\) we consider \"Regularization by Denoising (RED)\" [23]. RED proposes a recovery method using a denoiser in an explicit regularizer of the form" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.497, + 0.891, + 0.526 + ], + "angle": 0, + "content": "\\[\n\\rho \\left(f _ {t}\\right) = \\frac {1}{2} f _ {t} ^ {T} \\left(f _ {t} - D \\left(f _ {t}\\right)\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.542, + 0.892, + 0.665 + ], + "angle": 0, + "content": "where \\(D:\\mathbb{R}^{J^2}\\to \\mathbb{R}^{J^2}\\) is the denoising operator. Recent works using RED provide impressive results for various static reconstruction tasks, including high-dimensional cases [27]. Providing significant flexibility for the type of denoisers that can be used, RED still requires \\(D\\) to be differentiable and locally homogeneous, and to satisfy the passivity condition \\(\\| G(f)\\| \\leq \\| f\\|\\), for its theoretical analysis to apply." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.667, + 0.814, + 0.68 + ], + "angle": 0, + "content": "For the conventional variational formulation" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.697, + 0.826, + 0.722 + ], + "angle": 0, + "content": "\\[\n\\hat {f} _ {t} = \\arg \\min _ {f _ {t}} \\| R _ {\\theta_ {t}} f _ {t} - g _ {t} \\| _ {2} ^ {2} + \\lambda \\rho (f _ {t}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.737, + 0.891, + 0.782 + ], + "angle": 0, + "content": "an efficient choice are iterative algorithms [23] that use the standard \"early termination\" approach [29], and only require a single use of the denoiser per iteration." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.785, + 0.892, + 0.845 + ], + "angle": 0, + "content": "However, the regularized PSM objective in (3) does not allow to propagate the RED updates on \\( f \\) to the respective basis functions in an efficient manner. To overcome this difficulty, we perform a bilinear variable splitting \\( f = \\Lambda \\Psi^T \\)" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.863, + 0.892, + 0.901 + ], + "angle": 0, + "content": "1While many powerful denoisers satisfy these conditions [23], recent work [28] provides an alternative framework to explain the good performance of RED with denoisers not satisfying conditions in [23]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.926, + 0.519, + 0.938 + ], + "angle": 0, + "content": "10597" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.294, + 0.106 + ], + "angle": 0, + "content": "and obtain our final formulation" + }, + { + "type": "equation", + "bbox": [ + 0.124, + 0.113, + 0.47, + 0.166 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {f, \\Lambda , \\Psi} \\sum_ {t} \\| R _ {\\theta_ {t}} \\Lambda \\Psi_ {k} ^ {T} e _ {t} - g _ {t} \\| _ {2} ^ {2} + \\lambda \\rho (f e _ {t}) \\tag {5} \\\\ + \\xi \\| \\Psi \\| _ {F} ^ {2} + \\xi \\| \\Lambda \\| _ {F} ^ {2} \\quad \\mathrm {s . t .} \\quad f = \\Lambda \\Psi^ {T}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.173, + 0.47, + 0.218 + ], + "angle": 0, + "content": "Since the PSM is enforced as a hard constraint, the estimated object \\( f \\) is constrained to have \\( \\mathrm{rank}(f) \\leq K \\). We propose an algorithm based on ADMM to solve (5)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.218, + 0.469, + 0.263 + ], + "angle": 0, + "content": "To cast the problem with the PSM constraint into the ADMM framework, we form the augmented Lagrangian in the scaled form, [30, 31]" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.27, + 0.469, + 0.352 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\beta} [ \\Lambda , \\Psi , f; \\gamma ] = \\sum_ {t} \\left\\| R _ {\\theta_ {t}} \\Lambda \\Psi^ {T} e _ {t} - g _ {t} \\right\\| _ {2} ^ {2} + \\lambda \\rho (f e _ {t}) \\\\ + \\xi \\| \\Psi \\| _ {F} ^ {2} + \\xi \\| \\Lambda \\| _ {F} ^ {2} - \\frac {\\beta}{2} \\| \\gamma \\| _ {F} ^ {2} + \\frac {\\beta}{2} \\| \\Lambda \\Psi^ {T} - f + \\gamma \\| _ {F} ^ {2}, \\tag {6} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.362, + 0.469, + 0.394 + ], + "angle": 0, + "content": "where \\(\\gamma \\in \\mathbb{R}^{P\\times J^2}\\) represents the scaled dual variable and \\(\\beta >0\\) is the penalty parameter." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.395, + 0.469, + 0.41 + ], + "angle": 0, + "content": "Then, ADMM can be used to solve (6) as in Algorithm 1." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.424, + 0.242, + 0.438 + ], + "angle": 0, + "content": "Algorithm 1 RED-PSM" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.441, + 0.469, + 0.473 + ], + "angle": 0, + "content": "input: \\(\\Lambda^{(0)},\\Psi^{(0)},\\gamma^{(0)},f^{(0)} = \\Lambda^{(0)}\\Psi^{(0)T},\\beta >0,\\) \\(\\lambda >0,\\xi >0\\)" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.476, + 0.252, + 0.49 + ], + "angle": 0, + "content": "1: for \\( i \\in \\{1, \\dots, I\\} \\) do" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.49, + 0.433, + 0.507 + ], + "angle": 0, + "content": "2: \\(\\Lambda^{(i)} = \\arg \\min_{\\Lambda}\\{\\sum_t\\| R_{\\theta_t}\\Lambda \\Psi^{(i - 1)T}e_t - g_t\\| _2^2\\)" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.527, + 0.419, + 0.544 + ], + "angle": 0, + "content": "3: \\(\\Psi^{(i)} = \\arg \\min_{\\Psi}\\{\\sum_t\\| R_{\\theta_t}\\Lambda^{(i)}\\Psi^T e_t - g_t\\| _2^2\\)" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.565, + 0.325, + 0.583 + ], + "angle": 0, + "content": "4: \\(\\forall t:f_t^{(i)} = \\arg \\min_{f_t}\\{\\lambda \\rho (f_t)\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.603, + 0.343, + 0.621 + ], + "angle": 0, + "content": "5: \\(\\gamma^{(i)} = \\gamma^{(i - 1)} + \\Lambda^{(i)}\\Psi^{(i)T} - f^{(i)}\\)" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.622, + 0.16, + 0.633 + ], + "angle": 0, + "content": "6: end for" + }, + { + "type": "equation", + "bbox": [ + 0.089, + 0.476, + 0.441, + 0.633 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} + \\frac {\\beta}{2} \\| \\Lambda \\Psi^ {(i - 1) T} - f ^ {(i - 1)} + \\gamma^ {(i - 1)} \\| _ {F} ^ {2} + \\xi \\| \\Lambda \\| _ {F} ^ {2} \\} \\\\ + \\frac {\\beta}{2} \\| \\Lambda^ {(i)} \\Psi^ {T} + \\gamma^ {(i - 1)} - f ^ {(i - 1)} \\| _ {F} ^ {2} + \\xi \\| \\Psi \\| _ {F} ^ {2} \\} \\\\ + \\frac {\\beta}{2} \\| (\\Lambda^ {(i)} \\Psi^ {(i) T} + \\gamma^ {(i - 1)}) e _ {t} - f _ {t} \\| _ {2} ^ {2} \\rbrace \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.655, + 0.47, + 0.73 + ], + "angle": 0, + "content": "Line 4 in Algorithm 1 corresponds to the variational denoising of \\((\\Lambda^{(i)}\\Psi^{(i)T} + \\gamma^{(i - 1)})e_t\\) with regularization \\(\\lambda \\rho (f_t)\\). Algorithm 1 is reformulated into Algorithm 2 to use RED as in [23] and [28], where \\(D_{\\phi}\\) is the denoiser for which we have the gradient rule" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.739, + 0.469, + 0.756 + ], + "angle": 0, + "content": "\\[\n\\nabla \\rho (f _ {t}) = f _ {t} - D _ {\\phi} (f _ {t}) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.764, + 0.47, + 0.839 + ], + "angle": 0, + "content": "and each \\( f_{t} \\) update in Step 4 is a single fixed-point iteration step using the approach of early stopping [29] (Sec. 4.3.2). In contrast to an iterative method to perform Line 4 in Algorithm 1, Step 4 in Algorithm 2 requires only single use of the denoiser per iteration of ADMM." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.848, + 0.303, + 0.864 + ], + "angle": 0, + "content": "4.3. Regularization Denoiser" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The regularization denoiser \\(D_{\\phi}\\) has a DnCNN [32] architecture and was trained in a supervised manner on a training" + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.092, + 0.8, + 0.107 + ], + "angle": 0, + "content": "Algorithm 2 RED-PSM with efficient \\(f\\) step" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.108, + 0.892, + 0.135 + ], + "angle": 0, + "content": "Note: Inputs, and Lines 1-3 & 5-6 are the same as Algorithm 1." + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.136, + 0.892, + 0.156 + ], + "angle": 0, + "content": "\\[\n4: \\forall t: f _ {t} ^ {(i)} = \\frac {\\lambda}{\\lambda + \\beta} D _ {\\phi} (f _ {t} ^ {(i - 1)}) + \\frac {\\beta}{\\lambda + \\beta} \\big (\\Lambda^ {(i)} \\Psi^ {(i) T} + \\gamma^ {(i - 1)} \\big) e _ {t}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.185, + 0.892, + 0.247 + ], + "angle": 0, + "content": "set of static 2D slices \\( f_{i} \\in \\mathbb{R}^{J^{2}} \\), \\( i = 1, \\dots, N \\) assuming that such data will be available in the settings of interest. Thus, the RED steps are agnostic to the specific motion type. The training objective for the denoiser is" + }, + { + "type": "equation", + "bbox": [ + 0.61, + 0.258, + 0.892, + 0.289 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\phi} \\sum_ {i} \\| f _ {i} - D _ {\\phi} (\\tilde {f} _ {i}) \\| _ {F} ^ {2} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.303, + 0.892, + 0.363 + ], + "angle": 0, + "content": "where \\(\\tilde{f}_i = f_i + \\eta_i\\), and the injected noise \\(\\eta_{i}\\sim \\mathcal{N}(0,\\sigma_{i}^{2}I)\\) has noise level \\(\\sigma_{i}\\sim U[0,\\sigma_{\\mathrm{max}}]\\) spanning a range of values, so that the denoiser learns to denoise data with various noise levels." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.375, + 0.706, + 0.391 + ], + "angle": 0, + "content": "4.4. Convergence Analysis" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.399, + 0.892, + 0.596 + ], + "angle": 0, + "content": "In [33](Section V.), we follow an approach along the lines of [34] to analyze convergence. We show that under mild technical conditions, the objective in Algorithm 1 is guaranteed to converge (with increasing number \\( I \\) of iterations) to a value corresponding to a stationary point of the Lagrangian, that is, satisfying the necessary conditions for first order optimality. In practice, Algorithm 2 with the efficient \\( f \\) step version, which we implemented and used in the experiments reported in Section 5 has better run times, and rapid empirical convergence. However, its analysis requires additional steps, which are not particularly illuminating. Thus, following the tradition in related analyses [29, 35], we focus on the analysis of the nominal Algorithm 1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.61, + 0.633, + 0.627 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.635, + 0.602, + 0.65 + ], + "angle": 0, + "content": "5.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.659, + 0.854, + 0.674 + ], + "angle": 0, + "content": "Three categories of data sets are used in this work." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.675, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Walnut Dataset: We use the CT reconstructions of two different (static) walnut objects from the publicly available 3D walnut CT dataset [36]. We create a dynamic test object by synthetically warping the central axial slice of one of the walnut objects using a sinusoidal piecewise-affine time-varying warp [37]. To be precise, the image is divided into a \\(J \\times J\\) uniformly spaced rectangular grid, and the following vertical displacement is applied on each row separately to drive the temporally varying warp \\(\\Delta_{j,t} = -C(t)\\sin(3\\pi j / J)\\), \\(j \\in \\{0, \\dots, J-1\\}\\), where \\(C(t)\\) is a linearly increasing function of \\(t\\) and \\(C(0) = 0\\). Static axial, coronal, and sagittal slices of the other walnut object are used to train the denoiser \\(D_{\\phi}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Compressed Object Dataset: This data set is obtained from a materials science experiment [38] with a sequence" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "10598" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "of nine increasing compression steps applied to an object, with a full set of radiographic projections collected (using Carl Zeiss Xradia 520 Versa) and reconstructed by the instrument's software at each step. Using this quasi-static data set, a fixed axial slice is extracted from each reconstruction. Nine extracted slices are interpolated to \\(P\\) time frames using a recent deep learning-based video interpolation algorithm [39]. The denoiser \\(D_{\\phi}\\) for our experiments on this data set was trained using the axial slices of the static pre-compression and post-compression objects, which would be available in actual dynamic loading experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.258, + 0.47, + 0.319 + ], + "angle": 0, + "content": "We note that all algorithms compared in this paper are agnostic to both the synthetic warp applied on the static walnut slice and to the data-driven interpolation method used for the compressed object." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.474, + 0.546 + ], + "angle": 0, + "content": "Spatio-temporal projection data for each dataset is simulated by a parallel-beam projection with \\( J = 128 \\) detector bins of the dynamic phantoms, a single projection at each of the \\( P \\) time instants. The sequence of projection angles \\( \\{\\theta_t\\}_{t=0}^{P-1} \\) (a free experimental design parameter) was chosen to follow the bit-reversed view angle sampling scheme, which has been shown [16] to provide an especially favorable conditioning of the recovery problem. The simulated measurements are corrupted using AWGN with standard deviation \\( \\sigma = 5 \\cdot 10^{-3} \\). This noise level leads to the FBP (with Ram-Lak filter) of the full set of \\( P = 512 \\) projections at each time instant having a PSNR of approximately 46 dB. When, in the actual experiments with sequentially sampled data, only \\( 1 / P \\) of this data is used, the PSNR of the reconstruction may be expected to be lower." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.547, + 0.456, + 0.561 + ], + "angle": 0, + "content": "Ground-truth frames for \\( P = 4 \\) are shown in Figure 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.562, + 0.47, + 0.651 + ], + "angle": 0, + "content": "Cardiac dMRI Dataset: For a more direct comparison with the setting and data used in dMRI works, we also test RED-PSM on the \"retrospective\" cardiac dMRI data in [20]. The data includes 23 distinct time frames for one cardiac cycle. Details of the data and experiments are in Section 5.4.3." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.664, + 0.46, + 0.773 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.774, + 0.47, + 0.817 + ], + "angle": 0, + "content": "Figure 2: Ground-truth frames for the time-varying walnut (top) and compressed object (bottom) datasets, uniformly sampled in time, \\( t \\in \\{0, \\dots, P - 1\\} \\), for \\( P = 4 \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.831, + 0.25, + 0.847 + ], + "angle": 0, + "content": "5.2. Baseline Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "PSM-TV: Similar to the proposed approach, this algorithm also uses a partially separable model to represent the object with a different regularization type. For PSM-TV," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.227 + ], + "angle": 0, + "content": "regularization penalizes the \\(\\ell_1\\)-norm of the discrete 2D total variation of the temporal slices of \\(f\\) at each time instant. To this end, the constraint \\(f = \\Lambda \\Psi^T\\) is implemented by substitution into the objective in (5), and the definition of \\(\\rho\\) is changed to \\(\\rho (\\Lambda \\Psi^T e_t) = \\mathrm{TV}(\\Lambda \\Psi^T e_t)\\), and the rest of the objective is kept the same. The unconstrained problem is then solved for \\(\\{\\hat{\\Lambda},\\hat{\\Psi}\\}\\) (using, as a convenient implementation, the Adam optimizer in Pytorch). Finally, the estimated object is obtained as \\(\\hat{f} = \\hat{\\Lambda}\\hat{\\Psi}^{T}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.228, + 0.892, + 0.334 + ], + "angle": 0, + "content": "TD-DIP [20]: TD-DIP is a recent method based on the Deep Image Prior (DIP) approach. It uses a mapping network \\(M_{\\alpha}\\) and a generative model \\(N_{\\beta}\\) sequentially to obtain the estimated object at each time instant \\(f_{t}\\) from fixed and handcrafted latent representations \\(\\chi_t\\). Because TD-DIP was originally proposed for dynamic MRI, we modified the objective minimally for dynamic tomography as" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.345, + 0.892, + 0.375 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\alpha , \\beta} \\sum_ {t} \\| g _ {t} - R _ {\\theta (t)} \\left(\\left(N _ {\\beta} \\circ M _ {\\alpha}\\right) (\\chi_ {t})\\right) \\| ^ {2}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.893, + 0.568 + ], + "angle": 0, + "content": "For the comparisons in this work, identical mapping network and generator architectures, latent representation dimensionality, optimizer, learning rate, and decay schemes are used as in the available online implementation [40]. The original work focuses on the beating heart problem and thus proposes a helix-shaped latent manifold for \\(\\chi_t\\) with cycles equal to the number of heartbeats during measurement acquisition. Since we do not have a repetition assumption for the motion types included in this paper, we use a linear manifold as explained in the original paper [20]. Thus, the method is sometimes denoted as \"TD-DIP (L)\" in Section 5.4 for clarification." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.579, + 0.707, + 0.595 + ], + "angle": 0, + "content": "5.3. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.603, + 0.892, + 0.693 + ], + "angle": 0, + "content": "All methods are run on a workstation with an Intel(R) Xeon(R) Gold 5320 CPU and NVIDIA RTX A6000 GPU. In practice, we used a minor variation of Algorithm 2, where we combined the subproblems in \\(\\Lambda\\) and \\(\\Psi\\), and minimized with respect to both basis functions simultaneously using gradient descent with Adam [41] optimizer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.694, + 0.892, + 0.83 + ], + "angle": 0, + "content": "Denoiser training. The upper limit for noise level used in training the denoiser was set to \\(\\sigma_{\\mathrm{max}} = 5 \\cdot 10^{-2}\\). For the dynamic walnut object, the denoiser \\(D_{\\phi}\\) is trained on the central 200 axial, 200 sagittal, and 200 coronal slices of another walnut CT reconstruction downsampled to size \\(128 \\times 128\\). For the compressed object, axial slices of precompression and post-compression static objects, containing 462 slices in total, are used to train \\(D_{\\phi}\\). For the cardiac MRI setting, the denoiser was trained on the static MRI" + }, + { + "type": "page_footnote", + "bbox": [ + 0.498, + 0.839, + 0.892, + 0.901 + ], + "angle": 0, + "content": "2It would be interesting to include yet another baseline method - the DIP-based PSM approach [22] (also developed for MRI). However we were unable to do so as an implementation of this method was not available, and because of potential issues with replicating its performance and adapting to our CT problem." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.926, + 0.519, + 0.938 + ], + "angle": 0, + "content": "10599" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.092, + 0.287, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.091, + 0.488, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.091, + 0.692, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.693, + 0.092, + 0.898, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.313, + 0.895, + 0.368 + ], + "angle": 0, + "content": "Figure 3: Reconstruction PSNR, SSIM, MAE, and HFEN for the time-varying walnut object (top) and compressed material (bottom) vs. \\( P \\) using different methods. For TD-DIP, accuracy statistics for the best PSNR reconstruction during optimization are reported assuming such an oracle is available. The minimum and maximum values are indicated with error bars and the mean values are connected by the dashed line for different \\( P \\) for three different runs." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.376, + 0.472, + 0.554 + ], + "angle": 0, + "content": "
(a) Walnut(b) Compressed Material
PMethodPSNR (dB)SSIMMAE (1e-3)HFENPSNR (dB)SSIMMAE (1e-2)HFEN
32PSM-TV (R)21.10.6782.91.0422.50.6972.911.6
TD-DIP (L)22.50.8822.10.8725.40.9091.58.1
RED-PSM (Pr)22.70.9141.50.7923.90.9161.29.9
64PSM-TV (R)24.00.8791.90.9425.60.8451.810.7
TD-DIP (L)25.60.9161.50.7429.00.9471.16.5
RED-PSM (Pr)26.40.9580.90.5729.30.9520.56.0
128PSM-TV (R)26.80.9121.40.7829.20.9071.19.6
TD-DIP (L)29.00.9531.00.5032.40.9530.85.1
RED-PSM (Pr)29.90.9780.60.4333.10.9720.44.7
256PSM-TV (R)30.10.9341.00.6331.90.9630.78.0
TD-DIP (L)31.70.9660.80.4534.70.9660.74.6
RED-PSM (Pr)33.80.9870.40.3235.90.9860.34.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.556, + 0.47, + 0.613 + ], + "angle": 0, + "content": "Table 1: Reconstruction accuracies for different \\( P \\). Random (R) and ProSep (Pr) initialization for the PSM methods. For TD-DIP, the reported accuracies are for the best PSNR using a \"stopping oracle\", averaged over three runs with random initial conditions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.622, + 0.469, + 0.744 + ], + "angle": 0, + "content": "training slices of the ACDC dataset [42]. For all datasets, \\( D_{\\phi} \\) is trained for 500 epochs using the Adam optimizer with a learning rate of \\( 5 \\cdot 10^{-3} \\). Each convolutional layer is followed by a ReLU nonlinearity except for the final layer, which has a single-channel output. We test both direct and residual DnCNN denoisers where the former predicts the denoised image and the latter estimates the noise from the noisy input." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.469, + 0.807 + ], + "angle": 0, + "content": "Architectural details for denoisers used in our experiments are provided in Table 6 in Supplementary Material C. We use a fixed pre-trained denoiser for all \\( P \\) for the same object type." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.809, + 0.469, + 0.854 + ], + "angle": 0, + "content": "Temporal Basis. In all experiments, we use a fixed basis \\(U\\) as a cubic spline interpolator to interpolate the low-dimensional temporal representation \\(Z\\) to \\(\\Psi\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Initialization. Unless stated otherwise, spatial and temporal basis functions are initialized using the SVD truncated to order \\(K\\) the rank of the dynamic object estimate pro" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.378, + 0.892, + 0.468 + ], + "angle": 0, + "content": "duced by a recent projection-domain PSM-based method \"ProSep\" [17]. If the ProSep estimate has rank smaller than \\(K\\), the remaining basis functions are initialized as 0. Otherwise, all spatial basis functions are initialized as 0 and the latent representations \\(z_{k}\\) of the temporal basis functions are initialized randomly as \\(z_{k} \\sim \\mathcal{N}(0, I)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.469, + 0.892, + 0.514 + ], + "angle": 0, + "content": "Tomographic Acquisition Scheme. All methods mentioned in this paper use the bit-reversed angular sampling scheme, over the range \\([0,\\pi ]\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.514, + 0.892, + 0.679 + ], + "angle": 0, + "content": "Run Times. For \\( P = 256 \\) and using the specified computational resources and parameter settings, To achieve the peak PSNR during optimization, RED-PSM with ProSep initialization requires \\( 50 < \\) iterations \\( < 150 \\) taking about 2 to 6 minutes whereas TD-DIP with batch size \\( P \\) typically requires \\( > 30k \\) steps, taking about 3.5 hours to complete. Hence, RED-PSM provides a speedup over TD-DIP by a factor of 35 to 105 to reach its peak performance. We note that based on the parameter configuration, the speedup factor may vary. However, the proposed method provides a significant run time reduction in all cases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.68, + 0.892, + 0.801 + ], + "angle": 0, + "content": "Evaluation Metrics. Four quantitative metrics were implemented for evaluating reconstruction accuracy (i) the peak signal-to-noise ratio (PSNR) in dB; (ii) the structural similarity index (SSIM) [43]; (iii) the mean absolute error (MAE); and (iv) the high-frequency error norm (HFEN) [44] defined as \\(\\mathrm{HFEN}(f, f_r) = \\| \\mathrm{LoG}(f) - \\mathrm{LoG}(f_r)\\|_2\\) where LoG is a rotationally symmetric Laplacian of Gaussian filter with a standard deviation of 1.5 pixels." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.809, + 0.593, + 0.823 + ], + "angle": 0, + "content": "5.4. Results" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.842, + 0.846 + ], + "angle": 0, + "content": "5.4.1 Reconstruction accuracies for different \\(P\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In Figure 3 and Table 1, the performance of RED-PSM is compared with PSM-TV and with TD-DIP that uses a linear latent representation for both objects. While Figure 3" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.927, + 0.519, + 0.938 + ], + "angle": 0, + "content": "10600" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.088, + 0.865, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.389, + 0.893, + 0.418 + ], + "angle": 0, + "content": "Figure 4: Comparison of reconstructed object frames at two time instants using different methods for \\( P = 256 \\), and the corresponding normalized absolute reconstruction errors for (A) the time-varying walnut, and (B) compressed object." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.473, + 0.637 + ], + "angle": 0, + "content": "facilitates the comparison of metrics for different \\( P \\) for the various methods, since the range of metrics is very large for varying \\( P \\). Table 1 emphasizes important differences between methods for the same \\( P \\), and provides detail for a more precise quantitative comparison. As expected, the estimates improve with increasing \\( P \\) for all methods. In terms of PSNR, the proposed algorithm performs on par with or better than the best PSNR TD-DIP estimate for various \\( P \\), with improvement for RED-PSM enhancing with the increase in \\( P \\). Moreover, in terms of SSIM, MAE, and HFEN, the improvements with RED-PSM are even more significant. Although these observations are valid for both objects, for the walnut, RED-PSM provides slightly greater improvement over TD-DIP." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.473, + 0.883 + ], + "angle": 0, + "content": "Figure 4 compares the reconstructions for both objects at two different \\( t \\) for \\( P = 256 \\). As expected, providing blurry reconstructions lacking finer details for both objects, PSM-TV performs the worst among the compared methods. The TD-DIP reconstructions contain visible noise-like artifacts on the piecewise constant regions of the walnut object, which are alleviated by RED-PSM. This observation manifests itself also in the absolute difference figures, with error for TD-DIP distributed throughout the interior regions of the walnut. Furthermore, RED-PSM preserves sharp details around the shell of the walnut better. Throughout the compressed material object for the given time frames, compared to TD-DIP, RED-PSM has an almost consistently smaller absolute error. This difference is more prominent around the highly dynamic regions of the object, emphasizing the advantage of the proposed method." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In Figure 5, the reconstructed \\( x - t \\) cross-sections of the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.427, + 0.895, + 0.533 + ], + "angle": 0, + "content": "dynamic walnut are shown for different methods. The location of the cross-section is highlighted by a yellow line on the static \\(x - y\\) frame at \\(t = 0\\). Consistent with the comparison in Figure 4, RED-PSM provides reduced absolute error values throughout the respective cross-section. Also, as more apparent in the error figures, TD-DIP produces higher background errors." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.555, + 0.709, + 0.57 + ], + "angle": 0, + "content": "5.4.2 Effect of Initialization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.895, + 0.763 + ], + "angle": 0, + "content": "The initialization of \\(\\Lambda\\), \\(\\Psi\\), and \\(f\\) plays an important role in the performance and convergence speed of RED-PSM. We observe significant speed-up when rather than a random initialization, we initialize the algorithm with ProSep [16] estimated reconstruction. Figure 7 shows PSNR vs. iterations comparison for different initialization techniques for the dynamic walnut object with \\(P = 256\\). The rest of the parameters were selected identically as indicated in Table 5 in Supplementary Material. This experiment highlights the advantages of initializing with ProSep estimated basis functions: eliminating the need for multiple runs for a best-case result; and speeding up convergence considerably." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.785, + 0.783, + 0.801 + ], + "angle": 0, + "content": "5.4.3 Cardiac dMRI data experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In this setting, different to the previous experiments, we used \\(4k\\)-space radial lines (\"spokes\") per frame at the bitreversed angles. We used 1.4 and 2.8 cardiac cycles, with \\(23 \\times 4 = 92\\) spokes/cycle, for a total of \\(P = 128\\) and \\(P = 256\\) spokes. The problem is still severely undersampled compared to the experiment in [20] where 13 spokes are used" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.927, + 0.518, + 0.938 + ], + "angle": 0, + "content": "10601" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.094, + 0.236, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.236, + 0.094, + 0.384, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.384, + 0.094, + 0.529, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.094, + 0.674, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.674, + 0.094, + 0.818, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.82, + 0.094, + 0.866, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.205, + 0.892, + 0.248 + ], + "angle": 0, + "content": "Figure 5: Comparison of reconstructed \\( x - t \\) cross-sections using different methods for \\( P = 256 \\) (top), with corresponding normalized absolute error counterparts (bottom). The location of the cross-section is indicated with a yellow line on the static object at time \\( t = 0 \\) (left). The \\( x - y - t \\) coordinates are indicated on the static object and bottom left absolute error figure in white text." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.254, + 0.468, + 0.299 + ], + "angle": 0, + "content": "per frame for 13 cycles, for a total of \\(13 \\times 23 \\times 13 = 3,887\\) spokes. Since the data is periodic, we also tested the helix latent scheme (H) for TD-DIP." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.3, + 0.468, + 0.358 + ], + "angle": 0, + "content": "The metrics in Table 2 and the qualitative comparison in Figure 6 with zoomed-in reconstructions and absolute error maps, show that RED-PSM performs better than both versions of TD-DIP." + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.37, + 0.455, + 0.584 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.585, + 0.468, + 0.626 + ], + "angle": 0, + "content": "Figure 6: Reconstructed frames for \\( P = 256 \\) for retrospective dMRI data [20] with zoomed-in frames (middle row), and absolute reconstruction errors (last row)." + }, + { + "type": "table", + "bbox": [ + 0.11, + 0.635, + 0.432, + 0.717 + ], + "angle": 0, + "content": "
PMethodPSNR (dB)SSIMMAE (1e-2)HFEN
128TD-DIP (L)34.60.9231.73.38
TD-DIP (H)34.60.9281.73.32
RED-PSM36.60.9391.42.73
256TD-DIP (L)36.20.9481.43.47
TD-DIP (H)36.40.9471.43.44
RED-PSM38.40.9621.12.99
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.719, + 0.468, + 0.747 + ], + "angle": 0, + "content": "Table 2: Reconstruction accuracies for RED-PSM and TD-DIP for the retrospective dMRI data [20]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.756, + 0.412, + 0.772 + ], + "angle": 0, + "content": "5.5. PSNR vs. \\( t \\), and a Patch-Based Scheme" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.468, + 0.84 + ], + "angle": 0, + "content": "In Supplementary Material A, we compare the PSNR of the reconstructed frames for each \\( t \\) for all methods for the walnut object with \\( P = 256 \\) and show the consistently better performance of RED-PSM." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Also, in Supplementary Material B, to improve scalability to high-resolution and high-dimensional settings, we propose and evaluate a patch-based version of RED-PSM with a patch-based denoiser \\(D_{\\phi}\\). In the experiments," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.254, + 0.89, + 0.285 + ], + "angle": 0, + "content": "the patch-based scheme provided reconstruction accuracies similar to those reported here for the original scheme." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.3, + 0.627, + 0.315 + ], + "angle": 0, + "content": "6. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.325, + 0.892, + 0.552 + ], + "angle": 0, + "content": "RED-PSM is the first PSM-based approach to dynamic imaging using a pre-trained and learned (RED-based) spatial prior. The objective in the proposed variational formulation is optimized using a novel and effective bilinear ADMM algorithm, which enforces the PSM as a hard constraint. Unlike existing PSM-based techniques, RED-PSM is supported by theoretical analysis, with a convergence guarantee to a stationary point of the objective. The results of the numerical experiments show better reconstruction accuracy and considerably faster run times compared to a recent DIP-based algorithm. A patch-based regularizer version of RED-PSM provides almost equivalent performance with a massive reduction of storage requirements, indicating the potential of our framework for dynamic high-resolution 2D or 3D settings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.659 + ], + "angle": 0, + "content": "Possible directions for future work include the application of RED-PSM to various imaging scenarios other than tomography and MRI, and robust denoiser training for the RED framework, since the deep denoisers encounter varying artifact distributions during optimization. This could also improve the generalizability of the framework to different input types." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.72 + ], + "angle": 0, + "content": "Acknowledgements. This research was supported in part by Los Alamos National Labs under Subcontract No. 599416/CW13995. We thank Dr. Brian M. Patterson for providing the data for the compressed material experiments." + }, + { + "type": "image", + "bbox": [ + 0.563, + 0.737, + 0.828, + 0.846 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.845, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Figure 7: PSNR vs. iteration comparison for RED-PSM as described in Section 5.4.2. The area between the best and the worst PSNR for each iteration is shown in blue to highlight the varying performances of five different runs with random initialization." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.926, + 0.519, + 0.938 + ], + "angle": 0, + "content": "10602" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] E. Maire, C. Le Bourlot, J. Adrien, A. Mortensen, and R. Mokso, “20 Hz X-ray tomography during an in situ tensile test,” International Journal of Fracture, vol. 200, no. 1, pp. 3–12, 2016." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.175, + 0.472, + 0.259 + ], + "angle": 0, + "content": "[2] I. Danad, J. Szymonifka, J. Schulman-Marcus, and J. K. 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Klasky2 + +Yoram Bresler + +berki2@illinois.edu + +mklasky@lanl.gov + +ybresler@illinois.edu + +1University of Illinois at Urbana-Champaign, USA 2Los Alamos National Laboratory, USA + +# Abstract + +Dynamic imaging involves the recovery of a time-varying 2D or 3D object at each time instant using its undersampled measurements. In particular, in dynamic tomography, only a single projection at a single view angle may be available at a time, making the problem severely ill-posed. In this work, we propose an approach, RED-PSM, which combines for the first time two powerful techniques to address this challenging imaging problem. The first, are partially separable models, which have been used to introduce a low-rank prior for the spatio-temporal object. The second is the recent Regularization by Denoising (RED), which provides a flexible framework to exploit the impressive performance of state-of-the-art image denoising algorithms, for various inverse problems. We propose a partially separable objective with RED and an optimization scheme with variable splitting and ADMM. Our objective is proved to converge to a value corresponding to a stationary point satisfying the first-order optimality conditions. Convergence is accelerated by a particular projection-domain-based initialization. We demonstrate the performance and computational improvements of our proposed RED-PSM with a learned image denoiser by comparing it to a recent deep-prior-based method TD-DIP. Although the emphasis is on dynamic tomography, we also demonstrate the performance advantages of RED-PSM in a dynamic cardiac MRI setting. + +# 1. Introduction + +Time-varying tomography is a challenging ill-posed inverse problem that involves reconstructing a dynamic object using its sequential projections at each time instant. Since the measurements are inconsistent due to the evolving object, traditional reconstruction algorithms lead to significant artifacts. + +The problem arises in micro-CT [1], myocardial perfusion imaging [2], thoracic CT [3], imaging of fluid flow processes [4, 5] and dynamic imaging of material samples undergoing compression [6, 7]. Also, it is closely related to the dynamic MRI (dMRI) problem, which typically arises + +in cardiac imaging [8]. + +Previous work [9, 10] treated the problem as time-sequential sampling of bandlimited signals and provided an optimal view angle sampling order and theoretical guarantees for unique and stable reconstruction. However, the approach is limited by its bandlimitedness assumptions. + +Several methods [11, 12] recover the underlying motion field from projections using the Radon transform properties. However, these methods require the object information a priori. Other algorithms [13, 14] alternate between estimating the motion field and the time-varying object. These methods assume the total density to be preserved for a given object at different times which may be a limiting assumption. For instance, imaging a fixed slice of a time-varying object under compression may violate this assumption due to perpendicularly evolving parts. + +In dynamic tomography and MRI, partially-separable models (PSM) have been used to represent the underlying object [15] and the time-sequential projections [16, 17]. The projection-domain PSM in [16, 17] carries the PSM to the projection domain using the harmonic representation of projections, and provides uniqueness and stability analysis for the problem. In spite of this advantage of the projection domain PSM over its object-domain counterparts, the performance of this approach is limited by the null space of the measurement operator. + +A different PSM-based method for dMRI [18] imposes the low-rank structure as a soft constraint. It uses a hybrid objective with the PSM model used in the data fidelity term and the object in a simple $l_{1}$ -norm penalty, with an additional penalty term to penalize the mismatch between the PSM and the object. The method does not use a guided initial guess for the object or for the PSM basis functions. A fast alternative low-rank (or PSM)-based method for dMRI [19] decomposes the object representation into three components: the mean signal, a low-rank PSM, and the residual, which is assumed to be sparse in the Fourier domain. Then, each component is estimated in order. Although on some of the data sets used for the comparison in [19] competing methods are either faster or more accurate, the method provides better results when averaged over all data sets. + +Recently, object-domain deep image prior (DIP)-based algorithms [20,21] have been proposed for dMRI. Providing impressive results, DIP-based algorithms such as [20] suffer from overfitting and usually require handcrafted early stopping criteria during the optimization of generator network parameters. In an attempt to overcome the overfitting and the need for handcrafted early stopping, the authors of [21] regularize the problem by constraining the geodesic distances between generated objects in proportion to the distances between their latent representation. However, this requires the computation of the Jacobian of the generator network at each iteration of the update of the weights and significantly increases the computational load and run time. + +A different approach [22] combines partially separable and generative models. It employs spatial and temporal regularization by penalizing the generator weights and a particular initialization scheme for the inputs to the generator networks. Although it combines the PSM with the recent DIP framework, this method has the following limitations, which are overcome by the proposed approach: (i) The spatial generator is an artifact removal network taking the full-sized spatial basis functions as input. Since this prevents a patch-based implementation, it may be difficult to scale to high-resolution 3D+temporal settings. (ii) The CNN prior for natural images may not be useful as a prior for the individual spatial basis functions, since the least-squares optimal spatial basis functions are the left singular vectors of the complete object, and as such may not have the structure of natural images. (iii) As with other DIP-based methods, if the additional penalty on the generator parameters is insufficient, this method can be prone to overfitting. + +# Contributions + +1. To the best of our knowledge, RED-PSM is the first PSM-based approach to dynamic imaging, that uses a pre-trained, learned (RED-based [23]) spatial prior. +2. A novel and effective ADMM algorithm for the resulting new minimization problem enforcing PSM as a hard constraint and incorporating the learned RED spatial regularizer is proposed. +3. The method is supported by theoretical analysis, with a convergence guarantee. +4. Compared to a recent DIP-based [20] algorithm, RED-PSM achieves better reconstruction accuracy with orders of magnitude faster run times. +5. A version of the approach with a patch-based regularizer is shown to provide almost equivalent reconstruction accuracy. This makes the proposed method conveniently scalable to high-resolution 3D or 4D settings. + +![](images/9e062c8cb60b485f4bcc5c1dbc0365ca5064edb7924296adc7dd2aea28d8060f.jpg) +Figure 1: Projection acquisition geometry for time-varying tomography of the object $f_{t}$ with single measurement $g_{t}$ at each time instant for $t \in \{0,1,2\}$ . + +# 2. Problem Statement + +In a 2D setting, the goal in the ill-posed dynamic tomography problem is to reconstruct a time-varying object $f(\mathbf{x},t)$ , $\mathbf{x} \in \mathbb{R}^2$ vanishing outside a disc of diameter $L$ , from its projections + +$$ +g (\cdot , \theta , t) = \mathcal {R} _ {\theta} \{f (\mathbf {x}, t) \} +$$ + +obtained using the Radon transform operator $\mathcal{R}_{\theta}$ at angle $\theta$ . Considering time-sequential sampling, in which only one projection is acquired at each time instant, and sampling uniform in time, the acquired measurements are + +$$ +\left\{g \left(s, \theta_ {p}, t _ {p}\right) \right\} _ {p = 0} ^ {P - 1}, \forall s, t _ {p} = p \Delta_ {t}, \tag {1} +$$ + +where $s$ is the offset of the line of integration from the origin (i.e., detector position), and $P$ is the total number of projections (and temporal samples) acquired. The sampling of the $s$ variable is assumed fine enough and is suppressed in the notation. The angular sampling scheme, the sequence $\{\theta_p\}_{p=0}^{P-1}$ , with $\theta_p \in [0,2\pi]$ , is considered as a free design parameter. Figure 1 shows a simplified time-sequential sampling scheme for a time-varying object. + +Our objective in dynamic tomography, and in dynamic imaging in general, is to reconstruct the underlying object with temporal variation $\{f(\mathbf{x},t_p)\}_{p = 0}^{P - 1}$ from the time-sequential measurements in (1). The challenge is that because each projection belongs to a different object, the projections in (1) are inconsistent. Therefore, a conventional, e.g., filtered backprojection (FBP) reconstruction as for a static object results in significant reconstruction artifacts. + +# 3. Partially Separable Models (PSM) + +For spatio-temporal inverse problems such as dynamic MRI and tomography, the underlying object can be accurately represented using a partially-separable model (PSM), which effectively introduces a low-rank prior to the problem. For dynamic tomography, a PSM can represent the + +imagined object $f$ , or its full set of projections $g$ . In this paper we use an object-domain PSM. + +The representation of a dynamic object $f(\mathbf{x}, t)$ by a $K$ -th order PSM is the series expansion + +$$ +f (\mathbf {x}, t) = \sum_ {k = 0} ^ {K - 1} \Lambda_ {k} (\mathbf {x}) \psi_ {k} (t). \tag {2} +$$ + +The model helps with interpretability by separating the spatial structure from the temporal dynamics. This expansion is dense in $\mathcal{L}_2$ [24], meaning that any finite energy object can be approximated arbitrarily well by such a model of sufficiently high order. Empirically, modest values of $K$ provide high accuracy in applications to MR cardiac imaging [15, 25, 26]. Theoretical analysis in [17] shows that for a spatially bandlimited object undergoing a time-varying affine transformation (i.e., combination of time-varying translation, scaling, and rotation) of bounded magnitude, a low order PSM provides a good approximation. + +The PSM using a $d$ -dimensional representation for the temporal functions leads to significant reduction of $\approx PL^2$ representation parameters for an unstructured object of diameter $L$ with $P$ temporal samples to $\approx KL^2 + Kd$ with $K \ll P$ and $d \ll P$ . Thus, it provides an effective parsimonious model for the spatio-temporal object $f$ . + +Also, by propagating the PSM object model to the projection domain, it enables quantitative analysis [17] of the choice of optimal sequential projection angular schedule. + +# 4. Proposed Method: RED-PSM + +# 4.1. Variational Formulation + +We use a discretized version of the PSM (2) for the dynamic object, with the object $f(\cdot ,t)$ at each time instant $t = 0,1,\ldots ,P - 1$ , represented by a $J\times J$ -pixel image. Vectorizing these images to vectors $f_{t}\in \mathbb{R}^{J^{2}}$ , the entire dynamic object is the $J^2\times P$ matrix $f = [f_0\dots f_{P - 1}] = \Lambda \Psi^T\in \mathbb{R}^{J^2\times P}$ . Denoting the $t$ -th column of the $P\times P$ identity matrix by $e_t$ , we have $f e_{t} = f_{t}$ for the $t$ -th individual time frame of $f$ . The columns $\Lambda_{k}$ and $\Psi_{k}$ of $\Lambda \in \mathbb{R}^{J^2\times K}$ and $\Psi \in \mathbb{R}^{P\times K}$ are the discretized spatial and temporal basis functions for the PSM representation, respectively. + +Assuming that the x-ray detector has $J$ bins, the projection of the object at time $t$ is $g_{t} = g(\cdot ,\theta_{t},t) = R_{\theta_{t}}f_{t}\in \mathbb{R}^{J}$ , where the measurement matrix $R_{\theta_t}\in \mathbb{R}^{J\times J^2}$ computes the projection at view angle $\theta_t$ . + +We formulate the recovery of $f$ as the solution $\hat{f} = \hat{\Lambda}\hat{\Psi}^T$ to the following variational problem + +$$ +\begin{array}{l} (\hat {\Lambda}, \hat {\Psi}) = \arg \min _ {\Lambda , \Psi} \sum_ {t = 0} ^ {P - 1} \| R _ {\theta_ {t}} \Lambda \Psi^ {T} e _ {t} - g _ {t} \| _ {2} ^ {2} + \lambda \rho (\Lambda \Psi^ {T} e _ {t}) \\ + \xi \| \Psi \| _ {F} ^ {2} + \xi \| \Lambda \| _ {F} ^ {2} \quad \text {w h e r e} \quad \Psi = U Z. \tag {3} \\ \end{array} +$$ + +The first term is the data fidelity term measuring the fit between available undersampled measurements $g_{t}$ of the true object and the measurements obtained from the estimated object $f = \Lambda \Psi^{T} \in \mathbb{R}^{J^{2} \times P}$ . The second term with weight $\lambda > 0$ is a spatial regularizer injecting relevant spatial prior to the problem. The last two terms with weight $\xi > 0$ prevent the bilinear factors $\Lambda$ or $\Psi$ from growing without limit. + +Finally, the constraint $\Psi = UZ$ is an implicit temporal regularizer that restricts the temporal basis functions $\Psi$ to a $d$ -dimensional subspace of $\mathbb{R}^P$ spanned by a fixed basis $U \in \mathbb{R}^{P \times d}$ . In practice, we incorporate this constraint by explicit substitution (reparametrization of $\Psi$ in terms of the free variable $Z \in \mathbb{Z}^{d \times K}$ ) into the objective, and the minimization in (3) over $\Psi$ is thus replaced by minimization over $Z$ . This reduces the number of degrees of freedom in $\Psi$ to a fixed number $dK$ , independent of the number $P$ of temporal sampling instants. For notational conciseness, We do not display this constraint/reparametrization in the sequel, but it is used throughout. + +# 4.2. Incorporating Regularization by Denoising + +For the spatial regularizer $\rho(\cdot)$ we consider "Regularization by Denoising (RED)" [23]. RED proposes a recovery method using a denoiser in an explicit regularizer of the form + +$$ +\rho \left(f _ {t}\right) = \frac {1}{2} f _ {t} ^ {T} \left(f _ {t} - D \left(f _ {t}\right)\right) \tag {4} +$$ + +where $D:\mathbb{R}^{J^2}\to \mathbb{R}^{J^2}$ is the denoising operator. Recent works using RED provide impressive results for various static reconstruction tasks, including high-dimensional cases [27]. Providing significant flexibility for the type of denoisers that can be used, RED still requires $D$ to be differentiable and locally homogeneous, and to satisfy the passivity condition $\| G(f)\| \leq \| f\|$ , for its theoretical analysis to apply. + +For the conventional variational formulation + +$$ +\hat {f} _ {t} = \arg \min _ {f _ {t}} \| R _ {\theta_ {t}} f _ {t} - g _ {t} \| _ {2} ^ {2} + \lambda \rho (f _ {t}), +$$ + +an efficient choice are iterative algorithms [23] that use the standard "early termination" approach [29], and only require a single use of the denoiser per iteration. + +However, the regularized PSM objective in (3) does not allow to propagate the RED updates on $f$ to the respective basis functions in an efficient manner. To overcome this difficulty, we perform a bilinear variable splitting $f = \Lambda \Psi^T$ + +and obtain our final formulation + +$$ +\begin{array}{l} \min _ {f, \Lambda , \Psi} \sum_ {t} \| R _ {\theta_ {t}} \Lambda \Psi_ {k} ^ {T} e _ {t} - g _ {t} \| _ {2} ^ {2} + \lambda \rho (f e _ {t}) \tag {5} \\ + \xi \| \Psi \| _ {F} ^ {2} + \xi \| \Lambda \| _ {F} ^ {2} \quad \mathrm {s . t .} \quad f = \Lambda \Psi^ {T}. \\ \end{array} +$$ + +Since the PSM is enforced as a hard constraint, the estimated object $f$ is constrained to have $\mathrm{rank}(f) \leq K$ . We propose an algorithm based on ADMM to solve (5). + +To cast the problem with the PSM constraint into the ADMM framework, we form the augmented Lagrangian in the scaled form, [30, 31] + +$$ +\begin{array}{l} \mathcal {L} _ {\beta} [ \Lambda , \Psi , f; \gamma ] = \sum_ {t} \left\| R _ {\theta_ {t}} \Lambda \Psi^ {T} e _ {t} - g _ {t} \right\| _ {2} ^ {2} + \lambda \rho (f e _ {t}) \\ + \xi \| \Psi \| _ {F} ^ {2} + \xi \| \Lambda \| _ {F} ^ {2} - \frac {\beta}{2} \| \gamma \| _ {F} ^ {2} + \frac {\beta}{2} \| \Lambda \Psi^ {T} - f + \gamma \| _ {F} ^ {2}, \tag {6} \\ \end{array} +$$ + +where $\gamma \in \mathbb{R}^{P\times J^2}$ represents the scaled dual variable and $\beta >0$ is the penalty parameter. + +Then, ADMM can be used to solve (6) as in Algorithm 1. + +# Algorithm 1 RED-PSM + +input: $\Lambda^{(0)},\Psi^{(0)},\gamma^{(0)},f^{(0)} = \Lambda^{(0)}\Psi^{(0)T},\beta >0,$ $\lambda >0,\xi >0$ + +1: for $i \in \{1, \dots, I\}$ do + +2: $\Lambda^{(i)} = \arg \min_{\Lambda}\{\sum_t\| R_{\theta_t}\Lambda \Psi^{(i - 1)T}e_t - g_t\| _2^2$ + +3: $\Psi^{(i)} = \arg \min_{\Psi}\{\sum_t\| R_{\theta_t}\Lambda^{(i)}\Psi^T e_t - g_t\| _2^2$ + +4: $\forall t:f_t^{(i)} = \arg \min_{f_t}\{\lambda \rho (f_t)\}$ + +5: $\gamma^{(i)} = \gamma^{(i - 1)} + \Lambda^{(i)}\Psi^{(i)T} - f^{(i)}$ + +6: end for + +$$ +\begin{array}{l} + \frac {\beta}{2} \| \Lambda \Psi^ {(i - 1) T} - f ^ {(i - 1)} + \gamma^ {(i - 1)} \| _ {F} ^ {2} + \xi \| \Lambda \| _ {F} ^ {2} \} \\ + \frac {\beta}{2} \| \Lambda^ {(i)} \Psi^ {T} + \gamma^ {(i - 1)} - f ^ {(i - 1)} \| _ {F} ^ {2} + \xi \| \Psi \| _ {F} ^ {2} \} \\ + \frac {\beta}{2} \| (\Lambda^ {(i)} \Psi^ {(i) T} + \gamma^ {(i - 1)}) e _ {t} - f _ {t} \| _ {2} ^ {2} \rbrace \\ \end{array} +$$ + +Line 4 in Algorithm 1 corresponds to the variational denoising of $(\Lambda^{(i)}\Psi^{(i)T} + \gamma^{(i - 1)})e_t$ with regularization $\lambda \rho (f_t)$ . Algorithm 1 is reformulated into Algorithm 2 to use RED as in [23] and [28], where $D_{\phi}$ is the denoiser for which we have the gradient rule + +$$ +\nabla \rho (f _ {t}) = f _ {t} - D _ {\phi} (f _ {t}) \tag {7} +$$ + +and each $f_{t}$ update in Step 4 is a single fixed-point iteration step using the approach of early stopping [29] (Sec. 4.3.2). In contrast to an iterative method to perform Line 4 in Algorithm 1, Step 4 in Algorithm 2 requires only single use of the denoiser per iteration of ADMM. + +# 4.3. Regularization Denoiser + +The regularization denoiser $D_{\phi}$ has a DnCNN [32] architecture and was trained in a supervised manner on a training + +# Algorithm 2 RED-PSM with efficient $f$ step + +Note: Inputs, and Lines 1-3 & 5-6 are the same as Algorithm 1. + +$$ +4: \forall t: f _ {t} ^ {(i)} = \frac {\lambda}{\lambda + \beta} D _ {\phi} (f _ {t} ^ {(i - 1)}) + \frac {\beta}{\lambda + \beta} \big (\Lambda^ {(i)} \Psi^ {(i) T} + \gamma^ {(i - 1)} \big) e _ {t} +$$ + +set of static 2D slices $f_{i} \in \mathbb{R}^{J^{2}}$ , $i = 1, \dots, N$ assuming that such data will be available in the settings of interest. Thus, the RED steps are agnostic to the specific motion type. The training objective for the denoiser is + +$$ +\min _ {\phi} \sum_ {i} \| f _ {i} - D _ {\phi} (\tilde {f} _ {i}) \| _ {F} ^ {2} \tag {8} +$$ + +where $\tilde{f}_i = f_i + \eta_i$ , and the injected noise $\eta_{i}\sim \mathcal{N}(0,\sigma_{i}^{2}I)$ has noise level $\sigma_{i}\sim U[0,\sigma_{\mathrm{max}}]$ spanning a range of values, so that the denoiser learns to denoise data with various noise levels. + +# 4.4. Convergence Analysis + +In [33](Section V.), we follow an approach along the lines of [34] to analyze convergence. We show that under mild technical conditions, the objective in Algorithm 1 is guaranteed to converge (with increasing number $I$ of iterations) to a value corresponding to a stationary point of the Lagrangian, that is, satisfying the necessary conditions for first order optimality. In practice, Algorithm 2 with the efficient $f$ step version, which we implemented and used in the experiments reported in Section 5 has better run times, and rapid empirical convergence. However, its analysis requires additional steps, which are not particularly illuminating. Thus, following the tradition in related analyses [29, 35], we focus on the analysis of the nominal Algorithm 1. + +# 5. Experiments + +# 5.1. Datasets + +Three categories of data sets are used in this work. + +Walnut Dataset: We use the CT reconstructions of two different (static) walnut objects from the publicly available 3D walnut CT dataset [36]. We create a dynamic test object by synthetically warping the central axial slice of one of the walnut objects using a sinusoidal piecewise-affine time-varying warp [37]. To be precise, the image is divided into a $J \times J$ uniformly spaced rectangular grid, and the following vertical displacement is applied on each row separately to drive the temporally varying warp $\Delta_{j,t} = -C(t)\sin(3\pi j / J)$ , $j \in \{0, \dots, J-1\}$ , where $C(t)$ is a linearly increasing function of $t$ and $C(0) = 0$ . Static axial, coronal, and sagittal slices of the other walnut object are used to train the denoiser $D_{\phi}$ . + +Compressed Object Dataset: This data set is obtained from a materials science experiment [38] with a sequence + +of nine increasing compression steps applied to an object, with a full set of radiographic projections collected (using Carl Zeiss Xradia 520 Versa) and reconstructed by the instrument's software at each step. Using this quasi-static data set, a fixed axial slice is extracted from each reconstruction. Nine extracted slices are interpolated to $P$ time frames using a recent deep learning-based video interpolation algorithm [39]. The denoiser $D_{\phi}$ for our experiments on this data set was trained using the axial slices of the static pre-compression and post-compression objects, which would be available in actual dynamic loading experiments. + +We note that all algorithms compared in this paper are agnostic to both the synthetic warp applied on the static walnut slice and to the data-driven interpolation method used for the compressed object. + +Spatio-temporal projection data for each dataset is simulated by a parallel-beam projection with $J = 128$ detector bins of the dynamic phantoms, a single projection at each of the $P$ time instants. The sequence of projection angles $\{\theta_t\}_{t=0}^{P-1}$ (a free experimental design parameter) was chosen to follow the bit-reversed view angle sampling scheme, which has been shown [16] to provide an especially favorable conditioning of the recovery problem. The simulated measurements are corrupted using AWGN with standard deviation $\sigma = 5 \cdot 10^{-3}$ . This noise level leads to the FBP (with Ram-Lak filter) of the full set of $P = 512$ projections at each time instant having a PSNR of approximately 46 dB. When, in the actual experiments with sequentially sampled data, only $1 / P$ of this data is used, the PSNR of the reconstruction may be expected to be lower. + +Ground-truth frames for $P = 4$ are shown in Figure 2. + +Cardiac dMRI Dataset: For a more direct comparison with the setting and data used in dMRI works, we also test RED-PSM on the "retrospective" cardiac dMRI data in [20]. The data includes 23 distinct time frames for one cardiac cycle. Details of the data and experiments are in Section 5.4.3. + +![](images/167e7ee59929a2e09799f5eb620bee3fe2b5b7151ec889e57e91482f07e5ab23.jpg) +Figure 2: Ground-truth frames for the time-varying walnut (top) and compressed object (bottom) datasets, uniformly sampled in time, $t \in \{0, \dots, P - 1\}$ , for $P = 4$ . + +# 5.2. Baseline Methods + +PSM-TV: Similar to the proposed approach, this algorithm also uses a partially separable model to represent the object with a different regularization type. For PSM-TV, + +regularization penalizes the $\ell_1$ -norm of the discrete 2D total variation of the temporal slices of $f$ at each time instant. To this end, the constraint $f = \Lambda \Psi^T$ is implemented by substitution into the objective in (5), and the definition of $\rho$ is changed to $\rho (\Lambda \Psi^T e_t) = \mathrm{TV}(\Lambda \Psi^T e_t)$ , and the rest of the objective is kept the same. The unconstrained problem is then solved for $\{\hat{\Lambda},\hat{\Psi}\}$ (using, as a convenient implementation, the Adam optimizer in Pytorch). Finally, the estimated object is obtained as $\hat{f} = \hat{\Lambda}\hat{\Psi}^{T}$ . + +TD-DIP [20]: TD-DIP is a recent method based on the Deep Image Prior (DIP) approach. It uses a mapping network $M_{\alpha}$ and a generative model $N_{\beta}$ sequentially to obtain the estimated object at each time instant $f_{t}$ from fixed and handcrafted latent representations $\chi_t$ . Because TD-DIP was originally proposed for dynamic MRI, we modified the objective minimally for dynamic tomography as + +$$ +\min _ {\alpha , \beta} \sum_ {t} \| g _ {t} - R _ {\theta (t)} \left(\left(N _ {\beta} \circ M _ {\alpha}\right) (\chi_ {t})\right) \| ^ {2}. \tag {9} +$$ + +For the comparisons in this work, identical mapping network and generator architectures, latent representation dimensionality, optimizer, learning rate, and decay schemes are used as in the available online implementation [40]. The original work focuses on the beating heart problem and thus proposes a helix-shaped latent manifold for $\chi_t$ with cycles equal to the number of heartbeats during measurement acquisition. Since we do not have a repetition assumption for the motion types included in this paper, we use a linear manifold as explained in the original paper [20]. Thus, the method is sometimes denoted as "TD-DIP (L)" in Section 5.4 for clarification. + +# 5.3. Experimental Settings + +All methods are run on a workstation with an Intel(R) Xeon(R) Gold 5320 CPU and NVIDIA RTX A6000 GPU. In practice, we used a minor variation of Algorithm 2, where we combined the subproblems in $\Lambda$ and $\Psi$ , and minimized with respect to both basis functions simultaneously using gradient descent with Adam [41] optimizer. + +Denoiser training. The upper limit for noise level used in training the denoiser was set to $\sigma_{\mathrm{max}} = 5 \cdot 10^{-2}$ . For the dynamic walnut object, the denoiser $D_{\phi}$ is trained on the central 200 axial, 200 sagittal, and 200 coronal slices of another walnut CT reconstruction downsampled to size $128 \times 128$ . For the compressed object, axial slices of precompression and post-compression static objects, containing 462 slices in total, are used to train $D_{\phi}$ . For the cardiac MRI setting, the denoiser was trained on the static MRI + +![](images/e0541d9605d18db12e067518136d5ba9e4b6eb2c29d7eb6b551fa239663f906f.jpg) +Figure 3: Reconstruction PSNR, SSIM, MAE, and HFEN for the time-varying walnut object (top) and compressed material (bottom) vs. $P$ using different methods. For TD-DIP, accuracy statistics for the best PSNR reconstruction during optimization are reported assuming such an oracle is available. The minimum and maximum values are indicated with error bars and the mean values are connected by the dashed line for different $P$ for three different runs. + +![](images/9f646b60d1e06fdcbfa357f67ec74177b15273069d3abf96a20fa5aaaa1bd6ac.jpg) + +![](images/6f97db83192577f02658f4ef1b4145ce0fa26e8dcc8b9ae4a2cdaebb931cee81.jpg) + +![](images/151dd039336443623d6b5a98dadac46eb6981e548f13e1e3a5192876a50d4d55.jpg) + +
(a) Walnut(b) Compressed Material
PMethodPSNR (dB)SSIMMAE (1e-3)HFENPSNR (dB)SSIMMAE (1e-2)HFEN
32PSM-TV (R)21.10.6782.91.0422.50.6972.911.6
TD-DIP (L)22.50.8822.10.8725.40.9091.58.1
RED-PSM (Pr)22.70.9141.50.7923.90.9161.29.9
64PSM-TV (R)24.00.8791.90.9425.60.8451.810.7
TD-DIP (L)25.60.9161.50.7429.00.9471.16.5
RED-PSM (Pr)26.40.9580.90.5729.30.9520.56.0
128PSM-TV (R)26.80.9121.40.7829.20.9071.19.6
TD-DIP (L)29.00.9531.00.5032.40.9530.85.1
RED-PSM (Pr)29.90.9780.60.4333.10.9720.44.7
256PSM-TV (R)30.10.9341.00.6331.90.9630.78.0
TD-DIP (L)31.70.9660.80.4534.70.9660.74.6
RED-PSM (Pr)33.80.9870.40.3235.90.9860.34.4
+ +Table 1: Reconstruction accuracies for different $P$ . Random (R) and ProSep (Pr) initialization for the PSM methods. For TD-DIP, the reported accuracies are for the best PSNR using a "stopping oracle", averaged over three runs with random initial conditions. + +training slices of the ACDC dataset [42]. For all datasets, $D_{\phi}$ is trained for 500 epochs using the Adam optimizer with a learning rate of $5 \cdot 10^{-3}$ . Each convolutional layer is followed by a ReLU nonlinearity except for the final layer, which has a single-channel output. We test both direct and residual DnCNN denoisers where the former predicts the denoised image and the latter estimates the noise from the noisy input. + +Architectural details for denoisers used in our experiments are provided in Table 6 in Supplementary Material C. We use a fixed pre-trained denoiser for all $P$ for the same object type. + +Temporal Basis. In all experiments, we use a fixed basis $U$ as a cubic spline interpolator to interpolate the low-dimensional temporal representation $Z$ to $\Psi$ . + +Initialization. Unless stated otherwise, spatial and temporal basis functions are initialized using the SVD truncated to order $K$ the rank of the dynamic object estimate pro + +duced by a recent projection-domain PSM-based method "ProSep" [17]. If the ProSep estimate has rank smaller than $K$ , the remaining basis functions are initialized as 0. Otherwise, all spatial basis functions are initialized as 0 and the latent representations $z_{k}$ of the temporal basis functions are initialized randomly as $z_{k} \sim \mathcal{N}(0, I)$ . + +Tomographic Acquisition Scheme. All methods mentioned in this paper use the bit-reversed angular sampling scheme, over the range $[0,\pi ]$ . + +Run Times. For $P = 256$ and using the specified computational resources and parameter settings, To achieve the peak PSNR during optimization, RED-PSM with ProSep initialization requires $50 <$ iterations $< 150$ taking about 2 to 6 minutes whereas TD-DIP with batch size $P$ typically requires $> 30k$ steps, taking about 3.5 hours to complete. Hence, RED-PSM provides a speedup over TD-DIP by a factor of 35 to 105 to reach its peak performance. We note that based on the parameter configuration, the speedup factor may vary. However, the proposed method provides a significant run time reduction in all cases. + +Evaluation Metrics. Four quantitative metrics were implemented for evaluating reconstruction accuracy (i) the peak signal-to-noise ratio (PSNR) in dB; (ii) the structural similarity index (SSIM) [43]; (iii) the mean absolute error (MAE); and (iv) the high-frequency error norm (HFEN) [44] defined as $\mathrm{HFEN}(f, f_r) = \| \mathrm{LoG}(f) - \mathrm{LoG}(f_r)\|_2$ where LoG is a rotationally symmetric Laplacian of Gaussian filter with a standard deviation of 1.5 pixels. + +# 5.4. Results + +# 5.4.1 Reconstruction accuracies for different $P$ + +In Figure 3 and Table 1, the performance of RED-PSM is compared with PSM-TV and with TD-DIP that uses a linear latent representation for both objects. While Figure 3 + +![](images/f25bcfea3f73944bbeba99e933c8adedc629c6e5457815e6e72036b47ad23ff2.jpg) +Figure 4: Comparison of reconstructed object frames at two time instants using different methods for $P = 256$ , and the corresponding normalized absolute reconstruction errors for (A) the time-varying walnut, and (B) compressed object. + +facilitates the comparison of metrics for different $P$ for the various methods, since the range of metrics is very large for varying $P$ . Table 1 emphasizes important differences between methods for the same $P$ , and provides detail for a more precise quantitative comparison. As expected, the estimates improve with increasing $P$ for all methods. In terms of PSNR, the proposed algorithm performs on par with or better than the best PSNR TD-DIP estimate for various $P$ , with improvement for RED-PSM enhancing with the increase in $P$ . Moreover, in terms of SSIM, MAE, and HFEN, the improvements with RED-PSM are even more significant. Although these observations are valid for both objects, for the walnut, RED-PSM provides slightly greater improvement over TD-DIP. + +Figure 4 compares the reconstructions for both objects at two different $t$ for $P = 256$ . As expected, providing blurry reconstructions lacking finer details for both objects, PSM-TV performs the worst among the compared methods. The TD-DIP reconstructions contain visible noise-like artifacts on the piecewise constant regions of the walnut object, which are alleviated by RED-PSM. This observation manifests itself also in the absolute difference figures, with error for TD-DIP distributed throughout the interior regions of the walnut. Furthermore, RED-PSM preserves sharp details around the shell of the walnut better. Throughout the compressed material object for the given time frames, compared to TD-DIP, RED-PSM has an almost consistently smaller absolute error. This difference is more prominent around the highly dynamic regions of the object, emphasizing the advantage of the proposed method. + +In Figure 5, the reconstructed $x - t$ cross-sections of the + +dynamic walnut are shown for different methods. The location of the cross-section is highlighted by a yellow line on the static $x - y$ frame at $t = 0$ . Consistent with the comparison in Figure 4, RED-PSM provides reduced absolute error values throughout the respective cross-section. Also, as more apparent in the error figures, TD-DIP produces higher background errors. + +# 5.4.2 Effect of Initialization + +The initialization of $\Lambda$ , $\Psi$ , and $f$ plays an important role in the performance and convergence speed of RED-PSM. We observe significant speed-up when rather than a random initialization, we initialize the algorithm with ProSep [16] estimated reconstruction. Figure 7 shows PSNR vs. iterations comparison for different initialization techniques for the dynamic walnut object with $P = 256$ . The rest of the parameters were selected identically as indicated in Table 5 in Supplementary Material. This experiment highlights the advantages of initializing with ProSep estimated basis functions: eliminating the need for multiple runs for a best-case result; and speeding up convergence considerably. + +# 5.4.3 Cardiac dMRI data experiments + +In this setting, different to the previous experiments, we used $4k$ -space radial lines ("spokes") per frame at the bitreversed angles. We used 1.4 and 2.8 cardiac cycles, with $23 \times 4 = 92$ spokes/cycle, for a total of $P = 128$ and $P = 256$ spokes. The problem is still severely undersampled compared to the experiment in [20] where 13 spokes are used + +![](images/b933e3c8c0dfc105bc8e7b8061f2343b10eea044acef736e2dfbca0b107ab5c4.jpg) +Figure 5: Comparison of reconstructed $x - t$ cross-sections using different methods for $P = 256$ (top), with corresponding normalized absolute error counterparts (bottom). The location of the cross-section is indicated with a yellow line on the static object at time $t = 0$ (left). The $x - y - t$ coordinates are indicated on the static object and bottom left absolute error figure in white text. + +![](images/09d3208231d9d75f956e27c02d09e12340b28f2da42d61a0a394b6a44ee1f344.jpg) + +![](images/4e2d324213887fee614a4ee031ae5c2b834b2f48514acae517041474796ec816.jpg) + +![](images/384f4706bf41f52296a3ca8b7a7e1a1c5b27979073f392095ed59fce9c1668d1.jpg) + +![](images/d974b72d97dc6fcba4f6cd5a0e071a5534fa77c08d9962816882c193d3ee48d3.jpg) + +![](images/30a4e5748de863c9924f0b2bd603c64adeb56c3c50c06f8d172bc7cf2b2eb4f2.jpg) + +per frame for 13 cycles, for a total of $13 \times 23 \times 13 = 3,887$ spokes. Since the data is periodic, we also tested the helix latent scheme (H) for TD-DIP. + +The metrics in Table 2 and the qualitative comparison in Figure 6 with zoomed-in reconstructions and absolute error maps, show that RED-PSM performs better than both versions of TD-DIP. + +![](images/c740dcf4dde0c91aa3c47502dc6ccc5c48d1690e962dc99a7e4f0cf0100b3b18.jpg) +Figure 6: Reconstructed frames for $P = 256$ for retrospective dMRI data [20] with zoomed-in frames (middle row), and absolute reconstruction errors (last row). + +
PMethodPSNR (dB)SSIMMAE (1e-2)HFEN
128TD-DIP (L)34.60.9231.73.38
TD-DIP (H)34.60.9281.73.32
RED-PSM36.60.9391.42.73
256TD-DIP (L)36.20.9481.43.47
TD-DIP (H)36.40.9471.43.44
RED-PSM38.40.9621.12.99
+ +Table 2: Reconstruction accuracies for RED-PSM and TD-DIP for the retrospective dMRI data [20]. + +# 5.5. PSNR vs. $t$ , and a Patch-Based Scheme + +In Supplementary Material A, we compare the PSNR of the reconstructed frames for each $t$ for all methods for the walnut object with $P = 256$ and show the consistently better performance of RED-PSM. + +Also, in Supplementary Material B, to improve scalability to high-resolution and high-dimensional settings, we propose and evaluate a patch-based version of RED-PSM with a patch-based denoiser $D_{\phi}$ . In the experiments, + +the patch-based scheme provided reconstruction accuracies similar to those reported here for the original scheme. + +# 6. Conclusions + +RED-PSM is the first PSM-based approach to dynamic imaging using a pre-trained and learned (RED-based) spatial prior. The objective in the proposed variational formulation is optimized using a novel and effective bilinear ADMM algorithm, which enforces the PSM as a hard constraint. Unlike existing PSM-based techniques, RED-PSM is supported by theoretical analysis, with a convergence guarantee to a stationary point of the objective. The results of the numerical experiments show better reconstruction accuracy and considerably faster run times compared to a recent DIP-based algorithm. A patch-based regularizer version of RED-PSM provides almost equivalent performance with a massive reduction of storage requirements, indicating the potential of our framework for dynamic high-resolution 2D or 3D settings. + +Possible directions for future work include the application of RED-PSM to various imaging scenarios other than tomography and MRI, and robust denoiser training for the RED framework, since the deep denoisers encounter varying artifact distributions during optimization. This could also improve the generalizability of the framework to different input types. + +Acknowledgements. This research was supported in part by Los Alamos National Labs under Subcontract No. 599416/CW13995. We thank Dr. Brian M. Patterson for providing the data for the compressed material experiments. + +![](images/6e8a2d405e3c354bf6928f9c643f0eb52a0818eb616d9694215e3f2c3ebb2ec0.jpg) +Figure 7: PSNR vs. iteration comparison for RED-PSM as described in Section 5.4.2. The area between the best and the worst PSNR for each iteration is shown in blue to highlight the varying performances of five different runs with random initialization. + +# References + +[1] E. Maire, C. Le Bourlot, J. Adrien, A. Mortensen, and R. Mokso, “20 Hz X-ray tomography during an in situ tensile test,” International Journal of Fracture, vol. 200, no. 1, pp. 3–12, 2016. +[2] I. Danad, J. Szymonifka, J. Schulman-Marcus, and J. K. 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In particular, in dynamic tomography, only a single projection at a single view angle may be available at a time, making the problem severely ill-posed. In this work, we propose an approach, RED-PSM, which combines for the first time two powerful techniques to address this challenging imaging problem. The first, are partially separable models, which have been used to introduce a low-rank prior for the spatio-temporal object. The second is the recent Regularization by Denoising (RED), which provides a flexible framework to exploit the impressive performance of state-of-the-art image denoising algorithms, for various inverse problems. We propose a partially separable objective with RED and an optimization scheme with variable splitting and ADMM. Our objective is proved to converge to a value corresponding to a stationary point satisfying the first-order optimality conditions. Convergence is accelerated by a particular projection-domain-based initialization. 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Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 581, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 581, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 581, + 287, + 653 + ], + "type": "text", + "content": "Time-varying tomography is a challenging ill-posed inverse problem that involves reconstructing a dynamic object using its sequential projections at each time instant. 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Also, it is closely related to the dynamic MRI (dMRI) problem, which typically arises" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 217, + 400, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 217, + 400, + 228 + ], + "spans": [ + { + "bbox": [ + 306, + 217, + 400, + 228 + ], + "type": "text", + "content": "in cardiac imaging [8]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 230, + 545, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 230, + 545, + 290 + ], + "spans": [ + { + "bbox": [ + 304, + 230, + 545, + 290 + ], + "type": "text", + "content": "Previous work [9, 10] treated the problem as time-sequential sampling of bandlimited signals and provided an optimal view angle sampling order and theoretical guarantees for unique and stable reconstruction. However, the approach is limited by its bandlimitedness assumptions." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 291, + 546, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 291, + 546, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 291, + 546, + 411 + ], + "type": "text", + "content": "Several methods [11, 12] recover the underlying motion field from projections using the Radon transform properties. However, these methods require the object information a priori. Other algorithms [13, 14] alternate between estimating the motion field and the time-varying object. These methods assume the total density to be preserved for a given object at different times which may be a limiting assumption. For instance, imaging a fixed slice of a time-varying object under compression may violate this assumption due to perpendicularly evolving parts." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 412, + 546, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 546, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 546, + 533 + ], + "type": "text", + "content": "In dynamic tomography and MRI, partially-separable models (PSM) have been used to represent the underlying object [15] and the time-sequential projections [16, 17]. The projection-domain PSM in [16, 17] carries the PSM to the projection domain using the harmonic representation of projections, and provides uniqueness and stability analysis for the problem. In spite of this advantage of the projection domain PSM over its object-domain counterparts, the performance of this approach is limited by the null space of the measurement operator." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "type": "text", + "content": "A different PSM-based method for dMRI [18] imposes the low-rank structure as a soft constraint. It uses a hybrid objective with the PSM model used in the data fidelity term and the object in a simple " + }, + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "type": "inline_equation", + "content": "l_{1}" + }, + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "type": "text", + "content": "-norm penalty, with an additional penalty term to penalize the mismatch between the PSM and the object. The method does not use a guided initial guess for the object or for the PSM basis functions. A fast alternative low-rank (or PSM)-based method for dMRI [19] decomposes the object representation into three components: the mean signal, a low-rank PSM, and the residual, which is assumed to be sparse in the Fourier domain. Then, each component is estimated in order. Although on some of the data sets used for the comparison in [19] competing methods are either faster or more accurate, the method provides better results when averaged over all data sets." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "type": "text", + "content": "10595" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "Recently, object-domain deep image prior (DIP)-based algorithms [20,21] have been proposed for dMRI. Providing impressive results, DIP-based algorithms such as [20] suffer from overfitting and usually require handcrafted early stopping criteria during the optimization of generator network parameters. In an attempt to overcome the overfitting and the need for handcrafted early stopping, the authors of [21] regularize the problem by constraining the geodesic distances between generated objects in proportion to the distances between their latent representation. However, this requires the computation of the Jacobian of the generator network at each iteration of the update of the weights and significantly increases the computational load and run time." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 289, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 445 + ], + "type": "text", + "content": "A different approach [22] combines partially separable and generative models. It employs spatial and temporal regularization by penalizing the generator weights and a particular initialization scheme for the inputs to the generator networks. Although it combines the PSM with the recent DIP framework, this method has the following limitations, which are overcome by the proposed approach: (i) The spatial generator is an artifact removal network taking the full-sized spatial basis functions as input. Since this prevents a patch-based implementation, it may be difficult to scale to high-resolution 3D+temporal settings. (ii) The CNN prior for natural images may not be useful as a prior for the individual spatial basis functions, since the least-squares optimal spatial basis functions are the left singular vectors of the complete object, and as such may not have the structure of natural images. (iii) As with other DIP-based methods, if the additional penalty on the generator parameters is insufficient, this method can be prone to overfitting." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 449, + 118, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 449, + 118, + 460 + ], + "spans": [ + { + "bbox": [ + 59, + 449, + 118, + 460 + ], + "type": "text", + "content": "Contributions" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 472, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 55, + 472, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 472, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 55, + 472, + 287, + 510 + ], + "type": "text", + "content": "1. To the best of our knowledge, RED-PSM is the first PSM-based approach to dynamic imaging, that uses a pre-trained, learned (RED-based [23]) spatial prior." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 521, + 287, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 521, + 287, + 570 + ], + "spans": [ + { + "bbox": [ + 54, + 521, + 287, + 570 + ], + "type": "text", + "content": "2. A novel and effective ADMM algorithm for the resulting new minimization problem enforcing PSM as a hard constraint and incorporating the learned RED spatial regularizer is proposed." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 580, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 580, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 54, + 580, + 287, + 605 + ], + "type": "text", + "content": "3. The method is supported by theoretical analysis, with a convergence guarantee." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 617, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 617, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 54, + 617, + 287, + 653 + ], + "type": "text", + "content": "4. Compared to a recent DIP-based [20] algorithm, RED-PSM achieves better reconstruction accuracy with orders of magnitude faster run times." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 54, + 665, + 287, + 714 + ], + "type": "text", + "content": "5. A version of the approach with a patch-based regularizer is shown to provide almost equivalent reconstruction accuracy. This makes the proposed method conveniently scalable to high-resolution 3D or 4D settings." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "type": "image", + "bbox": [ + 312, + 72, + 537, + 203 + ], + "blocks": [ + { + "bbox": [ + 312, + 72, + 537, + 203 + ], + "lines": [ + { + "bbox": [ + 312, + 72, + 537, + 203 + ], + "spans": [ + { + "bbox": [ + 312, + 72, + 537, + 203 + ], + "type": "image", + "image_path": "9e062c8cb60b485f4bcc5c1dbc0365ca5064edb7924296adc7dd2aea28d8060f.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 207, + 547, + 242 + ], + "lines": [ + { + "bbox": [ + 305, + 207, + 547, + 242 + ], + "spans": [ + { + "bbox": [ + 305, + 207, + 547, + 242 + ], + "type": "text", + "content": "Figure 1: Projection acquisition geometry for time-varying tomography of the object " + }, + { + "bbox": [ + 305, + 207, + 547, + 242 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 305, + 207, + 547, + 242 + ], + "type": "text", + "content": " with single measurement " + }, + { + "bbox": [ + 305, + 207, + 547, + 242 + ], + "type": "inline_equation", + "content": "g_{t}" + }, + { + "bbox": [ + 305, + 207, + 547, + 242 + ], + "type": "text", + "content": " at each time instant for " + }, + { + "bbox": [ + 305, + 207, + 547, + 242 + ], + "type": "inline_equation", + "content": "t \\in \\{0,1,2\\}" + }, + { + "bbox": [ + 305, + 207, + 547, + 242 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 249, + 421, + 262 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 249, + 421, + 262 + ], + "spans": [ + { + "bbox": [ + 306, + 249, + 421, + 262 + ], + "type": "text", + "content": "2. Problem Statement" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 269, + 547, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 269, + 547, + 318 + ], + "spans": [ + { + "bbox": [ + 305, + 269, + 547, + 318 + ], + "type": "text", + "content": "In a 2D setting, the goal in the ill-posed dynamic tomography problem is to reconstruct a time-varying object " + }, + { + "bbox": [ + 305, + 269, + 547, + 318 + ], + "type": "inline_equation", + "content": "f(\\mathbf{x},t)" + }, + { + "bbox": [ + 305, + 269, + 547, + 318 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 269, + 547, + 318 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^2" + }, + { + "bbox": [ + 305, + 269, + 547, + 318 + ], + "type": "text", + "content": " vanishing outside a disc of diameter " + }, + { + "bbox": [ + 305, + 269, + 547, + 318 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 305, + 269, + 547, + 318 + ], + "type": "text", + "content": ", from its projections" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 375, + 327, + 476, + 341 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 327, + 476, + 341 + ], + "spans": [ + { + "bbox": [ + 375, + 327, + 476, + 341 + ], + "type": "interline_equation", + "content": "g (\\cdot , \\theta , t) = \\mathcal {R} _ {\\theta} \\{f (\\mathbf {x}, t) \\}", + "image_path": "495cccef14c055a66b71fb8ba9d74e3f06d0e2dd81826b309c2931c64b9ff13a.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 350, + 546, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 350, + 546, + 398 + ], + "spans": [ + { + "bbox": [ + 305, + 350, + 546, + 398 + ], + "type": "text", + "content": "obtained using the Radon transform operator " + }, + { + "bbox": [ + 305, + 350, + 546, + 398 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\theta}" + }, + { + "bbox": [ + 305, + 350, + 546, + 398 + ], + "type": "text", + "content": " at angle " + }, + { + "bbox": [ + 305, + 350, + 546, + 398 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 305, + 350, + 546, + 398 + ], + "type": "text", + "content": ". Considering time-sequential sampling, in which only one projection is acquired at each time instant, and sampling uniform in time, the acquired measurements are" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 357, + 406, + 545, + 422 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 406, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 357, + 406, + 545, + 422 + ], + "type": "interline_equation", + "content": "\\left\\{g \\left(s, \\theta_ {p}, t _ {p}\\right) \\right\\} _ {p = 0} ^ {P - 1}, \\forall s, t _ {p} = p \\Delta_ {t}, \\tag {1}", + "image_path": "ea1b72b60cc0062d7f92d8831726d9ba83cf3ffe7b707d583493ba81dc1c6bae.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 430, + 547, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 430, + 547, + 526 + ], + "spans": [ + { + "bbox": [ + 305, + 430, + 547, + 526 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 430, + 547, + 526 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 430, + 547, + 526 + ], + "type": "text", + "content": " is the offset of the line of integration from the origin (i.e., detector position), and " + }, + { + "bbox": [ + 305, + 430, + 547, + 526 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 305, + 430, + 547, + 526 + ], + "type": "text", + "content": " is the total number of projections (and temporal samples) acquired. The sampling of the " + }, + { + "bbox": [ + 305, + 430, + 547, + 526 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 430, + 547, + 526 + ], + "type": "text", + "content": " variable is assumed fine enough and is suppressed in the notation. The angular sampling scheme, the sequence " + }, + { + "bbox": [ + 305, + 430, + 547, + 526 + ], + "type": "inline_equation", + "content": "\\{\\theta_p\\}_{p=0}^{P-1}" + }, + { + "bbox": [ + 305, + 430, + 547, + 526 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 305, + 430, + 547, + 526 + ], + "type": "inline_equation", + "content": "\\theta_p \\in [0,2\\pi]" + }, + { + "bbox": [ + 305, + 430, + 547, + 526 + ], + "type": "text", + "content": ", is considered as a free design parameter. Figure 1 shows a simplified time-sequential sampling scheme for a time-varying object." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 526, + 547, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 526, + 547, + 622 + ], + "spans": [ + { + "bbox": [ + 304, + 526, + 547, + 622 + ], + "type": "text", + "content": "Our objective in dynamic tomography, and in dynamic imaging in general, is to reconstruct the underlying object with temporal variation " + }, + { + "bbox": [ + 304, + 526, + 547, + 622 + ], + "type": "inline_equation", + "content": "\\{f(\\mathbf{x},t_p)\\}_{p = 0}^{P - 1}" + }, + { + "bbox": [ + 304, + 526, + 547, + 622 + ], + "type": "text", + "content": " from the time-sequential measurements in (1). The challenge is that because each projection belongs to a different object, the projections in (1) are inconsistent. Therefore, a conventional, e.g., filtered backprojection (FBP) reconstruction as for a static object results in significant reconstruction artifacts." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 633, + 497, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 633, + 497, + 647 + ], + "spans": [ + { + "bbox": [ + 305, + 633, + 497, + 647 + ], + "type": "text", + "content": "3. Partially Separable Models (PSM)" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "type": "text", + "content": "For spatio-temporal inverse problems such as dynamic MRI and tomography, the underlying object can be accurately represented using a partially-separable model (PSM), which effectively introduces a low-rank prior to the problem. For dynamic tomography, a PSM can represent the" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 318, + 742 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 318, + 742 + ], + "type": "text", + "content": "10596" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "imagined object " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": ", or its full set of projections " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": ". In this paper we use an object-domain PSM." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 95, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 95, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 95, + 287, + 120 + ], + "type": "text", + "content": "The representation of a dynamic object " + }, + { + "bbox": [ + 46, + 95, + 287, + 120 + ], + "type": "inline_equation", + "content": "f(\\mathbf{x}, t)" + }, + { + "bbox": [ + 46, + 95, + 287, + 120 + ], + "type": "text", + "content": " by a " + }, + { + "bbox": [ + 46, + 95, + 287, + 120 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 95, + 287, + 120 + ], + "type": "text", + "content": "-th order PSM is the series expansion" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 110, + 125, + 287, + 158 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 125, + 287, + 158 + ], + "spans": [ + { + "bbox": [ + 110, + 125, + 287, + 158 + ], + "type": "interline_equation", + "content": "f (\\mathbf {x}, t) = \\sum_ {k = 0} ^ {K - 1} \\Lambda_ {k} (\\mathbf {x}) \\psi_ {k} (t). \\tag {2}", + "image_path": "d5b853041688ef4fef3bb4023f93efc212ef5e3c049cdc4cd9af34028e7c0934.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 163, + 288, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 163, + 288, + 294 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 288, + 294 + ], + "type": "text", + "content": "The model helps with interpretability by separating the spatial structure from the temporal dynamics. This expansion is dense in " + }, + { + "bbox": [ + 46, + 163, + 288, + 294 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2" + }, + { + "bbox": [ + 46, + 163, + 288, + 294 + ], + "type": "text", + "content": " [24], meaning that any finite energy object can be approximated arbitrarily well by such a model of sufficiently high order. Empirically, modest values of " + }, + { + "bbox": [ + 46, + 163, + 288, + 294 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 163, + 288, + 294 + ], + "type": "text", + "content": " provide high accuracy in applications to MR cardiac imaging [15, 25, 26]. Theoretical analysis in [17] shows that for a spatially bandlimited object undergoing a time-varying affine transformation (i.e., combination of time-varying translation, scaling, and rotation) of bounded magnitude, a low order PSM provides a good approximation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "type": "text", + "content": "The PSM using a " + }, + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "type": "text", + "content": "-dimensional representation for the temporal functions leads to significant reduction of " + }, + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "type": "inline_equation", + "content": "\\approx PL^2" + }, + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "type": "text", + "content": " representation parameters for an unstructured object of diameter " + }, + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "type": "text", + "content": " temporal samples to " + }, + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "type": "inline_equation", + "content": "\\approx KL^2 + Kd" + }, + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "type": "inline_equation", + "content": "K \\ll P" + }, + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "type": "inline_equation", + "content": "d \\ll P" + }, + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "type": "text", + "content": ". Thus, it provides an effective parsimonious model for the spatio-temporal object " + }, + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 294, + 287, + 366 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 366, + 287, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 366, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 366, + 287, + 403 + ], + "type": "text", + "content": "Also, by propagating the PSM object model to the projection domain, it enables quantitative analysis [17] of the choice of optimal sequential projection angular schedule." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 411, + 216, + 425 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 411, + 216, + 425 + ], + "spans": [ + { + "bbox": [ + 47, + 411, + 216, + 425 + ], + "type": "text", + "content": "4. Proposed Method: RED-PSM" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 431, + 185, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 431, + 185, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 431, + 185, + 443 + ], + "type": "text", + "content": "4.1. Variational Formulation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "text", + "content": "We use a discretized version of the PSM (2) for the dynamic object, with the object " + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "inline_equation", + "content": "f(\\cdot ,t)" + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "text", + "content": " at each time instant " + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "inline_equation", + "content": "t = 0,1,\\ldots ,P - 1" + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "text", + "content": ", represented by a " + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "inline_equation", + "content": "J\\times J" + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "text", + "content": "-pixel image. Vectorizing these images to vectors " + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "inline_equation", + "content": "f_{t}\\in \\mathbb{R}^{J^{2}}" + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "text", + "content": ", the entire dynamic object is the " + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "inline_equation", + "content": "J^2\\times P" + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "text", + "content": " matrix " + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "inline_equation", + "content": "f = [f_0\\dots f_{P - 1}] = \\Lambda \\Psi^T\\in \\mathbb{R}^{J^2\\times P}" + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "text", + "content": ". Denoting the " + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "text", + "content": "-th column of the " + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "inline_equation", + "content": "P\\times P" + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "text", + "content": " identity matrix by " + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "inline_equation", + "content": "e_t" + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "text", + "content": ", we have " + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "inline_equation", + "content": "f e_{t} = f_{t}" + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "text", + "content": "-th individual time frame of " + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "text", + "content": ". The columns " + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "inline_equation", + "content": "\\Lambda_{k}" + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "inline_equation", + "content": "\\Psi_{k}" + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "inline_equation", + "content": "\\Lambda \\in \\mathbb{R}^{J^2\\times K}" + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "inline_equation", + "content": "\\Psi \\in \\mathbb{R}^{P\\times K}" + }, + { + "bbox": [ + 46, + 449, + 287, + 582 + ], + "type": "text", + "content": " are the discretized spatial and temporal basis functions for the PSM representation, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 583, + 287, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 583, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 583, + 287, + 632 + ], + "type": "text", + "content": "Assuming that the x-ray detector has " + }, + { + "bbox": [ + 46, + 583, + 287, + 632 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 46, + 583, + 287, + 632 + ], + "type": "text", + "content": " bins, the projection of the object at time " + }, + { + "bbox": [ + 46, + 583, + 287, + 632 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 583, + 287, + 632 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 46, + 583, + 287, + 632 + ], + "type": "inline_equation", + "content": "g_{t} = g(\\cdot ,\\theta_{t},t) = R_{\\theta_{t}}f_{t}\\in \\mathbb{R}^{J}" + }, + { + "bbox": [ + 46, + 583, + 287, + 632 + ], + "type": "text", + "content": ", where the measurement matrix " + }, + { + "bbox": [ + 46, + 583, + 287, + 632 + ], + "type": "inline_equation", + "content": "R_{\\theta_t}\\in \\mathbb{R}^{J\\times J^2}" + }, + { + "bbox": [ + 46, + 583, + 287, + 632 + ], + "type": "text", + "content": " computes the projection at view angle " + }, + { + "bbox": [ + 46, + 583, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\theta_t" + }, + { + "bbox": [ + 46, + 583, + 287, + 632 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 632, + 287, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 632, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 46, + 632, + 287, + 657 + ], + "type": "text", + "content": "We formulate the recovery of " + }, + { + "bbox": [ + 46, + 632, + 287, + 657 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 632, + 287, + 657 + ], + "type": "text", + "content": " as the solution " + }, + { + "bbox": [ + 46, + 632, + 287, + 657 + ], + "type": "inline_equation", + "content": "\\hat{f} = \\hat{\\Lambda}\\hat{\\Psi}^T" + }, + { + "bbox": [ + 46, + 632, + 287, + 657 + ], + "type": "text", + "content": " to the following variational problem" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 50, + 662, + 287, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 662, + 287, + 711 + ], + "spans": [ + { + "bbox": [ + 50, + 662, + 287, + 711 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} (\\hat {\\Lambda}, \\hat {\\Psi}) = \\arg \\min _ {\\Lambda , \\Psi} \\sum_ {t = 0} ^ {P - 1} \\| R _ {\\theta_ {t}} \\Lambda \\Psi^ {T} e _ {t} - g _ {t} \\| _ {2} ^ {2} + \\lambda \\rho (\\Lambda \\Psi^ {T} e _ {t}) \\\\ + \\xi \\| \\Psi \\| _ {F} ^ {2} + \\xi \\| \\Lambda \\| _ {F} ^ {2} \\quad \\text {w h e r e} \\quad \\Psi = U Z. \\tag {3} \\\\ \\end{array}", + "image_path": "7457b8cd58c9079b5c7f4f8e247d679dce2dd18685150937a41c528a4d425e50.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "text", + "content": "The first term is the data fidelity term measuring the fit between available undersampled measurements " + }, + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "inline_equation", + "content": "g_{t}" + }, + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "text", + "content": " of the true object and the measurements obtained from the estimated object " + }, + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "inline_equation", + "content": "f = \\Lambda \\Psi^{T} \\in \\mathbb{R}^{J^{2} \\times P}" + }, + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "text", + "content": ". The second term with weight " + }, + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "inline_equation", + "content": "\\lambda > 0" + }, + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "text", + "content": " is a spatial regularizer injecting relevant spatial prior to the problem. The last two terms with weight " + }, + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "inline_equation", + "content": "\\xi > 0" + }, + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "text", + "content": " prevent the bilinear factors " + }, + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "inline_equation", + "content": "\\Lambda" + }, + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 304, + 72, + 545, + 157 + ], + "type": "text", + "content": " from growing without limit." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "spans": [ + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "text", + "content": "Finally, the constraint " + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "inline_equation", + "content": "\\Psi = UZ" + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "text", + "content": " is an implicit temporal regularizer that restricts the temporal basis functions " + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "text", + "content": " to a " + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "text", + "content": "-dimensional subspace of " + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^P" + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "text", + "content": " spanned by a fixed basis " + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "inline_equation", + "content": "U \\in \\mathbb{R}^{P \\times d}" + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "text", + "content": ". In practice, we incorporate this constraint by explicit substitution (reparametrization of " + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "text", + "content": " in terms of the free variable " + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "inline_equation", + "content": "Z \\in \\mathbb{Z}^{d \\times K}" + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "text", + "content": ") into the objective, and the minimization in (3) over " + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "text", + "content": " is thus replaced by minimization over " + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "text", + "content": ". This reduces the number of degrees of freedom in " + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "text", + "content": " to a fixed number " + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "inline_equation", + "content": "dK" + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "text", + "content": ", independent of the number " + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 158, + 546, + 302 + ], + "type": "text", + "content": " of temporal sampling instants. For notational conciseness, We do not display this constraint/reparametrization in the sequel, but it is used throughout." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 315, + 529, + 328 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 315, + 529, + 328 + ], + "spans": [ + { + "bbox": [ + 305, + 315, + 529, + 328 + ], + "type": "text", + "content": "4.2. Incorporating Regularization by Denoising" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 335, + 545, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 545, + 382 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 545, + 382 + ], + "type": "text", + "content": "For the spatial regularizer " + }, + { + "bbox": [ + 304, + 335, + 545, + 382 + ], + "type": "inline_equation", + "content": "\\rho(\\cdot)" + }, + { + "bbox": [ + 304, + 335, + 545, + 382 + ], + "type": "text", + "content": " we consider \"Regularization by Denoising (RED)\" [23]. RED proposes a recovery method using a denoiser in an explicit regularizer of the form" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 369, + 393, + 545, + 416 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 393, + 545, + 416 + ], + "spans": [ + { + "bbox": [ + 369, + 393, + 545, + 416 + ], + "type": "interline_equation", + "content": "\\rho \\left(f _ {t}\\right) = \\frac {1}{2} f _ {t} ^ {T} \\left(f _ {t} - D \\left(f _ {t}\\right)\\right) \\tag {4}", + "image_path": "817c290d915ef7beb8449d923c9d76bf30c27e2bfd02a31fd772c4608ae3179d.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 429, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 429, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 429, + 545, + 526 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 429, + 545, + 526 + ], + "type": "inline_equation", + "content": "D:\\mathbb{R}^{J^2}\\to \\mathbb{R}^{J^2}" + }, + { + "bbox": [ + 304, + 429, + 545, + 526 + ], + "type": "text", + "content": " is the denoising operator. Recent works using RED provide impressive results for various static reconstruction tasks, including high-dimensional cases [27]. Providing significant flexibility for the type of denoisers that can be used, RED still requires " + }, + { + "bbox": [ + 304, + 429, + 545, + 526 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 429, + 545, + 526 + ], + "type": "text", + "content": " to be differentiable and locally homogeneous, and to satisfy the passivity condition " + }, + { + "bbox": [ + 304, + 429, + 545, + 526 + ], + "type": "inline_equation", + "content": "\\| G(f)\\| \\leq \\| f\\|" + }, + { + "bbox": [ + 304, + 429, + 545, + 526 + ], + "type": "text", + "content": ", for its theoretical analysis to apply." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 317, + 528, + 498, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 528, + 498, + 538 + ], + "spans": [ + { + "bbox": [ + 317, + 528, + 498, + 538 + ], + "type": "text", + "content": "For the conventional variational formulation" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 345, + 552, + 505, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 552, + 505, + 571 + ], + "spans": [ + { + "bbox": [ + 345, + 552, + 505, + 571 + ], + "type": "interline_equation", + "content": "\\hat {f} _ {t} = \\arg \\min _ {f _ {t}} \\| R _ {\\theta_ {t}} f _ {t} - g _ {t} \\| _ {2} ^ {2} + \\lambda \\rho (f _ {t}),", + "image_path": "33fa8663abadcb901ef914d1e4dafd7267b0513617a6316c4ef8a5740677a146.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 583, + 545, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 583, + 545, + 619 + ], + "spans": [ + { + "bbox": [ + 304, + 583, + 545, + 619 + ], + "type": "text", + "content": "an efficient choice are iterative algorithms [23] that use the standard \"early termination\" approach [29], and only require a single use of the denoiser per iteration." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 621, + 545, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 621, + 545, + 669 + ], + "spans": [ + { + "bbox": [ + 304, + 621, + 545, + 669 + ], + "type": "text", + "content": "However, the regularized PSM objective in (3) does not allow to propagate the RED updates on " + }, + { + "bbox": [ + 304, + 621, + 545, + 669 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 621, + 545, + 669 + ], + "type": "text", + "content": " to the respective basis functions in an efficient manner. To overcome this difficulty, we perform a bilinear variable splitting " + }, + { + "bbox": [ + 304, + 621, + 545, + 669 + ], + "type": "inline_equation", + "content": "f = \\Lambda \\Psi^T" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "text", + "content": "1While many powerful denoisers satisfy these conditions [23], recent work [28] provides an alternative framework to explain the good performance of RED with denoisers not satisfying conditions in [23]." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "text", + "content": "10597" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 179, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 179, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 179, + 83 + ], + "type": "text", + "content": "and obtain our final formulation" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 75, + 89, + 287, + 131 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 89, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 75, + 89, + 287, + 131 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {f, \\Lambda , \\Psi} \\sum_ {t} \\| R _ {\\theta_ {t}} \\Lambda \\Psi_ {k} ^ {T} e _ {t} - g _ {t} \\| _ {2} ^ {2} + \\lambda \\rho (f e _ {t}) \\tag {5} \\\\ + \\xi \\| \\Psi \\| _ {F} ^ {2} + \\xi \\| \\Lambda \\| _ {F} ^ {2} \\quad \\mathrm {s . t .} \\quad f = \\Lambda \\Psi^ {T}. \\\\ \\end{array}", + "image_path": "93e68263a2fc1d98d32d09f0193cf2763993ba22b6a25667efd22aea064d478c.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 137, + 287, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 137, + 287, + 172 + ], + "spans": [ + { + "bbox": [ + 47, + 137, + 287, + 172 + ], + "type": "text", + "content": "Since the PSM is enforced as a hard constraint, the estimated object " + }, + { + "bbox": [ + 47, + 137, + 287, + 172 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 137, + 287, + 172 + ], + "type": "text", + "content": " is constrained to have " + }, + { + "bbox": [ + 47, + 137, + 287, + 172 + ], + "type": "inline_equation", + "content": "\\mathrm{rank}(f) \\leq K" + }, + { + "bbox": [ + 47, + 137, + 287, + 172 + ], + "type": "text", + "content": ". We propose an algorithm based on ADMM to solve (5)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 172, + 287, + 208 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 172, + 287, + 208 + ], + "spans": [ + { + "bbox": [ + 47, + 172, + 287, + 208 + ], + "type": "text", + "content": "To cast the problem with the PSM constraint into the ADMM framework, we form the augmented Lagrangian in the scaled form, [30, 31]" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 213, + 287, + 278 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 213, + 287, + 278 + ], + "spans": [ + { + "bbox": [ + 55, + 213, + 287, + 278 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\beta} [ \\Lambda , \\Psi , f; \\gamma ] = \\sum_ {t} \\left\\| R _ {\\theta_ {t}} \\Lambda \\Psi^ {T} e _ {t} - g _ {t} \\right\\| _ {2} ^ {2} + \\lambda \\rho (f e _ {t}) \\\\ + \\xi \\| \\Psi \\| _ {F} ^ {2} + \\xi \\| \\Lambda \\| _ {F} ^ {2} - \\frac {\\beta}{2} \\| \\gamma \\| _ {F} ^ {2} + \\frac {\\beta}{2} \\| \\Lambda \\Psi^ {T} - f + \\gamma \\| _ {F} ^ {2}, \\tag {6} \\\\ \\end{array}", + "image_path": "3a94f961d5d9ba6c1d1b35e982b12c3fb06aaf29c47aef4a03132243cc5908d0.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 286, + 287, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 286, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 286, + 287, + 312 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 286, + 287, + 312 + ], + "type": "inline_equation", + "content": "\\gamma \\in \\mathbb{R}^{P\\times J^2}" + }, + { + "bbox": [ + 47, + 286, + 287, + 312 + ], + "type": "text", + "content": " represents the scaled dual variable and " + }, + { + "bbox": [ + 47, + 286, + 287, + 312 + ], + "type": "inline_equation", + "content": "\\beta >0" + }, + { + "bbox": [ + 47, + 286, + 287, + 312 + ], + "type": "text", + "content": " is the penalty parameter." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 312, + 287, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 312, + 287, + 324 + ], + "spans": [ + { + "bbox": [ + 59, + 312, + 287, + 324 + ], + "type": "text", + "content": "Then, ADMM can be used to solve (6) as in Algorithm 1." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 48, + 335, + 148, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 335, + 148, + 346 + ], + "spans": [ + { + "bbox": [ + 48, + 335, + 148, + 346 + ], + "type": "text", + "content": "Algorithm 1 RED-PSM" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 349, + 287, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 349, + 287, + 374 + ], + "spans": [ + { + "bbox": [ + 47, + 349, + 287, + 374 + ], + "type": "text", + "content": "input: " + }, + { + "bbox": [ + 47, + 349, + 287, + 374 + ], + "type": "inline_equation", + "content": "\\Lambda^{(0)},\\Psi^{(0)},\\gamma^{(0)},f^{(0)} = \\Lambda^{(0)}\\Psi^{(0)T},\\beta >0," + }, + { + "bbox": [ + 47, + 349, + 287, + 374 + ], + "type": "inline_equation", + "content": "\\lambda >0,\\xi >0" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 54, + 376, + 154, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 376, + 154, + 388 + ], + "spans": [ + { + "bbox": [ + 54, + 376, + 154, + 388 + ], + "type": "text", + "content": "1: for " + }, + { + "bbox": [ + 54, + 376, + 154, + 388 + ], + "type": "inline_equation", + "content": "i \\in \\{1, \\dots, I\\}" + }, + { + "bbox": [ + 54, + 376, + 154, + 388 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 54, + 388, + 264, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 388, + 264, + 401 + ], + "spans": [ + { + "bbox": [ + 54, + 388, + 264, + 401 + ], + "type": "text", + "content": "2: " + }, + { + "bbox": [ + 54, + 388, + 264, + 401 + ], + "type": "inline_equation", + "content": "\\Lambda^{(i)} = \\arg \\min_{\\Lambda}\\{\\sum_t\\| R_{\\theta_t}\\Lambda \\Psi^{(i - 1)T}e_t - g_t\\| _2^2" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 54, + 417, + 256, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 417, + 256, + 430 + ], + "spans": [ + { + "bbox": [ + 54, + 417, + 256, + 430 + ], + "type": "text", + "content": "3: " + }, + { + "bbox": [ + 54, + 417, + 256, + 430 + ], + "type": "inline_equation", + "content": "\\Psi^{(i)} = \\arg \\min_{\\Psi}\\{\\sum_t\\| R_{\\theta_t}\\Lambda^{(i)}\\Psi^T e_t - g_t\\| _2^2" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 54, + 447, + 198, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 447, + 198, + 461 + ], + "spans": [ + { + "bbox": [ + 54, + 447, + 198, + 461 + ], + "type": "text", + "content": "4: " + }, + { + "bbox": [ + 54, + 447, + 198, + 461 + ], + "type": "inline_equation", + "content": "\\forall t:f_t^{(i)} = \\arg \\min_{f_t}\\{\\lambda \\rho (f_t)\\}" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 54, + 477, + 209, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 477, + 209, + 491 + ], + "spans": [ + { + "bbox": [ + 54, + 477, + 209, + 491 + ], + "type": "text", + "content": "5: " + }, + { + "bbox": [ + 54, + 477, + 209, + 491 + ], + "type": "inline_equation", + "content": "\\gamma^{(i)} = \\gamma^{(i - 1)} + \\Lambda^{(i)}\\Psi^{(i)T} - f^{(i)}" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 54, + 492, + 97, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 492, + 97, + 501 + ], + "spans": [ + { + "bbox": [ + 54, + 492, + 97, + 501 + ], + "type": "text", + "content": "6: end for" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 54, + 376, + 269, + 501 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 376, + 269, + 501 + ], + "spans": [ + { + "bbox": [ + 54, + 376, + 269, + 501 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} + \\frac {\\beta}{2} \\| \\Lambda \\Psi^ {(i - 1) T} - f ^ {(i - 1)} + \\gamma^ {(i - 1)} \\| _ {F} ^ {2} + \\xi \\| \\Lambda \\| _ {F} ^ {2} \\} \\\\ + \\frac {\\beta}{2} \\| \\Lambda^ {(i)} \\Psi^ {T} + \\gamma^ {(i - 1)} - f ^ {(i - 1)} \\| _ {F} ^ {2} + \\xi \\| \\Psi \\| _ {F} ^ {2} \\} \\\\ + \\frac {\\beta}{2} \\| (\\Lambda^ {(i)} \\Psi^ {(i) T} + \\gamma^ {(i - 1)}) e _ {t} - f _ {t} \\| _ {2} ^ {2} \\rbrace \\\\ \\end{array}", + "image_path": "90e6a108bd77d0cf815d88dde1d6d1b1d7b06ba4764e428e033ceeb0e31ffd94.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 518, + 287, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 518, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 47, + 518, + 287, + 578 + ], + "type": "text", + "content": "Line 4 in Algorithm 1 corresponds to the variational denoising of " + }, + { + "bbox": [ + 47, + 518, + 287, + 578 + ], + "type": "inline_equation", + "content": "(\\Lambda^{(i)}\\Psi^{(i)T} + \\gamma^{(i - 1)})e_t" + }, + { + "bbox": [ + 47, + 518, + 287, + 578 + ], + "type": "text", + "content": " with regularization " + }, + { + "bbox": [ + 47, + 518, + 287, + 578 + ], + "type": "inline_equation", + "content": "\\lambda \\rho (f_t)" + }, + { + "bbox": [ + 47, + 518, + 287, + 578 + ], + "type": "text", + "content": ". Algorithm 1 is reformulated into Algorithm 2 to use RED as in [23] and [28], where " + }, + { + "bbox": [ + 47, + 518, + 287, + 578 + ], + "type": "inline_equation", + "content": "D_{\\phi}" + }, + { + "bbox": [ + 47, + 518, + 287, + 578 + ], + "type": "text", + "content": " is the denoiser for which we have the gradient rule" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 119, + 585, + 287, + 598 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 585, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 119, + 585, + 287, + 598 + ], + "type": "interline_equation", + "content": "\\nabla \\rho (f _ {t}) = f _ {t} - D _ {\\phi} (f _ {t}) \\tag {7}", + "image_path": "08d2838551246c9296ff27aefc96707cdc142b3c16f4993a3ccb2e1df2b8029a.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 605, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 287, + 664 + ], + "type": "text", + "content": "and each " + }, + { + "bbox": [ + 47, + 605, + 287, + 664 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 47, + 605, + 287, + 664 + ], + "type": "text", + "content": " update in Step 4 is a single fixed-point iteration step using the approach of early stopping [29] (Sec. 4.3.2). In contrast to an iterative method to perform Line 4 in Algorithm 1, Step 4 in Algorithm 2 requires only single use of the denoiser per iteration of ADMM." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 47, + 671, + 185, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 185, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 185, + 684 + ], + "type": "text", + "content": "4.3. Regularization Denoiser" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "The regularization denoiser " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "D_{\\phi}" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " has a DnCNN [32] architecture and was trained in a supervised manner on a training" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 72, + 489, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 489, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 489, + 84 + ], + "type": "text", + "content": "Algorithm 2 RED-PSM with efficient " + }, + { + "bbox": [ + 306, + 72, + 489, + 84 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 306, + 72, + 489, + 84 + ], + "type": "text", + "content": " step" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 85, + 545, + 106 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 85, + 545, + 106 + ], + "spans": [ + { + "bbox": [ + 306, + 85, + 545, + 106 + ], + "type": "text", + "content": "Note: Inputs, and Lines 1-3 & 5-6 are the same as Algorithm 1." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 310, + 107, + 545, + 123 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 107, + 545, + 123 + ], + "spans": [ + { + "bbox": [ + 310, + 107, + 545, + 123 + ], + "type": "interline_equation", + "content": "4: \\forall t: f _ {t} ^ {(i)} = \\frac {\\lambda}{\\lambda + \\beta} D _ {\\phi} (f _ {t} ^ {(i - 1)}) + \\frac {\\beta}{\\lambda + \\beta} \\big (\\Lambda^ {(i)} \\Psi^ {(i) T} + \\gamma^ {(i - 1)} \\big) e _ {t}", + "image_path": "4c94c84ba2280aa946f7aaf77607c30728db9940536668f6316f0acd4bb27ef3.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 146, + 545, + 195 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 146, + 545, + 195 + ], + "spans": [ + { + "bbox": [ + 305, + 146, + 545, + 195 + ], + "type": "text", + "content": "set of static 2D slices " + }, + { + "bbox": [ + 305, + 146, + 545, + 195 + ], + "type": "inline_equation", + "content": "f_{i} \\in \\mathbb{R}^{J^{2}}" + }, + { + "bbox": [ + 305, + 146, + 545, + 195 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 146, + 545, + 195 + ], + "type": "inline_equation", + "content": "i = 1, \\dots, N" + }, + { + "bbox": [ + 305, + 146, + 545, + 195 + ], + "type": "text", + "content": " assuming that such data will be available in the settings of interest. Thus, the RED steps are agnostic to the specific motion type. The training objective for the denoiser is" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 373, + 204, + 545, + 228 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 204, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 373, + 204, + 545, + 228 + ], + "type": "interline_equation", + "content": "\\min _ {\\phi} \\sum_ {i} \\| f _ {i} - D _ {\\phi} (\\tilde {f} _ {i}) \\| _ {F} ^ {2} \\tag {8}", + "image_path": "93ebb057e848fe5b78c892edcc8ad9c834dae164845299733f9ad27f5e510fd5.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 239, + 545, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 239, + 545, + 287 + ], + "spans": [ + { + "bbox": [ + 305, + 239, + 545, + 287 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 239, + 545, + 287 + ], + "type": "inline_equation", + "content": "\\tilde{f}_i = f_i + \\eta_i" + }, + { + "bbox": [ + 305, + 239, + 545, + 287 + ], + "type": "text", + "content": ", and the injected noise " + }, + { + "bbox": [ + 305, + 239, + 545, + 287 + ], + "type": "inline_equation", + "content": "\\eta_{i}\\sim \\mathcal{N}(0,\\sigma_{i}^{2}I)" + }, + { + "bbox": [ + 305, + 239, + 545, + 287 + ], + "type": "text", + "content": " has noise level " + }, + { + "bbox": [ + 305, + 239, + 545, + 287 + ], + "type": "inline_equation", + "content": "\\sigma_{i}\\sim U[0,\\sigma_{\\mathrm{max}}]" + }, + { + "bbox": [ + 305, + 239, + 545, + 287 + ], + "type": "text", + "content": " spanning a range of values, so that the denoiser learns to denoise data with various noise levels." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 297, + 432, + 309 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 297, + 432, + 309 + ], + "spans": [ + { + "bbox": [ + 306, + 297, + 432, + 309 + ], + "type": "text", + "content": "4.4. Convergence Analysis" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 316, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 316, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 316, + 545, + 472 + ], + "type": "text", + "content": "In [33](Section V.), we follow an approach along the lines of [34] to analyze convergence. We show that under mild technical conditions, the objective in Algorithm 1 is guaranteed to converge (with increasing number " + }, + { + "bbox": [ + 305, + 316, + 545, + 472 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 305, + 316, + 545, + 472 + ], + "type": "text", + "content": " of iterations) to a value corresponding to a stationary point of the Lagrangian, that is, satisfying the necessary conditions for first order optimality. In practice, Algorithm 2 with the efficient " + }, + { + "bbox": [ + 305, + 316, + 545, + 472 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 305, + 316, + 545, + 472 + ], + "type": "text", + "content": " step version, which we implemented and used in the experiments reported in Section 5 has better run times, and rapid empirical convergence. However, its analysis requires additional steps, which are not particularly illuminating. Thus, following the tradition in related analyses [29, 35], we focus on the analysis of the nominal Algorithm 1." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 483, + 387, + 496 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 483, + 387, + 496 + ], + "spans": [ + { + "bbox": [ + 306, + 483, + 387, + 496 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 502, + 368, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 502, + 368, + 514 + ], + "spans": [ + { + "bbox": [ + 306, + 502, + 368, + 514 + ], + "type": "text", + "content": "5.1. Datasets" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 317, + 521, + 522, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 521, + 522, + 533 + ], + "spans": [ + { + "bbox": [ + 317, + 521, + 522, + 533 + ], + "type": "text", + "content": "Three categories of data sets are used in this work." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 305, + 534, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 534, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 305, + 534, + 545, + 689 + ], + "type": "text", + "content": "Walnut Dataset: We use the CT reconstructions of two different (static) walnut objects from the publicly available 3D walnut CT dataset [36]. We create a dynamic test object by synthetically warping the central axial slice of one of the walnut objects using a sinusoidal piecewise-affine time-varying warp [37]. To be precise, the image is divided into a " + }, + { + "bbox": [ + 305, + 534, + 545, + 689 + ], + "type": "inline_equation", + "content": "J \\times J" + }, + { + "bbox": [ + 305, + 534, + 545, + 689 + ], + "type": "text", + "content": " uniformly spaced rectangular grid, and the following vertical displacement is applied on each row separately to drive the temporally varying warp " + }, + { + "bbox": [ + 305, + 534, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\Delta_{j,t} = -C(t)\\sin(3\\pi j / J)" + }, + { + "bbox": [ + 305, + 534, + 545, + 689 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 534, + 545, + 689 + ], + "type": "inline_equation", + "content": "j \\in \\{0, \\dots, J-1\\}" + }, + { + "bbox": [ + 305, + 534, + 545, + 689 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 534, + 545, + 689 + ], + "type": "inline_equation", + "content": "C(t)" + }, + { + "bbox": [ + 305, + 534, + 545, + 689 + ], + "type": "text", + "content": " is a linearly increasing function of " + }, + { + "bbox": [ + 305, + 534, + 545, + 689 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 534, + 545, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 534, + 545, + 689 + ], + "type": "inline_equation", + "content": "C(0) = 0" + }, + { + "bbox": [ + 305, + 534, + 545, + 689 + ], + "type": "text", + "content": ". Static axial, coronal, and sagittal slices of the other walnut object are used to train the denoiser " + }, + { + "bbox": [ + 305, + 534, + 545, + 689 + ], + "type": "inline_equation", + "content": "D_{\\phi}" + }, + { + "bbox": [ + 305, + 534, + 545, + 689 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Compressed Object Dataset: This data set is obtained from a materials science experiment [38] with a sequence" + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "type": "text", + "content": "10598" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "of nine increasing compression steps applied to an object, with a full set of radiographic projections collected (using Carl Zeiss Xradia 520 Versa) and reconstructed by the instrument's software at each step. Using this quasi-static data set, a fixed axial slice is extracted from each reconstruction. Nine extracted slices are interpolated to " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " time frames using a recent deep learning-based video interpolation algorithm [39]. The denoiser " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "D_{\\phi}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " for our experiments on this data set was trained using the axial slices of the static pre-compression and post-compression objects, which would be available in actual dynamic loading experiments." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 204, + 287, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 204, + 287, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 287, + 252 + ], + "type": "text", + "content": "We note that all algorithms compared in this paper are agnostic to both the synthetic warp applied on the static walnut slice and to the data-driven interpolation method used for the compressed object." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 252, + 290, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 290, + 432 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 290, + 432 + ], + "type": "text", + "content": "Spatio-temporal projection data for each dataset is simulated by a parallel-beam projection with " + }, + { + "bbox": [ + 46, + 252, + 290, + 432 + ], + "type": "inline_equation", + "content": "J = 128" + }, + { + "bbox": [ + 46, + 252, + 290, + 432 + ], + "type": "text", + "content": " detector bins of the dynamic phantoms, a single projection at each of the " + }, + { + "bbox": [ + 46, + 252, + 290, + 432 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 252, + 290, + 432 + ], + "type": "text", + "content": " time instants. The sequence of projection angles " + }, + { + "bbox": [ + 46, + 252, + 290, + 432 + ], + "type": "inline_equation", + "content": "\\{\\theta_t\\}_{t=0}^{P-1}" + }, + { + "bbox": [ + 46, + 252, + 290, + 432 + ], + "type": "text", + "content": " (a free experimental design parameter) was chosen to follow the bit-reversed view angle sampling scheme, which has been shown [16] to provide an especially favorable conditioning of the recovery problem. The simulated measurements are corrupted using AWGN with standard deviation " + }, + { + "bbox": [ + 46, + 252, + 290, + 432 + ], + "type": "inline_equation", + "content": "\\sigma = 5 \\cdot 10^{-3}" + }, + { + "bbox": [ + 46, + 252, + 290, + 432 + ], + "type": "text", + "content": ". This noise level leads to the FBP (with Ram-Lak filter) of the full set of " + }, + { + "bbox": [ + 46, + 252, + 290, + 432 + ], + "type": "inline_equation", + "content": "P = 512" + }, + { + "bbox": [ + 46, + 252, + 290, + 432 + ], + "type": "text", + "content": " projections at each time instant having a PSNR of approximately 46 dB. When, in the actual experiments with sequentially sampled data, only " + }, + { + "bbox": [ + 46, + 252, + 290, + 432 + ], + "type": "inline_equation", + "content": "1 / P" + }, + { + "bbox": [ + 46, + 252, + 290, + 432 + ], + "type": "text", + "content": " of this data is used, the PSNR of the reconstruction may be expected to be lower." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 433, + 279, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 433, + 279, + 444 + ], + "spans": [ + { + "bbox": [ + 59, + 433, + 279, + 444 + ], + "type": "text", + "content": "Ground-truth frames for " + }, + { + "bbox": [ + 59, + 433, + 279, + 444 + ], + "type": "inline_equation", + "content": "P = 4" + }, + { + "bbox": [ + 59, + 433, + 279, + 444 + ], + "type": "text", + "content": " are shown in Figure 2." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 445, + 287, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 515 + ], + "type": "text", + "content": "Cardiac dMRI Dataset: For a more direct comparison with the setting and data used in dMRI works, we also test RED-PSM on the \"retrospective\" cardiac dMRI data in [20]. The data includes 23 distinct time frames for one cardiac cycle. Details of the data and experiments are in Section 5.4.3." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 53, + 525, + 281, + 612 + ], + "blocks": [ + { + "bbox": [ + 53, + 525, + 281, + 612 + ], + "lines": [ + { + "bbox": [ + 53, + 525, + 281, + 612 + ], + "spans": [ + { + "bbox": [ + 53, + 525, + 281, + 612 + ], + "type": "image", + "image_path": "167e7ee59929a2e09799f5eb620bee3fe2b5b7151ec889e57e91482f07e5ab23.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 613, + 287, + 647 + ], + "lines": [ + { + "bbox": [ + 46, + 613, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 613, + 287, + 647 + ], + "type": "text", + "content": "Figure 2: Ground-truth frames for the time-varying walnut (top) and compressed object (bottom) datasets, uniformly sampled in time, " + }, + { + "bbox": [ + 46, + 613, + 287, + 647 + ], + "type": "inline_equation", + "content": "t \\in \\{0, \\dots, P - 1\\}" + }, + { + "bbox": [ + 46, + 613, + 287, + 647 + ], + "type": "text", + "content": ", for " + }, + { + "bbox": [ + 46, + 613, + 287, + 647 + ], + "type": "inline_equation", + "content": "P = 4" + }, + { + "bbox": [ + 46, + 613, + 287, + 647 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 658, + 153, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 153, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 153, + 670 + ], + "type": "text", + "content": "5.2. Baseline Methods" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": "PSM-TV: Similar to the proposed approach, this algorithm also uses a partially separable model to represent the object with a different regularization type. For PSM-TV," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": "regularization penalizes the " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": "-norm of the discrete 2D total variation of the temporal slices of " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": " at each time instant. To this end, the constraint " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "f = \\Lambda \\Psi^T" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": " is implemented by substitution into the objective in (5), and the definition of " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": " is changed to " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "\\rho (\\Lambda \\Psi^T e_t) = \\mathrm{TV}(\\Lambda \\Psi^T e_t)" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": ", and the rest of the objective is kept the same. The unconstrained problem is then solved for " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "\\{\\hat{\\Lambda},\\hat{\\Psi}\\}" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": " (using, as a convenient implementation, the Adam optimizer in Pytorch). Finally, the estimated object is obtained as " + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "inline_equation", + "content": "\\hat{f} = \\hat{\\Lambda}\\hat{\\Psi}^{T}" + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "text", + "content": "TD-DIP [20]: TD-DIP is a recent method based on the Deep Image Prior (DIP) approach. It uses a mapping network " + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "inline_equation", + "content": "M_{\\alpha}" + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "text", + "content": " and a generative model " + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "inline_equation", + "content": "N_{\\beta}" + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "text", + "content": " sequentially to obtain the estimated object at each time instant " + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "text", + "content": " from fixed and handcrafted latent representations " + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "inline_equation", + "content": "\\chi_t" + }, + { + "bbox": [ + 304, + 180, + 545, + 264 + ], + "type": "text", + "content": ". Because TD-DIP was originally proposed for dynamic MRI, we modified the objective minimally for dynamic tomography as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 341, + 273, + 545, + 297 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 273, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 341, + 273, + 545, + 297 + ], + "type": "interline_equation", + "content": "\\min _ {\\alpha , \\beta} \\sum_ {t} \\| g _ {t} - R _ {\\theta (t)} \\left(\\left(N _ {\\beta} \\circ M _ {\\alpha}\\right) (\\chi_ {t})\\right) \\| ^ {2}. \\tag {9}", + "image_path": "79b0d2abeea894a28c8ac26c2f86f3346a3f7bdb343ea56d27d02b367bcc1ff7.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 306, + 546, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 546, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 546, + 449 + ], + "type": "text", + "content": "For the comparisons in this work, identical mapping network and generator architectures, latent representation dimensionality, optimizer, learning rate, and decay schemes are used as in the available online implementation [40]. The original work focuses on the beating heart problem and thus proposes a helix-shaped latent manifold for " + }, + { + "bbox": [ + 304, + 306, + 546, + 449 + ], + "type": "inline_equation", + "content": "\\chi_t" + }, + { + "bbox": [ + 304, + 306, + 546, + 449 + ], + "type": "text", + "content": " with cycles equal to the number of heartbeats during measurement acquisition. Since we do not have a repetition assumption for the motion types included in this paper, we use a linear manifold as explained in the original paper [20]. Thus, the method is sometimes denoted as \"TD-DIP (L)\" in Section 5.4 for clarification." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 458, + 432, + 471 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 458, + 432, + 471 + ], + "spans": [ + { + "bbox": [ + 306, + 458, + 432, + 471 + ], + "type": "text", + "content": "5.3. Experimental Settings" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 477, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 477, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 477, + 545, + 548 + ], + "type": "text", + "content": "All methods are run on a workstation with an Intel(R) Xeon(R) Gold 5320 CPU and NVIDIA RTX A6000 GPU. In practice, we used a minor variation of Algorithm 2, where we combined the subproblems in " + }, + { + "bbox": [ + 304, + 477, + 545, + 548 + ], + "type": "inline_equation", + "content": "\\Lambda" + }, + { + "bbox": [ + 304, + 477, + 545, + 548 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 477, + 545, + 548 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 304, + 477, + 545, + 548 + ], + "type": "text", + "content": ", and minimized with respect to both basis functions simultaneously using gradient descent with Adam [41] optimizer." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 549, + 545, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 549, + 545, + 657 + ], + "spans": [ + { + "bbox": [ + 304, + 549, + 545, + 657 + ], + "type": "text", + "content": "Denoiser training. The upper limit for noise level used in training the denoiser was set to " + }, + { + "bbox": [ + 304, + 549, + 545, + 657 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{max}} = 5 \\cdot 10^{-2}" + }, + { + "bbox": [ + 304, + 549, + 545, + 657 + ], + "type": "text", + "content": ". For the dynamic walnut object, the denoiser " + }, + { + "bbox": [ + 304, + 549, + 545, + 657 + ], + "type": "inline_equation", + "content": "D_{\\phi}" + }, + { + "bbox": [ + 304, + 549, + 545, + 657 + ], + "type": "text", + "content": " is trained on the central 200 axial, 200 sagittal, and 200 coronal slices of another walnut CT reconstruction downsampled to size " + }, + { + "bbox": [ + 304, + 549, + 545, + 657 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 304, + 549, + 545, + 657 + ], + "type": "text", + "content": ". For the compressed object, axial slices of precompression and post-compression static objects, containing 462 slices in total, are used to train " + }, + { + "bbox": [ + 304, + 549, + 545, + 657 + ], + "type": "inline_equation", + "content": "D_{\\phi}" + }, + { + "bbox": [ + 304, + 549, + 545, + 657 + ], + "type": "text", + "content": ". For the cardiac MRI setting, the denoiser was trained on the static MRI" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "text", + "content": "2It would be interesting to include yet another baseline method - the DIP-based PSM approach [22] (also developed for MRI). However we were unable to do so as an implementation of this method was not available, and because of potential issues with replicating its performance and adapting to our CT problem." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "text", + "content": "10599" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 72, + 175, + 247 + ], + "blocks": [ + { + "bbox": [ + 47, + 72, + 175, + 247 + ], + "lines": [ + { + "bbox": [ + 47, + 72, + 175, + 247 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 175, + 247 + ], + "type": "image", + "image_path": "e0541d9605d18db12e067518136d5ba9e4b6eb2c29d7eb6b551fa239663f906f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 247, + 547, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 247, + 547, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 547, + 291 + ], + "type": "text", + "content": "Figure 3: Reconstruction PSNR, SSIM, MAE, and HFEN for the time-varying walnut object (top) and compressed material (bottom) vs. " + }, + { + "bbox": [ + 46, + 247, + 547, + 291 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 247, + 547, + 291 + ], + "type": "text", + "content": " using different methods. For TD-DIP, accuracy statistics for the best PSNR reconstruction during optimization are reported assuming such an oracle is available. The minimum and maximum values are indicated with error bars and the mean values are connected by the dashed line for different " + }, + { + "bbox": [ + 46, + 247, + 547, + 291 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 247, + 547, + 291 + ], + "type": "text", + "content": " for three different runs." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 173, + 72, + 298, + 247 + ], + "blocks": [ + { + "bbox": [ + 173, + 72, + 298, + 247 + ], + "lines": [ + { + "bbox": [ + 173, + 72, + 298, + 247 + ], + "spans": [ + { + "bbox": [ + 173, + 72, + 298, + 247 + ], + "type": "image", + "image_path": "9f646b60d1e06fdcbfa357f67ec74177b15273069d3abf96a20fa5aaaa1bd6ac.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 299, + 72, + 423, + 247 + ], + "blocks": [ + { + "bbox": [ + 299, + 72, + 423, + 247 + ], + "lines": [ + { + "bbox": [ + 299, + 72, + 423, + 247 + ], + "spans": [ + { + "bbox": [ + 299, + 72, + 423, + 247 + ], + "type": "image", + "image_path": "6f97db83192577f02658f4ef1b4145ce0fa26e8dcc8b9ae4a2cdaebb931cee81.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 424, + 72, + 549, + 247 + ], + "blocks": [ + { + "bbox": [ + 424, + 72, + 549, + 247 + ], + "lines": [ + { + "bbox": [ + 424, + 72, + 549, + 247 + ], + "spans": [ + { + "bbox": [ + 424, + 72, + 549, + 247 + ], + "type": "image", + "image_path": "151dd039336443623d6b5a98dadac46eb6981e548f13e1e3a5192876a50d4d55.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 48, + 297, + 288, + 438 + ], + "blocks": [ + { + "bbox": [ + 48, + 297, + 288, + 438 + ], + "lines": [ + { + "bbox": [ + 48, + 297, + 288, + 438 + ], + "spans": [ + { + "bbox": [ + 48, + 297, + 288, + 438 + ], + "type": "table", + "html": "
(a) Walnut(b) Compressed Material
PMethodPSNR (dB)SSIMMAE (1e-3)HFENPSNR (dB)SSIMMAE (1e-2)HFEN
32PSM-TV (R)21.10.6782.91.0422.50.6972.911.6
TD-DIP (L)22.50.8822.10.8725.40.9091.58.1
RED-PSM (Pr)22.70.9141.50.7923.90.9161.29.9
64PSM-TV (R)24.00.8791.90.9425.60.8451.810.7
TD-DIP (L)25.60.9161.50.7429.00.9471.16.5
RED-PSM (Pr)26.40.9580.90.5729.30.9520.56.0
128PSM-TV (R)26.80.9121.40.7829.20.9071.19.6
TD-DIP (L)29.00.9531.00.5032.40.9530.85.1
RED-PSM (Pr)29.90.9780.60.4333.10.9720.44.7
256PSM-TV (R)30.10.9341.00.6331.90.9630.78.0
TD-DIP (L)31.70.9660.80.4534.70.9660.74.6
RED-PSM (Pr)33.80.9870.40.3235.90.9860.34.4
", + "image_path": "978668ae12f3598e4d34b50d8566c5318abed270d3f8ccef1a876144535b7cdf.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 440, + 287, + 485 + ], + "lines": [ + { + "bbox": [ + 46, + 440, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 440, + 287, + 485 + ], + "type": "text", + "content": "Table 1: Reconstruction accuracies for different " + }, + { + "bbox": [ + 46, + 440, + 287, + 485 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 440, + 287, + 485 + ], + "type": "text", + "content": ". Random (R) and ProSep (Pr) initialization for the PSM methods. For TD-DIP, the reported accuracies are for the best PSNR using a \"stopping oracle\", averaged over three runs with random initial conditions." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 492, + 287, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 492, + 287, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 492, + 287, + 589 + ], + "type": "text", + "content": "training slices of the ACDC dataset [42]. For all datasets, " + }, + { + "bbox": [ + 46, + 492, + 287, + 589 + ], + "type": "inline_equation", + "content": "D_{\\phi}" + }, + { + "bbox": [ + 46, + 492, + 287, + 589 + ], + "type": "text", + "content": " is trained for 500 epochs using the Adam optimizer with a learning rate of " + }, + { + "bbox": [ + 46, + 492, + 287, + 589 + ], + "type": "inline_equation", + "content": "5 \\cdot 10^{-3}" + }, + { + "bbox": [ + 46, + 492, + 287, + 589 + ], + "type": "text", + "content": ". Each convolutional layer is followed by a ReLU nonlinearity except for the final layer, which has a single-channel output. We test both direct and residual DnCNN denoisers where the former predicts the denoised image and the latter estimates the noise from the noisy input." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 590, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 287, + 639 + ], + "type": "text", + "content": "Architectural details for denoisers used in our experiments are provided in Table 6 in Supplementary Material C. We use a fixed pre-trained denoiser for all " + }, + { + "bbox": [ + 46, + 590, + 287, + 639 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 590, + 287, + 639 + ], + "type": "text", + "content": " for the same object type." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 640, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 640, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 640, + 287, + 676 + ], + "type": "text", + "content": "Temporal Basis. In all experiments, we use a fixed basis " + }, + { + "bbox": [ + 46, + 640, + 287, + 676 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 46, + 640, + 287, + 676 + ], + "type": "text", + "content": " as a cubic spline interpolator to interpolate the low-dimensional temporal representation " + }, + { + "bbox": [ + 46, + 640, + 287, + 676 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 640, + 287, + 676 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 640, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 46, + 640, + 287, + 676 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Initialization. Unless stated otherwise, spatial and temporal basis functions are initialized using the SVD truncated to order " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " the rank of the dynamic object estimate pro" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 299, + 545, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 299, + 545, + 370 + ], + "spans": [ + { + "bbox": [ + 304, + 299, + 545, + 370 + ], + "type": "text", + "content": "duced by a recent projection-domain PSM-based method \"ProSep\" [17]. If the ProSep estimate has rank smaller than " + }, + { + "bbox": [ + 304, + 299, + 545, + 370 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 299, + 545, + 370 + ], + "type": "text", + "content": ", the remaining basis functions are initialized as 0. Otherwise, all spatial basis functions are initialized as 0 and the latent representations " + }, + { + "bbox": [ + 304, + 299, + 545, + 370 + ], + "type": "inline_equation", + "content": "z_{k}" + }, + { + "bbox": [ + 304, + 299, + 545, + 370 + ], + "type": "text", + "content": " of the temporal basis functions are initialized randomly as " + }, + { + "bbox": [ + 304, + 299, + 545, + 370 + ], + "type": "inline_equation", + "content": "z_{k} \\sim \\mathcal{N}(0, I)" + }, + { + "bbox": [ + 304, + 299, + 545, + 370 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 371, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 371, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 371, + 545, + 407 + ], + "type": "text", + "content": "Tomographic Acquisition Scheme. All methods mentioned in this paper use the bit-reversed angular sampling scheme, over the range " + }, + { + "bbox": [ + 304, + 371, + 545, + 407 + ], + "type": "inline_equation", + "content": "[0,\\pi ]" + }, + { + "bbox": [ + 304, + 371, + 545, + 407 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 407, + 545, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 537 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 537 + ], + "type": "text", + "content": "Run Times. For " + }, + { + "bbox": [ + 304, + 407, + 545, + 537 + ], + "type": "inline_equation", + "content": "P = 256" + }, + { + "bbox": [ + 304, + 407, + 545, + 537 + ], + "type": "text", + "content": " and using the specified computational resources and parameter settings, To achieve the peak PSNR during optimization, RED-PSM with ProSep initialization requires " + }, + { + "bbox": [ + 304, + 407, + 545, + 537 + ], + "type": "inline_equation", + "content": "50 <" + }, + { + "bbox": [ + 304, + 407, + 545, + 537 + ], + "type": "text", + "content": " iterations " + }, + { + "bbox": [ + 304, + 407, + 545, + 537 + ], + "type": "inline_equation", + "content": "< 150" + }, + { + "bbox": [ + 304, + 407, + 545, + 537 + ], + "type": "text", + "content": " taking about 2 to 6 minutes whereas TD-DIP with batch size " + }, + { + "bbox": [ + 304, + 407, + 545, + 537 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 407, + 545, + 537 + ], + "type": "text", + "content": " typically requires " + }, + { + "bbox": [ + 304, + 407, + 545, + 537 + ], + "type": "inline_equation", + "content": "> 30k" + }, + { + "bbox": [ + 304, + 407, + 545, + 537 + ], + "type": "text", + "content": " steps, taking about 3.5 hours to complete. Hence, RED-PSM provides a speedup over TD-DIP by a factor of 35 to 105 to reach its peak performance. We note that based on the parameter configuration, the speedup factor may vary. However, the proposed method provides a significant run time reduction in all cases." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 538, + 545, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 538, + 545, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 538, + 545, + 634 + ], + "type": "text", + "content": "Evaluation Metrics. Four quantitative metrics were implemented for evaluating reconstruction accuracy (i) the peak signal-to-noise ratio (PSNR) in dB; (ii) the structural similarity index (SSIM) [43]; (iii) the mean absolute error (MAE); and (iv) the high-frequency error norm (HFEN) [44] defined as " + }, + { + "bbox": [ + 304, + 538, + 545, + 634 + ], + "type": "inline_equation", + "content": "\\mathrm{HFEN}(f, f_r) = \\| \\mathrm{LoG}(f) - \\mathrm{LoG}(f_r)\\|_2" + }, + { + "bbox": [ + 304, + 538, + 545, + 634 + ], + "type": "text", + "content": " where LoG is a rotationally symmetric Laplacian of Gaussian filter with a standard deviation of 1.5 pixels." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 640, + 362, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 640, + 362, + 651 + ], + "spans": [ + { + "bbox": [ + 306, + 640, + 362, + 651 + ], + "type": "text", + "content": "5.4. Results" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 658, + 515, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 515, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 515, + 670 + ], + "type": "text", + "content": "5.4.1 Reconstruction accuracies for different " + }, + { + "bbox": [ + 306, + 658, + 515, + 670 + ], + "type": "inline_equation", + "content": "P" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "In Figure 3 and Table 1, the performance of RED-PSM is compared with PSM-TV and with TD-DIP that uses a linear latent representation for both objects. While Figure 3" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "type": "text", + "content": "10600" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 69, + 529, + 305 + ], + "blocks": [ + { + "bbox": [ + 58, + 69, + 529, + 305 + ], + "lines": [ + { + "bbox": [ + 58, + 69, + 529, + 305 + ], + "spans": [ + { + "bbox": [ + 58, + 69, + 529, + 305 + ], + "type": "image", + "image_path": "f25bcfea3f73944bbeba99e933c8adedc629c6e5457815e6e72036b47ad23ff2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 308, + 546, + 331 + ], + "lines": [ + { + "bbox": [ + 46, + 308, + 546, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 546, + 331 + ], + "type": "text", + "content": "Figure 4: Comparison of reconstructed object frames at two time instants using different methods for " + }, + { + "bbox": [ + 46, + 308, + 546, + 331 + ], + "type": "inline_equation", + "content": "P = 256" + }, + { + "bbox": [ + 46, + 308, + 546, + 331 + ], + "type": "text", + "content": ", and the corresponding normalized absolute reconstruction errors for (A) the time-varying walnut, and (B) compressed object." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 338, + 289, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 289, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 289, + 504 + ], + "type": "text", + "content": "facilitates the comparison of metrics for different " + }, + { + "bbox": [ + 46, + 338, + 289, + 504 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 338, + 289, + 504 + ], + "type": "text", + "content": " for the various methods, since the range of metrics is very large for varying " + }, + { + "bbox": [ + 46, + 338, + 289, + 504 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 338, + 289, + 504 + ], + "type": "text", + "content": ". Table 1 emphasizes important differences between methods for the same " + }, + { + "bbox": [ + 46, + 338, + 289, + 504 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 338, + 289, + 504 + ], + "type": "text", + "content": ", and provides detail for a more precise quantitative comparison. As expected, the estimates improve with increasing " + }, + { + "bbox": [ + 46, + 338, + 289, + 504 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 338, + 289, + 504 + ], + "type": "text", + "content": " for all methods. In terms of PSNR, the proposed algorithm performs on par with or better than the best PSNR TD-DIP estimate for various " + }, + { + "bbox": [ + 46, + 338, + 289, + 504 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 338, + 289, + 504 + ], + "type": "text", + "content": ", with improvement for RED-PSM enhancing with the increase in " + }, + { + "bbox": [ + 46, + 338, + 289, + 504 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 338, + 289, + 504 + ], + "type": "text", + "content": ". Moreover, in terms of SSIM, MAE, and HFEN, the improvements with RED-PSM are even more significant. Although these observations are valid for both objects, for the walnut, RED-PSM provides slightly greater improvement over TD-DIP." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 508, + 289, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 289, + 699 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 289, + 699 + ], + "type": "text", + "content": "Figure 4 compares the reconstructions for both objects at two different " + }, + { + "bbox": [ + 46, + 508, + 289, + 699 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 508, + 289, + 699 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 508, + 289, + 699 + ], + "type": "inline_equation", + "content": "P = 256" + }, + { + "bbox": [ + 46, + 508, + 289, + 699 + ], + "type": "text", + "content": ". As expected, providing blurry reconstructions lacking finer details for both objects, PSM-TV performs the worst among the compared methods. The TD-DIP reconstructions contain visible noise-like artifacts on the piecewise constant regions of the walnut object, which are alleviated by RED-PSM. This observation manifests itself also in the absolute difference figures, with error for TD-DIP distributed throughout the interior regions of the walnut. Furthermore, RED-PSM preserves sharp details around the shell of the walnut better. Throughout the compressed material object for the given time frames, compared to TD-DIP, RED-PSM has an almost consistently smaller absolute error. This difference is more prominent around the highly dynamic regions of the object, emphasizing the advantage of the proposed method." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "In Figure 5, the reconstructed " + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "inline_equation", + "content": "x - t" + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": " cross-sections of the" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 338, + 547, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 547, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 547, + 422 + ], + "type": "text", + "content": "dynamic walnut are shown for different methods. The location of the cross-section is highlighted by a yellow line on the static " + }, + { + "bbox": [ + 304, + 338, + 547, + 422 + ], + "type": "inline_equation", + "content": "x - y" + }, + { + "bbox": [ + 304, + 338, + 547, + 422 + ], + "type": "text", + "content": " frame at " + }, + { + "bbox": [ + 304, + 338, + 547, + 422 + ], + "type": "inline_equation", + "content": "t = 0" + }, + { + "bbox": [ + 304, + 338, + 547, + 422 + ], + "type": "text", + "content": ". Consistent with the comparison in Figure 4, RED-PSM provides reduced absolute error values throughout the respective cross-section. Also, as more apparent in the error figures, TD-DIP produces higher background errors." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 439, + 433, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 439, + 433, + 451 + ], + "spans": [ + { + "bbox": [ + 305, + 439, + 433, + 451 + ], + "type": "text", + "content": "5.4.2 Effect of Initialization" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 460, + 547, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 547, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 547, + 604 + ], + "type": "text", + "content": "The initialization of " + }, + { + "bbox": [ + 304, + 460, + 547, + 604 + ], + "type": "inline_equation", + "content": "\\Lambda" + }, + { + "bbox": [ + 304, + 460, + 547, + 604 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 460, + 547, + 604 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 304, + 460, + 547, + 604 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 460, + 547, + 604 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 460, + 547, + 604 + ], + "type": "text", + "content": " plays an important role in the performance and convergence speed of RED-PSM. We observe significant speed-up when rather than a random initialization, we initialize the algorithm with ProSep [16] estimated reconstruction. Figure 7 shows PSNR vs. iterations comparison for different initialization techniques for the dynamic walnut object with " + }, + { + "bbox": [ + 304, + 460, + 547, + 604 + ], + "type": "inline_equation", + "content": "P = 256" + }, + { + "bbox": [ + 304, + 460, + 547, + 604 + ], + "type": "text", + "content": ". The rest of the parameters were selected identically as indicated in Table 5 in Supplementary Material. This experiment highlights the advantages of initializing with ProSep estimated basis functions: eliminating the need for multiple runs for a best-case result; and speeding up convergence considerably." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 621, + 479, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 621, + 479, + 634 + ], + "spans": [ + { + "bbox": [ + 305, + 621, + 479, + 634 + ], + "type": "text", + "content": "5.4.3 Cardiac dMRI data experiments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": "In this setting, different to the previous experiments, we used " + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "inline_equation", + "content": "4k" + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": "-space radial lines (\"spokes\") per frame at the bitreversed angles. 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Since the data is periodic, we also tested the helix latent scheme (H) for TD-DIP." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 237, + 286, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 237, + 286, + 283 + ], + "spans": [ + { + "bbox": [ + 46, + 237, + 286, + 283 + ], + "type": "text", + "content": "The metrics in Table 2 and the qualitative comparison in Figure 6 with zoomed-in reconstructions and absolute error maps, show that RED-PSM performs better than both versions of TD-DIP." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 52, + 293, + 278, + 462 + ], + "blocks": [ + { + "bbox": [ + 52, + 293, + 278, + 462 + ], + "lines": [ + { + "bbox": [ + 52, + 293, + 278, + 462 + ], + "spans": [ + { + "bbox": [ + 52, + 293, + 278, + 462 + ], + "type": "image", + "image_path": "c740dcf4dde0c91aa3c47502dc6ccc5c48d1690e962dc99a7e4f0cf0100b3b18.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 463, + 286, + 495 + ], + "lines": [ + { + "bbox": [ + 46, + 463, + 286, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 463, + 286, + 495 + ], + "type": "text", + "content": "Figure 6: Reconstructed frames for " + }, + { + "bbox": [ + 46, + 463, + 286, + 495 + ], + "type": "inline_equation", + "content": "P = 256" + }, + { + "bbox": [ + 46, + 463, + 286, + 495 + ], + "type": "text", + "content": " for retrospective dMRI data [20] with zoomed-in frames (middle row), and absolute reconstruction errors (last row)." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 67, + 502, + 264, + 567 + ], + "blocks": [ + { + "bbox": [ + 67, + 502, + 264, + 567 + ], + "lines": [ + { + "bbox": [ + 67, + 502, + 264, + 567 + ], + "spans": [ + { + "bbox": [ + 67, + 502, + 264, + 567 + ], + "type": "table", + "html": "
PMethodPSNR (dB)SSIMMAE (1e-2)HFEN
128TD-DIP (L)34.60.9231.73.38
TD-DIP (H)34.60.9281.73.32
RED-PSM36.60.9391.42.73
256TD-DIP (L)36.20.9481.43.47
TD-DIP (H)36.40.9471.43.44
RED-PSM38.40.9621.12.99
", + "image_path": "21f04080e7e1edf1048618b3e87f02bbc9267efe4a152e6a3e4478b35b0c8644.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 569, + 286, + 591 + ], + "lines": [ + { + "bbox": [ + 46, + 569, + 286, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 569, + 286, + 591 + ], + "type": "text", + "content": "Table 2: Reconstruction accuracies for RED-PSM and TD-DIP for the retrospective dMRI data [20]." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 598, + 252, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 598, + 252, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 598, + 252, + 611 + ], + "type": "text", + "content": "5.5. PSNR vs. " + }, + { + "bbox": [ + 47, + 598, + 252, + 611 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 598, + 252, + 611 + ], + "type": "text", + "content": ", and a Patch-Based Scheme" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 617, + 286, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 286, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 286, + 665 + ], + "type": "text", + "content": "In Supplementary Material A, we compare the PSNR of the reconstructed frames for each " + }, + { + "bbox": [ + 46, + 617, + 286, + 665 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 617, + 286, + 665 + ], + "type": "text", + "content": " for all methods for the walnut object with " + }, + { + "bbox": [ + 46, + 617, + 286, + 665 + ], + "type": "inline_equation", + "content": "P = 256" + }, + { + "bbox": [ + 46, + 617, + 286, + 665 + ], + "type": "text", + "content": " and show the consistently better performance of RED-PSM." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "content": "Also, in Supplementary Material B, to improve scalability to high-resolution and high-dimensional settings, we propose and evaluate a patch-based version of RED-PSM with a patch-based denoiser " + }, + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "inline_equation", + "content": "D_{\\phi}" + }, + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "content": ". In the experiments," + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 201, + 544, + 225 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 201, + 544, + 225 + ], + "spans": [ + { + "bbox": [ + 305, + 201, + 544, + 225 + ], + "type": "text", + "content": "the patch-based scheme provided reconstruction accuracies similar to those reported here for the original scheme." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 237, + 383, + 249 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 237, + 383, + 249 + ], + "spans": [ + { + "bbox": [ + 306, + 237, + 383, + 249 + ], + "type": "text", + "content": "6. Conclusions" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 257, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 257, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 257, + 545, + 437 + ], + "type": "text", + "content": "RED-PSM is the first PSM-based approach to dynamic imaging using a pre-trained and learned (RED-based) spatial prior. The objective in the proposed variational formulation is optimized using a novel and effective bilinear ADMM algorithm, which enforces the PSM as a hard constraint. Unlike existing PSM-based techniques, RED-PSM is supported by theoretical analysis, with a convergence guarantee to a stationary point of the objective. The results of the numerical experiments show better reconstruction accuracy and considerably faster run times compared to a recent DIP-based algorithm. A patch-based regularizer version of RED-PSM provides almost equivalent performance with a massive reduction of storage requirements, indicating the potential of our framework for dynamic high-resolution 2D or 3D settings." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "text", + "content": "Possible directions for future work include the application of RED-PSM to various imaging scenarios other than tomography and MRI, and robust denoiser training for the RED framework, since the deep denoisers encounter varying artifact distributions during optimization. This could also improve the generalizability of the framework to different input types." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 522, + 545, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 570 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 570 + ], + "type": "text", + "content": "Acknowledgements. This research was supported in part by Los Alamos National Labs under Subcontract No. 599416/CW13995. We thank Dr. Brian M. Patterson for providing the data for the compressed material experiments." + } + ] + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 344, + 583, + 506, + 670 + ], + "blocks": [ + { + "bbox": [ + 344, + 583, + 506, + 670 + ], + "lines": [ + { + "bbox": [ + 344, + 583, + 506, + 670 + ], + "spans": [ + { + "bbox": [ + 344, + 583, + 506, + 670 + ], + "type": "image", + "image_path": "6e8a2d405e3c354bf6928f9c643f0eb52a0818eb616d9694215e3f2c3ebb2ec0.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 669, + 545, + 713 + ], + "lines": [ + { + "bbox": [ + 304, + 669, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 669, + 545, + 713 + ], + "type": "text", + "content": "Figure 7: PSNR vs. iteration comparison for RED-PSM as described in Section 5.4.2. The area between the best and the worst PSNR for each iteration is shown in blue to highlight the varying performances of five different runs with random initialization." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "text", + "content": "10602" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] E. 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Bresler, \"MR image reconstruction from highly undersampled k-space data by dictionary learning,\" IEEE Transactions on Medical Imaging, vol. 30, no. 5, pp. 1028-1041, 2010." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 734, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 734, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 734, + 318, + 742 + ], + "type": "text", + "content": "10604" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/RFD-ECNet_ Extreme Underwater Image Compression with Reference to Feature Dictionary/cdd3e31c-4266-47f7-a8c7-755cca493958_content_list.json b/2023/RFD-ECNet_ Extreme Underwater Image Compression with Reference to Feature Dictionary/cdd3e31c-4266-47f7-a8c7-755cca493958_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9657d768ed435984de74645255b5c5eee388df79 --- /dev/null +++ b/2023/RFD-ECNet_ Extreme Underwater Image Compression with Reference to Feature Dictionary/cdd3e31c-4266-47f7-a8c7-755cca493958_content_list.json @@ -0,0 +1,1790 @@ +[ + { + "type": "text", + "text": "RFD-ECNet: Extreme Underwater Image Compression with Reference to Feature Dictionary", + "text_level": 1, + "bbox": [ + 204, + 130, + 767, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Mengyao Li $^{1}$ , Liquan Shen $^{1*}$ , Peng Ye $^{2}$ , Guorui Feng $^{1}$ , Zheyin Wang $^{1}$ $^{1}$ Shanghai Universit, Shanghai, China \n $^{2}$ Fudan University, Shanghai, China \nsdlmy@shu.edu.cn, jsslq@163.com, 20110720039@fudan.edu.cn \ngrfeng@shu.edu.cn, wangzy_0831@163.com", + "bbox": [ + 117, + 202, + 849, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Thriving underwater applications demand efficient extreme compression technology to realize the transmission of underwater images (UWIs) in very narrow underwater bandwidth. However, existing image compression methods achieve inferior performance on UWIs because they do not consider the characteristics of UWIs: (1) Multifarious underwater styles of color shift and distance-dependent clarity, caused by the unique underwater physical imaging; (2) Massive redundancy between different UWIs, caused by the fact that different UWIs contain several common ocean objects, which have plenty of similarities in structures and semantics. To remove redundancy among UWIs, we first construct an exhaustive underwater multi-scale feature dictionary to provide coarse-to-fine reference features for UWI compression. Subsequently, an extreme UWI compression network with reference to the feature dictionary $(RFD-ECNet)^{1}$ is creatively proposed, which utilizes feature match and reference feature variant to significantly remove redundancy among UWIs. To align the multifarious underwater styles and improve the accuracy of feature match, an underwater style normalized block (USNB) is proposed, which utilizes underwater physical priors extracted from the underwater physical imaging model to normalize the underwater styles of dictionary features toward the input. Moreover, a reference feature variant module (RFVM) is designed to adaptively morph the reference features, improving the similarity between the reference and input features. Experimental results on four UWI datasets show that our RFD-ECNet is the first work that achieves a significant BD-rate saving of $31\\%$ over the most advanced VVC.", + "bbox": [ + 75, + 338, + 473, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 811, + 209, + 828 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, underwater exploration attracts great attention from governments, scientists, and the public due to", + "bbox": [ + 76, + 837, + 468, + 867 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2f34891c46e60dc4cce2753262fbe0c4f40f7e4e9aa262349ecd7b7fbb5a3c19.jpg", + "image_caption": [ + "(a) Existing image compression pipeline" + ], + "image_footnote": [], + "bbox": [ + 501, + 308, + 890, + 358 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9442e45745d070d366734a86db7eca7c681e3cdedd491ab1c9d59bb42beccf70.jpg", + "image_caption": [ + "(b) Our motivation and pipeline", + "Figure 1: Key ideas of our work. Different UWIs have similarities in texture, structure and semantic, which can be included in an underwater feature dictionary to provide reference for UWI compression. E/D indicates encoder/decoder." + ], + "image_footnote": [], + "bbox": [ + 503, + 377, + 890, + 563 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the growing underwater applications. For example, mine search, nuclear-reactors detection, and underwater power inspection [1] are parts of homeland security operations. In addition, marine biology [2] and archaeology [3] are important scientific research for ocean resource development. Moreover, underwater entertainment [4] such as underwater live broadcasts is becoming greatly popular with the public.", + "bbox": [ + 496, + 667, + 893, + 775 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In these underwater applications, images taken underwater play an essential role. To be transmitted from the deep sea to the board or ground, underwater images (UWIs) must be compressed at extremely low bitrates due to the very narrow underwater wireless acoustic bandwidth of about 20 kbps [5]. However, existing image compression approaches severely degrade the pixel fidelity (e.g., MSE) of UWIs at extremely low bitrates (<0.1bpp), which greatly impairs the", + "bbox": [ + 496, + 780, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Corresponding Author.", + "bbox": [ + 96, + 875, + 235, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{1}$ Code is available at https://github.com/lilala0/RFD-ECNet", + "bbox": [ + 96, + 887, + 455, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12980", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "broad application of UWIs. Hence, it is highly urgent to design a more powerful extreme UWI compression algorithm.", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Different from general images, UWIs present two unique underwater characteristics: (1) UWIs present multifarious underwater styles of color shift and distance-dependent clarity. This is because the underwater imaging process is quite different from that in the open air [6]. When light travels through water, it suffers from absorption and scattering. Specifically, the blueish/greenish color shift is caused by the fact that the red light of the shortest wavelength is absorbed first, and then the green and blue light are followed [7]. In addition, light is scattered by the particles in water, which change the direction of light propagation [8], resulting in the spatially varying distance dependencies of clarity, i.e., the image clarity decreases as the distance to the objects increases. (2) Different UWIs contain some common underwater objects at diverse morphologies and sizes. Due to the special underwater natural environment, there are some common underwater objects such as fish, corals, and rocks that widely exist in different UWIs in diverse morphologies and sizes. Hence, there are plenty of similar representations between UWIs. As shown in Fig. 1 (b), although the UWIs are captured at different times and in various underwater scenes, they contain some same underwater objects such as water, corals, and rocks, which share plenty of similarities in textures, structures, and semantics.", + "bbox": [ + 75, + 125, + 472, + 487 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given the characteristics of UWIs, there are two main drawbacks for existing image compression methods [9-21]: (1) They only remove redundancy within an image and do not consider redundancy between UWIs. Conventional image compression CODEs such as JPEG2000 [9], BPG [10] and the latest VVC-intra [11] reduce the intra-redundancy through transform and intra-prediction. Recently, learnt image compression methods [12-18] have shown greater potential than conventional CODEs. Based on variational autoencoder (VAE), [12] designs a hyperprior model to remove the statistic redundancy within an image. After that, [13] proposes an autoregressive model to further remove the local context redundancy. However, all of them are limited to removing redundancy in only an image. (2) They utilize a unitary compression that cannot handle the multifarious underwater styles of color shift and distance-dependent clarity. It is reasonable to use the unitary compression for the general terrestrial images because the colors (r, g, b) of terrestrial images are evenly distributed [22] and the internal clarity is steady broadly. However, it limits their performance on UWIs because the UWIs are full of multifarious color shift and distance-dependent clarity. To design an efficient extreme UWI compression method, it needs to both remove redundancy between UWIs and align the multifarious underwater styles.", + "bbox": [ + 75, + 489, + 472, + 867 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Accordingly, we creatively propose to compress UWIs by referencing a dictionary to remove redundancy between", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "UWIs. First, we construct an exhaustive underwater multiscale feature dictionary to provide from coarse to fine reference information for the UWI compression. Specifically, the features in the dictionary are extracted from plenty of representative UWIs, which are strictly selected according to various underwater scenes, including different underwater objects, water types, and water depths. As such, our dictionary could cover a wide range of underwater common objects, assisting the UWI compression to fully remove redundancy between UWIs. Subsequently, we design a novel extreme UWI compression network with reference to the underwater feature dictionary (RFD-ECNet), shown in Fig 2, where the features of input UWI are matched with the dictionary to select the reference features, and then the residuals between the input and reference features are compressed, significantly reducing the coding bits of UWIs.", + "bbox": [ + 496, + 90, + 890, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Additionally, an underwater styles normalization block-based feature match (USN-FMM) is proposed to ensure that the match is not interfered by the multifarious underwater styles and focuses on selecting the references that have the most similar texture to the input. To be specific, the USNB utilizes the underwater physical priors (UPPs) extracted from the underwater imaging physical model [6] to normalize the underwater style of reference features towards that of the input. Moreover, to improve the similarity between the reference and input features, a reference feature variant module (RFVM) is designed to adaptively morph the reference features based on their dependency relevance to the input feature. Extensive experimental results show that our RFD-ECNet outperforms state-of-the-art (SOTA) compression methods. Overall, our main contributions are summarized as follows:", + "bbox": [ + 496, + 333, + 892, + 571 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We make the first attempt to remove the massive redundancy between UWIs, and the proposed dictionary-based compression network RFD-ECNet is the first work that achieves significantly better BD-rate/PSNR than the latest VVC and other learnt methods.", + "- We construct an exhaustive underwater feature dictionary from representative UWIs manually selected based on various underwater scenes, water types, and water depths. Besides, detailed analyses are conducted to verify the comprehensiveness and compactness of the dictionary.", + "- To eliminate the effect of underwater styles on feature match, we utilize the underwater physical priors to design USNB to improve feature match accuracy. Moreover, we design RFVM to adaptively morph the reference features based on the dependency map, improving their similarity." + ], + "bbox": [ + 516, + 574, + 893, + 833 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 844, + 650, + 861 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learnt Image Compression. Recently, learnt image compression approaches have developed rapidly and", + "bbox": [ + 500, + 869, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12981", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c88cb3b234852270807a38f8dbd6e7c605e9146847a6b6ed352621945f9eb128.jpg", + "image_caption": [ + "Figure 2: Overview of the proposed RFD-ECNet. Q indicates the quantizer. AE/AD represents the arithmetic en/decoding." + ], + "image_footnote": [], + "bbox": [ + 78, + 89, + 697, + 383 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/cc6868b93d08ba9672fe13e862aca36c2843ddd0b173071e97f4eefda6ad1da3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 90, + 890, + 381 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "achieved great breakthroughs, which can be divided into VAE-based and GAN-based. Generally, VAE-based methods [12-18] utilize an encoder, which includes some parametric linear and nonlinear transforms, to compress image to compact latent features. After quantization and entropy coding, the latent features are compressed into bit-stream. Then a decoder, which usually has a symmetrical structure with the encoder, is used to reconstruct the image.", + "bbox": [ + 75, + 443, + 468, + 565 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To improve the rate-distortion (R-D) performance, some works focus on designing more efficient learnt model to capture redundancy in an image. [13] proposes auto-regressive model to combine the context model with the hyperprior model [12] for entropy estimation. [18] proposes window-based local attention block to capture local redundancy such as non-repetitive textures. [17] proposes Gaussian Mixture Model to estimate likelihoods of latent features more accurately. Although VAE-based methods achieve admirable R-D performance, they often present unpleasant artifacts at extremely low bitrates.", + "bbox": [ + 75, + 565, + 468, + 731 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To this end, some works [19-21] combine VAE with the generative adversarial network (GAN) to generate visually pleasing textures to counteract compression artifacts. Nevertheless, the pixel fidelity (e.g., MSE) of the image reconstructed by the GAN-based methods is quite low because the generated content is fake and deceptive. Hence, it is difficult for existing methods to achieve high pixel fidelity UWI reconstruction at extremely low bitrates by only removing redundancy within an image.", + "bbox": [ + 75, + 732, + 468, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image Set Compression. This direction aims to compress a batch of images captured at the same place from", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "different view angles and focal distances [23], which can be divided into local-based and cloud-based. The local-based methods [24-26] construct the reference by first preprocessing all the images in a set. For example, [25] creates a new low frequency template as reference image by averaging the low frequency components of all images. The cloud-based methods such as [27] select reference images from the massive images in the cloud.", + "bbox": [ + 496, + 443, + 890, + 564 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Obviously, the local-based methods must obtain all images before compression, which limits their usage flexibility. The cloud-based methods rely on the wide transmission channel to access the cloud disk, which cannot be achieved by the very narrow underwater wireless acoustic channel. Moreover, since these methods can only be applied to the small image subset captured at the same place, they cannot deal with UWIs captured at different underwater scenes and depths in the vast underwater world.", + "bbox": [ + 496, + 565, + 892, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Reference-based Model. To the best of our knowledge, there exists no image compression method based on image/feature reference. The closest area to our work is reference-based super-resolution (RefSR), which utilizes the high-frequency information in high-resolution (HR) reference image/patch to rich the details of low resolution (LR) image. Given an arbitrary HR image, [28] uses the VGG network to simultaneously extract the referenced HR and LR features, and swaps the most similar features of reference and the LR. To overcome the inherent information deficit of a single reference, [29] uses multiple reference images to provide a more diverse pool of image features. Besides, [30] builds a face dictionary from HR face images", + "bbox": [ + 496, + 703, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12982", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/836f6807d027e6e82c7443a0e41cea7cfa9a5981d1060a6d2fb7025f70103a62.jpg", + "image_caption": [ + "Figure 3: Construction of underwater multi-scale feature dictionary. $B$ is the number of the representative UWIs." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 467, + 214 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to provide the high-frequency reference to construct more and richer features for the LR image.", + "bbox": [ + 75, + 273, + 468, + 303 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The differences between our work and the RefSR works are as follows: (1) The RefSR task aims to learn more/richer features from the HR reference, which is a process of increasing information. In contrast, our compression task aims to learn fewer/more compact features, a process of removing redundant information. To our best knowledge, we are the first image compression work referring to the feature dictionary. (2) In [30], their dictionary only contains face images with eyes, nose and mouth, which are relatively more simple and similar than the vast UWI domain. Instead, UWIs contain multifarious underwater styles, where the common underwater objects are at diverse morphologies and sizes. To construct an exhaustive underwater dictionary, we manually select the representative UWIs based on various underwater scenes, water types, and water depths. (3) We design USNB to align the underwater styles of dictionary features and input, improving feature match accuracy. Additionally, we design RFVM to adaptively morph the reference features, further improving their similarity.", + "bbox": [ + 75, + 304, + 468, + 592 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. The Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 606, + 287, + 622 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Exhaustive Underwater Feature Dictionary", + "text_level": 1, + "bbox": [ + 76, + 630, + 444, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To achieve extremely low bitrate UWI compression, we propose RFD-ECNet, a novel image compression network referring to underwater feature dictionary, to remove redundancy between UWIs. First of all, an exhaustive dictionary is constructed, which is offline and shared at the encoder and decoder. The pipeline of the construction of underwater multi-scale feature dictionary is shown in Fig. 3.", + "bbox": [ + 75, + 654, + 468, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To build the feature dictionary, a series of representative UWIs are selected from the largest public underwater image dataset UGWI ${}^{2}$ . UGWI contains 2150 various UWIs, which are collected during oceanic explorations, humanrobot collaborative experiments, or from websites such as Google and YouTube. To select representative UWIs that cover the richest and most comprehensive common contents", + "bbox": [ + 75, + 760, + 468, + 864 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/573ce1a6f589bf9fdf7c52cca384f6888d071c05b3e4f1aaf8053a9296e33c38.jpg", + "image_caption": [ + "Figure 4: SI and CF of images used to build the dictionary." + ], + "image_footnote": [], + "bbox": [ + 596, + 88, + 790, + 223 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of UWIs, we manually divided the two thousand images into 300 groups according to two rules. 1) Different Objects. Based on [8], the common objects in UWIs can be divided into marine faunas of fish, turtles, sharks, snails and shellfish, etc.; marine plants of corals, seaweed, fringing reefs, etc.; non-biology of rocks, wreckage and sculpture, etc. 2) Different water types and depths. The water type is distinguished from clear to turbid, and the water depth is distinguished from shoal water, deep sea and seabed. UWIs captured in clear and shoal water present lighter color shift and better clarity, and vice versa.", + "bbox": [ + 496, + 266, + 890, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After grouping the UGWI manually, 1-2 images from each group are selected to build our dictionary, which is then cropped into non-overlapping $128 \\times 128$ image patches $P$ . For each image patch, we use the pre-trained popular deep image compression network DICN [12] to extract its compression features at multi-scales, shown in Fig. 3. The generation process of dictionary can be described as,", + "bbox": [ + 496, + 431, + 890, + 537 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nD _ {s} = \\mathcal {F} (P; \\theta_ {D I C N} ^ {s}) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 551, + 890, + 569 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $s \\in \\{2,3,4\\}$ is the scale and $\\theta_{DICN}^{s}$ is the parameters of the pre-trained DICN at scale $s$ .", + "bbox": [ + 496, + 582, + 888, + 611 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To verify the diversity of these representative UWIs, the Spatial Information (SI) and Colorfulness (CF) indices are computed respectively for the content variation along the spatial and color dimensions. Higher SI / CF indicates more complex image content / colorful. The CF versus SI distribution is plotted in Fig. 4. As shown, the distribution range is quite broad, which indicates that the content of these patches is diverse. Additionally, some points are distributed closely, which also verifies that there are many similar common content between UWIs.", + "bbox": [ + 496, + 613, + 890, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To compact the features in dictionary, we adopt K-means to create $K$ clusters. Considering the high computational complexity of directly performing K-means on massive features of multifarious UWIs, we first perform principal components analysis (PCA) on the features of per UWI to reduce their dimension. Finally, $K$ typical features at each scale are preserved, constructing our multi-scale feature dictionary. The effect of cluster number $K$ on the compression performance is shown in the supplementary materials.", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "$^{2}$ UGWI is a public underwater image dataset and is available online at https://github.com/Underwater-Lab-SHU", + "bbox": [ + 76, + 875, + 468, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12983", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ea4623a437f6280850fb3a4eaa8ce5efaa395aec2bb4ae750e43f55de80c50ec.jpg", + "image_caption": [ + "Figure 5: The structure of the proposed USNB." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 467, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Overall of the proposed RFD-ECNet", + "text_level": 1, + "bbox": [ + 76, + 300, + 393, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The framework of our RFD-ECNet is shown in Fig. 2, which performs feature match at multiple scales ( $s \\in \\{2,3,4\\}$ ) in a progressive manner to remove the underwater common redundancy from coarse to fine. Let $F_{s}$ be the input features at scale $s$ , and $D_{s,i}$ denotes the $i$ -th dictionary features at scale $s$ . In the encoder, the input UWI is down-sampled by two convolutional sampling layers to obtain its features $F_{2}$ , which are matched with the dictionary $D$ to select its reference features $D_{2,i}$ . To guarantee the input features $F_{2}$ and $D$ in the same feature space, the first-two sampling layers of RFD-ECNet are filled with that of the pre-trained DICN, which are fixed during the training of our RFD-ECNet.", + "bbox": [ + 75, + 323, + 468, + 518 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For more accurate feature match, USNB is proposed to normalize the dictionary features based on the underwater style of the input, eliminating the effect of the underwater styles diversity on feature match. Specifically, USNB utilizes the UPPs extracted from an UPPs extractor [7] to simulate the underwater imaging process [6], which dictate the underwater styles of UWIs. Moreover, the selected $D_{2,i}$ is further refined by the proposed RFVM to obtain $RD_{2,i}$ based on the similarity map $W_{2}$ between $F_{2}$ and $D_{2,i}$ , greatly improving their similarity.", + "bbox": [ + 75, + 520, + 468, + 671 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After removing redundancy on three scales, the latent features $z$ and the dependency maps $(W_{2}, W_{3}, W_{4})$ are quantized by the uniform noise approximated method [12], and then entropy coded by the Gaussian mixture entropy model [17] to the bit-stream.", + "bbox": [ + 75, + 671, + 468, + 746 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.USNB-based Feature Match (USN-FMM)", + "text_level": 1, + "bbox": [ + 76, + 755, + 431, + 771 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Feature match aims to select the reference features that have the most similar textures to the input features. However, the UWIs sharing similarity may have multifarious underwater styles of color shift and distance-dependent clarity. Hence, it is necessary to normalize the underwater styles of dictionary features toward that of the input before the feature match.", + "bbox": [ + 75, + 779, + 468, + 883 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Underwater Style Normalize. By studying the process", + "bbox": [ + 96, + 885, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9ca943d6dddd9d85d49f81daada5571a07a0029a445ccd8b21ab89cf593c9749.jpg", + "image_caption": [ + "Figure 6: The structure of the proposed RFVM." + ], + "image_footnote": [], + "bbox": [ + 501, + 89, + 893, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "of underwater imaging, it can be observed that the underwater styles are dictated by underwater physical priors such as ambient light and imaging transmission map, which can be described by the underwater physical scattering model:", + "bbox": [ + 496, + 300, + 890, + 361 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} J = I \\times T + A \\times (1 - T) \\\\ = \\quad_ {c d} \\end{array} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 369, + 890, + 396 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nT = e ^ {- \\alpha d}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 392, + 676, + 406 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $I$ denotes the clear scene without underwater style and $J$ is the captured UWI with multifarious underwater styles. Under the effect of underwater physical priors, including $T$ and $A$ , $I$ is evolved to $J$ . $T$ and $A$ respectively represent the transmission map and the global ambient light, and their visual examples are presented in the supplementary materials. $T$ is calculated by $\\alpha$ and $d$ , which respectively refer to light attenuation coefficient and the distance between camera and object, which leads to the distance-dependent clarity. Derived from Eq. (2), the clear scene can be modeled as:", + "bbox": [ + 496, + 417, + 890, + 583 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nI = \\frac {J - A \\times (1 - T)}{T} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 590, + 890, + 621 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on Eq. (2) and Eq. (3), the dictionary features can be normalized towards the underwater style of input by", + "bbox": [ + 496, + 628, + 890, + 659 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} J ^ {d i c. i n p u t} = I ^ {d i c} \\times T ^ {i n p u t} + A ^ {i n p u t} \\times \\left(1 - T ^ {i n p u t}\\right) \\\\ = \\frac {J ^ {d i c} - A ^ {d i c} \\times (1 - T ^ {d i c})}{T ^ {d i c}} \\times T ^ {\\text {i n p u t}} \\tag {4} \\\\ + A ^ {i n p u t} \\times (1 - T ^ {i n p u t}) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 667, + 890, + 739 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on the above analysis, we propose the USNB to parametrically implement Eq. (4), as shown in Fig. 5, which is used before the feature match to normalize the underwater styles of dictionary features toward the input. In Fig. 5, $D_{s}$ and $ND_{s}$ respectively correspond to $J_{dic}$ and $J_{dic\\_input}$ in Eq. (4). Underwater physical priors of dictionary features $(T^{dic}$ and $A^{dic})$ and that of the input $(T^{in}$ and $A^{in})$ are fed to several convention layers to normalize $D_{s}$ to $ND_{s}$ by following the data flow in Eq. (4). Notably, the network parameters for processing $T^{dic}$ and $A^{dic}$ are shared", + "bbox": [ + 496, + 750, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12984", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/dbd5c30f339ff620b6302813d4978b4b9ac75b32c3e7250614ec24dd1c1c433b.jpg", + "image_caption": [ + "(a) UGWI, Rate-PSNR" + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 279, + 215 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5742289e86852ac1d2e15f3df0c57b61ded123a36489912acec123fb11aa4214.jpg", + "image_caption": [ + "(b) EUVP, Rate-PSNR" + ], + "image_footnote": [], + "bbox": [ + 279, + 87, + 483, + 218 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/21522237f422887d94a37d5491ff8c8e5911e84594a4a24a1c5e63315837d7b6.jpg", + "image_caption": [ + "(c) UFO, Rate-PSNR" + ], + "image_footnote": [], + "bbox": [ + 486, + 89, + 686, + 217 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e2d5a46de4f775b9f764d485d1fea9e168989b4328f8cc21800aa4c1b205a17a.jpg", + "image_caption": [ + "(d) UIEB, Rate-PSNR", + "Figure 7: R-D curves of different image compression methods on UGWI, EUVP [31], UFO [32], and UIEB [8] datasets." + ], + "image_footnote": [], + "bbox": [ + 689, + 88, + 890, + 218 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "with that for $T^{dic}$ and $A^{dic}$ to guarantee that all underwater physical priors are in the same feature space. As such, the proposed USNB is able to normalize the underwater styles of the dictionary features toward the input for more accurate feature match. The effectiveness of USNB is verified in the ablation studies.", + "bbox": [ + 75, + 277, + 468, + 369 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Feature Match. To select the reference features $D_{s,i}$ from the dictionary features $D_{s}$ for input features $F_{s}$ , we adopt the widely used inner product to measure the similarity score between $F_{s}$ and $D_{s}$ . The similarity scores between $F_{s}$ and $D_{s}$ is defined as:", + "bbox": [ + 76, + 373, + 468, + 449 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nS _ {s} = \\left\\langle F _ {s}, \\frac {D _ {s}}{\\| D _ {s} \\|} \\right\\rangle \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 455, + 468, + 491 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Following the procedure in [33], Eq. (5) is implemented by a convolution operation, where the kernel weights are set as $D_{s}$ , to accelerate the similarity calculations. The $i$ -th dictionary feature with the highest similarity score is selected as the reference feature $D_{s,i}$ .", + "bbox": [ + 76, + 503, + 468, + 580 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. Reference Feature Variant Module (RFVM)", + "text_level": 1, + "bbox": [ + 76, + 601, + 449, + 617 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Although the reference features $D_{s,i}$ and the input features $F_{s}$ share some similarities, the relative position and shape of the similar areas in $D_{s,i}$ and $F_{s}$ may be dramatically different. To achieve the highest possible similarity, we develop the RFVM to adaptively morph the $D_{s,i}$ based on $F_{s}$ , shown in Fig. 6. RFVM utilizes the spatial variant recursive convolution (SVRConv) [34] to implement the feature variant on a large receptive field, which is able to facilitate the dramatic spatial variant by the long-distance information propagation of recurrent convolution and the learned weights for different locations. The weights of SVRConv are learned by exploring the dependency between $D_{s,i}$ and $F_{s}$ . To obtain the global dependency map $W$ , dilated convolutions with different dilation rates are used to exploit the spatial information at different receptive fields. As such, our RFVM is able to morph the reference features in a large receptive field to improve the similarity with the input features.", + "bbox": [ + 75, + 628, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 277, + 633, + 295 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Extensive experiments are conducted to evaluate the extreme compression performance of our RFD-ECNet. First, we test RFD-ECNet on four different UWI datasets objectively and subjectively to verify our excellent generalization. After that, a series of ablation studies are presented to respectively verify the effectiveness of our multi-scale manner, USNB and RFVM.", + "bbox": [ + 496, + 303, + 890, + 407 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 498, + 419, + 705, + 435 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We perform experiments on four public UWI datasets, including the UGWI dataset, EUVP dataset [31], UFO dataset [32], and UIEB dataset [8]. These UWI datasets are collected during different oceanic explorations and hence include various underwater scenes and rich ocean species. As stated in Section 3.1, some representative UWIs selected from UGWI dataset are utilized to construct our underwater multi-scale feature dictionary. The rest of UGWI are divided into 1550 UWIs for training and 300 UWIs for testing. Additionally, we randomly select 100 images respectively from EUVP [31], UFO [32], and UIEB [8] to test the pre-trained RFD-ECNet to verify the generalization of our RFD-ECNet.", + "bbox": [ + 496, + 441, + 890, + 637 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training. As the most VAE-based methods, our RFD-ECNet is optimized by the rate-distortion trade-off loss function, which can be described as:", + "bbox": [ + 498, + 638, + 890, + 683 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda \\cdot D + R, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 640, + 696, + 890, + 712 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda$ is a trade-off parameter to balance bitrate $R$ and distortion $D$ . In our work, MSE is used as the $D$ , and $\\lambda$ belongs to the set $\\{512, 256, 128, 64, 32\\}$ for 5 different compression ratios. The channel width of RFD-ECNet is set as 192, and the bottleneck layer is set as 64. Detailed network architecture is introduced in the supplementary materials. All model are trained using the Adam optimizer [35] with standard parameters and learning rate of $1 \\times 10^{-4}$ .", + "bbox": [ + 496, + 719, + 890, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation. The compression performance is measured by bitrate $R$ and distortion $D$ , which are respectively calculated by bits-per-pixel (bpp) and Peak Signal to Noise Ratio (PSNR). Lower bpp and higher PSNR indicate better com", + "bbox": [ + 496, + 840, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12985", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0e275f700fa3e83cb578b71f1cb5c28d6f64dcac05035c8dda62fdb923c28885.jpg", + "table_caption": [ + "Table 1: Comparison of BD-rate and BD-PSNR on UGWI, EUVP [31], UIEB [8], and UFO [32] testsets. The BD-rate and BD-PSNR are calculated from PSNR-BPP curve over data points with $\\mathrm{bpp} < 0.1$ , when BPG [10] is set as the anchor. The performance of SOTA compression codec VVC is marked in red. The best performance is bolded." + ], + "table_footnote": [], + "table_body": "
MethodsBD-rate ↓ (%)BD-PSNR ↑ (dB)Computation complexity
UGWIEUVPUIEBUFOAvg.UGWIEUVPUIEBUFOAvg.Param. (M)FLOPs (G)
VVC-intra [11]-19.0-16.2-16.0-16.1-16.80.690.430.520.470.53//
JPEG2000 [9]61.768.467.266.966.1-1.62-1.71-1.84-1.56-1.68//
BPG [10]0000000000//
Minnen (NIPS'18) [13]-3.814.89.819.09.90.16-0.36-0.33-0.59-0.2814.127.2
Cheng (CVPR'20) [17]-12.8-8.4-1.3-8.3-7.70.430.200.040.240.2320.561.3
Zou (CVPR'22) [18]-13.8-10.3-12.4-14.7-12.80.480.250.360.430.3875.033.3
Ours-slim-50.2-44.6-42.6-34.7-43.01.731.011.110.651.1215.440.7
Ours-53.7-50.3-52.9-37.3-48.51.971.181.560.991.4335.886.7
", + "bbox": [ + 84, + 141, + 888, + 313 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ed7f1f7ffb8c29a475d1dcb4f85652794d515b678a95d3d80a8831494dd3730c.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 81, + 327, + 207, + 425 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6cd66ba37bc674914d16936909987879ac0dfef73638c2d1dcdc3f78d3b79a93.jpg", + "image_caption": [ + "JPEG2000, Bpp=0.137" + ], + "image_footnote": [], + "bbox": [ + 209, + 328, + 331, + 425 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/18fdcdc8d372a937d8f31bb9a94939f5f5d3764f6b62c13e9ec552cc5aa9b5d1.jpg", + "image_caption": [ + "VVC-intra, Bpp=0.139" + ], + "image_footnote": [], + "bbox": [ + 334, + 328, + 459, + 425 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c2d1109353d3f5723c1fd4b7cf4e8c9256b96b948811415ea453e9a8f96cc021.jpg", + "image_caption": [ + "Cheng(CVPR'20), Bpp=0.146" + ], + "image_footnote": [], + "bbox": [ + 460, + 328, + 586, + 425 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/364b1820a1c05f2030bd2f108310a5459d50dce3f040211e00a01b561cfc3b6e.jpg", + "image_caption": [ + "Ours, Bpp=0.137" + ], + "image_footnote": [], + "bbox": [ + 588, + 328, + 712, + 425 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e635477c759e220f74a8b4f3912cd018f8f0d0985d3bf75d2aac3b1653026c4b.jpg", + "image_caption": [ + "Cheng" + ], + "image_footnote": [], + "bbox": [ + 717, + 328, + 772, + 425 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c03d2bf8cc2ad1e909f772e9fcabba702a3e841699f4ba78830e9c43ccc416f8.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 774, + 328, + 831, + 425 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5459c8b9750990424f2431b60b52b91fd23bd564bbf9820658a06e9da338e400.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 833, + 356, + 887, + 398 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4b8fe94809da9ba7a9e1be6d6486ed448e684826366f12b75867dff7304e5a15.jpg", + "image_caption": [ + "Input", + "Figure 8: Visual examples of the reconstructed images. The examples in two rows are respectively from UGWI and EUVP [31] testset. The metrics are bpp $(\\downarrow)$ and PSNR $(\\uparrow)$ . At extremely low bpp, our reconstructed images have more details and higher pixel fidelity (measured by PSNR) than others." + ], + "image_footnote": [], + "bbox": [ + 81, + 446, + 207, + 545 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/df8e0e8512a9ace11245e66ec7e2fa5f8f2b1b84bf0affb457fc920d4b6e18b6.jpg", + "image_caption": [ + "PSNR=27.37 dB", + "JPEG2000, Bpp=0.049", + "PSNR=22.17 dB" + ], + "image_footnote": [], + "bbox": [ + 209, + 446, + 331, + 545 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2089c8741a4effc676835531c47abbb75e43601bea8e04f625f0bc3bf2bb815d.jpg", + "image_caption": [ + "PSNR=29.35 dB", + "VVC-intra, Bpp=0.049", + "PSNR=25.22 dB" + ], + "image_footnote": [], + "bbox": [ + 334, + 446, + 459, + 545 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0dc4ad8d2c12b3f92b2b6b28cff600122ad73bf910bf7387b6227dbdd9bb2338.jpg", + "image_caption": [ + "PSNR=29.13 dB", + "Cheng(CVPR'20), Bpp=0.049", + "PSNR=25.28 dB" + ], + "image_footnote": [], + "bbox": [ + 460, + 446, + 586, + 545 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/16baf89ba433e4b6c1602ceb61de6c12fd203216b73ea984f0aad8bc58fe286a.jpg", + "image_caption": [ + "PSNR=30.16 dB", + "Ours, Bpp=0.048", + "PSNR=26.15 dB" + ], + "image_footnote": [], + "bbox": [ + 588, + 446, + 712, + 545 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/25880dac893654e0f369ac32e2bcf8fdd7b3367887eaa9554a67726ff7c19ef9.jpg", + "image_caption": [ + "JPEG2000", + "VVC-intra" + ], + "image_footnote": [], + "bbox": [ + 717, + 446, + 774, + 489 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3e9e198bf0961f321d1ad607ce4f9b69fda0e7341b7940b513e40747df987b2b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 774, + 446, + 831, + 489 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "VVC-intra", + "bbox": [ + 779, + 491, + 825, + 500 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/af86153ceb0aa98e7e2a52146198cd918cc8435843f55478117b18b971245805.jpg", + "image_caption": [ + "Cheng" + ], + "image_footnote": [], + "bbox": [ + 717, + 501, + 772, + 544 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/28dde335b884709b5906c590c0153e1f9dd49740795facbfced6ebf00ba495a8.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 774, + 501, + 831, + 544 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2d5f7a27e9e660bf6a4d5f9ff20abb8bdcef51e0a57840e59487ff0185342d59.jpg", + "image_caption": [ + "${13}/{14}$" + ], + "image_footnote": [], + "bbox": [ + 833, + 446, + 887, + 489 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/780053d874d19f625a1a8a44ab00ab0809ce020623ac19fd06e989e86f9dd9dc.jpg", + "image_caption": [ + "" + ], + "image_footnote": [], + "bbox": [ + 833, + 501, + 887, + 544 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "pression performance. Notably, our bpp is calculated by,", + "bbox": [ + 75, + 640, + 468, + 657 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nb p p = \\frac {b i t s _ {z} + b i t s _ {W} + b i t s _ {i n d e x}}{N _ {\\text {p i x e l s}}} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 665, + 468, + 699 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $\\text{bits}_z$ and $\\text{bits}_W$ respectively represent the bits of latent features $z$ and dependency map $W$ . $\\text{bits}_{index}$ denotes the bits for coding the index numbers of reference features, which are directly coded by Huffman coding. In addition to R-D curves, the widely used Bjøntegaard delta rate (BD-rate) and BD-PSNR are also evaluated. Lower BD-rate and higher BD-PSNR indicate more efficient compression.", + "bbox": [ + 75, + 704, + 468, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For the comparative methods, we compare our RFDECNet with influential and SOTA image compression networks, including Minnen (NIPS'18) [13], Cheng (CVPR'20) [17], and Zou (CVPR'22) [18]. For fair comparisons, all networks are trained on the UGWI dataset. Additionally, some conventional CODECs are compared, includ", + "bbox": [ + 75, + 810, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ing popular JPEG2000 [9], BPG (HEVC-intra) [10] and the latest VVC-intra (VTM 11.0) [11]. For BPG and VVC, the highest PSNR setting (4:4:4) is tested.", + "bbox": [ + 498, + 640, + 890, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Comparison against SOTA methods", + "text_level": 1, + "bbox": [ + 500, + 696, + 812, + 712 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "R-D Performance. Fig. 7 presents the R-D curves on four UWI testsets of UGWI, EUVP [31], UIEB [8], and UFO [32]. As shown, the R-D curves of our RFD-ECNet are above the curves of all comparative methods on four testsets, which demonstrates that our method achieves better compression performance than all comparative methods and our excellent generalization and robustness. Notably, as bpp decreases, our RFD-ECNet achieves higher PSNR improvements than comparative methods. This indicates that the reference features provided by our underwater feature dictionary are very efficient for the reconstruction, especially at extremely low bitrates.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12986", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/15c11c5dac874482504cab77501fe9dbfd4e2c38f71baa132ff95d0abbeadfa0.jpg", + "table_caption": [ + "Table 2: BD-rate $(\\%)$ and BD-PSNR (dB) of VVC/HEVC at inter/intra modes, where Minnen [13] is set as the anchor." + ], + "table_footnote": [], + "table_body": "
MethodsVVC-interVVC-intraHEVC-interHEVC-intraOurs
BD-rate ↓-22.1-21.00.23.2-59.5
BD-PSNR ↑0.850.82-0.10-0.122.25
", + "bbox": [ + 84, + 126, + 467, + 176 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The BD-rate of different image compression methods with BPG [10] as the anchor is presented in Table 1. As shown, our method achieves the best BD-rate and BD-PSNR results on four testsets, which indicates that we use the smallest amount of bits to achieve the highest PSNR among all methods. Specially, our average BD-rate of $-48.5\\%$ and BD-PSNR of $1.43\\mathrm{dB}$ are much better than the most advanced codec VVC-intra' - $16.8\\%$ and $0.53\\mathrm{dB}$ . More intuitively, when VVC is set as the anchor, our RFD-ECNet achieves breakthrough BD-rate saving of $31.7\\%$ and BD-PSNR of $0.90\\mathrm{dB}$ , demonstrating the advanced performance of our RFD-ECNet on UWI extreme compression.", + "bbox": [ + 75, + 189, + 468, + 371 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visual Quality. Fig. 8 shows visual examples of reconstructed images by our RFD-ECNet, Cheng (CVPR'20), the most advanced VVC-intra, and the widely used JPEG2000. As shown, our reconstructed images retain more details, while the reconstructed images of VVC-intra and JPEG2000 present obvious blurring and blocking effects at extremely low bpp. As shown in the second row, when bpp=0.049, VVC-intra, Cheng (CVPR'20) and JPEG2000 completely lose the common object of sand, while our RFD-ECNet can roughly reconstruct the sand by referencing our dictionary. Overall, our pixel fidelity is higher than others at the similar extremely low bpp, which can be verified by our higher PSNR. More visual results tested on underwater videos are provided at https://github.com/lilala0/RFD-ECNet.", + "bbox": [ + 75, + 371, + 468, + 597 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparison with video CODECs. To verify that the redundancy between UWIs cannot be efficiently removed by video CODEcs, our RFD-ECNet is compared with the latest video CODEcs of VVC-inter and HEVC-inter. Their performance on UGWI testset measured by BD-rate and BD-PSNR with the Minnen [13] as the anchor is shown in Table 2. As shown, we achieve better results than both VVC-inter and HEVC-inter, verifying that our RFD-ECNet referencing to dictionary is more efficient than video CODEcs to remove the redundancy between UWIs. Moreover, both video CODEcs at inter-mode only achieve tiny improvement of BD-rate/PSNR than the intra-mode. This verifies that there is redundancy between UWIs indeed.", + "bbox": [ + 75, + 598, + 468, + 794 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparison of complexity. The trainable parameters and FLOPs of all approaches are compared in Table 1. As shown, our parameters (35.8 M) is much less than that (99.8 M) of compression network [18]. Additionally, we also provide a slim version of Our RFD-ECNet by narrowing our network channels of 192 to 128 (denoted as Ours-slim), which only have 15.4M parameters and 40.7G FLOPs. No", + "bbox": [ + 75, + 795, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/027c8e35a372c2f5fc75014ade006adcded17935e458b9d8dfb65548b7ce7438.jpg", + "table_caption": [ + "Table 3: BD-rate $(\\%)$ and BD-PSNR (dB) of ablation studies about our USNB and RFVM, where BPG [10] is set as the anchor." + ], + "table_footnote": [], + "table_body": "
SettingOursw/o USNBw/o RFVMw/o USNB&RFVM
BD-rate ↓-53.7-33.6-43.1-24.6
BD-PSNR ↑1.971.141.490.83
", + "bbox": [ + 506, + 141, + 888, + 195 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f254b2491b3ceacc0b5799d679ccd050b5085e168bb667e9da50ff96f20cc1c0.jpg", + "table_caption": [ + "Table 4: BD-rate $(\\%)$ and BD-PSNR (dB) of ablation studies about the multi-scale manner, where BPG [10] is set as the anchor." + ], + "table_footnote": [], + "table_body": "
Scale settingScale-{2}Scales-{2,3}Scales-{2,3,4}
BD-rate ↓-46.1-49.8-53.7
BD-PSNR ↑1.671.831.97
", + "bbox": [ + 506, + 263, + 888, + 314 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tably, ours-slim still achieves better performance than all SOTA methods with lower complexity, illustrating our excellent UWI extreme compression performance.", + "bbox": [ + 498, + 340, + 890, + 388 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 412, + 651, + 430 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of USNB and RFVM. To verify the effectiveness of the proposed USNB and RFVM, a series of ablation experiments are conducted, where the USNB and RFVM are removed from our RFD-ECNet in sequence. The performance of each ablation is measured by the BD-rate and BD-PSNR with the BPG as the anchor, shown in Table 3. w/o USNB indicates the network that directly performs feature match by inner product without using our USNB to normalize the dictionary features. w/o RFVM is the network where the matched reference features are not fed into our RFVM and therefore cannot be varied adaptively based on the input features. w/o USNB&RFVM is the network without both USNB and RFVM. As can be seen from Table 3, the removal of either USNB or RFVM degrades the performance of our RFD-ECNet. Moreover, the performance degrades most when USNB and RFVM are removed simultaneously, verifying the effectiveness of USNB and RFVM.", + "bbox": [ + 496, + 441, + 890, + 700 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of multi-scale reference. In our RFD-ECNet, the input features are matched with the feature dictionary at three scales (\\(s = 2,3,4\\)), considering that the similarity between UWIs is reflected on the textures, structures, and semantics. Here we conduct ablations to verify the effectiveness of the multi-scale manner, and provide the results in Table 4. Since the features on scale-1 contain more noise less semantic information, we perform feature match starting from scale-2. As shown, our RFD-ECNet referring dictionary at scales-\\{2,3,4\\} achieves the best performance, followed by scales-\\{2,3\\} and scale-\\{2\\}\\), which verifies that it is efficient to remove the underwater common redundancy at multiple scales from coarse to fine.", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12987", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion", + "text_level": 1, + "bbox": [ + 76, + 89, + 189, + 104 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work creatively removes redundancy between UWIs and proposes a novel reference-based image compression framework. Actually, the redundancy between images exists not only in UWIs but also in other image domains where independent images contain some common objects specific to the image domain. For example, all Martian images [36] contain rocks and sand; all face images [37] contain eyes, nose and mouth; most remote sensing images [38] contain buildings, road and so on. However, existing image compression works neglect this nature and only remove redundancy in an image, which may limit the development of image compression.", + "bbox": [ + 75, + 114, + 472, + 297 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "To validate our hypothesis, we additionally conduct preliminary experiments on Martian images [36] by adjusting our network. Experimental results presented in the supplementary materials show that we also achieve better performance than VVC and Ding (VCIP'22) [36], illustrating the efficiency and feasibility of removing redundancy between images in other image domains.", + "bbox": [ + 75, + 297, + 472, + 405 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 420, + 194, + 436 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we explore the characteristics of UWIs and find that UWIs present multifarious underwater styles and different UWIs share some common ocean objects at diverse morphologies and sizes, resulting in plenty of redundancy between UWIs. Hence, we construct an exhaustive and compact underwater multi-scale feature dictionary from the manually selected representative UWIs, which provides coarse-to-fine reference for our RFD-ECNet to fully remove redundancy between UWIs. Meanwhile, to eliminate the effect of underwater styles on feature match, we utilize UPPs to design the USNB to align the multifarious underwater styles of dictionary towards that of input features. Moreover, to improve the similarity between the input and reference features, we propose RFVM to perform adaptive reference feature variant. Finally, extensive comparisons are conducted to verify our significant performance improvement than SOTA methods including the latest VVC, and comprehensive ablation studies verify the effectiveness of each module in our RFD-ECNet.", + "bbox": [ + 75, + 446, + 472, + 750 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 76, + 762, + 235, + 779 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work is supported in part by the National Natural Science Foundation of China under Grant 61931022 and Grant 62271301; in part by the Shanghai Science and Technology Program under Grant 22511105200; in part by the Shanghai Excellent Academic Leaders Program under Grant 23XD1401400; in part by the Natural Science Foundation of Shandong Province under Grant ZR2022ZD38.", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 501, + 90, + 596, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] G.L. 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In ISPRS TC VII Symposium, 2010. 9" + ], + "bbox": [ + 501, + 92, + 890, + 704 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "12989", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/RFD-ECNet_ Extreme Underwater Image Compression with Reference to Feature Dictionary/cdd3e31c-4266-47f7-a8c7-755cca493958_model.json b/2023/RFD-ECNet_ Extreme Underwater Image Compression with Reference to Feature Dictionary/cdd3e31c-4266-47f7-a8c7-755cca493958_model.json new file mode 100644 index 0000000000000000000000000000000000000000..96b8b87c234c9df251f6316adc370cf69e3374c5 --- /dev/null +++ b/2023/RFD-ECNet_ Extreme Underwater Image Compression with Reference to Feature Dictionary/cdd3e31c-4266-47f7-a8c7-755cca493958_model.json @@ -0,0 +1,2541 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.205, + 0.131, + 0.768, + 0.177 + ], + "angle": 0, + "content": "RFD-ECNet: Extreme Underwater Image Compression with Reference to Feature Dictionary" + }, + { + "type": "text", + "bbox": [ + 0.119, + 0.203, + 0.851, + 0.275 + ], + "angle": 0, + "content": "Mengyao Li\\(^{1}\\), Liquan Shen\\(^{1*}\\), Peng Ye\\(^{2}\\), Guorui Feng\\(^{1}\\), Zheyin Wang\\(^{1}\\) \n\\(^{1}\\)Shanghai Universit, Shanghai, China \n\\(^{2}\\)Fudan University, Shanghai, China \nsdlmy@shu.edu.cn, jsslq@163.com, 20110720039@fudan.edu.cn \ngrfeng@shu.edu.cn, wangzy_0831@163.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.326 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.339, + 0.474, + 0.794 + ], + "angle": 0, + "content": "Thriving underwater applications demand efficient extreme compression technology to realize the transmission of underwater images (UWIs) in very narrow underwater bandwidth. However, existing image compression methods achieve inferior performance on UWIs because they do not consider the characteristics of UWIs: (1) Multifarious underwater styles of color shift and distance-dependent clarity, caused by the unique underwater physical imaging; (2) Massive redundancy between different UWIs, caused by the fact that different UWIs contain several common ocean objects, which have plenty of similarities in structures and semantics. To remove redundancy among UWIs, we first construct an exhaustive underwater multi-scale feature dictionary to provide coarse-to-fine reference features for UWI compression. Subsequently, an extreme UWI compression network with reference to the feature dictionary \\((RFD-ECNet)^{1}\\) is creatively proposed, which utilizes feature match and reference feature variant to significantly remove redundancy among UWIs. To align the multifarious underwater styles and improve the accuracy of feature match, an underwater style normalized block (USNB) is proposed, which utilizes underwater physical priors extracted from the underwater physical imaging model to normalize the underwater styles of dictionary features toward the input. Moreover, a reference feature variant module (RFVM) is designed to adaptively morph the reference features, improving the similarity between the reference and input features. Experimental results on four UWI datasets show that our RFD-ECNet is the first work that achieves a significant BD-rate saving of \\(31\\%\\) over the most advanced VVC." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.812, + 0.21, + 0.829 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.838, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Recently, underwater exploration attracts great attention from governments, scientists, and the public due to" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.309, + 0.891, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.579, + 0.361, + 0.815, + 0.375 + ], + "angle": 0, + "content": "(a) Existing image compression pipeline" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.378, + 0.891, + 0.564 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.604, + 0.566, + 0.792, + 0.58 + ], + "angle": 0, + "content": "(b) Our motivation and pipeline" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.585, + 0.893, + 0.645 + ], + "angle": 0, + "content": "Figure 1: Key ideas of our work. Different UWIs have similarities in texture, structure and semantic, which can be included in an underwater feature dictionary to provide reference for UWI compression. E/D indicates encoder/decoder." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.669, + 0.894, + 0.776 + ], + "angle": 0, + "content": "the growing underwater applications. For example, mine search, nuclear-reactors detection, and underwater power inspection [1] are parts of homeland security operations. In addition, marine biology [2] and archaeology [3] are important scientific research for ocean resource development. Moreover, underwater entertainment [4] such as underwater live broadcasts is becoming greatly popular with the public." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.895, + 0.902 + ], + "angle": 0, + "content": "In these underwater applications, images taken underwater play an essential role. To be transmitted from the deep sea to the board or ground, underwater images (UWIs) must be compressed at extremely low bitrates due to the very narrow underwater wireless acoustic bandwidth of about 20 kbps [5]. However, existing image compression approaches severely degrade the pixel fidelity (e.g., MSE) of UWIs at extremely low bitrates (<0.1bpp), which greatly impairs the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.875, + 0.236, + 0.888 + ], + "angle": 0, + "content": "* Corresponding Author." + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.457, + 0.9 + ], + "angle": 0, + "content": "\\(^{1}\\)Code is available at https://github.com/lilala0/RFD-ECNet" + }, + { + "type": "list", + "bbox": [ + 0.098, + 0.875, + 0.457, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12980" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "broad application of UWIs. Hence, it is highly urgent to design a more powerful extreme UWI compression algorithm." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.125, + 0.473, + 0.488 + ], + "angle": 0, + "content": "Different from general images, UWIs present two unique underwater characteristics: (1) UWIs present multifarious underwater styles of color shift and distance-dependent clarity. This is because the underwater imaging process is quite different from that in the open air [6]. When light travels through water, it suffers from absorption and scattering. Specifically, the blueish/greenish color shift is caused by the fact that the red light of the shortest wavelength is absorbed first, and then the green and blue light are followed [7]. In addition, light is scattered by the particles in water, which change the direction of light propagation [8], resulting in the spatially varying distance dependencies of clarity, i.e., the image clarity decreases as the distance to the objects increases. (2) Different UWIs contain some common underwater objects at diverse morphologies and sizes. Due to the special underwater natural environment, there are some common underwater objects such as fish, corals, and rocks that widely exist in different UWIs in diverse morphologies and sizes. Hence, there are plenty of similar representations between UWIs. As shown in Fig. 1 (b), although the UWIs are captured at different times and in various underwater scenes, they contain some same underwater objects such as water, corals, and rocks, which share plenty of similarities in textures, structures, and semantics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.473, + 0.868 + ], + "angle": 0, + "content": "Given the characteristics of UWIs, there are two main drawbacks for existing image compression methods [9-21]: (1) They only remove redundancy within an image and do not consider redundancy between UWIs. Conventional image compression CODEs such as JPEG2000 [9], BPG [10] and the latest VVC-intra [11] reduce the intra-redundancy through transform and intra-prediction. Recently, learnt image compression methods [12-18] have shown greater potential than conventional CODEs. Based on variational autoencoder (VAE), [12] designs a hyperprior model to remove the statistic redundancy within an image. After that, [13] proposes an autoregressive model to further remove the local context redundancy. However, all of them are limited to removing redundancy in only an image. (2) They utilize a unitary compression that cannot handle the multifarious underwater styles of color shift and distance-dependent clarity. It is reasonable to use the unitary compression for the general terrestrial images because the colors (r, g, b) of terrestrial images are evenly distributed [22] and the internal clarity is steady broadly. However, it limits their performance on UWIs because the UWIs are full of multifarious color shift and distance-dependent clarity. To design an efficient extreme UWI compression method, it needs to both remove redundancy between UWIs and align the multifarious underwater styles." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Accordingly, we creatively propose to compress UWIs by referencing a dictionary to remove redundancy between" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.333 + ], + "angle": 0, + "content": "UWIs. First, we construct an exhaustive underwater multiscale feature dictionary to provide from coarse to fine reference information for the UWI compression. Specifically, the features in the dictionary are extracted from plenty of representative UWIs, which are strictly selected according to various underwater scenes, including different underwater objects, water types, and water depths. As such, our dictionary could cover a wide range of underwater common objects, assisting the UWI compression to fully remove redundancy between UWIs. Subsequently, we design a novel extreme UWI compression network with reference to the underwater feature dictionary (RFD-ECNet), shown in Fig 2, where the features of input UWI are matched with the dictionary to select the reference features, and then the residuals between the input and reference features are compressed, significantly reducing the coding bits of UWIs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.334, + 0.893, + 0.573 + ], + "angle": 0, + "content": "Additionally, an underwater styles normalization block-based feature match (USN-FMM) is proposed to ensure that the match is not interfered by the multifarious underwater styles and focuses on selecting the references that have the most similar texture to the input. To be specific, the USNB utilizes the underwater physical priors (UPPs) extracted from the underwater imaging physical model [6] to normalize the underwater style of reference features towards that of the input. Moreover, to improve the similarity between the reference and input features, a reference feature variant module (RFVM) is designed to adaptively morph the reference features based on their dependency relevance to the input feature. Extensive experimental results show that our RFD-ECNet outperforms state-of-the-art (SOTA) compression methods. Overall, our main contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.575, + 0.892, + 0.649 + ], + "angle": 0, + "content": "- We make the first attempt to remove the massive redundancy between UWIs, and the proposed dictionary-based compression network RFD-ECNet is the first work that achieves significantly better BD-rate/PSNR than the latest VVC and other learnt methods." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.652, + 0.894, + 0.741 + ], + "angle": 0, + "content": "- We construct an exhaustive underwater feature dictionary from representative UWIs manually selected based on various underwater scenes, water types, and water depths. Besides, detailed analyses are conducted to verify the comprehensiveness and compactness of the dictionary." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.744, + 0.894, + 0.834 + ], + "angle": 0, + "content": "- To eliminate the effect of underwater styles on feature match, we utilize the underwater physical priors to design USNB to improve feature match accuracy. Moreover, we design RFVM to adaptively morph the reference features based on the dependency map, improving their similarity." + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.575, + 0.894, + 0.834 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.845, + 0.651, + 0.862 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Learnt Image Compression. Recently, learnt image compression approaches have developed rapidly and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12981" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.09, + 0.699, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.091, + 0.891, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.08, + 0.402, + 0.888, + 0.419 + ], + "angle": 0, + "content": "Figure 2: Overview of the proposed RFD-ECNet. Q indicates the quantizer. AE/AD represents the arithmetic en/decoding." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.444, + 0.47, + 0.566 + ], + "angle": 0, + "content": "achieved great breakthroughs, which can be divided into VAE-based and GAN-based. Generally, VAE-based methods [12-18] utilize an encoder, which includes some parametric linear and nonlinear transforms, to compress image to compact latent features. After quantization and entropy coding, the latent features are compressed into bit-stream. Then a decoder, which usually has a symmetrical structure with the encoder, is used to reconstruct the image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.566, + 0.47, + 0.732 + ], + "angle": 0, + "content": "To improve the rate-distortion (R-D) performance, some works focus on designing more efficient learnt model to capture redundancy in an image. [13] proposes auto-regressive model to combine the context model with the hyperprior model [12] for entropy estimation. [18] proposes window-based local attention block to capture local redundancy such as non-repetitive textures. [17] proposes Gaussian Mixture Model to estimate likelihoods of latent features more accurately. Although VAE-based methods achieve admirable R-D performance, they often present unpleasant artifacts at extremely low bitrates." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.469, + 0.87 + ], + "angle": 0, + "content": "To this end, some works [19-21] combine VAE with the generative adversarial network (GAN) to generate visually pleasing textures to counteract compression artifacts. Nevertheless, the pixel fidelity (e.g., MSE) of the image reconstructed by the GAN-based methods is quite low because the generated content is fake and deceptive. Hence, it is difficult for existing methods to achieve high pixel fidelity UWI reconstruction at extremely low bitrates by only removing redundancy within an image." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Image Set Compression. This direction aims to compress a batch of images captured at the same place from" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.444, + 0.892, + 0.565 + ], + "angle": 0, + "content": "different view angles and focal distances [23], which can be divided into local-based and cloud-based. The local-based methods [24-26] construct the reference by first preprocessing all the images in a set. For example, [25] creates a new low frequency template as reference image by averaging the low frequency components of all images. The cloud-based methods such as [27] select reference images from the massive images in the cloud." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.893, + 0.702 + ], + "angle": 0, + "content": "Obviously, the local-based methods must obtain all images before compression, which limits their usage flexibility. The cloud-based methods rely on the wide transmission channel to access the cloud disk, which cannot be achieved by the very narrow underwater wireless acoustic channel. Moreover, since these methods can only be applied to the small image subset captured at the same place, they cannot deal with UWIs captured at different underwater scenes and depths in the vast underwater world." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Reference-based Model. To the best of our knowledge, there exists no image compression method based on image/feature reference. The closest area to our work is reference-based super-resolution (RefSR), which utilizes the high-frequency information in high-resolution (HR) reference image/patch to rich the details of low resolution (LR) image. Given an arbitrary HR image, [28] uses the VGG network to simultaneously extract the referenced HR and LR features, and swaps the most similar features of reference and the LR. To overcome the inherent information deficit of a single reference, [29] uses multiple reference images to provide a more diverse pool of image features. Besides, [30] builds a face dictionary from HR face images" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12982" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.224, + 0.47, + 0.254 + ], + "angle": 0, + "content": "Figure 3: Construction of underwater multi-scale feature dictionary. \\( B \\) is the number of the representative UWIs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.275, + 0.469, + 0.304 + ], + "angle": 0, + "content": "to provide the high-frequency reference to construct more and richer features for the LR image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.305, + 0.47, + 0.593 + ], + "angle": 0, + "content": "The differences between our work and the RefSR works are as follows: (1) The RefSR task aims to learn more/richer features from the HR reference, which is a process of increasing information. In contrast, our compression task aims to learn fewer/more compact features, a process of removing redundant information. To our best knowledge, we are the first image compression work referring to the feature dictionary. (2) In [30], their dictionary only contains face images with eyes, nose and mouth, which are relatively more simple and similar than the vast UWI domain. Instead, UWIs contain multifarious underwater styles, where the common underwater objects are at diverse morphologies and sizes. To construct an exhaustive underwater dictionary, we manually select the representative UWIs based on various underwater scenes, water types, and water depths. (3) We design USNB to align the underwater styles of dictionary features and input, improving feature match accuracy. Additionally, we design RFVM to adaptively morph the reference features, further improving their similarity." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.607, + 0.289, + 0.623 + ], + "angle": 0, + "content": "3. The Proposed Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.631, + 0.445, + 0.648 + ], + "angle": 0, + "content": "3.1. Exhaustive Underwater Feature Dictionary" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.469, + 0.759 + ], + "angle": 0, + "content": "To achieve extremely low bitrate UWI compression, we propose RFD-ECNet, a novel image compression network referring to underwater feature dictionary, to remove redundancy between UWIs. First of all, an exhaustive dictionary is constructed, which is offline and shared at the encoder and decoder. The pipeline of the construction of underwater multi-scale feature dictionary is shown in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.761, + 0.469, + 0.866 + ], + "angle": 0, + "content": "To build the feature dictionary, a series of representative UWIs are selected from the largest public underwater image dataset UGWI \\( {}^{2} \\) . UGWI contains 2150 various UWIs, which are collected during oceanic explorations, humanrobot collaborative experiments, or from websites such as Google and YouTube. To select representative UWIs that cover the richest and most comprehensive common contents" + }, + { + "type": "image", + "bbox": [ + 0.597, + 0.089, + 0.791, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.501, + 0.23, + 0.889, + 0.245 + ], + "angle": 0, + "content": "Figure 4: SI and CF of images used to build the dictionary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.267, + 0.892, + 0.432 + ], + "angle": 0, + "content": "of UWIs, we manually divided the two thousand images into 300 groups according to two rules. 1) Different Objects. Based on [8], the common objects in UWIs can be divided into marine faunas of fish, turtles, sharks, snails and shellfish, etc.; marine plants of corals, seaweed, fringing reefs, etc.; non-biology of rocks, wreckage and sculpture, etc. 2) Different water types and depths. The water type is distinguished from clear to turbid, and the water depth is distinguished from shoal water, deep sea and seabed. UWIs captured in clear and shoal water present lighter color shift and better clarity, and vice versa." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.433, + 0.892, + 0.538 + ], + "angle": 0, + "content": "After grouping the UGWI manually, 1-2 images from each group are selected to build our dictionary, which is then cropped into non-overlapping \\(128 \\times 128\\) image patches \\(P\\). For each image patch, we use the pre-trained popular deep image compression network DICN [12] to extract its compression features at multi-scales, shown in Fig. 3. The generation process of dictionary can be described as," + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.553, + 0.891, + 0.57 + ], + "angle": 0, + "content": "\\[\nD _ {s} = \\mathcal {F} (P; \\theta_ {D I C N} ^ {s}) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.89, + 0.612 + ], + "angle": 0, + "content": "where \\( s \\in \\{2,3,4\\} \\) is the scale and \\( \\theta_{DICN}^{s} \\) is the parameters of the pre-trained DICN at scale \\( s \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.763 + ], + "angle": 0, + "content": "To verify the diversity of these representative UWIs, the Spatial Information (SI) and Colorfulness (CF) indices are computed respectively for the content variation along the spatial and color dimensions. Higher SI / CF indicates more complex image content / colorful. The CF versus SI distribution is plotted in Fig. 4. As shown, the distribution range is quite broad, which indicates that the content of these patches is diverse. Additionally, some points are distributed closely, which also verifies that there are many similar common content between UWIs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To compact the features in dictionary, we adopt K-means to create \\(K\\) clusters. Considering the high computational complexity of directly performing K-means on massive features of multifarious UWIs, we first perform principal components analysis (PCA) on the features of per UWI to reduce their dimension. Finally, \\(K\\) typical features at each scale are preserved, constructing our multi-scale feature dictionary. The effect of cluster number \\(K\\) on the compression performance is shown in the supplementary materials." + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.469, + 0.9 + ], + "angle": 0, + "content": "\\(^{2}\\)UGWI is a public underwater image dataset and is available online at https://github.com/Underwater-Lab-SHU" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12983" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.468, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.116, + 0.265, + 0.431, + 0.281 + ], + "angle": 0, + "content": "Figure 5: The structure of the proposed USNB." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.301, + 0.395, + 0.318 + ], + "angle": 0, + "content": "3.2. Overall of the proposed RFD-ECNet" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.47, + 0.519 + ], + "angle": 0, + "content": "The framework of our RFD-ECNet is shown in Fig. 2, which performs feature match at multiple scales (\\(s \\in \\{2,3,4\\}\\)) in a progressive manner to remove the underwater common redundancy from coarse to fine. Let \\(F_{s}\\) be the input features at scale \\(s\\), and \\(D_{s,i}\\) denotes the \\(i\\)-th dictionary features at scale \\(s\\). In the encoder, the input UWI is down-sampled by two convolutional sampling layers to obtain its features \\(F_{2}\\), which are matched with the dictionary \\(D\\) to select its reference features \\(D_{2,i}\\). To guarantee the input features \\(F_{2}\\) and \\(D\\) in the same feature space, the first-two sampling layers of RFD-ECNet are filled with that of the pre-trained DICN, which are fixed during the training of our RFD-ECNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.521, + 0.47, + 0.672 + ], + "angle": 0, + "content": "For more accurate feature match, USNB is proposed to normalize the dictionary features based on the underwater style of the input, eliminating the effect of the underwater styles diversity on feature match. Specifically, USNB utilizes the UPPs extracted from an UPPs extractor [7] to simulate the underwater imaging process [6], which dictate the underwater styles of UWIs. Moreover, the selected \\(D_{2,i}\\) is further refined by the proposed RFVM to obtain \\(RD_{2,i}\\) based on the similarity map \\(W_{2}\\) between \\(F_{2}\\) and \\(D_{2,i}\\), greatly improving their similarity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.47, + 0.747 + ], + "angle": 0, + "content": "After removing redundancy on three scales, the latent features \\(z\\) and the dependency maps \\((W_{2}, W_{3}, W_{4})\\) are quantized by the uniform noise approximated method [12], and then entropy coded by the Gaussian mixture entropy model [17] to the bit-stream." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.756, + 0.433, + 0.772 + ], + "angle": 0, + "content": "3.3.USNB-based Feature Match (USN-FMM)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.884 + ], + "angle": 0, + "content": "Feature match aims to select the reference features that have the most similar textures to the input features. However, the UWIs sharing similarity may have multifarious underwater styles of color shift and distance-dependent clarity. Hence, it is necessary to normalize the underwater styles of dictionary features toward that of the input before the feature match." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Underwater Style Normalize. By studying the process" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.09, + 0.895, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.266, + 0.855, + 0.282 + ], + "angle": 0, + "content": "Figure 6: The structure of the proposed RFVM." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.301, + 0.892, + 0.362 + ], + "angle": 0, + "content": "of underwater imaging, it can be observed that the underwater styles are dictated by underwater physical priors such as ambient light and imaging transmission map, which can be described by the underwater physical scattering model:" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.371, + 0.892, + 0.397 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} J = I \\times T + A \\times (1 - T) \\\\ = \\quad_ {c d} \\end{array} \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.393, + 0.678, + 0.407 + ], + "angle": 0, + "content": "\\[\nT = e ^ {- \\alpha d}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.419, + 0.892, + 0.584 + ], + "angle": 0, + "content": "where \\(I\\) denotes the clear scene without underwater style and \\(J\\) is the captured UWI with multifarious underwater styles. Under the effect of underwater physical priors, including \\(T\\) and \\(A\\), \\(I\\) is evolved to \\(J\\). \\(T\\) and \\(A\\) respectively represent the transmission map and the global ambient light, and their visual examples are presented in the supplementary materials. \\(T\\) is calculated by \\(\\alpha\\) and \\(d\\), which respectively refer to light attenuation coefficient and the distance between camera and object, which leads to the distance-dependent clarity. Derived from Eq. (2), the clear scene can be modeled as:" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.591, + 0.891, + 0.622 + ], + "angle": 0, + "content": "\\[\nI = \\frac {J - A \\times (1 - T)}{T} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.891, + 0.66 + ], + "angle": 0, + "content": "Based on Eq. (2) and Eq. (3), the dictionary features can be normalized towards the underwater style of input by" + }, + { + "type": "equation", + "bbox": [ + 0.511, + 0.668, + 0.892, + 0.741 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} J ^ {d i c. i n p u t} = I ^ {d i c} \\times T ^ {i n p u t} + A ^ {i n p u t} \\times \\left(1 - T ^ {i n p u t}\\right) \\\\ = \\frac {J ^ {d i c} - A ^ {d i c} \\times (1 - T ^ {d i c})}{T ^ {d i c}} \\times T ^ {\\text {i n p u t}} \\tag {4} \\\\ + A ^ {i n p u t} \\times (1 - T ^ {i n p u t}) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Based on the above analysis, we propose the USNB to parametrically implement Eq. (4), as shown in Fig. 5, which is used before the feature match to normalize the underwater styles of dictionary features toward the input. In Fig. 5, \\(D_{s}\\) and \\(ND_{s}\\) respectively correspond to \\(J_{dic}\\) and \\(J_{dic\\_input}\\) in Eq. (4). Underwater physical priors of dictionary features \\((T^{dic}\\) and \\(A^{dic})\\) and that of the input \\((T^{in}\\) and \\(A^{in})\\) are fed to several convention layers to normalize \\(D_{s}\\) to \\(ND_{s}\\) by following the data flow in Eq. (4). Notably, the network parameters for processing \\(T^{dic}\\) and \\(A^{dic}\\) are shared" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12984" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.28, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.22, + 0.25, + 0.233 + ], + "angle": 0, + "content": "(a) UGWI, Rate-PSNR" + }, + { + "type": "image", + "bbox": [ + 0.281, + 0.088, + 0.485, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.316, + 0.222, + 0.452, + 0.236 + ], + "angle": 0, + "content": "(b) EUVP, Rate-PSNR" + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.09, + 0.687, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.523, + 0.22, + 0.651, + 0.233 + ], + "angle": 0, + "content": "(c) UFO, Rate-PSNR" + }, + { + "type": "image", + "bbox": [ + 0.69, + 0.089, + 0.892, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.724, + 0.222, + 0.857, + 0.236 + ], + "angle": 0, + "content": "(d) UIEB, Rate-PSNR" + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.243, + 0.879, + 0.26 + ], + "angle": 0, + "content": "Figure 7: R-D curves of different image compression methods on UGWI, EUVP [31], UFO [32], and UIEB [8] datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.279, + 0.47, + 0.37 + ], + "angle": 0, + "content": "with that for \\( T^{dic} \\) and \\( A^{dic} \\) to guarantee that all underwater physical priors are in the same feature space. As such, the proposed USNB is able to normalize the underwater styles of the dictionary features toward the input for more accurate feature match. The effectiveness of USNB is verified in the ablation studies." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.374, + 0.47, + 0.45 + ], + "angle": 0, + "content": "Feature Match. To select the reference features \\( D_{s,i} \\) from the dictionary features \\( D_{s} \\) for input features \\( F_{s} \\), we adopt the widely used inner product to measure the similarity score between \\( F_{s} \\) and \\( D_{s} \\). The similarity scores between \\( F_{s} \\) and \\( D_{s} \\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.457, + 0.469, + 0.492 + ], + "angle": 0, + "content": "\\[\nS _ {s} = \\left\\langle F _ {s}, \\frac {D _ {s}}{\\| D _ {s} \\|} \\right\\rangle \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.505, + 0.47, + 0.581 + ], + "angle": 0, + "content": "Following the procedure in [33], Eq. (5) is implemented by a convolution operation, where the kernel weights are set as \\( D_{s} \\), to accelerate the similarity calculations. The \\( i \\)-th dictionary feature with the highest similarity score is selected as the reference feature \\( D_{s,i} \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.602, + 0.45, + 0.618 + ], + "angle": 0, + "content": "3.4. Reference Feature Variant Module (RFVM)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Although the reference features \\( D_{s,i} \\) and the input features \\( F_{s} \\) share some similarities, the relative position and shape of the similar areas in \\( D_{s,i} \\) and \\( F_{s} \\) may be dramatically different. To achieve the highest possible similarity, we develop the RFVM to adaptively morph the \\( D_{s,i} \\) based on \\( F_{s} \\), shown in Fig. 6. RFVM utilizes the spatial variant recursive convolution (SVRConv) [34] to implement the feature variant on a large receptive field, which is able to facilitate the dramatic spatial variant by the long-distance information propagation of recurrent convolution and the learned weights for different locations. The weights of SVRConv are learned by exploring the dependency between \\( D_{s,i} \\) and \\( F_{s} \\). To obtain the global dependency map \\( W \\), dilated convolutions with different dilation rates are used to exploit the spatial information at different receptive fields. As such, our RFVM is able to morph the reference features in a large receptive field to improve the similarity with the input features." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.279, + 0.634, + 0.296 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.304, + 0.892, + 0.409 + ], + "angle": 0, + "content": "Extensive experiments are conducted to evaluate the extreme compression performance of our RFD-ECNet. First, we test RFD-ECNet on four different UWI datasets objectively and subjectively to verify our excellent generalization. After that, a series of ablation studies are presented to respectively verify the effectiveness of our multi-scale manner, USNB and RFVM." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.42, + 0.707, + 0.436 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.443, + 0.892, + 0.638 + ], + "angle": 0, + "content": "Datasets. We perform experiments on four public UWI datasets, including the UGWI dataset, EUVP dataset [31], UFO dataset [32], and UIEB dataset [8]. These UWI datasets are collected during different oceanic explorations and hence include various underwater scenes and rich ocean species. As stated in Section 3.1, some representative UWIs selected from UGWI dataset are utilized to construct our underwater multi-scale feature dictionary. The rest of UGWI are divided into 1550 UWIs for training and 300 UWIs for testing. Additionally, we randomly select 100 images respectively from EUVP [31], UFO [32], and UIEB [8] to test the pre-trained RFD-ECNet to verify the generalization of our RFD-ECNet." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.64, + 0.892, + 0.684 + ], + "angle": 0, + "content": "Training. As the most VAE-based methods, our RFD-ECNet is optimized by the rate-distortion trade-off loss function, which can be described as:" + }, + { + "type": "equation", + "bbox": [ + 0.641, + 0.698, + 0.891, + 0.713 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda \\cdot D + R, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.84 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is a trade-off parameter to balance bitrate \\(R\\) and distortion \\(D\\). In our work, MSE is used as the \\(D\\), and \\(\\lambda\\) belongs to the set \\(\\{512, 256, 128, 64, 32\\}\\) for 5 different compression ratios. The channel width of RFD-ECNet is set as 192, and the bottleneck layer is set as 64. Detailed network architecture is introduced in the supplementary materials. All model are trained using the Adam optimizer [35] with standard parameters and learning rate of \\(1 \\times 10^{-4}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Evaluation. The compression performance is measured by bitrate \\( R \\) and distortion \\( D \\), which are respectively calculated by bits-per-pixel (bpp) and Peak Signal to Noise Ratio (PSNR). Lower bpp and higher PSNR indicate better com" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12985" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.137 + ], + "angle": 0, + "content": "Table 1: Comparison of BD-rate and BD-PSNR on UGWI, EUVP [31], UIEB [8], and UFO [32] testsets. The BD-rate and BD-PSNR are calculated from PSNR-BPP curve over data points with \\( \\mathrm{bpp} < 0.1 \\), when BPG [10] is set as the anchor. The performance of SOTA compression codec VVC is marked in red. The best performance is bolded." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.142, + 0.89, + 0.314 + ], + "angle": 0, + "content": "
MethodsBD-rate ↓ (%)BD-PSNR ↑ (dB)Computation complexity
UGWIEUVPUIEBUFOAvg.UGWIEUVPUIEBUFOAvg.Param. (M)FLOPs (G)
VVC-intra [11]-19.0-16.2-16.0-16.1-16.80.690.430.520.470.53//
JPEG2000 [9]61.768.467.266.966.1-1.62-1.71-1.84-1.56-1.68//
BPG [10]0000000000//
Minnen (NIPS'18) [13]-3.814.89.819.09.90.16-0.36-0.33-0.59-0.2814.127.2
Cheng (CVPR'20) [17]-12.8-8.4-1.3-8.3-7.70.430.200.040.240.2320.561.3
Zou (CVPR'22) [18]-13.8-10.3-12.4-14.7-12.80.480.250.360.430.3875.033.3
Ours-slim-50.2-44.6-42.6-34.7-43.01.731.011.110.651.1215.440.7
Ours-53.7-50.3-52.9-37.3-48.51.971.181.560.991.4335.886.7
" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.328, + 0.209, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.134, + 0.427, + 0.157, + 0.436 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.21, + 0.329, + 0.333, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.225, + 0.427, + 0.318, + 0.436 + ], + "angle": 0, + "content": "JPEG2000, Bpp=0.137" + }, + { + "type": "image_caption", + "bbox": [ + 0.236, + 0.436, + 0.305, + 0.444 + ], + "angle": 0, + "content": "PSNR=27.37 dB" + }, + { + "type": "image", + "bbox": [ + 0.335, + 0.329, + 0.46, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.427, + 0.444, + 0.436 + ], + "angle": 0, + "content": "VVC-intra, Bpp=0.139" + }, + { + "type": "image_caption", + "bbox": [ + 0.362, + 0.436, + 0.432, + 0.444 + ], + "angle": 0, + "content": "PSNR=29.35 dB" + }, + { + "type": "image", + "bbox": [ + 0.462, + 0.329, + 0.587, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.465, + 0.427, + 0.585, + 0.436 + ], + "angle": 0, + "content": "Cheng(CVPR'20), Bpp=0.146" + }, + { + "type": "image_caption", + "bbox": [ + 0.49, + 0.436, + 0.558, + 0.444 + ], + "angle": 0, + "content": "PSNR=29.13 dB" + }, + { + "type": "image", + "bbox": [ + 0.589, + 0.329, + 0.713, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.616, + 0.427, + 0.686, + 0.436 + ], + "angle": 0, + "content": "Ours, Bpp=0.137" + }, + { + "type": "image_caption", + "bbox": [ + 0.617, + 0.436, + 0.685, + 0.444 + ], + "angle": 0, + "content": "PSNR=30.16 dB" + }, + { + "type": "image", + "bbox": [ + 0.718, + 0.329, + 0.774, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.734, + 0.427, + 0.762, + 0.436 + ], + "angle": 0, + "content": "Cheng" + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.329, + 0.832, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.794, + 0.427, + 0.815, + 0.435 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.834, + 0.357, + 0.888, + 0.4 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.848, + 0.401, + 0.872, + 0.409 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.448, + 0.209, + 0.546 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.134, + 0.547, + 0.157, + 0.556 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.21, + 0.448, + 0.333, + 0.546 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.225, + 0.547, + 0.318, + 0.556 + ], + "angle": 0, + "content": "JPEG2000, Bpp=0.049" + }, + { + "type": "image_caption", + "bbox": [ + 0.236, + 0.556, + 0.305, + 0.564 + ], + "angle": 0, + "content": "PSNR=22.17 dB" + }, + { + "type": "image", + "bbox": [ + 0.335, + 0.448, + 0.46, + 0.546 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.547, + 0.444, + 0.556 + ], + "angle": 0, + "content": "VVC-intra, Bpp=0.049" + }, + { + "type": "image_caption", + "bbox": [ + 0.362, + 0.556, + 0.432, + 0.563 + ], + "angle": 0, + "content": "PSNR=25.22 dB" + }, + { + "type": "image", + "bbox": [ + 0.462, + 0.448, + 0.587, + 0.546 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.465, + 0.547, + 0.585, + 0.556 + ], + "angle": 0, + "content": "Cheng(CVPR'20), Bpp=0.049" + }, + { + "type": "image_caption", + "bbox": [ + 0.49, + 0.556, + 0.558, + 0.564 + ], + "angle": 0, + "content": "PSNR=25.28 dB" + }, + { + "type": "image", + "bbox": [ + 0.589, + 0.448, + 0.714, + 0.546 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.616, + 0.547, + 0.686, + 0.556 + ], + "angle": 0, + "content": "Ours, Bpp=0.048" + }, + { + "type": "image_caption", + "bbox": [ + 0.617, + 0.556, + 0.685, + 0.564 + ], + "angle": 0, + "content": "PSNR=26.15 dB" + }, + { + "type": "image", + "bbox": [ + 0.718, + 0.448, + 0.775, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.724, + 0.492, + 0.768, + 0.499 + ], + "angle": 0, + "content": "JPEG2000" + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.448, + 0.832, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.781, + 0.492, + 0.826, + 0.5 + ], + "angle": 0, + "content": "VVC-intra" + }, + { + "type": "image", + "bbox": [ + 0.718, + 0.502, + 0.774, + 0.545 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.733, + 0.546, + 0.761, + 0.554 + ], + "angle": 0, + "content": "Cheng" + }, + { + "type": "image_caption", + "bbox": [ + 0.775, + 0.492, + 0.832, + 0.5 + ], + "angle": 0, + "content": "VVC-intra" + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.502, + 0.832, + 0.545 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.794, + 0.546, + 0.815, + 0.554 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.834, + 0.448, + 0.888, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.834, + 0.492, + 0.89, + 0.5 + ], + "angle": 0, + "content": "\\( {13}/{14} \\)" + }, + { + "type": "image", + "bbox": [ + 0.834, + 0.502, + 0.888, + 0.545 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.849, + 0.547, + 0.872, + 0.555 + ], + "angle": 0, + "content": "" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.569, + 0.895, + 0.615 + ], + "angle": 0, + "content": "Figure 8: Visual examples of the reconstructed images. The examples in two rows are respectively from UGWI and EUVP [31] testset. The metrics are bpp \\((\\downarrow)\\) and PSNR \\((\\uparrow)\\). At extremely low bpp, our reconstructed images have more details and higher pixel fidelity (measured by PSNR) than others." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.641, + 0.47, + 0.658 + ], + "angle": 0, + "content": "pression performance. Notably, our bpp is calculated by," + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.666, + 0.47, + 0.7 + ], + "angle": 0, + "content": "\\[\nb p p = \\frac {b i t s _ {z} + b i t s _ {W} + b i t s _ {i n d e x}}{N _ {\\text {p i x e l s}}} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.469, + 0.81 + ], + "angle": 0, + "content": "where \\( \\text{bits}_z \\) and \\( \\text{bits}_W \\) respectively represent the bits of latent features \\( z \\) and dependency map \\( W \\). \\( \\text{bits}_{index} \\) denotes the bits for coding the index numbers of reference features, which are directly coded by Huffman coding. In addition to R-D curves, the widely used Bjøntegaard delta rate (BD-rate) and BD-PSNR are also evaluated. Lower BD-rate and higher BD-PSNR indicate more efficient compression." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.901 + ], + "angle": 0, + "content": "For the comparative methods, we compare our RFDECNet with influential and SOTA image compression networks, including Minnen (NIPS'18) [13], Cheng (CVPR'20) [17], and Zou (CVPR'22) [18]. For fair comparisons, all networks are trained on the UGWI dataset. Additionally, some conventional CODECs are compared, includ" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.641, + 0.892, + 0.688 + ], + "angle": 0, + "content": "ing popular JPEG2000 [9], BPG (HEVC-intra) [10] and the latest VVC-intra (VTM 11.0) [11]. For BPG and VVC, the highest PSNR setting (4:4:4) is tested." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.697, + 0.813, + 0.713 + ], + "angle": 0, + "content": "4.2. Comparison against SOTA methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "R-D Performance. Fig. 7 presents the R-D curves on four UWI testsets of UGWI, EUVP [31], UIEB [8], and UFO [32]. As shown, the R-D curves of our RFD-ECNet are above the curves of all comparative methods on four testsets, which demonstrates that our method achieves better compression performance than all comparative methods and our excellent generalization and robustness. Notably, as bpp decreases, our RFD-ECNet achieves higher PSNR improvements than comparative methods. This indicates that the reference features provided by our underwater feature dictionary are very efficient for the reconstruction, especially at extremely low bitrates." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12986" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.472, + 0.121 + ], + "angle": 0, + "content": "Table 2: BD-rate \\((\\%)\\) and BD-PSNR (dB) of VVC/HEVC at inter/intra modes, where Minnen [13] is set as the anchor." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.127, + 0.468, + 0.178 + ], + "angle": 0, + "content": "
MethodsVVC-interVVC-intraHEVC-interHEVC-intraOurs
BD-rate ↓-22.1-21.00.23.2-59.5
BD-PSNR ↑0.850.82-0.10-0.122.25
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.19, + 0.47, + 0.372 + ], + "angle": 0, + "content": "The BD-rate of different image compression methods with BPG [10] as the anchor is presented in Table 1. As shown, our method achieves the best BD-rate and BD-PSNR results on four testsets, which indicates that we use the smallest amount of bits to achieve the highest PSNR among all methods. Specially, our average BD-rate of \\(-48.5\\%\\) and BD-PSNR of \\(1.43\\mathrm{dB}\\) are much better than the most advanced codec VVC-intra' - \\(16.8\\%\\) and \\(0.53\\mathrm{dB}\\). More intuitively, when VVC is set as the anchor, our RFD-ECNet achieves breakthrough BD-rate saving of \\(31.7\\%\\) and BD-PSNR of \\(0.90\\mathrm{dB}\\), demonstrating the advanced performance of our RFD-ECNet on UWI extreme compression." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.372, + 0.47, + 0.598 + ], + "angle": 0, + "content": "Visual Quality. Fig. 8 shows visual examples of reconstructed images by our RFD-ECNet, Cheng (CVPR'20), the most advanced VVC-intra, and the widely used JPEG2000. As shown, our reconstructed images retain more details, while the reconstructed images of VVC-intra and JPEG2000 present obvious blurring and blocking effects at extremely low bpp. As shown in the second row, when bpp=0.049, VVC-intra, Cheng (CVPR'20) and JPEG2000 completely lose the common object of sand, while our RFD-ECNet can roughly reconstruct the sand by referencing our dictionary. Overall, our pixel fidelity is higher than others at the similar extremely low bpp, which can be verified by our higher PSNR. More visual results tested on underwater videos are provided at https://github.com/lilala0/RFD-ECNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.795 + ], + "angle": 0, + "content": "Comparison with video CODECs. To verify that the redundancy between UWIs cannot be efficiently removed by video CODEcs, our RFD-ECNet is compared with the latest video CODEcs of VVC-inter and HEVC-inter. Their performance on UGWI testset measured by BD-rate and BD-PSNR with the Minnen [13] as the anchor is shown in Table 2. As shown, we achieve better results than both VVC-inter and HEVC-inter, verifying that our RFD-ECNet referencing to dictionary is more efficient than video CODEcs to remove the redundancy between UWIs. Moreover, both video CODEcs at inter-mode only achieve tiny improvement of BD-rate/PSNR than the intra-mode. This verifies that there is redundancy between UWIs indeed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Comparison of complexity. The trainable parameters and FLOPs of all approaches are compared in Table 1. As shown, our parameters (35.8 M) is much less than that (99.8 M) of compression network [18]. Additionally, we also provide a slim version of Our RFD-ECNet by narrowing our network channels of 192 to 128 (denoted as Ours-slim), which only have 15.4M parameters and 40.7G FLOPs. No" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.135 + ], + "angle": 0, + "content": "Table 3: BD-rate \\((\\%)\\) and BD-PSNR (dB) of ablation studies about our USNB and RFVM, where BPG [10] is set as the anchor." + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.142, + 0.89, + 0.196 + ], + "angle": 0, + "content": "
SettingOursw/o USNBw/o RFVMw/o USNB&RFVM
BD-rate ↓-53.7-33.6-43.1-24.6
BD-PSNR ↑1.971.141.490.83
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.212, + 0.892, + 0.257 + ], + "angle": 0, + "content": "Table 4: BD-rate \\((\\%)\\) and BD-PSNR (dB) of ablation studies about the multi-scale manner, where BPG [10] is set as the anchor." + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.264, + 0.89, + 0.315 + ], + "angle": 0, + "content": "
Scale settingScale-{2}Scales-{2,3}Scales-{2,3,4}
BD-rate ↓-46.1-49.8-53.7
BD-PSNR ↑1.671.831.97
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.342, + 0.892, + 0.389 + ], + "angle": 0, + "content": "tably, ours-slim still achieves better performance than all SOTA methods with lower complexity, illustrating our excellent UWI extreme compression performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.414, + 0.652, + 0.431 + ], + "angle": 0, + "content": "5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.443, + 0.892, + 0.701 + ], + "angle": 0, + "content": "Effectiveness of USNB and RFVM. To verify the effectiveness of the proposed USNB and RFVM, a series of ablation experiments are conducted, where the USNB and RFVM are removed from our RFD-ECNet in sequence. The performance of each ablation is measured by the BD-rate and BD-PSNR with the BPG as the anchor, shown in Table 3. w/o USNB indicates the network that directly performs feature match by inner product without using our USNB to normalize the dictionary features. w/o RFVM is the network where the matched reference features are not fed into our RFVM and therefore cannot be varied adaptively based on the input features. w/o USNB&RFVM is the network without both USNB and RFVM. As can be seen from Table 3, the removal of either USNB or RFVM degrades the performance of our RFD-ECNet. Moreover, the performance degrades most when USNB and RFVM are removed simultaneously, verifying the effectiveness of USNB and RFVM." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of multi-scale reference. In our RFD-ECNet, the input features are matched with the feature dictionary at three scales (\\(s = 2,3,4\\)), considering that the similarity between UWIs is reflected on the textures, structures, and semantics. Here we conduct ablations to verify the effectiveness of the multi-scale manner, and provide the results in Table 4. Since the features on scale-1 contain more noise less semantic information, we perform feature match starting from scale-2. As shown, our RFD-ECNet referring dictionary at scales-\\{2,3,4\\} achieves the best performance, followed by scales-\\{2,3\\} and scale-\\{2\\}\\), which verifies that it is efficient to remove the underwater common redundancy at multiple scales from coarse to fine." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12987" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.191, + 0.106 + ], + "angle": 0, + "content": "6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.116, + 0.473, + 0.299 + ], + "angle": 0, + "content": "This work creatively removes redundancy between UWIs and proposes a novel reference-based image compression framework. Actually, the redundancy between images exists not only in UWIs but also in other image domains where independent images contain some common objects specific to the image domain. For example, all Martian images [36] contain rocks and sand; all face images [37] contain eyes, nose and mouth; most remote sensing images [38] contain buildings, road and so on. However, existing image compression works neglect this nature and only remove redundancy in an image, which may limit the development of image compression." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.299, + 0.473, + 0.406 + ], + "angle": 0, + "content": "To validate our hypothesis, we additionally conduct preliminary experiments on Martian images [36] by adjusting our network. Experimental results presented in the supplementary materials show that we also achieve better performance than VVC and Ding (VCIP'22) [36], illustrating the efficiency and feasibility of removing redundancy between images in other image domains." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.421, + 0.196, + 0.437 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.447, + 0.473, + 0.751 + ], + "angle": 0, + "content": "In this paper, we explore the characteristics of UWIs and find that UWIs present multifarious underwater styles and different UWIs share some common ocean objects at diverse morphologies and sizes, resulting in plenty of redundancy between UWIs. Hence, we construct an exhaustive and compact underwater multi-scale feature dictionary from the manually selected representative UWIs, which provides coarse-to-fine reference for our RFD-ECNet to fully remove redundancy between UWIs. Meanwhile, to eliminate the effect of underwater styles on feature match, we utilize UPPs to design the USNB to align the multifarious underwater styles of dictionary towards that of input features. Moreover, to improve the similarity between the input and reference features, we propose RFVM to perform adaptive reference feature variant. Finally, extensive comparisons are conducted to verify our significant performance improvement than SOTA methods including the latest VVC, and comprehensive ablation studies verify the effectiveness of each module in our RFD-ECNet." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.763, + 0.236, + 0.78 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "This work is supported in part by the National Natural Science Foundation of China under Grant 61931022 and Grant 62271301; in part by the Shanghai Science and Technology Program under Grant 22511105200; in part by the Shanghai Excellent Academic Leaders Program under Grant 23XD1401400; in part by the Natural Science Foundation of Shandong Province under Grant ZR2022ZD38." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.091, + 0.598, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.509, + 0.115, + 0.892, + 0.171 + ], + "angle": 0, + "content": "[1] G.L. 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However, existing image compression methods achieve inferior performance on UWIs because they do not consider the characteristics of UWIs: (1) Multifarious underwater styles of color shift and distance-dependent clarity, caused by the unique underwater physical imaging; (2) Massive redundancy between different UWIs, caused by the fact that different UWIs contain several common ocean objects, which have plenty of similarities in structures and semantics. To remove redundancy among UWIs, we first construct an exhaustive underwater multi-scale feature dictionary to provide coarse-to-fine reference features for UWI compression. Subsequently, an extreme UWI compression network with reference to the feature dictionary $(RFD-ECNet)^{1}$ is creatively proposed, which utilizes feature match and reference feature variant to significantly remove redundancy among UWIs. To align the multifarious underwater styles and improve the accuracy of feature match, an underwater style normalized block (USNB) is proposed, which utilizes underwater physical priors extracted from the underwater physical imaging model to normalize the underwater styles of dictionary features toward the input. Moreover, a reference feature variant module (RFVM) is designed to adaptively morph the reference features, improving the similarity between the reference and input features. Experimental results on four UWI datasets show that our RFD-ECNet is the first work that achieves a significant BD-rate saving of $31\%$ over the most advanced VVC. + +# 1. Introduction + +Recently, underwater exploration attracts great attention from governments, scientists, and the public due to + +![](images/2f34891c46e60dc4cce2753262fbe0c4f40f7e4e9aa262349ecd7b7fbb5a3c19.jpg) +(a) Existing image compression pipeline + +![](images/9442e45745d070d366734a86db7eca7c681e3cdedd491ab1c9d59bb42beccf70.jpg) +(b) Our motivation and pipeline +Figure 1: Key ideas of our work. Different UWIs have similarities in texture, structure and semantic, which can be included in an underwater feature dictionary to provide reference for UWI compression. E/D indicates encoder/decoder. + +the growing underwater applications. For example, mine search, nuclear-reactors detection, and underwater power inspection [1] are parts of homeland security operations. In addition, marine biology [2] and archaeology [3] are important scientific research for ocean resource development. Moreover, underwater entertainment [4] such as underwater live broadcasts is becoming greatly popular with the public. + +In these underwater applications, images taken underwater play an essential role. To be transmitted from the deep sea to the board or ground, underwater images (UWIs) must be compressed at extremely low bitrates due to the very narrow underwater wireless acoustic bandwidth of about 20 kbps [5]. However, existing image compression approaches severely degrade the pixel fidelity (e.g., MSE) of UWIs at extremely low bitrates (<0.1bpp), which greatly impairs the + +broad application of UWIs. Hence, it is highly urgent to design a more powerful extreme UWI compression algorithm. + +Different from general images, UWIs present two unique underwater characteristics: (1) UWIs present multifarious underwater styles of color shift and distance-dependent clarity. This is because the underwater imaging process is quite different from that in the open air [6]. When light travels through water, it suffers from absorption and scattering. Specifically, the blueish/greenish color shift is caused by the fact that the red light of the shortest wavelength is absorbed first, and then the green and blue light are followed [7]. In addition, light is scattered by the particles in water, which change the direction of light propagation [8], resulting in the spatially varying distance dependencies of clarity, i.e., the image clarity decreases as the distance to the objects increases. (2) Different UWIs contain some common underwater objects at diverse morphologies and sizes. Due to the special underwater natural environment, there are some common underwater objects such as fish, corals, and rocks that widely exist in different UWIs in diverse morphologies and sizes. Hence, there are plenty of similar representations between UWIs. As shown in Fig. 1 (b), although the UWIs are captured at different times and in various underwater scenes, they contain some same underwater objects such as water, corals, and rocks, which share plenty of similarities in textures, structures, and semantics. + +Given the characteristics of UWIs, there are two main drawbacks for existing image compression methods [9-21]: (1) They only remove redundancy within an image and do not consider redundancy between UWIs. Conventional image compression CODEs such as JPEG2000 [9], BPG [10] and the latest VVC-intra [11] reduce the intra-redundancy through transform and intra-prediction. Recently, learnt image compression methods [12-18] have shown greater potential than conventional CODEs. Based on variational autoencoder (VAE), [12] designs a hyperprior model to remove the statistic redundancy within an image. After that, [13] proposes an autoregressive model to further remove the local context redundancy. However, all of them are limited to removing redundancy in only an image. (2) They utilize a unitary compression that cannot handle the multifarious underwater styles of color shift and distance-dependent clarity. It is reasonable to use the unitary compression for the general terrestrial images because the colors (r, g, b) of terrestrial images are evenly distributed [22] and the internal clarity is steady broadly. However, it limits their performance on UWIs because the UWIs are full of multifarious color shift and distance-dependent clarity. To design an efficient extreme UWI compression method, it needs to both remove redundancy between UWIs and align the multifarious underwater styles. + +Accordingly, we creatively propose to compress UWIs by referencing a dictionary to remove redundancy between + +UWIs. First, we construct an exhaustive underwater multiscale feature dictionary to provide from coarse to fine reference information for the UWI compression. Specifically, the features in the dictionary are extracted from plenty of representative UWIs, which are strictly selected according to various underwater scenes, including different underwater objects, water types, and water depths. As such, our dictionary could cover a wide range of underwater common objects, assisting the UWI compression to fully remove redundancy between UWIs. Subsequently, we design a novel extreme UWI compression network with reference to the underwater feature dictionary (RFD-ECNet), shown in Fig 2, where the features of input UWI are matched with the dictionary to select the reference features, and then the residuals between the input and reference features are compressed, significantly reducing the coding bits of UWIs. + +Additionally, an underwater styles normalization block-based feature match (USN-FMM) is proposed to ensure that the match is not interfered by the multifarious underwater styles and focuses on selecting the references that have the most similar texture to the input. To be specific, the USNB utilizes the underwater physical priors (UPPs) extracted from the underwater imaging physical model [6] to normalize the underwater style of reference features towards that of the input. Moreover, to improve the similarity between the reference and input features, a reference feature variant module (RFVM) is designed to adaptively morph the reference features based on their dependency relevance to the input feature. Extensive experimental results show that our RFD-ECNet outperforms state-of-the-art (SOTA) compression methods. Overall, our main contributions are summarized as follows: + +- We make the first attempt to remove the massive redundancy between UWIs, and the proposed dictionary-based compression network RFD-ECNet is the first work that achieves significantly better BD-rate/PSNR than the latest VVC and other learnt methods. +- We construct an exhaustive underwater feature dictionary from representative UWIs manually selected based on various underwater scenes, water types, and water depths. Besides, detailed analyses are conducted to verify the comprehensiveness and compactness of the dictionary. +- To eliminate the effect of underwater styles on feature match, we utilize the underwater physical priors to design USNB to improve feature match accuracy. Moreover, we design RFVM to adaptively morph the reference features based on the dependency map, improving their similarity. + +# 2. Related Works + +Learnt Image Compression. Recently, learnt image compression approaches have developed rapidly and + +![](images/c88cb3b234852270807a38f8dbd6e7c605e9146847a6b6ed352621945f9eb128.jpg) +Figure 2: Overview of the proposed RFD-ECNet. Q indicates the quantizer. AE/AD represents the arithmetic en/decoding. + +![](images/cc6868b93d08ba9672fe13e862aca36c2843ddd0b173071e97f4eefda6ad1da3.jpg) + +achieved great breakthroughs, which can be divided into VAE-based and GAN-based. Generally, VAE-based methods [12-18] utilize an encoder, which includes some parametric linear and nonlinear transforms, to compress image to compact latent features. After quantization and entropy coding, the latent features are compressed into bit-stream. Then a decoder, which usually has a symmetrical structure with the encoder, is used to reconstruct the image. + +To improve the rate-distortion (R-D) performance, some works focus on designing more efficient learnt model to capture redundancy in an image. [13] proposes auto-regressive model to combine the context model with the hyperprior model [12] for entropy estimation. [18] proposes window-based local attention block to capture local redundancy such as non-repetitive textures. [17] proposes Gaussian Mixture Model to estimate likelihoods of latent features more accurately. Although VAE-based methods achieve admirable R-D performance, they often present unpleasant artifacts at extremely low bitrates. + +To this end, some works [19-21] combine VAE with the generative adversarial network (GAN) to generate visually pleasing textures to counteract compression artifacts. Nevertheless, the pixel fidelity (e.g., MSE) of the image reconstructed by the GAN-based methods is quite low because the generated content is fake and deceptive. Hence, it is difficult for existing methods to achieve high pixel fidelity UWI reconstruction at extremely low bitrates by only removing redundancy within an image. + +Image Set Compression. This direction aims to compress a batch of images captured at the same place from + +different view angles and focal distances [23], which can be divided into local-based and cloud-based. The local-based methods [24-26] construct the reference by first preprocessing all the images in a set. For example, [25] creates a new low frequency template as reference image by averaging the low frequency components of all images. The cloud-based methods such as [27] select reference images from the massive images in the cloud. + +Obviously, the local-based methods must obtain all images before compression, which limits their usage flexibility. The cloud-based methods rely on the wide transmission channel to access the cloud disk, which cannot be achieved by the very narrow underwater wireless acoustic channel. Moreover, since these methods can only be applied to the small image subset captured at the same place, they cannot deal with UWIs captured at different underwater scenes and depths in the vast underwater world. + +Reference-based Model. To the best of our knowledge, there exists no image compression method based on image/feature reference. The closest area to our work is reference-based super-resolution (RefSR), which utilizes the high-frequency information in high-resolution (HR) reference image/patch to rich the details of low resolution (LR) image. Given an arbitrary HR image, [28] uses the VGG network to simultaneously extract the referenced HR and LR features, and swaps the most similar features of reference and the LR. To overcome the inherent information deficit of a single reference, [29] uses multiple reference images to provide a more diverse pool of image features. Besides, [30] builds a face dictionary from HR face images + +![](images/836f6807d027e6e82c7443a0e41cea7cfa9a5981d1060a6d2fb7025f70103a62.jpg) +Figure 3: Construction of underwater multi-scale feature dictionary. $B$ is the number of the representative UWIs. + +to provide the high-frequency reference to construct more and richer features for the LR image. + +The differences between our work and the RefSR works are as follows: (1) The RefSR task aims to learn more/richer features from the HR reference, which is a process of increasing information. In contrast, our compression task aims to learn fewer/more compact features, a process of removing redundant information. To our best knowledge, we are the first image compression work referring to the feature dictionary. (2) In [30], their dictionary only contains face images with eyes, nose and mouth, which are relatively more simple and similar than the vast UWI domain. Instead, UWIs contain multifarious underwater styles, where the common underwater objects are at diverse morphologies and sizes. To construct an exhaustive underwater dictionary, we manually select the representative UWIs based on various underwater scenes, water types, and water depths. (3) We design USNB to align the underwater styles of dictionary features and input, improving feature match accuracy. Additionally, we design RFVM to adaptively morph the reference features, further improving their similarity. + +# 3. The Proposed Method + +# 3.1. Exhaustive Underwater Feature Dictionary + +To achieve extremely low bitrate UWI compression, we propose RFD-ECNet, a novel image compression network referring to underwater feature dictionary, to remove redundancy between UWIs. First of all, an exhaustive dictionary is constructed, which is offline and shared at the encoder and decoder. The pipeline of the construction of underwater multi-scale feature dictionary is shown in Fig. 3. + +To build the feature dictionary, a series of representative UWIs are selected from the largest public underwater image dataset UGWI ${}^{2}$ . UGWI contains 2150 various UWIs, which are collected during oceanic explorations, humanrobot collaborative experiments, or from websites such as Google and YouTube. To select representative UWIs that cover the richest and most comprehensive common contents + +![](images/573ce1a6f589bf9fdf7c52cca384f6888d071c05b3e4f1aaf8053a9296e33c38.jpg) +Figure 4: SI and CF of images used to build the dictionary. + +of UWIs, we manually divided the two thousand images into 300 groups according to two rules. 1) Different Objects. Based on [8], the common objects in UWIs can be divided into marine faunas of fish, turtles, sharks, snails and shellfish, etc.; marine plants of corals, seaweed, fringing reefs, etc.; non-biology of rocks, wreckage and sculpture, etc. 2) Different water types and depths. The water type is distinguished from clear to turbid, and the water depth is distinguished from shoal water, deep sea and seabed. UWIs captured in clear and shoal water present lighter color shift and better clarity, and vice versa. + +After grouping the UGWI manually, 1-2 images from each group are selected to build our dictionary, which is then cropped into non-overlapping $128 \times 128$ image patches $P$ . For each image patch, we use the pre-trained popular deep image compression network DICN [12] to extract its compression features at multi-scales, shown in Fig. 3. The generation process of dictionary can be described as, + +$$ +D _ {s} = \mathcal {F} (P; \theta_ {D I C N} ^ {s}) \tag {1} +$$ + +where $s \in \{2,3,4\}$ is the scale and $\theta_{DICN}^{s}$ is the parameters of the pre-trained DICN at scale $s$ . + +To verify the diversity of these representative UWIs, the Spatial Information (SI) and Colorfulness (CF) indices are computed respectively for the content variation along the spatial and color dimensions. Higher SI / CF indicates more complex image content / colorful. The CF versus SI distribution is plotted in Fig. 4. As shown, the distribution range is quite broad, which indicates that the content of these patches is diverse. Additionally, some points are distributed closely, which also verifies that there are many similar common content between UWIs. + +To compact the features in dictionary, we adopt K-means to create $K$ clusters. Considering the high computational complexity of directly performing K-means on massive features of multifarious UWIs, we first perform principal components analysis (PCA) on the features of per UWI to reduce their dimension. Finally, $K$ typical features at each scale are preserved, constructing our multi-scale feature dictionary. The effect of cluster number $K$ on the compression performance is shown in the supplementary materials. + +![](images/ea4623a437f6280850fb3a4eaa8ce5efaa395aec2bb4ae750e43f55de80c50ec.jpg) +Figure 5: The structure of the proposed USNB. + +# 3.2. Overall of the proposed RFD-ECNet + +The framework of our RFD-ECNet is shown in Fig. 2, which performs feature match at multiple scales ( $s \in \{2,3,4\}$ ) in a progressive manner to remove the underwater common redundancy from coarse to fine. Let $F_{s}$ be the input features at scale $s$ , and $D_{s,i}$ denotes the $i$ -th dictionary features at scale $s$ . In the encoder, the input UWI is down-sampled by two convolutional sampling layers to obtain its features $F_{2}$ , which are matched with the dictionary $D$ to select its reference features $D_{2,i}$ . To guarantee the input features $F_{2}$ and $D$ in the same feature space, the first-two sampling layers of RFD-ECNet are filled with that of the pre-trained DICN, which are fixed during the training of our RFD-ECNet. + +For more accurate feature match, USNB is proposed to normalize the dictionary features based on the underwater style of the input, eliminating the effect of the underwater styles diversity on feature match. Specifically, USNB utilizes the UPPs extracted from an UPPs extractor [7] to simulate the underwater imaging process [6], which dictate the underwater styles of UWIs. Moreover, the selected $D_{2,i}$ is further refined by the proposed RFVM to obtain $RD_{2,i}$ based on the similarity map $W_{2}$ between $F_{2}$ and $D_{2,i}$ , greatly improving their similarity. + +After removing redundancy on three scales, the latent features $z$ and the dependency maps $(W_{2}, W_{3}, W_{4})$ are quantized by the uniform noise approximated method [12], and then entropy coded by the Gaussian mixture entropy model [17] to the bit-stream. + +# 3.3.USNB-based Feature Match (USN-FMM) + +Feature match aims to select the reference features that have the most similar textures to the input features. However, the UWIs sharing similarity may have multifarious underwater styles of color shift and distance-dependent clarity. Hence, it is necessary to normalize the underwater styles of dictionary features toward that of the input before the feature match. + +Underwater Style Normalize. By studying the process + +![](images/9ca943d6dddd9d85d49f81daada5571a07a0029a445ccd8b21ab89cf593c9749.jpg) +Figure 6: The structure of the proposed RFVM. + +of underwater imaging, it can be observed that the underwater styles are dictated by underwater physical priors such as ambient light and imaging transmission map, which can be described by the underwater physical scattering model: + +$$ +\begin{array}{l} J = I \times T + A \times (1 - T) \\ = \quad_ {c d} \end{array} \tag {2} +$$ + +$$ +T = e ^ {- \alpha d} +$$ + +where $I$ denotes the clear scene without underwater style and $J$ is the captured UWI with multifarious underwater styles. Under the effect of underwater physical priors, including $T$ and $A$ , $I$ is evolved to $J$ . $T$ and $A$ respectively represent the transmission map and the global ambient light, and their visual examples are presented in the supplementary materials. $T$ is calculated by $\alpha$ and $d$ , which respectively refer to light attenuation coefficient and the distance between camera and object, which leads to the distance-dependent clarity. Derived from Eq. (2), the clear scene can be modeled as: + +$$ +I = \frac {J - A \times (1 - T)}{T} \tag {3} +$$ + +Based on Eq. (2) and Eq. (3), the dictionary features can be normalized towards the underwater style of input by + +$$ +\begin{array}{l} J ^ {d i c. i n p u t} = I ^ {d i c} \times T ^ {i n p u t} + A ^ {i n p u t} \times \left(1 - T ^ {i n p u t}\right) \\ = \frac {J ^ {d i c} - A ^ {d i c} \times (1 - T ^ {d i c})}{T ^ {d i c}} \times T ^ {\text {i n p u t}} \tag {4} \\ + A ^ {i n p u t} \times (1 - T ^ {i n p u t}) \\ \end{array} +$$ + +Based on the above analysis, we propose the USNB to parametrically implement Eq. (4), as shown in Fig. 5, which is used before the feature match to normalize the underwater styles of dictionary features toward the input. In Fig. 5, $D_{s}$ and $ND_{s}$ respectively correspond to $J_{dic}$ and $J_{dic\_input}$ in Eq. (4). Underwater physical priors of dictionary features $(T^{dic}$ and $A^{dic})$ and that of the input $(T^{in}$ and $A^{in})$ are fed to several convention layers to normalize $D_{s}$ to $ND_{s}$ by following the data flow in Eq. (4). Notably, the network parameters for processing $T^{dic}$ and $A^{dic}$ are shared + +![](images/dbd5c30f339ff620b6302813d4978b4b9ac75b32c3e7250614ec24dd1c1c433b.jpg) +(a) UGWI, Rate-PSNR + +![](images/5742289e86852ac1d2e15f3df0c57b61ded123a36489912acec123fb11aa4214.jpg) +(b) EUVP, Rate-PSNR + +![](images/21522237f422887d94a37d5491ff8c8e5911e84594a4a24a1c5e63315837d7b6.jpg) +(c) UFO, Rate-PSNR + +![](images/e2d5a46de4f775b9f764d485d1fea9e168989b4328f8cc21800aa4c1b205a17a.jpg) +(d) UIEB, Rate-PSNR +Figure 7: R-D curves of different image compression methods on UGWI, EUVP [31], UFO [32], and UIEB [8] datasets. + +with that for $T^{dic}$ and $A^{dic}$ to guarantee that all underwater physical priors are in the same feature space. As such, the proposed USNB is able to normalize the underwater styles of the dictionary features toward the input for more accurate feature match. The effectiveness of USNB is verified in the ablation studies. + +Feature Match. To select the reference features $D_{s,i}$ from the dictionary features $D_{s}$ for input features $F_{s}$ , we adopt the widely used inner product to measure the similarity score between $F_{s}$ and $D_{s}$ . The similarity scores between $F_{s}$ and $D_{s}$ is defined as: + +$$ +S _ {s} = \left\langle F _ {s}, \frac {D _ {s}}{\| D _ {s} \|} \right\rangle \tag {5} +$$ + +Following the procedure in [33], Eq. (5) is implemented by a convolution operation, where the kernel weights are set as $D_{s}$ , to accelerate the similarity calculations. The $i$ -th dictionary feature with the highest similarity score is selected as the reference feature $D_{s,i}$ . + +# 3.4. Reference Feature Variant Module (RFVM) + +Although the reference features $D_{s,i}$ and the input features $F_{s}$ share some similarities, the relative position and shape of the similar areas in $D_{s,i}$ and $F_{s}$ may be dramatically different. To achieve the highest possible similarity, we develop the RFVM to adaptively morph the $D_{s,i}$ based on $F_{s}$ , shown in Fig. 6. RFVM utilizes the spatial variant recursive convolution (SVRConv) [34] to implement the feature variant on a large receptive field, which is able to facilitate the dramatic spatial variant by the long-distance information propagation of recurrent convolution and the learned weights for different locations. The weights of SVRConv are learned by exploring the dependency between $D_{s,i}$ and $F_{s}$ . To obtain the global dependency map $W$ , dilated convolutions with different dilation rates are used to exploit the spatial information at different receptive fields. As such, our RFVM is able to morph the reference features in a large receptive field to improve the similarity with the input features. + +# 4. Experiments + +Extensive experiments are conducted to evaluate the extreme compression performance of our RFD-ECNet. First, we test RFD-ECNet on four different UWI datasets objectively and subjectively to verify our excellent generalization. After that, a series of ablation studies are presented to respectively verify the effectiveness of our multi-scale manner, USNB and RFVM. + +# 4.1. Experimental Settings + +Datasets. We perform experiments on four public UWI datasets, including the UGWI dataset, EUVP dataset [31], UFO dataset [32], and UIEB dataset [8]. These UWI datasets are collected during different oceanic explorations and hence include various underwater scenes and rich ocean species. As stated in Section 3.1, some representative UWIs selected from UGWI dataset are utilized to construct our underwater multi-scale feature dictionary. The rest of UGWI are divided into 1550 UWIs for training and 300 UWIs for testing. Additionally, we randomly select 100 images respectively from EUVP [31], UFO [32], and UIEB [8] to test the pre-trained RFD-ECNet to verify the generalization of our RFD-ECNet. + +Training. As the most VAE-based methods, our RFD-ECNet is optimized by the rate-distortion trade-off loss function, which can be described as: + +$$ +\mathcal {L} = \lambda \cdot D + R, \tag {6} +$$ + +where $\lambda$ is a trade-off parameter to balance bitrate $R$ and distortion $D$ . In our work, MSE is used as the $D$ , and $\lambda$ belongs to the set $\{512, 256, 128, 64, 32\}$ for 5 different compression ratios. The channel width of RFD-ECNet is set as 192, and the bottleneck layer is set as 64. Detailed network architecture is introduced in the supplementary materials. All model are trained using the Adam optimizer [35] with standard parameters and learning rate of $1 \times 10^{-4}$ . + +Evaluation. The compression performance is measured by bitrate $R$ and distortion $D$ , which are respectively calculated by bits-per-pixel (bpp) and Peak Signal to Noise Ratio (PSNR). Lower bpp and higher PSNR indicate better com + +Table 1: Comparison of BD-rate and BD-PSNR on UGWI, EUVP [31], UIEB [8], and UFO [32] testsets. The BD-rate and BD-PSNR are calculated from PSNR-BPP curve over data points with $\mathrm{bpp} < 0.1$ , when BPG [10] is set as the anchor. The performance of SOTA compression codec VVC is marked in red. The best performance is bolded. + +
MethodsBD-rate ↓ (%)BD-PSNR ↑ (dB)Computation complexity
UGWIEUVPUIEBUFOAvg.UGWIEUVPUIEBUFOAvg.Param. (M)FLOPs (G)
VVC-intra [11]-19.0-16.2-16.0-16.1-16.80.690.430.520.470.53//
JPEG2000 [9]61.768.467.266.966.1-1.62-1.71-1.84-1.56-1.68//
BPG [10]0000000000//
Minnen (NIPS'18) [13]-3.814.89.819.09.90.16-0.36-0.33-0.59-0.2814.127.2
Cheng (CVPR'20) [17]-12.8-8.4-1.3-8.3-7.70.430.200.040.240.2320.561.3
Zou (CVPR'22) [18]-13.8-10.3-12.4-14.7-12.80.480.250.360.430.3875.033.3
Ours-slim-50.2-44.6-42.6-34.7-43.01.731.011.110.651.1215.440.7
Ours-53.7-50.3-52.9-37.3-48.51.971.181.560.991.4335.886.7
+ +![](images/ed7f1f7ffb8c29a475d1dcb4f85652794d515b678a95d3d80a8831494dd3730c.jpg) +Input + +![](images/6cd66ba37bc674914d16936909987879ac0dfef73638c2d1dcdc3f78d3b79a93.jpg) +JPEG2000, Bpp=0.137 + +![](images/18fdcdc8d372a937d8f31bb9a94939f5f5d3764f6b62c13e9ec552cc5aa9b5d1.jpg) +VVC-intra, Bpp=0.139 + +![](images/c2d1109353d3f5723c1fd4b7cf4e8c9256b96b948811415ea453e9a8f96cc021.jpg) +Cheng(CVPR'20), Bpp=0.146 + +![](images/364b1820a1c05f2030bd2f108310a5459d50dce3f040211e00a01b561cfc3b6e.jpg) +Ours, Bpp=0.137 + +![](images/e635477c759e220f74a8b4f3912cd018f8f0d0985d3bf75d2aac3b1653026c4b.jpg) +Cheng + +![](images/c03d2bf8cc2ad1e909f772e9fcabba702a3e841699f4ba78830e9c43ccc416f8.jpg) +Ours + +![](images/5459c8b9750990424f2431b60b52b91fd23bd564bbf9820658a06e9da338e400.jpg) +Input + +![](images/4b8fe94809da9ba7a9e1be6d6486ed448e684826366f12b75867dff7304e5a15.jpg) +Input +Figure 8: Visual examples of the reconstructed images. The examples in two rows are respectively from UGWI and EUVP [31] testset. The metrics are bpp $(\downarrow)$ and PSNR $(\uparrow)$ . At extremely low bpp, our reconstructed images have more details and higher pixel fidelity (measured by PSNR) than others. + +![](images/df8e0e8512a9ace11245e66ec7e2fa5f8f2b1b84bf0affb457fc920d4b6e18b6.jpg) +PSNR=27.37 dB +JPEG2000, Bpp=0.049 +PSNR=22.17 dB + +![](images/2089c8741a4effc676835531c47abbb75e43601bea8e04f625f0bc3bf2bb815d.jpg) +PSNR=29.35 dB +VVC-intra, Bpp=0.049 +PSNR=25.22 dB + +![](images/0dc4ad8d2c12b3f92b2b6b28cff600122ad73bf910bf7387b6227dbdd9bb2338.jpg) +PSNR=29.13 dB +Cheng(CVPR'20), Bpp=0.049 +PSNR=25.28 dB + +![](images/16baf89ba433e4b6c1602ceb61de6c12fd203216b73ea984f0aad8bc58fe286a.jpg) +PSNR=30.16 dB +Ours, Bpp=0.048 +PSNR=26.15 dB + +![](images/25880dac893654e0f369ac32e2bcf8fdd7b3367887eaa9554a67726ff7c19ef9.jpg) +JPEG2000 +VVC-intra + +![](images/3e9e198bf0961f321d1ad607ce4f9b69fda0e7341b7940b513e40747df987b2b.jpg) + +VVC-intra + +![](images/af86153ceb0aa98e7e2a52146198cd918cc8435843f55478117b18b971245805.jpg) +Cheng + +![](images/28dde335b884709b5906c590c0153e1f9dd49740795facbfced6ebf00ba495a8.jpg) +Ours + +![](images/2d5f7a27e9e660bf6a4d5f9ff20abb8bdcef51e0a57840e59487ff0185342d59.jpg) +${13}/{14}$ + +![](images/780053d874d19f625a1a8a44ab00ab0809ce020623ac19fd06e989e86f9dd9dc.jpg) + +pression performance. Notably, our bpp is calculated by, + +$$ +b p p = \frac {b i t s _ {z} + b i t s _ {W} + b i t s _ {i n d e x}}{N _ {\text {p i x e l s}}} \tag {7} +$$ + +where $\text{bits}_z$ and $\text{bits}_W$ respectively represent the bits of latent features $z$ and dependency map $W$ . $\text{bits}_{index}$ denotes the bits for coding the index numbers of reference features, which are directly coded by Huffman coding. In addition to R-D curves, the widely used Bjøntegaard delta rate (BD-rate) and BD-PSNR are also evaluated. Lower BD-rate and higher BD-PSNR indicate more efficient compression. + +For the comparative methods, we compare our RFDECNet with influential and SOTA image compression networks, including Minnen (NIPS'18) [13], Cheng (CVPR'20) [17], and Zou (CVPR'22) [18]. For fair comparisons, all networks are trained on the UGWI dataset. Additionally, some conventional CODECs are compared, includ + +ing popular JPEG2000 [9], BPG (HEVC-intra) [10] and the latest VVC-intra (VTM 11.0) [11]. For BPG and VVC, the highest PSNR setting (4:4:4) is tested. + +# 4.2. Comparison against SOTA methods + +R-D Performance. Fig. 7 presents the R-D curves on four UWI testsets of UGWI, EUVP [31], UIEB [8], and UFO [32]. As shown, the R-D curves of our RFD-ECNet are above the curves of all comparative methods on four testsets, which demonstrates that our method achieves better compression performance than all comparative methods and our excellent generalization and robustness. Notably, as bpp decreases, our RFD-ECNet achieves higher PSNR improvements than comparative methods. This indicates that the reference features provided by our underwater feature dictionary are very efficient for the reconstruction, especially at extremely low bitrates. + +Table 2: BD-rate $(\%)$ and BD-PSNR (dB) of VVC/HEVC at inter/intra modes, where Minnen [13] is set as the anchor. + +
MethodsVVC-interVVC-intraHEVC-interHEVC-intraOurs
BD-rate ↓-22.1-21.00.23.2-59.5
BD-PSNR ↑0.850.82-0.10-0.122.25
+ +The BD-rate of different image compression methods with BPG [10] as the anchor is presented in Table 1. As shown, our method achieves the best BD-rate and BD-PSNR results on four testsets, which indicates that we use the smallest amount of bits to achieve the highest PSNR among all methods. Specially, our average BD-rate of $-48.5\%$ and BD-PSNR of $1.43\mathrm{dB}$ are much better than the most advanced codec VVC-intra' - $16.8\%$ and $0.53\mathrm{dB}$ . More intuitively, when VVC is set as the anchor, our RFD-ECNet achieves breakthrough BD-rate saving of $31.7\%$ and BD-PSNR of $0.90\mathrm{dB}$ , demonstrating the advanced performance of our RFD-ECNet on UWI extreme compression. + +Visual Quality. Fig. 8 shows visual examples of reconstructed images by our RFD-ECNet, Cheng (CVPR'20), the most advanced VVC-intra, and the widely used JPEG2000. As shown, our reconstructed images retain more details, while the reconstructed images of VVC-intra and JPEG2000 present obvious blurring and blocking effects at extremely low bpp. As shown in the second row, when bpp=0.049, VVC-intra, Cheng (CVPR'20) and JPEG2000 completely lose the common object of sand, while our RFD-ECNet can roughly reconstruct the sand by referencing our dictionary. Overall, our pixel fidelity is higher than others at the similar extremely low bpp, which can be verified by our higher PSNR. More visual results tested on underwater videos are provided at https://github.com/lilala0/RFD-ECNet. + +Comparison with video CODECs. To verify that the redundancy between UWIs cannot be efficiently removed by video CODEcs, our RFD-ECNet is compared with the latest video CODEcs of VVC-inter and HEVC-inter. Their performance on UGWI testset measured by BD-rate and BD-PSNR with the Minnen [13] as the anchor is shown in Table 2. As shown, we achieve better results than both VVC-inter and HEVC-inter, verifying that our RFD-ECNet referencing to dictionary is more efficient than video CODEcs to remove the redundancy between UWIs. Moreover, both video CODEcs at inter-mode only achieve tiny improvement of BD-rate/PSNR than the intra-mode. This verifies that there is redundancy between UWIs indeed. + +Comparison of complexity. The trainable parameters and FLOPs of all approaches are compared in Table 1. As shown, our parameters (35.8 M) is much less than that (99.8 M) of compression network [18]. Additionally, we also provide a slim version of Our RFD-ECNet by narrowing our network channels of 192 to 128 (denoted as Ours-slim), which only have 15.4M parameters and 40.7G FLOPs. No + +Table 3: BD-rate $(\%)$ and BD-PSNR (dB) of ablation studies about our USNB and RFVM, where BPG [10] is set as the anchor. + +
SettingOursw/o USNBw/o RFVMw/o USNB&RFVM
BD-rate ↓-53.7-33.6-43.1-24.6
BD-PSNR ↑1.971.141.490.83
+ +Table 4: BD-rate $(\%)$ and BD-PSNR (dB) of ablation studies about the multi-scale manner, where BPG [10] is set as the anchor. + +
Scale settingScale-{2}Scales-{2,3}Scales-{2,3,4}
BD-rate ↓-46.1-49.8-53.7
BD-PSNR ↑1.671.831.97
+ +tably, ours-slim still achieves better performance than all SOTA methods with lower complexity, illustrating our excellent UWI extreme compression performance. + +# 5. Ablation Study + +Effectiveness of USNB and RFVM. To verify the effectiveness of the proposed USNB and RFVM, a series of ablation experiments are conducted, where the USNB and RFVM are removed from our RFD-ECNet in sequence. The performance of each ablation is measured by the BD-rate and BD-PSNR with the BPG as the anchor, shown in Table 3. w/o USNB indicates the network that directly performs feature match by inner product without using our USNB to normalize the dictionary features. w/o RFVM is the network where the matched reference features are not fed into our RFVM and therefore cannot be varied adaptively based on the input features. w/o USNB&RFVM is the network without both USNB and RFVM. As can be seen from Table 3, the removal of either USNB or RFVM degrades the performance of our RFD-ECNet. Moreover, the performance degrades most when USNB and RFVM are removed simultaneously, verifying the effectiveness of USNB and RFVM. + +Effectiveness of multi-scale reference. In our RFD-ECNet, the input features are matched with the feature dictionary at three scales (\(s = 2,3,4\)), considering that the similarity between UWIs is reflected on the textures, structures, and semantics. Here we conduct ablations to verify the effectiveness of the multi-scale manner, and provide the results in Table 4. Since the features on scale-1 contain more noise less semantic information, we perform feature match starting from scale-2. As shown, our RFD-ECNet referring dictionary at scales-\{2,3,4\} achieves the best performance, followed by scales-\{2,3\} and scale-\{2\}\), which verifies that it is efficient to remove the underwater common redundancy at multiple scales from coarse to fine. + +# 6. Discussion + +This work creatively removes redundancy between UWIs and proposes a novel reference-based image compression framework. Actually, the redundancy between images exists not only in UWIs but also in other image domains where independent images contain some common objects specific to the image domain. For example, all Martian images [36] contain rocks and sand; all face images [37] contain eyes, nose and mouth; most remote sensing images [38] contain buildings, road and so on. However, existing image compression works neglect this nature and only remove redundancy in an image, which may limit the development of image compression. + +To validate our hypothesis, we additionally conduct preliminary experiments on Martian images [36] by adjusting our network. Experimental results presented in the supplementary materials show that we also achieve better performance than VVC and Ding (VCIP'22) [36], illustrating the efficiency and feasibility of removing redundancy between images in other image domains. + +# 7. Conclusion + +In this paper, we explore the characteristics of UWIs and find that UWIs present multifarious underwater styles and different UWIs share some common ocean objects at diverse morphologies and sizes, resulting in plenty of redundancy between UWIs. Hence, we construct an exhaustive and compact underwater multi-scale feature dictionary from the manually selected representative UWIs, which provides coarse-to-fine reference for our RFD-ECNet to fully remove redundancy between UWIs. Meanwhile, to eliminate the effect of underwater styles on feature match, we utilize UPPs to design the USNB to align the multifarious underwater styles of dictionary towards that of input features. Moreover, to improve the similarity between the input and reference features, we propose RFVM to perform adaptive reference feature variant. Finally, extensive comparisons are conducted to verify our significant performance improvement than SOTA methods including the latest VVC, and comprehensive ablation studies verify the effectiveness of each module in our RFD-ECNet. + +# Acknowledgments + +This work is supported in part by the National Natural Science Foundation of China under Grant 61931022 and Grant 62271301; in part by the Shanghai Science and Technology Program under Grant 22511105200; in part by the Shanghai Excellent Academic Leaders Program under Grant 23XD1401400; in part by the Natural Science Foundation of Shandong Province under Grant ZR2022ZD38. + +# References + +[1] G.L. Foresti. Visual inspection of sea bottom structures by an autonomous underwater vehicle. 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Different UWIs have similarities in texture, structure and semantic, which can be included in an underwater feature dictionary to provide reference for UWI compression. E/D indicates encoder/decoder." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 529, + 547, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 547, + 614 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 547, + 614 + ], + "type": "text", + "content": "the growing underwater applications. For example, mine search, nuclear-reactors detection, and underwater power inspection [1] are parts of homeland security operations. In addition, marine biology [2] and archaeology [3] are important scientific research for ocean resource development. Moreover, underwater entertainment [4] such as underwater live broadcasts is becoming greatly popular with the public." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "type": "text", + "content": "In these underwater applications, images taken underwater play an essential role. To be transmitted from the deep sea to the board or ground, underwater images (UWIs) must be compressed at extremely low bitrates due to the very narrow underwater wireless acoustic bandwidth of about 20 kbps [5]. However, existing image compression approaches severely degrade the pixel fidelity (e.g., MSE) of UWIs at extremely low bitrates (<0.1bpp), which greatly impairs the" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 693, + 144, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 693, + 144, + 703 + ], + "spans": [ + { + "bbox": [ + 59, + 693, + 144, + 703 + ], + "type": "text", + "content": "* Corresponding Author." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 59, + 703, + 279, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 279, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 279, + 712 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 59, + 703, + 279, + 712 + ], + "type": "text", + "content": "Code is available at https://github.com/lilala0/RFD-ECNet" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "12980" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "broad application of UWIs. Hence, it is highly urgent to design a more powerful extreme UWI compression algorithm." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 99, + 289, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 99, + 289, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 99, + 289, + 386 + ], + "type": "text", + "content": "Different from general images, UWIs present two unique underwater characteristics: (1) UWIs present multifarious underwater styles of color shift and distance-dependent clarity. This is because the underwater imaging process is quite different from that in the open air [6]. When light travels through water, it suffers from absorption and scattering. Specifically, the blueish/greenish color shift is caused by the fact that the red light of the shortest wavelength is absorbed first, and then the green and blue light are followed [7]. In addition, light is scattered by the particles in water, which change the direction of light propagation [8], resulting in the spatially varying distance dependencies of clarity, i.e., the image clarity decreases as the distance to the objects increases. (2) Different UWIs contain some common underwater objects at diverse morphologies and sizes. Due to the special underwater natural environment, there are some common underwater objects such as fish, corals, and rocks that widely exist in different UWIs in diverse morphologies and sizes. Hence, there are plenty of similar representations between UWIs. As shown in Fig. 1 (b), although the UWIs are captured at different times and in various underwater scenes, they contain some same underwater objects such as water, corals, and rocks, which share plenty of similarities in textures, structures, and semantics." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 388, + 289, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 289, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 289, + 687 + ], + "type": "text", + "content": "Given the characteristics of UWIs, there are two main drawbacks for existing image compression methods [9-21]: (1) They only remove redundancy within an image and do not consider redundancy between UWIs. Conventional image compression CODEs such as JPEG2000 [9], BPG [10] and the latest VVC-intra [11] reduce the intra-redundancy through transform and intra-prediction. Recently, learnt image compression methods [12-18] have shown greater potential than conventional CODEs. Based on variational autoencoder (VAE), [12] designs a hyperprior model to remove the statistic redundancy within an image. After that, [13] proposes an autoregressive model to further remove the local context redundancy. However, all of them are limited to removing redundancy in only an image. (2) They utilize a unitary compression that cannot handle the multifarious underwater styles of color shift and distance-dependent clarity. It is reasonable to use the unitary compression for the general terrestrial images because the colors (r, g, b) of terrestrial images are evenly distributed [22] and the internal clarity is steady broadly. However, it limits their performance on UWIs because the UWIs are full of multifarious color shift and distance-dependent clarity. To design an efficient extreme UWI compression method, it needs to both remove redundancy between UWIs and align the multifarious underwater styles." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "Accordingly, we creatively propose to compress UWIs by referencing a dictionary to remove redundancy between" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": "UWIs. First, we construct an exhaustive underwater multiscale feature dictionary to provide from coarse to fine reference information for the UWI compression. Specifically, the features in the dictionary are extracted from plenty of representative UWIs, which are strictly selected according to various underwater scenes, including different underwater objects, water types, and water depths. As such, our dictionary could cover a wide range of underwater common objects, assisting the UWI compression to fully remove redundancy between UWIs. Subsequently, we design a novel extreme UWI compression network with reference to the underwater feature dictionary (RFD-ECNet), shown in Fig 2, where the features of input UWI are matched with the dictionary to select the reference features, and then the residuals between the input and reference features are compressed, significantly reducing the coding bits of UWIs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 264, + 546, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 264, + 546, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 264, + 546, + 453 + ], + "type": "text", + "content": "Additionally, an underwater styles normalization block-based feature match (USN-FMM) is proposed to ensure that the match is not interfered by the multifarious underwater styles and focuses on selecting the references that have the most similar texture to the input. To be specific, the USNB utilizes the underwater physical priors (UPPs) extracted from the underwater imaging physical model [6] to normalize the underwater style of reference features towards that of the input. Moreover, to improve the similarity between the reference and input features, a reference feature variant module (RFVM) is designed to adaptively morph the reference features based on their dependency relevance to the input feature. Extensive experimental results show that our RFD-ECNet outperforms state-of-the-art (SOTA) compression methods. Overall, our main contributions are summarized as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 316, + 455, + 547, + 660 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 316, + 455, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 455, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 316, + 455, + 545, + 514 + ], + "type": "text", + "content": "- We make the first attempt to remove the massive redundancy between UWIs, and the proposed dictionary-based compression network RFD-ECNet is the first work that achieves significantly better BD-rate/PSNR than the latest VVC and other learnt methods." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 316, + 516, + 547, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 516, + 547, + 586 + ], + "spans": [ + { + "bbox": [ + 316, + 516, + 547, + 586 + ], + "type": "text", + "content": "- We construct an exhaustive underwater feature dictionary from representative UWIs manually selected based on various underwater scenes, water types, and water depths. Besides, detailed analyses are conducted to verify the comprehensiveness and compactness of the dictionary." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 316, + 589, + 547, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 589, + 547, + 660 + ], + "spans": [ + { + "bbox": [ + 316, + 589, + 547, + 660 + ], + "type": "text", + "content": "- To eliminate the effect of underwater styles on feature match, we utilize the underwater physical priors to design USNB to improve feature match accuracy. Moreover, we design RFVM to adaptively morph the reference features based on the dependency map, improving their similarity." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 669, + 398, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 398, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 398, + 682 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 715 + ], + "type": "text", + "content": "Learnt Image Compression. Recently, learnt image compression approaches have developed rapidly and" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "12981" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 71, + 427, + 304 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 427, + 304 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 427, + 304 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 427, + 304 + ], + "type": "image", + "image_path": "c88cb3b234852270807a38f8dbd6e7c605e9146847a6b6ed352621945f9eb128.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 48, + 318, + 543, + 331 + ], + "lines": [ + { + "bbox": [ + 48, + 318, + 543, + 331 + ], + "spans": [ + { + "bbox": [ + 48, + 318, + 543, + 331 + ], + "type": "text", + "content": "Figure 2: Overview of the proposed RFD-ECNet. Q indicates the quantizer. AE/AD represents the arithmetic en/decoding." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 427, + 72, + 545, + 302 + ], + "blocks": [ + { + "bbox": [ + 427, + 72, + 545, + 302 + ], + "lines": [ + { + "bbox": [ + 427, + 72, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 427, + 72, + 545, + 302 + ], + "type": "image", + "image_path": "cc6868b93d08ba9672fe13e862aca36c2843ddd0b173071e97f4eefda6ad1da3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 351, + 287, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 351, + 287, + 448 + ], + "spans": [ + { + "bbox": [ + 46, + 351, + 287, + 448 + ], + "type": "text", + "content": "achieved great breakthroughs, which can be divided into VAE-based and GAN-based. Generally, VAE-based methods [12-18] utilize an encoder, which includes some parametric linear and nonlinear transforms, to compress image to compact latent features. After quantization and entropy coding, the latent features are compressed into bit-stream. Then a decoder, which usually has a symmetrical structure with the encoder, is used to reconstruct the image." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 448, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 448, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 287, + 579 + ], + "type": "text", + "content": "To improve the rate-distortion (R-D) performance, some works focus on designing more efficient learnt model to capture redundancy in an image. [13] proposes auto-regressive model to combine the context model with the hyperprior model [12] for entropy estimation. [18] proposes window-based local attention block to capture local redundancy such as non-repetitive textures. [17] proposes Gaussian Mixture Model to estimate likelihoods of latent features more accurately. Although VAE-based methods achieve admirable R-D performance, they often present unpleasant artifacts at extremely low bitrates." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 580, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 287, + 689 + ], + "type": "text", + "content": "To this end, some works [19-21] combine VAE with the generative adversarial network (GAN) to generate visually pleasing textures to counteract compression artifacts. Nevertheless, the pixel fidelity (e.g., MSE) of the image reconstructed by the GAN-based methods is quite low because the generated content is fake and deceptive. Hence, it is difficult for existing methods to achieve high pixel fidelity UWI reconstruction at extremely low bitrates by only removing redundancy within an image." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "Image Set Compression. This direction aims to compress a batch of images captured at the same place from" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 351, + 545, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 351, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 545, + 447 + ], + "type": "text", + "content": "different view angles and focal distances [23], which can be divided into local-based and cloud-based. The local-based methods [24-26] construct the reference by first preprocessing all the images in a set. For example, [25] creates a new low frequency template as reference image by averaging the low frequency components of all images. The cloud-based methods such as [27] select reference images from the massive images in the cloud." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 448, + 546, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 546, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 546, + 555 + ], + "type": "text", + "content": "Obviously, the local-based methods must obtain all images before compression, which limits their usage flexibility. The cloud-based methods rely on the wide transmission channel to access the cloud disk, which cannot be achieved by the very narrow underwater wireless acoustic channel. Moreover, since these methods can only be applied to the small image subset captured at the same place, they cannot deal with UWIs captured at different underwater scenes and depths in the vast underwater world." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "type": "text", + "content": "Reference-based Model. To the best of our knowledge, there exists no image compression method based on image/feature reference. The closest area to our work is reference-based super-resolution (RefSR), which utilizes the high-frequency information in high-resolution (HR) reference image/patch to rich the details of low resolution (LR) image. Given an arbitrary HR image, [28] uses the VGG network to simultaneously extract the referenced HR and LR features, and swaps the most similar features of reference and the LR. To overcome the inherent information deficit of a single reference, [29] uses multiple reference images to provide a more diverse pool of image features. Besides, [30] builds a face dictionary from HR face images" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "12982" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 286, + 170 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 170 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 170 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 170 + ], + "type": "image", + "image_path": "836f6807d027e6e82c7443a0e41cea7cfa9a5981d1060a6d2fb7025f70103a62.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 177, + 287, + 201 + ], + "lines": [ + { + "bbox": [ + 46, + 177, + 287, + 201 + ], + "spans": [ + { + "bbox": [ + 46, + 177, + 287, + 201 + ], + "type": "text", + "content": "Figure 3: Construction of underwater multi-scale feature dictionary. " + }, + { + "bbox": [ + 46, + 177, + 287, + 201 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 177, + 287, + 201 + ], + "type": "text", + "content": " is the number of the representative UWIs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 217, + 287, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 287, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 287, + 240 + ], + "type": "text", + "content": "to provide the high-frequency reference to construct more and richer features for the LR image." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 241, + 287, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 241, + 287, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 287, + 469 + ], + "type": "text", + "content": "The differences between our work and the RefSR works are as follows: (1) The RefSR task aims to learn more/richer features from the HR reference, which is a process of increasing information. In contrast, our compression task aims to learn fewer/more compact features, a process of removing redundant information. To our best knowledge, we are the first image compression work referring to the feature dictionary. (2) In [30], their dictionary only contains face images with eyes, nose and mouth, which are relatively more simple and similar than the vast UWI domain. Instead, UWIs contain multifarious underwater styles, where the common underwater objects are at diverse morphologies and sizes. To construct an exhaustive underwater dictionary, we manually select the representative UWIs based on various underwater scenes, water types, and water depths. (3) We design USNB to align the underwater styles of dictionary features and input, improving feature match accuracy. Additionally, we design RFVM to adaptively morph the reference features, further improving their similarity." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 480, + 176, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 480, + 176, + 493 + ], + "spans": [ + { + "bbox": [ + 47, + 480, + 176, + 493 + ], + "type": "text", + "content": "3. The Proposed Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 499, + 272, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 499, + 272, + 513 + ], + "spans": [ + { + "bbox": [ + 47, + 499, + 272, + 513 + ], + "type": "text", + "content": "3.1. Exhaustive Underwater Feature Dictionary" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 518, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 518, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 287, + 601 + ], + "type": "text", + "content": "To achieve extremely low bitrate UWI compression, we propose RFD-ECNet, a novel image compression network referring to underwater feature dictionary, to remove redundancy between UWIs. First of all, an exhaustive dictionary is constructed, which is offline and shared at the encoder and decoder. The pipeline of the construction of underwater multi-scale feature dictionary is shown in Fig. 3." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "type": "text", + "content": "To build the feature dictionary, a series of representative UWIs are selected from the largest public underwater image dataset UGWI " + }, + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "type": "inline_equation", + "content": "{}^{2}" + }, + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "type": "text", + "content": " . UGWI contains 2150 various UWIs, which are collected during oceanic explorations, humanrobot collaborative experiments, or from websites such as Google and YouTube. To select representative UWIs that cover the richest and most comprehensive common contents" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 365, + 70, + 484, + 177 + ], + "blocks": [ + { + "bbox": [ + 365, + 70, + 484, + 177 + ], + "lines": [ + { + "bbox": [ + 365, + 70, + 484, + 177 + ], + "spans": [ + { + "bbox": [ + 365, + 70, + 484, + 177 + ], + "type": "image", + "image_path": "573ce1a6f589bf9fdf7c52cca384f6888d071c05b3e4f1aaf8053a9296e33c38.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 182, + 544, + 194 + ], + "lines": [ + { + "bbox": [ + 306, + 182, + 544, + 194 + ], + "spans": [ + { + "bbox": [ + 306, + 182, + 544, + 194 + ], + "type": "text", + "content": "Figure 4: SI and CF of images used to build the dictionary." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 211, + 545, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 211, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 211, + 545, + 342 + ], + "type": "text", + "content": "of UWIs, we manually divided the two thousand images into 300 groups according to two rules. 1) Different Objects. Based on [8], the common objects in UWIs can be divided into marine faunas of fish, turtles, sharks, snails and shellfish, etc.; marine plants of corals, seaweed, fringing reefs, etc.; non-biology of rocks, wreckage and sculpture, etc. 2) Different water types and depths. The water type is distinguished from clear to turbid, and the water depth is distinguished from shoal water, deep sea and seabed. UWIs captured in clear and shoal water present lighter color shift and better clarity, and vice versa." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "text", + "content": "After grouping the UGWI manually, 1-2 images from each group are selected to build our dictionary, which is then cropped into non-overlapping " + }, + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "text", + "content": " image patches " + }, + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 342, + 545, + 426 + ], + "type": "text", + "content": ". For each image patch, we use the pre-trained popular deep image compression network DICN [12] to extract its compression features at multi-scales, shown in Fig. 3. The generation process of dictionary can be described as," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 382, + 437, + 545, + 451 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 437, + 545, + 451 + ], + "spans": [ + { + "bbox": [ + 382, + 437, + 545, + 451 + ], + "type": "interline_equation", + "content": "D _ {s} = \\mathcal {F} (P; \\theta_ {D I C N} ^ {s}) \\tag {1}", + "image_path": "3c82a9033abdf587fa82f5f1e9cbcc2b2a0478b54ba0f14c0a9ff6b8b58104f9.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 461, + 544, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 544, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 544, + 484 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 461, + 544, + 484 + ], + "type": "inline_equation", + "content": "s \\in \\{2,3,4\\}" + }, + { + "bbox": [ + 304, + 461, + 544, + 484 + ], + "type": "text", + "content": " is the scale and " + }, + { + "bbox": [ + 304, + 461, + 544, + 484 + ], + "type": "inline_equation", + "content": "\\theta_{DICN}^{s}" + }, + { + "bbox": [ + 304, + 461, + 544, + 484 + ], + "type": "text", + "content": " is the parameters of the pre-trained DICN at scale " + }, + { + "bbox": [ + 304, + 461, + 544, + 484 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 461, + 544, + 484 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 486, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 604 + ], + "type": "text", + "content": "To verify the diversity of these representative UWIs, the Spatial Information (SI) and Colorfulness (CF) indices are computed respectively for the content variation along the spatial and color dimensions. Higher SI / CF indicates more complex image content / colorful. The CF versus SI distribution is plotted in Fig. 4. As shown, the distribution range is quite broad, which indicates that the content of these patches is diverse. Additionally, some points are distributed closely, which also verifies that there are many similar common content between UWIs." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "To compact the features in dictionary, we adopt K-means to create " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " clusters. Considering the high computational complexity of directly performing K-means on massive features of multifarious UWIs, we first perform principal components analysis (PCA) on the features of per UWI to reduce their dimension. Finally, " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " typical features at each scale are preserved, constructing our multi-scale feature dictionary. The effect of cluster number " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " on the compression performance is shown in the supplementary materials." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "text", + "content": "UGWI is a public underwater image dataset and is available online at https://github.com/Underwater-Lab-SHU" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12983" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 286, + 205 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 286, + 205 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 286, + 205 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 286, + 205 + ], + "type": "image", + "image_path": "ea4623a437f6280850fb3a4eaa8ce5efaa395aec2bb4ae750e43f55de80c50ec.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 70, + 209, + 263, + 222 + ], + "lines": [ + { + "bbox": [ + 70, + 209, + 263, + 222 + ], + "spans": [ + { + "bbox": [ + 70, + 209, + 263, + 222 + ], + "type": "text", + "content": "Figure 5: The structure of the proposed USNB." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 238, + 241, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 238, + 241, + 251 + ], + "spans": [ + { + "bbox": [ + 47, + 238, + 241, + 251 + ], + "type": "text", + "content": "3.2. Overall of the proposed RFD-ECNet" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "text", + "content": "The framework of our RFD-ECNet is shown in Fig. 2, which performs feature match at multiple scales (" + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "inline_equation", + "content": "s \\in \\{2,3,4\\}" + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "text", + "content": ") in a progressive manner to remove the underwater common redundancy from coarse to fine. Let " + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "inline_equation", + "content": "F_{s}" + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "text", + "content": " be the input features at scale " + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "inline_equation", + "content": "D_{s,i}" + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "text", + "content": "-th dictionary features at scale " + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "text", + "content": ". In the encoder, the input UWI is down-sampled by two convolutional sampling layers to obtain its features " + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "inline_equation", + "content": "F_{2}" + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "text", + "content": ", which are matched with the dictionary " + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "text", + "content": " to select its reference features " + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "inline_equation", + "content": "D_{2,i}" + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "text", + "content": ". To guarantee the input features " + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "inline_equation", + "content": "F_{2}" + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 256, + 287, + 411 + ], + "type": "text", + "content": " in the same feature space, the first-two sampling layers of RFD-ECNet are filled with that of the pre-trained DICN, which are fixed during the training of our RFD-ECNet." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 412, + 287, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 412, + 287, + 532 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 287, + 532 + ], + "type": "text", + "content": "For more accurate feature match, USNB is proposed to normalize the dictionary features based on the underwater style of the input, eliminating the effect of the underwater styles diversity on feature match. Specifically, USNB utilizes the UPPs extracted from an UPPs extractor [7] to simulate the underwater imaging process [6], which dictate the underwater styles of UWIs. Moreover, the selected " + }, + { + "bbox": [ + 46, + 412, + 287, + 532 + ], + "type": "inline_equation", + "content": "D_{2,i}" + }, + { + "bbox": [ + 46, + 412, + 287, + 532 + ], + "type": "text", + "content": " is further refined by the proposed RFVM to obtain " + }, + { + "bbox": [ + 46, + 412, + 287, + 532 + ], + "type": "inline_equation", + "content": "RD_{2,i}" + }, + { + "bbox": [ + 46, + 412, + 287, + 532 + ], + "type": "text", + "content": " based on the similarity map " + }, + { + "bbox": [ + 46, + 412, + 287, + 532 + ], + "type": "inline_equation", + "content": "W_{2}" + }, + { + "bbox": [ + 46, + 412, + 287, + 532 + ], + "type": "text", + "content": " between " + }, + { + "bbox": [ + 46, + 412, + 287, + 532 + ], + "type": "inline_equation", + "content": "F_{2}" + }, + { + "bbox": [ + 46, + 412, + 287, + 532 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 412, + 287, + 532 + ], + "type": "inline_equation", + "content": "D_{2,i}" + }, + { + "bbox": [ + 46, + 412, + 287, + 532 + ], + "type": "text", + "content": ", greatly improving their similarity." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "text", + "content": "After removing redundancy on three scales, the latent features " + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "text", + "content": " and the dependency maps " + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "inline_equation", + "content": "(W_{2}, W_{3}, W_{4})" + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "text", + "content": " are quantized by the uniform noise approximated method [12], and then entropy coded by the Gaussian mixture entropy model [17] to the bit-stream." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 598, + 264, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 598, + 264, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 598, + 264, + 611 + ], + "type": "text", + "content": "3.3.USNB-based Feature Match (USN-FMM)" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 617, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 700 + ], + "type": "text", + "content": "Feature match aims to select the reference features that have the most similar textures to the input features. However, the UWIs sharing similarity may have multifarious underwater styles of color shift and distance-dependent clarity. Hence, it is necessary to normalize the underwater styles of dictionary features toward that of the input before the feature match." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "content": "Underwater Style Normalize. By studying the process" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 71, + 547, + 205 + ], + "blocks": [ + { + "bbox": [ + 307, + 71, + 547, + 205 + ], + "lines": [ + { + "bbox": [ + 307, + 71, + 547, + 205 + ], + "spans": [ + { + "bbox": [ + 307, + 71, + 547, + 205 + ], + "type": "image", + "image_path": "9ca943d6dddd9d85d49f81daada5571a07a0029a445ccd8b21ab89cf593c9749.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 329, + 210, + 523, + 223 + ], + "lines": [ + { + "bbox": [ + 329, + 210, + 523, + 223 + ], + "spans": [ + { + "bbox": [ + 329, + 210, + 523, + 223 + ], + "type": "text", + "content": "Figure 6: The structure of the proposed RFVM." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 238, + 545, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 238, + 545, + 286 + ], + "spans": [ + { + "bbox": [ + 304, + 238, + 545, + 286 + ], + "type": "text", + "content": "of underwater imaging, it can be observed that the underwater styles are dictated by underwater physical priors such as ambient light and imaging transmission map, which can be described by the underwater physical scattering model:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 369, + 293, + 545, + 314 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 293, + 545, + 314 + ], + "spans": [ + { + "bbox": [ + 369, + 293, + 545, + 314 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} J = I \\times T + A \\times (1 - T) \\\\ = \\quad_ {c d} \\end{array} \\tag {2}", + "image_path": "6daa4151b40c9bd4125cc5a0625e8c7e2a94498f295cf6f83e7cdb5716738bfb.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 370, + 311, + 414, + 322 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 311, + 414, + 322 + ], + "spans": [ + { + "bbox": [ + 370, + 311, + 414, + 322 + ], + "type": "interline_equation", + "content": "T = e ^ {- \\alpha d}", + "image_path": "fcc3035590fb2f3501a439ad6ebee88f4e86efeaf641661c3e573bd21bf2544c.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "text", + "content": " denotes the clear scene without underwater style and " + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "text", + "content": " is the captured UWI with multifarious underwater styles. Under the effect of underwater physical priors, including " + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "text", + "content": " is evolved to " + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "text", + "content": " respectively represent the transmission map and the global ambient light, and their visual examples are presented in the supplementary materials. " + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "text", + "content": " is calculated by " + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 331, + 545, + 462 + ], + "type": "text", + "content": ", which respectively refer to light attenuation coefficient and the distance between camera and object, which leads to the distance-dependent clarity. Derived from Eq. (2), the clear scene can be modeled as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 378, + 468, + 545, + 492 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 468, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 378, + 468, + 545, + 492 + ], + "type": "interline_equation", + "content": "I = \\frac {J - A \\times (1 - T)}{T} \\tag {3}", + "image_path": "49ed059662af7a1275ec1816227849badccbb0ec9abd84c566052cff4f1ab251.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 498, + 545, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 522 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 522 + ], + "type": "text", + "content": "Based on Eq. (2) and Eq. (3), the dictionary features can be normalized towards the underwater style of input by" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 312, + 529, + 545, + 586 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 529, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 312, + 529, + 545, + 586 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} J ^ {d i c. i n p u t} = I ^ {d i c} \\times T ^ {i n p u t} + A ^ {i n p u t} \\times \\left(1 - T ^ {i n p u t}\\right) \\\\ = \\frac {J ^ {d i c} - A ^ {d i c} \\times (1 - T ^ {d i c})}{T ^ {d i c}} \\times T ^ {\\text {i n p u t}} \\tag {4} \\\\ + A ^ {i n p u t} \\times (1 - T ^ {i n p u t}) \\\\ \\end{array}", + "image_path": "e0226eec64a6d618a122cf746744bc8511372343ea84716b2314785a5d3b9c6f.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": "Based on the above analysis, we propose the USNB to parametrically implement Eq. (4), as shown in Fig. 5, which is used before the feature match to normalize the underwater styles of dictionary features toward the input. In Fig. 5, " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "D_{s}" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "ND_{s}" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " respectively correspond to " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "J_{dic}" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "J_{dic\\_input}" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " in Eq. (4). Underwater physical priors of dictionary features " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "(T^{dic}" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "A^{dic})" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " and that of the input " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "(T^{in}" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "A^{in})" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " are fed to several convention layers to normalize " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "D_{s}" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "ND_{s}" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " by following the data flow in Eq. (4). Notably, the network parameters for processing " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "T^{dic}" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "A^{dic}" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " are shared" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "12984" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 171, + 171 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 171, + 171 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 171, + 171 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 171, + 171 + ], + "type": "image", + "image_path": "dbd5c30f339ff620b6302813d4978b4b9ac75b32c3e7250614ec24dd1c1c433b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 67, + 174, + 153, + 184 + ], + "lines": [ + { + "bbox": [ + 67, + 174, + 153, + 184 + ], + "spans": [ + { + "bbox": [ + 67, + 174, + 153, + 184 + ], + "type": "text", + "content": "(a) UGWI, Rate-PSNR" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 171, + 69, + 296, + 173 + ], + "blocks": [ + { + "bbox": [ + 171, + 69, + 296, + 173 + ], + "lines": [ + { + "bbox": [ + 171, + 69, + 296, + 173 + ], + "spans": [ + { + "bbox": [ + 171, + 69, + 296, + 173 + ], + "type": "image", + "image_path": "5742289e86852ac1d2e15f3df0c57b61ded123a36489912acec123fb11aa4214.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 193, + 175, + 276, + 186 + ], + "lines": [ + { + "bbox": [ + 193, + 175, + 276, + 186 + ], + "spans": [ + { + "bbox": [ + 193, + 175, + 276, + 186 + ], + "type": "text", + "content": "(b) EUVP, Rate-PSNR" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 298, + 71, + 420, + 172 + ], + "blocks": [ + { + "bbox": [ + 298, + 71, + 420, + 172 + ], + "lines": [ + { + "bbox": [ + 298, + 71, + 420, + 172 + ], + "spans": [ + { + "bbox": [ + 298, + 71, + 420, + 172 + ], + "type": "image", + "image_path": "21522237f422887d94a37d5491ff8c8e5911e84594a4a24a1c5e63315837d7b6.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 320, + 174, + 398, + 184 + ], + "lines": [ + { + "bbox": [ + 320, + 174, + 398, + 184 + ], + "spans": [ + { + "bbox": [ + 320, + 174, + 398, + 184 + ], + "type": "text", + "content": "(c) UFO, Rate-PSNR" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 422, + 70, + 545, + 173 + ], + "blocks": [ + { + "bbox": [ + 422, + 70, + 545, + 173 + ], + "lines": [ + { + "bbox": [ + 422, + 70, + 545, + 173 + ], + "spans": [ + { + "bbox": [ + 422, + 70, + 545, + 173 + ], + "type": "image", + "image_path": "e2d5a46de4f775b9f764d485d1fea9e168989b4328f8cc21800aa4c1b205a17a.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 443, + 175, + 524, + 186 + ], + "lines": [ + { + "bbox": [ + 443, + 175, + 524, + 186 + ], + "spans": [ + { + "bbox": [ + 443, + 175, + 524, + 186 + ], + "type": "text", + "content": "(d) UIEB, Rate-PSNR" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 54, + 192, + 537, + 205 + ], + "lines": [ + { + "bbox": [ + 54, + 192, + 537, + 205 + ], + "spans": [ + { + "bbox": [ + 54, + 192, + 537, + 205 + ], + "type": "text", + "content": "Figure 7: R-D curves of different image compression methods on UGWI, EUVP [31], UFO [32], and UIEB [8] datasets." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "text", + "content": "with that for " + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "inline_equation", + "content": "T^{dic}" + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "inline_equation", + "content": "A^{dic}" + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "text", + "content": " to guarantee that all underwater physical priors are in the same feature space. As such, the proposed USNB is able to normalize the underwater styles of the dictionary features toward the input for more accurate feature match. The effectiveness of USNB is verified in the ablation studies." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 296, + 287, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 296, + 287, + 356 + ], + "spans": [ + { + "bbox": [ + 47, + 296, + 287, + 356 + ], + "type": "text", + "content": "Feature Match. To select the reference features " + }, + { + "bbox": [ + 47, + 296, + 287, + 356 + ], + "type": "inline_equation", + "content": "D_{s,i}" + }, + { + "bbox": [ + 47, + 296, + 287, + 356 + ], + "type": "text", + "content": " from the dictionary features " + }, + { + "bbox": [ + 47, + 296, + 287, + 356 + ], + "type": "inline_equation", + "content": "D_{s}" + }, + { + "bbox": [ + 47, + 296, + 287, + 356 + ], + "type": "text", + "content": " for input features " + }, + { + "bbox": [ + 47, + 296, + 287, + 356 + ], + "type": "inline_equation", + "content": "F_{s}" + }, + { + "bbox": [ + 47, + 296, + 287, + 356 + ], + "type": "text", + "content": ", we adopt the widely used inner product to measure the similarity score between " + }, + { + "bbox": [ + 47, + 296, + 287, + 356 + ], + "type": "inline_equation", + "content": "F_{s}" + }, + { + "bbox": [ + 47, + 296, + 287, + 356 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 296, + 287, + 356 + ], + "type": "inline_equation", + "content": "D_{s}" + }, + { + "bbox": [ + 47, + 296, + 287, + 356 + ], + "type": "text", + "content": ". The similarity scores between " + }, + { + "bbox": [ + 47, + 296, + 287, + 356 + ], + "type": "inline_equation", + "content": "F_{s}" + }, + { + "bbox": [ + 47, + 296, + 287, + 356 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 296, + 287, + 356 + ], + "type": "inline_equation", + "content": "D_{s}" + }, + { + "bbox": [ + 47, + 296, + 287, + 356 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 125, + 361, + 287, + 389 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 361, + 287, + 389 + ], + "spans": [ + { + "bbox": [ + 125, + 361, + 287, + 389 + ], + "type": "interline_equation", + "content": "S _ {s} = \\left\\langle F _ {s}, \\frac {D _ {s}}{\\| D _ {s} \\|} \\right\\rangle \\tag {5}", + "image_path": "752658cca00ffa12243e8b29ef9e9916c133eca97fe6431a54c57e16d54a2467.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 399, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 399, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 399, + 287, + 460 + ], + "type": "text", + "content": "Following the procedure in [33], Eq. (5) is implemented by a convolution operation, where the kernel weights are set as " + }, + { + "bbox": [ + 47, + 399, + 287, + 460 + ], + "type": "inline_equation", + "content": "D_{s}" + }, + { + "bbox": [ + 47, + 399, + 287, + 460 + ], + "type": "text", + "content": ", to accelerate the similarity calculations. The " + }, + { + "bbox": [ + 47, + 399, + 287, + 460 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 399, + 287, + 460 + ], + "type": "text", + "content": "-th dictionary feature with the highest similarity score is selected as the reference feature " + }, + { + "bbox": [ + 47, + 399, + 287, + 460 + ], + "type": "inline_equation", + "content": "D_{s,i}" + }, + { + "bbox": [ + 47, + 399, + 287, + 460 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 476, + 275, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 476, + 275, + 489 + ], + "spans": [ + { + "bbox": [ + 47, + 476, + 275, + 489 + ], + "type": "text", + "content": "3.4. Reference Feature Variant Module (RFVM)" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "text", + "content": "Although the reference features " + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "inline_equation", + "content": "D_{s,i}" + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "text", + "content": " and the input features " + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "inline_equation", + "content": "F_{s}" + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "text", + "content": " share some similarities, the relative position and shape of the similar areas in " + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "inline_equation", + "content": "D_{s,i}" + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "inline_equation", + "content": "F_{s}" + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "text", + "content": " may be dramatically different. To achieve the highest possible similarity, we develop the RFVM to adaptively morph the " + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "inline_equation", + "content": "D_{s,i}" + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "text", + "content": " based on " + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "inline_equation", + "content": "F_{s}" + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "text", + "content": ", shown in Fig. 6. RFVM utilizes the spatial variant recursive convolution (SVRConv) [34] to implement the feature variant on a large receptive field, which is able to facilitate the dramatic spatial variant by the long-distance information propagation of recurrent convolution and the learned weights for different locations. The weights of SVRConv are learned by exploring the dependency between " + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "inline_equation", + "content": "D_{s,i}" + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "inline_equation", + "content": "F_{s}" + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "text", + "content": ". To obtain the global dependency map " + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "text", + "content": ", dilated convolutions with different dilation rates are used to exploit the spatial information at different receptive fields. As such, our RFVM is able to morph the reference features in a large receptive field to improve the similarity with the input features." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 220, + 388, + 234 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 220, + 388, + 234 + ], + "spans": [ + { + "bbox": [ + 306, + 220, + 388, + 234 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 240, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 240, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 240, + 545, + 323 + ], + "type": "text", + "content": "Extensive experiments are conducted to evaluate the extreme compression performance of our RFD-ECNet. First, we test RFD-ECNet on four different UWI datasets objectively and subjectively to verify our excellent generalization. After that, a series of ablation studies are presented to respectively verify the effectiveness of our multi-scale manner, USNB and RFVM." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 332, + 432, + 345 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 332, + 432, + 345 + ], + "spans": [ + { + "bbox": [ + 305, + 332, + 432, + 345 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 350, + 545, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 545, + 505 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 545, + 505 + ], + "type": "text", + "content": "Datasets. We perform experiments on four public UWI datasets, including the UGWI dataset, EUVP dataset [31], UFO dataset [32], and UIEB dataset [8]. These UWI datasets are collected during different oceanic explorations and hence include various underwater scenes and rich ocean species. As stated in Section 3.1, some representative UWIs selected from UGWI dataset are utilized to construct our underwater multi-scale feature dictionary. The rest of UGWI are divided into 1550 UWIs for training and 300 UWIs for testing. Additionally, we randomly select 100 images respectively from EUVP [31], UFO [32], and UIEB [8] to test the pre-trained RFD-ECNet to verify the generalization of our RFD-ECNet." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 506, + 545, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 506, + 545, + 541 + ], + "spans": [ + { + "bbox": [ + 305, + 506, + 545, + 541 + ], + "type": "text", + "content": "Training. As the most VAE-based methods, our RFD-ECNet is optimized by the rate-distortion trade-off loss function, which can be described as:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 392, + 552, + 545, + 564 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 392, + 552, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 392, + 552, + 545, + 564 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda \\cdot D + R, \\tag {6}", + "image_path": "69d894184fe7e5db73a382de99d0d0ab5ad3d6473f42a41c5667e2b667b2607e.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "content": " is a trade-off parameter to balance bitrate " + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "content": " and distortion " + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "content": ". In our work, MSE is used as the " + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "content": " belongs to the set " + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\{512, 256, 128, 64, 32\\}" + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "content": " for 5 different compression ratios. The channel width of RFD-ECNet is set as 192, and the bottleneck layer is set as 64. Detailed network architecture is introduced in the supplementary materials. All model are trained using the Adam optimizer [35] with standard parameters and learning rate of " + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": "Evaluation. The compression performance is measured by bitrate " + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": " and distortion " + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": ", which are respectively calculated by bits-per-pixel (bpp) and Peak Signal to Noise Ratio (PSNR). Lower bpp and higher PSNR indicate better com" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12985" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 112, + 544, + 248 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 108 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 108 + ], + "type": "text", + "content": "Table 1: Comparison of BD-rate and BD-PSNR on UGWI, EUVP [31], UIEB [8], and UFO [32] testsets. The BD-rate and BD-PSNR are calculated from PSNR-BPP curve over data points with " + }, + { + "bbox": [ + 46, + 70, + 547, + 108 + ], + "type": "inline_equation", + "content": "\\mathrm{bpp} < 0.1" + }, + { + "bbox": [ + 46, + 70, + 547, + 108 + ], + "type": "text", + "content": ", when BPG [10] is set as the anchor. The performance of SOTA compression codec VVC is marked in red. The best performance is bolded." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 112, + 544, + 248 + ], + "lines": [ + { + "bbox": [ + 52, + 112, + 544, + 248 + ], + "spans": [ + { + "bbox": [ + 52, + 112, + 544, + 248 + ], + "type": "table", + "html": "
MethodsBD-rate ↓ (%)BD-PSNR ↑ (dB)Computation complexity
UGWIEUVPUIEBUFOAvg.UGWIEUVPUIEBUFOAvg.Param. (M)FLOPs (G)
VVC-intra [11]-19.0-16.2-16.0-16.1-16.80.690.430.520.470.53//
JPEG2000 [9]61.768.467.266.966.1-1.62-1.71-1.84-1.56-1.68//
BPG [10]0000000000//
Minnen (NIPS'18) [13]-3.814.89.819.09.90.16-0.36-0.33-0.59-0.2814.127.2
Cheng (CVPR'20) [17]-12.8-8.4-1.3-8.3-7.70.430.200.040.240.2320.561.3
Zou (CVPR'22) [18]-13.8-10.3-12.4-14.7-12.80.480.250.360.430.3875.033.3
Ours-slim-50.2-44.6-42.6-34.7-43.01.731.011.110.651.1215.440.7
Ours-53.7-50.3-52.9-37.3-48.51.971.181.560.991.4335.886.7
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Notably, our bpp is calculated by," + } + ] + } + ], + "index": 50 + }, + { + "bbox": [ + 96, + 527, + 287, + 554 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 527, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 96, + 527, + 287, + 554 + ], + "type": "interline_equation", + "content": "b p p = \\frac {b i t s _ {z} + b i t s _ {W} + b i t s _ {i n d e x}}{N _ {\\text {p i x e l s}}} \\tag {7}", + "image_path": "e5f93ff6907c843b47474e57f3a7a63ad9532b7a191b4e1e8209112d3f61d4af.jpg" + } + ] + } + ], + "index": 51 + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\text{bits}_z" + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\text{bits}_W" + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "text", + "content": " respectively represent the bits of latent features " + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "text", + "content": " and dependency map " + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\text{bits}_{index}" + }, + { + "bbox": [ + 46, + 558, + 287, + 641 + ], + "type": "text", + "content": " denotes the bits for coding the index numbers of reference features, which are directly coded by Huffman coding. In addition to R-D curves, the widely used Bjøntegaard delta rate (BD-rate) and BD-PSNR are also evaluated. Lower BD-rate and higher BD-PSNR indicate more efficient compression." + } + ] + } + ], + "index": 52 + }, + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "content": "For the comparative methods, we compare our RFDECNet with influential and SOTA image compression networks, including Minnen (NIPS'18) [13], Cheng (CVPR'20) [17], and Zou (CVPR'22) [18]. For fair comparisons, all networks are trained on the UGWI dataset. Additionally, some conventional CODECs are compared, includ" + } + ] + } + ], + "index": 53 + }, + { + "bbox": [ + 305, + 507, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 507, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 305, + 507, + 545, + 544 + ], + "type": "text", + "content": "ing popular JPEG2000 [9], BPG (HEVC-intra) [10] and the latest VVC-intra (VTM 11.0) [11]. For BPG and VVC, the highest PSNR setting (4:4:4) is tested." + } + ] + } + ], + "index": 54 + }, + { + "bbox": [ + 306, + 552, + 497, + 564 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 552, + 497, + 564 + ], + "spans": [ + { + "bbox": [ + 306, + 552, + 497, + 564 + ], + "type": "text", + "content": "4.2. Comparison against SOTA methods" + } + ] + } + ], + "index": 55 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "R-D Performance. Fig. 7 presents the R-D curves on four UWI testsets of UGWI, EUVP [31], UIEB [8], and UFO [32]. As shown, the R-D curves of our RFD-ECNet are above the curves of all comparative methods on four testsets, which demonstrates that our method achieves better compression performance than all comparative methods and our excellent generalization and robustness. Notably, as bpp decreases, our RFD-ECNet achieves higher PSNR improvements than comparative methods. This indicates that the reference features provided by our underwater feature dictionary are very efficient for the reconstruction, especially at extremely low bitrates." + } + ] + } + ], + "index": 56 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "12986" + } + ] + } + ], + "index": 57 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 100, + 286, + 140 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 95 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 95 + ], + "type": "text", + "content": "Table 2: BD-rate " + }, + { + "bbox": [ + 47, + 70, + 288, + 95 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 47, + 70, + 288, + 95 + ], + "type": "text", + "content": " and BD-PSNR (dB) of VVC/HEVC at inter/intra modes, where Minnen [13] is set as the anchor." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 100, + 286, + 140 + ], + "lines": [ + { + "bbox": [ + 52, + 100, + 286, + 140 + ], + "spans": [ + { + "bbox": [ + 52, + 100, + 286, + 140 + ], + "type": "table", + "html": "
MethodsVVC-interVVC-intraHEVC-interHEVC-intraOurs
BD-rate ↓-22.1-21.00.23.2-59.5
BD-PSNR ↑0.850.82-0.10-0.122.25
", + "image_path": "15c11c5dac874482504cab77501fe9dbfd4e2c38f71baa132ff95d0abbeadfa0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 150, + 287, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 150, + 287, + 294 + ], + "spans": [ + { + "bbox": [ + 46, + 150, + 287, + 294 + ], + "type": "text", + "content": "The BD-rate of different image compression methods with BPG [10] as the anchor is presented in Table 1. As shown, our method achieves the best BD-rate and BD-PSNR results on four testsets, which indicates that we use the smallest amount of bits to achieve the highest PSNR among all methods. Specially, our average BD-rate of " + }, + { + "bbox": [ + 46, + 150, + 287, + 294 + ], + "type": "inline_equation", + "content": "-48.5\\%" + }, + { + "bbox": [ + 46, + 150, + 287, + 294 + ], + "type": "text", + "content": " and BD-PSNR of " + }, + { + "bbox": [ + 46, + 150, + 287, + 294 + ], + "type": "inline_equation", + "content": "1.43\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 150, + 287, + 294 + ], + "type": "text", + "content": " are much better than the most advanced codec VVC-intra' - " + }, + { + "bbox": [ + 46, + 150, + 287, + 294 + ], + "type": "inline_equation", + "content": "16.8\\%" + }, + { + "bbox": [ + 46, + 150, + 287, + 294 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 150, + 287, + 294 + ], + "type": "inline_equation", + "content": "0.53\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 150, + 287, + 294 + ], + "type": "text", + "content": ". More intuitively, when VVC is set as the anchor, our RFD-ECNet achieves breakthrough BD-rate saving of " + }, + { + "bbox": [ + 46, + 150, + 287, + 294 + ], + "type": "inline_equation", + "content": "31.7\\%" + }, + { + "bbox": [ + 46, + 150, + 287, + 294 + ], + "type": "text", + "content": " and BD-PSNR of " + }, + { + "bbox": [ + 46, + 150, + 287, + 294 + ], + "type": "inline_equation", + "content": "0.90\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 150, + 287, + 294 + ], + "type": "text", + "content": ", demonstrating the advanced performance of our RFD-ECNet on UWI extreme compression." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 294, + 287, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 294, + 287, + 473 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 287, + 473 + ], + "type": "text", + "content": "Visual Quality. Fig. 8 shows visual examples of reconstructed images by our RFD-ECNet, Cheng (CVPR'20), the most advanced VVC-intra, and the widely used JPEG2000. As shown, our reconstructed images retain more details, while the reconstructed images of VVC-intra and JPEG2000 present obvious blurring and blocking effects at extremely low bpp. As shown in the second row, when bpp=0.049, VVC-intra, Cheng (CVPR'20) and JPEG2000 completely lose the common object of sand, while our RFD-ECNet can roughly reconstruct the sand by referencing our dictionary. Overall, our pixel fidelity is higher than others at the similar extremely low bpp, which can be verified by our higher PSNR. More visual results tested on underwater videos are provided at https://github.com/lilala0/RFD-ECNet." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 474, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 629 + ], + "type": "text", + "content": "Comparison with video CODECs. To verify that the redundancy between UWIs cannot be efficiently removed by video CODEcs, our RFD-ECNet is compared with the latest video CODEcs of VVC-inter and HEVC-inter. Their performance on UGWI testset measured by BD-rate and BD-PSNR with the Minnen [13] as the anchor is shown in Table 2. As shown, we achieve better results than both VVC-inter and HEVC-inter, verifying that our RFD-ECNet referencing to dictionary is more efficient than video CODEcs to remove the redundancy between UWIs. Moreover, both video CODEcs at inter-mode only achieve tiny improvement of BD-rate/PSNR than the intra-mode. This verifies that there is redundancy between UWIs indeed." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": "Comparison of complexity. The trainable parameters and FLOPs of all approaches are compared in Table 1. As shown, our parameters (35.8 M) is much less than that (99.8 M) of compression network [18]. Additionally, we also provide a slim version of Our RFD-ECNet by narrowing our network channels of 192 to 128 (denoted as Ours-slim), which only have 15.4M parameters and 40.7G FLOPs. No" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 310, + 112, + 544, + 155 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 106 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 106 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 106 + ], + "type": "text", + "content": "Table 3: BD-rate " + }, + { + "bbox": [ + 305, + 70, + 545, + 106 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 70, + 545, + 106 + ], + "type": "text", + "content": " and BD-PSNR (dB) of ablation studies about our USNB and RFVM, where BPG [10] is set as the anchor." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 112, + 544, + 155 + ], + "lines": [ + { + "bbox": [ + 310, + 112, + 544, + 155 + ], + "spans": [ + { + "bbox": [ + 310, + 112, + 544, + 155 + ], + "type": "table", + "html": "
SettingOursw/o USNBw/o RFVMw/o USNB&RFVM
BD-rate ↓-53.7-33.6-43.1-24.6
BD-PSNR ↑1.971.141.490.83
", + "image_path": "027c8e35a372c2f5fc75014ade006adcded17935e458b9d8dfb65548b7ce7438.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 310, + 209, + 544, + 249 + ], + "blocks": [ + { + "bbox": [ + 305, + 167, + 545, + 203 + ], + "lines": [ + { + "bbox": [ + 305, + 167, + 545, + 203 + ], + "spans": [ + { + "bbox": [ + 305, + 167, + 545, + 203 + ], + "type": "text", + "content": "Table 4: BD-rate " + }, + { + "bbox": [ + 305, + 167, + 545, + 203 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 167, + 545, + 203 + ], + "type": "text", + "content": " and BD-PSNR (dB) of ablation studies about the multi-scale manner, where BPG [10] is set as the anchor." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 209, + 544, + 249 + ], + "lines": [ + { + "bbox": [ + 310, + 209, + 544, + 249 + ], + "spans": [ + { + "bbox": [ + 310, + 209, + 544, + 249 + ], + "type": "table", + "html": "
Scale settingScale-{2}Scales-{2,3}Scales-{2,3,4}
BD-rate ↓-46.1-49.8-53.7
BD-PSNR ↑1.671.831.97
", + "image_path": "f254b2491b3ceacc0b5799d679ccd050b5085e168bb667e9da50ff96f20cc1c0.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 270, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 270, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 305, + 270, + 545, + 308 + ], + "type": "text", + "content": "tably, ours-slim still achieves better performance than all SOTA methods with lower complexity, illustrating our excellent UWI extreme compression performance." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 327, + 399, + 341 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 327, + 399, + 341 + ], + "spans": [ + { + "bbox": [ + 306, + 327, + 399, + 341 + ], + "type": "text", + "content": "5. Ablation Study" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 350, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 545, + 555 + ], + "type": "text", + "content": "Effectiveness of USNB and RFVM. To verify the effectiveness of the proposed USNB and RFVM, a series of ablation experiments are conducted, where the USNB and RFVM are removed from our RFD-ECNet in sequence. The performance of each ablation is measured by the BD-rate and BD-PSNR with the BPG as the anchor, shown in Table 3. w/o USNB indicates the network that directly performs feature match by inner product without using our USNB to normalize the dictionary features. w/o RFVM is the network where the matched reference features are not fed into our RFVM and therefore cannot be varied adaptively based on the input features. w/o USNB&RFVM is the network without both USNB and RFVM. As can be seen from Table 3, the removal of either USNB or RFVM degrades the performance of our RFD-ECNet. Moreover, the performance degrades most when USNB and RFVM are removed simultaneously, verifying the effectiveness of USNB and RFVM." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "Effectiveness of multi-scale reference. In our RFD-ECNet, the input features are matched with the feature dictionary at three scales (\\(s = 2,3,4\\)), considering that the similarity between UWIs is reflected on the textures, structures, and semantics. Here we conduct ablations to verify the effectiveness of the multi-scale manner, and provide the results in Table 4. Since the features on scale-1 contain more noise less semantic information, we perform feature match starting from scale-2. As shown, our RFD-ECNet referring dictionary at scales-\\{2,3,4\\} achieves the best performance, followed by scales-\\{2,3\\} and scale-\\{2\\}\\), which verifies that it is efficient to remove the underwater common redundancy at multiple scales from coarse to fine." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12987" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 116, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 116, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 116, + 83 + ], + "type": "text", + "content": "6. Discussion" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 289, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 289, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 289, + 236 + ], + "type": "text", + "content": "This work creatively removes redundancy between UWIs and proposes a novel reference-based image compression framework. Actually, the redundancy between images exists not only in UWIs but also in other image domains where independent images contain some common objects specific to the image domain. For example, all Martian images [36] contain rocks and sand; all face images [37] contain eyes, nose and mouth; most remote sensing images [38] contain buildings, road and so on. However, existing image compression works neglect this nature and only remove redundancy in an image, which may limit the development of image compression." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 236, + 289, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 236, + 289, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 289, + 321 + ], + "type": "text", + "content": "To validate our hypothesis, we additionally conduct preliminary experiments on Martian images [36] by adjusting our network. Experimental results presented in the supplementary materials show that we also achieve better performance than VVC and Ding (VCIP'22) [36], illustrating the efficiency and feasibility of removing redundancy between images in other image domains." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 333, + 119, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 333, + 119, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 333, + 119, + 346 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 354, + 289, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 289, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 289, + 594 + ], + "type": "text", + "content": "In this paper, we explore the characteristics of UWIs and find that UWIs present multifarious underwater styles and different UWIs share some common ocean objects at diverse morphologies and sizes, resulting in plenty of redundancy between UWIs. Hence, we construct an exhaustive and compact underwater multi-scale feature dictionary from the manually selected representative UWIs, which provides coarse-to-fine reference for our RFD-ECNet to fully remove redundancy between UWIs. Meanwhile, to eliminate the effect of underwater styles on feature match, we utilize UPPs to design the USNB to align the multifarious underwater styles of dictionary towards that of input features. Moreover, to improve the similarity between the input and reference features, we propose RFVM to perform adaptive reference feature variant. Finally, extensive comparisons are conducted to verify our significant performance improvement than SOTA methods including the latest VVC, and comprehensive ablation studies verify the effectiveness of each module in our RFD-ECNet." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 604, + 144, + 617 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 604, + 144, + 617 + ], + "spans": [ + { + "bbox": [ + 47, + 604, + 144, + 617 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "This work is supported in part by the National Natural Science Foundation of China under Grant 61931022 and Grant 62271301; in part by the Shanghai Science and Technology Program under Grant 22511105200; in part by the Shanghai Excellent Academic Leaders Program under Grant 23XD1401400; in part by the Natural Science Foundation of Shandong Province under Grant ZR2022ZD38." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 307, + 72, + 365, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 72, + 365, + 83 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 365, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 307, + 91, + 547, + 712 + ], + "type": "list", + "angle": 0, + "index": 22, + "blocks": [ + { + "bbox": [ + 311, + 91, + 545, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 91, + 545, + 135 + ], + "spans": [ + { + "bbox": [ + 311, + 91, + 545, + 135 + ], + "type": "text", + "content": "[1] G.L. 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Vggface2: A dataset for recognising faces across pose and age. In IEEE International Conference on Automatic Face & Gesture Recognition (FG 2018), pages 67-74, 2018. 9" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 307, + 525, + 545, + 558 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 525, + 545, + 558 + ], + "spans": [ + { + "bbox": [ + 307, + 525, + 545, + 558 + ], + "type": "text", + "content": "[38] G. S. Xia, W. Yang, J. Delon, Y. Gousseau, and S. Hong. Structural high-resolution satellite image indexing. In ISPRS TC VII Symposium, 2010. 9" + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "12989" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/RFLA_ A Stealthy Reflected Light Adversarial Attack in the Physical World/bdd5612c-711f-444e-bf67-fd043897ebe9_content_list.json b/2023/RFLA_ A Stealthy Reflected Light Adversarial Attack in the Physical World/bdd5612c-711f-444e-bf67-fd043897ebe9_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..48d144f8ae9169d23f4798bfc9fbf1f05abd14fd --- /dev/null +++ b/2023/RFLA_ A Stealthy Reflected Light Adversarial Attack in the Physical World/bdd5612c-711f-444e-bf67-fd043897ebe9_content_list.json @@ -0,0 +1,2424 @@ +[ + { + "type": "text", + "text": "RFLA: A Stealthy Reflected Light Adversarial Attack in the Physical World", + "text_level": 1, + "bbox": [ + 102, + 128, + 867, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Donghua Wang $^{1}$ , Wen Yao $^{*2}$ , Tingsong Jiang $^{*2}$ , Chao Li $^{3}$ , and Xiaojian Chen $^{2}$", + "bbox": [ + 171, + 191, + 795, + 212 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1College of Computer Science and Technology, Zhejiang University", + "bbox": [ + 212, + 223, + 751, + 241 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "2Defense Innovation Institute, Chinese Academy of Military Science", + "bbox": [ + 212, + 241, + 754, + 258 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ School of Artificial Intelligence, Xidian University", + "bbox": [ + 279, + 258, + 689, + 276 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "wangdonghua@zju.edu.cn, {wendy0782,lichaoedu} @ 126.com, tingsong@pku.edu.cn,", + "bbox": [ + 143, + 277, + 828, + 295 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "chenxiaogian@nudt.edu.cn", + "bbox": [ + 375, + 295, + 594, + 311 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 357, + 313, + 372 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Physical adversarial attacks against deep neural networks (DNNs) have recently gained increasing attention. The current mainstream physical attacks use printed adversarial patches or camouflage to alter the appearance of the target object. However, these approaches generate conspicuous adversarial patterns that show poor stealthiness. Another physical deployable attack is the optical attack, featuring stealthiness while exhibiting weakly in the daytime with sunlight. In this paper, we propose a novel Reflected Light Attack (RFLA), featuring effective and stealthy in both the digital and physical world, which is implemented by placing the color transparent plastic sheet and a paper cut of a specific shape in front of the mirror to create different colored geometries on the target object. To achieve these goals, we devise a general framework based on the circle to model the reflected light on the target object. Specifically, we optimize a circle (composed of a coordinate and radius) to carry various geometrical shapes determined by the optimized angle. The fill color of the geometry shape and its corresponding transparency are also optimized. We extensively evaluate the effectiveness of RFLA on different datasets and models. Experiment results suggest that the proposed method achieves over $99\\%$ success rate on different datasets and models in the digital world. Additionally, we verify the effectiveness of the proposed method in different physical environments by using sunlight or a flashlight.", + "bbox": [ + 76, + 388, + 472, + 782 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 823, + 209, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep neural networks (DNNs) have increasingly been applied to daily life as their dramatic capabilities, such as", + "bbox": [ + 76, + 848, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/39a1f360014eed5c64a3195c1f15d70de79d86a80763a17d5a7f71ed5cd20484.jpg", + "image_caption": [ + "Figure 1. The reflected light is modulated by the color transparency plastic sheet and paper cut of the specific shape for better attack performance. The Reflected light source can be sunlight or a flashlight (when the sunlight is unreachable)." + ], + "image_footnote": [], + "bbox": [ + 504, + 357, + 864, + 545 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "automatic driving, facial payment, and computer-aided diagnosis. However, DNN-based systems have exposed security risks caused by adversarial examples [39]. Adversarial examples are crafted by carefully designed noise that is invisible to humans but can deceive the DNNs. Furthermore, recent researches [34, 21] reported that physically deployed DNN-based systems are also exposed to such security risks. Therefore, exploring various potential risks in security-sensitive systems to avoid possible loss is urgent.", + "bbox": [ + 496, + 627, + 890, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing adversarial attack methods can be categorized into digital attacks and physical attacks. The former focus on pursuing higher attack performance on limitation conditions, such as breaking the model equipped with adversarial defense [20, 3, 7, 24], preventing the attacker from accessing the target model's information (e.g., architecture or dataset), i.e., black-box attack [1, 22, 23]. Although some researchers suggested that adversarial examples generated by the digital attack can be applied to physical attacks [21],", + "bbox": [ + 496, + 765, + 892, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author.", + "bbox": [ + 94, + 886, + 225, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4455", + "bbox": [ + 482, + 924, + 514, + 936 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the attack performance is not satisfying. The possible reason is that the adversarial perturbation is too small to resist the environmental noise in the physical world. In contrast, physical attacks are designed to be physically deployable, where one crucial change is eliminating the perturbation's magnitude constraint.", + "bbox": [ + 75, + 90, + 470, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A line of physical adversarial attack methods [10, 9, 43, 44] has been proposed, which can be grouped into contact attacks and contactless attacks. The former requires the attacker to approach the target object and then modify the appearance of the target object by pasting the adversarial patch or camouflage. However, the adversarial pattern generated by these methods is conspicuous, which easily alerts humans and results in attack failure. By contrast, contactless physical attacks do not require the attacker to approach the target object while modifying the appearance of the target object by projecting or emitting light or laser on the target object to perform attacks, making it stealthy and dangerous. Optical attacks are representative contactless attacks. Although several optical attacks have been proposed [28, 32, 8, 17], they merely work in dark environments as the strong light (e.g., sunlight) environment would disturb the emitted light, limiting their usability.", + "bbox": [ + 75, + 184, + 470, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we get inspiration from the fact that the driver is easily affected by the strong reflected light, resulting in a potential car accident, and such potential risks to the automatic driving system remain unexplored. We explore the vulnerability of the DNNs toward the reflected light attack by elaborately designing the position, geometry, and color of the reflected light. Specifically, we propose a Reflected Light Attack (RFLA), which can solve the issue of the poor attack performance of existing optical attacks in strong-light environments, as our light source is sunlight. To perform physical attacks, we use a mirror to reflect the sunlight toward the target object to modify its appearance. However, the monotonous sunlight (usually white) may not obtain the desired performance. Therefore, we first use different colored transparent plastic sheets to modulate the color of the reflected light, then apply a paper cut of a specific shape to control the shape of reflected light on the target object (see Figure 1). Finally, we can create different colors and shapes of the reflected light on the target object's specific region to achieve desired attack performance.", + "bbox": [ + 75, + 444, + 468, + 746 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To achieve the above goals, we present a general framework based on the circle to model the above problem. Specifically, we first initialize a circle with a random coordinate and radius. On this circle, we create a point on the circle using sine and cosine with a randomly selected angle. Then, we customize a shape by adding a new angle, which is used to create a new point in the circumference. The other points required to create a geometry can be obtained by applying the center symmetry of the circle. Moreover, the fill color and its transparency are also considered in", + "bbox": [ + 75, + 750, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the optimization. Finally, we adopt the particle swarm optimization (PSO) algorithm to find the optimal result. Our contributions are listed as follows.", + "bbox": [ + 498, + 90, + 890, + 135 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel reflect-light-based physical adversarial attack under the black-box scenario. It reflects the natural sunlight toward the target object using a mirror, making it controllable and stealthy.", + "- We devise a general framework based on a circle to search for the best position, geometry, and color of the reflected light to achieve better attack performance.", + "- We comprehensively investigate the influence of the geometry, position, and color of the reflected light on attack performance in the digital world. We conduct the physical adversarial attack by using sunlight for daytime and a flashlight for sunlight unavailable, and the experiment results verify the effectiveness of the proposed method." + ], + "bbox": [ + 517, + 151, + 890, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 411, + 648, + 426 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Digital Adversarial Attacks", + "text_level": 1, + "bbox": [ + 500, + 436, + 746, + 454 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Digital adversarial attacks have enjoyed decade development, which can be roughly divided into white-box attack methods and black-box attack methods. The former grants the adversary access to the target model, allowing them to develop attack algorithms with the model's gradient. The most represented gradient-based attack is the fast gradient sign method (i.e., FGSM [13]), which updates adversarial examples along the ascending direction of the gradient under one iteration step. Since then, a line of variants has been proposed, including an iterative variant of FGSM (i.e., I-FGSM [21]), random initialization has been adopted (i.e., PGD [27]), momentum term is introduced to enhance the transferability (i.e., MI-FGSM [6]), and various data augmentation technique like diversity input (i.e., DIFGSM[47]), translation-invariant (i.e., TI-FGSM [7]) and scale-invariant (i.e., SI-FGSM [24]). In contrast, black-box attacks prohibit the attacker from accessing any information about the target model but are open for queries, which makes black-box attacks more challenging. Nonetheless, many black-box attacks are proposed, such as exploiting the differential evolution algorithm [22], genetic algorithm [1], particle swarm optimization [51], and so on [2]. In addition, several works suggested that adversarial perturbation's position [45], pattern [49], and geometry [4] on the clean image significantly impact attack performance. However, current works only investigate one or two of these factors. In this work, we systematically investigate the influence of the adversarial perturbation's position, geometry, and pattern on attack performance under the black-box scenario.", + "bbox": [ + 496, + 462, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4456", + "bbox": [ + 482, + 924, + 514, + 936 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Physical Adversarial Attacks", + "text_level": 1, + "bbox": [ + 76, + 90, + 334, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "According to whether it requires the attacker to access the target object in the real attack scenario, physical adversarial attacks can be grouped into contact and contactless physical attacks. Contact attacks can be further categorized into patch-based attacks and camouflage-based attacks. Patch-based attacks mainly focus on optimizing an adversarial image patch, which is then printed out and stuck on the target object or held by the attacker to deceive the target DNNs. Patch-based attacks are usually applied in attacking the facial recognition model [34, 35, 45, 46], pedestrian detection model [41, 40, 16, 5], and traffic sign recognition model [10, 25, 51]. Camouflage-based attacks [44, 43, 9] slightly differ from patch-based, as they concentrate on modifying the appearance of the target object via UV Texture. Thus, camouflage-based attacks show better attack performance in the multi-view scenario by painting the full coverage camouflage over the appearance of the target object. However, although contact physical attacks achieve good physical attack performance, the pattern of the adversarial patch/camouflage is conspicuous, which leads to poor stealthiness. In contrast, contactless physical attacks are performed by projecting/emitting light [12, 17], or a laser beam [8], usually called optical attacks. However, existing optical attacks work in dark environments [8, 17] while performing poorly in strong-light environments. The reason is that the light beam emitted by a light source is easily affected by environmental light, resulting in attacking failure. Recently, Zhang et al. [51] proposed a shadow-based attack, but it can only create a triangle shape with one monotonous color (e.g., gray). In this work, we solve the situation of poor attacks in strong-light (i.e., sunlight) environments to perform attacks since we directly use sunlight to perform attacks. Moreover, we create reflected light with different geometrical shapes and colors using the color transparency plastic sheet and paper cut.", + "bbox": [ + 75, + 114, + 473, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 662, + 212, + 679 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Statement", + "text_level": 1, + "bbox": [ + 76, + 688, + 261, + 703 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $\\mathcal{X}$ denote the data distribution, and the corresponding ground truth label is $\\mathcal{V}$ . Given an image $x\\in \\mathcal{X}$ that has the resolution of $x\\in \\mathbb{R}^{C\\times H\\times W}$ , a well trained neural network $f$ output $\\hat{y} = f(x)$ and $\\hat{y} = y$ , where the $\\hat{y}$ is prediction of the $f$ and $y$ is the ground truth label, $\\hat{y},y\\in \\mathbb{R}^{|\\mathcal{V}|}$ . Adversarial attack aims to generate adversarial examples $x_{adv}$ to make the $f$ output the wrong prediction by adding small perturbation $\\delta$ into the clean image $x$ , i.e., $x_{adv} = x + \\delta$ . Mathematically, the $\\delta$ is obtained by solving the following problem", + "bbox": [ + 75, + 712, + 468, + 864 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min \\delta \\quad s. t. f (x + \\delta) \\neq f (x), | | \\delta | | _ {p} \\leq \\epsilon , \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 883, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a0506e345e55c38f94f4b6613696819082eee2da2ede0883c6a8c2ee4bf2f620.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 89, + 633, + 179 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d55d70caf5b1dba2d088c44bb859b115dee41ede8817ab348a6cc483cfcf1cfd.jpg", + "image_caption": [ + "(a) Base circle", + "(d) Rectangle", + "Figure 2. Visualization explanation of the circle modeling. Different geometries are constructed by adjusting the angle. For example, the triangle is created by adding a new angle $\\angle a_{2}$ on the base circle (a), where three vertices are composed of two points $(p_{1}$ and $p_2)$ determined by two angles $(\\angle a_{1}$ and $\\angle a_{2})$ and one symmetry point $(p_1^{\\prime})$" + ], + "image_footnote": [], + "bbox": [ + 517, + 196, + 633, + 289 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a405cf57134d85fc4b2159f2c4d8655e9a7e6b0bf5cc4eec1f8455f1450e2292.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 638, + 89, + 754, + 179 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/32224686e0b467cb699c9a3e1d9311c04afcdb961992ef57e18705bd90fcf1b2.jpg", + "image_caption": [ + "(b) Line", + "(e) Pentagon" + ], + "image_footnote": [], + "bbox": [ + 638, + 196, + 753, + 287 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9eb653c354c24f917a8085193ba6d3b226985036e10457065a67a7a20c06d772.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 88, + 874, + 179 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/fe178b4f050668981db212a1f8835229b8788e147ac808edd81e3efb18935e5a.jpg", + "image_caption": [ + "(c) Triangle", + "(f) Hexagon" + ], + "image_footnote": [], + "bbox": [ + 759, + 196, + 872, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $||\\cdot ||_p$ is the $L_{p}$ norm, which bound the maximum allowable magnitude of $\\delta$ .", + "bbox": [ + 496, + 412, + 890, + 441 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The optimization objective of Equation 1 is the general formal for constructing the full-pixel-wise perturbation, which is unsuitable for physical adversarial attacks as the background of the physical world is unchangeable. Therefore, we reformulate Equation 1 to optimize the physical deployable perturbation by modifying the construction of $x_{adv}$ . Specifically, we define an apply function $\\mathcal{A}(x,p,l,M)$ to construct adversarial examples $x_{adv}$ , which indicates that apply the perturbation $p$ at the location $l$ of the clean image $x$ , where $M$ is the binary mask to indicate whether the position is allowed to modify (one denote allow while zero not).", + "bbox": [ + 496, + 443, + 892, + 623 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we aim to reflect the sunlight toward the target object to perform stealthy physical adversarial attacks, where the representation (e.g., geometry, fill color and position) of reflected light on the target object is the key to a successful attack. Therefore, the parameters of $\\mathcal{A}(x,p,l,M)$ comprise geometry and fill color of $p$ , and the location of $l$ are variables to be optimized.", + "bbox": [ + 496, + 625, + 890, + 731 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Reflected Light Attack", + "text_level": 1, + "bbox": [ + 500, + 739, + 709, + 757 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Sunlight is the most common and indispensable natural phenomenon in daily life. People can reflect the sunlight toward the wall to construct various shapes by using different shapes of mirrors. However, the danger of such reflected light against DNN-based systems has been ignored, which may pose a potential risk as it featured extremely stealthy and controllable. In this work, we aim to modulate the reflected light to perform adversarial attacks in the digital and physical world.", + "bbox": [ + 496, + 763, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4457", + "bbox": [ + 480, + 925, + 514, + 936 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Previous work [51] modeled the triangle shadow by optimizing three points, which requires complex constraints on points to construct a rational geometry shape if they extend to other geometric shapes. To address this issue, we exploit the characteristic of the circle and propose a novel general framework based on the circle, which can generate various shapes by adjusting the number of angles (see Figure 2). The details process is described as follows.", + "bbox": [ + 76, + 90, + 472, + 212 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Select a radius $r$ from the region of $[0, \\min(H, W)/2]$ .", + "- Spawn a center $o(x, y)$ of the circle from the region of $[r, H - r]$ and $[r, W - r]$ .", + "- Randomly select an angle $a_1$ and spawn a point $p_1(x_1, y_1)$ on circle by the follow equation" + ], + "bbox": [ + 94, + 223, + 468, + 319 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} x _ {1} = x + r \\times \\sin \\left(\\frac {a _ {1} \\times \\pi}{1 8 0}\\right), \\\\ y _ {1} = y + r \\times \\cos \\left(\\frac {a _ {1} \\times \\pi}{1 8 0}\\right), \\end{array} \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 329, + 468, + 364 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Calculate the symmetry point $p_1'(x_1', y_1')$ of the point $p_1$ against the center of the circle by $x_1' = 2 \\times x - x_1$ and $y_1' = 2 \\times y - y_1$ .", + "- Randomly select a color tuple (red, green, blue) from the region of [0, 255], and the transparency $\\alpha$ from [0, 1]." + ], + "bbox": [ + 94, + 377, + 468, + 478 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The above process can plot a line on the clean image. To construct varying geometries like a triangle, rectangle, pentagon, or hexagon, one can repeat the third and fourth steps to create a new point by adding a new angle. Algorithm A1 in describes the detailed particle initialization process.", + "bbox": [ + 76, + 489, + 468, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Optimization", + "text_level": 1, + "bbox": [ + 76, + 575, + 217, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As aforementioned, we have eight base variables that need to be optimized, expressed as eight-tuples $(x,y,r,\\alpha ,red,green,\\text{blue},a_{1})$ , which can be used to plot a line on the clean image. To generate various geometries, more additional variables are required to generate various geometries, which depend on the shape to be generated. For example, there is one extra variable for the triangle and rectangle; two extra for the pentagon and hexagon. Note that the proposed method is easily extended to more complex geometry. Recall that our goal is to deceive the DNNs by plotting geometry on the clean image. Thus, we adopt the particle swarm optimization algorithm (PSO) to seek the best geometry, fill color, and position.", + "bbox": [ + 76, + 598, + 468, + 794 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In PSO, we represent the optimization variables tuple as a particle (i.e., the solution vector $q$ ). The update direction of the particle is determined by a velocity vector $v$ . Every particle stands for a potential solution, which requires to be optimized. We treat the personal historical best solution of a particle as $q_{best}$ , and the global best solution of a particle as $q_{gbest}$ . Moreover, for every solution, we fix the circle's", + "bbox": [ + 75, + 795, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6a34e550aa31c58d7fe8235533908287514bd0b603a8dba3b7a76bf7cb206f60.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 540, + 87, + 694, + 193 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/46318297295131d00c8972c7edf6b60052fa0bcbe3391637d98f7d6dd34d3476.jpg", + "image_caption": [ + "(b)", + "Figure 3. The color discrepancy between the color transparency plastic sheet (a) and its reflected light(b)." + ], + "image_footnote": [], + "bbox": [ + 696, + 88, + 856, + 210 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "position and merely optimize the geometry, fill color, and transparency. Therefore, to represent the best solution of a circle, we devised an additional metric $q_{sgbest}$ , which is the sum of the fitness score of all geometrical shapes in a specific circle. Finally, the update criterion is defined as follows:", + "bbox": [ + 496, + 277, + 890, + 366 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} v _ {i} (t) = W v _ {i} (t - 1) + C _ {1} \\kappa_ {1} \\left(q _ {p b e s t} - q _ {i} (t)\\right) \\\\ + C _ {2} \\kappa_ {2} \\left(q _ {\\text {g b e s t}} - q _ {i} (t)\\right) \\tag {3} \\\\ + C _ {3} \\kappa_ {3} \\left(q _ {s g b e s t} - q _ {i} (t)\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 390, + 890, + 445 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq _ {i} (t) = q _ {i} (t - 1) + v _ {i} (t), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 460, + 890, + 477 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $W$ is the inertia weight used to control the impact of the previous velocity on the current velocity. $C_1, C_2$ , and $C_3$ indicate the learning factors, which balance the impact of different parts empirical on current velocity. $\\kappa_1, \\kappa_2$ , and $\\kappa_3$ are random values uniformly sampled from [0, 1], which are used to increase the randomness of the search.", + "bbox": [ + 496, + 483, + 890, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Apart from the solution and velocity of a particle, the fitness function is crucial for optimizing in PSO algorithm. In this work, we adopt the following fitness function to evaluate each particle.", + "bbox": [ + 496, + 574, + 890, + 633 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min F (q) = \\Pr_ {\\hat {y}} (\\mathcal {A} (x, q, M)), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 648, + 890, + 666 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{A}(x,q,M)$ denotes an applied function that paints the geometry with color (red,green,blue) and transparency $\\alpha$ at the coordinate of $o$ on the clean image $x$ , where $M$ is a binary mask indicates the allowed modification area. $\\operatorname{Pr}_{\\hat{y}}(\\cdot)$ is the predicted label $\\hat{y}$ probability of the target model $f$ on the input. By minimizing the $F(q)$ , the confidence of prediction label $\\hat{y}$ gradually decreases. We stop the search until it reaches the maximum iteration or finds the adversarial example. Algorithm 1 describes the optimization process.", + "bbox": [ + 496, + 671, + 890, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Physical Deployable Attack", + "text_level": 1, + "bbox": [ + 500, + 832, + 746, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In digital worlds, we can construct $256^{3}$ color tuples by blending different RGB values, which is impractical in the physical world as the limitation of the device and material.", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4458", + "bbox": [ + 480, + 924, + 514, + 936 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [], + "code_body": "Algorithm 1 Reflected Light Adversarial Attack (RFLA) \nInput: input image $x$ , target model $f$ , max iteration MaxIter \nOutput: Best solution $q^*$ \n1: $q \\gets \\text{Initialization}()$ ▷ Algorithm A1 \n2: $x_{adv} \\gets \\text{GenSample}(q)$ ▷ Algorithm A2 \n3: if $f(x_{adv}) \\neq f(x)$ then \n4: return $q^*$ \n5: end if \n6: for $itr = i, \\dots, \\text{MaxIter}$ do \n7: Update velocity vector $v$ by Equation 3 \n8: Update position vector $q$ by Equation 4 \n9: $x_{adv} \\gets \\text{GenSample}(q)$ ▷ Algorithm A2 \n10: if $f(x_{adv}) \\neq f(x)$ then \n11: return $q^*$ \n12: end if \n13: end for", + "bbox": [ + 76, + 89, + 468, + 352 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Therefore, we constrain the search space of the color to ensure physically deployable. Specifically, we use seven color transparency plastic sheets to change the color of the reflected light. However, we find discrepancies exist between the color transparency plastic sheet and its reflected light (see Figure 3), which may lead to attack failure. To decrease such discrepancy, we collect the light color reflected by the color transparency plastic sheet and adopt it as the searched color. In such a way, we can decrease color discrepancies when performing physical attacks.", + "bbox": [ + 75, + 382, + 472, + 536 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 550, + 209, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Settings", + "text_level": 1, + "bbox": [ + 76, + 575, + 174, + 592 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets: To investigate the effectiveness of the proposed method, we conduct the digital attack on the ImageNet-compatible dataset provided by the NIPS 2017 adversarial competition1, which includes 1000 images. Moreover, two commonly used traffic sign datasets: GTSRB [37] and LISA [29], are also considered to investigate the extensibility of the proposed method.", + "bbox": [ + 75, + 599, + 468, + 705 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Target models: We conduct the proposed method on two tasks: image classification and traffic sign recognition. As for image classification, we select six ImageNet pre-trained networks: ResNet50 (RN50) [15], VGG16 [36], DenseNet121 (DN121) [18], ResNeXt50 (RNX50) [48], WiderResNet50 (WRN50) [50] and SqueezeNet (SN) [19], which are all provided by PyTorch [30]. As for traffic sign recognition, we follow the setting reported in previous works [10, 25] to train GTSRB CNN and LISA CNN on GTSRB and LISA dataset, which obtains the accuracy of $95.06\\%$ and $100\\%$ on the test set, respectively.", + "bbox": [ + 75, + 707, + 470, + 875 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/a1963f95ce82db73e5a0ab05b0d7ee7689e5b4bcf562b34fed9f5a2f5578f756.jpg", + "table_caption": [ + "Table 1. Comparison results with the line-based method in terms of ASR (%) on ImageNet-compatible dataset. The best results are highlighted with bold." + ], + "table_footnote": [], + "table_body": "
RN50VGG16DN121RNX50WRN50SN
Bezier [11]72.477.774.172.769.689.3
RFLA-Line76.977.476.575.771.789.2
", + "bbox": [ + 501, + 128, + 898, + 176 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation metrics: We adopt the attack success rate (ASR) as the evaluation metric, defined as the ratio of the number of the network's prediction flipped caused by adversarial examples to the total test dataset.", + "bbox": [ + 498, + 200, + 890, + 260 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details: We adopt the OpenCV-Python package to plot different geometries in the clean image. For the settings of parameters of PSO, we set the max iteration number to 200, $C_1$ , $C_2$ , and $C_3$ set to 2.05, $W$ is set to 0.7298, the particle size and the geometry number at a circle are set to 50. The particle and velocity bound are provided in Appendix A (The upper bound of the transparency $\\alpha$ is set to 0.7 to evade occluding the clean image.). Unless otherwise specified, the mask $M$ is set to all one value matrix in our experiments. All experiments were conducted on an NVIDIA RTX 3090ti 24GB GPU $^2$ .", + "bbox": [ + 496, + 261, + 892, + 428 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Digital Adversarial Attacks", + "text_level": 1, + "bbox": [ + 500, + 436, + 746, + 452 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we quantitatively and qualitatively evaluate the effectiveness of the proposed method in the digital world. For comparison, we adopt two patch-based attack methods: TPA [49] and DAPatch [4]; one line-based attack method Bezier [11]. TPA [49] utilized the feature texture image extracted from DNNs as the adversarial patch, which is pasted on the clean image, where the paste position is optimized by reinforcement learning. DAPatch [4] optimized the pattern and mask simultaneously, which can create a deformable shape adversarial patch. In contrast, Bezier [11] generated adversarial examples by scratching theBezier curve on the clean image, where theBezier curve depends on three points optimized by the optimizer (e.g., PSO). We reproduce the above three methods on the ImageNet-compatible dataset using the default settings.", + "bbox": [ + 496, + 459, + 893, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.1 Quantitatively Result", + "text_level": 1, + "bbox": [ + 500, + 704, + 702, + 719 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1 reported the comparison results of the proposed RFLA-Line with the Bezier method. As we can observe, the proposed method outperforms the Bezier method on four of six models and obtains an improvement by $1.93\\%$ in average ASR, indicating the proposed method's effectiveness. Additionally, we can get an $8.95\\%$ improvement by widening the line thickness two times. Although the length of the Bezier curve may be shorter than ours, the discrepancy is trivial as modifications caused by the line is neglectable. Moreover, our method can be extended to more geometries.", + "bbox": [ + 496, + 727, + 893, + 878 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "1https://www.kaggle.com/c/nips-2017-non-targeted-adversarial-attack", + "bbox": [ + 94, + 886, + 465, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "$^{2}$ Code will be released after published.", + "bbox": [ + 517, + 886, + 725, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4459", + "bbox": [ + 482, + 926, + 514, + 936 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1b3386f0e862e9a3b67a08c3b9023b9a092cc32f3f90289b57cd4fd961594382.jpg", + "image_caption": [ + "balloon" + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 158, + 155 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fc99541260d87d6bbd5b5dc2116c7be31bc605b976c99b541de543d3e229d5af.jpg", + "image_caption": [ + "balloon" + ], + "image_footnote": [], + "bbox": [ + 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Visualization comparison of adversarial examples generated by different methods on ResNet50." + ], + "image_footnote": [], + "bbox": [ + 449, + 311, + 522, + 367 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cf4f723b1e7b68f01725892bb0f288e0d4332ab80da79f4bea7c0950238e1547.jpg", + "image_caption": [ + "cheetah" + ], + "image_footnote": [], + "bbox": [ + 539, + 311, + 612, + 367 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9d4440c9779adc2b99c15f49b265a7a75756a57ec797b75c25b929c4ffcf716c.jpg", + "image_caption": [ + "ounce" + ], + "image_footnote": [], + "bbox": [ + 630, + 311, + 702, + 367 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b415952c7654092d2231919d6e33713a1bc56561a5f822d6b44faff5fda25a1c.jpg", + "image_caption": [ + "ounce" + ], + "image_footnote": [], + "bbox": [ + 722, + 311, + 794, + 367 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/dec4262063827417f1141b6dfd2875ba1f35e3f76a01174f36d8e91012f68607.jpg", + "image_caption": [ + "cheetah" + ], + "image_footnote": [], + "bbox": [ + 812, + 311, + 885, + 367 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8e99c4f16ff4ea6b500453dbe2da332d1b461e3697a1544fab210c8e9131d838.jpg", + "table_caption": [ + "Table 2. Comparison results with patch-based methods in terms of ASR (\\%) on ImageNet-compatible dataset. The best results are highlighted with bold." + ], + "table_footnote": [], + "table_body": "
RN50VGG16DN121RNX50WRN50SN
TPA [49]66.1364024.723.444.6
DAPatch [4]74.371.679.373.776.756
RFLA-Triangle98.197.897.297.298.199.5
RFLA-Rectangle99.399.199.298.999.199.8
RFLA-Pentagon99.699.199.299.299.499.8
RFLA-Hexagon99.599.599.599.599.499.8
", + "bbox": [ + 78, + 455, + 472, + 555 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Then, the comparison results of patch-based methods are listed in Table 2. We conclude that the proposed geometry variants of RFLA outperform the existing method significantly. Specifically, the average ASR of the RFLA-triangle, RFLA-rectangle, RFLA-pentagon, and RFLA-hexagon are $97.98\\%$ , $99.23\\%$ , $99.38\\%$ , and $99.53\\%$ , obtaining the maximum improvement against TPA and DAPatch by $60.32\\%$ and $27.52\\%$ . We observe that the attack performance of comparison methods fails to achieve such results reported in their paper. The possible reason is that TPA may require two or more patches occluding $8\\%$ of the image to achieve higher attack performance. As for DAPatch [4], the position of the adversarial patch is ignored, which makes them fail to seek the model-decision-sensitive position. In contrast, our method simultaneously optimizes the position, geometry, and adversarial pattern, resulting in better performance. Moreover, the ASR gains with increasing vertex of geometry shape are attenuations, such as $20.08\\%$ gains from Line (two vertices) to Triangle(three vertices), while only $0.15\\%$ from Rectangle to Pentagon, which may be attributed to the improvement room of ASR is limited.", + "bbox": [ + 75, + 583, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/817702727fff026d88b7b128bde5cf91b4695513764f42ac3a3de76fd25187ee.jpg", + "table_caption": [ + "Table 3. Comparison results of transferability of adversarial examples generated by RNX50 in terms of ASR $(\\%)$ on ImageNet-compatible dataset. Item indicates the white-box attack result, while the others are black-box results. The best results are highlighted with bold." + ], + "table_footnote": [], + "table_body": "
methodRN50VGG16DN121RNX50WRN50SN
Bezier [11]18.116.816.472.712.426.6
RFLA-LINE17.615.517.575.71427.1
TPA [49]28.93626.724.720.445.4
DAPatch [4]32.352.542.373.726.428.8
RFLA-Triangle37.834.933.197.233.750
RFLA-Rectangle47.643.244.398.945.5259.9
RFLA-Pentagon47.54546.499.245.261.9
RFLA-Hexagon50.84447.699.54763.9
", + "bbox": [ + 501, + 483, + 895, + 612 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In addition, we compare the transferability of the proposed method with the comparison methods. Specifically, we use adversarial examples generated on RNX50 to attack other models. Evaluation results are reported in Table 3. As we can observe, RFLA outperforms the comparison methods in most cases, and the magnitude of fall behind cases is small. Concretely, we obtain the maximum average improvement of ASR of Bezier, TPA, and DAPatch are $0.28\\%$ (RFLA-Line), $19.18\\%$ , and $14.2\\%$ , indicating the effectiveness of the proposed method. In addition, we provide other transferability comparison results in Appendix B1.", + "bbox": [ + 496, + 640, + 890, + 806 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.2 Qualitatively Result", + "text_level": 1, + "bbox": [ + 500, + 829, + 692, + 845 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We provide the visualization result of adversarial examples generated by different methods in Figure 4. As we can observe, on the one hand, the Bezier and RFLA-Line obtain", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4460", + "bbox": [ + 482, + 926, + 514, + 936 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/31d54a1cae4007428d1fb3794b967ba093bf9a11b0c5a6bcbc12a975dd4d3040.jpg", + "image_caption": [ + "Figure 5. Model attention analysis of adversarial examples generated by RFLA on ResNet50." + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 454, + 193 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the most natural visuality quality, and the scratched line is hardly observed at a glance. Meanwhile, RFLA-Line fools the DNNs in all displayed cases, but Bezier only has two success cases. On the other hand, TPA and DAPatch failed in all displayed cases. Such qualitative results can be used to explain their inferior attack performance. The adversarial patch generated by their method covers the noncontent areas, which may be insignificant to the model decision. Although the proposed method affects more image content than TPA and DAPatch, the covered contents are recognizable. In other words, our method does not modify the semantics of the image. We provide more visualization results of adversarial examples in Appendix B1.", + "bbox": [ + 75, + 247, + 467, + 443 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In addition, we use the Grad-CAM [33] to investigate why the proposed method can work. Figure 5 illustrates the model attention visualization results. As we can observe, the painted geometry suppresses the model's attention areas, which makes the model output the wrong results. We also provide the visualization analysis result of comparison methods on model attention in Appendix B2.", + "bbox": [ + 75, + 443, + 467, + 549 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Extend to Traffic Sign Recognition Task", + "text_level": 1, + "bbox": [ + 76, + 558, + 418, + 574 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To further investigate the effectiveness of the proposed method, we use RFLA to attack the traffic sign recognition (TSR) model. Specifically, we collect 200 stop sign images from the GTSRB and LISA test set for evaluation. To avoid the geometry being out of the scope of the stop sign, we use a mask to indicate the allowable modification positions. We get the mask by averaging 200 test images and binary it. Table 4 lists the digital adversarial performance. As we can observe, the proposed method obtains superior attack performances on two TSR models, especially for GTSRB CNN (100% ASR). In addition, as for LISA-CNN, the attack performance increase with the geometries. One possible reason is that the affected area of the clean image is larger with the change of geometries under a similar circle.", + "bbox": [ + 75, + 580, + 467, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Adversarial Defense", + "text_level": 1, + "bbox": [ + 76, + 801, + 267, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this part, we investigate the attack performance under the following adversarial defense methods: preprocess-based method and adversarial trained model. The former includes Total Variance Minimization (TVM) [14], standard Pixel Deflection (Pixel) [31], JPEG compression with qual", + "bbox": [ + 75, + 825, + 467, + 898 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6fc5bc7e1c0eac01758edbec21f10607194bdea508eeef87194736d4d56da80b.jpg", + "table_caption": [ + "Table 4. Quantitative results of RELA on TSR model in terms of ASR $(\\%)$" + ], + "table_footnote": [], + "table_body": "
LISA-CNNGTSRB-CNN
RFLA-Triangle68.5100
RFLA-Rectangle92.5100
RFLA-Pentagon93.5100
RFLA-Hexagon97.5100
", + "bbox": [ + 522, + 113, + 866, + 191 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1ebb8e2c2d20c54850647cd45ca11692ec940355803160a907a9573b2727e51f.jpg", + "table_caption": [ + "Table 5. Comparison results of attack methods under different defense strategies in terms of ASR $(\\%)$" + ], + "table_footnote": [], + "table_body": "
methodTVMPixelJPEGBlurAdvIncV3EnvAdvV2
Bezier [11]74.45439.851.737.524.2
RFLA-LINE73.750.238.349.337.123.3
TPA [49]76.537.241.549.853.744.6
DAPatch [4]79.328.23242.859.547.4
RFLA-Triangle84.474.564.47557.345.1
RFLA-Rectangle8880.370.580.167.857.6
RFLA-Pentagon84.545.155.564.471.864.3
RFLA-Hexagon88.881.673.684.668.962.9
", + "bbox": [ + 516, + 231, + 875, + 342 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2f05c810d1d7aca9504bbcaa54a63e7a660ddffc1208ad80e5de224967982fef.jpg", + "table_caption": [ + "Table 6. Physical adversarial attacks under different light sources on different models in terms of ASR (\\%)." + ], + "table_footnote": [], + "table_body": "
RN50VGG16DN121
Sunlight81.2581.2581.25
Flashlight87.587.587.5
", + "bbox": [ + 550, + 378, + 834, + 428 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ity factor 75 [26], and Gaussian blur with the kernel size 5, while the latter includes the adversarial trained model consisting of Adv-Inc-v3 (AdvIncV3) [38] and Ens-Adv-IncRes-v2 (EnvAdvV2) $[42]^3$ . Table 5 reports the attack performance after the adversarial defense. As we can observe, on the one hand, the proposed method falls behind Bezier under defense strategy by $1.58\\%$ in terms of average ASR, which may attribute to the curve generated by Bezier exhibiting more robustness to the defense strategy than the line. On the other hand, other geometries generated by the proposed method significantly outperform the comparison method under the defense strategy. Specifically, the proposed method obtains the average ASR of RFLA-Triangle, RFLA-Rectangle, RFLA-Pentagon, and RFLA-Hexagon under defense is $63.37\\%$ , $70.77\\%$ , $63.11\\%$ , and $73.43\\%$ . In contrast, TPA and DAPatch are $49.24\\%$ and $46.77\\%$ . Such a result suggests that our method is more robust than the comparison method under different defense strategies.", + "bbox": [ + 496, + 452, + 890, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Physical Adversarial Attacks", + "text_level": 1, + "bbox": [ + 500, + 750, + 756, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Unlike the previous physical attacks that generate the adversarial pattern for the physically captured images, we generate the adversarial pattern (i.e., colored geometries) for digital images (the target model is RN50) and then reflect the light according to the optimized variables toward the corresponding printed images. In physical adversarial attacks, we use sunlight and a flashlight as the light source", + "bbox": [ + 496, + 772, + 890, + 877 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "$^{3}$ https://github.com/rwrightman/pytorch-image-models", + "bbox": [ + 514, + 886, + 803, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4461", + "bbox": [ + 482, + 926, + 513, + 936 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e16f37eea950b7bfba2e921ff567051a6c31c87b9b2f7f6a19173797c8961934.jpg", + "image_caption": [ + "Camera $\\rightarrow$ Rubber" + ], + "image_footnote": [], + "bbox": [ + 91, + 92, + 210, + 186 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7050c534024039837f483a3e21dea00a47fa0606fd38c795ac16a40c93316872.jpg", + "image_caption": [ + "Camera $\\rightarrow$ Laptop" + ], + "image_footnote": [], + "bbox": [ + 215, + 93, + 336, + 186 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/19ec2a320a61bd72d533a62b4464095c79a86c7cba1180a0336012003c31df05.jpg", + "image_caption": [ + "Camera $\\rightarrow$ Television" + ], + "image_footnote": [], + "bbox": [ + 341, + 93, + 460, + 186 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/337d46f9647f84ab8c4e96ecdf0219fe4a39965039bd0ec4c7d9790b78db14e4.jpg", + "image_caption": [ + "Arch bridge $\\rightarrow$", + "Window screen" + ], + "image_footnote": [], + "bbox": [ + 91, + 203, + 210, + 297 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cffec0562726bf792d65a1fab24102c3687a5a5e2c0c89a1122204d3b7b3392a.jpg", + "image_caption": [ + "Arch bridge $\\rightarrow$ Screen" + ], + "image_footnote": [], + "bbox": [ + 214, + 210, + 333, + 297 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/38eb1ac50082753b31bd8f5ea03646f08d79253a40108519472cafa17fad18e8.jpg", + "image_caption": [ + "Arch bridge $\\rightarrow$ Screen" + ], + "image_footnote": [], + "bbox": [ + 339, + 203, + 460, + 297 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6b61c2cc483f6142c0bd4e270bcf6bc383f1a62d88bebcdb2811024658dbb079.jpg", + "image_caption": [ + "Figure 6. Physical adversarial examples.", + "Light source: flashlight", + "Predict: Speed Limited 30 \nConfidence: $99.99\\%$", + "Figure 7. Examples of the \"stop\" sign with the reflected light and its prediction result on GTSRB CNN." + ], + "image_footnote": [], + "bbox": [ + 91, + 372, + 176, + 436 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/730a7fa04926883bee73031f7ce2fbe6220a46ce3304c157ee803fabb5848ba4.jpg", + "image_caption": [ + "Predict: Yield Confidence: $71.94\\%$" + ], + "image_footnote": [], + "bbox": [ + 187, + 372, + 269, + 436 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/91e0d0df7c914a5fb3c3be3809e487bf5fe6757ce05856e4c41b412469f40426.jpg", + "image_caption": [ + "Predict: Road Work Confidence: $75.44\\%$", + "ource: sunlight" + ], + "image_footnote": [], + "bbox": [ + 279, + 372, + 361, + 436 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/559735413c96bdb06a4ae470fe7aa606fa99ad196cbc5f647ee403d3480dbb6a.jpg", + "image_caption": [ + "Predict: Road Work Confidence: 85.57%" + ], + "image_footnote": [], + "bbox": [ + 372, + 372, + 454, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "to mimic two different scenarios. We only evaluate one geometry (i.e., rectangle) for simplicity. Specifically, we randomly select six images from the dataset and generate the corresponding adversarial examples, where the color set is fixed during the optimization for physical deployment. Note that all selected images can be correctly classified as their original label after printing out. We use eight colors: seven colors created by seven transparent color plastic sheets and one white reflected sunlight. Finally, we capture the physical adversarial examples from 2 meters away, collecting 48 images for each light source.", + "bbox": [ + 75, + 516, + 467, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6 lists the evaluation results. As we can observe, the ASR against the three models is above $80\\%$ on physical adversarial examples created by two different light sources. Interestingly, we find that physical adversarial examples created by the reflected light against RN50 can consistently mislead the different models, indicating the reflected light is well-transferable even in the physical world. Figure 6 illustrates the physical adversarial examples. Furthermore, we study the effectiveness of reflected light attacks using sunlight and a flashlight on the TSR model. Figure 7 illustrates examples generated by different geometrical shapes.", + "bbox": [ + 75, + 683, + 467, + 849 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 861, + 228, + 877 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Attack performance v.s. transparency. The trans", + "bbox": [ + 96, + 885, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/810433e5e5122343388681dc191992d58fc6b2841000094338c787e74c573a7e.jpg", + "image_caption": [ + "(a) Confidence v.s. $\\alpha$" + ], + "image_footnote": [], + "bbox": [ + 526, + 99, + 679, + 190 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1e5a7e88350ea679c4445a12b484a633b61f5f50bf81b34547bf327367d72236.jpg", + "image_caption": [ + "(b) Frequency v.s. $\\alpha$" + ], + "image_footnote": [], + "bbox": [ + 697, + 99, + 856, + 190 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2d41281fec03a6400f8c6429599e2b17ddba53d7c2c9d285debe0cd477d1bb76.jpg", + "image_caption": [ + "Figure 8. From left to right: (a) The trend of ground-truth label confidence with changing transparency, where blue points denote the successful attack. (b) The frequency of successful attacks (RFLA-Triangle) with changing of transparency.", + "Figure 9. The confidence distribution of the ground-truth label on adversarial examples. Blue points denote the attack fail color tuple, while red points denote the attack success color tuple." + ], + "image_footnote": [], + "bbox": [ + 526, + 276, + 622, + 347 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/144090df2b0ce29f84babc79eebdc0ee4bdb83e418e7a317fb9a72d23201322b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 653, + 276, + 751, + 347 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/316343832edbb4dda5f593d14746b5acead2fc955fa767d5352f5af036a2e7e6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 781, + 276, + 879, + 347 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "parency $\\alpha$ determined the cover intensity of the color. When $\\alpha$ is set to one, the pixel value of the clean image at the specific position is substituted by the pure color, while the smaller value is the lower transparency of the color. We study how transparency changes the attack performance. Specifically, we fixed the other variables except for transparency, which traveled from [0,1] with a step size of 0.01. Figure 8 (a) illustrates the evaluation results of various geometries. As expectedly, the confidence of the ground-truth label decrease with enlarges of $\\alpha$ . In contrast, the attack performance (represented in the number of blue points) rises with the increases in transparency, as more content of the clean image is covered due to deeper pure color. Moreover, we statistics the frequency of successful and failed attacks of the RFLA-Triangle on 100 test images, which is depicted in Figure 8 (b), consistent with the previous analysis.", + "bbox": [ + 496, + 416, + 890, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Attack performance v.s. color. The pattern of adversarial perturbation is crucial for a successful attack. Unlike the previous works that optimize the pixel-wise perturbation, we focus on the channel-wise perturbation (perturb a channel with one value) as we must ensure the perturbation is physically realizable by reflecting the light. Furthermore, channel-wise perturbation is visually more acceptable than pixel-wise perturbation. Specifically, we select the color tuple set in intervals of 16 pixels across the three RGB channels to investigate how color influences the attack performance. Figure 9 illustrates the evaluation results. As we can observe, the success cases almost cluster in specific areas near the searched optimal color tuple when other variables are fixed. In other words, the optimal color tuple has certain robustness to a slight change of color, which makes our attacks can undertake some distortions when applied in", + "bbox": [ + 496, + 659, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4462", + "bbox": [ + 482, + 926, + 514, + 936 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a27d43e49ab23b40cba44a91801574a91c5982885cea7ac88d226b84443619a1.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 102, + 90, + 202, + 169 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/d385084e00138a70f7fbd3d6196702a3225d7d697a048308186a71f43294a0dd.jpg", + "image_caption": [ + "(b)", + "Figure 10. From left to right: (a) Model attention on the clean image; (b) Adversarial examples; (c) Prediction confidence distribution of the clean image with the change of position, where blue points (the center of the circle) denote the successful attacks." + ], + "image_footnote": [], + "bbox": [ + 205, + 90, + 303, + 167 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/ab45607ec9343a952d4819f477e7ec9a98ae5709b4e93d6d18bdf18d5dc08378.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 312, + 95, + 424, + 166 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/cf66136a93408cc410d4fa145a5723813a967c4041660b77403edc206db4930f.jpg", + "image_caption": [ + "Figure 11. Comparison result with RFLA and random search in terms of ASR." + ], + "image_footnote": [], + "bbox": [ + 107, + 291, + 415, + 459 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "the physical world.", + "bbox": [ + 76, + 537, + 205, + 551 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Attack performance vs. position. To investigate the influence of the position of the adversarial perturbation to attack performance, we fixed the optimal variable except for position. Then, we sample the position in intervals of two steps. Furthermore, we also give the Grad-Cam for comparison. Figure 10 provides the evaluation results. As we can see, the adversarial geometry plotted around the content areas significantly drops the prediction confidence of the model on the clean image. Meanwhile, the attack success area is consistent with the model attention area, which indicates that our method can automatically locate the model attention areas to perform attacks.", + "bbox": [ + 75, + 560, + 468, + 741 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "RFLA v.s. Random search. To investigate the effectiveness of the proposed algorithm, we use the proposed method to find the optimal triangle reflected light with white sunlight. For comparison, we conduct the random search algorithm under the same settings. The evaluation result is illustrated in Figure 11. As we can see, RFLA outperforms the random baseline significantly. Specifically, RFLA achieves the average ASR of $95.13\\%$ , obtaining an improvement of $13.63\\%$ than the random search (i.e., $81.5\\%$ ), which shows the effectiveness of our method.", + "bbox": [ + 75, + 750, + 467, + 900 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 89, + 617, + 104 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we propose a novel reflected light attack to realize effective and stealthy attacks in both digital and physical worlds, which may impose potential risks to automatic driving systems. Specifically, to explore how to control the reflected light's position, geometry, and pattern, we exploit the characteristic of the circle and propose a general framework based on the circle. To create a geometry, we first generate a specific number of angles to construct the point in circumference, followed by applying point symmetry against the center of a circle to generate a new point. These obtained points fence a geometrical shape where the fill color and transparency are optimized. Finally, we apply the PSO algorithm to find the best position, geometry, fill color, and transparency. Experiment results on digital and physical attacks verify the effectiveness of the proposed method. Moreover, our method can not only use sunlight but also can use flashlights to perform physical attacks for adapting to different environments.", + "bbox": [ + 496, + 117, + 890, + 388 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Limitations. Though the reflected-light attack can perform in different environments, it is hard to remain effective in bad weather, such as fog and rain. A more penetrating light source (e.g., the traffic light and foglight) may work in such conditions.", + "bbox": [ + 496, + 391, + 890, + 465 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Potential negative societal impact and mitigation. Similar to other types of attack, the adversarial attack is inevitable to cause potential security risks, especially for those physically deployed systems. However, we aim to arouse people's attention to such related applications and then encourage people to develop defense techniques to counter the reflected-light attack. To thwart the RFLA attack proposed in this paper, one can develop multimodal-based DNN systems.", + "bbox": [ + 496, + 468, + 890, + 604 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 625, + 678, + 641 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The authors are grateful to the anonymous reviewers for their insightful comments. This work was supported by the National Natural Science Foundation of China (No.11725211 and 52005505).", + "bbox": [ + 496, + 651, + 890, + 710 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 731, + 596, + 746 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Moustafa Alzantot, Yash Sharma, Supriyo Chakraborty, Huan Zhang, Cho-Jui Hsieh, and Mani B Srivastava. Genattack: Practical black-box attacks with gradient-free optimization. In Proceedings of the Genetic and Evolutionary Computation Conference, pages 1111-1119, 2019. 1, 2", + "[2] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. Square attack: a query-efficient black-box adversarial attack via random search. In European Conference on Computer Vision, pages 484-501. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15345-15354, 2022. 2, 3, 4" + ], + "bbox": [ + 501, + 90, + 892, + 892 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "4465", + "bbox": [ + 482, + 926, + 514, + 936 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/RFLA_ A Stealthy Reflected Light Adversarial Attack in the Physical World/bdd5612c-711f-444e-bf67-fd043897ebe9_model.json b/2023/RFLA_ A Stealthy Reflected Light Adversarial Attack in the Physical World/bdd5612c-711f-444e-bf67-fd043897ebe9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8e06becfb2e1ed035e230350c202cb2987e18561 --- /dev/null +++ b/2023/RFLA_ A Stealthy Reflected Light Adversarial Attack in the Physical World/bdd5612c-711f-444e-bf67-fd043897ebe9_model.json @@ -0,0 +1,3566 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.103, + 0.13, + 0.868, + 0.152 + ], + "angle": 0, + "content": "RFLA: A Stealthy Reflected Light Adversarial Attack in the Physical World" + }, + { + "type": "text", + "bbox": [ + 0.173, + 0.193, + 0.796, + 0.213 + ], + "angle": 0, + "content": "Donghua Wang\\(^{1}\\), Wen Yao\\(^{*2}\\), Tingsong Jiang\\(^{*2}\\), Chao Li\\(^{3}\\), and Xiaojian Chen\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.214, + 0.224, + 0.753, + 0.242 + ], + "angle": 0, + "content": "1College of Computer Science and Technology, Zhejiang University" + }, + { + "type": "text", + "bbox": [ + 0.214, + 0.242, + 0.756, + 0.259 + ], + "angle": 0, + "content": "2Defense Innovation Institute, Chinese Academy of Military Science" + }, + { + "type": "text", + "bbox": [ + 0.28, + 0.26, + 0.69, + 0.277 + ], + "angle": 0, + "content": "\\(^{3}\\)School of Artificial Intelligence, Xidian University" + }, + { + "type": "text", + "bbox": [ + 0.144, + 0.278, + 0.83, + 0.296 + ], + "angle": 0, + "content": "wangdonghua@zju.edu.cn, {wendy0782,lichaoedu} @ 126.com, tingsong@pku.edu.cn," + }, + { + "type": "text", + "bbox": [ + 0.377, + 0.296, + 0.595, + 0.312 + ], + "angle": 0, + "content": "chenxiaogian@nudt.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.358, + 0.314, + 0.373 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.39, + 0.473, + 0.784 + ], + "angle": 0, + "content": "Physical adversarial attacks against deep neural networks (DNNs) have recently gained increasing attention. The current mainstream physical attacks use printed adversarial patches or camouflage to alter the appearance of the target object. However, these approaches generate conspicuous adversarial patterns that show poor stealthiness. Another physical deployable attack is the optical attack, featuring stealthiness while exhibiting weakly in the daytime with sunlight. In this paper, we propose a novel Reflected Light Attack (RFLA), featuring effective and stealthy in both the digital and physical world, which is implemented by placing the color transparent plastic sheet and a paper cut of a specific shape in front of the mirror to create different colored geometries on the target object. To achieve these goals, we devise a general framework based on the circle to model the reflected light on the target object. Specifically, we optimize a circle (composed of a coordinate and radius) to carry various geometrical shapes determined by the optimized angle. The fill color of the geometry shape and its corresponding transparency are also optimized. We extensively evaluate the effectiveness of RFLA on different datasets and models. Experiment results suggest that the proposed method achieves over \\(99\\%\\) success rate on different datasets and models in the digital world. Additionally, we verify the effectiveness of the proposed method in different physical environments by using sunlight or a flashlight." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.824, + 0.21, + 0.84 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.849, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Deep neural networks (DNNs) have increasingly been applied to daily life as their dramatic capabilities, such as" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.358, + 0.865, + 0.546 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.547, + 0.892, + 0.603 + ], + "angle": 0, + "content": "Figure 1. The reflected light is modulated by the color transparency plastic sheet and paper cut of the specific shape for better attack performance. The Reflected light source can be sunlight or a flashlight (when the sunlight is unreachable)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.892, + 0.765 + ], + "angle": 0, + "content": "automatic driving, facial payment, and computer-aided diagnosis. However, DNN-based systems have exposed security risks caused by adversarial examples [39]. Adversarial examples are crafted by carefully designed noise that is invisible to humans but can deceive the DNNs. Furthermore, recent researches [34, 21] reported that physically deployed DNN-based systems are also exposed to such security risks. Therefore, exploring various potential risks in security-sensitive systems to avoid possible loss is urgent." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.766, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Existing adversarial attack methods can be categorized into digital attacks and physical attacks. The former focus on pursuing higher attack performance on limitation conditions, such as breaking the model equipped with adversarial defense [20, 3, 7, 24], preventing the attacker from accessing the target model's information (e.g., architecture or dataset), i.e., black-box attack [1, 22, 23]. Although some researchers suggested that adversarial examples generated by the digital attack can be applied to physical attacks [21]," + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.227, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "4455" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.182 + ], + "angle": 0, + "content": "the attack performance is not satisfying. The possible reason is that the adversarial perturbation is too small to resist the environmental noise in the physical world. In contrast, physical attacks are designed to be physically deployable, where one crucial change is eliminating the perturbation's magnitude constraint." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.185, + 0.471, + 0.442 + ], + "angle": 0, + "content": "A line of physical adversarial attack methods [10, 9, 43, 44] has been proposed, which can be grouped into contact attacks and contactless attacks. The former requires the attacker to approach the target object and then modify the appearance of the target object by pasting the adversarial patch or camouflage. However, the adversarial pattern generated by these methods is conspicuous, which easily alerts humans and results in attack failure. By contrast, contactless physical attacks do not require the attacker to approach the target object while modifying the appearance of the target object by projecting or emitting light or laser on the target object to perform attacks, making it stealthy and dangerous. Optical attacks are representative contactless attacks. Although several optical attacks have been proposed [28, 32, 8, 17], they merely work in dark environments as the strong light (e.g., sunlight) environment would disturb the emitted light, limiting their usability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.47, + 0.747 + ], + "angle": 0, + "content": "In this paper, we get inspiration from the fact that the driver is easily affected by the strong reflected light, resulting in a potential car accident, and such potential risks to the automatic driving system remain unexplored. We explore the vulnerability of the DNNs toward the reflected light attack by elaborately designing the position, geometry, and color of the reflected light. Specifically, we propose a Reflected Light Attack (RFLA), which can solve the issue of the poor attack performance of existing optical attacks in strong-light environments, as our light source is sunlight. To perform physical attacks, we use a mirror to reflect the sunlight toward the target object to modify its appearance. However, the monotonous sunlight (usually white) may not obtain the desired performance. Therefore, we first use different colored transparent plastic sheets to modulate the color of the reflected light, then apply a paper cut of a specific shape to control the shape of reflected light on the target object (see Figure 1). Finally, we can create different colors and shapes of the reflected light on the target object's specific region to achieve desired attack performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.901 + ], + "angle": 0, + "content": "To achieve the above goals, we present a general framework based on the circle to model the above problem. Specifically, we first initialize a circle with a random coordinate and radius. On this circle, we create a point on the circle using sine and cosine with a randomly selected angle. Then, we customize a shape by adding a new angle, which is used to create a new point in the circumference. The other points required to create a geometry can be obtained by applying the center symmetry of the circle. Moreover, the fill color and its transparency are also considered in" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "the optimization. Finally, we adopt the particle swarm optimization (PSO) algorithm to find the optimal result. Our contributions are listed as follows." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.152, + 0.892, + 0.213 + ], + "angle": 0, + "content": "- We propose a novel reflect-light-based physical adversarial attack under the black-box scenario. It reflects the natural sunlight toward the target object using a mirror, making it controllable and stealthy." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.228, + 0.892, + 0.273 + ], + "angle": 0, + "content": "- We devise a general framework based on a circle to search for the best position, geometry, and color of the reflected light to achieve better attack performance." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.289, + 0.892, + 0.394 + ], + "angle": 0, + "content": "- We comprehensively investigate the influence of the geometry, position, and color of the reflected light on attack performance in the digital world. We conduct the physical adversarial attack by using sunlight for daytime and a flashlight for sunlight unavailable, and the experiment results verify the effectiveness of the proposed method." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.152, + 0.892, + 0.394 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.412, + 0.65, + 0.428 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.438, + 0.747, + 0.455 + ], + "angle": 0, + "content": "2.1. Digital Adversarial Attacks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Digital adversarial attacks have enjoyed decade development, which can be roughly divided into white-box attack methods and black-box attack methods. The former grants the adversary access to the target model, allowing them to develop attack algorithms with the model's gradient. The most represented gradient-based attack is the fast gradient sign method (i.e., FGSM [13]), which updates adversarial examples along the ascending direction of the gradient under one iteration step. Since then, a line of variants has been proposed, including an iterative variant of FGSM (i.e., I-FGSM [21]), random initialization has been adopted (i.e., PGD [27]), momentum term is introduced to enhance the transferability (i.e., MI-FGSM [6]), and various data augmentation technique like diversity input (i.e., DIFGSM[47]), translation-invariant (i.e., TI-FGSM [7]) and scale-invariant (i.e., SI-FGSM [24]). In contrast, black-box attacks prohibit the attacker from accessing any information about the target model but are open for queries, which makes black-box attacks more challenging. Nonetheless, many black-box attacks are proposed, such as exploiting the differential evolution algorithm [22], genetic algorithm [1], particle swarm optimization [51], and so on [2]. In addition, several works suggested that adversarial perturbation's position [45], pattern [49], and geometry [4] on the clean image significantly impact attack performance. However, current works only investigate one or two of these factors. In this work, we systematically investigate the influence of the adversarial perturbation's position, geometry, and pattern on attack performance under the black-box scenario." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "4456" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.336, + 0.107 + ], + "angle": 0, + "content": "2.2. Physical Adversarial Attacks" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.116, + 0.474, + 0.645 + ], + "angle": 0, + "content": "According to whether it requires the attacker to access the target object in the real attack scenario, physical adversarial attacks can be grouped into contact and contactless physical attacks. Contact attacks can be further categorized into patch-based attacks and camouflage-based attacks. Patch-based attacks mainly focus on optimizing an adversarial image patch, which is then printed out and stuck on the target object or held by the attacker to deceive the target DNNs. Patch-based attacks are usually applied in attacking the facial recognition model [34, 35, 45, 46], pedestrian detection model [41, 40, 16, 5], and traffic sign recognition model [10, 25, 51]. Camouflage-based attacks [44, 43, 9] slightly differ from patch-based, as they concentrate on modifying the appearance of the target object via UV Texture. Thus, camouflage-based attacks show better attack performance in the multi-view scenario by painting the full coverage camouflage over the appearance of the target object. However, although contact physical attacks achieve good physical attack performance, the pattern of the adversarial patch/camouflage is conspicuous, which leads to poor stealthiness. In contrast, contactless physical attacks are performed by projecting/emitting light [12, 17], or a laser beam [8], usually called optical attacks. However, existing optical attacks work in dark environments [8, 17] while performing poorly in strong-light environments. The reason is that the light beam emitted by a light source is easily affected by environmental light, resulting in attacking failure. Recently, Zhang et al. [51] proposed a shadow-based attack, but it can only create a triangle shape with one monotonous color (e.g., gray). In this work, we solve the situation of poor attacks in strong-light (i.e., sunlight) environments to perform attacks since we directly use sunlight to perform attacks. Moreover, we create reflected light with different geometrical shapes and colors using the color transparency plastic sheet and paper cut." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.663, + 0.214, + 0.68 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.689, + 0.262, + 0.704 + ], + "angle": 0, + "content": "3.1. Problem Statement" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.713, + 0.47, + 0.866 + ], + "angle": 0, + "content": "Let \\(\\mathcal{X}\\) denote the data distribution, and the corresponding ground truth label is \\(\\mathcal{V}\\). Given an image \\(x\\in \\mathcal{X}\\) that has the resolution of \\(x\\in \\mathbb{R}^{C\\times H\\times W}\\), a well trained neural network \\(f\\) output \\(\\hat{y} = f(x)\\) and \\(\\hat{y} = y\\), where the \\(\\hat{y}\\) is prediction of the \\(f\\) and \\(y\\) is the ground truth label, \\(\\hat{y},y\\in \\mathbb{R}^{|\\mathcal{V}|}\\). Adversarial attack aims to generate adversarial examples \\(x_{adv}\\) to make the \\(f\\) output the wrong prediction by adding small perturbation \\(\\delta\\) into the clean image \\(x\\), i.e., \\(x_{adv} = x + \\delta\\). Mathematically, the \\(\\delta\\) is obtained by solving the following problem" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.885, + 0.469, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\min \\delta \\quad s. t. f (x + \\delta) \\neq f (x), | | \\delta | | _ {p} \\leq \\epsilon , \\tag {1}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.09, + 0.635, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.187, + 0.616, + 0.197 + ], + "angle": 0, + "content": "(a) Base circle" + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.198, + 0.635, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.54, + 0.294, + 0.613, + 0.306 + ], + "angle": 0, + "content": "(d) Rectangle" + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.09, + 0.755, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.675, + 0.187, + 0.72, + 0.198 + ], + "angle": 0, + "content": "(b) Line" + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.198, + 0.754, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.663, + 0.295, + 0.731, + 0.306 + ], + "angle": 0, + "content": "(e) Pentagon" + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.089, + 0.875, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.785, + 0.186, + 0.849, + 0.198 + ], + "angle": 0, + "content": "(c) Triangle" + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.198, + 0.874, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.785, + 0.295, + 0.849, + 0.305 + ], + "angle": 0, + "content": "(f) Hexagon" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.305, + 0.892, + 0.388 + ], + "angle": 0, + "content": "Figure 2. Visualization explanation of the circle modeling. Different geometries are constructed by adjusting the angle. For example, the triangle is created by adding a new angle \\(\\angle a_{2}\\) on the base circle (a), where three vertices are composed of two points \\((p_{1}\\) and \\(p_2)\\) determined by two angles \\((\\angle a_{1}\\) and \\(\\angle a_{2})\\) and one symmetry point \\((p_1^{\\prime})\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.413, + 0.892, + 0.443 + ], + "angle": 0, + "content": "where \\(||\\cdot ||_p\\) is the \\(L_{p}\\) norm, which bound the maximum allowable magnitude of \\(\\delta\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.444, + 0.893, + 0.624 + ], + "angle": 0, + "content": "The optimization objective of Equation 1 is the general formal for constructing the full-pixel-wise perturbation, which is unsuitable for physical adversarial attacks as the background of the physical world is unchangeable. Therefore, we reformulate Equation 1 to optimize the physical deployable perturbation by modifying the construction of \\( x_{adv} \\). Specifically, we define an apply function \\( \\mathcal{A}(x,p,l,M) \\) to construct adversarial examples \\( x_{adv} \\), which indicates that apply the perturbation \\( p \\) at the location \\( l \\) of the clean image \\( x \\), where \\( M \\) is the binary mask to indicate whether the position is allowed to modify (one denote allow while zero not)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.892, + 0.732 + ], + "angle": 0, + "content": "In this work, we aim to reflect the sunlight toward the target object to perform stealthy physical adversarial attacks, where the representation (e.g., geometry, fill color and position) of reflected light on the target object is the key to a successful attack. Therefore, the parameters of \\( \\mathcal{A}(x,p,l,M) \\) comprise geometry and fill color of \\( p \\), and the location of \\( l \\) are variables to be optimized." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.741, + 0.71, + 0.758 + ], + "angle": 0, + "content": "3.2. Reflected Light Attack" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Sunlight is the most common and indispensable natural phenomenon in daily life. People can reflect the sunlight toward the wall to construct various shapes by using different shapes of mirrors. However, the danger of such reflected light against DNN-based systems has been ignored, which may pose a potential risk as it featured extremely stealthy and controllable. In this work, we aim to modulate the reflected light to perform adversarial attacks in the digital and physical world." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.926, + 0.516, + 0.938 + ], + "angle": 0, + "content": "4457" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "Previous work [51] modeled the triangle shadow by optimizing three points, which requires complex constraints on points to construct a rational geometry shape if they extend to other geometric shapes. To address this issue, we exploit the characteristic of the circle and propose a novel general framework based on the circle, which can generate various shapes by adjusting the number of angles (see Figure 2). The details process is described as follows." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.224, + 0.468, + 0.242 + ], + "angle": 0, + "content": "- Select a radius \\( r \\) from the region of \\( [0, \\min(H, W)/2] \\)." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.249, + 0.47, + 0.282 + ], + "angle": 0, + "content": "- Spawn a center \\( o(x, y) \\) of the circle from the region of \\( [r, H - r] \\) and \\( [r, W - r] \\)." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.29, + 0.469, + 0.32 + ], + "angle": 0, + "content": "- Randomly select an angle \\( a_1 \\) and spawn a point \\( p_1(x_1, y_1) \\) on circle by the follow equation" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.224, + 0.47, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.33, + 0.469, + 0.365 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} x _ {1} = x + r \\times \\sin \\left(\\frac {a _ {1} \\times \\pi}{1 8 0}\\right), \\\\ y _ {1} = y + r \\times \\cos \\left(\\frac {a _ {1} \\times \\pi}{1 8 0}\\right), \\end{array} \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.378, + 0.469, + 0.425 + ], + "angle": 0, + "content": "- Calculate the symmetry point \\( p_1'(x_1', y_1') \\) of the point \\( p_1 \\) against the center of the circle by \\( x_1' = 2 \\times x - x_1 \\) and \\( y_1' = 2 \\times y - y_1 \\)." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.434, + 0.469, + 0.479 + ], + "angle": 0, + "content": "- Randomly select a color tuple (red, green, blue) from the region of [0, 255], and the transparency \\(\\alpha\\) from [0, 1]." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.378, + 0.469, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.491, + 0.469, + 0.567 + ], + "angle": 0, + "content": "The above process can plot a line on the clean image. To construct varying geometries like a triangle, rectangle, pentagon, or hexagon, one can repeat the third and fourth steps to create a new point by adding a new angle. Algorithm A1 in describes the detailed particle initialization process." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.576, + 0.218, + 0.592 + ], + "angle": 0, + "content": "3.3. Optimization" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.599, + 0.469, + 0.795 + ], + "angle": 0, + "content": "As aforementioned, we have eight base variables that need to be optimized, expressed as eight-tuples \\((x,y,r,\\alpha ,red,green,\\text{blue},a_{1})\\), which can be used to plot a line on the clean image. To generate various geometries, more additional variables are required to generate various geometries, which depend on the shape to be generated. For example, there is one extra variable for the triangle and rectangle; two extra for the pentagon and hexagon. Note that the proposed method is easily extended to more complex geometry. Recall that our goal is to deceive the DNNs by plotting geometry on the clean image. Thus, we adopt the particle swarm optimization algorithm (PSO) to seek the best geometry, fill color, and position." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.903 + ], + "angle": 0, + "content": "In PSO, we represent the optimization variables tuple as a particle (i.e., the solution vector \\( q \\)). The update direction of the particle is determined by a velocity vector \\( v \\). Every particle stands for a potential solution, which requires to be optimized. We treat the personal historical best solution of a particle as \\( q_{best} \\), and the global best solution of a particle as \\( q_{gbest} \\). Moreover, for every solution, we fix the circle's" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.088, + 0.695, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.609, + 0.202, + 0.627, + 0.213 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.089, + 0.857, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.767, + 0.216, + 0.785, + 0.226 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.226, + 0.892, + 0.253 + ], + "angle": 0, + "content": "Figure 3. The color discrepancy between the color transparency plastic sheet (a) and its reflected light(b)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.278, + 0.892, + 0.367 + ], + "angle": 0, + "content": "position and merely optimize the geometry, fill color, and transparency. Therefore, to represent the best solution of a circle, we devised an additional metric \\( q_{sgbest} \\), which is the sum of the fitness score of all geometrical shapes in a specific circle. Finally, the update criterion is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.548, + 0.391, + 0.891, + 0.446 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} v _ {i} (t) = W v _ {i} (t - 1) + C _ {1} \\kappa_ {1} \\left(q _ {p b e s t} - q _ {i} (t)\\right) \\\\ + C _ {2} \\kappa_ {2} \\left(q _ {\\text {g b e s t}} - q _ {i} (t)\\right) \\tag {3} \\\\ + C _ {3} \\kappa_ {3} \\left(q _ {s g b e s t} - q _ {i} (t)\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.462, + 0.891, + 0.478 + ], + "angle": 0, + "content": "\\[\nq _ {i} (t) = q _ {i} (t - 1) + v _ {i} (t), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.484, + 0.892, + 0.573 + ], + "angle": 0, + "content": "where \\( W \\) is the inertia weight used to control the impact of the previous velocity on the current velocity. \\( C_1, C_2 \\), and \\( C_3 \\) indicate the learning factors, which balance the impact of different parts empirical on current velocity. \\( \\kappa_1, \\kappa_2 \\), and \\( \\kappa_3 \\) are random values uniformly sampled from [0, 1], which are used to increase the randomness of the search." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.575, + 0.892, + 0.635 + ], + "angle": 0, + "content": "Apart from the solution and velocity of a particle, the fitness function is crucial for optimizing in PSO algorithm. In this work, we adopt the following fitness function to evaluate each particle." + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.65, + 0.891, + 0.667 + ], + "angle": 0, + "content": "\\[\n\\min F (q) = \\Pr_ {\\hat {y}} (\\mathcal {A} (x, q, M)), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.892, + 0.824 + ], + "angle": 0, + "content": "where \\(\\mathcal{A}(x,q,M)\\) denotes an applied function that paints the geometry with color (red,green,blue) and transparency \\(\\alpha\\) at the coordinate of \\(o\\) on the clean image \\(x\\), where \\(M\\) is a binary mask indicates the allowed modification area. \\(\\operatorname{Pr}_{\\hat{y}}(\\cdot)\\) is the predicted label \\(\\hat{y}\\) probability of the target model \\(f\\) on the input. By minimizing the \\(F(q)\\), the confidence of prediction label \\(\\hat{y}\\) gradually decreases. We stop the search until it reaches the maximum iteration or finds the adversarial example. Algorithm 1 describes the optimization process." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.747, + 0.849 + ], + "angle": 0, + "content": "3.4. Physical Deployable Attack" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In digital worlds, we can construct \\(256^{3}\\) color tuples by blending different RGB values, which is impractical in the physical world as the limitation of the device and material." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "4458" + } + ], + [ + { + "type": "algorithm", + "bbox": [ + 0.078, + 0.09, + 0.47, + 0.353 + ], + "angle": 0, + "content": "Algorithm 1 Reflected Light Adversarial Attack (RFLA) \nInput: input image \\( x \\), target model \\( f \\), max iteration MaxIter \nOutput: Best solution \\( q^* \\) \n1: \\( q \\gets \\text{Initialization}() \\) ▷ Algorithm A1 \n2: \\( x_{adv} \\gets \\text{GenSample}(q) \\) ▷ Algorithm A2 \n3: if \\( f(x_{adv}) \\neq f(x) \\) then \n4: return \\( q^* \\) \n5: end if \n6: for \\( itr = i, \\dots, \\text{MaxIter} \\) do \n7: Update velocity vector \\( v \\) by Equation 3 \n8: Update position vector \\( q \\) by Equation 4 \n9: \\( x_{adv} \\gets \\text{GenSample}(q) \\) ▷ Algorithm A2 \n10: if \\( f(x_{adv}) \\neq f(x) \\) then \n11: return \\( q^* \\) \n12: end if \n13: end for" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.383, + 0.473, + 0.537 + ], + "angle": 0, + "content": "Therefore, we constrain the search space of the color to ensure physically deployable. Specifically, we use seven color transparency plastic sheets to change the color of the reflected light. However, we find discrepancies exist between the color transparency plastic sheet and its reflected light (see Figure 3), which may lead to attack failure. To decrease such discrepancy, we collect the light color reflected by the color transparency plastic sheet and adopt it as the searched color. In such a way, we can decrease color discrepancies when performing physical attacks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.551, + 0.21, + 0.568 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.577, + 0.176, + 0.593 + ], + "angle": 0, + "content": "4.1. Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.601, + 0.47, + 0.707 + ], + "angle": 0, + "content": "Datasets: To investigate the effectiveness of the proposed method, we conduct the digital attack on the ImageNet-compatible dataset provided by the NIPS 2017 adversarial competition1, which includes 1000 images. Moreover, two commonly used traffic sign datasets: GTSRB [37] and LISA [29], are also considered to investigate the extensibility of the proposed method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.708, + 0.471, + 0.875 + ], + "angle": 0, + "content": "Target models: We conduct the proposed method on two tasks: image classification and traffic sign recognition. As for image classification, we select six ImageNet pre-trained networks: ResNet50 (RN50) [15], VGG16 [36], DenseNet121 (DN121) [18], ResNeXt50 (RNX50) [48], WiderResNet50 (WRN50) [50] and SqueezeNet (SN) [19], which are all provided by PyTorch [30]. As for traffic sign recognition, we follow the setting reported in previous works [10, 25] to train GTSRB CNN and LISA CNN on GTSRB and LISA dataset, which obtains the accuracy of \\(95.06\\%\\) and \\(100\\%\\) on the test set, respectively." + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.088, + 0.895, + 0.129 + ], + "angle": 0, + "content": "Table 1. Comparison results with the line-based method in terms of ASR (%) on ImageNet-compatible dataset. The best results are highlighted with bold." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.129, + 0.9, + 0.178 + ], + "angle": 0, + "content": "
RN50VGG16DN121RNX50WRN50SN
Bezier [11]72.477.774.172.769.689.3
RFLA-Line76.977.476.575.771.789.2
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.202, + 0.892, + 0.261 + ], + "angle": 0, + "content": "Evaluation metrics: We adopt the attack success rate (ASR) as the evaluation metric, defined as the ratio of the number of the network's prediction flipped caused by adversarial examples to the total test dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.262, + 0.893, + 0.429 + ], + "angle": 0, + "content": "Implementation details: We adopt the OpenCV-Python package to plot different geometries in the clean image. For the settings of parameters of PSO, we set the max iteration number to 200, \\( C_1 \\), \\( C_2 \\), and \\( C_3 \\) set to 2.05, \\( W \\) is set to 0.7298, the particle size and the geometry number at a circle are set to 50. The particle and velocity bound are provided in Appendix A (The upper bound of the transparency \\( \\alpha \\) is set to 0.7 to evade occluding the clean image.). Unless otherwise specified, the mask \\( M \\) is set to all one value matrix in our experiments. All experiments were conducted on an NVIDIA RTX 3090ti 24GB GPU\\(^2\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.437, + 0.747, + 0.453 + ], + "angle": 0, + "content": "4.2. Digital Adversarial Attacks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.895, + 0.689 + ], + "angle": 0, + "content": "In this section, we quantitatively and qualitatively evaluate the effectiveness of the proposed method in the digital world. For comparison, we adopt two patch-based attack methods: TPA [49] and DAPatch [4]; one line-based attack method Bezier [11]. TPA [49] utilized the feature texture image extracted from DNNs as the adversarial patch, which is pasted on the clean image, where the paste position is optimized by reinforcement learning. DAPatch [4] optimized the pattern and mask simultaneously, which can create a deformable shape adversarial patch. In contrast, Bezier [11] generated adversarial examples by scratching theBezier curve on the clean image, where theBezier curve depends on three points optimized by the optimizer (e.g., PSO). We reproduce the above three methods on the ImageNet-compatible dataset using the default settings." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.705, + 0.704, + 0.72 + ], + "angle": 0, + "content": "4.2.1 Quantitatively Result" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.728, + 0.894, + 0.88 + ], + "angle": 0, + "content": "Table 1 reported the comparison results of the proposed RFLA-Line with the Bezier method. As we can observe, the proposed method outperforms the Bezier method on four of six models and obtains an improvement by \\(1.93\\%\\) in average ASR, indicating the proposed method's effectiveness. Additionally, we can get an \\(8.95\\%\\) improvement by widening the line thickness two times. Although the length of the Bezier curve may be shorter than ours, the discrepancy is trivial as modifications caused by the line is neglectable. Moreover, our method can be extended to more geometries." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.466, + 0.901 + ], + "angle": 0, + "content": "1https://www.kaggle.com/c/nips-2017-non-targeted-adversarial-attack" + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.887, + 0.726, + 0.901 + ], + "angle": 0, + "content": "\\(^{2}\\)Code will be released after published." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.927, + 0.516, + 0.938 + ], + "angle": 0, + "content": "4459" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.159, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.157, + 0.14, + 0.167 + ], + "angle": 0, + "content": "balloon" + }, + { + "type": "image", + "bbox": [ + 0.175, + 0.091, + 0.249, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.185, + 0.157, + 0.231, + 0.167 + ], + "angle": 0, + "content": 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"cheetah" + }, + { + "type": "image_caption", + "bbox": [ + 0.173, + 0.38, + 0.796, + 0.395 + ], + "angle": 0, + "content": "Figure 4. Visualization comparison of adversarial examples generated by different methods on ResNet50." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.415, + 0.471, + 0.456 + ], + "angle": 0, + "content": "Table 2. Comparison results with patch-based methods in terms of ASR (\\%) on ImageNet-compatible dataset. The best results are highlighted with bold." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.457, + 0.473, + 0.556 + ], + "angle": 0, + "content": "
RN50VGG16DN121RNX50WRN50SN
TPA [49]66.1364024.723.444.6
DAPatch [4]74.371.679.373.776.756
RFLA-Triangle98.197.897.297.298.199.5
RFLA-Rectangle99.399.199.298.999.199.8
RFLA-Pentagon99.699.199.299.299.499.8
RFLA-Hexagon99.599.599.599.599.499.8
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Then, the comparison results of patch-based methods are listed in Table 2. We conclude that the proposed geometry variants of RFLA outperform the existing method significantly. Specifically, the average ASR of the RFLA-triangle, RFLA-rectangle, RFLA-pentagon, and RFLA-hexagon are \\(97.98\\%\\), \\(99.23\\%\\), \\(99.38\\%\\), and \\(99.53\\%\\), obtaining the maximum improvement against TPA and DAPatch by \\(60.32\\%\\) and \\(27.52\\%\\). We observe that the attack performance of comparison methods fails to achieve such results reported in their paper. The possible reason is that TPA may require two or more patches occluding \\(8\\%\\) of the image to achieve higher attack performance. As for DAPatch [4], the position of the adversarial patch is ignored, which makes them fail to seek the model-decision-sensitive position. In contrast, our method simultaneously optimizes the position, geometry, and adversarial pattern, resulting in better performance. Moreover, the ASR gains with increasing vertex of geometry shape are attenuations, such as \\(20.08\\%\\) gains from Line (two vertices) to Triangle(three vertices), while only \\(0.15\\%\\) from Rectangle to Pentagon, which may be attributed to the improvement room of ASR is limited." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.415, + 0.892, + 0.484 + ], + "angle": 0, + "content": "Table 3. Comparison results of transferability of adversarial examples generated by RNX50 in terms of ASR \\((\\%)\\) on ImageNet-compatible dataset. Item indicates the white-box attack result, while the others are black-box results. The best results are highlighted with bold." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.484, + 0.896, + 0.613 + ], + "angle": 0, + "content": "
methodRN50VGG16DN121RNX50WRN50SN
Bezier [11]18.116.816.472.712.426.6
RFLA-LINE17.615.517.575.71427.1
TPA [49]28.93626.724.720.445.4
DAPatch [4]32.352.542.373.726.428.8
RFLA-Triangle37.834.933.197.233.750
RFLA-Rectangle47.643.244.398.945.5259.9
RFLA-Pentagon47.54546.499.245.261.9
RFLA-Hexagon50.84447.699.54763.9
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.892, + 0.807 + ], + "angle": 0, + "content": "In addition, we compare the transferability of the proposed method with the comparison methods. Specifically, we use adversarial examples generated on RNX50 to attack other models. Evaluation results are reported in Table 3. As we can observe, RFLA outperforms the comparison methods in most cases, and the magnitude of fall behind cases is small. Concretely, we obtain the maximum average improvement of ASR of Bezier, TPA, and DAPatch are \\(0.28\\%\\) (RFLA-Line), \\(19.18\\%\\), and \\(14.2\\%\\), indicating the effectiveness of the proposed method. In addition, we provide other transferability comparison results in Appendix B1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.83, + 0.694, + 0.846 + ], + "angle": 0, + "content": "4.2.2 Qualitatively Result" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We provide the visualization result of adversarial examples generated by different methods in Figure 4. As we can observe, on the one hand, the Bezier and RFLA-Line obtain" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.927, + 0.516, + 0.938 + ], + "angle": 0, + "content": "4460" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.455, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.197, + 0.468, + 0.224 + ], + "angle": 0, + "content": "Figure 5. Model attention analysis of adversarial examples generated by RFLA on ResNet50." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.248, + 0.468, + 0.444 + ], + "angle": 0, + "content": "the most natural visuality quality, and the scratched line is hardly observed at a glance. Meanwhile, RFLA-Line fools the DNNs in all displayed cases, but Bezier only has two success cases. On the other hand, TPA and DAPatch failed in all displayed cases. Such qualitative results can be used to explain their inferior attack performance. The adversarial patch generated by their method covers the noncontent areas, which may be insignificant to the model decision. Although the proposed method affects more image content than TPA and DAPatch, the covered contents are recognizable. In other words, our method does not modify the semantics of the image. We provide more visualization results of adversarial examples in Appendix B1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.444, + 0.468, + 0.55 + ], + "angle": 0, + "content": "In addition, we use the Grad-CAM [33] to investigate why the proposed method can work. Figure 5 illustrates the model attention visualization results. As we can observe, the painted geometry suppresses the model's attention areas, which makes the model output the wrong results. We also provide the visualization analysis result of comparison methods on model attention in Appendix B2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.559, + 0.419, + 0.575 + ], + "angle": 0, + "content": "4.3. Extend to Traffic Sign Recognition Task" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.582, + 0.468, + 0.793 + ], + "angle": 0, + "content": "To further investigate the effectiveness of the proposed method, we use RFLA to attack the traffic sign recognition (TSR) model. Specifically, we collect 200 stop sign images from the GTSRB and LISA test set for evaluation. To avoid the geometry being out of the scope of the stop sign, we use a mask to indicate the allowable modification positions. We get the mask by averaging 200 test images and binary it. Table 4 lists the digital adversarial performance. As we can observe, the proposed method obtains superior attack performances on two TSR models, especially for GTSRB CNN (100% ASR). In addition, as for LISA-CNN, the attack performance increase with the geometries. One possible reason is that the affected area of the clean image is larger with the change of geometries under a similar circle." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.268, + 0.817 + ], + "angle": 0, + "content": "4.4. Adversarial Defense" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.468, + 0.9 + ], + "angle": 0, + "content": "In this part, we investigate the attack performance under the following adversarial defense methods: preprocess-based method and adversarial trained model. The former includes Total Variance Minimization (TVM) [14], standard Pixel Deflection (Pixel) [31], JPEG compression with qual" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.088, + 0.892, + 0.113 + ], + "angle": 0, + "content": "Table 4. Quantitative results of RELA on TSR model in terms of ASR \\((\\%)\\)" + }, + { + "type": "table", + "bbox": [ + 0.524, + 0.114, + 0.867, + 0.193 + ], + "angle": 0, + "content": "
LISA-CNNGTSRB-CNN
RFLA-Triangle68.5100
RFLA-Rectangle92.5100
RFLA-Pentagon93.5100
RFLA-Hexagon97.5100
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.204, + 0.89, + 0.231 + ], + "angle": 0, + "content": "Table 5. Comparison results of attack methods under different defense strategies in terms of ASR \\((\\%)\\)" + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.232, + 0.877, + 0.343 + ], + "angle": 0, + "content": "
methodTVMPixelJPEGBlurAdvIncV3EnvAdvV2
Bezier [11]74.45439.851.737.524.2
RFLA-LINE73.750.238.349.337.123.3
TPA [49]76.537.241.549.853.744.6
DAPatch [4]79.328.23242.859.547.4
RFLA-Triangle84.474.564.47557.345.1
RFLA-Rectangle8880.370.580.167.857.6
RFLA-Pentagon84.545.155.564.471.864.3
RFLA-Hexagon88.881.673.684.668.962.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.354, + 0.89, + 0.38 + ], + "angle": 0, + "content": "Table 6. Physical adversarial attacks under different light sources on different models in terms of ASR (\\%)." + }, + { + "type": "table", + "bbox": [ + 0.552, + 0.38, + 0.836, + 0.429 + ], + "angle": 0, + "content": "
RN50VGG16DN121
Sunlight81.2581.2581.25
Flashlight87.587.587.5
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.453, + 0.892, + 0.74 + ], + "angle": 0, + "content": "ity factor 75 [26], and Gaussian blur with the kernel size 5, while the latter includes the adversarial trained model consisting of Adv-Inc-v3 (AdvIncV3) [38] and Ens-Adv-IncRes-v2 (EnvAdvV2) \\([42]^3\\). Table 5 reports the attack performance after the adversarial defense. As we can observe, on the one hand, the proposed method falls behind Bezier under defense strategy by \\(1.58\\%\\) in terms of average ASR, which may attribute to the curve generated by Bezier exhibiting more robustness to the defense strategy than the line. On the other hand, other geometries generated by the proposed method significantly outperform the comparison method under the defense strategy. Specifically, the proposed method obtains the average ASR of RFLA-Triangle, RFLA-Rectangle, RFLA-Pentagon, and RFLA-Hexagon under defense is \\(63.37\\%\\), \\(70.77\\%\\), \\(63.11\\%\\), and \\(73.43\\%\\). In contrast, TPA and DAPatch are \\(49.24\\%\\) and \\(46.77\\%\\). Such a result suggests that our method is more robust than the comparison method under different defense strategies." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.75, + 0.757, + 0.765 + ], + "angle": 0, + "content": "4.5. Physical Adversarial Attacks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.773, + 0.891, + 0.878 + ], + "angle": 0, + "content": "Unlike the previous physical attacks that generate the adversarial pattern for the physically captured images, we generate the adversarial pattern (i.e., colored geometries) for digital images (the target model is RN50) and then reflect the light according to the optimized variables toward the corresponding printed images. In physical adversarial attacks, we use sunlight and a flashlight as the light source" + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.887, + 0.805, + 0.9 + ], + "angle": 0, + "content": "\\(^{3}\\)https://github.com/rwrightman/pytorch-image-models" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.927, + 0.514, + 0.938 + ], + "angle": 0, + "content": "4461" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.093, + 0.212, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.106, + 0.192, + 0.198, + 0.202 + ], + "angle": 0, + "content": "Camera \\(\\rightarrow\\) Rubber" + }, + { + "type": "image", + "bbox": [ + 0.217, + 0.094, + 0.338, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.234, + 0.192, + 0.324, + 0.203 + ], + "angle": 0, + "content": "Camera \\(\\rightarrow\\) Laptop" + }, + { + "type": "image", + "bbox": [ + 0.343, + 0.094, + 0.461, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.346, + 0.192, + 0.451, + 0.202 + ], + "angle": 0, + "content": "Camera \\(\\rightarrow\\) Television" + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.204, + 0.211, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.301, + 0.191, + 0.311 + ], + "angle": 0, + "content": "Arch bridge \\(\\rightarrow\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.313, + 0.191, + 0.323 + ], + "angle": 0, + "content": "Window screen" + }, + { + "type": "image", + "bbox": [ + 0.215, + 0.211, + 0.334, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.215, + 0.302, + 0.332, + 0.313 + ], + "angle": 0, + "content": "Arch bridge \\(\\rightarrow\\) Screen" + }, + { + "type": "image", + "bbox": [ + 0.34, + 0.204, + 0.461, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.347, + 0.301, + 0.455, + 0.313 + ], + "angle": 0, + "content": "Arch bridge \\(\\rightarrow\\) Screen" + }, + { + "type": "image_caption", + "bbox": [ + 0.152, + 0.33, + 0.393, + 0.344 + ], + "angle": 0, + "content": "Figure 6. Physical adversarial examples." + }, + { + "type": "image_caption", + "bbox": [ + 0.142, + 0.363, + 0.221, + 0.372 + ], + "angle": 0, + "content": "Light source: flashlight" + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.373, + 0.177, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.44, + 0.178, + 0.453 + ], + "angle": 0, + "content": "Predict: Speed Limited 30 \nConfidence: \\(99.99\\%\\)" + }, + { + "type": "image", + "bbox": [ + 0.188, + 0.373, + 0.271, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.195, + 0.44, + 0.267, + 0.453 + ], + "angle": 0, + "content": "Predict: Yield Confidence: \\(71.94\\%\\)" + }, + { + "type": "image", + "bbox": [ + 0.28, + 0.373, + 0.362, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.288, + 0.44, + 0.358, + 0.453 + ], + "angle": 0, + "content": "Predict: Road Work Confidence: \\(75.44\\%\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.364, + 0.4, + 0.372 + ], + "angle": 0, + "content": "ource: sunlight" + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.373, + 0.455, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.38, + 0.44, + 0.448, + 0.454 + ], + "angle": 0, + "content": "Predict: Road Work Confidence: 85.57%" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.462, + 0.468, + 0.49 + ], + "angle": 0, + "content": "Figure 7. Examples of the \"stop\" sign with the reflected light and its prediction result on GTSRB CNN." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.468, + 0.682 + ], + "angle": 0, + "content": "to mimic two different scenarios. We only evaluate one geometry (i.e., rectangle) for simplicity. Specifically, we randomly select six images from the dataset and generate the corresponding adversarial examples, where the color set is fixed during the optimization for physical deployment. Note that all selected images can be correctly classified as their original label after printing out. We use eight colors: seven colors created by seven transparent color plastic sheets and one white reflected sunlight. Finally, we capture the physical adversarial examples from 2 meters away, collecting 48 images for each light source." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.684, + 0.468, + 0.851 + ], + "angle": 0, + "content": "Table 6 lists the evaluation results. As we can observe, the ASR against the three models is above \\(80\\%\\) on physical adversarial examples created by two different light sources. Interestingly, we find that physical adversarial examples created by the reflected light against RN50 can consistently mislead the different models, indicating the reflected light is well-transferable even in the physical world. Figure 6 illustrates the physical adversarial examples. Furthermore, we study the effectiveness of reflected light attacks using sunlight and a flashlight on the TSR model. Figure 7 illustrates examples generated by different geometrical shapes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.862, + 0.229, + 0.878 + ], + "angle": 0, + "content": "4.6. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Attack performance v.s. transparency. The trans" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.101, + 0.68, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.551, + 0.197, + 0.664, + 0.208 + ], + "angle": 0, + "content": "(a) Confidence v.s. \\(\\alpha\\)" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.101, + 0.857, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.73, + 0.197, + 0.84, + 0.208 + ], + "angle": 0, + "content": "(b) Frequency v.s. \\(\\alpha\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.208, + 0.892, + 0.263 + ], + "angle": 0, + "content": "Figure 8. From left to right: (a) The trend of ground-truth label confidence with changing transparency, where blue points denote the successful attack. (b) The frequency of successful attacks (RFLA-Triangle) with changing of transparency." + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.277, + 0.624, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.654, + 0.277, + 0.753, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.782, + 0.277, + 0.88, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.349, + 0.892, + 0.39 + ], + "angle": 0, + "content": "Figure 9. The confidence distribution of the ground-truth label on adversarial examples. Blue points denote the attack fail color tuple, while red points denote the attack success color tuple." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.417, + 0.892, + 0.659 + ], + "angle": 0, + "content": "parency \\(\\alpha\\) determined the cover intensity of the color. When \\(\\alpha\\) is set to one, the pixel value of the clean image at the specific position is substituted by the pure color, while the smaller value is the lower transparency of the color. We study how transparency changes the attack performance. Specifically, we fixed the other variables except for transparency, which traveled from [0,1] with a step size of 0.01. Figure 8 (a) illustrates the evaluation results of various geometries. As expectedly, the confidence of the ground-truth label decrease with enlarges of \\(\\alpha\\). In contrast, the attack performance (represented in the number of blue points) rises with the increases in transparency, as more content of the clean image is covered due to deeper pure color. Moreover, we statistics the frequency of successful and failed attacks of the RFLA-Triangle on 100 test images, which is depicted in Figure 8 (b), consistent with the previous analysis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Attack performance v.s. color. The pattern of adversarial perturbation is crucial for a successful attack. Unlike the previous works that optimize the pixel-wise perturbation, we focus on the channel-wise perturbation (perturb a channel with one value) as we must ensure the perturbation is physically realizable by reflecting the light. Furthermore, channel-wise perturbation is visually more acceptable than pixel-wise perturbation. Specifically, we select the color tuple set in intervals of 16 pixels across the three RGB channels to investigate how color influences the attack performance. Figure 9 illustrates the evaluation results. As we can observe, the success cases almost cluster in specific areas near the searched optimal color tuple when other variables are fixed. In other words, the optimal color tuple has certain robustness to a slight change of color, which makes our attacks can undertake some distortions when applied in" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.927, + 0.516, + 0.938 + ], + "angle": 0, + "content": "4462" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.091, + 0.203, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.146, + 0.173, + 0.163, + 0.184 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.206, + 0.091, + 0.305, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.245, + 0.173, + 0.264, + 0.184 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.313, + 0.096, + 0.426, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.366, + 0.175, + 0.383, + 0.185 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.185, + 0.47, + 0.24 + ], + "angle": 0, + "content": "Figure 10. From left to right: (a) Model attention on the clean image; (b) Adversarial examples; (c) Prediction confidence distribution of the clean image with the change of position, where blue points (the center of the circle) denote the successful attacks." + }, + { + "type": "image", + "bbox": [ + 0.108, + 0.292, + 0.416, + 0.46 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.47, + 0.468, + 0.497 + ], + "angle": 0, + "content": "Figure 11. Comparison result with RFLA and random search in terms of ASR." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.538, + 0.206, + 0.552 + ], + "angle": 0, + "content": "the physical world." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.47, + 0.742 + ], + "angle": 0, + "content": "Attack performance vs. position. To investigate the influence of the position of the adversarial perturbation to attack performance, we fixed the optimal variable except for position. Then, we sample the position in intervals of two steps. Furthermore, we also give the Grad-Cam for comparison. Figure 10 provides the evaluation results. As we can see, the adversarial geometry plotted around the content areas significantly drops the prediction confidence of the model on the clean image. Meanwhile, the attack success area is consistent with the model attention area, which indicates that our method can automatically locate the model attention areas to perform attacks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.468, + 0.901 + ], + "angle": 0, + "content": "RFLA v.s. Random search. To investigate the effectiveness of the proposed algorithm, we use the proposed method to find the optimal triangle reflected light with white sunlight. For comparison, we conduct the random search algorithm under the same settings. The evaluation result is illustrated in Figure 11. As we can see, RFLA outperforms the random baseline significantly. Specifically, RFLA achieves the average ASR of \\(95.13\\%\\), obtaining an improvement of \\(13.63\\%\\) than the random search (i.e., \\(81.5\\%\\)), which shows the effectiveness of our method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.619, + 0.106 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.118, + 0.892, + 0.389 + ], + "angle": 0, + "content": "In this paper, we propose a novel reflected light attack to realize effective and stealthy attacks in both digital and physical worlds, which may impose potential risks to automatic driving systems. Specifically, to explore how to control the reflected light's position, geometry, and pattern, we exploit the characteristic of the circle and propose a general framework based on the circle. To create a geometry, we first generate a specific number of angles to construct the point in circumference, followed by applying point symmetry against the center of a circle to generate a new point. These obtained points fence a geometrical shape where the fill color and transparency are optimized. Finally, we apply the PSO algorithm to find the best position, geometry, fill color, and transparency. Experiment results on digital and physical attacks verify the effectiveness of the proposed method. Moreover, our method can not only use sunlight but also can use flashlights to perform physical attacks for adapting to different environments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.392, + 0.892, + 0.466 + ], + "angle": 0, + "content": "Limitations. Though the reflected-light attack can perform in different environments, it is hard to remain effective in bad weather, such as fog and rain. A more penetrating light source (e.g., the traffic light and foglight) may work in such conditions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.469, + 0.892, + 0.605 + ], + "angle": 0, + "content": "Potential negative societal impact and mitigation. Similar to other types of attack, the adversarial attack is inevitable to cause potential security risks, especially for those physically deployed systems. However, we aim to arouse people's attention to such related applications and then encourage people to develop defense techniques to counter the reflected-light attack. To thwart the RFLA attack proposed in this paper, one can develop multimodal-based DNN systems." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.625, + 0.679, + 0.642 + ], + "angle": 0, + "content": "6. Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.652, + 0.892, + 0.712 + ], + "angle": 0, + "content": "The authors are grateful to the anonymous reviewers for their insightful comments. 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The current mainstream physical attacks use printed adversarial patches or camouflage to alter the appearance of the target object. However, these approaches generate conspicuous adversarial patterns that show poor stealthiness. Another physical deployable attack is the optical attack, featuring stealthiness while exhibiting weakly in the daytime with sunlight. In this paper, we propose a novel Reflected Light Attack (RFLA), featuring effective and stealthy in both the digital and physical world, which is implemented by placing the color transparent plastic sheet and a paper cut of a specific shape in front of the mirror to create different colored geometries on the target object. To achieve these goals, we devise a general framework based on the circle to model the reflected light on the target object. Specifically, we optimize a circle (composed of a coordinate and radius) to carry various geometrical shapes determined by the optimized angle. The fill color of the geometry shape and its corresponding transparency are also optimized. We extensively evaluate the effectiveness of RFLA on different datasets and models. Experiment results suggest that the proposed method achieves over $99\%$ success rate on different datasets and models in the digital world. Additionally, we verify the effectiveness of the proposed method in different physical environments by using sunlight or a flashlight. + +# 1. Introduction + +Deep neural networks (DNNs) have increasingly been applied to daily life as their dramatic capabilities, such as + +![](images/39a1f360014eed5c64a3195c1f15d70de79d86a80763a17d5a7f71ed5cd20484.jpg) +Figure 1. The reflected light is modulated by the color transparency plastic sheet and paper cut of the specific shape for better attack performance. The Reflected light source can be sunlight or a flashlight (when the sunlight is unreachable). + +automatic driving, facial payment, and computer-aided diagnosis. However, DNN-based systems have exposed security risks caused by adversarial examples [39]. Adversarial examples are crafted by carefully designed noise that is invisible to humans but can deceive the DNNs. Furthermore, recent researches [34, 21] reported that physically deployed DNN-based systems are also exposed to such security risks. Therefore, exploring various potential risks in security-sensitive systems to avoid possible loss is urgent. + +Existing adversarial attack methods can be categorized into digital attacks and physical attacks. The former focus on pursuing higher attack performance on limitation conditions, such as breaking the model equipped with adversarial defense [20, 3, 7, 24], preventing the attacker from accessing the target model's information (e.g., architecture or dataset), i.e., black-box attack [1, 22, 23]. Although some researchers suggested that adversarial examples generated by the digital attack can be applied to physical attacks [21], + +the attack performance is not satisfying. The possible reason is that the adversarial perturbation is too small to resist the environmental noise in the physical world. In contrast, physical attacks are designed to be physically deployable, where one crucial change is eliminating the perturbation's magnitude constraint. + +A line of physical adversarial attack methods [10, 9, 43, 44] has been proposed, which can be grouped into contact attacks and contactless attacks. The former requires the attacker to approach the target object and then modify the appearance of the target object by pasting the adversarial patch or camouflage. However, the adversarial pattern generated by these methods is conspicuous, which easily alerts humans and results in attack failure. By contrast, contactless physical attacks do not require the attacker to approach the target object while modifying the appearance of the target object by projecting or emitting light or laser on the target object to perform attacks, making it stealthy and dangerous. Optical attacks are representative contactless attacks. Although several optical attacks have been proposed [28, 32, 8, 17], they merely work in dark environments as the strong light (e.g., sunlight) environment would disturb the emitted light, limiting their usability. + +In this paper, we get inspiration from the fact that the driver is easily affected by the strong reflected light, resulting in a potential car accident, and such potential risks to the automatic driving system remain unexplored. We explore the vulnerability of the DNNs toward the reflected light attack by elaborately designing the position, geometry, and color of the reflected light. Specifically, we propose a Reflected Light Attack (RFLA), which can solve the issue of the poor attack performance of existing optical attacks in strong-light environments, as our light source is sunlight. To perform physical attacks, we use a mirror to reflect the sunlight toward the target object to modify its appearance. However, the monotonous sunlight (usually white) may not obtain the desired performance. Therefore, we first use different colored transparent plastic sheets to modulate the color of the reflected light, then apply a paper cut of a specific shape to control the shape of reflected light on the target object (see Figure 1). Finally, we can create different colors and shapes of the reflected light on the target object's specific region to achieve desired attack performance. + +To achieve the above goals, we present a general framework based on the circle to model the above problem. Specifically, we first initialize a circle with a random coordinate and radius. On this circle, we create a point on the circle using sine and cosine with a randomly selected angle. Then, we customize a shape by adding a new angle, which is used to create a new point in the circumference. The other points required to create a geometry can be obtained by applying the center symmetry of the circle. Moreover, the fill color and its transparency are also considered in + +the optimization. Finally, we adopt the particle swarm optimization (PSO) algorithm to find the optimal result. Our contributions are listed as follows. + +- We propose a novel reflect-light-based physical adversarial attack under the black-box scenario. It reflects the natural sunlight toward the target object using a mirror, making it controllable and stealthy. +- We devise a general framework based on a circle to search for the best position, geometry, and color of the reflected light to achieve better attack performance. +- We comprehensively investigate the influence of the geometry, position, and color of the reflected light on attack performance in the digital world. We conduct the physical adversarial attack by using sunlight for daytime and a flashlight for sunlight unavailable, and the experiment results verify the effectiveness of the proposed method. + +# 2. Related Works + +# 2.1. Digital Adversarial Attacks + +Digital adversarial attacks have enjoyed decade development, which can be roughly divided into white-box attack methods and black-box attack methods. The former grants the adversary access to the target model, allowing them to develop attack algorithms with the model's gradient. The most represented gradient-based attack is the fast gradient sign method (i.e., FGSM [13]), which updates adversarial examples along the ascending direction of the gradient under one iteration step. Since then, a line of variants has been proposed, including an iterative variant of FGSM (i.e., I-FGSM [21]), random initialization has been adopted (i.e., PGD [27]), momentum term is introduced to enhance the transferability (i.e., MI-FGSM [6]), and various data augmentation technique like diversity input (i.e., DIFGSM[47]), translation-invariant (i.e., TI-FGSM [7]) and scale-invariant (i.e., SI-FGSM [24]). In contrast, black-box attacks prohibit the attacker from accessing any information about the target model but are open for queries, which makes black-box attacks more challenging. Nonetheless, many black-box attacks are proposed, such as exploiting the differential evolution algorithm [22], genetic algorithm [1], particle swarm optimization [51], and so on [2]. In addition, several works suggested that adversarial perturbation's position [45], pattern [49], and geometry [4] on the clean image significantly impact attack performance. However, current works only investigate one or two of these factors. In this work, we systematically investigate the influence of the adversarial perturbation's position, geometry, and pattern on attack performance under the black-box scenario. + +# 2.2. Physical Adversarial Attacks + +According to whether it requires the attacker to access the target object in the real attack scenario, physical adversarial attacks can be grouped into contact and contactless physical attacks. Contact attacks can be further categorized into patch-based attacks and camouflage-based attacks. Patch-based attacks mainly focus on optimizing an adversarial image patch, which is then printed out and stuck on the target object or held by the attacker to deceive the target DNNs. Patch-based attacks are usually applied in attacking the facial recognition model [34, 35, 45, 46], pedestrian detection model [41, 40, 16, 5], and traffic sign recognition model [10, 25, 51]. Camouflage-based attacks [44, 43, 9] slightly differ from patch-based, as they concentrate on modifying the appearance of the target object via UV Texture. Thus, camouflage-based attacks show better attack performance in the multi-view scenario by painting the full coverage camouflage over the appearance of the target object. However, although contact physical attacks achieve good physical attack performance, the pattern of the adversarial patch/camouflage is conspicuous, which leads to poor stealthiness. In contrast, contactless physical attacks are performed by projecting/emitting light [12, 17], or a laser beam [8], usually called optical attacks. However, existing optical attacks work in dark environments [8, 17] while performing poorly in strong-light environments. The reason is that the light beam emitted by a light source is easily affected by environmental light, resulting in attacking failure. Recently, Zhang et al. [51] proposed a shadow-based attack, but it can only create a triangle shape with one monotonous color (e.g., gray). In this work, we solve the situation of poor attacks in strong-light (i.e., sunlight) environments to perform attacks since we directly use sunlight to perform attacks. Moreover, we create reflected light with different geometrical shapes and colors using the color transparency plastic sheet and paper cut. + +# 3. Methodology + +# 3.1. Problem Statement + +Let $\mathcal{X}$ denote the data distribution, and the corresponding ground truth label is $\mathcal{V}$ . Given an image $x\in \mathcal{X}$ that has the resolution of $x\in \mathbb{R}^{C\times H\times W}$ , a well trained neural network $f$ output $\hat{y} = f(x)$ and $\hat{y} = y$ , where the $\hat{y}$ is prediction of the $f$ and $y$ is the ground truth label, $\hat{y},y\in \mathbb{R}^{|\mathcal{V}|}$ . Adversarial attack aims to generate adversarial examples $x_{adv}$ to make the $f$ output the wrong prediction by adding small perturbation $\delta$ into the clean image $x$ , i.e., $x_{adv} = x + \delta$ . Mathematically, the $\delta$ is obtained by solving the following problem + +$$ +\min \delta \quad s. t. f (x + \delta) \neq f (x), | | \delta | | _ {p} \leq \epsilon , \tag {1} +$$ + +![](images/a0506e345e55c38f94f4b6613696819082eee2da2ede0883c6a8c2ee4bf2f620.jpg) + +![](images/d55d70caf5b1dba2d088c44bb859b115dee41ede8817ab348a6cc483cfcf1cfd.jpg) +(a) Base circle +(d) Rectangle +Figure 2. Visualization explanation of the circle modeling. Different geometries are constructed by adjusting the angle. For example, the triangle is created by adding a new angle $\angle a_{2}$ on the base circle (a), where three vertices are composed of two points $(p_{1}$ and $p_2)$ determined by two angles $(\angle a_{1}$ and $\angle a_{2})$ and one symmetry point $(p_1^{\prime})$ + +![](images/a405cf57134d85fc4b2159f2c4d8655e9a7e6b0bf5cc4eec1f8455f1450e2292.jpg) + +![](images/32224686e0b467cb699c9a3e1d9311c04afcdb961992ef57e18705bd90fcf1b2.jpg) +(b) Line +(e) Pentagon + +![](images/9eb653c354c24f917a8085193ba6d3b226985036e10457065a67a7a20c06d772.jpg) + +![](images/fe178b4f050668981db212a1f8835229b8788e147ac808edd81e3efb18935e5a.jpg) +(c) Triangle +(f) Hexagon + +where $||\cdot ||_p$ is the $L_{p}$ norm, which bound the maximum allowable magnitude of $\delta$ . + +The optimization objective of Equation 1 is the general formal for constructing the full-pixel-wise perturbation, which is unsuitable for physical adversarial attacks as the background of the physical world is unchangeable. Therefore, we reformulate Equation 1 to optimize the physical deployable perturbation by modifying the construction of $x_{adv}$ . Specifically, we define an apply function $\mathcal{A}(x,p,l,M)$ to construct adversarial examples $x_{adv}$ , which indicates that apply the perturbation $p$ at the location $l$ of the clean image $x$ , where $M$ is the binary mask to indicate whether the position is allowed to modify (one denote allow while zero not). + +In this work, we aim to reflect the sunlight toward the target object to perform stealthy physical adversarial attacks, where the representation (e.g., geometry, fill color and position) of reflected light on the target object is the key to a successful attack. Therefore, the parameters of $\mathcal{A}(x,p,l,M)$ comprise geometry and fill color of $p$ , and the location of $l$ are variables to be optimized. + +# 3.2. Reflected Light Attack + +Sunlight is the most common and indispensable natural phenomenon in daily life. People can reflect the sunlight toward the wall to construct various shapes by using different shapes of mirrors. However, the danger of such reflected light against DNN-based systems has been ignored, which may pose a potential risk as it featured extremely stealthy and controllable. In this work, we aim to modulate the reflected light to perform adversarial attacks in the digital and physical world. + +Previous work [51] modeled the triangle shadow by optimizing three points, which requires complex constraints on points to construct a rational geometry shape if they extend to other geometric shapes. To address this issue, we exploit the characteristic of the circle and propose a novel general framework based on the circle, which can generate various shapes by adjusting the number of angles (see Figure 2). The details process is described as follows. + +- Select a radius $r$ from the region of $[0, \min(H, W)/2]$ . +- Spawn a center $o(x, y)$ of the circle from the region of $[r, H - r]$ and $[r, W - r]$ . +- Randomly select an angle $a_1$ and spawn a point $p_1(x_1, y_1)$ on circle by the follow equation + +$$ +\left\{ \begin{array}{l} x _ {1} = x + r \times \sin \left(\frac {a _ {1} \times \pi}{1 8 0}\right), \\ y _ {1} = y + r \times \cos \left(\frac {a _ {1} \times \pi}{1 8 0}\right), \end{array} \right. \tag {2} +$$ + +- Calculate the symmetry point $p_1'(x_1', y_1')$ of the point $p_1$ against the center of the circle by $x_1' = 2 \times x - x_1$ and $y_1' = 2 \times y - y_1$ . +- Randomly select a color tuple (red, green, blue) from the region of [0, 255], and the transparency $\alpha$ from [0, 1]. + +The above process can plot a line on the clean image. To construct varying geometries like a triangle, rectangle, pentagon, or hexagon, one can repeat the third and fourth steps to create a new point by adding a new angle. Algorithm A1 in describes the detailed particle initialization process. + +# 3.3. Optimization + +As aforementioned, we have eight base variables that need to be optimized, expressed as eight-tuples $(x,y,r,\alpha ,red,green,\text{blue},a_{1})$ , which can be used to plot a line on the clean image. To generate various geometries, more additional variables are required to generate various geometries, which depend on the shape to be generated. For example, there is one extra variable for the triangle and rectangle; two extra for the pentagon and hexagon. Note that the proposed method is easily extended to more complex geometry. Recall that our goal is to deceive the DNNs by plotting geometry on the clean image. Thus, we adopt the particle swarm optimization algorithm (PSO) to seek the best geometry, fill color, and position. + +In PSO, we represent the optimization variables tuple as a particle (i.e., the solution vector $q$ ). The update direction of the particle is determined by a velocity vector $v$ . Every particle stands for a potential solution, which requires to be optimized. We treat the personal historical best solution of a particle as $q_{best}$ , and the global best solution of a particle as $q_{gbest}$ . Moreover, for every solution, we fix the circle's + +![](images/6a34e550aa31c58d7fe8235533908287514bd0b603a8dba3b7a76bf7cb206f60.jpg) +(a) + +![](images/46318297295131d00c8972c7edf6b60052fa0bcbe3391637d98f7d6dd34d3476.jpg) +(b) +Figure 3. The color discrepancy between the color transparency plastic sheet (a) and its reflected light(b). + +position and merely optimize the geometry, fill color, and transparency. Therefore, to represent the best solution of a circle, we devised an additional metric $q_{sgbest}$ , which is the sum of the fitness score of all geometrical shapes in a specific circle. Finally, the update criterion is defined as follows: + +$$ +\begin{array}{l} v _ {i} (t) = W v _ {i} (t - 1) + C _ {1} \kappa_ {1} \left(q _ {p b e s t} - q _ {i} (t)\right) \\ + C _ {2} \kappa_ {2} \left(q _ {\text {g b e s t}} - q _ {i} (t)\right) \tag {3} \\ + C _ {3} \kappa_ {3} \left(q _ {s g b e s t} - q _ {i} (t)\right), \\ \end{array} +$$ + +$$ +q _ {i} (t) = q _ {i} (t - 1) + v _ {i} (t), \tag {4} +$$ + +where $W$ is the inertia weight used to control the impact of the previous velocity on the current velocity. $C_1, C_2$ , and $C_3$ indicate the learning factors, which balance the impact of different parts empirical on current velocity. $\kappa_1, \kappa_2$ , and $\kappa_3$ are random values uniformly sampled from [0, 1], which are used to increase the randomness of the search. + +Apart from the solution and velocity of a particle, the fitness function is crucial for optimizing in PSO algorithm. In this work, we adopt the following fitness function to evaluate each particle. + +$$ +\min F (q) = \Pr_ {\hat {y}} (\mathcal {A} (x, q, M)), \tag {5} +$$ + +where $\mathcal{A}(x,q,M)$ denotes an applied function that paints the geometry with color (red,green,blue) and transparency $\alpha$ at the coordinate of $o$ on the clean image $x$ , where $M$ is a binary mask indicates the allowed modification area. $\operatorname{Pr}_{\hat{y}}(\cdot)$ is the predicted label $\hat{y}$ probability of the target model $f$ on the input. By minimizing the $F(q)$ , the confidence of prediction label $\hat{y}$ gradually decreases. We stop the search until it reaches the maximum iteration or finds the adversarial example. Algorithm 1 describes the optimization process. + +# 3.4. Physical Deployable Attack + +In digital worlds, we can construct $256^{3}$ color tuples by blending different RGB values, which is impractical in the physical world as the limitation of the device and material. + +Algorithm 1 Reflected Light Adversarial Attack (RFLA) +Input: input image $x$ , target model $f$ , max iteration MaxIter +Output: Best solution $q^*$ +1: $q \gets \text{Initialization}()$ ▷ Algorithm A1 +2: $x_{adv} \gets \text{GenSample}(q)$ ▷ Algorithm A2 +3: if $f(x_{adv}) \neq f(x)$ then +4: return $q^*$ +5: end if +6: for $itr = i, \dots, \text{MaxIter}$ do +7: Update velocity vector $v$ by Equation 3 +8: Update position vector $q$ by Equation 4 +9: $x_{adv} \gets \text{GenSample}(q)$ ▷ Algorithm A2 +10: if $f(x_{adv}) \neq f(x)$ then +11: return $q^*$ +12: end if +13: end for + +Therefore, we constrain the search space of the color to ensure physically deployable. Specifically, we use seven color transparency plastic sheets to change the color of the reflected light. However, we find discrepancies exist between the color transparency plastic sheet and its reflected light (see Figure 3), which may lead to attack failure. To decrease such discrepancy, we collect the light color reflected by the color transparency plastic sheet and adopt it as the searched color. In such a way, we can decrease color discrepancies when performing physical attacks. + +# 4. Experiments + +# 4.1. Settings + +Datasets: To investigate the effectiveness of the proposed method, we conduct the digital attack on the ImageNet-compatible dataset provided by the NIPS 2017 adversarial competition1, which includes 1000 images. Moreover, two commonly used traffic sign datasets: GTSRB [37] and LISA [29], are also considered to investigate the extensibility of the proposed method. + +Target models: We conduct the proposed method on two tasks: image classification and traffic sign recognition. As for image classification, we select six ImageNet pre-trained networks: ResNet50 (RN50) [15], VGG16 [36], DenseNet121 (DN121) [18], ResNeXt50 (RNX50) [48], WiderResNet50 (WRN50) [50] and SqueezeNet (SN) [19], which are all provided by PyTorch [30]. As for traffic sign recognition, we follow the setting reported in previous works [10, 25] to train GTSRB CNN and LISA CNN on GTSRB and LISA dataset, which obtains the accuracy of $95.06\%$ and $100\%$ on the test set, respectively. + +Table 1. Comparison results with the line-based method in terms of ASR (%) on ImageNet-compatible dataset. The best results are highlighted with bold. + +
RN50VGG16DN121RNX50WRN50SN
Bezier [11]72.477.774.172.769.689.3
RFLA-Line76.977.476.575.771.789.2
+ +Evaluation metrics: We adopt the attack success rate (ASR) as the evaluation metric, defined as the ratio of the number of the network's prediction flipped caused by adversarial examples to the total test dataset. + +Implementation details: We adopt the OpenCV-Python package to plot different geometries in the clean image. For the settings of parameters of PSO, we set the max iteration number to 200, $C_1$ , $C_2$ , and $C_3$ set to 2.05, $W$ is set to 0.7298, the particle size and the geometry number at a circle are set to 50. The particle and velocity bound are provided in Appendix A (The upper bound of the transparency $\alpha$ is set to 0.7 to evade occluding the clean image.). Unless otherwise specified, the mask $M$ is set to all one value matrix in our experiments. All experiments were conducted on an NVIDIA RTX 3090ti 24GB GPU $^2$ . + +# 4.2. Digital Adversarial Attacks + +In this section, we quantitatively and qualitatively evaluate the effectiveness of the proposed method in the digital world. For comparison, we adopt two patch-based attack methods: TPA [49] and DAPatch [4]; one line-based attack method Bezier [11]. TPA [49] utilized the feature texture image extracted from DNNs as the adversarial patch, which is pasted on the clean image, where the paste position is optimized by reinforcement learning. DAPatch [4] optimized the pattern and mask simultaneously, which can create a deformable shape adversarial patch. In contrast, Bezier [11] generated adversarial examples by scratching theBezier curve on the clean image, where theBezier curve depends on three points optimized by the optimizer (e.g., PSO). We reproduce the above three methods on the ImageNet-compatible dataset using the default settings. + +# 4.2.1 Quantitatively Result + +Table 1 reported the comparison results of the proposed RFLA-Line with the Bezier method. As we can observe, the proposed method outperforms the Bezier method on four of six models and obtains an improvement by $1.93\%$ in average ASR, indicating the proposed method's effectiveness. Additionally, we can get an $8.95\%$ improvement by widening the line thickness two times. Although the length of the Bezier curve may be shorter than ours, the discrepancy is trivial as modifications caused by the line is neglectable. Moreover, our method can be extended to more geometries. + +![](images/1b3386f0e862e9a3b67a08c3b9023b9a092cc32f3f90289b57cd4fd961594382.jpg) +balloon + +![](images/fc99541260d87d6bbd5b5dc2116c7be31bc605b976c99b541de543d3e229d5af.jpg) +balloon + +![](images/56ed5affb18eec1f55452cf9025f64e76175ad90b81137c2c1c45341d223c0fd.jpg) +balloon + +![](images/b431b462c36b4e45d575901a3a5765ffaa468af19bc1831e0ce78a1f91e06aa2.jpg) +balloon + +![](images/6aaddda060989288fe1cf78f0869440dad0427b8333bad835bea2b56a87f38e5.jpg) +parachute + +![](images/c33b07f417b4ab31bf050dd42046ed56e20cd06207630c7126b9f7336f59c3d8.jpg) +parachute + +![](images/1de3e984946f45a4f0c3c00fdce9572e41374a996003939c374856d1217737e3.jpg) +parachute + +![](images/253e025ea3c62b1c2749320e009b87e901df8671a9386f53359eb12230d50d08.jpg) +parachute + +![](images/f9ff5a637918d99319225b79e24d0a3bbbb8da1ab980c77b47518141ea74a932.jpg) +parachute + +![](images/5341866405e3f180f935c42a94600c4bdecff03b3bf52375a3c704f5761bf72f.jpg) +scabbard + +![](images/2f5331c4a4c642dfb7416c033a900fb5a8b5b3d6ccdcdb33918800d3885f227a.jpg) +scabbard + +![](images/d2f06eae2797aa7c3d673617400e88caa4b6bb3ffc7f5e9fd00bddde13e31a10.jpg) +scabbard + +![](images/ddc26aa18a384130eafd5698435894b1f61e273ac6aab8fa2e5712410701d29c.jpg) +scabbard + +![](images/cd5bb1a0233795fb0f7bd8823049abde719475003a898f2dd0e69aa22ddd2858.jpg) +pen + +![](images/dc069633fa905021c6faa5cfe61f91d03ce527dd410aec0bee6e2b26aac31a09.jpg) +pen + +![](images/f6a209ef7922cf0cf6615a178b0c593e6e1c6586e56d87fae558e78b89870a89.jpg) +holster + +![](images/2cdd9ba6847992a8f6cbc8afb3829eee7949ea36938343bdf84fcb5f3784b797.jpg) +pen + +![](images/04bf5a05b9b26d7b2984e5897ee68e7f982ce210e6531f1a9608b49aa1d4d93d.jpg) +wallet + +![](images/652994bffba262a14dd35a3d9aba955b00eb6e0c0c2b18492523a590c6ee647d.jpg) +hip + +![](images/455cd175c726cefd5a55d69fb83e1f897e4bb819345feda96a0df7d6f2c2a528.jpg) +hip + +![](images/2e324cd5a45dd089bec394a1a4f4dc67576f72da997d85ba31c17fa6e733b661.jpg) +hip + +![](images/d175cfd440254a51b34aa7c2e37233a4d803367eb5ba55e2a51de9e16b5a6df4.jpg) +hip + +![](images/1a6844e707c01785990fd2c7622d2712d0afcee8926bf1e8b82eed6809b2a6a0.jpg) +syringe + +![](images/570389eefc253bb945183f0c83d0923d144560169d92914230749c72e38f8fe0.jpg) +pinwheel + +![](images/c672fdd24d16b24be299a4d91500448933355e6d2759fb8db6cd466b87742b79.jpg) +birdhouse + +![](images/fc03e134c5972c27a19414278a8d2dffa001c627108501bf899abfe1afcdd6f7.jpg) +birdhouse + +![](images/cd0c93f756a09ecaf295d73c341a66b0a046218bb475ce4fbc32d1297bda6dac.jpg) +handkerchief + +![](images/f81371252ffd4c8ab237fae3a7238561d48ab676eaddbcc601dceeda335dce90.jpg) +lynx + +![](images/d2d8e517c8d02ec681f21db8c0636587734efa4ca3032f35506d64f5d52d1988.jpg) +lynx + +![](images/d93238c0bed9ae2672a7d693ec69ed444417e1c1ae824138e9c419810789586c.jpg) +lynx + +![](images/d0d664e04c924d78993f03743879544197589d408d78b8721d71d2a1b86b68c0.jpg) +ounce + +![](images/7ee696f976228a86327d1be28e7e713debe73da6a6398bacb279694f9836f26f.jpg) +ounce +Figure 4. Visualization comparison of adversarial examples generated by different methods on ResNet50. + +![](images/cf4f723b1e7b68f01725892bb0f288e0d4332ab80da79f4bea7c0950238e1547.jpg) +cheetah + +![](images/9d4440c9779adc2b99c15f49b265a7a75756a57ec797b75c25b929c4ffcf716c.jpg) +ounce + +![](images/b415952c7654092d2231919d6e33713a1bc56561a5f822d6b44faff5fda25a1c.jpg) +ounce + +![](images/dec4262063827417f1141b6dfd2875ba1f35e3f76a01174f36d8e91012f68607.jpg) +cheetah + +Table 2. Comparison results with patch-based methods in terms of ASR (\%) on ImageNet-compatible dataset. The best results are highlighted with bold. + +
RN50VGG16DN121RNX50WRN50SN
TPA [49]66.1364024.723.444.6
DAPatch [4]74.371.679.373.776.756
RFLA-Triangle98.197.897.297.298.199.5
RFLA-Rectangle99.399.199.298.999.199.8
RFLA-Pentagon99.699.199.299.299.499.8
RFLA-Hexagon99.599.599.599.599.499.8
+ +Then, the comparison results of patch-based methods are listed in Table 2. We conclude that the proposed geometry variants of RFLA outperform the existing method significantly. Specifically, the average ASR of the RFLA-triangle, RFLA-rectangle, RFLA-pentagon, and RFLA-hexagon are $97.98\%$ , $99.23\%$ , $99.38\%$ , and $99.53\%$ , obtaining the maximum improvement against TPA and DAPatch by $60.32\%$ and $27.52\%$ . We observe that the attack performance of comparison methods fails to achieve such results reported in their paper. The possible reason is that TPA may require two or more patches occluding $8\%$ of the image to achieve higher attack performance. As for DAPatch [4], the position of the adversarial patch is ignored, which makes them fail to seek the model-decision-sensitive position. In contrast, our method simultaneously optimizes the position, geometry, and adversarial pattern, resulting in better performance. Moreover, the ASR gains with increasing vertex of geometry shape are attenuations, such as $20.08\%$ gains from Line (two vertices) to Triangle(three vertices), while only $0.15\%$ from Rectangle to Pentagon, which may be attributed to the improvement room of ASR is limited. + +Table 3. Comparison results of transferability of adversarial examples generated by RNX50 in terms of ASR $(\%)$ on ImageNet-compatible dataset. Item indicates the white-box attack result, while the others are black-box results. The best results are highlighted with bold. + +
methodRN50VGG16DN121RNX50WRN50SN
Bezier [11]18.116.816.472.712.426.6
RFLA-LINE17.615.517.575.71427.1
TPA [49]28.93626.724.720.445.4
DAPatch [4]32.352.542.373.726.428.8
RFLA-Triangle37.834.933.197.233.750
RFLA-Rectangle47.643.244.398.945.5259.9
RFLA-Pentagon47.54546.499.245.261.9
RFLA-Hexagon50.84447.699.54763.9
+ +In addition, we compare the transferability of the proposed method with the comparison methods. Specifically, we use adversarial examples generated on RNX50 to attack other models. Evaluation results are reported in Table 3. As we can observe, RFLA outperforms the comparison methods in most cases, and the magnitude of fall behind cases is small. Concretely, we obtain the maximum average improvement of ASR of Bezier, TPA, and DAPatch are $0.28\%$ (RFLA-Line), $19.18\%$ , and $14.2\%$ , indicating the effectiveness of the proposed method. In addition, we provide other transferability comparison results in Appendix B1. + +# 4.2.2 Qualitatively Result + +We provide the visualization result of adversarial examples generated by different methods in Figure 4. As we can observe, on the one hand, the Bezier and RFLA-Line obtain + +![](images/31d54a1cae4007428d1fb3794b967ba093bf9a11b0c5a6bcbc12a975dd4d3040.jpg) +Figure 5. Model attention analysis of adversarial examples generated by RFLA on ResNet50. + +the most natural visuality quality, and the scratched line is hardly observed at a glance. Meanwhile, RFLA-Line fools the DNNs in all displayed cases, but Bezier only has two success cases. On the other hand, TPA and DAPatch failed in all displayed cases. Such qualitative results can be used to explain their inferior attack performance. The adversarial patch generated by their method covers the noncontent areas, which may be insignificant to the model decision. Although the proposed method affects more image content than TPA and DAPatch, the covered contents are recognizable. In other words, our method does not modify the semantics of the image. We provide more visualization results of adversarial examples in Appendix B1. + +In addition, we use the Grad-CAM [33] to investigate why the proposed method can work. Figure 5 illustrates the model attention visualization results. As we can observe, the painted geometry suppresses the model's attention areas, which makes the model output the wrong results. We also provide the visualization analysis result of comparison methods on model attention in Appendix B2. + +# 4.3. Extend to Traffic Sign Recognition Task + +To further investigate the effectiveness of the proposed method, we use RFLA to attack the traffic sign recognition (TSR) model. Specifically, we collect 200 stop sign images from the GTSRB and LISA test set for evaluation. To avoid the geometry being out of the scope of the stop sign, we use a mask to indicate the allowable modification positions. We get the mask by averaging 200 test images and binary it. Table 4 lists the digital adversarial performance. As we can observe, the proposed method obtains superior attack performances on two TSR models, especially for GTSRB CNN (100% ASR). In addition, as for LISA-CNN, the attack performance increase with the geometries. One possible reason is that the affected area of the clean image is larger with the change of geometries under a similar circle. + +# 4.4. Adversarial Defense + +In this part, we investigate the attack performance under the following adversarial defense methods: preprocess-based method and adversarial trained model. The former includes Total Variance Minimization (TVM) [14], standard Pixel Deflection (Pixel) [31], JPEG compression with qual + +Table 4. Quantitative results of RELA on TSR model in terms of ASR $(\%)$ + +
LISA-CNNGTSRB-CNN
RFLA-Triangle68.5100
RFLA-Rectangle92.5100
RFLA-Pentagon93.5100
RFLA-Hexagon97.5100
+ +Table 5. Comparison results of attack methods under different defense strategies in terms of ASR $(\%)$ + +
methodTVMPixelJPEGBlurAdvIncV3EnvAdvV2
Bezier [11]74.45439.851.737.524.2
RFLA-LINE73.750.238.349.337.123.3
TPA [49]76.537.241.549.853.744.6
DAPatch [4]79.328.23242.859.547.4
RFLA-Triangle84.474.564.47557.345.1
RFLA-Rectangle8880.370.580.167.857.6
RFLA-Pentagon84.545.155.564.471.864.3
RFLA-Hexagon88.881.673.684.668.962.9
+ +Table 6. Physical adversarial attacks under different light sources on different models in terms of ASR (\%). + +
RN50VGG16DN121
Sunlight81.2581.2581.25
Flashlight87.587.587.5
+ +ity factor 75 [26], and Gaussian blur with the kernel size 5, while the latter includes the adversarial trained model consisting of Adv-Inc-v3 (AdvIncV3) [38] and Ens-Adv-IncRes-v2 (EnvAdvV2) $[42]^3$ . Table 5 reports the attack performance after the adversarial defense. As we can observe, on the one hand, the proposed method falls behind Bezier under defense strategy by $1.58\%$ in terms of average ASR, which may attribute to the curve generated by Bezier exhibiting more robustness to the defense strategy than the line. On the other hand, other geometries generated by the proposed method significantly outperform the comparison method under the defense strategy. Specifically, the proposed method obtains the average ASR of RFLA-Triangle, RFLA-Rectangle, RFLA-Pentagon, and RFLA-Hexagon under defense is $63.37\%$ , $70.77\%$ , $63.11\%$ , and $73.43\%$ . In contrast, TPA and DAPatch are $49.24\%$ and $46.77\%$ . Such a result suggests that our method is more robust than the comparison method under different defense strategies. + +# 4.5. Physical Adversarial Attacks + +Unlike the previous physical attacks that generate the adversarial pattern for the physically captured images, we generate the adversarial pattern (i.e., colored geometries) for digital images (the target model is RN50) and then reflect the light according to the optimized variables toward the corresponding printed images. In physical adversarial attacks, we use sunlight and a flashlight as the light source + +![](images/e16f37eea950b7bfba2e921ff567051a6c31c87b9b2f7f6a19173797c8961934.jpg) +Camera $\rightarrow$ Rubber + +![](images/7050c534024039837f483a3e21dea00a47fa0606fd38c795ac16a40c93316872.jpg) +Camera $\rightarrow$ Laptop + +![](images/19ec2a320a61bd72d533a62b4464095c79a86c7cba1180a0336012003c31df05.jpg) +Camera $\rightarrow$ Television + +![](images/337d46f9647f84ab8c4e96ecdf0219fe4a39965039bd0ec4c7d9790b78db14e4.jpg) +Arch bridge $\rightarrow$ +Window screen + +![](images/cffec0562726bf792d65a1fab24102c3687a5a5e2c0c89a1122204d3b7b3392a.jpg) +Arch bridge $\rightarrow$ Screen + +![](images/38eb1ac50082753b31bd8f5ea03646f08d79253a40108519472cafa17fad18e8.jpg) +Arch bridge $\rightarrow$ Screen + +![](images/6b61c2cc483f6142c0bd4e270bcf6bc383f1a62d88bebcdb2811024658dbb079.jpg) +Figure 6. Physical adversarial examples. +Light source: flashlight +Predict: Speed Limited 30 +Confidence: $99.99\%$ +Figure 7. Examples of the "stop" sign with the reflected light and its prediction result on GTSRB CNN. + +![](images/730a7fa04926883bee73031f7ce2fbe6220a46ce3304c157ee803fabb5848ba4.jpg) +Predict: Yield Confidence: $71.94\%$ + +![](images/91e0d0df7c914a5fb3c3be3809e487bf5fe6757ce05856e4c41b412469f40426.jpg) +Predict: Road Work Confidence: $75.44\%$ +ource: sunlight + +![](images/559735413c96bdb06a4ae470fe7aa606fa99ad196cbc5f647ee403d3480dbb6a.jpg) +Predict: Road Work Confidence: 85.57% + +to mimic two different scenarios. We only evaluate one geometry (i.e., rectangle) for simplicity. Specifically, we randomly select six images from the dataset and generate the corresponding adversarial examples, where the color set is fixed during the optimization for physical deployment. Note that all selected images can be correctly classified as their original label after printing out. We use eight colors: seven colors created by seven transparent color plastic sheets and one white reflected sunlight. Finally, we capture the physical adversarial examples from 2 meters away, collecting 48 images for each light source. + +Table 6 lists the evaluation results. As we can observe, the ASR against the three models is above $80\%$ on physical adversarial examples created by two different light sources. Interestingly, we find that physical adversarial examples created by the reflected light against RN50 can consistently mislead the different models, indicating the reflected light is well-transferable even in the physical world. Figure 6 illustrates the physical adversarial examples. Furthermore, we study the effectiveness of reflected light attacks using sunlight and a flashlight on the TSR model. Figure 7 illustrates examples generated by different geometrical shapes. + +# 4.6. Ablation Study + +Attack performance v.s. transparency. The trans + +![](images/810433e5e5122343388681dc191992d58fc6b2841000094338c787e74c573a7e.jpg) +(a) Confidence v.s. $\alpha$ + +![](images/1e5a7e88350ea679c4445a12b484a633b61f5f50bf81b34547bf327367d72236.jpg) +(b) Frequency v.s. $\alpha$ + +![](images/2d41281fec03a6400f8c6429599e2b17ddba53d7c2c9d285debe0cd477d1bb76.jpg) +Figure 8. From left to right: (a) The trend of ground-truth label confidence with changing transparency, where blue points denote the successful attack. (b) The frequency of successful attacks (RFLA-Triangle) with changing of transparency. +Figure 9. The confidence distribution of the ground-truth label on adversarial examples. Blue points denote the attack fail color tuple, while red points denote the attack success color tuple. + +![](images/144090df2b0ce29f84babc79eebdc0ee4bdb83e418e7a317fb9a72d23201322b.jpg) + +![](images/316343832edbb4dda5f593d14746b5acead2fc955fa767d5352f5af036a2e7e6.jpg) + +parency $\alpha$ determined the cover intensity of the color. When $\alpha$ is set to one, the pixel value of the clean image at the specific position is substituted by the pure color, while the smaller value is the lower transparency of the color. We study how transparency changes the attack performance. Specifically, we fixed the other variables except for transparency, which traveled from [0,1] with a step size of 0.01. Figure 8 (a) illustrates the evaluation results of various geometries. As expectedly, the confidence of the ground-truth label decrease with enlarges of $\alpha$ . In contrast, the attack performance (represented in the number of blue points) rises with the increases in transparency, as more content of the clean image is covered due to deeper pure color. Moreover, we statistics the frequency of successful and failed attacks of the RFLA-Triangle on 100 test images, which is depicted in Figure 8 (b), consistent with the previous analysis. + +Attack performance v.s. color. The pattern of adversarial perturbation is crucial for a successful attack. Unlike the previous works that optimize the pixel-wise perturbation, we focus on the channel-wise perturbation (perturb a channel with one value) as we must ensure the perturbation is physically realizable by reflecting the light. Furthermore, channel-wise perturbation is visually more acceptable than pixel-wise perturbation. Specifically, we select the color tuple set in intervals of 16 pixels across the three RGB channels to investigate how color influences the attack performance. Figure 9 illustrates the evaluation results. As we can observe, the success cases almost cluster in specific areas near the searched optimal color tuple when other variables are fixed. In other words, the optimal color tuple has certain robustness to a slight change of color, which makes our attacks can undertake some distortions when applied in + +![](images/a27d43e49ab23b40cba44a91801574a91c5982885cea7ac88d226b84443619a1.jpg) +(a) + +![](images/d385084e00138a70f7fbd3d6196702a3225d7d697a048308186a71f43294a0dd.jpg) +(b) +Figure 10. From left to right: (a) Model attention on the clean image; (b) Adversarial examples; (c) Prediction confidence distribution of the clean image with the change of position, where blue points (the center of the circle) denote the successful attacks. + +![](images/ab45607ec9343a952d4819f477e7ec9a98ae5709b4e93d6d18bdf18d5dc08378.jpg) +(c) + +![](images/cf66136a93408cc410d4fa145a5723813a967c4041660b77403edc206db4930f.jpg) +Figure 11. Comparison result with RFLA and random search in terms of ASR. + +the physical world. + +Attack performance vs. position. To investigate the influence of the position of the adversarial perturbation to attack performance, we fixed the optimal variable except for position. Then, we sample the position in intervals of two steps. Furthermore, we also give the Grad-Cam for comparison. Figure 10 provides the evaluation results. As we can see, the adversarial geometry plotted around the content areas significantly drops the prediction confidence of the model on the clean image. Meanwhile, the attack success area is consistent with the model attention area, which indicates that our method can automatically locate the model attention areas to perform attacks. + +RFLA v.s. Random search. To investigate the effectiveness of the proposed algorithm, we use the proposed method to find the optimal triangle reflected light with white sunlight. For comparison, we conduct the random search algorithm under the same settings. The evaluation result is illustrated in Figure 11. As we can see, RFLA outperforms the random baseline significantly. Specifically, RFLA achieves the average ASR of $95.13\%$ , obtaining an improvement of $13.63\%$ than the random search (i.e., $81.5\%$ ), which shows the effectiveness of our method. + +# 5. Conclusion + +In this paper, we propose a novel reflected light attack to realize effective and stealthy attacks in both digital and physical worlds, which may impose potential risks to automatic driving systems. Specifically, to explore how to control the reflected light's position, geometry, and pattern, we exploit the characteristic of the circle and propose a general framework based on the circle. To create a geometry, we first generate a specific number of angles to construct the point in circumference, followed by applying point symmetry against the center of a circle to generate a new point. These obtained points fence a geometrical shape where the fill color and transparency are optimized. Finally, we apply the PSO algorithm to find the best position, geometry, fill color, and transparency. Experiment results on digital and physical attacks verify the effectiveness of the proposed method. Moreover, our method can not only use sunlight but also can use flashlights to perform physical attacks for adapting to different environments. + +Limitations. Though the reflected-light attack can perform in different environments, it is hard to remain effective in bad weather, such as fog and rain. A more penetrating light source (e.g., the traffic light and foglight) may work in such conditions. + +Potential negative societal impact and mitigation. Similar to other types of attack, the adversarial attack is inevitable to cause potential security risks, especially for those physically deployed systems. However, we aim to arouse people's attention to such related applications and then encourage people to develop defense techniques to counter the reflected-light attack. 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+ 620 + ], + "type": "text", + "content": "Physical adversarial attacks against deep neural networks (DNNs) have recently gained increasing attention. The current mainstream physical attacks use printed adversarial patches or camouflage to alter the appearance of the target object. However, these approaches generate conspicuous adversarial patterns that show poor stealthiness. Another physical deployable attack is the optical attack, featuring stealthiness while exhibiting weakly in the daytime with sunlight. In this paper, we propose a novel Reflected Light Attack (RFLA), featuring effective and stealthy in both the digital and physical world, which is implemented by placing the color transparent plastic sheet and a paper cut of a specific shape in front of the mirror to create different colored geometries on the target object. To achieve these goals, we devise a general framework based on the circle to model the reflected light on the target object. Specifically, we optimize a circle (composed of a coordinate and radius) to carry various geometrical shapes determined by the optimized angle. The fill color of the geometry shape and its corresponding transparency are also optimized. We extensively evaluate the effectiveness of RFLA on different datasets and models. Experiment results suggest that the proposed method achieves over " + }, + { + "bbox": [ + 47, + 308, + 289, + 620 + ], + "type": "inline_equation", + "content": "99\\%" + }, + { + "bbox": [ + 47, + 308, + 289, + 620 + ], + "type": "text", + "content": " success rate on different datasets and models in the digital world. Additionally, we verify the effectiveness of the proposed method in different physical environments by using sunlight or a flashlight." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 652, + 128, + 665 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 652, + 128, + 665 + ], + "spans": [ + { + "bbox": [ + 47, + 652, + 128, + 665 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 672, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 672, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 672, + 287, + 696 + ], + "type": "text", + "content": "Deep neural networks (DNNs) have increasingly been applied to daily life as their dramatic capabilities, such as" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 309, + 283, + 529, + 432 + ], + "blocks": [ + { + "bbox": [ + 309, + 283, + 529, + 432 + ], + "lines": [ + { + "bbox": [ + 309, + 283, + 529, + 432 + ], + "spans": [ + { + "bbox": [ + 309, + 283, + 529, + 432 + ], + "type": "image", + "image_path": "39a1f360014eed5c64a3195c1f15d70de79d86a80763a17d5a7f71ed5cd20484.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 433, + 545, + 477 + ], + "lines": [ + { + "bbox": [ + 305, + 433, + 545, + 477 + ], + "spans": [ + { + "bbox": [ + 305, + 433, + 545, + 477 + ], + "type": "text", + "content": "Figure 1. The reflected light is modulated by the color transparency plastic sheet and paper cut of the specific shape for better attack performance. The Reflected light source can be sunlight or a flashlight (when the sunlight is unreachable)." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 497, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 545, + 605 + ], + "type": "text", + "content": "automatic driving, facial payment, and computer-aided diagnosis. However, DNN-based systems have exposed security risks caused by adversarial examples [39]. Adversarial examples are crafted by carefully designed noise that is invisible to humans but can deceive the DNNs. Furthermore, recent researches [34, 21] reported that physically deployed DNN-based systems are also exposed to such security risks. Therefore, exploring various potential risks in security-sensitive systems to avoid possible loss is urgent." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 606, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 606, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 606, + 546, + 714 + ], + "type": "text", + "content": "Existing adversarial attack methods can be categorized into digital attacks and physical attacks. The former focus on pursuing higher attack performance on limitation conditions, such as breaking the model equipped with adversarial defense [20, 3, 7, 24], preventing the attacker from accessing the target model's information (e.g., architecture or dataset), i.e., black-box attack [1, 22, 23]. Although some researchers suggested that adversarial examples generated by the digital attack can be applied to physical attacks [21]," + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "type": "text", + "content": "*Corresponding Author." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "type": "text", + "content": "4455" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "content": "the attack performance is not satisfying. The possible reason is that the adversarial perturbation is too small to resist the environmental noise in the physical world. In contrast, physical attacks are designed to be physically deployable, where one crucial change is eliminating the perturbation's magnitude constraint." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 146, + 288, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 146, + 288, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 146, + 288, + 350 + ], + "type": "text", + "content": "A line of physical adversarial attack methods [10, 9, 43, 44] has been proposed, which can be grouped into contact attacks and contactless attacks. The former requires the attacker to approach the target object and then modify the appearance of the target object by pasting the adversarial patch or camouflage. However, the adversarial pattern generated by these methods is conspicuous, which easily alerts humans and results in attack failure. By contrast, contactless physical attacks do not require the attacker to approach the target object while modifying the appearance of the target object by projecting or emitting light or laser on the target object to perform attacks, making it stealthy and dangerous. Optical attacks are representative contactless attacks. Although several optical attacks have been proposed [28, 32, 8, 17], they merely work in dark environments as the strong light (e.g., sunlight) environment would disturb the emitted light, limiting their usability." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 352, + 287, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 287, + 591 + ], + "type": "text", + "content": "In this paper, we get inspiration from the fact that the driver is easily affected by the strong reflected light, resulting in a potential car accident, and such potential risks to the automatic driving system remain unexplored. We explore the vulnerability of the DNNs toward the reflected light attack by elaborately designing the position, geometry, and color of the reflected light. Specifically, we propose a Reflected Light Attack (RFLA), which can solve the issue of the poor attack performance of existing optical attacks in strong-light environments, as our light source is sunlight. To perform physical attacks, we use a mirror to reflect the sunlight toward the target object to modify its appearance. However, the monotonous sunlight (usually white) may not obtain the desired performance. Therefore, we first use different colored transparent plastic sheets to modulate the color of the reflected light, then apply a paper cut of a specific shape to control the shape of reflected light on the target object (see Figure 1). Finally, we can create different colors and shapes of the reflected light on the target object's specific region to achieve desired attack performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": "To achieve the above goals, we present a general framework based on the circle to model the above problem. Specifically, we first initialize a circle with a random coordinate and radius. On this circle, we create a point on the circle using sine and cosine with a randomly selected angle. Then, we customize a shape by adding a new angle, which is used to create a new point in the circumference. The other points required to create a geometry can be obtained by applying the center symmetry of the circle. Moreover, the fill color and its transparency are also considered in" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": "the optimization. Finally, we adopt the particle swarm optimization (PSO) algorithm to find the optimal result. Our contributions are listed as follows." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 120, + 545, + 312 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 317, + 120, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 120, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 317, + 120, + 545, + 168 + ], + "type": "text", + "content": "- We propose a novel reflect-light-based physical adversarial attack under the black-box scenario. It reflects the natural sunlight toward the target object using a mirror, making it controllable and stealthy." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 180, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 180, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 317, + 180, + 545, + 216 + ], + "type": "text", + "content": "- We devise a general framework based on a circle to search for the best position, geometry, and color of the reflected light to achieve better attack performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 228, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 228, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 317, + 228, + 545, + 312 + ], + "type": "text", + "content": "- We comprehensively investigate the influence of the geometry, position, and color of the reflected light on attack performance in the digital world. We conduct the physical adversarial attack by using sunlight for daytime and a flashlight for sunlight unavailable, and the experiment results verify the effectiveness of the proposed method." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 326, + 397, + 338 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 326, + 397, + 338 + ], + "spans": [ + { + "bbox": [ + 306, + 326, + 397, + 338 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 346, + 457, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 346, + 457, + 360 + ], + "spans": [ + { + "bbox": [ + 306, + 346, + 457, + 360 + ], + "type": "text", + "content": "2.1. Digital Adversarial Attacks" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 366, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 545, + 713 + ], + "type": "text", + "content": "Digital adversarial attacks have enjoyed decade development, which can be roughly divided into white-box attack methods and black-box attack methods. The former grants the adversary access to the target model, allowing them to develop attack algorithms with the model's gradient. The most represented gradient-based attack is the fast gradient sign method (i.e., FGSM [13]), which updates adversarial examples along the ascending direction of the gradient under one iteration step. Since then, a line of variants has been proposed, including an iterative variant of FGSM (i.e., I-FGSM [21]), random initialization has been adopted (i.e., PGD [27]), momentum term is introduced to enhance the transferability (i.e., MI-FGSM [6]), and various data augmentation technique like diversity input (i.e., DIFGSM[47]), translation-invariant (i.e., TI-FGSM [7]) and scale-invariant (i.e., SI-FGSM [24]). In contrast, black-box attacks prohibit the attacker from accessing any information about the target model but are open for queries, which makes black-box attacks more challenging. Nonetheless, many black-box attacks are proposed, such as exploiting the differential evolution algorithm [22], genetic algorithm [1], particle swarm optimization [51], and so on [2]. In addition, several works suggested that adversarial perturbation's position [45], pattern [49], and geometry [4] on the clean image significantly impact attack performance. However, current works only investigate one or two of these factors. In this work, we systematically investigate the influence of the adversarial perturbation's position, geometry, and pattern on attack performance under the black-box scenario." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "type": "text", + "content": "4456" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 205, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 205, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 205, + 84 + ], + "type": "text", + "content": "2.2. Physical Adversarial Attacks" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 290, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 290, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 290, + 510 + ], + "type": "text", + "content": "According to whether it requires the attacker to access the target object in the real attack scenario, physical adversarial attacks can be grouped into contact and contactless physical attacks. Contact attacks can be further categorized into patch-based attacks and camouflage-based attacks. Patch-based attacks mainly focus on optimizing an adversarial image patch, which is then printed out and stuck on the target object or held by the attacker to deceive the target DNNs. Patch-based attacks are usually applied in attacking the facial recognition model [34, 35, 45, 46], pedestrian detection model [41, 40, 16, 5], and traffic sign recognition model [10, 25, 51]. Camouflage-based attacks [44, 43, 9] slightly differ from patch-based, as they concentrate on modifying the appearance of the target object via UV Texture. Thus, camouflage-based attacks show better attack performance in the multi-view scenario by painting the full coverage camouflage over the appearance of the target object. However, although contact physical attacks achieve good physical attack performance, the pattern of the adversarial patch/camouflage is conspicuous, which leads to poor stealthiness. In contrast, contactless physical attacks are performed by projecting/emitting light [12, 17], or a laser beam [8], usually called optical attacks. However, existing optical attacks work in dark environments [8, 17] while performing poorly in strong-light environments. The reason is that the light beam emitted by a light source is easily affected by environmental light, resulting in attacking failure. Recently, Zhang et al. [51] proposed a shadow-based attack, but it can only create a triangle shape with one monotonous color (e.g., gray). In this work, we solve the situation of poor attacks in strong-light (i.e., sunlight) environments to perform attacks since we directly use sunlight to perform attacks. Moreover, we create reflected light with different geometrical shapes and colors using the color transparency plastic sheet and paper cut." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 525, + 130, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 130, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 130, + 538 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 545, + 160, + 557 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 545, + 160, + 557 + ], + "spans": [ + { + "bbox": [ + 47, + 545, + 160, + 557 + ], + "type": "text", + "content": "3.1. Problem Statement" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 564, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 564, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 564, + 287, + 685 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 46, + 564, + 287, + 685 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 564, + 287, + 685 + ], + "type": "text", + "content": " denote the data distribution, and the corresponding ground truth label is " + }, + { + "bbox": [ + 46, + 564, + 287, + 685 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 564, + 287, + 685 + ], + "type": "text", + "content": ". 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Visualization explanation of the circle modeling. Different geometries are constructed by adjusting the angle. For example, the triangle is created by adding a new angle " + }, + { + "bbox": [ + 304, + 241, + 545, + 307 + ], + "type": "inline_equation", + "content": "\\angle a_{2}" + }, + { + "bbox": [ + 304, + 241, + 545, + 307 + ], + "type": "text", + "content": " on the base circle (a), where three vertices are composed of two points " + }, + { + "bbox": [ + 304, + 241, + 545, + 307 + ], + "type": "inline_equation", + "content": "(p_{1}" + }, + { + "bbox": [ + 304, + 241, + 545, + 307 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 241, + 545, + 307 + ], + "type": "inline_equation", + "content": "p_2)" + }, + { + "bbox": [ + 304, + 241, + 545, + 307 + ], + "type": "text", + "content": " determined by two angles " + }, + { + "bbox": [ + 304, + 241, + 545, + 307 + ], + "type": "inline_equation", + "content": "(\\angle a_{1}" + }, + { + "bbox": [ + 304, + 241, + 545, + 307 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 241, + 545, + 307 + ], 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norm, which bound the maximum allowable magnitude of " + }, + { + "bbox": [ + 304, + 327, + 545, + 350 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 327, + 545, + 350 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 351, + 546, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 351, + 546, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 546, + 494 + ], + "type": "text", + "content": "The optimization objective of Equation 1 is the general formal for constructing the full-pixel-wise perturbation, which is unsuitable for physical adversarial attacks as the background of the physical world is unchangeable. Therefore, we reformulate Equation 1 to optimize the physical deployable perturbation by modifying the construction of " + }, + { + "bbox": [ + 304, + 351, + 546, + 494 + ], + "type": "inline_equation", + "content": "x_{adv}" + }, + { + "bbox": [ + 304, + 351, + 546, + 494 + ], + "type": "text", + "content": ". Specifically, we define an apply function " + }, + { + "bbox": [ + 304, + 351, + 546, + 494 + ], + "type": "inline_equation", + "content": "\\mathcal{A}(x,p,l,M)" + }, + { + "bbox": [ + 304, + 351, + 546, + 494 + ], + "type": "text", + "content": " to construct adversarial examples " + }, + { + "bbox": [ + 304, + 351, + 546, + 494 + ], + "type": "inline_equation", + "content": "x_{adv}" + }, + { + "bbox": [ + 304, + 351, + 546, + 494 + ], + "type": "text", + "content": ", which indicates that apply the perturbation " + }, + { + "bbox": [ + 304, + 351, + 546, + 494 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 351, + 546, + 494 + ], + "type": "text", + "content": " at the location " + }, + { + "bbox": [ + 304, + 351, + 546, + 494 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 351, + 546, + 494 + ], + "type": "text", + "content": " of the clean image " + }, + { + "bbox": [ + 304, + 351, + 546, + 494 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 351, + 546, + 494 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 351, + 546, + 494 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 351, + 546, + 494 + ], + "type": "text", + "content": " is the binary mask to indicate whether the position is allowed to modify (one denote allow while zero not)." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 495, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 579 + ], + "type": "text", + "content": "In this work, we aim to reflect the sunlight toward the target object to perform stealthy physical adversarial attacks, where the representation (e.g., geometry, fill color and position) of reflected light on the target object is the key to a successful attack. Therefore, the parameters of " + }, + { + "bbox": [ + 304, + 495, + 545, + 579 + ], + "type": "inline_equation", + "content": "\\mathcal{A}(x,p,l,M)" + }, + { + "bbox": [ + 304, + 495, + 545, + 579 + ], + "type": "text", + "content": " comprise geometry and fill color of " + }, + { + "bbox": [ + 304, + 495, + 545, + 579 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 495, + 545, + 579 + ], + "type": "text", + "content": ", and the location of " + }, + { + "bbox": [ + 304, + 495, + 545, + 579 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 495, + 545, + 579 + ], + "type": "text", + "content": " are variables to be optimized." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 586, + 434, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 434, + 600 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 434, + 600 + ], + "type": "text", + "content": "3.2. Reflected Light Attack" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": "Sunlight is the most common and indispensable natural phenomenon in daily life. People can reflect the sunlight toward the wall to construct various shapes by using different shapes of mirrors. However, the danger of such reflected light against DNN-based systems has been ignored, which may pose a potential risk as it featured extremely stealthy and controllable. In this work, we aim to modulate the reflected light to perform adversarial attacks in the digital and physical world." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 733, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 733, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 733, + 315, + 742 + ], + "type": "text", + "content": "4457" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 168 + ], + "type": "text", + "content": "Previous work [51] modeled the triangle shadow by optimizing three points, which requires complex constraints on points to construct a rational geometry shape if they extend to other geometric shapes. To address this issue, we exploit the characteristic of the circle and propose a novel general framework based on the circle, which can generate various shapes by adjusting the number of angles (see Figure 2). The details process is described as follows." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 58, + 177, + 287, + 253 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 58, + 177, + 286, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 177, + 286, + 191 + ], + "spans": [ + { + "bbox": [ + 58, + 177, + 286, + 191 + ], + "type": "text", + "content": "- Select a radius " + }, + { + "bbox": [ + 58, + 177, + 286, + 191 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 58, + 177, + 286, + 191 + ], + "type": "text", + "content": " from the region of " + }, + { + "bbox": [ + 58, + 177, + 286, + 191 + ], + "type": "inline_equation", + "content": "[0, \\min(H, W)/2]" + }, + { + "bbox": [ + 58, + 177, + 286, + 191 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 197, + 287, + 223 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 197, + 287, + 223 + ], + "spans": [ + { + "bbox": [ + 58, + 197, + 287, + 223 + ], + "type": "text", + "content": "- Spawn a center " + }, + { + "bbox": [ + 58, + 197, + 287, + 223 + ], + "type": "inline_equation", + "content": "o(x, y)" + }, + { + "bbox": [ + 58, + 197, + 287, + 223 + ], + "type": "text", + "content": " of the circle from the region of " + }, + { + "bbox": [ + 58, + 197, + 287, + 223 + ], + "type": "inline_equation", + "content": "[r, H - r]" + }, + { + "bbox": [ + 58, + 197, + 287, + 223 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 58, + 197, + 287, + 223 + ], + "type": "inline_equation", + "content": "[r, W - r]" + }, + { + "bbox": [ + 58, + 197, + 287, + 223 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 229, + 287, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 229, + 287, + 253 + ], + "spans": [ + { + "bbox": [ + 58, + 229, + 287, + 253 + ], + "type": "text", + "content": "- Randomly select an angle " + }, + { + "bbox": [ + 58, + 229, + 287, + 253 + ], + "type": "inline_equation", + "content": "a_1" + }, + { + "bbox": [ + 58, + 229, + 287, + 253 + ], + "type": "text", + "content": " and spawn a point " + }, + { + "bbox": [ + 58, + 229, + 287, + 253 + ], + "type": "inline_equation", + "content": "p_1(x_1, y_1)" + }, + { + "bbox": [ + 58, + 229, + 287, + 253 + ], + "type": "text", + "content": " on circle by the follow equation" + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 110, + 261, + 287, + 289 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 261, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 110, + 261, + 287, + 289 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} x _ {1} = x + r \\times \\sin \\left(\\frac {a _ {1} \\times \\pi}{1 8 0}\\right), \\\\ y _ {1} = y + r \\times \\cos \\left(\\frac {a _ {1} \\times \\pi}{1 8 0}\\right), \\end{array} \\right. \\tag {2}", + "image_path": "8465d462200be11de84485885ca29f46f2b18c610e194ad14a94c249bd0e425b.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 299, + 287, + 379 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 58, + 299, + 287, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 299, + 287, + 336 + ], + "spans": [ + { + "bbox": [ + 58, + 299, + 287, + 336 + ], + "type": "text", + "content": "- Calculate the symmetry point " + }, + { + "bbox": [ + 58, + 299, + 287, + 336 + ], + "type": "inline_equation", + "content": "p_1'(x_1', y_1')" + }, + { + "bbox": [ + 58, + 299, + 287, + 336 + ], + "type": "text", + "content": " of the point " + }, + { + "bbox": [ + 58, + 299, + 287, + 336 + ], + "type": "inline_equation", + "content": "p_1" + }, + { + "bbox": [ + 58, + 299, + 287, + 336 + ], + "type": "text", + "content": " against the center of the circle by " + }, + { + "bbox": [ + 58, + 299, + 287, + 336 + ], + "type": "inline_equation", + "content": "x_1' = 2 \\times x - x_1" + }, + { + "bbox": [ + 58, + 299, + 287, + 336 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 58, + 299, + 287, + 336 + ], + "type": "inline_equation", + "content": "y_1' = 2 \\times y - y_1" + }, + { + "bbox": [ + 58, + 299, + 287, + 336 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 343, + 287, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 343, + 287, + 379 + ], + "spans": [ + { + "bbox": [ + 58, + 343, + 287, + 379 + ], + "type": "text", + "content": "- Randomly select a color tuple (red, green, blue) from the region of [0, 255], and the transparency " + }, + { + "bbox": [ + 58, + 343, + 287, + 379 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 58, + 343, + 287, + 379 + ], + "type": "text", + "content": " from [0, 1]." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 388, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 388, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 47, + 388, + 287, + 449 + ], + "type": "text", + "content": "The above process can plot a line on the clean image. To construct varying geometries like a triangle, rectangle, pentagon, or hexagon, one can repeat the third and fourth steps to create a new point by adding a new angle. Algorithm A1 in describes the detailed particle initialization process." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 456, + 133, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 133, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 133, + 468 + ], + "type": "text", + "content": "3.3. Optimization" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 474, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 474, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 47, + 474, + 287, + 629 + ], + "type": "text", + "content": "As aforementioned, we have eight base variables that need to be optimized, expressed as eight-tuples " + }, + { + "bbox": [ + 47, + 474, + 287, + 629 + ], + "type": "inline_equation", + "content": "(x,y,r,\\alpha ,red,green,\\text{blue},a_{1})" + }, + { + "bbox": [ + 47, + 474, + 287, + 629 + ], + "type": "text", + "content": ", which can be used to plot a line on the clean image. To generate various geometries, more additional variables are required to generate various geometries, which depend on the shape to be generated. For example, there is one extra variable for the triangle and rectangle; two extra for the pentagon and hexagon. Note that the proposed method is easily extended to more complex geometry. Recall that our goal is to deceive the DNNs by plotting geometry on the clean image. Thus, we adopt the particle swarm optimization algorithm (PSO) to seek the best geometry, fill color, and position." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": "In PSO, we represent the optimization variables tuple as a particle (i.e., the solution vector " + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": "). The update direction of the particle is determined by a velocity vector " + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": ". Every particle stands for a potential solution, which requires to be optimized. We treat the personal historical best solution of a particle as " + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "inline_equation", + "content": "q_{best}" + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": ", and the global best solution of a particle as " + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "inline_equation", + "content": "q_{gbest}" + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": ". Moreover, for every solution, we fix the circle's" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 331, + 69, + 425, + 153 + ], + "blocks": [ + { + "bbox": [ + 331, + 69, + 425, + 153 + ], + "lines": [ + { + "bbox": [ + 331, + 69, + 425, + 153 + ], + "spans": [ + { + "bbox": [ + 331, + 69, + 425, + 153 + ], + "type": "image", + "image_path": "6a34e550aa31c58d7fe8235533908287514bd0b603a8dba3b7a76bf7cb206f60.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 372, + 159, + 383, + 168 + ], + "lines": [ + { + "bbox": [ + 372, + 159, + 383, + 168 + ], + "spans": [ + { + "bbox": [ + 372, + 159, + 383, + 168 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 426, + 70, + 524, + 167 + ], + "blocks": [ + { + "bbox": [ + 426, + 70, + 524, + 167 + ], + "lines": [ + { + "bbox": [ + 426, + 70, + 524, + 167 + ], + "spans": [ + { + "bbox": [ + 426, + 70, + 524, + 167 + ], + "type": "image", + "image_path": "46318297295131d00c8972c7edf6b60052fa0bcbe3391637d98f7d6dd34d3476.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 469, + 171, + 480, + 178 + ], + "lines": [ + { + "bbox": [ + 469, + 171, + 480, + 178 + ], + "spans": [ + { + "bbox": [ + 469, + 171, + 480, + 178 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 178, + 545, + 200 + ], + "lines": [ + { + "bbox": [ + 305, + 178, + 545, + 200 + ], + "spans": [ + { + "bbox": [ + 305, + 178, + 545, + 200 + ], + "type": "text", + "content": "Figure 3. The color discrepancy between the color transparency plastic sheet (a) and its reflected light(b)." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 220, + 545, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 220, + 545, + 290 + ], + "spans": [ + { + "bbox": [ + 304, + 220, + 545, + 290 + ], + "type": "text", + "content": "position and merely optimize the geometry, fill color, and transparency. Therefore, to represent the best solution of a circle, we devised an additional metric " + }, + { + "bbox": [ + 304, + 220, + 545, + 290 + ], + "type": "inline_equation", + "content": "q_{sgbest}" + }, + { + "bbox": [ + 304, + 220, + 545, + 290 + ], + "type": "text", + "content": ", which is the sum of the fitness score of all geometrical shapes in a specific circle. Finally, the update criterion is defined as follows:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 335, + 309, + 545, + 353 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 309, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 335, + 309, + 545, + 353 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} v _ {i} (t) = W v _ {i} (t - 1) + C _ {1} \\kappa_ {1} \\left(q _ {p b e s t} - q _ {i} (t)\\right) \\\\ + C _ {2} \\kappa_ {2} \\left(q _ {\\text {g b e s t}} - q _ {i} (t)\\right) \\tag {3} \\\\ + C _ {3} \\kappa_ {3} \\left(q _ {s g b e s t} - q _ {i} (t)\\right), \\\\ \\end{array}", + "image_path": "d76ac77aa58d977db2efc3eec3ebc7d5ae2bab0d9cb936a8b149a2d1d52ca739.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 372, + 365, + 545, + 378 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 365, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 372, + 365, + 545, + 378 + ], + "type": "interline_equation", + "content": "q _ {i} (t) = q _ {i} (t - 1) + v _ {i} (t), \\tag {4}", + "image_path": "654daf43ebd4ab837eb6e4ade4ca2531f25af6246ea83feb2cdd6928ff195d31.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 383, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 383, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 383, + 545, + 453 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 383, + 545, + 453 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 383, + 545, + 453 + ], + "type": "text", + "content": " is the inertia weight used to control the impact of the previous velocity on the current velocity. " + }, + { + "bbox": [ + 304, + 383, + 545, + 453 + ], + "type": "inline_equation", + "content": "C_1, C_2" + }, + { + "bbox": [ + 304, + 383, + 545, + 453 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 383, + 545, + 453 + ], + "type": "inline_equation", + "content": "C_3" + }, + { + "bbox": [ + 304, + 383, + 545, + 453 + ], + "type": "text", + "content": " indicate the learning factors, which balance the impact of different parts empirical on current velocity. " + }, + { + "bbox": [ + 304, + 383, + 545, + 453 + ], + "type": "inline_equation", + "content": "\\kappa_1, \\kappa_2" + }, + { + "bbox": [ + 304, + 383, + 545, + 453 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 383, + 545, + 453 + ], + "type": "inline_equation", + "content": "\\kappa_3" + }, + { + "bbox": [ + 304, + 383, + 545, + 453 + ], + "type": "text", + "content": " are random values uniformly sampled from [0, 1], which are used to increase the randomness of the search." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 455, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 455, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 455, + 545, + 502 + ], + "type": "text", + "content": "Apart from the solution and velocity of a particle, the fitness function is crucial for optimizing in PSO algorithm. In this work, we adopt the following fitness function to evaluate each particle." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 359, + 514, + 545, + 528 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 514, + 545, + 528 + ], + "spans": [ + { + "bbox": [ + 359, + 514, + 545, + 528 + ], + "type": "interline_equation", + "content": "\\min F (q) = \\Pr_ {\\hat {y}} (\\mathcal {A} (x, q, M)), \\tag {5}", + "image_path": "05efba755ce61a316ed934a74792c26a24a7346fa199624b567353323da97973.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{A}(x,q,M)" + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "text", + "content": " denotes an applied function that paints the geometry with color (red,green,blue) and transparency " + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "text", + "content": " at the coordinate of " + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "text", + "content": " on the clean image " + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "text", + "content": " is a binary mask indicates the allowed modification area. " + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\operatorname{Pr}_{\\hat{y}}(\\cdot)" + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "text", + "content": " is the predicted label " + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "text", + "content": " probability of the target model " + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "text", + "content": " on the input. By minimizing the " + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "inline_equation", + "content": "F(q)" + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "text", + "content": ", the confidence of prediction label " + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "text", + "content": " gradually decreases. We stop the search until it reaches the maximum iteration or finds the adversarial example. Algorithm 1 describes the optimization process." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 659, + 457, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 457, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 457, + 672 + ], + "type": "text", + "content": "3.4. Physical Deployable Attack" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "In digital worlds, we can construct " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "256^{3}" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " color tuples by blending different RGB values, which is impractical in the physical world as the limitation of the device and material." + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "text", + "content": "4458" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 47, + 71, + 287, + 279 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "text", + "content": "Algorithm 1 Reflected Light Adversarial Attack (RFLA) \nInput: input image " + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "text", + "content": ", target model " + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "text", + "content": ", max iteration MaxIter \nOutput: Best solution " + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "inline_equation", + "content": "q^*" + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "text", + "content": " \n1: " + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "inline_equation", + "content": "q \\gets \\text{Initialization}()" + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "text", + "content": " ▷ Algorithm A1 \n2: " + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "inline_equation", + "content": "x_{adv} \\gets \\text{GenSample}(q)" + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "text", + "content": " ▷ Algorithm A2 \n3: if " + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "inline_equation", + "content": "f(x_{adv}) \\neq f(x)" + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "text", + "content": " then \n4: return " + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "inline_equation", + "content": "q^*" + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "text", + "content": " \n5: end if \n6: for " + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "inline_equation", + "content": "itr = i, \\dots, \\text{MaxIter}" + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "text", + "content": " do \n7: Update velocity vector " + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "text", + "content": " by Equation 3 \n8: Update position vector " + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "text", + "content": " by Equation 4 \n9: " + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "inline_equation", + "content": "x_{adv} \\gets \\text{GenSample}(q)" + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "text", + "content": " ▷ Algorithm A2 \n10: if " + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "inline_equation", + "content": "f(x_{adv}) \\neq f(x)" + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "text", + "content": " then \n11: return " + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "inline_equation", + "content": "q^*" + }, + { + "bbox": [ + 47, + 71, + 287, + 279 + ], + "type": "text", + "content": " \n12: end if \n13: end for" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_body" + } + ], + "index": 0, + "sub_type": "algorithm" + }, + { + "bbox": [ + 46, + 303, + 289, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 303, + 289, + 425 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 289, + 425 + ], + "type": "text", + "content": "Therefore, we constrain the search space of the color to ensure physically deployable. Specifically, we use seven color transparency plastic sheets to change the color of the reflected light. However, we find discrepancies exist between the color transparency plastic sheet and its reflected light (see Figure 3), which may lead to attack failure. To decrease such discrepancy, we collect the light color reflected by the color transparency plastic sheet and adopt it as the searched color. In such a way, we can decrease color discrepancies when performing physical attacks." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 436, + 128, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 436, + 128, + 449 + ], + "spans": [ + { + "bbox": [ + 47, + 436, + 128, + 449 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 456, + 107, + 469 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 107, + 469 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 107, + 469 + ], + "type": "text", + "content": "4.1. Settings" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 475, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 287, + 559 + ], + "type": "text", + "content": "Datasets: To investigate the effectiveness of the proposed method, we conduct the digital attack on the ImageNet-compatible dataset provided by the NIPS 2017 adversarial competition1, which includes 1000 images. Moreover, two commonly used traffic sign datasets: GTSRB [37] and LISA [29], are also considered to investigate the extensibility of the proposed method." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 560, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 560, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 560, + 288, + 693 + ], + "type": "text", + "content": "Target models: We conduct the proposed method on two tasks: image classification and traffic sign recognition. As for image classification, we select six ImageNet pre-trained networks: ResNet50 (RN50) [15], VGG16 [36], DenseNet121 (DN121) [18], ResNeXt50 (RNX50) [48], WiderResNet50 (WRN50) [50] and SqueezeNet (SN) [19], which are all provided by PyTorch [30]. As for traffic sign recognition, we follow the setting reported in previous works [10, 25] to train GTSRB CNN and LISA CNN on GTSRB and LISA dataset, which obtains the accuracy of " + }, + { + "bbox": [ + 46, + 560, + 288, + 693 + ], + "type": "inline_equation", + "content": "95.06\\%" + }, + { + "bbox": [ + 46, + 560, + 288, + 693 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 560, + 288, + 693 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 560, + 288, + 693 + ], + "type": "text", + "content": " on the test set, respectively." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 307, + 102, + 550, + 140 + ], + "blocks": [ + { + "bbox": [ + 306, + 69, + 547, + 102 + ], + "lines": [ + { + "bbox": [ + 306, + 69, + 547, + 102 + ], + "spans": [ + { + "bbox": [ + 306, + 69, + 547, + 102 + ], + "type": "text", + "content": "Table 1. Comparison results with the line-based method in terms of ASR (%) on ImageNet-compatible dataset. The best results are highlighted with bold." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 102, + 550, + 140 + ], + "lines": [ + { + "bbox": [ + 307, + 102, + 550, + 140 + ], + "spans": [ + { + "bbox": [ + 307, + 102, + 550, + 140 + ], + "type": "table", + "html": "
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", + "image_path": "a1963f95ce82db73e5a0ab05b0d7ee7689e5b4bcf562b34fed9f5a2f5578f756.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 159, + 545, + 206 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 159, + 545, + 206 + ], + "spans": [ + { + "bbox": [ + 305, + 159, + 545, + 206 + ], + "type": "text", + "content": "Evaluation metrics: We adopt the attack success rate (ASR) as the evaluation metric, defined as the ratio of the number of the network's prediction flipped caused by adversarial examples to the total test dataset." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 207, + 546, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 207, + 546, + 339 + ], + "spans": [ + { + "bbox": [ + 304, + 207, + 546, + 339 + ], + "type": "text", + "content": "Implementation details: We adopt the OpenCV-Python package to plot different geometries in the clean image. For the settings of parameters of PSO, we set the max iteration number to 200, " + }, + { + "bbox": [ + 304, + 207, + 546, + 339 + ], + "type": "inline_equation", + "content": "C_1" + }, + { + "bbox": [ + 304, + 207, + 546, + 339 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 207, + 546, + 339 + ], + "type": "inline_equation", + "content": "C_2" + }, + { + "bbox": [ + 304, + 207, + 546, + 339 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 207, + 546, + 339 + ], + "type": "inline_equation", + "content": "C_3" + }, + { + "bbox": [ + 304, + 207, + 546, + 339 + ], + "type": "text", + "content": " set to 2.05, " + }, + { + "bbox": [ + 304, + 207, + 546, + 339 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 207, + 546, + 339 + ], + "type": "text", + "content": " is set to 0.7298, the particle size and the geometry number at a circle are set to 50. The particle and velocity bound are provided in Appendix A (The upper bound of the transparency " + }, + { + "bbox": [ + 304, + 207, + 546, + 339 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 207, + 546, + 339 + ], + "type": "text", + "content": " is set to 0.7 to evade occluding the clean image.). Unless otherwise specified, the mask " + }, + { + "bbox": [ + 304, + 207, + 546, + 339 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 207, + 546, + 339 + ], + "type": "text", + "content": " is set to all one value matrix in our experiments. All experiments were conducted on an NVIDIA RTX 3090ti 24GB GPU" + }, + { + "bbox": [ + 304, + 207, + 546, + 339 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 207, + 546, + 339 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 346, + 457, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 346, + 457, + 358 + ], + "spans": [ + { + "bbox": [ + 306, + 346, + 457, + 358 + ], + "type": "text", + "content": "4.2. Digital Adversarial Attacks" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 364, + 547, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 547, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 547, + 545 + ], + "type": "text", + "content": "In this section, we quantitatively and qualitatively evaluate the effectiveness of the proposed method in the digital world. For comparison, we adopt two patch-based attack methods: TPA [49] and DAPatch [4]; one line-based attack method Bezier [11]. TPA [49] utilized the feature texture image extracted from DNNs as the adversarial patch, which is pasted on the clean image, where the paste position is optimized by reinforcement learning. DAPatch [4] optimized the pattern and mask simultaneously, which can create a deformable shape adversarial patch. In contrast, Bezier [11] generated adversarial examples by scratching theBezier curve on the clean image, where theBezier curve depends on three points optimized by the optimizer (e.g., PSO). We reproduce the above three methods on the ImageNet-compatible dataset using the default settings." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 558, + 430, + 570 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 558, + 430, + 570 + ], + "spans": [ + { + "bbox": [ + 306, + 558, + 430, + 570 + ], + "type": "text", + "content": "4.2.1 Quantitatively Result" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 576, + 547, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 576, + 547, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 576, + 547, + 696 + ], + "type": "text", + "content": "Table 1 reported the comparison results of the proposed RFLA-Line with the Bezier method. As we can observe, the proposed method outperforms the Bezier method on four of six models and obtains an improvement by " + }, + { + "bbox": [ + 304, + 576, + 547, + 696 + ], + "type": "inline_equation", + "content": "1.93\\%" + }, + { + "bbox": [ + 304, + 576, + 547, + 696 + ], + "type": "text", + "content": " in average ASR, indicating the proposed method's effectiveness. Additionally, we can get an " + }, + { + "bbox": [ + 304, + 576, + 547, + 696 + ], + "type": "inline_equation", + "content": "8.95\\%" + }, + { + "bbox": [ + 304, + 576, + 547, + 696 + ], + "type": "text", + "content": " improvement by widening the line thickness two times. Although the length of the Bezier curve may be shorter than ours, the discrepancy is trivial as modifications caused by the line is neglectable. Moreover, our method can be extended to more geometries." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 285, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 285, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 285, + 713 + ], + "type": "text", + "content": "1https://www.kaggle.com/c/nips-2017-non-targeted-adversarial-attack" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 702, + 444, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 702, + 444, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 702, + 444, + 713 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 317, + 702, + 444, + 713 + ], + "type": "text", + "content": "Code will be released after published." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + 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Comparison results with patch-based methods in terms of ASR (\\%) on ImageNet-compatible dataset. The best results are highlighted with bold." + } + ] + } + ], + "index": 73, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 361, + 289, + 440 + ], + "lines": [ + { + "bbox": [ + 48, + 361, + 289, + 440 + ], + "spans": [ + { + "bbox": [ + 48, + 361, + 289, + 440 + ], + "type": "table", + "html": "
RN50VGG16DN121RNX50WRN50SN
TPA [49]66.1364024.723.444.6
DAPatch [4]74.371.679.373.776.756
RFLA-Triangle98.197.897.297.298.199.5
RFLA-Rectangle99.399.199.298.999.199.8
RFLA-Pentagon99.699.199.299.299.499.8
RFLA-Hexagon99.599.599.599.599.499.8
", + "image_path": "8e99c4f16ff4ea6b500453dbe2da332d1b461e3697a1544fab210c8e9131d838.jpg" + } + ] + } + ], + "index": 74, + "angle": 0, + "type": "table_body" + } + ], + "index": 74 + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "content": "Then, the comparison results of patch-based methods are listed in Table 2. We conclude that the proposed geometry variants of RFLA outperform the existing method significantly. Specifically, the average ASR of the RFLA-triangle, RFLA-rectangle, RFLA-pentagon, and RFLA-hexagon are " + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "inline_equation", + "content": "97.98\\%" + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "inline_equation", + "content": "99.23\\%" + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "inline_equation", + "content": "99.38\\%" + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "inline_equation", + "content": "99.53\\%" + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "content": ", obtaining the maximum improvement against TPA and DAPatch by " + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "inline_equation", + "content": "60.32\\%" + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "inline_equation", + "content": "27.52\\%" + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "content": ". We observe that the attack performance of comparison methods fails to achieve such results reported in their paper. The possible reason is that TPA may require two or more patches occluding " + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "inline_equation", + "content": "8\\%" + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "content": " of the image to achieve higher attack performance. As for DAPatch [4], the position of the adversarial patch is ignored, which makes them fail to seek the model-decision-sensitive position. In contrast, our method simultaneously optimizes the position, geometry, and adversarial pattern, resulting in better performance. Moreover, the ASR gains with increasing vertex of geometry shape are attenuations, such as " + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "inline_equation", + "content": "20.08\\%" + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "content": " gains from Line (two vertices) to Triangle(three vertices), while only " + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "inline_equation", + "content": "0.15\\%" + }, + { + "bbox": [ + 46, + 462, + 287, + 713 + ], + "type": "text", + "content": " from Rectangle to Pentagon, which may be attributed to the improvement room of ASR is limited." + } + ] + } + ], + "index": 75 + }, + { + "type": "table", + "bbox": [ + 307, + 383, + 548, + 485 + ], + "blocks": [ + { + "bbox": [ + 305, + 328, + 545, + 383 + ], + "lines": [ + { + "bbox": [ + 305, + 328, + 545, + 383 + ], + "spans": [ + { + "bbox": [ + 305, + 328, + 545, + 383 + ], + "type": "text", + "content": "Table 3. Comparison results of transferability of adversarial examples generated by RNX50 in terms of ASR " + }, + { + "bbox": [ + 305, + 328, + 545, + 383 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 328, + 545, + 383 + ], + "type": "text", + "content": " on ImageNet-compatible dataset. Item indicates the white-box attack result, while the others are black-box results. The best results are highlighted with bold." + } + ] + } + ], + "index": 76, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 383, + 548, + 485 + ], + "lines": [ + { + "bbox": [ + 307, + 383, + 548, + 485 + ], + "spans": [ + { + "bbox": [ + 307, + 383, + 548, + 485 + ], + "type": "table", + "html": "
methodRN50VGG16DN121RNX50WRN50SN
Bezier [11]18.116.816.472.712.426.6
RFLA-LINE17.615.517.575.71427.1
TPA [49]28.93626.724.720.445.4
DAPatch [4]32.352.542.373.726.428.8
RFLA-Triangle37.834.933.197.233.750
RFLA-Rectangle47.643.244.398.945.5259.9
RFLA-Pentagon47.54546.499.245.261.9
RFLA-Hexagon50.84447.699.54763.9
", + "image_path": "817702727fff026d88b7b128bde5cf91b4695513764f42ac3a3de76fd25187ee.jpg" + } + ] + } + ], + "index": 77, + "angle": 0, + "type": "table_body" + } + ], + "index": 77 + }, + { + "bbox": [ + 304, + 507, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 507, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 507, + 545, + 639 + ], + "type": "text", + "content": "In addition, we compare the transferability of the proposed method with the comparison methods. Specifically, we use adversarial examples generated on RNX50 to attack other models. Evaluation results are reported in Table 3. As we can observe, RFLA outperforms the comparison methods in most cases, and the magnitude of fall behind cases is small. Concretely, we obtain the maximum average improvement of ASR of Bezier, TPA, and DAPatch are " + }, + { + "bbox": [ + 304, + 507, + 545, + 639 + ], + "type": "inline_equation", + "content": "0.28\\%" + }, + { + "bbox": [ + 304, + 507, + 545, + 639 + ], + "type": "text", + "content": " (RFLA-Line), " + }, + { + "bbox": [ + 304, + 507, + 545, + 639 + ], + "type": "inline_equation", + "content": "19.18\\%" + }, + { + "bbox": [ + 304, + 507, + 545, + 639 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 507, + 545, + 639 + ], + "type": "inline_equation", + "content": "14.2\\%" + }, + { + "bbox": [ + 304, + 507, + 545, + 639 + ], + "type": "text", + "content": ", indicating the effectiveness of the proposed method. In addition, we provide other transferability comparison results in Appendix B1." + } + ] + } + ], + "index": 78 + }, + { + "bbox": [ + 306, + 657, + 424, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 657, + 424, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 657, + 424, + 670 + ], + "type": "text", + "content": "4.2.2 Qualitatively Result" + } + ] + } + ], + "index": 79 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "We provide the visualization result of adversarial examples generated by different methods in Figure 4. As we can observe, on the one hand, the Bezier and RFLA-Line obtain" + } + ] + } + ], + "index": 80 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "type": "text", + "content": "4460" + } + ] + } + ], + "index": 81 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 278, + 153 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 278, + 153 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 278, + 153 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 278, + 153 + ], + "type": "image", + "image_path": "31d54a1cae4007428d1fb3794b967ba093bf9a11b0c5a6bcbc12a975dd4d3040.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 156, + 286, + 177 + ], + "lines": [ + { + "bbox": [ + 47, + 156, + 286, + 177 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 286, + 177 + ], + "type": "text", + "content": "Figure 5. Model attention analysis of adversarial examples generated by RFLA on ResNet50." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 196, + 286, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 196, + 286, + 351 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 286, + 351 + ], + "type": "text", + "content": "the most natural visuality quality, and the scratched line is hardly observed at a glance. Meanwhile, RFLA-Line fools the DNNs in all displayed cases, but Bezier only has two success cases. On the other hand, TPA and DAPatch failed in all displayed cases. Such qualitative results can be used to explain their inferior attack performance. The adversarial patch generated by their method covers the noncontent areas, which may be insignificant to the model decision. Although the proposed method affects more image content than TPA and DAPatch, the covered contents are recognizable. In other words, our method does not modify the semantics of the image. We provide more visualization results of adversarial examples in Appendix B1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 351, + 286, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 351, + 286, + 435 + ], + "spans": [ + { + "bbox": [ + 46, + 351, + 286, + 435 + ], + "type": "text", + "content": "In addition, we use the Grad-CAM [33] to investigate why the proposed method can work. Figure 5 illustrates the model attention visualization results. As we can observe, the painted geometry suppresses the model's attention areas, which makes the model output the wrong results. We also provide the visualization analysis result of comparison methods on model attention in Appendix B2." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 442, + 256, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 442, + 256, + 455 + ], + "spans": [ + { + "bbox": [ + 47, + 442, + 256, + 455 + ], + "type": "text", + "content": "4.3. Extend to Traffic Sign Recognition Task" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 460, + 286, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 286, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 286, + 628 + ], + "type": "text", + "content": "To further investigate the effectiveness of the proposed method, we use RFLA to attack the traffic sign recognition (TSR) model. Specifically, we collect 200 stop sign images from the GTSRB and LISA test set for evaluation. To avoid the geometry being out of the scope of the stop sign, we use a mask to indicate the allowable modification positions. We get the mask by averaging 200 test images and binary it. Table 4 lists the digital adversarial performance. As we can observe, the proposed method obtains superior attack performances on two TSR models, especially for GTSRB CNN (100% ASR). In addition, as for LISA-CNN, the attack performance increase with the geometries. One possible reason is that the affected area of the clean image is larger with the change of geometries under a similar circle." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 635, + 164, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 164, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 164, + 647 + ], + "type": "text", + "content": "4.4. Adversarial Defense" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 654, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 286, + 712 + ], + "type": "text", + "content": "In this part, we investigate the attack performance under the following adversarial defense methods: preprocess-based method and adversarial trained model. The former includes Total Variance Minimization (TVM) [14], standard Pixel Deflection (Pixel) [31], JPEG compression with qual" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 320, + 90, + 530, + 152 + ], + "blocks": [ + { + "bbox": [ + 306, + 69, + 545, + 89 + ], + "lines": [ + { + "bbox": [ + 306, + 69, + 545, + 89 + ], + "spans": [ + { + "bbox": [ + 306, + 69, + 545, + 89 + ], + "type": "text", + "content": "Table 4. Quantitative results of RELA on TSR model in terms of ASR " + }, + { + "bbox": [ + 306, + 69, + 545, + 89 + ], + "type": "inline_equation", + "content": "(\\%)" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 320, + 90, + 530, + 152 + ], + "lines": [ + { + "bbox": [ + 320, + 90, + 530, + 152 + ], + "spans": [ + { + "bbox": [ + 320, + 90, + 530, + 152 + ], + "type": "table", + "html": "
LISA-CNNGTSRB-CNN
RFLA-Triangle68.5100
RFLA-Rectangle92.5100
RFLA-Pentagon93.5100
RFLA-Hexagon97.5100
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methodTVMPixelJPEGBlurAdvIncV3EnvAdvV2
Bezier [11]74.45439.851.737.524.2
RFLA-LINE73.750.238.349.337.123.3
TPA [49]76.537.241.549.853.744.6
DAPatch [4]79.328.23242.859.547.4
RFLA-Triangle84.474.564.47557.345.1
RFLA-Rectangle8880.370.580.167.857.6
RFLA-Pentagon84.545.155.564.471.864.3
RFLA-Hexagon88.881.673.684.668.962.9
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RN50VGG16DN121
Sunlight81.2581.2581.25
Flashlight87.587.587.5
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As we can observe, on the one hand, the proposed method falls behind Bezier under defense strategy by " + }, + { + "bbox": [ + 304, + 358, + 545, + 586 + ], + "type": "inline_equation", + "content": "1.58\\%" + }, + { + "bbox": [ + 304, + 358, + 545, + 586 + ], + "type": "text", + "content": " in terms of average ASR, which may attribute to the curve generated by Bezier exhibiting more robustness to the defense strategy than the line. On the other hand, other geometries generated by the proposed method significantly outperform the comparison method under the defense strategy. Specifically, the proposed method obtains the average ASR of RFLA-Triangle, RFLA-Rectangle, RFLA-Pentagon, and RFLA-Hexagon under defense is " + }, + { + "bbox": [ + 304, + 358, + 545, + 586 + ], + "type": "inline_equation", + "content": "63.37\\%" + }, + { + "bbox": [ + 304, + 358, + 545, + 586 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 358, + 545, + 586 + ], + "type": "inline_equation", + "content": "70.77\\%" + }, + { + "bbox": [ + 304, + 358, + 545, + 586 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 358, + 545, + 586 + ], + "type": "inline_equation", + "content": "63.11\\%" + }, + { + "bbox": [ + 304, + 358, + 545, + 586 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 358, + 545, + 586 + ], + "type": "inline_equation", + "content": "73.43\\%" + }, + { + "bbox": [ + 304, + 358, + 545, + 586 + ], + "type": "text", + "content": ". In contrast, TPA and DAPatch are " + }, + { + "bbox": [ + 304, + 358, + 545, + 586 + ], + "type": "inline_equation", + "content": "49.24\\%" + }, + { + "bbox": [ + 304, + 358, + 545, + 586 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 358, + 545, + 586 + ], + "type": "inline_equation", + "content": "46.77\\%" + }, + { + "bbox": [ + 304, + 358, + 545, + 586 + ], + "type": "text", + "content": ". Such a result suggests that our method is more robust than the comparison method under different defense strategies." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 594, + 463, + 605 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 594, + 463, + 605 + ], + "spans": [ + { + "bbox": [ + 306, + 594, + 463, + 605 + ], + "type": "text", + "content": "4.5. 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In physical adversarial attacks, we use sunlight and a flashlight as the light source" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 315, + 702, + 492, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 702, + 492, + 712 + ], + "spans": [ + { + "bbox": [ + 315, + 702, + 492, + 712 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 315, + 702, + 492, + 712 + ], + "type": "text", + "content": "https://github.com/rwrightman/pytorch-image-models" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 295, + 734, + 314, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 734, + 314, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 734, + 314, + 742 + ], + "type": "text", + "content": "4461" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 73, + 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Physical adversarial examples." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 86, + 287, + 135, + 294 + ], + "lines": [ + { + "bbox": [ + 86, + 287, + 135, + 294 + ], + "spans": [ + { + "bbox": [ + 86, + 287, + 135, + 294 + ], + "type": "text", + "content": "Light source: flashlight" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 56, + 295, + 108, + 346 + ], + "lines": [ + { + "bbox": [ + 56, + 295, + 108, + 346 + ], + "spans": [ + { + "bbox": [ + 56, + 295, + 108, + 346 + ], + "type": "image", + "image_path": "6b61c2cc483f6142c0bd4e270bcf6bc383f1a62d88bebcdb2811024658dbb079.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 348, + 108, + 358 + ], + "lines": [ + { + "bbox": [ + 54, + 348, + 108, + 358 + ], + "spans": [ + { + "bbox": [ + 54, + 348, + 108, + 358 + ], + "type": "text", + "content": "Predict: Speed Limited 30 \nConfidence: " + }, + { + "bbox": [ + 54, + 348, + 108, + 358 + ], + "type": "inline_equation", + "content": "99.99\\%" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 365, + 286, + 388 + ], + "lines": [ + { + "bbox": [ + 47, + 365, + 286, + 388 + ], + "spans": [ + { + "bbox": [ + 47, + 365, + 286, + 388 + ], + "type": "text", + "content": "Figure 7. Examples of the \"stop\" sign with the reflected light and its prediction result on GTSRB CNN." + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 115, + 295, + 165, + 346 + ], + "blocks": [ + { + "bbox": [ + 115, + 295, + 165, + 346 + ], + "lines": [ + { + "bbox": [ + 115, + 295, + 165, + 346 + ], + "spans": [ + { + "bbox": [ + 115, + 295, + 165, + 346 + ], + "type": "image", + "image_path": "730a7fa04926883bee73031f7ce2fbe6220a46ce3304c157ee803fabb5848ba4.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 119, + 348, + 163, + 358 + ], + "lines": [ + { + "bbox": [ + 119, + 348, + 163, + 358 + ], + "spans": [ + { + "bbox": [ + 119, + 348, + 163, + 358 + ], + "type": "text", + "content": "Predict: Yield Confidence: " + }, + { + "bbox": [ + 119, + 348, + 163, + 358 + ], + "type": "inline_equation", + "content": "71.94\\%" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 171, + 295, + 221, + 346 + ], + "blocks": [ + { + "bbox": [ + 171, + 295, + 221, + 346 + ], + "lines": [ + { + "bbox": [ + 171, + 295, + 221, + 346 + ], + "spans": [ + { + "bbox": [ + 171, + 295, + 221, + 346 + ], + "type": "image", + "image_path": "91e0d0df7c914a5fb3c3be3809e487bf5fe6757ce05856e4c41b412469f40426.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 176, + 348, + 219, + 358 + ], + "lines": [ + { + "bbox": [ + 176, + 348, + 219, + 358 + ], + "spans": [ + { + "bbox": [ + 176, + 348, + 219, + 358 + ], + "type": "text", + "content": "Predict: Road Work Confidence: " + }, + { + "bbox": [ + 176, + 348, + 219, + 358 + ], + "type": "inline_equation", + "content": "75.44\\%" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 214, + 288, + 244, + 294 + ], + "lines": [ + { + "bbox": [ + 214, + 288, + 244, + 294 + ], + "spans": [ + { + "bbox": [ + 214, + 288, + 244, + 294 + ], + "type": "text", + "content": "ource: sunlight" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 228, + 295, + 278, + 346 + ], + "blocks": [ + { + "bbox": [ + 228, + 295, + 278, + 346 + ], + "lines": [ + { + "bbox": [ + 228, + 295, + 278, + 346 + ], + "spans": [ + { + "bbox": [ + 228, + 295, + 278, + 346 + ], + "type": "image", + "image_path": "559735413c96bdb06a4ae470fe7aa606fa99ad196cbc5f647ee403d3480dbb6a.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 232, + 348, + 274, + 359 + ], + "lines": [ + { + "bbox": [ + 232, + 348, + 274, + 359 + ], + "spans": [ + { + "bbox": [ + 232, + 348, + 274, + 359 + ], + "type": "text", + "content": "Predict: Road Work Confidence: 85.57%" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 409, + 286, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 286, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 286, + 540 + ], + "type": "text", + "content": "to mimic two different scenarios. We only evaluate one geometry (i.e., rectangle) for simplicity. Specifically, we randomly select six images from the dataset and generate the corresponding adversarial examples, where the color set is fixed during the optimization for physical deployment. Note that all selected images can be correctly classified as their original label after printing out. We use eight colors: seven colors created by seven transparent color plastic sheets and one white reflected sunlight. Finally, we capture the physical adversarial examples from 2 meters away, collecting 48 images for each light source." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 541, + 286, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 541, + 286, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 541, + 286, + 673 + ], + "type": "text", + "content": "Table 6 lists the evaluation results. As we can observe, the ASR against the three models is above " + }, + { + "bbox": [ + 46, + 541, + 286, + 673 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 46, + 541, + 286, + 673 + ], + "type": "text", + "content": " on physical adversarial examples created by two different light sources. Interestingly, we find that physical adversarial examples created by the reflected light against RN50 can consistently mislead the different models, indicating the reflected light is well-transferable even in the physical world. Figure 6 illustrates the physical adversarial examples. Furthermore, we study the effectiveness of reflected light attacks using sunlight and a flashlight on the TSR model. Figure 7 illustrates examples generated by different geometrical shapes." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 47, + 682, + 140, + 695 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 682, + 140, + 695 + ], + "spans": [ + { + "bbox": [ + 47, + 682, + 140, + 695 + ], + "type": "text", + "content": "4.6. Ablation Study" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "content": "Attack performance v.s. transparency. The trans" + } + ] + } + ], + "index": 28 + }, + { + "type": "image", + "bbox": [ + 322, + 79, + 416, + 151 + ], + "blocks": [ + { + "bbox": [ + 322, + 79, + 416, + 151 + ], + "lines": [ + { + "bbox": [ + 322, + 79, + 416, + 151 + ], + "spans": [ + { + "bbox": [ + 322, + 79, + 416, + 151 + ], + "type": "image", + "image_path": "810433e5e5122343388681dc191992d58fc6b2841000094338c787e74c573a7e.jpg" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 337, + 156, + 406, + 164 + ], + "lines": [ + { + "bbox": [ + 337, + 156, + 406, + 164 + ], + "spans": [ + { + "bbox": [ + 337, + 156, + 406, + 164 + ], + "type": "text", + "content": "(a) Confidence v.s. " + }, + { + "bbox": [ + 337, + 156, + 406, + 164 + ], + "type": "inline_equation", + "content": "\\alpha" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_caption" + } + ], + "index": 29 + }, + { + "type": "image", + "bbox": [ + 427, + 79, + 524, + 151 + ], + "blocks": [ + { + "bbox": [ + 427, + 79, + 524, + 151 + ], + "lines": [ + { + "bbox": [ + 427, + 79, + 524, + 151 + ], + "spans": [ + { + "bbox": [ + 427, + 79, + 524, + 151 + ], + "type": "image", + "image_path": "1e5a7e88350ea679c4445a12b484a633b61f5f50bf81b34547bf327367d72236.jpg" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 446, + 156, + 514, + 164 + ], + "lines": [ + { + "bbox": [ + 446, + 156, + 514, + 164 + ], + "spans": [ + { + "bbox": [ + 446, + 156, + 514, + 164 + ], + "type": "text", + "content": "(b) Frequency v.s. " + }, + { + "bbox": [ + 446, + 156, + 514, + 164 + ], + "type": "inline_equation", + "content": "\\alpha" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_caption" + } + ], + "index": 31 + }, + { + "type": "image", + "bbox": [ + 322, + 219, + 381, + 275 + ], + "blocks": [ + { + "bbox": [ + 305, + 164, + 545, + 208 + ], + "lines": [ + { + "bbox": [ + 305, + 164, + 545, + 208 + ], + "spans": [ + { + "bbox": [ + 305, + 164, + 545, + 208 + ], + "type": "text", + "content": "Figure 8. From left to right: (a) The trend of ground-truth label confidence with changing transparency, where blue points denote the successful attack. (b) The frequency of successful attacks (RFLA-Triangle) with changing of transparency." + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 322, + 219, + 381, + 275 + ], + "lines": [ + { + "bbox": [ + 322, + 219, + 381, + 275 + ], + "spans": [ + { + "bbox": [ + 322, + 219, + 381, + 275 + ], + "type": "image", + "image_path": "2d41281fec03a6400f8c6429599e2b17ddba53d7c2c9d285debe0cd477d1bb76.jpg" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 276, + 545, + 308 + ], + "lines": [ + { + "bbox": [ + 305, + 276, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 305, + 276, + 545, + 308 + ], + "type": "text", + "content": "Figure 9. The confidence distribution of the ground-truth label on adversarial examples. Blue points denote the attack fail color tuple, while red points denote the attack success color tuple." + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "image_caption" + } + ], + "index": 34 + }, + { + "type": "image", + "bbox": [ + 400, + 219, + 460, + 275 + ], + "blocks": [ + { + "bbox": [ + 400, + 219, + 460, + 275 + ], + "lines": [ + { + "bbox": [ + 400, + 219, + 460, + 275 + ], + "spans": [ + { + "bbox": [ + 400, + 219, + 460, + 275 + ], + "type": "image", + "image_path": "144090df2b0ce29f84babc79eebdc0ee4bdb83e418e7a317fb9a72d23201322b.jpg" + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "image_body" + } + ], + "index": 35 + }, + { + "type": "image", + "bbox": [ + 478, + 219, + 538, + 275 + ], + "blocks": [ + { + "bbox": [ + 478, + 219, + 538, + 275 + ], + "lines": [ + { + "bbox": [ + 478, + 219, + 538, + 275 + ], + "spans": [ + { + "bbox": [ + 478, + 219, + 538, + 275 + ], + "type": "image", + "image_path": "316343832edbb4dda5f593d14746b5acead2fc955fa767d5352f5af036a2e7e6.jpg" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_body" + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 330, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 330, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 330, + 545, + 521 + ], + "type": "text", + "content": "parency " + }, + { + "bbox": [ + 304, + 330, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 330, + 545, + 521 + ], + "type": "text", + "content": " determined the cover intensity of the color. When " + }, + { + "bbox": [ + 304, + 330, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 330, + 545, + 521 + ], + "type": "text", + "content": " is set to one, the pixel value of the clean image at the specific position is substituted by the pure color, while the smaller value is the lower transparency of the color. We study how transparency changes the attack performance. Specifically, we fixed the other variables except for transparency, which traveled from [0,1] with a step size of 0.01. Figure 8 (a) illustrates the evaluation results of various geometries. As expectedly, the confidence of the ground-truth label decrease with enlarges of " + }, + { + "bbox": [ + 304, + 330, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 330, + 545, + 521 + ], + "type": "text", + "content": ". In contrast, the attack performance (represented in the number of blue points) rises with the increases in transparency, as more content of the clean image is covered due to deeper pure color. Moreover, we statistics the frequency of successful and failed attacks of the RFLA-Triangle on 100 test images, which is depicted in Figure 8 (b), consistent with the previous analysis." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": "Attack performance v.s. color. The pattern of adversarial perturbation is crucial for a successful attack. Unlike the previous works that optimize the pixel-wise perturbation, we focus on the channel-wise perturbation (perturb a channel with one value) as we must ensure the perturbation is physically realizable by reflecting the light. Furthermore, channel-wise perturbation is visually more acceptable than pixel-wise perturbation. Specifically, we select the color tuple set in intervals of 16 pixels across the three RGB channels to investigate how color influences the attack performance. Figure 9 illustrates the evaluation results. As we can observe, the success cases almost cluster in specific areas near the searched optimal color tuple when other variables are fixed. In other words, the optimal color tuple has certain robustness to a slight change of color, which makes our attacks can undertake some distortions when applied in" + } + ] + } + ], + "index": 39 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "type": "text", + "content": "4462" + } + ] + } + ], + "index": 40 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 72, + 124, + 134 + ], + "blocks": [ + { + "bbox": [ + 63, + 72, + 124, + 134 + ], + "lines": [ + { + "bbox": [ + 63, + 72, + 124, + 134 + ], + "spans": [ + { + "bbox": [ + 63, + 72, + 124, + 134 + ], + "type": "image", + "image_path": "a27d43e49ab23b40cba44a91801574a91c5982885cea7ac88d226b84443619a1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 89, + 137, + 99, + 145 + ], + "lines": [ + { + "bbox": [ + 89, + 137, + 99, + 145 + ], + "spans": [ + { + "bbox": [ + 89, + 137, + 99, + 145 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 126, + 72, + 186, + 133 + ], + "blocks": [ + { + "bbox": [ + 126, + 72, + 186, + 133 + ], + "lines": [ + { + "bbox": [ + 126, + 72, + 186, + 133 + ], + "spans": [ + { + "bbox": [ + 126, + 72, + 186, + 133 + ], + "type": "image", + "image_path": "d385084e00138a70f7fbd3d6196702a3225d7d697a048308186a71f43294a0dd.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 149, + 137, + 161, + 145 + ], + "lines": [ + { + "bbox": [ + 149, + 137, + 161, + 145 + ], + "spans": [ + { + "bbox": [ + 149, + 137, + 161, + 145 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 146, + 287, + 190 + ], + "lines": [ + { + "bbox": [ + 46, + 146, + 287, + 190 + ], + "spans": [ + { + "bbox": [ + 46, + 146, + 287, + 190 + ], + "type": "text", + "content": "Figure 10. From left to right: (a) Model attention on the clean image; (b) Adversarial examples; (c) Prediction confidence distribution of the clean image with the change of position, where blue points (the center of the circle) denote the successful attacks." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 191, + 76, + 260, + 132 + ], + "blocks": [ + { + "bbox": [ + 191, + 76, + 260, + 132 + ], + "lines": [ + { + "bbox": [ + 191, + 76, + 260, + 132 + ], + "spans": [ + { + "bbox": [ + 191, + 76, + 260, + 132 + ], + "type": "image", + "image_path": "ab45607ec9343a952d4819f477e7ec9a98ae5709b4e93d6d18bdf18d5dc08378.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 223, + 138, + 234, + 146 + ], + "lines": [ + { + "bbox": [ + 223, + 138, + 234, + 146 + ], + "spans": [ + { + "bbox": [ + 223, + 138, + 234, + 146 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 66, + 231, + 254, + 364 + ], + "blocks": [ + { + "bbox": [ + 66, + 231, + 254, + 364 + ], + "lines": [ + { + "bbox": [ + 66, + 231, + 254, + 364 + ], + "spans": [ + { + "bbox": [ + 66, + 231, + 254, + 364 + ], + "type": "image", + "image_path": "cf66136a93408cc410d4fa145a5723813a967c4041660b77403edc206db4930f.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 372, + 286, + 393 + ], + "lines": [ + { + "bbox": [ + 46, + 372, + 286, + 393 + ], + "spans": [ + { + "bbox": [ + 46, + 372, + 286, + 393 + ], + "type": "text", + "content": "Figure 11. Comparison result with RFLA and random search in terms of ASR." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 426, + 126, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 426, + 126, + 437 + ], + "spans": [ + { + "bbox": [ + 47, + 426, + 126, + 437 + ], + "type": "text", + "content": "the physical world." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 444, + 287, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 444, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 287, + 587 + ], + "type": "text", + "content": "Attack performance vs. position. To investigate the influence of the position of the adversarial perturbation to attack performance, we fixed the optimal variable except for position. Then, we sample the position in intervals of two steps. Furthermore, we also give the Grad-Cam for comparison. Figure 10 provides the evaluation results. As we can see, the adversarial geometry plotted around the content areas significantly drops the prediction confidence of the model on the clean image. Meanwhile, the attack success area is consistent with the model attention area, which indicates that our method can automatically locate the model attention areas to perform attacks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": "RFLA v.s. Random search. To investigate the effectiveness of the proposed algorithm, we use the proposed method to find the optimal triangle reflected light with white sunlight. For comparison, we conduct the random search algorithm under the same settings. The evaluation result is illustrated in Figure 11. As we can see, RFLA outperforms the random baseline significantly. Specifically, RFLA achieves the average ASR of " + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "inline_equation", + "content": "95.13\\%" + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": ", obtaining an improvement of " + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "inline_equation", + "content": "13.63\\%" + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": " than the random search (i.e., " + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "inline_equation", + "content": "81.5\\%" + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": "), which shows the effectiveness of our method." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 71, + 378, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 378, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 378, + 83 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 93, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 93, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 93, + 545, + 308 + ], + "type": "text", + "content": "In this paper, we propose a novel reflected light attack to realize effective and stealthy attacks in both digital and physical worlds, which may impose potential risks to automatic driving systems. Specifically, to explore how to control the reflected light's position, geometry, and pattern, we exploit the characteristic of the circle and propose a general framework based on the circle. To create a geometry, we first generate a specific number of angles to construct the point in circumference, followed by applying point symmetry against the center of a circle to generate a new point. These obtained points fence a geometrical shape where the fill color and transparency are optimized. Finally, we apply the PSO algorithm to find the best position, geometry, fill color, and transparency. Experiment results on digital and physical attacks verify the effectiveness of the proposed method. Moreover, our method can not only use sunlight but also can use flashlights to perform physical attacks for adapting to different environments." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 310, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 310, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 310, + 545, + 369 + ], + "type": "text", + "content": "Limitations. Though the reflected-light attack can perform in different environments, it is hard to remain effective in bad weather, such as fog and rain. A more penetrating light source (e.g., the traffic light and foglight) may work in such conditions." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 371, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 371, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 371, + 545, + 479 + ], + "type": "text", + "content": "Potential negative societal impact and mitigation. Similar to other types of attack, the adversarial attack is inevitable to cause potential security risks, especially for those physically deployed systems. However, we aim to arouse people's attention to such related applications and then encourage people to develop defense techniques to counter the reflected-light attack. To thwart the RFLA attack proposed in this paper, one can develop multimodal-based DNN systems." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 495, + 415, + 508 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 495, + 415, + 508 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 415, + 508 + ], + "type": "text", + "content": "6. Acknowledgments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 516, + 545, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 516, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 304, + 516, + 545, + 563 + ], + "type": "text", + "content": "The authors are grateful to the anonymous reviewers for their insightful comments. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15345-15354, 2022. 2, 3, 4" + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 734, + 315, + 742 + ], + "type": "text", + "content": "4465" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/RICO_ Regularizing the Unobservable for Indoor Compositional Reconstruction/9a248d4c-688f-46d5-8671-0975c0bef03f_content_list.json b/2023/RICO_ Regularizing the Unobservable for Indoor Compositional Reconstruction/9a248d4c-688f-46d5-8671-0975c0bef03f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..938a9b332a6ecd1bb541237d38990d220749d4d4 --- /dev/null +++ b/2023/RICO_ Regularizing the Unobservable for Indoor Compositional Reconstruction/9a248d4c-688f-46d5-8671-0975c0bef03f_content_list.json @@ -0,0 +1,1998 @@ +[ + { + "type": "text", + "text": "RICO: Regularizing the Unobservable for Indoor Compositional Reconstruction", + "text_level": 1, + "bbox": [ + 80, + 130, + 888, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zizhang Li $^{1}$ , Xiaoyang Lyu $^{2}$ , Yuanyuan Ding $^{1}$ , Mengmeng Wang $^{1}$ , Yiyi Liao $^{1*}$ , Yong Liu $^{1*}$ $^{1}$ Zhejiang University, $^{2}$ The University of Hong Kong", + "bbox": [ + 111, + 179, + 849, + 229 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 262, + 313, + 277 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, neural implicit surfaces have become popular for multi-view reconstruction. To facilitate practical applications like scene editing and manipulation, some works extend the framework with semantic masks input for the object-compositional reconstruction rather than the holistic perspective. Though achieving plausible disentanglement, the performance drops significantly when processing the indoor scenes where objects are usually partially observed. We propose RICO to address this by regularizing the unobservable regions for indoor compositional reconstruction. Our key idea is to first regularize the smoothness of the occluded background, which then in turn guides the foreground object reconstruction in unobservable regions based on the object-background relationship. Particularly, we regularize the geometry smoothness of occluded background patches. With the improved background surface, the signed distance function and the reversedly rendered depth of objects can be optimized to bound them within the background range. Extensive experiments show our method outperforms other methods on synthetic and real-world indoor scenes and prove the effectiveness of proposed regularizations. The code is available at https://github.com/kyleleey/RICO", + "bbox": [ + 75, + 295, + 473, + 643 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 671, + 209, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Reconstructing 3D geometry from images is a fundamental problem in computer vision and has many downstream applications like VR/AR and game assets creation. With the advance of neural implicit representations [20], recent reconstruction methods [25, 36, 41, 43] can recover accurate geometry from multi-view images. However, existing methods typically regard the whole scene as an entirety and reconstruct everything altogether, thus preventing applications like scene editing. In indoor scenes with plenty of reconfigurable objects, a disentangled object-compositional reconstruction, i.e. decomposing the geometry into different instantiated objects and background, can be more suitable", + "bbox": [ + 75, + 696, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/363124f5ae2b360c85afe7ca2a2ee00751a566213077d418f1450f1039a4a6eb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 261, + 883, + 414 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/892f31bbdde9e28a568301862d77543b832f9644b7c815734b87a1596128ecab.jpg", + "image_caption": [ + "Figure 1. Comparison of [37] (Top) and ours (Bottom). Different objects are visualized in different colors. Previous reconstructions are connected with large artifacts. Taking the partially observed cubic object's front and back views (in red and green rectangles respectively) as an example, [37] can only get the visible surface, while ours can complement the complete body." + ], + "image_footnote": [], + "bbox": [ + 522, + 415, + 883, + 563 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "for further applications like moving the sofa in the scene.", + "bbox": [ + 500, + 688, + 877, + 703 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we aim to recover the room-level indoor scenes with decomposed geometry of individual objects and background. We assume that multi-view posed images and semantic masks that assign different labels to each instantiated object and the background are given as input. Existing object-compositional methods [9, 45, 40] concentrate more on the rendering performance rather than the underlying geometry, and thus can not be directly used for reconstruction. The most recent work ObjSDF [37] learns an object-compositional signed distance function (SDF) field by proposing a transform function between SDF values and semantic logits. Specifically speaking, ObjSDF predicts multiple SDF values at each 3D point for different seman", + "bbox": [ + 496, + 704, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding authors.", + "bbox": [ + 94, + 887, + 228, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17761", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tic classes, and converts them to semantic logits, allowing for separating object SDF values from the background when supervised by semantic masks. Although achieving plausible shape disentanglement, it suffers from a common problem in indoor scenes: objects and background can only be partially observed due to occlusions. When the object is partially observed, e.g. a cubic object against the wall, ObjSDF can not properly reconstruct the geometry between them (see Fig. 1 top-right). The reason is that the existing works [45, 37] can only effectively regularize semantic labels and geometry of observed regions, and have little impact on the unobserved regions. When processing the indoor scenes where a large portion of objects are partially observed, the reconstruction results of these objects will be visible surface connected with the unconstrained structures (as shown in Fig. 1, see Section 3.3 for a detailed analysis). Fig. 2 shows that even with reasonable reconstruction when composing all the objects together, each object's result in the unobserved region is far from satisfactory and can hinder further applications like manipulating the object.", + "bbox": [ + 75, + 90, + 472, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We propose RICO, which realizes the proper geometry disentanglement for indoor scenes (see Fig. 1 bottom) by explicitly regularizing the unobserved regions. To be more specific, when the object is partially observed, recovering its geometry is an ill-posed problem even with corresponding masks. Thus, introducing prior regularization for unobserved regions is necessary. We exploit two types of prior knowledge for indoor scenes in this work: 1) background smoothness and 2) object-background relations. First, when one ray hits the object surface, the existing method [37] can properly regularize the geometry and appearance on the hitting point, but can not account for the background surface behind this object. This drawback leads to artifacts and holes on the unobserved background surface (see Fig. 2). We propose a patch-based smoothness loss to regularize the SDF values of unobserved background regions. Then, since the background reconstruction is improved, we can leverage another strong prior: the objects are all within the room, i.e. using the background surface to regularize the SDF field of objects. We design two regularization terms: an object point-SDF loss for sampled points behind the background surface and a reversed depth loss to regularize the SDF distribution of the entire ray. Both terms aim to bound the object within the background surface's range, thus preventing the aforementioned unmeaning structure, making the object reconstruction a watertight and plausible shape instead of an open surface with severe artifacts.", + "bbox": [ + 75, + 397, + 472, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, we propose RICO to realize compositional reconstruction in indoor scenes where a large portion of objects are partially observed. Our main contributions are: i) A patch-based background smoothness regularizer for unobserved background surface geometry. ii) Guided by the improved background surface, we exploit the object-", + "bbox": [ + 75, + 810, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/cd75785997efa7f925afd81f2cb9042b67fce0bdedb4f4024dc7b06c24fb6dff.jpg", + "image_caption": [ + "Figure 2. ObjSDF results. Interested objects are dyed in blue. Despite of the plausible composition, the disentangled backgrounds have artifacts and sunk holes, and partially observed objects can only get the visible surface (illustrated in 'Object Backward')." + ], + "image_footnote": [], + "bbox": [ + 506, + 90, + 883, + 244 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "background relation as prior knowledge and design objectives that effectively regularize objects' unobserved regions. iii) Extensive experiments on both real-world and synthetic datasets prove our superior reconstruction performance compared to previous works, especially for the partially observed objects.", + "bbox": [ + 496, + 335, + 893, + 429 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 441, + 640, + 458 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Implicit Representation for Reconstruction: Recently, neural implicit representations have emerged as a popular representation for 3D reconstruction. While early approaches [19, 26] rely on 3D supervision, a few works [24, 42] exploit surface rendering to use multi-view image supervision only, but also suffer from the unstable training. Neural radiance field (NeRF) [20] adopts volume rendering technique to achieve photorealistic scene representation and stable optimization. However, NeRF's formulation can not guarantee accurate underlying geometry. Therefore, [25, 36, 41] combine the geometry representation with iso-surface (e.g. occupancy [19], SDF [36, 41]) and volume density to accurately reconstruct object-level scenes from RGB images. [8] further applies the planar regularization for scene-level reconstruction. To tackle the problem in texture-less regions, [35, 43] utilize results from pretrained normal and depth estimation networks to guide the SDF training and boost the reconstruction performance.", + "bbox": [ + 496, + 472, + 890, + 743 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, despite the promising reconstruction performance, the aforementioned methods all consider the whole scene as an entirety. Our method focuses on decomposing the scene reconstruction into the background and different foreground objects, which can be regarded as compositional scene reconstruction.", + "bbox": [ + 496, + 744, + 893, + 835 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Compositional Scene Reconstruction: Decomposing a scene into its different components could benefit downstream applications like scene editing. Many works have been proposed to recover the scene in a compositional man", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17762", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b72291283a923880577c0df11df758eb200167fc4546dde72e95123639f5181b.jpg", + "image_caption": [ + "Figure 3. Overview. In this work, we propose two different regularizations. We first regularize the geometry smoothness of the unobserved background regions in a sampled patch. Then, we exploit the background surface as the prior to constrain the objects' surface. In detail, a per-point SDF loss and a reversed depth loss are introduced to regularize the manifold of objects' SDF functions. Combined with other reconstruction losses, our method reaches a neat and disentangled compositional reconstruction in indoor scenes." + ], + "image_footnote": [], + "bbox": [ + 98, + 85, + 867, + 324 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ner from different perspectives. [22, 44, 10, 21] detect and reconstruct different objects in the given monocular image, and predict the scene's layout at the same time. But most of these methods require large-scale datasets with 3D ground truth for training. [14, 32, 18] optimize a feature field from a large pretrained model [1, 16], which enables deep feature based decomposition and manipulation. [38, 31] exploit the self-supervise paradigm to decompose the scenes into static and dynamic parts. More works [9, 45, 40, 39, 34, 6, 15, 33] focus on recovering the object-compositional scenes given semantic masks with images. However, this line of works concerns the rendering outputs rather than the geometry, i.e. the reconstruction results are sub-optimal.", + "bbox": [ + 75, + 417, + 470, + 614 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, ObjSDF [37] proposes a transform function between semantic logits and SDFs of different objects, which enables optimizing SDF fields with image and semantic mask supervision, and decomposing the whole scene with accurate reconstruction. However, in the indoor scenes where many objects are in partial observation, its reconstruction results are far from satisfactory and can not be used for further applications (see Fig. 2). On the contrary, our method introduces geometry prior to unobserved regions, yielding better compositional scene reconstruction.", + "bbox": [ + 75, + 618, + 468, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Prior Regularization in Neural Implicit Reconstruction: In addition to the commonly used RGB image supervision, many different priors have been proposed to benefit the neural implicit representation. For example, [4, 30] use explicit point cloud as the depth prior, [23] employs regularization in unseen views and [11] introduces pretrained model's feature consistency. [12, 28] adopt explicit human model as the structural prior for the human-centric scenes. As for surface", + "bbox": [ + 75, + 780, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "reconstruction, [8] proposes a Manhattan-world assumption for the planar regions, [43] utilizes the normal and depth prediction from off-the-shelf model [5] as prior to regularize the texture-less regions.", + "bbox": [ + 496, + 417, + 890, + 478 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method exploits the geometry prior in the unobserved region for compositional scene reconstruction. The proposed regularization can effectively reconstruct the objects and disentangle them from the background, even if the object itself is partially observed.", + "bbox": [ + 496, + 479, + 892, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 573, + 635, + 590 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to recover decomposed geometry surface of the objects and background within a scene from the images and semantic masks inputs. To this end, we first review the SDF-based neural implicit representation and how to use the semantic logits for compositional reconstruction in Section 3.1. Next, we propose two types of regularizations on unobserved regions to address the partial observation problem: patch-based background smoothness (Section 3.2) and object-background relation (Section 3.3). Finally, we introduce the overall optimization procedure in Section 3.4. An overview of our method is provided in Fig 3.", + "bbox": [ + 496, + 599, + 893, + 767 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Background", + "text_level": 1, + "bbox": [ + 500, + 780, + 632, + 797 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Volume Rendering of SDF-based Implicit Surface: For implicit reconstruction, the geometry of the scene is represented as the signed distance function (SDF) $s(\\mathbf{p})$ of each spatial point $\\mathbf{p}$ , which is the point's distance to the closest surface. In practice, the SDF function is implemented as a multi-layer perceptron (MLP) network $f(\\cdot)$ . The appear-", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17763", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ance of the scene is also defined as an MLP $g(\\cdot)$ ..", + "bbox": [ + 76, + 90, + 400, + 107 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} f: \\mathbf {p} \\in \\mathbb {R} ^ {3} \\mapsto (s \\in \\mathbb {R}, \\mathbf {f} \\in \\mathbb {R} ^ {2 5 6}) \\\\ g: (\\mathbf {p} \\in \\mathbb {R} ^ {3}, \\mathbf {n} \\in \\mathbb {R} ^ {3}, \\mathbf {v} \\in \\mathbb {S} ^ {2}, \\mathbf {f} \\in \\mathbb {R} ^ {2 5 6}) \\mapsto \\mathbf {c} \\in \\mathbb {R} ^ {3} \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 114, + 468, + 154 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{f}$ is a geometry feature vector, $\\mathbf{n}$ is the normal at $\\mathbf{p}$ , $\\mathbf{v}$ is the viewing direction and $\\mathbf{c}$ is the view-dependent color. We adopt the unbiased rendering proposed in [36] to render the image. For each camera ray $\\mathbf{r} = (\\mathbf{o},\\mathbf{v})$ with $\\mathbf{o}$ as the ray origin, $n$ points $\\{\\mathbf{p}(t_i) = \\mathbf{o} + t_i\\mathbf{v}|i = 0,1,\\dots ,n - 1\\}$ are sampled, and the pixel color can be approximated as:", + "bbox": [ + 76, + 165, + 468, + 255 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {C}} (\\mathbf {r}) = \\sum_ {i = 0} ^ {n - 1} T _ {i} \\alpha_ {i} \\mathbf {c} _ {i}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 266, + 468, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The $T_{i}$ is the discrete accumulated transmittance derived from $T_{i} = \\prod_{j=0}^{i-1}(1 - \\alpha_{j})$ , and $\\alpha_{i}$ is the discrete density value defined as", + "bbox": [ + 76, + 316, + 468, + 361 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {i} = \\max \\left(\\frac {\\Phi_ {u} (s (\\mathbf {p} (t _ {i}))) - \\Phi_ {u} (s (\\mathbf {p} (t _ {i + 1})))}{\\Phi_ {u} (s (\\mathbf {p} (t _ {i})))}, 0\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 93, + 369, + 468, + 404 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Phi_u(x) = (1 + e^{-ux})^{-1}$ and $u$ is a learnable parameter. By minimizing the difference between predicted and ground-truth pixel colors, we can learn the SDF and appearance function of the desired scene.", + "bbox": [ + 76, + 412, + 468, + 473 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning SDF with Semantic Logits: In this work, we consider compositional reconstruction of $k$ objects given their masks. Note that we also consider the background as an instantiated object for brevity as in [37] and follow their network structure. In detail, for a scene with $k$ objects, the SDF MLP $f(\\cdot)$ now outputs $k$ SDFs at each point, and the $j$ -th $(1 \\leq j \\leq k)$ SDF represents the geometry of $j$ -th object. Without loss of generality, we set $j = 1$ as the background category and others for objects in Fig. 3 and the rest of the paper. The scene SDF is the minimum of $\\{s_j\\}$ , which is used for sampling points along the ray and aforementioned volume rendering (Eq. 2). Moreover, each point's $k$ SDFs can be transformed into semantic logits $\\mathbf{h}(\\mathbf{p})$ as", + "bbox": [ + 76, + 479, + 468, + 676 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\begin{array}{l} h _ {j} (\\mathbf {p}) = \\gamma / (1 + \\exp (\\gamma \\cdot s _ {j} (\\mathbf {p}))), \\\\ \\mathbf {p} (.) = [ 1, (.) ] \\end{array} \\tag {4} \\\\ \\mathbf {h} (\\mathbf {p}) = \\left[ h _ {1} (\\mathbf {p}), h _ {2} (\\mathbf {p}), \\dots , h _ {k} (\\mathbf {p}) \\right], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 686, + 468, + 722 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\gamma$ is a fixed parameter. Using volume rendering to accumulate the semantic logits of all the points along a ray, we can get the semantic logits $\\mathbf{H}(\\mathbf{r})\\in \\mathbb{R}^k$ of each pixel. During training, the cross-entropy loss applied to $\\mathbf{H}(\\mathbf{r})$ is backpropagated to the SDF values, allowing for learning the compositional geometry.", + "bbox": [ + 76, + 732, + 468, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Patch-based Background Smoothness", + "text_level": 1, + "bbox": [ + 76, + 832, + 401, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although the volume rendering can propagate gradients along the entire ray, the optimization mainly focuses on the surface-hitting point, as its accumulated weight can be", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "much larger than the others. As a result, the geometry of the points behind the first-hit surface can not be optimized correctly. In the indoor scenes, the occluded part of the background surface is invisible in all the images, which can be with holes and random artifacts (see Fig. 2).", + "bbox": [ + 496, + 90, + 890, + 166 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since we cannot tell the exact color, depth or normal of the occluded part, it is intractable to optimize this region wrt. its ground truth. Therefore, we propose to regularize the geometry of the occluded background to be smooth, thus preventing some clearly wrong artifacts.", + "bbox": [ + 496, + 167, + 890, + 241 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In detail, we regularize the smoothness of rendered depth and normal of background surface within a small patch region. To save the computation budget, we randomly sample a $\\mathcal{P} \\times \\mathcal{P}$ size patch every $\\mathcal{T}_{\\mathcal{P}}$ iterations in the given image and sample points along the patch rays using the background SDF only. We compute depth map $\\hat{D}(\\mathbf{r})$ and normal map $\\hat{N}(\\mathbf{r})$ of the sampled patch following [43], $\\mathbf{r}$ denotes the sampled ray in patch. The semantic map of the patch is also computed and transformed into a patch Mask $\\hat{M}(\\mathbf{r})$ :", + "bbox": [ + 496, + 242, + 890, + 378 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {M} (\\mathbf {r}) = \\mathbb {1} [ \\arg \\max (\\mathbf {H} (\\mathbf {r})) \\neq 1 ], \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 387, + 890, + 405 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which means the mask value is 1 if the rendered class is not the background, so that only the occluded background is regularized. Taking rendered depth as an example, the patch-based background smoothness loss is", + "bbox": [ + 496, + 414, + 890, + 474 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} (\\hat {D}) = \\sum_ {d = 0} ^ {3} \\sum_ {m, n = 0} ^ {\\mathcal {P} - 1 - 2 ^ {d}} \\hat {M} \\left(\\mathbf {r} _ {m, n}\\right) \\odot (| \\hat {D} \\left(\\mathbf {r} _ {m, n}\\right) - \\tag {6} \\\\ \\hat {D} \\left(\\mathbf {r} _ {m, n + 2 ^ {d}}\\right) | + | \\hat {D} (\\mathbf {r} _ {m, n}) - \\hat {D} \\left(\\mathbf {r} _ {m + 2 ^ {d}, n}\\right) |\\left. \\right). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 484, + 890, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here the smoothness is applied on different intervals controlled by $d$ . $m$ and $n$ are the pixel indices within the patch and the mask is multiplied at each position with hadamard product $\\odot$ . The normal smoothness loss $\\mathcal{L}(\\hat{N})$ can be obtained similarly. We define the overall background smoothness loss $\\mathcal{L}_{bs}$ as:", + "bbox": [ + 496, + 560, + 890, + 650 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {b s}} = \\mathcal {L} (\\hat {D}) + \\mathcal {L} (\\hat {N}). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 659, + 890, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here in contrast to [23] which applies a patch-based regularization to visible regions in other views, we instead regularize the occluded regions of the background.", + "bbox": [ + 496, + 686, + 890, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Object-background Relation as Regularization", + "text_level": 1, + "bbox": [ + 500, + 741, + 890, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With the help of the patch-based background smoothness loss, most artifacts of the background are resolved, yielding a smooth surface. We further leverage this smooth background surface to regularize the SDF fields of other objects, leveraging a key prior knowledge that all the other objects are confined to the room, i.e., the background surface.", + "bbox": [ + 496, + 763, + 890, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the original framework of [37], if an object is partially observed, e.g. against the background, the object's reconstructed surface won't be a \"closed\" surface (see Fig. 1 and", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17764", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1197c88105231b5d4c8de329e887c8d3b41bfefb9fa3b462786546145bf3b2aa.jpg", + "image_caption": [ + "Figure 4. Toy-case analysis. A bird-eye view of an object against the background is shown here, the SDF and surface of object is shown in red and background's in blue. (a) In [37] the minimum SDF is used for volume rendering and semantic loss, so on object's visible surface where object SDF is optimized to 0 and the background SDF here is positive, and similar for the visible background surface. Since the scene is partially observed from left, the right part of object surface is open and unobserved background region is unconstrained. (b) With the smoothness prior the background surface can be plausible, (c) and object point SDF loss close the object surface but still have intersections, (d) finally the reversed depth loss optimizes the entire ray thus the object can be within the background." + ], + "image_footnote": [], + "bbox": [ + 86, + 85, + 450, + 296 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fig. 2). We refer to the toy-case analysis shown in Fig. 4 for the reason of the current unsatisfactory reconstruction. To encourage the reconstruction to be watertight, we design two types of regularization on the SDF fields of objects.", + "bbox": [ + 75, + 516, + 468, + 578 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Object Point-SDF Loss: A straightforward solution is to directly regularize the objects' SDFs on every sampled point behind the background surface. To be more specific, the regular volume rendering only guarantees a single change of the sign (positive SDF to negative) when a ray hits a visible surface. For watertight objects, the ray should hit another occluded surface (negative SDF to positive). With the prior that the object is confined within the room, the occluded object surface should be closer than the background surface, meaning that the object SDFs of points behind the background surface should all be positive (Fig. 4 (c)).", + "bbox": [ + 75, + 582, + 468, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We implement an object point-SDF loss based on the above analysis. For the sampled points along the rays, we first utilize the root-finding algorithm among the background SDF of these points and find the zero-SDF ray depth $t'$ . Then the object point-SDF loss can be formulated as", + "bbox": [ + 76, + 750, + 470, + 825 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {o p}} = \\frac {1}{k - 1} \\sum_ {j = 2} ^ {k} \\max \\left(0, \\epsilon - \\mathbf {s} _ {j} (\\mathbf {p} (t _ {i}))\\right) \\cdot \\mathbb {1} [ t _ {i} > t ^ {\\prime} ], \\quad (8)\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 834, + 468, + 877 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which pushes the objects' SDFs at points behind the surface", + "bbox": [ + 76, + 885, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "larger than a positive threshold $\\epsilon$ .", + "bbox": [ + 500, + 90, + 720, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Reversed Depth Loss: Although the $\\mathcal{L}_{\\mathrm{op}}$ can effectively regularize the SDF fields of each object, in practice we find the reconstructed object surface can still have intersections with the background surface (Fig. 4 (c)). The reason is that the sampled points are discrete and in most cases, the background surface is between two sampled points. Therefore, the sign change of the occluded surface may still occur after hitting the background surface.", + "bbox": [ + 496, + 109, + 893, + 232 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since per-point optimization can not effectively propagate to the distribution of the entire ray. To optimize the entire ray's SDF distribution for better regularization, we compute a reversed depth along each ray. With the help of $\\mathcal{L}_{\\mathrm{op}}$ , the sign of the object SDF along one ray now is positive-negative-positive, which enables rendering a depth value backward. We first transform the ray depth $\\{t_i|i = 0,1,\\dots ,n - 1\\}$ into the reversed ray depth named $\\{\\hat{t}_i|i = 0,1,\\dots ,n - 1\\}$ , where", + "bbox": [ + 496, + 232, + 892, + 368 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {t} _ {i} = \\left(t _ {0} + t _ {n - 1}\\right) - t _ {n - 1 - i}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 601, + 373, + 890, + 390 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the reversed ray depth values, we use the background and object SDF both in reversed order to compute the accumulated weight and get the reversed depth respectively. Remarkably, in order to compute the exact correct depth, the points should be re-sampled along the reverse direction. Here we directly use the sampled points to avoid computation overhead, and empirical results prove its effectiveness. We only compute the reverse depth of one pixel if satisfying two conditions: 1) this pixel's $\\hat{M}(\\mathbf{r}) = 1$ ; 2) the SDF value of the rendered object at the furthest point is positive. Note that the second condition is usually satisfied when the object point-SDF loss is applied. By computing the reversed depth $d_{o}$ of the hitting object (determined by the pixel's rendered semantic) and $d_{b}$ of the background, we can get the reversed depth loss:", + "bbox": [ + 496, + 396, + 892, + 623 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {r d}} = \\max \\left(0, d _ {b} - d _ {o}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 628, + 890, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which pushes the object surface within the background as illustrated in Fig. 4 (d).", + "bbox": [ + 496, + 650, + 890, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training Objectives Details", + "text_level": 1, + "bbox": [ + 500, + 686, + 746, + 704 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Monocular geometric cues are essential for indoor scene reconstruction as proved in [43]. Following [43], we add the depth and normal consistency loss $(\\mathcal{L}_{\\mathrm{D}},\\mathcal{L}_{\\mathrm{N}})$ with pseudo ground truth from Omnidata [5] model. In experiments, we also add the monocular cues on [37] to get a stronger baseline for a fair comparison.", + "bbox": [ + 496, + 710, + 890, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The SDF network is also regularized by an Eikonal [7] loss item $\\mathcal{L}_{\\mathrm{E}}$ . We further use the semantic loss $\\mathcal{L}_{\\mathrm{S}}$ proposed in [37] to learn the compositional geometry. The overall loss function for compositional reconstruction is:", + "bbox": [ + 496, + 801, + 890, + 862 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\mathrm {R G B}} + \\lambda_ {\\mathrm {D}} \\mathcal {L} _ {\\mathrm {D}} + \\lambda_ {\\mathrm {N}} \\mathcal {L} _ {\\mathrm {N}} + \\lambda_ {\\mathrm {E}} \\mathcal {L} _ {\\mathrm {E}} + \\lambda_ {\\mathrm {S}} \\mathcal {L} _ {\\mathrm {S}} \\tag {11} \\\\ + \\lambda_ {\\mathrm {b s}} \\mathcal {L} _ {\\mathrm {b s}} + \\lambda_ {\\mathrm {o p}} \\mathcal {L} _ {\\mathrm {o p}} + \\lambda_ {\\mathrm {r d}} \\mathcal {L} _ {\\mathrm {r d}}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 867, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17765", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We set $\\lambda_{\\mathrm{bs}}, \\lambda_{\\mathrm{op}}, \\lambda_{\\mathrm{rd}} = 0.1$ in our experiments. For other loss terms, given the weight of RGB reconstruction loss as 1, we set $\\lambda_{\\mathrm{D}} = 0.1$ and $\\lambda_{\\mathrm{N}} = \\lambda_{\\mathrm{E}} = 0.05$ following [43]. For the semantic loss, we follow the implementation in [37] and set $\\lambda_{\\mathrm{D}} = 0.04$ . The detailed calculation of other losses can be found in supplementary.", + "bbox": [ + 76, + 90, + 472, + 183 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 195, + 210, + 212 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first conduct ablation study on each proposed component. Then we provide quantitative and qualitative results of object-compositional reconstruction on real-world and synthetic scenes. Finally, we show some possible object manipulation with our compositional reconstruction.", + "bbox": [ + 75, + 220, + 468, + 297 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets: We consider three types of indoor datasets with multi-view RGB images and masks: 1) ScanNet [3], a real-world dataset widely used in previous works [8, 35, 37, 43]; 2) ToyDesk dataset, a real-world dataset with two scenes and each has four objects placed on the table plane. This dataset has also been widely used in previous compositional works [40, 37] 3) a hand-crafted synthetic dataset with five scenes, each containing $5 \\sim 10$ objects. The synthetic dataset is considered such that the ground truth geometry of both, occluded and non-occluded regions are available.", + "bbox": [ + 75, + 301, + 470, + 452 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics: For reconstruction performance, we report Chamfer Distance, F-score for evaluation on ScanNet, following [8, 43]. On synthetic scenes we divide metrics for two aspects: objects and background. For objects we report the reconstruction performance compared to the complete ground truth object mesh, and the final results are averaged across all the objects in all the scenes. For background we report the reconstruction metrics and rendered depth errors of the occluded regions only to highlight the effectiveness of our regularization. The results are also averaged across all the scenes. See supplementary for a detailed introduction to datasets and metrics. We also report two 2D metrics, PSNR and mIoU, on the ToyDesk and ScanNet scenes. Here we omit the synthetic dataset considering its relatively simple texture. For the test image set, on ToyDesk dataset we use the official split, and on ScanNet we sample frames from their original camera trajectories. The metrics are averaged across different images of different scenes.", + "bbox": [ + 75, + 457, + 470, + 729 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines: We mainly compare with ObjSDF [37] in this work, as it is the only method that focuses on the same task, a specific discussion is provided in the supplementary. Since we focus on the indoor scene where monocular cues can benefit a lot [43], we add losses proposed in [43] to our method for better performance. For a fair comparison, we also combine [37] and [43] for a stronger baseline, named ObjSDF*. Moreover, since ObjSDF*’s object reconstructions inevitably have artifacts, we develop a postprocess method to cull the parts outside the background range and name this baseline ObjSDF*-C. We provide the", + "bbox": [ + 75, + 734, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8be90f091193a28a1bd84740061f197622c5d8c3210a967e50ae9102ded83a20.jpg", + "image_caption": [ + "Figure 5. Effects of Regularizations. The first row shows two backgrounds, the $\\mathcal{L}_{\\mathrm{bs}}$ clearly mitigates most of the artifacts. The last row shows that with $\\mathcal{L}_{\\mathrm{op}}$ we can get the watertight object and $\\mathcal{L}_{\\mathrm{rd}}$ further constrains the unobserved surface." + ], + "image_footnote": [], + "bbox": [ + 521, + 88, + 870, + 224 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "details of how to set the range in the supplementary. Note that our method directly generates clean watertight meshes and doesn't need such post-processing. In ScanNet experiments, we also report results for MonoSDF [43] as a reference since we can only evaluate the overall reconstruction (details in Section 4.3).", + "bbox": [ + 496, + 319, + 890, + 411 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details: We implement our method in PyTorch [27]. We use the Adam [13] optimizer with a learning rate of 5e-4 for 50k iterations and sample 1024 rays per iteration. The weight initialization scheme for SDF MLP is identical to [41, 36, 37]. The $u$ is initialized as 0.05 and we set $\\gamma = 20$ as proposed in [37]. $\\mathcal{P}$ , $\\mathcal{T}_{\\mathcal{P}}$ and $\\epsilon$ are set as 32, 10 and 0.05 respectively. All the reconstructions are acquired by using marching cube [17] at the resolution of 512.", + "bbox": [ + 496, + 415, + 892, + 536 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Moreover, we adopt the geometric initialization [7] for the geometry network, which initializes the reconstruction with a unit sphere and the surface normals are facing inside at the beginning of the optimization. For the ScanNet dataset, we follow the protocol in [43] to crop the input image to $384 \\times 384$ and adjust the intrinsics accordingly. For the synthetic dataset, we directly render the image at the same resolution. Since we focus on the indoor scenes in this paper, we adopt the common practice to process the \"bounded\" scene. For each scene, we normalize the camera poses so that all the cameras lie in a unit sphere. The rays intersection, i.e. the furthest sampling location, is computed based on this sphere and we also conduct Marching Cubes [17] within the same area for the final reconstruction.", + "bbox": [ + 496, + 537, + 893, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 756, + 653, + 772 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first quantitatively analyze the effectiveness of the proposed regularizations on synthetic scenes by comparing our full method to four variants in Tab. 1. First, adding the smoothness loss (V2) significantly decreases the depth error of occluded background regions. Next, the $\\mathcal{L}_{\\mathrm{op}}$ makes the object reconstruction watertight and the object-level metrics are greatly improved (V3). The $\\mathcal{L}_{\\mathrm{rd}}$ further improves the object reconstruction performance (Full). Results of V4 prove", + "bbox": [ + 496, + 779, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17766", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/98b5ebb6ab51af2e72435b447d56b2ff4bdb7d9ec54adb66921b989ccf47524e.jpg", + "image_caption": [ + "ObjSDF" + ], + "image_footnote": [], + "bbox": [ + 101, + 98, + 285, + 166 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b878686d54219a3f49abae12ac2b97c5df17047c31b1a4c6e7d1f74e2c5f04d4.jpg", + "image_caption": [ + "ObjSDF*" + ], + "image_footnote": [], + "bbox": [ + 297, + 98, + 480, + 167 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/663c0da969b18e7a84b7e8620f07d86a27cea434e771445a7a663930fd8d9eb9.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 491, + 98, + 673, + 167 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fda326be0808fb2cb22717cb189e6c213dddd651be38467e56ddfa46971a14bc.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 684, + 98, + 774, + 167 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/646374c948a90d7b869901439be331fc98c230e4bcdf48bf7f4c23fac18f19cd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 777, + 98, + 864, + 167 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/36095fbbc845631d7844521c339f08be34d24d5c9dad304a29067163e9b7096b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 98, + 196, + 282, + 277 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/45aeb756c6bc6207b4cf11456e08a174f133318c1e6761bc3cc76954c21c7da4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 101, + 277, + 282, + 319 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4d78525bbf8976f0ed2ce38f1357471fb89a40a08ed8920c51593e3e8f239286.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 204, + 480, + 319 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/062d8fc40fdd76808ab421abe972cbbbf7a55d7eec354699886ffec338749fb3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 204, + 674, + 319 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8b6a98c45f6d0932ef60164e2593d0f3930df1cc4d784209752d80f9aba6a5f2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 204, + 870, + 319 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/27d9cce436b0167bf77ec6c7587bb07d4dc2329d4fd0a788494d73f1a2be331e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 101, + 325, + 282, + 407 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c3e120a6b05231b2cb8d2145666bd443c86b31b4d7f257b5236563876caa1171.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 101, + 407, + 282, + 448 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/350efbd0d53781870cc086ed1a30febce2cf59202458cd25d5699e6159184621.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 335, + 478, + 449 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fda0c6112815a274759db63926206cf8408fa8a89d6c8cd5adf318833e8bcd10.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 335, + 674, + 449 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/18790fc8024a2746c51d937fc92fec8289db44a78421bbe021c3f80585e761b8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 335, + 870, + 449 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e8c47d26bb8357e34628e23c648f935efca6ed74ba67da79b1a5c19fe4ada79b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 101, + 450, + 282, + 531 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/981b928025d74b595b0ff2c4e17f6ebef687ed3c3e0e1b1a1dd6d715bb3033b8.jpg", + "image_caption": [ + "ObjSDF*" + ], + "image_footnote": [], + "bbox": [ + 101, + 532, + 282, + 573 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ac4064f45b56cbfa5ced7158cd74ba295ead14328ec4036ff77b3a3c96a0126c.jpg", + "image_caption": [ + "ObjSDF*-C" + ], + "image_footnote": [], + "bbox": [ + 295, + 460, + 478, + 573 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/577c32901b308d80eb51a26a30a99d7cff17f45c6606e7312695905177f35489.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 491, + 460, + 674, + 573 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/546666e584f0549f1a2594c3e4934fbed47389f3d3c067297121d8f3d626e8b3.jpg", + "image_caption": [ + "GT", + "Figure 6. Qualitative Results on Synthetic Scenes. Above the blue line we show the comparison of different methods on two background scenes. Below we provide results of two scenes where only the object results are shown. In red rectangles at the bottom of each picture, we show the back (left part) and front (right part) views of an example object. Detailed descriptions in Section 4.2." + ], + "image_footnote": [], + "bbox": [ + 686, + 460, + 870, + 573 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0777a375ec01635cc3ea1b98be134b07892c78d47ae5b4abf0b8771d219d95d6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
BackgroundObject
LbsLopLrdD.↓C.↓F.↑C.↓F.↑
V1---0.0210.0450.7681.240.065
V2✓--0.0040.0090.991.250.066
V3✓✓-0.0030.0090.990.0450.735
V4-✓✓0.0150.0290.8880.0390.785
Full✓✓✓0.0030.0090.990.0330.817
", + "bbox": [ + 78, + 672, + 460, + 785 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "that without $\\mathcal{L}_{\\mathrm{bs}}$ to improve the background, the object re", + "bbox": [ + 76, + 885, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b8a3df5bb4084c316e451e4aa9bbcbfa742f0e32602fb75c51351a954b5210e1.jpg", + "table_caption": [ + "Table 1. Ablation Study. The D. denotes the depth error of the occluded background. The C. and F. mean the Chamfer- $L_{1}$ and F-score respectively, for the reconstruction of occluded background regions and full complete objects. Details in Section 4.1." + ], + "table_footnote": [], + "table_body": "
BackgroundObjects
D.↓C.↓F.↑C.↓F.↑
ObjSDF0.0330.0760.6691.0400.084
ObjSDF*0.0210.0440.7721.0300.085
ObjSDF*-C0.0210.0440.7720.1340.681
Ours0.0030.0090.9900.0330.817
", + "bbox": [ + 500, + 672, + 880, + 768 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Synthetic Scenes Reconstruction Quantitative Results. The D. C. and F. have the same meanings as in Tab. 1.", + "bbox": [ + 498, + 777, + 890, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "construction quality also drops. Note that $\\mathcal{L}_{\\mathrm{rd}}$ needs to be applied jointly with $\\mathcal{L}_{\\mathrm{op}}$ to guarantee its second condition.", + "bbox": [ + 498, + 837, + 890, + 867 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "A qualitative case is shown in Fig. 5 for better illustration. In the first row, the occluded part of the background", + "bbox": [ + 498, + 869, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17767", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cb7f2718715fc2a664165b459a3013415e8443565fb897e3f1affa4851d96945.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 98, + 90, + 277, + 170 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/874f6c0812581415957cd6b0ae8fde13fac9d5fba19fcc33a95abcf3c4e9618a.jpg", + "image_caption": [ + "MonoSDF" + ], + "image_footnote": [], + "bbox": [ + 96, + 215, + 272, + 295 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f3ba0e8f513ec3c6917ea4b4563a69261d78144abd7160b75c05554615bae46f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 313, + 90, + 493, + 167 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e062d16d96920772da9475e00319ccf8c3bc58f03f7aaca5f8ad76bb8dfdd304.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 315, + 170, + 491, + 209 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d07266c13f534f6e9b21cc65e7f5ef800c85d3a48490f3e501b20e996ead8ff1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 316, + 215, + 491, + 295 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d5b89d778eea6245591442f5a36b87146f80d40806019b25bbd0ce53fd9f61e7.jpg", + "image_caption": [ + "ObjSDF*", + "Figure 7. Qualitative Results on ScanNet [3]. On the left of blue line we show the overall reconstruction from [43] as the reference. On the right we show the comparison between our method and two baselines. Similarly, the back and front views of objects with partial observations are provided in red rectangles. Detailed descriptions in Section 4.3." + ], + "image_footnote": [], + "bbox": [ + 316, + 296, + 491, + 335 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ea21c52063173b9fcebf2f67ee32b6c41d96c056b1767301dcefc0f88b8c3a2b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 90, + 679, + 209 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a947811aab529bfe5960a944e87026d8d49644dd69d4302040ba3b061146d7b8.jpg", + "image_caption": [ + "ObjSDF*-C" + ], + "image_footnote": [], + "bbox": [ + 504, + 234, + 679, + 335 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4d2a3477b241dbbd671290b4e04c9ccb68c07a7fcc40dab1c178caa6cbe0ba23.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 692, + 90, + 870, + 209 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9474bddb929044755c5613b9fa0f737e14ca1e5c5c34d1c4f046bcadcd1ed758.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 692, + 234, + 870, + 335 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "can have many artifacts because of occlusion. With the smoothness regularization, the reconstructed backgrounds are much cleaner. Since the $\\mathcal{L}_{\\mathrm{bs}}$ only applies to the occluded region, the other parts won't be affected. In the second row, the sofa is pushed against the wall and reconstruction from [37] contains only visible open surface. The $\\mathcal{L}_{\\mathrm{op}}$ first regularizes the SDF field to be a watertight mesh. The $\\mathcal{L}_{\\mathrm{rd}}$ further mitigates the flaws at the back by regularizing the object to be confined to the background.", + "bbox": [ + 75, + 435, + 468, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2. Reconstruction in Synthetic Scenes", + "text_level": 1, + "bbox": [ + 76, + 585, + 382, + 602 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Since the synthetic scenes are rendered with objects that have accurate object-level 3D ground truth geometry, we compare our methods with previous object-compositional reconstruction method [37] on the 5 generated scenes and report the quantitative results in Tab. 2.", + "bbox": [ + 75, + 611, + 468, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Tab. 2 we provide detailed metrics on object-level reconstruction. A qualitative comparison is shown in Fig. 6. The computation procedure of all the metrics is available in the supplementary. With monocular cues, ObjSDF* can achieve better performance than the original ObjSDF. However, their performance on object reconstruction is far from satisfactory, since they can only accurately obtain the visible surface with large parts of irrelevant structures in the indoor scenes as pointed out in the analysis before. Though ObjSDF*-C can eliminate most of the outliers and get improved performance, it can only reconstruct visible regions as an open surface as shown in Fig. 6. On the contrary, our regularizations help to smoothen the background and recover the object as a watertight mesh, which promotes", + "bbox": [ + 75, + 688, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ecc2d50995e606d9d75b6b8b7072c7fc618d38c2a3a3fc89fb1770a57e46a8ed.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ObjSDFObjSDF*OursMonoSDF
Chamfer-L1↓0.1700.0920.0880.090
F-Score ↑0.3570.5670.6240.610
", + "bbox": [ + 511, + 431, + 875, + 489 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. ScanNet Reconstruction Quantitative Results.", + "bbox": [ + 519, + 500, + 866, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "performance by a large margin and leads to broader downstream applications. As shown in Fig. 6, RICO can reconstruct the unobservable (back view as in the caption) regions of the objects where the previous methods fail.", + "bbox": [ + 498, + 542, + 890, + 602 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Reconstruction in Real-world Scenes", + "text_level": 1, + "bbox": [ + 500, + 616, + 818, + 631 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conduct experiments on 7 scenes of ScanNet [3] to show the effectiveness of our method on real-world data. Since ScanNet only provides ground truth for the visible surface, here we follow the protocol in [8] and report the reconstruction performance of the entire scene in Tab. 3. By utilizing the rendering formulation in [36] which explicitly models the angle between surface normal and ray, our method can achieve slightly better performance compared to ObjSDF* and [43] on visible surfaces.", + "bbox": [ + 496, + 640, + 890, + 776 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Tab. 4 we evaluate the 2D rendering and segmentation performance and provide the PSNR and mIoU results on two real-world datasets. As our method constrains mainly the unobservable, the PSNR and mIoU metrics are not with significant difference.", + "bbox": [ + 496, + 777, + 890, + 853 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Fig. 7 we also provide the comparisons over two scenes. Note that the ScanNet images are blurry and noisy, and the masks are sometimes inaccurate (e.g., legs of chairs", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17768", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/85e5b0d5f92245b146cd3bf9c1573aa01d4fee305ae12505cddb461aa541ca4c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ObjSDFObjSDF*Ours
PSNR↑ToyDesk21.1021.2121.33
ScanNet22.7823.1523.30
mIoU↑ToyDesk0.880.890.89
ScanNet0.890.910.92
", + "bbox": [ + 86, + 88, + 452, + 190 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 4. PSNR and mIoU Results of different methods on scenes from ScanNet and ToyDesk datasets.", + "bbox": [ + 76, + 202, + 468, + 229 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/6d8924b9eb6ad605d9e9a9239a6f09634ca3396a36e0cc004731b4d99856cfd3.jpg", + "image_caption": [ + "Figure 8. Qualitative Results on ToyDesk. Here we show the reconstruction results both with and without the background for better visualization." + ], + "image_footnote": [], + "bbox": [ + 91, + 255, + 460, + 449 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "missing), leading to less accurate reconstructions. However, it can still be seen that our method can successfully regularize the unobservable regions to get the watertight mesh, while the baselines always result in open surface. For example, the piano in the first row and the sofas in the second row can only be reconstructed on visible surfaces.", + "bbox": [ + 75, + 529, + 468, + 619 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "And in Fig. 8 we provide the qualitative results of our method and two baselines on two ToyDesk scenes. It can be seen that the baseline methods generate non-watertight surface with undesired artifacts (using table plane to cut the mesh will result in holes on the cut face), while our method can directly get clean results.", + "bbox": [ + 75, + 621, + 468, + 712 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.4. Object Manipulation", + "text_level": 1, + "bbox": [ + 76, + 724, + 274, + 742 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "As aforementioned, the reconstruction results from ObjSDF* are sub-optimal for downstream applications like object manipulation. On the contrary, since RICO can get a watertight mesh, it can be easily used for such applications. In Fig. 9 we show the volume rendered normal maps and segmentation masks before and after moving an object in the scene. An illustration of how to manipulate one object in our framework and conduct volume rendering accordingly is applicable in the supplementary. As illustrated, after manipulation, the rendered segmentation and normal map are", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/3141be343c1f8c90113ab61d9d3bf56bb0afead7e6960b8e57ac33e26f04d4ec.jpg", + "image_caption": [ + "Figure 9. Object Manipulation Cases. Here we show the volume rendered normal maps and segmentation masks in two scenes, before (top row) and after (bottom row) the manipulation." + ], + "image_footnote": [], + "bbox": [ + 500, + 89, + 692, + 200 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/0c64a3fabcf57952f021702a1c077cd9ffe1aafada9a2d0830beedcc3769f83c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 89, + 893, + 199 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "still clean for RICO. In contrast, the results of ObjSDF* are messy because their reconstruction is connected with artifacts that were originally outside of the scenes.", + "bbox": [ + 498, + 282, + 890, + 329 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 342, + 619, + 357 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We have presented RICO, a novel approach for compositional reconstruction in indoor scenes. Our key motivation is to regularize the unobservable regions for the objects with partial observations in indoor scenes. We exploit the geometry smoothness for the occluded background, and then adopt the improved background as the prior to regularize the objects' geometry. Our experimental results prove that our method achieves compositional reconstruction with fewer artifacts and watertight object geometry, which further facilitates applicable applications like object manipulation.", + "bbox": [ + 496, + 367, + 890, + 518 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Future work: Currently, each object's pose is baked with its geometry. An interesting future direction would be represent each object in scene as the combination of its own canonical coordinates and the pose, i.e. the rotated 3D bounding box in the world coordinate. With these disentangled representations, we can cast more regularizations from the shape and box perspectives, and the disentanglement also allows more flexible downstream applications. Another interesting direction would be developing more semantic-based prior knowledge for systemic regularization. Now the geometry motivated regularizations are lack of the understanding of the actual shape of each object. With the general knowledge emerged in recent large vision-language model, like StableDiffusion, it's interesting to distill its knowledge in our compositional reconstruction task. The learnt semantic knowledge can provide a holistic understanding of each object and provide a more comprehensive regularization.", + "bbox": [ + 496, + 523, + 892, + 780 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements: We thank Kechun Xu and Huaijin Pi for detailed feedback on the paper. We thank all authors and reviewers for the contributions. This work is in part supported by a Grant from the National Natural Science Foundation of China (No.U21A20484), the NSFC under grant U21B2004, 62202418, and the Zhejiang University Education Foundation Qizhen Scholar Foundation.", + "bbox": [ + 496, + 785, + 890, + 891 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "17769", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mathilde Caron, Hugo Touvron, Ishan Misra, Hervé Jégou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. Emerging properties in self-supervised vision transformers. In Proc. of the IEEE International Conf. on Computer Vision (ICCV), 2021. 3", + "[2] Blender Online Community. *Blender - a 3D modelling and rendering package*. 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In Proc. of the IEEE International Conf. on Computer Vision (ICCV), 2021. 1, 2, 3" + ], + "bbox": [ + 501, + 92, + 890, + 540 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "17771", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/RICO_ Regularizing the Unobservable for Indoor Compositional Reconstruction/9a248d4c-688f-46d5-8671-0975c0bef03f_model.json b/2023/RICO_ Regularizing the Unobservable for Indoor Compositional Reconstruction/9a248d4c-688f-46d5-8671-0975c0bef03f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e5e2347e9f8c3677519a0ecb5d4fff5ccec6f5c1 --- /dev/null +++ b/2023/RICO_ Regularizing the Unobservable for Indoor Compositional Reconstruction/9a248d4c-688f-46d5-8671-0975c0bef03f_model.json @@ -0,0 +1,2565 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.131, + 0.89, + 0.152 + ], + "angle": 0, + "content": "RICO: Regularizing the Unobservable for Indoor Compositional Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.18, + 0.851, + 0.23 + ], + "angle": 0, + "content": "Zizhang Li\\(^{1}\\), Xiaoyang Lyu\\(^{2}\\), Yuanyuan Ding\\(^{1}\\), Mengmeng Wang\\(^{1}\\), Yiyi Liao\\(^{1*}\\), Yong Liu\\(^{1*}\\) \n\\(^{1}\\) Zhejiang University, \\(^{2}\\) The University of Hong Kong" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.263, + 0.314, + 0.279 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.296, + 0.474, + 0.645 + ], + "angle": 0, + "content": "Recently, neural implicit surfaces have become popular for multi-view reconstruction. To facilitate practical applications like scene editing and manipulation, some works extend the framework with semantic masks input for the object-compositional reconstruction rather than the holistic perspective. Though achieving plausible disentanglement, the performance drops significantly when processing the indoor scenes where objects are usually partially observed. We propose RICO to address this by regularizing the unobservable regions for indoor compositional reconstruction. Our key idea is to first regularize the smoothness of the occluded background, which then in turn guides the foreground object reconstruction in unobservable regions based on the object-background relationship. Particularly, we regularize the geometry smoothness of occluded background patches. With the improved background surface, the signed distance function and the reversedly rendered depth of objects can be optimized to bound them within the background range. Extensive experiments show our method outperforms other methods on synthetic and real-world indoor scenes and prove the effectiveness of proposed regularizations. The code is available at https://github.com/kyleleey/RICO" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.672, + 0.21, + 0.687 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.697, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Reconstructing 3D geometry from images is a fundamental problem in computer vision and has many downstream applications like VR/AR and game assets creation. With the advance of neural implicit representations [20], recent reconstruction methods [25, 36, 41, 43] can recover accurate geometry from multi-view images. However, existing methods typically regard the whole scene as an entirety and reconstruct everything altogether, thus preventing applications like scene editing. In indoor scenes with plenty of reconfigurable objects, a disentangled object-compositional reconstruction, i.e. decomposing the geometry into different instantiated objects and background, can be more suitable" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.262, + 0.885, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.416, + 0.884, + 0.564 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.578, + 0.895, + 0.662 + ], + "angle": 0, + "content": "Figure 1. Comparison of [37] (Top) and ours (Bottom). Different objects are visualized in different colors. Previous reconstructions are connected with large artifacts. Taking the partially observed cubic object's front and back views (in red and green rectangles respectively) as an example, [37] can only get the visible surface, while ours can complement the complete body." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.689, + 0.878, + 0.704 + ], + "angle": 0, + "content": "for further applications like moving the sofa in the scene." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In this paper, we aim to recover the room-level indoor scenes with decomposed geometry of individual objects and background. We assume that multi-view posed images and semantic masks that assign different labels to each instantiated object and the background are given as input. Existing object-compositional methods [9, 45, 40] concentrate more on the rendering performance rather than the underlying geometry, and thus can not be directly used for reconstruction. The most recent work ObjSDF [37] learns an object-compositional signed distance function (SDF) field by proposing a transform function between SDF values and semantic logits. Specifically speaking, ObjSDF predicts multiple SDF values at each 3D point for different seman" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.229, + 0.9 + ], + "angle": 0, + "content": "*Corresponding authors." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17761" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.395 + ], + "angle": 0, + "content": "tic classes, and converts them to semantic logits, allowing for separating object SDF values from the background when supervised by semantic masks. Although achieving plausible shape disentanglement, it suffers from a common problem in indoor scenes: objects and background can only be partially observed due to occlusions. When the object is partially observed, e.g. a cubic object against the wall, ObjSDF can not properly reconstruct the geometry between them (see Fig. 1 top-right). The reason is that the existing works [45, 37] can only effectively regularize semantic labels and geometry of observed regions, and have little impact on the unobserved regions. When processing the indoor scenes where a large portion of objects are partially observed, the reconstruction results of these objects will be visible surface connected with the unconstrained structures (as shown in Fig. 1, see Section 3.3 for a detailed analysis). Fig. 2 shows that even with reasonable reconstruction when composing all the objects together, each object's result in the unobserved region is far from satisfactory and can hinder further applications like manipulating the object." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.398, + 0.473, + 0.807 + ], + "angle": 0, + "content": "We propose RICO, which realizes the proper geometry disentanglement for indoor scenes (see Fig. 1 bottom) by explicitly regularizing the unobserved regions. To be more specific, when the object is partially observed, recovering its geometry is an ill-posed problem even with corresponding masks. Thus, introducing prior regularization for unobserved regions is necessary. We exploit two types of prior knowledge for indoor scenes in this work: 1) background smoothness and 2) object-background relations. First, when one ray hits the object surface, the existing method [37] can properly regularize the geometry and appearance on the hitting point, but can not account for the background surface behind this object. This drawback leads to artifacts and holes on the unobserved background surface (see Fig. 2). We propose a patch-based smoothness loss to regularize the SDF values of unobserved background regions. Then, since the background reconstruction is improved, we can leverage another strong prior: the objects are all within the room, i.e. using the background surface to regularize the SDF field of objects. We design two regularization terms: an object point-SDF loss for sampled points behind the background surface and a reversed depth loss to regularize the SDF distribution of the entire ray. Both terms aim to bound the object within the background surface's range, thus preventing the aforementioned unmeaning structure, making the object reconstruction a watertight and plausible shape instead of an open surface with severe artifacts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In summary, we propose RICO to realize compositional reconstruction in indoor scenes where a large portion of objects are partially observed. Our main contributions are: i) A patch-based background smoothness regularizer for unobserved background surface geometry. ii) Guided by the improved background surface, we exploit the object-" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.092, + 0.885, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.256, + 0.895, + 0.314 + ], + "angle": 0, + "content": "Figure 2. ObjSDF results. Interested objects are dyed in blue. Despite of the plausible composition, the disentangled backgrounds have artifacts and sunk holes, and partially observed objects can only get the visible surface (illustrated in 'Object Backward')." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.337, + 0.895, + 0.43 + ], + "angle": 0, + "content": "background relation as prior knowledge and design objectives that effectively regularize objects' unobserved regions. iii) Extensive experiments on both real-world and synthetic datasets prove our superior reconstruction performance compared to previous works, especially for the partially observed objects." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.442, + 0.642, + 0.459 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.892, + 0.744 + ], + "angle": 0, + "content": "Neural Implicit Representation for Reconstruction: Recently, neural implicit representations have emerged as a popular representation for 3D reconstruction. While early approaches [19, 26] rely on 3D supervision, a few works [24, 42] exploit surface rendering to use multi-view image supervision only, but also suffer from the unstable training. Neural radiance field (NeRF) [20] adopts volume rendering technique to achieve photorealistic scene representation and stable optimization. However, NeRF's formulation can not guarantee accurate underlying geometry. Therefore, [25, 36, 41] combine the geometry representation with iso-surface (e.g. occupancy [19], SDF [36, 41]) and volume density to accurately reconstruct object-level scenes from RGB images. [8] further applies the planar regularization for scene-level reconstruction. To tackle the problem in texture-less regions, [35, 43] utilize results from pretrained normal and depth estimation networks to guide the SDF training and boost the reconstruction performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.746, + 0.894, + 0.837 + ], + "angle": 0, + "content": "However, despite the promising reconstruction performance, the aforementioned methods all consider the whole scene as an entirety. Our method focuses on decomposing the scene reconstruction into the background and different foreground objects, which can be regarded as compositional scene reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Compositional Scene Reconstruction: Decomposing a scene into its different components could benefit downstream applications like scene editing. Many works have been proposed to recover the scene in a compositional man" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "17762" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.087, + 0.868, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.338, + 0.895, + 0.396 + ], + "angle": 0, + "content": "Figure 3. Overview. In this work, we propose two different regularizations. We first regularize the geometry smoothness of the unobserved background regions in a sampled patch. Then, we exploit the background surface as the prior to constrain the objects' surface. In detail, a per-point SDF loss and a reversed depth loss are introduced to regularize the manifold of objects' SDF functions. Combined with other reconstruction losses, our method reaches a neat and disentangled compositional reconstruction in indoor scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.419, + 0.471, + 0.616 + ], + "angle": 0, + "content": "ner from different perspectives. [22, 44, 10, 21] detect and reconstruct different objects in the given monocular image, and predict the scene's layout at the same time. But most of these methods require large-scale datasets with 3D ground truth for training. [14, 32, 18] optimize a feature field from a large pretrained model [1, 16], which enables deep feature based decomposition and manipulation. [38, 31] exploit the self-supervise paradigm to decompose the scenes into static and dynamic parts. More works [9, 45, 40, 39, 34, 6, 15, 33] focus on recovering the object-compositional scenes given semantic masks with images. However, this line of works concerns the rendering outputs rather than the geometry, i.e. the reconstruction results are sub-optimal." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.619, + 0.47, + 0.773 + ], + "angle": 0, + "content": "Recently, ObjSDF [37] proposes a transform function between semantic logits and SDFs of different objects, which enables optimizing SDF fields with image and semantic mask supervision, and decomposing the whole scene with accurate reconstruction. However, in the indoor scenes where many objects are in partial observation, its reconstruction results are far from satisfactory and can not be used for further applications (see Fig. 2). On the contrary, our method introduces geometry prior to unobserved regions, yielding better compositional scene reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Prior Regularization in Neural Implicit Reconstruction: In addition to the commonly used RGB image supervision, many different priors have been proposed to benefit the neural implicit representation. For example, [4, 30] use explicit point cloud as the depth prior, [23] employs regularization in unseen views and [11] introduces pretrained model's feature consistency. [12, 28] adopt explicit human model as the structural prior for the human-centric scenes. As for surface" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.419, + 0.892, + 0.479 + ], + "angle": 0, + "content": "reconstruction, [8] proposes a Manhattan-world assumption for the planar regions, [43] utilizes the normal and depth prediction from off-the-shelf model [5] as prior to regularize the texture-less regions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.481, + 0.893, + 0.557 + ], + "angle": 0, + "content": "Our method exploits the geometry prior in the unobserved region for compositional scene reconstruction. The proposed regularization can effectively reconstruct the objects and disentangle them from the background, even if the object itself is partially observed." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.574, + 0.637, + 0.592 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.601, + 0.895, + 0.768 + ], + "angle": 0, + "content": "Our goal is to recover decomposed geometry surface of the objects and background within a scene from the images and semantic masks inputs. To this end, we first review the SDF-based neural implicit representation and how to use the semantic logits for compositional reconstruction in Section 3.1. Next, we propose two types of regularizations on unobserved regions to address the partial observation problem: patch-based background smoothness (Section 3.2) and object-background relation (Section 3.3). Finally, we introduce the overall optimization procedure in Section 3.4. An overview of our method is provided in Fig 3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.781, + 0.633, + 0.798 + ], + "angle": 0, + "content": "3.1. Background" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Volume Rendering of SDF-based Implicit Surface: For implicit reconstruction, the geometry of the scene is represented as the signed distance function (SDF) \\( s(\\mathbf{p}) \\) of each spatial point \\( \\mathbf{p} \\), which is the point's distance to the closest surface. In practice, the SDF function is implemented as a multi-layer perceptron (MLP) network \\( f(\\cdot) \\). The appear-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17763" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.401, + 0.108 + ], + "angle": 0, + "content": "ance of the scene is also defined as an MLP \\(g(\\cdot)\\) .." + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.116, + 0.469, + 0.155 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} f: \\mathbf {p} \\in \\mathbb {R} ^ {3} \\mapsto (s \\in \\mathbb {R}, \\mathbf {f} \\in \\mathbb {R} ^ {2 5 6}) \\\\ g: (\\mathbf {p} \\in \\mathbb {R} ^ {3}, \\mathbf {n} \\in \\mathbb {R} ^ {3}, \\mathbf {v} \\in \\mathbb {S} ^ {2}, \\mathbf {f} \\in \\mathbb {R} ^ {2 5 6}) \\mapsto \\mathbf {c} \\in \\mathbb {R} ^ {3} \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.166, + 0.47, + 0.256 + ], + "angle": 0, + "content": "where \\(\\mathbf{f}\\) is a geometry feature vector, \\(\\mathbf{n}\\) is the normal at \\(\\mathbf{p}\\), \\(\\mathbf{v}\\) is the viewing direction and \\(\\mathbf{c}\\) is the view-dependent color. We adopt the unbiased rendering proposed in [36] to render the image. For each camera ray \\(\\mathbf{r} = (\\mathbf{o},\\mathbf{v})\\) with \\(\\mathbf{o}\\) as the ray origin, \\(n\\) points \\(\\{\\mathbf{p}(t_i) = \\mathbf{o} + t_i\\mathbf{v}|i = 0,1,\\dots ,n - 1\\}\\) are sampled, and the pixel color can be approximated as:" + }, + { + "type": "equation", + "bbox": [ + 0.204, + 0.267, + 0.47, + 0.307 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {C}} (\\mathbf {r}) = \\sum_ {i = 0} ^ {n - 1} T _ {i} \\alpha_ {i} \\mathbf {c} _ {i}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.317, + 0.469, + 0.362 + ], + "angle": 0, + "content": "The \\(T_{i}\\) is the discrete accumulated transmittance derived from \\(T_{i} = \\prod_{j=0}^{i-1}(1 - \\alpha_{j})\\), and \\(\\alpha_{i}\\) is the discrete density value defined as" + }, + { + "type": "equation", + "bbox": [ + 0.094, + 0.37, + 0.469, + 0.405 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {i} = \\max \\left(\\frac {\\Phi_ {u} (s (\\mathbf {p} (t _ {i}))) - \\Phi_ {u} (s (\\mathbf {p} (t _ {i + 1})))}{\\Phi_ {u} (s (\\mathbf {p} (t _ {i})))}, 0\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.414, + 0.469, + 0.474 + ], + "angle": 0, + "content": "where \\(\\Phi_u(x) = (1 + e^{-ux})^{-1}\\) and \\(u\\) is a learnable parameter. By minimizing the difference between predicted and ground-truth pixel colors, we can learn the SDF and appearance function of the desired scene." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.48, + 0.47, + 0.678 + ], + "angle": 0, + "content": "Learning SDF with Semantic Logits: In this work, we consider compositional reconstruction of \\( k \\) objects given their masks. Note that we also consider the background as an instantiated object for brevity as in [37] and follow their network structure. In detail, for a scene with \\( k \\) objects, the SDF MLP \\( f(\\cdot) \\) now outputs \\( k \\) SDFs at each point, and the \\( j \\)-th \\( (1 \\leq j \\leq k) \\) SDF represents the geometry of \\( j \\)-th object. Without loss of generality, we set \\( j = 1 \\) as the background category and others for objects in Fig. 3 and the rest of the paper. The scene SDF is the minimum of \\( \\{s_j\\} \\), which is used for sampling points along the ray and aforementioned volume rendering (Eq. 2). Moreover, each point's \\( k \\) SDFs can be transformed into semantic logits \\( \\mathbf{h}(\\mathbf{p}) \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.687, + 0.47, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\begin{array}{l} h _ {j} (\\mathbf {p}) = \\gamma / (1 + \\exp (\\gamma \\cdot s _ {j} (\\mathbf {p}))), \\\\ \\mathbf {p} (.) = [ 1, (.) ] \\end{array} \\tag {4} \\\\ \\mathbf {h} (\\mathbf {p}) = \\left[ h _ {1} (\\mathbf {p}), h _ {2} (\\mathbf {p}), \\dots , h _ {k} (\\mathbf {p}) \\right], \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.733, + 0.469, + 0.824 + ], + "angle": 0, + "content": "where \\(\\gamma\\) is a fixed parameter. Using volume rendering to accumulate the semantic logits of all the points along a ray, we can get the semantic logits \\(\\mathbf{H}(\\mathbf{r})\\in \\mathbb{R}^k\\) of each pixel. During training, the cross-entropy loss applied to \\(\\mathbf{H}(\\mathbf{r})\\) is backpropagated to the SDF values, allowing for learning the compositional geometry." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.833, + 0.402, + 0.849 + ], + "angle": 0, + "content": "3.2. Patch-based Background Smoothness" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Although the volume rendering can propagate gradients along the entire ray, the optimization mainly focuses on the surface-hitting point, as its accumulated weight can be" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.167 + ], + "angle": 0, + "content": "much larger than the others. As a result, the geometry of the points behind the first-hit surface can not be optimized correctly. In the indoor scenes, the occluded part of the background surface is invisible in all the images, which can be with holes and random artifacts (see Fig. 2)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.892, + 0.242 + ], + "angle": 0, + "content": "Since we cannot tell the exact color, depth or normal of the occluded part, it is intractable to optimize this region wrt. its ground truth. Therefore, we propose to regularize the geometry of the occluded background to be smooth, thus preventing some clearly wrong artifacts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.892, + 0.379 + ], + "angle": 0, + "content": "In detail, we regularize the smoothness of rendered depth and normal of background surface within a small patch region. To save the computation budget, we randomly sample a \\(\\mathcal{P} \\times \\mathcal{P}\\) size patch every \\(\\mathcal{T}_{\\mathcal{P}}\\) iterations in the given image and sample points along the patch rays using the background SDF only. We compute depth map \\(\\hat{D}(\\mathbf{r})\\) and normal map \\(\\hat{N}(\\mathbf{r})\\) of the sampled patch following [43], \\(\\mathbf{r}\\) denotes the sampled ray in patch. The semantic map of the patch is also computed and transformed into a patch Mask \\(\\hat{M}(\\mathbf{r})\\):" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.388, + 0.891, + 0.406 + ], + "angle": 0, + "content": "\\[\n\\hat {M} (\\mathbf {r}) = \\mathbb {1} [ \\arg \\max (\\mathbf {H} (\\mathbf {r})) \\neq 1 ], \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.892, + 0.476 + ], + "angle": 0, + "content": "which means the mask value is 1 if the rendered class is not the background, so that only the occluded background is regularized. Taking rendered depth as an example, the patch-based background smoothness loss is" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.486, + 0.891, + 0.552 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} (\\hat {D}) = \\sum_ {d = 0} ^ {3} \\sum_ {m, n = 0} ^ {\\mathcal {P} - 1 - 2 ^ {d}} \\hat {M} \\left(\\mathbf {r} _ {m, n}\\right) \\odot (| \\hat {D} \\left(\\mathbf {r} _ {m, n}\\right) - \\tag {6} \\\\ \\hat {D} \\left(\\mathbf {r} _ {m, n + 2 ^ {d}}\\right) | + | \\hat {D} (\\mathbf {r} _ {m, n}) - \\hat {D} \\left(\\mathbf {r} _ {m + 2 ^ {d}, n}\\right) |\\left. \\right). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.651 + ], + "angle": 0, + "content": "Here the smoothness is applied on different intervals controlled by \\(d\\). \\(m\\) and \\(n\\) are the pixel indices within the patch and the mask is multiplied at each position with hadamard product \\(\\odot\\). The normal smoothness loss \\(\\mathcal{L}(\\hat{N})\\) can be obtained similarly. We define the overall background smoothness loss \\(\\mathcal{L}_{bs}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.621, + 0.66, + 0.891, + 0.678 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {b s}} = \\mathcal {L} (\\hat {D}) + \\mathcal {L} (\\hat {N}). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.891, + 0.734 + ], + "angle": 0, + "content": "Here in contrast to [23] which applies a patch-based regularization to visible regions in other views, we instead regularize the occluded regions of the background." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.742, + 0.892, + 0.759 + ], + "angle": 0, + "content": "3.3. Object-background Relation as Regularization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.855 + ], + "angle": 0, + "content": "With the help of the patch-based background smoothness loss, most artifacts of the background are resolved, yielding a smooth surface. We further leverage this smooth background surface to regularize the SDF fields of other objects, leveraging a key prior knowledge that all the other objects are confined to the room, i.e., the background surface." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In the original framework of [37], if an object is partially observed, e.g. against the background, the object's reconstructed surface won't be a \"closed\" surface (see Fig. 1 and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17764" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.087, + 0.452, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.314, + 0.473, + 0.495 + ], + "angle": 0, + "content": "Figure 4. Toy-case analysis. A bird-eye view of an object against the background is shown here, the SDF and surface of object is shown in red and background's in blue. (a) In [37] the minimum SDF is used for volume rendering and semantic loss, so on object's visible surface where object SDF is optimized to 0 and the background SDF here is positive, and similar for the visible background surface. Since the scene is partially observed from left, the right part of object surface is open and unobserved background region is unconstrained. (b) With the smoothness prior the background surface can be plausible, (c) and object point SDF loss close the object surface but still have intersections, (d) finally the reversed depth loss optimizes the entire ray thus the object can be within the background." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.47, + 0.579 + ], + "angle": 0, + "content": "Fig. 2). We refer to the toy-case analysis shown in Fig. 4 for the reason of the current unsatisfactory reconstruction. To encourage the reconstruction to be watertight, we design two types of regularization on the SDF fields of objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.47, + 0.749 + ], + "angle": 0, + "content": "Object Point-SDF Loss: A straightforward solution is to directly regularize the objects' SDFs on every sampled point behind the background surface. To be more specific, the regular volume rendering only guarantees a single change of the sign (positive SDF to negative) when a ray hits a visible surface. For watertight objects, the ray should hit another occluded surface (negative SDF to positive). With the prior that the object is confined within the room, the occluded object surface should be closer than the background surface, meaning that the object SDFs of points behind the background surface should all be positive (Fig. 4 (c))." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.75, + 0.471, + 0.826 + ], + "angle": 0, + "content": "We implement an object point-SDF loss based on the above analysis. For the sampled points along the rays, we first utilize the root-finding algorithm among the background SDF of these points and find the zero-SDF ray depth \\( t' \\). Then the object point-SDF loss can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.835, + 0.47, + 0.878 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {o p}} = \\frac {1}{k - 1} \\sum_ {j = 2} ^ {k} \\max \\left(0, \\epsilon - \\mathbf {s} _ {j} (\\mathbf {p} (t _ {i}))\\right) \\cdot \\mathbb {1} [ t _ {i} > t ^ {\\prime} ], \\quad (8)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.886, + 0.471, + 0.902 + ], + "angle": 0, + "content": "which pushes the objects' SDFs at points behind the surface" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.722, + 0.107 + ], + "angle": 0, + "content": "larger than a positive threshold \\(\\epsilon\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.111, + 0.894, + 0.233 + ], + "angle": 0, + "content": "Reversed Depth Loss: Although the \\(\\mathcal{L}_{\\mathrm{op}}\\) can effectively regularize the SDF fields of each object, in practice we find the reconstructed object surface can still have intersections with the background surface (Fig. 4 (c)). The reason is that the sampled points are discrete and in most cases, the background surface is between two sampled points. Therefore, the sign change of the occluded surface may still occur after hitting the background surface." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.233, + 0.893, + 0.369 + ], + "angle": 0, + "content": "Since per-point optimization can not effectively propagate to the distribution of the entire ray. To optimize the entire ray's SDF distribution for better regularization, we compute a reversed depth along each ray. With the help of \\(\\mathcal{L}_{\\mathrm{op}}\\), the sign of the object SDF along one ray now is positive-negative-positive, which enables rendering a depth value backward. We first transform the ray depth \\(\\{t_i|i = 0,1,\\dots ,n - 1\\}\\) into the reversed ray depth named \\(\\{\\hat{t}_i|i = 0,1,\\dots ,n - 1\\}\\), where" + }, + { + "type": "equation", + "bbox": [ + 0.602, + 0.374, + 0.892, + 0.391 + ], + "angle": 0, + "content": "\\[\n\\hat {t} _ {i} = \\left(t _ {0} + t _ {n - 1}\\right) - t _ {n - 1 - i}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.397, + 0.893, + 0.624 + ], + "angle": 0, + "content": "With the reversed ray depth values, we use the background and object SDF both in reversed order to compute the accumulated weight and get the reversed depth respectively. Remarkably, in order to compute the exact correct depth, the points should be re-sampled along the reverse direction. Here we directly use the sampled points to avoid computation overhead, and empirical results prove its effectiveness. We only compute the reverse depth of one pixel if satisfying two conditions: 1) this pixel's \\(\\hat{M}(\\mathbf{r}) = 1\\); 2) the SDF value of the rendered object at the furthest point is positive. Note that the second condition is usually satisfied when the object point-SDF loss is applied. By computing the reversed depth \\(d_{o}\\) of the hitting object (determined by the pixel's rendered semantic) and \\(d_{b}\\) of the background, we can get the reversed depth loss:" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.629, + 0.892, + 0.645 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {r d}} = \\max \\left(0, d _ {b} - d _ {o}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.651, + 0.892, + 0.682 + ], + "angle": 0, + "content": "which pushes the object surface within the background as illustrated in Fig. 4 (d)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.688, + 0.747, + 0.705 + ], + "angle": 0, + "content": "3.4. Training Objectives Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.712, + 0.892, + 0.802 + ], + "angle": 0, + "content": "Monocular geometric cues are essential for indoor scene reconstruction as proved in [43]. Following [43], we add the depth and normal consistency loss \\((\\mathcal{L}_{\\mathrm{D}},\\mathcal{L}_{\\mathrm{N}})\\) with pseudo ground truth from Omnidata [5] model. In experiments, we also add the monocular cues on [37] to get a stronger baseline for a fair comparison." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.802, + 0.892, + 0.863 + ], + "angle": 0, + "content": "The SDF network is also regularized by an Eikonal [7] loss item \\(\\mathcal{L}_{\\mathrm{E}}\\). We further use the semantic loss \\(\\mathcal{L}_{\\mathrm{S}}\\) proposed in [37] to learn the compositional geometry. The overall loss function for compositional reconstruction is:" + }, + { + "type": "equation", + "bbox": [ + 0.533, + 0.868, + 0.891, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\mathrm {R G B}} + \\lambda_ {\\mathrm {D}} \\mathcal {L} _ {\\mathrm {D}} + \\lambda_ {\\mathrm {N}} \\mathcal {L} _ {\\mathrm {N}} + \\lambda_ {\\mathrm {E}} \\mathcal {L} _ {\\mathrm {E}} + \\lambda_ {\\mathrm {S}} \\mathcal {L} _ {\\mathrm {S}} \\tag {11} \\\\ + \\lambda_ {\\mathrm {b s}} \\mathcal {L} _ {\\mathrm {b s}} + \\lambda_ {\\mathrm {o p}} \\mathcal {L} _ {\\mathrm {o p}} + \\lambda_ {\\mathrm {r d}} \\mathcal {L} _ {\\mathrm {r d}}. \\\\ \\end{array}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17765" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.184 + ], + "angle": 0, + "content": "We set \\(\\lambda_{\\mathrm{bs}}, \\lambda_{\\mathrm{op}}, \\lambda_{\\mathrm{rd}} = 0.1\\) in our experiments. For other loss terms, given the weight of RGB reconstruction loss as 1, we set \\(\\lambda_{\\mathrm{D}} = 0.1\\) and \\(\\lambda_{\\mathrm{N}} = \\lambda_{\\mathrm{E}} = 0.05\\) following [43]. For the semantic loss, we follow the implementation in [37] and set \\(\\lambda_{\\mathrm{D}} = 0.04\\). The detailed calculation of other losses can be found in supplementary." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.196, + 0.212, + 0.213 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.222, + 0.47, + 0.298 + ], + "angle": 0, + "content": "We first conduct ablation study on each proposed component. Then we provide quantitative and qualitative results of object-compositional reconstruction on real-world and synthetic scenes. Finally, we show some possible object manipulation with our compositional reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.471, + 0.453 + ], + "angle": 0, + "content": "Datasets: We consider three types of indoor datasets with multi-view RGB images and masks: 1) ScanNet [3], a real-world dataset widely used in previous works [8, 35, 37, 43]; 2) ToyDesk dataset, a real-world dataset with two scenes and each has four objects placed on the table plane. This dataset has also been widely used in previous compositional works [40, 37] 3) a hand-crafted synthetic dataset with five scenes, each containing \\(5 \\sim 10\\) objects. The synthetic dataset is considered such that the ground truth geometry of both, occluded and non-occluded regions are available." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.458, + 0.471, + 0.73 + ], + "angle": 0, + "content": "Metrics: For reconstruction performance, we report Chamfer Distance, F-score for evaluation on ScanNet, following [8, 43]. On synthetic scenes we divide metrics for two aspects: objects and background. For objects we report the reconstruction performance compared to the complete ground truth object mesh, and the final results are averaged across all the objects in all the scenes. For background we report the reconstruction metrics and rendered depth errors of the occluded regions only to highlight the effectiveness of our regularization. The results are also averaged across all the scenes. See supplementary for a detailed introduction to datasets and metrics. We also report two 2D metrics, PSNR and mIoU, on the ToyDesk and ScanNet scenes. Here we omit the synthetic dataset considering its relatively simple texture. For the test image set, on ToyDesk dataset we use the official split, and on ScanNet we sample frames from their original camera trajectories. The metrics are averaged across different images of different scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Baselines: We mainly compare with ObjSDF [37] in this work, as it is the only method that focuses on the same task, a specific discussion is provided in the supplementary. Since we focus on the indoor scene where monocular cues can benefit a lot [43], we add losses proposed in [43] to our method for better performance. For a fair comparison, we also combine [37] and [43] for a stronger baseline, named ObjSDF*. Moreover, since ObjSDF*’s object reconstructions inevitably have artifacts, we develop a postprocess method to cull the parts outside the background range and name this baseline ObjSDF*-C. We provide the" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.089, + 0.872, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.242, + 0.895, + 0.298 + ], + "angle": 0, + "content": "Figure 5. Effects of Regularizations. The first row shows two backgrounds, the \\(\\mathcal{L}_{\\mathrm{bs}}\\) clearly mitigates most of the artifacts. The last row shows that with \\(\\mathcal{L}_{\\mathrm{op}}\\) we can get the watertight object and \\(\\mathcal{L}_{\\mathrm{rd}}\\) further constrains the unobserved surface." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.32, + 0.892, + 0.412 + ], + "angle": 0, + "content": "details of how to set the range in the supplementary. Note that our method directly generates clean watertight meshes and doesn't need such post-processing. In ScanNet experiments, we also report results for MonoSDF [43] as a reference since we can only evaluate the overall reconstruction (details in Section 4.3)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.893, + 0.537 + ], + "angle": 0, + "content": "Implementation Details: We implement our method in PyTorch [27]. We use the Adam [13] optimizer with a learning rate of 5e-4 for 50k iterations and sample 1024 rays per iteration. The weight initialization scheme for SDF MLP is identical to [41, 36, 37]. The \\( u \\) is initialized as 0.05 and we set \\( \\gamma = 20 \\) as proposed in [37]. \\( \\mathcal{P} \\), \\( \\mathcal{T}_{\\mathcal{P}} \\) and \\( \\epsilon \\) are set as 32, 10 and 0.05 respectively. All the reconstructions are acquired by using marching cube [17] at the resolution of 512." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.895, + 0.749 + ], + "angle": 0, + "content": "Moreover, we adopt the geometric initialization [7] for the geometry network, which initializes the reconstruction with a unit sphere and the surface normals are facing inside at the beginning of the optimization. For the ScanNet dataset, we follow the protocol in [43] to crop the input image to \\( 384 \\times 384 \\) and adjust the intrinsics accordingly. For the synthetic dataset, we directly render the image at the same resolution. Since we focus on the indoor scenes in this paper, we adopt the common practice to process the \"bounded\" scene. For each scene, we normalize the camera poses so that all the cameras lie in a unit sphere. The rays intersection, i.e. the furthest sampling location, is computed based on this sphere and we also conduct Marching Cubes [17] within the same area for the final reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.655, + 0.773 + ], + "angle": 0, + "content": "4.1. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We first quantitatively analyze the effectiveness of the proposed regularizations on synthetic scenes by comparing our full method to four variants in Tab. 1. First, adding the smoothness loss (V2) significantly decreases the depth error of occluded background regions. Next, the \\(\\mathcal{L}_{\\mathrm{op}}\\) makes the object reconstruction watertight and the object-level metrics are greatly improved (V3). The \\(\\mathcal{L}_{\\mathrm{rd}}\\) further improves the object reconstruction performance (Full). Results of V4 prove" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17766" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.099, + 0.287, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.167, + 0.171, + 0.22, + 0.184 + ], + "angle": 0, + "content": "ObjSDF" + }, + { + "type": "image", + "bbox": [ + 0.298, + 0.099, + 0.481, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.359, + 0.171, + 0.418, + 0.184 + ], + "angle": 0, + "content": "ObjSDF*" + }, + { + "type": "image", + "bbox": [ + 0.492, + 0.099, + 0.674, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.565, + 0.171, + 0.599, + 0.184 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.099, + 0.775, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.765, + 0.171, + 0.786, + 0.183 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image", + "bbox": [ + 0.778, + 0.099, + 0.866, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.197, + 0.284, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.279, + 0.284, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.205, + 0.481, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.492, + 0.205, + 0.675, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.205, + 0.871, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.327, + 0.283, + 0.408 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.409, + 0.283, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.297, + 0.336, + 0.48, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.492, + 0.336, + 0.675, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.336, + 0.871, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.452, + 0.284, + 0.532 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.533, + 0.284, + 0.574 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.16, + 0.579, + 0.22, + 0.593 + ], + "angle": 0, + "content": "ObjSDF*" + }, + { + "type": "image", + "bbox": [ + 0.297, + 0.462, + 0.48, + 0.574 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.35, + 0.579, + 0.424, + 0.593 + ], + "angle": 0, + "content": "ObjSDF*-C" + }, + { + "type": "image", + "bbox": [ + 0.492, + 0.462, + 0.675, + 0.574 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.567, + 0.58, + 0.6, + 0.592 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.462, + 0.871, + 0.574 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.77, + 0.579, + 0.792, + 0.591 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.61, + 0.895, + 0.655 + ], + "angle": 0, + "content": "Figure 6. Qualitative Results on Synthetic Scenes. Above the blue line we show the comparison of different methods on two background scenes. Below we provide results of two scenes where only the object results are shown. In red rectangles at the bottom of each picture, we show the back (left part) and front (right part) views of an example object. Detailed descriptions in Section 4.2." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.674, + 0.462, + 0.786 + ], + "angle": 0, + "content": "
BackgroundObject
LbsLopLrdD.↓C.↓F.↑C.↓F.↑
V1---0.0210.0450.7681.240.065
V2✓--0.0040.0090.991.250.066
V3✓✓-0.0030.0090.990.0450.735
V4-✓✓0.0150.0290.8880.0390.785
Full✓✓✓0.0030.0090.990.0330.817
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.794, + 0.471, + 0.851 + ], + "angle": 0, + "content": "Table 1. Ablation Study. The D. denotes the depth error of the occluded background. The C. and F. mean the Chamfer- \\( L_{1} \\) and F-score respectively, for the reconstruction of occluded background regions and full complete objects. Details in Section 4.1." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.471, + 0.902 + ], + "angle": 0, + "content": "that without \\(\\mathcal{L}_{\\mathrm{bs}}\\) to improve the background, the object re" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.674, + 0.882, + 0.769 + ], + "angle": 0, + "content": "
BackgroundObjects
D.↓C.↓F.↑C.↓F.↑
ObjSDF0.0330.0760.6691.0400.084
ObjSDF*0.0210.0440.7721.0300.085
ObjSDF*-C0.0210.0440.7720.1340.681
Ours0.0030.0090.9900.0330.817
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.778, + 0.892, + 0.808 + ], + "angle": 0, + "content": "Table 2. Synthetic Scenes Reconstruction Quantitative Results. The D. C. and F. have the same meanings as in Tab. 1." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.838, + 0.892, + 0.868 + ], + "angle": 0, + "content": "construction quality also drops. Note that \\(\\mathcal{L}_{\\mathrm{rd}}\\) needs to be applied jointly with \\(\\mathcal{L}_{\\mathrm{op}}\\) to guarantee its second condition." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.901 + ], + "angle": 0, + "content": "A qualitative case is shown in Fig. 5 for better illustration. In the first row, the occluded part of the background" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17767" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.091, + 0.278, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.217, + 0.274, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.153, + 0.338, + 0.218, + 0.351 + ], + "angle": 0, + "content": "MonoSDF" + }, + { + "type": "image", + "bbox": [ + 0.315, + 0.091, + 0.495, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.316, + 0.171, + 0.493, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.317, + 0.217, + 0.492, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.317, + 0.297, + 0.492, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.376, + 0.339, + 0.433, + 0.352 + ], + "angle": 0, + "content": "ObjSDF*" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.091, + 0.681, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.236, + 0.681, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.557, + 0.339, + 0.629, + 0.352 + ], + "angle": 0, + "content": "ObjSDF*-C" + }, + { + "type": "image", + "bbox": [ + 0.694, + 0.091, + 0.871, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.694, + 0.236, + 0.871, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.766, + 0.339, + 0.798, + 0.35 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.369, + 0.894, + 0.412 + ], + "angle": 0, + "content": "Figure 7. Qualitative Results on ScanNet [3]. On the left of blue line we show the overall reconstruction from [43] as the reference. On the right we show the comparison between our method and two baselines. Similarly, the back and front views of objects with partial observations are provided in red rectangles. Detailed descriptions in Section 4.3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.436, + 0.47, + 0.572 + ], + "angle": 0, + "content": "can have many artifacts because of occlusion. With the smoothness regularization, the reconstructed backgrounds are much cleaner. Since the \\(\\mathcal{L}_{\\mathrm{bs}}\\) only applies to the occluded region, the other parts won't be affected. In the second row, the sofa is pushed against the wall and reconstruction from [37] contains only visible open surface. The \\(\\mathcal{L}_{\\mathrm{op}}\\) first regularizes the SDF field to be a watertight mesh. The \\(\\mathcal{L}_{\\mathrm{rd}}\\) further mitigates the flaws at the back by regularizing the object to be confined to the background." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.587, + 0.383, + 0.603 + ], + "angle": 0, + "content": "4.2. Reconstruction in Synthetic Scenes" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.47, + 0.687 + ], + "angle": 0, + "content": "Since the synthetic scenes are rendered with objects that have accurate object-level 3D ground truth geometry, we compare our methods with previous object-compositional reconstruction method [37] on the 5 generated scenes and report the quantitative results in Tab. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.901 + ], + "angle": 0, + "content": "In Tab. 2 we provide detailed metrics on object-level reconstruction. A qualitative comparison is shown in Fig. 6. The computation procedure of all the metrics is available in the supplementary. With monocular cues, ObjSDF* can achieve better performance than the original ObjSDF. However, their performance on object reconstruction is far from satisfactory, since they can only accurately obtain the visible surface with large parts of irrelevant structures in the indoor scenes as pointed out in the analysis before. Though ObjSDF*-C can eliminate most of the outliers and get improved performance, it can only reconstruct visible regions as an open surface as shown in Fig. 6. On the contrary, our regularizations help to smoothen the background and recover the object as a watertight mesh, which promotes" + }, + { + "type": "table", + "bbox": [ + 0.512, + 0.433, + 0.876, + 0.49 + ], + "angle": 0, + "content": "
ObjSDFObjSDF*OursMonoSDF
Chamfer-L1↓0.1700.0920.0880.090
F-Score ↑0.3570.5670.6240.610
" + }, + { + "type": "table_caption", + "bbox": [ + 0.52, + 0.501, + 0.867, + 0.515 + ], + "angle": 0, + "content": "Table 3. ScanNet Reconstruction Quantitative Results." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.543, + 0.892, + 0.603 + ], + "angle": 0, + "content": "performance by a large margin and leads to broader downstream applications. As shown in Fig. 6, RICO can reconstruct the unobservable (back view as in the caption) regions of the objects where the previous methods fail." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.617, + 0.819, + 0.632 + ], + "angle": 0, + "content": "4.3. Reconstruction in Real-world Scenes" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.892, + 0.777 + ], + "angle": 0, + "content": "We conduct experiments on 7 scenes of ScanNet [3] to show the effectiveness of our method on real-world data. Since ScanNet only provides ground truth for the visible surface, here we follow the protocol in [8] and report the reconstruction performance of the entire scene in Tab. 3. By utilizing the rendering formulation in [36] which explicitly models the angle between surface normal and ray, our method can achieve slightly better performance compared to ObjSDF* and [43] on visible surfaces." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.779, + 0.892, + 0.854 + ], + "angle": 0, + "content": "In Tab. 4 we evaluate the 2D rendering and segmentation performance and provide the PSNR and mIoU results on two real-world datasets. As our method constrains mainly the unobservable, the PSNR and mIoU metrics are not with significant difference." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In Fig. 7 we also provide the comparisons over two scenes. Note that the ScanNet images are blurry and noisy, and the masks are sometimes inaccurate (e.g., legs of chairs" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "17768" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.088, + 0.089, + 0.454, + 0.191 + ], + "angle": 0, + "content": "
ObjSDFObjSDF*Ours
PSNR↑ToyDesk21.1021.2121.33
ScanNet22.7823.1523.30
mIoU↑ToyDesk0.880.890.89
ScanNet0.890.910.92
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.203, + 0.47, + 0.231 + ], + "angle": 0, + "content": "Table 4. PSNR and mIoU Results of different methods on scenes from ScanNet and ToyDesk datasets." + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.256, + 0.462, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.463, + 0.47, + 0.505 + ], + "angle": 0, + "content": "Figure 8. Qualitative Results on ToyDesk. Here we show the reconstruction results both with and without the background for better visualization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.47, + 0.621 + ], + "angle": 0, + "content": "missing), leading to less accurate reconstructions. However, it can still be seen that our method can successfully regularize the unobservable regions to get the watertight mesh, while the baselines always result in open surface. For example, the piano in the first row and the sofas in the second row can only be reconstructed on visible surfaces." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.622, + 0.47, + 0.713 + ], + "angle": 0, + "content": "And in Fig. 8 we provide the qualitative results of our method and two baselines on two ToyDesk scenes. It can be seen that the baseline methods generate non-watertight surface with undesired artifacts (using table plane to cut the mesh will result in holes on the cut face), while our method can directly get clean results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.726, + 0.276, + 0.743 + ], + "angle": 0, + "content": "4.4. Object Manipulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.903 + ], + "angle": 0, + "content": "As aforementioned, the reconstruction results from ObjSDF* are sub-optimal for downstream applications like object manipulation. On the contrary, since RICO can get a watertight mesh, it can be easily used for such applications. In Fig. 9 we show the volume rendered normal maps and segmentation masks before and after moving an object in the scene. An illustration of how to manipulate one object in our framework and conduct volume rendering accordingly is applicable in the supplementary. As illustrated, after manipulation, the rendered segmentation and normal map are" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.09, + 0.693, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.09, + 0.894, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.217, + 0.892, + 0.26 + ], + "angle": 0, + "content": "Figure 9. Object Manipulation Cases. Here we show the volume rendered normal maps and segmentation masks in two scenes, before (top row) and after (bottom row) the manipulation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.283, + 0.892, + 0.33 + ], + "angle": 0, + "content": "still clean for RICO. In contrast, the results of ObjSDF* are messy because their reconstruction is connected with artifacts that were originally outside of the scenes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.343, + 0.62, + 0.358 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.368, + 0.892, + 0.52 + ], + "angle": 0, + "content": "We have presented RICO, a novel approach for compositional reconstruction in indoor scenes. Our key motivation is to regularize the unobservable regions for the objects with partial observations in indoor scenes. We exploit the geometry smoothness for the occluded background, and then adopt the improved background as the prior to regularize the objects' geometry. Our experimental results prove that our method achieves compositional reconstruction with fewer artifacts and watertight object geometry, which further facilitates applicable applications like object manipulation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.893, + 0.781 + ], + "angle": 0, + "content": "Future work: Currently, each object's pose is baked with its geometry. An interesting future direction would be represent each object in scene as the combination of its own canonical coordinates and the pose, i.e. the rotated 3D bounding box in the world coordinate. With these disentangled representations, we can cast more regularizations from the shape and box perspectives, and the disentanglement also allows more flexible downstream applications. Another interesting direction would be developing more semantic-based prior knowledge for systemic regularization. Now the geometry motivated regularizations are lack of the understanding of the actual shape of each object. With the general knowledge emerged in recent large vision-language model, like StableDiffusion, it's interesting to distill its knowledge in our compositional reconstruction task. The learnt semantic knowledge can provide a holistic understanding of each object and provide a more comprehensive regularization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.786, + 0.892, + 0.892 + ], + "angle": 0, + "content": "Acknowledgements: We thank Kechun Xu and Huaijin Pi for detailed feedback on the paper. We thank all authors and reviewers for the contributions. This work is in part supported by a Grant from the National Natural Science Foundation of China (No.U21A20484), the NSFC under grant U21B2004, 62202418, and the Zhejiang University Education Foundation Qizhen Scholar Foundation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17769" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Mathilde Caron, Hugo Touvron, Ishan Misra, Hervé Jégou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. Emerging properties in self-supervised vision transformers. 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To facilitate practical applications like scene editing and manipulation, some works extend the framework with semantic masks input for the object-compositional reconstruction rather than the holistic perspective. Though achieving plausible disentanglement, the performance drops significantly when processing the indoor scenes where objects are usually partially observed. We propose RICO to address this by regularizing the unobservable regions for indoor compositional reconstruction. Our key idea is to first regularize the smoothness of the occluded background, which then in turn guides the foreground object reconstruction in unobservable regions based on the object-background relationship. Particularly, we regularize the geometry smoothness of occluded background patches. With the improved background surface, the signed distance function and the reversedly rendered depth of objects can be optimized to bound them within the background range. Extensive experiments show our method outperforms other methods on synthetic and real-world indoor scenes and prove the effectiveness of proposed regularizations. The code is available at https://github.com/kyleleey/RICO + +# 1. Introduction + +Reconstructing 3D geometry from images is a fundamental problem in computer vision and has many downstream applications like VR/AR and game assets creation. With the advance of neural implicit representations [20], recent reconstruction methods [25, 36, 41, 43] can recover accurate geometry from multi-view images. However, existing methods typically regard the whole scene as an entirety and reconstruct everything altogether, thus preventing applications like scene editing. In indoor scenes with plenty of reconfigurable objects, a disentangled object-compositional reconstruction, i.e. decomposing the geometry into different instantiated objects and background, can be more suitable + +![](images/363124f5ae2b360c85afe7ca2a2ee00751a566213077d418f1450f1039a4a6eb.jpg) + +![](images/892f31bbdde9e28a568301862d77543b832f9644b7c815734b87a1596128ecab.jpg) +Figure 1. Comparison of [37] (Top) and ours (Bottom). Different objects are visualized in different colors. Previous reconstructions are connected with large artifacts. Taking the partially observed cubic object's front and back views (in red and green rectangles respectively) as an example, [37] can only get the visible surface, while ours can complement the complete body. + +for further applications like moving the sofa in the scene. + +In this paper, we aim to recover the room-level indoor scenes with decomposed geometry of individual objects and background. We assume that multi-view posed images and semantic masks that assign different labels to each instantiated object and the background are given as input. Existing object-compositional methods [9, 45, 40] concentrate more on the rendering performance rather than the underlying geometry, and thus can not be directly used for reconstruction. The most recent work ObjSDF [37] learns an object-compositional signed distance function (SDF) field by proposing a transform function between SDF values and semantic logits. Specifically speaking, ObjSDF predicts multiple SDF values at each 3D point for different seman + +tic classes, and converts them to semantic logits, allowing for separating object SDF values from the background when supervised by semantic masks. Although achieving plausible shape disentanglement, it suffers from a common problem in indoor scenes: objects and background can only be partially observed due to occlusions. When the object is partially observed, e.g. a cubic object against the wall, ObjSDF can not properly reconstruct the geometry between them (see Fig. 1 top-right). The reason is that the existing works [45, 37] can only effectively regularize semantic labels and geometry of observed regions, and have little impact on the unobserved regions. When processing the indoor scenes where a large portion of objects are partially observed, the reconstruction results of these objects will be visible surface connected with the unconstrained structures (as shown in Fig. 1, see Section 3.3 for a detailed analysis). Fig. 2 shows that even with reasonable reconstruction when composing all the objects together, each object's result in the unobserved region is far from satisfactory and can hinder further applications like manipulating the object. + +We propose RICO, which realizes the proper geometry disentanglement for indoor scenes (see Fig. 1 bottom) by explicitly regularizing the unobserved regions. To be more specific, when the object is partially observed, recovering its geometry is an ill-posed problem even with corresponding masks. Thus, introducing prior regularization for unobserved regions is necessary. We exploit two types of prior knowledge for indoor scenes in this work: 1) background smoothness and 2) object-background relations. First, when one ray hits the object surface, the existing method [37] can properly regularize the geometry and appearance on the hitting point, but can not account for the background surface behind this object. This drawback leads to artifacts and holes on the unobserved background surface (see Fig. 2). We propose a patch-based smoothness loss to regularize the SDF values of unobserved background regions. Then, since the background reconstruction is improved, we can leverage another strong prior: the objects are all within the room, i.e. using the background surface to regularize the SDF field of objects. We design two regularization terms: an object point-SDF loss for sampled points behind the background surface and a reversed depth loss to regularize the SDF distribution of the entire ray. Both terms aim to bound the object within the background surface's range, thus preventing the aforementioned unmeaning structure, making the object reconstruction a watertight and plausible shape instead of an open surface with severe artifacts. + +In summary, we propose RICO to realize compositional reconstruction in indoor scenes where a large portion of objects are partially observed. Our main contributions are: i) A patch-based background smoothness regularizer for unobserved background surface geometry. ii) Guided by the improved background surface, we exploit the object- + +![](images/cd75785997efa7f925afd81f2cb9042b67fce0bdedb4f4024dc7b06c24fb6dff.jpg) +Figure 2. ObjSDF results. Interested objects are dyed in blue. Despite of the plausible composition, the disentangled backgrounds have artifacts and sunk holes, and partially observed objects can only get the visible surface (illustrated in 'Object Backward'). + +background relation as prior knowledge and design objectives that effectively regularize objects' unobserved regions. iii) Extensive experiments on both real-world and synthetic datasets prove our superior reconstruction performance compared to previous works, especially for the partially observed objects. + +# 2. Related Work + +Neural Implicit Representation for Reconstruction: Recently, neural implicit representations have emerged as a popular representation for 3D reconstruction. While early approaches [19, 26] rely on 3D supervision, a few works [24, 42] exploit surface rendering to use multi-view image supervision only, but also suffer from the unstable training. Neural radiance field (NeRF) [20] adopts volume rendering technique to achieve photorealistic scene representation and stable optimization. However, NeRF's formulation can not guarantee accurate underlying geometry. Therefore, [25, 36, 41] combine the geometry representation with iso-surface (e.g. occupancy [19], SDF [36, 41]) and volume density to accurately reconstruct object-level scenes from RGB images. [8] further applies the planar regularization for scene-level reconstruction. To tackle the problem in texture-less regions, [35, 43] utilize results from pretrained normal and depth estimation networks to guide the SDF training and boost the reconstruction performance. + +However, despite the promising reconstruction performance, the aforementioned methods all consider the whole scene as an entirety. Our method focuses on decomposing the scene reconstruction into the background and different foreground objects, which can be regarded as compositional scene reconstruction. + +Compositional Scene Reconstruction: Decomposing a scene into its different components could benefit downstream applications like scene editing. Many works have been proposed to recover the scene in a compositional man + +![](images/b72291283a923880577c0df11df758eb200167fc4546dde72e95123639f5181b.jpg) +Figure 3. Overview. In this work, we propose two different regularizations. We first regularize the geometry smoothness of the unobserved background regions in a sampled patch. Then, we exploit the background surface as the prior to constrain the objects' surface. In detail, a per-point SDF loss and a reversed depth loss are introduced to regularize the manifold of objects' SDF functions. Combined with other reconstruction losses, our method reaches a neat and disentangled compositional reconstruction in indoor scenes. + +ner from different perspectives. [22, 44, 10, 21] detect and reconstruct different objects in the given monocular image, and predict the scene's layout at the same time. But most of these methods require large-scale datasets with 3D ground truth for training. [14, 32, 18] optimize a feature field from a large pretrained model [1, 16], which enables deep feature based decomposition and manipulation. [38, 31] exploit the self-supervise paradigm to decompose the scenes into static and dynamic parts. More works [9, 45, 40, 39, 34, 6, 15, 33] focus on recovering the object-compositional scenes given semantic masks with images. However, this line of works concerns the rendering outputs rather than the geometry, i.e. the reconstruction results are sub-optimal. + +Recently, ObjSDF [37] proposes a transform function between semantic logits and SDFs of different objects, which enables optimizing SDF fields with image and semantic mask supervision, and decomposing the whole scene with accurate reconstruction. However, in the indoor scenes where many objects are in partial observation, its reconstruction results are far from satisfactory and can not be used for further applications (see Fig. 2). On the contrary, our method introduces geometry prior to unobserved regions, yielding better compositional scene reconstruction. + +Prior Regularization in Neural Implicit Reconstruction: In addition to the commonly used RGB image supervision, many different priors have been proposed to benefit the neural implicit representation. For example, [4, 30] use explicit point cloud as the depth prior, [23] employs regularization in unseen views and [11] introduces pretrained model's feature consistency. [12, 28] adopt explicit human model as the structural prior for the human-centric scenes. As for surface + +reconstruction, [8] proposes a Manhattan-world assumption for the planar regions, [43] utilizes the normal and depth prediction from off-the-shelf model [5] as prior to regularize the texture-less regions. + +Our method exploits the geometry prior in the unobserved region for compositional scene reconstruction. The proposed regularization can effectively reconstruct the objects and disentangle them from the background, even if the object itself is partially observed. + +# 3. Methodology + +Our goal is to recover decomposed geometry surface of the objects and background within a scene from the images and semantic masks inputs. To this end, we first review the SDF-based neural implicit representation and how to use the semantic logits for compositional reconstruction in Section 3.1. Next, we propose two types of regularizations on unobserved regions to address the partial observation problem: patch-based background smoothness (Section 3.2) and object-background relation (Section 3.3). Finally, we introduce the overall optimization procedure in Section 3.4. An overview of our method is provided in Fig 3. + +# 3.1. Background + +Volume Rendering of SDF-based Implicit Surface: For implicit reconstruction, the geometry of the scene is represented as the signed distance function (SDF) $s(\mathbf{p})$ of each spatial point $\mathbf{p}$ , which is the point's distance to the closest surface. In practice, the SDF function is implemented as a multi-layer perceptron (MLP) network $f(\cdot)$ . The appear- + +ance of the scene is also defined as an MLP $g(\cdot)$ .. + +$$ +\begin{array}{l} f: \mathbf {p} \in \mathbb {R} ^ {3} \mapsto (s \in \mathbb {R}, \mathbf {f} \in \mathbb {R} ^ {2 5 6}) \\ g: (\mathbf {p} \in \mathbb {R} ^ {3}, \mathbf {n} \in \mathbb {R} ^ {3}, \mathbf {v} \in \mathbb {S} ^ {2}, \mathbf {f} \in \mathbb {R} ^ {2 5 6}) \mapsto \mathbf {c} \in \mathbb {R} ^ {3} \tag {1} \\ \end{array} +$$ + +where $\mathbf{f}$ is a geometry feature vector, $\mathbf{n}$ is the normal at $\mathbf{p}$ , $\mathbf{v}$ is the viewing direction and $\mathbf{c}$ is the view-dependent color. We adopt the unbiased rendering proposed in [36] to render the image. For each camera ray $\mathbf{r} = (\mathbf{o},\mathbf{v})$ with $\mathbf{o}$ as the ray origin, $n$ points $\{\mathbf{p}(t_i) = \mathbf{o} + t_i\mathbf{v}|i = 0,1,\dots ,n - 1\}$ are sampled, and the pixel color can be approximated as: + +$$ +\hat {\mathbf {C}} (\mathbf {r}) = \sum_ {i = 0} ^ {n - 1} T _ {i} \alpha_ {i} \mathbf {c} _ {i}. \tag {2} +$$ + +The $T_{i}$ is the discrete accumulated transmittance derived from $T_{i} = \prod_{j=0}^{i-1}(1 - \alpha_{j})$ , and $\alpha_{i}$ is the discrete density value defined as + +$$ +\alpha_ {i} = \max \left(\frac {\Phi_ {u} (s (\mathbf {p} (t _ {i}))) - \Phi_ {u} (s (\mathbf {p} (t _ {i + 1})))}{\Phi_ {u} (s (\mathbf {p} (t _ {i})))}, 0\right), \tag {3} +$$ + +where $\Phi_u(x) = (1 + e^{-ux})^{-1}$ and $u$ is a learnable parameter. By minimizing the difference between predicted and ground-truth pixel colors, we can learn the SDF and appearance function of the desired scene. + +Learning SDF with Semantic Logits: In this work, we consider compositional reconstruction of $k$ objects given their masks. Note that we also consider the background as an instantiated object for brevity as in [37] and follow their network structure. In detail, for a scene with $k$ objects, the SDF MLP $f(\cdot)$ now outputs $k$ SDFs at each point, and the $j$ -th $(1 \leq j \leq k)$ SDF represents the geometry of $j$ -th object. Without loss of generality, we set $j = 1$ as the background category and others for objects in Fig. 3 and the rest of the paper. The scene SDF is the minimum of $\{s_j\}$ , which is used for sampling points along the ray and aforementioned volume rendering (Eq. 2). Moreover, each point's $k$ SDFs can be transformed into semantic logits $\mathbf{h}(\mathbf{p})$ as + +$$ +\begin{array}{l} \begin{array}{l} h _ {j} (\mathbf {p}) = \gamma / (1 + \exp (\gamma \cdot s _ {j} (\mathbf {p}))), \\ \mathbf {p} (.) = [ 1, (.) ] \end{array} \tag {4} \\ \mathbf {h} (\mathbf {p}) = \left[ h _ {1} (\mathbf {p}), h _ {2} (\mathbf {p}), \dots , h _ {k} (\mathbf {p}) \right], \\ \end{array} +$$ + +where $\gamma$ is a fixed parameter. Using volume rendering to accumulate the semantic logits of all the points along a ray, we can get the semantic logits $\mathbf{H}(\mathbf{r})\in \mathbb{R}^k$ of each pixel. During training, the cross-entropy loss applied to $\mathbf{H}(\mathbf{r})$ is backpropagated to the SDF values, allowing for learning the compositional geometry. + +# 3.2. Patch-based Background Smoothness + +Although the volume rendering can propagate gradients along the entire ray, the optimization mainly focuses on the surface-hitting point, as its accumulated weight can be + +much larger than the others. As a result, the geometry of the points behind the first-hit surface can not be optimized correctly. In the indoor scenes, the occluded part of the background surface is invisible in all the images, which can be with holes and random artifacts (see Fig. 2). + +Since we cannot tell the exact color, depth or normal of the occluded part, it is intractable to optimize this region wrt. its ground truth. Therefore, we propose to regularize the geometry of the occluded background to be smooth, thus preventing some clearly wrong artifacts. + +In detail, we regularize the smoothness of rendered depth and normal of background surface within a small patch region. To save the computation budget, we randomly sample a $\mathcal{P} \times \mathcal{P}$ size patch every $\mathcal{T}_{\mathcal{P}}$ iterations in the given image and sample points along the patch rays using the background SDF only. We compute depth map $\hat{D}(\mathbf{r})$ and normal map $\hat{N}(\mathbf{r})$ of the sampled patch following [43], $\mathbf{r}$ denotes the sampled ray in patch. The semantic map of the patch is also computed and transformed into a patch Mask $\hat{M}(\mathbf{r})$ : + +$$ +\hat {M} (\mathbf {r}) = \mathbb {1} [ \arg \max (\mathbf {H} (\mathbf {r})) \neq 1 ], \tag {5} +$$ + +which means the mask value is 1 if the rendered class is not the background, so that only the occluded background is regularized. Taking rendered depth as an example, the patch-based background smoothness loss is + +$$ +\begin{array}{l} \mathcal {L} (\hat {D}) = \sum_ {d = 0} ^ {3} \sum_ {m, n = 0} ^ {\mathcal {P} - 1 - 2 ^ {d}} \hat {M} \left(\mathbf {r} _ {m, n}\right) \odot (| \hat {D} \left(\mathbf {r} _ {m, n}\right) - \tag {6} \\ \hat {D} \left(\mathbf {r} _ {m, n + 2 ^ {d}}\right) | + | \hat {D} (\mathbf {r} _ {m, n}) - \hat {D} \left(\mathbf {r} _ {m + 2 ^ {d}, n}\right) |\left. \right). \\ \end{array} +$$ + +Here the smoothness is applied on different intervals controlled by $d$ . $m$ and $n$ are the pixel indices within the patch and the mask is multiplied at each position with hadamard product $\odot$ . The normal smoothness loss $\mathcal{L}(\hat{N})$ can be obtained similarly. We define the overall background smoothness loss $\mathcal{L}_{bs}$ as: + +$$ +\mathcal {L} _ {\mathrm {b s}} = \mathcal {L} (\hat {D}) + \mathcal {L} (\hat {N}). \tag {7} +$$ + +Here in contrast to [23] which applies a patch-based regularization to visible regions in other views, we instead regularize the occluded regions of the background. + +# 3.3. Object-background Relation as Regularization + +With the help of the patch-based background smoothness loss, most artifacts of the background are resolved, yielding a smooth surface. We further leverage this smooth background surface to regularize the SDF fields of other objects, leveraging a key prior knowledge that all the other objects are confined to the room, i.e., the background surface. + +In the original framework of [37], if an object is partially observed, e.g. against the background, the object's reconstructed surface won't be a "closed" surface (see Fig. 1 and + +![](images/1197c88105231b5d4c8de329e887c8d3b41bfefb9fa3b462786546145bf3b2aa.jpg) +Figure 4. Toy-case analysis. A bird-eye view of an object against the background is shown here, the SDF and surface of object is shown in red and background's in blue. (a) In [37] the minimum SDF is used for volume rendering and semantic loss, so on object's visible surface where object SDF is optimized to 0 and the background SDF here is positive, and similar for the visible background surface. Since the scene is partially observed from left, the right part of object surface is open and unobserved background region is unconstrained. (b) With the smoothness prior the background surface can be plausible, (c) and object point SDF loss close the object surface but still have intersections, (d) finally the reversed depth loss optimizes the entire ray thus the object can be within the background. + +Fig. 2). We refer to the toy-case analysis shown in Fig. 4 for the reason of the current unsatisfactory reconstruction. To encourage the reconstruction to be watertight, we design two types of regularization on the SDF fields of objects. + +Object Point-SDF Loss: A straightforward solution is to directly regularize the objects' SDFs on every sampled point behind the background surface. To be more specific, the regular volume rendering only guarantees a single change of the sign (positive SDF to negative) when a ray hits a visible surface. For watertight objects, the ray should hit another occluded surface (negative SDF to positive). With the prior that the object is confined within the room, the occluded object surface should be closer than the background surface, meaning that the object SDFs of points behind the background surface should all be positive (Fig. 4 (c)). + +We implement an object point-SDF loss based on the above analysis. For the sampled points along the rays, we first utilize the root-finding algorithm among the background SDF of these points and find the zero-SDF ray depth $t'$ . Then the object point-SDF loss can be formulated as + +$$ +\mathcal {L} _ {\mathrm {o p}} = \frac {1}{k - 1} \sum_ {j = 2} ^ {k} \max \left(0, \epsilon - \mathbf {s} _ {j} (\mathbf {p} (t _ {i}))\right) \cdot \mathbb {1} [ t _ {i} > t ^ {\prime} ], \quad (8) +$$ + +which pushes the objects' SDFs at points behind the surface + +larger than a positive threshold $\epsilon$ . + +Reversed Depth Loss: Although the $\mathcal{L}_{\mathrm{op}}$ can effectively regularize the SDF fields of each object, in practice we find the reconstructed object surface can still have intersections with the background surface (Fig. 4 (c)). The reason is that the sampled points are discrete and in most cases, the background surface is between two sampled points. Therefore, the sign change of the occluded surface may still occur after hitting the background surface. + +Since per-point optimization can not effectively propagate to the distribution of the entire ray. To optimize the entire ray's SDF distribution for better regularization, we compute a reversed depth along each ray. With the help of $\mathcal{L}_{\mathrm{op}}$ , the sign of the object SDF along one ray now is positive-negative-positive, which enables rendering a depth value backward. We first transform the ray depth $\{t_i|i = 0,1,\dots ,n - 1\}$ into the reversed ray depth named $\{\hat{t}_i|i = 0,1,\dots ,n - 1\}$ , where + +$$ +\hat {t} _ {i} = \left(t _ {0} + t _ {n - 1}\right) - t _ {n - 1 - i}. \tag {9} +$$ + +With the reversed ray depth values, we use the background and object SDF both in reversed order to compute the accumulated weight and get the reversed depth respectively. Remarkably, in order to compute the exact correct depth, the points should be re-sampled along the reverse direction. Here we directly use the sampled points to avoid computation overhead, and empirical results prove its effectiveness. We only compute the reverse depth of one pixel if satisfying two conditions: 1) this pixel's $\hat{M}(\mathbf{r}) = 1$ ; 2) the SDF value of the rendered object at the furthest point is positive. Note that the second condition is usually satisfied when the object point-SDF loss is applied. By computing the reversed depth $d_{o}$ of the hitting object (determined by the pixel's rendered semantic) and $d_{b}$ of the background, we can get the reversed depth loss: + +$$ +\mathcal {L} _ {\mathrm {r d}} = \max \left(0, d _ {b} - d _ {o}\right), \tag {10} +$$ + +which pushes the object surface within the background as illustrated in Fig. 4 (d). + +# 3.4. Training Objectives Details + +Monocular geometric cues are essential for indoor scene reconstruction as proved in [43]. Following [43], we add the depth and normal consistency loss $(\mathcal{L}_{\mathrm{D}},\mathcal{L}_{\mathrm{N}})$ with pseudo ground truth from Omnidata [5] model. In experiments, we also add the monocular cues on [37] to get a stronger baseline for a fair comparison. + +The SDF network is also regularized by an Eikonal [7] loss item $\mathcal{L}_{\mathrm{E}}$ . We further use the semantic loss $\mathcal{L}_{\mathrm{S}}$ proposed in [37] to learn the compositional geometry. The overall loss function for compositional reconstruction is: + +$$ +\begin{array}{l} \mathcal {L} = \mathcal {L} _ {\mathrm {R G B}} + \lambda_ {\mathrm {D}} \mathcal {L} _ {\mathrm {D}} + \lambda_ {\mathrm {N}} \mathcal {L} _ {\mathrm {N}} + \lambda_ {\mathrm {E}} \mathcal {L} _ {\mathrm {E}} + \lambda_ {\mathrm {S}} \mathcal {L} _ {\mathrm {S}} \tag {11} \\ + \lambda_ {\mathrm {b s}} \mathcal {L} _ {\mathrm {b s}} + \lambda_ {\mathrm {o p}} \mathcal {L} _ {\mathrm {o p}} + \lambda_ {\mathrm {r d}} \mathcal {L} _ {\mathrm {r d}}. \\ \end{array} +$$ + +We set $\lambda_{\mathrm{bs}}, \lambda_{\mathrm{op}}, \lambda_{\mathrm{rd}} = 0.1$ in our experiments. For other loss terms, given the weight of RGB reconstruction loss as 1, we set $\lambda_{\mathrm{D}} = 0.1$ and $\lambda_{\mathrm{N}} = \lambda_{\mathrm{E}} = 0.05$ following [43]. For the semantic loss, we follow the implementation in [37] and set $\lambda_{\mathrm{D}} = 0.04$ . The detailed calculation of other losses can be found in supplementary. + +# 4. Experiments + +We first conduct ablation study on each proposed component. Then we provide quantitative and qualitative results of object-compositional reconstruction on real-world and synthetic scenes. Finally, we show some possible object manipulation with our compositional reconstruction. + +Datasets: We consider three types of indoor datasets with multi-view RGB images and masks: 1) ScanNet [3], a real-world dataset widely used in previous works [8, 35, 37, 43]; 2) ToyDesk dataset, a real-world dataset with two scenes and each has four objects placed on the table plane. This dataset has also been widely used in previous compositional works [40, 37] 3) a hand-crafted synthetic dataset with five scenes, each containing $5 \sim 10$ objects. The synthetic dataset is considered such that the ground truth geometry of both, occluded and non-occluded regions are available. + +Metrics: For reconstruction performance, we report Chamfer Distance, F-score for evaluation on ScanNet, following [8, 43]. On synthetic scenes we divide metrics for two aspects: objects and background. For objects we report the reconstruction performance compared to the complete ground truth object mesh, and the final results are averaged across all the objects in all the scenes. For background we report the reconstruction metrics and rendered depth errors of the occluded regions only to highlight the effectiveness of our regularization. The results are also averaged across all the scenes. See supplementary for a detailed introduction to datasets and metrics. We also report two 2D metrics, PSNR and mIoU, on the ToyDesk and ScanNet scenes. Here we omit the synthetic dataset considering its relatively simple texture. For the test image set, on ToyDesk dataset we use the official split, and on ScanNet we sample frames from their original camera trajectories. The metrics are averaged across different images of different scenes. + +Baselines: We mainly compare with ObjSDF [37] in this work, as it is the only method that focuses on the same task, a specific discussion is provided in the supplementary. Since we focus on the indoor scene where monocular cues can benefit a lot [43], we add losses proposed in [43] to our method for better performance. For a fair comparison, we also combine [37] and [43] for a stronger baseline, named ObjSDF*. Moreover, since ObjSDF*’s object reconstructions inevitably have artifacts, we develop a postprocess method to cull the parts outside the background range and name this baseline ObjSDF*-C. We provide the + +![](images/8be90f091193a28a1bd84740061f197622c5d8c3210a967e50ae9102ded83a20.jpg) +Figure 5. Effects of Regularizations. The first row shows two backgrounds, the $\mathcal{L}_{\mathrm{bs}}$ clearly mitigates most of the artifacts. The last row shows that with $\mathcal{L}_{\mathrm{op}}$ we can get the watertight object and $\mathcal{L}_{\mathrm{rd}}$ further constrains the unobserved surface. + +details of how to set the range in the supplementary. Note that our method directly generates clean watertight meshes and doesn't need such post-processing. In ScanNet experiments, we also report results for MonoSDF [43] as a reference since we can only evaluate the overall reconstruction (details in Section 4.3). + +Implementation Details: We implement our method in PyTorch [27]. We use the Adam [13] optimizer with a learning rate of 5e-4 for 50k iterations and sample 1024 rays per iteration. The weight initialization scheme for SDF MLP is identical to [41, 36, 37]. The $u$ is initialized as 0.05 and we set $\gamma = 20$ as proposed in [37]. $\mathcal{P}$ , $\mathcal{T}_{\mathcal{P}}$ and $\epsilon$ are set as 32, 10 and 0.05 respectively. All the reconstructions are acquired by using marching cube [17] at the resolution of 512. + +Moreover, we adopt the geometric initialization [7] for the geometry network, which initializes the reconstruction with a unit sphere and the surface normals are facing inside at the beginning of the optimization. For the ScanNet dataset, we follow the protocol in [43] to crop the input image to $384 \times 384$ and adjust the intrinsics accordingly. For the synthetic dataset, we directly render the image at the same resolution. Since we focus on the indoor scenes in this paper, we adopt the common practice to process the "bounded" scene. For each scene, we normalize the camera poses so that all the cameras lie in a unit sphere. The rays intersection, i.e. the furthest sampling location, is computed based on this sphere and we also conduct Marching Cubes [17] within the same area for the final reconstruction. + +# 4.1. Ablation Study + +We first quantitatively analyze the effectiveness of the proposed regularizations on synthetic scenes by comparing our full method to four variants in Tab. 1. First, adding the smoothness loss (V2) significantly decreases the depth error of occluded background regions. Next, the $\mathcal{L}_{\mathrm{op}}$ makes the object reconstruction watertight and the object-level metrics are greatly improved (V3). The $\mathcal{L}_{\mathrm{rd}}$ further improves the object reconstruction performance (Full). Results of V4 prove + +![](images/98b5ebb6ab51af2e72435b447d56b2ff4bdb7d9ec54adb66921b989ccf47524e.jpg) +ObjSDF + +![](images/b878686d54219a3f49abae12ac2b97c5df17047c31b1a4c6e7d1f74e2c5f04d4.jpg) +ObjSDF* + +![](images/663c0da969b18e7a84b7e8620f07d86a27cea434e771445a7a663930fd8d9eb9.jpg) +Ours + +![](images/fda326be0808fb2cb22717cb189e6c213dddd651be38467e56ddfa46971a14bc.jpg) +GT + +![](images/646374c948a90d7b869901439be331fc98c230e4bcdf48bf7f4c23fac18f19cd.jpg) + +![](images/36095fbbc845631d7844521c339f08be34d24d5c9dad304a29067163e9b7096b.jpg) + +![](images/45aeb756c6bc6207b4cf11456e08a174f133318c1e6761bc3cc76954c21c7da4.jpg) + +![](images/4d78525bbf8976f0ed2ce38f1357471fb89a40a08ed8920c51593e3e8f239286.jpg) + +![](images/062d8fc40fdd76808ab421abe972cbbbf7a55d7eec354699886ffec338749fb3.jpg) + +![](images/8b6a98c45f6d0932ef60164e2593d0f3930df1cc4d784209752d80f9aba6a5f2.jpg) + +![](images/27d9cce436b0167bf77ec6c7587bb07d4dc2329d4fd0a788494d73f1a2be331e.jpg) + +![](images/c3e120a6b05231b2cb8d2145666bd443c86b31b4d7f257b5236563876caa1171.jpg) + +![](images/350efbd0d53781870cc086ed1a30febce2cf59202458cd25d5699e6159184621.jpg) + +![](images/fda0c6112815a274759db63926206cf8408fa8a89d6c8cd5adf318833e8bcd10.jpg) + +![](images/18790fc8024a2746c51d937fc92fec8289db44a78421bbe021c3f80585e761b8.jpg) + +![](images/e8c47d26bb8357e34628e23c648f935efca6ed74ba67da79b1a5c19fe4ada79b.jpg) + +![](images/981b928025d74b595b0ff2c4e17f6ebef687ed3c3e0e1b1a1dd6d715bb3033b8.jpg) +ObjSDF* + +![](images/ac4064f45b56cbfa5ced7158cd74ba295ead14328ec4036ff77b3a3c96a0126c.jpg) +ObjSDF*-C + +![](images/577c32901b308d80eb51a26a30a99d7cff17f45c6606e7312695905177f35489.jpg) +Ours + +![](images/546666e584f0549f1a2594c3e4934fbed47389f3d3c067297121d8f3d626e8b3.jpg) +GT +Figure 6. Qualitative Results on Synthetic Scenes. Above the blue line we show the comparison of different methods on two background scenes. Below we provide results of two scenes where only the object results are shown. In red rectangles at the bottom of each picture, we show the back (left part) and front (right part) views of an example object. Detailed descriptions in Section 4.2. + +
BackgroundObject
LbsLopLrdD.↓C.↓F.↑C.↓F.↑
V1---0.0210.0450.7681.240.065
V2✓--0.0040.0090.991.250.066
V3✓✓-0.0030.0090.990.0450.735
V4-✓✓0.0150.0290.8880.0390.785
Full✓✓✓0.0030.0090.990.0330.817
+ +that without $\mathcal{L}_{\mathrm{bs}}$ to improve the background, the object re + +Table 1. Ablation Study. The D. denotes the depth error of the occluded background. The C. and F. mean the Chamfer- $L_{1}$ and F-score respectively, for the reconstruction of occluded background regions and full complete objects. Details in Section 4.1. + +
BackgroundObjects
D.↓C.↓F.↑C.↓F.↑
ObjSDF0.0330.0760.6691.0400.084
ObjSDF*0.0210.0440.7721.0300.085
ObjSDF*-C0.0210.0440.7720.1340.681
Ours0.0030.0090.9900.0330.817
+ +Table 2. Synthetic Scenes Reconstruction Quantitative Results. The D. C. and F. have the same meanings as in Tab. 1. + +construction quality also drops. Note that $\mathcal{L}_{\mathrm{rd}}$ needs to be applied jointly with $\mathcal{L}_{\mathrm{op}}$ to guarantee its second condition. + +A qualitative case is shown in Fig. 5 for better illustration. In the first row, the occluded part of the background + +![](images/cb7f2718715fc2a664165b459a3013415e8443565fb897e3f1affa4851d96945.jpg) + +![](images/874f6c0812581415957cd6b0ae8fde13fac9d5fba19fcc33a95abcf3c4e9618a.jpg) +MonoSDF + +![](images/f3ba0e8f513ec3c6917ea4b4563a69261d78144abd7160b75c05554615bae46f.jpg) + +![](images/e062d16d96920772da9475e00319ccf8c3bc58f03f7aaca5f8ad76bb8dfdd304.jpg) + +![](images/d07266c13f534f6e9b21cc65e7f5ef800c85d3a48490f3e501b20e996ead8ff1.jpg) + +![](images/d5b89d778eea6245591442f5a36b87146f80d40806019b25bbd0ce53fd9f61e7.jpg) +ObjSDF* +Figure 7. Qualitative Results on ScanNet [3]. On the left of blue line we show the overall reconstruction from [43] as the reference. On the right we show the comparison between our method and two baselines. Similarly, the back and front views of objects with partial observations are provided in red rectangles. Detailed descriptions in Section 4.3. + +![](images/ea21c52063173b9fcebf2f67ee32b6c41d96c056b1767301dcefc0f88b8c3a2b.jpg) + +![](images/a947811aab529bfe5960a944e87026d8d49644dd69d4302040ba3b061146d7b8.jpg) +ObjSDF*-C + +![](images/4d2a3477b241dbbd671290b4e04c9ccb68c07a7fcc40dab1c178caa6cbe0ba23.jpg) + +![](images/9474bddb929044755c5613b9fa0f737e14ca1e5c5c34d1c4f046bcadcd1ed758.jpg) +Ours + +can have many artifacts because of occlusion. With the smoothness regularization, the reconstructed backgrounds are much cleaner. Since the $\mathcal{L}_{\mathrm{bs}}$ only applies to the occluded region, the other parts won't be affected. In the second row, the sofa is pushed against the wall and reconstruction from [37] contains only visible open surface. The $\mathcal{L}_{\mathrm{op}}$ first regularizes the SDF field to be a watertight mesh. The $\mathcal{L}_{\mathrm{rd}}$ further mitigates the flaws at the back by regularizing the object to be confined to the background. + +# 4.2. Reconstruction in Synthetic Scenes + +Since the synthetic scenes are rendered with objects that have accurate object-level 3D ground truth geometry, we compare our methods with previous object-compositional reconstruction method [37] on the 5 generated scenes and report the quantitative results in Tab. 2. + +In Tab. 2 we provide detailed metrics on object-level reconstruction. A qualitative comparison is shown in Fig. 6. The computation procedure of all the metrics is available in the supplementary. With monocular cues, ObjSDF* can achieve better performance than the original ObjSDF. However, their performance on object reconstruction is far from satisfactory, since they can only accurately obtain the visible surface with large parts of irrelevant structures in the indoor scenes as pointed out in the analysis before. Though ObjSDF*-C can eliminate most of the outliers and get improved performance, it can only reconstruct visible regions as an open surface as shown in Fig. 6. On the contrary, our regularizations help to smoothen the background and recover the object as a watertight mesh, which promotes + +
ObjSDFObjSDF*OursMonoSDF
Chamfer-L1↓0.1700.0920.0880.090
F-Score ↑0.3570.5670.6240.610
+ +Table 3. ScanNet Reconstruction Quantitative Results. + +performance by a large margin and leads to broader downstream applications. As shown in Fig. 6, RICO can reconstruct the unobservable (back view as in the caption) regions of the objects where the previous methods fail. + +# 4.3. Reconstruction in Real-world Scenes + +We conduct experiments on 7 scenes of ScanNet [3] to show the effectiveness of our method on real-world data. Since ScanNet only provides ground truth for the visible surface, here we follow the protocol in [8] and report the reconstruction performance of the entire scene in Tab. 3. By utilizing the rendering formulation in [36] which explicitly models the angle between surface normal and ray, our method can achieve slightly better performance compared to ObjSDF* and [43] on visible surfaces. + +In Tab. 4 we evaluate the 2D rendering and segmentation performance and provide the PSNR and mIoU results on two real-world datasets. As our method constrains mainly the unobservable, the PSNR and mIoU metrics are not with significant difference. + +In Fig. 7 we also provide the comparisons over two scenes. Note that the ScanNet images are blurry and noisy, and the masks are sometimes inaccurate (e.g., legs of chairs + +
ObjSDFObjSDF*Ours
PSNR↑ToyDesk21.1021.2121.33
ScanNet22.7823.1523.30
mIoU↑ToyDesk0.880.890.89
ScanNet0.890.910.92
+ +Table 4. PSNR and mIoU Results of different methods on scenes from ScanNet and ToyDesk datasets. + +![](images/6d8924b9eb6ad605d9e9a9239a6f09634ca3396a36e0cc004731b4d99856cfd3.jpg) +Figure 8. Qualitative Results on ToyDesk. Here we show the reconstruction results both with and without the background for better visualization. + +missing), leading to less accurate reconstructions. However, it can still be seen that our method can successfully regularize the unobservable regions to get the watertight mesh, while the baselines always result in open surface. For example, the piano in the first row and the sofas in the second row can only be reconstructed on visible surfaces. + +And in Fig. 8 we provide the qualitative results of our method and two baselines on two ToyDesk scenes. It can be seen that the baseline methods generate non-watertight surface with undesired artifacts (using table plane to cut the mesh will result in holes on the cut face), while our method can directly get clean results. + +# 4.4. Object Manipulation + +As aforementioned, the reconstruction results from ObjSDF* are sub-optimal for downstream applications like object manipulation. On the contrary, since RICO can get a watertight mesh, it can be easily used for such applications. In Fig. 9 we show the volume rendered normal maps and segmentation masks before and after moving an object in the scene. An illustration of how to manipulate one object in our framework and conduct volume rendering accordingly is applicable in the supplementary. As illustrated, after manipulation, the rendered segmentation and normal map are + +![](images/3141be343c1f8c90113ab61d9d3bf56bb0afead7e6960b8e57ac33e26f04d4ec.jpg) +Figure 9. Object Manipulation Cases. Here we show the volume rendered normal maps and segmentation masks in two scenes, before (top row) and after (bottom row) the manipulation. + +![](images/0c64a3fabcf57952f021702a1c077cd9ffe1aafada9a2d0830beedcc3769f83c.jpg) + +still clean for RICO. In contrast, the results of ObjSDF* are messy because their reconstruction is connected with artifacts that were originally outside of the scenes. + +# 5. Conclusion + +We have presented RICO, a novel approach for compositional reconstruction in indoor scenes. Our key motivation is to regularize the unobservable regions for the objects with partial observations in indoor scenes. We exploit the geometry smoothness for the occluded background, and then adopt the improved background as the prior to regularize the objects' geometry. Our experimental results prove that our method achieves compositional reconstruction with fewer artifacts and watertight object geometry, which further facilitates applicable applications like object manipulation. + +Future work: Currently, each object's pose is baked with its geometry. An interesting future direction would be represent each object in scene as the combination of its own canonical coordinates and the pose, i.e. the rotated 3D bounding box in the world coordinate. With these disentangled representations, we can cast more regularizations from the shape and box perspectives, and the disentanglement also allows more flexible downstream applications. Another interesting direction would be developing more semantic-based prior knowledge for systemic regularization. Now the geometry motivated regularizations are lack of the understanding of the actual shape of each object. With the general knowledge emerged in recent large vision-language model, like StableDiffusion, it's interesting to distill its knowledge in our compositional reconstruction task. The learnt semantic knowledge can provide a holistic understanding of each object and provide a more comprehensive regularization. + +Acknowledgements: We thank Kechun Xu and Huaijin Pi for detailed feedback on the paper. We thank all authors and reviewers for the contributions. This work is in part supported by a Grant from the National Natural Science Foundation of China (No.U21A20484), the NSFC under grant U21B2004, 62202418, and the Zhejiang University Education Foundation Qizhen Scholar Foundation. + +# References + +[1] Mathilde Caron, Hugo Touvron, Ishan Misra, Hervé Jégou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. Emerging properties in self-supervised vision transformers. 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To facilitate practical applications like scene editing and manipulation, some works extend the framework with semantic masks input for the object-compositional reconstruction rather than the holistic perspective. Though achieving plausible disentanglement, the performance drops significantly when processing the indoor scenes where objects are usually partially observed. We propose RICO to address this by regularizing the unobservable regions for indoor compositional reconstruction. Our key idea is to first regularize the smoothness of the occluded background, which then in turn guides the foreground object reconstruction in unobservable regions based on the object-background relationship. Particularly, we regularize the geometry smoothness of occluded background patches. With the improved background surface, the signed distance function and the reversedly rendered depth of objects can be optimized to bound them within the background range. 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Comparison of [37] (Top) and ours (Bottom). Different objects are visualized in different colors. Previous reconstructions are connected with large artifacts. Taking the partially observed cubic object's front and back views (in red and green rectangles respectively) as an example, [37] can only get the visible surface, while ours can complement the complete body." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 545, + 537, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 545, + 537, + 557 + ], + "spans": [ + { + "bbox": [ + 306, + 545, + 537, + 557 + ], + "type": "text", + "content": "for further applications like moving the sofa in the scene." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": "In this paper, we aim to recover the room-level indoor scenes with decomposed geometry of individual objects and background. We assume that multi-view posed images and semantic masks that assign different labels to each instantiated object and the background are given as input. Existing object-compositional methods [9, 45, 40] concentrate more on the rendering performance rather than the underlying geometry, and thus can not be directly used for reconstruction. The most recent work ObjSDF [37] learns an object-compositional signed distance function (SDF) field by proposing a transform function between SDF values and semantic logits. Specifically speaking, ObjSDF predicts multiple SDF values at each 3D point for different seman" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 140, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 140, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 140, + 712 + ], + "type": "text", + "content": "*Corresponding authors." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17761" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 312 + ], + "type": "text", + "content": "tic classes, and converts them to semantic logits, allowing for separating object SDF values from the background when supervised by semantic masks. Although achieving plausible shape disentanglement, it suffers from a common problem in indoor scenes: objects and background can only be partially observed due to occlusions. When the object is partially observed, e.g. a cubic object against the wall, ObjSDF can not properly reconstruct the geometry between them (see Fig. 1 top-right). The reason is that the existing works [45, 37] can only effectively regularize semantic labels and geometry of observed regions, and have little impact on the unobserved regions. When processing the indoor scenes where a large portion of objects are partially observed, the reconstruction results of these objects will be visible surface connected with the unconstrained structures (as shown in Fig. 1, see Section 3.3 for a detailed analysis). Fig. 2 shows that even with reasonable reconstruction when composing all the objects together, each object's result in the unobserved region is far from satisfactory and can hinder further applications like manipulating the object." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 315, + 289, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 315, + 289, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 315, + 289, + 639 + ], + "type": "text", + "content": "We propose RICO, which realizes the proper geometry disentanglement for indoor scenes (see Fig. 1 bottom) by explicitly regularizing the unobserved regions. To be more specific, when the object is partially observed, recovering its geometry is an ill-posed problem even with corresponding masks. Thus, introducing prior regularization for unobserved regions is necessary. We exploit two types of prior knowledge for indoor scenes in this work: 1) background smoothness and 2) object-background relations. First, when one ray hits the object surface, the existing method [37] can properly regularize the geometry and appearance on the hitting point, but can not account for the background surface behind this object. This drawback leads to artifacts and holes on the unobserved background surface (see Fig. 2). We propose a patch-based smoothness loss to regularize the SDF values of unobserved background regions. Then, since the background reconstruction is improved, we can leverage another strong prior: the objects are all within the room, i.e. using the background surface to regularize the SDF field of objects. We design two regularization terms: an object point-SDF loss for sampled points behind the background surface and a reversed depth loss to regularize the SDF distribution of the entire ray. Both terms aim to bound the object within the background surface's range, thus preventing the aforementioned unmeaning structure, making the object reconstruction a watertight and plausible shape instead of an open surface with severe artifacts." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 642, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 289, + 715 + ], + "type": "text", + "content": "In summary, we propose RICO to realize compositional reconstruction in indoor scenes where a large portion of objects are partially observed. Our main contributions are: i) A patch-based background smoothness regularizer for unobserved background surface geometry. ii) Guided by the improved background surface, we exploit the object-" + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 541, + 194 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 541, + 194 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 541, + 194 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 541, + 194 + ], + "type": "image", + "image_path": "cd75785997efa7f925afd81f2cb9042b67fce0bdedb4f4024dc7b06c24fb6dff.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 202, + 547, + 248 + ], + "lines": [ + { + "bbox": [ + 304, + 202, + 547, + 248 + ], + "spans": [ + { + "bbox": [ + 304, + 202, + 547, + 248 + ], + "type": "text", + "content": "Figure 2. ObjSDF results. Interested objects are dyed in blue. Despite of the plausible composition, the disentangled backgrounds have artifacts and sunk holes, and partially observed objects can only get the visible surface (illustrated in 'Object Backward')." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 266, + 547, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 547, + 340 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 547, + 340 + ], + "type": "text", + "content": "background relation as prior knowledge and design objectives that effectively regularize objects' unobserved regions. iii) Extensive experiments on both real-world and synthetic datasets prove our superior reconstruction performance compared to previous works, especially for the partially observed objects." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 350, + 392, + 363 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 350, + 392, + 363 + ], + "spans": [ + { + "bbox": [ + 306, + 350, + 392, + 363 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 374, + 545, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 545, + 589 + ], + "type": "text", + "content": "Neural Implicit Representation for Reconstruction: Recently, neural implicit representations have emerged as a popular representation for 3D reconstruction. While early approaches [19, 26] rely on 3D supervision, a few works [24, 42] exploit surface rendering to use multi-view image supervision only, but also suffer from the unstable training. Neural radiance field (NeRF) [20] adopts volume rendering technique to achieve photorealistic scene representation and stable optimization. However, NeRF's formulation can not guarantee accurate underlying geometry. Therefore, [25, 36, 41] combine the geometry representation with iso-surface (e.g. occupancy [19], SDF [36, 41]) and volume density to accurately reconstruct object-level scenes from RGB images. [8] further applies the planar regularization for scene-level reconstruction. To tackle the problem in texture-less regions, [35, 43] utilize results from pretrained normal and depth estimation networks to guide the SDF training and boost the reconstruction performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 590, + 547, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 590, + 547, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 590, + 547, + 662 + ], + "type": "text", + "content": "However, despite the promising reconstruction performance, the aforementioned methods all consider the whole scene as an entirety. Our method focuses on decomposing the scene reconstruction into the background and different foreground objects, which can be regarded as compositional scene reconstruction." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Compositional Scene Reconstruction: Decomposing a scene into its different components could benefit downstream applications like scene editing. Many works have been proposed to recover the scene in a compositional man" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "17762" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 68, + 531, + 257 + ], + "blocks": [ + { + "bbox": [ + 60, + 68, + 531, + 257 + ], + "lines": [ + { + "bbox": [ + 60, + 68, + 531, + 257 + ], + "spans": [ + { + "bbox": [ + 60, + 68, + 531, + 257 + ], + "type": "image", + "image_path": "b72291283a923880577c0df11df758eb200167fc4546dde72e95123639f5181b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 267, + 547, + 313 + ], + "lines": [ + { + "bbox": [ + 46, + 267, + 547, + 313 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 547, + 313 + ], + "type": "text", + "content": "Figure 3. Overview. In this work, we propose two different regularizations. We first regularize the geometry smoothness of the unobserved background regions in a sampled patch. Then, we exploit the background surface as the prior to constrain the objects' surface. In detail, a per-point SDF loss and a reversed depth loss are introduced to regularize the manifold of objects' SDF functions. Combined with other reconstruction losses, our method reaches a neat and disentangled compositional reconstruction in indoor scenes." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 331, + 288, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 288, + 487 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 288, + 487 + ], + "type": "text", + "content": "ner from different perspectives. [22, 44, 10, 21] detect and reconstruct different objects in the given monocular image, and predict the scene's layout at the same time. But most of these methods require large-scale datasets with 3D ground truth for training. [14, 32, 18] optimize a feature field from a large pretrained model [1, 16], which enables deep feature based decomposition and manipulation. [38, 31] exploit the self-supervise paradigm to decompose the scenes into static and dynamic parts. More works [9, 45, 40, 39, 34, 6, 15, 33] focus on recovering the object-compositional scenes given semantic masks with images. However, this line of works concerns the rendering outputs rather than the geometry, i.e. the reconstruction results are sub-optimal." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 490, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 490, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 490, + 287, + 612 + ], + "type": "text", + "content": "Recently, ObjSDF [37] proposes a transform function between semantic logits and SDFs of different objects, which enables optimizing SDF fields with image and semantic mask supervision, and decomposing the whole scene with accurate reconstruction. However, in the indoor scenes where many objects are in partial observation, its reconstruction results are far from satisfactory and can not be used for further applications (see Fig. 2). On the contrary, our method introduces geometry prior to unobserved regions, yielding better compositional scene reconstruction." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 618, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 715 + ], + "type": "text", + "content": "Prior Regularization in Neural Implicit Reconstruction: In addition to the commonly used RGB image supervision, many different priors have been proposed to benefit the neural implicit representation. For example, [4, 30] use explicit point cloud as the depth prior, [23] employs regularization in unseen views and [11] introduces pretrained model's feature consistency. [12, 28] adopt explicit human model as the structural prior for the human-centric scenes. As for surface" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 331, + 545, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 545, + 379 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 545, + 379 + ], + "type": "text", + "content": "reconstruction, [8] proposes a Manhattan-world assumption for the planar regions, [43] utilizes the normal and depth prediction from off-the-shelf model [5] as prior to regularize the texture-less regions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 380, + 546, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 546, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 546, + 441 + ], + "type": "text", + "content": "Our method exploits the geometry prior in the unobserved region for compositional scene reconstruction. The proposed regularization can effectively reconstruct the objects and disentangle them from the background, even if the object itself is partially observed." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 454, + 389, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 454, + 389, + 468 + ], + "spans": [ + { + "bbox": [ + 306, + 454, + 389, + 468 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 475, + 547, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 547, + 608 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 547, + 608 + ], + "type": "text", + "content": "Our goal is to recover decomposed geometry surface of the objects and background within a scene from the images and semantic masks inputs. To this end, we first review the SDF-based neural implicit representation and how to use the semantic logits for compositional reconstruction in Section 3.1. Next, we propose two types of regularizations on unobserved regions to address the partial observation problem: patch-based background smoothness (Section 3.2) and object-background relation (Section 3.3). Finally, we introduce the overall optimization procedure in Section 3.4. An overview of our method is provided in Fig 3." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 618, + 387, + 632 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 618, + 387, + 632 + ], + "spans": [ + { + "bbox": [ + 306, + 618, + 387, + 632 + ], + "type": "text", + "content": "3.1. 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In practice, the SDF function is implemented as a multi-layer perceptron (MLP) network " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": ". The appear-" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17763" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 245, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 245, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 245, + 85 + ], + "type": "text", + "content": "ance of the scene is also defined as an MLP " + }, + { + "bbox": [ + 47, + 72, + 245, + 85 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 47, + 72, + 245, + 85 + ], + "type": "text", + "content": " .." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 91, + 287, + 122 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 91, + 287, + 122 + ], + "spans": [ + { + "bbox": [ + 56, + 91, + 287, + 122 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} f: \\mathbf {p} \\in \\mathbb {R} ^ {3} \\mapsto (s \\in \\mathbb {R}, \\mathbf {f} \\in \\mathbb {R} ^ {2 5 6}) \\\\ g: (\\mathbf {p} \\in \\mathbb {R} ^ {3}, \\mathbf {n} \\in \\mathbb {R} ^ {3}, \\mathbf {v} \\in \\mathbb {S} ^ {2}, \\mathbf {f} \\in \\mathbb {R} ^ {2 5 6}) \\mapsto \\mathbf {c} \\in \\mathbb {R} ^ {3} \\tag {1} \\\\ \\end{array}", + "image_path": "48af86ae10fe6279bba0ea7e4ca49256b5c556da9767416059a241928e5ae816.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "spans": [ + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "text", + "content": " is a geometry feature vector, " + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "inline_equation", + "content": "\\mathbf{n}" + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "text", + "content": " is the normal at " + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "text", + "content": " is the viewing direction and " + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "text", + "content": " is the view-dependent color. We adopt the unbiased rendering proposed in [36] to render the image. For each camera ray " + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "inline_equation", + "content": "\\mathbf{r} = (\\mathbf{o},\\mathbf{v})" + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "inline_equation", + "content": "\\mathbf{o}" + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "text", + "content": " as the ray origin, " + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "text", + "content": " points " + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{p}(t_i) = \\mathbf{o} + t_i\\mathbf{v}|i = 0,1,\\dots ,n - 1\\}" + }, + { + "bbox": [ + 47, + 131, + 287, + 202 + ], + "type": "text", + "content": " are sampled, and the pixel color can be approximated as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 124, + 211, + 287, + 243 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 211, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 124, + 211, + 287, + 243 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {C}} (\\mathbf {r}) = \\sum_ {i = 0} ^ {n - 1} T _ {i} \\alpha_ {i} \\mathbf {c} _ {i}. \\tag {2}", + "image_path": "e5efef4ea6db12ae702df311c487012f4a56ce37067dec0202d5e4f39bacc399.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 251, + 287, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 251, + 287, + 286 + ], + "spans": [ + { + "bbox": [ + 47, + 251, + 287, + 286 + ], + "type": "text", + "content": "The " + }, + { + "bbox": [ + 47, + 251, + 287, + 286 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 47, + 251, + 287, + 286 + ], + "type": "text", + "content": " is the discrete accumulated transmittance derived from " + }, + { + "bbox": [ + 47, + 251, + 287, + 286 + ], + "type": "inline_equation", + "content": "T_{i} = \\prod_{j=0}^{i-1}(1 - \\alpha_{j})" + }, + { + "bbox": [ + 47, + 251, + 287, + 286 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 251, + 287, + 286 + ], + "type": "inline_equation", + "content": "\\alpha_{i}" + }, + { + "bbox": [ + 47, + 251, + 287, + 286 + ], + "type": "text", + "content": " is the discrete density value defined as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 57, + 293, + 287, + 320 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 293, + 287, + 320 + ], + "spans": [ + { + "bbox": [ + 57, + 293, + 287, + 320 + ], + "type": "interline_equation", + "content": "\\alpha_ {i} = \\max \\left(\\frac {\\Phi_ {u} (s (\\mathbf {p} (t _ {i}))) - \\Phi_ {u} (s (\\mathbf {p} (t _ {i + 1})))}{\\Phi_ {u} (s (\\mathbf {p} (t _ {i})))}, 0\\right), \\tag {3}", + "image_path": "676fb0e889f215b51bc4e1a85bf240e2f345318df71dcba10b3a18fee6b8fcdc.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 327, + 287, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 327, + 287, + 375 + ], + "spans": [ + { + "bbox": [ + 47, + 327, + 287, + 375 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 327, + 287, + 375 + ], + "type": "inline_equation", + "content": "\\Phi_u(x) = (1 + e^{-ux})^{-1}" + }, + { + "bbox": [ + 47, + 327, + 287, + 375 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 327, + 287, + 375 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 47, + 327, + 287, + 375 + ], + "type": "text", + "content": " is a learnable parameter. By minimizing the difference between predicted and ground-truth pixel colors, we can learn the SDF and appearance function of the desired scene." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "text", + "content": "Learning SDF with Semantic Logits: In this work, we consider compositional reconstruction of " + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "text", + "content": " objects given their masks. Note that we also consider the background as an instantiated object for brevity as in [37] and follow their network structure. In detail, for a scene with " + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "text", + "content": " objects, the SDF MLP " + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "text", + "content": " now outputs " + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "text", + "content": " SDFs at each point, and the " + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "text", + "content": "-th " + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "inline_equation", + "content": "(1 \\leq j \\leq k)" + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "text", + "content": " SDF represents the geometry of " + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "text", + "content": "-th object. Without loss of generality, we set " + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "inline_equation", + "content": "j = 1" + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "text", + "content": " as the background category and others for objects in Fig. 3 and the rest of the paper. The scene SDF is the minimum of " + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "inline_equation", + "content": "\\{s_j\\}" + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "text", + "content": ", which is used for sampling points along the ray and aforementioned volume rendering (Eq. 2). Moreover, each point's " + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "text", + "content": " SDFs can be transformed into semantic logits " + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "inline_equation", + "content": "\\mathbf{h}(\\mathbf{p})" + }, + { + "bbox": [ + 47, + 380, + 287, + 536 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 94, + 544, + 287, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 544, + 287, + 572 + ], + "spans": [ + { + "bbox": [ + 94, + 544, + 287, + 572 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\begin{array}{l} h _ {j} (\\mathbf {p}) = \\gamma / (1 + \\exp (\\gamma \\cdot s _ {j} (\\mathbf {p}))), \\\\ \\mathbf {p} (.) = [ 1, (.) ] \\end{array} \\tag {4} \\\\ \\mathbf {h} (\\mathbf {p}) = \\left[ h _ {1} (\\mathbf {p}), h _ {2} (\\mathbf {p}), \\dots , h _ {k} (\\mathbf {p}) \\right], \\\\ \\end{array}", + "image_path": "1e69dd0b3532afdf07ba125e9ccff03014d28043a171651823dc761661e8523c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 580, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 580, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 47, + 580, + 287, + 652 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 580, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 47, + 580, + 287, + 652 + ], + "type": "text", + "content": " is a fixed parameter. Using volume rendering to accumulate the semantic logits of all the points along a ray, we can get the semantic logits " + }, + { + "bbox": [ + 47, + 580, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\mathbf{H}(\\mathbf{r})\\in \\mathbb{R}^k" + }, + { + "bbox": [ + 47, + 580, + 287, + 652 + ], + "type": "text", + "content": " of each pixel. During training, the cross-entropy loss applied to " + }, + { + "bbox": [ + 47, + 580, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\mathbf{H}(\\mathbf{r})" + }, + { + "bbox": [ + 47, + 580, + 287, + 652 + ], + "type": "text", + "content": " is backpropagated to the SDF values, allowing for learning the compositional geometry." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 659, + 246, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 246, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 246, + 672 + ], + "type": "text", + "content": "3.2. Patch-based Background Smoothness" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "Although the volume rendering can propagate gradients along the entire ray, the optimization mainly focuses on the surface-hitting point, as its accumulated weight can be" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": "much larger than the others. As a result, the geometry of the points behind the first-hit surface can not be optimized correctly. In the indoor scenes, the occluded part of the background surface is invisible in all the images, which can be with holes and random artifacts (see Fig. 2)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 133, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 545, + 191 + ], + "type": "text", + "content": "Since we cannot tell the exact color, depth or normal of the occluded part, it is intractable to optimize this region wrt. its ground truth. Therefore, we propose to regularize the geometry of the occluded background to be smooth, thus preventing some clearly wrong artifacts." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 192, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 545, + 300 + ], + "type": "text", + "content": "In detail, we regularize the smoothness of rendered depth and normal of background surface within a small patch region. To save the computation budget, we randomly sample a " + }, + { + "bbox": [ + 304, + 192, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{P} \\times \\mathcal{P}" + }, + { + "bbox": [ + 304, + 192, + 545, + 300 + ], + "type": "text", + "content": " size patch every " + }, + { + "bbox": [ + 304, + 192, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_{\\mathcal{P}}" + }, + { + "bbox": [ + 304, + 192, + 545, + 300 + ], + "type": "text", + "content": " iterations in the given image and sample points along the patch rays using the background SDF only. We compute depth map " + }, + { + "bbox": [ + 304, + 192, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\hat{D}(\\mathbf{r})" + }, + { + "bbox": [ + 304, + 192, + 545, + 300 + ], + "type": "text", + "content": " and normal map " + }, + { + "bbox": [ + 304, + 192, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\hat{N}(\\mathbf{r})" + }, + { + "bbox": [ + 304, + 192, + 545, + 300 + ], + "type": "text", + "content": " of the sampled patch following [43], " + }, + { + "bbox": [ + 304, + 192, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 304, + 192, + 545, + 300 + ], + "type": "text", + "content": " denotes the sampled ray in patch. The semantic map of the patch is also computed and transformed into a patch Mask " + }, + { + "bbox": [ + 304, + 192, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\hat{M}(\\mathbf{r})" + }, + { + "bbox": [ + 304, + 192, + 545, + 300 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 358, + 307, + 545, + 321 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 307, + 545, + 321 + ], + "spans": [ + { + "bbox": [ + 358, + 307, + 545, + 321 + ], + "type": "interline_equation", + "content": "\\hat {M} (\\mathbf {r}) = \\mathbb {1} [ \\arg \\max (\\mathbf {H} (\\mathbf {r})) \\neq 1 ], \\tag {5}", + "image_path": "4284d65f4e809865401da1559e555132e8f2f28e9d9c78408eca51a4f0429f9a.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 328, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 328, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 545, + 376 + ], + "type": "text", + "content": "which means the mask value is 1 if the rendered class is not the background, so that only the occluded background is regularized. Taking rendered depth as an example, the patch-based background smoothness loss is" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 384, + 545, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 384, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 384, + 545, + 437 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} (\\hat {D}) = \\sum_ {d = 0} ^ {3} \\sum_ {m, n = 0} ^ {\\mathcal {P} - 1 - 2 ^ {d}} \\hat {M} \\left(\\mathbf {r} _ {m, n}\\right) \\odot (| \\hat {D} \\left(\\mathbf {r} _ {m, n}\\right) - \\tag {6} \\\\ \\hat {D} \\left(\\mathbf {r} _ {m, n + 2 ^ {d}}\\right) | + | \\hat {D} (\\mathbf {r} _ {m, n}) - \\hat {D} \\left(\\mathbf {r} _ {m + 2 ^ {d}, n}\\right) |\\left. \\right). \\\\ \\end{array}", + "image_path": "012c795395872d7a79610971d463484bbcaa754a8428b828b7ee2c19046542c5.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 444, + 545, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 545, + 515 + ], + "type": "text", + "content": "Here the smoothness is applied on different intervals controlled by " + }, + { + "bbox": [ + 304, + 444, + 545, + 515 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 444, + 545, + 515 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 444, + 545, + 515 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 444, + 545, + 515 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 444, + 545, + 515 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 444, + 545, + 515 + ], + "type": "text", + "content": " are the pixel indices within the patch and the mask is multiplied at each position with hadamard product " + }, + { + "bbox": [ + 304, + 444, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 304, + 444, + 545, + 515 + ], + "type": "text", + "content": ". The normal smoothness loss " + }, + { + "bbox": [ + 304, + 444, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\hat{N})" + }, + { + "bbox": [ + 304, + 444, + 545, + 515 + ], + "type": "text", + "content": " can be obtained similarly. We define the overall background smoothness loss " + }, + { + "bbox": [ + 304, + 444, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{bs}" + }, + { + "bbox": [ + 304, + 444, + 545, + 515 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 380, + 522, + 545, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 522, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 380, + 522, + 545, + 536 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {b s}} = \\mathcal {L} (\\hat {D}) + \\mathcal {L} (\\hat {N}). \\tag {7}", + "image_path": "b9551f61f381b863093b96e71c7a7fb01ba5ee123b92003079c14e801b0b44db.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 544, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 581 + ], + "type": "text", + "content": "Here in contrast to [23] which applies a patch-based regularization to visible regions in other views, we instead regularize the occluded regions of the background." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 587, + 545, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 587, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 306, + 587, + 545, + 601 + ], + "type": "text", + "content": "3.3. Object-background Relation as Regularization" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 605, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 677 + ], + "type": "text", + "content": "With the help of the patch-based background smoothness loss, most artifacts of the background are resolved, yielding a smooth surface. We further leverage this smooth background surface to regularize the SDF fields of other objects, leveraging a key prior knowledge that all the other objects are confined to the room, i.e., the background surface." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "In the original framework of [37], if an object is partially observed, e.g. against the background, the object's reconstructed surface won't be a \"closed\" surface (see Fig. 1 and" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17764" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 68, + 276, + 235 + ], + "blocks": [ + { + "bbox": [ + 53, + 68, + 276, + 235 + ], + "lines": [ + { + "bbox": [ + 53, + 68, + 276, + 235 + ], + "spans": [ + { + "bbox": [ + 53, + 68, + 276, + 235 + ], + "type": "image", + "image_path": "1197c88105231b5d4c8de329e887c8d3b41bfefb9fa3b462786546145bf3b2aa.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 248, + 289, + 392 + ], + "lines": [ + { + "bbox": [ + 46, + 248, + 289, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 248, + 289, + 392 + ], + "type": "text", + "content": "Figure 4. Toy-case analysis. A bird-eye view of an object against the background is shown here, the SDF and surface of object is shown in red and background's in blue. (a) In [37] the minimum SDF is used for volume rendering and semantic loss, so on object's visible surface where object SDF is optimized to 0 and the background SDF here is positive, and similar for the visible background surface. Since the scene is partially observed from left, the right part of object surface is open and unobserved background region is unconstrained. (b) With the smoothness prior the background surface can be plausible, (c) and object point SDF loss close the object surface but still have intersections, (d) finally the reversed depth loss optimizes the entire ray thus the object can be within the background." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 409, + 287, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 287, + 458 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 287, + 458 + ], + "type": "text", + "content": "Fig. 2). We refer to the toy-case analysis shown in Fig. 4 for the reason of the current unsatisfactory reconstruction. To encourage the reconstruction to be watertight, we design two types of regularization on the SDF fields of objects." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 461, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 593 + ], + "type": "text", + "content": "Object Point-SDF Loss: A straightforward solution is to directly regularize the objects' SDFs on every sampled point behind the background surface. To be more specific, the regular volume rendering only guarantees a single change of the sign (positive SDF to negative) when a ray hits a visible surface. For watertight objects, the ray should hit another occluded surface (negative SDF to positive). With the prior that the object is confined within the room, the occluded object surface should be closer than the background surface, meaning that the object SDFs of points behind the background surface should all be positive (Fig. 4 (c))." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 594, + 288, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 594, + 288, + 654 + ], + "spans": [ + { + "bbox": [ + 47, + 594, + 288, + 654 + ], + "type": "text", + "content": "We implement an object point-SDF loss based on the above analysis. For the sampled points along the rays, we first utilize the root-finding algorithm among the background SDF of these points and find the zero-SDF ray depth " + }, + { + "bbox": [ + 47, + 594, + 288, + 654 + ], + "type": "inline_equation", + "content": "t'" + }, + { + "bbox": [ + 47, + 594, + 288, + 654 + ], + "type": "text", + "content": ". Then the object point-SDF loss can be formulated as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 661, + 287, + 695 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 661, + 287, + 695 + ], + "spans": [ + { + "bbox": [ + 55, + 661, + 287, + 695 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {o p}} = \\frac {1}{k - 1} \\sum_ {j = 2} ^ {k} \\max \\left(0, \\epsilon - \\mathbf {s} _ {j} (\\mathbf {p} (t _ {i}))\\right) \\cdot \\mathbb {1} [ t _ {i} > t ^ {\\prime} ], \\quad (8)", + "image_path": "ade320acca6e17160b383c4def153812603f877ba45385a69a6a400ac2c81e37.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 701, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 288, + 714 + ], + "type": "text", + "content": "which pushes the objects' SDFs at points behind the surface" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 441, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 441, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 441, + 84 + ], + "type": "text", + "content": "larger than a positive threshold " + }, + { + "bbox": [ + 306, + 72, + 441, + 84 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 306, + 72, + 441, + 84 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 87, + 547, + 184 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 87, + 547, + 184 + ], + "spans": [ + { + "bbox": [ + 304, + 87, + 547, + 184 + ], + "type": "text", + "content": "Reversed Depth Loss: Although the " + }, + { + "bbox": [ + 304, + 87, + 547, + 184 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{op}}" + }, + { + "bbox": [ + 304, + 87, + 547, + 184 + ], + "type": "text", + "content": " can effectively regularize the SDF fields of each object, in practice we find the reconstructed object surface can still have intersections with the background surface (Fig. 4 (c)). The reason is that the sampled points are discrete and in most cases, the background surface is between two sampled points. Therefore, the sign change of the occluded surface may still occur after hitting the background surface." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 184, + 546, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 184, + 546, + 292 + ], + "spans": [ + { + "bbox": [ + 304, + 184, + 546, + 292 + ], + "type": "text", + "content": "Since per-point optimization can not effectively propagate to the distribution of the entire ray. To optimize the entire ray's SDF distribution for better regularization, we compute a reversed depth along each ray. With the help of " + }, + { + "bbox": [ + 304, + 184, + 546, + 292 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{op}}" + }, + { + "bbox": [ + 304, + 184, + 546, + 292 + ], + "type": "text", + "content": ", the sign of the object SDF along one ray now is positive-negative-positive, which enables rendering a depth value backward. We first transform the ray depth " + }, + { + "bbox": [ + 304, + 184, + 546, + 292 + ], + "type": "inline_equation", + "content": "\\{t_i|i = 0,1,\\dots ,n - 1\\}" + }, + { + "bbox": [ + 304, + 184, + 546, + 292 + ], + "type": "text", + "content": " into the reversed ray depth named " + }, + { + "bbox": [ + 304, + 184, + 546, + 292 + ], + "type": "inline_equation", + "content": "\\{\\hat{t}_i|i = 0,1,\\dots ,n - 1\\}" + }, + { + "bbox": [ + 304, + 184, + 546, + 292 + ], + "type": "text", + "content": ", where" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 368, + 296, + 545, + 309 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 368, + 296, + 545, + 309 + ], + "spans": [ + { + "bbox": [ + 368, + 296, + 545, + 309 + ], + "type": "interline_equation", + "content": "\\hat {t} _ {i} = \\left(t _ {0} + t _ {n - 1}\\right) - t _ {n - 1 - i}. \\tag {9}", + "image_path": "34ff464e82d360c42714c5660a14e9de8faace7890856aa697d57b94dcabbf49.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 314, + 546, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 314, + 546, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 546, + 494 + ], + "type": "text", + "content": "With the reversed ray depth values, we use the background and object SDF both in reversed order to compute the accumulated weight and get the reversed depth respectively. Remarkably, in order to compute the exact correct depth, the points should be re-sampled along the reverse direction. Here we directly use the sampled points to avoid computation overhead, and empirical results prove its effectiveness. We only compute the reverse depth of one pixel if satisfying two conditions: 1) this pixel's " + }, + { + "bbox": [ + 304, + 314, + 546, + 494 + ], + "type": "inline_equation", + "content": "\\hat{M}(\\mathbf{r}) = 1" + }, + { + "bbox": [ + 304, + 314, + 546, + 494 + ], + "type": "text", + "content": "; 2) the SDF value of the rendered object at the furthest point is positive. Note that the second condition is usually satisfied when the object point-SDF loss is applied. By computing the reversed depth " + }, + { + "bbox": [ + 304, + 314, + 546, + 494 + ], + "type": "inline_equation", + "content": "d_{o}" + }, + { + "bbox": [ + 304, + 314, + 546, + 494 + ], + "type": "text", + "content": " of the hitting object (determined by the pixel's rendered semantic) and " + }, + { + "bbox": [ + 304, + 314, + 546, + 494 + ], + "type": "inline_equation", + "content": "d_{b}" + }, + { + "bbox": [ + 304, + 314, + 546, + 494 + ], + "type": "text", + "content": " of the background, we can get the reversed depth loss:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 376, + 498, + 545, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 498, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 376, + 498, + 545, + 510 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {r d}} = \\max \\left(0, d _ {b} - d _ {o}\\right), \\tag {10}", + "image_path": "bd7c29ebc705218059e5e9d2a710e16265b6e414f63cd4119c15e72d6c635347.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 515, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 515, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 515, + 545, + 540 + ], + "type": "text", + "content": "which pushes the object surface within the background as illustrated in Fig. 4 (d)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 544, + 457, + 558 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 544, + 457, + 558 + ], + "spans": [ + { + "bbox": [ + 306, + 544, + 457, + 558 + ], + "type": "text", + "content": "3.4. Training Objectives Details" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 563, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 563, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 563, + 545, + 635 + ], + "type": "text", + "content": "Monocular geometric cues are essential for indoor scene reconstruction as proved in [43]. Following [43], we add the depth and normal consistency loss " + }, + { + "bbox": [ + 304, + 563, + 545, + 635 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{\\mathrm{D}},\\mathcal{L}_{\\mathrm{N}})" + }, + { + "bbox": [ + 304, + 563, + 545, + 635 + ], + "type": "text", + "content": " with pseudo ground truth from Omnidata [5] model. In experiments, we also add the monocular cues on [37] to get a stronger baseline for a fair comparison." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 635, + 545, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 635, + 545, + 683 + ], + "spans": [ + { + "bbox": [ + 304, + 635, + 545, + 683 + ], + "type": "text", + "content": "The SDF network is also regularized by an Eikonal [7] loss item " + }, + { + "bbox": [ + 304, + 635, + 545, + 683 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{E}}" + }, + { + "bbox": [ + 304, + 635, + 545, + 683 + ], + "type": "text", + "content": ". We further use the semantic loss " + }, + { + "bbox": [ + 304, + 635, + 545, + 683 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{S}}" + }, + { + "bbox": [ + 304, + 635, + 545, + 683 + ], + "type": "text", + "content": " proposed in [37] to learn the compositional geometry. The overall loss function for compositional reconstruction is:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 326, + 687, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 687, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 326, + 687, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\mathrm {R G B}} + \\lambda_ {\\mathrm {D}} \\mathcal {L} _ {\\mathrm {D}} + \\lambda_ {\\mathrm {N}} \\mathcal {L} _ {\\mathrm {N}} + \\lambda_ {\\mathrm {E}} \\mathcal {L} _ {\\mathrm {E}} + \\lambda_ {\\mathrm {S}} \\mathcal {L} _ {\\mathrm {S}} \\tag {11} \\\\ + \\lambda_ {\\mathrm {b s}} \\mathcal {L} _ {\\mathrm {b s}} + \\lambda_ {\\mathrm {o p}} \\mathcal {L} _ {\\mathrm {o p}} + \\lambda_ {\\mathrm {r d}} \\mathcal {L} _ {\\mathrm {r d}}. \\\\ \\end{array}", + "image_path": "558ecda1054e07d587734f10966366a849ed82c8ea67292c4e54b01fbf2beef1.jpg" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "17765" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "text", + "content": "We set " + }, + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{bs}}, \\lambda_{\\mathrm{op}}, \\lambda_{\\mathrm{rd}} = 0.1" + }, + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "text", + "content": " in our experiments. For other loss terms, given the weight of RGB reconstruction loss as 1, we set " + }, + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{D}} = 0.1" + }, + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{N}} = \\lambda_{\\mathrm{E}} = 0.05" + }, + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "text", + "content": " following [43]. For the semantic loss, we follow the implementation in [37] and set " + }, + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{D}} = 0.04" + }, + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "text", + "content": ". The detailed calculation of other losses can be found in supplementary." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 155, + 129, + 168 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 155, + 129, + 168 + ], + "spans": [ + { + "bbox": [ + 47, + 155, + 129, + 168 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 175, + 287, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 175, + 287, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 287, + 236 + ], + "type": "text", + "content": "We first conduct ablation study on each proposed component. Then we provide quantitative and qualitative results of object-compositional reconstruction on real-world and synthetic scenes. Finally, we show some possible object manipulation with our compositional reconstruction." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 239, + 288, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 288, + 358 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 288, + 358 + ], + "type": "text", + "content": "Datasets: We consider three types of indoor datasets with multi-view RGB images and masks: 1) ScanNet [3], a real-world dataset widely used in previous works [8, 35, 37, 43]; 2) ToyDesk dataset, a real-world dataset with two scenes and each has four objects placed on the table plane. This dataset has also been widely used in previous compositional works [40, 37] 3) a hand-crafted synthetic dataset with five scenes, each containing " + }, + { + "bbox": [ + 46, + 239, + 288, + 358 + ], + "type": "inline_equation", + "content": "5 \\sim 10" + }, + { + "bbox": [ + 46, + 239, + 288, + 358 + ], + "type": "text", + "content": " objects. The synthetic dataset is considered such that the ground truth geometry of both, occluded and non-occluded regions are available." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 362, + 288, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 362, + 288, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 362, + 288, + 578 + ], + "type": "text", + "content": "Metrics: For reconstruction performance, we report Chamfer Distance, F-score for evaluation on ScanNet, following [8, 43]. On synthetic scenes we divide metrics for two aspects: objects and background. For objects we report the reconstruction performance compared to the complete ground truth object mesh, and the final results are averaged across all the objects in all the scenes. For background we report the reconstruction metrics and rendered depth errors of the occluded regions only to highlight the effectiveness of our regularization. The results are also averaged across all the scenes. See supplementary for a detailed introduction to datasets and metrics. We also report two 2D metrics, PSNR and mIoU, on the ToyDesk and ScanNet scenes. Here we omit the synthetic dataset considering its relatively simple texture. For the test image set, on ToyDesk dataset we use the official split, and on ScanNet we sample frames from their original camera trajectories. The metrics are averaged across different images of different scenes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": "Baselines: We mainly compare with ObjSDF [37] in this work, as it is the only method that focuses on the same task, a specific discussion is provided in the supplementary. Since we focus on the indoor scene where monocular cues can benefit a lot [43], we add losses proposed in [43] to our method for better performance. For a fair comparison, we also combine [37] and [43] for a stronger baseline, named ObjSDF*. Moreover, since ObjSDF*’s object reconstructions inevitably have artifacts, we develop a postprocess method to cull the parts outside the background range and name this baseline ObjSDF*-C. We provide the" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 319, + 70, + 533, + 178 + ], + "blocks": [ + { + "bbox": [ + 319, + 70, + 533, + 178 + ], + "lines": [ + { + "bbox": [ + 319, + 70, + 533, + 178 + ], + "spans": [ + { + "bbox": [ + 319, + 70, + 533, + 178 + ], + "type": "image", + "image_path": "8be90f091193a28a1bd84740061f197622c5d8c3210a967e50ae9102ded83a20.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 191, + 547, + 236 + ], + "lines": [ + { + "bbox": [ + 305, + 191, + 547, + 236 + ], + "spans": [ + { + "bbox": [ + 305, + 191, + 547, + 236 + ], + "type": "text", + "content": "Figure 5. Effects of Regularizations. The first row shows two backgrounds, the " + }, + { + "bbox": [ + 305, + 191, + 547, + 236 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{bs}}" + }, + { + "bbox": [ + 305, + 191, + 547, + 236 + ], + "type": "text", + "content": " clearly mitigates most of the artifacts. The last row shows that with " + }, + { + "bbox": [ + 305, + 191, + 547, + 236 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{op}}" + }, + { + "bbox": [ + 305, + 191, + 547, + 236 + ], + "type": "text", + "content": " we can get the watertight object and " + }, + { + "bbox": [ + 305, + 191, + 547, + 236 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rd}}" + }, + { + "bbox": [ + 305, + 191, + 547, + 236 + ], + "type": "text", + "content": " further constrains the unobserved surface." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 253, + 545, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 253, + 545, + 326 + ], + "spans": [ + { + "bbox": [ + 304, + 253, + 545, + 326 + ], + "type": "text", + "content": "details of how to set the range in the supplementary. Note that our method directly generates clean watertight meshes and doesn't need such post-processing. In ScanNet experiments, we also report results for MonoSDF [43] as a reference since we can only evaluate the overall reconstruction (details in Section 4.3)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 329, + 546, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 546, + 425 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 546, + 425 + ], + "type": "text", + "content": "Implementation Details: We implement our method in PyTorch [27]. We use the Adam [13] optimizer with a learning rate of 5e-4 for 50k iterations and sample 1024 rays per iteration. The weight initialization scheme for SDF MLP is identical to [41, 36, 37]. The " + }, + { + "bbox": [ + 304, + 329, + 546, + 425 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 304, + 329, + 546, + 425 + ], + "type": "text", + "content": " is initialized as 0.05 and we set " + }, + { + "bbox": [ + 304, + 329, + 546, + 425 + ], + "type": "inline_equation", + "content": "\\gamma = 20" + }, + { + "bbox": [ + 304, + 329, + 546, + 425 + ], + "type": "text", + "content": " as proposed in [37]. " + }, + { + "bbox": [ + 304, + 329, + 546, + 425 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 329, + 546, + 425 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 329, + 546, + 425 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_{\\mathcal{P}}" + }, + { + "bbox": [ + 304, + 329, + 546, + 425 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 329, + 546, + 425 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 329, + 546, + 425 + ], + "type": "text", + "content": " are set as 32, 10 and 0.05 respectively. All the reconstructions are acquired by using marching cube [17] at the resolution of 512." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 426, + 547, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 547, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 547, + 593 + ], + "type": "text", + "content": "Moreover, we adopt the geometric initialization [7] for the geometry network, which initializes the reconstruction with a unit sphere and the surface normals are facing inside at the beginning of the optimization. For the ScanNet dataset, we follow the protocol in [43] to crop the input image to " + }, + { + "bbox": [ + 304, + 426, + 547, + 593 + ], + "type": "inline_equation", + "content": "384 \\times 384" + }, + { + "bbox": [ + 304, + 426, + 547, + 593 + ], + "type": "text", + "content": " and adjust the intrinsics accordingly. For the synthetic dataset, we directly render the image at the same resolution. Since we focus on the indoor scenes in this paper, we adopt the common practice to process the \"bounded\" scene. For each scene, we normalize the camera poses so that all the cameras lie in a unit sphere. The rays intersection, i.e. the furthest sampling location, is computed based on this sphere and we also conduct Marching Cubes [17] within the same area for the final reconstruction." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 599, + 400, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 400, + 612 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 400, + 612 + ], + "type": "text", + "content": "4.1. 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Qualitative Results on Synthetic Scenes. Above the blue line we show the comparison of different methods on two background scenes. Below we provide results of two scenes where only the object results are shown. In red rectangles at the bottom of each picture, we show the back (left part) and front (right part) views of an example object. Detailed descriptions in Section 4.2." + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + } + ], + "index": 26 + }, + { + "type": "table", + "bbox": [ + 48, + 533, + 282, + 622 + ], + "blocks": [ + { + "bbox": [ + 48, + 533, + 282, + 622 + ], + "lines": [ + { + "bbox": [ + 48, + 533, + 282, + 622 + ], + "spans": [ + { + "bbox": [ + 48, + 533, + 282, + 622 + ], + "type": "table", + "html": "
BackgroundObject
LbsLopLrdD.↓C.↓F.↑C.↓F.↑
V1---0.0210.0450.7681.240.065
V2✓--0.0040.0090.991.250.066
V3✓✓-0.0030.0090.990.0450.735
V4-✓✓0.0150.0290.8880.0390.785
Full✓✓✓0.0030.0090.990.0330.817
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D.↓C.↓F.↑C.↓F.↑
ObjSDF0.0330.0760.6691.0400.084
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ObjSDF*-C0.0210.0440.7720.1340.681
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Note that " + }, + { + "bbox": [ + 305, + 663, + 545, + 687 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rd}}" + }, + { + "bbox": [ + 305, + 663, + 545, + 687 + ], + "type": "text", + "content": " needs to be applied jointly with " + }, + { + "bbox": [ + 305, + 663, + 545, + 687 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{op}}" + }, + { + "bbox": [ + 305, + 663, + 545, + 687 + ], + "type": "text", + "content": " to guarantee its second condition." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "content": "A qualitative case is shown in Fig. 5 for better illustration. 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Qualitative Results on ScanNet [3]. On the left of blue line we show the overall reconstruction from [43] as the reference. On the right we show the comparison between our method and two baselines. Similarly, the back and front views of objects with partial observations are provided in red rectangles. Detailed descriptions in Section 4.3." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 309, + 72, + 416, + 166 + ], + "blocks": [ + { + "bbox": [ + 309, + 72, + 416, + 166 + ], + "lines": [ + { + "bbox": [ + 309, + 72, + 416, + 166 + ], + "spans": [ + { + "bbox": [ + 309, + 72, + 416, + 166 + ], + "type": "image", + "image_path": "ea21c52063173b9fcebf2f67ee32b6c41d96c056b1767301dcefc0f88b8c3a2b.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 186, + 416, + 266 + ], + "blocks": [ + { + "bbox": [ + 309, + 186, + 416, + 266 + ], + "lines": [ + { + "bbox": [ + 309, + 186, + 416, + 266 + ], + "spans": [ + { + "bbox": [ + 309, + 186, + 416, + 266 + ], + "type": "image", + "image_path": "a947811aab529bfe5960a944e87026d8d49644dd69d4302040ba3b061146d7b8.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 340, + 268, + 384, + 278 + ], + "lines": [ + { + "bbox": [ + 340, + 268, + 384, + 278 + ], + "spans": [ + { + "bbox": [ + 340, + 268, + 384, + 278 + ], + "type": "text", + "content": "ObjSDF*-C" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 424, + 72, + 533, + 166 + ], + "blocks": [ + { + "bbox": [ + 424, + 72, + 533, + 166 + ], + "lines": [ + { + "bbox": [ + 424, + 72, + 533, + 166 + ], + "spans": [ + { + "bbox": [ + 424, + 72, + 533, + 166 + ], + "type": "image", + "image_path": "4d2a3477b241dbbd671290b4e04c9ccb68c07a7fcc40dab1c178caa6cbe0ba23.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 424, + 186, + 533, + 266 + ], + "blocks": [ + { + "bbox": [ + 424, + 186, + 533, + 266 + ], + "lines": [ + { + "bbox": [ + 424, + 186, + 533, + 266 + ], + "spans": [ + { + "bbox": [ + 424, + 186, + 533, + 266 + ], + "type": "image", + "image_path": "9474bddb929044755c5613b9fa0f737e14ca1e5c5c34d1c4f046bcadcd1ed758.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 468, + 268, + 488, + 277 + ], + "lines": [ + { + "bbox": [ + 468, + 268, + 488, + 277 + ], + "spans": [ + { + "bbox": [ + 468, + 268, + 488, + 277 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 345, + 287, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 345, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 345, + 287, + 453 + ], + "type": "text", + "content": "can have many artifacts because of occlusion. With the smoothness regularization, the reconstructed backgrounds are much cleaner. Since the " + }, + { + "bbox": [ + 46, + 345, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{bs}}" + }, + { + "bbox": [ + 46, + 345, + 287, + 453 + ], + "type": "text", + "content": " only applies to the occluded region, the other parts won't be affected. In the second row, the sofa is pushed against the wall and reconstruction from [37] contains only visible open surface. The " + }, + { + "bbox": [ + 46, + 345, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{op}}" + }, + { + "bbox": [ + 46, + 345, + 287, + 453 + ], + "type": "text", + "content": " first regularizes the SDF field to be a watertight mesh. The " + }, + { + "bbox": [ + 46, + 345, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rd}}" + }, + { + "bbox": [ + 46, + 345, + 287, + 453 + ], + "type": "text", + "content": " further mitigates the flaws at the back by regularizing the object to be confined to the background." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 464, + 234, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 234, + 477 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 234, + 477 + ], + "type": "text", + "content": "4.2. Reconstruction in Synthetic Scenes" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 484, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 544 + ], + "type": "text", + "content": "Since the synthetic scenes are rendered with objects that have accurate object-level 3D ground truth geometry, we compare our methods with previous object-compositional reconstruction method [37] on the 5 generated scenes and report the quantitative results in Tab. 2." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": "In Tab. 2 we provide detailed metrics on object-level reconstruction. A qualitative comparison is shown in Fig. 6. The computation procedure of all the metrics is available in the supplementary. With monocular cues, ObjSDF* can achieve better performance than the original ObjSDF. However, their performance on object reconstruction is far from satisfactory, since they can only accurately obtain the visible surface with large parts of irrelevant structures in the indoor scenes as pointed out in the analysis before. Though ObjSDF*-C can eliminate most of the outliers and get improved performance, it can only reconstruct visible regions as an open surface as shown in Fig. 6. On the contrary, our regularizations help to smoothen the background and recover the object as a watertight mesh, which promotes" + } + ] + } + ], + "index": 18 + }, + { + "type": "table", + "bbox": [ + 313, + 342, + 536, + 388 + ], + "blocks": [ + { + "bbox": [ + 313, + 342, + 536, + 388 + ], + "lines": [ + { + "bbox": [ + 313, + 342, + 536, + 388 + ], + "spans": [ + { + "bbox": [ + 313, + 342, + 536, + 388 + ], + "type": "table", + "html": "
ObjSDFObjSDF*OursMonoSDF
Chamfer-L1↓0.1700.0920.0880.090
F-Score ↑0.3570.5670.6240.610
", + "image_path": "ecc2d50995e606d9d75b6b8b7072c7fc618d38c2a3a3fc89fb1770a57e46a8ed.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "table_body" + } + ], + "index": 19 + }, + { + "bbox": [ + 318, + 396, + 530, + 407 + ], + "lines": [ + { + "bbox": [ + 318, + 396, + 530, + 407 + ], + "spans": [ + { + "bbox": [ + 318, + 396, + 530, + 407 + ], + "type": "text", + "content": "Table 3. ScanNet Reconstruction Quantitative Results." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 430, + 545, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 430, + 545, + 477 + ], + "spans": [ + { + "bbox": [ + 305, + 430, + 545, + 477 + ], + "type": "text", + "content": "performance by a large margin and leads to broader downstream applications. As shown in Fig. 6, RICO can reconstruct the unobservable (back view as in the caption) regions of the objects where the previous methods fail." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 488, + 501, + 500 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 488, + 501, + 500 + ], + "spans": [ + { + "bbox": [ + 306, + 488, + 501, + 500 + ], + "type": "text", + "content": "4.3. Reconstruction in Real-world Scenes" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 507, + 545, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 507, + 545, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 507, + 545, + 615 + ], + "type": "text", + "content": "We conduct experiments on 7 scenes of ScanNet [3] to show the effectiveness of our method on real-world data. Since ScanNet only provides ground truth for the visible surface, here we follow the protocol in [8] and report the reconstruction performance of the entire scene in Tab. 3. By utilizing the rendering formulation in [36] which explicitly models the angle between surface normal and ray, our method can achieve slightly better performance compared to ObjSDF* and [43] on visible surfaces." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 616, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 616, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 616, + 545, + 676 + ], + "type": "text", + "content": "In Tab. 4 we evaluate the 2D rendering and segmentation performance and provide the PSNR and mIoU results on two real-world datasets. As our method constrains mainly the unobservable, the PSNR and mIoU metrics are not with significant difference." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "In Fig. 7 we also provide the comparisons over two scenes. Note that the ScanNet images are blurry and noisy, and the masks are sometimes inaccurate (e.g., legs of chairs" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17768" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 70, + 277, + 151 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 277, + 151 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 277, + 151 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 277, + 151 + ], + "type": "table", + "html": "
ObjSDFObjSDF*Ours
PSNR↑ToyDesk21.1021.2121.33
ScanNet22.7823.1523.30
mIoU↑ToyDesk0.880.890.89
ScanNet0.890.910.92
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PSNR and mIoU Results of different methods on scenes from ScanNet and ToyDesk datasets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 56, + 202, + 282, + 356 + ], + "blocks": [ + { + "bbox": [ + 56, + 202, + 282, + 356 + ], + "lines": [ + { + "bbox": [ + 56, + 202, + 282, + 356 + ], + "spans": [ + { + "bbox": [ + 56, + 202, + 282, + 356 + ], + "type": "image", + "image_path": "6d8924b9eb6ad605d9e9a9239a6f09634ca3396a36e0cc004731b4d99856cfd3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 366, + 287, + 399 + ], + "lines": [ + { + "bbox": [ + 46, + 366, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 366, + 287, + 399 + ], + "type": "text", + "content": "Figure 8. Qualitative Results on ToyDesk. Here we show the reconstruction results both with and without the background for better visualization." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 419, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 419, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 287, + 491 + ], + "type": "text", + "content": "missing), leading to less accurate reconstructions. However, it can still be seen that our method can successfully regularize the unobservable regions to get the watertight mesh, while the baselines always result in open surface. For example, the piano in the first row and the sofas in the second row can only be reconstructed on visible surfaces." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 492, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 492, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 492, + 287, + 564 + ], + "type": "text", + "content": "And in Fig. 8 we provide the qualitative results of our method and two baselines on two ToyDesk scenes. It can be seen that the baseline methods generate non-watertight surface with undesired artifacts (using table plane to cut the mesh will result in holes on the cut face), while our method can directly get clean results." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 574, + 168, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 168, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 168, + 588 + ], + "type": "text", + "content": "4.4. Object Manipulation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "As aforementioned, the reconstruction results from ObjSDF* are sub-optimal for downstream applications like object manipulation. On the contrary, since RICO can get a watertight mesh, it can be easily used for such applications. In Fig. 9 we show the volume rendered normal maps and segmentation masks before and after moving an object in the scene. An illustration of how to manipulate one object in our framework and conduct volume rendering accordingly is applicable in the supplementary. As illustrated, after manipulation, the rendered segmentation and normal map are" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 306, + 71, + 424, + 159 + ], + "blocks": [ + { + "bbox": [ + 306, + 71, + 424, + 159 + ], + "lines": [ + { + "bbox": [ + 306, + 71, + 424, + 159 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 424, + 159 + ], + "type": "image", + "image_path": "3141be343c1f8c90113ab61d9d3bf56bb0afead7e6960b8e57ac33e26f04d4ec.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 171, + 545, + 205 + ], + "lines": [ + { + "bbox": [ + 305, + 171, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 305, + 171, + 545, + 205 + ], + "type": "text", + "content": "Figure 9. Object Manipulation Cases. Here we show the volume rendered normal maps and segmentation masks in two scenes, before (top row) and after (bottom row) the manipulation." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 429, + 71, + 547, + 158 + ], + "blocks": [ + { + "bbox": [ + 429, + 71, + 547, + 158 + ], + "lines": [ + { + "bbox": [ + 429, + 71, + 547, + 158 + ], + "spans": [ + { + "bbox": [ + 429, + 71, + 547, + 158 + ], + "type": "image", + "image_path": "0c64a3fabcf57952f021702a1c077cd9ffe1aafada9a2d0830beedcc3769f83c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 224, + 545, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 224, + 545, + 261 + ], + "spans": [ + { + "bbox": [ + 305, + 224, + 545, + 261 + ], + "type": "text", + "content": "still clean for RICO. In contrast, the results of ObjSDF* are messy because their reconstruction is connected with artifacts that were originally outside of the scenes." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 271, + 379, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 271, + 379, + 283 + ], + "spans": [ + { + "bbox": [ + 306, + 271, + 379, + 283 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 291, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 291, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 291, + 545, + 411 + ], + "type": "text", + "content": "We have presented RICO, a novel approach for compositional reconstruction in indoor scenes. Our key motivation is to regularize the unobservable regions for the objects with partial observations in indoor scenes. We exploit the geometry smoothness for the occluded background, and then adopt the improved background as the prior to regularize the objects' geometry. Our experimental results prove that our method achieves compositional reconstruction with fewer artifacts and watertight object geometry, which further facilitates applicable applications like object manipulation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 415, + 546, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 546, + 618 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 546, + 618 + ], + "type": "text", + "content": "Future work: Currently, each object's pose is baked with its geometry. An interesting future direction would be represent each object in scene as the combination of its own canonical coordinates and the pose, i.e. the rotated 3D bounding box in the world coordinate. With these disentangled representations, we can cast more regularizations from the shape and box perspectives, and the disentanglement also allows more flexible downstream applications. Another interesting direction would be developing more semantic-based prior knowledge for systemic regularization. Now the geometry motivated regularizations are lack of the understanding of the actual shape of each object. With the general knowledge emerged in recent large vision-language model, like StableDiffusion, it's interesting to distill its knowledge in our compositional reconstruction task. The learnt semantic knowledge can provide a holistic understanding of each object and provide a more comprehensive regularization." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 622, + 545, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 622, + 545, + 706 + ], + "spans": [ + { + "bbox": [ + 304, + 622, + 545, + 706 + ], + "type": "text", + "content": "Acknowledgements: We thank Kechun Xu and Huaijin Pi for detailed feedback on the paper. We thank all authors and reviewers for the contributions. This work is in part supported by a Grant from the National Natural Science Foundation of China (No.U21A20484), the NSFC under grant U21B2004, 62202418, and the Zhejiang University Education Foundation Qizhen Scholar Foundation." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17769" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Mathilde Caron, Hugo Touvron, Ishan Misra, Hervé Jégou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. 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Wong $^{1}$ , and Ping Luo $^{1,3*}$", + "bbox": [ + 205, + 179, + 769, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Deapartment of Computer Science, The University of Hong Kong", + "bbox": [ + 220, + 199, + 748, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ School of Computing and Information Systems, Singapore Management University", + "bbox": [ + 153, + 217, + 816, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ Shanghai AI Laboratory", + "bbox": [ + 383, + 234, + 584, + 252 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8806412aeddf979edbc31c9a6a9d8427ec3148851997e5c29ffaec556c2d4c93.jpg", + "image_caption": [ + "Figure 1: Comparisons of video inversion and editing with existing methods. Number in each column denotes the average editing time over 100 frames. Our RIGID achieves temporal coherent inversion and editing performances with much less time cost. s. Please refer to the arXiv version to watch this figure as a video clip." + ], + "image_footnote": [], + "bbox": [ + 86, + 271, + 888, + 494 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 590, + 313, + 606 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "GAN inversion is indispensable for applying the powerful editability of GAN to real images. However, existing methods invert video frames individually often leading to undesired inconsistent results over time. In this paper, we propose a unified recurrent framework, named Recurrent vIDEo GAN Inversion and eDiting (RIGID), to explicitly and simultaneously enforce temporally coherent GAN inversion and facial editing of real videos. Our approach models the temporal relations between current and previous frames from three aspects. To enable a faithful real video reconstruction, we first maximize the inversion fidelity and consistency by learning a temporal compensated latent code. Second, we observe incoherent noises lie in the high-frequency domain that can be disentangled from the latent space. Third, to remove the inconsistency after attribute manipulation, we propose an in-between frame composition constraint such that the arbitrary frame must be a direct composite of its neighboring", + "bbox": [ + 75, + 617, + 472, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "frames. Our unified framework learns the inherent coherence between input frames in an end-to-end manner, and therefore it is agnostic to a specific attribute and can be applied to arbitrary editing of the same video without re-training. Extensive experiments demonstrate that RIGID outperforms state-of-the-art methods qualitatively and quantitatively in both inversion and editing tasks. The deliverables can be found in https://cnn1stm.github.io/RIGID.", + "bbox": [ + 496, + 590, + 893, + 713 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 738, + 630, + 753 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Generative adversarial networks (GANs) have demonstrated powerful generative ability in synthesizing high-quality faces from a latent code [9, 11, 12, 47]. It is evidenced that the latent space of a well-trained GAN is semantically organized, and shifting the latent code along with a specific direction results in the manipulation of a corresponding attribute [23, 24, 5, 19, 45, 32]. Hence, many works migrate this power to real face processing by inverting a real face image to a latent code [49, 16, 39, 48, 40, 38]. Although", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author: pingluo@hku.hk.", + "bbox": [ + 94, + 886, + 318, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13691", + "bbox": [ + 480, + 924, + 517, + 936 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "this two-comb strategy becomes a standard for editing high-resolution images, applying it to real videos has less been explored. A naive inversion and editing for each frame can undoubtedly produce incoherence in the resulted video.", + "bbox": [ + 75, + 90, + 470, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Different from processing images, maintaining temporal coherence is the core issue for video editing [18, 28, 26]. Specifically, both the GAN inversion and attribute manipulation may introduce discontinuity across frames. IGCI [39] proposes the first attempt to invert consecutive images simultaneously. They leverage the continuity of the inputs to optimize both the reconstruction fidelity and editability of the outputs, but they fail to consider the temporal correlation between results (see flickering in Fig. 1b). Recent work STIT [30] implicitly recovers the original temporal correlations by the faithful inversion of each frame. It fine-tunes an individual generator for every input video such that the generator can capture all the reconstruction details, and TCSVE [37] extends this idea by proposing a temporal consistency loss that applies on the edited videos. Although they works well for most cases, they are video- and attribute-specific (needs to retrain the model for a new video or a new target attribute), and thus suffers from the expensive training cost and poor generalization ability.", + "bbox": [ + 75, + 155, + 473, + 444 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we aim to design a unified approach that learns the temporal correlations between successive frames for both inversion and editing, and it can be generalized to other target attributes without re-training. To this end, we propose a Recurrent vVideo GAN Inversion and eDiting (RIGID) framework, which evolves and enables the image-based StyleGAN [11, 12] generator to output temporally coherent frames. The coherence is realized in both inversion and editing tasks. Given the current and previous frames, we formulate the inversion as the combination of an image-based inverted code and a temporal compensated code, while the latter amends the code with inter-frame similarity for an accurate and consistent inversion. On the other hand, we observe that the main sources of temporal incoherence, like \"flickering\", belong to high-frequency artifacts. This motivates us to disentangle the main video content from high-frequency artifacts in the latent space, and thus the \"incoherence\" can be shared with all the other frames. To build the temporal correlations after attribute manipulation, we propose a self-supervised \"in-between frame composition constraint\" that applies to consecutive edited frames. It enforces any intermediate frame that can be composed by the warping results of their neighbors, which guarantees the smoothness of generated videos. RIGID is trained on the video episodes with several tailored losses. During the inference, it inverts video frames sequentially and therefore can handle videos with arbitrary lengths and support live stream editing. More importantly, once our model is trained, it is attribute-agnostic that can be reused for arbitrary attribute manipulations without re-training. As shown in Fig. 1f,", + "bbox": [ + 75, + 446, + 473, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "RIGID achieves temporal coherent inversion and editing with far less inference time (compared to those scene- and attribute-specific methods like STIT). Extensive experiments demonstrate the superiority over state-of-the-art methods in terms of quantitative and qualitative evaluations.", + "bbox": [ + 496, + 90, + 893, + 166 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are three-fold:", + "bbox": [ + 517, + 167, + 818, + 181 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a recurrent video GAN inversion framework that unifies video inversion and editing. It learns the temporal correlation of generated videos explicitly.", + "- We model temporal coherence from both inversion and editing ends. For inversion, we discover the temporal compensated code and disentangle high-frequency artifacts in the latent space. For editing, we present a novel \"in-between frame composition constraint\" to confine a continuous video transformation.", + "- We achieve attribute-agnostic editing that can vary editing attributes on the fly, avoiding expensive re-training of the model. Extensive experiments demonstrate the effectiveness of our method over state-of-the-arts." + ], + "bbox": [ + 517, + 191, + 893, + 409 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 434, + 650, + 450 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "GAN Inversion. GAN inversion aims at inverting real images into the latent space of pre-trained generators for reconstruct and edit the real images [1, 39, 21, 33, 35, 29, 27]. Early works optimize the latent code directly for a specific image with expensive computational cost [4, 1]. Another class trains a general encoder that maps the real image to the latent code directly [21, 29, 33]. Particularly, pSp [21] proposes an encoder with pyramid architecture that inverts the real images into the $\\mathcal{W}+$ latent space of StyleGAN. Based on the same architecture, e4e [29] analyzes the trade-offs between reconstruction and editability in StyleGAN's inversion. HFGI [33] introduces the distortion map for improving the fidelity reconstitution. Existing works mainly focus on the image-based GAN inversion, inverting the real videos into GANs has not been well studied.", + "bbox": [ + 496, + 455, + 893, + 681 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "StyleGAN-based Video Generation and Editing. State-of-the-art video GANs still cannot generate high quality results as their image counterparts [28, 6, 34, 30]. Opposite to design a video generator directly, many works use the pretrained image generator (e.g., StyleGAN) for synthesizing high-quality videos [18, 28, 43, 26]. MoCoGAN-HD [28] decomposes the motion and content in videos and generates motion trajectory in StyleGAN's latent space. Style-HEAT [43] shares the same decomposition idea, it exploits the flow field as the motion descriptor for talking face generation. Recently, StyleGAN-V [26] injects the continuous motion representations into the StyleGAN. In this paper, we aim at inverting a real video into a pre-trained StyleGAN for temporal coherence reconstruction and editing. Few works", + "bbox": [ + 496, + 688, + 895, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13692", + "bbox": [ + 480, + 924, + 519, + 936 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/72b447ebbfafccb7a852722b57f90b853c70aafef9d9d9c3fca271a9cdadb18a.jpg", + "image_caption": [ + "Figure 2: Overview of our RIGID. We first align the faces on two neighbor frames $(I_{t-1}$ and $I_t)$ . Then we concatenate them with the inverted face $O_{t-1}$ and edited face $E_{t-1}$ in the previous step as the inputs of the recurrent encoder. The encoder learns the temporal compensated code $w_t'$ and spatial noise map $n_t$ , as a complement to the initial latent code $w_t$ (acquired by the \"e4e\" encoder). In addition, we share the latter part of latent codes across all frames using $w_1^l$ for eliminating the high-frequency temporal flickering. Both the final inverted latent code $w_t^{lfd}$ and the edited one are fed to the generator, producing the inverted and edited faces $O_t^a$ and $E_t^a$ . The generated faces are unaligned and blended with the original frames. Dotted lines denote recurrent inputs from the last time step or outputs to the next step. In addition, a novel in-between frame composition constraint is proposed that learns the temporal correlation during editing (details can be found in Fig. 3)." + ], + "image_footnote": [], + "bbox": [ + 81, + 85, + 890, + 305 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "concentrate on this task. Latent-Transformer [42] presents a pipeline for facial video editing by inverting each frame individually, resulting in the temporal inconsistency in the edited videos. IGCI [39] introduces the consecutive frames into GAN inversion for improving the reconstruction quality and editability. STIT [30] edits the facial videos using StyleGAN2 [12] by fine-tuning the generator. TCSVE [37] also optimizes generators with a temporal consistency loss that applies on the edited videos. Above two optimization-based work need to re-optimize the generator for a new video or edit, which is time-consuming. In this paper, we propose a recurrent framework that learns the temporal correlations both in inverted and edited videos. Once it is properly trained, it supports various semantic editing methods with low computational costs.", + "bbox": [ + 75, + 465, + 472, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 76, + 710, + 187, + 728 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Formulation", + "text_level": 1, + "bbox": [ + 76, + 737, + 210, + 752 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a real face video $\\{I_t|t = 1,\\dots T\\}$ , our goal is to invert it to the latent space of pre-trained StyleGAN $G$ to obtain a set of latent codes, and output the inverted video $\\{O_t|t = 1,\\dots T\\}$ , where $O_{t}$ is obtained by feeding the latent code to $G$ . Meanwhile, we can also obtain an edited video $\\{E_t|t = 1,\\dots T\\}$ by manipulating the latent codes. The key is that both inverted and edited video should be temporal coherent.", + "bbox": [ + 76, + 762, + 468, + 882 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To address that, we propose a recurrent video GAN inver", + "bbox": [ + 96, + 885, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "sion and editing framework to explicitly and simultaneously enforce temporally coherent GAN inversion and facial editing of real videos. For video inversion, as the original video of inborn temporal coherence, the best way to maintain inversion consistency is a faithful reconstruction. In addition, we propose a \"latent frequency disentanglement\" strategy for eliminating the high-frequency temporal flickering in the latent space. We also propose an in-between frame composition constraint that builds the temporal correlations of edited video. The overview of our RIGID can be seen in Fig. 2.", + "bbox": [ + 496, + 465, + 893, + 618 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Coherent Video Inversion", + "text_level": 1, + "bbox": [ + 500, + 626, + 733, + 642 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1 Temporal Compensated Inversion", + "text_level": 1, + "bbox": [ + 500, + 650, + 790, + 666 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a real video, we can deliver its temporal correlation to the generated video by a faithful reconstruction. Before inversion, face alignment is necessary since StyleGAN cannot handle the entire frame. After the alignment on each frame, we can obtain a set of aligned faces $\\{I_t^a | t = 1, \\dots, T\\}$ . We first encode them to the $\\mathcal{W}+$ space using image-based inversion method (e4e [29] in this paper), and obtain the initial latent codes $\\{w_t | t = 1, \\dots, T\\}$ , $w_t \\in \\mathcal{W}+$ . However, directly using the initial latent codes cannot reconstruct original faces accurately due to the missing of temporal context. We use a recurrent encoder that learns a temporal compensated code as a complement to the initialized one. Moreover, recovering a high-fidelity face solely in StyleGAN's $\\mathcal{W}+$ latent space is too difficult due to the lack of spatial information [13, 33]. Inspired by [2], the encoder also learns a", + "bbox": [ + 496, + 674, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13693", + "bbox": [ + 478, + 924, + 517, + 936 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "noise map in StyleGAN's $\\mathcal{N}$ space for injecting the spatial information.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our goal is to unify inversion and editing in the same framework. As a result, both the inverted and edited faces from previous and current time steps are fed to the encoder to generate the temporal compensated code and the noise map. Here a ConvLSTM layer [25] is integrated into the encoder for modeling the spatial-temporal correlations. Specifically, at time step $t$ , we concatenate the aligned faces $I_{t-1}^a$ , $I_t^a$ , the last inverted face $O_{t-1}^a$ , and last edited face $E_{t-1}^a$ as inputs. It outputs a temporal compensated code $w_t'$ and spatial noise map $n_t$ , we add $w_t'$ with the initialized code $w_t$ . Then both added code and noise map $n_t$ are sent to the generator for inversion, that is:", + "bbox": [ + 75, + 121, + 470, + 303 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{w _ {t} ^ {\\prime}, n _ {t} \\right\\} = E \\left(\\operatorname {c a t} \\left(I _ {t - 1} ^ {a}, I _ {t} ^ {a}, O _ {t - 1} ^ {a}, E _ {t - 1} ^ {a}\\right)\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 316, + 468, + 333 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nO _ {t} ^ {a} = G \\left(w _ {t} + w _ {t} ^ {\\prime}, n _ {t}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 335, + 468, + 352 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $E$ denotes the recurrent encoder and $\\operatorname{cat}(\\cdot, \\cdot, \\cdot, \\cdot)$ denotes the concatenation operator.", + "bbox": [ + 75, + 364, + 472, + 396 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Latent Frequency Disentanglement", + "text_level": 1, + "bbox": [ + 76, + 417, + 375, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The fidelity inversion delivers the temporal relations from the original video to the inverted one. However, frames are inverted one by one and may lead to subtle inconsistency, i.e., the unique high-frequency information in a single frame will be accumulated in a video and leads to temporal flickering. We notice that high-frequency temporal flickering mainly exists in the appearance of an image. Recent works evidenced that $\\mathcal{W}+$ space is highly disentangled, and the appearance of the image is synthesized at the higher layer of StyleGAN, which is controlled by the latter part of the $w$ latent code [12, 21]. Hence we propose a \"latent frequency disentanglement\" strategy that eliminates the temporal flickering by sharing the latter part of $w$ latent code across all the frames.", + "bbox": [ + 75, + 441, + 468, + 651 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, we first decompose a latent code into the former part and the latter part, then we reuse the latter part (corresponding to high layers of StyleGAN) of the first frame in all the following frames that unify the high frequency information, that is:", + "bbox": [ + 75, + 652, + 468, + 728 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nw _ {t} ^ {l f d} = \\operatorname {c a t} \\left(\\left(w _ {t} + w _ {t} ^ {\\prime}\\right) ^ {f}, w _ {1} ^ {l}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 739, + 468, + 760 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $w_{t}^{lfd}$ is the latent code after latent frequency disentanglement, $(w_{t} + w_{t}^{\\prime})^{f}$ is the former part of latent code $w_{t} + w_{t}^{\\prime}$ , and $w_{1}^{l}$ denotes the latter part of the first latent code. Now, we can get the final latent codes $\\{c_{t} = \\{w_{t}^{lfd}, n_{t}\\} | t = 1, \\dots, T\\}$ for reconstructing a temporal coherent video. That is, we replace Eq. 2 with following equation:", + "bbox": [ + 75, + 773, + 470, + 867 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nO _ {t} ^ {a} = G \\left(w _ {t} ^ {l f d}, n _ {t}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 877, + 468, + 897 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The face can be edited by manipulating the latent code $w_{t}^{lfd}$ :", + "bbox": [ + 500, + 90, + 890, + 122 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nE _ {t} ^ {a} = G \\left(\\left(w _ {t} ^ {l f d} + \\vec {\\mathbf {n}}\\right), n _ {t}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 128, + 890, + 148 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\vec{\\mathbf{n}}$ denotes the semantic direction acquired by arbitrary semantic editing techniques [23, 24, 5, 42, 41]. It is noticed that the $n_t$ is also determined by edited face $E_{t-1}^a$ , and it can be well cooperated with both inverted and edited code.", + "bbox": [ + 496, + 156, + 893, + 231 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Coherent Video Editing", + "text_level": 1, + "bbox": [ + 500, + 239, + 718, + 257 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.1 Post Processing", + "text_level": 1, + "bbox": [ + 500, + 263, + 663, + 279 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The generated faces are naturally aligned that lost the temporal coherence. We need to unaligned generated faces and blend them with the original frame $I_{t}$ . Here we follow [42, 30] that blends the face region only. In particular, we first segment the face region on an original frame by a pre-trained face parsing model [44] to get the inner face mask $M_{I_t}$ , then we blend the inverted face $O_{t}^{a}$ with the original frame according to mask $M_{I_t}$ , which can be presented as:", + "bbox": [ + 496, + 287, + 893, + 421 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nO _ {t} = \\mathrm {B} \\left(\\mathrm {U A} \\left(O _ {t} ^ {a}\\right), I _ {t}, M _ {I _ {t}}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 422, + 890, + 440 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where B and UA denote the blending and unalignment respectively.", + "bbox": [ + 496, + 444, + 893, + 473 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the edited face $E_{t}^{a}$ , its face region may be modified after editing, and the face mask of the original frame $M_{I_t}$ cannot well fit with the edited faces. Besides, directly using the face mask of the edited face also suffers a similar problem. Hence we use the union of two masks as the blending mask, that is:", + "bbox": [ + 496, + 474, + 893, + 564 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nE _ {t} = \\mathbb {B} \\left(\\mathrm {U A} \\left(E _ {t} ^ {a}\\right), I _ {t}, M _ {E _ {t}} \\cup M _ {I _ {t}}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 574, + 890, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.2 In-between Frame Composition Constraint", + "text_level": 1, + "bbox": [ + 500, + 607, + 841, + 622 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After post processing, we can obtain the inverted and edited videos. Compared with the inverted videos, temporal correlation in an edited video is more difficult to learn, since there is no GT edited videos for supervision. We propose a self-supervised in-between frame composition constraint that models the temporal correlation in an edited video.", + "bbox": [ + 496, + 631, + 893, + 720 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Generally, for a triplet of consecutive frames $\\{E_{t - 1}, E_t, E_{t + 1}\\}$ , the intermediate frame $E_t$ can be composed by flow-based warping results of its neighbor frames [8, 20, 36]. Specifically, as shown in Fig. 3, let $f_{t \\Rightarrow t - 1}$ denotes the optical flow from $E_t$ to $E_{t - 1}$ and $f_{t \\Rightarrow t + 1}$ is the flow from $E_t$ to $E_{t + 1}$ , then frames $E_{t - 1}$ and $E_{t + 1}$ are warped using different flow. And the intermediate frame can be composed using two warped results according to a visibility map, that is:", + "bbox": [ + 496, + 722, + 893, + 857 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {E} _ {t} = V _ {t \\leftarrow t - 1} \\odot \\mathbb {W} \\left(E _ {t - 1}, f _ {t \\Rightarrow t - 1}\\right) + \\tag {8} \\\\ \\left(1 - V _ {t \\Leftarrow t - 1}\\right) \\odot \\mathrm {w} \\left(E _ {t + 1}, f _ {t \\Rightarrow t + 1}\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 866, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13694", + "bbox": [ + 478, + 924, + 517, + 936 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/af40d372d8c762bd5856a4099ab3e851fc9ad624859043df685ff607582d7f40.jpg", + "image_caption": [ + "Figure 3: The in-between frame can be composed by flow-based warping results of its neighboring frames according to a visibility map $V_{t \\Leftarrow t-1}$ ." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 486, + 256 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{E}_t$ is the composed intermediate frame, $V_{t\\Leftarrow t - 1}$ is the visibility map from frame $E_{t}$ to $E_{t - 1}$ , it is a one channel mask with the same resolution with aligned face frames. It denotes whether a pixel remains visible when moving from frame $t - 1$ to $t$ (0 is fully occluded and 1 is fully visible). $\\mathbb{W}$ is the warping operator, and $\\odot$ denotes elementwise multiplication. This equation models the temporal correlations among three consecutive frames.", + "bbox": [ + 75, + 340, + 468, + 462 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the edited videos, both $f_{t \\Rightarrow t-1}$ and $f_{t \\Rightarrow t+1}$ are available, the remaining challenge is to estimate the visibility mask $V_{t \\Leftarrow t-1}$ . Since there is no GT for edited videos, we turn to train a visible net $V$ for estimating the mask. Particularly, we compose the in-between frame $\\hat{I}_t$ on the real videos using Eq. 8. Then we align the $l_1$ distance between $\\hat{I}_t$ and $I_t$ for training visible net $V$ . After training, we fix the $V$ and adopt it to the edited frames for estimating the visibility mask and composing the in-between frame $\\hat{E}_t$ . We minimize the distance between $\\hat{E}_t$ and $E_t$ to form in-between frame composition constraint:", + "bbox": [ + 75, + 464, + 470, + 630 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i b f c c} = \\sum_ {t = 2} ^ {T - 1} \\left| \\left| E _ {t} - \\hat {E} _ {t} \\right| \\right| _ {1}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 643, + 468, + 683 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This constraint enforces the edited video as smooth as real video, which guarantees the temporal coherence effectively. Note that we train the encoder on the video episodes. Particularly, we first collect the outputs $\\{E_0,\\dots ,E_T\\}$ in an episode via forward propagation, then we apply this constraint to train the encoder in backward propagation (we use differentiable unalignment).", + "bbox": [ + 75, + 696, + 470, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Loss Functions", + "text_level": 1, + "bbox": [ + 76, + 815, + 228, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our RIGID is trained under several tailored losses. Besides the in-between frame composition constraint $\\mathcal{L}_{ifsc}$ applied on the edited videos, it also includes reconstruction and temporal consistency losses on the inverted videos.", + "bbox": [ + 75, + 839, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Reconstruction Loss. We first introduce the reconstruction loss $\\mathcal{L}_{rec}$ on the inverted faces. Following [21, 33], it includes a pixel-wise $\\mathcal{L}_2$ loss for minimizing the reconstruction error, and LPIPS loss for a better image quality preservation [46], which can be represented as:", + "bbox": [ + 496, + 90, + 893, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {2} = \\sum_ {t = 1} ^ {T} \\left| \\left| I _ {t} ^ {a} - O _ {t} ^ {a} \\right| \\right| _ {2}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 616, + 176, + 892, + 217 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {l p i p s} = \\sum_ {t = 1} ^ {T} | | P \\left(I _ {t} ^ {a}\\right) - P \\left(O _ {t} ^ {a}\\right) | | _ {2}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 220, + 892, + 261 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r e c} = \\mathcal {L} _ {2} + \\alpha \\mathcal {L} _ {l p i p s}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 265, + 892, + 282 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $T$ is the number of frame in each training episode, $P(\\cdot)$ denotes the perceptual feature extractor, and $\\alpha$ is the balance weight. Following [21], we set $\\alpha = 0.8$ .", + "bbox": [ + 500, + 291, + 892, + 335 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Temporal Consistency Loss. We also introduce a warping-based temporal consistency loss $\\mathcal{L}_{tc}$ for preserving the temporal consistency of inverted videos. In particular, we first calculate the optical flow between two real neighbor frames, then we warp a real frame according to the flow, meanwhile, we also warp the inverted frame by the same flow. Then we minimize the distance on two warped frames to form the temporal consistency loss, that is:", + "bbox": [ + 496, + 337, + 893, + 457 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {I} _ {t - 1} = \\mathbb {W} \\left(I _ {t - 1}, f _ {t \\Rightarrow t - 1}\\right), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 465, + 890, + 484 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {O} _ {t - 1} = \\mathbb {W} \\left(O _ {t - 1}, f _ {t \\Rightarrow t - 1}\\right), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 488, + 890, + 505 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {t c} = \\sum_ {t = 2} ^ {T} \\left| \\left| \\hat {I} _ {t - 1} - \\hat {O} _ {t - 1} \\right| \\right| _ {1}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 511, + 890, + 550 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $f_{t \\Rightarrow t-1}$ is the flow from frame $I_{t-1}$ to $I_t$ . This loss enforces the temporal correlation in the videos to be the same as the input video, and improves the temporal smoothness.", + "bbox": [ + 496, + 560, + 890, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Final Loss. We get the final loss function for training the RIGID:", + "bbox": [ + 500, + 604, + 890, + 633 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\mathcal {L} _ {\\text {r e c}} + \\lambda_ {2} \\mathcal {L} _ {t c} + \\lambda_ {3} \\mathcal {L} _ {i b f c c}, \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 646, + 890, + 664 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\{\\lambda_i\\}$ denote the weight factors for balancing loss terms.", + "bbox": [ + 496, + 672, + 890, + 702 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 715, + 632, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 741, + 715, + 757 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We implement the proposed framework in Pytorch on a PC with an Nvidia GeForce RTX 3090. We chose the StyleGAN2 [12] pre-trained on the FFHQ dataset [11] with the resolution of $256 \\times 256$ as our generator due to its strong edit ability. The corresponding $w$ latent code has the dimension of $14 \\times 512$ , and we set the early $10 \\times 512$ as the former part and the rest of $4 \\times 512$ as the latter part in the latent frequency disentanglement. The framework is optimized by the Adam optimizer [14] with the learning rate of", + "bbox": [ + 496, + 763, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13695", + "bbox": [ + 480, + 924, + 517, + 936 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9ce25133724c76ddd661a39c1e8b2d4d95a508d60932623f02dc9a7894dd9868.jpg", + "image_caption": [ + "Figure 4: Qualitative comparison on the video inversion task. Our learning-based RIGID can faithfully reconstruct the video frames that is comparable to those expensive optimization-based works." + ], + "image_footnote": [], + "bbox": [ + 89, + 99, + 883, + 439 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$1e^{-4}$ . We empirically set the balancing weights in Eq. 16 as $\\lambda_1 = 1$ , $\\lambda_2 = 2$ , and $\\lambda_3 = 5$ . Limited by the memory size of GPU, we set $T = 6$ in Eq. 15, which indicates each training episode contains 6 consecutive frames. In addition, we inject the noise map $n_t$ at the resolution of $32 \\times 32$ to the generator.", + "bbox": [ + 75, + 507, + 468, + 597 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The recurrent encoder consists of 7 convolutional (Conv) layers, a ConvLSTM layer, and a fully connected (FC) layer. We take \"Fused Leaky ReLU\" as activation in-between Conv layers. The ConvLSTM layer is integrated between the Conv and FC layers. The visible net has a U-Net structure [22], it takes 5 Conv layers as encoder, and 5 Transposed convolutional layers as a decoder. BatchNorm layer and leakyReLU activation are integrated into between layers. Besides, a Sigmoid function is applied on output U-Net for normalizing the visibility map values. Visible net takes the concatenation of two warped results with 6 channels as input and outputs a visibility map with 1 channel. It is trained using Adam optimizer [14] with the learning rate of $1e^{-4}$ with 100,000 iterations. Besides, we use pre-trained FlowNet2 [7] for predicting optical flow, and we implement warping operation using bi-linear interpolation.", + "bbox": [ + 75, + 598, + 470, + 840 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experimental Settings", + "text_level": 1, + "bbox": [ + 76, + 847, + 284, + 864 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We collect datasets both under control and in the wild environment. We select 72 videos from the con", + "bbox": [ + 76, + 869, + 470, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "trolled RAVDESS dataset [17], which we called RAVDESS-72 Dataset. It contains 9,045 frames and each video contains about 120 frames. We also collect 36 videos from the Internet with the various poses, expressions, and backgrounds. We name them as In-the-Wild-36 Dataset, it contains 7,532 frames in total. We combine two datasets together, use 85 videos for training our RIGID and the rest 23 videos for testing.", + "bbox": [ + 496, + 507, + 893, + 628 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Competitors and Evaluation Metrics. We compare RIGID with three works, including IGCI [39], Latent-Transformer [42], STIT [30], and TCSVE [37]. Note that STIT [30] and TCSVE [37] use the same method for inversion. We use several metrics for evaluating different methods. For the video inversion task, we use the pixel-wise Mean Square Error (MSE) and Learned Perceptual Image Patch Similarity (LPIPS) [46] that evaluates the reconstruction quality. For evaluating the temporal stability, we use the flow-based Warp Error (WE) metric. For the edited task, we follow STIT [30] that use Temporally-Local (TL-ID) and Temporally-Global (TG-ID) identity preservation metrics for evaluating the temporal coherence of edited videos. We also use Fréchet Video Distance (FVD) [31] metric on both edited and inverted videos. Inference Times (IT) over 100 frames is also reported. Please refer to supplementary for more details of competitors and evaluation metrics.", + "bbox": [ + 496, + 643, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13696", + "bbox": [ + 480, + 924, + 517, + 936 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/68928e6f53866b6c627f3011944b987d0c1f32b143e13f19c27a39e172892b72.jpg", + "table_caption": [ + "Table 1: Video inversion comparisons on two datasets. $\\downarrow$ denotes the lower the better and the best results are marked in bold, and the values of MSE are magnified 100 times." + ], + "table_footnote": [], + "table_body": "
Metrics MethodsRAVDESS-72 DatasetIn-the-Wild-36 DatasetIT↓(s)
MSE↓LPIPS↓WE↓FVD↓MSE↓(×e-2)LPIPS↓WE↓FVD↓
IGCI [39]0.990.05154.21412.332.010.13432.98276.921.2×e5
Latent-T. [42]5.680.1286.356220.465.310.22367.32165.3549.2
STIT [30]/TCSVE [37]0.990.0583.21171.232.320.11293.8381.03851.5
RIGID1.040.0584.62174.552.310.12287.3274.1154.5
", + "bbox": [ + 106, + 121, + 867, + 219 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7cc575105a515aa5a46af2f0c3bfe8217ea380e67c714693928e3250ab5b8e2d.jpg", + "image_caption": [ + "+Chubby", + "Figure 5: Qualitative comparison on video editing. RIGID uses the same post processing as IGCI and Latent-Transformer, but the edited faces can be better blended with the original background. Besides, compared with STIT and TCSVE, our RIGID supports shape editing on the face boundary (e.g., \"Chubby\")." + ], + "image_footnote": [], + "bbox": [ + 89, + 234, + 348, + 641 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2162523261d195162bea22842e024e17c26528ae85eadd93fb24464bac87d4f2.jpg", + "image_caption": [ + "+EyeGlasses" + ], + "image_footnote": [], + "bbox": [ + 348, + 237, + 606, + 640 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0b8623991dd8183079a9d7ce8665b8e3488218f980fe043ead7b3af89add0c6f.jpg", + "image_caption": [ + "+NarrowEyes", + "Original IGCI Latent-T. STIT TCSVE RIGID" + ], + "image_footnote": [], + "bbox": [ + 607, + 237, + 861, + 640 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Evaluation on Video Inversion", + "text_level": 1, + "bbox": [ + 76, + 731, + 344, + 746 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative Evaluation. We first evaluate the fidelity and temporal coherence of inverted videos. Quantitative comparison can be seen in Tab. 1. We can see that both STIT, IGCI, and TCSVE have lower MSE and LPIPIS values, they optimize latent codes or generator specifically according to the video frames, which can reconstruct the target frames faithfully. IGCI presents the worse performance on WE and FVD metrics, since it optimizes the latent code for each image but fails to consider the temporal coherence of consec-", + "bbox": [ + 75, + 763, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "utive frames, making the inverted latent codes less consistent. In addition, optimization-based methods cost a lot of time during the inference, especially for IGCI, which takes about 20 minutes for a single frame. Latent-Transformer uses a learning-based encoder that accelerates the inference speed, but it processes each frame individually, both the temporal coherence and reconstruction quality cannot be guaranteed. With about $15 \\times$ faster inference than STIT, RIGID achieves a comparable result on the RAVDESS-72 and In-the-Wild-36 datasets. RIGID not only inverts the frame faithfully but also preserves the original temporal relations across frames.", + "bbox": [ + 496, + 732, + 893, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13697", + "bbox": [ + 478, + 924, + 517, + 936 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/25ea9445359bdb5d80c212de9b933cf46c8f67eeb379d34ed3a38be7f384c762.jpg", + "table_caption": [ + "Table 2: Video editing comparisons on two datasets. $\\downarrow$ denotes the lower the better and vice versa, the best results are marked in bold." + ], + "table_footnote": [], + "table_body": "
Metrics MethodsRAVDESS-72In-the-Wild-36IT↓(s)
TL-ID↑TG-ID↑FVD↓TL-ID↑TG-ID↑FVD↓
IGCI [39]0.940.79834.330.930.71499.221.2×e5
Latent-T. [42]0.990.93311.840.990.87267.4249.2
STIT [30]0.990.97212.040.990.91211.341.6×e3
TCSVE [37]0.990.97201.320.990.92198.463.4×e3
RIGID0.990.97198.540.990.93183.3654.5
", + "bbox": [ + 109, + 121, + 859, + 233 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Thanks to temporal compensated inversion, RIGID guarantees the fidelity of inverted faces.", + "bbox": [ + 75, + 252, + 470, + 282 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative Evaluation. The quantitative comparison of video inversion can be seen in Fig. 4. We can see that two optimization-based works, IGCI and STIT reconstruct the frames well. Latent-Transformer utilizes the pSp encoder for inversion [21], and the results present different skin colors with original frames. Thanks to the temporal compensation inversion, our learning-based RIGID presents the competitive results with optimization-based IGCI and STIT on pixelwise reconstruction. The video comparison can be seen in Fig. 1. Latent-Transformer cannot provide accurate reconstruction. IGCI inverts each frame faithfully, but it cannot guarantee the temporal coherence across frames, resulting in serious temporal flickering. STIT achieves high-quality inversion on a specific video at the cost of long computational times. In contrast, RIGID builds temporal relations of inverted videos by the temporal compensated inversion, yielding temporal coherent inverted videos with much less time cost.", + "bbox": [ + 75, + 284, + 473, + 555 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Evaluation on Video Editing", + "text_level": 1, + "bbox": [ + 76, + 571, + 331, + 588 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Quantitative Evaluation. The quantitative comparison of video editing can be seen in Tab. 2. We can see that IGCI [39] has high FVD values on both two datasets. As discussed above, it cannot produce consistent latent codes, making the edited frames discontinuous. In addition, IGCI has lower values on both TL-ID and TG-ID, which evidences that identity information cannot be preserved locally and globally. Compared with IGCI, Latent-Transformer [42] uses an encoder for producing latent codes, and the edited frames are more consistent. STIT [30] optimizes the generator for each video hence requires many inference times. RIGID achieves a comparable result on the RAVDESS-72 dataset with $30 \\times$ faster during the inference. As for the In-the-Wild-36 Dataset, RIGID outperforms all competitors with three metrics. This should contribute to our in-between frame composition constraint. It enforces the smoothness of edited frames and brings temporal coherence into edited videos.", + "bbox": [ + 73, + 595, + 470, + 866 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative Evaluation. We present the qualitative comparison on video editing in Fig. 1 and Fig. 5. We can see that", + "bbox": [ + 75, + 869, + 472, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ICGI presents blurry edited faces with temporal flickering, and Latent-Transformer loses temporal coherence on local details (see bangs in Fig. 1c). In addition, though they use the same post processing as our RIGID, their edited faces cannot be well blended with the original background. Without considering the temporal coherence of edited frames, their edited faces have large structure deformations from the original faces. STIT proposes a \"stitching tuning\" strategy for the seamless blending, it enforces the edit frames have similar transitions around the face boundary with originals. However, when the target face's boundary is close to the background, this method does not support its shape-related editing (e.g., \"Chubby\" or \"Double Chins\"). As shown in the $1_{st}$ sample in Fig. 5, STIT fails on the \"Chubby\" editing. TCSVE uses the same strategy, hence it fails on this editing. More video comparisons can be found in the supplementary materials.", + "bbox": [ + 496, + 252, + 893, + 508 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablation Study", + "text_level": 1, + "bbox": [ + 498, + 525, + 653, + 542 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this section, we perform an ablation study to evaluate our RIGID on the RAVDESS-72 dataset. We develop five variants with the modification of the modules and the loss functions: 1) $w / o$ TCC, by removing temporal compensated code $w_{t}^{\\prime}$ . 2) $w / o$ NM, by removing noise map $n_t$ . 3) $w / o$ LFD, by removing the latent frequency disentanglement in the framework. In this variant, frames in the same video have different latter codes $w_{t}^{l}$ . 4) $w / o$ $L_{ibfcc}$ , by removing in-between frame composition constraint. 5) $w / o$ $\\mathcal{L}_{tc}$ , by removing the temporal consistent loss $\\mathcal{L}_{tc}$ .", + "bbox": [ + 496, + 550, + 893, + 702 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The quantitative comparisons with various variants can be seen in Tab. 3. Compared with RIGID, variant $w / o$ TCC has a large WE value. Code $w_{t}^{\\prime}$ introduces the temporal compensation to the image-based latent code, and brings the temporal coherence in inverted videos. Variant $w / o$ NM has large MSE and LPIPS values. Since noise map $n_t$ injects the spatial information to the generator, and improves the inversion accuracy. Both variant $w / o$ LFD and $w / o$ $\\mathcal{L}_{tc}$ have large WE numbers. Our latent frequency disentangle-ment strategy unifies the high-frequency information in a video, and $\\mathcal{L}_{tc}$ preserves the temporal consistency from the original to the inverted video. They learn the temporal relations effectively. We observe that variant $w / o$ $\\mathcal{L}_{ibfcc}$ has", + "bbox": [ + 496, + 704, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13698", + "bbox": [ + 478, + 924, + 519, + 936 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/228b49c9ef960fb1d58e130bcbf8690329bf4c4b95ef4493cb7dc02c46504f74.jpg", + "table_caption": [ + "Table 3: Quantitative comparisons with various variants on video inversion and editing. $\\downarrow$ denotes the lower the better and vice visa, the best results are marked in bold. The values of MSE are magnified 100 times." + ], + "table_footnote": [], + "table_body": "
Metrics\nVariantsVideo InversionVideo Editing
MSE↓LPIPS↓WE↓FVD↓TL-ID↑TG-ID↑FVD↓
w/o TCC1.310.07106.52208.740.980.94321.98
w/o NM2.280.0896.52201.220.990.92334.98
w/o LFD1.100.06103.61215.960.990.94309.04
w/o Lfccc0.930.05705.22358.040.980.90299.12
w/o Ltc1.080.05122.08203.540.990.97299.34
RIGID1.040.0584.62174.550.990.97198.54
", + "bbox": [ + 120, + 122, + 849, + 250 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/57ba392c6dcf27f9e26958b02ac786ebd644d29af1aa7d54b79e122349184819.jpg", + "image_caption": [ + "Figure 6: Qualitative comparison with different variants. Variant $w / o$ LFD and $w / o \\mathcal{L}_{ibfcc}$ present noticeable temporal flickering. Please refer to the arXiv version to watch this figure as a video clip." + ], + "image_footnote": [], + "bbox": [ + 81, + 280, + 468, + 439 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "the largest WE and FVD values on inverted videos, though it is applied to the edited frames. That is because the constraint enforces the smoothness of edited frames, and can be propagated to the latent codes that control the coherence of inverted frames. Meanwhile, variant $w / o \\mathcal{L}_{ibfcc}$ has the worse performance on metrics TL-ID and TG-ID. Without the in-between constraint, the framework cannot guarantee the identity similarity across frames. By learning the temporal correlations in inverted and edited videos, the final RIGID achieves the best performance on two tasks.", + "bbox": [ + 75, + 521, + 470, + 672 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Qualitative comparison with different variants can be seen in Fig. 6. We can see variant $w / o \\mathcal{L}_{ibfcc}$ presents annoying flickering both on the inverted and edited videos, which evidences the effectiveness of in-between frame composition constraint. As talked about in the main paper, it builds the temporal relations of video frames, which guarantees the smoothness of generated videos. Variant $w / o$ NM cannot invert the video faithfully. Variant $w / o$ LFD may present temporal flickering. The final RIGID presents temporal coherent inversion and editing videos.", + "bbox": [ + 75, + 674, + 470, + 828 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion and Discussions", + "text_level": 1, + "bbox": [ + 76, + 843, + 333, + 859 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we propose RIGID, a novel recurrent framework that learns the temporal correlations between succes", + "bbox": [ + 76, + 869, + 472, + 902 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "sive frames for both inversion and editing. RIGID first learn the temporal correlation of inverted videos by a temporal-compensated reconstruction. It takes previous and current faces as input, and produces a temporal compensated code with a spatial noise map. They, together with the image-based latent code, are fed to the StyleGAN generator to reconstruct the video frames. Meanwhile, RIGID disentangles high-frequency artifacts in the latent space for eliminating the temporal flickering. Furthermore, for learning the temporal correlation of edited video, we enforce an edited frame can be composed by the flow-based warping of its neighbor frames. RIGID achieves attribute-agnostic editing with much less time cost. Extensive experiments demonstrate the superiority of RIGID.", + "bbox": [ + 496, + 267, + 893, + 479 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Limitations. As cropping and alignment of faces are needed before the inversion, those hair portions outside the cropped region cannot be edited by our method, which leads to unnatural conflicts after blending. It may be addressed by using StyleGAN3 [10] since it can generate unaligned faces. However, as indicated in [3], StyleGAN3 has a worse edit ability than StyleGAN2, which is essential in GAN inversion.", + "bbox": [ + 496, + 488, + 893, + 609 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Broader Impact. RIGID can potentially be used for academic research and commercial applications. It provides a pipeline for video-based GAN inversion, and benefits the design of temporal coherent video GANs. Besides, RIGID can create more facial videos in the media industry. On the other hand, although not the purpose of this work, it can potentially be misused for the violation of portrait rights and privacy. The risk can be mitigated by face forgery detection methods, i.e., we can detect the blending boundary using [15].", + "bbox": [ + 496, + 619, + 895, + 771 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgement. This paper is partially supported by the National Key R&D Program of China No.2022ZD0161000; the General Research Fund of Hong Kong No.17200622; National Natural Science Foundation of China (No. 61972162); Guangdong Natural Science Funds for Distinguished Young Scholars (No. 2023B1515020097); and Singapore Ministry of Education Academic Research Fund Tier 1 (MSS23C002).", + "bbox": [ + 496, + 780, + 895, + 902 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "13699", + "bbox": [ + 478, + 924, + 519, + 936 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rameen Abdal, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? In CVPR, pages 4432-4441, 2019. 2", + "[2] Rameen Abdul, Yipeng Qin, and Peter Wonka. 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IEEE TIP, 31:1230-1242, 2022. 1", + "bbox": [ + 532, + 90, + 893, + 119 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "13701", + "bbox": [ + 478, + 924, + 517, + 936 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/RIGID_ Recurrent GAN Inversion and Editing of Real Face Videos/0ac9c66e-6779-4caf-9449-892ceb58d43e_model.json b/2023/RIGID_ Recurrent GAN Inversion and Editing of Real Face Videos/0ac9c66e-6779-4caf-9449-892ceb58d43e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..9d34720581a470daa2c38612e11d25f50f357bc0 --- /dev/null +++ b/2023/RIGID_ Recurrent GAN Inversion and Editing of Real Face Videos/0ac9c66e-6779-4caf-9449-892ceb58d43e_model.json @@ -0,0 +1,2191 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.149, + 0.131, + 0.823, + 0.152 + ], + "angle": 0, + "content": "RIGID: Recurrent GAN Inversion and Editing of Real Face Videos" + }, + { + "type": "text", + "bbox": [ + 0.207, + 0.18, + 0.77, + 0.2 + ], + "angle": 0, + "content": "Yangyang Xu\\(^{1}\\), Shengfeng He\\(^{2}\\), Kwan-Yee K. Wong\\(^{1}\\), and Ping Luo\\(^{1,3*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.222, + 0.2, + 0.749, + 0.218 + ], + "angle": 0, + "content": "1Deapartment of Computer Science, The University of Hong Kong" + }, + { + "type": "text", + "bbox": [ + 0.155, + 0.218, + 0.817, + 0.234 + ], + "angle": 0, + "content": "\\(^{2}\\)School of Computing and Information Systems, Singapore Management University" + }, + { + "type": "text", + "bbox": [ + 0.385, + 0.235, + 0.585, + 0.253 + ], + "angle": 0, + "content": "\\(^{3}\\)Shanghai AI Laboratory" + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.272, + 0.889, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.503, + 0.893, + 0.551 + ], + "angle": 0, + "content": "Figure 1: Comparisons of video inversion and editing with existing methods. Number in each column denotes the average editing time over 100 frames. Our RIGID achieves temporal coherent inversion and editing performances with much less time cost. s. Please refer to the arXiv version to watch this figure as a video clip." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.591, + 0.314, + 0.607 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.618, + 0.473, + 0.876 + ], + "angle": 0, + "content": "GAN inversion is indispensable for applying the powerful editability of GAN to real images. However, existing methods invert video frames individually often leading to undesired inconsistent results over time. In this paper, we propose a unified recurrent framework, named Recurrent vIDEo GAN Inversion and eDiting (RIGID), to explicitly and simultaneously enforce temporally coherent GAN inversion and facial editing of real videos. Our approach models the temporal relations between current and previous frames from three aspects. To enable a faithful real video reconstruction, we first maximize the inversion fidelity and consistency by learning a temporal compensated latent code. Second, we observe incoherent noises lie in the high-frequency domain that can be disentangled from the latent space. Third, to remove the inconsistency after attribute manipulation, we propose an in-between frame composition constraint such that the arbitrary frame must be a direct composite of its neighboring" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.592, + 0.895, + 0.714 + ], + "angle": 0, + "content": "frames. Our unified framework learns the inherent coherence between input frames in an end-to-end manner, and therefore it is agnostic to a specific attribute and can be applied to arbitrary editing of the same video without re-training. Extensive experiments demonstrate that RIGID outperforms state-of-the-art methods qualitatively and quantitatively in both inversion and editing tasks. The deliverables can be found in https://cnn1stm.github.io/RIGID." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.739, + 0.631, + 0.755 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Generative adversarial networks (GANs) have demonstrated powerful generative ability in synthesizing high-quality faces from a latent code [9, 11, 12, 47]. It is evidenced that the latent space of a well-trained GAN is semantically organized, and shifting the latent code along with a specific direction results in the manipulation of a corresponding attribute [23, 24, 5, 19, 45, 32]. Hence, many works migrate this power to real face processing by inverting a real face image to a latent code [49, 16, 39, 48, 40, 38]. Although" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.319, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author: pingluo@hku.hk." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.925, + 0.518, + 0.937 + ], + "angle": 0, + "content": "13691" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.152 + ], + "angle": 0, + "content": "this two-comb strategy becomes a standard for editing high-resolution images, applying it to real videos has less been explored. A naive inversion and editing for each frame can undoubtedly produce incoherence in the resulted video." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.156, + 0.474, + 0.445 + ], + "angle": 0, + "content": "Different from processing images, maintaining temporal coherence is the core issue for video editing [18, 28, 26]. Specifically, both the GAN inversion and attribute manipulation may introduce discontinuity across frames. IGCI [39] proposes the first attempt to invert consecutive images simultaneously. They leverage the continuity of the inputs to optimize both the reconstruction fidelity and editability of the outputs, but they fail to consider the temporal correlation between results (see flickering in Fig. 1b). Recent work STIT [30] implicitly recovers the original temporal correlations by the faithful inversion of each frame. It fine-tunes an individual generator for every input video such that the generator can capture all the reconstruction details, and TCSVE [37] extends this idea by proposing a temporal consistency loss that applies on the edited videos. Although they works well for most cases, they are video- and attribute-specific (needs to retrain the model for a new video or a new target attribute), and thus suffers from the expensive training cost and poor generalization ability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.448, + 0.474, + 0.903 + ], + "angle": 0, + "content": "In this paper, we aim to design a unified approach that learns the temporal correlations between successive frames for both inversion and editing, and it can be generalized to other target attributes without re-training. To this end, we propose a Recurrent vVideo GAN Inversion and eDiting (RIGID) framework, which evolves and enables the image-based StyleGAN [11, 12] generator to output temporally coherent frames. The coherence is realized in both inversion and editing tasks. Given the current and previous frames, we formulate the inversion as the combination of an image-based inverted code and a temporal compensated code, while the latter amends the code with inter-frame similarity for an accurate and consistent inversion. On the other hand, we observe that the main sources of temporal incoherence, like \"flickering\", belong to high-frequency artifacts. This motivates us to disentangle the main video content from high-frequency artifacts in the latent space, and thus the \"incoherence\" can be shared with all the other frames. To build the temporal correlations after attribute manipulation, we propose a self-supervised \"in-between frame composition constraint\" that applies to consecutive edited frames. It enforces any intermediate frame that can be composed by the warping results of their neighbors, which guarantees the smoothness of generated videos. RIGID is trained on the video episodes with several tailored losses. During the inference, it inverts video frames sequentially and therefore can handle videos with arbitrary lengths and support live stream editing. More importantly, once our model is trained, it is attribute-agnostic that can be reused for arbitrary attribute manipulations without re-training. As shown in Fig. 1f," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.167 + ], + "angle": 0, + "content": "RIGID achieves temporal coherent inversion and editing with far less inference time (compared to those scene- and attribute-specific methods like STIT). Extensive experiments demonstrate the superiority over state-of-the-art methods in terms of quantitative and qualitative evaluations." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.168, + 0.819, + 0.182 + ], + "angle": 0, + "content": "In summary, our contributions are three-fold:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.193, + 0.895, + 0.24 + ], + "angle": 0, + "content": "- We propose a recurrent video GAN inversion framework that unifies video inversion and editing. It learns the temporal correlation of generated videos explicitly." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.249, + 0.895, + 0.339 + ], + "angle": 0, + "content": "- We model temporal coherence from both inversion and editing ends. For inversion, we discover the temporal compensated code and disentangle high-frequency artifacts in the latent space. For editing, we present a novel \"in-between frame composition constraint\" to confine a continuous video transformation." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.35, + 0.895, + 0.41 + ], + "angle": 0, + "content": "- We achieve attribute-agnostic editing that can vary editing attributes on the fly, avoiding expensive re-training of the model. Extensive experiments demonstrate the effectiveness of our method over state-of-the-arts." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.193, + 0.895, + 0.41 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.435, + 0.651, + 0.451 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.895, + 0.683 + ], + "angle": 0, + "content": "GAN Inversion. GAN inversion aims at inverting real images into the latent space of pre-trained generators for reconstruct and edit the real images [1, 39, 21, 33, 35, 29, 27]. Early works optimize the latent code directly for a specific image with expensive computational cost [4, 1]. Another class trains a general encoder that maps the real image to the latent code directly [21, 29, 33]. Particularly, pSp [21] proposes an encoder with pyramid architecture that inverts the real images into the \\(\\mathcal{W}+\\) latent space of StyleGAN. Based on the same architecture, e4e [29] analyzes the trade-offs between reconstruction and editability in StyleGAN's inversion. HFGI [33] introduces the distortion map for improving the fidelity reconstitution. Existing works mainly focus on the image-based GAN inversion, inverting the real videos into GANs has not been well studied." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.897, + 0.902 + ], + "angle": 0, + "content": "StyleGAN-based Video Generation and Editing. State-of-the-art video GANs still cannot generate high quality results as their image counterparts [28, 6, 34, 30]. Opposite to design a video generator directly, many works use the pretrained image generator (e.g., StyleGAN) for synthesizing high-quality videos [18, 28, 43, 26]. MoCoGAN-HD [28] decomposes the motion and content in videos and generates motion trajectory in StyleGAN's latent space. Style-HEAT [43] shares the same decomposition idea, it exploits the flow field as the motion descriptor for talking face generation. Recently, StyleGAN-V [26] injects the continuous motion representations into the StyleGAN. In this paper, we aim at inverting a real video into a pre-trained StyleGAN for temporal coherence reconstruction and editing. Few works" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.925, + 0.521, + 0.937 + ], + "angle": 0, + "content": "13692" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.087, + 0.891, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.318, + 0.896, + 0.442 + ], + "angle": 0, + "content": "Figure 2: Overview of our RIGID. We first align the faces on two neighbor frames \\((I_{t-1}\\) and \\(I_t)\\). Then we concatenate them with the inverted face \\(O_{t-1}\\) and edited face \\(E_{t-1}\\) in the previous step as the inputs of the recurrent encoder. The encoder learns the temporal compensated code \\(w_t'\\) and spatial noise map \\(n_t\\), as a complement to the initial latent code \\(w_t\\) (acquired by the \"e4e\" encoder). In addition, we share the latter part of latent codes across all frames using \\(w_1^l\\) for eliminating the high-frequency temporal flickering. Both the final inverted latent code \\(w_t^{lfd}\\) and the edited one are fed to the generator, producing the inverted and edited faces \\(O_t^a\\) and \\(E_t^a\\). The generated faces are unaligned and blended with the original frames. Dotted lines denote recurrent inputs from the last time step or outputs to the next step. In addition, a novel in-between frame composition constraint is proposed that learns the temporal correlation during editing (details can be found in Fig. 3)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.467, + 0.473, + 0.693 + ], + "angle": 0, + "content": "concentrate on this task. Latent-Transformer [42] presents a pipeline for facial video editing by inverting each frame individually, resulting in the temporal inconsistency in the edited videos. IGCI [39] introduces the consecutive frames into GAN inversion for improving the reconstruction quality and editability. STIT [30] edits the facial videos using StyleGAN2 [12] by fine-tuning the generator. TCSVE [37] also optimizes generators with a temporal consistency loss that applies on the edited videos. Above two optimization-based work need to re-optimize the generator for a new video or edit, which is time-consuming. In this paper, we propose a recurrent framework that learns the temporal correlations both in inverted and edited videos. Once it is properly trained, it supports various semantic editing methods with low computational costs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.712, + 0.188, + 0.729 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.738, + 0.212, + 0.753 + ], + "angle": 0, + "content": "3.1. Formulation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.763, + 0.47, + 0.883 + ], + "angle": 0, + "content": "Given a real face video \\(\\{I_t|t = 1,\\dots T\\}\\), our goal is to invert it to the latent space of pre-trained StyleGAN \\(G\\) to obtain a set of latent codes, and output the inverted video \\(\\{O_t|t = 1,\\dots T\\}\\), where \\(O_{t}\\) is obtained by feeding the latent code to \\(G\\). Meanwhile, we can also obtain an edited video \\(\\{E_t|t = 1,\\dots T\\}\\) by manipulating the latent codes. The key is that both inverted and edited video should be temporal coherent." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.472, + 0.901 + ], + "angle": 0, + "content": "To address that, we propose a recurrent video GAN inver" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.467, + 0.895, + 0.619 + ], + "angle": 0, + "content": "sion and editing framework to explicitly and simultaneously enforce temporally coherent GAN inversion and facial editing of real videos. For video inversion, as the original video of inborn temporal coherence, the best way to maintain inversion consistency is a faithful reconstruction. In addition, we propose a \"latent frequency disentanglement\" strategy for eliminating the high-frequency temporal flickering in the latent space. We also propose an in-between frame composition constraint that builds the temporal correlations of edited video. The overview of our RIGID can be seen in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.627, + 0.734, + 0.643 + ], + "angle": 0, + "content": "3.2. Coherent Video Inversion" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.792, + 0.667 + ], + "angle": 0, + "content": "3.2.1 Temporal Compensated Inversion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Given a real video, we can deliver its temporal correlation to the generated video by a faithful reconstruction. Before inversion, face alignment is necessary since StyleGAN cannot handle the entire frame. After the alignment on each frame, we can obtain a set of aligned faces \\(\\{I_t^a | t = 1, \\dots, T\\}\\). We first encode them to the \\(\\mathcal{W}+\\) space using image-based inversion method (e4e [29] in this paper), and obtain the initial latent codes \\(\\{w_t | t = 1, \\dots, T\\}\\), \\(w_t \\in \\mathcal{W}+\\). However, directly using the initial latent codes cannot reconstruct original faces accurately due to the missing of temporal context. We use a recurrent encoder that learns a temporal compensated code as a complement to the initialized one. Moreover, recovering a high-fidelity face solely in StyleGAN's \\(\\mathcal{W}+\\) latent space is too difficult due to the lack of spatial information [13, 33]. Inspired by [2], the encoder also learns a" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "13693" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.12 + ], + "angle": 0, + "content": "noise map in StyleGAN's \\(\\mathcal{N}\\) space for injecting the spatial information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.471, + 0.304 + ], + "angle": 0, + "content": "Our goal is to unify inversion and editing in the same framework. As a result, both the inverted and edited faces from previous and current time steps are fed to the encoder to generate the temporal compensated code and the noise map. Here a ConvLSTM layer [25] is integrated into the encoder for modeling the spatial-temporal correlations. Specifically, at time step \\( t \\), we concatenate the aligned faces \\( I_{t-1}^a \\), \\( I_t^a \\), the last inverted face \\( O_{t-1}^a \\), and last edited face \\( E_{t-1}^a \\) as inputs. It outputs a temporal compensated code \\( w_t' \\) and spatial noise map \\( n_t \\), we add \\( w_t' \\) with the initialized code \\( w_t \\). Then both added code and noise map \\( n_t \\) are sent to the generator for inversion, that is:" + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.317, + 0.47, + 0.334 + ], + "angle": 0, + "content": "\\[\n\\left\\{w _ {t} ^ {\\prime}, n _ {t} \\right\\} = E \\left(\\operatorname {c a t} \\left(I _ {t - 1} ^ {a}, I _ {t} ^ {a}, O _ {t - 1} ^ {a}, E _ {t - 1} ^ {a}\\right)\\right), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.198, + 0.337, + 0.47, + 0.353 + ], + "angle": 0, + "content": "\\[\nO _ {t} ^ {a} = G \\left(w _ {t} + w _ {t} ^ {\\prime}, n _ {t}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.473, + 0.397 + ], + "angle": 0, + "content": "where \\(E\\) denotes the recurrent encoder and \\(\\operatorname{cat}(\\cdot, \\cdot, \\cdot, \\cdot)\\) denotes the concatenation operator." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.418, + 0.377, + 0.433 + ], + "angle": 0, + "content": "3.2.2 Latent Frequency Disentanglement" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.47, + 0.652 + ], + "angle": 0, + "content": "The fidelity inversion delivers the temporal relations from the original video to the inverted one. However, frames are inverted one by one and may lead to subtle inconsistency, i.e., the unique high-frequency information in a single frame will be accumulated in a video and leads to temporal flickering. We notice that high-frequency temporal flickering mainly exists in the appearance of an image. Recent works evidenced that \\(\\mathcal{W}+\\) space is highly disentangled, and the appearance of the image is synthesized at the higher layer of StyleGAN, which is controlled by the latter part of the \\(w\\) latent code [12, 21]. Hence we propose a \"latent frequency disentanglement\" strategy that eliminates the temporal flickering by sharing the latter part of \\(w\\) latent code across all the frames." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.654, + 0.47, + 0.729 + ], + "angle": 0, + "content": "Specifically, we first decompose a latent code into the former part and the latter part, then we reuse the latter part (corresponding to high layers of StyleGAN) of the first frame in all the following frames that unify the high frequency information, that is:" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.74, + 0.47, + 0.761 + ], + "angle": 0, + "content": "\\[\nw _ {t} ^ {l f d} = \\operatorname {c a t} \\left(\\left(w _ {t} + w _ {t} ^ {\\prime}\\right) ^ {f}, w _ {1} ^ {l}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.774, + 0.471, + 0.868 + ], + "angle": 0, + "content": "where \\( w_{t}^{lfd} \\) is the latent code after latent frequency disentanglement, \\( (w_{t} + w_{t}^{\\prime})^{f} \\) is the former part of latent code \\( w_{t} + w_{t}^{\\prime} \\), and \\( w_{1}^{l} \\) denotes the latter part of the first latent code. Now, we can get the final latent codes \\( \\{c_{t} = \\{w_{t}^{lfd}, n_{t}\\} | t = 1, \\dots, T\\} \\) for reconstructing a temporal coherent video. That is, we replace Eq. 2 with following equation:" + }, + { + "type": "equation", + "bbox": [ + 0.207, + 0.878, + 0.47, + 0.898 + ], + "angle": 0, + "content": "\\[\nO _ {t} ^ {a} = G \\left(w _ {t} ^ {l f d}, n _ {t}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.123 + ], + "angle": 0, + "content": "The face can be edited by manipulating the latent code \\( w_{t}^{lfd} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.13, + 0.892, + 0.15 + ], + "angle": 0, + "content": "\\[\nE _ {t} ^ {a} = G \\left(\\left(w _ {t} ^ {l f d} + \\vec {\\mathbf {n}}\\right), n _ {t}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.157, + 0.894, + 0.232 + ], + "angle": 0, + "content": "where \\(\\vec{\\mathbf{n}}\\) denotes the semantic direction acquired by arbitrary semantic editing techniques [23, 24, 5, 42, 41]. It is noticed that the \\(n_t\\) is also determined by edited face \\(E_{t-1}^a\\), and it can be well cooperated with both inverted and edited code." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.241, + 0.719, + 0.258 + ], + "angle": 0, + "content": "3.3. Coherent Video Editing" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.265, + 0.664, + 0.28 + ], + "angle": 0, + "content": "3.3.1 Post Processing" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.288, + 0.895, + 0.422 + ], + "angle": 0, + "content": "The generated faces are naturally aligned that lost the temporal coherence. We need to unaligned generated faces and blend them with the original frame \\( I_{t} \\). Here we follow [42, 30] that blends the face region only. In particular, we first segment the face region on an original frame by a pre-trained face parsing model [44] to get the inner face mask \\( M_{I_t} \\), then we blend the inverted face \\( O_{t}^{a} \\) with the original frame according to mask \\( M_{I_t} \\), which can be presented as:" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.424, + 0.892, + 0.441 + ], + "angle": 0, + "content": "\\[\nO _ {t} = \\mathrm {B} \\left(\\mathrm {U A} \\left(O _ {t} ^ {a}\\right), I _ {t}, M _ {I _ {t}}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.445, + 0.894, + 0.474 + ], + "angle": 0, + "content": "where B and UA denote the blending and unalignment respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.894, + 0.565 + ], + "angle": 0, + "content": "For the edited face \\( E_{t}^{a} \\), its face region may be modified after editing, and the face mask of the original frame \\( M_{I_t} \\) cannot well fit with the edited faces. Besides, directly using the face mask of the edited face also suffers a similar problem. Hence we use the union of two masks as the blending mask, that is:" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.575, + 0.892, + 0.592 + ], + "angle": 0, + "content": "\\[\nE _ {t} = \\mathbb {B} \\left(\\mathrm {U A} \\left(E _ {t} ^ {a}\\right), I _ {t}, M _ {E _ {t}} \\cup M _ {I _ {t}}\\right). \\tag {7}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.608, + 0.843, + 0.623 + ], + "angle": 0, + "content": "3.3.2 In-between Frame Composition Constraint" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.632, + 0.894, + 0.721 + ], + "angle": 0, + "content": "After post processing, we can obtain the inverted and edited videos. Compared with the inverted videos, temporal correlation in an edited video is more difficult to learn, since there is no GT edited videos for supervision. We propose a self-supervised in-between frame composition constraint that models the temporal correlation in an edited video." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.723, + 0.894, + 0.858 + ], + "angle": 0, + "content": "Generally, for a triplet of consecutive frames \\(\\{E_{t - 1}, E_t, E_{t + 1}\\}\\), the intermediate frame \\(E_t\\) can be composed by flow-based warping results of its neighbor frames [8, 20, 36]. Specifically, as shown in Fig. 3, let \\(f_{t \\Rightarrow t - 1}\\) denotes the optical flow from \\(E_t\\) to \\(E_{t - 1}\\) and \\(f_{t \\Rightarrow t + 1}\\) is the flow from \\(E_t\\) to \\(E_{t + 1}\\), then frames \\(E_{t - 1}\\) and \\(E_{t + 1}\\) are warped using different flow. And the intermediate frame can be composed using two warped results according to a visibility map, that is:" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.867, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {E} _ {t} = V _ {t \\leftarrow t - 1} \\odot \\mathbb {W} \\left(E _ {t - 1}, f _ {t \\Rightarrow t - 1}\\right) + \\tag {8} \\\\ \\left(1 - V _ {t \\Leftarrow t - 1}\\right) \\odot \\mathrm {w} \\left(E _ {t + 1}, f _ {t \\Rightarrow t + 1}\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "13694" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.487, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.268, + 0.471, + 0.315 + ], + "angle": 0, + "content": "Figure 3: The in-between frame can be composed by flow-based warping results of its neighboring frames according to a visibility map \\( V_{t \\Leftarrow t-1} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.47, + 0.463 + ], + "angle": 0, + "content": "where \\(\\hat{E}_t\\) is the composed intermediate frame, \\(V_{t\\Leftarrow t - 1}\\) is the visibility map from frame \\(E_{t}\\) to \\(E_{t - 1}\\), it is a one channel mask with the same resolution with aligned face frames. It denotes whether a pixel remains visible when moving from frame \\(t - 1\\) to \\(t\\) (0 is fully occluded and 1 is fully visible). \\(\\mathbb{W}\\) is the warping operator, and \\(\\odot\\) denotes elementwise multiplication. This equation models the temporal correlations among three consecutive frames." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.465, + 0.471, + 0.631 + ], + "angle": 0, + "content": "For the edited videos, both \\( f_{t \\Rightarrow t-1} \\) and \\( f_{t \\Rightarrow t+1} \\) are available, the remaining challenge is to estimate the visibility mask \\( V_{t \\Leftarrow t-1} \\). Since there is no GT for edited videos, we turn to train a visible net \\( V \\) for estimating the mask. Particularly, we compose the in-between frame \\( \\hat{I}_t \\) on the real videos using Eq. 8. Then we align the \\( l_1 \\) distance between \\( \\hat{I}_t \\) and \\( I_t \\) for training visible net \\( V \\). After training, we fix the \\( V \\) and adopt it to the edited frames for estimating the visibility mask and composing the in-between frame \\( \\hat{E}_t \\). We minimize the distance between \\( \\hat{E}_t \\) and \\( E_t \\) to form in-between frame composition constraint:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.644, + 0.47, + 0.684 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i b f c c} = \\sum_ {t = 2} ^ {T - 1} \\left| \\left| E _ {t} - \\hat {E} _ {t} \\right| \\right| _ {1}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.697, + 0.471, + 0.803 + ], + "angle": 0, + "content": "This constraint enforces the edited video as smooth as real video, which guarantees the temporal coherence effectively. Note that we train the encoder on the video episodes. Particularly, we first collect the outputs \\(\\{E_0,\\dots ,E_T\\}\\) in an episode via forward propagation, then we apply this constraint to train the encoder in backward propagation (we use differentiable unalignment)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.816, + 0.229, + 0.831 + ], + "angle": 0, + "content": "3.4. Loss Functions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Our RIGID is trained under several tailored losses. Besides the in-between frame composition constraint \\(\\mathcal{L}_{ifsc}\\) applied on the edited videos, it also includes reconstruction and temporal consistency losses on the inverted videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.894, + 0.168 + ], + "angle": 0, + "content": "Reconstruction Loss. We first introduce the reconstruction loss \\(\\mathcal{L}_{rec}\\) on the inverted faces. Following [21, 33], it includes a pixel-wise \\(\\mathcal{L}_2\\) loss for minimizing the reconstruction error, and LPIPS loss for a better image quality preservation [46], which can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.617, + 0.177, + 0.893, + 0.218 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {2} = \\sum_ {t = 1} ^ {T} \\left| \\left| I _ {t} ^ {a} - O _ {t} ^ {a} \\right| \\right| _ {2}, \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.222, + 0.893, + 0.262 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {l p i p s} = \\sum_ {t = 1} ^ {T} | | P \\left(I _ {t} ^ {a}\\right) - P \\left(O _ {t} ^ {a}\\right) | | _ {2}, \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.621, + 0.266, + 0.893, + 0.283 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r e c} = \\mathcal {L} _ {2} + \\alpha \\mathcal {L} _ {l p i p s}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.292, + 0.893, + 0.337 + ], + "angle": 0, + "content": "where \\(T\\) is the number of frame in each training episode, \\(P(\\cdot)\\) denotes the perceptual feature extractor, and \\(\\alpha\\) is the balance weight. Following [21], we set \\(\\alpha = 0.8\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.338, + 0.894, + 0.458 + ], + "angle": 0, + "content": "Temporal Consistency Loss. We also introduce a warping-based temporal consistency loss \\(\\mathcal{L}_{tc}\\) for preserving the temporal consistency of inverted videos. In particular, we first calculate the optical flow between two real neighbor frames, then we warp a real frame according to the flow, meanwhile, we also warp the inverted frame by the same flow. Then we minimize the distance on two warped frames to form the temporal consistency loss, that is:" + }, + { + "type": "equation", + "bbox": [ + 0.611, + 0.467, + 0.892, + 0.485 + ], + "angle": 0, + "content": "\\[\n\\hat {I} _ {t - 1} = \\mathbb {W} \\left(I _ {t - 1}, f _ {t \\Rightarrow t - 1}\\right), \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.489, + 0.892, + 0.506 + ], + "angle": 0, + "content": "\\[\n\\hat {O} _ {t - 1} = \\mathbb {W} \\left(O _ {t - 1}, f _ {t \\Rightarrow t - 1}\\right), \\tag {14}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.512, + 0.892, + 0.551 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {t c} = \\sum_ {t = 2} ^ {T} \\left| \\left| \\hat {I} _ {t - 1} - \\hat {O} _ {t - 1} \\right| \\right| _ {1}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.891, + 0.606 + ], + "angle": 0, + "content": "where \\( f_{t \\Rightarrow t-1} \\) is the flow from frame \\( I_{t-1} \\) to \\( I_t \\). This loss enforces the temporal correlation in the videos to be the same as the input video, and improves the temporal smoothness." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.606, + 0.891, + 0.634 + ], + "angle": 0, + "content": "Final Loss. We get the final loss function for training the RIGID:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.647, + 0.892, + 0.665 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\mathcal {L} _ {\\text {r e c}} + \\lambda_ {2} \\mathcal {L} _ {t c} + \\lambda_ {3} \\mathcal {L} _ {i b f c c}, \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.891, + 0.703 + ], + "angle": 0, + "content": "where \\(\\{\\lambda_i\\}\\) denote the weight factors for balancing loss terms." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.717, + 0.633, + 0.734 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.742, + 0.717, + 0.758 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.894, + 0.901 + ], + "angle": 0, + "content": "We implement the proposed framework in Pytorch on a PC with an Nvidia GeForce RTX 3090. We chose the StyleGAN2 [12] pre-trained on the FFHQ dataset [11] with the resolution of \\(256 \\times 256\\) as our generator due to its strong edit ability. The corresponding \\(w\\) latent code has the dimension of \\(14 \\times 512\\), and we set the early \\(10 \\times 512\\) as the former part and the rest of \\(4 \\times 512\\) as the latter part in the latent frequency disentanglement. The framework is optimized by the Adam optimizer [14] with the learning rate of" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "13695" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.101, + 0.885, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.45, + 0.893, + 0.482 + ], + "angle": 0, + "content": "Figure 4: Qualitative comparison on the video inversion task. Our learning-based RIGID can faithfully reconstruct the video frames that is comparable to those expensive optimization-based works." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.598 + ], + "angle": 0, + "content": "\\(1e^{-4}\\). We empirically set the balancing weights in Eq. 16 as \\(\\lambda_1 = 1\\), \\(\\lambda_2 = 2\\), and \\(\\lambda_3 = 5\\). Limited by the memory size of GPU, we set \\(T = 6\\) in Eq. 15, which indicates each training episode contains 6 consecutive frames. In addition, we inject the noise map \\(n_t\\) at the resolution of \\(32 \\times 32\\) to the generator." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.471, + 0.841 + ], + "angle": 0, + "content": "The recurrent encoder consists of 7 convolutional (Conv) layers, a ConvLSTM layer, and a fully connected (FC) layer. We take \"Fused Leaky ReLU\" as activation in-between Conv layers. The ConvLSTM layer is integrated between the Conv and FC layers. The visible net has a U-Net structure [22], it takes 5 Conv layers as encoder, and 5 Transposed convolutional layers as a decoder. BatchNorm layer and leakyReLU activation are integrated into between layers. Besides, a Sigmoid function is applied on output U-Net for normalizing the visibility map values. Visible net takes the concatenation of two warped results with 6 channels as input and outputs a visibility map with 1 channel. It is trained using Adam optimizer [14] with the learning rate of \\(1e^{-4}\\) with 100,000 iterations. Besides, we use pre-trained FlowNet2 [7] for predicting optical flow, and we implement warping operation using bi-linear interpolation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.285, + 0.865 + ], + "angle": 0, + "content": "4.2. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.9 + ], + "angle": 0, + "content": "Datasets. We collect datasets both under control and in the wild environment. We select 72 videos from the con" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.895, + 0.63 + ], + "angle": 0, + "content": "trolled RAVDESS dataset [17], which we called RAVDESS-72 Dataset. It contains 9,045 frames and each video contains about 120 frames. We also collect 36 videos from the Internet with the various poses, expressions, and backgrounds. We name them as In-the-Wild-36 Dataset, it contains 7,532 frames in total. We combine two datasets together, use 85 videos for training our RIGID and the rest 23 videos for testing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Competitors and Evaluation Metrics. We compare RIGID with three works, including IGCI [39], Latent-Transformer [42], STIT [30], and TCSVE [37]. Note that STIT [30] and TCSVE [37] use the same method for inversion. We use several metrics for evaluating different methods. For the video inversion task, we use the pixel-wise Mean Square Error (MSE) and Learned Perceptual Image Patch Similarity (LPIPS) [46] that evaluates the reconstruction quality. For evaluating the temporal stability, we use the flow-based Warp Error (WE) metric. For the edited task, we follow STIT [30] that use Temporally-Local (TL-ID) and Temporally-Global (TG-ID) identity preservation metrics for evaluating the temporal coherence of edited videos. We also use Fréchet Video Distance (FVD) [31] metric on both edited and inverted videos. Inference Times (IT) over 100 frames is also reported. Please refer to supplementary for more details of competitors and evaluation metrics." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "13696" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.892, + 0.119 + ], + "angle": 0, + "content": "Table 1: Video inversion comparisons on two datasets. \\( \\downarrow \\) denotes the lower the better and the best results are marked in bold, and the values of MSE are magnified 100 times." + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.122, + 0.868, + 0.22 + ], + "angle": 0, + "content": "
Metrics MethodsRAVDESS-72 DatasetIn-the-Wild-36 DatasetIT↓(s)
MSE↓LPIPS↓WE↓FVD↓MSE↓(×e-2)LPIPS↓WE↓FVD↓
IGCI [39]0.990.05154.21412.332.010.13432.98276.921.2×e5
Latent-T. [42]5.680.1286.356220.465.310.22367.32165.3549.2
STIT [30]/TCSVE [37]0.990.0583.21171.232.320.11293.8381.03851.5
RIGID1.040.0584.62174.552.310.12287.3274.1154.5
" + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.236, + 0.349, + 0.642 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.192, + 0.645, + 0.249, + 0.657 + ], + "angle": 0, + "content": "+Chubby" + }, + { + "type": "image", + "bbox": [ + 0.349, + 0.238, + 0.607, + 0.641 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.434, + 0.645, + 0.522, + 0.656 + ], + "angle": 0, + "content": "+EyeGlasses" + }, + { + "type": "image", + "bbox": [ + 0.608, + 0.238, + 0.862, + 0.641 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.691, + 0.645, + 0.779, + 0.656 + ], + "angle": 0, + "content": "+NarrowEyes" + }, + { + "type": "image_caption", + "bbox": [ + 0.863, + 0.253, + 0.88, + 0.629 + ], + "angle": 0, + "content": "Original IGCI Latent-T. STIT TCSVE RIGID" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.661, + 0.893, + 0.708 + ], + "angle": 0, + "content": "Figure 5: Qualitative comparison on video editing. RIGID uses the same post processing as IGCI and Latent-Transformer, but the edited faces can be better blended with the original background. Besides, compared with STIT and TCSVE, our RIGID supports shape editing on the face boundary (e.g., \"Chubby\")." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.732, + 0.345, + 0.747 + ], + "angle": 0, + "content": "4.3. Evaluation on Video Inversion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Quantitative Evaluation. We first evaluate the fidelity and temporal coherence of inverted videos. Quantitative comparison can be seen in Tab. 1. We can see that both STIT, IGCI, and TCSVE have lower MSE and LPIPIS values, they optimize latent codes or generator specifically according to the video frames, which can reconstruct the target frames faithfully. IGCI presents the worse performance on WE and FVD metrics, since it optimizes the latent code for each image but fails to consider the temporal coherence of consec-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.895, + 0.9 + ], + "angle": 0, + "content": "utive frames, making the inverted latent codes less consistent. In addition, optimization-based methods cost a lot of time during the inference, especially for IGCI, which takes about 20 minutes for a single frame. Latent-Transformer uses a learning-based encoder that accelerates the inference speed, but it processes each frame individually, both the temporal coherence and reconstruction quality cannot be guaranteed. With about \\(15 \\times\\) faster inference than STIT, RIGID achieves a comparable result on the RAVDESS-72 and In-the-Wild-36 datasets. RIGID not only inverts the frame faithfully but also preserves the original temporal relations across frames." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "13697" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.119 + ], + "angle": 0, + "content": "Table 2: Video editing comparisons on two datasets. \\( \\downarrow \\) denotes the lower the better and vice versa, the best results are marked in bold." + }, + { + "type": "table", + "bbox": [ + 0.111, + 0.122, + 0.861, + 0.234 + ], + "angle": 0, + "content": "
Metrics MethodsRAVDESS-72In-the-Wild-36IT↓(s)
TL-ID↑TG-ID↑FVD↓TL-ID↑TG-ID↑FVD↓
IGCI [39]0.940.79834.330.930.71499.221.2×e5
Latent-T. [42]0.990.93311.840.990.87267.4249.2
STIT [30]0.990.97212.040.990.91211.341.6×e3
TCSVE [37]0.990.97201.320.990.92198.463.4×e3
RIGID0.990.97198.540.990.93183.3654.5
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.253, + 0.471, + 0.283 + ], + "angle": 0, + "content": "Thanks to temporal compensated inversion, RIGID guarantees the fidelity of inverted faces." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.285, + 0.474, + 0.556 + ], + "angle": 0, + "content": "Qualitative Evaluation. The quantitative comparison of video inversion can be seen in Fig. 4. We can see that two optimization-based works, IGCI and STIT reconstruct the frames well. Latent-Transformer utilizes the pSp encoder for inversion [21], and the results present different skin colors with original frames. Thanks to the temporal compensation inversion, our learning-based RIGID presents the competitive results with optimization-based IGCI and STIT on pixelwise reconstruction. The video comparison can be seen in Fig. 1. Latent-Transformer cannot provide accurate reconstruction. IGCI inverts each frame faithfully, but it cannot guarantee the temporal coherence across frames, resulting in serious temporal flickering. STIT achieves high-quality inversion on a specific video at the cost of long computational times. In contrast, RIGID builds temporal relations of inverted videos by the temporal compensated inversion, yielding temporal coherent inverted videos with much less time cost." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.572, + 0.333, + 0.589 + ], + "angle": 0, + "content": "4.4. Evaluation on Video Editing" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.597, + 0.471, + 0.867 + ], + "angle": 0, + "content": "Quantitative Evaluation. The quantitative comparison of video editing can be seen in Tab. 2. We can see that IGCI [39] has high FVD values on both two datasets. As discussed above, it cannot produce consistent latent codes, making the edited frames discontinuous. In addition, IGCI has lower values on both TL-ID and TG-ID, which evidences that identity information cannot be preserved locally and globally. Compared with IGCI, Latent-Transformer [42] uses an encoder for producing latent codes, and the edited frames are more consistent. STIT [30] optimizes the generator for each video hence requires many inference times. RIGID achieves a comparable result on the RAVDESS-72 dataset with \\(30 \\times\\) faster during the inference. As for the In-the-Wild-36 Dataset, RIGID outperforms all competitors with three metrics. This should contribute to our in-between frame composition constraint. It enforces the smoothness of edited frames and brings temporal coherence into edited videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Qualitative Evaluation. We present the qualitative comparison on video editing in Fig. 1 and Fig. 5. We can see that" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.253, + 0.895, + 0.51 + ], + "angle": 0, + "content": "ICGI presents blurry edited faces with temporal flickering, and Latent-Transformer loses temporal coherence on local details (see bangs in Fig. 1c). In addition, though they use the same post processing as our RIGID, their edited faces cannot be well blended with the original background. Without considering the temporal coherence of edited frames, their edited faces have large structure deformations from the original faces. STIT proposes a \"stitching tuning\" strategy for the seamless blending, it enforces the edit frames have similar transitions around the face boundary with originals. However, when the target face's boundary is close to the background, this method does not support its shape-related editing (e.g., \"Chubby\" or \"Double Chins\"). As shown in the \\(1_{st}\\) sample in Fig. 5, STIT fails on the \"Chubby\" editing. TCSVE uses the same strategy, hence it fails on this editing. More video comparisons can be found in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.526, + 0.655, + 0.543 + ], + "angle": 0, + "content": "4.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.551, + 0.894, + 0.703 + ], + "angle": 0, + "content": "In this section, we perform an ablation study to evaluate our RIGID on the RAVDESS-72 dataset. We develop five variants with the modification of the modules and the loss functions: 1) \\( w / o \\) TCC, by removing temporal compensated code \\( w_{t}^{\\prime} \\). 2) \\( w / o \\) NM, by removing noise map \\( n_t \\). 3) \\( w / o \\) LFD, by removing the latent frequency disentanglement in the framework. In this variant, frames in the same video have different latter codes \\( w_{t}^{l} \\). 4) \\( w / o \\) \\( L_{ibfcc} \\), by removing in-between frame composition constraint. 5) \\( w / o \\) \\( \\mathcal{L}_{tc} \\), by removing the temporal consistent loss \\( \\mathcal{L}_{tc} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.903 + ], + "angle": 0, + "content": "The quantitative comparisons with various variants can be seen in Tab. 3. Compared with RIGID, variant \\( w / o \\) TCC has a large WE value. Code \\( w_{t}^{\\prime} \\) introduces the temporal compensation to the image-based latent code, and brings the temporal coherence in inverted videos. Variant \\( w / o \\) NM has large MSE and LPIPS values. Since noise map \\( n_t \\) injects the spatial information to the generator, and improves the inversion accuracy. Both variant \\( w / o \\) LFD and \\( w / o \\) \\( \\mathcal{L}_{tc} \\) have large WE numbers. Our latent frequency disentangle-ment strategy unifies the high-frequency information in a video, and \\( \\mathcal{L}_{tc} \\) preserves the temporal consistency from the original to the inverted video. They learn the temporal relations effectively. We observe that variant \\( w / o \\) \\( \\mathcal{L}_{ibfcc} \\) has" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.521, + 0.937 + ], + "angle": 0, + "content": "13698" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.121 + ], + "angle": 0, + "content": "Table 3: Quantitative comparisons with various variants on video inversion and editing. \\( \\downarrow \\) denotes the lower the better and vice visa, the best results are marked in bold. The values of MSE are magnified 100 times." + }, + { + "type": "table", + "bbox": [ + 0.122, + 0.123, + 0.85, + 0.25 + ], + "angle": 0, + "content": "
Metrics\nVariantsVideo InversionVideo Editing
MSE↓LPIPS↓WE↓FVD↓TL-ID↑TG-ID↑FVD↓
w/o TCC1.310.07106.52208.740.980.94321.98
w/o NM2.280.0896.52201.220.990.92334.98
w/o LFD1.100.06103.61215.960.990.94309.04
w/o Lfccc0.930.05705.22358.040.980.90299.12
w/o Ltc1.080.05122.08203.540.990.97299.34
RIGID1.040.0584.62174.550.990.97198.54
" + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.281, + 0.47, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.45, + 0.474, + 0.512 + ], + "angle": 0, + "content": "Figure 6: Qualitative comparison with different variants. Variant \\( w / o \\) LFD and \\( w / o \\mathcal{L}_{ibfcc} \\) present noticeable temporal flickering. Please refer to the arXiv version to watch this figure as a video clip." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.471, + 0.674 + ], + "angle": 0, + "content": "the largest WE and FVD values on inverted videos, though it is applied to the edited frames. That is because the constraint enforces the smoothness of edited frames, and can be propagated to the latent codes that control the coherence of inverted frames. Meanwhile, variant \\( w / o \\mathcal{L}_{ibfcc} \\) has the worse performance on metrics TL-ID and TG-ID. Without the in-between constraint, the framework cannot guarantee the identity similarity across frames. By learning the temporal correlations in inverted and edited videos, the final RIGID achieves the best performance on two tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.471, + 0.829 + ], + "angle": 0, + "content": "Qualitative comparison with different variants can be seen in Fig. 6. We can see variant \\( w / o \\mathcal{L}_{ibfcc} \\) presents annoying flickering both on the inverted and edited videos, which evidences the effectiveness of in-between frame composition constraint. As talked about in the main paper, it builds the temporal relations of video frames, which guarantees the smoothness of generated videos. Variant \\( w / o \\) NM cannot invert the video faithfully. Variant \\( w / o \\) LFD may present temporal flickering. The final RIGID presents temporal coherent inversion and editing videos." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.844, + 0.334, + 0.86 + ], + "angle": 0, + "content": "5. Conclusion and Discussions" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In this paper, we propose RIGID, a novel recurrent framework that learns the temporal correlations between succes" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.268, + 0.895, + 0.48 + ], + "angle": 0, + "content": "sive frames for both inversion and editing. RIGID first learn the temporal correlation of inverted videos by a temporal-compensated reconstruction. It takes previous and current faces as input, and produces a temporal compensated code with a spatial noise map. They, together with the image-based latent code, are fed to the StyleGAN generator to reconstruct the video frames. Meanwhile, RIGID disentangles high-frequency artifacts in the latent space for eliminating the temporal flickering. Furthermore, for learning the temporal correlation of edited video, we enforce an edited frame can be composed by the flow-based warping of its neighbor frames. RIGID achieves attribute-agnostic editing with much less time cost. Extensive experiments demonstrate the superiority of RIGID." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.489, + 0.895, + 0.61 + ], + "angle": 0, + "content": "Limitations. As cropping and alignment of faces are needed before the inversion, those hair portions outside the cropped region cannot be edited by our method, which leads to unnatural conflicts after blending. It may be addressed by using StyleGAN3 [10] since it can generate unaligned faces. However, as indicated in [3], StyleGAN3 has a worse edit ability than StyleGAN2, which is essential in GAN inversion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.896, + 0.772 + ], + "angle": 0, + "content": "Broader Impact. RIGID can potentially be used for academic research and commercial applications. It provides a pipeline for video-based GAN inversion, and benefits the design of temporal coherent video GANs. Besides, RIGID can create more facial videos in the media industry. On the other hand, although not the purpose of this work, it can potentially be misused for the violation of portrait rights and privacy. The risk can be mitigated by face forgery detection methods, i.e., we can detect the blending boundary using [15]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Acknowledgement. This paper is partially supported by the National Key R&D Program of China No.2022ZD0161000; the General Research Fund of Hong Kong No.17200622; National Natural Science Foundation of China (No. 61972162); Guangdong Natural Science Funds for Distinguished Young Scholars (No. 2023B1515020097); and Singapore Ministry of Education Academic Research Fund Tier 1 (MSS23C002)." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.521, + 0.938 + ], + "angle": 0, + "content": "13699" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.471, + 0.157 + ], + "angle": 0, + "content": "[1] Rameen Abdal, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? 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IEEE TIP, 31:1230-1242, 2022. 1" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.518, + 0.937 + ], + "angle": 0, + "content": "13701" + } + ] +] \ No newline at end of file diff --git a/2023/RIGID_ Recurrent GAN Inversion and Editing of Real Face Videos/0ac9c66e-6779-4caf-9449-892ceb58d43e_origin.pdf b/2023/RIGID_ Recurrent GAN Inversion and Editing of Real Face Videos/0ac9c66e-6779-4caf-9449-892ceb58d43e_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..15febf18b4f37029bcdbec801e21bde3c01c5d70 --- /dev/null +++ b/2023/RIGID_ Recurrent GAN Inversion and Editing of Real Face Videos/0ac9c66e-6779-4caf-9449-892ceb58d43e_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a7280fe57c4710855219d814821921ba2d5fd49416340fd27b9658ba7f85c537 +size 6065524 diff --git a/2023/RIGID_ Recurrent GAN Inversion and Editing of Real Face Videos/full.md b/2023/RIGID_ Recurrent GAN Inversion and Editing of Real Face Videos/full.md new file mode 100644 index 0000000000000000000000000000000000000000..bb5d83b8808c114d985ec1dcbeae3df0aec322f2 --- /dev/null +++ b/2023/RIGID_ Recurrent GAN Inversion and Editing of Real Face Videos/full.md @@ -0,0 +1,331 @@ +# RIGID: Recurrent GAN Inversion and Editing of Real Face Videos + +Yangyang Xu $^{1}$ , Shengfeng He $^{2}$ , Kwan-Yee K. Wong $^{1}$ , and Ping Luo $^{1,3*}$ + +1Deapartment of Computer Science, The University of Hong Kong + +$^{2}$ School of Computing and Information Systems, Singapore Management University + +$^{3}$ Shanghai AI Laboratory + +![](images/8806412aeddf979edbc31c9a6a9d8427ec3148851997e5c29ffaec556c2d4c93.jpg) +Figure 1: Comparisons of video inversion and editing with existing methods. Number in each column denotes the average editing time over 100 frames. Our RIGID achieves temporal coherent inversion and editing performances with much less time cost. s. Please refer to the arXiv version to watch this figure as a video clip. + +# Abstract + +GAN inversion is indispensable for applying the powerful editability of GAN to real images. However, existing methods invert video frames individually often leading to undesired inconsistent results over time. In this paper, we propose a unified recurrent framework, named Recurrent vIDEo GAN Inversion and eDiting (RIGID), to explicitly and simultaneously enforce temporally coherent GAN inversion and facial editing of real videos. Our approach models the temporal relations between current and previous frames from three aspects. To enable a faithful real video reconstruction, we first maximize the inversion fidelity and consistency by learning a temporal compensated latent code. Second, we observe incoherent noises lie in the high-frequency domain that can be disentangled from the latent space. Third, to remove the inconsistency after attribute manipulation, we propose an in-between frame composition constraint such that the arbitrary frame must be a direct composite of its neighboring + +frames. Our unified framework learns the inherent coherence between input frames in an end-to-end manner, and therefore it is agnostic to a specific attribute and can be applied to arbitrary editing of the same video without re-training. Extensive experiments demonstrate that RIGID outperforms state-of-the-art methods qualitatively and quantitatively in both inversion and editing tasks. The deliverables can be found in https://cnn1stm.github.io/RIGID. + +# 1. Introduction + +Generative adversarial networks (GANs) have demonstrated powerful generative ability in synthesizing high-quality faces from a latent code [9, 11, 12, 47]. It is evidenced that the latent space of a well-trained GAN is semantically organized, and shifting the latent code along with a specific direction results in the manipulation of a corresponding attribute [23, 24, 5, 19, 45, 32]. Hence, many works migrate this power to real face processing by inverting a real face image to a latent code [49, 16, 39, 48, 40, 38]. Although + +this two-comb strategy becomes a standard for editing high-resolution images, applying it to real videos has less been explored. A naive inversion and editing for each frame can undoubtedly produce incoherence in the resulted video. + +Different from processing images, maintaining temporal coherence is the core issue for video editing [18, 28, 26]. Specifically, both the GAN inversion and attribute manipulation may introduce discontinuity across frames. IGCI [39] proposes the first attempt to invert consecutive images simultaneously. They leverage the continuity of the inputs to optimize both the reconstruction fidelity and editability of the outputs, but they fail to consider the temporal correlation between results (see flickering in Fig. 1b). Recent work STIT [30] implicitly recovers the original temporal correlations by the faithful inversion of each frame. It fine-tunes an individual generator for every input video such that the generator can capture all the reconstruction details, and TCSVE [37] extends this idea by proposing a temporal consistency loss that applies on the edited videos. Although they works well for most cases, they are video- and attribute-specific (needs to retrain the model for a new video or a new target attribute), and thus suffers from the expensive training cost and poor generalization ability. + +In this paper, we aim to design a unified approach that learns the temporal correlations between successive frames for both inversion and editing, and it can be generalized to other target attributes without re-training. To this end, we propose a Recurrent vVideo GAN Inversion and eDiting (RIGID) framework, which evolves and enables the image-based StyleGAN [11, 12] generator to output temporally coherent frames. The coherence is realized in both inversion and editing tasks. Given the current and previous frames, we formulate the inversion as the combination of an image-based inverted code and a temporal compensated code, while the latter amends the code with inter-frame similarity for an accurate and consistent inversion. On the other hand, we observe that the main sources of temporal incoherence, like "flickering", belong to high-frequency artifacts. This motivates us to disentangle the main video content from high-frequency artifacts in the latent space, and thus the "incoherence" can be shared with all the other frames. To build the temporal correlations after attribute manipulation, we propose a self-supervised "in-between frame composition constraint" that applies to consecutive edited frames. It enforces any intermediate frame that can be composed by the warping results of their neighbors, which guarantees the smoothness of generated videos. RIGID is trained on the video episodes with several tailored losses. During the inference, it inverts video frames sequentially and therefore can handle videos with arbitrary lengths and support live stream editing. More importantly, once our model is trained, it is attribute-agnostic that can be reused for arbitrary attribute manipulations without re-training. As shown in Fig. 1f, + +RIGID achieves temporal coherent inversion and editing with far less inference time (compared to those scene- and attribute-specific methods like STIT). Extensive experiments demonstrate the superiority over state-of-the-art methods in terms of quantitative and qualitative evaluations. + +In summary, our contributions are three-fold: + +- We propose a recurrent video GAN inversion framework that unifies video inversion and editing. It learns the temporal correlation of generated videos explicitly. +- We model temporal coherence from both inversion and editing ends. For inversion, we discover the temporal compensated code and disentangle high-frequency artifacts in the latent space. For editing, we present a novel "in-between frame composition constraint" to confine a continuous video transformation. +- We achieve attribute-agnostic editing that can vary editing attributes on the fly, avoiding expensive re-training of the model. Extensive experiments demonstrate the effectiveness of our method over state-of-the-arts. + +# 2. Related Works + +GAN Inversion. GAN inversion aims at inverting real images into the latent space of pre-trained generators for reconstruct and edit the real images [1, 39, 21, 33, 35, 29, 27]. Early works optimize the latent code directly for a specific image with expensive computational cost [4, 1]. Another class trains a general encoder that maps the real image to the latent code directly [21, 29, 33]. Particularly, pSp [21] proposes an encoder with pyramid architecture that inverts the real images into the $\mathcal{W}+$ latent space of StyleGAN. Based on the same architecture, e4e [29] analyzes the trade-offs between reconstruction and editability in StyleGAN's inversion. HFGI [33] introduces the distortion map for improving the fidelity reconstitution. Existing works mainly focus on the image-based GAN inversion, inverting the real videos into GANs has not been well studied. + +StyleGAN-based Video Generation and Editing. State-of-the-art video GANs still cannot generate high quality results as their image counterparts [28, 6, 34, 30]. Opposite to design a video generator directly, many works use the pretrained image generator (e.g., StyleGAN) for synthesizing high-quality videos [18, 28, 43, 26]. MoCoGAN-HD [28] decomposes the motion and content in videos and generates motion trajectory in StyleGAN's latent space. Style-HEAT [43] shares the same decomposition idea, it exploits the flow field as the motion descriptor for talking face generation. Recently, StyleGAN-V [26] injects the continuous motion representations into the StyleGAN. In this paper, we aim at inverting a real video into a pre-trained StyleGAN for temporal coherence reconstruction and editing. Few works + +![](images/72b447ebbfafccb7a852722b57f90b853c70aafef9d9d9c3fca271a9cdadb18a.jpg) +Figure 2: Overview of our RIGID. We first align the faces on two neighbor frames $(I_{t-1}$ and $I_t)$ . Then we concatenate them with the inverted face $O_{t-1}$ and edited face $E_{t-1}$ in the previous step as the inputs of the recurrent encoder. The encoder learns the temporal compensated code $w_t'$ and spatial noise map $n_t$ , as a complement to the initial latent code $w_t$ (acquired by the "e4e" encoder). In addition, we share the latter part of latent codes across all frames using $w_1^l$ for eliminating the high-frequency temporal flickering. Both the final inverted latent code $w_t^{lfd}$ and the edited one are fed to the generator, producing the inverted and edited faces $O_t^a$ and $E_t^a$ . The generated faces are unaligned and blended with the original frames. Dotted lines denote recurrent inputs from the last time step or outputs to the next step. In addition, a novel in-between frame composition constraint is proposed that learns the temporal correlation during editing (details can be found in Fig. 3). + +concentrate on this task. Latent-Transformer [42] presents a pipeline for facial video editing by inverting each frame individually, resulting in the temporal inconsistency in the edited videos. IGCI [39] introduces the consecutive frames into GAN inversion for improving the reconstruction quality and editability. STIT [30] edits the facial videos using StyleGAN2 [12] by fine-tuning the generator. TCSVE [37] also optimizes generators with a temporal consistency loss that applies on the edited videos. Above two optimization-based work need to re-optimize the generator for a new video or edit, which is time-consuming. In this paper, we propose a recurrent framework that learns the temporal correlations both in inverted and edited videos. Once it is properly trained, it supports various semantic editing methods with low computational costs. + +# 3. Approach + +# 3.1. Formulation + +Given a real face video $\{I_t|t = 1,\dots T\}$ , our goal is to invert it to the latent space of pre-trained StyleGAN $G$ to obtain a set of latent codes, and output the inverted video $\{O_t|t = 1,\dots T\}$ , where $O_{t}$ is obtained by feeding the latent code to $G$ . Meanwhile, we can also obtain an edited video $\{E_t|t = 1,\dots T\}$ by manipulating the latent codes. The key is that both inverted and edited video should be temporal coherent. + +To address that, we propose a recurrent video GAN inver + +sion and editing framework to explicitly and simultaneously enforce temporally coherent GAN inversion and facial editing of real videos. For video inversion, as the original video of inborn temporal coherence, the best way to maintain inversion consistency is a faithful reconstruction. In addition, we propose a "latent frequency disentanglement" strategy for eliminating the high-frequency temporal flickering in the latent space. We also propose an in-between frame composition constraint that builds the temporal correlations of edited video. The overview of our RIGID can be seen in Fig. 2. + +# 3.2. Coherent Video Inversion + +# 3.2.1 Temporal Compensated Inversion + +Given a real video, we can deliver its temporal correlation to the generated video by a faithful reconstruction. Before inversion, face alignment is necessary since StyleGAN cannot handle the entire frame. After the alignment on each frame, we can obtain a set of aligned faces $\{I_t^a | t = 1, \dots, T\}$ . We first encode them to the $\mathcal{W}+$ space using image-based inversion method (e4e [29] in this paper), and obtain the initial latent codes $\{w_t | t = 1, \dots, T\}$ , $w_t \in \mathcal{W}+$ . However, directly using the initial latent codes cannot reconstruct original faces accurately due to the missing of temporal context. We use a recurrent encoder that learns a temporal compensated code as a complement to the initialized one. Moreover, recovering a high-fidelity face solely in StyleGAN's $\mathcal{W}+$ latent space is too difficult due to the lack of spatial information [13, 33]. Inspired by [2], the encoder also learns a + +noise map in StyleGAN's $\mathcal{N}$ space for injecting the spatial information. + +Our goal is to unify inversion and editing in the same framework. As a result, both the inverted and edited faces from previous and current time steps are fed to the encoder to generate the temporal compensated code and the noise map. Here a ConvLSTM layer [25] is integrated into the encoder for modeling the spatial-temporal correlations. Specifically, at time step $t$ , we concatenate the aligned faces $I_{t-1}^a$ , $I_t^a$ , the last inverted face $O_{t-1}^a$ , and last edited face $E_{t-1}^a$ as inputs. It outputs a temporal compensated code $w_t'$ and spatial noise map $n_t$ , we add $w_t'$ with the initialized code $w_t$ . Then both added code and noise map $n_t$ are sent to the generator for inversion, that is: + +$$ +\left\{w _ {t} ^ {\prime}, n _ {t} \right\} = E \left(\operatorname {c a t} \left(I _ {t - 1} ^ {a}, I _ {t} ^ {a}, O _ {t - 1} ^ {a}, E _ {t - 1} ^ {a}\right)\right), \tag {1} +$$ + +$$ +O _ {t} ^ {a} = G \left(w _ {t} + w _ {t} ^ {\prime}, n _ {t}\right), \tag {2} +$$ + +where $E$ denotes the recurrent encoder and $\operatorname{cat}(\cdot, \cdot, \cdot, \cdot)$ denotes the concatenation operator. + +# 3.2.2 Latent Frequency Disentanglement + +The fidelity inversion delivers the temporal relations from the original video to the inverted one. However, frames are inverted one by one and may lead to subtle inconsistency, i.e., the unique high-frequency information in a single frame will be accumulated in a video and leads to temporal flickering. We notice that high-frequency temporal flickering mainly exists in the appearance of an image. Recent works evidenced that $\mathcal{W}+$ space is highly disentangled, and the appearance of the image is synthesized at the higher layer of StyleGAN, which is controlled by the latter part of the $w$ latent code [12, 21]. Hence we propose a "latent frequency disentanglement" strategy that eliminates the temporal flickering by sharing the latter part of $w$ latent code across all the frames. + +Specifically, we first decompose a latent code into the former part and the latter part, then we reuse the latter part (corresponding to high layers of StyleGAN) of the first frame in all the following frames that unify the high frequency information, that is: + +$$ +w _ {t} ^ {l f d} = \operatorname {c a t} \left(\left(w _ {t} + w _ {t} ^ {\prime}\right) ^ {f}, w _ {1} ^ {l}\right), \tag {3} +$$ + +where $w_{t}^{lfd}$ is the latent code after latent frequency disentanglement, $(w_{t} + w_{t}^{\prime})^{f}$ is the former part of latent code $w_{t} + w_{t}^{\prime}$ , and $w_{1}^{l}$ denotes the latter part of the first latent code. Now, we can get the final latent codes $\{c_{t} = \{w_{t}^{lfd}, n_{t}\} | t = 1, \dots, T\}$ for reconstructing a temporal coherent video. That is, we replace Eq. 2 with following equation: + +$$ +O _ {t} ^ {a} = G \left(w _ {t} ^ {l f d}, n _ {t}\right). \tag {4} +$$ + +The face can be edited by manipulating the latent code $w_{t}^{lfd}$ : + +$$ +E _ {t} ^ {a} = G \left(\left(w _ {t} ^ {l f d} + \vec {\mathbf {n}}\right), n _ {t}\right), \tag {5} +$$ + +where $\vec{\mathbf{n}}$ denotes the semantic direction acquired by arbitrary semantic editing techniques [23, 24, 5, 42, 41]. It is noticed that the $n_t$ is also determined by edited face $E_{t-1}^a$ , and it can be well cooperated with both inverted and edited code. + +# 3.3. Coherent Video Editing + +# 3.3.1 Post Processing + +The generated faces are naturally aligned that lost the temporal coherence. We need to unaligned generated faces and blend them with the original frame $I_{t}$ . Here we follow [42, 30] that blends the face region only. In particular, we first segment the face region on an original frame by a pre-trained face parsing model [44] to get the inner face mask $M_{I_t}$ , then we blend the inverted face $O_{t}^{a}$ with the original frame according to mask $M_{I_t}$ , which can be presented as: + +$$ +O _ {t} = \mathrm {B} \left(\mathrm {U A} \left(O _ {t} ^ {a}\right), I _ {t}, M _ {I _ {t}}\right), \tag {6} +$$ + +where B and UA denote the blending and unalignment respectively. + +For the edited face $E_{t}^{a}$ , its face region may be modified after editing, and the face mask of the original frame $M_{I_t}$ cannot well fit with the edited faces. Besides, directly using the face mask of the edited face also suffers a similar problem. Hence we use the union of two masks as the blending mask, that is: + +$$ +E _ {t} = \mathbb {B} \left(\mathrm {U A} \left(E _ {t} ^ {a}\right), I _ {t}, M _ {E _ {t}} \cup M _ {I _ {t}}\right). \tag {7} +$$ + +# 3.3.2 In-between Frame Composition Constraint + +After post processing, we can obtain the inverted and edited videos. Compared with the inverted videos, temporal correlation in an edited video is more difficult to learn, since there is no GT edited videos for supervision. We propose a self-supervised in-between frame composition constraint that models the temporal correlation in an edited video. + +Generally, for a triplet of consecutive frames $\{E_{t - 1}, E_t, E_{t + 1}\}$ , the intermediate frame $E_t$ can be composed by flow-based warping results of its neighbor frames [8, 20, 36]. Specifically, as shown in Fig. 3, let $f_{t \Rightarrow t - 1}$ denotes the optical flow from $E_t$ to $E_{t - 1}$ and $f_{t \Rightarrow t + 1}$ is the flow from $E_t$ to $E_{t + 1}$ , then frames $E_{t - 1}$ and $E_{t + 1}$ are warped using different flow. And the intermediate frame can be composed using two warped results according to a visibility map, that is: + +$$ +\begin{array}{l} \hat {E} _ {t} = V _ {t \leftarrow t - 1} \odot \mathbb {W} \left(E _ {t - 1}, f _ {t \Rightarrow t - 1}\right) + \tag {8} \\ \left(1 - V _ {t \Leftarrow t - 1}\right) \odot \mathrm {w} \left(E _ {t + 1}, f _ {t \Rightarrow t + 1}\right), \\ \end{array} +$$ + +![](images/af40d372d8c762bd5856a4099ab3e851fc9ad624859043df685ff607582d7f40.jpg) +Figure 3: The in-between frame can be composed by flow-based warping results of its neighboring frames according to a visibility map $V_{t \Leftarrow t-1}$ . + +where $\hat{E}_t$ is the composed intermediate frame, $V_{t\Leftarrow t - 1}$ is the visibility map from frame $E_{t}$ to $E_{t - 1}$ , it is a one channel mask with the same resolution with aligned face frames. It denotes whether a pixel remains visible when moving from frame $t - 1$ to $t$ (0 is fully occluded and 1 is fully visible). $\mathbb{W}$ is the warping operator, and $\odot$ denotes elementwise multiplication. This equation models the temporal correlations among three consecutive frames. + +For the edited videos, both $f_{t \Rightarrow t-1}$ and $f_{t \Rightarrow t+1}$ are available, the remaining challenge is to estimate the visibility mask $V_{t \Leftarrow t-1}$ . Since there is no GT for edited videos, we turn to train a visible net $V$ for estimating the mask. Particularly, we compose the in-between frame $\hat{I}_t$ on the real videos using Eq. 8. Then we align the $l_1$ distance between $\hat{I}_t$ and $I_t$ for training visible net $V$ . After training, we fix the $V$ and adopt it to the edited frames for estimating the visibility mask and composing the in-between frame $\hat{E}_t$ . We minimize the distance between $\hat{E}_t$ and $E_t$ to form in-between frame composition constraint: + +$$ +\mathcal {L} _ {i b f c c} = \sum_ {t = 2} ^ {T - 1} \left| \left| E _ {t} - \hat {E} _ {t} \right| \right| _ {1}. \tag {9} +$$ + +This constraint enforces the edited video as smooth as real video, which guarantees the temporal coherence effectively. Note that we train the encoder on the video episodes. Particularly, we first collect the outputs $\{E_0,\dots ,E_T\}$ in an episode via forward propagation, then we apply this constraint to train the encoder in backward propagation (we use differentiable unalignment). + +# 3.4. Loss Functions + +Our RIGID is trained under several tailored losses. Besides the in-between frame composition constraint $\mathcal{L}_{ifsc}$ applied on the edited videos, it also includes reconstruction and temporal consistency losses on the inverted videos. + +Reconstruction Loss. We first introduce the reconstruction loss $\mathcal{L}_{rec}$ on the inverted faces. Following [21, 33], it includes a pixel-wise $\mathcal{L}_2$ loss for minimizing the reconstruction error, and LPIPS loss for a better image quality preservation [46], which can be represented as: + +$$ +\mathcal {L} _ {2} = \sum_ {t = 1} ^ {T} \left| \left| I _ {t} ^ {a} - O _ {t} ^ {a} \right| \right| _ {2}, \tag {10} +$$ + +$$ +\mathcal {L} _ {l p i p s} = \sum_ {t = 1} ^ {T} | | P \left(I _ {t} ^ {a}\right) - P \left(O _ {t} ^ {a}\right) | | _ {2}, \tag {11} +$$ + +$$ +\mathcal {L} _ {r e c} = \mathcal {L} _ {2} + \alpha \mathcal {L} _ {l p i p s}, \tag {12} +$$ + +where $T$ is the number of frame in each training episode, $P(\cdot)$ denotes the perceptual feature extractor, and $\alpha$ is the balance weight. Following [21], we set $\alpha = 0.8$ . + +Temporal Consistency Loss. We also introduce a warping-based temporal consistency loss $\mathcal{L}_{tc}$ for preserving the temporal consistency of inverted videos. In particular, we first calculate the optical flow between two real neighbor frames, then we warp a real frame according to the flow, meanwhile, we also warp the inverted frame by the same flow. Then we minimize the distance on two warped frames to form the temporal consistency loss, that is: + +$$ +\hat {I} _ {t - 1} = \mathbb {W} \left(I _ {t - 1}, f _ {t \Rightarrow t - 1}\right), \tag {13} +$$ + +$$ +\hat {O} _ {t - 1} = \mathbb {W} \left(O _ {t - 1}, f _ {t \Rightarrow t - 1}\right), \tag {14} +$$ + +$$ +\mathcal {L} _ {t c} = \sum_ {t = 2} ^ {T} \left| \left| \hat {I} _ {t - 1} - \hat {O} _ {t - 1} \right| \right| _ {1}, \tag {15} +$$ + +where $f_{t \Rightarrow t-1}$ is the flow from frame $I_{t-1}$ to $I_t$ . This loss enforces the temporal correlation in the videos to be the same as the input video, and improves the temporal smoothness. + +Final Loss. We get the final loss function for training the RIGID: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \lambda_ {1} \mathcal {L} _ {\text {r e c}} + \lambda_ {2} \mathcal {L} _ {t c} + \lambda_ {3} \mathcal {L} _ {i b f c c}, \tag {16} +$$ + +where $\{\lambda_i\}$ denote the weight factors for balancing loss terms. + +# 4. Experiments + +# 4.1. Implementation Details + +We implement the proposed framework in Pytorch on a PC with an Nvidia GeForce RTX 3090. We chose the StyleGAN2 [12] pre-trained on the FFHQ dataset [11] with the resolution of $256 \times 256$ as our generator due to its strong edit ability. The corresponding $w$ latent code has the dimension of $14 \times 512$ , and we set the early $10 \times 512$ as the former part and the rest of $4 \times 512$ as the latter part in the latent frequency disentanglement. The framework is optimized by the Adam optimizer [14] with the learning rate of + +![](images/9ce25133724c76ddd661a39c1e8b2d4d95a508d60932623f02dc9a7894dd9868.jpg) +Figure 4: Qualitative comparison on the video inversion task. Our learning-based RIGID can faithfully reconstruct the video frames that is comparable to those expensive optimization-based works. + +$1e^{-4}$ . We empirically set the balancing weights in Eq. 16 as $\lambda_1 = 1$ , $\lambda_2 = 2$ , and $\lambda_3 = 5$ . Limited by the memory size of GPU, we set $T = 6$ in Eq. 15, which indicates each training episode contains 6 consecutive frames. In addition, we inject the noise map $n_t$ at the resolution of $32 \times 32$ to the generator. + +The recurrent encoder consists of 7 convolutional (Conv) layers, a ConvLSTM layer, and a fully connected (FC) layer. We take "Fused Leaky ReLU" as activation in-between Conv layers. The ConvLSTM layer is integrated between the Conv and FC layers. The visible net has a U-Net structure [22], it takes 5 Conv layers as encoder, and 5 Transposed convolutional layers as a decoder. BatchNorm layer and leakyReLU activation are integrated into between layers. Besides, a Sigmoid function is applied on output U-Net for normalizing the visibility map values. Visible net takes the concatenation of two warped results with 6 channels as input and outputs a visibility map with 1 channel. It is trained using Adam optimizer [14] with the learning rate of $1e^{-4}$ with 100,000 iterations. Besides, we use pre-trained FlowNet2 [7] for predicting optical flow, and we implement warping operation using bi-linear interpolation. + +# 4.2. Experimental Settings + +Datasets. We collect datasets both under control and in the wild environment. We select 72 videos from the con + +trolled RAVDESS dataset [17], which we called RAVDESS-72 Dataset. It contains 9,045 frames and each video contains about 120 frames. We also collect 36 videos from the Internet with the various poses, expressions, and backgrounds. We name them as In-the-Wild-36 Dataset, it contains 7,532 frames in total. We combine two datasets together, use 85 videos for training our RIGID and the rest 23 videos for testing. + +Competitors and Evaluation Metrics. We compare RIGID with three works, including IGCI [39], Latent-Transformer [42], STIT [30], and TCSVE [37]. Note that STIT [30] and TCSVE [37] use the same method for inversion. We use several metrics for evaluating different methods. For the video inversion task, we use the pixel-wise Mean Square Error (MSE) and Learned Perceptual Image Patch Similarity (LPIPS) [46] that evaluates the reconstruction quality. For evaluating the temporal stability, we use the flow-based Warp Error (WE) metric. For the edited task, we follow STIT [30] that use Temporally-Local (TL-ID) and Temporally-Global (TG-ID) identity preservation metrics for evaluating the temporal coherence of edited videos. We also use Fréchet Video Distance (FVD) [31] metric on both edited and inverted videos. Inference Times (IT) over 100 frames is also reported. Please refer to supplementary for more details of competitors and evaluation metrics. + +Table 1: Video inversion comparisons on two datasets. $\downarrow$ denotes the lower the better and the best results are marked in bold, and the values of MSE are magnified 100 times. + +
Metrics MethodsRAVDESS-72 DatasetIn-the-Wild-36 DatasetIT↓(s)
MSE↓LPIPS↓WE↓FVD↓MSE↓(×e-2)LPIPS↓WE↓FVD↓
IGCI [39]0.990.05154.21412.332.010.13432.98276.921.2×e5
Latent-T. [42]5.680.1286.356220.465.310.22367.32165.3549.2
STIT [30]/TCSVE [37]0.990.0583.21171.232.320.11293.8381.03851.5
RIGID1.040.0584.62174.552.310.12287.3274.1154.5
+ +![](images/7cc575105a515aa5a46af2f0c3bfe8217ea380e67c714693928e3250ab5b8e2d.jpg) ++Chubby +Figure 5: Qualitative comparison on video editing. RIGID uses the same post processing as IGCI and Latent-Transformer, but the edited faces can be better blended with the original background. Besides, compared with STIT and TCSVE, our RIGID supports shape editing on the face boundary (e.g., "Chubby"). + +![](images/2162523261d195162bea22842e024e17c26528ae85eadd93fb24464bac87d4f2.jpg) ++EyeGlasses + +![](images/0b8623991dd8183079a9d7ce8665b8e3488218f980fe043ead7b3af89add0c6f.jpg) ++NarrowEyes +Original IGCI Latent-T. STIT TCSVE RIGID + +# 4.3. Evaluation on Video Inversion + +Quantitative Evaluation. We first evaluate the fidelity and temporal coherence of inverted videos. Quantitative comparison can be seen in Tab. 1. We can see that both STIT, IGCI, and TCSVE have lower MSE and LPIPIS values, they optimize latent codes or generator specifically according to the video frames, which can reconstruct the target frames faithfully. IGCI presents the worse performance on WE and FVD metrics, since it optimizes the latent code for each image but fails to consider the temporal coherence of consec- + +utive frames, making the inverted latent codes less consistent. In addition, optimization-based methods cost a lot of time during the inference, especially for IGCI, which takes about 20 minutes for a single frame. Latent-Transformer uses a learning-based encoder that accelerates the inference speed, but it processes each frame individually, both the temporal coherence and reconstruction quality cannot be guaranteed. With about $15 \times$ faster inference than STIT, RIGID achieves a comparable result on the RAVDESS-72 and In-the-Wild-36 datasets. RIGID not only inverts the frame faithfully but also preserves the original temporal relations across frames. + +Table 2: Video editing comparisons on two datasets. $\downarrow$ denotes the lower the better and vice versa, the best results are marked in bold. + +
Metrics MethodsRAVDESS-72In-the-Wild-36IT↓(s)
TL-ID↑TG-ID↑FVD↓TL-ID↑TG-ID↑FVD↓
IGCI [39]0.940.79834.330.930.71499.221.2×e5
Latent-T. [42]0.990.93311.840.990.87267.4249.2
STIT [30]0.990.97212.040.990.91211.341.6×e3
TCSVE [37]0.990.97201.320.990.92198.463.4×e3
RIGID0.990.97198.540.990.93183.3654.5
+ +Thanks to temporal compensated inversion, RIGID guarantees the fidelity of inverted faces. + +Qualitative Evaluation. The quantitative comparison of video inversion can be seen in Fig. 4. We can see that two optimization-based works, IGCI and STIT reconstruct the frames well. Latent-Transformer utilizes the pSp encoder for inversion [21], and the results present different skin colors with original frames. Thanks to the temporal compensation inversion, our learning-based RIGID presents the competitive results with optimization-based IGCI and STIT on pixelwise reconstruction. The video comparison can be seen in Fig. 1. Latent-Transformer cannot provide accurate reconstruction. IGCI inverts each frame faithfully, but it cannot guarantee the temporal coherence across frames, resulting in serious temporal flickering. STIT achieves high-quality inversion on a specific video at the cost of long computational times. In contrast, RIGID builds temporal relations of inverted videos by the temporal compensated inversion, yielding temporal coherent inverted videos with much less time cost. + +# 4.4. Evaluation on Video Editing + +Quantitative Evaluation. The quantitative comparison of video editing can be seen in Tab. 2. We can see that IGCI [39] has high FVD values on both two datasets. As discussed above, it cannot produce consistent latent codes, making the edited frames discontinuous. In addition, IGCI has lower values on both TL-ID and TG-ID, which evidences that identity information cannot be preserved locally and globally. Compared with IGCI, Latent-Transformer [42] uses an encoder for producing latent codes, and the edited frames are more consistent. STIT [30] optimizes the generator for each video hence requires many inference times. RIGID achieves a comparable result on the RAVDESS-72 dataset with $30 \times$ faster during the inference. As for the In-the-Wild-36 Dataset, RIGID outperforms all competitors with three metrics. This should contribute to our in-between frame composition constraint. It enforces the smoothness of edited frames and brings temporal coherence into edited videos. + +Qualitative Evaluation. We present the qualitative comparison on video editing in Fig. 1 and Fig. 5. We can see that + +ICGI presents blurry edited faces with temporal flickering, and Latent-Transformer loses temporal coherence on local details (see bangs in Fig. 1c). In addition, though they use the same post processing as our RIGID, their edited faces cannot be well blended with the original background. Without considering the temporal coherence of edited frames, their edited faces have large structure deformations from the original faces. STIT proposes a "stitching tuning" strategy for the seamless blending, it enforces the edit frames have similar transitions around the face boundary with originals. However, when the target face's boundary is close to the background, this method does not support its shape-related editing (e.g., "Chubby" or "Double Chins"). As shown in the $1_{st}$ sample in Fig. 5, STIT fails on the "Chubby" editing. TCSVE uses the same strategy, hence it fails on this editing. More video comparisons can be found in the supplementary materials. + +# 4.5. Ablation Study + +In this section, we perform an ablation study to evaluate our RIGID on the RAVDESS-72 dataset. We develop five variants with the modification of the modules and the loss functions: 1) $w / o$ TCC, by removing temporal compensated code $w_{t}^{\prime}$ . 2) $w / o$ NM, by removing noise map $n_t$ . 3) $w / o$ LFD, by removing the latent frequency disentanglement in the framework. In this variant, frames in the same video have different latter codes $w_{t}^{l}$ . 4) $w / o$ $L_{ibfcc}$ , by removing in-between frame composition constraint. 5) $w / o$ $\mathcal{L}_{tc}$ , by removing the temporal consistent loss $\mathcal{L}_{tc}$ . + +The quantitative comparisons with various variants can be seen in Tab. 3. Compared with RIGID, variant $w / o$ TCC has a large WE value. Code $w_{t}^{\prime}$ introduces the temporal compensation to the image-based latent code, and brings the temporal coherence in inverted videos. Variant $w / o$ NM has large MSE and LPIPS values. Since noise map $n_t$ injects the spatial information to the generator, and improves the inversion accuracy. Both variant $w / o$ LFD and $w / o$ $\mathcal{L}_{tc}$ have large WE numbers. Our latent frequency disentangle-ment strategy unifies the high-frequency information in a video, and $\mathcal{L}_{tc}$ preserves the temporal consistency from the original to the inverted video. They learn the temporal relations effectively. We observe that variant $w / o$ $\mathcal{L}_{ibfcc}$ has + +Table 3: Quantitative comparisons with various variants on video inversion and editing. $\downarrow$ denotes the lower the better and vice visa, the best results are marked in bold. The values of MSE are magnified 100 times. + +
Metrics +VariantsVideo InversionVideo Editing
MSE↓LPIPS↓WE↓FVD↓TL-ID↑TG-ID↑FVD↓
w/o TCC1.310.07106.52208.740.980.94321.98
w/o NM2.280.0896.52201.220.990.92334.98
w/o LFD1.100.06103.61215.960.990.94309.04
w/o Lfccc0.930.05705.22358.040.980.90299.12
w/o Ltc1.080.05122.08203.540.990.97299.34
RIGID1.040.0584.62174.550.990.97198.54
+ +![](images/57ba392c6dcf27f9e26958b02ac786ebd644d29af1aa7d54b79e122349184819.jpg) +Figure 6: Qualitative comparison with different variants. Variant $w / o$ LFD and $w / o \mathcal{L}_{ibfcc}$ present noticeable temporal flickering. Please refer to the arXiv version to watch this figure as a video clip. + +the largest WE and FVD values on inverted videos, though it is applied to the edited frames. That is because the constraint enforces the smoothness of edited frames, and can be propagated to the latent codes that control the coherence of inverted frames. Meanwhile, variant $w / o \mathcal{L}_{ibfcc}$ has the worse performance on metrics TL-ID and TG-ID. Without the in-between constraint, the framework cannot guarantee the identity similarity across frames. By learning the temporal correlations in inverted and edited videos, the final RIGID achieves the best performance on two tasks. + +Qualitative comparison with different variants can be seen in Fig. 6. We can see variant $w / o \mathcal{L}_{ibfcc}$ presents annoying flickering both on the inverted and edited videos, which evidences the effectiveness of in-between frame composition constraint. As talked about in the main paper, it builds the temporal relations of video frames, which guarantees the smoothness of generated videos. Variant $w / o$ NM cannot invert the video faithfully. Variant $w / o$ LFD may present temporal flickering. The final RIGID presents temporal coherent inversion and editing videos. + +# 5. Conclusion and Discussions + +In this paper, we propose RIGID, a novel recurrent framework that learns the temporal correlations between succes + +sive frames for both inversion and editing. RIGID first learn the temporal correlation of inverted videos by a temporal-compensated reconstruction. It takes previous and current faces as input, and produces a temporal compensated code with a spatial noise map. They, together with the image-based latent code, are fed to the StyleGAN generator to reconstruct the video frames. Meanwhile, RIGID disentangles high-frequency artifacts in the latent space for eliminating the temporal flickering. Furthermore, for learning the temporal correlation of edited video, we enforce an edited frame can be composed by the flow-based warping of its neighbor frames. RIGID achieves attribute-agnostic editing with much less time cost. Extensive experiments demonstrate the superiority of RIGID. + +Limitations. As cropping and alignment of faces are needed before the inversion, those hair portions outside the cropped region cannot be edited by our method, which leads to unnatural conflicts after blending. It may be addressed by using StyleGAN3 [10] since it can generate unaligned faces. However, as indicated in [3], StyleGAN3 has a worse edit ability than StyleGAN2, which is essential in GAN inversion. + +Broader Impact. RIGID can potentially be used for academic research and commercial applications. It provides a pipeline for video-based GAN inversion, and benefits the design of temporal coherent video GANs. Besides, RIGID can create more facial videos in the media industry. On the other hand, although not the purpose of this work, it can potentially be misused for the violation of portrait rights and privacy. The risk can be mitigated by face forgery detection methods, i.e., we can detect the blending boundary using [15]. + +Acknowledgement. This paper is partially supported by the National Key R&D Program of China No.2022ZD0161000; the General Research Fund of Hong Kong No.17200622; National Natural Science Foundation of China (No. 61972162); Guangdong Natural Science Funds for Distinguished Young Scholars (No. 2023B1515020097); and Singapore Ministry of Education Academic Research Fund Tier 1 (MSS23C002). + +# References + +[1] Rameen Abdal, Yipeng Qin, and Peter Wonka. 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In CVPR, pages 5708-5717, 2022. 1 +[49] Yang Zhou, Yangyang Xu, Yong Du, Qiang Wen, and Shengfeng He. Pro-pulse: Learning progressive encoders + +of latent semantics in gans for photo upsampling. 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Number in each column denotes the average editing time over 100 frames. Our RIGID achieves temporal coherent inversion and editing performances with much less time cost. s. Please refer to the arXiv version to watch this figure as a video clip." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 143, + 468, + 192, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 468, + 192, + 480 + ], + "spans": [ + { + "bbox": [ + 143, + 468, + 192, + 480 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 489, + 289, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 489, + 289, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 489, + 289, + 693 + ], + "type": "text", + "content": "GAN inversion is indispensable for applying the powerful editability of GAN to real images. However, existing methods invert video frames individually often leading to undesired inconsistent results over time. In this paper, we propose a unified recurrent framework, named Recurrent vIDEo GAN Inversion and eDiting (RIGID), to explicitly and simultaneously enforce temporally coherent GAN inversion and facial editing of real videos. Our approach models the temporal relations between current and previous frames from three aspects. To enable a faithful real video reconstruction, we first maximize the inversion fidelity and consistency by learning a temporal compensated latent code. Second, we observe incoherent noises lie in the high-frequency domain that can be disentangled from the latent space. Third, to remove the inconsistency after attribute manipulation, we propose an in-between frame composition constraint such that the arbitrary frame must be a direct composite of its neighboring" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 468, + 547, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 547, + 565 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 547, + 565 + ], + "type": "text", + "content": "frames. Our unified framework learns the inherent coherence between input frames in an end-to-end manner, and therefore it is agnostic to a specific attribute and can be applied to arbitrary editing of the same video without re-training. Extensive experiments demonstrate that RIGID outperforms state-of-the-art methods qualitatively and quantitatively in both inversion and editing tasks. The deliverables can be found in https://cnn1stm.github.io/RIGID." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 585, + 386, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 585, + 386, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 585, + 386, + 597 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "Generative adversarial networks (GANs) have demonstrated powerful generative ability in synthesizing high-quality faces from a latent code [9, 11, 12, 47]. It is evidenced that the latent space of a well-trained GAN is semantically organized, and shifting the latent code along with a specific direction results in the manipulation of a corresponding attribute [23, 24, 5, 19, 45, 32]. Hence, many works migrate this power to real face processing by inverting a real face image to a latent code [49, 16, 39, 48, 40, 38]. Although" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 195, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 195, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 195, + 713 + ], + "type": "text", + "content": "*Corresponding author: pingluo@hku.hk." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "type": "text", + "content": "13691" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": "this two-comb strategy becomes a standard for editing high-resolution images, applying it to real videos has less been explored. A naive inversion and editing for each frame can undoubtedly produce incoherence in the resulted video." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 123, + 290, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 123, + 290, + 352 + ], + "spans": [ + { + "bbox": [ + 46, + 123, + 290, + 352 + ], + "type": "text", + "content": "Different from processing images, maintaining temporal coherence is the core issue for video editing [18, 28, 26]. Specifically, both the GAN inversion and attribute manipulation may introduce discontinuity across frames. IGCI [39] proposes the first attempt to invert consecutive images simultaneously. They leverage the continuity of the inputs to optimize both the reconstruction fidelity and editability of the outputs, but they fail to consider the temporal correlation between results (see flickering in Fig. 1b). Recent work STIT [30] implicitly recovers the original temporal correlations by the faithful inversion of each frame. It fine-tunes an individual generator for every input video such that the generator can capture all the reconstruction details, and TCSVE [37] extends this idea by proposing a temporal consistency loss that applies on the edited videos. Although they works well for most cases, they are video- and attribute-specific (needs to retrain the model for a new video or a new target attribute), and thus suffers from the expensive training cost and poor generalization ability." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 354, + 290, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 290, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 290, + 715 + ], + "type": "text", + "content": "In this paper, we aim to design a unified approach that learns the temporal correlations between successive frames for both inversion and editing, and it can be generalized to other target attributes without re-training. To this end, we propose a Recurrent vVideo GAN Inversion and eDiting (RIGID) framework, which evolves and enables the image-based StyleGAN [11, 12] generator to output temporally coherent frames. The coherence is realized in both inversion and editing tasks. Given the current and previous frames, we formulate the inversion as the combination of an image-based inverted code and a temporal compensated code, while the latter amends the code with inter-frame similarity for an accurate and consistent inversion. On the other hand, we observe that the main sources of temporal incoherence, like \"flickering\", belong to high-frequency artifacts. This motivates us to disentangle the main video content from high-frequency artifacts in the latent space, and thus the \"incoherence\" can be shared with all the other frames. To build the temporal correlations after attribute manipulation, we propose a self-supervised \"in-between frame composition constraint\" that applies to consecutive edited frames. It enforces any intermediate frame that can be composed by the warping results of their neighbors, which guarantees the smoothness of generated videos. RIGID is trained on the video episodes with several tailored losses. During the inference, it inverts video frames sequentially and therefore can handle videos with arbitrary lengths and support live stream editing. More importantly, once our model is trained, it is attribute-agnostic that can be reused for arbitrary attribute manipulations without re-training. As shown in Fig. 1f," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 132 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 132 + ], + "type": "text", + "content": "RIGID achieves temporal coherent inversion and editing with far less inference time (compared to those scene- and attribute-specific methods like STIT). Extensive experiments demonstrate the superiority over state-of-the-art methods in terms of quantitative and qualitative evaluations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 317, + 133, + 501, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 133, + 501, + 144 + ], + "spans": [ + { + "bbox": [ + 317, + 133, + 501, + 144 + ], + "type": "text", + "content": "In summary, our contributions are three-fold:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 152, + 547, + 324 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 317, + 152, + 547, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 152, + 547, + 190 + ], + "spans": [ + { + "bbox": [ + 317, + 152, + 547, + 190 + ], + "type": "text", + "content": "- We propose a recurrent video GAN inversion framework that unifies video inversion and editing. It learns the temporal correlation of generated videos explicitly." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 197, + 547, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 197, + 547, + 268 + ], + "spans": [ + { + "bbox": [ + 317, + 197, + 547, + 268 + ], + "type": "text", + "content": "- We model temporal coherence from both inversion and editing ends. For inversion, we discover the temporal compensated code and disentangle high-frequency artifacts in the latent space. For editing, we present a novel \"in-between frame composition constraint\" to confine a continuous video transformation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 277, + 547, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 277, + 547, + 324 + ], + "spans": [ + { + "bbox": [ + 317, + 277, + 547, + 324 + ], + "type": "text", + "content": "- We achieve attribute-agnostic editing that can vary editing attributes on the fly, avoiding expensive re-training of the model. Extensive experiments demonstrate the effectiveness of our method over state-of-the-arts." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 344, + 398, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 344, + 398, + 357 + ], + "spans": [ + { + "bbox": [ + 306, + 344, + 398, + 357 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 361, + 547, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 547, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 547, + 540 + ], + "type": "text", + "content": "GAN Inversion. GAN inversion aims at inverting real images into the latent space of pre-trained generators for reconstruct and edit the real images [1, 39, 21, 33, 35, 29, 27]. Early works optimize the latent code directly for a specific image with expensive computational cost [4, 1]. Another class trains a general encoder that maps the real image to the latent code directly [21, 29, 33]. Particularly, pSp [21] proposes an encoder with pyramid architecture that inverts the real images into the " + }, + { + "bbox": [ + 304, + 361, + 547, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{W}+" + }, + { + "bbox": [ + 304, + 361, + 547, + 540 + ], + "type": "text", + "content": " latent space of StyleGAN. Based on the same architecture, e4e [29] analyzes the trade-offs between reconstruction and editability in StyleGAN's inversion. HFGI [33] introduces the distortion map for improving the fidelity reconstitution. Existing works mainly focus on the image-based GAN inversion, inverting the real videos into GANs has not been well studied." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 545, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 548, + 714 + ], + "type": "text", + "content": "StyleGAN-based Video Generation and Editing. State-of-the-art video GANs still cannot generate high quality results as their image counterparts [28, 6, 34, 30]. Opposite to design a video generator directly, many works use the pretrained image generator (e.g., StyleGAN) for synthesizing high-quality videos [18, 28, 43, 26]. MoCoGAN-HD [28] decomposes the motion and content in videos and generates motion trajectory in StyleGAN's latent space. Style-HEAT [43] shares the same decomposition idea, it exploits the flow field as the motion descriptor for talking face generation. Recently, StyleGAN-V [26] injects the continuous motion representations into the StyleGAN. In this paper, we aim at inverting a real video into a pre-trained StyleGAN for temporal coherence reconstruction and editing. Few works" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 318, + 742 + ], + "type": "text", + "content": "13692" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 68, + 545, + 242 + ], + "blocks": [ + { + "bbox": [ + 50, + 68, + 545, + 242 + ], + "lines": [ + { + "bbox": [ + 50, + 68, + 545, + 242 + ], + "spans": [ + { + "bbox": [ + 50, + 68, + 545, + 242 + ], + "type": "image", + "image_path": "72b447ebbfafccb7a852722b57f90b853c70aafef9d9d9c3fca271a9cdadb18a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "lines": [ + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "text", + "content": "Figure 2: Overview of our RIGID. We first align the faces on two neighbor frames " + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "inline_equation", + "content": "(I_{t-1}" + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "inline_equation", + "content": "I_t)" + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "text", + "content": ". Then we concatenate them with the inverted face " + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "inline_equation", + "content": "O_{t-1}" + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "text", + "content": " and edited face " + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "inline_equation", + "content": "E_{t-1}" + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "text", + "content": " in the previous step as the inputs of the recurrent encoder. The encoder learns the temporal compensated code " + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "inline_equation", + "content": "w_t'" + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "text", + "content": " and spatial noise map " + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "inline_equation", + "content": "n_t" + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "text", + "content": ", as a complement to the initial latent code " + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "inline_equation", + "content": "w_t" + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "text", + "content": " (acquired by the \"e4e\" encoder). In addition, we share the latter part of latent codes across all frames using " + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "inline_equation", + "content": "w_1^l" + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "text", + "content": " for eliminating the high-frequency temporal flickering. Both the final inverted latent code " + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "inline_equation", + "content": "w_t^{lfd}" + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "text", + "content": " and the edited one are fed to the generator, producing the inverted and edited faces " + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "inline_equation", + "content": "O_t^a" + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "inline_equation", + "content": "E_t^a" + }, + { + "bbox": [ + 46, + 251, + 548, + 350 + ], + "type": "text", + "content": ". The generated faces are unaligned and blended with the original frames. Dotted lines denote recurrent inputs from the last time step or outputs to the next step. In addition, a novel in-between frame composition constraint is proposed that learns the temporal correlation during editing (details can be found in Fig. 3)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 369, + 289, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 289, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 289, + 548 + ], + "type": "text", + "content": "concentrate on this task. Latent-Transformer [42] presents a pipeline for facial video editing by inverting each frame individually, resulting in the temporal inconsistency in the edited videos. IGCI [39] introduces the consecutive frames into GAN inversion for improving the reconstruction quality and editability. STIT [30] edits the facial videos using StyleGAN2 [12] by fine-tuning the generator. TCSVE [37] also optimizes generators with a temporal consistency loss that applies on the edited videos. Above two optimization-based work need to re-optimize the generator for a new video or edit, which is time-consuming. In this paper, we propose a recurrent framework that learns the temporal correlations both in inverted and edited videos. Once it is properly trained, it supports various semantic editing methods with low computational costs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 563, + 115, + 577 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 115, + 577 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 115, + 577 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 584, + 129, + 596 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 584, + 129, + 596 + ], + "spans": [ + { + "bbox": [ + 47, + 584, + 129, + 596 + ], + "type": "text", + "content": "3.1. Formulation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 604, + 287, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 604, + 287, + 699 + ], + "spans": [ + { + "bbox": [ + 47, + 604, + 287, + 699 + ], + "type": "text", + "content": "Given a real face video " + }, + { + "bbox": [ + 47, + 604, + 287, + 699 + ], + "type": "inline_equation", + "content": "\\{I_t|t = 1,\\dots T\\}" + }, + { + "bbox": [ + 47, + 604, + 287, + 699 + ], + "type": "text", + "content": ", our goal is to invert it to the latent space of pre-trained StyleGAN " + }, + { + "bbox": [ + 47, + 604, + 287, + 699 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 47, + 604, + 287, + 699 + ], + "type": "text", + "content": " to obtain a set of latent codes, and output the inverted video " + }, + { + "bbox": [ + 47, + 604, + 287, + 699 + ], + "type": "inline_equation", + "content": "\\{O_t|t = 1,\\dots T\\}" + }, + { + "bbox": [ + 47, + 604, + 287, + 699 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 604, + 287, + 699 + ], + "type": "inline_equation", + "content": "O_{t}" + }, + { + "bbox": [ + 47, + 604, + 287, + 699 + ], + "type": "text", + "content": " is obtained by feeding the latent code to " + }, + { + "bbox": [ + 47, + 604, + 287, + 699 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 47, + 604, + 287, + 699 + ], + "type": "text", + "content": ". Meanwhile, we can also obtain an edited video " + }, + { + "bbox": [ + 47, + 604, + 287, + 699 + ], + "type": "inline_equation", + "content": "\\{E_t|t = 1,\\dots T\\}" + }, + { + "bbox": [ + 47, + 604, + 287, + 699 + ], + "type": "text", + "content": " by manipulating the latent codes. The key is that both inverted and edited video should be temporal coherent." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 701, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 288, + 713 + ], + "type": "text", + "content": "To address that, we propose a recurrent video GAN inver" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 369, + 547, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 547, + 490 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 547, + 490 + ], + "type": "text", + "content": "sion and editing framework to explicitly and simultaneously enforce temporally coherent GAN inversion and facial editing of real videos. For video inversion, as the original video of inborn temporal coherence, the best way to maintain inversion consistency is a faithful reconstruction. In addition, we propose a \"latent frequency disentanglement\" strategy for eliminating the high-frequency temporal flickering in the latent space. We also propose an in-between frame composition constraint that builds the temporal correlations of edited video. The overview of our RIGID can be seen in Fig. 2." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 496, + 449, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 496, + 449, + 509 + ], + "spans": [ + { + "bbox": [ + 306, + 496, + 449, + 509 + ], + "type": "text", + "content": "3.2. Coherent Video Inversion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 515, + 484, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 484, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 484, + 528 + ], + "type": "text", + "content": "3.2.1 Temporal Compensated Inversion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "content": "Given a real video, we can deliver its temporal correlation to the generated video by a faithful reconstruction. Before inversion, face alignment is necessary since StyleGAN cannot handle the entire frame. After the alignment on each frame, we can obtain a set of aligned faces " + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\{I_t^a | t = 1, \\dots, T\\}" + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "content": ". We first encode them to the " + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{W}+" + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "content": " space using image-based inversion method (e4e [29] in this paper), and obtain the initial latent codes " + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\{w_t | t = 1, \\dots, T\\}" + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "inline_equation", + "content": "w_t \\in \\mathcal{W}+" + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "content": ". However, directly using the initial latent codes cannot reconstruct original faces accurately due to the missing of temporal context. We use a recurrent encoder that learns a temporal compensated code as a complement to the initialized one. Moreover, recovering a high-fidelity face solely in StyleGAN's " + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{W}+" + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "content": " latent space is too difficult due to the lack of spatial information [13, 33]. Inspired by [2], the encoder also learns a" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "13693" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "noise map in StyleGAN's " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": " space for injecting the spatial information." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "text", + "content": "Our goal is to unify inversion and editing in the same framework. As a result, both the inverted and edited faces from previous and current time steps are fed to the encoder to generate the temporal compensated code and the noise map. Here a ConvLSTM layer [25] is integrated into the encoder for modeling the spatial-temporal correlations. Specifically, at time step " + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "text", + "content": ", we concatenate the aligned faces " + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "inline_equation", + "content": "I_{t-1}^a" + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "inline_equation", + "content": "I_t^a" + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "text", + "content": ", the last inverted face " + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "inline_equation", + "content": "O_{t-1}^a" + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "text", + "content": ", and last edited face " + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "inline_equation", + "content": "E_{t-1}^a" + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "text", + "content": " as inputs. It outputs a temporal compensated code " + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "inline_equation", + "content": "w_t'" + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "text", + "content": " and spatial noise map " + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "inline_equation", + "content": "n_t" + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "text", + "content": ", we add " + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "inline_equation", + "content": "w_t'" + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "text", + "content": " with the initialized code " + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "inline_equation", + "content": "w_t" + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "text", + "content": ". Then both added code and noise map " + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "inline_equation", + "content": "n_t" + }, + { + "bbox": [ + 46, + 96, + 288, + 240 + ], + "type": "text", + "content": " are sent to the generator for inversion, that is:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 78, + 251, + 287, + 264 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 251, + 287, + 264 + ], + "spans": [ + { + "bbox": [ + 78, + 251, + 287, + 264 + ], + "type": "interline_equation", + "content": "\\left\\{w _ {t} ^ {\\prime}, n _ {t} \\right\\} = E \\left(\\operatorname {c a t} \\left(I _ {t - 1} ^ {a}, I _ {t} ^ {a}, O _ {t - 1} ^ {a}, E _ {t - 1} ^ {a}\\right)\\right), \\tag {1}", + "image_path": "b9cb2ea99b67b799a4934b893547625d392a87541e1f26e76e8f591f9f8e5d5b.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 121, + 266, + 287, + 279 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 266, + 287, + 279 + ], + "spans": [ + { + "bbox": [ + 121, + 266, + 287, + 279 + ], + "type": "interline_equation", + "content": "O _ {t} ^ {a} = G \\left(w _ {t} + w _ {t} ^ {\\prime}, n _ {t}\\right), \\tag {2}", + "image_path": "14042ad30facfb414e380741e6da24d0fb273c383f2a2f8aab8f26efd9274f3a.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 289, + 289, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 289, + 314 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 289, + 314 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 289, + 289, + 314 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 289, + 289, + 314 + ], + "type": "text", + "content": " denotes the recurrent encoder and " + }, + { + "bbox": [ + 46, + 289, + 289, + 314 + ], + "type": "inline_equation", + "content": "\\operatorname{cat}(\\cdot, \\cdot, \\cdot, \\cdot)" + }, + { + "bbox": [ + 46, + 289, + 289, + 314 + ], + "type": "text", + "content": " denotes the concatenation operator." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 331, + 230, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 331, + 230, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 331, + 230, + 342 + ], + "type": "text", + "content": "3.2.2 Latent Frequency Disentanglement" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 350, + 287, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 516 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 516 + ], + "type": "text", + "content": "The fidelity inversion delivers the temporal relations from the original video to the inverted one. However, frames are inverted one by one and may lead to subtle inconsistency, i.e., the unique high-frequency information in a single frame will be accumulated in a video and leads to temporal flickering. We notice that high-frequency temporal flickering mainly exists in the appearance of an image. Recent works evidenced that " + }, + { + "bbox": [ + 46, + 350, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\mathcal{W}+" + }, + { + "bbox": [ + 46, + 350, + 287, + 516 + ], + "type": "text", + "content": " space is highly disentangled, and the appearance of the image is synthesized at the higher layer of StyleGAN, which is controlled by the latter part of the " + }, + { + "bbox": [ + 46, + 350, + 287, + 516 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 350, + 287, + 516 + ], + "type": "text", + "content": " latent code [12, 21]. Hence we propose a \"latent frequency disentanglement\" strategy that eliminates the temporal flickering by sharing the latter part of " + }, + { + "bbox": [ + 46, + 350, + 287, + 516 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 350, + 287, + 516 + ], + "type": "text", + "content": " latent code across all the frames." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 517, + 287, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 517, + 287, + 577 + ], + "spans": [ + { + "bbox": [ + 46, + 517, + 287, + 577 + ], + "type": "text", + "content": "Specifically, we first decompose a latent code into the former part and the latter part, then we reuse the latter part (corresponding to high layers of StyleGAN) of the first frame in all the following frames that unify the high frequency information, that is:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 586, + 287, + 602 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 586, + 287, + 602 + ], + "spans": [ + { + "bbox": [ + 104, + 586, + 287, + 602 + ], + "type": "interline_equation", + "content": "w _ {t} ^ {l f d} = \\operatorname {c a t} \\left(\\left(w _ {t} + w _ {t} ^ {\\prime}\\right) ^ {f}, w _ {1} ^ {l}\\right), \\tag {3}", + "image_path": "e26f291b607f393854f951549d32d5a7e01268868ca7111482749b3bdc3230b6.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 613, + 288, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 613, + 288, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 613, + 288, + 687 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 613, + 288, + 687 + ], + "type": "inline_equation", + "content": "w_{t}^{lfd}" + }, + { + "bbox": [ + 46, + 613, + 288, + 687 + ], + "type": "text", + "content": " is the latent code after latent frequency disentanglement, " + }, + { + "bbox": [ + 46, + 613, + 288, + 687 + ], + "type": "inline_equation", + "content": "(w_{t} + w_{t}^{\\prime})^{f}" + }, + { + "bbox": [ + 46, + 613, + 288, + 687 + ], + "type": "text", + "content": " is the former part of latent code " + }, + { + "bbox": [ + 46, + 613, + 288, + 687 + ], + "type": "inline_equation", + "content": "w_{t} + w_{t}^{\\prime}" + }, + { + "bbox": [ + 46, + 613, + 288, + 687 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 613, + 288, + 687 + ], + "type": "inline_equation", + "content": "w_{1}^{l}" + }, + { + "bbox": [ + 46, + 613, + 288, + 687 + ], + "type": "text", + "content": " denotes the latter part of the first latent code. Now, we can get the final latent codes " + }, + { + "bbox": [ + 46, + 613, + 288, + 687 + ], + "type": "inline_equation", + "content": "\\{c_{t} = \\{w_{t}^{lfd}, n_{t}\\} | t = 1, \\dots, T\\}" + }, + { + "bbox": [ + 46, + 613, + 288, + 687 + ], + "type": "text", + "content": " for reconstructing a temporal coherent video. That is, we replace Eq. 2 with following equation:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 126, + 695, + 287, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 695, + 287, + 711 + ], + "spans": [ + { + "bbox": [ + 126, + 695, + 287, + 711 + ], + "type": "interline_equation", + "content": "O _ {t} ^ {a} = G \\left(w _ {t} ^ {l f d}, n _ {t}\\right). \\tag {4}", + "image_path": "14e167a38b9649538cbb722c2cf1d3ec078f401f700f27063707f46f2fe4ec55.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "content": "The face can be edited by manipulating the latent code " + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "w_{t}^{lfd}" + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 370, + 102, + 545, + 118 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 102, + 545, + 118 + ], + "spans": [ + { + "bbox": [ + 370, + 102, + 545, + 118 + ], + "type": "interline_equation", + "content": "E _ {t} ^ {a} = G \\left(\\left(w _ {t} ^ {l f d} + \\vec {\\mathbf {n}}\\right), n _ {t}\\right), \\tag {5}", + "image_path": "a8a11c04314566a44ead7e26503d547954e423a77e83fd535a16f5644f37263d.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 124, + 547, + 183 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 124, + 547, + 183 + ], + "spans": [ + { + "bbox": [ + 304, + 124, + 547, + 183 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 124, + 547, + 183 + ], + "type": "inline_equation", + "content": "\\vec{\\mathbf{n}}" + }, + { + "bbox": [ + 304, + 124, + 547, + 183 + ], + "type": "text", + "content": " denotes the semantic direction acquired by arbitrary semantic editing techniques [23, 24, 5, 42, 41]. It is noticed that the " + }, + { + "bbox": [ + 304, + 124, + 547, + 183 + ], + "type": "inline_equation", + "content": "n_t" + }, + { + "bbox": [ + 304, + 124, + 547, + 183 + ], + "type": "text", + "content": " is also determined by edited face " + }, + { + "bbox": [ + 304, + 124, + 547, + 183 + ], + "type": "inline_equation", + "content": "E_{t-1}^a" + }, + { + "bbox": [ + 304, + 124, + 547, + 183 + ], + "type": "text", + "content": ", and it can be well cooperated with both inverted and edited code." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 190, + 440, + 204 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 190, + 440, + 204 + ], + "spans": [ + { + "bbox": [ + 306, + 190, + 440, + 204 + ], + "type": "text", + "content": "3.3. Coherent Video Editing" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 209, + 406, + 221 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 209, + 406, + 221 + ], + "spans": [ + { + "bbox": [ + 306, + 209, + 406, + 221 + ], + "type": "text", + "content": "3.3.1 Post Processing" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 228, + 547, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 547, + 334 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 547, + 334 + ], + "type": "text", + "content": "The generated faces are naturally aligned that lost the temporal coherence. We need to unaligned generated faces and blend them with the original frame " + }, + { + "bbox": [ + 304, + 228, + 547, + 334 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 304, + 228, + 547, + 334 + ], + "type": "text", + "content": ". Here we follow [42, 30] that blends the face region only. In particular, we first segment the face region on an original frame by a pre-trained face parsing model [44] to get the inner face mask " + }, + { + "bbox": [ + 304, + 228, + 547, + 334 + ], + "type": "inline_equation", + "content": "M_{I_t}" + }, + { + "bbox": [ + 304, + 228, + 547, + 334 + ], + "type": "text", + "content": ", then we blend the inverted face " + }, + { + "bbox": [ + 304, + 228, + 547, + 334 + ], + "type": "inline_equation", + "content": "O_{t}^{a}" + }, + { + "bbox": [ + 304, + 228, + 547, + 334 + ], + "type": "text", + "content": " with the original frame according to mask " + }, + { + "bbox": [ + 304, + 228, + 547, + 334 + ], + "type": "inline_equation", + "content": "M_{I_t}" + }, + { + "bbox": [ + 304, + 228, + 547, + 334 + ], + "type": "text", + "content": ", which can be presented as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 370, + 335, + 545, + 349 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 335, + 545, + 349 + ], + "spans": [ + { + "bbox": [ + 370, + 335, + 545, + 349 + ], + "type": "interline_equation", + "content": "O _ {t} = \\mathrm {B} \\left(\\mathrm {U A} \\left(O _ {t} ^ {a}\\right), I _ {t}, M _ {I _ {t}}\\right), \\tag {6}", + "image_path": "8eaa0ad7af7b3857edc21c72cb2fc5951fb41465a3bcbda13e71d14e2f218712.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 352, + 547, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 352, + 547, + 375 + ], + "spans": [ + { + "bbox": [ + 304, + 352, + 547, + 375 + ], + "type": "text", + "content": "where B and UA denote the blending and unalignment respectively." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 376, + 547, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 547, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 547, + 447 + ], + "type": "text", + "content": "For the edited face " + }, + { + "bbox": [ + 304, + 376, + 547, + 447 + ], + "type": "inline_equation", + "content": "E_{t}^{a}" + }, + { + "bbox": [ + 304, + 376, + 547, + 447 + ], + "type": "text", + "content": ", its face region may be modified after editing, and the face mask of the original frame " + }, + { + "bbox": [ + 304, + 376, + 547, + 447 + ], + "type": "inline_equation", + "content": "M_{I_t}" + }, + { + "bbox": [ + 304, + 376, + 547, + 447 + ], + "type": "text", + "content": " cannot well fit with the edited faces. Besides, directly using the face mask of the edited face also suffers a similar problem. Hence we use the union of two masks as the blending mask, that is:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 355, + 455, + 545, + 468 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 455, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 355, + 455, + 545, + 468 + ], + "type": "interline_equation", + "content": "E _ {t} = \\mathbb {B} \\left(\\mathrm {U A} \\left(E _ {t} ^ {a}\\right), I _ {t}, M _ {E _ {t}} \\cup M _ {I _ {t}}\\right). \\tag {7}", + "image_path": "d3c154eda31135fa56248bba63f64bf527df939fdd91283c780a8349404a7b14.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 481, + 515, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 481, + 515, + 493 + ], + "spans": [ + { + "bbox": [ + 306, + 481, + 515, + 493 + ], + "type": "text", + "content": "3.3.2 In-between Frame Composition Constraint" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 500, + 547, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 500, + 547, + 571 + ], + "spans": [ + { + "bbox": [ + 304, + 500, + 547, + 571 + ], + "type": "text", + "content": "After post processing, we can obtain the inverted and edited videos. Compared with the inverted videos, temporal correlation in an edited video is more difficult to learn, since there is no GT edited videos for supervision. We propose a self-supervised in-between frame composition constraint that models the temporal correlation in an edited video." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "spans": [ + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "text", + "content": "Generally, for a triplet of consecutive frames " + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "inline_equation", + "content": "\\{E_{t - 1}, E_t, E_{t + 1}\\}" + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "text", + "content": ", the intermediate frame " + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "inline_equation", + "content": "E_t" + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "text", + "content": " can be composed by flow-based warping results of its neighbor frames [8, 20, 36]. Specifically, as shown in Fig. 3, let " + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "inline_equation", + "content": "f_{t \\Rightarrow t - 1}" + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "text", + "content": " denotes the optical flow from " + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "inline_equation", + "content": "E_t" + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "inline_equation", + "content": "E_{t - 1}" + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "inline_equation", + "content": "f_{t \\Rightarrow t + 1}" + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "text", + "content": " is the flow from " + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "inline_equation", + "content": "E_t" + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "inline_equation", + "content": "E_{t + 1}" + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "text", + "content": ", then frames " + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "inline_equation", + "content": "E_{t - 1}" + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "inline_equation", + "content": "E_{t + 1}" + }, + { + "bbox": [ + 304, + 572, + 547, + 679 + ], + "type": "text", + "content": " are warped using different flow. And the intermediate frame can be composed using two warped results according to a visibility map, that is:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 344, + 686, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 686, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 344, + 686, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {E} _ {t} = V _ {t \\leftarrow t - 1} \\odot \\mathbb {W} \\left(E _ {t - 1}, f _ {t \\Rightarrow t - 1}\\right) + \\tag {8} \\\\ \\left(1 - V _ {t \\Leftarrow t - 1}\\right) \\odot \\mathrm {w} \\left(E _ {t + 1}, f _ {t \\Rightarrow t + 1}\\right), \\\\ \\end{array}", + "image_path": "d6ecb3ff3f98e1268091f32d394f8ecae5839e9e0c4d62727f2b35fc92658aeb.jpg" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "13694" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 298, + 203 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 298, + 203 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 298, + 203 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 298, + 203 + ], + "type": "image", + "image_path": "af40d372d8c762bd5856a4099ab3e851fc9ad624859043df685ff607582d7f40.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 212, + 288, + 249 + ], + "lines": [ + { + "bbox": [ + 46, + 212, + 288, + 249 + ], + "spans": [ + { + "bbox": [ + 46, + 212, + 288, + 249 + ], + "type": "text", + "content": "Figure 3: The in-between frame can be composed by flow-based warping results of its neighboring frames according to a visibility map " + }, + { + "bbox": [ + 46, + 212, + 288, + 249 + ], + "type": "inline_equation", + "content": "V_{t \\Leftarrow t-1}" + }, + { + "bbox": [ + 46, + 212, + 288, + 249 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "type": "inline_equation", + "content": "\\hat{E}_t" + }, + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "type": "text", + "content": " is the composed intermediate frame, " + }, + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "type": "inline_equation", + "content": "V_{t\\Leftarrow t - 1}" + }, + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "type": "text", + "content": " is the visibility map from frame " + }, + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "type": "inline_equation", + "content": "E_{t}" + }, + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "type": "inline_equation", + "content": "E_{t - 1}" + }, + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "type": "text", + "content": ", it is a one channel mask with the same resolution with aligned face frames. It denotes whether a pixel remains visible when moving from frame " + }, + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "type": "inline_equation", + "content": "t - 1" + }, + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "type": "text", + "content": " (0 is fully occluded and 1 is fully visible). " + }, + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "type": "inline_equation", + "content": "\\mathbb{W}" + }, + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "type": "text", + "content": " is the warping operator, and " + }, + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 270, + 287, + 366 + ], + "type": "text", + "content": " denotes elementwise multiplication. This equation models the temporal correlations among three consecutive frames." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "text", + "content": "For the edited videos, both " + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "inline_equation", + "content": "f_{t \\Rightarrow t-1}" + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "inline_equation", + "content": "f_{t \\Rightarrow t+1}" + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "text", + "content": " are available, the remaining challenge is to estimate the visibility mask " + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "inline_equation", + "content": "V_{t \\Leftarrow t-1}" + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "text", + "content": ". Since there is no GT for edited videos, we turn to train a visible net " + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "text", + "content": " for estimating the mask. Particularly, we compose the in-between frame " + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "inline_equation", + "content": "\\hat{I}_t" + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "text", + "content": " on the real videos using Eq. 8. Then we align the " + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "inline_equation", + "content": "l_1" + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "text", + "content": " distance between " + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "inline_equation", + "content": "\\hat{I}_t" + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "inline_equation", + "content": "I_t" + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "text", + "content": " for training visible net " + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "text", + "content": ". After training, we fix the " + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "text", + "content": " and adopt it to the edited frames for estimating the visibility mask and composing the in-between frame " + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "inline_equation", + "content": "\\hat{E}_t" + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "text", + "content": ". We minimize the distance between " + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "inline_equation", + "content": "\\hat{E}_t" + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "inline_equation", + "content": "E_t" + }, + { + "bbox": [ + 46, + 368, + 288, + 499 + ], + "type": "text", + "content": " to form in-between frame composition constraint:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 111, + 510, + 287, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 510, + 287, + 541 + ], + "spans": [ + { + "bbox": [ + 111, + 510, + 287, + 541 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i b f c c} = \\sum_ {t = 2} ^ {T - 1} \\left| \\left| E _ {t} - \\hat {E} _ {t} \\right| \\right| _ {1}. \\tag {9}", + "image_path": "75ca334076005332040a9ad224ebfe2f797b801f3a407575899b24704895dd58.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 552, + 288, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 288, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 288, + 635 + ], + "type": "text", + "content": "This constraint enforces the edited video as smooth as real video, which guarantees the temporal coherence effectively. Note that we train the encoder on the video episodes. Particularly, we first collect the outputs " + }, + { + "bbox": [ + 46, + 552, + 288, + 635 + ], + "type": "inline_equation", + "content": "\\{E_0,\\dots ,E_T\\}" + }, + { + "bbox": [ + 46, + 552, + 288, + 635 + ], + "type": "text", + "content": " in an episode via forward propagation, then we apply this constraint to train the encoder in backward propagation (we use differentiable unalignment)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 646, + 140, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 646, + 140, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 646, + 140, + 658 + ], + "type": "text", + "content": "3.4. Loss Functions" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "content": "Our RIGID is trained under several tailored losses. Besides the in-between frame composition constraint " + }, + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ifsc}" + }, + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "content": " applied on the edited videos, it also includes reconstruction and temporal consistency losses on the inverted videos." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": "Reconstruction Loss. We first introduce the reconstruction loss " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec}" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " on the inverted faces. Following [21, 33], it includes a pixel-wise " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " loss for minimizing the reconstruction error, and LPIPS loss for a better image quality preservation [46], which can be represented as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 377, + 140, + 546, + 172 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 377, + 140, + 546, + 172 + ], + "spans": [ + { + "bbox": [ + 377, + 140, + 546, + 172 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {2} = \\sum_ {t = 1} ^ {T} \\left| \\left| I _ {t} ^ {a} - O _ {t} ^ {a} \\right| \\right| _ {2}, \\tag {10}", + "image_path": "2e8869cd1bbce8d3da3d8f722d187db13995e7c27cbe210b65ddde8f8b990b3d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 355, + 175, + 546, + 207 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 175, + 546, + 207 + ], + "spans": [ + { + "bbox": [ + 355, + 175, + 546, + 207 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {l p i p s} = \\sum_ {t = 1} ^ {T} | | P \\left(I _ {t} ^ {a}\\right) - P \\left(O _ {t} ^ {a}\\right) | | _ {2}, \\tag {11}", + "image_path": "57ac8c2d5922b1a14fb750f9ef9195ca6609cea80341be993b1b193c9d91a03e.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 380, + 210, + 546, + 224 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 210, + 546, + 224 + ], + "spans": [ + { + "bbox": [ + 380, + 210, + 546, + 224 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r e c} = \\mathcal {L} _ {2} + \\alpha \\mathcal {L} _ {l p i p s}, \\tag {12}", + "image_path": "cdddfe6a0486c7dd6f6dc134e73f4ce4de556e507111f1107643c0fc89c8a730.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 231, + 546, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 231, + 546, + 266 + ], + "spans": [ + { + "bbox": [ + 306, + 231, + 546, + 266 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 231, + 546, + 266 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 306, + 231, + 546, + 266 + ], + "type": "text", + "content": " is the number of frame in each training episode, " + }, + { + "bbox": [ + 306, + 231, + 546, + 266 + ], + "type": "inline_equation", + "content": "P(\\cdot)" + }, + { + "bbox": [ + 306, + 231, + 546, + 266 + ], + "type": "text", + "content": " denotes the perceptual feature extractor, and " + }, + { + "bbox": [ + 306, + 231, + 546, + 266 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 306, + 231, + 546, + 266 + ], + "type": "text", + "content": " is the balance weight. Following [21], we set " + }, + { + "bbox": [ + 306, + 231, + 546, + 266 + ], + "type": "inline_equation", + "content": "\\alpha = 0.8" + }, + { + "bbox": [ + 306, + 231, + 546, + 266 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 267, + 547, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 267, + 547, + 362 + ], + "spans": [ + { + "bbox": [ + 304, + 267, + 547, + 362 + ], + "type": "text", + "content": "Temporal Consistency Loss. We also introduce a warping-based temporal consistency loss " + }, + { + "bbox": [ + 304, + 267, + 547, + 362 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{tc}" + }, + { + "bbox": [ + 304, + 267, + 547, + 362 + ], + "type": "text", + "content": " for preserving the temporal consistency of inverted videos. In particular, we first calculate the optical flow between two real neighbor frames, then we warp a real frame according to the flow, meanwhile, we also warp the inverted frame by the same flow. Then we minimize the distance on two warped frames to form the temporal consistency loss, that is:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 373, + 369, + 545, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 369, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 373, + 369, + 545, + 384 + ], + "type": "interline_equation", + "content": "\\hat {I} _ {t - 1} = \\mathbb {W} \\left(I _ {t - 1}, f _ {t \\Rightarrow t - 1}\\right), \\tag {13}", + "image_path": "abceffb5352eb8f9b1295457ff4b0243d5b3183d35b3ed269e1b8ae2e6af8d59.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 371, + 387, + 545, + 400 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 387, + 545, + 400 + ], + "spans": [ + { + "bbox": [ + 371, + 387, + 545, + 400 + ], + "type": "interline_equation", + "content": "\\hat {O} _ {t - 1} = \\mathbb {W} \\left(O _ {t - 1}, f _ {t \\Rightarrow t - 1}\\right), \\tag {14}", + "image_path": "aaf1f89876c6f77f3c56ec1479622580155a729ef75ed37945eca9e744d9aed1.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 367, + 405, + 545, + 436 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 405, + 545, + 436 + ], + "spans": [ + { + "bbox": [ + 367, + 405, + 545, + 436 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {t c} = \\sum_ {t = 2} ^ {T} \\left| \\left| \\hat {I} _ {t - 1} - \\hat {O} _ {t - 1} \\right| \\right| _ {1}, \\tag {15}", + "image_path": "02e262695db823042b23944ba841772b4d574c97d32712d477d9facbf417166e.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 444, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 545, + 479 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 444, + 545, + 479 + ], + "type": "inline_equation", + "content": "f_{t \\Rightarrow t-1}" + }, + { + "bbox": [ + 304, + 444, + 545, + 479 + ], + "type": "text", + "content": " is the flow from frame " + }, + { + "bbox": [ + 304, + 444, + 545, + 479 + ], + "type": "inline_equation", + "content": "I_{t-1}" + }, + { + "bbox": [ + 304, + 444, + 545, + 479 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 444, + 545, + 479 + ], + "type": "inline_equation", + "content": "I_t" + }, + { + "bbox": [ + 304, + 444, + 545, + 479 + ], + "type": "text", + "content": ". This loss enforces the temporal correlation in the videos to be the same as the input video, and improves the temporal smoothness." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 479, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 545, + 502 + ], + "type": "text", + "content": "Final Loss. We get the final loss function for training the RIGID:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 347, + 512, + 545, + 526 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 512, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 347, + 512, + 545, + 526 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\mathcal {L} _ {\\text {r e c}} + \\lambda_ {2} \\mathcal {L} _ {t c} + \\lambda_ {3} \\mathcal {L} _ {i b f c c}, \\tag {16}", + "image_path": "6ebf70718dfc101290dfbe7dad01a4afead4c3ba3679b6f2eb4d321d6dd8be71.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 533, + 545, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 556 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 533, + 545, + 556 + ], + "type": "inline_equation", + "content": "\\{\\lambda_i\\}" + }, + { + "bbox": [ + 304, + 533, + 545, + 556 + ], + "type": "text", + "content": " denote the weight factors for balancing loss terms." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 567, + 387, + 581 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 567, + 387, + 581 + ], + "spans": [ + { + "bbox": [ + 306, + 567, + 387, + 581 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 587, + 438, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 587, + 438, + 600 + ], + "spans": [ + { + "bbox": [ + 306, + 587, + 438, + 600 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": "We implement the proposed framework in Pytorch on a PC with an Nvidia GeForce RTX 3090. We chose the StyleGAN2 [12] pre-trained on the FFHQ dataset [11] with the resolution of " + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": " as our generator due to its strong edit ability. The corresponding " + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": " latent code has the dimension of " + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "inline_equation", + "content": "14 \\times 512" + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": ", and we set the early " + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "inline_equation", + "content": "10 \\times 512" + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": " as the former part and the rest of " + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "inline_equation", + "content": "4 \\times 512" + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": " as the latter part in the latent frequency disentanglement. The framework is optimized by the Adam optimizer [14] with the learning rate of" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "type": "text", + "content": "13695" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 79, + 541, + 348 + ], + "blocks": [ + { + "bbox": [ + 55, + 79, + 541, + 348 + ], + "lines": [ + { + "bbox": [ + 55, + 79, + 541, + 348 + ], + "spans": [ + { + "bbox": [ + 55, + 79, + 541, + 348 + ], + "type": "image", + "image_path": "9ce25133724c76ddd661a39c1e8b2d4d95a508d60932623f02dc9a7894dd9868.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 356, + 546, + 381 + ], + "lines": [ + { + "bbox": [ + 46, + 356, + 546, + 381 + ], + "spans": [ + { + "bbox": [ + 46, + 356, + 546, + 381 + ], + "type": "text", + "content": "Figure 4: Qualitative comparison on the video inversion task. Our learning-based RIGID can faithfully reconstruct the video frames that is comparable to those expensive optimization-based works." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 402, + 287, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 473 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 473 + ], + "type": "inline_equation", + "content": "1e^{-4}" + }, + { + "bbox": [ + 46, + 402, + 287, + 473 + ], + "type": "text", + "content": ". We empirically set the balancing weights in Eq. 16 as " + }, + { + "bbox": [ + 46, + 402, + 287, + 473 + ], + "type": "inline_equation", + "content": "\\lambda_1 = 1" + }, + { + "bbox": [ + 46, + 402, + 287, + 473 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 402, + 287, + 473 + ], + "type": "inline_equation", + "content": "\\lambda_2 = 2" + }, + { + "bbox": [ + 46, + 402, + 287, + 473 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 402, + 287, + 473 + ], + "type": "inline_equation", + "content": "\\lambda_3 = 5" + }, + { + "bbox": [ + 46, + 402, + 287, + 473 + ], + "type": "text", + "content": ". Limited by the memory size of GPU, we set " + }, + { + "bbox": [ + 46, + 402, + 287, + 473 + ], + "type": "inline_equation", + "content": "T = 6" + }, + { + "bbox": [ + 46, + 402, + 287, + 473 + ], + "type": "text", + "content": " in Eq. 15, which indicates each training episode contains 6 consecutive frames. In addition, we inject the noise map " + }, + { + "bbox": [ + 46, + 402, + 287, + 473 + ], + "type": "inline_equation", + "content": "n_t" + }, + { + "bbox": [ + 46, + 402, + 287, + 473 + ], + "type": "text", + "content": " at the resolution of " + }, + { + "bbox": [ + 46, + 402, + 287, + 473 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 46, + 402, + 287, + 473 + ], + "type": "text", + "content": " to the generator." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 474, + 288, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 288, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 288, + 666 + ], + "type": "text", + "content": "The recurrent encoder consists of 7 convolutional (Conv) layers, a ConvLSTM layer, and a fully connected (FC) layer. We take \"Fused Leaky ReLU\" as activation in-between Conv layers. The ConvLSTM layer is integrated between the Conv and FC layers. The visible net has a U-Net structure [22], it takes 5 Conv layers as encoder, and 5 Transposed convolutional layers as a decoder. BatchNorm layer and leakyReLU activation are integrated into between layers. Besides, a Sigmoid function is applied on output U-Net for normalizing the visibility map values. Visible net takes the concatenation of two warped results with 6 channels as input and outputs a visibility map with 1 channel. It is trained using Adam optimizer [14] with the learning rate of " + }, + { + "bbox": [ + 46, + 474, + 288, + 666 + ], + "type": "inline_equation", + "content": "1e^{-4}" + }, + { + "bbox": [ + 46, + 474, + 288, + 666 + ], + "type": "text", + "content": " with 100,000 iterations. Besides, we use pre-trained FlowNet2 [7] for predicting optical flow, and we implement warping operation using bi-linear interpolation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 671, + 174, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 174, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 174, + 685 + ], + "type": "text", + "content": "4.2. Experimental Settings" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 689, + 288, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 712 + ], + "type": "text", + "content": "Datasets. We collect datasets both under control and in the wild environment. We select 72 videos from the con" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 402, + 547, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 547, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 547, + 498 + ], + "type": "text", + "content": "trolled RAVDESS dataset [17], which we called RAVDESS-72 Dataset. It contains 9,045 frames and each video contains about 120 frames. We also collect 36 videos from the Internet with the various poses, expressions, and backgrounds. We name them as In-the-Wild-36 Dataset, it contains 7,532 frames in total. We combine two datasets together, use 85 videos for training our RIGID and the rest 23 videos for testing." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "text", + "content": "Competitors and Evaluation Metrics. We compare RIGID with three works, including IGCI [39], Latent-Transformer [42], STIT [30], and TCSVE [37]. Note that STIT [30] and TCSVE [37] use the same method for inversion. We use several metrics for evaluating different methods. For the video inversion task, we use the pixel-wise Mean Square Error (MSE) and Learned Perceptual Image Patch Similarity (LPIPS) [46] that evaluates the reconstruction quality. For evaluating the temporal stability, we use the flow-based Warp Error (WE) metric. For the edited task, we follow STIT [30] that use Temporally-Local (TL-ID) and Temporally-Global (TG-ID) identity preservation metrics for evaluating the temporal coherence of edited videos. We also use Fréchet Video Distance (FVD) [31] metric on both edited and inverted videos. Inference Times (IT) over 100 frames is also reported. Please refer to supplementary for more details of competitors and evaluation metrics." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "type": "text", + "content": "13696" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 65, + 96, + 531, + 174 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 545, + 94 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 545, + 94 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 545, + 94 + ], + "type": "text", + "content": "Table 1: Video inversion comparisons on two datasets. " + }, + { + "bbox": [ + 46, + 70, + 545, + 94 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 70, + 545, + 94 + ], + "type": "text", + "content": " denotes the lower the better and the best results are marked in bold, and the values of MSE are magnified 100 times." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 65, + 96, + 531, + 174 + ], + "lines": [ + { + "bbox": [ + 65, + 96, + 531, + 174 + ], + "spans": [ + { + "bbox": [ + 65, + 96, + 531, + 174 + ], + "type": "table", + "html": "
Metrics MethodsRAVDESS-72 DatasetIn-the-Wild-36 DatasetIT↓(s)
MSE↓LPIPS↓WE↓FVD↓MSE↓(×e-2)LPIPS↓WE↓FVD↓
IGCI [39]0.990.05154.21412.332.010.13432.98276.921.2×e5
Latent-T. [42]5.680.1286.356220.465.310.22367.32165.3549.2
STIT [30]/TCSVE [37]0.990.0583.21171.232.320.11293.8381.03851.5
RIGID1.040.0584.62174.552.310.12287.3274.1154.5
", + "image_path": "68928e6f53866b6c627f3011944b987d0c1f32b143e13f19c27a39e172892b72.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 55, + 186, + 213, + 508 + ], + "blocks": [ + { + "bbox": [ + 55, + 186, + 213, + 508 + ], + "lines": [ + { + "bbox": [ + 55, + 186, + 213, + 508 + ], + "spans": [ + { + "bbox": [ + 55, + 186, + 213, + 508 + ], + "type": "image", + "image_path": "7cc575105a515aa5a46af2f0c3bfe8217ea380e67c714693928e3250ab5b8e2d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 117, + 510, + 152, + 520 + ], + "lines": [ + { + "bbox": [ + 117, + 510, + 152, + 520 + ], + "spans": [ + { + "bbox": [ + 117, + 510, + 152, + 520 + ], + "type": "text", + "content": "+Chubby" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 523, + 546, + 560 + ], + "lines": [ + { + "bbox": [ + 46, + 523, + 546, + 560 + ], + "spans": [ + { + "bbox": [ + 46, + 523, + 546, + 560 + ], + "type": "text", + "content": "Figure 5: Qualitative comparison on video editing. RIGID uses the same post processing as IGCI and Latent-Transformer, but the edited faces can be better blended with the original background. Besides, compared with STIT and TCSVE, our RIGID supports shape editing on the face boundary (e.g., \"Chubby\")." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 213, + 188, + 371, + 507 + ], + "blocks": [ + { + "bbox": [ + 213, + 188, + 371, + 507 + ], + "lines": [ + { + "bbox": [ + 213, + 188, + 371, + 507 + ], + "spans": [ + { + "bbox": [ + 213, + 188, + 371, + 507 + ], + "type": "image", + "image_path": "2162523261d195162bea22842e024e17c26528ae85eadd93fb24464bac87d4f2.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 265, + 510, + 319, + 519 + ], + "lines": [ + { + "bbox": [ + 265, + 510, + 319, + 519 + ], + "spans": [ + { + "bbox": [ + 265, + 510, + 319, + 519 + ], + "type": "text", + "content": "+EyeGlasses" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 372, + 188, + 527, + 507 + ], + "blocks": [ + { + "bbox": [ + 372, + 188, + 527, + 507 + ], + "lines": [ + { + "bbox": [ + 372, + 188, + 527, + 507 + ], + "spans": [ + { + "bbox": [ + 372, + 188, + 527, + 507 + ], + "type": "image", + "image_path": "0b8623991dd8183079a9d7ce8665b8e3488218f980fe043ead7b3af89add0c6f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 422, + 510, + 476, + 519 + ], + "lines": [ + { + "bbox": [ + 422, + 510, + 476, + 519 + ], + "spans": [ + { + "bbox": [ + 422, + 510, + 476, + 519 + ], + "type": "text", + "content": "+NarrowEyes" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 528, + 200, + 538, + 498 + ], + "lines": [ + { + "bbox": [ + 528, + 200, + 538, + 498 + ], + "spans": [ + { + "bbox": [ + 528, + 200, + 538, + 498 + ], + "type": "text", + "content": "Original IGCI Latent-T. STIT TCSVE RIGID" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 579, + 211, + 591 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 579, + 211, + 591 + ], + "spans": [ + { + "bbox": [ + 47, + 579, + 211, + 591 + ], + "type": "text", + "content": "4.3. Evaluation on Video Inversion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "text", + "content": "Quantitative Evaluation. We first evaluate the fidelity and temporal coherence of inverted videos. Quantitative comparison can be seen in Tab. 1. We can see that both STIT, IGCI, and TCSVE have lower MSE and LPIPIS values, they optimize latent codes or generator specifically according to the video frames, which can reconstruct the target frames faithfully. IGCI presents the worse performance on WE and FVD metrics, since it optimizes the latent code for each image but fails to consider the temporal coherence of consec-" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 580, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 547, + 712 + ], + "type": "text", + "content": "utive frames, making the inverted latent codes less consistent. In addition, optimization-based methods cost a lot of time during the inference, especially for IGCI, which takes about 20 minutes for a single frame. Latent-Transformer uses a learning-based encoder that accelerates the inference speed, but it processes each frame individually, both the temporal coherence and reconstruction quality cannot be guaranteed. With about " + }, + { + "bbox": [ + 304, + 580, + 547, + 712 + ], + "type": "inline_equation", + "content": "15 \\times" + }, + { + "bbox": [ + 304, + 580, + 547, + 712 + ], + "type": "text", + "content": " faster inference than STIT, RIGID achieves a comparable result on the RAVDESS-72 and In-the-Wild-36 datasets. RIGID not only inverts the frame faithfully but also preserves the original temporal relations across frames." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "13697" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 96, + 526, + 185 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": "Table 2: Video editing comparisons on two datasets. " + }, + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": " denotes the lower the better and vice versa, the best results are marked in bold." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 67, + 96, + 526, + 185 + ], + "lines": [ + { + "bbox": [ + 67, + 96, + 526, + 185 + ], + "spans": [ + { + "bbox": [ + 67, + 96, + 526, + 185 + ], + "type": "table", + "html": "
Metrics MethodsRAVDESS-72In-the-Wild-36IT↓(s)
TL-ID↑TG-ID↑FVD↓TL-ID↑TG-ID↑FVD↓
IGCI [39]0.940.79834.330.930.71499.221.2×e5
Latent-T. [42]0.990.93311.840.990.87267.4249.2
STIT [30]0.990.97212.040.990.91211.341.6×e3
TCSVE [37]0.990.97201.320.990.92198.463.4×e3
RIGID0.990.97198.540.990.93183.3654.5
", + "image_path": "25ea9445359bdb5d80c212de9b933cf46c8f67eeb379d34ed3a38be7f384c762.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 200, + 288, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 200, + 288, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 200, + 288, + 224 + ], + "type": "text", + "content": "Thanks to temporal compensated inversion, RIGID guarantees the fidelity of inverted faces." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 225, + 290, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 225, + 290, + 440 + ], + "spans": [ + { + "bbox": [ + 46, + 225, + 290, + 440 + ], + "type": "text", + "content": "Qualitative Evaluation. The quantitative comparison of video inversion can be seen in Fig. 4. We can see that two optimization-based works, IGCI and STIT reconstruct the frames well. Latent-Transformer utilizes the pSp encoder for inversion [21], and the results present different skin colors with original frames. Thanks to the temporal compensation inversion, our learning-based RIGID presents the competitive results with optimization-based IGCI and STIT on pixelwise reconstruction. The video comparison can be seen in Fig. 1. Latent-Transformer cannot provide accurate reconstruction. IGCI inverts each frame faithfully, but it cannot guarantee the temporal coherence across frames, resulting in serious temporal flickering. STIT achieves high-quality inversion on a specific video at the cost of long computational times. In contrast, RIGID builds temporal relations of inverted videos by the temporal compensated inversion, yielding temporal coherent inverted videos with much less time cost." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 453, + 203, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 203, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 203, + 466 + ], + "type": "text", + "content": "4.4. Evaluation on Video Editing" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 472, + 288, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 472, + 288, + 686 + ], + "spans": [ + { + "bbox": [ + 45, + 472, + 288, + 686 + ], + "type": "text", + "content": "Quantitative Evaluation. The quantitative comparison of video editing can be seen in Tab. 2. We can see that IGCI [39] has high FVD values on both two datasets. As discussed above, it cannot produce consistent latent codes, making the edited frames discontinuous. In addition, IGCI has lower values on both TL-ID and TG-ID, which evidences that identity information cannot be preserved locally and globally. Compared with IGCI, Latent-Transformer [42] uses an encoder for producing latent codes, and the edited frames are more consistent. STIT [30] optimizes the generator for each video hence requires many inference times. RIGID achieves a comparable result on the RAVDESS-72 dataset with " + }, + { + "bbox": [ + 45, + 472, + 288, + 686 + ], + "type": "inline_equation", + "content": "30 \\times" + }, + { + "bbox": [ + 45, + 472, + 288, + 686 + ], + "type": "text", + "content": " faster during the inference. As for the In-the-Wild-36 Dataset, RIGID outperforms all competitors with three metrics. This should contribute to our in-between frame composition constraint. It enforces the smoothness of edited frames and brings temporal coherence into edited videos." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 689, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 289, + 714 + ], + "type": "text", + "content": "Qualitative Evaluation. We present the qualitative comparison on video editing in Fig. 1 and Fig. 5. We can see that" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 200, + 547, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 200, + 547, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 200, + 547, + 403 + ], + "type": "text", + "content": "ICGI presents blurry edited faces with temporal flickering, and Latent-Transformer loses temporal coherence on local details (see bangs in Fig. 1c). In addition, though they use the same post processing as our RIGID, their edited faces cannot be well blended with the original background. Without considering the temporal coherence of edited frames, their edited faces have large structure deformations from the original faces. STIT proposes a \"stitching tuning\" strategy for the seamless blending, it enforces the edit frames have similar transitions around the face boundary with originals. However, when the target face's boundary is close to the background, this method does not support its shape-related editing (e.g., \"Chubby\" or \"Double Chins\"). As shown in the " + }, + { + "bbox": [ + 304, + 200, + 547, + 403 + ], + "type": "inline_equation", + "content": "1_{st}" + }, + { + "bbox": [ + 304, + 200, + 547, + 403 + ], + "type": "text", + "content": " sample in Fig. 5, STIT fails on the \"Chubby\" editing. TCSVE uses the same strategy, hence it fails on this editing. More video comparisons can be found in the supplementary materials." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 416, + 400, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 416, + 400, + 430 + ], + "spans": [ + { + "bbox": [ + 305, + 416, + 400, + 430 + ], + "type": "text", + "content": "4.5. Ablation Study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "text", + "content": "In this section, we perform an ablation study to evaluate our RIGID on the RAVDESS-72 dataset. We develop five variants with the modification of the modules and the loss functions: 1) " + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "inline_equation", + "content": "w / o" + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "text", + "content": " TCC, by removing temporal compensated code " + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "inline_equation", + "content": "w_{t}^{\\prime}" + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "text", + "content": ". 2) " + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "inline_equation", + "content": "w / o" + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "text", + "content": " NM, by removing noise map " + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "inline_equation", + "content": "n_t" + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "text", + "content": ". 3) " + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "inline_equation", + "content": "w / o" + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "text", + "content": " LFD, by removing the latent frequency disentanglement in the framework. In this variant, frames in the same video have different latter codes " + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "inline_equation", + "content": "w_{t}^{l}" + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "text", + "content": ". 4) " + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "inline_equation", + "content": "w / o" + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "inline_equation", + "content": "L_{ibfcc}" + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "text", + "content": ", by removing in-between frame composition constraint. 5) " + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "inline_equation", + "content": "w / o" + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{tc}" + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "text", + "content": ", by removing the temporal consistent loss " + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{tc}" + }, + { + "bbox": [ + 304, + 436, + 547, + 556 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": "The quantitative comparisons with various variants can be seen in Tab. 3. Compared with RIGID, variant " + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "inline_equation", + "content": "w / o" + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": " TCC has a large WE value. Code " + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "inline_equation", + "content": "w_{t}^{\\prime}" + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": " introduces the temporal compensation to the image-based latent code, and brings the temporal coherence in inverted videos. Variant " + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "inline_equation", + "content": "w / o" + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": " NM has large MSE and LPIPS values. Since noise map " + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "inline_equation", + "content": "n_t" + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": " injects the spatial information to the generator, and improves the inversion accuracy. Both variant " + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "inline_equation", + "content": "w / o" + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": " LFD and " + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "inline_equation", + "content": "w / o" + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{tc}" + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": " have large WE numbers. Our latent frequency disentangle-ment strategy unifies the high-frequency information in a video, and " + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{tc}" + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": " preserves the temporal consistency from the original to the inverted video. They learn the temporal relations effectively. We observe that variant " + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "inline_equation", + "content": "w / o" + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ibfcc}" + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": " has" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "text", + "content": "13698" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 74, + 97, + 520, + 198 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "type": "text", + "content": "Table 3: Quantitative comparisons with various variants on video inversion and editing. " + }, + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 70, + 547, + 95 + ], + "type": "text", + "content": " denotes the lower the better and vice visa, the best results are marked in bold. The values of MSE are magnified 100 times." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 74, + 97, + 520, + 198 + ], + "lines": [ + { + "bbox": [ + 74, + 97, + 520, + 198 + ], + "spans": [ + { + "bbox": [ + 74, + 97, + 520, + 198 + ], + "type": "table", + "html": "
Metrics\nVariantsVideo InversionVideo Editing
MSE↓LPIPS↓WE↓FVD↓TL-ID↑TG-ID↑FVD↓
w/o TCC1.310.07106.52208.740.980.94321.98
w/o NM2.280.0896.52201.220.990.92334.98
w/o LFD1.100.06103.61215.960.990.94309.04
w/o Lfccc0.930.05705.22358.040.980.90299.12
w/o Ltc1.080.05122.08203.540.990.97299.34
RIGID1.040.0584.62174.550.990.97198.54
", + "image_path": "228b49c9ef960fb1d58e130bcbf8690329bf4c4b95ef4493cb7dc02c46504f74.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 50, + 222, + 287, + 348 + ], + "blocks": [ + { + "bbox": [ + 50, + 222, + 287, + 348 + ], + "lines": [ + { + "bbox": [ + 50, + 222, + 287, + 348 + ], + "spans": [ + { + "bbox": [ + 50, + 222, + 287, + 348 + ], + "type": "image", + "image_path": "57ba392c6dcf27f9e26958b02ac786ebd644d29af1aa7d54b79e122349184819.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 356, + 290, + 405 + ], + "lines": [ + { + "bbox": [ + 46, + 356, + 290, + 405 + ], + "spans": [ + { + "bbox": [ + 46, + 356, + 290, + 405 + ], + "type": "text", + "content": "Figure 6: Qualitative comparison with different variants. Variant " + }, + { + "bbox": [ + 46, + 356, + 290, + 405 + ], + "type": "inline_equation", + "content": "w / o" + }, + { + "bbox": [ + 46, + 356, + 290, + 405 + ], + "type": "text", + "content": " LFD and " + }, + { + "bbox": [ + 46, + 356, + 290, + 405 + ], + "type": "inline_equation", + "content": "w / o \\mathcal{L}_{ibfcc}" + }, + { + "bbox": [ + 46, + 356, + 290, + 405 + ], + "type": "text", + "content": " present noticeable temporal flickering. Please refer to the arXiv version to watch this figure as a video clip." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 413, + 288, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 288, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 288, + 533 + ], + "type": "text", + "content": "the largest WE and FVD values on inverted videos, though it is applied to the edited frames. That is because the constraint enforces the smoothness of edited frames, and can be propagated to the latent codes that control the coherence of inverted frames. Meanwhile, variant " + }, + { + "bbox": [ + 46, + 413, + 288, + 533 + ], + "type": "inline_equation", + "content": "w / o \\mathcal{L}_{ibfcc}" + }, + { + "bbox": [ + 46, + 413, + 288, + 533 + ], + "type": "text", + "content": " has the worse performance on metrics TL-ID and TG-ID. Without the in-between constraint, the framework cannot guarantee the identity similarity across frames. By learning the temporal correlations in inverted and edited videos, the final RIGID achieves the best performance on two tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 534, + 288, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 288, + 656 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 288, + 656 + ], + "type": "text", + "content": "Qualitative comparison with different variants can be seen in Fig. 6. We can see variant " + }, + { + "bbox": [ + 46, + 534, + 288, + 656 + ], + "type": "inline_equation", + "content": "w / o \\mathcal{L}_{ibfcc}" + }, + { + "bbox": [ + 46, + 534, + 288, + 656 + ], + "type": "text", + "content": " presents annoying flickering both on the inverted and edited videos, which evidences the effectiveness of in-between frame composition constraint. As talked about in the main paper, it builds the temporal relations of video frames, which guarantees the smoothness of generated videos. Variant " + }, + { + "bbox": [ + 46, + 534, + 288, + 656 + ], + "type": "inline_equation", + "content": "w / o" + }, + { + "bbox": [ + 46, + 534, + 288, + 656 + ], + "type": "text", + "content": " NM cannot invert the video faithfully. Variant " + }, + { + "bbox": [ + 46, + 534, + 288, + 656 + ], + "type": "inline_equation", + "content": "w / o" + }, + { + "bbox": [ + 46, + 534, + 288, + 656 + ], + "type": "text", + "content": " LFD may present temporal flickering. The final RIGID presents temporal coherent inversion and editing videos." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 668, + 204, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 668, + 204, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 668, + 204, + 681 + ], + "type": "text", + "content": "5. Conclusion and Discussions" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 289, + 715 + ], + "type": "text", + "content": "In this paper, we propose RIGID, a novel recurrent framework that learns the temporal correlations between succes" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 212, + 547, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 212, + 547, + 380 + ], + "spans": [ + { + "bbox": [ + 304, + 212, + 547, + 380 + ], + "type": "text", + "content": "sive frames for both inversion and editing. RIGID first learn the temporal correlation of inverted videos by a temporal-compensated reconstruction. It takes previous and current faces as input, and produces a temporal compensated code with a spatial noise map. They, together with the image-based latent code, are fed to the StyleGAN generator to reconstruct the video frames. Meanwhile, RIGID disentangles high-frequency artifacts in the latent space for eliminating the temporal flickering. Furthermore, for learning the temporal correlation of edited video, we enforce an edited frame can be composed by the flow-based warping of its neighbor frames. RIGID achieves attribute-agnostic editing with much less time cost. Extensive experiments demonstrate the superiority of RIGID." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 387, + 547, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 387, + 547, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 547, + 483 + ], + "type": "text", + "content": "Limitations. As cropping and alignment of faces are needed before the inversion, those hair portions outside the cropped region cannot be edited by our method, which leads to unnatural conflicts after blending. It may be addressed by using StyleGAN3 [10] since it can generate unaligned faces. However, as indicated in [3], StyleGAN3 has a worse edit ability than StyleGAN2, which is essential in GAN inversion." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 491, + 548, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 548, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 548, + 611 + ], + "type": "text", + "content": "Broader Impact. RIGID can potentially be used for academic research and commercial applications. It provides a pipeline for video-based GAN inversion, and benefits the design of temporal coherent video GANs. Besides, RIGID can create more facial videos in the media industry. On the other hand, although not the purpose of this work, it can potentially be misused for the violation of portrait rights and privacy. The risk can be mitigated by face forgery detection methods, i.e., we can detect the blending boundary using [15]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 618, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 548, + 715 + ], + "type": "text", + "content": "Acknowledgement. This paper is partially supported by the National Key R&D Program of China No.2022ZD0161000; the General Research Fund of Hong Kong No.17200622; National Natural Science Foundation of China (No. 61972162); Guangdong Natural Science Funds for Distinguished Young Scholars (No. 2023B1515020097); and Singapore Ministry of Education Academic Research Fund Tier 1 (MSS23C002)." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "text", + "content": "13699" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 288, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 288, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 288, + 124 + ], + "type": "text", + "content": "[1] Rameen Abdal, Yipeng Qin, and Peter Wonka. 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IEEE TIP, 31:1230-1242, 2022. 1" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "13701" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/RLIPv2_ Fast Scaling of Relational Language-Image Pre-Training/dedbf300-120b-4912-a26e-f96e152258fe_content_list.json b/2023/RLIPv2_ Fast Scaling of Relational Language-Image Pre-Training/dedbf300-120b-4912-a26e-f96e152258fe_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..915e47a34644d3b2b65711a4aaf90be04869c0fe --- /dev/null +++ b/2023/RLIPv2_ Fast Scaling of Relational Language-Image Pre-Training/dedbf300-120b-4912-a26e-f96e152258fe_content_list.json @@ -0,0 +1,1813 @@ +[ + { + "type": "text", + "text": "RLIPv2: Fast Scaling of Relational Language-Image Pre-training", + "text_level": 1, + "bbox": [ + 153, + 130, + 818, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hangjie Yuan $^{1*}$ Shiwei Zhang $^{2}$ Xiang Wang $^{3*}$ Samuel Albanie $^{4}$ Yining Pan $^{5*}$ Tao Feng $^{2}$ Jianwen Jiang $^{2}$ Dong Ni $^{1\\dagger}$ Yingya Zhang $^{2}$ Deli Zhao $^{2}$", + "bbox": [ + 151, + 178, + 813, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Zhejiang University $^{2}$ Alibaba Group $^{3}$ Huazhong University of Science and Technology $^{4}$ CAML Lab, University of Cambridge $^{5}$ Singapore University of Technology and Design", + "bbox": [ + 202, + 220, + 779, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{hj.yuan, dni}@zju.edu.cn wxiang@hust.edu.cn {pyn.sigrid, fengtao.hi, zhaodeli}@gmail.com \nsma71@cam.ac.uk {zhangjin.zsw, jianwen.jjw, yingya.zyy}@alibaba-inc.com", + "bbox": [ + 86, + 253, + 890, + 286 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 316, + 313, + 333 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Relational Language-Image Pre-training (RLIP) aims to align vision representations with relational texts, thereby advancing the capability of relational reasoning in computer vision tasks. However, hindered by the slow convergence of RLIPv1 architecture and the limited availability of existing scene graph data, scaling RLIPv1 is challenging. In this paper, we propose RLIPv2, a fast converging model that enables the scaling of relational pre-training to large-scale pseudo-labelled scene graph data. To enable fast scaling, RLIPv2 introduces Asymmetric Language-Image Fusion (ALIF), a mechanism that facilitates earlier and deeper gated cross-modal fusion with sparsified language encoding layers. ALIF leads to comparable or better performance than RLIPv1 in a fraction of the time for pre-training and fine-tuning. To obtain scene graph data at scale, we extend object detection datasets with free-form relation labels by introducing a captioner (e.g., BLIP) and a designed Relation Tagger. The Relation Tagger assigns BLIP-generated relation texts to region pairs, thus enabling larger-scale relational pre-training. Through extensive experiments conducted on Human-Object Interaction Detection and Scene Graph Generation, RLIPv2 shows state-of-the-art performance on three benchmarks under fully-finetuning, few-shot and zero-shot settings. Notably, the largest RLIPv2 achieves 23.29mAP on HICO-DET without any fine-tuning, yields 32.22mAP with just $1\\%$ data and yields 45.09mAP with $100\\%$ data. Code and models are publicly available at https://github.com/JacobYuan7/RLIPv2.", + "bbox": [ + 75, + 348, + 473, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 787, + 209, + 803 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The pretraining-finetuning paradigm has achieved major breakthroughs in vision and language domains [58, 13,", + "bbox": [ + 75, + 813, + 468, + 844 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7560613fa90b2d6d31e9a47fa3f982bb4c342884fe937d906b1704e9b4a5445c.jpg", + "image_caption": [ + "Figure 1: Left: Fine-tuning comparison on HICO-DET. Right: Pre-training epoch and zero-shot (NF) comparison on HICO-DET. Except where stated, RLIPv2-ParSeDA architecture is adopted." + ], + "image_footnote": [], + "bbox": [ + 506, + 316, + 733, + 426 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bd75ed80e18b9ed3dd7e4fe9d1fb69a3213f2f65243d54e895fbdb4584423403.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 738, + 316, + 880, + 426 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "23, 103, 65, 77]. In this context, a number of particularly notable results have been obtained through aligned Vision-Language Pre-training (VLP) [65, 42, 41, 78, 95, 91]. These research efforts have typically employed a robust base model [14, 25, 12, 74] that is trained on language-image paired data to produce foundation models.", + "bbox": [ + 496, + 500, + 890, + 590 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "RLIPv1 [86] presents the first attempt to specifically align vision representations and relational texts using VLP. By pre-training on open-vocabulary scene graph data like Visual Genome (VG) [38], RLIPv1 demonstrates its usefulness in zero-shot, few-shot and fully-finetuned Human-Object Interaction (HOI) Detection. Although RLIPv1 is proven effective, we find it challenging to scale for the following reasons:", + "bbox": [ + 496, + 592, + 892, + 712 + ], + "page_idx": 0 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(i) Model perspective: RLIPv1 converges slowly, as exemplified by DETR [3]-based RLIPv1, which requires 150/90 epochs to converge during pre-training/fine-tuning. Even when building on Deformable DETR (DDETR) [102] and DAB-DDETR [56], 50/60 epochs are still required.", + "(ii) Data perspective: as observed by the authors of RLIPv1, data with relation triplet annotations is scarce, impeding RLIPv1's scaling. Annotating triplets in the form of $\\langle$ subject, relations, object $\\rangle$ is both time- and cost-intensive." + ], + "bbox": [ + 496, + 715, + 890, + 853 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To resolve the aforementioned challenges, we introduce RLIPv2, a fast converging model that enables relational pretraining on larger-scale pseudo-labelled scene graph data.", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work conducted during their research internships at DAMO Academy.", + "bbox": [ + 93, + 849, + 467, + 863 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 96, + 863, + 222, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{1}$ RLIPv1 refers to the model presented in [86], and RLIPv2 refers to the model presented in this paper.", + "bbox": [ + 78, + 875, + 468, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21649", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "From both the model and data perspectives, we summarize the contributions of RLIPv2 as follows.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "From the model perspective, we observe that the slow convergence of DDETR can be attributed to the late language-image fusion strategy: fusion after decoding. Prior works [15, 44] have demonstrated an earlier and deeper fusion mechanism facilitates cross-modal alignment. In light of this, we propose Asymmetric Language-Image Fusion (ALIF) in RLIPv2 that encourages fusion in the encoding stage with sparsified language layers. Without sacrificing inference speed thanks to sparsification, RLIPv2 requires only 20 epochs to pre-train and fine-tune based on DDETR family models [102, 56] as shown in Fig. 1, while performing better than or comparably to RLIPv1.", + "bbox": [ + 75, + 121, + 468, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "From the data perspective, we leverage well-established object detection datasets [53, 69, 39]. Specifically, we extend these datasets with relational annotations by pseudolabelling. To perform pseudo-labelling, we must tackle two challenges: (i) sorting out the relations contained in the image and (ii) tagging relation texts to region pairs. Regarding the first challenge, we employ external captioners (e.g. BLIP [42]) that generate captions containing relation descriptions. Regarding the second challenge, we reuse RLIPv2 model as a Relation Tagger (R-Tagger) that enables assigning the generated open-vocabulary relation texts to region pairs. Equipped with such a pipeline, we investigate the scaling behavior of both the model and the data for RLIPv2, which demonstrates improved zero-shot, few-shot and fine-tuning performance.", + "bbox": [ + 75, + 301, + 470, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Furthermore, we introduce Scene Graph Generation (SGG), an analogously defined task to HOI detection for evaluating RLIPv2. RLIPv2 achieves state-of-the-art performance on Open Images v6 [39] for SGG, which underscores its robustness and efficacy in tackling relational reasoning tasks.", + "bbox": [ + 75, + 529, + 468, + 619 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 633, + 218, + 648 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Language-image pre-training for detection. Recently, there has been a growing interest in learning visual representations from language supervision [42, 41, 65, 1, 32, 34, 15, 44, 95, 76]. This paradigm of learning from language supervision has also proven effective in improving detection performance. MDETR [34] was the first work to learn region-text correspondences in an end-to-end manner, while X-DETR [2] improved upon MDETR by removing the cross-modal fusion part that improves its training efficiency. GLIP [44] extended this line of research by scaling to web-scale data, leading to significant advances in zero-shot object detection and data efficiency. DetCLIP [84] proposed a paralleled concept formulation and a concept dictionary to enable semantically rich region-text alignment. RLIPv1 [86] was the first work to seek language-image alignment via relations, and our work follows its footsteps", + "bbox": [ + 75, + 659, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "to achieve fast scaling of relational pre-training.", + "bbox": [ + 498, + 90, + 815, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "End-to-end HOI detection and scene graph generation. Relations can interpret visual content in a fine-grained perspective [10, 31, 33]. Detecting and recognizing relations utilizing HOI detection and scene graph generation have been verified effective in image captioning [85], image retrieval [33, 75], synthesis [83, 18], activity understanding [31, 88, 87] and . The aim of these tasks is to detect relation triplets from a given input image. Before the emergence of DETR [3], the commonly adopted pipeline was to adopt an off-the-shelf object detector [66, 24] and design reasoning modules to infer relations [20, 19, 63, 49, 48, 90, 7, 54, 46, 47, 81]. Initial end-to-end design efforts extended detectors to support relation recognition [50, 99, 82, 35, 55]. Further attempts focus on the adaptation of DETR to the field of HOI detection [89, 6, 36, 104, 71, 93, 94, 79, 37, 57, 101, 62, 64, 97] and SGG [45, 11]. RLIPv1 [86] demonstrated the effectiveness of relational pre-training in improving performance and data efficiency. RLIPv2 builds upon RLIPv1, but seeks to solve its scaling problem. The most related work [100] also seeks scaling with the help of language. However, it remains a two-stage detection pipeline, lacks semantic richness and adopts a naive matching algorithm that hinders its performance.", + "bbox": [ + 496, + 107, + 890, + 468 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Recap of RLIPv1", + "text_level": 1, + "bbox": [ + 500, + 483, + 668, + 500 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we will briefly review RLIPv1 [86], a model that leverages both entity and relation descriptions to perform VLP and that forms the basis for our approach. As triplet detection architecture, RLIPv1 proposes a ParSeD model that allocates decoupled embeddings for subjects, objects and relations. The collective model RLIPv1-ParSeD consists of three stages: Parallel Entity Detection, Sequential Relation Inference and Cross-Modal Fusion, as shown in Fig. 2(a).", + "bbox": [ + 496, + 508, + 890, + 645 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For Parallel Entity Detection, RLIPv1-ParSeD defines two sets of queries $Q_{s}, Q_{o} \\in \\mathbb{R}^{N_{Q} \\times D}$ with $N_{Q}$ pairs of subjects and objects to perform subject and object detection. For Sequential Relation Inference, the model generates relation queries $Q_{r} \\in \\mathbb{R}^{N_{Q} \\times D}$ based on the decoded subject and object queries $\\tilde{Q}_{s}, \\tilde{Q}_{o} \\in \\mathbb{R}^{N_{Q} \\times D}$ , and performs decoding to obtain $\\tilde{Q}_{r} \\in \\mathbb{R}^{N_{Q} \\times D}$ for relation recognition. The design of RLIPv1-ParSeD obeys the following probabilistic factorization:", + "bbox": [ + 496, + 645, + 890, + 781 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbb {P} \\left(\\boldsymbol {G} \\mid \\boldsymbol {Q} _ {s}, \\boldsymbol {Q} _ {o}, \\boldsymbol {C} _ {E}; \\boldsymbol {\\theta} _ {P a r}, \\boldsymbol {\\theta} _ {S e}\\right) = \\tag {1} \\\\ \\mathbb {P} \\left(\\boldsymbol {B} _ {s}, \\boldsymbol {B} _ {o} \\mid \\boldsymbol {Q} _ {s}, \\boldsymbol {Q} _ {o}, \\boldsymbol {C} _ {E}; \\boldsymbol {\\theta} _ {P a r}\\right) \\cdot \\mathbb {P} \\left(\\boldsymbol {R} \\mid \\boldsymbol {B} _ {s}, \\boldsymbol {B} _ {o}, \\boldsymbol {C} _ {E}; \\boldsymbol {\\theta} _ {S e}\\right) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 789, + 890, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $C_E$ denotes features from the DDETR encoder; $\\theta_{Par},\\theta_{Se}$ denote parameters for Parallel Entity Detection", + "bbox": [ + 498, + 833, + 890, + 864 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "2Since RLIPv2 targets fast scaling, we only focus on DDETR-based detection architecture.", + "bbox": [ + 500, + 875, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21650", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/809772b0dbebb81a18fa65cc11dde1fb8e0f984dfa613a154803b94d7c597e00.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 444, + 261 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b78474a5ee4a6c050624c514035213567af73368922067822a98756661849224.jpg", + "image_caption": [ + "(b)", + "Figure 2: The overview of (a) RLIPv1-ParSeD and (b) RLIPv2-ParSeD and R-Tagger. The red part (loss calculation and noise injection) is only valid during training. In (a), Cross-Modal Fusion is achieved by the cross encoder. In (b), Cross-Modal Fusion is achieved by ALIF. The two architectures have an equivalent number of DDETR layers." + ], + "image_footnote": [], + "bbox": [ + 450, + 89, + 890, + 268 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and Sequential Relation Inference; $B_{s}, B_{o}, R$ are sets of detected subject boxes, object boxes and relations, respectively. They collectively comprise the detection results $G$ .", + "bbox": [ + 75, + 362, + 468, + 407 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For Cross-Modal Fusion, RLIPv1-ParSeD appends additional Transformer encoding layers [74, 34, 43] to perform language-image feature fusion on top of the decoded relation features $\\tilde{Q}_r$ , entity label features $L_{E} \\in \\mathbb{R}^{N_{E} \\times D}$ and relation label features $L_{R} \\in \\mathbb{R}^{N_{R} \\times D}$ . $L_{E}, L_{R}$ are extracted from RoBERTa [58].", + "bbox": [ + 75, + 407, + 468, + 498 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Methodology", + "text_level": 1, + "bbox": [ + 76, + 511, + 210, + 527 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we will introduce: (i) Asymmetric Language-Image Fusion (ALIF) as an efficient CrossModal Fusion mechanism in RLIPv2, as shown in Fig. 2(b); (ii) the overall framework of extending the off-the-shelf object detection datasets [53, 69] to support relational pretraining.", + "bbox": [ + 75, + 536, + 468, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Asymmetric Language-Image Fusion", + "text_level": 1, + "bbox": [ + 76, + 635, + 398, + 652 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The core idea underpinning ALIF is to perform efficient cross-modal fusion in the early stages of RLIPv2 as highlighted by [15, 44]. Unlike RLIPv1 that encourages cross-modal alignment for entities and relations after the decoding phase, ALIF performs this during the detection encoding phase. This is particularly challenging for DDETR's encoder, since it relies on deformable attention that makes it challenging to adopt dedicated encoder layers during the detection encoding phase like [34, 60, 16].", + "bbox": [ + 75, + 659, + 468, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To address this, we propose ALIF, a mechanism that leverages DDETR encoding for the vision branch, RoBERTa encoding for the language branch and gated cross-attention for fusion. In contrast to previous work that encodes image and language with an equivalent number of layers [34, 16, 44, 15], we experimentally find that excessive RoBERTa layers do not improve its generalization", + "bbox": [ + 75, + 795, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "capability due to its potential for overfitting to pre-trained data. Moreover, such a paradigm results in training difficulty due to the increased model complexity. As a result, we perform DDETR encoding densely while performing RoBERTa encoding sparsely. We denote the vision features from the backbone as $C^{(0)}$ and language features from RoBERTa as $L^{(0)}$ (the concatenation of $L_{E}$ and $L_{R}$ ). The first ALIF module can be formulated as:", + "bbox": [ + 496, + 362, + 890, + 482 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\boldsymbol {C}} ^ {(0)}, \\tilde {\\boldsymbol {L}} ^ {(0)} = \\operatorname {C r o s s - a t t n} \\left(\\boldsymbol {C} ^ {(0)}, \\boldsymbol {L} ^ {(0)}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 491, + 890, + 511 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {C} ^ {\\left(N _ {v}\\right)} = \\mathrm {D D E T R} ^ {N _ {v}} \\left(\\boldsymbol {C} ^ {(0)} + \\mathrm {G} \\left(\\tilde {\\boldsymbol {C}} ^ {(0)}\\right)\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 534, + 890, + 551 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {L} ^ {(1)} = \\operatorname {R o B E R T a} ^ {1} \\left(\\boldsymbol {L} ^ {(0)} + \\mathrm {G} \\left(\\tilde {\\boldsymbol {L}} ^ {(0)}\\right)\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 571, + 890, + 590 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\tilde{C}^{(0)}$ denotes language features aggregated by cross attention, and $\\tilde{L}^{(0)}$ is analogously defined; $N_{v}$ is the number of DDETR layers in one ALIF; $\\mathrm{G}(\\pmb{x})$ defines a gating function that gates the aggregated cross-modal features. Note that $C_E$ is $C^{(N_v)}$ after stacking $N_{ALIF}$ ALIF layers for encoding. For the instantiation of $\\mathrm{G}(\\pmb{x})$ , we experiment with three options: (i) $\\mathrm{G}(\\pmb{x}) = \\alpha \\pmb{x}$ where $\\alpha$ is a learnable scalar; (ii) $\\mathrm{G}(\\pmb{x}) = \\pmb{a}\\pmb{x}$ where $\\pmb{a}$ is a learnable vector; (iii) $\\mathrm{G}(\\pmb{x}) = \\mathrm{SE}(\\pmb{x})$ where SE denotes a Squeeze-and-Excitation block [30] with a reduction ratio of 4. We also experiment augmenting $\\mathrm{G}(\\pmb{x})$ with $\\tanh()$ introduced in [1] (e.g. $\\tanh(\\alpha\\pmb{x})$ ), while only observing side effects. This indicates the magnitude of language and vision features are disparate, and a proper gating method is desired.", + "bbox": [ + 496, + 595, + 890, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.2. Relational Pseudo-labelling", + "text_level": 1, + "bbox": [ + 500, + 816, + 746, + 833 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "RLIPv2 reuses object detection datasets to benefit pretraining by pseudo-labelling, as shown in Fig. 3. We assume that during the pre-training phase, the downstream entity and relation distributions are unavailable to us. Then, to tag", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21651", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5a79babf17dc25c766b90dff8b11df6a40499ac58d065545e589486b6e3a42f1.jpg", + "image_caption": [ + "Figure 3: An overview of relational pseudo-labeling, which tags object detection data with free-form relation texts. This process enables pre-training to be performed on two kinds of data." + ], + "image_footnote": [], + "bbox": [ + 86, + 88, + 455, + 188 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "relation texts, we need to sort out the relations contained in the image as detailed in Sec. 4.2.1, and to tag relation texts to region pairs as detailed in Sec. 4.2.2.", + "bbox": [ + 75, + 261, + 467, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2.1 Relation Candidate Set Generation", + "text_level": 1, + "bbox": [ + 76, + 321, + 375, + 335 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For a given image, relation candidate set generation aims to generate a coarse-grained set of candidate subject-object (SO) region pairs $\\pmb{P}$ and their candidate relation texts $\\pmb{T}$ . First, we adopt BLIP to generate $N_{Cap}$ captions for each image. Note that when $N_{Cap} = 1$ , we generate the caption via beam search, a deterministic generation method; when $N_{Cap} > 1$ , we generate captions via nucleus sampling [26], a stochastic generation methods with cumulative probability threshold set to 0.9. Nucleus sampling adds semantic diversity to the generated captions, which contributes to diversity in the relations.", + "bbox": [ + 75, + 345, + 467, + 511 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Second, we adopt a scene graph parser [68] to parse the obtained captions into relation triplets. To filter out invalid parsed triplets, we perform string matching and keep those whose subjects and objects can be matched with any entities' names or entities' synonyms within the image [86]. This operation encloses a small set of possible SO region pairs $P$ and possible relation texts $T$ for the pairs (which are inputs to R-Tagger), without needing to traverse all possible pairs.", + "bbox": [ + 75, + 513, + 467, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2.2 Relation Tagger via RLIPv2 Architecture", + "text_level": 1, + "bbox": [ + 76, + 664, + 418, + 679 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The R-Tagger aims to assign candidate relation texts $T$ to candidate SO region pairs $P$ for a given image. While one alternative is executing the pre-trained RLIPv2 model to perform SGG on object detection datasets to obtain pseudotriplets, the informative object annotations fail to be utilized directly during the execution of RLIPv2. As a result, the quality of pseudo-labels is degraded. A prior work [100] adopts a coarse rule-based pseudo-labelling method that employed a greedy matching algorithm to randomly assign one relation text to an SO region pair as long as the relation texts' corresponding SO texts match with the SO region pair. An \"overlap\" prior was applied to further filter the triplets (i.e., a triplet is deemed valid only if the subject and object are overlapped). This method, however,", + "bbox": [ + 75, + 688, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "introduces excessive false positives, causing degraded pretraining. Thus, we propose to reuse the RLIPv2 architecture to perform relation prediction given ground-truth SO region pairs as shown in Figure Fig. 2(b).", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As outlined in Sec. 3, RLIPv2 also utilizes subject queries $Q_{s}$ and object queries $Q_{o}$ as input. To allow for the utilization of object annotations as the input, we propose to replace the detection queries $Q_{s}$ and $Q_{o}$ with object embeddings [40], which aims to encourage Parallel Entity Detection to reconstruct object representations and Sequential Relation Inference to recognize relations. Compared with Eq. (1), the probabilistic factorisation of R-Tagger during inference can be reformulated as:", + "bbox": [ + 496, + 151, + 890, + 286 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbb {P} (\\boldsymbol {R} | \\hat {\\boldsymbol {B}} _ {s}, \\hat {\\boldsymbol {B}} _ {o}, \\boldsymbol {C} _ {E}; \\boldsymbol {\\theta} _ {P a r}, \\boldsymbol {\\theta} _ {S e}) = \\tag {5} \\\\ \\mathbb {P} \\left(\\hat {\\boldsymbol {B}} _ {s}, \\hat {\\boldsymbol {B}} _ {o} \\mid \\hat {\\boldsymbol {B}} _ {s}, \\hat {\\boldsymbol {B}} _ {o}, \\boldsymbol {C} _ {E}; \\boldsymbol {\\theta} _ {P a r}\\right) \\cdot \\mathbb {P} \\left(\\boldsymbol {R} \\mid \\hat {\\boldsymbol {B}} _ {s}, \\hat {\\boldsymbol {B}} _ {o}, \\boldsymbol {C} _ {E}; \\boldsymbol {\\theta} _ {S e}\\right) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 294, + 890, + 330 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\hat{B}_s, \\hat{B}_o$ denote the ground-truth SO boxes from the region pair set $P$ that include their positions and labels); $\\tilde{B}_s, \\tilde{B}_o$ denote contextualized SO representations. To allow for decoding, we embed $\\hat{B}_s, \\hat{B}_o$ to have an equivalent dimension with queries. Specifically, we use MLPs to project positions and label text embeddings, and concatenate them along the channel dimension to obtain query-like input.", + "bbox": [ + 496, + 338, + 890, + 444 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Denoising training of R-Tagger. The training losses of R-Tagger are identical to RLIPv1:", + "bbox": [ + 498, + 445, + 890, + 474 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda_ {1} \\mathcal {L} _ {l 1} + \\lambda_ {2} \\mathcal {L} _ {G I o U} + \\lambda_ {3} \\left(\\mathcal {L} _ {s} + \\mathcal {L} _ {o}\\right) + \\lambda_ {4} \\mathcal {L} _ {r} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 483, + 890, + 500 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}$ is comprised of the $\\ell_1$ loss for box regression $\\mathcal{L}_{l1}$ , GIoU loss [67] $\\mathcal{L}_{G IoU}$ , Cross-Entropy (CE) loss for subject and object classes $\\mathcal{L}_s, \\mathcal{L}_o$ , and Focal loss [52] for relations $\\mathcal{L}_r$ . $\\lambda_1, \\lambda_2, \\lambda_3, \\lambda_4$ are set to 2.5, 1, 1, 1 as fixed weights to balance multi-task training [86, 89, 71].", + "bbox": [ + 496, + 508, + 890, + 583 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, due to the identical input and training objectives of Parallel Entity Detection, the model will attempt to find a shortcut, i.e., identity mapping, to achieve the minimum loss value. To avoid this, we draw inspiration from [40] which adds noise to $\\hat{B}_s, \\hat{B}_o$ during training. Specifically, we follow [40] to add center shifting and box scaling noise to box positions and add label flipping noise to box labels. The noise scale of center shifting and box scaling is set to 0.4, and the noise scale of label flipping is set to 0.2 following [40]. Furthermore, to prevent the information leakage between the same region with different noise, we apply attention masks to block the information flow between the same regions in Parallel Entity Detection.", + "bbox": [ + 496, + 583, + 890, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inference of R-Tagger. After the training of R-Tagger, we can use it to infer relations without additional noise based on Eq. (5). For each inference, the maximum number of region pairs is $N_{Q}$ . If candidate SO region pairs exceed $N_{Q}$ , we infer multiple times and merge the results. To quantify the confidence of a relation, we calculate the product of the top-1 score from the softmax distribution over the subject, the object and the original relation sigmoid score. To", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21652", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/4d3f3be4e1ab78385eb766b15ef8d44a9b705456fb287d671b0b93163c4286b1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
NvNALIFRareNon-RareFull#ParamsFPS
1610.9213.9913.28246.8M18.93
2312.1214.0713.62206.6M21.49
3210.5714.0513.25193.2M22.15
6111.2613.9013.30179.8M23.17
", + "bbox": [ + 80, + 89, + 462, + 183 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "select pseudo-labels, we choose those whose relation confidence exceeds a threshold $\\eta$ . $\\eta$ is set to 0.2 by default (details can be found in the Appendix).", + "bbox": [ + 75, + 267, + 468, + 313 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Pre-training, Fine-tuning and Inference", + "text_level": 1, + "bbox": [ + 76, + 323, + 416, + 339 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Regarding pre-training and fine-tuning of RLIPv2, we first merge results from Parallel Entity Detection and Sequential Relation Inference to obtain $N_{Q}$ triplets. Next, we employ the bipartite matching algorithm originally proposed in [71] to match the predicted and ground-truth triplet annotations. The overall loss is identical to Eq. (6). The techniques introduced in RLIPv1, i.e. Label Sequence Extension, Relation Quality Labels and Relation Pseudo-Labels, are employed by default for a fair comparison. Regarding the inference of RLIPv2, we sort the relation confidence (defined in Sec. 4.2.2) of the correctly localised triplets (IoU > 0.5) and select the Top-K triplets. $K$ is set to 100 by default following [86, 71, 45, 11].", + "bbox": [ + 75, + 345, + 468, + 544 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 556, + 209, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pre-training datasets. To pre-train RLIPv2, we utilize VG [38], COCO [53] and Objects365 [69]. VG has $108k$ images annotated with free-form relation and object annotations. COCO has $117k$ images with only object annotations in 80 classes, and Objects365 has $1,742k$ images with only object annotations in 365 classes. Thus, we use relational pseudo-labelling to tag relation labels for COCO and Objects365, enabling them to support relational pre-training.", + "bbox": [ + 75, + 582, + 468, + 704 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Downstream datasets. For HOI detection, we follow [71, 86, 89, 93] to evaluate on HICO-DET [4] and V-COCO [22]. For HICO-DET that contains 117 verbs and 80 objects, we evaluate under the Default setting on Full, Rare and Non-Rare sets. For V-COCO that contains 24 interactions and 80 objects, we evaluate following the official evaluation code [22] under two scenarios: $\\mathrm{AP}_{role}^{\\#1}$ and $\\mathrm{AP}_{role}^{\\#2}$ . For SGG, we assess RLIPv2 on the widely-used Open Images v6 [39] dataset, which is annotated with 288 objects and 30 relations. We evaluate RLIPv2 using standard evaluation metrics [39, 96]: Recall@50 (R@50), weighted mean Average Precision for relation detection ( $\\mathrm{wmAP}_{rel}$ ) and phrase detection ( $\\mathrm{wmAP}_{phr}$ ). The final score is calculated", + "bbox": [ + 75, + 704, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/3d99d69b03594671deb6ca8ac798b3e7b79fb6114126ac88da5f68331940b777.jpg", + "table_caption": [ + "Table 1: The effect of the sparsification of language encoding layers in Cross-Modal Fusion. Results are evaluated on HICODET under zero-shot (NF) setting. FPS (frames per second) is tested on a single NVIDIA A100 with a minibatch size 1." + ], + "table_footnote": [], + "table_body": "
Gatingtanh()RareNon-RareFull
α10.4713.8313.05
a✓9.9113.5412.70
SE11.0713.8913.24
α12.1214.0713.62
ax10.9814.0713.36
SE11.0714.0013.32
", + "bbox": [ + 501, + 88, + 890, + 202 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2: Comparisons of different gating functions introduced in Sec. 4.1. We report zero-shot (NF) results on HICO-DET.", + "bbox": [ + 498, + 208, + 890, + 237 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "as: $\\mathrm{score}_{wtd} = 0.2 * \\mathrm{R} @ 50 + 0.4 * \\mathrm{wmAP}_{rel} + 0.4 * \\mathrm{wmAP}_{phr}$ .", + "bbox": [ + 498, + 257, + 890, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. To assess the effectiveness of RLIPv2, we choose to adopt DDETR [102] to compose RLIPv2-ParSeD and adopt DAB-DDETR [56] to compose RLIPv2-ParSeDA. To perform a fair comparison with previous works, we ensure that RLIPv2 has $N_v * N_{ALIF} = 6$ DDETR/DAB-DDETR encoding layers. For Parallel Entity Detection and Sequential Relation Inference, 3 layers are adopted following [86, 89, 71, 93]. $N_Q$ is set to 100 during pre-training and fine-tuning, except when we finetune on HICO-DET where $N_Q$ is set to 64 following [93]. Regarding model initialization, we use COCO detection parameters as initialisation when using VG or VG and COCO for pre-training; when using VG, COCO and Objects365 for pre-training, we use COCO and Object365 detection parameters as initialisation. Regarding the configuration of minibatch sizes and learning rate (LR), we set the minibatch size to 64, LR for the text encoder to 1.41e-5 and LR for other modules to 1.41e-4 when using ResNet-50 [25] and Swin-T [59]; We set the minibatch size to 32, LR for the text encoder to 1e-5 and LR for other modules to 1e-4 when using Swin-L [59]. RLIPv2 and R-Tagger are pre-trained and fine-tuned for 20 epochs unless otherwise stated, with LR dropping by a factor of 10 at the 15th epoch. For the BLIP captioner, we adopt the ViT-L/16 [14] model fine-tuned on COCO Caption [8].", + "bbox": [ + 496, + 287, + 892, + 666 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 675, + 653, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We perform the ablation study using RLIPv2-ParSeD with ResNet-50 as the backbone, and VG as the pre-training dataset unless otherwise stated. We pre-train for 20 epochs and evaluate performance on HICO-DET under the zero-shot with no fine-tuning (NF) setting.", + "bbox": [ + 496, + 698, + 890, + 773 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1.1 Asymmetric Language-Image Fusion", + "text_level": 1, + "bbox": [ + 498, + 786, + 812, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sparsification of the language layers. First of all, we ablate on the number of language layers to investigate the effect of sparsifying language encoding layers in CrossModal Fusion. As introduced in Sec. 4.1, dense language layers cause difficult training. To avoid training collapse, we compute classification losses $(\\mathcal{L}_s,\\mathcal{L}_o$ and $\\mathcal{L}_r)$ using all", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21653", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/33d246fd37d65749840f938a7139fe379462ba0b70959b3cb9cd8a3c8f3beacf.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelPre-trainingFully-finetuningFPS
Ep.TimeZero-shot (NF)Ep.Result
RLIPv1-ParSeD5025.9h11.20 / 14.73 / 13.926024.67 / 32.50 / 30.7021.89
RLIPv2-ParSeD2010.9h12.12 / 14.07 / 13.622026.47 / 33.51 / 31.8921.49
RLIPv1-ParSeDA5027.2h11.34 / 14.56 / 13.826022.85 / 30.87 / 29.0319.41
RLIPv2-ParSeDA2011.3h13.03 / 14.98 / 14.532027.01 / 35.21 / 33.3218.94
", + "bbox": [ + 78, + 88, + 589, + 186 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2b1b6d5cad210d6b428a5fb6744fc9475a1d3c238736e0fa188466805564644a.jpg", + "table_caption": [ + "Table 3: Comparisons of RLIPv1 and RLIPv2 under zero-shot (NF) and fully-finetuning settings on HICO-DET pre-trained on VG. Results are reported on Rare/Non-Rare/Full sets. FPS is tested on a single NVIDIA A100 with minibatch size 1. Pretraining time is tested on 8 NVIDIA A100. \"Ep.\" denotes number of epochs." + ], + "table_footnote": [], + "table_body": "
InitializationRareNon-RareFull
COCO (default)12.1214.0713.62
R-Tagger12.5513.6413.39
w/o noise9.9412.7412.09
w/o attn masks8.5511.2210.61
", + "bbox": [ + 602, + 89, + 895, + 183 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "intermediate language features rather than using only the last layer of language features in Cross-Modal Fusion. Results are shown in Tab. 1. Our findings suggest that sparsifying the language encoder does not compromise zero-shot performance and improves parameter efficiency. We attribute this to overfitting effects on upstream datasets impairing models' generalization. We choose $N_{v} = 2$ and $N_{ALIF} = 3$ as the default hyper-parameters for the following experiments.", + "bbox": [ + 75, + 268, + 468, + 404 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The choice of the gating function $\\mathrm{G}(\\boldsymbol{x})$ . To investigate the effect of the gating function on cross-modal fusion, we experiment with variants of the gating function as described in Sec. 4.1. The results are shown in Tab. 2. We note that tanh consistently degrades performance for the three gating methods. We conjecture that the output range of tanh can constrain the magnitude of the features to be fused, thus limiting the performance. Based on the results, we choose the simplest one: the learnable scalar gating method parameterised by $\\alpha$ .", + "bbox": [ + 75, + 405, + 470, + 556 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparisons of RLIPv2 with RLIPv1. To compare the architectural benefit of RLIPv2 with RLIPv1, we adopt DDETR [102] and DAB-DDETR [56] to follow two designs, and evaluate performance under zero-shot (NF) and fully-finetuning setting. Results are shown in Tab. 3. From this table, we can observe that by modifying the architecture without compromising much inference speed, RLIPv2 generally outperforms its RLIPv1 counterpart. Specifically, RLIPv2 obtains comparable zero-shot results to RLIPv1, while costing about $0.4 \\times$ pre-training time. In terms of fine-tuning results, RLIPv2 surpasses RLIPv1 with $0.33 \\times$ fine-tuning time due to earlier and deeper fusion.", + "bbox": [ + 75, + 556, + 470, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1.2 Relational Pseudo-labelling", + "text_level": 1, + "bbox": [ + 76, + 753, + 321, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "By default, we use RLIPv2-ParSeD with ResNet-50 backbone as the basic structure of R-Tagger.", + "bbox": [ + 75, + 777, + 468, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The necessity of denoising pre-training and attention masks for R-Tagger. If noise is not added during R-Tagger's pre-training, the loss will fluctuate instead of steadily decreasing as the optimization proceeds. If attention masks are not utilized to prevent information leakage, the model will tend to learn an identity mapping, thus de", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/082dbfc465be71a5410a2f424c9e4a44293f1266fc1e80225fd76e88e6cd0bce.jpg", + "table_caption": [ + "Table 4: The quality of R-Tagger parameters. Results are evaluated using RLIPv2-ParSeD with ResNet-50 under zero-shot (NF) setting." + ], + "table_footnote": [], + "table_body": "
Tagging MethodOverlapRareNon-RareFull
Greedy [100]×11.1511.6511.55
✓13.1614.7014.35
CLIP (ViT-L/14) [65]×12.6612.7612.74
✓14.6314.9414.87
R-Tagger (ResNet-50)×15.3315.5415.49
✓15.3615.3715.36
", + "bbox": [ + 501, + 266, + 890, + 393 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1b2369b9d46f5fbfba5939faa2d7674c93173753ffdca8633e17b9ecd3a296bb.jpg", + "table_caption": [ + "Table 5: Comparisons of relation tagging methods. \"Overlap\" denotes the \"overlap\" prior for SO pairs introduced in Sec. 4.2.2. We report zero-shot (NF) results pre-trained on VG and COCO. We use oracle captions from COCO Caption [8] ( $N_{Cap} = 5$ )." + ], + "table_footnote": [], + "table_body": "
Caption typeNCapRareNon-RareFull
Oracle515.3315.5415.49
BLIP (beam)19.8612.0211.52
BLIP (nucleus)514.6714.7614.74
BLIP (nucleus)1015.0815.1015.09
BLIP (nucleus)2014.2414.9114.75
BLIP (nucleus)*512.3114.3713.89
", + "bbox": [ + 501, + 467, + 888, + 588 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 6: Comparisons of different caption types. \"beam\" and \"nucleus\" denote beam search and nucleus sampling. \"Oracle\" denotes captions from COCO Caption. By default, we adopt COCO Caption fine-tuned BLIP model. * denotes that we adopt the pretrained BLIP model.", + "bbox": [ + 498, + 595, + 890, + 664 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "grading its ability to infer relations. R-Tagger is pre-trained for 20 epochs. To assess the quality of R-Tagger's parameters, thanks to R-Tagger's identical structure to RLIPv2-ParSeD, we initialize RLIPv2-ParSeD with R-Tagger's parameters and pre-train for 10 epochs. We evaluate the zero-shot (NF) performance on HICO-DET as shown in Tab. 4. We observe that removing additional noise or attention masks both impair performance, highlighting their importance.", + "bbox": [ + 496, + 686, + 890, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparisons of different relation tagging strategies. We compare R-Tagger with other two methods: (i) the greedy matching algorithm [100]; (ii) the CLIP [65] tagging method. Specifically, to tag relations for a given SO region pair with a candidate relation text, the CLIP tagging", + "bbox": [ + 496, + 824, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21654", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0fafe1e5172c89508a137ceee5a470fd96fb4e5e41236ecebba4643369909785.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetRelation candidateRareNon-RareFull
VG-12.1214.0713.62
VG+COCOBLIP15.0815.1015.09
VG+COCOSelection from VG10.3411.3311.11
", + "bbox": [ + 80, + 89, + 460, + 162 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/32ef1707c76c2c3c3ccef2c914c2f1fc65ca943fe3a8f3919823a18e453f1fa2.jpg", + "table_caption": [ + "Table 7: Comparisons of methods to generate relation candidate sets. We report zero-shot (NF) results on HICO-DET." + ], + "table_footnote": [], + "table_body": "
VGVG+COCOVG+COCO+O365
ResNet-5013.03 / 14.98 / 14.5315.00 / 16.60 / 16.2319.64 / 17.24 / 17.79
Swin-T13.01 / 16.06 / 15.3517.13 / 18.74 / 18.3721.24 / 19.47 / 19.87
Swin-L19.93 / 18.74 / 19.0222.59 / 21.09 / 21.4427.97 / 21.90 / 23.29
", + "bbox": [ + 78, + 212, + 467, + 271 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d08dc12069963d4d077ec1ed73bd8fde4c060be95baecf9174a7c12cb8ec2bde.jpg", + "table_caption": [ + "Table 8: Model and dataset scaling experiments using RLIPv2-ParSeDA. Results are evaluated on HICO-DET Rare/Non-Rare/Full sets under zero-shot (NF) setting." + ], + "table_footnote": [], + "table_body": "
ModelBackboneExtramR@50R@50wmAPscore_wtd
relphr
VCTree [73]X101-F-33.9174.0834.1633.1140.21
G-RCNN [82]X101-F-34.0474.5133.5134.2141.84
Motifs [90]X101-F-32.6871.6329.9131.5938.93
Unbiased [72]X101-F-35.4769.3030.7432.8039.27
GPS-Net [54]X101-F-35.2674.8132.8533.9841.69
RelDN [96]R101-36.8072.7529.8730.4238.67
BGNN [46]R101-39.4174.9331.1531.3740.00
SGTR [45]R101-42.6159.9136.9838.7342.28
RelTR [11]R50--64.4734.1737.4441.54
RLIPv2-ParSeDR50*-44.5858.0443.3043.1246.18
R50*-44.8860.2044.7343.3647.28
R50†-45.5961.1545.7143.7348.01
RLIPv2-ParSeDAR50(i)50.4263.3547.6545.2349.82
R50(ii)52.0764.5349.1446.1451.01
R50(iii)51.3165.9949.5445.7151.30
Swin-T(iii)59.6168.8152.7048.0154.05
Swin-L(iii)64.7272.4956.3850.7057.34
", + "bbox": [ + 78, + 335, + 470, + 554 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "method clips the minimum bounding box of the SO region pair, creates two prompts (\"a photo of {subject} {relation} {object}\" and \"a photo of {subject} not interacting with {object}\" are adopted as positive and negative prompts.), and performs zero-shot prediction. If the softmax probability of the positive prompt is greater than a pre-defined threshold, we tag this relation text to this SO region pair. (We traverse the threshold and find the optimal one for the CLIP tagging method, as detailed in the Appendix.) We also ablate on the \"overlap\" prior [100] to observe whether a given tagging method relies on strong prior knowledge to filter out false positive relations. The results are shown in Tab. 5. From this table, we conclude that greedy matching and CLIP tagging method generate a significant number of low-quality non-overlapped triplets. Thus, the \"overlap\" prior is essential for them. R-Tagger, however, suf", + "bbox": [ + 75, + 657, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cc82df002864da9ade466256a3d093b76db5da5606b4192f2a26d896ccd54cf2.jpg", + "table_caption": [ + "Table 9: Comparisons with previous methods on Open Images v6 SGG benchmark. X101-F denote ResNeXt-101 FPN [80]. ${}^{ * }$ and ${}^{ \\dagger }$ denote ImageNet pretrained and COCO object detection pretrained. \"Extra\" denotes extra relations adopted from (i) VG, (ii) VG+COCO and (iii) VG+COCO+O365." + ], + "table_footnote": [], + "table_body": "
MethodBackboneUC-RFUC-NF
VCL [27]ResNet-5010.06 / 24.28 / 21.4316.22 / 18.52 / 18.06
ATL [28]ResNet-509.18 / 24.67 / 21.5718.25 / 18.78 / 18.67
FCL [29]ResNet-5013.16 / 24.23 / 22.0118.66 / 19.55 / 19.37
GEN-VLKT [51]ResNet-5021,36 / 32.91 / 30.5625.05 / 23.38 / 23.71
RLIPv1-ParSeD [86]ResNet-5016.43 / 30.59 / 27.7616.99 / 24.71 / 22.93
RLIPv1-ParSe [86]ResNet-5019.19 / 33.35 / 30.5220.27 / 27.67 / 26.19
RLIPv2-ParSeDAResNet-5021.45 / 35.85 / 32.9722.81 / 29.52 / 28.18
RLIPv2-ParSeDASwin-T26.95 / 39.92 / 37.3221.07 / 35.07 / 32.27
RLIPv2-ParSeDASwin-L31.23 / 45.01 / 42.2622.65 / 40.51 / 36.94
", + "bbox": [ + 501, + 89, + 893, + 204 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/72b1a99a17bd59af3507b3bbe058452b3a2e36554fafe9521b9134e026d010dc.jpg", + "table_caption": [ + "Table 10: Comparisons with methods on HICO-DET under UC-RF and UC-NF settings. We adopt ResNet-50 as the backbone. Results are reported on Unseen/Seen/Full sets." + ], + "table_footnote": [], + "table_body": "
MethodBackbone1% Data10% Data
RLIPv1-ParSeD [86]ResNet-5016.22 / 18.92 / 18.3015.89 / 23.94 / 22.09
RLIPv1-ParSe [86]ResNet-5017.47 / 18.76 / 18.4620.16 / 23.32 / 22.59
RLIPv2-ParSeDAResNet-5022.13 / 24.51 / 23.9623.28 / 30.02 / 28.46
RLIPv2-ParSeDASwin-T24.26 / 28.92 / 27.8528.31 / 32.93 / 31.87
RLIPv2-ParSeDASwin-L31.89 / 32.32 / 32.2234.75 / 38.27 / 37.46
", + "bbox": [ + 501, + 263, + 893, + 343 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 11: Comparisons on HICO-DET under few-shot settings. Results are reported on Rare/Non-Rare/Full sets.", + "bbox": [ + 500, + 353, + 890, + 380 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "fers a slight performance drop when using the \"overlap\" prior, indicating that R-Tagger generates more reliable non-overlapped triplets. Besides, although CLIP is pre-trained on a massive quantity of language-image pairs, it struggles in recognizing relations, which R-Tagger is expert in.", + "bbox": [ + 496, + 401, + 890, + 477 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparisons of different caption types. Previous experiments demonstrate that oracle COCO captions can benefit pre-training. However, most datasets lack such high-quality captions. Thus, BLIP provides an alternative for caption generation. We conduct experiments on various caption types, as shown in Tab. 6. From this table, we can observe that: (i) BLIP-generated captions achieve a decent performance compared to oracle captions, indicating the practicality of adopting generated captions for pseudolabelling. (ii) If we compare BLIP model with different parameters (COCO Caption fine-tuned or only pre-trained), we can see that the fine-tuned model generates better captions with more boost on the Rare set $(12.31\\rightarrow 14.67)$ . We conjecture that the caption quality of the curated style dataset COCO Caption is better than pre-training captions harvested from the web. (iii) By adopting generated captions, we can increase the number of captions per image, thus diversifying the relations contained in captions and boost RLIPv2 $(11.52\\rightarrow 15.09)$ . Besides, although datasets like Conceptual Caption [70] (CC3M) also provide captions, the quantity of captions (average one caption per image) is not enough to describe many relations in an image. In comparison, our pipeline can work without caption annotation while performing better.", + "bbox": [ + 496, + 478, + 892, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The necessity of using captioners. By default, we use BLIP to generate relation texts. Another option is to query all possible SO pairs and select all possible relation texts from VG as it contains an enormous quantity of relations", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21655", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/956bbfefde550206c4dff3de40d1934b0f7fca82a774fa5129841dd16946e2e2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelBackboneExtra RelationsHICO-DETV-COCO
Zero-shot (NF)Fully-finetuningAP#1roleAP#2role
InteractNet [21]R50-FPN--7.16 / 10.77 / 9.9440.0-
UnionDet [35]R50-FPN--11.72 / 19.33 / 17.5847.556.2
PPDM [50]HG104--13.97 / 24.32 / 21.94--
HOTR [36]R50--17.34 / 27.42 / 25.1055.264.4
QPIC [71]R50--21.85 / 31.23 / 29.0758.861.0
OCN [89]R50--25.56 / 32.51 / 30.9164.266.3
CDN [93]R50--27.39 / 32.64 / 31.4461.763.8
GEN-VLKT [51]R50--29.25 / 35.10 / 33.7562.464.5
QAHOI [5]Swin-L*--29.80 / 37.56 / 35.78--
UniVRD [98]ViT-H/14†--31.65 / 39.99 / 38.0765.866.9
RLIPv1-ParSeD [86]R50VG11.20 / 14.73 / 13.9224.67 / 32.50 / 30.7061.763.8
RLIPv1-ParSe [86]R50VG15.08 / 15.50 / 15.4026.85 / 34.63 / 32.8461.964.2
RLIPv2-ParSeDAR50VG13.03 / 14.98 / 14.5327.01 / 35.21 / 33.3263.065.1
RLIPv2-ParSeDAR50VG+COCO15.00 / 16.60 / 16.2327.89 / 35.27 / 33.5764.566.7
RLIPv2-ParSeDAR50VG+COCO+O36519.64 / 17.24 / 17.7929.61 / 37.10 / 35.3865.968.0
RLIPv2-ParSeDASwin-TVG+COCO+O36521.24 / 19.47 / 19.8733.66 / 40.07 / 38.6068.870.8
RLIPv2-ParSeDASwin-LVG+COCO+O36527.97 / 21.90 / 23.2943.23 / 45.64 / 45.0972.174.1
", + "bbox": [ + 120, + 88, + 848, + 354 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 12: Comparisons with previous methods on HICO-DET and V-COCO. Results on HICO-DET are reported on Rare/Non-Rare/Full sets. R50 and HG denote ResNet-50 [25] and Hourglass [61]. * denotes the backbone is pre-trained with $384 \\times 384$ resolution, while others use $224 \\times 224$ . † indicates the backbone is pre-trained using LiT [92], then fine-tuned on Objects365, COCO and HICO with the objective of object detection.", + "bbox": [ + 75, + 362, + 890, + 419 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(36,515 kinds). Then, we run R-Tagger with selected relation texts as $T$ and all region pairs as $P$ . The results are shown in Tab. 7. We can observe that selecting from VG generates low-quality candidates, harming performance.", + "bbox": [ + 75, + 438, + 468, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Model scaling and dataset scaling. Equipped with the labelling pipeline introduced above, we can scale RLIPv2 to larger models and datasets. In Tab. 8, we adopt RLIPv2-ParSeDA as the base architecture and observe the benefit of scaling by zero-shot (NF) performance on HICO-DET. In terms of data, adding COCO and Objects365 can both boost performance, and the benefit of adding data exhibits a log scaling trend [9]. Models pre-trained with Objects365 consistently have better Rare result, which we attribute to the distribution misalignment of Objects365 and HICO-DET [17]. In terms of models, switching to stronger backbone models can improve the data efficiency at the cost of larger amounts of computation. Regarding scaling experiments using RLIPv2-ParSeD, we present it in the Appendix.", + "bbox": [ + 75, + 500, + 470, + 712 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2. Comparisons with State-of-the-Arts", + "text_level": 1, + "bbox": [ + 76, + 724, + 387, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Scene graph generation. We compare RLIPv2 series models with previous methods on Open Images v6 in Tab. 9. We also report mean Recall@50 (mR@50) to better show the usefulness of RLIPv2. Our findings suggest that (i) with the assistance of DDETR family models, RLIPv2 can serve as a strong baseline without any pre-training; (ii) naive object detection pre-training can boost the performance to some extent $(47.28 \\rightarrow 48.01)$ , while pre-training on VG can further boost the performance especially on mR@50 $(45.59 \\rightarrow 50.42)$ ; (iii) adding pseudo-labelled relation an-", + "bbox": [ + 75, + 750, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "notations in pre-training or switching to stronger backbones both contribute to better performance. However, the boost of adding Objects365 is negligible. We attribute this to the distribution discrepancy of Objects365 and Open Images v6.", + "bbox": [ + 496, + 438, + 890, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "HOI Detection under UC-NF and UC-RF settings. We report results in Tab. 10 on unseen combinations (UC) under UC-RF and UC-NF settings following [27, 28]. We only fine-tune for 10 epochs under UC-NF setting. Our method outperforms previous methods except on one metric. We attribute this to the strong transferability of CLIP features that GEN-VLKT adopts. Regarding experiments using RLIPv2-ParSeD, we present it in the Appendix.", + "bbox": [ + 496, + 521, + 890, + 643 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Few-shot HOI Detection. We follow [86] to only fine-tune 10 epochs on partial data (1% and 10%), results of which are shown in Tab. 11. We can observe significant improvements upon all metrics by scaling up pre-training compared with previous methods. This improves the practicality of RLIPv2 in low-data scenarios. Regarding experiments using RLIPv2-ParSeD, we present it in the Appendix.", + "bbox": [ + 496, + 650, + 890, + 757 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "HOI detection under fully-finetuning and zero-shot (NF) settings. We compare the performance of RLIPv2 series models with previous methods on HICO-DET and V-COCO in Tab. 12. We can observe from the table that (i) dataset and model scaling can both boost the final performance on two datasets; (ii) on HICO-DET, the benefit of pre-training is more prominent on zero-shot than fully-finetuning, especially on the Rare set. Regarding experiments using RLIPv2-ParSeD, we present it in the Appendix.", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21656", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0d2b7df2ed4ced0f1ed688c46233d9a8df44cfd3331660ae0c161c4dfa6a61c4.jpg", + "image_caption": [ + "Figure 4: (a) Visualization of pseudo-labelled relations on COCO. Left column: R-Tagger; right column: CLIP tagging method. (b) Visualization of failure cases of R-Tagger." + ], + "image_footnote": [], + "bbox": [ + 94, + 74, + 447, + 294 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5.3. Qualitative Analysis", + "text_level": 1, + "bbox": [ + 76, + 352, + 267, + 369 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Comparisons of relation tagging methods. We visualize three examples to compare the quality of pseudolabelled relations by R-Tagger and CLIP tagging method in Fig. 4(a). Generally, CLIP is more object-centric and position-agnostic, and thus struggles in discriminating relations. It tends to tag relations as long as the subject and object have strong co-occurrence priors. However, R-Tagger tags more reasonable relations.", + "bbox": [ + 75, + 376, + 468, + 496 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Failure cases of R-Tagger. Recognizing relations is challenging, especially in complex scenes. In Fig. 4(b), we present three examples of R-Tagger's failure cases. In particular, we observe failure cases when the scene contains multiple similar subjects or objects.", + "bbox": [ + 75, + 497, + 468, + 574 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 585, + 194, + 602 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we propose RLIPv2, a fast converging model that enables the scaling of relational pre-training to larger-scale pseudo-labelled datasets. Comprehensive experiments on HOI detection and scene graph generation under various settings demonstrate its effectiveness compared to previous methods. We anticipate that our work can galvanize further research efforts to focus on relational reasoning, fostering advancements that yield tangible benefits not only to the research community but also to broader society and humanity.", + "bbox": [ + 75, + 611, + 470, + 762 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 76, + 771, + 223, + 787 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We would like to extend our sincere gratitude to the anonymous reviewers for their invaluable feedback. Additionally, we appreciate the Fundamental Vision Intelligence Team of Alibaba DAMO Academy for their generous provision of essential computational resources. This research received support from the National Natural Science Foundation of China under Grant No. 62173298 and was addi", + "bbox": [ + 75, + 794, + 468, + 898 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "tionally backed by Alibaba Group via the Alibaba Research Intern Program.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 501, + 136, + 596, + 150 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, et al. Flamingo: a visual language model for few-shot learning. arXiv preprint arXiv:2204.14198, 2022. 2, 3", + "[2] Zhaowei Cai, Gukyeong Kwon, Avinash Ravichandran, Erhan Bas, Zhuowen Tu, Rahul Bhotika, and Stefano Soatto. 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In CVPR, pages 11825-11834, 2021. 2" + ], + "bbox": [ + 78, + 90, + 468, + 272 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "21661", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 12 + } +] \ No newline at end of file diff --git a/2023/RLIPv2_ Fast Scaling of Relational Language-Image Pre-Training/dedbf300-120b-4912-a26e-f96e152258fe_model.json b/2023/RLIPv2_ Fast Scaling of Relational Language-Image Pre-Training/dedbf300-120b-4912-a26e-f96e152258fe_model.json new file mode 100644 index 0000000000000000000000000000000000000000..f0c82e1ca821c76a35eac6084fa7375dc02007bc --- /dev/null +++ b/2023/RLIPv2_ Fast Scaling of Relational Language-Image Pre-Training/dedbf300-120b-4912-a26e-f96e152258fe_model.json @@ -0,0 +1,2965 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.155, + 0.131, + 0.819, + 0.154 + ], + "angle": 0, + "content": "RLIPv2: Fast Scaling of Relational Language-Image Pre-training" + }, + { + "type": "text", + "bbox": [ + 0.153, + 0.179, + 0.815, + 0.218 + ], + "angle": 0, + "content": "Hangjie Yuan\\(^{1*}\\) Shiwei Zhang\\(^{2}\\) Xiang Wang\\(^{3*}\\) Samuel Albanie\\(^{4}\\) Yining Pan\\(^{5*}\\) Tao Feng\\(^{2}\\) Jianwen Jiang\\(^{2}\\) Dong Ni\\(^{1\\dagger}\\) Yingya Zhang\\(^{2}\\) Deli Zhao\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.204, + 0.221, + 0.78, + 0.251 + ], + "angle": 0, + "content": "\\(^{1}\\)Zhejiang University \\(^{2}\\)Alibaba Group \\(^{3}\\)Huazhong University of Science and Technology \\(^{4}\\)CAML Lab, University of Cambridge \\(^{5}\\)Singapore University of Technology and Design" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.254, + 0.892, + 0.287 + ], + "angle": 0, + "content": "{hj.yuan, dni}@zju.edu.cn wxiang@hust.edu.cn {pyn.sigrid, fengtao.hi, zhaodeli}@gmail.com \nsma71@cam.ac.uk {zhangjin.zsw, jianwen.jjw, yingya.zyy}@alibaba-inc.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.318, + 0.314, + 0.334 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.474, + 0.775 + ], + "angle": 0, + "content": "Relational Language-Image Pre-training (RLIP) aims to align vision representations with relational texts, thereby advancing the capability of relational reasoning in computer vision tasks. However, hindered by the slow convergence of RLIPv1 architecture and the limited availability of existing scene graph data, scaling RLIPv1 is challenging. In this paper, we propose RLIPv2, a fast converging model that enables the scaling of relational pre-training to large-scale pseudo-labelled scene graph data. To enable fast scaling, RLIPv2 introduces Asymmetric Language-Image Fusion (ALIF), a mechanism that facilitates earlier and deeper gated cross-modal fusion with sparsified language encoding layers. ALIF leads to comparable or better performance than RLIPv1 in a fraction of the time for pre-training and fine-tuning. To obtain scene graph data at scale, we extend object detection datasets with free-form relation labels by introducing a captioner (e.g., BLIP) and a designed Relation Tagger. The Relation Tagger assigns BLIP-generated relation texts to region pairs, thus enabling larger-scale relational pre-training. Through extensive experiments conducted on Human-Object Interaction Detection and Scene Graph Generation, RLIPv2 shows state-of-the-art performance on three benchmarks under fully-finetuning, few-shot and zero-shot settings. Notably, the largest RLIPv2 achieves 23.29mAP on HICO-DET without any fine-tuning, yields 32.22mAP with just \\(1\\%\\) data and yields 45.09mAP with \\(100\\%\\) data. Code and models are publicly available at https://github.com/JacobYuan7/RLIPv2." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.789, + 0.21, + 0.804 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.814, + 0.47, + 0.845 + ], + "angle": 0, + "content": "The pretraining-finetuning paradigm has achieved major breakthroughs in vision and language domains [58, 13," + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.317, + 0.735, + 0.427 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.739, + 0.317, + 0.882, + 0.427 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.435, + 0.893, + 0.478 + ], + "angle": 0, + "content": "Figure 1: Left: Fine-tuning comparison on HICO-DET. Right: Pre-training epoch and zero-shot (NF) comparison on HICO-DET. Except where stated, RLIPv2-ParSeDA architecture is adopted." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.501, + 0.892, + 0.591 + ], + "angle": 0, + "content": "23, 103, 65, 77]. In this context, a number of particularly notable results have been obtained through aligned Vision-Language Pre-training (VLP) [65, 42, 41, 78, 95, 91]. These research efforts have typically employed a robust base model [14, 25, 12, 74] that is trained on language-image paired data to produce foundation models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.593, + 0.893, + 0.713 + ], + "angle": 0, + "content": "RLIPv1 [86] presents the first attempt to specifically align vision representations and relational texts using VLP. By pre-training on open-vocabulary scene graph data like Visual Genome (VG) [38], RLIPv1 demonstrates its usefulness in zero-shot, few-shot and fully-finetuned Human-Object Interaction (HOI) Detection. Although RLIPv1 is proven effective, we find it challenging to scale for the following reasons:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.716, + 0.892, + 0.791 + ], + "angle": 0, + "content": "(i) Model perspective: RLIPv1 converges slowly, as exemplified by DETR [3]-based RLIPv1, which requires 150/90 epochs to converge during pre-training/fine-tuning. Even when building on Deformable DETR (DDETR) [102] and DAB-DDETR [56], 50/60 epochs are still required." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.793, + 0.892, + 0.854 + ], + "angle": 0, + "content": "(ii) Data perspective: as observed by the authors of RLIPv1, data with relation triplet annotations is scarce, impeding RLIPv1's scaling. Annotating triplets in the form of \\(\\langle\\) subject, relations, object \\(\\rangle\\) is both time- and cost-intensive." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.716, + 0.892, + 0.854 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To resolve the aforementioned challenges, we introduce RLIPv2, a fast converging model that enables relational pretraining on larger-scale pseudo-labelled scene graph data." + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.851, + 0.468, + 0.864 + ], + "angle": 0, + "content": "*Work conducted during their research internships at DAMO Academy." + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.864, + 0.223, + 0.876 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "page_footnote", + "bbox": [ + 0.08, + 0.876, + 0.469, + 0.9 + ], + "angle": 0, + "content": "\\(^{1}\\)RLIPv1 refers to the model presented in [86], and RLIPv2 refers to the model presented in this paper." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.851, + 0.469, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21649" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.12 + ], + "angle": 0, + "content": "From both the model and data perspectives, we summarize the contributions of RLIPv2 as follows." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.47, + 0.303 + ], + "angle": 0, + "content": "From the model perspective, we observe that the slow convergence of DDETR can be attributed to the late language-image fusion strategy: fusion after decoding. Prior works [15, 44] have demonstrated an earlier and deeper fusion mechanism facilitates cross-modal alignment. In light of this, we propose Asymmetric Language-Image Fusion (ALIF) in RLIPv2 that encourages fusion in the encoding stage with sparsified language layers. Without sacrificing inference speed thanks to sparsification, RLIPv2 requires only 20 epochs to pre-train and fine-tune based on DDETR family models [102, 56] as shown in Fig. 1, while performing better than or comparably to RLIPv1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.471, + 0.529 + ], + "angle": 0, + "content": "From the data perspective, we leverage well-established object detection datasets [53, 69, 39]. Specifically, we extend these datasets with relational annotations by pseudolabelling. To perform pseudo-labelling, we must tackle two challenges: (i) sorting out the relations contained in the image and (ii) tagging relation texts to region pairs. Regarding the first challenge, we employ external captioners (e.g. BLIP [42]) that generate captions containing relation descriptions. Regarding the second challenge, we reuse RLIPv2 model as a Relation Tagger (R-Tagger) that enables assigning the generated open-vocabulary relation texts to region pairs. Equipped with such a pipeline, we investigate the scaling behavior of both the model and the data for RLIPv2, which demonstrates improved zero-shot, few-shot and fine-tuning performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.47, + 0.621 + ], + "angle": 0, + "content": "Furthermore, we introduce Scene Graph Generation (SGG), an analogously defined task to HOI detection for evaluating RLIPv2. RLIPv2 achieves state-of-the-art performance on Open Images v6 [39] for SGG, which underscores its robustness and efficacy in tackling relational reasoning tasks." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.634, + 0.22, + 0.649 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Language-image pre-training for detection. Recently, there has been a growing interest in learning visual representations from language supervision [42, 41, 65, 1, 32, 34, 15, 44, 95, 76]. This paradigm of learning from language supervision has also proven effective in improving detection performance. MDETR [34] was the first work to learn region-text correspondences in an end-to-end manner, while X-DETR [2] improved upon MDETR by removing the cross-modal fusion part that improves its training efficiency. GLIP [44] extended this line of research by scaling to web-scale data, leading to significant advances in zero-shot object detection and data efficiency. DetCLIP [84] proposed a paralleled concept formulation and a concept dictionary to enable semantically rich region-text alignment. RLIPv1 [86] was the first work to seek language-image alignment via relations, and our work follows its footsteps" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.816, + 0.107 + ], + "angle": 0, + "content": "to achieve fast scaling of relational pre-training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.108, + 0.892, + 0.469 + ], + "angle": 0, + "content": "End-to-end HOI detection and scene graph generation. Relations can interpret visual content in a fine-grained perspective [10, 31, 33]. Detecting and recognizing relations utilizing HOI detection and scene graph generation have been verified effective in image captioning [85], image retrieval [33, 75], synthesis [83, 18], activity understanding [31, 88, 87] and . The aim of these tasks is to detect relation triplets from a given input image. Before the emergence of DETR [3], the commonly adopted pipeline was to adopt an off-the-shelf object detector [66, 24] and design reasoning modules to infer relations [20, 19, 63, 49, 48, 90, 7, 54, 46, 47, 81]. Initial end-to-end design efforts extended detectors to support relation recognition [50, 99, 82, 35, 55]. Further attempts focus on the adaptation of DETR to the field of HOI detection [89, 6, 36, 104, 71, 93, 94, 79, 37, 57, 101, 62, 64, 97] and SGG [45, 11]. RLIPv1 [86] demonstrated the effectiveness of relational pre-training in improving performance and data efficiency. RLIPv2 builds upon RLIPv1, but seeks to solve its scaling problem. The most related work [100] also seeks scaling with the help of language. However, it remains a two-stage detection pipeline, lacks semantic richness and adopts a naive matching algorithm that hinders its performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.484, + 0.669, + 0.501 + ], + "angle": 0, + "content": "3. Recap of RLIPv1" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.51, + 0.892, + 0.646 + ], + "angle": 0, + "content": "In this section, we will briefly review RLIPv1 [86], a model that leverages both entity and relation descriptions to perform VLP and that forms the basis for our approach. As triplet detection architecture, RLIPv1 proposes a ParSeD model that allocates decoupled embeddings for subjects, objects and relations. The collective model RLIPv1-ParSeD consists of three stages: Parallel Entity Detection, Sequential Relation Inference and Cross-Modal Fusion, as shown in Fig. 2(a)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.646, + 0.892, + 0.782 + ], + "angle": 0, + "content": "For Parallel Entity Detection, RLIPv1-ParSeD defines two sets of queries \\( Q_{s}, Q_{o} \\in \\mathbb{R}^{N_{Q} \\times D} \\) with \\( N_{Q} \\) pairs of subjects and objects to perform subject and object detection. For Sequential Relation Inference, the model generates relation queries \\( Q_{r} \\in \\mathbb{R}^{N_{Q} \\times D} \\) based on the decoded subject and object queries \\( \\tilde{Q}_{s}, \\tilde{Q}_{o} \\in \\mathbb{R}^{N_{Q} \\times D} \\), and performs decoding to obtain \\( \\tilde{Q}_{r} \\in \\mathbb{R}^{N_{Q} \\times D} \\) for relation recognition. The design of RLIPv1-ParSeD obeys the following probabilistic factorization:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.79, + 0.891, + 0.823 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbb {P} \\left(\\boldsymbol {G} \\mid \\boldsymbol {Q} _ {s}, \\boldsymbol {Q} _ {o}, \\boldsymbol {C} _ {E}; \\boldsymbol {\\theta} _ {P a r}, \\boldsymbol {\\theta} _ {S e}\\right) = \\tag {1} \\\\ \\mathbb {P} \\left(\\boldsymbol {B} _ {s}, \\boldsymbol {B} _ {o} \\mid \\boldsymbol {Q} _ {s}, \\boldsymbol {Q} _ {o}, \\boldsymbol {C} _ {E}; \\boldsymbol {\\theta} _ {P a r}\\right) \\cdot \\mathbb {P} \\left(\\boldsymbol {R} \\mid \\boldsymbol {B} _ {s}, \\boldsymbol {B} _ {o}, \\boldsymbol {C} _ {E}; \\boldsymbol {\\theta} _ {S e}\\right) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.834, + 0.892, + 0.866 + ], + "angle": 0, + "content": "where \\(C_E\\) denotes features from the DDETR encoder; \\(\\theta_{Par},\\theta_{Se}\\) denote parameters for Parallel Entity Detection" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.9 + ], + "angle": 0, + "content": "2Since RLIPv2 targets fast scaling, we only focus on DDETR-based detection architecture." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21650" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.446, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.245, + 0.271, + 0.27, + 0.286 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.452, + 0.09, + 0.891, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.684, + 0.271, + 0.708, + 0.286 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.301, + 0.893, + 0.345 + ], + "angle": 0, + "content": "Figure 2: The overview of (a) RLIPv1-ParSeD and (b) RLIPv2-ParSeD and R-Tagger. The red part (loss calculation and noise injection) is only valid during training. In (a), Cross-Modal Fusion is achieved by the cross encoder. In (b), Cross-Modal Fusion is achieved by ALIF. The two architectures have an equivalent number of DDETR layers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.363, + 0.47, + 0.408 + ], + "angle": 0, + "content": "and Sequential Relation Inference; \\( B_{s}, B_{o}, R \\) are sets of detected subject boxes, object boxes and relations, respectively. They collectively comprise the detection results \\( G \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.408, + 0.47, + 0.499 + ], + "angle": 0, + "content": "For Cross-Modal Fusion, RLIPv1-ParSeD appends additional Transformer encoding layers [74, 34, 43] to perform language-image feature fusion on top of the decoded relation features \\(\\tilde{Q}_r\\), entity label features \\(L_{E} \\in \\mathbb{R}^{N_{E} \\times D}\\) and relation label features \\(L_{R} \\in \\mathbb{R}^{N_{R} \\times D}\\). \\(L_{E}, L_{R}\\) are extracted from RoBERTa [58]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.512, + 0.212, + 0.529 + ], + "angle": 0, + "content": "4. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.469, + 0.629 + ], + "angle": 0, + "content": "In this section, we will introduce: (i) Asymmetric Language-Image Fusion (ALIF) as an efficient CrossModal Fusion mechanism in RLIPv2, as shown in Fig. 2(b); (ii) the overall framework of extending the off-the-shelf object detection datasets [53, 69] to support relational pretraining." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.636, + 0.399, + 0.654 + ], + "angle": 0, + "content": "4.1. Asymmetric Language-Image Fusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.469, + 0.795 + ], + "angle": 0, + "content": "The core idea underpinning ALIF is to perform efficient cross-modal fusion in the early stages of RLIPv2 as highlighted by [15, 44]. Unlike RLIPv1 that encourages cross-modal alignment for entities and relations after the decoding phase, ALIF performs this during the detection encoding phase. This is particularly challenging for DDETR's encoder, since it relies on deformable attention that makes it challenging to adopt dedicated encoder layers during the detection encoding phase like [34, 60, 16]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.901 + ], + "angle": 0, + "content": "To address this, we propose ALIF, a mechanism that leverages DDETR encoding for the vision branch, RoBERTa encoding for the language branch and gated cross-attention for fusion. In contrast to previous work that encodes image and language with an equivalent number of layers [34, 16, 44, 15], we experimentally find that excessive RoBERTa layers do not improve its generalization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.363, + 0.892, + 0.483 + ], + "angle": 0, + "content": "capability due to its potential for overfitting to pre-trained data. Moreover, such a paradigm results in training difficulty due to the increased model complexity. As a result, we perform DDETR encoding densely while performing RoBERTa encoding sparsely. We denote the vision features from the backbone as \\( C^{(0)} \\) and language features from RoBERTa as \\( L^{(0)} \\) (the concatenation of \\( L_{E} \\) and \\( L_{R} \\)). The first ALIF module can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.492, + 0.891, + 0.512 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\boldsymbol {C}} ^ {(0)}, \\tilde {\\boldsymbol {L}} ^ {(0)} = \\operatorname {C r o s s - a t t n} \\left(\\boldsymbol {C} ^ {(0)}, \\boldsymbol {L} ^ {(0)}\\right) \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.535, + 0.891, + 0.553 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {C} ^ {\\left(N _ {v}\\right)} = \\mathrm {D D E T R} ^ {N _ {v}} \\left(\\boldsymbol {C} ^ {(0)} + \\mathrm {G} \\left(\\tilde {\\boldsymbol {C}} ^ {(0)}\\right)\\right) \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.572, + 0.891, + 0.591 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {L} ^ {(1)} = \\operatorname {R o B E R T a} ^ {1} \\left(\\boldsymbol {L} ^ {(0)} + \\mathrm {G} \\left(\\tilde {\\boldsymbol {L}} ^ {(0)}\\right)\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.892, + 0.809 + ], + "angle": 0, + "content": "where \\(\\tilde{C}^{(0)}\\) denotes language features aggregated by cross attention, and \\(\\tilde{L}^{(0)}\\) is analogously defined; \\(N_{v}\\) is the number of DDETR layers in one ALIF; \\(\\mathrm{G}(\\pmb{x})\\) defines a gating function that gates the aggregated cross-modal features. Note that \\(C_E\\) is \\(C^{(N_v)}\\) after stacking \\(N_{ALIF}\\) ALIF layers for encoding. For the instantiation of \\(\\mathrm{G}(\\pmb{x})\\), we experiment with three options: (i) \\(\\mathrm{G}(\\pmb{x}) = \\alpha \\pmb{x}\\) where \\(\\alpha\\) is a learnable scalar; (ii) \\(\\mathrm{G}(\\pmb{x}) = \\pmb{a}\\pmb{x}\\) where \\(\\pmb{a}\\) is a learnable vector; (iii) \\(\\mathrm{G}(\\pmb{x}) = \\mathrm{SE}(\\pmb{x})\\) where SE denotes a Squeeze-and-Excitation block [30] with a reduction ratio of 4. We also experiment augmenting \\(\\mathrm{G}(\\pmb{x})\\) with \\(\\tanh()\\) introduced in [1] (e.g. \\(\\tanh(\\alpha\\pmb{x})\\)), while only observing side effects. This indicates the magnitude of language and vision features are disparate, and a proper gating method is desired." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.818, + 0.748, + 0.834 + ], + "angle": 0, + "content": "4.2. Relational Pseudo-labelling" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "RLIPv2 reuses object detection datasets to benefit pretraining by pseudo-labelling, as shown in Fig. 3. We assume that during the pre-training phase, the downstream entity and relation distributions are unavailable to us. Then, to tag" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21651" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.089, + 0.457, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.199, + 0.47, + 0.242 + ], + "angle": 0, + "content": "Figure 3: An overview of relational pseudo-labeling, which tags object detection data with free-form relation texts. This process enables pre-training to be performed on two kinds of data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.262, + 0.468, + 0.307 + ], + "angle": 0, + "content": "relation texts, we need to sort out the relations contained in the image as detailed in Sec. 4.2.1, and to tag relation texts to region pairs as detailed in Sec. 4.2.2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.322, + 0.376, + 0.336 + ], + "angle": 0, + "content": "4.2.1 Relation Candidate Set Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.347, + 0.468, + 0.512 + ], + "angle": 0, + "content": "For a given image, relation candidate set generation aims to generate a coarse-grained set of candidate subject-object (SO) region pairs \\( \\pmb{P} \\) and their candidate relation texts \\( \\pmb{T} \\). First, we adopt BLIP to generate \\( N_{Cap} \\) captions for each image. Note that when \\( N_{Cap} = 1 \\), we generate the caption via beam search, a deterministic generation method; when \\( N_{Cap} > 1 \\), we generate captions via nucleus sampling [26], a stochastic generation methods with cumulative probability threshold set to 0.9. Nucleus sampling adds semantic diversity to the generated captions, which contributes to diversity in the relations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.514, + 0.468, + 0.65 + ], + "angle": 0, + "content": "Second, we adopt a scene graph parser [68] to parse the obtained captions into relation triplets. To filter out invalid parsed triplets, we perform string matching and keep those whose subjects and objects can be matched with any entities' names or entities' synonyms within the image [86]. This operation encloses a small set of possible SO region pairs \\( P \\) and possible relation texts \\( T \\) for the pairs (which are inputs to R-Tagger), without needing to traverse all possible pairs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.665, + 0.419, + 0.68 + ], + "angle": 0, + "content": "4.2.2 Relation Tagger via RLIPv2 Architecture" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.468, + 0.901 + ], + "angle": 0, + "content": "The R-Tagger aims to assign candidate relation texts \\( T \\) to candidate SO region pairs \\( P \\) for a given image. While one alternative is executing the pre-trained RLIPv2 model to perform SGG on object detection datasets to obtain pseudotriplets, the informative object annotations fail to be utilized directly during the execution of RLIPv2. As a result, the quality of pseudo-labels is degraded. A prior work [100] adopts a coarse rule-based pseudo-labelling method that employed a greedy matching algorithm to randomly assign one relation text to an SO region pair as long as the relation texts' corresponding SO texts match with the SO region pair. An \"overlap\" prior was applied to further filter the triplets (i.e., a triplet is deemed valid only if the subject and object are overlapped). This method, however," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "introduces excessive false positives, causing degraded pretraining. Thus, we propose to reuse the RLIPv2 architecture to perform relation prediction given ground-truth SO region pairs as shown in Figure Fig. 2(b)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.152, + 0.892, + 0.287 + ], + "angle": 0, + "content": "As outlined in Sec. 3, RLIPv2 also utilizes subject queries \\( Q_{s} \\) and object queries \\( Q_{o} \\) as input. To allow for the utilization of object annotations as the input, we propose to replace the detection queries \\( Q_{s} \\) and \\( Q_{o} \\) with object embeddings [40], which aims to encourage Parallel Entity Detection to reconstruct object representations and Sequential Relation Inference to recognize relations. Compared with Eq. (1), the probabilistic factorisation of R-Tagger during inference can be reformulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.295, + 0.892, + 0.331 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbb {P} (\\boldsymbol {R} | \\hat {\\boldsymbol {B}} _ {s}, \\hat {\\boldsymbol {B}} _ {o}, \\boldsymbol {C} _ {E}; \\boldsymbol {\\theta} _ {P a r}, \\boldsymbol {\\theta} _ {S e}) = \\tag {5} \\\\ \\mathbb {P} \\left(\\hat {\\boldsymbol {B}} _ {s}, \\hat {\\boldsymbol {B}} _ {o} \\mid \\hat {\\boldsymbol {B}} _ {s}, \\hat {\\boldsymbol {B}} _ {o}, \\boldsymbol {C} _ {E}; \\boldsymbol {\\theta} _ {P a r}\\right) \\cdot \\mathbb {P} \\left(\\boldsymbol {R} \\mid \\hat {\\boldsymbol {B}} _ {s}, \\hat {\\boldsymbol {B}} _ {o}, \\boldsymbol {C} _ {E}; \\boldsymbol {\\theta} _ {S e}\\right) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.892, + 0.445 + ], + "angle": 0, + "content": "where \\(\\hat{B}_s, \\hat{B}_o\\) denote the ground-truth SO boxes from the region pair set \\(P\\) that include their positions and labels); \\(\\tilde{B}_s, \\tilde{B}_o\\) denote contextualized SO representations. To allow for decoding, we embed \\(\\hat{B}_s, \\hat{B}_o\\) to have an equivalent dimension with queries. Specifically, we use MLPs to project positions and label text embeddings, and concatenate them along the channel dimension to obtain query-like input." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.446, + 0.892, + 0.476 + ], + "angle": 0, + "content": "Denoising training of R-Tagger. The training losses of R-Tagger are identical to RLIPv1:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.484, + 0.891, + 0.5 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda_ {1} \\mathcal {L} _ {l 1} + \\lambda_ {2} \\mathcal {L} _ {G I o U} + \\lambda_ {3} \\left(\\mathcal {L} _ {s} + \\mathcal {L} _ {o}\\right) + \\lambda_ {4} \\mathcal {L} _ {r} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.584 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}\\) is comprised of the \\(\\ell_1\\) loss for box regression \\(\\mathcal{L}_{l1}\\), GIoU loss [67] \\(\\mathcal{L}_{G IoU}\\), Cross-Entropy (CE) loss for subject and object classes \\(\\mathcal{L}_s, \\mathcal{L}_o\\), and Focal loss [52] for relations \\(\\mathcal{L}_r\\). \\(\\lambda_1, \\lambda_2, \\lambda_3, \\lambda_4\\) are set to 2.5, 1, 1, 1 as fixed weights to balance multi-task training [86, 89, 71]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.78 + ], + "angle": 0, + "content": "However, due to the identical input and training objectives of Parallel Entity Detection, the model will attempt to find a shortcut, i.e., identity mapping, to achieve the minimum loss value. To avoid this, we draw inspiration from [40] which adds noise to \\(\\hat{B}_s, \\hat{B}_o\\) during training. Specifically, we follow [40] to add center shifting and box scaling noise to box positions and add label flipping noise to box labels. The noise scale of center shifting and box scaling is set to 0.4, and the noise scale of label flipping is set to 0.2 following [40]. Furthermore, to prevent the information leakage between the same region with different noise, we apply attention masks to block the information flow between the same regions in Parallel Entity Detection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Inference of R-Tagger. After the training of R-Tagger, we can use it to infer relations without additional noise based on Eq. (5). For each inference, the maximum number of region pairs is \\( N_{Q} \\). If candidate SO region pairs exceed \\( N_{Q} \\), we infer multiple times and merge the results. To quantify the confidence of a relation, we calculate the product of the top-1 score from the softmax distribution over the subject, the object and the original relation sigmoid score. To" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21652" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.09, + 0.464, + 0.184 + ], + "angle": 0, + "content": "
NvNALIFRareNon-RareFull#ParamsFPS
1610.9213.9913.28246.8M18.93
2312.1214.0713.62206.6M21.49
3210.5714.0513.25193.2M22.15
6111.2613.9013.30179.8M23.17
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.192, + 0.47, + 0.248 + ], + "angle": 0, + "content": "Table 1: The effect of the sparsification of language encoding layers in Cross-Modal Fusion. Results are evaluated on HICODET under zero-shot (NF) setting. FPS (frames per second) is tested on a single NVIDIA A100 with a minibatch size 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.268, + 0.469, + 0.314 + ], + "angle": 0, + "content": "select pseudo-labels, we choose those whose relation confidence exceeds a threshold \\(\\eta\\). \\(\\eta\\) is set to 0.2 by default (details can be found in the Appendix)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.324, + 0.418, + 0.34 + ], + "angle": 0, + "content": "4.3. Pre-training, Fine-tuning and Inference" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.347, + 0.47, + 0.545 + ], + "angle": 0, + "content": "Regarding pre-training and fine-tuning of RLIPv2, we first merge results from Parallel Entity Detection and Sequential Relation Inference to obtain \\( N_{Q} \\) triplets. Next, we employ the bipartite matching algorithm originally proposed in [71] to match the predicted and ground-truth triplet annotations. The overall loss is identical to Eq. (6). The techniques introduced in RLIPv1, i.e. Label Sequence Extension, Relation Quality Labels and Relation Pseudo-Labels, are employed by default for a fair comparison. Regarding the inference of RLIPv2, we sort the relation confidence (defined in Sec. 4.2.2) of the correctly localised triplets (IoU > 0.5) and select the Top-K triplets. \\( K \\) is set to 100 by default following [86, 71, 45, 11]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.558, + 0.21, + 0.575 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.469, + 0.705 + ], + "angle": 0, + "content": "Pre-training datasets. To pre-train RLIPv2, we utilize VG [38], COCO [53] and Objects365 [69]. VG has \\(108k\\) images annotated with free-form relation and object annotations. COCO has \\(117k\\) images with only object annotations in 80 classes, and Objects365 has \\(1,742k\\) images with only object annotations in 365 classes. Thus, we use relational pseudo-labelling to tag relation labels for COCO and Objects365, enabling them to support relational pre-training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Downstream datasets. For HOI detection, we follow [71, 86, 89, 93] to evaluate on HICO-DET [4] and V-COCO [22]. For HICO-DET that contains 117 verbs and 80 objects, we evaluate under the Default setting on Full, Rare and Non-Rare sets. For V-COCO that contains 24 interactions and 80 objects, we evaluate following the official evaluation code [22] under two scenarios: \\(\\mathrm{AP}_{role}^{\\#1}\\) and \\(\\mathrm{AP}_{role}^{\\#2}\\). For SGG, we assess RLIPv2 on the widely-used Open Images v6 [39] dataset, which is annotated with 288 objects and 30 relations. We evaluate RLIPv2 using standard evaluation metrics [39, 96]: Recall@50 (R@50), weighted mean Average Precision for relation detection (\\(\\mathrm{wmAP}_{rel}\\)) and phrase detection (\\(\\mathrm{wmAP}_{phr}\\)). The final score is calculated" + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.089, + 0.892, + 0.203 + ], + "angle": 0, + "content": "
Gatingtanh()RareNon-RareFull
α10.4713.8313.05
a✓9.9113.5412.70
SE11.0713.8913.24
α12.1214.0713.62
ax10.9814.0713.36
SE11.0714.0013.32
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.209, + 0.892, + 0.238 + ], + "angle": 0, + "content": "Table 2: Comparisons of different gating functions introduced in Sec. 4.1. We report zero-shot (NF) results on HICO-DET." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.258, + 0.892, + 0.288 + ], + "angle": 0, + "content": "as: \\(\\mathrm{score}_{wtd} = 0.2 * \\mathrm{R} @ 50 + 0.4 * \\mathrm{wmAP}_{rel} + 0.4 * \\mathrm{wmAP}_{phr}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.893, + 0.667 + ], + "angle": 0, + "content": "Implementation details. To assess the effectiveness of RLIPv2, we choose to adopt DDETR [102] to compose RLIPv2-ParSeD and adopt DAB-DDETR [56] to compose RLIPv2-ParSeDA. To perform a fair comparison with previous works, we ensure that RLIPv2 has \\( N_v * N_{ALIF} = 6 \\) DDETR/DAB-DDETR encoding layers. For Parallel Entity Detection and Sequential Relation Inference, 3 layers are adopted following [86, 89, 71, 93]. \\( N_Q \\) is set to 100 during pre-training and fine-tuning, except when we finetune on HICO-DET where \\( N_Q \\) is set to 64 following [93]. Regarding model initialization, we use COCO detection parameters as initialisation when using VG or VG and COCO for pre-training; when using VG, COCO and Objects365 for pre-training, we use COCO and Object365 detection parameters as initialisation. Regarding the configuration of minibatch sizes and learning rate (LR), we set the minibatch size to 64, LR for the text encoder to 1.41e-5 and LR for other modules to 1.41e-4 when using ResNet-50 [25] and Swin-T [59]; We set the minibatch size to 32, LR for the text encoder to 1e-5 and LR for other modules to 1e-4 when using Swin-L [59]. RLIPv2 and R-Tagger are pre-trained and fine-tuned for 20 epochs unless otherwise stated, with LR dropping by a factor of 10 at the 15th epoch. For the BLIP captioner, we adopt the ViT-L/16 [14] model fine-tuned on COCO Caption [8]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.676, + 0.655, + 0.692 + ], + "angle": 0, + "content": "5.1. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.699, + 0.892, + 0.775 + ], + "angle": 0, + "content": "We perform the ablation study using RLIPv2-ParSeD with ResNet-50 as the backbone, and VG as the pre-training dataset unless otherwise stated. We pre-train for 20 epochs and evaluate performance on HICO-DET under the zero-shot with no fine-tuning (NF) setting." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.787, + 0.813, + 0.802 + ], + "angle": 0, + "content": "5.1.1 Asymmetric Language-Image Fusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Sparsification of the language layers. First of all, we ablate on the number of language layers to investigate the effect of sparsifying language encoding layers in CrossModal Fusion. As introduced in Sec. 4.1, dense language layers cause difficult training. To avoid training collapse, we compute classification losses \\((\\mathcal{L}_s,\\mathcal{L}_o\\) and \\(\\mathcal{L}_r)\\) using all" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21653" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.59, + 0.187 + ], + "angle": 0, + "content": "
ModelPre-trainingFully-finetuningFPS
Ep.TimeZero-shot (NF)Ep.Result
RLIPv1-ParSeD5025.9h11.20 / 14.73 / 13.926024.67 / 32.50 / 30.7021.89
RLIPv2-ParSeD2010.9h12.12 / 14.07 / 13.622026.47 / 33.51 / 31.8921.49
RLIPv1-ParSeDA5027.2h11.34 / 14.56 / 13.826022.85 / 30.87 / 29.0319.41
RLIPv2-ParSeDA2011.3h13.03 / 14.98 / 14.532027.01 / 35.21 / 33.3218.94
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.194, + 0.593, + 0.251 + ], + "angle": 0, + "content": "Table 3: Comparisons of RLIPv1 and RLIPv2 under zero-shot (NF) and fully-finetuning settings on HICO-DET pre-trained on VG. Results are reported on Rare/Non-Rare/Full sets. FPS is tested on a single NVIDIA A100 with minibatch size 1. Pretraining time is tested on 8 NVIDIA A100. \"Ep.\" denotes number of epochs." + }, + { + "type": "table", + "bbox": [ + 0.604, + 0.09, + 0.896, + 0.184 + ], + "angle": 0, + "content": "
InitializationRareNon-RareFull
COCO (default)12.1214.0713.62
R-Tagger12.5513.6413.39
w/o noise9.9412.7412.09
w/o attn masks8.5511.2210.61
" + }, + { + "type": "table_caption", + "bbox": [ + 0.601, + 0.193, + 0.892, + 0.249 + ], + "angle": 0, + "content": "Table 4: The quality of R-Tagger parameters. Results are evaluated using RLIPv2-ParSeD with ResNet-50 under zero-shot (NF) setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.27, + 0.47, + 0.405 + ], + "angle": 0, + "content": "intermediate language features rather than using only the last layer of language features in Cross-Modal Fusion. Results are shown in Tab. 1. Our findings suggest that sparsifying the language encoder does not compromise zero-shot performance and improves parameter efficiency. We attribute this to overfitting effects on upstream datasets impairing models' generalization. We choose \\( N_{v} = 2 \\) and \\( N_{ALIF} = 3 \\) as the default hyper-parameters for the following experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.406, + 0.471, + 0.557 + ], + "angle": 0, + "content": "The choice of the gating function \\( \\mathrm{G}(\\boldsymbol{x}) \\). To investigate the effect of the gating function on cross-modal fusion, we experiment with variants of the gating function as described in Sec. 4.1. The results are shown in Tab. 2. We note that tanh consistently degrades performance for the three gating methods. We conjecture that the output range of tanh can constrain the magnitude of the features to be fused, thus limiting the performance. Based on the results, we choose the simplest one: the learnable scalar gating method parameterised by \\( \\alpha \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.558, + 0.471, + 0.74 + ], + "angle": 0, + "content": "Comparisons of RLIPv2 with RLIPv1. To compare the architectural benefit of RLIPv2 with RLIPv1, we adopt DDETR [102] and DAB-DDETR [56] to follow two designs, and evaluate performance under zero-shot (NF) and fully-finetuning setting. Results are shown in Tab. 3. From this table, we can observe that by modifying the architecture without compromising much inference speed, RLIPv2 generally outperforms its RLIPv1 counterpart. Specifically, RLIPv2 obtains comparable zero-shot results to RLIPv1, while costing about \\(0.4 \\times\\) pre-training time. In terms of fine-tuning results, RLIPv2 surpasses RLIPv1 with \\(0.33 \\times\\) fine-tuning time due to earlier and deeper fusion." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.755, + 0.323, + 0.77 + ], + "angle": 0, + "content": "5.1.2 Relational Pseudo-labelling" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.469, + 0.81 + ], + "angle": 0, + "content": "By default, we use RLIPv2-ParSeD with ResNet-50 backbone as the basic structure of R-Tagger." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "The necessity of denoising pre-training and attention masks for R-Tagger. If noise is not added during R-Tagger's pre-training, the loss will fluctuate instead of steadily decreasing as the optimization proceeds. If attention masks are not utilized to prevent information leakage, the model will tend to learn an identity mapping, thus de" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.267, + 0.892, + 0.395 + ], + "angle": 0, + "content": "
Tagging MethodOverlapRareNon-RareFull
Greedy [100]×11.1511.6511.55
✓13.1614.7014.35
CLIP (ViT-L/14) [65]×12.6612.7612.74
✓14.6314.9414.87
R-Tagger (ResNet-50)×15.3315.5415.49
✓15.3615.3715.36
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.402, + 0.892, + 0.46 + ], + "angle": 0, + "content": "Table 5: Comparisons of relation tagging methods. \"Overlap\" denotes the \"overlap\" prior for SO pairs introduced in Sec. 4.2.2. We report zero-shot (NF) results pre-trained on VG and COCO. We use oracle captions from COCO Caption [8] (\\(N_{Cap} = 5\\))." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.468, + 0.889, + 0.589 + ], + "angle": 0, + "content": "
Caption typeNCapRareNon-RareFull
Oracle515.3315.5415.49
BLIP (beam)19.8612.0211.52
BLIP (nucleus)514.6714.7614.74
BLIP (nucleus)1015.0815.1015.09
BLIP (nucleus)2014.2414.9114.75
BLIP (nucleus)*512.3114.3713.89
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.596, + 0.892, + 0.665 + ], + "angle": 0, + "content": "Table 6: Comparisons of different caption types. \"beam\" and \"nucleus\" denote beam search and nucleus sampling. \"Oracle\" denotes captions from COCO Caption. By default, we adopt COCO Caption fine-tuned BLIP model. * denotes that we adopt the pretrained BLIP model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.822 + ], + "angle": 0, + "content": "grading its ability to infer relations. R-Tagger is pre-trained for 20 epochs. To assess the quality of R-Tagger's parameters, thanks to R-Tagger's identical structure to RLIPv2-ParSeD, we initialize RLIPv2-ParSeD with R-Tagger's parameters and pre-train for 10 epochs. We evaluate the zero-shot (NF) performance on HICO-DET as shown in Tab. 4. We observe that removing additional noise or attention masks both impair performance, highlighting their importance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Comparisons of different relation tagging strategies. We compare R-Tagger with other two methods: (i) the greedy matching algorithm [100]; (ii) the CLIP [65] tagging method. Specifically, to tag relations for a given SO region pair with a candidate relation text, the CLIP tagging" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21654" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.09, + 0.462, + 0.164 + ], + "angle": 0, + "content": "
DatasetRelation candidateRareNon-RareFull
VG-12.1214.0713.62
VG+COCOBLIP15.0815.1015.09
VG+COCOSelection from VG10.3411.3311.11
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.172, + 0.468, + 0.201 + ], + "angle": 0, + "content": "Table 7: Comparisons of methods to generate relation candidate sets. We report zero-shot (NF) results on HICO-DET." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.213, + 0.468, + 0.272 + ], + "angle": 0, + "content": "
VGVG+COCOVG+COCO+O365
ResNet-5013.03 / 14.98 / 14.5315.00 / 16.60 / 16.2319.64 / 17.24 / 17.79
Swin-T13.01 / 16.06 / 15.3517.13 / 18.74 / 18.3721.24 / 19.47 / 19.87
Swin-L19.93 / 18.74 / 19.0222.59 / 21.09 / 21.4427.97 / 21.90 / 23.29
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.282, + 0.468, + 0.324 + ], + "angle": 0, + "content": "Table 8: Model and dataset scaling experiments using RLIPv2-ParSeDA. Results are evaluated on HICO-DET Rare/Non-Rare/Full sets under zero-shot (NF) setting." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.337, + 0.472, + 0.555 + ], + "angle": 0, + "content": "
ModelBackboneExtramR@50R@50wmAPscore_wtd
relphr
VCTree [73]X101-F-33.9174.0834.1633.1140.21
G-RCNN [82]X101-F-34.0474.5133.5134.2141.84
Motifs [90]X101-F-32.6871.6329.9131.5938.93
Unbiased [72]X101-F-35.4769.3030.7432.8039.27
GPS-Net [54]X101-F-35.2674.8132.8533.9841.69
RelDN [96]R101-36.8072.7529.8730.4238.67
BGNN [46]R101-39.4174.9331.1531.3740.00
SGTR [45]R101-42.6159.9136.9838.7342.28
RelTR [11]R50--64.4734.1737.4441.54
RLIPv2-ParSeDR50*-44.5858.0443.3043.1246.18
R50*-44.8860.2044.7343.3647.28
R50†-45.5961.1545.7143.7348.01
RLIPv2-ParSeDAR50(i)50.4263.3547.6545.2349.82
R50(ii)52.0764.5349.1446.1451.01
R50(iii)51.3165.9949.5445.7151.30
Swin-T(iii)59.6168.8152.7048.0154.05
Swin-L(iii)64.7272.4956.3850.7057.34
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.565, + 0.468, + 0.634 + ], + "angle": 0, + "content": "Table 9: Comparisons with previous methods on Open Images v6 SGG benchmark. X101-F denote ResNeXt-101 FPN [80]. \\( {}^{ * } \\) and \\( {}^{ \\dagger } \\) denote ImageNet pretrained and COCO object detection pretrained. \"Extra\" denotes extra relations adopted from (i) VG, (ii) VG+COCO and (iii) VG+COCO+O365." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.468, + 0.901 + ], + "angle": 0, + "content": "method clips the minimum bounding box of the SO region pair, creates two prompts (\"a photo of {subject} {relation} {object}\" and \"a photo of {subject} not interacting with {object}\" are adopted as positive and negative prompts.), and performs zero-shot prediction. If the softmax probability of the positive prompt is greater than a pre-defined threshold, we tag this relation text to this SO region pair. (We traverse the threshold and find the optimal one for the CLIP tagging method, as detailed in the Appendix.) We also ablate on the \"overlap\" prior [100] to observe whether a given tagging method relies on strong prior knowledge to filter out false positive relations. The results are shown in Tab. 5. From this table, we conclude that greedy matching and CLIP tagging method generate a significant number of low-quality non-overlapped triplets. Thus, the \"overlap\" prior is essential for them. R-Tagger, however, suf" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.09, + 0.894, + 0.205 + ], + "angle": 0, + "content": "
MethodBackboneUC-RFUC-NF
VCL [27]ResNet-5010.06 / 24.28 / 21.4316.22 / 18.52 / 18.06
ATL [28]ResNet-509.18 / 24.67 / 21.5718.25 / 18.78 / 18.67
FCL [29]ResNet-5013.16 / 24.23 / 22.0118.66 / 19.55 / 19.37
GEN-VLKT [51]ResNet-5021,36 / 32.91 / 30.5625.05 / 23.38 / 23.71
RLIPv1-ParSeD [86]ResNet-5016.43 / 30.59 / 27.7616.99 / 24.71 / 22.93
RLIPv1-ParSe [86]ResNet-5019.19 / 33.35 / 30.5220.27 / 27.67 / 26.19
RLIPv2-ParSeDAResNet-5021.45 / 35.85 / 32.9722.81 / 29.52 / 28.18
RLIPv2-ParSeDASwin-T26.95 / 39.92 / 37.3221.07 / 35.07 / 32.27
RLIPv2-ParSeDASwin-L31.23 / 45.01 / 42.2622.65 / 40.51 / 36.94
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.214, + 0.892, + 0.257 + ], + "angle": 0, + "content": "Table 10: Comparisons with methods on HICO-DET under UC-RF and UC-NF settings. We adopt ResNet-50 as the backbone. Results are reported on Unseen/Seen/Full sets." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.265, + 0.894, + 0.344 + ], + "angle": 0, + "content": "
MethodBackbone1% Data10% Data
RLIPv1-ParSeD [86]ResNet-5016.22 / 18.92 / 18.3015.89 / 23.94 / 22.09
RLIPv1-ParSe [86]ResNet-5017.47 / 18.76 / 18.4620.16 / 23.32 / 22.59
RLIPv2-ParSeDAResNet-5022.13 / 24.51 / 23.9623.28 / 30.02 / 28.46
RLIPv2-ParSeDASwin-T24.26 / 28.92 / 27.8528.31 / 32.93 / 31.87
RLIPv2-ParSeDASwin-L31.89 / 32.32 / 32.2234.75 / 38.27 / 37.46
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.354, + 0.892, + 0.381 + ], + "angle": 0, + "content": "Table 11: Comparisons on HICO-DET under few-shot settings. Results are reported on Rare/Non-Rare/Full sets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.402, + 0.892, + 0.478 + ], + "angle": 0, + "content": "fers a slight performance drop when using the \"overlap\" prior, indicating that R-Tagger generates more reliable non-overlapped triplets. Besides, although CLIP is pre-trained on a massive quantity of language-image pairs, it struggles in recognizing relations, which R-Tagger is expert in." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.479, + 0.893, + 0.84 + ], + "angle": 0, + "content": "Comparisons of different caption types. Previous experiments demonstrate that oracle COCO captions can benefit pre-training. However, most datasets lack such high-quality captions. Thus, BLIP provides an alternative for caption generation. We conduct experiments on various caption types, as shown in Tab. 6. From this table, we can observe that: (i) BLIP-generated captions achieve a decent performance compared to oracle captions, indicating the practicality of adopting generated captions for pseudolabelling. (ii) If we compare BLIP model with different parameters (COCO Caption fine-tuned or only pre-trained), we can see that the fine-tuned model generates better captions with more boost on the Rare set \\((12.31\\rightarrow 14.67)\\). We conjecture that the caption quality of the curated style dataset COCO Caption is better than pre-training captions harvested from the web. (iii) By adopting generated captions, we can increase the number of captions per image, thus diversifying the relations contained in captions and boost RLIPv2 \\((11.52\\rightarrow 15.09)\\). Besides, although datasets like Conceptual Caption [70] (CC3M) also provide captions, the quantity of captions (average one caption per image) is not enough to describe many relations in an image. In comparison, our pipeline can work without caption annotation while performing better." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The necessity of using captioners. By default, we use BLIP to generate relation texts. Another option is to query all possible SO pairs and select all possible relation texts from VG as it contains an enormous quantity of relations" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21655" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.122, + 0.089, + 0.849, + 0.356 + ], + "angle": 0, + "content": "
ModelBackboneExtra RelationsHICO-DETV-COCO
Zero-shot (NF)Fully-finetuningAP#1roleAP#2role
InteractNet [21]R50-FPN--7.16 / 10.77 / 9.9440.0-
UnionDet [35]R50-FPN--11.72 / 19.33 / 17.5847.556.2
PPDM [50]HG104--13.97 / 24.32 / 21.94--
HOTR [36]R50--17.34 / 27.42 / 25.1055.264.4
QPIC [71]R50--21.85 / 31.23 / 29.0758.861.0
OCN [89]R50--25.56 / 32.51 / 30.9164.266.3
CDN [93]R50--27.39 / 32.64 / 31.4461.763.8
GEN-VLKT [51]R50--29.25 / 35.10 / 33.7562.464.5
QAHOI [5]Swin-L*--29.80 / 37.56 / 35.78--
UniVRD [98]ViT-H/14†--31.65 / 39.99 / 38.0765.866.9
RLIPv1-ParSeD [86]R50VG11.20 / 14.73 / 13.9224.67 / 32.50 / 30.7061.763.8
RLIPv1-ParSe [86]R50VG15.08 / 15.50 / 15.4026.85 / 34.63 / 32.8461.964.2
RLIPv2-ParSeDAR50VG13.03 / 14.98 / 14.5327.01 / 35.21 / 33.3263.065.1
RLIPv2-ParSeDAR50VG+COCO15.00 / 16.60 / 16.2327.89 / 35.27 / 33.5764.566.7
RLIPv2-ParSeDAR50VG+COCO+O36519.64 / 17.24 / 17.7929.61 / 37.10 / 35.3865.968.0
RLIPv2-ParSeDASwin-TVG+COCO+O36521.24 / 19.47 / 19.8733.66 / 40.07 / 38.6068.870.8
RLIPv2-ParSeDASwin-LVG+COCO+O36527.97 / 21.90 / 23.2943.23 / 45.64 / 45.0972.174.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.363, + 0.892, + 0.42 + ], + "angle": 0, + "content": "Table 12: Comparisons with previous methods on HICO-DET and V-COCO. Results on HICO-DET are reported on Rare/Non-Rare/Full sets. R50 and HG denote ResNet-50 [25] and Hourglass [61]. * denotes the backbone is pre-trained with \\(384 \\times 384\\) resolution, while others use \\(224 \\times 224\\). † indicates the backbone is pre-trained using LiT [92], then fine-tuned on Objects365, COCO and HICO with the objective of object detection." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.47, + 0.5 + ], + "angle": 0, + "content": "(36,515 kinds). Then, we run R-Tagger with selected relation texts as \\( T \\) and all region pairs as \\( P \\). The results are shown in Tab. 7. We can observe that selecting from VG generates low-quality candidates, harming performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.471, + 0.713 + ], + "angle": 0, + "content": "Model scaling and dataset scaling. Equipped with the labelling pipeline introduced above, we can scale RLIPv2 to larger models and datasets. In Tab. 8, we adopt RLIPv2-ParSeDA as the base architecture and observe the benefit of scaling by zero-shot (NF) performance on HICO-DET. In terms of data, adding COCO and Objects365 can both boost performance, and the benefit of adding data exhibits a log scaling trend [9]. Models pre-trained with Objects365 consistently have better Rare result, which we attribute to the distribution misalignment of Objects365 and HICO-DET [17]. In terms of models, switching to stronger backbone models can improve the data efficiency at the cost of larger amounts of computation. Regarding scaling experiments using RLIPv2-ParSeD, we present it in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.726, + 0.388, + 0.741 + ], + "angle": 0, + "content": "5.2. Comparisons with State-of-the-Arts" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Scene graph generation. We compare RLIPv2 series models with previous methods on Open Images v6 in Tab. 9. We also report mean Recall@50 (mR@50) to better show the usefulness of RLIPv2. Our findings suggest that (i) with the assistance of DDETR family models, RLIPv2 can serve as a strong baseline without any pre-training; (ii) naive object detection pre-training can boost the performance to some extent \\((47.28 \\rightarrow 48.01)\\), while pre-training on VG can further boost the performance especially on mR@50 \\((45.59 \\rightarrow 50.42)\\); (iii) adding pseudo-labelled relation an-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.892, + 0.514 + ], + "angle": 0, + "content": "notations in pre-training or switching to stronger backbones both contribute to better performance. However, the boost of adding Objects365 is negligible. We attribute this to the distribution discrepancy of Objects365 and Open Images v6." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.892, + 0.644 + ], + "angle": 0, + "content": "HOI Detection under UC-NF and UC-RF settings. We report results in Tab. 10 on unseen combinations (UC) under UC-RF and UC-NF settings following [27, 28]. We only fine-tune for 10 epochs under UC-NF setting. Our method outperforms previous methods except on one metric. We attribute this to the strong transferability of CLIP features that GEN-VLKT adopts. Regarding experiments using RLIPv2-ParSeD, we present it in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.651, + 0.892, + 0.758 + ], + "angle": 0, + "content": "Few-shot HOI Detection. We follow [86] to only fine-tune 10 epochs on partial data (1% and 10%), results of which are shown in Tab. 11. We can observe significant improvements upon all metrics by scaling up pre-training compared with previous methods. This improves the practicality of RLIPv2 in low-data scenarios. Regarding experiments using RLIPv2-ParSeD, we present it in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "HOI detection under fully-finetuning and zero-shot (NF) settings. We compare the performance of RLIPv2 series models with previous methods on HICO-DET and V-COCO in Tab. 12. We can observe from the table that (i) dataset and model scaling can both boost the final performance on two datasets; (ii) on HICO-DET, the benefit of pre-training is more prominent on zero-shot than fully-finetuning, especially on the Rare set. Regarding experiments using RLIPv2-ParSeD, we present it in the Appendix." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21656" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.075, + 0.449, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.3, + 0.47, + 0.342 + ], + "angle": 0, + "content": "Figure 4: (a) Visualization of pseudo-labelled relations on COCO. Left column: R-Tagger; right column: CLIP tagging method. (b) Visualization of failure cases of R-Tagger." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.353, + 0.269, + 0.37 + ], + "angle": 0, + "content": "5.3. Qualitative Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.377, + 0.47, + 0.497 + ], + "angle": 0, + "content": "Comparisons of relation tagging methods. We visualize three examples to compare the quality of pseudolabelled relations by R-Tagger and CLIP tagging method in Fig. 4(a). Generally, CLIP is more object-centric and position-agnostic, and thus struggles in discriminating relations. It tends to tag relations as long as the subject and object have strong co-occurrence priors. However, R-Tagger tags more reasonable relations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.498, + 0.47, + 0.575 + ], + "angle": 0, + "content": "Failure cases of R-Tagger. Recognizing relations is challenging, especially in complex scenes. In Fig. 4(b), we present three examples of R-Tagger's failure cases. In particular, we observe failure cases when the scene contains multiple similar subjects or objects." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.587, + 0.196, + 0.603 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.471, + 0.763 + ], + "angle": 0, + "content": "In this paper, we propose RLIPv2, a fast converging model that enables the scaling of relational pre-training to larger-scale pseudo-labelled datasets. Comprehensive experiments on HOI detection and scene graph generation under various settings demonstrate its effectiveness compared to previous methods. We anticipate that our work can galvanize further research efforts to focus on relational reasoning, fostering advancements that yield tangible benefits not only to the research community but also to broader society and humanity." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.772, + 0.224, + 0.789 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.9 + ], + "angle": 0, + "content": "We would like to extend our sincere gratitude to the anonymous reviewers for their invaluable feedback. Additionally, we appreciate the Fundamental Vision Intelligence Team of Alibaba DAMO Academy for their generous provision of essential computational resources. This research received support from the National Natural Science Foundation of China under Grant No. 62173298 and was addi" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "tionally backed by Alibaba Group via the Alibaba Research Intern Program." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.137, + 0.597, + 0.151 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.516, + 0.162, + 0.892, + 0.231 + ], + "angle": 0, + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, et al. 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However, hindered by the slow convergence of RLIPv1 architecture and the limited availability of existing scene graph data, scaling RLIPv1 is challenging. In this paper, we propose RLIPv2, a fast converging model that enables the scaling of relational pre-training to large-scale pseudo-labelled scene graph data. To enable fast scaling, RLIPv2 introduces Asymmetric Language-Image Fusion (ALIF), a mechanism that facilitates earlier and deeper gated cross-modal fusion with sparsified language encoding layers. ALIF leads to comparable or better performance than RLIPv1 in a fraction of the time for pre-training and fine-tuning. To obtain scene graph data at scale, we extend object detection datasets with free-form relation labels by introducing a captioner (e.g., BLIP) and a designed Relation Tagger. The Relation Tagger assigns BLIP-generated relation texts to region pairs, thus enabling larger-scale relational pre-training. Through extensive experiments conducted on Human-Object Interaction Detection and Scene Graph Generation, RLIPv2 shows state-of-the-art performance on three benchmarks under fully-finetuning, few-shot and zero-shot settings. Notably, the largest RLIPv2 achieves 23.29mAP on HICO-DET without any fine-tuning, yields 32.22mAP with just $1\%$ data and yields 45.09mAP with $100\%$ data. Code and models are publicly available at https://github.com/JacobYuan7/RLIPv2. + +# 1. Introduction + +The pretraining-finetuning paradigm has achieved major breakthroughs in vision and language domains [58, 13, + +![](images/7560613fa90b2d6d31e9a47fa3f982bb4c342884fe937d906b1704e9b4a5445c.jpg) +Figure 1: Left: Fine-tuning comparison on HICO-DET. Right: Pre-training epoch and zero-shot (NF) comparison on HICO-DET. Except where stated, RLIPv2-ParSeDA architecture is adopted. + +![](images/bd75ed80e18b9ed3dd7e4fe9d1fb69a3213f2f65243d54e895fbdb4584423403.jpg) + +23, 103, 65, 77]. In this context, a number of particularly notable results have been obtained through aligned Vision-Language Pre-training (VLP) [65, 42, 41, 78, 95, 91]. These research efforts have typically employed a robust base model [14, 25, 12, 74] that is trained on language-image paired data to produce foundation models. + +RLIPv1 [86] presents the first attempt to specifically align vision representations and relational texts using VLP. By pre-training on open-vocabulary scene graph data like Visual Genome (VG) [38], RLIPv1 demonstrates its usefulness in zero-shot, few-shot and fully-finetuned Human-Object Interaction (HOI) Detection. Although RLIPv1 is proven effective, we find it challenging to scale for the following reasons: + +(i) Model perspective: RLIPv1 converges slowly, as exemplified by DETR [3]-based RLIPv1, which requires 150/90 epochs to converge during pre-training/fine-tuning. Even when building on Deformable DETR (DDETR) [102] and DAB-DDETR [56], 50/60 epochs are still required. +(ii) Data perspective: as observed by the authors of RLIPv1, data with relation triplet annotations is scarce, impeding RLIPv1's scaling. Annotating triplets in the form of $\langle$ subject, relations, object $\rangle$ is both time- and cost-intensive. + +To resolve the aforementioned challenges, we introduce RLIPv2, a fast converging model that enables relational pretraining on larger-scale pseudo-labelled scene graph data. + +From both the model and data perspectives, we summarize the contributions of RLIPv2 as follows. + +From the model perspective, we observe that the slow convergence of DDETR can be attributed to the late language-image fusion strategy: fusion after decoding. Prior works [15, 44] have demonstrated an earlier and deeper fusion mechanism facilitates cross-modal alignment. In light of this, we propose Asymmetric Language-Image Fusion (ALIF) in RLIPv2 that encourages fusion in the encoding stage with sparsified language layers. Without sacrificing inference speed thanks to sparsification, RLIPv2 requires only 20 epochs to pre-train and fine-tune based on DDETR family models [102, 56] as shown in Fig. 1, while performing better than or comparably to RLIPv1. + +From the data perspective, we leverage well-established object detection datasets [53, 69, 39]. Specifically, we extend these datasets with relational annotations by pseudolabelling. To perform pseudo-labelling, we must tackle two challenges: (i) sorting out the relations contained in the image and (ii) tagging relation texts to region pairs. Regarding the first challenge, we employ external captioners (e.g. BLIP [42]) that generate captions containing relation descriptions. Regarding the second challenge, we reuse RLIPv2 model as a Relation Tagger (R-Tagger) that enables assigning the generated open-vocabulary relation texts to region pairs. Equipped with such a pipeline, we investigate the scaling behavior of both the model and the data for RLIPv2, which demonstrates improved zero-shot, few-shot and fine-tuning performance. + +Furthermore, we introduce Scene Graph Generation (SGG), an analogously defined task to HOI detection for evaluating RLIPv2. RLIPv2 achieves state-of-the-art performance on Open Images v6 [39] for SGG, which underscores its robustness and efficacy in tackling relational reasoning tasks. + +# 2. Related Work + +Language-image pre-training for detection. Recently, there has been a growing interest in learning visual representations from language supervision [42, 41, 65, 1, 32, 34, 15, 44, 95, 76]. This paradigm of learning from language supervision has also proven effective in improving detection performance. MDETR [34] was the first work to learn region-text correspondences in an end-to-end manner, while X-DETR [2] improved upon MDETR by removing the cross-modal fusion part that improves its training efficiency. GLIP [44] extended this line of research by scaling to web-scale data, leading to significant advances in zero-shot object detection and data efficiency. DetCLIP [84] proposed a paralleled concept formulation and a concept dictionary to enable semantically rich region-text alignment. RLIPv1 [86] was the first work to seek language-image alignment via relations, and our work follows its footsteps + +to achieve fast scaling of relational pre-training. + +End-to-end HOI detection and scene graph generation. Relations can interpret visual content in a fine-grained perspective [10, 31, 33]. Detecting and recognizing relations utilizing HOI detection and scene graph generation have been verified effective in image captioning [85], image retrieval [33, 75], synthesis [83, 18], activity understanding [31, 88, 87] and . The aim of these tasks is to detect relation triplets from a given input image. Before the emergence of DETR [3], the commonly adopted pipeline was to adopt an off-the-shelf object detector [66, 24] and design reasoning modules to infer relations [20, 19, 63, 49, 48, 90, 7, 54, 46, 47, 81]. Initial end-to-end design efforts extended detectors to support relation recognition [50, 99, 82, 35, 55]. Further attempts focus on the adaptation of DETR to the field of HOI detection [89, 6, 36, 104, 71, 93, 94, 79, 37, 57, 101, 62, 64, 97] and SGG [45, 11]. RLIPv1 [86] demonstrated the effectiveness of relational pre-training in improving performance and data efficiency. RLIPv2 builds upon RLIPv1, but seeks to solve its scaling problem. The most related work [100] also seeks scaling with the help of language. However, it remains a two-stage detection pipeline, lacks semantic richness and adopts a naive matching algorithm that hinders its performance. + +# 3. Recap of RLIPv1 + +In this section, we will briefly review RLIPv1 [86], a model that leverages both entity and relation descriptions to perform VLP and that forms the basis for our approach. As triplet detection architecture, RLIPv1 proposes a ParSeD model that allocates decoupled embeddings for subjects, objects and relations. The collective model RLIPv1-ParSeD consists of three stages: Parallel Entity Detection, Sequential Relation Inference and Cross-Modal Fusion, as shown in Fig. 2(a). + +For Parallel Entity Detection, RLIPv1-ParSeD defines two sets of queries $Q_{s}, Q_{o} \in \mathbb{R}^{N_{Q} \times D}$ with $N_{Q}$ pairs of subjects and objects to perform subject and object detection. For Sequential Relation Inference, the model generates relation queries $Q_{r} \in \mathbb{R}^{N_{Q} \times D}$ based on the decoded subject and object queries $\tilde{Q}_{s}, \tilde{Q}_{o} \in \mathbb{R}^{N_{Q} \times D}$ , and performs decoding to obtain $\tilde{Q}_{r} \in \mathbb{R}^{N_{Q} \times D}$ for relation recognition. The design of RLIPv1-ParSeD obeys the following probabilistic factorization: + +$$ +\begin{array}{l} \mathbb {P} \left(\boldsymbol {G} \mid \boldsymbol {Q} _ {s}, \boldsymbol {Q} _ {o}, \boldsymbol {C} _ {E}; \boldsymbol {\theta} _ {P a r}, \boldsymbol {\theta} _ {S e}\right) = \tag {1} \\ \mathbb {P} \left(\boldsymbol {B} _ {s}, \boldsymbol {B} _ {o} \mid \boldsymbol {Q} _ {s}, \boldsymbol {Q} _ {o}, \boldsymbol {C} _ {E}; \boldsymbol {\theta} _ {P a r}\right) \cdot \mathbb {P} \left(\boldsymbol {R} \mid \boldsymbol {B} _ {s}, \boldsymbol {B} _ {o}, \boldsymbol {C} _ {E}; \boldsymbol {\theta} _ {S e}\right) \\ \end{array} +$$ + +where $C_E$ denotes features from the DDETR encoder; $\theta_{Par},\theta_{Se}$ denote parameters for Parallel Entity Detection + +![](images/809772b0dbebb81a18fa65cc11dde1fb8e0f984dfa613a154803b94d7c597e00.jpg) +(a) + +![](images/b78474a5ee4a6c050624c514035213567af73368922067822a98756661849224.jpg) +(b) +Figure 2: The overview of (a) RLIPv1-ParSeD and (b) RLIPv2-ParSeD and R-Tagger. The red part (loss calculation and noise injection) is only valid during training. In (a), Cross-Modal Fusion is achieved by the cross encoder. In (b), Cross-Modal Fusion is achieved by ALIF. The two architectures have an equivalent number of DDETR layers. + +and Sequential Relation Inference; $B_{s}, B_{o}, R$ are sets of detected subject boxes, object boxes and relations, respectively. They collectively comprise the detection results $G$ . + +For Cross-Modal Fusion, RLIPv1-ParSeD appends additional Transformer encoding layers [74, 34, 43] to perform language-image feature fusion on top of the decoded relation features $\tilde{Q}_r$ , entity label features $L_{E} \in \mathbb{R}^{N_{E} \times D}$ and relation label features $L_{R} \in \mathbb{R}^{N_{R} \times D}$ . $L_{E}, L_{R}$ are extracted from RoBERTa [58]. + +# 4. Methodology + +In this section, we will introduce: (i) Asymmetric Language-Image Fusion (ALIF) as an efficient CrossModal Fusion mechanism in RLIPv2, as shown in Fig. 2(b); (ii) the overall framework of extending the off-the-shelf object detection datasets [53, 69] to support relational pretraining. + +# 4.1. Asymmetric Language-Image Fusion + +The core idea underpinning ALIF is to perform efficient cross-modal fusion in the early stages of RLIPv2 as highlighted by [15, 44]. Unlike RLIPv1 that encourages cross-modal alignment for entities and relations after the decoding phase, ALIF performs this during the detection encoding phase. This is particularly challenging for DDETR's encoder, since it relies on deformable attention that makes it challenging to adopt dedicated encoder layers during the detection encoding phase like [34, 60, 16]. + +To address this, we propose ALIF, a mechanism that leverages DDETR encoding for the vision branch, RoBERTa encoding for the language branch and gated cross-attention for fusion. In contrast to previous work that encodes image and language with an equivalent number of layers [34, 16, 44, 15], we experimentally find that excessive RoBERTa layers do not improve its generalization + +capability due to its potential for overfitting to pre-trained data. Moreover, such a paradigm results in training difficulty due to the increased model complexity. As a result, we perform DDETR encoding densely while performing RoBERTa encoding sparsely. We denote the vision features from the backbone as $C^{(0)}$ and language features from RoBERTa as $L^{(0)}$ (the concatenation of $L_{E}$ and $L_{R}$ ). The first ALIF module can be formulated as: + +$$ +\tilde {\boldsymbol {C}} ^ {(0)}, \tilde {\boldsymbol {L}} ^ {(0)} = \operatorname {C r o s s - a t t n} \left(\boldsymbol {C} ^ {(0)}, \boldsymbol {L} ^ {(0)}\right) \tag {2} +$$ + +$$ +\boldsymbol {C} ^ {\left(N _ {v}\right)} = \mathrm {D D E T R} ^ {N _ {v}} \left(\boldsymbol {C} ^ {(0)} + \mathrm {G} \left(\tilde {\boldsymbol {C}} ^ {(0)}\right)\right) \tag {3} +$$ + +$$ +\boldsymbol {L} ^ {(1)} = \operatorname {R o B E R T a} ^ {1} \left(\boldsymbol {L} ^ {(0)} + \mathrm {G} \left(\tilde {\boldsymbol {L}} ^ {(0)}\right)\right) \tag {4} +$$ + +where $\tilde{C}^{(0)}$ denotes language features aggregated by cross attention, and $\tilde{L}^{(0)}$ is analogously defined; $N_{v}$ is the number of DDETR layers in one ALIF; $\mathrm{G}(\pmb{x})$ defines a gating function that gates the aggregated cross-modal features. Note that $C_E$ is $C^{(N_v)}$ after stacking $N_{ALIF}$ ALIF layers for encoding. For the instantiation of $\mathrm{G}(\pmb{x})$ , we experiment with three options: (i) $\mathrm{G}(\pmb{x}) = \alpha \pmb{x}$ where $\alpha$ is a learnable scalar; (ii) $\mathrm{G}(\pmb{x}) = \pmb{a}\pmb{x}$ where $\pmb{a}$ is a learnable vector; (iii) $\mathrm{G}(\pmb{x}) = \mathrm{SE}(\pmb{x})$ where SE denotes a Squeeze-and-Excitation block [30] with a reduction ratio of 4. We also experiment augmenting $\mathrm{G}(\pmb{x})$ with $\tanh()$ introduced in [1] (e.g. $\tanh(\alpha\pmb{x})$ ), while only observing side effects. This indicates the magnitude of language and vision features are disparate, and a proper gating method is desired. + +# 4.2. Relational Pseudo-labelling + +RLIPv2 reuses object detection datasets to benefit pretraining by pseudo-labelling, as shown in Fig. 3. We assume that during the pre-training phase, the downstream entity and relation distributions are unavailable to us. Then, to tag + +![](images/5a79babf17dc25c766b90dff8b11df6a40499ac58d065545e589486b6e3a42f1.jpg) +Figure 3: An overview of relational pseudo-labeling, which tags object detection data with free-form relation texts. This process enables pre-training to be performed on two kinds of data. + +relation texts, we need to sort out the relations contained in the image as detailed in Sec. 4.2.1, and to tag relation texts to region pairs as detailed in Sec. 4.2.2. + +# 4.2.1 Relation Candidate Set Generation + +For a given image, relation candidate set generation aims to generate a coarse-grained set of candidate subject-object (SO) region pairs $\pmb{P}$ and their candidate relation texts $\pmb{T}$ . First, we adopt BLIP to generate $N_{Cap}$ captions for each image. Note that when $N_{Cap} = 1$ , we generate the caption via beam search, a deterministic generation method; when $N_{Cap} > 1$ , we generate captions via nucleus sampling [26], a stochastic generation methods with cumulative probability threshold set to 0.9. Nucleus sampling adds semantic diversity to the generated captions, which contributes to diversity in the relations. + +Second, we adopt a scene graph parser [68] to parse the obtained captions into relation triplets. To filter out invalid parsed triplets, we perform string matching and keep those whose subjects and objects can be matched with any entities' names or entities' synonyms within the image [86]. This operation encloses a small set of possible SO region pairs $P$ and possible relation texts $T$ for the pairs (which are inputs to R-Tagger), without needing to traverse all possible pairs. + +# 4.2.2 Relation Tagger via RLIPv2 Architecture + +The R-Tagger aims to assign candidate relation texts $T$ to candidate SO region pairs $P$ for a given image. While one alternative is executing the pre-trained RLIPv2 model to perform SGG on object detection datasets to obtain pseudotriplets, the informative object annotations fail to be utilized directly during the execution of RLIPv2. As a result, the quality of pseudo-labels is degraded. A prior work [100] adopts a coarse rule-based pseudo-labelling method that employed a greedy matching algorithm to randomly assign one relation text to an SO region pair as long as the relation texts' corresponding SO texts match with the SO region pair. An "overlap" prior was applied to further filter the triplets (i.e., a triplet is deemed valid only if the subject and object are overlapped). This method, however, + +introduces excessive false positives, causing degraded pretraining. Thus, we propose to reuse the RLIPv2 architecture to perform relation prediction given ground-truth SO region pairs as shown in Figure Fig. 2(b). + +As outlined in Sec. 3, RLIPv2 also utilizes subject queries $Q_{s}$ and object queries $Q_{o}$ as input. To allow for the utilization of object annotations as the input, we propose to replace the detection queries $Q_{s}$ and $Q_{o}$ with object embeddings [40], which aims to encourage Parallel Entity Detection to reconstruct object representations and Sequential Relation Inference to recognize relations. Compared with Eq. (1), the probabilistic factorisation of R-Tagger during inference can be reformulated as: + +$$ +\begin{array}{l} \mathbb {P} (\boldsymbol {R} | \hat {\boldsymbol {B}} _ {s}, \hat {\boldsymbol {B}} _ {o}, \boldsymbol {C} _ {E}; \boldsymbol {\theta} _ {P a r}, \boldsymbol {\theta} _ {S e}) = \tag {5} \\ \mathbb {P} \left(\hat {\boldsymbol {B}} _ {s}, \hat {\boldsymbol {B}} _ {o} \mid \hat {\boldsymbol {B}} _ {s}, \hat {\boldsymbol {B}} _ {o}, \boldsymbol {C} _ {E}; \boldsymbol {\theta} _ {P a r}\right) \cdot \mathbb {P} \left(\boldsymbol {R} \mid \hat {\boldsymbol {B}} _ {s}, \hat {\boldsymbol {B}} _ {o}, \boldsymbol {C} _ {E}; \boldsymbol {\theta} _ {S e}\right) \\ \end{array} +$$ + +where $\hat{B}_s, \hat{B}_o$ denote the ground-truth SO boxes from the region pair set $P$ that include their positions and labels); $\tilde{B}_s, \tilde{B}_o$ denote contextualized SO representations. To allow for decoding, we embed $\hat{B}_s, \hat{B}_o$ to have an equivalent dimension with queries. Specifically, we use MLPs to project positions and label text embeddings, and concatenate them along the channel dimension to obtain query-like input. + +Denoising training of R-Tagger. The training losses of R-Tagger are identical to RLIPv1: + +$$ +\mathcal {L} = \lambda_ {1} \mathcal {L} _ {l 1} + \lambda_ {2} \mathcal {L} _ {G I o U} + \lambda_ {3} \left(\mathcal {L} _ {s} + \mathcal {L} _ {o}\right) + \lambda_ {4} \mathcal {L} _ {r} \tag {6} +$$ + +where $\mathcal{L}$ is comprised of the $\ell_1$ loss for box regression $\mathcal{L}_{l1}$ , GIoU loss [67] $\mathcal{L}_{G IoU}$ , Cross-Entropy (CE) loss for subject and object classes $\mathcal{L}_s, \mathcal{L}_o$ , and Focal loss [52] for relations $\mathcal{L}_r$ . $\lambda_1, \lambda_2, \lambda_3, \lambda_4$ are set to 2.5, 1, 1, 1 as fixed weights to balance multi-task training [86, 89, 71]. + +However, due to the identical input and training objectives of Parallel Entity Detection, the model will attempt to find a shortcut, i.e., identity mapping, to achieve the minimum loss value. To avoid this, we draw inspiration from [40] which adds noise to $\hat{B}_s, \hat{B}_o$ during training. Specifically, we follow [40] to add center shifting and box scaling noise to box positions and add label flipping noise to box labels. The noise scale of center shifting and box scaling is set to 0.4, and the noise scale of label flipping is set to 0.2 following [40]. Furthermore, to prevent the information leakage between the same region with different noise, we apply attention masks to block the information flow between the same regions in Parallel Entity Detection. + +Inference of R-Tagger. After the training of R-Tagger, we can use it to infer relations without additional noise based on Eq. (5). For each inference, the maximum number of region pairs is $N_{Q}$ . If candidate SO region pairs exceed $N_{Q}$ , we infer multiple times and merge the results. To quantify the confidence of a relation, we calculate the product of the top-1 score from the softmax distribution over the subject, the object and the original relation sigmoid score. To + +
NvNALIFRareNon-RareFull#ParamsFPS
1610.9213.9913.28246.8M18.93
2312.1214.0713.62206.6M21.49
3210.5714.0513.25193.2M22.15
6111.2613.9013.30179.8M23.17
+ +select pseudo-labels, we choose those whose relation confidence exceeds a threshold $\eta$ . $\eta$ is set to 0.2 by default (details can be found in the Appendix). + +# 4.3. Pre-training, Fine-tuning and Inference + +Regarding pre-training and fine-tuning of RLIPv2, we first merge results from Parallel Entity Detection and Sequential Relation Inference to obtain $N_{Q}$ triplets. Next, we employ the bipartite matching algorithm originally proposed in [71] to match the predicted and ground-truth triplet annotations. The overall loss is identical to Eq. (6). The techniques introduced in RLIPv1, i.e. Label Sequence Extension, Relation Quality Labels and Relation Pseudo-Labels, are employed by default for a fair comparison. Regarding the inference of RLIPv2, we sort the relation confidence (defined in Sec. 4.2.2) of the correctly localised triplets (IoU > 0.5) and select the Top-K triplets. $K$ is set to 100 by default following [86, 71, 45, 11]. + +# 5. Experiments + +Pre-training datasets. To pre-train RLIPv2, we utilize VG [38], COCO [53] and Objects365 [69]. VG has $108k$ images annotated with free-form relation and object annotations. COCO has $117k$ images with only object annotations in 80 classes, and Objects365 has $1,742k$ images with only object annotations in 365 classes. Thus, we use relational pseudo-labelling to tag relation labels for COCO and Objects365, enabling them to support relational pre-training. + +Downstream datasets. For HOI detection, we follow [71, 86, 89, 93] to evaluate on HICO-DET [4] and V-COCO [22]. For HICO-DET that contains 117 verbs and 80 objects, we evaluate under the Default setting on Full, Rare and Non-Rare sets. For V-COCO that contains 24 interactions and 80 objects, we evaluate following the official evaluation code [22] under two scenarios: $\mathrm{AP}_{role}^{\#1}$ and $\mathrm{AP}_{role}^{\#2}$ . For SGG, we assess RLIPv2 on the widely-used Open Images v6 [39] dataset, which is annotated with 288 objects and 30 relations. We evaluate RLIPv2 using standard evaluation metrics [39, 96]: Recall@50 (R@50), weighted mean Average Precision for relation detection ( $\mathrm{wmAP}_{rel}$ ) and phrase detection ( $\mathrm{wmAP}_{phr}$ ). The final score is calculated + +Table 1: The effect of the sparsification of language encoding layers in Cross-Modal Fusion. Results are evaluated on HICODET under zero-shot (NF) setting. FPS (frames per second) is tested on a single NVIDIA A100 with a minibatch size 1. + +
Gatingtanh()RareNon-RareFull
α10.4713.8313.05
a✓9.9113.5412.70
SE11.0713.8913.24
α12.1214.0713.62
ax10.9814.0713.36
SE11.0714.0013.32
+ +Table 2: Comparisons of different gating functions introduced in Sec. 4.1. We report zero-shot (NF) results on HICO-DET. + +as: $\mathrm{score}_{wtd} = 0.2 * \mathrm{R} @ 50 + 0.4 * \mathrm{wmAP}_{rel} + 0.4 * \mathrm{wmAP}_{phr}$ . + +Implementation details. To assess the effectiveness of RLIPv2, we choose to adopt DDETR [102] to compose RLIPv2-ParSeD and adopt DAB-DDETR [56] to compose RLIPv2-ParSeDA. To perform a fair comparison with previous works, we ensure that RLIPv2 has $N_v * N_{ALIF} = 6$ DDETR/DAB-DDETR encoding layers. For Parallel Entity Detection and Sequential Relation Inference, 3 layers are adopted following [86, 89, 71, 93]. $N_Q$ is set to 100 during pre-training and fine-tuning, except when we finetune on HICO-DET where $N_Q$ is set to 64 following [93]. Regarding model initialization, we use COCO detection parameters as initialisation when using VG or VG and COCO for pre-training; when using VG, COCO and Objects365 for pre-training, we use COCO and Object365 detection parameters as initialisation. Regarding the configuration of minibatch sizes and learning rate (LR), we set the minibatch size to 64, LR for the text encoder to 1.41e-5 and LR for other modules to 1.41e-4 when using ResNet-50 [25] and Swin-T [59]; We set the minibatch size to 32, LR for the text encoder to 1e-5 and LR for other modules to 1e-4 when using Swin-L [59]. RLIPv2 and R-Tagger are pre-trained and fine-tuned for 20 epochs unless otherwise stated, with LR dropping by a factor of 10 at the 15th epoch. For the BLIP captioner, we adopt the ViT-L/16 [14] model fine-tuned on COCO Caption [8]. + +# 5.1. Ablation Study + +We perform the ablation study using RLIPv2-ParSeD with ResNet-50 as the backbone, and VG as the pre-training dataset unless otherwise stated. We pre-train for 20 epochs and evaluate performance on HICO-DET under the zero-shot with no fine-tuning (NF) setting. + +# 5.1.1 Asymmetric Language-Image Fusion + +Sparsification of the language layers. First of all, we ablate on the number of language layers to investigate the effect of sparsifying language encoding layers in CrossModal Fusion. As introduced in Sec. 4.1, dense language layers cause difficult training. To avoid training collapse, we compute classification losses $(\mathcal{L}_s,\mathcal{L}_o$ and $\mathcal{L}_r)$ using all + +
ModelPre-trainingFully-finetuningFPS
Ep.TimeZero-shot (NF)Ep.Result
RLIPv1-ParSeD5025.9h11.20 / 14.73 / 13.926024.67 / 32.50 / 30.7021.89
RLIPv2-ParSeD2010.9h12.12 / 14.07 / 13.622026.47 / 33.51 / 31.8921.49
RLIPv1-ParSeDA5027.2h11.34 / 14.56 / 13.826022.85 / 30.87 / 29.0319.41
RLIPv2-ParSeDA2011.3h13.03 / 14.98 / 14.532027.01 / 35.21 / 33.3218.94
+ +Table 3: Comparisons of RLIPv1 and RLIPv2 under zero-shot (NF) and fully-finetuning settings on HICO-DET pre-trained on VG. Results are reported on Rare/Non-Rare/Full sets. FPS is tested on a single NVIDIA A100 with minibatch size 1. Pretraining time is tested on 8 NVIDIA A100. "Ep." denotes number of epochs. + +
InitializationRareNon-RareFull
COCO (default)12.1214.0713.62
R-Tagger12.5513.6413.39
w/o noise9.9412.7412.09
w/o attn masks8.5511.2210.61
+ +intermediate language features rather than using only the last layer of language features in Cross-Modal Fusion. Results are shown in Tab. 1. Our findings suggest that sparsifying the language encoder does not compromise zero-shot performance and improves parameter efficiency. We attribute this to overfitting effects on upstream datasets impairing models' generalization. We choose $N_{v} = 2$ and $N_{ALIF} = 3$ as the default hyper-parameters for the following experiments. + +The choice of the gating function $\mathrm{G}(\boldsymbol{x})$ . To investigate the effect of the gating function on cross-modal fusion, we experiment with variants of the gating function as described in Sec. 4.1. The results are shown in Tab. 2. We note that tanh consistently degrades performance for the three gating methods. We conjecture that the output range of tanh can constrain the magnitude of the features to be fused, thus limiting the performance. Based on the results, we choose the simplest one: the learnable scalar gating method parameterised by $\alpha$ . + +Comparisons of RLIPv2 with RLIPv1. To compare the architectural benefit of RLIPv2 with RLIPv1, we adopt DDETR [102] and DAB-DDETR [56] to follow two designs, and evaluate performance under zero-shot (NF) and fully-finetuning setting. Results are shown in Tab. 3. From this table, we can observe that by modifying the architecture without compromising much inference speed, RLIPv2 generally outperforms its RLIPv1 counterpart. Specifically, RLIPv2 obtains comparable zero-shot results to RLIPv1, while costing about $0.4 \times$ pre-training time. In terms of fine-tuning results, RLIPv2 surpasses RLIPv1 with $0.33 \times$ fine-tuning time due to earlier and deeper fusion. + +# 5.1.2 Relational Pseudo-labelling + +By default, we use RLIPv2-ParSeD with ResNet-50 backbone as the basic structure of R-Tagger. + +The necessity of denoising pre-training and attention masks for R-Tagger. If noise is not added during R-Tagger's pre-training, the loss will fluctuate instead of steadily decreasing as the optimization proceeds. If attention masks are not utilized to prevent information leakage, the model will tend to learn an identity mapping, thus de + +Table 4: The quality of R-Tagger parameters. Results are evaluated using RLIPv2-ParSeD with ResNet-50 under zero-shot (NF) setting. + +
Tagging MethodOverlapRareNon-RareFull
Greedy [100]×11.1511.6511.55
✓13.1614.7014.35
CLIP (ViT-L/14) [65]×12.6612.7612.74
✓14.6314.9414.87
R-Tagger (ResNet-50)×15.3315.5415.49
✓15.3615.3715.36
+ +Table 5: Comparisons of relation tagging methods. "Overlap" denotes the "overlap" prior for SO pairs introduced in Sec. 4.2.2. We report zero-shot (NF) results pre-trained on VG and COCO. We use oracle captions from COCO Caption [8] ( $N_{Cap} = 5$ ). + +
Caption typeNCapRareNon-RareFull
Oracle515.3315.5415.49
BLIP (beam)19.8612.0211.52
BLIP (nucleus)514.6714.7614.74
BLIP (nucleus)1015.0815.1015.09
BLIP (nucleus)2014.2414.9114.75
BLIP (nucleus)*512.3114.3713.89
+ +Table 6: Comparisons of different caption types. "beam" and "nucleus" denote beam search and nucleus sampling. "Oracle" denotes captions from COCO Caption. By default, we adopt COCO Caption fine-tuned BLIP model. * denotes that we adopt the pretrained BLIP model. + +grading its ability to infer relations. R-Tagger is pre-trained for 20 epochs. To assess the quality of R-Tagger's parameters, thanks to R-Tagger's identical structure to RLIPv2-ParSeD, we initialize RLIPv2-ParSeD with R-Tagger's parameters and pre-train for 10 epochs. We evaluate the zero-shot (NF) performance on HICO-DET as shown in Tab. 4. We observe that removing additional noise or attention masks both impair performance, highlighting their importance. + +Comparisons of different relation tagging strategies. We compare R-Tagger with other two methods: (i) the greedy matching algorithm [100]; (ii) the CLIP [65] tagging method. Specifically, to tag relations for a given SO region pair with a candidate relation text, the CLIP tagging + +
DatasetRelation candidateRareNon-RareFull
VG-12.1214.0713.62
VG+COCOBLIP15.0815.1015.09
VG+COCOSelection from VG10.3411.3311.11
+ +Table 7: Comparisons of methods to generate relation candidate sets. We report zero-shot (NF) results on HICO-DET. + +
VGVG+COCOVG+COCO+O365
ResNet-5013.03 / 14.98 / 14.5315.00 / 16.60 / 16.2319.64 / 17.24 / 17.79
Swin-T13.01 / 16.06 / 15.3517.13 / 18.74 / 18.3721.24 / 19.47 / 19.87
Swin-L19.93 / 18.74 / 19.0222.59 / 21.09 / 21.4427.97 / 21.90 / 23.29
+ +Table 8: Model and dataset scaling experiments using RLIPv2-ParSeDA. Results are evaluated on HICO-DET Rare/Non-Rare/Full sets under zero-shot (NF) setting. + +
ModelBackboneExtramR@50R@50wmAPscore_wtd
relphr
VCTree [73]X101-F-33.9174.0834.1633.1140.21
G-RCNN [82]X101-F-34.0474.5133.5134.2141.84
Motifs [90]X101-F-32.6871.6329.9131.5938.93
Unbiased [72]X101-F-35.4769.3030.7432.8039.27
GPS-Net [54]X101-F-35.2674.8132.8533.9841.69
RelDN [96]R101-36.8072.7529.8730.4238.67
BGNN [46]R101-39.4174.9331.1531.3740.00
SGTR [45]R101-42.6159.9136.9838.7342.28
RelTR [11]R50--64.4734.1737.4441.54
RLIPv2-ParSeDR50*-44.5858.0443.3043.1246.18
R50*-44.8860.2044.7343.3647.28
R50†-45.5961.1545.7143.7348.01
RLIPv2-ParSeDAR50(i)50.4263.3547.6545.2349.82
R50(ii)52.0764.5349.1446.1451.01
R50(iii)51.3165.9949.5445.7151.30
Swin-T(iii)59.6168.8152.7048.0154.05
Swin-L(iii)64.7272.4956.3850.7057.34
+ +method clips the minimum bounding box of the SO region pair, creates two prompts ("a photo of {subject} {relation} {object}" and "a photo of {subject} not interacting with {object}" are adopted as positive and negative prompts.), and performs zero-shot prediction. If the softmax probability of the positive prompt is greater than a pre-defined threshold, we tag this relation text to this SO region pair. (We traverse the threshold and find the optimal one for the CLIP tagging method, as detailed in the Appendix.) We also ablate on the "overlap" prior [100] to observe whether a given tagging method relies on strong prior knowledge to filter out false positive relations. The results are shown in Tab. 5. From this table, we conclude that greedy matching and CLIP tagging method generate a significant number of low-quality non-overlapped triplets. Thus, the "overlap" prior is essential for them. R-Tagger, however, suf + +Table 9: Comparisons with previous methods on Open Images v6 SGG benchmark. X101-F denote ResNeXt-101 FPN [80]. ${}^{ * }$ and ${}^{ \dagger }$ denote ImageNet pretrained and COCO object detection pretrained. "Extra" denotes extra relations adopted from (i) VG, (ii) VG+COCO and (iii) VG+COCO+O365. + +
MethodBackboneUC-RFUC-NF
VCL [27]ResNet-5010.06 / 24.28 / 21.4316.22 / 18.52 / 18.06
ATL [28]ResNet-509.18 / 24.67 / 21.5718.25 / 18.78 / 18.67
FCL [29]ResNet-5013.16 / 24.23 / 22.0118.66 / 19.55 / 19.37
GEN-VLKT [51]ResNet-5021,36 / 32.91 / 30.5625.05 / 23.38 / 23.71
RLIPv1-ParSeD [86]ResNet-5016.43 / 30.59 / 27.7616.99 / 24.71 / 22.93
RLIPv1-ParSe [86]ResNet-5019.19 / 33.35 / 30.5220.27 / 27.67 / 26.19
RLIPv2-ParSeDAResNet-5021.45 / 35.85 / 32.9722.81 / 29.52 / 28.18
RLIPv2-ParSeDASwin-T26.95 / 39.92 / 37.3221.07 / 35.07 / 32.27
RLIPv2-ParSeDASwin-L31.23 / 45.01 / 42.2622.65 / 40.51 / 36.94
+ +Table 10: Comparisons with methods on HICO-DET under UC-RF and UC-NF settings. We adopt ResNet-50 as the backbone. Results are reported on Unseen/Seen/Full sets. + +
MethodBackbone1% Data10% Data
RLIPv1-ParSeD [86]ResNet-5016.22 / 18.92 / 18.3015.89 / 23.94 / 22.09
RLIPv1-ParSe [86]ResNet-5017.47 / 18.76 / 18.4620.16 / 23.32 / 22.59
RLIPv2-ParSeDAResNet-5022.13 / 24.51 / 23.9623.28 / 30.02 / 28.46
RLIPv2-ParSeDASwin-T24.26 / 28.92 / 27.8528.31 / 32.93 / 31.87
RLIPv2-ParSeDASwin-L31.89 / 32.32 / 32.2234.75 / 38.27 / 37.46
+ +Table 11: Comparisons on HICO-DET under few-shot settings. Results are reported on Rare/Non-Rare/Full sets. + +fers a slight performance drop when using the "overlap" prior, indicating that R-Tagger generates more reliable non-overlapped triplets. Besides, although CLIP is pre-trained on a massive quantity of language-image pairs, it struggles in recognizing relations, which R-Tagger is expert in. + +Comparisons of different caption types. Previous experiments demonstrate that oracle COCO captions can benefit pre-training. However, most datasets lack such high-quality captions. Thus, BLIP provides an alternative for caption generation. We conduct experiments on various caption types, as shown in Tab. 6. From this table, we can observe that: (i) BLIP-generated captions achieve a decent performance compared to oracle captions, indicating the practicality of adopting generated captions for pseudolabelling. (ii) If we compare BLIP model with different parameters (COCO Caption fine-tuned or only pre-trained), we can see that the fine-tuned model generates better captions with more boost on the Rare set $(12.31\rightarrow 14.67)$ . We conjecture that the caption quality of the curated style dataset COCO Caption is better than pre-training captions harvested from the web. (iii) By adopting generated captions, we can increase the number of captions per image, thus diversifying the relations contained in captions and boost RLIPv2 $(11.52\rightarrow 15.09)$ . Besides, although datasets like Conceptual Caption [70] (CC3M) also provide captions, the quantity of captions (average one caption per image) is not enough to describe many relations in an image. In comparison, our pipeline can work without caption annotation while performing better. + +The necessity of using captioners. By default, we use BLIP to generate relation texts. Another option is to query all possible SO pairs and select all possible relation texts from VG as it contains an enormous quantity of relations + +
ModelBackboneExtra RelationsHICO-DETV-COCO
Zero-shot (NF)Fully-finetuningAP#1roleAP#2role
InteractNet [21]R50-FPN--7.16 / 10.77 / 9.9440.0-
UnionDet [35]R50-FPN--11.72 / 19.33 / 17.5847.556.2
PPDM [50]HG104--13.97 / 24.32 / 21.94--
HOTR [36]R50--17.34 / 27.42 / 25.1055.264.4
QPIC [71]R50--21.85 / 31.23 / 29.0758.861.0
OCN [89]R50--25.56 / 32.51 / 30.9164.266.3
CDN [93]R50--27.39 / 32.64 / 31.4461.763.8
GEN-VLKT [51]R50--29.25 / 35.10 / 33.7562.464.5
QAHOI [5]Swin-L*--29.80 / 37.56 / 35.78--
UniVRD [98]ViT-H/14†--31.65 / 39.99 / 38.0765.866.9
RLIPv1-ParSeD [86]R50VG11.20 / 14.73 / 13.9224.67 / 32.50 / 30.7061.763.8
RLIPv1-ParSe [86]R50VG15.08 / 15.50 / 15.4026.85 / 34.63 / 32.8461.964.2
RLIPv2-ParSeDAR50VG13.03 / 14.98 / 14.5327.01 / 35.21 / 33.3263.065.1
RLIPv2-ParSeDAR50VG+COCO15.00 / 16.60 / 16.2327.89 / 35.27 / 33.5764.566.7
RLIPv2-ParSeDAR50VG+COCO+O36519.64 / 17.24 / 17.7929.61 / 37.10 / 35.3865.968.0
RLIPv2-ParSeDASwin-TVG+COCO+O36521.24 / 19.47 / 19.8733.66 / 40.07 / 38.6068.870.8
RLIPv2-ParSeDASwin-LVG+COCO+O36527.97 / 21.90 / 23.2943.23 / 45.64 / 45.0972.174.1
+ +Table 12: Comparisons with previous methods on HICO-DET and V-COCO. Results on HICO-DET are reported on Rare/Non-Rare/Full sets. R50 and HG denote ResNet-50 [25] and Hourglass [61]. * denotes the backbone is pre-trained with $384 \times 384$ resolution, while others use $224 \times 224$ . † indicates the backbone is pre-trained using LiT [92], then fine-tuned on Objects365, COCO and HICO with the objective of object detection. + +(36,515 kinds). Then, we run R-Tagger with selected relation texts as $T$ and all region pairs as $P$ . The results are shown in Tab. 7. We can observe that selecting from VG generates low-quality candidates, harming performance. + +Model scaling and dataset scaling. Equipped with the labelling pipeline introduced above, we can scale RLIPv2 to larger models and datasets. In Tab. 8, we adopt RLIPv2-ParSeDA as the base architecture and observe the benefit of scaling by zero-shot (NF) performance on HICO-DET. In terms of data, adding COCO and Objects365 can both boost performance, and the benefit of adding data exhibits a log scaling trend [9]. Models pre-trained with Objects365 consistently have better Rare result, which we attribute to the distribution misalignment of Objects365 and HICO-DET [17]. In terms of models, switching to stronger backbone models can improve the data efficiency at the cost of larger amounts of computation. Regarding scaling experiments using RLIPv2-ParSeD, we present it in the Appendix. + +# 5.2. Comparisons with State-of-the-Arts + +Scene graph generation. We compare RLIPv2 series models with previous methods on Open Images v6 in Tab. 9. We also report mean Recall@50 (mR@50) to better show the usefulness of RLIPv2. Our findings suggest that (i) with the assistance of DDETR family models, RLIPv2 can serve as a strong baseline without any pre-training; (ii) naive object detection pre-training can boost the performance to some extent $(47.28 \rightarrow 48.01)$ , while pre-training on VG can further boost the performance especially on mR@50 $(45.59 \rightarrow 50.42)$ ; (iii) adding pseudo-labelled relation an- + +notations in pre-training or switching to stronger backbones both contribute to better performance. However, the boost of adding Objects365 is negligible. We attribute this to the distribution discrepancy of Objects365 and Open Images v6. + +HOI Detection under UC-NF and UC-RF settings. We report results in Tab. 10 on unseen combinations (UC) under UC-RF and UC-NF settings following [27, 28]. We only fine-tune for 10 epochs under UC-NF setting. Our method outperforms previous methods except on one metric. We attribute this to the strong transferability of CLIP features that GEN-VLKT adopts. Regarding experiments using RLIPv2-ParSeD, we present it in the Appendix. + +Few-shot HOI Detection. We follow [86] to only fine-tune 10 epochs on partial data (1% and 10%), results of which are shown in Tab. 11. We can observe significant improvements upon all metrics by scaling up pre-training compared with previous methods. This improves the practicality of RLIPv2 in low-data scenarios. Regarding experiments using RLIPv2-ParSeD, we present it in the Appendix. + +HOI detection under fully-finetuning and zero-shot (NF) settings. We compare the performance of RLIPv2 series models with previous methods on HICO-DET and V-COCO in Tab. 12. We can observe from the table that (i) dataset and model scaling can both boost the final performance on two datasets; (ii) on HICO-DET, the benefit of pre-training is more prominent on zero-shot than fully-finetuning, especially on the Rare set. Regarding experiments using RLIPv2-ParSeD, we present it in the Appendix. + +![](images/0d2b7df2ed4ced0f1ed688c46233d9a8df44cfd3331660ae0c161c4dfa6a61c4.jpg) +Figure 4: (a) Visualization of pseudo-labelled relations on COCO. Left column: R-Tagger; right column: CLIP tagging method. (b) Visualization of failure cases of R-Tagger. + +# 5.3. Qualitative Analysis + +Comparisons of relation tagging methods. We visualize three examples to compare the quality of pseudolabelled relations by R-Tagger and CLIP tagging method in Fig. 4(a). Generally, CLIP is more object-centric and position-agnostic, and thus struggles in discriminating relations. It tends to tag relations as long as the subject and object have strong co-occurrence priors. However, R-Tagger tags more reasonable relations. + +Failure cases of R-Tagger. Recognizing relations is challenging, especially in complex scenes. In Fig. 4(b), we present three examples of R-Tagger's failure cases. In particular, we observe failure cases when the scene contains multiple similar subjects or objects. + +# 6. Conclusion + +In this paper, we propose RLIPv2, a fast converging model that enables the scaling of relational pre-training to larger-scale pseudo-labelled datasets. Comprehensive experiments on HOI detection and scene graph generation under various settings demonstrate its effectiveness compared to previous methods. We anticipate that our work can galvanize further research efforts to focus on relational reasoning, fostering advancements that yield tangible benefits not only to the research community but also to broader society and humanity. + +# Acknowledgments + +We would like to extend our sincere gratitude to the anonymous reviewers for their invaluable feedback. Additionally, we appreciate the Fundamental Vision Intelligence Team of Alibaba DAMO Academy for their generous provision of essential computational resources. 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In CVPR, pages 11825-11834, 2021. 2 \ No newline at end of file diff --git a/2023/RLIPv2_ Fast Scaling of Relational Language-Image Pre-Training/images.zip b/2023/RLIPv2_ Fast Scaling of Relational Language-Image Pre-Training/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..1e7fdc6794c52a070494a745187ab272a1cf40f2 --- /dev/null +++ b/2023/RLIPv2_ Fast Scaling of Relational Language-Image Pre-Training/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2ce4028a56e4cda4514271335d2ff00a818ceb36d6f20d09c3e757d24f3f35fa +size 694000 diff --git a/2023/RLIPv2_ Fast Scaling of Relational Language-Image Pre-Training/layout.json b/2023/RLIPv2_ Fast Scaling of Relational Language-Image Pre-Training/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..320109ffe9c799db1f5ebd3e42d18d9bf6f6219c --- /dev/null +++ b/2023/RLIPv2_ Fast Scaling of Relational Language-Image Pre-Training/layout.json @@ -0,0 +1,11260 @@ 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+ ], + "spans": [ + { + "bbox": [ + 53, + 201, + 545, + 227 + ], + "type": "text", + "content": "{hj.yuan, dni}@zju.edu.cn wxiang@hust.edu.cn {pyn.sigrid, fengtao.hi, zhaodeli}@gmail.com \nsma71@cam.ac.uk {zhangjin.zsw, jianwen.jjw, yingya.zyy}@alibaba-inc.com" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 251, + 192, + 264 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 251, + 192, + 264 + ], + "spans": [ + { + "bbox": [ + 143, + 251, + 192, + 264 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 276, + 290, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 290, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 290, + 613 + ], + "type": "text", + "content": "Relational Language-Image Pre-training (RLIP) aims to align vision representations with relational texts, thereby advancing the capability of relational reasoning in computer vision tasks. However, hindered by the slow convergence of RLIPv1 architecture and the limited availability of existing scene graph data, scaling RLIPv1 is challenging. In this paper, we propose RLIPv2, a fast converging model that enables the scaling of relational pre-training to large-scale pseudo-labelled scene graph data. To enable fast scaling, RLIPv2 introduces Asymmetric Language-Image Fusion (ALIF), a mechanism that facilitates earlier and deeper gated cross-modal fusion with sparsified language encoding layers. ALIF leads to comparable or better performance than RLIPv1 in a fraction of the time for pre-training and fine-tuning. To obtain scene graph data at scale, we extend object detection datasets with free-form relation labels by introducing a captioner (e.g., BLIP) and a designed Relation Tagger. The Relation Tagger assigns BLIP-generated relation texts to region pairs, thus enabling larger-scale relational pre-training. Through extensive experiments conducted on Human-Object Interaction Detection and Scene Graph Generation, RLIPv2 shows state-of-the-art performance on three benchmarks under fully-finetuning, few-shot and zero-shot settings. Notably, the largest RLIPv2 achieves 23.29mAP on HICO-DET without any fine-tuning, yields 32.22mAP with just " + }, + { + "bbox": [ + 46, + 276, + 290, + 613 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 276, + 290, + 613 + ], + "type": "text", + "content": " data and yields 45.09mAP with " + }, + { + "bbox": [ + 46, + 276, + 290, + 613 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 276, + 290, + 613 + ], + "type": "text", + "content": " data. Code and models are publicly available at https://github.com/JacobYuan7/RLIPv2." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 624, + 128, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 624, + 128, + 636 + ], + "spans": [ + { + "bbox": [ + 47, + 624, + 128, + 636 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 644, + 287, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 644, + 287, + 669 + ], + "spans": [ + { + "bbox": [ + 46, + 644, + 287, + 669 + ], + "type": "text", + "content": "The pretraining-finetuning paradigm has achieved major breakthroughs in vision and language domains [58, 13," + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 251, + 449, + 338 + ], + "blocks": [ + { + "bbox": [ + 310, + 251, + 449, + 338 + ], + "lines": [ + { + "bbox": [ + 310, + 251, + 449, + 338 + ], + "spans": [ + { + "bbox": [ + 310, + 251, + 449, + 338 + ], + "type": "image", + "image_path": "7560613fa90b2d6d31e9a47fa3f982bb4c342884fe937d906b1704e9b4a5445c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 344, + 546, + 378 + ], + "lines": [ + { + "bbox": [ + 305, + 344, + 546, + 378 + ], + "spans": [ + { + "bbox": [ + 305, + 344, + 546, + 378 + ], + "type": "text", + "content": "Figure 1: Left: Fine-tuning comparison on HICO-DET. Right: Pre-training epoch and zero-shot (NF) comparison on HICO-DET. Except where stated, RLIPv2-ParSeDA architecture is adopted." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 452, + 251, + 539, + 338 + ], + "blocks": [ + { + "bbox": [ + 452, + 251, + 539, + 338 + ], + "lines": [ + { + "bbox": [ + 452, + 251, + 539, + 338 + ], + "spans": [ + { + "bbox": [ + 452, + 251, + 539, + 338 + ], + "type": "image", + "image_path": "bd75ed80e18b9ed3dd7e4fe9d1fb69a3213f2f65243d54e895fbdb4584423403.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 396, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 545, + 468 + ], + "type": "text", + "content": "23, 103, 65, 77]. In this context, a number of particularly notable results have been obtained through aligned Vision-Language Pre-training (VLP) [65, 42, 41, 78, 95, 91]. These research efforts have typically employed a robust base model [14, 25, 12, 74] that is trained on language-image paired data to produce foundation models." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 469, + 546, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 469, + 546, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 546, + 564 + ], + "type": "text", + "content": "RLIPv1 [86] presents the first attempt to specifically align vision representations and relational texts using VLP. By pre-training on open-vocabulary scene graph data like Visual Genome (VG) [38], RLIPv1 demonstrates its usefulness in zero-shot, few-shot and fully-finetuned Human-Object Interaction (HOI) Detection. Although RLIPv1 is proven effective, we find it challenging to scale for the following reasons:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 567, + 545, + 676 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 304, + 567, + 545, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 545, + 626 + ], + "type": "text", + "content": "(i) Model perspective: RLIPv1 converges slowly, as exemplified by DETR [3]-based RLIPv1, which requires 150/90 epochs to converge during pre-training/fine-tuning. Even when building on Deformable DETR (DDETR) [102] and DAB-DDETR [56], 50/60 epochs are still required." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 628, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 628, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 628, + 545, + 676 + ], + "type": "text", + "content": "(ii) Data perspective: as observed by the authors of RLIPv1, data with relation triplet annotations is scarce, impeding RLIPv1's scaling. Annotating triplets in the form of " + }, + { + "bbox": [ + 304, + 628, + 545, + 676 + ], + "type": "inline_equation", + "content": "\\langle" + }, + { + "bbox": [ + 304, + 628, + 545, + 676 + ], + "type": "text", + "content": " subject, relations, object " + }, + { + "bbox": [ + 304, + 628, + 545, + 676 + ], + "type": "inline_equation", + "content": "\\rangle" + }, + { + "bbox": [ + 304, + 628, + 545, + 676 + ], + "type": "text", + "content": " is both time- and cost-intensive." + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "To resolve the aforementioned challenges, we introduce RLIPv2, a fast converging model that enables relational pretraining on larger-scale pseudo-labelled scene graph data." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 673, + 286, + 684 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 673, + 286, + 684 + ], + "spans": [ + { + "bbox": [ + 57, + 673, + 286, + 684 + ], + "type": "text", + "content": "*Work conducted during their research internships at DAMO Academy." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 59, + 684, + 136, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 684, + 136, + 693 + ], + "spans": [ + { + "bbox": [ + 59, + 684, + 136, + 693 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 48, + 693, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 693, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 693, + 287, + 712 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 48, + 693, + 287, + 712 + ], + "type": "text", + "content": "RLIPv1 refers to the model presented in [86], and RLIPv2 refers to the model presented in this paper." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21649" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "From both the model and data perspectives, we summarize the contributions of RLIPv2 as follows." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 287, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 287, + 239 + ], + "type": "text", + "content": "From the model perspective, we observe that the slow convergence of DDETR can be attributed to the late language-image fusion strategy: fusion after decoding. Prior works [15, 44] have demonstrated an earlier and deeper fusion mechanism facilitates cross-modal alignment. In light of this, we propose Asymmetric Language-Image Fusion (ALIF) in RLIPv2 that encourages fusion in the encoding stage with sparsified language layers. Without sacrificing inference speed thanks to sparsification, RLIPv2 requires only 20 epochs to pre-train and fine-tune based on DDETR family models [102, 56] as shown in Fig. 1, while performing better than or comparably to RLIPv1." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 239, + 288, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 288, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 288, + 418 + ], + "type": "text", + "content": "From the data perspective, we leverage well-established object detection datasets [53, 69, 39]. Specifically, we extend these datasets with relational annotations by pseudolabelling. To perform pseudo-labelling, we must tackle two challenges: (i) sorting out the relations contained in the image and (ii) tagging relation texts to region pairs. Regarding the first challenge, we employ external captioners (e.g. BLIP [42]) that generate captions containing relation descriptions. Regarding the second challenge, we reuse RLIPv2 model as a Relation Tagger (R-Tagger) that enables assigning the generated open-vocabulary relation texts to region pairs. Equipped with such a pipeline, we investigate the scaling behavior of both the model and the data for RLIPv2, which demonstrates improved zero-shot, few-shot and fine-tuning performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 419, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 419, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 287, + 491 + ], + "type": "text", + "content": "Furthermore, we introduce Scene Graph Generation (SGG), an analogously defined task to HOI detection for evaluating RLIPv2. RLIPv2 achieves state-of-the-art performance on Open Images v6 [39] for SGG, which underscores its robustness and efficacy in tackling relational reasoning tasks." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 502, + 134, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 134, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 134, + 514 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": "Language-image pre-training for detection. Recently, there has been a growing interest in learning visual representations from language supervision [42, 41, 65, 1, 32, 34, 15, 44, 95, 76]. This paradigm of learning from language supervision has also proven effective in improving detection performance. MDETR [34] was the first work to learn region-text correspondences in an end-to-end manner, while X-DETR [2] improved upon MDETR by removing the cross-modal fusion part that improves its training efficiency. GLIP [44] extended this line of research by scaling to web-scale data, leading to significant advances in zero-shot object detection and data efficiency. DetCLIP [84] proposed a paralleled concept formulation and a concept dictionary to enable semantically rich region-text alignment. RLIPv1 [86] was the first work to seek language-image alignment via relations, and our work follows its footsteps" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 72, + 499, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 499, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 499, + 84 + ], + "type": "text", + "content": "to achieve fast scaling of relational pre-training." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 85, + 545, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 85, + 545, + 371 + ], + "spans": [ + { + "bbox": [ + 304, + 85, + 545, + 371 + ], + "type": "text", + "content": "End-to-end HOI detection and scene graph generation. Relations can interpret visual content in a fine-grained perspective [10, 31, 33]. Detecting and recognizing relations utilizing HOI detection and scene graph generation have been verified effective in image captioning [85], image retrieval [33, 75], synthesis [83, 18], activity understanding [31, 88, 87] and . The aim of these tasks is to detect relation triplets from a given input image. Before the emergence of DETR [3], the commonly adopted pipeline was to adopt an off-the-shelf object detector [66, 24] and design reasoning modules to infer relations [20, 19, 63, 49, 48, 90, 7, 54, 46, 47, 81]. Initial end-to-end design efforts extended detectors to support relation recognition [50, 99, 82, 35, 55]. Further attempts focus on the adaptation of DETR to the field of HOI detection [89, 6, 36, 104, 71, 93, 94, 79, 37, 57, 101, 62, 64, 97] and SGG [45, 11]. RLIPv1 [86] demonstrated the effectiveness of relational pre-training in improving performance and data efficiency. RLIPv2 builds upon RLIPv1, but seeks to solve its scaling problem. The most related work [100] also seeks scaling with the help of language. However, it remains a two-stage detection pipeline, lacks semantic richness and adopts a naive matching algorithm that hinders its performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 383, + 409, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 383, + 409, + 396 + ], + "spans": [ + { + "bbox": [ + 306, + 383, + 409, + 396 + ], + "type": "text", + "content": "3. Recap of RLIPv1" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 403, + 545, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 511 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 511 + ], + "type": "text", + "content": "In this section, we will briefly review RLIPv1 [86], a model that leverages both entity and relation descriptions to perform VLP and that forms the basis for our approach. As triplet detection architecture, RLIPv1 proposes a ParSeD model that allocates decoupled embeddings for subjects, objects and relations. The collective model RLIPv1-ParSeD consists of three stages: Parallel Entity Detection, Sequential Relation Inference and Cross-Modal Fusion, as shown in Fig. 2(a)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 511, + 545, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 511, + 545, + 619 + ], + "spans": [ + { + "bbox": [ + 304, + 511, + 545, + 619 + ], + "type": "text", + "content": "For Parallel Entity Detection, RLIPv1-ParSeD defines two sets of queries " + }, + { + "bbox": [ + 304, + 511, + 545, + 619 + ], + "type": "inline_equation", + "content": "Q_{s}, Q_{o} \\in \\mathbb{R}^{N_{Q} \\times D}" + }, + { + "bbox": [ + 304, + 511, + 545, + 619 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 511, + 545, + 619 + ], + "type": "inline_equation", + "content": "N_{Q}" + }, + { + "bbox": [ + 304, + 511, + 545, + 619 + ], + "type": "text", + "content": " pairs of subjects and objects to perform subject and object detection. For Sequential Relation Inference, the model generates relation queries " + }, + { + "bbox": [ + 304, + 511, + 545, + 619 + ], + "type": "inline_equation", + "content": "Q_{r} \\in \\mathbb{R}^{N_{Q} \\times D}" + }, + { + "bbox": [ + 304, + 511, + 545, + 619 + ], + "type": "text", + "content": " based on the decoded subject and object queries " + }, + { + "bbox": [ + 304, + 511, + 545, + 619 + ], + "type": "inline_equation", + "content": "\\tilde{Q}_{s}, \\tilde{Q}_{o} \\in \\mathbb{R}^{N_{Q} \\times D}" + }, + { + "bbox": [ + 304, + 511, + 545, + 619 + ], + "type": "text", + "content": ", and performs decoding to obtain " + }, + { + "bbox": [ + 304, + 511, + 545, + 619 + ], + "type": "inline_equation", + "content": "\\tilde{Q}_{r} \\in \\mathbb{R}^{N_{Q} \\times D}" + }, + { + "bbox": [ + 304, + 511, + 545, + 619 + ], + "type": "text", + "content": " for relation recognition. The design of RLIPv1-ParSeD obeys the following probabilistic factorization:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 315, + 625, + 545, + 651 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 625, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 315, + 625, + 545, + 651 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbb {P} \\left(\\boldsymbol {G} \\mid \\boldsymbol {Q} _ {s}, \\boldsymbol {Q} _ {o}, \\boldsymbol {C} _ {E}; \\boldsymbol {\\theta} _ {P a r}, \\boldsymbol {\\theta} _ {S e}\\right) = \\tag {1} \\\\ \\mathbb {P} \\left(\\boldsymbol {B} _ {s}, \\boldsymbol {B} _ {o} \\mid \\boldsymbol {Q} _ {s}, \\boldsymbol {Q} _ {o}, \\boldsymbol {C} _ {E}; \\boldsymbol {\\theta} _ {P a r}\\right) \\cdot \\mathbb {P} \\left(\\boldsymbol {R} \\mid \\boldsymbol {B} _ {s}, \\boldsymbol {B} _ {o}, \\boldsymbol {C} _ {E}; \\boldsymbol {\\theta} _ {S e}\\right) \\\\ \\end{array}", + "image_path": "5025358e4cce238beb8539f5303d4a0ed35b9df50e12e6c4043605b6837b25a7.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 660, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 660, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 305, + 660, + 545, + 685 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 660, + 545, + 685 + ], + "type": "inline_equation", + "content": "C_E" + }, + { + "bbox": [ + 305, + 660, + 545, + 685 + ], + "type": "text", + "content": " denotes features from the DDETR encoder; " + }, + { + "bbox": [ + 305, + 660, + 545, + 685 + ], + "type": "inline_equation", + "content": "\\theta_{Par},\\theta_{Se}" + }, + { + "bbox": [ + 305, + 660, + 545, + 685 + ], + "type": "text", + "content": " denote parameters for Parallel Entity Detection" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "text", + "content": "2Since RLIPv2 targets fast scaling, we only focus on DDETR-based detection architecture." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21650" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 272, + 207 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 272, + 207 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 272, + 207 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 272, + 207 + ], + "type": "image", + "image_path": "809772b0dbebb81a18fa65cc11dde1fb8e0f984dfa613a154803b94d7c597e00.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 149, + 214, + 165, + 226 + ], + "lines": [ + { + "bbox": [ + 149, + 214, + 165, + 226 + ], + "spans": [ + { + "bbox": [ + 149, + 214, + 165, + 226 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 276, + 71, + 545, + 213 + ], + "blocks": [ + { + "bbox": [ + 276, + 71, + 545, + 213 + ], + "lines": [ + { + "bbox": [ + 276, + 71, + 545, + 213 + ], + "spans": [ + { + "bbox": [ + 276, + 71, + 545, + 213 + ], + "type": "image", + "image_path": "b78474a5ee4a6c050624c514035213567af73368922067822a98756661849224.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 418, + 214, + 433, + 226 + ], + "lines": [ + { + "bbox": [ + 418, + 214, + 433, + 226 + ], + "spans": [ + { + "bbox": [ + 418, + 214, + 433, + 226 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 238, + 546, + 273 + ], + "lines": [ + { + "bbox": [ + 46, + 238, + 546, + 273 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 546, + 273 + ], + "type": "text", + "content": "Figure 2: The overview of (a) RLIPv1-ParSeD and (b) RLIPv2-ParSeD and R-Tagger. The red part (loss calculation and noise injection) is only valid during training. In (a), Cross-Modal Fusion is achieved by the cross encoder. In (b), Cross-Modal Fusion is achieved by ALIF. The two architectures have an equivalent number of DDETR layers." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 287, + 287, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 287, + 287, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 287, + 323 + ], + "type": "text", + "content": "and Sequential Relation Inference; " + }, + { + "bbox": [ + 46, + 287, + 287, + 323 + ], + "type": "inline_equation", + "content": "B_{s}, B_{o}, R" + }, + { + "bbox": [ + 46, + 287, + 287, + 323 + ], + "type": "text", + "content": " are sets of detected subject boxes, object boxes and relations, respectively. They collectively comprise the detection results " + }, + { + "bbox": [ + 46, + 287, + 287, + 323 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 287, + 287, + 323 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 323, + 287, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 287, + 395 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 287, + 395 + ], + "type": "text", + "content": "For Cross-Modal Fusion, RLIPv1-ParSeD appends additional Transformer encoding layers [74, 34, 43] to perform language-image feature fusion on top of the decoded relation features " + }, + { + "bbox": [ + 46, + 323, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\tilde{Q}_r" + }, + { + "bbox": [ + 46, + 323, + 287, + 395 + ], + "type": "text", + "content": ", entity label features " + }, + { + "bbox": [ + 46, + 323, + 287, + 395 + ], + "type": "inline_equation", + "content": "L_{E} \\in \\mathbb{R}^{N_{E} \\times D}" + }, + { + "bbox": [ + 46, + 323, + 287, + 395 + ], + "type": "text", + "content": " and relation label features " + }, + { + "bbox": [ + 46, + 323, + 287, + 395 + ], + "type": "inline_equation", + "content": "L_{R} \\in \\mathbb{R}^{N_{R} \\times D}" + }, + { + "bbox": [ + 46, + 323, + 287, + 395 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 323, + 287, + 395 + ], + "type": "inline_equation", + "content": "L_{E}, L_{R}" + }, + { + "bbox": [ + 46, + 323, + 287, + 395 + ], + "type": "text", + "content": " are extracted from RoBERTa [58]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 405, + 129, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 405, + 129, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 405, + 129, + 418 + ], + "type": "text", + "content": "4. Methodology" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 425, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 287, + 498 + ], + "type": "text", + "content": "In this section, we will introduce: (i) Asymmetric Language-Image Fusion (ALIF) as an efficient CrossModal Fusion mechanism in RLIPv2, as shown in Fig. 2(b); (ii) the overall framework of extending the off-the-shelf object detection datasets [53, 69] to support relational pretraining." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 503, + 244, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 503, + 244, + 517 + ], + "spans": [ + { + "bbox": [ + 47, + 503, + 244, + 517 + ], + "type": "text", + "content": "4.1. Asymmetric Language-Image Fusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "text", + "content": "The core idea underpinning ALIF is to perform efficient cross-modal fusion in the early stages of RLIPv2 as highlighted by [15, 44]. Unlike RLIPv1 that encourages cross-modal alignment for entities and relations after the decoding phase, ALIF performs this during the detection encoding phase. This is particularly challenging for DDETR's encoder, since it relies on deformable attention that makes it challenging to adopt dedicated encoder layers during the detection encoding phase like [34, 60, 16]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "To address this, we propose ALIF, a mechanism that leverages DDETR encoding for the vision branch, RoBERTa encoding for the language branch and gated cross-attention for fusion. In contrast to previous work that encodes image and language with an equivalent number of layers [34, 16, 44, 15], we experimentally find that excessive RoBERTa layers do not improve its generalization" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 287, + 545, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 287, + 545, + 382 + ], + "spans": [ + { + "bbox": [ + 304, + 287, + 545, + 382 + ], + "type": "text", + "content": "capability due to its potential for overfitting to pre-trained data. Moreover, such a paradigm results in training difficulty due to the increased model complexity. As a result, we perform DDETR encoding densely while performing RoBERTa encoding sparsely. We denote the vision features from the backbone as " + }, + { + "bbox": [ + 304, + 287, + 545, + 382 + ], + "type": "inline_equation", + "content": "C^{(0)}" + }, + { + "bbox": [ + 304, + 287, + 545, + 382 + ], + "type": "text", + "content": " and language features from RoBERTa as " + }, + { + "bbox": [ + 304, + 287, + 545, + 382 + ], + "type": "inline_equation", + "content": "L^{(0)}" + }, + { + "bbox": [ + 304, + 287, + 545, + 382 + ], + "type": "text", + "content": " (the concatenation of " + }, + { + "bbox": [ + 304, + 287, + 545, + 382 + ], + "type": "inline_equation", + "content": "L_{E}" + }, + { + "bbox": [ + 304, + 287, + 545, + 382 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 287, + 545, + 382 + ], + "type": "inline_equation", + "content": "L_{R}" + }, + { + "bbox": [ + 304, + 287, + 545, + 382 + ], + "type": "text", + "content": "). The first ALIF module can be formulated as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 348, + 389, + 545, + 405 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 389, + 545, + 405 + ], + "spans": [ + { + "bbox": [ + 348, + 389, + 545, + 405 + ], + "type": "interline_equation", + "content": "\\tilde {\\boldsymbol {C}} ^ {(0)}, \\tilde {\\boldsymbol {L}} ^ {(0)} = \\operatorname {C r o s s - a t t n} \\left(\\boldsymbol {C} ^ {(0)}, \\boldsymbol {L} ^ {(0)}\\right) \\tag {2}", + "image_path": "47d2077b0b98e1242d4b9d82847b468feaa96845ac6d3b3f9cd26fd1b0e4a5ea.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 343, + 423, + 545, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 423, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 343, + 423, + 545, + 437 + ], + "type": "interline_equation", + "content": "\\boldsymbol {C} ^ {\\left(N _ {v}\\right)} = \\mathrm {D D E T R} ^ {N _ {v}} \\left(\\boldsymbol {C} ^ {(0)} + \\mathrm {G} \\left(\\tilde {\\boldsymbol {C}} ^ {(0)}\\right)\\right) \\tag {3}", + "image_path": "17b04336a6a12e8d1d49ab8063cb7edf271327b7bd8fef5dee810d14ab873ad9.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 348, + 453, + 545, + 468 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 453, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 348, + 453, + 545, + 468 + ], + "type": "interline_equation", + "content": "\\boldsymbol {L} ^ {(1)} = \\operatorname {R o B E R T a} ^ {1} \\left(\\boldsymbol {L} ^ {(0)} + \\mathrm {G} \\left(\\tilde {\\boldsymbol {L}} ^ {(0)}\\right)\\right) \\tag {4}", + "image_path": "296446e1094c4075682dfc795c5da86f4cf0757f95ad89ffdfa98e9135e33da0.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "inline_equation", + "content": "\\tilde{C}^{(0)}" + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": " denotes language features aggregated by cross attention, and " + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "inline_equation", + "content": "\\tilde{L}^{(0)}" + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": " is analogously defined; " + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "inline_equation", + "content": "N_{v}" + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": " is the number of DDETR layers in one ALIF; " + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "inline_equation", + "content": "\\mathrm{G}(\\pmb{x})" + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": " defines a gating function that gates the aggregated cross-modal features. Note that " + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "inline_equation", + "content": "C_E" + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "inline_equation", + "content": "C^{(N_v)}" + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": " after stacking " + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "inline_equation", + "content": "N_{ALIF}" + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": " ALIF layers for encoding. For the instantiation of " + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "inline_equation", + "content": "\\mathrm{G}(\\pmb{x})" + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": ", we experiment with three options: (i) " + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "inline_equation", + "content": "\\mathrm{G}(\\pmb{x}) = \\alpha \\pmb{x}" + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": " is a learnable scalar; (ii) " + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "inline_equation", + "content": "\\mathrm{G}(\\pmb{x}) = \\pmb{a}\\pmb{x}" + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "inline_equation", + "content": "\\pmb{a}" + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": " is a learnable vector; (iii) " + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "inline_equation", + "content": "\\mathrm{G}(\\pmb{x}) = \\mathrm{SE}(\\pmb{x})" + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": " where SE denotes a Squeeze-and-Excitation block [30] with a reduction ratio of 4. We also experiment augmenting " + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "inline_equation", + "content": "\\mathrm{G}(\\pmb{x})" + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "inline_equation", + "content": "\\tanh()" + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": " introduced in [1] (e.g. " + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "inline_equation", + "content": "\\tanh(\\alpha\\pmb{x})" + }, + { + "bbox": [ + 304, + 472, + 545, + 640 + ], + "type": "text", + "content": "), while only observing side effects. This indicates the magnitude of language and vision features are disparate, and a proper gating method is desired." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 647, + 457, + 660 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 457, + 660 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 457, + 660 + ], + "type": "text", + "content": "4.2. Relational Pseudo-labelling" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "RLIPv2 reuses object detection datasets to benefit pretraining by pseudo-labelling, as shown in Fig. 3. We assume that during the pre-training phase, the downstream entity and relation distributions are unavailable to us. Then, to tag" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21651" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 70, + 279, + 149 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 279, + 149 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 279, + 149 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 279, + 149 + ], + "type": "image", + "image_path": "5a79babf17dc25c766b90dff8b11df6a40499ac58d065545e589486b6e3a42f1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 157, + 287, + 191 + ], + "lines": [ + { + "bbox": [ + 46, + 157, + 287, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 157, + 287, + 191 + ], + "type": "text", + "content": "Figure 3: An overview of relational pseudo-labeling, which tags object detection data with free-form relation texts. This process enables pre-training to be performed on two kinds of data." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 207, + 286, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 207, + 286, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 207, + 286, + 243 + ], + "type": "text", + "content": "relation texts, we need to sort out the relations contained in the image as detailed in Sec. 4.2.1, and to tag relation texts to region pairs as detailed in Sec. 4.2.2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 255, + 230, + 266 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 255, + 230, + 266 + ], + "spans": [ + { + "bbox": [ + 47, + 255, + 230, + 266 + ], + "type": "text", + "content": "4.2.1 Relation Candidate Set Generation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 274, + 286, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 274, + 286, + 405 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 286, + 405 + ], + "type": "text", + "content": "For a given image, relation candidate set generation aims to generate a coarse-grained set of candidate subject-object (SO) region pairs " + }, + { + "bbox": [ + 46, + 274, + 286, + 405 + ], + "type": "inline_equation", + "content": "\\pmb{P}" + }, + { + "bbox": [ + 46, + 274, + 286, + 405 + ], + "type": "text", + "content": " and their candidate relation texts " + }, + { + "bbox": [ + 46, + 274, + 286, + 405 + ], + "type": "inline_equation", + "content": "\\pmb{T}" + }, + { + "bbox": [ + 46, + 274, + 286, + 405 + ], + "type": "text", + "content": ". First, we adopt BLIP to generate " + }, + { + "bbox": [ + 46, + 274, + 286, + 405 + ], + "type": "inline_equation", + "content": "N_{Cap}" + }, + { + "bbox": [ + 46, + 274, + 286, + 405 + ], + "type": "text", + "content": " captions for each image. Note that when " + }, + { + "bbox": [ + 46, + 274, + 286, + 405 + ], + "type": "inline_equation", + "content": "N_{Cap} = 1" + }, + { + "bbox": [ + 46, + 274, + 286, + 405 + ], + "type": "text", + "content": ", we generate the caption via beam search, a deterministic generation method; when " + }, + { + "bbox": [ + 46, + 274, + 286, + 405 + ], + "type": "inline_equation", + "content": "N_{Cap} > 1" + }, + { + "bbox": [ + 46, + 274, + 286, + 405 + ], + "type": "text", + "content": ", we generate captions via nucleus sampling [26], a stochastic generation methods with cumulative probability threshold set to 0.9. Nucleus sampling adds semantic diversity to the generated captions, which contributes to diversity in the relations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 407, + 286, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 286, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 286, + 514 + ], + "type": "text", + "content": "Second, we adopt a scene graph parser [68] to parse the obtained captions into relation triplets. To filter out invalid parsed triplets, we perform string matching and keep those whose subjects and objects can be matched with any entities' names or entities' synonyms within the image [86]. This operation encloses a small set of possible SO region pairs " + }, + { + "bbox": [ + 46, + 407, + 286, + 514 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 407, + 286, + 514 + ], + "type": "text", + "content": " and possible relation texts " + }, + { + "bbox": [ + 46, + 407, + 286, + 514 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 407, + 286, + 514 + ], + "type": "text", + "content": " for the pairs (which are inputs to R-Tagger), without needing to traverse all possible pairs." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 526, + 256, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 526, + 256, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 526, + 256, + 538 + ], + "type": "text", + "content": "4.2.2 Relation Tagger via RLIPv2 Architecture" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "type": "text", + "content": "The R-Tagger aims to assign candidate relation texts " + }, + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "type": "text", + "content": " to candidate SO region pairs " + }, + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "type": "text", + "content": " for a given image. While one alternative is executing the pre-trained RLIPv2 model to perform SGG on object detection datasets to obtain pseudotriplets, the informative object annotations fail to be utilized directly during the execution of RLIPv2. As a result, the quality of pseudo-labels is degraded. A prior work [100] adopts a coarse rule-based pseudo-labelling method that employed a greedy matching algorithm to randomly assign one relation text to an SO region pair as long as the relation texts' corresponding SO texts match with the SO region pair. An \"overlap\" prior was applied to further filter the triplets (i.e., a triplet is deemed valid only if the subject and object are overlapped). This method, however," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "introduces excessive false positives, causing degraded pretraining. Thus, we propose to reuse the RLIPv2 architecture to perform relation prediction given ground-truth SO region pairs as shown in Figure Fig. 2(b)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "spans": [ + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "text", + "content": "As outlined in Sec. 3, RLIPv2 also utilizes subject queries " + }, + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "inline_equation", + "content": "Q_{s}" + }, + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "text", + "content": " and object queries " + }, + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "inline_equation", + "content": "Q_{o}" + }, + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "text", + "content": " as input. To allow for the utilization of object annotations as the input, we propose to replace the detection queries " + }, + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "inline_equation", + "content": "Q_{s}" + }, + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "inline_equation", + "content": "Q_{o}" + }, + { + "bbox": [ + 304, + 120, + 545, + 227 + ], + "type": "text", + "content": " with object embeddings [40], which aims to encourage Parallel Entity Detection to reconstruct object representations and Sequential Relation Inference to recognize relations. Compared with Eq. (1), the probabilistic factorisation of R-Tagger during inference can be reformulated as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 315, + 233, + 545, + 262 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 233, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 315, + 233, + 545, + 262 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbb {P} (\\boldsymbol {R} | \\hat {\\boldsymbol {B}} _ {s}, \\hat {\\boldsymbol {B}} _ {o}, \\boldsymbol {C} _ {E}; \\boldsymbol {\\theta} _ {P a r}, \\boldsymbol {\\theta} _ {S e}) = \\tag {5} \\\\ \\mathbb {P} \\left(\\hat {\\boldsymbol {B}} _ {s}, \\hat {\\boldsymbol {B}} _ {o} \\mid \\hat {\\boldsymbol {B}} _ {s}, \\hat {\\boldsymbol {B}} _ {o}, \\boldsymbol {C} _ {E}; \\boldsymbol {\\theta} _ {P a r}\\right) \\cdot \\mathbb {P} \\left(\\boldsymbol {R} \\mid \\hat {\\boldsymbol {B}} _ {s}, \\hat {\\boldsymbol {B}} _ {o}, \\boldsymbol {C} _ {E}; \\boldsymbol {\\theta} _ {S e}\\right) \\\\ \\end{array}", + "image_path": "8e69a3501c5ee4353aa41945302e22fa1fa159b9121729956bd5cb638d9f928e.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 268, + 545, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 268, + 545, + 352 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 545, + 352 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 268, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\hat{B}_s, \\hat{B}_o" + }, + { + "bbox": [ + 304, + 268, + 545, + 352 + ], + "type": "text", + "content": " denote the ground-truth SO boxes from the region pair set " + }, + { + "bbox": [ + 304, + 268, + 545, + 352 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 268, + 545, + 352 + ], + "type": "text", + "content": " that include their positions and labels); " + }, + { + "bbox": [ + 304, + 268, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\tilde{B}_s, \\tilde{B}_o" + }, + { + "bbox": [ + 304, + 268, + 545, + 352 + ], + "type": "text", + "content": " denote contextualized SO representations. To allow for decoding, we embed " + }, + { + "bbox": [ + 304, + 268, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\hat{B}_s, \\hat{B}_o" + }, + { + "bbox": [ + 304, + 268, + 545, + 352 + ], + "type": "text", + "content": " to have an equivalent dimension with queries. Specifically, we use MLPs to project positions and label text embeddings, and concatenate them along the channel dimension to obtain query-like input." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 353, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 353, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 305, + 353, + 545, + 376 + ], + "type": "text", + "content": "Denoising training of R-Tagger. The training losses of R-Tagger are identical to RLIPv1:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 321, + 383, + 545, + 396 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 383, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 321, + 383, + 545, + 396 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda_ {1} \\mathcal {L} _ {l 1} + \\lambda_ {2} \\mathcal {L} _ {G I o U} + \\lambda_ {3} \\left(\\mathcal {L} _ {s} + \\mathcal {L} _ {o}\\right) + \\lambda_ {4} \\mathcal {L} _ {r} \\tag {6}", + "image_path": "6311c54b17c97ad7f123f9411b83f7f0c44756a53e0ccf6731b0af7c83b4f3bc.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 403, + 545, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 462 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 462 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 403, + 545, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 304, + 403, + 545, + 462 + ], + "type": "text", + "content": " is comprised of the " + }, + { + "bbox": [ + 304, + 403, + 545, + 462 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 304, + 403, + 545, + 462 + ], + "type": "text", + "content": " loss for box regression " + }, + { + "bbox": [ + 304, + 403, + 545, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{l1}" + }, + { + "bbox": [ + 304, + 403, + 545, + 462 + ], + "type": "text", + "content": ", GIoU loss [67] " + }, + { + "bbox": [ + 304, + 403, + 545, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{G IoU}" + }, + { + "bbox": [ + 304, + 403, + 545, + 462 + ], + "type": "text", + "content": ", Cross-Entropy (CE) loss for subject and object classes " + }, + { + "bbox": [ + 304, + 403, + 545, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_s, \\mathcal{L}_o" + }, + { + "bbox": [ + 304, + 403, + 545, + 462 + ], + "type": "text", + "content": ", and Focal loss [52] for relations " + }, + { + "bbox": [ + 304, + 403, + 545, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_r" + }, + { + "bbox": [ + 304, + 403, + 545, + 462 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 403, + 545, + 462 + ], + "type": "inline_equation", + "content": "\\lambda_1, \\lambda_2, \\lambda_3, \\lambda_4" + }, + { + "bbox": [ + 304, + 403, + 545, + 462 + ], + "type": "text", + "content": " are set to 2.5, 1, 1, 1 as fixed weights to balance multi-task training [86, 89, 71]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 462, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 617 + ], + "type": "text", + "content": "However, due to the identical input and training objectives of Parallel Entity Detection, the model will attempt to find a shortcut, i.e., identity mapping, to achieve the minimum loss value. To avoid this, we draw inspiration from [40] which adds noise to " + }, + { + "bbox": [ + 304, + 462, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\hat{B}_s, \\hat{B}_o" + }, + { + "bbox": [ + 304, + 462, + 545, + 617 + ], + "type": "text", + "content": " during training. Specifically, we follow [40] to add center shifting and box scaling noise to box positions and add label flipping noise to box labels. The noise scale of center shifting and box scaling is set to 0.4, and the noise scale of label flipping is set to 0.2 following [40]. Furthermore, to prevent the information leakage between the same region with different noise, we apply attention masks to block the information flow between the same regions in Parallel Entity Detection." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Inference of R-Tagger. After the training of R-Tagger, we can use it to infer relations without additional noise based on Eq. (5). For each inference, the maximum number of region pairs is " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "N_{Q}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": ". If candidate SO region pairs exceed " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "N_{Q}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": ", we infer multiple times and merge the results. To quantify the confidence of a relation, we calculate the product of the top-1 score from the softmax distribution over the subject, the object and the original relation sigmoid score. To" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21652" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 71, + 283, + 145 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 283, + 145 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 283, + 145 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 283, + 145 + ], + "type": "table", + "html": "
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", + "image_path": "4d3f3be4e1ab78385eb766b15ef8d44a9b705456fb287d671b0b93163c4286b1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 212, + 287, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 212, + 287, + 248 + ], + "spans": [ + { + "bbox": [ + 46, + 212, + 287, + 248 + ], + "type": "text", + "content": "select pseudo-labels, we choose those whose relation confidence exceeds a threshold " + }, + { + "bbox": [ + 46, + 212, + 287, + 248 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 212, + 287, + 248 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 212, + 287, + 248 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 212, + 287, + 248 + ], + "type": "text", + "content": " is set to 0.2 by default (details can be found in the Appendix)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 256, + 255, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 256, + 255, + 269 + ], + "spans": [ + { + "bbox": [ + 47, + 256, + 255, + 269 + ], + "type": "text", + "content": "4.3. Pre-training, Fine-tuning and Inference" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 274, + 287, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 274, + 287, + 431 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 287, + 431 + ], + "type": "text", + "content": "Regarding pre-training and fine-tuning of RLIPv2, we first merge results from Parallel Entity Detection and Sequential Relation Inference to obtain " + }, + { + "bbox": [ + 46, + 274, + 287, + 431 + ], + "type": "inline_equation", + "content": "N_{Q}" + }, + { + "bbox": [ + 46, + 274, + 287, + 431 + ], + "type": "text", + "content": " triplets. Next, we employ the bipartite matching algorithm originally proposed in [71] to match the predicted and ground-truth triplet annotations. The overall loss is identical to Eq. (6). The techniques introduced in RLIPv1, i.e. Label Sequence Extension, Relation Quality Labels and Relation Pseudo-Labels, are employed by default for a fair comparison. Regarding the inference of RLIPv2, we sort the relation confidence (defined in Sec. 4.2.2) of the correctly localised triplets (IoU > 0.5) and select the Top-K triplets. " + }, + { + "bbox": [ + 46, + 274, + 287, + 431 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 274, + 287, + 431 + ], + "type": "text", + "content": " is set to 100 by default following [86, 71, 45, 11]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 441, + 128, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 128, + 455 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 128, + 455 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 461, + 287, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 558 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 558 + ], + "type": "text", + "content": "Pre-training datasets. To pre-train RLIPv2, we utilize VG [38], COCO [53] and Objects365 [69]. VG has " + }, + { + "bbox": [ + 46, + 461, + 287, + 558 + ], + "type": "inline_equation", + "content": "108k" + }, + { + "bbox": [ + 46, + 461, + 287, + 558 + ], + "type": "text", + "content": " images annotated with free-form relation and object annotations. COCO has " + }, + { + "bbox": [ + 46, + 461, + 287, + 558 + ], + "type": "inline_equation", + "content": "117k" + }, + { + "bbox": [ + 46, + 461, + 287, + 558 + ], + "type": "text", + "content": " images with only object annotations in 80 classes, and Objects365 has " + }, + { + "bbox": [ + 46, + 461, + 287, + 558 + ], + "type": "inline_equation", + "content": "1,742k" + }, + { + "bbox": [ + 46, + 461, + 287, + 558 + ], + "type": "text", + "content": " images with only object annotations in 365 classes. Thus, we use relational pseudo-labelling to tag relation labels for COCO and Objects365, enabling them to support relational pre-training." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 558, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 714 + ], + "type": "text", + "content": "Downstream datasets. For HOI detection, we follow [71, 86, 89, 93] to evaluate on HICO-DET [4] and V-COCO [22]. For HICO-DET that contains 117 verbs and 80 objects, we evaluate under the Default setting on Full, Rare and Non-Rare sets. For V-COCO that contains 24 interactions and 80 objects, we evaluate following the official evaluation code [22] under two scenarios: " + }, + { + "bbox": [ + 46, + 558, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{role}^{\\#1}" + }, + { + "bbox": [ + 46, + 558, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 558, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{role}^{\\#2}" + }, + { + "bbox": [ + 46, + 558, + 287, + 714 + ], + "type": "text", + "content": ". For SGG, we assess RLIPv2 on the widely-used Open Images v6 [39] dataset, which is annotated with 288 objects and 30 relations. We evaluate RLIPv2 using standard evaluation metrics [39, 96]: Recall@50 (R@50), weighted mean Average Precision for relation detection (" + }, + { + "bbox": [ + 46, + 558, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{wmAP}_{rel}" + }, + { + "bbox": [ + 46, + 558, + 287, + 714 + ], + "type": "text", + "content": ") and phrase detection (" + }, + { + "bbox": [ + 46, + 558, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{wmAP}_{phr}" + }, + { + "bbox": [ + 46, + 558, + 287, + 714 + ], + "type": "text", + "content": "). The final score is calculated" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 70, + 545, + 160 + ], + "blocks": [ + { + "bbox": [ + 46, + 152, + 287, + 196 + ], + "lines": [ + { + "bbox": [ + 46, + 152, + 287, + 196 + ], + "spans": [ + { + "bbox": [ + 46, + 152, + 287, + 196 + ], + "type": "text", + "content": "Table 1: The effect of the sparsification of language encoding layers in Cross-Modal Fusion. Results are evaluated on HICODET under zero-shot (NF) setting. FPS (frames per second) is tested on a single NVIDIA A100 with a minibatch size 1." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 70, + 545, + 160 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 160 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 160 + ], + "type": "table", + "html": "
Gatingtanh()RareNon-RareFull
α10.4713.8313.05
a✓9.9113.5412.70
SE11.0713.8913.24
α12.1214.0713.62
ax10.9814.0713.36
SE11.0714.0013.32
", + "image_path": "3d99d69b03594671deb6ca8ac798b3e7b79fb6114126ac88da5f68331940b777.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 165, + 545, + 188 + ], + "lines": [ + { + "bbox": [ + 305, + 165, + 545, + 188 + ], + "spans": [ + { + "bbox": [ + 305, + 165, + 545, + 188 + ], + "type": "text", + "content": "Table 2: Comparisons of different gating functions introduced in Sec. 4.1. We report zero-shot (NF) results on HICO-DET." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 204, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 204, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 305, + 204, + 545, + 228 + ], + "type": "text", + "content": "as: " + }, + { + "bbox": [ + 305, + 204, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\mathrm{score}_{wtd} = 0.2 * \\mathrm{R} @ 50 + 0.4 * \\mathrm{wmAP}_{rel} + 0.4 * \\mathrm{wmAP}_{phr}" + }, + { + "bbox": [ + 305, + 204, + 545, + 228 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 228, + 546, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 546, + 528 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 546, + 528 + ], + "type": "text", + "content": "Implementation details. To assess the effectiveness of RLIPv2, we choose to adopt DDETR [102] to compose RLIPv2-ParSeD and adopt DAB-DDETR [56] to compose RLIPv2-ParSeDA. To perform a fair comparison with previous works, we ensure that RLIPv2 has " + }, + { + "bbox": [ + 304, + 228, + 546, + 528 + ], + "type": "inline_equation", + "content": "N_v * N_{ALIF} = 6" + }, + { + "bbox": [ + 304, + 228, + 546, + 528 + ], + "type": "text", + "content": " DDETR/DAB-DDETR encoding layers. For Parallel Entity Detection and Sequential Relation Inference, 3 layers are adopted following [86, 89, 71, 93]. " + }, + { + "bbox": [ + 304, + 228, + 546, + 528 + ], + "type": "inline_equation", + "content": "N_Q" + }, + { + "bbox": [ + 304, + 228, + 546, + 528 + ], + "type": "text", + "content": " is set to 100 during pre-training and fine-tuning, except when we finetune on HICO-DET where " + }, + { + "bbox": [ + 304, + 228, + 546, + 528 + ], + "type": "inline_equation", + "content": "N_Q" + }, + { + "bbox": [ + 304, + 228, + 546, + 528 + ], + "type": "text", + "content": " is set to 64 following [93]. Regarding model initialization, we use COCO detection parameters as initialisation when using VG or VG and COCO for pre-training; when using VG, COCO and Objects365 for pre-training, we use COCO and Object365 detection parameters as initialisation. Regarding the configuration of minibatch sizes and learning rate (LR), we set the minibatch size to 64, LR for the text encoder to 1.41e-5 and LR for other modules to 1.41e-4 when using ResNet-50 [25] and Swin-T [59]; We set the minibatch size to 32, LR for the text encoder to 1e-5 and LR for other modules to 1e-4 when using Swin-L [59]. RLIPv2 and R-Tagger are pre-trained and fine-tuned for 20 epochs unless otherwise stated, with LR dropping by a factor of 10 at the 15th epoch. For the BLIP captioner, we adopt the ViT-L/16 [14] model fine-tuned on COCO Caption [8]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 535, + 400, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 535, + 400, + 548 + ], + "spans": [ + { + "bbox": [ + 306, + 535, + 400, + 548 + ], + "type": "text", + "content": "5.1. Ablation Study" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 553, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 553, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 553, + 545, + 613 + ], + "type": "text", + "content": "We perform the ablation study using RLIPv2-ParSeD with ResNet-50 as the backbone, and VG as the pre-training dataset unless otherwise stated. We pre-train for 20 epochs and evaluate performance on HICO-DET under the zero-shot with no fine-tuning (NF) setting." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 623, + 497, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 623, + 497, + 635 + ], + "spans": [ + { + "bbox": [ + 305, + 623, + 497, + 635 + ], + "type": "text", + "content": "5.1.1 Asymmetric Language-Image Fusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "Sparsification of the language layers. First of all, we ablate on the number of language layers to investigate the effect of sparsifying language encoding layers in CrossModal Fusion. As introduced in Sec. 4.1, dense language layers cause difficult training. To avoid training collapse, we compute classification losses " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_s,\\mathcal{L}_o" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_r)" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " using all" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21653" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 361, + 148 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 361, + 148 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 361, + 148 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 361, + 148 + ], + "type": "table", + "html": "
ModelPre-trainingFully-finetuningFPS
Ep.TimeZero-shot (NF)Ep.Result
RLIPv1-ParSeD5025.9h11.20 / 14.73 / 13.926024.67 / 32.50 / 30.7021.89
RLIPv2-ParSeD2010.9h12.12 / 14.07 / 13.622026.47 / 33.51 / 31.8921.49
RLIPv1-ParSeDA5027.2h11.34 / 14.56 / 13.826022.85 / 30.87 / 29.0319.41
RLIPv2-ParSeDA2011.3h13.03 / 14.98 / 14.532027.01 / 35.21 / 33.3218.94
", + "image_path": "33d246fd37d65749840f938a7139fe379462ba0b70959b3cb9cd8a3c8f3beacf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 369, + 71, + 548, + 145 + ], + "blocks": [ + { + "bbox": [ + 46, + 153, + 362, + 198 + ], + "lines": [ + { + "bbox": [ + 46, + 153, + 362, + 198 + ], + "spans": [ + { + "bbox": [ + 46, + 153, + 362, + 198 + ], + "type": "text", + "content": "Table 3: Comparisons of RLIPv1 and RLIPv2 under zero-shot (NF) and fully-finetuning settings on HICO-DET pre-trained on VG. Results are reported on Rare/Non-Rare/Full sets. FPS is tested on a single NVIDIA A100 with minibatch size 1. Pretraining time is tested on 8 NVIDIA A100. \"Ep.\" denotes number of epochs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 369, + 71, + 548, + 145 + ], + "lines": [ + { + "bbox": [ + 369, + 71, + 548, + 145 + ], + "spans": [ + { + "bbox": [ + 369, + 71, + 548, + 145 + ], + "type": "table", + "html": "
InitializationRareNon-RareFull
COCO (default)12.1214.0713.62
R-Tagger12.5513.6413.39
w/o noise9.9412.7412.09
w/o attn masks8.5511.2210.61
", + "image_path": "2b1b6d5cad210d6b428a5fb6744fc9475a1d3c238736e0fa188466805564644a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 213, + 287, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 213, + 287, + 320 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 287, + 320 + ], + "type": "text", + "content": "intermediate language features rather than using only the last layer of language features in Cross-Modal Fusion. Results are shown in Tab. 1. Our findings suggest that sparsifying the language encoder does not compromise zero-shot performance and improves parameter efficiency. We attribute this to overfitting effects on upstream datasets impairing models' generalization. We choose " + }, + { + "bbox": [ + 46, + 213, + 287, + 320 + ], + "type": "inline_equation", + "content": "N_{v} = 2" + }, + { + "bbox": [ + 46, + 213, + 287, + 320 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 213, + 287, + 320 + ], + "type": "inline_equation", + "content": "N_{ALIF} = 3" + }, + { + "bbox": [ + 46, + 213, + 287, + 320 + ], + "type": "text", + "content": " as the default hyper-parameters for the following experiments." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 321, + 288, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 321, + 288, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 321, + 288, + 441 + ], + "type": "text", + "content": "The choice of the gating function " + }, + { + "bbox": [ + 46, + 321, + 288, + 441 + ], + "type": "inline_equation", + "content": "\\mathrm{G}(\\boldsymbol{x})" + }, + { + "bbox": [ + 46, + 321, + 288, + 441 + ], + "type": "text", + "content": ". To investigate the effect of the gating function on cross-modal fusion, we experiment with variants of the gating function as described in Sec. 4.1. The results are shown in Tab. 2. We note that tanh consistently degrades performance for the three gating methods. We conjecture that the output range of tanh can constrain the magnitude of the features to be fused, thus limiting the performance. Based on the results, we choose the simplest one: the learnable scalar gating method parameterised by " + }, + { + "bbox": [ + 46, + 321, + 288, + 441 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 321, + 288, + 441 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 441, + 288, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 441, + 288, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 441, + 288, + 586 + ], + "type": "text", + "content": "Comparisons of RLIPv2 with RLIPv1. To compare the architectural benefit of RLIPv2 with RLIPv1, we adopt DDETR [102] and DAB-DDETR [56] to follow two designs, and evaluate performance under zero-shot (NF) and fully-finetuning setting. Results are shown in Tab. 3. From this table, we can observe that by modifying the architecture without compromising much inference speed, RLIPv2 generally outperforms its RLIPv1 counterpart. Specifically, RLIPv2 obtains comparable zero-shot results to RLIPv1, while costing about " + }, + { + "bbox": [ + 46, + 441, + 288, + 586 + ], + "type": "inline_equation", + "content": "0.4 \\times" + }, + { + "bbox": [ + 46, + 441, + 288, + 586 + ], + "type": "text", + "content": " pre-training time. In terms of fine-tuning results, RLIPv2 surpasses RLIPv1 with " + }, + { + "bbox": [ + 46, + 441, + 288, + 586 + ], + "type": "inline_equation", + "content": "0.33 \\times" + }, + { + "bbox": [ + 46, + 441, + 288, + 586 + ], + "type": "text", + "content": " fine-tuning time due to earlier and deeper fusion." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 597, + 197, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 197, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 197, + 609 + ], + "type": "text", + "content": "5.1.2 Relational Pseudo-labelling" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 616, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 641 + ], + "type": "text", + "content": "By default, we use RLIPv2-ParSeD with ResNet-50 backbone as the basic structure of R-Tagger." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "The necessity of denoising pre-training and attention masks for R-Tagger. If noise is not added during R-Tagger's pre-training, the loss will fluctuate instead of steadily decreasing as the optimization proceeds. If attention masks are not utilized to prevent information leakage, the model will tend to learn an identity mapping, thus de" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 307, + 211, + 545, + 312 + ], + "blocks": [ + { + "bbox": [ + 367, + 152, + 545, + 197 + ], + "lines": [ + { + "bbox": [ + 367, + 152, + 545, + 197 + ], + "spans": [ + { + "bbox": [ + 367, + 152, + 545, + 197 + ], + "type": "text", + "content": "Table 4: The quality of R-Tagger parameters. Results are evaluated using RLIPv2-ParSeD with ResNet-50 under zero-shot (NF) setting." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 211, + 545, + 312 + ], + "lines": [ + { + "bbox": [ + 307, + 211, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 307, + 211, + 545, + 312 + ], + "type": "table", + "html": "
Tagging MethodOverlapRareNon-RareFull
Greedy [100]×11.1511.6511.55
✓13.1614.7014.35
CLIP (ViT-L/14) [65]×12.6612.7612.74
✓14.6314.9414.87
R-Tagger (ResNet-50)×15.3315.5415.49
✓15.3615.3715.36
", + "image_path": "082dbfc465be71a5410a2f424c9e4a44293f1266fc1e80225fd76e88e6cd0bce.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 307, + 370, + 544, + 466 + ], + "blocks": [ + { + "bbox": [ + 305, + 318, + 545, + 364 + ], + "lines": [ + { + "bbox": [ + 305, + 318, + 545, + 364 + ], + "spans": [ + { + "bbox": [ + 305, + 318, + 545, + 364 + ], + "type": "text", + "content": "Table 5: Comparisons of relation tagging methods. \"Overlap\" denotes the \"overlap\" prior for SO pairs introduced in Sec. 4.2.2. We report zero-shot (NF) results pre-trained on VG and COCO. We use oracle captions from COCO Caption [8] (" + }, + { + "bbox": [ + 305, + 318, + 545, + 364 + ], + "type": "inline_equation", + "content": "N_{Cap} = 5" + }, + { + "bbox": [ + 305, + 318, + 545, + 364 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 370, + 544, + 466 + ], + "lines": [ + { + "bbox": [ + 307, + 370, + 544, + 466 + ], + "spans": [ + { + "bbox": [ + 307, + 370, + 544, + 466 + ], + "type": "table", + "html": "
Caption typeNCapRareNon-RareFull
Oracle515.3315.5415.49
BLIP (beam)19.8612.0211.52
BLIP (nucleus)514.6714.7614.74
BLIP (nucleus)1015.0815.1015.09
BLIP (nucleus)2014.2414.9114.75
BLIP (nucleus)*512.3114.3713.89
", + "image_path": "1b2369b9d46f5fbfba5939faa2d7674c93173753ffdca8633e17b9ecd3a296bb.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 472, + 545, + 526 + ], + "lines": [ + { + "bbox": [ + 305, + 472, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 305, + 472, + 545, + 526 + ], + "type": "text", + "content": "Table 6: Comparisons of different caption types. \"beam\" and \"nucleus\" denote beam search and nucleus sampling. \"Oracle\" denotes captions from COCO Caption. By default, we adopt COCO Caption fine-tuned BLIP model. * denotes that we adopt the pretrained BLIP model." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 544, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 651 + ], + "type": "text", + "content": "grading its ability to infer relations. R-Tagger is pre-trained for 20 epochs. To assess the quality of R-Tagger's parameters, thanks to R-Tagger's identical structure to RLIPv2-ParSeD, we initialize RLIPv2-ParSeD with R-Tagger's parameters and pre-train for 10 epochs. We evaluate the zero-shot (NF) performance on HICO-DET as shown in Tab. 4. We observe that removing additional noise or attention masks both impair performance, highlighting their importance." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": "Comparisons of different relation tagging strategies. We compare R-Tagger with other two methods: (i) the greedy matching algorithm [100]; (ii) the CLIP [65] tagging method. Specifically, to tag relations for a given SO region pair with a candidate relation text, the CLIP tagging" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21654" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 71, + 282, + 129 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 282, + 129 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 282, + 129 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 282, + 129 + ], + "type": "table", + "html": "
DatasetRelation candidateRareNon-RareFull
VG-12.1214.0713.62
VG+COCOBLIP15.0815.1015.09
VG+COCOSelection from VG10.3411.3311.11
", + "image_path": "0fafe1e5172c89508a137ceee5a470fd96fb4e5e41236ecebba4643369909785.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 168, + 286, + 215 + ], + "blocks": [ + { + "bbox": [ + 47, + 136, + 286, + 159 + ], + "lines": [ + { + "bbox": [ + 47, + 136, + 286, + 159 + ], + "spans": [ + { + "bbox": [ + 47, + 136, + 286, + 159 + ], + "type": "text", + "content": "Table 7: Comparisons of methods to generate relation candidate sets. We report zero-shot (NF) results on HICO-DET." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 168, + 286, + 215 + ], + "lines": [ + { + "bbox": [ + 48, + 168, + 286, + 215 + ], + "spans": [ + { + "bbox": [ + 48, + 168, + 286, + 215 + ], + "type": "table", + "html": "
VGVG+COCOVG+COCO+O365
ResNet-5013.03 / 14.98 / 14.5315.00 / 16.60 / 16.2319.64 / 17.24 / 17.79
Swin-T13.01 / 16.06 / 15.3517.13 / 18.74 / 18.3721.24 / 19.47 / 19.87
Swin-L19.93 / 18.74 / 19.0222.59 / 21.09 / 21.4427.97 / 21.90 / 23.29
", + "image_path": "32ef1707c76c2c3c3ccef2c914c2f1fc65ca943fe3a8f3919823a18e453f1fa2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 48, + 266, + 288, + 439 + ], + "blocks": [ + { + "bbox": [ + 47, + 223, + 286, + 256 + ], + "lines": [ + { + "bbox": [ + 47, + 223, + 286, + 256 + ], + "spans": [ + { + "bbox": [ + 47, + 223, + 286, + 256 + ], + "type": "text", + "content": "Table 8: Model and dataset scaling experiments using RLIPv2-ParSeDA. Results are evaluated on HICO-DET Rare/Non-Rare/Full sets under zero-shot (NF) setting." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 266, + 288, + 439 + ], + "lines": [ + { + "bbox": [ + 48, + 266, + 288, + 439 + ], + "spans": [ + { + "bbox": [ + 48, + 266, + 288, + 439 + ], + "type": "table", + "html": "
ModelBackboneExtramR@50R@50wmAPscore_wtd
relphr
VCTree [73]X101-F-33.9174.0834.1633.1140.21
G-RCNN [82]X101-F-34.0474.5133.5134.2141.84
Motifs [90]X101-F-32.6871.6329.9131.5938.93
Unbiased [72]X101-F-35.4769.3030.7432.8039.27
GPS-Net [54]X101-F-35.2674.8132.8533.9841.69
RelDN [96]R101-36.8072.7529.8730.4238.67
BGNN [46]R101-39.4174.9331.1531.3740.00
SGTR [45]R101-42.6159.9136.9838.7342.28
RelTR [11]R50--64.4734.1737.4441.54
RLIPv2-ParSeDR50*-44.5858.0443.3043.1246.18
R50*-44.8860.2044.7343.3647.28
R50†-45.5961.1545.7143.7348.01
RLIPv2-ParSeDAR50(i)50.4263.3547.6545.2349.82
R50(ii)52.0764.5349.1446.1451.01
R50(iii)51.3165.9949.5445.7151.30
Swin-T(iii)59.6168.8152.7048.0154.05
Swin-L(iii)64.7272.4956.3850.7057.34
", + "image_path": "d08dc12069963d4d077ec1ed73bd8fde4c060be95baecf9174a7c12cb8ec2bde.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 521, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 286, + 713 + ], + "type": "text", + "content": "method clips the minimum bounding box of the SO region pair, creates two prompts (\"a photo of {subject} {relation} {object}\" and \"a photo of {subject} not interacting with {object}\" are adopted as positive and negative prompts.), and performs zero-shot prediction. If the softmax probability of the positive prompt is greater than a pre-defined threshold, we tag this relation text to this SO region pair. (We traverse the threshold and find the optimal one for the CLIP tagging method, as detailed in the Appendix.) We also ablate on the \"overlap\" prior [100] to observe whether a given tagging method relies on strong prior knowledge to filter out false positive relations. The results are shown in Tab. 5. From this table, we conclude that greedy matching and CLIP tagging method generate a significant number of low-quality non-overlapped triplets. Thus, the \"overlap\" prior is essential for them. R-Tagger, however, suf" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 71, + 547, + 162 + ], + "blocks": [ + { + "bbox": [ + 47, + 447, + 286, + 502 + ], + "lines": [ + { + "bbox": [ + 47, + 447, + 286, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 447, + 286, + 502 + ], + "type": "text", + "content": "Table 9: Comparisons with previous methods on Open Images v6 SGG benchmark. X101-F denote ResNeXt-101 FPN [80]. " + }, + { + "bbox": [ + 47, + 447, + 286, + 502 + ], + "type": "inline_equation", + "content": "{}^{ * }" + }, + { + "bbox": [ + 47, + 447, + 286, + 502 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 447, + 286, + 502 + ], + "type": "inline_equation", + "content": "{}^{ \\dagger }" + }, + { + "bbox": [ + 47, + 447, + 286, + 502 + ], + "type": "text", + "content": " denote ImageNet pretrained and COCO object detection pretrained. \"Extra\" denotes extra relations adopted from (i) VG, (ii) VG+COCO and (iii) VG+COCO+O365." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 71, + 547, + 162 + ], + "lines": [ + { + "bbox": [ + 307, + 71, + 547, + 162 + ], + "spans": [ + { + "bbox": [ + 307, + 71, + 547, + 162 + ], + "type": "table", + "html": "
MethodBackboneUC-RFUC-NF
VCL [27]ResNet-5010.06 / 24.28 / 21.4316.22 / 18.52 / 18.06
ATL [28]ResNet-509.18 / 24.67 / 21.5718.25 / 18.78 / 18.67
FCL [29]ResNet-5013.16 / 24.23 / 22.0118.66 / 19.55 / 19.37
GEN-VLKT [51]ResNet-5021,36 / 32.91 / 30.5625.05 / 23.38 / 23.71
RLIPv1-ParSeD [86]ResNet-5016.43 / 30.59 / 27.7616.99 / 24.71 / 22.93
RLIPv1-ParSe [86]ResNet-5019.19 / 33.35 / 30.5220.27 / 27.67 / 26.19
RLIPv2-ParSeDAResNet-5021.45 / 35.85 / 32.9722.81 / 29.52 / 28.18
RLIPv2-ParSeDASwin-T26.95 / 39.92 / 37.3221.07 / 35.07 / 32.27
RLIPv2-ParSeDASwin-L31.23 / 45.01 / 42.2622.65 / 40.51 / 36.94
", + "image_path": "cc82df002864da9ade466256a3d093b76db5da5606b4192f2a26d896ccd54cf2.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 209, + 547, + 272 + ], + "blocks": [ + { + "bbox": [ + 306, + 169, + 545, + 203 + ], + "lines": [ + { + "bbox": [ + 306, + 169, + 545, + 203 + ], + "spans": [ + { + "bbox": [ + 306, + 169, + 545, + 203 + ], + "type": "text", + "content": "Table 10: Comparisons with methods on HICO-DET under UC-RF and UC-NF settings. We adopt ResNet-50 as the backbone. Results are reported on Unseen/Seen/Full sets." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 209, + 547, + 272 + ], + "lines": [ + { + "bbox": [ + 307, + 209, + 547, + 272 + ], + "spans": [ + { + "bbox": [ + 307, + 209, + 547, + 272 + ], + "type": "table", + "html": "
MethodBackbone1% Data10% Data
RLIPv1-ParSeD [86]ResNet-5016.22 / 18.92 / 18.3015.89 / 23.94 / 22.09
RLIPv1-ParSe [86]ResNet-5017.47 / 18.76 / 18.4620.16 / 23.32 / 22.59
RLIPv2-ParSeDAResNet-5022.13 / 24.51 / 23.9623.28 / 30.02 / 28.46
RLIPv2-ParSeDASwin-T24.26 / 28.92 / 27.8528.31 / 32.93 / 31.87
RLIPv2-ParSeDASwin-L31.89 / 32.32 / 32.2234.75 / 38.27 / 37.46
", + "image_path": "72b1a99a17bd59af3507b3bbe058452b3a2e36554fafe9521b9134e026d010dc.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 280, + 545, + 301 + ], + "lines": [ + { + "bbox": [ + 306, + 280, + 545, + 301 + ], + "spans": [ + { + "bbox": [ + 306, + 280, + 545, + 301 + ], + "type": "text", + "content": "Table 11: Comparisons on HICO-DET under few-shot settings. Results are reported on Rare/Non-Rare/Full sets." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 318, + 545, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 318, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 304, + 318, + 545, + 378 + ], + "type": "text", + "content": "fers a slight performance drop when using the \"overlap\" prior, indicating that R-Tagger generates more reliable non-overlapped triplets. Besides, although CLIP is pre-trained on a massive quantity of language-image pairs, it struggles in recognizing relations, which R-Tagger is expert in." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 379, + 546, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 379, + 546, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 379, + 546, + 665 + ], + "type": "text", + "content": "Comparisons of different caption types. Previous experiments demonstrate that oracle COCO captions can benefit pre-training. However, most datasets lack such high-quality captions. Thus, BLIP provides an alternative for caption generation. We conduct experiments on various caption types, as shown in Tab. 6. From this table, we can observe that: (i) BLIP-generated captions achieve a decent performance compared to oracle captions, indicating the practicality of adopting generated captions for pseudolabelling. (ii) If we compare BLIP model with different parameters (COCO Caption fine-tuned or only pre-trained), we can see that the fine-tuned model generates better captions with more boost on the Rare set " + }, + { + "bbox": [ + 304, + 379, + 546, + 665 + ], + "type": "inline_equation", + "content": "(12.31\\rightarrow 14.67)" + }, + { + "bbox": [ + 304, + 379, + 546, + 665 + ], + "type": "text", + "content": ". We conjecture that the caption quality of the curated style dataset COCO Caption is better than pre-training captions harvested from the web. (iii) By adopting generated captions, we can increase the number of captions per image, thus diversifying the relations contained in captions and boost RLIPv2 " + }, + { + "bbox": [ + 304, + 379, + 546, + 665 + ], + "type": "inline_equation", + "content": "(11.52\\rightarrow 15.09)" + }, + { + "bbox": [ + 304, + 379, + 546, + 665 + ], + "type": "text", + "content": ". Besides, although datasets like Conceptual Caption [70] (CC3M) also provide captions, the quantity of captions (average one caption per image) is not enough to describe many relations in an image. In comparison, our pipeline can work without caption annotation while performing better." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "The necessity of using captioners. By default, we use BLIP to generate relation texts. Another option is to query all possible SO pairs and select all possible relation texts from VG as it contains an enormous quantity of relations" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21655" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 74, + 70, + 519, + 281 + ], + "blocks": [ + { + "bbox": [ + 74, + 70, + 519, + 281 + ], + "lines": [ + { + "bbox": [ + 74, + 70, + 519, + 281 + ], + "spans": [ + { + "bbox": [ + 74, + 70, + 519, + 281 + ], + "type": "table", + "html": "
ModelBackboneExtra RelationsHICO-DETV-COCO
Zero-shot (NF)Fully-finetuningAP#1roleAP#2role
InteractNet [21]R50-FPN--7.16 / 10.77 / 9.9440.0-
UnionDet [35]R50-FPN--11.72 / 19.33 / 17.5847.556.2
PPDM [50]HG104--13.97 / 24.32 / 21.94--
HOTR [36]R50--17.34 / 27.42 / 25.1055.264.4
QPIC [71]R50--21.85 / 31.23 / 29.0758.861.0
OCN [89]R50--25.56 / 32.51 / 30.9164.266.3
CDN [93]R50--27.39 / 32.64 / 31.4461.763.8
GEN-VLKT [51]R50--29.25 / 35.10 / 33.7562.464.5
QAHOI [5]Swin-L*--29.80 / 37.56 / 35.78--
UniVRD [98]ViT-H/14†--31.65 / 39.99 / 38.0765.866.9
RLIPv1-ParSeD [86]R50VG11.20 / 14.73 / 13.9224.67 / 32.50 / 30.7061.763.8
RLIPv1-ParSe [86]R50VG15.08 / 15.50 / 15.4026.85 / 34.63 / 32.8461.964.2
RLIPv2-ParSeDAR50VG13.03 / 14.98 / 14.5327.01 / 35.21 / 33.3263.065.1
RLIPv2-ParSeDAR50VG+COCO15.00 / 16.60 / 16.2327.89 / 35.27 / 33.5764.566.7
RLIPv2-ParSeDAR50VG+COCO+O36519.64 / 17.24 / 17.7929.61 / 37.10 / 35.3865.968.0
RLIPv2-ParSeDASwin-TVG+COCO+O36521.24 / 19.47 / 19.8733.66 / 40.07 / 38.6068.870.8
RLIPv2-ParSeDASwin-LVG+COCO+O36527.97 / 21.90 / 23.2943.23 / 45.64 / 45.0972.174.1
", + "image_path": "956bbfefde550206c4dff3de40d1934b0f7fca82a774fa5129841dd16946e2e2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 287, + 545, + 332 + ], + "lines": [ + { + "bbox": [ + 46, + 287, + 545, + 332 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 545, + 332 + ], + "type": "text", + "content": "Table 12: Comparisons with previous methods on HICO-DET and V-COCO. Results on HICO-DET are reported on Rare/Non-Rare/Full sets. R50 and HG denote ResNet-50 [25] and Hourglass [61]. * denotes the backbone is pre-trained with " + }, + { + "bbox": [ + 46, + 287, + 545, + 332 + ], + "type": "inline_equation", + "content": "384 \\times 384" + }, + { + "bbox": [ + 46, + 287, + 545, + 332 + ], + "type": "text", + "content": " resolution, while others use " + }, + { + "bbox": [ + 46, + 287, + 545, + 332 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 287, + 545, + 332 + ], + "type": "text", + "content": ". † indicates the backbone is pre-trained using LiT [92], then fine-tuned on Objects365, COCO and HICO with the objective of object detection." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 347, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 287, + 396 + ], + "type": "text", + "content": "(36,515 kinds). Then, we run R-Tagger with selected relation texts as " + }, + { + "bbox": [ + 46, + 347, + 287, + 396 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 347, + 287, + 396 + ], + "type": "text", + "content": " and all region pairs as " + }, + { + "bbox": [ + 46, + 347, + 287, + 396 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 347, + 287, + 396 + ], + "type": "text", + "content": ". The results are shown in Tab. 7. We can observe that selecting from VG generates low-quality candidates, harming performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 396, + 288, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 288, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 288, + 564 + ], + "type": "text", + "content": "Model scaling and dataset scaling. Equipped with the labelling pipeline introduced above, we can scale RLIPv2 to larger models and datasets. In Tab. 8, we adopt RLIPv2-ParSeDA as the base architecture and observe the benefit of scaling by zero-shot (NF) performance on HICO-DET. In terms of data, adding COCO and Objects365 can both boost performance, and the benefit of adding data exhibits a log scaling trend [9]. Models pre-trained with Objects365 consistently have better Rare result, which we attribute to the distribution misalignment of Objects365 and HICO-DET [17]. In terms of models, switching to stronger backbone models can improve the data efficiency at the cost of larger amounts of computation. Regarding scaling experiments using RLIPv2-ParSeD, we present it in the Appendix." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 574, + 237, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 237, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 237, + 586 + ], + "type": "text", + "content": "5.2. Comparisons with State-of-the-Arts" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "content": "Scene graph generation. We compare RLIPv2 series models with previous methods on Open Images v6 in Tab. 9. We also report mean Recall@50 (mR@50) to better show the usefulness of RLIPv2. Our findings suggest that (i) with the assistance of DDETR family models, RLIPv2 can serve as a strong baseline without any pre-training; (ii) naive object detection pre-training can boost the performance to some extent " + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "inline_equation", + "content": "(47.28 \\rightarrow 48.01)" + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "content": ", while pre-training on VG can further boost the performance especially on mR@50 " + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "inline_equation", + "content": "(45.59 \\rightarrow 50.42)" + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "content": "; (iii) adding pseudo-labelled relation an-" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 347, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 545, + 407 + ], + "type": "text", + "content": "notations in pre-training or switching to stronger backbones both contribute to better performance. However, the boost of adding Objects365 is negligible. We attribute this to the distribution discrepancy of Objects365 and Open Images v6." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 413, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 545, + 510 + ], + "type": "text", + "content": "HOI Detection under UC-NF and UC-RF settings. We report results in Tab. 10 on unseen combinations (UC) under UC-RF and UC-NF settings following [27, 28]. We only fine-tune for 10 epochs under UC-NF setting. Our method outperforms previous methods except on one metric. We attribute this to the strong transferability of CLIP features that GEN-VLKT adopts. Regarding experiments using RLIPv2-ParSeD, we present it in the Appendix." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 515, + 545, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 515, + 545, + 600 + ], + "spans": [ + { + "bbox": [ + 304, + 515, + 545, + 600 + ], + "type": "text", + "content": "Few-shot HOI Detection. We follow [86] to only fine-tune 10 epochs on partial data (1% and 10%), results of which are shown in Tab. 11. We can observe significant improvements upon all metrics by scaling up pre-training compared with previous methods. This improves the practicality of RLIPv2 in low-data scenarios. Regarding experiments using RLIPv2-ParSeD, we present it in the Appendix." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "HOI detection under fully-finetuning and zero-shot (NF) settings. We compare the performance of RLIPv2 series models with previous methods on HICO-DET and V-COCO in Tab. 12. We can observe from the table that (i) dataset and model scaling can both boost the final performance on two datasets; (ii) on HICO-DET, the benefit of pre-training is more prominent on zero-shot than fully-finetuning, especially on the Rare set. Regarding experiments using RLIPv2-ParSeD, we present it in the Appendix." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21656" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 59, + 274, + 233 + ], + "blocks": [ + { + "bbox": [ + 58, + 59, + 274, + 233 + ], + "lines": [ + { + "bbox": [ + 58, + 59, + 274, + 233 + ], + "spans": [ + { + "bbox": [ + 58, + 59, + 274, + 233 + ], + "type": "image", + "image_path": "0d2b7df2ed4ced0f1ed688c46233d9a8df44cfd3331660ae0c161c4dfa6a61c4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 237, + 287, + 270 + ], + "lines": [ + { + "bbox": [ + 46, + 237, + 287, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 237, + 287, + 270 + ], + "type": "text", + "content": "Figure 4: (a) Visualization of pseudo-labelled relations on COCO. Left column: R-Tagger; right column: CLIP tagging method. (b) Visualization of failure cases of R-Tagger." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 279, + 164, + 293 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 279, + 164, + 293 + ], + "spans": [ + { + "bbox": [ + 47, + 279, + 164, + 293 + ], + "type": "text", + "content": "5.3. Qualitative Analysis" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 298, + 287, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 298, + 287, + 393 + ], + "spans": [ + { + "bbox": [ + 46, + 298, + 287, + 393 + ], + "type": "text", + "content": "Comparisons of relation tagging methods. We visualize three examples to compare the quality of pseudolabelled relations by R-Tagger and CLIP tagging method in Fig. 4(a). Generally, CLIP is more object-centric and position-agnostic, and thus struggles in discriminating relations. It tends to tag relations as long as the subject and object have strong co-occurrence priors. However, R-Tagger tags more reasonable relations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 394, + 287, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 394, + 287, + 455 + ], + "spans": [ + { + "bbox": [ + 46, + 394, + 287, + 455 + ], + "type": "text", + "content": "Failure cases of R-Tagger. Recognizing relations is challenging, especially in complex scenes. In Fig. 4(b), we present three examples of R-Tagger's failure cases. In particular, we observe failure cases when the scene contains multiple similar subjects or objects." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 464, + 119, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 119, + 477 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 119, + 477 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 484, + 288, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 288, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 288, + 604 + ], + "type": "text", + "content": "In this paper, we propose RLIPv2, a fast converging model that enables the scaling of relational pre-training to larger-scale pseudo-labelled datasets. Comprehensive experiments on HOI detection and scene graph generation under various settings demonstrate its effectiveness compared to previous methods. We anticipate that our work can galvanize further research efforts to focus on relational reasoning, fostering advancements that yield tangible benefits not only to the research community but also to broader society and humanity." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 611, + 137, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 137, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 137, + 624 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 629, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 712 + ], + "type": "text", + "content": "We would like to extend our sincere gratitude to the anonymous reviewers for their invaluable feedback. Additionally, we appreciate the Fundamental Vision Intelligence Team of Alibaba DAMO Academy for their generous provision of essential computational resources. This research received support from the National Natural Science Foundation of China under Grant No. 62173298 and was addi" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "tionally backed by Alibaba Group via the Alibaba Research Intern Program." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 307, + 108, + 365, + 119 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 108, + 365, + 119 + ], + "spans": [ + { + "bbox": [ + 307, + 108, + 365, + 119 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 128, + 547, + 712 + ], + "type": "list", + "angle": 0, + "index": 24, + "blocks": [ + { + "bbox": [ + 315, + 128, + 545, + 182 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 128, + 545, + 182 + ], + "spans": [ + { + "bbox": [ + 315, + 128, + 545, + 182 + ], + "type": "text", + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, et al. 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In CVPR, pages 11825-11834, 2021. 2" + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "21661" + } + ] + } + ], + "index": 4 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 12 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/RLSAC_ Reinforcement Learning Enhanced Sample Consensus for End-to-End Robust Estimation/253f2fc2-5243-41a5-8404-4467c420f19c_content_list.json b/2023/RLSAC_ Reinforcement Learning Enhanced Sample Consensus for End-to-End Robust Estimation/253f2fc2-5243-41a5-8404-4467c420f19c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..136d8d169d4c016c22ae8333023e09a18caf21f0 --- /dev/null +++ b/2023/RLSAC_ Reinforcement Learning Enhanced Sample Consensus for End-to-End Robust Estimation/253f2fc2-5243-41a5-8404-4467c420f19c_content_list.json @@ -0,0 +1,1626 @@ +[ + { + "type": "text", + "text": "RLSAC: Reinforcement Learning enhanced Sample Consensus for End-to-End Robust Estimation", + "text_level": 1, + "bbox": [ + 166, + 130, + 803, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chang Nie1, Guangming Wang1,3, Zhe Liu2*, Luca Cavalli3, Marc Pollefeys3,4, Hesheng Wang1* \n1Department of Automation, Key Laboratory of System Control and Information Processing of Ministry of Education, Shanghai Jiao Tong University \n2MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University \n3Department of Computer Science, ETH Zürich 4 Microsoft Mixed Reality and AI Zürich Lab", + "bbox": [ + 104, + 202, + 866, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{changnie, wangguangming, liuzhesjtu, wanghesheng}@sjtu.edu.cn \nlcaballi@ethz.ch marc.poliffeys@inf.ethz.ch", + "bbox": [ + 223, + 294, + 745, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 361, + 313, + 378 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Robust estimation is a crucial and still challenging task, which involves estimating model parameters in noisy environments. Although conventional sampling consensus-based algorithms sample several times to achieve robustness, these algorithms cannot use data features and historical information effectively. In this paper, we propose RLSAC, a novel Reinforcement Learning enhanced SAmple Consensus framework for end-to-end robust estimation. RLSAC employs a graph neural network to utilize both data and memory features to guide exploring directions for sampling the next minimum set. The feedback of downstream tasks serves as the reward for unsupervised training. Therefore, RLSAC can avoid differentiating to learn the features and the feedback of downstream tasks for end-to-end robust estimation. In addition, RLSAC integrates a state transition module that encodes both data and memory features. Our experimental results demonstrate that RLSAC can learn from features to gradually explore a better hypothesis. Through analysis, it is apparent that RLSAC can be easily transferred to other sampling consensus-based robust estimation tasks. To the best of our knowledge, RLSAC is also the first method that uses reinforcement learning to sample consensus for end-to-end robust estimation. We release our codes at https://github.com/IRMVLab/RLSAC.", + "bbox": [ + 75, + 393, + 473, + 758 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 787, + 209, + 803 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As a fundamental module in computer vision, robust estimation is crucial for many tasks, such as camera pose estimation [10, 33, 31, 32], motion segmentation [26, 19, 29, 30], short and wide baseline matching [22, 28], plane fitting [18],", + "bbox": [ + 75, + 814, + 470, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6f6d8b71cfab04db83270a37b5d186a9b2615142a6fca5511b60647f774992ec.jpg", + "image_caption": [ + "Figure 1. RLSAC remodel the sampling consensus process. By modeling the sampling consensus as a reinforcement learning process, RLSAC can achieve end-to-end learning on various robust estimation tasks." + ], + "image_footnote": [], + "bbox": [ + 500, + 361, + 890, + 641 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "and line fitting [12, 20]. However, it is still difficult to exclude disturbances while estimating accurate models. To address this issue, sampling consensus-based algorithms are widely used, which are represented by the RANdom SAmple Consensus (RANSAC) [16] algorithm. It first samples the minimum set required for the task, e.g., a minimum set size of 2 for 2D line fitting. Then, the hypothesis is solved by the minimum set. Next, all data is divided into inliers and outliers, according to their residuals to the hypothesis. Finally, the above process is repeated and the best hypothesis is selected based on the highest inlier ratio. RANSAC", + "bbox": [ + 496, + 734, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Authors. The first two authors contributed equally.", + "bbox": [ + 94, + 886, + 467, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "9891", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "can provide strong robustness and generalization, but as the outlier rate increases, the probability of sampling inliers decreases. As a result, the performance of RANSAC degrades rapidly. This is because RANSAC samples each data evenly, regardless of data features that can be used for classifying inliers and outliers. Additionally, the non-differentiable deterministic random sampling of RANSAC also limits it to be integrated into the learning-based pipeline.", + "bbox": [ + 80, + 90, + 468, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Since sampling the minimum set from the data is quite similar to the process of sampling an action from the action space in reinforcement learning [17, 13], the sampling consensus can be integrated into the reinforcement learning framework. Sampling in reinforcement learning can be achieved through a neural network, which extracts the data features. In addition, the reward from the environment can be used to train the reinforcement learning framework without differentiation. Therefore, to learn from data features and avoid differentiating, we propose the RLSAC: Reinforcement Learning enhanced SAmple Consensus for end-to-end robust estimation. As shown in Figure 1, RLSAC regards sampling consensus as the process of interaction between the agent and environment in reinforcement learning. Specifically, the agent uses a neural network to sample the minimal set from the data as an action. The environment then performs model generation and evaluation based on the action and outputs the next state, which is used in the next iteration.", + "bbox": [ + 80, + 214, + 468, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, designing appropriate reward and state are very important and challenging in reinforcement learning. To achieve reinforcement learning enhanced sampling consensus, RLSAC proposes new state transition and reward modules. Specifically, the state is encoded by augmenting the original data features with memory features, including the current action, data residuals, and historical information. When the state is input into the agent, these features can provide more information about the quality of the previous action. This allows RLSAC to gradually explore a better hypothesis by utilizing this memory information.", + "bbox": [ + 80, + 488, + 468, + 654 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Additionally, the evaluation result of the generated hypothesis can be used as the reward signal to train the neural network without differentiation. The reward signal enables the learning-based sampling consensus for end-to-end robust estimation. Furthermore, the evaluation result is the feedback from the downstream task. Thus, the neural network can learn to effectively use the data features and optimize the output to meet the requirements of the downstream task.", + "bbox": [ + 80, + 656, + 468, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Moreover, instead of directly predicting the final result from the data in one shot [27], RLSAC employs multiple episodes, each containing several sampling processes. In addition, RLSAC performs one random sampling at the beginning of each episode to form the initial state. This approach preserves the robustness of multiple random sampling and provides basic performance for RLSAC. Besides, RLSAC can be extended to other robust estimation tasks since it is", + "bbox": [ + 80, + 779, + 468, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "not restricted to any specific task.", + "bbox": [ + 503, + 92, + 720, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The proposed RLSAC is tested on two classic robust estimation tasks, which are the 2D line fitting task and the fundamental matrix estimation task. The experimental results show that RLSAC achieves great performance.", + "bbox": [ + 503, + 107, + 893, + 166 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions are as follows:", + "bbox": [ + 522, + 167, + 772, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We propose RLSAC: a novel Reinforcement Learning enhanced SAmple Consensus framework for end-to-end robust estimation. It learns data features to sample the minimum set. RLSAC retains the robustness of the multiple sampling process, while the initial random sampling can provide the basic performance.", + "bbox": [ + 519, + 186, + 890, + 276 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- RLSAC proposes an approach for state encoding, which includes both current and historical information. This enables the agent to assess the quality of the previous actions and gradually explore better hypotheses. RL-SAC is trained unsupervised using the reward function, which avoids differentiating the sampling process and achieves end-to-end robust estimation.", + "bbox": [ + 519, + 281, + 890, + 385 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- RLSAC is evaluated on two robust estimation tasks. The 2D line fitting task demonstrates its robustness to disturbances and effective progressive exploration capability. In the fundamental matrix estimation task, RLSAC achieves state-of-the-art performance. Furthermore, RLSAC can be easily applied to other sampling consensus-based robust estimation tasks.", + "bbox": [ + 519, + 391, + 890, + 494 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 503, + 511, + 638, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Robust estimation is a basic module for many tasks. Although the simple repetitive random sampling strategy of RANSAC [16] is robust and generalized, it has some limitations, such as no further optimization, inefficient sampling, and non-differentiability.", + "bbox": [ + 503, + 537, + 893, + 612 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "There are several methods observing that local features help to optimize the sampling result. LO-RANSAC [15] continues to sample in the inliers with a smaller threshold after sampling the best model so far, aiming to find a better hypothesis near the current one. NAPSAC [25] uses a fixed hypersphere to acquire local data and samples from it, but this approach loses global features and may get stuck in local data. To address this, progressive NAPSAC [4] gradually expands the hypersphere to extend the sampling from local to global. GC-RANSAC [5] considers spatial continuity between inliers and surrounding points, modeling the connections of the data through graph-cut to divide inliers and outliers. MAGSAC++ [6] assesses the model quality by weighting various thresholds to reduce the sensitivity to the choice of a specific noise scale.", + "bbox": [ + 503, + 613, + 890, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To improve sampling efficiency, some methods use guided sampling instead of random sampling. PROSAC [14] sorts the data based on a quality function and then samples the sorted data sequentially to improve efficiency. USAC", + "bbox": [ + 503, + 840, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "9892", + "bbox": [ + 483, + 946, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/59c17724da94bb19eb2b15ebcb13eb1de92e540c4885cde55ad685955987e416.jpg", + "image_caption": [ + "Figure 2. The pipeline of the proposed RLSAC. The fundamental matrix estimation problem is used as an example. The black, green, and blue lines represent outliers, inliers, and the minimum set, respectively. The yellow arrows are only used once during initialization. The red and orange arrows indicate the loop in an episode. The initial states are randomly sampled. The best hypothesis for this scene is selected by scoring all hypotheses. The collected experience is recorded in the replay buffer for training." + ], + "image_footnote": [], + "bbox": [ + 99, + 88, + 872, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "[24] integrates the advantages of various methods to achieve robustness and efficiency. To learn from the data, Yi et al. [36] are the first to use a neural network based on PointNet to directly classify inliers and outliers. Then, Zhang et al. [37] improve this work by proposing pooling and unpooling blocks to learn the local context of correspondences. NG-RANSAC [9] uses a neural network to calculate the sample probability for each point, achieving probability-based sampling. The neural network is trained using reinforcement learning, but it did not use reinforcement learning to achieve sampling consensus and progressive exploration. Barath et al. [2] propose the MQ-Net to learn from residual histograms and evaluate the quality of the model. Additionally, the authors design the MF-Net to learn to reject bad minimum sets early, further improving efficiency. NeFSAC [11] uses a neural network to reject the motion-inconsistent and poorly-conditioned minimal samples.", + "bbox": [ + 75, + 431, + 472, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The non-differentiability of RANSAC makes it challenging to integrate into an end-to-end learning pipeline. Some methods propose the differentiable RANSAC. For example, DSAC [8] replaces the deterministic selection process with probabilistic selection, allowing for differentiation with respect to the data. Wei et al. [35] achieve gradient propagation by predicting the probabilities of being inliers to guide sampling. To avoid differentiation, some methods use the loss as reward signals through reinforcement learning to train the network. Bhowmik et al. [7] use reinforcement learning to train the feature point detection network but not for the sampling consensus process. Truong et al. [27] iteratively delete points with reinforcement learning, seeking the maximum consensus model that meets the threshold. However,", + "bbox": [ + 75, + 688, + 472, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the authors encode the attributes of the points into the state, but does not include long-range historical information or the position of the hypothesis in the state space. In addition, this method does not include the sampling consensus process and may overlook better solutions.", + "bbox": [ + 496, + 431, + 893, + 506 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 518, + 591, + 534 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 500, + 544, + 702, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Robust estimation can be considered as generating a good hypothesis $h$ given a set of data $\\chi = \\{\\mathbf{x}_i\\}_{i=1}^N$ , which may be disturbed by noise. For instance, the hypothesis $h$ could represent the parameters of a 2D line, and $\\chi$ could be all the points in the 2D plane. Or $h$ could be the fundamental matrix that represents the epipolar geometry of a pair of images, and $\\chi$ could be all the correspondences. Similarly, the data contained in $\\mathbf{x}_i$ varies with the task. As a commonly used robust estimation method, the sampling consensus method samples $n$ minimum sets $\\mathcal{M}$ from $\\chi$ . The size $m$ of a minimum set varies depending on the task. For example, when fitting a 2D line, the size $m = 2$ . Then, these minimum sets $\\mathcal{M}$ are solved by the minimum solver $S$ to output hypotheses:", + "bbox": [ + 496, + 566, + 893, + 763 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nH = \\left\\{S \\left(\\mathcal {M} _ {j}\\right) \\mid \\mathcal {M} _ {j} \\in M, j = 1, 2, \\dots , n \\right\\}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 767, + 893, + 782 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Next, the hypotheses $H$ are evaluated using a scoring function $f$ . The residuals of all data points $\\chi$ can be computed and used to calculate the inlier ratio, which is commonly used as a metric for the hypothesis quality [16]. Finally, the hypothesis with the highest score is chosen as the best hypothesis $h_{Best}$ :", + "bbox": [ + 496, + 786, + 893, + 876 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nh _ {B e s t} = \\underset {h \\in H} {\\arg \\max } f (h, \\chi). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 878, + 892, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "9893", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "By solving the problem using several minimum sets $\\mathcal{M}$ , the model can achieve robust estimation, which is less sensitive to outliers and can lead to more accurate results.", + "bbox": [ + 76, + 90, + 468, + 135 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The RANSAC [16] algorithm performs random sampling to sample the minimum sets $\\mathcal{M}$ , which cannot fully exploit the data features. As shown in Figure 1, One alternative is to consider the sampling of a minimum set as an action taken by an agent based on the current state, within the reinforcement learning framework:", + "bbox": [ + 76, + 136, + 468, + 227 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\na _ {t + 1} \\sim \\pi_ {\\phi} \\left(a _ {t} \\mid s _ {t}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 232, + 468, + 250 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, the policy network $\\pi_{\\phi}$ depends on the weights $\\phi$ . The action $a_{t + 1}$ is sampled by the policy $\\pi_{\\phi}$ from the state $s_t$ and $a_{t}$ at time $t + 1$ , which can also be viewed as the process of sampling a minimum set $\\mathcal{M}_j$ from all data $\\chi$ . So the Eq. 2 can be rewritten that the best hypothesis is selected by a reinforcement learning enhanced sample consensus method:", + "bbox": [ + 76, + 261, + 470, + 351 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nh _ {B e s t} = \\underset {t = 1, 2, \\dots , j} {\\arg \\max } f (S (a _ {t}), \\chi). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 359, + 468, + 383 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In addition, the policy $\\pi_{\\phi}$ is a trainable neural network, and the state $s_t$ contains the features of the data $\\chi$ . Therefore, the minimum set can be selected based on sufficient learned knowledge of the data features, rather than being chosen randomly. Furthermore, the evaluation result $f(S(a_t), \\chi)$ of the minimum solver $S$ can serve as the reward in reinforcement learning to achieve unsupervised learning.", + "bbox": [ + 76, + 383, + 470, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. System Framework", + "text_level": 1, + "bbox": [ + 76, + 500, + 264, + 513 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With the problem formulation of modeling the process of sampling consensus as a reinforcement learning problem, we introduce RLSAC, which is illustrated in Figure 2. Although the fundamental matrix estimation task is used as an example, the pipeline is also applicable to other robust estimation tasks. Firstly, RLSAC initiates multiple episodes for the correspondences of a pair of images $\\chi$ at (1). An episode contains many steps. At the start of each episode, a random sampling of the minimum set $\\mathcal{M}_0$ is performed to generate the initial state $s_0$ through state transition at (2). Specifically, the initial state $s_0$ is obtained by concatenating each data point with the memory features, which are consisting of action, residual, and historical features (see Section 3.5).", + "bbox": [ + 76, + 522, + 468, + 718 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, the initial state $s_0$ is input into the sampling consensus loop. The agent receives the current state $s_t$ and feeds it into the policy network $\\pi_{\\phi}$ at ③, as shown in Section 3.3. The network generates a probability for each data point. The $m$ points with the highest probabilities are selected as the minimum set $\\mathcal{M}_t$ , instead of random sampling.", + "bbox": [ + 76, + 719, + 468, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, the minimum set $\\mathcal{M}_t$ serves as the action $a_t$ for the agent, which generates a hypothesis $h_t$ in the environment at ④, as shown in Section 3.4. The residuals of points to the hypothesis are compared with a threshold to classify points into inliers and outliers at ⑤. The ratio of inliers is utilized as the reward $r_t$ for the current action $a_t$ to train the", + "bbox": [ + 76, + 810, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "policy network $\\pi_{\\phi}$ at ⑥. Additionally, the action, inliers, and residuals are used for the state transition to generate the next state $s_{t + 1}$ at ⑦, as shown in Section 3.5. Finally, the environment outputs the next state $s_{t + 1}$ and the reward $r_t$ which are used by the agent to start the next step at ⑧.", + "bbox": [ + 496, + 90, + 893, + 167 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Furthermore, the state $s_t$ , action $a_t$ , reward $r_t$ , and the next state $s_{t+1}$ in every step are collected as experiences in the replay buffer [13] for training. After all episodes are complete, the hypothesis with the highest inlier ratio across all episodes is output as the best hypothesis $h_{Best}$ for this pair of images.", + "bbox": [ + 496, + 167, + 893, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Sampling Minimum Set by Agent", + "text_level": 1, + "bbox": [ + 498, + 268, + 794, + 286 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The agent receives the state $s_t \\in \\mathbb{R}^{N \\times C}$ , where $N$ is the number of the correspondences of a pair of images. The channel $C = c + 3$ , with $c$ denoting the dimension of data features and 3 representing the dimension of memory features (see Section 3.5). In addition, the first hypothesis $h_0$ of each episode is generated using a randomly sampled minimum set, which provides a basic performance for RLSAC.", + "bbox": [ + 496, + 292, + 893, + 398 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then the state $s_t$ is fed into the policy network $\\pi_{\\phi}$ . To achieve permutation invariance for the input data, RLSAC uses edge convolution (EdgeConv) from the DGCNN [34] as the basic module to establish the policy network $\\pi_{\\phi}$ . The EdgeConv can model the interrelationship of correspondences by graph neural networks. It can extract features from neighboring nodes in a graph and aggregate them into a central node. The policy network $\\pi_{\\phi}$ extracts data features and calculates the probabilities by softmax for each point of being in the minimum set. The probability can be interpreted as the probability of obtaining a greater return on the action for the long term, rather than the probability of achieving the best result in the current state. Consequently, the $m$ points with the highest probability are selected as the minimum set $\\mathcal{M}_t$ in the current state $s_t$ . Importantly, all previously used minimum sets are recorded to avoid selecting a duplicate minimum set. Thus, when a new minimum set is selected, it is checked whether it has been used. If the new minimum set has already been used, then another $m$ data set is selected following the probability, which will be checked as well. Until the unused data set is found, it is output as the minimum set. Ultimately, the minimum set is as the action $a_t \\in \\mathbb{R}^{m \\times C}$ output by the agent.", + "bbox": [ + 496, + 398, + 893, + 748 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Evaluating Hypothesis in Environment", + "text_level": 1, + "bbox": [ + 498, + 757, + 834, + 773 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The environment generates a hypothesis $h_t$ based on the received action $a_t$ from the agent. Next, the residuals $R$ are calculated for all data $\\chi$ with respect to the hypothesis:", + "bbox": [ + 496, + 782, + 892, + 828 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nR _ {t} = \\left\\{D \\left(x _ {i}, h _ {t}\\right) \\mid x _ {i} \\in \\chi , i = 1, 2, \\dots , N \\right\\}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 840, + 892, + 858 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the function $D$ is for residual calculation. The scalar valued residuals $R$ are calculated at all data $\\chi$ . With the", + "bbox": [ + 496, + 869, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "9894", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3483b80179bce9e3ec851cdf19e8d71cef60f7aa612424f5fd60a60ce3567196.jpg", + "image_caption": [ + "Figure 3. The state transition in RLSAC. To form the next state, the data features are added with the memory features, which contain action features, residual features, and historical features." + ], + "image_footnote": [], + "bbox": [ + 86, + 90, + 450, + 234 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "pre-defined threshold, the data $\\chi$ is divided into inliers $I_{t}\\in$ $\\mathbb{R}^{z\\times C}$ and outliers $O_{t}\\in \\mathbb{R}^{(N - z)\\times C}$ based to the residuals.", + "bbox": [ + 76, + 303, + 468, + 333 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the sampling consensus methods, the inlier ratio commonly represents the quality of the hypothesis. Since the hypothesis $h_t$ is generated by the action $a_t$ in RLSAC, the inlier ratio can be considered as the reward $r_t$ of the current action $a_t$ to train the policy network $\\pi_\\phi$ without ground truth.", + "bbox": [ + 76, + 335, + 468, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the hypotheses related-rewards, RLSAC can update weights $\\phi$ of the policy network $\\pi$ without differentiating the sampling process. By modeling sampling consensus as an interactive process in reinforcement learning, RLSAC achieves end-to-end robust estimation while avoiding differentiating.", + "bbox": [ + 76, + 411, + 468, + 486 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. State Transition", + "text_level": 1, + "bbox": [ + 76, + 498, + 235, + 512 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The state transition module allows RLSAC to encode the previous state and action, enabling RLSAC to explore the state space effectively. As illustrated in Figure 3, the next state $s_{t + 1}$ is obtained by concatenating the original data features $N \\times c$ with memory features $\\{A, R, \\mathcal{H}\\}$ , which comprise action features $N \\times 1$ , residual features $N \\times 1$ and historical features $N \\times 1$ .", + "bbox": [ + 76, + 522, + 468, + 626 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The action features are derived from the current action $a_{t}$ . If a data point $x_{i}$ is used in the action $a_{t}$ , the corresponding entry in the action features $\\alpha_{i}$ is set to 1, otherwise it is -1:", + "bbox": [ + 76, + 628, + 468, + 674 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nA _ {t} = \\left\\{\\alpha_ {i} \\right\\}, \\alpha_ {i} = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} x _ {i} \\in a _ {t} \\\\ - 1 & \\text {o t h e r w i s e} \\end{array} , i = 1, 2, \\dots , N. \\right. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 686, + 468, + 731 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The action features could provide the agent with information on the current action, like the current location in the data for the next state.", + "bbox": [ + 76, + 733, + 468, + 775 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The residual features are obtained from the residuals $R_{t}$ computed in Eq. 5. They encode the relative relationship between the hypothesis and the data, which can be thought of as the direction for the agent.", + "bbox": [ + 76, + 779, + 468, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The historical features collect how often is a data point used up to the current step. They are initialized to 0 and updated as follow: for each data point $x_{i}$ used in the current action $a_{t}$ , the corresponding entry in the historical features", + "bbox": [ + 76, + 839, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\tau_{i}$ is incremented by 1:", + "bbox": [ + 500, + 92, + 653, + 106 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {H} _ {t} = \\left\\{\\tau_ {i} \\right\\}, \\tau_ {i} = \\tau_ {i} + 1 \\text {i f} x _ {i} \\in a _ {\\mathrm {t}}, i = 1, 2, \\dots , N. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 118, + 893, + 135 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The historical features can provide the agent with information on the actions taken so far, enabling it to keep track of its path through the data.", + "bbox": [ + 498, + 147, + 893, + 191 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By encoding the state in this way, the agent has access to both current and historical information, allowing it to reach the goal state. Furthermore, the memory features serve as a director of local navigation, guiding the agent to explore the data features and reach its destination gradually.", + "bbox": [ + 498, + 193, + 892, + 268 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 282, + 630, + 299 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate the performance of RLSAC on classic tasks, including 2D line fitting and fundamental matrix estimation. The 2D line fitting task serves as a basic benchmark to assess the performance of the robust estimation algorithm and provides visualization of the sampling process. The fundamental matrix estimation task can show the performance of algorithms on complex camera pose estimation task in the real world, which is a critical task in computer vision.", + "bbox": [ + 498, + 306, + 893, + 429 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Settings", + "text_level": 1, + "bbox": [ + 500, + 439, + 596, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "RLSAC is built on the widely used reinforcement learning framework SAC-Discrete [13]. As shown in Figure 2, the collected replay buffer is retrieved for off-policy to update the actor and critic network in reinforcement learning.", + "bbox": [ + 498, + 462, + 890, + 522 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since RLSAC uses the inlier ratio as the reward for training, it is an unsupervised method. To explore more images, only one episode with multiple steps is collected per image pair during training. The framework is trained for 100 epochs. During training, the episode termination conditions are set as follows: (i) if the number of inliers is unchanged for $\\kappa = 2$ steps; (ii) if the inlier ratio does not exceed the maximum inlier ratio in the episode for $\\varsigma = 3$ steps; (iii) if the maximum number of steps $\\psi = 15$ is reached. During testing, only the third condition is valid, and each pair of images can be tested in $\\nu$ episodes.", + "bbox": [ + 496, + 523, + 893, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As with the standard reinforcement learning [13], RLSAC uses probabilistic sampling during training and max sampling during testing. For the EdgeConv module in the policy network, the value of k-nearest neighbors is set to $k = 15$ . The network architecture and additional information can be found in the supplementary material. Moreover, we have included ablation experiments to analyze the impact of specific network details, also provided in the supplementary material. Similar to the RANSAC implementation, RLSAC also employs refinement using the inliers of the final best hypothesis as the final model polishing.", + "bbox": [ + 496, + 689, + 893, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The experiments are conducted on a Linux computer with an Intel i7 3.6GHz CPU and an NVIDIA RTX 2080Ti GPU. Our implementation is based on PyTorch.", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "9895", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/5aeb7a7c55c5c16a2846def5cb3c3ef18505105332e3d3e05ca45129de121de4.jpg", + "table_caption": [ + "Table 1. 2D line fitting. The mAA@0.5° and median error(°) on various outlier rates are reported." + ], + "table_footnote": [], + "table_body": "
Method0.10.20.30.40.50.60.7
mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓
RANSAC [16]0.8700.0490.8630.0520.8500.0560.8290.0610.7960.0710.7460.0870.6080.135
Ours0.8750.0470.8740.0490.8720.0480.8650.0500.8580.0520.8450.0560.8240.062
Ours-0.50.8490.0530.8500.0550.8540.0530.8580.0520.8580.0520.8640.0500.8490.054
", + "bbox": [ + 78, + 101, + 893, + 176 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Case Study 1: 2D Line Fitting", + "text_level": 1, + "bbox": [ + 76, + 191, + 344, + 209 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The 2D line fitting task is a basic problem in robust estimation, which can visualize the process of robust estimation and assess the robustness quantitatively to different outlier rates. In this task, each data point contains only the coordinates, thus all data points can be expressed as: $\\chi = \\{[x_i,y_i]\\mid i = 1,2,\\dots,N\\}$ , where $\\chi$ represents the data features $N\\times c$ , with $c = 2$ . Since two points are sufficient to determine a 2D line, the agent can generate a hypothesis by selecting two points from the set of all data points as the minimum set $N\\times m$ , where $m = 2$ . For comparison, the RANSAC [16] algorithm is evaluated with the same task.", + "bbox": [ + 75, + 215, + 470, + 381 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate the performance of RLSAC in the 2D line fitting task, we synthesize $N = 100$ data points for both training and testing. Specifically, a ground truth 2D line is randomly generated in a $10 \\times 10$ picture. True inliers are then randomly generated on the line based on the set outlier rate. Next, the true inliers are uniformly disturbed within a range of 0.1 around the line. Thus, the inlier threshold could be set to $\\varepsilon = 0.1$ . Additionally, true outliers are randomly scattered throughout the picture. Moreover, it is possible for true outliers to be located within the inlier region, as is often the case in real-world scenes.", + "bbox": [ + 75, + 383, + 468, + 547 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For accurately evaluating and comparing the performance of different methods, we adopt the mean Average Accuracy (mAA) metric in [2]. The angular difference between the estimated line and the ground truth line is used as the error metric, which is used to calculate the mAA metric with a tolerance threshold of $0.5^{\\circ}$ .", + "bbox": [ + 75, + 550, + 468, + 641 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The performance of RLSAC and RANSAC at different outlier rates with 150 iterations is evaluated and the results are presented in Table 1. When the outlier rate is lower than 0.5, RANSAC can achieve a similar performance to RLSAC. This is because the repeated random selection of the minimum set can achieve good performance in simple low outlier rate scenes. However, the performance of RANSAC degrades more quickly than that of RLSAC as the outlier rate increases. This suggests that RLSAC can explore hypotheses closer to the ground truth in noisy scenes.", + "bbox": [ + 75, + 642, + 470, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As the outlier rate increases beyond 0.5, RLSAC can still maintain a low error and high mAA score. This indicates that RLSAC is more robust to disturbances, providing a more stable performance compared to RANSAC.", + "bbox": [ + 75, + 792, + 468, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The qualitative results of RLSAC are shown in Figure 4, which demonstrates its ability to quickly find the better hypothesis even from a bad initial state. This means that the", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bc069480173fb3a2d266ea9fbc5cfa63090baed83b8d8e887faaf9f02977e050.jpg", + "image_caption": [ + "Figure 4. The qualitative results of RLSAC on 2D line fitting. The hypothesis converges to the ground truth as the number of steps increases. The green points represent inliers, while the red points represent outliers. The sampled minimum set points are denoted by black edges. The ground truth is represented by a yellow line, while the hypothesis and inlier threshold are represented by blue and dashed lines respectively." + ], + "image_footnote": [], + "bbox": [ + 509, + 189, + 883, + 327 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "memory features can serve as a director of local navigation, allowing RLSAC to move towards a better state through outputting actions. Moreover, once RLSAC finds a high inlier ratio hypothesis that is close to the ground truth, it continues to explore the local state to further improve the result, rather than randomly transitioning to other states.", + "bbox": [ + 496, + 455, + 893, + 546 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The results of the 2D line fitting task show that RLSAC can effectively utilize both data features and memory features, maintaining robust and stable performance in noisy environments. In addition, it can gradually explore a better hypothesis with the help of memory features.", + "bbox": [ + 496, + 547, + 893, + 623 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Case Study 2: Fundamental Matrix Estimation", + "text_level": 1, + "bbox": [ + 498, + 633, + 890, + 650 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The fundamental matrix estimation is a crucial robust estimation task in computer vision, which solves the fundamental matrix by correspondences in a pair of images. In this study, we use the data and settings in CVPR tutorial RANSAC in 2020 [3], where the correspondences are detected by RootSIFT [1] and matched by the nearest neighbor. The training data comprises 12 scenes, each with $100\\mathrm{k}$ image pairs, while the test data includes 2 scenes, with 4950 image pairs. The dataset uses Second Nearest Neighbor (SNN) ratio as the matching score. The correspondences are sorted in descending order by SNN. Then the top $N = 150$ SNN correspondences are selected. Next, each point extracts a 128-dimensional descriptor desc through the SIFT algorithm. Thus, the data points are: $\\chi = \\left\\{\\left[x_1^i,y_1^i,x_2^i,y_2^i,SNN^i,desc_1^i,desc_2^i\\right]\\mid i = 1,2,\\dots,N\\right\\} \\in \\mathbb{R}^{N\\times c}$ , where $c = 261$ . The 8-point solver is used to solve", + "bbox": [ + 496, + 659, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "9896", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/788ebfd0ae17fc5f7303ab1135cb1af5e17527cda0eeb9b2818e83f758a55228.jpg", + "table_caption": [ + "Table 2. Fundamental matrix estimation. The mAA@ $10^{\\circ}$ and median error $(\\epsilon_{\\mathbf{R}}$ and $\\epsilon_{\\mathrm{t}})$ of rotation and the direction of translation at 1k iterations are reported in degrees." + ], + "table_footnote": [], + "table_body": "
MethodmAA@10°↑Median (°) ↓
RtεRεt
RANSAC[16]0.6440.4882.3075.100
USAC[24]0.7410.6041.0362.157
MAGSAC++[6]0.7530.6140.9241.895
Ours0.7600.6220.9261.751
", + "bbox": [ + 107, + 128, + 436, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8772cc2cbf6043a90e7ca5da0af72b8b30f3bb983a685e1e61e7b53df8c09ca8.jpg", + "image_caption": [ + "Figure 5. The mAA@10° at different iterations. The results on the fundamental matrix estimation task at different iterations." + ], + "image_footnote": [], + "bbox": [ + 96, + 227, + 269, + 354 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6ab1e5df281150369ba941dda5d7ce7f98580c00af2ad49a00749c43516559bc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 227, + 447, + 356 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5d231a319ac116fb8b45335a114f72e178de5a85a2e720e881f9168960a9a76f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 400, + 269, + 465 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/91d9c4e1a98e7b6344e2844548e1d93b8f2620bebfcd28119a2a2063412aa606.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 400, + 449, + 465 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2a76fbecb79966cfbb3ab3d0ff00f4dab8a019af789d34d7a68fed46fd1b8a11.jpg", + "image_caption": [ + "Figure 6. The qualitative results of RLSAC on the fundamental matrix estimation task. Inlier rate, rotation and translation errors are reported. The blue lines represent the sampled minimum set points, and the green lines represent the inliers." + ], + "image_footnote": [], + "bbox": [ + 94, + 467, + 267, + 532 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/83f7938764bc6ef25635ca581599a57b77938b16500eb6a6974e69fd794cee36.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 467, + 449, + 532 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/97be18e718c7e873181d70151440925b4249201e1104425819dfc6812f8be658.jpg", + "image_caption": [ + "Figure 7. The step results of RLSAC on the fundamental matrix estimation task. The meaning of the lines and the evaluation metrics are consistent with Figure 6." + ], + "image_footnote": [], + "bbox": [ + 94, + 609, + 267, + 781 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5351c4637327432fcbb7eb8e2d4a9bbbdf91fc6bca50da60127fc1861a68792a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 276, + 609, + 452, + 781 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the hypotheses [21]. The inlier threshold of RLSAC is set to $\\varepsilon = 4$ . The evaluation settings follow [3]. To compare with other methods, RANSAC [16], USAC [24], MAGSAC++ [6] are tested, which use the recommended settings in [3].", + "bbox": [ + 76, + 839, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Figure 5, RLSAC outperforms other methods in estimating both the rotation matrix and translation vector. Remarkably, RLSAC can achieve high accuracy with only 100 iterations. Comparisons reveals that RLSAC possesses a higher upper bound in performance than MAGSAC.", + "bbox": [ + 496, + 90, + 890, + 166 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The quantitative results of the methods at 1k iterations are presented in Table 2. RLSAC achieves great performance with small errors, a little higher than MAGSAC++[6]. Specifically, RLSAC shows high performance in estimating the direction of the translation vector compared to other methods. Since RLSAC could effectively learn features from the data to exclude noise disturbances, it has significant performance on translation vector estimation.", + "bbox": [ + 496, + 167, + 892, + 285 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 6 shows the qualitative results of the fundamental matrix estimation of RLSAC in each scene. The figure demonstrates that RLSAC selects rigid and fixed feature points on buildings as the minimum sets, which can help to find better poses. Furthermore, the step-by-step fundamental matrix estimation results of RLSAC are visualized in Figure 7. It demonstrates a gradual increase in the inlier ratio of the hypothesis and a decrease in the rotation and translation errors. This illustrates that RLSAC can progressively explore the state space to find a better hypothesis.", + "bbox": [ + 496, + 287, + 890, + 438 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 452, + 650, + 468 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We perform ablation studies by modifying or removing modules to analyze their effectiveness. The experimental data and settings remain the same as in Section 4.", + "bbox": [ + 496, + 477, + 890, + 522 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Robustness and Generalization of RLSAC in 2D Line Fitting: The Ours-0.5 in Table 1 shows the result of evaluating the robustness and generalization of RLSAC in 2D Line Fitting. We train RLSAC on data with the outlier rate of 0.5 and then test it on various outlier rates. In most cases, Ours-0.5 can outperform RANSAC. Notably, when the outlier rate exceeds 0.5, Ours-0.5 performs even better than the model trained at that outlier rate. This is because, in scenes with high outlier rates, the point distribution is closer to a uniform distribution, which lacks the features of a dense distribution. As a result, the model $RLSAC_{High}$ trained on high outlier rates may not have learned the dense distribution in low outlier rates. This results in a mediocre performance of $RLSAC_{High}$ in low outlier rates scenes. Conversely, scenes of low outlier rates exhibit both sparse and dense point distributions in different regions, providing more diverse features for the model $RLSAC_{Low}$ to learn. Consequently, the $RLSAC_{Low}$ can predict better results when the dense distribution of points is occasionally present in the high outlier scene. These results demonstrate that RLSAC can effectively learn the distribution in point groups to classify inliers and outliers.", + "bbox": [ + 496, + 523, + 892, + 853 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of Descriptors: To investigate the effect of descriptors with image semantic features, we conduct experiments as shown in Table 3 (a). This suggests that descriptors with", + "bbox": [ + 496, + 854, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "9897", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/712bea5e4c1df71c190dd0874158521badd3fdeb4d2e53d8c5ede29895b3d8b4.jpg", + "table_caption": [ + "Table 3. The ablation study results of RLSAC on fundamental matrix estimation." + ], + "table_footnote": [], + "table_body": "
MethodmAA@10^↑Median (°) ↓
RtεRεt
(a)Ours (w/o descriptors)0.7020.5681.4002.963
Ours (full, with 128 DIM descriptors)0.7600.6220.9261.751
(b)Ours (with max sampling in training and max sampling in testing)0.7300.5911.1322.331
Ours (with max sampling in training and probabilistic sampling in testing)0.7060.5311.4152.893
Ours (with probabilistic sampling in training and probabilistic sampling in testing)0.7200.5811.1502.508
Ours (full, with probabilistic sampling in training and max sampling in testing)0.7600.6220.9261.751
(c)Ours (with N=100 points)0.7270.5881.2162.464
Ours (with N=200 points)0.7470.6041.0502.108
Ours (with N=300 points)0.7330.5941.1802.364
Ours (full, with N=150 points)0.7600.6220.9261.751
", + "bbox": [ + 78, + 112, + 486, + 297 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "semantic features are helpful for RLSAC to effectively learn and sample minimum sets.", + "bbox": [ + 76, + 310, + 467, + 339 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Different Sampling Approaches: In Table 3 (b), four different sampling strategies are compared. The results illustrate that the best performance can be achieved by probabilistic sampling during training and max sampling during testing. This is consistent with the sampling strategy for actions in reinforcement learning. Specifically, probabilistic sampling can provide randomness and exploratory during training, while max sampling can output the optimal strategy during testing to improve performance and efficiency.", + "bbox": [ + 75, + 340, + 468, + 477 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Number of State Points: In RLSAC, the state points are selected from the top $N$ correspondences sorted by SNN. Different values of $N$ are evaluated in Table 3 (c). The best performance is obtained when $N = 150$ . We count the number of correspondences in images at $SNN < 0.8$ recommended in [3], which is also around 150 points. This is reasonable that a smaller number of points may exclude points, which would solve the better hypothesis. While more points will introduce more noise, making it more difficult for RLSAC to learn effective sampling strategies.", + "bbox": [ + 75, + 479, + 468, + 630 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion", + "text_level": 1, + "bbox": [ + 76, + 646, + 191, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The methods of estimating results directly with neural networks in one shot [23] are not robust and generalized in the scenes that have not been learned. Moreover, their poor interpretability leads to poor practicality in engineering applications. In contrast, traditional methods based on mathematical theory, such as multiple sampling consensus for model estimation and noise covariance matrix estimation in simultaneous localization and mapping (SLAM), offer clear interpretability and well-defined scopes of application. However, many traditional methods cannot be integrated into a learning-based framework due to their non-differentiability.", + "bbox": [ + 75, + 672, + 468, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Therefore, combining these traditional methods with learning-based methods can provide both interpretability and high performance. RLSAC combines sampling consensus with reinforcement learning to avoid differentiation of", + "bbox": [ + 75, + 839, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "sampling while better extracting data features and memory features. In addition, RLSAC can be easily transferred to other sampling consensus tasks due to:", + "bbox": [ + 498, + 90, + 890, + 136 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- The input data of RLSAC is not limited to coordinates and descriptors. Additional features such as depth estimation information and semantic segmentation information can also be used as input for the policy network.", + "- RLSAC retains random sampling at the beginning of each episode and each sample result is deduplicated. This provides basic performance for sampling consensus-based tasks.", + "- The rewards in RLSAC are linked with the evaluation of the hypothesis. Therefore, RLSAC can be extended to other robust estimation tasks, which require different evaluation methods. Moreover, RLSAC does not require differentiation of the sampling process, the hypothesis solving process, and the evaluation process." + ], + "bbox": [ + 517, + 140, + 893, + 359 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this way, RLSAC enables end-to-end learning that incorporates traditional methods. This allows for consistent optimization objectives across modules.", + "bbox": [ + 498, + 367, + 893, + 412 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 426, + 617, + 441 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose RLSAC, a reinforcement learning enhanced sample consensus framework for end-to-end robust estimation. RLSAC models the sampling consensus process as a reinforcement learning task to achieve end-to-end robust estimation. The basic performance of RLSAC is provided by the initial random sampling in each episode. In RLSAC, a new state transition strategy is designed to effectively extract current and historical information, which can guide RLSAC to explore state space. Furthermore, the inlier ratio of the hypothesis is used as a reward to realize unsupervised policy network learning. In experiments, the 2D line fitting task illustrates that RLSAC is robust to various disturbances and exhibits strong generalization. The visualization of the sampling process shows that RLSAC can progressively explore to better models and continues to explore locally. Additionally, the fundamental matrix estimation task demonstrates that RLSAC outperforms other methods in the complex camera pose estimation problem. Notably, RLSAC is not limited to specific tasks and can easily perform end-to-end learning on various sampling consensus-based tasks. In future work, it is worthwhile to explore the integration of traditional and learning-based methods within this framework, while trying to maintain the strengths of each method.", + "bbox": [ + 496, + 452, + 893, + 800 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8. Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 814, + 679, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported in part by the Natural Science Foundation of China under Grant 62225309, 62073222, U21A20480 and U1913204. The authors gratefully appreciate the contribution of Yiqing Xu from CUMT.", + "bbox": [ + 498, + 839, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "9898", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Relja Arandjelovic and Andrew Zisserman. Three things everyone should know to improve object retrieval. In 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 2911-2918, 2012.", + "[2] Daniel Barath, Luca Cavalli, and Marc Pollefeys. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 5845-5854, 2019." + ], + "bbox": [ + 78, + 90, + 470, + 598 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "9900", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/RLSAC_ Reinforcement Learning Enhanced Sample Consensus for End-to-End Robust Estimation/253f2fc2-5243-41a5-8404-4467c420f19c_model.json b/2023/RLSAC_ Reinforcement Learning Enhanced Sample Consensus for End-to-End Robust Estimation/253f2fc2-5243-41a5-8404-4467c420f19c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e985d1d1bd635ba8c7448649398445afca4d5289 --- /dev/null +++ b/2023/RLSAC_ Reinforcement Learning Enhanced Sample Consensus for End-to-End Robust Estimation/253f2fc2-5243-41a5-8404-4467c420f19c_model.json @@ -0,0 +1,2079 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.168, + 0.131, + 0.804, + 0.175 + ], + "angle": 0, + "content": "RLSAC: Reinforcement Learning enhanced Sample Consensus for End-to-End Robust Estimation" + }, + { + "type": "text", + "bbox": [ + 0.106, + 0.203, + 0.867, + 0.293 + ], + "angle": 0, + "content": "Chang Nie1, Guangming Wang1,3, Zhe Liu2*, Luca Cavalli3, Marc Pollefeys3,4, Hesheng Wang1* \n1Department of Automation, Key Laboratory of System Control and Information Processing of Ministry of Education, Shanghai Jiao Tong University \n2MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University \n3Department of Computer Science, ETH Zürich 4 Microsoft Mixed Reality and AI Zürich Lab" + }, + { + "type": "text", + "bbox": [ + 0.224, + 0.295, + 0.746, + 0.327 + ], + "angle": 0, + "content": "{changnie, wangguangming, liuzhesjtu, wanghesheng}@sjtu.edu.cn \nlcaballi@ethz.ch marc.poliffeys@inf.ethz.ch" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.362, + 0.314, + 0.379 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.474, + 0.759 + ], + "angle": 0, + "content": "Robust estimation is a crucial and still challenging task, which involves estimating model parameters in noisy environments. Although conventional sampling consensus-based algorithms sample several times to achieve robustness, these algorithms cannot use data features and historical information effectively. In this paper, we propose RLSAC, a novel Reinforcement Learning enhanced SAmple Consensus framework for end-to-end robust estimation. RLSAC employs a graph neural network to utilize both data and memory features to guide exploring directions for sampling the next minimum set. The feedback of downstream tasks serves as the reward for unsupervised training. Therefore, RLSAC can avoid differentiating to learn the features and the feedback of downstream tasks for end-to-end robust estimation. In addition, RLSAC integrates a state transition module that encodes both data and memory features. Our experimental results demonstrate that RLSAC can learn from features to gradually explore a better hypothesis. Through analysis, it is apparent that RLSAC can be easily transferred to other sampling consensus-based robust estimation tasks. To the best of our knowledge, RLSAC is also the first method that uses reinforcement learning to sample consensus for end-to-end robust estimation. We release our codes at https://github.com/IRMVLab/RLSAC." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.788, + 0.21, + 0.804 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.815, + 0.472, + 0.876 + ], + "angle": 0, + "content": "As a fundamental module in computer vision, robust estimation is crucial for many tasks, such as camera pose estimation [10, 33, 31, 32], motion segmentation [26, 19, 29, 30], short and wide baseline matching [22, 28], plane fitting [18]," + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.362, + 0.892, + 0.642 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.643, + 0.895, + 0.698 + ], + "angle": 0, + "content": "Figure 1. RLSAC remodel the sampling consensus process. By modeling the sampling consensus as a reinforcement learning process, RLSAC can achieve end-to-end learning on various robust estimation tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.897, + 0.903 + ], + "angle": 0, + "content": "and line fitting [12, 20]. However, it is still difficult to exclude disturbances while estimating accurate models. To address this issue, sampling consensus-based algorithms are widely used, which are represented by the RANdom SAmple Consensus (RANSAC) [16] algorithm. It first samples the minimum set required for the task, e.g., a minimum set size of 2 for 2D line fitting. Then, the hypothesis is solved by the minimum set. Next, all data is divided into inliers and outliers, according to their residuals to the hypothesis. Finally, the above process is repeated and the best hypothesis is selected based on the highest inlier ratio. RANSAC" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.468, + 0.901 + ], + "angle": 0, + "content": "*Corresponding Authors. The first two authors contributed equally." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "9891" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.081, + 0.092, + 0.47, + 0.212 + ], + "angle": 0, + "content": "can provide strong robustness and generalization, but as the outlier rate increases, the probability of sampling inliers decreases. As a result, the performance of RANSAC degrades rapidly. This is because RANSAC samples each data evenly, regardless of data features that can be used for classifying inliers and outliers. Additionally, the non-differentiable deterministic random sampling of RANSAC also limits it to be integrated into the learning-based pipeline." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.215, + 0.47, + 0.486 + ], + "angle": 0, + "content": "Since sampling the minimum set from the data is quite similar to the process of sampling an action from the action space in reinforcement learning [17, 13], the sampling consensus can be integrated into the reinforcement learning framework. Sampling in reinforcement learning can be achieved through a neural network, which extracts the data features. In addition, the reward from the environment can be used to train the reinforcement learning framework without differentiation. Therefore, to learn from data features and avoid differentiating, we propose the RLSAC: Reinforcement Learning enhanced SAmple Consensus for end-to-end robust estimation. As shown in Figure 1, RLSAC regards sampling consensus as the process of interaction between the agent and environment in reinforcement learning. Specifically, the agent uses a neural network to sample the minimal set from the data as an action. The environment then performs model generation and evaluation based on the action and outputs the next state, which is used in the next iteration." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.489, + 0.47, + 0.655 + ], + "angle": 0, + "content": "However, designing appropriate reward and state are very important and challenging in reinforcement learning. To achieve reinforcement learning enhanced sampling consensus, RLSAC proposes new state transition and reward modules. Specifically, the state is encoded by augmenting the original data features with memory features, including the current action, data residuals, and historical information. When the state is input into the agent, these features can provide more information about the quality of the previous action. This allows RLSAC to gradually explore a better hypothesis by utilizing this memory information." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.657, + 0.47, + 0.778 + ], + "angle": 0, + "content": "Additionally, the evaluation result of the generated hypothesis can be used as the reward signal to train the neural network without differentiation. The reward signal enables the learning-based sampling consensus for end-to-end robust estimation. Furthermore, the evaluation result is the feedback from the downstream task. Thus, the neural network can learn to effectively use the data features and optimize the output to meet the requirements of the downstream task." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.78, + 0.47, + 0.9 + ], + "angle": 0, + "content": "Moreover, instead of directly predicting the final result from the data in one shot [27], RLSAC employs multiple episodes, each containing several sampling processes. In addition, RLSAC performs one random sampling at the beginning of each episode to form the initial state. This approach preserves the robustness of multiple random sampling and provides basic performance for RLSAC. Besides, RLSAC can be extended to other robust estimation tasks since it is" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.093, + 0.722, + 0.107 + ], + "angle": 0, + "content": "not restricted to any specific task." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.108, + 0.894, + 0.167 + ], + "angle": 0, + "content": "The proposed RLSAC is tested on two classic robust estimation tasks, which are the 2D line fitting task and the fundamental matrix estimation task. The experimental results show that RLSAC achieves great performance." + }, + { + "type": "text", + "bbox": [ + 0.523, + 0.169, + 0.774, + 0.182 + ], + "angle": 0, + "content": "Our main contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.187, + 0.892, + 0.277 + ], + "angle": 0, + "content": "- We propose RLSAC: a novel Reinforcement Learning enhanced SAmple Consensus framework for end-to-end robust estimation. It learns data features to sample the minimum set. RLSAC retains the robustness of the multiple sampling process, while the initial random sampling can provide the basic performance." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.282, + 0.892, + 0.386 + ], + "angle": 0, + "content": "- RLSAC proposes an approach for state encoding, which includes both current and historical information. This enables the agent to assess the quality of the previous actions and gradually explore better hypotheses. RL-SAC is trained unsupervised using the reward function, which avoids differentiating the sampling process and achieves end-to-end robust estimation." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.392, + 0.892, + 0.496 + ], + "angle": 0, + "content": "- RLSAC is evaluated on two robust estimation tasks. The 2D line fitting task demonstrates its robustness to disturbances and effective progressive exploration capability. In the fundamental matrix estimation task, RLSAC achieves state-of-the-art performance. Furthermore, RLSAC can be easily applied to other sampling consensus-based robust estimation tasks." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.512, + 0.64, + 0.528 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.538, + 0.894, + 0.613 + ], + "angle": 0, + "content": "Robust estimation is a basic module for many tasks. Although the simple repetitive random sampling strategy of RANSAC [16] is robust and generalized, it has some limitations, such as no further optimization, inefficient sampling, and non-differentiability." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.614, + 0.892, + 0.839 + ], + "angle": 0, + "content": "There are several methods observing that local features help to optimize the sampling result. LO-RANSAC [15] continues to sample in the inliers with a smaller threshold after sampling the best model so far, aiming to find a better hypothesis near the current one. NAPSAC [25] uses a fixed hypersphere to acquire local data and samples from it, but this approach loses global features and may get stuck in local data. To address this, progressive NAPSAC [4] gradually expands the hypersphere to extend the sampling from local to global. GC-RANSAC [5] considers spatial continuity between inliers and surrounding points, modeling the connections of the data through graph-cut to divide inliers and outliers. MAGSAC++ [6] assesses the model quality by weighting various thresholds to reduce the sensitivity to the choice of a specific noise scale." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.841, + 0.892, + 0.9 + ], + "angle": 0, + "content": "To improve sampling efficiency, some methods use guided sampling instead of random sampling. PROSAC [14] sorts the data based on a quality function and then samples the sorted data sequentially to improve efficiency. USAC" + }, + { + "type": "page_number", + "bbox": [ + 0.485, + 0.947, + 0.514, + 0.957 + ], + "angle": 0, + "content": "9892" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.089, + 0.873, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.351, + 0.895, + 0.409 + ], + "angle": 0, + "content": "Figure 2. The pipeline of the proposed RLSAC. The fundamental matrix estimation problem is used as an example. The black, green, and blue lines represent outliers, inliers, and the minimum set, respectively. The yellow arrows are only used once during initialization. The red and orange arrows indicate the loop in an episode. The initial states are randomly sampled. The best hypothesis for this scene is selected by scoring all hypotheses. The collected experience is recorded in the replay buffer for training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.432, + 0.473, + 0.688 + ], + "angle": 0, + "content": "[24] integrates the advantages of various methods to achieve robustness and efficiency. To learn from the data, Yi et al. [36] are the first to use a neural network based on PointNet to directly classify inliers and outliers. Then, Zhang et al. [37] improve this work by proposing pooling and unpooling blocks to learn the local context of correspondences. NG-RANSAC [9] uses a neural network to calculate the sample probability for each point, achieving probability-based sampling. The neural network is trained using reinforcement learning, but it did not use reinforcement learning to achieve sampling consensus and progressive exploration. Barath et al. [2] propose the MQ-Net to learn from residual histograms and evaluate the quality of the model. Additionally, the authors design the MF-Net to learn to reject bad minimum sets early, further improving efficiency. NeFSAC [11] uses a neural network to reject the motion-inconsistent and poorly-conditioned minimal samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.473, + 0.901 + ], + "angle": 0, + "content": "The non-differentiability of RANSAC makes it challenging to integrate into an end-to-end learning pipeline. Some methods propose the differentiable RANSAC. For example, DSAC [8] replaces the deterministic selection process with probabilistic selection, allowing for differentiation with respect to the data. Wei et al. [35] achieve gradient propagation by predicting the probabilities of being inliers to guide sampling. To avoid differentiation, some methods use the loss as reward signals through reinforcement learning to train the network. Bhowmik et al. [7] use reinforcement learning to train the feature point detection network but not for the sampling consensus process. Truong et al. [27] iteratively delete points with reinforcement learning, seeking the maximum consensus model that meets the threshold. However," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.432, + 0.895, + 0.507 + ], + "angle": 0, + "content": "the authors encode the attributes of the points into the state, but does not include long-range historical information or the position of the hypothesis in the state space. In addition, this method does not include the sampling consensus process and may overlook better solutions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.52, + 0.593, + 0.535 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.545, + 0.704, + 0.56 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.895, + 0.765 + ], + "angle": 0, + "content": "Robust estimation can be considered as generating a good hypothesis \\( h \\) given a set of data \\( \\chi = \\{\\mathbf{x}_i\\}_{i=1}^N \\), which may be disturbed by noise. For instance, the hypothesis \\( h \\) could represent the parameters of a 2D line, and \\( \\chi \\) could be all the points in the 2D plane. Or \\( h \\) could be the fundamental matrix that represents the epipolar geometry of a pair of images, and \\( \\chi \\) could be all the correspondences. Similarly, the data contained in \\( \\mathbf{x}_i \\) varies with the task. As a commonly used robust estimation method, the sampling consensus method samples \\( n \\) minimum sets \\( \\mathcal{M} \\) from \\( \\chi \\). The size \\( m \\) of a minimum set varies depending on the task. For example, when fitting a 2D line, the size \\( m = 2 \\). Then, these minimum sets \\( \\mathcal{M} \\) are solved by the minimum solver \\( S \\) to output hypotheses:" + }, + { + "type": "equation", + "bbox": [ + 0.552, + 0.768, + 0.894, + 0.784 + ], + "angle": 0, + "content": "\\[\nH = \\left\\{S \\left(\\mathcal {M} _ {j}\\right) \\mid \\mathcal {M} _ {j} \\in M, j = 1, 2, \\dots , n \\right\\}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.787, + 0.895, + 0.877 + ], + "angle": 0, + "content": "Next, the hypotheses \\( H \\) are evaluated using a scoring function \\( f \\). The residuals of all data points \\( \\chi \\) can be computed and used to calculate the inlier ratio, which is commonly used as a metric for the hypothesis quality [16]. Finally, the hypothesis with the highest score is chosen as the best hypothesis \\( h_{Best} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.88, + 0.893, + 0.904 + ], + "angle": 0, + "content": "\\[\nh _ {B e s t} = \\underset {h \\in H} {\\arg \\max } f (h, \\chi). \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9893" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.136 + ], + "angle": 0, + "content": "By solving the problem using several minimum sets \\(\\mathcal{M}\\), the model can achieve robust estimation, which is less sensitive to outliers and can lead to more accurate results." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.137, + 0.47, + 0.228 + ], + "angle": 0, + "content": "The RANSAC [16] algorithm performs random sampling to sample the minimum sets \\(\\mathcal{M}\\), which cannot fully exploit the data features. As shown in Figure 1, One alternative is to consider the sampling of a minimum set as an action taken by an agent based on the current state, within the reinforcement learning framework:" + }, + { + "type": "equation", + "bbox": [ + 0.203, + 0.233, + 0.47, + 0.25 + ], + "angle": 0, + "content": "\\[\na _ {t + 1} \\sim \\pi_ {\\phi} \\left(a _ {t} \\mid s _ {t}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.262, + 0.471, + 0.352 + ], + "angle": 0, + "content": "Here, the policy network \\(\\pi_{\\phi}\\) depends on the weights \\(\\phi\\). The action \\(a_{t + 1}\\) is sampled by the policy \\(\\pi_{\\phi}\\) from the state \\(s_t\\) and \\(a_{t}\\) at time \\(t + 1\\), which can also be viewed as the process of sampling a minimum set \\(\\mathcal{M}_j\\) from all data \\(\\chi\\). So the Eq. 2 can be rewritten that the best hypothesis is selected by a reinforcement learning enhanced sample consensus method:" + }, + { + "type": "equation", + "bbox": [ + 0.164, + 0.36, + 0.47, + 0.385 + ], + "angle": 0, + "content": "\\[\nh _ {B e s t} = \\underset {t = 1, 2, \\dots , j} {\\arg \\max } f (S (a _ {t}), \\chi). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.385, + 0.472, + 0.491 + ], + "angle": 0, + "content": "In addition, the policy \\(\\pi_{\\phi}\\) is a trainable neural network, and the state \\(s_t\\) contains the features of the data \\(\\chi\\). Therefore, the minimum set can be selected based on sufficient learned knowledge of the data features, rather than being chosen randomly. Furthermore, the evaluation result \\(f(S(a_t), \\chi)\\) of the minimum solver \\(S\\) can serve as the reward in reinforcement learning to achieve unsupervised learning." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.5, + 0.265, + 0.515 + ], + "angle": 0, + "content": "3.2. System Framework" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.523, + 0.47, + 0.719 + ], + "angle": 0, + "content": "With the problem formulation of modeling the process of sampling consensus as a reinforcement learning problem, we introduce RLSAC, which is illustrated in Figure 2. Although the fundamental matrix estimation task is used as an example, the pipeline is also applicable to other robust estimation tasks. Firstly, RLSAC initiates multiple episodes for the correspondences of a pair of images \\(\\chi\\) at (1). An episode contains many steps. At the start of each episode, a random sampling of the minimum set \\(\\mathcal{M}_0\\) is performed to generate the initial state \\(s_0\\) through state transition at (2). Specifically, the initial state \\(s_0\\) is obtained by concatenating each data point with the memory features, which are consisting of action, residual, and historical features (see Section 3.5)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.72, + 0.47, + 0.81 + ], + "angle": 0, + "content": "Next, the initial state \\( s_0 \\) is input into the sampling consensus loop. The agent receives the current state \\( s_t \\) and feeds it into the policy network \\( \\pi_{\\phi} \\) at ③, as shown in Section 3.3. The network generates a probability for each data point. The \\( m \\) points with the highest probabilities are selected as the minimum set \\( \\mathcal{M}_t \\), instead of random sampling." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.811, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Then, the minimum set \\(\\mathcal{M}_t\\) serves as the action \\(a_t\\) for the agent, which generates a hypothesis \\(h_t\\) in the environment at ④, as shown in Section 3.4. The residuals of points to the hypothesis are compared with a threshold to classify points into inliers and outliers at ⑤. The ratio of inliers is utilized as the reward \\(r_t\\) for the current action \\(a_t\\) to train the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.894, + 0.168 + ], + "angle": 0, + "content": "policy network \\(\\pi_{\\phi}\\) at ⑥. Additionally, the action, inliers, and residuals are used for the state transition to generate the next state \\(s_{t + 1}\\) at ⑦, as shown in Section 3.5. Finally, the environment outputs the next state \\(s_{t + 1}\\) and the reward \\(r_t\\) which are used by the agent to start the next step at ⑧." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.894, + 0.259 + ], + "angle": 0, + "content": "Furthermore, the state \\( s_t \\), action \\( a_t \\), reward \\( r_t \\), and the next state \\( s_{t+1} \\) in every step are collected as experiences in the replay buffer [13] for training. After all episodes are complete, the hypothesis with the highest inlier ratio across all episodes is output as the best hypothesis \\( h_{Best} \\) for this pair of images." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.27, + 0.795, + 0.287 + ], + "angle": 0, + "content": "3.3. Sampling Minimum Set by Agent" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.293, + 0.894, + 0.399 + ], + "angle": 0, + "content": "The agent receives the state \\( s_t \\in \\mathbb{R}^{N \\times C} \\), where \\( N \\) is the number of the correspondences of a pair of images. The channel \\( C = c + 3 \\), with \\( c \\) denoting the dimension of data features and 3 representing the dimension of memory features (see Section 3.5). In addition, the first hypothesis \\( h_0 \\) of each episode is generated using a randomly sampled minimum set, which provides a basic performance for RLSAC." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.4, + 0.894, + 0.749 + ], + "angle": 0, + "content": "Then the state \\( s_t \\) is fed into the policy network \\( \\pi_{\\phi} \\). To achieve permutation invariance for the input data, RLSAC uses edge convolution (EdgeConv) from the DGCNN [34] as the basic module to establish the policy network \\( \\pi_{\\phi} \\). The EdgeConv can model the interrelationship of correspondences by graph neural networks. It can extract features from neighboring nodes in a graph and aggregate them into a central node. The policy network \\( \\pi_{\\phi} \\) extracts data features and calculates the probabilities by softmax for each point of being in the minimum set. The probability can be interpreted as the probability of obtaining a greater return on the action for the long term, rather than the probability of achieving the best result in the current state. Consequently, the \\( m \\) points with the highest probability are selected as the minimum set \\( \\mathcal{M}_t \\) in the current state \\( s_t \\). Importantly, all previously used minimum sets are recorded to avoid selecting a duplicate minimum set. Thus, when a new minimum set is selected, it is checked whether it has been used. If the new minimum set has already been used, then another \\( m \\) data set is selected following the probability, which will be checked as well. Until the unused data set is found, it is output as the minimum set. Ultimately, the minimum set is as the action \\( a_t \\in \\mathbb{R}^{m \\times C} \\) output by the agent." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.758, + 0.836, + 0.775 + ], + "angle": 0, + "content": "3.4. Evaluating Hypothesis in Environment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.783, + 0.893, + 0.829 + ], + "angle": 0, + "content": "The environment generates a hypothesis \\( h_t \\) based on the received action \\( a_t \\) from the agent. Next, the residuals \\( R \\) are calculated for all data \\( \\chi \\) with respect to the hypothesis:" + }, + { + "type": "equation", + "bbox": [ + 0.551, + 0.841, + 0.893, + 0.859 + ], + "angle": 0, + "content": "\\[\nR _ {t} = \\left\\{D \\left(x _ {i}, h _ {t}\\right) \\mid x _ {i} \\in \\chi , i = 1, 2, \\dots , N \\right\\}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.893, + 0.901 + ], + "angle": 0, + "content": "where the function \\(D\\) is for residual calculation. The scalar valued residuals \\(R\\) are calculated at all data \\(\\chi\\). With the" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9894" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.092, + 0.452, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.236, + 0.47, + 0.278 + ], + "angle": 0, + "content": "Figure 3. The state transition in RLSAC. To form the next state, the data features are added with the memory features, which contain action features, residual features, and historical features." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.304, + 0.469, + 0.334 + ], + "angle": 0, + "content": "pre-defined threshold, the data \\(\\chi\\) is divided into inliers \\(I_{t}\\in\\) \\(\\mathbb{R}^{z\\times C}\\) and outliers \\(O_{t}\\in \\mathbb{R}^{(N - z)\\times C}\\) based to the residuals." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.336, + 0.47, + 0.41 + ], + "angle": 0, + "content": "In the sampling consensus methods, the inlier ratio commonly represents the quality of the hypothesis. Since the hypothesis \\( h_t \\) is generated by the action \\( a_t \\) in RLSAC, the inlier ratio can be considered as the reward \\( r_t \\) of the current action \\( a_t \\) to train the policy network \\( \\pi_\\phi \\) without ground truth." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.412, + 0.47, + 0.487 + ], + "angle": 0, + "content": "With the hypotheses related-rewards, RLSAC can update weights \\(\\phi\\) of the policy network \\(\\pi\\) without differentiating the sampling process. By modeling sampling consensus as an interactive process in reinforcement learning, RLSAC achieves end-to-end robust estimation while avoiding differentiating." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.499, + 0.236, + 0.513 + ], + "angle": 0, + "content": "3.5. State Transition" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.523, + 0.469, + 0.627 + ], + "angle": 0, + "content": "The state transition module allows RLSAC to encode the previous state and action, enabling RLSAC to explore the state space effectively. As illustrated in Figure 3, the next state \\( s_{t + 1} \\) is obtained by concatenating the original data features \\( N \\times c \\) with memory features \\( \\{A, R, \\mathcal{H}\\} \\), which comprise action features \\( N \\times 1 \\), residual features \\( N \\times 1 \\) and historical features \\( N \\times 1 \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.63, + 0.47, + 0.675 + ], + "angle": 0, + "content": "The action features are derived from the current action \\( a_{t} \\). If a data point \\( x_{i} \\) is used in the action \\( a_{t} \\), the corresponding entry in the action features \\( \\alpha_{i} \\) is set to 1, otherwise it is -1:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.687, + 0.47, + 0.732 + ], + "angle": 0, + "content": "\\[\nA _ {t} = \\left\\{\\alpha_ {i} \\right\\}, \\alpha_ {i} = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} x _ {i} \\in a _ {t} \\\\ - 1 & \\text {o t h e r w i s e} \\end{array} , i = 1, 2, \\dots , N. \\right. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.734, + 0.469, + 0.776 + ], + "angle": 0, + "content": "The action features could provide the agent with information on the current action, like the current location in the data for the next state." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.78, + 0.469, + 0.839 + ], + "angle": 0, + "content": "The residual features are obtained from the residuals \\( R_{t} \\) computed in Eq. 5. They encode the relative relationship between the hypothesis and the data, which can be thought of as the direction for the agent." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The historical features collect how often is a data point used up to the current step. They are initialized to 0 and updated as follow: for each data point \\( x_{i} \\) used in the current action \\( a_{t} \\), the corresponding entry in the historical features" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.093, + 0.655, + 0.107 + ], + "angle": 0, + "content": "\\(\\tau_{i}\\) is incremented by 1:" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.119, + 0.894, + 0.136 + ], + "angle": 0, + "content": "\\[\n\\mathcal {H} _ {t} = \\left\\{\\tau_ {i} \\right\\}, \\tau_ {i} = \\tau_ {i} + 1 \\text {i f} x _ {i} \\in a _ {\\mathrm {t}}, i = 1, 2, \\dots , N. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.148, + 0.894, + 0.193 + ], + "angle": 0, + "content": "The historical features can provide the agent with information on the actions taken so far, enabling it to keep track of its path through the data." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.194, + 0.893, + 0.269 + ], + "angle": 0, + "content": "By encoding the state in this way, the agent has access to both current and historical information, allowing it to reach the goal state. Furthermore, the memory features serve as a director of local navigation, guiding the agent to explore the data features and reach its destination gradually." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.283, + 0.632, + 0.3 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.308, + 0.894, + 0.43 + ], + "angle": 0, + "content": "We evaluate the performance of RLSAC on classic tasks, including 2D line fitting and fundamental matrix estimation. The 2D line fitting task serves as a basic benchmark to assess the performance of the robust estimation algorithm and provides visualization of the sampling process. The fundamental matrix estimation task can show the performance of algorithms on complex camera pose estimation task in the real world, which is a critical task in computer vision." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.44, + 0.597, + 0.455 + ], + "angle": 0, + "content": "4.1. Settings" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.463, + 0.892, + 0.523 + ], + "angle": 0, + "content": "RLSAC is built on the widely used reinforcement learning framework SAC-Discrete [13]. As shown in Figure 2, the collected replay buffer is retrieved for off-policy to update the actor and critic network in reinforcement learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.894, + 0.689 + ], + "angle": 0, + "content": "Since RLSAC uses the inlier ratio as the reward for training, it is an unsupervised method. To explore more images, only one episode with multiple steps is collected per image pair during training. The framework is trained for 100 epochs. During training, the episode termination conditions are set as follows: (i) if the number of inliers is unchanged for \\(\\kappa = 2\\) steps; (ii) if the inlier ratio does not exceed the maximum inlier ratio in the episode for \\(\\varsigma = 3\\) steps; (iii) if the maximum number of steps \\(\\psi = 15\\) is reached. During testing, only the third condition is valid, and each pair of images can be tested in \\(\\nu\\) episodes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.894, + 0.855 + ], + "angle": 0, + "content": "As with the standard reinforcement learning [13], RLSAC uses probabilistic sampling during training and max sampling during testing. For the EdgeConv module in the policy network, the value of k-nearest neighbors is set to \\(k = 15\\). The network architecture and additional information can be found in the supplementary material. Moreover, we have included ablation experiments to analyze the impact of specific network details, also provided in the supplementary material. Similar to the RANSAC implementation, RLSAC also employs refinement using the inliers of the final best hypothesis as the final model polishing." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "The experiments are conducted on a Linux computer with an Intel i7 3.6GHz CPU and an NVIDIA RTX 2080Ti GPU. Our implementation is based on PyTorch." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.515, + 0.957 + ], + "angle": 0, + "content": "9895" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.192, + 0.088, + 0.776, + 0.102 + ], + "angle": 0, + "content": "Table 1. 2D line fitting. The mAA@0.5° and median error(°) on various outlier rates are reported." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.102, + 0.894, + 0.178 + ], + "angle": 0, + "content": "
Method0.10.20.30.40.50.60.7
mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓
RANSAC [16]0.8700.0490.8630.0520.8500.0560.8290.0610.7960.0710.7460.0870.6080.135
Ours0.8750.0470.8740.0490.8720.0480.8650.0500.8580.0520.8450.0560.8240.062
Ours-0.50.8490.0530.8500.0550.8540.0530.8580.0520.8580.0520.8640.0500.8490.054
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.193, + 0.345, + 0.21 + ], + "angle": 0, + "content": "4.2. Case Study 1: 2D Line Fitting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.217, + 0.471, + 0.382 + ], + "angle": 0, + "content": "The 2D line fitting task is a basic problem in robust estimation, which can visualize the process of robust estimation and assess the robustness quantitatively to different outlier rates. In this task, each data point contains only the coordinates, thus all data points can be expressed as: \\(\\chi = \\{[x_i,y_i]\\mid i = 1,2,\\dots,N\\}\\), where \\(\\chi\\) represents the data features \\(N\\times c\\), with \\(c = 2\\). Since two points are sufficient to determine a 2D line, the agent can generate a hypothesis by selecting two points from the set of all data points as the minimum set \\(N\\times m\\), where \\(m = 2\\). For comparison, the RANSAC [16] algorithm is evaluated with the same task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.384, + 0.47, + 0.549 + ], + "angle": 0, + "content": "To evaluate the performance of RLSAC in the 2D line fitting task, we synthesize \\( N = 100 \\) data points for both training and testing. Specifically, a ground truth 2D line is randomly generated in a \\( 10 \\times 10 \\) picture. True inliers are then randomly generated on the line based on the set outlier rate. Next, the true inliers are uniformly disturbed within a range of 0.1 around the line. Thus, the inlier threshold could be set to \\( \\varepsilon = 0.1 \\). Additionally, true outliers are randomly scattered throughout the picture. Moreover, it is possible for true outliers to be located within the inlier region, as is often the case in real-world scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.47, + 0.642 + ], + "angle": 0, + "content": "For accurately evaluating and comparing the performance of different methods, we adopt the mean Average Accuracy (mAA) metric in [2]. The angular difference between the estimated line and the ground truth line is used as the error metric, which is used to calculate the mAA metric with a tolerance threshold of \\(0.5^{\\circ}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.471, + 0.793 + ], + "angle": 0, + "content": "The performance of RLSAC and RANSAC at different outlier rates with 150 iterations is evaluated and the results are presented in Table 1. When the outlier rate is lower than 0.5, RANSAC can achieve a similar performance to RLSAC. This is because the repeated random selection of the minimum set can achieve good performance in simple low outlier rate scenes. However, the performance of RANSAC degrades more quickly than that of RLSAC as the outlier rate increases. This suggests that RLSAC can explore hypotheses closer to the ground truth in noisy scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.794, + 0.47, + 0.855 + ], + "angle": 0, + "content": "As the outlier rate increases beyond 0.5, RLSAC can still maintain a low error and high mAA score. This indicates that RLSAC is more robust to disturbances, providing a more stable performance compared to RANSAC." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "The qualitative results of RLSAC are shown in Figure 4, which demonstrates its ability to quickly find the better hypothesis even from a bad initial state. This means that the" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.19, + 0.885, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.333, + 0.895, + 0.431 + ], + "angle": 0, + "content": "Figure 4. The qualitative results of RLSAC on 2D line fitting. The hypothesis converges to the ground truth as the number of steps increases. The green points represent inliers, while the red points represent outliers. The sampled minimum set points are denoted by black edges. The ground truth is represented by a yellow line, while the hypothesis and inlier threshold are represented by blue and dashed lines respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.895, + 0.547 + ], + "angle": 0, + "content": "memory features can serve as a director of local navigation, allowing RLSAC to move towards a better state through outputting actions. Moreover, once RLSAC finds a high inlier ratio hypothesis that is close to the ground truth, it continues to explore the local state to further improve the result, rather than randomly transitioning to other states." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.895, + 0.624 + ], + "angle": 0, + "content": "The results of the 2D line fitting task show that RLSAC can effectively utilize both data features and memory features, maintaining robust and stable performance in noisy environments. In addition, it can gradually explore a better hypothesis with the help of memory features." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.635, + 0.892, + 0.651 + ], + "angle": 0, + "content": "4.3. Case Study 2: Fundamental Matrix Estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.895, + 0.901 + ], + "angle": 0, + "content": "The fundamental matrix estimation is a crucial robust estimation task in computer vision, which solves the fundamental matrix by correspondences in a pair of images. In this study, we use the data and settings in CVPR tutorial RANSAC in 2020 [3], where the correspondences are detected by RootSIFT [1] and matched by the nearest neighbor. The training data comprises 12 scenes, each with \\(100\\mathrm{k}\\) image pairs, while the test data includes 2 scenes, with 4950 image pairs. The dataset uses Second Nearest Neighbor (SNN) ratio as the matching score. The correspondences are sorted in descending order by SNN. Then the top \\(N = 150\\) SNN correspondences are selected. Next, each point extracts a 128-dimensional descriptor desc through the SIFT algorithm. Thus, the data points are: \\(\\chi = \\left\\{\\left[x_1^i,y_1^i,x_2^i,y_2^i,SNN^i,desc_1^i,desc_2^i\\right]\\mid i = 1,2,\\dots,N\\right\\} \\in \\mathbb{R}^{N\\times c}\\), where \\(c = 261\\). The 8-point solver is used to solve" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9896" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.47, + 0.129 + ], + "angle": 0, + "content": "Table 2. Fundamental matrix estimation. The mAA@ \\(10^{\\circ}\\) and median error \\((\\epsilon_{\\mathbf{R}}\\) and \\(\\epsilon_{\\mathrm{t}})\\) of rotation and the direction of translation at 1k iterations are reported in degrees." + }, + { + "type": "table", + "bbox": [ + 0.108, + 0.13, + 0.437, + 0.221 + ], + "angle": 0, + "content": "
MethodmAA@10°↑Median (°) ↓
RtεRεt
RANSAC[16]0.6440.4882.3075.100
USAC[24]0.7410.6041.0362.157
MAGSAC++[6]0.7530.6140.9241.895
Ours0.7600.6220.9261.751
" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.228, + 0.27, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.228, + 0.449, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.36, + 0.468, + 0.387 + ], + "angle": 0, + "content": "Figure 5. The mAA@10° at different iterations. The results on the fundamental matrix estimation task at different iterations." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.401, + 0.27, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.401, + 0.45, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.468, + 0.269, + 0.533 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.468, + 0.45, + 0.533 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.54, + 0.468, + 0.596 + ], + "angle": 0, + "content": "Figure 6. The qualitative results of RLSAC on the fundamental matrix estimation task. Inlier rate, rotation and translation errors are reported. The blue lines represent the sampled minimum set points, and the green lines represent the inliers." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.61, + 0.269, + 0.782 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.611, + 0.453, + 0.782 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.789, + 0.468, + 0.83 + ], + "angle": 0, + "content": "Figure 7. The step results of RLSAC on the fundamental matrix estimation task. The meaning of the lines and the evaluation metrics are consistent with Figure 6." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.47, + 0.901 + ], + "angle": 0, + "content": "the hypotheses [21]. The inlier threshold of RLSAC is set to \\(\\varepsilon = 4\\). The evaluation settings follow [3]. To compare with other methods, RANSAC [16], USAC [24], MAGSAC++ [6] are tested, which use the recommended settings in [3]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.167 + ], + "angle": 0, + "content": "As shown in Figure 5, RLSAC outperforms other methods in estimating both the rotation matrix and translation vector. Remarkably, RLSAC can achieve high accuracy with only 100 iterations. Comparisons reveals that RLSAC possesses a higher upper bound in performance than MAGSAC." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.893, + 0.286 + ], + "angle": 0, + "content": "The quantitative results of the methods at 1k iterations are presented in Table 2. RLSAC achieves great performance with small errors, a little higher than MAGSAC++[6]. Specifically, RLSAC shows high performance in estimating the direction of the translation vector compared to other methods. Since RLSAC could effectively learn features from the data to exclude noise disturbances, it has significant performance on translation vector estimation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.288, + 0.892, + 0.439 + ], + "angle": 0, + "content": "Figure 6 shows the qualitative results of the fundamental matrix estimation of RLSAC in each scene. The figure demonstrates that RLSAC selects rigid and fixed feature points on buildings as the minimum sets, which can help to find better poses. Furthermore, the step-by-step fundamental matrix estimation results of RLSAC are visualized in Figure 7. It demonstrates a gradual increase in the inlier ratio of the hypothesis and a decrease in the rotation and translation errors. This illustrates that RLSAC can progressively explore the state space to find a better hypothesis." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.453, + 0.651, + 0.469 + ], + "angle": 0, + "content": "5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.891, + 0.523 + ], + "angle": 0, + "content": "We perform ablation studies by modifying or removing modules to analyze their effectiveness. The experimental data and settings remain the same as in Section 4." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.893, + 0.854 + ], + "angle": 0, + "content": "Robustness and Generalization of RLSAC in 2D Line Fitting: The Ours-0.5 in Table 1 shows the result of evaluating the robustness and generalization of RLSAC in 2D Line Fitting. We train RLSAC on data with the outlier rate of 0.5 and then test it on various outlier rates. In most cases, Ours-0.5 can outperform RANSAC. Notably, when the outlier rate exceeds 0.5, Ours-0.5 performs even better than the model trained at that outlier rate. This is because, in scenes with high outlier rates, the point distribution is closer to a uniform distribution, which lacks the features of a dense distribution. As a result, the model \\(RLSAC_{High}\\) trained on high outlier rates may not have learned the dense distribution in low outlier rates. This results in a mediocre performance of \\(RLSAC_{High}\\) in low outlier rates scenes. Conversely, scenes of low outlier rates exhibit both sparse and dense point distributions in different regions, providing more diverse features for the model \\(RLSAC_{Low}\\) to learn. Consequently, the \\(RLSAC_{Low}\\) can predict better results when the dense distribution of points is occasionally present in the high outlier scene. These results demonstrate that RLSAC can effectively learn the distribution in point groups to classify inliers and outliers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Effect of Descriptors: To investigate the effect of descriptors with image semantic features, we conduct experiments as shown in Table 3 (a). This suggests that descriptors with" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.956 + ], + "angle": 0, + "content": "9897" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.088, + 0.468, + 0.113 + ], + "angle": 0, + "content": "Table 3. The ablation study results of RLSAC on fundamental matrix estimation." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.113, + 0.487, + 0.299 + ], + "angle": 0, + "content": "
MethodmAA@10^↑Median (°) ↓
RtεRεt
(a)Ours (w/o descriptors)0.7020.5681.4002.963
Ours (full, with 128 DIM descriptors)0.7600.6220.9261.751
(b)Ours (with max sampling in training and max sampling in testing)0.7300.5911.1322.331
Ours (with max sampling in training and probabilistic sampling in testing)0.7060.5311.4152.893
Ours (with probabilistic sampling in training and probabilistic sampling in testing)0.7200.5811.1502.508
Ours (full, with probabilistic sampling in training and max sampling in testing)0.7600.6220.9261.751
(c)Ours (with N=100 points)0.7270.5881.2162.464
Ours (with N=200 points)0.7470.6041.0502.108
Ours (with N=300 points)0.7330.5941.1802.364
Ours (full, with N=150 points)0.7600.6220.9261.751
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.311, + 0.468, + 0.34 + ], + "angle": 0, + "content": "semantic features are helpful for RLSAC to effectively learn and sample minimum sets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.47, + 0.478 + ], + "angle": 0, + "content": "Different Sampling Approaches: In Table 3 (b), four different sampling strategies are compared. The results illustrate that the best performance can be achieved by probabilistic sampling during training and max sampling during testing. This is consistent with the sampling strategy for actions in reinforcement learning. Specifically, probabilistic sampling can provide randomness and exploratory during training, while max sampling can output the optimal strategy during testing to improve performance and efficiency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.48, + 0.47, + 0.631 + ], + "angle": 0, + "content": "Number of State Points: In RLSAC, the state points are selected from the top \\(N\\) correspondences sorted by SNN. Different values of \\(N\\) are evaluated in Table 3 (c). The best performance is obtained when \\(N = 150\\). We count the number of correspondences in images at \\(SNN < 0.8\\) recommended in [3], which is also around 150 points. This is reasonable that a smaller number of points may exclude points, which would solve the better hypothesis. While more points will introduce more noise, making it more difficult for RLSAC to learn effective sampling strategies." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.647, + 0.192, + 0.663 + ], + "angle": 0, + "content": "6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.47, + 0.839 + ], + "angle": 0, + "content": "The methods of estimating results directly with neural networks in one shot [23] are not robust and generalized in the scenes that have not been learned. Moreover, their poor interpretability leads to poor practicality in engineering applications. In contrast, traditional methods based on mathematical theory, such as multiple sampling consensus for model estimation and noise covariance matrix estimation in simultaneous localization and mapping (SLAM), offer clear interpretability and well-defined scopes of application. However, many traditional methods cannot be integrated into a learning-based framework due to their non-differentiability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Therefore, combining these traditional methods with learning-based methods can provide both interpretability and high performance. RLSAC combines sampling consensus with reinforcement learning to avoid differentiation of" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "sampling while better extracting data features and memory features. In addition, RLSAC can be easily transferred to other sampling consensus tasks due to:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.141, + 0.894, + 0.201 + ], + "angle": 0, + "content": "- The input data of RLSAC is not limited to coordinates and descriptors. Additional features such as depth estimation information and semantic segmentation information can also be used as input for the policy network." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.206, + 0.894, + 0.265 + ], + "angle": 0, + "content": "- RLSAC retains random sampling at the beginning of each episode and each sample result is deduplicated. This provides basic performance for sampling consensus-based tasks." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.269, + 0.894, + 0.36 + ], + "angle": 0, + "content": "- The rewards in RLSAC are linked with the evaluation of the hypothesis. Therefore, RLSAC can be extended to other robust estimation tasks, which require different evaluation methods. Moreover, RLSAC does not require differentiation of the sampling process, the hypothesis solving process, and the evaluation process." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.141, + 0.894, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.368, + 0.894, + 0.413 + ], + "angle": 0, + "content": "In this way, RLSAC enables end-to-end learning that incorporates traditional methods. This allows for consistent optimization objectives across modules." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.428, + 0.619, + 0.443 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.453, + 0.895, + 0.801 + ], + "angle": 0, + "content": "In this paper, we propose RLSAC, a reinforcement learning enhanced sample consensus framework for end-to-end robust estimation. RLSAC models the sampling consensus process as a reinforcement learning task to achieve end-to-end robust estimation. The basic performance of RLSAC is provided by the initial random sampling in each episode. In RLSAC, a new state transition strategy is designed to effectively extract current and historical information, which can guide RLSAC to explore state space. Furthermore, the inlier ratio of the hypothesis is used as a reward to realize unsupervised policy network learning. In experiments, the 2D line fitting task illustrates that RLSAC is robust to various disturbances and exhibits strong generalization. The visualization of the sampling process shows that RLSAC can progressively explore to better models and continues to explore locally. Additionally, the fundamental matrix estimation task demonstrates that RLSAC outperforms other methods in the complex camera pose estimation problem. Notably, RLSAC is not limited to specific tasks and can easily perform end-to-end learning on various sampling consensus-based tasks. In future work, it is worthwhile to explore the integration of traditional and learning-based methods within this framework, while trying to maintain the strengths of each method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.815, + 0.681, + 0.832 + ], + "angle": 0, + "content": "8. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "This work was supported in part by the Natural Science Foundation of China under Grant 62225309, 62073222, U21A20480 and U1913204. The authors gratefully appreciate the contribution of Yiqing Xu from CUMT." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9898" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Relja Arandjelovic and Andrew Zisserman. Three things everyone should know to improve object retrieval. In 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 2911-2918, 2012." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.171, + 0.472, + 0.227 + ], + "angle": 0, + "content": "[2] Daniel Barath, Luca Cavalli, and Marc Pollefeys. Learning to Find Good Models in RANSAC. 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Although conventional sampling consensus-based algorithms sample several times to achieve robustness, these algorithms cannot use data features and historical information effectively. In this paper, we propose RLSAC, a novel Reinforcement Learning enhanced SAmple Consensus framework for end-to-end robust estimation. RLSAC employs a graph neural network to utilize both data and memory features to guide exploring directions for sampling the next minimum set. The feedback of downstream tasks serves as the reward for unsupervised training. Therefore, RLSAC can avoid differentiating to learn the features and the feedback of downstream tasks for end-to-end robust estimation. In addition, RLSAC integrates a state transition module that encodes both data and memory features. Our experimental results demonstrate that RLSAC can learn from features to gradually explore a better hypothesis. Through analysis, it is apparent that RLSAC can be easily transferred to other sampling consensus-based robust estimation tasks. To the best of our knowledge, RLSAC is also the first method that uses reinforcement learning to sample consensus for end-to-end robust estimation. We release our codes at https://github.com/IRMVLab/RLSAC. + +# 1. Introduction + +As a fundamental module in computer vision, robust estimation is crucial for many tasks, such as camera pose estimation [10, 33, 31, 32], motion segmentation [26, 19, 29, 30], short and wide baseline matching [22, 28], plane fitting [18], + +![](images/6f6d8b71cfab04db83270a37b5d186a9b2615142a6fca5511b60647f774992ec.jpg) +Figure 1. RLSAC remodel the sampling consensus process. By modeling the sampling consensus as a reinforcement learning process, RLSAC can achieve end-to-end learning on various robust estimation tasks. + +and line fitting [12, 20]. However, it is still difficult to exclude disturbances while estimating accurate models. To address this issue, sampling consensus-based algorithms are widely used, which are represented by the RANdom SAmple Consensus (RANSAC) [16] algorithm. It first samples the minimum set required for the task, e.g., a minimum set size of 2 for 2D line fitting. Then, the hypothesis is solved by the minimum set. Next, all data is divided into inliers and outliers, according to their residuals to the hypothesis. Finally, the above process is repeated and the best hypothesis is selected based on the highest inlier ratio. RANSAC + +can provide strong robustness and generalization, but as the outlier rate increases, the probability of sampling inliers decreases. As a result, the performance of RANSAC degrades rapidly. This is because RANSAC samples each data evenly, regardless of data features that can be used for classifying inliers and outliers. Additionally, the non-differentiable deterministic random sampling of RANSAC also limits it to be integrated into the learning-based pipeline. + +Since sampling the minimum set from the data is quite similar to the process of sampling an action from the action space in reinforcement learning [17, 13], the sampling consensus can be integrated into the reinforcement learning framework. Sampling in reinforcement learning can be achieved through a neural network, which extracts the data features. In addition, the reward from the environment can be used to train the reinforcement learning framework without differentiation. Therefore, to learn from data features and avoid differentiating, we propose the RLSAC: Reinforcement Learning enhanced SAmple Consensus for end-to-end robust estimation. As shown in Figure 1, RLSAC regards sampling consensus as the process of interaction between the agent and environment in reinforcement learning. Specifically, the agent uses a neural network to sample the minimal set from the data as an action. The environment then performs model generation and evaluation based on the action and outputs the next state, which is used in the next iteration. + +However, designing appropriate reward and state are very important and challenging in reinforcement learning. To achieve reinforcement learning enhanced sampling consensus, RLSAC proposes new state transition and reward modules. Specifically, the state is encoded by augmenting the original data features with memory features, including the current action, data residuals, and historical information. When the state is input into the agent, these features can provide more information about the quality of the previous action. This allows RLSAC to gradually explore a better hypothesis by utilizing this memory information. + +Additionally, the evaluation result of the generated hypothesis can be used as the reward signal to train the neural network without differentiation. The reward signal enables the learning-based sampling consensus for end-to-end robust estimation. Furthermore, the evaluation result is the feedback from the downstream task. Thus, the neural network can learn to effectively use the data features and optimize the output to meet the requirements of the downstream task. + +Moreover, instead of directly predicting the final result from the data in one shot [27], RLSAC employs multiple episodes, each containing several sampling processes. In addition, RLSAC performs one random sampling at the beginning of each episode to form the initial state. This approach preserves the robustness of multiple random sampling and provides basic performance for RLSAC. Besides, RLSAC can be extended to other robust estimation tasks since it is + +not restricted to any specific task. + +The proposed RLSAC is tested on two classic robust estimation tasks, which are the 2D line fitting task and the fundamental matrix estimation task. The experimental results show that RLSAC achieves great performance. + +Our main contributions are as follows: + +- We propose RLSAC: a novel Reinforcement Learning enhanced SAmple Consensus framework for end-to-end robust estimation. It learns data features to sample the minimum set. RLSAC retains the robustness of the multiple sampling process, while the initial random sampling can provide the basic performance. + +- RLSAC proposes an approach for state encoding, which includes both current and historical information. This enables the agent to assess the quality of the previous actions and gradually explore better hypotheses. RL-SAC is trained unsupervised using the reward function, which avoids differentiating the sampling process and achieves end-to-end robust estimation. + +- RLSAC is evaluated on two robust estimation tasks. The 2D line fitting task demonstrates its robustness to disturbances and effective progressive exploration capability. In the fundamental matrix estimation task, RLSAC achieves state-of-the-art performance. Furthermore, RLSAC can be easily applied to other sampling consensus-based robust estimation tasks. + +# 2. Related Work + +Robust estimation is a basic module for many tasks. Although the simple repetitive random sampling strategy of RANSAC [16] is robust and generalized, it has some limitations, such as no further optimization, inefficient sampling, and non-differentiability. + +There are several methods observing that local features help to optimize the sampling result. LO-RANSAC [15] continues to sample in the inliers with a smaller threshold after sampling the best model so far, aiming to find a better hypothesis near the current one. NAPSAC [25] uses a fixed hypersphere to acquire local data and samples from it, but this approach loses global features and may get stuck in local data. To address this, progressive NAPSAC [4] gradually expands the hypersphere to extend the sampling from local to global. GC-RANSAC [5] considers spatial continuity between inliers and surrounding points, modeling the connections of the data through graph-cut to divide inliers and outliers. MAGSAC++ [6] assesses the model quality by weighting various thresholds to reduce the sensitivity to the choice of a specific noise scale. + +To improve sampling efficiency, some methods use guided sampling instead of random sampling. PROSAC [14] sorts the data based on a quality function and then samples the sorted data sequentially to improve efficiency. USAC + +![](images/59c17724da94bb19eb2b15ebcb13eb1de92e540c4885cde55ad685955987e416.jpg) +Figure 2. The pipeline of the proposed RLSAC. The fundamental matrix estimation problem is used as an example. The black, green, and blue lines represent outliers, inliers, and the minimum set, respectively. The yellow arrows are only used once during initialization. The red and orange arrows indicate the loop in an episode. The initial states are randomly sampled. The best hypothesis for this scene is selected by scoring all hypotheses. The collected experience is recorded in the replay buffer for training. + +[24] integrates the advantages of various methods to achieve robustness and efficiency. To learn from the data, Yi et al. [36] are the first to use a neural network based on PointNet to directly classify inliers and outliers. Then, Zhang et al. [37] improve this work by proposing pooling and unpooling blocks to learn the local context of correspondences. NG-RANSAC [9] uses a neural network to calculate the sample probability for each point, achieving probability-based sampling. The neural network is trained using reinforcement learning, but it did not use reinforcement learning to achieve sampling consensus and progressive exploration. Barath et al. [2] propose the MQ-Net to learn from residual histograms and evaluate the quality of the model. Additionally, the authors design the MF-Net to learn to reject bad minimum sets early, further improving efficiency. NeFSAC [11] uses a neural network to reject the motion-inconsistent and poorly-conditioned minimal samples. + +The non-differentiability of RANSAC makes it challenging to integrate into an end-to-end learning pipeline. Some methods propose the differentiable RANSAC. For example, DSAC [8] replaces the deterministic selection process with probabilistic selection, allowing for differentiation with respect to the data. Wei et al. [35] achieve gradient propagation by predicting the probabilities of being inliers to guide sampling. To avoid differentiation, some methods use the loss as reward signals through reinforcement learning to train the network. Bhowmik et al. [7] use reinforcement learning to train the feature point detection network but not for the sampling consensus process. Truong et al. [27] iteratively delete points with reinforcement learning, seeking the maximum consensus model that meets the threshold. However, + +the authors encode the attributes of the points into the state, but does not include long-range historical information or the position of the hypothesis in the state space. In addition, this method does not include the sampling consensus process and may overlook better solutions. + +# 3. Method + +# 3.1. Problem Formulation + +Robust estimation can be considered as generating a good hypothesis $h$ given a set of data $\chi = \{\mathbf{x}_i\}_{i=1}^N$ , which may be disturbed by noise. For instance, the hypothesis $h$ could represent the parameters of a 2D line, and $\chi$ could be all the points in the 2D plane. Or $h$ could be the fundamental matrix that represents the epipolar geometry of a pair of images, and $\chi$ could be all the correspondences. Similarly, the data contained in $\mathbf{x}_i$ varies with the task. As a commonly used robust estimation method, the sampling consensus method samples $n$ minimum sets $\mathcal{M}$ from $\chi$ . The size $m$ of a minimum set varies depending on the task. For example, when fitting a 2D line, the size $m = 2$ . Then, these minimum sets $\mathcal{M}$ are solved by the minimum solver $S$ to output hypotheses: + +$$ +H = \left\{S \left(\mathcal {M} _ {j}\right) \mid \mathcal {M} _ {j} \in M, j = 1, 2, \dots , n \right\}. \tag {1} +$$ + +Next, the hypotheses $H$ are evaluated using a scoring function $f$ . The residuals of all data points $\chi$ can be computed and used to calculate the inlier ratio, which is commonly used as a metric for the hypothesis quality [16]. Finally, the hypothesis with the highest score is chosen as the best hypothesis $h_{Best}$ : + +$$ +h _ {B e s t} = \underset {h \in H} {\arg \max } f (h, \chi). \tag {2} +$$ + +By solving the problem using several minimum sets $\mathcal{M}$ , the model can achieve robust estimation, which is less sensitive to outliers and can lead to more accurate results. + +The RANSAC [16] algorithm performs random sampling to sample the minimum sets $\mathcal{M}$ , which cannot fully exploit the data features. As shown in Figure 1, One alternative is to consider the sampling of a minimum set as an action taken by an agent based on the current state, within the reinforcement learning framework: + +$$ +a _ {t + 1} \sim \pi_ {\phi} \left(a _ {t} \mid s _ {t}\right). \tag {3} +$$ + +Here, the policy network $\pi_{\phi}$ depends on the weights $\phi$ . The action $a_{t + 1}$ is sampled by the policy $\pi_{\phi}$ from the state $s_t$ and $a_{t}$ at time $t + 1$ , which can also be viewed as the process of sampling a minimum set $\mathcal{M}_j$ from all data $\chi$ . So the Eq. 2 can be rewritten that the best hypothesis is selected by a reinforcement learning enhanced sample consensus method: + +$$ +h _ {B e s t} = \underset {t = 1, 2, \dots , j} {\arg \max } f (S (a _ {t}), \chi). \tag {4} +$$ + +In addition, the policy $\pi_{\phi}$ is a trainable neural network, and the state $s_t$ contains the features of the data $\chi$ . Therefore, the minimum set can be selected based on sufficient learned knowledge of the data features, rather than being chosen randomly. Furthermore, the evaluation result $f(S(a_t), \chi)$ of the minimum solver $S$ can serve as the reward in reinforcement learning to achieve unsupervised learning. + +# 3.2. System Framework + +With the problem formulation of modeling the process of sampling consensus as a reinforcement learning problem, we introduce RLSAC, which is illustrated in Figure 2. Although the fundamental matrix estimation task is used as an example, the pipeline is also applicable to other robust estimation tasks. Firstly, RLSAC initiates multiple episodes for the correspondences of a pair of images $\chi$ at (1). An episode contains many steps. At the start of each episode, a random sampling of the minimum set $\mathcal{M}_0$ is performed to generate the initial state $s_0$ through state transition at (2). Specifically, the initial state $s_0$ is obtained by concatenating each data point with the memory features, which are consisting of action, residual, and historical features (see Section 3.5). + +Next, the initial state $s_0$ is input into the sampling consensus loop. The agent receives the current state $s_t$ and feeds it into the policy network $\pi_{\phi}$ at ③, as shown in Section 3.3. The network generates a probability for each data point. The $m$ points with the highest probabilities are selected as the minimum set $\mathcal{M}_t$ , instead of random sampling. + +Then, the minimum set $\mathcal{M}_t$ serves as the action $a_t$ for the agent, which generates a hypothesis $h_t$ in the environment at ④, as shown in Section 3.4. The residuals of points to the hypothesis are compared with a threshold to classify points into inliers and outliers at ⑤. The ratio of inliers is utilized as the reward $r_t$ for the current action $a_t$ to train the + +policy network $\pi_{\phi}$ at ⑥. Additionally, the action, inliers, and residuals are used for the state transition to generate the next state $s_{t + 1}$ at ⑦, as shown in Section 3.5. Finally, the environment outputs the next state $s_{t + 1}$ and the reward $r_t$ which are used by the agent to start the next step at ⑧. + +Furthermore, the state $s_t$ , action $a_t$ , reward $r_t$ , and the next state $s_{t+1}$ in every step are collected as experiences in the replay buffer [13] for training. After all episodes are complete, the hypothesis with the highest inlier ratio across all episodes is output as the best hypothesis $h_{Best}$ for this pair of images. + +# 3.3. Sampling Minimum Set by Agent + +The agent receives the state $s_t \in \mathbb{R}^{N \times C}$ , where $N$ is the number of the correspondences of a pair of images. The channel $C = c + 3$ , with $c$ denoting the dimension of data features and 3 representing the dimension of memory features (see Section 3.5). In addition, the first hypothesis $h_0$ of each episode is generated using a randomly sampled minimum set, which provides a basic performance for RLSAC. + +Then the state $s_t$ is fed into the policy network $\pi_{\phi}$ . To achieve permutation invariance for the input data, RLSAC uses edge convolution (EdgeConv) from the DGCNN [34] as the basic module to establish the policy network $\pi_{\phi}$ . The EdgeConv can model the interrelationship of correspondences by graph neural networks. It can extract features from neighboring nodes in a graph and aggregate them into a central node. The policy network $\pi_{\phi}$ extracts data features and calculates the probabilities by softmax for each point of being in the minimum set. The probability can be interpreted as the probability of obtaining a greater return on the action for the long term, rather than the probability of achieving the best result in the current state. Consequently, the $m$ points with the highest probability are selected as the minimum set $\mathcal{M}_t$ in the current state $s_t$ . Importantly, all previously used minimum sets are recorded to avoid selecting a duplicate minimum set. Thus, when a new minimum set is selected, it is checked whether it has been used. If the new minimum set has already been used, then another $m$ data set is selected following the probability, which will be checked as well. Until the unused data set is found, it is output as the minimum set. Ultimately, the minimum set is as the action $a_t \in \mathbb{R}^{m \times C}$ output by the agent. + +# 3.4. Evaluating Hypothesis in Environment + +The environment generates a hypothesis $h_t$ based on the received action $a_t$ from the agent. Next, the residuals $R$ are calculated for all data $\chi$ with respect to the hypothesis: + +$$ +R _ {t} = \left\{D \left(x _ {i}, h _ {t}\right) \mid x _ {i} \in \chi , i = 1, 2, \dots , N \right\}, \tag {5} +$$ + +where the function $D$ is for residual calculation. The scalar valued residuals $R$ are calculated at all data $\chi$ . With the + +![](images/3483b80179bce9e3ec851cdf19e8d71cef60f7aa612424f5fd60a60ce3567196.jpg) +Figure 3. The state transition in RLSAC. To form the next state, the data features are added with the memory features, which contain action features, residual features, and historical features. + +pre-defined threshold, the data $\chi$ is divided into inliers $I_{t}\in$ $\mathbb{R}^{z\times C}$ and outliers $O_{t}\in \mathbb{R}^{(N - z)\times C}$ based to the residuals. + +In the sampling consensus methods, the inlier ratio commonly represents the quality of the hypothesis. Since the hypothesis $h_t$ is generated by the action $a_t$ in RLSAC, the inlier ratio can be considered as the reward $r_t$ of the current action $a_t$ to train the policy network $\pi_\phi$ without ground truth. + +With the hypotheses related-rewards, RLSAC can update weights $\phi$ of the policy network $\pi$ without differentiating the sampling process. By modeling sampling consensus as an interactive process in reinforcement learning, RLSAC achieves end-to-end robust estimation while avoiding differentiating. + +# 3.5. State Transition + +The state transition module allows RLSAC to encode the previous state and action, enabling RLSAC to explore the state space effectively. As illustrated in Figure 3, the next state $s_{t + 1}$ is obtained by concatenating the original data features $N \times c$ with memory features $\{A, R, \mathcal{H}\}$ , which comprise action features $N \times 1$ , residual features $N \times 1$ and historical features $N \times 1$ . + +The action features are derived from the current action $a_{t}$ . If a data point $x_{i}$ is used in the action $a_{t}$ , the corresponding entry in the action features $\alpha_{i}$ is set to 1, otherwise it is -1: + +$$ +A _ {t} = \left\{\alpha_ {i} \right\}, \alpha_ {i} = \left\{ \begin{array}{l l} 1 & \text {i f} x _ {i} \in a _ {t} \\ - 1 & \text {o t h e r w i s e} \end{array} , i = 1, 2, \dots , N. \right. \tag {6} +$$ + +The action features could provide the agent with information on the current action, like the current location in the data for the next state. + +The residual features are obtained from the residuals $R_{t}$ computed in Eq. 5. They encode the relative relationship between the hypothesis and the data, which can be thought of as the direction for the agent. + +The historical features collect how often is a data point used up to the current step. They are initialized to 0 and updated as follow: for each data point $x_{i}$ used in the current action $a_{t}$ , the corresponding entry in the historical features + +$\tau_{i}$ is incremented by 1: + +$$ +\mathcal {H} _ {t} = \left\{\tau_ {i} \right\}, \tau_ {i} = \tau_ {i} + 1 \text {i f} x _ {i} \in a _ {\mathrm {t}}, i = 1, 2, \dots , N. \tag {7} +$$ + +The historical features can provide the agent with information on the actions taken so far, enabling it to keep track of its path through the data. + +By encoding the state in this way, the agent has access to both current and historical information, allowing it to reach the goal state. Furthermore, the memory features serve as a director of local navigation, guiding the agent to explore the data features and reach its destination gradually. + +# 4. Experiments + +We evaluate the performance of RLSAC on classic tasks, including 2D line fitting and fundamental matrix estimation. The 2D line fitting task serves as a basic benchmark to assess the performance of the robust estimation algorithm and provides visualization of the sampling process. The fundamental matrix estimation task can show the performance of algorithms on complex camera pose estimation task in the real world, which is a critical task in computer vision. + +# 4.1. Settings + +RLSAC is built on the widely used reinforcement learning framework SAC-Discrete [13]. As shown in Figure 2, the collected replay buffer is retrieved for off-policy to update the actor and critic network in reinforcement learning. + +Since RLSAC uses the inlier ratio as the reward for training, it is an unsupervised method. To explore more images, only one episode with multiple steps is collected per image pair during training. The framework is trained for 100 epochs. During training, the episode termination conditions are set as follows: (i) if the number of inliers is unchanged for $\kappa = 2$ steps; (ii) if the inlier ratio does not exceed the maximum inlier ratio in the episode for $\varsigma = 3$ steps; (iii) if the maximum number of steps $\psi = 15$ is reached. During testing, only the third condition is valid, and each pair of images can be tested in $\nu$ episodes. + +As with the standard reinforcement learning [13], RLSAC uses probabilistic sampling during training and max sampling during testing. For the EdgeConv module in the policy network, the value of k-nearest neighbors is set to $k = 15$ . The network architecture and additional information can be found in the supplementary material. Moreover, we have included ablation experiments to analyze the impact of specific network details, also provided in the supplementary material. Similar to the RANSAC implementation, RLSAC also employs refinement using the inliers of the final best hypothesis as the final model polishing. + +The experiments are conducted on a Linux computer with an Intel i7 3.6GHz CPU and an NVIDIA RTX 2080Ti GPU. Our implementation is based on PyTorch. + +Table 1. 2D line fitting. The mAA@0.5° and median error(°) on various outlier rates are reported. + +
Method0.10.20.30.40.50.60.7
mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓
RANSAC [16]0.8700.0490.8630.0520.8500.0560.8290.0610.7960.0710.7460.0870.6080.135
Ours0.8750.0470.8740.0490.8720.0480.8650.0500.8580.0520.8450.0560.8240.062
Ours-0.50.8490.0530.8500.0550.8540.0530.8580.0520.8580.0520.8640.0500.8490.054
+ +# 4.2. Case Study 1: 2D Line Fitting + +The 2D line fitting task is a basic problem in robust estimation, which can visualize the process of robust estimation and assess the robustness quantitatively to different outlier rates. In this task, each data point contains only the coordinates, thus all data points can be expressed as: $\chi = \{[x_i,y_i]\mid i = 1,2,\dots,N\}$ , where $\chi$ represents the data features $N\times c$ , with $c = 2$ . Since two points are sufficient to determine a 2D line, the agent can generate a hypothesis by selecting two points from the set of all data points as the minimum set $N\times m$ , where $m = 2$ . For comparison, the RANSAC [16] algorithm is evaluated with the same task. + +To evaluate the performance of RLSAC in the 2D line fitting task, we synthesize $N = 100$ data points for both training and testing. Specifically, a ground truth 2D line is randomly generated in a $10 \times 10$ picture. True inliers are then randomly generated on the line based on the set outlier rate. Next, the true inliers are uniformly disturbed within a range of 0.1 around the line. Thus, the inlier threshold could be set to $\varepsilon = 0.1$ . Additionally, true outliers are randomly scattered throughout the picture. Moreover, it is possible for true outliers to be located within the inlier region, as is often the case in real-world scenes. + +For accurately evaluating and comparing the performance of different methods, we adopt the mean Average Accuracy (mAA) metric in [2]. The angular difference between the estimated line and the ground truth line is used as the error metric, which is used to calculate the mAA metric with a tolerance threshold of $0.5^{\circ}$ . + +The performance of RLSAC and RANSAC at different outlier rates with 150 iterations is evaluated and the results are presented in Table 1. When the outlier rate is lower than 0.5, RANSAC can achieve a similar performance to RLSAC. This is because the repeated random selection of the minimum set can achieve good performance in simple low outlier rate scenes. However, the performance of RANSAC degrades more quickly than that of RLSAC as the outlier rate increases. This suggests that RLSAC can explore hypotheses closer to the ground truth in noisy scenes. + +As the outlier rate increases beyond 0.5, RLSAC can still maintain a low error and high mAA score. This indicates that RLSAC is more robust to disturbances, providing a more stable performance compared to RANSAC. + +The qualitative results of RLSAC are shown in Figure 4, which demonstrates its ability to quickly find the better hypothesis even from a bad initial state. This means that the + +![](images/bc069480173fb3a2d266ea9fbc5cfa63090baed83b8d8e887faaf9f02977e050.jpg) +Figure 4. The qualitative results of RLSAC on 2D line fitting. The hypothesis converges to the ground truth as the number of steps increases. The green points represent inliers, while the red points represent outliers. The sampled minimum set points are denoted by black edges. The ground truth is represented by a yellow line, while the hypothesis and inlier threshold are represented by blue and dashed lines respectively. + +memory features can serve as a director of local navigation, allowing RLSAC to move towards a better state through outputting actions. Moreover, once RLSAC finds a high inlier ratio hypothesis that is close to the ground truth, it continues to explore the local state to further improve the result, rather than randomly transitioning to other states. + +The results of the 2D line fitting task show that RLSAC can effectively utilize both data features and memory features, maintaining robust and stable performance in noisy environments. In addition, it can gradually explore a better hypothesis with the help of memory features. + +# 4.3. Case Study 2: Fundamental Matrix Estimation + +The fundamental matrix estimation is a crucial robust estimation task in computer vision, which solves the fundamental matrix by correspondences in a pair of images. In this study, we use the data and settings in CVPR tutorial RANSAC in 2020 [3], where the correspondences are detected by RootSIFT [1] and matched by the nearest neighbor. The training data comprises 12 scenes, each with $100\mathrm{k}$ image pairs, while the test data includes 2 scenes, with 4950 image pairs. The dataset uses Second Nearest Neighbor (SNN) ratio as the matching score. The correspondences are sorted in descending order by SNN. Then the top $N = 150$ SNN correspondences are selected. Next, each point extracts a 128-dimensional descriptor desc through the SIFT algorithm. Thus, the data points are: $\chi = \left\{\left[x_1^i,y_1^i,x_2^i,y_2^i,SNN^i,desc_1^i,desc_2^i\right]\mid i = 1,2,\dots,N\right\} \in \mathbb{R}^{N\times c}$ , where $c = 261$ . The 8-point solver is used to solve + +Table 2. Fundamental matrix estimation. The mAA@ $10^{\circ}$ and median error $(\epsilon_{\mathbf{R}}$ and $\epsilon_{\mathrm{t}})$ of rotation and the direction of translation at 1k iterations are reported in degrees. + +
MethodmAA@10°↑Median (°) ↓
RtεRεt
RANSAC[16]0.6440.4882.3075.100
USAC[24]0.7410.6041.0362.157
MAGSAC++[6]0.7530.6140.9241.895
Ours0.7600.6220.9261.751
+ +![](images/8772cc2cbf6043a90e7ca5da0af72b8b30f3bb983a685e1e61e7b53df8c09ca8.jpg) +Figure 5. The mAA@10° at different iterations. The results on the fundamental matrix estimation task at different iterations. + +![](images/6ab1e5df281150369ba941dda5d7ce7f98580c00af2ad49a00749c43516559bc.jpg) + +![](images/5d231a319ac116fb8b45335a114f72e178de5a85a2e720e881f9168960a9a76f.jpg) + +![](images/91d9c4e1a98e7b6344e2844548e1d93b8f2620bebfcd28119a2a2063412aa606.jpg) + +![](images/2a76fbecb79966cfbb3ab3d0ff00f4dab8a019af789d34d7a68fed46fd1b8a11.jpg) +Figure 6. The qualitative results of RLSAC on the fundamental matrix estimation task. Inlier rate, rotation and translation errors are reported. The blue lines represent the sampled minimum set points, and the green lines represent the inliers. + +![](images/83f7938764bc6ef25635ca581599a57b77938b16500eb6a6974e69fd794cee36.jpg) + +![](images/97be18e718c7e873181d70151440925b4249201e1104425819dfc6812f8be658.jpg) +Figure 7. The step results of RLSAC on the fundamental matrix estimation task. The meaning of the lines and the evaluation metrics are consistent with Figure 6. + +![](images/5351c4637327432fcbb7eb8e2d4a9bbbdf91fc6bca50da60127fc1861a68792a.jpg) + +the hypotheses [21]. The inlier threshold of RLSAC is set to $\varepsilon = 4$ . The evaluation settings follow [3]. To compare with other methods, RANSAC [16], USAC [24], MAGSAC++ [6] are tested, which use the recommended settings in [3]. + +As shown in Figure 5, RLSAC outperforms other methods in estimating both the rotation matrix and translation vector. Remarkably, RLSAC can achieve high accuracy with only 100 iterations. Comparisons reveals that RLSAC possesses a higher upper bound in performance than MAGSAC. + +The quantitative results of the methods at 1k iterations are presented in Table 2. RLSAC achieves great performance with small errors, a little higher than MAGSAC++[6]. Specifically, RLSAC shows high performance in estimating the direction of the translation vector compared to other methods. Since RLSAC could effectively learn features from the data to exclude noise disturbances, it has significant performance on translation vector estimation. + +Figure 6 shows the qualitative results of the fundamental matrix estimation of RLSAC in each scene. The figure demonstrates that RLSAC selects rigid and fixed feature points on buildings as the minimum sets, which can help to find better poses. Furthermore, the step-by-step fundamental matrix estimation results of RLSAC are visualized in Figure 7. It demonstrates a gradual increase in the inlier ratio of the hypothesis and a decrease in the rotation and translation errors. This illustrates that RLSAC can progressively explore the state space to find a better hypothesis. + +# 5. Ablation Study + +We perform ablation studies by modifying or removing modules to analyze their effectiveness. The experimental data and settings remain the same as in Section 4. + +Robustness and Generalization of RLSAC in 2D Line Fitting: The Ours-0.5 in Table 1 shows the result of evaluating the robustness and generalization of RLSAC in 2D Line Fitting. We train RLSAC on data with the outlier rate of 0.5 and then test it on various outlier rates. In most cases, Ours-0.5 can outperform RANSAC. Notably, when the outlier rate exceeds 0.5, Ours-0.5 performs even better than the model trained at that outlier rate. This is because, in scenes with high outlier rates, the point distribution is closer to a uniform distribution, which lacks the features of a dense distribution. As a result, the model $RLSAC_{High}$ trained on high outlier rates may not have learned the dense distribution in low outlier rates. This results in a mediocre performance of $RLSAC_{High}$ in low outlier rates scenes. Conversely, scenes of low outlier rates exhibit both sparse and dense point distributions in different regions, providing more diverse features for the model $RLSAC_{Low}$ to learn. Consequently, the $RLSAC_{Low}$ can predict better results when the dense distribution of points is occasionally present in the high outlier scene. These results demonstrate that RLSAC can effectively learn the distribution in point groups to classify inliers and outliers. + +Effect of Descriptors: To investigate the effect of descriptors with image semantic features, we conduct experiments as shown in Table 3 (a). This suggests that descriptors with + +Table 3. The ablation study results of RLSAC on fundamental matrix estimation. + +
MethodmAA@10^↑Median (°) ↓
RtεRεt
(a)Ours (w/o descriptors)0.7020.5681.4002.963
Ours (full, with 128 DIM descriptors)0.7600.6220.9261.751
(b)Ours (with max sampling in training and max sampling in testing)0.7300.5911.1322.331
Ours (with max sampling in training and probabilistic sampling in testing)0.7060.5311.4152.893
Ours (with probabilistic sampling in training and probabilistic sampling in testing)0.7200.5811.1502.508
Ours (full, with probabilistic sampling in training and max sampling in testing)0.7600.6220.9261.751
(c)Ours (with N=100 points)0.7270.5881.2162.464
Ours (with N=200 points)0.7470.6041.0502.108
Ours (with N=300 points)0.7330.5941.1802.364
Ours (full, with N=150 points)0.7600.6220.9261.751
+ +semantic features are helpful for RLSAC to effectively learn and sample minimum sets. + +Different Sampling Approaches: In Table 3 (b), four different sampling strategies are compared. The results illustrate that the best performance can be achieved by probabilistic sampling during training and max sampling during testing. This is consistent with the sampling strategy for actions in reinforcement learning. Specifically, probabilistic sampling can provide randomness and exploratory during training, while max sampling can output the optimal strategy during testing to improve performance and efficiency. + +Number of State Points: In RLSAC, the state points are selected from the top $N$ correspondences sorted by SNN. Different values of $N$ are evaluated in Table 3 (c). The best performance is obtained when $N = 150$ . We count the number of correspondences in images at $SNN < 0.8$ recommended in [3], which is also around 150 points. This is reasonable that a smaller number of points may exclude points, which would solve the better hypothesis. While more points will introduce more noise, making it more difficult for RLSAC to learn effective sampling strategies. + +# 6. Discussion + +The methods of estimating results directly with neural networks in one shot [23] are not robust and generalized in the scenes that have not been learned. Moreover, their poor interpretability leads to poor practicality in engineering applications. In contrast, traditional methods based on mathematical theory, such as multiple sampling consensus for model estimation and noise covariance matrix estimation in simultaneous localization and mapping (SLAM), offer clear interpretability and well-defined scopes of application. However, many traditional methods cannot be integrated into a learning-based framework due to their non-differentiability. + +Therefore, combining these traditional methods with learning-based methods can provide both interpretability and high performance. RLSAC combines sampling consensus with reinforcement learning to avoid differentiation of + +sampling while better extracting data features and memory features. In addition, RLSAC can be easily transferred to other sampling consensus tasks due to: + +- The input data of RLSAC is not limited to coordinates and descriptors. Additional features such as depth estimation information and semantic segmentation information can also be used as input for the policy network. +- RLSAC retains random sampling at the beginning of each episode and each sample result is deduplicated. This provides basic performance for sampling consensus-based tasks. +- The rewards in RLSAC are linked with the evaluation of the hypothesis. Therefore, RLSAC can be extended to other robust estimation tasks, which require different evaluation methods. Moreover, RLSAC does not require differentiation of the sampling process, the hypothesis solving process, and the evaluation process. + +In this way, RLSAC enables end-to-end learning that incorporates traditional methods. This allows for consistent optimization objectives across modules. + +# 7. Conclusion + +In this paper, we propose RLSAC, a reinforcement learning enhanced sample consensus framework for end-to-end robust estimation. RLSAC models the sampling consensus process as a reinforcement learning task to achieve end-to-end robust estimation. The basic performance of RLSAC is provided by the initial random sampling in each episode. In RLSAC, a new state transition strategy is designed to effectively extract current and historical information, which can guide RLSAC to explore state space. Furthermore, the inlier ratio of the hypothesis is used as a reward to realize unsupervised policy network learning. In experiments, the 2D line fitting task illustrates that RLSAC is robust to various disturbances and exhibits strong generalization. The visualization of the sampling process shows that RLSAC can progressively explore to better models and continues to explore locally. Additionally, the fundamental matrix estimation task demonstrates that RLSAC outperforms other methods in the complex camera pose estimation problem. Notably, RLSAC is not limited to specific tasks and can easily perform end-to-end learning on various sampling consensus-based tasks. In future work, it is worthwhile to explore the integration of traditional and learning-based methods within this framework, while trying to maintain the strengths of each method. + +# 8. Acknowledgement + +This work was supported in part by the Natural Science Foundation of China under Grant 62225309, 62073222, U21A20480 and U1913204. The authors gratefully appreciate the contribution of Yiqing Xu from CUMT. + +# References + +[1] Relja Arandjelovic and Andrew Zisserman. Three things everyone should know to improve object retrieval. In 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 2911-2918, 2012. +[2] Daniel Barath, Luca Cavalli, and Marc Pollefeys. Learning to Find Good Models in RANSAC. In 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 15723-15732, 2022. +[3] D Barath, TJ Chin, O Chum, D Mishkin, R Ranftl, and J Matas. RANSAC in 2020 tutorial. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2020. +[4] Daniel Barath, Maksym Ivashechkin, and Jiri Matas. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 5845-5854, 2019. \ No newline at end of file diff --git a/2023/RLSAC_ Reinforcement Learning Enhanced Sample Consensus for End-to-End Robust Estimation/images.zip b/2023/RLSAC_ Reinforcement Learning Enhanced Sample Consensus for End-to-End Robust Estimation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..1b172eb655e37ea903b4e533fa84166869049580 --- /dev/null +++ b/2023/RLSAC_ Reinforcement Learning Enhanced Sample Consensus for End-to-End Robust Estimation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3882a9f235f63fddc792825e1de2ebfaf5f327c2a84d14d33fdab268881f0dd6 +size 515572 diff --git a/2023/RLSAC_ Reinforcement Learning Enhanced Sample Consensus for End-to-End Robust Estimation/layout.json b/2023/RLSAC_ Reinforcement Learning Enhanced Sample Consensus for End-to-End Robust Estimation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..749cb4f969dfe624483e4af9973426de5d22f27f --- /dev/null +++ b/2023/RLSAC_ Reinforcement Learning Enhanced Sample Consensus for End-to-End Robust Estimation/layout.json @@ -0,0 +1,9061 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 102, + 103, + 492, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 103, + 492, + 138 + ], + "spans": [ + { + "bbox": [ + 102, + 103, + 492, + 138 + ], + "type": "text", + "content": "RLSAC: Reinforcement Learning enhanced Sample Consensus for End-to-End Robust Estimation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 64, + 160, + 530, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 160, + 530, + 232 + ], + "spans": [ + { + "bbox": [ + 64, + 160, + 530, + 232 + ], + "type": "text", + "content": "Chang Nie1, Guangming Wang1,3, Zhe Liu2*, Luca Cavalli3, Marc Pollefeys3,4, Hesheng Wang1* \n1Department of Automation, Key Laboratory of System Control and Information Processing of Ministry of Education, Shanghai Jiao Tong University \n2MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University \n3Department of Computer Science, ETH Zürich 4 Microsoft Mixed Reality and AI Zürich Lab" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 137, + 233, + 456, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 137, + 233, + 456, + 258 + ], + "spans": [ + { + "bbox": [ + 137, + 233, + 456, + 258 + ], + "type": "text", + "content": "{changnie, wangguangming, liuzhesjtu, wanghesheng}@sjtu.edu.cn \nlcaballi@ethz.ch marc.poliffeys@inf.ethz.ch" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 286, + 192, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 286, + 192, + 300 + ], + "spans": [ + { + "bbox": [ + 143, + 286, + 192, + 300 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 312, + 290, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 290, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 290, + 601 + ], + "type": "text", + "content": "Robust estimation is a crucial and still challenging task, which involves estimating model parameters in noisy environments. Although conventional sampling consensus-based algorithms sample several times to achieve robustness, these algorithms cannot use data features and historical information effectively. In this paper, we propose RLSAC, a novel Reinforcement Learning enhanced SAmple Consensus framework for end-to-end robust estimation. RLSAC employs a graph neural network to utilize both data and memory features to guide exploring directions for sampling the next minimum set. The feedback of downstream tasks serves as the reward for unsupervised training. Therefore, RLSAC can avoid differentiating to learn the features and the feedback of downstream tasks for end-to-end robust estimation. In addition, RLSAC integrates a state transition module that encodes both data and memory features. Our experimental results demonstrate that RLSAC can learn from features to gradually explore a better hypothesis. Through analysis, it is apparent that RLSAC can be easily transferred to other sampling consensus-based robust estimation tasks. To the best of our knowledge, RLSAC is also the first method that uses reinforcement learning to sample consensus for end-to-end robust estimation. We release our codes at https://github.com/IRMVLab/RLSAC." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 624, + 128, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 624, + 128, + 636 + ], + "spans": [ + { + "bbox": [ + 47, + 624, + 128, + 636 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 645, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 645, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 645, + 288, + 693 + ], + "type": "text", + "content": "As a fundamental module in computer vision, robust estimation is crucial for many tasks, such as camera pose estimation [10, 33, 31, 32], motion segmentation [26, 19, 29, 30], short and wide baseline matching [22, 28], plane fitting [18]," + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 306, + 286, + 545, + 508 + ], + "blocks": [ + { + "bbox": [ + 306, + 286, + 545, + 508 + ], + "lines": [ + { + "bbox": [ + 306, + 286, + 545, + 508 + ], + "spans": [ + { + "bbox": [ + 306, + 286, + 545, + 508 + ], + "type": "image", + "image_path": "6f6d8b71cfab04db83270a37b5d186a9b2615142a6fca5511b60647f774992ec.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 509, + 547, + 552 + ], + "lines": [ + { + "bbox": [ + 305, + 509, + 547, + 552 + ], + "spans": [ + { + "bbox": [ + 305, + 509, + 547, + 552 + ], + "type": "text", + "content": "Figure 1. RLSAC remodel the sampling consensus process. By modeling the sampling consensus as a reinforcement learning process, RLSAC can achieve end-to-end learning on various robust estimation tasks." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": "and line fitting [12, 20]. However, it is still difficult to exclude disturbances while estimating accurate models. To address this issue, sampling consensus-based algorithms are widely used, which are represented by the RANdom SAmple Consensus (RANSAC) [16] algorithm. It first samples the minimum set required for the task, e.g., a minimum set size of 2 for 2D line fitting. Then, the hypothesis is solved by the minimum set. Next, all data is divided into inliers and outliers, according to their residuals to the hypothesis. Finally, the above process is repeated and the best hypothesis is selected based on the highest inlier ratio. RANSAC" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 286, + 713 + ], + "type": "text", + "content": "*Corresponding Authors. The first two authors contributed equally." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "9891" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 72, + 287, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 72, + 287, + 167 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 287, + 167 + ], + "type": "text", + "content": "can provide strong robustness and generalization, but as the outlier rate increases, the probability of sampling inliers decreases. As a result, the performance of RANSAC degrades rapidly. This is because RANSAC samples each data evenly, regardless of data features that can be used for classifying inliers and outliers. Additionally, the non-differentiable deterministic random sampling of RANSAC also limits it to be integrated into the learning-based pipeline." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 170, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 170, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 49, + 170, + 287, + 384 + ], + "type": "text", + "content": "Since sampling the minimum set from the data is quite similar to the process of sampling an action from the action space in reinforcement learning [17, 13], the sampling consensus can be integrated into the reinforcement learning framework. Sampling in reinforcement learning can be achieved through a neural network, which extracts the data features. In addition, the reward from the environment can be used to train the reinforcement learning framework without differentiation. Therefore, to learn from data features and avoid differentiating, we propose the RLSAC: Reinforcement Learning enhanced SAmple Consensus for end-to-end robust estimation. As shown in Figure 1, RLSAC regards sampling consensus as the process of interaction between the agent and environment in reinforcement learning. Specifically, the agent uses a neural network to sample the minimal set from the data as an action. The environment then performs model generation and evaluation based on the action and outputs the next state, which is used in the next iteration." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 387, + 287, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 387, + 287, + 518 + ], + "spans": [ + { + "bbox": [ + 49, + 387, + 287, + 518 + ], + "type": "text", + "content": "However, designing appropriate reward and state are very important and challenging in reinforcement learning. To achieve reinforcement learning enhanced sampling consensus, RLSAC proposes new state transition and reward modules. Specifically, the state is encoded by augmenting the original data features with memory features, including the current action, data residuals, and historical information. When the state is input into the agent, these features can provide more information about the quality of the previous action. This allows RLSAC to gradually explore a better hypothesis by utilizing this memory information." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 520, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 520, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 49, + 520, + 287, + 616 + ], + "type": "text", + "content": "Additionally, the evaluation result of the generated hypothesis can be used as the reward signal to train the neural network without differentiation. The reward signal enables the learning-based sampling consensus for end-to-end robust estimation. Furthermore, the evaluation result is the feedback from the downstream task. Thus, the neural network can learn to effectively use the data features and optimize the output to meet the requirements of the downstream task." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 49, + 617, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 617, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 49, + 617, + 287, + 712 + ], + "type": "text", + "content": "Moreover, instead of directly predicting the final result from the data in one shot [27], RLSAC employs multiple episodes, each containing several sampling processes. In addition, RLSAC performs one random sampling at the beginning of each episode to form the initial state. This approach preserves the robustness of multiple random sampling and provides basic performance for RLSAC. Besides, RLSAC can be extended to other robust estimation tasks since it is" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 308, + 73, + 441, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 73, + 441, + 84 + ], + "spans": [ + { + "bbox": [ + 308, + 73, + 441, + 84 + ], + "type": "text", + "content": "not restricted to any specific task." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 85, + 547, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 85, + 547, + 132 + ], + "spans": [ + { + "bbox": [ + 308, + 85, + 547, + 132 + ], + "type": "text", + "content": "The proposed RLSAC is tested on two classic robust estimation tasks, which are the 2D line fitting task and the fundamental matrix estimation task. The experimental results show that RLSAC achieves great performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 320, + 133, + 473, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 133, + 473, + 144 + ], + "spans": [ + { + "bbox": [ + 320, + 133, + 473, + 144 + ], + "type": "text", + "content": "Our main contributions are as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 318, + 148, + 545, + 219 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 148, + 545, + 219 + ], + "spans": [ + { + "bbox": [ + 318, + 148, + 545, + 219 + ], + "type": "text", + "content": "- We propose RLSAC: a novel Reinforcement Learning enhanced SAmple Consensus framework for end-to-end robust estimation. It learns data features to sample the minimum set. RLSAC retains the robustness of the multiple sampling process, while the initial random sampling can provide the basic performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 318, + 223, + 545, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 223, + 545, + 305 + ], + "spans": [ + { + "bbox": [ + 318, + 223, + 545, + 305 + ], + "type": "text", + "content": "- RLSAC proposes an approach for state encoding, which includes both current and historical information. This enables the agent to assess the quality of the previous actions and gradually explore better hypotheses. RL-SAC is trained unsupervised using the reward function, which avoids differentiating the sampling process and achieves end-to-end robust estimation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 318, + 310, + 545, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 310, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 318, + 310, + 545, + 392 + ], + "type": "text", + "content": "- RLSAC is evaluated on two robust estimation tasks. The 2D line fitting task demonstrates its robustness to disturbances and effective progressive exploration capability. In the fundamental matrix estimation task, RLSAC achieves state-of-the-art performance. Furthermore, RLSAC can be easily applied to other sampling consensus-based robust estimation tasks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 405, + 391, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 405, + 391, + 418 + ], + "spans": [ + { + "bbox": [ + 308, + 405, + 391, + 418 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 308, + 426, + 547, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 426, + 547, + 485 + ], + "spans": [ + { + "bbox": [ + 308, + 426, + 547, + 485 + ], + "type": "text", + "content": "Robust estimation is a basic module for many tasks. Although the simple repetitive random sampling strategy of RANSAC [16] is robust and generalized, it has some limitations, such as no further optimization, inefficient sampling, and non-differentiability." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 308, + 486, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 486, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 308, + 486, + 545, + 664 + ], + "type": "text", + "content": "There are several methods observing that local features help to optimize the sampling result. LO-RANSAC [15] continues to sample in the inliers with a smaller threshold after sampling the best model so far, aiming to find a better hypothesis near the current one. NAPSAC [25] uses a fixed hypersphere to acquire local data and samples from it, but this approach loses global features and may get stuck in local data. To address this, progressive NAPSAC [4] gradually expands the hypersphere to extend the sampling from local to global. GC-RANSAC [5] considers spatial continuity between inliers and surrounding points, modeling the connections of the data through graph-cut to divide inliers and outliers. MAGSAC++ [6] assesses the model quality by weighting various thresholds to reduce the sensitivity to the choice of a specific noise scale." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 308, + 666, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 666, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 666, + 545, + 712 + ], + "type": "text", + "content": "To improve sampling efficiency, some methods use guided sampling instead of random sampling. PROSAC [14] sorts the data based on a quality function and then samples the sorted data sequentially to improve efficiency. USAC" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "type": "text", + "content": "9892" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 534, + 277 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 534, + 277 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 534, + 277 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 534, + 277 + ], + "type": "image", + "image_path": "59c17724da94bb19eb2b15ebcb13eb1de92e540c4885cde55ad685955987e416.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 277, + 547, + 323 + ], + "lines": [ + { + "bbox": [ + 46, + 277, + 547, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 547, + 323 + ], + "type": "text", + "content": "Figure 2. The pipeline of the proposed RLSAC. The fundamental matrix estimation problem is used as an example. The black, green, and blue lines represent outliers, inliers, and the minimum set, respectively. The yellow arrows are only used once during initialization. The red and orange arrows indicate the loop in an episode. The initial states are randomly sampled. The best hypothesis for this scene is selected by scoring all hypotheses. The collected experience is recorded in the replay buffer for training." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 342, + 289, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 289, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 289, + 544 + ], + "type": "text", + "content": "[24] integrates the advantages of various methods to achieve robustness and efficiency. To learn from the data, Yi et al. [36] are the first to use a neural network based on PointNet to directly classify inliers and outliers. Then, Zhang et al. [37] improve this work by proposing pooling and unpooling blocks to learn the local context of correspondences. NG-RANSAC [9] uses a neural network to calculate the sample probability for each point, achieving probability-based sampling. The neural network is trained using reinforcement learning, but it did not use reinforcement learning to achieve sampling consensus and progressive exploration. Barath et al. [2] propose the MQ-Net to learn from residual histograms and evaluate the quality of the model. Additionally, the authors design the MF-Net to learn to reject bad minimum sets early, further improving efficiency. NeFSAC [11] uses a neural network to reject the motion-inconsistent and poorly-conditioned minimal samples." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 545, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 289, + 713 + ], + "type": "text", + "content": "The non-differentiability of RANSAC makes it challenging to integrate into an end-to-end learning pipeline. Some methods propose the differentiable RANSAC. For example, DSAC [8] replaces the deterministic selection process with probabilistic selection, allowing for differentiation with respect to the data. Wei et al. [35] achieve gradient propagation by predicting the probabilities of being inliers to guide sampling. To avoid differentiation, some methods use the loss as reward signals through reinforcement learning to train the network. Bhowmik et al. [7] use reinforcement learning to train the feature point detection network but not for the sampling consensus process. Truong et al. [27] iteratively delete points with reinforcement learning, seeking the maximum consensus model that meets the threshold. However," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 342, + 547, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 547, + 401 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 547, + 401 + ], + "type": "text", + "content": "the authors encode the attributes of the points into the state, but does not include long-range historical information or the position of the hypothesis in the state space. In addition, this method does not include the sampling consensus process and may overlook better solutions." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 411, + 362, + 423 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 411, + 362, + 423 + ], + "spans": [ + { + "bbox": [ + 306, + 411, + 362, + 423 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 431, + 430, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 431, + 430, + 443 + ], + "spans": [ + { + "bbox": [ + 306, + 431, + 430, + 443 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "text", + "content": "Robust estimation can be considered as generating a good hypothesis " + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "text", + "content": " given a set of data " + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\chi = \\{\\mathbf{x}_i\\}_{i=1}^N" + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "text", + "content": ", which may be disturbed by noise. For instance, the hypothesis " + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "text", + "content": " could represent the parameters of a 2D line, and " + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "text", + "content": " could be all the points in the 2D plane. Or " + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "text", + "content": " could be the fundamental matrix that represents the epipolar geometry of a pair of images, and " + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "text", + "content": " could be all the correspondences. Similarly, the data contained in " + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "text", + "content": " varies with the task. As a commonly used robust estimation method, the sampling consensus method samples " + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "text", + "content": " minimum sets " + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "text", + "content": ". The size " + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "text", + "content": " of a minimum set varies depending on the task. For example, when fitting a 2D line, the size " + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "inline_equation", + "content": "m = 2" + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "text", + "content": ". Then, these minimum sets " + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "text", + "content": " are solved by the minimum solver " + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 449, + 547, + 605 + ], + "type": "text", + "content": " to output hypotheses:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 337, + 608, + 547, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 608, + 547, + 620 + ], + "spans": [ + { + "bbox": [ + 337, + 608, + 547, + 620 + ], + "type": "interline_equation", + "content": "H = \\left\\{S \\left(\\mathcal {M} _ {j}\\right) \\mid \\mathcal {M} _ {j} \\in M, j = 1, 2, \\dots , n \\right\\}. \\tag {1}", + "image_path": "01184af632a1eeb52da7868d10fe059742b9d6d32c5f54a8e8419d713171aecc.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 623, + 547, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 623, + 547, + 694 + ], + "spans": [ + { + "bbox": [ + 304, + 623, + 547, + 694 + ], + "type": "text", + "content": "Next, the hypotheses " + }, + { + "bbox": [ + 304, + 623, + 547, + 694 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 623, + 547, + 694 + ], + "type": "text", + "content": " are evaluated using a scoring function " + }, + { + "bbox": [ + 304, + 623, + 547, + 694 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 623, + 547, + 694 + ], + "type": "text", + "content": ". The residuals of all data points " + }, + { + "bbox": [ + 304, + 623, + 547, + 694 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 304, + 623, + 547, + 694 + ], + "type": "text", + "content": " can be computed and used to calculate the inlier ratio, which is commonly used as a metric for the hypothesis quality [16]. Finally, the hypothesis with the highest score is chosen as the best hypothesis " + }, + { + "bbox": [ + 304, + 623, + 547, + 694 + ], + "type": "inline_equation", + "content": "h_{Best}" + }, + { + "bbox": [ + 304, + 623, + 547, + 694 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 369, + 696, + 546, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 696, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 369, + 696, + 546, + 715 + ], + "type": "interline_equation", + "content": "h _ {B e s t} = \\underset {h \\in H} {\\arg \\max } f (h, \\chi). \\tag {2}", + "image_path": "082db9806ce781086adc1de0e034784c96468bece90a64777d5fd9073abe4940.jpg" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9893" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": "By solving the problem using several minimum sets " + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": ", the model can achieve robust estimation, which is less sensitive to outliers and can lead to more accurate results." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 108, + 287, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 108, + 287, + 180 + ], + "spans": [ + { + "bbox": [ + 47, + 108, + 287, + 180 + ], + "type": "text", + "content": "The RANSAC [16] algorithm performs random sampling to sample the minimum sets " + }, + { + "bbox": [ + 47, + 108, + 287, + 180 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 47, + 108, + 287, + 180 + ], + "type": "text", + "content": ", which cannot fully exploit the data features. As shown in Figure 1, One alternative is to consider the sampling of a minimum set as an action taken by an agent based on the current state, within the reinforcement learning framework:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 124, + 184, + 287, + 198 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 184, + 287, + 198 + ], + "spans": [ + { + "bbox": [ + 124, + 184, + 287, + 198 + ], + "type": "interline_equation", + "content": "a _ {t + 1} \\sim \\pi_ {\\phi} \\left(a _ {t} \\mid s _ {t}\\right). \\tag {3}", + "image_path": "3b8131e33b912369b9562424367943477c2bbdb988055ec745c9497ed6106a5a.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "spans": [ + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "text", + "content": "Here, the policy network " + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "inline_equation", + "content": "\\pi_{\\phi}" + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "text", + "content": " depends on the weights " + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "text", + "content": ". The action " + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "inline_equation", + "content": "a_{t + 1}" + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "text", + "content": " is sampled by the policy " + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "inline_equation", + "content": "\\pi_{\\phi}" + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "text", + "content": " from the state " + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "inline_equation", + "content": "s_t" + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "inline_equation", + "content": "a_{t}" + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "text", + "content": ", which can also be viewed as the process of sampling a minimum set " + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_j" + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "text", + "content": " from all data " + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 47, + 207, + 288, + 278 + ], + "type": "text", + "content": ". So the Eq. 2 can be rewritten that the best hypothesis is selected by a reinforcement learning enhanced sample consensus method:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 100, + 285, + 287, + 304 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 285, + 287, + 304 + ], + "spans": [ + { + "bbox": [ + 100, + 285, + 287, + 304 + ], + "type": "interline_equation", + "content": "h _ {B e s t} = \\underset {t = 1, 2, \\dots , j} {\\arg \\max } f (S (a _ {t}), \\chi). \\tag {4}", + "image_path": "48c70b8c89b6f88ab0adffd4f240780daa67ac8be439925542417bd5bdfdb8e1.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 304, + 288, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 304, + 288, + 388 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 288, + 388 + ], + "type": "text", + "content": "In addition, the policy " + }, + { + "bbox": [ + 47, + 304, + 288, + 388 + ], + "type": "inline_equation", + "content": "\\pi_{\\phi}" + }, + { + "bbox": [ + 47, + 304, + 288, + 388 + ], + "type": "text", + "content": " is a trainable neural network, and the state " + }, + { + "bbox": [ + 47, + 304, + 288, + 388 + ], + "type": "inline_equation", + "content": "s_t" + }, + { + "bbox": [ + 47, + 304, + 288, + 388 + ], + "type": "text", + "content": " contains the features of the data " + }, + { + "bbox": [ + 47, + 304, + 288, + 388 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 47, + 304, + 288, + 388 + ], + "type": "text", + "content": ". Therefore, the minimum set can be selected based on sufficient learned knowledge of the data features, rather than being chosen randomly. Furthermore, the evaluation result " + }, + { + "bbox": [ + 47, + 304, + 288, + 388 + ], + "type": "inline_equation", + "content": "f(S(a_t), \\chi)" + }, + { + "bbox": [ + 47, + 304, + 288, + 388 + ], + "type": "text", + "content": " of the minimum solver " + }, + { + "bbox": [ + 47, + 304, + 288, + 388 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 304, + 288, + 388 + ], + "type": "text", + "content": " can serve as the reward in reinforcement learning to achieve unsupervised learning." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 396, + 162, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 162, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 162, + 407 + ], + "type": "text", + "content": "3.2. System Framework" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 414, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 414, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 47, + 414, + 287, + 569 + ], + "type": "text", + "content": "With the problem formulation of modeling the process of sampling consensus as a reinforcement learning problem, we introduce RLSAC, which is illustrated in Figure 2. Although the fundamental matrix estimation task is used as an example, the pipeline is also applicable to other robust estimation tasks. Firstly, RLSAC initiates multiple episodes for the correspondences of a pair of images " + }, + { + "bbox": [ + 47, + 414, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 47, + 414, + 287, + 569 + ], + "type": "text", + "content": " at (1). An episode contains many steps. At the start of each episode, a random sampling of the minimum set " + }, + { + "bbox": [ + 47, + 414, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_0" + }, + { + "bbox": [ + 47, + 414, + 287, + 569 + ], + "type": "text", + "content": " is performed to generate the initial state " + }, + { + "bbox": [ + 47, + 414, + 287, + 569 + ], + "type": "inline_equation", + "content": "s_0" + }, + { + "bbox": [ + 47, + 414, + 287, + 569 + ], + "type": "text", + "content": " through state transition at (2). Specifically, the initial state " + }, + { + "bbox": [ + 47, + 414, + 287, + 569 + ], + "type": "inline_equation", + "content": "s_0" + }, + { + "bbox": [ + 47, + 414, + 287, + 569 + ], + "type": "text", + "content": " is obtained by concatenating each data point with the memory features, which are consisting of action, residual, and historical features (see Section 3.5)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "text", + "content": "Next, the initial state " + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "inline_equation", + "content": "s_0" + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "text", + "content": " is input into the sampling consensus loop. The agent receives the current state " + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "inline_equation", + "content": "s_t" + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "text", + "content": " and feeds it into the policy network " + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\pi_{\\phi}" + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "text", + "content": " at ③, as shown in Section 3.3. The network generates a probability for each data point. The " + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "text", + "content": " points with the highest probabilities are selected as the minimum set " + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t" + }, + { + "bbox": [ + 47, + 570, + 287, + 641 + ], + "type": "text", + "content": ", instead of random sampling." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "type": "text", + "content": "Then, the minimum set " + }, + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t" + }, + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "type": "text", + "content": " serves as the action " + }, + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "type": "inline_equation", + "content": "a_t" + }, + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "type": "text", + "content": " for the agent, which generates a hypothesis " + }, + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "type": "inline_equation", + "content": "h_t" + }, + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "type": "text", + "content": " in the environment at ④, as shown in Section 3.4. The residuals of points to the hypothesis are compared with a threshold to classify points into inliers and outliers at ⑤. The ratio of inliers is utilized as the reward " + }, + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "type": "inline_equation", + "content": "r_t" + }, + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "type": "text", + "content": " for the current action " + }, + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "type": "inline_equation", + "content": "a_t" + }, + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "type": "text", + "content": " to train the" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": "policy network " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "\\pi_{\\phi}" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " at ⑥. Additionally, the action, inliers, and residuals are used for the state transition to generate the next state " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "s_{t + 1}" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " at ⑦, as shown in Section 3.5. Finally, the environment outputs the next state " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "s_{t + 1}" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " and the reward " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "r_t" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " which are used by the agent to start the next step at ⑧." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 133, + 547, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 547, + 205 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 547, + 205 + ], + "type": "text", + "content": "Furthermore, the state " + }, + { + "bbox": [ + 304, + 133, + 547, + 205 + ], + "type": "inline_equation", + "content": "s_t" + }, + { + "bbox": [ + 304, + 133, + 547, + 205 + ], + "type": "text", + "content": ", action " + }, + { + "bbox": [ + 304, + 133, + 547, + 205 + ], + "type": "inline_equation", + "content": "a_t" + }, + { + "bbox": [ + 304, + 133, + 547, + 205 + ], + "type": "text", + "content": ", reward " + }, + { + "bbox": [ + 304, + 133, + 547, + 205 + ], + "type": "inline_equation", + "content": "r_t" + }, + { + "bbox": [ + 304, + 133, + 547, + 205 + ], + "type": "text", + "content": ", and the next state " + }, + { + "bbox": [ + 304, + 133, + 547, + 205 + ], + "type": "inline_equation", + "content": "s_{t+1}" + }, + { + "bbox": [ + 304, + 133, + 547, + 205 + ], + "type": "text", + "content": " in every step are collected as experiences in the replay buffer [13] for training. After all episodes are complete, the hypothesis with the highest inlier ratio across all episodes is output as the best hypothesis " + }, + { + "bbox": [ + 304, + 133, + 547, + 205 + ], + "type": "inline_equation", + "content": "h_{Best}" + }, + { + "bbox": [ + 304, + 133, + 547, + 205 + ], + "type": "text", + "content": " for this pair of images." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 213, + 486, + 227 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 213, + 486, + 227 + ], + "spans": [ + { + "bbox": [ + 305, + 213, + 486, + 227 + ], + "type": "text", + "content": "3.3. Sampling Minimum Set by Agent" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 232, + 547, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 547, + 316 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 547, + 316 + ], + "type": "text", + "content": "The agent receives the state " + }, + { + "bbox": [ + 304, + 232, + 547, + 316 + ], + "type": "inline_equation", + "content": "s_t \\in \\mathbb{R}^{N \\times C}" + }, + { + "bbox": [ + 304, + 232, + 547, + 316 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 232, + 547, + 316 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 232, + 547, + 316 + ], + "type": "text", + "content": " is the number of the correspondences of a pair of images. The channel " + }, + { + "bbox": [ + 304, + 232, + 547, + 316 + ], + "type": "inline_equation", + "content": "C = c + 3" + }, + { + "bbox": [ + 304, + 232, + 547, + 316 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 304, + 232, + 547, + 316 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 232, + 547, + 316 + ], + "type": "text", + "content": " denoting the dimension of data features and 3 representing the dimension of memory features (see Section 3.5). In addition, the first hypothesis " + }, + { + "bbox": [ + 304, + 232, + 547, + 316 + ], + "type": "inline_equation", + "content": "h_0" + }, + { + "bbox": [ + 304, + 232, + 547, + 316 + ], + "type": "text", + "content": " of each episode is generated using a randomly sampled minimum set, which provides a basic performance for RLSAC." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "text", + "content": "Then the state " + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "inline_equation", + "content": "s_t" + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "text", + "content": " is fed into the policy network " + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "inline_equation", + "content": "\\pi_{\\phi}" + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "text", + "content": ". To achieve permutation invariance for the input data, RLSAC uses edge convolution (EdgeConv) from the DGCNN [34] as the basic module to establish the policy network " + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "inline_equation", + "content": "\\pi_{\\phi}" + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "text", + "content": ". The EdgeConv can model the interrelationship of correspondences by graph neural networks. It can extract features from neighboring nodes in a graph and aggregate them into a central node. The policy network " + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "inline_equation", + "content": "\\pi_{\\phi}" + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "text", + "content": " extracts data features and calculates the probabilities by softmax for each point of being in the minimum set. The probability can be interpreted as the probability of obtaining a greater return on the action for the long term, rather than the probability of achieving the best result in the current state. Consequently, the " + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "text", + "content": " points with the highest probability are selected as the minimum set " + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t" + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "text", + "content": " in the current state " + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "inline_equation", + "content": "s_t" + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "text", + "content": ". Importantly, all previously used minimum sets are recorded to avoid selecting a duplicate minimum set. Thus, when a new minimum set is selected, it is checked whether it has been used. If the new minimum set has already been used, then another " + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "text", + "content": " data set is selected following the probability, which will be checked as well. Until the unused data set is found, it is output as the minimum set. Ultimately, the minimum set is as the action " + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "inline_equation", + "content": "a_t \\in \\mathbb{R}^{m \\times C}" + }, + { + "bbox": [ + 304, + 316, + 547, + 593 + ], + "type": "text", + "content": " output by the agent." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 600, + 511, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 600, + 511, + 613 + ], + "spans": [ + { + "bbox": [ + 305, + 600, + 511, + 613 + ], + "type": "text", + "content": "3.4. Evaluating Hypothesis in Environment" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 620, + 546, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 620, + 546, + 656 + ], + "spans": [ + { + "bbox": [ + 304, + 620, + 546, + 656 + ], + "type": "text", + "content": "The environment generates a hypothesis " + }, + { + "bbox": [ + 304, + 620, + 546, + 656 + ], + "type": "inline_equation", + "content": "h_t" + }, + { + "bbox": [ + 304, + 620, + 546, + 656 + ], + "type": "text", + "content": " based on the received action " + }, + { + "bbox": [ + 304, + 620, + 546, + 656 + ], + "type": "inline_equation", + "content": "a_t" + }, + { + "bbox": [ + 304, + 620, + 546, + 656 + ], + "type": "text", + "content": " from the agent. Next, the residuals " + }, + { + "bbox": [ + 304, + 620, + 546, + 656 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 620, + 546, + 656 + ], + "type": "text", + "content": " are calculated for all data " + }, + { + "bbox": [ + 304, + 620, + 546, + 656 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 304, + 620, + 546, + 656 + ], + "type": "text", + "content": " with respect to the hypothesis:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 337, + 666, + 546, + 680 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 666, + 546, + 680 + ], + "spans": [ + { + "bbox": [ + 337, + 666, + 546, + 680 + ], + "type": "interline_equation", + "content": "R _ {t} = \\left\\{D \\left(x _ {i}, h _ {t}\\right) \\mid x _ {i} \\in \\chi , i = 1, 2, \\dots , N \\right\\}, \\tag {5}", + "image_path": "f38ccccb9aa75aaa48ea12cd6c164e4e887421b647866b48f48243a81ee89e0e.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 689, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 546, + 713 + ], + "type": "text", + "content": "where the function " + }, + { + "bbox": [ + 304, + 689, + 546, + 713 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 689, + 546, + 713 + ], + "type": "text", + "content": " is for residual calculation. The scalar valued residuals " + }, + { + "bbox": [ + 304, + 689, + 546, + 713 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 689, + 546, + 713 + ], + "type": "text", + "content": " are calculated at all data " + }, + { + "bbox": [ + 304, + 689, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 304, + 689, + 546, + 713 + ], + "type": "text", + "content": ". With the" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9894" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 72, + 276, + 186 + ], + "blocks": [ + { + "bbox": [ + 53, + 72, + 276, + 186 + ], + "lines": [ + { + "bbox": [ + 53, + 72, + 276, + 186 + ], + "spans": [ + { + "bbox": [ + 53, + 72, + 276, + 186 + ], + "type": "image", + "image_path": "3483b80179bce9e3ec851cdf19e8d71cef60f7aa612424f5fd60a60ce3567196.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 186, + 287, + 220 + ], + "lines": [ + { + "bbox": [ + 47, + 186, + 287, + 220 + ], + "spans": [ + { + "bbox": [ + 47, + 186, + 287, + 220 + ], + "type": "text", + "content": "Figure 3. The state transition in RLSAC. To form the next state, the data features are added with the memory features, which contain action features, residual features, and historical features." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 240, + 287, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 240, + 287, + 264 + ], + "spans": [ + { + "bbox": [ + 47, + 240, + 287, + 264 + ], + "type": "text", + "content": "pre-defined threshold, the data " + }, + { + "bbox": [ + 47, + 240, + 287, + 264 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 47, + 240, + 287, + 264 + ], + "type": "text", + "content": " is divided into inliers " + }, + { + "bbox": [ + 47, + 240, + 287, + 264 + ], + "type": "inline_equation", + "content": "I_{t}\\in" + }, + { + "bbox": [ + 47, + 240, + 287, + 264 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{z\\times C}" + }, + { + "bbox": [ + 47, + 240, + 287, + 264 + ], + "type": "text", + "content": " and outliers " + }, + { + "bbox": [ + 47, + 240, + 287, + 264 + ], + "type": "inline_equation", + "content": "O_{t}\\in \\mathbb{R}^{(N - z)\\times C}" + }, + { + "bbox": [ + 47, + 240, + 287, + 264 + ], + "type": "text", + "content": " based to the residuals." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 266, + 287, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 266, + 287, + 324 + ], + "spans": [ + { + "bbox": [ + 47, + 266, + 287, + 324 + ], + "type": "text", + "content": "In the sampling consensus methods, the inlier ratio commonly represents the quality of the hypothesis. Since the hypothesis " + }, + { + "bbox": [ + 47, + 266, + 287, + 324 + ], + "type": "inline_equation", + "content": "h_t" + }, + { + "bbox": [ + 47, + 266, + 287, + 324 + ], + "type": "text", + "content": " is generated by the action " + }, + { + "bbox": [ + 47, + 266, + 287, + 324 + ], + "type": "inline_equation", + "content": "a_t" + }, + { + "bbox": [ + 47, + 266, + 287, + 324 + ], + "type": "text", + "content": " in RLSAC, the inlier ratio can be considered as the reward " + }, + { + "bbox": [ + 47, + 266, + 287, + 324 + ], + "type": "inline_equation", + "content": "r_t" + }, + { + "bbox": [ + 47, + 266, + 287, + 324 + ], + "type": "text", + "content": " of the current action " + }, + { + "bbox": [ + 47, + 266, + 287, + 324 + ], + "type": "inline_equation", + "content": "a_t" + }, + { + "bbox": [ + 47, + 266, + 287, + 324 + ], + "type": "text", + "content": " to train the policy network " + }, + { + "bbox": [ + 47, + 266, + 287, + 324 + ], + "type": "inline_equation", + "content": "\\pi_\\phi" + }, + { + "bbox": [ + 47, + 266, + 287, + 324 + ], + "type": "text", + "content": " without ground truth." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 326, + 287, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 326, + 287, + 385 + ], + "spans": [ + { + "bbox": [ + 47, + 326, + 287, + 385 + ], + "type": "text", + "content": "With the hypotheses related-rewards, RLSAC can update weights " + }, + { + "bbox": [ + 47, + 326, + 287, + 385 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 47, + 326, + 287, + 385 + ], + "type": "text", + "content": " of the policy network " + }, + { + "bbox": [ + 47, + 326, + 287, + 385 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 47, + 326, + 287, + 385 + ], + "type": "text", + "content": " without differentiating the sampling process. By modeling sampling consensus as an interactive process in reinforcement learning, RLSAC achieves end-to-end robust estimation while avoiding differentiating." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 395, + 144, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 395, + 144, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 395, + 144, + 406 + ], + "type": "text", + "content": "3.5. State Transition" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 414, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 414, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 47, + 414, + 287, + 496 + ], + "type": "text", + "content": "The state transition module allows RLSAC to encode the previous state and action, enabling RLSAC to explore the state space effectively. As illustrated in Figure 3, the next state " + }, + { + "bbox": [ + 47, + 414, + 287, + 496 + ], + "type": "inline_equation", + "content": "s_{t + 1}" + }, + { + "bbox": [ + 47, + 414, + 287, + 496 + ], + "type": "text", + "content": " is obtained by concatenating the original data features " + }, + { + "bbox": [ + 47, + 414, + 287, + 496 + ], + "type": "inline_equation", + "content": "N \\times c" + }, + { + "bbox": [ + 47, + 414, + 287, + 496 + ], + "type": "text", + "content": " with memory features " + }, + { + "bbox": [ + 47, + 414, + 287, + 496 + ], + "type": "inline_equation", + "content": "\\{A, R, \\mathcal{H}\\}" + }, + { + "bbox": [ + 47, + 414, + 287, + 496 + ], + "type": "text", + "content": ", which comprise action features " + }, + { + "bbox": [ + 47, + 414, + 287, + 496 + ], + "type": "inline_equation", + "content": "N \\times 1" + }, + { + "bbox": [ + 47, + 414, + 287, + 496 + ], + "type": "text", + "content": ", residual features " + }, + { + "bbox": [ + 47, + 414, + 287, + 496 + ], + "type": "inline_equation", + "content": "N \\times 1" + }, + { + "bbox": [ + 47, + 414, + 287, + 496 + ], + "type": "text", + "content": " and historical features " + }, + { + "bbox": [ + 47, + 414, + 287, + 496 + ], + "type": "inline_equation", + "content": "N \\times 1" + }, + { + "bbox": [ + 47, + 414, + 287, + 496 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "type": "text", + "content": "The action features are derived from the current action " + }, + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "type": "inline_equation", + "content": "a_{t}" + }, + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "type": "text", + "content": ". If a data point " + }, + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "type": "text", + "content": " is used in the action " + }, + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "type": "inline_equation", + "content": "a_{t}" + }, + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "type": "text", + "content": ", the corresponding entry in the action features " + }, + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "type": "inline_equation", + "content": "\\alpha_{i}" + }, + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "type": "text", + "content": " is set to 1, otherwise it is -1:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 544, + 287, + 579 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 544, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 55, + 544, + 287, + 579 + ], + "type": "interline_equation", + "content": "A _ {t} = \\left\\{\\alpha_ {i} \\right\\}, \\alpha_ {i} = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} x _ {i} \\in a _ {t} \\\\ - 1 & \\text {o t h e r w i s e} \\end{array} , i = 1, 2, \\dots , N. \\right. \\tag {6}", + "image_path": "f0480fb61ac84a4a4c1c2e439cfd871e48dd123dd6ab6eb3aad2842631e16a42.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 581, + 287, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 581, + 287, + 614 + ], + "spans": [ + { + "bbox": [ + 47, + 581, + 287, + 614 + ], + "type": "text", + "content": "The action features could provide the agent with information on the current action, like the current location in the data for the next state." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 617, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 617, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 617, + 287, + 664 + ], + "type": "text", + "content": "The residual features are obtained from the residuals " + }, + { + "bbox": [ + 47, + 617, + 287, + 664 + ], + "type": "inline_equation", + "content": "R_{t}" + }, + { + "bbox": [ + 47, + 617, + 287, + 664 + ], + "type": "text", + "content": " computed in Eq. 5. They encode the relative relationship between the hypothesis and the data, which can be thought of as the direction for the agent." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "content": "The historical features collect how often is a data point used up to the current step. They are initialized to 0 and updated as follow: for each data point " + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "content": " used in the current action " + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "a_{t}" + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "content": ", the corresponding entry in the historical features" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 73, + 400, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 73, + 400, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 73, + 400, + 84 + ], + "type": "inline_equation", + "content": "\\tau_{i}" + }, + { + "bbox": [ + 306, + 73, + 400, + 84 + ], + "type": "text", + "content": " is incremented by 1:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 318, + 94, + 547, + 107 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 94, + 547, + 107 + ], + "spans": [ + { + "bbox": [ + 318, + 94, + 547, + 107 + ], + "type": "interline_equation", + "content": "\\mathcal {H} _ {t} = \\left\\{\\tau_ {i} \\right\\}, \\tau_ {i} = \\tau_ {i} + 1 \\text {i f} x _ {i} \\in a _ {\\mathrm {t}}, i = 1, 2, \\dots , N. \\tag {7}", + "image_path": "fa3a8754dd4e39177850bfa4df06b0e8727eebe51999a3184d188f807e2fcf5e.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 117, + 547, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 117, + 547, + 152 + ], + "spans": [ + { + "bbox": [ + 305, + 117, + 547, + 152 + ], + "type": "text", + "content": "The historical features can provide the agent with information on the actions taken so far, enabling it to keep track of its path through the data." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 153, + 546, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 153, + 546, + 213 + ], + "spans": [ + { + "bbox": [ + 305, + 153, + 546, + 213 + ], + "type": "text", + "content": "By encoding the state in this way, the agent has access to both current and historical information, allowing it to reach the goal state. Furthermore, the memory features serve as a director of local navigation, guiding the agent to explore the data features and reach its destination gradually." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 224, + 386, + 237 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 224, + 386, + 237 + ], + "spans": [ + { + "bbox": [ + 306, + 224, + 386, + 237 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 243, + 547, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 243, + 547, + 340 + ], + "spans": [ + { + "bbox": [ + 305, + 243, + 547, + 340 + ], + "type": "text", + "content": "We evaluate the performance of RLSAC on classic tasks, including 2D line fitting and fundamental matrix estimation. The 2D line fitting task serves as a basic benchmark to assess the performance of the robust estimation algorithm and provides visualization of the sampling process. The fundamental matrix estimation task can show the performance of algorithms on complex camera pose estimation task in the real world, which is a critical task in computer vision." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 348, + 365, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 348, + 365, + 360 + ], + "spans": [ + { + "bbox": [ + 306, + 348, + 365, + 360 + ], + "type": "text", + "content": "4.1. Settings" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 366, + 545, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 366, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 305, + 366, + 545, + 414 + ], + "type": "text", + "content": "RLSAC is built on the widely used reinforcement learning framework SAC-Discrete [13]. As shown in Figure 2, the collected replay buffer is retrieved for off-policy to update the actor and critic network in reinforcement learning." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 415, + 547, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 547, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 547, + 545 + ], + "type": "text", + "content": "Since RLSAC uses the inlier ratio as the reward for training, it is an unsupervised method. To explore more images, only one episode with multiple steps is collected per image pair during training. The framework is trained for 100 epochs. During training, the episode termination conditions are set as follows: (i) if the number of inliers is unchanged for " + }, + { + "bbox": [ + 304, + 415, + 547, + 545 + ], + "type": "inline_equation", + "content": "\\kappa = 2" + }, + { + "bbox": [ + 304, + 415, + 547, + 545 + ], + "type": "text", + "content": " steps; (ii) if the inlier ratio does not exceed the maximum inlier ratio in the episode for " + }, + { + "bbox": [ + 304, + 415, + 547, + 545 + ], + "type": "inline_equation", + "content": "\\varsigma = 3" + }, + { + "bbox": [ + 304, + 415, + 547, + 545 + ], + "type": "text", + "content": " steps; (iii) if the maximum number of steps " + }, + { + "bbox": [ + 304, + 415, + 547, + 545 + ], + "type": "inline_equation", + "content": "\\psi = 15" + }, + { + "bbox": [ + 304, + 415, + 547, + 545 + ], + "type": "text", + "content": " is reached. During testing, only the third condition is valid, and each pair of images can be tested in " + }, + { + "bbox": [ + 304, + 415, + 547, + 545 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 304, + 415, + 547, + 545 + ], + "type": "text", + "content": " episodes." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 546, + 547, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 547, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 547, + 677 + ], + "type": "text", + "content": "As with the standard reinforcement learning [13], RLSAC uses probabilistic sampling during training and max sampling during testing. For the EdgeConv module in the policy network, the value of k-nearest neighbors is set to " + }, + { + "bbox": [ + 304, + 546, + 547, + 677 + ], + "type": "inline_equation", + "content": "k = 15" + }, + { + "bbox": [ + 304, + 546, + 547, + 677 + ], + "type": "text", + "content": ". The network architecture and additional information can be found in the supplementary material. Moreover, we have included ablation experiments to analyze the impact of specific network details, also provided in the supplementary material. Similar to the RANSAC implementation, RLSAC also employs refinement using the inliers of the final best hypothesis as the final model polishing." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "The experiments are conducted on a Linux computer with an Intel i7 3.6GHz CPU and an NVIDIA RTX 2080Ti GPU. Our implementation is based on PyTorch." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "9895" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 80, + 547, + 140 + ], + "blocks": [ + { + "bbox": [ + 117, + 69, + 474, + 80 + ], + "lines": [ + { + "bbox": [ + 117, + 69, + 474, + 80 + ], + "spans": [ + { + "bbox": [ + 117, + 69, + 474, + 80 + ], + "type": "text", + "content": "Table 1. 2D line fitting. The mAA@0.5° and median error(°) on various outlier rates are reported." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 80, + 547, + 140 + ], + "lines": [ + { + "bbox": [ + 48, + 80, + 547, + 140 + ], + "spans": [ + { + "bbox": [ + 48, + 80, + 547, + 140 + ], + "type": "table", + "html": "
Method0.10.20.30.40.50.60.7
mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓mAA ↑Mid. ↓
RANSAC [16]0.8700.0490.8630.0520.8500.0560.8290.0610.7960.0710.7460.0870.6080.135
Ours0.8750.0470.8740.0490.8720.0480.8650.0500.8580.0520.8450.0560.8240.062
Ours-0.50.8490.0530.8500.0550.8540.0530.8580.0520.8580.0520.8640.0500.8490.054
", + "image_path": "5aeb7a7c55c5c16a2846def5cb3c3ef18505105332e3d3e05ca45129de121de4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 152, + 211, + 166 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 152, + 211, + 166 + ], + "spans": [ + { + "bbox": [ + 47, + 152, + 211, + 166 + ], + "type": "text", + "content": "4.2. Case Study 1: 2D Line Fitting" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 171, + 288, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 171, + 288, + 302 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 288, + 302 + ], + "type": "text", + "content": "The 2D line fitting task is a basic problem in robust estimation, which can visualize the process of robust estimation and assess the robustness quantitatively to different outlier rates. In this task, each data point contains only the coordinates, thus all data points can be expressed as: " + }, + { + "bbox": [ + 46, + 171, + 288, + 302 + ], + "type": "inline_equation", + "content": "\\chi = \\{[x_i,y_i]\\mid i = 1,2,\\dots,N\\}" + }, + { + "bbox": [ + 46, + 171, + 288, + 302 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 171, + 288, + 302 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 171, + 288, + 302 + ], + "type": "text", + "content": " represents the data features " + }, + { + "bbox": [ + 46, + 171, + 288, + 302 + ], + "type": "inline_equation", + "content": "N\\times c" + }, + { + "bbox": [ + 46, + 171, + 288, + 302 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 46, + 171, + 288, + 302 + ], + "type": "inline_equation", + "content": "c = 2" + }, + { + "bbox": [ + 46, + 171, + 288, + 302 + ], + "type": "text", + "content": ". Since two points are sufficient to determine a 2D line, the agent can generate a hypothesis by selecting two points from the set of all data points as the minimum set " + }, + { + "bbox": [ + 46, + 171, + 288, + 302 + ], + "type": "inline_equation", + "content": "N\\times m" + }, + { + "bbox": [ + 46, + 171, + 288, + 302 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 171, + 288, + 302 + ], + "type": "inline_equation", + "content": "m = 2" + }, + { + "bbox": [ + 46, + 171, + 288, + 302 + ], + "type": "text", + "content": ". For comparison, the RANSAC [16] algorithm is evaluated with the same task." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 304, + 287, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 434 + ], + "type": "text", + "content": "To evaluate the performance of RLSAC in the 2D line fitting task, we synthesize " + }, + { + "bbox": [ + 46, + 304, + 287, + 434 + ], + "type": "inline_equation", + "content": "N = 100" + }, + { + "bbox": [ + 46, + 304, + 287, + 434 + ], + "type": "text", + "content": " data points for both training and testing. Specifically, a ground truth 2D line is randomly generated in a " + }, + { + "bbox": [ + 46, + 304, + 287, + 434 + ], + "type": "inline_equation", + "content": "10 \\times 10" + }, + { + "bbox": [ + 46, + 304, + 287, + 434 + ], + "type": "text", + "content": " picture. True inliers are then randomly generated on the line based on the set outlier rate. Next, the true inliers are uniformly disturbed within a range of 0.1 around the line. Thus, the inlier threshold could be set to " + }, + { + "bbox": [ + 46, + 304, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\varepsilon = 0.1" + }, + { + "bbox": [ + 46, + 304, + 287, + 434 + ], + "type": "text", + "content": ". Additionally, true outliers are randomly scattered throughout the picture. Moreover, it is possible for true outliers to be located within the inlier region, as is often the case in real-world scenes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 436, + 287, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 287, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 287, + 508 + ], + "type": "text", + "content": "For accurately evaluating and comparing the performance of different methods, we adopt the mean Average Accuracy (mAA) metric in [2]. The angular difference between the estimated line and the ground truth line is used as the error metric, which is used to calculate the mAA metric with a tolerance threshold of " + }, + { + "bbox": [ + 46, + 436, + 287, + 508 + ], + "type": "inline_equation", + "content": "0.5^{\\circ}" + }, + { + "bbox": [ + 46, + 436, + 287, + 508 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 509, + 288, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 288, + 628 + ], + "type": "text", + "content": "The performance of RLSAC and RANSAC at different outlier rates with 150 iterations is evaluated and the results are presented in Table 1. When the outlier rate is lower than 0.5, RANSAC can achieve a similar performance to RLSAC. This is because the repeated random selection of the minimum set can achieve good performance in simple low outlier rate scenes. However, the performance of RANSAC degrades more quickly than that of RLSAC as the outlier rate increases. This suggests that RLSAC can explore hypotheses closer to the ground truth in noisy scenes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 628, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 287, + 677 + ], + "type": "text", + "content": "As the outlier rate increases beyond 0.5, RLSAC can still maintain a low error and high mAA score. This indicates that RLSAC is more robust to disturbances, providing a more stable performance compared to RANSAC." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "The qualitative results of RLSAC are shown in Figure 4, which demonstrates its ability to quickly find the better hypothesis even from a bad initial state. This means that the" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 312, + 150, + 541, + 259 + ], + "blocks": [ + { + "bbox": [ + 312, + 150, + 541, + 259 + ], + "lines": [ + { + "bbox": [ + 312, + 150, + 541, + 259 + ], + "spans": [ + { + "bbox": [ + 312, + 150, + 541, + 259 + ], + "type": "image", + "image_path": "bc069480173fb3a2d266ea9fbc5cfa63090baed83b8d8e887faaf9f02977e050.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 263, + 547, + 341 + ], + "lines": [ + { + "bbox": [ + 304, + 263, + 547, + 341 + ], + "spans": [ + { + "bbox": [ + 304, + 263, + 547, + 341 + ], + "type": "text", + "content": "Figure 4. The qualitative results of RLSAC on 2D line fitting. The hypothesis converges to the ground truth as the number of steps increases. The green points represent inliers, while the red points represent outliers. The sampled minimum set points are denoted by black edges. The ground truth is represented by a yellow line, while the hypothesis and inlier threshold are represented by blue and dashed lines respectively." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 361, + 547, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 547, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 547, + 433 + ], + "type": "text", + "content": "memory features can serve as a director of local navigation, allowing RLSAC to move towards a better state through outputting actions. Moreover, once RLSAC finds a high inlier ratio hypothesis that is close to the ground truth, it continues to explore the local state to further improve the result, rather than randomly transitioning to other states." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 434, + 547, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 547, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 547, + 494 + ], + "type": "text", + "content": "The results of the 2D line fitting task show that RLSAC can effectively utilize both data features and memory features, maintaining robust and stable performance in noisy environments. In addition, it can gradually explore a better hypothesis with the help of memory features." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 502, + 545, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 502, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 305, + 502, + 545, + 515 + ], + "type": "text", + "content": "4.3. Case Study 2: Fundamental Matrix Estimation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "type": "text", + "content": "The fundamental matrix estimation is a crucial robust estimation task in computer vision, which solves the fundamental matrix by correspondences in a pair of images. In this study, we use the data and settings in CVPR tutorial RANSAC in 2020 [3], where the correspondences are detected by RootSIFT [1] and matched by the nearest neighbor. The training data comprises 12 scenes, each with " + }, + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "type": "inline_equation", + "content": "100\\mathrm{k}" + }, + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "type": "text", + "content": " image pairs, while the test data includes 2 scenes, with 4950 image pairs. The dataset uses Second Nearest Neighbor (SNN) ratio as the matching score. The correspondences are sorted in descending order by SNN. Then the top " + }, + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "type": "inline_equation", + "content": "N = 150" + }, + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "type": "text", + "content": " SNN correspondences are selected. Next, each point extracts a 128-dimensional descriptor desc through the SIFT algorithm. Thus, the data points are: " + }, + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\chi = \\left\\{\\left[x_1^i,y_1^i,x_2^i,y_2^i,SNN^i,desc_1^i,desc_2^i\\right]\\mid i = 1,2,\\dots,N\\right\\} \\in \\mathbb{R}^{N\\times c}" + }, + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "type": "inline_equation", + "content": "c = 261" + }, + { + "bbox": [ + 304, + 522, + 547, + 713 + ], + "type": "text", + "content": ". The 8-point solver is used to solve" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "9896" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 66, + 102, + 267, + 175 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "type": "text", + "content": "Table 2. Fundamental matrix estimation. The mAA@ " + }, + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "type": "inline_equation", + "content": "10^{\\circ}" + }, + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "type": "text", + "content": " and median error " + }, + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "type": "inline_equation", + "content": "(\\epsilon_{\\mathbf{R}}" + }, + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\mathrm{t}})" + }, + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "type": "text", + "content": " of rotation and the direction of translation at 1k iterations are reported in degrees." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 102, + 267, + 175 + ], + "lines": [ + { + "bbox": [ + 66, + 102, + 267, + 175 + ], + "spans": [ + { + "bbox": [ + 66, + 102, + 267, + 175 + ], + "type": "table", + "html": "
MethodmAA@10°↑Median (°) ↓
RtεRεt
RANSAC[16]0.6440.4882.3075.100
USAC[24]0.7410.6041.0362.157
MAGSAC++[6]0.7530.6140.9241.895
Ours0.7600.6220.9261.751
", + "image_path": "788ebfd0ae17fc5f7303ab1135cb1af5e17527cda0eeb9b2818e83f758a55228.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 59, + 180, + 165, + 281 + ], + "blocks": [ + { + "bbox": [ + 59, + 180, + 165, + 281 + ], + "lines": [ + { + "bbox": [ + 59, + 180, + 165, + 281 + ], + "spans": [ + { + "bbox": [ + 59, + 180, + 165, + 281 + ], + "type": "image", + "image_path": "8772cc2cbf6043a90e7ca5da0af72b8b30f3bb983a685e1e61e7b53df8c09ca8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 285, + 286, + 306 + ], + "lines": [ + { + "bbox": [ + 47, + 285, + 286, + 306 + ], + "spans": [ + { + "bbox": [ + 47, + 285, + 286, + 306 + ], + "type": "text", + "content": "Figure 5. The mAA@10° at different iterations. The results on the fundamental matrix estimation task at different iterations." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 168, + 180, + 274, + 282 + ], + "blocks": [ + { + "bbox": [ + 168, + 180, + 274, + 282 + ], + "lines": [ + { + "bbox": [ + 168, + 180, + 274, + 282 + ], + "spans": [ + { + "bbox": [ + 168, + 180, + 274, + 282 + ], + "type": "image", + "image_path": "6ab1e5df281150369ba941dda5d7ce7f98580c00af2ad49a00749c43516559bc.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 58, + 317, + 165, + 369 + ], + "blocks": [ + { + "bbox": [ + 58, + 317, + 165, + 369 + ], + "lines": [ + { + "bbox": [ + 58, + 317, + 165, + 369 + ], + "spans": [ + { + "bbox": [ + 58, + 317, + 165, + 369 + ], + "type": "image", + "image_path": "5d231a319ac116fb8b45335a114f72e178de5a85a2e720e881f9168960a9a76f.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 168, + 317, + 275, + 369 + ], + "blocks": [ + { + "bbox": [ + 168, + 317, + 275, + 369 + ], + "lines": [ + { + "bbox": [ + 168, + 317, + 275, + 369 + ], + "spans": [ + { + "bbox": [ + 168, + 317, + 275, + 369 + ], + "type": "image", + "image_path": "91d9c4e1a98e7b6344e2844548e1d93b8f2620bebfcd28119a2a2063412aa606.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 58, + 370, + 164, + 422 + ], + "blocks": [ + { + "bbox": [ + 58, + 370, + 164, + 422 + ], + "lines": [ + { + "bbox": [ + 58, + 370, + 164, + 422 + ], + "spans": [ + { + "bbox": [ + 58, + 370, + 164, + 422 + ], + "type": "image", + "image_path": "2a76fbecb79966cfbb3ab3d0ff00f4dab8a019af789d34d7a68fed46fd1b8a11.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 427, + 286, + 472 + ], + "lines": [ + { + "bbox": [ + 47, + 427, + 286, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 427, + 286, + 472 + ], + "type": "text", + "content": "Figure 6. The qualitative results of RLSAC on the fundamental matrix estimation task. Inlier rate, rotation and translation errors are reported. The blue lines represent the sampled minimum set points, and the green lines represent the inliers." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 168, + 370, + 275, + 422 + ], + "blocks": [ + { + "bbox": [ + 168, + 370, + 275, + 422 + ], + "lines": [ + { + "bbox": [ + 168, + 370, + 275, + 422 + ], + "spans": [ + { + "bbox": [ + 168, + 370, + 275, + 422 + ], + "type": "image", + "image_path": "83f7938764bc6ef25635ca581599a57b77938b16500eb6a6974e69fd794cee36.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 58, + 483, + 164, + 619 + ], + "blocks": [ + { + "bbox": [ + 58, + 483, + 164, + 619 + ], + "lines": [ + { + "bbox": [ + 58, + 483, + 164, + 619 + ], + "spans": [ + { + "bbox": [ + 58, + 483, + 164, + 619 + ], + "type": "image", + "image_path": "97be18e718c7e873181d70151440925b4249201e1104425819dfc6812f8be658.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 624, + 286, + 657 + ], + "lines": [ + { + "bbox": [ + 47, + 624, + 286, + 657 + ], + "spans": [ + { + "bbox": [ + 47, + 624, + 286, + 657 + ], + "type": "text", + "content": "Figure 7. The step results of RLSAC on the fundamental matrix estimation task. The meaning of the lines and the evaluation metrics are consistent with Figure 6." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 169, + 483, + 277, + 619 + ], + "blocks": [ + { + "bbox": [ + 169, + 483, + 277, + 619 + ], + "lines": [ + { + "bbox": [ + 169, + 483, + 277, + 619 + ], + "spans": [ + { + "bbox": [ + 169, + 483, + 277, + 619 + ], + "type": "image", + "image_path": "5351c4637327432fcbb7eb8e2d4a9bbbdf91fc6bca50da60127fc1861a68792a.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "content": "the hypotheses [21]. The inlier threshold of RLSAC is set to " + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\varepsilon = 4" + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "content": ". The evaluation settings follow [3]. To compare with other methods, RANSAC [16], USAC [24], MAGSAC++ [6] are tested, which use the recommended settings in [3]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": "As shown in Figure 5, RLSAC outperforms other methods in estimating both the rotation matrix and translation vector. Remarkably, RLSAC can achieve high accuracy with only 100 iterations. Comparisons reveals that RLSAC possesses a higher upper bound in performance than MAGSAC." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 133, + 546, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 546, + 226 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 546, + 226 + ], + "type": "text", + "content": "The quantitative results of the methods at 1k iterations are presented in Table 2. RLSAC achieves great performance with small errors, a little higher than MAGSAC++[6]. Specifically, RLSAC shows high performance in estimating the direction of the translation vector compared to other methods. Since RLSAC could effectively learn features from the data to exclude noise disturbances, it has significant performance on translation vector estimation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 228, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 347 + ], + "type": "text", + "content": "Figure 6 shows the qualitative results of the fundamental matrix estimation of RLSAC in each scene. The figure demonstrates that RLSAC selects rigid and fixed feature points on buildings as the minimum sets, which can help to find better poses. Furthermore, the step-by-step fundamental matrix estimation results of RLSAC are visualized in Figure 7. It demonstrates a gradual increase in the inlier ratio of the hypothesis and a decrease in the rotation and translation errors. This illustrates that RLSAC can progressively explore the state space to find a better hypothesis." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 358, + 398, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 358, + 398, + 371 + ], + "spans": [ + { + "bbox": [ + 306, + 358, + 398, + 371 + ], + "type": "text", + "content": "5. Ablation Study" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 378, + 545, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 545, + 414 + ], + "type": "text", + "content": "We perform ablation studies by modifying or removing modules to analyze their effectiveness. The experimental data and settings remain the same as in Section 4." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 415, + 546, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 546, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 546, + 676 + ], + "type": "text", + "content": "Robustness and Generalization of RLSAC in 2D Line Fitting: The Ours-0.5 in Table 1 shows the result of evaluating the robustness and generalization of RLSAC in 2D Line Fitting. We train RLSAC on data with the outlier rate of 0.5 and then test it on various outlier rates. In most cases, Ours-0.5 can outperform RANSAC. Notably, when the outlier rate exceeds 0.5, Ours-0.5 performs even better than the model trained at that outlier rate. This is because, in scenes with high outlier rates, the point distribution is closer to a uniform distribution, which lacks the features of a dense distribution. As a result, the model " + }, + { + "bbox": [ + 304, + 415, + 546, + 676 + ], + "type": "inline_equation", + "content": "RLSAC_{High}" + }, + { + "bbox": [ + 304, + 415, + 546, + 676 + ], + "type": "text", + "content": " trained on high outlier rates may not have learned the dense distribution in low outlier rates. This results in a mediocre performance of " + }, + { + "bbox": [ + 304, + 415, + 546, + 676 + ], + "type": "inline_equation", + "content": "RLSAC_{High}" + }, + { + "bbox": [ + 304, + 415, + 546, + 676 + ], + "type": "text", + "content": " in low outlier rates scenes. Conversely, scenes of low outlier rates exhibit both sparse and dense point distributions in different regions, providing more diverse features for the model " + }, + { + "bbox": [ + 304, + 415, + 546, + 676 + ], + "type": "inline_equation", + "content": "RLSAC_{Low}" + }, + { + "bbox": [ + 304, + 415, + 546, + 676 + ], + "type": "text", + "content": " to learn. Consequently, the " + }, + { + "bbox": [ + 304, + 415, + 546, + 676 + ], + "type": "inline_equation", + "content": "RLSAC_{Low}" + }, + { + "bbox": [ + 304, + 415, + 546, + 676 + ], + "type": "text", + "content": " can predict better results when the dense distribution of points is occasionally present in the high outlier scene. These results demonstrate that RLSAC can effectively learn the distribution in point groups to classify inliers and outliers." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "content": "Effect of Descriptors: To investigate the effect of descriptors with image semantic features, we conduct experiments as shown in Table 3 (a). This suggests that descriptors with" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9897" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 89, + 298, + 236 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 286, + 89 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 286, + 89 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 286, + 89 + ], + "type": "text", + "content": "Table 3. The ablation study results of RLSAC on fundamental matrix estimation." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 89, + 298, + 236 + ], + "lines": [ + { + "bbox": [ + 48, + 89, + 298, + 236 + ], + "spans": [ + { + "bbox": [ + 48, + 89, + 298, + 236 + ], + "type": "table", + "html": "
MethodmAA@10^↑Median (°) ↓
RtεRεt
(a)Ours (w/o descriptors)0.7020.5681.4002.963
Ours (full, with 128 DIM descriptors)0.7600.6220.9261.751
(b)Ours (with max sampling in training and max sampling in testing)0.7300.5911.1322.331
Ours (with max sampling in training and probabilistic sampling in testing)0.7060.5311.4152.893
Ours (with probabilistic sampling in training and probabilistic sampling in testing)0.7200.5811.1502.508
Ours (full, with probabilistic sampling in training and max sampling in testing)0.7600.6220.9261.751
(c)Ours (with N=100 points)0.7270.5881.2162.464
Ours (with N=200 points)0.7470.6041.0502.108
Ours (with N=300 points)0.7330.5941.1802.364
Ours (full, with N=150 points)0.7600.6220.9261.751
", + "image_path": "712bea5e4c1df71c190dd0874158521badd3fdeb4d2e53d8c5ede29895b3d8b4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 246, + 286, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 246, + 286, + 269 + ], + "spans": [ + { + "bbox": [ + 47, + 246, + 286, + 269 + ], + "type": "text", + "content": "semantic features are helpful for RLSAC to effectively learn and sample minimum sets." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 270, + 287, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 287, + 378 + ], + "type": "text", + "content": "Different Sampling Approaches: In Table 3 (b), four different sampling strategies are compared. The results illustrate that the best performance can be achieved by probabilistic sampling during training and max sampling during testing. This is consistent with the sampling strategy for actions in reinforcement learning. Specifically, probabilistic sampling can provide randomness and exploratory during training, while max sampling can output the optimal strategy during testing to improve performance and efficiency." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "text", + "content": "Number of State Points: In RLSAC, the state points are selected from the top " + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "text", + "content": " correspondences sorted by SNN. Different values of " + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "text", + "content": " are evaluated in Table 3 (c). The best performance is obtained when " + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "inline_equation", + "content": "N = 150" + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "text", + "content": ". We count the number of correspondences in images at " + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "inline_equation", + "content": "SNN < 0.8" + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "text", + "content": " recommended in [3], which is also around 150 points. This is reasonable that a smaller number of points may exclude points, which would solve the better hypothesis. While more points will introduce more noise, making it more difficult for RLSAC to learn effective sampling strategies." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 512, + 117, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 512, + 117, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 512, + 117, + 525 + ], + "type": "text", + "content": "6. Discussion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 533, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 664 + ], + "type": "text", + "content": "The methods of estimating results directly with neural networks in one shot [23] are not robust and generalized in the scenes that have not been learned. Moreover, their poor interpretability leads to poor practicality in engineering applications. In contrast, traditional methods based on mathematical theory, such as multiple sampling consensus for model estimation and noise covariance matrix estimation in simultaneous localization and mapping (SLAM), offer clear interpretability and well-defined scopes of application. However, many traditional methods cannot be integrated into a learning-based framework due to their non-differentiability." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "content": "Therefore, combining these traditional methods with learning-based methods can provide both interpretability and high performance. RLSAC combines sampling consensus with reinforcement learning to avoid differentiation of" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": "sampling while better extracting data features and memory features. In addition, RLSAC can be easily transferred to other sampling consensus tasks due to:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 111, + 547, + 285 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 317, + 111, + 547, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 111, + 547, + 159 + ], + "spans": [ + { + "bbox": [ + 317, + 111, + 547, + 159 + ], + "type": "text", + "content": "- The input data of RLSAC is not limited to coordinates and descriptors. Additional features such as depth estimation information and semantic segmentation information can also be used as input for the policy network." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 163, + 547, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 163, + 547, + 209 + ], + "spans": [ + { + "bbox": [ + 317, + 163, + 547, + 209 + ], + "type": "text", + "content": "- RLSAC retains random sampling at the beginning of each episode and each sample result is deduplicated. This provides basic performance for sampling consensus-based tasks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 213, + 547, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 213, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 317, + 213, + 547, + 285 + ], + "type": "text", + "content": "- The rewards in RLSAC are linked with the evaluation of the hypothesis. Therefore, RLSAC can be extended to other robust estimation tasks, which require different evaluation methods. Moreover, RLSAC does not require differentiation of the sampling process, the hypothesis solving process, and the evaluation process." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 291, + 547, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 291, + 547, + 327 + ], + "spans": [ + { + "bbox": [ + 305, + 291, + 547, + 327 + ], + "type": "text", + "content": "In this way, RLSAC enables end-to-end learning that incorporates traditional methods. This allows for consistent optimization objectives across modules." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 338, + 378, + 350 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 338, + 378, + 350 + ], + "spans": [ + { + "bbox": [ + 306, + 338, + 378, + 350 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 358, + 547, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 358, + 547, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 358, + 547, + 634 + ], + "type": "text", + "content": "In this paper, we propose RLSAC, a reinforcement learning enhanced sample consensus framework for end-to-end robust estimation. RLSAC models the sampling consensus process as a reinforcement learning task to achieve end-to-end robust estimation. The basic performance of RLSAC is provided by the initial random sampling in each episode. In RLSAC, a new state transition strategy is designed to effectively extract current and historical information, which can guide RLSAC to explore state space. Furthermore, the inlier ratio of the hypothesis is used as a reward to realize unsupervised policy network learning. In experiments, the 2D line fitting task illustrates that RLSAC is robust to various disturbances and exhibits strong generalization. The visualization of the sampling process shows that RLSAC can progressively explore to better models and continues to explore locally. Additionally, the fundamental matrix estimation task demonstrates that RLSAC outperforms other methods in the complex camera pose estimation problem. Notably, RLSAC is not limited to specific tasks and can easily perform end-to-end learning on various sampling consensus-based tasks. In future work, it is worthwhile to explore the integration of traditional and learning-based methods within this framework, while trying to maintain the strengths of each method." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 645, + 416, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 645, + 416, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 645, + 416, + 658 + ], + "type": "text", + "content": "8. Acknowledgement" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "type": "text", + "content": "This work was supported in part by the Natural Science Foundation of China under Grant 62225309, 62073222, U21A20480 and U1913204. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 5845-5854, 2019." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "9900" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/RMP-Loss_ Regularizing Membrane Potential Distribution for Spiking Neural Networks/8dd5399b-d34f-43a1-82f0-9e644d0103b9_content_list.json b/2023/RMP-Loss_ Regularizing Membrane Potential Distribution for Spiking Neural Networks/8dd5399b-d34f-43a1-82f0-9e644d0103b9_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..6e4d9d843b1ffd2feefb6e2182c86948441c8f7e --- /dev/null +++ b/2023/RMP-Loss_ Regularizing Membrane Potential Distribution for Spiking Neural Networks/8dd5399b-d34f-43a1-82f0-9e644d0103b9_content_list.json @@ -0,0 +1,1640 @@ +[ + { + "type": "text", + "text": "RMP-Loss: Regularizing Membrane Potential Distribution for Spiking Neural Networks", + "text_level": 1, + "bbox": [ + 91, + 128, + 880, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yufei Guo\\*, Xiaode Liu\\*, Yuanpei Chen, Liwen Zhang, Weihang Peng, Yuhan Zhang, Xuhui Huang, Zhe Ma† \nIntelligent Science & Technology Academy of CASIC, China \nScientific Research Laboratory of Aerospace Intelligent Systems and Technology, China", + "bbox": [ + 133, + 202, + 833, + 276 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Spiking Neural Networks (SNNs) as one of the biology-inspired models have received much attention recently. It can significantly reduce energy consumption since they quantize the real-valued membrane potentials to 0/1 spikes to transmit information thus the multiplications of activations and weights can be replaced by additions when implemented on hardware. However, this quantization mechanism will inevitably introduce quantization error, thus causing catastrophic information loss. To address the quantization error problem, we propose a regularizing membrane potential loss (RMP-Loss) to adjust the distribution which is directly related to quantization error to a range close to the spikes. Our method is extremely simple to implement and straightforward to train an SNN. Furthermore, it is shown to consistently outperform previous state-of-the-art methods over different network architectures and datasets.", + "bbox": [ + 75, + 340, + 473, + 583 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 612, + 209, + 628 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, many efforts have been done to make deep neural networks (DNNs) lightweight, so that they can be deployed in devices where energy consumption is limited. To this end, several approaches have been proposed, including network pruning [61], network quantization [18, 37, 15], knowledge transfer/distillation [46], neural architecture search [65, 39], and spiking neural networks (SNNs) [23, 19, 22, 17, 52, 36, 44, 55, 54, 63, 49, 56, 57]. The SNN provides a special way to reduce energy consumption following the working mechanism of the brain neuron. Its neurons accumulate spikes from previous neurons and present spikes to posterior neurons when the membrane potential exceeds the firing threshold. This information transmission paradigm will convert the computationally expensive multiplication to computationally convenient additions", + "bbox": [ + 75, + 638, + 470, + 864 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "thus making SNNs energy-efficient when implemented on hardware. Specialized neuromorphic hardware based on an event-driven processing paradigm is currently under various stages of development, e.g., SpiNNaker [31], TrueNorth [1], Tianjic [45], and Loihi [9], where SNNs can be efficiently implemented further. Due to the advantage of computational efficiency and rapid development of neuromorphic hardware, the SNN has gained more and more attention.", + "bbox": [ + 500, + 310, + 890, + 430 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although SNNs have been widely studied, their performance is still not comparable with that of DNNs. This performance gap is largely related to the quantization of the real-valued membrane potential to $0/1$ spikes for the firing of the SNN in implementation [21]. The excessive information loss induced by the firing activity forcing all information only to two values will cause accuracy to decrease. Although information loss is important for computer vision tasks and the quantization will cause information loss too, the essential role of the activation function is to introduce non-linearity for neural networks [43]. Therefore, how to effectively reduce the information loss of membrane potential quantization is of high research importance. However, as far as we know, few studies have focused on directly solving this problem. The quantization error problem also exists in these methods that convert the ANN model to an SNN model [11, 4, 36]. However, these methods solve the problem by changing the activation function in ANNs or increasing timesteps in SNNs, which don't work for SNN training. InfLoR-SNN [21] adds a membrane potential redistribution function in the spiking neuron to reduce the quantization error via redistributing the membrane potential. However, it will decrease the biological plausibility of the SNN and increase the inference burden. This paper focuses on reducing the quantization error in SNN training directly and aims to introduce no burden for the SNN.", + "bbox": [ + 496, + 431, + 892, + 823 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Quantization error is smaller when the membrane potential is close to the spiking threshold or reset values [21]. Hence, to mitigate the information loss, we suggest redistributing the membrane potential to where the membrane potential is closer to the 0/1 spike. Then an additional", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution. \n†Corresponding author, mazhe_thu@163.com.", + "bbox": [ + 94, + 875, + 339, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17391", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c3c77f985f3c56210ab83c59702ab261b8b8bfca03585555542ec4fc261d4b7d.jpg", + "image_caption": [ + "Figure 1: The overall workflow of the proposed method. We embed a membrane potential regularization loss in the task loss to redistribute the membrane potential in the training phase to reduce the quantization error." + ], + "image_footnote": [], + "bbox": [ + 86, + 98, + 888, + 280 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "loss term aims at regularizing membrane potential is presented, called RMP-Loss, which can encourage the membrane potentials to gather around binary spike values during the training phase. The workflow of our method is shown in Fig. 1. Our main contributions can be concluded as follows:", + "bbox": [ + 75, + 349, + 468, + 425 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- To our best knowledge, there have been few works noticing the quantization error in direct training of SNNs. To mitigate the quantization error, we present the RMP-Loss, which is of benefit to training an SNN model that enjoys a narrow gap between the membrane potential and its corresponding $0/1$ spike. Furthermore, we also provide theoretical proof to clarify why the RMP-Loss can prevent information loss.", + "- Some existing methods can address information loss too. While achieving comparable performance, more parameters or computation burdens are also introduced in the inference phase. Different from those methods, the RMP-Loss can handle information loss directly without introducing any additional parameters or inference burden.", + "- Extensive experiments on both static and dynamic datasets show that our method performs better than many state-of-the-art SNN models." + ], + "bbox": [ + 94, + 436, + 468, + 726 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 739, + 218, + 753 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "There are two main problems to train an SNN model [22]. The first is that the firing activity is non-differentiable thus the SNN model cannot be trained with these back-propagation methods directly. One way to mitigate the optimization difficulty is through surrogate functions. This kind of method replaces the non-differentiable firing activity with a differentiable surrogate function to calculate the gradient in the back-propagation [34, 51, 42, 50]. In [2], the derivative of a truncated quadratic function was", + "bbox": [ + 75, + 763, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "used to approximate the derivative of the firing activity function. In [59] and [7], the derivatives of a sigmoid [59] and a rectangular function were respectively adopted to construct the surrogate gradient. Furthermore, a dynamic evolutionary surrogate gradient that could maintain accurate gradients during the training was proposed in [38, 20, 5, 6]. Another way to solve the non-differentiable problem is converting an ANN model to an SNN model, known as ANN-SNN conversion methods [27, 26, 36, 32, 3, 29, 28]. The ANN-SNN method trains a high-accuracy ANN with ReLU activation first and then transforms the network parameters into an SNN under the supposition that the activation of the ANN can be approximated by the average firing rates of an SNN. However, conversion methods will introduce conversion errors inevitably. Many efforts were made to tackle this problem, such as long inference time [14], threshold rescaling [48], soft reset [27], threshold shift [36], and the quantization clip-floor-shift activation function [4]. This paper adopts the surrogate gradient method.", + "bbox": [ + 496, + 349, + 890, + 636 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The second problem is information loss. Though transmitting information with binary spikes is more efficient than that with real values, quantizing these real-valued membrane potentials to 0/1 spikes will cause information loss. There have been some works handling this problem indirectly. Such as learning the appropriate membrane leak-and-firing threshold [47, 64]. These are of benefit to finding a preferable quantization choice. Similarly, in [17, 58], some learnable neuron parameters are incorporated into the SNN to optimize the quantization choice. In [24], three regularization losses are introduced to penalize three undesired shifts of membrane potential distribution to make easy optimization and convergence for the SNN. The regularization is also beneficial to reduce quantization error. However, all these methods do not handle the information loss problem directly and most of them require more parameters. InfLoR-SNN [21] suggests adding a membrane potential redistribution", + "bbox": [ + 496, + 643, + 892, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17392", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tion function in the spiking neuron to redistribute the membrane potential closer to spike values, which can be seen as a direct method to reduce the quantization error. However, adding another function in spiking neurons will decrease the biological plausibility of the SNN and increase the inference burden. In this work, we focus on handling the quantization error problem directly without introducing extra parameters or computation burden in the inference phase.", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 228, + 202, + 246 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, a brief review of the primary computing element of SNNs is first provided in Sec. 3.1. Then we introduce the proposed surrogate gradient that handles the non-differentiability challenge in Sec. 3.2. Finally, in Sec. 3.3, we describe the threshold-dependent batch normalization technique used in this work.", + "bbox": [ + 75, + 253, + 468, + 345 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Spiking Neuron Model", + "text_level": 1, + "bbox": [ + 76, + 356, + 287, + 372 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Spiking neuron. The primary computing element, i.e., the neuron of an SNN is much different from that of an ANN. The neuron of an ANN plays the role of nonlinear transformation and can output real-valued values. Meanwhile, the neuron in an SNN accumulates the information from previous neurons into its membrane potential and presents the spike to the following neurons when its membrane potential exceeds the firing threshold. The SNN is more efficient with this special information transmission paradigm while suffering the information loss problem. A unified form of this spiking neuron model can be formulated as follows,", + "bbox": [ + 75, + 380, + 472, + 559 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nu ^ {(t), \\text {p r e}} = \\tau u ^ {(t - 1)} + x ^ {(t)}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 561, + 468, + 579 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\no ^ {(t)} = \\left\\{ \\begin{array}{l} 1, \\text {i f} u ^ {(t), \\text {p r e}} \\geq V _ {\\text {t h}} \\\\ 0, \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 589, + 468, + 622 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nu ^ {(t)} = u ^ {(t), \\mathrm {p r e}} (1 - o ^ {(t)}). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 632, + 468, + 651 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Where $u^{(t),\\mathrm{pre}}$ and $u^{(t)}$ are pre-membrane potential and membrane potential, respectively, $x^{(t)}$ is input information, $o^{(t)}$ is output spike at the timestep $t$ . The range of constant leaky factor $\\tau$ is (0, 1), and we set $\\tau$ as 0.25. $V_{\\mathrm{th}}$ is the firing threshold and is set to 0.5 here.", + "bbox": [ + 75, + 659, + 468, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Output layer neuron. In the general classification task, the output of the last layer will be presented to the Softmax function first and then find the winner class. We make the neuron model in the output layer only accumulate the incoming inputs without any leakage as final output like doing in recent practices[47, 62], described by", + "bbox": [ + 75, + 736, + 468, + 827 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nu ^ {(t)} = u ^ {(t - 1)} + x ^ {(t)}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 838, + 468, + 856 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Then the cross-entropy loss is calculated according to the final membrane potential at the last timesteps, $u^{(T)}$ .", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Surrogate Gradients of SNNs", + "text_level": 1, + "bbox": [ + 500, + 90, + 761, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Eq. 2, the firing activity of SNNs can be seen as a step function. Its derivative is 0 everywhere except at $V_{\\mathrm{th}}$ . This non-differentiability problem of firing activity will cause gradient vanishing or explosion and make the back-propagation unsuitable for training SNNs, directly. As mentioned before, many prior works adopted the surrogate function to replace the firing function to obtain a suitable gradient [7, 62, 52]. In InfLoR-SNN [21], an extra membrane potential redistribution function is added before the firing function. It argues that this redistribution function will reduce the information loss in forward propagation. However, investigating it from a backward propagation perspective and considering the redistribution function being next to the firing function, it can be seen as a more suitable surrogate gradient if we gather the STE (used in [21]) gradients of the firing function and redistribution function together. In this sense, the suitable surrogate gradient can also be seen as a route to reduce quantization error. Therefore, in this paper, we adopt the gathered redistribution function in InfLoR-SNN as our surrogate function, which indeed performs better than other methods [7, 62, 52] in our experiments, denoted as", + "bbox": [ + 496, + 114, + 893, + 446 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\varphi (u) = \\left\\{ \\begin{array}{l l} 0, & u < 0, \\\\ \\frac {1}{2 \\tanh (3 / 2)} \\tanh (3 (u - 1 / 2)) + 1 / 2, & 0 \\leq u \\leq 1, \\\\ 1, & u > 1. \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 458, + 906, + 521 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Threshold-dependent Batch Normalization", + "text_level": 1, + "bbox": [ + 500, + 531, + 864, + 547 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Normalization techniques can effectively reduce the training time and alleviate the gradient vanishing or explosion problem for training DNNs. A most widely used technique called batch normalization (BN) [30] uses the distribution of the summed input to a neuron over a mini-batch of training cases to compute a mean and variance which are then used to normalize the summed input to that neuron on each training case. This is significantly effective for convolutional neural networks (CNNs). However, directly applying BN to SNNs will ignore the temporal characteristic and can not achieve the desired effect. To this end, a more suitable normalization technique for SNNs, named threshold-dependent BN (tdBN) was further proposed in [62]. It normalizes feature inputs on both temporal and spatial dimensions. Besides, as its name implies, tdBN makes normalized variance dependent on the firing threshold, i.e., the pre-activations are normalized to $N(0,(\\alpha V_{\\mathrm{th}})^2)$ instead of $N(0,1)$ . This can balance pre-synaptic input and threshold to maintain a reasonable firing rate. In this paper, we also adopt the tdBN, as follows,", + "bbox": [ + 496, + 555, + 893, + 858 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\mathbf {X}} = \\alpha V _ {\\mathrm {t h}} \\frac {\\mathbf {X} - \\operatorname {m e a n} (\\mathbf {X})}{\\sqrt {\\operatorname {m e a n} ((\\mathbf {X} - \\operatorname {m e a n} (\\mathbf {X})) ^ {2}) + \\epsilon}}, \\qquad (6)\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 869, + 890, + 905 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17393", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {X}} = \\lambda \\bar {\\mathbf {X}} + \\beta . \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 223, + 89, + 468, + 106 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{X} \\in \\mathbb{R}^{T \\times B \\times C \\times H \\times W}$ ( $T$ : timesteps; $B$ : batch size; $C$ : channel; $(H, W)$ : spatial domain) is a 5D tensor and $\\alpha$ is a hyper-parameter set as 1.", + "bbox": [ + 76, + 111, + 468, + 157 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. RMP-Loss", + "text_level": 1, + "bbox": [ + 76, + 170, + 191, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As aforementioned, we suggest reducing the quantization error to avoid information loss in supervised training-based SNNs. In this section, we first try to provide a metric to measure the quantization error in SNNs. Then based on the metric, we introduce our method, a loss term for regularizing membrane potential, i.e., RMP-Loss, which can push the membrane potentials close to spike values to reduce the quantization error. Finally, theoretical proof to clarify why the RMP-Loss can prevent information loss is given.", + "bbox": [ + 75, + 196, + 470, + 332 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Quantization Error Estimation", + "text_level": 1, + "bbox": [ + 76, + 340, + 352, + 356 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Estimating the quantization error precisely is important for designing a method to reduce the prediction error. Hence, before giving the full details of the RMP-Loss, here we try to formulate the quantization error first. As shown in Eq. 2, the output of a neuron is dependent on the magnitude of the membrane potential. When the membrane potential exceeds the firing threshold, the output is 1, otherwise, is 0; that is, these full-precision values will be mapped to only two spike values. The difference between output, $o$ , and membrane potential, $u$ , can be measured as", + "bbox": [ + 75, + 364, + 468, + 515 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {D i s} (o, u) = \\left\\{ \\begin{array}{l l} 1 - u, & \\text {i f} u \\geq V _ {\\mathrm {t h}} \\\\ 0 - u, & \\text {o t h e r w i s e} \\end{array} \\right.. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 523, + 468, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Obviously, the closer a membrane potential is to its corresponding spike, the smaller the quantization error. The quantization error depends on the margin between the membrane potential and its corresponding spike. Then we define the quantization error as", + "bbox": [ + 75, + 565, + 468, + 642 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq (u) = \\left| \\operatorname {D i s} (o, u) \\right| ^ {p}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 651, + 468, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $p > 0$ , which is usually set to 1 and/or 2 corresponding to L1-norm and/or L2-norm. Unless otherwise specified, we set it as 2 in the paper.", + "bbox": [ + 75, + 676, + 468, + 723 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Regularizing Membrane Potential Distribution", + "text_level": 1, + "bbox": [ + 76, + 731, + 468, + 747 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To mitigate the information loss problem in SNNs, the quantization error should be reduced to some extent. To this end, we propose RMP-Loss to carve the distribution to a range close to the spikes based on $q(u)$ , as", + "bbox": [ + 75, + 753, + 468, + 815 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {R M P}} = \\frac {1}{T L B C W H} \\sum_ {t, l, b, c, w, h} q (u). \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 823, + 468, + 861 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $T$ , $L$ , $B$ , $C$ , $W$ , and $H$ denote the number of timesteps, the number of layers, batch size, channel length,", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1 Training an SNN with RMP-Loss.", + "bbox": [ + 500, + 90, + 816, + 106 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Input: An SNN to be trained; Training dataset, total number of training epochs $N$ , total number of training iterations per epoch $I$ .", + "bbox": [ + 500, + 108, + 890, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Output: The trained SNN.", + "bbox": [ + 500, + 152, + 679, + 166 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: for All $n = 1,2,\\ldots ,N - th$ epoch do", + "2: for All $i = 1,2,\\ldots ,I - th$ iteration do", + "3: Feed-Forward:", + "4: Calculate the SNN output, $\\mathbf{O}^i$ , membrane potential, $\\mathbf{U}$ , and class label, $\\mathbf{Y}^i$ ;", + "5: Compute classification loss $\\mathcal{L}_{\\mathrm{CE}} = \\mathcal{L}_{\\mathrm{CE}}(\\mathbf{O},\\mathbf{Y}^i)$", + "6: Compute RMP-Loss $\\mathcal{L}_{\\mathrm{RMP}} = \\mathcal{L}_{\\mathrm{RMP}}(\\mathbf{U})$", + "7: Compute the total loss $\\mathcal{L}_{\\mathrm{CE - RMP}} = \\mathcal{L}_{\\mathrm{CE}} + \\lambda (n)\\mathcal{L}_{\\mathrm{RMP}}$" + ], + "bbox": [ + 509, + 170, + 890, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Backward-Propagation:", + "text_level": 1, + "bbox": [ + 560, + 306, + 730, + 320 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "8: Calculate the gradients $\\Delta \\mathbf{W} = \\frac{\\partial\\mathcal{L}_{\\mathrm{CE - RMP}}}{\\partial\\mathbf{W}} = \\sum_{t}\\frac{\\partial(\\mathcal{L}_{\\mathrm{CE}} + \\lambda(n)\\mathcal{L}_{\\mathrm{RMP}})}{\\partial\\mathbf{y}^t}\\frac{\\partial\\mathbf{y}^t}{\\partial\\mathbf{U}}\\frac{\\partial\\mathbf{U}}{\\partial\\mathbf{W}}$ where $\\mathbf{y}^t$ is feature maps at $t$ -th timesteps and $\\frac{\\partial\\mathbf{y}^t}{\\partial\\mathbf{U}}$ is the gradient of firing function, which can be calculated as $\\frac{\\partial\\varphi(\\mathbf{U})}{\\partial\\mathbf{U}}$ . Parameters Update:", + "9: Update all parameters with the learning rate $\\eta$ .", + "10: end for", + "11: end for", + "12: return the trained SNN." + ], + "bbox": [ + 504, + 320, + 890, + 468 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "width, and height of the membrane potential map, respectively. Finally, taking classification loss into consideration, the total loss can be written as", + "bbox": [ + 498, + 494, + 890, + 537 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {C E} - \\mathrm {R M P}} = \\mathcal {L} _ {\\mathrm {C E}} + \\lambda (n) \\mathcal {L} _ {\\mathrm {R M P}}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 547, + 890, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{CE}$ is the cross-entropy loss, and $\\lambda (n)$ is a balanced coefficient, which changes dynamically with the training epoch. Obviously, $\\mathcal{L}_{RMP}$ does not take into account the classification problem at hand and will add a new constraint in the network optimization. To make the network parameter update have enough freedom at the beginning, which is important to train a well-performance network, and still focus on the classification task at the end. We adopt a strategy of increasing first and decreasing later to adjust the $\\lambda (n)$ as follows,", + "bbox": [ + 496, + 569, + 890, + 719 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\lambda (n) = \\left\\{ \\begin{array}{l} 2 k \\frac {n}{N}, \\text {i f} n \\leq N / 2 \\\\ 2 k \\left(1 - \\frac {n}{N}\\right), \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 724, + 890, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $n$ is the $n$ -th epoch and $k$ is a coefficient, which controls the amplitude of regularization. Unless otherwise specified, we set it as 0.1 in the paper.", + "bbox": [ + 496, + 763, + 890, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The final resulting RMP-Loss training method is defined in Algo. 1.", + "bbox": [ + 498, + 809, + 890, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Analysis and Discussion", + "text_level": 1, + "bbox": [ + 500, + 847, + 725, + 862 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this work, we assume that RMP-Loss can help reduce the quantization loss of the SNNs. To verify our assumption, we first consider a linear model with a single input $x$ and a single output $y$ . Then, we use the following linear model to obtain the output $y$ from the input $x$ :", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17394", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tion, a theoretical analysis is conducted by using the information entropy concept. To mitigate the information loss, the output spike tensor $\\mathbf{O}$ should reflect the information of the membrane potential tensor $\\mathbf{U}$ as much as possible. Since KL-divergence is a metric to measure the difference between two random variable distributions. We use KLdivergence to compute the difference between $\\mathbf{O}$ and $\\mathbf{U}$ , which refers to the difficulty of reconstructing $\\mathbf{U}$ from $\\mathbf{O}$ , i.e., information loss degree. Then we provide the theoretical analysis below.", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Let $x^u\\sim \\mathcal{U}$ where $x^{u}$ are samples $\\in \\mathbf{U}$ and $\\mathcal{U}$ represents the distribution of $x^{u}$ . Similarly, we have $x^{o}\\sim \\mathcal{O}$ where $x^{o}\\in \\mathbf{O}$ . We use $P_U(x)$ and $P_O(x)$ to denote the probability density function for $\\mathcal{U}$ and $\\mathcal{O}$ , respectively. Then the information loss for the spike firing process can be described as", + "bbox": [ + 76, + 242, + 468, + 318 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {K L} (\\mathcal {U} | | \\mathcal {O}) = \\int_ {- \\infty} ^ {\\infty} P _ {U} \\left(x ^ {u}\\right) \\log \\frac {P _ {U} \\left(x ^ {u}\\right)}{P _ {O} \\left(x ^ {o}\\right)} d x. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 111, + 327, + 468, + 362 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since output spike $x^{o}$ is discrete, we can update it as", + "bbox": [ + 76, + 371, + 426, + 386 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {K L} (\\mathcal {U} \\| \\mathcal {O}) = \\int_ {o - \\epsilon} ^ {o + \\epsilon} P _ {U} \\left(x ^ {u}\\right) \\log \\frac {P _ {U} \\left(x ^ {u}\\right)}{P _ {O} \\left(x ^ {o}\\right)} d x, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 106, + 396, + 468, + 431 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\epsilon$ is a small constant, $o$ is the spike value, $P_O(x^o)$ can be seen as a very large constant in this situation, and $\\int_{o - \\epsilon}^{o + \\epsilon}P_O(x^o)dx = 1$ . With RMP-Loss, it will become", + "bbox": [ + 76, + 441, + 468, + 489 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {K L} (\\hat {\\mathcal {U}} | | \\mathcal {O}) = \\int_ {o - \\epsilon} ^ {o + \\epsilon} P _ {\\hat {U}} (x ^ {\\hat {u}}) \\log \\frac {P _ {\\hat {U}} (x ^ {\\hat {u}})}{P _ {O} (x ^ {o})} d x, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 106, + 502, + 468, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $x^{\\hat{u}} \\in \\hat{\\mathcal{U}}$ and $\\hat{\\mathcal{U}}$ is the new distribution of $x^{\\hat{u}}$ adjusted by RMP-Loss. Here, we have the following propositions.", + "bbox": [ + 75, + 549, + 468, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proposition 1 $\\frac{d\\mathcal{L}_{KL}}{dP_U(x^u)} < 0$ i.e., $\\mathcal{L}_{KL}\\downarrow asP_U(x^u)\\uparrow$", + "bbox": [ + 76, + 580, + 437, + 597 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proof: When a membrane potential $u$ is below the firing threshold, it will be pushed to 0 by the RMP-Loss, considering its effect, and otherwise, 1. Hence the firing rate of the neuron can be seen as the same, whether using the RMP-Loss or not, i.e., $P_O(x^o)$ keep the same for $\\hat{\\mathbf{U}}$ and $\\mathbf{U}$ .", + "bbox": [ + 75, + 597, + 468, + 672 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\frac {d \\mathcal {L} _ {K L}}{d P _ {U} \\left(x ^ {u}\\right)} = \\frac {d \\int_ {o - \\epsilon} ^ {o + \\epsilon} P _ {U} \\left(x ^ {u}\\right) \\log \\frac {P _ {U} \\left(x ^ {u}\\right)}{P _ {O} \\left(x ^ {o}\\right)} d x}{d P _ {U} \\left(x ^ {u}\\right)} (16) \\\\ = \\int_ {o - \\epsilon} ^ {o + \\epsilon} \\left(\\log \\frac {P _ {U} \\left(x ^ {u}\\right)}{P _ {O} \\left(x ^ {o}\\right)} + \\frac {1}{\\ln 2}\\right) d x. (17) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 683, + 468, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since $P_O(x^o)$ is much larger than $P_U(x^u)$ , we can get $\\int_{o - \\epsilon}^{o + \\epsilon} (\\log \\frac{P_U(x^u)}{P_O(x^o)} + \\frac{1}{\\ln 2}) dx < 0$ , then $\\frac{d\\mathcal{L}_{KL}}{dP_U(x^u)} < 0$ .", + "bbox": [ + 76, + 768, + 468, + 805 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proposition 2 $P_{\\hat{U}}(x^{\\hat{u}}) > P_{U}(x^{u})|x = o.$", + "bbox": [ + 76, + 805, + 359, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proof: We assume that there are $n_{\\epsilon}^{u}$ samples in the interval $(o - \\epsilon, o + \\epsilon)$ for $\\mathcal{U}$ , where $\\epsilon$ is a small constant. Then we can get $P_U(x^u) \\approx \\frac{n_{\\epsilon}^u}{2\\epsilon}$ . And we can simply see the RMP-Loss as a function to push the vanilla $\\mathbf{U}$ to $\\hat{\\mathbf{U}}$ , which is closer to $\\mathbf{O}$ , based on its effect. Therefore, we can assume that", + "bbox": [ + 75, + 821, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "these samples will be gathered to a new interval $(o - \\epsilon_l, o + \\epsilon_r)$ , where $\\epsilon_l, \\epsilon_r < \\epsilon$ . Then we can get $P_{\\hat{U}(x^{\\hat{u}})} \\approx \\frac{n_\\epsilon^u}{\\epsilon_l + \\epsilon_r}$ . Thereby we can have $P_{\\hat{U}(x^{\\hat{u}})} > P_U(x^u)|_{x = o}$ .", + "bbox": [ + 498, + 90, + 890, + 142 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Along with Proposition 1 and Proposition 2, we can conclude that $\\mathcal{L}_{KL}(\\hat{U} ||O) < \\mathcal{L}_{KL}(U||O)$ , i.e., our method with RMP-Loss enjoys lesser information loss.", + "bbox": [ + 498, + 141, + 890, + 186 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiment", + "text_level": 1, + "bbox": [ + 500, + 202, + 624, + 219 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we first conducted extensive ablation studies to compare the SNNs with RMP-Loss and their vanilla counterparts to verify the effectiveness of the method. Next, we fully compared our method with other state-of-the-art (SoTA) methods. Finally, some further experimental visualizations are provided to understand the RMP-Loss.", + "bbox": [ + 496, + 229, + 890, + 332 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Datasets and Settings", + "text_level": 1, + "bbox": [ + 500, + 345, + 700, + 363 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We conducted experiments on four benchmark datasets: CIFAR-10 (100) [33], CIFAR10-DVS [35], and ImageNet (ILSVRC12) [10]. The CIFAR-10 (100) dataset includes 60,000 images in 10 (100) classes with $32 \\times 32$ pixels. The numbers of training images and test images are 50,000 and 10,000. The CIFAR10-DVS dataset is the neuromorphic version of the CIFAR-10 dataset. It is composed of 10,000 images in 10 classes. We split the dataset into 9000 training images and 1000 test images similar to [52]. ImageNet dataset consists of 1,250,000 training images and 50,000 test images.", + "bbox": [ + 496, + 369, + 890, + 536 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Preprocessing. We applied data normalization on all static datasets to make input images have 0 mean and 1 variance. Besides, we conducted random horizontal flipping and cropping on these datasets to avoid overfitting. For CIFAR, the AutoAugment [8] and Cutout [13] were also used for data augmentation as doing in [24, 20]. For the neuromorphic dataset, we resized the training image frames to $48 \\times 48$ as in [62] and adopted random horizontal flip and random roll within 5 pixels for augmentation. And the test images were merely resized to $48 \\times 48$ without any additional processing.", + "bbox": [ + 496, + 537, + 890, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training setup. For all the datasets, the firing threshold $V_{\\mathrm{th}}$ was set as 0.5. For static image datasets, the images were encoded to binary spike using the first layer of the SNN, as in recent works [47, 17, 16]. This is similar to rate coding. For the neuromorphic image dataset, we used the 0/1 spike format directly. The neuron models in the output layer accumulated the incoming inputs without generating any spike as the output like in [47]. For CIFAR-10 (100) and CIFAR10-DVS datasets, we used the SGD optimizer with the momentum of 0.9 and learning rate of 0.01 with cosine decayed [40] to 0 as in [21]. All models were trained within 400 epochs with the same batch size of 128. For the ImageNet dataset, we adopted the SGD optimizer with", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17395", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/1a17c849bb2ae1ef60b14e240e0263c24ae31b6b8b44b90850fb178e48ca2cdc.jpg", + "table_caption": [ + "Table 1: Ablation Study for RMP-Loss" + ], + "table_footnote": [], + "table_body": "
DatasetArchitectureTypeTimestepAccuracyQuantization error
CIFAR-10ResNet20Without RMP-Loss491.26%0.186
With RMP-Loss491.89%0.121
ResNet19Without RMP-Loss495.04%0.128
With RMP-Loss495.51%0.104
VGG16Without RMP-Loss492.80%0.174
With RMP-Loss493.33%0.135
", + "bbox": [ + 151, + 114, + 816, + 237 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "a momentum of 0.9 and a learning rate of 0.1 with cosine decayed to 0. All models are trained within 320 epochs.", + "bbox": [ + 75, + 261, + 470, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Ablation Study for RMP-Loss", + "text_level": 1, + "bbox": [ + 76, + 301, + 344, + 318 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conducted a set of ablation experiments on CIFAR-10 using ResNet20, ResNet19, and VGG16 as backbones. The results are shown in Tab. 1. It can be seen that with the RMP-Loss, these SNNs can achieve higher accuracy than their vanilla counterparts. We also show the membrane potential distribution of the first layer of the second block in the ResNet20 with and without RMP-Loss on the test set of CIFAR-10 in Fig. 2. It can be seen that the models trained with RMP-Loss can shrink the membrane potential distribution range which enjoys less quantization error.", + "bbox": [ + 75, + 325, + 470, + 477 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fd640d50c0ba50ab93102761c751ca3fdd18f36b440a35f18de86eb040735164.jpg", + "image_caption": [ + "Figure 2: The effect of RMP-Loss. The overall original membrane potential distribution (left) and the redistributed membrane potential distribution by RMP-Loss (right) of the first layer of the second block in ResNet20 on CIFAR-10 test sets." + ], + "image_footnote": [], + "bbox": [ + 98, + 503, + 272, + 604 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a366d32d76c28737a96fda340ef8744f76ebfc4070f7f7f0318c1b374a0e8f13.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 300, + 503, + 473, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Comparison with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 76, + 724, + 441, + 742 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluated the proposed method with the accuracy performance on various widely used static and neuromorphic datasets using spiking ResNet20 [47, 48], VGG16 [47], ResNet18 [16], ResNet19 [62], and ResNet34 [16]. The results with the mean accuracy and standard deviation of 3-trials are listed in Tab. 2.", + "bbox": [ + 75, + 750, + 467, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CIFAR-10. For CIFAR-10, we tested three different network architectures. The performance of our method is shown in Tab. 2. It can be seen that our method achieves the best results in most of these cases. In special, us", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ing ResNet19 [62], the RMP-Loss achieves $96.10\\%$ averaged top-1 accuracy, which improves $1.60\\%$ absolute accuracy compared with the existing state-of-the-art TET [12]. Though InfLoR-SNN [21] is slightly better than our method for 4 and 6 timesteps, it will decrease the biological plausibility of the SNN and increase the inference burden since a complex transform function is added in its spiking neuron. On ResNet20, our method can achieve higher accuracy with only 6 timesteps, while Diet-SNN [47] with 10 timesteps. On VGG16, the RMP-Loss also shows obvious advantages.", + "bbox": [ + 496, + 261, + 890, + 412 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CIFAR-100. For CIFAR-100, we also experimented with these three different network structures. For all these configurations, our method achieves consistent and significant accuracy over prior work. ResNet20-based and VGG16-based RMP-Loss achieve $66.65\\%$ and $72.55\\%$ top-1 accuracy with only 4 timesteps, which outperform their Diet-SNN counterparts with $2.58\\%$ and $2.88\\%$ higher accuracy and Real spike counterparts with $0.05\\%$ and $1.93\\%$ respectively but with fewer timesteps. Noteworthy, our method significantly surpasses TET with $4.26\\%$ higher accuracy on ResNet19, which is not easy to achieve in the SNN field. Overall, our results on CIFAR-100 show that, when applied to a more complex dataset, the RMP-Loss achieves an even more favorable performance compared to competing methods.", + "bbox": [ + 496, + 412, + 892, + 641 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CIFAR10-DVS. We also verified our method on the popular neuromorphic dataset, CIFAR10-DVS. It can be seen that RMP-Loss also shows amazing performance. RMP-Loss outperforms STBP-tdBN by $12.39\\%$ , RecDis-SNN by $3.78\\%$ , and InfLoR-SNN by $0.70\\%$ respectively with $76.20\\%$ top-1 accuracy in 10 timesteps using ResNet19 as the backbone. With ResNet20 as the backbone, RMP-Loss can also achieve well-performed results.", + "bbox": [ + 496, + 642, + 890, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ImageNet. For ImageNet, we conducted experiments with ResNet18 and ResNet34 as backbones. Our results are presented in Tab. 4. In these normal spiking structures, our method achieves the highest accuracy among these SoTA prior works. However, our method is slightly worse than SEW ResNet [16]. This is because that SEW ResNet uses an atypical architecture, which abandons binary spike forms but will output arbitrary integers to transmit information, thus enjoying higher accuracy but the efficiency from mul", + "bbox": [ + 496, + 763, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17396", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/da3c6d202bc15737f7a6ae01da18e54496d2efad560380977908f8e32550e234.jpg", + "table_caption": [ + "Table 2: Comparison with SoTA methods on CIFAR-10/100." + ], + "table_footnote": [], + "table_body": "
DatasetMethodTypeArchitectureTimestepAccuracy
CIFAR-10STBP [52]SNN trainingCIFARNet1290.53%
TSSL-BP [60]SNN trainingCIFARNet591.41%
PLIF [17]SNN trainingPLIFNet893.50%
DSR [41]SNN trainingResNet182095.40%
Joint A-SNN [23]SNN trainingResNet18495.45%
Diet-SNN [47]SNN trainingVGG16592.70%
1093.44%
ResNet20591.78%
1092.54%
RecDis-SNN [24]SNN trainingResNet19293.64%
495.53%
695.55%
STBP-tdBN [62]SNN trainingResNet19292.34%
492.92%
693.16%
TET [12]SNN trainingResNet19294.16%
494.44%
694.50%
InfLoR-SNN [21]SNN trainingResNet19294.44%
496.27%
696.49%
RMP-LossSNN trainingResNet19295.31%±0.07
495.51%±0.08
696.10%±0.08
ResNet20491.89%±0.05
692.55%±0.06
VGG16493.33%±0.07
1094.39%±0.08
CIFAR-100DSR [41]SNN trainingResNet182078.50%
InfLoR-SNN [21]SNN trainingVGG16571.56%
IM-Loss [20]SNN trainingVGG16570.18%
Diet-SNN [47]SNN trainingResNet20564.07%
VGG16569.67%
Real Spike [25]SNN trainingResNet20566.60%
VGG16570.62%
TET [12]SNN trainingResNet19272.87%
474.47%
674.72%
RMP-LossSNN trainingResNet20466.65%±0.10
VGG16472.55%±0.08
1073.30%±0.11
ResNet19274.66%±0.12
478.28%±0.10
678.98%±0.08
", + "bbox": [ + 166, + 114, + 805, + 813 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tlication free of SNNs will be lost. Hence, it would be limited in some applications while our method not.", + "bbox": [ + 76, + 835, + 470, + 866 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Visualization", + "text_level": 1, + "bbox": [ + 500, + 834, + 637, + 849 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Furthermore, we also provide some experimental visualizations to show the regularizing effects of RMP-Loss.", + "bbox": [ + 500, + 869, + 890, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17397", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2a4072155043db1c9f6b0303681554e1335e8a057cb7a44c2b42f6ef39c7cbc9.jpg", + "table_caption": [ + "Table 3: Comparison with SoTA methods on CIFAR10-DVS." + ], + "table_footnote": [], + "table_body": "
DatasetMethodTypeArchitectureTimestepAccuracy
CIFAR10-DVSSTBP-tdBN [62]SNN trainingResNet191067.80%
LIAF [53]Conv3DLIAF-Net1071.70%
LIAF [53]LIAFLIAF-Net1070.40%
RecDis-SNN [24]SNN trainingResNet191072.42%
InfLoR-SNN [21]SNN trainingResNet191075.50%
ResNet201075.10%
RMP-LossSNN trainingResNet191076.20%±0.20
ResNet201075.60%±0.30
", + "bbox": [ + 153, + 114, + 818, + 268 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d98113f86c25204d2ed31afe6604d047865e2004c8f1c9b95eb7c79b0dd5836d.jpg", + "table_caption": [ + "Table 4: Comparison with SoTA methods on ImageNet." + ], + "table_footnote": [], + "table_body": "
MethodTypeArchitectureTimestepSpike formAccuracy
STBP-tdBN [62]SNN trainingResNet346Binary63.72%
TET [12]SNN trainingResNet346Binary64.79%
SEW ResNet [16]SNN trainingResNet184Integer63.18%
ResNet344Integer67.04%
Spiking ResNet [16]SNN trainingResNet184Binary62.32%
ResNet344Binary61.86%
RMP-LossSNN trainingResNet184Binary63.03%±0.07
ResNet344Binary65.17%±0.07
", + "bbox": [ + 161, + 306, + 810, + 459 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b1bef3d6c3b2f6327c4b946c901a56bde2cbdd61931ae070fddf612aa8f1d402.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 96, + 492, + 269, + 594 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4d7b7f0dd7bf3c0353f569782250851752ff4834ce31f953853886a8ab481a1b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 272, + 492, + 472, + 594 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/543136c1e205b41f0c229fe16ec42240d60197ce60101f28dce1860e4c9f4fe7.jpg", + "image_caption": [ + "ResNet19" + ], + "image_footnote": [], + "bbox": [ + 96, + 612, + 269, + 714 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/664f20942ecfe9c2e2aec0cb43a2cf884a71b589800b2c06e8450c7de36691d5.jpg", + "image_caption": [ + "Figure 3: The original membrane potential distribution (left) and the redistributed membrane potential distribution by RMP-Loss (right) of the first layer of the second block in ResNet20/19 on CIFAR-10 test sets." + ], + "image_footnote": [], + "bbox": [ + 272, + 612, + 472, + 714 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fig. 3 shows the membrane potential distribution of the first layer of the second block in the ResNet20/19 with and without RMP-Loss on the test set of CIFAR-10. It can be seen that the SNN models trained with RMP-Loss can shrink", + "bbox": [ + 75, + 839, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the membrane potential distribution range which enjoys less quantization error. On the other hand, comparing the membrane potential distribution difference between ResNet20 and ResNet19, it can be found that the membrane potential distribution of ResNet19 is thinner than that of ResNet20 too. Considering that ResNet19 can achieve higher accuracy than ResNet20, it also shows that reducing quantization error is effective to improve the accuracy of SNN models and our route to improve the SNN accuracy by reducing the quantization error is reasonable.", + "bbox": [ + 496, + 483, + 893, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 650, + 617, + 666 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper aims at addressing the information loss problem caused by the $0/1$ spike quantization of SNNs. We introduce RMP-Loss to adjust the membrane potential to reduce the quantization error. Different from other methods that reduce the quantization error indirectly or will induce more parameters, RMP-Loss focuses on handling this problem directly and will introduce no extra parameters in the inference phase. We show that our method outperforms SoTA methods on both static and neuromorphic datasets.", + "bbox": [ + 496, + 676, + 893, + 813 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment", + "text_level": 1, + "bbox": [ + 500, + 829, + 651, + 845 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is supported by grants from the National Natural Science Foundation of China under contracts No.12202412 and No.12202413.", + "bbox": [ + 498, + 854, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17398", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] F. Akopyan, J. Sawada, A. Cassidy, R. Alvarez-Icaza, and Dharmendra S. Modha. 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Neural architecture search with reinforcement learning, 2016. 1" + ], + "bbox": [ + 78, + 90, + 468, + 275 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "17401", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/RMP-Loss_ Regularizing Membrane Potential Distribution for Spiking Neural Networks/8dd5399b-d34f-43a1-82f0-9e644d0103b9_model.json b/2023/RMP-Loss_ Regularizing Membrane Potential Distribution for Spiking Neural Networks/8dd5399b-d34f-43a1-82f0-9e644d0103b9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..665c57f683333d703135f2f3464372f960d5dcd9 --- /dev/null +++ b/2023/RMP-Loss_ Regularizing Membrane Potential Distribution for Spiking Neural Networks/8dd5399b-d34f-43a1-82f0-9e644d0103b9_model.json @@ -0,0 +1,2455 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.13, + 0.882, + 0.175 + ], + "angle": 0, + "content": "RMP-Loss: Regularizing Membrane Potential Distribution for Spiking Neural Networks" + }, + { + "type": "text", + "bbox": [ + 0.134, + 0.203, + 0.834, + 0.277 + ], + "angle": 0, + "content": "Yufei Guo\\*, Xiaode Liu\\*, Yuanpei Chen, Liwen Zhang, Weihang Peng, Yuhan Zhang, Xuhui Huang, Zhe Ma† \nIntelligent Science & Technology Academy of CASIC, China \nScientific Research Laboratory of Aerospace Intelligent Systems and Technology, China" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.341, + 0.474, + 0.584 + ], + "angle": 0, + "content": "Spiking Neural Networks (SNNs) as one of the biology-inspired models have received much attention recently. It can significantly reduce energy consumption since they quantize the real-valued membrane potentials to 0/1 spikes to transmit information thus the multiplications of activations and weights can be replaced by additions when implemented on hardware. However, this quantization mechanism will inevitably introduce quantization error, thus causing catastrophic information loss. To address the quantization error problem, we propose a regularizing membrane potential loss (RMP-Loss) to adjust the distribution which is directly related to quantization error to a range close to the spikes. Our method is extremely simple to implement and straightforward to train an SNN. Furthermore, it is shown to consistently outperform previous state-of-the-art methods over different network architectures and datasets." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.613, + 0.21, + 0.629 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.639, + 0.471, + 0.866 + ], + "angle": 0, + "content": "Recently, many efforts have been done to make deep neural networks (DNNs) lightweight, so that they can be deployed in devices where energy consumption is limited. To this end, several approaches have been proposed, including network pruning [61], network quantization [18, 37, 15], knowledge transfer/distillation [46], neural architecture search [65, 39], and spiking neural networks (SNNs) [23, 19, 22, 17, 52, 36, 44, 55, 54, 63, 49, 56, 57]. The SNN provides a special way to reduce energy consumption following the working mechanism of the brain neuron. Its neurons accumulate spikes from previous neurons and present spikes to posterior neurons when the membrane potential exceeds the firing threshold. This information transmission paradigm will convert the computationally expensive multiplication to computationally convenient additions" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.311, + 0.892, + 0.431 + ], + "angle": 0, + "content": "thus making SNNs energy-efficient when implemented on hardware. Specialized neuromorphic hardware based on an event-driven processing paradigm is currently under various stages of development, e.g., SpiNNaker [31], TrueNorth [1], Tianjic [45], and Loihi [9], where SNNs can be efficiently implemented further. Due to the advantage of computational efficiency and rapid development of neuromorphic hardware, the SNN has gained more and more attention." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.432, + 0.893, + 0.824 + ], + "angle": 0, + "content": "Although SNNs have been widely studied, their performance is still not comparable with that of DNNs. This performance gap is largely related to the quantization of the real-valued membrane potential to \\(0/1\\) spikes for the firing of the SNN in implementation [21]. The excessive information loss induced by the firing activity forcing all information only to two values will cause accuracy to decrease. Although information loss is important for computer vision tasks and the quantization will cause information loss too, the essential role of the activation function is to introduce non-linearity for neural networks [43]. Therefore, how to effectively reduce the information loss of membrane potential quantization is of high research importance. However, as far as we know, few studies have focused on directly solving this problem. The quantization error problem also exists in these methods that convert the ANN model to an SNN model [11, 4, 36]. However, these methods solve the problem by changing the activation function in ANNs or increasing timesteps in SNNs, which don't work for SNN training. InfLoR-SNN [21] adds a membrane potential redistribution function in the spiking neuron to reduce the quantization error via redistributing the membrane potential. However, it will decrease the biological plausibility of the SNN and increase the inference burden. This paper focuses on reducing the quantization error in SNN training directly and aims to introduce no burden for the SNN." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Quantization error is smaller when the membrane potential is close to the spiking threshold or reset values [21]. Hence, to mitigate the information loss, we suggest redistributing the membrane potential to where the membrane potential is closer to the 0/1 spike. Then an additional" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.341, + 0.901 + ], + "angle": 0, + "content": "*Equal contribution. \n†Corresponding author, mazhe_thu@163.com." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17391" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.099, + 0.889, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.293, + 0.893, + 0.325 + ], + "angle": 0, + "content": "Figure 1: The overall workflow of the proposed method. We embed a membrane potential regularization loss in the task loss to redistribute the membrane potential in the training phase to reduce the quantization error." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.351, + 0.47, + 0.426 + ], + "angle": 0, + "content": "loss term aims at regularizing membrane potential is presented, called RMP-Loss, which can encourage the membrane potentials to gather around binary spike values during the training phase. The workflow of our method is shown in Fig. 1. Our main contributions can be concluded as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.437, + 0.47, + 0.558 + ], + "angle": 0, + "content": "- To our best knowledge, there have been few works noticing the quantization error in direct training of SNNs. To mitigate the quantization error, we present the RMP-Loss, which is of benefit to training an SNN model that enjoys a narrow gap between the membrane potential and its corresponding \\(0/1\\) spike. Furthermore, we also provide theoretical proof to clarify why the RMP-Loss can prevent information loss." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.567, + 0.47, + 0.673 + ], + "angle": 0, + "content": "- Some existing methods can address information loss too. While achieving comparable performance, more parameters or computation burdens are also introduced in the inference phase. Different from those methods, the RMP-Loss can handle information loss directly without introducing any additional parameters or inference burden." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.682, + 0.47, + 0.727 + ], + "angle": 0, + "content": "- Extensive experiments on both static and dynamic datasets show that our method performs better than many state-of-the-art SNN models." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.437, + 0.47, + 0.727 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.74, + 0.219, + 0.755 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.903 + ], + "angle": 0, + "content": "There are two main problems to train an SNN model [22]. The first is that the firing activity is non-differentiable thus the SNN model cannot be trained with these back-propagation methods directly. One way to mitigate the optimization difficulty is through surrogate functions. This kind of method replaces the non-differentiable firing activity with a differentiable surrogate function to calculate the gradient in the back-propagation [34, 51, 42, 50]. In [2], the derivative of a truncated quadratic function was" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.351, + 0.892, + 0.637 + ], + "angle": 0, + "content": "used to approximate the derivative of the firing activity function. In [59] and [7], the derivatives of a sigmoid [59] and a rectangular function were respectively adopted to construct the surrogate gradient. Furthermore, a dynamic evolutionary surrogate gradient that could maintain accurate gradients during the training was proposed in [38, 20, 5, 6]. Another way to solve the non-differentiable problem is converting an ANN model to an SNN model, known as ANN-SNN conversion methods [27, 26, 36, 32, 3, 29, 28]. The ANN-SNN method trains a high-accuracy ANN with ReLU activation first and then transforms the network parameters into an SNN under the supposition that the activation of the ANN can be approximated by the average firing rates of an SNN. However, conversion methods will introduce conversion errors inevitably. Many efforts were made to tackle this problem, such as long inference time [14], threshold rescaling [48], soft reset [27], threshold shift [36], and the quantization clip-floor-shift activation function [4]. This paper adopts the surrogate gradient method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.893, + 0.901 + ], + "angle": 0, + "content": "The second problem is information loss. Though transmitting information with binary spikes is more efficient than that with real values, quantizing these real-valued membrane potentials to 0/1 spikes will cause information loss. There have been some works handling this problem indirectly. Such as learning the appropriate membrane leak-and-firing threshold [47, 64]. These are of benefit to finding a preferable quantization choice. Similarly, in [17, 58], some learnable neuron parameters are incorporated into the SNN to optimize the quantization choice. In [24], three regularization losses are introduced to penalize three undesired shifts of membrane potential distribution to make easy optimization and convergence for the SNN. The regularization is also beneficial to reduce quantization error. However, all these methods do not handle the information loss problem directly and most of them require more parameters. InfLoR-SNN [21] suggests adding a membrane potential redistribution" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17392" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "tion function in the spiking neuron to redistribute the membrane potential closer to spike values, which can be seen as a direct method to reduce the quantization error. However, adding another function in spiking neurons will decrease the biological plausibility of the SNN and increase the inference burden. In this work, we focus on handling the quantization error problem directly without introducing extra parameters or computation burden in the inference phase." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.229, + 0.203, + 0.247 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.255, + 0.47, + 0.346 + ], + "angle": 0, + "content": "In this section, a brief review of the primary computing element of SNNs is first provided in Sec. 3.1. Then we introduce the proposed surrogate gradient that handles the non-differentiability challenge in Sec. 3.2. Finally, in Sec. 3.3, we describe the threshold-dependent batch normalization technique used in this work." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.357, + 0.289, + 0.373 + ], + "angle": 0, + "content": "3.1. Spiking Neuron Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.473, + 0.56 + ], + "angle": 0, + "content": "Spiking neuron. The primary computing element, i.e., the neuron of an SNN is much different from that of an ANN. The neuron of an ANN plays the role of nonlinear transformation and can output real-valued values. Meanwhile, the neuron in an SNN accumulates the information from previous neurons into its membrane potential and presents the spike to the following neurons when its membrane potential exceeds the firing threshold. The SNN is more efficient with this special information transmission paradigm while suffering the information loss problem. A unified form of this spiking neuron model can be formulated as follows," + }, + { + "type": "equation", + "bbox": [ + 0.186, + 0.562, + 0.47, + 0.58 + ], + "angle": 0, + "content": "\\[\nu ^ {(t), \\text {p r e}} = \\tau u ^ {(t - 1)} + x ^ {(t)}, \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.59, + 0.47, + 0.623 + ], + "angle": 0, + "content": "\\[\no ^ {(t)} = \\left\\{ \\begin{array}{l} 1, \\text {i f} u ^ {(t), \\text {p r e}} \\geq V _ {\\text {t h}} \\\\ 0, \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.633, + 0.469, + 0.652 + ], + "angle": 0, + "content": "\\[\nu ^ {(t)} = u ^ {(t), \\mathrm {p r e}} (1 - o ^ {(t)}). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.47, + 0.735 + ], + "angle": 0, + "content": "Where \\( u^{(t),\\mathrm{pre}} \\) and \\( u^{(t)} \\) are pre-membrane potential and membrane potential, respectively, \\( x^{(t)} \\) is input information, \\( o^{(t)} \\) is output spike at the timestep \\( t \\). The range of constant leaky factor \\( \\tau \\) is (0, 1), and we set \\( \\tau \\) as 0.25. \\( V_{\\mathrm{th}} \\) is the firing threshold and is set to 0.5 here." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.737, + 0.469, + 0.828 + ], + "angle": 0, + "content": "Output layer neuron. In the general classification task, the output of the last layer will be presented to the Softmax function first and then find the winner class. We make the neuron model in the output layer only accumulate the incoming inputs without any leakage as final output like doing in recent practices[47, 62], described by" + }, + { + "type": "equation", + "bbox": [ + 0.201, + 0.839, + 0.47, + 0.857 + ], + "angle": 0, + "content": "\\[\nu ^ {(t)} = u ^ {(t - 1)} + x ^ {(t)}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Then the cross-entropy loss is calculated according to the final membrane potential at the last timesteps, \\( u^{(T)} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.763, + 0.108 + ], + "angle": 0, + "content": "3.2. Surrogate Gradients of SNNs" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.895, + 0.448 + ], + "angle": 0, + "content": "As shown in Eq. 2, the firing activity of SNNs can be seen as a step function. Its derivative is 0 everywhere except at \\( V_{\\mathrm{th}} \\). This non-differentiability problem of firing activity will cause gradient vanishing or explosion and make the back-propagation unsuitable for training SNNs, directly. As mentioned before, many prior works adopted the surrogate function to replace the firing function to obtain a suitable gradient [7, 62, 52]. In InfLoR-SNN [21], an extra membrane potential redistribution function is added before the firing function. It argues that this redistribution function will reduce the information loss in forward propagation. However, investigating it from a backward propagation perspective and considering the redistribution function being next to the firing function, it can be seen as a more suitable surrogate gradient if we gather the STE (used in [21]) gradients of the firing function and redistribution function together. In this sense, the suitable surrogate gradient can also be seen as a route to reduce quantization error. Therefore, in this paper, we adopt the gathered redistribution function in InfLoR-SNN as our surrogate function, which indeed performs better than other methods [7, 62, 52] in our experiments, denoted as" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.459, + 0.908, + 0.522 + ], + "angle": 0, + "content": "\\[\n\\varphi (u) = \\left\\{ \\begin{array}{l l} 0, & u < 0, \\\\ \\frac {1}{2 \\tanh (3 / 2)} \\tanh (3 (u - 1 / 2)) + 1 / 2, & 0 \\leq u \\leq 1, \\\\ 1, & u > 1. \\end{array} \\right. \\tag {5}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.532, + 0.866, + 0.548 + ], + "angle": 0, + "content": "3.3. Threshold-dependent Batch Normalization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.556, + 0.894, + 0.859 + ], + "angle": 0, + "content": "Normalization techniques can effectively reduce the training time and alleviate the gradient vanishing or explosion problem for training DNNs. A most widely used technique called batch normalization (BN) [30] uses the distribution of the summed input to a neuron over a mini-batch of training cases to compute a mean and variance which are then used to normalize the summed input to that neuron on each training case. This is significantly effective for convolutional neural networks (CNNs). However, directly applying BN to SNNs will ignore the temporal characteristic and can not achieve the desired effect. To this end, a more suitable normalization technique for SNNs, named threshold-dependent BN (tdBN) was further proposed in [62]. It normalizes feature inputs on both temporal and spatial dimensions. Besides, as its name implies, tdBN makes normalized variance dependent on the firing threshold, i.e., the pre-activations are normalized to \\( N(0,(\\alpha V_{\\mathrm{th}})^2) \\) instead of \\( N(0,1) \\). This can balance pre-synaptic input and threshold to maintain a reasonable firing rate. In this paper, we also adopt the tdBN, as follows," + }, + { + "type": "equation", + "bbox": [ + 0.549, + 0.87, + 0.892, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\bar {\\mathbf {X}} = \\alpha V _ {\\mathrm {t h}} \\frac {\\mathbf {X} - \\operatorname {m e a n} (\\mathbf {X})}{\\sqrt {\\operatorname {m e a n} ((\\mathbf {X} - \\operatorname {m e a n} (\\mathbf {X})) ^ {2}) + \\epsilon}}, \\qquad (6)\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17393" + } + ], + [ + { + "type": "equation", + "bbox": [ + 0.225, + 0.09, + 0.469, + 0.107 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {X}} = \\lambda \\bar {\\mathbf {X}} + \\beta . \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.112, + 0.47, + 0.158 + ], + "angle": 0, + "content": "where \\(\\mathbf{X} \\in \\mathbb{R}^{T \\times B \\times C \\times H \\times W}\\) (\\(T\\): timesteps; \\(B\\): batch size; \\(C\\): channel; \\((H, W)\\): spatial domain) is a 5D tensor and \\(\\alpha\\) is a hyper-parameter set as 1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.171, + 0.192, + 0.187 + ], + "angle": 0, + "content": "4. RMP-Loss" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.197, + 0.471, + 0.333 + ], + "angle": 0, + "content": "As aforementioned, we suggest reducing the quantization error to avoid information loss in supervised training-based SNNs. In this section, we first try to provide a metric to measure the quantization error in SNNs. Then based on the metric, we introduce our method, a loss term for regularizing membrane potential, i.e., RMP-Loss, which can push the membrane potentials close to spike values to reduce the quantization error. Finally, theoretical proof to clarify why the RMP-Loss can prevent information loss is given." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.341, + 0.353, + 0.357 + ], + "angle": 0, + "content": "4.1. Quantization Error Estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.47, + 0.516 + ], + "angle": 0, + "content": "Estimating the quantization error precisely is important for designing a method to reduce the prediction error. Hence, before giving the full details of the RMP-Loss, here we try to formulate the quantization error first. As shown in Eq. 2, the output of a neuron is dependent on the magnitude of the membrane potential. When the membrane potential exceeds the firing threshold, the output is 1, otherwise, is 0; that is, these full-precision values will be mapped to only two spike values. The difference between output, \\(o\\), and membrane potential, \\(u\\), can be measured as" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.524, + 0.47, + 0.557 + ], + "angle": 0, + "content": "\\[\n\\operatorname {D i s} (o, u) = \\left\\{ \\begin{array}{l l} 1 - u, & \\text {i f} u \\geq V _ {\\mathrm {t h}} \\\\ 0 - u, & \\text {o t h e r w i s e} \\end{array} \\right.. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.566, + 0.47, + 0.643 + ], + "angle": 0, + "content": "Obviously, the closer a membrane potential is to its corresponding spike, the smaller the quantization error. The quantization error depends on the margin between the membrane potential and its corresponding spike. Then we define the quantization error as" + }, + { + "type": "equation", + "bbox": [ + 0.204, + 0.652, + 0.469, + 0.669 + ], + "angle": 0, + "content": "\\[\nq (u) = \\left| \\operatorname {D i s} (o, u) \\right| ^ {p}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.678, + 0.469, + 0.724 + ], + "angle": 0, + "content": "where \\( p > 0 \\), which is usually set to 1 and/or 2 corresponding to L1-norm and/or L2-norm. Unless otherwise specified, we set it as 2 in the paper." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.732, + 0.469, + 0.748 + ], + "angle": 0, + "content": "4.2. Regularizing Membrane Potential Distribution" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.755, + 0.469, + 0.816 + ], + "angle": 0, + "content": "To mitigate the information loss problem in SNNs, the quantization error should be reduced to some extent. To this end, we propose RMP-Loss to carve the distribution to a range close to the spikes based on \\( q(u) \\), as" + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.824, + 0.469, + 0.862 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {R M P}} = \\frac {1}{T L B C W H} \\sum_ {t, l, b, c, w, h} q (u). \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.87, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(T\\), \\(L\\), \\(B\\), \\(C\\), \\(W\\), and \\(H\\) denote the number of timesteps, the number of layers, batch size, channel length," + }, + { + "type": "code_caption", + "bbox": [ + 0.501, + 0.091, + 0.818, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 Training an SNN with RMP-Loss." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.109, + 0.892, + 0.152 + ], + "angle": 0, + "content": "Input: An SNN to be trained; Training dataset, total number of training epochs \\(N\\), total number of training iterations per epoch \\(I\\)." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.154, + 0.681, + 0.167 + ], + "angle": 0, + "content": "Output: The trained SNN." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.171, + 0.788, + 0.186 + ], + "angle": 0, + "content": "1: for All \\( n = 1,2,\\ldots ,N - th \\) epoch do" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.187, + 0.809, + 0.2 + ], + "angle": 0, + "content": "2: for All \\( i = 1,2,\\ldots ,I - th \\) iteration do" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.202, + 0.669, + 0.215 + ], + "angle": 0, + "content": "3: Feed-Forward:" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.217, + 0.891, + 0.245 + ], + "angle": 0, + "content": "4: Calculate the SNN output, \\(\\mathbf{O}^i\\), membrane potential, \\(\\mathbf{U}\\), and class label, \\(\\mathbf{Y}^i\\);" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.246, + 0.888, + 0.262 + ], + "angle": 0, + "content": "5: Compute classification loss \\(\\mathcal{L}_{\\mathrm{CE}} = \\mathcal{L}_{\\mathrm{CE}}(\\mathbf{O},\\mathbf{Y}^i)\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.263, + 0.842, + 0.277 + ], + "angle": 0, + "content": "6: Compute RMP-Loss \\(\\mathcal{L}_{\\mathrm{RMP}} = \\mathcal{L}_{\\mathrm{RMP}}(\\mathbf{U})\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.278, + 0.891, + 0.307 + ], + "angle": 0, + "content": "7: Compute the total loss \\(\\mathcal{L}_{\\mathrm{CE - RMP}} = \\mathcal{L}_{\\mathrm{CE}} + \\lambda (n)\\mathcal{L}_{\\mathrm{RMP}}\\)" + }, + { + "type": "list", + "bbox": [ + 0.511, + 0.171, + 0.891, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.562, + 0.308, + 0.732, + 0.321 + ], + "angle": 0, + "content": "Backward-Propagation:" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.321, + 0.892, + 0.411 + ], + "angle": 0, + "content": "8: Calculate the gradients \\(\\Delta \\mathbf{W} = \\frac{\\partial\\mathcal{L}_{\\mathrm{CE - RMP}}}{\\partial\\mathbf{W}} = \\sum_{t}\\frac{\\partial(\\mathcal{L}_{\\mathrm{CE}} + \\lambda(n)\\mathcal{L}_{\\mathrm{RMP}})}{\\partial\\mathbf{y}^t}\\frac{\\partial\\mathbf{y}^t}{\\partial\\mathbf{U}}\\frac{\\partial\\mathbf{U}}{\\partial\\mathbf{W}}\\) where \\(\\mathbf{y}^t\\) is feature maps at \\(t\\)-th timesteps and \\(\\frac{\\partial\\mathbf{y}^t}{\\partial\\mathbf{U}}\\) is the gradient of firing function, which can be calculated as \\(\\frac{\\partial\\varphi(\\mathbf{U})}{\\partial\\mathbf{U}}\\). Parameters Update:" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.411, + 0.868, + 0.426 + ], + "angle": 0, + "content": "9: Update all parameters with the learning rate \\(\\eta\\)." + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.427, + 0.599, + 0.438 + ], + "angle": 0, + "content": "10: end for" + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.441, + 0.583, + 0.453 + ], + "angle": 0, + "content": "11: end for" + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.456, + 0.692, + 0.469 + ], + "angle": 0, + "content": "12: return the trained SNN." + }, + { + "type": "list", + "bbox": [ + 0.506, + 0.321, + 0.892, + 0.469 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.495, + 0.891, + 0.539 + ], + "angle": 0, + "content": "width, and height of the membrane potential map, respectively. Finally, taking classification loss into consideration, the total loss can be written as" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.548, + 0.891, + 0.563 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {C E} - \\mathrm {R M P}} = \\mathcal {L} _ {\\mathrm {C E}} + \\lambda (n) \\mathcal {L} _ {\\mathrm {R M P}}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.57, + 0.892, + 0.72 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{CE}\\) is the cross-entropy loss, and \\(\\lambda (n)\\) is a balanced coefficient, which changes dynamically with the training epoch. Obviously, \\(\\mathcal{L}_{RMP}\\) does not take into account the classification problem at hand and will add a new constraint in the network optimization. To make the network parameter update have enough freedom at the beginning, which is important to train a well-performance network, and still focus on the classification task at the end. We adopt a strategy of increasing first and decreasing later to adjust the \\(\\lambda (n)\\) as follows," + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.726, + 0.891, + 0.76 + ], + "angle": 0, + "content": "\\[\n\\lambda (n) = \\left\\{ \\begin{array}{l} 2 k \\frac {n}{N}, \\text {i f} n \\leq N / 2 \\\\ 2 k \\left(1 - \\frac {n}{N}\\right), \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.891, + 0.81 + ], + "angle": 0, + "content": "where \\( n \\) is the \\( n \\)-th epoch and \\( k \\) is a coefficient, which controls the amplitude of regularization. Unless otherwise specified, we set it as 0.1 in the paper." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.81, + 0.891, + 0.84 + ], + "angle": 0, + "content": "The final resulting RMP-Loss training method is defined in Algo. 1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.727, + 0.863 + ], + "angle": 0, + "content": "4.3. Analysis and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.891, + 0.902 + ], + "angle": 0, + "content": "In this work, we assume that RMP-Loss can help reduce the quantization loss of the SNNs. To verify our assumption, we first consider a linear model with a single input \\( x \\) and a single output \\( y \\). Then, we use the following linear model to obtain the output \\( y \\) from the input \\( x \\):" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17394" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.242 + ], + "angle": 0, + "content": "tion, a theoretical analysis is conducted by using the information entropy concept. To mitigate the information loss, the output spike tensor \\(\\mathbf{O}\\) should reflect the information of the membrane potential tensor \\(\\mathbf{U}\\) as much as possible. Since KL-divergence is a metric to measure the difference between two random variable distributions. We use KLdivergence to compute the difference between \\(\\mathbf{O}\\) and \\(\\mathbf{U}\\), which refers to the difficulty of reconstructing \\(\\mathbf{U}\\) from \\(\\mathbf{O}\\), i.e., information loss degree. Then we provide the theoretical analysis below." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.243, + 0.47, + 0.319 + ], + "angle": 0, + "content": "Let \\(x^u\\sim \\mathcal{U}\\) where \\(x^{u}\\) are samples \\(\\in \\mathbf{U}\\) and \\(\\mathcal{U}\\) represents the distribution of \\(x^{u}\\). Similarly, we have \\(x^{o}\\sim \\mathcal{O}\\) where \\(x^{o}\\in \\mathbf{O}\\). We use \\(P_U(x)\\) and \\(P_O(x)\\) to denote the probability density function for \\(\\mathcal{U}\\) and \\(\\mathcal{O}\\), respectively. Then the information loss for the spike firing process can be described as" + }, + { + "type": "equation", + "bbox": [ + 0.112, + 0.328, + 0.47, + 0.363 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {K L} (\\mathcal {U} | | \\mathcal {O}) = \\int_ {- \\infty} ^ {\\infty} P _ {U} \\left(x ^ {u}\\right) \\log \\frac {P _ {U} \\left(x ^ {u}\\right)}{P _ {O} \\left(x ^ {o}\\right)} d x. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.372, + 0.427, + 0.387 + ], + "angle": 0, + "content": "Since output spike \\( x^{o} \\) is discrete, we can update it as" + }, + { + "type": "equation", + "bbox": [ + 0.107, + 0.397, + 0.47, + 0.432 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {K L} (\\mathcal {U} \\| \\mathcal {O}) = \\int_ {o - \\epsilon} ^ {o + \\epsilon} P _ {U} \\left(x ^ {u}\\right) \\log \\frac {P _ {U} \\left(x ^ {u}\\right)}{P _ {O} \\left(x ^ {o}\\right)} d x, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.443, + 0.47, + 0.491 + ], + "angle": 0, + "content": "where \\(\\epsilon\\) is a small constant, \\(o\\) is the spike value, \\(P_O(x^o)\\) can be seen as a very large constant in this situation, and \\(\\int_{o - \\epsilon}^{o + \\epsilon}P_O(x^o)dx = 1\\). With RMP-Loss, it will become" + }, + { + "type": "equation", + "bbox": [ + 0.107, + 0.503, + 0.47, + 0.539 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {K L} (\\hat {\\mathcal {U}} | | \\mathcal {O}) = \\int_ {o - \\epsilon} ^ {o + \\epsilon} P _ {\\hat {U}} (x ^ {\\hat {u}}) \\log \\frac {P _ {\\hat {U}} (x ^ {\\hat {u}})}{P _ {O} (x ^ {o})} d x, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.469, + 0.581 + ], + "angle": 0, + "content": "where \\(x^{\\hat{u}} \\in \\hat{\\mathcal{U}}\\) and \\(\\hat{\\mathcal{U}}\\) is the new distribution of \\(x^{\\hat{u}}\\) adjusted by RMP-Loss. Here, we have the following propositions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.581, + 0.439, + 0.598 + ], + "angle": 0, + "content": "Proposition 1 \\(\\frac{d\\mathcal{L}_{KL}}{dP_U(x^u)} < 0\\) i.e., \\(\\mathcal{L}_{KL}\\downarrow asP_U(x^u)\\uparrow\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.47, + 0.674 + ], + "angle": 0, + "content": "Proof: When a membrane potential \\( u \\) is below the firing threshold, it will be pushed to 0 by the RMP-Loss, considering its effect, and otherwise, 1. Hence the firing rate of the neuron can be seen as the same, whether using the RMP-Loss or not, i.e., \\( P_O(x^o) \\) keep the same for \\( \\hat{\\mathbf{U}} \\) and \\( \\mathbf{U} \\)." + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.684, + 0.47, + 0.76 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\frac {d \\mathcal {L} _ {K L}}{d P _ {U} \\left(x ^ {u}\\right)} = \\frac {d \\int_ {o - \\epsilon} ^ {o + \\epsilon} P _ {U} \\left(x ^ {u}\\right) \\log \\frac {P _ {U} \\left(x ^ {u}\\right)}{P _ {O} \\left(x ^ {o}\\right)} d x}{d P _ {U} \\left(x ^ {u}\\right)} (16) \\\\ = \\int_ {o - \\epsilon} ^ {o + \\epsilon} \\left(\\log \\frac {P _ {U} \\left(x ^ {u}\\right)}{P _ {O} \\left(x ^ {o}\\right)} + \\frac {1}{\\ln 2}\\right) d x. (17) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.77, + 0.47, + 0.806 + ], + "angle": 0, + "content": "Since \\(P_O(x^o)\\) is much larger than \\(P_U(x^u)\\), we can get \\(\\int_{o - \\epsilon}^{o + \\epsilon} (\\log \\frac{P_U(x^u)}{P_O(x^o)} + \\frac{1}{\\ln 2}) dx < 0\\), then \\(\\frac{d\\mathcal{L}_{KL}}{dP_U(x^u)} < 0\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.806, + 0.361, + 0.822 + ], + "angle": 0, + "content": "Proposition 2 \\(P_{\\hat{U}}(x^{\\hat{u}}) > P_{U}(x^{u})|x = o.\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.822, + 0.47, + 0.9 + ], + "angle": 0, + "content": "Proof: We assume that there are \\(n_{\\epsilon}^{u}\\) samples in the interval \\((o - \\epsilon, o + \\epsilon)\\) for \\(\\mathcal{U}\\), where \\(\\epsilon\\) is a small constant. Then we can get \\(P_U(x^u) \\approx \\frac{n_{\\epsilon}^u}{2\\epsilon}\\). And we can simply see the RMP-Loss as a function to push the vanilla \\(\\mathbf{U}\\) to \\(\\hat{\\mathbf{U}}\\), which is closer to \\(\\mathbf{O}\\), based on its effect. Therefore, we can assume that" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.143 + ], + "angle": 0, + "content": "these samples will be gathered to a new interval \\((o - \\epsilon_l, o + \\epsilon_r)\\), where \\(\\epsilon_l, \\epsilon_r < \\epsilon\\). Then we can get \\(P_{\\hat{U}(x^{\\hat{u}})} \\approx \\frac{n_\\epsilon^u}{\\epsilon_l + \\epsilon_r}\\). Thereby we can have \\(P_{\\hat{U}(x^{\\hat{u}})} > P_U(x^u)|_{x = o}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.142, + 0.892, + 0.187 + ], + "angle": 0, + "content": "Along with Proposition 1 and Proposition 2, we can conclude that \\(\\mathcal{L}_{KL}(\\hat{U} ||O) < \\mathcal{L}_{KL}(U||O)\\), i.e., our method with RMP-Loss enjoys lesser information loss." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.203, + 0.625, + 0.22 + ], + "angle": 0, + "content": "5. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.23, + 0.892, + 0.333 + ], + "angle": 0, + "content": "In this section, we first conducted extensive ablation studies to compare the SNNs with RMP-Loss and their vanilla counterparts to verify the effectiveness of the method. Next, we fully compared our method with other state-of-the-art (SoTA) methods. Finally, some further experimental visualizations are provided to understand the RMP-Loss." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.347, + 0.702, + 0.364 + ], + "angle": 0, + "content": "5.1. Datasets and Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.371, + 0.892, + 0.537 + ], + "angle": 0, + "content": "Datasets. We conducted experiments on four benchmark datasets: CIFAR-10 (100) [33], CIFAR10-DVS [35], and ImageNet (ILSVRC12) [10]. The CIFAR-10 (100) dataset includes 60,000 images in 10 (100) classes with \\(32 \\times 32\\) pixels. The numbers of training images and test images are 50,000 and 10,000. The CIFAR10-DVS dataset is the neuromorphic version of the CIFAR-10 dataset. It is composed of 10,000 images in 10 classes. We split the dataset into 9000 training images and 1000 test images similar to [52]. ImageNet dataset consists of 1,250,000 training images and 50,000 test images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.892, + 0.704 + ], + "angle": 0, + "content": "Preprocessing. We applied data normalization on all static datasets to make input images have 0 mean and 1 variance. Besides, we conducted random horizontal flipping and cropping on these datasets to avoid overfitting. For CIFAR, the AutoAugment [8] and Cutout [13] were also used for data augmentation as doing in [24, 20]. For the neuromorphic dataset, we resized the training image frames to \\(48 \\times 48\\) as in [62] and adopted random horizontal flip and random roll within 5 pixels for augmentation. And the test images were merely resized to \\(48 \\times 48\\) without any additional processing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Training setup. For all the datasets, the firing threshold \\( V_{\\mathrm{th}} \\) was set as 0.5. For static image datasets, the images were encoded to binary spike using the first layer of the SNN, as in recent works [47, 17, 16]. This is similar to rate coding. For the neuromorphic image dataset, we used the 0/1 spike format directly. The neuron models in the output layer accumulated the incoming inputs without generating any spike as the output like in [47]. For CIFAR-10 (100) and CIFAR10-DVS datasets, we used the SGD optimizer with the momentum of 0.9 and learning rate of 0.01 with cosine decayed [40] to 0 as in [21]. All models were trained within 400 epochs with the same batch size of 128. For the ImageNet dataset, we adopted the SGD optimizer with" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17395" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.356, + 0.09, + 0.616, + 0.105 + ], + "angle": 0, + "content": "Table 1: Ablation Study for RMP-Loss" + }, + { + "type": "table", + "bbox": [ + 0.153, + 0.116, + 0.817, + 0.238 + ], + "angle": 0, + "content": "
DatasetArchitectureTypeTimestepAccuracyQuantization error
CIFAR-10ResNet20Without RMP-Loss491.26%0.186
With RMP-Loss491.89%0.121
ResNet19Without RMP-Loss495.04%0.128
With RMP-Loss495.51%0.104
VGG16Without RMP-Loss492.80%0.174
With RMP-Loss493.33%0.135
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.262, + 0.471, + 0.294 + ], + "angle": 0, + "content": "a momentum of 0.9 and a learning rate of 0.1 with cosine decayed to 0. All models are trained within 320 epochs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.303, + 0.345, + 0.319 + ], + "angle": 0, + "content": "5.2. Ablation Study for RMP-Loss" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.471, + 0.478 + ], + "angle": 0, + "content": "We conducted a set of ablation experiments on CIFAR-10 using ResNet20, ResNet19, and VGG16 as backbones. The results are shown in Tab. 1. It can be seen that with the RMP-Loss, these SNNs can achieve higher accuracy than their vanilla counterparts. We also show the membrane potential distribution of the first layer of the second block in the ResNet20 with and without RMP-Loss on the test set of CIFAR-10 in Fig. 2. It can be seen that the models trained with RMP-Loss can shrink the membrane potential distribution range which enjoys less quantization error." + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.504, + 0.273, + 0.605 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.504, + 0.474, + 0.605 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.623, + 0.471, + 0.699 + ], + "angle": 0, + "content": "Figure 2: The effect of RMP-Loss. The overall original membrane potential distribution (left) and the redistributed membrane potential distribution by RMP-Loss (right) of the first layer of the second block in ResNet20 on CIFAR-10 test sets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.726, + 0.442, + 0.743 + ], + "angle": 0, + "content": "5.3. Comparison with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.468, + 0.839 + ], + "angle": 0, + "content": "We evaluated the proposed method with the accuracy performance on various widely used static and neuromorphic datasets using spiking ResNet20 [47, 48], VGG16 [47], ResNet18 [16], ResNet19 [62], and ResNet34 [16]. The results with the mean accuracy and standard deviation of 3-trials are listed in Tab. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "CIFAR-10. For CIFAR-10, we tested three different network architectures. The performance of our method is shown in Tab. 2. It can be seen that our method achieves the best results in most of these cases. In special, us" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.262, + 0.892, + 0.413 + ], + "angle": 0, + "content": "ing ResNet19 [62], the RMP-Loss achieves \\(96.10\\%\\) averaged top-1 accuracy, which improves \\(1.60\\%\\) absolute accuracy compared with the existing state-of-the-art TET [12]. Though InfLoR-SNN [21] is slightly better than our method for 4 and 6 timesteps, it will decrease the biological plausibility of the SNN and increase the inference burden since a complex transform function is added in its spiking neuron. On ResNet20, our method can achieve higher accuracy with only 6 timesteps, while Diet-SNN [47] with 10 timesteps. On VGG16, the RMP-Loss also shows obvious advantages." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.414, + 0.893, + 0.642 + ], + "angle": 0, + "content": "CIFAR-100. For CIFAR-100, we also experimented with these three different network structures. For all these configurations, our method achieves consistent and significant accuracy over prior work. ResNet20-based and VGG16-based RMP-Loss achieve \\(66.65\\%\\) and \\(72.55\\%\\) top-1 accuracy with only 4 timesteps, which outperform their Diet-SNN counterparts with \\(2.58\\%\\) and \\(2.88\\%\\) higher accuracy and Real spike counterparts with \\(0.05\\%\\) and \\(1.93\\%\\) respectively but with fewer timesteps. Noteworthy, our method significantly surpasses TET with \\(4.26\\%\\) higher accuracy on ResNet19, which is not easy to achieve in the SNN field. Overall, our results on CIFAR-100 show that, when applied to a more complex dataset, the RMP-Loss achieves an even more favorable performance compared to competing methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.763 + ], + "angle": 0, + "content": "CIFAR10-DVS. We also verified our method on the popular neuromorphic dataset, CIFAR10-DVS. It can be seen that RMP-Loss also shows amazing performance. RMP-Loss outperforms STBP-tdBN by \\(12.39\\%\\), RecDis-SNN by \\(3.78\\%\\), and InfLoR-SNN by \\(0.70\\%\\) respectively with \\(76.20\\%\\) top-1 accuracy in 10 timesteps using ResNet19 as the backbone. With ResNet20 as the backbone, RMP-Loss can also achieve well-performed results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.902 + ], + "angle": 0, + "content": "ImageNet. For ImageNet, we conducted experiments with ResNet18 and ResNet34 as backbones. Our results are presented in Tab. 4. In these normal spiking structures, our method achieves the highest accuracy among these SoTA prior works. However, our method is slightly worse than SEW ResNet [16]. This is because that SEW ResNet uses an atypical architecture, which abandons binary spike forms but will output arbitrary integers to transmit information, thus enjoying higher accuracy but the efficiency from mul" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17396" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.284, + 0.089, + 0.687, + 0.105 + ], + "angle": 0, + "content": "Table 2: Comparison with SoTA methods on CIFAR-10/100." + }, + { + "type": "table", + "bbox": [ + 0.168, + 0.116, + 0.806, + 0.814 + ], + "angle": 0, + "content": "
DatasetMethodTypeArchitectureTimestepAccuracy
CIFAR-10STBP [52]SNN trainingCIFARNet1290.53%
TSSL-BP [60]SNN trainingCIFARNet591.41%
PLIF [17]SNN trainingPLIFNet893.50%
DSR [41]SNN trainingResNet182095.40%
Joint A-SNN [23]SNN trainingResNet18495.45%
Diet-SNN [47]SNN trainingVGG16592.70%
1093.44%
ResNet20591.78%
1092.54%
RecDis-SNN [24]SNN trainingResNet19293.64%
495.53%
695.55%
STBP-tdBN [62]SNN trainingResNet19292.34%
492.92%
693.16%
TET [12]SNN trainingResNet19294.16%
494.44%
694.50%
InfLoR-SNN [21]SNN trainingResNet19294.44%
496.27%
696.49%
RMP-LossSNN trainingResNet19295.31%±0.07
495.51%±0.08
696.10%±0.08
ResNet20491.89%±0.05
692.55%±0.06
VGG16493.33%±0.07
1094.39%±0.08
CIFAR-100DSR [41]SNN trainingResNet182078.50%
InfLoR-SNN [21]SNN trainingVGG16571.56%
IM-Loss [20]SNN trainingVGG16570.18%
Diet-SNN [47]SNN trainingResNet20564.07%
VGG16569.67%
Real Spike [25]SNN trainingResNet20566.60%
VGG16570.62%
TET [12]SNN trainingResNet19272.87%
474.47%
674.72%
RMP-LossSNN trainingResNet20466.65%±0.10
VGG16472.55%±0.08
1073.30%±0.11
ResNet19274.66%±0.12
478.28%±0.10
678.98%±0.08
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.836, + 0.471, + 0.867 + ], + "angle": 0, + "content": "tlication free of SNNs will be lost. Hence, it would be limited in some applications while our method not." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.835, + 0.638, + 0.851 + ], + "angle": 0, + "content": "5.4. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Furthermore, we also provide some experimental visualizations to show the regularizing effects of RMP-Loss." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17397" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.282, + 0.089, + 0.687, + 0.105 + ], + "angle": 0, + "content": "Table 3: Comparison with SoTA methods on CIFAR10-DVS." + }, + { + "type": "table", + "bbox": [ + 0.155, + 0.116, + 0.819, + 0.27 + ], + "angle": 0, + "content": "
DatasetMethodTypeArchitectureTimestepAccuracy
CIFAR10-DVSSTBP-tdBN [62]SNN trainingResNet191067.80%
LIAF [53]Conv3DLIAF-Net1071.70%
LIAF [53]LIAFLIAF-Net1070.40%
RecDis-SNN [24]SNN trainingResNet191072.42%
InfLoR-SNN [21]SNN trainingResNet191075.50%
ResNet201075.10%
RMP-LossSNN trainingResNet191076.20%±0.20
ResNet201075.60%±0.30
" + }, + { + "type": "table_caption", + "bbox": [ + 0.3, + 0.28, + 0.668, + 0.296 + ], + "angle": 0, + "content": "Table 4: Comparison with SoTA methods on ImageNet." + }, + { + "type": "table", + "bbox": [ + 0.162, + 0.307, + 0.812, + 0.46 + ], + "angle": 0, + "content": "
MethodTypeArchitectureTimestepSpike formAccuracy
STBP-tdBN [62]SNN trainingResNet346Binary63.72%
TET [12]SNN trainingResNet346Binary64.79%
SEW ResNet [16]SNN trainingResNet184Integer63.18%
ResNet344Integer67.04%
Spiking ResNet [16]SNN trainingResNet184Binary62.32%
ResNet344Binary61.86%
RMP-LossSNN trainingResNet184Binary63.03%±0.07
ResNet344Binary65.17%±0.07
" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.493, + 0.271, + 0.595 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.273, + 0.493, + 0.473, + 0.595 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.613, + 0.27, + 0.715 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.273, + 0.613, + 0.473, + 0.715 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.264, + 0.716, + 0.302, + 0.726 + ], + "angle": 0, + "content": "ResNet19" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.742, + 0.47, + 0.802 + ], + "angle": 0, + "content": "Figure 3: The original membrane potential distribution (left) and the redistributed membrane potential distribution by RMP-Loss (right) of the first layer of the second block in ResNet20/19 on CIFAR-10 test sets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Fig. 3 shows the membrane potential distribution of the first layer of the second block in the ResNet20/19 with and without RMP-Loss on the test set of CIFAR-10. It can be seen that the SNN models trained with RMP-Loss can shrink" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.484, + 0.895, + 0.635 + ], + "angle": 0, + "content": "the membrane potential distribution range which enjoys less quantization error. On the other hand, comparing the membrane potential distribution difference between ResNet20 and ResNet19, it can be found that the membrane potential distribution of ResNet19 is thinner than that of ResNet20 too. Considering that ResNet19 can achieve higher accuracy than ResNet20, it also shows that reducing quantization error is effective to improve the accuracy of SNN models and our route to improve the SNN accuracy by reducing the quantization error is reasonable." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.619, + 0.667 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.677, + 0.894, + 0.814 + ], + "angle": 0, + "content": "This paper aims at addressing the information loss problem caused by the \\(0/1\\) spike quantization of SNNs. We introduce RMP-Loss to adjust the membrane potential to reduce the quantization error. Different from other methods that reduce the quantization error indirectly or will induce more parameters, RMP-Loss focuses on handling this problem directly and will introduce no extra parameters in the inference phase. We show that our method outperforms SoTA methods on both static and neuromorphic datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.83, + 0.652, + 0.847 + ], + "angle": 0, + "content": "Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "This work is supported by grants from the National Natural Science Foundation of China under contracts No.12202412 and No.12202413." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17398" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] F. Akopyan, J. Sawada, A. Cassidy, R. Alvarez-Icaza, and Dharmendra S. Modha. Truenorth: Design and tool flow of a 65 mw 1 million neuron programmable neurosynaptic chip. 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Neural architecture search with reinforcement learning, 2016. 1" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "17401" + } + ] +] \ No newline at end of file diff --git a/2023/RMP-Loss_ Regularizing Membrane Potential Distribution for Spiking Neural Networks/8dd5399b-d34f-43a1-82f0-9e644d0103b9_origin.pdf b/2023/RMP-Loss_ Regularizing Membrane Potential Distribution for Spiking Neural Networks/8dd5399b-d34f-43a1-82f0-9e644d0103b9_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..6559cb6cab598987d16fdebc3d7d28ab51accf0e --- /dev/null +++ b/2023/RMP-Loss_ Regularizing Membrane Potential Distribution for Spiking Neural Networks/8dd5399b-d34f-43a1-82f0-9e644d0103b9_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:77daf3c37f7a59f9251f725b61559d24957d9b2a28d945286e656e596934a9cd +size 541331 diff --git a/2023/RMP-Loss_ Regularizing Membrane Potential Distribution for Spiking Neural Networks/full.md b/2023/RMP-Loss_ Regularizing Membrane Potential Distribution for Spiking Neural Networks/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ddd848aa52e34c6dbe8a4b504b544e836793cd1c --- /dev/null +++ b/2023/RMP-Loss_ Regularizing Membrane Potential Distribution for Spiking Neural Networks/full.md @@ -0,0 +1,355 @@ +# RMP-Loss: Regularizing Membrane Potential Distribution for Spiking Neural Networks + +Yufei Guo\*, Xiaode Liu\*, Yuanpei Chen, Liwen Zhang, Weihang Peng, Yuhan Zhang, Xuhui Huang, Zhe Ma† +Intelligent Science & Technology Academy of CASIC, China +Scientific Research Laboratory of Aerospace Intelligent Systems and Technology, China + +# Abstract + +Spiking Neural Networks (SNNs) as one of the biology-inspired models have received much attention recently. It can significantly reduce energy consumption since they quantize the real-valued membrane potentials to 0/1 spikes to transmit information thus the multiplications of activations and weights can be replaced by additions when implemented on hardware. However, this quantization mechanism will inevitably introduce quantization error, thus causing catastrophic information loss. To address the quantization error problem, we propose a regularizing membrane potential loss (RMP-Loss) to adjust the distribution which is directly related to quantization error to a range close to the spikes. Our method is extremely simple to implement and straightforward to train an SNN. Furthermore, it is shown to consistently outperform previous state-of-the-art methods over different network architectures and datasets. + +# 1. Introduction + +Recently, many efforts have been done to make deep neural networks (DNNs) lightweight, so that they can be deployed in devices where energy consumption is limited. To this end, several approaches have been proposed, including network pruning [61], network quantization [18, 37, 15], knowledge transfer/distillation [46], neural architecture search [65, 39], and spiking neural networks (SNNs) [23, 19, 22, 17, 52, 36, 44, 55, 54, 63, 49, 56, 57]. The SNN provides a special way to reduce energy consumption following the working mechanism of the brain neuron. Its neurons accumulate spikes from previous neurons and present spikes to posterior neurons when the membrane potential exceeds the firing threshold. This information transmission paradigm will convert the computationally expensive multiplication to computationally convenient additions + +thus making SNNs energy-efficient when implemented on hardware. Specialized neuromorphic hardware based on an event-driven processing paradigm is currently under various stages of development, e.g., SpiNNaker [31], TrueNorth [1], Tianjic [45], and Loihi [9], where SNNs can be efficiently implemented further. Due to the advantage of computational efficiency and rapid development of neuromorphic hardware, the SNN has gained more and more attention. + +Although SNNs have been widely studied, their performance is still not comparable with that of DNNs. This performance gap is largely related to the quantization of the real-valued membrane potential to $0/1$ spikes for the firing of the SNN in implementation [21]. The excessive information loss induced by the firing activity forcing all information only to two values will cause accuracy to decrease. Although information loss is important for computer vision tasks and the quantization will cause information loss too, the essential role of the activation function is to introduce non-linearity for neural networks [43]. Therefore, how to effectively reduce the information loss of membrane potential quantization is of high research importance. However, as far as we know, few studies have focused on directly solving this problem. The quantization error problem also exists in these methods that convert the ANN model to an SNN model [11, 4, 36]. However, these methods solve the problem by changing the activation function in ANNs or increasing timesteps in SNNs, which don't work for SNN training. InfLoR-SNN [21] adds a membrane potential redistribution function in the spiking neuron to reduce the quantization error via redistributing the membrane potential. However, it will decrease the biological plausibility of the SNN and increase the inference burden. This paper focuses on reducing the quantization error in SNN training directly and aims to introduce no burden for the SNN. + +Quantization error is smaller when the membrane potential is close to the spiking threshold or reset values [21]. Hence, to mitigate the information loss, we suggest redistributing the membrane potential to where the membrane potential is closer to the 0/1 spike. Then an additional + +![](images/c3c77f985f3c56210ab83c59702ab261b8b8bfca03585555542ec4fc261d4b7d.jpg) +Figure 1: The overall workflow of the proposed method. We embed a membrane potential regularization loss in the task loss to redistribute the membrane potential in the training phase to reduce the quantization error. + +loss term aims at regularizing membrane potential is presented, called RMP-Loss, which can encourage the membrane potentials to gather around binary spike values during the training phase. The workflow of our method is shown in Fig. 1. Our main contributions can be concluded as follows: + +- To our best knowledge, there have been few works noticing the quantization error in direct training of SNNs. To mitigate the quantization error, we present the RMP-Loss, which is of benefit to training an SNN model that enjoys a narrow gap between the membrane potential and its corresponding $0/1$ spike. Furthermore, we also provide theoretical proof to clarify why the RMP-Loss can prevent information loss. +- Some existing methods can address information loss too. While achieving comparable performance, more parameters or computation burdens are also introduced in the inference phase. Different from those methods, the RMP-Loss can handle information loss directly without introducing any additional parameters or inference burden. +- Extensive experiments on both static and dynamic datasets show that our method performs better than many state-of-the-art SNN models. + +# 2. Related Work + +There are two main problems to train an SNN model [22]. The first is that the firing activity is non-differentiable thus the SNN model cannot be trained with these back-propagation methods directly. One way to mitigate the optimization difficulty is through surrogate functions. This kind of method replaces the non-differentiable firing activity with a differentiable surrogate function to calculate the gradient in the back-propagation [34, 51, 42, 50]. In [2], the derivative of a truncated quadratic function was + +used to approximate the derivative of the firing activity function. In [59] and [7], the derivatives of a sigmoid [59] and a rectangular function were respectively adopted to construct the surrogate gradient. Furthermore, a dynamic evolutionary surrogate gradient that could maintain accurate gradients during the training was proposed in [38, 20, 5, 6]. Another way to solve the non-differentiable problem is converting an ANN model to an SNN model, known as ANN-SNN conversion methods [27, 26, 36, 32, 3, 29, 28]. The ANN-SNN method trains a high-accuracy ANN with ReLU activation first and then transforms the network parameters into an SNN under the supposition that the activation of the ANN can be approximated by the average firing rates of an SNN. However, conversion methods will introduce conversion errors inevitably. Many efforts were made to tackle this problem, such as long inference time [14], threshold rescaling [48], soft reset [27], threshold shift [36], and the quantization clip-floor-shift activation function [4]. This paper adopts the surrogate gradient method. + +The second problem is information loss. Though transmitting information with binary spikes is more efficient than that with real values, quantizing these real-valued membrane potentials to 0/1 spikes will cause information loss. There have been some works handling this problem indirectly. Such as learning the appropriate membrane leak-and-firing threshold [47, 64]. These are of benefit to finding a preferable quantization choice. Similarly, in [17, 58], some learnable neuron parameters are incorporated into the SNN to optimize the quantization choice. In [24], three regularization losses are introduced to penalize three undesired shifts of membrane potential distribution to make easy optimization and convergence for the SNN. The regularization is also beneficial to reduce quantization error. However, all these methods do not handle the information loss problem directly and most of them require more parameters. InfLoR-SNN [21] suggests adding a membrane potential redistribution + +tion function in the spiking neuron to redistribute the membrane potential closer to spike values, which can be seen as a direct method to reduce the quantization error. However, adding another function in spiking neurons will decrease the biological plausibility of the SNN and increase the inference burden. In this work, we focus on handling the quantization error problem directly without introducing extra parameters or computation burden in the inference phase. + +# 3. Preliminary + +In this section, a brief review of the primary computing element of SNNs is first provided in Sec. 3.1. Then we introduce the proposed surrogate gradient that handles the non-differentiability challenge in Sec. 3.2. Finally, in Sec. 3.3, we describe the threshold-dependent batch normalization technique used in this work. + +# 3.1. Spiking Neuron Model + +Spiking neuron. The primary computing element, i.e., the neuron of an SNN is much different from that of an ANN. The neuron of an ANN plays the role of nonlinear transformation and can output real-valued values. Meanwhile, the neuron in an SNN accumulates the information from previous neurons into its membrane potential and presents the spike to the following neurons when its membrane potential exceeds the firing threshold. The SNN is more efficient with this special information transmission paradigm while suffering the information loss problem. A unified form of this spiking neuron model can be formulated as follows, + +$$ +u ^ {(t), \text {p r e}} = \tau u ^ {(t - 1)} + x ^ {(t)}, \tag {1} +$$ + +$$ +o ^ {(t)} = \left\{ \begin{array}{l} 1, \text {i f} u ^ {(t), \text {p r e}} \geq V _ {\text {t h}} \\ 0, \text {o t h e r w i s e} \end{array} , \right. \tag {2} +$$ + +$$ +u ^ {(t)} = u ^ {(t), \mathrm {p r e}} (1 - o ^ {(t)}). \tag {3} +$$ + +Where $u^{(t),\mathrm{pre}}$ and $u^{(t)}$ are pre-membrane potential and membrane potential, respectively, $x^{(t)}$ is input information, $o^{(t)}$ is output spike at the timestep $t$ . The range of constant leaky factor $\tau$ is (0, 1), and we set $\tau$ as 0.25. $V_{\mathrm{th}}$ is the firing threshold and is set to 0.5 here. + +Output layer neuron. In the general classification task, the output of the last layer will be presented to the Softmax function first and then find the winner class. We make the neuron model in the output layer only accumulate the incoming inputs without any leakage as final output like doing in recent practices[47, 62], described by + +$$ +u ^ {(t)} = u ^ {(t - 1)} + x ^ {(t)}. \tag {4} +$$ + +Then the cross-entropy loss is calculated according to the final membrane potential at the last timesteps, $u^{(T)}$ . + +# 3.2. Surrogate Gradients of SNNs + +As shown in Eq. 2, the firing activity of SNNs can be seen as a step function. Its derivative is 0 everywhere except at $V_{\mathrm{th}}$ . This non-differentiability problem of firing activity will cause gradient vanishing or explosion and make the back-propagation unsuitable for training SNNs, directly. As mentioned before, many prior works adopted the surrogate function to replace the firing function to obtain a suitable gradient [7, 62, 52]. In InfLoR-SNN [21], an extra membrane potential redistribution function is added before the firing function. It argues that this redistribution function will reduce the information loss in forward propagation. However, investigating it from a backward propagation perspective and considering the redistribution function being next to the firing function, it can be seen as a more suitable surrogate gradient if we gather the STE (used in [21]) gradients of the firing function and redistribution function together. In this sense, the suitable surrogate gradient can also be seen as a route to reduce quantization error. Therefore, in this paper, we adopt the gathered redistribution function in InfLoR-SNN as our surrogate function, which indeed performs better than other methods [7, 62, 52] in our experiments, denoted as + +$$ +\varphi (u) = \left\{ \begin{array}{l l} 0, & u < 0, \\ \frac {1}{2 \tanh (3 / 2)} \tanh (3 (u - 1 / 2)) + 1 / 2, & 0 \leq u \leq 1, \\ 1, & u > 1. \end{array} \right. \tag {5} +$$ + +# 3.3. Threshold-dependent Batch Normalization + +Normalization techniques can effectively reduce the training time and alleviate the gradient vanishing or explosion problem for training DNNs. A most widely used technique called batch normalization (BN) [30] uses the distribution of the summed input to a neuron over a mini-batch of training cases to compute a mean and variance which are then used to normalize the summed input to that neuron on each training case. This is significantly effective for convolutional neural networks (CNNs). However, directly applying BN to SNNs will ignore the temporal characteristic and can not achieve the desired effect. To this end, a more suitable normalization technique for SNNs, named threshold-dependent BN (tdBN) was further proposed in [62]. It normalizes feature inputs on both temporal and spatial dimensions. Besides, as its name implies, tdBN makes normalized variance dependent on the firing threshold, i.e., the pre-activations are normalized to $N(0,(\alpha V_{\mathrm{th}})^2)$ instead of $N(0,1)$ . This can balance pre-synaptic input and threshold to maintain a reasonable firing rate. In this paper, we also adopt the tdBN, as follows, + +$$ +\bar {\mathbf {X}} = \alpha V _ {\mathrm {t h}} \frac {\mathbf {X} - \operatorname {m e a n} (\mathbf {X})}{\sqrt {\operatorname {m e a n} ((\mathbf {X} - \operatorname {m e a n} (\mathbf {X})) ^ {2}) + \epsilon}}, \qquad (6) +$$ + +$$ +\tilde {\mathbf {X}} = \lambda \bar {\mathbf {X}} + \beta . \tag {7} +$$ + +where $\mathbf{X} \in \mathbb{R}^{T \times B \times C \times H \times W}$ ( $T$ : timesteps; $B$ : batch size; $C$ : channel; $(H, W)$ : spatial domain) is a 5D tensor and $\alpha$ is a hyper-parameter set as 1. + +# 4. RMP-Loss + +As aforementioned, we suggest reducing the quantization error to avoid information loss in supervised training-based SNNs. In this section, we first try to provide a metric to measure the quantization error in SNNs. Then based on the metric, we introduce our method, a loss term for regularizing membrane potential, i.e., RMP-Loss, which can push the membrane potentials close to spike values to reduce the quantization error. Finally, theoretical proof to clarify why the RMP-Loss can prevent information loss is given. + +# 4.1. Quantization Error Estimation + +Estimating the quantization error precisely is important for designing a method to reduce the prediction error. Hence, before giving the full details of the RMP-Loss, here we try to formulate the quantization error first. As shown in Eq. 2, the output of a neuron is dependent on the magnitude of the membrane potential. When the membrane potential exceeds the firing threshold, the output is 1, otherwise, is 0; that is, these full-precision values will be mapped to only two spike values. The difference between output, $o$ , and membrane potential, $u$ , can be measured as + +$$ +\operatorname {D i s} (o, u) = \left\{ \begin{array}{l l} 1 - u, & \text {i f} u \geq V _ {\mathrm {t h}} \\ 0 - u, & \text {o t h e r w i s e} \end{array} \right.. \tag {8} +$$ + +Obviously, the closer a membrane potential is to its corresponding spike, the smaller the quantization error. The quantization error depends on the margin between the membrane potential and its corresponding spike. Then we define the quantization error as + +$$ +q (u) = \left| \operatorname {D i s} (o, u) \right| ^ {p}, \tag {9} +$$ + +where $p > 0$ , which is usually set to 1 and/or 2 corresponding to L1-norm and/or L2-norm. Unless otherwise specified, we set it as 2 in the paper. + +# 4.2. Regularizing Membrane Potential Distribution + +To mitigate the information loss problem in SNNs, the quantization error should be reduced to some extent. To this end, we propose RMP-Loss to carve the distribution to a range close to the spikes based on $q(u)$ , as + +$$ +\mathcal {L} _ {\mathrm {R M P}} = \frac {1}{T L B C W H} \sum_ {t, l, b, c, w, h} q (u). \tag {10} +$$ + +where $T$ , $L$ , $B$ , $C$ , $W$ , and $H$ denote the number of timesteps, the number of layers, batch size, channel length, + +Algorithm 1 Training an SNN with RMP-Loss. + +Input: An SNN to be trained; Training dataset, total number of training epochs $N$ , total number of training iterations per epoch $I$ . + +Output: The trained SNN. + +1: for All $n = 1,2,\ldots ,N - th$ epoch do +2: for All $i = 1,2,\ldots ,I - th$ iteration do +3: Feed-Forward: +4: Calculate the SNN output, $\mathbf{O}^i$ , membrane potential, $\mathbf{U}$ , and class label, $\mathbf{Y}^i$ ; +5: Compute classification loss $\mathcal{L}_{\mathrm{CE}} = \mathcal{L}_{\mathrm{CE}}(\mathbf{O},\mathbf{Y}^i)$ +6: Compute RMP-Loss $\mathcal{L}_{\mathrm{RMP}} = \mathcal{L}_{\mathrm{RMP}}(\mathbf{U})$ +7: Compute the total loss $\mathcal{L}_{\mathrm{CE - RMP}} = \mathcal{L}_{\mathrm{CE}} + \lambda (n)\mathcal{L}_{\mathrm{RMP}}$ + +# Backward-Propagation: + +8: Calculate the gradients $\Delta \mathbf{W} = \frac{\partial\mathcal{L}_{\mathrm{CE - RMP}}}{\partial\mathbf{W}} = \sum_{t}\frac{\partial(\mathcal{L}_{\mathrm{CE}} + \lambda(n)\mathcal{L}_{\mathrm{RMP}})}{\partial\mathbf{y}^t}\frac{\partial\mathbf{y}^t}{\partial\mathbf{U}}\frac{\partial\mathbf{U}}{\partial\mathbf{W}}$ where $\mathbf{y}^t$ is feature maps at $t$ -th timesteps and $\frac{\partial\mathbf{y}^t}{\partial\mathbf{U}}$ is the gradient of firing function, which can be calculated as $\frac{\partial\varphi(\mathbf{U})}{\partial\mathbf{U}}$ . Parameters Update: +9: Update all parameters with the learning rate $\eta$ . +10: end for +11: end for +12: return the trained SNN. + +width, and height of the membrane potential map, respectively. Finally, taking classification loss into consideration, the total loss can be written as + +$$ +\mathcal {L} _ {\mathrm {C E} - \mathrm {R M P}} = \mathcal {L} _ {\mathrm {C E}} + \lambda (n) \mathcal {L} _ {\mathrm {R M P}}, \tag {11} +$$ + +where $\mathcal{L}_{CE}$ is the cross-entropy loss, and $\lambda (n)$ is a balanced coefficient, which changes dynamically with the training epoch. Obviously, $\mathcal{L}_{RMP}$ does not take into account the classification problem at hand and will add a new constraint in the network optimization. To make the network parameter update have enough freedom at the beginning, which is important to train a well-performance network, and still focus on the classification task at the end. We adopt a strategy of increasing first and decreasing later to adjust the $\lambda (n)$ as follows, + +$$ +\lambda (n) = \left\{ \begin{array}{l} 2 k \frac {n}{N}, \text {i f} n \leq N / 2 \\ 2 k \left(1 - \frac {n}{N}\right), \text {o t h e r w i s e} \end{array} , \right. \tag {12} +$$ + +where $n$ is the $n$ -th epoch and $k$ is a coefficient, which controls the amplitude of regularization. Unless otherwise specified, we set it as 0.1 in the paper. + +The final resulting RMP-Loss training method is defined in Algo. 1. + +# 4.3. Analysis and Discussion + +In this work, we assume that RMP-Loss can help reduce the quantization loss of the SNNs. To verify our assumption, we first consider a linear model with a single input $x$ and a single output $y$ . Then, we use the following linear model to obtain the output $y$ from the input $x$ : + +tion, a theoretical analysis is conducted by using the information entropy concept. To mitigate the information loss, the output spike tensor $\mathbf{O}$ should reflect the information of the membrane potential tensor $\mathbf{U}$ as much as possible. Since KL-divergence is a metric to measure the difference between two random variable distributions. We use KLdivergence to compute the difference between $\mathbf{O}$ and $\mathbf{U}$ , which refers to the difficulty of reconstructing $\mathbf{U}$ from $\mathbf{O}$ , i.e., information loss degree. Then we provide the theoretical analysis below. + +Let $x^u\sim \mathcal{U}$ where $x^{u}$ are samples $\in \mathbf{U}$ and $\mathcal{U}$ represents the distribution of $x^{u}$ . Similarly, we have $x^{o}\sim \mathcal{O}$ where $x^{o}\in \mathbf{O}$ . We use $P_U(x)$ and $P_O(x)$ to denote the probability density function for $\mathcal{U}$ and $\mathcal{O}$ , respectively. Then the information loss for the spike firing process can be described as + +$$ +\mathcal {L} _ {K L} (\mathcal {U} | | \mathcal {O}) = \int_ {- \infty} ^ {\infty} P _ {U} \left(x ^ {u}\right) \log \frac {P _ {U} \left(x ^ {u}\right)}{P _ {O} \left(x ^ {o}\right)} d x. \tag {13} +$$ + +Since output spike $x^{o}$ is discrete, we can update it as + +$$ +\mathcal {L} _ {K L} (\mathcal {U} \| \mathcal {O}) = \int_ {o - \epsilon} ^ {o + \epsilon} P _ {U} \left(x ^ {u}\right) \log \frac {P _ {U} \left(x ^ {u}\right)}{P _ {O} \left(x ^ {o}\right)} d x, \tag {14} +$$ + +where $\epsilon$ is a small constant, $o$ is the spike value, $P_O(x^o)$ can be seen as a very large constant in this situation, and $\int_{o - \epsilon}^{o + \epsilon}P_O(x^o)dx = 1$ . With RMP-Loss, it will become + +$$ +\mathcal {L} _ {K L} (\hat {\mathcal {U}} | | \mathcal {O}) = \int_ {o - \epsilon} ^ {o + \epsilon} P _ {\hat {U}} (x ^ {\hat {u}}) \log \frac {P _ {\hat {U}} (x ^ {\hat {u}})}{P _ {O} (x ^ {o})} d x, \tag {15} +$$ + +where $x^{\hat{u}} \in \hat{\mathcal{U}}$ and $\hat{\mathcal{U}}$ is the new distribution of $x^{\hat{u}}$ adjusted by RMP-Loss. Here, we have the following propositions. + +Proposition 1 $\frac{d\mathcal{L}_{KL}}{dP_U(x^u)} < 0$ i.e., $\mathcal{L}_{KL}\downarrow asP_U(x^u)\uparrow$ + +Proof: When a membrane potential $u$ is below the firing threshold, it will be pushed to 0 by the RMP-Loss, considering its effect, and otherwise, 1. Hence the firing rate of the neuron can be seen as the same, whether using the RMP-Loss or not, i.e., $P_O(x^o)$ keep the same for $\hat{\mathbf{U}}$ and $\mathbf{U}$ . + +$$ +\begin{array}{l} \frac {d \mathcal {L} _ {K L}}{d P _ {U} \left(x ^ {u}\right)} = \frac {d \int_ {o - \epsilon} ^ {o + \epsilon} P _ {U} \left(x ^ {u}\right) \log \frac {P _ {U} \left(x ^ {u}\right)}{P _ {O} \left(x ^ {o}\right)} d x}{d P _ {U} \left(x ^ {u}\right)} (16) \\ = \int_ {o - \epsilon} ^ {o + \epsilon} \left(\log \frac {P _ {U} \left(x ^ {u}\right)}{P _ {O} \left(x ^ {o}\right)} + \frac {1}{\ln 2}\right) d x. (17) \\ \end{array} +$$ + +Since $P_O(x^o)$ is much larger than $P_U(x^u)$ , we can get $\int_{o - \epsilon}^{o + \epsilon} (\log \frac{P_U(x^u)}{P_O(x^o)} + \frac{1}{\ln 2}) dx < 0$ , then $\frac{d\mathcal{L}_{KL}}{dP_U(x^u)} < 0$ . + +Proposition 2 $P_{\hat{U}}(x^{\hat{u}}) > P_{U}(x^{u})|x = o.$ + +Proof: We assume that there are $n_{\epsilon}^{u}$ samples in the interval $(o - \epsilon, o + \epsilon)$ for $\mathcal{U}$ , where $\epsilon$ is a small constant. Then we can get $P_U(x^u) \approx \frac{n_{\epsilon}^u}{2\epsilon}$ . And we can simply see the RMP-Loss as a function to push the vanilla $\mathbf{U}$ to $\hat{\mathbf{U}}$ , which is closer to $\mathbf{O}$ , based on its effect. Therefore, we can assume that + +these samples will be gathered to a new interval $(o - \epsilon_l, o + \epsilon_r)$ , where $\epsilon_l, \epsilon_r < \epsilon$ . Then we can get $P_{\hat{U}(x^{\hat{u}})} \approx \frac{n_\epsilon^u}{\epsilon_l + \epsilon_r}$ . Thereby we can have $P_{\hat{U}(x^{\hat{u}})} > P_U(x^u)|_{x = o}$ . + +Along with Proposition 1 and Proposition 2, we can conclude that $\mathcal{L}_{KL}(\hat{U} ||O) < \mathcal{L}_{KL}(U||O)$ , i.e., our method with RMP-Loss enjoys lesser information loss. + +# 5. Experiment + +In this section, we first conducted extensive ablation studies to compare the SNNs with RMP-Loss and their vanilla counterparts to verify the effectiveness of the method. Next, we fully compared our method with other state-of-the-art (SoTA) methods. Finally, some further experimental visualizations are provided to understand the RMP-Loss. + +# 5.1. Datasets and Settings + +Datasets. We conducted experiments on four benchmark datasets: CIFAR-10 (100) [33], CIFAR10-DVS [35], and ImageNet (ILSVRC12) [10]. The CIFAR-10 (100) dataset includes 60,000 images in 10 (100) classes with $32 \times 32$ pixels. The numbers of training images and test images are 50,000 and 10,000. The CIFAR10-DVS dataset is the neuromorphic version of the CIFAR-10 dataset. It is composed of 10,000 images in 10 classes. We split the dataset into 9000 training images and 1000 test images similar to [52]. ImageNet dataset consists of 1,250,000 training images and 50,000 test images. + +Preprocessing. We applied data normalization on all static datasets to make input images have 0 mean and 1 variance. Besides, we conducted random horizontal flipping and cropping on these datasets to avoid overfitting. For CIFAR, the AutoAugment [8] and Cutout [13] were also used for data augmentation as doing in [24, 20]. For the neuromorphic dataset, we resized the training image frames to $48 \times 48$ as in [62] and adopted random horizontal flip and random roll within 5 pixels for augmentation. And the test images were merely resized to $48 \times 48$ without any additional processing. + +Training setup. For all the datasets, the firing threshold $V_{\mathrm{th}}$ was set as 0.5. For static image datasets, the images were encoded to binary spike using the first layer of the SNN, as in recent works [47, 17, 16]. This is similar to rate coding. For the neuromorphic image dataset, we used the 0/1 spike format directly. The neuron models in the output layer accumulated the incoming inputs without generating any spike as the output like in [47]. For CIFAR-10 (100) and CIFAR10-DVS datasets, we used the SGD optimizer with the momentum of 0.9 and learning rate of 0.01 with cosine decayed [40] to 0 as in [21]. All models were trained within 400 epochs with the same batch size of 128. For the ImageNet dataset, we adopted the SGD optimizer with + +Table 1: Ablation Study for RMP-Loss + +
DatasetArchitectureTypeTimestepAccuracyQuantization error
CIFAR-10ResNet20Without RMP-Loss491.26%0.186
With RMP-Loss491.89%0.121
ResNet19Without RMP-Loss495.04%0.128
With RMP-Loss495.51%0.104
VGG16Without RMP-Loss492.80%0.174
With RMP-Loss493.33%0.135
+ +a momentum of 0.9 and a learning rate of 0.1 with cosine decayed to 0. All models are trained within 320 epochs. + +# 5.2. Ablation Study for RMP-Loss + +We conducted a set of ablation experiments on CIFAR-10 using ResNet20, ResNet19, and VGG16 as backbones. The results are shown in Tab. 1. It can be seen that with the RMP-Loss, these SNNs can achieve higher accuracy than their vanilla counterparts. We also show the membrane potential distribution of the first layer of the second block in the ResNet20 with and without RMP-Loss on the test set of CIFAR-10 in Fig. 2. It can be seen that the models trained with RMP-Loss can shrink the membrane potential distribution range which enjoys less quantization error. + +![](images/fd640d50c0ba50ab93102761c751ca3fdd18f36b440a35f18de86eb040735164.jpg) +Figure 2: The effect of RMP-Loss. The overall original membrane potential distribution (left) and the redistributed membrane potential distribution by RMP-Loss (right) of the first layer of the second block in ResNet20 on CIFAR-10 test sets. + +![](images/a366d32d76c28737a96fda340ef8744f76ebfc4070f7f7f0318c1b374a0e8f13.jpg) + +# 5.3. Comparison with State-of-the-art Methods + +We evaluated the proposed method with the accuracy performance on various widely used static and neuromorphic datasets using spiking ResNet20 [47, 48], VGG16 [47], ResNet18 [16], ResNet19 [62], and ResNet34 [16]. The results with the mean accuracy and standard deviation of 3-trials are listed in Tab. 2. + +CIFAR-10. For CIFAR-10, we tested three different network architectures. The performance of our method is shown in Tab. 2. It can be seen that our method achieves the best results in most of these cases. In special, us + +ing ResNet19 [62], the RMP-Loss achieves $96.10\%$ averaged top-1 accuracy, which improves $1.60\%$ absolute accuracy compared with the existing state-of-the-art TET [12]. Though InfLoR-SNN [21] is slightly better than our method for 4 and 6 timesteps, it will decrease the biological plausibility of the SNN and increase the inference burden since a complex transform function is added in its spiking neuron. On ResNet20, our method can achieve higher accuracy with only 6 timesteps, while Diet-SNN [47] with 10 timesteps. On VGG16, the RMP-Loss also shows obvious advantages. + +CIFAR-100. For CIFAR-100, we also experimented with these three different network structures. For all these configurations, our method achieves consistent and significant accuracy over prior work. ResNet20-based and VGG16-based RMP-Loss achieve $66.65\%$ and $72.55\%$ top-1 accuracy with only 4 timesteps, which outperform their Diet-SNN counterparts with $2.58\%$ and $2.88\%$ higher accuracy and Real spike counterparts with $0.05\%$ and $1.93\%$ respectively but with fewer timesteps. Noteworthy, our method significantly surpasses TET with $4.26\%$ higher accuracy on ResNet19, which is not easy to achieve in the SNN field. Overall, our results on CIFAR-100 show that, when applied to a more complex dataset, the RMP-Loss achieves an even more favorable performance compared to competing methods. + +CIFAR10-DVS. We also verified our method on the popular neuromorphic dataset, CIFAR10-DVS. It can be seen that RMP-Loss also shows amazing performance. RMP-Loss outperforms STBP-tdBN by $12.39\%$ , RecDis-SNN by $3.78\%$ , and InfLoR-SNN by $0.70\%$ respectively with $76.20\%$ top-1 accuracy in 10 timesteps using ResNet19 as the backbone. With ResNet20 as the backbone, RMP-Loss can also achieve well-performed results. + +ImageNet. For ImageNet, we conducted experiments with ResNet18 and ResNet34 as backbones. Our results are presented in Tab. 4. In these normal spiking structures, our method achieves the highest accuracy among these SoTA prior works. However, our method is slightly worse than SEW ResNet [16]. This is because that SEW ResNet uses an atypical architecture, which abandons binary spike forms but will output arbitrary integers to transmit information, thus enjoying higher accuracy but the efficiency from mul + +Table 2: Comparison with SoTA methods on CIFAR-10/100. + +
DatasetMethodTypeArchitectureTimestepAccuracy
CIFAR-10STBP [52]SNN trainingCIFARNet1290.53%
TSSL-BP [60]SNN trainingCIFARNet591.41%
PLIF [17]SNN trainingPLIFNet893.50%
DSR [41]SNN trainingResNet182095.40%
Joint A-SNN [23]SNN trainingResNet18495.45%
Diet-SNN [47]SNN trainingVGG16592.70%
1093.44%
ResNet20591.78%
1092.54%
RecDis-SNN [24]SNN trainingResNet19293.64%
495.53%
695.55%
STBP-tdBN [62]SNN trainingResNet19292.34%
492.92%
693.16%
TET [12]SNN trainingResNet19294.16%
494.44%
694.50%
InfLoR-SNN [21]SNN trainingResNet19294.44%
496.27%
696.49%
RMP-LossSNN trainingResNet19295.31%±0.07
495.51%±0.08
696.10%±0.08
ResNet20491.89%±0.05
692.55%±0.06
VGG16493.33%±0.07
1094.39%±0.08
CIFAR-100DSR [41]SNN trainingResNet182078.50%
InfLoR-SNN [21]SNN trainingVGG16571.56%
IM-Loss [20]SNN trainingVGG16570.18%
Diet-SNN [47]SNN trainingResNet20564.07%
VGG16569.67%
Real Spike [25]SNN trainingResNet20566.60%
VGG16570.62%
TET [12]SNN trainingResNet19272.87%
474.47%
674.72%
RMP-LossSNN trainingResNet20466.65%±0.10
VGG16472.55%±0.08
1073.30%±0.11
ResNet19274.66%±0.12
478.28%±0.10
678.98%±0.08
+ +tlication free of SNNs will be lost. Hence, it would be limited in some applications while our method not. + +# 5.4. Visualization + +Furthermore, we also provide some experimental visualizations to show the regularizing effects of RMP-Loss. + +Table 3: Comparison with SoTA methods on CIFAR10-DVS. + +
DatasetMethodTypeArchitectureTimestepAccuracy
CIFAR10-DVSSTBP-tdBN [62]SNN trainingResNet191067.80%
LIAF [53]Conv3DLIAF-Net1071.70%
LIAF [53]LIAFLIAF-Net1070.40%
RecDis-SNN [24]SNN trainingResNet191072.42%
InfLoR-SNN [21]SNN trainingResNet191075.50%
ResNet201075.10%
RMP-LossSNN trainingResNet191076.20%±0.20
ResNet201075.60%±0.30
+ +Table 4: Comparison with SoTA methods on ImageNet. + +
MethodTypeArchitectureTimestepSpike formAccuracy
STBP-tdBN [62]SNN trainingResNet346Binary63.72%
TET [12]SNN trainingResNet346Binary64.79%
SEW ResNet [16]SNN trainingResNet184Integer63.18%
ResNet344Integer67.04%
Spiking ResNet [16]SNN trainingResNet184Binary62.32%
ResNet344Binary61.86%
RMP-LossSNN trainingResNet184Binary63.03%±0.07
ResNet344Binary65.17%±0.07
+ +![](images/b1bef3d6c3b2f6327c4b946c901a56bde2cbdd61931ae070fddf612aa8f1d402.jpg) + +![](images/4d7b7f0dd7bf3c0353f569782250851752ff4834ce31f953853886a8ab481a1b.jpg) + +![](images/543136c1e205b41f0c229fe16ec42240d60197ce60101f28dce1860e4c9f4fe7.jpg) +ResNet19 + +![](images/664f20942ecfe9c2e2aec0cb43a2cf884a71b589800b2c06e8450c7de36691d5.jpg) +Figure 3: The original membrane potential distribution (left) and the redistributed membrane potential distribution by RMP-Loss (right) of the first layer of the second block in ResNet20/19 on CIFAR-10 test sets. + +Fig. 3 shows the membrane potential distribution of the first layer of the second block in the ResNet20/19 with and without RMP-Loss on the test set of CIFAR-10. It can be seen that the SNN models trained with RMP-Loss can shrink + +the membrane potential distribution range which enjoys less quantization error. On the other hand, comparing the membrane potential distribution difference between ResNet20 and ResNet19, it can be found that the membrane potential distribution of ResNet19 is thinner than that of ResNet20 too. Considering that ResNet19 can achieve higher accuracy than ResNet20, it also shows that reducing quantization error is effective to improve the accuracy of SNN models and our route to improve the SNN accuracy by reducing the quantization error is reasonable. + +# 6. Conclusion + +This paper aims at addressing the information loss problem caused by the $0/1$ spike quantization of SNNs. We introduce RMP-Loss to adjust the membrane potential to reduce the quantization error. Different from other methods that reduce the quantization error indirectly or will induce more parameters, RMP-Loss focuses on handling this problem directly and will introduce no extra parameters in the inference phase. 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Neural architecture search with reinforcement learning, 2016. 1 \ No newline at end of file diff --git a/2023/RMP-Loss_ Regularizing Membrane Potential Distribution for Spiking Neural Networks/images.zip b/2023/RMP-Loss_ Regularizing Membrane Potential Distribution for Spiking Neural Networks/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..51509597d01a3af64de7b3d83bd2fbd196b5b92f --- /dev/null +++ b/2023/RMP-Loss_ Regularizing Membrane Potential Distribution for Spiking Neural Networks/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:756b33f076c82545df691ecbe07d05eb0614b9cc8d91c1720633891423ce41d8 +size 515527 diff --git a/2023/RMP-Loss_ Regularizing Membrane Potential Distribution for Spiking Neural Networks/layout.json b/2023/RMP-Loss_ Regularizing Membrane Potential Distribution for Spiking Neural Networks/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..43ab967664b05bea741f9b698293cb5924ec6fa4 --- /dev/null +++ b/2023/RMP-Loss_ Regularizing Membrane Potential Distribution for Spiking Neural Networks/layout.json @@ -0,0 +1,9850 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 56, + 102, + 539, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 102, + 539, + 138 + ], + "spans": [ + { + "bbox": [ + 56, + 102, + 539, + 138 + ], + "type": "text", + "content": "RMP-Loss: Regularizing Membrane Potential Distribution for Spiking Neural Networks" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 82, + 160, + 510, + 219 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 160, + 510, + 219 + ], + "spans": [ + { + "bbox": [ + 82, + 160, + 510, + 219 + ], + "type": "text", + "content": "Yufei Guo\\*, Xiaode Liu\\*, Yuanpei Chen, Liwen Zhang, Weihang Peng, Yuhan Zhang, Xuhui Huang, Zhe Ma† \nIntelligent Science & Technology Academy of CASIC, China \nScientific Research Laboratory of Aerospace Intelligent Systems and Technology, China" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "spans": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 270, + 290, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 290, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 290, + 462 + ], + "type": "text", + "content": "Spiking Neural Networks (SNNs) as one of the biology-inspired models have received much attention recently. It can significantly reduce energy consumption since they quantize the real-valued membrane potentials to 0/1 spikes to transmit information thus the multiplications of activations and weights can be replaced by additions when implemented on hardware. However, this quantization mechanism will inevitably introduce quantization error, thus causing catastrophic information loss. To address the quantization error problem, we propose a regularizing membrane potential loss (RMP-Loss) to adjust the distribution which is directly related to quantization error to a range close to the spikes. Our method is extremely simple to implement and straightforward to train an SNN. Furthermore, it is shown to consistently outperform previous state-of-the-art methods over different network architectures and datasets." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 485, + 128, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 485, + 128, + 498 + ], + "spans": [ + { + "bbox": [ + 47, + 485, + 128, + 498 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 506, + 288, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 506, + 288, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 506, + 288, + 685 + ], + "type": "text", + "content": "Recently, many efforts have been done to make deep neural networks (DNNs) lightweight, so that they can be deployed in devices where energy consumption is limited. To this end, several approaches have been proposed, including network pruning [61], network quantization [18, 37, 15], knowledge transfer/distillation [46], neural architecture search [65, 39], and spiking neural networks (SNNs) [23, 19, 22, 17, 52, 36, 44, 55, 54, 63, 49, 56, 57]. The SNN provides a special way to reduce energy consumption following the working mechanism of the brain neuron. Its neurons accumulate spikes from previous neurons and present spikes to posterior neurons when the membrane potential exceeds the firing threshold. This information transmission paradigm will convert the computationally expensive multiplication to computationally convenient additions" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 246, + 545, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 246, + 545, + 341 + ], + "spans": [ + { + "bbox": [ + 306, + 246, + 545, + 341 + ], + "type": "text", + "content": "thus making SNNs energy-efficient when implemented on hardware. Specialized neuromorphic hardware based on an event-driven processing paradigm is currently under various stages of development, e.g., SpiNNaker [31], TrueNorth [1], Tianjic [45], and Loihi [9], where SNNs can be efficiently implemented further. Due to the advantage of computational efficiency and rapid development of neuromorphic hardware, the SNN has gained more and more attention." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 342, + 546, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 546, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 546, + 652 + ], + "type": "text", + "content": "Although SNNs have been widely studied, their performance is still not comparable with that of DNNs. This performance gap is largely related to the quantization of the real-valued membrane potential to " + }, + { + "bbox": [ + 304, + 342, + 546, + 652 + ], + "type": "inline_equation", + "content": "0/1" + }, + { + "bbox": [ + 304, + 342, + 546, + 652 + ], + "type": "text", + "content": " spikes for the firing of the SNN in implementation [21]. The excessive information loss induced by the firing activity forcing all information only to two values will cause accuracy to decrease. Although information loss is important for computer vision tasks and the quantization will cause information loss too, the essential role of the activation function is to introduce non-linearity for neural networks [43]. Therefore, how to effectively reduce the information loss of membrane potential quantization is of high research importance. However, as far as we know, few studies have focused on directly solving this problem. The quantization error problem also exists in these methods that convert the ANN model to an SNN model [11, 4, 36]. However, these methods solve the problem by changing the activation function in ANNs or increasing timesteps in SNNs, which don't work for SNN training. InfLoR-SNN [21] adds a membrane potential redistribution function in the spiking neuron to reduce the quantization error via redistributing the membrane potential. However, it will decrease the biological plausibility of the SNN and increase the inference burden. This paper focuses on reducing the quantization error in SNN training directly and aims to introduce no burden for the SNN." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "Quantization error is smaller when the membrane potential is close to the spiking threshold or reset values [21]. Hence, to mitigate the information loss, we suggest redistributing the membrane potential to where the membrane potential is closer to the 0/1 spike. Then an additional" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 208, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 208, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 208, + 713 + ], + "type": "text", + "content": "*Equal contribution. \n†Corresponding author, mazhe_thu@163.com." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17391" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 78, + 544, + 222 + ], + "blocks": [ + { + "bbox": [ + 53, + 78, + 544, + 222 + ], + "lines": [ + { + "bbox": [ + 53, + 78, + 544, + 222 + ], + "spans": [ + { + "bbox": [ + 53, + 78, + 544, + 222 + ], + "type": "image", + "image_path": "c3c77f985f3c56210ab83c59702ab261b8b8bfca03585555542ec4fc261d4b7d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 232, + 546, + 257 + ], + "lines": [ + { + "bbox": [ + 46, + 232, + 546, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 232, + 546, + 257 + ], + "type": "text", + "content": "Figure 1: The overall workflow of the proposed method. We embed a membrane potential regularization loss in the task loss to redistribute the membrane potential in the training phase to reduce the quantization error." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 277, + 287, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 287, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 287, + 337 + ], + "type": "text", + "content": "loss term aims at regularizing membrane potential is presented, called RMP-Loss, which can encourage the membrane potentials to gather around binary spike values during the training phase. The workflow of our method is shown in Fig. 1. Our main contributions can be concluded as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 346, + 287, + 575 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 58, + 346, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 346, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 58, + 346, + 287, + 441 + ], + "type": "text", + "content": "- To our best knowledge, there have been few works noticing the quantization error in direct training of SNNs. To mitigate the quantization error, we present the RMP-Loss, which is of benefit to training an SNN model that enjoys a narrow gap between the membrane potential and its corresponding " + }, + { + "bbox": [ + 58, + 346, + 287, + 441 + ], + "type": "inline_equation", + "content": "0/1" + }, + { + "bbox": [ + 58, + 346, + 287, + 441 + ], + "type": "text", + "content": " spike. Furthermore, we also provide theoretical proof to clarify why the RMP-Loss can prevent information loss." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 449, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 449, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 58, + 449, + 287, + 533 + ], + "type": "text", + "content": "- Some existing methods can address information loss too. While achieving comparable performance, more parameters or computation burdens are also introduced in the inference phase. Different from those methods, the RMP-Loss can handle information loss directly without introducing any additional parameters or inference burden." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 540, + 287, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 540, + 287, + 575 + ], + "spans": [ + { + "bbox": [ + 58, + 540, + 287, + 575 + ], + "type": "text", + "content": "- Extensive experiments on both static and dynamic datasets show that our method performs better than many state-of-the-art SNN models." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 586, + 134, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 134, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 134, + 597 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": "There are two main problems to train an SNN model [22]. The first is that the firing activity is non-differentiable thus the SNN model cannot be trained with these back-propagation methods directly. One way to mitigate the optimization difficulty is through surrogate functions. This kind of method replaces the non-differentiable firing activity with a differentiable surrogate function to calculate the gradient in the back-propagation [34, 51, 42, 50]. In [2], the derivative of a truncated quadratic function was" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 277, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 545, + 504 + ], + "type": "text", + "content": "used to approximate the derivative of the firing activity function. In [59] and [7], the derivatives of a sigmoid [59] and a rectangular function were respectively adopted to construct the surrogate gradient. Furthermore, a dynamic evolutionary surrogate gradient that could maintain accurate gradients during the training was proposed in [38, 20, 5, 6]. Another way to solve the non-differentiable problem is converting an ANN model to an SNN model, known as ANN-SNN conversion methods [27, 26, 36, 32, 3, 29, 28]. The ANN-SNN method trains a high-accuracy ANN with ReLU activation first and then transforms the network parameters into an SNN under the supposition that the activation of the ANN can be approximated by the average firing rates of an SNN. However, conversion methods will introduce conversion errors inevitably. Many efforts were made to tackle this problem, such as long inference time [14], threshold rescaling [48], soft reset [27], threshold shift [36], and the quantization clip-floor-shift activation function [4]. This paper adopts the surrogate gradient method." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "content": "The second problem is information loss. Though transmitting information with binary spikes is more efficient than that with real values, quantizing these real-valued membrane potentials to 0/1 spikes will cause information loss. There have been some works handling this problem indirectly. Such as learning the appropriate membrane leak-and-firing threshold [47, 64]. These are of benefit to finding a preferable quantization choice. Similarly, in [17, 58], some learnable neuron parameters are incorporated into the SNN to optimize the quantization choice. In [24], three regularization losses are introduced to penalize three undesired shifts of membrane potential distribution to make easy optimization and convergence for the SNN. The regularization is also beneficial to reduce quantization error. However, all these methods do not handle the information loss problem directly and most of them require more parameters. InfLoR-SNN [21] suggests adding a membrane potential redistribution" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17392" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "tion function in the spiking neuron to redistribute the membrane potential closer to spike values, which can be seen as a direct method to reduce the quantization error. However, adding another function in spiking neurons will decrease the biological plausibility of the SNN and increase the inference burden. In this work, we focus on handling the quantization error problem directly without introducing extra parameters or computation burden in the inference phase." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 181, + 124, + 195 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 181, + 124, + 195 + ], + "spans": [ + { + "bbox": [ + 47, + 181, + 124, + 195 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 201, + 287, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 201, + 287, + 274 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 287, + 274 + ], + "type": "text", + "content": "In this section, a brief review of the primary computing element of SNNs is first provided in Sec. 3.1. Then we introduce the proposed surrogate gradient that handles the non-differentiability challenge in Sec. 3.2. Finally, in Sec. 3.3, we describe the threshold-dependent batch normalization technique used in this work." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 282, + 176, + 295 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 282, + 176, + 295 + ], + "spans": [ + { + "bbox": [ + 47, + 282, + 176, + 295 + ], + "type": "text", + "content": "3.1. Spiking Neuron Model" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 301, + 289, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 289, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 289, + 443 + ], + "type": "text", + "content": "Spiking neuron. The primary computing element, i.e., the neuron of an SNN is much different from that of an ANN. The neuron of an ANN plays the role of nonlinear transformation and can output real-valued values. Meanwhile, the neuron in an SNN accumulates the information from previous neurons into its membrane potential and presents the spike to the following neurons when its membrane potential exceeds the firing threshold. The SNN is more efficient with this special information transmission paradigm while suffering the information loss problem. A unified form of this spiking neuron model can be formulated as follows," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 113, + 445, + 287, + 459 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 445, + 287, + 459 + ], + "spans": [ + { + "bbox": [ + 113, + 445, + 287, + 459 + ], + "type": "interline_equation", + "content": "u ^ {(t), \\text {p r e}} = \\tau u ^ {(t - 1)} + x ^ {(t)}, \\tag {1}", + "image_path": "7dbd6e226a44a19bacf013a2547422ebce7fae3515b624acde60a1aa08a7167a.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 99, + 467, + 287, + 493 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 467, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 99, + 467, + 287, + 493 + ], + "type": "interline_equation", + "content": "o ^ {(t)} = \\left\\{ \\begin{array}{l} 1, \\text {i f} u ^ {(t), \\text {p r e}} \\geq V _ {\\text {t h}} \\\\ 0, \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {2}", + "image_path": "1ef0ef9de9ae76b2be8206f135e861c93a7d4c5f10b7919e9ae6417d175838e9.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 116, + 501, + 287, + 516 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 501, + 287, + 516 + ], + "spans": [ + { + "bbox": [ + 116, + 501, + 287, + 516 + ], + "type": "interline_equation", + "content": "u ^ {(t)} = u ^ {(t), \\mathrm {p r e}} (1 - o ^ {(t)}). \\tag {3}", + "image_path": "d0558c5d395f4c18fa85e5c59018188e57da2afeedaa161a5e95791bf445caac.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "type": "inline_equation", + "content": "u^{(t),\\mathrm{pre}}" + }, + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "type": "inline_equation", + "content": "u^{(t)}" + }, + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "type": "text", + "content": " are pre-membrane potential and membrane potential, respectively, " + }, + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "type": "inline_equation", + "content": "x^{(t)}" + }, + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "type": "text", + "content": " is input information, " + }, + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "type": "inline_equation", + "content": "o^{(t)}" + }, + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "type": "text", + "content": " is output spike at the timestep " + }, + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "type": "text", + "content": ". The range of constant leaky factor " + }, + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "type": "text", + "content": " is (0, 1), and we set " + }, + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "type": "text", + "content": " as 0.25. " + }, + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{th}}" + }, + { + "bbox": [ + 46, + 522, + 287, + 582 + ], + "type": "text", + "content": " is the firing threshold and is set to 0.5 here." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 583, + 287, + 655 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 583, + 287, + 655 + ], + "spans": [ + { + "bbox": [ + 46, + 583, + 287, + 655 + ], + "type": "text", + "content": "Output layer neuron. In the general classification task, the output of the last layer will be presented to the Softmax function first and then find the winner class. We make the neuron model in the output layer only accumulate the incoming inputs without any leakage as final output like doing in recent practices[47, 62], described by" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 123, + 664, + 287, + 678 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 664, + 287, + 678 + ], + "spans": [ + { + "bbox": [ + 123, + 664, + 287, + 678 + ], + "type": "interline_equation", + "content": "u ^ {(t)} = u ^ {(t - 1)} + x ^ {(t)}. \\tag {4}", + "image_path": "2b33cb6dac9efe275655b459d547a317261de387bdd0969f245b5368c2d6dd54.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "Then the cross-entropy loss is calculated according to the final membrane potential at the last timesteps, " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "u^{(T)}" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 72, + 466, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 466, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 466, + 85 + ], + "type": "text", + "content": "3.2. Surrogate Gradients of SNNs" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 91, + 547, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 354 + ], + "type": "text", + "content": "As shown in Eq. 2, the firing activity of SNNs can be seen as a step function. Its derivative is 0 everywhere except at " + }, + { + "bbox": [ + 304, + 91, + 547, + 354 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{th}}" + }, + { + "bbox": [ + 304, + 91, + 547, + 354 + ], + "type": "text", + "content": ". This non-differentiability problem of firing activity will cause gradient vanishing or explosion and make the back-propagation unsuitable for training SNNs, directly. As mentioned before, many prior works adopted the surrogate function to replace the firing function to obtain a suitable gradient [7, 62, 52]. In InfLoR-SNN [21], an extra membrane potential redistribution function is added before the firing function. It argues that this redistribution function will reduce the information loss in forward propagation. However, investigating it from a backward propagation perspective and considering the redistribution function being next to the firing function, it can be seen as a more suitable surrogate gradient if we gather the STE (used in [21]) gradients of the firing function and redistribution function together. In this sense, the suitable surrogate gradient can also be seen as a route to reduce quantization error. Therefore, in this paper, we adopt the gathered redistribution function in InfLoR-SNN as our surrogate function, which indeed performs better than other methods [7, 62, 52] in our experiments, denoted as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 363, + 555, + 413 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 363, + 555, + 413 + ], + "spans": [ + { + "bbox": [ + 306, + 363, + 555, + 413 + ], + "type": "interline_equation", + "content": "\\varphi (u) = \\left\\{ \\begin{array}{l l} 0, & u < 0, \\\\ \\frac {1}{2 \\tanh (3 / 2)} \\tanh (3 (u - 1 / 2)) + 1 / 2, & 0 \\leq u \\leq 1, \\\\ 1, & u > 1. \\end{array} \\right. \\tag {5}", + "image_path": "64cc3bf72b69eafc8c8f5192bd1bcbea74824c45175f5236eae5589c77f74519.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 421, + 529, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 421, + 529, + 434 + ], + "spans": [ + { + "bbox": [ + 306, + 421, + 529, + 434 + ], + "type": "text", + "content": "3.3. Threshold-dependent Batch Normalization" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 440, + 547, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 440, + 547, + 680 + ], + "spans": [ + { + "bbox": [ + 304, + 440, + 547, + 680 + ], + "type": "text", + "content": "Normalization techniques can effectively reduce the training time and alleviate the gradient vanishing or explosion problem for training DNNs. A most widely used technique called batch normalization (BN) [30] uses the distribution of the summed input to a neuron over a mini-batch of training cases to compute a mean and variance which are then used to normalize the summed input to that neuron on each training case. This is significantly effective for convolutional neural networks (CNNs). However, directly applying BN to SNNs will ignore the temporal characteristic and can not achieve the desired effect. To this end, a more suitable normalization technique for SNNs, named threshold-dependent BN (tdBN) was further proposed in [62]. It normalizes feature inputs on both temporal and spatial dimensions. Besides, as its name implies, tdBN makes normalized variance dependent on the firing threshold, i.e., the pre-activations are normalized to " + }, + { + "bbox": [ + 304, + 440, + 547, + 680 + ], + "type": "inline_equation", + "content": "N(0,(\\alpha V_{\\mathrm{th}})^2)" + }, + { + "bbox": [ + 304, + 440, + 547, + 680 + ], + "type": "text", + "content": " instead of " + }, + { + "bbox": [ + 304, + 440, + 547, + 680 + ], + "type": "inline_equation", + "content": "N(0,1)" + }, + { + "bbox": [ + 304, + 440, + 547, + 680 + ], + "type": "text", + "content": ". This can balance pre-synaptic input and threshold to maintain a reasonable firing rate. In this paper, we also adopt the tdBN, as follows," + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 335, + 689, + 545, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 689, + 545, + 717 + ], + "spans": [ + { + "bbox": [ + 335, + 689, + 545, + 717 + ], + "type": "interline_equation", + "content": "\\bar {\\mathbf {X}} = \\alpha V _ {\\mathrm {t h}} \\frac {\\mathbf {X} - \\operatorname {m e a n} (\\mathbf {X})}{\\sqrt {\\operatorname {m e a n} ((\\mathbf {X} - \\operatorname {m e a n} (\\mathbf {X})) ^ {2}) + \\epsilon}}, \\qquad (6)", + "image_path": "fb24c7237e83c2556c63b63fd72cb85407b5a785be279d89d21f7b09c5f2f0da.jpg" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17393" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 137, + 71, + 287, + 84 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 137, + 71, + 287, + 84 + ], + "spans": [ + { + "bbox": [ + 137, + 71, + 287, + 84 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {X}} = \\lambda \\bar {\\mathbf {X}} + \\beta . \\tag {7}", + "image_path": "f317072068360d42eaa814db741f81f5c03e2a1fe8b0e4437348ec74b2c9b081.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 88, + 287, + 125 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 88, + 287, + 125 + ], + "spans": [ + { + "bbox": [ + 47, + 88, + 287, + 125 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 88, + 287, + 125 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{T \\times B \\times C \\times H \\times W}" + }, + { + "bbox": [ + 47, + 88, + 287, + 125 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 47, + 88, + 287, + 125 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 88, + 287, + 125 + ], + "type": "text", + "content": ": timesteps; " + }, + { + "bbox": [ + 47, + 88, + 287, + 125 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 47, + 88, + 287, + 125 + ], + "type": "text", + "content": ": batch size; " + }, + { + "bbox": [ + 47, + 88, + 287, + 125 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 88, + 287, + 125 + ], + "type": "text", + "content": ": channel; " + }, + { + "bbox": [ + 47, + 88, + 287, + 125 + ], + "type": "inline_equation", + "content": "(H, W)" + }, + { + "bbox": [ + 47, + 88, + 287, + 125 + ], + "type": "text", + "content": ": spatial domain) is a 5D tensor and " + }, + { + "bbox": [ + 47, + 88, + 287, + 125 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 88, + 287, + 125 + ], + "type": "text", + "content": " is a hyper-parameter set as 1." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 135, + 117, + 148 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 135, + 117, + 148 + ], + "spans": [ + { + "bbox": [ + 47, + 135, + 117, + 148 + ], + "type": "text", + "content": "4. RMP-Loss" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 156, + 288, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 156, + 288, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 288, + 263 + ], + "type": "text", + "content": "As aforementioned, we suggest reducing the quantization error to avoid information loss in supervised training-based SNNs. In this section, we first try to provide a metric to measure the quantization error in SNNs. Then based on the metric, we introduce our method, a loss term for regularizing membrane potential, i.e., RMP-Loss, which can push the membrane potentials close to spike values to reduce the quantization error. Finally, theoretical proof to clarify why the RMP-Loss can prevent information loss is given." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 270, + 216, + 282 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 270, + 216, + 282 + ], + "spans": [ + { + "bbox": [ + 47, + 270, + 216, + 282 + ], + "type": "text", + "content": "4.1. Quantization Error Estimation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "type": "text", + "content": "Estimating the quantization error precisely is important for designing a method to reduce the prediction error. Hence, before giving the full details of the RMP-Loss, here we try to formulate the quantization error first. As shown in Eq. 2, the output of a neuron is dependent on the magnitude of the membrane potential. When the membrane potential exceeds the firing threshold, the output is 1, otherwise, is 0; that is, these full-precision values will be mapped to only two spike values. The difference between output, " + }, + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "type": "text", + "content": ", and membrane potential, " + }, + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "type": "text", + "content": ", can be measured as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 91, + 415, + 287, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 415, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 91, + 415, + 287, + 441 + ], + "type": "interline_equation", + "content": "\\operatorname {D i s} (o, u) = \\left\\{ \\begin{array}{l l} 1 - u, & \\text {i f} u \\geq V _ {\\mathrm {t h}} \\\\ 0 - u, & \\text {o t h e r w i s e} \\end{array} \\right.. \\tag {8}", + "image_path": "7bc2d7463cb8fea0810a5c3e23e69a3f0263564444196fb4e7f2a5fc543be607.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 448, + 287, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 448, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 287, + 509 + ], + "type": "text", + "content": "Obviously, the closer a membrane potential is to its corresponding spike, the smaller the quantization error. The quantization error depends on the margin between the membrane potential and its corresponding spike. Then we define the quantization error as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 124, + 516, + 287, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 516, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 124, + 516, + 287, + 529 + ], + "type": "interline_equation", + "content": "q (u) = \\left| \\operatorname {D i s} (o, u) \\right| ^ {p}, \\tag {9}", + "image_path": "93ce08aecb3b38dced146a8711416065ec5a3570138cd6d2fad2b6ed40f2c78a.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 536, + 287, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 287, + 573 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 287, + 573 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 536, + 287, + 573 + ], + "type": "inline_equation", + "content": "p > 0" + }, + { + "bbox": [ + 46, + 536, + 287, + 573 + ], + "type": "text", + "content": ", which is usually set to 1 and/or 2 corresponding to L1-norm and/or L2-norm. Unless otherwise specified, we set it as 2 in the paper." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 579, + 287, + 592 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 579, + 287, + 592 + ], + "spans": [ + { + "bbox": [ + 47, + 579, + 287, + 592 + ], + "type": "text", + "content": "4.2. Regularizing Membrane Potential Distribution" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 597, + 287, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 287, + 646 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 287, + 646 + ], + "type": "text", + "content": "To mitigate the information loss problem in SNNs, the quantization error should be reduced to some extent. To this end, we propose RMP-Loss to carve the distribution to a range close to the spikes based on " + }, + { + "bbox": [ + 46, + 597, + 287, + 646 + ], + "type": "inline_equation", + "content": "q(u)" + }, + { + "bbox": [ + 46, + 597, + 287, + 646 + ], + "type": "text", + "content": ", as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 89, + 652, + 287, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 652, + 287, + 682 + ], + "spans": [ + { + "bbox": [ + 89, + 652, + 287, + 682 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {R M P}} = \\frac {1}{T L B C W H} \\sum_ {t, l, b, c, w, h} q (u). \\tag {10}", + "image_path": "e6f5fc6e2d61f0d1294e8340e8f6115773f6725d3bc917937ceea278c1cb1572.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " denote the number of timesteps, the number of layers, batch size, channel length," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 72, + 500, + 84 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 500, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 500, + 84 + ], + "type": "text", + "content": "Algorithm 1 Training an SNN with RMP-Loss." + } + ] + } + ], + "index": 14, + "type": "text" + }, + { + "bbox": [ + 306, + 86, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 86, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 306, + 86, + 545, + 120 + ], + "type": "text", + "content": "Input: An SNN to be trained; Training dataset, total number of training epochs " + }, + { + "bbox": [ + 306, + 86, + 545, + 120 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 306, + 86, + 545, + 120 + ], + "type": "text", + "content": ", total number of training iterations per epoch " + }, + { + "bbox": [ + 306, + 86, + 545, + 120 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 306, + 86, + 545, + 120 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 121, + 416, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 121, + 416, + 132 + ], + "spans": [ + { + "bbox": [ + 306, + 121, + 416, + 132 + ], + "type": "text", + "content": "Output: The trained SNN." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 312, + 135, + 545, + 243 + ], + "type": "list", + "angle": 0, + "index": 24, + "blocks": [ + { + "bbox": [ + 312, + 135, + 482, + 147 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 135, + 482, + 147 + ], + "spans": [ + { + "bbox": [ + 312, + 135, + 482, + 147 + ], + "type": "text", + "content": "1: for All " + }, + { + "bbox": [ + 312, + 135, + 482, + 147 + ], + "type": "inline_equation", + "content": "n = 1,2,\\ldots ,N - 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Finally, taking classification loss into consideration, the total loss can be written as" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 357, + 434, + 545, + 445 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 434, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 357, + 434, + 545, + 445 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {C E} - \\mathrm {R M P}} = \\mathcal {L} _ {\\mathrm {C E}} + \\lambda (n) \\mathcal {L} _ {\\mathrm {R M P}}, \\tag {11}", + "image_path": "83e9bac9e67c6ed1e0fa6a9002f93c95017316981034d2d80174a46fa237339f.jpg" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 304, + 451, + 545, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 451, + 545, + 570 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 545, + 570 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 451, + 545, + 570 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{CE}" + }, + { + "bbox": [ + 304, + 451, + 545, + 570 + ], + "type": "text", + "content": " is the cross-entropy loss, and " + }, + { + "bbox": [ + 304, + 451, + 545, + 570 + ], + "type": "inline_equation", + "content": "\\lambda (n)" + }, + { + "bbox": [ + 304, + 451, + 545, + 570 + ], + "type": "text", + "content": " is a balanced coefficient, which changes dynamically with the training epoch. Obviously, " + }, + { + "bbox": [ + 304, + 451, + 545, + 570 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{RMP}" + }, + { + "bbox": [ + 304, + 451, + 545, + 570 + ], + "type": "text", + "content": " does not take into account the classification problem at hand and will add a new constraint in the network optimization. To make the network parameter update have enough freedom at the beginning, which is important to train a well-performance network, and still focus on the classification task at the end. We adopt a strategy of increasing first and decreasing later to adjust the " + }, + { + "bbox": [ + 304, + 451, + 545, + 570 + ], + "type": "inline_equation", + "content": "\\lambda (n)" + }, + { + "bbox": [ + 304, + 451, + 545, + 570 + ], + "type": "text", + "content": " as follows," + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 348, + 574, + 545, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 574, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 348, + 574, + 545, + 601 + ], + "type": "interline_equation", + "content": "\\lambda (n) = \\left\\{ \\begin{array}{l} 2 k \\frac {n}{N}, \\text {i f} n \\leq N / 2 \\\\ 2 k \\left(1 - \\frac {n}{N}\\right), \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {12}", + "image_path": "443284f480a0da2aa1b32701a1f9e69882db0f4b2cc118589170c67de71541ef.jpg" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 304, + 605, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 641 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 605, + 545, + 641 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 605, + 545, + 641 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 304, + 605, + 545, + 641 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 605, + 545, + 641 + ], + "type": "text", + "content": "-th epoch and " + }, + { + "bbox": [ + 304, + 605, + 545, + 641 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 605, + 545, + 641 + ], + "type": "text", + "content": " is a coefficient, which controls the amplitude of regularization. Unless otherwise specified, we set it as 0.1 in the paper." + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 305, + 641, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 641, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 305, + 641, + 545, + 665 + ], + "type": "text", + "content": "The final resulting RMP-Loss training method is defined in Algo. 1." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 306, + 671, + 444, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 444, + 683 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 444, + 683 + ], + "type": "text", + "content": "4.3. Analysis and Discussion" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "In this work, we assume that RMP-Loss can help reduce the quantization loss of the SNNs. To verify our assumption, we first consider a linear model with a single input " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " and a single output " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": ". Then, we use the following linear model to obtain the output " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " from the input " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 39 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17394" + } + ] + } + ], + "index": 40 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "tion, a theoretical analysis is conducted by using the information entropy concept. To mitigate the information loss, the output spike tensor " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "\\mathbf{O}" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": " should reflect the information of the membrane potential tensor " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": " as much as possible. Since KL-divergence is a metric to measure the difference between two random variable distributions. We use KLdivergence to compute the difference between " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "\\mathbf{O}" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": ", which refers to the difficulty of reconstructing " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "\\mathbf{O}" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": ", i.e., information loss degree. Then we provide the theoretical analysis below." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "spans": [ + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "inline_equation", + "content": "x^u\\sim \\mathcal{U}" + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "inline_equation", + "content": "x^{u}" + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "text", + "content": " are samples " + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "inline_equation", + "content": "\\in \\mathbf{U}" + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "text", + "content": " represents the distribution of " + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "inline_equation", + "content": "x^{u}" + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "text", + "content": ". Similarly, we have " + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "inline_equation", + "content": "x^{o}\\sim \\mathcal{O}" + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "inline_equation", + "content": "x^{o}\\in \\mathbf{O}" + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "text", + "content": ". We use " + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "inline_equation", + "content": "P_U(x)" + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "inline_equation", + "content": "P_O(x)" + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "text", + "content": " to denote the probability density function for " + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 47, + 192, + 287, + 252 + ], + "type": "text", + "content": ", respectively. Then the information loss for the spike firing process can be described as" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 68, + 259, + 287, + 287 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 259, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 68, + 259, + 287, + 287 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {K L} (\\mathcal {U} | | \\mathcal {O}) = \\int_ {- \\infty} ^ {\\infty} P _ {U} \\left(x ^ {u}\\right) \\log \\frac {P _ {U} \\left(x ^ {u}\\right)}{P _ {O} \\left(x ^ {o}\\right)} d x. \\tag {13}", + "image_path": "d72eb4764d601c33a8f794ecfbf6245c8e610b1008971e96470deace9539017f.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 294, + 261, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 294, + 261, + 306 + ], + "spans": [ + { + "bbox": [ + 47, + 294, + 261, + 306 + ], + "type": "text", + "content": "Since output spike " + }, + { + "bbox": [ + 47, + 294, + 261, + 306 + ], + "type": "inline_equation", + "content": "x^{o}" + }, + { + "bbox": [ + 47, + 294, + 261, + 306 + ], + "type": "text", + "content": " is discrete, we can update it as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 65, + 314, + 287, + 342 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 314, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 65, + 314, + 287, + 342 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {K L} (\\mathcal {U} \\| \\mathcal {O}) = \\int_ {o - \\epsilon} ^ {o + \\epsilon} P _ {U} \\left(x ^ {u}\\right) \\log \\frac {P _ {U} \\left(x ^ {u}\\right)}{P _ {O} \\left(x ^ {o}\\right)} d x, \\tag {14}", + "image_path": "53e44c62f779dbc194ff6f897a7851cf3912987fc73c7d5648b62de850e6640d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 350, + 287, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 350, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 47, + 350, + 287, + 388 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 350, + 287, + 388 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 47, + 350, + 287, + 388 + ], + "type": "text", + "content": " is a small constant, " + }, + { + "bbox": [ + 47, + 350, + 287, + 388 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 47, + 350, + 287, + 388 + ], + "type": "text", + "content": " is the spike value, " + }, + { + "bbox": [ + 47, + 350, + 287, + 388 + ], + "type": "inline_equation", + "content": "P_O(x^o)" + }, + { + "bbox": [ + 47, + 350, + 287, + 388 + ], + "type": "text", + "content": " can be seen as a very large constant in this situation, and " + }, + { + "bbox": [ + 47, + 350, + 287, + 388 + ], + "type": "inline_equation", + "content": "\\int_{o - \\epsilon}^{o + \\epsilon}P_O(x^o)dx = 1" + }, + { + "bbox": [ + 47, + 350, + 287, + 388 + ], + "type": "text", + "content": ". With RMP-Loss, it will become" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 65, + 398, + 287, + 426 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 398, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 65, + 398, + 287, + 426 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {K L} (\\hat {\\mathcal {U}} | | \\mathcal {O}) = \\int_ {o - \\epsilon} ^ {o + \\epsilon} P _ {\\hat {U}} (x ^ {\\hat {u}}) \\log \\frac {P _ {\\hat {U}} (x ^ {\\hat {u}})}{P _ {O} (x ^ {o})} d x, \\tag {15}", + "image_path": "5ddc12881df2c06ba47ec3e5e4ed551d18ea77b1d50be09bfb77c645501908a9.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 435, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 287, + 460 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 435, + 287, + 460 + ], + "type": "inline_equation", + "content": "x^{\\hat{u}} \\in \\hat{\\mathcal{U}}" + }, + { + "bbox": [ + 46, + 435, + 287, + 460 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 435, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{U}}" + }, + { + "bbox": [ + 46, + 435, + 287, + 460 + ], + "type": "text", + "content": " is the new distribution of " + }, + { + "bbox": [ + 46, + 435, + 287, + 460 + ], + "type": "inline_equation", + "content": "x^{\\hat{u}}" + }, + { + "bbox": [ + 46, + 435, + 287, + 460 + ], + "type": "text", + "content": " adjusted by RMP-Loss. Here, we have the following propositions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 460, + 268, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 460, + 268, + 473 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 268, + 473 + ], + "type": "text", + "content": "Proposition 1 " + }, + { + "bbox": [ + 47, + 460, + 268, + 473 + ], + "type": "inline_equation", + "content": "\\frac{d\\mathcal{L}_{KL}}{dP_U(x^u)} < 0" + }, + { + "bbox": [ + 47, + 460, + 268, + 473 + ], + "type": "text", + "content": " i.e., " + }, + { + "bbox": [ + 47, + 460, + 268, + 473 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{KL}\\downarrow asP_U(x^u)\\uparrow" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 473, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 287, + 533 + ], + "type": "text", + "content": "Proof: When a membrane potential " + }, + { + "bbox": [ + 46, + 473, + 287, + 533 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 473, + 287, + 533 + ], + "type": "text", + "content": " is below the firing threshold, it will be pushed to 0 by the RMP-Loss, considering its effect, and otherwise, 1. Hence the firing rate of the neuron can be seen as the same, whether using the RMP-Loss or not, i.e., " + }, + { + "bbox": [ + 46, + 473, + 287, + 533 + ], + "type": "inline_equation", + "content": "P_O(x^o)" + }, + { + "bbox": [ + 46, + 473, + 287, + 533 + ], + "type": "text", + "content": " keep the same for " + }, + { + "bbox": [ + 46, + 473, + 287, + 533 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{U}}" + }, + { + "bbox": [ + 46, + 473, + 287, + 533 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 473, + 287, + 533 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 46, + 473, + 287, + 533 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 70, + 541, + 287, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 541, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 70, + 541, + 287, + 601 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\frac {d \\mathcal {L} _ {K L}}{d P _ {U} \\left(x ^ {u}\\right)} = \\frac {d \\int_ {o - \\epsilon} ^ {o + \\epsilon} P _ {U} \\left(x ^ {u}\\right) \\log \\frac {P _ {U} \\left(x ^ {u}\\right)}{P _ {O} \\left(x ^ {o}\\right)} d x}{d P _ {U} \\left(x ^ {u}\\right)} (16) \\\\ = \\int_ {o - \\epsilon} ^ {o + \\epsilon} \\left(\\log \\frac {P _ {U} \\left(x ^ {u}\\right)}{P _ {O} \\left(x ^ {o}\\right)} + \\frac {1}{\\ln 2}\\right) d x. (17) \\\\ \\end{array}", + "image_path": "348ae2dd3b3c216bdab65142d0aec2d140029f6b38815e5c8be89284ff064a22.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 609, + 287, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 287, + 638 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 287, + 638 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 47, + 609, + 287, + 638 + ], + "type": "inline_equation", + "content": "P_O(x^o)" + }, + { + "bbox": [ + 47, + 609, + 287, + 638 + ], + "type": "text", + "content": " is much larger than " + }, + { + "bbox": [ + 47, + 609, + 287, + 638 + ], + "type": "inline_equation", + "content": "P_U(x^u)" + }, + { + "bbox": [ + 47, + 609, + 287, + 638 + ], + "type": "text", + "content": ", we can get " + }, + { + "bbox": [ + 47, + 609, + 287, + 638 + ], + "type": "inline_equation", + "content": "\\int_{o - \\epsilon}^{o + \\epsilon} (\\log \\frac{P_U(x^u)}{P_O(x^o)} + \\frac{1}{\\ln 2}) dx < 0" + }, + { + "bbox": [ + 47, + 609, + 287, + 638 + ], + "type": "text", + "content": ", then " + }, + { + "bbox": [ + 47, + 609, + 287, + 638 + ], + "type": "inline_equation", + "content": "\\frac{d\\mathcal{L}_{KL}}{dP_U(x^u)} < 0" + }, + { + "bbox": [ + 47, + 609, + 287, + 638 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 638, + 220, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 638, + 220, + 651 + ], + "spans": [ + { + "bbox": [ + 47, + 638, + 220, + 651 + ], + "type": "text", + "content": "Proposition 2 " + }, + { + "bbox": [ + 47, + 638, + 220, + 651 + ], + "type": "inline_equation", + "content": "P_{\\hat{U}}(x^{\\hat{u}}) > P_{U}(x^{u})|x = o." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "type": "text", + "content": "Proof: We assume that there are " + }, + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "type": "inline_equation", + "content": "n_{\\epsilon}^{u}" + }, + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "type": "text", + "content": " samples in the interval " + }, + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "type": "inline_equation", + "content": "(o - \\epsilon, o + \\epsilon)" + }, + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "type": "text", + "content": " is a small constant. Then we can get " + }, + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "type": "inline_equation", + "content": "P_U(x^u) \\approx \\frac{n_{\\epsilon}^u}{2\\epsilon}" + }, + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "type": "text", + "content": ". And we can simply see the RMP-Loss as a function to push the vanilla " + }, + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{U}}" + }, + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "type": "text", + "content": ", which is closer to " + }, + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{O}" + }, + { + "bbox": [ + 46, + 651, + 287, + 712 + ], + "type": "text", + "content": ", based on its effect. Therefore, we can assume that" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 72, + 545, + 113 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 113 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 113 + ], + "type": "text", + "content": "these samples will be gathered to a new interval " + }, + { + "bbox": [ + 305, + 72, + 545, + 113 + ], + "type": "inline_equation", + "content": "(o - \\epsilon_l, o + \\epsilon_r)" + }, + { + "bbox": [ + 305, + 72, + 545, + 113 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 72, + 545, + 113 + ], + "type": "inline_equation", + "content": "\\epsilon_l, \\epsilon_r < \\epsilon" + }, + { + "bbox": [ + 305, + 72, + 545, + 113 + ], + "type": "text", + "content": ". Then we can get " + }, + { + "bbox": [ + 305, + 72, + 545, + 113 + ], + "type": "inline_equation", + "content": "P_{\\hat{U}(x^{\\hat{u}})} \\approx \\frac{n_\\epsilon^u}{\\epsilon_l + \\epsilon_r}" + }, + { + "bbox": [ + 305, + 72, + 545, + 113 + ], + "type": "text", + "content": ". Thereby we can have " + }, + { + "bbox": [ + 305, + 72, + 545, + 113 + ], + "type": "inline_equation", + "content": "P_{\\hat{U}(x^{\\hat{u}})} > P_U(x^u)|_{x = o}" + }, + { + "bbox": [ + 305, + 72, + 545, + 113 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 112, + 545, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 112, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 305, + 112, + 545, + 148 + ], + "type": "text", + "content": "Along with Proposition 1 and Proposition 2, we can conclude that " + }, + { + "bbox": [ + 305, + 112, + 545, + 148 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{KL}(\\hat{U} ||O) < \\mathcal{L}_{KL}(U||O)" + }, + { + "bbox": [ + 305, + 112, + 545, + 148 + ], + "type": "text", + "content": ", i.e., our method with RMP-Loss enjoys lesser information loss." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 160, + 382, + 174 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 160, + 382, + 174 + ], + "spans": [ + { + "bbox": [ + 306, + 160, + 382, + 174 + ], + "type": "text", + "content": "5. Experiment" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 182, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 182, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 545, + 263 + ], + "type": "text", + "content": "In this section, we first conducted extensive ablation studies to compare the SNNs with RMP-Loss and their vanilla counterparts to verify the effectiveness of the method. Next, we fully compared our method with other state-of-the-art (SoTA) methods. Finally, some further experimental visualizations are provided to understand the RMP-Loss." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 274, + 429, + 288 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 274, + 429, + 288 + ], + "spans": [ + { + "bbox": [ + 306, + 274, + 429, + 288 + ], + "type": "text", + "content": "5.1. Datasets and Settings" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 293, + 545, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 545, + 425 + ], + "type": "text", + "content": "Datasets. We conducted experiments on four benchmark datasets: CIFAR-10 (100) [33], CIFAR10-DVS [35], and ImageNet (ILSVRC12) [10]. The CIFAR-10 (100) dataset includes 60,000 images in 10 (100) classes with " + }, + { + "bbox": [ + 304, + 293, + 545, + 425 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 304, + 293, + 545, + 425 + ], + "type": "text", + "content": " pixels. The numbers of training images and test images are 50,000 and 10,000. The CIFAR10-DVS dataset is the neuromorphic version of the CIFAR-10 dataset. It is composed of 10,000 images in 10 classes. We split the dataset into 9000 training images and 1000 test images similar to [52]. ImageNet dataset consists of 1,250,000 training images and 50,000 test images." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 426, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 557 + ], + "type": "text", + "content": "Preprocessing. We applied data normalization on all static datasets to make input images have 0 mean and 1 variance. Besides, we conducted random horizontal flipping and cropping on these datasets to avoid overfitting. For CIFAR, the AutoAugment [8] and Cutout [13] were also used for data augmentation as doing in [24, 20]. For the neuromorphic dataset, we resized the training image frames to " + }, + { + "bbox": [ + 304, + 426, + 545, + 557 + ], + "type": "inline_equation", + "content": "48 \\times 48" + }, + { + "bbox": [ + 304, + 426, + 545, + 557 + ], + "type": "text", + "content": " as in [62] and adopted random horizontal flip and random roll within 5 pixels for augmentation. And the test images were merely resized to " + }, + { + "bbox": [ + 304, + 426, + 545, + 557 + ], + "type": "inline_equation", + "content": "48 \\times 48" + }, + { + "bbox": [ + 304, + 426, + 545, + 557 + ], + "type": "text", + "content": " without any additional processing." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "Training setup. For all the datasets, the firing threshold " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{th}}" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " was set as 0.5. For static image datasets, the images were encoded to binary spike using the first layer of the SNN, as in recent works [47, 17, 16]. This is similar to rate coding. For the neuromorphic image dataset, we used the 0/1 spike format directly. The neuron models in the output layer accumulated the incoming inputs without generating any spike as the output like in [47]. For CIFAR-10 (100) and CIFAR10-DVS datasets, we used the SGD optimizer with the momentum of 0.9 and learning rate of 0.01 with cosine decayed [40] to 0 as in [21]. All models were trained within 400 epochs with the same batch size of 128. For the ImageNet dataset, we adopted the SGD optimizer with" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17395" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 93, + 91, + 500, + 188 + ], + "blocks": [ + { + "bbox": [ + 217, + 71, + 376, + 83 + ], + "lines": [ + { + "bbox": [ + 217, + 71, + 376, + 83 + ], + "spans": [ + { + "bbox": [ + 217, + 71, + 376, + 83 + ], + "type": "text", + "content": "Table 1: Ablation Study for RMP-Loss" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 93, + 91, + 500, + 188 + ], + "lines": [ + { + "bbox": [ + 93, + 91, + 500, + 188 + ], + "spans": [ + { + "bbox": [ + 93, + 91, + 500, + 188 + ], + "type": "table", + "html": "
DatasetArchitectureTypeTimestepAccuracyQuantization error
CIFAR-10ResNet20Without RMP-Loss491.26%0.186
With RMP-Loss491.89%0.121
ResNet19Without RMP-Loss495.04%0.128
With RMP-Loss495.51%0.104
VGG16Without RMP-Loss492.80%0.174
With RMP-Loss493.33%0.135
", + "image_path": "1a17c849bb2ae1ef60b14e240e0263c24ae31b6b8b44b90850fb178e48ca2cdc.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 207, + 288, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 207, + 288, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 207, + 288, + 232 + ], + "type": "text", + "content": "a momentum of 0.9 and a learning rate of 0.1 with cosine decayed to 0. All models are trained within 320 epochs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 239, + 211, + 252 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 211, + 252 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 211, + 252 + ], + "type": "text", + "content": "5.2. Ablation Study for RMP-Loss" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 258, + 288, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 288, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 288, + 378 + ], + "type": "text", + "content": "We conducted a set of ablation experiments on CIFAR-10 using ResNet20, ResNet19, and VGG16 as backbones. The results are shown in Tab. 1. It can be seen that with the RMP-Loss, these SNNs can achieve higher accuracy than their vanilla counterparts. We also show the membrane potential distribution of the first layer of the second block in the ResNet20 with and without RMP-Loss on the test set of CIFAR-10 in Fig. 2. It can be seen that the models trained with RMP-Loss can shrink the membrane potential distribution range which enjoys less quantization error." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 60, + 399, + 167, + 479 + ], + "blocks": [ + { + "bbox": [ + 60, + 399, + 167, + 479 + ], + "lines": [ + { + "bbox": [ + 60, + 399, + 167, + 479 + ], + "spans": [ + { + "bbox": [ + 60, + 399, + 167, + 479 + ], + "type": "image", + "image_path": "fd640d50c0ba50ab93102761c751ca3fdd18f36b440a35f18de86eb040735164.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 493, + 288, + 553 + ], + "lines": [ + { + "bbox": [ + 46, + 493, + 288, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 493, + 288, + 553 + ], + "type": "text", + "content": "Figure 2: The effect of RMP-Loss. The overall original membrane potential distribution (left) and the redistributed membrane potential distribution by RMP-Loss (right) of the first layer of the second block in ResNet20 on CIFAR-10 test sets." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 184, + 399, + 290, + 479 + ], + "blocks": [ + { + "bbox": [ + 184, + 399, + 290, + 479 + ], + "lines": [ + { + "bbox": [ + 184, + 399, + 290, + 479 + ], + "spans": [ + { + "bbox": [ + 184, + 399, + 290, + 479 + ], + "type": "image", + "image_path": "a366d32d76c28737a96fda340ef8744f76ebfc4070f7f7f0318c1b374a0e8f13.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 574, + 270, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 270, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 270, + 588 + ], + "type": "text", + "content": "5.3. Comparison with State-of-the-art Methods" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 594, + 286, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 664 + ], + "type": "text", + "content": "We evaluated the proposed method with the accuracy performance on various widely used static and neuromorphic datasets using spiking ResNet20 [47, 48], VGG16 [47], ResNet18 [16], ResNet19 [62], and ResNet34 [16]. The results with the mean accuracy and standard deviation of 3-trials are listed in Tab. 2." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "CIFAR-10. For CIFAR-10, we tested three different network architectures. The performance of our method is shown in Tab. 2. It can be seen that our method achieves the best results in most of these cases. In special, us" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 207, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 207, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 304, + 207, + 545, + 327 + ], + "type": "text", + "content": "ing ResNet19 [62], the RMP-Loss achieves " + }, + { + "bbox": [ + 304, + 207, + 545, + 327 + ], + "type": "inline_equation", + "content": "96.10\\%" + }, + { + "bbox": [ + 304, + 207, + 545, + 327 + ], + "type": "text", + "content": " averaged top-1 accuracy, which improves " + }, + { + "bbox": [ + 304, + 207, + 545, + 327 + ], + "type": "inline_equation", + "content": "1.60\\%" + }, + { + "bbox": [ + 304, + 207, + 545, + 327 + ], + "type": "text", + "content": " absolute accuracy compared with the existing state-of-the-art TET [12]. Though InfLoR-SNN [21] is slightly better than our method for 4 and 6 timesteps, it will decrease the biological plausibility of the SNN and increase the inference burden since a complex transform function is added in its spiking neuron. On ResNet20, our method can achieve higher accuracy with only 6 timesteps, while Diet-SNN [47] with 10 timesteps. On VGG16, the RMP-Loss also shows obvious advantages." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 327, + 546, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 546, + 508 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 546, + 508 + ], + "type": "text", + "content": "CIFAR-100. For CIFAR-100, we also experimented with these three different network structures. For all these configurations, our method achieves consistent and significant accuracy over prior work. ResNet20-based and VGG16-based RMP-Loss achieve " + }, + { + "bbox": [ + 304, + 327, + 546, + 508 + ], + "type": "inline_equation", + "content": "66.65\\%" + }, + { + "bbox": [ + 304, + 327, + 546, + 508 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 327, + 546, + 508 + ], + "type": "inline_equation", + "content": "72.55\\%" + }, + { + "bbox": [ + 304, + 327, + 546, + 508 + ], + "type": "text", + "content": " top-1 accuracy with only 4 timesteps, which outperform their Diet-SNN counterparts with " + }, + { + "bbox": [ + 304, + 327, + 546, + 508 + ], + "type": "inline_equation", + "content": "2.58\\%" + }, + { + "bbox": [ + 304, + 327, + 546, + 508 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 327, + 546, + 508 + ], + "type": "inline_equation", + "content": "2.88\\%" + }, + { + "bbox": [ + 304, + 327, + 546, + 508 + ], + "type": "text", + "content": " higher accuracy and Real spike counterparts with " + }, + { + "bbox": [ + 304, + 327, + 546, + 508 + ], + "type": "inline_equation", + "content": "0.05\\%" + }, + { + "bbox": [ + 304, + 327, + 546, + 508 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 327, + 546, + 508 + ], + "type": "inline_equation", + "content": "1.93\\%" + }, + { + "bbox": [ + 304, + 327, + 546, + 508 + ], + "type": "text", + "content": " respectively but with fewer timesteps. Noteworthy, our method significantly surpasses TET with " + }, + { + "bbox": [ + 304, + 327, + 546, + 508 + ], + "type": "inline_equation", + "content": "4.26\\%" + }, + { + "bbox": [ + 304, + 327, + 546, + 508 + ], + "type": "text", + "content": " higher accuracy on ResNet19, which is not easy to achieve in the SNN field. Overall, our results on CIFAR-100 show that, when applied to a more complex dataset, the RMP-Loss achieves an even more favorable performance compared to competing methods." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "text", + "content": "CIFAR10-DVS. We also verified our method on the popular neuromorphic dataset, CIFAR10-DVS. It can be seen that RMP-Loss also shows amazing performance. RMP-Loss outperforms STBP-tdBN by " + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "inline_equation", + "content": "12.39\\%" + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "text", + "content": ", RecDis-SNN by " + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "inline_equation", + "content": "3.78\\%" + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "text", + "content": ", and InfLoR-SNN by " + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "inline_equation", + "content": "0.70\\%" + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "text", + "content": " respectively with " + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "inline_equation", + "content": "76.20\\%" + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "text", + "content": " top-1 accuracy in 10 timesteps using ResNet19 as the backbone. With ResNet20 as the backbone, RMP-Loss can also achieve well-performed results." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": "ImageNet. For ImageNet, we conducted experiments with ResNet18 and ResNet34 as backbones. Our results are presented in Tab. 4. In these normal spiking structures, our method achieves the highest accuracy among these SoTA prior works. However, our method is slightly worse than SEW ResNet [16]. This is because that SEW ResNet uses an atypical architecture, which abandons binary spike forms but will output arbitrary integers to transmit information, thus enjoying higher accuracy but the efficiency from mul" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17396" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 102, + 91, + 493, + 644 + ], + "blocks": [ + { + "bbox": [ + 173, + 70, + 420, + 83 + ], + "lines": [ + { + "bbox": [ + 173, + 70, + 420, + 83 + ], + "spans": [ + { + "bbox": [ + 173, + 70, + 420, + 83 + ], + "type": "text", + "content": "Table 2: Comparison with SoTA methods on CIFAR-10/100." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 102, + 91, + 493, + 644 + ], + "lines": [ + { + "bbox": [ + 102, + 91, + 493, + 644 + ], + "spans": [ + { + "bbox": [ + 102, + 91, + 493, + 644 + ], + "type": "table", + "html": "
DatasetMethodTypeArchitectureTimestepAccuracy
CIFAR-10STBP [52]SNN trainingCIFARNet1290.53%
TSSL-BP [60]SNN trainingCIFARNet591.41%
PLIF [17]SNN trainingPLIFNet893.50%
DSR [41]SNN trainingResNet182095.40%
Joint A-SNN [23]SNN trainingResNet18495.45%
Diet-SNN [47]SNN trainingVGG16592.70%
1093.44%
ResNet20591.78%
1092.54%
RecDis-SNN [24]SNN trainingResNet19293.64%
495.53%
695.55%
STBP-tdBN [62]SNN trainingResNet19292.34%
492.92%
693.16%
TET [12]SNN trainingResNet19294.16%
494.44%
694.50%
InfLoR-SNN [21]SNN trainingResNet19294.44%
496.27%
696.49%
RMP-LossSNN trainingResNet19295.31%±0.07
495.51%±0.08
696.10%±0.08
ResNet20491.89%±0.05
692.55%±0.06
VGG16493.33%±0.07
1094.39%±0.08
CIFAR-100DSR [41]SNN trainingResNet182078.50%
InfLoR-SNN [21]SNN trainingVGG16571.56%
IM-Loss [20]SNN trainingVGG16570.18%
Diet-SNN [47]SNN trainingResNet20564.07%
VGG16569.67%
Real Spike [25]SNN trainingResNet20566.60%
VGG16570.62%
TET [12]SNN trainingResNet19272.87%
474.47%
674.72%
RMP-LossSNN trainingResNet20466.65%±0.10
VGG16472.55%±0.08
1073.30%±0.11
ResNet19274.66%±0.12
478.28%±0.10
678.98%±0.08
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DatasetMethodTypeArchitectureTimestepAccuracy
CIFAR10-DVSSTBP-tdBN [62]SNN trainingResNet191067.80%
LIAF [53]Conv3DLIAF-Net1071.70%
LIAF [53]LIAFLIAF-Net1070.40%
RecDis-SNN [24]SNN trainingResNet191072.42%
InfLoR-SNN [21]SNN trainingResNet191075.50%
ResNet201075.10%
RMP-LossSNN trainingResNet191076.20%±0.20
ResNet201075.60%±0.30
", + "image_path": "2a4072155043db1c9f6b0303681554e1335e8a057cb7a44c2b42f6ef39c7cbc9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 99, + 243, + 496, + 364 + ], + "blocks": [ + { + "bbox": [ + 183, + 221, + 408, + 234 + ], + "lines": [ + { + "bbox": [ + 183, + 221, + 408, + 234 + ], + "spans": [ + { + "bbox": [ + 183, + 221, + 408, + 234 + ], + "type": "text", + "content": "Table 4: Comparison with SoTA methods on ImageNet." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 99, + 243, + 496, + 364 + ], + "lines": [ + { + "bbox": [ + 99, + 243, + 496, + 364 + ], + "spans": [ + { + "bbox": [ + 99, + 243, + 496, + 364 + ], + "type": "table", + "html": "
MethodTypeArchitectureTimestepSpike formAccuracy
STBP-tdBN [62]SNN trainingResNet346Binary63.72%
TET [12]SNN trainingResNet346Binary64.79%
SEW ResNet [16]SNN trainingResNet184Integer63.18%
ResNet344Integer67.04%
Spiking ResNet [16]SNN trainingResNet184Binary62.32%
ResNet344Binary61.86%
RMP-LossSNN trainingResNet184Binary63.03%±0.07
ResNet344Binary65.17%±0.07
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It can be seen that the SNN models trained with RMP-Loss can shrink" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 383, + 547, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 383, + 547, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 383, + 547, + 502 + ], + "type": "text", + "content": "the membrane potential distribution range which enjoys less quantization error. On the other hand, comparing the membrane potential distribution difference between ResNet20 and ResNet19, it can be found that the membrane potential distribution of ResNet19 is thinner than that of ResNet20 too. Considering that ResNet19 can achieve higher accuracy than ResNet20, it also shows that reducing quantization error is effective to improve the accuracy of SNN models and our route to improve the SNN accuracy by reducing the quantization error is reasonable." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 515, + 378, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 378, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 378, + 528 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 536, + 547, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 536, + 547, + 644 + ], + "spans": [ + { + "bbox": [ + 304, + 536, + 547, + 644 + ], + "type": "text", + "content": "This paper aims at addressing the information loss problem caused by the " + }, + { + "bbox": [ + 304, + 536, + 547, + 644 + ], + "type": "inline_equation", + "content": "0/1" + }, + { + "bbox": [ + 304, + 536, + 547, + 644 + ], + "type": "text", + "content": " spike quantization of SNNs. We introduce RMP-Loss to adjust the membrane potential to reduce the quantization error. Different from other methods that reduce the quantization error indirectly or will induce more parameters, RMP-Loss focuses on handling this problem directly and will introduce no extra parameters in the inference phase. We show that our method outperforms SoTA methods on both static and neuromorphic datasets." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 657, + 399, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 657, + 399, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 657, + 399, + 670 + ], + "type": "text", + "content": "Acknowledgment" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "type": "text", + "content": "This work is supported by grants from the National Natural Science Foundation of China under contracts No.12202412 and No.12202413." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17398" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] F. 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Neural architecture search with reinforcement learning, 2016. 1" + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "17401" + } + ] + } + ], + "index": 5 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/ROME_ Robustifying Memory-Efficient NAS via Topology Disentanglement and Gradient Accumulation/6ade4227-5686-42c9-830e-da85efbc5dca_content_list.json b/2023/ROME_ Robustifying Memory-Efficient NAS via Topology Disentanglement and Gradient Accumulation/6ade4227-5686-42c9-830e-da85efbc5dca_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..4ae05220cdd0f608a33d074b7c282db82519b1e6 --- /dev/null +++ b/2023/ROME_ Robustifying Memory-Efficient NAS via Topology Disentanglement and Gradient Accumulation/6ade4227-5686-42c9-830e-da85efbc5dca_content_list.json @@ -0,0 +1,1984 @@ +[ + { + "type": "text", + "text": "ROME: Robustifying Memory-Efficient NAS via Topology Disentanglement and Gradient Accumulation", + "text_level": 1, + "bbox": [ + 81, + 128, + 888, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xiaoxing Wang\\*, Xiangxiang Chu\\*, Yuda Fan\\*, Zhexi Zhang\\*, Bo Zhang\\*, Xiaokang Yang\\*, and Junchi Yan", + "bbox": [ + 94, + 214, + 875, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Dep. of Computer Science and Engineering & MoE Key Lab of AI, Shanghai Jiao Tong University $^{2}$ Meituan", + "bbox": [ + 91, + 263, + 879, + 297 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 340, + 313, + 358 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Albeit being a prevalent architecture searching approach, differentiable architecture search (DARTS) is largely hindered by its substantial memory cost since the entire supernet resides in the memory. This is where the single-path DARTS comes in, which only chooses a single-path submodel at each step. While being memory-friendly, it also comes with low computational costs. Nonetheless, we discover a critical issue of single-path DARTS that has not been primarily noticed. Namely, it also suffers from severe performance collapse since too many parameter-free operations like skip connections are derived, just like DARTS does. In this paper, we propose a new algorithm called RObustifying Memory-Efficient NAS (ROME) to give a cure. First, we disentangle the topology search from the operation search to make searching and evaluation consistent. We then adopt Gumbel-Top2 reparameterization and gradient accumulation to robustify the unwieldy bi-level optimization. We verify ROME extensively across 15 benchmarks to demonstrate its effectiveness and robustness.", + "bbox": [ + 75, + 372, + 473, + 660 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 686, + 209, + 703 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the fast development of neural architecture search (NAS) [52] to aid network design in vision tasks like classification [32, 6, 41, 42], object detection [11, 36], and segmentation [22], there has been an urging demand for faster searching algorithms. Early methods based on the evaluation of a huge number of candidate models [52, 31, 16] require unaffordable costs (typically 2k GPU days). In the light of weight-sharing mechanism introduced in SMASH [2], a variety of low-cost approaches have emerged [1, 27, 24]. DARTS [24] has taken the dominance with a myriad of follow-up works [38, 3, 39, 10, 5, 47]. In", + "bbox": [ + 75, + 712, + 470, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "this paper, we investigate a single-path based variation of DARTS, typically GDAS [10], for its fast speed and low GPU memory.", + "bbox": [ + 500, + 342, + 893, + 387 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unlike many DARTS variants that have to perform all candidate operations, single-path methods [30, 10, 39], also termed as memory-efficient $\\mathrm{NAS}^1$ , are developed to sample and activate only a subset of operations in the supernet. For differentiable search, Gumbel-Softmax reparameterization tricks [17, 25] are generally employed [38, 10, 39].", + "bbox": [ + 496, + 388, + 892, + 479 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we show that single-path methods also suffer from severe performance collapse where many parameterless operations accumulate, akin to that of DARTS as broadly discussed in [48, 4, 39, 8, 20]. We propose a robust algorithm called ROME to resolve this issue.", + "bbox": [ + 496, + 479, + 893, + 555 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We observe that single-path methods usually intertwine topology search with operation search, which creates inconsistency between searching and evaluation. We first disentangle the two from each other. Specifically, in addition to the existing architectural parameters $(\\alpha)$ that represent the significance of each operation, we involve topology parameters $(\\beta)$ to denote the relative importance of edges. A single-path architecture can then be induced by both $\\alpha$ and $\\beta$ . Moreover, to further robustify the searching process, we propose a gradient accumulation strategy during the bilevel optimization. We sketch the framework of ROME in Fig. 1. In a nutshell, our contributions are,", + "bbox": [ + 496, + 556, + 893, + 736 + ], + "page_idx": 0 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1) Revealing performance collapse in single-path differentiable NAS. Similar to the performance collapse problem in DARTS, the architectures searched by single-path based methods can also be dominated by parameterless operations, especially skip connections. However, this issue hasn't been deeply explored, which motivates us to propose a new robust, lower memory cost and search cost method.", + "2) Consistent search and evaluation by disentangling topology search from operation selection. We introduce" + ], + "bbox": [ + 496, + 738, + 893, + 875 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution, † Correspondence author.", + "bbox": [ + 94, + 886, + 344, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1We interchangeably use the term 'single-path' and 'memory-efficient'.", + "bbox": [ + 517, + 886, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5939", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/510a98dc79c64467dc83d6cf82d97ed64bc1db16539c218fa3a17ec8b5f6f226.jpg", + "image_caption": [ + "Figure 1: ROME (v2): Gumbel-Top2 is devised to sample edges to satisfy the restriction that each node has in-degree 2. Subnetworks apply forward and backward independently. Gradients are accumulated to update the supernet weights at once." + ], + "image_footnote": [], + "bbox": [ + 166, + 89, + 816, + 333 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "independent topology parameters to unwind topology from operations, which avoids structure inconsistency between the search and evaluation stage. We further devise Gumbel-Top2 re-parameterization to make our method differentiable and provide its theoretical validity. To our best knowledge, this is the first work to achieve consistent search and evaluation for single-path differentiable NAS.", + "bbox": [ + 75, + 386, + 470, + 491 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "3) Robustifying bi-level optimization via gradient accumulation. We devise two gradient accumulation techniques to address the aforementioned issue. One helps fair training for each candidate operations. The other instead reduces the estimation variance on architectural weights.", + "4) Strong performance while maintaining low memory cost. Tested on the popular settings² for NAS [48, 21, 6], our approach achieves state-of-the-art on various search spaces and datasets across 15 benchmarks. Our approach is fast, robust, and memory efficient. Compared with GDAS and PC-DARTS, our approach costs $26\\%$ and $38\\%$ lower memory in the standard search space of DARTS respectively. The source code will be made publicly available." + ], + "bbox": [ + 75, + 492, + 470, + 690 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 702, + 218, + 718 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Differentiable Neural Architecture Search. Similar to [53, 27] that uses a directed acyclic graph to represent a cell, DARTS [24] constructs a cell-based supernet and further introduces architectural weights to represent the importance of each operation. DARTS proposes two types (first-order and second-order) of approximation that alternatively update operation parameters and architectural weights with stochastic gradient descent. However, since the supernet subsumes all connections and operations within the search", + "bbox": [ + 75, + 728, + 468, + 864 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "space, DARTS risks exhausting GPU memory. A possible attempt to resolve this issue is done by progressively pruning operations [5], which is still an indirect approach and requires strong regularization tricks. Apart from that, recent works [48, 4] also point out an instability phenomenon of DARTS. These issues significantly restrict its application.", + "bbox": [ + 496, + 386, + 890, + 477 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Memory-efficient NAS. To reduce GPU memory cost, several prior works have revised the forward procedure of the supernet. PC-DARTS [40] makes use of partial connections instead of the full-fledged supernet. Some works [37, 36, 35] proposes to merge all parametric operations into one convolution, a similar super-kernel strategy is also used in single-path NAS [30]. ProxylessNAS [3] samples two operations on each edge during the search process, which enables proxyless searching on large datasets. Single-path supernets like SPOS [13] and FairNAS [7] sample only a single path at each iteration, however, both require an additional searching stage to choose the final models. Single-path differentiable methods like GDAS [10] sample a subgraph of the DAG at each iteration, which is by far the most efficient. However, we observe that a severe instability issue occurs, which has been previously neglected.", + "bbox": [ + 496, + 477, + 892, + 718 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Performance collapse of DARTS. The collapse issue is one of the most critical problems in differentiable architecture search [20, 40, 8, 4, 48]. It has been shown that DARTS [24] prefers to choose parameterless operations, leading to its performance collapse [20, 8]. Recent works [48, 4] utilize the eigenvalue of the Hessian matrix as an indicator of collapse and design various techniques to regularize high eigenvalues. Instead, other works [20, 5] directly constrain the number of skip connections as 2 to avoid collapse. Nonetheless, the previous methods are specifically designed for the full-path training scheme. Whereas the collapse problem in single-path has been rarely studied.", + "bbox": [ + 496, + 719, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "2Independently search under different random seeds instead of multiple training of a single best-searched model.", + "bbox": [ + 75, + 875, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5940", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/681004bbaecc4fe22c067ee049d168dccb30ea1c88b002c09746cb8f0bb694bc.jpg", + "image_caption": [ + "Figure 2: Two failure examples of GDAS [10] in the DARTS search space in our experiment by running the authors' code, where normal cells are full of parameterless operations. The average accuracy is $96.52\\%$ on CIFAR-10, while models searched by our method can achieve $97.42\\%$ ." + ], + "image_footnote": [], + "bbox": [ + 106, + 98, + 261, + 207 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3df73e556531c05f594fe0450b2378de71194b0a758c28cd2b3d378f5121ba37.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 98, + 436, + 209 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/958a61914769f1d324bf6dde42b4390d1807a5f559f72a6d793f12b94f7e11c1.jpg", + "image_caption": [ + "Figure 3: Evolution of the number of skip connections in a normal cell of GDAS vs. ROME." + ], + "image_footnote": [], + "bbox": [ + 91, + 321, + 444, + 448 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 523, + 212, + 542 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Collapse in Single-Path Differentiable NAS", + "text_level": 1, + "bbox": [ + 76, + 553, + 442, + 571 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "DARTS [24] optimizes a supernet stacked by normal cells and reduction cells. A cell owns $N$ nodes $\\{x_{i}\\}_{i = 1}^{N}$ denoting latent representation. Edge $e_{i,j}$ from node $x_{i}$ to $x_{j}$ integrates all candidate operations $\\mathcal{O}$ whose importance is represented by architecture parameter $\\alpha_{i,j}^{o}$ . Since the weights of all operations are involved in the forward and backward process, DARTS is very memory-consuming.", + "bbox": [ + 75, + 582, + 468, + 688 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To reduce memory cost, GDAS [10] proposes to sample a sub-set of operations at each iteration. For edge $e_{i,j}$ , a one-hot random vector $z_{i,j} \\in \\{0,1\\}^{|\\mathcal{O}|}$ is sampled, indicating only one candidate operation is selected during the forward pass and back-propagation.", + "bbox": [ + 75, + 694, + 470, + 771 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, we observe that the normal cell learned by GDAS has 4 skip connections, and GDAS (FRC) even contains 5 skip connections, implying performance collapse issue also exists in single-path based methods.", + "bbox": [ + 75, + 773, + 470, + 835 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We rerun the released code of GDAS [10] for several times and observe that the normal cells are dominated by skip connections and max pooling, shown in Fig. 2. We also draw the evolution of skip connections of GDAS in Fig. 3.", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Possible Reasons of Performance Collapse", + "text_level": 1, + "bbox": [ + 500, + 90, + 857, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We conjecture that the following two factors contribute most to the collapse issue, which motivates us to provide a remedy in each regard.", + "bbox": [ + 498, + 118, + 893, + 164 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inconsistency between the searching and evaluation stage. Structural inconsistency between the supernet and the final network mainly appears at the operation level and the topology level. Operation-level inconsistency, i.e., searching with many operations but evaluating only with the most significant one, has been alleviated in recent single-path methods [10, 39] by sampling one operation on each edge at each iteration in the search phase. However, topology-level inconsistency has long been neglected. Specifically, the nodes in the supernet connect with all its predecessors, while the nodes in the final network must only have in-degree 2. In this paper, we eliminate such inconsistency by disentangling topology and operation search.", + "bbox": [ + 496, + 167, + 892, + 364 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Insufficient sampling for candidate operations. The instability issue for single-bath methods can be largely attributed to its stochastic nature that involves sub-sampling. Specifically, at each iteration, only one operation is sampled for each edge, resulting in an insufficient training of weights $\\theta$ . It also causes high variance for the gradients of $\\alpha$ , hence influencing the searching convergence. To this end, we propose multiple sampling and gradient accumulation to train the supernet and reduce the gradient variance of architectural weights.", + "bbox": [ + 496, + 368, + 893, + 520 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Based on the above reasoning, we propose topology disentanglement (Sec 3.3) to resolve inconsistency and gradient accumulation (Sec 3.6) to rectify the instability caused by insufficient sampling. Fig. 3 illustrate the number of skip connections in a normal cell searched by GDAS and our method (ROME), showing that our method can effectively alleviate the collapse issue.", + "bbox": [ + 496, + 523, + 893, + 630 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Topology Disentanglement", + "text_level": 1, + "bbox": [ + 500, + 652, + 740, + 669 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To disentangle the search for topology and operations on each edge, we use an indicator $B_{i,j} \\in \\{0,1\\}$ to denote whether edge $e_{i,j}$ is selected, and $A_{i,j}^{o} \\in \\{0,1\\}$ for whether operation $o$ on edge $e_{i,j}$ is selected. Sampling architecture $z$ with $M$ connections can be decomposed into two parts: sample $M$ edges first, and their operations second.", + "bbox": [ + 496, + 680, + 890, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Sampling for edges. Topology inconsistency exists in single-path based methods [10, 39], as all 14 edges in a cell are selected in the search stage but the final architecture only has 8 edges. To address this issue, we propose to sample the same number of edges in search.", + "bbox": [ + 496, + 775, + 893, + 851 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Each intermediate node should connect with exact two predecessors, satisfying DARTS's constraints. Formally, we use $B_{i,j}$ to indicate whether the edge $e_{i,j}$ between node", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5941", + "bbox": [ + 482, + 944, + 513, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$x_{i}$ and $x_{j}$ is sampled, and we enforce,", + "bbox": [ + 76, + 90, + 331, + 106 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sum_ {i < j} \\boldsymbol {B} _ {i, j} = 2, \\quad \\forall j. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 116, + 468, + 148 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We give two techniques of edge sampling in Sec 3.4.", + "bbox": [ + 94, + 157, + 444, + 172 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Sampling for operations. We use $A_{i,j}^{o}$ to denote whether the operator $o$ is sampled on the edge $e_{i,j}$ , and we adopt Gumbel-Max technique to sample operations, where $g_{i,j}^{o}$ is sampled from Gumbel(0,1) distribution3, and $\\tilde{\\alpha}_{i,j}^{o} = \\frac{\\exp(\\alpha_{i,j}^{o})}{\\sum_{o' \\in \\mathcal{O}} \\exp(\\alpha_{i,j}^{o'})}$ is the normalized architectural weights:", + "bbox": [ + 76, + 172, + 468, + 273 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {A} _ {i, j} = \\text {o n e} \\_ \\text {h o t} \\left[ \\arg \\max _ {o \\in \\mathcal {O}} \\left(\\log \\tilde {\\boldsymbol {\\alpha}} _ {i, j} ^ {o} + \\boldsymbol {g} _ {i, j} ^ {o}\\right) \\right] \\in \\mathbb {R} ^ {| \\mathcal {O} |}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 281, + 468, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To make the objective function differentiable to architectural weights $\\alpha$ , we relax the discrete distribution to a continuous one by Gumbel-Softmax:", + "bbox": [ + 76, + 323, + 468, + 369 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\tilde {\\boldsymbol {A}} _ {i, j} ^ {o} = \\frac {\\exp \\left[ (\\log \\tilde {\\boldsymbol {\\alpha}} _ {i , j} ^ {o} + \\boldsymbol {g} _ {i , j} ^ {o}) / \\tau \\right]}{\\sum_ {o ^ {\\prime} = 1} ^ {| \\mathcal {O} |} \\exp \\left[ (\\log \\tilde {\\boldsymbol {\\alpha}} _ {i , j} ^ {o ^ {\\prime}} + \\boldsymbol {g} _ {i , j} ^ {o ^ {\\prime}}) / \\tau \\right]}, \\\\ \\boldsymbol {A} _ {i, j} = \\mathrm {o n e \\_ h o t} \\left[ \\arg \\max _ {o \\in \\mathcal {O}} \\tilde {\\boldsymbol {A}} _ {i, j} ^ {o} \\right], \\tag {3} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 377, + 468, + 454 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the temperature $\\tau$ gradually decreases in search.", + "bbox": [ + 76, + 462, + 439, + 477 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. From Gumbel-Max to Gumbel-Top2 Reparameterization", + "text_level": 1, + "bbox": [ + 76, + 484, + 468, + 515 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We propose two variations of edge sampling techniques, i.e. Gumbel-Max and Gumbel-Top2, based on which we derive two versions of ROME (v1 and v2).", + "bbox": [ + 76, + 523, + 468, + 568 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4.1 Gumbel-Max (ROME-v1).", + "text_level": 1, + "bbox": [ + 76, + 585, + 313, + 602 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Suppose node $x_{j}$ has $j$ possible predecessors, there are $\\frac{j \\times (j - 1)}{2}$ types of edge choices. We use $I_{j}^{(i,k)} (i < k < j)$ to indicate whether node $x_{j}$ is connected both to $x_{i}$ and $x_{k}$ , i.e. when $I_{j}^{(i,k)} = 1$ , we have $B_{i,j} = B_{k,j} = 1$ and $B_{m,j} = 0 (\\forall m < j, m \\neq i,j)$ .", + "bbox": [ + 76, + 609, + 468, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We then set a trainable variable $\\beta_j^{(i,k)}$ to denote the importance of each edge choice for node $x_{j}$ , such that", + "bbox": [ + 76, + 691, + 468, + 724 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np \\left(\\boldsymbol {I} _ {j} ^ {(i, k)} = 1\\right) = \\frac {\\exp \\left(\\boldsymbol {\\beta} _ {j} ^ {(i , k)}\\right)}{\\sum_ {i ^ {\\prime} < k ^ {\\prime} < j} \\exp \\left(\\boldsymbol {\\beta} _ {j} ^ {(i ^ {\\prime} , k ^ {\\prime})}\\right)} \\triangleq \\tilde {\\boldsymbol {\\beta}} _ {j} ^ {(i, k)}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 734, + 468, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We use Gumbel-Max technique where $\\pmb{g}_j^{(i,k)}$ obeys Gumbel (0,1) distribution,", + "bbox": [ + 76, + 787, + 468, + 820 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {I} _ {j} = \\text {o n e} _ {-} \\operatorname {h o t} \\left[ \\arg \\max _ {i < k < j} \\left(\\log \\tilde {\\boldsymbol {\\beta}} _ {j} ^ {(i, k)} + \\boldsymbol {g} _ {j} ^ {(i, k)}\\right) \\right] \\in \\mathbb {R} ^ {\\frac {j \\times (j - 1)}{2}}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 828, + 472, + 876 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Take a cell as a whole, if edge $e_{i,j}$ is sampled, there must be another chosen $e_{k,j}$ . Thus $\\mathbf{B}_{i,j}$ can be formulated by $\\mathbf{I}_j$ :", + "bbox": [ + 498, + 90, + 890, + 122 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {B} _ {i, j} = \\sum_ {k < i} \\boldsymbol {I} _ {j} ^ {(k, i)} + \\sum_ {k > i} \\boldsymbol {I} _ {j} ^ {(i, k)}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 132, + 890, + 165 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Gumbel-Softmax reparameterization is used to retain gradient information,", + "bbox": [ + 498, + 175, + 890, + 205 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\tilde {\\boldsymbol {I}} _ {j} ^ {(i, k)} = \\frac {\\exp \\left\\{\\left[ \\log \\tilde {\\boldsymbol {\\beta}} _ {j} ^ {(i , k)} + \\boldsymbol {g} _ {j} ^ {(i , k)} \\right] / \\tau \\right\\}}{\\sum_ {s < t < j} \\exp \\left\\{\\left[ \\log \\tilde {\\boldsymbol {\\beta}} _ {j} ^ {(s , t)} + \\boldsymbol {g} _ {j} ^ {(s , t)} \\right] / \\tau \\right\\}}, \\\\ \\boldsymbol {I} _ {j} = \\mathrm {o n e \\_ h o t} \\left[ \\arg \\max _ {i < k < j} \\tilde {\\boldsymbol {I}} _ {j} ^ {(i, k)} \\right]. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 215, + 852, + 304 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4.2 Gumbel-Top2 (ROME-v2).", + "text_level": 1, + "bbox": [ + 500, + 319, + 741, + 334 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Enumerating all possible edge combinations as in ROME-v1 is straightforward but superfluous, hence in ROME-v2 we directly sample two edges per node. We define the probability of each edge $e_{i,j}$ as $p(e_{i,j})$ . Given edge importance is denoted by $\\beta$ , the sampling probability $p(e_{i,j}) = \\frac{\\exp(\\beta_{i,j})}{\\sum_{k < j} \\exp(\\beta_{k,j})} \\triangleq \\tilde{\\beta}_{i,j}$ .", + "bbox": [ + 498, + 342, + 890, + 440 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To satisfy the constraints on the cell topology (Eq. 1), ROME-v2 extends Gumbel-Max to Gumbel-Top2:", + "bbox": [ + 500, + 440, + 890, + 469 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\boldsymbol {B}} _ {i, j} = \\frac {\\exp \\left(\\left(\\log \\tilde {\\boldsymbol {\\beta}} _ {i , j} + \\boldsymbol {g} _ {i , j}\\right) / \\tau\\right)}{\\sum_ {i ^ {\\prime} < j} \\exp \\left(\\left(\\log \\tilde {\\boldsymbol {\\beta}} _ {i ^ {\\prime} , j} + \\boldsymbol {g} _ {i ^ {\\prime} , j}\\right) / \\tau\\right)}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 479, + 890, + 531 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {B} _ {i, j} = \\left\\{ \\begin{array}{l l} 1, & i \\in \\underset {i ^ {\\prime} < j} {\\arg \\operatorname {t o p} 2} \\left(\\tilde {\\boldsymbol {B}} _ {i ^ {\\prime}, j}\\right) \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 532, + 890, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We also demonstrate that the Gumbel-Top2 technique is equivalent to sampling two different edges without replacement with probability simplex $p_i$ , so that Gumbel-Top2 sampling can be made differentiable.", + "bbox": [ + 500, + 592, + 890, + 651 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Theoretical Proof on Gumbel-Top2", + "text_level": 1, + "bbox": [ + 500, + 660, + 803, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We show that our Gumbel-Top2 technique is equivalent to sampling two different edges without replacement with probability simplex $p_i$ , so that Gumbel-Top2 sampling can be made differentiable. We sketch our proof as follows.", + "bbox": [ + 498, + 684, + 890, + 744 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $p_i$ be the probability of sampling $e_i$ by a single choice among $n$ predecessors. Without loss of generality, we compute the probability of sampling $e_1$ in two schemes, and show they are in fact equivalent.", + "bbox": [ + 498, + 744, + 890, + 806 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Sampling two edges without replacement: the probability of $e_1$ being sampled is $p_1 + \\sum_{i=2}^{n} p_i \\frac{p_1}{1 - p_i}$ .", + "2. Sampling with Gumbel-Top2: Gumbel random variable $g_{i}$ is obtained by sampling a uniform random variable $\\epsilon_{i}$ from [0, 1], i.e. $g_{i} = -\\log (-\\log \\epsilon_{i})$ . Then the" + ], + "bbox": [ + 511, + 815, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "3 $g_{i,j}^{o} = -\\log (-\\log (\\epsilon_{i,j}^{o}))$ $\\pmb{\\epsilon}_{i,j}^{o}$ obeys uniform distribution", + "bbox": [ + 91, + 885, + 419, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5942", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "edges are ranked by $(\\log p_i + g_i)$ among which the top two are chosen. There are two cases when $e_1$ is sampled,", + "bbox": [ + 107, + 90, + 468, + 137 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(a) $e_1$ ranks first, and the probability of $e_1$ being sampled is $p_1$ due to Gumbel-Max scheme.", + "(b) $e_1$ ranks second, and $e_i$ ranks first. We can directly get its probability," + ], + "bbox": [ + 117, + 147, + 468, + 213 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\int_ {0} ^ {1} \\epsilon_ {1} ^ {p _ {2} / p _ {1}} \\epsilon_ {1} ^ {p _ {3} / p _ {1}} \\dots (1 - \\epsilon_ {1} ^ {p _ {i} / p _ {1}}) \\dots \\epsilon_ {1} ^ {p _ {n} / p _ {1}} d \\epsilon_ {1} \\\\ = \\int_ {0} ^ {1} (1 - \\epsilon_ {1} ^ {p _ {i} / p _ {1}}) \\epsilon_ {1} ^ {\\frac {1 - p _ {i}}{p _ {1}} - 1} d \\epsilon_ {1} = p _ {i} \\frac {p _ {1}}{1 - p _ {i}}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 223, + 468, + 295 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The probability of edge $e_1$ being sampled is thus $p_1 + \\sum_{i=2}^{n} p_i \\frac{p_1}{1 - p_i}$ .", + "bbox": [ + 107, + 306, + 468, + 342 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Gradient Accumulation", + "text_level": 1, + "bbox": [ + 76, + 349, + 295, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Lastly, we tackle the issues caused by insufficient sampling. Suppose architectural weights $\\alpha$ and $\\beta$ be the parameters of a distribution for architectures. A candidate architecture $z$ is obtained by independently sampling edges and operations. Suppose $z$ owns $M$ edges $\\{e_1,\\dots,e_M\\}$ and the corresponding operations $\\{o_1,\\dots,o_M\\}$ , then the probability of $z$ being selected is given by", + "bbox": [ + 75, + 372, + 468, + 479 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np (z; \\boldsymbol {\\alpha}, \\boldsymbol {\\beta}) = \\prod_ {i = 1} ^ {M} p \\left(e _ {i}; \\boldsymbol {\\beta}\\right) \\times p \\left(o _ {i} \\mid e _ {i}; \\boldsymbol {\\alpha}\\right). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 489, + 468, + 531 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The search process can be thus modeled as finding optimal $\\alpha$ and $\\beta$ to minimize the expectation of validation loss of the architectures as Eq. 10, where $\\theta_z^*$ denotes the optimal operation parameters for the sampled architecture $z$ .", + "bbox": [ + 76, + 542, + 468, + 602 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {\\boldsymbol {\\alpha}, \\boldsymbol {\\beta}} \\quad \\mathbb {E} _ {z \\sim p (z; \\boldsymbol {\\alpha}, \\boldsymbol {\\beta})} \\left[ L _ {v a l} \\left(\\boldsymbol {\\theta} _ {z} ^ {*}, z\\right) \\right], \\tag {10} \\\\ \\text {s . t .} \\quad \\boldsymbol {\\theta} _ {z} ^ {*} = \\arg \\min _ {\\boldsymbol {\\theta}} L _ {\\text {t r a i n}} (\\boldsymbol {\\theta}, z) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 613, + 468, + 662 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, architecture $z$ changes at each iteration while the corresponding operation weights $\\omega$ are updated only once. Apparently, single-path approaches suffer from two problems: unfair and biased training for candidate operations, and creating large variance for architectural weights.", + "bbox": [ + 75, + 672, + 468, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We propose two effective techniques based on gradient accumulation. First, to boost fair training for operations, we sample $K$ sub-models from the supernet and accumulate gradients for each sub-model within one iteration. Weights $\\omega$ are updated by the accumulation of gradients from $K$ sub-models. Second, to reduce the variance for architectural weights, we sample another $K$ sub-models and average the gradients of architectural weights. Suppose that the gradient of $\\alpha$ be a random variable whose variance is $\\sigma^2$ , then averaging among $K$ samples reduces the variance to", + "bbox": [ + 75, + 750, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 ROME (with two versions v1 and v2).", + "bbox": [ + 500, + 90, + 841, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Input: iteration count $T$ ; number of sampling $K$ ; initialized operation parameters $\\theta$ ; and architectural weights $\\alpha$ , $\\beta$ ;", + "bbox": [ + 500, + 107, + 890, + 137 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Output: optimal architecture $z^{*}$", + "bbox": [ + 500, + 138, + 720, + 152 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: for $t = 1 \\rightarrow T$ do", + "2: Sample two batches of data samples $D_{s}$ and $D_{t}$ from two disjoint datasets;", + "3: for $k = 1 \\rightarrow K$ do", + "4: Topology sampling by Eq. 6 (v1) or Eq. 7 (v2); Operation sampling by Eq. 3;", + "5: Get sampled architecture $z_{k}$ ;", + "6: end for", + "7: Gradient accumulation and update $\\alpha, \\beta$ by Eq. 11 on $D_{s}$ , where $L_{val}$ is cross entropy;", + "8: for $k = 1 \\rightarrow K$ do", + "9: Topology sampling by Eq. 6 (v1) or Eq. 7 (v2); Operation sampling by Eq. 3;", + "10: Get sampled architecture $z_k'$ ;", + "11: end for", + "12: Gradient accumulation and update $\\theta$ by Eq. 12 on $D_{t}$ , where $L_{train}$ is cross entropy;", + "13: end for", + "14: return: $z^{*} = \\arg \\max_{z} p(z; \\boldsymbol{\\alpha}, \\boldsymbol{\\beta})$" + ], + "bbox": [ + 504, + 155, + 890, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\sigma^2 /K$ . Specifically, we alternately update operation parameters $\\pmb{\\theta}$ and architectural parameters $\\alpha$ (similar for $\\beta$ ) as:", + "bbox": [ + 498, + 478, + 890, + 508 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\alpha} \\leftarrow \\boldsymbol {\\alpha} - \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\nabla_ {\\boldsymbol {\\alpha}} L _ {v a l} (\\boldsymbol {\\theta}, z _ {k}), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 531, + 890, + 571 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\theta} \\leftarrow \\boldsymbol {\\theta} - \\sum_ {k = 1} ^ {K} \\nabla_ {\\boldsymbol {\\theta}} L _ {\\text {t r a i n}} \\left(\\boldsymbol {\\theta}, z _ {k} ^ {\\prime}\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 575, + 890, + 617 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $z_k, z_k'$ denote the sampled architectures. We can now summarize our ROME method wholly in Alg. 1.", + "bbox": [ + 500, + 627, + 890, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 671, + 630, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Protocols", + "text_level": 1, + "bbox": [ + 500, + 696, + 607, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Search spaces. In this paper, we denote DARTS's search space as S0, which comprises a stack of duplicate normal cells and reduction cells. Each cell is represented by a DAG with 4 intermediate nodes. Candidate operations between each two nodes are {maxpool, avgpool, skip_connect, sep_conv $3 \\times 3$ and $5 \\times 5$ , dil_conv $3 \\times 3$ and $5 \\times 5$ }. We exclude {none} operation from the default DARTS search space to satisfy the topology constraint in Eq. 1. Under S0 space, we search and evaluate on CIFAR-10 [18] and ImageNet [9] respectively.", + "bbox": [ + 496, + 719, + 890, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We also conduct experiments on four reduced search spaces, S1-S4, introduced by R-DARTS [48] to evaluate the", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5943", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/022543a81aa06c457c4697fa4b05dd88a42d13edef2472100a6032dbbbb58553.jpg", + "image_caption": [ + "(a) S1" + ], + "image_footnote": [], + "bbox": [ + 104, + 98, + 316, + 167 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0c064bda7c10bf6123d69e727b71f7d4af27bb875dc77f702aaca6e54b513acb.jpg", + "image_caption": [ + "(b) S2" + ], + "image_footnote": [], + "bbox": [ + 362, + 104, + 581, + 161 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7e57b257f35677a14141449f451437098da54fc0546eb44a4001592ef44d18a5.jpg", + "image_caption": [ + "(c) S3" + ], + "image_footnote": [], + "bbox": [ + 627, + 98, + 843, + 167 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/543890a0abbe3e34fb153af29dd3581485a1c3036ae9aead27cccf0f656bf3f4.jpg", + "image_caption": [ + "(a) S1" + ], + "image_footnote": [], + "bbox": [ + 101, + 266, + 316, + 319 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/043e9a62e1ef4f07e43c25cf6d9113a5b29230074c47ac06a1ce7dcb3d4fa6ce.jpg", + "image_caption": [ + "(b) S2", + "Figure 5: ROME-V2 resolves the aggregation of skip connections on NAS-Bench-1Shot1 [49]. Notice intermediate nodes concatenate their outputs as the input for the output node, while some have loose ends and don't feed to the output node." + ], + "image_footnote": [], + "bbox": [ + 364, + 265, + 578, + 321 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6ffc9c8b9bdbfaf8e3414368004b526d8bc13be3f8a1096c179465a6bf682f2f.jpg", + "image_caption": [ + "Figure 4: GDAS fails on NAS-Bench-1Shot1 [49] when searching on CIFAR-10 in all three search spaces when skip connection are added into choices. In each MixedOp, we have three choices: {maxpool3x3, conv3x3-bn-relu, skip-connect}.", + "(c) S3" + ], + "image_footnote": [], + "bbox": [ + 630, + 263, + 839, + 323 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "stability of our method. S1 is a pre-optimized search space, where each edge in the supernet has a predefined set of candidate operations. In the other 3 search spaces, candidate operations on each edge are the same (see the details in the supplementary). Following [48], we search and evaluate in these 4 search spaces on CIFAR-10, CIFAR-100 [18], and SVHN [26] (12 benchmarks in total).", + "bbox": [ + 75, + 422, + 468, + 527 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Search settings. Similar to DARTS, the supernet consists of 8 cells with 16 initial channels. We search for 50 epochs and set the sampling number $K = 7$ . Unless explicitly written, ROME-v2 is used by default throughout the paper since it is more efficient and robust. For operation parameters, we use the SGD optimizer with a momentum of 0.9 and an initial $lr$ of 0.05; For architectural weights, we adopt the Adam optimizer with an initial $lr$ of $3 \\times 10^{-4}$ .", + "bbox": [ + 75, + 529, + 468, + 650 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation settings. We use standard evaluation settings as DARTS [24] by training the inferred model for 600 epochs using SGD with a batch size of 96. For search space S0, inferred models are constructed by stacking 20 cells with 36 initial channels, and trained under the same settings following [5, 24]. For S1-S4, we strictly follow the settings in R-DARTS [48] for a fair comparison.", + "bbox": [ + 75, + 651, + 468, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Robustness Evaluation", + "text_level": 1, + "bbox": [ + 76, + 770, + 287, + 784 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For comprehensive evaluation, we follow the recommended best practices for NAS by [21, 48, 4, 6, 8] to report the mean and variance across several times of parallel searching with various random seeds, through which the robustness of a method can be measured. We appeal to the community for avoiding a common mistake that trains a single best-searched model several times, which only tests the", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "convergence stability of a single model.", + "bbox": [ + 500, + 422, + 763, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Discussion on collapse behavior across popular NAS benchmarks. We argue that excluding an important operation for search space can cause illusive conclusions. Specifically, NAS-Bench-1Shot1 [49] suggests that Gumbel-based NAS is quite robust. However, this observation is laying on the basis that popular skip connections are not included in the search space [44]. After adding skip connection into the choices, we perform GDAS using their released code, whose best model found is full of skip connections, which again supports our discovery of collapse issue in single-path based NAS, as shown in Fig. 4. In contrast, ROME does not suffer the same issue in these search spaces, as shown in Fig. 5.", + "bbox": [ + 496, + 438, + 890, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Robustness evaluation on 12 hard benchmarks. We follow R-DARTS [48] to evaluate the performance and across 3 datasets in S1-S4 search spaces, see Table 1. Our methods robustly outperform other methods with a clear margin across all these benchmarks.", + "bbox": [ + 496, + 633, + 890, + 709 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Additionally, we observe that parameterless operations in GDAS dominate the normal cell in both S2 and S3, while our method effectively handles their numbers and thus stabilizes the searching stage.", + "bbox": [ + 496, + 710, + 890, + 771 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Performance Comparison", + "text_level": 1, + "bbox": [ + 500, + 780, + 735, + 797 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Performance in S0 on CIFAR. We follow DARTS [24] and search on the CIFAR-10. Table 2 shows that ROME achieves state-of-the-art performance with only 0.3 GPU-days $^4$ . ROME has an average of $2.58 \\pm 0.07\\%$ error rate,", + "bbox": [ + 496, + 804, + 890, + 864 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "4GDAS searches 250 epochs and costs 0.2 GPU-days. ROME searches 50 epochs with $K = 7$ , equivalent to searching 350 epochs by GDAS.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5944", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ffdba8bd562294f4ea868cf34e6c81965c11cc143de6787c64a89a63773da2a1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
BenchmarkDARTS†ES†ADA†GDASROME
Error (%)Error (%)Error (%)Error (%)NumError(%)Num
C10S14.66±0.713.05±0.073.03±0.082.89±0.093.8±0.42.66±0.061.3±0.4
S24.42±0.403.41±0.143.59±0.313.89±0.176.0±0.73.14±0.142.0±0.0
S34.12±0.853.71±1.142.99±0.343.04±0.106.5±0.52.61±0.002.0±0.0
S46.95±0.184.17±0.213.89±0.673.34±0.100.0±0.03.21±0.120.0±0.0
C100S129.93±0.4128.90±0.8124.94±0.8124.49±0.084.0±0.022.71±0.712.3±0.4
S228.75±0.9224.68±1.4326.88±1.1124.57±0.476.3±0.422.91±0.753.5±0.5
S329.01±0.2426.99±1.7924.55±0.6322.86±0.173.0±0.722.43±0.362.5±0.5
S424.77±1.5123.90±2.0123.66±0.9024.14±0.892.3±1.120.95±0.450.0±0.0
SVHNS19.88±5.502.80±0.092.59±0.072.48±0.042.8±0.42.34±0.060.8±0.4
S23.69±0.122.68±0.182.79±0.223.05±0.027.8±0.42.41±0.071.0±0.0
S34.00±1.012.78±0.292.58±0.073.62±0.367.5±0.52.56±0.031.5±0.5
S42.90±0.022.55±0.152.52±0.062.51±0.061.5±1.52.34±0.000.0±0.0
", + "bbox": [ + 196, + 88, + 776, + 318 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/979313aca8e9613e589cfe38bbb57ba3aa96dafdcfe840f6d18926139dc7b183.jpg", + "table_caption": [ + "Table 1: Comparison in 4 search spaces and 3 datasets. For each algorithm, we independently search for 3 times under the settings in R-DARTS [48] and report the averaged performance. 'EA' and 'ADA' are two methods proposed by R-DARTS. 'Num': To reveal the collapse issue, we also report the average number of parameterless operations in the discovered normal cell for GDAS and ROME †: Results are obtained from R-DARTS." + ], + "table_footnote": [], + "table_body": "
ModelsParams (M)FLOPs (M)Error (%)Cost GPU DaysSP
DARTS-V1 [45]--3.38±0.230.4X
P-DARTS [5]‡3.3±0.2540±342.81±0.140.3X
PC-DARTS [40]‡3.6±0.5592±902.89±0.220.1X
PR-DARTS [51]‡3.4-2.68±0.100.2X
ISTA-NAS [43]‡3.3-2.71±0.100.05X
R-DARTS [48]--2.95±0.211.6X
SDARTS-ADV [4]3.3-2.61±0.021.3X
DARTS-PT [33]3.0-2.61±0.080.8X
NASI-FIX [29]3.9-2.79±0.070.24X
ZARTS [34]3.7-2.54±0.071.0X
Few-shot NAS [50]3.8-2.31±0.081.35X
GDAS [10]3.4-2.930.2✓
SNAS [39]2.8-2.85±0.021.5✓
ROME-v1 (best)4.56832.530.3✓
ROME-v1 (avg.)4.0±0.6670±212.63±0.090.3✓
ROME-v2 (best)3.65912.480.3✓
ROME-v2 (avg.)3.7±0.2595±282.58±0.070.3✓
", + "bbox": [ + 84, + 412, + 460, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "which is slightly higher than up-to-date SOTAs such as SDARTS-ADV [4]. However, ROME is more than $4 \\times$ faster. Compared with R-DARTS [48], ROME robustly outperforms it with $5 \\times$ fewer search costs. Our best model achieves $97.52\\%$ accuracy with 3.6M parameters.", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9f38d5c9118fe2981a936d45cb0dce0ba70e60a2632353a3260a071c813fb2d4.jpg", + "table_caption": [ + "Table 2: Averaged performance among 4 independent runs of search on CIFAR-10. $\\ddagger$ : reproduced result using their released code since they didn't report the average performance. $\\dagger$ : FLOPs are calculated by their released architecture. SP: single-path based method" + ], + "table_footnote": [], + "table_body": "
ModelsParams (M)Error (%)Cost GPU Days
ResNet [14]1.722.10°-
AmoebaNet [28]3.118.93°3150
PNAS [23]3.219.53°150
ENAS [27]4.619.43°0.45
DARTS [24]-20.58±0.44*0.4
GDAS [10]3.418.380.2
P-DARTS [5]3.617.49‡0.3
R-DARTS [48]-18.01±0.261.6
NASI-FIX [29]4.016.12±0.380.24
ZARTS [34]4.116.29±0.531.0
ROME-V1 (avg.)4.4±0.217.41±0.120.3
ROME-V1 (best)4.417.330.3
ROME-V2 (avg.)3.4±0.317.71±0.110.3
ROME-V2 (best)3.317.570.3
", + "bbox": [ + 504, + 412, + 890, + 678 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3: Comparison of searched models on CIFAR-100. Reported by [10], $\\star$ :Reported by [48], $\\ddagger$ :Rerun their code.", + "bbox": [ + 500, + 688, + 890, + 720 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also search on CIFAR-100 and show the results in Table 3. ROME surpasses all the methods and achieves state-of-the-art with only 0.3 GPU-days search cost.", + "bbox": [ + 498, + 747, + 890, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Performance in S0 on ImageNet. First, we transfer the architecture searched on CIFAR-10 to ImageNet following the common practice [24, 5, 19, 8]. Same as [19, 8], we train models for 250 epochs with a batch size of 1024 by SGD optimizer with a momentum of 0.9 and an initial $lr$ of 0.5 base learning rate. We also utilize an auxiliary classifier strategy. The results are shown in Table 4, where ROME", + "bbox": [ + 496, + 795, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5945", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/32a2707b90f17fb9fd2ace415d208c9b34cee0941b186a2750ec0ec106d570b1.jpg", + "table_caption": [], + "table_footnote": [ + "Table 4: Performance on ImageNet. The first block indicates the models transferred from CIFAR-10; The second block indicates that the models are directly searched on ImageNet. $\\ddagger$ : reproduced using their released code." + ], + "table_body": "
ModelsFLOPsTop-1Cost
(M)(M)(%)(GPU days)
AmoebaNet-A [28]5555.174.53150
NASNet-A [53]5645.374.02000
PNAS [23]5885.174.2225
DARTS [24]5744.773.30.4
P-DARTS [5]5775.175.30.3
FairDARTS-B [8]5414.875.10.4
SNAS [39]5224.372.71.5
PC-DARTS [40]5865.374.90.1
GDAS [10]5815.374.00.2
ROME (ours)5765.275.30.3
DARTS, P-DARTSOOM when batch-size ≥ 32
FairNAS-C [7]3214.474.712
ProxylessNAS [3]4657.175.18.3
FBNet-C [38]3755.574.99
PC-DARTS [40]‡5975.375.43.8
GDAS [10]‡4053.672.50.8
ROME (ours)5565.175.50.5
", + "bbox": [ + 80, + 88, + 467, + 397 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "achieves $75.3\\%$ top-1 accuracy.", + "bbox": [ + 76, + 492, + 287, + 508 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Second, as ROME features low memory cost and great robustness, we directly search on ImageNet as well. We randomly sample $10\\%$ images to train operation parameters and another $10\\%$ to train architectural weights. A supernet is constructed by stacking 8 cells with 16 initial channels. We search for 30 epochs with $K = 3$ . The batch size is set as 256. Our search cost is reduced to 0.4 GPU days on a single Tesla V100. We fully train the discovered model for 250 epochs with the same evaluation settings as above. Results are illustrated in Tabel 4, showing that ROME achieves $75.5\\%$ top-1 accuracy. To make fair comparisons, we reproduce GDAS [10] under the same settings (90 epochs). However, the network is dominated by skip connections and only achieves $72.5\\%$ top-1 accuracy.", + "bbox": [ + 75, + 508, + 468, + 720 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 737, + 227, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Sensitivity to the Sampling Number $K$ . $K$ is a hyperparameter in our gradient accumulation strategy, which is designed to reduce the variance of noise on $\\nabla_{\\alpha}L_{val}$ and stabilizes the search as analyzed in Sec. 3.6.", + "bbox": [ + 75, + 763, + 468, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5 compares the performance by setting $K$ as 1, 4, 7, 10 in ROME. We search and evaluate on CIFAR-10. Three parallel tests on each setting are conducted. Note we adjust the number of search epochs to have same number of iterations per test. We observe that the performance in", + "bbox": [ + 75, + 824, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/bc88bb136bf7f5245cdee457f8c407ea0147e4f1a949e74d46f5a926b4875f90.jpg", + "table_caption": [], + "table_footnote": [ + "Table 5: Sensitivity study of sampling number $K$ . For each setting, we adjust the number of search epochs according to $K$ for fair comparison. We do three parallel tests on each setting and report the mean and standard deviation." + ], + "table_body": "
KAcc (%)# Params# Epochs
197.12±0.063.34M350
497.28±0.073.57M87
797.42±0.073.73M50
1097.46±0.124.06M35
", + "bbox": [ + 542, + 88, + 849, + 180 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/91e91ad0848cabf213b4e083fb584abb6db1c587929d7c7bd434ec52f3a38a4c.jpg", + "table_caption": [], + "table_footnote": [ + "Table 6: Component study of ROME on CIFAR-10." + ], + "table_body": "
TDGAAcc (%)TDGAAcc (%)
θαθα
×××96.52±0.07✓××97.12±0.06
××✓96.85±0.31✓×✓97.22±0.07
×✓×96.98±0.05✓✓×97.34±0.07
×✓✓97.14±0.05✓✓✓97.42±0.07
", + "bbox": [ + 514, + 267, + 879, + 373 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "creases monotonically with $K$ which verifies our analysis that biased training shall be alleviated. The result demonstrates the effectiveness of our gradient accumulation strategy. Also, as the accuracy saturates at $K = 7$ , we set $K = 7$ .", + "bbox": [ + 496, + 428, + 890, + 488 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Component analysis for instability issue. There are two major components that contribute to the cure for instability in ROME: topology disentanglement (TD) and gradient accumulation (GA) for $\\theta$ and $\\alpha$ . To show their efficacy, we conduct ablation studies in S0 space on CIFAR-10.", + "bbox": [ + 496, + 489, + 890, + 565 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results are shown in Table 6, where 'GA for $\\theta$ indicates that gradient accumulation is applied over $K = 7$ sampled architectures to train operation parameters; 'GA for $\\alpha$ indicates that gradients for architectural parameters over $K = 7$ sampled architectures is accumulated and averaged. The setting without TD and GA (first line in Table 6) degenerates to GDAS [10]. Our ROME adopts both TD and GA, which is the last line in Table 6.", + "bbox": [ + 496, + 565, + 890, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We observe that TD alone can significantly improve the searching performance, showing that the inconsistency issue is the principal reason for performance collapse. This is as expected. On the one hand, inconsistent topology between search and evaluation results in an inconsistent searching objective; On the other hand, training the weights of 14 operations (w/o TD) is much more difficult than training 8 operations (w/ TD), which degrades the convergence.", + "bbox": [ + 496, + 686, + 890, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Moreover, we observe that gradient accumulation on $\\theta$ and $\\alpha$ can further improve the search performance, which confirms our analysis that performance collapse issue also comes from insufficient sampling.", + "bbox": [ + 496, + 809, + 890, + 869 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Memory Analysis. Table 7 compares GPU memory cost in S0 search space on CIFAR-10. ROME has the lowest", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5946", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/67444f35de88c5e7701df5a6542f689a8f7c50bec359de69e4b93fb7201d5fde.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodDARTSGDASPC-DARTSROME
M=4M=2
Memory (G)9.43.13.75.72.3
", + "bbox": [ + 80, + 89, + 467, + 152 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 7: GPU Memory cost comparison. We measured the cost based on a batch size of 64, where the supernet has 16 initial channels, and 8 layers.", + "bbox": [ + 75, + 162, + 468, + 209 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "memory cost thanks to our disentanglement of the search for topology. Unlike GDAS that preserves multiple edges for each node, we strictly sample 2 edges for each node leading to $26\\%$ memory reduction compared to GDAS.", + "bbox": [ + 75, + 234, + 468, + 296 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "PC-DARTS [40] uses partial channels during the search stage to reduce GPU memory cost, in which the partial ratio is controlled by a hyperparameter $M$ . But $M$ requires careful calibration for different tasks. In contrast, ROME doesn't require calibrating such an extra hyperparameter and is more memory-efficient.", + "bbox": [ + 75, + 299, + 468, + 390 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Comparison with Prior Works", + "text_level": 1, + "bbox": [ + 76, + 412, + 356, + 430 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Here we highlight the difference of ROME from the existing works. 1) ROME vs. DOTS. DOTS [12] explores an edge importance representation for one-shot NAS in a multi-stage fashion but the operations are divided into two groups (parameter-free and parameter-bearing, following DropNAS [15]) beforehand, which is a very strong prior. The length of each stage has to be tuned carefully from dataset to dataset. In contrast, no prior or extra hyperparameters are used in ROME; 2) ROME vs. DDW. Unlike DDW [46] that belongs to dynamic networks with a changeable topology dependent on inputs, ROME is a NAS method designed to search for a static architecture. 3) ROME vs. SNAS. SNAS [3] adopts Gumbel-softmax via masking, whose supernet still resides in the memory and thus not memory-efficient. In contrast, ROME is a truly single-path NAS method and inherits the property of low memory cost. SNAS didn't deal with the collapse issue either.", + "bbox": [ + 75, + 441, + 468, + 698 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 720, + 194, + 736 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we highlight the performance collapse issue of single-path differentiable NAS, and attribute the cause to topology inconsistency between searching and evaluation, as well as the stochastic nature of sampling for candidate operations. To address the above issues, we propose ROME that features topology disentanglement and gradient accumulation strategy to stabilize the searching process. ROME achieves state-of-the-art results across 15 recent popular benchmarks, which manifests its strong performance, low memory cost and robustness.", + "bbox": [ + 75, + 750, + 468, + 900 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 90, + 658, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Xiaoxing Wang and Yuda Fan partly contributed to this work when they were intern at Meituan and now Yuda Fan is with ETHZ. This work was partly supported by National Key R&D Program of China (No. 2022ZD0118700), NSFC (62222607), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102).", + "bbox": [ + 498, + 114, + 890, + 205 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 501, + 219, + 596, + 234 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Gabriel Bender, Pieter-Jan Kindermans, Barret Zoph, Vijay Vasudevan, and Quoc Le. Understanding and Simplifying One-Shot Architecture Search. In ICML, pages 549-558, 2018. 1", + "[2] Andrew Brock, Theodore Lim, James M Ritchie, and Nick Weston. SMASH: One-Shot Model Architecture. Search Through HyperNetworks. In ICLR, 2018. 1", + "[3] Han Cai, Ligeng Zhu, and Song Han. ProxylessNAS: Direct Neural Architecture Search on Target Task and Hardware. In ICLR, 2019. 1, 2, 8, 9", + "[4] Xiangning Chen and Cho-Jui Hsieh. 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In CVPR, volume 2, 2018. 2, 8" + ], + "bbox": [ + 78, + 90, + 468, + 417 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "5949", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/ROME_ Robustifying Memory-Efficient NAS via Topology Disentanglement and Gradient Accumulation/6ade4227-5686-42c9-830e-da85efbc5dca_model.json b/2023/ROME_ Robustifying Memory-Efficient NAS via Topology Disentanglement and Gradient Accumulation/6ade4227-5686-42c9-830e-da85efbc5dca_model.json new file mode 100644 index 0000000000000000000000000000000000000000..215c169b38b93cd30975f52ac8cad8b01b88b588 --- /dev/null +++ b/2023/ROME_ Robustifying Memory-Efficient NAS via Topology Disentanglement and Gradient Accumulation/6ade4227-5686-42c9-830e-da85efbc5dca_model.json @@ -0,0 +1,2807 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.082, + 0.13, + 0.89, + 0.175 + ], + "angle": 0, + "content": "ROME: Robustifying Memory-Efficient NAS via Topology Disentanglement and Gradient Accumulation" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.215, + 0.877, + 0.251 + ], + "angle": 0, + "content": "Xiaoxing Wang\\*, Xiangxiang Chu\\*, Yuda Fan\\*, Zhexi Zhang\\*, Bo Zhang\\*, Xiaokang Yang\\*, and Junchi Yan" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.264, + 0.88, + 0.299 + ], + "angle": 0, + "content": "\\(^{1}\\)Dep. of Computer Science and Engineering & MoE Key Lab of AI, Shanghai Jiao Tong University \\(^{2}\\)Meituan" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.342, + 0.314, + 0.359 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.373, + 0.474, + 0.661 + ], + "angle": 0, + "content": "Albeit being a prevalent architecture searching approach, differentiable architecture search (DARTS) is largely hindered by its substantial memory cost since the entire supernet resides in the memory. This is where the single-path DARTS comes in, which only chooses a single-path submodel at each step. While being memory-friendly, it also comes with low computational costs. Nonetheless, we discover a critical issue of single-path DARTS that has not been primarily noticed. Namely, it also suffers from severe performance collapse since too many parameter-free operations like skip connections are derived, just like DARTS does. In this paper, we propose a new algorithm called RObustifying Memory-Efficient NAS (ROME) to give a cure. First, we disentangle the topology search from the operation search to make searching and evaluation consistent. We then adopt Gumbel-Top2 reparameterization and gradient accumulation to robustify the unwieldy bi-level optimization. We verify ROME extensively across 15 benchmarks to demonstrate its effectiveness and robustness." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.688, + 0.21, + 0.704 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.713, + 0.471, + 0.88 + ], + "angle": 0, + "content": "Despite the fast development of neural architecture search (NAS) [52] to aid network design in vision tasks like classification [32, 6, 41, 42], object detection [11, 36], and segmentation [22], there has been an urging demand for faster searching algorithms. Early methods based on the evaluation of a huge number of candidate models [52, 31, 16] require unaffordable costs (typically 2k GPU days). In the light of weight-sharing mechanism introduced in SMASH [2], a variety of low-cost approaches have emerged [1, 27, 24]. DARTS [24] has taken the dominance with a myriad of follow-up works [38, 3, 39, 10, 5, 47]. In" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.343, + 0.894, + 0.388 + ], + "angle": 0, + "content": "this paper, we investigate a single-path based variation of DARTS, typically GDAS [10], for its fast speed and low GPU memory." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.389, + 0.893, + 0.48 + ], + "angle": 0, + "content": "Unlike many DARTS variants that have to perform all candidate operations, single-path methods [30, 10, 39], also termed as memory-efficient \\(\\mathrm{NAS}^1\\), are developed to sample and activate only a subset of operations in the supernet. For differentiable search, Gumbel-Softmax reparameterization tricks [17, 25] are generally employed [38, 10, 39]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.481, + 0.894, + 0.556 + ], + "angle": 0, + "content": "In this paper, we show that single-path methods also suffer from severe performance collapse where many parameterless operations accumulate, akin to that of DARTS as broadly discussed in [48, 4, 39, 8, 20]. We propose a robust algorithm called ROME to resolve this issue." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.557, + 0.895, + 0.737 + ], + "angle": 0, + "content": "We observe that single-path methods usually intertwine topology search with operation search, which creates inconsistency between searching and evaluation. We first disentangle the two from each other. Specifically, in addition to the existing architectural parameters \\((\\alpha)\\) that represent the significance of each operation, we involve topology parameters \\((\\beta)\\) to denote the relative importance of edges. A single-path architecture can then be induced by both \\(\\alpha\\) and \\(\\beta\\). Moreover, to further robustify the searching process, we propose a gradient accumulation strategy during the bilevel optimization. We sketch the framework of ROME in Fig. 1. In a nutshell, our contributions are," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.739, + 0.894, + 0.844 + ], + "angle": 0, + "content": "1) Revealing performance collapse in single-path differentiable NAS. Similar to the performance collapse problem in DARTS, the architectures searched by single-path based methods can also be dominated by parameterless operations, especially skip connections. However, this issue hasn't been deeply explored, which motivates us to propose a new robust, lower memory cost and search cost method." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.845, + 0.894, + 0.876 + ], + "angle": 0, + "content": "2) Consistent search and evaluation by disentangling topology search from operation selection. We introduce" + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.739, + 0.894, + 0.876 + ], + "angle": 0, + "content": null + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.345, + 0.901 + ], + "angle": 0, + "content": "*Equal contribution, † Correspondence author." + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.887, + 0.892, + 0.901 + ], + "angle": 0, + "content": "1We interchangeably use the term 'single-path' and 'memory-efficient'." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5939" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.168, + 0.09, + 0.817, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.343, + 0.895, + 0.377 + ], + "angle": 0, + "content": "Figure 1: ROME (v2): Gumbel-Top2 is devised to sample edges to satisfy the restriction that each node has in-degree 2. Subnetworks apply forward and backward independently. Gradients are accumulated to update the supernet weights at once." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.387, + 0.471, + 0.492 + ], + "angle": 0, + "content": "independent topology parameters to unwind topology from operations, which avoids structure inconsistency between the search and evaluation stage. We further devise Gumbel-Top2 re-parameterization to make our method differentiable and provide its theoretical validity. To our best knowledge, this is the first work to achieve consistent search and evaluation for single-path differentiable NAS." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.493, + 0.471, + 0.569 + ], + "angle": 0, + "content": "3) Robustifying bi-level optimization via gradient accumulation. We devise two gradient accumulation techniques to address the aforementioned issue. One helps fair training for each candidate operations. The other instead reduces the estimation variance on architectural weights." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.691 + ], + "angle": 0, + "content": "4) Strong performance while maintaining low memory cost. Tested on the popular settings² for NAS [48, 21, 6], our approach achieves state-of-the-art on various search spaces and datasets across 15 benchmarks. Our approach is fast, robust, and memory efficient. Compared with GDAS and PC-DARTS, our approach costs \\(26\\%\\) and \\(38\\%\\) lower memory in the standard search space of DARTS respectively. The source code will be made publicly available." + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.493, + 0.471, + 0.691 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.703, + 0.22, + 0.719 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.729, + 0.47, + 0.866 + ], + "angle": 0, + "content": "Differentiable Neural Architecture Search. Similar to [53, 27] that uses a directed acyclic graph to represent a cell, DARTS [24] constructs a cell-based supernet and further introduces architectural weights to represent the importance of each operation. DARTS proposes two types (first-order and second-order) of approximation that alternatively update operation parameters and architectural weights with stochastic gradient descent. However, since the supernet subsumes all connections and operations within the search" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.471, + 0.903 + ], + "angle": 0, + "content": "2Independently search under different random seeds instead of multiple training of a single best-searched model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.892, + 0.478 + ], + "angle": 0, + "content": "space, DARTS risks exhausting GPU memory. A possible attempt to resolve this issue is done by progressively pruning operations [5], which is still an indirect approach and requires strong regularization tricks. Apart from that, recent works [48, 4] also point out an instability phenomenon of DARTS. These issues significantly restrict its application." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.893, + 0.719 + ], + "angle": 0, + "content": "Memory-efficient NAS. To reduce GPU memory cost, several prior works have revised the forward procedure of the supernet. PC-DARTS [40] makes use of partial connections instead of the full-fledged supernet. Some works [37, 36, 35] proposes to merge all parametric operations into one convolution, a similar super-kernel strategy is also used in single-path NAS [30]. ProxylessNAS [3] samples two operations on each edge during the search process, which enables proxyless searching on large datasets. Single-path supernets like SPOS [13] and FairNAS [7] sample only a single path at each iteration, however, both require an additional searching stage to choose the final models. Single-path differentiable methods like GDAS [10] sample a subgraph of the DAG at each iteration, which is by far the most efficient. However, we observe that a severe instability issue occurs, which has been previously neglected." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Performance collapse of DARTS. The collapse issue is one of the most critical problems in differentiable architecture search [20, 40, 8, 4, 48]. It has been shown that DARTS [24] prefers to choose parameterless operations, leading to its performance collapse [20, 8]. Recent works [48, 4] utilize the eigenvalue of the Hessian matrix as an indicator of collapse and design various techniques to regularize high eigenvalues. Instead, other works [20, 5] directly constrain the number of skip connections as 2 to avoid collapse. Nonetheless, the previous methods are specifically designed for the full-path training scheme. Whereas the collapse problem in single-path has been rarely studied." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5940" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.099, + 0.262, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.099, + 0.437, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.217, + 0.471, + 0.295 + ], + "angle": 0, + "content": "Figure 2: Two failure examples of GDAS [10] in the DARTS search space in our experiment by running the authors' code, where normal cells are full of parameterless operations. The average accuracy is \\(96.52\\%\\) on CIFAR-10, while models searched by our method can achieve \\(97.42\\%\\)." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.322, + 0.446, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.458, + 0.471, + 0.489 + ], + "angle": 0, + "content": "Figure 3: Evolution of the number of skip connections in a normal cell of GDAS vs. ROME." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.524, + 0.214, + 0.543 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.554, + 0.444, + 0.573 + ], + "angle": 0, + "content": "3.1. Collapse in Single-Path Differentiable NAS" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.47, + 0.689 + ], + "angle": 0, + "content": "DARTS [24] optimizes a supernet stacked by normal cells and reduction cells. A cell owns \\(N\\) nodes \\(\\{x_{i}\\}_{i = 1}^{N}\\) denoting latent representation. Edge \\(e_{i,j}\\) from node \\(x_{i}\\) to \\(x_{j}\\) integrates all candidate operations \\(\\mathcal{O}\\) whose importance is represented by architecture parameter \\(\\alpha_{i,j}^{o}\\). Since the weights of all operations are involved in the forward and backward process, DARTS is very memory-consuming." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.695, + 0.471, + 0.772 + ], + "angle": 0, + "content": "To reduce memory cost, GDAS [10] proposes to sample a sub-set of operations at each iteration. For edge \\( e_{i,j} \\), a one-hot random vector \\( z_{i,j} \\in \\{0,1\\}^{|\\mathcal{O}|} \\) is sampled, indicating only one candidate operation is selected during the forward pass and back-propagation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.775, + 0.471, + 0.837 + ], + "angle": 0, + "content": "However, we observe that the normal cell learned by GDAS has 4 skip connections, and GDAS (FRC) even contains 5 skip connections, implying performance collapse issue also exists in single-path based methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We rerun the released code of GDAS [10] for several times and observe that the normal cells are dominated by skip connections and max pooling, shown in Fig. 2. We also draw the evolution of skip connections of GDAS in Fig. 3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.859, + 0.108 + ], + "angle": 0, + "content": "3.2. Possible Reasons of Performance Collapse" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.119, + 0.894, + 0.165 + ], + "angle": 0, + "content": "We conjecture that the following two factors contribute most to the collapse issue, which motivates us to provide a remedy in each regard." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.169, + 0.893, + 0.366 + ], + "angle": 0, + "content": "Inconsistency between the searching and evaluation stage. Structural inconsistency between the supernet and the final network mainly appears at the operation level and the topology level. Operation-level inconsistency, i.e., searching with many operations but evaluating only with the most significant one, has been alleviated in recent single-path methods [10, 39] by sampling one operation on each edge at each iteration in the search phase. However, topology-level inconsistency has long been neglected. Specifically, the nodes in the supernet connect with all its predecessors, while the nodes in the final network must only have in-degree 2. In this paper, we eliminate such inconsistency by disentangling topology and operation search." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.369, + 0.895, + 0.521 + ], + "angle": 0, + "content": "Insufficient sampling for candidate operations. The instability issue for single-bath methods can be largely attributed to its stochastic nature that involves sub-sampling. Specifically, at each iteration, only one operation is sampled for each edge, resulting in an insufficient training of weights \\(\\theta\\). It also causes high variance for the gradients of \\(\\alpha\\), hence influencing the searching convergence. To this end, we propose multiple sampling and gradient accumulation to train the supernet and reduce the gradient variance of architectural weights." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.525, + 0.894, + 0.631 + ], + "angle": 0, + "content": "Based on the above reasoning, we propose topology disentanglement (Sec 3.3) to resolve inconsistency and gradient accumulation (Sec 3.6) to rectify the instability caused by insufficient sampling. Fig. 3 illustrate the number of skip connections in a normal cell searched by GDAS and our method (ROME), showing that our method can effectively alleviate the collapse issue." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.653, + 0.741, + 0.67 + ], + "angle": 0, + "content": "3.3. Topology Disentanglement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.681, + 0.892, + 0.773 + ], + "angle": 0, + "content": "To disentangle the search for topology and operations on each edge, we use an indicator \\( B_{i,j} \\in \\{0,1\\} \\) to denote whether edge \\( e_{i,j} \\) is selected, and \\( A_{i,j}^{o} \\in \\{0,1\\} \\) for whether operation \\( o \\) on edge \\( e_{i,j} \\) is selected. Sampling architecture \\( z \\) with \\( M \\) connections can be decomposed into two parts: sample \\( M \\) edges first, and their operations second." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.776, + 0.894, + 0.852 + ], + "angle": 0, + "content": "Sampling for edges. Topology inconsistency exists in single-path based methods [10, 39], as all 14 edges in a cell are selected in the search stage but the final architecture only has 8 edges. To address this issue, we propose to sample the same number of edges in search." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Each intermediate node should connect with exact two predecessors, satisfying DARTS's constraints. Formally, we use \\( B_{i,j} \\) to indicate whether the edge \\( e_{i,j} \\) between node" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.958 + ], + "angle": 0, + "content": "5941" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.332, + 0.107 + ], + "angle": 0, + "content": "\\(x_{i}\\) and \\(x_{j}\\) is sampled, and we enforce," + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.117, + 0.47, + 0.15 + ], + "angle": 0, + "content": "\\[\n\\sum_ {i < j} \\boldsymbol {B} _ {i, j} = 2, \\quad \\forall j. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.159, + 0.446, + 0.174 + ], + "angle": 0, + "content": "We give two techniques of edge sampling in Sec 3.4." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.174, + 0.47, + 0.275 + ], + "angle": 0, + "content": "Sampling for operations. We use \\( A_{i,j}^{o} \\) to denote whether the operator \\( o \\) is sampled on the edge \\( e_{i,j} \\), and we adopt Gumbel-Max technique to sample operations, where \\( g_{i,j}^{o} \\) is sampled from Gumbel(0,1) distribution3, and \\( \\tilde{\\alpha}_{i,j}^{o} = \\frac{\\exp(\\alpha_{i,j}^{o})}{\\sum_{o' \\in \\mathcal{O}} \\exp(\\alpha_{i,j}^{o'})} \\) is the normalized architectural weights:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.282, + 0.469, + 0.317 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {A} _ {i, j} = \\text {o n e} \\_ \\text {h o t} \\left[ \\arg \\max _ {o \\in \\mathcal {O}} \\left(\\log \\tilde {\\boldsymbol {\\alpha}} _ {i, j} ^ {o} + \\boldsymbol {g} _ {i, j} ^ {o}\\right) \\right] \\in \\mathbb {R} ^ {| \\mathcal {O} |}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.324, + 0.47, + 0.37 + ], + "angle": 0, + "content": "To make the objective function differentiable to architectural weights \\(\\alpha\\), we relax the discrete distribution to a continuous one by Gumbel-Softmax:" + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.378, + 0.469, + 0.455 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\tilde {\\boldsymbol {A}} _ {i, j} ^ {o} = \\frac {\\exp \\left[ (\\log \\tilde {\\boldsymbol {\\alpha}} _ {i , j} ^ {o} + \\boldsymbol {g} _ {i , j} ^ {o}) / \\tau \\right]}{\\sum_ {o ^ {\\prime} = 1} ^ {| \\mathcal {O} |} \\exp \\left[ (\\log \\tilde {\\boldsymbol {\\alpha}} _ {i , j} ^ {o ^ {\\prime}} + \\boldsymbol {g} _ {i , j} ^ {o ^ {\\prime}}) / \\tau \\right]}, \\\\ \\boldsymbol {A} _ {i, j} = \\mathrm {o n e \\_ h o t} \\left[ \\arg \\max _ {o \\in \\mathcal {O}} \\tilde {\\boldsymbol {A}} _ {i, j} ^ {o} \\right], \\tag {3} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.463, + 0.44, + 0.478 + ], + "angle": 0, + "content": "where the temperature \\(\\tau\\) gradually decreases in search." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.485, + 0.469, + 0.516 + ], + "angle": 0, + "content": "3.4. From Gumbel-Max to Gumbel-Top2 Reparameterization" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.524, + 0.469, + 0.569 + ], + "angle": 0, + "content": "We propose two variations of edge sampling techniques, i.e. Gumbel-Max and Gumbel-Top2, based on which we derive two versions of ROME (v1 and v2)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.587, + 0.315, + 0.603 + ], + "angle": 0, + "content": "3.4.1 Gumbel-Max (ROME-v1)." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.611, + 0.469, + 0.692 + ], + "angle": 0, + "content": "Suppose node \\( x_{j} \\) has \\( j \\) possible predecessors, there are \\( \\frac{j \\times (j - 1)}{2} \\) types of edge choices. We use \\( I_{j}^{(i,k)} (i < k < j) \\) to indicate whether node \\( x_{j} \\) is connected both to \\( x_{i} \\) and \\( x_{k} \\), i.e. when \\( I_{j}^{(i,k)} = 1 \\), we have \\( B_{i,j} = B_{k,j} = 1 \\) and \\( B_{m,j} = 0 (\\forall m < j, m \\neq i,j) \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.693, + 0.469, + 0.726 + ], + "angle": 0, + "content": "We then set a trainable variable \\(\\beta_j^{(i,k)}\\) to denote the importance of each edge choice for node \\(x_{j}\\), such that" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.735, + 0.469, + 0.78 + ], + "angle": 0, + "content": "\\[\np \\left(\\boldsymbol {I} _ {j} ^ {(i, k)} = 1\\right) = \\frac {\\exp \\left(\\boldsymbol {\\beta} _ {j} ^ {(i , k)}\\right)}{\\sum_ {i ^ {\\prime} < k ^ {\\prime} < j} \\exp \\left(\\boldsymbol {\\beta} _ {j} ^ {(i ^ {\\prime} , k ^ {\\prime})}\\right)} \\triangleq \\tilde {\\boldsymbol {\\beta}} _ {j} ^ {(i, k)}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.788, + 0.469, + 0.821 + ], + "angle": 0, + "content": "We use Gumbel-Max technique where \\( \\pmb{g}_j^{(i,k)} \\) obeys Gumbel (0,1) distribution," + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.829, + 0.473, + 0.877 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {I} _ {j} = \\text {o n e} _ {-} \\operatorname {h o t} \\left[ \\arg \\max _ {i < k < j} \\left(\\log \\tilde {\\boldsymbol {\\beta}} _ {j} ^ {(i, k)} + \\boldsymbol {g} _ {j} ^ {(i, k)}\\right) \\right] \\in \\mathbb {R} ^ {\\frac {j \\times (j - 1)}{2}}. \\tag {5}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.093, + 0.886, + 0.421, + 0.904 + ], + "angle": 0, + "content": "3 \\(g_{i,j}^{o} = -\\log (-\\log (\\epsilon_{i,j}^{o}))\\) \\(\\pmb{\\epsilon}_{i,j}^{o}\\) obeys uniform distribution" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.123 + ], + "angle": 0, + "content": "Take a cell as a whole, if edge \\( e_{i,j} \\) is sampled, there must be another chosen \\( e_{k,j} \\). Thus \\( \\mathbf{B}_{i,j} \\) can be formulated by \\( \\mathbf{I}_j \\):" + }, + { + "type": "equation", + "bbox": [ + 0.593, + 0.133, + 0.892, + 0.166 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {B} _ {i, j} = \\sum_ {k < i} \\boldsymbol {I} _ {j} ^ {(k, i)} + \\sum_ {k > i} \\boldsymbol {I} _ {j} ^ {(i, k)}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.176, + 0.892, + 0.207 + ], + "angle": 0, + "content": "Gumbel-Softmax reparameterization is used to retain gradient information," + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.216, + 0.854, + 0.305 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\tilde {\\boldsymbol {I}} _ {j} ^ {(i, k)} = \\frac {\\exp \\left\\{\\left[ \\log \\tilde {\\boldsymbol {\\beta}} _ {j} ^ {(i , k)} + \\boldsymbol {g} _ {j} ^ {(i , k)} \\right] / \\tau \\right\\}}{\\sum_ {s < t < j} \\exp \\left\\{\\left[ \\log \\tilde {\\boldsymbol {\\beta}} _ {j} ^ {(s , t)} + \\boldsymbol {g} _ {j} ^ {(s , t)} \\right] / \\tau \\right\\}}, \\\\ \\boldsymbol {I} _ {j} = \\mathrm {o n e \\_ h o t} \\left[ \\arg \\max _ {i < k < j} \\tilde {\\boldsymbol {I}} _ {j} ^ {(i, k)} \\right]. \\\\ \\end{array}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.32, + 0.742, + 0.335 + ], + "angle": 0, + "content": "3.4.2 Gumbel-Top2 (ROME-v2)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.343, + 0.892, + 0.441 + ], + "angle": 0, + "content": "Enumerating all possible edge combinations as in ROME-v1 is straightforward but superfluous, hence in ROME-v2 we directly sample two edges per node. We define the probability of each edge \\( e_{i,j} \\) as \\( p(e_{i,j}) \\). Given edge importance is denoted by \\( \\beta \\), the sampling probability \\( p(e_{i,j}) = \\frac{\\exp(\\beta_{i,j})}{\\sum_{k < j} \\exp(\\beta_{k,j})} \\triangleq \\tilde{\\beta}_{i,j} \\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.441, + 0.891, + 0.47 + ], + "angle": 0, + "content": "To satisfy the constraints on the cell topology (Eq. 1), ROME-v2 extends Gumbel-Max to Gumbel-Top2:" + }, + { + "type": "equation", + "bbox": [ + 0.542, + 0.48, + 0.891, + 0.532 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\boldsymbol {B}} _ {i, j} = \\frac {\\exp \\left(\\left(\\log \\tilde {\\boldsymbol {\\beta}} _ {i , j} + \\boldsymbol {g} _ {i , j}\\right) / \\tau\\right)}{\\sum_ {i ^ {\\prime} < j} \\exp \\left(\\left(\\log \\tilde {\\boldsymbol {\\beta}} _ {i ^ {\\prime} , j} + \\boldsymbol {g} _ {i ^ {\\prime} , j}\\right) / \\tau\\right)}, \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.534, + 0.891, + 0.582 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {B} _ {i, j} = \\left\\{ \\begin{array}{l l} 1, & i \\in \\underset {i ^ {\\prime} < j} {\\arg \\operatorname {t o p} 2} \\left(\\tilde {\\boldsymbol {B}} _ {i ^ {\\prime}, j}\\right) \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.593, + 0.892, + 0.652 + ], + "angle": 0, + "content": "We also demonstrate that the Gumbel-Top2 technique is equivalent to sampling two different edges without replacement with probability simplex \\( p_i \\), so that Gumbel-Top2 sampling can be made differentiable." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.661, + 0.805, + 0.678 + ], + "angle": 0, + "content": "3.5. Theoretical Proof on Gumbel-Top2" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.685, + 0.892, + 0.746 + ], + "angle": 0, + "content": "We show that our Gumbel-Top2 technique is equivalent to sampling two different edges without replacement with probability simplex \\( p_i \\), so that Gumbel-Top2 sampling can be made differentiable. We sketch our proof as follows." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.746, + 0.892, + 0.807 + ], + "angle": 0, + "content": "Let \\( p_i \\) be the probability of sampling \\( e_i \\) by a single choice among \\( n \\) predecessors. Without loss of generality, we compute the probability of sampling \\( e_1 \\) in two schemes, and show they are in fact equivalent." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.816, + 0.892, + 0.85 + ], + "angle": 0, + "content": "1. Sampling two edges without replacement: the probability of \\( e_1 \\) being sampled is \\( p_1 + \\sum_{i=2}^{n} p_i \\frac{p_1}{1 - p_i} \\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "2. Sampling with Gumbel-Top2: Gumbel random variable \\( g_{i} \\) is obtained by sampling a uniform random variable \\( \\epsilon_{i} \\) from [0, 1], i.e. \\( g_{i} = -\\log (-\\log \\epsilon_{i}) \\). Then the" + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.816, + 0.892, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5942" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.109, + 0.092, + 0.47, + 0.138 + ], + "angle": 0, + "content": "edges are ranked by \\((\\log p_i + g_i)\\) among which the top two are chosen. There are two cases when \\(e_1\\) is sampled," + }, + { + "type": "text", + "bbox": [ + 0.119, + 0.148, + 0.469, + 0.178 + ], + "angle": 0, + "content": "(a) \\(e_1\\) ranks first, and the probability of \\(e_1\\) being sampled is \\(p_1\\) due to Gumbel-Max scheme." + }, + { + "type": "text", + "bbox": [ + 0.119, + 0.183, + 0.469, + 0.214 + ], + "angle": 0, + "content": "(b) \\(e_1\\) ranks second, and \\(e_i\\) ranks first. We can directly get its probability," + }, + { + "type": "list", + "bbox": [ + 0.119, + 0.148, + 0.469, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.224, + 0.469, + 0.296 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\int_ {0} ^ {1} \\epsilon_ {1} ^ {p _ {2} / p _ {1}} \\epsilon_ {1} ^ {p _ {3} / p _ {1}} \\dots (1 - \\epsilon_ {1} ^ {p _ {i} / p _ {1}}) \\dots \\epsilon_ {1} ^ {p _ {n} / p _ {1}} d \\epsilon_ {1} \\\\ = \\int_ {0} ^ {1} (1 - \\epsilon_ {1} ^ {p _ {i} / p _ {1}}) \\epsilon_ {1} ^ {\\frac {1 - p _ {i}}{p _ {1}} - 1} d \\epsilon_ {1} = p _ {i} \\frac {p _ {1}}{1 - p _ {i}}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.109, + 0.308, + 0.469, + 0.343 + ], + "angle": 0, + "content": "The probability of edge \\(e_1\\) being sampled is thus \\(p_1 + \\sum_{i=2}^{n} p_i \\frac{p_1}{1 - p_i}\\)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.35, + 0.296, + 0.365 + ], + "angle": 0, + "content": "3.6. Gradient Accumulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.373, + 0.469, + 0.48 + ], + "angle": 0, + "content": "Lastly, we tackle the issues caused by insufficient sampling. Suppose architectural weights \\(\\alpha\\) and \\(\\beta\\) be the parameters of a distribution for architectures. A candidate architecture \\(z\\) is obtained by independently sampling edges and operations. Suppose \\(z\\) owns \\(M\\) edges \\(\\{e_1,\\dots,e_M\\}\\) and the corresponding operations \\(\\{o_1,\\dots,o_M\\}\\), then the probability of \\(z\\) being selected is given by" + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.49, + 0.469, + 0.532 + ], + "angle": 0, + "content": "\\[\np (z; \\boldsymbol {\\alpha}, \\boldsymbol {\\beta}) = \\prod_ {i = 1} ^ {M} p \\left(e _ {i}; \\boldsymbol {\\beta}\\right) \\times p \\left(o _ {i} \\mid e _ {i}; \\boldsymbol {\\alpha}\\right). \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.543, + 0.469, + 0.603 + ], + "angle": 0, + "content": "The search process can be thus modeled as finding optimal \\(\\alpha\\) and \\(\\beta\\) to minimize the expectation of validation loss of the architectures as Eq. 10, where \\(\\theta_z^*\\) denotes the optimal operation parameters for the sampled architecture \\(z\\)." + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.614, + 0.469, + 0.663 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {\\boldsymbol {\\alpha}, \\boldsymbol {\\beta}} \\quad \\mathbb {E} _ {z \\sim p (z; \\boldsymbol {\\alpha}, \\boldsymbol {\\beta})} \\left[ L _ {v a l} \\left(\\boldsymbol {\\theta} _ {z} ^ {*}, z\\right) \\right], \\tag {10} \\\\ \\text {s . t .} \\quad \\boldsymbol {\\theta} _ {z} ^ {*} = \\arg \\min _ {\\boldsymbol {\\theta}} L _ {\\text {t r a i n}} (\\boldsymbol {\\theta}, z) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.469, + 0.75 + ], + "angle": 0, + "content": "However, architecture \\( z \\) changes at each iteration while the corresponding operation weights \\( \\omega \\) are updated only once. Apparently, single-path approaches suffer from two problems: unfair and biased training for candidate operations, and creating large variance for architectural weights." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We propose two effective techniques based on gradient accumulation. First, to boost fair training for operations, we sample \\(K\\) sub-models from the supernet and accumulate gradients for each sub-model within one iteration. Weights \\(\\omega\\) are updated by the accumulation of gradients from \\(K\\) sub-models. Second, to reduce the variance for architectural weights, we sample another \\(K\\) sub-models and average the gradients of architectural weights. Suppose that the gradient of \\(\\alpha\\) be a random variable whose variance is \\(\\sigma^2\\), then averaging among \\(K\\) samples reduces the variance to" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.092, + 0.842, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 ROME (with two versions v1 and v2)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.108, + 0.892, + 0.138 + ], + "angle": 0, + "content": "Input: iteration count \\(T\\); number of sampling \\(K\\); initialized operation parameters \\(\\theta\\); and architectural weights \\(\\alpha\\), \\(\\beta\\);" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.139, + 0.721, + 0.153 + ], + "angle": 0, + "content": "Output: optimal architecture \\( z^{*} \\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.156, + 0.653, + 0.169 + ], + "angle": 0, + "content": "1: for \\( t = 1 \\rightarrow T \\) do" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.171, + 0.892, + 0.201 + ], + "angle": 0, + "content": "2: Sample two batches of data samples \\( D_{s} \\) and \\( D_{t} \\) from two disjoint datasets;" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.202, + 0.675, + 0.215 + ], + "angle": 0, + "content": "3: for \\( k = 1 \\rightarrow K \\) do" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.217, + 0.892, + 0.247 + ], + "angle": 0, + "content": "4: Topology sampling by Eq. 6 (v1) or Eq. 7 (v2); Operation sampling by Eq. 3;" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.248, + 0.753, + 0.262 + ], + "angle": 0, + "content": "5: Get sampled architecture \\( z_{k} \\);" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.263, + 0.6, + 0.275 + ], + "angle": 0, + "content": "6: end for" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.277, + 0.892, + 0.307 + ], + "angle": 0, + "content": "7: Gradient accumulation and update \\(\\alpha, \\beta\\) by Eq. 11 on \\(D_{s}\\), where \\(L_{val}\\) is cross entropy;" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.308, + 0.675, + 0.321 + ], + "angle": 0, + "content": "8: for \\( k = 1 \\rightarrow K \\) do" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.322, + 0.892, + 0.352 + ], + "angle": 0, + "content": "9: Topology sampling by Eq. 6 (v1) or Eq. 7 (v2); Operation sampling by Eq. 3;" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.353, + 0.753, + 0.368 + ], + "angle": 0, + "content": "10: Get sampled architecture \\(z_k'\\);" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.369, + 0.6, + 0.381 + ], + "angle": 0, + "content": "11: end for" + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.383, + 0.892, + 0.413 + ], + "angle": 0, + "content": "12: Gradient accumulation and update \\(\\theta\\) by Eq. 12 on \\(D_{t}\\), where \\(L_{train}\\) is cross entropy;" + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.414, + 0.583, + 0.426 + ], + "angle": 0, + "content": "13: end for" + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.428, + 0.75, + 0.448 + ], + "angle": 0, + "content": "14: return: \\( z^{*} = \\arg \\max_{z} p(z; \\boldsymbol{\\alpha}, \\boldsymbol{\\beta}) \\)" + }, + { + "type": "list", + "bbox": [ + 0.506, + 0.156, + 0.892, + 0.448 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.479, + 0.892, + 0.51 + ], + "angle": 0, + "content": "\\(\\sigma^2 /K\\) . Specifically, we alternately update operation parameters \\(\\pmb{\\theta}\\) and architectural parameters \\(\\alpha\\) (similar for \\(\\beta\\) ) as:" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.532, + 0.892, + 0.573 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\alpha} \\leftarrow \\boldsymbol {\\alpha} - \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\nabla_ {\\boldsymbol {\\alpha}} L _ {v a l} (\\boldsymbol {\\theta}, z _ {k}), \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.576, + 0.891, + 0.618 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\theta} \\leftarrow \\boldsymbol {\\theta} - \\sum_ {k = 1} ^ {K} \\nabla_ {\\boldsymbol {\\theta}} L _ {\\text {t r a i n}} \\left(\\boldsymbol {\\theta}, z _ {k} ^ {\\prime}\\right), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.628, + 0.891, + 0.659 + ], + "angle": 0, + "content": "where \\( z_k, z_k' \\) denote the sampled architectures. We can now summarize our ROME method wholly in Alg. 1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.672, + 0.632, + 0.689 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.697, + 0.609, + 0.711 + ], + "angle": 0, + "content": "4.1. Protocols" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.871 + ], + "angle": 0, + "content": "Search spaces. In this paper, we denote DARTS's search space as S0, which comprises a stack of duplicate normal cells and reduction cells. Each cell is represented by a DAG with 4 intermediate nodes. Candidate operations between each two nodes are {maxpool, avgpool, skip_connect, sep_conv \\(3 \\times 3\\) and \\(5 \\times 5\\), dil_conv \\(3 \\times 3\\) and \\(5 \\times 5\\)}. We exclude {none} operation from the default DARTS search space to satisfy the topology constraint in Eq. 1. Under S0 space, we search and evaluate on CIFAR-10 [18] and ImageNet [9] respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We also conduct experiments on four reduced search spaces, S1-S4, introduced by R-DARTS [48] to evaluate the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5943" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.105, + 0.099, + 0.318, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.203, + 0.183, + 0.241, + 0.196 + ], + "angle": 0, + "content": "(a) S1" + }, + { + "type": "image", + "bbox": [ + 0.364, + 0.106, + 0.583, + 0.162 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.466, + 0.173, + 0.506, + 0.187 + ], + "angle": 0, + "content": "(b) S2" + }, + { + "type": "image", + "bbox": [ + 0.629, + 0.099, + 0.844, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.729, + 0.183, + 0.768, + 0.197 + ], + "angle": 0, + "content": "(c) S3" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.209, + 0.89, + 0.242 + ], + "angle": 0, + "content": "Figure 4: GDAS fails on NAS-Bench-1Shot1 [49] when searching on CIFAR-10 in all three search spaces when skip connection are added into choices. In each MixedOp, we have three choices: {maxpool3x3, conv3x3-bn-relu, skip-connect}." + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.267, + 0.317, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.203, + 0.333, + 0.241, + 0.347 + ], + "angle": 0, + "content": "(a) S1" + }, + { + "type": "image", + "bbox": [ + 0.365, + 0.266, + 0.58, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.466, + 0.336, + 0.506, + 0.349 + ], + "angle": 0, + "content": "(b) S2" + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.264, + 0.841, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.729, + 0.34, + 0.768, + 0.353 + ], + "angle": 0, + "content": "(c) S3" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.366, + 0.893, + 0.397 + ], + "angle": 0, + "content": "Figure 5: ROME-V2 resolves the aggregation of skip connections on NAS-Bench-1Shot1 [49]. Notice intermediate nodes concatenate their outputs as the input for the output node, while some have loose ends and don't feed to the output node." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.423, + 0.469, + 0.528 + ], + "angle": 0, + "content": "stability of our method. S1 is a pre-optimized search space, where each edge in the supernet has a predefined set of candidate operations. In the other 3 search spaces, candidate operations on each edge are the same (see the details in the supplementary). Following [48], we search and evaluate in these 4 search spaces on CIFAR-10, CIFAR-100 [18], and SVHN [26] (12 benchmarks in total)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.47, + 0.651 + ], + "angle": 0, + "content": "Search settings. Similar to DARTS, the supernet consists of 8 cells with 16 initial channels. We search for 50 epochs and set the sampling number \\( K = 7 \\). Unless explicitly written, ROME-v2 is used by default throughout the paper since it is more efficient and robust. For operation parameters, we use the SGD optimizer with a momentum of 0.9 and an initial \\( lr \\) of 0.05; For architectural weights, we adopt the Adam optimizer with an initial \\( lr \\) of \\( 3 \\times 10^{-4} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.652, + 0.47, + 0.759 + ], + "angle": 0, + "content": "Evaluation settings. We use standard evaluation settings as DARTS [24] by training the inferred model for 600 epochs using SGD with a batch size of 96. For search space S0, inferred models are constructed by stacking 20 cells with 36 initial channels, and trained under the same settings following [5, 24]. For S1-S4, we strictly follow the settings in R-DARTS [48] for a fair comparison." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.289, + 0.785 + ], + "angle": 0, + "content": "4.2. Robustness Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.901 + ], + "angle": 0, + "content": "For comprehensive evaluation, we follow the recommended best practices for NAS by [21, 48, 4, 6, 8] to report the mean and variance across several times of parallel searching with various random seeds, through which the robustness of a method can be measured. We appeal to the community for avoiding a common mistake that trains a single best-searched model several times, which only tests the" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.424, + 0.764, + 0.438 + ], + "angle": 0, + "content": "convergence stability of a single model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.892, + 0.635 + ], + "angle": 0, + "content": "Discussion on collapse behavior across popular NAS benchmarks. We argue that excluding an important operation for search space can cause illusive conclusions. Specifically, NAS-Bench-1Shot1 [49] suggests that Gumbel-based NAS is quite robust. However, this observation is laying on the basis that popular skip connections are not included in the search space [44]. After adding skip connection into the choices, we perform GDAS using their released code, whose best model found is full of skip connections, which again supports our discovery of collapse issue in single-path based NAS, as shown in Fig. 4. In contrast, ROME does not suffer the same issue in these search spaces, as shown in Fig. 5." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.635, + 0.892, + 0.71 + ], + "angle": 0, + "content": "Robustness evaluation on 12 hard benchmarks. We follow R-DARTS [48] to evaluate the performance and across 3 datasets in S1-S4 search spaces, see Table 1. Our methods robustly outperform other methods with a clear margin across all these benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.711, + 0.892, + 0.772 + ], + "angle": 0, + "content": "Additionally, we observe that parameterless operations in GDAS dominate the normal cell in both S2 and S3, while our method effectively handles their numbers and thus stabilizes the searching stage." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.781, + 0.736, + 0.798 + ], + "angle": 0, + "content": "4.3. Performance Comparison" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.805, + 0.892, + 0.866 + ], + "angle": 0, + "content": "Performance in S0 on CIFAR. We follow DARTS [24] and search on the CIFAR-10. Table 2 shows that ROME achieves state-of-the-art performance with only 0.3 GPU-days\\(^4\\). ROME has an average of \\(2.58 \\pm 0.07\\%\\) error rate," + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "4GDAS searches 250 epochs and costs 0.2 GPU-days. ROME searches 50 epochs with \\( K = 7 \\), equivalent to searching 350 epochs by GDAS." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5944" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.197, + 0.089, + 0.777, + 0.319 + ], + "angle": 0, + "content": "
BenchmarkDARTS†ES†ADA†GDASROME
Error (%)Error (%)Error (%)Error (%)NumError(%)Num
C10S14.66±0.713.05±0.073.03±0.082.89±0.093.8±0.42.66±0.061.3±0.4
S24.42±0.403.41±0.143.59±0.313.89±0.176.0±0.73.14±0.142.0±0.0
S34.12±0.853.71±1.142.99±0.343.04±0.106.5±0.52.61±0.002.0±0.0
S46.95±0.184.17±0.213.89±0.673.34±0.100.0±0.03.21±0.120.0±0.0
C100S129.93±0.4128.90±0.8124.94±0.8124.49±0.084.0±0.022.71±0.712.3±0.4
S228.75±0.9224.68±1.4326.88±1.1124.57±0.476.3±0.422.91±0.753.5±0.5
S329.01±0.2426.99±1.7924.55±0.6322.86±0.173.0±0.722.43±0.362.5±0.5
S424.77±1.5123.90±2.0123.66±0.9024.14±0.892.3±1.120.95±0.450.0±0.0
SVHNS19.88±5.502.80±0.092.59±0.072.48±0.042.8±0.42.34±0.060.8±0.4
S23.69±0.122.68±0.182.79±0.223.05±0.027.8±0.42.41±0.071.0±0.0
S34.00±1.012.78±0.292.58±0.073.62±0.367.5±0.52.56±0.031.5±0.5
S42.90±0.022.55±0.152.52±0.062.51±0.061.5±1.52.34±0.000.0±0.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.329, + 0.892, + 0.39 + ], + "angle": 0, + "content": "Table 1: Comparison in 4 search spaces and 3 datasets. For each algorithm, we independently search for 3 times under the settings in R-DARTS [48] and report the averaged performance. 'EA' and 'ADA' are two methods proposed by R-DARTS. 'Num': To reveal the collapse issue, we also report the average number of parameterless operations in the discovered normal cell for GDAS and ROME †: Results are obtained from R-DARTS." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.414, + 0.462, + 0.701 + ], + "angle": 0, + "content": "
ModelsParams (M)FLOPs (M)Error (%)Cost GPU DaysSP
DARTS-V1 [45]--3.38±0.230.4X
P-DARTS [5]‡3.3±0.2540±342.81±0.140.3X
PC-DARTS [40]‡3.6±0.5592±902.89±0.220.1X
PR-DARTS [51]‡3.4-2.68±0.100.2X
ISTA-NAS [43]‡3.3-2.71±0.100.05X
R-DARTS [48]--2.95±0.211.6X
SDARTS-ADV [4]3.3-2.61±0.021.3X
DARTS-PT [33]3.0-2.61±0.080.8X
NASI-FIX [29]3.9-2.79±0.070.24X
ZARTS [34]3.7-2.54±0.071.0X
Few-shot NAS [50]3.8-2.31±0.081.35X
GDAS [10]3.4-2.930.2✓
SNAS [39]2.8-2.85±0.021.5✓
ROME-v1 (best)4.56832.530.3✓
ROME-v1 (avg.)4.0±0.6670±212.63±0.090.3✓
ROME-v2 (best)3.65912.480.3✓
ROME-v2 (avg.)3.7±0.2595±282.58±0.070.3✓
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.712, + 0.47, + 0.788 + ], + "angle": 0, + "content": "Table 2: Averaged performance among 4 independent runs of search on CIFAR-10. \\(\\ddagger\\): reproduced result using their released code since they didn't report the average performance. \\(\\dagger\\): FLOPs are calculated by their released architecture. SP: single-path based method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "which is slightly higher than up-to-date SOTAs such as SDARTS-ADV [4]. However, ROME is more than \\(4 \\times\\) faster. Compared with R-DARTS [48], ROME robustly outperforms it with \\(5 \\times\\) fewer search costs. Our best model achieves \\(97.52\\%\\) accuracy with 3.6M parameters." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.414, + 0.891, + 0.679 + ], + "angle": 0, + "content": "
ModelsParams (M)Error (%)Cost GPU Days
ResNet [14]1.722.10°-
AmoebaNet [28]3.118.93°3150
PNAS [23]3.219.53°150
ENAS [27]4.619.43°0.45
DARTS [24]-20.58±0.44*0.4
GDAS [10]3.418.380.2
P-DARTS [5]3.617.49‡0.3
R-DARTS [48]-18.01±0.261.6
NASI-FIX [29]4.016.12±0.380.24
ZARTS [34]4.116.29±0.531.0
ROME-V1 (avg.)4.4±0.217.41±0.120.3
ROME-V1 (best)4.417.330.3
ROME-V2 (avg.)3.4±0.317.71±0.110.3
ROME-V2 (best)3.317.570.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.689, + 0.892, + 0.721 + ], + "angle": 0, + "content": "Table 3: Comparison of searched models on CIFAR-100. Reported by [10], \\(\\star\\):Reported by [48], \\(\\ddagger\\):Rerun their code." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.748, + 0.892, + 0.794 + ], + "angle": 0, + "content": "We also search on CIFAR-100 and show the results in Table 3. ROME surpasses all the methods and achieves state-of-the-art with only 0.3 GPU-days search cost." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Performance in S0 on ImageNet. First, we transfer the architecture searched on CIFAR-10 to ImageNet following the common practice [24, 5, 19, 8]. Same as [19, 8], we train models for 250 epochs with a batch size of 1024 by SGD optimizer with a momentum of 0.9 and an initial \\( lr \\) of 0.5 base learning rate. We also utilize an auxiliary classifier strategy. The results are shown in Table 4, where ROME" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5945" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.089, + 0.468, + 0.398 + ], + "angle": 0, + "content": "
ModelsFLOPsTop-1Cost
(M)(M)(%)(GPU days)
AmoebaNet-A [28]5555.174.53150
NASNet-A [53]5645.374.02000
PNAS [23]5885.174.2225
DARTS [24]5744.773.30.4
P-DARTS [5]5775.175.30.3
FairDARTS-B [8]5414.875.10.4
SNAS [39]5224.372.71.5
PC-DARTS [40]5865.374.90.1
GDAS [10]5815.374.00.2
ROME (ours)5765.275.30.3
DARTS, P-DARTSOOM when batch-size ≥ 32
FairNAS-C [7]3214.474.712
ProxylessNAS [3]4657.175.18.3
FBNet-C [38]3755.574.99
PC-DARTS [40]‡5975.375.43.8
GDAS [10]‡4053.672.50.8
ROME (ours)5565.175.50.5
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.409, + 0.47, + 0.471 + ], + "angle": 0, + "content": "Table 4: Performance on ImageNet. The first block indicates the models transferred from CIFAR-10; The second block indicates that the models are directly searched on ImageNet. \\(\\ddagger\\): reproduced using their released code." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.493, + 0.288, + 0.509 + ], + "angle": 0, + "content": "achieves \\(75.3\\%\\) top-1 accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.47, + 0.722 + ], + "angle": 0, + "content": "Second, as ROME features low memory cost and great robustness, we directly search on ImageNet as well. We randomly sample \\(10\\%\\) images to train operation parameters and another \\(10\\%\\) to train architectural weights. A supernet is constructed by stacking 8 cells with 16 initial channels. We search for 30 epochs with \\(K = 3\\). The batch size is set as 256. Our search cost is reduced to 0.4 GPU days on a single Tesla V100. We fully train the discovered model for 250 epochs with the same evaluation settings as above. Results are illustrated in Tabel 4, showing that ROME achieves \\(75.5\\%\\) top-1 accuracy. To make fair comparisons, we reproduce GDAS [10] under the same settings (90 epochs). However, the network is dominated by skip connections and only achieves \\(72.5\\%\\) top-1 accuracy." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.738, + 0.228, + 0.755 + ], + "angle": 0, + "content": "5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.764, + 0.469, + 0.825 + ], + "angle": 0, + "content": "Sensitivity to the Sampling Number \\(K\\). \\(K\\) is a hyperparameter in our gradient accumulation strategy, which is designed to reduce the variance of noise on \\(\\nabla_{\\alpha}L_{val}\\) and stabilizes the search as analyzed in Sec. 3.6." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Table 5 compares the performance by setting \\( K \\) as 1, 4, 7, 10 in ROME. We search and evaluate on CIFAR-10. Three parallel tests on each setting are conducted. Note we adjust the number of search epochs to have same number of iterations per test. We observe that the performance in" + }, + { + "type": "table", + "bbox": [ + 0.544, + 0.089, + 0.851, + 0.181 + ], + "angle": 0, + "content": "
KAcc (%)# Params# Epochs
197.12±0.063.34M350
497.28±0.073.57M87
797.42±0.073.73M50
1097.46±0.124.06M35
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.499, + 0.191, + 0.892, + 0.253 + ], + "angle": 0, + "content": "Table 5: Sensitivity study of sampling number \\( K \\). For each setting, we adjust the number of search epochs according to \\( K \\) for fair comparison. We do three parallel tests on each setting and report the mean and standard deviation." + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.268, + 0.88, + 0.374 + ], + "angle": 0, + "content": "
TDGAAcc (%)TDGAAcc (%)
θαθα
×××96.52±0.07✓××97.12±0.06
××✓96.85±0.31✓×✓97.22±0.07
×✓×96.98±0.05✓✓×97.34±0.07
×✓✓97.14±0.05✓✓✓97.42±0.07
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.524, + 0.384, + 0.868, + 0.4 + ], + "angle": 0, + "content": "Table 6: Component study of ROME on CIFAR-10." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.892, + 0.489 + ], + "angle": 0, + "content": "creases monotonically with \\( K \\) which verifies our analysis that biased training shall be alleviated. The result demonstrates the effectiveness of our gradient accumulation strategy. Also, as the accuracy saturates at \\( K = 7 \\), we set \\( K = 7 \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.892, + 0.566 + ], + "angle": 0, + "content": "Component analysis for instability issue. There are two major components that contribute to the cure for instability in ROME: topology disentanglement (TD) and gradient accumulation (GA) for \\(\\theta\\) and \\(\\alpha\\). To show their efficacy, we conduct ablation studies in S0 space on CIFAR-10." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.892, + 0.687 + ], + "angle": 0, + "content": "Results are shown in Table 6, where 'GA for \\(\\theta\\) indicates that gradient accumulation is applied over \\(K = 7\\) sampled architectures to train operation parameters; 'GA for \\(\\alpha\\) indicates that gradients for architectural parameters over \\(K = 7\\) sampled architectures is accumulated and averaged. The setting without TD and GA (first line in Table 6) degenerates to GDAS [10]. Our ROME adopts both TD and GA, which is the last line in Table 6." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.809 + ], + "angle": 0, + "content": "We observe that TD alone can significantly improve the searching performance, showing that the inconsistency issue is the principal reason for performance collapse. This is as expected. On the one hand, inconsistent topology between search and evaluation results in an inconsistent searching objective; On the other hand, training the weights of 14 operations (w/o TD) is much more difficult than training 8 operations (w/ TD), which degrades the convergence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Moreover, we observe that gradient accumulation on \\(\\theta\\) and \\(\\alpha\\) can further improve the search performance, which confirms our analysis that performance collapse issue also comes from insufficient sampling." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Memory Analysis. Table 7 compares GPU memory cost in S0 search space on CIFAR-10. ROME has the lowest" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5946" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.09, + 0.468, + 0.153 + ], + "angle": 0, + "content": "
MethodDARTSGDASPC-DARTSROME
M=4M=2
Memory (G)9.43.13.75.72.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.163, + 0.47, + 0.21 + ], + "angle": 0, + "content": "Table 7: GPU Memory cost comparison. We measured the cost based on a batch size of 64, where the supernet has 16 initial channels, and 8 layers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.236, + 0.469, + 0.297 + ], + "angle": 0, + "content": "memory cost thanks to our disentanglement of the search for topology. Unlike GDAS that preserves multiple edges for each node, we strictly sample 2 edges for each node leading to \\(26\\%\\) memory reduction compared to GDAS." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.3, + 0.469, + 0.391 + ], + "angle": 0, + "content": "PC-DARTS [40] uses partial channels during the search stage to reduce GPU memory cost, in which the partial ratio is controlled by a hyperparameter \\( M \\). But \\( M \\) requires careful calibration for different tasks. In contrast, ROME doesn't require calibrating such an extra hyperparameter and is more memory-efficient." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.413, + 0.357, + 0.431 + ], + "angle": 0, + "content": "6. Comparison with Prior Works" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.47, + 0.699 + ], + "angle": 0, + "content": "Here we highlight the difference of ROME from the existing works. 1) ROME vs. DOTS. DOTS [12] explores an edge importance representation for one-shot NAS in a multi-stage fashion but the operations are divided into two groups (parameter-free and parameter-bearing, following DropNAS [15]) beforehand, which is a very strong prior. The length of each stage has to be tuned carefully from dataset to dataset. In contrast, no prior or extra hyperparameters are used in ROME; 2) ROME vs. DDW. Unlike DDW [46] that belongs to dynamic networks with a changeable topology dependent on inputs, ROME is a NAS method designed to search for a static architecture. 3) ROME vs. SNAS. SNAS [3] adopts Gumbel-softmax via masking, whose supernet still resides in the memory and thus not memory-efficient. In contrast, ROME is a truly single-path NAS method and inherits the property of low memory cost. SNAS didn't deal with the collapse issue either." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.722, + 0.195, + 0.737 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.469, + 0.901 + ], + "angle": 0, + "content": "In this paper, we highlight the performance collapse issue of single-path differentiable NAS, and attribute the cause to topology inconsistency between searching and evaluation, as well as the stochastic nature of sampling for candidate operations. To address the above issues, we propose ROME that features topology disentanglement and gradient accumulation strategy to stabilize the searching process. ROME achieves state-of-the-art results across 15 recent popular benchmarks, which manifests its strong performance, low memory cost and robustness." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.091, + 0.659, + 0.108 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.115, + 0.892, + 0.207 + ], + "angle": 0, + "content": "Xiaoxing Wang and Yuda Fan partly contributed to this work when they were intern at Meituan and now Yuda Fan is with ETHZ. This work was partly supported by National Key R&D Program of China (No. 2022ZD0118700), NSFC (62222607), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102)." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.22, + 0.597, + 0.236 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.245, + 0.892, + 0.3 + ], + "angle": 0, + "content": "[1] Gabriel Bender, Pieter-Jan Kindermans, Barret Zoph, Vijay Vasudevan, and Quoc Le. Understanding and Simplifying One-Shot Architecture Search. In ICML, pages 549-558, 2018. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.509, + 0.302, + 0.893, + 0.344 + ], + "angle": 0, + "content": "[2] Andrew Brock, Theodore Lim, James M Ritchie, and Nick Weston. SMASH: One-Shot Model Architecture. Search Through HyperNetworks. In ICLR, 2018. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.509, + 0.346, + 0.894, + 0.386 + ], + "angle": 0, + "content": "[3] Han Cai, Ligeng Zhu, and Song Han. 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This is where the single-path DARTS comes in, which only chooses a single-path submodel at each step. While being memory-friendly, it also comes with low computational costs. Nonetheless, we discover a critical issue of single-path DARTS that has not been primarily noticed. Namely, it also suffers from severe performance collapse since too many parameter-free operations like skip connections are derived, just like DARTS does. In this paper, we propose a new algorithm called RObustifying Memory-Efficient NAS (ROME) to give a cure. First, we disentangle the topology search from the operation search to make searching and evaluation consistent. We then adopt Gumbel-Top2 reparameterization and gradient accumulation to robustify the unwieldy bi-level optimization. We verify ROME extensively across 15 benchmarks to demonstrate its effectiveness and robustness. + +# 1. Introduction + +Despite the fast development of neural architecture search (NAS) [52] to aid network design in vision tasks like classification [32, 6, 41, 42], object detection [11, 36], and segmentation [22], there has been an urging demand for faster searching algorithms. Early methods based on the evaluation of a huge number of candidate models [52, 31, 16] require unaffordable costs (typically 2k GPU days). In the light of weight-sharing mechanism introduced in SMASH [2], a variety of low-cost approaches have emerged [1, 27, 24]. DARTS [24] has taken the dominance with a myriad of follow-up works [38, 3, 39, 10, 5, 47]. In + +this paper, we investigate a single-path based variation of DARTS, typically GDAS [10], for its fast speed and low GPU memory. + +Unlike many DARTS variants that have to perform all candidate operations, single-path methods [30, 10, 39], also termed as memory-efficient $\mathrm{NAS}^1$ , are developed to sample and activate only a subset of operations in the supernet. For differentiable search, Gumbel-Softmax reparameterization tricks [17, 25] are generally employed [38, 10, 39]. + +In this paper, we show that single-path methods also suffer from severe performance collapse where many parameterless operations accumulate, akin to that of DARTS as broadly discussed in [48, 4, 39, 8, 20]. We propose a robust algorithm called ROME to resolve this issue. + +We observe that single-path methods usually intertwine topology search with operation search, which creates inconsistency between searching and evaluation. We first disentangle the two from each other. Specifically, in addition to the existing architectural parameters $(\alpha)$ that represent the significance of each operation, we involve topology parameters $(\beta)$ to denote the relative importance of edges. A single-path architecture can then be induced by both $\alpha$ and $\beta$ . Moreover, to further robustify the searching process, we propose a gradient accumulation strategy during the bilevel optimization. We sketch the framework of ROME in Fig. 1. In a nutshell, our contributions are, + +1) Revealing performance collapse in single-path differentiable NAS. Similar to the performance collapse problem in DARTS, the architectures searched by single-path based methods can also be dominated by parameterless operations, especially skip connections. However, this issue hasn't been deeply explored, which motivates us to propose a new robust, lower memory cost and search cost method. +2) Consistent search and evaluation by disentangling topology search from operation selection. We introduce + +![](images/510a98dc79c64467dc83d6cf82d97ed64bc1db16539c218fa3a17ec8b5f6f226.jpg) +Figure 1: ROME (v2): Gumbel-Top2 is devised to sample edges to satisfy the restriction that each node has in-degree 2. Subnetworks apply forward and backward independently. Gradients are accumulated to update the supernet weights at once. + +independent topology parameters to unwind topology from operations, which avoids structure inconsistency between the search and evaluation stage. We further devise Gumbel-Top2 re-parameterization to make our method differentiable and provide its theoretical validity. To our best knowledge, this is the first work to achieve consistent search and evaluation for single-path differentiable NAS. + +3) Robustifying bi-level optimization via gradient accumulation. We devise two gradient accumulation techniques to address the aforementioned issue. One helps fair training for each candidate operations. The other instead reduces the estimation variance on architectural weights. +4) Strong performance while maintaining low memory cost. Tested on the popular settings² for NAS [48, 21, 6], our approach achieves state-of-the-art on various search spaces and datasets across 15 benchmarks. Our approach is fast, robust, and memory efficient. Compared with GDAS and PC-DARTS, our approach costs $26\%$ and $38\%$ lower memory in the standard search space of DARTS respectively. The source code will be made publicly available. + +# 2. Related Work + +Differentiable Neural Architecture Search. Similar to [53, 27] that uses a directed acyclic graph to represent a cell, DARTS [24] constructs a cell-based supernet and further introduces architectural weights to represent the importance of each operation. DARTS proposes two types (first-order and second-order) of approximation that alternatively update operation parameters and architectural weights with stochastic gradient descent. However, since the supernet subsumes all connections and operations within the search + +space, DARTS risks exhausting GPU memory. A possible attempt to resolve this issue is done by progressively pruning operations [5], which is still an indirect approach and requires strong regularization tricks. Apart from that, recent works [48, 4] also point out an instability phenomenon of DARTS. These issues significantly restrict its application. + +Memory-efficient NAS. To reduce GPU memory cost, several prior works have revised the forward procedure of the supernet. PC-DARTS [40] makes use of partial connections instead of the full-fledged supernet. Some works [37, 36, 35] proposes to merge all parametric operations into one convolution, a similar super-kernel strategy is also used in single-path NAS [30]. ProxylessNAS [3] samples two operations on each edge during the search process, which enables proxyless searching on large datasets. Single-path supernets like SPOS [13] and FairNAS [7] sample only a single path at each iteration, however, both require an additional searching stage to choose the final models. Single-path differentiable methods like GDAS [10] sample a subgraph of the DAG at each iteration, which is by far the most efficient. However, we observe that a severe instability issue occurs, which has been previously neglected. + +Performance collapse of DARTS. The collapse issue is one of the most critical problems in differentiable architecture search [20, 40, 8, 4, 48]. It has been shown that DARTS [24] prefers to choose parameterless operations, leading to its performance collapse [20, 8]. Recent works [48, 4] utilize the eigenvalue of the Hessian matrix as an indicator of collapse and design various techniques to regularize high eigenvalues. Instead, other works [20, 5] directly constrain the number of skip connections as 2 to avoid collapse. Nonetheless, the previous methods are specifically designed for the full-path training scheme. Whereas the collapse problem in single-path has been rarely studied. + +![](images/681004bbaecc4fe22c067ee049d168dccb30ea1c88b002c09746cb8f0bb694bc.jpg) +Figure 2: Two failure examples of GDAS [10] in the DARTS search space in our experiment by running the authors' code, where normal cells are full of parameterless operations. The average accuracy is $96.52\%$ on CIFAR-10, while models searched by our method can achieve $97.42\%$ . + +![](images/3df73e556531c05f594fe0450b2378de71194b0a758c28cd2b3d378f5121ba37.jpg) + +![](images/958a61914769f1d324bf6dde42b4390d1807a5f559f72a6d793f12b94f7e11c1.jpg) +Figure 3: Evolution of the number of skip connections in a normal cell of GDAS vs. ROME. + +# 3. Methodology + +# 3.1. Collapse in Single-Path Differentiable NAS + +DARTS [24] optimizes a supernet stacked by normal cells and reduction cells. A cell owns $N$ nodes $\{x_{i}\}_{i = 1}^{N}$ denoting latent representation. Edge $e_{i,j}$ from node $x_{i}$ to $x_{j}$ integrates all candidate operations $\mathcal{O}$ whose importance is represented by architecture parameter $\alpha_{i,j}^{o}$ . Since the weights of all operations are involved in the forward and backward process, DARTS is very memory-consuming. + +To reduce memory cost, GDAS [10] proposes to sample a sub-set of operations at each iteration. For edge $e_{i,j}$ , a one-hot random vector $z_{i,j} \in \{0,1\}^{|\mathcal{O}|}$ is sampled, indicating only one candidate operation is selected during the forward pass and back-propagation. + +However, we observe that the normal cell learned by GDAS has 4 skip connections, and GDAS (FRC) even contains 5 skip connections, implying performance collapse issue also exists in single-path based methods. + +We rerun the released code of GDAS [10] for several times and observe that the normal cells are dominated by skip connections and max pooling, shown in Fig. 2. We also draw the evolution of skip connections of GDAS in Fig. 3. + +# 3.2. Possible Reasons of Performance Collapse + +We conjecture that the following two factors contribute most to the collapse issue, which motivates us to provide a remedy in each regard. + +Inconsistency between the searching and evaluation stage. Structural inconsistency between the supernet and the final network mainly appears at the operation level and the topology level. Operation-level inconsistency, i.e., searching with many operations but evaluating only with the most significant one, has been alleviated in recent single-path methods [10, 39] by sampling one operation on each edge at each iteration in the search phase. However, topology-level inconsistency has long been neglected. Specifically, the nodes in the supernet connect with all its predecessors, while the nodes in the final network must only have in-degree 2. In this paper, we eliminate such inconsistency by disentangling topology and operation search. + +Insufficient sampling for candidate operations. The instability issue for single-bath methods can be largely attributed to its stochastic nature that involves sub-sampling. Specifically, at each iteration, only one operation is sampled for each edge, resulting in an insufficient training of weights $\theta$ . It also causes high variance for the gradients of $\alpha$ , hence influencing the searching convergence. To this end, we propose multiple sampling and gradient accumulation to train the supernet and reduce the gradient variance of architectural weights. + +Based on the above reasoning, we propose topology disentanglement (Sec 3.3) to resolve inconsistency and gradient accumulation (Sec 3.6) to rectify the instability caused by insufficient sampling. Fig. 3 illustrate the number of skip connections in a normal cell searched by GDAS and our method (ROME), showing that our method can effectively alleviate the collapse issue. + +# 3.3. Topology Disentanglement + +To disentangle the search for topology and operations on each edge, we use an indicator $B_{i,j} \in \{0,1\}$ to denote whether edge $e_{i,j}$ is selected, and $A_{i,j}^{o} \in \{0,1\}$ for whether operation $o$ on edge $e_{i,j}$ is selected. Sampling architecture $z$ with $M$ connections can be decomposed into two parts: sample $M$ edges first, and their operations second. + +Sampling for edges. Topology inconsistency exists in single-path based methods [10, 39], as all 14 edges in a cell are selected in the search stage but the final architecture only has 8 edges. To address this issue, we propose to sample the same number of edges in search. + +Each intermediate node should connect with exact two predecessors, satisfying DARTS's constraints. Formally, we use $B_{i,j}$ to indicate whether the edge $e_{i,j}$ between node + +$x_{i}$ and $x_{j}$ is sampled, and we enforce, + +$$ +\sum_ {i < j} \boldsymbol {B} _ {i, j} = 2, \quad \forall j. \tag {1} +$$ + +We give two techniques of edge sampling in Sec 3.4. + +Sampling for operations. We use $A_{i,j}^{o}$ to denote whether the operator $o$ is sampled on the edge $e_{i,j}$ , and we adopt Gumbel-Max technique to sample operations, where $g_{i,j}^{o}$ is sampled from Gumbel(0,1) distribution3, and $\tilde{\alpha}_{i,j}^{o} = \frac{\exp(\alpha_{i,j}^{o})}{\sum_{o' \in \mathcal{O}} \exp(\alpha_{i,j}^{o'})}$ is the normalized architectural weights: + +$$ +\boldsymbol {A} _ {i, j} = \text {o n e} \_ \text {h o t} \left[ \arg \max _ {o \in \mathcal {O}} \left(\log \tilde {\boldsymbol {\alpha}} _ {i, j} ^ {o} + \boldsymbol {g} _ {i, j} ^ {o}\right) \right] \in \mathbb {R} ^ {| \mathcal {O} |}, \tag {2} +$$ + +To make the objective function differentiable to architectural weights $\alpha$ , we relax the discrete distribution to a continuous one by Gumbel-Softmax: + +$$ +\begin{array}{l} \tilde {\boldsymbol {A}} _ {i, j} ^ {o} = \frac {\exp \left[ (\log \tilde {\boldsymbol {\alpha}} _ {i , j} ^ {o} + \boldsymbol {g} _ {i , j} ^ {o}) / \tau \right]}{\sum_ {o ^ {\prime} = 1} ^ {| \mathcal {O} |} \exp \left[ (\log \tilde {\boldsymbol {\alpha}} _ {i , j} ^ {o ^ {\prime}} + \boldsymbol {g} _ {i , j} ^ {o ^ {\prime}}) / \tau \right]}, \\ \boldsymbol {A} _ {i, j} = \mathrm {o n e \_ h o t} \left[ \arg \max _ {o \in \mathcal {O}} \tilde {\boldsymbol {A}} _ {i, j} ^ {o} \right], \tag {3} \\ \end{array} +$$ + +where the temperature $\tau$ gradually decreases in search. + +# 3.4. From Gumbel-Max to Gumbel-Top2 Reparameterization + +We propose two variations of edge sampling techniques, i.e. Gumbel-Max and Gumbel-Top2, based on which we derive two versions of ROME (v1 and v2). + +# 3.4.1 Gumbel-Max (ROME-v1). + +Suppose node $x_{j}$ has $j$ possible predecessors, there are $\frac{j \times (j - 1)}{2}$ types of edge choices. We use $I_{j}^{(i,k)} (i < k < j)$ to indicate whether node $x_{j}$ is connected both to $x_{i}$ and $x_{k}$ , i.e. when $I_{j}^{(i,k)} = 1$ , we have $B_{i,j} = B_{k,j} = 1$ and $B_{m,j} = 0 (\forall m < j, m \neq i,j)$ . + +We then set a trainable variable $\beta_j^{(i,k)}$ to denote the importance of each edge choice for node $x_{j}$ , such that + +$$ +p \left(\boldsymbol {I} _ {j} ^ {(i, k)} = 1\right) = \frac {\exp \left(\boldsymbol {\beta} _ {j} ^ {(i , k)}\right)}{\sum_ {i ^ {\prime} < k ^ {\prime} < j} \exp \left(\boldsymbol {\beta} _ {j} ^ {(i ^ {\prime} , k ^ {\prime})}\right)} \triangleq \tilde {\boldsymbol {\beta}} _ {j} ^ {(i, k)}. \tag {4} +$$ + +We use Gumbel-Max technique where $\pmb{g}_j^{(i,k)}$ obeys Gumbel (0,1) distribution, + +$$ +\boldsymbol {I} _ {j} = \text {o n e} _ {-} \operatorname {h o t} \left[ \arg \max _ {i < k < j} \left(\log \tilde {\boldsymbol {\beta}} _ {j} ^ {(i, k)} + \boldsymbol {g} _ {j} ^ {(i, k)}\right) \right] \in \mathbb {R} ^ {\frac {j \times (j - 1)}{2}}. \tag {5} +$$ + +Take a cell as a whole, if edge $e_{i,j}$ is sampled, there must be another chosen $e_{k,j}$ . Thus $\mathbf{B}_{i,j}$ can be formulated by $\mathbf{I}_j$ : + +$$ +\boldsymbol {B} _ {i, j} = \sum_ {k < i} \boldsymbol {I} _ {j} ^ {(k, i)} + \sum_ {k > i} \boldsymbol {I} _ {j} ^ {(i, k)}. \tag {6} +$$ + +Gumbel-Softmax reparameterization is used to retain gradient information, + +$$ +\begin{array}{l} \tilde {\boldsymbol {I}} _ {j} ^ {(i, k)} = \frac {\exp \left\{\left[ \log \tilde {\boldsymbol {\beta}} _ {j} ^ {(i , k)} + \boldsymbol {g} _ {j} ^ {(i , k)} \right] / \tau \right\}}{\sum_ {s < t < j} \exp \left\{\left[ \log \tilde {\boldsymbol {\beta}} _ {j} ^ {(s , t)} + \boldsymbol {g} _ {j} ^ {(s , t)} \right] / \tau \right\}}, \\ \boldsymbol {I} _ {j} = \mathrm {o n e \_ h o t} \left[ \arg \max _ {i < k < j} \tilde {\boldsymbol {I}} _ {j} ^ {(i, k)} \right]. \\ \end{array} +$$ + +# 3.4.2 Gumbel-Top2 (ROME-v2). + +Enumerating all possible edge combinations as in ROME-v1 is straightforward but superfluous, hence in ROME-v2 we directly sample two edges per node. We define the probability of each edge $e_{i,j}$ as $p(e_{i,j})$ . Given edge importance is denoted by $\beta$ , the sampling probability $p(e_{i,j}) = \frac{\exp(\beta_{i,j})}{\sum_{k < j} \exp(\beta_{k,j})} \triangleq \tilde{\beta}_{i,j}$ . + +To satisfy the constraints on the cell topology (Eq. 1), ROME-v2 extends Gumbel-Max to Gumbel-Top2: + +$$ +\tilde {\boldsymbol {B}} _ {i, j} = \frac {\exp \left(\left(\log \tilde {\boldsymbol {\beta}} _ {i , j} + \boldsymbol {g} _ {i , j}\right) / \tau\right)}{\sum_ {i ^ {\prime} < j} \exp \left(\left(\log \tilde {\boldsymbol {\beta}} _ {i ^ {\prime} , j} + \boldsymbol {g} _ {i ^ {\prime} , j}\right) / \tau\right)}, \tag {7} +$$ + +$$ +\boldsymbol {B} _ {i, j} = \left\{ \begin{array}{l l} 1, & i \in \underset {i ^ {\prime} < j} {\arg \operatorname {t o p} 2} \left(\tilde {\boldsymbol {B}} _ {i ^ {\prime}, j}\right) \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {8} +$$ + +We also demonstrate that the Gumbel-Top2 technique is equivalent to sampling two different edges without replacement with probability simplex $p_i$ , so that Gumbel-Top2 sampling can be made differentiable. + +# 3.5. Theoretical Proof on Gumbel-Top2 + +We show that our Gumbel-Top2 technique is equivalent to sampling two different edges without replacement with probability simplex $p_i$ , so that Gumbel-Top2 sampling can be made differentiable. We sketch our proof as follows. + +Let $p_i$ be the probability of sampling $e_i$ by a single choice among $n$ predecessors. Without loss of generality, we compute the probability of sampling $e_1$ in two schemes, and show they are in fact equivalent. + +1. Sampling two edges without replacement: the probability of $e_1$ being sampled is $p_1 + \sum_{i=2}^{n} p_i \frac{p_1}{1 - p_i}$ . +2. Sampling with Gumbel-Top2: Gumbel random variable $g_{i}$ is obtained by sampling a uniform random variable $\epsilon_{i}$ from [0, 1], i.e. $g_{i} = -\log (-\log \epsilon_{i})$ . Then the + +edges are ranked by $(\log p_i + g_i)$ among which the top two are chosen. There are two cases when $e_1$ is sampled, + +(a) $e_1$ ranks first, and the probability of $e_1$ being sampled is $p_1$ due to Gumbel-Max scheme. +(b) $e_1$ ranks second, and $e_i$ ranks first. We can directly get its probability, + +$$ +\begin{array}{l} \int_ {0} ^ {1} \epsilon_ {1} ^ {p _ {2} / p _ {1}} \epsilon_ {1} ^ {p _ {3} / p _ {1}} \dots (1 - \epsilon_ {1} ^ {p _ {i} / p _ {1}}) \dots \epsilon_ {1} ^ {p _ {n} / p _ {1}} d \epsilon_ {1} \\ = \int_ {0} ^ {1} (1 - \epsilon_ {1} ^ {p _ {i} / p _ {1}}) \epsilon_ {1} ^ {\frac {1 - p _ {i}}{p _ {1}} - 1} d \epsilon_ {1} = p _ {i} \frac {p _ {1}}{1 - p _ {i}}. \\ \end{array} +$$ + +The probability of edge $e_1$ being sampled is thus $p_1 + \sum_{i=2}^{n} p_i \frac{p_1}{1 - p_i}$ . + +# 3.6. Gradient Accumulation + +Lastly, we tackle the issues caused by insufficient sampling. Suppose architectural weights $\alpha$ and $\beta$ be the parameters of a distribution for architectures. A candidate architecture $z$ is obtained by independently sampling edges and operations. Suppose $z$ owns $M$ edges $\{e_1,\dots,e_M\}$ and the corresponding operations $\{o_1,\dots,o_M\}$ , then the probability of $z$ being selected is given by + +$$ +p (z; \boldsymbol {\alpha}, \boldsymbol {\beta}) = \prod_ {i = 1} ^ {M} p \left(e _ {i}; \boldsymbol {\beta}\right) \times p \left(o _ {i} \mid e _ {i}; \boldsymbol {\alpha}\right). \tag {9} +$$ + +The search process can be thus modeled as finding optimal $\alpha$ and $\beta$ to minimize the expectation of validation loss of the architectures as Eq. 10, where $\theta_z^*$ denotes the optimal operation parameters for the sampled architecture $z$ . + +$$ +\begin{array}{l} \min _ {\boldsymbol {\alpha}, \boldsymbol {\beta}} \quad \mathbb {E} _ {z \sim p (z; \boldsymbol {\alpha}, \boldsymbol {\beta})} \left[ L _ {v a l} \left(\boldsymbol {\theta} _ {z} ^ {*}, z\right) \right], \tag {10} \\ \text {s . t .} \quad \boldsymbol {\theta} _ {z} ^ {*} = \arg \min _ {\boldsymbol {\theta}} L _ {\text {t r a i n}} (\boldsymbol {\theta}, z) \\ \end{array} +$$ + +However, architecture $z$ changes at each iteration while the corresponding operation weights $\omega$ are updated only once. Apparently, single-path approaches suffer from two problems: unfair and biased training for candidate operations, and creating large variance for architectural weights. + +We propose two effective techniques based on gradient accumulation. First, to boost fair training for operations, we sample $K$ sub-models from the supernet and accumulate gradients for each sub-model within one iteration. Weights $\omega$ are updated by the accumulation of gradients from $K$ sub-models. Second, to reduce the variance for architectural weights, we sample another $K$ sub-models and average the gradients of architectural weights. Suppose that the gradient of $\alpha$ be a random variable whose variance is $\sigma^2$ , then averaging among $K$ samples reduces the variance to + +Algorithm 1 ROME (with two versions v1 and v2). + +Input: iteration count $T$ ; number of sampling $K$ ; initialized operation parameters $\theta$ ; and architectural weights $\alpha$ , $\beta$ ; + +Output: optimal architecture $z^{*}$ + +1: for $t = 1 \rightarrow T$ do +2: Sample two batches of data samples $D_{s}$ and $D_{t}$ from two disjoint datasets; +3: for $k = 1 \rightarrow K$ do +4: Topology sampling by Eq. 6 (v1) or Eq. 7 (v2); Operation sampling by Eq. 3; +5: Get sampled architecture $z_{k}$ ; +6: end for +7: Gradient accumulation and update $\alpha, \beta$ by Eq. 11 on $D_{s}$ , where $L_{val}$ is cross entropy; +8: for $k = 1 \rightarrow K$ do +9: Topology sampling by Eq. 6 (v1) or Eq. 7 (v2); Operation sampling by Eq. 3; +10: Get sampled architecture $z_k'$ ; +11: end for +12: Gradient accumulation and update $\theta$ by Eq. 12 on $D_{t}$ , where $L_{train}$ is cross entropy; +13: end for +14: return: $z^{*} = \arg \max_{z} p(z; \boldsymbol{\alpha}, \boldsymbol{\beta})$ + +$\sigma^2 /K$ . Specifically, we alternately update operation parameters $\pmb{\theta}$ and architectural parameters $\alpha$ (similar for $\beta$ ) as: + +$$ +\boldsymbol {\alpha} \leftarrow \boldsymbol {\alpha} - \frac {1}{K} \sum_ {k = 1} ^ {K} \nabla_ {\boldsymbol {\alpha}} L _ {v a l} (\boldsymbol {\theta}, z _ {k}), \tag {11} +$$ + +$$ +\boldsymbol {\theta} \leftarrow \boldsymbol {\theta} - \sum_ {k = 1} ^ {K} \nabla_ {\boldsymbol {\theta}} L _ {\text {t r a i n}} \left(\boldsymbol {\theta}, z _ {k} ^ {\prime}\right), \tag {12} +$$ + +where $z_k, z_k'$ denote the sampled architectures. We can now summarize our ROME method wholly in Alg. 1. + +# 4. Experiments + +# 4.1. Protocols + +Search spaces. In this paper, we denote DARTS's search space as S0, which comprises a stack of duplicate normal cells and reduction cells. Each cell is represented by a DAG with 4 intermediate nodes. Candidate operations between each two nodes are {maxpool, avgpool, skip_connect, sep_conv $3 \times 3$ and $5 \times 5$ , dil_conv $3 \times 3$ and $5 \times 5$ }. We exclude {none} operation from the default DARTS search space to satisfy the topology constraint in Eq. 1. Under S0 space, we search and evaluate on CIFAR-10 [18] and ImageNet [9] respectively. + +We also conduct experiments on four reduced search spaces, S1-S4, introduced by R-DARTS [48] to evaluate the + +![](images/022543a81aa06c457c4697fa4b05dd88a42d13edef2472100a6032dbbbb58553.jpg) +(a) S1 + +![](images/0c064bda7c10bf6123d69e727b71f7d4af27bb875dc77f702aaca6e54b513acb.jpg) +(b) S2 + +![](images/7e57b257f35677a14141449f451437098da54fc0546eb44a4001592ef44d18a5.jpg) +(c) S3 + +![](images/543890a0abbe3e34fb153af29dd3581485a1c3036ae9aead27cccf0f656bf3f4.jpg) +(a) S1 + +![](images/043e9a62e1ef4f07e43c25cf6d9113a5b29230074c47ac06a1ce7dcb3d4fa6ce.jpg) +(b) S2 +Figure 5: ROME-V2 resolves the aggregation of skip connections on NAS-Bench-1Shot1 [49]. Notice intermediate nodes concatenate their outputs as the input for the output node, while some have loose ends and don't feed to the output node. + +![](images/6ffc9c8b9bdbfaf8e3414368004b526d8bc13be3f8a1096c179465a6bf682f2f.jpg) +Figure 4: GDAS fails on NAS-Bench-1Shot1 [49] when searching on CIFAR-10 in all three search spaces when skip connection are added into choices. In each MixedOp, we have three choices: {maxpool3x3, conv3x3-bn-relu, skip-connect}. +(c) S3 + +stability of our method. S1 is a pre-optimized search space, where each edge in the supernet has a predefined set of candidate operations. In the other 3 search spaces, candidate operations on each edge are the same (see the details in the supplementary). Following [48], we search and evaluate in these 4 search spaces on CIFAR-10, CIFAR-100 [18], and SVHN [26] (12 benchmarks in total). + +Search settings. Similar to DARTS, the supernet consists of 8 cells with 16 initial channels. We search for 50 epochs and set the sampling number $K = 7$ . Unless explicitly written, ROME-v2 is used by default throughout the paper since it is more efficient and robust. For operation parameters, we use the SGD optimizer with a momentum of 0.9 and an initial $lr$ of 0.05; For architectural weights, we adopt the Adam optimizer with an initial $lr$ of $3 \times 10^{-4}$ . + +Evaluation settings. We use standard evaluation settings as DARTS [24] by training the inferred model for 600 epochs using SGD with a batch size of 96. For search space S0, inferred models are constructed by stacking 20 cells with 36 initial channels, and trained under the same settings following [5, 24]. For S1-S4, we strictly follow the settings in R-DARTS [48] for a fair comparison. + +# 4.2. Robustness Evaluation + +For comprehensive evaluation, we follow the recommended best practices for NAS by [21, 48, 4, 6, 8] to report the mean and variance across several times of parallel searching with various random seeds, through which the robustness of a method can be measured. We appeal to the community for avoiding a common mistake that trains a single best-searched model several times, which only tests the + +convergence stability of a single model. + +Discussion on collapse behavior across popular NAS benchmarks. We argue that excluding an important operation for search space can cause illusive conclusions. Specifically, NAS-Bench-1Shot1 [49] suggests that Gumbel-based NAS is quite robust. However, this observation is laying on the basis that popular skip connections are not included in the search space [44]. After adding skip connection into the choices, we perform GDAS using their released code, whose best model found is full of skip connections, which again supports our discovery of collapse issue in single-path based NAS, as shown in Fig. 4. In contrast, ROME does not suffer the same issue in these search spaces, as shown in Fig. 5. + +Robustness evaluation on 12 hard benchmarks. We follow R-DARTS [48] to evaluate the performance and across 3 datasets in S1-S4 search spaces, see Table 1. Our methods robustly outperform other methods with a clear margin across all these benchmarks. + +Additionally, we observe that parameterless operations in GDAS dominate the normal cell in both S2 and S3, while our method effectively handles their numbers and thus stabilizes the searching stage. + +# 4.3. Performance Comparison + +Performance in S0 on CIFAR. We follow DARTS [24] and search on the CIFAR-10. Table 2 shows that ROME achieves state-of-the-art performance with only 0.3 GPU-days $^4$ . ROME has an average of $2.58 \pm 0.07\%$ error rate, + +
BenchmarkDARTS†ES†ADA†GDASROME
Error (%)Error (%)Error (%)Error (%)NumError(%)Num
C10S14.66±0.713.05±0.073.03±0.082.89±0.093.8±0.42.66±0.061.3±0.4
S24.42±0.403.41±0.143.59±0.313.89±0.176.0±0.73.14±0.142.0±0.0
S34.12±0.853.71±1.142.99±0.343.04±0.106.5±0.52.61±0.002.0±0.0
S46.95±0.184.17±0.213.89±0.673.34±0.100.0±0.03.21±0.120.0±0.0
C100S129.93±0.4128.90±0.8124.94±0.8124.49±0.084.0±0.022.71±0.712.3±0.4
S228.75±0.9224.68±1.4326.88±1.1124.57±0.476.3±0.422.91±0.753.5±0.5
S329.01±0.2426.99±1.7924.55±0.6322.86±0.173.0±0.722.43±0.362.5±0.5
S424.77±1.5123.90±2.0123.66±0.9024.14±0.892.3±1.120.95±0.450.0±0.0
SVHNS19.88±5.502.80±0.092.59±0.072.48±0.042.8±0.42.34±0.060.8±0.4
S23.69±0.122.68±0.182.79±0.223.05±0.027.8±0.42.41±0.071.0±0.0
S34.00±1.012.78±0.292.58±0.073.62±0.367.5±0.52.56±0.031.5±0.5
S42.90±0.022.55±0.152.52±0.062.51±0.061.5±1.52.34±0.000.0±0.0
+ +Table 1: Comparison in 4 search spaces and 3 datasets. For each algorithm, we independently search for 3 times under the settings in R-DARTS [48] and report the averaged performance. 'EA' and 'ADA' are two methods proposed by R-DARTS. 'Num': To reveal the collapse issue, we also report the average number of parameterless operations in the discovered normal cell for GDAS and ROME †: Results are obtained from R-DARTS. + +
ModelsParams (M)FLOPs (M)Error (%)Cost GPU DaysSP
DARTS-V1 [45]--3.38±0.230.4X
P-DARTS [5]‡3.3±0.2540±342.81±0.140.3X
PC-DARTS [40]‡3.6±0.5592±902.89±0.220.1X
PR-DARTS [51]‡3.4-2.68±0.100.2X
ISTA-NAS [43]‡3.3-2.71±0.100.05X
R-DARTS [48]--2.95±0.211.6X
SDARTS-ADV [4]3.3-2.61±0.021.3X
DARTS-PT [33]3.0-2.61±0.080.8X
NASI-FIX [29]3.9-2.79±0.070.24X
ZARTS [34]3.7-2.54±0.071.0X
Few-shot NAS [50]3.8-2.31±0.081.35X
GDAS [10]3.4-2.930.2✓
SNAS [39]2.8-2.85±0.021.5✓
ROME-v1 (best)4.56832.530.3✓
ROME-v1 (avg.)4.0±0.6670±212.63±0.090.3✓
ROME-v2 (best)3.65912.480.3✓
ROME-v2 (avg.)3.7±0.2595±282.58±0.070.3✓
+ +which is slightly higher than up-to-date SOTAs such as SDARTS-ADV [4]. However, ROME is more than $4 \times$ faster. Compared with R-DARTS [48], ROME robustly outperforms it with $5 \times$ fewer search costs. Our best model achieves $97.52\%$ accuracy with 3.6M parameters. + +Table 2: Averaged performance among 4 independent runs of search on CIFAR-10. $\ddagger$ : reproduced result using their released code since they didn't report the average performance. $\dagger$ : FLOPs are calculated by their released architecture. SP: single-path based method + +
ModelsParams (M)Error (%)Cost GPU Days
ResNet [14]1.722.10°-
AmoebaNet [28]3.118.93°3150
PNAS [23]3.219.53°150
ENAS [27]4.619.43°0.45
DARTS [24]-20.58±0.44*0.4
GDAS [10]3.418.380.2
P-DARTS [5]3.617.49‡0.3
R-DARTS [48]-18.01±0.261.6
NASI-FIX [29]4.016.12±0.380.24
ZARTS [34]4.116.29±0.531.0
ROME-V1 (avg.)4.4±0.217.41±0.120.3
ROME-V1 (best)4.417.330.3
ROME-V2 (avg.)3.4±0.317.71±0.110.3
ROME-V2 (best)3.317.570.3
+ +Table 3: Comparison of searched models on CIFAR-100. Reported by [10], $\star$ :Reported by [48], $\ddagger$ :Rerun their code. + +We also search on CIFAR-100 and show the results in Table 3. ROME surpasses all the methods and achieves state-of-the-art with only 0.3 GPU-days search cost. + +Performance in S0 on ImageNet. First, we transfer the architecture searched on CIFAR-10 to ImageNet following the common practice [24, 5, 19, 8]. Same as [19, 8], we train models for 250 epochs with a batch size of 1024 by SGD optimizer with a momentum of 0.9 and an initial $lr$ of 0.5 base learning rate. We also utilize an auxiliary classifier strategy. The results are shown in Table 4, where ROME + +
ModelsFLOPsTop-1Cost
(M)(M)(%)(GPU days)
AmoebaNet-A [28]5555.174.53150
NASNet-A [53]5645.374.02000
PNAS [23]5885.174.2225
DARTS [24]5744.773.30.4
P-DARTS [5]5775.175.30.3
FairDARTS-B [8]5414.875.10.4
SNAS [39]5224.372.71.5
PC-DARTS [40]5865.374.90.1
GDAS [10]5815.374.00.2
ROME (ours)5765.275.30.3
DARTS, P-DARTSOOM when batch-size ≥ 32
FairNAS-C [7]3214.474.712
ProxylessNAS [3]4657.175.18.3
FBNet-C [38]3755.574.99
PC-DARTS [40]‡5975.375.43.8
GDAS [10]‡4053.672.50.8
ROME (ours)5565.175.50.5
+ +Table 4: Performance on ImageNet. The first block indicates the models transferred from CIFAR-10; The second block indicates that the models are directly searched on ImageNet. $\ddagger$ : reproduced using their released code. + +achieves $75.3\%$ top-1 accuracy. + +Second, as ROME features low memory cost and great robustness, we directly search on ImageNet as well. We randomly sample $10\%$ images to train operation parameters and another $10\%$ to train architectural weights. A supernet is constructed by stacking 8 cells with 16 initial channels. We search for 30 epochs with $K = 3$ . The batch size is set as 256. Our search cost is reduced to 0.4 GPU days on a single Tesla V100. We fully train the discovered model for 250 epochs with the same evaluation settings as above. Results are illustrated in Tabel 4, showing that ROME achieves $75.5\%$ top-1 accuracy. To make fair comparisons, we reproduce GDAS [10] under the same settings (90 epochs). However, the network is dominated by skip connections and only achieves $72.5\%$ top-1 accuracy. + +# 5. Ablation Study + +Sensitivity to the Sampling Number $K$ . $K$ is a hyperparameter in our gradient accumulation strategy, which is designed to reduce the variance of noise on $\nabla_{\alpha}L_{val}$ and stabilizes the search as analyzed in Sec. 3.6. + +Table 5 compares the performance by setting $K$ as 1, 4, 7, 10 in ROME. We search and evaluate on CIFAR-10. Three parallel tests on each setting are conducted. Note we adjust the number of search epochs to have same number of iterations per test. We observe that the performance in + +
KAcc (%)# Params# Epochs
197.12±0.063.34M350
497.28±0.073.57M87
797.42±0.073.73M50
1097.46±0.124.06M35
+ +Table 5: Sensitivity study of sampling number $K$ . For each setting, we adjust the number of search epochs according to $K$ for fair comparison. We do three parallel tests on each setting and report the mean and standard deviation. + +
TDGAAcc (%)TDGAAcc (%)
θαθα
×××96.52±0.07✓××97.12±0.06
××✓96.85±0.31✓×✓97.22±0.07
×✓×96.98±0.05✓✓×97.34±0.07
×✓✓97.14±0.05✓✓✓97.42±0.07
+ +Table 6: Component study of ROME on CIFAR-10. + +creases monotonically with $K$ which verifies our analysis that biased training shall be alleviated. The result demonstrates the effectiveness of our gradient accumulation strategy. Also, as the accuracy saturates at $K = 7$ , we set $K = 7$ . + +Component analysis for instability issue. There are two major components that contribute to the cure for instability in ROME: topology disentanglement (TD) and gradient accumulation (GA) for $\theta$ and $\alpha$ . To show their efficacy, we conduct ablation studies in S0 space on CIFAR-10. + +Results are shown in Table 6, where 'GA for $\theta$ indicates that gradient accumulation is applied over $K = 7$ sampled architectures to train operation parameters; 'GA for $\alpha$ indicates that gradients for architectural parameters over $K = 7$ sampled architectures is accumulated and averaged. The setting without TD and GA (first line in Table 6) degenerates to GDAS [10]. Our ROME adopts both TD and GA, which is the last line in Table 6. + +We observe that TD alone can significantly improve the searching performance, showing that the inconsistency issue is the principal reason for performance collapse. This is as expected. On the one hand, inconsistent topology between search and evaluation results in an inconsistent searching objective; On the other hand, training the weights of 14 operations (w/o TD) is much more difficult than training 8 operations (w/ TD), which degrades the convergence. + +Moreover, we observe that gradient accumulation on $\theta$ and $\alpha$ can further improve the search performance, which confirms our analysis that performance collapse issue also comes from insufficient sampling. + +Memory Analysis. Table 7 compares GPU memory cost in S0 search space on CIFAR-10. ROME has the lowest + +
MethodDARTSGDASPC-DARTSROME
M=4M=2
Memory (G)9.43.13.75.72.3
+ +Table 7: GPU Memory cost comparison. We measured the cost based on a batch size of 64, where the supernet has 16 initial channels, and 8 layers. + +memory cost thanks to our disentanglement of the search for topology. Unlike GDAS that preserves multiple edges for each node, we strictly sample 2 edges for each node leading to $26\%$ memory reduction compared to GDAS. + +PC-DARTS [40] uses partial channels during the search stage to reduce GPU memory cost, in which the partial ratio is controlled by a hyperparameter $M$ . But $M$ requires careful calibration for different tasks. In contrast, ROME doesn't require calibrating such an extra hyperparameter and is more memory-efficient. + +# 6. Comparison with Prior Works + +Here we highlight the difference of ROME from the existing works. 1) ROME vs. DOTS. DOTS [12] explores an edge importance representation for one-shot NAS in a multi-stage fashion but the operations are divided into two groups (parameter-free and parameter-bearing, following DropNAS [15]) beforehand, which is a very strong prior. The length of each stage has to be tuned carefully from dataset to dataset. In contrast, no prior or extra hyperparameters are used in ROME; 2) ROME vs. DDW. Unlike DDW [46] that belongs to dynamic networks with a changeable topology dependent on inputs, ROME is a NAS method designed to search for a static architecture. 3) ROME vs. SNAS. SNAS [3] adopts Gumbel-softmax via masking, whose supernet still resides in the memory and thus not memory-efficient. In contrast, ROME is a truly single-path NAS method and inherits the property of low memory cost. SNAS didn't deal with the collapse issue either. + +# 7. Conclusion + +In this paper, we highlight the performance collapse issue of single-path differentiable NAS, and attribute the cause to topology inconsistency between searching and evaluation, as well as the stochastic nature of sampling for candidate operations. To address the above issues, we propose ROME that features topology disentanglement and gradient accumulation strategy to stabilize the searching process. ROME achieves state-of-the-art results across 15 recent popular benchmarks, which manifests its strong performance, low memory cost and robustness. + +# Acknowledgments + +Xiaoxing Wang and Yuda Fan partly contributed to this work when they were intern at Meituan and now Yuda Fan is with ETHZ. This work was partly supported by National Key R&D Program of China (No. 2022ZD0118700), NSFC (62222607), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102). + +# References + +[1] Gabriel Bender, Pieter-Jan Kindermans, Barret Zoph, Vijay Vasudevan, and Quoc Le. 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This is where the single-path DARTS comes in, which only chooses a single-path submodel at each step. While being memory-friendly, it also comes with low computational costs. Nonetheless, we discover a critical issue of single-path DARTS that has not been primarily noticed. Namely, it also suffers from severe performance collapse since too many parameter-free operations like skip connections are derived, just like DARTS does. In this paper, we propose a new algorithm called RObustifying Memory-Efficient NAS (ROME) to give a cure. First, we disentangle the topology search from the operation search to make searching and evaluation consistent. We then adopt Gumbel-Top2 reparameterization and gradient accumulation to robustify the unwieldy bi-level optimization. We verify ROME extensively across 15 benchmarks to demonstrate its effectiveness and robustness." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 544, + 128, + 557 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 128, + 557 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 128, + 557 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 564, + 288, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 564, + 288, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 564, + 288, + 696 + ], + "type": "text", + "content": "Despite the fast development of neural architecture search (NAS) [52] to aid network design in vision tasks like classification [32, 6, 41, 42], object detection [11, 36], and segmentation [22], there has been an urging demand for faster searching algorithms. Early methods based on the evaluation of a huge number of candidate models [52, 31, 16] require unaffordable costs (typically 2k GPU days). In the light of weight-sharing mechanism introduced in SMASH [2], a variety of low-cost approaches have emerged [1, 27, 24]. DARTS [24] has taken the dominance with a myriad of follow-up works [38, 3, 39, 10, 5, 47]. In" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 271, + 547, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 271, + 547, + 307 + ], + "spans": [ + { + "bbox": [ + 306, + 271, + 547, + 307 + ], + "type": "text", + "content": "this paper, we investigate a single-path based variation of DARTS, typically GDAS [10], for its fast speed and low GPU memory." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 308, + 546, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 546, + 380 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 546, + 380 + ], + "type": "text", + "content": "Unlike many DARTS variants that have to perform all candidate operations, single-path methods [30, 10, 39], also termed as memory-efficient " + }, + { + "bbox": [ + 304, + 308, + 546, + 380 + ], + "type": "inline_equation", + "content": "\\mathrm{NAS}^1" + }, + { + "bbox": [ + 304, + 308, + 546, + 380 + ], + "type": "text", + "content": ", are developed to sample and activate only a subset of operations in the supernet. For differentiable search, Gumbel-Softmax reparameterization tricks [17, 25] are generally employed [38, 10, 39]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 380, + 547, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 547, + 440 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 547, + 440 + ], + "type": "text", + "content": "In this paper, we show that single-path methods also suffer from severe performance collapse where many parameterless operations accumulate, akin to that of DARTS as broadly discussed in [48, 4, 39, 8, 20]. We propose a robust algorithm called ROME to resolve this issue." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 441, + 547, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 441, + 547, + 583 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 547, + 583 + ], + "type": "text", + "content": "We observe that single-path methods usually intertwine topology search with operation search, which creates inconsistency between searching and evaluation. We first disentangle the two from each other. Specifically, in addition to the existing architectural parameters " + }, + { + "bbox": [ + 304, + 441, + 547, + 583 + ], + "type": "inline_equation", + "content": "(\\alpha)" + }, + { + "bbox": [ + 304, + 441, + 547, + 583 + ], + "type": "text", + "content": " that represent the significance of each operation, we involve topology parameters " + }, + { + "bbox": [ + 304, + 441, + 547, + 583 + ], + "type": "inline_equation", + "content": "(\\beta)" + }, + { + "bbox": [ + 304, + 441, + 547, + 583 + ], + "type": "text", + "content": " to denote the relative importance of edges. A single-path architecture can then be induced by both " + }, + { + "bbox": [ + 304, + 441, + 547, + 583 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 441, + 547, + 583 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 441, + 547, + 583 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 441, + 547, + 583 + ], + "type": "text", + "content": ". Moreover, to further robustify the searching process, we propose a gradient accumulation strategy during the bilevel optimization. We sketch the framework of ROME in Fig. 1. In a nutshell, our contributions are," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 585, + 547, + 693 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 304, + 585, + 547, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 585, + 547, + 668 + ], + "spans": [ + { + "bbox": [ + 304, + 585, + 547, + 668 + ], + "type": "text", + "content": "1) Revealing performance collapse in single-path differentiable NAS. Similar to the performance collapse problem in DARTS, the architectures searched by single-path based methods can also be dominated by parameterless operations, especially skip connections. However, this issue hasn't been deeply explored, which motivates us to propose a new robust, lower memory cost and search cost method." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 669, + 547, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 669, + 547, + 693 + ], + "spans": [ + { + "bbox": [ + 305, + 669, + 547, + 693 + ], + "type": "text", + "content": "2) Consistent search and evaluation by disentangling topology search from operation selection. We introduce" + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 211, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 211, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 211, + 713 + ], + "type": "text", + "content": "*Equal contribution, † Correspondence author." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 702, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 702, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 702, + 545, + 713 + ], + "type": "text", + "content": "1We interchangeably use the term 'single-path' and 'memory-efficient'." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5939" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 102, + 71, + 500, + 264 + ], + "blocks": [ + { + "bbox": [ + 102, + 71, + 500, + 264 + ], + "lines": [ + { + "bbox": [ + 102, + 71, + 500, + 264 + ], + "spans": [ + { + "bbox": [ + 102, + 71, + 500, + 264 + ], + "type": "image", + "image_path": "510a98dc79c64467dc83d6cf82d97ed64bc1db16539c218fa3a17ec8b5f6f226.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 271, + 547, + 298 + ], + "lines": [ + { + "bbox": [ + 46, + 271, + 547, + 298 + ], + "spans": [ + { + "bbox": [ + 46, + 271, + 547, + 298 + ], + "type": "text", + "content": "Figure 1: ROME (v2): Gumbel-Top2 is devised to sample edges to satisfy the restriction that each node has in-degree 2. Subnetworks apply forward and backward independently. Gradients are accumulated to update the supernet weights at once." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 306, + 288, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 306, + 288, + 389 + ], + "spans": [ + { + "bbox": [ + 46, + 306, + 288, + 389 + ], + "type": "text", + "content": "independent topology parameters to unwind topology from operations, which avoids structure inconsistency between the search and evaluation stage. We further devise Gumbel-Top2 re-parameterization to make our method differentiable and provide its theoretical validity. To our best knowledge, this is the first work to achieve consistent search and evaluation for single-path differentiable NAS." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 390, + 288, + 547 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 46, + 390, + 288, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 390, + 288, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 288, + 450 + ], + "type": "text", + "content": "3) Robustifying bi-level optimization via gradient accumulation. We devise two gradient accumulation techniques to address the aforementioned issue. One helps fair training for each candidate operations. The other instead reduces the estimation variance on architectural weights." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 450, + 287, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 547 + ], + "type": "text", + "content": "4) Strong performance while maintaining low memory cost. Tested on the popular settings² for NAS [48, 21, 6], our approach achieves state-of-the-art on various search spaces and datasets across 15 benchmarks. Our approach is fast, robust, and memory efficient. Compared with GDAS and PC-DARTS, our approach costs " + }, + { + "bbox": [ + 46, + 450, + 287, + 547 + ], + "type": "inline_equation", + "content": "26\\%" + }, + { + "bbox": [ + 46, + 450, + 287, + 547 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 450, + 287, + 547 + ], + "type": "inline_equation", + "content": "38\\%" + }, + { + "bbox": [ + 46, + 450, + 287, + 547 + ], + "type": "text", + "content": " lower memory in the standard search space of DARTS respectively. The source code will be made publicly available." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 556, + 134, + 569 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 556, + 134, + 569 + ], + "spans": [ + { + "bbox": [ + 47, + 556, + 134, + 569 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 577, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 577, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 577, + 287, + 685 + ], + "type": "text", + "content": "Differentiable Neural Architecture Search. Similar to [53, 27] that uses a directed acyclic graph to represent a cell, DARTS [24] constructs a cell-based supernet and further introduces architectural weights to represent the importance of each operation. DARTS proposes two types (first-order and second-order) of approximation that alternatively update operation parameters and architectural weights with stochastic gradient descent. However, since the supernet subsumes all connections and operations within the search" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 306, + 545, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 545, + 378 + ], + "type": "text", + "content": "space, DARTS risks exhausting GPU memory. A possible attempt to resolve this issue is done by progressively pruning operations [5], which is still an indirect approach and requires strong regularization tricks. Apart from that, recent works [48, 4] also point out an instability phenomenon of DARTS. These issues significantly restrict its application." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 378, + 546, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 546, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 546, + 569 + ], + "type": "text", + "content": "Memory-efficient NAS. To reduce GPU memory cost, several prior works have revised the forward procedure of the supernet. PC-DARTS [40] makes use of partial connections instead of the full-fledged supernet. Some works [37, 36, 35] proposes to merge all parametric operations into one convolution, a similar super-kernel strategy is also used in single-path NAS [30]. ProxylessNAS [3] samples two operations on each edge during the search process, which enables proxyless searching on large datasets. Single-path supernets like SPOS [13] and FairNAS [7] sample only a single path at each iteration, however, both require an additional searching stage to choose the final models. Single-path differentiable methods like GDAS [10] sample a subgraph of the DAG at each iteration, which is by far the most efficient. However, we observe that a severe instability issue occurs, which has been previously neglected." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "content": "Performance collapse of DARTS. The collapse issue is one of the most critical problems in differentiable architecture search [20, 40, 8, 4, 48]. It has been shown that DARTS [24] prefers to choose parameterless operations, leading to its performance collapse [20, 8]. Recent works [48, 4] utilize the eigenvalue of the Hessian matrix as an indicator of collapse and design various techniques to regularize high eigenvalues. Instead, other works [20, 5] directly constrain the number of skip connections as 2 to avoid collapse. Nonetheless, the previous methods are specifically designed for the full-path training scheme. Whereas the collapse problem in single-path has been rarely studied." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 693, + 288, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 288, + 715 + ], + "type": "text", + "content": "2Independently search under different random seeds instead of multiple training of a single best-searched model." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5940" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 78, + 160, + 164 + ], + "blocks": [ + { + "bbox": [ + 65, + 78, + 160, + 164 + ], + "lines": [ + { + "bbox": [ + 65, + 78, + 160, + 164 + ], + "spans": [ + { + "bbox": [ + 65, + 78, + 160, + 164 + ], + "type": "image", + "image_path": "681004bbaecc4fe22c067ee049d168dccb30ea1c88b002c09746cb8f0bb694bc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 171, + 288, + 233 + ], + "lines": [ + { + "bbox": [ + 46, + 171, + 288, + 233 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 288, + 233 + ], + "type": "text", + "content": "Figure 2: Two failure examples of GDAS [10] in the DARTS search space in our experiment by running the authors' code, where normal cells are full of parameterless operations. The average accuracy is " + }, + { + "bbox": [ + 46, + 171, + 288, + 233 + ], + "type": "inline_equation", + "content": "96.52\\%" + }, + { + "bbox": [ + 46, + 171, + 288, + 233 + ], + "type": "text", + "content": " on CIFAR-10, while models searched by our method can achieve " + }, + { + "bbox": [ + 46, + 171, + 288, + 233 + ], + "type": "inline_equation", + "content": "97.42\\%" + }, + { + "bbox": [ + 46, + 171, + 288, + 233 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 173, + 78, + 267, + 166 + ], + "blocks": [ + { + "bbox": [ + 173, + 78, + 267, + 166 + ], + "lines": [ + { + "bbox": [ + 173, + 78, + 267, + 166 + ], + "spans": [ + { + "bbox": [ + 173, + 78, + 267, + 166 + ], + "type": "image", + "image_path": "3df73e556531c05f594fe0450b2378de71194b0a758c28cd2b3d378f5121ba37.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 56, + 255, + 272, + 355 + ], + "blocks": [ + { + "bbox": [ + 56, + 255, + 272, + 355 + ], + "lines": [ + { + "bbox": [ + 56, + 255, + 272, + 355 + ], + "spans": [ + { + "bbox": [ + 56, + 255, + 272, + 355 + ], + "type": "image", + "image_path": "958a61914769f1d324bf6dde42b4390d1807a5f559f72a6d793f12b94f7e11c1.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 362, + 288, + 387 + ], + "lines": [ + { + "bbox": [ + 46, + 362, + 288, + 387 + ], + "spans": [ + { + "bbox": [ + 46, + 362, + 288, + 387 + ], + "type": "text", + "content": "Figure 3: Evolution of the number of skip connections in a normal cell of GDAS vs. ROME." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 415, + 130, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 415, + 130, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 415, + 130, + 430 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 438, + 271, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 438, + 271, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 438, + 271, + 453 + ], + "type": "text", + "content": "3.1. Collapse in Single-Path Differentiable NAS" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 461, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 545 + ], + "type": "text", + "content": "DARTS [24] optimizes a supernet stacked by normal cells and reduction cells. A cell owns " + }, + { + "bbox": [ + 46, + 461, + 287, + 545 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 461, + 287, + 545 + ], + "type": "text", + "content": " nodes " + }, + { + "bbox": [ + 46, + 461, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\{x_{i}\\}_{i = 1}^{N}" + }, + { + "bbox": [ + 46, + 461, + 287, + 545 + ], + "type": "text", + "content": " denoting latent representation. Edge " + }, + { + "bbox": [ + 46, + 461, + 287, + 545 + ], + "type": "inline_equation", + "content": "e_{i,j}" + }, + { + "bbox": [ + 46, + 461, + 287, + 545 + ], + "type": "text", + "content": " from node " + }, + { + "bbox": [ + 46, + 461, + 287, + 545 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 46, + 461, + 287, + 545 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 461, + 287, + 545 + ], + "type": "inline_equation", + "content": "x_{j}" + }, + { + "bbox": [ + 46, + 461, + 287, + 545 + ], + "type": "text", + "content": " integrates all candidate operations " + }, + { + "bbox": [ + 46, + 461, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 46, + 461, + 287, + 545 + ], + "type": "text", + "content": " whose importance is represented by architecture parameter " + }, + { + "bbox": [ + 46, + 461, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\alpha_{i,j}^{o}" + }, + { + "bbox": [ + 46, + 461, + 287, + 545 + ], + "type": "text", + "content": ". Since the weights of all operations are involved in the forward and backward process, DARTS is very memory-consuming." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 550, + 288, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 550, + 288, + 611 + ], + "spans": [ + { + "bbox": [ + 46, + 550, + 288, + 611 + ], + "type": "text", + "content": "To reduce memory cost, GDAS [10] proposes to sample a sub-set of operations at each iteration. For edge " + }, + { + "bbox": [ + 46, + 550, + 288, + 611 + ], + "type": "inline_equation", + "content": "e_{i,j}" + }, + { + "bbox": [ + 46, + 550, + 288, + 611 + ], + "type": "text", + "content": ", a one-hot random vector " + }, + { + "bbox": [ + 46, + 550, + 288, + 611 + ], + "type": "inline_equation", + "content": "z_{i,j} \\in \\{0,1\\}^{|\\mathcal{O}|}" + }, + { + "bbox": [ + 46, + 550, + 288, + 611 + ], + "type": "text", + "content": " is sampled, indicating only one candidate operation is selected during the forward pass and back-propagation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 613, + 288, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 613, + 288, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 613, + 288, + 662 + ], + "type": "text", + "content": "However, we observe that the normal cell learned by GDAS has 4 skip connections, and GDAS (FRC) even contains 5 skip connections, implying performance collapse issue also exists in single-path based methods." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "We rerun the released code of GDAS [10] for several times and observe that the normal cells are dominated by skip connections and max pooling, shown in Fig. 2. We also draw the evolution of skip connections of GDAS in Fig. 3." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 72, + 525, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 525, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 525, + 85 + ], + "type": "text", + "content": "3.2. Possible Reasons of Performance Collapse" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 94, + 547, + 130 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 94, + 547, + 130 + ], + "spans": [ + { + "bbox": [ + 305, + 94, + 547, + 130 + ], + "type": "text", + "content": "We conjecture that the following two factors contribute most to the collapse issue, which motivates us to provide a remedy in each regard." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 133, + 546, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 546, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 546, + 289 + ], + "type": "text", + "content": "Inconsistency between the searching and evaluation stage. Structural inconsistency between the supernet and the final network mainly appears at the operation level and the topology level. Operation-level inconsistency, i.e., searching with many operations but evaluating only with the most significant one, has been alleviated in recent single-path methods [10, 39] by sampling one operation on each edge at each iteration in the search phase. However, topology-level inconsistency has long been neglected. Specifically, the nodes in the supernet connect with all its predecessors, while the nodes in the final network must only have in-degree 2. In this paper, we eliminate such inconsistency by disentangling topology and operation search." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 292, + 547, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 292, + 547, + 412 + ], + "spans": [ + { + "bbox": [ + 304, + 292, + 547, + 412 + ], + "type": "text", + "content": "Insufficient sampling for candidate operations. The instability issue for single-bath methods can be largely attributed to its stochastic nature that involves sub-sampling. Specifically, at each iteration, only one operation is sampled for each edge, resulting in an insufficient training of weights " + }, + { + "bbox": [ + 304, + 292, + 547, + 412 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 292, + 547, + 412 + ], + "type": "text", + "content": ". It also causes high variance for the gradients of " + }, + { + "bbox": [ + 304, + 292, + 547, + 412 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 292, + 547, + 412 + ], + "type": "text", + "content": ", hence influencing the searching convergence. To this end, we propose multiple sampling and gradient accumulation to train the supernet and reduce the gradient variance of architectural weights." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 415, + 547, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 547, + 499 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 547, + 499 + ], + "type": "text", + "content": "Based on the above reasoning, we propose topology disentanglement (Sec 3.3) to resolve inconsistency and gradient accumulation (Sec 3.6) to rectify the instability caused by insufficient sampling. Fig. 3 illustrate the number of skip connections in a normal cell searched by GDAS and our method (ROME), showing that our method can effectively alleviate the collapse issue." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 517, + 453, + 530 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 517, + 453, + 530 + ], + "spans": [ + { + "bbox": [ + 306, + 517, + 453, + 530 + ], + "type": "text", + "content": "3.3. Topology Disentanglement" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "type": "text", + "content": "To disentangle the search for topology and operations on each edge, we use an indicator " + }, + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "type": "inline_equation", + "content": "B_{i,j} \\in \\{0,1\\}" + }, + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "type": "text", + "content": " to denote whether edge " + }, + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "type": "inline_equation", + "content": "e_{i,j}" + }, + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "type": "text", + "content": " is selected, and " + }, + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "type": "inline_equation", + "content": "A_{i,j}^{o} \\in \\{0,1\\}" + }, + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "type": "text", + "content": " for whether operation " + }, + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "type": "text", + "content": " on edge " + }, + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "type": "inline_equation", + "content": "e_{i,j}" + }, + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "type": "text", + "content": " is selected. Sampling architecture " + }, + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "type": "text", + "content": " connections can be decomposed into two parts: sample " + }, + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 539, + 545, + 612 + ], + "type": "text", + "content": " edges first, and their operations second." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 614, + 547, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 614, + 547, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 614, + 547, + 674 + ], + "type": "text", + "content": "Sampling for edges. Topology inconsistency exists in single-path based methods [10, 39], as all 14 edges in a cell are selected in the search stage but the final architecture only has 8 edges. To address this issue, we propose to sample the same number of edges in search." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "Each intermediate node should connect with exact two predecessors, satisfying DARTS's constraints. Formally, we use " + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "inline_equation", + "content": "B_{i,j}" + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": " to indicate whether the edge " + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "inline_equation", + "content": "e_{i,j}" + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": " between node" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 758 + ], + "type": "text", + "content": "5941" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 203, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 203, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 203, + 84 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 47, + 72, + 203, + 84 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 203, + 84 + ], + "type": "inline_equation", + "content": "x_{j}" + }, + { + "bbox": [ + 47, + 72, + 203, + 84 + ], + "type": "text", + "content": " is sampled, and we enforce," + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 125, + 92, + 287, + 118 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 92, + 287, + 118 + ], + "spans": [ + { + "bbox": [ + 125, + 92, + 287, + 118 + ], + "type": "interline_equation", + "content": "\\sum_ {i < j} \\boldsymbol {B} _ {i, j} = 2, \\quad \\forall j. \\tag {1}", + "image_path": "fc5199dc6edf4a06b0327ab44afa16eef9bb592eb2774d51592556e6d3501b88.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 125, + 272, + 137 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 125, + 272, + 137 + ], + "spans": [ + { + "bbox": [ + 58, + 125, + 272, + 137 + ], + "type": "text", + "content": "We give two techniques of edge sampling in Sec 3.4." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 137, + 287, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 137, + 287, + 217 + ], + "spans": [ + { + "bbox": [ + 47, + 137, + 287, + 217 + ], + "type": "text", + "content": "Sampling for operations. We use " + }, + { + "bbox": [ + 47, + 137, + 287, + 217 + ], + "type": "inline_equation", + "content": "A_{i,j}^{o}" + }, + { + "bbox": [ + 47, + 137, + 287, + 217 + ], + "type": "text", + "content": " to denote whether the operator " + }, + { + "bbox": [ + 47, + 137, + 287, + 217 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 47, + 137, + 287, + 217 + ], + "type": "text", + "content": " is sampled on the edge " + }, + { + "bbox": [ + 47, + 137, + 287, + 217 + ], + "type": "inline_equation", + "content": "e_{i,j}" + }, + { + "bbox": [ + 47, + 137, + 287, + 217 + ], + "type": "text", + "content": ", and we adopt Gumbel-Max technique to sample operations, where " + }, + { + "bbox": [ + 47, + 137, + 287, + 217 + ], + "type": "inline_equation", + "content": "g_{i,j}^{o}" + }, + { + "bbox": [ + 47, + 137, + 287, + 217 + ], + "type": "text", + "content": " is sampled from Gumbel(0,1) distribution3, and " + }, + { + "bbox": [ + 47, + 137, + 287, + 217 + ], + "type": "inline_equation", + "content": "\\tilde{\\alpha}_{i,j}^{o} = \\frac{\\exp(\\alpha_{i,j}^{o})}{\\sum_{o' \\in \\mathcal{O}} \\exp(\\alpha_{i,j}^{o'})}" + }, + { + "bbox": [ + 47, + 137, + 287, + 217 + ], + "type": "text", + "content": " is the normalized architectural weights:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 223, + 287, + 251 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 223, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 53, + 223, + 287, + 251 + ], + "type": "interline_equation", + "content": "\\boldsymbol {A} _ {i, j} = \\text {o n e} \\_ \\text {h o t} \\left[ \\arg \\max _ {o \\in \\mathcal {O}} \\left(\\log \\tilde {\\boldsymbol {\\alpha}} _ {i, j} ^ {o} + \\boldsymbol {g} _ {i, j} ^ {o}\\right) \\right] \\in \\mathbb {R} ^ {| \\mathcal {O} |}, \\tag {2}", + "image_path": "16ee6b2332eaa182041acb7d3925e9b9606b7698a49e7fcd8c2c84c1833cacf7.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 256, + 287, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 256, + 287, + 293 + ], + "spans": [ + { + "bbox": [ + 47, + 256, + 287, + 293 + ], + "type": "text", + "content": "To make the objective function differentiable to architectural weights " + }, + { + "bbox": [ + 47, + 256, + 287, + 293 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 256, + 287, + 293 + ], + "type": "text", + "content": ", we relax the discrete distribution to a continuous one by Gumbel-Softmax:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 77, + 299, + 287, + 360 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 299, + 287, + 360 + ], + "spans": [ + { + "bbox": [ + 77, + 299, + 287, + 360 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\tilde {\\boldsymbol {A}} _ {i, j} ^ {o} = \\frac {\\exp \\left[ (\\log \\tilde {\\boldsymbol {\\alpha}} _ {i , j} ^ {o} + \\boldsymbol {g} _ {i , j} ^ {o}) / \\tau \\right]}{\\sum_ {o ^ {\\prime} = 1} ^ {| \\mathcal {O} |} \\exp \\left[ (\\log \\tilde {\\boldsymbol {\\alpha}} _ {i , j} ^ {o ^ {\\prime}} + \\boldsymbol {g} _ {i , j} ^ {o ^ {\\prime}}) / \\tau \\right]}, \\\\ \\boldsymbol {A} _ {i, j} = \\mathrm {o n e \\_ h o t} \\left[ \\arg \\max _ {o \\in \\mathcal {O}} \\tilde {\\boldsymbol {A}} _ {i, j} ^ {o} \\right], \\tag {3} \\\\ \\end{array}", + "image_path": "42733d822b629436da47689dca727d362b05d5e6c34bce4f222ed6ba036953fa.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 366, + 269, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 366, + 269, + 378 + ], + "spans": [ + { + "bbox": [ + 47, + 366, + 269, + 378 + ], + "type": "text", + "content": "where the temperature " + }, + { + "bbox": [ + 47, + 366, + 269, + 378 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 47, + 366, + 269, + 378 + ], + "type": "text", + "content": " gradually decreases in search." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 384, + 287, + 408 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 287, + 408 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 287, + 408 + ], + "type": "text", + "content": "3.4. From Gumbel-Max to Gumbel-Top2 Reparameterization" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 415, + 287, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 415, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 47, + 415, + 287, + 450 + ], + "type": "text", + "content": "We propose two variations of edge sampling techniques, i.e. Gumbel-Max and Gumbel-Top2, based on which we derive two versions of ROME (v1 and v2)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 464, + 192, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 192, + 477 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 192, + 477 + ], + "type": "text", + "content": "3.4.1 Gumbel-Max (ROME-v1)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "text", + "content": "Suppose node " + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "inline_equation", + "content": "x_{j}" + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "text", + "content": " has " + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "text", + "content": " possible predecessors, there are " + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\frac{j \\times (j - 1)}{2}" + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "text", + "content": " types of edge choices. We use " + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "inline_equation", + "content": "I_{j}^{(i,k)} (i < k < j)" + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "text", + "content": " to indicate whether node " + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "inline_equation", + "content": "x_{j}" + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "text", + "content": " is connected both to " + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "inline_equation", + "content": "x_{k}" + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "text", + "content": ", i.e. when " + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "inline_equation", + "content": "I_{j}^{(i,k)} = 1" + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "text", + "content": ", we have " + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "inline_equation", + "content": "B_{i,j} = B_{k,j} = 1" + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "inline_equation", + "content": "B_{m,j} = 0 (\\forall m < j, m \\neq i,j)" + }, + { + "bbox": [ + 47, + 483, + 287, + 548 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 548, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 287, + 574 + ], + "type": "text", + "content": "We then set a trainable variable " + }, + { + "bbox": [ + 47, + 548, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\beta_j^{(i,k)}" + }, + { + "bbox": [ + 47, + 548, + 287, + 574 + ], + "type": "text", + "content": " to denote the importance of each edge choice for node " + }, + { + "bbox": [ + 47, + 548, + 287, + 574 + ], + "type": "inline_equation", + "content": "x_{j}" + }, + { + "bbox": [ + 47, + 548, + 287, + 574 + ], + "type": "text", + "content": ", such that" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 55, + 582, + 287, + 617 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 582, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 55, + 582, + 287, + 617 + ], + "type": "interline_equation", + "content": "p \\left(\\boldsymbol {I} _ {j} ^ {(i, k)} = 1\\right) = \\frac {\\exp \\left(\\boldsymbol {\\beta} _ {j} ^ {(i , k)}\\right)}{\\sum_ {i ^ {\\prime} < k ^ {\\prime} < j} \\exp \\left(\\boldsymbol {\\beta} _ {j} ^ {(i ^ {\\prime} , k ^ {\\prime})}\\right)} \\triangleq \\tilde {\\boldsymbol {\\beta}} _ {j} ^ {(i, k)}. \\tag {4}", + "image_path": "adfee3b3db9064be68c7a28a0b5f4e359bbda546700979494f413817d80d401a.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 624, + 287, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 624, + 287, + 650 + ], + "spans": [ + { + "bbox": [ + 47, + 624, + 287, + 650 + ], + "type": "text", + "content": "We use Gumbel-Max technique where " + }, + { + "bbox": [ + 47, + 624, + 287, + 650 + ], + "type": "inline_equation", + "content": "\\pmb{g}_j^{(i,k)}" + }, + { + "bbox": [ + 47, + 624, + 287, + 650 + ], + "type": "text", + "content": " obeys Gumbel (0,1) distribution," + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 656, + 289, + 694 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 656, + 289, + 694 + ], + "spans": [ + { + "bbox": [ + 47, + 656, + 289, + 694 + ], + "type": "interline_equation", + "content": "\\boldsymbol {I} _ {j} = \\text {o n e} _ {-} \\operatorname {h o t} \\left[ \\arg \\max _ {i < k < j} \\left(\\log \\tilde {\\boldsymbol {\\beta}} _ {j} ^ {(i, k)} + \\boldsymbol {g} _ {j} ^ {(i, k)}\\right) \\right] \\in \\mathbb {R} ^ {\\frac {j \\times (j - 1)}{2}}. \\tag {5}", + "image_path": "9923a25b235335a01b1bf0a713be19e8a9e4ae15fd4a779ccd16bb51c9388f76.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "text", + "content": "Take a cell as a whole, if edge " + }, + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "e_{i,j}" + }, + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "text", + "content": " is sampled, there must be another chosen " + }, + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "e_{k,j}" + }, + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "text", + "content": ". Thus " + }, + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_{i,j}" + }, + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "text", + "content": " can be formulated by " + }, + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_j" + }, + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 362, + 105, + 545, + 131 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 105, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 362, + 105, + 545, + 131 + ], + "type": "interline_equation", + "content": "\\boldsymbol {B} _ {i, j} = \\sum_ {k < i} \\boldsymbol {I} _ {j} ^ {(k, i)} + \\sum_ {k > i} \\boldsymbol {I} _ {j} ^ {(i, k)}. \\tag {6}", + "image_path": "57aa2fd8634ca9cbda783f92e17511ae8d50504f216c4bb9dd9d2f4237ae3fc4.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 139, + 545, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 139, + 545, + 163 + ], + "spans": [ + { + "bbox": [ + 305, + 139, + 545, + 163 + ], + "type": "text", + "content": "Gumbel-Softmax reparameterization is used to retain gradient information," + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 319, + 171, + 522, + 241 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 171, + 522, + 241 + ], + "spans": [ + { + "bbox": [ + 319, + 171, + 522, + 241 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\tilde {\\boldsymbol {I}} _ {j} ^ {(i, k)} = \\frac {\\exp \\left\\{\\left[ \\log \\tilde {\\boldsymbol {\\beta}} _ {j} ^ {(i , k)} + \\boldsymbol {g} _ {j} ^ {(i , k)} \\right] / \\tau \\right\\}}{\\sum_ {s < t < j} \\exp \\left\\{\\left[ \\log \\tilde {\\boldsymbol {\\beta}} _ {j} ^ {(s , t)} + \\boldsymbol {g} _ {j} ^ {(s , t)} \\right] / \\tau \\right\\}}, \\\\ \\boldsymbol {I} _ {j} = \\mathrm {o n e \\_ h o t} \\left[ \\arg \\max _ {i < k < j} \\tilde {\\boldsymbol {I}} _ {j} ^ {(i, k)} \\right]. \\\\ \\end{array}", + "image_path": "0f711e953ba60c8c25c0bddac7e6d27d0d0cbf6db8ff2d8f2ae9e523762c7518.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 253, + 454, + 265 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 253, + 454, + 265 + ], + "spans": [ + { + "bbox": [ + 306, + 253, + 454, + 265 + ], + "type": "text", + "content": "3.4.2 Gumbel-Top2 (ROME-v2)." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 271, + 545, + 349 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 271, + 545, + 349 + ], + "spans": [ + { + "bbox": [ + 305, + 271, + 545, + 349 + ], + "type": "text", + "content": "Enumerating all possible edge combinations as in ROME-v1 is straightforward but superfluous, hence in ROME-v2 we directly sample two edges per node. We define the probability of each edge " + }, + { + "bbox": [ + 305, + 271, + 545, + 349 + ], + "type": "inline_equation", + "content": "e_{i,j}" + }, + { + "bbox": [ + 305, + 271, + 545, + 349 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 305, + 271, + 545, + 349 + ], + "type": "inline_equation", + "content": "p(e_{i,j})" + }, + { + "bbox": [ + 305, + 271, + 545, + 349 + ], + "type": "text", + "content": ". Given edge importance is denoted by " + }, + { + "bbox": [ + 305, + 271, + 545, + 349 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 271, + 545, + 349 + ], + "type": "text", + "content": ", the sampling probability " + }, + { + "bbox": [ + 305, + 271, + 545, + 349 + ], + "type": "inline_equation", + "content": "p(e_{i,j}) = \\frac{\\exp(\\beta_{i,j})}{\\sum_{k < j} \\exp(\\beta_{k,j})} \\triangleq \\tilde{\\beta}_{i,j}" + }, + { + "bbox": [ + 305, + 271, + 545, + 349 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 349, + 545, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 349, + 545, + 372 + ], + "spans": [ + { + "bbox": [ + 306, + 349, + 545, + 372 + ], + "type": "text", + "content": "To satisfy the constraints on the cell topology (Eq. 1), ROME-v2 extends Gumbel-Max to Gumbel-Top2:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 331, + 380, + 545, + 421 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 380, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 331, + 380, + 545, + 421 + ], + "type": "interline_equation", + "content": "\\tilde {\\boldsymbol {B}} _ {i, j} = \\frac {\\exp \\left(\\left(\\log \\tilde {\\boldsymbol {\\beta}} _ {i , j} + \\boldsymbol {g} _ {i , j}\\right) / \\tau\\right)}{\\sum_ {i ^ {\\prime} < j} \\exp \\left(\\left(\\log \\tilde {\\boldsymbol {\\beta}} _ {i ^ {\\prime} , j} + \\boldsymbol {g} _ {i ^ {\\prime} , j}\\right) / \\tau\\right)}, \\tag {7}", + "image_path": "3fb0b655610f3c48d7b4228062d676e7a49247ddfc86902c0d87895dc73c4aba.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 332, + 422, + 545, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 422, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 332, + 422, + 545, + 460 + ], + "type": "interline_equation", + "content": "\\boldsymbol {B} _ {i, j} = \\left\\{ \\begin{array}{l l} 1, & i \\in \\underset {i ^ {\\prime} < j} {\\arg \\operatorname {t o p} 2} \\left(\\tilde {\\boldsymbol {B}} _ {i ^ {\\prime}, j}\\right) \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {8}", + "image_path": "3310cb0a4b7438521adb4d812e39a4e2b22aaa73ddf973206e618e38e82e5576.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 469, + 545, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 469, + 545, + 516 + ], + "spans": [ + { + "bbox": [ + 306, + 469, + 545, + 516 + ], + "type": "text", + "content": "We also demonstrate that the Gumbel-Top2 technique is equivalent to sampling two different edges without replacement with probability simplex " + }, + { + "bbox": [ + 306, + 469, + 545, + 516 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 306, + 469, + 545, + 516 + ], + "type": "text", + "content": ", so that Gumbel-Top2 sampling can be made differentiable." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 523, + 492, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 523, + 492, + 536 + ], + "spans": [ + { + "bbox": [ + 306, + 523, + 492, + 536 + ], + "type": "text", + "content": "3.5. Theoretical Proof on Gumbel-Top2" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 542, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 542, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 305, + 542, + 545, + 590 + ], + "type": "text", + "content": "We show that our Gumbel-Top2 technique is equivalent to sampling two different edges without replacement with probability simplex " + }, + { + "bbox": [ + 305, + 542, + 545, + 590 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 305, + 542, + 545, + 590 + ], + "type": "text", + "content": ", so that Gumbel-Top2 sampling can be made differentiable. We sketch our proof as follows." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 305, + 590, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 590, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 305, + 590, + 545, + 639 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 305, + 590, + 545, + 639 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 305, + 590, + 545, + 639 + ], + "type": "text", + "content": " be the probability of sampling " + }, + { + "bbox": [ + 305, + 590, + 545, + 639 + ], + "type": "inline_equation", + "content": "e_i" + }, + { + "bbox": [ + 305, + 590, + 545, + 639 + ], + "type": "text", + "content": " by a single choice among " + }, + { + "bbox": [ + 305, + 590, + 545, + 639 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 590, + 545, + 639 + ], + "type": "text", + "content": " predecessors. Without loss of generality, we compute the probability of sampling " + }, + { + "bbox": [ + 305, + 590, + 545, + 639 + ], + "type": "inline_equation", + "content": "e_1" + }, + { + "bbox": [ + 305, + 590, + 545, + 639 + ], + "type": "text", + "content": " in two schemes, and show they are in fact equivalent." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 313, + 646, + 545, + 714 + ], + "type": "list", + "angle": 0, + "index": 32, + "blocks": [ + { + "bbox": [ + 313, + 646, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 646, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 313, + 646, + 545, + 673 + ], + "type": "text", + "content": "1. Sampling two edges without replacement: the probability of " + }, + { + "bbox": [ + 313, + 646, + 545, + 673 + ], + "type": "inline_equation", + "content": "e_1" + }, + { + "bbox": [ + 313, + 646, + 545, + 673 + ], + "type": "text", + "content": " being sampled is " + }, + { + "bbox": [ + 313, + 646, + 545, + 673 + ], + "type": "inline_equation", + "content": "p_1 + \\sum_{i=2}^{n} p_i \\frac{p_1}{1 - p_i}" + }, + { + "bbox": [ + 313, + 646, + 545, + 673 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 313, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 545, + 714 + ], + "type": "text", + "content": "2. Sampling with Gumbel-Top2: Gumbel random variable " + }, + { + "bbox": [ + 313, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "g_{i}" + }, + { + "bbox": [ + 313, + 677, + 545, + 714 + ], + "type": "text", + "content": " is obtained by sampling a uniform random variable " + }, + { + "bbox": [ + 313, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{i}" + }, + { + "bbox": [ + 313, + 677, + 545, + 714 + ], + "type": "text", + "content": " from [0, 1], i.e. " + }, + { + "bbox": [ + 313, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "g_{i} = -\\log (-\\log \\epsilon_{i})" + }, + { + "bbox": [ + 313, + 677, + 545, + 714 + ], + "type": "text", + "content": ". Then the" + } + ] + } + ], + "index": 31 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 56, + 701, + 257, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 701, + 257, + 715 + ], + "spans": [ + { + "bbox": [ + 56, + 701, + 257, + 715 + ], + "type": "text", + "content": "3 " + }, + { + "bbox": [ + 56, + 701, + 257, + 715 + ], + "type": "inline_equation", + "content": "g_{i,j}^{o} = -\\log (-\\log (\\epsilon_{i,j}^{o}))" + }, + { + "bbox": [ + 56, + 701, + 257, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{\\epsilon}_{i,j}^{o}" + }, + { + "bbox": [ + 56, + 701, + 257, + 715 + ], + "type": "text", + "content": " obeys uniform distribution" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5942" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 66, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 66, + 72, + 287, + 109 + ], + "type": "text", + "content": "edges are ranked by " + }, + { + "bbox": [ + 66, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "(\\log p_i + g_i)" + }, + { + "bbox": [ + 66, + 72, + 287, + 109 + ], + "type": "text", + "content": " among which the top two are chosen. There are two cases when " + }, + { + "bbox": [ + 66, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "e_1" + }, + { + "bbox": [ + 66, + 72, + 287, + 109 + ], + "type": "text", + "content": " is sampled," + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 72, + 117, + 287, + 169 + ], + "type": "list", + "angle": 0, + "index": 3, + "blocks": [ + { + "bbox": [ + 72, + 117, + 287, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 117, + 287, + 140 + ], + "spans": [ + { + "bbox": [ + 72, + 117, + 287, + 140 + ], + "type": "text", + "content": "(a) " + }, + { + "bbox": [ + 72, + 117, + 287, + 140 + ], + "type": "inline_equation", + "content": "e_1" + }, + { + "bbox": [ + 72, + 117, + 287, + 140 + ], + "type": "text", + "content": " ranks first, and the probability of " + }, + { + "bbox": [ + 72, + 117, + 287, + 140 + ], + "type": "inline_equation", + "content": "e_1" + }, + { + "bbox": [ + 72, + 117, + 287, + 140 + ], + "type": "text", + "content": " being sampled is " + }, + { + "bbox": [ + 72, + 117, + 287, + 140 + ], + "type": "inline_equation", + "content": "p_1" + }, + { + "bbox": [ + 72, + 117, + 287, + 140 + ], + "type": "text", + "content": " due to Gumbel-Max scheme." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 72, + 144, + 287, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 144, + 287, + 169 + ], + "spans": [ + { + "bbox": [ + 72, + 144, + 287, + 169 + ], + "type": "text", + "content": "(b) " + }, + { + "bbox": [ + 72, + 144, + 287, + 169 + ], + "type": "inline_equation", + "content": "e_1" + }, + { + "bbox": [ + 72, + 144, + 287, + 169 + ], + "type": "text", + "content": " ranks second, and " + }, + { + "bbox": [ + 72, + 144, + 287, + 169 + ], + "type": "inline_equation", + "content": "e_i" + }, + { + "bbox": [ + 72, + 144, + 287, + 169 + ], + "type": "text", + "content": " ranks first. We can directly get its probability," + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 90, + 177, + 287, + 234 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 177, + 287, + 234 + ], + "spans": [ + { + "bbox": [ + 90, + 177, + 287, + 234 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\int_ {0} ^ {1} \\epsilon_ {1} ^ {p _ {2} / p _ {1}} \\epsilon_ {1} ^ {p _ {3} / p _ {1}} \\dots (1 - \\epsilon_ {1} ^ {p _ {i} / p _ {1}}) \\dots \\epsilon_ {1} ^ {p _ {n} / p _ {1}} d \\epsilon_ {1} \\\\ = \\int_ {0} ^ {1} (1 - \\epsilon_ {1} ^ {p _ {i} / p _ {1}}) \\epsilon_ {1} ^ {\\frac {1 - p _ {i}}{p _ {1}} - 1} d \\epsilon_ {1} = p _ {i} \\frac {p _ {1}}{1 - p _ {i}}. \\\\ \\end{array}", + "image_path": "1ea3801a4985b8c6345e6ead1e140e278e7cbdb2d057b9f0512f9f92e3c40927.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 66, + 243, + 287, + 271 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 243, + 287, + 271 + ], + "spans": [ + { + "bbox": [ + 66, + 243, + 287, + 271 + ], + "type": "text", + "content": "The probability of edge " + }, + { + "bbox": [ + 66, + 243, + 287, + 271 + ], + "type": "inline_equation", + "content": "e_1" + }, + { + "bbox": [ + 66, + 243, + 287, + 271 + ], + "type": "text", + "content": " being sampled is thus " + }, + { + "bbox": [ + 66, + 243, + 287, + 271 + ], + "type": "inline_equation", + "content": "p_1 + \\sum_{i=2}^{n} p_i \\frac{p_1}{1 - p_i}" + }, + { + "bbox": [ + 66, + 243, + 287, + 271 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 277, + 181, + 289 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 277, + 181, + 289 + ], + "spans": [ + { + "bbox": [ + 47, + 277, + 181, + 289 + ], + "type": "text", + "content": "3.6. Gradient Accumulation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "type": "text", + "content": "Lastly, we tackle the issues caused by insufficient sampling. Suppose architectural weights " + }, + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "type": "text", + "content": " be the parameters of a distribution for architectures. A candidate architecture " + }, + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "type": "text", + "content": " is obtained by independently sampling edges and operations. Suppose " + }, + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "type": "text", + "content": " owns " + }, + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "type": "text", + "content": " edges " + }, + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "type": "inline_equation", + "content": "\\{e_1,\\dots,e_M\\}" + }, + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "type": "text", + "content": " and the corresponding operations " + }, + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "type": "inline_equation", + "content": "\\{o_1,\\dots,o_M\\}" + }, + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "type": "text", + "content": ", then the probability of " + }, + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 295, + 287, + 380 + ], + "type": "text", + "content": " being selected is given by" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 85, + 388, + 287, + 421 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 388, + 287, + 421 + ], + "spans": [ + { + "bbox": [ + 85, + 388, + 287, + 421 + ], + "type": "interline_equation", + "content": "p (z; \\boldsymbol {\\alpha}, \\boldsymbol {\\beta}) = \\prod_ {i = 1} ^ {M} p \\left(e _ {i}; \\boldsymbol {\\beta}\\right) \\times p \\left(o _ {i} \\mid e _ {i}; \\boldsymbol {\\alpha}\\right). \\tag {9}", + "image_path": "07eb63f6532878e431fe63246c9491d418bb7dc813dbdeb19d4cb421bebd4b59.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 430, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 287, + 477 + ], + "type": "text", + "content": "The search process can be thus modeled as finding optimal " + }, + { + "bbox": [ + 47, + 430, + 287, + 477 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 430, + 287, + 477 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 430, + 287, + 477 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 430, + 287, + 477 + ], + "type": "text", + "content": " to minimize the expectation of validation loss of the architectures as Eq. 10, where " + }, + { + "bbox": [ + 47, + 430, + 287, + 477 + ], + "type": "inline_equation", + "content": "\\theta_z^*" + }, + { + "bbox": [ + 47, + 430, + 287, + 477 + ], + "type": "text", + "content": " denotes the optimal operation parameters for the sampled architecture " + }, + { + "bbox": [ + 47, + 430, + 287, + 477 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 47, + 430, + 287, + 477 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 87, + 486, + 287, + 525 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 486, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 87, + 486, + 287, + 525 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {\\boldsymbol {\\alpha}, \\boldsymbol {\\beta}} \\quad \\mathbb {E} _ {z \\sim p (z; \\boldsymbol {\\alpha}, \\boldsymbol {\\beta})} \\left[ L _ {v a l} \\left(\\boldsymbol {\\theta} _ {z} ^ {*}, z\\right) \\right], \\tag {10} \\\\ \\text {s . t .} \\quad \\boldsymbol {\\theta} _ {z} ^ {*} = \\arg \\min _ {\\boldsymbol {\\theta}} L _ {\\text {t r a i n}} (\\boldsymbol {\\theta}, z) \\\\ \\end{array}", + "image_path": "84b9de3b9e3a4cea60bbb3d4dc6ce4edf0c93e44206307cec1aee1eff0964e51.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 533, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 594 + ], + "type": "text", + "content": "However, architecture " + }, + { + "bbox": [ + 46, + 533, + 287, + 594 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 533, + 287, + 594 + ], + "type": "text", + "content": " changes at each iteration while the corresponding operation weights " + }, + { + "bbox": [ + 46, + 533, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 533, + 287, + 594 + ], + "type": "text", + "content": " are updated only once. Apparently, single-path approaches suffer from two problems: unfair and biased training for candidate operations, and creating large variance for architectural weights." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": "We propose two effective techniques based on gradient accumulation. First, to boost fair training for operations, we sample " + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": " sub-models from the supernet and accumulate gradients for each sub-model within one iteration. Weights " + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": " are updated by the accumulation of gradients from " + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": " sub-models. Second, to reduce the variance for architectural weights, we sample another " + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": " sub-models and average the gradients of architectural weights. Suppose that the gradient of " + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": " be a random variable whose variance is " + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": ", then averaging among " + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": " samples reduces the variance to" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 72, + 515, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 515, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 515, + 84 + ], + "type": "text", + "content": "Algorithm 1 ROME (with two versions v1 and v2)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 85, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 85, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 306, + 85, + 545, + 109 + ], + "type": "text", + "content": "Input: iteration count " + }, + { + "bbox": [ + 306, + 85, + 545, + 109 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 306, + 85, + 545, + 109 + ], + "type": "text", + "content": "; number of sampling " + }, + { + "bbox": [ + 306, + 85, + 545, + 109 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 306, + 85, + 545, + 109 + ], + "type": "text", + "content": "; initialized operation parameters " + }, + { + "bbox": [ + 306, + 85, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 306, + 85, + 545, + 109 + ], + "type": "text", + "content": "; and architectural weights " + }, + { + "bbox": [ + 306, + 85, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 306, + 85, + 545, + 109 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 85, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 306, + 85, + 545, + 109 + ], + "type": "text", + "content": ";" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 110, + 441, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 110, + 441, + 121 + ], + "spans": [ + { + "bbox": [ + 306, + 110, + 441, + 121 + ], + "type": "text", + "content": "Output: optimal architecture " + }, + { + "bbox": [ + 306, + 110, + 441, + 121 + ], + "type": "inline_equation", + "content": "z^{*}" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 309, + 123, + 545, + 354 + ], + "type": "list", + "angle": 0, + "index": 30, + "blocks": [ + { + "bbox": [ + 312, + 123, + 399, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 123, + 399, + 133 + ], + "spans": [ + { + "bbox": [ + 312, + 123, + 399, + 133 + ], + "type": "text", + "content": "1: for " + }, + { + "bbox": [ + 312, + 123, + 399, + 133 + ], + "type": "inline_equation", + "content": "t = 1 \\rightarrow T" + }, + { + "bbox": [ + 312, + 123, + 399, + 133 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 312, + 135, + 545, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 135, + 545, + 159 + ], + "spans": [ + { + "bbox": [ + 312, + 135, + 545, + 159 + ], + "type": "text", + "content": "2: Sample two batches of data samples " + }, + { + "bbox": [ + 312, + 135, + 545, + 159 + ], + "type": "inline_equation", + "content": "D_{s}" + }, + { + "bbox": [ + 312, + 135, + 545, + 159 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 312, + 135, + 545, + 159 + ], + "type": "inline_equation", + "content": "D_{t}" + }, + { + "bbox": [ + 312, + 135, + 545, + 159 + ], + "type": "text", + "content": " from two disjoint datasets;" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 312, + 159, + 413, + 170 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 159, + 413, + 170 + ], + "spans": [ + { + "bbox": [ + 312, + 159, + 413, + 170 + ], + "type": "text", + "content": "3: for " + }, + { + "bbox": [ + 312, + 159, + 413, + 170 + ], + "type": "inline_equation", + "content": "k = 1 \\rightarrow K" + }, + { + "bbox": [ + 312, + 159, + 413, + 170 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 312, + 171, + 545, + 195 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 171, + 545, + 195 + ], + "spans": [ + { + "bbox": [ + 312, + 171, + 545, + 195 + ], + "type": "text", + "content": "4: Topology sampling by Eq. 6 (v1) or Eq. 7 (v2); 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Specifically, we alternately update operation parameters " + }, + { + "bbox": [ + 305, + 379, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}" + }, + { + "bbox": [ + 305, + 379, + 545, + 403 + ], + "type": "text", + "content": " and architectural parameters " + }, + { + "bbox": [ + 305, + 379, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 379, + 545, + 403 + ], + "type": "text", + "content": " (similar for " + }, + { + "bbox": [ + 305, + 379, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 379, + 545, + 403 + ], + "type": "text", + "content": " ) as:" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 351, + 421, + 545, + 453 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 421, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 351, + 421, + 545, + 453 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\alpha} \\leftarrow \\boldsymbol {\\alpha} - \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\nabla_ {\\boldsymbol {\\alpha}} L _ {v a l} (\\boldsymbol {\\theta}, z _ {k}), \\tag {11}", + "image_path": "58eb9d44207240fd29fe525de4295a01cb12b39e1195a167400c40796d7f42cb.jpg" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 372, + 456, + 545, + 489 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 456, + 545, + 489 + ], + "spans": [ + { + "bbox": [ + 372, + 456, + 545, + 489 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\theta} \\leftarrow \\boldsymbol {\\theta} - \\sum_ {k = 1} ^ {K} \\nabla_ {\\boldsymbol {\\theta}} L _ {\\text {t r a i n}} \\left(\\boldsymbol {\\theta}, z _ {k} ^ {\\prime}\\right), \\tag {12}", + "image_path": "54479ab70d403b486bfd93cd8394f38fe2f6dee6a8873cbaada10969e8bcd013.jpg" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 306, + 497, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 497, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 497, + 545, + 521 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 497, + 545, + 521 + ], + "type": "inline_equation", + "content": "z_k, z_k'" + }, + { + "bbox": [ + 306, + 497, + 545, + 521 + ], + "type": "text", + "content": " denote the sampled architectures. We can now summarize our ROME method wholly in Alg. 1." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 306, + 532, + 386, + 545 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 532, + 386, + 545 + ], + "spans": [ + { + "bbox": [ + 306, + 532, + 386, + 545 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 306, + 552, + 372, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 552, + 372, + 563 + ], + "spans": [ + { + "bbox": [ + 306, + 552, + 372, + 563 + ], + "type": "text", + "content": "4.1. Protocols" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "content": "Search spaces. In this paper, we denote DARTS's search space as S0, which comprises a stack of duplicate normal cells and reduction cells. Each cell is represented by a DAG with 4 intermediate nodes. Candidate operations between each two nodes are {maxpool, avgpool, skip_connect, sep_conv " + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "inline_equation", + "content": "5 \\times 5" + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "content": ", dil_conv " + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "inline_equation", + "content": "5 \\times 5" + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "content": "}. We exclude {none} operation from the default DARTS search space to satisfy the topology constraint in Eq. 1. Under S0 space, we search and evaluate on CIFAR-10 [18] and ImageNet [9] respectively." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "We also conduct experiments on four reduced search spaces, S1-S4, introduced by R-DARTS [48] to evaluate the" + } + ] + } + ], + "index": 38 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5943" + } + ] + } + ], + "index": 39 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 64, + 78, + 194, + 133 + ], + "blocks": [ + { + "bbox": [ + 64, + 78, + 194, + 133 + ], + "lines": [ + { + "bbox": [ + 64, + 78, + 194, + 133 + ], + "spans": [ + { + "bbox": [ + 64, + 78, + 194, + 133 + ], + "type": "image", + "image_path": "022543a81aa06c457c4697fa4b05dd88a42d13edef2472100a6032dbbbb58553.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 124, + 144, + 147, + 155 + ], + "lines": [ + { + "bbox": [ + 124, + 144, + 147, + 155 + ], + "spans": [ + { + "bbox": [ + 124, + 144, + 147, + 155 + ], + "type": "text", + "content": "(a) S1" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 222, + 83, + 356, + 128 + ], + "blocks": [ + { + "bbox": [ + 222, + 83, + 356, + 128 + ], + "lines": [ + { + "bbox": [ + 222, + 83, + 356, + 128 + ], + "spans": [ + { + "bbox": [ + 222, + 83, + 356, + 128 + ], + "type": "image", + "image_path": "0c064bda7c10bf6123d69e727b71f7d4af27bb875dc77f702aaca6e54b513acb.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 285, + 137, + 309, + 148 + ], + "lines": [ + { + "bbox": [ + 285, + 137, + 309, + 148 + ], + "spans": [ + { + "bbox": [ + 285, + 137, + 309, + 148 + ], + "type": "text", + "content": "(b) S2" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 384, + 78, + 516, + 133 + ], + "blocks": [ + { + "bbox": [ + 384, + 78, + 516, + 133 + ], + "lines": [ + { + "bbox": [ + 384, + 78, + 516, + 133 + ], + "spans": [ + { + "bbox": [ + 384, + 78, + 516, + 133 + ], + "type": "image", + "image_path": "7e57b257f35677a14141449f451437098da54fc0546eb44a4001592ef44d18a5.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 446, + 144, + 470, + 156 + ], + "lines": [ + { + "bbox": [ + 446, + 144, + 470, + 156 + ], + "spans": [ + { + "bbox": [ + 446, + 144, + 470, + 156 + ], + "type": "text", + "content": "(c) S3" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 62, + 211, + 194, + 253 + ], + "blocks": [ + { + "bbox": [ + 62, + 211, + 194, + 253 + ], + "lines": [ + { + "bbox": [ + 62, + 211, + 194, + 253 + ], + "spans": [ + { + "bbox": [ + 62, + 211, + 194, + 253 + ], + "type": "image", + "image_path": "543890a0abbe3e34fb153af29dd3581485a1c3036ae9aead27cccf0f656bf3f4.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 124, + 263, + 147, + 274 + ], + "lines": [ + { + "bbox": [ + 124, + 263, + 147, + 274 + ], + "spans": [ + { + "bbox": [ + 124, + 263, + 147, + 274 + ], + "type": "text", + "content": "(a) S1" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 223, + 210, + 354, + 255 + ], + "blocks": [ + { + "bbox": [ + 223, + 210, + 354, + 255 + ], + "lines": [ + { + "bbox": [ + 223, + 210, + 354, + 255 + ], + "spans": [ + { + "bbox": [ + 223, + 210, + 354, + 255 + ], + "type": "image", + "image_path": "043e9a62e1ef4f07e43c25cf6d9113a5b29230074c47ac06a1ce7dcb3d4fa6ce.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 285, + 266, + 309, + 276 + ], + "lines": [ + { + "bbox": [ + 285, + 266, + 309, + 276 + ], + "spans": [ + { + "bbox": [ + 285, + 266, + 309, + 276 + ], + "type": "text", + "content": "(b) S2" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 289, + 546, + 314 + ], + "lines": [ + { + "bbox": [ + 46, + 289, + 546, + 314 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 546, + 314 + ], + "type": "text", + "content": "Figure 5: ROME-V2 resolves the aggregation of skip connections on NAS-Bench-1Shot1 [49]. Notice intermediate nodes concatenate their outputs as the input for the output node, while some have loose ends and don't feed to the output node." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 386, + 209, + 514, + 256 + ], + "blocks": [ + { + "bbox": [ + 46, + 165, + 544, + 191 + ], + "lines": [ + { + "bbox": [ + 46, + 165, + 544, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 165, + 544, + 191 + ], + "type": "text", + "content": "Figure 4: GDAS fails on NAS-Bench-1Shot1 [49] when searching on CIFAR-10 in all three search spaces when skip connection are added into choices. In each MixedOp, we have three choices: {maxpool3x3, conv3x3-bn-relu, skip-connect}." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 386, + 209, + 514, + 256 + ], + "lines": [ + { + "bbox": [ + 386, + 209, + 514, + 256 + ], + "spans": [ + { + "bbox": [ + 386, + 209, + 514, + 256 + ], + "type": "image", + "image_path": "6ffc9c8b9bdbfaf8e3414368004b526d8bc13be3f8a1096c179465a6bf682f2f.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 446, + 269, + 470, + 279 + ], + "lines": [ + { + "bbox": [ + 446, + 269, + 470, + 279 + ], + "spans": [ + { + "bbox": [ + 446, + 269, + 470, + 279 + ], + "type": "text", + "content": "(c) S3" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 335, + 287, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 287, + 418 + ], + "type": "text", + "content": "stability of our method. S1 is a pre-optimized search space, where each edge in the supernet has a predefined set of candidate operations. In the other 3 search spaces, candidate operations on each edge are the same (see the details in the supplementary). Following [48], we search and evaluate in these 4 search spaces on CIFAR-10, CIFAR-100 [18], and SVHN [26] (12 benchmarks in total)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "text", + "content": "Search settings. Similar to DARTS, the supernet consists of 8 cells with 16 initial channels. We search for 50 epochs and set the sampling number " + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "inline_equation", + "content": "K = 7" + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "text", + "content": ". Unless explicitly written, ROME-v2 is used by default throughout the paper since it is more efficient and robust. For operation parameters, we use the SGD optimizer with a momentum of 0.9 and an initial " + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "inline_equation", + "content": "lr" + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "text", + "content": " of 0.05; For architectural weights, we adopt the Adam optimizer with an initial " + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "inline_equation", + "content": "lr" + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "inline_equation", + "content": "3 \\times 10^{-4}" + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 516, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 516, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 516, + 287, + 601 + ], + "type": "text", + "content": "Evaluation settings. We use standard evaluation settings as DARTS [24] by training the inferred model for 600 epochs using SGD with a batch size of 96. For search space S0, inferred models are constructed by stacking 20 cells with 36 initial channels, and trained under the same settings following [5, 24]. For S1-S4, we strictly follow the settings in R-DARTS [48] for a fair comparison." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 610, + 176, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 176, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 176, + 621 + ], + "type": "text", + "content": "4.2. Robustness Evaluation" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "For comprehensive evaluation, we follow the recommended best practices for NAS by [21, 48, 4, 6, 8] to report the mean and variance across several times of parallel searching with various random seeds, through which the robustness of a method can be measured. We appeal to the community for avoiding a common mistake that trains a single best-searched model several times, which only tests the" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 335, + 467, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 335, + 467, + 346 + ], + "spans": [ + { + "bbox": [ + 306, + 335, + 467, + 346 + ], + "type": "text", + "content": "convergence stability of a single model." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 347, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 545, + 502 + ], + "type": "text", + "content": "Discussion on collapse behavior across popular NAS benchmarks. We argue that excluding an important operation for search space can cause illusive conclusions. Specifically, NAS-Bench-1Shot1 [49] suggests that Gumbel-based NAS is quite robust. However, this observation is laying on the basis that popular skip connections are not included in the search space [44]. After adding skip connection into the choices, we perform GDAS using their released code, whose best model found is full of skip connections, which again supports our discovery of collapse issue in single-path based NAS, as shown in Fig. 4. In contrast, ROME does not suffer the same issue in these search spaces, as shown in Fig. 5." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 502, + 545, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 545, + 562 + ], + "type": "text", + "content": "Robustness evaluation on 12 hard benchmarks. We follow R-DARTS [48] to evaluate the performance and across 3 datasets in S1-S4 search spaces, see Table 1. Our methods robustly outperform other methods with a clear margin across all these benchmarks." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 563, + 545, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 563, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 563, + 545, + 611 + ], + "type": "text", + "content": "Additionally, we observe that parameterless operations in GDAS dominate the normal cell in both S2 and S3, while our method effectively handles their numbers and thus stabilizes the searching stage." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 618, + 450, + 632 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 618, + 450, + 632 + ], + "spans": [ + { + "bbox": [ + 306, + 618, + 450, + 632 + ], + "type": "text", + "content": "4.3. Performance Comparison" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 637, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 637, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 637, + 545, + 685 + ], + "type": "text", + "content": "Performance in S0 on CIFAR. We follow DARTS [24] and search on the CIFAR-10. Table 2 shows that ROME achieves state-of-the-art performance with only 0.3 GPU-days" + }, + { + "bbox": [ + 304, + 637, + 545, + 685 + ], + "type": "inline_equation", + "content": "^4" + }, + { + "bbox": [ + 304, + 637, + 545, + 685 + ], + "type": "text", + "content": ". ROME has an average of " + }, + { + "bbox": [ + 304, + 637, + 545, + 685 + ], + "type": "inline_equation", + "content": "2.58 \\pm 0.07\\%" + }, + { + "bbox": [ + 304, + 637, + 545, + 685 + ], + "type": "text", + "content": " error rate," + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "4GDAS searches 250 epochs and costs 0.2 GPU-days. ROME searches 50 epochs with " + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "K = 7" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": ", equivalent to searching 350 epochs by GDAS." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5944" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 120, + 70, + 475, + 252 + ], + "blocks": [ + { + "bbox": [ + 120, + 70, + 475, + 252 + ], + "lines": [ + { + "bbox": [ + 120, + 70, + 475, + 252 + ], + "spans": [ + { + "bbox": [ + 120, + 70, + 475, + 252 + ], + "type": "table", + "html": "
BenchmarkDARTS†ES†ADA†GDASROME
Error (%)Error (%)Error (%)Error (%)NumError(%)Num
C10S14.66±0.713.05±0.073.03±0.082.89±0.093.8±0.42.66±0.061.3±0.4
S24.42±0.403.41±0.143.59±0.313.89±0.176.0±0.73.14±0.142.0±0.0
S34.12±0.853.71±1.142.99±0.343.04±0.106.5±0.52.61±0.002.0±0.0
S46.95±0.184.17±0.213.89±0.673.34±0.100.0±0.03.21±0.120.0±0.0
C100S129.93±0.4128.90±0.8124.94±0.8124.49±0.084.0±0.022.71±0.712.3±0.4
S228.75±0.9224.68±1.4326.88±1.1124.57±0.476.3±0.422.91±0.753.5±0.5
S329.01±0.2426.99±1.7924.55±0.6322.86±0.173.0±0.722.43±0.362.5±0.5
S424.77±1.5123.90±2.0123.66±0.9024.14±0.892.3±1.120.95±0.450.0±0.0
SVHNS19.88±5.502.80±0.092.59±0.072.48±0.042.8±0.42.34±0.060.8±0.4
S23.69±0.122.68±0.182.79±0.223.05±0.027.8±0.42.41±0.071.0±0.0
S34.00±1.012.78±0.292.58±0.073.62±0.367.5±0.52.56±0.031.5±0.5
S42.90±0.022.55±0.152.52±0.062.51±0.061.5±1.52.34±0.000.0±0.0
", + "image_path": "ffdba8bd562294f4ea868cf34e6c81965c11cc143de6787c64a89a63773da2a1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 52, + 327, + 282, + 555 + ], + "blocks": [ + { + "bbox": [ + 46, + 260, + 545, + 308 + ], + "lines": [ + { + "bbox": [ + 46, + 260, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 260, + 545, + 308 + ], + "type": "text", + "content": "Table 1: Comparison in 4 search spaces and 3 datasets. For each algorithm, we independently search for 3 times under the settings in R-DARTS [48] and report the averaged performance. 'EA' and 'ADA' are two methods proposed by R-DARTS. 'Num': To reveal the collapse issue, we also report the average number of parameterless operations in the discovered normal cell for GDAS and ROME †: Results are obtained from R-DARTS." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 327, + 282, + 555 + ], + "lines": [ + { + "bbox": [ + 52, + 327, + 282, + 555 + ], + "spans": [ + { + "bbox": [ + 52, + 327, + 282, + 555 + ], + "type": "table", + "html": "
ModelsParams (M)FLOPs (M)Error (%)Cost GPU DaysSP
DARTS-V1 [45]--3.38±0.230.4X
P-DARTS [5]‡3.3±0.2540±342.81±0.140.3X
PC-DARTS [40]‡3.6±0.5592±902.89±0.220.1X
PR-DARTS [51]‡3.4-2.68±0.100.2X
ISTA-NAS [43]‡3.3-2.71±0.100.05X
R-DARTS [48]--2.95±0.211.6X
SDARTS-ADV [4]3.3-2.61±0.021.3X
DARTS-PT [33]3.0-2.61±0.080.8X
NASI-FIX [29]3.9-2.79±0.070.24X
ZARTS [34]3.7-2.54±0.071.0X
Few-shot NAS [50]3.8-2.31±0.081.35X
GDAS [10]3.4-2.930.2✓
SNAS [39]2.8-2.85±0.021.5✓
ROME-v1 (best)4.56832.530.3✓
ROME-v1 (avg.)4.0±0.6670±212.63±0.090.3✓
ROME-v2 (best)3.65912.480.3✓
ROME-v2 (avg.)3.7±0.2595±282.58±0.070.3✓
", + "image_path": "979313aca8e9613e589cfe38bbb57ba3aa96dafdcfe840f6d18926139dc7b183.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "which is slightly higher than up-to-date SOTAs such as SDARTS-ADV [4]. However, ROME is more than " + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": " faster. Compared with R-DARTS [48], ROME robustly outperforms it with " + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "inline_equation", + "content": "5 \\times" + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": " fewer search costs. Our best model achieves " + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "inline_equation", + "content": "97.52\\%" + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": " accuracy with 3.6M parameters." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 309, + 327, + 545, + 537 + ], + "blocks": [ + { + "bbox": [ + 46, + 563, + 287, + 624 + ], + "lines": [ + { + "bbox": [ + 46, + 563, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 287, + 624 + ], + "type": "text", + "content": "Table 2: Averaged performance among 4 independent runs of search on CIFAR-10. " + }, + { + "bbox": [ + 46, + 563, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\ddagger" + }, + { + "bbox": [ + 46, + 563, + 287, + 624 + ], + "type": "text", + "content": ": reproduced result using their released code since they didn't report the average performance. " + }, + { + "bbox": [ + 46, + 563, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 46, + 563, + 287, + 624 + ], + "type": "text", + "content": ": FLOPs are calculated by their released architecture. SP: single-path based method" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 327, + 545, + 537 + ], + "lines": [ + { + "bbox": [ + 309, + 327, + 545, + 537 + ], + "spans": [ + { + "bbox": [ + 309, + 327, + 545, + 537 + ], + "type": "table", + "html": "
ModelsParams (M)Error (%)Cost GPU Days
ResNet [14]1.722.10°-
AmoebaNet [28]3.118.93°3150
PNAS [23]3.219.53°150
ENAS [27]4.619.43°0.45
DARTS [24]-20.58±0.44*0.4
GDAS [10]3.418.380.2
P-DARTS [5]3.617.49‡0.3
R-DARTS [48]-18.01±0.261.6
NASI-FIX [29]4.016.12±0.380.24
ZARTS [34]4.116.29±0.531.0
ROME-V1 (avg.)4.4±0.217.41±0.120.3
ROME-V1 (best)4.417.330.3
ROME-V2 (avg.)3.4±0.317.71±0.110.3
ROME-V2 (best)3.317.570.3
", + "image_path": "9f38d5c9118fe2981a936d45cb0dce0ba70e60a2632353a3260a071c813fb2d4.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 545, + 545, + 571 + ], + "lines": [ + { + "bbox": [ + 306, + 545, + 545, + 571 + ], + "spans": [ + { + "bbox": [ + 306, + 545, + 545, + 571 + ], + "type": "text", + "content": "Table 3: Comparison of searched models on CIFAR-100. Reported by [10], " + }, + { + "bbox": [ + 306, + 545, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\star" + }, + { + "bbox": [ + 306, + 545, + 545, + 571 + ], + "type": "text", + "content": ":Reported by [48], " + }, + { + "bbox": [ + 306, + 545, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\ddagger" + }, + { + "bbox": [ + 306, + 545, + 545, + 571 + ], + "type": "text", + "content": ":Rerun their code." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 592, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 592, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 305, + 592, + 545, + 628 + ], + "type": "text", + "content": "We also search on CIFAR-100 and show the results in Table 3. ROME surpasses all the methods and achieves state-of-the-art with only 0.3 GPU-days search cost." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": "Performance in S0 on ImageNet. First, we transfer the architecture searched on CIFAR-10 to ImageNet following the common practice [24, 5, 19, 8]. Same as [19, 8], we train models for 250 epochs with a batch size of 1024 by SGD optimizer with a momentum of 0.9 and an initial " + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "inline_equation", + "content": "lr" + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": " of 0.5 base learning rate. We also utilize an auxiliary classifier strategy. The results are shown in Table 4, where ROME" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5945" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 70, + 286, + 315 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 286, + 315 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 286, + 315 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 286, + 315 + ], + "type": "table", + "html": "
ModelsFLOPsTop-1Cost
(M)(M)(%)(GPU days)
AmoebaNet-A [28]5555.174.53150
NASNet-A [53]5645.374.02000
PNAS [23]5885.174.2225
DARTS [24]5744.773.30.4
P-DARTS [5]5775.175.30.3
FairDARTS-B [8]5414.875.10.4
SNAS [39]5224.372.71.5
PC-DARTS [40]5865.374.90.1
GDAS [10]5815.374.00.2
ROME (ours)5765.275.30.3
DARTS, P-DARTSOOM when batch-size ≥ 32
FairNAS-C [7]3214.474.712
ProxylessNAS [3]4657.175.18.3
FBNet-C [38]3755.574.99
PC-DARTS [40]‡5975.375.43.8
GDAS [10]‡4053.672.50.8
ROME (ours)5565.175.50.5
", + "image_path": "32a2707b90f17fb9fd2ace415d208c9b34cee0941b186a2750ec0ec106d570b1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 323, + 287, + 373 + ], + "lines": [ + { + "bbox": [ + 46, + 323, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 287, + 373 + ], + "type": "text", + "content": "Table 4: Performance on ImageNet. The first block indicates the models transferred from CIFAR-10; The second block indicates that the models are directly searched on ImageNet. " + }, + { + "bbox": [ + 46, + 323, + 287, + 373 + ], + "type": "inline_equation", + "content": "\\ddagger" + }, + { + "bbox": [ + 46, + 323, + 287, + 373 + ], + "type": "text", + "content": ": reproduced using their released code." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 390, + 176, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 390, + 176, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 390, + 176, + 403 + ], + "type": "text", + "content": "achieves " + }, + { + "bbox": [ + 47, + 390, + 176, + 403 + ], + "type": "inline_equation", + "content": "75.3\\%" + }, + { + "bbox": [ + 47, + 390, + 176, + 403 + ], + "type": "text", + "content": " top-1 accuracy." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 403, + 287, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 571 + ], + "type": "text", + "content": "Second, as ROME features low memory cost and great robustness, we directly search on ImageNet as well. We randomly sample " + }, + { + "bbox": [ + 46, + 403, + 287, + 571 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 403, + 287, + 571 + ], + "type": "text", + "content": " images to train operation parameters and another " + }, + { + "bbox": [ + 46, + 403, + 287, + 571 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 403, + 287, + 571 + ], + "type": "text", + "content": " to train architectural weights. A supernet is constructed by stacking 8 cells with 16 initial channels. We search for 30 epochs with " + }, + { + "bbox": [ + 46, + 403, + 287, + 571 + ], + "type": "inline_equation", + "content": "K = 3" + }, + { + "bbox": [ + 46, + 403, + 287, + 571 + ], + "type": "text", + "content": ". The batch size is set as 256. Our search cost is reduced to 0.4 GPU days on a single Tesla V100. We fully train the discovered model for 250 epochs with the same evaluation settings as above. Results are illustrated in Tabel 4, showing that ROME achieves " + }, + { + "bbox": [ + 46, + 403, + 287, + 571 + ], + "type": "inline_equation", + "content": "75.5\\%" + }, + { + "bbox": [ + 46, + 403, + 287, + 571 + ], + "type": "text", + "content": " top-1 accuracy. To make fair comparisons, we reproduce GDAS [10] under the same settings (90 epochs). However, the network is dominated by skip connections and only achieves " + }, + { + "bbox": [ + 46, + 403, + 287, + 571 + ], + "type": "inline_equation", + "content": "72.5\\%" + }, + { + "bbox": [ + 46, + 403, + 287, + 571 + ], + "type": "text", + "content": " top-1 accuracy." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 584, + 139, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 584, + 139, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 584, + 139, + 597 + ], + "type": "text", + "content": "5. Ablation Study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "text", + "content": "Sensitivity to the Sampling Number " + }, + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "text", + "content": " is a hyperparameter in our gradient accumulation strategy, which is designed to reduce the variance of noise on " + }, + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\nabla_{\\alpha}L_{val}" + }, + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "text", + "content": " and stabilizes the search as analyzed in Sec. 3.6." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": "Table 5 compares the performance by setting " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " as 1, 4, 7, 10 in ROME. We search and evaluate on CIFAR-10. Three parallel tests on each setting are conducted. Note we adjust the number of search epochs to have same number of iterations per test. We observe that the performance in" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 332, + 70, + 520, + 143 + ], + "blocks": [ + { + "bbox": [ + 332, + 70, + 520, + 143 + ], + "lines": [ + { + "bbox": [ + 332, + 70, + 520, + 143 + ], + "spans": [ + { + "bbox": [ + 332, + 70, + 520, + 143 + ], + "type": "table", + "html": "
KAcc (%)# Params# Epochs
197.12±0.063.34M350
497.28±0.073.57M87
797.42±0.073.73M50
1097.46±0.124.06M35
", + "image_path": "bc88bb136bf7f5245cdee457f8c407ea0147e4f1a949e74d46f5a926b4875f90.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 305, + 151, + 545, + 200 + ], + "lines": [ + { + "bbox": [ + 305, + 151, + 545, + 200 + ], + "spans": [ + { + "bbox": [ + 305, + 151, + 545, + 200 + ], + "type": "text", + "content": "Table 5: Sensitivity study of sampling number " + }, + { + "bbox": [ + 305, + 151, + 545, + 200 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 151, + 545, + 200 + ], + "type": "text", + "content": ". For each setting, we adjust the number of search epochs according to " + }, + { + "bbox": [ + 305, + 151, + 545, + 200 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 151, + 545, + 200 + ], + "type": "text", + "content": " for fair comparison. We do three parallel tests on each setting and report the mean and standard deviation." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 315, + 212, + 538, + 296 + ], + "blocks": [ + { + "bbox": [ + 315, + 212, + 538, + 296 + ], + "lines": [ + { + "bbox": [ + 315, + 212, + 538, + 296 + ], + "spans": [ + { + "bbox": [ + 315, + 212, + 538, + 296 + ], + "type": "table", + "html": "
TDGAAcc (%)TDGAAcc (%)
θαθα
×××96.52±0.07✓××97.12±0.06
××✓96.85±0.31✓×✓97.22±0.07
×✓×96.98±0.05✓✓×97.34±0.07
×✓✓97.14±0.05✓✓✓97.42±0.07
", + "image_path": "91e91ad0848cabf213b4e083fb584abb6db1c587929d7c7bd434ec52f3a38a4c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 320, + 304, + 531, + 316 + ], + "lines": [ + { + "bbox": [ + 320, + 304, + 531, + 316 + ], + "spans": [ + { + "bbox": [ + 320, + 304, + 531, + 316 + ], + "type": "text", + "content": "Table 6: Component study of ROME on CIFAR-10." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 339, + 545, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 545, + 387 + ], + "type": "text", + "content": "creases monotonically with " + }, + { + "bbox": [ + 304, + 339, + 545, + 387 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 339, + 545, + 387 + ], + "type": "text", + "content": " which verifies our analysis that biased training shall be alleviated. The result demonstrates the effectiveness of our gradient accumulation strategy. Also, as the accuracy saturates at " + }, + { + "bbox": [ + 304, + 339, + 545, + 387 + ], + "type": "inline_equation", + "content": "K = 7" + }, + { + "bbox": [ + 304, + 339, + 545, + 387 + ], + "type": "text", + "content": ", we set " + }, + { + "bbox": [ + 304, + 339, + 545, + 387 + ], + "type": "inline_equation", + "content": "K = 7" + }, + { + "bbox": [ + 304, + 339, + 545, + 387 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 388, + 545, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 448 + ], + "type": "text", + "content": "Component analysis for instability issue. There are two major components that contribute to the cure for instability in ROME: topology disentanglement (TD) and gradient accumulation (GA) for " + }, + { + "bbox": [ + 304, + 388, + 545, + 448 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 388, + 545, + 448 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 388, + 545, + 448 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 388, + 545, + 448 + ], + "type": "text", + "content": ". To show their efficacy, we conduct ablation studies in S0 space on CIFAR-10." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 448, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 545, + 544 + ], + "type": "text", + "content": "Results are shown in Table 6, where 'GA for " + }, + { + "bbox": [ + 304, + 448, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 448, + 545, + 544 + ], + "type": "text", + "content": " indicates that gradient accumulation is applied over " + }, + { + "bbox": [ + 304, + 448, + 545, + 544 + ], + "type": "inline_equation", + "content": "K = 7" + }, + { + "bbox": [ + 304, + 448, + 545, + 544 + ], + "type": "text", + "content": " sampled architectures to train operation parameters; 'GA for " + }, + { + "bbox": [ + 304, + 448, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 448, + 545, + 544 + ], + "type": "text", + "content": " indicates that gradients for architectural parameters over " + }, + { + "bbox": [ + 304, + 448, + 545, + 544 + ], + "type": "inline_equation", + "content": "K = 7" + }, + { + "bbox": [ + 304, + 448, + 545, + 544 + ], + "type": "text", + "content": " sampled architectures is accumulated and averaged. The setting without TD and GA (first line in Table 6) degenerates to GDAS [10]. Our ROME adopts both TD and GA, which is the last line in Table 6." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 544, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 640 + ], + "type": "text", + "content": "We observe that TD alone can significantly improve the searching performance, showing that the inconsistency issue is the principal reason for performance collapse. This is as expected. On the one hand, inconsistent topology between search and evaluation results in an inconsistent searching objective; On the other hand, training the weights of 14 operations (w/o TD) is much more difficult than training 8 operations (w/ TD), which degrades the convergence." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "text", + "content": "Moreover, we observe that gradient accumulation on " + }, + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 641, + 545, + 689 + ], + "type": "text", + "content": " can further improve the search performance, which confirms our analysis that performance collapse issue also comes from insufficient sampling." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Memory Analysis. Table 7 compares GPU memory cost in S0 search space on CIFAR-10. ROME has the lowest" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5946" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 71, + 286, + 121 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 286, + 121 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 286, + 121 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 286, + 121 + ], + "type": "table", + "html": "
MethodDARTSGDASPC-DARTSROME
M=4M=2
Memory (G)9.43.13.75.72.3
", + "image_path": "67444f35de88c5e7701df5a6542f689a8f7c50bec359de69e4b93fb7201d5fde.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 129, + 287, + 166 + ], + "lines": [ + { + "bbox": [ + 46, + 129, + 287, + 166 + ], + "spans": [ + { + "bbox": [ + 46, + 129, + 287, + 166 + ], + "type": "text", + "content": "Table 7: GPU Memory cost comparison. We measured the cost based on a batch size of 64, where the supernet has 16 initial channels, and 8 layers." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 186, + 287, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 186, + 287, + 235 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 287, + 235 + ], + "type": "text", + "content": "memory cost thanks to our disentanglement of the search for topology. Unlike GDAS that preserves multiple edges for each node, we strictly sample 2 edges for each node leading to " + }, + { + "bbox": [ + 46, + 186, + 287, + 235 + ], + "type": "inline_equation", + "content": "26\\%" + }, + { + "bbox": [ + 46, + 186, + 287, + 235 + ], + "type": "text", + "content": " memory reduction compared to GDAS." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 237, + 287, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 237, + 287, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 237, + 287, + 309 + ], + "type": "text", + "content": "PC-DARTS [40] uses partial channels during the search stage to reduce GPU memory cost, in which the partial ratio is controlled by a hyperparameter " + }, + { + "bbox": [ + 46, + 237, + 287, + 309 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 237, + 287, + 309 + ], + "type": "text", + "content": ". But " + }, + { + "bbox": [ + 46, + 237, + 287, + 309 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 237, + 287, + 309 + ], + "type": "text", + "content": " requires careful calibration for different tasks. In contrast, ROME doesn't require calibrating such an extra hyperparameter and is more memory-efficient." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 327, + 218, + 341 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 327, + 218, + 341 + ], + "spans": [ + { + "bbox": [ + 47, + 327, + 218, + 341 + ], + "type": "text", + "content": "6. Comparison with Prior Works" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 350, + 287, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 553 + ], + "type": "text", + "content": "Here we highlight the difference of ROME from the existing works. 1) ROME vs. DOTS. DOTS [12] explores an edge importance representation for one-shot NAS in a multi-stage fashion but the operations are divided into two groups (parameter-free and parameter-bearing, following DropNAS [15]) beforehand, which is a very strong prior. The length of each stage has to be tuned carefully from dataset to dataset. In contrast, no prior or extra hyperparameters are used in ROME; 2) ROME vs. DDW. Unlike DDW [46] that belongs to dynamic networks with a changeable topology dependent on inputs, ROME is a NAS method designed to search for a static architecture. 3) ROME vs. SNAS. SNAS [3] adopts Gumbel-softmax via masking, whose supernet still resides in the memory and thus not memory-efficient. In contrast, ROME is a truly single-path NAS method and inherits the property of low memory cost. SNAS didn't deal with the collapse issue either." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 571, + 119, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 119, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 119, + 583 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": "In this paper, we highlight the performance collapse issue of single-path differentiable NAS, and attribute the cause to topology inconsistency between searching and evaluation, as well as the stochastic nature of sampling for candidate operations. To address the above issues, we propose ROME that features topology disentanglement and gradient accumulation strategy to stabilize the searching process. ROME achieves state-of-the-art results across 15 recent popular benchmarks, which manifests its strong performance, low memory cost and robustness." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 72, + 403, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 403, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 403, + 85 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 91, + 545, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 91, + 545, + 163 + ], + "spans": [ + { + "bbox": [ + 305, + 91, + 545, + 163 + ], + "type": "text", + "content": "Xiaoxing Wang and Yuda Fan partly contributed to this work when they were intern at Meituan and now Yuda Fan is with ETHZ. This work was partly supported by National Key R&D Program of China (No. 2022ZD0118700), NSFC (62222607), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 307, + 174, + 365, + 186 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 174, + 365, + 186 + ], + "spans": [ + { + "bbox": [ + 307, + 174, + 365, + 186 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 307, + 194, + 547, + 713 + ], + "type": "list", + "angle": 0, + "index": 25, + "blocks": [ + { + "bbox": [ + 310, + 194, + 545, + 237 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 194, + 545, + 237 + ], + "spans": [ + { + "bbox": [ + 310, + 194, + 545, + 237 + ], + "type": "text", + "content": "[1] Gabriel Bender, Pieter-Jan Kindermans, Barret Zoph, Vijay Vasudevan, and Quoc Le. Understanding and Simplifying One-Shot Architecture Search. 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However, as both conventional RGB cameras and LiDAR sensors adopt a frame-based data acquisition mechanism, their performance is limited by the fixed low sampling rates, especially in highly-dynamic scenes. By contrast, the event camera can asynchronously capture the intensity changes with a very high temporal resolution, providing complementary dynamic information of the observed scenes. In this paper, we incorporate RGB images, Point clouds and Events for joint optical flow and scene flow estimation with our proposed multi-stage multimodal fusion model, RPEFlow. First, we present an attention fusion module with a cross-attention mechanism to implicitly explore the internal cross-modal correlation for 2D and 3D branches, respectively. Second, we introduce a mutual information regularization term to explicitly model the complementary information of three modalities for effective multimodal feature learning. We also contribute a new synthetic dataset to advocate further research. Experiments on both synthetic and real datasets show that our model outperforms the existing state-of-the-art by a wide margin. Code and dataset is available at https://npucvr.github.io/RPEFlow.", + "bbox": [ + 75, + 338, + 473, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 729, + 209, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Optical flow estimation, i.e., estimating the dense 2D motion between consecutive image frames, has been extensively studied and significantly advanced with the development of deep neural networks [1-3]. Scene flow estimation, on the other hand, aims to estimate the 3D motion field with various input configurations, ranging from monocular images [4, 5], stereo images [6, 7], two frames of point clouds [8, 9], images combined with depth maps [10, 11]", + "bbox": [ + 75, + 755, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "or point clouds [12, 13]. Both are fundamental to downstream applications such as autonomous driving [14, 15], object tracking [16, 17], scene reconstruction [18, 19], etc.", + "bbox": [ + 500, + 292, + 890, + 338 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Due to the strong correlation between 2D and 3D motion, i.e., 2D motion can be regarded as the projection of 3D motion on the image plane, recent works [10, 12, 13] make efforts to jointly estimate optical flow and scene flow by combining RGB images and point clouds (or depth maps). Their success indicates that joint 2D and 3D motion estimation within a framework can obtain more accurate results than separate tasks. However, as both conventional RGB cameras and LiDAR (or depth) sensors adopt a fixed frame-by-frame data acquisition mechanism, these methods show unsatisfactory performance when dealing with complex motion scenes (see Fig. 3), which motivates us to alleviate this problem by introducing the event camera.", + "bbox": [ + 496, + 339, + 892, + 535 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Event camera, as a bio-inspired imaging sensor, can asynchronously capture the brightness change with very high temporal resolution (in the order of $\\mu s$ ) and output an event signal quickly [20]. As each pixel adapts its sampling rate according to the captured changes, the amount of output events usually depends on the complexity of motion (the faster the motion, the more triggered events), thus providing abundant motion information of the observed scene. Based on this, some works use event data alone to estimate optical flow [21, 22], but they show limitations in estimating reliable motion at regions with no events [23]. As compensation for this, image and event data are fused together to estimate dense optical flow [24, 25]. As far as we know, there is no method to incorporate event data within a multimodal learning framework for both 2D and 3D motion estimation.", + "bbox": [ + 496, + 537, + 893, + 762 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we propose to fuse RGB images, point clouds and events for joint optical flow and scene flow estimation. We find the ability of the event camera to asynchronously capture the brightness changes caused by motion makes it complementary to image cameras and LiDAR sensors, especially for complex dynamics and high-contrast brightness changes. We believe that combining these three modalities together for 2D and 3D motion estimation meets the practical needs, which has been further confirmed by", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author (daiyuchao@gmail.com).", + "bbox": [ + 99, + 887, + 401, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10030", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "existing datasets, such as MVSEC [26] and DSEC [22] that contain these data for driving scenarios.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We formulate this task as a representation-based multimodal learning problem, and exploit the complementary information between these three very different modalities implicitly and explicitly. We aim to exploit the relationships between multimodal and multi-dimensional space observations (images and events in 2D with point clouds in 3D) and explore their contributions to 2D and 3D motion. Specifically, in our RPEFlow framework, we first propose a multimodal attention fusion module with cross-attention mechanism to implicitly explore the correlations between three modalities, based on which a pyramid multi-stage fusion structure is introduced to extensively modeling. We observe that each modality can contribute a part to 2D and 3D motion estimation, making representation learning [27] suitable for our multimodal learning framework. Then we introduce cross-modal mutual information minimization in feature space to explicitly maximize the complementary information. We also contribute a new synthetic dataset with simulations that conform to the gravity model and collision detection and contain a larger variety of moving objects and richer annotations than FlyingThings3D [28]. Extensive experimental results validate both our implicit multimodal attention fusion and explicit representation regularization towards effective multimodal learning, leading to a new benchmark on both synthetic and real-captured datasets.", + "bbox": [ + 75, + 122, + 472, + 500 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions are summarized as follows:", + "bbox": [ + 96, + 501, + 434, + 515 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1) We propose to incorporate event cameras with RGB cameras and LiDAR sensors to jointly estimate optical flow and scene flow for complex dynamic scenes, which constitutes a new and practical problem.", + "2) An implicit multimodal attention fusion module and an explicit representation learning via mutual information regularization are presented in our RPEFlow model, achieving extensive cross-modal relationship modeling.", + "3) We contribute a large-scale synthetic dataset with ground-truth motion annotations. Experimental results on both synthetic and real datasets show that the proposed RPEFlow outperforms existing state-of-the-art and demonstrates the effectiveness of event data for motion estimation of complex dynamics." + ], + "bbox": [ + 76, + 516, + 468, + 728 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 744, + 218, + 758 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Unimodal 2D/3D Motion Estimation", + "text_level": 1, + "bbox": [ + 76, + 770, + 390, + 785 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image only. For learning-based 2D optical flow estimation, FlowNet series [29, 30] first propose end-to-end CNN models for regression. PwC-Net [1] work on constructing feature pyramids with coarse-to-fine refinement. RAFT [2] and its variants [3, 31] build all-pairs correlation and update the optical flow iteratively. For 3D scene flow estimation, learning-based studies [6, 7] use a sequence of stereo im", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ages as input [32], achieving faster and better performance compared with earlier optimization-based methods [15, 33]. Some recent works [4, 5, 34] use only monocular image sequences, which are more difficult to model accurate 3D structure and motion than stereo images. Due to the limited frame rate of input images and the difficulty in obtaining 3D structure, the performance of image-only methods is still unsatisfactory when dealing with complex dynamics.", + "bbox": [ + 496, + 90, + 890, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Point Cloud only. Point cloud data from the LiDAR sensor is favorable for 3D motion estimation. Due to the unique data structure, existing methods [8, 9, 35] focus on studying the model structure to represent the point cloud data for scene flow estimation. However, the point cloud lacks semantic information and leads to the difficulty of estimating accurate motion only by the structural information [13].", + "bbox": [ + 496, + 212, + 890, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Event only. Event-based motion estimation is dedicated to extracting motion information from event-encoded brightness changes. Some early optimization-based methods estimate the motion flow of moving boundaries [36,37]. Recent learning-based methods [21, 22, 38] are proposed to regress the dense optical flow directly. Even though the predictions of some of them are densely supervised, the sparse input event data leads to unreliable optical flow estimation in the regions without triggered events [23, 24].", + "bbox": [ + 496, + 318, + 890, + 454 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Multimodal 2D/3D Motion Estimation", + "text_level": 1, + "bbox": [ + 500, + 465, + 828, + 479 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As unimodal data only provides partial information, multimodal methods are presented to comprehensively learn from multiple observations. For optical flow estimation, event-based studies [24, 25, 39] combine the advantages of the image in dense representation and events in motion perception for reliable estimation. Besides, [40, 41] incorporate gyroscope or depth sensor to guide the optical flow. For scene flow estimation, using a sequences of RGB-Depth images [10, 11] becomes another trend, then [12, 13] replace depth with point clouds to deal with the limited ideal range of depth camera when applied outdoors. But again, they are still limited by the frame-by-frame acquisition mechanism, which leads us to introduce event data.", + "bbox": [ + 496, + 488, + 890, + 684 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Multimodal Fusion", + "text_level": 1, + "bbox": [ + 500, + 695, + 684, + 709 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given multimodal data, effective multimodal fusion is critical to extensively explore the contribution of each modality [42]. Two main directions have been explored: 1) attention based [43-45] and 2) representation learning [46-49] based. For the former, a specific attention module [50, 51] is designed to implicitly control the contribution of each modal. For the latter, representation similarity is measured to explicitly constrain the reliability of the feature embedding. Within this direction, mutual information (MI) estimation and optimization [48, 52-54] is the widely studied strategy, which is typically used as a regularizer to encourage (via MI maximization) or limit dependency (via", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10031", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/587b1c74b4b66448bb5364fa26640483d2178fcd4e842725bc5f0abfe2b64d98.jpg", + "image_caption": [ + "Figure 1: Our RPEFlow Structure. We learn motion correlations from the input three modalities (RGB-PointCloud-Event, RPE) by multi-stage fusion (FS, MS and ES) incorporating explicit multimodal attentional fusion (MAF) and implicit representing learning with mutual information regularization (MIR), and perform pyramidal updates from coarse to fine to estimate the optical flow in the 2D branch (top) and the scene flow in the 3D branch (bottom), respectively. Best viewed on screen." + ], + "image_footnote": [], + "bbox": [ + 88, + 87, + 883, + 345 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "MI minimization) between variables.", + "bbox": [ + 76, + 431, + 323, + 446 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Our Method", + "text_level": 1, + "bbox": [ + 76, + 460, + 207, + 477 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We introduce two main strategies to achieve effective multimodal learning, one is explicit multimodal attention fusion (Sec. 3.1) and the other is implicit mutual information regularization (Sec. 3.2). Based on them, we propose a pyramid multi-stage framework (see Fig. 1) for RGB-PointCloud-Event fusion and joint optical flow and scene flow estimation in 2D and 3D branches (Sec. 3.3).", + "bbox": [ + 75, + 486, + 470, + 592 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Multimodal Attention Fusion (MAF)", + "text_level": 1, + "bbox": [ + 76, + 603, + 395, + 618 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 1, we have both 2D and 3D branches for optical flow and scene flow estimation. Due to the different data structures of the two branches [8, 13], we design symmetric attention fusion strategy for both two branches in Fig. 2, which consists of two steps, namely feature projection and cross-attention fusion. In the 2D branch, we treat the RGB image as the primary modality and project point cloud feature into the image plane, then fuse with auxiliary features, i.e., event and point cloud. For the 3D branch, we define the point cloud data as the primary modality, then project the others into the 3D space and fuse them together. Multimodal Attention Fusion in 3D branch (MAF RPE-3D). We take the fusion module in the 3D branch of a single pyramid level as a detailed example, where the encoded image feature is $e_r \\in \\mathbb{R}^{H \\times W \\times C_{2D}}$ , event feature is $e_{ev} \\in \\mathbb{R}^{H \\times W \\times C_{2D}}$ , and point cloud feature is $e_{pc} \\in \\mathbb{R}^{N \\times C_{3D}}$ with the point positions $\\mathbf{p} = \\{\\mathbf{p}_{x_i}, \\mathbf{p}_{y_i}, \\mathbf{p}_{z_i}\\}^N \\in \\mathbb{R}^{N \\times 3}$ in 3D space. Note that $H, W$ and $N$ are the feature size at", + "bbox": [ + 75, + 626, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the current pyramid level, not the original input size. We first use the point position to sample the corresponding image and event feature into 3D space with focal length $f$ and denote the projected point position at the image plane as:", + "bbox": [ + 498, + 431, + 890, + 492 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\left(u _ {i}, v _ {i}\\right) \\right\\} ^ {N} = \\left\\{\\left(f \\frac {\\mathbf {P} _ {x _ {i}}}{\\mathbf {P} _ {z _ {i}}}, f \\frac {\\mathbf {P} _ {y _ {i}}}{\\mathbf {P} _ {z _ {i}}}\\right) \\right\\} ^ {N} \\in \\mathbb {R} ^ {N \\times 2}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 500, + 890, + 530 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Thus, the projected image and event features are:", + "bbox": [ + 517, + 536, + 844, + 551 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ne _ {r} ^ {p j} = \\left\\{e _ {r} (u _ {i}, v _ {i}) \\right\\} ^ {N}, e _ {e v} ^ {p j} = \\left\\{e _ {e v} (u _ {i}, v _ {i}) \\right\\} ^ {N} \\in \\mathbb {R} ^ {N \\times C _ {2 D}}, (2)\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 559, + 890, + 579 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $e_r(u_i, v_i)$ represents the feature obtained by bilinear interpolation sampling at $(u_i, v_i)$ position in image plane.", + "bbox": [ + 498, + 585, + 890, + 617 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "After projection, we feed the features of auxiliary modalities $e_r^{pj}$ and $e_{ev}^{pj}$ with the primary modality feature $X_{pri}^{3D} = e_{pc}$ into the attention fusion module. In the original self-attention mechanism [50, 51], all of the keys $K$ , values $V$ and queries $Q$ come from the same modality. Here we adapt it to accommodate inputs from multiple modalities and propose our cross-attention fusion structure. Specifically, we first combine the auxiliary features and align the number of channels with the master feature by $1 \\times 1$ convolution, yielding the aligned auxiliary feature $Y_{aux}^{3D} = W_a \\left[ e_r^{pj}, e_{ev}^{pj} \\right] (\\mathbb{R}^N \\times C_{3D} \\Leftarrow \\mathbb{R}^N \\times (C_{2D} + C_{2D}))$ , where $[\\cdot, \\cdot]$ is the concatenation operation. With layer normalization [55] (LN), we apply $3 \\times 3$ depth-wise convolution to encode spatial and channel information with queries $Q_{pri}^{3D} = W_d^Q \\mathrm{LN}(X_{pri}^{3D})$ , keys $K_{aux}^{3D} = W_d^K \\mathrm{LN}(Y_{aux}^{3D})$ and values $V_{aux}^{3D} = W_d^V \\mathrm{LN}(Y_{aux}^{3D})$ , respectively, obtaining the cross-modal self-attention as:", + "bbox": [ + 496, + 618, + 890, + 862 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A t t e n t i o n} (Q, K, V) = V \\operatorname {S o f t m a x} \\left(\\frac {Q ^ {T} K}{\\tau}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 869, + 890, + 905 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10032", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/95b692fa3cc413c5628c2ba7471a90769d59dc7b2d65f9f719caf21fa4b40e6a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 98, + 89, + 447, + 297 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f583210d2a194248f00c58dc935825a93fedd91a42d52950f1594c326131bdef.jpg", + "image_caption": [ + "Figure 2: Our proposed Multimodal Attention Fusion Module fuses both three modal features in 2D (top) and 3D (bottom) branches, including feature projection and cross-attention fusion. In particular, only image and point features are fused in Feature Stage (FS)." + ], + "image_footnote": [], + "bbox": [ + 80, + 303, + 467, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tau$ is a learnable scaling factor. We input $Q_{pri}^{3D}$ , $K_{aux}^{3D}$ , $V_{aux}^{3D}$ to the above attention module, and the resultant attention map with dimension $\\mathbb{R}^{C_{3D} \\times C_{3D}}$ is much smaller and more efficient than the original implementation [51] with dimension $\\mathbb{R}^{HW \\times HW}$ adopted from [56]. With the cross-modal attention in Eq. 3, we obtain the fused feature $X_{pri}^{3D'}$ corresponding to the primary modality $e_{pc}$ by another $1 \\times 1$ convolution projection and residual connection as:", + "bbox": [ + 75, + 598, + 468, + 723 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX _ {p r i} ^ {3 D ^ {\\prime}} = W _ {p} \\mathbf {A t t e n t i o n} (Q _ {p r i} ^ {3 D}, K _ {a u x} ^ {3 D}, V _ {a u x} ^ {3 D}) + X _ {p r i} ^ {3 D}. \\qquad (4)\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 729, + 468, + 752 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multimodal Attention Fusion in 2D branch (MAF RPE-2D). The fusion process in 2D is similar to the 3D branch above. To project the sparse point feature into a dense feature at the image plane, we adopt a learnable fusion-aware interpolation [13] and get the projected point feature $e_{pc}^{pj} \\in \\mathbb{R}^{H \\times W \\times C_{3D}}$ . Then we regard the image feature as the primary modality feature $X_{pri}^{2D} = e_r$ , then the aligned auxiliary feature $Y_{aux}^{2D} = W_a^{2D}\\left[e_{pc}^{pj}, e_{ev}\\right]$ . After similar cross-attention, the fused feature $X_{pri}^{2D'}$ is obtained as:", + "bbox": [ + 75, + 757, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX _ {p r i} ^ {2 D ^ {\\prime}} = W _ {p} \\mathbf {A t t e n t i o n} \\left(Q _ {p r i} ^ {2 D} K _ {a u x} ^ {2 D}, V _ {a u x} ^ {2 D}\\right) + X _ {p r i} ^ {2 D}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 117, + 890, + 138 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Mutual Information Regularization (MIR)", + "text_level": 1, + "bbox": [ + 500, + 150, + 861, + 166 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We incorporate mutual information minimization as a regularizer to explicitly model the cross-modal dependency following disentangled representation learning [27] based on the observation that each modality, i.e. RGB image, point cloud and event data, contributes partially to the output, and mutual information minimization is suitable for our task to explore the complementary information of each modality.", + "bbox": [ + 496, + 174, + 890, + 280 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We start with the case of two modalities with RGB image and event feature embeddings $e_r$ and $e_{ev}$ . Note that these feature embeddings are the features that have been projected into the same spatial space (2D or 3D) in Sec. 3.1.", + "bbox": [ + 496, + 281, + 890, + 340 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To explicitly model the cross-modal correlation, we define cross-modal mutual information between $e_r$ and $e_{ev}$ as $I(e_r;e_{ev}) = \\mathbb{E}_{p(e_r,e_{ev})}\\left[\\log \\frac{p(e_{ev}|e_r)}{p(e_{ev})}\\right]$ , where $p(e_r,e_{ev})$ is the joint distribution, $p(e_{ev}|e_r)$ is the conditional distribution and $p(e_{ev})$ is the marginal distribution. With importance sampling [57], we introduce a variational marginal approximation $q(e_{ev})$ with a variational upper bound $I^{vub}$ [54] of mutual information $I(e_r;e_{ev})$ as:", + "bbox": [ + 496, + 342, + 890, + 469 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} I \\left(e _ {r}; e _ {e v}\\right) \\leq \\mathbb {E} _ {p \\left(e _ {r}, e _ {e v}\\right)} \\left[ \\log \\frac {p \\left(e _ {e v} \\mid e _ {r}\\right)}{q \\left(e _ {e v}\\right)} \\right] \\tag {6} \\\\ = D _ {K L} \\left(p \\left(e _ {e v} \\mid e _ {r}\\right) \\| q \\left(e _ {e v}\\right)\\right) = I ^ {v u b} = \\mathcal {L} _ {\\mathrm {m i}}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 479, + 890, + 534 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $q(e_{ev})$ can be fixed as a standard normal distribution [58], i.e. $q(e_{ev}) = \\mathcal{N}(e_{ev};0,\\mathbf{I})$ , and $p(e_{ev}|e_r)$ can be modeled with the reparameterization trick [59], thus the Kullback-Leibler (KL) divergence term $D_{KL}$ within $I^{vub}$ can be solved in closed form.", + "bbox": [ + 496, + 547, + 890, + 622 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the case of three modalities feature embeddings $e_r$ , $e_{pc}$ and $e_{ev}$ , respectively, the interaction information $II(e_r; e_{pc}; e_{ev})$ [60], as a multivariate generalization of the mutual information, is upper bounded by:", + "bbox": [ + 498, + 625, + 890, + 685 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} I I \\left(e _ {r}; e _ {p c}; e _ {e v}\\right) \\leq \\min \\left\\{I \\left(e _ {r}; e _ {p c}\\right), I \\left(e _ {p c}; e _ {e v}\\right), I \\left(e _ {r}; e _ {e v}\\right) \\right\\} \\tag {7} \\\\ \\leq \\min \\left\\{I ^ {v u b} \\left(e _ {r}; e _ {p c}\\right), I ^ {v u b} \\left(e _ {p c}; e _ {e v}\\right), I ^ {v u b} \\left(e _ {r}; e _ {e v}\\right) \\right\\}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 696, + 890, + 734 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To compute $I^{vub}$ , we need to design a transition function, achieving the transformation of one modality to the other and assume the variational marginal approximation $q$ as the standard normal distribution for closed-form KL divergence computation. In practice, the standard normal distribution assumption of $q$ leads to high-bias mutual information estimation. Alternatively, we first map the representation of each modality $(e_r, e_{pc}, e_{ev})$ to a common manifold, with reparameterization trick [59] in the end to achieve Gaussian latent code of each modality. Then, we compute KL", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10033", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "divergence between the two Gaussian latent codes, leading to the final mutual information regularization term:", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {i i}} = I ^ {v u b} \\left(e _ {r}; e _ {p c}\\right) + I ^ {v u b} \\left(e _ {p c}; e _ {e v}\\right) + I ^ {v u b} \\left(e _ {r}; e _ {e v}\\right), (8)\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 140, + 468, + 159 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we compute the sum of $I^{vub}$ instead of choosing the minimum for stable training.", + "bbox": [ + 76, + 179, + 468, + 209 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Pyramid Fusion and Joint Estimation Model", + "text_level": 1, + "bbox": [ + 76, + 229, + 455, + 247 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the proposed multimodal attention fusion and the mutual information regularization term, we achieve once multimodal feature fusion. Inspired by CamLiFlow [13], we further perform multi-stage feature fusion implicitly and explicitly. Here we present the details of multi-stage feature fusion, and more details about the network structure are given in the supplementary materials. As shown in Fig. 1, our model contains both 2D and 3D branches, where each branch consists of feature extraction, correlation construction and flow estimation.", + "bbox": [ + 75, + 258, + 468, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In feature extraction, we first voxelized the raw events $E = \\{x_{i},y_{i},t_{i},p_{i}\\}^{K}$ into one event voxel $EV\\in \\mathbb{R}^{H\\times W\\times B}$ that can be used as input to our network, where $K$ is the number of events during the period between two frames and $B$ is the manually set number of time intervals to sample events. We apply three Siamese encoders to construct feature pyramids $(\\{e_{r_1},e_{r_2}\\} _l,\\{e_{pc_1},e_{pc_2}\\} _l$ and $e_{ev_l}$ with pyramid layers $l\\in [1,L])$ for three modalities respectively. As spans between two frames, the event data is not included in Feature Stage Fusion, which is applied to fuse the features of two frames RGB images and corresponding point clouds with two-modal attention fusion, i.e. simplify the auxiliary feature to a single modality in Eq. 4, 5 and mutual information regularization in Eq. 6 for both 2D and 3D branches.", + "bbox": [ + 75, + 412, + 468, + 625 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In correlation construction, we first warp the second frame of image and point cloud features using the coarse optical flow and scene flow (initialize with zero) from the previous pyramid layer, then construct correlation motion features by computing 2D and 3D cost volumes and fused them with the event feature at Motion Stage Fusion. In flow estimation, we construct a motion decoder and flow estimator, and perform an Estimation Stage Fusion between them to fuse the hidden motion features from the two branches decoder with the event feature. In these two fusion stages, we conduct multimodal attention fusion in Eq. 4, 5 and mutual information regularization in Eq. 8 for 2D and 3D motion features and event feature, because events can provide complementary information to enhance the motion correlation construction. The estimated optical flow and scene flow are fed into the next pyramid layer to achieve coarse-to-fine predictions. We take the optical flow and scene flow from the last pyramid layer as our final joint estimations.", + "bbox": [ + 75, + 628, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Objective Functions", + "text_level": 1, + "bbox": [ + 500, + 90, + 691, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The objective functions in the training of our model are divided into feature representation loss and task loss. The former consists of multiple mutual information regularizations at each fusion stage. $\\mathcal{L}_{\\mathrm{mi}}^{fs1}$ , $\\mathcal{L}_{\\mathrm{mi}}^{fs2}$ represent the mutual information minimization loss imposed on the RGB image and point cloud features of the first and the second frame at the Feature Stage fusion, and $\\mathcal{L}_{\\mathrm{ii}}^{ms}$ and $\\mathcal{L}_{\\mathrm{ii}}^{es}$ represent on both RGB image, point cloud and event features at the Motion Stage and Estimation Stage fusion. Thus the feature representation loss is the sum of all stages and is weighted at each pyramid level:", + "bbox": [ + 496, + 114, + 890, + 281 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {f e a t}} = \\sum_ {l = 1} ^ {L} \\lambda_ {l} \\left[ \\mathcal {L} _ {\\mathrm {m i}} ^ {f s 1} _ {l} + \\mathcal {L} _ {\\mathrm {m i}} ^ {f s 2} _ {l} + \\mathcal {L} _ {\\mathrm {i i}} ^ {m s} _ {l} + \\mathcal {L} _ {\\mathrm {i i}} ^ {e s} _ {l} \\right], \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 292, + 890, + 334 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $l$ is the pyramid level, and $\\lambda_{l}$ is used to reweight the contribution of each pyramid level.", + "bbox": [ + 498, + 345, + 890, + 375 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The latter task loss measures the $L_{2}$ distance between the ground-truth and the model output at each pyramid level by:", + "bbox": [ + 500, + 376, + 890, + 407 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {t a s k}} = \\sum_ {l = 1} ^ {L} \\lambda_ {l} \\left[ \\sum_ {\\mathbf {x}} \\left(\\| f _ {l} ^ {\\text {p r e d}} (\\mathbf {x}) - f _ {l} ^ {\\text {g t}} (\\mathbf {x}) \\| _ {2}\\right) + \\right. \\tag {10} \\\\ \\alpha \\sum_ {\\mathbf {p}} (\\| s _ {l} ^ {p r e d} (\\mathbf {p}) - s _ {l} ^ {g t} (\\mathbf {p}) \\| _ {2}) \\Big ], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 431, + 890, + 508 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{x}$ , $\\mathbf{p}$ are the valid image positions and point coordinates, $f_{l}^{pred}$ , $s_{l}^{pred}$ are the estimated 2D optical flow and 3D scene flow and $f_{l}^{gt}$ , $s_{l}^{gt}$ are the corresponding resized ground truth at the $l$ -th pyramid level, respectively. $\\alpha$ is the weight to balance 2D and 3D errors.", + "bbox": [ + 498, + 521, + 890, + 597 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The total loss is a weighted sum of the above:", + "bbox": [ + 517, + 598, + 821, + 613 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {t a s k}} + \\beta \\mathcal {L} _ {\\text {f e a t}}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 629, + 626, + 890, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\beta$ is the weight to balance two losses in training.", + "bbox": [ + 500, + 655, + 862, + 671 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 500, + 685, + 624, + 702 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 710, + 715, + 726 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. Since there is no large-scale scene flow dataset with real event data, we use synthetic data for pretraining. Follow the preprocess pipeline [13, 62], we generate point clouds from depth images for FlyingThings3D [28] dataset, which contains 19,640 and 3,824 RGB-PointColud pairs for \"train\" and \"val\" splits. We use the popular video-to-events conversion method [63] to generate the corresponding events. In addition, we use kubric [64] to simulate 15,367 RGB-PointCloud-Event pairs with rich annotations (including optical flow and scene flow ground truths), denoted as EKubric, which aims to simulate photo-realistic", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10034", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/68d25ed7f006533cd1f8e419c0ff09fab54126b0ea0a7653c773b8d2aa993abe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 88, + 212, + 265 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a55df57847bbda136569dc62793df4e4fc8e96da95b4a51d58f6eaaff0a95c99.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 215, + 89, + 348, + 265 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9d9f6ffb8832fe637bf53898eeff4d723091de7172c0f7f5cfb2b29ce15d8576.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 88, + 483, + 265 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4df0d62db1c7114a4d411a2a77e515b221f402ea95ebc5d2d982433fa9a905d6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 485, + 88, + 619, + 265 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/587c73308d86d3cc18f6e6fe8ec2b8eb28433928e8f954b6137658560166e8c3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 88, + 754, + 265 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0fc0e13953a9ac22706a191996313c0bc9102e30b2efb704f86f352116fb3466.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 756, + 88, + 890, + 265 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5b5cec11028640e8b27cea53d3cc13f1ab022f5f47bf88ba0b723e6793afdaa6.jpg", + "image_caption": [ + "Figure 3: Visual comparisons on simulated data, in which the top row is on the \"val\" split of FlyingThings3D [28] dataset and the reset two are on the test split of our simulated EKubric dataset. For the bottom 3D comparisons, blue indicates a lower error, red indicates a higher error, and green indicates the median. Best to zoom in on the screen for detailed comparisons." + ], + "image_footnote": [], + "bbox": [ + 86, + 266, + 243, + 438 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c45a81f6e6fbdd687c659d595151234811beb8d73f54b84a6539f7f8156bd26c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 253, + 266, + 401, + 438 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6b9d875b28fa6c96052c5310d5bf3fe23c86fac9f0f088b80b7fd7a620a651d8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 410, + 266, + 558, + 438 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/726718d4579b85a2bf57d0dcd59073e495375b21e4d7d228bac33b639e4c3947.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 566, + 266, + 717, + 436 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/aa1f90830d0616e47029b4517645fbbeb9fe8b464401e64d7ddfe91079d1cd79.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 723, + 266, + 923, + 438 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c8036b96e9ea67ea17bab80a6c978819b34372e59b072193a1a08edf4f5c785c.jpg", + "table_caption": [ + "Table 1: Performance comparison on the \"val\" split of the FlyingThings3D [28] subset." + ], + "table_footnote": [], + "table_body": "
InputMethodEPE2DACC1pxEPEN.Occ3DACCN.Occ05EPEFull3DACCFull05
RGBRAFT [2]3.1281.1%----
FlowFormer [3]3.0282.6%----
PCMeteornet* [61]----0.209-
PointPWC [8]--0.11251.8%--
SCTN [9]--0.03884.7%--
RGB+DepthRAFT-3D [10]2.3787.1%0.06284.5%0.08971.1%
RGB+PCDeepLiDARFlow [12]6.0447.1%-27.2%--
CamLiFlow [13]2.2084.6%0.03391.7%0.05986.0%
RGB+EventRAFT+Event2.4984.6%----
RGB+PC+EventCamLiFlow+Event1.5684.4%0.02891.7%0.04885.9%
RPEFlow (Ours)1.4086.2%0.02493.1%0.04288.0%
", + "bbox": [ + 94, + 536, + 874, + 718 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "scenes with collision detection, gravity model and ambient illumination and has more object kinds than FlyingThings3D. We also use the DSEC [22] dataset, which contains 8,170 pairs of real-captured samples in driving scenarios.", + "bbox": [ + 75, + 742, + 468, + 803 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training, Hyper-parameters and Metrics. Our model is trained with PyTorch on four RTX3090 GPUs and evaluated on one. We use the Adam optimizer with weight decay $10^{-6}$ . The number of event bins is $B = 10$ , pyramid layers is $L = 5$ . Loss weights are $\\alpha = 10.0$ , $\\beta = 0.01$ , $\\lambda_l = 2^{(l - 2)}$ for $l \\in [1, L]$ . Following [10, 13], we evalu", + "bbox": [ + 75, + 809, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ate using 2D and 3D end-point error (EPE $_{2\\mathrm{D}}$ and EPE $_{3\\mathrm{D}}$ ), and $\\mathrm{ACC}_{1\\mathrm{px}}$ and $\\mathrm{ACC}_{.05}$ to measure the portion of accuracy within 1 pixel and $5\\mathrm{cm}$ . The scene flow metrics with N.Occ superscript indicates only the not occluded positions are calculated, while Full or none indicates all positions including occlusion. More details about datasets and training are provided in the supplementary materials.", + "bbox": [ + 496, + 742, + 890, + 849 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10035", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5376542b1c2a3ca12b250b3841737389dd880aa3d624309150af7f8cfc386da5.jpg", + "table_caption": [ + "Table 2: Finetuned performance comparison on the test split of our simulated EKubric dataset." + ], + "table_footnote": [], + "table_body": "
InputMethodEPE2DACC1pxEPEN.Occ3DACCN.Occ05EPEFull3DACCFull05
RGBRAFT [2]0.75793.70%----
FlowFormer [3]0.68393.92%----
RGB+DepthRAFT-3D [10]0.71594.33%0.01695.20%0.04992.62%
RGB+PCCamLiFlow [13]0.76195.00%0.00998.39%0.03294.90%
RGB+EventRAFT+Event0.48795.25%----
RGB+PC+EventCamLiFlow+Event0.50595.41%0.00898.48%0.03195.01%
RPEFlow (Ours)0.44296.08%0.00798.68%0.02795.30%
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Comparisons with Synthetic Events", + "text_level": 1, + "bbox": [ + 75, + 564, + 387, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Following the conventional setting, our model is first pre-trained on FlyingThings3D [28], and Table 1 shows the quantitative comparison performance on the \"val\" split. Both results are evaluated using their pre-trained model on FlyingThings3D. Meteornet* [61] has not released model for scene flow estimation, so we compare the EPE3D result from its paper. We also finetune them on our simulated EKubric dataset, and the performance comparisons on the test set are shown in Table 2, where the compared models were all pre-trained on FlyingThings3D and then finetuned on EKubric with the same training settings. Note that we did not evaluate the PC-only methods on our EKubric dataset due to their different data preprocessing strategies.", + "bbox": [ + 75, + 593, + 468, + 789 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We report the results of two representative methods [2, 8] and two latest methods [3, 9] using only one modal for one task, and find that combining multiple modalities can significantly improve model accuracy for both optical flow and scene flow estimation. Furthermore, the methods that combine all three modalities, i.e. RGB+PC+Event, achieve better results than the rest [10, 12, 13], which illustrates the sig-", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "nificant benefit of introducing event data for accurate motion estimation. With the same input setting, we compare our model with CamLiFlow+Event and observe improved accuracy, which is because our proposed multimodal attention fusion module is able to fully mine valuable information from continuous event data for accurate motion estimation. The comparison of visualization results in Fig. 3 and in the supplementary materials is also consistent with the above observations, especially in high dynamic and detail moving or motion-blurred areas.", + "bbox": [ + 496, + 564, + 890, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Comparisons with Real Events", + "text_level": 1, + "bbox": [ + 500, + 726, + 772, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We further conduct experiments on the real-captured DSEC [22] dataset. We divide the public set into \"train\" and \"val\" splits for finetuning and evaluation. Since the dense depth required by RAFT-3D [10] is not available, we use CFNet [65] to obtain a pseudo-dense depth map by stereo matching as input. E-RAFT* [22] does not have a publicly available training code, thus we can only use the pretrained model on the entire DSEC dataset including the \"val\" split (marked with *). Both quantitative and qualitative (Table 3 and Fig. 4) comparisons demonstrate the superiority of our", + "bbox": [ + 496, + 750, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10036", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/787c43ba14c4890f580a8b2b8c6baee063b8e1c091f22df5736cacedd7a45979.jpg", + "table_caption": [ + "Table 3: Finetuned Performance comparison on the \"val\" split of DSEC [22] dataset." + ], + "table_footnote": [], + "table_body": "
MethodEPE2DACC1pxEPEFull3DACCFull.05
RAFT [2]0.57289.63%--
E-RAFT* [22]0.47392.11%--
RAFT-3D [10]0.56790.55%0.14051.30%
CamLiFlow [13]0.38394.92%0.12053.49%
RAFT+Event0.53790.08%--
CamLiFlow+Event0.36195.07%0.11655.26%
RPEFlow (Ours)0.33295.27%0.10460.50%
", + "bbox": [ + 86, + 130, + 455, + 256 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3a303e504bb1429b6c3f495bd336e384d48f16b4af37a9eee3f5d4c737608209.jpg", + "table_caption": [ + "Table 4: Ablation Studies. The results validate the effectiveness for introducing event data, attention fusion and mutual information regularization, respectively." + ], + "table_footnote": [], + "table_body": "
EventFusionMI EPE2DACC1pxEPEFull3DACCFull05
(a)-Concat-2.20084.62%0.059
(b)-Attention-2.13384.74%0.058
(c)-Attention✓2.06784.92%0.055
(d)✓ConcatW/oE-1.56184.37%0.048
(e)✓ConcatW/E-1.51985.34%0.046
(f)✓Attention-1.49486.01%0.043
(g)✓Attention✓1.40286.22%0.042
88.01%
", + "bbox": [ + 86, + 325, + 460, + 435 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "model for real-captured data, which is consistent with the observations on synthetic datasets above. In particular, our method performs better in night driving (the 2nd sample in Fig. 4), because the event camera is still sensitive to brightness changes even in low-light scenes. These comparisons further illustrate the importance of introducing events and the applicability of our model to practical needs.", + "bbox": [ + 75, + 460, + 468, + 566 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 575, + 241, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Table 4, We conduct ablation experiments to verify the contribution of each component in our model. All variations are trained on the \"training\" split and evaluated on the \"val\" split of FlyingThings3D [28] dataset. In addition to the following discussion, in the supplementary materials we analyze the impact of real and simulated events and the role of combining the two tasks.", + "bbox": [ + 75, + 598, + 468, + 703 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Event data. As we are the first to introduce the event data for joint optical flow and scene flow estimation, we explore the effectiveness of event data in two aspects. Firstly, we remove the event data in our framework (see Table 4 (a)-(d) and (c)-(g)), leading to significant performance degradation, especially in optical flow error. This is in line with our claim that event data with continuous observations of scene brightness changes can provide significant help for accurate motion estimation. Secondly, in order to validate the benefit of introducing events to other methods, we concatenate the extracted event feature as an additional input of flow decoder for RAFT [2] and CamLiFlow [13], denoted as RAFT+Event and CamLiFlow+Event, respectively. Re-", + "bbox": [ + 75, + 704, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/bdf9cacdf64263f69f23b1ed05feab571a38c08e5456621c847eca8e47bfcb86.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SettingEPE2DACC1pxEPE3DN.OccACC05N.OccEPEFull3DACC05
2D only1.93783.17%------
3D only--0.04386.37%0.07879.05%
2D&3D1.40286.22%0.02493.14%0.04288.01%
", + "bbox": [ + 506, + 88, + 885, + 152 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5: Joint vs independent tasks. These models both use three modalities and the results validate that combining the two tasks makes better use of motion information.", + "bbox": [ + 498, + 162, + 890, + 207 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "sults in Table 1, 2 and 3 show that introducing event data to existing models can also significantly improve the performance, rather than just on our proposed framework.", + "bbox": [ + 496, + 232, + 890, + 277 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fusion Structure. Unlike CamLiFlow [13] that concat the features from two modalities, we propose an attention-based multimodal fusion module. We conduct experiments with both no-event and with event settings (see Table 4 (a)-(b) and (d)(e)-(f)), and our proposed attention fusion improves both 2D and 3D motion estimation performance. This shows that our multimodal attention fusion module can effectively explore the complementary information and correlations among the three modalities and generate fused features that are suitable for subsequent motion estimation.", + "bbox": [ + 496, + 277, + 892, + 428 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Mutual Information. The purpose of the mutual information regularization term is to explicitly constrain the network to learn complementary information from different modalities of data. To verify its contribution to motion estimation, we conduct experiments with both no-event and with event settings (see Table 4 (b)-(c) and (f)-(g)). The results show that with this explicit constraint, the fused features can further improve the accuracy of motion estimation. In addition, we believe that the multimodal attention fusion module and mutual information regularization term both play an important role in motion estimation, because their contribution to 2D and 3D motion estimation is significant in both the with-event and without-event settings.", + "bbox": [ + 496, + 429, + 893, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Computation Cost", + "text_level": 1, + "bbox": [ + 498, + 633, + 679, + 650 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our model is relatively efficient compared to the latest unimodal and multimodal methods in model size and runtime, i.e., FlowFormer [3]: 17.6M, 1.35s, SCTN [9]: 7.8M, 242ms, RAFT-3D [10]: 45M, 593ms, CamLiFlow [13]: 7.7M, 88ms ( $\\approx$ 2s with refine) and Ours: 9.75M, 112ms (both on a single RTX3090 GPU with $1280 \\times 720$ size).", + "bbox": [ + 496, + 657, + 890, + 748 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Joint 2D and 3D estimation.", + "text_level": 1, + "bbox": [ + 498, + 756, + 750, + 771 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In previous comparisons, the methods of joint optical flow and scene flow estimation perform significantly better than independent methods. To further verify the necessity of jointing these two tasks, we compare the models that only supervise the optical flow or scene flow estimation in Table 5. Although using all three modalities for a single task (2D only and 3D only) is more beneficial than the methods using fewer modality data in Table 1 of main paper.", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10037", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "However, combining the two tasks in 2D and 3D benefits from the tight correlation between the two deeply supervised branches, allowing more adequate exploiting of the correlation between 2D and 3D input modalities and more accurate estimating of 2D and 3D motion jointly.", + "bbox": [ + 75, + 90, + 472, + 167 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 183, + 194, + 199 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We introduce a multimodal fusion framework for joint 2D optical flow and 3D scene flow estimation by fusing RGB images, point clouds and event data. Our contributions are threefold: 1) By incorporating event data, our new framework could handle highly dynamic scenes. 2) We fuse representations of the three very different modalities both implicitly and explicitly through multimodal attention and mutual information regularization, respectively. 3) We contribute a new simulation dataset to further advocate research in this direction. Our work shows that event cameras can play an important role in 2D and 3D motion estimation, and reveals the prospect of event-based 3D vision.", + "bbox": [ + 75, + 209, + 472, + 390 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Limitation. Our model is not specially designed for extreme situations such as dark nights or sensor failures, and we plan to address them in the future.", + "bbox": [ + 75, + 391, + 470, + 436 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Acknowledgments", + "text_level": 1, + "bbox": [ + 76, + 454, + 256, + 470 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This research was supported in part by National Natural Science Foundation of China (62271410), the Fundamental Research Funds for the Central Universities, and Zhejiang Lab (NO.2021MC0AB05). Zhexiong Wan is sponsored by the scholarship from China Scholarship Council (202306290193) and the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (CX2023013).", + "bbox": [ + 75, + 479, + 468, + 602 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 617, + 174, + 633 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Deqing Sun, Xiaodong Yang, Ming-Yu Liu, and Jan Kautz. Pwc-net: Cnns for optical flow using pyramid, warping, and cost volume. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 8934-8943, 2018. 1, 2", + "[2] Zachary Teed and Jia Deng. Raft: Recurrent all-pairs field transforms for optical flow. In European Conference on Computer Vision (ECCV), pages 402-419, 2020. 1, 2, 6, 7, 8", + "[3] Zhaoyang Huang, Xiaoyu Shi, Chao Zhang, Qiang Wang, Ka Chun Cheung, Hongwei Qin, Jifeng Dai, and Hongsheng Li. 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In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 13906-13915, 2021. 7" + ], + "bbox": [ + 501, + 92, + 890, + 885 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "10040", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/RPEFlow_ Multimodal Fusion of RGB-PointCloud-Event for Joint Optical Flow and Scene Flow Estimation/d027f499-898c-464c-acf6-a1eba174840a_model.json b/2023/RPEFlow_ Multimodal Fusion of RGB-PointCloud-Event for Joint Optical Flow and Scene Flow Estimation/d027f499-898c-464c-acf6-a1eba174840a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8e90b80b416c49233c3bba912b0b19bdd1fbddaa --- /dev/null +++ b/2023/RPEFlow_ Multimodal Fusion of RGB-PointCloud-Event for Joint Optical Flow and Scene Flow Estimation/d027f499-898c-464c-acf6-a1eba174840a_model.json @@ -0,0 +1,2554 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.197, + 0.131, + 0.777, + 0.177 + ], + "angle": 0, + "content": "RPEFlow: Multimodal Fusion of RGB-PointCloud-Event for Joint Optical Flow and Scene Flow Estimation" + }, + { + "type": "text", + "bbox": [ + 0.236, + 0.203, + 0.732, + 0.221 + ], + "angle": 0, + "content": "Zhexiong Wan\\(^{1}\\) Yuxin Mao\\(^{1}\\) Jing Zhang\\(^{2}\\) Yuchao Dai\\(^{1\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.19, + 0.222, + 0.78, + 0.259 + ], + "angle": 0, + "content": "\\(^{1}\\)Northwestern Polytechnical University & Shaanxi Key Laboratory of Information Acquisition and Processing \\(^{2}\\)Australian National University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.307, + 0.314, + 0.323 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.339, + 0.474, + 0.701 + ], + "angle": 0, + "content": "Recently, the RGB images and point clouds fusion methods have been proposed to jointly estimate 2D optical flow and 3D scene flow. However, as both conventional RGB cameras and LiDAR sensors adopt a frame-based data acquisition mechanism, their performance is limited by the fixed low sampling rates, especially in highly-dynamic scenes. By contrast, the event camera can asynchronously capture the intensity changes with a very high temporal resolution, providing complementary dynamic information of the observed scenes. In this paper, we incorporate RGB images, Point clouds and Events for joint optical flow and scene flow estimation with our proposed multi-stage multimodal fusion model, RPEFlow. First, we present an attention fusion module with a cross-attention mechanism to implicitly explore the internal cross-modal correlation for 2D and 3D branches, respectively. Second, we introduce a mutual information regularization term to explicitly model the complementary information of three modalities for effective multimodal feature learning. We also contribute a new synthetic dataset to advocate further research. Experiments on both synthetic and real datasets show that our model outperforms the existing state-of-the-art by a wide margin. Code and dataset is available at https://npucvr.github.io/RPEFlow." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.731, + 0.21, + 0.746 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.756, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Optical flow estimation, i.e., estimating the dense 2D motion between consecutive image frames, has been extensively studied and significantly advanced with the development of deep neural networks [1-3]. Scene flow estimation, on the other hand, aims to estimate the 3D motion field with various input configurations, ranging from monocular images [4, 5], stereo images [6, 7], two frames of point clouds [8, 9], images combined with depth maps [10, 11]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.293, + 0.892, + 0.339 + ], + "angle": 0, + "content": "or point clouds [12, 13]. Both are fundamental to downstream applications such as autonomous driving [14, 15], object tracking [16, 17], scene reconstruction [18, 19], etc." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.34, + 0.893, + 0.536 + ], + "angle": 0, + "content": "Due to the strong correlation between 2D and 3D motion, i.e., 2D motion can be regarded as the projection of 3D motion on the image plane, recent works [10, 12, 13] make efforts to jointly estimate optical flow and scene flow by combining RGB images and point clouds (or depth maps). Their success indicates that joint 2D and 3D motion estimation within a framework can obtain more accurate results than separate tasks. However, as both conventional RGB cameras and LiDAR (or depth) sensors adopt a fixed frame-by-frame data acquisition mechanism, these methods show unsatisfactory performance when dealing with complex motion scenes (see Fig. 3), which motivates us to alleviate this problem by introducing the event camera." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.895, + 0.763 + ], + "angle": 0, + "content": "Event camera, as a bio-inspired imaging sensor, can asynchronously capture the brightness change with very high temporal resolution (in the order of \\(\\mu s\\)) and output an event signal quickly [20]. As each pixel adapts its sampling rate according to the captured changes, the amount of output events usually depends on the complexity of motion (the faster the motion, the more triggered events), thus providing abundant motion information of the observed scene. Based on this, some works use event data alone to estimate optical flow [21, 22], but they show limitations in estimating reliable motion at regions with no events [23]. As compensation for this, image and event data are fused together to estimate dense optical flow [24, 25]. As far as we know, there is no method to incorporate event data within a multimodal learning framework for both 2D and 3D motion estimation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In this paper, we propose to fuse RGB images, point clouds and events for joint optical flow and scene flow estimation. We find the ability of the event camera to asynchronously capture the brightness changes caused by motion makes it complementary to image cameras and LiDAR sensors, especially for complex dynamics and high-contrast brightness changes. We believe that combining these three modalities together for 2D and 3D motion estimation meets the practical needs, which has been further confirmed by" + }, + { + "type": "page_footnote", + "bbox": [ + 0.101, + 0.888, + 0.403, + 0.901 + ], + "angle": 0, + "content": "† Corresponding author (daiyuchao@gmail.com)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10030" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "existing datasets, such as MVSEC [26] and DSEC [22] that contain these data for driving scenarios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.123, + 0.473, + 0.5 + ], + "angle": 0, + "content": "We formulate this task as a representation-based multimodal learning problem, and exploit the complementary information between these three very different modalities implicitly and explicitly. We aim to exploit the relationships between multimodal and multi-dimensional space observations (images and events in 2D with point clouds in 3D) and explore their contributions to 2D and 3D motion. Specifically, in our RPEFlow framework, we first propose a multimodal attention fusion module with cross-attention mechanism to implicitly explore the correlations between three modalities, based on which a pyramid multi-stage fusion structure is introduced to extensively modeling. We observe that each modality can contribute a part to 2D and 3D motion estimation, making representation learning [27] suitable for our multimodal learning framework. Then we introduce cross-modal mutual information minimization in feature space to explicitly maximize the complementary information. We also contribute a new synthetic dataset with simulations that conform to the gravity model and collision detection and contain a larger variety of moving objects and richer annotations than FlyingThings3D [28]. Extensive experimental results validate both our implicit multimodal attention fusion and explicit representation regularization towards effective multimodal learning, leading to a new benchmark on both synthetic and real-captured datasets." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.502, + 0.436, + 0.516 + ], + "angle": 0, + "content": "Our main contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.517, + 0.469, + 0.577 + ], + "angle": 0, + "content": "1) We propose to incorporate event cameras with RGB cameras and LiDAR sensors to jointly estimate optical flow and scene flow for complex dynamic scenes, which constitutes a new and practical problem." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.578, + 0.469, + 0.638 + ], + "angle": 0, + "content": "2) An implicit multimodal attention fusion module and an explicit representation learning via mutual information regularization are presented in our RPEFlow model, achieving extensive cross-modal relationship modeling." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.639, + 0.469, + 0.729 + ], + "angle": 0, + "content": "3) We contribute a large-scale synthetic dataset with ground-truth motion annotations. Experimental results on both synthetic and real datasets show that the proposed RPEFlow outperforms existing state-of-the-art and demonstrates the effectiveness of event data for motion estimation of complex dynamics." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.517, + 0.469, + 0.729 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.745, + 0.22, + 0.76 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.392, + 0.786 + ], + "angle": 0, + "content": "2.1. Unimodal 2D/3D Motion Estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Image only. For learning-based 2D optical flow estimation, FlowNet series [29, 30] first propose end-to-end CNN models for regression. PwC-Net [1] work on constructing feature pyramids with coarse-to-fine refinement. RAFT [2] and its variants [3, 31] build all-pairs correlation and update the optical flow iteratively. For 3D scene flow estimation, learning-based studies [6, 7] use a sequence of stereo im" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.212 + ], + "angle": 0, + "content": "ages as input [32], achieving faster and better performance compared with earlier optimization-based methods [15, 33]. Some recent works [4, 5, 34] use only monocular image sequences, which are more difficult to model accurate 3D structure and motion than stereo images. Due to the limited frame rate of input images and the difficulty in obtaining 3D structure, the performance of image-only methods is still unsatisfactory when dealing with complex dynamics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.213, + 0.892, + 0.318 + ], + "angle": 0, + "content": "Point Cloud only. Point cloud data from the LiDAR sensor is favorable for 3D motion estimation. Due to the unique data structure, existing methods [8, 9, 35] focus on studying the model structure to represent the point cloud data for scene flow estimation. However, the point cloud lacks semantic information and leads to the difficulty of estimating accurate motion only by the structural information [13]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.319, + 0.892, + 0.455 + ], + "angle": 0, + "content": "Event only. Event-based motion estimation is dedicated to extracting motion information from event-encoded brightness changes. Some early optimization-based methods estimate the motion flow of moving boundaries [36,37]. Recent learning-based methods [21, 22, 38] are proposed to regress the dense optical flow directly. Even though the predictions of some of them are densely supervised, the sparse input event data leads to unreliable optical flow estimation in the regions without triggered events [23, 24]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.466, + 0.829, + 0.481 + ], + "angle": 0, + "content": "2.2. Multimodal 2D/3D Motion Estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.489, + 0.892, + 0.685 + ], + "angle": 0, + "content": "As unimodal data only provides partial information, multimodal methods are presented to comprehensively learn from multiple observations. For optical flow estimation, event-based studies [24, 25, 39] combine the advantages of the image in dense representation and events in motion perception for reliable estimation. Besides, [40, 41] incorporate gyroscope or depth sensor to guide the optical flow. For scene flow estimation, using a sequences of RGB-Depth images [10, 11] becomes another trend, then [12, 13] replace depth with point clouds to deal with the limited ideal range of depth camera when applied outdoors. But again, they are still limited by the frame-by-frame acquisition mechanism, which leads us to introduce event data." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.696, + 0.685, + 0.71 + ], + "angle": 0, + "content": "2.3. Multimodal Fusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Given multimodal data, effective multimodal fusion is critical to extensively explore the contribution of each modality [42]. Two main directions have been explored: 1) attention based [43-45] and 2) representation learning [46-49] based. For the former, a specific attention module [50, 51] is designed to implicitly control the contribution of each modal. For the latter, representation similarity is measured to explicitly constrain the reliability of the feature embedding. Within this direction, mutual information (MI) estimation and optimization [48, 52-54] is the widely studied strategy, which is typically used as a regularizer to encourage (via MI maximization) or limit dependency (via" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10031" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.089, + 0.088, + 0.885, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.35, + 0.895, + 0.414 + ], + "angle": 0, + "content": "Figure 1: Our RPEFlow Structure. We learn motion correlations from the input three modalities (RGB-PointCloud-Event, RPE) by multi-stage fusion (FS, MS and ES) incorporating explicit multimodal attentional fusion (MAF) and implicit representing learning with mutual information regularization (MIR), and perform pyramidal updates from coarse to fine to estimate the optical flow in the 2D branch (top) and the scene flow in the 3D branch (bottom), respectively. Best viewed on screen." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.432, + 0.325, + 0.447 + ], + "angle": 0, + "content": "MI minimization) between variables." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.462, + 0.208, + 0.478 + ], + "angle": 0, + "content": "3. Our Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.487, + 0.471, + 0.593 + ], + "angle": 0, + "content": "We introduce two main strategies to achieve effective multimodal learning, one is explicit multimodal attention fusion (Sec. 3.1) and the other is implicit mutual information regularization (Sec. 3.2). Based on them, we propose a pyramid multi-stage framework (see Fig. 1) for RGB-PointCloud-Event fusion and joint optical flow and scene flow estimation in 2D and 3D branches (Sec. 3.3)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.604, + 0.396, + 0.619 + ], + "angle": 0, + "content": "3.1. Multimodal Attention Fusion (MAF)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.473, + 0.902 + ], + "angle": 0, + "content": "As shown in Fig. 1, we have both 2D and 3D branches for optical flow and scene flow estimation. Due to the different data structures of the two branches [8, 13], we design symmetric attention fusion strategy for both two branches in Fig. 2, which consists of two steps, namely feature projection and cross-attention fusion. In the 2D branch, we treat the RGB image as the primary modality and project point cloud feature into the image plane, then fuse with auxiliary features, i.e., event and point cloud. For the 3D branch, we define the point cloud data as the primary modality, then project the others into the 3D space and fuse them together. Multimodal Attention Fusion in 3D branch (MAF RPE-3D). We take the fusion module in the 3D branch of a single pyramid level as a detailed example, where the encoded image feature is \\( e_r \\in \\mathbb{R}^{H \\times W \\times C_{2D}} \\), event feature is \\( e_{ev} \\in \\mathbb{R}^{H \\times W \\times C_{2D}} \\), and point cloud feature is \\( e_{pc} \\in \\mathbb{R}^{N \\times C_{3D}} \\) with the point positions \\( \\mathbf{p} = \\{\\mathbf{p}_{x_i}, \\mathbf{p}_{y_i}, \\mathbf{p}_{z_i}\\}^N \\in \\mathbb{R}^{N \\times 3} \\) in 3D space. Note that \\( H, W \\) and \\( N \\) are the feature size at" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.432, + 0.892, + 0.493 + ], + "angle": 0, + "content": "the current pyramid level, not the original input size. We first use the point position to sample the corresponding image and event feature into 3D space with focal length \\( f \\) and denote the projected point position at the image plane as:" + }, + { + "type": "equation", + "bbox": [ + 0.551, + 0.5, + 0.892, + 0.531 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\left(u _ {i}, v _ {i}\\right) \\right\\} ^ {N} = \\left\\{\\left(f \\frac {\\mathbf {P} _ {x _ {i}}}{\\mathbf {P} _ {z _ {i}}}, f \\frac {\\mathbf {P} _ {y _ {i}}}{\\mathbf {P} _ {z _ {i}}}\\right) \\right\\} ^ {N} \\in \\mathbb {R} ^ {N \\times 2}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.537, + 0.845, + 0.552 + ], + "angle": 0, + "content": "Thus, the projected image and event features are:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.56, + 0.892, + 0.58 + ], + "angle": 0, + "content": "\\[\ne _ {r} ^ {p j} = \\left\\{e _ {r} (u _ {i}, v _ {i}) \\right\\} ^ {N}, e _ {e v} ^ {p j} = \\left\\{e _ {e v} (u _ {i}, v _ {i}) \\right\\} ^ {N} \\in \\mathbb {R} ^ {N \\times C _ {2 D}}, (2)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.587, + 0.891, + 0.618 + ], + "angle": 0, + "content": "where \\( e_r(u_i, v_i) \\) represents the feature obtained by bilinear interpolation sampling at \\( (u_i, v_i) \\) position in image plane." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.619, + 0.892, + 0.863 + ], + "angle": 0, + "content": "After projection, we feed the features of auxiliary modalities \\( e_r^{pj} \\) and \\( e_{ev}^{pj} \\) with the primary modality feature \\( X_{pri}^{3D} = e_{pc} \\) into the attention fusion module. In the original self-attention mechanism [50, 51], all of the keys \\( K \\), values \\( V \\) and queries \\( Q \\) come from the same modality. Here we adapt it to accommodate inputs from multiple modalities and propose our cross-attention fusion structure. Specifically, we first combine the auxiliary features and align the number of channels with the master feature by \\( 1 \\times 1 \\) convolution, yielding the aligned auxiliary feature \\( Y_{aux}^{3D} = W_a \\left[ e_r^{pj}, e_{ev}^{pj} \\right] (\\mathbb{R}^N \\times C_{3D} \\Leftarrow \\mathbb{R}^N \\times (C_{2D} + C_{2D})) \\), where \\( [\\cdot, \\cdot] \\) is the concatenation operation. With layer normalization [55] (LN), we apply \\( 3 \\times 3 \\) depth-wise convolution to encode spatial and channel information with queries \\( Q_{pri}^{3D} = W_d^Q \\mathrm{LN}(X_{pri}^{3D}) \\), keys \\( K_{aux}^{3D} = W_d^K \\mathrm{LN}(Y_{aux}^{3D}) \\) and values \\( V_{aux}^{3D} = W_d^V \\mathrm{LN}(Y_{aux}^{3D}) \\), respectively, obtaining the cross-modal self-attention as:" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.871, + 0.892, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A t t e n t i o n} (Q, K, V) = V \\operatorname {S o f t m a x} \\left(\\frac {Q ^ {T} K}{\\tau}\\right), \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10032" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.09, + 0.448, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.304, + 0.468, + 0.496 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.5, + 0.471, + 0.576 + ], + "angle": 0, + "content": "Figure 2: Our proposed Multimodal Attention Fusion Module fuses both three modal features in 2D (top) and 3D (bottom) branches, including feature projection and cross-attention fusion. In particular, only image and point features are fused in Feature Stage (FS)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.724 + ], + "angle": 0, + "content": "where \\(\\tau\\) is a learnable scaling factor. We input \\(Q_{pri}^{3D}\\), \\(K_{aux}^{3D}\\), \\(V_{aux}^{3D}\\) to the above attention module, and the resultant attention map with dimension \\(\\mathbb{R}^{C_{3D} \\times C_{3D}}\\) is much smaller and more efficient than the original implementation [51] with dimension \\(\\mathbb{R}^{HW \\times HW}\\) adopted from [56]. With the cross-modal attention in Eq. 3, we obtain the fused feature \\(X_{pri}^{3D'}\\) corresponding to the primary modality \\(e_{pc}\\) by another \\(1 \\times 1\\) convolution projection and residual connection as:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.731, + 0.469, + 0.753 + ], + "angle": 0, + "content": "\\[\nX _ {p r i} ^ {3 D ^ {\\prime}} = W _ {p} \\mathbf {A t t e n t i o n} (Q _ {p r i} ^ {3 D}, K _ {a u x} ^ {3 D}, V _ {a u x} ^ {3 D}) + X _ {p r i} ^ {3 D}. \\qquad (4)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.758, + 0.47, + 0.904 + ], + "angle": 0, + "content": "Multimodal Attention Fusion in 2D branch (MAF RPE-2D). The fusion process in 2D is similar to the 3D branch above. To project the sparse point feature into a dense feature at the image plane, we adopt a learnable fusion-aware interpolation [13] and get the projected point feature \\( e_{pc}^{pj} \\in \\mathbb{R}^{H \\times W \\times C_{3D}} \\). Then we regard the image feature as the primary modality feature \\( X_{pri}^{2D} = e_r \\), then the aligned auxiliary feature \\( Y_{aux}^{2D} = W_a^{2D}\\left[e_{pc}^{pj}, e_{ev}\\right] \\). After similar cross-attention, the fused feature \\( X_{pri}^{2D'} \\) is obtained as:" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.118, + 0.892, + 0.14 + ], + "angle": 0, + "content": "\\[\nX _ {p r i} ^ {2 D ^ {\\prime}} = W _ {p} \\mathbf {A t t e n t i o n} \\left(Q _ {p r i} ^ {2 D} K _ {a u x} ^ {2 D}, V _ {a u x} ^ {2 D}\\right) + X _ {p r i} ^ {2 D}. \\tag {5}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.151, + 0.862, + 0.167 + ], + "angle": 0, + "content": "3.2. Mutual Information Regularization (MIR)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.175, + 0.892, + 0.281 + ], + "angle": 0, + "content": "We incorporate mutual information minimization as a regularizer to explicitly model the cross-modal dependency following disentangled representation learning [27] based on the observation that each modality, i.e. RGB image, point cloud and event data, contributes partially to the output, and mutual information minimization is suitable for our task to explore the complementary information of each modality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.282, + 0.892, + 0.342 + ], + "angle": 0, + "content": "We start with the case of two modalities with RGB image and event feature embeddings \\( e_r \\) and \\( e_{ev} \\). Note that these feature embeddings are the features that have been projected into the same spatial space (2D or 3D) in Sec. 3.1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.343, + 0.892, + 0.47 + ], + "angle": 0, + "content": "To explicitly model the cross-modal correlation, we define cross-modal mutual information between \\( e_r \\) and \\( e_{ev} \\) as \\( I(e_r;e_{ev}) = \\mathbb{E}_{p(e_r,e_{ev})}\\left[\\log \\frac{p(e_{ev}|e_r)}{p(e_{ev})}\\right] \\), where \\( p(e_r,e_{ev}) \\) is the joint distribution, \\( p(e_{ev}|e_r) \\) is the conditional distribution and \\( p(e_{ev}) \\) is the marginal distribution. With importance sampling [57], we introduce a variational marginal approximation \\( q(e_{ev}) \\) with a variational upper bound \\( I^{vub} \\) [54] of mutual information \\( I(e_r;e_{ev}) \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.481, + 0.891, + 0.535 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} I \\left(e _ {r}; e _ {e v}\\right) \\leq \\mathbb {E} _ {p \\left(e _ {r}, e _ {e v}\\right)} \\left[ \\log \\frac {p \\left(e _ {e v} \\mid e _ {r}\\right)}{q \\left(e _ {e v}\\right)} \\right] \\tag {6} \\\\ = D _ {K L} \\left(p \\left(e _ {e v} \\mid e _ {r}\\right) \\| q \\left(e _ {e v}\\right)\\right) = I ^ {v u b} = \\mathcal {L} _ {\\mathrm {m i}}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.892, + 0.623 + ], + "angle": 0, + "content": "where \\( q(e_{ev}) \\) can be fixed as a standard normal distribution [58], i.e. \\( q(e_{ev}) = \\mathcal{N}(e_{ev};0,\\mathbf{I}) \\), and \\( p(e_{ev}|e_r) \\) can be modeled with the reparameterization trick [59], thus the Kullback-Leibler (KL) divergence term \\( D_{KL} \\) within \\( I^{vub} \\) can be solved in closed form." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.625, + 0.892, + 0.686 + ], + "angle": 0, + "content": "In the case of three modalities feature embeddings \\( e_r \\), \\( e_{pc} \\) and \\( e_{ev} \\), respectively, the interaction information \\( II(e_r; e_{pc}; e_{ev}) \\) [60], as a multivariate generalization of the mutual information, is upper bounded by:" + }, + { + "type": "equation", + "bbox": [ + 0.506, + 0.697, + 0.892, + 0.736 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} I I \\left(e _ {r}; e _ {p c}; e _ {e v}\\right) \\leq \\min \\left\\{I \\left(e _ {r}; e _ {p c}\\right), I \\left(e _ {p c}; e _ {e v}\\right), I \\left(e _ {r}; e _ {e v}\\right) \\right\\} \\tag {7} \\\\ \\leq \\min \\left\\{I ^ {v u b} \\left(e _ {r}; e _ {p c}\\right), I ^ {v u b} \\left(e _ {p c}; e _ {e v}\\right), I ^ {v u b} \\left(e _ {r}; e _ {e v}\\right) \\right\\}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To compute \\( I^{vub} \\), we need to design a transition function, achieving the transformation of one modality to the other and assume the variational marginal approximation \\( q \\) as the standard normal distribution for closed-form KL divergence computation. In practice, the standard normal distribution assumption of \\( q \\) leads to high-bias mutual information estimation. Alternatively, we first map the representation of each modality \\( (e_r, e_{pc}, e_{ev}) \\) to a common manifold, with reparameterization trick [59] in the end to achieve Gaussian latent code of each modality. Then, we compute KL" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10033" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "divergence between the two Gaussian latent codes, leading to the final mutual information regularization term:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.141, + 0.47, + 0.16 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {i i}} = I ^ {v u b} \\left(e _ {r}; e _ {p c}\\right) + I ^ {v u b} \\left(e _ {p c}; e _ {e v}\\right) + I ^ {v u b} \\left(e _ {r}; e _ {e v}\\right), (8)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.18, + 0.469, + 0.21 + ], + "angle": 0, + "content": "where we compute the sum of \\( I^{vub} \\) instead of choosing the minimum for stable training." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.231, + 0.456, + 0.248 + ], + "angle": 0, + "content": "3.3. Pyramid Fusion and Joint Estimation Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.259, + 0.469, + 0.41 + ], + "angle": 0, + "content": "With the proposed multimodal attention fusion and the mutual information regularization term, we achieve once multimodal feature fusion. Inspired by CamLiFlow [13], we further perform multi-stage feature fusion implicitly and explicitly. Here we present the details of multi-stage feature fusion, and more details about the network structure are given in the supplementary materials. As shown in Fig. 1, our model contains both 2D and 3D branches, where each branch consists of feature extraction, correlation construction and flow estimation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.414, + 0.469, + 0.626 + ], + "angle": 0, + "content": "In feature extraction, we first voxelized the raw events \\( E = \\{x_{i},y_{i},t_{i},p_{i}\\}^{K} \\) into one event voxel \\( EV\\in \\mathbb{R}^{H\\times W\\times B} \\) that can be used as input to our network, where \\( K \\) is the number of events during the period between two frames and \\( B \\) is the manually set number of time intervals to sample events. We apply three Siamese encoders to construct feature pyramids \\( (\\{e_{r_1},e_{r_2}\\} _l,\\{e_{pc_1},e_{pc_2}\\} _l \\) and \\( e_{ev_l} \\) with pyramid layers \\( l\\in [1,L]) \\) for three modalities respectively. As spans between two frames, the event data is not included in Feature Stage Fusion, which is applied to fuse the features of two frames RGB images and corresponding point clouds with two-modal attention fusion, i.e. simplify the auxiliary feature to a single modality in Eq. 4, 5 and mutual information regularization in Eq. 6 for both 2D and 3D branches." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In correlation construction, we first warp the second frame of image and point cloud features using the coarse optical flow and scene flow (initialize with zero) from the previous pyramid layer, then construct correlation motion features by computing 2D and 3D cost volumes and fused them with the event feature at Motion Stage Fusion. In flow estimation, we construct a motion decoder and flow estimator, and perform an Estimation Stage Fusion between them to fuse the hidden motion features from the two branches decoder with the event feature. In these two fusion stages, we conduct multimodal attention fusion in Eq. 4, 5 and mutual information regularization in Eq. 8 for 2D and 3D motion features and event feature, because events can provide complementary information to enhance the motion correlation construction. The estimated optical flow and scene flow are fed into the next pyramid layer to achieve coarse-to-fine predictions. We take the optical flow and scene flow from the last pyramid layer as our final joint estimations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.692, + 0.108 + ], + "angle": 0, + "content": "3.4. Objective Functions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.892, + 0.282 + ], + "angle": 0, + "content": "The objective functions in the training of our model are divided into feature representation loss and task loss. The former consists of multiple mutual information regularizations at each fusion stage. \\(\\mathcal{L}_{\\mathrm{mi}}^{fs1}\\), \\(\\mathcal{L}_{\\mathrm{mi}}^{fs2}\\) represent the mutual information minimization loss imposed on the RGB image and point cloud features of the first and the second frame at the Feature Stage fusion, and \\(\\mathcal{L}_{\\mathrm{ii}}^{ms}\\) and \\(\\mathcal{L}_{\\mathrm{ii}}^{es}\\) represent on both RGB image, point cloud and event features at the Motion Stage and Estimation Stage fusion. Thus the feature representation loss is the sum of all stages and is weighted at each pyramid level:" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.293, + 0.892, + 0.335 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {f e a t}} = \\sum_ {l = 1} ^ {L} \\lambda_ {l} \\left[ \\mathcal {L} _ {\\mathrm {m i}} ^ {f s 1} _ {l} + \\mathcal {L} _ {\\mathrm {m i}} ^ {f s 2} _ {l} + \\mathcal {L} _ {\\mathrm {i i}} ^ {m s} _ {l} + \\mathcal {L} _ {\\mathrm {i i}} ^ {e s} _ {l} \\right], \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.346, + 0.891, + 0.376 + ], + "angle": 0, + "content": "where \\(l\\) is the pyramid level, and \\(\\lambda_{l}\\) is used to reweight the contribution of each pyramid level." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.377, + 0.892, + 0.408 + ], + "angle": 0, + "content": "The latter task loss measures the \\(L_{2}\\) distance between the ground-truth and the model output at each pyramid level by:" + }, + { + "type": "equation", + "bbox": [ + 0.531, + 0.432, + 0.891, + 0.51 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {t a s k}} = \\sum_ {l = 1} ^ {L} \\lambda_ {l} \\left[ \\sum_ {\\mathbf {x}} \\left(\\| f _ {l} ^ {\\text {p r e d}} (\\mathbf {x}) - f _ {l} ^ {\\text {g t}} (\\mathbf {x}) \\| _ {2}\\right) + \\right. \\tag {10} \\\\ \\alpha \\sum_ {\\mathbf {p}} (\\| s _ {l} ^ {p r e d} (\\mathbf {p}) - s _ {l} ^ {g t} (\\mathbf {p}) \\| _ {2}) \\Big ], \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.522, + 0.892, + 0.598 + ], + "angle": 0, + "content": "where \\(\\mathbf{x}\\), \\(\\mathbf{p}\\) are the valid image positions and point coordinates, \\(f_{l}^{pred}\\), \\(s_{l}^{pred}\\) are the estimated 2D optical flow and 3D scene flow and \\(f_{l}^{gt}\\), \\(s_{l}^{gt}\\) are the corresponding resized ground truth at the \\(l\\)-th pyramid level, respectively. \\(\\alpha\\) is the weight to balance 2D and 3D errors." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.599, + 0.822, + 0.614 + ], + "angle": 0, + "content": "The total loss is a weighted sum of the above:" + }, + { + "type": "equation", + "bbox": [ + 0.63, + 0.627, + 0.892, + 0.643 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {t a s k}} + \\beta \\mathcal {L} _ {\\text {f e a t}}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.656, + 0.863, + 0.672 + ], + "angle": 0, + "content": "where \\(\\beta\\) is the weight to balance two losses in training." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.686, + 0.625, + 0.703 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.711, + 0.717, + 0.727 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Datasets. Since there is no large-scale scene flow dataset with real event data, we use synthetic data for pretraining. Follow the preprocess pipeline [13, 62], we generate point clouds from depth images for FlyingThings3D [28] dataset, which contains 19,640 and 3,824 RGB-PointColud pairs for \"train\" and \"val\" splits. We use the popular video-to-events conversion method [63] to generate the corresponding events. In addition, we use kubric [64] to simulate 15,367 RGB-PointCloud-Event pairs with rich annotations (including optical flow and scene flow ground truths), denoted as EKubric, which aims to simulate photo-realistic" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10034" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.213, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.217, + 0.09, + 0.349, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.089, + 0.484, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.089, + 0.62, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.622, + 0.089, + 0.755, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.089, + 0.892, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.267, + 0.245, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.254, + 0.267, + 0.402, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.411, + 0.267, + 0.56, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.567, + 0.267, + 0.718, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.725, + 0.267, + 0.924, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.45, + 0.893, + 0.496 + ], + "angle": 0, + "content": "Figure 3: Visual comparisons on simulated data, in which the top row is on the \"val\" split of FlyingThings3D [28] dataset and the reset two are on the test split of our simulated EKubric dataset. For the bottom 3D comparisons, blue indicates a lower error, red indicates a higher error, and green indicates the median. Best to zoom in on the screen for detailed comparisons." + }, + { + "type": "table_caption", + "bbox": [ + 0.191, + 0.51, + 0.776, + 0.526 + ], + "angle": 0, + "content": "Table 1: Performance comparison on the \"val\" split of the FlyingThings3D [28] subset." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.537, + 0.875, + 0.719 + ], + "angle": 0, + "content": "
InputMethodEPE2DACC1pxEPEN.Occ3DACCN.Occ05EPEFull3DACCFull05
RGBRAFT [2]3.1281.1%----
FlowFormer [3]3.0282.6%----
PCMeteornet* [61]----0.209-
PointPWC [8]--0.11251.8%--
SCTN [9]--0.03884.7%--
RGB+DepthRAFT-3D [10]2.3787.1%0.06284.5%0.08971.1%
RGB+PCDeepLiDARFlow [12]6.0447.1%-27.2%--
CamLiFlow [13]2.2084.6%0.03391.7%0.05986.0%
RGB+EventRAFT+Event2.4984.6%----
RGB+PC+EventCamLiFlow+Event1.5684.4%0.02891.7%0.04885.9%
RPEFlow (Ours)1.4086.2%0.02493.1%0.04288.0%
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.743, + 0.47, + 0.804 + ], + "angle": 0, + "content": "scenes with collision detection, gravity model and ambient illumination and has more object kinds than FlyingThings3D. We also use the DSEC [22] dataset, which contains 8,170 pairs of real-captured samples in driving scenarios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Training, Hyper-parameters and Metrics. Our model is trained with PyTorch on four RTX3090 GPUs and evaluated on one. We use the Adam optimizer with weight decay \\(10^{-6}\\). The number of event bins is \\(B = 10\\), pyramid layers is \\(L = 5\\). Loss weights are \\(\\alpha = 10.0\\), \\(\\beta = 0.01\\), \\(\\lambda_l = 2^{(l - 2)}\\) for \\(l \\in [1, L]\\). Following [10, 13], we evalu" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.743, + 0.892, + 0.85 + ], + "angle": 0, + "content": "ate using 2D and 3D end-point error (EPE\\(_{2\\mathrm{D}}\\) and EPE\\(_{3\\mathrm{D}}\\)), and \\(\\mathrm{ACC}_{1\\mathrm{px}}\\) and \\(\\mathrm{ACC}_{.05}\\) to measure the portion of accuracy within 1 pixel and \\(5\\mathrm{cm}\\). The scene flow metrics with N.Occ superscript indicates only the not occluded positions are calculated, while Full or none indicates all positions including occlusion. More details about datasets and training are provided in the supplementary materials." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10035" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.165, + 0.09, + 0.804, + 0.105 + ], + "angle": 0, + "content": "Table 2: Finetuned performance comparison on the test split of our simulated EKubric dataset." + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.117, + 0.86, + 0.248 + ], + "angle": 0, + "content": "
InputMethodEPE2DACC1pxEPEN.Occ3DACCN.Occ05EPEFull3DACCFull05
RGBRAFT [2]0.75793.70%----
FlowFormer [3]0.68393.92%----
RGB+DepthRAFT-3D [10]0.71594.33%0.01695.20%0.04992.62%
RGB+PCCamLiFlow [13]0.76195.00%0.00998.39%0.03294.90%
RGB+EventRAFT+Event0.48795.25%----
RGB+PC+EventCamLiFlow+Event0.50595.41%0.00898.48%0.03195.01%
RPEFlow (Ours)0.44296.08%0.00798.68%0.02795.30%
" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.261, + 0.212, + 0.338 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.339, + 0.212, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.217, + 0.261, + 0.348, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.217, + 0.339, + 0.348, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.261, + 0.483, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.339, + 0.483, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.261, + 0.62, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.339, + 0.62, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.261, + 0.755, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.339, + 0.755, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.261, + 0.892, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.339, + 0.892, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.089, + 0.42, + 0.245, + 0.512 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.258, + 0.419, + 0.402, + 0.512 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.412, + 0.419, + 0.56, + 0.513 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.419, + 0.716, + 0.512 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.725, + 0.419, + 0.922, + 0.512 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.175, + 0.523, + 0.793, + 0.539 + ], + "angle": 0, + "content": "Figure 4: Visual comparisons on real-captured data, i.e. the \"val\" split of DSEC [22] dataset." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.565, + 0.388, + 0.581 + ], + "angle": 0, + "content": "4.2. Comparisons with Synthetic Events" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.594, + 0.47, + 0.79 + ], + "angle": 0, + "content": "Following the conventional setting, our model is first pre-trained on FlyingThings3D [28], and Table 1 shows the quantitative comparison performance on the \"val\" split. Both results are evaluated using their pre-trained model on FlyingThings3D. Meteornet* [61] has not released model for scene flow estimation, so we compare the EPE3D result from its paper. We also finetune them on our simulated EKubric dataset, and the performance comparisons on the test set are shown in Table 2, where the compared models were all pre-trained on FlyingThings3D and then finetuned on EKubric with the same training settings. Note that we did not evaluate the PC-only methods on our EKubric dataset due to their different data preprocessing strategies." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We report the results of two representative methods [2, 8] and two latest methods [3, 9] using only one modal for one task, and find that combining multiple modalities can significantly improve model accuracy for both optical flow and scene flow estimation. Furthermore, the methods that combine all three modalities, i.e. RGB+PC+Event, achieve better results than the rest [10, 12, 13], which illustrates the sig-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.892, + 0.716 + ], + "angle": 0, + "content": "nificant benefit of introducing event data for accurate motion estimation. With the same input setting, we compare our model with CamLiFlow+Event and observe improved accuracy, which is because our proposed multimodal attention fusion module is able to fully mine valuable information from continuous event data for accurate motion estimation. The comparison of visualization results in Fig. 3 and in the supplementary materials is also consistent with the above observations, especially in high dynamic and detail moving or motion-blurred areas." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.774, + 0.743 + ], + "angle": 0, + "content": "4.3. Comparisons with Real Events" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.894, + 0.901 + ], + "angle": 0, + "content": "We further conduct experiments on the real-captured DSEC [22] dataset. We divide the public set into \"train\" and \"val\" splits for finetuning and evaluation. Since the dense depth required by RAFT-3D [10] is not available, we use CFNet [65] to obtain a pseudo-dense depth map by stereo matching as input. E-RAFT* [22] does not have a publicly available training code, thus we can only use the pretrained model on the entire DSEC dataset including the \"val\" split (marked with *). Both quantitative and qualitative (Table 3 and Fig. 4) comparisons demonstrate the superiority of our" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10036" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.121 + ], + "angle": 0, + "content": "Table 3: Finetuned Performance comparison on the \"val\" split of DSEC [22] dataset." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.131, + 0.457, + 0.257 + ], + "angle": 0, + "content": "
MethodEPE2DACC1pxEPEFull3DACCFull.05
RAFT [2]0.57289.63%--
E-RAFT* [22]0.47392.11%--
RAFT-3D [10]0.56790.55%0.14051.30%
CamLiFlow [13]0.38394.92%0.12053.49%
RAFT+Event0.53790.08%--
CamLiFlow+Event0.36195.07%0.11655.26%
RPEFlow (Ours)0.33295.27%0.10460.50%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.269, + 0.47, + 0.316 + ], + "angle": 0, + "content": "Table 4: Ablation Studies. The results validate the effectiveness for introducing event data, attention fusion and mutual information regularization, respectively." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.326, + 0.462, + 0.436 + ], + "angle": 0, + "content": "
EventFusionMI EPE2DACC1pxEPEFull3DACCFull05
(a)-Concat-2.20084.62%0.059
(b)-Attention-2.13384.74%0.058
(c)-Attention✓2.06784.92%0.055
(d)✓ConcatW/oE-1.56184.37%0.048
(e)✓ConcatW/E-1.51985.34%0.046
(f)✓Attention-1.49486.01%0.043
(g)✓Attention✓1.40286.22%0.042
88.01%
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.47, + 0.568 + ], + "angle": 0, + "content": "model for real-captured data, which is consistent with the observations on synthetic datasets above. In particular, our method performs better in night driving (the 2nd sample in Fig. 4), because the event camera is still sensitive to brightness changes even in low-light scenes. These comparisons further illustrate the importance of introducing events and the applicability of our model to practical needs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.576, + 0.242, + 0.59 + ], + "angle": 0, + "content": "4.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.469, + 0.704 + ], + "angle": 0, + "content": "In Table 4, We conduct ablation experiments to verify the contribution of each component in our model. All variations are trained on the \"training\" split and evaluated on the \"val\" split of FlyingThings3D [28] dataset. In addition to the following discussion, in the supplementary materials we analyze the impact of real and simulated events and the role of combining the two tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Event data. As we are the first to introduce the event data for joint optical flow and scene flow estimation, we explore the effectiveness of event data in two aspects. Firstly, we remove the event data in our framework (see Table 4 (a)-(d) and (c)-(g)), leading to significant performance degradation, especially in optical flow error. This is in line with our claim that event data with continuous observations of scene brightness changes can provide significant help for accurate motion estimation. Secondly, in order to validate the benefit of introducing events to other methods, we concatenate the extracted event feature as an additional input of flow decoder for RAFT [2] and CamLiFlow [13], denoted as RAFT+Event and CamLiFlow+Event, respectively. Re-" + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.089, + 0.887, + 0.153 + ], + "angle": 0, + "content": "
SettingEPE2DACC1pxEPE3DN.OccACC05N.OccEPEFull3DACC05
2D only1.93783.17%------
3D only--0.04386.37%0.07879.05%
2D&3D1.40286.22%0.02493.14%0.04288.01%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.163, + 0.892, + 0.208 + ], + "angle": 0, + "content": "Table 5: Joint vs independent tasks. These models both use three modalities and the results validate that combining the two tasks makes better use of motion information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.233, + 0.892, + 0.278 + ], + "angle": 0, + "content": "sults in Table 1, 2 and 3 show that introducing event data to existing models can also significantly improve the performance, rather than just on our proposed framework." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.279, + 0.893, + 0.429 + ], + "angle": 0, + "content": "Fusion Structure. Unlike CamLiFlow [13] that concat the features from two modalities, we propose an attention-based multimodal fusion module. We conduct experiments with both no-event and with event settings (see Table 4 (a)-(b) and (d)(e)-(f)), and our proposed attention fusion improves both 2D and 3D motion estimation performance. This shows that our multimodal attention fusion module can effectively explore the complementary information and correlations among the three modalities and generate fused features that are suitable for subsequent motion estimation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.43, + 0.894, + 0.626 + ], + "angle": 0, + "content": "Mutual Information. The purpose of the mutual information regularization term is to explicitly constrain the network to learn complementary information from different modalities of data. To verify its contribution to motion estimation, we conduct experiments with both no-event and with event settings (see Table 4 (b)-(c) and (f)-(g)). The results show that with this explicit constraint, the fused features can further improve the accuracy of motion estimation. In addition, we believe that the multimodal attention fusion module and mutual information regularization term both play an important role in motion estimation, because their contribution to 2D and 3D motion estimation is significant in both the with-event and without-event settings." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.635, + 0.68, + 0.651 + ], + "angle": 0, + "content": "4.5. Computation Cost" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.749 + ], + "angle": 0, + "content": "Our model is relatively efficient compared to the latest unimodal and multimodal methods in model size and runtime, i.e., FlowFormer [3]: 17.6M, 1.35s, SCTN [9]: 7.8M, 242ms, RAFT-3D [10]: 45M, 593ms, CamLiFlow [13]: 7.7M, 88ms (\\(\\approx\\)2s with refine) and Ours: 9.75M, 112ms (both on a single RTX3090 GPU with \\(1280 \\times 720\\) size)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.757, + 0.75, + 0.772 + ], + "angle": 0, + "content": "4.6. Joint 2D and 3D estimation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In previous comparisons, the methods of joint optical flow and scene flow estimation perform significantly better than independent methods. To further verify the necessity of jointing these two tasks, we compare the models that only supervise the optical flow or scene flow estimation in Table 5. Although using all three modalities for a single task (2D only and 3D only) is more beneficial than the methods using fewer modality data in Table 1 of main paper." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10037" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.168 + ], + "angle": 0, + "content": "However, combining the two tasks in 2D and 3D benefits from the tight correlation between the two deeply supervised branches, allowing more adequate exploiting of the correlation between 2D and 3D input modalities and more accurate estimating of 2D and 3D motion jointly." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.184, + 0.196, + 0.2 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.21, + 0.473, + 0.391 + ], + "angle": 0, + "content": "We introduce a multimodal fusion framework for joint 2D optical flow and 3D scene flow estimation by fusing RGB images, point clouds and event data. Our contributions are threefold: 1) By incorporating event data, our new framework could handle highly dynamic scenes. 2) We fuse representations of the three very different modalities both implicitly and explicitly through multimodal attention and mutual information regularization, respectively. 3) We contribute a new simulation dataset to further advocate research in this direction. Our work shows that event cameras can play an important role in 2D and 3D motion estimation, and reveals the prospect of event-based 3D vision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.392, + 0.471, + 0.438 + ], + "angle": 0, + "content": "Limitation. Our model is not specially designed for extreme situations such as dark nights or sensor failures, and we plan to address them in the future." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.455, + 0.258, + 0.472 + ], + "angle": 0, + "content": "6. Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.481, + 0.47, + 0.603 + ], + "angle": 0, + "content": "This research was supported in part by National Natural Science Foundation of China (62271410), the Fundamental Research Funds for the Central Universities, and Zhejiang Lab (NO.2021MC0AB05). Zhexiong Wan is sponsored by the scholarship from China Scholarship Council (202306290193) and the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (CX2023013)." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.618, + 0.175, + 0.634 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.644, + 0.47, + 0.7 + ], + "angle": 0, + "content": "[1] Deqing Sun, Xiaodong Yang, Ming-Yu Liu, and Jan Kautz. Pwc-net: Cnns for optical flow using pyramid, warping, and cost volume. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 8934-8943, 2018. 1, 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.707, + 0.47, + 0.761 + ], + "angle": 0, + "content": "[2] Zachary Teed and Jia Deng. Raft: Recurrent all-pairs field transforms for optical flow. 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However, as both conventional RGB cameras and LiDAR sensors adopt a frame-based data acquisition mechanism, their performance is limited by the fixed low sampling rates, especially in highly-dynamic scenes. By contrast, the event camera can asynchronously capture the intensity changes with a very high temporal resolution, providing complementary dynamic information of the observed scenes. In this paper, we incorporate RGB images, Point clouds and Events for joint optical flow and scene flow estimation with our proposed multi-stage multimodal fusion model, RPEFlow. First, we present an attention fusion module with a cross-attention mechanism to implicitly explore the internal cross-modal correlation for 2D and 3D branches, respectively. Second, we introduce a mutual information regularization term to explicitly model the complementary information of three modalities for effective multimodal feature learning. We also contribute a new synthetic dataset to advocate further research. Experiments on both synthetic and real datasets show that our model outperforms the existing state-of-the-art by a wide margin. Code and dataset is available at https://npucvr.github.io/RPEFlow. + +# 1. Introduction + +Optical flow estimation, i.e., estimating the dense 2D motion between consecutive image frames, has been extensively studied and significantly advanced with the development of deep neural networks [1-3]. Scene flow estimation, on the other hand, aims to estimate the 3D motion field with various input configurations, ranging from monocular images [4, 5], stereo images [6, 7], two frames of point clouds [8, 9], images combined with depth maps [10, 11] + +or point clouds [12, 13]. Both are fundamental to downstream applications such as autonomous driving [14, 15], object tracking [16, 17], scene reconstruction [18, 19], etc. + +Due to the strong correlation between 2D and 3D motion, i.e., 2D motion can be regarded as the projection of 3D motion on the image plane, recent works [10, 12, 13] make efforts to jointly estimate optical flow and scene flow by combining RGB images and point clouds (or depth maps). Their success indicates that joint 2D and 3D motion estimation within a framework can obtain more accurate results than separate tasks. However, as both conventional RGB cameras and LiDAR (or depth) sensors adopt a fixed frame-by-frame data acquisition mechanism, these methods show unsatisfactory performance when dealing with complex motion scenes (see Fig. 3), which motivates us to alleviate this problem by introducing the event camera. + +Event camera, as a bio-inspired imaging sensor, can asynchronously capture the brightness change with very high temporal resolution (in the order of $\mu s$ ) and output an event signal quickly [20]. As each pixel adapts its sampling rate according to the captured changes, the amount of output events usually depends on the complexity of motion (the faster the motion, the more triggered events), thus providing abundant motion information of the observed scene. Based on this, some works use event data alone to estimate optical flow [21, 22], but they show limitations in estimating reliable motion at regions with no events [23]. As compensation for this, image and event data are fused together to estimate dense optical flow [24, 25]. As far as we know, there is no method to incorporate event data within a multimodal learning framework for both 2D and 3D motion estimation. + +In this paper, we propose to fuse RGB images, point clouds and events for joint optical flow and scene flow estimation. We find the ability of the event camera to asynchronously capture the brightness changes caused by motion makes it complementary to image cameras and LiDAR sensors, especially for complex dynamics and high-contrast brightness changes. We believe that combining these three modalities together for 2D and 3D motion estimation meets the practical needs, which has been further confirmed by + +existing datasets, such as MVSEC [26] and DSEC [22] that contain these data for driving scenarios. + +We formulate this task as a representation-based multimodal learning problem, and exploit the complementary information between these three very different modalities implicitly and explicitly. We aim to exploit the relationships between multimodal and multi-dimensional space observations (images and events in 2D with point clouds in 3D) and explore their contributions to 2D and 3D motion. Specifically, in our RPEFlow framework, we first propose a multimodal attention fusion module with cross-attention mechanism to implicitly explore the correlations between three modalities, based on which a pyramid multi-stage fusion structure is introduced to extensively modeling. We observe that each modality can contribute a part to 2D and 3D motion estimation, making representation learning [27] suitable for our multimodal learning framework. Then we introduce cross-modal mutual information minimization in feature space to explicitly maximize the complementary information. We also contribute a new synthetic dataset with simulations that conform to the gravity model and collision detection and contain a larger variety of moving objects and richer annotations than FlyingThings3D [28]. Extensive experimental results validate both our implicit multimodal attention fusion and explicit representation regularization towards effective multimodal learning, leading to a new benchmark on both synthetic and real-captured datasets. + +Our main contributions are summarized as follows: + +1) We propose to incorporate event cameras with RGB cameras and LiDAR sensors to jointly estimate optical flow and scene flow for complex dynamic scenes, which constitutes a new and practical problem. +2) An implicit multimodal attention fusion module and an explicit representation learning via mutual information regularization are presented in our RPEFlow model, achieving extensive cross-modal relationship modeling. +3) We contribute a large-scale synthetic dataset with ground-truth motion annotations. Experimental results on both synthetic and real datasets show that the proposed RPEFlow outperforms existing state-of-the-art and demonstrates the effectiveness of event data for motion estimation of complex dynamics. + +# 2. Related Work + +# 2.1. Unimodal 2D/3D Motion Estimation + +Image only. For learning-based 2D optical flow estimation, FlowNet series [29, 30] first propose end-to-end CNN models for regression. PwC-Net [1] work on constructing feature pyramids with coarse-to-fine refinement. RAFT [2] and its variants [3, 31] build all-pairs correlation and update the optical flow iteratively. For 3D scene flow estimation, learning-based studies [6, 7] use a sequence of stereo im + +ages as input [32], achieving faster and better performance compared with earlier optimization-based methods [15, 33]. Some recent works [4, 5, 34] use only monocular image sequences, which are more difficult to model accurate 3D structure and motion than stereo images. Due to the limited frame rate of input images and the difficulty in obtaining 3D structure, the performance of image-only methods is still unsatisfactory when dealing with complex dynamics. + +Point Cloud only. Point cloud data from the LiDAR sensor is favorable for 3D motion estimation. Due to the unique data structure, existing methods [8, 9, 35] focus on studying the model structure to represent the point cloud data for scene flow estimation. However, the point cloud lacks semantic information and leads to the difficulty of estimating accurate motion only by the structural information [13]. + +Event only. Event-based motion estimation is dedicated to extracting motion information from event-encoded brightness changes. Some early optimization-based methods estimate the motion flow of moving boundaries [36,37]. Recent learning-based methods [21, 22, 38] are proposed to regress the dense optical flow directly. Even though the predictions of some of them are densely supervised, the sparse input event data leads to unreliable optical flow estimation in the regions without triggered events [23, 24]. + +# 2.2. Multimodal 2D/3D Motion Estimation + +As unimodal data only provides partial information, multimodal methods are presented to comprehensively learn from multiple observations. For optical flow estimation, event-based studies [24, 25, 39] combine the advantages of the image in dense representation and events in motion perception for reliable estimation. Besides, [40, 41] incorporate gyroscope or depth sensor to guide the optical flow. For scene flow estimation, using a sequences of RGB-Depth images [10, 11] becomes another trend, then [12, 13] replace depth with point clouds to deal with the limited ideal range of depth camera when applied outdoors. But again, they are still limited by the frame-by-frame acquisition mechanism, which leads us to introduce event data. + +# 2.3. Multimodal Fusion + +Given multimodal data, effective multimodal fusion is critical to extensively explore the contribution of each modality [42]. Two main directions have been explored: 1) attention based [43-45] and 2) representation learning [46-49] based. For the former, a specific attention module [50, 51] is designed to implicitly control the contribution of each modal. For the latter, representation similarity is measured to explicitly constrain the reliability of the feature embedding. Within this direction, mutual information (MI) estimation and optimization [48, 52-54] is the widely studied strategy, which is typically used as a regularizer to encourage (via MI maximization) or limit dependency (via + +![](images/587b1c74b4b66448bb5364fa26640483d2178fcd4e842725bc5f0abfe2b64d98.jpg) +Figure 1: Our RPEFlow Structure. We learn motion correlations from the input three modalities (RGB-PointCloud-Event, RPE) by multi-stage fusion (FS, MS and ES) incorporating explicit multimodal attentional fusion (MAF) and implicit representing learning with mutual information regularization (MIR), and perform pyramidal updates from coarse to fine to estimate the optical flow in the 2D branch (top) and the scene flow in the 3D branch (bottom), respectively. Best viewed on screen. + +MI minimization) between variables. + +# 3. Our Method + +We introduce two main strategies to achieve effective multimodal learning, one is explicit multimodal attention fusion (Sec. 3.1) and the other is implicit mutual information regularization (Sec. 3.2). Based on them, we propose a pyramid multi-stage framework (see Fig. 1) for RGB-PointCloud-Event fusion and joint optical flow and scene flow estimation in 2D and 3D branches (Sec. 3.3). + +# 3.1. Multimodal Attention Fusion (MAF) + +As shown in Fig. 1, we have both 2D and 3D branches for optical flow and scene flow estimation. Due to the different data structures of the two branches [8, 13], we design symmetric attention fusion strategy for both two branches in Fig. 2, which consists of two steps, namely feature projection and cross-attention fusion. In the 2D branch, we treat the RGB image as the primary modality and project point cloud feature into the image plane, then fuse with auxiliary features, i.e., event and point cloud. For the 3D branch, we define the point cloud data as the primary modality, then project the others into the 3D space and fuse them together. Multimodal Attention Fusion in 3D branch (MAF RPE-3D). We take the fusion module in the 3D branch of a single pyramid level as a detailed example, where the encoded image feature is $e_r \in \mathbb{R}^{H \times W \times C_{2D}}$ , event feature is $e_{ev} \in \mathbb{R}^{H \times W \times C_{2D}}$ , and point cloud feature is $e_{pc} \in \mathbb{R}^{N \times C_{3D}}$ with the point positions $\mathbf{p} = \{\mathbf{p}_{x_i}, \mathbf{p}_{y_i}, \mathbf{p}_{z_i}\}^N \in \mathbb{R}^{N \times 3}$ in 3D space. Note that $H, W$ and $N$ are the feature size at + +the current pyramid level, not the original input size. We first use the point position to sample the corresponding image and event feature into 3D space with focal length $f$ and denote the projected point position at the image plane as: + +$$ +\left\{\left(u _ {i}, v _ {i}\right) \right\} ^ {N} = \left\{\left(f \frac {\mathbf {P} _ {x _ {i}}}{\mathbf {P} _ {z _ {i}}}, f \frac {\mathbf {P} _ {y _ {i}}}{\mathbf {P} _ {z _ {i}}}\right) \right\} ^ {N} \in \mathbb {R} ^ {N \times 2}. \tag {1} +$$ + +Thus, the projected image and event features are: + +$$ +e _ {r} ^ {p j} = \left\{e _ {r} (u _ {i}, v _ {i}) \right\} ^ {N}, e _ {e v} ^ {p j} = \left\{e _ {e v} (u _ {i}, v _ {i}) \right\} ^ {N} \in \mathbb {R} ^ {N \times C _ {2 D}}, (2) +$$ + +where $e_r(u_i, v_i)$ represents the feature obtained by bilinear interpolation sampling at $(u_i, v_i)$ position in image plane. + +After projection, we feed the features of auxiliary modalities $e_r^{pj}$ and $e_{ev}^{pj}$ with the primary modality feature $X_{pri}^{3D} = e_{pc}$ into the attention fusion module. In the original self-attention mechanism [50, 51], all of the keys $K$ , values $V$ and queries $Q$ come from the same modality. Here we adapt it to accommodate inputs from multiple modalities and propose our cross-attention fusion structure. Specifically, we first combine the auxiliary features and align the number of channels with the master feature by $1 \times 1$ convolution, yielding the aligned auxiliary feature $Y_{aux}^{3D} = W_a \left[ e_r^{pj}, e_{ev}^{pj} \right] (\mathbb{R}^N \times C_{3D} \Leftarrow \mathbb{R}^N \times (C_{2D} + C_{2D}))$ , where $[\cdot, \cdot]$ is the concatenation operation. With layer normalization [55] (LN), we apply $3 \times 3$ depth-wise convolution to encode spatial and channel information with queries $Q_{pri}^{3D} = W_d^Q \mathrm{LN}(X_{pri}^{3D})$ , keys $K_{aux}^{3D} = W_d^K \mathrm{LN}(Y_{aux}^{3D})$ and values $V_{aux}^{3D} = W_d^V \mathrm{LN}(Y_{aux}^{3D})$ , respectively, obtaining the cross-modal self-attention as: + +$$ +\operatorname {A t t e n t i o n} (Q, K, V) = V \operatorname {S o f t m a x} \left(\frac {Q ^ {T} K}{\tau}\right), \tag {3} +$$ + +![](images/95b692fa3cc413c5628c2ba7471a90769d59dc7b2d65f9f719caf21fa4b40e6a.jpg) + +![](images/f583210d2a194248f00c58dc935825a93fedd91a42d52950f1594c326131bdef.jpg) +Figure 2: Our proposed Multimodal Attention Fusion Module fuses both three modal features in 2D (top) and 3D (bottom) branches, including feature projection and cross-attention fusion. In particular, only image and point features are fused in Feature Stage (FS). + +where $\tau$ is a learnable scaling factor. We input $Q_{pri}^{3D}$ , $K_{aux}^{3D}$ , $V_{aux}^{3D}$ to the above attention module, and the resultant attention map with dimension $\mathbb{R}^{C_{3D} \times C_{3D}}$ is much smaller and more efficient than the original implementation [51] with dimension $\mathbb{R}^{HW \times HW}$ adopted from [56]. With the cross-modal attention in Eq. 3, we obtain the fused feature $X_{pri}^{3D'}$ corresponding to the primary modality $e_{pc}$ by another $1 \times 1$ convolution projection and residual connection as: + +$$ +X _ {p r i} ^ {3 D ^ {\prime}} = W _ {p} \mathbf {A t t e n t i o n} (Q _ {p r i} ^ {3 D}, K _ {a u x} ^ {3 D}, V _ {a u x} ^ {3 D}) + X _ {p r i} ^ {3 D}. \qquad (4) +$$ + +Multimodal Attention Fusion in 2D branch (MAF RPE-2D). The fusion process in 2D is similar to the 3D branch above. To project the sparse point feature into a dense feature at the image plane, we adopt a learnable fusion-aware interpolation [13] and get the projected point feature $e_{pc}^{pj} \in \mathbb{R}^{H \times W \times C_{3D}}$ . Then we regard the image feature as the primary modality feature $X_{pri}^{2D} = e_r$ , then the aligned auxiliary feature $Y_{aux}^{2D} = W_a^{2D}\left[e_{pc}^{pj}, e_{ev}\right]$ . After similar cross-attention, the fused feature $X_{pri}^{2D'}$ is obtained as: + +$$ +X _ {p r i} ^ {2 D ^ {\prime}} = W _ {p} \mathbf {A t t e n t i o n} \left(Q _ {p r i} ^ {2 D} K _ {a u x} ^ {2 D}, V _ {a u x} ^ {2 D}\right) + X _ {p r i} ^ {2 D}. \tag {5} +$$ + +# 3.2. Mutual Information Regularization (MIR) + +We incorporate mutual information minimization as a regularizer to explicitly model the cross-modal dependency following disentangled representation learning [27] based on the observation that each modality, i.e. RGB image, point cloud and event data, contributes partially to the output, and mutual information minimization is suitable for our task to explore the complementary information of each modality. + +We start with the case of two modalities with RGB image and event feature embeddings $e_r$ and $e_{ev}$ . Note that these feature embeddings are the features that have been projected into the same spatial space (2D or 3D) in Sec. 3.1. + +To explicitly model the cross-modal correlation, we define cross-modal mutual information between $e_r$ and $e_{ev}$ as $I(e_r;e_{ev}) = \mathbb{E}_{p(e_r,e_{ev})}\left[\log \frac{p(e_{ev}|e_r)}{p(e_{ev})}\right]$ , where $p(e_r,e_{ev})$ is the joint distribution, $p(e_{ev}|e_r)$ is the conditional distribution and $p(e_{ev})$ is the marginal distribution. With importance sampling [57], we introduce a variational marginal approximation $q(e_{ev})$ with a variational upper bound $I^{vub}$ [54] of mutual information $I(e_r;e_{ev})$ as: + +$$ +\begin{array}{l} I \left(e _ {r}; e _ {e v}\right) \leq \mathbb {E} _ {p \left(e _ {r}, e _ {e v}\right)} \left[ \log \frac {p \left(e _ {e v} \mid e _ {r}\right)}{q \left(e _ {e v}\right)} \right] \tag {6} \\ = D _ {K L} \left(p \left(e _ {e v} \mid e _ {r}\right) \| q \left(e _ {e v}\right)\right) = I ^ {v u b} = \mathcal {L} _ {\mathrm {m i}}, \\ \end{array} +$$ + +where $q(e_{ev})$ can be fixed as a standard normal distribution [58], i.e. $q(e_{ev}) = \mathcal{N}(e_{ev};0,\mathbf{I})$ , and $p(e_{ev}|e_r)$ can be modeled with the reparameterization trick [59], thus the Kullback-Leibler (KL) divergence term $D_{KL}$ within $I^{vub}$ can be solved in closed form. + +In the case of three modalities feature embeddings $e_r$ , $e_{pc}$ and $e_{ev}$ , respectively, the interaction information $II(e_r; e_{pc}; e_{ev})$ [60], as a multivariate generalization of the mutual information, is upper bounded by: + +$$ +\begin{array}{l} I I \left(e _ {r}; e _ {p c}; e _ {e v}\right) \leq \min \left\{I \left(e _ {r}; e _ {p c}\right), I \left(e _ {p c}; e _ {e v}\right), I \left(e _ {r}; e _ {e v}\right) \right\} \tag {7} \\ \leq \min \left\{I ^ {v u b} \left(e _ {r}; e _ {p c}\right), I ^ {v u b} \left(e _ {p c}; e _ {e v}\right), I ^ {v u b} \left(e _ {r}; e _ {e v}\right) \right\}. \\ \end{array} +$$ + +To compute $I^{vub}$ , we need to design a transition function, achieving the transformation of one modality to the other and assume the variational marginal approximation $q$ as the standard normal distribution for closed-form KL divergence computation. In practice, the standard normal distribution assumption of $q$ leads to high-bias mutual information estimation. Alternatively, we first map the representation of each modality $(e_r, e_{pc}, e_{ev})$ to a common manifold, with reparameterization trick [59] in the end to achieve Gaussian latent code of each modality. Then, we compute KL + +divergence between the two Gaussian latent codes, leading to the final mutual information regularization term: + +$$ +\mathcal {L} _ {\mathrm {i i}} = I ^ {v u b} \left(e _ {r}; e _ {p c}\right) + I ^ {v u b} \left(e _ {p c}; e _ {e v}\right) + I ^ {v u b} \left(e _ {r}; e _ {e v}\right), (8) +$$ + +where we compute the sum of $I^{vub}$ instead of choosing the minimum for stable training. + +# 3.3. Pyramid Fusion and Joint Estimation Model + +With the proposed multimodal attention fusion and the mutual information regularization term, we achieve once multimodal feature fusion. Inspired by CamLiFlow [13], we further perform multi-stage feature fusion implicitly and explicitly. Here we present the details of multi-stage feature fusion, and more details about the network structure are given in the supplementary materials. As shown in Fig. 1, our model contains both 2D and 3D branches, where each branch consists of feature extraction, correlation construction and flow estimation. + +In feature extraction, we first voxelized the raw events $E = \{x_{i},y_{i},t_{i},p_{i}\}^{K}$ into one event voxel $EV\in \mathbb{R}^{H\times W\times B}$ that can be used as input to our network, where $K$ is the number of events during the period between two frames and $B$ is the manually set number of time intervals to sample events. We apply three Siamese encoders to construct feature pyramids $(\{e_{r_1},e_{r_2}\} _l,\{e_{pc_1},e_{pc_2}\} _l$ and $e_{ev_l}$ with pyramid layers $l\in [1,L])$ for three modalities respectively. As spans between two frames, the event data is not included in Feature Stage Fusion, which is applied to fuse the features of two frames RGB images and corresponding point clouds with two-modal attention fusion, i.e. simplify the auxiliary feature to a single modality in Eq. 4, 5 and mutual information regularization in Eq. 6 for both 2D and 3D branches. + +In correlation construction, we first warp the second frame of image and point cloud features using the coarse optical flow and scene flow (initialize with zero) from the previous pyramid layer, then construct correlation motion features by computing 2D and 3D cost volumes and fused them with the event feature at Motion Stage Fusion. In flow estimation, we construct a motion decoder and flow estimator, and perform an Estimation Stage Fusion between them to fuse the hidden motion features from the two branches decoder with the event feature. In these two fusion stages, we conduct multimodal attention fusion in Eq. 4, 5 and mutual information regularization in Eq. 8 for 2D and 3D motion features and event feature, because events can provide complementary information to enhance the motion correlation construction. The estimated optical flow and scene flow are fed into the next pyramid layer to achieve coarse-to-fine predictions. We take the optical flow and scene flow from the last pyramid layer as our final joint estimations. + +# 3.4. Objective Functions + +The objective functions in the training of our model are divided into feature representation loss and task loss. The former consists of multiple mutual information regularizations at each fusion stage. $\mathcal{L}_{\mathrm{mi}}^{fs1}$ , $\mathcal{L}_{\mathrm{mi}}^{fs2}$ represent the mutual information minimization loss imposed on the RGB image and point cloud features of the first and the second frame at the Feature Stage fusion, and $\mathcal{L}_{\mathrm{ii}}^{ms}$ and $\mathcal{L}_{\mathrm{ii}}^{es}$ represent on both RGB image, point cloud and event features at the Motion Stage and Estimation Stage fusion. Thus the feature representation loss is the sum of all stages and is weighted at each pyramid level: + +$$ +\mathcal {L} _ {\text {f e a t}} = \sum_ {l = 1} ^ {L} \lambda_ {l} \left[ \mathcal {L} _ {\mathrm {m i}} ^ {f s 1} _ {l} + \mathcal {L} _ {\mathrm {m i}} ^ {f s 2} _ {l} + \mathcal {L} _ {\mathrm {i i}} ^ {m s} _ {l} + \mathcal {L} _ {\mathrm {i i}} ^ {e s} _ {l} \right], \tag {9} +$$ + +where $l$ is the pyramid level, and $\lambda_{l}$ is used to reweight the contribution of each pyramid level. + +The latter task loss measures the $L_{2}$ distance between the ground-truth and the model output at each pyramid level by: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {t a s k}} = \sum_ {l = 1} ^ {L} \lambda_ {l} \left[ \sum_ {\mathbf {x}} \left(\| f _ {l} ^ {\text {p r e d}} (\mathbf {x}) - f _ {l} ^ {\text {g t}} (\mathbf {x}) \| _ {2}\right) + \right. \tag {10} \\ \alpha \sum_ {\mathbf {p}} (\| s _ {l} ^ {p r e d} (\mathbf {p}) - s _ {l} ^ {g t} (\mathbf {p}) \| _ {2}) \Big ], \\ \end{array} +$$ + +where $\mathbf{x}$ , $\mathbf{p}$ are the valid image positions and point coordinates, $f_{l}^{pred}$ , $s_{l}^{pred}$ are the estimated 2D optical flow and 3D scene flow and $f_{l}^{gt}$ , $s_{l}^{gt}$ are the corresponding resized ground truth at the $l$ -th pyramid level, respectively. $\alpha$ is the weight to balance 2D and 3D errors. + +The total loss is a weighted sum of the above: + +$$ +\mathcal {L} = \mathcal {L} _ {\text {t a s k}} + \beta \mathcal {L} _ {\text {f e a t}}, \tag {11} +$$ + +where $\beta$ is the weight to balance two losses in training. + +# 4. Experiment + +# 4.1. Implementation Details + +Datasets. Since there is no large-scale scene flow dataset with real event data, we use synthetic data for pretraining. Follow the preprocess pipeline [13, 62], we generate point clouds from depth images for FlyingThings3D [28] dataset, which contains 19,640 and 3,824 RGB-PointColud pairs for "train" and "val" splits. We use the popular video-to-events conversion method [63] to generate the corresponding events. In addition, we use kubric [64] to simulate 15,367 RGB-PointCloud-Event pairs with rich annotations (including optical flow and scene flow ground truths), denoted as EKubric, which aims to simulate photo-realistic + +![](images/68d25ed7f006533cd1f8e419c0ff09fab54126b0ea0a7653c773b8d2aa993abe.jpg) + +![](images/a55df57847bbda136569dc62793df4e4fc8e96da95b4a51d58f6eaaff0a95c99.jpg) + +![](images/9d9f6ffb8832fe637bf53898eeff4d723091de7172c0f7f5cfb2b29ce15d8576.jpg) + +![](images/4df0d62db1c7114a4d411a2a77e515b221f402ea95ebc5d2d982433fa9a905d6.jpg) + +![](images/587c73308d86d3cc18f6e6fe8ec2b8eb28433928e8f954b6137658560166e8c3.jpg) + +![](images/0fc0e13953a9ac22706a191996313c0bc9102e30b2efb704f86f352116fb3466.jpg) + +![](images/5b5cec11028640e8b27cea53d3cc13f1ab022f5f47bf88ba0b723e6793afdaa6.jpg) +Figure 3: Visual comparisons on simulated data, in which the top row is on the "val" split of FlyingThings3D [28] dataset and the reset two are on the test split of our simulated EKubric dataset. For the bottom 3D comparisons, blue indicates a lower error, red indicates a higher error, and green indicates the median. Best to zoom in on the screen for detailed comparisons. + +![](images/c45a81f6e6fbdd687c659d595151234811beb8d73f54b84a6539f7f8156bd26c.jpg) + +![](images/6b9d875b28fa6c96052c5310d5bf3fe23c86fac9f0f088b80b7fd7a620a651d8.jpg) + +![](images/726718d4579b85a2bf57d0dcd59073e495375b21e4d7d228bac33b639e4c3947.jpg) + +![](images/aa1f90830d0616e47029b4517645fbbeb9fe8b464401e64d7ddfe91079d1cd79.jpg) + +Table 1: Performance comparison on the "val" split of the FlyingThings3D [28] subset. + +
InputMethodEPE2DACC1pxEPEN.Occ3DACCN.Occ05EPEFull3DACCFull05
RGBRAFT [2]3.1281.1%----
FlowFormer [3]3.0282.6%----
PCMeteornet* [61]----0.209-
PointPWC [8]--0.11251.8%--
SCTN [9]--0.03884.7%--
RGB+DepthRAFT-3D [10]2.3787.1%0.06284.5%0.08971.1%
RGB+PCDeepLiDARFlow [12]6.0447.1%-27.2%--
CamLiFlow [13]2.2084.6%0.03391.7%0.05986.0%
RGB+EventRAFT+Event2.4984.6%----
RGB+PC+EventCamLiFlow+Event1.5684.4%0.02891.7%0.04885.9%
RPEFlow (Ours)1.4086.2%0.02493.1%0.04288.0%
+ +scenes with collision detection, gravity model and ambient illumination and has more object kinds than FlyingThings3D. We also use the DSEC [22] dataset, which contains 8,170 pairs of real-captured samples in driving scenarios. + +Training, Hyper-parameters and Metrics. Our model is trained with PyTorch on four RTX3090 GPUs and evaluated on one. We use the Adam optimizer with weight decay $10^{-6}$ . The number of event bins is $B = 10$ , pyramid layers is $L = 5$ . Loss weights are $\alpha = 10.0$ , $\beta = 0.01$ , $\lambda_l = 2^{(l - 2)}$ for $l \in [1, L]$ . Following [10, 13], we evalu + +ate using 2D and 3D end-point error (EPE $_{2\mathrm{D}}$ and EPE $_{3\mathrm{D}}$ ), and $\mathrm{ACC}_{1\mathrm{px}}$ and $\mathrm{ACC}_{.05}$ to measure the portion of accuracy within 1 pixel and $5\mathrm{cm}$ . The scene flow metrics with N.Occ superscript indicates only the not occluded positions are calculated, while Full or none indicates all positions including occlusion. More details about datasets and training are provided in the supplementary materials. + +Table 2: Finetuned performance comparison on the test split of our simulated EKubric dataset. + +
InputMethodEPE2DACC1pxEPEN.Occ3DACCN.Occ05EPEFull3DACCFull05
RGBRAFT [2]0.75793.70%----
FlowFormer [3]0.68393.92%----
RGB+DepthRAFT-3D [10]0.71594.33%0.01695.20%0.04992.62%
RGB+PCCamLiFlow [13]0.76195.00%0.00998.39%0.03294.90%
RGB+EventRAFT+Event0.48795.25%----
RGB+PC+EventCamLiFlow+Event0.50595.41%0.00898.48%0.03195.01%
RPEFlow (Ours)0.44296.08%0.00798.68%0.02795.30%
+ +![](images/704b051972ee0f8a6cb261c9e33f4c3ff812e759a48b7871eec1686f862b03ab.jpg) + +![](images/1f306705a1ae8b3736582e029ace1080e9cda4ad2430a761e7ff0b605e805871.jpg) + +![](images/8c56eb9672fb1228145bf6f875c57a5116bec2530d28fcbe4bc2ca8d16917958.jpg) + +![](images/b6359e8468a61e037eb0567767ad9da06ff286936c60583ca60968fb696ce281.jpg) + +![](images/292578f879c043fdbacd86d70763750e0daa5ae7a3a47d1492f555668d363773.jpg) + +![](images/91572ec4831b943cbbf8ae031a34aa1321e80bbe96a5b412b82b787c7f3d6038.jpg) + +![](images/174ad864feb652aa2b0d88663d0c8b95273ca3ab18e4b2da9f1cd18b0a99d0fa.jpg) + +![](images/3a7e3773add81391ad4c31b5120420df3dfa4470deb495c08e96b1101fdb4600.jpg) + +![](images/39af1f8d1b54614f0cacd5cbd90cfad0e1338fb86ba42d4d3da8fe046eb83c7a.jpg) + +![](images/f5b47ba9fe3b06954403fb7cf1bbd73704b72edde0ab2da30afdf2ac0b1e77a7.jpg) + +![](images/5654dfa448f58b85d71f90da640c01e9f7306481723032ce4e2a95caba7b214c.jpg) + +![](images/686ee3371d8cf5d56b643da08ed9698352b3b4169cff477c0b6411ecf067529b.jpg) + +![](images/dbedb5c2154ceeda9c49b0dd4f8f7946d26d2ec186f4bae5fb902d0563a4bee1.jpg) +Figure 4: Visual comparisons on real-captured data, i.e. the "val" split of DSEC [22] dataset. + +![](images/caa30dc4e5e561046a14c8c090424623f42f3cc7884315e65e8baabf5e411eb5.jpg) + +![](images/6ce0c57069a35eeb0f902850a17f5f977f5b8b6f32bf186519f4de0c31ecdd15.jpg) + +![](images/d98e946b653dc7381573229b1973f54b0d808384521cbb32866a99b728299944.jpg) + +![](images/05e14465915b54f1780eab8124907d564b8c62da6f11a368d0c832c5a8699047.jpg) + +# 4.2. Comparisons with Synthetic Events + +Following the conventional setting, our model is first pre-trained on FlyingThings3D [28], and Table 1 shows the quantitative comparison performance on the "val" split. Both results are evaluated using their pre-trained model on FlyingThings3D. Meteornet* [61] has not released model for scene flow estimation, so we compare the EPE3D result from its paper. We also finetune them on our simulated EKubric dataset, and the performance comparisons on the test set are shown in Table 2, where the compared models were all pre-trained on FlyingThings3D and then finetuned on EKubric with the same training settings. Note that we did not evaluate the PC-only methods on our EKubric dataset due to their different data preprocessing strategies. + +We report the results of two representative methods [2, 8] and two latest methods [3, 9] using only one modal for one task, and find that combining multiple modalities can significantly improve model accuracy for both optical flow and scene flow estimation. Furthermore, the methods that combine all three modalities, i.e. RGB+PC+Event, achieve better results than the rest [10, 12, 13], which illustrates the sig- + +nificant benefit of introducing event data for accurate motion estimation. With the same input setting, we compare our model with CamLiFlow+Event and observe improved accuracy, which is because our proposed multimodal attention fusion module is able to fully mine valuable information from continuous event data for accurate motion estimation. The comparison of visualization results in Fig. 3 and in the supplementary materials is also consistent with the above observations, especially in high dynamic and detail moving or motion-blurred areas. + +# 4.3. Comparisons with Real Events + +We further conduct experiments on the real-captured DSEC [22] dataset. We divide the public set into "train" and "val" splits for finetuning and evaluation. Since the dense depth required by RAFT-3D [10] is not available, we use CFNet [65] to obtain a pseudo-dense depth map by stereo matching as input. E-RAFT* [22] does not have a publicly available training code, thus we can only use the pretrained model on the entire DSEC dataset including the "val" split (marked with *). Both quantitative and qualitative (Table 3 and Fig. 4) comparisons demonstrate the superiority of our + +Table 3: Finetuned Performance comparison on the "val" split of DSEC [22] dataset. + +
MethodEPE2DACC1pxEPEFull3DACCFull.05
RAFT [2]0.57289.63%--
E-RAFT* [22]0.47392.11%--
RAFT-3D [10]0.56790.55%0.14051.30%
CamLiFlow [13]0.38394.92%0.12053.49%
RAFT+Event0.53790.08%--
CamLiFlow+Event0.36195.07%0.11655.26%
RPEFlow (Ours)0.33295.27%0.10460.50%
+ +Table 4: Ablation Studies. The results validate the effectiveness for introducing event data, attention fusion and mutual information regularization, respectively. + +
EventFusionMI EPE2DACC1pxEPEFull3DACCFull05
(a)-Concat-2.20084.62%0.059
(b)-Attention-2.13384.74%0.058
(c)-Attention✓2.06784.92%0.055
(d)✓ConcatW/oE-1.56184.37%0.048
(e)✓ConcatW/E-1.51985.34%0.046
(f)✓Attention-1.49486.01%0.043
(g)✓Attention✓1.40286.22%0.042
88.01%
+ +model for real-captured data, which is consistent with the observations on synthetic datasets above. In particular, our method performs better in night driving (the 2nd sample in Fig. 4), because the event camera is still sensitive to brightness changes even in low-light scenes. These comparisons further illustrate the importance of introducing events and the applicability of our model to practical needs. + +# 4.4. Ablation Studies + +In Table 4, We conduct ablation experiments to verify the contribution of each component in our model. All variations are trained on the "training" split and evaluated on the "val" split of FlyingThings3D [28] dataset. In addition to the following discussion, in the supplementary materials we analyze the impact of real and simulated events and the role of combining the two tasks. + +Event data. As we are the first to introduce the event data for joint optical flow and scene flow estimation, we explore the effectiveness of event data in two aspects. Firstly, we remove the event data in our framework (see Table 4 (a)-(d) and (c)-(g)), leading to significant performance degradation, especially in optical flow error. This is in line with our claim that event data with continuous observations of scene brightness changes can provide significant help for accurate motion estimation. Secondly, in order to validate the benefit of introducing events to other methods, we concatenate the extracted event feature as an additional input of flow decoder for RAFT [2] and CamLiFlow [13], denoted as RAFT+Event and CamLiFlow+Event, respectively. Re- + +
SettingEPE2DACC1pxEPE3DN.OccACC05N.OccEPEFull3DACC05
2D only1.93783.17%------
3D only--0.04386.37%0.07879.05%
2D&3D1.40286.22%0.02493.14%0.04288.01%
+ +Table 5: Joint vs independent tasks. These models both use three modalities and the results validate that combining the two tasks makes better use of motion information. + +sults in Table 1, 2 and 3 show that introducing event data to existing models can also significantly improve the performance, rather than just on our proposed framework. + +Fusion Structure. Unlike CamLiFlow [13] that concat the features from two modalities, we propose an attention-based multimodal fusion module. We conduct experiments with both no-event and with event settings (see Table 4 (a)-(b) and (d)(e)-(f)), and our proposed attention fusion improves both 2D and 3D motion estimation performance. This shows that our multimodal attention fusion module can effectively explore the complementary information and correlations among the three modalities and generate fused features that are suitable for subsequent motion estimation. + +Mutual Information. The purpose of the mutual information regularization term is to explicitly constrain the network to learn complementary information from different modalities of data. To verify its contribution to motion estimation, we conduct experiments with both no-event and with event settings (see Table 4 (b)-(c) and (f)-(g)). The results show that with this explicit constraint, the fused features can further improve the accuracy of motion estimation. In addition, we believe that the multimodal attention fusion module and mutual information regularization term both play an important role in motion estimation, because their contribution to 2D and 3D motion estimation is significant in both the with-event and without-event settings. + +# 4.5. Computation Cost + +Our model is relatively efficient compared to the latest unimodal and multimodal methods in model size and runtime, i.e., FlowFormer [3]: 17.6M, 1.35s, SCTN [9]: 7.8M, 242ms, RAFT-3D [10]: 45M, 593ms, CamLiFlow [13]: 7.7M, 88ms ( $\approx$ 2s with refine) and Ours: 9.75M, 112ms (both on a single RTX3090 GPU with $1280 \times 720$ size). + +# 4.6. Joint 2D and 3D estimation. + +In previous comparisons, the methods of joint optical flow and scene flow estimation perform significantly better than independent methods. To further verify the necessity of jointing these two tasks, we compare the models that only supervise the optical flow or scene flow estimation in Table 5. Although using all three modalities for a single task (2D only and 3D only) is more beneficial than the methods using fewer modality data in Table 1 of main paper. + +However, combining the two tasks in 2D and 3D benefits from the tight correlation between the two deeply supervised branches, allowing more adequate exploiting of the correlation between 2D and 3D input modalities and more accurate estimating of 2D and 3D motion jointly. + +# 5. Conclusion + +We introduce a multimodal fusion framework for joint 2D optical flow and 3D scene flow estimation by fusing RGB images, point clouds and event data. Our contributions are threefold: 1) By incorporating event data, our new framework could handle highly dynamic scenes. 2) We fuse representations of the three very different modalities both implicitly and explicitly through multimodal attention and mutual information regularization, respectively. 3) We contribute a new simulation dataset to further advocate research in this direction. 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Club: A contrastive log-ratio upper bound of mutual information. In International Conference on Machine Learning (ICML), pages 1779-1788, 2020. 2, 4 +[55] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. Layer normalization. arXiv preprint arXiv:1607.06450, 2016.3 +[56] Syed Waqas Zamir, Aditya Arora, Salman Khan, Munawar Hayat, Fahad Shahbaz Khan, and Ming-Hsuan Yang. Restormer: Efficient transformer for high-resolution image restoration. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 5728-5739, 2022. 4 +[57] Yuri Burda, Roger Grosse, and Ruslan Salakhutdinov. Importance weighted autoencoders. In International Conference on Learning Representations (ICLR), 2016. 4 +[58] Alexander A. Alemi, Ian Fischer, Joshua V. Dillon, and Kevin Murphy. Deep variational information bottleneck. In International Conference on Learning Representations (ICLR), 2017. 4 +[59] Diederik Kingma and Max Welling. Auto-encoding variational bayes. 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However, as both conventional RGB cameras and LiDAR sensors adopt a frame-based data acquisition mechanism, their performance is limited by the fixed low sampling rates, especially in highly-dynamic scenes. By contrast, the event camera can asynchronously capture the intensity changes with a very high temporal resolution, providing complementary dynamic information of the observed scenes. In this paper, we incorporate RGB images, Point clouds and Events for joint optical flow and scene flow estimation with our proposed multi-stage multimodal fusion model, RPEFlow. First, we present an attention fusion module with a cross-attention mechanism to implicitly explore the internal cross-modal correlation for 2D and 3D branches, respectively. Second, we introduce a mutual information regularization term to explicitly model the complementary information of three modalities for effective multimodal feature learning. We also contribute a new synthetic dataset to advocate further research. 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Both are fundamental to downstream applications such as autonomous driving [14, 15], object tracking [16, 17], scene reconstruction [18, 19], etc." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 269, + 546, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 269, + 546, + 424 + ], + "spans": [ + { + "bbox": [ + 304, + 269, + 546, + 424 + ], + "type": "text", + "content": "Due to the strong correlation between 2D and 3D motion, i.e., 2D motion can be regarded as the projection of 3D motion on the image plane, recent works [10, 12, 13] make efforts to jointly estimate optical flow and scene flow by combining RGB images and point clouds (or depth maps). Their success indicates that joint 2D and 3D motion estimation within a framework can obtain more accurate results than separate tasks. However, as both conventional RGB cameras and LiDAR (or depth) sensors adopt a fixed frame-by-frame data acquisition mechanism, these methods show unsatisfactory performance when dealing with complex motion scenes (see Fig. 3), which motivates us to alleviate this problem by introducing the event camera." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 426, + 547, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 547, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 547, + 604 + ], + "type": "text", + "content": "Event camera, as a bio-inspired imaging sensor, can asynchronously capture the brightness change with very high temporal resolution (in the order of " + }, + { + "bbox": [ + 304, + 426, + 547, + 604 + ], + "type": "inline_equation", + "content": "\\mu s" + }, + { + "bbox": [ + 304, + 426, + 547, + 604 + ], + "type": "text", + "content": ") and output an event signal quickly [20]. 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As far as we know, there is no method to incorporate event data within a multimodal learning framework for both 2D and 3D motion estimation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "In this paper, we propose to fuse RGB images, point clouds and events for joint optical flow and scene flow estimation. We find the ability of the event camera to asynchronously capture the brightness changes caused by motion makes it complementary to image cameras and LiDAR sensors, especially for complex dynamics and high-contrast brightness changes. We believe that combining these three modalities together for 2D and 3D motion estimation meets the practical needs, which has been further confirmed by" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 703, + 246, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 703, + 246, + 713 + ], + "spans": [ + { + "bbox": [ + 61, + 703, + 246, + 713 + ], + "type": "text", + "content": "† Corresponding author (daiyuchao@gmail.com)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10030" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "existing datasets, such as MVSEC [26] and DSEC [22] that contain these data for driving scenarios." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 97, + 289, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 97, + 289, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 97, + 289, + 396 + ], + "type": "text", + "content": "We formulate this task as a representation-based multimodal learning problem, and exploit the complementary information between these three very different modalities implicitly and explicitly. We aim to exploit the relationships between multimodal and multi-dimensional space observations (images and events in 2D with point clouds in 3D) and explore their contributions to 2D and 3D motion. Specifically, in our RPEFlow framework, we first propose a multimodal attention fusion module with cross-attention mechanism to implicitly explore the correlations between three modalities, based on which a pyramid multi-stage fusion structure is introduced to extensively modeling. We observe that each modality can contribute a part to 2D and 3D motion estimation, making representation learning [27] suitable for our multimodal learning framework. Then we introduce cross-modal mutual information minimization in feature space to explicitly maximize the complementary information. We also contribute a new synthetic dataset with simulations that conform to the gravity model and collision detection and contain a larger variety of moving objects and richer annotations than FlyingThings3D [28]. Extensive experimental results validate both our implicit multimodal attention fusion and explicit representation regularization towards effective multimodal learning, leading to a new benchmark on both synthetic and real-captured datasets." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 397, + 266, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 397, + 266, + 408 + ], + "spans": [ + { + "bbox": [ + 59, + 397, + 266, + 408 + ], + "type": "text", + "content": "Our main contributions are summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 409, + 287, + 577 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 48, + 409, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 409, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 48, + 409, + 287, + 456 + ], + "type": "text", + "content": "1) We propose to incorporate event cameras with RGB cameras and LiDAR sensors to jointly estimate optical flow and scene flow for complex dynamic scenes, which constitutes a new and practical problem." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 457, + 287, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 457, + 287, + 505 + ], + "spans": [ + { + "bbox": [ + 47, + 457, + 287, + 505 + ], + "type": "text", + "content": "2) An implicit multimodal attention fusion module and an explicit representation learning via mutual information regularization are presented in our RPEFlow model, achieving extensive cross-modal relationship modeling." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 506, + 287, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 506, + 287, + 577 + ], + "spans": [ + { + "bbox": [ + 47, + 506, + 287, + 577 + ], + "type": "text", + "content": "3) We contribute a large-scale synthetic dataset with ground-truth motion annotations. Experimental results on both synthetic and real datasets show that the proposed RPEFlow outperforms existing state-of-the-art and demonstrates the effectiveness of event data for motion estimation of complex dynamics." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 590, + 134, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 590, + 134, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 590, + 134, + 601 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 610, + 239, + 622 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 239, + 622 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 239, + 622 + ], + "type": "text", + "content": "2.1. Unimodal 2D/3D Motion Estimation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "Image only. For learning-based 2D optical flow estimation, FlowNet series [29, 30] first propose end-to-end CNN models for regression. PwC-Net [1] work on constructing feature pyramids with coarse-to-fine refinement. RAFT [2] and its variants [3, 31] build all-pairs correlation and update the optical flow iteratively. For 3D scene flow estimation, learning-based studies [6, 7] use a sequence of stereo im" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": "ages as input [32], achieving faster and better performance compared with earlier optimization-based methods [15, 33]. Some recent works [4, 5, 34] use only monocular image sequences, which are more difficult to model accurate 3D structure and motion than stereo images. Due to the limited frame rate of input images and the difficulty in obtaining 3D structure, the performance of image-only methods is still unsatisfactory when dealing with complex dynamics." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 168, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 545, + 251 + ], + "type": "text", + "content": "Point Cloud only. Point cloud data from the LiDAR sensor is favorable for 3D motion estimation. Due to the unique data structure, existing methods [8, 9, 35] focus on studying the model structure to represent the point cloud data for scene flow estimation. However, the point cloud lacks semantic information and leads to the difficulty of estimating accurate motion only by the structural information [13]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 252, + 545, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 252, + 545, + 360 + ], + "spans": [ + { + "bbox": [ + 304, + 252, + 545, + 360 + ], + "type": "text", + "content": "Event only. Event-based motion estimation is dedicated to extracting motion information from event-encoded brightness changes. Some early optimization-based methods estimate the motion flow of moving boundaries [36,37]. Recent learning-based methods [21, 22, 38] are proposed to regress the dense optical flow directly. Even though the predictions of some of them are densely supervised, the sparse input event data leads to unreliable optical flow estimation in the regions without triggered events [23, 24]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 369, + 507, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 369, + 507, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 369, + 507, + 380 + ], + "type": "text", + "content": "2.2. Multimodal 2D/3D Motion Estimation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 387, + 545, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 387, + 545, + 542 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 545, + 542 + ], + "type": "text", + "content": "As unimodal data only provides partial information, multimodal methods are presented to comprehensively learn from multiple observations. For optical flow estimation, event-based studies [24, 25, 39] combine the advantages of the image in dense representation and events in motion perception for reliable estimation. Besides, [40, 41] incorporate gyroscope or depth sensor to guide the optical flow. For scene flow estimation, using a sequences of RGB-Depth images [10, 11] becomes another trend, then [12, 13] replace depth with point clouds to deal with the limited ideal range of depth camera when applied outdoors. But again, they are still limited by the frame-by-frame acquisition mechanism, which leads us to introduce event data." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 551, + 419, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 551, + 419, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 551, + 419, + 562 + ], + "type": "text", + "content": "2.3. Multimodal Fusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Given multimodal data, effective multimodal fusion is critical to extensively explore the contribution of each modality [42]. Two main directions have been explored: 1) attention based [43-45] and 2) representation learning [46-49] based. For the former, a specific attention module [50, 51] is designed to implicitly control the contribution of each modal. For the latter, representation similarity is measured to explicitly constrain the reliability of the feature embedding. Within this direction, mutual information (MI) estimation and optimization [48, 52-54] is the widely studied strategy, which is typically used as a regularizer to encourage (via MI maximization) or limit dependency (via" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10031" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 54, + 69, + 541, + 274 + ], + "blocks": [ + { + "bbox": [ + 54, + 69, + 541, + 274 + ], + "lines": [ + { + "bbox": [ + 54, + 69, + 541, + 274 + ], + "spans": [ + { + "bbox": [ + 54, + 69, + 541, + 274 + ], + "type": "image", + "image_path": "587b1c74b4b66448bb5364fa26640483d2178fcd4e842725bc5f0abfe2b64d98.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 277, + 547, + 327 + ], + "lines": [ + { + "bbox": [ + 46, + 277, + 547, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 547, + 327 + ], + "type": "text", + "content": "Figure 1: Our RPEFlow Structure. We learn motion correlations from the input three modalities (RGB-PointCloud-Event, RPE) by multi-stage fusion (FS, MS and ES) incorporating explicit multimodal attentional fusion (MAF) and implicit representing learning with mutual information regularization (MIR), and perform pyramidal updates from coarse to fine to estimate the optical flow in the 2D branch (top) and the scene flow in the 3D branch (bottom), respectively. Best viewed on screen." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 342, + 198, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 342, + 198, + 354 + ], + "spans": [ + { + "bbox": [ + 47, + 342, + 198, + 354 + ], + "type": "text", + "content": "MI minimization) between variables." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 365, + 127, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 365, + 127, + 378 + ], + "spans": [ + { + "bbox": [ + 47, + 365, + 127, + 378 + ], + "type": "text", + "content": "3. Our Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 385, + 288, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 385, + 288, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 385, + 288, + 469 + ], + "type": "text", + "content": "We introduce two main strategies to achieve effective multimodal learning, one is explicit multimodal attention fusion (Sec. 3.1) and the other is implicit mutual information regularization (Sec. 3.2). Based on them, we propose a pyramid multi-stage framework (see Fig. 1) for RGB-PointCloud-Event fusion and joint optical flow and scene flow estimation in 2D and 3D branches (Sec. 3.3)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 478, + 242, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 478, + 242, + 490 + ], + "spans": [ + { + "bbox": [ + 47, + 478, + 242, + 490 + ], + "type": "text", + "content": "3.1. Multimodal Attention Fusion (MAF)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 496, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 289, + 714 + ], + "type": "text", + "content": "As shown in Fig. 1, we have both 2D and 3D branches for optical flow and scene flow estimation. Due to the different data structures of the two branches [8, 13], we design symmetric attention fusion strategy for both two branches in Fig. 2, which consists of two steps, namely feature projection and cross-attention fusion. In the 2D branch, we treat the RGB image as the primary modality and project point cloud feature into the image plane, then fuse with auxiliary features, i.e., event and point cloud. For the 3D branch, we define the point cloud data as the primary modality, then project the others into the 3D space and fuse them together. Multimodal Attention Fusion in 3D branch (MAF RPE-3D). We take the fusion module in the 3D branch of a single pyramid level as a detailed example, where the encoded image feature is " + }, + { + "bbox": [ + 46, + 496, + 289, + 714 + ], + "type": "inline_equation", + "content": "e_r \\in \\mathbb{R}^{H \\times W \\times C_{2D}}" + }, + { + "bbox": [ + 46, + 496, + 289, + 714 + ], + "type": "text", + "content": ", event feature is " + }, + { + "bbox": [ + 46, + 496, + 289, + 714 + ], + "type": "inline_equation", + "content": "e_{ev} \\in \\mathbb{R}^{H \\times W \\times C_{2D}}" + }, + { + "bbox": [ + 46, + 496, + 289, + 714 + ], + "type": "text", + "content": ", and point cloud feature is " + }, + { + "bbox": [ + 46, + 496, + 289, + 714 + ], + "type": "inline_equation", + "content": "e_{pc} \\in \\mathbb{R}^{N \\times C_{3D}}" + }, + { + "bbox": [ + 46, + 496, + 289, + 714 + ], + "type": "text", + "content": " with the point positions " + }, + { + "bbox": [ + 46, + 496, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{p} = \\{\\mathbf{p}_{x_i}, \\mathbf{p}_{y_i}, \\mathbf{p}_{z_i}\\}^N \\in \\mathbb{R}^{N \\times 3}" + }, + { + "bbox": [ + 46, + 496, + 289, + 714 + ], + "type": "text", + "content": " in 3D space. Note that " + }, + { + "bbox": [ + 46, + 496, + 289, + 714 + ], + "type": "inline_equation", + "content": "H, W" + }, + { + "bbox": [ + 46, + 496, + 289, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 496, + 289, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 496, + 289, + 714 + ], + "type": "text", + "content": " are the feature size at" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 342, + 545, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 342, + 545, + 390 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 545, + 390 + ], + "type": "text", + "content": "the current pyramid level, not the original input size. We first use the point position to sample the corresponding image and event feature into 3D space with focal length " + }, + { + "bbox": [ + 305, + 342, + 545, + 390 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 305, + 342, + 545, + 390 + ], + "type": "text", + "content": " and denote the projected point position at the image plane as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 337, + 396, + 545, + 420 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 396, + 545, + 420 + ], + "spans": [ + { + "bbox": [ + 337, + 396, + 545, + 420 + ], + "type": "interline_equation", + "content": "\\left\\{\\left(u _ {i}, v _ {i}\\right) \\right\\} ^ {N} = \\left\\{\\left(f \\frac {\\mathbf {P} _ {x _ {i}}}{\\mathbf {P} _ {z _ {i}}}, f \\frac {\\mathbf {P} _ {y _ {i}}}{\\mathbf {P} _ {z _ {i}}}\\right) \\right\\} ^ {N} \\in \\mathbb {R} ^ {N \\times 2}. \\tag {1}", + "image_path": "b99e990ae9c0b9a98a5c1771dc12fe58d0bd3db9fffccb1a6fa45a4f3a586d55.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 425, + 517, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 425, + 517, + 437 + ], + "spans": [ + { + "bbox": [ + 317, + 425, + 517, + 437 + ], + "type": "text", + "content": "Thus, the projected image and event features are:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 310, + 443, + 545, + 459 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 443, + 545, + 459 + ], + "spans": [ + { + "bbox": [ + 310, + 443, + 545, + 459 + ], + "type": "interline_equation", + "content": "e _ {r} ^ {p j} = \\left\\{e _ {r} (u _ {i}, v _ {i}) \\right\\} ^ {N}, e _ {e v} ^ {p j} = \\left\\{e _ {e v} (u _ {i}, v _ {i}) \\right\\} ^ {N} \\in \\mathbb {R} ^ {N \\times C _ {2 D}}, (2)", + "image_path": "a7e12352038cbc792eb9bd4a5f3be1bf6581d1cfbd78592be2b9900ff1d97bc7.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 464, + 545, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 464, + 545, + 489 + ], + "spans": [ + { + "bbox": [ + 305, + 464, + 545, + 489 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 464, + 545, + 489 + ], + "type": "inline_equation", + "content": "e_r(u_i, v_i)" + }, + { + "bbox": [ + 305, + 464, + 545, + 489 + ], + "type": "text", + "content": " represents the feature obtained by bilinear interpolation sampling at " + }, + { + "bbox": [ + 305, + 464, + 545, + 489 + ], + "type": "inline_equation", + "content": "(u_i, v_i)" + }, + { + "bbox": [ + 305, + 464, + 545, + 489 + ], + "type": "text", + "content": " position in image plane." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "spans": [ + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "text", + "content": "After projection, we feed the features of auxiliary modalities " + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "inline_equation", + "content": "e_r^{pj}" + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "inline_equation", + "content": "e_{ev}^{pj}" + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "text", + "content": " with the primary modality feature " + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "inline_equation", + "content": "X_{pri}^{3D} = e_{pc}" + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "text", + "content": " into the attention fusion module. In the original self-attention mechanism [50, 51], all of the keys " + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "text", + "content": ", values " + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "text", + "content": " and queries " + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "text", + "content": " come from the same modality. Here we adapt it to accommodate inputs from multiple modalities and propose our cross-attention fusion structure. Specifically, we first combine the auxiliary features and align the number of channels with the master feature by " + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "text", + "content": " convolution, yielding the aligned auxiliary feature " + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "inline_equation", + "content": "Y_{aux}^{3D} = W_a \\left[ e_r^{pj}, e_{ev}^{pj} \\right] (\\mathbb{R}^N \\times C_{3D} \\Leftarrow \\mathbb{R}^N \\times (C_{2D} + C_{2D}))" + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "inline_equation", + "content": "[\\cdot, \\cdot]" + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "text", + "content": " is the concatenation operation. With layer normalization [55] (LN), we apply " + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "text", + "content": " depth-wise convolution to encode spatial and channel information with queries " + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "inline_equation", + "content": "Q_{pri}^{3D} = W_d^Q \\mathrm{LN}(X_{pri}^{3D})" + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "text", + "content": ", keys " + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "inline_equation", + "content": "K_{aux}^{3D} = W_d^K \\mathrm{LN}(Y_{aux}^{3D})" + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "text", + "content": " and values " + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "inline_equation", + "content": "V_{aux}^{3D} = W_d^V \\mathrm{LN}(Y_{aux}^{3D})" + }, + { + "bbox": [ + 304, + 490, + 545, + 683 + ], + "type": "text", + "content": ", respectively, obtaining the cross-modal self-attention as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 689, + 545, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 689, + 545, + 717 + ], + "spans": [ + { + "bbox": [ + 315, + 689, + 545, + 717 + ], + "type": "interline_equation", + "content": "\\operatorname {A t t e n t i o n} (Q, K, V) = V \\operatorname {S o f t m a x} \\left(\\frac {Q ^ {T} K}{\\tau}\\right), \\tag {3}", + "image_path": "6ece4334a62efd27a21af0fb36b302a75fc4f20a60c10acd50c8ce5fbdd4ac0e.jpg" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10032" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 71, + 274, + 236 + ], + "blocks": [ + { + "bbox": [ + 60, + 71, + 274, + 236 + ], + "lines": [ + { + "bbox": [ + 60, + 71, + 274, + 236 + ], + "spans": [ + { + "bbox": [ + 60, + 71, + 274, + 236 + ], + "type": "image", + "image_path": "95b692fa3cc413c5628c2ba7471a90769d59dc7b2d65f9f719caf21fa4b40e6a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 49, + 240, + 286, + 392 + ], + "blocks": [ + { + "bbox": [ + 49, + 240, + 286, + 392 + ], + "lines": [ + { + "bbox": [ + 49, + 240, + 286, + 392 + ], + "spans": [ + { + "bbox": [ + 49, + 240, + 286, + 392 + ], + "type": "image", + "image_path": "f583210d2a194248f00c58dc935825a93fedd91a42d52950f1594c326131bdef.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 396, + 288, + 456 + ], + "lines": [ + { + "bbox": [ + 46, + 396, + 288, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 288, + 456 + ], + "type": "text", + "content": "Figure 2: Our proposed Multimodal Attention Fusion Module fuses both three modal features in 2D (top) and 3D (bottom) branches, including feature projection and cross-attention fusion. In particular, only image and point features are fused in Feature Stage (FS)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "text", + "content": " is a learnable scaling factor. We input " + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "inline_equation", + "content": "Q_{pri}^{3D}" + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "inline_equation", + "content": "K_{aux}^{3D}" + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "inline_equation", + "content": "V_{aux}^{3D}" + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "text", + "content": " to the above attention module, and the resultant attention map with dimension " + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{C_{3D} \\times C_{3D}}" + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "text", + "content": " is much smaller and more efficient than the original implementation [51] with dimension " + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{HW \\times HW}" + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "text", + "content": " adopted from [56]. With the cross-modal attention in Eq. 3, we obtain the fused feature " + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "inline_equation", + "content": "X_{pri}^{3D'}" + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "text", + "content": " corresponding to the primary modality " + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "inline_equation", + "content": "e_{pc}" + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "text", + "content": " by another " + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 474, + 287, + 573 + ], + "type": "text", + "content": " convolution projection and residual connection as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 578, + 287, + 596 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 578, + 287, + 596 + ], + "spans": [ + { + "bbox": [ + 53, + 578, + 287, + 596 + ], + "type": "interline_equation", + "content": "X _ {p r i} ^ {3 D ^ {\\prime}} = W _ {p} \\mathbf {A t t e n t i o n} (Q _ {p r i} ^ {3 D}, K _ {a u x} ^ {3 D}, V _ {a u x} ^ {3 D}) + X _ {p r i} ^ {3 D}. \\qquad (4)", + "image_path": "948102facb6a8b8bee1f75de19f99ecf28a08fd97777e0f116705dd1c893536d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 600, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 600, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 600, + 287, + 715 + ], + "type": "text", + "content": "Multimodal Attention Fusion in 2D branch (MAF RPE-2D). The fusion process in 2D is similar to the 3D branch above. To project the sparse point feature into a dense feature at the image plane, we adopt a learnable fusion-aware interpolation [13] and get the projected point feature " + }, + { + "bbox": [ + 46, + 600, + 287, + 715 + ], + "type": "inline_equation", + "content": "e_{pc}^{pj} \\in \\mathbb{R}^{H \\times W \\times C_{3D}}" + }, + { + "bbox": [ + 46, + 600, + 287, + 715 + ], + "type": "text", + "content": ". Then we regard the image feature as the primary modality feature " + }, + { + "bbox": [ + 46, + 600, + 287, + 715 + ], + "type": "inline_equation", + "content": "X_{pri}^{2D} = e_r" + }, + { + "bbox": [ + 46, + 600, + 287, + 715 + ], + "type": "text", + "content": ", then the aligned auxiliary feature " + }, + { + "bbox": [ + 46, + 600, + 287, + 715 + ], + "type": "inline_equation", + "content": "Y_{aux}^{2D} = W_a^{2D}\\left[e_{pc}^{pj}, e_{ev}\\right]" + }, + { + "bbox": [ + 46, + 600, + 287, + 715 + ], + "type": "text", + "content": ". After similar cross-attention, the fused feature " + }, + { + "bbox": [ + 46, + 600, + 287, + 715 + ], + "type": "inline_equation", + "content": "X_{pri}^{2D'}" + }, + { + "bbox": [ + 46, + 600, + 287, + 715 + ], + "type": "text", + "content": " is obtained as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 312, + 93, + 545, + 110 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 93, + 545, + 110 + ], + "spans": [ + { + "bbox": [ + 312, + 93, + 545, + 110 + ], + "type": "interline_equation", + "content": "X _ {p r i} ^ {2 D ^ {\\prime}} = W _ {p} \\mathbf {A t t e n t i o n} \\left(Q _ {p r i} ^ {2 D} K _ {a u x} ^ {2 D}, V _ {a u x} ^ {2 D}\\right) + X _ {p r i} ^ {2 D}. \\tag {5}", + "image_path": "304072c1a1a5e131ca022e480c7ab408b7ddc3f25fd7ad5ae87cc61960ab21d1.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 119, + 527, + 132 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 119, + 527, + 132 + ], + "spans": [ + { + "bbox": [ + 306, + 119, + 527, + 132 + ], + "type": "text", + "content": "3.2. Mutual Information Regularization (MIR)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 138, + 545, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 138, + 545, + 222 + ], + "spans": [ + { + "bbox": [ + 304, + 138, + 545, + 222 + ], + "type": "text", + "content": "We incorporate mutual information minimization as a regularizer to explicitly model the cross-modal dependency following disentangled representation learning [27] based on the observation that each modality, i.e. RGB image, point cloud and event data, contributes partially to the output, and mutual information minimization is suitable for our task to explore the complementary information of each modality." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 223, + 545, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 223, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 304, + 223, + 545, + 270 + ], + "type": "text", + "content": "We start with the case of two modalities with RGB image and event feature embeddings " + }, + { + "bbox": [ + 304, + 223, + 545, + 270 + ], + "type": "inline_equation", + "content": "e_r" + }, + { + "bbox": [ + 304, + 223, + 545, + 270 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 223, + 545, + 270 + ], + "type": "inline_equation", + "content": "e_{ev}" + }, + { + "bbox": [ + 304, + 223, + 545, + 270 + ], + "type": "text", + "content": ". Note that these feature embeddings are the features that have been projected into the same spatial space (2D or 3D) in Sec. 3.1." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "spans": [ + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "text", + "content": "To explicitly model the cross-modal correlation, we define cross-modal mutual information between " + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "inline_equation", + "content": "e_r" + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "inline_equation", + "content": "e_{ev}" + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "inline_equation", + "content": "I(e_r;e_{ev}) = \\mathbb{E}_{p(e_r,e_{ev})}\\left[\\log \\frac{p(e_{ev}|e_r)}{p(e_{ev})}\\right]" + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "inline_equation", + "content": "p(e_r,e_{ev})" + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "text", + "content": " is the joint distribution, " + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "inline_equation", + "content": "p(e_{ev}|e_r)" + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "text", + "content": " is the conditional distribution and " + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "inline_equation", + "content": "p(e_{ev})" + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "text", + "content": " is the marginal distribution. With importance sampling [57], we introduce a variational marginal approximation " + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "inline_equation", + "content": "q(e_{ev})" + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "text", + "content": " with a variational upper bound " + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "inline_equation", + "content": "I^{vub}" + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "text", + "content": " [54] of mutual information " + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "inline_equation", + "content": "I(e_r;e_{ev})" + }, + { + "bbox": [ + 304, + 271, + 545, + 372 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 315, + 380, + 545, + 423 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 380, + 545, + 423 + ], + "spans": [ + { + "bbox": [ + 315, + 380, + 545, + 423 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} I \\left(e _ {r}; e _ {e v}\\right) \\leq \\mathbb {E} _ {p \\left(e _ {r}, e _ {e v}\\right)} \\left[ \\log \\frac {p \\left(e _ {e v} \\mid e _ {r}\\right)}{q \\left(e _ {e v}\\right)} \\right] \\tag {6} \\\\ = D _ {K L} \\left(p \\left(e _ {e v} \\mid e _ {r}\\right) \\| q \\left(e _ {e v}\\right)\\right) = I ^ {v u b} = \\mathcal {L} _ {\\mathrm {m i}}, \\\\ \\end{array}", + "image_path": "c801f9ef59913586469c80615c9463fc0fa307f1837f3850641a44d94daa8512.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "type": "inline_equation", + "content": "q(e_{ev})" + }, + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "type": "text", + "content": " can be fixed as a standard normal distribution [58], i.e. " + }, + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "type": "inline_equation", + "content": "q(e_{ev}) = \\mathcal{N}(e_{ev};0,\\mathbf{I})" + }, + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "type": "inline_equation", + "content": "p(e_{ev}|e_r)" + }, + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "type": "text", + "content": " can be modeled with the reparameterization trick [59], thus the Kullback-Leibler (KL) divergence term " + }, + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "type": "inline_equation", + "content": "D_{KL}" + }, + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "type": "text", + "content": " within " + }, + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "type": "inline_equation", + "content": "I^{vub}" + }, + { + "bbox": [ + 304, + 434, + 545, + 493 + ], + "type": "text", + "content": " can be solved in closed form." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 495, + 545, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 495, + 545, + 543 + ], + "spans": [ + { + "bbox": [ + 305, + 495, + 545, + 543 + ], + "type": "text", + "content": "In the case of three modalities feature embeddings " + }, + { + "bbox": [ + 305, + 495, + 545, + 543 + ], + "type": "inline_equation", + "content": "e_r" + }, + { + "bbox": [ + 305, + 495, + 545, + 543 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 495, + 545, + 543 + ], + "type": "inline_equation", + "content": "e_{pc}" + }, + { + "bbox": [ + 305, + 495, + 545, + 543 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 495, + 545, + 543 + ], + "type": "inline_equation", + "content": "e_{ev}" + }, + { + "bbox": [ + 305, + 495, + 545, + 543 + ], + "type": "text", + "content": ", respectively, the interaction information " + }, + { + "bbox": [ + 305, + 495, + 545, + 543 + ], + "type": "inline_equation", + "content": "II(e_r; e_{pc}; e_{ev})" + }, + { + "bbox": [ + 305, + 495, + 545, + 543 + ], + "type": "text", + "content": " [60], as a multivariate generalization of the mutual information, is upper bounded by:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 309, + 552, + 545, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 552, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 309, + 552, + 545, + 582 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} I I \\left(e _ {r}; e _ {p c}; e _ {e v}\\right) \\leq \\min \\left\\{I \\left(e _ {r}; e _ {p c}\\right), I \\left(e _ {p c}; e _ {e v}\\right), I \\left(e _ {r}; e _ {e v}\\right) \\right\\} \\tag {7} \\\\ \\leq \\min \\left\\{I ^ {v u b} \\left(e _ {r}; e _ {p c}\\right), I ^ {v u b} \\left(e _ {p c}; e _ {e v}\\right), I ^ {v u b} \\left(e _ {r}; e _ {e v}\\right) \\right\\}. \\\\ \\end{array}", + "image_path": "07462bd3e590c1f37e95301d5a5b3441f2be677304acd18d3e4e1e937d07edd7.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "To compute " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "I^{vub}" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ", we need to design a transition function, achieving the transformation of one modality to the other and assume the variational marginal approximation " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " as the standard normal distribution for closed-form KL divergence computation. In practice, the standard normal distribution assumption of " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " leads to high-bias mutual information estimation. Alternatively, we first map the representation of each modality " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "(e_r, e_{pc}, e_{ev})" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " to a common manifold, with reparameterization trick [59] in the end to achieve Gaussian latent code of each modality. Then, we compute KL" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10033" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "divergence between the two Gaussian latent codes, leading to the final mutual information regularization term:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 53, + 111, + 287, + 126 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 111, + 287, + 126 + ], + "spans": [ + { + "bbox": [ + 53, + 111, + 287, + 126 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {i i}} = I ^ {v u b} \\left(e _ {r}; e _ {p c}\\right) + I ^ {v u b} \\left(e _ {p c}; e _ {e v}\\right) + I ^ {v u b} \\left(e _ {r}; e _ {e v}\\right), (8)", + "image_path": "bb155969efe9dde8f7db4d9db7ea5ad4cfdfabab3d6755a4e7a2c9deb40236f8.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 142, + 287, + 166 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 142, + 287, + 166 + ], + "spans": [ + { + "bbox": [ + 47, + 142, + 287, + 166 + ], + "type": "text", + "content": "where we compute the sum of " + }, + { + "bbox": [ + 47, + 142, + 287, + 166 + ], + "type": "inline_equation", + "content": "I^{vub}" + }, + { + "bbox": [ + 47, + 142, + 287, + 166 + ], + "type": "text", + "content": " instead of choosing the minimum for stable training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 182, + 279, + 196 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 182, + 279, + 196 + ], + "spans": [ + { + "bbox": [ + 47, + 182, + 279, + 196 + ], + "type": "text", + "content": "3.3. Pyramid Fusion and Joint Estimation Model" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 205, + 287, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 205, + 287, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 287, + 324 + ], + "type": "text", + "content": "With the proposed multimodal attention fusion and the mutual information regularization term, we achieve once multimodal feature fusion. Inspired by CamLiFlow [13], we further perform multi-stage feature fusion implicitly and explicitly. Here we present the details of multi-stage feature fusion, and more details about the network structure are given in the supplementary materials. As shown in Fig. 1, our model contains both 2D and 3D branches, where each branch consists of feature extraction, correlation construction and flow estimation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 327, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 287, + 495 + ], + "type": "text", + "content": "In feature extraction, we first voxelized the raw events " + }, + { + "bbox": [ + 46, + 327, + 287, + 495 + ], + "type": "inline_equation", + "content": "E = \\{x_{i},y_{i},t_{i},p_{i}\\}^{K}" + }, + { + "bbox": [ + 46, + 327, + 287, + 495 + ], + "type": "text", + "content": " into one event voxel " + }, + { + "bbox": [ + 46, + 327, + 287, + 495 + ], + "type": "inline_equation", + "content": "EV\\in \\mathbb{R}^{H\\times W\\times B}" + }, + { + "bbox": [ + 46, + 327, + 287, + 495 + ], + "type": "text", + "content": " that can be used as input to our network, where " + }, + { + "bbox": [ + 46, + 327, + 287, + 495 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 327, + 287, + 495 + ], + "type": "text", + "content": " is the number of events during the period between two frames and " + }, + { + "bbox": [ + 46, + 327, + 287, + 495 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 327, + 287, + 495 + ], + "type": "text", + "content": " is the manually set number of time intervals to sample events. We apply three Siamese encoders to construct feature pyramids " + }, + { + "bbox": [ + 46, + 327, + 287, + 495 + ], + "type": "inline_equation", + "content": "(\\{e_{r_1},e_{r_2}\\} _l,\\{e_{pc_1},e_{pc_2}\\} _l" + }, + { + "bbox": [ + 46, + 327, + 287, + 495 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 327, + 287, + 495 + ], + "type": "inline_equation", + "content": "e_{ev_l}" + }, + { + "bbox": [ + 46, + 327, + 287, + 495 + ], + "type": "text", + "content": " with pyramid layers " + }, + { + "bbox": [ + 46, + 327, + 287, + 495 + ], + "type": "inline_equation", + "content": "l\\in [1,L])" + }, + { + "bbox": [ + 46, + 327, + 287, + 495 + ], + "type": "text", + "content": " for three modalities respectively. As spans between two frames, the event data is not included in Feature Stage Fusion, which is applied to fuse the features of two frames RGB images and corresponding point clouds with two-modal attention fusion, i.e. simplify the auxiliary feature to a single modality in Eq. 4, 5 and mutual information regularization in Eq. 6 for both 2D and 3D branches." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 498, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 714 + ], + "type": "text", + "content": "In correlation construction, we first warp the second frame of image and point cloud features using the coarse optical flow and scene flow (initialize with zero) from the previous pyramid layer, then construct correlation motion features by computing 2D and 3D cost volumes and fused them with the event feature at Motion Stage Fusion. In flow estimation, we construct a motion decoder and flow estimator, and perform an Estimation Stage Fusion between them to fuse the hidden motion features from the two branches decoder with the event feature. In these two fusion stages, we conduct multimodal attention fusion in Eq. 4, 5 and mutual information regularization in Eq. 8 for 2D and 3D motion features and event feature, because events can provide complementary information to enhance the motion correlation construction. The estimated optical flow and scene flow are fed into the next pyramid layer to achieve coarse-to-fine predictions. We take the optical flow and scene flow from the last pyramid layer as our final joint estimations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 423, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 423, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 423, + 85 + ], + "type": "text", + "content": "3.4. 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" + }, + { + "bbox": [ + 304, + 91, + 545, + 223 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mi}}^{fs1}" + }, + { + "bbox": [ + 304, + 91, + 545, + 223 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 91, + 545, + 223 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mi}}^{fs2}" + }, + { + "bbox": [ + 304, + 91, + 545, + 223 + ], + "type": "text", + "content": " represent the mutual information minimization loss imposed on the RGB image and point cloud features of the first and the second frame at the Feature Stage fusion, and " + }, + { + "bbox": [ + 304, + 91, + 545, + 223 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ii}}^{ms}" + }, + { + "bbox": [ + 304, + 91, + 545, + 223 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 91, + 545, + 223 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ii}}^{es}" + }, + { + "bbox": [ + 304, + 91, + 545, + 223 + ], + "type": "text", + "content": " represent on both RGB image, point cloud and event features at the Motion Stage and Estimation Stage fusion. 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Experiment" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 563, + 438, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 438, + 575 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 438, + 575 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Datasets. Since there is no large-scale scene flow dataset with real event data, we use synthetic data for pretraining. Follow the preprocess pipeline [13, 62], we generate point clouds from depth images for FlyingThings3D [28] dataset, which contains 19,640 and 3,824 RGB-PointColud pairs for \"train\" and \"val\" splits. 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For the bottom 3D comparisons, blue indicates a lower error, red indicates a higher error, and green indicates the median. Best to zoom in on the screen for detailed comparisons." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 155, + 211, + 246, + 347 + ], + "blocks": [ + { + "bbox": [ + 155, + 211, + 246, + 347 + ], + "lines": [ + { + "bbox": [ + 155, + 211, + 246, + 347 + ], + "spans": [ + { + "bbox": [ + 155, + 211, + 246, + 347 + ], + "type": "image", + "image_path": "c45a81f6e6fbdd687c659d595151234811beb8d73f54b84a6539f7f8156bd26c.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 251, + 211, + 342, + 347 + ], + "blocks": [ + { + "bbox": [ + 251, + 211, + 342, + 347 + ], + "lines": [ + { + "bbox": [ + 251, + 211, + 342, + 347 + ], + "spans": [ + { + "bbox": [ + 251, + 211, + 342, + 347 + ], + "type": "image", + "image_path": "6b9d875b28fa6c96052c5310d5bf3fe23c86fac9f0f088b80b7fd7a620a651d8.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 347, + 211, + 439, + 346 + ], + "blocks": [ + { + "bbox": [ + 347, + 211, + 439, + 346 + ], + "lines": [ + { + "bbox": [ + 347, + 211, + 439, + 346 + ], + "spans": [ + { + "bbox": [ + 347, + 211, + 439, + 346 + ], + "type": "image", + "image_path": "726718d4579b85a2bf57d0dcd59073e495375b21e4d7d228bac33b639e4c3947.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 443, + 211, + 565, + 347 + ], + "blocks": [ + { + "bbox": [ + 443, + 211, + 565, + 347 + ], + "lines": [ + { + "bbox": [ + 443, + 211, + 565, + 347 + ], + "spans": [ + { + "bbox": [ + 443, + 211, + 565, + 347 + ], + "type": "image", + "image_path": "aa1f90830d0616e47029b4517645fbbeb9fe8b464401e64d7ddfe91079d1cd79.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 58, + 425, + 535, + 569 + ], + "blocks": [ + { + "bbox": [ + 116, + 403, + 474, + 416 + ], + "lines": [ + { + "bbox": [ + 116, + 403, + 474, + 416 + ], + "spans": [ + { + "bbox": [ + 116, + 403, + 474, + 416 + ], + "type": "text", + "content": "Table 1: Performance comparison on the \"val\" split of the FlyingThings3D [28] subset." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 425, + 535, + 569 + ], + "lines": [ + { + "bbox": [ + 58, + 425, + 535, + 569 + ], + "spans": [ + { + "bbox": [ + 58, + 425, + 535, + 569 + ], + "type": "table", + "html": "
InputMethodEPE2DACC1pxEPEN.Occ3DACCN.Occ05EPEFull3DACCFull05
RGBRAFT [2]3.1281.1%----
FlowFormer [3]3.0282.6%----
PCMeteornet* [61]----0.209-
PointPWC [8]--0.11251.8%--
SCTN [9]--0.03884.7%--
RGB+DepthRAFT-3D [10]2.3787.1%0.06284.5%0.08971.1%
RGB+PCDeepLiDARFlow [12]6.0447.1%-27.2%--
CamLiFlow [13]2.2084.6%0.03391.7%0.05986.0%
RGB+EventRAFT+Event2.4984.6%----
RGB+PC+EventCamLiFlow+Event1.5684.4%0.02891.7%0.04885.9%
RPEFlow (Ours)1.4086.2%0.02493.1%0.04288.0%
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Our model is trained with PyTorch on four RTX3090 GPUs and evaluated on one. We use the Adam optimizer with weight decay " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "10^{-6}" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": ". The number of event bins is " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "B = 10" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": ", pyramid layers is " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "L = 5" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": ". Loss weights are " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\alpha = 10.0" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\beta = 0.01" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_l = 2^{(l - 2)}" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "l \\in [1, L]" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": ". Following [10, 13], we evalu" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 588, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 588, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 588, + 545, + 673 + ], + "type": "text", + "content": "ate using 2D and 3D end-point error (EPE" + }, + { + "bbox": [ + 304, + 588, + 545, + 673 + ], + "type": "inline_equation", + "content": "_{2\\mathrm{D}}" + }, + { + "bbox": [ + 304, + 588, + 545, + 673 + ], + "type": "text", + "content": " and EPE" + }, + { + "bbox": [ + 304, + 588, + 545, + 673 + ], + "type": "inline_equation", + "content": "_{3\\mathrm{D}}" + }, + { + "bbox": [ + 304, + 588, + 545, + 673 + ], + "type": "text", + "content": "), and " + }, + { + "bbox": [ + 304, + 588, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathrm{ACC}_{1\\mathrm{px}}" + }, + { + "bbox": [ + 304, + 588, + 545, + 673 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 588, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathrm{ACC}_{.05}" + }, + { + "bbox": [ + 304, + 588, + 545, + 673 + ], + "type": "text", + "content": " to measure the portion of accuracy within 1 pixel and " + }, + { + "bbox": [ + 304, + 588, + 545, + 673 + ], + "type": "inline_equation", + "content": "5\\mathrm{cm}" + }, + { + "bbox": [ + 304, + 588, + 545, + 673 + ], + "type": "text", + "content": ". The scene flow metrics with N.Occ superscript indicates only the not occluded positions are calculated, while Full or none indicates all positions including occlusion. More details about datasets and training are provided in the supplementary materials." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10035" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 63, + 92, + 526, + 196 + ], + "blocks": [ + { + "bbox": [ + 100, + 71, + 492, + 83 + ], + "lines": [ + { + "bbox": [ + 100, + 71, + 492, + 83 + ], + "spans": [ + { + "bbox": [ + 100, + 71, + 492, + 83 + ], + "type": "text", + "content": "Table 2: Finetuned performance comparison on the test split of our simulated EKubric dataset." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 63, + 92, + 526, + 196 + ], + "lines": [ + { + "bbox": [ + 63, + 92, + 526, + 196 + ], + "spans": [ + { + "bbox": [ + 63, + 92, + 526, + 196 + ], + "type": "table", + "html": "
InputMethodEPE2DACC1pxEPEN.Occ3DACCN.Occ05EPEFull3DACCFull05
RGBRAFT [2]0.75793.70%----
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RGB+DepthRAFT-3D [10]0.71594.33%0.01695.20%0.04992.62%
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RGB+EventRAFT+Event0.48795.25%----
RGB+PC+EventCamLiFlow+Event0.50595.41%0.00898.48%0.03195.01%
RPEFlow (Ours)0.44296.08%0.00798.68%0.02795.30%
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Comparisons with Synthetic Events" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 470, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 470, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 470, + 287, + 625 + ], + "type": "text", + "content": "Following the conventional setting, our model is first pre-trained on FlyingThings3D [28], and Table 1 shows the quantitative comparison performance on the \"val\" split. Both results are evaluated using their pre-trained model on FlyingThings3D. Meteornet* [61] has not released model for scene flow estimation, so we compare the EPE3D result from its paper. We also finetune them on our simulated EKubric dataset, and the performance comparisons on the test set are shown in Table 2, where the compared models were all pre-trained on FlyingThings3D and then finetuned on EKubric with the same training settings. Note that we did not evaluate the PC-only methods on our EKubric dataset due to their different data preprocessing strategies." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "We report the results of two representative methods [2, 8] and two latest methods [3, 9] using only one modal for one task, and find that combining multiple modalities can significantly improve model accuracy for both optical flow and scene flow estimation. Furthermore, the methods that combine all three modalities, i.e. RGB+PC+Event, achieve better results than the rest [10, 12, 13], which illustrates the sig-" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 447, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 545, + 567 + ], + "type": "text", + "content": "nificant benefit of introducing event data for accurate motion estimation. With the same input setting, we compare our model with CamLiFlow+Event and observe improved accuracy, which is because our proposed multimodal attention fusion module is able to fully mine valuable information from continuous event data for accurate motion estimation. The comparison of visualization results in Fig. 3 and in the supplementary materials is also consistent with the above observations, especially in high dynamic and detail moving or motion-blurred areas." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 575, + 473, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 473, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 473, + 588 + ], + "type": "text", + "content": "4.3. Comparisons with Real Events" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": "We further conduct experiments on the real-captured DSEC [22] dataset. We divide the public set into \"train\" and \"val\" splits for finetuning and evaluation. Since the dense depth required by RAFT-3D [10] is not available, we use CFNet [65] to obtain a pseudo-dense depth map by stereo matching as input. E-RAFT* [22] does not have a publicly available training code, thus we can only use the pretrained model on the entire DSEC dataset including the \"val\" split (marked with *). Both quantitative and qualitative (Table 3 and Fig. 4) comparisons demonstrate the superiority of our" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10036" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 103, + 279, + 203 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 95 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 95 + ], + "type": "text", + "content": "Table 3: Finetuned Performance comparison on the \"val\" split of DSEC [22] dataset." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 103, + 279, + 203 + ], + "lines": [ + { + "bbox": [ + 53, + 103, + 279, + 203 + ], + "spans": [ + { + "bbox": [ + 53, + 103, + 279, + 203 + ], + "type": "table", + "html": "
MethodEPE2DACC1pxEPEFull3DACCFull.05
RAFT [2]0.57289.63%--
E-RAFT* [22]0.47392.11%--
RAFT-3D [10]0.56790.55%0.14051.30%
CamLiFlow [13]0.38394.92%0.12053.49%
RAFT+Event0.53790.08%--
CamLiFlow+Event0.36195.07%0.11655.26%
RPEFlow (Ours)0.33295.27%0.10460.50%
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EventFusionMI EPE2DACC1pxEPEFull3DACCFull05
(a)-Concat-2.20084.62%0.059
(b)-Attention-2.13384.74%0.058
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", + "image_path": "3a303e504bb1429b6c3f495bd336e384d48f16b4af37a9eee3f5d4c737608209.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 365, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 449 + ], + "type": "text", + "content": "model for real-captured data, which is consistent with the observations on synthetic datasets above. In particular, our method performs better in night driving (the 2nd sample in Fig. 4), because the event camera is still sensitive to brightness changes even in low-light scenes. These comparisons further illustrate the importance of introducing events and the applicability of our model to practical needs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 456, + 148, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 148, + 467 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 148, + 467 + ], + "type": "text", + "content": "4.4. Ablation Studies" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 474, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 557 + ], + "type": "text", + "content": "In Table 4, We conduct ablation experiments to verify the contribution of each component in our model. All variations are trained on the \"training\" split and evaluated on the \"val\" split of FlyingThings3D [28] dataset. In addition to the following discussion, in the supplementary materials we analyze the impact of real and simulated events and the role of combining the two tasks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": "Event data. As we are the first to introduce the event data for joint optical flow and scene flow estimation, we explore the effectiveness of event data in two aspects. Firstly, we remove the event data in our framework (see Table 4 (a)-(d) and (c)-(g)), leading to significant performance degradation, especially in optical flow error. This is in line with our claim that event data with continuous observations of scene brightness changes can provide significant help for accurate motion estimation. Secondly, in order to validate the benefit of introducing events to other methods, we concatenate the extracted event feature as an additional input of flow decoder for RAFT [2] and CamLiFlow [13], denoted as RAFT+Event and CamLiFlow+Event, respectively. Re-" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 310, + 70, + 542, + 121 + ], + "blocks": [ + { + "bbox": [ + 310, + 70, + 542, + 121 + ], + "lines": [ + { + "bbox": [ + 310, + 70, + 542, + 121 + ], + "spans": [ + { + "bbox": [ + 310, + 70, + 542, + 121 + ], + "type": "table", + "html": "
SettingEPE2DACC1pxEPE3DN.OccACC05N.OccEPEFull3DACC05
2D only1.93783.17%------
3D only--0.04386.37%0.07879.05%
2D&3D1.40286.22%0.02493.14%0.04288.01%
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These models both use three modalities and the results validate that combining the two tasks makes better use of motion information." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "text", + "content": "sults in Table 1, 2 and 3 show that introducing event data to existing models can also significantly improve the performance, rather than just on our proposed framework." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 220, + 546, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 220, + 546, + 339 + ], + "spans": [ + { + "bbox": [ + 304, + 220, + 546, + 339 + ], + "type": "text", + "content": "Fusion Structure. Unlike CamLiFlow [13] that concat the features from two modalities, we propose an attention-based multimodal fusion module. We conduct experiments with both no-event and with event settings (see Table 4 (a)-(b) and (d)(e)-(f)), and our proposed attention fusion improves both 2D and 3D motion estimation performance. This shows that our multimodal attention fusion module can effectively explore the complementary information and correlations among the three modalities and generate fused features that are suitable for subsequent motion estimation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 340, + 547, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 340, + 547, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 340, + 547, + 495 + ], + "type": "text", + "content": "Mutual Information. The purpose of the mutual information regularization term is to explicitly constrain the network to learn complementary information from different modalities of data. To verify its contribution to motion estimation, we conduct experiments with both no-event and with event settings (see Table 4 (b)-(c) and (f)-(g)). The results show that with this explicit constraint, the fused features can further improve the accuracy of motion estimation. In addition, we believe that the multimodal attention fusion module and mutual information regularization term both play an important role in motion estimation, because their contribution to 2D and 3D motion estimation is significant in both the with-event and without-event settings." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 502, + 416, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 502, + 416, + 515 + ], + "spans": [ + { + "bbox": [ + 305, + 502, + 416, + 515 + ], + "type": "text", + "content": "4.5. Computation Cost" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "text", + "content": "Our model is relatively efficient compared to the latest unimodal and multimodal methods in model size and runtime, i.e., FlowFormer [3]: 17.6M, 1.35s, SCTN [9]: 7.8M, 242ms, RAFT-3D [10]: 45M, 593ms, CamLiFlow [13]: 7.7M, 88ms (" + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "inline_equation", + "content": "\\approx" + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "text", + "content": "2s with refine) and Ours: 9.75M, 112ms (both on a single RTX3090 GPU with " + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "inline_equation", + "content": "1280 \\times 720" + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "text", + "content": " size)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 599, + 459, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 599, + 459, + 611 + ], + "spans": [ + { + "bbox": [ + 305, + 599, + 459, + 611 + ], + "type": "text", + "content": "4.6. Joint 2D and 3D estimation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "In previous comparisons, the methods of joint optical flow and scene flow estimation perform significantly better than independent methods. To further verify the necessity of jointing these two tasks, we compare the models that only supervise the optical flow or scene flow estimation in Table 5. Although using all three modalities for a single task (2D only and 3D only) is more beneficial than the methods using fewer modality data in Table 1 of main paper." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10037" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "content": "However, combining the two tasks in 2D and 3D benefits from the tight correlation between the two deeply supervised branches, allowing more adequate exploiting of the correlation between 2D and 3D input modalities and more accurate estimating of 2D and 3D motion jointly." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 145, + 119, + 158 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 145, + 119, + 158 + ], + "spans": [ + { + "bbox": [ + 47, + 145, + 119, + 158 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 166, + 289, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 166, + 289, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 166, + 289, + 309 + ], + "type": "text", + "content": "We introduce a multimodal fusion framework for joint 2D optical flow and 3D scene flow estimation by fusing RGB images, point clouds and event data. Our contributions are threefold: 1) By incorporating event data, our new framework could handle highly dynamic scenes. 2) We fuse representations of the three very different modalities both implicitly and explicitly through multimodal attention and mutual information regularization, respectively. 3) We contribute a new simulation dataset to further advocate research in this direction. Our work shows that event cameras can play an important role in 2D and 3D motion estimation, and reveals the prospect of event-based 3D vision." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 310, + 288, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 310, + 288, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 288, + 346 + ], + "type": "text", + "content": "Limitation. Our model is not specially designed for extreme situations such as dark nights or sensor failures, and we plan to address them in the future." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 360, + 157, + 373 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 360, + 157, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 360, + 157, + 373 + ], + "type": "text", + "content": "6. Acknowledgments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 380, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 477 + ], + "type": "text", + "content": "This research was supported in part by National Natural Science Foundation of China (62271410), the Fundamental Research Funds for the Central Universities, and Zhejiang Lab (NO.2021MC0AB05). Zhexiong Wan is sponsored by the scholarship from China Scholarship Council (202306290193) and the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (CX2023013)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 48, + 489, + 107, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 489, + 107, + 502 + ], + "spans": [ + { + "bbox": [ + 48, + 489, + 107, + 502 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 53, + 510, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 53, + 510, + 287, + 554 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 510, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 53, + 510, + 287, + 554 + ], + "type": "text", + "content": "[1] Deqing Sun, Xiaodong Yang, Ming-Yu Liu, and Jan Kautz. Pwc-net: Cnns for optical flow using pyramid, warping, and cost volume. 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450, + 535, + 467 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "jiawei@hfut.edu.cn", + "bbox": [ + 403, + 472, + 565, + 484 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 521, + 312, + 536 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Palmprint recently shows great potential in recognition applications as it is a privacy-friendly and stable biometric. However, the lack of large-scale public palmprint datasets limits further research and development of palmprint recognition. In this paper, we propose a novel realistic pseudo-palmprint generation (RPG) model to synthesize palmprints with massive identities. We first introduce a conditional modulation generator to improve the intraclass diversity. Then an identity-aware loss is proposed to ensure identity consistency against unpaired training. We further improve the Bézier palm creases generation strategy to guarantee identity independence. Extensive experimental results demonstrate that synthetic pretraining significantly boosts the recognition model performance. For example, our model improves the state-of-the-art Bézier Palm by more than $5\\%$ and $14\\%$ in terms of TAR@FAR=1e-6 under the 1:1 and 1:3 Open-set protocol. When accessing only $10\\%$ of the real training data, our method still outperforms ArcFace with $100\\%$ real training data, indicating that we are closer to real-data-free palmprint recognition.", + "bbox": [ + 75, + 542, + 472, + 845 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 520, + 630, + 536 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Palmprint is an excellent biometric in terms of privacy, willingness, convenience, and security. Since the palmprint locates on the inner side of the palm, obtaining the palmprint without one's permission is nearly impossible, which is more privacy-friendliness over the face. Compared to iris and fingerprints, palmprint has fewer usage restrictions, which makes palmprint more user-friendly. Furthermore, Palmprints and palm veins can be collected simultaneously to form a highly secure dual-modal system.", + "bbox": [ + 496, + 547, + 890, + 684 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Due to these advantages, big companies such as Amazon [1] and Tencent [69] begin to apply palmprint recognition in their payment services. However, for the same reason, palmprints are rare in public and expensive to collect. To our best knowledge, publicly available datasets [2, 21, 29, 30, 36, 41, 52, 57, 68] only contain thousands of identities and tens of thousands of images in total. Meanwhile, face recognition has several million-level publicly available datasets [4, 9, 27, 38, 44, 62] that contain tens to hundreds of thousands of identities. The lack of large-scale public dataset seriously inhibits the research on palmprint recognition.", + "bbox": [ + 496, + 686, + 890, + 866 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To solve this problem, one way is to collect a large-scale palmprint dataset. However, this way is very time-", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 805, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution.", + "bbox": [ + 94, + 875, + 205, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding authors.", + "bbox": [ + 96, + 887, + 225, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19605", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e7c68c9c6f70d258629d13f6986ba984a0f7b6d9e69a90dc8d0899e9ac595b98.jpg", + "image_caption": [ + "Figure 1: Synthetic Bezier palm creases are used as the identity control condition to guide the generator to produce diverse synthetic data. Recognition models are pretrained with pseudo-data and then finetuned on real data, achieving significant performance boosts. Besides, even if only accessing $10\\%$ of the real training data for generation and recognition model, our method still gets comparable performance to $100\\%$ of real data direct training." + ], + "image_footnote": [], + "bbox": [ + 98, + 88, + 439, + 361 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "consuming and expensive. In addition, collecting biometric data causes more and more privacy and ethical concerns [7] and is strictly restricted by legislation in many countries. Another way is to augment the training dataset with synthetic palmprints. To better benefit palmprint recognition applications, the synthetic method should support generating massive identities with inter-class and intra-class diversity, and the gap between synthetic palmprints and real palmprints should be small.", + "bbox": [ + 75, + 521, + 468, + 655 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, BézierPalm [69] synthesizes fake palmprint images by generating palmprint creases with several parameterized Bézier curves for recognition model pretraining. BézierPalm first shows the ability to output massive new identities without using real palmprints and significantly improves the performance of the palmprint recognition models. However, BézierPalm has some problems unsolved. Firstly, synthetic palmprints have a large gap to real ones, resulting in non-neglectable finetune data requirements in real-world applications. Secondly, the curve parameter difference of each identity cannot ensure inter-class independence when generating massive data. Thirdly, the intra-class diversity only contains small curve deformation in BézierPalm, while real palmprints have diverse textures, lighting and et al.", + "bbox": [ + 75, + 657, + 468, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a realistic pseudo-palmprint", + "bbox": [ + 96, + 885, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "generation (RPG) model. As shown in Fig.1, the RPG model takes synthetic Bezier palm creases as an identity (ID) condition and outputs realistic pseudo-palmprints with a bidirectional mapping from the Gaussian noise domain to the palmprints domain. Since there is no correspondence between synthetic Bezier palm creases and real palmprints, the generation model can only use unpaired data and will lose intra-class identity consistency easily during training. To solve this problem, we introduce an identity-aware loss that restrains the identity consistency between palmprints generated from the same Bezier palm creases. In addition, we design a conditional modulation generator to generate diversified intra-class textures and lighting conditions using a latent control vector encoded from random noises. To further reduce the distribution gap between synthetic palm creases and real-world palmprints, we refined the synthetic palmprint creases generation strategy with a more reasonable parameter design and identity independence check.", + "bbox": [ + 496, + 90, + 893, + 364 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions of this paper are as follows:", + "bbox": [ + 519, + 375, + 823, + 388 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a realistic pseudo-palmprint generation (RPG) model with a conditional modulation generator to improve the intra-class diversity and an ID-aware loss to help the RPG model ensure identity consistency under unpaired training.", + "- We improve the Bezier palm creases synthetic method to get more reasonable palm creases and independent identities.", + "- Extensive experimental results on 13 public datasets demonstrate that recognition models pretrained with our synthetic pseudo-palmprints achieve state-of-the-art recognition accuracy.", + "- With our RPG pretraining, even if accessing only $10\\%$ of the real data, the recognition model performance still outperforms $100\\%$ real data direct training. Showing we are closer to real-data-free palmprint recognition." + ], + "bbox": [ + 516, + 402, + 890, + 696 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 714, + 640, + 729 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Palmprint Recognition Methods", + "text_level": 1, + "bbox": [ + 500, + 739, + 782, + 757 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Palmprint recognition methods can be divided into two categories: traditional-based and deep-learning based [18]. Traditional methods extract various kinds of local or global features to make different palmprints more discriminative. Local-based methods [19, 28, 34, 40, 43, 57, 70] manually design effective local features for recognition. Global-based methods [3, 20, 32, 42, 51, 59] extract low-dimensional features from the whole image to distinguish different palmprints. Deep Learning based methods [16, 25, 35, 58] train", + "bbox": [ + 496, + 763, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19606", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "modified neural networks to extract features with classification or pair-wise loss [14, 55, 71]. However, the lack of large-scale public palmprint datasets limits the potential of existing palmprint recognition methods.", + "bbox": [ + 75, + 90, + 470, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Generation Model for Image Transformation", + "text_level": 1, + "bbox": [ + 76, + 186, + 457, + 204 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "With the development of image generation models, such as generative adversarial network (GAN)-based models [26, 37] and diffusion-based models [47, 48], image-to-image generation/translation methods have achieved impressive performance [11, 12, 33]. However, many typical models, e.g., conditional generation model pix2pixHD [61], multidomain transformation model StarGAN [12], dual-domain mapping model BicycleGAN [74] and recent conditional diffusion model [50, 60], rely on paired training data, which is unavailable in many applications. Therefore, some unpaired image-to-image translation models have been proposed [39, 54, 64, 72], which usually adopt cycle consistency loss to train the models without paired data. However, these models are not designed for recognition tasks, and thus ignore the ID preservation in the generation process. Overall, there is still a lack of research on generating diversified and realistic palmprints with ID consistency from limited unpaired samples.", + "bbox": [ + 75, + 219, + 468, + 492 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Data generation for Recognition Tasks", + "text_level": 1, + "bbox": [ + 76, + 527, + 408, + 544 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In order to improve the recognition performance, data generation can be used to expand the depth (diversity of each identity) and width (total number of identities) of training data. For example, in face recognition field, several facial image generation methods [15, 24, 45, 46, 65, 22, 23] have been proposed to generate facial samples based on the priors of facial attributes, facial structures and 3D faces [6]. Also, in field of fingerprint recognition, some methods based on hand-crafted or learning-based approaches [5, 17, 63] have been proposed to generate high-fidelity fingerprint images.", + "bbox": [ + 75, + 560, + 468, + 727 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For palm recognition tasks, BezierPalm [69] use Bezier curves to synthesize fake palm creases by changing the Bezier control parameters. PalmGAN [53] improves the cross-domain recognition performances by using CycleGAN to transfer the styles between normal and multispectral palmprints. However, PalmGAN doesn't create virtual identities, and the BezierPalm suffers from the domain gap between palmprint images and geometry curves. By introducing the new generation model and ID-aware loss, our method can expand the inter-class diversity and intra-class diversity of palmprint dataset simultaneously.", + "bbox": [ + 75, + 734, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 89, + 591, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overall Framework", + "text_level": 1, + "bbox": [ + 500, + 116, + 689, + 132 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fig.2 illustrates the whole framework of the proposed realistic pseudo-palmprint generation (RPG) model, which includes a training stage and a forward palmprint generation stage. In the training phase, palmprint $B$ is first mapped from the palmprint image domain to the latent vector $Q(z|B)$ in the Gaussian noise domain through the encoder $E$ . Then, the generator $G$ utilizes the unpaired palm creases $A$ as condition, and remaps the encoded noise vector $Q(z|B)$ back to the palmprint image domain. In order to increase the diversity and randomness of the generated palmprints, a conditional modulation structure is designed for $G$ , which uses the input noise vector to control the modulation of intermediate features.", + "bbox": [ + 496, + 141, + 890, + 335 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In order to constrain the ID consistency of the generated pseudo palmprints, an ID-aware loss is presented to enforce the generator to maintain the ID information of input palm creases. As shown in Fig.2 (a), a siamese generator $G$ is used to produce another palmprint $B''$ with the same palm creases $A$ . Then, a pretrained palmprint recognition discriminator is used to measure the ID consistency between $B'$ and $B''$ .", + "bbox": [ + 496, + 339, + 890, + 459 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the forward pseudo-palmprint generation stage, synthetic Bézier creases are input into the generator $G$ to obtain corresponding palmprint images for virtual identities. Motivated by BézierPalm [69], we improve the random Bézier curves generation strategy to obtain a more reasonable layout of principal lines and wrinkle lines. Then, a classic palmprint recognition method RLOC [34] is applied to ensure the inter-class difference.", + "bbox": [ + 496, + 463, + 890, + 582 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the following, we will introduce the details of generator $G$ , encoder $E$ , ID-aware loss, and the improved Bézier palm creases synthesis strategy.", + "bbox": [ + 496, + 585, + 890, + 632 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Conditional Modulation Palmprint Generator", + "text_level": 1, + "bbox": [ + 500, + 646, + 887, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The proposed generator $G$ takes Gaussian noise vector as input, palm creases image $A$ as condition, and reproduces the pseudo-palmprint image $B'$ . As a typical image generation task, the common UNet [49] architecture is adopted. The detailed structure of $G$ is illustrated in Fig.3 (a). To generate diversified results, a conditional adaptive instance normalization module (CAdaIN) is introduced to modulate the generated details in each down-block and up-block.", + "bbox": [ + 496, + 672, + 890, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the CAdaIN module, the input noise vector $N(z)$ is first encoded into a latent control vector $w(z)$ through two fully-connected (FC) layers. Note that the parameters of these two FC layers are shared for the whole generator $G$ , so that the generated style can be consistent by means of the same $w(z)$ . Then, two other FC layers are used to modulate the mean and variance of intermediate feature maps", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19607", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d6cd1dc5128a85b9460c8fe86a56f8d4d0125447034522d1b81d02acf68bacf6.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 98, + 87, + 624, + 339 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ec0965eb017ddcba28253a0c760e59ca1840a25ba66d1d8350b8040c1d8e16fa.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 627, + 89, + 861, + 335 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a28b25984f8d1eed882a312bd1bb34003e505013327317ad86e293c1316777c3.jpg", + "image_caption": [ + "Figure 2: Framework of the proposed realistic pseudo-palmprint generation model, (a) training stage, (b) forward pseudopalmprint generation stage.", + "(a)" + ], + "image_footnote": [], + "bbox": [ + 112, + 397, + 588, + 652 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/933dc0990bc1760dae615ab716cae2353e6abaaed7243905be0d779e29664519.jpg", + "image_caption": [ + "(b)", + "Figure 3: The network structure of the proposed method, (a) structure of generator $G$ , (b) structure of encoder $E$ ." + ], + "image_footnote": [], + "bbox": [ + 609, + 397, + 846, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "respectively, which can be calculated as,", + "bbox": [ + 76, + 715, + 344, + 729 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {X} _ {o} = f _ {c 1} (w (z)) \\boldsymbol {X} _ {i} + f _ {c 2} (w (z)) + \\boldsymbol {n} _ {0}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 739, + 468, + 756 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $X_{i}$ and $X_{o}$ denote the input and output features of CAdaIN, and $f_{c1}, f_{c2}$ represent two FC layers. By using a latent control vector encoded from random noise, the CAdaIN can modulate the features to produce different distributions, resulting in diversified palmprint images. In addition, in order to further improve the diversity, random noise $n_{0}$ with the same spatial resolution as the feature map is added to the modulated features to inject more randomness.", + "bbox": [ + 75, + 763, + 468, + 898 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For producing realistic results, the loss $\\mathcal{L}_1$ and adversarial loss $\\mathcal{L}_D$ are used to restrain the learning of $G$ , as follows,", + "bbox": [ + 500, + 715, + 888, + 746 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {G} = \\lambda_ {1} \\mathcal {L} _ {1} \\left(B, B ^ {\\prime}\\right) + \\lambda_ {2} \\mathcal {L} _ {D} \\left(B, B ^ {\\prime}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 753, + 888, + 771 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda_{1}$ and $\\lambda_{2}$ are weights. The $\\mathcal{L}_1$ is a commonly used pixel-wise loss, which can ensure the numerical similarity between the generated image and real palmprint. But note that the palm creases image $A$ is not matched with palmprint $B$ , so that too strong pixel-wise constraint may cause wrong overfitting to the details in $B$ . Hence, adversarial loss $\\mathcal{L}_D$ is also used to relax the constraint and restrain the semantic similarity between $B$ and $B'$ . For the discriminator in $\\mathcal{L}_D$ ,", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19608", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "we adopt the PatchGAN [13], which determines patch-wise authenticity by mapping the image to a $70 \\times 70$ grid.", + "bbox": [ + 76, + 90, + 468, + 122 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Palmprint Encoder", + "text_level": 1, + "bbox": [ + 76, + 128, + 261, + 143 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The encoder $E$ is used to map the palmprint image to the Gaussian noise domain. Its structure is shown in Fig.3 (b), which is a straightforward ResNet structure. The original size of the feature map is $256 \\times 256$ , and it gradually decreases to $16 \\times 16$ through several residual blocks (RB). Then, a FC layer is used to estimate the target mean $\\mu_{Q}$ and variance $\\sigma_{Q}^{2}$ from flattened features. Finally, the noise vector $Q(z|B)$ is sampled from Gaussian space $\\mathcal{N}(\\mu_{Q}, \\sigma_{Q}^{2})$ via reparameterization trick [74].", + "bbox": [ + 75, + 152, + 468, + 289 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the training stage, we constrain the KL divergence between $Q(z|B) \\sim \\mathcal{N}(\\mu_Q,\\sigma_Q^2)$ and noise vector $N(z) \\sim \\mathcal{N}(0,1)$ sampled from Gaussian space, so that the target domain of $E$ can keep approximating to the standard normal distribution. This loss can be computed as,", + "bbox": [ + 76, + 290, + 468, + 364 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {K L} = - \\frac {1}{2} \\left(1 + \\log \\sigma_ {Q} ^ {2} - \\sigma_ {Q} ^ {2} - \\mu_ {Q} ^ {2}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 372, + 468, + 401 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this paper, $E$ and $G$ are combined to learn a domain-to-domain mapping from unpaired training data, instead of using a fully supervised manner. Firstly, this structure can avoid the dependence on manual labeling of paired data. Secondly, conditional bidirectional domain-to-domain mapping can reproduce random and realistic images and keep the information of palm creases condition as well.", + "bbox": [ + 75, + 407, + 468, + 512 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. ID-aware Loss", + "text_level": 1, + "bbox": [ + 76, + 521, + 225, + 535 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For training recognition models, the generated palmprints not only need to be diversified, but also have to preserve ID information. For a synthetic palm creases image $A$ , the generated palmprints should have the same ID information. Therefore, an ID-aware loss $\\mathcal{L}_{ID}$ is added to restrain the generator. As shown in Fig.2 (a), a siamese generator $G$ is used to produce another palmprint image $B''$ with the same creases $A$ and random noise vector $N(z)$ . Then the $\\mathcal{L}_{ID}$ restricts the ID consistency of two generated results of $B'$ and $B''$ , as follows,", + "bbox": [ + 75, + 544, + 468, + 694 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {I D} = 1 - \\frac {D _ {M B} \\left(B ^ {\\prime}\\right) \\cdot D _ {M B} \\left(B ^ {\\prime \\prime}\\right)}{\\left| \\left| D _ {M B} \\left(B ^ {\\prime}\\right) \\right| \\right| \\times \\left| \\left| D _ {M B} \\left(B ^ {\\prime \\prime}\\right) \\right| \\right|}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 700, + 468, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where “.” denotes the vector dot product operation, $D_{MB}$ is a pretrained palmprint recognition model using MobileFaceNet [10] and extracts the $512 \\times 1$ feature of $B'$ and $B''$ . That is, $\\mathcal{L}_{ID}$ calculates cosine similarity between the extracted features of two generated images for the same ID. Owing to the ID-aware loss, increasing the randomness and diversity of the generator will not destroy the intra-class ID consistency.", + "bbox": [ + 75, + 739, + 468, + 859 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The total loss of entire model, as follows,", + "bbox": [ + 96, + 861, + 372, + 875 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {D} \\mathcal {L} _ {D} + \\lambda_ {1} \\mathcal {L} _ {1} + \\lambda_ {K L} \\mathcal {L} _ {K L} + \\lambda_ {I D} \\mathcal {L} _ {I D}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 885, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9568da3a9c46797694078c9ab589e2f133c13a234d47ef86a5965be3a29d80f6.jpg", + "image_caption": [ + "Real Palmprint" + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 686, + 229 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/212acf0840641701b563cc05068d160b838397423273e1a062611cf3ab2dd1ee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 89, + 777, + 157 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8e3698e83ab49bbe7e890588b2a6ceef9cd945fd3c10558d12a1db1ce2f6e033.jpg", + "image_caption": [ + "BézierPalm Creases", + "Our Improved Bézier Palm Creases" + ], + "image_footnote": [], + "bbox": [ + 687, + 160, + 776, + 229 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/04425f16a86dd6df0d8f95985d11b23e7113b972b73aa50faa94e9e8cc591e74.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 779, + 90, + 867, + 157 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5e9e9e0b0abccbf0b822c490ef7f0bc03ae2407726d0844d2b227164b33f8d68.jpg", + "image_caption": [ + "Figure 4: Examples of some synthetic palm creases in BezierPalm [69] and our method." + ], + "image_footnote": [], + "bbox": [ + 779, + 160, + 867, + 229 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_D$ denotes GAN loss, $\\mathcal{L}_1$ denotes absolute error loss, $\\mathcal{L}_{KL}$ denotes KL divergence loss, and $\\mathcal{L}_{ID}$ denotes ID-aware loss. We will add the total loss in final version.", + "bbox": [ + 498, + 309, + 890, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Improved Bezier Palm Creases Synthesis", + "text_level": 1, + "bbox": [ + 500, + 364, + 849, + 380 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the forward stage, only the generator $G$ is used to produce palmprint images from synthetic palm creases, as shown in Fig.2 (b). Motivated by BézierPalm [69], we also adopt the two-level Bézier curves to synthesize palm creases image that contains three principal lines and random wrinkle lines. The parametric control points of the Bézier curve can be adjusted randomly within a preset range to obtain a large number of fake palm creases for virtual ID.", + "bbox": [ + 496, + 387, + 890, + 507 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, we have observed that randomly adjusted Bézier curves may lead to some unreasonable results. As shown in Fig.4, the layout of some randomly generated creases is quite different from that of the real palmprints.", + "bbox": [ + 496, + 508, + 890, + 568 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As a result, this paper improves the Bézier curves synthesis strategy based on real palmprint prior from the following three aspects. Firstly, we observe and adjust the rough range of the parameter points (i.e., start point, control point, and end point) of three principal lines according to real palmprints. So that the layout of synthetic principal lines becomes more similar to that of real palms. Secondly, we adjust the synthesis rules to generate more wrinkle lines with moderate length and more uniform distribution. Thirdly, a similarity constraint based on RLOC [34] is added, which makes the principal lines of different IDs sufficiently distinguishable. RLOC is a classic palmprint recognition method that can measure the similarity of two creases images. In order to avoid very similar principal lines being generated for different IDs, we filter out some creases images which exceed the RLOC inter-class similarity threshold. We ablate the threshold of RLOC with 0.1, 0.5, 0.9, 0.95 and experimentally set it as 0.9. More details of improved Bézier palm creases can be found in supplementary materials.", + "bbox": [ + 496, + 569, + 890, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, the improved random Bézier curves are input into the generator $G$ to obtain corresponding palmprint images. This generation process can be repeated until a large-", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19609", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "scale realistic pseudo-palmprint dataset is established.", + "bbox": [ + 76, + 90, + 434, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experimental Settings", + "text_level": 1, + "bbox": [ + 76, + 119, + 287, + 137 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We adopt the same experimental datasets and Open-set evaluation protocol following BézierPalm [69]. The identities of the training and test set are isolated. TAR(True Acceptance Rate) @FAR(False Accept Rate) is used to evaluate model performance. Details about Open-set and evaluation protocol can be found in supplementary materials.", + "bbox": [ + 76, + 143, + 468, + 234 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 244, + 181, + 258 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We adopt 13 public datasets in our experiments as in BezierPalm [69], including 3,268 IDs and 59,162 palmprint images. Detailed descriptions of these datasets are shown in Tab.1. We follow the detect-then-crop protocol in [67] to extract the Region Of Interests(ROIs).", + "bbox": [ + 76, + 268, + 468, + 344 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e11cb4946b2ca8ea63f579c399e9bc8e493322304b3e537ec00e783606f73502.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1: Details of the 13 public palmprint datasets." + ], + "table_body": "
Name#IDs#ImagesDevice
MPD [68]40016,000Phone
TCD [68]60012,000Contactless
IITD [41]4602,601Contactless
CASIA [57]6205,502Contactless
CASIA-MS [29]2007,200Contactless
COEP [2]1671,344Digital camera
MOHI [30]2003,000Phone
WEHI [30]2003,000Web cam
GPDS [21]1002,000Web cam
XJTU_UP [52]20030,000Phone
XJTU_A [52]1141,130CMOS camera
PolyU-MS [66]50024,000Contactless
PolyU(2D+3D) [36]4008,000Web cam
", + "bbox": [ + 102, + 354, + 447, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 590, + 294, + 606 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Generation Model Training. We generate 4000 identities and 100 samples for each identity by default following BézierPalm [69]. For training the generation model, the weights of $\\mathcal{L}_1$ , $\\mathcal{L}_D$ and $\\mathcal{L}_{KL}$ are set as 10.0 1.0 and 0.01 according to [74]. We ablate the weight of $\\mathcal{L}_{ID}$ with 1.0, 5.0, 10.0 and experimentally set it as 5.0. The resolution of input and output images is $256 \\times 256$ . The learning rate is 0.0002 in the first 30 epochs and linearly decays to 1e-8 in the last 30 epochs. The generation model is trained using Adam optimizer with parameters (0.5, 0.99). For comparative experiment, we use the source codes of pix2pixHD [61], CycleGAN [73] and BicycleGAN [74] in their original papers.", + "bbox": [ + 75, + 613, + 470, + 796 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Recognition Model Training. For our recognition model, we use ResNet50 [31] and MobileFaceNet [10] as the backbone with the input resolution of $224 \\times 224$ . The model is first pretrained on synthesized data for 25 epochs and then finetuned on real datasets for 50 epochs. For the baseline model, we train the model on real datasets for 50", + "bbox": [ + 75, + 809, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "epochs. The feature extractor in ID-aware Loss uses the same training setting as the baseline. We use Arcface [14] with margin $m = 0.5$ and scale factor $s = 48$ for the pretraining, finetuning and baseline training supervision. We use the cosine learning rate schedule with a warmup start for one epoch. The maximum learning rate is 1e-2 and the minimum learning rate is 1e-6 for pretraining and finetuning. All recognition models are trained with a mini-batch SGD optimizer. We use 4 NVIDIA Tesla V100 GPUs for training with total batch size of 128.", + "bbox": [ + 496, + 90, + 890, + 241 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "It should be emphasized that the generation model, the feature extractor in ID-aware loss, and the recognition model all ensure that the training and test sets are completely isolated.", + "bbox": [ + 496, + 242, + 890, + 301 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experimental Results", + "text_level": 1, + "bbox": [ + 500, + 315, + 705, + 332 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Open-set Palmprint Recognition", + "text_level": 1, + "bbox": [ + 500, + 340, + 784, + 357 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first test our method under the open-set protocol with two different training and test ratios 1:1 and 1:3 (trainIDs: testIDs = 1634:1632, 818:2448). Details about the \"Open-set\" protocol can be found in supplementary materials. The quantitative results are shown in Tab.2. The TAR v.s. FAR curves of the 1:1 setting are in Fig.5. Our method outperforms BézierPalm by $5.09\\%$ and $14.73\\%$ under 1:1 and 1:3 settings @FAR = 1e-6 using 'MB', which establishes a new state-of-the-art. Our method achieves more significant improvement under 1:3 setting than 1:1 setting, which demonstrates the effectiveness of our method in scenarios with only a small amount of real training data.", + "bbox": [ + 496, + 363, + 890, + 545 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a6739fa4c450f8c01fc7a8bdaba2579a688cfebfa07b7940d86d07d07d442df5.jpg", + "image_caption": [ + "Figure 5: TAR@FAR curves of different methods under the open-set 1:1 setting. The backbone of ArcFace, BézierPalm and our method is MobileFaceNet." + ], + "image_footnote": [], + "bbox": [ + 504, + 559, + 885, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Palmprint Recognition with Limited Identities", + "text_level": 1, + "bbox": [ + 500, + 832, + 890, + 848 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To further verify the performance of our method with limited real training IDs, we test our method with different sizes of real training IDs and fix the test set under the 1:1", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19610", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/492b258f461d877d6d1c6c30f7a3e6a9b68d7dd95258f2bc8de309e4444cf9d9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBackbonetrain : test = 1 : 1train : test = 1 : 3
TAR@1e-3TAR@1e-4TAR@1e-5TAR@1e-6TAR@1e-3TAR@1e-4TAR@1e-5TAR@1e-6
CompCode [40]N/A0.48000.42920.36250.21030.45010.39320.34940.2648
LLDP [43]N/A0.73820.67620.52220.12470.73720.67850.61710.2108
BOCV [28]N/A0.49300.45150.39560.21030.45270.39750.35270.2422
RLOC [34]N/A0.64900.58840.44750.14430.64820.58400.52240.3366
DOC [19]N/A0.49750.44090.37120.16670.48860.43290.38890.2007
PalmNet [25]N/A0.71740.66610.59920.10690.72170.66990.61550.2877
C-LMCL [71]MB0.92900.85540.77320.62390.85090.75540.74350.5932
ArcFace [14]MB0.92920.85680.78120.70490.85160.75310.66080.5825
BézierPalm [69]MB0.96400.94380.91020.84370.94070.88610.79340.7012
OursMB0.98020.97140.94860.89460.94960.92670.89690.8485
C-LMCL [71]R500.95450.90270.83170.75340.86010.77010.68210.6254
ArcFace [14]R500.94670.89250.82520.74620.87090.78840.71560.6580
BézierPalm [69]R500.96710.95210.92740.89560.94240.89500.82170.7649
OursR500.98210.97320.95690.93470.95330.93190.90160.8698
", + "bbox": [ + 119, + 87, + 846, + 344 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "open-set protocol. We synthesize 4000 identities and 100 samples for each identity in all experiments. As shown in Tab.3, the performance of ArcFace and BézierPalm drops quickly with the reduction of real data, while our method still performs well with few real training IDs. Note that our method with $160(10\\%)$ real IDs even outperforms Arcface with 1600 real IDs. Besides, our method significantly improves the TAR by $20.81\\%$ @FAR=1e-6 against BézierPalm [69] with 80 training IDs, which shows the superiority of our method under few real training IDs.", + "bbox": [ + 75, + 401, + 470, + 551 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Palmprint Recognition at Million Scale", + "text_level": 1, + "bbox": [ + 76, + 561, + 413, + 579 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In order to verify the effectiveness of our method on large-scale real-world datasets, we test our method on our internal dataset with millions of palmprint images. Our dataset contains 19,286 training identities with 2,871,073 images and 1,000 test identities with 182,732 images. For a fair comparison with BézierPalm, we generate 20,000 IDs with 100 samples in each ID for pretraining. Quantitative results are shown in Tab.4. Our method outperforms ArcFace and BézierPalm with a clear margin, showing its practical application value on large-scale datasets.", + "bbox": [ + 75, + 585, + 468, + 737 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 750, + 228, + 767 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we conduct ablation studies to verify different components and design choices of our method. The MobileFaceNet is used as the backbone for all experiments under the same Open-set protocol.", + "bbox": [ + 76, + 776, + 468, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.1. Components and design choices", + "text_level": 1, + "bbox": [ + 76, + 847, + 356, + 864 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The main components and design choices of our method are ID-aware loss, conditional modulation generator and", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a03825e6b469c31ed48c26ee70f99ae45d42d2ed40dc26d3a014e0d8a55e25ea.jpg", + "table_caption": [ + "Table 2: Quantitative performances under the open-set protocol where the performances are evaluated in terms of TAR@FAR. 'MB' represents the MobileFaceNet [10] backbone and 'R50' is resnet50 [31] backbone." + ], + "table_footnote": [], + "table_body": "
Method#IDTAR@FAR=
1e-31e-41e-51e-6
ArcFace0.92920.85680.78120.7049
BézierPalm1,6000.96400.94380.91020.8437
Ours0.98020.97140.94860.8946
ArcFace0.89340.74320.71040.6437
BézierPalm8000.95340.93900.90250.8164
Ours0.97830.96870.93560.8741
ArcFace0.81020.70500.66680.3320
BézierPalm4000.91890.84970.75420.6899
Ours0.95730.93240.88360.8162
ArcFace0.67610.52940.47830.2437
BézierPalm1600.81790.69980.58260.4832
Ours0.93560.86410.80630.7246
ArcFace0.53840.46820.32490.1173
BézierPalm800.65470.55110.44900.3743
Ours0.89740.80920.69470.5824
", + "bbox": [ + 521, + 398, + 867, + 681 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3: Performance under different real training identities. The generation model, feature extractor in ID-aware loss, and the recognition model access the same number of real training identities. The backbone is MobileFaceNet.", + "bbox": [ + 498, + 683, + 890, + 743 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "improved strategy for Bezier palm creases synthesis. Tab.5 shows the results of recognition models with or without these components. 'I', 'C', 'S' represent the three components respectively. For baseline without 'C', the normal UNet [49] as in [74] is used to take place of 'C'. ID-aware loss achieves the greatest improvement by $11.72\\%$ @FAR=1e-6 against the baseline, which reflects its advantage for preserving intra-class consistency. The con", + "bbox": [ + 498, + 779, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19611", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3e943a01d8c85b3db10ec0b1c12c0fd69cb39afbd456f5d05f16fe848cf396cf.jpg", + "image_caption": [ + "Input Synthetic Palm Creases" + ], + "image_footnote": [], + "bbox": [ + 109, + 118, + 199, + 186 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b61da0dbb0af2677cefdea6362db662053a61eed02e529e500546ce414eddb3f.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 200, + 88, + 366, + 217 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2af07fb735b4511a652a62082cfcde84f68ab6e0ed76d5a7f4e12ba341a25168.jpg", + "image_caption": [ + "(b)", + "Figure 6: Generated palmprint images of different methods, (a) pix2pixHD [61], (b) CycleGAN [73], (c) BicycleGAN [74], (d) the proposed method." + ], + "image_footnote": [], + "bbox": [ + 367, + 88, + 532, + 218 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d518ded8a104cfbcd562df09e347300eb3b3949a41cb57099b4bb31fec73cb87.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 532, + 88, + 700, + 218 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b6c7a0a501528e55f44686a478fedededdd6d2ead50a0ae9dd71ffcf4324ba98.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 702, + 88, + 870, + 218 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/13371b3e614a57a5bc1712e536776b9698234562bcb01731daea16788d9fd903.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBackboneTAR@FAR=
1e-61e-71e-81e-9
ArcFace0.97700.95500.92510.8833
BézierPalmMB0.98030.96050.93010.9015
Ours0.98710.96840.94160.9194
ArcFace0.99860.99640.99310.9879
BézierPalmR500.99960.99750.99430.9911
Ours0.99980.99830.99720.9954
", + "bbox": [ + 99, + 287, + 444, + 412 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1a5ea341115d6091b8c65c2407330264eef157ddec3ecb0a577b6e71a1d9b046.jpg", + "image_caption": [ + "Figure 7: Diverse synthetic palmprints can be generated by adjusting the input noise vector $N(z)$ ." + ], + "image_footnote": [], + "bbox": [ + 84, + 459, + 459, + 652 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ditional modulation generator also significantly improves the performance by $4.49\\%$ @FAR=1e-6, which reflects its advantage for improving the intra-class diversity. The improved Bezier palm creases bring an improvement by $1.15\\%$ @FAR=1e-6.", + "bbox": [ + 75, + 714, + 467, + 789 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.2. Comparison of Generation Methods", + "text_level": 1, + "bbox": [ + 76, + 801, + 390, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Three generation methods pix2pixHD [61], CycleGAN [73], BicycleGAN [74] are used for comparison, and all of them are retrained on the same training set with unpaired data. Fig.6 illustrates the generated palmprints of different generation methods. It can be found that pix2pixHD", + "bbox": [ + 75, + 824, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6717d460c3ce9c90142c8cf9f465c619193d7732af8426b6bd1df4ef9f371443.jpg", + "table_caption": [ + "Table 4: Palmprint recognition performance on million scale dataset." + ], + "table_footnote": [], + "table_body": "
ICSTAR@FAR=
1e-31e-41e-51e-6
X(UNet)X0.93990.89050.81640.7210
✓(UNet)X0.96870.95710.90760.8382
✓✓X0.97960.96890.94410.8831
✓✓✓0.98020.97140.94860.8946
", + "bbox": [ + 521, + 289, + 867, + 377 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9868838b6e37d5670f3406dd7d6a1ba8ec9f3c26062fd579b35ad194daf717dd.jpg", + "table_caption": [ + "Table 5: Ablation of different components in our method. 'I', 'C' and 'S' denote ID-aware loss, conditional modulation generator and improved synthetic creases, respectively." + ], + "table_footnote": [], + "table_body": "
MethodFID↓train:test=1:1train:test=1:3
TAR↑@1e-5TAR↑@1e-6TAR↑@1e-5TAR↑@1e-6
ArcFace [14]--0.78120.70490.66080.5825
BézierPalm [69]--0.91020.84370.79340.7012
pix2pixHD [61]97.58010.91560.87340.80520.7244
CycleGAN [73]50.77040.91360.87030.78630.7189
BicycleGAN [74]35.28010.81730.72540.67830.5929
Ours16.47620.94860.89460.89690.8485
", + "bbox": [ + 503, + 440, + 888, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6: Quantitative recognition results using different generation methods under the open-set protocol.", + "bbox": [ + 500, + 582, + 890, + 613 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and CycleGAN tend to synthesize blurred results. As marked in blue rectangle, BicycleGAN may generate some creases that are inconsistent with the input Bézier curves. Our method can synthesize clearer and sharper principal lines and faithfully preserve the ID information of the input Bézier curves. For intra-class diversity, as shown in Fig.7, our method is able to randomly generate high-fidelity palmprints with diverse lighting and skin types by adjusting the input noise vector $N(z)$ .", + "bbox": [ + 496, + 642, + 890, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Quantitative results are shown in Tab.6. Our method substantially outperforms the existing methods in terms of TAR@FAR. Also, we use FID [8] to evaluate the quality of generated results and our method also effectively decreases the FID score by more than $50\\%$ against other methods. Besides, we reproduced some other generation methods [54, 56] for unpaired image-to-image transfer, including diffusion-based models, but the generated results are unsat", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19612", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "isfying. Related details and more subjective results can be found in supplementary material.", + "bbox": [ + 76, + 90, + 468, + 122 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6.3. Number of Synthesized Identities and Images", + "text_level": 1, + "bbox": [ + 76, + 132, + 460, + 148 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this ablation, we investigate the influence of the number of synthesized identities and images. Specifically, we generate 4000 identities and 100 samples by default, and fix one number and vary the other under the open-set protocol(train:test=1:1). The results are shown in Fig.8. With the increase of \"width\" and \"depth\" of synthetic data, our method can continuously improve the performance of the recognition model and achieve a higher upper bound than BezierPalm. The performance reaches the upper bound with $80k$ synthetic identities and 160 samples per identity.", + "bbox": [ + 75, + 155, + 470, + 308 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/1ac102ce60b6e200fc27ff174294da7ae2a6d23d8d9571a9691eeaf6d83089b4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 324, + 464, + 439 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/15f05bbdd3b695e4556e419208310951d587e3c3f5ec78b84e4668061418fb15.jpg", + "image_caption": [ + "Figure 8: TAR@FAR=1e-6 of recognition models pretrained with different numbers of synthetic identities and samples. The backbone is MobileFaceNet." + ], + "image_footnote": [], + "bbox": [ + 83, + 441, + 464, + 556 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 633, + 194, + 648 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This paper proposed an ID-aware conditional modulation generation model which can produce realistic and diversified palmprint images. Specifically, a conditional modulation generator was designed, which adopted synthetic palm creases as condition, and used encoded Gaussian noise vector to modulate the generated diversity. An ID-aware loss was proposed to preserve the identity information of input palm creases during the unpaired training process. In the forward pseudo-palmprint generation stage, we improved the Bezier curves generation strategy to produce more realistic synthetic palm creases. From experimental results, we can obtain the following findings. Firstly, the generated pseudo-palmprint samples can effectively improve the performance of palmprint recognition models. Secondly, by using the synthetic palmprints, our method can effectively reduce the dependence of real data by $90\\%$ . In", + "bbox": [ + 75, + 659, + 472, + 901 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "future work, we hope to implement complete real-data-free palmprint recognition with synthetic data.", + "bbox": [ + 498, + 90, + 890, + 122 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "8. Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 136, + 687, + 152 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work is partly supported by the grants of the National Natural Science Foundation of China, Nos.62076086, 62272142 and 61972129.", + "bbox": [ + 498, + 161, + 890, + 205 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 220, + 596, + 236 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Amazon one. https://one.amazon.com/.", + "[2] The ceop dataset. https://www.coep.org.in/resources/coeppalmprintdatabase.", + "[3] Denise Almeida, Konstantin Shmarko, and Elizabeth Lomas. The ethics of facial recognition technologies, surveillance, and accountability in an age of artificial intelligence: a comparative analysis of us, eu, and uk regulatory frameworks. 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In Advances in Neural Information Processing Systems, 2017." + ], + "bbox": [ + 78, + 90, + 468, + 273 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "19616", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/RPG-Palm_ Realistic Pseudo-data Generation for Palmprint Recognition/6f1b3792-7545-4d6e-8992-4404f77414a4_model.json b/2023/RPG-Palm_ Realistic Pseudo-data Generation for Palmprint Recognition/6f1b3792-7545-4d6e-8992-4404f77414a4_model.json new file mode 100644 index 0000000000000000000000000000000000000000..89f648265fd0c24f6f707209c6ac7c966e26b9c9 --- /dev/null +++ b/2023/RPG-Palm_ Realistic Pseudo-data Generation for Palmprint Recognition/6f1b3792-7545-4d6e-8992-4404f77414a4_model.json @@ -0,0 +1,3150 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.807, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. 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However, the lack of large-scale public palmprint datasets limits further research and development of palmprint recognition. In this paper, we propose a novel realistic pseudo-palmprint generation (RPG) model to synthesize palmprints with massive identities. We first introduce a conditional modulation generator to improve the intraclass diversity. Then an identity-aware loss is proposed to ensure identity consistency against unpaired training. We further improve the Bézier palm creases generation strategy to guarantee identity independence. Extensive experimental results demonstrate that synthetic pretraining significantly boosts the recognition model performance. For example, our model improves the state-of-the-art Bézier Palm by more than \\(5\\%\\) and \\(14\\%\\) in terms of TAR@FAR=1e-6 under the 1:1 and 1:3 Open-set protocol. When accessing only \\(10\\%\\) of the real training data, our method still outperforms ArcFace with \\(100\\%\\) real training data, indicating that we are closer to real-data-free palmprint recognition." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.521, + 0.631, + 0.537 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.549, + 0.892, + 0.685 + ], + "angle": 0, + "content": "Palmprint is an excellent biometric in terms of privacy, willingness, convenience, and security. Since the palmprint locates on the inner side of the palm, obtaining the palmprint without one's permission is nearly impossible, which is more privacy-friendliness over the face. Compared to iris and fingerprints, palmprint has fewer usage restrictions, which makes palmprint more user-friendly. Furthermore, Palmprints and palm veins can be collected simultaneously to form a highly secure dual-modal system." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Due to these advantages, big companies such as Amazon [1] and Tencent [69] begin to apply palmprint recognition in their payment services. However, for the same reason, palmprints are rare in public and expensive to collect. To our best knowledge, publicly available datasets [2, 21, 29, 30, 36, 41, 52, 57, 68] only contain thousands of identities and tens of thousands of images in total. Meanwhile, face recognition has several million-level publicly available datasets [4, 9, 27, 38, 44, 62] that contain tens to hundreds of thousands of identities. The lack of large-scale public dataset seriously inhibits the research on palmprint recognition." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "To solve this problem, one way is to collect a large-scale palmprint dataset. However, this way is very time-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.875, + 0.206, + 0.888 + ], + "angle": 0, + "content": "*Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.227, + 0.9 + ], + "angle": 0, + "content": "† Corresponding authors." + }, + { + "type": "list", + "bbox": [ + 0.095, + 0.871, + 0.227, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19605" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.089, + 0.44, + 0.362 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.371, + 0.473, + 0.493 + ], + "angle": 0, + "content": "Figure 1: Synthetic Bezier palm creases are used as the identity control condition to guide the generator to produce diverse synthetic data. Recognition models are pretrained with pseudo-data and then finetuned on real data, achieving significant performance boosts. Besides, even if only accessing \\(10\\%\\) of the real training data for generation and recognition model, our method still gets comparable performance to \\(100\\%\\) of real data direct training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.47, + 0.656 + ], + "angle": 0, + "content": "consuming and expensive. In addition, collecting biometric data causes more and more privacy and ethical concerns [7] and is strictly restricted by legislation in many countries. Another way is to augment the training dataset with synthetic palmprints. To better benefit palmprint recognition applications, the synthetic method should support generating massive identities with inter-class and intra-class diversity, and the gap between synthetic palmprints and real palmprints should be small." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.47, + 0.884 + ], + "angle": 0, + "content": "Recently, BézierPalm [69] synthesizes fake palmprint images by generating palmprint creases with several parameterized Bézier curves for recognition model pretraining. BézierPalm first shows the ability to output massive new identities without using real palmprints and significantly improves the performance of the palmprint recognition models. However, BézierPalm has some problems unsolved. Firstly, synthetic palmprints have a large gap to real ones, resulting in non-neglectable finetune data requirements in real-world applications. Secondly, the curve parameter difference of each identity cannot ensure inter-class independence when generating massive data. Thirdly, the intra-class diversity only contains small curve deformation in BézierPalm, while real palmprints have diverse textures, lighting and et al." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In this paper, we propose a realistic pseudo-palmprint" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.365 + ], + "angle": 0, + "content": "generation (RPG) model. As shown in Fig.1, the RPG model takes synthetic Bezier palm creases as an identity (ID) condition and outputs realistic pseudo-palmprints with a bidirectional mapping from the Gaussian noise domain to the palmprints domain. Since there is no correspondence between synthetic Bezier palm creases and real palmprints, the generation model can only use unpaired data and will lose intra-class identity consistency easily during training. To solve this problem, we introduce an identity-aware loss that restrains the identity consistency between palmprints generated from the same Bezier palm creases. In addition, we design a conditional modulation generator to generate diversified intra-class textures and lighting conditions using a latent control vector encoded from random noises. To further reduce the distribution gap between synthetic palm creases and real-world palmprints, we refined the synthetic palmprint creases generation strategy with a more reasonable parameter design and identity independence check." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.375, + 0.825, + 0.39 + ], + "angle": 0, + "content": "The contributions of this paper are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.403, + 0.892, + 0.479 + ], + "angle": 0, + "content": "- We propose a realistic pseudo-palmprint generation (RPG) model with a conditional modulation generator to improve the intra-class diversity and an ID-aware loss to help the RPG model ensure identity consistency under unpaired training." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.491, + 0.892, + 0.536 + ], + "angle": 0, + "content": "- We improve the Bezier palm creases synthetic method to get more reasonable palm creases and independent identities." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.55, + 0.892, + 0.611 + ], + "angle": 0, + "content": "- Extensive experimental results on 13 public datasets demonstrate that recognition models pretrained with our synthetic pseudo-palmprints achieve state-of-the-art recognition accuracy." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.624, + 0.892, + 0.698 + ], + "angle": 0, + "content": "- With our RPG pretraining, even if accessing only \\(10\\%\\) of the real data, the recognition model performance still outperforms \\(100\\%\\) real data direct training. Showing we are closer to real-data-free palmprint recognition." + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.403, + 0.892, + 0.698 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.715, + 0.642, + 0.731 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.741, + 0.783, + 0.758 + ], + "angle": 0, + "content": "2.1. Palmprint Recognition Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Palmprint recognition methods can be divided into two categories: traditional-based and deep-learning based [18]. Traditional methods extract various kinds of local or global features to make different palmprints more discriminative. Local-based methods [19, 28, 34, 40, 43, 57, 70] manually design effective local features for recognition. Global-based methods [3, 20, 32, 42, 51, 59] extract low-dimensional features from the whole image to distinguish different palmprints. Deep Learning based methods [16, 25, 35, 58] train" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19606" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.472, + 0.152 + ], + "angle": 0, + "content": "modified neural networks to extract features with classification or pair-wise loss [14, 55, 71]. However, the lack of large-scale public palmprint datasets limits the potential of existing palmprint recognition methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.188, + 0.459, + 0.205 + ], + "angle": 0, + "content": "2.2. Generation Model for Image Transformation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.22, + 0.47, + 0.493 + ], + "angle": 0, + "content": "With the development of image generation models, such as generative adversarial network (GAN)-based models [26, 37] and diffusion-based models [47, 48], image-to-image generation/translation methods have achieved impressive performance [11, 12, 33]. However, many typical models, e.g., conditional generation model pix2pixHD [61], multidomain transformation model StarGAN [12], dual-domain mapping model BicycleGAN [74] and recent conditional diffusion model [50, 60], rely on paired training data, which is unavailable in many applications. Therefore, some unpaired image-to-image translation models have been proposed [39, 54, 64, 72], which usually adopt cycle consistency loss to train the models without paired data. However, these models are not designed for recognition tasks, and thus ignore the ID preservation in the generation process. Overall, there is still a lack of research on generating diversified and realistic palmprints with ID consistency from limited unpaired samples." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.528, + 0.409, + 0.545 + ], + "angle": 0, + "content": "2.3. Data generation for Recognition Tasks" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.47, + 0.728 + ], + "angle": 0, + "content": "In order to improve the recognition performance, data generation can be used to expand the depth (diversity of each identity) and width (total number of identities) of training data. For example, in face recognition field, several facial image generation methods [15, 24, 45, 46, 65, 22, 23] have been proposed to generate facial samples based on the priors of facial attributes, facial structures and 3D faces [6]. Also, in field of fingerprint recognition, some methods based on hand-crafted or learning-based approaches [5, 17, 63] have been proposed to generate high-fidelity fingerprint images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.736, + 0.47, + 0.903 + ], + "angle": 0, + "content": "For palm recognition tasks, BezierPalm [69] use Bezier curves to synthesize fake palm creases by changing the Bezier control parameters. PalmGAN [53] improves the cross-domain recognition performances by using CycleGAN to transfer the styles between normal and multispectral palmprints. However, PalmGAN doesn't create virtual identities, and the BezierPalm suffers from the domain gap between palmprint images and geometry curves. By introducing the new generation model and ID-aware loss, our method can expand the inter-class diversity and intra-class diversity of palmprint dataset simultaneously." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.593, + 0.107 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.117, + 0.691, + 0.133 + ], + "angle": 0, + "content": "3.1. Overall Framework" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.142, + 0.892, + 0.337 + ], + "angle": 0, + "content": "Fig.2 illustrates the whole framework of the proposed realistic pseudo-palmprint generation (RPG) model, which includes a training stage and a forward palmprint generation stage. In the training phase, palmprint \\( B \\) is first mapped from the palmprint image domain to the latent vector \\( Q(z|B) \\) in the Gaussian noise domain through the encoder \\( E \\). Then, the generator \\( G \\) utilizes the unpaired palm creases \\( A \\) as condition, and remaps the encoded noise vector \\( Q(z|B) \\) back to the palmprint image domain. In order to increase the diversity and randomness of the generated palmprints, a conditional modulation structure is designed for \\( G \\), which uses the input noise vector to control the modulation of intermediate features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.34, + 0.892, + 0.46 + ], + "angle": 0, + "content": "In order to constrain the ID consistency of the generated pseudo palmprints, an ID-aware loss is presented to enforce the generator to maintain the ID information of input palm creases. As shown in Fig.2 (a), a siamese generator \\( G \\) is used to produce another palmprint \\( B'' \\) with the same palm creases \\( A \\). Then, a pretrained palmprint recognition discriminator is used to measure the ID consistency between \\( B' \\) and \\( B'' \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.464, + 0.892, + 0.583 + ], + "angle": 0, + "content": "In the forward pseudo-palmprint generation stage, synthetic Bézier creases are input into the generator \\( G \\) to obtain corresponding palmprint images for virtual identities. Motivated by BézierPalm [69], we improve the random Bézier curves generation strategy to obtain a more reasonable layout of principal lines and wrinkle lines. Then, a classic palmprint recognition method RLOC [34] is applied to ensure the inter-class difference." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.587, + 0.892, + 0.633 + ], + "angle": 0, + "content": "In the following, we will introduce the details of generator \\( G \\), encoder \\( E \\), ID-aware loss, and the improved Bézier palm creases synthesis strategy." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.647, + 0.888, + 0.664 + ], + "angle": 0, + "content": "3.2. Conditional Modulation Palmprint Generator" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.793 + ], + "angle": 0, + "content": "The proposed generator \\( G \\) takes Gaussian noise vector as input, palm creases image \\( A \\) as condition, and reproduces the pseudo-palmprint image \\( B' \\). As a typical image generation task, the common UNet [49] architecture is adopted. The detailed structure of \\( G \\) is illustrated in Fig.3 (a). To generate diversified results, a conditional adaptive instance normalization module (CAdaIN) is introduced to modulate the generated details in each down-block and up-block." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In the CAdaIN module, the input noise vector \\( N(z) \\) is first encoded into a latent control vector \\( w(z) \\) through two fully-connected (FC) layers. Note that the parameters of these two FC layers are shared for the whole generator \\( G \\), so that the generated style can be consistent by means of the same \\( w(z) \\). Then, two other FC layers are used to modulate the mean and variance of intermediate feature maps" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19607" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.088, + 0.625, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.335, + 0.343, + 0.357, + 0.355 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.629, + 0.09, + 0.862, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.713, + 0.342, + 0.736, + 0.355 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.355, + 0.89, + 0.384 + ], + "angle": 0, + "content": "Figure 2: Framework of the proposed realistic pseudo-palmprint generation model, (a) training stage, (b) forward pseudopalmprint generation stage." + }, + { + "type": "image", + "bbox": [ + 0.114, + 0.398, + 0.589, + 0.653 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.349, + 0.653, + 0.371, + 0.667 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.61, + 0.398, + 0.848, + 0.653 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.699, + 0.655, + 0.724, + 0.67 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.674, + 0.855, + 0.69 + ], + "angle": 0, + "content": "Figure 3: The network structure of the proposed method, (a) structure of generator \\( G \\), (b) structure of encoder \\( E \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.717, + 0.345, + 0.731 + ], + "angle": 0, + "content": "respectively, which can be calculated as," + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.74, + 0.469, + 0.757 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {X} _ {o} = f _ {c 1} (w (z)) \\boldsymbol {X} _ {i} + f _ {c 2} (w (z)) + \\boldsymbol {n} _ {0}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.9 + ], + "angle": 0, + "content": "where \\( X_{i} \\) and \\( X_{o} \\) denote the input and output features of CAdaIN, and \\( f_{c1}, f_{c2} \\) represent two FC layers. By using a latent control vector encoded from random noise, the CAdaIN can modulate the features to produce different distributions, resulting in diversified palmprint images. In addition, in order to further improve the diversity, random noise \\( n_{0} \\) with the same spatial resolution as the feature map is added to the modulated features to inject more randomness." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.717, + 0.89, + 0.747 + ], + "angle": 0, + "content": "For producing realistic results, the loss \\(\\mathcal{L}_1\\) and adversarial loss \\(\\mathcal{L}_D\\) are used to restrain the learning of \\(G\\), as follows," + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.755, + 0.89, + 0.772 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {G} = \\lambda_ {1} \\mathcal {L} _ {1} \\left(B, B ^ {\\prime}\\right) + \\lambda_ {2} \\mathcal {L} _ {D} \\left(B, B ^ {\\prime}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are weights. The \\(\\mathcal{L}_1\\) is a commonly used pixel-wise loss, which can ensure the numerical similarity between the generated image and real palmprint. But note that the palm creases image \\(A\\) is not matched with palmprint \\(B\\), so that too strong pixel-wise constraint may cause wrong overfitting to the details in \\(B\\). Hence, adversarial loss \\(\\mathcal{L}_D\\) is also used to relax the constraint and restrain the semantic similarity between \\(B\\) and \\(B'\\). For the discriminator in \\(\\mathcal{L}_D\\)," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19608" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.123 + ], + "angle": 0, + "content": "we adopt the PatchGAN [13], which determines patch-wise authenticity by mapping the image to a \\(70 \\times 70\\) grid." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.13, + 0.262, + 0.145 + ], + "angle": 0, + "content": "3.3. Palmprint Encoder" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.153, + 0.469, + 0.29 + ], + "angle": 0, + "content": "The encoder \\( E \\) is used to map the palmprint image to the Gaussian noise domain. Its structure is shown in Fig.3 (b), which is a straightforward ResNet structure. The original size of the feature map is \\( 256 \\times 256 \\), and it gradually decreases to \\( 16 \\times 16 \\) through several residual blocks (RB). Then, a FC layer is used to estimate the target mean \\( \\mu_{Q} \\) and variance \\( \\sigma_{Q}^{2} \\) from flattened features. Finally, the noise vector \\( Q(z|B) \\) is sampled from Gaussian space \\( \\mathcal{N}(\\mu_{Q}, \\sigma_{Q}^{2}) \\) via reparameterization trick [74]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.291, + 0.469, + 0.366 + ], + "angle": 0, + "content": "In the training stage, we constrain the KL divergence between \\( Q(z|B) \\sim \\mathcal{N}(\\mu_Q,\\sigma_Q^2) \\) and noise vector \\( N(z) \\sim \\mathcal{N}(0,1) \\) sampled from Gaussian space, so that the target domain of \\( E \\) can keep approximating to the standard normal distribution. This loss can be computed as," + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.373, + 0.469, + 0.402 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {K L} = - \\frac {1}{2} \\left(1 + \\log \\sigma_ {Q} ^ {2} - \\sigma_ {Q} ^ {2} - \\mu_ {Q} ^ {2}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.408, + 0.469, + 0.513 + ], + "angle": 0, + "content": "In this paper, \\( E \\) and \\( G \\) are combined to learn a domain-to-domain mapping from unpaired training data, instead of using a fully supervised manner. Firstly, this structure can avoid the dependence on manual labeling of paired data. Secondly, conditional bidirectional domain-to-domain mapping can reproduce random and realistic images and keep the information of palm creases condition as well." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.522, + 0.226, + 0.536 + ], + "angle": 0, + "content": "3.4. ID-aware Loss" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.545, + 0.47, + 0.695 + ], + "angle": 0, + "content": "For training recognition models, the generated palmprints not only need to be diversified, but also have to preserve ID information. For a synthetic palm creases image \\(A\\), the generated palmprints should have the same ID information. Therefore, an ID-aware loss \\(\\mathcal{L}_{ID}\\) is added to restrain the generator. As shown in Fig.2 (a), a siamese generator \\(G\\) is used to produce another palmprint image \\(B''\\) with the same creases \\(A\\) and random noise vector \\(N(z)\\). Then the \\(\\mathcal{L}_{ID}\\) restricts the ID consistency of two generated results of \\(B'\\) and \\(B''\\), as follows," + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.701, + 0.469, + 0.735 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {I D} = 1 - \\frac {D _ {M B} \\left(B ^ {\\prime}\\right) \\cdot D _ {M B} \\left(B ^ {\\prime \\prime}\\right)}{\\left| \\left| D _ {M B} \\left(B ^ {\\prime}\\right) \\right| \\right| \\times \\left| \\left| D _ {M B} \\left(B ^ {\\prime \\prime}\\right) \\right| \\right|}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.741, + 0.469, + 0.861 + ], + "angle": 0, + "content": "where “.” denotes the vector dot product operation, \\( D_{MB} \\) is a pretrained palmprint recognition model using MobileFaceNet [10] and extracts the \\( 512 \\times 1 \\) feature of \\( B' \\) and \\( B'' \\). That is, \\( \\mathcal{L}_{ID} \\) calculates cosine similarity between the extracted features of two generated images for the same ID. Owing to the ID-aware loss, increasing the randomness and diversity of the generator will not destroy the intra-class ID consistency." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.862, + 0.373, + 0.876 + ], + "angle": 0, + "content": "The total loss of entire model, as follows," + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.886, + 0.469, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {D} \\mathcal {L} _ {D} + \\lambda_ {1} \\mathcal {L} _ {1} + \\lambda_ {K L} \\mathcal {L} _ {K L} + \\lambda_ {I D} \\mathcal {L} _ {I D}, \\tag {5}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.687, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.552, + 0.238, + 0.633, + 0.25 + ], + "angle": 0, + "content": "Real Palmprint" + }, + { + "type": "image", + "bbox": [ + 0.688, + 0.09, + 0.778, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.689, + 0.161, + 0.777, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.701, + 0.233, + 0.762, + 0.253 + ], + "angle": 0, + "content": "BézierPalm Creases" + }, + { + "type": "image", + "bbox": [ + 0.78, + 0.091, + 0.869, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.78, + 0.161, + 0.869, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.771, + 0.233, + 0.879, + 0.253 + ], + "angle": 0, + "content": "Our Improved Bézier Palm Creases" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.255, + 0.892, + 0.284 + ], + "angle": 0, + "content": "Figure 4: Examples of some synthetic palm creases in BezierPalm [69] and our method." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.31, + 0.892, + 0.355 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_D\\) denotes GAN loss, \\(\\mathcal{L}_1\\) denotes absolute error loss, \\(\\mathcal{L}_{KL}\\) denotes KL divergence loss, and \\(\\mathcal{L}_{ID}\\) denotes ID-aware loss. We will add the total loss in final version." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.365, + 0.85, + 0.381 + ], + "angle": 0, + "content": "3.5. Improved Bezier Palm Creases Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.388, + 0.892, + 0.508 + ], + "angle": 0, + "content": "In the forward stage, only the generator \\( G \\) is used to produce palmprint images from synthetic palm creases, as shown in Fig.2 (b). Motivated by BézierPalm [69], we also adopt the two-level Bézier curves to synthesize palm creases image that contains three principal lines and random wrinkle lines. The parametric control points of the Bézier curve can be adjusted randomly within a preset range to obtain a large number of fake palm creases for virtual ID." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.569 + ], + "angle": 0, + "content": "However, we have observed that randomly adjusted Bézier curves may lead to some unreasonable results. As shown in Fig.4, the layout of some randomly generated creases is quite different from that of the real palmprints." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.57, + 0.892, + 0.855 + ], + "angle": 0, + "content": "As a result, this paper improves the Bézier curves synthesis strategy based on real palmprint prior from the following three aspects. Firstly, we observe and adjust the rough range of the parameter points (i.e., start point, control point, and end point) of three principal lines according to real palmprints. So that the layout of synthetic principal lines becomes more similar to that of real palms. Secondly, we adjust the synthesis rules to generate more wrinkle lines with moderate length and more uniform distribution. Thirdly, a similarity constraint based on RLOC [34] is added, which makes the principal lines of different IDs sufficiently distinguishable. RLOC is a classic palmprint recognition method that can measure the similarity of two creases images. In order to avoid very similar principal lines being generated for different IDs, we filter out some creases images which exceed the RLOC inter-class similarity threshold. We ablate the threshold of RLOC with 0.1, 0.5, 0.9, 0.95 and experimentally set it as 0.9. More details of improved Bézier palm creases can be found in supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Finally, the improved random Bézier curves are input into the generator \\( G \\) to obtain corresponding palmprint images. This generation process can be repeated until a large-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19609" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.435, + 0.108 + ], + "angle": 0, + "content": "scale realistic pseudo-palmprint dataset is established." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.12, + 0.289, + 0.138 + ], + "angle": 0, + "content": "4. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.145, + 0.47, + 0.236 + ], + "angle": 0, + "content": "We adopt the same experimental datasets and Open-set evaluation protocol following BézierPalm [69]. The identities of the training and test set are isolated. TAR(True Acceptance Rate) @FAR(False Accept Rate) is used to evaluate model performance. Details about Open-set and evaluation protocol can be found in supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.245, + 0.182, + 0.26 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.269, + 0.47, + 0.345 + ], + "angle": 0, + "content": "We adopt 13 public datasets in our experiments as in BezierPalm [69], including 3,268 IDs and 59,162 palmprint images. Detailed descriptions of these datasets are shown in Tab.1. We follow the detect-then-crop protocol in [67] to extract the Region Of Interests(ROIs)." + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.356, + 0.449, + 0.562 + ], + "angle": 0, + "content": "
Name#IDs#ImagesDevice
MPD [68]40016,000Phone
TCD [68]60012,000Contactless
IITD [41]4602,601Contactless
CASIA [57]6205,502Contactless
CASIA-MS [29]2007,200Contactless
COEP [2]1671,344Digital camera
MOHI [30]2003,000Phone
WEHI [30]2003,000Web cam
GPDS [21]1002,000Web cam
XJTU_UP [52]20030,000Phone
XJTU_A [52]1141,130CMOS camera
PolyU-MS [66]50024,000Contactless
PolyU(2D+3D) [36]4008,000Web cam
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.103, + 0.562, + 0.444, + 0.576 + ], + "angle": 0, + "content": "Table 1: Details of the 13 public palmprint datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.591, + 0.295, + 0.607 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.471, + 0.797 + ], + "angle": 0, + "content": "Generation Model Training. We generate 4000 identities and 100 samples for each identity by default following BézierPalm [69]. For training the generation model, the weights of \\(\\mathcal{L}_1\\), \\(\\mathcal{L}_D\\) and \\(\\mathcal{L}_{KL}\\) are set as 10.0 1.0 and 0.01 according to [74]. We ablate the weight of \\(\\mathcal{L}_{ID}\\) with 1.0, 5.0, 10.0 and experimentally set it as 5.0. The resolution of input and output images is \\(256 \\times 256\\). The learning rate is 0.0002 in the first 30 epochs and linearly decays to 1e-8 in the last 30 epochs. The generation model is trained using Adam optimizer with parameters (0.5, 0.99). For comparative experiment, we use the source codes of pix2pixHD [61], CycleGAN [73] and BicycleGAN [74] in their original papers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Recognition Model Training. For our recognition model, we use ResNet50 [31] and MobileFaceNet [10] as the backbone with the input resolution of \\(224 \\times 224\\). The model is first pretrained on synthesized data for 25 epochs and then finetuned on real datasets for 50 epochs. For the baseline model, we train the model on real datasets for 50" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.242 + ], + "angle": 0, + "content": "epochs. The feature extractor in ID-aware Loss uses the same training setting as the baseline. We use Arcface [14] with margin \\( m = 0.5 \\) and scale factor \\( s = 48 \\) for the pretraining, finetuning and baseline training supervision. We use the cosine learning rate schedule with a warmup start for one epoch. The maximum learning rate is 1e-2 and the minimum learning rate is 1e-6 for pretraining and finetuning. All recognition models are trained with a mini-batch SGD optimizer. We use 4 NVIDIA Tesla V100 GPUs for training with total batch size of 128." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.892, + 0.303 + ], + "angle": 0, + "content": "It should be emphasized that the generation model, the feature extractor in ID-aware loss, and the recognition model all ensure that the training and test sets are completely isolated." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.316, + 0.706, + 0.333 + ], + "angle": 0, + "content": "5. Experimental Results" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.341, + 0.785, + 0.358 + ], + "angle": 0, + "content": "5.1. Open-set Palmprint Recognition" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.364, + 0.892, + 0.546 + ], + "angle": 0, + "content": "We first test our method under the open-set protocol with two different training and test ratios 1:1 and 1:3 (trainIDs: testIDs = 1634:1632, 818:2448). Details about the \"Open-set\" protocol can be found in supplementary materials. The quantitative results are shown in Tab.2. The TAR v.s. FAR curves of the 1:1 setting are in Fig.5. Our method outperforms BézierPalm by \\(5.09\\%\\) and \\(14.73\\%\\) under 1:1 and 1:3 settings @FAR = 1e-6 using 'MB', which establishes a new state-of-the-art. Our method achieves more significant improvement under 1:3 setting than 1:1 setting, which demonstrates the effectiveness of our method in scenarios with only a small amount of real training data." + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.56, + 0.887, + 0.763 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.763, + 0.892, + 0.807 + ], + "angle": 0, + "content": "Figure 5: TAR@FAR curves of different methods under the open-set 1:1 setting. The backbone of ArcFace, BézierPalm and our method is MobileFaceNet." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.892, + 0.849 + ], + "angle": 0, + "content": "5.2. Palmprint Recognition with Limited Identities" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To further verify the performance of our method with limited real training IDs, we test our method with different sizes of real training IDs and fix the test set under the 1:1" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19610" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.12, + 0.088, + 0.847, + 0.345 + ], + "angle": 0, + "content": "
MethodBackbonetrain : test = 1 : 1train : test = 1 : 3
TAR@1e-3TAR@1e-4TAR@1e-5TAR@1e-6TAR@1e-3TAR@1e-4TAR@1e-5TAR@1e-6
CompCode [40]N/A0.48000.42920.36250.21030.45010.39320.34940.2648
LLDP [43]N/A0.73820.67620.52220.12470.73720.67850.61710.2108
BOCV [28]N/A0.49300.45150.39560.21030.45270.39750.35270.2422
RLOC [34]N/A0.64900.58840.44750.14430.64820.58400.52240.3366
DOC [19]N/A0.49750.44090.37120.16670.48860.43290.38890.2007
PalmNet [25]N/A0.71740.66610.59920.10690.72170.66990.61550.2877
C-LMCL [71]MB0.92900.85540.77320.62390.85090.75540.74350.5932
ArcFace [14]MB0.92920.85680.78120.70490.85160.75310.66080.5825
BézierPalm [69]MB0.96400.94380.91020.84370.94070.88610.79340.7012
OursMB0.98020.97140.94860.89460.94960.92670.89690.8485
C-LMCL [71]R500.95450.90270.83170.75340.86010.77010.68210.6254
ArcFace [14]R500.94670.89250.82520.74620.87090.78840.71560.6580
BézierPalm [69]R500.96710.95210.92740.89560.94240.89500.82170.7649
OursR500.98210.97320.95690.93470.95330.93190.90160.8698
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.346, + 0.892, + 0.375 + ], + "angle": 0, + "content": "Table 2: Quantitative performances under the open-set protocol where the performances are evaluated in terms of TAR@FAR. 'MB' represents the MobileFaceNet [10] backbone and 'R50' is resnet50 [31] backbone." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.402, + 0.471, + 0.553 + ], + "angle": 0, + "content": "open-set protocol. We synthesize 4000 identities and 100 samples for each identity in all experiments. As shown in Tab.3, the performance of ArcFace and BézierPalm drops quickly with the reduction of real data, while our method still performs well with few real training IDs. Note that our method with \\(160(10\\%)\\) real IDs even outperforms Arcface with 1600 real IDs. Besides, our method significantly improves the TAR by \\(20.81\\%\\) @FAR=1e-6 against BézierPalm [69] with 80 training IDs, which shows the superiority of our method under few real training IDs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.563, + 0.414, + 0.58 + ], + "angle": 0, + "content": "5.3. Palmprint Recognition at Million Scale" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.587, + 0.47, + 0.738 + ], + "angle": 0, + "content": "In order to verify the effectiveness of our method on large-scale real-world datasets, we test our method on our internal dataset with millions of palmprint images. Our dataset contains 19,286 training identities with 2,871,073 images and 1,000 test identities with 182,732 images. For a fair comparison with BézierPalm, we generate 20,000 IDs with 100 samples in each ID for pretraining. Quantitative results are shown in Tab.4. Our method outperforms ArcFace and BézierPalm with a clear margin, showing its practical application value on large-scale datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.751, + 0.229, + 0.768 + ], + "angle": 0, + "content": "6. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.777, + 0.47, + 0.839 + ], + "angle": 0, + "content": "In this section, we conduct ablation studies to verify different components and design choices of our method. The MobileFaceNet is used as the backbone for all experiments under the same Open-set protocol." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.357, + 0.865 + ], + "angle": 0, + "content": "6.1. Components and design choices" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "The main components and design choices of our method are ID-aware loss, conditional modulation generator and" + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.399, + 0.868, + 0.683 + ], + "angle": 0, + "content": "
Method#IDTAR@FAR=
1e-31e-41e-51e-6
ArcFace0.92920.85680.78120.7049
BézierPalm1,6000.96400.94380.91020.8437
Ours0.98020.97140.94860.8946
ArcFace0.89340.74320.71040.6437
BézierPalm8000.95340.93900.90250.8164
Ours0.97830.96870.93560.8741
ArcFace0.81020.70500.66680.3320
BézierPalm4000.91890.84970.75420.6899
Ours0.95730.93240.88360.8162
ArcFace0.67610.52940.47830.2437
BézierPalm1600.81790.69980.58260.4832
Ours0.93560.86410.80630.7246
ArcFace0.53840.46820.32490.1173
BézierPalm800.65470.55110.44900.3743
Ours0.89740.80920.69470.5824
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.684, + 0.892, + 0.744 + ], + "angle": 0, + "content": "Table 3: Performance under different real training identities. The generation model, feature extractor in ID-aware loss, and the recognition model access the same number of real training identities. The backbone is MobileFaceNet." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "improved strategy for Bezier palm creases synthesis. Tab.5 shows the results of recognition models with or without these components. 'I', 'C', 'S' represent the three components respectively. For baseline without 'C', the normal UNet [49] as in [74] is used to take place of 'C'. ID-aware loss achieves the greatest improvement by \\(11.72\\%\\) @FAR=1e-6 against the baseline, which reflects its advantage for preserving intra-class consistency. The con" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19611" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.111, + 0.119, + 0.2, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.19, + 0.2, + 0.211 + ], + "angle": 0, + "content": "Input Synthetic Palm Creases" + }, + { + "type": "image", + "bbox": [ + 0.201, + 0.089, + 0.367, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.271, + 0.222, + 0.296, + 0.236 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.368, + 0.089, + 0.533, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.435, + 0.223, + 0.459, + 0.238 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.089, + 0.701, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.614, + 0.222, + 0.636, + 0.236 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.089, + 0.871, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.78, + 0.222, + 0.804, + 0.236 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.236, + 0.892, + 0.266 + ], + "angle": 0, + "content": "Figure 6: Generated palmprint images of different methods, (a) pix2pixHD [61], (b) CycleGAN [73], (c) BicycleGAN [74], (d) the proposed method." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.289, + 0.445, + 0.414 + ], + "angle": 0, + "content": "
MethodBackboneTAR@FAR=
1e-61e-71e-81e-9
ArcFace0.97700.95500.92510.8833
BézierPalmMB0.98030.96050.93010.9015
Ours0.98710.96840.94160.9194
ArcFace0.99860.99640.99310.9879
BézierPalmR500.99960.99750.99430.9911
Ours0.99980.99830.99720.9954
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.415, + 0.468, + 0.444 + ], + "angle": 0, + "content": "Table 4: Palmprint recognition performance on million scale dataset." + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.46, + 0.46, + 0.654 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.657, + 0.468, + 0.687 + ], + "angle": 0, + "content": "Figure 7: Diverse synthetic palmprints can be generated by adjusting the input noise vector \\( N(z) \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.715, + 0.468, + 0.79 + ], + "angle": 0, + "content": "ditional modulation generator also significantly improves the performance by \\(4.49\\%\\) @FAR=1e-6, which reflects its advantage for improving the intra-class diversity. The improved Bezier palm creases bring an improvement by \\(1.15\\%\\) @FAR=1e-6." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.391, + 0.817 + ], + "angle": 0, + "content": "6.2. Comparison of Generation Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Three generation methods pix2pixHD [61], CycleGAN [73], BicycleGAN [74] are used for comparison, and all of them are retrained on the same training set with unpaired data. Fig.6 illustrates the generated palmprints of different generation methods. It can be found that pix2pixHD" + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.29, + 0.868, + 0.378 + ], + "angle": 0, + "content": "
ICSTAR@FAR=
1e-31e-41e-51e-6
X(UNet)X0.93990.89050.81640.7210
✓(UNet)X0.96870.95710.90760.8382
✓✓X0.97960.96890.94410.8831
✓✓✓0.98020.97140.94860.8946
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.379, + 0.892, + 0.425 + ], + "angle": 0, + "content": "Table 5: Ablation of different components in our method. 'I', 'C' and 'S' denote ID-aware loss, conditional modulation generator and improved synthetic creases, respectively." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.441, + 0.889, + 0.581 + ], + "angle": 0, + "content": "
MethodFID↓train:test=1:1train:test=1:3
TAR↑@1e-5TAR↑@1e-6TAR↑@1e-5TAR↑@1e-6
ArcFace [14]--0.78120.70490.66080.5825
BézierPalm [69]--0.91020.84370.79340.7012
pix2pixHD [61]97.58010.91560.87340.80520.7244
CycleGAN [73]50.77040.91360.87030.78630.7189
BicycleGAN [74]35.28010.81730.72540.67830.5929
Ours16.47620.94860.89460.89690.8485
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.583, + 0.891, + 0.614 + ], + "angle": 0, + "content": "Table 6: Quantitative recognition results using different generation methods under the open-set protocol." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.779 + ], + "angle": 0, + "content": "and CycleGAN tend to synthesize blurred results. As marked in blue rectangle, BicycleGAN may generate some creases that are inconsistent with the input Bézier curves. Our method can synthesize clearer and sharper principal lines and faithfully preserve the ID information of the input Bézier curves. For intra-class diversity, as shown in Fig.7, our method is able to randomly generate high-fidelity palmprints with diverse lighting and skin types by adjusting the input noise vector \\( N(z) \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Quantitative results are shown in Tab.6. Our method substantially outperforms the existing methods in terms of TAR@FAR. Also, we use FID [8] to evaluate the quality of generated results and our method also effectively decreases the FID score by more than \\(50\\%\\) against other methods. Besides, we reproduced some other generation methods [54, 56] for unpaired image-to-image transfer, including diffusion-based models, but the generated results are unsat" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19612" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.123 + ], + "angle": 0, + "content": "isfying. Related details and more subjective results can be found in supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.133, + 0.462, + 0.15 + ], + "angle": 0, + "content": "6.3. Number of Synthesized Identities and Images" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.156, + 0.471, + 0.309 + ], + "angle": 0, + "content": "In this ablation, we investigate the influence of the number of synthesized identities and images. Specifically, we generate 4000 identities and 100 samples by default, and fix one number and vary the other under the open-set protocol(train:test=1:1). The results are shown in Fig.8. With the increase of \"width\" and \"depth\" of synthetic data, our method can continuously improve the performance of the recognition model and achieve a higher upper bound than BezierPalm. The performance reaches the upper bound with \\(80k\\) synthetic identities and 160 samples per identity." + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.325, + 0.465, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.442, + 0.465, + 0.557 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.557, + 0.47, + 0.603 + ], + "angle": 0, + "content": "Figure 8: TAR@FAR=1e-6 of recognition models pretrained with different numbers of synthetic identities and samples. The backbone is MobileFaceNet." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.634, + 0.196, + 0.649 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.473, + 0.902 + ], + "angle": 0, + "content": "This paper proposed an ID-aware conditional modulation generation model which can produce realistic and diversified palmprint images. Specifically, a conditional modulation generator was designed, which adopted synthetic palm creases as condition, and used encoded Gaussian noise vector to modulate the generated diversity. An ID-aware loss was proposed to preserve the identity information of input palm creases during the unpaired training process. In the forward pseudo-palmprint generation stage, we improved the Bezier curves generation strategy to produce more realistic synthetic palm creases. From experimental results, we can obtain the following findings. Firstly, the generated pseudo-palmprint samples can effectively improve the performance of palmprint recognition models. Secondly, by using the synthetic palmprints, our method can effectively reduce the dependence of real data by \\(90\\%\\). In" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.123 + ], + "angle": 0, + "content": "future work, we hope to implement complete real-data-free palmprint recognition with synthetic data." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.137, + 0.688, + 0.154 + ], + "angle": 0, + "content": "8. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.162, + 0.892, + 0.207 + ], + "angle": 0, + "content": "This work is partly supported by the grants of the National Natural Science Foundation of China, Nos.62076086, 62272142 and 61972129." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.222, + 0.597, + 0.237 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.509, + 0.248, + 0.829, + 0.261 + ], + "angle": 0, + "content": "[1] Amazon one. https://one.amazon.com/." + }, + { + "type": "ref_text", + "bbox": [ + 0.509, + 0.263, + 0.892, + 0.289 + ], + "angle": 0, + "content": "[2] The ceop dataset. https://www.coep.org.in/resources/coeppalmprintdatabase." + }, + { + "type": "ref_text", + "bbox": [ + 0.509, + 0.292, + 0.892, + 0.36 + ], + "angle": 0, + "content": "[3] Denise Almeida, Konstantin Shmarko, and Elizabeth Lomas. 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In Advances in Neural Information Processing Systems, 2017." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19616" + } + ] +] \ No newline at end of file diff --git a/2023/RPG-Palm_ Realistic Pseudo-data Generation for Palmprint Recognition/6f1b3792-7545-4d6e-8992-4404f77414a4_origin.pdf b/2023/RPG-Palm_ Realistic Pseudo-data Generation for Palmprint Recognition/6f1b3792-7545-4d6e-8992-4404f77414a4_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4a79865159de0264c514c8dc2894441ffd476fc6 --- /dev/null +++ b/2023/RPG-Palm_ Realistic Pseudo-data Generation for Palmprint Recognition/6f1b3792-7545-4d6e-8992-4404f77414a4_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7c4f6a14819cc372d0d95d1009982e33dbd79e3effa8a6eb336836fa38438592 +size 3499149 diff --git a/2023/RPG-Palm_ Realistic Pseudo-data Generation for Palmprint Recognition/full.md b/2023/RPG-Palm_ Realistic Pseudo-data Generation for Palmprint Recognition/full.md new file mode 100644 index 0000000000000000000000000000000000000000..6ff1791340f9fa119ee4a148361cf2b68fd09636 --- /dev/null +++ b/2023/RPG-Palm_ Realistic Pseudo-data Generation for Palmprint Recognition/full.md @@ -0,0 +1,438 @@ +# RPG-Palm: Realistic Pseudo-data Generation for Palmprint Recognition + +Lei Shen* + +Youtu Lab, Tencent + +Shanghai, China + +shenlei1996@gmail.com + +Jianlong Jin* + +Hefei University of Technology + +Hefei, China + +2022111048@mail.hfut.edu.cn + +Ruixin Zhang + +Youtu Lab, Tencent + +Shanghai, China + +ruixinzhang@tencent.com + +Huaen Li + +Hefei University of Technology + +Hefei, China + +huaenli@mail.hfut.edu.cn + +Kai Zhao + +UCLA + +California, USA + +kz@kaizhao.net + +Yingyi Zhang + +Youtu Lab, Tencent + +Shanghai, China + +sherlyzhang@tencent.com + +Jingyun Zhang + +WeChat Pay Lab33, Tencent + +Shenzhen, China + +naskyzhang@tencent.com + +Shouhong Ding† + +Youtu Lab, Tencent + +Shanghai, China + +ericshding@tencent.com + +Yang Zhao† + +Hefei University of Technology + +Hefei, China + +YZhao@hfut.edu.cn + +Wei Jia† + +Hefei University of Technology + +Hefei, China + +jiawei@hfut.edu.cn + +# Abstract + +Palmprint recently shows great potential in recognition applications as it is a privacy-friendly and stable biometric. However, the lack of large-scale public palmprint datasets limits further research and development of palmprint recognition. In this paper, we propose a novel realistic pseudo-palmprint generation (RPG) model to synthesize palmprints with massive identities. We first introduce a conditional modulation generator to improve the intraclass diversity. Then an identity-aware loss is proposed to ensure identity consistency against unpaired training. We further improve the Bézier palm creases generation strategy to guarantee identity independence. Extensive experimental results demonstrate that synthetic pretraining significantly boosts the recognition model performance. For example, our model improves the state-of-the-art Bézier Palm by more than $5\%$ and $14\%$ in terms of TAR@FAR=1e-6 under the 1:1 and 1:3 Open-set protocol. When accessing only $10\%$ of the real training data, our method still outperforms ArcFace with $100\%$ real training data, indicating that we are closer to real-data-free palmprint recognition. + +# 1. Introduction + +Palmprint is an excellent biometric in terms of privacy, willingness, convenience, and security. Since the palmprint locates on the inner side of the palm, obtaining the palmprint without one's permission is nearly impossible, which is more privacy-friendliness over the face. Compared to iris and fingerprints, palmprint has fewer usage restrictions, which makes palmprint more user-friendly. Furthermore, Palmprints and palm veins can be collected simultaneously to form a highly secure dual-modal system. + +Due to these advantages, big companies such as Amazon [1] and Tencent [69] begin to apply palmprint recognition in their payment services. However, for the same reason, palmprints are rare in public and expensive to collect. To our best knowledge, publicly available datasets [2, 21, 29, 30, 36, 41, 52, 57, 68] only contain thousands of identities and tens of thousands of images in total. Meanwhile, face recognition has several million-level publicly available datasets [4, 9, 27, 38, 44, 62] that contain tens to hundreds of thousands of identities. The lack of large-scale public dataset seriously inhibits the research on palmprint recognition. + +To solve this problem, one way is to collect a large-scale palmprint dataset. However, this way is very time- + +![](images/e7c68c9c6f70d258629d13f6986ba984a0f7b6d9e69a90dc8d0899e9ac595b98.jpg) +Figure 1: Synthetic Bezier palm creases are used as the identity control condition to guide the generator to produce diverse synthetic data. Recognition models are pretrained with pseudo-data and then finetuned on real data, achieving significant performance boosts. Besides, even if only accessing $10\%$ of the real training data for generation and recognition model, our method still gets comparable performance to $100\%$ of real data direct training. + +consuming and expensive. In addition, collecting biometric data causes more and more privacy and ethical concerns [7] and is strictly restricted by legislation in many countries. Another way is to augment the training dataset with synthetic palmprints. To better benefit palmprint recognition applications, the synthetic method should support generating massive identities with inter-class and intra-class diversity, and the gap between synthetic palmprints and real palmprints should be small. + +Recently, BézierPalm [69] synthesizes fake palmprint images by generating palmprint creases with several parameterized Bézier curves for recognition model pretraining. BézierPalm first shows the ability to output massive new identities without using real palmprints and significantly improves the performance of the palmprint recognition models. However, BézierPalm has some problems unsolved. Firstly, synthetic palmprints have a large gap to real ones, resulting in non-neglectable finetune data requirements in real-world applications. Secondly, the curve parameter difference of each identity cannot ensure inter-class independence when generating massive data. Thirdly, the intra-class diversity only contains small curve deformation in BézierPalm, while real palmprints have diverse textures, lighting and et al. + +In this paper, we propose a realistic pseudo-palmprint + +generation (RPG) model. As shown in Fig.1, the RPG model takes synthetic Bezier palm creases as an identity (ID) condition and outputs realistic pseudo-palmprints with a bidirectional mapping from the Gaussian noise domain to the palmprints domain. Since there is no correspondence between synthetic Bezier palm creases and real palmprints, the generation model can only use unpaired data and will lose intra-class identity consistency easily during training. To solve this problem, we introduce an identity-aware loss that restrains the identity consistency between palmprints generated from the same Bezier palm creases. In addition, we design a conditional modulation generator to generate diversified intra-class textures and lighting conditions using a latent control vector encoded from random noises. To further reduce the distribution gap between synthetic palm creases and real-world palmprints, we refined the synthetic palmprint creases generation strategy with a more reasonable parameter design and identity independence check. + +The contributions of this paper are as follows: + +- We propose a realistic pseudo-palmprint generation (RPG) model with a conditional modulation generator to improve the intra-class diversity and an ID-aware loss to help the RPG model ensure identity consistency under unpaired training. +- We improve the Bezier palm creases synthetic method to get more reasonable palm creases and independent identities. +- Extensive experimental results on 13 public datasets demonstrate that recognition models pretrained with our synthetic pseudo-palmprints achieve state-of-the-art recognition accuracy. +- With our RPG pretraining, even if accessing only $10\%$ of the real data, the recognition model performance still outperforms $100\%$ real data direct training. Showing we are closer to real-data-free palmprint recognition. + +# 2. Related Work + +# 2.1. Palmprint Recognition Methods + +Palmprint recognition methods can be divided into two categories: traditional-based and deep-learning based [18]. Traditional methods extract various kinds of local or global features to make different palmprints more discriminative. Local-based methods [19, 28, 34, 40, 43, 57, 70] manually design effective local features for recognition. Global-based methods [3, 20, 32, 42, 51, 59] extract low-dimensional features from the whole image to distinguish different palmprints. Deep Learning based methods [16, 25, 35, 58] train + +modified neural networks to extract features with classification or pair-wise loss [14, 55, 71]. However, the lack of large-scale public palmprint datasets limits the potential of existing palmprint recognition methods. + +# 2.2. Generation Model for Image Transformation + +With the development of image generation models, such as generative adversarial network (GAN)-based models [26, 37] and diffusion-based models [47, 48], image-to-image generation/translation methods have achieved impressive performance [11, 12, 33]. However, many typical models, e.g., conditional generation model pix2pixHD [61], multidomain transformation model StarGAN [12], dual-domain mapping model BicycleGAN [74] and recent conditional diffusion model [50, 60], rely on paired training data, which is unavailable in many applications. Therefore, some unpaired image-to-image translation models have been proposed [39, 54, 64, 72], which usually adopt cycle consistency loss to train the models without paired data. However, these models are not designed for recognition tasks, and thus ignore the ID preservation in the generation process. Overall, there is still a lack of research on generating diversified and realistic palmprints with ID consistency from limited unpaired samples. + +# 2.3. Data generation for Recognition Tasks + +In order to improve the recognition performance, data generation can be used to expand the depth (diversity of each identity) and width (total number of identities) of training data. For example, in face recognition field, several facial image generation methods [15, 24, 45, 46, 65, 22, 23] have been proposed to generate facial samples based on the priors of facial attributes, facial structures and 3D faces [6]. Also, in field of fingerprint recognition, some methods based on hand-crafted or learning-based approaches [5, 17, 63] have been proposed to generate high-fidelity fingerprint images. + +For palm recognition tasks, BezierPalm [69] use Bezier curves to synthesize fake palm creases by changing the Bezier control parameters. PalmGAN [53] improves the cross-domain recognition performances by using CycleGAN to transfer the styles between normal and multispectral palmprints. However, PalmGAN doesn't create virtual identities, and the BezierPalm suffers from the domain gap between palmprint images and geometry curves. By introducing the new generation model and ID-aware loss, our method can expand the inter-class diversity and intra-class diversity of palmprint dataset simultaneously. + +# 3. Method + +# 3.1. Overall Framework + +Fig.2 illustrates the whole framework of the proposed realistic pseudo-palmprint generation (RPG) model, which includes a training stage and a forward palmprint generation stage. In the training phase, palmprint $B$ is first mapped from the palmprint image domain to the latent vector $Q(z|B)$ in the Gaussian noise domain through the encoder $E$ . Then, the generator $G$ utilizes the unpaired palm creases $A$ as condition, and remaps the encoded noise vector $Q(z|B)$ back to the palmprint image domain. In order to increase the diversity and randomness of the generated palmprints, a conditional modulation structure is designed for $G$ , which uses the input noise vector to control the modulation of intermediate features. + +In order to constrain the ID consistency of the generated pseudo palmprints, an ID-aware loss is presented to enforce the generator to maintain the ID information of input palm creases. As shown in Fig.2 (a), a siamese generator $G$ is used to produce another palmprint $B''$ with the same palm creases $A$ . Then, a pretrained palmprint recognition discriminator is used to measure the ID consistency between $B'$ and $B''$ . + +In the forward pseudo-palmprint generation stage, synthetic Bézier creases are input into the generator $G$ to obtain corresponding palmprint images for virtual identities. Motivated by BézierPalm [69], we improve the random Bézier curves generation strategy to obtain a more reasonable layout of principal lines and wrinkle lines. Then, a classic palmprint recognition method RLOC [34] is applied to ensure the inter-class difference. + +In the following, we will introduce the details of generator $G$ , encoder $E$ , ID-aware loss, and the improved Bézier palm creases synthesis strategy. + +# 3.2. Conditional Modulation Palmprint Generator + +The proposed generator $G$ takes Gaussian noise vector as input, palm creases image $A$ as condition, and reproduces the pseudo-palmprint image $B'$ . As a typical image generation task, the common UNet [49] architecture is adopted. The detailed structure of $G$ is illustrated in Fig.3 (a). To generate diversified results, a conditional adaptive instance normalization module (CAdaIN) is introduced to modulate the generated details in each down-block and up-block. + +In the CAdaIN module, the input noise vector $N(z)$ is first encoded into a latent control vector $w(z)$ through two fully-connected (FC) layers. Note that the parameters of these two FC layers are shared for the whole generator $G$ , so that the generated style can be consistent by means of the same $w(z)$ . Then, two other FC layers are used to modulate the mean and variance of intermediate feature maps + +![](images/d6cd1dc5128a85b9460c8fe86a56f8d4d0125447034522d1b81d02acf68bacf6.jpg) +(a) + +![](images/ec0965eb017ddcba28253a0c760e59ca1840a25ba66d1d8350b8040c1d8e16fa.jpg) +(b) + +![](images/a28b25984f8d1eed882a312bd1bb34003e505013327317ad86e293c1316777c3.jpg) +Figure 2: Framework of the proposed realistic pseudo-palmprint generation model, (a) training stage, (b) forward pseudopalmprint generation stage. +(a) + +![](images/933dc0990bc1760dae615ab716cae2353e6abaaed7243905be0d779e29664519.jpg) +(b) +Figure 3: The network structure of the proposed method, (a) structure of generator $G$ , (b) structure of encoder $E$ . + +respectively, which can be calculated as, + +$$ +\boldsymbol {X} _ {o} = f _ {c 1} (w (z)) \boldsymbol {X} _ {i} + f _ {c 2} (w (z)) + \boldsymbol {n} _ {0}, \tag {1} +$$ + +where $X_{i}$ and $X_{o}$ denote the input and output features of CAdaIN, and $f_{c1}, f_{c2}$ represent two FC layers. By using a latent control vector encoded from random noise, the CAdaIN can modulate the features to produce different distributions, resulting in diversified palmprint images. In addition, in order to further improve the diversity, random noise $n_{0}$ with the same spatial resolution as the feature map is added to the modulated features to inject more randomness. + +For producing realistic results, the loss $\mathcal{L}_1$ and adversarial loss $\mathcal{L}_D$ are used to restrain the learning of $G$ , as follows, + +$$ +\mathcal {L} _ {G} = \lambda_ {1} \mathcal {L} _ {1} \left(B, B ^ {\prime}\right) + \lambda_ {2} \mathcal {L} _ {D} \left(B, B ^ {\prime}\right), \tag {2} +$$ + +where $\lambda_{1}$ and $\lambda_{2}$ are weights. The $\mathcal{L}_1$ is a commonly used pixel-wise loss, which can ensure the numerical similarity between the generated image and real palmprint. But note that the palm creases image $A$ is not matched with palmprint $B$ , so that too strong pixel-wise constraint may cause wrong overfitting to the details in $B$ . Hence, adversarial loss $\mathcal{L}_D$ is also used to relax the constraint and restrain the semantic similarity between $B$ and $B'$ . For the discriminator in $\mathcal{L}_D$ , + +we adopt the PatchGAN [13], which determines patch-wise authenticity by mapping the image to a $70 \times 70$ grid. + +# 3.3. Palmprint Encoder + +The encoder $E$ is used to map the palmprint image to the Gaussian noise domain. Its structure is shown in Fig.3 (b), which is a straightforward ResNet structure. The original size of the feature map is $256 \times 256$ , and it gradually decreases to $16 \times 16$ through several residual blocks (RB). Then, a FC layer is used to estimate the target mean $\mu_{Q}$ and variance $\sigma_{Q}^{2}$ from flattened features. Finally, the noise vector $Q(z|B)$ is sampled from Gaussian space $\mathcal{N}(\mu_{Q}, \sigma_{Q}^{2})$ via reparameterization trick [74]. + +In the training stage, we constrain the KL divergence between $Q(z|B) \sim \mathcal{N}(\mu_Q,\sigma_Q^2)$ and noise vector $N(z) \sim \mathcal{N}(0,1)$ sampled from Gaussian space, so that the target domain of $E$ can keep approximating to the standard normal distribution. This loss can be computed as, + +$$ +\mathcal {L} _ {K L} = - \frac {1}{2} \left(1 + \log \sigma_ {Q} ^ {2} - \sigma_ {Q} ^ {2} - \mu_ {Q} ^ {2}\right). \tag {3} +$$ + +In this paper, $E$ and $G$ are combined to learn a domain-to-domain mapping from unpaired training data, instead of using a fully supervised manner. Firstly, this structure can avoid the dependence on manual labeling of paired data. Secondly, conditional bidirectional domain-to-domain mapping can reproduce random and realistic images and keep the information of palm creases condition as well. + +# 3.4. ID-aware Loss + +For training recognition models, the generated palmprints not only need to be diversified, but also have to preserve ID information. For a synthetic palm creases image $A$ , the generated palmprints should have the same ID information. Therefore, an ID-aware loss $\mathcal{L}_{ID}$ is added to restrain the generator. As shown in Fig.2 (a), a siamese generator $G$ is used to produce another palmprint image $B''$ with the same creases $A$ and random noise vector $N(z)$ . Then the $\mathcal{L}_{ID}$ restricts the ID consistency of two generated results of $B'$ and $B''$ , as follows, + +$$ +\mathcal {L} _ {I D} = 1 - \frac {D _ {M B} \left(B ^ {\prime}\right) \cdot D _ {M B} \left(B ^ {\prime \prime}\right)}{\left| \left| D _ {M B} \left(B ^ {\prime}\right) \right| \right| \times \left| \left| D _ {M B} \left(B ^ {\prime \prime}\right) \right| \right|}, \tag {4} +$$ + +where “.” denotes the vector dot product operation, $D_{MB}$ is a pretrained palmprint recognition model using MobileFaceNet [10] and extracts the $512 \times 1$ feature of $B'$ and $B''$ . That is, $\mathcal{L}_{ID}$ calculates cosine similarity between the extracted features of two generated images for the same ID. Owing to the ID-aware loss, increasing the randomness and diversity of the generator will not destroy the intra-class ID consistency. + +The total loss of entire model, as follows, + +$$ +\mathcal {L} _ {\text {t o t a l}} = \lambda_ {D} \mathcal {L} _ {D} + \lambda_ {1} \mathcal {L} _ {1} + \lambda_ {K L} \mathcal {L} _ {K L} + \lambda_ {I D} \mathcal {L} _ {I D}, \tag {5} +$$ + +![](images/9568da3a9c46797694078c9ab589e2f133c13a234d47ef86a5965be3a29d80f6.jpg) +Real Palmprint + +![](images/212acf0840641701b563cc05068d160b838397423273e1a062611cf3ab2dd1ee.jpg) + +![](images/8e3698e83ab49bbe7e890588b2a6ceef9cd945fd3c10558d12a1db1ce2f6e033.jpg) +BézierPalm Creases +Our Improved Bézier Palm Creases + +![](images/04425f16a86dd6df0d8f95985d11b23e7113b972b73aa50faa94e9e8cc591e74.jpg) + +![](images/5e9e9e0b0abccbf0b822c490ef7f0bc03ae2407726d0844d2b227164b33f8d68.jpg) +Figure 4: Examples of some synthetic palm creases in BezierPalm [69] and our method. + +where $\mathcal{L}_D$ denotes GAN loss, $\mathcal{L}_1$ denotes absolute error loss, $\mathcal{L}_{KL}$ denotes KL divergence loss, and $\mathcal{L}_{ID}$ denotes ID-aware loss. We will add the total loss in final version. + +# 3.5. Improved Bezier Palm Creases Synthesis + +In the forward stage, only the generator $G$ is used to produce palmprint images from synthetic palm creases, as shown in Fig.2 (b). Motivated by BézierPalm [69], we also adopt the two-level Bézier curves to synthesize palm creases image that contains three principal lines and random wrinkle lines. The parametric control points of the Bézier curve can be adjusted randomly within a preset range to obtain a large number of fake palm creases for virtual ID. + +However, we have observed that randomly adjusted Bézier curves may lead to some unreasonable results. As shown in Fig.4, the layout of some randomly generated creases is quite different from that of the real palmprints. + +As a result, this paper improves the Bézier curves synthesis strategy based on real palmprint prior from the following three aspects. Firstly, we observe and adjust the rough range of the parameter points (i.e., start point, control point, and end point) of three principal lines according to real palmprints. So that the layout of synthetic principal lines becomes more similar to that of real palms. Secondly, we adjust the synthesis rules to generate more wrinkle lines with moderate length and more uniform distribution. Thirdly, a similarity constraint based on RLOC [34] is added, which makes the principal lines of different IDs sufficiently distinguishable. RLOC is a classic palmprint recognition method that can measure the similarity of two creases images. In order to avoid very similar principal lines being generated for different IDs, we filter out some creases images which exceed the RLOC inter-class similarity threshold. We ablate the threshold of RLOC with 0.1, 0.5, 0.9, 0.95 and experimentally set it as 0.9. More details of improved Bézier palm creases can be found in supplementary materials. + +Finally, the improved random Bézier curves are input into the generator $G$ to obtain corresponding palmprint images. This generation process can be repeated until a large- + +scale realistic pseudo-palmprint dataset is established. + +# 4. Experimental Settings + +We adopt the same experimental datasets and Open-set evaluation protocol following BézierPalm [69]. The identities of the training and test set are isolated. TAR(True Acceptance Rate) @FAR(False Accept Rate) is used to evaluate model performance. Details about Open-set and evaluation protocol can be found in supplementary materials. + +# 4.1. Datasets + +We adopt 13 public datasets in our experiments as in BezierPalm [69], including 3,268 IDs and 59,162 palmprint images. Detailed descriptions of these datasets are shown in Tab.1. We follow the detect-then-crop protocol in [67] to extract the Region Of Interests(ROIs). + +
Name#IDs#ImagesDevice
MPD [68]40016,000Phone
TCD [68]60012,000Contactless
IITD [41]4602,601Contactless
CASIA [57]6205,502Contactless
CASIA-MS [29]2007,200Contactless
COEP [2]1671,344Digital camera
MOHI [30]2003,000Phone
WEHI [30]2003,000Web cam
GPDS [21]1002,000Web cam
XJTU_UP [52]20030,000Phone
XJTU_A [52]1141,130CMOS camera
PolyU-MS [66]50024,000Contactless
PolyU(2D+3D) [36]4008,000Web cam
+ +Table 1: Details of the 13 public palmprint datasets. + +# 4.2. Implementation Details + +Generation Model Training. We generate 4000 identities and 100 samples for each identity by default following BézierPalm [69]. For training the generation model, the weights of $\mathcal{L}_1$ , $\mathcal{L}_D$ and $\mathcal{L}_{KL}$ are set as 10.0 1.0 and 0.01 according to [74]. We ablate the weight of $\mathcal{L}_{ID}$ with 1.0, 5.0, 10.0 and experimentally set it as 5.0. The resolution of input and output images is $256 \times 256$ . The learning rate is 0.0002 in the first 30 epochs and linearly decays to 1e-8 in the last 30 epochs. The generation model is trained using Adam optimizer with parameters (0.5, 0.99). For comparative experiment, we use the source codes of pix2pixHD [61], CycleGAN [73] and BicycleGAN [74] in their original papers. + +Recognition Model Training. For our recognition model, we use ResNet50 [31] and MobileFaceNet [10] as the backbone with the input resolution of $224 \times 224$ . The model is first pretrained on synthesized data for 25 epochs and then finetuned on real datasets for 50 epochs. For the baseline model, we train the model on real datasets for 50 + +epochs. The feature extractor in ID-aware Loss uses the same training setting as the baseline. We use Arcface [14] with margin $m = 0.5$ and scale factor $s = 48$ for the pretraining, finetuning and baseline training supervision. We use the cosine learning rate schedule with a warmup start for one epoch. The maximum learning rate is 1e-2 and the minimum learning rate is 1e-6 for pretraining and finetuning. All recognition models are trained with a mini-batch SGD optimizer. We use 4 NVIDIA Tesla V100 GPUs for training with total batch size of 128. + +It should be emphasized that the generation model, the feature extractor in ID-aware loss, and the recognition model all ensure that the training and test sets are completely isolated. + +# 5. Experimental Results + +# 5.1. Open-set Palmprint Recognition + +We first test our method under the open-set protocol with two different training and test ratios 1:1 and 1:3 (trainIDs: testIDs = 1634:1632, 818:2448). Details about the "Open-set" protocol can be found in supplementary materials. The quantitative results are shown in Tab.2. The TAR v.s. FAR curves of the 1:1 setting are in Fig.5. Our method outperforms BézierPalm by $5.09\%$ and $14.73\%$ under 1:1 and 1:3 settings @FAR = 1e-6 using 'MB', which establishes a new state-of-the-art. Our method achieves more significant improvement under 1:3 setting than 1:1 setting, which demonstrates the effectiveness of our method in scenarios with only a small amount of real training data. + +![](images/a6739fa4c450f8c01fc7a8bdaba2579a688cfebfa07b7940d86d07d07d442df5.jpg) +Figure 5: TAR@FAR curves of different methods under the open-set 1:1 setting. The backbone of ArcFace, BézierPalm and our method is MobileFaceNet. + +# 5.2. Palmprint Recognition with Limited Identities + +To further verify the performance of our method with limited real training IDs, we test our method with different sizes of real training IDs and fix the test set under the 1:1 + +
MethodBackbonetrain : test = 1 : 1train : test = 1 : 3
TAR@1e-3TAR@1e-4TAR@1e-5TAR@1e-6TAR@1e-3TAR@1e-4TAR@1e-5TAR@1e-6
CompCode [40]N/A0.48000.42920.36250.21030.45010.39320.34940.2648
LLDP [43]N/A0.73820.67620.52220.12470.73720.67850.61710.2108
BOCV [28]N/A0.49300.45150.39560.21030.45270.39750.35270.2422
RLOC [34]N/A0.64900.58840.44750.14430.64820.58400.52240.3366
DOC [19]N/A0.49750.44090.37120.16670.48860.43290.38890.2007
PalmNet [25]N/A0.71740.66610.59920.10690.72170.66990.61550.2877
C-LMCL [71]MB0.92900.85540.77320.62390.85090.75540.74350.5932
ArcFace [14]MB0.92920.85680.78120.70490.85160.75310.66080.5825
BézierPalm [69]MB0.96400.94380.91020.84370.94070.88610.79340.7012
OursMB0.98020.97140.94860.89460.94960.92670.89690.8485
C-LMCL [71]R500.95450.90270.83170.75340.86010.77010.68210.6254
ArcFace [14]R500.94670.89250.82520.74620.87090.78840.71560.6580
BézierPalm [69]R500.96710.95210.92740.89560.94240.89500.82170.7649
OursR500.98210.97320.95690.93470.95330.93190.90160.8698
+ +open-set protocol. We synthesize 4000 identities and 100 samples for each identity in all experiments. As shown in Tab.3, the performance of ArcFace and BézierPalm drops quickly with the reduction of real data, while our method still performs well with few real training IDs. Note that our method with $160(10\%)$ real IDs even outperforms Arcface with 1600 real IDs. Besides, our method significantly improves the TAR by $20.81\%$ @FAR=1e-6 against BézierPalm [69] with 80 training IDs, which shows the superiority of our method under few real training IDs. + +# 5.3. Palmprint Recognition at Million Scale + +In order to verify the effectiveness of our method on large-scale real-world datasets, we test our method on our internal dataset with millions of palmprint images. Our dataset contains 19,286 training identities with 2,871,073 images and 1,000 test identities with 182,732 images. For a fair comparison with BézierPalm, we generate 20,000 IDs with 100 samples in each ID for pretraining. Quantitative results are shown in Tab.4. Our method outperforms ArcFace and BézierPalm with a clear margin, showing its practical application value on large-scale datasets. + +# 6. Ablation Study + +In this section, we conduct ablation studies to verify different components and design choices of our method. The MobileFaceNet is used as the backbone for all experiments under the same Open-set protocol. + +# 6.1. Components and design choices + +The main components and design choices of our method are ID-aware loss, conditional modulation generator and + +Table 2: Quantitative performances under the open-set protocol where the performances are evaluated in terms of TAR@FAR. 'MB' represents the MobileFaceNet [10] backbone and 'R50' is resnet50 [31] backbone. + +
Method#IDTAR@FAR=
1e-31e-41e-51e-6
ArcFace0.92920.85680.78120.7049
BézierPalm1,6000.96400.94380.91020.8437
Ours0.98020.97140.94860.8946
ArcFace0.89340.74320.71040.6437
BézierPalm8000.95340.93900.90250.8164
Ours0.97830.96870.93560.8741
ArcFace0.81020.70500.66680.3320
BézierPalm4000.91890.84970.75420.6899
Ours0.95730.93240.88360.8162
ArcFace0.67610.52940.47830.2437
BézierPalm1600.81790.69980.58260.4832
Ours0.93560.86410.80630.7246
ArcFace0.53840.46820.32490.1173
BézierPalm800.65470.55110.44900.3743
Ours0.89740.80920.69470.5824
+ +Table 3: Performance under different real training identities. The generation model, feature extractor in ID-aware loss, and the recognition model access the same number of real training identities. The backbone is MobileFaceNet. + +improved strategy for Bezier palm creases synthesis. Tab.5 shows the results of recognition models with or without these components. 'I', 'C', 'S' represent the three components respectively. For baseline without 'C', the normal UNet [49] as in [74] is used to take place of 'C'. ID-aware loss achieves the greatest improvement by $11.72\%$ @FAR=1e-6 against the baseline, which reflects its advantage for preserving intra-class consistency. The con + +![](images/3e943a01d8c85b3db10ec0b1c12c0fd69cb39afbd456f5d05f16fe848cf396cf.jpg) +Input Synthetic Palm Creases + +![](images/b61da0dbb0af2677cefdea6362db662053a61eed02e529e500546ce414eddb3f.jpg) +(a) + +![](images/2af07fb735b4511a652a62082cfcde84f68ab6e0ed76d5a7f4e12ba341a25168.jpg) +(b) +Figure 6: Generated palmprint images of different methods, (a) pix2pixHD [61], (b) CycleGAN [73], (c) BicycleGAN [74], (d) the proposed method. + +![](images/d518ded8a104cfbcd562df09e347300eb3b3949a41cb57099b4bb31fec73cb87.jpg) +(c) + +![](images/b6c7a0a501528e55f44686a478fedededdd6d2ead50a0ae9dd71ffcf4324ba98.jpg) +(d) + +
MethodBackboneTAR@FAR=
1e-61e-71e-81e-9
ArcFace0.97700.95500.92510.8833
BézierPalmMB0.98030.96050.93010.9015
Ours0.98710.96840.94160.9194
ArcFace0.99860.99640.99310.9879
BézierPalmR500.99960.99750.99430.9911
Ours0.99980.99830.99720.9954
+ +![](images/1a5ea341115d6091b8c65c2407330264eef157ddec3ecb0a577b6e71a1d9b046.jpg) +Figure 7: Diverse synthetic palmprints can be generated by adjusting the input noise vector $N(z)$ . + +ditional modulation generator also significantly improves the performance by $4.49\%$ @FAR=1e-6, which reflects its advantage for improving the intra-class diversity. The improved Bezier palm creases bring an improvement by $1.15\%$ @FAR=1e-6. + +# 6.2. Comparison of Generation Methods + +Three generation methods pix2pixHD [61], CycleGAN [73], BicycleGAN [74] are used for comparison, and all of them are retrained on the same training set with unpaired data. Fig.6 illustrates the generated palmprints of different generation methods. It can be found that pix2pixHD + +Table 4: Palmprint recognition performance on million scale dataset. + +
ICSTAR@FAR=
1e-31e-41e-51e-6
X(UNet)X0.93990.89050.81640.7210
✓(UNet)X0.96870.95710.90760.8382
✓✓X0.97960.96890.94410.8831
✓✓✓0.98020.97140.94860.8946
+ +Table 5: Ablation of different components in our method. 'I', 'C' and 'S' denote ID-aware loss, conditional modulation generator and improved synthetic creases, respectively. + +
MethodFID↓train:test=1:1train:test=1:3
TAR↑@1e-5TAR↑@1e-6TAR↑@1e-5TAR↑@1e-6
ArcFace [14]--0.78120.70490.66080.5825
BézierPalm [69]--0.91020.84370.79340.7012
pix2pixHD [61]97.58010.91560.87340.80520.7244
CycleGAN [73]50.77040.91360.87030.78630.7189
BicycleGAN [74]35.28010.81730.72540.67830.5929
Ours16.47620.94860.89460.89690.8485
+ +Table 6: Quantitative recognition results using different generation methods under the open-set protocol. + +and CycleGAN tend to synthesize blurred results. As marked in blue rectangle, BicycleGAN may generate some creases that are inconsistent with the input Bézier curves. Our method can synthesize clearer and sharper principal lines and faithfully preserve the ID information of the input Bézier curves. For intra-class diversity, as shown in Fig.7, our method is able to randomly generate high-fidelity palmprints with diverse lighting and skin types by adjusting the input noise vector $N(z)$ . + +Quantitative results are shown in Tab.6. Our method substantially outperforms the existing methods in terms of TAR@FAR. Also, we use FID [8] to evaluate the quality of generated results and our method also effectively decreases the FID score by more than $50\%$ against other methods. Besides, we reproduced some other generation methods [54, 56] for unpaired image-to-image transfer, including diffusion-based models, but the generated results are unsat + +isfying. Related details and more subjective results can be found in supplementary material. + +# 6.3. Number of Synthesized Identities and Images + +In this ablation, we investigate the influence of the number of synthesized identities and images. Specifically, we generate 4000 identities and 100 samples by default, and fix one number and vary the other under the open-set protocol(train:test=1:1). The results are shown in Fig.8. With the increase of "width" and "depth" of synthetic data, our method can continuously improve the performance of the recognition model and achieve a higher upper bound than BezierPalm. The performance reaches the upper bound with $80k$ synthetic identities and 160 samples per identity. + +![](images/1ac102ce60b6e200fc27ff174294da7ae2a6d23d8d9571a9691eeaf6d83089b4.jpg) + +![](images/15f05bbdd3b695e4556e419208310951d587e3c3f5ec78b84e4668061418fb15.jpg) +Figure 8: TAR@FAR=1e-6 of recognition models pretrained with different numbers of synthetic identities and samples. The backbone is MobileFaceNet. + +# 7. Conclusion + +This paper proposed an ID-aware conditional modulation generation model which can produce realistic and diversified palmprint images. Specifically, a conditional modulation generator was designed, which adopted synthetic palm creases as condition, and used encoded Gaussian noise vector to modulate the generated diversity. An ID-aware loss was proposed to preserve the identity information of input palm creases during the unpaired training process. In the forward pseudo-palmprint generation stage, we improved the Bezier curves generation strategy to produce more realistic synthetic palm creases. From experimental results, we can obtain the following findings. Firstly, the generated pseudo-palmprint samples can effectively improve the performance of palmprint recognition models. Secondly, by using the synthetic palmprints, our method can effectively reduce the dependence of real data by $90\%$ . In + +future work, we hope to implement complete real-data-free palmprint recognition with synthetic data. + +# 8. Acknowledgements + +This work is partly supported by the grants of the National Natural Science Foundation of China, Nos.62076086, 62272142 and 61972129. + +# References + +[1] Amazon one. https://one.amazon.com/. +[2] The ceop dataset. https://www.coep.org.in/resources/coeppalmprintdatabase. +[3] Denise Almeida, Konstantin Shmarko, and Elizabeth Lomas. 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However, the lack of large-scale public palmprint datasets limits further research and development of palmprint recognition. In this paper, we propose a novel realistic pseudo-palmprint generation (RPG) model to synthesize palmprints with massive identities. We first introduce a conditional modulation generator to improve the intraclass diversity. Then an identity-aware loss is proposed to ensure identity consistency against unpaired training. We further improve the Bézier palm creases generation strategy to guarantee identity independence. Extensive experimental results demonstrate that synthetic pretraining significantly boosts the recognition model performance. For example, our model improves the state-of-the-art Bézier Palm by more than " + }, + { + "bbox": [ + 46, + 430, + 289, + 670 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 430, + 289, + 670 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 430, + 289, + 670 + ], + "type": "inline_equation", + "content": "14\\%" + }, + { + "bbox": [ + 46, + 430, + 289, + 670 + ], + "type": "text", + "content": " in terms of TAR@FAR=1e-6 under the 1:1 and 1:3 Open-set protocol. When accessing only " + }, + { + "bbox": [ + 46, + 430, + 289, + 670 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 430, + 289, + 670 + ], + "type": "text", + "content": " of the real training data, our method still outperforms ArcFace with " + }, + { + "bbox": [ + 46, + 430, + 289, + 670 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 430, + 289, + 670 + ], + "type": "text", + "content": " real training data, indicating that we are closer to real-data-free palmprint recognition." + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 307, + 412, + 386, + 425 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 412, + 386, + 425 + ], + "spans": [ + { + "bbox": [ + 307, + 412, + 386, + 425 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 304, + 434, + 545, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 542 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 542 + ], + "type": "text", + "content": "Palmprint is an excellent biometric in terms of privacy, willingness, convenience, and security. Since the palmprint locates on the inner side of the palm, obtaining the palmprint without one's permission is nearly impossible, which is more privacy-friendliness over the face. Compared to iris and fingerprints, palmprint has fewer usage restrictions, which makes palmprint more user-friendly. Furthermore, Palmprints and palm veins can be collected simultaneously to form a highly secure dual-modal system." + } + ] + } + ], + "index": 46 + }, + { + "bbox": [ + 304, + 544, + 545, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 686 + ], + "type": "text", + "content": "Due to these advantages, big companies such as Amazon [1] and Tencent [69] begin to apply palmprint recognition in their payment services. However, for the same reason, palmprints are rare in public and expensive to collect. To our best knowledge, publicly available datasets [2, 21, 29, 30, 36, 41, 52, 57, 68] only contain thousands of identities and tens of thousands of images in total. Meanwhile, face recognition has several million-level publicly available datasets [4, 9, 27, 38, 44, 62] that contain tens to hundreds of thousands of identities. The lack of large-scale public dataset seriously inhibits the research on palmprint recognition." + } + ] + } + ], + "index": 47 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "To solve this problem, one way is to collect a large-scale palmprint dataset. However, this way is very time-" + } + ] + } + ], + "index": 48 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 126, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 126, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 126, + 703 + ], + "type": "text", + "content": "*Equal contribution." + } + ] + } + ], + "index": 49 + }, + { + "bbox": [ + 59, + 703, + 138, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 138, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 138, + 712 + ], + "type": "text", + "content": "† Corresponding authors." + } + ] + } + ], + "index": 50 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19605" + } + ] + } + ], + "index": 52 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 70, + 269, + 286 + ], + "blocks": [ + { + "bbox": [ + 60, + 70, + 269, + 286 + ], + "lines": [ + { + "bbox": [ + 60, + 70, + 269, + 286 + ], + "spans": [ + { + "bbox": [ + 60, + 70, + 269, + 286 + ], + "type": "image", + "image_path": "e7c68c9c6f70d258629d13f6986ba984a0f7b6d9e69a90dc8d0899e9ac595b98.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 293, + 289, + 390 + ], + "lines": [ + { + "bbox": [ + 46, + 293, + 289, + 390 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 289, + 390 + ], + "type": "text", + "content": "Figure 1: Synthetic Bezier palm creases are used as the identity control condition to guide the generator to produce diverse synthetic data. Recognition models are pretrained with pseudo-data and then finetuned on real data, achieving significant performance boosts. Besides, even if only accessing " + }, + { + "bbox": [ + 46, + 293, + 289, + 390 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 293, + 289, + 390 + ], + "type": "text", + "content": " of the real training data for generation and recognition model, our method still gets comparable performance to " + }, + { + "bbox": [ + 46, + 293, + 289, + 390 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 293, + 289, + 390 + ], + "type": "text", + "content": " of real data direct training." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 413, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 519 + ], + "type": "text", + "content": "consuming and expensive. In addition, collecting biometric data causes more and more privacy and ethical concerns [7] and is strictly restricted by legislation in many countries. Another way is to augment the training dataset with synthetic palmprints. To better benefit palmprint recognition applications, the synthetic method should support generating massive identities with inter-class and intra-class diversity, and the gap between synthetic palmprints and real palmprints should be small." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "text", + "content": "Recently, BézierPalm [69] synthesizes fake palmprint images by generating palmprint creases with several parameterized Bézier curves for recognition model pretraining. BézierPalm first shows the ability to output massive new identities without using real palmprints and significantly improves the performance of the palmprint recognition models. However, BézierPalm has some problems unsolved. Firstly, synthetic palmprints have a large gap to real ones, resulting in non-neglectable finetune data requirements in real-world applications. Secondly, the curve parameter difference of each identity cannot ensure inter-class independence when generating massive data. Thirdly, the intra-class diversity only contains small curve deformation in BézierPalm, while real palmprints have diverse textures, lighting and et al." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 701, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 288, + 714 + ], + "type": "text", + "content": "In this paper, we propose a realistic pseudo-palmprint" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 289 + ], + "type": "text", + "content": "generation (RPG) model. As shown in Fig.1, the RPG model takes synthetic Bezier palm creases as an identity (ID) condition and outputs realistic pseudo-palmprints with a bidirectional mapping from the Gaussian noise domain to the palmprints domain. Since there is no correspondence between synthetic Bezier palm creases and real palmprints, the generation model can only use unpaired data and will lose intra-class identity consistency easily during training. To solve this problem, we introduce an identity-aware loss that restrains the identity consistency between palmprints generated from the same Bezier palm creases. In addition, we design a conditional modulation generator to generate diversified intra-class textures and lighting conditions using a latent control vector encoded from random noises. To further reduce the distribution gap between synthetic palm creases and real-world palmprints, we refined the synthetic palmprint creases generation strategy with a more reasonable parameter design and identity independence check." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 318, + 297, + 504, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 297, + 504, + 308 + ], + "spans": [ + { + "bbox": [ + 318, + 297, + 504, + 308 + ], + "type": "text", + "content": "The contributions of this paper are as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 316, + 319, + 545, + 552 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 316, + 319, + 545, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 319, + 545, + 379 + ], + "spans": [ + { + "bbox": [ + 316, + 319, + 545, + 379 + ], + "type": "text", + "content": "- We propose a realistic pseudo-palmprint generation (RPG) model with a conditional modulation generator to improve the intra-class diversity and an ID-aware loss to help the RPG model ensure identity consistency under unpaired training." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 316, + 388, + 545, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 388, + 545, + 424 + ], + "spans": [ + { + "bbox": [ + 316, + 388, + 545, + 424 + ], + "type": "text", + "content": "- We improve the Bezier palm creases synthetic method to get more reasonable palm creases and independent identities." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 316, + 435, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 435, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 316, + 435, + 545, + 483 + ], + "type": "text", + "content": "- Extensive experimental results on 13 public datasets demonstrate that recognition models pretrained with our synthetic pseudo-palmprints achieve state-of-the-art recognition accuracy." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 316, + 494, + 545, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 494, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 316, + 494, + 545, + 552 + ], + "type": "text", + "content": "- With our RPG pretraining, even if accessing only " + }, + { + "bbox": [ + 316, + 494, + 545, + 552 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 316, + 494, + 545, + 552 + ], + "type": "text", + "content": " of the real data, the recognition model performance still outperforms " + }, + { + "bbox": [ + 316, + 494, + 545, + 552 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 316, + 494, + 545, + 552 + ], + "type": "text", + "content": " real data direct training. Showing we are closer to real-data-free palmprint recognition." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 566, + 392, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 566, + 392, + 578 + ], + "spans": [ + { + "bbox": [ + 306, + 566, + 392, + 578 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 586, + 479, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 479, + 600 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 479, + 600 + ], + "type": "text", + "content": "2.1. Palmprint Recognition Methods" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "content": "Palmprint recognition methods can be divided into two categories: traditional-based and deep-learning based [18]. Traditional methods extract various kinds of local or global features to make different palmprints more discriminative. Local-based methods [19, 28, 34, 40, 43, 57, 70] manually design effective local features for recognition. Global-based methods [3, 20, 32, 42, 51, 59] extract low-dimensional features from the whole image to distinguish different palmprints. Deep Learning based methods [16, 25, 35, 58] train" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19606" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": "modified neural networks to extract features with classification or pair-wise loss [14, 55, 71]. However, the lack of large-scale public palmprint datasets limits the potential of existing palmprint recognition methods." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 148, + 280, + 162 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 148, + 280, + 162 + ], + "spans": [ + { + "bbox": [ + 47, + 148, + 280, + 162 + ], + "type": "text", + "content": "2.2. Generation Model for Image Transformation" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 174, + 287, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 174, + 287, + 390 + ], + "spans": [ + { + "bbox": [ + 46, + 174, + 287, + 390 + ], + "type": "text", + "content": "With the development of image generation models, such as generative adversarial network (GAN)-based models [26, 37] and diffusion-based models [47, 48], image-to-image generation/translation methods have achieved impressive performance [11, 12, 33]. However, many typical models, e.g., conditional generation model pix2pixHD [61], multidomain transformation model StarGAN [12], dual-domain mapping model BicycleGAN [74] and recent conditional diffusion model [50, 60], rely on paired training data, which is unavailable in many applications. Therefore, some unpaired image-to-image translation models have been proposed [39, 54, 64, 72], which usually adopt cycle consistency loss to train the models without paired data. However, these models are not designed for recognition tasks, and thus ignore the ID preservation in the generation process. Overall, there is still a lack of research on generating diversified and realistic palmprints with ID consistency from limited unpaired samples." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 418, + 250, + 431 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 418, + 250, + 431 + ], + "spans": [ + { + "bbox": [ + 47, + 418, + 250, + 431 + ], + "type": "text", + "content": "2.3. Data generation for Recognition Tasks" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 444, + 287, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 444, + 287, + 576 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 287, + 576 + ], + "type": "text", + "content": "In order to improve the recognition performance, data generation can be used to expand the depth (diversity of each identity) and width (total number of identities) of training data. For example, in face recognition field, several facial image generation methods [15, 24, 45, 46, 65, 22, 23] have been proposed to generate facial samples based on the priors of facial attributes, facial structures and 3D faces [6]. Also, in field of fingerprint recognition, some methods based on hand-crafted or learning-based approaches [5, 17, 63] have been proposed to generate high-fidelity fingerprint images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": "For palm recognition tasks, BezierPalm [69] use Bezier curves to synthesize fake palm creases by changing the Bezier control parameters. PalmGAN [53] improves the cross-domain recognition performances by using CycleGAN to transfer the styles between normal and multispectral palmprints. However, PalmGAN doesn't create virtual identities, and the BezierPalm suffers from the domain gap between palmprint images and geometry curves. By introducing the new generation model and ID-aware loss, our method can expand the inter-class diversity and intra-class diversity of palmprint dataset simultaneously." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 71, + 362, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 362, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 362, + 84 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 92, + 422, + 105 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 92, + 422, + 105 + ], + "spans": [ + { + "bbox": [ + 306, + 92, + 422, + 105 + ], + "type": "text", + "content": "3.1. Overall Framework" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 112, + 545, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 112, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 304, + 112, + 545, + 266 + ], + "type": "text", + "content": "Fig.2 illustrates the whole framework of the proposed realistic pseudo-palmprint generation (RPG) model, which includes a training stage and a forward palmprint generation stage. In the training phase, palmprint " + }, + { + "bbox": [ + 304, + 112, + 545, + 266 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 112, + 545, + 266 + ], + "type": "text", + "content": " is first mapped from the palmprint image domain to the latent vector " + }, + { + "bbox": [ + 304, + 112, + 545, + 266 + ], + "type": "inline_equation", + "content": "Q(z|B)" + }, + { + "bbox": [ + 304, + 112, + 545, + 266 + ], + "type": "text", + "content": " in the Gaussian noise domain through the encoder " + }, + { + "bbox": [ + 304, + 112, + 545, + 266 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 112, + 545, + 266 + ], + "type": "text", + "content": ". Then, the generator " + }, + { + "bbox": [ + 304, + 112, + 545, + 266 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 112, + 545, + 266 + ], + "type": "text", + "content": " utilizes the unpaired palm creases " + }, + { + "bbox": [ + 304, + 112, + 545, + 266 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 112, + 545, + 266 + ], + "type": "text", + "content": " as condition, and remaps the encoded noise vector " + }, + { + "bbox": [ + 304, + 112, + 545, + 266 + ], + "type": "inline_equation", + "content": "Q(z|B)" + }, + { + "bbox": [ + 304, + 112, + 545, + 266 + ], + "type": "text", + "content": " back to the palmprint image domain. In order to increase the diversity and randomness of the generated palmprints, a conditional modulation structure is designed for " + }, + { + "bbox": [ + 304, + 112, + 545, + 266 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 112, + 545, + 266 + ], + "type": "text", + "content": ", which uses the input noise vector to control the modulation of intermediate features." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 269, + 545, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 269, + 545, + 364 + ], + "spans": [ + { + "bbox": [ + 304, + 269, + 545, + 364 + ], + "type": "text", + "content": "In order to constrain the ID consistency of the generated pseudo palmprints, an ID-aware loss is presented to enforce the generator to maintain the ID information of input palm creases. As shown in Fig.2 (a), a siamese generator " + }, + { + "bbox": [ + 304, + 269, + 545, + 364 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 269, + 545, + 364 + ], + "type": "text", + "content": " is used to produce another palmprint " + }, + { + "bbox": [ + 304, + 269, + 545, + 364 + ], + "type": "inline_equation", + "content": "B''" + }, + { + "bbox": [ + 304, + 269, + 545, + 364 + ], + "type": "text", + "content": " with the same palm creases " + }, + { + "bbox": [ + 304, + 269, + 545, + 364 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 269, + 545, + 364 + ], + "type": "text", + "content": ". Then, a pretrained palmprint recognition discriminator is used to measure the ID consistency between " + }, + { + "bbox": [ + 304, + 269, + 545, + 364 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 304, + 269, + 545, + 364 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 269, + 545, + 364 + ], + "type": "inline_equation", + "content": "B''" + }, + { + "bbox": [ + 304, + 269, + 545, + 364 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 367, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 367, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 367, + 545, + 461 + ], + "type": "text", + "content": "In the forward pseudo-palmprint generation stage, synthetic Bézier creases are input into the generator " + }, + { + "bbox": [ + 304, + 367, + 545, + 461 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 367, + 545, + 461 + ], + "type": "text", + "content": " to obtain corresponding palmprint images for virtual identities. Motivated by BézierPalm [69], we improve the random Bézier curves generation strategy to obtain a more reasonable layout of principal lines and wrinkle lines. Then, a classic palmprint recognition method RLOC [34] is applied to ensure the inter-class difference." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 464, + 545, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 464, + 545, + 501 + ], + "spans": [ + { + "bbox": [ + 304, + 464, + 545, + 501 + ], + "type": "text", + "content": "In the following, we will introduce the details of generator " + }, + { + "bbox": [ + 304, + 464, + 545, + 501 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 464, + 545, + 501 + ], + "type": "text", + "content": ", encoder " + }, + { + "bbox": [ + 304, + 464, + 545, + 501 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 464, + 545, + 501 + ], + "type": "text", + "content": ", ID-aware loss, and the improved Bézier palm creases synthesis strategy." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 512, + 543, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 512, + 543, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 512, + 543, + 525 + ], + "type": "text", + "content": "3.2. Conditional Modulation Palmprint Generator" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 533, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 628 + ], + "type": "text", + "content": "The proposed generator " + }, + { + "bbox": [ + 304, + 533, + 545, + 628 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 533, + 545, + 628 + ], + "type": "text", + "content": " takes Gaussian noise vector as input, palm creases image " + }, + { + "bbox": [ + 304, + 533, + 545, + 628 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 533, + 545, + 628 + ], + "type": "text", + "content": " as condition, and reproduces the pseudo-palmprint image " + }, + { + "bbox": [ + 304, + 533, + 545, + 628 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 304, + 533, + 545, + 628 + ], + "type": "text", + "content": ". As a typical image generation task, the common UNet [49] architecture is adopted. The detailed structure of " + }, + { + "bbox": [ + 304, + 533, + 545, + 628 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 533, + 545, + 628 + ], + "type": "text", + "content": " is illustrated in Fig.3 (a). To generate diversified results, a conditional adaptive instance normalization module (CAdaIN) is introduced to modulate the generated details in each down-block and up-block." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "In the CAdaIN module, the input noise vector " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "N(z)" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " is first encoded into a latent control vector " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "w(z)" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " through two fully-connected (FC) layers. Note that the parameters of these two FC layers are shared for the whole generator " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": ", so that the generated style can be consistent by means of the same " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "w(z)" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": ". 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+ "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "text", + "content": " denote the input and output features of CAdaIN, and " + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "inline_equation", + "content": "f_{c1}, f_{c2}" + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "text", + "content": " represent two FC layers. By using a latent control vector encoded from random noise, the CAdaIN can modulate the features to produce different distributions, resulting in diversified palmprint images. In addition, in order to further improve the diversity, random noise " + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "inline_equation", + "content": "n_{0}" + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "text", + "content": " with the same spatial resolution as the feature map is added to the modulated features to inject more randomness." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 567, + 544, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 567, + 544, + 591 + ], + "spans": [ + { + "bbox": [ + 306, + 567, + 544, + 591 + ], + "type": "text", + "content": "For producing realistic results, the loss " + }, + { + "bbox": [ + 306, + 567, + 544, + 591 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 306, + 567, + 544, + 591 + ], + "type": "text", + "content": " and adversarial loss " + }, + { + "bbox": [ + 306, + 567, + 544, + 591 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_D" + }, + { + "bbox": [ + 306, + 567, + 544, + 591 + ], + "type": "text", + "content": " are used to restrain the learning of " + }, + { + "bbox": [ + 306, + 567, + 544, + 591 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 306, + 567, + 544, + 591 + ], + "type": "text", + "content": ", as follows," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 349, + 597, + 544, + 611 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 597, + 544, + 611 + ], + "spans": [ + { + "bbox": [ + 349, + 597, + 544, + 611 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {G} = \\lambda_ {1} \\mathcal {L} _ {1} \\left(B, B ^ {\\prime}\\right) + \\lambda_ {2} \\mathcal {L} _ {D} \\left(B, B ^ {\\prime}\\right), \\tag {2}", + "image_path": "fe65a5cf03fc818ab3056314904ba2cb39e5b6936839a2ab037678396aec8b45.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " are weights. The " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " is a commonly used pixel-wise loss, which can ensure the numerical similarity between the generated image and real palmprint. But note that the palm creases image " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " is not matched with palmprint " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": ", so that too strong pixel-wise constraint may cause wrong overfitting to the details in " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": ". Hence, adversarial loss " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_D" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " is also used to relax the constraint and restrain the semantic similarity between " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": ". For the discriminator in " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_D" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19608" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "content": "we adopt the PatchGAN [13], which determines patch-wise authenticity by mapping the image to a " + }, + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "inline_equation", + "content": "70 \\times 70" + }, + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "content": " grid." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 102, + 160, + 114 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 102, + 160, + 114 + ], + "spans": [ + { + "bbox": [ + 47, + 102, + 160, + 114 + ], + "type": "text", + "content": "3.3. Palmprint Encoder" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 121, + 287, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 287, + 229 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 287, + 229 + ], + "type": "text", + "content": "The encoder " + }, + { + "bbox": [ + 46, + 121, + 287, + 229 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 121, + 287, + 229 + ], + "type": "text", + "content": " is used to map the palmprint image to the Gaussian noise domain. Its structure is shown in Fig.3 (b), which is a straightforward ResNet structure. The original size of the feature map is " + }, + { + "bbox": [ + 46, + 121, + 287, + 229 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 121, + 287, + 229 + ], + "type": "text", + "content": ", and it gradually decreases to " + }, + { + "bbox": [ + 46, + 121, + 287, + 229 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 46, + 121, + 287, + 229 + ], + "type": "text", + "content": " through several residual blocks (RB). Then, a FC layer is used to estimate the target mean " + }, + { + "bbox": [ + 46, + 121, + 287, + 229 + ], + "type": "inline_equation", + "content": "\\mu_{Q}" + }, + { + "bbox": [ + 46, + 121, + 287, + 229 + ], + "type": "text", + "content": " and variance " + }, + { + "bbox": [ + 46, + 121, + 287, + 229 + ], + "type": "inline_equation", + "content": "\\sigma_{Q}^{2}" + }, + { + "bbox": [ + 46, + 121, + 287, + 229 + ], + "type": "text", + "content": " from flattened features. Finally, the noise vector " + }, + { + "bbox": [ + 46, + 121, + 287, + 229 + ], + "type": "inline_equation", + "content": "Q(z|B)" + }, + { + "bbox": [ + 46, + 121, + 287, + 229 + ], + "type": "text", + "content": " is sampled from Gaussian space " + }, + { + "bbox": [ + 46, + 121, + 287, + 229 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\mu_{Q}, \\sigma_{Q}^{2})" + }, + { + "bbox": [ + 46, + 121, + 287, + 229 + ], + "type": "text", + "content": " via reparameterization trick [74]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "text", + "content": "In the training stage, we constrain the KL divergence between " + }, + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "inline_equation", + "content": "Q(z|B) \\sim \\mathcal{N}(\\mu_Q,\\sigma_Q^2)" + }, + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "text", + "content": " and noise vector " + }, + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "inline_equation", + "content": "N(z) \\sim \\mathcal{N}(0,1)" + }, + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "text", + "content": " sampled from Gaussian space, so that the target domain of " + }, + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "text", + "content": " can keep approximating to the standard normal distribution. This loss can be computed as," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 88, + 295, + 287, + 318 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 295, + 287, + 318 + ], + "spans": [ + { + "bbox": [ + 88, + 295, + 287, + 318 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {K L} = - \\frac {1}{2} \\left(1 + \\log \\sigma_ {Q} ^ {2} - \\sigma_ {Q} ^ {2} - \\mu_ {Q} ^ {2}\\right). \\tag {3}", + "image_path": "d2d84608d278f12457bcdb5b39df5c51b96ce828952b7813a7870ea4f1d04788.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 323, + 287, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 287, + 406 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 287, + 406 + ], + "type": "text", + "content": "In this paper, " + }, + { + "bbox": [ + 46, + 323, + 287, + 406 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 323, + 287, + 406 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 323, + 287, + 406 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 323, + 287, + 406 + ], + "type": "text", + "content": " are combined to learn a domain-to-domain mapping from unpaired training data, instead of using a fully supervised manner. Firstly, this structure can avoid the dependence on manual labeling of paired data. Secondly, conditional bidirectional domain-to-domain mapping can reproduce random and realistic images and keep the information of palm creases condition as well." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 413, + 138, + 424 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 413, + 138, + 424 + ], + "spans": [ + { + "bbox": [ + 47, + 413, + 138, + 424 + ], + "type": "text", + "content": "3.4. ID-aware Loss" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "text", + "content": "For training recognition models, the generated palmprints not only need to be diversified, but also have to preserve ID information. For a synthetic palm creases image " + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "text", + "content": ", the generated palmprints should have the same ID information. Therefore, an ID-aware loss " + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ID}" + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "text", + "content": " is added to restrain the generator. As shown in Fig.2 (a), a siamese generator " + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "text", + "content": " is used to produce another palmprint image " + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "inline_equation", + "content": "B''" + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "text", + "content": " with the same creases " + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "text", + "content": " and random noise vector " + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "inline_equation", + "content": "N(z)" + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "text", + "content": ". Then the " + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ID}" + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "text", + "content": " restricts the ID consistency of two generated results of " + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "inline_equation", + "content": "B''" + }, + { + "bbox": [ + 46, + 431, + 287, + 550 + ], + "type": "text", + "content": ", as follows," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 78, + 555, + 287, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 555, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 78, + 555, + 287, + 582 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {I D} = 1 - \\frac {D _ {M B} \\left(B ^ {\\prime}\\right) \\cdot D _ {M B} \\left(B ^ {\\prime \\prime}\\right)}{\\left| \\left| D _ {M B} \\left(B ^ {\\prime}\\right) \\right| \\right| \\times \\left| \\left| D _ {M B} \\left(B ^ {\\prime \\prime}\\right) \\right| \\right|}, \\tag {4}", + "image_path": "673b75ce7d296499305158eaf70284cf1e2c6b6cd40efdb99781217ab3d87394.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 586, + 287, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 586, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 46, + 586, + 287, + 681 + ], + "type": "text", + "content": "where “.” denotes the vector dot product operation, " + }, + { + "bbox": [ + 46, + 586, + 287, + 681 + ], + "type": "inline_equation", + "content": "D_{MB}" + }, + { + "bbox": [ + 46, + 586, + 287, + 681 + ], + "type": "text", + "content": " is a pretrained palmprint recognition model using MobileFaceNet [10] and extracts the " + }, + { + "bbox": [ + 46, + 586, + 287, + 681 + ], + "type": "inline_equation", + "content": "512 \\times 1" + }, + { + "bbox": [ + 46, + 586, + 287, + 681 + ], + "type": "text", + "content": " feature of " + }, + { + "bbox": [ + 46, + 586, + 287, + 681 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 46, + 586, + 287, + 681 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 586, + 287, + 681 + ], + "type": "inline_equation", + "content": "B''" + }, + { + "bbox": [ + 46, + 586, + 287, + 681 + ], + "type": "text", + "content": ". That is, " + }, + { + "bbox": [ + 46, + 586, + 287, + 681 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ID}" + }, + { + "bbox": [ + 46, + 586, + 287, + 681 + ], + "type": "text", + "content": " calculates cosine similarity between the extracted features of two generated images for the same ID. Owing to the ID-aware loss, increasing the randomness and diversity of the generator will not destroy the intra-class ID consistency." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 59, + 682, + 228, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 682, + 228, + 693 + ], + "spans": [ + { + "bbox": [ + 59, + 682, + 228, + 693 + ], + "type": "text", + "content": "The total loss of entire model, as follows," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {D} \\mathcal {L} _ {D} + \\lambda_ {1} \\mathcal {L} _ {1} + \\lambda_ {K L} \\mathcal {L} _ {K L} + \\lambda_ {I D} \\mathcal {L} _ {I D}, \\tag {5}", + "image_path": "396a85ef48fd4409a74eff488390a76217ab0336b415710d53c77f576e6e8c2b.jpg" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 420, + 182 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 420, + 182 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 420, + 182 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 420, + 182 + ], + "type": "image", + "image_path": "9568da3a9c46797694078c9ab589e2f133c13a234d47ef86a5965be3a29d80f6.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 337, + 188, + 387, + 198 + ], + "lines": [ + { + "bbox": [ + 337, + 188, + 387, + 198 + ], + "spans": [ + { + "bbox": [ + 337, + 188, + 387, + 198 + ], + "type": "text", + "content": "Real Palmprint" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 421, + 71, + 476, + 125 + ], + "blocks": [ + { + "bbox": [ + 421, + 71, + 476, + 125 + ], + "lines": [ + { + 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0, + "type": "image_caption" + }, + { + "bbox": [ + 471, + 184, + 537, + 200 + ], + "lines": [ + { + "bbox": [ + 471, + 184, + 537, + 200 + ], + "spans": [ + { + "bbox": [ + 471, + 184, + 537, + 200 + ], + "type": "text", + "content": "Our Improved Bézier Palm Creases" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 477, + 72, + 531, + 125 + ], + "blocks": [ + { + "bbox": [ + 477, + 72, + 531, + 125 + ], + "lines": [ + { + "bbox": [ + 477, + 72, + 531, + 125 + ], + "spans": [ + { + "bbox": [ + 477, + 72, + 531, + 125 + ], + "type": "image", + "image_path": "04425f16a86dd6df0d8f95985d11b23e7113b972b73aa50faa94e9e8cc591e74.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 477, + 127, + 531, + 182 + ], + "blocks": [ + { + "bbox": [ + 477, + 127, + 531, + 182 + ], + "lines": [ + { + "bbox": [ + 477, + 127, + 531, + 182 + ], + "spans": [ + { + "bbox": [ + 477, + 127, + 531, + 182 + ], + "type": "image", + "image_path": "5e9e9e0b0abccbf0b822c490ef7f0bc03ae2407726d0844d2b227164b33f8d68.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 201, + 545, + 224 + ], + "lines": [ + { + "bbox": [ + 306, + 201, + 545, + 224 + ], + "spans": [ + { + "bbox": [ + 306, + 201, + 545, + 224 + ], + "type": "text", + "content": "Figure 4: Examples of some synthetic palm creases in BezierPalm [69] and our method." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 245, + 545, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 245, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 305, + 245, + 545, + 281 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 245, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_D" + }, + { + "bbox": [ + 305, + 245, + 545, + 281 + ], + "type": "text", + "content": " denotes GAN loss, " + }, + { + "bbox": [ + 305, + 245, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 305, + 245, + 545, + 281 + ], + "type": "text", + "content": " denotes absolute error loss, " + }, + { + "bbox": [ + 305, + 245, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{KL}" + }, + { + "bbox": [ + 305, + 245, + 545, + 281 + ], + "type": "text", + "content": " denotes KL divergence loss, and " + }, + { + "bbox": [ + 305, + 245, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ID}" + }, + { + "bbox": [ + 305, + 245, + 545, + 281 + ], + "type": "text", + "content": " denotes ID-aware loss. We will add the total loss in final version." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 289, + 520, + 301 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 289, + 520, + 301 + ], + "spans": [ + { + "bbox": [ + 306, + 289, + 520, + 301 + ], + "type": "text", + "content": "3.5. Improved Bezier Palm Creases Synthesis" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 307, + 545, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 307, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 545, + 402 + ], + "type": "text", + "content": "In the forward stage, only the generator " + }, + { + "bbox": [ + 304, + 307, + 545, + 402 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 307, + 545, + 402 + ], + "type": "text", + "content": " is used to produce palmprint images from synthetic palm creases, as shown in Fig.2 (b). Motivated by BézierPalm [69], we also adopt the two-level Bézier curves to synthesize palm creases image that contains three principal lines and random wrinkle lines. The parametric control points of the Bézier curve can be adjusted randomly within a preset range to obtain a large number of fake palm creases for virtual ID." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 403, + 545, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 450 + ], + "type": "text", + "content": "However, we have observed that randomly adjusted Bézier curves may lead to some unreasonable results. As shown in Fig.4, the layout of some randomly generated creases is quite different from that of the real palmprints." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 451, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 451, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 545, + 677 + ], + "type": "text", + "content": "As a result, this paper improves the Bézier curves synthesis strategy based on real palmprint prior from the following three aspects. Firstly, we observe and adjust the rough range of the parameter points (i.e., start point, control point, and end point) of three principal lines according to real palmprints. So that the layout of synthetic principal lines becomes more similar to that of real palms. Secondly, we adjust the synthesis rules to generate more wrinkle lines with moderate length and more uniform distribution. Thirdly, a similarity constraint based on RLOC [34] is added, which makes the principal lines of different IDs sufficiently distinguishable. RLOC is a classic palmprint recognition method that can measure the similarity of two creases images. In order to avoid very similar principal lines being generated for different IDs, we filter out some creases images which exceed the RLOC inter-class similarity threshold. We ablate the threshold of RLOC with 0.1, 0.5, 0.9, 0.95 and experimentally set it as 0.9. More details of improved Bézier palm creases can be found in supplementary materials." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Finally, the improved random Bézier curves are input into the generator " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " to obtain corresponding palmprint images. This generation process can be repeated until a large-" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19609" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 266, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 266, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 266, + 85 + ], + "type": "text", + "content": "scale realistic pseudo-palmprint dataset is established." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 95, + 176, + 109 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 95, + 176, + 109 + ], + "spans": [ + { + "bbox": [ + 47, + 95, + 176, + 109 + ], + "type": "text", + "content": "4. Experimental Settings" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 114, + 287, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 114, + 287, + 186 + ], + "spans": [ + { + "bbox": [ + 47, + 114, + 287, + 186 + ], + "type": "text", + "content": "We adopt the same experimental datasets and Open-set evaluation protocol following BézierPalm [69]. The identities of the training and test set are isolated. TAR(True Acceptance Rate) @FAR(False Accept Rate) is used to evaluate model performance. Details about Open-set and evaluation protocol can be found in supplementary materials." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 194, + 111, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 194, + 111, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 194, + 111, + 205 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 213, + 287, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 213, + 287, + 273 + ], + "spans": [ + { + "bbox": [ + 47, + 213, + 287, + 273 + ], + "type": "text", + "content": "We adopt 13 public datasets in our experiments as in BezierPalm [69], including 3,268 IDs and 59,162 palmprint images. Detailed descriptions of these datasets are shown in Tab.1. We follow the detect-then-crop protocol in [67] to extract the Region Of Interests(ROIs)." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 63, + 281, + 274, + 445 + ], + "blocks": [ + { + "bbox": [ + 63, + 281, + 274, + 445 + ], + "lines": [ + { + "bbox": [ + 63, + 281, + 274, + 445 + ], + "spans": [ + { + "bbox": [ + 63, + 281, + 274, + 445 + ], + "type": "table", + "html": "
Name#IDs#ImagesDevice
MPD [68]40016,000Phone
TCD [68]60012,000Contactless
IITD [41]4602,601Contactless
CASIA [57]6205,502Contactless
CASIA-MS [29]2007,200Contactless
COEP [2]1671,344Digital camera
MOHI [30]2003,000Phone
WEHI [30]2003,000Web cam
GPDS [21]1002,000Web cam
XJTU_UP [52]20030,000Phone
XJTU_A [52]1141,130CMOS camera
PolyU-MS [66]50024,000Contactless
PolyU(2D+3D) [36]4008,000Web cam
", + "image_path": "e11cb4946b2ca8ea63f579c399e9bc8e493322304b3e537ec00e783606f73502.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 63, + 445, + 271, + 456 + ], + "lines": [ + { + "bbox": [ + 63, + 445, + 271, + 456 + ], + "spans": [ + { + "bbox": [ + 63, + 445, + 271, + 456 + ], + "type": "text", + "content": "Table 1: Details of the 13 public palmprint datasets." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 468, + 180, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 468, + 180, + 480 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 180, + 480 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 486, + 288, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 288, + 631 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 288, + 631 + ], + "type": "text", + "content": "Generation Model Training. We generate 4000 identities and 100 samples for each identity by default following BézierPalm [69]. For training the generation model, the weights of " + }, + { + "bbox": [ + 46, + 486, + 288, + 631 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 46, + 486, + 288, + 631 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 486, + 288, + 631 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_D" + }, + { + "bbox": [ + 46, + 486, + 288, + 631 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 486, + 288, + 631 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{KL}" + }, + { + "bbox": [ + 46, + 486, + 288, + 631 + ], + "type": "text", + "content": " are set as 10.0 1.0 and 0.01 according to [74]. We ablate the weight of " + }, + { + "bbox": [ + 46, + 486, + 288, + 631 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ID}" + }, + { + "bbox": [ + 46, + 486, + 288, + 631 + ], + "type": "text", + "content": " with 1.0, 5.0, 10.0 and experimentally set it as 5.0. The resolution of input and output images is " + }, + { + "bbox": [ + 46, + 486, + 288, + 631 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 486, + 288, + 631 + ], + "type": "text", + "content": ". The learning rate is 0.0002 in the first 30 epochs and linearly decays to 1e-8 in the last 30 epochs. The generation model is trained using Adam optimizer with parameters (0.5, 0.99). For comparative experiment, we use the source codes of pix2pixHD [61], CycleGAN [73] and BicycleGAN [74] in their original papers." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "content": "Recognition Model Training. For our recognition model, we use ResNet50 [31] and MobileFaceNet [10] as the backbone with the input resolution of " + }, + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "content": ". The model is first pretrained on synthesized data for 25 epochs and then finetuned on real datasets for 50 epochs. For the baseline model, we train the model on real datasets for 50" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": "epochs. The feature extractor in ID-aware Loss uses the same training setting as the baseline. We use Arcface [14] with margin " + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "inline_equation", + "content": "m = 0.5" + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": " and scale factor " + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "inline_equation", + "content": "s = 48" + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": " for the pretraining, finetuning and baseline training supervision. We use the cosine learning rate schedule with a warmup start for one epoch. The maximum learning rate is 1e-2 and the minimum learning rate is 1e-6 for pretraining and finetuning. All recognition models are trained with a mini-batch SGD optimizer. We use 4 NVIDIA Tesla V100 GPUs for training with total batch size of 128." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "text", + "content": "It should be emphasized that the generation model, the feature extractor in ID-aware loss, and the recognition model all ensure that the training and test sets are completely isolated." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 250, + 432, + 263 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 250, + 432, + 263 + ], + "spans": [ + { + "bbox": [ + 306, + 250, + 432, + 263 + ], + "type": "text", + "content": "5. Experimental Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 270, + 480, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 270, + 480, + 283 + ], + "spans": [ + { + "bbox": [ + 306, + 270, + 480, + 283 + ], + "type": "text", + "content": "5.1. Open-set Palmprint Recognition" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 288, + 545, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 288, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 304, + 288, + 545, + 432 + ], + "type": "text", + "content": "We first test our method under the open-set protocol with two different training and test ratios 1:1 and 1:3 (trainIDs: testIDs = 1634:1632, 818:2448). Details about the \"Open-set\" protocol can be found in supplementary materials. The quantitative results are shown in Tab.2. The TAR v.s. FAR curves of the 1:1 setting are in Fig.5. Our method outperforms BézierPalm by " + }, + { + "bbox": [ + 304, + 288, + 545, + 432 + ], + "type": "inline_equation", + "content": "5.09\\%" + }, + { + "bbox": [ + 304, + 288, + 545, + 432 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 288, + 545, + 432 + ], + "type": "inline_equation", + "content": "14.73\\%" + }, + { + "bbox": [ + 304, + 288, + 545, + 432 + ], + "type": "text", + "content": " under 1:1 and 1:3 settings @FAR = 1e-6 using 'MB', which establishes a new state-of-the-art. Our method achieves more significant improvement under 1:3 setting than 1:1 setting, which demonstrates the effectiveness of our method in scenarios with only a small amount of real training data." + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 309, + 443, + 542, + 604 + ], + "blocks": [ + { + "bbox": [ + 309, + 443, + 542, + 604 + ], + "lines": [ + { + "bbox": [ + 309, + 443, + 542, + 604 + ], + "spans": [ + { + "bbox": [ + 309, + 443, + 542, + 604 + ], + "type": "image", + "image_path": "a6739fa4c450f8c01fc7a8bdaba2579a688cfebfa07b7940d86d07d07d442df5.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 604, + 545, + 639 + ], + "lines": [ + { + "bbox": [ + 304, + 604, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 545, + 639 + ], + "type": "text", + "content": "Figure 5: TAR@FAR curves of different methods under the open-set 1:1 setting. The backbone of ArcFace, BézierPalm and our method is MobileFaceNet." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 659, + 545, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 545, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 545, + 672 + ], + "type": "text", + "content": "5.2. Palmprint Recognition with Limited Identities" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "To further verify the performance of our method with limited real training IDs, we test our method with different sizes of real training IDs and fix the test set under the 1:1" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19610" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 69, + 518, + 273 + ], + "blocks": [ + { + "bbox": [ + 73, + 69, + 518, + 273 + ], + "lines": [ + { + "bbox": [ + 73, + 69, + 518, + 273 + ], + "spans": [ + { + "bbox": [ + 73, + 69, + 518, + 273 + ], + "type": "table", + "html": "
MethodBackbonetrain : test = 1 : 1train : test = 1 : 3
TAR@1e-3TAR@1e-4TAR@1e-5TAR@1e-6TAR@1e-3TAR@1e-4TAR@1e-5TAR@1e-6
CompCode [40]N/A0.48000.42920.36250.21030.45010.39320.34940.2648
LLDP [43]N/A0.73820.67620.52220.12470.73720.67850.61710.2108
BOCV [28]N/A0.49300.45150.39560.21030.45270.39750.35270.2422
RLOC [34]N/A0.64900.58840.44750.14430.64820.58400.52240.3366
DOC [19]N/A0.49750.44090.37120.16670.48860.43290.38890.2007
PalmNet [25]N/A0.71740.66610.59920.10690.72170.66990.61550.2877
C-LMCL [71]MB0.92900.85540.77320.62390.85090.75540.74350.5932
ArcFace [14]MB0.92920.85680.78120.70490.85160.75310.66080.5825
BézierPalm [69]MB0.96400.94380.91020.84370.94070.88610.79340.7012
OursMB0.98020.97140.94860.89460.94960.92670.89690.8485
C-LMCL [71]R500.95450.90270.83170.75340.86010.77010.68210.6254
ArcFace [14]R500.94670.89250.82520.74620.87090.78840.71560.6580
BézierPalm [69]R500.96710.95210.92740.89560.94240.89500.82170.7649
OursR500.98210.97320.95690.93470.95330.93190.90160.8698
", + "image_path": "492b258f461d877d6d1c6c30f7a3e6a9b68d7dd95258f2bc8de309e4444cf9d9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 318, + 288, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 318, + 288, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 318, + 288, + 437 + ], + "type": "text", + "content": "open-set protocol. We synthesize 4000 identities and 100 samples for each identity in all experiments. As shown in Tab.3, the performance of ArcFace and BézierPalm drops quickly with the reduction of real data, while our method still performs well with few real training IDs. Note that our method with " + }, + { + "bbox": [ + 46, + 318, + 288, + 437 + ], + "type": "inline_equation", + "content": "160(10\\%)" + }, + { + "bbox": [ + 46, + 318, + 288, + 437 + ], + "type": "text", + "content": " real IDs even outperforms Arcface with 1600 real IDs. Besides, our method significantly improves the TAR by " + }, + { + "bbox": [ + 46, + 318, + 288, + 437 + ], + "type": "inline_equation", + "content": "20.81\\%" + }, + { + "bbox": [ + 46, + 318, + 288, + 437 + ], + "type": "text", + "content": " @FAR=1e-6 against BézierPalm [69] with 80 training IDs, which shows the superiority of our method under few real training IDs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 445, + 253, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 445, + 253, + 459 + ], + "spans": [ + { + "bbox": [ + 47, + 445, + 253, + 459 + ], + "type": "text", + "content": "5.3. Palmprint Recognition at Million Scale" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 464, + 287, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 584 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 584 + ], + "type": "text", + "content": "In order to verify the effectiveness of our method on large-scale real-world datasets, we test our method on our internal dataset with millions of palmprint images. Our dataset contains 19,286 training identities with 2,871,073 images and 1,000 test identities with 182,732 images. For a fair comparison with BézierPalm, we generate 20,000 IDs with 100 samples in each ID for pretraining. Quantitative results are shown in Tab.4. Our method outperforms ArcFace and BézierPalm with a clear margin, showing its practical application value on large-scale datasets." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 594, + 140, + 608 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 594, + 140, + 608 + ], + "spans": [ + { + "bbox": [ + 47, + 594, + 140, + 608 + ], + "type": "text", + "content": "6. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 615, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 615, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 615, + 287, + 664 + ], + "type": "text", + "content": "In this section, we conduct ablation studies to verify different components and design choices of our method. The MobileFaceNet is used as the backbone for all experiments under the same Open-set protocol." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 671, + 218, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 218, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 218, + 685 + ], + "type": "text", + "content": "6.1. Components and design choices" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "The main components and design choices of our method are ID-aware loss, conditional modulation generator and" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 319, + 316, + 531, + 540 + ], + "blocks": [ + { + "bbox": [ + 47, + 274, + 545, + 297 + ], + "lines": [ + { + "bbox": [ + 47, + 274, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 47, + 274, + 545, + 297 + ], + "type": "text", + "content": "Table 2: Quantitative performances under the open-set protocol where the performances are evaluated in terms of TAR@FAR. 'MB' represents the MobileFaceNet [10] backbone and 'R50' is resnet50 [31] backbone." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 319, + 316, + 531, + 540 + ], + "lines": [ + { + "bbox": [ + 319, + 316, + 531, + 540 + ], + "spans": [ + { + "bbox": [ + 319, + 316, + 531, + 540 + ], + "type": "table", + "html": "
Method#IDTAR@FAR=
1e-31e-41e-51e-6
ArcFace0.92920.85680.78120.7049
BézierPalm1,6000.96400.94380.91020.8437
Ours0.98020.97140.94860.8946
ArcFace0.89340.74320.71040.6437
BézierPalm8000.95340.93900.90250.8164
Ours0.97830.96870.93560.8741
ArcFace0.81020.70500.66680.3320
BézierPalm4000.91890.84970.75420.6899
Ours0.95730.93240.88360.8162
ArcFace0.67610.52940.47830.2437
BézierPalm1600.81790.69980.58260.4832
Ours0.93560.86410.80630.7246
ArcFace0.53840.46820.32490.1173
BézierPalm800.65470.55110.44900.3743
Ours0.89740.80920.69470.5824
", + "image_path": "a03825e6b469c31ed48c26ee70f99ae45d42d2ed40dc26d3a014e0d8a55e25ea.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 541, + 545, + 589 + ], + "lines": [ + { + "bbox": [ + 305, + 541, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 305, + 541, + 545, + 589 + ], + "type": "text", + "content": "Table 3: Performance under different real training identities. The generation model, feature extractor in ID-aware loss, and the recognition model access the same number of real training identities. The backbone is MobileFaceNet." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "text", + "content": "improved strategy for Bezier palm creases synthesis. Tab.5 shows the results of recognition models with or without these components. 'I', 'C', 'S' represent the three components respectively. For baseline without 'C', the normal UNet [49] as in [74] is used to take place of 'C'. ID-aware loss achieves the greatest improvement by " + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "11.72\\%" + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "text", + "content": " @FAR=1e-6 against the baseline, which reflects its advantage for preserving intra-class consistency. The con" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19611" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 67, + 94, + 122, + 148 + ], + "blocks": [ + { + "bbox": [ + 67, + 94, + 122, + 148 + ], + "lines": [ + { + "bbox": [ + 67, + 94, + 122, + 148 + ], + "spans": [ + { + "bbox": [ + 67, + 94, + 122, + 148 + ], + "type": "image", + "image_path": "3e943a01d8c85b3db10ec0b1c12c0fd69cb39afbd456f5d05f16fe848cf396cf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 69, + 150, + 122, + 167 + ], + "lines": [ + { + "bbox": [ + 69, + 150, + 122, + 167 + ], + "spans": [ + { + "bbox": [ + 69, + 150, + 122, + 167 + ], + "type": "text", + "content": "Input Synthetic Palm Creases" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 123, + 70, + 224, + 172 + ], + "blocks": [ + { + "bbox": [ + 123, + 70, + 224, + 172 + ], + "lines": [ + { + "bbox": [ + 123, + 70, + 224, + 172 + ], + "spans": [ + { + "bbox": [ + 123, + 70, + 224, + 172 + ], + "type": "image", + "image_path": "b61da0dbb0af2677cefdea6362db662053a61eed02e529e500546ce414eddb3f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 165, + 175, + 181, + 186 + ], + "lines": [ + { + "bbox": [ + 165, + 175, + 181, + 186 + ], + "spans": [ + { + "bbox": [ + 165, + 175, + 181, + 186 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 225, + 70, + 326, + 173 + ], + "blocks": [ + { + "bbox": [ + 225, + 70, + 326, + 173 + ], + "lines": [ + { + "bbox": [ + 225, + 70, + 326, + 173 + ], + "spans": [ + { + "bbox": [ + 225, + 70, + 326, + 173 + ], + "type": "image", + "image_path": "2af07fb735b4511a652a62082cfcde84f68ab6e0ed76d5a7f4e12ba341a25168.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 266, + 176, + 280, + 188 + ], + "lines": [ + { + "bbox": [ + 266, + 176, + 280, + 188 + ], + "spans": [ + { + "bbox": [ + 266, + 176, + 280, + 188 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 186, + 545, + 210 + ], + "lines": [ + { + "bbox": [ + 46, + 186, + 545, + 210 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 545, + 210 + ], + "type": "text", + "content": "Figure 6: Generated palmprint images of different methods, (a) pix2pixHD [61], (b) CycleGAN [73], (c) BicycleGAN [74], (d) the proposed method." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 326, + 70, + 429, + 173 + ], + "blocks": [ + { + "bbox": [ + 326, + 70, + 429, + 173 + ], + "lines": [ + { + "bbox": [ + 326, + 70, + 429, + 173 + ], + "spans": [ + { + "bbox": [ + 326, + 70, + 429, + 173 + ], + "type": "image", + "image_path": "d518ded8a104cfbcd562df09e347300eb3b3949a41cb57099b4bb31fec73cb87.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 375, + 175, + 389, + 186 + ], + "lines": [ + { + "bbox": [ + 375, + 175, + 389, + 186 + ], + "spans": [ + { + "bbox": [ + 375, + 175, + 389, + 186 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 430, + 70, + 533, + 173 + ], + "blocks": [ + { + "bbox": [ + 430, + 70, + 533, + 173 + ], + "lines": [ + { + "bbox": [ + 430, + 70, + 533, + 173 + ], + "spans": [ + { + "bbox": [ + 430, + 70, + 533, + 173 + ], + "type": "image", + "image_path": "b6c7a0a501528e55f44686a478fedededdd6d2ead50a0ae9dd71ffcf4324ba98.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 477, + 175, + 492, + 186 + ], + "lines": [ + { + "bbox": [ + 477, + 175, + 492, + 186 + ], + "spans": [ + { + "bbox": [ + 477, + 175, + 492, + 186 + ], + "type": "text", + "content": "(d)" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 61, + 228, + 272, + 327 + ], + "blocks": [ + { + "bbox": [ + 61, + 228, + 272, + 327 + ], + "lines": [ + { + "bbox": [ + 61, + 228, + 272, + 327 + ], + "spans": [ + { + "bbox": [ + 61, + 228, + 272, + 327 + ], + "type": "table", + "html": "
MethodBackboneTAR@FAR=
1e-61e-71e-81e-9
ArcFace0.97700.95500.92510.8833
BézierPalmMB0.98030.96050.93010.9015
Ours0.98710.96840.94160.9194
ArcFace0.99860.99640.99310.9879
BézierPalmR500.99960.99750.99430.9911
Ours0.99980.99830.99720.9954
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ICSTAR@FAR=
1e-31e-41e-51e-6
X(UNet)X0.93990.89050.81640.7210
✓(UNet)X0.96870.95710.90760.8382
✓✓X0.97960.96890.94410.8831
✓✓✓0.98020.97140.94860.8946
", + "image_path": "6717d460c3ce9c90142c8cf9f465c619193d7732af8426b6bd1df4ef9f371443.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_body" + } + ], + "index": 18 + }, + { + "type": "table", + "bbox": [ + 308, + 349, + 544, + 460 + ], + "blocks": [ + { + "bbox": [ + 306, + 300, + 545, + 336 + ], + "lines": [ + { + "bbox": [ + 306, + 300, + 545, + 336 + ], + "spans": [ + { + "bbox": [ + 306, + 300, + 545, + 336 + ], + "type": "text", + "content": "Table 5: Ablation of different components in our method. 'I', 'C' and 'S' denote ID-aware loss, conditional modulation generator and improved synthetic creases, respectively." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 349, + 544, + 460 + ], + "lines": [ + { + "bbox": [ + 308, + 349, + 544, + 460 + ], + "spans": [ + { + "bbox": [ + 308, + 349, + 544, + 460 + ], + "type": "table", + "html": "
MethodFID↓train:test=1:1train:test=1:3
TAR↑@1e-5TAR↑@1e-6TAR↑@1e-5TAR↑@1e-6
ArcFace [14]--0.78120.70490.66080.5825
BézierPalm [69]--0.91020.84370.79340.7012
pix2pixHD [61]97.58010.91560.87340.80520.7244
CycleGAN [73]50.77040.91360.87030.78630.7189
BicycleGAN [74]35.28010.81730.72540.67830.5929
Ours16.47620.94860.89460.89690.8485
", + "image_path": "9868838b6e37d5670f3406dd7d6a1ba8ec9f3c26062fd579b35ad194daf717dd.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "table_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 461, + 545, + 486 + ], + "lines": [ + { + "bbox": [ + 306, + 461, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 306, + 461, + 545, + 486 + ], + "type": "text", + "content": "Table 6: Quantitative recognition results using different generation methods under the open-set protocol." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 509, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 616 + ], + "type": "text", + "content": "and CycleGAN tend to synthesize blurred results. As marked in blue rectangle, BicycleGAN may generate some creases that are inconsistent with the input Bézier curves. Our method can synthesize clearer and sharper principal lines and faithfully preserve the ID information of the input Bézier curves. For intra-class diversity, as shown in Fig.7, our method is able to randomly generate high-fidelity palmprints with diverse lighting and skin types by adjusting the input noise vector " + }, + { + "bbox": [ + 304, + 509, + 545, + 616 + ], + "type": "inline_equation", + "content": "N(z)" + }, + { + "bbox": [ + 304, + 509, + 545, + 616 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Quantitative results are shown in Tab.6. Our method substantially outperforms the existing methods in terms of TAR@FAR. Also, we use FID [8] to evaluate the quality of generated results and our method also effectively decreases the FID score by more than " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " against other methods. Besides, we reproduced some other generation methods [54, 56] for unpaired image-to-image transfer, including diffusion-based models, but the generated results are unsat" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19612" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "content": "isfying. Related details and more subjective results can be found in supplementary material." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 105, + 282, + 118 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 105, + 282, + 118 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 282, + 118 + ], + "type": "text", + "content": "6.3. Number of Synthesized Identities and Images" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 123, + 288, + 244 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 123, + 288, + 244 + ], + "spans": [ + { + "bbox": [ + 46, + 123, + 288, + 244 + ], + "type": "text", + "content": "In this ablation, we investigate the influence of the number of synthesized identities and images. Specifically, we generate 4000 identities and 100 samples by default, and fix one number and vary the other under the open-set protocol(train:test=1:1). The results are shown in Fig.8. With the increase of \"width\" and \"depth\" of synthetic data, our method can continuously improve the performance of the recognition model and achieve a higher upper bound than BezierPalm. The performance reaches the upper bound with " + }, + { + "bbox": [ + 46, + 123, + 288, + 244 + ], + "type": "inline_equation", + "content": "80k" + }, + { + "bbox": [ + 46, + 123, + 288, + 244 + ], + "type": "text", + "content": " synthetic identities and 160 samples per identity." + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 51, + 257, + 284, + 348 + ], + "blocks": [ + { + "bbox": [ + 51, + 257, + 284, + 348 + ], + "lines": [ + { + "bbox": [ + 51, + 257, + 284, + 348 + ], + "spans": [ + { + "bbox": [ + 51, + 257, + 284, + 348 + ], + "type": "image", + "image_path": "1ac102ce60b6e200fc27ff174294da7ae2a6d23d8d9571a9691eeaf6d83089b4.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 51, + 350, + 284, + 441 + ], + "blocks": [ + { + "bbox": [ + 51, + 350, + 284, + 441 + ], + "lines": [ + { + "bbox": [ + 51, + 350, + 284, + 441 + ], + "spans": [ + { + "bbox": [ + 51, + 350, + 284, + 441 + ], + "type": "image", + "image_path": "15f05bbdd3b695e4556e419208310951d587e3c3f5ec78b84e4668061418fb15.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 441, + 287, + 477 + ], + "lines": [ + { + "bbox": [ + 46, + 441, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 441, + 287, + 477 + ], + "type": "text", + "content": "Figure 8: TAR@FAR=1e-6 of recognition models pretrained with different numbers of synthetic identities and samples. The backbone is MobileFaceNet." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 502, + 119, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 119, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 119, + 514 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "text", + "content": "This paper proposed an ID-aware conditional modulation generation model which can produce realistic and diversified palmprint images. Specifically, a conditional modulation generator was designed, which adopted synthetic palm creases as condition, and used encoded Gaussian noise vector to modulate the generated diversity. An ID-aware loss was proposed to preserve the identity information of input palm creases during the unpaired training process. In the forward pseudo-palmprint generation stage, we improved the Bezier curves generation strategy to produce more realistic synthetic palm creases. From experimental results, we can obtain the following findings. Firstly, the generated pseudo-palmprint samples can effectively improve the performance of palmprint recognition models. Secondly, by using the synthetic palmprints, our method can effectively reduce the dependence of real data by " + }, + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "text", + "content": ". In" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "text", + "content": "future work, we hope to implement complete real-data-free palmprint recognition with synthetic data." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 108, + 421, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 108, + 421, + 121 + ], + "spans": [ + { + "bbox": [ + 306, + 108, + 421, + 121 + ], + "type": "text", + "content": "8. Acknowledgements" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 128, + 545, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 128, + 545, + 163 + ], + "spans": [ + { + "bbox": [ + 305, + 128, + 545, + 163 + ], + "type": "text", + "content": "This work is partly supported by the grants of the National Natural Science Foundation of China, Nos.62076086, 62272142 and 61972129." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 175, + 365, + 187 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 175, + 365, + 187 + ], + "spans": [ + { + "bbox": [ + 306, + 175, + 365, + 187 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 307, + 196, + 545, + 712 + ], + "type": "list", + "angle": 0, + "index": 24, + "blocks": [ + { + "bbox": [ + 311, + 196, + 507, + 206 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 196, + 507, + 206 + ], + "spans": [ + { + "bbox": [ + 311, + 196, + 507, + 206 + ], + "type": "text", + "content": "[1] Amazon one. https://one.amazon.com/." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 311, + 208, + 545, + 228 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 208, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 311, + 208, + 545, + 228 + ], + "type": "text", + "content": "[2] The ceop dataset. https://www.coep.org.in/resources/coeppalmprintdatabase." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 311, + 231, + 545, + 285 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 231, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 311, + 231, + 545, + 285 + ], + "type": "text", + "content": "[3] Denise Almeida, Konstantin Shmarko, and Elizabeth Lomas. 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Although users often share common aesthetic preferences, their retouching methods may vary based on their individual preferences. Therefore, there is a need for white-box approaches that produce satisfying results and enable users to conveniently edit their images simultaneously. Recent white-box retouching methods rely on cascaded global filters that provide image-level filter arguments but cannot perform fine-grained retouching. In contrast, colorists typically employ a divide-and-conquer approach, performing a series of region-specific fine-grained enhancements when using traditional tools like Davinci Resolve. We draw on this insight to develop a white-box framework for photo retouching using parallel region-specific filters, called RSFNet. Our model generates filter arguments (e.g., saturation, contrast, hue) and attention maps of regions for each filter simultaneously. Instead of cascading filters, RSFNet employs linear summations of filters, allowing for a more diverse range of filter classes that can be trained more easily. Our experiments demonstrate that RSFNet achieves state-of-the-art results, offering satisfying aesthetic appeal and increased user convenience for editable white-box retouching. Code is available at https://github.com/Vicky0522/RSFNet.", + "bbox": [ + 75, + 342, + 473, + 705 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 737, + 209, + 753 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Photos and videos recorded by the camera usually lack aesthetic quality due to poor shooting condition and inexperienced photographer. Artists often use professional-grade softwares (e.g., PhotoShop for image, Davinci Resolve for video) to enhance image and video quality. However, it requires professional retouching skills to conduct a series of sophisticated manual adjustments. The use of fool-proof applications that present various style templates simplifies the retouching procedure, but it is unable to achieve opti", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/674e39577ef6977caea0f5c63d4025f2a9122acc3d3cfe231479c2b3f468170d.jpg", + "image_caption": [ + "Figure 1: Architecture of our white-box retouching framework. Our model generates filter arguments (e.g., saturation, midtones, highlights) and attention maps of regions for corresponding filter simultaneously. Final result is obtained by conducting linear summations on filtered results." + ], + "image_footnote": [], + "bbox": [ + 511, + 306, + 883, + 470 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "mal results due to the lack of enhancement capability.", + "bbox": [ + 498, + 580, + 854, + 595 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent learning-based methods have demonstrated the strong capability of deep neural nets for automatic photo retouching. Automatic systems are established to generate the optimal result end-to-end. However, one of the most significant considerations is that retouching is not a problem with an exclusive solution. People have different retouching preferences. Even the same artist may retouch the same image in different styles to meet various demands. In order to provide convenience for manual edits, automatic retouching systems must provide not only the suggested result, but also the retouching strategy in a way understandable by humans.", + "bbox": [ + 496, + 595, + 892, + 762 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Taking these considerations into account, we propose a white-box framework that uses the divide-and-conquer strategy employed by artists in traditional retouching tools. Our model generates attention maps of regions as well as filter arguments for traditional edits for these regions. This allows users to alter the suggested results to their preferences.", + "bbox": [ + 496, + 762, + 890, + 866 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The main contributions of this work are as follows:", + "bbox": [ + 517, + 867, + 864, + 882 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "- We redefine the retouching problem according to the", + "bbox": [ + 517, + 885, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12160", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "divide-and-conquer strategy, focusing on finding attention maps for regions and human-understandable filter adjustments per map to achieve the best results.", + "bbox": [ + 107, + 90, + 467, + 135 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose RSFNet, which generates pixel-level attention maps of regions and filter arguments simultaneously. By conducting linear summations on the filtered results, our model demonstrates superior performance to global white-box retouching methods, with a wider range of filter classes for fine-grained enhancement and a simpler training procedure.", + "- We propose a scheme that allows users to edit RSFNet suggested results, demonstrating its effectiveness and convenience in image applications." + ], + "bbox": [ + 96, + 136, + 467, + 286 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 76, + 301, + 225, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deep Image Enhancement. Many attempts have been made in image enhancement using learning-based methods. These methods can broadly be classified into two categories: deep-convolutional-based models and physical-inspired models. The former [3, 4, 6, 25, 29] view enhancement as a synthesis problem and use fully convolutional generators [15] to achieve dense image-to-image translation. While these methods exhibit strong capability for generating and enhancing details, they suffer from heavy structure and low inference speed. The latter category of works defines enhancement as the parameter prediction of a physical model and uses deep learning strategies to fit the model. These models include 3D-LUT [21, 28, 27], parametric filters [16], conditional sequential global modulation [8], affine color transformations [7, 20], 1D mapping curves [19, 12, 17]. Their enhancement capabilities depend on the range of transformation functions the physical model covers. Among those, models based on global 3D-LUT [27, 28] are well-designed for retouching and could achieve high performance with fast inference speed. However, they suffer from uneven transitions in smooth areas due to lack of fine-grained local adjustment. Spatial-Aware 3D-LUT [21] alleviate the problem of global 3D-LUT by computing pixel-level weight maps. All these methods have a black-box structure or unintuitive parameters that are hard for humans to understand. DeepLPF [16] has been a significant milestone in the field of region-specific color enhancement via local parametric filters but suffers from low inference speed and limited filter shapes. The three types of filters with three implementations each results in complex maps that are hard to understand.", + "bbox": [ + 76, + 325, + 468, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "White-box Image Editing. Recent white-box methods [10, 11, 26, 30] have decoupled image editing into a series of human understandable operations and deep learning strategies to predict them. Of these, our work is most related to [11, 10]. However, they train networks with cascaded filter argument prediction modules to perform global retouching step-by-step. Our model utilizes pixel-wise region-", + "bbox": [ + 75, + 795, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "specific filters to capture local features and employs linear summations to combine filters, thus having stronger capability to cover a wider range of color transformation functions.", + "bbox": [ + 496, + 90, + 890, + 148 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 167, + 589, + 183 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Design Motivation", + "text_level": 1, + "bbox": [ + 500, + 194, + 676, + 209 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Traditional Retouching Strategy. In the traditional retouching process, local adjustments for different regions are conducted separately and then aggregated together to accomplish fine-grained enhancement. All the adjustments could be accomplished in one Layer, where filters are all conducted on the same image instead of results from previous filters. We adopt this divide-and-conquer strategy to build our framework. We select 10 commonly used retouching filters from traditional tools(e.g., Davinci Resolve) to represent adjustment manipulations, including contrast, saturation, hue, temperature, shadows, midtones, highlights and shift. For more details about filters, please refer to our supplementary material. Therefore, retouching is defined as finding pixel-level attention maps and corresponding adjustments for each map to achieve the most desirable result. We adopt this convention and represent retouching result $Y$ as adding linear summations of increments resulted by filters to the original image as:", + "bbox": [ + 496, + 217, + 890, + 489 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nY = X + \\sum_ {m} \\sum_ {n} \\left(F _ {m, n} \\left(\\theta_ {m, n}, X\\right) - X\\right) \\odot M _ {m} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 516, + 890, + 547 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Where $\\theta_{m,n}$ and $F_{m,n} \\in \\{\\text{contrast}, \\dots, \\text{shift}\\}$ are the argument value and filter function of the $n$ th filter for the $m$ th attention map of input image $X$ respectively, $M_{m}$ is the $m$ th attention map for image $X$ . It should be noticed that this linear representation makes our optimization process much simpler than other white-box methods.", + "bbox": [ + 496, + 561, + 890, + 652 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.2. Architecture", + "text_level": 1, + "bbox": [ + 500, + 665, + 633, + 679 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our model consists of two modules, the parameter predictor and the renderer. The architecture of the parameter predictor shares a similar overall structure with previous segmentation models [22, 23]. As illustrated in Figure 2, the network $g$ is composed of a backbone $g_{\\text{backbone}}$ , a FPN neck $g_{\\text{neck}}$ , a map generator $h_{\\text{map}}$ for attention map prediction and an argument regressor $h_{\\text{arg}}$ for arguments regression. We set the last layer of map generator $h_{\\text{map}}$ to sigmoid, followed by an upsampling layer to match the size of the original input image. We use $f(X)$ to represent the output features of FPN neck. Maps generated by $h_{\\text{map}}$ after upsampling are:", + "bbox": [ + 496, + 689, + 890, + 869 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nM _ {m} = h _ {\\text {m a p}} (f (X)) _ {m}, m \\in \\{1, \\dots ., K \\} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 883, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12161", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/1fa1e6a7ff4eeef981125cee46064f989a073c8f2da72da946887fbfb672e634.jpg", + "image_caption": [ + "Figure 2: Our network comprises two modules: the parameter predictor and renderer. The input image is transformed into feature embeddings $f(X)$ through a backbone $g_{\\text{backbone}}$ and FPN neck $g_{\\text{neck}}$ , which are then utilized by the map generator $h_{\\text{map}}$ and argument regressor $h_{\\text{arg}}$ to generate region maps and filter arguments (e.g. contrast, hue, saturation), respectively. The renderer applies the filter arguments to each region map and aggregates them to produce the final retouching result." + ], + "image_footnote": [], + "bbox": [ + 117, + 85, + 851, + 348 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$K$ is the number of output channels of the last layer. The argument regressor $h_{arg}$ consists of 4 units of convolutional modules. Each module consists of a convolution layer followed by group normalization, $\\text{relu}$ activation and average pooling. Output feature $f(X)$ is finally reduced by $h_{arg}$ to a $K \\times N$ vector representing arguments of all filters for every map:", + "bbox": [ + 75, + 450, + 468, + 556 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {m, n} = h _ {\\arg} (f (X)) _ {m, n}, m \\in \\{1, \\dots ., K \\}, n \\in \\{1, \\dots ., N \\} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 80, + 561, + 468, + 593 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$K$ is the number of color filters per map. Given the maps and arguments from the parameter predictor, the renderer applies filter functions $F_{m,n} \\in \\{\\text{contrast}, \\dots, \\text{shift}\\}$ to the input image and merges filtered results via linear summations of increments. The final output image $Y$ in Equation 1 is:", + "bbox": [ + 75, + 594, + 468, + 681 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nY = X + \\sum_ {m = 1} ^ {K} \\sum_ {n = 1} ^ {N} \\left(F _ {m, n} \\left(\\theta_ {m, n}, X\\right) - X\\right) \\odot M _ {m} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 688, + 468, + 729 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In our implementation, we set the number of filters per map as $N = 1$ , indicating that there is one specific filter assigned to each map. This is illustrated in the second row of filter boxes depicted in Figure 2. We also consider the filter Shift as a global function that is applied to the entire image without an attention map. Through our experimentation, we observe that this configuration is sufficient for generating satisfactory results while also providing convenience for users to edit.", + "bbox": [ + 75, + 734, + 468, + 868 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Training Loss. The overall framework can be trained end-to-end. Our training loss function is defined as follows:", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/069589aeb25c49168e0a8e104ef4ac02ded19d73908a3fff6f9fd3fbebc760e7.jpg", + "image_caption": [ + "Figure 3: A variation of RSFNet could be used to generate masks with controlled shapes. We generate ground truth masks for training via three types of region masks derived from off-the-shelf models: palette-based segmentation, semantic segmentation, and saliency detection." + ], + "image_footnote": [], + "bbox": [ + 519, + 448, + 888, + 604 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL = L _ {\\text {r e c o n}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 651, + 736, + 890, + 752 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $L_{\\text{recon}}$ is the $l1$ loss for reconstruction.", + "bbox": [ + 500, + 760, + 803, + 775 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. A Variation of RSFNet with Controlled Region Shape", + "text_level": 1, + "bbox": [ + 500, + 785, + 890, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our proposed framework has the capability to generate region masks with controlled shapes, with minimal modifications to the training data and loss function. In our observation, artists tend to select regions based on their main color, saliency, or other high-level semantic informa", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12162", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4dca9de783795fce137d9e2c4b210daf9bf36b7201b051d2e9e573f0f84df63d.jpg", + "image_caption": [ + "Figure 4: Editable white-box retouching. The second column illustrates the arguments and masks generated by RSFNet-saliency that is trained with saliency masks. The third column displays the retouched result. On the right-hand side, the figure showcases three versions of adjustments conducted on the retouched results, with numbers denoted in green boxes indicating the relative incremental value of filters." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 885, + 441 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tion. To leverage this insight, we utilize palette-based methods [2], saliency detection [14], and panoptic segmentation networks [5] to generate palette-based, saliency, and semantic masks of the input images used for training, as depicted in Figure 3. Further implementation details can be found in the supplementary material. Our training loss function in Equation 5 is modified as follows:", + "bbox": [ + 75, + 537, + 472, + 643 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL = L _ {\\text {r e c o n}} + \\lambda L _ {\\text {m a s k}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 676, + 468, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $L_{\\text{recon}}$ is the $l1$ loss for reconstruction. When training with palette-based masks and saliency masks, $L_{\\text{mask}}$ is the Dice Loss for mask prediction following loss functions in [22, 23]. We change it to the Cross Entropy Loss when training with semantic masks, at the time map generator $h_{\\text{map}}$ ends with a softmax layer.", + "bbox": [ + 75, + 724, + 468, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The model generates region masks and corresponding filter arguments for the input image simultaneously. Users can select region maps and adjust filter arguments to edit results. We show an example of RSFNet-saliency trained with saliency masks in Figure 4.", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 536, + 633, + 553 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Datasets and Application Settings", + "text_level": 1, + "bbox": [ + 500, + 570, + 794, + 588 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We conduct experiments on two publicly available datasets: MIT-Adobe FiveK [1] and PPR10K [13]. The MIT-Adobe FiveK consists of 5,000 RAW images with their retouched versions. We follow prior works [8, 12, 28, 27] to adopt images retouched by expert C as ground truths and split the dataset into 4,500 pairs for training and 500 pairs for validation. Images are resized to $480\\mathrm{p}$ during training stage, whereas both of $480\\mathrm{p}$ resolution and original resolution are used during validation. We follow the official split [13] to split PPR10K dataset into 8,875 pairs for training and 2,286 pairs for testing. Images are resized to $360\\mathrm{p}$ resolution for training and validation.", + "bbox": [ + 496, + 604, + 893, + 785 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the MIT-Adobe FiveK dataset, we conduct experiments on two input settings: input zeroed with expertC white balance and input zeroed as shot. The second set of inputs is more challenging as it also deteriorates in white balance. Therefore, to restore its visual appeal, our framework's ability to perform color temperature correction and hue adjustment is required.", + "bbox": [ + 496, + 794, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12163", + "bbox": [ + 480, + 944, + 517, + 957 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/92f36291aa38a5cb1b569a699527499a3e6b12b5eb4c332b4db37ad5b9e9b57b.jpg", + "table_caption": [], + "table_footnote": [ + "(a) Analysis on using mask as input and different mask types. Bracket after \"mask type\" indicates number of masks." + ], + "table_body": "
mask as inputmask typePSNR↑SSIM↑
w/saliency(1)23.830.906
w/palette(5)23.450.903
w/semantic(10)21.650.866
w/semantic(5)21.770.867
w/osaliency(1)24.010.909
w/opalette(5)24.140.906
w/osemantic(10)24.090.908
w/osemantic(5)24.170.909
w/osemantic(133)23.750.905
", + "bbox": [ + 78, + 89, + 336, + 236 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/dc273e5f6b576c7e488c4cb1f912a0af5722e33bbf0797100170cf57554c474a.jpg", + "table_caption": [], + "table_footnote": [ + "(b) Analysis of training order. \"Mask first\" refers to building model on pre-trained PoolNet [14]." + ], + "table_body": "
mask firstmasktypePSNR↑SSIM↑
w/saliency(1)23.260.890
w/osaliency(1)24.010.909
", + "bbox": [ + 385, + 125, + 614, + 199 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/7d6e07dd2fbe97d307bd5c2df0ee3df670fb11d7b3cc03df98ca455cac5395c3.jpg", + "table_caption": [], + "table_footnote": [ + "(c) Trade off between speed and accuracy." + ], + "table_body": "
backbonedownscaling factorPSNR↑Runtime↓
resnet18x824.659.98
resnet18x424.8312.38
resnet10x824.507.98
resnet10x424.388.71
", + "bbox": [ + 651, + 132, + 923, + 220 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1: Ablation analysis of our framework. Models are trained on the FiveK dataset [1] with inputs zeroed as shot.", + "bbox": [ + 101, + 296, + 864, + 311 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b580ce3d2e6f88e4c3bfae6e43ae112e56813c24e4a3f0f299f0cbc3e174e4f4.jpg", + "image_caption": [ + "Figure 5: Comparison between sequential and parallel methods under the same filter functions and network structures." + ], + "image_footnote": [], + "bbox": [ + 88, + 335, + 259, + 474 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/797b51d18273ef8e24923f1dd0dd02751e38eb9943d1aa820313ce50a205dbf1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 267, + 335, + 455, + 474 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 559, + 294, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To implement our proposed framework as described in Section 3.2, we employ ResNet18 [9] as the backbone and utilize the output features of layer $(0,1,2,3)$ as concatenated input with $256\\times 4$ channels for the FPN neck. The FPN neck reduces the features to $64\\times 4$ channels and feeds them into the map generator and argument regressor. We set the output numbers $K$ of region maps to 10 and 16 for the Adobe-MIT FiveK and PPR10K datasets, respectively. The number of filters per map $N$ is set to $N = 1$ , with 10 filters used for MIT-Adobe FiveK, 1 each for shadow, midtones, highlights, where arguments for RGB channels are set equal. For PPR10K, we use 16 filters, with 3 each for shadow, midtones, highlights, where arguments for RGB channels are set differently.", + "bbox": [ + 75, + 583, + 468, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To implement the variation of RSFNet with controlled region shapes, as described in Section 3.3, we generate ground truth masks for the MIT-Adobe FiveK dataset. Specifically, we generate five palette-based masks, one saliency mask, and five semantic masks for each image. For the PPR10K dataset, we directly use the human-region masks provided in the dataset as ground truth masks for", + "bbox": [ + 75, + 795, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "training. The map generator is designed to output 5 channels for the palette-based version, 2 channels for the saliency version, and 5 channels for the semantic version. We use 10 filters for the MIT-Adobe FiveK and 16 filters for the PPR10K, as mentioned above.", + "bbox": [ + 496, + 338, + 890, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use the standard Adam optimizer [18] to minimize the loss function in Equation 5 and 6. The mini-batch size is 16. We train models for 1,000,000 iterations with initial learning rate $l_{r} = 2 \\times 10^{-4}$ . We use a cosine strategy to gradually decay the learning rate every 250,000 iterations. All experiments are conducted on NVIDIA Tesla V100 GPU.", + "bbox": [ + 496, + 414, + 890, + 517 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the following sections, we denote our main model in Section 3.2 as $RSFNet$ -map. Variations depicted in Section 3.3 are denoted as $RSFNet$ -palette, $RSFNet$ -saliency and $RSFNet$ -semantic.", + "bbox": [ + 496, + 518, + 890, + 579 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 590, + 663, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we evaluate the ability of our frameworks in different settings.", + "bbox": [ + 496, + 613, + 890, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Comparative study of parallel and sequential approaches. We conduct experiments to compare parallel and sequential approaches under the same set of filter functions and backbone structures. For sequential implementations, we modify the network structure to mimic artistic workflows and resemble Harmonizer [11]. We train the network using randomly shuffled 20 unique sequences of filter functions. The results are shown in Figure 5. The parallel approach shows Pareto-optimality with near-maximum PSNR and a lower PSNR standard deviation (std). It also outperforms all sequential approaches in terms of SSIM and SSIM std. We find that altering the sequence of applying filters can lead to considerable changes in performance. Nearly half of these sequences fail to produce satisfactory results. Moreover, during training, the parallel approach converges faster than its sequential counterparts. In addition, the parallel method can be faster than the sequential one.", + "bbox": [ + 496, + 643, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12164", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/a5252d0bb0ece520a3109feac145e21a056d4772d479b847df08a804bd95a825.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method480p zeroed with C's480p zeroed as shotFull Resolution zeroed as shot
PSNR↑SSIM↑△Eab↓PSNR↑SSIM↑△Eab↓Runtime↓PSNR↑SSIM↑Runtime↓
UPE [20]21.88*0.853*10.80*///////
DPE [4]23.75*0.908*9.34*///////
HDRNet [7]24.66*0.915*8.06*///////
DeepLPF [16]24.73*0.916*7.99*23.380.88010.0344.2523.400.8631133.90
CSRNet [8]25.17*0.924*7.75*24.240.9109.703.4923.040.87480.6
SA-3DLUT [21]25.50*/////////
3D-LUT [28]25.29*0.923*7.55*///////
3D-LUT+AdaInt [27]25.49*0.926*7.47*24.500.9129.221.5924.240.8571.80
Harmonizer [11]24.110.9048.2323.230.89310.1416.7422.570.87027.98
RSFNet-map25.490.9247.2324.640.9159.169.9824.390.89412.35
RSFNet-palette25.010.9147.6224.220.9119.5219.7623.880.88868.57
RSFNet-saliency24.780.9167.8624.200.9129.4214.0924.000.89059.42
RSFNet-semantic24.760.9157.7724.190.9129.4524.0723.890.89171.18
RSFNet-global24.310.9118.2123.430.90410.169.4223.260.88510.99
", + "bbox": [ + 129, + 88, + 844, + 353 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/31fcf8c6197ac17a41c594dccfde0bbfefa71adc175d932de8472dd740d563df.jpg", + "table_caption": [ + "Table 2: Quantitative comparisons for retouching tasks on FiveK dataset [1]. Runtime is measured in milliseconds. “*” means the result is adopted from the paper [27]. “/” means the result is not available. Runtime shown in previous works are not adopted due to different hardware settings. Results with the first and second performance are colored as red and blue respectively. White-box methods are colored as violet. Full resolution images results are evaluated using Python, while others are evaluated on Matlab." + ], + "table_footnote": [], + "table_body": "
Method360p expert a360p expert b360p expert c
PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑
DeepLPF [16]23.470.89222.770.87523.730.896
CSRNet [8]24.010.93623.910.93824.310.931
3D-LUT+AdaInt [27]25.980.94724.910.93625.480.919
Harmonizer [11]24.760.92922.790.88524.560.902
RSFNet-map25.580.94924.810.94525.520.939
RSFNet-saliency25.530.94624.720.94425.110.939
", + "bbox": [ + 230, + 452, + 743, + 608 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3: Quantitative comparisons for retouching tasks on PPR10K dataset [13]. All the models are trained on data without augmentations. White-box methods are colored as violet.", + "bbox": [ + 75, + 617, + 893, + 650 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training map generation and arguments regression separately. To train models with controlled region shapes, we experiment with using pre-trained PoolNet [14] and adding an FPN neck followed by an argument regressor to the backbone instead of training from scratch. During training, we fix the weights of the backbone to keep the saliency mask generated by the network unchanged. The quantitative results are shown in Table 1b, which indicates that there is no superiority over training from scratch. The reason for this might be that a network trained only on semantic data lacks sufficient information for retouching. Therefore, it is better to train the map generation and arguments regression tasks simultaneously.", + "bbox": [ + 75, + 674, + 472, + 872 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Using Masks as Input. For training models with controlled region shapes, we can use masks concatenated with the image as input for our model. We train three models using three sets of masks as input, respectively. The results are shown in Table 1a. The retouching results evaluated on PSNR and SSIM [24] are lower than in other settings. This may be because the ground truth masks are generated by off-the-shelf models, which may differ from the underlying real masks of the dataset. Masks are slightly modified by the map generator in the inference stage to achieve better retouching results. Therefore, simple concatenation of masks with the input image can lead to worse performance compared to our design of the variant of RSFNet, which generates masks and filter arguments simultaneously.", + "bbox": [ + 496, + 674, + 893, + 888 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12165", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fe072dae96562455a2c04aa476d03a45dd0a8ccb0d4a6614f3b101af5d457999.jpg", + "image_caption": [ + "Figure 6: Qualitative comparison of selected methods. \"RSFNet-map\" means our main model explained in Section 3.2" + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 885, + 422 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/899cd8149a655c259275fd724506b3c48c996843590f9952e460c91d4e0e3501.jpg", + "image_caption": [ + "Figure 7: Boxplot of user study. The dashed green line and the solid black line inside the box are the mean and the median preference percentage respectively." + ], + "image_footnote": [], + "bbox": [ + 98, + 496, + 424, + 672 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Trade Off Between Speed and Accuracy. As we decrease the number of downsample operations in the backbone, the feature size grows larger and time costs increase. However, quantitative results of retouching also become better, as shown in 1c. Speed is measured in milliseconds.", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Comparison with State-of-the-Art", + "text_level": 1, + "bbox": [ + 500, + 473, + 797, + 489 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our methods with the state-of-the-art for black-box and white-box image retouching tasks. The selected methods are compared on PSNR, SSIM [24], the $L_{2}$ -distance in CIE LAB color space $(\\triangle E_{ab})$ and the inference speed. We follow the practice in [27] to measure the GPU inference time on 100 images and report the average. Quantitative results are shown in Table 2 and 3. RSFNet-map refers to our main model in Section 3.2, RSFNet-saliency, RSFNet-palette and RSFNet-semantic refers to models trained with three sets of masks respectively in Section 3.3. In addition, we evaluate a global retouching model without the map generator, denoted as RSFNet-global. Other models are trained using their official public codes and default configurations. All experiments are executed on an NVIDIA Tesla V100 GPU.", + "bbox": [ + 496, + 502, + 890, + 729 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our proposed method, $RSFNet$ -map, demonstrates its effectiveness in temperature correction and color enhancement, especially for the second set of inputs under more deteriorating shooting conditions. Although $RSFNet$ -map achieves state-of-the-art results with negligible increase, while other RSFNet variations lag behind the state of the art, it is important to note that our white-box framework provides human-understandable ways for retouching, which makes it more convenient for users to edit and assess retouching results compared to other black-box methods. When compared with state-of-the-art white-box methods", + "bbox": [ + 496, + 734, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12166", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ecdc78af2604b0e3704b6e4005ae955f8d970292043771ec0f2d5ac1c3a2a2d4.jpg", + "image_caption": [ + "Figure 8: Editable image retouching. \"RSFNet-saliency\", \"RSFNet-semantic\" means RSFNet trained with saliency masks and semantic masks respectively." + ], + "image_footnote": [], + "bbox": [ + 86, + 99, + 854, + 506 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "such as Harmonizer [11], all of our models exhibit better performance with faster speed. Furthermore, using 3D-LUTs to encode filter functions could potentially accelerate our models, a technique commonly implemented in traditional retouching tools. For PPR10K [13], we also evaluate our methods using a random split setup. The results are provided in supplementary material, consistently reinforcing the conclusions drawn from previous experiments.", + "bbox": [ + 75, + 575, + 468, + 698 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The qualitative results presented in Figure 6 demonstrate that our proposed method, $RSFNet$ -map, exhibits superior performance in handling color transitions across regions, particularly in highlight areas, compared to 3D-LUT based methods such as AdaInt, as shown in the first row of the figure. Furthermore, we conduct a comparison with Harmonizer [11] on editable retouching, as shown in Figure 8. Our white-box framework offers more degrees of freedom than global-retouching manipulations to achieve region-specific retouching. For instance, when the temperature is adjusted globally using Harmonizer, the sky in the first image turns yellow. On the other hand, our $RSFNet$ -saliency model can modify the temperature of the foreground girl while leav-", + "bbox": [ + 75, + 703, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing other regions unaffected. In the second image, global temperature adjustment by Harmonizer turns the lake and mountains blue. In contrast, $RSFNet$ -semantic only modifies the sky temperature, leaving the mountains and lake unchanged.", + "bbox": [ + 496, + 575, + 890, + 652 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To further validate the effectiveness of our proposed framework, we conduct a user study to evaluate human preferences for RSFNet and other state-of-the-art methods, including CSRNet [8], AdaInt [27], and Hormonizer [11]. To form the test set, we randomly select 58 images from the validation set of Adobe-MIT FiveK using the input zeroed with expertC white balance and input zeroed as shot settings, as well as an additional 20 images downloaded from the internet. During the experiment, we display retouched images produced by all methods, including the original input, to 22 participants. Participants are asked to select the best result from a randomly shuffled set of retouched images generated by all methods. We calculate the preferences of participants for each method and plot the results using a box plot, as shown in Figure 7.", + "bbox": [ + 496, + 655, + 892, + 882 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Among the compared methods, AdaInt [27] achieves", + "bbox": [ + 519, + 885, + 890, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12167", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "higher mean and median percentages. RSFNet exhibits more stable performance with a higher bottom percentage and the smallest standard variance percentage than the other methods. In comparison to the white-box method Harmonizer [11], RSFNet demonstrates superior user preference percentages. The boxplot illustrates the varying preferences of different users, highlighting the significance of editable capability. As RSFNet utilizes traditional color filters for retouching, it can be readily integrated into traditional retouching tools. Users can further enhance the visual appeal of the retouched results according to their own preferences through an interface.", + "bbox": [ + 75, + 90, + 472, + 271 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Video Retouching. Our proposed RSFNet model also demonstrates applicability to video retouching, as shown in Figure 8. The filter arguments remain constant within a single video clip for all frames, ensuring consistency throughout the retouching process. However, for RSFNet variations with controlled region shapes, such as $RSFNet$ -saliency, the retouching consistency across frames relies on the consistency of region masks across frames. Although filter arguments can alleviate the inconsistency caused by masks, severe inconsistency problems in masks may still affect retouching results. With the assistance of a more robust tracking algorithm, these models can achieve better performance in editable video retouching, highlighting the potential of RSFNet in various retouching applications.", + "bbox": [ + 75, + 272, + 472, + 484 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Limitation and Conclusion", + "text_level": 1, + "bbox": [ + 76, + 497, + 326, + 513 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We develop our framework under the assumption that all adjustments are done in one layer, which is then combined via linear summations of increments of all filters to obtain the final result. Therefore, although our model provides a white-box retouching framework that aligns with the intuition of human artists, it is unable to cover all adjustments that artists could conduct using professional software. However, we believe that if the cache data in the retouching process of artists is available, such as the region masks used for region-specific retouching, our model equipped with a more complicated structure, such as a cascaded structure in [10, 11], could behave more similarly to a real human artist by learning from this data.", + "bbox": [ + 75, + 523, + 468, + 718 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This paper introduces RSFNet, a white-box framework for image retouching that utilizes a divide-and-conquer strategy to generate region maps and human-understandable filter arguments. The resulting filtered images are combined using linear summations, allowing for a wider range of filter classes and achieving fine-grained enhancement with superior performance. A variation of RSFNet with controlled shape region masks is also proposed for user convenience. Extensive experiments are presented to demonstrate the effectiveness of RSFNet.", + "bbox": [ + 75, + 719, + 470, + 869 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgement This work was supported by Alibaba", + "bbox": [ + 76, + 885, + 468, + 901 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Group through Alibaba Innovative Research (AIR) Program and Alibaba-NTU Singapore Joint Research Institute (JRI), Nanyang Technological University, Singapore. We appreciate Mr. Wang Yuxi's efforts in generating additional experimental results during the rebuttal period.", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 501, + 180, + 596, + 196 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Vladimir Bychkovsky, Sylvain Paris, Eric Chan, and Frédo Durand. 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Adaint: Learning adaptive intervals for 3d lookup tables on real-time image enhancement. In CVPR, pages 17501-17510, 2022.", + "[28] Hui Zeng, Jianrui Cai, Lida Li, Zisheng Cao, and Lei Zhang. Learning image-adaptive 3d lookup tables for high performance photo enhancement in real-time. IEEE TPAMI, 2020.", + "[29] Yonghua Zhang, Jiawan Zhang, and Xiaojie Guo. Kindling the darkness: A practical low-light image enhancer. In Laurent Amsaleg, Benoit Huet, Martha A. Larson, Guillaume Gravier, Hayley Hung, Chong-Wah Ngo, and Wei Tsang Ooi, editors, ACM MM, pages 1632-1640. ACM, 2019.", + "[30] Zhengxia Zou, Tianyang Shi, Shuang Qiu, Yi Yuan, and Zhenwei Shi. Stylized neural painting. In CVPR, pages 15689-15698, 2021." + ], + "bbox": [ + 78, + 90, + 467, + 886 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "12169", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/RSFNet_ A White-Box Image Retouching Approach using Region-Specific Color Filters/a1a06f38-ffb3-49f3-88a3-88bb8d7af4de_model.json b/2023/RSFNet_ A White-Box Image Retouching Approach using Region-Specific Color Filters/a1a06f38-ffb3-49f3-88a3-88bb8d7af4de_model.json new file mode 100644 index 0000000000000000000000000000000000000000..efa13fa6f9c87df67cb24a45441f62dee98bc62a --- /dev/null +++ b/2023/RSFNet_ A White-Box Image Retouching Approach using Region-Specific Color Filters/a1a06f38-ffb3-49f3-88a3-88bb8d7af4de_model.json @@ -0,0 +1,1650 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.082, + 0.13, + 0.89, + 0.175 + ], + "angle": 0, + "content": "RSFNet: A White-Box Image Retouching Approach using Region-Specific Color Filters" + }, + { + "type": "text", + "bbox": [ + 0.153, + 0.203, + 0.816, + 0.24 + ], + "angle": 0, + "content": "Wenqi Ouyang\\(^{1}\\), Yi Dong\\(^{2}\\), Xiaoyang Kang\\(^{1}\\), Peiran Ren\\(^{1}\\), Xin Xu\\(^{1}\\), Xuansong Xie\\(^{1}\\) \n\\(^{1}\\)DAMO Academy, Alibaba Group, \\(^{2}\\)Nanyang Technological University" + }, + { + "type": "text", + "bbox": [ + 0.272, + 0.243, + 0.694, + 0.258 + ], + "angle": 0, + "content": "wenqi.oywq@alibaba-inc.com, ydong004@ntu.edu.sg," + }, + { + "type": "text", + "bbox": [ + 0.176, + 0.26, + 0.794, + 0.275 + ], + "angle": 0, + "content": "{peiran.rpr, kangxiaoyang.kxy, chris.xx, xingtong.xxs}@alibaba-inc.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.343, + 0.474, + 0.707 + ], + "angle": 0, + "content": "Retouching images is an essential aspect of enhancing the visual appeal of photos. Although users often share common aesthetic preferences, their retouching methods may vary based on their individual preferences. Therefore, there is a need for white-box approaches that produce satisfying results and enable users to conveniently edit their images simultaneously. Recent white-box retouching methods rely on cascaded global filters that provide image-level filter arguments but cannot perform fine-grained retouching. In contrast, colorists typically employ a divide-and-conquer approach, performing a series of region-specific fine-grained enhancements when using traditional tools like Davinci Resolve. We draw on this insight to develop a white-box framework for photo retouching using parallel region-specific filters, called RSFNet. Our model generates filter arguments (e.g., saturation, contrast, hue) and attention maps of regions for each filter simultaneously. Instead of cascading filters, RSFNet employs linear summations of filters, allowing for a more diverse range of filter classes that can be trained more easily. Our experiments demonstrate that RSFNet achieves state-of-the-art results, offering satisfying aesthetic appeal and increased user convenience for editable white-box retouching. Code is available at https://github.com/Vicky0522/RSFNet." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.738, + 0.21, + 0.755 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Photos and videos recorded by the camera usually lack aesthetic quality due to poor shooting condition and inexperienced photographer. Artists often use professional-grade softwares (e.g., PhotoShop for image, Davinci Resolve for video) to enhance image and video quality. However, it requires professional retouching skills to conduct a series of sophisticated manual adjustments. The use of fool-proof applications that present various style templates simplifies the retouching procedure, but it is unable to achieve opti" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.308, + 0.885, + 0.471 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.479, + 0.895, + 0.556 + ], + "angle": 0, + "content": "Figure 1: Architecture of our white-box retouching framework. Our model generates filter arguments (e.g., saturation, midtones, highlights) and attention maps of regions for corresponding filter simultaneously. Final result is obtained by conducting linear summations on filtered results." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.581, + 0.856, + 0.597 + ], + "angle": 0, + "content": "mal results due to the lack of enhancement capability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.597, + 0.893, + 0.763 + ], + "angle": 0, + "content": "Recent learning-based methods have demonstrated the strong capability of deep neural nets for automatic photo retouching. Automatic systems are established to generate the optimal result end-to-end. However, one of the most significant considerations is that retouching is not a problem with an exclusive solution. People have different retouching preferences. Even the same artist may retouch the same image in different styles to meet various demands. In order to provide convenience for manual edits, automatic retouching systems must provide not only the suggested result, but also the retouching strategy in a way understandable by humans." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Taking these considerations into account, we propose a white-box framework that uses the divide-and-conquer strategy employed by artists in traditional retouching tools. Our model generates attention maps of regions as well as filter arguments for traditional edits for these regions. This allows users to alter the suggested results to their preferences." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.868, + 0.865, + 0.883 + ], + "angle": 0, + "content": "The main contributions of this work are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "- We redefine the retouching problem according to the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12160" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.109, + 0.092, + 0.468, + 0.136 + ], + "angle": 0, + "content": "divide-and-conquer strategy, focusing on finding attention maps for regions and human-understandable filter adjustments per map to achieve the best results." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.137, + 0.468, + 0.242 + ], + "angle": 0, + "content": "- We propose RSFNet, which generates pixel-level attention maps of regions and filter arguments simultaneously. By conducting linear summations on the filtered results, our model demonstrates superior performance to global white-box retouching methods, with a wider range of filter classes for fine-grained enhancement and a simpler training procedure." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.243, + 0.468, + 0.287 + ], + "angle": 0, + "content": "- We propose a scheme that allows users to edit RSFNet suggested results, demonstrating its effectiveness and convenience in image applications." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.137, + 0.468, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.302, + 0.226, + 0.317 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.327, + 0.47, + 0.793 + ], + "angle": 0, + "content": "Deep Image Enhancement. Many attempts have been made in image enhancement using learning-based methods. These methods can broadly be classified into two categories: deep-convolutional-based models and physical-inspired models. The former [3, 4, 6, 25, 29] view enhancement as a synthesis problem and use fully convolutional generators [15] to achieve dense image-to-image translation. While these methods exhibit strong capability for generating and enhancing details, they suffer from heavy structure and low inference speed. The latter category of works defines enhancement as the parameter prediction of a physical model and uses deep learning strategies to fit the model. These models include 3D-LUT [21, 28, 27], parametric filters [16], conditional sequential global modulation [8], affine color transformations [7, 20], 1D mapping curves [19, 12, 17]. Their enhancement capabilities depend on the range of transformation functions the physical model covers. Among those, models based on global 3D-LUT [27, 28] are well-designed for retouching and could achieve high performance with fast inference speed. However, they suffer from uneven transitions in smooth areas due to lack of fine-grained local adjustment. Spatial-Aware 3D-LUT [21] alleviate the problem of global 3D-LUT by computing pixel-level weight maps. All these methods have a black-box structure or unintuitive parameters that are hard for humans to understand. DeepLPF [16] has been a significant milestone in the field of region-specific color enhancement via local parametric filters but suffers from low inference speed and limited filter shapes. The three types of filters with three implementations each results in complex maps that are hard to understand." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.468, + 0.901 + ], + "angle": 0, + "content": "White-box Image Editing. Recent white-box methods [10, 11, 26, 30] have decoupled image editing into a series of human understandable operations and deep learning strategies to predict them. Of these, our work is most related to [11, 10]. However, they train networks with cascaded filter argument prediction modules to perform global retouching step-by-step. Our model utilizes pixel-wise region-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.15 + ], + "angle": 0, + "content": "specific filters to capture local features and employs linear summations to combine filters, thus having stronger capability to cover a wider range of color transformation functions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.169, + 0.59, + 0.184 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.195, + 0.677, + 0.21 + ], + "angle": 0, + "content": "3.1. Design Motivation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.218, + 0.892, + 0.491 + ], + "angle": 0, + "content": "Traditional Retouching Strategy. In the traditional retouching process, local adjustments for different regions are conducted separately and then aggregated together to accomplish fine-grained enhancement. All the adjustments could be accomplished in one Layer, where filters are all conducted on the same image instead of results from previous filters. We adopt this divide-and-conquer strategy to build our framework. We select 10 commonly used retouching filters from traditional tools(e.g., Davinci Resolve) to represent adjustment manipulations, including contrast, saturation, hue, temperature, shadows, midtones, highlights and shift. For more details about filters, please refer to our supplementary material. Therefore, retouching is defined as finding pixel-level attention maps and corresponding adjustments for each map to achieve the most desirable result. We adopt this convention and represent retouching result \\( Y \\) as adding linear summations of increments resulted by filters to the original image as:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.517, + 0.891, + 0.548 + ], + "angle": 0, + "content": "\\[\nY = X + \\sum_ {m} \\sum_ {n} \\left(F _ {m, n} \\left(\\theta_ {m, n}, X\\right) - X\\right) \\odot M _ {m} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.892, + 0.653 + ], + "angle": 0, + "content": "Where \\( \\theta_{m,n} \\) and \\( F_{m,n} \\in \\{\\text{contrast}, \\dots, \\text{shift}\\} \\) are the argument value and filter function of the \\( n \\)th filter for the \\( m \\)th attention map of input image \\( X \\) respectively, \\( M_{m} \\) is the \\( m \\)th attention map for image \\( X \\). It should be noticed that this linear representation makes our optimization process much simpler than other white-box methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.666, + 0.634, + 0.68 + ], + "angle": 0, + "content": "3.2. Architecture" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.892, + 0.871 + ], + "angle": 0, + "content": "Our model consists of two modules, the parameter predictor and the renderer. The architecture of the parameter predictor shares a similar overall structure with previous segmentation models [22, 23]. As illustrated in Figure 2, the network \\( g \\) is composed of a backbone \\( g_{\\text{backbone}} \\), a FPN neck \\( g_{\\text{neck}} \\), a map generator \\( h_{\\text{map}} \\) for attention map prediction and an argument regressor \\( h_{\\text{arg}} \\) for arguments regression. We set the last layer of map generator \\( h_{\\text{map}} \\) to sigmoid, followed by an upsampling layer to match the size of the original input image. We use \\( f(X) \\) to represent the output features of FPN neck. Maps generated by \\( h_{\\text{map}} \\) after upsampling are:" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.885, + 0.891, + 0.902 + ], + "angle": 0, + "content": "\\[\nM _ {m} = h _ {\\text {m a p}} (f (X)) _ {m}, m \\in \\{1, \\dots ., K \\} \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12161" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.119, + 0.087, + 0.852, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.364, + 0.892, + 0.427 + ], + "angle": 0, + "content": "Figure 2: Our network comprises two modules: the parameter predictor and renderer. The input image is transformed into feature embeddings \\( f(X) \\) through a backbone \\( g_{\\text{backbone}} \\) and FPN neck \\( g_{\\text{neck}} \\), which are then utilized by the map generator \\( h_{\\text{map}} \\) and argument regressor \\( h_{\\text{arg}} \\) to generate region maps and filter arguments (e.g. contrast, hue, saturation), respectively. The renderer applies the filter arguments to each region map and aggregates them to produce the final retouching result." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.451, + 0.47, + 0.558 + ], + "angle": 0, + "content": "\\(K\\) is the number of output channels of the last layer. The argument regressor \\(h_{arg}\\) consists of 4 units of convolutional modules. Each module consists of a convolution layer followed by group normalization, \\(\\text{relu}\\) activation and average pooling. Output feature \\(f(X)\\) is finally reduced by \\(h_{arg}\\) to a \\(K \\times N\\) vector representing arguments of all filters for every map:" + }, + { + "type": "equation", + "bbox": [ + 0.081, + 0.563, + 0.469, + 0.594 + ], + "angle": 0, + "content": "\\[\n\\theta_ {m, n} = h _ {\\arg} (f (X)) _ {m, n}, m \\in \\{1, \\dots ., K \\}, n \\in \\{1, \\dots ., N \\} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.469, + 0.683 + ], + "angle": 0, + "content": "\\(K\\) is the number of color filters per map. Given the maps and arguments from the parameter predictor, the renderer applies filter functions \\(F_{m,n} \\in \\{\\text{contrast}, \\dots, \\text{shift}\\}\\) to the input image and merges filtered results via linear summations of increments. The final output image \\(Y\\) in Equation 1 is:" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.689, + 0.469, + 0.731 + ], + "angle": 0, + "content": "\\[\nY = X + \\sum_ {m = 1} ^ {K} \\sum_ {n = 1} ^ {N} \\left(F _ {m, n} \\left(\\theta_ {m, n}, X\\right) - X\\right) \\odot M _ {m} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.869 + ], + "angle": 0, + "content": "In our implementation, we set the number of filters per map as \\( N = 1 \\), indicating that there is one specific filter assigned to each map. This is illustrated in the second row of filter boxes depicted in Figure 2. We also consider the filter Shift as a global function that is applied to the entire image without an attention map. Through our experimentation, we observe that this configuration is sufficient for generating satisfactory results while also providing convenience for users to edit." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Training Loss. The overall framework can be trained end-to-end. Our training loss function is defined as follows:" + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.449, + 0.889, + 0.605 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.616, + 0.892, + 0.692 + ], + "angle": 0, + "content": "Figure 3: A variation of RSFNet could be used to generate masks with controlled shapes. We generate ground truth masks for training via three types of region masks derived from off-the-shelf models: palette-based segmentation, semantic segmentation, and saliency detection." + }, + { + "type": "equation", + "bbox": [ + 0.653, + 0.737, + 0.891, + 0.753 + ], + "angle": 0, + "content": "\\[\nL = L _ {\\text {r e c o n}}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.761, + 0.804, + 0.776 + ], + "angle": 0, + "content": "where \\(L_{\\text{recon}}\\) is the \\(l1\\) loss for reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.786, + 0.891, + 0.817 + ], + "angle": 0, + "content": "3.3. A Variation of RSFNet with Controlled Region Shape" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Our proposed framework has the capability to generate region masks with controlled shapes, with minimal modifications to the training data and loss function. In our observation, artists tend to select regions based on their main color, saliency, or other high-level semantic informa" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12162" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.887, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.451, + 0.896, + 0.514 + ], + "angle": 0, + "content": "Figure 4: Editable white-box retouching. The second column illustrates the arguments and masks generated by RSFNet-saliency that is trained with saliency masks. The third column displays the retouched result. On the right-hand side, the figure showcases three versions of adjustments conducted on the retouched results, with numbers denoted in green boxes indicating the relative incremental value of filters." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.473, + 0.645 + ], + "angle": 0, + "content": "tion. To leverage this insight, we utilize palette-based methods [2], saliency detection [14], and panoptic segmentation networks [5] to generate palette-based, saliency, and semantic masks of the input images used for training, as depicted in Figure 3. Further implementation details can be found in the supplementary material. Our training loss function in Equation 5 is modified as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.677, + 0.47, + 0.693 + ], + "angle": 0, + "content": "\\[\nL = L _ {\\text {r e c o n}} + \\lambda L _ {\\text {m a s k}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.725, + 0.47, + 0.817 + ], + "angle": 0, + "content": "where \\( L_{\\text{recon}} \\) is the \\( l1 \\) loss for reconstruction. When training with palette-based masks and saliency masks, \\( L_{\\text{mask}} \\) is the Dice Loss for mask prediction following loss functions in [22, 23]. We change it to the Cross Entropy Loss when training with semantic masks, at the time map generator \\( h_{\\text{map}} \\) ends with a softmax layer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The model generates region masks and corresponding filter arguments for the input image simultaneously. Users can select region maps and adjust filter arguments to edit results. We show an example of RSFNet-saliency trained with saliency masks in Figure 4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.537, + 0.634, + 0.554 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.571, + 0.795, + 0.589 + ], + "angle": 0, + "content": "4.1. Datasets and Application Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.605, + 0.895, + 0.786 + ], + "angle": 0, + "content": "We conduct experiments on two publicly available datasets: MIT-Adobe FiveK [1] and PPR10K [13]. The MIT-Adobe FiveK consists of 5,000 RAW images with their retouched versions. We follow prior works [8, 12, 28, 27] to adopt images retouched by expert C as ground truths and split the dataset into 4,500 pairs for training and 500 pairs for validation. Images are resized to \\(480\\mathrm{p}\\) during training stage, whereas both of \\(480\\mathrm{p}\\) resolution and original resolution are used during validation. We follow the official split [13] to split PPR10K dataset into 8,875 pairs for training and 2,286 pairs for testing. Images are resized to \\(360\\mathrm{p}\\) resolution for training and validation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.903 + ], + "angle": 0, + "content": "For the MIT-Adobe FiveK dataset, we conduct experiments on two input settings: input zeroed with expertC white balance and input zeroed as shot. The second set of inputs is more challenging as it also deteriorates in white balance. Therefore, to restore its visual appeal, our framework's ability to perform color temperature correction and hue adjustment is required." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "12163" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.09, + 0.337, + 0.237 + ], + "angle": 0, + "content": "
mask as inputmask typePSNR↑SSIM↑
w/saliency(1)23.830.906
w/palette(5)23.450.903
w/semantic(10)21.650.866
w/semantic(5)21.770.867
w/osaliency(1)24.010.909
w/opalette(5)24.140.906
w/osemantic(10)24.090.908
w/osemantic(5)24.170.909
w/osemantic(133)23.750.905
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.077, + 0.242, + 0.351, + 0.283 + ], + "angle": 0, + "content": "(a) Analysis on using mask as input and different mask types. Bracket after \"mask type\" indicates number of masks." + }, + { + "type": "table", + "bbox": [ + 0.387, + 0.125, + 0.615, + 0.2 + ], + "angle": 0, + "content": "
mask firstmasktypePSNR↑SSIM↑
w/saliency(1)23.260.890
w/osaliency(1)24.010.909
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.363, + 0.206, + 0.636, + 0.248 + ], + "angle": 0, + "content": "(b) Analysis of training order. \"Mask first\" refers to building model on pre-trained PoolNet [14]." + }, + { + "type": "table", + "bbox": [ + 0.652, + 0.133, + 0.924, + 0.221 + ], + "angle": 0, + "content": "
backbonedownscaling factorPSNR↑Runtime↓
resnet18x824.659.98
resnet18x424.8312.38
resnet10x824.507.98
resnet10x424.388.71
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.661, + 0.226, + 0.912, + 0.241 + ], + "angle": 0, + "content": "(c) Trade off between speed and accuracy." + }, + { + "type": "table_caption", + "bbox": [ + 0.102, + 0.297, + 0.866, + 0.312 + ], + "angle": 0, + "content": "Table 1: Ablation analysis of our framework. Models are trained on the FiveK dataset [1] with inputs zeroed as shot." + }, + { + "type": "image", + "bbox": [ + 0.089, + 0.336, + 0.26, + 0.476 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.269, + 0.336, + 0.457, + 0.476 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.487, + 0.47, + 0.531 + ], + "angle": 0, + "content": "Figure 5: Comparison between sequential and parallel methods under the same filter functions and network structures." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.56, + 0.295, + 0.575 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.47, + 0.794 + ], + "angle": 0, + "content": "To implement our proposed framework as described in Section 3.2, we employ ResNet18 [9] as the backbone and utilize the output features of layer \\((0,1,2,3)\\) as concatenated input with \\(256\\times 4\\) channels for the FPN neck. The FPN neck reduces the features to \\(64\\times 4\\) channels and feeds them into the map generator and argument regressor. We set the output numbers \\(K\\) of region maps to 10 and 16 for the Adobe-MIT FiveK and PPR10K datasets, respectively. The number of filters per map \\(N\\) is set to \\(N = 1\\), with 10 filters used for MIT-Adobe FiveK, 1 each for shadow, midtones, highlights, where arguments for RGB channels are set equal. For PPR10K, we use 16 filters, with 3 each for shadow, midtones, highlights, where arguments for RGB channels are set differently." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.468, + 0.901 + ], + "angle": 0, + "content": "To implement the variation of RSFNet with controlled region shapes, as described in Section 3.3, we generate ground truth masks for the MIT-Adobe FiveK dataset. Specifically, we generate five palette-based masks, one saliency mask, and five semantic masks for each image. For the PPR10K dataset, we directly use the human-region masks provided in the dataset as ground truth masks for" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.892, + 0.413 + ], + "angle": 0, + "content": "training. The map generator is designed to output 5 channels for the palette-based version, 2 channels for the saliency version, and 5 channels for the semantic version. We use 10 filters for the MIT-Adobe FiveK and 16 filters for the PPR10K, as mentioned above." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.892, + 0.518 + ], + "angle": 0, + "content": "We use the standard Adam optimizer [18] to minimize the loss function in Equation 5 and 6. The mini-batch size is 16. We train models for 1,000,000 iterations with initial learning rate \\( l_{r} = 2 \\times 10^{-4} \\). We use a cosine strategy to gradually decay the learning rate every 250,000 iterations. All experiments are conducted on NVIDIA Tesla V100 GPU." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.892, + 0.58 + ], + "angle": 0, + "content": "In the following sections, we denote our main model in Section 3.2 as \\( RSFNet \\)-map. Variations depicted in Section 3.3 are denoted as \\( RSFNet \\)-palette, \\( RSFNet \\)-saliency and \\( RSFNet \\)-semantic." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.591, + 0.664, + 0.605 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.891, + 0.644 + ], + "angle": 0, + "content": "In this section, we evaluate the ability of our frameworks in different settings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Comparative study of parallel and sequential approaches. We conduct experiments to compare parallel and sequential approaches under the same set of filter functions and backbone structures. For sequential implementations, we modify the network structure to mimic artistic workflows and resemble Harmonizer [11]. We train the network using randomly shuffled 20 unique sequences of filter functions. The results are shown in Figure 5. The parallel approach shows Pareto-optimality with near-maximum PSNR and a lower PSNR standard deviation (std). It also outperforms all sequential approaches in terms of SSIM and SSIM std. We find that altering the sequence of applying filters can lead to considerable changes in performance. Nearly half of these sequences fail to produce satisfactory results. Moreover, during training, the parallel approach converges faster than its sequential counterparts. In addition, the parallel method can be faster than the sequential one." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12164" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.13, + 0.089, + 0.845, + 0.354 + ], + "angle": 0, + "content": "
Method480p zeroed with C's480p zeroed as shotFull Resolution zeroed as shot
PSNR↑SSIM↑△Eab↓PSNR↑SSIM↑△Eab↓Runtime↓PSNR↑SSIM↑Runtime↓
UPE [20]21.88*0.853*10.80*///////
DPE [4]23.75*0.908*9.34*///////
HDRNet [7]24.66*0.915*8.06*///////
DeepLPF [16]24.73*0.916*7.99*23.380.88010.0344.2523.400.8631133.90
CSRNet [8]25.17*0.924*7.75*24.240.9109.703.4923.040.87480.6
SA-3DLUT [21]25.50*/////////
3D-LUT [28]25.29*0.923*7.55*///////
3D-LUT+AdaInt [27]25.49*0.926*7.47*24.500.9129.221.5924.240.8571.80
Harmonizer [11]24.110.9048.2323.230.89310.1416.7422.570.87027.98
RSFNet-map25.490.9247.2324.640.9159.169.9824.390.89412.35
RSFNet-palette25.010.9147.6224.220.9119.5219.7623.880.88868.57
RSFNet-saliency24.780.9167.8624.200.9129.4214.0924.000.89059.42
RSFNet-semantic24.760.9157.7724.190.9129.4524.0723.890.89171.18
RSFNet-global24.310.9118.2123.430.90410.169.4223.260.88510.99
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.363, + 0.895, + 0.44 + ], + "angle": 0, + "content": "Table 2: Quantitative comparisons for retouching tasks on FiveK dataset [1]. Runtime is measured in milliseconds. “*” means the result is adopted from the paper [27]. “/” means the result is not available. Runtime shown in previous works are not adopted due to different hardware settings. Results with the first and second performance are colored as red and blue respectively. White-box methods are colored as violet. Full resolution images results are evaluated using Python, while others are evaluated on Matlab." + }, + { + "type": "table", + "bbox": [ + 0.231, + 0.453, + 0.744, + 0.609 + ], + "angle": 0, + "content": "
Method360p expert a360p expert b360p expert c
PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑
DeepLPF [16]23.470.89222.770.87523.730.896
CSRNet [8]24.010.93623.910.93824.310.931
3D-LUT+AdaInt [27]25.980.94724.910.93625.480.919
Harmonizer [11]24.760.92922.790.88524.560.902
RSFNet-map25.580.94924.810.94525.520.939
RSFNet-saliency25.530.94624.720.94425.110.939
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.618, + 0.895, + 0.651 + ], + "angle": 0, + "content": "Table 3: Quantitative comparisons for retouching tasks on PPR10K dataset [13]. All the models are trained on data without augmentations. White-box methods are colored as violet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.473, + 0.873 + ], + "angle": 0, + "content": "Training map generation and arguments regression separately. To train models with controlled region shapes, we experiment with using pre-trained PoolNet [14] and adding an FPN neck followed by an argument regressor to the backbone instead of training from scratch. During training, we fix the weights of the backbone to keep the saliency mask generated by the network unchanged. The quantitative results are shown in Table 1b, which indicates that there is no superiority over training from scratch. The reason for this might be that a network trained only on semantic data lacks sufficient information for retouching. Therefore, it is better to train the map generation and arguments regression tasks simultaneously." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.889 + ], + "angle": 0, + "content": "Using Masks as Input. For training models with controlled region shapes, we can use masks concatenated with the image as input for our model. We train three models using three sets of masks as input, respectively. The results are shown in Table 1a. The retouching results evaluated on PSNR and SSIM [24] are lower than in other settings. This may be because the ground truth masks are generated by off-the-shelf models, which may differ from the underlying real masks of the dataset. Masks are slightly modified by the map generator in the inference stage to achieve better retouching results. Therefore, simple concatenation of masks with the input image can lead to worse performance compared to our design of the variant of RSFNet, which generates masks and filter arguments simultaneously." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12165" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.887, + 0.423 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.095, + 0.432, + 0.877, + 0.45 + ], + "angle": 0, + "content": "Figure 6: Qualitative comparison of selected methods. \"RSFNet-map\" means our main model explained in Section 3.2" + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.497, + 0.425, + 0.673 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.696, + 0.471, + 0.743 + ], + "angle": 0, + "content": "Figure 7: Boxplot of user study. The dashed green line and the solid black line inside the box are the mean and the median preference percentage respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Trade Off Between Speed and Accuracy. As we decrease the number of downsample operations in the backbone, the feature size grows larger and time costs increase. However, quantitative results of retouching also become better, as shown in 1c. Speed is measured in milliseconds." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.474, + 0.799, + 0.491 + ], + "angle": 0, + "content": "4.4. Comparison with State-of-the-Art" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.503, + 0.892, + 0.73 + ], + "angle": 0, + "content": "We compare our methods with the state-of-the-art for black-box and white-box image retouching tasks. The selected methods are compared on PSNR, SSIM [24], the \\(L_{2}\\)-distance in CIE LAB color space \\((\\triangle E_{ab})\\) and the inference speed. We follow the practice in [27] to measure the GPU inference time on 100 images and report the average. Quantitative results are shown in Table 2 and 3. RSFNet-map refers to our main model in Section 3.2, RSFNet-saliency, RSFNet-palette and RSFNet-semantic refers to models trained with three sets of masks respectively in Section 3.3. In addition, we evaluate a global retouching model without the map generator, denoted as RSFNet-global. Other models are trained using their official public codes and default configurations. All experiments are executed on an NVIDIA Tesla V100 GPU." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Our proposed method, \\(RSFNet\\)-map, demonstrates its effectiveness in temperature correction and color enhancement, especially for the second set of inputs under more deteriorating shooting conditions. Although \\(RSFNet\\)-map achieves state-of-the-art results with negligible increase, while other RSFNet variations lag behind the state of the art, it is important to note that our white-box framework provides human-understandable ways for retouching, which makes it more convenient for users to edit and assess retouching results compared to other black-box methods. When compared with state-of-the-art white-box methods" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12166" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.101, + 0.856, + 0.507 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.52, + 0.895, + 0.552 + ], + "angle": 0, + "content": "Figure 8: Editable image retouching. \"RSFNet-saliency\", \"RSFNet-semantic\" means RSFNet trained with saliency masks and semantic masks respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.577, + 0.47, + 0.699 + ], + "angle": 0, + "content": "such as Harmonizer [11], all of our models exhibit better performance with faster speed. Furthermore, using 3D-LUTs to encode filter functions could potentially accelerate our models, a technique commonly implemented in traditional retouching tools. For PPR10K [13], we also evaluate our methods using a random split setup. The results are provided in supplementary material, consistently reinforcing the conclusions drawn from previous experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The qualitative results presented in Figure 6 demonstrate that our proposed method, \\( RSFNet \\)-map, exhibits superior performance in handling color transitions across regions, particularly in highlight areas, compared to 3D-LUT based methods such as AdaInt, as shown in the first row of the figure. Furthermore, we conduct a comparison with Harmonizer [11] on editable retouching, as shown in Figure 8. Our white-box framework offers more degrees of freedom than global-retouching manipulations to achieve region-specific retouching. For instance, when the temperature is adjusted globally using Harmonizer, the sky in the first image turns yellow. On the other hand, our \\( RSFNet \\)-saliency model can modify the temperature of the foreground girl while leav-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.654 + ], + "angle": 0, + "content": "ing other regions unaffected. In the second image, global temperature adjustment by Harmonizer turns the lake and mountains blue. In contrast, \\( RSFNet \\)-semantic only modifies the sky temperature, leaving the mountains and lake unchanged." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.893, + 0.883 + ], + "angle": 0, + "content": "To further validate the effectiveness of our proposed framework, we conduct a user study to evaluate human preferences for RSFNet and other state-of-the-art methods, including CSRNet [8], AdaInt [27], and Hormonizer [11]. To form the test set, we randomly select 58 images from the validation set of Adobe-MIT FiveK using the input zeroed with expertC white balance and input zeroed as shot settings, as well as an additional 20 images downloaded from the internet. During the experiment, we display retouched images produced by all methods, including the original input, to 22 participants. Participants are asked to select the best result from a randomly shuffled set of retouched images generated by all methods. We calculate the preferences of participants for each method and plot the results using a box plot, as shown in Figure 7." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Among the compared methods, AdaInt [27] achieves" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12167" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.272 + ], + "angle": 0, + "content": "higher mean and median percentages. RSFNet exhibits more stable performance with a higher bottom percentage and the smallest standard variance percentage than the other methods. In comparison to the white-box method Harmonizer [11], RSFNet demonstrates superior user preference percentages. The boxplot illustrates the varying preferences of different users, highlighting the significance of editable capability. As RSFNet utilizes traditional color filters for retouching, it can be readily integrated into traditional retouching tools. Users can further enhance the visual appeal of the retouched results according to their own preferences through an interface." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.473, + 0.485 + ], + "angle": 0, + "content": "Video Retouching. Our proposed RSFNet model also demonstrates applicability to video retouching, as shown in Figure 8. The filter arguments remain constant within a single video clip for all frames, ensuring consistency throughout the retouching process. However, for RSFNet variations with controlled region shapes, such as \\(RSFNet\\)-saliency, the retouching consistency across frames relies on the consistency of region masks across frames. Although filter arguments can alleviate the inconsistency caused by masks, severe inconsistency problems in masks may still affect retouching results. With the assistance of a more robust tracking algorithm, these models can achieve better performance in editable video retouching, highlighting the potential of RSFNet in various retouching applications." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.498, + 0.327, + 0.515 + ], + "angle": 0, + "content": "5. Limitation and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.47, + 0.719 + ], + "angle": 0, + "content": "We develop our framework under the assumption that all adjustments are done in one layer, which is then combined via linear summations of increments of all filters to obtain the final result. Therefore, although our model provides a white-box retouching framework that aligns with the intuition of human artists, it is unable to cover all adjustments that artists could conduct using professional software. However, we believe that if the cache data in the retouching process of artists is available, such as the region masks used for region-specific retouching, our model equipped with a more complicated structure, such as a cascaded structure in [10, 11], could behave more similarly to a real human artist by learning from this data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.871 + ], + "angle": 0, + "content": "This paper introduces RSFNet, a white-box framework for image retouching that utilizes a divide-and-conquer strategy to generate region maps and human-understandable filter arguments. The resulting filtered images are combined using linear summations, allowing for a wider range of filter classes and achieving fine-grained enhancement with superior performance. A variation of RSFNet with controlled shape region masks is also proposed for user convenience. Extensive experiments are presented to demonstrate the effectiveness of RSFNet." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Acknowledgement This work was supported by Alibaba" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "Group through Alibaba Innovative Research (AIR) Program and Alibaba-NTU Singapore Joint Research Institute (JRI), Nanyang Technological University, Singapore. We appreciate Mr. Wang Yuxi's efforts in generating additional experimental results during the rebuttal period." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.181, + 0.597, + 0.197 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.205, + 0.895, + 0.262 + ], + "angle": 0, + "content": "[1] Vladimir Bychkovsky, Sylvain Paris, Eric Chan, and Frédo Durand. 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In CVPR, pages 15689-15698, 2021." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.887 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12169" + } + ] +] \ No newline at end of file diff --git a/2023/RSFNet_ A White-Box Image Retouching Approach using Region-Specific Color Filters/a1a06f38-ffb3-49f3-88a3-88bb8d7af4de_origin.pdf b/2023/RSFNet_ A White-Box Image Retouching Approach using Region-Specific Color Filters/a1a06f38-ffb3-49f3-88a3-88bb8d7af4de_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8d2baf5dea7720bd3e71eeaa23550b9adaf1b7a7 --- /dev/null +++ b/2023/RSFNet_ A White-Box Image Retouching Approach using Region-Specific Color Filters/a1a06f38-ffb3-49f3-88a3-88bb8d7af4de_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:69d59576142923f5fac373868040fd938e4f2543f422d12f5eb238facd6e3ef6 +size 5641561 diff --git a/2023/RSFNet_ A White-Box Image Retouching Approach using Region-Specific Color Filters/full.md b/2023/RSFNet_ A White-Box Image Retouching Approach using Region-Specific Color Filters/full.md new file mode 100644 index 0000000000000000000000000000000000000000..8b458dcb8feac1d3980f1b6695e98f926992962f --- /dev/null +++ b/2023/RSFNet_ A White-Box Image Retouching Approach using Region-Specific Color Filters/full.md @@ -0,0 +1,239 @@ +# RSFNet: A White-Box Image Retouching Approach using Region-Specific Color Filters + +Wenqi Ouyang $^{1}$ , Yi Dong $^{2}$ , Xiaoyang Kang $^{1}$ , Peiran Ren $^{1}$ , Xin Xu $^{1}$ , Xuansong Xie $^{1}$ $^{1}$ DAMO Academy, Alibaba Group, $^{2}$ Nanyang Technological University + +wenqi.oywq@alibaba-inc.com, ydong004@ntu.edu.sg, + +{peiran.rpr, kangxiaoyang.kxy, chris.xx, xingtong.xxs}@alibaba-inc.com + +# Abstract + +Retouching images is an essential aspect of enhancing the visual appeal of photos. Although users often share common aesthetic preferences, their retouching methods may vary based on their individual preferences. Therefore, there is a need for white-box approaches that produce satisfying results and enable users to conveniently edit their images simultaneously. Recent white-box retouching methods rely on cascaded global filters that provide image-level filter arguments but cannot perform fine-grained retouching. In contrast, colorists typically employ a divide-and-conquer approach, performing a series of region-specific fine-grained enhancements when using traditional tools like Davinci Resolve. We draw on this insight to develop a white-box framework for photo retouching using parallel region-specific filters, called RSFNet. Our model generates filter arguments (e.g., saturation, contrast, hue) and attention maps of regions for each filter simultaneously. Instead of cascading filters, RSFNet employs linear summations of filters, allowing for a more diverse range of filter classes that can be trained more easily. Our experiments demonstrate that RSFNet achieves state-of-the-art results, offering satisfying aesthetic appeal and increased user convenience for editable white-box retouching. Code is available at https://github.com/Vicky0522/RSFNet. + +# 1. Introduction + +Photos and videos recorded by the camera usually lack aesthetic quality due to poor shooting condition and inexperienced photographer. Artists often use professional-grade softwares (e.g., PhotoShop for image, Davinci Resolve for video) to enhance image and video quality. However, it requires professional retouching skills to conduct a series of sophisticated manual adjustments. The use of fool-proof applications that present various style templates simplifies the retouching procedure, but it is unable to achieve opti + +![](images/674e39577ef6977caea0f5c63d4025f2a9122acc3d3cfe231479c2b3f468170d.jpg) +Figure 1: Architecture of our white-box retouching framework. Our model generates filter arguments (e.g., saturation, midtones, highlights) and attention maps of regions for corresponding filter simultaneously. Final result is obtained by conducting linear summations on filtered results. + +mal results due to the lack of enhancement capability. + +Recent learning-based methods have demonstrated the strong capability of deep neural nets for automatic photo retouching. Automatic systems are established to generate the optimal result end-to-end. However, one of the most significant considerations is that retouching is not a problem with an exclusive solution. People have different retouching preferences. Even the same artist may retouch the same image in different styles to meet various demands. In order to provide convenience for manual edits, automatic retouching systems must provide not only the suggested result, but also the retouching strategy in a way understandable by humans. + +Taking these considerations into account, we propose a white-box framework that uses the divide-and-conquer strategy employed by artists in traditional retouching tools. Our model generates attention maps of regions as well as filter arguments for traditional edits for these regions. This allows users to alter the suggested results to their preferences. + +The main contributions of this work are as follows: + +- We redefine the retouching problem according to the + +divide-and-conquer strategy, focusing on finding attention maps for regions and human-understandable filter adjustments per map to achieve the best results. + +- We propose RSFNet, which generates pixel-level attention maps of regions and filter arguments simultaneously. By conducting linear summations on the filtered results, our model demonstrates superior performance to global white-box retouching methods, with a wider range of filter classes for fine-grained enhancement and a simpler training procedure. +- We propose a scheme that allows users to edit RSFNet suggested results, demonstrating its effectiveness and convenience in image applications. + +# 2. Related Works + +Deep Image Enhancement. Many attempts have been made in image enhancement using learning-based methods. These methods can broadly be classified into two categories: deep-convolutional-based models and physical-inspired models. The former [3, 4, 6, 25, 29] view enhancement as a synthesis problem and use fully convolutional generators [15] to achieve dense image-to-image translation. While these methods exhibit strong capability for generating and enhancing details, they suffer from heavy structure and low inference speed. The latter category of works defines enhancement as the parameter prediction of a physical model and uses deep learning strategies to fit the model. These models include 3D-LUT [21, 28, 27], parametric filters [16], conditional sequential global modulation [8], affine color transformations [7, 20], 1D mapping curves [19, 12, 17]. Their enhancement capabilities depend on the range of transformation functions the physical model covers. Among those, models based on global 3D-LUT [27, 28] are well-designed for retouching and could achieve high performance with fast inference speed. However, they suffer from uneven transitions in smooth areas due to lack of fine-grained local adjustment. Spatial-Aware 3D-LUT [21] alleviate the problem of global 3D-LUT by computing pixel-level weight maps. All these methods have a black-box structure or unintuitive parameters that are hard for humans to understand. DeepLPF [16] has been a significant milestone in the field of region-specific color enhancement via local parametric filters but suffers from low inference speed and limited filter shapes. The three types of filters with three implementations each results in complex maps that are hard to understand. + +White-box Image Editing. Recent white-box methods [10, 11, 26, 30] have decoupled image editing into a series of human understandable operations and deep learning strategies to predict them. Of these, our work is most related to [11, 10]. However, they train networks with cascaded filter argument prediction modules to perform global retouching step-by-step. Our model utilizes pixel-wise region- + +specific filters to capture local features and employs linear summations to combine filters, thus having stronger capability to cover a wider range of color transformation functions. + +# 3. Method + +# 3.1. Design Motivation + +Traditional Retouching Strategy. In the traditional retouching process, local adjustments for different regions are conducted separately and then aggregated together to accomplish fine-grained enhancement. All the adjustments could be accomplished in one Layer, where filters are all conducted on the same image instead of results from previous filters. We adopt this divide-and-conquer strategy to build our framework. We select 10 commonly used retouching filters from traditional tools(e.g., Davinci Resolve) to represent adjustment manipulations, including contrast, saturation, hue, temperature, shadows, midtones, highlights and shift. For more details about filters, please refer to our supplementary material. Therefore, retouching is defined as finding pixel-level attention maps and corresponding adjustments for each map to achieve the most desirable result. We adopt this convention and represent retouching result $Y$ as adding linear summations of increments resulted by filters to the original image as: + +$$ +Y = X + \sum_ {m} \sum_ {n} \left(F _ {m, n} \left(\theta_ {m, n}, X\right) - X\right) \odot M _ {m} \tag {1} +$$ + +Where $\theta_{m,n}$ and $F_{m,n} \in \{\text{contrast}, \dots, \text{shift}\}$ are the argument value and filter function of the $n$ th filter for the $m$ th attention map of input image $X$ respectively, $M_{m}$ is the $m$ th attention map for image $X$ . It should be noticed that this linear representation makes our optimization process much simpler than other white-box methods. + +# 3.2. Architecture + +Our model consists of two modules, the parameter predictor and the renderer. The architecture of the parameter predictor shares a similar overall structure with previous segmentation models [22, 23]. As illustrated in Figure 2, the network $g$ is composed of a backbone $g_{\text{backbone}}$ , a FPN neck $g_{\text{neck}}$ , a map generator $h_{\text{map}}$ for attention map prediction and an argument regressor $h_{\text{arg}}$ for arguments regression. We set the last layer of map generator $h_{\text{map}}$ to sigmoid, followed by an upsampling layer to match the size of the original input image. We use $f(X)$ to represent the output features of FPN neck. Maps generated by $h_{\text{map}}$ after upsampling are: + +$$ +M _ {m} = h _ {\text {m a p}} (f (X)) _ {m}, m \in \{1, \dots ., K \} \tag {2} +$$ + +![](images/1fa1e6a7ff4eeef981125cee46064f989a073c8f2da72da946887fbfb672e634.jpg) +Figure 2: Our network comprises two modules: the parameter predictor and renderer. The input image is transformed into feature embeddings $f(X)$ through a backbone $g_{\text{backbone}}$ and FPN neck $g_{\text{neck}}$ , which are then utilized by the map generator $h_{\text{map}}$ and argument regressor $h_{\text{arg}}$ to generate region maps and filter arguments (e.g. contrast, hue, saturation), respectively. The renderer applies the filter arguments to each region map and aggregates them to produce the final retouching result. + +$K$ is the number of output channels of the last layer. The argument regressor $h_{arg}$ consists of 4 units of convolutional modules. Each module consists of a convolution layer followed by group normalization, $\text{relu}$ activation and average pooling. Output feature $f(X)$ is finally reduced by $h_{arg}$ to a $K \times N$ vector representing arguments of all filters for every map: + +$$ +\theta_ {m, n} = h _ {\arg} (f (X)) _ {m, n}, m \in \{1, \dots ., K \}, n \in \{1, \dots ., N \} \tag {3} +$$ + +$K$ is the number of color filters per map. Given the maps and arguments from the parameter predictor, the renderer applies filter functions $F_{m,n} \in \{\text{contrast}, \dots, \text{shift}\}$ to the input image and merges filtered results via linear summations of increments. The final output image $Y$ in Equation 1 is: + +$$ +Y = X + \sum_ {m = 1} ^ {K} \sum_ {n = 1} ^ {N} \left(F _ {m, n} \left(\theta_ {m, n}, X\right) - X\right) \odot M _ {m} \tag {4} +$$ + +In our implementation, we set the number of filters per map as $N = 1$ , indicating that there is one specific filter assigned to each map. This is illustrated in the second row of filter boxes depicted in Figure 2. We also consider the filter Shift as a global function that is applied to the entire image without an attention map. Through our experimentation, we observe that this configuration is sufficient for generating satisfactory results while also providing convenience for users to edit. + +Training Loss. The overall framework can be trained end-to-end. Our training loss function is defined as follows: + +![](images/069589aeb25c49168e0a8e104ef4ac02ded19d73908a3fff6f9fd3fbebc760e7.jpg) +Figure 3: A variation of RSFNet could be used to generate masks with controlled shapes. We generate ground truth masks for training via three types of region masks derived from off-the-shelf models: palette-based segmentation, semantic segmentation, and saliency detection. + +$$ +L = L _ {\text {r e c o n}}, \tag {5} +$$ + +where $L_{\text{recon}}$ is the $l1$ loss for reconstruction. + +# 3.3. A Variation of RSFNet with Controlled Region Shape + +Our proposed framework has the capability to generate region masks with controlled shapes, with minimal modifications to the training data and loss function. In our observation, artists tend to select regions based on their main color, saliency, or other high-level semantic informa + +![](images/4dca9de783795fce137d9e2c4b210daf9bf36b7201b051d2e9e573f0f84df63d.jpg) +Figure 4: Editable white-box retouching. The second column illustrates the arguments and masks generated by RSFNet-saliency that is trained with saliency masks. The third column displays the retouched result. On the right-hand side, the figure showcases three versions of adjustments conducted on the retouched results, with numbers denoted in green boxes indicating the relative incremental value of filters. + +tion. To leverage this insight, we utilize palette-based methods [2], saliency detection [14], and panoptic segmentation networks [5] to generate palette-based, saliency, and semantic masks of the input images used for training, as depicted in Figure 3. Further implementation details can be found in the supplementary material. Our training loss function in Equation 5 is modified as follows: + +$$ +L = L _ {\text {r e c o n}} + \lambda L _ {\text {m a s k}}, \tag {6} +$$ + +where $L_{\text{recon}}$ is the $l1$ loss for reconstruction. When training with palette-based masks and saliency masks, $L_{\text{mask}}$ is the Dice Loss for mask prediction following loss functions in [22, 23]. We change it to the Cross Entropy Loss when training with semantic masks, at the time map generator $h_{\text{map}}$ ends with a softmax layer. + +The model generates region masks and corresponding filter arguments for the input image simultaneously. Users can select region maps and adjust filter arguments to edit results. We show an example of RSFNet-saliency trained with saliency masks in Figure 4. + +# 4. Experiments + +# 4.1. Datasets and Application Settings + +We conduct experiments on two publicly available datasets: MIT-Adobe FiveK [1] and PPR10K [13]. The MIT-Adobe FiveK consists of 5,000 RAW images with their retouched versions. We follow prior works [8, 12, 28, 27] to adopt images retouched by expert C as ground truths and split the dataset into 4,500 pairs for training and 500 pairs for validation. Images are resized to $480\mathrm{p}$ during training stage, whereas both of $480\mathrm{p}$ resolution and original resolution are used during validation. We follow the official split [13] to split PPR10K dataset into 8,875 pairs for training and 2,286 pairs for testing. Images are resized to $360\mathrm{p}$ resolution for training and validation. + +For the MIT-Adobe FiveK dataset, we conduct experiments on two input settings: input zeroed with expertC white balance and input zeroed as shot. The second set of inputs is more challenging as it also deteriorates in white balance. Therefore, to restore its visual appeal, our framework's ability to perform color temperature correction and hue adjustment is required. + +
mask as inputmask typePSNR↑SSIM↑
w/saliency(1)23.830.906
w/palette(5)23.450.903
w/semantic(10)21.650.866
w/semantic(5)21.770.867
w/osaliency(1)24.010.909
w/opalette(5)24.140.906
w/osemantic(10)24.090.908
w/osemantic(5)24.170.909
w/osemantic(133)23.750.905
+ +(a) Analysis on using mask as input and different mask types. Bracket after "mask type" indicates number of masks. + +
mask firstmasktypePSNR↑SSIM↑
w/saliency(1)23.260.890
w/osaliency(1)24.010.909
+ +(b) Analysis of training order. "Mask first" refers to building model on pre-trained PoolNet [14]. + +
backbonedownscaling factorPSNR↑Runtime↓
resnet18x824.659.98
resnet18x424.8312.38
resnet10x824.507.98
resnet10x424.388.71
+ +(c) Trade off between speed and accuracy. + +Table 1: Ablation analysis of our framework. Models are trained on the FiveK dataset [1] with inputs zeroed as shot. + +![](images/b580ce3d2e6f88e4c3bfae6e43ae112e56813c24e4a3f0f299f0cbc3e174e4f4.jpg) +Figure 5: Comparison between sequential and parallel methods under the same filter functions and network structures. + +![](images/797b51d18273ef8e24923f1dd0dd02751e38eb9943d1aa820313ce50a205dbf1.jpg) + +# 4.2. Implementation Details + +To implement our proposed framework as described in Section 3.2, we employ ResNet18 [9] as the backbone and utilize the output features of layer $(0,1,2,3)$ as concatenated input with $256\times 4$ channels for the FPN neck. The FPN neck reduces the features to $64\times 4$ channels and feeds them into the map generator and argument regressor. We set the output numbers $K$ of region maps to 10 and 16 for the Adobe-MIT FiveK and PPR10K datasets, respectively. The number of filters per map $N$ is set to $N = 1$ , with 10 filters used for MIT-Adobe FiveK, 1 each for shadow, midtones, highlights, where arguments for RGB channels are set equal. For PPR10K, we use 16 filters, with 3 each for shadow, midtones, highlights, where arguments for RGB channels are set differently. + +To implement the variation of RSFNet with controlled region shapes, as described in Section 3.3, we generate ground truth masks for the MIT-Adobe FiveK dataset. Specifically, we generate five palette-based masks, one saliency mask, and five semantic masks for each image. For the PPR10K dataset, we directly use the human-region masks provided in the dataset as ground truth masks for + +training. The map generator is designed to output 5 channels for the palette-based version, 2 channels for the saliency version, and 5 channels for the semantic version. We use 10 filters for the MIT-Adobe FiveK and 16 filters for the PPR10K, as mentioned above. + +We use the standard Adam optimizer [18] to minimize the loss function in Equation 5 and 6. The mini-batch size is 16. We train models for 1,000,000 iterations with initial learning rate $l_{r} = 2 \times 10^{-4}$ . We use a cosine strategy to gradually decay the learning rate every 250,000 iterations. All experiments are conducted on NVIDIA Tesla V100 GPU. + +In the following sections, we denote our main model in Section 3.2 as $RSFNet$ -map. Variations depicted in Section 3.3 are denoted as $RSFNet$ -palette, $RSFNet$ -saliency and $RSFNet$ -semantic. + +# 4.3. Ablation Studies + +In this section, we evaluate the ability of our frameworks in different settings. + +Comparative study of parallel and sequential approaches. We conduct experiments to compare parallel and sequential approaches under the same set of filter functions and backbone structures. For sequential implementations, we modify the network structure to mimic artistic workflows and resemble Harmonizer [11]. We train the network using randomly shuffled 20 unique sequences of filter functions. The results are shown in Figure 5. The parallel approach shows Pareto-optimality with near-maximum PSNR and a lower PSNR standard deviation (std). It also outperforms all sequential approaches in terms of SSIM and SSIM std. We find that altering the sequence of applying filters can lead to considerable changes in performance. Nearly half of these sequences fail to produce satisfactory results. Moreover, during training, the parallel approach converges faster than its sequential counterparts. In addition, the parallel method can be faster than the sequential one. + +
Method480p zeroed with C's480p zeroed as shotFull Resolution zeroed as shot
PSNR↑SSIM↑△Eab↓PSNR↑SSIM↑△Eab↓Runtime↓PSNR↑SSIM↑Runtime↓
UPE [20]21.88*0.853*10.80*///////
DPE [4]23.75*0.908*9.34*///////
HDRNet [7]24.66*0.915*8.06*///////
DeepLPF [16]24.73*0.916*7.99*23.380.88010.0344.2523.400.8631133.90
CSRNet [8]25.17*0.924*7.75*24.240.9109.703.4923.040.87480.6
SA-3DLUT [21]25.50*/////////
3D-LUT [28]25.29*0.923*7.55*///////
3D-LUT+AdaInt [27]25.49*0.926*7.47*24.500.9129.221.5924.240.8571.80
Harmonizer [11]24.110.9048.2323.230.89310.1416.7422.570.87027.98
RSFNet-map25.490.9247.2324.640.9159.169.9824.390.89412.35
RSFNet-palette25.010.9147.6224.220.9119.5219.7623.880.88868.57
RSFNet-saliency24.780.9167.8624.200.9129.4214.0924.000.89059.42
RSFNet-semantic24.760.9157.7724.190.9129.4524.0723.890.89171.18
RSFNet-global24.310.9118.2123.430.90410.169.4223.260.88510.99
+ +Table 2: Quantitative comparisons for retouching tasks on FiveK dataset [1]. Runtime is measured in milliseconds. “*” means the result is adopted from the paper [27]. “/” means the result is not available. Runtime shown in previous works are not adopted due to different hardware settings. Results with the first and second performance are colored as red and blue respectively. White-box methods are colored as violet. Full resolution images results are evaluated using Python, while others are evaluated on Matlab. + +
Method360p expert a360p expert b360p expert c
PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑
DeepLPF [16]23.470.89222.770.87523.730.896
CSRNet [8]24.010.93623.910.93824.310.931
3D-LUT+AdaInt [27]25.980.94724.910.93625.480.919
Harmonizer [11]24.760.92922.790.88524.560.902
RSFNet-map25.580.94924.810.94525.520.939
RSFNet-saliency25.530.94624.720.94425.110.939
+ +Table 3: Quantitative comparisons for retouching tasks on PPR10K dataset [13]. All the models are trained on data without augmentations. White-box methods are colored as violet. + +Training map generation and arguments regression separately. To train models with controlled region shapes, we experiment with using pre-trained PoolNet [14] and adding an FPN neck followed by an argument regressor to the backbone instead of training from scratch. During training, we fix the weights of the backbone to keep the saliency mask generated by the network unchanged. The quantitative results are shown in Table 1b, which indicates that there is no superiority over training from scratch. The reason for this might be that a network trained only on semantic data lacks sufficient information for retouching. Therefore, it is better to train the map generation and arguments regression tasks simultaneously. + +Using Masks as Input. For training models with controlled region shapes, we can use masks concatenated with the image as input for our model. We train three models using three sets of masks as input, respectively. The results are shown in Table 1a. The retouching results evaluated on PSNR and SSIM [24] are lower than in other settings. This may be because the ground truth masks are generated by off-the-shelf models, which may differ from the underlying real masks of the dataset. Masks are slightly modified by the map generator in the inference stage to achieve better retouching results. Therefore, simple concatenation of masks with the input image can lead to worse performance compared to our design of the variant of RSFNet, which generates masks and filter arguments simultaneously. + +![](images/fe072dae96562455a2c04aa476d03a45dd0a8ccb0d4a6614f3b101af5d457999.jpg) +Figure 6: Qualitative comparison of selected methods. "RSFNet-map" means our main model explained in Section 3.2 + +![](images/899cd8149a655c259275fd724506b3c48c996843590f9952e460c91d4e0e3501.jpg) +Figure 7: Boxplot of user study. The dashed green line and the solid black line inside the box are the mean and the median preference percentage respectively. + +Trade Off Between Speed and Accuracy. As we decrease the number of downsample operations in the backbone, the feature size grows larger and time costs increase. However, quantitative results of retouching also become better, as shown in 1c. Speed is measured in milliseconds. + +# 4.4. Comparison with State-of-the-Art + +We compare our methods with the state-of-the-art for black-box and white-box image retouching tasks. The selected methods are compared on PSNR, SSIM [24], the $L_{2}$ -distance in CIE LAB color space $(\triangle E_{ab})$ and the inference speed. We follow the practice in [27] to measure the GPU inference time on 100 images and report the average. Quantitative results are shown in Table 2 and 3. RSFNet-map refers to our main model in Section 3.2, RSFNet-saliency, RSFNet-palette and RSFNet-semantic refers to models trained with three sets of masks respectively in Section 3.3. In addition, we evaluate a global retouching model without the map generator, denoted as RSFNet-global. Other models are trained using their official public codes and default configurations. All experiments are executed on an NVIDIA Tesla V100 GPU. + +Our proposed method, $RSFNet$ -map, demonstrates its effectiveness in temperature correction and color enhancement, especially for the second set of inputs under more deteriorating shooting conditions. Although $RSFNet$ -map achieves state-of-the-art results with negligible increase, while other RSFNet variations lag behind the state of the art, it is important to note that our white-box framework provides human-understandable ways for retouching, which makes it more convenient for users to edit and assess retouching results compared to other black-box methods. When compared with state-of-the-art white-box methods + +![](images/ecdc78af2604b0e3704b6e4005ae955f8d970292043771ec0f2d5ac1c3a2a2d4.jpg) +Figure 8: Editable image retouching. "RSFNet-saliency", "RSFNet-semantic" means RSFNet trained with saliency masks and semantic masks respectively. + +such as Harmonizer [11], all of our models exhibit better performance with faster speed. Furthermore, using 3D-LUTs to encode filter functions could potentially accelerate our models, a technique commonly implemented in traditional retouching tools. For PPR10K [13], we also evaluate our methods using a random split setup. The results are provided in supplementary material, consistently reinforcing the conclusions drawn from previous experiments. + +The qualitative results presented in Figure 6 demonstrate that our proposed method, $RSFNet$ -map, exhibits superior performance in handling color transitions across regions, particularly in highlight areas, compared to 3D-LUT based methods such as AdaInt, as shown in the first row of the figure. Furthermore, we conduct a comparison with Harmonizer [11] on editable retouching, as shown in Figure 8. Our white-box framework offers more degrees of freedom than global-retouching manipulations to achieve region-specific retouching. For instance, when the temperature is adjusted globally using Harmonizer, the sky in the first image turns yellow. On the other hand, our $RSFNet$ -saliency model can modify the temperature of the foreground girl while leav- + +ing other regions unaffected. In the second image, global temperature adjustment by Harmonizer turns the lake and mountains blue. In contrast, $RSFNet$ -semantic only modifies the sky temperature, leaving the mountains and lake unchanged. + +To further validate the effectiveness of our proposed framework, we conduct a user study to evaluate human preferences for RSFNet and other state-of-the-art methods, including CSRNet [8], AdaInt [27], and Hormonizer [11]. To form the test set, we randomly select 58 images from the validation set of Adobe-MIT FiveK using the input zeroed with expertC white balance and input zeroed as shot settings, as well as an additional 20 images downloaded from the internet. During the experiment, we display retouched images produced by all methods, including the original input, to 22 participants. Participants are asked to select the best result from a randomly shuffled set of retouched images generated by all methods. We calculate the preferences of participants for each method and plot the results using a box plot, as shown in Figure 7. + +Among the compared methods, AdaInt [27] achieves + +higher mean and median percentages. RSFNet exhibits more stable performance with a higher bottom percentage and the smallest standard variance percentage than the other methods. In comparison to the white-box method Harmonizer [11], RSFNet demonstrates superior user preference percentages. The boxplot illustrates the varying preferences of different users, highlighting the significance of editable capability. As RSFNet utilizes traditional color filters for retouching, it can be readily integrated into traditional retouching tools. Users can further enhance the visual appeal of the retouched results according to their own preferences through an interface. + +Video Retouching. Our proposed RSFNet model also demonstrates applicability to video retouching, as shown in Figure 8. The filter arguments remain constant within a single video clip for all frames, ensuring consistency throughout the retouching process. However, for RSFNet variations with controlled region shapes, such as $RSFNet$ -saliency, the retouching consistency across frames relies on the consistency of region masks across frames. Although filter arguments can alleviate the inconsistency caused by masks, severe inconsistency problems in masks may still affect retouching results. With the assistance of a more robust tracking algorithm, these models can achieve better performance in editable video retouching, highlighting the potential of RSFNet in various retouching applications. + +# 5. Limitation and Conclusion + +We develop our framework under the assumption that all adjustments are done in one layer, which is then combined via linear summations of increments of all filters to obtain the final result. Therefore, although our model provides a white-box retouching framework that aligns with the intuition of human artists, it is unable to cover all adjustments that artists could conduct using professional software. However, we believe that if the cache data in the retouching process of artists is available, such as the region masks used for region-specific retouching, our model equipped with a more complicated structure, such as a cascaded structure in [10, 11], could behave more similarly to a real human artist by learning from this data. + +This paper introduces RSFNet, a white-box framework for image retouching that utilizes a divide-and-conquer strategy to generate region maps and human-understandable filter arguments. The resulting filtered images are combined using linear summations, allowing for a wider range of filter classes and achieving fine-grained enhancement with superior performance. 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In CVPR, pages 15689-15698, 2021. \ No newline at end of file diff --git a/2023/RSFNet_ A White-Box Image Retouching Approach using Region-Specific Color Filters/images.zip b/2023/RSFNet_ A White-Box Image Retouching Approach using Region-Specific Color Filters/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..ee39ba4cb04dc37d70b91fe6ee10ffcfa41d46cf --- /dev/null +++ b/2023/RSFNet_ A White-Box Image Retouching Approach using Region-Specific Color Filters/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f12396d0fcb36e0550be7ace62e40f5d4ac8ac37fb3e1471d1011be644d1d5ff +size 944194 diff --git a/2023/RSFNet_ A White-Box Image Retouching Approach using Region-Specific Color Filters/layout.json b/2023/RSFNet_ A White-Box Image Retouching Approach using Region-Specific Color Filters/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..6f56e5d27de7a9e6a4f15fe8abd66c94515d0024 --- /dev/null +++ b/2023/RSFNet_ A White-Box Image Retouching Approach using Region-Specific Color Filters/layout.json @@ -0,0 +1,6452 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 50, + 102, + 544, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 102, + 544, + 138 + ], + "spans": [ + { + "bbox": [ + 50, + 102, + 544, + 138 + ], + "type": "text", + "content": "RSFNet: A White-Box Image Retouching Approach using Region-Specific Color Filters" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 93, + 160, + 499, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 160, + 499, + 190 + ], + "spans": [ + { + "bbox": [ + 93, + 160, + 499, + 190 + ], + "type": "text", + "content": "Wenqi Ouyang" + }, + { + "bbox": [ + 93, + 160, + 499, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 93, + 160, + 499, + 190 + ], + "type": "text", + "content": ", Yi Dong" + }, + { + "bbox": [ + 93, + 160, + 499, + 190 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 93, + 160, + 499, + 190 + ], + "type": "text", + "content": ", Xiaoyang Kang" + }, + { + "bbox": [ + 93, + 160, + 499, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 93, + 160, + 499, + 190 + ], + "type": "text", + "content": ", Peiran Ren" + }, + { + "bbox": [ + 93, + 160, + 499, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 93, + 160, + 499, + 190 + ], + "type": "text", + "content": ", Xin Xu" + }, + { + "bbox": [ + 93, + 160, + 499, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 93, + 160, + 499, + 190 + ], + "type": "text", + "content": ", Xuansong Xie" + }, + { + "bbox": [ + 93, + 160, + 499, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 93, + 160, + 499, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 93, + 160, + 499, + 190 + ], + "type": "text", + "content": "DAMO Academy, Alibaba Group, " + }, + { + "bbox": [ + 93, + 160, + 499, + 190 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 93, + 160, + 499, + 190 + ], + "type": "text", + "content": "Nanyang Technological University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 166, + 192, + 424, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 166, + 192, + 424, + 204 + ], + "spans": [ + { + "bbox": [ + 166, + 192, + 424, + 204 + ], + "type": "text", + "content": "wenqi.oywq@alibaba-inc.com, ydong004@ntu.edu.sg," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 107, + 205, + 485, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 205, + 485, + 217 + ], + "spans": [ + { + "bbox": [ + 107, + 205, + 485, + 217 + ], + "type": "text", + "content": "{peiran.rpr, kangxiaoyang.kxy, chris.xx, xingtong.xxs}@alibaba-inc.com" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "spans": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 271, + 290, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 271, + 290, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 271, + 290, + 559 + ], + "type": "text", + "content": "Retouching images is an essential aspect of enhancing the visual appeal of photos. Although users often share common aesthetic preferences, their retouching methods may vary based on their individual preferences. Therefore, there is a need for white-box approaches that produce satisfying results and enable users to conveniently edit their images simultaneously. Recent white-box retouching methods rely on cascaded global filters that provide image-level filter arguments but cannot perform fine-grained retouching. In contrast, colorists typically employ a divide-and-conquer approach, performing a series of region-specific fine-grained enhancements when using traditional tools like Davinci Resolve. We draw on this insight to develop a white-box framework for photo retouching using parallel region-specific filters, called RSFNet. Our model generates filter arguments (e.g., saturation, contrast, hue) and attention maps of regions for each filter simultaneously. Instead of cascading filters, RSFNet employs linear summations of filters, allowing for a more diverse range of filter classes that can be trained more easily. Our experiments demonstrate that RSFNet achieves state-of-the-art results, offering satisfying aesthetic appeal and increased user convenience for editable white-box retouching. Code is available at https://github.com/Vicky0522/RSFNet." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 584, + 128, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 584, + 128, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 584, + 128, + 597 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Photos and videos recorded by the camera usually lack aesthetic quality due to poor shooting condition and inexperienced photographer. Artists often use professional-grade softwares (e.g., PhotoShop for image, Davinci Resolve for video) to enhance image and video quality. However, it requires professional retouching skills to conduct a series of sophisticated manual adjustments. The use of fool-proof applications that present various style templates simplifies the retouching procedure, but it is unable to achieve opti" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 313, + 243, + 541, + 373 + ], + "blocks": [ + { + "bbox": [ + 313, + 243, + 541, + 373 + ], + "lines": [ + { + "bbox": [ + 313, + 243, + 541, + 373 + ], + "spans": [ + { + "bbox": [ + 313, + 243, + 541, + 373 + ], + "type": "image", + "image_path": "674e39577ef6977caea0f5c63d4025f2a9122acc3d3cfe231479c2b3f468170d.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 379, + 547, + 440 + ], + "lines": [ + { + "bbox": [ + 304, + 379, + 547, + 440 + ], + "spans": [ + { + "bbox": [ + 304, + 379, + 547, + 440 + ], + "type": "text", + "content": "Figure 1: Architecture of our white-box retouching framework. Our model generates filter arguments (e.g., saturation, midtones, highlights) and attention maps of regions for corresponding filter simultaneously. Final result is obtained by conducting linear summations on filtered results." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 460, + 523, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 460, + 523, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 460, + 523, + 472 + ], + "type": "text", + "content": "mal results due to the lack of enhancement capability." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 472, + 546, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 546, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 546, + 604 + ], + "type": "text", + "content": "Recent learning-based methods have demonstrated the strong capability of deep neural nets for automatic photo retouching. Automatic systems are established to generate the optimal result end-to-end. However, one of the most significant considerations is that retouching is not a problem with an exclusive solution. People have different retouching preferences. Even the same artist may retouch the same image in different styles to meet various demands. In order to provide convenience for manual edits, automatic retouching systems must provide not only the suggested result, but also the retouching strategy in a way understandable by humans." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 604, + 545, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 545, + 686 + ], + "type": "text", + "content": "Taking these considerations into account, we propose a white-box framework that uses the divide-and-conquer strategy employed by artists in traditional retouching tools. Our model generates attention maps of regions as well as filter arguments for traditional edits for these regions. This allows users to alter the suggested results to their preferences." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 687, + 529, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 687, + 529, + 699 + ], + "spans": [ + { + "bbox": [ + 317, + 687, + 529, + 699 + ], + "type": "text", + "content": "The main contributions of this work are as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": "- We redefine the retouching problem according to the" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12160" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 66, + 72, + 286, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 72, + 286, + 107 + ], + "spans": [ + { + "bbox": [ + 66, + 72, + 286, + 107 + ], + "type": "text", + "content": "divide-and-conquer strategy, focusing on finding attention maps for regions and human-understandable filter adjustments per map to achieve the best results." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 108, + 286, + 227 + ], + "type": "list", + "angle": 0, + "index": 3, + "blocks": [ + { + "bbox": [ + 59, + 108, + 286, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 108, + 286, + 191 + ], + "spans": [ + { + "bbox": [ + 59, + 108, + 286, + 191 + ], + "type": "text", + "content": "- We propose RSFNet, which generates pixel-level attention maps of regions and filter arguments simultaneously. By conducting linear summations on the filtered results, our model demonstrates superior performance to global white-box retouching methods, with a wider range of filter classes for fine-grained enhancement and a simpler training procedure." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 192, + 286, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 192, + 286, + 227 + ], + "spans": [ + { + "bbox": [ + 59, + 192, + 286, + 227 + ], + "type": "text", + "content": "- We propose a scheme that allows users to edit RSFNet suggested results, demonstrating its effectiveness and convenience in image applications." + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 239, + 138, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 138, + 251 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 138, + 251 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 258, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 258, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 258, + 287, + 628 + ], + "type": "text", + "content": "Deep Image Enhancement. Many attempts have been made in image enhancement using learning-based methods. These methods can broadly be classified into two categories: deep-convolutional-based models and physical-inspired models. The former [3, 4, 6, 25, 29] view enhancement as a synthesis problem and use fully convolutional generators [15] to achieve dense image-to-image translation. While these methods exhibit strong capability for generating and enhancing details, they suffer from heavy structure and low inference speed. The latter category of works defines enhancement as the parameter prediction of a physical model and uses deep learning strategies to fit the model. These models include 3D-LUT [21, 28, 27], parametric filters [16], conditional sequential global modulation [8], affine color transformations [7, 20], 1D mapping curves [19, 12, 17]. Their enhancement capabilities depend on the range of transformation functions the physical model covers. Among those, models based on global 3D-LUT [27, 28] are well-designed for retouching and could achieve high performance with fast inference speed. However, they suffer from uneven transitions in smooth areas due to lack of fine-grained local adjustment. Spatial-Aware 3D-LUT [21] alleviate the problem of global 3D-LUT by computing pixel-level weight maps. All these methods have a black-box structure or unintuitive parameters that are hard for humans to understand. DeepLPF [16] has been a significant milestone in the field of region-specific color enhancement via local parametric filters but suffers from low inference speed and limited filter shapes. The three types of filters with three implementations each results in complex maps that are hard to understand." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": "White-box Image Editing. Recent white-box methods [10, 11, 26, 30] have decoupled image editing into a series of human understandable operations and deep learning strategies to predict them. Of these, our work is most related to [11, 10]. However, they train networks with cascaded filter argument prediction modules to perform global retouching step-by-step. Our model utilizes pixel-wise region-" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 118 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 118 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 118 + ], + "type": "text", + "content": "specific filters to capture local features and employs linear summations to combine filters, thus having stronger capability to cover a wider range of color transformation functions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 133, + 361, + 145 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 133, + 361, + 145 + ], + "spans": [ + { + "bbox": [ + 306, + 133, + 361, + 145 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 154, + 414, + 166 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 154, + 414, + 166 + ], + "spans": [ + { + "bbox": [ + 306, + 154, + 414, + 166 + ], + "type": "text", + "content": "3.1. Design Motivation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 172, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 172, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 304, + 172, + 545, + 388 + ], + "type": "text", + "content": "Traditional Retouching Strategy. In the traditional retouching process, local adjustments for different regions are conducted separately and then aggregated together to accomplish fine-grained enhancement. All the adjustments could be accomplished in one Layer, where filters are all conducted on the same image instead of results from previous filters. We adopt this divide-and-conquer strategy to build our framework. We select 10 commonly used retouching filters from traditional tools(e.g., Davinci Resolve) to represent adjustment manipulations, including contrast, saturation, hue, temperature, shadows, midtones, highlights and shift. For more details about filters, please refer to our supplementary material. Therefore, retouching is defined as finding pixel-level attention maps and corresponding adjustments for each map to achieve the most desirable result. We adopt this convention and represent retouching result " + }, + { + "bbox": [ + 304, + 172, + 545, + 388 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 172, + 545, + 388 + ], + "type": "text", + "content": " as adding linear summations of increments resulted by filters to the original image as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 321, + 409, + 545, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 409, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 321, + 409, + 545, + 434 + ], + "type": "interline_equation", + "content": "Y = X + \\sum_ {m} \\sum_ {n} \\left(F _ {m, n} \\left(\\theta_ {m, n}, X\\right) - X\\right) \\odot M _ {m} \\tag {1}", + "image_path": "cc7949822b97a9acb236f1c6c43b048374f39a47af6d1a825241420c386a6720.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "type": "inline_equation", + "content": "\\theta_{m,n}" + }, + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "type": "inline_equation", + "content": "F_{m,n} \\in \\{\\text{contrast}, \\dots, \\text{shift}\\}" + }, + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "type": "text", + "content": " are the argument value and filter function of the " + }, + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "type": "text", + "content": "th filter for the " + }, + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "type": "text", + "content": "th attention map of input image " + }, + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "type": "text", + "content": " respectively, " + }, + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "type": "inline_equation", + "content": "M_{m}" + }, + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "type": "text", + "content": "th attention map for image " + }, + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 445, + 545, + 517 + ], + "type": "text", + "content": ". It should be noticed that this linear representation makes our optimization process much simpler than other white-box methods." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 527, + 388, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 527, + 388, + 538 + ], + "spans": [ + { + "bbox": [ + 306, + 527, + 388, + 538 + ], + "type": "text", + "content": "3.2. Architecture" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "type": "text", + "content": "Our model consists of two modules, the parameter predictor and the renderer. The architecture of the parameter predictor shares a similar overall structure with previous segmentation models [22, 23]. As illustrated in Figure 2, the network " + }, + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "type": "text", + "content": " is composed of a backbone " + }, + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "type": "inline_equation", + "content": "g_{\\text{backbone}}" + }, + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "type": "text", + "content": ", a FPN neck " + }, + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "type": "inline_equation", + "content": "g_{\\text{neck}}" + }, + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "type": "text", + "content": ", a map generator " + }, + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "type": "inline_equation", + "content": "h_{\\text{map}}" + }, + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "type": "text", + "content": " for attention map prediction and an argument regressor " + }, + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "type": "inline_equation", + "content": "h_{\\text{arg}}" + }, + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "type": "text", + "content": " for arguments regression. We set the last layer of map generator " + }, + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "type": "inline_equation", + "content": "h_{\\text{map}}" + }, + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "type": "text", + "content": " to sigmoid, followed by an upsampling layer to match the size of the original input image. We use " + }, + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "type": "inline_equation", + "content": "f(X)" + }, + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "type": "text", + "content": " to represent the output features of FPN neck. Maps generated by " + }, + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "type": "inline_equation", + "content": "h_{\\text{map}}" + }, + { + "bbox": [ + 304, + 546, + 545, + 689 + ], + "type": "text", + "content": " after upsampling are:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 344, + 700, + 545, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 700, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 344, + 700, + 545, + 714 + ], + "type": "interline_equation", + "content": "M _ {m} = h _ {\\text {m a p}} (f (X)) _ {m}, m \\in \\{1, \\dots ., K \\} \\tag {2}", + "image_path": "2868604a3a032abbed2a8e81cd4b20e1111154d69a79bf038ea27e84654a54f9.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12161" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 68, + 521, + 276 + ], + "blocks": [ + { + "bbox": [ + 72, + 68, + 521, + 276 + ], + "lines": [ + { + "bbox": [ + 72, + 68, + 521, + 276 + ], + "spans": [ + { + "bbox": [ + 72, + 68, + 521, + 276 + ], + "type": "image", + "image_path": "1fa1e6a7ff4eeef981125cee46064f989a073c8f2da72da946887fbfb672e634.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 288, + 545, + 338 + ], + "lines": [ + { + "bbox": [ + 46, + 288, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 545, + 338 + ], + "type": "text", + "content": "Figure 2: Our network comprises two modules: the parameter predictor and renderer. The input image is transformed into feature embeddings " + }, + { + "bbox": [ + 46, + 288, + 545, + 338 + ], + "type": "inline_equation", + "content": "f(X)" + }, + { + "bbox": [ + 46, + 288, + 545, + 338 + ], + "type": "text", + "content": " through a backbone " + }, + { + "bbox": [ + 46, + 288, + 545, + 338 + ], + "type": "inline_equation", + "content": "g_{\\text{backbone}}" + }, + { + "bbox": [ + 46, + 288, + 545, + 338 + ], + "type": "text", + "content": " and FPN neck " + }, + { + "bbox": [ + 46, + 288, + 545, + 338 + ], + "type": "inline_equation", + "content": "g_{\\text{neck}}" + }, + { + "bbox": [ + 46, + 288, + 545, + 338 + ], + "type": "text", + "content": ", which are then utilized by the map generator " + }, + { + "bbox": [ + 46, + 288, + 545, + 338 + ], + "type": "inline_equation", + "content": "h_{\\text{map}}" + }, + { + "bbox": [ + 46, + 288, + 545, + 338 + ], + "type": "text", + "content": " and argument regressor " + }, + { + "bbox": [ + 46, + 288, + 545, + 338 + ], + "type": "inline_equation", + "content": "h_{\\text{arg}}" + }, + { + "bbox": [ + 46, + 288, + 545, + 338 + ], + "type": "text", + "content": " to generate region maps and filter arguments (e.g. contrast, hue, saturation), respectively. The renderer applies the filter arguments to each region map and aggregates them to produce the final retouching result." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 357, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 287, + 441 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 357, + 287, + 441 + ], + "type": "text", + "content": " is the number of output channels of the last layer. The argument regressor " + }, + { + "bbox": [ + 46, + 357, + 287, + 441 + ], + "type": "inline_equation", + "content": "h_{arg}" + }, + { + "bbox": [ + 46, + 357, + 287, + 441 + ], + "type": "text", + "content": " consists of 4 units of convolutional modules. Each module consists of a convolution layer followed by group normalization, " + }, + { + "bbox": [ + 46, + 357, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\text{relu}" + }, + { + "bbox": [ + 46, + 357, + 287, + 441 + ], + "type": "text", + "content": " activation and average pooling. Output feature " + }, + { + "bbox": [ + 46, + 357, + 287, + 441 + ], + "type": "inline_equation", + "content": "f(X)" + }, + { + "bbox": [ + 46, + 357, + 287, + 441 + ], + "type": "text", + "content": " is finally reduced by " + }, + { + "bbox": [ + 46, + 357, + 287, + 441 + ], + "type": "inline_equation", + "content": "h_{arg}" + }, + { + "bbox": [ + 46, + 357, + 287, + 441 + ], + "type": "text", + "content": " to a " + }, + { + "bbox": [ + 46, + 357, + 287, + 441 + ], + "type": "inline_equation", + "content": "K \\times N" + }, + { + "bbox": [ + 46, + 357, + 287, + 441 + ], + "type": "text", + "content": " vector representing arguments of all filters for every map:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 445, + 287, + 470 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 445, + 287, + 470 + ], + "spans": [ + { + "bbox": [ + 49, + 445, + 287, + 470 + ], + "type": "interline_equation", + "content": "\\theta_ {m, n} = h _ {\\arg} (f (X)) _ {m, n}, m \\in \\{1, \\dots ., K \\}, n \\in \\{1, \\dots ., N \\} \\tag {3}", + "image_path": "654900883fd4fdb8238e8943f6db52641e41634c9d8dc0cb363394263ef0abc1.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 471, + 287, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 287, + 540 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 471, + 287, + 540 + ], + "type": "text", + "content": " is the number of color filters per map. Given the maps and arguments from the parameter predictor, the renderer applies filter functions " + }, + { + "bbox": [ + 46, + 471, + 287, + 540 + ], + "type": "inline_equation", + "content": "F_{m,n} \\in \\{\\text{contrast}, \\dots, \\text{shift}\\}" + }, + { + "bbox": [ + 46, + 471, + 287, + 540 + ], + "type": "text", + "content": " to the input image and merges filtered results via linear summations of increments. The final output image " + }, + { + "bbox": [ + 46, + 471, + 287, + 540 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 46, + 471, + 287, + 540 + ], + "type": "text", + "content": " in Equation 1 is:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 60, + 545, + 287, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 545, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 60, + 545, + 287, + 578 + ], + "type": "interline_equation", + "content": "Y = X + \\sum_ {m = 1} ^ {K} \\sum_ {n = 1} ^ {N} \\left(F _ {m, n} \\left(\\theta_ {m, n}, X\\right) - X\\right) \\odot M _ {m} \\tag {4}", + "image_path": "c2e4e2b9cd06f928836c15ce4c8c4f004004b6e52641c03fd365103f08396414.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 688 + ], + "type": "text", + "content": "In our implementation, we set the number of filters per map as " + }, + { + "bbox": [ + 46, + 582, + 287, + 688 + ], + "type": "inline_equation", + "content": "N = 1" + }, + { + "bbox": [ + 46, + 582, + 287, + 688 + ], + "type": "text", + "content": ", indicating that there is one specific filter assigned to each map. This is illustrated in the second row of filter boxes depicted in Figure 2. We also consider the filter Shift as a global function that is applied to the entire image without an attention map. Through our experimentation, we observe that this configuration is sufficient for generating satisfactory results while also providing convenience for users to edit." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Training Loss. The overall framework can be trained end-to-end. Our training loss function is defined as follows:" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 318, + 355, + 544, + 479 + ], + "blocks": [ + { + "bbox": [ + 318, + 355, + 544, + 479 + ], + "lines": [ + { + "bbox": [ + 318, + 355, + 544, + 479 + ], + "spans": [ + { + "bbox": [ + 318, + 355, + 544, + 479 + ], + "type": "image", + "image_path": "069589aeb25c49168e0a8e104ef4ac02ded19d73908a3fff6f9fd3fbebc760e7.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 487, + 545, + 548 + ], + "lines": [ + { + "bbox": [ + 304, + 487, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 545, + 548 + ], + "type": "text", + "content": "Figure 3: A variation of RSFNet could be used to generate masks with controlled shapes. We generate ground truth masks for training via three types of region masks derived from off-the-shelf models: palette-based segmentation, semantic segmentation, and saliency detection." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 399, + 583, + 545, + 596 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 399, + 583, + 545, + 596 + ], + "spans": [ + { + "bbox": [ + 399, + 583, + 545, + 596 + ], + "type": "interline_equation", + "content": "L = L _ {\\text {r e c o n}}, \\tag {5}", + "image_path": "8e495f95a754f74339eccccfeb1681d1478b77c1ce8928e177066857713dd9bd.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 602, + 492, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 602, + 492, + 614 + ], + "spans": [ + { + "bbox": [ + 306, + 602, + 492, + 614 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 602, + 492, + 614 + ], + "type": "inline_equation", + "content": "L_{\\text{recon}}" + }, + { + "bbox": [ + 306, + 602, + 492, + 614 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 306, + 602, + 492, + 614 + ], + "type": "inline_equation", + "content": "l1" + }, + { + "bbox": [ + 306, + 602, + 492, + 614 + ], + "type": "text", + "content": " loss for reconstruction." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 622, + 545, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 622, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 622, + 545, + 647 + ], + "type": "text", + "content": "3.3. A Variation of RSFNet with Controlled Region Shape" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Our proposed framework has the capability to generate region masks with controlled shapes, with minimal modifications to the training data and loss function. In our observation, artists tend to select regions based on their main color, saliency, or other high-level semantic informa" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12162" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 542, + 350 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 542, + 350 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 542, + 350 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 542, + 350 + ], + "type": "image", + "image_path": "4dca9de783795fce137d9e2c4b210daf9bf36b7201b051d2e9e573f0f84df63d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 357, + 548, + 407 + ], + "lines": [ + { + "bbox": [ + 46, + 357, + 548, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 548, + 407 + ], + "type": "text", + "content": "Figure 4: Editable white-box retouching. The second column illustrates the arguments and masks generated by RSFNet-saliency that is trained with saliency masks. The third column displays the retouched result. On the right-hand side, the figure showcases three versions of adjustments conducted on the retouched results, with numbers denoted in green boxes indicating the relative incremental value of filters." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 426, + 289, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 289, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 289, + 510 + ], + "type": "text", + "content": "tion. To leverage this insight, we utilize palette-based methods [2], saliency detection [14], and panoptic segmentation networks [5] to generate palette-based, saliency, and semantic masks of the input images used for training, as depicted in Figure 3. Further implementation details can be found in the supplementary material. Our training loss function in Equation 5 is modified as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 117, + 536, + 287, + 548 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 536, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 117, + 536, + 287, + 548 + ], + "type": "interline_equation", + "content": "L = L _ {\\text {r e c o n}} + \\lambda L _ {\\text {m a s k}}, \\tag {6}", + "image_path": "e0cc2a687ad38e25018ebd5f3de42494acf87a7d44041b07b08587f7799c9594.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 574, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 287, + 647 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 574, + 287, + 647 + ], + "type": "inline_equation", + "content": "L_{\\text{recon}}" + }, + { + "bbox": [ + 46, + 574, + 287, + 647 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 574, + 287, + 647 + ], + "type": "inline_equation", + "content": "l1" + }, + { + "bbox": [ + 46, + 574, + 287, + 647 + ], + "type": "text", + "content": " loss for reconstruction. When training with palette-based masks and saliency masks, " + }, + { + "bbox": [ + 46, + 574, + 287, + 647 + ], + "type": "inline_equation", + "content": "L_{\\text{mask}}" + }, + { + "bbox": [ + 46, + 574, + 287, + 647 + ], + "type": "text", + "content": " is the Dice Loss for mask prediction following loss functions in [22, 23]. We change it to the Cross Entropy Loss when training with semantic masks, at the time map generator " + }, + { + "bbox": [ + 46, + 574, + 287, + 647 + ], + "type": "inline_equation", + "content": "h_{\\text{map}}" + }, + { + "bbox": [ + 46, + 574, + 287, + 647 + ], + "type": "text", + "content": " ends with a softmax layer." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "The model generates region masks and corresponding filter arguments for the input image simultaneously. Users can select region maps and adjust filter arguments to edit results. We show an example of RSFNet-saliency trained with saliency masks in Figure 4." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 425, + 388, + 438 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 425, + 388, + 438 + ], + "spans": [ + { + "bbox": [ + 306, + 425, + 388, + 438 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 452, + 486, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 452, + 486, + 466 + ], + "spans": [ + { + "bbox": [ + 306, + 452, + 486, + 466 + ], + "type": "text", + "content": "4.1. Datasets and Application Settings" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 479, + 547, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 547, + 622 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 547, + 622 + ], + "type": "text", + "content": "We conduct experiments on two publicly available datasets: MIT-Adobe FiveK [1] and PPR10K [13]. The MIT-Adobe FiveK consists of 5,000 RAW images with their retouched versions. We follow prior works [8, 12, 28, 27] to adopt images retouched by expert C as ground truths and split the dataset into 4,500 pairs for training and 500 pairs for validation. Images are resized to " + }, + { + "bbox": [ + 304, + 479, + 547, + 622 + ], + "type": "inline_equation", + "content": "480\\mathrm{p}" + }, + { + "bbox": [ + 304, + 479, + 547, + 622 + ], + "type": "text", + "content": " during training stage, whereas both of " + }, + { + "bbox": [ + 304, + 479, + 547, + 622 + ], + "type": "inline_equation", + "content": "480\\mathrm{p}" + }, + { + "bbox": [ + 304, + 479, + 547, + 622 + ], + "type": "text", + "content": " resolution and original resolution are used during validation. We follow the official split [13] to split PPR10K dataset into 8,875 pairs for training and 2,286 pairs for testing. Images are resized to " + }, + { + "bbox": [ + 304, + 479, + 547, + 622 + ], + "type": "inline_equation", + "content": "360\\mathrm{p}" + }, + { + "bbox": [ + 304, + 479, + 547, + 622 + ], + "type": "text", + "content": " resolution for training and validation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "For the MIT-Adobe FiveK dataset, we conduct experiments on two input settings: input zeroed with expertC white balance and input zeroed as shot. The second set of inputs is more challenging as it also deteriorates in white balance. Therefore, to restore its visual appeal, our framework's ability to perform color temperature correction and hue adjustment is required." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "type": "text", + "content": "12163" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 71, + 206, + 187 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 206, + 187 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 206, + 187 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 206, + 187 + ], + "type": "table", + "html": "
mask as inputmask typePSNR↑SSIM↑
w/saliency(1)23.830.906
w/palette(5)23.450.903
w/semantic(10)21.650.866
w/semantic(5)21.770.867
w/osaliency(1)24.010.909
w/opalette(5)24.140.906
w/osemantic(10)24.090.908
w/osemantic(5)24.170.909
w/osemantic(133)23.750.905
", + "image_path": "92f36291aa38a5cb1b569a699527499a3e6b12b5eb4c332b4db37ad5b9e9b57b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 47, + 191, + 214, + 224 + ], + "lines": [ + { + "bbox": [ + 47, + 191, + 214, + 224 + ], + "spans": [ + { + "bbox": [ + 47, + 191, + 214, + 224 + ], + "type": "text", + "content": "(a) Analysis on using mask as input and different mask types. Bracket after \"mask type\" indicates number of masks." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 236, + 99, + 376, + 158 + ], + "blocks": [ + { + "bbox": [ + 236, + 99, + 376, + 158 + ], + "lines": [ + { + "bbox": [ + 236, + 99, + 376, + 158 + ], + "spans": [ + { + "bbox": [ + 236, + 99, + 376, + 158 + ], + "type": "table", + "html": "
mask firstmasktypePSNR↑SSIM↑
w/saliency(1)23.260.890
w/osaliency(1)24.010.909
", + "image_path": "dc273e5f6b576c7e488c4cb1f912a0af5722e33bbf0797100170cf57554c474a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 222, + 163, + 389, + 196 + ], + "lines": [ + { + "bbox": [ + 222, + 163, + 389, + 196 + ], + "spans": [ + { + "bbox": [ + 222, + 163, + 389, + 196 + ], + "type": "text", + "content": "(b) Analysis of training order. \"Mask first\" refers to building model on pre-trained PoolNet [14]." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 399, + 105, + 565, + 175 + ], + "blocks": [ + { + "bbox": [ + 399, + 105, + 565, + 175 + ], + "lines": [ + { + "bbox": [ + 399, + 105, + 565, + 175 + ], + "spans": [ + { + "bbox": [ + 399, + 105, + 565, + 175 + ], + "type": "table", + "html": "
backbonedownscaling factorPSNR↑Runtime↓
resnet18x824.659.98
resnet18x424.8312.38
resnet10x824.507.98
resnet10x424.388.71
", + "image_path": "7d6e07dd2fbe97d307bd5c2df0ee3df670fb11d7b3cc03df98ca455cac5395c3.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 404, + 178, + 558, + 190 + ], + "lines": [ + { + "bbox": [ + 404, + 178, + 558, + 190 + ], + "spans": [ + { + "bbox": [ + 404, + 178, + 558, + 190 + ], + "type": "text", + "content": "(c) Trade off between speed and accuracy." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 4 + }, + { + "bbox": [ + 62, + 235, + 529, + 247 + ], + "lines": [ + { + "bbox": [ + 62, + 235, + 529, + 247 + ], + "spans": [ + { + "bbox": [ + 62, + 235, + 529, + 247 + ], + "type": "text", + "content": "Table 1: Ablation analysis of our framework. Models are trained on the FiveK dataset [1] with inputs zeroed as shot." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 54, + 266, + 159, + 376 + ], + "blocks": [ + { + "bbox": [ + 54, + 266, + 159, + 376 + ], + "lines": [ + { + "bbox": [ + 54, + 266, + 159, + 376 + ], + "spans": [ + { + "bbox": [ + 54, + 266, + 159, + 376 + ], + "type": "image", + "image_path": "b580ce3d2e6f88e4c3bfae6e43ae112e56813c24e4a3f0f299f0cbc3e174e4f4.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 385, + 287, + 420 + ], + "lines": [ + { + "bbox": [ + 46, + 385, + 287, + 420 + ], + "spans": [ + { + "bbox": [ + 46, + 385, + 287, + 420 + ], + "type": "text", + "content": "Figure 5: Comparison between sequential and parallel methods under the same filter functions and network structures." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 164, + 266, + 279, + 376 + ], + "blocks": [ + { + "bbox": [ + 164, + 266, + 279, + 376 + ], + "lines": [ + { + "bbox": [ + 164, + 266, + 279, + 376 + ], + "spans": [ + { + "bbox": [ + 164, + 266, + 279, + 376 + ], + "type": "image", + "image_path": "797b51d18273ef8e24923f1dd0dd02751e38eb9943d1aa820313ce50a205dbf1.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 443, + 180, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 443, + 180, + 455 + ], + "spans": [ + { + "bbox": [ + 47, + 443, + 180, + 455 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 462, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 287, + 628 + ], + "type": "text", + "content": "To implement our proposed framework as described in Section 3.2, we employ ResNet18 [9] as the backbone and utilize the output features of layer " + }, + { + "bbox": [ + 46, + 462, + 287, + 628 + ], + "type": "inline_equation", + "content": "(0,1,2,3)" + }, + { + "bbox": [ + 46, + 462, + 287, + 628 + ], + "type": "text", + "content": " as concatenated input with " + }, + { + "bbox": [ + 46, + 462, + 287, + 628 + ], + "type": "inline_equation", + "content": "256\\times 4" + }, + { + "bbox": [ + 46, + 462, + 287, + 628 + ], + "type": "text", + "content": " channels for the FPN neck. The FPN neck reduces the features to " + }, + { + "bbox": [ + 46, + 462, + 287, + 628 + ], + "type": "inline_equation", + "content": "64\\times 4" + }, + { + "bbox": [ + 46, + 462, + 287, + 628 + ], + "type": "text", + "content": " channels and feeds them into the map generator and argument regressor. We set the output numbers " + }, + { + "bbox": [ + 46, + 462, + 287, + 628 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 462, + 287, + 628 + ], + "type": "text", + "content": " of region maps to 10 and 16 for the Adobe-MIT FiveK and PPR10K datasets, respectively. The number of filters per map " + }, + { + "bbox": [ + 46, + 462, + 287, + 628 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 462, + 287, + 628 + ], + "type": "text", + "content": " is set to " + }, + { + "bbox": [ + 46, + 462, + 287, + 628 + ], + "type": "inline_equation", + "content": "N = 1" + }, + { + "bbox": [ + 46, + 462, + 287, + 628 + ], + "type": "text", + "content": ", with 10 filters used for MIT-Adobe FiveK, 1 each for shadow, midtones, highlights, where arguments for RGB channels are set equal. For PPR10K, we use 16 filters, with 3 each for shadow, midtones, highlights, where arguments for RGB channels are set differently." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": "To implement the variation of RSFNet with controlled region shapes, as described in Section 3.3, we generate ground truth masks for the MIT-Adobe FiveK dataset. Specifically, we generate five palette-based masks, one saliency mask, and five semantic masks for each image. For the PPR10K dataset, we directly use the human-region masks provided in the dataset as ground truth masks for" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 268, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 268, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 545, + 327 + ], + "type": "text", + "content": "training. The map generator is designed to output 5 channels for the palette-based version, 2 channels for the saliency version, and 5 channels for the semantic version. We use 10 filters for the MIT-Adobe FiveK and 16 filters for the PPR10K, as mentioned above." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 328, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 328, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 545, + 410 + ], + "type": "text", + "content": "We use the standard Adam optimizer [18] to minimize the loss function in Equation 5 and 6. The mini-batch size is 16. We train models for 1,000,000 iterations with initial learning rate " + }, + { + "bbox": [ + 304, + 328, + 545, + 410 + ], + "type": "inline_equation", + "content": "l_{r} = 2 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 328, + 545, + 410 + ], + "type": "text", + "content": ". We use a cosine strategy to gradually decay the learning rate every 250,000 iterations. All experiments are conducted on NVIDIA Tesla V100 GPU." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 411, + 545, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 459 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 459 + ], + "type": "text", + "content": "In the following sections, we denote our main model in Section 3.2 as " + }, + { + "bbox": [ + 304, + 411, + 545, + 459 + ], + "type": "inline_equation", + "content": "RSFNet" + }, + { + "bbox": [ + 304, + 411, + 545, + 459 + ], + "type": "text", + "content": "-map. Variations depicted in Section 3.3 are denoted as " + }, + { + "bbox": [ + 304, + 411, + 545, + 459 + ], + "type": "inline_equation", + "content": "RSFNet" + }, + { + "bbox": [ + 304, + 411, + 545, + 459 + ], + "type": "text", + "content": "-palette, " + }, + { + "bbox": [ + 304, + 411, + 545, + 459 + ], + "type": "inline_equation", + "content": "RSFNet" + }, + { + "bbox": [ + 304, + 411, + 545, + 459 + ], + "type": "text", + "content": "-saliency and " + }, + { + "bbox": [ + 304, + 411, + 545, + 459 + ], + "type": "inline_equation", + "content": "RSFNet" + }, + { + "bbox": [ + 304, + 411, + 545, + 459 + ], + "type": "text", + "content": "-semantic." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 468, + 406, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 468, + 406, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 468, + 406, + 479 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 486, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 510 + ], + "type": "text", + "content": "In this section, we evaluate the ability of our frameworks in different settings." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": "Comparative study of parallel and sequential approaches. We conduct experiments to compare parallel and sequential approaches under the same set of filter functions and backbone structures. For sequential implementations, we modify the network structure to mimic artistic workflows and resemble Harmonizer [11]. We train the network using randomly shuffled 20 unique sequences of filter functions. The results are shown in Figure 5. The parallel approach shows Pareto-optimality with near-maximum PSNR and a lower PSNR standard deviation (std). It also outperforms all sequential approaches in terms of SSIM and SSIM std. We find that altering the sequence of applying filters can lead to considerable changes in performance. Nearly half of these sequences fail to produce satisfactory results. Moreover, during training, the parallel approach converges faster than its sequential counterparts. In addition, the parallel method can be faster than the sequential one." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12164" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 79, + 70, + 517, + 280 + ], + "blocks": [ + { + "bbox": [ + 79, + 70, + 517, + 280 + ], + "lines": [ + { + "bbox": [ + 79, + 70, + 517, + 280 + ], + "spans": [ + { + "bbox": [ + 79, + 70, + 517, + 280 + ], + "type": "table", + "html": "
Method480p zeroed with C's480p zeroed as shotFull Resolution zeroed as shot
PSNR↑SSIM↑△Eab↓PSNR↑SSIM↑△Eab↓Runtime↓PSNR↑SSIM↑Runtime↓
UPE [20]21.88*0.853*10.80*///////
DPE [4]23.75*0.908*9.34*///////
HDRNet [7]24.66*0.915*8.06*///////
DeepLPF [16]24.73*0.916*7.99*23.380.88010.0344.2523.400.8631133.90
CSRNet [8]25.17*0.924*7.75*24.240.9109.703.4923.040.87480.6
SA-3DLUT [21]25.50*/////////
3D-LUT [28]25.29*0.923*7.55*///////
3D-LUT+AdaInt [27]25.49*0.926*7.47*24.500.9129.221.5924.240.8571.80
Harmonizer [11]24.110.9048.2323.230.89310.1416.7422.570.87027.98
RSFNet-map25.490.9247.2324.640.9159.169.9824.390.89412.35
RSFNet-palette25.010.9147.6224.220.9119.5219.7623.880.88868.57
RSFNet-saliency24.780.9167.8624.200.9129.4214.0924.000.89059.42
RSFNet-semantic24.760.9157.7724.190.9129.4524.0723.890.89171.18
RSFNet-global24.310.9118.2123.430.90410.169.4223.260.88510.99
", + "image_path": "a5252d0bb0ece520a3109feac145e21a056d4772d479b847df08a804bd95a825.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 141, + 358, + 455, + 482 + ], + "blocks": [ + { + "bbox": [ + 46, + 287, + 547, + 348 + ], + "lines": [ + { + "bbox": [ + 46, + 287, + 547, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 547, + 348 + ], + "type": "text", + "content": "Table 2: Quantitative comparisons for retouching tasks on FiveK dataset [1]. Runtime is measured in milliseconds. “*” means the result is adopted from the paper [27]. “/” means the result is not available. Runtime shown in previous works are not adopted due to different hardware settings. Results with the first and second performance are colored as red and blue respectively. White-box methods are colored as violet. Full resolution images results are evaluated using Python, while others are evaluated on Matlab." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 141, + 358, + 455, + 482 + ], + "lines": [ + { + "bbox": [ + 141, + 358, + 455, + 482 + ], + "spans": [ + { + "bbox": [ + 141, + 358, + 455, + 482 + ], + "type": "table", + "html": "
Method360p expert a360p expert b360p expert c
PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑
DeepLPF [16]23.470.89222.770.87523.730.896
CSRNet [8]24.010.93623.910.93824.310.931
3D-LUT+AdaInt [27]25.980.94724.910.93625.480.919
Harmonizer [11]24.760.92922.790.88524.560.902
RSFNet-map25.580.94924.810.94525.520.939
RSFNet-saliency25.530.94624.720.94425.110.939
", + "image_path": "31fcf8c6197ac17a41c594dccfde0bbfefa71adc175d932de8472dd740d563df.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 489, + 547, + 515 + ], + "lines": [ + { + "bbox": [ + 46, + 489, + 547, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 489, + 547, + 515 + ], + "type": "text", + "content": "Table 3: Quantitative comparisons for retouching tasks on PPR10K dataset [13]. All the models are trained on data without augmentations. White-box methods are colored as violet." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 534, + 289, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 289, + 691 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 289, + 691 + ], + "type": "text", + "content": "Training map generation and arguments regression separately. To train models with controlled region shapes, we experiment with using pre-trained PoolNet [14] and adding an FPN neck followed by an argument regressor to the backbone instead of training from scratch. During training, we fix the weights of the backbone to keep the saliency mask generated by the network unchanged. The quantitative results are shown in Table 1b, which indicates that there is no superiority over training from scratch. The reason for this might be that a network trained only on semantic data lacks sufficient information for retouching. Therefore, it is better to train the map generation and arguments regression tasks simultaneously." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 534, + 547, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 704 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 704 + ], + "type": "text", + "content": "Using Masks as Input. For training models with controlled region shapes, we can use masks concatenated with the image as input for our model. We train three models using three sets of masks as input, respectively. The results are shown in Table 1a. The retouching results evaluated on PSNR and SSIM [24] are lower than in other settings. This may be because the ground truth masks are generated by off-the-shelf models, which may differ from the underlying real masks of the dataset. Masks are slightly modified by the map generator in the inference stage to achieve better retouching results. Therefore, simple concatenation of masks with the input image can lead to worse performance compared to our design of the variant of RSFNet, which generates masks and filter arguments simultaneously." + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12165" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 542, + 335 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 542, + 335 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 542, + 335 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 542, + 335 + ], + "type": "image", + "image_path": "fe072dae96562455a2c04aa476d03a45dd0a8ccb0d4a6614f3b101af5d457999.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 58, + 342, + 536, + 356 + ], + "lines": [ + { + "bbox": [ + 58, + 342, + 536, + 356 + ], + "spans": [ + { + "bbox": [ + 58, + 342, + 536, + 356 + ], + "type": "text", + "content": "Figure 6: Qualitative comparison of selected methods. \"RSFNet-map\" means our main model explained in Section 3.2" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 60, + 393, + 260, + 533 + ], + "blocks": [ + { + "bbox": [ + 60, + 393, + 260, + 533 + ], + "lines": [ + { + "bbox": [ + 60, + 393, + 260, + 533 + ], + "spans": [ + { + "bbox": [ + 60, + 393, + 260, + 533 + ], + "type": "image", + "image_path": "899cd8149a655c259275fd724506b3c48c996843590f9952e460c91d4e0e3501.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 551, + 288, + 588 + ], + "lines": [ + { + "bbox": [ + 46, + 551, + 288, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 551, + 288, + 588 + ], + "type": "text", + "content": "Figure 7: Boxplot of user study. The dashed green line and the solid black line inside the box are the mean and the median preference percentage respectively." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Trade Off Between Speed and Accuracy. As we decrease the number of downsample operations in the backbone, the feature size grows larger and time costs increase. However, quantitative results of retouching also become better, as shown in 1c. Speed is measured in milliseconds." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 375, + 488, + 388 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 375, + 488, + 388 + ], + "spans": [ + { + "bbox": [ + 306, + 375, + 488, + 388 + ], + "type": "text", + "content": "4.4. Comparison with State-of-the-Art" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 398, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 398, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 398, + 545, + 578 + ], + "type": "text", + "content": "We compare our methods with the state-of-the-art for black-box and white-box image retouching tasks. The selected methods are compared on PSNR, SSIM [24], the " + }, + { + "bbox": [ + 304, + 398, + 545, + 578 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 304, + 398, + 545, + 578 + ], + "type": "text", + "content": "-distance in CIE LAB color space " + }, + { + "bbox": [ + 304, + 398, + 545, + 578 + ], + "type": "inline_equation", + "content": "(\\triangle E_{ab})" + }, + { + "bbox": [ + 304, + 398, + 545, + 578 + ], + "type": "text", + "content": " and the inference speed. We follow the practice in [27] to measure the GPU inference time on 100 images and report the average. Quantitative results are shown in Table 2 and 3. RSFNet-map refers to our main model in Section 3.2, RSFNet-saliency, RSFNet-palette and RSFNet-semantic refers to models trained with three sets of masks respectively in Section 3.3. In addition, we evaluate a global retouching model without the map generator, denoted as RSFNet-global. Other models are trained using their official public codes and default configurations. All experiments are executed on an NVIDIA Tesla V100 GPU." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": "Our proposed method, " + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "inline_equation", + "content": "RSFNet" + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": "-map, demonstrates its effectiveness in temperature correction and color enhancement, especially for the second set of inputs under more deteriorating shooting conditions. Although " + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "inline_equation", + "content": "RSFNet" + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": "-map achieves state-of-the-art results with negligible increase, while other RSFNet variations lag behind the state of the art, it is important to note that our white-box framework provides human-understandable ways for retouching, which makes it more convenient for users to edit and assess retouching results compared to other black-box methods. When compared with state-of-the-art white-box methods" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12166" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 79, + 523, + 401 + ], + "blocks": [ + { + "bbox": [ + 53, + 79, + 523, + 401 + ], + "lines": [ + { + "bbox": [ + 53, + 79, + 523, + 401 + ], + "spans": [ + { + "bbox": [ + 53, + 79, + 523, + 401 + ], + "type": "image", + "image_path": "ecdc78af2604b0e3704b6e4005ae955f8d970292043771ec0f2d5ac1c3a2a2d4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 411, + 547, + 437 + ], + "lines": [ + { + "bbox": [ + 46, + 411, + 547, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 547, + 437 + ], + "type": "text", + "content": "Figure 8: Editable image retouching. \"RSFNet-saliency\", \"RSFNet-semantic\" means RSFNet trained with saliency masks and semantic masks respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 456, + 287, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 553 + ], + "type": "text", + "content": "such as Harmonizer [11], all of our models exhibit better performance with faster speed. Furthermore, using 3D-LUTs to encode filter functions could potentially accelerate our models, a technique commonly implemented in traditional retouching tools. For PPR10K [13], we also evaluate our methods using a random split setup. The results are provided in supplementary material, consistently reinforcing the conclusions drawn from previous experiments." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": "The qualitative results presented in Figure 6 demonstrate that our proposed method, " + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "inline_equation", + "content": "RSFNet" + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": "-map, exhibits superior performance in handling color transitions across regions, particularly in highlight areas, compared to 3D-LUT based methods such as AdaInt, as shown in the first row of the figure. Furthermore, we conduct a comparison with Harmonizer [11] on editable retouching, as shown in Figure 8. Our white-box framework offers more degrees of freedom than global-retouching manipulations to achieve region-specific retouching. For instance, when the temperature is adjusted globally using Harmonizer, the sky in the first image turns yellow. On the other hand, our " + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "inline_equation", + "content": "RSFNet" + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": "-saliency model can modify the temperature of the foreground girl while leav-" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 456, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 517 + ], + "type": "text", + "content": "ing other regions unaffected. In the second image, global temperature adjustment by Harmonizer turns the lake and mountains blue. In contrast, " + }, + { + "bbox": [ + 304, + 456, + 545, + 517 + ], + "type": "inline_equation", + "content": "RSFNet" + }, + { + "bbox": [ + 304, + 456, + 545, + 517 + ], + "type": "text", + "content": "-semantic only modifies the sky temperature, leaving the mountains and lake unchanged." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 519, + 546, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 519, + 546, + 699 + ], + "spans": [ + { + "bbox": [ + 304, + 519, + 546, + 699 + ], + "type": "text", + "content": "To further validate the effectiveness of our proposed framework, we conduct a user study to evaluate human preferences for RSFNet and other state-of-the-art methods, including CSRNet [8], AdaInt [27], and Hormonizer [11]. To form the test set, we randomly select 58 images from the validation set of Adobe-MIT FiveK using the input zeroed with expertC white balance and input zeroed as shot settings, as well as an additional 20 images downloaded from the internet. During the experiment, we display retouched images produced by all methods, including the original input, to 22 participants. Participants are asked to select the best result from a randomly shuffled set of retouched images generated by all methods. We calculate the preferences of participants for each method and plot the results using a box plot, as shown in Figure 7." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "content": "Among the compared methods, AdaInt [27] achieves" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12167" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": "higher mean and median percentages. RSFNet exhibits more stable performance with a higher bottom percentage and the smallest standard variance percentage than the other methods. In comparison to the white-box method Harmonizer [11], RSFNet demonstrates superior user preference percentages. The boxplot illustrates the varying preferences of different users, highlighting the significance of editable capability. As RSFNet utilizes traditional color filters for retouching, it can be readily integrated into traditional retouching tools. Users can further enhance the visual appeal of the retouched results according to their own preferences through an interface." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 216, + 289, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 289, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 289, + 384 + ], + "type": "text", + "content": "Video Retouching. Our proposed RSFNet model also demonstrates applicability to video retouching, as shown in Figure 8. The filter arguments remain constant within a single video clip for all frames, ensuring consistency throughout the retouching process. However, for RSFNet variations with controlled region shapes, such as " + }, + { + "bbox": [ + 46, + 216, + 289, + 384 + ], + "type": "inline_equation", + "content": "RSFNet" + }, + { + "bbox": [ + 46, + 216, + 289, + 384 + ], + "type": "text", + "content": "-saliency, the retouching consistency across frames relies on the consistency of region masks across frames. Although filter arguments can alleviate the inconsistency caused by masks, severe inconsistency problems in masks may still affect retouching results. With the assistance of a more robust tracking algorithm, these models can achieve better performance in editable video retouching, highlighting the potential of RSFNet in various retouching applications." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 394, + 200, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 394, + 200, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 394, + 200, + 407 + ], + "type": "text", + "content": "5. Limitation and Conclusion" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 415, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 569 + ], + "type": "text", + "content": "We develop our framework under the assumption that all adjustments are done in one layer, which is then combined via linear summations of increments of all filters to obtain the final result. Therefore, although our model provides a white-box retouching framework that aligns with the intuition of human artists, it is unable to cover all adjustments that artists could conduct using professional software. However, we believe that if the cache data in the retouching process of artists is available, such as the region masks used for region-specific retouching, our model equipped with a more complicated structure, such as a cascaded structure in [10, 11], could behave more similarly to a real human artist by learning from this data." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 570, + 288, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 689 + ], + "type": "text", + "content": "This paper introduces RSFNet, a white-box framework for image retouching that utilizes a divide-and-conquer strategy to generate region maps and human-understandable filter arguments. The resulting filtered images are combined using linear summations, allowing for a wider range of filter classes and achieving fine-grained enhancement with superior performance. A variation of RSFNet with controlled shape region masks is also proposed for user convenience. Extensive experiments are presented to demonstrate the effectiveness of RSFNet." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "content": "Acknowledgement This work was supported by Alibaba" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "Group through Alibaba Innovative Research (AIR) Program and Alibaba-NTU Singapore Joint Research Institute (JRI), Nanyang Technological University, Singapore. We appreciate Mr. Wang Yuxi's efforts in generating additional experimental results during the rebuttal period." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 307, + 143, + 365, + 156 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 143, + 365, + 156 + ], + "spans": [ + { + "bbox": [ + 307, + 143, + 365, + 156 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 307, + 162, + 547, + 714 + ], + "type": "list", + "angle": 0, + "index": 22, + "blocks": [ + { + "bbox": [ + 310, + 162, + 547, + 207 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 162, + 547, + 207 + ], + "spans": [ + { + "bbox": [ + 310, + 162, + 547, + 207 + ], + "type": "text", + "content": "[1] Vladimir Bychkovsky, Sylvain Paris, Eric Chan, and Frédo Durand. Learning photographic global tonal adjustment with a database of input / output image pairs. 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Specifically, we propose RandBox, a Fast R-CNN based architecture trained on random proposals at each training iteration, surpassing existing Faster R-CNN and Transformer based OWOD. Its effectiveness stems from the following two benefits introduced by randomness. First, as the randomization is independent of the distribution of the limited known objects, the random proposals become the instrumental variable that prevents the training from being confounded by the known objects. Second, the unbiased training encourages more proposal explorations by using our proposed matching score that does not penalize the random proposals whose prediction scores do not match the known objects. On two benchmarks: Pascal-VOC/MS-COCO and LVIS, RandBox significantly outperforms the previous state-of-the-art in all metrics. We also detail the ablations on randomization and loss designs. Codes are available at https://github.com/scuwyh2000/RandBox.", + "bbox": [ + 75, + 300, + 473, + 648 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 676, + 209, + 694 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Different objects may share common visual features. For example, the detection of \"horse\" helps that of \"cow\" as they are both \"four-legged\" cattle. Therefore, it is possible to generalize the detector trained from a limited object class inventory to detect visually similar objects whose classes are out of the inventory. As shown in the right column of Figure 1, besides the conventional detection of a close-world object inventory, Open-wolrd Object Detection [23] (OWOD) can detect out-of-inventory objects and label them as \"unknown\".", + "bbox": [ + 75, + 703, + 468, + 852 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To exploit the feature transfer from \"known\" to \"unknown\", the training loss of existing OWOD methods [23, 20, 55] has the following break-downs (Figure 1):", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9b286709c785ae8db1ab321a9a5791ac69766ae665828a495d21638c3204be10.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 524, + 267, + 767, + 364 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a3e8a21443a7cc0ee6107e0eedf59eb5a1935c0c8df8d8b3031f9144948d00a8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 777, + 267, + 890, + 366 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f84ace50b37abd0b0afe38f29cb1c94014282d117bfd5f4697a13aabcd57d577.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 526, + 371, + 767, + 465 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/92c099588aa27cb906703cda762af5e0b59dba09f982864820a420b4c11934ab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 777, + 369, + 890, + 465 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1eff90579158a71545ace3b223253ad83331db8db346fb3cd957737a63fa34cc.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 527, + 474, + 767, + 558 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/dda8f9351725741a80fed17db0753650cc29e9973d803e3c0b4da74653ea7d2d.jpg", + "image_caption": [ + "Figure 1: The paradigm of (a) closed-world object detection, (b) existing open-world object detection, and (c) our RandBox that uses random proposals." + ], + "image_footnote": [], + "bbox": [ + 777, + 470, + 890, + 561 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Known-FG (foreground): like conventional closed-world detection (Figure 1a), we calculate the matching scores between the predicted region proposal labels and the ground-truth labels of known objects, where the label is a pair of class andbbox (bounding box). In particular, for two-stage detectors like Faster R-CNN [42], the \"proposal sampler\" and \"matching score\" are region proposal network andbbox IoU (intersection over union); for end-to-end detectors like DETR [9], they are query transformer decoder and bipartite matching score. For the matched proposals, the loss is class cross-entropy $\\mathcal{L}_{cls}$ andbbox regression $\\mathcal{L}_{reg}$ .", + "bbox": [ + 496, + 654, + 893, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "BG (background): for conventional detection, all the mismatched proposals are considered background, whose loss is only $\\mathcal{L}_{cls}$ with the label \"BG\"; for OWOD, we only use the mismatched proposals excluding the Unknown-FG proposals below.", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 47 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "6233", + "bbox": [ + 482, + 943, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f4b4d37380d21027c4fa6d489a4ab185a4ae8c1b05f126554f97eba4d9073351.jpg", + "image_caption": [ + "Figure 2: The sorted foreground confidence assigned by two baselines (ORE [23], OW-DETR [20]) and our Rand-Box to the generated proposals in training. Green, red and black correspond to \"known\", \"unknown\" and \"BG\", respectively, with examples showing on the top row." + ], + "image_footnote": [], + "bbox": [ + 86, + 87, + 455, + 213 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unknown-FG: this is the key difference from conventional detection. Its design heuristic is that, for the mismatched proposals with class confidence larger than a threshold—probably unknown objects—the loss is only $\\mathcal{L}_{cls}$ with a special label \"unknown\" w/o bbox regression. Note that this heuristic is based on the assumption of feature transfer [56, 10]—visually similar proposals have similar class confidences (see Section 3.1 for the review of the loss implementation in two-stage and end-to-end detection)—the more unknown objects the Unknown-FG collects, the better the OWOD.", + "bbox": [ + 75, + 325, + 468, + 491 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, in practice, Unknown-FG usually has a low recall of unknown objects. As shown in Figure 2, in existing methods, most proposals of high confidence are matched as Known-FG; the mismatched proposals, mixed with both unknown objects and BG, all have low confidence, losing a gradual confidence decrease to differentiate Unknown-FG from BG (the red and black colors are inseparable). One may easily understand that this failure is predictable because, yet, we don't have the ground-truth labels for unknown objects, so the proposal sampler trained on known objects will be inevitably biased towards them. In fact, such bias is ubiquitously in any bootstrapping learning [43] with limited supervision, such as semi-supervised learning [34, 49] and reinforcement learning [24, 53]. Unfortunately, existing OWOD methods do not properly address the bias.", + "bbox": [ + 75, + 493, + 468, + 733 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we point out that the bias is caused by the confounding effect [37, 39] of the training data with limited known object labels that mislead the feature transfer. The effect can be understood in this way: if we only let the training data determine what region proposals to be used to extract the region features for detector training (Figure 1b), we cannot avoid the trivial loss minimization from only detecting the known objects. To this end, we propose to remove the confounding effect by introducing a random Instrumental Variable [5]—the proposed RandBox—that is independent of the training data. Intuitively, RandBox sim", + "bbox": [ + 75, + 734, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ulates a Randomized Controlled Experiment (RCT) [8] to learn a causal detector from region features to object labels, by inviting an independent 3rd-party proposal sampler to explore more possible locations of unknown objects. As shown in Figure 2 RandBox, the recall of unknown objects is greatly improved by RandBox, due to the fact that the confidence score change of the proposals from known to unknown is much more separable. We will detail the theory behind RandBox in Section 4. To get a qualitative sense of open-world detection task, see Figures 3.", + "bbox": [ + 496, + 90, + 890, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "RandBox is simple yet effective (Section 3.2). For each training image in every iteration, we sample 500 random boxes as proposals from a 4-dimensional Gaussian noise (center_x, center_y, height, width). For these random boxes, we crop their RoI (region of interest) features from a backbone feature map, and feed them into a detection head to obtain $\\mathcal{L}_{cls}$ and $\\mathcal{L}_{reg}$ as in (Figure 1c), where the proposed matching score that encourages exploration is detailed in Section 3.2. At inference, we remove the randomness and grid-sample 10,000 boxes per image by 10 scales, 10 shapes, and 100 spatial locations. We use NMS [35] (Non-maximum Suppression) to prune the 10,000 boxes for final detection. Overall, our contributions include:", + "bbox": [ + 496, + 242, + 890, + 438 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Our proposed RandBox is a Fast R-CNN based architecture for OWOD, which leverages random proposals to remove the confounding effect from the known objects, and uses an improved matching score to encourage proposal exploration.", + "- By removing the confounding effect, we learn an unbiased detector that improves both known and unknown detection accuracy. In particular, we achieve new state-of-the-art results on Pascal-VOC/MS-COCO [29].", + "- We show that our RandBox detector trained on PascalVOC/MS-COCO remains robust when transferring to long-tailed datasets such as LVIS [19]." + ], + "bbox": [ + 514, + 443, + 890, + 632 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 647, + 640, + 662 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Open-World Object Detection (OWOD). Object detection systems are significantly advanced recently [41, 57, 42, 18, 48]. Yet they are based on the conventional close-world paradigm, which assumes that all objects of interests are annotated. In practice, an object detector deployed in real life is constantly challenged by the vast open and dynamic visual world [33, 23, 25]. To bridge the gap, open-set detection [33, 32, 14] aims to reject out-of-inventory objects as “unknown”, and other works focus on incrementally learning [40, 1, 31] a detector to recognize new object classes without forgetting old ones. Inspired by the open-world setting proposed in image classification [6, 7], recent works [23, 20, 55, 58] unify open-set detection and incremental learning as OWOD, which are based on two stage detectors like Faster R-CNN [42], or end-to-end ones like", + "bbox": [ + 496, + 672, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "6234", + "bbox": [ + 482, + 943, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3b9bea2127c63d1f0459a739ed637af63ecdee11c0412bbaf74c8f734db1a0c8.jpg", + "image_caption": [ + "Figure 3: Example results. We show the ground-truth (GT) locations of unknown objects, those predicted by OWDETR [20], and those predicted by our RandBox. RandBox not only detects the annotated unknown objects (first 2 images), but even discovers valid unknown ones without annotations (e.g., camp in image 3, bracelet in image 5, banner in image 6)." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 883, + 270 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "DETR [57]. We systematically analyze the failure of these existing works—low recall of unknown objects—which is caused by the confounding effect [37, 36], and remove it using random proposals to learn a causal detector.", + "bbox": [ + 75, + 352, + 468, + 412 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Debiasing by Randomization. Randomization is an effective tool to debias across many tasks and domains. For example, using randomization as an instrument variable [12, 4, 5] is a classic tool to identify causal effect in social studies [15]. In reinforcement learning [53], randomization is used to encourage exploration [54, 27], such that the agent is not biased to exploiting spurious shortcuts. Several works [3, 50] in adversarial training [17] leverages randomization to build a robust model not biased to feature that can be manipulated in adversarial attack, e.g., by image perturbation [59]. In fact, data augmentation that is prevailing in vision [45, 21, 47] and language [46, 44] also leverages randomness to remove augmentation-related context bias in training (e.g., using green grass to classify cow). In our work, we present a novel detection framework that leverages random proposals to learn causal effect in OWOD.", + "bbox": [ + 75, + 415, + 473, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 676, + 169, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In OWOD, the task is to detect a gradually expanding set of known inventory classes $K$ , while simultaneously rejecting the out-of-inventory classes set $U$ as \"unknown\". The training dataset contains images where known objects are labelled. Specifically, for a training image containing $n$ known objects, it is labelled with a set $\\{(b_i, y_i)\\}_{i=1}^n$ , where $b_i$ specifies the bounding box (bbox) of the $i$ -th object (i.e., center_x, center_y, height, width), and $y_i \\in K$ is its class label. We drop the subscript $i$ for simplicity when the context is clear. The goal in OWOD is to train a detector, whose input is an image, and output is a set of $m$ predictions $P = \\{(\\hat{b}_i, \\hat{y}_i)\\}_{i=1}^m$ , where $\\hat{b}_i$ is the $i$ -th bounding box prediction (predictedbbox), and $\\hat{y}_i \\in \\mathbb{R}^{|K| + 2}$ denotes the clas-", + "bbox": [ + 75, + 703, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "sification logit for each class in $K\\cup \\{\\text{\"unknown\",\"BG\"}\\}$", + "bbox": [ + 498, + 352, + 883, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries: Existing OWOD Methods", + "text_level": 1, + "bbox": [ + 498, + 375, + 849, + 392 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Existing methods adopt either the two-stage Faster R-CNN [42] or the end-to-end DETR [9] as the detector. In training, the predictions $P$ generated by the detector are partitioned into three subsets: Known-FG, Unknown-FG and BG, which are used to calculate the classification loss and bbox regression loss. We detail each part below:", + "bbox": [ + 496, + 398, + 892, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Detector. Given an image, a detector generates $m$ proposals, extracts ROI features $x_{i}$ for each proposal, and finally computes bounding box $\\hat{b}_{i}$ and logits $\\hat{y}_{i}$ using a classifier to form $P$ . The two detector frameworks mainly differ in the first step: 1) Faster R-CNN leverages a region proposal network (RPN) pre-trained on the labelled data. It outputs the top- $m$ proposals with the largest objectness (i.e., probability of containing a known object). 2) DETR is an end-to-end detector. It first transforms an image into tokens using a combination of CNN backbone and transformer encoder. Then a transformer decoder uses the image tokens to generate the proposals. More details are in Appendix.", + "bbox": [ + 496, + 489, + 892, + 671 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Known-FG is selected from all predictions $P$ by matching with the labels $\\{(b_i, y_i)\\}_{i=1}^n$ based on a Known-FG score. To compute the score for a prediction $(\\hat{b}, \\hat{y}) \\in P$ with a ground-truth $(b, y)$ , Faster R-CNN uses the IoU between $\\hat{b}$ and $b$ , and DETR uses the bipartite matching score, which additionally considers if $\\hat{y}$ has a large value on the class $y$ . As the process is the same as that in closed-set detection, we leave other details in Appendix. After matching, we denote the Known-FG subset as $P^K$ . For $(\\hat{b}, \\hat{y}) \\in P^K$ , we denote its matched ground-truth as $(b^*, y^*)$ .", + "bbox": [ + 496, + 671, + 893, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unknown-FG & BG are selected from the unmatched predictions $P \\setminus P^K$ . Specifically, current methods compute an Unknown-FG score for each prediction, and select 5 predictions with the largest score as the Unknown-FG. For the score, methods based on Faster R-CNN [42, 23] use object-", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "6235", + "bbox": [ + 482, + 943, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/38b4cc5bf9d0d3dfda7ef97229d3c461488cb39db93e84e53c7f3fc7cf8d5b27.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 509, + 244 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d48657afbad43da15183e417247cbc33e73532b5f647925cde41af954b475a3c.jpg", + "image_caption": [ + "(b)", + "Figure 4: (a) RandBox Pipeline. Our proposals are randomly generated. We obtain the Known-FG subset using a dynamic- $k$ matcher, and the Unknown-FG subset based on our proposed matching score. Our training losses follow existing methods. (b) Proposed Matching Score is the sum of likelihood of belonging to each foreground classes (including \"unknown\"). The proposals of known (green) and unknown (red) objects both have large matching score, i.e., high likelihood on the ground-truth class (solid arrows) or by feature transfer (dashed arrow), while BG proposals (black) have low score." + ], + "image_footnote": [], + "bbox": [ + 542, + 88, + 890, + 247 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ness, and those based on DETR [20] use the average value of the ROI feature. We denote the Unknown-FG subset as $P^U$ . Finally, the rest predictions become the BG subset $P^B$ . Training Loss.", + "bbox": [ + 76, + 377, + 468, + 436 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We calculate the loss on each of the three subsets. The loss on Known-FG $\\mathcal{L}^K$ has the same form with closed-set detection:", + "bbox": [ + 76, + 438, + 468, + 481 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} ^ {K} = \\sum_ {i = 1} ^ {| P ^ {K} |} \\mathcal {L} _ {c l s} \\left(\\hat {y} _ {i}, y _ {i} ^ {*}\\right) + \\lambda \\mathcal {L} _ {r e g} \\left(\\hat {b} _ {i}, b _ {i} ^ {*}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 489, + 468, + 534 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{cls}$ is the cross-entropy loss or focal loss [28] to handle class-imbalance, $\\lambda$ is a balancing weight, and $\\mathcal{L}_{reg}$ is the smooth L1 regression loss [18] to rectify the predicted bbox. Details of $\\mathcal{L}_{cls}$ and $\\mathcal{L}_{reg}$ are in Appendix. As Unknown-FG and BG have no annotated bbox, we only calculate $\\mathcal{L}_{cls}$ on them:", + "bbox": [ + 76, + 541, + 468, + 632 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} ^ {U B} = \\sum_ {i = 1} ^ {| P ^ {U} |} \\mathcal {L} _ {c l s} \\left(\\hat {y} _ {i}, \\text {\" u n k n o w n\"}\\right) + \\sum_ {i = 1} ^ {| P ^ {B} |} \\mathcal {L} _ {c l s} \\left(\\hat {y} _ {i}, \\text {\" B G\"}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 652, + 468, + 709 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Overall, the detector parameters $\\theta$ are optimized with:", + "bbox": [ + 76, + 710, + 433, + 724 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta} \\mathcal {L} ^ {K} + \\beta \\mathcal {L} ^ {U B}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 209, + 732, + 468, + 756 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\beta$ is a weight with ablation in Section 5.2.", + "bbox": [ + 76, + 763, + 398, + 777 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "OWOD Pipeline. The detector is first randomly initialized. Then it is trained with the labelled data on $K$ , and evaluated with data on both $K$ and $U$ (Task 1). Next, additional labelled data on a subset of classes $K' \\subset U$ is provided, i.e., the known classes set expands as $K \\gets K \\cup K'$ , and the unknown one becomes $U \\gets U \\setminus K'$ . The detector trained on Task 1 is fine-tuned and evaluated with the updated $K$ and $U$ (Task 2). This continues for the following tasks.", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Proposed RandBox", + "text_level": 1, + "bbox": [ + 500, + 376, + 684, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Existing methods suffer from the low recall of the unknown objects in Unknown-FG. To tackle this, our proposed RandBox has two improvements: 1) We propose to generate region proposals randomly, instead of using a proposal sampler trained on the known objects, which explores more possible unknown object locations. 2) We propose a matching score without penalizing proposals that are not matched with the known objects, which explores more possible unknown object proposals. We detail the two improvements below, and explain why our RandBox solves the existing problems from a causal view in Section 4.", + "bbox": [ + 496, + 405, + 890, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Detector with Random Proposals. In training, we randomly generate 500 bboxes as region proposals on each image (Figure 4a). For each bbox, we sample 4 random real numbers in [0, 1], where each number is first drawn from the standard Gaussian distribution, truncated to $[-2, 2]$ and then scaled linearly to [0, 1]. The 4 numbers correspond to the horizontal and vertical coordinate of the bbox center, as well as the width and height of the bbox, respectively (proportional to image size). The width and height of out-of-boundary bboxes are adjusted to stay in the image. In testing, to remove the prediction randomness, we use 10,000 pre-defined bboxes as proposals on each image, which cover 10 scales, 10 aspect ratios and 100 spatial locations (details in Appendix). We use non-maximum suppression to prune the bboxes as per standard practice [35]. We highlight the following points:", + "bbox": [ + 496, + 575, + 890, + 818 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Our region proposals are randomly sampled for every image in each iteration throughout the training.", + "- While we use random sampling, the number of our random proposals is in fact comparable with that used in the existing methods, e.g., ORE [23] uses 1024 proposals." + ], + "bbox": [ + 496, + 823, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "6236", + "bbox": [ + 482, + 943, + 514, + 954 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Known-FG. We adopted the dynamic- $k$ matcher [11] as shown in Figure 4a. Specifically, each ground-truth bbox $b$ is matched with $k$ proposals based on the bipartite matching score, where $k$ is dynamically selected as the sum of the IoU between each proposal and $b$ .", + "bbox": [ + 75, + 90, + 468, + 166 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Unknown-FG. We propose a novel matching score to form Unknown-FG. Specifically, we select the top $N$ proposals with the largest matching score (ablation of $N$ in Section 5.2). Among the selected proposals, those already in Known-FG are removed to form our Unknown-FG subset. We use the following equation to compute our matching score for a proposal with the classification logits $\\hat{y}$ :", + "bbox": [ + 75, + 167, + 467, + 272 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ns (\\hat {y}) = \\sum_ {i = 1} ^ {| K | + 1} \\frac {1}{1 + \\exp (- \\hat {y} _ {i})}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 282, + 468, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we compute and sum the sigmoid of the $|K|$ known classes and “+1” unknown class, and $\\hat{y}_i$ denotes the logit for the class $i$ . Note that we implement $\\mathcal{L}_{cls}$ with the BCE loss [28]. Hence our score essentially computes how likely $\\hat{y}$ corresponds to the foreground. Specifically, the top- $N$ (largest matching score) proposals that are not in KnownFG are pseudo-labeled as “unknown” to train the UnknownFG logit (Eq. 2 first loss). This design is based on the assumption of feature transfer [38, 52]—similarity between Unknown-FG and Known-FG is larger than that between BG and Known-FG. As shown in Figure 4b, an unknown object proposal can have non-trivial likelihood of belonging to a known class due to shared feature (dashed arrow), while BG proposal almost shares no feature with known. Hence future unknown object proposals can have large likelihood of belonging to “unknown” (solid red arrow), increasing the unknown recall. We have the following comparisons with existing methods:", + "bbox": [ + 75, + 335, + 467, + 608 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Methods based on Faster R-CNN use the objectness predicted by RPN as the matching score to select UnknownFG. However, RPN is trained to produce large scores only on the proposals matched with the known objects, thus penalizing those unmatched ones.", + "- Without RPN, methods based on DETR use the mean activation of the ROI feature instead. However, this heuristic is extremely unreliable (Figure 3b), and unknown object proposals are often mistakenly placed in the BG subset and penalized as \"background\".", + "- In contrast, our matching score fairly evaluates each proposal by checking both known classes (first $|K|$ logits), as well as \"unknown\" ( $|K| + 1$ -th logit). Hence unknown object proposals can be reliably selected in the Unknown-FG subset with high likelihood of belonging to \"unknown\"." + ], + "bbox": [ + 73, + 609, + 467, + 837 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Other Details. Our training objective is the same as Eq. (3). We used ResNet-50 [22] as backbone. Our RandBox is Fast R-CNN [18] based architecture and detection head is borrowed from Sparse R-CNN [48].", + "bbox": [ + 75, + 839, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8077c57287447c75085f30fe3a1e9a9adc352e17347bad1dc786d4cad30f41b9.jpg", + "image_caption": [ + "Figure 5: Causal graph of (a) existing OWOD methods, and (b) our RandBox." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 676, + 157 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/63e8fc6aa531d0cc95adcfed96a7a8146e719165260ea48837b1cc4aef59af23.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 717, + 89, + 890, + 157 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Theory", + "text_level": 1, + "bbox": [ + 500, + 224, + 584, + 242 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use a Structural Causal Model (SCM) to analyze the causalities between the key components in OWOD: training data $D$ , region proposal $R$ , ROI feature $X$ , and label $Y$ on $K \\cup \\{\\text{\"unknown\", \"BG\"}\\}$ . Note that $D$ only contains labelled data of the known classes $K$ . The SCM is illustrated with a causal graph in Figure 5, where each directed link denotes a causal relation between the two connected nodes. $R \\rightarrow X \\rightarrow Y$ represents the desired causal effect from region proposal $R$ to label $Y$ , as label $Y$ describes what a region $R$ (or its ROI feature $X$ ) contains. A detector is unbiased if it identifies $R \\rightarrow X \\rightarrow Y$ , i.e., given any region, the detector can fairly evaluate what it contains.", + "bbox": [ + 496, + 250, + 890, + 430 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$R \\to X \\gets D$ . The ROI feature $X$ is jointly determined by what the region contains ( $R \\to X$ ), as well as the feature representation learned on the training data ( $D \\to X$ ).", + "bbox": [ + 496, + 431, + 890, + 476 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$D \\to Y$ is because the detector leverages the training knowledge obtained from $D$ to predict $Y$ , e.g., identifying the BG subset with prediction \"BG\" (Section 3.1).", + "bbox": [ + 496, + 477, + 888, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$D \\to R$ exists in current OWOD methods as shown in Figure 5a. This is because the region proposal network in Faster R-CNN and the transformer decoder in DETR are both trained on $D$ to generate proposal $R$ .", + "bbox": [ + 496, + 522, + 888, + 582 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Confounding Effect. In Figure 5a, $R \\gets D \\to Y$ is known as a backdoor path, which leads to the undesired confounding effect [37]. Specifically, as the proposal sampler is supervised by the labelled data of known objects $D$ , the generated proposals $R$ are inevitably biased to them $(D \\to R)$ , i.e., $R$ only faithfully reflects the known object locations. Consequently, the training is dominated by the loss $\\mathcal{L}^K$ on Known-FG, and the detector recklessly exploits any discriminative feature in $D$ towards the known objects $(D \\to Y)$ , which may not transfer to the unknown ones. This causes the low recall of Unknown-FG in Figure 2.", + "bbox": [ + 496, + 582, + 890, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Removing Confounding Effect. In our RandBox, $R$ is randomly generated with no influence from $D$ , i.e., $D \\nRightarrow R$ in Figure 5b. This makes $R$ an Instrument Variable [5], which removes the confounding effect by simulating a Randomized Controlled Experiment [8]. We provide a threefold intuitive explanation: 1) The backdoor path is cut, i.e., $R \\nLeftarrow D \\to Y$ ; 2) The path $R \\to X \\gets D \\to Y$ is blocked due to the collider [37] $X$ (i.e., with two incoming arrows). 3) This makes $R \\to X \\to Y$ the only unblocked path from $R$ to $Y$ . Hence when learning to predict $Y$ from $R$ , our de", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "6237", + "bbox": [ + 482, + 943, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/41f2618ae022df8f5833594762c2babe79e276f0300a4a53d4709a5d34ec7cd0.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodTask 1Task 2Task 3Task 4
K-mAPU-RWIA-OSEK-mAPU-RWIA-OSEK-mAPU-RWIA-OSEK-mAP
Faster-RCNN [42]56.4-0.069913,39615.2-0.037112,2916.7-0.02139,1744.2
Faster-RCNN+Finetuning56.4-0.069913,39638.0-0.037512,49730.0-0.02799,62225.6
DDETR [57]60.3-0.060833,27017.9-0.036818,1158.5-0.01979,3926.0
DDETR+Finetuning60.3-0.060833,27044.8-0.033717,83433.3-0.019510,09529.4
ORE [23]56.04.90.062110,45939.42.90.028210,44529.73.90.01566,80325.3
OST [55]56.2-0.04174,88939.9-0.02132,54629.6-0.01462,12025.9
OW-DETR [20]59.37.50.057110,24042.96.20.02788,44130.85.70.01566,80327.8
RandBox61.810.60.02404,49845.36.30.00781,88039.47.80.00541,45235.4
", + "bbox": [ + 96, + 88, + 883, + 220 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1: OWOD Evaluation results and comparison with existing methods. We can also achieve SOTA on previously/currently known scores, more details are in Appendix.", + "bbox": [ + 75, + 229, + 892, + 261 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tector captures the causal effect free from the confounding one. The formal definition and proof are in Appendix.", + "bbox": [ + 75, + 276, + 470, + 306 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 324, + 209, + 343 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We introduce important experiment setups below, and leave other details in Appendix.", + "bbox": [ + 75, + 351, + 468, + 382 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We extensively evaluated RandBox on three tasks: OWOD, transfer learning and open-set detection. For OWOD, we used Pascal VOC [16] and MS-COCO [29] following the standard setups [23, 20]. In Task 1, the known set $K$ contains the 20 classes in Pascal VOC, and the unknown set $U$ contains the 60 classes unique to MS-COCO. For each of the Task 2-4, 20 classes in $U$ are added to $K$ , i.e., Task 4 corresponds to closed-set detection with 80 classes. The training and testing images are selected from the respective split of the two datasets. For transfer learning, we evaluated models trained on Task 1 on the 4,809 validation images of LVIS v1.0 [19], which are from over 1000 classes that exhibits long-tailed distribution. For open-set detection, we followed [33] to train models on Pascal VOC train split, and evaluate them on WR1 [33].", + "bbox": [ + 75, + 383, + 468, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics: On known classes, we used the standard Known-class mAP (K-mAP). On unknown classes, we used three metrics: 1) Unknown class Recall (U-R) is the recall of unknown classes at IoU threshold of 0.5. 2) Wilderness Impact (WI) [14] is computed by (closed-set precision)/(open-set precision) - 1. A small WI is desired in OWOD, i.e., precision does not drop when unknown objects are introduced in evaluation. 3) Absolute Open-Set Error (A-OSE) [33] is the predictions that are misclassified as one of the known classes.", + "bbox": [ + 75, + 611, + 468, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details: In training, we used the ResNet-50 [22] pre-trained on ImageNet [13] as our backbone. We trained RandBox using AdamW [30] optimizer with learning rate as $2.5e^{-5}$ and weight decay as $1e^{-4}$ . We used the same methodology as prior work [23, 2, 51, 26] to mitigate forgetting, i.e., by storing a balanced set of exemplars for model fine-tuning after each incremental step. In inference, after getting the predictions on the 10,000 pre-defined bboxes, we used Non-Maximum Suppression (NMS) [35]", + "bbox": [ + 75, + 763, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "to prune redundant bboxes. After pruning, the final predictions are the bboxes whose probability of belonging to a class in $K \\cup \\{ \"unknown\" \\}$ are at least 0.1.", + "bbox": [ + 496, + 276, + 892, + 321 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Main Results", + "text_level": 1, + "bbox": [ + 500, + 330, + 638, + 347 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1 presents the results of OWOD evaluation. We have the following observations:", + "bbox": [ + 496, + 354, + 892, + 385 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1) For the conventional framework Faster-RCNN [42] and Deformable-DETR (DDETR) [57], their K-mAP drops significantly in Task 2-4, showing that they suffer from catastrophic forgetting when new classes are incrementally added. By using data replay [23] (+Finetuning), their K-mAP results improve significantly (e.g., 6.0 to 29.4 on Task 4 for DDETR). Note that they are not capable to detect unknown objects (e.g., U-R is not applicable).", + "2) By comparing existing OWOD methods with the conventional frameworks, we notice that all of them have reduced K-mAP (e.g., the DDETR-based OW-DETR reduced 1.6 mAP on Task 4 compared with DDETR+Finetuning). This means that their capabilities of unknown detection are at the cost of known detection accuracy.", + "3) By comparing RandBox with existing OWOD methods on U-R and A-OSE, we observe significant improvements, e.g., $3.1\\%$ U-R improvement and 391 A-OSE reduction on Task 1. This suggests that our training scheme with random boxes and the proposed matching score encourage proposal explorations, which detects and learn on more unknown objects to improve their evaluation performance.", + "4) In particular, by comparing K-mAP and WI of Rand-Box and OWOD methods, we see that RandBox also achieves the state-of-the-art (SOTA) performance, e.g., absolute gains ranging from $2.4\\%$ to $8.6\\%$ in terms of K-mAP and relatively reduces ranging from $42\\%$ to $64\\%$ in terms of WI. Remarkably, our RandBox even outperforms the conventional detection frameworks, e.g., Faster-RCNN and DDETR. This means that instead of sacrificing \"known\" to detect \"unknown\", RandBox learns \"unknown\" to benefit \"known\". This strongly validates that our approach removes confounding bias by simulating Randomized Controlled Experiment with random boxes, where our detector captures the causal effect from any region proposal (known," + ], + "bbox": [ + 496, + 386, + 893, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6238", + "bbox": [ + 482, + 943, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2b2f24145c0f83192917b2129b0fd59aa3b37e1865b946d3293d3f09adb3add5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ProposalsK-mAPU-RWIA-OSE
Selective search57.39.10.0295,433
RPN59.08.60.0315,128
Query based59.79.10.0434,679
Random (Ours)61.810.60.0244,498
", + "bbox": [ + 86, + 89, + 486, + 174 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/89cc9132ea1786b03ed49898d3aed844ba17f225a53a22bcc7640efb2a0d2be1.jpg", + "table_caption": [ + "(a) Ablation on proposal generation method." + ], + "table_footnote": [], + "table_body": "
MatchRandK-mAPU-RWIA-OSE
51.8-0.0427,652
Ours59.79.10.0434,679
Mean activation✓60.37.10.0245,929
Ours✓61.810.60.0244,498
", + "bbox": [ + 86, + 199, + 486, + 277 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cda5719c2d6d11d93e6324dace8f66125d9f4659979998e7687cf8edcef2489e.jpg", + "table_caption": [ + "(c) Ablation on components." + ], + "table_footnote": [], + "table_body": "
distributionnumK-mAPU-RWIA-OSE
Uniform10060.28.70.0274,877
Gaussian10060.79.30.0264,732
Uniform50062.010.10.0264,588
Gaussian50061.810.60.0244,498
Uniform1,00061.710.40.0284,975
Gaussian1,00061.810.60.0304,763
", + "bbox": [ + 506, + 89, + 887, + 174 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/fcfd106155c258d752da7b25fd608430aba8dcffa1a650bb1e38a8e2758c3325.jpg", + "table_caption": [ + "(b) Strategy for Random Proposals." + ], + "table_footnote": [], + "table_body": "
ratioscalelocationK-mAPU-RWIA-OSE
552060.28.20.0413,001
10102061.69.60.0323,715
10104061.310.20.0294,098
101010061.810.60.0244,498
", + "bbox": [ + 506, + 199, + 890, + 277 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(d) Ablation on inference bboxes.", + "bbox": [ + 589, + 286, + 797, + 299 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2: Ablation results. Models are trained on Task 1. We adopted the best performing setting as our default (in gray).", + "bbox": [ + 84, + 311, + 879, + 328 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7c5ee4532117f0bc2390ded4aeede6355cfef423b510254405c3f2fce565d8fa.jpg", + "image_caption": [ + "Figure 6: Ablation on $N$ by training RandBox on Task 1." + ], + "image_footnote": [], + "bbox": [ + 81, + 352, + 455, + 497 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "unknown or BG) to its label (Section 4). Hence we observe unconditional improvements overall.", + "bbox": [ + 76, + 550, + 467, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Ablation Experiments", + "text_level": 1, + "bbox": [ + 76, + 590, + 282, + 606 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Choice of $N$ . Recall that in training, we identify the top $N$ proposals with the largest matching score to form Unknown-FG (by removing those already in Known-FG). Hence $N$ is directly correlated with the size of Unknown-FG. The ablation results on $N$ are given in Figure 6. Initially, increasing $N$ benefits both known detection (K-mAP) and unknown recall (U-R). This is because 1) With more unknown proposals for optimizing Eq. (3), the detector improves in recognizing \"unknown\" (increased U-R). 2) To differentiate \"unknown\" from \"known\", the detector also avoids spurious correlations of known classes in training (i.e., captures causal effect), which may not generalize to known objects in testing (increased K-mAP). However, further increasing $N$ leads to the drop in K-mAP. This is because increasing the size of Unknown-FG by large $N$ essentially increases the weight of the classification loss on \"unknown\" in Eq. (2). Hence the detector learning on known classes is adversely impacted when the weight is too large. We used $N = 10$ in all our experiments.", + "bbox": [ + 75, + 612, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Proposal generation methods Its ablation is in Table 2a. We use our matching score Eq. 4 and fix the same proposal number (500) to ablate the proposal generation methods. We compared our Random Proposals with Selective search, RPN and Query based proposals. We can find that our Random proposals surpass all other methods which means the randomness can make more explorations on more image regions, without biased towards the training data.", + "bbox": [ + 496, + 354, + 890, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Strategy for Random Proposals. When generating random proposals in training, we experimented with different distribution (for drawing random numbers) and the number of random proposals (num), and the results are in Table 2b. Using the same number of proposals, the results on the two distributions are both competitive. Regarding the number of proposals, we observe that increasing it beyond 500 does not bring any improvement. This shows that the image locations are already sufficiently explored using 500 random bboxes. Overall, we used 500 random proposals drawn from Gaussian distribution.", + "bbox": [ + 496, + 477, + 892, + 642 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Components. The main components in RandBox are the use of random proposals (Rand), and the matching process for Known-FG and Unknown-FG (Match). Their ablations are given in Table 2c. The first line corresponds to the baseline Sparse R-CNN [48]. Comparing the second line, by combining our matching process with NMS, our matching score can improve all metrics and already achieved SOTA (e.g., by comparing with other OWOD methods in Table 1 Task 1). In the third and forth lines, we introduce the Random proposals and compare two kinds of matching score, i.e., Mean activation and our matching score. We can find that our matching score improve all metrics significantly (e.g., $1.5\\%$ on K-mAP and $3.5\\%$ on U-R) compared with the Mean activation. This strongly validates the effectiveness of each component in RandBox.", + "bbox": [ + 496, + 643, + 892, + 868 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training schedule. We show the change of U-R and K-mAP over the training and compare RandBox with ORE", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "6239", + "bbox": [ + 482, + 943, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/89b8051312ac2baebdda29a4bd647c44a73fb1f2b2987c45ad95fc3b9f304000.jpg", + "image_caption": [ + "Figure 7: Training schedule compared with existing works." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 261, + 212 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8b9cdb80118d491765c19d1d1d1b1885733b2ee623d4ab6710ec3df3f5fdc18d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 279, + 89, + 459, + 213 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f44f404188911a61c77235d4fd5c7fb81b87649ff3aab85a39922e89b811ce50.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodK-mAPU-RWIA-OSE
ORE [23]23.23.50.174323,225
OW-DETR [20]25.16.30.154819,672
RandBox27.78.40.07357,842
", + "bbox": [ + 89, + 252, + 460, + 310 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1b6d4d7cd51a12e8044e5dfd36ab67d4a951968064535f46682e855e782c4403.jpg", + "table_caption": [ + "Table 3: Transfer evaluation results on LVIS v1.0 [19]." + ], + "table_footnote": [], + "table_body": "
Evaluated on →Pascal-VOCOpen-Set (WR1)
Faster R-CNN [42]81.877.1
RetinaNet [28]79.273.8
Dropout Sampling [33]78.173.8
ORE [23]81.371.7
OW-DETR [20]82.178.6
RandBox84.482.0
", + "bbox": [ + 91, + 349, + 459, + 435 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4: Results on Pascal-VOC [16] (closed-set) and WR1 [33] (open-set).", + "bbox": [ + 76, + 446, + 468, + 477 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and OW-DETR in Figure 7. Our RandBox converges quickly and trains stably, outperforming the two methods.", + "bbox": [ + 75, + 503, + 467, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Inference Bboxes. We ablation on the number of predefined bbox ratios, scales and locations in Table 2d. Increasing the bbox number generally improves the performance due to the increased recall on both known and unknown classes. However, it also increases the number of mis-classified unknown predictions, leading to a larger A-OSE. As the performance tends to saturate with 10,000 bboxes (last row), we use this configuration for efficiency.", + "bbox": [ + 75, + 534, + 467, + 654 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Transfer and Open-Set Evaluations", + "text_level": 1, + "bbox": [ + 76, + 662, + 383, + 679 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Transfer to LVIS v1.0. We evaluated the models trained on Task 1 on LVIS 1.0. [19] We observe significant improvements on all metrics compared to ORE and OW-DETR in Table 3 This validates the robustness of RandBox over the existing works under distribution shift.", + "bbox": [ + 75, + 686, + 467, + 761 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Open-Set Object Detection. Detectors in OWOD can naturally tackle open-set detection. We followed [33] and evaluated models trained on Task 1 on Pascal-VOC test split (closed-set) and WR1 (open-set). We significantly improve existing SOTAs on both evaluations (Table 4).", + "bbox": [ + 75, + 762, + 467, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Additional Qualitative Results", + "text_level": 1, + "bbox": [ + 76, + 847, + 346, + 863 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Figure 8 first column, OW-DETR misses the known objects \"mouse\" and \"chair\" due to confusing", + "bbox": [ + 76, + 869, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/af384c3d8d84492f1b10b215b1542496491c9bf5c6d6328956978d71aa990143.jpg", + "image_caption": [ + "Figure 8: Additional qualitative results. We show the ground-truth labels of known objects in the first row, and compare the predictions from OW-DETR and our RandBox. Green: known. Red: unknown." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 890, + 281 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "background and partial view, respectively. Our RandBox not only detects all known objects, but also identify many valid unknown objects. In the second column, RandBox predicts the overlapping spoons as \"unknown\", which is indeed plausible without other prior knowledge. The third column shows that our RandBox detects the unknown object \"picture frame\" both in the real world and in the mirror.", + "bbox": [ + 496, + 383, + 890, + 489 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 508, + 617, + 525 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We presented a novel Open-World Object Detection (OWOD) method called RandBox, trained on random proposals and surpassing existing Faster R-CNN and Transformer based OWOD. We show from a causality theoretical perspective that RandBox simulates a Randomized Controlled Experiment, which removes the confounding effect of the training data with limited known object labels. In addition, we propose a matching score without penalizing random proposals that are not matched with the known objects, which further encourages proposal explorations. Extensive evaluations of our proposed RandBox show that it significantly improves both the accuracy of the known objects and the recall of unknown ones. As future direction, we will seek additional inductive bias to remove the confounding effect and extend our approach to other detection tasks.", + "bbox": [ + 496, + 537, + 890, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 782, + 686, + 799 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The authors would like to thank all reviewers and ACs for their constructive suggestions. This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-RP-2021-022) and Alibaba-NTU Singapore Joint Research Institute.", + "bbox": [ + 496, + 809, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "6240", + "bbox": [ + 482, + 943, + 514, + 954 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware synapses: Learning what (not) to forget. In Proceedings of the European conference on computer vision (ECCV), pages 139-154, 2018. 2", + "[2] Takeshi Amemiya and Thomas E MaCurdy. 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Scientific reports, 9(1):614, 2019. 3" + ], + "bbox": [ + 78, + 90, + 468, + 204 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "6243", + "bbox": [ + 482, + 943, + 516, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Random Boxes Are Open-world Object Detectors/99919d69-2dc0-454c-a4b9-63b911115db6_model.json b/2023/Random Boxes Are Open-world Object Detectors/99919d69-2dc0-454c-a4b9-63b911115db6_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d187834d33f906c72bc85504b4177a50db45e064 --- /dev/null +++ b/2023/Random Boxes Are Open-world Object Detectors/99919d69-2dc0-454c-a4b9-63b911115db6_model.json @@ -0,0 +1,2433 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.048 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.236, + 0.131, + 0.738, + 0.154 + ], + "angle": 0, + "content": "Random Boxes Are Open-world Object Detectors" + }, + { + "type": "text", + "bbox": [ + 0.163, + 0.18, + 0.806, + 0.2 + ], + "angle": 0, + "content": "Yanghao Wang\\(^{1}\\), Zhongqi Yue\\(^{1,2}\\), Xian-Sheng Hua\\(^{3}\\), Hanwang Zhang\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.212, + 0.201, + 0.762, + 0.217 + ], + "angle": 0, + "content": "\\(^{1}\\)Nanyang Technological University, \\(^{2}\\)Damo Academy, Alibaba Group, \\(^{3}\\)Terminus Group" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.22, + 0.885, + 0.235 + ], + "angle": 0, + "content": "scuwyh2000@gmail.com, yuez0003@ntu.edu.sg, huaxiansheng@gmail.com, hanwangzhang@ntu.edu.sg" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.65 + ], + "angle": 0, + "content": "We show that classifiers trained with random region proposals achieve state-of-the-art Open-world Object Detection (OWOD): they can not only maintain the accuracy of the known objects (w/ training labels), but also considerably improve the recall of unknown ones (w/o training labels). Specifically, we propose RandBox, a Fast R-CNN based architecture trained on random proposals at each training iteration, surpassing existing Faster R-CNN and Transformer based OWOD. Its effectiveness stems from the following two benefits introduced by randomness. First, as the randomization is independent of the distribution of the limited known objects, the random proposals become the instrumental variable that prevents the training from being confounded by the known objects. Second, the unbiased training encourages more proposal explorations by using our proposed matching score that does not penalize the random proposals whose prediction scores do not match the known objects. On two benchmarks: Pascal-VOC/MS-COCO and LVIS, RandBox significantly outperforms the previous state-of-the-art in all metrics. We also detail the ablations on randomization and loss designs. Codes are available at https://github.com/scuwyh2000/RandBox." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.678, + 0.21, + 0.695 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.853 + ], + "angle": 0, + "content": "Different objects may share common visual features. For example, the detection of \"horse\" helps that of \"cow\" as they are both \"four-legged\" cattle. Therefore, it is possible to generalize the detector trained from a limited object class inventory to detect visually similar objects whose classes are out of the inventory. As shown in the right column of Figure 1, besides the conventional detection of a close-world object inventory, Open-wolrd Object Detection [23] (OWOD) can detect out-of-inventory objects and label them as \"unknown\"." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "To exploit the feature transfer from \"known\" to \"unknown\", the training loss of existing OWOD methods [23, 20, 55] has the following break-downs (Figure 1):" + }, + { + "type": "image_caption", + "bbox": [ + 0.501, + 0.317, + 0.518, + 0.329 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.268, + 0.769, + 0.365 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.779, + 0.268, + 0.892, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.503, + 0.419, + 0.518, + 0.431 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.372, + 0.769, + 0.467 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.779, + 0.371, + 0.892, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.503, + 0.511, + 0.518, + 0.523 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.528, + 0.475, + 0.769, + 0.559 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.779, + 0.471, + 0.892, + 0.563 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.574, + 0.894, + 0.621 + ], + "angle": 0, + "content": "Figure 1: The paradigm of (a) closed-world object detection, (b) existing open-world object detection, and (c) our RandBox that uses random proposals." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.895, + 0.822 + ], + "angle": 0, + "content": "Known-FG (foreground): like conventional closed-world detection (Figure 1a), we calculate the matching scores between the predicted region proposal labels and the ground-truth labels of known objects, where the label is a pair of class andbbox (bounding box). In particular, for two-stage detectors like Faster R-CNN [42], the \"proposal sampler\" and \"matching score\" are region proposal network andbbox IoU (intersection over union); for end-to-end detectors like DETR [9], they are query transformer decoder and bipartite matching score. For the matched proposals, the loss is class cross-entropy \\(\\mathcal{L}_{cls}\\) andbbox regression \\(\\mathcal{L}_{reg}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.894, + 0.903 + ], + "angle": 0, + "content": "BG (background): for conventional detection, all the mismatched proposals are considered background, whose loss is only \\(\\mathcal{L}_{cls}\\) with the label \"BG\"; for OWOD, we only use the mismatched proposals excluding the Unknown-FG proposals below." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.944, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6233" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.088, + 0.457, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.224, + 0.47, + 0.302 + ], + "angle": 0, + "content": "Figure 2: The sorted foreground confidence assigned by two baselines (ORE [23], OW-DETR [20]) and our Rand-Box to the generated proposals in training. Green, red and black correspond to \"known\", \"unknown\" and \"BG\", respectively, with examples showing on the top row." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.327, + 0.47, + 0.492 + ], + "angle": 0, + "content": "Unknown-FG: this is the key difference from conventional detection. Its design heuristic is that, for the mismatched proposals with class confidence larger than a threshold—probably unknown objects—the loss is only \\(\\mathcal{L}_{cls}\\) with a special label \"unknown\" w/o bbox regression. Note that this heuristic is based on the assumption of feature transfer [56, 10]—visually similar proposals have similar class confidences (see Section 3.1 for the review of the loss implementation in two-stage and end-to-end detection)—the more unknown objects the Unknown-FG collects, the better the OWOD." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.494, + 0.47, + 0.734 + ], + "angle": 0, + "content": "However, in practice, Unknown-FG usually has a low recall of unknown objects. As shown in Figure 2, in existing methods, most proposals of high confidence are matched as Known-FG; the mismatched proposals, mixed with both unknown objects and BG, all have low confidence, losing a gradual confidence decrease to differentiate Unknown-FG from BG (the red and black colors are inseparable). One may easily understand that this failure is predictable because, yet, we don't have the ground-truth labels for unknown objects, so the proposal sampler trained on known objects will be inevitably biased towards them. In fact, such bias is ubiquitously in any bootstrapping learning [43] with limited supervision, such as semi-supervised learning [34, 49] and reinforcement learning [24, 53]. Unfortunately, existing OWOD methods do not properly address the bias." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In this paper, we point out that the bias is caused by the confounding effect [37, 39] of the training data with limited known object labels that mislead the feature transfer. The effect can be understood in this way: if we only let the training data determine what region proposals to be used to extract the region features for detector training (Figure 1b), we cannot avoid the trivial loss minimization from only detecting the known objects. To this end, we propose to remove the confounding effect by introducing a random Instrumental Variable [5]—the proposed RandBox—that is independent of the training data. Intuitively, RandBox sim" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.242 + ], + "angle": 0, + "content": "ulates a Randomized Controlled Experiment (RCT) [8] to learn a causal detector from region features to object labels, by inviting an independent 3rd-party proposal sampler to explore more possible locations of unknown objects. As shown in Figure 2 RandBox, the recall of unknown objects is greatly improved by RandBox, due to the fact that the confidence score change of the proposals from known to unknown is much more separable. We will detail the theory behind RandBox in Section 4. To get a qualitative sense of open-world detection task, see Figures 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.892, + 0.439 + ], + "angle": 0, + "content": "RandBox is simple yet effective (Section 3.2). For each training image in every iteration, we sample 500 random boxes as proposals from a 4-dimensional Gaussian noise (center_x, center_y, height, width). For these random boxes, we crop their RoI (region of interest) features from a backbone feature map, and feed them into a detection head to obtain \\(\\mathcal{L}_{cls}\\) and \\(\\mathcal{L}_{reg}\\) as in (Figure 1c), where the proposed matching score that encourages exploration is detailed in Section 3.2. At inference, we remove the randomness and grid-sample 10,000 boxes per image by 10 scales, 10 shapes, and 100 spatial locations. We use NMS [35] (Non-maximum Suppression) to prune the 10,000 boxes for final detection. Overall, our contributions include:" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.444, + 0.892, + 0.52 + ], + "angle": 0, + "content": "- Our proposed RandBox is a Fast R-CNN based architecture for OWOD, which leverages random proposals to remove the confounding effect from the known objects, and uses an improved matching score to encourage proposal exploration." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.523, + 0.892, + 0.584 + ], + "angle": 0, + "content": "- By removing the confounding effect, we learn an unbiased detector that improves both known and unknown detection accuracy. In particular, we achieve new state-of-the-art results on Pascal-VOC/MS-COCO [29]." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.587, + 0.892, + 0.633 + ], + "angle": 0, + "content": "- We show that our RandBox detector trained on PascalVOC/MS-COCO remains robust when transferring to long-tailed datasets such as LVIS [19]." + }, + { + "type": "list", + "bbox": [ + 0.515, + 0.444, + 0.892, + 0.633 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.648, + 0.642, + 0.664 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Open-World Object Detection (OWOD). Object detection systems are significantly advanced recently [41, 57, 42, 18, 48]. Yet they are based on the conventional close-world paradigm, which assumes that all objects of interests are annotated. In practice, an object detector deployed in real life is constantly challenged by the vast open and dynamic visual world [33, 23, 25]. To bridge the gap, open-set detection [33, 32, 14] aims to reject out-of-inventory objects as “unknown”, and other works focus on incrementally learning [40, 1, 31] a detector to recognize new object classes without forgetting old ones. Inspired by the open-world setting proposed in image classification [6, 7], recent works [23, 20, 55, 58] unify open-set detection and incremental learning as OWOD, which are based on two stage detectors like Faster R-CNN [42], or end-to-end ones like" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.944, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6234" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.885, + 0.271 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.281, + 0.893, + 0.327 + ], + "angle": 0, + "content": "Figure 3: Example results. We show the ground-truth (GT) locations of unknown objects, those predicted by OWDETR [20], and those predicted by our RandBox. RandBox not only detects the annotated unknown objects (first 2 images), but even discovers valid unknown ones without annotations (e.g., camp in image 3, bracelet in image 5, banner in image 6)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.47, + 0.414 + ], + "angle": 0, + "content": "DETR [57]. We systematically analyze the failure of these existing works—low recall of unknown objects—which is caused by the confounding effect [37, 36], and remove it using random proposals to learn a causal detector." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.416, + 0.474, + 0.658 + ], + "angle": 0, + "content": "Debiasing by Randomization. Randomization is an effective tool to debias across many tasks and domains. For example, using randomization as an instrument variable [12, 4, 5] is a classic tool to identify causal effect in social studies [15]. In reinforcement learning [53], randomization is used to encourage exploration [54, 27], such that the agent is not biased to exploiting spurious shortcuts. Several works [3, 50] in adversarial training [17] leverages randomization to build a robust model not biased to feature that can be manipulated in adversarial attack, e.g., by image perturbation [59]. In fact, data augmentation that is prevailing in vision [45, 21, 47] and language [46, 44] also leverages randomness to remove augmentation-related context bias in training (e.g., using green grass to classify cow). In our work, we present a novel detection framework that leverages random proposals to learn causal effect in OWOD." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.677, + 0.17, + 0.693 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In OWOD, the task is to detect a gradually expanding set of known inventory classes \\( K \\), while simultaneously rejecting the out-of-inventory classes set \\( U \\) as \"unknown\". The training dataset contains images where known objects are labelled. Specifically, for a training image containing \\( n \\) known objects, it is labelled with a set \\( \\{(b_i, y_i)\\}_{i=1}^n \\), where \\( b_i \\) specifies the bounding box (bbox) of the \\( i \\)-th object (i.e., center_x, center_y, height, width), and \\( y_i \\in K \\) is its class label. We drop the subscript \\( i \\) for simplicity when the context is clear. The goal in OWOD is to train a detector, whose input is an image, and output is a set of \\( m \\) predictions \\( P = \\{(\\hat{b}_i, \\hat{y}_i)\\}_{i=1}^m \\), where \\( \\hat{b}_i \\) is the \\( i \\)-th bounding box prediction (predictedbbox), and \\( \\hat{y}_i \\in \\mathbb{R}^{|K| + 2} \\) denotes the clas-" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.353, + 0.885, + 0.371 + ], + "angle": 0, + "content": "sification logit for each class in \\(K\\cup \\{\\text{\"unknown\",\"BG\"}\\}\\)" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.376, + 0.851, + 0.393 + ], + "angle": 0, + "content": "3.1. Preliminaries: Existing OWOD Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.4, + 0.893, + 0.491 + ], + "angle": 0, + "content": "Existing methods adopt either the two-stage Faster R-CNN [42] or the end-to-end DETR [9] as the detector. In training, the predictions \\( P \\) generated by the detector are partitioned into three subsets: Known-FG, Unknown-FG and BG, which are used to calculate the classification loss and bbox regression loss. We detail each part below:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.491, + 0.893, + 0.672 + ], + "angle": 0, + "content": "Detector. Given an image, a detector generates \\( m \\) proposals, extracts ROI features \\( x_{i} \\) for each proposal, and finally computes bounding box \\( \\hat{b}_{i} \\) and logits \\( \\hat{y}_{i} \\) using a classifier to form \\( P \\). The two detector frameworks mainly differ in the first step: 1) Faster R-CNN leverages a region proposal network (RPN) pre-trained on the labelled data. It outputs the top- \\( m \\) proposals with the largest objectness (i.e., probability of containing a known object). 2) DETR is an end-to-end detector. It first transforms an image into tokens using a combination of CNN backbone and transformer encoder. Then a transformer decoder uses the image tokens to generate the proposals. More details are in Appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.895, + 0.825 + ], + "angle": 0, + "content": "Known-FG is selected from all predictions \\( P \\) by matching with the labels \\( \\{(b_i, y_i)\\}_{i=1}^n \\) based on a Known-FG score. To compute the score for a prediction \\( (\\hat{b}, \\hat{y}) \\in P \\) with a ground-truth \\( (b, y) \\), Faster R-CNN uses the IoU between \\( \\hat{b} \\) and \\( b \\), and DETR uses the bipartite matching score, which additionally considers if \\( \\hat{y} \\) has a large value on the class \\( y \\). As the process is the same as that in closed-set detection, we leave other details in Appendix. After matching, we denote the Known-FG subset as \\( P^K \\). For \\( (\\hat{b}, \\hat{y}) \\in P^K \\), we denote its matched ground-truth as \\( (b^*, y^*) \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Unknown-FG & BG are selected from the unmatched predictions \\( P \\setminus P^K \\). Specifically, current methods compute an Unknown-FG score for each prediction, and select 5 predictions with the largest score as the Unknown-FG. For the score, methods based on Faster R-CNN [42, 23] use object-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.944, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6235" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.51, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.192, + 0.25, + 0.208, + 0.262 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.544, + 0.089, + 0.891, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.711, + 0.251, + 0.728, + 0.264 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.276, + 0.893, + 0.352 + ], + "angle": 0, + "content": "Figure 4: (a) RandBox Pipeline. Our proposals are randomly generated. We obtain the Known-FG subset using a dynamic-\\(k\\) matcher, and the Unknown-FG subset based on our proposed matching score. Our training losses follow existing methods. (b) Proposed Matching Score is the sum of likelihood of belonging to each foreground classes (including \"unknown\"). The proposals of known (green) and unknown (red) objects both have large matching score, i.e., high likelihood on the ground-truth class (solid arrows) or by feature transfer (dashed arrow), while BG proposals (black) have low score." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.378, + 0.469, + 0.438 + ], + "angle": 0, + "content": "ness, and those based on DETR [20] use the average value of the ROI feature. We denote the Unknown-FG subset as \\( P^U \\). Finally, the rest predictions become the BG subset \\( P^B \\). Training Loss." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.439, + 0.469, + 0.482 + ], + "angle": 0, + "content": "We calculate the loss on each of the three subsets. The loss on Known-FG \\(\\mathcal{L}^K\\) has the same form with closed-set detection:" + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.49, + 0.469, + 0.535 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} ^ {K} = \\sum_ {i = 1} ^ {| P ^ {K} |} \\mathcal {L} _ {c l s} \\left(\\hat {y} _ {i}, y _ {i} ^ {*}\\right) + \\lambda \\mathcal {L} _ {r e g} \\left(\\hat {b} _ {i}, b _ {i} ^ {*}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.542, + 0.47, + 0.633 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{cls}\\) is the cross-entropy loss or focal loss [28] to handle class-imbalance, \\(\\lambda\\) is a balancing weight, and \\(\\mathcal{L}_{reg}\\) is the smooth L1 regression loss [18] to rectify the predicted bbox. Details of \\(\\mathcal{L}_{cls}\\) and \\(\\mathcal{L}_{reg}\\) are in Appendix. As Unknown-FG and BG have no annotated bbox, we only calculate \\(\\mathcal{L}_{cls}\\) on them:" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.653, + 0.469, + 0.71 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} ^ {U B} = \\sum_ {i = 1} ^ {| P ^ {U} |} \\mathcal {L} _ {c l s} \\left(\\hat {y} _ {i}, \\text {\" u n k n o w n\"}\\right) + \\sum_ {i = 1} ^ {| P ^ {B} |} \\mathcal {L} _ {c l s} \\left(\\hat {y} _ {i}, \\text {\" B G\"}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.711, + 0.434, + 0.726 + ], + "angle": 0, + "content": "Overall, the detector parameters \\(\\theta\\) are optimized with:" + }, + { + "type": "equation", + "bbox": [ + 0.21, + 0.733, + 0.469, + 0.757 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta} \\mathcal {L} ^ {K} + \\beta \\mathcal {L} ^ {U B}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.765, + 0.399, + 0.779 + ], + "angle": 0, + "content": "where \\(\\beta\\) is a weight with ablation in Section 5.2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.901 + ], + "angle": 0, + "content": "OWOD Pipeline. The detector is first randomly initialized. Then it is trained with the labelled data on \\( K \\), and evaluated with data on both \\( K \\) and \\( U \\) (Task 1). Next, additional labelled data on a subset of classes \\( K' \\subset U \\) is provided, i.e., the known classes set expands as \\( K \\gets K \\cup K' \\), and the unknown one becomes \\( U \\gets U \\setminus K' \\). The detector trained on Task 1 is fine-tuned and evaluated with the updated \\( K \\) and \\( U \\) (Task 2). This continues for the following tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.377, + 0.685, + 0.394 + ], + "angle": 0, + "content": "3.2. Proposed RandBox" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.406, + 0.892, + 0.572 + ], + "angle": 0, + "content": "Existing methods suffer from the low recall of the unknown objects in Unknown-FG. To tackle this, our proposed RandBox has two improvements: 1) We propose to generate region proposals randomly, instead of using a proposal sampler trained on the known objects, which explores more possible unknown object locations. 2) We propose a matching score without penalizing proposals that are not matched with the known objects, which explores more possible unknown object proposals. We detail the two improvements below, and explain why our RandBox solves the existing problems from a causal view in Section 4." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.819 + ], + "angle": 0, + "content": "Detector with Random Proposals. In training, we randomly generate 500 bboxes as region proposals on each image (Figure 4a). For each bbox, we sample 4 random real numbers in [0, 1], where each number is first drawn from the standard Gaussian distribution, truncated to \\([-2, 2]\\) and then scaled linearly to [0, 1]. The 4 numbers correspond to the horizontal and vertical coordinate of the bbox center, as well as the width and height of the bbox, respectively (proportional to image size). The width and height of out-of-boundary bboxes are adjusted to stay in the image. In testing, to remove the prediction randomness, we use 10,000 pre-defined bboxes as proposals on each image, which cover 10 scales, 10 aspect ratios and 100 spatial locations (details in Appendix). We use non-maximum suppression to prune the bboxes as per standard practice [35]. We highlight the following points:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.824, + 0.89, + 0.854 + ], + "angle": 0, + "content": "- Our region proposals are randomly sampled for every image in each iteration throughout the training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.891, + 0.901 + ], + "angle": 0, + "content": "- While we use random sampling, the number of our random proposals is in fact comparable with that used in the existing methods, e.g., ORE [23] uses 1024 proposals." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.824, + 0.891, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.944, + 0.516, + 0.955 + ], + "angle": 0, + "content": "6236" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.167 + ], + "angle": 0, + "content": "Known-FG. We adopted the dynamic-\\(k\\) matcher [11] as shown in Figure 4a. Specifically, each ground-truth bbox \\(b\\) is matched with \\(k\\) proposals based on the bipartite matching score, where \\(k\\) is dynamically selected as the sum of the IoU between each proposal and \\(b\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.468, + 0.273 + ], + "angle": 0, + "content": "Unknown-FG. We propose a novel matching score to form Unknown-FG. Specifically, we select the top \\(N\\) proposals with the largest matching score (ablation of \\(N\\) in Section 5.2). Among the selected proposals, those already in Known-FG are removed to form our Unknown-FG subset. We use the following equation to compute our matching score for a proposal with the classification logits \\(\\hat{y}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.284, + 0.469, + 0.327 + ], + "angle": 0, + "content": "\\[\ns (\\hat {y}) = \\sum_ {i = 1} ^ {| K | + 1} \\frac {1}{1 + \\exp (- \\hat {y} _ {i})}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.468, + 0.609 + ], + "angle": 0, + "content": "where we compute and sum the sigmoid of the \\(|K|\\) known classes and “+1” unknown class, and \\(\\hat{y}_i\\) denotes the logit for the class \\(i\\). Note that we implement \\(\\mathcal{L}_{cls}\\) with the BCE loss [28]. Hence our score essentially computes how likely \\(\\hat{y}\\) corresponds to the foreground. Specifically, the top-\\(N\\) (largest matching score) proposals that are not in KnownFG are pseudo-labeled as “unknown” to train the UnknownFG logit (Eq. 2 first loss). This design is based on the assumption of feature transfer [38, 52]—similarity between Unknown-FG and Known-FG is larger than that between BG and Known-FG. As shown in Figure 4b, an unknown object proposal can have non-trivial likelihood of belonging to a known class due to shared feature (dashed arrow), while BG proposal almost shares no feature with known. Hence future unknown object proposals can have large likelihood of belonging to “unknown” (solid red arrow), increasing the unknown recall. We have the following comparisons with existing methods:" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.611, + 0.468, + 0.685 + ], + "angle": 0, + "content": "- Methods based on Faster R-CNN use the objectness predicted by RPN as the matching score to select UnknownFG. However, RPN is trained to produce large scores only on the proposals matched with the known objects, thus penalizing those unmatched ones." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.687, + 0.468, + 0.761 + ], + "angle": 0, + "content": "- Without RPN, methods based on DETR use the mean activation of the ROI feature instead. However, this heuristic is extremely unreliable (Figure 3b), and unknown object proposals are often mistakenly placed in the BG subset and penalized as \"background\"." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.764, + 0.468, + 0.838 + ], + "angle": 0, + "content": "- In contrast, our matching score fairly evaluates each proposal by checking both known classes (first \\(|K|\\) logits), as well as \"unknown\" (\\(|K| + 1\\)-th logit). Hence unknown object proposals can be reliably selected in the Unknown-FG subset with high likelihood of belonging to \"unknown\"." + }, + { + "type": "list", + "bbox": [ + 0.075, + 0.611, + 0.468, + 0.838 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Other Details. Our training objective is the same as Eq. (3). We used ResNet-50 [22] as backbone. Our RandBox is Fast R-CNN [18] based architecture and detection head is borrowed from Sparse R-CNN [48]." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.677, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.718, + 0.09, + 0.892, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.168, + 0.89, + 0.198 + ], + "angle": 0, + "content": "Figure 5: Causal graph of (a) existing OWOD methods, and (b) our RandBox." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.225, + 0.586, + 0.243 + ], + "angle": 0, + "content": "4. Theory" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.25, + 0.892, + 0.431 + ], + "angle": 0, + "content": "We use a Structural Causal Model (SCM) to analyze the causalities between the key components in OWOD: training data \\(D\\), region proposal \\(R\\), ROI feature \\(X\\), and label \\(Y\\) on \\(K \\cup \\{\\text{\"unknown\", \"BG\"}\\}\\). Note that \\(D\\) only contains labelled data of the known classes \\(K\\). The SCM is illustrated with a causal graph in Figure 5, where each directed link denotes a causal relation between the two connected nodes. \\(R \\rightarrow X \\rightarrow Y\\) represents the desired causal effect from region proposal \\(R\\) to label \\(Y\\), as label \\(Y\\) describes what a region \\(R\\) (or its ROI feature \\(X\\)) contains. A detector is unbiased if it identifies \\(R \\rightarrow X \\rightarrow Y\\), i.e., given any region, the detector can fairly evaluate what it contains." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.432, + 0.892, + 0.477 + ], + "angle": 0, + "content": "\\(R \\to X \\gets D\\). The ROI feature \\(X\\) is jointly determined by what the region contains (\\(R \\to X\\)), as well as the feature representation learned on the training data (\\(D \\to X\\))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.89, + 0.522 + ], + "angle": 0, + "content": "\\(D \\to Y\\) is because the detector leverages the training knowledge obtained from \\(D\\) to predict \\(Y\\), e.g., identifying the BG subset with prediction \"BG\" (Section 3.1)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.89, + 0.583 + ], + "angle": 0, + "content": "\\(D \\to R\\) exists in current OWOD methods as shown in Figure 5a. This is because the region proposal network in Faster R-CNN and the transformer decoder in DETR are both trained on \\(D\\) to generate proposal \\(R\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.749 + ], + "angle": 0, + "content": "Confounding Effect. In Figure 5a, \\( R \\gets D \\to Y \\) is known as a backdoor path, which leads to the undesired confounding effect [37]. Specifically, as the proposal sampler is supervised by the labelled data of known objects \\( D \\), the generated proposals \\( R \\) are inevitably biased to them \\( (D \\to R) \\), i.e., \\( R \\) only faithfully reflects the known object locations. Consequently, the training is dominated by the loss \\( \\mathcal{L}^K \\) on Known-FG, and the detector recklessly exploits any discriminative feature in \\( D \\) towards the known objects \\( (D \\to Y) \\), which may not transfer to the unknown ones. This causes the low recall of Unknown-FG in Figure 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Removing Confounding Effect. In our RandBox, \\( R \\) is randomly generated with no influence from \\( D \\), i.e., \\( D \\nRightarrow R \\) in Figure 5b. This makes \\( R \\) an Instrument Variable [5], which removes the confounding effect by simulating a Randomized Controlled Experiment [8]. We provide a threefold intuitive explanation: 1) The backdoor path is cut, i.e., \\( R \\nLeftarrow D \\to Y \\); 2) The path \\( R \\to X \\gets D \\to Y \\) is blocked due to the collider [37] \\( X \\) (i.e., with two incoming arrows). 3) This makes \\( R \\to X \\to Y \\) the only unblocked path from \\( R \\) to \\( Y \\). Hence when learning to predict \\( Y \\) from \\( R \\), our de" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.944, + 0.515, + 0.956 + ], + "angle": 0, + "content": "6237" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.097, + 0.089, + 0.885, + 0.221 + ], + "angle": 0, + "content": "
MethodTask 1Task 2Task 3Task 4
K-mAPU-RWIA-OSEK-mAPU-RWIA-OSEK-mAPU-RWIA-OSEK-mAP
Faster-RCNN [42]56.4-0.069913,39615.2-0.037112,2916.7-0.02139,1744.2
Faster-RCNN+Finetuning56.4-0.069913,39638.0-0.037512,49730.0-0.02799,62225.6
DDETR [57]60.3-0.060833,27017.9-0.036818,1158.5-0.01979,3926.0
DDETR+Finetuning60.3-0.060833,27044.8-0.033717,83433.3-0.019510,09529.4
ORE [23]56.04.90.062110,45939.42.90.028210,44529.73.90.01566,80325.3
OST [55]56.2-0.04174,88939.9-0.02132,54629.6-0.01462,12025.9
OW-DETR [20]59.37.50.057110,24042.96.20.02788,44130.85.70.01566,80327.8
RandBox61.810.60.02404,49845.36.30.00781,88039.47.80.00541,45235.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.23, + 0.893, + 0.262 + ], + "angle": 0, + "content": "Table 1: OWOD Evaluation results and comparison with existing methods. We can also achieve SOTA on previously/currently known scores, more details are in Appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.277, + 0.471, + 0.308 + ], + "angle": 0, + "content": "tector captures the causal effect free from the confounding one. The formal definition and proof are in Appendix." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.325, + 0.21, + 0.344 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.352, + 0.47, + 0.383 + ], + "angle": 0, + "content": "We introduce important experiment setups below, and leave other details in Appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.47, + 0.61 + ], + "angle": 0, + "content": "Datasets. We extensively evaluated RandBox on three tasks: OWOD, transfer learning and open-set detection. For OWOD, we used Pascal VOC [16] and MS-COCO [29] following the standard setups [23, 20]. In Task 1, the known set \\( K \\) contains the 20 classes in Pascal VOC, and the unknown set \\( U \\) contains the 60 classes unique to MS-COCO. For each of the Task 2-4, 20 classes in \\( U \\) are added to \\( K \\), i.e., Task 4 corresponds to closed-set detection with 80 classes. The training and testing images are selected from the respective split of the two datasets. For transfer learning, we evaluated models trained on Task 1 on the 4,809 validation images of LVIS v1.0 [19], which are from over 1000 classes that exhibits long-tailed distribution. For open-set detection, we followed [33] to train models on Pascal VOC train split, and evaluate them on WR1 [33]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.47, + 0.763 + ], + "angle": 0, + "content": "Evaluation Metrics: On known classes, we used the standard Known-class mAP (K-mAP). On unknown classes, we used three metrics: 1) Unknown class Recall (U-R) is the recall of unknown classes at IoU threshold of 0.5. 2) Wilderness Impact (WI) [14] is computed by (closed-set precision)/(open-set precision) - 1. A small WI is desired in OWOD, i.e., precision does not drop when unknown objects are introduced in evaluation. 3) Absolute Open-Set Error (A-OSE) [33] is the predictions that are misclassified as one of the known classes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Implementation Details: In training, we used the ResNet-50 [22] pre-trained on ImageNet [13] as our backbone. We trained RandBox using AdamW [30] optimizer with learning rate as \\( 2.5e^{-5} \\) and weight decay as \\( 1e^{-4} \\). We used the same methodology as prior work [23, 2, 51, 26] to mitigate forgetting, i.e., by storing a balanced set of exemplars for model fine-tuning after each incremental step. In inference, after getting the predictions on the 10,000 pre-defined bboxes, we used Non-Maximum Suppression (NMS) [35]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.277, + 0.893, + 0.322 + ], + "angle": 0, + "content": "to prune redundant bboxes. After pruning, the final predictions are the bboxes whose probability of belonging to a class in \\( K \\cup \\{ \"unknown\" \\} \\) are at least 0.1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.332, + 0.64, + 0.348 + ], + "angle": 0, + "content": "5.1. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.356, + 0.893, + 0.386 + ], + "angle": 0, + "content": "Table 1 presents the results of OWOD evaluation. We have the following observations:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.893, + 0.508 + ], + "angle": 0, + "content": "1) For the conventional framework Faster-RCNN [42] and Deformable-DETR (DDETR) [57], their K-mAP drops significantly in Task 2-4, showing that they suffer from catastrophic forgetting when new classes are incrementally added. By using data replay [23] (+Finetuning), their K-mAP results improve significantly (e.g., 6.0 to 29.4 on Task 4 for DDETR). Note that they are not capable to detect unknown objects (e.g., U-R is not applicable)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.893, + 0.599 + ], + "angle": 0, + "content": "2) By comparing existing OWOD methods with the conventional frameworks, we notice that all of them have reduced K-mAP (e.g., the DDETR-based OW-DETR reduced 1.6 mAP on Task 4 compared with DDETR+Finetuning). This means that their capabilities of unknown detection are at the cost of known detection accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.893, + 0.704 + ], + "angle": 0, + "content": "3) By comparing RandBox with existing OWOD methods on U-R and A-OSE, we observe significant improvements, e.g., \\(3.1\\%\\) U-R improvement and 391 A-OSE reduction on Task 1. This suggests that our training scheme with random boxes and the proposed matching score encourage proposal explorations, which detects and learn on more unknown objects to improve their evaluation performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.902 + ], + "angle": 0, + "content": "4) In particular, by comparing K-mAP and WI of Rand-Box and OWOD methods, we see that RandBox also achieves the state-of-the-art (SOTA) performance, e.g., absolute gains ranging from \\(2.4\\%\\) to \\(8.6\\%\\) in terms of K-mAP and relatively reduces ranging from \\(42\\%\\) to \\(64\\%\\) in terms of WI. Remarkably, our RandBox even outperforms the conventional detection frameworks, e.g., Faster-RCNN and DDETR. This means that instead of sacrificing \"known\" to detect \"unknown\", RandBox learns \"unknown\" to benefit \"known\". This strongly validates that our approach removes confounding bias by simulating Randomized Controlled Experiment with random boxes, where our detector captures the causal effect from any region proposal (known," + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.387, + 0.895, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.944, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6238" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.088, + 0.09, + 0.487, + 0.175 + ], + "angle": 0, + "content": "
ProposalsK-mAPU-RWIA-OSE
Selective search57.39.10.0295,433
RPN59.08.60.0315,128
Query based59.79.10.0434,679
Random (Ours)61.810.60.0244,498
" + }, + { + "type": "table_caption", + "bbox": [ + 0.127, + 0.184, + 0.404, + 0.197 + ], + "angle": 0, + "content": "(a) Ablation on proposal generation method." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.2, + 0.488, + 0.278 + ], + "angle": 0, + "content": "
MatchRandK-mAPU-RWIA-OSE
51.8-0.0427,652
Ours59.79.10.0434,679
Mean activation✓60.37.10.0245,929
Ours✓61.810.60.0244,498
" + }, + { + "type": "table_caption", + "bbox": [ + 0.186, + 0.286, + 0.364, + 0.3 + ], + "angle": 0, + "content": "(c) Ablation on components." + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.09, + 0.888, + 0.175 + ], + "angle": 0, + "content": "
distributionnumK-mAPU-RWIA-OSE
Uniform10060.28.70.0274,877
Gaussian10060.79.30.0264,732
Uniform50062.010.10.0264,588
Gaussian50061.810.60.0244,498
Uniform1,00061.710.40.0284,975
Gaussian1,00061.810.60.0304,763
" + }, + { + "type": "table_caption", + "bbox": [ + 0.573, + 0.185, + 0.796, + 0.198 + ], + "angle": 0, + "content": "(b) Strategy for Random Proposals." + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.2, + 0.892, + 0.278 + ], + "angle": 0, + "content": "
ratioscalelocationK-mAPU-RWIA-OSE
552060.28.20.0413,001
10102061.69.60.0323,715
10104061.310.20.0294,098
101010061.810.60.0244,498
" + }, + { + "type": "table_caption", + "bbox": [ + 0.59, + 0.287, + 0.798, + 0.3 + ], + "angle": 0, + "content": "(d) Ablation on inference bboxes." + }, + { + "type": "table_caption", + "bbox": [ + 0.086, + 0.313, + 0.88, + 0.329 + ], + "angle": 0, + "content": "Table 2: Ablation results. Models are trained on Task 1. We adopted the best performing setting as our default (in gray)." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.353, + 0.457, + 0.498 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.51, + 0.461, + 0.525 + ], + "angle": 0, + "content": "Figure 6: Ablation on \\(N\\) by training RandBox on Task 1." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.551, + 0.468, + 0.581 + ], + "angle": 0, + "content": "unknown or BG) to its label (Section 4). Hence we observe unconditional improvements overall." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.591, + 0.283, + 0.607 + ], + "angle": 0, + "content": "5.2. Ablation Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Choice of \\(N\\). Recall that in training, we identify the top \\(N\\) proposals with the largest matching score to form Unknown-FG (by removing those already in Known-FG). Hence \\(N\\) is directly correlated with the size of Unknown-FG. The ablation results on \\(N\\) are given in Figure 6. Initially, increasing \\(N\\) benefits both known detection (K-mAP) and unknown recall (U-R). This is because 1) With more unknown proposals for optimizing Eq. (3), the detector improves in recognizing \"unknown\" (increased U-R). 2) To differentiate \"unknown\" from \"known\", the detector also avoids spurious correlations of known classes in training (i.e., captures causal effect), which may not generalize to known objects in testing (increased K-mAP). However, further increasing \\(N\\) leads to the drop in K-mAP. This is because increasing the size of Unknown-FG by large \\(N\\) essentially increases the weight of the classification loss on \"unknown\" in Eq. (2). Hence the detector learning on known classes is adversely impacted when the weight is too large. We used \\(N = 10\\) in all our experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.356, + 0.892, + 0.476 + ], + "angle": 0, + "content": "Proposal generation methods Its ablation is in Table 2a. We use our matching score Eq. 4 and fix the same proposal number (500) to ablate the proposal generation methods. We compared our Random Proposals with Selective search, RPN and Query based proposals. We can find that our Random proposals surpass all other methods which means the randomness can make more explorations on more image regions, without biased towards the training data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.893, + 0.643 + ], + "angle": 0, + "content": "Strategy for Random Proposals. When generating random proposals in training, we experimented with different distribution (for drawing random numbers) and the number of random proposals (num), and the results are in Table 2b. Using the same number of proposals, the results on the two distributions are both competitive. Regarding the number of proposals, we observe that increasing it beyond 500 does not bring any improvement. This shows that the image locations are already sufficiently explored using 500 random bboxes. Overall, we used 500 random proposals drawn from Gaussian distribution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.893, + 0.869 + ], + "angle": 0, + "content": "Components. The main components in RandBox are the use of random proposals (Rand), and the matching process for Known-FG and Unknown-FG (Match). Their ablations are given in Table 2c. The first line corresponds to the baseline Sparse R-CNN [48]. Comparing the second line, by combining our matching process with NMS, our matching score can improve all metrics and already achieved SOTA (e.g., by comparing with other OWOD methods in Table 1 Task 1). In the third and forth lines, we introduce the Random proposals and compare two kinds of matching score, i.e., Mean activation and our matching score. We can find that our matching score improve all metrics significantly (e.g., \\(1.5\\%\\) on K-mAP and \\(3.5\\%\\) on U-R) compared with the Mean activation. This strongly validates the effectiveness of each component in RandBox." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Training schedule. We show the change of U-R and K-mAP over the training and compare RandBox with ORE" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.944, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6239" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.262, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.281, + 0.09, + 0.46, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.224, + 0.468, + 0.24 + ], + "angle": 0, + "content": "Figure 7: Training schedule compared with existing works." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.253, + 0.462, + 0.311 + ], + "angle": 0, + "content": "
MethodK-mAPU-RWIA-OSE
ORE [23]23.23.50.174323,225
OW-DETR [20]25.16.30.154819,672
RandBox27.78.40.07357,842
" + }, + { + "type": "table_caption", + "bbox": [ + 0.092, + 0.322, + 0.454, + 0.337 + ], + "angle": 0, + "content": "Table 3: Transfer evaluation results on LVIS v1.0 [19]." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.351, + 0.46, + 0.436 + ], + "angle": 0, + "content": "
Evaluated on →Pascal-VOCOpen-Set (WR1)
Faster R-CNN [42]81.877.1
RetinaNet [28]79.273.8
Dropout Sampling [33]78.173.8
ORE [23]81.371.7
OW-DETR [20]82.178.6
RandBox84.482.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.448, + 0.47, + 0.478 + ], + "angle": 0, + "content": "Table 4: Results on Pascal-VOC [16] (closed-set) and WR1 [33] (open-set)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.468, + 0.534 + ], + "angle": 0, + "content": "and OW-DETR in Figure 7. Our RandBox converges quickly and trains stably, outperforming the two methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.468, + 0.655 + ], + "angle": 0, + "content": "Inference Bboxes. We ablation on the number of predefined bbox ratios, scales and locations in Table 2d. Increasing the bbox number generally improves the performance due to the increased recall on both known and unknown classes. However, it also increases the number of mis-classified unknown predictions, leading to a larger A-OSE. As the performance tends to saturate with 10,000 bboxes (last row), we use this configuration for efficiency." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.664, + 0.385, + 0.68 + ], + "angle": 0, + "content": "5.3. Transfer and Open-Set Evaluations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.468, + 0.762 + ], + "angle": 0, + "content": "Transfer to LVIS v1.0. We evaluated the models trained on Task 1 on LVIS 1.0. [19] We observe significant improvements on all metrics compared to ORE and OW-DETR in Table 3 This validates the robustness of RandBox over the existing works under distribution shift." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.763, + 0.468, + 0.839 + ], + "angle": 0, + "content": "Open-Set Object Detection. Detectors in OWOD can naturally tackle open-set detection. We followed [33] and evaluated models trained on Task 1 on Pascal-VOC test split (closed-set) and WR1 (open-set). We significantly improve existing SOTAs on both evaluations (Table 4)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.347, + 0.864 + ], + "angle": 0, + "content": "5.4. Additional Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "As shown in Figure 8 first column, OW-DETR misses the known objects \"mouse\" and \"chair\" due to confusing" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.892, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.294, + 0.892, + 0.354 + ], + "angle": 0, + "content": "Figure 8: Additional qualitative results. We show the ground-truth labels of known objects in the first row, and compare the predictions from OW-DETR and our RandBox. Green: known. Red: unknown." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.892, + 0.491 + ], + "angle": 0, + "content": "background and partial view, respectively. Our RandBox not only detects all known objects, but also identify many valid unknown objects. In the second column, RandBox predicts the overlapping spoons as \"unknown\", which is indeed plausible without other prior knowledge. The third column shows that our RandBox detects the unknown object \"picture frame\" both in the real world and in the mirror." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.51, + 0.618, + 0.526 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.892, + 0.765 + ], + "angle": 0, + "content": "We presented a novel Open-World Object Detection (OWOD) method called RandBox, trained on random proposals and surpassing existing Faster R-CNN and Transformer based OWOD. We show from a causality theoretical perspective that RandBox simulates a Randomized Controlled Experiment, which removes the confounding effect of the training data with limited known object labels. In addition, we propose a matching score without penalizing random proposals that are not matched with the known objects, which further encourages proposal explorations. Extensive evaluations of our proposed RandBox show that it significantly improves both the accuracy of the known objects and the recall of unknown ones. As future direction, we will seek additional inductive bias to remove the confounding effect and extend our approach to other detection tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.783, + 0.687, + 0.8 + ], + "angle": 0, + "content": "7. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.9 + ], + "angle": 0, + "content": "The authors would like to thank all reviewers and ACs for their constructive suggestions. This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-RP-2021-022) and Alibaba-NTU Singapore Joint Research Institute." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.944, + 0.516, + 0.955 + ], + "angle": 0, + "content": "6240" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware synapses: Learning what (not) to forget. In Proceedings of the European conference on computer vision (ECCV), pages 139-154, 2018. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.187, + 0.472, + 0.243 + ], + "angle": 0, + "content": "[2] Takeshi Amemiya and Thomas E MaCurdy. 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Specifically, we propose RandBox, a Fast R-CNN based architecture trained on random proposals at each training iteration, surpassing existing Faster R-CNN and Transformer based OWOD. Its effectiveness stems from the following two benefits introduced by randomness. First, as the randomization is independent of the distribution of the limited known objects, the random proposals become the instrumental variable that prevents the training from being confounded by the known objects. Second, the unbiased training encourages more proposal explorations by using our proposed matching score that does not penalize the random proposals whose prediction scores do not match the known objects. On two benchmarks: Pascal-VOC/MS-COCO and LVIS, RandBox significantly outperforms the previous state-of-the-art in all metrics. We also detail the ablations on randomization and loss designs. Codes are available at https://github.com/scuwyh2000/RandBox. + +# 1. Introduction + +Different objects may share common visual features. For example, the detection of "horse" helps that of "cow" as they are both "four-legged" cattle. Therefore, it is possible to generalize the detector trained from a limited object class inventory to detect visually similar objects whose classes are out of the inventory. As shown in the right column of Figure 1, besides the conventional detection of a close-world object inventory, Open-wolrd Object Detection [23] (OWOD) can detect out-of-inventory objects and label them as "unknown". + +To exploit the feature transfer from "known" to "unknown", the training loss of existing OWOD methods [23, 20, 55] has the following break-downs (Figure 1): + +![](images/9b286709c785ae8db1ab321a9a5791ac69766ae665828a495d21638c3204be10.jpg) +(a) + +![](images/a3e8a21443a7cc0ee6107e0eedf59eb5a1935c0c8df8d8b3031f9144948d00a8.jpg) + +![](images/f84ace50b37abd0b0afe38f29cb1c94014282d117bfd5f4697a13aabcd57d577.jpg) +(b) + +![](images/92c099588aa27cb906703cda762af5e0b59dba09f982864820a420b4c11934ab.jpg) + +![](images/1eff90579158a71545ace3b223253ad83331db8db346fb3cd957737a63fa34cc.jpg) +(c) + +![](images/dda8f9351725741a80fed17db0753650cc29e9973d803e3c0b4da74653ea7d2d.jpg) +Figure 1: The paradigm of (a) closed-world object detection, (b) existing open-world object detection, and (c) our RandBox that uses random proposals. + +Known-FG (foreground): like conventional closed-world detection (Figure 1a), we calculate the matching scores between the predicted region proposal labels and the ground-truth labels of known objects, where the label is a pair of class andbbox (bounding box). In particular, for two-stage detectors like Faster R-CNN [42], the "proposal sampler" and "matching score" are region proposal network andbbox IoU (intersection over union); for end-to-end detectors like DETR [9], they are query transformer decoder and bipartite matching score. For the matched proposals, the loss is class cross-entropy $\mathcal{L}_{cls}$ andbbox regression $\mathcal{L}_{reg}$ . + +BG (background): for conventional detection, all the mismatched proposals are considered background, whose loss is only $\mathcal{L}_{cls}$ with the label "BG"; for OWOD, we only use the mismatched proposals excluding the Unknown-FG proposals below. + +![](images/f4b4d37380d21027c4fa6d489a4ab185a4ae8c1b05f126554f97eba4d9073351.jpg) +Figure 2: The sorted foreground confidence assigned by two baselines (ORE [23], OW-DETR [20]) and our Rand-Box to the generated proposals in training. Green, red and black correspond to "known", "unknown" and "BG", respectively, with examples showing on the top row. + +Unknown-FG: this is the key difference from conventional detection. Its design heuristic is that, for the mismatched proposals with class confidence larger than a threshold—probably unknown objects—the loss is only $\mathcal{L}_{cls}$ with a special label "unknown" w/o bbox regression. Note that this heuristic is based on the assumption of feature transfer [56, 10]—visually similar proposals have similar class confidences (see Section 3.1 for the review of the loss implementation in two-stage and end-to-end detection)—the more unknown objects the Unknown-FG collects, the better the OWOD. + +However, in practice, Unknown-FG usually has a low recall of unknown objects. As shown in Figure 2, in existing methods, most proposals of high confidence are matched as Known-FG; the mismatched proposals, mixed with both unknown objects and BG, all have low confidence, losing a gradual confidence decrease to differentiate Unknown-FG from BG (the red and black colors are inseparable). One may easily understand that this failure is predictable because, yet, we don't have the ground-truth labels for unknown objects, so the proposal sampler trained on known objects will be inevitably biased towards them. In fact, such bias is ubiquitously in any bootstrapping learning [43] with limited supervision, such as semi-supervised learning [34, 49] and reinforcement learning [24, 53]. Unfortunately, existing OWOD methods do not properly address the bias. + +In this paper, we point out that the bias is caused by the confounding effect [37, 39] of the training data with limited known object labels that mislead the feature transfer. The effect can be understood in this way: if we only let the training data determine what region proposals to be used to extract the region features for detector training (Figure 1b), we cannot avoid the trivial loss minimization from only detecting the known objects. To this end, we propose to remove the confounding effect by introducing a random Instrumental Variable [5]—the proposed RandBox—that is independent of the training data. Intuitively, RandBox sim + +ulates a Randomized Controlled Experiment (RCT) [8] to learn a causal detector from region features to object labels, by inviting an independent 3rd-party proposal sampler to explore more possible locations of unknown objects. As shown in Figure 2 RandBox, the recall of unknown objects is greatly improved by RandBox, due to the fact that the confidence score change of the proposals from known to unknown is much more separable. We will detail the theory behind RandBox in Section 4. To get a qualitative sense of open-world detection task, see Figures 3. + +RandBox is simple yet effective (Section 3.2). For each training image in every iteration, we sample 500 random boxes as proposals from a 4-dimensional Gaussian noise (center_x, center_y, height, width). For these random boxes, we crop their RoI (region of interest) features from a backbone feature map, and feed them into a detection head to obtain $\mathcal{L}_{cls}$ and $\mathcal{L}_{reg}$ as in (Figure 1c), where the proposed matching score that encourages exploration is detailed in Section 3.2. At inference, we remove the randomness and grid-sample 10,000 boxes per image by 10 scales, 10 shapes, and 100 spatial locations. We use NMS [35] (Non-maximum Suppression) to prune the 10,000 boxes for final detection. Overall, our contributions include: + +- Our proposed RandBox is a Fast R-CNN based architecture for OWOD, which leverages random proposals to remove the confounding effect from the known objects, and uses an improved matching score to encourage proposal exploration. +- By removing the confounding effect, we learn an unbiased detector that improves both known and unknown detection accuracy. In particular, we achieve new state-of-the-art results on Pascal-VOC/MS-COCO [29]. +- We show that our RandBox detector trained on PascalVOC/MS-COCO remains robust when transferring to long-tailed datasets such as LVIS [19]. + +# 2. Related Work + +Open-World Object Detection (OWOD). Object detection systems are significantly advanced recently [41, 57, 42, 18, 48]. Yet they are based on the conventional close-world paradigm, which assumes that all objects of interests are annotated. In practice, an object detector deployed in real life is constantly challenged by the vast open and dynamic visual world [33, 23, 25]. To bridge the gap, open-set detection [33, 32, 14] aims to reject out-of-inventory objects as “unknown”, and other works focus on incrementally learning [40, 1, 31] a detector to recognize new object classes without forgetting old ones. Inspired by the open-world setting proposed in image classification [6, 7], recent works [23, 20, 55, 58] unify open-set detection and incremental learning as OWOD, which are based on two stage detectors like Faster R-CNN [42], or end-to-end ones like + +![](images/3b9bea2127c63d1f0459a739ed637af63ecdee11c0412bbaf74c8f734db1a0c8.jpg) +Figure 3: Example results. We show the ground-truth (GT) locations of unknown objects, those predicted by OWDETR [20], and those predicted by our RandBox. RandBox not only detects the annotated unknown objects (first 2 images), but even discovers valid unknown ones without annotations (e.g., camp in image 3, bracelet in image 5, banner in image 6). + +DETR [57]. We systematically analyze the failure of these existing works—low recall of unknown objects—which is caused by the confounding effect [37, 36], and remove it using random proposals to learn a causal detector. + +Debiasing by Randomization. Randomization is an effective tool to debias across many tasks and domains. For example, using randomization as an instrument variable [12, 4, 5] is a classic tool to identify causal effect in social studies [15]. In reinforcement learning [53], randomization is used to encourage exploration [54, 27], such that the agent is not biased to exploiting spurious shortcuts. Several works [3, 50] in adversarial training [17] leverages randomization to build a robust model not biased to feature that can be manipulated in adversarial attack, e.g., by image perturbation [59]. In fact, data augmentation that is prevailing in vision [45, 21, 47] and language [46, 44] also leverages randomness to remove augmentation-related context bias in training (e.g., using green grass to classify cow). In our work, we present a novel detection framework that leverages random proposals to learn causal effect in OWOD. + +# 3. Method + +In OWOD, the task is to detect a gradually expanding set of known inventory classes $K$ , while simultaneously rejecting the out-of-inventory classes set $U$ as "unknown". The training dataset contains images where known objects are labelled. Specifically, for a training image containing $n$ known objects, it is labelled with a set $\{(b_i, y_i)\}_{i=1}^n$ , where $b_i$ specifies the bounding box (bbox) of the $i$ -th object (i.e., center_x, center_y, height, width), and $y_i \in K$ is its class label. We drop the subscript $i$ for simplicity when the context is clear. The goal in OWOD is to train a detector, whose input is an image, and output is a set of $m$ predictions $P = \{(\hat{b}_i, \hat{y}_i)\}_{i=1}^m$ , where $\hat{b}_i$ is the $i$ -th bounding box prediction (predictedbbox), and $\hat{y}_i \in \mathbb{R}^{|K| + 2}$ denotes the clas- + +sification logit for each class in $K\cup \{\text{"unknown","BG"}\}$ + +# 3.1. Preliminaries: Existing OWOD Methods + +Existing methods adopt either the two-stage Faster R-CNN [42] or the end-to-end DETR [9] as the detector. In training, the predictions $P$ generated by the detector are partitioned into three subsets: Known-FG, Unknown-FG and BG, which are used to calculate the classification loss and bbox regression loss. We detail each part below: + +Detector. Given an image, a detector generates $m$ proposals, extracts ROI features $x_{i}$ for each proposal, and finally computes bounding box $\hat{b}_{i}$ and logits $\hat{y}_{i}$ using a classifier to form $P$ . The two detector frameworks mainly differ in the first step: 1) Faster R-CNN leverages a region proposal network (RPN) pre-trained on the labelled data. It outputs the top- $m$ proposals with the largest objectness (i.e., probability of containing a known object). 2) DETR is an end-to-end detector. It first transforms an image into tokens using a combination of CNN backbone and transformer encoder. Then a transformer decoder uses the image tokens to generate the proposals. More details are in Appendix. + +Known-FG is selected from all predictions $P$ by matching with the labels $\{(b_i, y_i)\}_{i=1}^n$ based on a Known-FG score. To compute the score for a prediction $(\hat{b}, \hat{y}) \in P$ with a ground-truth $(b, y)$ , Faster R-CNN uses the IoU between $\hat{b}$ and $b$ , and DETR uses the bipartite matching score, which additionally considers if $\hat{y}$ has a large value on the class $y$ . As the process is the same as that in closed-set detection, we leave other details in Appendix. After matching, we denote the Known-FG subset as $P^K$ . For $(\hat{b}, \hat{y}) \in P^K$ , we denote its matched ground-truth as $(b^*, y^*)$ . + +Unknown-FG & BG are selected from the unmatched predictions $P \setminus P^K$ . Specifically, current methods compute an Unknown-FG score for each prediction, and select 5 predictions with the largest score as the Unknown-FG. For the score, methods based on Faster R-CNN [42, 23] use object- + +![](images/38b4cc5bf9d0d3dfda7ef97229d3c461488cb39db93e84e53c7f3fc7cf8d5b27.jpg) +(a) + +![](images/d48657afbad43da15183e417247cbc33e73532b5f647925cde41af954b475a3c.jpg) +(b) +Figure 4: (a) RandBox Pipeline. Our proposals are randomly generated. We obtain the Known-FG subset using a dynamic- $k$ matcher, and the Unknown-FG subset based on our proposed matching score. Our training losses follow existing methods. (b) Proposed Matching Score is the sum of likelihood of belonging to each foreground classes (including "unknown"). The proposals of known (green) and unknown (red) objects both have large matching score, i.e., high likelihood on the ground-truth class (solid arrows) or by feature transfer (dashed arrow), while BG proposals (black) have low score. + +ness, and those based on DETR [20] use the average value of the ROI feature. We denote the Unknown-FG subset as $P^U$ . Finally, the rest predictions become the BG subset $P^B$ . Training Loss. + +We calculate the loss on each of the three subsets. The loss on Known-FG $\mathcal{L}^K$ has the same form with closed-set detection: + +$$ +\mathcal {L} ^ {K} = \sum_ {i = 1} ^ {| P ^ {K} |} \mathcal {L} _ {c l s} \left(\hat {y} _ {i}, y _ {i} ^ {*}\right) + \lambda \mathcal {L} _ {r e g} \left(\hat {b} _ {i}, b _ {i} ^ {*}\right), \tag {1} +$$ + +where $\mathcal{L}_{cls}$ is the cross-entropy loss or focal loss [28] to handle class-imbalance, $\lambda$ is a balancing weight, and $\mathcal{L}_{reg}$ is the smooth L1 regression loss [18] to rectify the predicted bbox. Details of $\mathcal{L}_{cls}$ and $\mathcal{L}_{reg}$ are in Appendix. As Unknown-FG and BG have no annotated bbox, we only calculate $\mathcal{L}_{cls}$ on them: + +$$ +\mathcal {L} ^ {U B} = \sum_ {i = 1} ^ {| P ^ {U} |} \mathcal {L} _ {c l s} \left(\hat {y} _ {i}, \text {" u n k n o w n"}\right) + \sum_ {i = 1} ^ {| P ^ {B} |} \mathcal {L} _ {c l s} \left(\hat {y} _ {i}, \text {" B G"}\right), \tag {2} +$$ + +Overall, the detector parameters $\theta$ are optimized with: + +$$ +\min _ {\theta} \mathcal {L} ^ {K} + \beta \mathcal {L} ^ {U B}, \tag {3} +$$ + +where $\beta$ is a weight with ablation in Section 5.2. + +OWOD Pipeline. The detector is first randomly initialized. Then it is trained with the labelled data on $K$ , and evaluated with data on both $K$ and $U$ (Task 1). Next, additional labelled data on a subset of classes $K' \subset U$ is provided, i.e., the known classes set expands as $K \gets K \cup K'$ , and the unknown one becomes $U \gets U \setminus K'$ . The detector trained on Task 1 is fine-tuned and evaluated with the updated $K$ and $U$ (Task 2). This continues for the following tasks. + +# 3.2. Proposed RandBox + +Existing methods suffer from the low recall of the unknown objects in Unknown-FG. To tackle this, our proposed RandBox has two improvements: 1) We propose to generate region proposals randomly, instead of using a proposal sampler trained on the known objects, which explores more possible unknown object locations. 2) We propose a matching score without penalizing proposals that are not matched with the known objects, which explores more possible unknown object proposals. We detail the two improvements below, and explain why our RandBox solves the existing problems from a causal view in Section 4. + +Detector with Random Proposals. In training, we randomly generate 500 bboxes as region proposals on each image (Figure 4a). For each bbox, we sample 4 random real numbers in [0, 1], where each number is first drawn from the standard Gaussian distribution, truncated to $[-2, 2]$ and then scaled linearly to [0, 1]. The 4 numbers correspond to the horizontal and vertical coordinate of the bbox center, as well as the width and height of the bbox, respectively (proportional to image size). The width and height of out-of-boundary bboxes are adjusted to stay in the image. In testing, to remove the prediction randomness, we use 10,000 pre-defined bboxes as proposals on each image, which cover 10 scales, 10 aspect ratios and 100 spatial locations (details in Appendix). We use non-maximum suppression to prune the bboxes as per standard practice [35]. We highlight the following points: + +- Our region proposals are randomly sampled for every image in each iteration throughout the training. +- While we use random sampling, the number of our random proposals is in fact comparable with that used in the existing methods, e.g., ORE [23] uses 1024 proposals. + +Known-FG. We adopted the dynamic- $k$ matcher [11] as shown in Figure 4a. Specifically, each ground-truth bbox $b$ is matched with $k$ proposals based on the bipartite matching score, where $k$ is dynamically selected as the sum of the IoU between each proposal and $b$ . + +Unknown-FG. We propose a novel matching score to form Unknown-FG. Specifically, we select the top $N$ proposals with the largest matching score (ablation of $N$ in Section 5.2). Among the selected proposals, those already in Known-FG are removed to form our Unknown-FG subset. We use the following equation to compute our matching score for a proposal with the classification logits $\hat{y}$ : + +$$ +s (\hat {y}) = \sum_ {i = 1} ^ {| K | + 1} \frac {1}{1 + \exp (- \hat {y} _ {i})}, \tag {4} +$$ + +where we compute and sum the sigmoid of the $|K|$ known classes and “+1” unknown class, and $\hat{y}_i$ denotes the logit for the class $i$ . Note that we implement $\mathcal{L}_{cls}$ with the BCE loss [28]. Hence our score essentially computes how likely $\hat{y}$ corresponds to the foreground. Specifically, the top- $N$ (largest matching score) proposals that are not in KnownFG are pseudo-labeled as “unknown” to train the UnknownFG logit (Eq. 2 first loss). This design is based on the assumption of feature transfer [38, 52]—similarity between Unknown-FG and Known-FG is larger than that between BG and Known-FG. As shown in Figure 4b, an unknown object proposal can have non-trivial likelihood of belonging to a known class due to shared feature (dashed arrow), while BG proposal almost shares no feature with known. Hence future unknown object proposals can have large likelihood of belonging to “unknown” (solid red arrow), increasing the unknown recall. We have the following comparisons with existing methods: + +- Methods based on Faster R-CNN use the objectness predicted by RPN as the matching score to select UnknownFG. However, RPN is trained to produce large scores only on the proposals matched with the known objects, thus penalizing those unmatched ones. +- Without RPN, methods based on DETR use the mean activation of the ROI feature instead. However, this heuristic is extremely unreliable (Figure 3b), and unknown object proposals are often mistakenly placed in the BG subset and penalized as "background". +- In contrast, our matching score fairly evaluates each proposal by checking both known classes (first $|K|$ logits), as well as "unknown" ( $|K| + 1$ -th logit). Hence unknown object proposals can be reliably selected in the Unknown-FG subset with high likelihood of belonging to "unknown". + +Other Details. Our training objective is the same as Eq. (3). We used ResNet-50 [22] as backbone. Our RandBox is Fast R-CNN [18] based architecture and detection head is borrowed from Sparse R-CNN [48]. + +![](images/8077c57287447c75085f30fe3a1e9a9adc352e17347bad1dc786d4cad30f41b9.jpg) +Figure 5: Causal graph of (a) existing OWOD methods, and (b) our RandBox. + +![](images/63e8fc6aa531d0cc95adcfed96a7a8146e719165260ea48837b1cc4aef59af23.jpg) + +# 4. Theory + +We use a Structural Causal Model (SCM) to analyze the causalities between the key components in OWOD: training data $D$ , region proposal $R$ , ROI feature $X$ , and label $Y$ on $K \cup \{\text{"unknown", "BG"}\}$ . Note that $D$ only contains labelled data of the known classes $K$ . The SCM is illustrated with a causal graph in Figure 5, where each directed link denotes a causal relation between the two connected nodes. $R \rightarrow X \rightarrow Y$ represents the desired causal effect from region proposal $R$ to label $Y$ , as label $Y$ describes what a region $R$ (or its ROI feature $X$ ) contains. A detector is unbiased if it identifies $R \rightarrow X \rightarrow Y$ , i.e., given any region, the detector can fairly evaluate what it contains. + +$R \to X \gets D$ . The ROI feature $X$ is jointly determined by what the region contains ( $R \to X$ ), as well as the feature representation learned on the training data ( $D \to X$ ). + +$D \to Y$ is because the detector leverages the training knowledge obtained from $D$ to predict $Y$ , e.g., identifying the BG subset with prediction "BG" (Section 3.1). + +$D \to R$ exists in current OWOD methods as shown in Figure 5a. This is because the region proposal network in Faster R-CNN and the transformer decoder in DETR are both trained on $D$ to generate proposal $R$ . + +Confounding Effect. In Figure 5a, $R \gets D \to Y$ is known as a backdoor path, which leads to the undesired confounding effect [37]. Specifically, as the proposal sampler is supervised by the labelled data of known objects $D$ , the generated proposals $R$ are inevitably biased to them $(D \to R)$ , i.e., $R$ only faithfully reflects the known object locations. Consequently, the training is dominated by the loss $\mathcal{L}^K$ on Known-FG, and the detector recklessly exploits any discriminative feature in $D$ towards the known objects $(D \to Y)$ , which may not transfer to the unknown ones. This causes the low recall of Unknown-FG in Figure 2. + +Removing Confounding Effect. In our RandBox, $R$ is randomly generated with no influence from $D$ , i.e., $D \nRightarrow R$ in Figure 5b. This makes $R$ an Instrument Variable [5], which removes the confounding effect by simulating a Randomized Controlled Experiment [8]. We provide a threefold intuitive explanation: 1) The backdoor path is cut, i.e., $R \nLeftarrow D \to Y$ ; 2) The path $R \to X \gets D \to Y$ is blocked due to the collider [37] $X$ (i.e., with two incoming arrows). 3) This makes $R \to X \to Y$ the only unblocked path from $R$ to $Y$ . Hence when learning to predict $Y$ from $R$ , our de + +
MethodTask 1Task 2Task 3Task 4
K-mAPU-RWIA-OSEK-mAPU-RWIA-OSEK-mAPU-RWIA-OSEK-mAP
Faster-RCNN [42]56.4-0.069913,39615.2-0.037112,2916.7-0.02139,1744.2
Faster-RCNN+Finetuning56.4-0.069913,39638.0-0.037512,49730.0-0.02799,62225.6
DDETR [57]60.3-0.060833,27017.9-0.036818,1158.5-0.01979,3926.0
DDETR+Finetuning60.3-0.060833,27044.8-0.033717,83433.3-0.019510,09529.4
ORE [23]56.04.90.062110,45939.42.90.028210,44529.73.90.01566,80325.3
OST [55]56.2-0.04174,88939.9-0.02132,54629.6-0.01462,12025.9
OW-DETR [20]59.37.50.057110,24042.96.20.02788,44130.85.70.01566,80327.8
RandBox61.810.60.02404,49845.36.30.00781,88039.47.80.00541,45235.4
+ +Table 1: OWOD Evaluation results and comparison with existing methods. We can also achieve SOTA on previously/currently known scores, more details are in Appendix. + +tector captures the causal effect free from the confounding one. The formal definition and proof are in Appendix. + +# 5. Experiments + +We introduce important experiment setups below, and leave other details in Appendix. + +Datasets. We extensively evaluated RandBox on three tasks: OWOD, transfer learning and open-set detection. For OWOD, we used Pascal VOC [16] and MS-COCO [29] following the standard setups [23, 20]. In Task 1, the known set $K$ contains the 20 classes in Pascal VOC, and the unknown set $U$ contains the 60 classes unique to MS-COCO. For each of the Task 2-4, 20 classes in $U$ are added to $K$ , i.e., Task 4 corresponds to closed-set detection with 80 classes. The training and testing images are selected from the respective split of the two datasets. For transfer learning, we evaluated models trained on Task 1 on the 4,809 validation images of LVIS v1.0 [19], which are from over 1000 classes that exhibits long-tailed distribution. For open-set detection, we followed [33] to train models on Pascal VOC train split, and evaluate them on WR1 [33]. + +Evaluation Metrics: On known classes, we used the standard Known-class mAP (K-mAP). On unknown classes, we used three metrics: 1) Unknown class Recall (U-R) is the recall of unknown classes at IoU threshold of 0.5. 2) Wilderness Impact (WI) [14] is computed by (closed-set precision)/(open-set precision) - 1. A small WI is desired in OWOD, i.e., precision does not drop when unknown objects are introduced in evaluation. 3) Absolute Open-Set Error (A-OSE) [33] is the predictions that are misclassified as one of the known classes. + +Implementation Details: In training, we used the ResNet-50 [22] pre-trained on ImageNet [13] as our backbone. We trained RandBox using AdamW [30] optimizer with learning rate as $2.5e^{-5}$ and weight decay as $1e^{-4}$ . We used the same methodology as prior work [23, 2, 51, 26] to mitigate forgetting, i.e., by storing a balanced set of exemplars for model fine-tuning after each incremental step. In inference, after getting the predictions on the 10,000 pre-defined bboxes, we used Non-Maximum Suppression (NMS) [35] + +to prune redundant bboxes. After pruning, the final predictions are the bboxes whose probability of belonging to a class in $K \cup \{ "unknown" \}$ are at least 0.1. + +# 5.1. Main Results + +Table 1 presents the results of OWOD evaluation. We have the following observations: + +1) For the conventional framework Faster-RCNN [42] and Deformable-DETR (DDETR) [57], their K-mAP drops significantly in Task 2-4, showing that they suffer from catastrophic forgetting when new classes are incrementally added. By using data replay [23] (+Finetuning), their K-mAP results improve significantly (e.g., 6.0 to 29.4 on Task 4 for DDETR). Note that they are not capable to detect unknown objects (e.g., U-R is not applicable). +2) By comparing existing OWOD methods with the conventional frameworks, we notice that all of them have reduced K-mAP (e.g., the DDETR-based OW-DETR reduced 1.6 mAP on Task 4 compared with DDETR+Finetuning). This means that their capabilities of unknown detection are at the cost of known detection accuracy. +3) By comparing RandBox with existing OWOD methods on U-R and A-OSE, we observe significant improvements, e.g., $3.1\%$ U-R improvement and 391 A-OSE reduction on Task 1. This suggests that our training scheme with random boxes and the proposed matching score encourage proposal explorations, which detects and learn on more unknown objects to improve their evaluation performance. +4) In particular, by comparing K-mAP and WI of Rand-Box and OWOD methods, we see that RandBox also achieves the state-of-the-art (SOTA) performance, e.g., absolute gains ranging from $2.4\%$ to $8.6\%$ in terms of K-mAP and relatively reduces ranging from $42\%$ to $64\%$ in terms of WI. Remarkably, our RandBox even outperforms the conventional detection frameworks, e.g., Faster-RCNN and DDETR. This means that instead of sacrificing "known" to detect "unknown", RandBox learns "unknown" to benefit "known". This strongly validates that our approach removes confounding bias by simulating Randomized Controlled Experiment with random boxes, where our detector captures the causal effect from any region proposal (known, + +
ProposalsK-mAPU-RWIA-OSE
Selective search57.39.10.0295,433
RPN59.08.60.0315,128
Query based59.79.10.0434,679
Random (Ours)61.810.60.0244,498
+ +(a) Ablation on proposal generation method. + +
MatchRandK-mAPU-RWIA-OSE
51.8-0.0427,652
Ours59.79.10.0434,679
Mean activation✓60.37.10.0245,929
Ours✓61.810.60.0244,498
+ +(c) Ablation on components. + +
distributionnumK-mAPU-RWIA-OSE
Uniform10060.28.70.0274,877
Gaussian10060.79.30.0264,732
Uniform50062.010.10.0264,588
Gaussian50061.810.60.0244,498
Uniform1,00061.710.40.0284,975
Gaussian1,00061.810.60.0304,763
+ +(b) Strategy for Random Proposals. + +
ratioscalelocationK-mAPU-RWIA-OSE
552060.28.20.0413,001
10102061.69.60.0323,715
10104061.310.20.0294,098
101010061.810.60.0244,498
+ +(d) Ablation on inference bboxes. + +Table 2: Ablation results. Models are trained on Task 1. We adopted the best performing setting as our default (in gray). + +![](images/7c5ee4532117f0bc2390ded4aeede6355cfef423b510254405c3f2fce565d8fa.jpg) +Figure 6: Ablation on $N$ by training RandBox on Task 1. + +unknown or BG) to its label (Section 4). Hence we observe unconditional improvements overall. + +# 5.2. Ablation Experiments + +Choice of $N$ . Recall that in training, we identify the top $N$ proposals with the largest matching score to form Unknown-FG (by removing those already in Known-FG). Hence $N$ is directly correlated with the size of Unknown-FG. The ablation results on $N$ are given in Figure 6. Initially, increasing $N$ benefits both known detection (K-mAP) and unknown recall (U-R). This is because 1) With more unknown proposals for optimizing Eq. (3), the detector improves in recognizing "unknown" (increased U-R). 2) To differentiate "unknown" from "known", the detector also avoids spurious correlations of known classes in training (i.e., captures causal effect), which may not generalize to known objects in testing (increased K-mAP). However, further increasing $N$ leads to the drop in K-mAP. This is because increasing the size of Unknown-FG by large $N$ essentially increases the weight of the classification loss on "unknown" in Eq. (2). Hence the detector learning on known classes is adversely impacted when the weight is too large. We used $N = 10$ in all our experiments. + +Proposal generation methods Its ablation is in Table 2a. We use our matching score Eq. 4 and fix the same proposal number (500) to ablate the proposal generation methods. We compared our Random Proposals with Selective search, RPN and Query based proposals. We can find that our Random proposals surpass all other methods which means the randomness can make more explorations on more image regions, without biased towards the training data. + +Strategy for Random Proposals. When generating random proposals in training, we experimented with different distribution (for drawing random numbers) and the number of random proposals (num), and the results are in Table 2b. Using the same number of proposals, the results on the two distributions are both competitive. Regarding the number of proposals, we observe that increasing it beyond 500 does not bring any improvement. This shows that the image locations are already sufficiently explored using 500 random bboxes. Overall, we used 500 random proposals drawn from Gaussian distribution. + +Components. The main components in RandBox are the use of random proposals (Rand), and the matching process for Known-FG and Unknown-FG (Match). Their ablations are given in Table 2c. The first line corresponds to the baseline Sparse R-CNN [48]. Comparing the second line, by combining our matching process with NMS, our matching score can improve all metrics and already achieved SOTA (e.g., by comparing with other OWOD methods in Table 1 Task 1). In the third and forth lines, we introduce the Random proposals and compare two kinds of matching score, i.e., Mean activation and our matching score. We can find that our matching score improve all metrics significantly (e.g., $1.5\%$ on K-mAP and $3.5\%$ on U-R) compared with the Mean activation. This strongly validates the effectiveness of each component in RandBox. + +Training schedule. We show the change of U-R and K-mAP over the training and compare RandBox with ORE + +![](images/89b8051312ac2baebdda29a4bd647c44a73fb1f2b2987c45ad95fc3b9f304000.jpg) +Figure 7: Training schedule compared with existing works. + +![](images/8b9cdb80118d491765c19d1d1d1b1885733b2ee623d4ab6710ec3df3f5fdc18d.jpg) + +
MethodK-mAPU-RWIA-OSE
ORE [23]23.23.50.174323,225
OW-DETR [20]25.16.30.154819,672
RandBox27.78.40.07357,842
+ +Table 3: Transfer evaluation results on LVIS v1.0 [19]. + +
Evaluated on →Pascal-VOCOpen-Set (WR1)
Faster R-CNN [42]81.877.1
RetinaNet [28]79.273.8
Dropout Sampling [33]78.173.8
ORE [23]81.371.7
OW-DETR [20]82.178.6
RandBox84.482.0
+ +Table 4: Results on Pascal-VOC [16] (closed-set) and WR1 [33] (open-set). + +and OW-DETR in Figure 7. Our RandBox converges quickly and trains stably, outperforming the two methods. + +Inference Bboxes. We ablation on the number of predefined bbox ratios, scales and locations in Table 2d. Increasing the bbox number generally improves the performance due to the increased recall on both known and unknown classes. However, it also increases the number of mis-classified unknown predictions, leading to a larger A-OSE. As the performance tends to saturate with 10,000 bboxes (last row), we use this configuration for efficiency. + +# 5.3. Transfer and Open-Set Evaluations + +Transfer to LVIS v1.0. We evaluated the models trained on Task 1 on LVIS 1.0. [19] We observe significant improvements on all metrics compared to ORE and OW-DETR in Table 3 This validates the robustness of RandBox over the existing works under distribution shift. + +Open-Set Object Detection. Detectors in OWOD can naturally tackle open-set detection. We followed [33] and evaluated models trained on Task 1 on Pascal-VOC test split (closed-set) and WR1 (open-set). We significantly improve existing SOTAs on both evaluations (Table 4). + +# 5.4. Additional Qualitative Results + +As shown in Figure 8 first column, OW-DETR misses the known objects "mouse" and "chair" due to confusing + +![](images/af384c3d8d84492f1b10b215b1542496491c9bf5c6d6328956978d71aa990143.jpg) +Figure 8: Additional qualitative results. We show the ground-truth labels of known objects in the first row, and compare the predictions from OW-DETR and our RandBox. Green: known. Red: unknown. + +background and partial view, respectively. Our RandBox not only detects all known objects, but also identify many valid unknown objects. In the second column, RandBox predicts the overlapping spoons as "unknown", which is indeed plausible without other prior knowledge. The third column shows that our RandBox detects the unknown object "picture frame" both in the real world and in the mirror. + +# 6. Conclusion + +We presented a novel Open-World Object Detection (OWOD) method called RandBox, trained on random proposals and surpassing existing Faster R-CNN and Transformer based OWOD. We show from a causality theoretical perspective that RandBox simulates a Randomized Controlled Experiment, which removes the confounding effect of the training data with limited known object labels. In addition, we propose a matching score without penalizing random proposals that are not matched with the known objects, which further encourages proposal explorations. Extensive evaluations of our proposed RandBox show that it significantly improves both the accuracy of the known objects and the recall of unknown ones. As future direction, we will seek additional inductive bias to remove the confounding effect and extend our approach to other detection tasks. + +# 7. Acknowledgements + +The authors would like to thank all reviewers and ACs for their constructive suggestions. This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-RP-2021-022) and Alibaba-NTU Singapore Joint Research Institute. + +# References + +[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware synapses: Learning what (not) to forget. In Proceedings of the European conference on computer vision (ECCV), pages 139-154, 2018. 2 +[2] Takeshi Amemiya and Thomas E MaCurdy. Instrumental-variable estimation of an error-components model. *Econometrica: Journal of the Econometric Society*, pages 869–880, 1986. 6 +[3] Alexandre Araujo, Laurent Meunier, Rafael Pinot, and Benjamin Negrevergne. Robust neural networks using randomized adversarial training. arXiv preprint arXiv:1903.10219, 2019. 3 +[4] Manuel Arellano and Olympia Bover. 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In particular, for two-stage detectors like Faster R-CNN [42], the \"proposal sampler\" and \"matching score\" are region proposal network andbbox IoU (intersection over union); for end-to-end detectors like DETR [9], they are query transformer decoder and bipartite matching score. For the matched proposals, the loss is class cross-entropy " + }, + { + "bbox": [ + 304, + 518, + 547, + 651 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 304, + 518, + 547, + 651 + ], + "type": "text", + "content": " andbbox regression " + }, + { + "bbox": [ + 304, + 518, + 547, + 651 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{reg}" + }, + { + "bbox": [ + 304, + 518, + 547, + 651 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "BG (background): for conventional detection, all the mismatched proposals are considered background, whose loss is only " + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": " with the label \"BG\"; for OWOD, we only use the mismatched proposals excluding the Unknown-FG proposals below." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 38 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 38 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 38 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 747, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 747, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 747, + 315, + 757 + ], + "type": "text", + "content": "6233" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 69, + 279, + 169 + ], + "blocks": [ + { + "bbox": [ + 53, + 69, + 279, + 169 + ], + "lines": [ + { + "bbox": [ + 53, + 69, + 279, + 169 + ], + "spans": [ + { + "bbox": [ + 53, + 69, + 279, + 169 + ], + "type": "image", + "image_path": "f4b4d37380d21027c4fa6d489a4ab185a4ae8c1b05f126554f97eba4d9073351.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 177, + 287, + 239 + ], + "lines": [ + { + "bbox": [ + 46, + 177, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 177, + 287, + 239 + ], + "type": "text", + "content": "Figure 2: The sorted foreground confidence assigned by two baselines (ORE [23], OW-DETR [20]) and our Rand-Box to the generated proposals in training. Green, red and black correspond to \"known\", \"unknown\" and \"BG\", respectively, with examples showing on the top row." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 258, + 287, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 287, + 389 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 287, + 389 + ], + "type": "text", + "content": "Unknown-FG: this is the key difference from conventional detection. Its design heuristic is that, for the mismatched proposals with class confidence larger than a threshold—probably unknown objects—the loss is only " + }, + { + "bbox": [ + 46, + 258, + 287, + 389 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 46, + 258, + 287, + 389 + ], + "type": "text", + "content": " with a special label \"unknown\" w/o bbox regression. Note that this heuristic is based on the assumption of feature transfer [56, 10]—visually similar proposals have similar class confidences (see Section 3.1 for the review of the loss implementation in two-stage and end-to-end detection)—the more unknown objects the Unknown-FG collects, the better the OWOD." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 391, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 391, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 391, + 287, + 581 + ], + "type": "text", + "content": "However, in practice, Unknown-FG usually has a low recall of unknown objects. As shown in Figure 2, in existing methods, most proposals of high confidence are matched as Known-FG; the mismatched proposals, mixed with both unknown objects and BG, all have low confidence, losing a gradual confidence decrease to differentiate Unknown-FG from BG (the red and black colors are inseparable). One may easily understand that this failure is predictable because, yet, we don't have the ground-truth labels for unknown objects, so the proposal sampler trained on known objects will be inevitably biased towards them. In fact, such bias is ubiquitously in any bootstrapping learning [43] with limited supervision, such as semi-supervised learning [34, 49] and reinforcement learning [24, 53]. Unfortunately, existing OWOD methods do not properly address the bias." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": "In this paper, we point out that the bias is caused by the confounding effect [37, 39] of the training data with limited known object labels that mislead the feature transfer. The effect can be understood in this way: if we only let the training data determine what region proposals to be used to extract the region features for detector training (Figure 1b), we cannot avoid the trivial loss minimization from only detecting the known objects. To this end, we propose to remove the confounding effect by introducing a random Instrumental Variable [5]—the proposed RandBox—that is independent of the training data. Intuitively, RandBox sim" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": "ulates a Randomized Controlled Experiment (RCT) [8] to learn a causal detector from region features to object labels, by inviting an independent 3rd-party proposal sampler to explore more possible locations of unknown objects. As shown in Figure 2 RandBox, the recall of unknown objects is greatly improved by RandBox, due to the fact that the confidence score change of the proposals from known to unknown is much more separable. We will detail the theory behind RandBox in Section 4. To get a qualitative sense of open-world detection task, see Figures 3." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 192, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 545, + 347 + ], + "type": "text", + "content": "RandBox is simple yet effective (Section 3.2). For each training image in every iteration, we sample 500 random boxes as proposals from a 4-dimensional Gaussian noise (center_x, center_y, height, width). For these random boxes, we crop their RoI (region of interest) features from a backbone feature map, and feed them into a detection head to obtain " + }, + { + "bbox": [ + 304, + 192, + 545, + 347 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 304, + 192, + 545, + 347 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 192, + 545, + 347 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{reg}" + }, + { + "bbox": [ + 304, + 192, + 545, + 347 + ], + "type": "text", + "content": " as in (Figure 1c), where the proposed matching score that encourages exploration is detailed in Section 3.2. At inference, we remove the randomness and grid-sample 10,000 boxes per image by 10 scales, 10 shapes, and 100 spatial locations. We use NMS [35] (Non-maximum Suppression) to prune the 10,000 boxes for final detection. Overall, our contributions include:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 315, + 351, + 545, + 501 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 315, + 351, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 351, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 315, + 351, + 545, + 411 + ], + "type": "text", + "content": "- Our proposed RandBox is a Fast R-CNN based architecture for OWOD, which leverages random proposals to remove the confounding effect from the known objects, and uses an improved matching score to encourage proposal exploration." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 315, + 414, + 545, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 414, + 545, + 462 + ], + "spans": [ + { + "bbox": [ + 315, + 414, + 545, + 462 + ], + "type": "text", + "content": "- By removing the confounding effect, we learn an unbiased detector that improves both known and unknown detection accuracy. In particular, we achieve new state-of-the-art results on Pascal-VOC/MS-COCO [29]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 315, + 464, + 545, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 464, + 545, + 501 + ], + "spans": [ + { + "bbox": [ + 315, + 464, + 545, + 501 + ], + "type": "text", + "content": "- We show that our RandBox detector trained on PascalVOC/MS-COCO remains robust when transferring to long-tailed datasets such as LVIS [19]." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 513, + 392, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 513, + 392, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 513, + 392, + 525 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "type": "text", + "content": "Open-World Object Detection (OWOD). Object detection systems are significantly advanced recently [41, 57, 42, 18, 48]. Yet they are based on the conventional close-world paradigm, which assumes that all objects of interests are annotated. In practice, an object detector deployed in real life is constantly challenged by the vast open and dynamic visual world [33, 23, 25]. To bridge the gap, open-set detection [33, 32, 14] aims to reject out-of-inventory objects as “unknown”, and other works focus on incrementally learning [40, 1, 31] a detector to recognize new object classes without forgetting old ones. Inspired by the open-world setting proposed in image classification [6, 7], recent works [23, 20, 55, 58] unify open-set detection and incremental learning as OWOD, which are based on two stage detectors like Faster R-CNN [42], or end-to-end ones like" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 747, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 747, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 747, + 315, + 757 + ], + "type": "text", + "content": "6234" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 541, + 214 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 541, + 214 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 541, + 214 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 541, + 214 + ], + "type": "image", + "image_path": "3b9bea2127c63d1f0459a739ed637af63ecdee11c0412bbaf74c8f734db1a0c8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 222, + 546, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 222, + 546, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 222, + 546, + 258 + ], + "type": "text", + "content": "Figure 3: Example results. We show the ground-truth (GT) locations of unknown objects, those predicted by OWDETR [20], and those predicted by our RandBox. RandBox not only detects the annotated unknown objects (first 2 images), but even discovers valid unknown ones without annotations (e.g., camp in image 3, bracelet in image 5, banner in image 6)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 279, + 287, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 287, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 287, + 327 + ], + "type": "text", + "content": "DETR [57]. We systematically analyze the failure of these existing works—low recall of unknown objects—which is caused by the confounding effect [37, 36], and remove it using random proposals to learn a causal detector." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 329, + 290, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 329, + 290, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 290, + 521 + ], + "type": "text", + "content": "Debiasing by Randomization. Randomization is an effective tool to debias across many tasks and domains. For example, using randomization as an instrument variable [12, 4, 5] is a classic tool to identify causal effect in social studies [15]. In reinforcement learning [53], randomization is used to encourage exploration [54, 27], such that the agent is not biased to exploiting spurious shortcuts. Several works [3, 50] in adversarial training [17] leverages randomization to build a robust model not biased to feature that can be manipulated in adversarial attack, e.g., by image perturbation [59]. In fact, data augmentation that is prevailing in vision [45, 21, 47] and language [46, 44] also leverages randomness to remove augmentation-related context bias in training (e.g., using green grass to classify cow). In our work, we present a novel detection framework that leverages random proposals to learn causal effect in OWOD." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 536, + 104, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 104, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 104, + 548 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": "In OWOD, the task is to detect a gradually expanding set of known inventory classes " + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": ", while simultaneously rejecting the out-of-inventory classes set " + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": " as \"unknown\". The training dataset contains images where known objects are labelled. Specifically, for a training image containing " + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": " known objects, it is labelled with a set " + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\{(b_i, y_i)\\}_{i=1}^n" + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "inline_equation", + "content": "b_i" + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": " specifies the bounding box (bbox) of the " + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": "-th object (i.e., center_x, center_y, height, width), and " + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "inline_equation", + "content": "y_i \\in K" + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": " is its class label. We drop the subscript " + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": " for simplicity when the context is clear. The goal in OWOD is to train a detector, whose input is an image, and output is a set of " + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": " predictions " + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "inline_equation", + "content": "P = \\{(\\hat{b}_i, \\hat{y}_i)\\}_{i=1}^m" + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\hat{b}_i" + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": "-th bounding box prediction (predictedbbox), and " + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\hat{y}_i \\in \\mathbb{R}^{|K| + 2}" + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": " denotes the clas-" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 279, + 541, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 279, + 541, + 293 + ], + "spans": [ + { + "bbox": [ + 305, + 279, + 541, + 293 + ], + "type": "text", + "content": "sification logit for each class in " + }, + { + "bbox": [ + 305, + 279, + 541, + 293 + ], + "type": "inline_equation", + "content": "K\\cup \\{\\text{\"unknown\",\"BG\"}\\}" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 297, + 520, + 311 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 297, + 520, + 311 + ], + "spans": [ + { + "bbox": [ + 305, + 297, + 520, + 311 + ], + "type": "text", + "content": "3.1. Preliminaries: Existing OWOD Methods" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 316, + 546, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 546, + 388 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 546, + 388 + ], + "type": "text", + "content": "Existing methods adopt either the two-stage Faster R-CNN [42] or the end-to-end DETR [9] as the detector. In training, the predictions " + }, + { + "bbox": [ + 304, + 316, + 546, + 388 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 316, + 546, + 388 + ], + "type": "text", + "content": " generated by the detector are partitioned into three subsets: Known-FG, Unknown-FG and BG, which are used to calculate the classification loss and bbox regression loss. We detail each part below:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 388, + 546, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 546, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 546, + 532 + ], + "type": "text", + "content": "Detector. Given an image, a detector generates " + }, + { + "bbox": [ + 304, + 388, + 546, + 532 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 388, + 546, + 532 + ], + "type": "text", + "content": " proposals, extracts ROI features " + }, + { + "bbox": [ + 304, + 388, + 546, + 532 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 304, + 388, + 546, + 532 + ], + "type": "text", + "content": " for each proposal, and finally computes bounding box " + }, + { + "bbox": [ + 304, + 388, + 546, + 532 + ], + "type": "inline_equation", + "content": "\\hat{b}_{i}" + }, + { + "bbox": [ + 304, + 388, + 546, + 532 + ], + "type": "text", + "content": " and logits " + }, + { + "bbox": [ + 304, + 388, + 546, + 532 + ], + "type": "inline_equation", + "content": "\\hat{y}_{i}" + }, + { + "bbox": [ + 304, + 388, + 546, + 532 + ], + "type": "text", + "content": " using a classifier to form " + }, + { + "bbox": [ + 304, + 388, + 546, + 532 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 388, + 546, + 532 + ], + "type": "text", + "content": ". The two detector frameworks mainly differ in the first step: 1) Faster R-CNN leverages a region proposal network (RPN) pre-trained on the labelled data. It outputs the top- " + }, + { + "bbox": [ + 304, + 388, + 546, + 532 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 388, + 546, + 532 + ], + "type": "text", + "content": " proposals with the largest objectness (i.e., probability of containing a known object). 2) DETR is an end-to-end detector. It first transforms an image into tokens using a combination of CNN backbone and transformer encoder. Then a transformer decoder uses the image tokens to generate the proposals. More details are in Appendix." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "text", + "content": "Known-FG is selected from all predictions " + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "text", + "content": " by matching with the labels " + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "inline_equation", + "content": "\\{(b_i, y_i)\\}_{i=1}^n" + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "text", + "content": " based on a Known-FG score. To compute the score for a prediction " + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "inline_equation", + "content": "(\\hat{b}, \\hat{y}) \\in P" + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "text", + "content": " with a ground-truth " + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "inline_equation", + "content": "(b, y)" + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "text", + "content": ", Faster R-CNN uses the IoU between " + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "inline_equation", + "content": "\\hat{b}" + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "text", + "content": ", and DETR uses the bipartite matching score, which additionally considers if " + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "text", + "content": " has a large value on the class " + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "text", + "content": ". As the process is the same as that in closed-set detection, we leave other details in Appendix. After matching, we denote the Known-FG subset as " + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "inline_equation", + "content": "P^K" + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "inline_equation", + "content": "(\\hat{b}, \\hat{y}) \\in P^K" + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "text", + "content": ", we denote its matched ground-truth as " + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "inline_equation", + "content": "(b^*, y^*)" + }, + { + "bbox": [ + 304, + 532, + 547, + 653 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "Unknown-FG & BG are selected from the unmatched predictions " + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "inline_equation", + "content": "P \\setminus P^K" + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": ". Specifically, current methods compute an Unknown-FG score for each prediction, and select 5 predictions with the largest score as the Unknown-FG. For the score, methods based on Faster R-CNN [42, 23] use object-" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 747, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 747, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 747, + 315, + 757 + ], + "type": "text", + "content": "6235" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 312, + 194 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 312, + 194 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 312, + 194 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 312, + 194 + ], + "type": "image", + "image_path": "38b4cc5bf9d0d3dfda7ef97229d3c461488cb39db93e84e53c7f3fc7cf8d5b27.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 117, + 198, + 127, + 207 + ], + "lines": [ + { + "bbox": [ + 117, + 198, + 127, + 207 + ], + "spans": [ + { + "bbox": [ + 117, + 198, + 127, + 207 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 332, + 70, + 545, + 196 + ], + "blocks": [ + { + "bbox": [ + 332, + 70, + 545, + 196 + ], + "lines": [ + { + "bbox": [ + 332, + 70, + 545, + 196 + ], + "spans": [ + { + "bbox": [ + 332, + 70, + 545, + 196 + ], + "type": "image", + "image_path": "d48657afbad43da15183e417247cbc33e73532b5f647925cde41af954b475a3c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 435, + 198, + 445, + 209 + ], + "lines": [ + { + "bbox": [ + 435, + 198, + 445, + 209 + ], + "spans": [ + { + "bbox": [ + 435, + 198, + 445, + 209 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 218, + 546, + 278 + ], + "lines": [ + { + "bbox": [ + 46, + 218, + 546, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 218, + 546, + 278 + ], + "type": "text", + "content": "Figure 4: (a) RandBox Pipeline. Our proposals are randomly generated. We obtain the Known-FG subset using a dynamic-" + }, + { + "bbox": [ + 46, + 218, + 546, + 278 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 218, + 546, + 278 + ], + "type": "text", + "content": " matcher, and the Unknown-FG subset based on our proposed matching score. Our training losses follow existing methods. (b) Proposed Matching Score is the sum of likelihood of belonging to each foreground classes (including \"unknown\"). The proposals of known (green) and unknown (red) objects both have large matching score, i.e., high likelihood on the ground-truth class (solid arrows) or by feature transfer (dashed arrow), while BG proposals (black) have low score." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 299, + 287, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 299, + 287, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 299, + 287, + 346 + ], + "type": "text", + "content": "ness, and those based on DETR [20] use the average value of the ROI feature. We denote the Unknown-FG subset as " + }, + { + "bbox": [ + 47, + 299, + 287, + 346 + ], + "type": "inline_equation", + "content": "P^U" + }, + { + "bbox": [ + 47, + 299, + 287, + 346 + ], + "type": "text", + "content": ". Finally, the rest predictions become the BG subset " + }, + { + "bbox": [ + 47, + 299, + 287, + 346 + ], + "type": "inline_equation", + "content": "P^B" + }, + { + "bbox": [ + 47, + 299, + 287, + 346 + ], + "type": "text", + "content": ". Training Loss." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 347, + 287, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 347, + 287, + 381 + ], + "spans": [ + { + "bbox": [ + 47, + 347, + 287, + 381 + ], + "type": "text", + "content": "We calculate the loss on each of the three subsets. The loss on Known-FG " + }, + { + "bbox": [ + 47, + 347, + 287, + 381 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^K" + }, + { + "bbox": [ + 47, + 347, + 287, + 381 + ], + "type": "text", + "content": " has the same form with closed-set detection:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 83, + 388, + 287, + 423 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 388, + 287, + 423 + ], + "spans": [ + { + "bbox": [ + 83, + 388, + 287, + 423 + ], + "type": "interline_equation", + "content": "\\mathcal {L} ^ {K} = \\sum_ {i = 1} ^ {| P ^ {K} |} \\mathcal {L} _ {c l s} \\left(\\hat {y} _ {i}, y _ {i} ^ {*}\\right) + \\lambda \\mathcal {L} _ {r e g} \\left(\\hat {b} _ {i}, b _ {i} ^ {*}\\right), \\tag {1}", + "image_path": "17051bcc847d4ee1624db4df1acf03e03b8ce9230abe3f350a0e40c0130b20ee.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 429, + 287, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 429, + 287, + 501 + ], + "spans": [ + { + "bbox": [ + 47, + 429, + 287, + 501 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 429, + 287, + 501 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 47, + 429, + 287, + 501 + ], + "type": "text", + "content": " is the cross-entropy loss or focal loss [28] to handle class-imbalance, " + }, + { + "bbox": [ + 47, + 429, + 287, + 501 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 429, + 287, + 501 + ], + "type": "text", + "content": " is a balancing weight, and " + }, + { + "bbox": [ + 47, + 429, + 287, + 501 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{reg}" + }, + { + "bbox": [ + 47, + 429, + 287, + 501 + ], + "type": "text", + "content": " is the smooth L1 regression loss [18] to rectify the predicted bbox. Details of " + }, + { + "bbox": [ + 47, + 429, + 287, + 501 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 47, + 429, + 287, + 501 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 429, + 287, + 501 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{reg}" + }, + { + "bbox": [ + 47, + 429, + 287, + 501 + ], + "type": "text", + "content": " are in Appendix. As Unknown-FG and BG have no annotated bbox, we only calculate " + }, + { + "bbox": [ + 47, + 429, + 287, + 501 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 47, + 429, + 287, + 501 + ], + "type": "text", + "content": " on them:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 51, + 517, + 287, + 562 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 517, + 287, + 562 + ], + "spans": [ + { + "bbox": [ + 51, + 517, + 287, + 562 + ], + "type": "interline_equation", + "content": "\\mathcal {L} ^ {U B} = \\sum_ {i = 1} ^ {| P ^ {U} |} \\mathcal {L} _ {c l s} \\left(\\hat {y} _ {i}, \\text {\" u n k n o w n\"}\\right) + \\sum_ {i = 1} ^ {| P ^ {B} |} \\mathcal {L} _ {c l s} \\left(\\hat {y} _ {i}, \\text {\" B G\"}\\right), \\tag {2}", + "image_path": "1aa84b2b0a2a5954d69e36a54971b5b1ef92ab116595293a62a28f60ef40b091.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 563, + 265, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 265, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 265, + 574 + ], + "type": "text", + "content": "Overall, the detector parameters " + }, + { + "bbox": [ + 47, + 563, + 265, + 574 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 563, + 265, + 574 + ], + "type": "text", + "content": " are optimized with:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 128, + 580, + 287, + 599 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 128, + 580, + 287, + 599 + ], + "spans": [ + { + "bbox": [ + 128, + 580, + 287, + 599 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta} \\mathcal {L} ^ {K} + \\beta \\mathcal {L} ^ {U B}, \\tag {3}", + "image_path": "bc3c9b8655a7cd8087a4695ec7add946908b0fb74e1af642c486ddb6f47f1264.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 605, + 244, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 244, + 616 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 244, + 616 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 605, + 244, + 616 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 605, + 244, + 616 + ], + "type": "text", + "content": " is a weight with ablation in Section 5.2." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "OWOD Pipeline. The detector is first randomly initialized. Then it is trained with the labelled data on " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": ", and evaluated with data on both " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " (Task 1). Next, additional labelled data on a subset of classes " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "K' \\subset U" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " is provided, i.e., the known classes set expands as " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "K \\gets K \\cup K'" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": ", and the unknown one becomes " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "U \\gets U \\setminus K'" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": ". The detector trained on Task 1 is fine-tuned and evaluated with the updated " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " (Task 2). This continues for the following tasks." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 298, + 419, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 298, + 419, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 298, + 419, + 312 + ], + "type": "text", + "content": "3.2. Proposed RandBox" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 321, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 321, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 321, + 545, + 453 + ], + "type": "text", + "content": "Existing methods suffer from the low recall of the unknown objects in Unknown-FG. To tackle this, our proposed RandBox has two improvements: 1) We propose to generate region proposals randomly, instead of using a proposal sampler trained on the known objects, which explores more possible unknown object locations. 2) We propose a matching score without penalizing proposals that are not matched with the known objects, which explores more possible unknown object proposals. We detail the two improvements below, and explain why our RandBox solves the existing problems from a causal view in Section 4." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 456, + 545, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 648 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 648 + ], + "type": "text", + "content": "Detector with Random Proposals. In training, we randomly generate 500 bboxes as region proposals on each image (Figure 4a). For each bbox, we sample 4 random real numbers in [0, 1], where each number is first drawn from the standard Gaussian distribution, truncated to " + }, + { + "bbox": [ + 304, + 456, + 545, + 648 + ], + "type": "inline_equation", + "content": "[-2, 2]" + }, + { + "bbox": [ + 304, + 456, + 545, + 648 + ], + "type": "text", + "content": " and then scaled linearly to [0, 1]. The 4 numbers correspond to the horizontal and vertical coordinate of the bbox center, as well as the width and height of the bbox, respectively (proportional to image size). The width and height of out-of-boundary bboxes are adjusted to stay in the image. In testing, to remove the prediction randomness, we use 10,000 pre-defined bboxes as proposals on each image, which cover 10 scales, 10 aspect ratios and 100 spatial locations (details in Appendix). We use non-maximum suppression to prune the bboxes as per standard practice [35]. We highlight the following points:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 652, + 545, + 713 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 304, + 652, + 544, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 652, + 544, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 652, + 544, + 676 + ], + "type": "text", + "content": "- Our region proposals are randomly sampled for every image in each iteration throughout the training." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "- While we use random sampling, the number of our random proposals is in fact comparable with that used in the existing methods, e.g., ORE [23] uses 1024 proposals." + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 747, + 315, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 747, + 315, + 756 + ], + "spans": [ + { + "bbox": [ + 295, + 747, + 315, + 756 + ], + "type": "text", + "content": "6236" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": "Known-FG. We adopted the dynamic-" + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": " matcher [11] as shown in Figure 4a. Specifically, each ground-truth bbox " + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": " is matched with " + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": " proposals based on the bipartite matching score, where " + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": " is dynamically selected as the sum of the IoU between each proposal and " + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 286, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 286, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 286, + 216 + ], + "type": "text", + "content": "Unknown-FG. We propose a novel matching score to form Unknown-FG. Specifically, we select the top " + }, + { + "bbox": [ + 46, + 133, + 286, + 216 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 133, + 286, + 216 + ], + "type": "text", + "content": " proposals with the largest matching score (ablation of " + }, + { + "bbox": [ + 46, + 133, + 286, + 216 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 133, + 286, + 216 + ], + "type": "text", + "content": " in Section 5.2). Among the selected proposals, those already in Known-FG are removed to form our Unknown-FG subset. We use the following equation to compute our matching score for a proposal with the classification logits " + }, + { + "bbox": [ + 46, + 133, + 286, + 216 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 46, + 133, + 286, + 216 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 107, + 224, + 287, + 258 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 224, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 107, + 224, + 287, + 258 + ], + "type": "interline_equation", + "content": "s (\\hat {y}) = \\sum_ {i = 1} ^ {| K | + 1} \\frac {1}{1 + \\exp (- \\hat {y} _ {i})}, \\tag {4}", + "image_path": "c3ebbb266d699c69c9a7de9c7564648fd9ae45d373004872d8ae1ab6cddff58c.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 266, + 286, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 286, + 482 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 286, + 482 + ], + "type": "text", + "content": "where we compute and sum the sigmoid of the " + }, + { + "bbox": [ + 46, + 266, + 286, + 482 + ], + "type": "inline_equation", + "content": "|K|" + }, + { + "bbox": [ + 46, + 266, + 286, + 482 + ], + "type": "text", + "content": " known classes and “+1” unknown class, and " + }, + { + "bbox": [ + 46, + 266, + 286, + 482 + ], + "type": "inline_equation", + "content": "\\hat{y}_i" + }, + { + "bbox": [ + 46, + 266, + 286, + 482 + ], + "type": "text", + "content": " denotes the logit for the class " + }, + { + "bbox": [ + 46, + 266, + 286, + 482 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 266, + 286, + 482 + ], + "type": "text", + "content": ". Note that we implement " + }, + { + "bbox": [ + 46, + 266, + 286, + 482 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 46, + 266, + 286, + 482 + ], + "type": "text", + "content": " with the BCE loss [28]. Hence our score essentially computes how likely " + }, + { + "bbox": [ + 46, + 266, + 286, + 482 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 46, + 266, + 286, + 482 + ], + "type": "text", + "content": " corresponds to the foreground. Specifically, the top-" + }, + { + "bbox": [ + 46, + 266, + 286, + 482 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 266, + 286, + 482 + ], + "type": "text", + "content": " (largest matching score) proposals that are not in KnownFG are pseudo-labeled as “unknown” to train the UnknownFG logit (Eq. 2 first loss). This design is based on the assumption of feature transfer [38, 52]—similarity between Unknown-FG and Known-FG is larger than that between BG and Known-FG. As shown in Figure 4b, an unknown object proposal can have non-trivial likelihood of belonging to a known class due to shared feature (dashed arrow), while BG proposal almost shares no feature with known. Hence future unknown object proposals can have large likelihood of belonging to “unknown” (solid red arrow), increasing the unknown recall. We have the following comparisons with existing methods:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 483, + 286, + 663 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 45, + 483, + 286, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 483, + 286, + 542 + ], + "spans": [ + { + "bbox": [ + 45, + 483, + 286, + 542 + ], + "type": "text", + "content": "- Methods based on Faster R-CNN use the objectness predicted by RPN as the matching score to select UnknownFG. However, RPN is trained to produce large scores only on the proposals matched with the known objects, thus penalizing those unmatched ones." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 544, + 286, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 544, + 286, + 602 + ], + "spans": [ + { + "bbox": [ + 45, + 544, + 286, + 602 + ], + "type": "text", + "content": "- Without RPN, methods based on DETR use the mean activation of the ROI feature instead. However, this heuristic is extremely unreliable (Figure 3b), and unknown object proposals are often mistakenly placed in the BG subset and penalized as \"background\"." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 605, + 286, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 605, + 286, + 663 + ], + "spans": [ + { + "bbox": [ + 45, + 605, + 286, + 663 + ], + "type": "text", + "content": "- In contrast, our matching score fairly evaluates each proposal by checking both known classes (first " + }, + { + "bbox": [ + 45, + 605, + 286, + 663 + ], + "type": "inline_equation", + "content": "|K|" + }, + { + "bbox": [ + 45, + 605, + 286, + 663 + ], + "type": "text", + "content": " logits), as well as \"unknown\" (" + }, + { + "bbox": [ + 45, + 605, + 286, + 663 + ], + "type": "inline_equation", + "content": "|K| + 1" + }, + { + "bbox": [ + 45, + 605, + 286, + 663 + ], + "type": "text", + "content": "-th logit). Hence unknown object proposals can be reliably selected in the Unknown-FG subset with high likelihood of belonging to \"unknown\"." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "content": "Other Details. Our training objective is the same as Eq. (3). We used ResNet-50 [22] as backbone. Our RandBox is Fast R-CNN [18] based architecture and detection head is borrowed from Sparse R-CNN [48]." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 414, + 125 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 414, + 125 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 414, + 125 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 414, + 125 + ], + "type": "image", + "image_path": "8077c57287447c75085f30fe3a1e9a9adc352e17347bad1dc786d4cad30f41b9.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 133, + 544, + 156 + ], + "lines": [ + { + "bbox": [ + 305, + 133, + 544, + 156 + ], + "spans": [ + { + "bbox": [ + 305, + 133, + 544, + 156 + ], + "type": "text", + "content": "Figure 5: Causal graph of (a) existing OWOD methods, and (b) our RandBox." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 439, + 71, + 545, + 125 + ], + "blocks": [ + { + "bbox": [ + 439, + 71, + 545, + 125 + ], + "lines": [ + { + "bbox": [ + 439, + 71, + 545, + 125 + ], + "spans": [ + { + "bbox": [ + 439, + 71, + 545, + 125 + ], + "type": "image", + "image_path": "63e8fc6aa531d0cc95adcfed96a7a8146e719165260ea48837b1cc4aef59af23.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 178, + 358, + 192 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 178, + 358, + 192 + ], + "spans": [ + { + "bbox": [ + 306, + 178, + 358, + 192 + ], + "type": "text", + "content": "4. Theory" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "text", + "content": "We use a Structural Causal Model (SCM) to analyze the causalities between the key components in OWOD: training data " + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "text", + "content": ", region proposal " + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "text", + "content": ", ROI feature " + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "text", + "content": ", and label " + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "inline_equation", + "content": "K \\cup \\{\\text{\"unknown\", \"BG\"}\\}" + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "text", + "content": ". Note that " + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "text", + "content": " only contains labelled data of the known classes " + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "text", + "content": ". The SCM is illustrated with a causal graph in Figure 5, where each directed link denotes a causal relation between the two connected nodes. " + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "inline_equation", + "content": "R \\rightarrow X \\rightarrow Y" + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "text", + "content": " represents the desired causal effect from region proposal " + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "text", + "content": " to label " + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "text", + "content": ", as label " + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "text", + "content": " describes what a region " + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "text", + "content": " (or its ROI feature " + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "text", + "content": ") contains. A detector is unbiased if it identifies " + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "inline_equation", + "content": "R \\rightarrow X \\rightarrow Y" + }, + { + "bbox": [ + 304, + 198, + 545, + 341 + ], + "type": "text", + "content": ", i.e., given any region, the detector can fairly evaluate what it contains." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 342, + 545, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 545, + 377 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 545, + 377 + ], + "type": "inline_equation", + "content": "R \\to X \\gets D" + }, + { + "bbox": [ + 304, + 342, + 545, + 377 + ], + "type": "text", + "content": ". The ROI feature " + }, + { + "bbox": [ + 304, + 342, + 545, + 377 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 342, + 545, + 377 + ], + "type": "text", + "content": " is jointly determined by what the region contains (" + }, + { + "bbox": [ + 304, + 342, + 545, + 377 + ], + "type": "inline_equation", + "content": "R \\to X" + }, + { + "bbox": [ + 304, + 342, + 545, + 377 + ], + "type": "text", + "content": "), as well as the feature representation learned on the training data (" + }, + { + "bbox": [ + 304, + 342, + 545, + 377 + ], + "type": "inline_equation", + "content": "D \\to X" + }, + { + "bbox": [ + 304, + 342, + 545, + 377 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 378, + 544, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 544, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 544, + 413 + ], + "type": "inline_equation", + "content": "D \\to Y" + }, + { + "bbox": [ + 304, + 378, + 544, + 413 + ], + "type": "text", + "content": " is because the detector leverages the training knowledge obtained from " + }, + { + "bbox": [ + 304, + 378, + 544, + 413 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 378, + 544, + 413 + ], + "type": "text", + "content": " to predict " + }, + { + "bbox": [ + 304, + 378, + 544, + 413 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 378, + 544, + 413 + ], + "type": "text", + "content": ", e.g., identifying the BG subset with prediction \"BG\" (Section 3.1)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 414, + 544, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 544, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 544, + 461 + ], + "type": "inline_equation", + "content": "D \\to R" + }, + { + "bbox": [ + 304, + 414, + 544, + 461 + ], + "type": "text", + "content": " exists in current OWOD methods as shown in Figure 5a. This is because the region proposal network in Faster R-CNN and the transformer decoder in DETR are both trained on " + }, + { + "bbox": [ + 304, + 414, + 544, + 461 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 414, + 544, + 461 + ], + "type": "text", + "content": " to generate proposal " + }, + { + "bbox": [ + 304, + 414, + 544, + 461 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 414, + 544, + 461 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "text", + "content": "Confounding Effect. In Figure 5a, " + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "inline_equation", + "content": "R \\gets D \\to Y" + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "text", + "content": " is known as a backdoor path, which leads to the undesired confounding effect [37]. Specifically, as the proposal sampler is supervised by the labelled data of known objects " + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "text", + "content": ", the generated proposals " + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "text", + "content": " are inevitably biased to them " + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "inline_equation", + "content": "(D \\to R)" + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "text", + "content": " only faithfully reflects the known object locations. Consequently, the training is dominated by the loss " + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^K" + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "text", + "content": " on Known-FG, and the detector recklessly exploits any discriminative feature in " + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "text", + "content": " towards the known objects " + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "inline_equation", + "content": "(D \\to Y)" + }, + { + "bbox": [ + 304, + 461, + 545, + 593 + ], + "type": "text", + "content": ", which may not transfer to the unknown ones. This causes the low recall of Unknown-FG in Figure 2." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Removing Confounding Effect. In our RandBox, " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " is randomly generated with no influence from " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "D \\nRightarrow R" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " in Figure 5b. This makes " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " an Instrument Variable [5], which removes the confounding effect by simulating a Randomized Controlled Experiment [8]. We provide a threefold intuitive explanation: 1) The backdoor path is cut, i.e., " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "R \\nLeftarrow D \\to Y" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "; 2) The path " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "R \\to X \\gets D \\to Y" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " is blocked due to the collider [37] " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " (i.e., with two incoming arrows). 3) This makes " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "R \\to X \\to Y" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " the only unblocked path from " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ". 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MethodTask 1Task 2Task 3Task 4
K-mAPU-RWIA-OSEK-mAPU-RWIA-OSEK-mAPU-RWIA-OSEK-mAP
Faster-RCNN [42]56.4-0.069913,39615.2-0.037112,2916.7-0.02139,1744.2
Faster-RCNN+Finetuning56.4-0.069913,39638.0-0.037512,49730.0-0.02799,62225.6
DDETR [57]60.3-0.060833,27017.9-0.036818,1158.5-0.01979,3926.0
DDETR+Finetuning60.3-0.060833,27044.8-0.033717,83433.3-0.019510,09529.4
ORE [23]56.04.90.062110,45939.42.90.028210,44529.73.90.01566,80325.3
OST [55]56.2-0.04174,88939.9-0.02132,54629.6-0.01462,12025.9
OW-DETR [20]59.37.50.057110,24042.96.20.02788,44130.85.70.01566,80327.8
RandBox61.810.60.02404,49845.36.30.00781,88039.47.80.00541,45235.4
", + "image_path": "41f2618ae022df8f5833594762c2babe79e276f0300a4a53d4709a5d34ec7cd0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 182, + 546, + 207 + ], + "lines": [ + { + "bbox": [ + 46, + 182, + 546, + 207 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 546, + 207 + ], + "type": "text", + "content": "Table 1: OWOD Evaluation results and comparison with existing methods. We can also achieve SOTA on previously/currently known scores, more details are in Appendix." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 219, + 288, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 219, + 288, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 288, + 243 + ], + "type": "text", + "content": "tector captures the causal effect free from the confounding one. The formal definition and proof are in Appendix." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 257, + 128, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 257, + 128, + 272 + ], + "spans": [ + { + "bbox": [ + 47, + 257, + 128, + 272 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 278, + 287, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 278, + 287, + 303 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 287, + 303 + ], + "type": "text", + "content": "We introduce important experiment setups below, and leave other details in Appendix." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 304, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 483 + ], + "type": "text", + "content": "Datasets. We extensively evaluated RandBox on three tasks: OWOD, transfer learning and open-set detection. For OWOD, we used Pascal VOC [16] and MS-COCO [29] following the standard setups [23, 20]. In Task 1, the known set " + }, + { + "bbox": [ + 46, + 304, + 287, + 483 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 304, + 287, + 483 + ], + "type": "text", + "content": " contains the 20 classes in Pascal VOC, and the unknown set " + }, + { + "bbox": [ + 46, + 304, + 287, + 483 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 46, + 304, + 287, + 483 + ], + "type": "text", + "content": " contains the 60 classes unique to MS-COCO. For each of the Task 2-4, 20 classes in " + }, + { + "bbox": [ + 46, + 304, + 287, + 483 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 46, + 304, + 287, + 483 + ], + "type": "text", + "content": " are added to " + }, + { + "bbox": [ + 46, + 304, + 287, + 483 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 304, + 287, + 483 + ], + "type": "text", + "content": ", i.e., Task 4 corresponds to closed-set detection with 80 classes. The training and testing images are selected from the respective split of the two datasets. For transfer learning, we evaluated models trained on Task 1 on the 4,809 validation images of LVIS v1.0 [19], which are from over 1000 classes that exhibits long-tailed distribution. For open-set detection, we followed [33] to train models on Pascal VOC train split, and evaluate them on WR1 [33]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "text", + "content": "Evaluation Metrics: On known classes, we used the standard Known-class mAP (K-mAP). On unknown classes, we used three metrics: 1) Unknown class Recall (U-R) is the recall of unknown classes at IoU threshold of 0.5. 2) Wilderness Impact (WI) [14] is computed by (closed-set precision)/(open-set precision) - 1. A small WI is desired in OWOD, i.e., precision does not drop when unknown objects are introduced in evaluation. 3) Absolute Open-Set Error (A-OSE) [33] is the predictions that are misclassified as one of the known classes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": "Implementation Details: In training, we used the ResNet-50 [22] pre-trained on ImageNet [13] as our backbone. We trained RandBox using AdamW [30] optimizer with learning rate as " + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "inline_equation", + "content": "2.5e^{-5}" + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": " and weight decay as " + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "inline_equation", + "content": "1e^{-4}" + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": ". We used the same methodology as prior work [23, 2, 51, 26] to mitigate forgetting, i.e., by storing a balanced set of exemplars for model fine-tuning after each incremental step. In inference, after getting the predictions on the 10,000 pre-defined bboxes, we used Non-Maximum Suppression (NMS) [35]" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 219, + 546, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 219, + 546, + 255 + ], + "spans": [ + { + "bbox": [ + 304, + 219, + 546, + 255 + ], + "type": "text", + "content": "to prune redundant bboxes. After pruning, the final predictions are the bboxes whose probability of belonging to a class in " + }, + { + "bbox": [ + 304, + 219, + 546, + 255 + ], + "type": "inline_equation", + "content": "K \\cup \\{ \"unknown\" \\}" + }, + { + "bbox": [ + 304, + 219, + 546, + 255 + ], + "type": "text", + "content": " are at least 0.1." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 262, + 391, + 275 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 262, + 391, + 275 + ], + "spans": [ + { + "bbox": [ + 306, + 262, + 391, + 275 + ], + "type": "text", + "content": "5.1. Main Results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 281, + 546, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 546, + 305 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 546, + 305 + ], + "type": "text", + "content": "Table 1 presents the results of OWOD evaluation. We have the following observations:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 306, + 547, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 304, + 306, + 546, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 546, + 402 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 546, + 402 + ], + "type": "text", + "content": "1) For the conventional framework Faster-RCNN [42] and Deformable-DETR (DDETR) [57], their K-mAP drops significantly in Task 2-4, showing that they suffer from catastrophic forgetting when new classes are incrementally added. By using data replay [23] (+Finetuning), their K-mAP results improve significantly (e.g., 6.0 to 29.4 on Task 4 for DDETR). Note that they are not capable to detect unknown objects (e.g., U-R is not applicable)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 402, + 546, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 546, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 546, + 474 + ], + "type": "text", + "content": "2) By comparing existing OWOD methods with the conventional frameworks, we notice that all of them have reduced K-mAP (e.g., the DDETR-based OW-DETR reduced 1.6 mAP on Task 4 compared with DDETR+Finetuning). This means that their capabilities of unknown detection are at the cost of known detection accuracy." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 474, + 546, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 546, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 546, + 557 + ], + "type": "text", + "content": "3) By comparing RandBox with existing OWOD methods on U-R and A-OSE, we observe significant improvements, e.g., " + }, + { + "bbox": [ + 304, + 474, + 546, + 557 + ], + "type": "inline_equation", + "content": "3.1\\%" + }, + { + "bbox": [ + 304, + 474, + 546, + 557 + ], + "type": "text", + "content": " U-R improvement and 391 A-OSE reduction on Task 1. This suggests that our training scheme with random boxes and the proposed matching score encourage proposal explorations, which detects and learn on more unknown objects to improve their evaluation performance." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "content": "4) In particular, by comparing K-mAP and WI of Rand-Box and OWOD methods, we see that RandBox also achieves the state-of-the-art (SOTA) performance, e.g., absolute gains ranging from " + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "inline_equation", + "content": "2.4\\%" + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "inline_equation", + "content": "8.6\\%" + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "content": " in terms of K-mAP and relatively reduces ranging from " + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "inline_equation", + "content": "42\\%" + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "inline_equation", + "content": "64\\%" + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "content": " in terms of WI. Remarkably, our RandBox even outperforms the conventional detection frameworks, e.g., Faster-RCNN and DDETR. This means that instead of sacrificing \"known\" to detect \"unknown\", RandBox learns \"unknown\" to benefit \"known\". This strongly validates that our approach removes confounding bias by simulating Randomized Controlled Experiment with random boxes, where our detector captures the causal effect from any region proposal (known," + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 747, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 747, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 747, + 315, + 757 + ], + "type": "text", + "content": "6238" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 71, + 298, + 138 + ], + "blocks": [ + { + "bbox": [ + 53, + 71, + 298, + 138 + ], + "lines": [ + { + "bbox": [ + 53, + 71, + 298, + 138 + ], + "spans": [ + { + "bbox": [ + 53, + 71, + 298, + 138 + ], + "type": "table", + "html": "
ProposalsK-mAPU-RWIA-OSE
Selective search57.39.10.0295,433
RPN59.08.60.0315,128
Query based59.79.10.0434,679
Random (Ours)61.810.60.0244,498
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MatchRandK-mAPU-RWIA-OSE
51.8-0.0427,652
Ours59.79.10.0434,679
Mean activation✓60.37.10.0245,929
Ours✓61.810.60.0244,498
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distributionnumK-mAPU-RWIA-OSE
Uniform10060.28.70.0274,877
Gaussian10060.79.30.0264,732
Uniform50062.010.10.0264,588
Gaussian50061.810.60.0244,498
Uniform1,00061.710.40.0284,975
Gaussian1,00061.810.60.0304,763
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ratioscalelocationK-mAPU-RWIA-OSE
552060.28.20.0413,001
10102061.69.60.0323,715
10104061.310.20.0294,098
101010061.810.60.0244,498
", + "image_path": "fcfd106155c258d752da7b25fd608430aba8dcffa1a650bb1e38a8e2758c3325.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 361, + 227, + 488, + 237 + ], + "lines": [ + { + "bbox": [ + 361, + 227, + 488, + 237 + ], + "spans": [ + { + "bbox": [ + 361, + 227, + 488, + 237 + ], + "type": "text", + "content": "(d) Ablation on inference bboxes." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 52, + 247, + 538, + 260 + ], + "lines": [ + { + "bbox": [ + 52, + 247, + 538, + 260 + ], + "spans": [ + { + "bbox": [ + 52, + 247, + 538, + 260 + ], + "type": "text", + "content": "Table 2: Ablation results. Models are trained on Task 1. We adopted the best performing setting as our default (in gray)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 50, + 279, + 279, + 394 + ], + "blocks": [ + { + "bbox": [ + 50, + 279, + 279, + 394 + ], + "lines": [ + { + "bbox": [ + 50, + 279, + 279, + 394 + ], + "spans": [ + { + "bbox": [ + 50, + 279, + 279, + 394 + ], + "type": "image", + "image_path": "7c5ee4532117f0bc2390ded4aeede6355cfef423b510254405c3f2fce565d8fa.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 51, + 403, + 282, + 415 + ], + "lines": [ + { + "bbox": [ + 51, + 403, + 282, + 415 + ], + "spans": [ + { + "bbox": [ + 51, + 403, + 282, + 415 + ], + "type": "text", + "content": "Figure 6: Ablation on " + }, + { + "bbox": [ + 51, + 403, + 282, + 415 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 51, + 403, + 282, + 415 + ], + "type": "text", + "content": " by training RandBox on Task 1." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 436, + 286, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 436, + 286, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 436, + 286, + 460 + ], + "type": "text", + "content": "unknown or BG) to its label (Section 4). Hence we observe unconditional improvements overall." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 468, + 173, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 468, + 173, + 480 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 173, + 480 + ], + "type": "text", + "content": "5.2. Ablation Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "type": "text", + "content": "Choice of " + }, + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "type": "text", + "content": ". Recall that in training, we identify the top " + }, + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "type": "text", + "content": " proposals with the largest matching score to form Unknown-FG (by removing those already in Known-FG). Hence " + }, + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "type": "text", + "content": " is directly correlated with the size of Unknown-FG. The ablation results on " + }, + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "type": "text", + "content": " are given in Figure 6. Initially, increasing " + }, + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "type": "text", + "content": " benefits both known detection (K-mAP) and unknown recall (U-R). This is because 1) With more unknown proposals for optimizing Eq. (3), the detector improves in recognizing \"unknown\" (increased U-R). 2) To differentiate \"unknown\" from \"known\", the detector also avoids spurious correlations of known classes in training (i.e., captures causal effect), which may not generalize to known objects in testing (increased K-mAP). However, further increasing " + }, + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "type": "text", + "content": " leads to the drop in K-mAP. This is because increasing the size of Unknown-FG by large " + }, + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "type": "text", + "content": " essentially increases the weight of the classification loss on \"unknown\" in Eq. (2). Hence the detector learning on known classes is adversely impacted when the weight is too large. We used " + }, + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "type": "inline_equation", + "content": "N = 10" + }, + { + "bbox": [ + 46, + 485, + 287, + 713 + ], + "type": "text", + "content": " in all our experiments." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 281, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 545, + 376 + ], + "type": "text", + "content": "Proposal generation methods Its ablation is in Table 2a. We use our matching score Eq. 4 and fix the same proposal number (500) to ablate the proposal generation methods. We compared our Random Proposals with Selective search, RPN and Query based proposals. We can find that our Random proposals surpass all other methods which means the randomness can make more explorations on more image regions, without biased towards the training data." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 378, + 546, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 546, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 546, + 509 + ], + "type": "text", + "content": "Strategy for Random Proposals. When generating random proposals in training, we experimented with different distribution (for drawing random numbers) and the number of random proposals (num), and the results are in Table 2b. Using the same number of proposals, the results on the two distributions are both competitive. Regarding the number of proposals, we observe that increasing it beyond 500 does not bring any improvement. This shows that the image locations are already sufficiently explored using 500 random bboxes. Overall, we used 500 random proposals drawn from Gaussian distribution." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 510, + 546, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 688 + ], + "type": "text", + "content": "Components. The main components in RandBox are the use of random proposals (Rand), and the matching process for Known-FG and Unknown-FG (Match). Their ablations are given in Table 2c. The first line corresponds to the baseline Sparse R-CNN [48]. Comparing the second line, by combining our matching process with NMS, our matching score can improve all metrics and already achieved SOTA (e.g., by comparing with other OWOD methods in Table 1 Task 1). In the third and forth lines, we introduce the Random proposals and compare two kinds of matching score, i.e., Mean activation and our matching score. We can find that our matching score improve all metrics significantly (e.g., " + }, + { + "bbox": [ + 304, + 510, + 546, + 688 + ], + "type": "inline_equation", + "content": "1.5\\%" + }, + { + "bbox": [ + 304, + 510, + 546, + 688 + ], + "type": "text", + "content": " on K-mAP and " + }, + { + "bbox": [ + 304, + 510, + 546, + 688 + ], + "type": "inline_equation", + "content": "3.5\\%" + }, + { + "bbox": [ + 304, + 510, + 546, + 688 + ], + "type": "text", + "content": " on U-R) compared with the Mean activation. This strongly validates the effectiveness of each component in RandBox." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Training schedule. We show the change of U-R and K-mAP over the training and compare RandBox with ORE" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 747, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 747, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 747, + 315, + 757 + ], + "type": "text", + "content": "6239" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 160, + 168 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 160, + 168 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 160, + 168 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 160, + 168 + ], + "type": "image", + "image_path": "89b8051312ac2baebdda29a4bd647c44a73fb1f2b2987c45ad95fc3b9f304000.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 177, + 286, + 190 + ], + "lines": [ + { + "bbox": [ + 47, + 177, + 286, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 177, + 286, + 190 + ], + "type": "text", + "content": "Figure 7: Training schedule compared with existing works." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 171, + 71, + 281, + 169 + ], + "blocks": [ + { + "bbox": [ + 171, + 71, + 281, + 169 + ], + "lines": [ + { + "bbox": [ + 171, + 71, + 281, + 169 + ], + "spans": [ + { + "bbox": [ + 171, + 71, + 281, + 169 + ], + "type": "image", + "image_path": "8b9cdb80118d491765c19d1d1d1b1885733b2ee623d4ab6710ec3df3f5fdc18d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 55, + 200, + 282, + 246 + ], + "blocks": [ + { + "bbox": [ + 55, + 200, + 282, + 246 + ], + "lines": [ + { + "bbox": [ + 55, + 200, + 282, + 246 + ], + "spans": [ + { + "bbox": [ + 55, + 200, + 282, + 246 + ], + "type": "table", + "html": "
MethodK-mAPU-RWIA-OSE
ORE [23]23.23.50.174323,225
OW-DETR [20]25.16.30.154819,672
RandBox27.78.40.07357,842
", + "image_path": "f44f404188911a61c77235d4fd5c7fb81b87649ff3aab85a39922e89b811ce50.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 56, + 277, + 281, + 345 + ], + "blocks": [ + { + "bbox": [ + 56, + 255, + 277, + 266 + ], + "lines": [ + { + "bbox": [ + 56, + 255, + 277, + 266 + ], + "spans": [ + { + "bbox": [ + 56, + 255, + 277, + 266 + ], + "type": "text", + "content": "Table 3: Transfer evaluation results on LVIS v1.0 [19]." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 277, + 281, + 345 + ], + "lines": [ + { + "bbox": [ + 56, + 277, + 281, + 345 + ], + "spans": [ + { + "bbox": [ + 56, + 277, + 281, + 345 + ], + "type": "table", + "html": "
Evaluated on →Pascal-VOCOpen-Set (WR1)
Faster R-CNN [42]81.877.1
RetinaNet [28]79.273.8
Dropout Sampling [33]78.173.8
ORE [23]81.371.7
OW-DETR [20]82.178.6
RandBox84.482.0
", + "image_path": "1b6d4d7cd51a12e8044e5dfd36ab67d4a951968064535f46682e855e782c4403.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 354, + 287, + 378 + ], + "lines": [ + { + "bbox": [ + 47, + 354, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 47, + 354, + 287, + 378 + ], + "type": "text", + "content": "Table 4: Results on Pascal-VOC [16] (closed-set) and WR1 [33] (open-set)." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 399, + 286, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 286, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 286, + 422 + ], + "type": "text", + "content": "and OW-DETR in Figure 7. Our RandBox converges quickly and trains stably, outperforming the two methods." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 423, + 286, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 286, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 286, + 518 + ], + "type": "text", + "content": "Inference Bboxes. We ablation on the number of predefined bbox ratios, scales and locations in Table 2d. Increasing the bbox number generally improves the performance due to the increased recall on both known and unknown classes. However, it also increases the number of mis-classified unknown predictions, leading to a larger A-OSE. As the performance tends to saturate with 10,000 bboxes (last row), we use this configuration for efficiency." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 525, + 235, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 235, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 235, + 538 + ], + "type": "text", + "content": "5.3. Transfer and Open-Set Evaluations" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 544, + 286, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 286, + 603 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 286, + 603 + ], + "type": "text", + "content": "Transfer to LVIS v1.0. We evaluated the models trained on Task 1 on LVIS 1.0. [19] We observe significant improvements on all metrics compared to ORE and OW-DETR in Table 3 This validates the robustness of RandBox over the existing works under distribution shift." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 604, + 286, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 604, + 286, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 604, + 286, + 664 + ], + "type": "text", + "content": "Open-Set Object Detection. Detectors in OWOD can naturally tackle open-set detection. We followed [33] and evaluated models trained on Task 1 on Pascal-VOC test split (closed-set) and WR1 (open-set). We significantly improve existing SOTAs on both evaluations (Table 4)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 671, + 212, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 212, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 212, + 684 + ], + "type": "text", + "content": "5.4. Additional Qualitative Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": "As shown in Figure 8 first column, OW-DETR misses the known objects \"mouse\" and \"chair\" due to confusing" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 545, + 223 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 223 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 223 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 223 + ], + "type": "image", + "image_path": "af384c3d8d84492f1b10b215b1542496491c9bf5c6d6328956978d71aa990143.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 232, + 545, + 280 + ], + "lines": [ + { + "bbox": [ + 305, + 232, + 545, + 280 + ], + "spans": [ + { + "bbox": [ + 305, + 232, + 545, + 280 + ], + "type": "text", + "content": "Figure 8: Additional qualitative results. We show the ground-truth labels of known objects in the first row, and compare the predictions from OW-DETR and our RandBox. Green: known. Red: unknown." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 304, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 545, + 388 + ], + "type": "text", + "content": "background and partial view, respectively. Our RandBox not only detects all known objects, but also identify many valid unknown objects. In the second column, RandBox predicts the overlapping spoons as \"unknown\", which is indeed plausible without other prior knowledge. The third column shows that our RandBox detects the unknown object \"picture frame\" both in the real world and in the mirror." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 403, + 378, + 416 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 403, + 378, + 416 + ], + "spans": [ + { + "bbox": [ + 306, + 403, + 378, + 416 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 426, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 605 + ], + "type": "text", + "content": "We presented a novel Open-World Object Detection (OWOD) method called RandBox, trained on random proposals and surpassing existing Faster R-CNN and Transformer based OWOD. We show from a causality theoretical perspective that RandBox simulates a Randomized Controlled Experiment, which removes the confounding effect of the training data with limited known object labels. In addition, we propose a matching score without penalizing random proposals that are not matched with the known objects, which further encourages proposal explorations. Extensive evaluations of our proposed RandBox show that it significantly improves both the accuracy of the known objects and the recall of unknown ones. As future direction, we will seek additional inductive bias to remove the confounding effect and extend our approach to other detection tasks." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 620, + 420, + 633 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 620, + 420, + 633 + ], + "spans": [ + { + "bbox": [ + 306, + 620, + 420, + 633 + ], + "type": "text", + "content": "7. Acknowledgements" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "content": "The authors would like to thank all reviewers and ACs for their constructive suggestions. This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-RP-2021-022) and Alibaba-NTU Singapore Joint Research Institute." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 747, + 315, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 747, + 315, + 756 + ], + "spans": [ + { + "bbox": [ + 295, + 747, + 315, + 756 + ], + "type": "text", + "content": "6240" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. 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However, it is still very challenging to widely utilize the supervised methods in real cases due to the lack of paired noisy-clean images. Meanwhile, most self-supervised denoising methods are ineffective as well when applied to the real-world denoising tasks because of their strict assumptions in applications. For example, as a typical method for self-supervised denoising, the original blind spot network (BSN) assumes that the noise is pixel-wise independent, which is much different from the real cases. To solve this problem, we propose a novel self-supervised real image denoising framework named Sampling Difference As Perturbation (SDAP) based on Random Sub-samples Generation (RSG) with a cyclic sample difference loss. Specifically, we dig deeper into the properties of BSN to make it more suitable for real noise. Surprisingly, we find that adding an appropriate perturbation to the training images can effectively improve the performance of BSN. Further, we propose that the sampling difference can be considered as perturbation to achieve better results. Finally we propose a new BSN framework in combination with our RSG strategy. The results show that it significantly outperforms other state-of-the-art self-supervised denoising methods on real-world datasets. The code is available at https://github.com/p1y2z3/SDAP.", + "bbox": [ + 76, + 318, + 473, + 712 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 742, + 209, + 758 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image denoising is a hot topic in low-level vision tasks, aiming to obtain high-quality images from noisy versions. In recent years, learning-based methods have been widely used in image denoising with their superior performance. Thanks to the construction of paired image datasets, the supervised approaches [44, 2, 28, 11, 33, 34] can be efficiently implemented. In these approaches, it is a common practice", + "bbox": [ + 76, + 768, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8fbacf789c4e458d42046085ca6396bc7fa49c0a349082f193067df8e6a1e994.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 284, + 629, + 378 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c1f18a120e36fb48bf471d8a63d4acf5ca79188f245e75b58e36dd168623b03e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 284, + 756, + 378 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a783399a381aa24e1d1d0d75493e230c3eca2c47e13f273d58474e176f1ca652.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 761, + 284, + 885, + 378 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6588ba477eb9b8f7fedfc027d64d44cf07e27075587671729059483b2c8c7635.jpg", + "image_caption": [ + "Noisy", + "CVF-SID [25]" + ], + "image_footnote": [], + "bbox": [ + 504, + 388, + 627, + 481 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/721555f91cb1dd3a1613bf4b26c79212d71fae1ed0c97966bec1a73796b773dd.jpg", + "image_caption": [ + "CBDNet [14]", + "AP-BSN [22]", + "Figure 1: Real-world image denoising results on DND [27]." + ], + "image_footnote": [], + "bbox": [ + 630, + 388, + 754, + 482 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8b8afde62f777128c984f02907f5a5c07b706c0bfc4ddb0f1d827f7561fa66cf.jpg", + "image_caption": [ + "C2N [18]", + "SDAP (S)(E) (Ours)" + ], + "image_footnote": [], + "bbox": [ + 761, + 388, + 883, + 482 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "to synthesize paired datasets directly using a specific noise model, such as the signal-independent additive white Gaussian noise (AWGN) model.", + "bbox": [ + 498, + 537, + 890, + 582 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, the real images are captured by cameras with image signal processing (ISP) pipelines [4]. The noise is usually signal-dependent and spatially correlated in the real world. Moreover, ISP includes many non-linear operations that can complicate the noise distribution. Due to the influence of ISP pipelines within the camera, the noise distribution of real images is difficult to predict. Therefore, it is difficult and challenging for us to model the noise for real images. To overcome the problem of directly and explicitly modelling noise distribution, paired real-world datasets have been constructed by researchers. However, collecting paired noisy-clean images is difficult and time-expensive.", + "bbox": [ + 496, + 583, + 892, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, a series of unsupervised and self-supervised methods have been introduced. These methods do not require paired datasets for training, and thus further avoiding the difficulty of collecting real-world paired datasets for denoising. Among them, Noise2Void [20] proposes Blind-Spot Network (BSN) that can be trained with only single noisy images. Unfortunately, BSN has strict assumptions, which can only be applied to pixel-wise independent noise. AP-BSN [22] applies pixel-shuffle downsampling", + "bbox": [ + 496, + 765, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Corresponding Author", + "bbox": [ + 89, + 886, + 223, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12150", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(PD) strategy [47] to BSN, remove the spatial correlation in the real-world noise, and thus the real image can also meet the conditions for BSN to some extent. However, real noisy datasets usually have relatively limited numbers of samples. AP-BSN directly adopts the strategy of PD, which can only obtain $s^2$ sub-images for a noisy image (the stride factor of PD is $s$ ). This will inevitably lead to the insufficient samples, and make the training of BSN less effective. Therefore, the optimal performance of BSN cannot be achieved.", + "bbox": [ + 75, + 90, + 467, + 224 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We observe that adding some perturbations to the training images can greatly expand the training data, which improves the performance of BSN. Further, we consider the samples difference as the perturbation. To obtain more random perturbations and more sub-samples, we propose random sub-samples generation (RSG) strategy to break the fixed sampling pattern of PD. Based on this, we propose a new cyclic sampling difference loss for BSN and a new BSN framework in combination with our RSG strategy. In summary, our contributions include:", + "bbox": [ + 75, + 227, + 467, + 378 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We provide a new idea about adding perturbations to the training data to improve the BSN performance. Then, we suggest that the sub-samples difference generated by sampling can be considered as perturbations for higher performance.", + "- We propose a new self-supervised framework for real image denoising with random sub-samples generation and cyclic sampling difference loss.", + "- Our method performs very favorably against state-of-the-art (SOTA) self-supervised denoising methods on real-world datasets." + ], + "bbox": [ + 96, + 391, + 467, + 583 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 602, + 217, + 617 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The image denoising task aims to restore a clean image from its noisy counterpart. There are two main types of non-learning-based image denoising: filtering-based methods and model-based methods. Filter-based methods involve using some artificially designed low-pass filter to remove image noise. Taking advantage of the condition of having many similar image blocks in the same image, noise can also be removed by the local similarity of image, such as NLM [5], BM3D [12], etc. Model-based methods involve modeling the distribution of natural images or noise and then using the model distribution before obtaining a clear image with an optimization algorithm, such as WNNM [13]. The learning-based methods are effective ways to reduce image noise. Usually, it can be divided into traditional and deep network-based methods. In recent years, due to the continuous development of the deep learning technology, deep network-based methods have achieved superior denoising results compared to previous methods, and thus", + "bbox": [ + 75, + 628, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "they have become the mainstream denoising methods. Generally, deep network-based methods can be further classified according to their training manners.", + "bbox": [ + 498, + 90, + 888, + 135 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Supervised Image Denoising", + "text_level": 1, + "bbox": [ + 498, + 146, + 754, + 161 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Most of the early works [24, 44, 31, 45, 46] assume that the noise is independent and uniformly distributed, and additive Gaussian white noise (AWGN) is usually used to model image noise and synthetic paired datasets. These methods achieve SOTA results on AWGN denoising tasks. However, the noise model in the real world is complex and unknown. Models trained with synthetic datasets are difficult to be applied to the real world. Recently, most of the methods [14, 2, 19, 41, 43, 6, 42, 29, 9] use produced real-world paired datasets for training. Due to the differences in camera parameters, these methods may not be widely used in the real world.", + "bbox": [ + 496, + 169, + 890, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Pseudo-Supervised Image denoising", + "text_level": 1, + "bbox": [ + 500, + 359, + 810, + 376 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The supervised denoising methods require paired noisy-clean images, while the pseudo-supervised denoising methods relax the data requirements. Noise2Noise [23] proposes that pairs of noisy images can be used to train the network when the noise mean is zero. When some unpaired noisy-clean images are available, some methods [8, 7, 15, 18] learn the noise distribution of noisy images by generative adversarial networks (GAN). Then, clean images are used to generate pseudo-paired noisy-clean images to train the denoising network. However, these methods are still difficult to be applied because the scene distribution of noisy images often does not match the available clean images [18].", + "bbox": [ + 496, + 383, + 890, + 565 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Self-Supervised Image Denoising", + "text_level": 1, + "bbox": [ + 500, + 575, + 785, + 590 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The self-supervised denoising methods require single noisy images for training. Noise2Void [20] finds that masking a portion of pixels in noisy images for pairing can train the denoising network, and thus proposes a BSN for self-supervised denoising. Laine19 [21] and D-BSN [36] further optimize the BSN and improve its performance. Noise2Same [37] and Blind2Unblind [35] propose new denoising losses for self-supervised training through mask-based blind-spot methods. Neighbor2Neighbor [17] samples the noisy image into two similar sub-images to form a noisy-noisy pair for training. CVF-SID [25] can disentangle the clean image, signal-dependent and signal-independent noises from the real-world noisy input via various self-supervised training objectives. AP-BSN [22] combines PD and BSN to process real-world sRGB noisy images and employs asymmetric PD stride factors for training and inference. However, current self-supervised methods for real noise removal usually still require a large number of noisy images and are challenging to train with less training data to achieve superior performance.", + "bbox": [ + 496, + 598, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12151", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 89, + 250, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Revisiting Noise2Void", + "text_level": 1, + "bbox": [ + 76, + 113, + 281, + 130 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Noise2Void (N2V) [20] requires only single noisy images for training, and it assumes that the noise $n$ is pixelwise independent (the noises at different pixel positions are independent) given the clean image $x$ . $y$ is the noisy image, i.e. $y = x + n$ . Due to the local correlation of the pixels within an image, clean central pixels can be estimated from the surrounding noisy pixels. Therefore, using the pixel of the noisy image as a target for its surrounding pixels will not obtain the noisy pixel. Thus, N2V can train the denoising network in a self-supervised approach. Specifically, N2V loss $L_{N2V}$ can be written as follows:", + "bbox": [ + 75, + 137, + 472, + 303 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {N 2 V} = E _ {y} \\left\\{\\| f \\left(y _ {r}\\right) - y _ {c} \\| _ {2} ^ {2} \\right\\}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 311, + 468, + 330 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $f(\\cdot)$ is the normal denoising network, $y_{r}$ is the patch of $y$ centered on $y_{c}$ with the same dimensions as the network receptive field. Note that $y_{r}$ does not contain $y_{c}$ .", + "bbox": [ + 75, + 340, + 468, + 385 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To facilitate the implementation of training with $L_{N2V}$ , N2V proposes BSN $B(\\cdot)$ capable of masking centroids. The noisy images used to train the BSN must satisfy the BSN assumption that the noise is pixel-wise independent and zero-mean. BSN can be trained by optimizing the following loss $L_{BSN}$ :", + "bbox": [ + 75, + 386, + 468, + 474 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {B S N} = E _ {y} \\left\\{\\left\\| B (y) - y \\right\\| _ {2} ^ {2} \\right\\}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 484, + 468, + 503 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$L_{N2V}$ and $L_{BSN}$ are equivalent for training BSN. For a known noise model (e.g. AWGN model), we can synthesize an infinite number of different noisy images. Thus, BSN can be easily trained. In contrast, since real image datasets often have a limited number of captured images, it is difficult to train BSN directly for real image denoising. Moreover, real images do not satisfy the pixel-wise independent noise assumptions of BSN. Therefore, the limitations of $L_{BSN}$ are significant, and it is not appropriate to use real images directly for BSN.", + "bbox": [ + 75, + 512, + 468, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. AP-BSN and Its Limitation", + "text_level": 1, + "bbox": [ + 76, + 672, + 321, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To make BSN better for the spatially correlated real image noise, AP-BSN [22] introduces PD [47] to break the spatial correlation among real noisy pixels, leading to near pixel-wise independent noise. Therefore, the real image after PD can be considered to meet the BSN assumption [22], and thus can be used as the input for BSN. The original APBSN loss is written as $\\left\\|PD^{-1}(B(PD(y))) - y\\right\\|_1$ , where $PD$ is the PD operator and $PD^{-1}$ is the inverse operator. To facilitate the analysis, we further write it as:", + "bbox": [ + 75, + 696, + 468, + 833 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {A P - B S N} = E _ {y} \\left\\{\\left\\| B (P D (y)) - P D (y) \\right\\| _ {1} \\right\\}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 843, + 468, + 862 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "It can be observed that the pattern of pairing is fixed in Eq. (3) (i.e. fixed $PD(y)$ to $PD(y)$ ). We consider that the", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/a27876a184f8c11ee31d92250432d741ef46b310430cd83183bc15fbde2d5a27.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetSet12BSD68Urban100
Fixed seed28.91/0.819227.26/0.747727.66/0.8172
Random seed29.36/0.839927.72/0.772828.81/0.8632
", + "bbox": [ + 519, + 88, + 874, + 148 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 1: The effect of different BSN training strategies on PSNR (dB)/SSIM.", + "bbox": [ + 498, + 156, + 890, + 186 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "training of fixed patterns does not affect the performance of BSN when the sample number is large enough. In contrast, it is well known that insufficient sample number may lead to overfitting [39]. Overfitting of noisy-clean pairing training can only have a superior effect on the training datasets and fail on other datasets. However, BSN requires noisy-noisy pairs for training. The overfitting of BSN will make the denoising result fit the noisy image and affect the denoising performance. For synthetic noise, because the noise modelling can generate an infinite number of noisy images, BSN can avoid fitting the noise, resulting in a clean image. But when BSN is used for real noise, real datasets tend to have a much smaller sample number than synthetic datasets. In this case, BSN may fail to get high-quality clean pixels.", + "bbox": [ + 496, + 212, + 890, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To verify the effect of the number of training images on the denoising results, we train BSN with synthetic images. In this way, we can synthesize any number of noisy images. We employ DIV2K dataset [32] and add Gaussian noise with a level $\\sigma = 25$ to synthesize noisy images. Two ways are adopted to train BSN with $L_{BSN}$ : (1) adding noise with fixed seed in each epoch, and (2) adding noise with random seed in each epoch. Then, we perform denoising experiments on the test datasets generated with Gaussian noise (Set12 [44], BSD68 [30], and Urban100 [16]). Table 1 shows the PSNR(dB) and SSIM results in the test datasets for different training strategies. We observe that when a limited number of noisy images (noisy images with fixed seeds) are used to train the BSN, the denoising performance degrades significantly. Therefore, the introduction of PD is practical. Still, considering that the training data of real images are often limited, the direct use of $L_{AP-BSN}$ may affect the denoising performance for real image denoising.", + "bbox": [ + 496, + 426, + 892, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Perturbation in BSN", + "text_level": 1, + "bbox": [ + 500, + 720, + 694, + 736 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In order to solve the above problems, we suggest adding perturbations to Eq. (3) to increase the number of training data and avoid fitting to the fixed pattern. We should ensure that the sub-images as inputs or targets remain consistent with the BSN assumption after adding perturbations. This is necessary for training the BSN using these sub-images for denoising purposes. A simple solution is using AWGN as the perturbation. Suppose $\\epsilon$ , $\\epsilon_{1}$ , and $\\epsilon_{2}$ are all perturbations of a Gaussian distribution with mean 0 and variance $\\sigma_{\\epsilon}^{2}$ . We propose three perturbation BSN losses $L_{PBSN_{1,2,3}}$", + "bbox": [ + 496, + 750, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12152", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/52989a3c797b92d9d8d1d7180206e0c397bfe720edf3252fdf102a4a17cab174.jpg", + "image_caption": [ + "Figure 2: Ablation study of $\\sigma_{\\epsilon}$ in $L_{PBSN_{1,2,3}}$ for training on the SIDD validation dataset [1]." + ], + "image_footnote": [], + "bbox": [ + 76, + 95, + 331, + 250 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9d69cdf5c784e2fb73ec2180f6f0be11c83be8abc637956d5681c61bb55457bb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 348, + 95, + 604, + 250 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/917afef4c8de27808351cc47a20aff06bbcd548ce7f0053b32d6643aae9bb3b0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 622, + 95, + 875, + 250 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f707db4f04ce4917a41ead15691d29397182d5a7e338ccddab8306202dec5f56.jpg", + "image_caption": [ + "Figure 3: Ablation study of $\\sigma_{\\epsilon}$ in $L_{PBSN_2}$ for training in different images." + ], + "image_footnote": [], + "bbox": [ + 86, + 292, + 460, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "as follows:", + "bbox": [ + 76, + 551, + 151, + 565 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {P B S N _ {1}} = E _ {y} \\left\\{\\left\\| B (P D (y) + \\epsilon) - P D (y) \\right\\| _ {1} \\right\\}, \\\\ L _ {P B S N _ {2}} = E _ {y} \\left\\{\\| B (P D (y)) - (P D (y) + \\epsilon) \\| _ {1} \\right\\}, \\tag {4} \\\\ L _ {P B S N _ {3}} = E _ {y} \\left\\{\\| B (P D (y) + \\epsilon_ {1}) - (P D (y) + \\epsilon_ {2}) \\| _ {1} \\right\\}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 575, + 468, + 632 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We test the effect of different variances of $\\epsilon$ or $(\\epsilon_{1},\\epsilon_{2})$ in Eq. (4) on the BSN training, and the results are shown in Figures 2 and 3. We observe that adding suitable perturbations can achieve improvements in BSN performance. Therefore, each of the losses in Eq. (4) fits our vision and can obtain a better BSN by training. In Section 4.3, we analyze the influence of perturbations in detail. The results in Figure 2 show that different perturbation levels' effects on BSN performance vary. The results in Figure 3 show that the appropriate optimal perturbation for different levels of noisy images also varies. Therefore, it is a challenge to choose the appropriate perturbation.", + "bbox": [ + 75, + 641, + 468, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Sampling Difference as Perturbation", + "text_level": 1, + "bbox": [ + 76, + 830, + 393, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "PD can produce a series of similar sub-images $(PD_{1}(y)$ , $PD_{2}(y)$ , ..., where $PD_{i}(\\cdot)$ denotes the $i$ -th sub-image obtained after PD). Since the PD sampling process does not", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/67121a6b1b4262ee1bd064b5f98878bea499944e46d985ac59dd8d03131edca2.jpg", + "image_caption": [ + "Figure 4: Results of sampling by different methods. The second row is the sampling difference obtained by subtracting the two sub-samples in the first row." + ], + "image_footnote": [], + "bbox": [ + 500, + 292, + 883, + 445 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "overlap, the pixels in the sub-images that are at the same position are not located at the same position in the original image. As a result, there are certain differences between these sub-images, which we refer to as sampling difference.", + "bbox": [ + 496, + 517, + 890, + 577 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on the previous analysis, it is evident that adding perturbation for training can enhance the performance of BSN, but how to add the appropriate perturbations is a challenge. Since there exists a sampling difference among the sub-images acquired through sampling, this difference can be viewed as a type of perturbation. First of all, according to [22], the sub-images obtained through PD sampling are naturally in line with the BSN assumption. Next, the difference between $PD_{1}(y)$ and $PD_{2}(y)$ can be considered as the perturbation, so we do not need to add additional perturbations as in Eq. (4). Therefore, $PD_{1}(y)$ and $PD_{2}(y)$ can be used as the input and target in the BSN training, respectively. Finally, we propose a new sampling difference BSN loss $L_{SDBSN}$ as follows:", + "bbox": [ + 496, + 578, + 892, + 789 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {S D B S N} = E _ {y} \\left\\{\\| B \\left(P D _ {1} (y)\\right) - P D _ {2} (y) \\| _ {1} \\right\\}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 797, + 890, + 815 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Random Sub-Samples Generation", + "text_level": 1, + "bbox": [ + 500, + 830, + 797, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The sampling difference generated by the PD strategy can be obtained by subtracting the two sub-images generated by the PD. The sub-images and the sampling difference", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12153", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5a9867a5838425102661ca3953fba7dffcbee5a30f5d659c79a5b9928866861d.jpg", + "image_caption": [ + "Figure 5: Example of generating sub-samples with RSG." + ], + "image_footnote": [], + "bbox": [ + 98, + 88, + 436, + 309 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d777ebf35cd49b5f436e9ee40c4ff4a63d423d9b5e4494b073a229806bc48190.jpg", + "image_caption": [ + "(a) SDAP" + ], + "image_footnote": [], + "bbox": [ + 81, + 340, + 171, + 411 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/714d4c0c98b9b44482049b67c07a9f0ef33793ae263aa2d55a7efb85febea54f.jpg", + "image_caption": [ + "Figure 6: Visual comparison between SDAP and SDAP (E)." + ], + "image_footnote": [], + "bbox": [ + 173, + 340, + 264, + 411 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/986fdd164fba912ead610f0337e258eacde0d0662bd10d4a34f1f65b969503c9.jpg", + "image_caption": [ + "(b) SDAP (E)" + ], + "image_footnote": [], + "bbox": [ + 274, + 340, + 364, + 411 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/88f183ad01f826b18d4e2ace78db7a458125faaf37986861699a4dd521455df4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 367, + 340, + 457, + 411 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "generated by PD are shown in Figure 4a. It can be observed that the sampling difference generated by PD is similar to the gradient map. Meanwhile, the PD strategy with a stride factor of $s$ can only generate $s^2$ fixed sub-images for the same image, which still faces the data-hungry issue for BSN training. To obtain more sub-samples and make the sampling difference closer to random perturbation, we propose the random sub-samples generation strategy (RSG).", + "bbox": [ + 75, + 465, + 467, + 585 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The diagram of sub-images generation with the RSG is shown in Figure 5. Assume that the noisy image $(y)$ length and width are $H$ and $W$ , respectively. The details of RSG are described below:", + "bbox": [ + 75, + 585, + 467, + 645 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Divide. The image $y$ is divided into $HW / s^2$ non-overlapping cells with size $s \\times s$ . Then, we stretch the cells into vectors of length $s^2$ . For better visualization, we set $s = 2$ in Figure 5.", + "2. Shuffle. Randomly shuffle the elements within each vector. Since this process is strictly random, the subsamples obtained are different each time.", + "3. Reform. Take the elements at the same position of each vector to form $s^2$ new vectors of length $HW / s^2$ .", + "4. Reshape. Reshape each vector into a sub-sample of size $[W / s] \\times [H / s]$ . In this way, $s^2$ similar sub-samples $(RSG_1(y), RSG_2(y), \\ldots, RSG_{s^2}(y))$ are obtained." + ], + "bbox": [ + 88, + 654, + 467, + 862 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To maximize the variance of each sub-sample, our sampling is non-overlapping.", + "bbox": [ + 76, + 869, + 467, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The sub-samples generated by the RSG strategy and their sampling difference is shown in Figure 4b. It can be observed that the use of RSG does make the sampling difference more random. Furthermore, we provide detailed analysis for this phenomenon. Both PD and RSG sample the image directly, so the calculation of the sampling difference can be considered as the deviation in the direction of the line connecting the sampling pixels of the two sub-samples. Since each pixel of the PD sub-sample has a fixed position in the original image, the difference has a fixed offset direction. Due to random sampling, the sampling difference of RSG sub-samples are not fixed in the direction of each pixel deviation, making the difference more random. In addition, as can also be seen from Figure 5, PD is equivalent to obtaining four fixed sub-images of yellow, blue, green and red. While RSG obtains random sub-images of $①②③④$ with different results for each sampling, which can provide a large number of samples for training. Therefore, RSG strategy can also be considered as a solution to the data-hungry issue of training BSN with real noisy images.", + "bbox": [ + 496, + 90, + 890, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Cyclic Sampling Difference BSN Loss", + "text_level": 1, + "bbox": [ + 500, + 402, + 823, + 419 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "According to Eq. (5), only two sub-samples are needed. However, because multiple sub-samples are generated by RSG, using the whole sub-images instead of only two samples in training can better utilize the features of the generated sub-samples, leading to higher performance. Moreover, if only two sub-samples are used for training, the loss of each training iteration will fluctuate seriously, and the training of BSN cannot converge. To preserve the stability of training and to make full use of each sample, we introduce the strategy of cyclic and RSG to propose a new cyclic samples difference BSN loss $L_{CSDBSN}$ :", + "bbox": [ + 496, + 426, + 890, + 592 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {C S D B S N} = \\sum_ {i = 1} ^ {s ^ {2}} \\underbrace {\\left\\| B \\left(R S G _ {i} (y)\\right) - R S G _ {i + 1} (y) \\right\\| _ {1}} _ {\\text {c r o s s - p a i r i n g}} \\tag {6} \\\\ (R S G _ {s ^ {2} + 1} (y) = R S G _ {1} (y)). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 604, + 890, + 674 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since the sub-samples are generated randomly, the training data is also random. The target corresponding to each input in $L_{CSDBSN}$ is different. Therefore, two sub-samples are avoided to form a fixed mapping during the cycle. This cyclic loss has the following merits: 1) it imposes constraints on the full pixel of the original noisy image; 2) it ensures that all the sub-samples generated by RSG are well exploited; 3) it makes the training of BSN more robust. Figure 7 visually illustrates our training scheme with the cyclic sampling difference BSN loss.", + "bbox": [ + 496, + 686, + 890, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.7. Proposed SDAP Framework", + "text_level": 1, + "bbox": [ + 500, + 847, + 753, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the training stage, we first sample the noisy images into $s^2$ sub-samples by RSG. Then, we denoise sub-samples", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12154", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/eeb438c784131578e87716403f4e0cd99def64150de071f3a8801fe180db714f.jpg", + "image_caption": [ + "Figure 7: Overview of our proposed SDAP framework." + ], + "image_footnote": [], + "bbox": [ + 133, + 87, + 831, + 258 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "by BSN. The loss is calculated by cross-pairing the subsamples after denoising with those before denoising. Finally, the above steps are iterated, and the loss function is updated to optimize the BSN until it converges. The training process is shown in the left half of Figure 7.", + "bbox": [ + 75, + 291, + 468, + 367 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the testing stage, due to the randomness of the single RSG, the test results are not fixed. Since the sampling pattern of PD is fixed, the test results are stable for testing. Therefore, for default setting, we directly adopt the strategy of PD. We denoise the sub-images after PD and then stitch them to obtain the final denoised image.", + "bbox": [ + 75, + 368, + 468, + 458 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The PD strategy is introduced in the testing stage to break the spatial correlation of real-world noise. However, this also makes the pixels of the denoised image discontinuous and produces checkerboard artifacts as shown in Figure 6a. To make the denoised image have better visual performance, we propose to denoise the initial denoised image again by BSN to remove the unpleasing artifacts. This performance enhancement method is denoted by \"SDAP (E)\" and is shown in the right half of Figure 7. The comparison of the final visual effect is shown in Figure 6b. The results show that our proposed test strategy can remove checkerboard artifacts and make the images more natural. More details about PD and RSG for testing are provided in Supplementary Material.", + "bbox": [ + 75, + 459, + 470, + 672 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 686, + 209, + 702 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 710, + 294, + 726 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use the general BSN architecture [36, 22] in our method. According to [22], we empirically set the stride factor $s$ of RSG to 5 for training. To ensure the stability of the test, we still use the PD with stride factor 2 for testing and ablation study. During the training, we use Adam as the optimizer with default settings. The initial learning rate is 0.0001, batch size and patch size are set to 16 and $160 \\times 160$ respectively, and epochs are taken as 15. 25600 patches are used in one epoch. To fine-tune the network, BSN continues to be optimised for 10 epochs. Meanwhile, we decay the learning rate by a factor of 10, reduce batch size to 8, and", + "bbox": [ + 75, + 734, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "adjust patch size to $250 \\times 250$ . We use PyTorch to implement our BSN and train it on an NVIDIA RTX 3090 GPU.", + "bbox": [ + 498, + 291, + 890, + 321 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Dataset", + "text_level": 1, + "bbox": [ + 500, + 330, + 594, + 344 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SIDD [1]. The SIDD dataset uses five representative mobile phone cameras to capture approximately 300,000 noisy images for 10 scenes under different lighting conditions and obtain the corresponding relatively clean images by specific statistical methods. The SIDD dataset provides an SIDD Medium dataset of 320 data pairs for training, an SIDD validation dataset of 1280 image blocks of size $256 \\times 256$ for validation, and an SIDD benchmark dataset of 40 high-resolution noisy images for testing.", + "bbox": [ + 496, + 352, + 890, + 489 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "DND [27]. The DND dataset contains 50 high-resolution test image pairs taken by consumer-grade cameras of various sensor sizes. However, because the images are too large, DND cropped all the images to $512 \\times 512$ image blocks, giving 1000 image blocks for testing. The DND dataset does not provide training images, and the clean images of the test dataset are not publicly available.", + "bbox": [ + 496, + 507, + 890, + 612 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Note that unless otherwise stated, we used SIDD Medium dataset for training in the following experiments.", + "bbox": [ + 498, + 612, + 890, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Analyzing Perturbation", + "text_level": 1, + "bbox": [ + 500, + 650, + 718, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first validate the effect of the perturbation in $L_{AP-BSN}$ for real-world sRGB image denoising. We train the BSN by $L_{PBSN_{1,2,3}}$ with different variances of $\\epsilon$ , i.e., $\\sigma_{\\epsilon} \\in \\{0,5,10,15,20,25\\}$ . Meanwhile, we also replace PD with RSG for a similar set of experiments. Figure 2 shows the PSNR(dB) results in the SIDD validation set.", + "bbox": [ + 498, + 674, + 890, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We observe that BSN performs best on SIDD validation dataset when $\\sigma_{\\epsilon} = 5$ for both PD and RSG. After this, the performance decreases as $\\sigma_{\\epsilon}$ increases. Specifically, for $L_{PBSN_{1,2,3}}$ , since the perturbation is added to the training data, when the perturbation is too large, it will significantly change the noise distribution of the training image, making it difficult for the BSN to adapt to the original noise. Therefore, the denoising performance of BSN decreases significantly when $\\sigma_{\\epsilon} > 15$ . Also, since RSG and perturbation", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12155", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e21e6ef90f8c2890378d137fa2c0ab6e064dffc60ad61e96120706b2cba2a39d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Type of supervisionTraining dataMethodSIDD validationSIDD benchmarkDND benchmark
Non-learning based-BM3D [12]31.75/0.706125.65/0.68534.51/0.8507
WNNM [13]26.31/0.524025.78/0.80934.67/0.8646
SupervisedPaired noisy-cleanDnCNN [44]26.20/0.441423.66/0.58332.43/0.7900
TNRD [10]26.99/0.744024.73/0.64333.65/0.8306
CBDNet [14]30.83/0.754133.28/0.86838.06/0.9421
RIDNet [2]38.76/0.913237.87/0.94339.25/0.9528
VDN [40]39.29/0.910939.26/0.95539.38/0.9518
Zhou et al. [47]-34.00/0.89838.40/0.945
DeamNet [28]39.40/0.916939.35/0.95539.63/0.9531
Pseudo-supervisedUnpaired noisy-cleanGCBD [8]--35.58/0.9217
D-BSN [36]--37.93/0.9373
C2N [18]35.36/0.890135.35/0.93737.28/0.9237
Paired noisy-noisyR2R [26]35.04/0.844034.78/0.89837.61/0.9368
Self-supervisedSingle noisyN2V [20]29.35/0.651027.68/0.668-
N2S [3]30.72/0.787029.56/0.808-
NAC [38]--36.20/0.9252
Neighbor2Neighbor [17]28.00/0.589027.96/0.67031.40/0.7880
CVF-SID [25]34.17/0.871934.71/0.91736.50/0.9233
AP-BSN [22]34.46/0.850134.90/0.90037.46/0.9244
SDAP (Ours)36.58/0.863036.54/0.91937.71/0.9278
SDAP (S) (Ours)36.71/0.864036.68/0.91938.18/0.9322
SDAP (E) (Ours)37.30/0.893737.24/0.93637.86/0.9366
SDAP (S)(E) (Ours)37.55/0.894337.53/0.93638.56/0.9402
", + "bbox": [ + 81, + 84, + 890, + 459 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2: Quantitative PSNR(dB)/SSIM Results on SIDD and DND Dataset.", + "bbox": [ + 233, + 468, + 733, + 484 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "have similar roles, both are designed to obtain more training data. When the perturbation is too large, the role of RSG is difficult to be reflected. Therefore, when the perturbation is small, the RSG strategy outperforms the PD strategy. When the perturbation is large, the RSG strategy and the PD strategy are used for BSN to obtain similar denoising results.", + "bbox": [ + 75, + 511, + 468, + 602 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In addition, we note that the most suitable perturbation standard deviation $\\sigma_{\\epsilon}$ is different for each of these images in Figure 3. Nevertheless, when we consider the sampling difference as the perturbation, the BSN performs the best regardless of the data. In Section 4.5, we analyze the sampling difference as perturbation in detail. Therefore, Eq. (6) is the final loss function of our proposed method.", + "bbox": [ + 75, + 603, + 470, + 709 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Denoising of Real Image", + "text_level": 1, + "bbox": [ + 76, + 724, + 302, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We use SIDD validation, SIDD benchmark, and DND benchmark datasets to evaluate the performance of our SDAP in real-world denoising tasks. For the SIDD validation dataset, because the paired noisy-clean images are provided, we can directly test the PSNR/SSIM results. For the SIDD and DND benchmarks, we submit the denoised images to websites for server-side evaluation to obtain the final results (PSNR/SSIM values). To evaluate our model on the three different datasets, we adopt two different strategies for training.", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training on SIDD Medium dataset. We train our self-supervised method with noisy images from the SIDD Medium dataset. Then, the obtained model is evaluated on different datasets. This training method is represented as \"SDAP\" in Table 2.", + "bbox": [ + 498, + 510, + 890, + 585 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training on test dataset. Since our method is fully self-supervised [25], instead of using the fixed SIDD Medium dataset for training, we can use the test images for self-supervised training as well. Therefore, we train our method on three test datasets in self-supervised manner, respectively. The trained models are evaluated with the corresponding test datasets. Since the noise distribution of training and test images are identical, this strategy can obtain a BSN model with better performance. Fully self-supervised training method is represented as \"SDAP (S)\" in Table 2.", + "bbox": [ + 496, + 611, + 890, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "It should be noted that \"(S)\" denotes the method to improve the performance in training, while \"(E)\" denotes the way to improve the performance in testing. Thus \"SDAP (S)(E)\" is the way in which the proposed method can achieve the best performance.", + "bbox": [ + 496, + 763, + 890, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The results in Table 2 show that this method achieves significantly better results than some traditional methods, such as BM3D, on the SIDD Benchmark test data. Even when compared with some supervised deep learning-based", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12156", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9cfb7647d011532775bf60b57b4a5ee9d664347ef50fb72735fe820143982045.jpg", + "image_caption": [ + "Noisy" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 176, + 311 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ed24440efac01904b610a71296cfc2eee3803bfafdd7c221d6e530cc401a4f49.jpg", + "image_caption": [ + "BM3D [12]" + ], + "image_footnote": [], + "bbox": [ + 181, + 88, + 277, + 311 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8291debe78c08100a3d8560c5edbe921c78190c7288511fb533af25db41a55e3.jpg", + "image_caption": [ + "DnCNN [44]" + ], + "image_footnote": [], + "bbox": [ + 282, + 88, + 380, + 311 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3da4a09e704a4c4e569d617a1c7694c3a849b646495eca68949639716d42d416.jpg", + "image_caption": [ + "CBDNet [14]" + ], + "image_footnote": [], + "bbox": [ + 383, + 88, + 480, + 311 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c7ae956ca553b0a608ad18b0e22b072b8d3be980abf7c9744476c633344559c3.jpg", + "image_caption": [ + "C2N [18]", + "Figure 8: Visual comparison of our method against other competing methods on the SIDD validation dataset [1]." + ], + "image_footnote": [], + "bbox": [ + 483, + 88, + 581, + 311 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/929760c5fddede94d0747ee7d0a6f06a7176a45d58c41f727a6f55c931880f29.jpg", + "image_caption": [ + "CVF-SID [25]" + ], + "image_footnote": [], + "bbox": [ + 586, + 88, + 681, + 311 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bbb5cf7db6ad6f385ef9e2bef352343029f09b4fa349573157dd04134fd86d85.jpg", + "image_caption": [ + "AP-BSN [22]" + ], + "image_footnote": [], + "bbox": [ + 686, + 88, + 782, + 311 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d2a73886287ba5d0254473b6d3a0d92c74534be7ccb335620b587dde35cd9141.jpg", + "image_caption": [ + "SDAP (S)(E) (Ours)" + ], + "image_footnote": [], + "bbox": [ + 787, + 88, + 885, + 311 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9d7c6af67e8d07089291ef569319f695a8ef9b5950415d8ce81389bd906abaf5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
PDRSG\\( L_{AP-BSN} \\)\\( L_{CSDBSN} \\)PSNR(dB)/SSIM
✓-✓-35.68/0.8382
✓--✓36.19/0.8472
-✓✓-36.03/0.8533
-✓-✓36.58/0.8630
", + "bbox": [ + 84, + 369, + 460, + 463 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3: Investigation of RSG and $L_{CSDBSN}$ on SIDD Validation Dataset.", + "bbox": [ + 75, + 470, + 467, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "image denoising methods, this method achieves superior denoising results. For example, the PSNR and SSIM results of this method are 3.40dB and 0.051 higher compared with CBDNet. When we compared with the SOTA self-supervised image denoising approaches, our method also has obvious advantages. For example, compared with APBSN, which has the same network structure as us, SDAP achieves 1.78dB and 0.019 increases in PSNR and SSIM metrics, respectively. The performance of SDAP on the DND dataset has similar findings as those on SIDD. Figures 1 and 8 provide visual comparisons of several methods, and the results further validate the visual superiority of our method to other methods.", + "bbox": [ + 75, + 531, + 468, + 727 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 739, + 228, + 757 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We examine two major determinants of our model: a) RSG; b) $L_{CSDBSN}$ . If there is a \"√\" in the column of $L_{CSDBSN}$ (or $L_{APBSN}$ ), it means that $L_{CSDBSN}$ (or $L_{APBSN}$ ) is used for training, and vice versa. If there is a \"√\" in the column of RSG, it means that the RSG strategy is used for training, and we replace all $PD$ in the loss with $RSG$ . If there is a \"√\" in the column of PD, it means that the PD strategy is used for training, and we replace all $RSG$ in the loss with $PD$ .", + "bbox": [ + 75, + 763, + 468, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Study of RSG. The performance of training with RSG in Table 3 is always higher than training with PD. A comparison between the first and third rows of Table 3 shows that replacing PD with RSG increases the PSNR/SSIM result by $0.35\\mathrm{dB} / 0.0151$ . The comparison between the second and fourth rows shows a similar conclusion. These results verify the effectiveness for RSG.", + "bbox": [ + 496, + 372, + 890, + 479 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Study of $L_{CSDBSN}$ . Rows 2 and 4 of Table 3 show the effect of our proposed $L_{CSDBSN}$ , where our proposed loss improves the denoising performance by 0.51dB/0.0090 in the case of training with PD and 0.55dB/0.0097 in the case of training with RSG. It is worth noting that, irrespective of whether PD or RSG is used in $L_{CSDBSN}$ for BSN training, the performance of BSN is superior to that achieved by directly adding Gaussian perturbations in $L_{AP-BSN}$ (i.e., using $L_{CSDBSN}$ for training is better than using $L_{PBSN_{1,2,3}}$ ).", + "bbox": [ + 496, + 496, + 892, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 645, + 617, + 660 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we first analyze the reasons for the limited performance of BSN when used for real image denoising. Based on this, we propose to add perturbations to the training data and consider sampling difference as perturbation. Further, we propose SDAP framework with random sub-samples generation and cyclic sampling difference loss. Our SDAP does not require clean images for training and outperforms existing pseudo-supervised/self-supervised methods. We believe that our approach can provide promising inspirations for various self-supervised real-world denoising methods.", + "bbox": [ + 496, + 670, + 890, + 837 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work was supported by the National Natural Science Foundation of China under Grant 62171304.", + "bbox": [ + 496, + 854, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12157", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S Brown. A high-quality denoising dataset for smartphone cameras. In CVPR, pages 1692-1700, 2018.", + "[2] Saeed Anwar and Nick Barnes. Real image denoising with feature attention. 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In AAAI, volume 34, pages 13074-13081, 2020." + ], + "bbox": [ + 501, + 92, + 890, + 401 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "12159", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Random Sub-Samples Generation for Self-Supervised Real Image Denoising/0ac3ef7d-9ebc-4369-9f12-6e7b6e92e896_model.json b/2023/Random Sub-Samples Generation for Self-Supervised Real Image Denoising/0ac3ef7d-9ebc-4369-9f12-6e7b6e92e896_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8a82953ba38ba259c147d3c36a85605caf91a70e --- /dev/null +++ b/2023/Random Sub-Samples Generation for Self-Supervised Real Image Denoising/0ac3ef7d-9ebc-4369-9f12-6e7b6e92e896_model.json @@ -0,0 +1,2431 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.101, + 0.131, + 0.872, + 0.154 + ], + "angle": 0, + "content": "Random Sub-Samples Generation for Self-Supervised Real Image Denoising" + }, + { + "type": "text", + "bbox": [ + 0.183, + 0.18, + 0.784, + 0.199 + ], + "angle": 0, + "content": "Yizhong Pan\\(^{1}\\), Xiao Liu\\(^{1}\\), Xiangyu Liao\\(^{1}\\), Yuanzhouhan Cao\\(^{2}\\), Chao Ren\\(^{1(\\boxtimes)}\\)" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.199, + 0.803, + 0.217 + ], + "angle": 0, + "content": "1College of Electronics and Information Engineering, Sichuan University, China" + }, + { + "type": "text", + "bbox": [ + 0.146, + 0.217, + 0.824, + 0.235 + ], + "angle": 0, + "content": "\\(^{2}\\)School of Computer and Information Technology, Beijing Jiaotong University, China" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.237, + 0.868, + 0.252 + ], + "angle": 0, + "content": "{panyizhong, liux, liaoxiangyul}@stu.scu.edu.cn, yzhcao@bjtu.edu.cn, chaoren@scu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.319, + 0.474, + 0.713 + ], + "angle": 0, + "content": "With sufficient paired training samples, the supervised deep learning methods have attracted much attention in image denoising because of their superior performance. However, it is still very challenging to widely utilize the supervised methods in real cases due to the lack of paired noisy-clean images. Meanwhile, most self-supervised denoising methods are ineffective as well when applied to the real-world denoising tasks because of their strict assumptions in applications. For example, as a typical method for self-supervised denoising, the original blind spot network (BSN) assumes that the noise is pixel-wise independent, which is much different from the real cases. To solve this problem, we propose a novel self-supervised real image denoising framework named Sampling Difference As Perturbation (SDAP) based on Random Sub-samples Generation (RSG) with a cyclic sample difference loss. Specifically, we dig deeper into the properties of BSN to make it more suitable for real noise. Surprisingly, we find that adding an appropriate perturbation to the training images can effectively improve the performance of BSN. Further, we propose that the sampling difference can be considered as perturbation to achieve better results. Finally we propose a new BSN framework in combination with our RSG strategy. The results show that it significantly outperforms other state-of-the-art self-supervised denoising methods on real-world datasets. The code is available at https://github.com/p1y2z3/SDAP." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.743, + 0.21, + 0.759 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.77, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Image denoising is a hot topic in low-level vision tasks, aiming to obtain high-quality images from noisy versions. In recent years, learning-based methods have been widely used in image denoising with their superior performance. Thanks to the construction of paired image datasets, the supervised approaches [44, 2, 28, 11, 33, 34] can be efficiently implemented. In these approaches, it is a common practice" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.285, + 0.63, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.556, + 0.381, + 0.584, + 0.39 + ], + "angle": 0, + "content": "Noisy" + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.285, + 0.758, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.665, + 0.381, + 0.728, + 0.39 + ], + "angle": 0, + "content": "CBDNet [14]" + }, + { + "type": "image", + "bbox": [ + 0.763, + 0.285, + 0.886, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.801, + 0.381, + 0.846, + 0.39 + ], + "angle": 0, + "content": "C2N [18]" + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.39, + 0.628, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.533, + 0.484, + 0.601, + 0.495 + ], + "angle": 0, + "content": "CVF-SID [25]" + }, + { + "type": "image", + "bbox": [ + 0.632, + 0.39, + 0.755, + 0.483 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.663, + 0.484, + 0.726, + 0.495 + ], + "angle": 0, + "content": "AP-BSN [22]" + }, + { + "type": "image", + "bbox": [ + 0.762, + 0.39, + 0.884, + 0.483 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.773, + 0.484, + 0.872, + 0.495 + ], + "angle": 0, + "content": "SDAP (S)(E) (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.502, + 0.892, + 0.518 + ], + "angle": 0, + "content": "Figure 1: Real-world image denoising results on DND [27]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.538, + 0.892, + 0.583 + ], + "angle": 0, + "content": "to synthesize paired datasets directly using a specific noise model, such as the signal-independent additive white Gaussian noise (AWGN) model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.893, + 0.765 + ], + "angle": 0, + "content": "However, the real images are captured by cameras with image signal processing (ISP) pipelines [4]. The noise is usually signal-dependent and spatially correlated in the real world. Moreover, ISP includes many non-linear operations that can complicate the noise distribution. Due to the influence of ISP pipelines within the camera, the noise distribution of real images is difficult to predict. Therefore, it is difficult and challenging for us to model the noise for real images. To overcome the problem of directly and explicitly modelling noise distribution, paired real-world datasets have been constructed by researchers. However, collecting paired noisy-clean images is difficult and time-expensive." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.766, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Recently, a series of unsupervised and self-supervised methods have been introduced. These methods do not require paired datasets for training, and thus further avoiding the difficulty of collecting real-world paired datasets for denoising. Among them, Noise2Void [20] proposes Blind-Spot Network (BSN) that can be trained with only single noisy images. Unfortunately, BSN has strict assumptions, which can only be applied to pixel-wise independent noise. AP-BSN [22] applies pixel-shuffle downsampling" + }, + { + "type": "page_footnote", + "bbox": [ + 0.091, + 0.887, + 0.225, + 0.9 + ], + "angle": 0, + "content": "Corresponding Author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12150" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.226 + ], + "angle": 0, + "content": "(PD) strategy [47] to BSN, remove the spatial correlation in the real-world noise, and thus the real image can also meet the conditions for BSN to some extent. However, real noisy datasets usually have relatively limited numbers of samples. AP-BSN directly adopts the strategy of PD, which can only obtain \\( s^2 \\) sub-images for a noisy image (the stride factor of PD is \\( s \\)). This will inevitably lead to the insufficient samples, and make the training of BSN less effective. Therefore, the optimal performance of BSN cannot be achieved." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.468, + 0.379 + ], + "angle": 0, + "content": "We observe that adding some perturbations to the training images can greatly expand the training data, which improves the performance of BSN. Further, we consider the samples difference as the perturbation. To obtain more random perturbations and more sub-samples, we propose random sub-samples generation (RSG) strategy to break the fixed sampling pattern of PD. Based on this, we propose a new cyclic sampling difference loss for BSN and a new BSN framework in combination with our RSG strategy. In summary, our contributions include:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.392, + 0.468, + 0.466 + ], + "angle": 0, + "content": "- We provide a new idea about adding perturbations to the training data to improve the BSN performance. Then, we suggest that the sub-samples difference generated by sampling can be considered as perturbations for higher performance." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.482, + 0.468, + 0.526 + ], + "angle": 0, + "content": "- We propose a new self-supervised framework for real image denoising with random sub-samples generation and cyclic sampling difference loss." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.541, + 0.468, + 0.584 + ], + "angle": 0, + "content": "- Our method performs very favorably against state-of-the-art (SOTA) self-supervised denoising methods on real-world datasets." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.392, + 0.468, + 0.584 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.603, + 0.218, + 0.618 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.468, + 0.899 + ], + "angle": 0, + "content": "The image denoising task aims to restore a clean image from its noisy counterpart. There are two main types of non-learning-based image denoising: filtering-based methods and model-based methods. Filter-based methods involve using some artificially designed low-pass filter to remove image noise. Taking advantage of the condition of having many similar image blocks in the same image, noise can also be removed by the local similarity of image, such as NLM [5], BM3D [12], etc. Model-based methods involve modeling the distribution of natural images or noise and then using the model distribution before obtaining a clear image with an optimization algorithm, such as WNNM [13]. The learning-based methods are effective ways to reduce image noise. Usually, it can be divided into traditional and deep network-based methods. In recent years, due to the continuous development of the deep learning technology, deep network-based methods have achieved superior denoising results compared to previous methods, and thus" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.89, + 0.136 + ], + "angle": 0, + "content": "they have become the mainstream denoising methods. Generally, deep network-based methods can be further classified according to their training manners." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.147, + 0.755, + 0.162 + ], + "angle": 0, + "content": "2.1. Supervised Image Denoising" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.17, + 0.892, + 0.35 + ], + "angle": 0, + "content": "Most of the early works [24, 44, 31, 45, 46] assume that the noise is independent and uniformly distributed, and additive Gaussian white noise (AWGN) is usually used to model image noise and synthetic paired datasets. These methods achieve SOTA results on AWGN denoising tasks. However, the noise model in the real world is complex and unknown. Models trained with synthetic datasets are difficult to be applied to the real world. Recently, most of the methods [14, 2, 19, 41, 43, 6, 42, 29, 9] use produced real-world paired datasets for training. Due to the differences in camera parameters, these methods may not be widely used in the real world." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.361, + 0.811, + 0.377 + ], + "angle": 0, + "content": "2.2. Pseudo-Supervised Image denoising" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.892, + 0.566 + ], + "angle": 0, + "content": "The supervised denoising methods require paired noisy-clean images, while the pseudo-supervised denoising methods relax the data requirements. Noise2Noise [23] proposes that pairs of noisy images can be used to train the network when the noise mean is zero. When some unpaired noisy-clean images are available, some methods [8, 7, 15, 18] learn the noise distribution of noisy images by generative adversarial networks (GAN). Then, clean images are used to generate pseudo-paired noisy-clean images to train the denoising network. However, these methods are still difficult to be applied because the scene distribution of noisy images often does not match the available clean images [18]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.576, + 0.787, + 0.591 + ], + "angle": 0, + "content": "2.3. Self-Supervised Image Denoising" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The self-supervised denoising methods require single noisy images for training. Noise2Void [20] finds that masking a portion of pixels in noisy images for pairing can train the denoising network, and thus proposes a BSN for self-supervised denoising. Laine19 [21] and D-BSN [36] further optimize the BSN and improve its performance. Noise2Same [37] and Blind2Unblind [35] propose new denoising losses for self-supervised training through mask-based blind-spot methods. Neighbor2Neighbor [17] samples the noisy image into two similar sub-images to form a noisy-noisy pair for training. CVF-SID [25] can disentangle the clean image, signal-dependent and signal-independent noises from the real-world noisy input via various self-supervised training objectives. AP-BSN [22] combines PD and BSN to process real-world sRGB noisy images and employs asymmetric PD stride factors for training and inference. However, current self-supervised methods for real noise removal usually still require a large number of noisy images and are challenging to train with less training data to achieve superior performance." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12151" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.251, + 0.108 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.114, + 0.282, + 0.131 + ], + "angle": 0, + "content": "3.1. Revisiting Noise2Void" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.473, + 0.304 + ], + "angle": 0, + "content": "Noise2Void (N2V) [20] requires only single noisy images for training, and it assumes that the noise \\( n \\) is pixelwise independent (the noises at different pixel positions are independent) given the clean image \\( x \\). \\( y \\) is the noisy image, i.e. \\( y = x + n \\). Due to the local correlation of the pixels within an image, clean central pixels can be estimated from the surrounding noisy pixels. Therefore, using the pixel of the noisy image as a target for its surrounding pixels will not obtain the noisy pixel. Thus, N2V can train the denoising network in a self-supervised approach. Specifically, N2V loss \\( L_{N2V} \\) can be written as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.171, + 0.313, + 0.47, + 0.332 + ], + "angle": 0, + "content": "\\[\nL _ {N 2 V} = E _ {y} \\left\\{\\| f \\left(y _ {r}\\right) - y _ {c} \\| _ {2} ^ {2} \\right\\}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.341, + 0.47, + 0.386 + ], + "angle": 0, + "content": "where \\( f(\\cdot) \\) is the normal denoising network, \\( y_{r} \\) is the patch of \\( y \\) centered on \\( y_{c} \\) with the same dimensions as the network receptive field. Note that \\( y_{r} \\) does not contain \\( y_{c} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.387, + 0.47, + 0.476 + ], + "angle": 0, + "content": "To facilitate the implementation of training with \\(L_{N2V}\\), N2V proposes BSN \\(B(\\cdot)\\) capable of masking centroids. The noisy images used to train the BSN must satisfy the BSN assumption that the noise is pixel-wise independent and zero-mean. BSN can be trained by optimizing the following loss \\(L_{BSN}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.485, + 0.47, + 0.505 + ], + "angle": 0, + "content": "\\[\nL _ {B S N} = E _ {y} \\left\\{\\left\\| B (y) - y \\right\\| _ {2} ^ {2} \\right\\}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.513, + 0.47, + 0.665 + ], + "angle": 0, + "content": "\\(L_{N2V}\\) and \\(L_{BSN}\\) are equivalent for training BSN. For a known noise model (e.g. AWGN model), we can synthesize an infinite number of different noisy images. Thus, BSN can be easily trained. In contrast, since real image datasets often have a limited number of captured images, it is difficult to train BSN directly for real image denoising. Moreover, real images do not satisfy the pixel-wise independent noise assumptions of BSN. Therefore, the limitations of \\(L_{BSN}\\) are significant, and it is not appropriate to use real images directly for BSN." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.673, + 0.323, + 0.688 + ], + "angle": 0, + "content": "3.2. AP-BSN and Its Limitation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.697, + 0.47, + 0.834 + ], + "angle": 0, + "content": "To make BSN better for the spatially correlated real image noise, AP-BSN [22] introduces PD [47] to break the spatial correlation among real noisy pixels, leading to near pixel-wise independent noise. Therefore, the real image after PD can be considered to meet the BSN assumption [22], and thus can be used as the input for BSN. The original APBSN loss is written as \\(\\left\\|PD^{-1}(B(PD(y))) - y\\right\\|_1\\), where \\(PD\\) is the PD operator and \\(PD^{-1}\\) is the inverse operator. To facilitate the analysis, we further write it as:" + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.844, + 0.469, + 0.863 + ], + "angle": 0, + "content": "\\[\nL _ {A P - B S N} = E _ {y} \\left\\{\\left\\| B (P D (y)) - P D (y) \\right\\| _ {1} \\right\\}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "It can be observed that the pattern of pairing is fixed in Eq. (3) (i.e. fixed \\( PD(y) \\) to \\( PD(y) \\)). We consider that the" + }, + { + "type": "table", + "bbox": [ + 0.52, + 0.089, + 0.875, + 0.149 + ], + "angle": 0, + "content": "
DatasetSet12BSD68Urban100
Fixed seed28.91/0.819227.26/0.747727.66/0.8172
Random seed29.36/0.839927.72/0.772828.81/0.8632
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.157, + 0.892, + 0.187 + ], + "angle": 0, + "content": "Table 1: The effect of different BSN training strategies on PSNR (dB)/SSIM." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.213, + 0.892, + 0.424 + ], + "angle": 0, + "content": "training of fixed patterns does not affect the performance of BSN when the sample number is large enough. In contrast, it is well known that insufficient sample number may lead to overfitting [39]. Overfitting of noisy-clean pairing training can only have a superior effect on the training datasets and fail on other datasets. However, BSN requires noisy-noisy pairs for training. The overfitting of BSN will make the denoising result fit the noisy image and affect the denoising performance. For synthetic noise, because the noise modelling can generate an infinite number of noisy images, BSN can avoid fitting the noise, resulting in a clean image. But when BSN is used for real noise, real datasets tend to have a much smaller sample number than synthetic datasets. In this case, BSN may fail to get high-quality clean pixels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.428, + 0.893, + 0.701 + ], + "angle": 0, + "content": "To verify the effect of the number of training images on the denoising results, we train BSN with synthetic images. In this way, we can synthesize any number of noisy images. We employ DIV2K dataset [32] and add Gaussian noise with a level \\(\\sigma = 25\\) to synthesize noisy images. Two ways are adopted to train BSN with \\(L_{BSN}\\): (1) adding noise with fixed seed in each epoch, and (2) adding noise with random seed in each epoch. Then, we perform denoising experiments on the test datasets generated with Gaussian noise (Set12 [44], BSD68 [30], and Urban100 [16]). Table 1 shows the PSNR(dB) and SSIM results in the test datasets for different training strategies. We observe that when a limited number of noisy images (noisy images with fixed seeds) are used to train the BSN, the denoising performance degrades significantly. Therefore, the introduction of PD is practical. Still, considering that the training data of real images are often limited, the direct use of \\(L_{AP-BSN}\\) may affect the denoising performance for real image denoising." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.722, + 0.695, + 0.737 + ], + "angle": 0, + "content": "3.3. Perturbation in BSN" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.903 + ], + "angle": 0, + "content": "In order to solve the above problems, we suggest adding perturbations to Eq. (3) to increase the number of training data and avoid fitting to the fixed pattern. We should ensure that the sub-images as inputs or targets remain consistent with the BSN assumption after adding perturbations. This is necessary for training the BSN using these sub-images for denoising purposes. A simple solution is using AWGN as the perturbation. Suppose \\(\\epsilon\\), \\(\\epsilon_{1}\\), and \\(\\epsilon_{2}\\) are all perturbations of a Gaussian distribution with mean 0 and variance \\(\\sigma_{\\epsilon}^{2}\\). We propose three perturbation BSN losses \\(L_{PBSN_{1,2,3}}\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12152" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.096, + 0.332, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.349, + 0.096, + 0.605, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.624, + 0.097, + 0.876, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.179, + 0.255, + 0.788, + 0.271 + ], + "angle": 0, + "content": "Figure 2: Ablation study of \\(\\sigma_{\\epsilon}\\) in \\(L_{PBSN_{1,2,3}}\\) for training on the SIDD validation dataset [1]." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.293, + 0.462, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.496, + 0.47, + 0.527 + ], + "angle": 0, + "content": "Figure 3: Ablation study of \\(\\sigma_{\\epsilon}\\) in \\(L_{PBSN_2}\\) for training in different images." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.553, + 0.152, + 0.566 + ], + "angle": 0, + "content": "as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.577, + 0.47, + 0.633 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {P B S N _ {1}} = E _ {y} \\left\\{\\left\\| B (P D (y) + \\epsilon) - P D (y) \\right\\| _ {1} \\right\\}, \\\\ L _ {P B S N _ {2}} = E _ {y} \\left\\{\\| B (P D (y)) - (P D (y) + \\epsilon) \\| _ {1} \\right\\}, \\tag {4} \\\\ L _ {P B S N _ {3}} = E _ {y} \\left\\{\\| B (P D (y) + \\epsilon_ {1}) - (P D (y) + \\epsilon_ {2}) \\| _ {1} \\right\\}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.47, + 0.824 + ], + "angle": 0, + "content": "We test the effect of different variances of \\(\\epsilon\\) or \\((\\epsilon_{1},\\epsilon_{2})\\) in Eq. (4) on the BSN training, and the results are shown in Figures 2 and 3. We observe that adding suitable perturbations can achieve improvements in BSN performance. Therefore, each of the losses in Eq. (4) fits our vision and can obtain a better BSN by training. In Section 4.3, we analyze the influence of perturbations in detail. The results in Figure 2 show that different perturbation levels' effects on BSN performance vary. The results in Figure 3 show that the appropriate optimal perturbation for different levels of noisy images also varies. Therefore, it is a challenge to choose the appropriate perturbation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.395, + 0.849 + ], + "angle": 0, + "content": "3.4. Sampling Difference as Perturbation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "PD can produce a series of similar sub-images \\((PD_{1}(y)\\), \\(PD_{2}(y)\\), ..., where \\(PD_{i}(\\cdot)\\) denotes the \\(i\\)-th sub-image obtained after PD). Since the PD sampling process does not" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.293, + 0.885, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.449, + 0.892, + 0.494 + ], + "angle": 0, + "content": "Figure 4: Results of sampling by different methods. The second row is the sampling difference obtained by subtracting the two sub-samples in the first row." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.892, + 0.578 + ], + "angle": 0, + "content": "overlap, the pixels in the sub-images that are at the same position are not located at the same position in the original image. As a result, there are certain differences between these sub-images, which we refer to as sampling difference." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.579, + 0.893, + 0.79 + ], + "angle": 0, + "content": "Based on the previous analysis, it is evident that adding perturbation for training can enhance the performance of BSN, but how to add the appropriate perturbations is a challenge. Since there exists a sampling difference among the sub-images acquired through sampling, this difference can be viewed as a type of perturbation. First of all, according to [22], the sub-images obtained through PD sampling are naturally in line with the BSN assumption. Next, the difference between \\(PD_{1}(y)\\) and \\(PD_{2}(y)\\) can be considered as the perturbation, so we do not need to add additional perturbations as in Eq. (4). Therefore, \\(PD_{1}(y)\\) and \\(PD_{2}(y)\\) can be used as the input and target in the BSN training, respectively. Finally, we propose a new sampling difference BSN loss \\(L_{SDBSN}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.799, + 0.891, + 0.816 + ], + "angle": 0, + "content": "\\[\nL _ {S D B S N} = E _ {y} \\left\\{\\| B \\left(P D _ {1} (y)\\right) - P D _ {2} (y) \\| _ {1} \\right\\}. \\tag {5}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.798, + 0.849 + ], + "angle": 0, + "content": "3.5. Random Sub-Samples Generation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The sampling difference generated by the PD strategy can be obtained by subtracting the two sub-images generated by the PD. The sub-images and the sampling difference" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12153" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.089, + 0.437, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.085, + 0.313, + 0.461, + 0.328 + ], + "angle": 0, + "content": "Figure 5: Example of generating sub-samples with RSG." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.341, + 0.172, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.144, + 0.417, + 0.204, + 0.43 + ], + "angle": 0, + "content": "(a) SDAP" + }, + { + "type": "image", + "bbox": [ + 0.174, + 0.341, + 0.266, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.341, + 0.365, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.368, + 0.342, + 0.459, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.326, + 0.417, + 0.408, + 0.431 + ], + "angle": 0, + "content": "(b) SDAP (E)" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.433, + 0.468, + 0.448 + ], + "angle": 0, + "content": "Figure 6: Visual comparison between SDAP and SDAP (E)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.468, + 0.587 + ], + "angle": 0, + "content": "generated by PD are shown in Figure 4a. It can be observed that the sampling difference generated by PD is similar to the gradient map. Meanwhile, the PD strategy with a stride factor of \\( s \\) can only generate \\( s^2 \\) fixed sub-images for the same image, which still faces the data-hungry issue for BSN training. To obtain more sub-samples and make the sampling difference closer to random perturbation, we propose the random sub-samples generation strategy (RSG)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.587, + 0.468, + 0.646 + ], + "angle": 0, + "content": "The diagram of sub-images generation with the RSG is shown in Figure 5. Assume that the noisy image \\((y)\\) length and width are \\(H\\) and \\(W\\), respectively. The details of RSG are described below:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.655, + 0.468, + 0.716 + ], + "angle": 0, + "content": "1. Divide. The image \\( y \\) is divided into \\( HW / s^2 \\) non-overlapping cells with size \\( s \\times s \\). Then, we stretch the cells into vectors of length \\( s^2 \\). For better visualization, we set \\( s = 2 \\) in Figure 5." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.724, + 0.468, + 0.769 + ], + "angle": 0, + "content": "2. Shuffle. Randomly shuffle the elements within each vector. Since this process is strictly random, the subsamples obtained are different each time." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.779, + 0.468, + 0.809 + ], + "angle": 0, + "content": "3. Reform. Take the elements at the same position of each vector to form \\( s^2 \\) new vectors of length \\( HW / s^2 \\)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.818, + 0.468, + 0.863 + ], + "angle": 0, + "content": "4. Reshape. Reshape each vector into a sub-sample of size \\([W / s] \\times [H / s]\\). In this way, \\(s^2\\) similar sub-samples \\((RSG_1(y), RSG_2(y), \\ldots, RSG_{s^2}(y))\\) are obtained." + }, + { + "type": "list", + "bbox": [ + 0.089, + 0.655, + 0.468, + 0.863 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.902 + ], + "angle": 0, + "content": "To maximize the variance of each sub-sample, our sampling is non-overlapping." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.394 + ], + "angle": 0, + "content": "The sub-samples generated by the RSG strategy and their sampling difference is shown in Figure 4b. It can be observed that the use of RSG does make the sampling difference more random. Furthermore, we provide detailed analysis for this phenomenon. Both PD and RSG sample the image directly, so the calculation of the sampling difference can be considered as the deviation in the direction of the line connecting the sampling pixels of the two sub-samples. Since each pixel of the PD sub-sample has a fixed position in the original image, the difference has a fixed offset direction. Due to random sampling, the sampling difference of RSG sub-samples are not fixed in the direction of each pixel deviation, making the difference more random. In addition, as can also be seen from Figure 5, PD is equivalent to obtaining four fixed sub-images of yellow, blue, green and red. While RSG obtains random sub-images of \\(①②③④\\) with different results for each sampling, which can provide a large number of samples for training. Therefore, RSG strategy can also be considered as a solution to the data-hungry issue of training BSN with real noisy images." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.403, + 0.824, + 0.42 + ], + "angle": 0, + "content": "3.6. Cyclic Sampling Difference BSN Loss" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.427, + 0.892, + 0.593 + ], + "angle": 0, + "content": "According to Eq. (5), only two sub-samples are needed. However, because multiple sub-samples are generated by RSG, using the whole sub-images instead of only two samples in training can better utilize the features of the generated sub-samples, leading to higher performance. Moreover, if only two sub-samples are used for training, the loss of each training iteration will fluctuate seriously, and the training of BSN cannot converge. To preserve the stability of training and to make full use of each sample, we introduce the strategy of cyclic and RSG to propose a new cyclic samples difference BSN loss \\( L_{CSDBSN} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.605, + 0.891, + 0.675 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {C S D B S N} = \\sum_ {i = 1} ^ {s ^ {2}} \\underbrace {\\left\\| B \\left(R S G _ {i} (y)\\right) - R S G _ {i + 1} (y) \\right\\| _ {1}} _ {\\text {c r o s s - p a i r i n g}} \\tag {6} \\\\ (R S G _ {s ^ {2} + 1} (y) = R S G _ {1} (y)). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.892, + 0.837 + ], + "angle": 0, + "content": "Since the sub-samples are generated randomly, the training data is also random. The target corresponding to each input in \\( L_{CSDBSN} \\) is different. Therefore, two sub-samples are avoided to form a fixed mapping during the cycle. This cyclic loss has the following merits: 1) it imposes constraints on the full pixel of the original noisy image; 2) it ensures that all the sub-samples generated by RSG are well exploited; 3) it makes the training of BSN more robust. Figure 7 visually illustrates our training scheme with the cyclic sampling difference BSN loss." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.754, + 0.864 + ], + "angle": 0, + "content": "3.7. Proposed SDAP Framework" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "For the training stage, we first sample the noisy images into \\( s^2 \\) sub-samples by RSG. Then, we denoise sub-samples" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12154" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.088, + 0.833, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.302, + 0.262, + 0.668, + 0.277 + ], + "angle": 0, + "content": "Figure 7: Overview of our proposed SDAP framework." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.292, + 0.47, + 0.368 + ], + "angle": 0, + "content": "by BSN. The loss is calculated by cross-pairing the subsamples after denoising with those before denoising. Finally, the above steps are iterated, and the loss function is updated to optimize the BSN until it converges. The training process is shown in the left half of Figure 7." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.369, + 0.47, + 0.459 + ], + "angle": 0, + "content": "For the testing stage, due to the randomness of the single RSG, the test results are not fixed. Since the sampling pattern of PD is fixed, the test results are stable for testing. Therefore, for default setting, we directly adopt the strategy of PD. We denoise the sub-images after PD and then stitch them to obtain the final denoised image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.471, + 0.673 + ], + "angle": 0, + "content": "The PD strategy is introduced in the testing stage to break the spatial correlation of real-world noise. However, this also makes the pixels of the denoised image discontinuous and produces checkerboard artifacts as shown in Figure 6a. To make the denoised image have better visual performance, we propose to denoise the initial denoised image again by BSN to remove the unpleasing artifacts. This performance enhancement method is denoted by \"SDAP (E)\" and is shown in the right half of Figure 7. The comparison of the final visual effect is shown in Figure 6b. The results show that our proposed test strategy can remove checkerboard artifacts and make the images more natural. More details about PD and RSG for testing are provided in Supplementary Material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.687, + 0.21, + 0.703 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.711, + 0.295, + 0.727 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We use the general BSN architecture [36, 22] in our method. According to [22], we empirically set the stride factor \\( s \\) of RSG to 5 for training. To ensure the stability of the test, we still use the PD with stride factor 2 for testing and ablation study. During the training, we use Adam as the optimizer with default settings. The initial learning rate is 0.0001, batch size and patch size are set to 16 and \\( 160 \\times 160 \\) respectively, and epochs are taken as 15. 25600 patches are used in one epoch. To fine-tune the network, BSN continues to be optimised for 10 epochs. Meanwhile, we decay the learning rate by a factor of 10, reduce batch size to 8, and" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.292, + 0.892, + 0.323 + ], + "angle": 0, + "content": "adjust patch size to \\(250 \\times 250\\). We use PyTorch to implement our BSN and train it on an NVIDIA RTX 3090 GPU." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.331, + 0.596, + 0.345 + ], + "angle": 0, + "content": "4.2. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.353, + 0.892, + 0.49 + ], + "angle": 0, + "content": "SIDD [1]. The SIDD dataset uses five representative mobile phone cameras to capture approximately 300,000 noisy images for 10 scenes under different lighting conditions and obtain the corresponding relatively clean images by specific statistical methods. The SIDD dataset provides an SIDD Medium dataset of 320 data pairs for training, an SIDD validation dataset of 1280 image blocks of size \\(256 \\times 256\\) for validation, and an SIDD benchmark dataset of 40 high-resolution noisy images for testing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.892, + 0.613 + ], + "angle": 0, + "content": "DND [27]. The DND dataset contains 50 high-resolution test image pairs taken by consumer-grade cameras of various sensor sizes. However, because the images are too large, DND cropped all the images to \\(512 \\times 512\\) image blocks, giving 1000 image blocks for testing. The DND dataset does not provide training images, and the clean images of the test dataset are not publicly available." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.613, + 0.892, + 0.644 + ], + "angle": 0, + "content": "Note that unless otherwise stated, we used SIDD Medium dataset for training in the following experiments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.719, + 0.667 + ], + "angle": 0, + "content": "4.3. Analyzing Perturbation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.675, + 0.892, + 0.764 + ], + "angle": 0, + "content": "We first validate the effect of the perturbation in \\(L_{AP-BSN}\\) for real-world sRGB image denoising. We train the BSN by \\(L_{PBSN_{1,2,3}}\\) with different variances of \\(\\epsilon\\), i.e., \\(\\sigma_{\\epsilon} \\in \\{0,5,10,15,20,25\\}\\). Meanwhile, we also replace PD with RSG for a similar set of experiments. Figure 2 shows the PSNR(dB) results in the SIDD validation set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We observe that BSN performs best on SIDD validation dataset when \\(\\sigma_{\\epsilon} = 5\\) for both PD and RSG. After this, the performance decreases as \\(\\sigma_{\\epsilon}\\) increases. Specifically, for \\(L_{PBSN_{1,2,3}}\\), since the perturbation is added to the training data, when the perturbation is too large, it will significantly change the noise distribution of the training image, making it difficult for the BSN to adapt to the original noise. Therefore, the denoising performance of BSN decreases significantly when \\(\\sigma_{\\epsilon} > 15\\). Also, since RSG and perturbation" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12155" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.085, + 0.891, + 0.46 + ], + "angle": 0, + "content": "
Type of supervisionTraining dataMethodSIDD validationSIDD benchmarkDND benchmark
Non-learning based-BM3D [12]31.75/0.706125.65/0.68534.51/0.8507
WNNM [13]26.31/0.524025.78/0.80934.67/0.8646
SupervisedPaired noisy-cleanDnCNN [44]26.20/0.441423.66/0.58332.43/0.7900
TNRD [10]26.99/0.744024.73/0.64333.65/0.8306
CBDNet [14]30.83/0.754133.28/0.86838.06/0.9421
RIDNet [2]38.76/0.913237.87/0.94339.25/0.9528
VDN [40]39.29/0.910939.26/0.95539.38/0.9518
Zhou et al. [47]-34.00/0.89838.40/0.945
DeamNet [28]39.40/0.916939.35/0.95539.63/0.9531
Pseudo-supervisedUnpaired noisy-cleanGCBD [8]--35.58/0.9217
D-BSN [36]--37.93/0.9373
C2N [18]35.36/0.890135.35/0.93737.28/0.9237
Paired noisy-noisyR2R [26]35.04/0.844034.78/0.89837.61/0.9368
Self-supervisedSingle noisyN2V [20]29.35/0.651027.68/0.668-
N2S [3]30.72/0.787029.56/0.808-
NAC [38]--36.20/0.9252
Neighbor2Neighbor [17]28.00/0.589027.96/0.67031.40/0.7880
CVF-SID [25]34.17/0.871934.71/0.91736.50/0.9233
AP-BSN [22]34.46/0.850134.90/0.90037.46/0.9244
SDAP (Ours)36.58/0.863036.54/0.91937.71/0.9278
SDAP (S) (Ours)36.71/0.864036.68/0.91938.18/0.9322
SDAP (E) (Ours)37.30/0.893737.24/0.93637.86/0.9366
SDAP (S)(E) (Ours)37.55/0.894337.53/0.93638.56/0.9402
" + }, + { + "type": "table_caption", + "bbox": [ + 0.235, + 0.469, + 0.735, + 0.485 + ], + "angle": 0, + "content": "Table 2: Quantitative PSNR(dB)/SSIM Results on SIDD and DND Dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.47, + 0.603 + ], + "angle": 0, + "content": "have similar roles, both are designed to obtain more training data. When the perturbation is too large, the role of RSG is difficult to be reflected. Therefore, when the perturbation is small, the RSG strategy outperforms the PD strategy. When the perturbation is large, the RSG strategy and the PD strategy are used for BSN to obtain similar denoising results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.604, + 0.471, + 0.71 + ], + "angle": 0, + "content": "In addition, we note that the most suitable perturbation standard deviation \\(\\sigma_{\\epsilon}\\) is different for each of these images in Figure 3. Nevertheless, when we consider the sampling difference as the perturbation, the BSN performs the best regardless of the data. In Section 4.5, we analyze the sampling difference as perturbation in detail. Therefore, Eq. (6) is the final loss function of our proposed method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.725, + 0.303, + 0.741 + ], + "angle": 0, + "content": "4.4. Denoising of Real Image" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We use SIDD validation, SIDD benchmark, and DND benchmark datasets to evaluate the performance of our SDAP in real-world denoising tasks. For the SIDD validation dataset, because the paired noisy-clean images are provided, we can directly test the PSNR/SSIM results. For the SIDD and DND benchmarks, we submit the denoised images to websites for server-side evaluation to obtain the final results (PSNR/SSIM values). To evaluate our model on the three different datasets, we adopt two different strategies for training." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.511, + 0.892, + 0.587 + ], + "angle": 0, + "content": "Training on SIDD Medium dataset. We train our self-supervised method with noisy images from the SIDD Medium dataset. Then, the obtained model is evaluated on different datasets. This training method is represented as \"SDAP\" in Table 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.892, + 0.763 + ], + "angle": 0, + "content": "Training on test dataset. Since our method is fully self-supervised [25], instead of using the fixed SIDD Medium dataset for training, we can use the test images for self-supervised training as well. Therefore, we train our method on three test datasets in self-supervised manner, respectively. The trained models are evaluated with the corresponding test datasets. Since the noise distribution of training and test images are identical, this strategy can obtain a BSN model with better performance. Fully self-supervised training method is represented as \"SDAP (S)\" in Table 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.764, + 0.892, + 0.84 + ], + "angle": 0, + "content": "It should be noted that \"(S)\" denotes the method to improve the performance in training, while \"(E)\" denotes the way to improve the performance in testing. Thus \"SDAP (S)(E)\" is the way in which the proposed method can achieve the best performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.903 + ], + "angle": 0, + "content": "The results in Table 2 show that this method achieves significantly better results than some traditional methods, such as BM3D, on the SIDD Benchmark test data. Even when compared with some supervised deep learning-based" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "12156" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.178, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.314, + 0.145, + 0.324 + ], + "angle": 0, + "content": "Noisy" + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.089, + 0.279, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.203, + 0.314, + 0.258, + 0.323 + ], + "angle": 0, + "content": "BM3D [12]" + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.089, + 0.381, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.301, + 0.314, + 0.363, + 0.323 + ], + "angle": 0, + "content": "DnCNN [44]" + }, + { + "type": "image", + "bbox": [ + 0.385, + 0.089, + 0.481, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.402, + 0.314, + 0.465, + 0.323 + ], + "angle": 0, + "content": "CBDNet [14]" + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.089, + 0.582, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.314, + 0.556, + 0.323 + ], + "angle": 0, + "content": "C2N [18]" + }, + { + "type": "image", + "bbox": [ + 0.587, + 0.089, + 0.683, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.601, + 0.314, + 0.669, + 0.323 + ], + "angle": 0, + "content": "CVF-SID [25]" + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.089, + 0.784, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.704, + 0.314, + 0.769, + 0.323 + ], + "angle": 0, + "content": "AP-BSN [22]" + }, + { + "type": "image", + "bbox": [ + 0.789, + 0.089, + 0.886, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.788, + 0.314, + 0.886, + 0.323 + ], + "angle": 0, + "content": "SDAP (S)(E) (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.115, + 0.331, + 0.853, + 0.347 + ], + "angle": 0, + "content": "Figure 8: Visual comparison of our method against other competing methods on the SIDD validation dataset [1]." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.371, + 0.462, + 0.464 + ], + "angle": 0, + "content": "
PDRSG\\( L_{AP-BSN} \\)\\( L_{CSDBSN} \\)PSNR(dB)/SSIM
✓-✓-35.68/0.8382
✓--✓36.19/0.8472
-✓✓-36.03/0.8533
-✓-✓36.58/0.8630
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.472, + 0.468, + 0.501 + ], + "angle": 0, + "content": "Table 3: Investigation of RSG and \\(L_{CSDBSN}\\) on SIDD Validation Dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.532, + 0.47, + 0.728 + ], + "angle": 0, + "content": "image denoising methods, this method achieves superior denoising results. For example, the PSNR and SSIM results of this method are 3.40dB and 0.051 higher compared with CBDNet. When we compared with the SOTA self-supervised image denoising approaches, our method also has obvious advantages. For example, compared with APBSN, which has the same network structure as us, SDAP achieves 1.78dB and 0.019 increases in PSNR and SSIM metrics, respectively. The performance of SDAP on the DND dataset has similar findings as those on SIDD. Figures 1 and 8 provide visual comparisons of several methods, and the results further validate the visual superiority of our method to other methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.741, + 0.229, + 0.758 + ], + "angle": 0, + "content": "4.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.9 + ], + "angle": 0, + "content": "We examine two major determinants of our model: a) RSG; b) \\( L_{CSDBSN} \\). If there is a \"√\" in the column of \\( L_{CSDBSN} \\) (or \\( L_{APBSN} \\)), it means that \\( L_{CSDBSN} \\) (or \\( L_{APBSN} \\)) is used for training, and vice versa. If there is a \"√\" in the column of RSG, it means that the RSG strategy is used for training, and we replace all \\( PD \\) in the loss with \\( RSG \\). If there is a \"√\" in the column of PD, it means that the PD strategy is used for training, and we replace all \\( RSG \\) in the loss with \\( PD \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.373, + 0.892, + 0.48 + ], + "angle": 0, + "content": "Study of RSG. The performance of training with RSG in Table 3 is always higher than training with PD. A comparison between the first and third rows of Table 3 shows that replacing PD with RSG increases the PSNR/SSIM result by \\(0.35\\mathrm{dB} / 0.0151\\). The comparison between the second and fourth rows shows a similar conclusion. These results verify the effectiveness for RSG." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.497, + 0.893, + 0.635 + ], + "angle": 0, + "content": "Study of \\(L_{CSDBSN}\\). Rows 2 and 4 of Table 3 show the effect of our proposed \\(L_{CSDBSN}\\), where our proposed loss improves the denoising performance by 0.51dB/0.0090 in the case of training with PD and 0.55dB/0.0097 in the case of training with RSG. It is worth noting that, irrespective of whether PD or RSG is used in \\(L_{CSDBSN}\\) for BSN training, the performance of BSN is superior to that achieved by directly adding Gaussian perturbations in \\(L_{AP-BSN}\\) (i.e., using \\(L_{CSDBSN}\\) for training is better than using \\(L_{PBSN_{1,2,3}}\\))." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.646, + 0.619, + 0.661 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.892, + 0.838 + ], + "angle": 0, + "content": "In this paper, we first analyze the reasons for the limited performance of BSN when used for real image denoising. Based on this, we propose to add perturbations to the training data and consider sampling difference as perturbation. Further, we propose SDAP framework with random sub-samples generation and cyclic sampling difference loss. Our SDAP does not require clean images for training and outperforms existing pseudo-supervised/self-supervised methods. We believe that our approach can provide promising inspirations for various self-supervised real-world denoising methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgement. This work was supported by the National Natural Science Foundation of China under Grant 62171304." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12157" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.469, + 0.156 + ], + "angle": 0, + "content": "[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S Brown. A high-quality denoising dataset for smartphone cameras. In CVPR, pages 1692-1700, 2018." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.469, + 0.185 + ], + "angle": 0, + "content": "[2] Saeed Anwar and Nick Barnes. Real image denoising with feature attention. In ICCV, pages 3155-3164, 2019." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.187, + 0.468, + 0.213 + ], + "angle": 0, + "content": "[3] Joshua Batson and Loic Royer. 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However, it is still very challenging to widely utilize the supervised methods in real cases due to the lack of paired noisy-clean images. Meanwhile, most self-supervised denoising methods are ineffective as well when applied to the real-world denoising tasks because of their strict assumptions in applications. For example, as a typical method for self-supervised denoising, the original blind spot network (BSN) assumes that the noise is pixel-wise independent, which is much different from the real cases. To solve this problem, we propose a novel self-supervised real image denoising framework named Sampling Difference As Perturbation (SDAP) based on Random Sub-samples Generation (RSG) with a cyclic sample difference loss. Specifically, we dig deeper into the properties of BSN to make it more suitable for real noise. Surprisingly, we find that adding an appropriate perturbation to the training images can effectively improve the performance of BSN. Further, we propose that the sampling difference can be considered as perturbation to achieve better results. Finally we propose a new BSN framework in combination with our RSG strategy. The results show that it significantly outperforms other state-of-the-art self-supervised denoising methods on real-world datasets. The code is available at https://github.com/p1y2z3/SDAP. + +# 1. Introduction + +Image denoising is a hot topic in low-level vision tasks, aiming to obtain high-quality images from noisy versions. In recent years, learning-based methods have been widely used in image denoising with their superior performance. Thanks to the construction of paired image datasets, the supervised approaches [44, 2, 28, 11, 33, 34] can be efficiently implemented. In these approaches, it is a common practice + +![](images/8fbacf789c4e458d42046085ca6396bc7fa49c0a349082f193067df8e6a1e994.jpg) + +![](images/c1f18a120e36fb48bf471d8a63d4acf5ca79188f245e75b58e36dd168623b03e.jpg) + +![](images/a783399a381aa24e1d1d0d75493e230c3eca2c47e13f273d58474e176f1ca652.jpg) + +![](images/6588ba477eb9b8f7fedfc027d64d44cf07e27075587671729059483b2c8c7635.jpg) +Noisy +CVF-SID [25] + +![](images/721555f91cb1dd3a1613bf4b26c79212d71fae1ed0c97966bec1a73796b773dd.jpg) +CBDNet [14] +AP-BSN [22] +Figure 1: Real-world image denoising results on DND [27]. + +![](images/8b8afde62f777128c984f02907f5a5c07b706c0bfc4ddb0f1d827f7561fa66cf.jpg) +C2N [18] +SDAP (S)(E) (Ours) + +to synthesize paired datasets directly using a specific noise model, such as the signal-independent additive white Gaussian noise (AWGN) model. + +However, the real images are captured by cameras with image signal processing (ISP) pipelines [4]. The noise is usually signal-dependent and spatially correlated in the real world. Moreover, ISP includes many non-linear operations that can complicate the noise distribution. Due to the influence of ISP pipelines within the camera, the noise distribution of real images is difficult to predict. Therefore, it is difficult and challenging for us to model the noise for real images. To overcome the problem of directly and explicitly modelling noise distribution, paired real-world datasets have been constructed by researchers. However, collecting paired noisy-clean images is difficult and time-expensive. + +Recently, a series of unsupervised and self-supervised methods have been introduced. These methods do not require paired datasets for training, and thus further avoiding the difficulty of collecting real-world paired datasets for denoising. Among them, Noise2Void [20] proposes Blind-Spot Network (BSN) that can be trained with only single noisy images. Unfortunately, BSN has strict assumptions, which can only be applied to pixel-wise independent noise. AP-BSN [22] applies pixel-shuffle downsampling + +(PD) strategy [47] to BSN, remove the spatial correlation in the real-world noise, and thus the real image can also meet the conditions for BSN to some extent. However, real noisy datasets usually have relatively limited numbers of samples. AP-BSN directly adopts the strategy of PD, which can only obtain $s^2$ sub-images for a noisy image (the stride factor of PD is $s$ ). This will inevitably lead to the insufficient samples, and make the training of BSN less effective. Therefore, the optimal performance of BSN cannot be achieved. + +We observe that adding some perturbations to the training images can greatly expand the training data, which improves the performance of BSN. Further, we consider the samples difference as the perturbation. To obtain more random perturbations and more sub-samples, we propose random sub-samples generation (RSG) strategy to break the fixed sampling pattern of PD. Based on this, we propose a new cyclic sampling difference loss for BSN and a new BSN framework in combination with our RSG strategy. In summary, our contributions include: + +- We provide a new idea about adding perturbations to the training data to improve the BSN performance. Then, we suggest that the sub-samples difference generated by sampling can be considered as perturbations for higher performance. +- We propose a new self-supervised framework for real image denoising with random sub-samples generation and cyclic sampling difference loss. +- Our method performs very favorably against state-of-the-art (SOTA) self-supervised denoising methods on real-world datasets. + +# 2. Related Work + +The image denoising task aims to restore a clean image from its noisy counterpart. There are two main types of non-learning-based image denoising: filtering-based methods and model-based methods. Filter-based methods involve using some artificially designed low-pass filter to remove image noise. Taking advantage of the condition of having many similar image blocks in the same image, noise can also be removed by the local similarity of image, such as NLM [5], BM3D [12], etc. Model-based methods involve modeling the distribution of natural images or noise and then using the model distribution before obtaining a clear image with an optimization algorithm, such as WNNM [13]. The learning-based methods are effective ways to reduce image noise. Usually, it can be divided into traditional and deep network-based methods. In recent years, due to the continuous development of the deep learning technology, deep network-based methods have achieved superior denoising results compared to previous methods, and thus + +they have become the mainstream denoising methods. Generally, deep network-based methods can be further classified according to their training manners. + +# 2.1. Supervised Image Denoising + +Most of the early works [24, 44, 31, 45, 46] assume that the noise is independent and uniformly distributed, and additive Gaussian white noise (AWGN) is usually used to model image noise and synthetic paired datasets. These methods achieve SOTA results on AWGN denoising tasks. However, the noise model in the real world is complex and unknown. Models trained with synthetic datasets are difficult to be applied to the real world. Recently, most of the methods [14, 2, 19, 41, 43, 6, 42, 29, 9] use produced real-world paired datasets for training. Due to the differences in camera parameters, these methods may not be widely used in the real world. + +# 2.2. Pseudo-Supervised Image denoising + +The supervised denoising methods require paired noisy-clean images, while the pseudo-supervised denoising methods relax the data requirements. Noise2Noise [23] proposes that pairs of noisy images can be used to train the network when the noise mean is zero. When some unpaired noisy-clean images are available, some methods [8, 7, 15, 18] learn the noise distribution of noisy images by generative adversarial networks (GAN). Then, clean images are used to generate pseudo-paired noisy-clean images to train the denoising network. However, these methods are still difficult to be applied because the scene distribution of noisy images often does not match the available clean images [18]. + +# 2.3. Self-Supervised Image Denoising + +The self-supervised denoising methods require single noisy images for training. Noise2Void [20] finds that masking a portion of pixels in noisy images for pairing can train the denoising network, and thus proposes a BSN for self-supervised denoising. Laine19 [21] and D-BSN [36] further optimize the BSN and improve its performance. Noise2Same [37] and Blind2Unblind [35] propose new denoising losses for self-supervised training through mask-based blind-spot methods. Neighbor2Neighbor [17] samples the noisy image into two similar sub-images to form a noisy-noisy pair for training. CVF-SID [25] can disentangle the clean image, signal-dependent and signal-independent noises from the real-world noisy input via various self-supervised training objectives. AP-BSN [22] combines PD and BSN to process real-world sRGB noisy images and employs asymmetric PD stride factors for training and inference. However, current self-supervised methods for real noise removal usually still require a large number of noisy images and are challenging to train with less training data to achieve superior performance. + +# 3. Proposed Method + +# 3.1. Revisiting Noise2Void + +Noise2Void (N2V) [20] requires only single noisy images for training, and it assumes that the noise $n$ is pixelwise independent (the noises at different pixel positions are independent) given the clean image $x$ . $y$ is the noisy image, i.e. $y = x + n$ . Due to the local correlation of the pixels within an image, clean central pixels can be estimated from the surrounding noisy pixels. Therefore, using the pixel of the noisy image as a target for its surrounding pixels will not obtain the noisy pixel. Thus, N2V can train the denoising network in a self-supervised approach. Specifically, N2V loss $L_{N2V}$ can be written as follows: + +$$ +L _ {N 2 V} = E _ {y} \left\{\| f \left(y _ {r}\right) - y _ {c} \| _ {2} ^ {2} \right\}, \tag {1} +$$ + +where $f(\cdot)$ is the normal denoising network, $y_{r}$ is the patch of $y$ centered on $y_{c}$ with the same dimensions as the network receptive field. Note that $y_{r}$ does not contain $y_{c}$ . + +To facilitate the implementation of training with $L_{N2V}$ , N2V proposes BSN $B(\cdot)$ capable of masking centroids. The noisy images used to train the BSN must satisfy the BSN assumption that the noise is pixel-wise independent and zero-mean. BSN can be trained by optimizing the following loss $L_{BSN}$ : + +$$ +L _ {B S N} = E _ {y} \left\{\left\| B (y) - y \right\| _ {2} ^ {2} \right\}. \tag {2} +$$ + +$L_{N2V}$ and $L_{BSN}$ are equivalent for training BSN. For a known noise model (e.g. AWGN model), we can synthesize an infinite number of different noisy images. Thus, BSN can be easily trained. In contrast, since real image datasets often have a limited number of captured images, it is difficult to train BSN directly for real image denoising. Moreover, real images do not satisfy the pixel-wise independent noise assumptions of BSN. Therefore, the limitations of $L_{BSN}$ are significant, and it is not appropriate to use real images directly for BSN. + +# 3.2. AP-BSN and Its Limitation + +To make BSN better for the spatially correlated real image noise, AP-BSN [22] introduces PD [47] to break the spatial correlation among real noisy pixels, leading to near pixel-wise independent noise. Therefore, the real image after PD can be considered to meet the BSN assumption [22], and thus can be used as the input for BSN. The original APBSN loss is written as $\left\|PD^{-1}(B(PD(y))) - y\right\|_1$ , where $PD$ is the PD operator and $PD^{-1}$ is the inverse operator. To facilitate the analysis, we further write it as: + +$$ +L _ {A P - B S N} = E _ {y} \left\{\left\| B (P D (y)) - P D (y) \right\| _ {1} \right\}. \tag {3} +$$ + +It can be observed that the pattern of pairing is fixed in Eq. (3) (i.e. fixed $PD(y)$ to $PD(y)$ ). We consider that the + +
DatasetSet12BSD68Urban100
Fixed seed28.91/0.819227.26/0.747727.66/0.8172
Random seed29.36/0.839927.72/0.772828.81/0.8632
+ +Table 1: The effect of different BSN training strategies on PSNR (dB)/SSIM. + +training of fixed patterns does not affect the performance of BSN when the sample number is large enough. In contrast, it is well known that insufficient sample number may lead to overfitting [39]. Overfitting of noisy-clean pairing training can only have a superior effect on the training datasets and fail on other datasets. However, BSN requires noisy-noisy pairs for training. The overfitting of BSN will make the denoising result fit the noisy image and affect the denoising performance. For synthetic noise, because the noise modelling can generate an infinite number of noisy images, BSN can avoid fitting the noise, resulting in a clean image. But when BSN is used for real noise, real datasets tend to have a much smaller sample number than synthetic datasets. In this case, BSN may fail to get high-quality clean pixels. + +To verify the effect of the number of training images on the denoising results, we train BSN with synthetic images. In this way, we can synthesize any number of noisy images. We employ DIV2K dataset [32] and add Gaussian noise with a level $\sigma = 25$ to synthesize noisy images. Two ways are adopted to train BSN with $L_{BSN}$ : (1) adding noise with fixed seed in each epoch, and (2) adding noise with random seed in each epoch. Then, we perform denoising experiments on the test datasets generated with Gaussian noise (Set12 [44], BSD68 [30], and Urban100 [16]). Table 1 shows the PSNR(dB) and SSIM results in the test datasets for different training strategies. We observe that when a limited number of noisy images (noisy images with fixed seeds) are used to train the BSN, the denoising performance degrades significantly. Therefore, the introduction of PD is practical. Still, considering that the training data of real images are often limited, the direct use of $L_{AP-BSN}$ may affect the denoising performance for real image denoising. + +# 3.3. Perturbation in BSN + +In order to solve the above problems, we suggest adding perturbations to Eq. (3) to increase the number of training data and avoid fitting to the fixed pattern. We should ensure that the sub-images as inputs or targets remain consistent with the BSN assumption after adding perturbations. This is necessary for training the BSN using these sub-images for denoising purposes. A simple solution is using AWGN as the perturbation. Suppose $\epsilon$ , $\epsilon_{1}$ , and $\epsilon_{2}$ are all perturbations of a Gaussian distribution with mean 0 and variance $\sigma_{\epsilon}^{2}$ . We propose three perturbation BSN losses $L_{PBSN_{1,2,3}}$ + +![](images/52989a3c797b92d9d8d1d7180206e0c397bfe720edf3252fdf102a4a17cab174.jpg) +Figure 2: Ablation study of $\sigma_{\epsilon}$ in $L_{PBSN_{1,2,3}}$ for training on the SIDD validation dataset [1]. + +![](images/9d69cdf5c784e2fb73ec2180f6f0be11c83be8abc637956d5681c61bb55457bb.jpg) + +![](images/917afef4c8de27808351cc47a20aff06bbcd548ce7f0053b32d6643aae9bb3b0.jpg) + +![](images/f707db4f04ce4917a41ead15691d29397182d5a7e338ccddab8306202dec5f56.jpg) +Figure 3: Ablation study of $\sigma_{\epsilon}$ in $L_{PBSN_2}$ for training in different images. + +as follows: + +$$ +\begin{array}{l} L _ {P B S N _ {1}} = E _ {y} \left\{\left\| B (P D (y) + \epsilon) - P D (y) \right\| _ {1} \right\}, \\ L _ {P B S N _ {2}} = E _ {y} \left\{\| B (P D (y)) - (P D (y) + \epsilon) \| _ {1} \right\}, \tag {4} \\ L _ {P B S N _ {3}} = E _ {y} \left\{\| B (P D (y) + \epsilon_ {1}) - (P D (y) + \epsilon_ {2}) \| _ {1} \right\}. \\ \end{array} +$$ + +We test the effect of different variances of $\epsilon$ or $(\epsilon_{1},\epsilon_{2})$ in Eq. (4) on the BSN training, and the results are shown in Figures 2 and 3. We observe that adding suitable perturbations can achieve improvements in BSN performance. Therefore, each of the losses in Eq. (4) fits our vision and can obtain a better BSN by training. In Section 4.3, we analyze the influence of perturbations in detail. The results in Figure 2 show that different perturbation levels' effects on BSN performance vary. The results in Figure 3 show that the appropriate optimal perturbation for different levels of noisy images also varies. Therefore, it is a challenge to choose the appropriate perturbation. + +# 3.4. Sampling Difference as Perturbation + +PD can produce a series of similar sub-images $(PD_{1}(y)$ , $PD_{2}(y)$ , ..., where $PD_{i}(\cdot)$ denotes the $i$ -th sub-image obtained after PD). Since the PD sampling process does not + +![](images/67121a6b1b4262ee1bd064b5f98878bea499944e46d985ac59dd8d03131edca2.jpg) +Figure 4: Results of sampling by different methods. The second row is the sampling difference obtained by subtracting the two sub-samples in the first row. + +overlap, the pixels in the sub-images that are at the same position are not located at the same position in the original image. As a result, there are certain differences between these sub-images, which we refer to as sampling difference. + +Based on the previous analysis, it is evident that adding perturbation for training can enhance the performance of BSN, but how to add the appropriate perturbations is a challenge. Since there exists a sampling difference among the sub-images acquired through sampling, this difference can be viewed as a type of perturbation. First of all, according to [22], the sub-images obtained through PD sampling are naturally in line with the BSN assumption. Next, the difference between $PD_{1}(y)$ and $PD_{2}(y)$ can be considered as the perturbation, so we do not need to add additional perturbations as in Eq. (4). Therefore, $PD_{1}(y)$ and $PD_{2}(y)$ can be used as the input and target in the BSN training, respectively. Finally, we propose a new sampling difference BSN loss $L_{SDBSN}$ as follows: + +$$ +L _ {S D B S N} = E _ {y} \left\{\| B \left(P D _ {1} (y)\right) - P D _ {2} (y) \| _ {1} \right\}. \tag {5} +$$ + +# 3.5. Random Sub-Samples Generation + +The sampling difference generated by the PD strategy can be obtained by subtracting the two sub-images generated by the PD. The sub-images and the sampling difference + +![](images/5a9867a5838425102661ca3953fba7dffcbee5a30f5d659c79a5b9928866861d.jpg) +Figure 5: Example of generating sub-samples with RSG. + +![](images/d777ebf35cd49b5f436e9ee40c4ff4a63d423d9b5e4494b073a229806bc48190.jpg) +(a) SDAP + +![](images/714d4c0c98b9b44482049b67c07a9f0ef33793ae263aa2d55a7efb85febea54f.jpg) +Figure 6: Visual comparison between SDAP and SDAP (E). + +![](images/986fdd164fba912ead610f0337e258eacde0d0662bd10d4a34f1f65b969503c9.jpg) +(b) SDAP (E) + +![](images/88f183ad01f826b18d4e2ace78db7a458125faaf37986861699a4dd521455df4.jpg) + +generated by PD are shown in Figure 4a. It can be observed that the sampling difference generated by PD is similar to the gradient map. Meanwhile, the PD strategy with a stride factor of $s$ can only generate $s^2$ fixed sub-images for the same image, which still faces the data-hungry issue for BSN training. To obtain more sub-samples and make the sampling difference closer to random perturbation, we propose the random sub-samples generation strategy (RSG). + +The diagram of sub-images generation with the RSG is shown in Figure 5. Assume that the noisy image $(y)$ length and width are $H$ and $W$ , respectively. The details of RSG are described below: + +1. Divide. The image $y$ is divided into $HW / s^2$ non-overlapping cells with size $s \times s$ . Then, we stretch the cells into vectors of length $s^2$ . For better visualization, we set $s = 2$ in Figure 5. +2. Shuffle. Randomly shuffle the elements within each vector. Since this process is strictly random, the subsamples obtained are different each time. +3. Reform. Take the elements at the same position of each vector to form $s^2$ new vectors of length $HW / s^2$ . +4. Reshape. Reshape each vector into a sub-sample of size $[W / s] \times [H / s]$ . In this way, $s^2$ similar sub-samples $(RSG_1(y), RSG_2(y), \ldots, RSG_{s^2}(y))$ are obtained. + +To maximize the variance of each sub-sample, our sampling is non-overlapping. + +The sub-samples generated by the RSG strategy and their sampling difference is shown in Figure 4b. It can be observed that the use of RSG does make the sampling difference more random. Furthermore, we provide detailed analysis for this phenomenon. Both PD and RSG sample the image directly, so the calculation of the sampling difference can be considered as the deviation in the direction of the line connecting the sampling pixels of the two sub-samples. Since each pixel of the PD sub-sample has a fixed position in the original image, the difference has a fixed offset direction. Due to random sampling, the sampling difference of RSG sub-samples are not fixed in the direction of each pixel deviation, making the difference more random. In addition, as can also be seen from Figure 5, PD is equivalent to obtaining four fixed sub-images of yellow, blue, green and red. While RSG obtains random sub-images of $①②③④$ with different results for each sampling, which can provide a large number of samples for training. Therefore, RSG strategy can also be considered as a solution to the data-hungry issue of training BSN with real noisy images. + +# 3.6. Cyclic Sampling Difference BSN Loss + +According to Eq. (5), only two sub-samples are needed. However, because multiple sub-samples are generated by RSG, using the whole sub-images instead of only two samples in training can better utilize the features of the generated sub-samples, leading to higher performance. Moreover, if only two sub-samples are used for training, the loss of each training iteration will fluctuate seriously, and the training of BSN cannot converge. To preserve the stability of training and to make full use of each sample, we introduce the strategy of cyclic and RSG to propose a new cyclic samples difference BSN loss $L_{CSDBSN}$ : + +$$ +\begin{array}{l} L _ {C S D B S N} = \sum_ {i = 1} ^ {s ^ {2}} \underbrace {\left\| B \left(R S G _ {i} (y)\right) - R S G _ {i + 1} (y) \right\| _ {1}} _ {\text {c r o s s - p a i r i n g}} \tag {6} \\ (R S G _ {s ^ {2} + 1} (y) = R S G _ {1} (y)). \\ \end{array} +$$ + +Since the sub-samples are generated randomly, the training data is also random. The target corresponding to each input in $L_{CSDBSN}$ is different. Therefore, two sub-samples are avoided to form a fixed mapping during the cycle. This cyclic loss has the following merits: 1) it imposes constraints on the full pixel of the original noisy image; 2) it ensures that all the sub-samples generated by RSG are well exploited; 3) it makes the training of BSN more robust. Figure 7 visually illustrates our training scheme with the cyclic sampling difference BSN loss. + +# 3.7. Proposed SDAP Framework + +For the training stage, we first sample the noisy images into $s^2$ sub-samples by RSG. Then, we denoise sub-samples + +![](images/eeb438c784131578e87716403f4e0cd99def64150de071f3a8801fe180db714f.jpg) +Figure 7: Overview of our proposed SDAP framework. + +by BSN. The loss is calculated by cross-pairing the subsamples after denoising with those before denoising. Finally, the above steps are iterated, and the loss function is updated to optimize the BSN until it converges. The training process is shown in the left half of Figure 7. + +For the testing stage, due to the randomness of the single RSG, the test results are not fixed. Since the sampling pattern of PD is fixed, the test results are stable for testing. Therefore, for default setting, we directly adopt the strategy of PD. We denoise the sub-images after PD and then stitch them to obtain the final denoised image. + +The PD strategy is introduced in the testing stage to break the spatial correlation of real-world noise. However, this also makes the pixels of the denoised image discontinuous and produces checkerboard artifacts as shown in Figure 6a. To make the denoised image have better visual performance, we propose to denoise the initial denoised image again by BSN to remove the unpleasing artifacts. This performance enhancement method is denoted by "SDAP (E)" and is shown in the right half of Figure 7. The comparison of the final visual effect is shown in Figure 6b. The results show that our proposed test strategy can remove checkerboard artifacts and make the images more natural. More details about PD and RSG for testing are provided in Supplementary Material. + +# 4. Experiments + +# 4.1. Implementation Details + +We use the general BSN architecture [36, 22] in our method. According to [22], we empirically set the stride factor $s$ of RSG to 5 for training. To ensure the stability of the test, we still use the PD with stride factor 2 for testing and ablation study. During the training, we use Adam as the optimizer with default settings. The initial learning rate is 0.0001, batch size and patch size are set to 16 and $160 \times 160$ respectively, and epochs are taken as 15. 25600 patches are used in one epoch. To fine-tune the network, BSN continues to be optimised for 10 epochs. Meanwhile, we decay the learning rate by a factor of 10, reduce batch size to 8, and + +adjust patch size to $250 \times 250$ . We use PyTorch to implement our BSN and train it on an NVIDIA RTX 3090 GPU. + +# 4.2. Dataset + +SIDD [1]. The SIDD dataset uses five representative mobile phone cameras to capture approximately 300,000 noisy images for 10 scenes under different lighting conditions and obtain the corresponding relatively clean images by specific statistical methods. The SIDD dataset provides an SIDD Medium dataset of 320 data pairs for training, an SIDD validation dataset of 1280 image blocks of size $256 \times 256$ for validation, and an SIDD benchmark dataset of 40 high-resolution noisy images for testing. + +DND [27]. The DND dataset contains 50 high-resolution test image pairs taken by consumer-grade cameras of various sensor sizes. However, because the images are too large, DND cropped all the images to $512 \times 512$ image blocks, giving 1000 image blocks for testing. The DND dataset does not provide training images, and the clean images of the test dataset are not publicly available. + +Note that unless otherwise stated, we used SIDD Medium dataset for training in the following experiments. + +# 4.3. Analyzing Perturbation + +We first validate the effect of the perturbation in $L_{AP-BSN}$ for real-world sRGB image denoising. We train the BSN by $L_{PBSN_{1,2,3}}$ with different variances of $\epsilon$ , i.e., $\sigma_{\epsilon} \in \{0,5,10,15,20,25\}$ . Meanwhile, we also replace PD with RSG for a similar set of experiments. Figure 2 shows the PSNR(dB) results in the SIDD validation set. + +We observe that BSN performs best on SIDD validation dataset when $\sigma_{\epsilon} = 5$ for both PD and RSG. After this, the performance decreases as $\sigma_{\epsilon}$ increases. Specifically, for $L_{PBSN_{1,2,3}}$ , since the perturbation is added to the training data, when the perturbation is too large, it will significantly change the noise distribution of the training image, making it difficult for the BSN to adapt to the original noise. Therefore, the denoising performance of BSN decreases significantly when $\sigma_{\epsilon} > 15$ . Also, since RSG and perturbation + +
Type of supervisionTraining dataMethodSIDD validationSIDD benchmarkDND benchmark
Non-learning based-BM3D [12]31.75/0.706125.65/0.68534.51/0.8507
WNNM [13]26.31/0.524025.78/0.80934.67/0.8646
SupervisedPaired noisy-cleanDnCNN [44]26.20/0.441423.66/0.58332.43/0.7900
TNRD [10]26.99/0.744024.73/0.64333.65/0.8306
CBDNet [14]30.83/0.754133.28/0.86838.06/0.9421
RIDNet [2]38.76/0.913237.87/0.94339.25/0.9528
VDN [40]39.29/0.910939.26/0.95539.38/0.9518
Zhou et al. [47]-34.00/0.89838.40/0.945
DeamNet [28]39.40/0.916939.35/0.95539.63/0.9531
Pseudo-supervisedUnpaired noisy-cleanGCBD [8]--35.58/0.9217
D-BSN [36]--37.93/0.9373
C2N [18]35.36/0.890135.35/0.93737.28/0.9237
Paired noisy-noisyR2R [26]35.04/0.844034.78/0.89837.61/0.9368
Self-supervisedSingle noisyN2V [20]29.35/0.651027.68/0.668-
N2S [3]30.72/0.787029.56/0.808-
NAC [38]--36.20/0.9252
Neighbor2Neighbor [17]28.00/0.589027.96/0.67031.40/0.7880
CVF-SID [25]34.17/0.871934.71/0.91736.50/0.9233
AP-BSN [22]34.46/0.850134.90/0.90037.46/0.9244
SDAP (Ours)36.58/0.863036.54/0.91937.71/0.9278
SDAP (S) (Ours)36.71/0.864036.68/0.91938.18/0.9322
SDAP (E) (Ours)37.30/0.893737.24/0.93637.86/0.9366
SDAP (S)(E) (Ours)37.55/0.894337.53/0.93638.56/0.9402
+ +Table 2: Quantitative PSNR(dB)/SSIM Results on SIDD and DND Dataset. + +have similar roles, both are designed to obtain more training data. When the perturbation is too large, the role of RSG is difficult to be reflected. Therefore, when the perturbation is small, the RSG strategy outperforms the PD strategy. When the perturbation is large, the RSG strategy and the PD strategy are used for BSN to obtain similar denoising results. + +In addition, we note that the most suitable perturbation standard deviation $\sigma_{\epsilon}$ is different for each of these images in Figure 3. Nevertheless, when we consider the sampling difference as the perturbation, the BSN performs the best regardless of the data. In Section 4.5, we analyze the sampling difference as perturbation in detail. Therefore, Eq. (6) is the final loss function of our proposed method. + +# 4.4. Denoising of Real Image + +We use SIDD validation, SIDD benchmark, and DND benchmark datasets to evaluate the performance of our SDAP in real-world denoising tasks. For the SIDD validation dataset, because the paired noisy-clean images are provided, we can directly test the PSNR/SSIM results. For the SIDD and DND benchmarks, we submit the denoised images to websites for server-side evaluation to obtain the final results (PSNR/SSIM values). To evaluate our model on the three different datasets, we adopt two different strategies for training. + +Training on SIDD Medium dataset. We train our self-supervised method with noisy images from the SIDD Medium dataset. Then, the obtained model is evaluated on different datasets. This training method is represented as "SDAP" in Table 2. + +Training on test dataset. Since our method is fully self-supervised [25], instead of using the fixed SIDD Medium dataset for training, we can use the test images for self-supervised training as well. Therefore, we train our method on three test datasets in self-supervised manner, respectively. The trained models are evaluated with the corresponding test datasets. Since the noise distribution of training and test images are identical, this strategy can obtain a BSN model with better performance. Fully self-supervised training method is represented as "SDAP (S)" in Table 2. + +It should be noted that "(S)" denotes the method to improve the performance in training, while "(E)" denotes the way to improve the performance in testing. Thus "SDAP (S)(E)" is the way in which the proposed method can achieve the best performance. + +The results in Table 2 show that this method achieves significantly better results than some traditional methods, such as BM3D, on the SIDD Benchmark test data. Even when compared with some supervised deep learning-based + +![](images/9cfb7647d011532775bf60b57b4a5ee9d664347ef50fb72735fe820143982045.jpg) +Noisy + +![](images/ed24440efac01904b610a71296cfc2eee3803bfafdd7c221d6e530cc401a4f49.jpg) +BM3D [12] + +![](images/8291debe78c08100a3d8560c5edbe921c78190c7288511fb533af25db41a55e3.jpg) +DnCNN [44] + +![](images/3da4a09e704a4c4e569d617a1c7694c3a849b646495eca68949639716d42d416.jpg) +CBDNet [14] + +![](images/c7ae956ca553b0a608ad18b0e22b072b8d3be980abf7c9744476c633344559c3.jpg) +C2N [18] +Figure 8: Visual comparison of our method against other competing methods on the SIDD validation dataset [1]. + +![](images/929760c5fddede94d0747ee7d0a6f06a7176a45d58c41f727a6f55c931880f29.jpg) +CVF-SID [25] + +![](images/bbb5cf7db6ad6f385ef9e2bef352343029f09b4fa349573157dd04134fd86d85.jpg) +AP-BSN [22] + +![](images/d2a73886287ba5d0254473b6d3a0d92c74534be7ccb335620b587dde35cd9141.jpg) +SDAP (S)(E) (Ours) + +
PDRSG\( L_{AP-BSN} \)\( L_{CSDBSN} \)PSNR(dB)/SSIM
✓-✓-35.68/0.8382
✓--✓36.19/0.8472
-✓✓-36.03/0.8533
-✓-✓36.58/0.8630
+ +Table 3: Investigation of RSG and $L_{CSDBSN}$ on SIDD Validation Dataset. + +image denoising methods, this method achieves superior denoising results. For example, the PSNR and SSIM results of this method are 3.40dB and 0.051 higher compared with CBDNet. When we compared with the SOTA self-supervised image denoising approaches, our method also has obvious advantages. For example, compared with APBSN, which has the same network structure as us, SDAP achieves 1.78dB and 0.019 increases in PSNR and SSIM metrics, respectively. The performance of SDAP on the DND dataset has similar findings as those on SIDD. Figures 1 and 8 provide visual comparisons of several methods, and the results further validate the visual superiority of our method to other methods. + +# 4.5. Ablation Study + +We examine two major determinants of our model: a) RSG; b) $L_{CSDBSN}$ . If there is a "√" in the column of $L_{CSDBSN}$ (or $L_{APBSN}$ ), it means that $L_{CSDBSN}$ (or $L_{APBSN}$ ) is used for training, and vice versa. If there is a "√" in the column of RSG, it means that the RSG strategy is used for training, and we replace all $PD$ in the loss with $RSG$ . If there is a "√" in the column of PD, it means that the PD strategy is used for training, and we replace all $RSG$ in the loss with $PD$ . + +Study of RSG. The performance of training with RSG in Table 3 is always higher than training with PD. A comparison between the first and third rows of Table 3 shows that replacing PD with RSG increases the PSNR/SSIM result by $0.35\mathrm{dB} / 0.0151$ . The comparison between the second and fourth rows shows a similar conclusion. These results verify the effectiveness for RSG. + +Study of $L_{CSDBSN}$ . Rows 2 and 4 of Table 3 show the effect of our proposed $L_{CSDBSN}$ , where our proposed loss improves the denoising performance by 0.51dB/0.0090 in the case of training with PD and 0.55dB/0.0097 in the case of training with RSG. It is worth noting that, irrespective of whether PD or RSG is used in $L_{CSDBSN}$ for BSN training, the performance of BSN is superior to that achieved by directly adding Gaussian perturbations in $L_{AP-BSN}$ (i.e., using $L_{CSDBSN}$ for training is better than using $L_{PBSN_{1,2,3}}$ ). + +# 5. Conclusion + +In this paper, we first analyze the reasons for the limited performance of BSN when used for real image denoising. Based on this, we propose to add perturbations to the training data and consider sampling difference as perturbation. Further, we propose SDAP framework with random sub-samples generation and cyclic sampling difference loss. 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"lines": [ + { + "bbox": [ + 490, + 301, + 517, + 308 + ], + "spans": [ + { + "bbox": [ + 490, + 301, + 517, + 308 + ], + "type": "text", + "content": "C2N [18]" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 466, + 308, + 541, + 382 + ], + "lines": [ + { + "bbox": [ + 466, + 308, + 541, + 382 + ], + "spans": [ + { + "bbox": [ + 466, + 308, + 541, + 382 + ], + "type": "image", + "image_path": "8b8afde62f777128c984f02907f5a5c07b706c0bfc4ddb0f1d827f7561fa66cf.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 473, + 383, + 533, + 392 + ], + "lines": [ + { + "bbox": [ + 473, + 383, + 533, + 392 + ], + "spans": [ + { + "bbox": [ + 473, + 383, + 533, + 392 + ], + "type": "text", + "content": "SDAP (S)(E) (Ours)" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 426, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 426, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 305, + 426, + 545, + 461 + ], + "type": "text", + "content": "to synthesize paired datasets directly using a specific noise model, such as the signal-independent additive white Gaussian noise (AWGN) model." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 462, + 546, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 546, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 546, + 605 + ], + "type": "text", + "content": "However, the real images are captured by cameras with image signal processing (ISP) pipelines [4]. The noise is usually signal-dependent and spatially correlated in the real world. Moreover, ISP includes many non-linear operations that can complicate the noise distribution. Due to the influence of ISP pipelines within the camera, the noise distribution of real images is difficult to predict. Therefore, it is difficult and challenging for us to model the noise for real images. To overcome the problem of directly and explicitly modelling noise distribution, paired real-world datasets have been constructed by researchers. However, collecting paired noisy-clean images is difficult and time-expensive." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 606, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 606, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 606, + 547, + 715 + ], + "type": "text", + "content": "Recently, a series of unsupervised and self-supervised methods have been introduced. These methods do not require paired datasets for training, and thus further avoiding the difficulty of collecting real-world paired datasets for denoising. Among them, Noise2Void [20] proposes Blind-Spot Network (BSN) that can be trained with only single noisy images. Unfortunately, BSN has strict assumptions, which can only be applied to pixel-wise independent noise. AP-BSN [22] applies pixel-shuffle downsampling" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 702, + 137, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 702, + 137, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 702, + 137, + 712 + ], + "type": "text", + "content": "Corresponding Author" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12150" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 178 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 178 + ], + "type": "text", + "content": "(PD) strategy [47] to BSN, remove the spatial correlation in the real-world noise, and thus the real image can also meet the conditions for BSN to some extent. However, real noisy datasets usually have relatively limited numbers of samples. AP-BSN directly adopts the strategy of PD, which can only obtain " + }, + { + "bbox": [ + 46, + 72, + 286, + 178 + ], + "type": "inline_equation", + "content": "s^2" + }, + { + "bbox": [ + 46, + 72, + 286, + 178 + ], + "type": "text", + "content": " sub-images for a noisy image (the stride factor of PD is " + }, + { + "bbox": [ + 46, + 72, + 286, + 178 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 72, + 286, + 178 + ], + "type": "text", + "content": "). This will inevitably lead to the insufficient samples, and make the training of BSN less effective. Therefore, the optimal performance of BSN cannot be achieved." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 286, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 286, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 286, + 300 + ], + "type": "text", + "content": "We observe that adding some perturbations to the training images can greatly expand the training data, which improves the performance of BSN. Further, we consider the samples difference as the perturbation. To obtain more random perturbations and more sub-samples, we propose random sub-samples generation (RSG) strategy to break the fixed sampling pattern of PD. Based on this, we propose a new cyclic sampling difference loss for BSN and a new BSN framework in combination with our RSG strategy. In summary, our contributions include:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 310, + 286, + 462 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 59, + 310, + 286, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 310, + 286, + 369 + ], + "spans": [ + { + "bbox": [ + 59, + 310, + 286, + 369 + ], + "type": "text", + "content": "- We provide a new idea about adding perturbations to the training data to improve the BSN performance. Then, we suggest that the sub-samples difference generated by sampling can be considered as perturbations for higher performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 381, + 286, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 381, + 286, + 416 + ], + "spans": [ + { + "bbox": [ + 59, + 381, + 286, + 416 + ], + "type": "text", + "content": "- We propose a new self-supervised framework for real image denoising with random sub-samples generation and cyclic sampling difference loss." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 428, + 286, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 428, + 286, + 462 + ], + "spans": [ + { + "bbox": [ + 59, + 428, + 286, + 462 + ], + "type": "text", + "content": "- Our method performs very favorably against state-of-the-art (SOTA) self-supervised denoising methods on real-world datasets." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 477, + 133, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 477, + 133, + 489 + ], + "spans": [ + { + "bbox": [ + 47, + 477, + 133, + 489 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 498, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 286, + 712 + ], + "type": "text", + "content": "The image denoising task aims to restore a clean image from its noisy counterpart. There are two main types of non-learning-based image denoising: filtering-based methods and model-based methods. Filter-based methods involve using some artificially designed low-pass filter to remove image noise. Taking advantage of the condition of having many similar image blocks in the same image, noise can also be removed by the local similarity of image, such as NLM [5], BM3D [12], etc. Model-based methods involve modeling the distribution of natural images or noise and then using the model distribution before obtaining a clear image with an optimization algorithm, such as WNNM [13]. The learning-based methods are effective ways to reduce image noise. Usually, it can be divided into traditional and deep network-based methods. In recent years, due to the continuous development of the deep learning technology, deep network-based methods have achieved superior denoising results compared to previous methods, and thus" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 544, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 544, + 107 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 544, + 107 + ], + "type": "text", + "content": "they have become the mainstream denoising methods. Generally, deep network-based methods can be further classified according to their training manners." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 116, + 462, + 128 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 116, + 462, + 128 + ], + "spans": [ + { + "bbox": [ + 305, + 116, + 462, + 128 + ], + "type": "text", + "content": "2.1. Supervised Image Denoising" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 134, + 545, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 134, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 134, + 545, + 277 + ], + "type": "text", + "content": "Most of the early works [24, 44, 31, 45, 46] assume that the noise is independent and uniformly distributed, and additive Gaussian white noise (AWGN) is usually used to model image noise and synthetic paired datasets. These methods achieve SOTA results on AWGN denoising tasks. However, the noise model in the real world is complex and unknown. Models trained with synthetic datasets are difficult to be applied to the real world. Recently, most of the methods [14, 2, 19, 41, 43, 6, 42, 29, 9] use produced real-world paired datasets for training. Due to the differences in camera parameters, these methods may not be widely used in the real world." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 285, + 496, + 298 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 285, + 496, + 298 + ], + "spans": [ + { + "bbox": [ + 306, + 285, + 496, + 298 + ], + "type": "text", + "content": "2.2. Pseudo-Supervised Image denoising" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 304, + 545, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 545, + 448 + ], + "type": "text", + "content": "The supervised denoising methods require paired noisy-clean images, while the pseudo-supervised denoising methods relax the data requirements. Noise2Noise [23] proposes that pairs of noisy images can be used to train the network when the noise mean is zero. When some unpaired noisy-clean images are available, some methods [8, 7, 15, 18] learn the noise distribution of noisy images by generative adversarial networks (GAN). Then, clean images are used to generate pseudo-paired noisy-clean images to train the denoising network. However, these methods are still difficult to be applied because the scene distribution of noisy images often does not match the available clean images [18]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 456, + 481, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 456, + 481, + 468 + ], + "spans": [ + { + "bbox": [ + 306, + 456, + 481, + 468 + ], + "type": "text", + "content": "2.3. Self-Supervised Image Denoising" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "content": "The self-supervised denoising methods require single noisy images for training. Noise2Void [20] finds that masking a portion of pixels in noisy images for pairing can train the denoising network, and thus proposes a BSN for self-supervised denoising. Laine19 [21] and D-BSN [36] further optimize the BSN and improve its performance. Noise2Same [37] and Blind2Unblind [35] propose new denoising losses for self-supervised training through mask-based blind-spot methods. Neighbor2Neighbor [17] samples the noisy image into two similar sub-images to form a noisy-noisy pair for training. CVF-SID [25] can disentangle the clean image, signal-dependent and signal-independent noises from the real-world noisy input via various self-supervised training objectives. AP-BSN [22] combines PD and BSN to process real-world sRGB noisy images and employs asymmetric PD stride factors for training and inference. However, current self-supervised methods for real noise removal usually still require a large number of noisy images and are challenging to train with less training data to achieve superior performance." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12151" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 153, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 153, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 153, + 85 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 90, + 172, + 103 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 90, + 172, + 103 + ], + "spans": [ + { + "bbox": [ + 47, + 90, + 172, + 103 + ], + "type": "text", + "content": "3.1. Revisiting Noise2Void" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 109, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 289, + 240 + ], + "type": "text", + "content": "Noise2Void (N2V) [20] requires only single noisy images for training, and it assumes that the noise " + }, + { + "bbox": [ + 46, + 109, + 289, + 240 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 109, + 289, + 240 + ], + "type": "text", + "content": " is pixelwise independent (the noises at different pixel positions are independent) given the clean image " + }, + { + "bbox": [ + 46, + 109, + 289, + 240 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 109, + 289, + 240 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 109, + 289, + 240 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 109, + 289, + 240 + ], + "type": "text", + "content": " is the noisy image, i.e. " + }, + { + "bbox": [ + 46, + 109, + 289, + 240 + ], + "type": "inline_equation", + "content": "y = x + n" + }, + { + "bbox": [ + 46, + 109, + 289, + 240 + ], + "type": "text", + "content": ". Due to the local correlation of the pixels within an image, clean central pixels can be estimated from the surrounding noisy pixels. Therefore, using the pixel of the noisy image as a target for its surrounding pixels will not obtain the noisy pixel. Thus, N2V can train the denoising network in a self-supervised approach. Specifically, N2V loss " + }, + { + "bbox": [ + 46, + 109, + 289, + 240 + ], + "type": "inline_equation", + "content": "L_{N2V}" + }, + { + "bbox": [ + 46, + 109, + 289, + 240 + ], + "type": "text", + "content": " can be written as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 247, + 287, + 262 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 247, + 287, + 262 + ], + "spans": [ + { + "bbox": [ + 104, + 247, + 287, + 262 + ], + "type": "interline_equation", + "content": "L _ {N 2 V} = E _ {y} \\left\\{\\| f \\left(y _ {r}\\right) - y _ {c} \\| _ {2} ^ {2} \\right\\}, \\tag {1}", + "image_path": "f8eeb2f548890cc4d11250b4671c0baa5171b3d46a916b71bca7802256f8028e.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 270, + 287, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 287, + 305 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 287, + 305 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 270, + 287, + 305 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 46, + 270, + 287, + 305 + ], + "type": "text", + "content": " is the normal denoising network, " + }, + { + "bbox": [ + 46, + 270, + 287, + 305 + ], + "type": "inline_equation", + "content": "y_{r}" + }, + { + "bbox": [ + 46, + 270, + 287, + 305 + ], + "type": "text", + "content": " is the patch of " + }, + { + "bbox": [ + 46, + 270, + 287, + 305 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 270, + 287, + 305 + ], + "type": "text", + "content": " centered on " + }, + { + "bbox": [ + 46, + 270, + 287, + 305 + ], + "type": "inline_equation", + "content": "y_{c}" + }, + { + "bbox": [ + 46, + 270, + 287, + 305 + ], + "type": "text", + "content": " with the same dimensions as the network receptive field. Note that " + }, + { + "bbox": [ + 46, + 270, + 287, + 305 + ], + "type": "inline_equation", + "content": "y_{r}" + }, + { + "bbox": [ + 46, + 270, + 287, + 305 + ], + "type": "text", + "content": " does not contain " + }, + { + "bbox": [ + 46, + 270, + 287, + 305 + ], + "type": "inline_equation", + "content": "y_{c}" + }, + { + "bbox": [ + 46, + 270, + 287, + 305 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 306, + 287, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 306, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 306, + 287, + 376 + ], + "type": "text", + "content": "To facilitate the implementation of training with " + }, + { + "bbox": [ + 46, + 306, + 287, + 376 + ], + "type": "inline_equation", + "content": "L_{N2V}" + }, + { + "bbox": [ + 46, + 306, + 287, + 376 + ], + "type": "text", + "content": ", N2V proposes BSN " + }, + { + "bbox": [ + 46, + 306, + 287, + 376 + ], + "type": "inline_equation", + "content": "B(\\cdot)" + }, + { + "bbox": [ + 46, + 306, + 287, + 376 + ], + "type": "text", + "content": " capable of masking centroids. The noisy images used to train the BSN must satisfy the BSN assumption that the noise is pixel-wise independent and zero-mean. BSN can be trained by optimizing the following loss " + }, + { + "bbox": [ + 46, + 306, + 287, + 376 + ], + "type": "inline_equation", + "content": "L_{BSN}" + }, + { + "bbox": [ + 46, + 306, + 287, + 376 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 107, + 384, + 287, + 399 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 384, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 107, + 384, + 287, + 399 + ], + "type": "interline_equation", + "content": "L _ {B S N} = E _ {y} \\left\\{\\left\\| B (y) - y \\right\\| _ {2} ^ {2} \\right\\}. \\tag {2}", + "image_path": "fe1384d82f6180efdbd299b7c9de502054f54fab27c086ab32f8de82041dbd46.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "spans": [ + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "inline_equation", + "content": "L_{N2V}" + }, + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "inline_equation", + "content": "L_{BSN}" + }, + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "text", + "content": " are equivalent for training BSN. For a known noise model (e.g. AWGN model), we can synthesize an infinite number of different noisy images. Thus, BSN can be easily trained. In contrast, since real image datasets often have a limited number of captured images, it is difficult to train BSN directly for real image denoising. Moreover, real images do not satisfy the pixel-wise independent noise assumptions of BSN. Therefore, the limitations of " + }, + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "inline_equation", + "content": "L_{BSN}" + }, + { + "bbox": [ + 46, + 406, + 287, + 526 + ], + "type": "text", + "content": " are significant, and it is not appropriate to use real images directly for BSN." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 533, + 197, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 197, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 197, + 544 + ], + "type": "text", + "content": "3.2. AP-BSN and Its Limitation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 552, + 287, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 287, + 660 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 287, + 660 + ], + "type": "text", + "content": "To make BSN better for the spatially correlated real image noise, AP-BSN [22] introduces PD [47] to break the spatial correlation among real noisy pixels, leading to near pixel-wise independent noise. Therefore, the real image after PD can be considered to meet the BSN assumption [22], and thus can be used as the input for BSN. The original APBSN loss is written as " + }, + { + "bbox": [ + 46, + 552, + 287, + 660 + ], + "type": "inline_equation", + "content": "\\left\\|PD^{-1}(B(PD(y))) - y\\right\\|_1" + }, + { + "bbox": [ + 46, + 552, + 287, + 660 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 552, + 287, + 660 + ], + "type": "inline_equation", + "content": "PD" + }, + { + "bbox": [ + 46, + 552, + 287, + 660 + ], + "type": "text", + "content": " is the PD operator and " + }, + { + "bbox": [ + 46, + 552, + 287, + 660 + ], + "type": "inline_equation", + "content": "PD^{-1}" + }, + { + "bbox": [ + 46, + 552, + 287, + 660 + ], + "type": "text", + "content": " is the inverse operator. To facilitate the analysis, we further write it as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 77, + 668, + 287, + 683 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 668, + 287, + 683 + ], + "spans": [ + { + "bbox": [ + 77, + 668, + 287, + 683 + ], + "type": "interline_equation", + "content": "L _ {A P - B S N} = E _ {y} \\left\\{\\left\\| B (P D (y)) - P D (y) \\right\\| _ {1} \\right\\}. \\tag {3}", + "image_path": "bee077f3c7b7ed4e4c31fbf73b7f8d5917ad47e2b0f3fbd5beb26bd808900270.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "It can be observed that the pattern of pairing is fixed in Eq. (3) (i.e. fixed " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "PD(y)" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "PD(y)" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "). We consider that the" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 318, + 70, + 535, + 118 + ], + "blocks": [ + { + "bbox": [ + 318, + 70, + 535, + 118 + ], + "lines": [ + { + "bbox": [ + 318, + 70, + 535, + 118 + ], + "spans": [ + { + "bbox": [ + 318, + 70, + 535, + 118 + ], + "type": "table", + "html": "
DatasetSet12BSD68Urban100
Fixed seed28.91/0.819227.26/0.747727.66/0.8172
Random seed29.36/0.839927.72/0.772828.81/0.8632
", + "image_path": "a27876a184f8c11ee31d92250432d741ef46b310430cd83183bc15fbde2d5a27.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 124, + 545, + 148 + ], + "lines": [ + { + "bbox": [ + 305, + 124, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 305, + 124, + 545, + 148 + ], + "type": "text", + "content": "Table 1: The effect of different BSN training strategies on PSNR (dB)/SSIM." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 168, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 545, + 335 + ], + "type": "text", + "content": "training of fixed patterns does not affect the performance of BSN when the sample number is large enough. In contrast, it is well known that insufficient sample number may lead to overfitting [39]. Overfitting of noisy-clean pairing training can only have a superior effect on the training datasets and fail on other datasets. However, BSN requires noisy-noisy pairs for training. The overfitting of BSN will make the denoising result fit the noisy image and affect the denoising performance. For synthetic noise, because the noise modelling can generate an infinite number of noisy images, BSN can avoid fitting the noise, resulting in a clean image. But when BSN is used for real noise, real datasets tend to have a much smaller sample number than synthetic datasets. In this case, BSN may fail to get high-quality clean pixels." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 338, + 546, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 546, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 546, + 555 + ], + "type": "text", + "content": "To verify the effect of the number of training images on the denoising results, we train BSN with synthetic images. In this way, we can synthesize any number of noisy images. We employ DIV2K dataset [32] and add Gaussian noise with a level " + }, + { + "bbox": [ + 304, + 338, + 546, + 555 + ], + "type": "inline_equation", + "content": "\\sigma = 25" + }, + { + "bbox": [ + 304, + 338, + 546, + 555 + ], + "type": "text", + "content": " to synthesize noisy images. Two ways are adopted to train BSN with " + }, + { + "bbox": [ + 304, + 338, + 546, + 555 + ], + "type": "inline_equation", + "content": "L_{BSN}" + }, + { + "bbox": [ + 304, + 338, + 546, + 555 + ], + "type": "text", + "content": ": (1) adding noise with fixed seed in each epoch, and (2) adding noise with random seed in each epoch. Then, we perform denoising experiments on the test datasets generated with Gaussian noise (Set12 [44], BSD68 [30], and Urban100 [16]). Table 1 shows the PSNR(dB) and SSIM results in the test datasets for different training strategies. We observe that when a limited number of noisy images (noisy images with fixed seeds) are used to train the BSN, the denoising performance degrades significantly. Therefore, the introduction of PD is practical. Still, considering that the training data of real images are often limited, the direct use of " + }, + { + "bbox": [ + 304, + 338, + 546, + 555 + ], + "type": "inline_equation", + "content": "L_{AP-BSN}" + }, + { + "bbox": [ + 304, + 338, + 546, + 555 + ], + "type": "text", + "content": " may affect the denoising performance for real image denoising." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 571, + 425, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 571, + 425, + 583 + ], + "spans": [ + { + "bbox": [ + 306, + 571, + 425, + 583 + ], + "type": "text", + "content": "3.3. Perturbation in BSN" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "content": "In order to solve the above problems, we suggest adding perturbations to Eq. (3) to increase the number of training data and avoid fitting to the fixed pattern. We should ensure that the sub-images as inputs or targets remain consistent with the BSN assumption after adding perturbations. This is necessary for training the BSN using these sub-images for denoising purposes. A simple solution is using AWGN as the perturbation. Suppose " + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon_{1}" + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon_{2}" + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "content": " are all perturbations of a Gaussian distribution with mean 0 and variance " + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\sigma_{\\epsilon}^{2}" + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "text", + "content": ". We propose three perturbation BSN losses " + }, + { + "bbox": [ + 304, + 594, + 545, + 715 + ], + "type": "inline_equation", + "content": "L_{PBSN_{1,2,3}}" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12152" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 76, + 203, + 198 + ], + "blocks": [ + { + "bbox": [ + 47, + 76, + 203, + 198 + ], + "lines": [ + { + "bbox": [ + 47, + 76, + 203, + 198 + ], + "spans": [ + { + "bbox": [ + 47, + 76, + 203, + 198 + ], + "type": "image", + "image_path": "52989a3c797b92d9d8d1d7180206e0c397bfe720edf3252fdf102a4a17cab174.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 109, + 201, + 482, + 214 + ], + "lines": [ + { + "bbox": [ + 109, + 201, + 482, + 214 + ], + "spans": [ + { + "bbox": [ + 109, + 201, + 482, + 214 + ], + "type": "text", + "content": "Figure 2: Ablation study of " + }, + { + "bbox": [ + 109, + 201, + 482, + 214 + ], + "type": "inline_equation", + "content": "\\sigma_{\\epsilon}" + }, + { + "bbox": [ + 109, + 201, + 482, + 214 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 109, + 201, + 482, + 214 + ], + "type": "inline_equation", + "content": "L_{PBSN_{1,2,3}}" + }, + { + "bbox": [ + 109, + 201, + 482, + 214 + ], + "type": "text", + "content": " for training on the SIDD validation dataset [1]." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 213, + 76, + 370, + 198 + ], + "blocks": [ + { + "bbox": [ + 213, + 76, + 370, + 198 + ], + "lines": [ + { + "bbox": [ + 213, + 76, + 370, + 198 + ], + "spans": [ + { + "bbox": [ + 213, + 76, + 370, + 198 + ], + "type": "image", + "image_path": "9d69cdf5c784e2fb73ec2180f6f0be11c83be8abc637956d5681c61bb55457bb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 381, + 76, + 536, + 198 + ], + "blocks": [ + { + "bbox": [ + 381, + 76, + 536, + 198 + ], + "lines": [ + { + "bbox": [ + 381, + 76, + 536, + 198 + ], + "spans": [ + { + "bbox": [ + 381, + 76, + 536, + 198 + ], + "type": "image", + "image_path": "917afef4c8de27808351cc47a20aff06bbcd548ce7f0053b32d6643aae9bb3b0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 53, + 232, + 282, + 388 + ], + "blocks": [ + { + "bbox": [ + 53, + 232, + 282, + 388 + ], + "lines": [ + { + "bbox": [ + 53, + 232, + 282, + 388 + ], + "spans": [ + { + "bbox": [ + 53, + 232, + 282, + 388 + ], + "type": "image", + "image_path": "f707db4f04ce4917a41ead15691d29397182d5a7e338ccddab8306202dec5f56.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 392, + 287, + 417 + ], + "lines": [ + { + "bbox": [ + 46, + 392, + 287, + 417 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 287, + 417 + ], + "type": "text", + "content": "Figure 3: Ablation study of " + }, + { + "bbox": [ + 46, + 392, + 287, + 417 + ], + "type": "inline_equation", + "content": "\\sigma_{\\epsilon}" + }, + { + "bbox": [ + 46, + 392, + 287, + 417 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 392, + 287, + 417 + ], + "type": "inline_equation", + "content": "L_{PBSN_2}" + }, + { + "bbox": [ + 46, + 392, + 287, + 417 + ], + "type": "text", + "content": " for training in different images." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 437, + 93, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 437, + 93, + 448 + ], + "spans": [ + { + "bbox": [ + 47, + 437, + 93, + 448 + ], + "type": "text", + "content": "as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 53, + 456, + 287, + 501 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 456, + 287, + 501 + ], + "spans": [ + { + "bbox": [ + 53, + 456, + 287, + 501 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {P B S N _ {1}} = E _ {y} \\left\\{\\left\\| B (P D (y) + \\epsilon) - P D (y) \\right\\| _ {1} \\right\\}, \\\\ L _ {P B S N _ {2}} = E _ {y} \\left\\{\\| B (P D (y)) - (P D (y) + \\epsilon) \\| _ {1} \\right\\}, \\tag {4} \\\\ L _ {P B S N _ {3}} = E _ {y} \\left\\{\\| B (P D (y) + \\epsilon_ {1}) - (P D (y) + \\epsilon_ {2}) \\| _ {1} \\right\\}. \\\\ \\end{array}", + "image_path": "24ebb625211d251e8040e380aa878fa540c8710613bc608ab2ce0fd1cc22cbd4.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 508, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 287, + 652 + ], + "type": "text", + "content": "We test the effect of different variances of " + }, + { + "bbox": [ + 46, + 508, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 508, + 287, + 652 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 508, + 287, + 652 + ], + "type": "inline_equation", + "content": "(\\epsilon_{1},\\epsilon_{2})" + }, + { + "bbox": [ + 46, + 508, + 287, + 652 + ], + "type": "text", + "content": " in Eq. (4) on the BSN training, and the results are shown in Figures 2 and 3. We observe that adding suitable perturbations can achieve improvements in BSN performance. Therefore, each of the losses in Eq. (4) fits our vision and can obtain a better BSN by training. In Section 4.3, we analyze the influence of perturbations in detail. The results in Figure 2 show that different perturbation levels' effects on BSN performance vary. The results in Figure 3 show that the appropriate optimal perturbation for different levels of noisy images also varies. Therefore, it is a challenge to choose the appropriate perturbation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 658, + 241, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 241, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 241, + 672 + ], + "type": "text", + "content": "3.4. Sampling Difference as Perturbation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "PD can produce a series of similar sub-images " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "(PD_{1}(y)" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "PD_{2}(y)" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": ", ..., where " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "PD_{i}(\\cdot)" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "-th sub-image obtained after PD). Since the PD sampling process does not" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 306, + 232, + 541, + 353 + ], + "blocks": [ + { + "bbox": [ + 306, + 232, + 541, + 353 + ], + "lines": [ + { + "bbox": [ + 306, + 232, + 541, + 353 + ], + "spans": [ + { + "bbox": [ + 306, + 232, + 541, + 353 + ], + "type": "image", + "image_path": "67121a6b1b4262ee1bd064b5f98878bea499944e46d985ac59dd8d03131edca2.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 355, + 545, + 391 + ], + "lines": [ + { + "bbox": [ + 305, + 355, + 545, + 391 + ], + "spans": [ + { + "bbox": [ + 305, + 355, + 545, + 391 + ], + "type": "text", + "content": "Figure 4: Results of sampling by different methods. The second row is the sampling difference obtained by subtracting the two sub-samples in the first row." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 410, + 545, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 410, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 545, + 457 + ], + "type": "text", + "content": "overlap, the pixels in the sub-images that are at the same position are not located at the same position in the original image. As a result, there are certain differences between these sub-images, which we refer to as sampling difference." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 458, + 546, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 458, + 546, + 625 + ], + "spans": [ + { + "bbox": [ + 304, + 458, + 546, + 625 + ], + "type": "text", + "content": "Based on the previous analysis, it is evident that adding perturbation for training can enhance the performance of BSN, but how to add the appropriate perturbations is a challenge. Since there exists a sampling difference among the sub-images acquired through sampling, this difference can be viewed as a type of perturbation. First of all, according to [22], the sub-images obtained through PD sampling are naturally in line with the BSN assumption. Next, the difference between " + }, + { + "bbox": [ + 304, + 458, + 546, + 625 + ], + "type": "inline_equation", + "content": "PD_{1}(y)" + }, + { + "bbox": [ + 304, + 458, + 546, + 625 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 458, + 546, + 625 + ], + "type": "inline_equation", + "content": "PD_{2}(y)" + }, + { + "bbox": [ + 304, + 458, + 546, + 625 + ], + "type": "text", + "content": " can be considered as the perturbation, so we do not need to add additional perturbations as in Eq. (4). Therefore, " + }, + { + "bbox": [ + 304, + 458, + 546, + 625 + ], + "type": "inline_equation", + "content": "PD_{1}(y)" + }, + { + "bbox": [ + 304, + 458, + 546, + 625 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 458, + 546, + 625 + ], + "type": "inline_equation", + "content": "PD_{2}(y)" + }, + { + "bbox": [ + 304, + 458, + 546, + 625 + ], + "type": "text", + "content": " can be used as the input and target in the BSN training, respectively. Finally, we propose a new sampling difference BSN loss " + }, + { + "bbox": [ + 304, + 458, + 546, + 625 + ], + "type": "inline_equation", + "content": "L_{SDBSN}" + }, + { + "bbox": [ + 304, + 458, + 546, + 625 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 333, + 632, + 545, + 646 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 632, + 545, + 646 + ], + "spans": [ + { + "bbox": [ + 333, + 632, + 545, + 646 + ], + "type": "interline_equation", + "content": "L _ {S D B S N} = E _ {y} \\left\\{\\| B \\left(P D _ {1} (y)\\right) - P D _ {2} (y) \\| _ {1} \\right\\}. \\tag {5}", + "image_path": "b500c81cf17d5067133b5f09dc85d950276319c62c1d3014a85fe72212e152e4.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 658, + 488, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 488, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 488, + 672 + ], + "type": "text", + "content": "3.5. Random Sub-Samples Generation" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "The sampling difference generated by the PD strategy can be obtained by subtracting the two sub-images generated by the PD. The sub-images and the sampling difference" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12153" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 70, + 267, + 245 + ], + "blocks": [ + { + "bbox": [ + 60, + 70, + 267, + 245 + ], + "lines": [ + { + "bbox": [ + 60, + 70, + 267, + 245 + ], + "spans": [ + { + "bbox": [ + 60, + 70, + 267, + 245 + ], + "type": "image", + "image_path": "5a9867a5838425102661ca3953fba7dffcbee5a30f5d659c79a5b9928866861d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 52, + 247, + 282, + 259 + ], + "lines": [ + { + "bbox": [ + 52, + 247, + 282, + 259 + ], + "spans": [ + { + "bbox": [ + 52, + 247, + 282, + 259 + ], + "type": "text", + "content": "Figure 5: Example of generating sub-samples with RSG." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 270, + 105, + 326 + ], + "blocks": [ + { + "bbox": [ + 50, + 270, + 105, + 326 + ], + "lines": [ + { + "bbox": [ + 50, + 270, + 105, + 326 + ], + "spans": [ + { + "bbox": [ + 50, + 270, + 105, + 326 + ], + "type": "image", + "image_path": "d777ebf35cd49b5f436e9ee40c4ff4a63d423d9b5e4494b073a229806bc48190.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 88, + 330, + 124, + 340 + ], + "lines": [ + { + "bbox": [ + 88, + 330, + 124, + 340 + ], + "spans": [ + { + "bbox": [ + 88, + 330, + 124, + 340 + ], + "type": "text", + "content": "(a) SDAP" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 106, + 270, + 162, + 326 + ], + "blocks": [ + { + "bbox": [ + 106, + 270, + 162, + 326 + ], + "lines": [ + { + "bbox": [ + 106, + 270, + 162, + 326 + ], + "spans": [ + { + "bbox": [ + 106, + 270, + 162, + 326 + ], + "type": "image", + "image_path": "714d4c0c98b9b44482049b67c07a9f0ef33793ae263aa2d55a7efb85febea54f.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 342, + 286, + 354 + ], + "lines": [ + { + "bbox": [ + 47, + 342, + 286, + 354 + ], + "spans": [ + { + "bbox": [ + 47, + 342, + 286, + 354 + ], + "type": "text", + "content": "Figure 6: Visual comparison between SDAP and SDAP (E)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 168, + 270, + 223, + 326 + ], + "blocks": [ + { + "bbox": [ + 168, + 270, + 223, + 326 + ], + "lines": [ + { + "bbox": [ + 168, + 270, + 223, + 326 + ], + "spans": [ + { + "bbox": [ + 168, + 270, + 223, + 326 + ], + "type": "image", + "image_path": "986fdd164fba912ead610f0337e258eacde0d0662bd10d4a34f1f65b969503c9.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 199, + 330, + 249, + 341 + ], + "lines": [ + { + "bbox": [ + 199, + 330, + 249, + 341 + ], + "spans": [ + { + "bbox": [ + 199, + 330, + 249, + 341 + ], + "type": "text", + "content": "(b) SDAP (E)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 225, + 270, + 280, + 326 + ], + "blocks": [ + { + "bbox": [ + 225, + 270, + 280, + 326 + ], + "lines": [ + { + "bbox": [ + 225, + 270, + 280, + 326 + ], + "spans": [ + { + "bbox": [ + 225, + 270, + 280, + 326 + ], + "type": "image", + "image_path": "88f183ad01f826b18d4e2ace78db7a458125faaf37986861699a4dd521455df4.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 369, + 286, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 286, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 286, + 464 + ], + "type": "text", + "content": "generated by PD are shown in Figure 4a. It can be observed that the sampling difference generated by PD is similar to the gradient map. Meanwhile, the PD strategy with a stride factor of " + }, + { + "bbox": [ + 46, + 369, + 286, + 464 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 369, + 286, + 464 + ], + "type": "text", + "content": " can only generate " + }, + { + "bbox": [ + 46, + 369, + 286, + 464 + ], + "type": "inline_equation", + "content": "s^2" + }, + { + "bbox": [ + 46, + 369, + 286, + 464 + ], + "type": "text", + "content": " fixed sub-images for the same image, which still faces the data-hungry issue for BSN training. To obtain more sub-samples and make the sampling difference closer to random perturbation, we propose the random sub-samples generation strategy (RSG)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 464, + 286, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 286, + 511 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 286, + 511 + ], + "type": "text", + "content": "The diagram of sub-images generation with the RSG is shown in Figure 5. Assume that the noisy image " + }, + { + "bbox": [ + 46, + 464, + 286, + 511 + ], + "type": "inline_equation", + "content": "(y)" + }, + { + "bbox": [ + 46, + 464, + 286, + 511 + ], + "type": "text", + "content": " length and width are " + }, + { + "bbox": [ + 46, + 464, + 286, + 511 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 464, + 286, + 511 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 464, + 286, + 511 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 464, + 286, + 511 + ], + "type": "text", + "content": ", respectively. The details of RSG are described below:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 54, + 518, + 286, + 683 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 55, + 518, + 286, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 518, + 286, + 567 + ], + "spans": [ + { + "bbox": [ + 55, + 518, + 286, + 567 + ], + "type": "text", + "content": "1. Divide. The image " + }, + { + "bbox": [ + 55, + 518, + 286, + 567 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 55, + 518, + 286, + 567 + ], + "type": "text", + "content": " is divided into " + }, + { + "bbox": [ + 55, + 518, + 286, + 567 + ], + "type": "inline_equation", + "content": "HW / s^2" + }, + { + "bbox": [ + 55, + 518, + 286, + 567 + ], + "type": "text", + "content": " non-overlapping cells with size " + }, + { + "bbox": [ + 55, + 518, + 286, + 567 + ], + "type": "inline_equation", + "content": "s \\times s" + }, + { + "bbox": [ + 55, + 518, + 286, + 567 + ], + "type": "text", + "content": ". Then, we stretch the cells into vectors of length " + }, + { + "bbox": [ + 55, + 518, + 286, + 567 + ], + "type": "inline_equation", + "content": "s^2" + }, + { + "bbox": [ + 55, + 518, + 286, + 567 + ], + "type": "text", + "content": ". For better visualization, we set " + }, + { + "bbox": [ + 55, + 518, + 286, + 567 + ], + "type": "inline_equation", + "content": "s = 2" + }, + { + "bbox": [ + 55, + 518, + 286, + 567 + ], + "type": "text", + "content": " in Figure 5." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 54, + 573, + 286, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 573, + 286, + 609 + ], + "spans": [ + { + "bbox": [ + 54, + 573, + 286, + 609 + ], + "type": "text", + "content": "2. Shuffle. Randomly shuffle the elements within each vector. Since this process is strictly random, the subsamples obtained are different each time." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 54, + 616, + 286, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 616, + 286, + 640 + ], + "spans": [ + { + "bbox": [ + 54, + 616, + 286, + 640 + ], + "type": "text", + "content": "3. Reform. Take the elements at the same position of each vector to form " + }, + { + "bbox": [ + 54, + 616, + 286, + 640 + ], + "type": "inline_equation", + "content": "s^2" + }, + { + "bbox": [ + 54, + 616, + 286, + 640 + ], + "type": "text", + "content": " new vectors of length " + }, + { + "bbox": [ + 54, + 616, + 286, + 640 + ], + "type": "inline_equation", + "content": "HW / s^2" + }, + { + "bbox": [ + 54, + 616, + 286, + 640 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 54, + 647, + 286, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 647, + 286, + 683 + ], + "spans": [ + { + "bbox": [ + 54, + 647, + 286, + 683 + ], + "type": "text", + "content": "4. Reshape. Reshape each vector into a sub-sample of size " + }, + { + "bbox": [ + 54, + 647, + 286, + 683 + ], + "type": "inline_equation", + "content": "[W / s] \\times [H / s]" + }, + { + "bbox": [ + 54, + 647, + 286, + 683 + ], + "type": "text", + "content": ". In this way, " + }, + { + "bbox": [ + 54, + 647, + 286, + 683 + ], + "type": "inline_equation", + "content": "s^2" + }, + { + "bbox": [ + 54, + 647, + 286, + 683 + ], + "type": "text", + "content": " similar sub-samples " + }, + { + "bbox": [ + 54, + 647, + 286, + 683 + ], + "type": "inline_equation", + "content": "(RSG_1(y), RSG_2(y), \\ldots, RSG_{s^2}(y))" + }, + { + "bbox": [ + 54, + 647, + 286, + 683 + ], + "type": "text", + "content": " are obtained." + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "text", + "content": "To maximize the variance of each sub-sample, our sampling is non-overlapping." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 72, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 312 + ], + "type": "text", + "content": "The sub-samples generated by the RSG strategy and their sampling difference is shown in Figure 4b. It can be observed that the use of RSG does make the sampling difference more random. Furthermore, we provide detailed analysis for this phenomenon. Both PD and RSG sample the image directly, so the calculation of the sampling difference can be considered as the deviation in the direction of the line connecting the sampling pixels of the two sub-samples. Since each pixel of the PD sub-sample has a fixed position in the original image, the difference has a fixed offset direction. Due to random sampling, the sampling difference of RSG sub-samples are not fixed in the direction of each pixel deviation, making the difference more random. In addition, as can also be seen from Figure 5, PD is equivalent to obtaining four fixed sub-images of yellow, blue, green and red. While RSG obtains random sub-images of " + }, + { + "bbox": [ + 304, + 72, + 545, + 312 + ], + "type": "inline_equation", + "content": "①②③④" + }, + { + "bbox": [ + 304, + 72, + 545, + 312 + ], + "type": "text", + "content": " with different results for each sampling, which can provide a large number of samples for training. Therefore, RSG strategy can also be considered as a solution to the data-hungry issue of training BSN with real noisy images." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 319, + 504, + 332 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 319, + 504, + 332 + ], + "spans": [ + { + "bbox": [ + 306, + 319, + 504, + 332 + ], + "type": "text", + "content": "3.6. Cyclic Sampling Difference BSN Loss" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 338, + 545, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 545, + 469 + ], + "type": "text", + "content": "According to Eq. (5), only two sub-samples are needed. However, because multiple sub-samples are generated by RSG, using the whole sub-images instead of only two samples in training can better utilize the features of the generated sub-samples, leading to higher performance. Moreover, if only two sub-samples are used for training, the loss of each training iteration will fluctuate seriously, and the training of BSN cannot converge. To preserve the stability of training and to make full use of each sample, we introduce the strategy of cyclic and RSG to propose a new cyclic samples difference BSN loss " + }, + { + "bbox": [ + 304, + 338, + 545, + 469 + ], + "type": "inline_equation", + "content": "L_{CSDBSN}" + }, + { + "bbox": [ + 304, + 338, + 545, + 469 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 319, + 479, + 545, + 534 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 479, + 545, + 534 + ], + "spans": [ + { + "bbox": [ + 319, + 479, + 545, + 534 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {C S D B S N} = \\sum_ {i = 1} ^ {s ^ {2}} \\underbrace {\\left\\| B \\left(R S G _ {i} (y)\\right) - R S G _ {i + 1} (y) \\right\\| _ {1}} _ {\\text {c r o s s - p a i r i n g}} \\tag {6} \\\\ (R S G _ {s ^ {2} + 1} (y) = R S G _ {1} (y)). \\\\ \\end{array}", + "image_path": "c056ca72d7230cf832bdceca9b58e412ccbea2ec28a43281f4df80eb6b0c04bf.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 544, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 662 + ], + "type": "text", + "content": "Since the sub-samples are generated randomly, the training data is also random. The target corresponding to each input in " + }, + { + "bbox": [ + 304, + 544, + 545, + 662 + ], + "type": "inline_equation", + "content": "L_{CSDBSN}" + }, + { + "bbox": [ + 304, + 544, + 545, + 662 + ], + "type": "text", + "content": " is different. Therefore, two sub-samples are avoided to form a fixed mapping during the cycle. This cyclic loss has the following merits: 1) it imposes constraints on the full pixel of the original noisy image; 2) it ensures that all the sub-samples generated by RSG are well exploited; 3) it makes the training of BSN more robust. Figure 7 visually illustrates our training scheme with the cyclic sampling difference BSN loss." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 671, + 461, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 461, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 461, + 684 + ], + "type": "text", + "content": "3.7. Proposed SDAP Framework" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "For the training stage, we first sample the noisy images into " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "s^2" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": " sub-samples by RSG. Then, we denoise sub-samples" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12154" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 69, + 509, + 205 + ], + "blocks": [ + { + "bbox": [ + 82, + 69, + 509, + 205 + ], + "lines": [ + { + "bbox": [ + 82, + 69, + 509, + 205 + ], + "spans": [ + { + "bbox": [ + 82, + 69, + 509, + 205 + ], + "type": "image", + "image_path": "eeb438c784131578e87716403f4e0cd99def64150de071f3a8801fe180db714f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 184, + 207, + 408, + 219 + ], + "lines": [ + { + "bbox": [ + 184, + 207, + 408, + 219 + ], + "spans": [ + { + "bbox": [ + 184, + 207, + 408, + 219 + ], + "type": "text", + "content": "Figure 7: Overview of our proposed SDAP framework." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 231, + 287, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 231, + 287, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 231, + 287, + 291 + ], + "type": "text", + "content": "by BSN. The loss is calculated by cross-pairing the subsamples after denoising with those before denoising. Finally, the above steps are iterated, and the loss function is updated to optimize the BSN until it converges. The training process is shown in the left half of Figure 7." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 292, + 287, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 292, + 287, + 363 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 287, + 363 + ], + "type": "text", + "content": "For the testing stage, due to the randomness of the single RSG, the test results are not fixed. Since the sampling pattern of PD is fixed, the test results are stable for testing. Therefore, for default setting, we directly adopt the strategy of PD. We denoise the sub-images after PD and then stitch them to obtain the final denoised image." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 364, + 288, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 288, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 288, + 533 + ], + "type": "text", + "content": "The PD strategy is introduced in the testing stage to break the spatial correlation of real-world noise. However, this also makes the pixels of the denoised image discontinuous and produces checkerboard artifacts as shown in Figure 6a. To make the denoised image have better visual performance, we propose to denoise the initial denoised image again by BSN to remove the unpleasing artifacts. This performance enhancement method is denoted by \"SDAP (E)\" and is shown in the right half of Figure 7. The comparison of the final visual effect is shown in Figure 6b. The results show that our proposed test strategy can remove checkerboard artifacts and make the images more natural. More details about PD and RSG for testing are provided in Supplementary Material." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 544, + 128, + 556 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 128, + 556 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 128, + 556 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 563, + 180, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 180, + 575 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 180, + 575 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 713 + ], + "type": "text", + "content": "We use the general BSN architecture [36, 22] in our method. According to [22], we empirically set the stride factor " + }, + { + "bbox": [ + 46, + 582, + 288, + 713 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 582, + 288, + 713 + ], + "type": "text", + "content": " of RSG to 5 for training. To ensure the stability of the test, we still use the PD with stride factor 2 for testing and ablation study. During the training, we use Adam as the optimizer with default settings. The initial learning rate is 0.0001, batch size and patch size are set to 16 and " + }, + { + "bbox": [ + 46, + 582, + 288, + 713 + ], + "type": "inline_equation", + "content": "160 \\times 160" + }, + { + "bbox": [ + 46, + 582, + 288, + 713 + ], + "type": "text", + "content": " respectively, and epochs are taken as 15. 25600 patches are used in one epoch. To fine-tune the network, BSN continues to be optimised for 10 epochs. Meanwhile, we decay the learning rate by a factor of 10, reduce batch size to 8, and" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 231, + 545, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 231, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 305, + 231, + 545, + 255 + ], + "type": "text", + "content": "adjust patch size to " + }, + { + "bbox": [ + 305, + 231, + 545, + 255 + ], + "type": "inline_equation", + "content": "250 \\times 250" + }, + { + "bbox": [ + 305, + 231, + 545, + 255 + ], + "type": "text", + "content": ". We use PyTorch to implement our BSN and train it on an NVIDIA RTX 3090 GPU." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 262, + 364, + 273 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 262, + 364, + 273 + ], + "spans": [ + { + "bbox": [ + 306, + 262, + 364, + 273 + ], + "type": "text", + "content": "4.2. Dataset" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 279, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 279, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 304, + 279, + 545, + 388 + ], + "type": "text", + "content": "SIDD [1]. The SIDD dataset uses five representative mobile phone cameras to capture approximately 300,000 noisy images for 10 scenes under different lighting conditions and obtain the corresponding relatively clean images by specific statistical methods. The SIDD dataset provides an SIDD Medium dataset of 320 data pairs for training, an SIDD validation dataset of 1280 image blocks of size " + }, + { + "bbox": [ + 304, + 279, + 545, + 388 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 279, + 545, + 388 + ], + "type": "text", + "content": " for validation, and an SIDD benchmark dataset of 40 high-resolution noisy images for testing." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "text", + "content": "DND [27]. The DND dataset contains 50 high-resolution test image pairs taken by consumer-grade cameras of various sensor sizes. However, because the images are too large, DND cropped all the images to " + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "text", + "content": " image blocks, giving 1000 image blocks for testing. The DND dataset does not provide training images, and the clean images of the test dataset are not publicly available." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 485, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 485, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 305, + 485, + 545, + 510 + ], + "type": "text", + "content": "Note that unless otherwise stated, we used SIDD Medium dataset for training in the following experiments." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 515, + 440, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 440, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 440, + 528 + ], + "type": "text", + "content": "4.3. Analyzing Perturbation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 534, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 534, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 305, + 534, + 545, + 605 + ], + "type": "text", + "content": "We first validate the effect of the perturbation in " + }, + { + "bbox": [ + 305, + 534, + 545, + 605 + ], + "type": "inline_equation", + "content": "L_{AP-BSN}" + }, + { + "bbox": [ + 305, + 534, + 545, + 605 + ], + "type": "text", + "content": " for real-world sRGB image denoising. We train the BSN by " + }, + { + "bbox": [ + 305, + 534, + 545, + 605 + ], + "type": "inline_equation", + "content": "L_{PBSN_{1,2,3}}" + }, + { + "bbox": [ + 305, + 534, + 545, + 605 + ], + "type": "text", + "content": " with different variances of " + }, + { + "bbox": [ + 305, + 534, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 305, + 534, + 545, + 605 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 305, + 534, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\sigma_{\\epsilon} \\in \\{0,5,10,15,20,25\\}" + }, + { + "bbox": [ + 305, + 534, + 545, + 605 + ], + "type": "text", + "content": ". Meanwhile, we also replace PD with RSG for a similar set of experiments. Figure 2 shows the PSNR(dB) results in the SIDD validation set." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "We observe that BSN performs best on SIDD validation dataset when " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\sigma_{\\epsilon} = 5" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " for both PD and RSG. After this, the performance decreases as " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\sigma_{\\epsilon}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " increases. Specifically, for " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "L_{PBSN_{1,2,3}}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ", since the perturbation is added to the training data, when the perturbation is too large, it will significantly change the noise distribution of the training image, making it difficult for the BSN to adapt to the original noise. Therefore, the denoising performance of BSN decreases significantly when " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\sigma_{\\epsilon} > 15" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ". Also, since RSG and perturbation" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12155" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 67, + 545, + 364 + ], + "blocks": [ + { + "bbox": [ + 50, + 67, + 545, + 364 + ], + "lines": [ + { + "bbox": [ + 50, + 67, + 545, + 364 + ], + "spans": [ + { + "bbox": [ + 50, + 67, + 545, + 364 + ], + "type": "table", + "html": "
Type of supervisionTraining dataMethodSIDD validationSIDD benchmarkDND benchmark
Non-learning based-BM3D [12]31.75/0.706125.65/0.68534.51/0.8507
WNNM [13]26.31/0.524025.78/0.80934.67/0.8646
SupervisedPaired noisy-cleanDnCNN [44]26.20/0.441423.66/0.58332.43/0.7900
TNRD [10]26.99/0.744024.73/0.64333.65/0.8306
CBDNet [14]30.83/0.754133.28/0.86838.06/0.9421
RIDNet [2]38.76/0.913237.87/0.94339.25/0.9528
VDN [40]39.29/0.910939.26/0.95539.38/0.9518
Zhou et al. [47]-34.00/0.89838.40/0.945
DeamNet [28]39.40/0.916939.35/0.95539.63/0.9531
Pseudo-supervisedUnpaired noisy-cleanGCBD [8]--35.58/0.9217
D-BSN [36]--37.93/0.9373
C2N [18]35.36/0.890135.35/0.93737.28/0.9237
Paired noisy-noisyR2R [26]35.04/0.844034.78/0.89837.61/0.9368
Self-supervisedSingle noisyN2V [20]29.35/0.651027.68/0.668-
N2S [3]30.72/0.787029.56/0.808-
NAC [38]--36.20/0.9252
Neighbor2Neighbor [17]28.00/0.589027.96/0.67031.40/0.7880
CVF-SID [25]34.17/0.871934.71/0.91736.50/0.9233
AP-BSN [22]34.46/0.850134.90/0.90037.46/0.9244
SDAP (Ours)36.58/0.863036.54/0.91937.71/0.9278
SDAP (S) (Ours)36.71/0.864036.68/0.91938.18/0.9322
SDAP (E) (Ours)37.30/0.893737.24/0.93637.86/0.9366
SDAP (S)(E) (Ours)37.55/0.894337.53/0.93638.56/0.9402
", + "image_path": "e21e6ef90f8c2890378d137fa2c0ab6e064dffc60ad61e96120706b2cba2a39d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 143, + 371, + 449, + 384 + ], + "lines": [ + { + "bbox": [ + 143, + 371, + 449, + 384 + ], + "spans": [ + { + "bbox": [ + 143, + 371, + 449, + 384 + ], + "type": "text", + "content": "Table 2: Quantitative PSNR(dB)/SSIM Results on SIDD and DND Dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 405, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 287, + 477 + ], + "type": "text", + "content": "have similar roles, both are designed to obtain more training data. When the perturbation is too large, the role of RSG is difficult to be reflected. Therefore, when the perturbation is small, the RSG strategy outperforms the PD strategy. When the perturbation is large, the RSG strategy and the PD strategy are used for BSN to obtain similar denoising results." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 478, + 288, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 478, + 288, + 562 + ], + "spans": [ + { + "bbox": [ + 46, + 478, + 288, + 562 + ], + "type": "text", + "content": "In addition, we note that the most suitable perturbation standard deviation " + }, + { + "bbox": [ + 46, + 478, + 288, + 562 + ], + "type": "inline_equation", + "content": "\\sigma_{\\epsilon}" + }, + { + "bbox": [ + 46, + 478, + 288, + 562 + ], + "type": "text", + "content": " is different for each of these images in Figure 3. Nevertheless, when we consider the sampling difference as the perturbation, the BSN performs the best regardless of the data. In Section 4.5, we analyze the sampling difference as perturbation in detail. Therefore, Eq. (6) is the final loss function of our proposed method." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 574, + 185, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 185, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 185, + 586 + ], + "type": "text", + "content": "4.4. Denoising of Real Image" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "We use SIDD validation, SIDD benchmark, and DND benchmark datasets to evaluate the performance of our SDAP in real-world denoising tasks. For the SIDD validation dataset, because the paired noisy-clean images are provided, we can directly test the PSNR/SSIM results. For the SIDD and DND benchmarks, we submit the denoised images to websites for server-side evaluation to obtain the final results (PSNR/SSIM values). To evaluate our model on the three different datasets, we adopt two different strategies for training." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 404, + 545, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 404, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 305, + 404, + 545, + 464 + ], + "type": "text", + "content": "Training on SIDD Medium dataset. We train our self-supervised method with noisy images from the SIDD Medium dataset. Then, the obtained model is evaluated on different datasets. This training method is represented as \"SDAP\" in Table 2." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 484, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 545, + 604 + ], + "type": "text", + "content": "Training on test dataset. Since our method is fully self-supervised [25], instead of using the fixed SIDD Medium dataset for training, we can use the test images for self-supervised training as well. Therefore, we train our method on three test datasets in self-supervised manner, respectively. The trained models are evaluated with the corresponding test datasets. Since the noise distribution of training and test images are identical, this strategy can obtain a BSN model with better performance. Fully self-supervised training method is represented as \"SDAP (S)\" in Table 2." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 605, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 665 + ], + "type": "text", + "content": "It should be noted that \"(S)\" denotes the method to improve the performance in training, while \"(E)\" denotes the way to improve the performance in testing. Thus \"SDAP (S)(E)\" is the way in which the proposed method can achieve the best performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "The results in Table 2 show that this method achieves significantly better results than some traditional methods, such as BM3D, on the SIDD Benchmark test data. Even when compared with some supervised deep learning-based" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12156" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 108, + 247 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 108, + 247 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 108, + 247 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 108, + 247 + ], + "type": "image", + "image_path": "9cfb7647d011532775bf60b57b4a5ee9d664347ef50fb72735fe820143982045.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 69, + 248, + 88, + 256 + ], + "lines": [ + { + "bbox": [ + 69, + 248, 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PDRSG\\( L_{AP-BSN} \\)\\( L_{CSDBSN} \\)PSNR(dB)/SSIM
✓-✓-35.68/0.8382
✓--✓36.19/0.8472
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", + "image_path": "9d7c6af67e8d07089291ef569319f695a8ef9b5950415d8ce81389bd906abaf5.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 373, + 286, + 396 + ], + "lines": [ + { + "bbox": [ + 46, + 373, + 286, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 286, + 396 + ], + "type": "text", + "content": "Table 3: Investigation of RSG and " + }, + { + "bbox": [ + 46, + 373, + 286, + 396 + ], + "type": "inline_equation", + "content": "L_{CSDBSN}" + }, + { + "bbox": [ + 46, + 373, + 286, + 396 + ], + "type": "text", + "content": " on SIDD Validation Dataset." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 421, + 287, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 421, + 287, + 576 + ], + "spans": [ + { + "bbox": [ + 46, + 421, + 287, + 576 + ], + "type": "text", + "content": "image denoising methods, this method achieves superior denoising results. For example, the PSNR and SSIM results of this method are 3.40dB and 0.051 higher compared with CBDNet. When we compared with the SOTA self-supervised image denoising approaches, our method also has obvious advantages. For example, compared with APBSN, which has the same network structure as us, SDAP achieves 1.78dB and 0.019 increases in PSNR and SSIM metrics, respectively. The performance of SDAP on the DND dataset has similar findings as those on SIDD. Figures 1 and 8 provide visual comparisons of several methods, and the results further validate the visual superiority of our method to other methods." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 47, + 586, + 140, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 140, + 600 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 140, + 600 + ], + "type": "text", + "content": "4.5. Ablation Study" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "text", + "content": "We examine two major determinants of our model: a) RSG; b) " + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "inline_equation", + "content": "L_{CSDBSN}" + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "text", + "content": ". If there is a \"√\" in the column of " + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "inline_equation", + "content": "L_{CSDBSN}" + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "inline_equation", + "content": "L_{APBSN}" + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "text", + "content": "), it means that " + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "inline_equation", + "content": "L_{CSDBSN}" + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "inline_equation", + "content": "L_{APBSN}" + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "text", + "content": ") is used for training, and vice versa. If there is a \"√\" in the column of RSG, it means that the RSG strategy is used for training, and we replace all " + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "inline_equation", + "content": "PD" + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "text", + "content": " in the loss with " + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "inline_equation", + "content": "RSG" + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "text", + "content": ". If there is a \"√\" in the column of PD, it means that the PD strategy is used for training, and we replace all " + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "inline_equation", + "content": "RSG" + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "text", + "content": " in the loss with " + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "inline_equation", + "content": "PD" + }, + { + "bbox": [ + 46, + 605, + 287, + 712 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 295, + 545, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 295, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 304, + 295, + 545, + 380 + ], + "type": "text", + "content": "Study of RSG. The performance of training with RSG in Table 3 is always higher than training with PD. A comparison between the first and third rows of Table 3 shows that replacing PD with RSG increases the PSNR/SSIM result by " + }, + { + "bbox": [ + 304, + 295, + 545, + 380 + ], + "type": "inline_equation", + "content": "0.35\\mathrm{dB} / 0.0151" + }, + { + "bbox": [ + 304, + 295, + 545, + 380 + ], + "type": "text", + "content": ". The comparison between the second and fourth rows shows a similar conclusion. These results verify the effectiveness for RSG." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "text", + "content": "Study of " + }, + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "inline_equation", + "content": "L_{CSDBSN}" + }, + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "text", + "content": ". Rows 2 and 4 of Table 3 show the effect of our proposed " + }, + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "inline_equation", + "content": "L_{CSDBSN}" + }, + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "text", + "content": ", where our proposed loss improves the denoising performance by 0.51dB/0.0090 in the case of training with PD and 0.55dB/0.0097 in the case of training with RSG. It is worth noting that, irrespective of whether PD or RSG is used in " + }, + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "inline_equation", + "content": "L_{CSDBSN}" + }, + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "text", + "content": " for BSN training, the performance of BSN is superior to that achieved by directly adding Gaussian perturbations in " + }, + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "inline_equation", + "content": "L_{AP-BSN}" + }, + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "text", + "content": " (i.e., using " + }, + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "inline_equation", + "content": "L_{CSDBSN}" + }, + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "text", + "content": " for training is better than using " + }, + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "inline_equation", + "content": "L_{PBSN_{1,2,3}}" + }, + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 511, + 378, + 523 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 511, + 378, + 523 + ], + "spans": [ + { + "bbox": [ + 306, + 511, + 378, + 523 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 531, + 545, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 545, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 545, + 663 + ], + "type": "text", + "content": "In this paper, we first analyze the reasons for the limited performance of BSN when used for real image denoising. Based on this, we propose to add perturbations to the training data and consider sampling difference as perturbation. Further, we propose SDAP framework with random sub-samples generation and cyclic sampling difference loss. Our SDAP does not require clean images for training and outperforms existing pseudo-supervised/self-supervised methods. We believe that our approach can provide promising inspirations for various self-supervised real-world denoising methods." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgement. This work was supported by the National Natural Science Foundation of China under Grant 62171304." + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12157" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S Brown. 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In AAAI, volume 34, pages 13074-13081, 2020." + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12159" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Randomized Quantization_ A Generic Augmentation for Data Agnostic Self-supervised Learning/35e2ad13-e7ee-4623-a3bb-087851f2da1d_content_list.json b/2023/Randomized Quantization_ A Generic Augmentation for Data Agnostic Self-supervised Learning/35e2ad13-e7ee-4623-a3bb-087851f2da1d_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..7d347a5a165cac683d4718a8b0ab2bc9e3004f68 --- /dev/null +++ b/2023/Randomized Quantization_ A Generic Augmentation for Data Agnostic Self-supervised Learning/35e2ad13-e7ee-4623-a3bb-087851f2da1d_content_list.json @@ -0,0 +1,1642 @@ +[ + { + "type": "text", + "text": "Randomized Quantization: A Generic Augmentation for Data Agnostic Self-supervised Learning", + "text_level": 1, + "bbox": [ + 218, + 130, + 751, + 176 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a0182e3adb250b05ba4be337b7cdbea430bfb423d6fd5d3cc5519784230d7855.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 200, + 916, + 262 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 295, + 313, + 311 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Self-supervised representation learning follows a paradigm of withholding some part of the data and tasking the network to predict it from the remaining part. Among many techniques, data augmentation lies at the core for creating the information gap. Towards this end, masking has emerged as a generic and powerful tool where content is withheld along the sequential dimension, e.g., spatial in images, temporal in audio, and syntactic in language. In this paper, we explore the orthogonal channel dimension for generic data augmentation by exploiting precision redundancy. The data for each channel is quantized through a non-uniform quantizer, with the quantized value sampled randomly within randomly sampled quantization bins. From another perspective, quantization is analogous to channel-wise masking, as it removes the information within each bin, but preserves the information across bins. Our approach significantly surpasses existing generic data augmentation methods, while showing on par performance against modality-specific augmentations. We comprehensively evaluate our approach on vision, audio, 3D point clouds, as well as the DABS benchmark which is comprised of various data modalities. The code is available at https://github.com/microsoft/random_QUantize.", + "bbox": [ + 76, + 328, + 473, + 691 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 717, + 209, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We are witnessing a convergence of multi-modal AI [23, 6] where the architecture and the learning algorithm are unified for various data modalities. This exciting direction abandons the domain-specific knowledge for an individual data modality, but rather pursues a solution far more generalizable.", + "bbox": [ + 76, + 742, + 468, + 830 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "For self-supervised representation learning, masked modeling [23] or simply masking input as an augmentation [75] has emerged as an effective approach. The in", + "bbox": [ + 76, + 834, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b132969fe43a9cf2c64a42fc8117276c67c87b7ec7d32940ba58ea661a50a159.jpg", + "image_caption": [ + "Figure 1. We represent data as a matrix with a sequential dimension and a channel dimension. As a generic data augmentation, masking drops tokens along the sequential dimension. The proposed randomized quantization instead withholds information along the channel dimension. In this figure, we use 1D data of 10 sequential tokens for illustration. Data values are coded in grayscale." + ], + "image_footnote": [], + "bbox": [ + 501, + 299, + 890, + 473 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "put data is represented by a 2D tensor with a sequential dimension and a channel dimension in a modality-agnostic way [3]. The sequential dimension can be spatial in images, temporal in audio, and syntactic in languages. The masking mechanism withholding information along the sequential dimension, and exploits it for supervision. As a result, models learned from the masking supervision demonstrate strong capability for capturing correlations between sequential tokens [38].", + "bbox": [ + 496, + 607, + 893, + 743 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The channel dimension describes the data feature at each sequential location, for example, RGB color at a spatial location or spectrogram frequency at a time step. Despite being generic, masking approaches have neglected to exploit supervision along the channel dimension. While the number of channels for images is as small as three, the channels for audio and tabular data can be as many as hundreds. Formulating the self-supervision from the channel dimension holds much potential for representation learning.", + "bbox": [ + 496, + 746, + 893, + 882 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we draw a connection between the sequen", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution. Work done during an internship at MSRA.", + "bbox": [ + 94, + 886, + 431, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16305", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tial masking operation and quantization by exploring quantization as a novel form of masking along the channel dimension. The data in each channel is dynamically quantized through a non-uniform quantizer, with the quantization value randomly sampled from randomly sampled quantization bins. In this way, information within each quantization bin is masked out, yet information across bins is retained. The information removed by quantization is controlled by the number of bins and the size of the bins, which has been rigorously studied in theory [62]. The larger the distortion rate, the stronger the quantization when it is used as an augmentation for representation learning. The extreme case of using only a single bin is equivalent to dropping the entire channel. We systematically study various quantization configurations for their effects as a data augmentation, for example, with respect to the number bins, uniform or non-uniform bins, and methods to select quantization values.", + "bbox": [ + 75, + 90, + 472, + 361 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We apply the randomized quantizer as the only augmentation, or in conjunction with augmentations along the sequential dimension on state-of-the-art Siamese representation learning methods MoCo-v3 [16] and BYOL [34]. In comparisons with domain-agnostic augmentations based on MixUp [85], our approach achieves state-of-the-art results by a large margin on vision, audio, 3d point cloud, and the DABS benchmark. Compared with domain-specific augmentations, our approach achieves competitive performance against handcrafted augmentations on vision, and state-of-the-art performance on audio and 3d point clouds.", + "bbox": [ + 75, + 363, + 472, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be summarized as follows:", + "bbox": [ + 96, + 529, + 423, + 544 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a simple yet effective data-agnostic augmentation for contrastive learning, based on quantization along the channel dimension.", + "- We design a randomization technique by varying the quantization value and the quantization bins, to enhance data augmentation.", + "- We demonstrate the generality and strong performance of our channel-wise randomized quantization for vision, audio, 3D point clouds and the DABS benchmark in a data-agnostic way." + ], + "bbox": [ + 94, + 550, + 468, + 724 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 76, + 739, + 227, + 753 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Self-supervised learning extracts labels from the data itself and tasks the network to learn transferable representations. Among the earliest forms of self-supervised models are auto-encoders [42] and generative models [41]. But since the input and the output are identical, a neural network may easily find shortcuts and use memorization to solve the generation task. Advances in recent years show that information needs to be withheld from the input to prevent cheating [25]. Pretext tasks such as colorization [86],", + "bbox": [ + 75, + 763, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": " inpainting [58], jigsaw puzzles [55] were proposed in vision, while masked modeling [23], next sentence prediction [46, 45], and replaced word prediction [17] were developed in natural language processing. Speediness [7, 43] and temporal order [73, 52] have been exploited for video representation learning. Due to space limitations, we omit the literature for speech [4], tabular data [1], graph-structured data [65] and many other modalities. The optimal pretext task for each target problem may be different. However, there exists enormous interest in obtaining a single foundation model [9] for all downstream applications.", + "bbox": [ + 496, + 90, + 893, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Instead of withholding data for supervision, contrastive models [78, 56] create new data via data augmentation and compare features extracted using a Siamese network for supervision. Siamese representation learning can be categorized by whether to use explicit negatives [34], ways to define negatives [2], and various loss formulations [13, 83]. However, the main driving signal for learning lies in the augmentations.", + "bbox": [ + 496, + 258, + 893, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Data augmentation enlarges the number of data instances by leveraging prior knowledge of the data and target problem properties. For supervised learning, data augmentation aids in reducing overfitting and regularization [84]. For self-supervised learning, the information gap created by two augmentations provides learning supervision. Typically, the data augmentation function extracts partial information from the data and optionally adds corruptions.", + "bbox": [ + 496, + 382, + 893, + 503 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Popular image-specific augmentations include cropping, scaling, color jittering, Gaussian blurring, cut-out [24], cutmix [82], and auto-augment, which searches for a data augmentation policy [21]. In natural language processing, synonym replacement [74], back translation [11], random word insertion and deletion are most common. For audio and speech, altering the pitch, changing the playback speed, and masking either along the time axis or the frequency axis [57] may improve performance. Additionally, augmenting data through a generative model [10] such as a GAN is a viable approach.", + "bbox": [ + 496, + 503, + 893, + 671 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Domain-agnostic augmentation aims to generalize modality-specific and domain-specific augmentations into a unified formulation. Finding such general priors in data is challenging. One line of work follows Mixup [85], which is initially proposed to improve empirical risk minimization of supervised learning by linearly interpolating data and labels. Because of its generality, later works have explored its application on other data modalities [35], a wide range of problems [50, 40], as well as representation learning [66, 48, 68]. Another important line of work generalizes masked modeling [23], which was initially proposed for language modeling, to other data modalities and domains [38, 67, 79]. The masking mechanism samples a subset of the input data, while Mixup introduces additional corruptions which are not observed in the original data", + "bbox": [ + 496, + 674, + 895, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16306", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/4056949339240c7b23d30d572cfd69596eec22a8cd838f64becb00f0df7e8c51.jpg", + "image_caption": [ + "Figure 2. Visualizing randomized quantization augmentation on images, 3d point clouds, and audio. The first row presents the original signal, and the bottom three rows are augmented views. Randomized quantization alters color and enhances edges on images, spatially samples coordinates on point clouds, and enhances frequency channels for audio." + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 893, + 325 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e8078d9c9c59999acbf47f17d732d091fdceabb0cd0743aebeb4af0de00e188d.jpg", + "image_caption": [ + "Figure 3. Illustration of a non-uniform quantizer with five bins. $a_{i}$ denotes the interval of the quantization bin and $y_{i}$ denotes the reproduction value from each bin." + ], + "image_footnote": [], + "bbox": [ + 78, + 396, + 467, + 433 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "instance. A third line of work tries to mine inherent regularities and structures in the data. NNCLR [26] and MSF [47] use nearest neighbors derived from the current representations as a novel form of augmentation for contrastive learning. Our randomized quantization differs from these works, and augments data along the channel dimension.", + "bbox": [ + 75, + 502, + 468, + 608 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Quantization represents numerical values with a fixed discrete set of numbers so as to reduce communication bandwidth and maintain representation quality. The rounding error was first analyzed a century ago [63], and the theory based on variable-rate quantization [61] and Huffman coding [44] revolutionized the communications industry. We refer readers to a survey [33] that describes this area from a theoretical perspective.", + "bbox": [ + 75, + 611, + 468, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Quantization for efficient neural networks [32] aims to reduce neural network latency while maintaining model accuracy. The advances of half-precision [5, 69] and mixed-precision training [18, 36, 51] has accelerated model training by an order of magnitude. Works have shown that neural networks can be completely binarized [49, 76, 19] with reasonable performance. Stochastic quantization [15, 28, 8] is a technique for learning and compressing model weights in a way that avoids local minima with the low-precision weight representations.", + "bbox": [ + 75, + 733, + 468, + 883 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "There exist two works [12, 30] that study the use of", + "bbox": [ + 96, + 885, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "quantization in contrastive representation learning. In both, quantization is applied on the intermediate features and model weights. Though effective for model compression, the quantization of features/weights can be viewed as unsuitable for augmentation due to the unpredictability of the corresponding change in the input. Our work additionally differs from these methods [12, 30] in its randomization of a non-uniform quantizer. This technique creates a much more complex augmentation space than uniform quantization, generating valid images of greater diversity.", + "bbox": [ + 496, + 396, + 893, + 547 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 500, + 561, + 609, + 579 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This paper proposes a novel generic data augmentation for representation learning based on quantization. We first provide preliminaries on quantization. We then introduce two factors to inject randomness into the quantization procedure.", + "bbox": [ + 496, + 585, + 893, + 660 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries: Quantization", + "text_level": 1, + "bbox": [ + 500, + 671, + 754, + 688 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A quantizer is a function which consists of a set of non-overlapping intervals or bins $S = \\{S_{i} = [a_{i},a_{i + 1})\\} ,i = 0,1,\\ldots n - 1$ , and a set of reproduction values $y_{i}$ . $n$ is the number of intervals and reproduction values. Let $x$ be a one-dimensional input signal. The quantizer maps values within an interval to a single scalar, defined as $q(x) = y_{i}$ for $x\\in S_i$ . Formally, it can be written as", + "bbox": [ + 496, + 695, + 893, + 801 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq (x) = \\sum_ {i} y _ {i} \\cdot 1 _ {S _ {i}} (x), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 616, + 811, + 890, + 844 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the indicator function $1_{S_i}(x) = 1$ if $x \\in S_i$ and $1_{S_i}(x) = 0$ otherwise. Figure 3 gives an illustration of a quantizer with five intervals. Quantization represents the", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16307", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2d5571991a90bf44f7dcabaeaf31f9e132ee3e10535ffffde0b694fdd8225a13.jpg", + "image_caption": [ + "Figure 4. Visualization of quantized images with different numbers of bins. The images are quantized by a uniform quantizer. Fewer than three quantization bins causes severe information reduction, while fifteen or more bins leads to negligible difference from the original image. An intermediate number of bins (e.g., five to ten) is well-suited for image augmentation." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 890, + 258 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2034fca5aec68f902fc1f8cb06c965ccca4cec5576c69ca1db19c0ec9e3187d2.jpg", + "image_caption": [ + "Figure 5. Ablation study on the number of quantization bins. The peak performance is reached at 8 bins. Fewer bins deliver heavier augmentations and larger bins lead to weaker augmentations." + ], + "image_footnote": [], + "bbox": [ + 86, + 334, + 446, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "original signal using a finite number of bits and hence introduces error to signal recovery. The central research problem is to find better tradeoffs between communication bandwidths and reproduction errors.", + "bbox": [ + 75, + 522, + 467, + 583 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Quantization can be categorized by uniform quantization and non-uniform quantization. A uniform quantizer has intervals and values which are evenly spaced, whereas a nonuniform quantizer allows either intervals or values to be unevenly spaced. Uniform quantizers are amenable to hardware deployment. However, non-uniform quantizers may perform better depending on the probabilistic distribution of $x$ .", + "bbox": [ + 75, + 585, + 467, + 705 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Randomized Quantization as Augmentation", + "text_level": 1, + "bbox": [ + 76, + 722, + 447, + 738 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We aim to exploit quantization as a data withholding tool for representation learning. The information within each quantization bin is withheld, while the information across bins are retained. For data augmentation, a key aspect is the complexity of the augmentation space. We design a complex quantization augmentation by randomizing the intervals and the reproduction values. Concretely, given $S_{i} = [a_{i},a_{i + 1})$ , $a_{i}$ is generated by", + "bbox": [ + 75, + 747, + 467, + 868 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\na _ {0}, a _ {1}, \\dots , a _ {n - 1} = \\operatorname {s o r t} \\left(a _ {0} ^ {\\prime}, a _ {1} ^ {\\prime}, \\dots , a _ {n - 1} ^ {\\prime}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 885, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/48dc98471da0236fd5c0348fa31abb9b1fef61fa619d24fc262bec854af1e77c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
random binsrandom valuestop1 acc
baselineXX50.0
+ quantizeXX54.8
+ quantizeX✓62.6
+ quantize✓X66.0
+ quantize✓✓67.9
", + "bbox": [ + 522, + 325, + 867, + 421 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. Ablation study of the two randomness factors for randomized quantization described in Eq. 3 and Eq. 4. We examine the effect of randomized bins and random reproduction values for each bin. These two factors increase the complexity of the augmentation and significantly improve the performance.", + "bbox": [ + 498, + 430, + 890, + 501 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\na _ {i} ^ {\\prime} = U (\\min (x), \\max (x)), i = 0, 1, \\dots , n - 1, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 537, + 890, + 555 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $U$ denotes random sampling with a uniform distribution over the interval, and $\\min(x) / \\max(x)$ refers to the minimum/maximum of the values $x$ per channel. The reproduction value $y_i$ is randomly sampled within the corresponding interval,", + "bbox": [ + 496, + 560, + 890, + 635 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ny _ {i} = U \\left(a _ {i}, a _ {i + 1}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 647, + 890, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The resultant randomized quantizer is non-uniform. The number of quantization bins $n$ is the hyperparameter of the augmentation.", + "bbox": [ + 496, + 672, + 890, + 717 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Data-Agnostic Augmentation", + "text_level": 1, + "bbox": [ + 500, + 726, + 758, + 742 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The proposed randomized quantization augmentation can be applied to the channel dimension for any arbitrary data modality. The physical interpretation of the augmentation depends on the nature of the data modality. In Figure 2, we visualize the augmentations for images, audio and point clouds. On images, it removes the high frequency details but highlights object boundaries and edges. It also alters color appearance significantly. On audio, we examine the augmented sound acoustically and we find the augmentation tends to enhance specific frequency signals, such as", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16308", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/85251e673c00b0885e96996d2bd1ea357ea1f8abb026b23eb91f435b41833ec8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
100-ep300-ep800-ep
MoCo-v367.971.672.1
BYOL67.271.071.6
", + "bbox": [ + 133, + 88, + 415, + 137 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/2947f654c2a6d2131dca6fb58ba104d03921958fcc800f513468c480df3c1e31.jpg", + "table_caption": [ + "Table 2. Representation learning with randomized quantization augmentation benefits from more training epochs without early saturation." + ], + "table_footnote": [], + "table_body": "
AugmentationsMoCo-v3BYOL
CR10.19.9
CR + DACL [68]32.733.2
CR + i-Mix [48]30.328.7
CR + SSQL [12]11.16.4
CR + Ours42.943.0
RRC50.049.3
RRC + DACL [68]57.257.6
RRC + i-Mix [48]55.449.9
RRC + SSQL [12]42.949.3
RRC + Ours67.967.2
", + "bbox": [ + 98, + 200, + 450, + 369 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "low-frequency sounds or high-frequency sounds. On point clouds where the channel dimension represents xyz coordinates, it tends to downsample local structures but highlight the global shape. Some discrete modalities such as language are not directly amenable to quantization, but can be mapped to a continuous representation via a frozen data embedding layer. In Section 5.4, we examine randomized quantization on such input embeddings.", + "bbox": [ + 75, + 474, + 468, + 597 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Siamese Representation Learning", + "text_level": 1, + "bbox": [ + 76, + 608, + 372, + 625 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Siamese representation learning or contrastive learning relies heavily on the quality of the augmentations [34, 87]. We apply the proposed augmentation on Siamese representation learning. At each training iteration, we sample two views from a data instance using randomized quantization by itself or in conjunction with other augmentations. Loss terms such as InfoNCE [56] and L2 are applied on the two views. The MoCo-v3 [16] and BYOL [34] frameworks are followed in this paper, and we refer readers to the original papers for details.", + "bbox": [ + 75, + 632, + 468, + 782 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 799, + 228, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We choose visual representation learning for an ablation study. Random resized cropping is taken as the baseline augmentation, and we apply our randomized quantization after it. Following the MoCo-v3 framework [16], we use ResNet-50 [39] as the backbone network. The optimizer", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/b35e19dfdff92f5c178404d93ea3b0d5eaeb44c60a5fdf6b27e39bc6897c1935.jpg", + "table_caption": [ + "Table 3. Comparisons with alternative domain-agnostic augmentation techniques under the linear classification protocol on ImageNet. CR is short for center crop, and RRC is short for random resized crop. Our randomized quantization approach achieves the best results against prior arts." + ], + "table_footnote": [], + "table_body": "
MethodMoCo-v3BYOL
Ours42.943.0
RRC50.049.4
RRC + CJ60.161.1
RRC + Ours67.967.2
Full68.968.9
", + "bbox": [ + 542, + 87, + 851, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 4. Comparisons with image-specific augmentations under the linear classification protocol on ImageNet. CJ stands for color jittering, and Full includes random resized crop, color jittering, grayscale, Gaussian blurring and solarization. Randomized quantization is stronger than color jittering by a large margin. It falls behind the full handcrafted augmentations by just $1\\%$ .", + "bbox": [ + 496, + 191, + 893, + 276 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "is consistent with MoCo-v3, and the network is optimized for 100 epochs. Representation learning is conducted on the ImageNet-1K dataset [22], and linear classification accuracy is reported on the validation set.", + "bbox": [ + 496, + 300, + 890, + 359 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We ablate three design factors of the proposed quantization-based augmentation which affect its ability to mask channel-wise information.", + "bbox": [ + 496, + 361, + 890, + 406 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Randomizing Bins. The performance of representation learning depends on the complexity of the pretext tasks created from random augmentations. In Table 1, the baseline approach using the random resized crop augmentation obtains $50.0\\%$ top-1 accuracy. Using a fixed uniform quantizer improves the performance mildly to $54.8\\%$ . Randomizing the locations and sizes of bins allows for uneven masking and creates more effective pretext tasks. It improves the performance significantly to $66.0\\%$ .", + "bbox": [ + 496, + 409, + 892, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Randomizing reproduction values. Quantization is also affected by how each bin is represented. Commonly, the values within a bin's range are represented by the midpoint. As an alternative, we also consider taking a random value in the range. Intuitively, random reproduction values lead to bias in the quantization error, making them no longer zero-mean and bringing a stronger augmentation effect. It is found to benefit representation learning, yielding an increase of 1.9 points upon randomizing the bins in Table 1.", + "bbox": [ + 496, + 547, + 893, + 684 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Number of quantization bins. Figure 5 illustrates the effect of various numbers of quantization bins. Intuitively, fewer bins leads to a stronger masking effect and higher cross-view variation. We vary the number of bins and find strong performance with 5-10 bins, peaking at 8 bins. This observation is similar to spatial masking in MAE [38] where an optimal masking ratio is found. In Figure 4, we visualize quantized images with different numbers of bins. To make the visualization consistent and comparable, we use the uniform quantizer in this case. It can be observed that too much information is withheld when using too few bins, and too many bins withdraws too little information.", + "bbox": [ + 496, + 686, + 893, + 867 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training epochs. We further study training the augmentations with more epochs. In Table 2, the performance im", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16309", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/71e6ba549108505ac34224a628fd31dc5995db386cc3d42d7c040efc9201a4a0.jpg", + "image_caption": [ + "Figure 6. Visual comparisons between color jittering and randomized quantization. Randomized quantization exhibits greater change in visual appearance and stronger edge enhancement." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 462, + 200 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "proves from $67.9\\%$ with 100 epochs to $71.6\\%$ with 300 epochs and $72.1\\%$ with 800 epochs. With this complex augmentation, the network benefits from longer training.", + "bbox": [ + 75, + 273, + 468, + 321 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments on Various Modalities", + "text_level": 1, + "bbox": [ + 76, + 335, + 397, + 353 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We examine pre-training with the proposed augmentation across a variety of modalities including 1) vision (Section 5.1); 2) 3D point clouds (Section 5.2); 3) audio (Section 5.3); and 4) the DABS benchmark [66] (Section 5.4) comprised of data from multiple domains. The hyperparameter $n$ indicating the number of bins is tuned for each modality. We leave the description of corresponding datasets, settings and evaluation metrics to each section.", + "bbox": [ + 75, + 361, + 468, + 482 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Images", + "text_level": 1, + "bbox": [ + 76, + 494, + 169, + 510 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare the proposed randomized quantization augmentation against domain-agnostic augmentation baselines, as well as domain-specific augmentations designed for images. The number of quantization bins is chosen as $n = 8$ . The experimental protocol follows the ablation study.", + "bbox": [ + 75, + 518, + 468, + 594 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparisons with domain-agnostic augmentations. Recent works on domain-agnostic augmentation are predominantly adapted from Mixup [85]. For example, i-Mix [48] linearly interpolates input data, and their corresponding virtual labels are generated from the current batch. Similarly, DACL [68] interpolates input but uses it as a way of adding noise to the original data. We also consider a baseline SSQL [12] which jointly performs quantization and contrastive learning for lower bit-width deployment.", + "bbox": [ + 75, + 597, + 468, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Table 3, we compare our approach to these methods on two spatial operations: center crop (CR) and random resize crop (RRC). Center crop amounts to no augmentation, and random resized crop is frequently used in vision applications. Our evaluation is based on two Siamese representation learning frameworks MoCo-v3 and BYOL, since BYOL is said to have different behavior on augmentations.", + "bbox": [ + 75, + 733, + 468, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Randomized quantization performs the best against Mixup-based augmentations. As a standalone augmentation, randomized quantization obtains an accuracy of $42.9\\%$ with MoCo-v3, which outperforms DACL and i-Mix by a", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e2f84bdf6aa44ba1dcfe8370d3c42d7604319da59b2430ec25495398f8145b20.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBackboneEpochsTop1 accuracy
MSF w/wR-5020066.3
OursR-5010067.9
OursR-5030071.6
", + "bbox": [ + 519, + 88, + 874, + 152 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a8eaa62a5787b8943abb722adba6eb79ae3b9256e095c1a43ed31c24f6a4d2ae.jpg", + "table_caption": [ + "Table 5. Comparison with weakly-augmented SSL baseline MSF." + ], + "table_footnote": [], + "table_body": "
1%2%5%10%20%100%
FoldingNet (lin)56.466.975.681.283.688.4
MID-FC (lin)61.573.180.284.286.990.3
Ours (lin)66.774.380.084.587.290.5
Scratch58.571.280.185.488.792.9
MID-FC (ft)67.376.583.688.490.293.0
Ours (ft)71.378.584.988.690.693.0
", + "bbox": [ + 516, + 189, + 875, + 301 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/bb90fce1e6dd2f10858e7dc89bb9d406fab8afd1a39e2afac612d44883dc123f.jpg", + "table_caption": [ + "Table 6. Linear probing (lin) and finetuning (ft) results for the shape classification task on the ModelNet40 dataset. Pre-training is conducted on the ShapeNet dataset. Our augmentation improves the classification accuracy substantially on various ratios of data, especially on very limited $(1\\%)$ data." + ], + "table_footnote": [], + "table_body": "
C.mIoUI.mIoU
1%5%100%1%5%100%
Multi-Task (lin)-73.9-68.280.7-
MID-FC (lin)66.276.582.872.480.984.1
Ours (lin)70.676.982.977.481.984.3
MID-FC (ft)67.677.884.376.282.185.5
Ours (ft)69.578.484.477.882.385.5
", + "bbox": [ + 514, + 392, + 877, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 7. Linear probing (lin) and finetuning (ft) results for the shape segmentation task on the ShapeNet Part dataset. Pre-training is conducted on ShapeNet. Our augmentation improves the performance substantially on various ratios.", + "bbox": [ + 498, + 512, + 890, + 568 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "large margin. In conjunction with random resized crop, a $10\\%$ margin is maintained. SSQL heavily relies on domain-specific augmentations, and in many cases, it fails to improve the baseline when handcrafted augmentations are removed. The results using MoCo-v3 and BYOL training objectives are similar. Overall, randomized quantization achieves state-of-the-art results against domain-agnostic baselines in the vision domain.", + "bbox": [ + 496, + 595, + 890, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparisons with domain-specific augmentations. We further compare with image-specific augmentations for visual representation learning in Table 4. We find that randomized quantization is much stronger than color jittering, which is heavily designed with prior knowledge such as brightness, contrast, and saturation for pixels. In Figure 6, we visualize color jittering and our augmentation. It can be observed that our augmentation leads to stronger and more diverse visual appearances than color jittering. Our augmentation is $1\\%$ weaker than the full augmentation, which includes random resized crop, color jittering, grayscale, Gaussian blurring and solarization successively.", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16310", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1e98045cc473e0542d40e177d1f821d7f4bdc3d0cfc6cc8de34385edf02c987a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
NameTask#ClassesData sizeAvg duration (s)
NSynth (NS) [27]Musical instrument classification11305,9794.0
UrbanSound8K (US8K) [60]Urban sound classification108,7324.0
VoxCeleb1 (VC1) [53]Speaker identification1,211153,5148.2
VoxForge (VF) [from Voxforge.org]Language identification6176,4385.8
Speech Commands V2 (SPCV2) [72]Command classification35105,8291.0
Speech Commands V2 (SPCV2/12) [72]Command classification12105,8291.0
", + "bbox": [ + 107, + 87, + 867, + 199 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/10491982224c7a0d72b153fb3dbca0ef3af9a268f254e3390fd1a406766c16f3.jpg", + "table_caption": [ + "Table 8. Downstream dataset details for audio representation learning." + ], + "table_footnote": [], + "table_body": "
MethodNSUS8KVC1VFSPCV2/12SPCV2Average
TRILL [64]--17.988.174.9--
COLA [59]63.4-29.971.371.762.4-
OpenL3 [20]-78.2-----
COALA [29]73.172.7-----
COLA [59]70.278.530.479.576.776.868.7
BYOL-A [54]74.179.140.190.291.092.277.8
Ours74.278.045.792.695.192.179.6
", + "bbox": [ + 129, + 232, + 844, + 359 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 9. Linear probing results for audio representation learning on six downstream datasets. Pre-training is conducted on the AudioSet dataset. Our model outperforms BYOL-A on four of the six datasets, with an average improvement of $1.8\\%$ .", + "bbox": [ + 75, + 367, + 893, + 398 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with weakly-augmented SSL baselines. We compare the performance with MSF [47] in a weak augmentation setting. MSF implicitly utilizes close nearest neighbors as a form of augmentation. In Table 5, our method is better, and it benefits from longer training (67.9 vs. 71.9). Additionally, we demonstrate our approach on diverse modalities, while MSF only focuses on vision.", + "bbox": [ + 75, + 421, + 473, + 529 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2.3D Point Clouds", + "text_level": 1, + "bbox": [ + 76, + 542, + 240, + 558 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We explore self-supervised representation learning on point clouds, represented by a disordered set of xyz coordinates. The pretraining is conducted on the ShapeNet [14] dataset consisting of 57,449 3D shapes. Octree-based Sparse CNN [70] is used as the backbone network, which takes 3D point clouds as input and extracts point features as well as shape features. We follow the MID-Net [71] model as the baseline, which is trained by a point-wise and instance-wise contrastive loss. The model is trained by a SGD optimizer with a batch size of 32 and a weight decay of $5\\mathrm{e - }4$ . The initial learning rate is 0.03 and decreases by a factor of 10 after 200 and 300 epochs, and the training process terminates after 400 epochs. We apply the randomized quantization augmentation after the base augmentations used in MID-Net. Unlike images and audio which are snapped to grids, strong quantization of point cloud coordinates drastically degrades 3d point data. We thus choose to use a larger number of bins, $n = 30$ , in order to maintain more information. In practice, since the 3d points are sparsified by quantization, we observe a substantial training speedup as a side benefit. For evaluation, we experiment on two downstream tasks: shape classification and segmentation.", + "bbox": [ + 75, + 568, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Shape classification is conducted on ModelNet40 [77] which is composed of 13,834 3D models from 40 categories. For each shape, we extract a global feature with the pre-trained backbone then train a linear classifier, or finetune the network, and report the average classification accuracy in Table 6. We do comparison with FoldingNet [80] and MID-FC [71]. With our augmentation, we improve the classification accuracy over the baseline MID-FC [71] substantially, especially when the training data is limited as shown in Table 6. For example, with $1\\%$ of the training data, we improve the classification accuracy by 5.2 and 4.0 points on linear probing and finetuning, respectively.", + "bbox": [ + 496, + 421, + 893, + 602 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Shape segmentation is conducted on ShapeNet Part [81] with 16,881 3D point clouds from 16 categories. For each shape, we extract point-wise features with the pre-trained backbone then train a segmentation head composed of two fully connected layers, or finetune the network, and report the mean IoU across all categories (C.mIoU) and the mean IoU across all instances (I.mIoU) in Table 7. We do comparison with two unsupervised pretraining methods: MIDFC [71] and Multi-Task [37]. Our results are consistently better than the baselines across different ratios of training data. And similarly to ModelNet40 classification, we observe significant improvements with limited (1% and 5%) training data. For example, with 1% of the training data, our method improves the segmentation performance by 4.4 and 1.9 IoU on linear probing and finetuning, respectively.", + "bbox": [ + 496, + 604, + 895, + 833 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Audio", + "text_level": 1, + "bbox": [ + 500, + 845, + 584, + 859 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We apply randomized quantization to audio representation learning. We use AudioSet [31] as the pretraining", + "bbox": [ + 498, + 869, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16311", + "bbox": [ + 480, + 944, + 517, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/43c72ecefcc6fa576c61fb2a31ec0952ef18e74c30e1527b03d6ca257e82ac94.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodNatural ImagesTextSpeechSensorsChest x-raysImages & TextAverage
Scratch10.142.324.969.868.157.545.5
e-Mix27.944.141.879.572.448.952.4
Ours32.144.744.584.973.454.555.6
", + "bbox": [ + 98, + 87, + 872, + 152 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 10. Evaluation of the representation performance over six modalities in the DABS benchmark. Representations are trained on a single primary dataset for each modality and evaluated on a number of downstream datasets. The performance for each modality is averaged across the downstream datasets and shown in the table.", + "bbox": [ + 75, + 161, + 893, + 205 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "dataset, with 1,963,807 audio samples of 527 classes. The pretrained representation is evaluated on six downstream audio classification datasets, summarized in Table 8.", + "bbox": [ + 75, + 228, + 468, + 272 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We largely follow the experimental settings of BYOL-A [54] and treat it as our baseline.", + "bbox": [ + 76, + 273, + 468, + 303 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We convert audio clips into the commonly used log-scaled spectrogram representation. Random resized crop is used to extract a $64 \\times 96$ frequency-temporal segment for training. We replaced the Mixup augmentation used in BYOL-A with our randomized quantization, with the number of bins set to 5. We follow prior works [54] by using a lightweight 2D convolutional network as the backbone. We train the network using the Adam optimizer with a base learning rate of 3e-4 and a batch size of 256 for 100 epochs.", + "bbox": [ + 75, + 304, + 468, + 439 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 9 summarizes the results on the six downstream classification tasks. Compared against BYOL-A with the Mixup augmentation, our randomized quantization outperforms it in four out of the six tasks. Our approach is particularly stronger by a margin of $5.6\\%$ on the VoxCeleb1 dataset, which is the hardest classification task with 1211 classes among all six tasks. Our improvements tend to be smaller for tasks with fewer classes. On average, the proposed augmentation surpasses the current state-the-of-art BYOL-A by a margin of $1.8\\%$ .", + "bbox": [ + 75, + 441, + 470, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. DABS", + "text_level": 1, + "bbox": [ + 76, + 601, + 161, + 616 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We additionally conduct experiments on the public benchmark DABS [66] which is designed to study domain-agnostic self-supervised representation learning. Since some of its domains are discrete in nature (e.g., language), we first embed the data with a frozen layer and then augment the data embeddings for all the modalities consistently. It contains six data modalities1, covering natural RGB images, multichannel sensor data, English text, audio, chest x-ray images, as well as captioned images. In each domain, pre-training is conducted on a large-scale dataset, and the learned representations are evaluated with linear probing on various in-domain downstream datasets. The average performance for the in-domain downstream datasets is reported. We refer the reader to the benchmark for a full description of the pretraining datasets and in-domain evaluation datasets.", + "bbox": [ + 75, + 625, + 470, + 864 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We follow a leading method e-Mix [66] with a Transformer architecture on this domain-agnostic benchmark. The network is optimized with the Adam optimizer with a learning rate of 1e-4 and weight decay of 1e-4. The training protocol follows e-Mix, and all modalities share the same recipe.", + "bbox": [ + 504, + 228, + 892, + 318 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We apply randomized quantization on the token embeddings before the Transformer. Since the quantization function has zero gradients everywhere, we randomly initialize the token embedding module without updating it. The straight-through estimator can be potentially useful, but it is not the focus of this work.", + "bbox": [ + 496, + 323, + 892, + 412 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 10 summarizes the results for this benchmark. Our model outperforms the baseline e-Mix on all modalities. The improvements on natural images, speech, and sensors are larger than $3\\%$ , while the improvements on text and chest x-rays are relatively smaller, less than $1\\%$ . Both e-Mix and our pretraining seem to hurt the representation quality for captioned images. We hypothesize that the two modalities of images and texts pose significant challenges for a naive contrastive learning approach.", + "bbox": [ + 496, + 419, + 893, + 555 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 583, + 619, + 599 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose randomized quantization as a novel data augmentation tool for self-supervised representation learning. Quantization effectively withholds information within the quantization bins but retains the information across bins. It could be applied on arbitrary data along the channel dimension without domain-specific knowledge. Randomized quantization significantly outperforms existing domain-agnostic augmentations based on Mixup. It compares favorably against domain-specific augmentations on vision, and attains state-of-the-art results on audio and 3D point clouds. We also explored randomized quantization on input data embeddings in a neural network for a wide range of data modalities. Experimental results on the DABS benchmark demonstrate state-of-the-art results for speech, text, images and multiple sensors. Randomized quantization could potentially be applied in a masked modeling framework, where the original images are reconstructed from quantized ones. This direction will be explored in future work.", + "bbox": [ + 496, + 613, + 893, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "1The benchmark also provides an additional multi-lingual text modality. However, it is not evaluated in the original paper. We thus omit this.", + "bbox": [ + 75, + 875, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16312", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Broader Impacts", + "text_level": 1, + "bbox": [ + 76, + 90, + 223, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Although the proposed augmentation is generic in its formulation, it is not guaranteed to work beyond the modalities investigated in this paper. Application of the augmentation for other self-supervised learning frameworks such as masked modeling or generalization to other downstream tasks remains under-explored.", + "bbox": [ + 75, + 114, + 468, + 205 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 76, + 217, + 243, + 234 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We sincerely appreciate Reviewer #5 and AC's unwavering efforts in saving this work from rejection. This research was supported in part by National Natural Science Foundation of China/HKSAR Research Grants Council Joint Research Scheme under Grant N_HKUST627/20, and in part by HKSAR RGC General Research Fund (GRF) #16203319.", + "bbox": [ + 75, + 242, + 468, + 348 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 359, + 174, + 376 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sercan Ö Arik and Tomas Pfister. Tabnet: Attentive interpretable tabular learning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, pages 6679-6687, 2021. 2", + "[2] Philip Bachman, R Devon Hjelm, and William Buchwalter. Learning representations by maximizing mutual information across views. Advances in neural information processing systems, 32, 2019. 2", + "[3] Alexei Baevski, Wei-Ning Hsu, Qiantong Xu, Arun Babu, Ji-atao Gu, and Michael Auli. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.219, + 0.131, + 0.753, + 0.177 + ], + "angle": 0, + "content": "Randomized Quantization: A Generic Augmentation for Data Agnostic Self-supervised Learning" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.202, + 0.918, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.296, + 0.314, + 0.312 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.329, + 0.474, + 0.692 + ], + "angle": 0, + "content": "Self-supervised representation learning follows a paradigm of withholding some part of the data and tasking the network to predict it from the remaining part. Among many techniques, data augmentation lies at the core for creating the information gap. Towards this end, masking has emerged as a generic and powerful tool where content is withheld along the sequential dimension, e.g., spatial in images, temporal in audio, and syntactic in language. In this paper, we explore the orthogonal channel dimension for generic data augmentation by exploiting precision redundancy. The data for each channel is quantized through a non-uniform quantizer, with the quantized value sampled randomly within randomly sampled quantization bins. From another perspective, quantization is analogous to channel-wise masking, as it removes the information within each bin, but preserves the information across bins. Our approach significantly surpasses existing generic data augmentation methods, while showing on par performance against modality-specific augmentations. We comprehensively evaluate our approach on vision, audio, 3D point clouds, as well as the DABS benchmark which is comprised of various data modalities. The code is available at https://github.com/microsoft/random_QUantize." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.718, + 0.21, + 0.734 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.743, + 0.47, + 0.832 + ], + "angle": 0, + "content": "We are witnessing a convergence of multi-modal AI [23, 6] where the architecture and the learning algorithm are unified for various data modalities. This exciting direction abandons the domain-specific knowledge for an individual data modality, but rather pursues a solution far more generalizable." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.835, + 0.47, + 0.88 + ], + "angle": 0, + "content": "For self-supervised representation learning, masked modeling [23] or simply masking input as an augmentation [75] has emerged as an effective approach. The in" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.3, + 0.891, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.479, + 0.895, + 0.577 + ], + "angle": 0, + "content": "Figure 1. We represent data as a matrix with a sequential dimension and a channel dimension. As a generic data augmentation, masking drops tokens along the sequential dimension. The proposed randomized quantization instead withholds information along the channel dimension. In this figure, we use 1D data of 10 sequential tokens for illustration. Data values are coded in grayscale." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.608, + 0.894, + 0.744 + ], + "angle": 0, + "content": "put data is represented by a 2D tensor with a sequential dimension and a channel dimension in a modality-agnostic way [3]. The sequential dimension can be spatial in images, temporal in audio, and syntactic in languages. The masking mechanism withholding information along the sequential dimension, and exploits it for supervision. As a result, models learned from the masking supervision demonstrate strong capability for capturing correlations between sequential tokens [38]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.747, + 0.895, + 0.883 + ], + "angle": 0, + "content": "The channel dimension describes the data feature at each sequential location, for example, RGB color at a spatial location or spectrogram frequency at a time step. Despite being generic, masking approaches have neglected to exploit supervision along the channel dimension. While the number of channels for images is as small as three, the channels for audio and tabular data can be as many as hundreds. Formulating the self-supervision from the channel dimension holds much potential for representation learning." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In this paper, we draw a connection between the sequen" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.432, + 0.9 + ], + "angle": 0, + "content": "*Equal contribution. Work done during an internship at MSRA." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16305" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.362 + ], + "angle": 0, + "content": "tial masking operation and quantization by exploring quantization as a novel form of masking along the channel dimension. The data in each channel is dynamically quantized through a non-uniform quantizer, with the quantization value randomly sampled from randomly sampled quantization bins. In this way, information within each quantization bin is masked out, yet information across bins is retained. The information removed by quantization is controlled by the number of bins and the size of the bins, which has been rigorously studied in theory [62]. The larger the distortion rate, the stronger the quantization when it is used as an augmentation for representation learning. The extreme case of using only a single bin is equivalent to dropping the entire channel. We systematically study various quantization configurations for their effects as a data augmentation, for example, with respect to the number bins, uniform or non-uniform bins, and methods to select quantization values." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.473, + 0.529 + ], + "angle": 0, + "content": "We apply the randomized quantizer as the only augmentation, or in conjunction with augmentations along the sequential dimension on state-of-the-art Siamese representation learning methods MoCo-v3 [16] and BYOL [34]. In comparisons with domain-agnostic augmentations based on MixUp [85], our approach achieves state-of-the-art results by a large margin on vision, audio, 3d point cloud, and the DABS benchmark. Compared with domain-specific augmentations, our approach achieves competitive performance against handcrafted augmentations on vision, and state-of-the-art performance on audio and 3d point clouds." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.53, + 0.424, + 0.545 + ], + "angle": 0, + "content": "Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.551, + 0.47, + 0.596 + ], + "angle": 0, + "content": "- We propose a simple yet effective data-agnostic augmentation for contrastive learning, based on quantization along the channel dimension." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.608, + 0.47, + 0.653 + ], + "angle": 0, + "content": "- We design a randomization technique by varying the quantization value and the quantization bins, to enhance data augmentation." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.664, + 0.47, + 0.725 + ], + "angle": 0, + "content": "- We demonstrate the generality and strong performance of our channel-wise randomized quantization for vision, audio, 3D point clouds and the DABS benchmark in a data-agnostic way." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.551, + 0.47, + 0.725 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.74, + 0.228, + 0.755 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Self-supervised learning extracts labels from the data itself and tasks the network to learn transferable representations. Among the earliest forms of self-supervised models are auto-encoders [42] and generative models [41]. But since the input and the output are identical, a neural network may easily find shortcuts and use memorization to solve the generation task. Advances in recent years show that information needs to be withheld from the input to prevent cheating [25]. Pretext tasks such as colorization [86]," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.258 + ], + "angle": 0, + "content": " inpainting [58], jigsaw puzzles [55] were proposed in vision, while masked modeling [23], next sentence prediction [46, 45], and replaced word prediction [17] were developed in natural language processing. Speediness [7, 43] and temporal order [73, 52] have been exploited for video representation learning. Due to space limitations, we omit the literature for speech [4], tabular data [1], graph-structured data [65] and many other modalities. The optimal pretext task for each target problem may be different. However, there exists enormous interest in obtaining a single foundation model [9] for all downstream applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.259, + 0.895, + 0.38 + ], + "angle": 0, + "content": "Instead of withholding data for supervision, contrastive models [78, 56] create new data via data augmentation and compare features extracted using a Siamese network for supervision. Siamese representation learning can be categorized by whether to use explicit negatives [34], ways to define negatives [2], and various loss formulations [13, 83]. However, the main driving signal for learning lies in the augmentations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.383, + 0.895, + 0.504 + ], + "angle": 0, + "content": "Data augmentation enlarges the number of data instances by leveraging prior knowledge of the data and target problem properties. For supervised learning, data augmentation aids in reducing overfitting and regularization [84]. For self-supervised learning, the information gap created by two augmentations provides learning supervision. Typically, the data augmentation function extracts partial information from the data and optionally adds corruptions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.505, + 0.895, + 0.672 + ], + "angle": 0, + "content": "Popular image-specific augmentations include cropping, scaling, color jittering, Gaussian blurring, cut-out [24], cutmix [82], and auto-augment, which searches for a data augmentation policy [21]. In natural language processing, synonym replacement [74], back translation [11], random word insertion and deletion are most common. For audio and speech, altering the pitch, changing the playback speed, and masking either along the time axis or the frequency axis [57] may improve performance. Additionally, augmenting data through a generative model [10] such as a GAN is a viable approach." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.897, + 0.902 + ], + "angle": 0, + "content": "Domain-agnostic augmentation aims to generalize modality-specific and domain-specific augmentations into a unified formulation. Finding such general priors in data is challenging. One line of work follows Mixup [85], which is initially proposed to improve empirical risk minimization of supervised learning by linearly interpolating data and labels. Because of its generality, later works have explored its application on other data modalities [35], a wide range of problems [50, 40], as well as representation learning [66, 48, 68]. Another important line of work generalizes masked modeling [23], which was initially proposed for language modeling, to other data modalities and domains [38, 67, 79]. The masking mechanism samples a subset of the input data, while Mixup introduces additional corruptions which are not observed in the original data" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "16306" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.894, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.33, + 0.895, + 0.375 + ], + "angle": 0, + "content": "Figure 2. Visualizing randomized quantization augmentation on images, 3d point clouds, and audio. The first row presents the original signal, and the bottom three rows are augmented views. Randomized quantization alters color and enhances edges on images, spatially samples coordinates on point clouds, and enhances frequency channels for audio." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.397, + 0.468, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.439, + 0.472, + 0.482 + ], + "angle": 0, + "content": "Figure 3. Illustration of a non-uniform quantizer with five bins. \\(a_{i}\\) denotes the interval of the quantization bin and \\(y_{i}\\) denotes the reproduction value from each bin." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.503, + 0.47, + 0.609 + ], + "angle": 0, + "content": "instance. A third line of work tries to mine inherent regularities and structures in the data. NNCLR [26] and MSF [47] use nearest neighbors derived from the current representations as a novel form of augmentation for contrastive learning. Our randomized quantization differs from these works, and augments data along the channel dimension." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.47, + 0.734 + ], + "angle": 0, + "content": "Quantization represents numerical values with a fixed discrete set of numbers so as to reduce communication bandwidth and maintain representation quality. The rounding error was first analyzed a century ago [63], and the theory based on variable-rate quantization [61] and Huffman coding [44] revolutionized the communications industry. We refer readers to a survey [33] that describes this area from a theoretical perspective." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.734, + 0.47, + 0.885 + ], + "angle": 0, + "content": "Quantization for efficient neural networks [32] aims to reduce neural network latency while maintaining model accuracy. The advances of half-precision [5, 69] and mixed-precision training [18, 36, 51] has accelerated model training by an order of magnitude. Works have shown that neural networks can be completely binarized [49, 76, 19] with reasonable performance. Stochastic quantization [15, 28, 8] is a technique for learning and compressing model weights in a way that avoids local minima with the low-precision weight representations." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.472, + 0.902 + ], + "angle": 0, + "content": "There exist two works [12, 30] that study the use of" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.397, + 0.895, + 0.549 + ], + "angle": 0, + "content": "quantization in contrastive representation learning. In both, quantization is applied on the intermediate features and model weights. Though effective for model compression, the quantization of features/weights can be viewed as unsuitable for augmentation due to the unpredictability of the corresponding change in the input. Our work additionally differs from these methods [12, 30] in its randomization of a non-uniform quantizer. This technique creates a much more complex augmentation space than uniform quantization, generating valid images of greater diversity." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.562, + 0.61, + 0.58 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.587, + 0.894, + 0.661 + ], + "angle": 0, + "content": "This paper proposes a novel generic data augmentation for representation learning based on quantization. We first provide preliminaries on quantization. We then introduce two factors to inject randomness into the quantization procedure." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.672, + 0.755, + 0.689 + ], + "angle": 0, + "content": "3.1. Preliminaries: Quantization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.696, + 0.894, + 0.803 + ], + "angle": 0, + "content": "A quantizer is a function which consists of a set of non-overlapping intervals or bins \\( S = \\{S_{i} = [a_{i},a_{i + 1})\\} ,i = 0,1,\\ldots n - 1 \\), and a set of reproduction values \\( y_{i} \\). \\( n \\) is the number of intervals and reproduction values. Let \\( x \\) be a one-dimensional input signal. The quantizer maps values within an interval to a single scalar, defined as \\( q(x) = y_{i} \\) for \\( x\\in S_i \\). Formally, it can be written as" + }, + { + "type": "equation", + "bbox": [ + 0.617, + 0.813, + 0.892, + 0.845 + ], + "angle": 0, + "content": "\\[\nq (x) = \\sum_ {i} y _ {i} \\cdot 1 _ {S _ {i}} (x), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "where the indicator function \\(1_{S_i}(x) = 1\\) if \\(x \\in S_i\\) and \\(1_{S_i}(x) = 0\\) otherwise. Figure 3 gives an illustration of a quantizer with five intervals. Quantization represents the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16307" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.891, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.263, + 0.893, + 0.307 + ], + "angle": 0, + "content": "Figure 4. Visualization of quantized images with different numbers of bins. The images are quantized by a uniform quantizer. Fewer than three quantization bins causes severe information reduction, while fifteen or more bins leads to negligible difference from the original image. An intermediate number of bins (e.g., five to ten) is well-suited for image augmentation." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.335, + 0.447, + 0.448 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.452, + 0.47, + 0.495 + ], + "angle": 0, + "content": "Figure 5. Ablation study on the number of quantization bins. The peak performance is reached at 8 bins. Fewer bins deliver heavier augmentations and larger bins lead to weaker augmentations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.468, + 0.584 + ], + "angle": 0, + "content": "original signal using a finite number of bits and hence introduces error to signal recovery. The central research problem is to find better tradeoffs between communication bandwidths and reproduction errors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.468, + 0.706 + ], + "angle": 0, + "content": "Quantization can be categorized by uniform quantization and non-uniform quantization. A uniform quantizer has intervals and values which are evenly spaced, whereas a nonuniform quantizer allows either intervals or values to be unevenly spaced. Uniform quantizers are amenable to hardware deployment. However, non-uniform quantizers may perform better depending on the probabilistic distribution of \\( x \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.723, + 0.449, + 0.739 + ], + "angle": 0, + "content": "3.2. Randomized Quantization as Augmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.748, + 0.468, + 0.869 + ], + "angle": 0, + "content": "We aim to exploit quantization as a data withholding tool for representation learning. The information within each quantization bin is withheld, while the information across bins are retained. For data augmentation, a key aspect is the complexity of the augmentation space. We design a complex quantization augmentation by randomizing the intervals and the reproduction values. Concretely, given \\( S_{i} = [a_{i},a_{i + 1}) \\), \\( a_{i} \\) is generated by" + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.886, + 0.469, + 0.902 + ], + "angle": 0, + "content": "\\[\na _ {0}, a _ {1}, \\dots , a _ {n - 1} = \\operatorname {s o r t} \\left(a _ {0} ^ {\\prime}, a _ {1} ^ {\\prime}, \\dots , a _ {n - 1} ^ {\\prime}\\right) \\tag {2}\n\\]" + }, + { + "type": "table", + "bbox": [ + 0.523, + 0.327, + 0.868, + 0.422 + ], + "angle": 0, + "content": "
random binsrandom valuestop1 acc
baselineXX50.0
+ quantizeXX54.8
+ quantizeX✓62.6
+ quantize✓X66.0
+ quantize✓✓67.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.431, + 0.892, + 0.502 + ], + "angle": 0, + "content": "Table 1. Ablation study of the two randomness factors for randomized quantization described in Eq. 3 and Eq. 4. We examine the effect of randomized bins and random reproduction values for each bin. These two factors increase the complexity of the augmentation and significantly improve the performance." + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.539, + 0.891, + 0.556 + ], + "angle": 0, + "content": "\\[\na _ {i} ^ {\\prime} = U (\\min (x), \\max (x)), i = 0, 1, \\dots , n - 1, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.636 + ], + "angle": 0, + "content": "where \\(U\\) denotes random sampling with a uniform distribution over the interval, and \\(\\min(x) / \\max(x)\\) refers to the minimum/maximum of the values \\(x\\) per channel. The reproduction value \\(y_i\\) is randomly sampled within the corresponding interval," + }, + { + "type": "equation", + "bbox": [ + 0.635, + 0.648, + 0.891, + 0.663 + ], + "angle": 0, + "content": "\\[\ny _ {i} = U \\left(a _ {i}, a _ {i + 1}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.891, + 0.718 + ], + "angle": 0, + "content": "The resultant randomized quantizer is non-uniform. The number of quantization bins \\( n \\) is the hyperparameter of the augmentation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.759, + 0.743 + ], + "angle": 0, + "content": "3.3. Data-Agnostic Augmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The proposed randomized quantization augmentation can be applied to the channel dimension for any arbitrary data modality. The physical interpretation of the augmentation depends on the nature of the data modality. In Figure 2, we visualize the augmentations for images, audio and point clouds. On images, it removes the high frequency details but highlights object boundaries and edges. It also alters color appearance significantly. On audio, we examine the augmented sound acoustically and we find the augmentation tends to enhance specific frequency signals, such as" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16308" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.134, + 0.089, + 0.416, + 0.138 + ], + "angle": 0, + "content": "
100-ep300-ep800-ep
MoCo-v367.971.672.1
BYOL67.271.071.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.147, + 0.47, + 0.188 + ], + "angle": 0, + "content": "Table 2. Representation learning with randomized quantization augmentation benefits from more training epochs without early saturation." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.201, + 0.451, + 0.37 + ], + "angle": 0, + "content": "
AugmentationsMoCo-v3BYOL
CR10.19.9
CR + DACL [68]32.733.2
CR + i-Mix [48]30.328.7
CR + SSQL [12]11.16.4
CR + Ours42.943.0
RRC50.049.3
RRC + DACL [68]57.257.6
RRC + i-Mix [48]55.449.9
RRC + SSQL [12]42.949.3
RRC + Ours67.967.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.38, + 0.47, + 0.45 + ], + "angle": 0, + "content": "Table 3. Comparisons with alternative domain-agnostic augmentation techniques under the linear classification protocol on ImageNet. CR is short for center crop, and RRC is short for random resized crop. Our randomized quantization approach achieves the best results against prior arts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.47, + 0.598 + ], + "angle": 0, + "content": "low-frequency sounds or high-frequency sounds. On point clouds where the channel dimension represents xyz coordinates, it tends to downsample local structures but highlight the global shape. Some discrete modalities such as language are not directly amenable to quantization, but can be mapped to a continuous representation via a frozen data embedding layer. In Section 5.4, we examine randomized quantization on such input embeddings." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.609, + 0.373, + 0.626 + ], + "angle": 0, + "content": "3.4. Siamese Representation Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.633, + 0.47, + 0.784 + ], + "angle": 0, + "content": "Siamese representation learning or contrastive learning relies heavily on the quality of the augmentations [34, 87]. We apply the proposed augmentation on Siamese representation learning. At each training iteration, we sample two views from a data instance using randomized quantization by itself or in conjunction with other augmentations. Loss terms such as InfoNCE [56] and L2 are applied on the two views. The MoCo-v3 [16] and BYOL [34] frameworks are followed in this paper, and we refer readers to the original papers for details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.8, + 0.229, + 0.817 + ], + "angle": 0, + "content": "4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We choose visual representation learning for an ablation study. Random resized cropping is taken as the baseline augmentation, and we apply our randomized quantization after it. Following the MoCo-v3 framework [16], we use ResNet-50 [39] as the backbone network. The optimizer" + }, + { + "type": "table", + "bbox": [ + 0.543, + 0.088, + 0.852, + 0.183 + ], + "angle": 0, + "content": "
MethodMoCo-v3BYOL
Ours42.943.0
RRC50.049.4
RRC + CJ60.161.1
RRC + Ours67.967.2
Full68.968.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.193, + 0.894, + 0.277 + ], + "angle": 0, + "content": "Table 4. Comparisons with image-specific augmentations under the linear classification protocol on ImageNet. CJ stands for color jittering, and Full includes random resized crop, color jittering, grayscale, Gaussian blurring and solarization. Randomized quantization is stronger than color jittering by a large margin. It falls behind the full handcrafted augmentations by just \\(1\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.301, + 0.892, + 0.361 + ], + "angle": 0, + "content": "is consistent with MoCo-v3, and the network is optimized for 100 epochs. Representation learning is conducted on the ImageNet-1K dataset [22], and linear classification accuracy is reported on the validation set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.362, + 0.892, + 0.407 + ], + "angle": 0, + "content": "We ablate three design factors of the proposed quantization-based augmentation which affect its ability to mask channel-wise information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.893, + 0.547 + ], + "angle": 0, + "content": "Randomizing Bins. The performance of representation learning depends on the complexity of the pretext tasks created from random augmentations. In Table 1, the baseline approach using the random resized crop augmentation obtains \\(50.0\\%\\) top-1 accuracy. Using a fixed uniform quantizer improves the performance mildly to \\(54.8\\%\\). Randomizing the locations and sizes of bins allows for uneven masking and creates more effective pretext tasks. It improves the performance significantly to \\(66.0\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.549, + 0.894, + 0.685 + ], + "angle": 0, + "content": "Randomizing reproduction values. Quantization is also affected by how each bin is represented. Commonly, the values within a bin's range are represented by the midpoint. As an alternative, we also consider taking a random value in the range. Intuitively, random reproduction values lead to bias in the quantization error, making them no longer zero-mean and bringing a stronger augmentation effect. It is found to benefit representation learning, yielding an increase of 1.9 points upon randomizing the bins in Table 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.894, + 0.868 + ], + "angle": 0, + "content": "Number of quantization bins. Figure 5 illustrates the effect of various numbers of quantization bins. Intuitively, fewer bins leads to a stronger masking effect and higher cross-view variation. We vary the number of bins and find strong performance with 5-10 bins, peaking at 8 bins. This observation is similar to spatial masking in MAE [38] where an optimal masking ratio is found. In Figure 4, we visualize quantized images with different numbers of bins. To make the visualization consistent and comparable, we use the uniform quantizer in this case. It can be observed that too much information is withheld when using too few bins, and too many bins withdraws too little information." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Training epochs. We further study training the augmentations with more epochs. In Table 2, the performance im" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16309" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.091, + 0.464, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.206, + 0.47, + 0.249 + ], + "angle": 0, + "content": "Figure 6. Visual comparisons between color jittering and randomized quantization. Randomized quantization exhibits greater change in visual appearance and stronger edge enhancement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.275, + 0.47, + 0.322 + ], + "angle": 0, + "content": "proves from \\(67.9\\%\\) with 100 epochs to \\(71.6\\%\\) with 300 epochs and \\(72.1\\%\\) with 800 epochs. With this complex augmentation, the network benefits from longer training." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.336, + 0.398, + 0.354 + ], + "angle": 0, + "content": "5. Experiments on Various Modalities" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.362, + 0.47, + 0.483 + ], + "angle": 0, + "content": "We examine pre-training with the proposed augmentation across a variety of modalities including 1) vision (Section 5.1); 2) 3D point clouds (Section 5.2); 3) audio (Section 5.3); and 4) the DABS benchmark [66] (Section 5.4) comprised of data from multiple domains. The hyperparameter \\( n \\) indicating the number of bins is tuned for each modality. We leave the description of corresponding datasets, settings and evaluation metrics to each section." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.495, + 0.17, + 0.511 + ], + "angle": 0, + "content": "5.1. Images" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.519, + 0.469, + 0.595 + ], + "angle": 0, + "content": "We compare the proposed randomized quantization augmentation against domain-agnostic augmentation baselines, as well as domain-specific augmentations designed for images. The number of quantization bins is chosen as \\( n = 8 \\). The experimental protocol follows the ablation study." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.469, + 0.734 + ], + "angle": 0, + "content": "Comparisons with domain-agnostic augmentations. Recent works on domain-agnostic augmentation are predominantly adapted from Mixup [85]. For example, i-Mix [48] linearly interpolates input data, and their corresponding virtual labels are generated from the current batch. Similarly, DACL [68] interpolates input but uses it as a way of adding noise to the original data. We also consider a baseline SSQL [12] which jointly performs quantization and contrastive learning for lower bit-width deployment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.734, + 0.469, + 0.84 + ], + "angle": 0, + "content": "In Table 3, we compare our approach to these methods on two spatial operations: center crop (CR) and random resize crop (RRC). Center crop amounts to no augmentation, and random resized crop is frequently used in vision applications. Our evaluation is based on two Siamese representation learning frameworks MoCo-v3 and BYOL, since BYOL is said to have different behavior on augmentations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Randomized quantization performs the best against Mixup-based augmentations. As a standalone augmentation, randomized quantization obtains an accuracy of \\(42.9\\%\\) with MoCo-v3, which outperforms DACL and i-Mix by a" + }, + { + "type": "table", + "bbox": [ + 0.52, + 0.089, + 0.875, + 0.153 + ], + "angle": 0, + "content": "
MethodBackboneEpochsTop1 accuracy
MSF w/wR-5020066.3
OursR-5010067.9
OursR-5030071.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.163, + 0.888, + 0.177 + ], + "angle": 0, + "content": "Table 5. Comparison with weakly-augmented SSL baseline MSF." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.19, + 0.877, + 0.302 + ], + "angle": 0, + "content": "
1%2%5%10%20%100%
FoldingNet (lin)56.466.975.681.283.688.4
MID-FC (lin)61.573.180.284.286.990.3
Ours (lin)66.774.380.084.587.290.5
Scratch58.571.280.185.488.792.9
MID-FC (ft)67.376.583.688.490.293.0
Ours (ft)71.378.584.988.690.693.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.31, + 0.892, + 0.38 + ], + "angle": 0, + "content": "Table 6. Linear probing (lin) and finetuning (ft) results for the shape classification task on the ModelNet40 dataset. Pre-training is conducted on the ShapeNet dataset. Our augmentation improves the classification accuracy substantially on various ratios of data, especially on very limited \\((1\\%)\\) data." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.393, + 0.878, + 0.505 + ], + "angle": 0, + "content": "
C.mIoUI.mIoU
1%5%100%1%5%100%
Multi-Task (lin)-73.9-68.280.7-
MID-FC (lin)66.276.582.872.480.984.1
Ours (lin)70.676.982.977.481.984.3
MID-FC (ft)67.677.884.376.282.185.5
Ours (ft)69.578.484.477.882.385.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.513, + 0.892, + 0.569 + ], + "angle": 0, + "content": "Table 7. Linear probing (lin) and finetuning (ft) results for the shape segmentation task on the ShapeNet Part dataset. Pre-training is conducted on ShapeNet. Our augmentation improves the performance substantially on various ratios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.892, + 0.716 + ], + "angle": 0, + "content": "large margin. In conjunction with random resized crop, a \\(10\\%\\) margin is maintained. SSQL heavily relies on domain-specific augmentations, and in many cases, it fails to improve the baseline when handcrafted augmentations are removed. The results using MoCo-v3 and BYOL training objectives are similar. Overall, randomized quantization achieves state-of-the-art results against domain-agnostic baselines in the vision domain." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Comparisons with domain-specific augmentations. We further compare with image-specific augmentations for visual representation learning in Table 4. We find that randomized quantization is much stronger than color jittering, which is heavily designed with prior knowledge such as brightness, contrast, and saturation for pixels. In Figure 6, we visualize color jittering and our augmentation. It can be observed that our augmentation leads to stronger and more diverse visual appearances than color jittering. Our augmentation is \\(1\\%\\) weaker than the full augmentation, which includes random resized crop, color jittering, grayscale, Gaussian blurring and solarization successively." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16310" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.109, + 0.088, + 0.868, + 0.2 + ], + "angle": 0, + "content": "
NameTask#ClassesData sizeAvg duration (s)
NSynth (NS) [27]Musical instrument classification11305,9794.0
UrbanSound8K (US8K) [60]Urban sound classification108,7324.0
VoxCeleb1 (VC1) [53]Speaker identification1,211153,5148.2
VoxForge (VF) [from Voxforge.org]Language identification6176,4385.8
Speech Commands V2 (SPCV2) [72]Command classification35105,8291.0
Speech Commands V2 (SPCV2/12) [72]Command classification12105,8291.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.277, + 0.208, + 0.694, + 0.223 + ], + "angle": 0, + "content": "Table 8. Downstream dataset details for audio representation learning." + }, + { + "type": "table", + "bbox": [ + 0.13, + 0.233, + 0.845, + 0.361 + ], + "angle": 0, + "content": "
MethodNSUS8KVC1VFSPCV2/12SPCV2Average
TRILL [64]--17.988.174.9--
COLA [59]63.4-29.971.371.762.4-
OpenL3 [20]-78.2-----
COALA [29]73.172.7-----
COLA [59]70.278.530.479.576.776.868.7
BYOL-A [54]74.179.140.190.291.092.277.8
Ours74.278.045.792.695.192.179.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.368, + 0.895, + 0.399 + ], + "angle": 0, + "content": "Table 9. Linear probing results for audio representation learning on six downstream datasets. Pre-training is conducted on the AudioSet dataset. Our model outperforms BYOL-A on four of the six datasets, with an average improvement of \\(1.8\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.422, + 0.475, + 0.53 + ], + "angle": 0, + "content": "Comparison with weakly-augmented SSL baselines. We compare the performance with MSF [47] in a weak augmentation setting. MSF implicitly utilizes close nearest neighbors as a form of augmentation. In Table 5, our method is better, and it benefits from longer training (67.9 vs. 71.9). Additionally, we demonstrate our approach on diverse modalities, while MSF only focuses on vision." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.543, + 0.241, + 0.559 + ], + "angle": 0, + "content": "5.2.3D Point Clouds" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We explore self-supervised representation learning on point clouds, represented by a disordered set of xyz coordinates. The pretraining is conducted on the ShapeNet [14] dataset consisting of 57,449 3D shapes. Octree-based Sparse CNN [70] is used as the backbone network, which takes 3D point clouds as input and extracts point features as well as shape features. We follow the MID-Net [71] model as the baseline, which is trained by a point-wise and instance-wise contrastive loss. The model is trained by a SGD optimizer with a batch size of 32 and a weight decay of \\(5\\mathrm{e - }4\\). The initial learning rate is 0.03 and decreases by a factor of 10 after 200 and 300 epochs, and the training process terminates after 400 epochs. We apply the randomized quantization augmentation after the base augmentations used in MID-Net. Unlike images and audio which are snapped to grids, strong quantization of point cloud coordinates drastically degrades 3d point data. We thus choose to use a larger number of bins, \\(n = 30\\), in order to maintain more information. In practice, since the 3d points are sparsified by quantization, we observe a substantial training speedup as a side benefit. For evaluation, we experiment on two downstream tasks: shape classification and segmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.422, + 0.895, + 0.603 + ], + "angle": 0, + "content": "Shape classification is conducted on ModelNet40 [77] which is composed of 13,834 3D models from 40 categories. For each shape, we extract a global feature with the pre-trained backbone then train a linear classifier, or finetune the network, and report the average classification accuracy in Table 6. We do comparison with FoldingNet [80] and MID-FC [71]. With our augmentation, we improve the classification accuracy over the baseline MID-FC [71] substantially, especially when the training data is limited as shown in Table 6. For example, with \\(1\\%\\) of the training data, we improve the classification accuracy by 5.2 and 4.0 points on linear probing and finetuning, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.605, + 0.896, + 0.834 + ], + "angle": 0, + "content": "Shape segmentation is conducted on ShapeNet Part [81] with 16,881 3D point clouds from 16 categories. For each shape, we extract point-wise features with the pre-trained backbone then train a segmentation head composed of two fully connected layers, or finetune the network, and report the mean IoU across all categories (C.mIoU) and the mean IoU across all instances (I.mIoU) in Table 7. We do comparison with two unsupervised pretraining methods: MIDFC [71] and Multi-Task [37]. Our results are consistently better than the baselines across different ratios of training data. And similarly to ModelNet40 classification, we observe significant improvements with limited (1% and 5%) training data. For example, with 1% of the training data, our method improves the segmentation performance by 4.4 and 1.9 IoU on linear probing and finetuning, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.846, + 0.585, + 0.861 + ], + "angle": 0, + "content": "5.3. Audio" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We apply randomized quantization to audio representation learning. We use AudioSet [31] as the pretraining" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "16311" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.099, + 0.088, + 0.873, + 0.153 + ], + "angle": 0, + "content": "
MethodNatural ImagesTextSpeechSensorsChest x-raysImages & TextAverage
Scratch10.142.324.969.868.157.545.5
e-Mix27.944.141.879.572.448.952.4
Ours32.144.744.584.973.454.555.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.162, + 0.895, + 0.207 + ], + "angle": 0, + "content": "Table 10. Evaluation of the representation performance over six modalities in the DABS benchmark. Representations are trained on a single primary dataset for each modality and evaluated on a number of downstream datasets. The performance for each modality is averaged across the downstream datasets and shown in the table." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.229, + 0.47, + 0.273 + ], + "angle": 0, + "content": "dataset, with 1,963,807 audio samples of 527 classes. The pretrained representation is evaluated on six downstream audio classification datasets, summarized in Table 8." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.275, + 0.47, + 0.304 + ], + "angle": 0, + "content": "We largely follow the experimental settings of BYOL-A [54] and treat it as our baseline." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.305, + 0.47, + 0.44 + ], + "angle": 0, + "content": "We convert audio clips into the commonly used log-scaled spectrogram representation. Random resized crop is used to extract a \\(64 \\times 96\\) frequency-temporal segment for training. We replaced the Mixup augmentation used in BYOL-A with our randomized quantization, with the number of bins set to 5. We follow prior works [54] by using a lightweight 2D convolutional network as the backbone. We train the network using the Adam optimizer with a base learning rate of 3e-4 and a batch size of 256 for 100 epochs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.471, + 0.593 + ], + "angle": 0, + "content": "Table 9 summarizes the results on the six downstream classification tasks. Compared against BYOL-A with the Mixup augmentation, our randomized quantization outperforms it in four out of the six tasks. Our approach is particularly stronger by a margin of \\(5.6\\%\\) on the VoxCeleb1 dataset, which is the hardest classification task with 1211 classes among all six tasks. Our improvements tend to be smaller for tasks with fewer classes. On average, the proposed augmentation surpasses the current state-the-of-art BYOL-A by a margin of \\(1.8\\%\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.602, + 0.163, + 0.617 + ], + "angle": 0, + "content": "5.4. DABS" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.471, + 0.866 + ], + "angle": 0, + "content": "We additionally conduct experiments on the public benchmark DABS [66] which is designed to study domain-agnostic self-supervised representation learning. Since some of its domains are discrete in nature (e.g., language), we first embed the data with a frozen layer and then augment the data embeddings for all the modalities consistently. It contains six data modalities1, covering natural RGB images, multichannel sensor data, English text, audio, chest x-ray images, as well as captioned images. In each domain, pre-training is conducted on a large-scale dataset, and the learned representations are evaluated with linear probing on various in-domain downstream datasets. The average performance for the in-domain downstream datasets is reported. We refer the reader to the benchmark for a full description of the pretraining datasets and in-domain evaluation datasets." + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.229, + 0.893, + 0.319 + ], + "angle": 0, + "content": "We follow a leading method e-Mix [66] with a Transformer architecture on this domain-agnostic benchmark. The network is optimized with the Adam optimizer with a learning rate of 1e-4 and weight decay of 1e-4. The training protocol follows e-Mix, and all modalities share the same recipe." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.324, + 0.893, + 0.414 + ], + "angle": 0, + "content": "We apply randomized quantization on the token embeddings before the Transformer. Since the quantization function has zero gradients everywhere, we randomly initialize the token embedding module without updating it. The straight-through estimator can be potentially useful, but it is not the focus of this work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.42, + 0.895, + 0.556 + ], + "angle": 0, + "content": "Table 10 summarizes the results for this benchmark. Our model outperforms the baseline e-Mix on all modalities. The improvements on natural images, speech, and sensors are larger than \\(3\\%\\), while the improvements on text and chest x-rays are relatively smaller, less than \\(1\\%\\). Both e-Mix and our pretraining seem to hurt the representation quality for captioned images. We hypothesize that the two modalities of images and texts pose significant challenges for a naive contrastive learning approach." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.584, + 0.62, + 0.6 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.9 + ], + "angle": 0, + "content": "We propose randomized quantization as a novel data augmentation tool for self-supervised representation learning. Quantization effectively withholds information within the quantization bins but retains the information across bins. It could be applied on arbitrary data along the channel dimension without domain-specific knowledge. Randomized quantization significantly outperforms existing domain-agnostic augmentations based on Mixup. It compares favorably against domain-specific augmentations on vision, and attains state-of-the-art results on audio and 3D point clouds. We also explored randomized quantization on input data embeddings in a neural network for a wide range of data modalities. Experimental results on the DABS benchmark demonstrate state-of-the-art results for speech, text, images and multiple sensors. Randomized quantization could potentially be applied in a masked modeling framework, where the original images are reconstructed from quantized ones. This direction will be explored in future work." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.47, + 0.903 + ], + "angle": 0, + "content": "1The benchmark also provides an additional multi-lingual text modality. However, it is not evaluated in the original paper. We thus omit this." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "16312" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.224, + 0.108 + ], + "angle": 0, + "content": "Broader Impacts" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.47, + 0.207 + ], + "angle": 0, + "content": "Although the proposed augmentation is generic in its formulation, it is not guaranteed to work beyond the modalities investigated in this paper. Application of the augmentation for other self-supervised learning frameworks such as masked modeling or generalization to other downstream tasks remains under-explored." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.218, + 0.245, + 0.236 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.47, + 0.349 + ], + "angle": 0, + "content": "We sincerely appreciate Reviewer #5 and AC's unwavering efforts in saving this work from rejection. This research was supported in part by National Natural Science Foundation of China/HKSAR Research Grants Council Joint Research Scheme under Grant N_HKUST627/20, and in part by HKSAR RGC General Research Fund (GRF) #16203319." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.361, + 0.175, + 0.377 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.385, + 0.47, + 0.439 + ], + "angle": 0, + "content": "[1] Sercan Ö Arik and Tomas Pfister. 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In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, pages 10990-10998, 2021. 5" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.53 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16316" + } + ] +] \ No newline at end of file diff --git a/2023/Randomized Quantization_ A Generic Augmentation for Data Agnostic Self-supervised Learning/35e2ad13-e7ee-4623-a3bb-087851f2da1d_origin.pdf b/2023/Randomized Quantization_ A Generic Augmentation for Data Agnostic Self-supervised Learning/35e2ad13-e7ee-4623-a3bb-087851f2da1d_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3d4ce2d24e69c99d5abaed6fd1959b6525316918 --- /dev/null +++ b/2023/Randomized Quantization_ A Generic Augmentation for Data Agnostic Self-supervised Learning/35e2ad13-e7ee-4623-a3bb-087851f2da1d_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0ec41b1e70b96ff25b9a7a329c5ba2356e7395f81a59c3f95879316d1a35d6eb +size 8844764 diff --git a/2023/Randomized Quantization_ A Generic Augmentation for Data Agnostic Self-supervised Learning/full.md b/2023/Randomized Quantization_ A Generic Augmentation for Data Agnostic Self-supervised Learning/full.md new file mode 100644 index 0000000000000000000000000000000000000000..bbfdff2b5f28f10a6bc67b21eb70273b21a4960a --- /dev/null +++ b/2023/Randomized Quantization_ A Generic Augmentation for Data Agnostic Self-supervised Learning/full.md @@ -0,0 +1,339 @@ +# Randomized Quantization: A Generic Augmentation for Data Agnostic Self-supervised Learning + +![](images/a0182e3adb250b05ba4be337b7cdbea430bfb423d6fd5d3cc5519784230d7855.jpg) + +# Abstract + +Self-supervised representation learning follows a paradigm of withholding some part of the data and tasking the network to predict it from the remaining part. Among many techniques, data augmentation lies at the core for creating the information gap. Towards this end, masking has emerged as a generic and powerful tool where content is withheld along the sequential dimension, e.g., spatial in images, temporal in audio, and syntactic in language. In this paper, we explore the orthogonal channel dimension for generic data augmentation by exploiting precision redundancy. The data for each channel is quantized through a non-uniform quantizer, with the quantized value sampled randomly within randomly sampled quantization bins. From another perspective, quantization is analogous to channel-wise masking, as it removes the information within each bin, but preserves the information across bins. Our approach significantly surpasses existing generic data augmentation methods, while showing on par performance against modality-specific augmentations. We comprehensively evaluate our approach on vision, audio, 3D point clouds, as well as the DABS benchmark which is comprised of various data modalities. The code is available at https://github.com/microsoft/random_QUantize. + +# 1. Introduction + +We are witnessing a convergence of multi-modal AI [23, 6] where the architecture and the learning algorithm are unified for various data modalities. This exciting direction abandons the domain-specific knowledge for an individual data modality, but rather pursues a solution far more generalizable. + +For self-supervised representation learning, masked modeling [23] or simply masking input as an augmentation [75] has emerged as an effective approach. The in + +![](images/b132969fe43a9cf2c64a42fc8117276c67c87b7ec7d32940ba58ea661a50a159.jpg) +Figure 1. We represent data as a matrix with a sequential dimension and a channel dimension. As a generic data augmentation, masking drops tokens along the sequential dimension. The proposed randomized quantization instead withholds information along the channel dimension. In this figure, we use 1D data of 10 sequential tokens for illustration. Data values are coded in grayscale. + +put data is represented by a 2D tensor with a sequential dimension and a channel dimension in a modality-agnostic way [3]. The sequential dimension can be spatial in images, temporal in audio, and syntactic in languages. The masking mechanism withholding information along the sequential dimension, and exploits it for supervision. As a result, models learned from the masking supervision demonstrate strong capability for capturing correlations between sequential tokens [38]. + +The channel dimension describes the data feature at each sequential location, for example, RGB color at a spatial location or spectrogram frequency at a time step. Despite being generic, masking approaches have neglected to exploit supervision along the channel dimension. While the number of channels for images is as small as three, the channels for audio and tabular data can be as many as hundreds. Formulating the self-supervision from the channel dimension holds much potential for representation learning. + +In this paper, we draw a connection between the sequen + +tial masking operation and quantization by exploring quantization as a novel form of masking along the channel dimension. The data in each channel is dynamically quantized through a non-uniform quantizer, with the quantization value randomly sampled from randomly sampled quantization bins. In this way, information within each quantization bin is masked out, yet information across bins is retained. The information removed by quantization is controlled by the number of bins and the size of the bins, which has been rigorously studied in theory [62]. The larger the distortion rate, the stronger the quantization when it is used as an augmentation for representation learning. The extreme case of using only a single bin is equivalent to dropping the entire channel. We systematically study various quantization configurations for their effects as a data augmentation, for example, with respect to the number bins, uniform or non-uniform bins, and methods to select quantization values. + +We apply the randomized quantizer as the only augmentation, or in conjunction with augmentations along the sequential dimension on state-of-the-art Siamese representation learning methods MoCo-v3 [16] and BYOL [34]. In comparisons with domain-agnostic augmentations based on MixUp [85], our approach achieves state-of-the-art results by a large margin on vision, audio, 3d point cloud, and the DABS benchmark. Compared with domain-specific augmentations, our approach achieves competitive performance against handcrafted augmentations on vision, and state-of-the-art performance on audio and 3d point clouds. + +Our contributions can be summarized as follows: + +- We propose a simple yet effective data-agnostic augmentation for contrastive learning, based on quantization along the channel dimension. +- We design a randomization technique by varying the quantization value and the quantization bins, to enhance data augmentation. +- We demonstrate the generality and strong performance of our channel-wise randomized quantization for vision, audio, 3D point clouds and the DABS benchmark in a data-agnostic way. + +# 2. Related Works + +Self-supervised learning extracts labels from the data itself and tasks the network to learn transferable representations. Among the earliest forms of self-supervised models are auto-encoders [42] and generative models [41]. But since the input and the output are identical, a neural network may easily find shortcuts and use memorization to solve the generation task. Advances in recent years show that information needs to be withheld from the input to prevent cheating [25]. Pretext tasks such as colorization [86], + +inpainting [58], jigsaw puzzles [55] were proposed in vision, while masked modeling [23], next sentence prediction [46, 45], and replaced word prediction [17] were developed in natural language processing. Speediness [7, 43] and temporal order [73, 52] have been exploited for video representation learning. Due to space limitations, we omit the literature for speech [4], tabular data [1], graph-structured data [65] and many other modalities. The optimal pretext task for each target problem may be different. However, there exists enormous interest in obtaining a single foundation model [9] for all downstream applications. + +Instead of withholding data for supervision, contrastive models [78, 56] create new data via data augmentation and compare features extracted using a Siamese network for supervision. Siamese representation learning can be categorized by whether to use explicit negatives [34], ways to define negatives [2], and various loss formulations [13, 83]. However, the main driving signal for learning lies in the augmentations. + +Data augmentation enlarges the number of data instances by leveraging prior knowledge of the data and target problem properties. For supervised learning, data augmentation aids in reducing overfitting and regularization [84]. For self-supervised learning, the information gap created by two augmentations provides learning supervision. Typically, the data augmentation function extracts partial information from the data and optionally adds corruptions. + +Popular image-specific augmentations include cropping, scaling, color jittering, Gaussian blurring, cut-out [24], cutmix [82], and auto-augment, which searches for a data augmentation policy [21]. In natural language processing, synonym replacement [74], back translation [11], random word insertion and deletion are most common. For audio and speech, altering the pitch, changing the playback speed, and masking either along the time axis or the frequency axis [57] may improve performance. Additionally, augmenting data through a generative model [10] such as a GAN is a viable approach. + +Domain-agnostic augmentation aims to generalize modality-specific and domain-specific augmentations into a unified formulation. Finding such general priors in data is challenging. One line of work follows Mixup [85], which is initially proposed to improve empirical risk minimization of supervised learning by linearly interpolating data and labels. Because of its generality, later works have explored its application on other data modalities [35], a wide range of problems [50, 40], as well as representation learning [66, 48, 68]. Another important line of work generalizes masked modeling [23], which was initially proposed for language modeling, to other data modalities and domains [38, 67, 79]. The masking mechanism samples a subset of the input data, while Mixup introduces additional corruptions which are not observed in the original data + +![](images/4056949339240c7b23d30d572cfd69596eec22a8cd838f64becb00f0df7e8c51.jpg) +Figure 2. Visualizing randomized quantization augmentation on images, 3d point clouds, and audio. The first row presents the original signal, and the bottom three rows are augmented views. Randomized quantization alters color and enhances edges on images, spatially samples coordinates on point clouds, and enhances frequency channels for audio. + +![](images/e8078d9c9c59999acbf47f17d732d091fdceabb0cd0743aebeb4af0de00e188d.jpg) +Figure 3. Illustration of a non-uniform quantizer with five bins. $a_{i}$ denotes the interval of the quantization bin and $y_{i}$ denotes the reproduction value from each bin. + +instance. A third line of work tries to mine inherent regularities and structures in the data. NNCLR [26] and MSF [47] use nearest neighbors derived from the current representations as a novel form of augmentation for contrastive learning. Our randomized quantization differs from these works, and augments data along the channel dimension. + +Quantization represents numerical values with a fixed discrete set of numbers so as to reduce communication bandwidth and maintain representation quality. The rounding error was first analyzed a century ago [63], and the theory based on variable-rate quantization [61] and Huffman coding [44] revolutionized the communications industry. We refer readers to a survey [33] that describes this area from a theoretical perspective. + +Quantization for efficient neural networks [32] aims to reduce neural network latency while maintaining model accuracy. The advances of half-precision [5, 69] and mixed-precision training [18, 36, 51] has accelerated model training by an order of magnitude. Works have shown that neural networks can be completely binarized [49, 76, 19] with reasonable performance. Stochastic quantization [15, 28, 8] is a technique for learning and compressing model weights in a way that avoids local minima with the low-precision weight representations. + +There exist two works [12, 30] that study the use of + +quantization in contrastive representation learning. In both, quantization is applied on the intermediate features and model weights. Though effective for model compression, the quantization of features/weights can be viewed as unsuitable for augmentation due to the unpredictability of the corresponding change in the input. Our work additionally differs from these methods [12, 30] in its randomization of a non-uniform quantizer. This technique creates a much more complex augmentation space than uniform quantization, generating valid images of greater diversity. + +# 3. Approach + +This paper proposes a novel generic data augmentation for representation learning based on quantization. We first provide preliminaries on quantization. We then introduce two factors to inject randomness into the quantization procedure. + +# 3.1. Preliminaries: Quantization + +A quantizer is a function which consists of a set of non-overlapping intervals or bins $S = \{S_{i} = [a_{i},a_{i + 1})\} ,i = 0,1,\ldots n - 1$ , and a set of reproduction values $y_{i}$ . $n$ is the number of intervals and reproduction values. Let $x$ be a one-dimensional input signal. The quantizer maps values within an interval to a single scalar, defined as $q(x) = y_{i}$ for $x\in S_i$ . Formally, it can be written as + +$$ +q (x) = \sum_ {i} y _ {i} \cdot 1 _ {S _ {i}} (x), \tag {1} +$$ + +where the indicator function $1_{S_i}(x) = 1$ if $x \in S_i$ and $1_{S_i}(x) = 0$ otherwise. Figure 3 gives an illustration of a quantizer with five intervals. Quantization represents the + +![](images/2d5571991a90bf44f7dcabaeaf31f9e132ee3e10535ffffde0b694fdd8225a13.jpg) +Figure 4. Visualization of quantized images with different numbers of bins. The images are quantized by a uniform quantizer. Fewer than three quantization bins causes severe information reduction, while fifteen or more bins leads to negligible difference from the original image. An intermediate number of bins (e.g., five to ten) is well-suited for image augmentation. + +![](images/2034fca5aec68f902fc1f8cb06c965ccca4cec5576c69ca1db19c0ec9e3187d2.jpg) +Figure 5. Ablation study on the number of quantization bins. The peak performance is reached at 8 bins. Fewer bins deliver heavier augmentations and larger bins lead to weaker augmentations. + +original signal using a finite number of bits and hence introduces error to signal recovery. The central research problem is to find better tradeoffs between communication bandwidths and reproduction errors. + +Quantization can be categorized by uniform quantization and non-uniform quantization. A uniform quantizer has intervals and values which are evenly spaced, whereas a nonuniform quantizer allows either intervals or values to be unevenly spaced. Uniform quantizers are amenable to hardware deployment. However, non-uniform quantizers may perform better depending on the probabilistic distribution of $x$ . + +# 3.2. Randomized Quantization as Augmentation + +We aim to exploit quantization as a data withholding tool for representation learning. The information within each quantization bin is withheld, while the information across bins are retained. For data augmentation, a key aspect is the complexity of the augmentation space. We design a complex quantization augmentation by randomizing the intervals and the reproduction values. Concretely, given $S_{i} = [a_{i},a_{i + 1})$ , $a_{i}$ is generated by + +$$ +a _ {0}, a _ {1}, \dots , a _ {n - 1} = \operatorname {s o r t} \left(a _ {0} ^ {\prime}, a _ {1} ^ {\prime}, \dots , a _ {n - 1} ^ {\prime}\right) \tag {2} +$$ + +
random binsrandom valuestop1 acc
baselineXX50.0
+ quantizeXX54.8
+ quantizeX✓62.6
+ quantize✓X66.0
+ quantize✓✓67.9
+ +Table 1. Ablation study of the two randomness factors for randomized quantization described in Eq. 3 and Eq. 4. We examine the effect of randomized bins and random reproduction values for each bin. These two factors increase the complexity of the augmentation and significantly improve the performance. + +$$ +a _ {i} ^ {\prime} = U (\min (x), \max (x)), i = 0, 1, \dots , n - 1, \tag {3} +$$ + +where $U$ denotes random sampling with a uniform distribution over the interval, and $\min(x) / \max(x)$ refers to the minimum/maximum of the values $x$ per channel. The reproduction value $y_i$ is randomly sampled within the corresponding interval, + +$$ +y _ {i} = U \left(a _ {i}, a _ {i + 1}\right). \tag {4} +$$ + +The resultant randomized quantizer is non-uniform. The number of quantization bins $n$ is the hyperparameter of the augmentation. + +# 3.3. Data-Agnostic Augmentation + +The proposed randomized quantization augmentation can be applied to the channel dimension for any arbitrary data modality. The physical interpretation of the augmentation depends on the nature of the data modality. In Figure 2, we visualize the augmentations for images, audio and point clouds. On images, it removes the high frequency details but highlights object boundaries and edges. It also alters color appearance significantly. On audio, we examine the augmented sound acoustically and we find the augmentation tends to enhance specific frequency signals, such as + +
100-ep300-ep800-ep
MoCo-v367.971.672.1
BYOL67.271.071.6
+ +Table 2. Representation learning with randomized quantization augmentation benefits from more training epochs without early saturation. + +
AugmentationsMoCo-v3BYOL
CR10.19.9
CR + DACL [68]32.733.2
CR + i-Mix [48]30.328.7
CR + SSQL [12]11.16.4
CR + Ours42.943.0
RRC50.049.3
RRC + DACL [68]57.257.6
RRC + i-Mix [48]55.449.9
RRC + SSQL [12]42.949.3
RRC + Ours67.967.2
+ +low-frequency sounds or high-frequency sounds. On point clouds where the channel dimension represents xyz coordinates, it tends to downsample local structures but highlight the global shape. Some discrete modalities such as language are not directly amenable to quantization, but can be mapped to a continuous representation via a frozen data embedding layer. In Section 5.4, we examine randomized quantization on such input embeddings. + +# 3.4. Siamese Representation Learning + +Siamese representation learning or contrastive learning relies heavily on the quality of the augmentations [34, 87]. We apply the proposed augmentation on Siamese representation learning. At each training iteration, we sample two views from a data instance using randomized quantization by itself or in conjunction with other augmentations. Loss terms such as InfoNCE [56] and L2 are applied on the two views. The MoCo-v3 [16] and BYOL [34] frameworks are followed in this paper, and we refer readers to the original papers for details. + +# 4. Ablation Study + +We choose visual representation learning for an ablation study. Random resized cropping is taken as the baseline augmentation, and we apply our randomized quantization after it. Following the MoCo-v3 framework [16], we use ResNet-50 [39] as the backbone network. The optimizer + +Table 3. Comparisons with alternative domain-agnostic augmentation techniques under the linear classification protocol on ImageNet. CR is short for center crop, and RRC is short for random resized crop. Our randomized quantization approach achieves the best results against prior arts. + +
MethodMoCo-v3BYOL
Ours42.943.0
RRC50.049.4
RRC + CJ60.161.1
RRC + Ours67.967.2
Full68.968.9
+ +Table 4. Comparisons with image-specific augmentations under the linear classification protocol on ImageNet. CJ stands for color jittering, and Full includes random resized crop, color jittering, grayscale, Gaussian blurring and solarization. Randomized quantization is stronger than color jittering by a large margin. It falls behind the full handcrafted augmentations by just $1\%$ . + +is consistent with MoCo-v3, and the network is optimized for 100 epochs. Representation learning is conducted on the ImageNet-1K dataset [22], and linear classification accuracy is reported on the validation set. + +We ablate three design factors of the proposed quantization-based augmentation which affect its ability to mask channel-wise information. + +Randomizing Bins. The performance of representation learning depends on the complexity of the pretext tasks created from random augmentations. In Table 1, the baseline approach using the random resized crop augmentation obtains $50.0\%$ top-1 accuracy. Using a fixed uniform quantizer improves the performance mildly to $54.8\%$ . Randomizing the locations and sizes of bins allows for uneven masking and creates more effective pretext tasks. It improves the performance significantly to $66.0\%$ . + +Randomizing reproduction values. Quantization is also affected by how each bin is represented. Commonly, the values within a bin's range are represented by the midpoint. As an alternative, we also consider taking a random value in the range. Intuitively, random reproduction values lead to bias in the quantization error, making them no longer zero-mean and bringing a stronger augmentation effect. It is found to benefit representation learning, yielding an increase of 1.9 points upon randomizing the bins in Table 1. + +Number of quantization bins. Figure 5 illustrates the effect of various numbers of quantization bins. Intuitively, fewer bins leads to a stronger masking effect and higher cross-view variation. We vary the number of bins and find strong performance with 5-10 bins, peaking at 8 bins. This observation is similar to spatial masking in MAE [38] where an optimal masking ratio is found. In Figure 4, we visualize quantized images with different numbers of bins. To make the visualization consistent and comparable, we use the uniform quantizer in this case. It can be observed that too much information is withheld when using too few bins, and too many bins withdraws too little information. + +Training epochs. We further study training the augmentations with more epochs. In Table 2, the performance im + +![](images/71e6ba549108505ac34224a628fd31dc5995db386cc3d42d7c040efc9201a4a0.jpg) +Figure 6. Visual comparisons between color jittering and randomized quantization. Randomized quantization exhibits greater change in visual appearance and stronger edge enhancement. + +proves from $67.9\%$ with 100 epochs to $71.6\%$ with 300 epochs and $72.1\%$ with 800 epochs. With this complex augmentation, the network benefits from longer training. + +# 5. Experiments on Various Modalities + +We examine pre-training with the proposed augmentation across a variety of modalities including 1) vision (Section 5.1); 2) 3D point clouds (Section 5.2); 3) audio (Section 5.3); and 4) the DABS benchmark [66] (Section 5.4) comprised of data from multiple domains. The hyperparameter $n$ indicating the number of bins is tuned for each modality. We leave the description of corresponding datasets, settings and evaluation metrics to each section. + +# 5.1. Images + +We compare the proposed randomized quantization augmentation against domain-agnostic augmentation baselines, as well as domain-specific augmentations designed for images. The number of quantization bins is chosen as $n = 8$ . The experimental protocol follows the ablation study. + +Comparisons with domain-agnostic augmentations. Recent works on domain-agnostic augmentation are predominantly adapted from Mixup [85]. For example, i-Mix [48] linearly interpolates input data, and their corresponding virtual labels are generated from the current batch. Similarly, DACL [68] interpolates input but uses it as a way of adding noise to the original data. We also consider a baseline SSQL [12] which jointly performs quantization and contrastive learning for lower bit-width deployment. + +In Table 3, we compare our approach to these methods on two spatial operations: center crop (CR) and random resize crop (RRC). Center crop amounts to no augmentation, and random resized crop is frequently used in vision applications. Our evaluation is based on two Siamese representation learning frameworks MoCo-v3 and BYOL, since BYOL is said to have different behavior on augmentations. + +Randomized quantization performs the best against Mixup-based augmentations. As a standalone augmentation, randomized quantization obtains an accuracy of $42.9\%$ with MoCo-v3, which outperforms DACL and i-Mix by a + +
MethodBackboneEpochsTop1 accuracy
MSF w/wR-5020066.3
OursR-5010067.9
OursR-5030071.6
+ +Table 5. Comparison with weakly-augmented SSL baseline MSF. + +
1%2%5%10%20%100%
FoldingNet (lin)56.466.975.681.283.688.4
MID-FC (lin)61.573.180.284.286.990.3
Ours (lin)66.774.380.084.587.290.5
Scratch58.571.280.185.488.792.9
MID-FC (ft)67.376.583.688.490.293.0
Ours (ft)71.378.584.988.690.693.0
+ +Table 6. Linear probing (lin) and finetuning (ft) results for the shape classification task on the ModelNet40 dataset. Pre-training is conducted on the ShapeNet dataset. Our augmentation improves the classification accuracy substantially on various ratios of data, especially on very limited $(1\%)$ data. + +
C.mIoUI.mIoU
1%5%100%1%5%100%
Multi-Task (lin)-73.9-68.280.7-
MID-FC (lin)66.276.582.872.480.984.1
Ours (lin)70.676.982.977.481.984.3
MID-FC (ft)67.677.884.376.282.185.5
Ours (ft)69.578.484.477.882.385.5
+ +Table 7. Linear probing (lin) and finetuning (ft) results for the shape segmentation task on the ShapeNet Part dataset. Pre-training is conducted on ShapeNet. Our augmentation improves the performance substantially on various ratios. + +large margin. In conjunction with random resized crop, a $10\%$ margin is maintained. SSQL heavily relies on domain-specific augmentations, and in many cases, it fails to improve the baseline when handcrafted augmentations are removed. The results using MoCo-v3 and BYOL training objectives are similar. Overall, randomized quantization achieves state-of-the-art results against domain-agnostic baselines in the vision domain. + +Comparisons with domain-specific augmentations. We further compare with image-specific augmentations for visual representation learning in Table 4. We find that randomized quantization is much stronger than color jittering, which is heavily designed with prior knowledge such as brightness, contrast, and saturation for pixels. In Figure 6, we visualize color jittering and our augmentation. It can be observed that our augmentation leads to stronger and more diverse visual appearances than color jittering. Our augmentation is $1\%$ weaker than the full augmentation, which includes random resized crop, color jittering, grayscale, Gaussian blurring and solarization successively. + +
NameTask#ClassesData sizeAvg duration (s)
NSynth (NS) [27]Musical instrument classification11305,9794.0
UrbanSound8K (US8K) [60]Urban sound classification108,7324.0
VoxCeleb1 (VC1) [53]Speaker identification1,211153,5148.2
VoxForge (VF) [from Voxforge.org]Language identification6176,4385.8
Speech Commands V2 (SPCV2) [72]Command classification35105,8291.0
Speech Commands V2 (SPCV2/12) [72]Command classification12105,8291.0
+ +Table 8. Downstream dataset details for audio representation learning. + +
MethodNSUS8KVC1VFSPCV2/12SPCV2Average
TRILL [64]--17.988.174.9--
COLA [59]63.4-29.971.371.762.4-
OpenL3 [20]-78.2-----
COALA [29]73.172.7-----
COLA [59]70.278.530.479.576.776.868.7
BYOL-A [54]74.179.140.190.291.092.277.8
Ours74.278.045.792.695.192.179.6
+ +Table 9. Linear probing results for audio representation learning on six downstream datasets. Pre-training is conducted on the AudioSet dataset. Our model outperforms BYOL-A on four of the six datasets, with an average improvement of $1.8\%$ . + +Comparison with weakly-augmented SSL baselines. We compare the performance with MSF [47] in a weak augmentation setting. MSF implicitly utilizes close nearest neighbors as a form of augmentation. In Table 5, our method is better, and it benefits from longer training (67.9 vs. 71.9). Additionally, we demonstrate our approach on diverse modalities, while MSF only focuses on vision. + +# 5.2.3D Point Clouds + +We explore self-supervised representation learning on point clouds, represented by a disordered set of xyz coordinates. The pretraining is conducted on the ShapeNet [14] dataset consisting of 57,449 3D shapes. Octree-based Sparse CNN [70] is used as the backbone network, which takes 3D point clouds as input and extracts point features as well as shape features. We follow the MID-Net [71] model as the baseline, which is trained by a point-wise and instance-wise contrastive loss. The model is trained by a SGD optimizer with a batch size of 32 and a weight decay of $5\mathrm{e - }4$ . The initial learning rate is 0.03 and decreases by a factor of 10 after 200 and 300 epochs, and the training process terminates after 400 epochs. We apply the randomized quantization augmentation after the base augmentations used in MID-Net. Unlike images and audio which are snapped to grids, strong quantization of point cloud coordinates drastically degrades 3d point data. We thus choose to use a larger number of bins, $n = 30$ , in order to maintain more information. In practice, since the 3d points are sparsified by quantization, we observe a substantial training speedup as a side benefit. For evaluation, we experiment on two downstream tasks: shape classification and segmentation. + +Shape classification is conducted on ModelNet40 [77] which is composed of 13,834 3D models from 40 categories. For each shape, we extract a global feature with the pre-trained backbone then train a linear classifier, or finetune the network, and report the average classification accuracy in Table 6. We do comparison with FoldingNet [80] and MID-FC [71]. With our augmentation, we improve the classification accuracy over the baseline MID-FC [71] substantially, especially when the training data is limited as shown in Table 6. For example, with $1\%$ of the training data, we improve the classification accuracy by 5.2 and 4.0 points on linear probing and finetuning, respectively. + +Shape segmentation is conducted on ShapeNet Part [81] with 16,881 3D point clouds from 16 categories. For each shape, we extract point-wise features with the pre-trained backbone then train a segmentation head composed of two fully connected layers, or finetune the network, and report the mean IoU across all categories (C.mIoU) and the mean IoU across all instances (I.mIoU) in Table 7. We do comparison with two unsupervised pretraining methods: MIDFC [71] and Multi-Task [37]. Our results are consistently better than the baselines across different ratios of training data. And similarly to ModelNet40 classification, we observe significant improvements with limited (1% and 5%) training data. For example, with 1% of the training data, our method improves the segmentation performance by 4.4 and 1.9 IoU on linear probing and finetuning, respectively. + +# 5.3. Audio + +We apply randomized quantization to audio representation learning. We use AudioSet [31] as the pretraining + +
MethodNatural ImagesTextSpeechSensorsChest x-raysImages & TextAverage
Scratch10.142.324.969.868.157.545.5
e-Mix27.944.141.879.572.448.952.4
Ours32.144.744.584.973.454.555.6
+ +Table 10. Evaluation of the representation performance over six modalities in the DABS benchmark. Representations are trained on a single primary dataset for each modality and evaluated on a number of downstream datasets. The performance for each modality is averaged across the downstream datasets and shown in the table. + +dataset, with 1,963,807 audio samples of 527 classes. The pretrained representation is evaluated on six downstream audio classification datasets, summarized in Table 8. + +We largely follow the experimental settings of BYOL-A [54] and treat it as our baseline. + +We convert audio clips into the commonly used log-scaled spectrogram representation. Random resized crop is used to extract a $64 \times 96$ frequency-temporal segment for training. We replaced the Mixup augmentation used in BYOL-A with our randomized quantization, with the number of bins set to 5. We follow prior works [54] by using a lightweight 2D convolutional network as the backbone. We train the network using the Adam optimizer with a base learning rate of 3e-4 and a batch size of 256 for 100 epochs. + +Table 9 summarizes the results on the six downstream classification tasks. Compared against BYOL-A with the Mixup augmentation, our randomized quantization outperforms it in four out of the six tasks. Our approach is particularly stronger by a margin of $5.6\%$ on the VoxCeleb1 dataset, which is the hardest classification task with 1211 classes among all six tasks. Our improvements tend to be smaller for tasks with fewer classes. On average, the proposed augmentation surpasses the current state-the-of-art BYOL-A by a margin of $1.8\%$ . + +# 5.4. DABS + +We additionally conduct experiments on the public benchmark DABS [66] which is designed to study domain-agnostic self-supervised representation learning. Since some of its domains are discrete in nature (e.g., language), we first embed the data with a frozen layer and then augment the data embeddings for all the modalities consistently. It contains six data modalities1, covering natural RGB images, multichannel sensor data, English text, audio, chest x-ray images, as well as captioned images. In each domain, pre-training is conducted on a large-scale dataset, and the learned representations are evaluated with linear probing on various in-domain downstream datasets. The average performance for the in-domain downstream datasets is reported. We refer the reader to the benchmark for a full description of the pretraining datasets and in-domain evaluation datasets. + +We follow a leading method e-Mix [66] with a Transformer architecture on this domain-agnostic benchmark. The network is optimized with the Adam optimizer with a learning rate of 1e-4 and weight decay of 1e-4. The training protocol follows e-Mix, and all modalities share the same recipe. + +We apply randomized quantization on the token embeddings before the Transformer. Since the quantization function has zero gradients everywhere, we randomly initialize the token embedding module without updating it. The straight-through estimator can be potentially useful, but it is not the focus of this work. + +Table 10 summarizes the results for this benchmark. Our model outperforms the baseline e-Mix on all modalities. The improvements on natural images, speech, and sensors are larger than $3\%$ , while the improvements on text and chest x-rays are relatively smaller, less than $1\%$ . Both e-Mix and our pretraining seem to hurt the representation quality for captioned images. We hypothesize that the two modalities of images and texts pose significant challenges for a naive contrastive learning approach. + +# 6. Conclusion + +We propose randomized quantization as a novel data augmentation tool for self-supervised representation learning. Quantization effectively withholds information within the quantization bins but retains the information across bins. It could be applied on arbitrary data along the channel dimension without domain-specific knowledge. Randomized quantization significantly outperforms existing domain-agnostic augmentations based on Mixup. It compares favorably against domain-specific augmentations on vision, and attains state-of-the-art results on audio and 3D point clouds. We also explored randomized quantization on input data embeddings in a neural network for a wide range of data modalities. Experimental results on the DABS benchmark demonstrate state-of-the-art results for speech, text, images and multiple sensors. Randomized quantization could potentially be applied in a masked modeling framework, where the original images are reconstructed from quantized ones. This direction will be explored in future work. + +# Broader Impacts + +Although the proposed augmentation is generic in its formulation, it is not guaranteed to work beyond the modalities investigated in this paper. Application of the augmentation for other self-supervised learning frameworks such as masked modeling or generalization to other downstream tasks remains under-explored. + +# Acknowledgements + +We sincerely appreciate Reviewer #5 and AC's unwavering efforts in saving this work from rejection. This research was supported in part by National Natural Science Foundation of China/HKSAR Research Grants Council Joint Research Scheme under Grant N_HKUST627/20, and in part by HKSAR RGC General Research Fund (GRF) #16203319. + +# References + +[1] Sercan Ö Arik and Tomas Pfister. Tabnet: Attentive interpretable tabular learning. 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Among many techniques, data augmentation lies at the core for creating the information gap. Towards this end, masking has emerged as a generic and powerful tool where content is withheld along the sequential dimension, e.g., spatial in images, temporal in audio, and syntactic in language. In this paper, we explore the orthogonal channel dimension for generic data augmentation by exploiting precision redundancy. The data for each channel is quantized through a non-uniform quantizer, with the quantized value sampled randomly within randomly sampled quantization bins. From another perspective, quantization is analogous to channel-wise masking, as it removes the information within each bin, but preserves the information across bins. Our approach significantly surpasses existing generic data augmentation methods, while showing on par performance against modality-specific augmentations. We comprehensively evaluate our approach on vision, audio, 3D point clouds, as well as the DABS benchmark which is comprised of various data modalities. The code is available at https://github.com/microsoft/random_QUantize." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 48, + 568, + 128, + 581 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 568, + 128, + 581 + ], + "spans": [ + { + "bbox": [ + 48, + 568, + 128, + 581 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 588, + 287, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 588, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 588, + 287, + 658 + ], + "type": "text", + "content": "We are witnessing a convergence of multi-modal AI [23, 6] where the architecture and the learning algorithm are unified for various data modalities. This exciting direction abandons the domain-specific knowledge for an individual data modality, but rather pursues a solution far more generalizable." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 661, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 661, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 661, + 287, + 696 + ], + "type": "text", + "content": "For self-supervised representation learning, masked modeling [23] or simply masking input as an augmentation [75] has emerged as an effective approach. The in" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 237, + 545, + 375 + ], + "blocks": [ + { + "bbox": [ + 307, + 237, + 545, + 375 + ], + "lines": [ + { + "bbox": [ + 307, + 237, + 545, + 375 + ], + "spans": [ + { + "bbox": [ + 307, + 237, + 545, + 375 + ], + "type": "image", + "image_path": "b132969fe43a9cf2c64a42fc8117276c67c87b7ec7d32940ba58ea661a50a159.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 379, + 547, + 456 + ], + "lines": [ + { + "bbox": [ + 305, + 379, + 547, + 456 + ], + "spans": [ + { + "bbox": [ + 305, + 379, + 547, + 456 + ], + "type": "text", + "content": "Figure 1. We represent data as a matrix with a sequential dimension and a channel dimension. As a generic data augmentation, masking drops tokens along the sequential dimension. The proposed randomized quantization instead withholds information along the channel dimension. In this figure, we use 1D data of 10 sequential tokens for illustration. Data values are coded in grayscale." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 481, + 547, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 481, + 547, + 589 + ], + "spans": [ + { + "bbox": [ + 304, + 481, + 547, + 589 + ], + "type": "text", + "content": "put data is represented by a 2D tensor with a sequential dimension and a channel dimension in a modality-agnostic way [3]. The sequential dimension can be spatial in images, temporal in audio, and syntactic in languages. The masking mechanism withholding information along the sequential dimension, and exploits it for supervision. As a result, models learned from the masking supervision demonstrate strong capability for capturing correlations between sequential tokens [38]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 591, + 547, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 591, + 547, + 699 + ], + "spans": [ + { + "bbox": [ + 304, + 591, + 547, + 699 + ], + "type": "text", + "content": "The channel dimension describes the data feature at each sequential location, for example, RGB color at a spatial location or spectrogram frequency at a time step. Despite being generic, masking approaches have neglected to exploit supervision along the channel dimension. While the number of channels for images is as small as three, the channels for audio and tabular data can be as many as hundreds. Formulating the self-supervision from the channel dimension holds much potential for representation learning." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "In this paper, we draw a connection between the sequen" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 264, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 264, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 264, + 712 + ], + "type": "text", + "content": "*Equal contribution. Work done during an internship at MSRA." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16305" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 286 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 286 + ], + "type": "text", + "content": "tial masking operation and quantization by exploring quantization as a novel form of masking along the channel dimension. The data in each channel is dynamically quantized through a non-uniform quantizer, with the quantization value randomly sampled from randomly sampled quantization bins. In this way, information within each quantization bin is masked out, yet information across bins is retained. The information removed by quantization is controlled by the number of bins and the size of the bins, which has been rigorously studied in theory [62]. The larger the distortion rate, the stronger the quantization when it is used as an augmentation for representation learning. The extreme case of using only a single bin is equivalent to dropping the entire channel. We systematically study various quantization configurations for their effects as a data augmentation, for example, with respect to the number bins, uniform or non-uniform bins, and methods to select quantization values." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 288, + 289, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 289, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 289, + 418 + ], + "type": "text", + "content": "We apply the randomized quantizer as the only augmentation, or in conjunction with augmentations along the sequential dimension on state-of-the-art Siamese representation learning methods MoCo-v3 [16] and BYOL [34]. In comparisons with domain-agnostic augmentations based on MixUp [85], our approach achieves state-of-the-art results by a large margin on vision, audio, 3d point cloud, and the DABS benchmark. Compared with domain-specific augmentations, our approach achieves competitive performance against handcrafted augmentations on vision, and state-of-the-art performance on audio and 3d point clouds." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 419, + 259, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 419, + 259, + 431 + ], + "spans": [ + { + "bbox": [ + 59, + 419, + 259, + 431 + ], + "type": "text", + "content": "Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 436, + 287, + 574 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 58, + 436, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 436, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 58, + 436, + 287, + 472 + ], + "type": "text", + "content": "- We propose a simple yet effective data-agnostic augmentation for contrastive learning, based on quantization along the channel dimension." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 481, + 287, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 481, + 287, + 517 + ], + "spans": [ + { + "bbox": [ + 58, + 481, + 287, + 517 + ], + "type": "text", + "content": "- We design a randomization technique by varying the quantization value and the quantization bins, to enhance data augmentation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 525, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 525, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 58, + 525, + 287, + 574 + ], + "type": "text", + "content": "- We demonstrate the generality and strong performance of our channel-wise randomized quantization for vision, audio, 3D point clouds and the DABS benchmark in a data-agnostic way." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 586, + 139, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 139, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 139, + 597 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": "Self-supervised learning extracts labels from the data itself and tasks the network to learn transferable representations. Among the earliest forms of self-supervised models are auto-encoders [42] and generative models [41]. But since the input and the output are identical, a neural network may easily find shortcuts and use memorization to solve the generation task. Advances in recent years show that information needs to be withheld from the input to prevent cheating [25]. Pretext tasks such as colorization [86]," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "content": " inpainting [58], jigsaw puzzles [55] were proposed in vision, while masked modeling [23], next sentence prediction [46, 45], and replaced word prediction [17] were developed in natural language processing. Speediness [7, 43] and temporal order [73, 52] have been exploited for video representation learning. Due to space limitations, we omit the literature for speech [4], tabular data [1], graph-structured data [65] and many other modalities. The optimal pretext task for each target problem may be different. However, there exists enormous interest in obtaining a single foundation model [9] for all downstream applications." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 205, + 547, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 205, + 547, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 205, + 547, + 300 + ], + "type": "text", + "content": "Instead of withholding data for supervision, contrastive models [78, 56] create new data via data augmentation and compare features extracted using a Siamese network for supervision. Siamese representation learning can be categorized by whether to use explicit negatives [34], ways to define negatives [2], and various loss formulations [13, 83]. However, the main driving signal for learning lies in the augmentations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 303, + 547, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 303, + 547, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 303, + 547, + 399 + ], + "type": "text", + "content": "Data augmentation enlarges the number of data instances by leveraging prior knowledge of the data and target problem properties. For supervised learning, data augmentation aids in reducing overfitting and regularization [84]. For self-supervised learning, the information gap created by two augmentations provides learning supervision. Typically, the data augmentation function extracts partial information from the data and optionally adds corruptions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 399, + 547, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 547, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 547, + 532 + ], + "type": "text", + "content": "Popular image-specific augmentations include cropping, scaling, color jittering, Gaussian blurring, cut-out [24], cutmix [82], and auto-augment, which searches for a data augmentation policy [21]. In natural language processing, synonym replacement [74], back translation [11], random word insertion and deletion are most common. For audio and speech, altering the pitch, changing the playback speed, and masking either along the time axis or the frequency axis [57] may improve performance. Additionally, augmenting data through a generative model [10] such as a GAN is a viable approach." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 534, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 548, + 714 + ], + "type": "text", + "content": "Domain-agnostic augmentation aims to generalize modality-specific and domain-specific augmentations into a unified formulation. Finding such general priors in data is challenging. One line of work follows Mixup [85], which is initially proposed to improve empirical risk minimization of supervised learning by linearly interpolating data and labels. Because of its generality, later works have explored its application on other data modalities [35], a wide range of problems [50, 40], as well as representation learning [66, 48, 68]. Another important line of work generalizes masked modeling [23], which was initially proposed for language modeling, to other data modalities and domains [38, 67, 79]. The masking mechanism samples a subset of the input data, while Mixup introduces additional corruptions which are not observed in the original data" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16306" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 547, + 258 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 547, + 258 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 547, + 258 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 547, + 258 + ], + "type": "image", + "image_path": "4056949339240c7b23d30d572cfd69596eec22a8cd838f64becb00f0df7e8c51.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 261, + 547, + 297 + ], + "lines": [ + { + "bbox": [ + 46, + 261, + 547, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 547, + 297 + ], + "type": "text", + "content": "Figure 2. Visualizing randomized quantization augmentation on images, 3d point clouds, and audio. The first row presents the original signal, and the bottom three rows are augmented views. Randomized quantization alters color and enhances edges on images, spatially samples coordinates on point clouds, and enhances frequency channels for audio." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 314, + 286, + 343 + ], + "blocks": [ + { + "bbox": [ + 48, + 314, + 286, + 343 + ], + "lines": [ + { + "bbox": [ + 48, + 314, + 286, + 343 + ], + "spans": [ + { + "bbox": [ + 48, + 314, + 286, + 343 + ], + "type": "image", + "image_path": "e8078d9c9c59999acbf47f17d732d091fdceabb0cd0743aebeb4af0de00e188d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 347, + 288, + 381 + ], + "lines": [ + { + "bbox": [ + 46, + 347, + 288, + 381 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 288, + 381 + ], + "type": "text", + "content": "Figure 3. Illustration of a non-uniform quantizer with five bins. " + }, + { + "bbox": [ + 46, + 347, + 288, + 381 + ], + "type": "inline_equation", + "content": "a_{i}" + }, + { + "bbox": [ + 46, + 347, + 288, + 381 + ], + "type": "text", + "content": " denotes the interval of the quantization bin and " + }, + { + "bbox": [ + 46, + 347, + 288, + 381 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 46, + 347, + 288, + 381 + ], + "type": "text", + "content": " denotes the reproduction value from each bin." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 398, + 287, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 398, + 287, + 482 + ], + "spans": [ + { + "bbox": [ + 46, + 398, + 287, + 482 + ], + "type": "text", + "content": "instance. A third line of work tries to mine inherent regularities and structures in the data. NNCLR [26] and MSF [47] use nearest neighbors derived from the current representations as a novel form of augmentation for contrastive learning. Our randomized quantization differs from these works, and augments data along the channel dimension." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 484, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 581 + ], + "type": "text", + "content": "Quantization represents numerical values with a fixed discrete set of numbers so as to reduce communication bandwidth and maintain representation quality. The rounding error was first analyzed a century ago [63], and the theory based on variable-rate quantization [61] and Huffman coding [44] revolutionized the communications industry. We refer readers to a survey [33] that describes this area from a theoretical perspective." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 581, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 581, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 581, + 287, + 700 + ], + "type": "text", + "content": "Quantization for efficient neural networks [32] aims to reduce neural network latency while maintaining model accuracy. The advances of half-precision [5, 69] and mixed-precision training [18, 36, 51] has accelerated model training by an order of magnitude. Works have shown that neural networks can be completely binarized [49, 76, 19] with reasonable performance. Stochastic quantization [15, 28, 8] is a technique for learning and compressing model weights in a way that avoids local minima with the low-precision weight representations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 59, + 701, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 288, + 714 + ], + "type": "text", + "content": "There exist two works [12, 30] that study the use of" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 314, + 547, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 314, + 547, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 547, + 434 + ], + "type": "text", + "content": "quantization in contrastive representation learning. In both, quantization is applied on the intermediate features and model weights. Though effective for model compression, the quantization of features/weights can be viewed as unsuitable for augmentation due to the unpredictability of the corresponding change in the input. Our work additionally differs from these methods [12, 30] in its randomization of a non-uniform quantizer. This technique creates a much more complex augmentation space than uniform quantization, generating valid images of greater diversity." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 445, + 373, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 445, + 373, + 459 + ], + "spans": [ + { + "bbox": [ + 306, + 445, + 373, + 459 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 464, + 547, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 464, + 547, + 523 + ], + "spans": [ + { + "bbox": [ + 304, + 464, + 547, + 523 + ], + "type": "text", + "content": "This paper proposes a novel generic data augmentation for representation learning based on quantization. We first provide preliminaries on quantization. We then introduce two factors to inject randomness into the quantization procedure." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 532, + 462, + 545 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 532, + 462, + 545 + ], + "spans": [ + { + "bbox": [ + 306, + 532, + 462, + 545 + ], + "type": "text", + "content": "3.1. Preliminaries: Quantization" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 551, + 547, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 551, + 547, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 551, + 547, + 635 + ], + "type": "text", + "content": "A quantizer is a function which consists of a set of non-overlapping intervals or bins " + }, + { + "bbox": [ + 304, + 551, + 547, + 635 + ], + "type": "inline_equation", + "content": "S = \\{S_{i} = [a_{i},a_{i + 1})\\} ,i = 0,1,\\ldots n - 1" + }, + { + "bbox": [ + 304, + 551, + 547, + 635 + ], + "type": "text", + "content": ", and a set of reproduction values " + }, + { + "bbox": [ + 304, + 551, + 547, + 635 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 304, + 551, + 547, + 635 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 551, + 547, + 635 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 551, + 547, + 635 + ], + "type": "text", + "content": " is the number of intervals and reproduction values. Let " + }, + { + "bbox": [ + 304, + 551, + 547, + 635 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 551, + 547, + 635 + ], + "type": "text", + "content": " be a one-dimensional input signal. The quantizer maps values within an interval to a single scalar, defined as " + }, + { + "bbox": [ + 304, + 551, + 547, + 635 + ], + "type": "inline_equation", + "content": "q(x) = y_{i}" + }, + { + "bbox": [ + 304, + 551, + 547, + 635 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 551, + 547, + 635 + ], + "type": "inline_equation", + "content": "x\\in S_i" + }, + { + "bbox": [ + 304, + 551, + 547, + 635 + ], + "type": "text", + "content": ". Formally, it can be written as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 377, + 643, + 545, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 377, + 643, + 545, + 669 + ], + "spans": [ + { + "bbox": [ + 377, + 643, + 545, + 669 + ], + "type": "interline_equation", + "content": "q (x) = \\sum_ {i} y _ {i} \\cdot 1 _ {S _ {i}} (x), \\tag {1}", + "image_path": "565415b11eaac9a06f951930dc6437d4222a3a482933f8153833b5152bdd2a1e.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "where the indicator function " + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "inline_equation", + "content": "1_{S_i}(x) = 1" + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "inline_equation", + "content": "x \\in S_i" + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "inline_equation", + "content": "1_{S_i}(x) = 0" + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": " otherwise. Figure 3 gives an illustration of a quantizer with five intervals. Quantization represents the" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16307" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 545, + 205 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 545, + 205 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 545, + 205 + ], + "type": "image", + "image_path": "2d5571991a90bf44f7dcabaeaf31f9e132ee3e10535ffffde0b694fdd8225a13.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 208, + 546, + 243 + ], + "lines": [ + { + "bbox": [ + 46, + 208, + 546, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 208, + 546, + 243 + ], + "type": "text", + "content": "Figure 4. Visualization of quantized images with different numbers of bins. The images are quantized by a uniform quantizer. Fewer than three quantization bins causes severe information reduction, while fifteen or more bins leads to negligible difference from the original image. An intermediate number of bins (e.g., five to ten) is well-suited for image augmentation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 53, + 265, + 273, + 354 + ], + "blocks": [ + { + "bbox": [ + 53, + 265, + 273, + 354 + ], + "lines": [ + { + "bbox": [ + 53, + 265, + 273, + 354 + ], + "spans": [ + { + "bbox": [ + 53, + 265, + 273, + 354 + ], + "type": "image", + "image_path": "2034fca5aec68f902fc1f8cb06c965ccca4cec5576c69ca1db19c0ec9e3187d2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 357, + 287, + 392 + ], + "lines": [ + { + "bbox": [ + 46, + 357, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 287, + 392 + ], + "type": "text", + "content": "Figure 5. Ablation study on the number of quantization bins. The peak performance is reached at 8 bins. Fewer bins deliver heavier augmentations and larger bins lead to weaker augmentations." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 414, + 286, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 286, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 286, + 462 + ], + "type": "text", + "content": "original signal using a finite number of bits and hence introduces error to signal recovery. The central research problem is to find better tradeoffs between communication bandwidths and reproduction errors." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 464, + 286, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 286, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 286, + 559 + ], + "type": "text", + "content": "Quantization can be categorized by uniform quantization and non-uniform quantization. A uniform quantizer has intervals and values which are evenly spaced, whereas a nonuniform quantizer allows either intervals or values to be unevenly spaced. Uniform quantizers are amenable to hardware deployment. However, non-uniform quantizers may perform better depending on the probabilistic distribution of " + }, + { + "bbox": [ + 46, + 464, + 286, + 559 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 464, + 286, + 559 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 572, + 274, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 572, + 274, + 585 + ], + "spans": [ + { + "bbox": [ + 47, + 572, + 274, + 585 + ], + "type": "text", + "content": "3.2. Randomized Quantization as Augmentation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 592, + 286, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 592, + 286, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 592, + 286, + 688 + ], + "type": "text", + "content": "We aim to exploit quantization as a data withholding tool for representation learning. The information within each quantization bin is withheld, while the information across bins are retained. For data augmentation, a key aspect is the complexity of the augmentation space. We design a complex quantization augmentation by randomizing the intervals and the reproduction values. Concretely, given " + }, + { + "bbox": [ + 46, + 592, + 286, + 688 + ], + "type": "inline_equation", + "content": "S_{i} = [a_{i},a_{i + 1})" + }, + { + "bbox": [ + 46, + 592, + 286, + 688 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 592, + 286, + 688 + ], + "type": "inline_equation", + "content": "a_{i}" + }, + { + "bbox": [ + 46, + 592, + 286, + 688 + ], + "type": "text", + "content": " is generated by" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 85, + 701, + 287, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 85, + 701, + 287, + 714 + ], + "type": "interline_equation", + "content": "a _ {0}, a _ {1}, \\dots , a _ {n - 1} = \\operatorname {s o r t} \\left(a _ {0} ^ {\\prime}, a _ {1} ^ {\\prime}, \\dots , a _ {n - 1} ^ {\\prime}\\right) \\tag {2}", + "image_path": "f524f499892acd563d540f40b5a365d4c6268ce687fb0299035593bb4822c40c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 320, + 258, + 531, + 334 + ], + "blocks": [ + { + "bbox": [ + 320, + 258, + 531, + 334 + ], + "lines": [ + { + "bbox": [ + 320, + 258, + 531, + 334 + ], + "spans": [ + { + "bbox": [ + 320, + 258, + 531, + 334 + ], + "type": "table", + "html": "
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+ quantizeXX54.8
+ quantizeX✓62.6
+ quantize✓X66.0
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", + "image_path": "48dc98471da0236fd5c0348fa31abb9b1fef61fa619d24fc262bec854af1e77c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 341, + 545, + 397 + ], + "lines": [ + { + "bbox": [ + 305, + 341, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 305, + 341, + 545, + 397 + ], + "type": "text", + "content": "Table 1. Ablation study of the two randomness factors for randomized quantization described in Eq. 3 and Eq. 4. We examine the effect of randomized bins and random reproduction values for each bin. These two factors increase the complexity of the augmentation and significantly improve the performance." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 333, + 426, + 545, + 440 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 426, + 545, + 440 + ], + "spans": [ + { + "bbox": [ + 333, + 426, + 545, + 440 + ], + "type": "interline_equation", + "content": "a _ {i} ^ {\\prime} = U (\\min (x), \\max (x)), i = 0, 1, \\dots , n - 1, \\tag {3}", + "image_path": "2ab431e6e562a1abe1804b74ecaa05ef7ea1b1e707b438baa304e058f377aab0.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 444, + 545, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 545, + 503 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 444, + 545, + 503 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 304, + 444, + 545, + 503 + ], + "type": "text", + "content": " denotes random sampling with a uniform distribution over the interval, and " + }, + { + "bbox": [ + 304, + 444, + 545, + 503 + ], + "type": "inline_equation", + "content": "\\min(x) / \\max(x)" + }, + { + "bbox": [ + 304, + 444, + 545, + 503 + ], + "type": "text", + "content": " refers to the minimum/maximum of the values " + }, + { + "bbox": [ + 304, + 444, + 545, + 503 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 444, + 545, + 503 + ], + "type": "text", + "content": " per channel. The reproduction value " + }, + { + "bbox": [ + 304, + 444, + 545, + 503 + ], + "type": "inline_equation", + "content": "y_i" + }, + { + "bbox": [ + 304, + 444, + 545, + 503 + ], + "type": "text", + "content": " is randomly sampled within the corresponding interval," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 388, + 513, + 545, + 525 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 513, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 388, + 513, + 545, + 525 + ], + "type": "interline_equation", + "content": "y _ {i} = U \\left(a _ {i}, a _ {i + 1}\\right). \\tag {4}", + "image_path": "f122f09d090a4e8064fa0a3053eacf0f49128d706e1905c1e51ed314ec72555a.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 533, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 568 + ], + "type": "text", + "content": "The resultant randomized quantizer is non-uniform. The number of quantization bins " + }, + { + "bbox": [ + 304, + 533, + 545, + 568 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 533, + 545, + 568 + ], + "type": "text", + "content": " is the hyperparameter of the augmentation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 575, + 464, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 464, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 464, + 588 + ], + "type": "text", + "content": "3.3. Data-Agnostic Augmentation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "The proposed randomized quantization augmentation can be applied to the channel dimension for any arbitrary data modality. The physical interpretation of the augmentation depends on the nature of the data modality. In Figure 2, we visualize the augmentations for images, audio and point clouds. On images, it removes the high frequency details but highlights object boundaries and edges. It also alters color appearance significantly. On audio, we examine the augmented sound acoustically and we find the augmentation tends to enhance specific frequency signals, such as" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16308" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 82, + 70, + 254, + 109 + ], + "blocks": [ + { + "bbox": [ + 82, + 70, + 254, + 109 + ], + "lines": [ + { + "bbox": [ + 82, + 70, + 254, + 109 + ], + "spans": [ + { + "bbox": [ + 82, + 70, + 254, + 109 + ], + "type": "table", + "html": "
100-ep300-ep800-ep
MoCo-v367.971.672.1
BYOL67.271.071.6
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AugmentationsMoCo-v3BYOL
CR10.19.9
CR + DACL [68]32.733.2
CR + i-Mix [48]30.328.7
CR + SSQL [12]11.16.4
CR + Ours42.943.0
RRC50.049.3
RRC + DACL [68]57.257.6
RRC + i-Mix [48]55.449.9
RRC + SSQL [12]42.949.3
RRC + Ours67.967.2
", + "image_path": "2947f654c2a6d2131dca6fb58ba104d03921958fcc800f513468c480df3c1e31.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 376, + 287, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 287, + 473 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 287, + 473 + ], + "type": "text", + "content": "low-frequency sounds or high-frequency sounds. On point clouds where the channel dimension represents xyz coordinates, it tends to downsample local structures but highlight the global shape. Some discrete modalities such as language are not directly amenable to quantization, but can be mapped to a continuous representation via a frozen data embedding layer. In Section 5.4, we examine randomized quantization on such input embeddings." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 482, + 228, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 482, + 228, + 495 + ], + "spans": [ + { + "bbox": [ + 47, + 482, + 228, + 495 + ], + "type": "text", + "content": "3.4. Siamese Representation Learning" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 501, + 287, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 501, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 46, + 501, + 287, + 620 + ], + "type": "text", + "content": "Siamese representation learning or contrastive learning relies heavily on the quality of the augmentations [34, 87]. We apply the proposed augmentation on Siamese representation learning. At each training iteration, we sample two views from a data instance using randomized quantization by itself or in conjunction with other augmentations. Loss terms such as InfoNCE [56] and L2 are applied on the two views. The MoCo-v3 [16] and BYOL [34] frameworks are followed in this paper, and we refer readers to the original papers for details." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 633, + 140, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 633, + 140, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 633, + 140, + 647 + ], + "type": "text", + "content": "4. Ablation Study" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "We choose visual representation learning for an ablation study. Random resized cropping is taken as the baseline augmentation, and we apply our randomized quantization after it. Following the MoCo-v3 framework [16], we use ResNet-50 [39] as the backbone network. The optimizer" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 332, + 69, + 521, + 144 + ], + "blocks": [ + { + "bbox": [ + 46, + 300, + 287, + 356 + ], + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 356 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 356 + ], + "type": "text", + "content": "Table 3. Comparisons with alternative domain-agnostic augmentation techniques under the linear classification protocol on ImageNet. CR is short for center crop, and RRC is short for random resized crop. Our randomized quantization approach achieves the best results against prior arts." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 332, + 69, + 521, + 144 + ], + "lines": [ + { + "bbox": [ + 332, + 69, + 521, + 144 + ], + "spans": [ + { + "bbox": [ + 332, + 69, + 521, + 144 + ], + "type": "table", + "html": "
MethodMoCo-v3BYOL
Ours42.943.0
RRC50.049.4
RRC + CJ60.161.1
RRC + Ours67.967.2
Full68.968.9
", + "image_path": "b35e19dfdff92f5c178404d93ea3b0d5eaeb44c60a5fdf6b27e39bc6897c1935.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 152, + 547, + 219 + ], + "lines": [ + { + "bbox": [ + 304, + 152, + 547, + 219 + ], + "spans": [ + { + "bbox": [ + 304, + 152, + 547, + 219 + ], + "type": "text", + "content": "Table 4. Comparisons with image-specific augmentations under the linear classification protocol on ImageNet. CJ stands for color jittering, and Full includes random resized crop, color jittering, grayscale, Gaussian blurring and solarization. Randomized quantization is stronger than color jittering by a large margin. It falls behind the full handcrafted augmentations by just " + }, + { + "bbox": [ + 304, + 152, + 547, + 219 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 152, + 547, + 219 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 238, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 238, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 304, + 238, + 545, + 285 + ], + "type": "text", + "content": "is consistent with MoCo-v3, and the network is optimized for 100 epochs. Representation learning is conducted on the ImageNet-1K dataset [22], and linear classification accuracy is reported on the validation set." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 286, + 545, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 286, + 545, + 322 + ], + "spans": [ + { + "bbox": [ + 304, + 286, + 545, + 322 + ], + "type": "text", + "content": "We ablate three design factors of the proposed quantization-based augmentation which affect its ability to mask channel-wise information." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 324, + 546, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 546, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 546, + 433 + ], + "type": "text", + "content": "Randomizing Bins. The performance of representation learning depends on the complexity of the pretext tasks created from random augmentations. In Table 1, the baseline approach using the random resized crop augmentation obtains " + }, + { + "bbox": [ + 304, + 324, + 546, + 433 + ], + "type": "inline_equation", + "content": "50.0\\%" + }, + { + "bbox": [ + 304, + 324, + 546, + 433 + ], + "type": "text", + "content": " top-1 accuracy. Using a fixed uniform quantizer improves the performance mildly to " + }, + { + "bbox": [ + 304, + 324, + 546, + 433 + ], + "type": "inline_equation", + "content": "54.8\\%" + }, + { + "bbox": [ + 304, + 324, + 546, + 433 + ], + "type": "text", + "content": ". Randomizing the locations and sizes of bins allows for uneven masking and creates more effective pretext tasks. It improves the performance significantly to " + }, + { + "bbox": [ + 304, + 324, + 546, + 433 + ], + "type": "inline_equation", + "content": "66.0\\%" + }, + { + "bbox": [ + 304, + 324, + 546, + 433 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 434, + 547, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 547, + 542 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 547, + 542 + ], + "type": "text", + "content": "Randomizing reproduction values. Quantization is also affected by how each bin is represented. Commonly, the values within a bin's range are represented by the midpoint. As an alternative, we also consider taking a random value in the range. Intuitively, random reproduction values lead to bias in the quantization error, making them no longer zero-mean and bringing a stronger augmentation effect. It is found to benefit representation learning, yielding an increase of 1.9 points upon randomizing the bins in Table 1." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 544, + 547, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 547, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 547, + 687 + ], + "type": "text", + "content": "Number of quantization bins. Figure 5 illustrates the effect of various numbers of quantization bins. Intuitively, fewer bins leads to a stronger masking effect and higher cross-view variation. We vary the number of bins and find strong performance with 5-10 bins, peaking at 8 bins. This observation is similar to spatial masking in MAE [38] where an optimal masking ratio is found. In Figure 4, we visualize quantized images with different numbers of bins. To make the visualization consistent and comparable, we use the uniform quantizer in this case. It can be observed that too much information is withheld when using too few bins, and too many bins withdraws too little information." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Training epochs. We further study training the augmentations with more epochs. In Table 2, the performance im" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16309" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 283, + 159 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 283, + 159 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 283, + 159 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 283, + 159 + ], + "type": "image", + "image_path": "71e6ba549108505ac34224a628fd31dc5995db386cc3d42d7c040efc9201a4a0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 163, + 287, + 197 + ], + "lines": [ + { + "bbox": [ + 46, + 163, + 287, + 197 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 287, + 197 + ], + "type": "text", + "content": "Figure 6. Visual comparisons between color jittering and randomized quantization. Randomized quantization exhibits greater change in visual appearance and stronger edge enhancement." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 217, + 287, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 287, + 255 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 287, + 255 + ], + "type": "text", + "content": "proves from " + }, + { + "bbox": [ + 46, + 217, + 287, + 255 + ], + "type": "inline_equation", + "content": "67.9\\%" + }, + { + "bbox": [ + 46, + 217, + 287, + 255 + ], + "type": "text", + "content": " with 100 epochs to " + }, + { + "bbox": [ + 46, + 217, + 287, + 255 + ], + "type": "inline_equation", + "content": "71.6\\%" + }, + { + "bbox": [ + 46, + 217, + 287, + 255 + ], + "type": "text", + "content": " with 300 epochs and " + }, + { + "bbox": [ + 46, + 217, + 287, + 255 + ], + "type": "inline_equation", + "content": "72.1\\%" + }, + { + "bbox": [ + 46, + 217, + 287, + 255 + ], + "type": "text", + "content": " with 800 epochs. With this complex augmentation, the network benefits from longer training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 266, + 243, + 280 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 266, + 243, + 280 + ], + "spans": [ + { + "bbox": [ + 47, + 266, + 243, + 280 + ], + "type": "text", + "content": "5. Experiments on Various Modalities" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 286, + 287, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 286, + 287, + 382 + ], + "spans": [ + { + "bbox": [ + 46, + 286, + 287, + 382 + ], + "type": "text", + "content": "We examine pre-training with the proposed augmentation across a variety of modalities including 1) vision (Section 5.1); 2) 3D point clouds (Section 5.2); 3) audio (Section 5.3); and 4) the DABS benchmark [66] (Section 5.4) comprised of data from multiple domains. The hyperparameter " + }, + { + "bbox": [ + 46, + 286, + 287, + 382 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 286, + 287, + 382 + ], + "type": "text", + "content": " indicating the number of bins is tuned for each modality. We leave the description of corresponding datasets, settings and evaluation metrics to each section." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 392, + 104, + 404 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 392, + 104, + 404 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 104, + 404 + ], + "type": "text", + "content": "5.1. Images" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 411, + 287, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 471 + ], + "type": "text", + "content": "We compare the proposed randomized quantization augmentation against domain-agnostic augmentation baselines, as well as domain-specific augmentations designed for images. The number of quantization bins is chosen as " + }, + { + "bbox": [ + 46, + 411, + 287, + 471 + ], + "type": "inline_equation", + "content": "n = 8" + }, + { + "bbox": [ + 46, + 411, + 287, + 471 + ], + "type": "text", + "content": ". The experimental protocol follows the ablation study." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 473, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 287, + 581 + ], + "type": "text", + "content": "Comparisons with domain-agnostic augmentations. Recent works on domain-agnostic augmentation are predominantly adapted from Mixup [85]. For example, i-Mix [48] linearly interpolates input data, and their corresponding virtual labels are generated from the current batch. Similarly, DACL [68] interpolates input but uses it as a way of adding noise to the original data. We also consider a baseline SSQL [12] which jointly performs quantization and contrastive learning for lower bit-width deployment." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 581, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 581, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 581, + 287, + 665 + ], + "type": "text", + "content": "In Table 3, we compare our approach to these methods on two spatial operations: center crop (CR) and random resize crop (RRC). Center crop amounts to no augmentation, and random resized crop is frequently used in vision applications. Our evaluation is based on two Siamese representation learning frameworks MoCo-v3 and BYOL, since BYOL is said to have different behavior on augmentations." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "Randomized quantization performs the best against Mixup-based augmentations. As a standalone augmentation, randomized quantization obtains an accuracy of " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "42.9\\%" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": " with MoCo-v3, which outperforms DACL and i-Mix by a" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 318, + 70, + 535, + 121 + ], + "blocks": [ + { + "bbox": [ + 318, + 70, + 535, + 121 + ], + "lines": [ + { + "bbox": [ + 318, + 70, + 535, + 121 + ], + "spans": [ + { + "bbox": [ + 318, + 70, + 535, + 121 + ], + "type": "table", + "html": "
MethodBackboneEpochsTop1 accuracy
MSF w/wR-5020066.3
OursR-5010067.9
OursR-5030071.6
", + "image_path": "e2f84bdf6aa44ba1dcfe8370d3c42d7604319da59b2430ec25495398f8145b20.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 316, + 150, + 536, + 239 + ], + "blocks": [ + { + "bbox": [ + 306, + 129, + 543, + 140 + ], + "lines": [ + { + "bbox": [ + 306, + 129, + 543, + 140 + ], + "spans": [ + { + "bbox": [ + 306, + 129, + 543, + 140 + ], + "type": "text", + "content": "Table 5. Comparison with weakly-augmented SSL baseline MSF." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 150, + 536, + 239 + ], + "lines": [ + { + "bbox": [ + 316, + 150, + 536, + 239 + ], + "spans": [ + { + "bbox": [ + 316, + 150, + 536, + 239 + ], + "type": "table", + "html": "
1%2%5%10%20%100%
FoldingNet (lin)56.466.975.681.283.688.4
MID-FC (lin)61.573.180.284.286.990.3
Ours (lin)66.774.380.084.587.290.5
Scratch58.571.280.185.488.792.9
MID-FC (ft)67.376.583.688.490.293.0
Ours (ft)71.378.584.988.690.693.0
", + "image_path": "a8eaa62a5787b8943abb722adba6eb79ae3b9256e095c1a43ed31c24f6a4d2ae.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 315, + 311, + 537, + 399 + ], + "blocks": [ + { + "bbox": [ + 305, + 245, + 545, + 300 + ], + "lines": [ + { + "bbox": [ + 305, + 245, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 305, + 245, + 545, + 300 + ], + "type": "text", + "content": "Table 6. Linear probing (lin) and finetuning (ft) results for the shape classification task on the ModelNet40 dataset. Pre-training is conducted on the ShapeNet dataset. Our augmentation improves the classification accuracy substantially on various ratios of data, especially on very limited " + }, + { + "bbox": [ + 305, + 245, + 545, + 300 + ], + "type": "inline_equation", + "content": "(1\\%)" + }, + { + "bbox": [ + 305, + 245, + 545, + 300 + ], + "type": "text", + "content": " data." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 311, + 537, + 399 + ], + "lines": [ + { + "bbox": [ + 315, + 311, + 537, + 399 + ], + "spans": [ + { + "bbox": [ + 315, + 311, + 537, + 399 + ], + "type": "table", + "html": "
C.mIoUI.mIoU
1%5%100%1%5%100%
Multi-Task (lin)-73.9-68.280.7-
MID-FC (lin)66.276.582.872.480.984.1
Ours (lin)70.676.982.977.481.984.3
MID-FC (ft)67.677.884.376.282.185.5
Ours (ft)69.578.484.477.882.385.5
", + "image_path": "bb90fce1e6dd2f10858e7dc89bb9d406fab8afd1a39e2afac612d44883dc123f.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 406, + 545, + 450 + ], + "lines": [ + { + "bbox": [ + 305, + 406, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 305, + 406, + 545, + 450 + ], + "type": "text", + "content": "Table 7. Linear probing (lin) and finetuning (ft) results for the shape segmentation task on the ShapeNet Part dataset. Pre-training is conducted on ShapeNet. Our augmentation improves the performance substantially on various ratios." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 472, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 545, + 567 + ], + "type": "text", + "content": "large margin. In conjunction with random resized crop, a " + }, + { + "bbox": [ + 304, + 472, + 545, + 567 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 472, + 545, + 567 + ], + "type": "text", + "content": " margin is maintained. SSQL heavily relies on domain-specific augmentations, and in many cases, it fails to improve the baseline when handcrafted augmentations are removed. The results using MoCo-v3 and BYOL training objectives are similar. Overall, randomized quantization achieves state-of-the-art results against domain-agnostic baselines in the vision domain." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": "Comparisons with domain-specific augmentations. We further compare with image-specific augmentations for visual representation learning in Table 4. We find that randomized quantization is much stronger than color jittering, which is heavily designed with prior knowledge such as brightness, contrast, and saturation for pixels. In Figure 6, we visualize color jittering and our augmentation. It can be observed that our augmentation leads to stronger and more diverse visual appearances than color jittering. Our augmentation is " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " weaker than the full augmentation, which includes random resized crop, color jittering, grayscale, Gaussian blurring and solarization successively." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16310" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 66, + 69, + 531, + 158 + ], + "blocks": [ + { + "bbox": [ + 66, + 69, + 531, + 158 + ], + "lines": [ + { + "bbox": [ + 66, + 69, + 531, + 158 + ], + "spans": [ + { + "bbox": [ + 66, + 69, + 531, + 158 + ], + "type": "table", + "html": "
NameTask#ClassesData sizeAvg duration (s)
NSynth (NS) [27]Musical instrument classification11305,9794.0
UrbanSound8K (US8K) [60]Urban sound classification108,7324.0
VoxCeleb1 (VC1) [53]Speaker identification1,211153,5148.2
VoxForge (VF) [from Voxforge.org]Language identification6176,4385.8
Speech Commands V2 (SPCV2) [72]Command classification35105,8291.0
Speech Commands V2 (SPCV2/12) [72]Command classification12105,8291.0
", + "image_path": "1e98045cc473e0542d40e177d1f821d7f4bdc3d0cfc6cc8de34385edf02c987a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 79, + 184, + 517, + 285 + ], + "blocks": [ + { + "bbox": [ + 169, + 164, + 424, + 176 + ], + "lines": [ + { + "bbox": [ + 169, + 164, + 424, + 176 + ], + "spans": [ + { + "bbox": [ + 169, + 164, + 424, + 176 + ], + "type": "text", + "content": "Table 8. Downstream dataset details for audio representation learning." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 79, + 184, + 517, + 285 + ], + "lines": [ + { + "bbox": [ + 79, + 184, + 517, + 285 + ], + "spans": [ + { + "bbox": [ + 79, + 184, + 517, + 285 + ], + "type": "table", + "html": "
MethodNSUS8KVC1VFSPCV2/12SPCV2Average
TRILL [64]--17.988.174.9--
COLA [59]63.4-29.971.371.762.4-
OpenL3 [20]-78.2-----
COALA [29]73.172.7-----
COLA [59]70.278.530.479.576.776.868.7
BYOL-A [54]74.179.140.190.291.092.277.8
Ours74.278.045.792.695.192.179.6
", + "image_path": "10491982224c7a0d72b153fb3dbca0ef3af9a268f254e3390fd1a406766c16f3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 291, + 547, + 316 + ], + "lines": [ + { + "bbox": [ + 46, + 291, + 547, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 291, + 547, + 316 + ], + "type": "text", + "content": "Table 9. Linear probing results for audio representation learning on six downstream datasets. Pre-training is conducted on the AudioSet dataset. Our model outperforms BYOL-A on four of the six datasets, with an average improvement of " + }, + { + "bbox": [ + 46, + 291, + 547, + 316 + ], + "type": "inline_equation", + "content": "1.8\\%" + }, + { + "bbox": [ + 46, + 291, + 547, + 316 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 334, + 290, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 334, + 290, + 419 + ], + "spans": [ + { + "bbox": [ + 46, + 334, + 290, + 419 + ], + "type": "text", + "content": "Comparison with weakly-augmented SSL baselines. We compare the performance with MSF [47] in a weak augmentation setting. MSF implicitly utilizes close nearest neighbors as a form of augmentation. In Table 5, our method is better, and it benefits from longer training (67.9 vs. 71.9). Additionally, we demonstrate our approach on diverse modalities, while MSF only focuses on vision." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 430, + 147, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 147, + 442 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 147, + 442 + ], + "type": "text", + "content": "5.2.3D Point Clouds" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": "We explore self-supervised representation learning on point clouds, represented by a disordered set of xyz coordinates. The pretraining is conducted on the ShapeNet [14] dataset consisting of 57,449 3D shapes. Octree-based Sparse CNN [70] is used as the backbone network, which takes 3D point clouds as input and extracts point features as well as shape features. We follow the MID-Net [71] model as the baseline, which is trained by a point-wise and instance-wise contrastive loss. The model is trained by a SGD optimizer with a batch size of 32 and a weight decay of " + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "inline_equation", + "content": "5\\mathrm{e - }4" + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": ". The initial learning rate is 0.03 and decreases by a factor of 10 after 200 and 300 epochs, and the training process terminates after 400 epochs. We apply the randomized quantization augmentation after the base augmentations used in MID-Net. Unlike images and audio which are snapped to grids, strong quantization of point cloud coordinates drastically degrades 3d point data. We thus choose to use a larger number of bins, " + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "inline_equation", + "content": "n = 30" + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": ", in order to maintain more information. In practice, since the 3d points are sparsified by quantization, we observe a substantial training speedup as a side benefit. For evaluation, we experiment on two downstream tasks: shape classification and segmentation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 334, + 547, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 334, + 547, + 477 + ], + "spans": [ + { + "bbox": [ + 304, + 334, + 547, + 477 + ], + "type": "text", + "content": "Shape classification is conducted on ModelNet40 [77] which is composed of 13,834 3D models from 40 categories. For each shape, we extract a global feature with the pre-trained backbone then train a linear classifier, or finetune the network, and report the average classification accuracy in Table 6. We do comparison with FoldingNet [80] and MID-FC [71]. With our augmentation, we improve the classification accuracy over the baseline MID-FC [71] substantially, especially when the training data is limited as shown in Table 6. For example, with " + }, + { + "bbox": [ + 304, + 334, + 547, + 477 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 334, + 547, + 477 + ], + "type": "text", + "content": " of the training data, we improve the classification accuracy by 5.2 and 4.0 points on linear probing and finetuning, respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 479, + 548, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 548, + 660 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 548, + 660 + ], + "type": "text", + "content": "Shape segmentation is conducted on ShapeNet Part [81] with 16,881 3D point clouds from 16 categories. For each shape, we extract point-wise features with the pre-trained backbone then train a segmentation head composed of two fully connected layers, or finetune the network, and report the mean IoU across all categories (C.mIoU) and the mean IoU across all instances (I.mIoU) in Table 7. We do comparison with two unsupervised pretraining methods: MIDFC [71] and Multi-Task [37]. Our results are consistently better than the baselines across different ratios of training data. And similarly to ModelNet40 classification, we observe significant improvements with limited (1% and 5%) training data. For example, with 1% of the training data, our method improves the segmentation performance by 4.4 and 1.9 IoU on linear probing and finetuning, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 670, + 358, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 358, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 358, + 681 + ], + "type": "text", + "content": "5.3. Audio" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "content": "We apply randomized quantization to audio representation learning. We use AudioSet [31] as the pretraining" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "type": "text", + "content": "16311" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 60, + 69, + 534, + 121 + ], + "blocks": [ + { + "bbox": [ + 60, + 69, + 534, + 121 + ], + "lines": [ + { + "bbox": [ + 60, + 69, + 534, + 121 + ], + "spans": [ + { + "bbox": [ + 60, + 69, + 534, + 121 + ], + "type": "table", + "html": "
MethodNatural ImagesTextSpeechSensorsChest x-raysImages & TextAverage
Scratch10.142.324.969.868.157.545.5
e-Mix27.944.141.879.572.448.952.4
Ours32.144.744.584.973.454.555.6
", + "image_path": "43c72ecefcc6fa576c61fb2a31ec0952ef18e74c30e1527b03d6ca257e82ac94.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 128, + 547, + 163 + ], + "lines": [ + { + "bbox": [ + 46, + 128, + 547, + 163 + ], + "spans": [ + { + "bbox": [ + 46, + 128, + 547, + 163 + ], + "type": "text", + "content": "Table 10. Evaluation of the representation performance over six modalities in the DABS benchmark. Representations are trained on a single primary dataset for each modality and evaluated on a number of downstream datasets. The performance for each modality is averaged across the downstream datasets and shown in the table." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 181, + 287, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 181, + 287, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 181, + 287, + 216 + ], + "type": "text", + "content": "dataset, with 1,963,807 audio samples of 527 classes. The pretrained representation is evaluated on six downstream audio classification datasets, summarized in Table 8." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 217, + 287, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 217, + 287, + 240 + ], + "spans": [ + { + "bbox": [ + 47, + 217, + 287, + 240 + ], + "type": "text", + "content": "We largely follow the experimental settings of BYOL-A [54] and treat it as our baseline." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 241, + 287, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 241, + 287, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 287, + 348 + ], + "type": "text", + "content": "We convert audio clips into the commonly used log-scaled spectrogram representation. Random resized crop is used to extract a " + }, + { + "bbox": [ + 46, + 241, + 287, + 348 + ], + "type": "inline_equation", + "content": "64 \\times 96" + }, + { + "bbox": [ + 46, + 241, + 287, + 348 + ], + "type": "text", + "content": " frequency-temporal segment for training. We replaced the Mixup augmentation used in BYOL-A with our randomized quantization, with the number of bins set to 5. We follow prior works [54] by using a lightweight 2D convolutional network as the backbone. We train the network using the Adam optimizer with a base learning rate of 3e-4 and a batch size of 256 for 100 epochs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 350, + 288, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 288, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 288, + 469 + ], + "type": "text", + "content": "Table 9 summarizes the results on the six downstream classification tasks. Compared against BYOL-A with the Mixup augmentation, our randomized quantization outperforms it in four out of the six tasks. Our approach is particularly stronger by a margin of " + }, + { + "bbox": [ + 46, + 350, + 288, + 469 + ], + "type": "inline_equation", + "content": "5.6\\%" + }, + { + "bbox": [ + 46, + 350, + 288, + 469 + ], + "type": "text", + "content": " on the VoxCeleb1 dataset, which is the hardest classification task with 1211 classes among all six tasks. Our improvements tend to be smaller for tasks with fewer classes. On average, the proposed augmentation surpasses the current state-the-of-art BYOL-A by a margin of " + }, + { + "bbox": [ + 46, + 350, + 288, + 469 + ], + "type": "inline_equation", + "content": "1.8\\%" + }, + { + "bbox": [ + 46, + 350, + 288, + 469 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 476, + 99, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 476, + 99, + 488 + ], + "spans": [ + { + "bbox": [ + 47, + 476, + 99, + 488 + ], + "type": "text", + "content": "5.4. DABS" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 495, + 288, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 288, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 288, + 685 + ], + "type": "text", + "content": "We additionally conduct experiments on the public benchmark DABS [66] which is designed to study domain-agnostic self-supervised representation learning. Since some of its domains are discrete in nature (e.g., language), we first embed the data with a frozen layer and then augment the data embeddings for all the modalities consistently. It contains six data modalities1, covering natural RGB images, multichannel sensor data, English text, audio, chest x-ray images, as well as captioned images. In each domain, pre-training is conducted on a large-scale dataset, and the learned representations are evaluated with linear probing on various in-domain downstream datasets. The average performance for the in-domain downstream datasets is reported. We refer the reader to the benchmark for a full description of the pretraining datasets and in-domain evaluation datasets." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 309, + 181, + 546, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 181, + 546, + 252 + ], + "spans": [ + { + "bbox": [ + 309, + 181, + 546, + 252 + ], + "type": "text", + "content": "We follow a leading method e-Mix [66] with a Transformer architecture on this domain-agnostic benchmark. The network is optimized with the Adam optimizer with a learning rate of 1e-4 and weight decay of 1e-4. The training protocol follows e-Mix, and all modalities share the same recipe." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 256, + 546, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 256, + 546, + 327 + ], + "spans": [ + { + "bbox": [ + 304, + 256, + 546, + 327 + ], + "type": "text", + "content": "We apply randomized quantization on the token embeddings before the Transformer. Since the quantization function has zero gradients everywhere, we randomly initialize the token embedding module without updating it. The straight-through estimator can be potentially useful, but it is not the focus of this work." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 332, + 547, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 332, + 547, + 440 + ], + "spans": [ + { + "bbox": [ + 304, + 332, + 547, + 440 + ], + "type": "text", + "content": "Table 10 summarizes the results for this benchmark. Our model outperforms the baseline e-Mix on all modalities. The improvements on natural images, speech, and sensors are larger than " + }, + { + "bbox": [ + 304, + 332, + 547, + 440 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 304, + 332, + 547, + 440 + ], + "type": "text", + "content": ", while the improvements on text and chest x-rays are relatively smaller, less than " + }, + { + "bbox": [ + 304, + 332, + 547, + 440 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 332, + 547, + 440 + ], + "type": "text", + "content": ". Both e-Mix and our pretraining seem to hurt the representation quality for captioned images. We hypothesize that the two modalities of images and texts pose significant challenges for a naive contrastive learning approach." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 462, + 379, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 462, + 379, + 475 + ], + "spans": [ + { + "bbox": [ + 306, + 462, + 379, + 475 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 486, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 712 + ], + "type": "text", + "content": "We propose randomized quantization as a novel data augmentation tool for self-supervised representation learning. Quantization effectively withholds information within the quantization bins but retains the information across bins. It could be applied on arbitrary data along the channel dimension without domain-specific knowledge. Randomized quantization significantly outperforms existing domain-agnostic augmentations based on Mixup. It compares favorably against domain-specific augmentations on vision, and attains state-of-the-art results on audio and 3D point clouds. We also explored randomized quantization on input data embeddings in a neural network for a wide range of data modalities. Experimental results on the DABS benchmark demonstrate state-of-the-art results for speech, text, images and multiple sensors. Randomized quantization could potentially be applied in a masked modeling framework, where the original images are reconstructed from quantized ones. This direction will be explored in future work." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 693, + 287, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 287, + 715 + ], + "type": "text", + "content": "1The benchmark also provides an additional multi-lingual text modality. However, it is not evaluated in the original paper. We thus omit this." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "16312" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 137, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 137, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 137, + 85 + ], + "type": "text", + "content": "Broader Impacts" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 163 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 163 + ], + "type": "text", + "content": "Although the proposed augmentation is generic in its formulation, it is not guaranteed to work beyond the modalities investigated in this paper. Application of the augmentation for other self-supervised learning frameworks such as masked modeling or generalization to other downstream tasks remains under-explored." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 172, + 149, + 186 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 172, + 149, + 186 + ], + "spans": [ + { + "bbox": [ + 47, + 172, + 149, + 186 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 192, + 287, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 287, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 287, + 276 + ], + "type": "text", + "content": "We sincerely appreciate Reviewer #5 and AC's unwavering efforts in saving this work from rejection. 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In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, pages 10990-10998, 2021. 5" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "16316" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/RankMatch_ Fostering Confidence and Consistency in Learning with Noisy Labels/0d715541-80cd-458e-81f4-423a1c46d83e_content_list.json b/2023/RankMatch_ Fostering Confidence and Consistency in Learning with Noisy Labels/0d715541-80cd-458e-81f4-423a1c46d83e_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..f5e38b7ca359d99e762940ca5620f3443516db6e --- /dev/null +++ b/2023/RankMatch_ Fostering Confidence and Consistency in Learning with Noisy Labels/0d715541-80cd-458e-81f4-423a1c46d83e_content_list.json @@ -0,0 +1,1710 @@ +[ + { + "type": "text", + "text": "RankMatch: Fostering Confidence and Consistency in Learning with Noisy Labels", + "text_level": 1, + "bbox": [ + 210, + 130, + 759, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ziyi Zhang $^{1,2}$ , Weikai Chen $^{3}$ , Chaowei Fang $^{4}$ , Zhen Li $^{5}$ , Lechao Chen $^{6}$ , Liang Lin $^{2}$ , Guanbin Li $^{2,7*}$", + "bbox": [ + 96, + 202, + 877, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ National Key Laboratory of Novel Software Technology, Nanjing University, Nanjing, China $^{2}$ Sun Yat-sen University, Guangzhou, China, $^{3}$ Tencent America", + "bbox": [ + 116, + 220, + 854, + 255 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{4}$ Xidian University, $^{5}$ The Chinese University of Hong Kong (Shenzhen), $^{6}$ Zhejiang Lab", + "bbox": [ + 132, + 256, + 836, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{7}$ Research Institute, Sun Yat-sen University, Shenzhen, China", + "bbox": [ + 241, + 273, + 728, + 291 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "zhangziyi@lamda.nju.edu.cn,liguanbin@mail.sysu.edu.cn", + "bbox": [ + 250, + 295, + 720, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 344, + 313, + 359 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Learning with noisy labels (LNL) is one of the most important and challenging problems in weakly-supervised learning. Recent advances adopt the sample selection strategy to mitigate the interference of noisy labels and use small-loss criteria to select clean samples. However, the one-dimensional loss is an over-simplified metric that fails to accommodate the complex feature landscape of various samples, and, hence, is prone to introduce classification errors during sample selection. In this paper, we propose RankMatch, a novel LNL framework that investigates additional dimensions of confidence and consistency in order to combat noisy labels. Confidence-wise, we propose a novel sample selection strategy based on confidence representation voting instead of the widely-used small-loss criterion. This new strategy is capable of increasing sample selection quantity without sacrificing labeling accuracy. Consistency-wise, instead of the widely adopted feature distance metric for measuring the consistency of inner-class samples, we advocate that the rank of principal features is a much more robust indicator. Based on this metric, we propose rank contrastive loss, which strengthens the consistency of similar samples regardless of their labels and facilitates feature representation learning. Experimental results on noisy versions of CIFAR-10, CIFAR-100, Clothing1M and WebVision have validated the superiority of our approach over existing state-of-the-art methods.", + "bbox": [ + 75, + 377, + 473, + 770 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 801, + 209, + 816 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The remarkable success of DNNs stems from the availability of large-scale datasets. However, it is highly laborious to obtain massive data with high-quality annotations.", + "bbox": [ + 76, + 828, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b9b9ee18a1798f29c2f62808d16d22753ef7663dba48715495aea1a22e4c9cf7.jpg", + "image_caption": [ + "Figure 1: Motivation of RankMatch. After being trained with noisy labels, the model is validated by the augmented images. Noisy labels leads to high-entropy outputs, which lack confidence. We advocate for the use of confidence criterion for sample selection, as the confident samples are more likely to have clean labels. Moreover, The weakly augmented image is similar to training Image 1 (classified as 'dog'), while the strongly augmented one is similar to training Image 2 (classified as 'deer'). Considering the model tends to produce similar predictions for similar images, the two views of the same image have inconsistent predictions. Consequently, we introduce the rank contrastive loss to enhance the semantic consistency." + ], + "image_footnote": [], + "bbox": [ + 521, + 344, + 879, + 484 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hence, training DNNs using inexpensive samples from the search engine or machine annotation [27, 33, 11] has become an attractive alternative. However, these methods inevitably introduce erroneous labels, which cause poor performance as DNNs can easily overfit to noises [58]. Hence, learning with noisy labels (LNL) has become an important yet challenging task.", + "bbox": [ + 496, + 729, + 893, + 835 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sample selection is a widely adopted strategy in LNL that identifies clean samples from the dataset to alleviate the negative impact of noisy labels. The small-loss criterion is a popular sample selection strategy, which regards", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1644", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "samples with lower loss as clean ones. However, such a one-dimensional loss is too simplified to accommodate the sophisticated distribution of high-dimensional data, such as the image features. As a result, a plethora of easy-but-noisy samples with small loss are often wrongly grouped into the clean set by using the loss-based strategy. This confirmation bias would be gradually amplified in the subsequent loss minimization training and severely impact the final performance [24, 44].", + "bbox": [ + 75, + 90, + 470, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another challenge of LNL lies in the difficulty of obtaining robust and consistent representation for samples across categories and subjects [24, 26, 19]. In semi-supervised learning, this issue can be largely addressed by enforcing consistent predictions given different views of the same sample [21]. However, in LNL, due to the existence of wrong labels, different views of the same object could be clustered into different categories, leading to inconsistent estimations (see Figure 1). Though the sample selection mechanism can identify a part of clean samples, the consistent representation learned from this set of clean data only works on simple samples with high confidence. Hence, how to achieve consistent prediction on difficult samples with low confidence remains an open question.", + "bbox": [ + 75, + 229, + 470, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we follow the line of sample selection to avoid the adverse impact of noisy labels. However, instead of relying on an over-simplified 1D loss function, we propose to combat the noises by incorporating new perspectives from confidence and consistency. Confidence-wise, to ensure robust selection of clean samples, we leverage the advances of confidence learning (CL) [37] while avoiding its vulnerability to noisy network predictions. In particular, we investigate the performance of clean sample selection using fixed confidence thresholds at different noise levels. The results (Figure 4) show that a fixed high threshold leads to a much more accurate sample selection even at the presence of strong noises. Therefore, we leverage one fixed high confidence threshold for all classes to ensure the purity of confident samples. To address the lack of clean data by using a high threshold, we further propose sample selection via confidence voting (SCV) to ensure an ample collection of clean labels. Specifically, we generate $K$ clusters from confident samples for each class and treat the cluster center as confident prototype. Each sample is considered clean if the label is consistent with the results voted by its $k$ nearest confident prototypes. We empirically find that the proposed confidence voting mechanism can generate reliable and clean samples in sufficient amounts, ensuring both the quality and quantity of clean samples.", + "bbox": [ + 75, + 444, + 470, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Consistency-wise, in addition to the classic consistency regularization, i.e. enforcing consistent outputs of different views from the same sample, we propose to encourage consistent predictions between similar hard samples of the same category. To achieve this goal, we introduce rank con", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "trastive loss (RCL), a novel metric that fully leverages the rank of principal image features for robust measurement of similar samples. Empirical experiments show that the conventional $l_{2}$ distance cannot exploit the inner structure of feature representation, and, hence, fails to foster consistent clustering in the complex feature space corrupted by noisy samples. Our key observation is that while similar hard samples (with low confidence) of the same class may have a large $l_{2}$ distance in the feature space, the underlying rank of their principal features still remains consistent (see Figure 2). Therefore, our proposed RCL loss is able to promote feature consistency by encouraging correct and discriminative clustering of similar samples with low confidence.", + "bbox": [ + 496, + 90, + 890, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We code our method as RankMatch as the two perspectives of the proposed framework can mutually benefit each other. While more reliable data segmentation based on high confidence can benefit the subsequent representation learning, the consistent representations further improve the confidence of uncertain data samples, and, in turn, strengthen our proposed confidence-based sample-selection mechanism. We validate the superiority of our method over the state-of-the-art approaches on several challenging benchmarks, including CIFAR, Clothing1M, and WebVision. Our contributions can be summarized as follows.", + "bbox": [ + 496, + 287, + 890, + 452 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A method with new state-of-the-art performance that is specially tailored for LNL problems by fostering both confidence and consistency.", + "- A novel sample-selection via confidence voting (SCV) strategy that generates reliable and ample clean samples for the subsequent training.", + "- Rank contrastive loss (RCL) based on the rank statistics of principal features that encourages consistency between hard samples of the same category. RCL can further benefit clean sample selection by promoting more discriminative features (see Fig. 1 in the supplementary material) for constructing intra-category clusters." + ], + "bbox": [ + 517, + 460, + 890, + 654 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 670, + 640, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Most existing methods on LNL can be categorized into two directions: 1) loss correction and 2) sample selection.", + "bbox": [ + 498, + 696, + 890, + 726 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Loss Correction. For loss correction, mainstream techniques [51, 46, 29, 47, 22] estimate noise transition matrix with a small set of clean samples as prior knowledge. However, estimating the noise transition matrix is challenging, and their assumptions may be too ideal to fit real-world scenarios. To rectify the noisy labels, another line of research proposes self-training architectures where noisy labels are replaced by network predictions [43, 56]. Some methods focus on the design of noisy-tolerant loss functions. For example, [2, 48, 13, 12] leverage bounded loss functions to improve their robustness to noisy labels. Besides, there are", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1645", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/78471bfa7668c0c88d787e59ef03525109ce850e44aeb845cb25c8173b776e88.jpg", + "image_caption": [ + "Figure 2: The training strategy of RankMatch. We use strong and weak augmentation to achieve consistency regularization in LNL. For the clean set, the given labels are used to regularize the network predictions on strongly augmented images via the supervised training loss $L_{c}$ . For the noisy set, we first generate pseudo labels from the predictions on weakly augmented images and then use them to regularize the predictions on strongly augmented images via training loss $L_{n}$ . Rank contrastive loss pulls similar samples together and pushes others away. The similarity matrix is defined by ranking feature channels instead of Euclidean distance. The final objective function is a joint loss, including a class diversity regularization term in addition." + ], + "image_footnote": [], + "bbox": [ + 130, + 98, + 848, + 253 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "some proposed unbiased loss function [35], information-based loss function called $L_{DMI}$ [54], punishment regularization [32], confidence regularization [8], early learning regularization [30], contrastive representation regularization [28] and over-parameterized term [31]. However, it is arduous for loss-correction-based methods to play an advantage in practical scenarios facing high noise ratios.", + "bbox": [ + 75, + 402, + 470, + 510 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Sample selection. Sample selection-based methods strive to reweight training samples and identify clean data to reduce the interference of noisy labels. Many existing methods propose introducing improved selection criteria to make the selected samples cleaner [23, 59, 3, 36, 24, 1]. Memorization effect [4] illuminates that DNNs learn clean and simple patterns faster than noisy labels, leading to a trend to consider small loss as a criterion for sample selection, which means that samples with smaller loss values are more likely to have clean labels. For instance, [3, 36, 24, 1] leverage clean data distribution as selection criterion by lower-loss component in mixture model fitted by per-sample loss. [55, 19] introduces JS-divergence between network prediction and labels as a selection criterion. [38] leverages the cross-entropy loss between disagreement distribution and labels as selection criterion. However, the loss value is just a scalar, contains limited information, and is prone to errors. For example, it is hard to distinguish between hard-to-learn clean samples and noisy samples after the warm-up stage since both have relatively large loss values. Besides, confirmation bias [44] is a common issue often encountered with the small-loss criterion. Once the noisy samples are wrongly grouped into the clean set by the small-loss criterion, their losses will keep small in the later train", + "bbox": [ + 75, + 537, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ing. It remains challenging to rectify the sample selection errors. Many methods mitigate this issue by training two networks [18, 34, 14, 57, 49, 24, 55]. But it is still a problem to get more accurate labels through the small-loss criterion. More recently, Confident Learning (CL) [37] proposes confident criterion as an alternative for sample selection. It computes a set of thresholds for every class and chooses confident samples whose network predicted highest probabilities are greater than the corresponding thresholds. However, CL directly estimates the noise transition matrix by confident samples, which is vulnerable to the network predictions and threshold setting. And it is prone to fail to perform well in large-scale cases and real-world scenarios with a high noise ratio.", + "bbox": [ + 496, + 402, + 890, + 614 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Semi-supervised Learning. The Semi-supervised Learning (SSL) has seen fast progress by leveraging consistency regularization [41, 53, 5, 21, 39, 40, 45], which is used to minimize the difference in network prediction between two views of the same image. FixMatch [21] simply but effectively combines strong and weak augmentation in consistency regularization with confidently pseudo-labeling to achieve great success in semi-supervised learning setting. Most recently, [39] propose an uncertainty-aware pseudolabels selection (UPS) framework to improve pseudo labeling accuracy. RankingMatch [45] introduces a triplet loss, where the similarity between samples is measured by the L2-norm outputs. Furthermore, it is worth noting that the rank statistics of principal features can serve as a metric to measure the pairwise similarity among samples [15]. There are similarities between Learning with Noisy Labels (LNL) problems and semi-supervised learning setting.", + "bbox": [ + 496, + 643, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1646", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In semi-supervised learning settings, confident predictions have strong connection with true labels as labeled data regularizing the unlabeled data, which are not easy to overconfident confused by noisy label. And leveraging confident predictions inevitably lacks sample diversity to make pseudo labels more reliable, while difficult samples always have uncertain predictions. Our approach finds a good balance of confidence, sample diversity and consistency.", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 227, + 168, + 242 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our method is introduced in three parts: the sample selection mechanism (Figure. 3), the consistency regularization and rank contrastive loss. Figure 2 shows the overview of RankMatch. The algorithm is included in the supplementary material.", + "bbox": [ + 75, + 253, + 468, + 328 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Preliminaries. For the $C$ -way image classification task with noisy labels, denoted by $\\mathcal{D} = (\\mathcal{X}, \\widetilde{\\mathcal{Y}})$ the training data, where $\\mathcal{X}$ is training images, and $\\widetilde{\\mathcal{Y}}$ is labels which may be wrongly annotated. We denote the DNNs in training stage as $P(F(\\mathbf{x}, \\theta))$ , where $\\mathbf{x} \\in \\mathbb{R}^I$ is the input image, $F: \\mathbb{R}^I \\to \\mathbb{R}^L$ is the feature extractor where $I$ and $L$ stand for the dimension of input space and embedding space respectively, and $P: \\mathbb{R}^L \\to \\mathbb{R}^C$ represents the classifier. $\\theta$ denotes the network parameters of the feature extractor. We use $\\mathbf{f}_i$ and $\\mathbf{p}_i$ as simplified forms of $F(\\mathbf{x}_i, \\theta)$ and $P(F(\\mathbf{x}_i, \\theta))$ respectively.", + "bbox": [ + 75, + 329, + 470, + 498 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Sample Selection via Confidence Voting", + "text_level": 1, + "bbox": [ + 76, + 508, + 416, + 525 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the sample selection, we leverage the advantage of confident learning [37] rather than the widely used small-loss criterion. We explore using a fixed confidence threshold to avoid the vulnerability of inaccurate network predictions. Figure 4 illustrates that confident predictions selected by a fixed high threshold are reliable but of a limited number. Hence, we propose a new sample selection strategy based on the confidence criterion that maintains reliability while ensuring sufficient confident samples across categories.", + "bbox": [ + 75, + 532, + 468, + 683 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Confident Samples. In the setting of LNL, it is hard to select confident samples just by a single threshold when facing different levels of noise rates. Some classes are easy-to-learn, and one threshold for all classes is likely to result in class-unbalanced selection. In order to avoid data imbalance among classes, we select the top $B$ basic confident samples $\\mathcal{I}_b$ in each class to ensure each class at least has $B$ samples:", + "bbox": [ + 75, + 690, + 468, + 811 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {I} _ {b} ^ {c} = \\underset {| \\hat {\\mathcal {X}} | = B, \\hat {\\mathcal {X}} \\subseteq \\mathcal {X}} {\\arg \\max } \\sum_ {\\mathbf {x} \\in \\hat {\\mathcal {X}}} \\mathbf {p} [ c ], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 813, + 468, + 845 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{p}[c]$ is the $c$ -th element of $\\mathbf{p}$ ( $= P(F(\\mathbf{x},\\theta))$ ), namely the probability value of the $c$ -th class. And additional samples with prediction probability greater than a threshold as", + "bbox": [ + 76, + 854, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7235a956e775513c21f6c228f280bd344eb80a7ebc64c02bda2cae3b67f428b3.jpg", + "image_caption": [ + "Figure 3: Sample-selection via Confidence Voting (SCV) module. We first select the most representative confident samples. Then, the selected confident samples generate prototypes as voting candidates. For each sample, its $k$ nearest prototypes are regarded as voters to identify whether the label is clean." + ], + "image_footnote": [], + "bbox": [ + 532, + 95, + 859, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the reliable confident samples:", + "bbox": [ + 500, + 388, + 705, + 402 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {I} _ {r} ^ {c} = \\left\\{\\mathbf {x} _ {i} \\mid \\mathbf {p} _ {i} [ c ] > \\tau , \\mathbf {x} _ {i} \\in \\mathcal {X} \\right\\}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 419, + 890, + 435 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The final selected confident samples is the union of the two sets $\\mathcal{I}^c = \\mathcal{I}_b^c\\cup \\mathcal{I}_r^c$", + "bbox": [ + 498, + 450, + 890, + 481 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Confident Prototype Generation. To guarantee the quality of the confident samples, we set high threshold $\\tau$ and small portion $B$ , but face the problem of low sample quantity. Although with a small number, the reliable representations of confident samples reflect some common intra-class patterns. Thus, we generate representation prototypes using the selected samples for further selection. Straightforwardly, a representative feature can be generated by averaging features of confident samples for each class:", + "bbox": [ + 496, + 488, + 892, + 625 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\phi^ {c} = \\frac {1}{| \\mathcal {I} ^ {c} |} \\sum_ {\\mathbf {x} \\in \\mathcal {I} ^ {c}} F (\\mathbf {x}, \\theta). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 637, + 890, + 674 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Even if the confident samples include some noise during the early training stage, the prototype generation process will predominantly rely on the most clean samples, rendering it robust to noisy labels. However, the mean vector is unable to represent a class with large intra-class variations. We further diversify the intra-class patterns by generating more prototypes of each class. Specifically, we split the confident samples into $K$ clusters for each class by $K$ -means. For the $c$ -th class, we define the average centers of the obtained clusters features as $\\Phi^c = \\{\\phi_j^c\\}_{j=1}^K$ . Our sample-selection module is based on the generated confident prototypes $\\Phi (= \\bigcup_{c=1}^{C} \\Phi^c)$ .", + "bbox": [ + 496, + 686, + 892, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Data Segmentation by Confidence Voting. After obtaining $C \\times K$ prototypes, we first find the $k$ nearest prototypes", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1647", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of $\\mathbf{x}_i$ measured by the cosine similarity:", + "bbox": [ + 76, + 90, + 341, + 104 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {V} _ {i} = \\underset {| \\hat {\\Phi} | = k, \\hat {\\Phi} \\subseteq \\Phi} {\\arg \\max } \\sum_ {\\phi \\in \\hat {\\Phi}} \\cos (\\mathbf {f} _ {i}, \\phi). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 168, + 119, + 468, + 152 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The class label to which the most prototypes belong in $\\mathcal{V}_i$ is considered as the voting result $\\mathbf{y}_i'$ . Clean samples $\\mathcal{D}_{\\mathrm{cln}}$ are identified by checking whether $\\mathbf{y}_i'$ is consistent with the provided label $\\widetilde{\\mathbf{y}}_i$ :", + "bbox": [ + 76, + 166, + 468, + 227 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} _ {\\mathrm {c l n}} = \\left\\{\\left(\\mathbf {x} _ {i}, \\widetilde {\\mathbf {y}} _ {i}\\right) \\mid \\widetilde {\\mathbf {y}} _ {i} = \\mathbf {y} _ {i} ^ {\\prime}, \\forall \\left(\\mathbf {x} _ {i}, \\widetilde {\\mathbf {y}} _ {i}\\right) \\in \\mathcal {D} \\right\\}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 239, + 468, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The remaining noisy set is $\\mathcal{D}_{\\mathrm{nsy}} = \\mathcal{D}\\setminus \\mathcal{D}_{\\mathrm{cln}}$", + "bbox": [ + 76, + 270, + 369, + 286 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Consistency Regularization", + "text_level": 1, + "bbox": [ + 76, + 296, + 323, + 313 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This paper argues that noisy labels lead to inconsistent predictions (Figure 1). To enhance the consistency of the predictions augmented from the same image, we apply two different augmentation methods to generate two views for training images, including \"weak\" augmentation $(\\mathcal{A}_w)$ and \"strong\" augmentation $(\\mathcal{A}_s)$ . Weak augmentation refers to random cropping and flipping, while strong augmentation refers to AutoAugment [9], which uses reinforcement learning to find augmentation strategies automatically and requires labeled data to learn. Note that our sample selection mechanism provides cleaner supervision signals, benefiting AutoAugment to accept a more effective augmentation policy.", + "bbox": [ + 75, + 320, + 468, + 516 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following [21], we transfer the training image $\\mathbf{x}$ with the two augmentation strategies, resulting in two views: $\\mathbf{v}^w = \\mathcal{A}_w(\\mathbf{x})$ , and $\\mathbf{v}^s = \\mathcal{A}_s(\\mathbf{x})$ . The corresponding network predictions are denoted as $\\mathbf{p}^w$ and $\\mathbf{p}^s$ , respectively. Given that the semantic information of the augmented images is not modified, we assume the two network predictions to be consistent.", + "bbox": [ + 76, + 517, + 468, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For clean samples, we direct use cross-entropy loss between predictions on strongly augmented images and the original labels:", + "bbox": [ + 76, + 623, + 468, + 667 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c} = - \\frac {1}{| \\mathcal {D} _ {\\mathrm {c l n}} |} \\sum_ {(\\mathbf {x}, \\widetilde {\\mathbf {y}}) \\in \\mathcal {D} _ {\\mathrm {c l n}}} \\widetilde {\\mathbf {y}} \\circ \\log (\\mathbf {p} ^ {s}), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 681, + 468, + 719 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\circ$ denotes the inner product.", + "bbox": [ + 76, + 731, + 307, + 746 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For noisy samples with high prediction confidence, we rectify their labels with predictions of weakly augmented images:", + "bbox": [ + 76, + 747, + 468, + 792 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathcal {D}} _ {\\mathrm {n s y}} = \\left\\{\\left(\\mathbf {x} _ {i}, \\hat {\\mathbf {y}} _ {i}\\right) | \\forall \\mathbf {x} _ {i} \\in \\mathcal {X} _ {\\mathrm {n s y}}, \\max _ {c} \\left\\{\\mathbf {p} ^ {w} [ c ] \\right\\} > \\nu , \\hat {\\mathbf {y}} _ {i} = c \\right\\}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 804, + 468, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\nu$ is the confidence threshold, we set it the same as that in Eq. 2 to avoid introducing another parameter. Inspired by [21], the cross entropy losses between the predictions of weakly and strongly augmented images are", + "bbox": [ + 76, + 840, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "employed as regularizing consistency for the CNN model learning:", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {n} = - \\frac {1}{| \\hat {\\mathcal {D}} _ {\\mathrm {n s y}} |} \\sum_ {(\\mathbf {x}, \\hat {\\mathbf {y}}) \\in \\hat {\\mathcal {D}} _ {\\mathrm {n s y}}} \\hat {\\mathbf {y}} \\circ \\log \\left(\\mathbf {p} ^ {s}\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 138, + 890, + 180 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Rank Contrastive Loss", + "text_level": 1, + "bbox": [ + 500, + 202, + 710, + 217 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Robust representations can benefit our samples selection strategy. However, some valuable information is excluded by Eq. 7 and Eq. 8 since the hard-to-learn noisy samples have less confident predictions and thus can not be optimized. To obtain complete and robust representations, we propose a rank contrastive loss (RCL) to strengthen the consistency of the \"similar\" samples while pushing \"dissimilar\" ones further.", + "bbox": [ + 496, + 229, + 890, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The widely used $L_{2}$ distance as the similarity metric is less robust in LNL, as overfitting to noisy labels tends to introduce spurious close euclidean distance. Every convolution kernel filters out certain kinds of attributes in the input image. Similar visual patterns are prone to activate the same representation channel of response maps produced by convolution layers. Hence, the indices of feature elements rank ordered in accordance with their magnitudes, can serve as a metric for assessing the pairwise representations similarity [15]. Although noisy labels affect the feature value, we leverage rank statistics of principal features to estimate the similarity matrix. Specifically, we rank the values in all channels of $\\mathbf{f}_i$ and regard the $r$ channels with the largest activation values as the principal feature dimensions,", + "bbox": [ + 496, + 354, + 890, + 566 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {R} _ {i} = \\underset {| \\hat {\\mathcal {R}} | = r, \\hat {\\mathcal {R}} \\subset \\{1, 2, \\dots , L \\}} {\\arg \\max } \\sum_ {n \\in \\hat {\\mathcal {R}}} \\mathbf {f} _ {i} [ n ], \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 584, + 890, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{f}_i[n]$ denote the $n$ -th channel of feature $\\mathbf{f}_i$ . If two samples $\\mathbf{x}_i$ and $\\mathbf{x}_j$ share the same principal feature dimensions, we assume they are \"similar\". The similarity $s_{ij}$ between $\\mathbf{x}_i$ and $\\mathbf{x}_j$ is evaluated as follows,", + "bbox": [ + 498, + 637, + 890, + 699 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ns _ {i j} = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\mathcal {R} _ {i} = \\mathcal {R} _ {j}; \\\\ 0 & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 717, + 890, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To achieve clustering in the feature space, we adopt the following binary cross-entropy loss as:", + "bbox": [ + 500, + 780, + 888, + 810 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {R C L}} = - \\frac {1}{N ^ {2}} \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {N} \\left[ s _ {i j} \\log \\left(\\mathbf {p} _ {i} \\circ \\mathbf {q} _ {j}\\right) + \\left(1 - s _ {i j}\\right) \\log \\left(1 - \\mathbf {p} _ {i} \\circ \\mathbf {q} _ {j}\\right) \\right], \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 829, + 915, + 883 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{p}_i = P(F(\\mathbf{v}_i^w,\\theta))$ and $\\mathbf{q}_i = P(F(\\mathbf{v}_i^s,\\theta))$ . The train-", + "bbox": [ + 500, + 885, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1648", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ing loss $\\mathcal{L}_{\\mathrm{RCL}}$ can be divided into two terms:", + "bbox": [ + 76, + 90, + 374, + 106 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Consistency regularization", + "bbox": [ + 253, + 118, + 379, + 130 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {R C L}} = - \\frac {1}{N ^ {2}} \\sum_ {i = 1} ^ {N} \\left[ s _ {i i} \\log \\left(\\mathbf {p} _ {i} \\circ \\mathbf {q} _ {i}\\right) + \\left(1 - s _ {i i}\\right) \\log \\left(1 - \\mathbf {p} _ {i} \\circ \\mathbf {q} _ {i}\\right) \\right] \\\\ - \\frac {1}{N ^ {2}} \\sum_ {i = 1} ^ {N} \\sum_ {j \\neq i} [ s _ {i j} \\log (\\mathbf {p} _ {i} \\circ \\mathbf {q} _ {j}) + (1 - s _ {i j}) \\log (1 - \\mathbf {p} _ {i} \\circ \\mathbf {q} _ {j}) ]. \\tag {12} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 80, + 138, + 496, + 237 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Since $s_{ii} = 1$ always holds, organize the first term as:", + "bbox": [ + 76, + 238, + 431, + 253 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n- \\frac {1}{N ^ {2}} \\sum_ {i = 1} ^ {N} \\log \\left(\\mathbf {p} _ {i} \\circ \\mathbf {q} _ {i}\\right) = - \\frac {1}{N ^ {2}} \\sum_ {i = 1} ^ {N} \\log \\left(\\mathbf {p} _ {i} ^ {w} \\circ \\mathbf {p} _ {i} ^ {s}\\right). \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 265, + 468, + 306 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Minimizing this term is equal to $\\max \\{\\mathbf{p}_i^w\\circ \\mathbf{p}_i^s\\}$ , which pulls the outputs of strongly and weakly augmented images closer. Thus, $\\mathcal{L}_{\\mathrm{RCL}}$ in the diagonal of $S$ can be regarded as consistency regularization. Even in the early training stage, $S$ is the identity matrix that removes the second term in Eq. 12, improving the network representation ability.", + "bbox": [ + 76, + 318, + 468, + 411 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. Overall Loss Function", + "text_level": 1, + "bbox": [ + 76, + 420, + 284, + 434 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Following [43, 24, 3], we apply the fair class diversity-promoting regularization $\\mathcal{L}_{div}$ to prevent assigning most samples into few classes:", + "bbox": [ + 76, + 444, + 468, + 489 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d i v} = \\sum_ {c = 1} ^ {C} \\frac {1}{C} \\log \\left(\\frac {1}{C} / \\frac {\\sum_ {i = 1} ^ {N} \\mathbf {p} _ {i} ^ {w} [ c ]}{N}\\right). \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 501, + 468, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The overall loss function for network optimization is as follows:", + "bbox": [ + 76, + 554, + 468, + 582 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {c} + \\lambda_ {n} \\mathcal {L} _ {n} + \\mathcal {L} _ {\\mathrm {R C L}} + \\mathcal {L} _ {\\text {d i v}}. \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 585, + 468, + 601 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We following [24, 14, 57, 36] to train two networks to combat the confirmation bias, detailed algorithm is included in supplementary material.", + "bbox": [ + 76, + 609, + 468, + 656 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 670, + 209, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 695, + 266, + 710 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate the proposed RankMatch on CIFAR-10, CIFAR-100 [20], as well as the real-world datasets Clothing1M [52] and WebVision [27]. Both CIFAR-10 and CIFAR-100 contain 50,000 training images and 10,000 test images of size $32 \\times 32$ . Following previous works [43, 25], we conduct experiments requiring noise augmentation, either symmetric or asymmetric [43, 25] label noise injection. We follow the identical implementation of generating symmetric and asymmetric noises on CIFAR datasets with DivideMix [24]. Symmetric noise is generated by randomly replacing the labels for a percentage of the training data with all possible labels. Asymmetric noise is to mimic the", + "bbox": [ + 75, + 719, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "structure of real-world label noise, where labels are only replaced by similar classes (e.g. deer $\\rightarrow$ horse, dog $\\leftrightarrow$ cat). We adopt 18-layer PreAct Resnet [17] as the backbone. During training, we train DNNs for 300 epochs using SGD optimizer with a momentum of 0.9, with weight decay of 0.0005 for CIFAR-10 and 0.001 for CIFAR-100. The batch size is 64 for CIFAR-10 and 128 for CIFAR-100. We set the initial learning rate as 0.02 and reduce it by a factor of 10 after 150 epochs. The warm-up period is 10 epochs for CIFAR-10 and 30 epochs for CIFAR-100, respectively. For all CIFAR experiments, we set $\\tau = 0.95$ , $r = 5$ , and choose $\\lambda_{n}$ from $\\{0.2, 0.5, 1, 2, 10, 15\\}$ for a small validation test. More experimental details are in supplementary materials.", + "bbox": [ + 496, + 90, + 890, + 287 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Clothing1M contains 1 million real-world shopping images belonging to 14 classes. We use ResNet-50 [16] with weights pretrained on ImageNet as the classification model. WebVision consists of web-crawled images with the same concepts from ImageNet ILSVRC12 [10]. We follow the previous work [24, 7] and compare baseline methods on the first 50 classes of the Google image subset using the inception-resnet v2 [42]. The training details are delineated in supplementary materials.", + "bbox": [ + 496, + 287, + 890, + 425 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experimental Results", + "text_level": 1, + "bbox": [ + 500, + 436, + 700, + 452 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on CIFAR. Table 1 illuminates RankMatch outperforms the state-of-the-art models across most noisy levels. RRL [26] combats noisy labels by learning robust representations and slightly outperforms our method on CIFAR-10 with $20\\%$ symmetric label noise. One possible explanation is that the massive clean labels make it easy to rectify the symmetric label noise. Thus, the sample selection strategy is less effective in this scenario but shows great advantages for a high noise ratio and real-world dataset. Benefiting from the advanced confidence sample selection mechanism, RankMatch boosts the averaged test accuracy of the last ten epochs from $77.4\\%$ to $92.1\\%$ on CIFAR-10 and $33.1\\%$ to $49.9\\%$ on CIFAR-100 under the extreme case of $90\\%$ noise. Even without MixMatch [6] technique, RankMatch achieves around 20 points improvement (50.6% vs. $31.5\\%$ ) compared to DivideMix [24] on CIFAR-100 with $90\\%$ noisy labels. We surpass CTRR [28], the most recent contrastive learning-based method, under all noise ratios, especially on the more challenging CIFAR-100 dataset.", + "bbox": [ + 496, + 460, + 890, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on real-world dataset. Table 2 and Table 3 demonstrate the results on Clothing1M and WebVision, respectively. Our method outperforms all the alternative methods in both noisy real-world datasets. We achieve the improvement of $0.18\\%$ over SFT [50], the most recent sample selection-based method with MixMatch [6]. Besides, the most recent baseline UNICON [19] well combines the advantages of semi-supervised learning (DivideMix-like) and contrastive learning (RRL-like) and achieves great per", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1649", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2f197df8d09c5803860e8c13465f02446770bc2573a1ac235e01fca00c4c6e08.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetCIFAR-10CIFAR-100
Method/Noise ratio20%50%80%90%Asym. 40%20%50%80%90%
Cross-EntropyBest86.879.462.942.785.062.046.719.910.1
Last82.757.926.116.872.361.837.38.83.5
PENCILBest92.489.177.558.988.569.457.531.115.3
[56]Last92.088.776.558.288.168.156.420.78.8
Meta-LearningBest92.989.377.458.789.268.559.242.419.5
[25]Last92.088.876.158.388.467.758.040.114.3
DivideMixBest96.194.693.276.093.477.374.660.231.5
[24]Last95.794.492.975.492.176.974.259.631.0
ELR [30]Best95.894.893.378.793.077.673.660.833.4
MOIT [38]Best94.191.175.870.193.275.970.151.424.5
RRL [26]Last96.495.393.377.493.380.376.061.133.1
CTRR [28]Best93.3-86.784.389.070.1-43.7-
RankMatchBest96.595.694.592.694.779.577.967.650.6
Last96.495.494.292.194.479.377.667.249.9
", + "bbox": [ + 187, + 88, + 782, + 357 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e1986ed7b1f0abd51b3a950aeebbc5f644410e4e6e68d732ae09c1d8a6cf085c.jpg", + "table_caption": [ + "Table 1: Comparison between RankMatch and state-of-the-art methods on CIFAR-10 and CIFAR-100 under symmetric and asymmetric noise. \"Best\" refers to the best test accuracy across all epochs and \"Last\" is the averaged test accuracy over the last 10 epochs." + ], + "table_footnote": [], + "table_body": "
MethodTest Accuracy
Cross-Entropy69.21
PENCIL [56]73.49
DivideMix [24]74.76
RRL [26]74.97
DSOS [1]73.63
UNICON [19]74.98
SOP [31]73.50
SFT [50]75.08
RankMatch75.22
", + "bbox": [ + 153, + 436, + 393, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "formance gain. In particular, RankMatch achieves $0.24\\%$ performance gain over UNICON on the challenging Clothing1M dataset. Moreover, RankMatch obtain over $2\\%$ Top-1 accuracy improvement over state-of-the-art on both mini-WebVison and ILSVRC12 validation sets, and guarantees state-of-the-art Top-5 accuracy on WebVision and ILSVRC12, indicating the effectiveness of our approach.", + "bbox": [ + 75, + 696, + 468, + 803 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 815, + 230, + 832 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The role of confidence in LNL. To explore the role of the fixed confidence threshold in the LNL setting, we focus on the relationship between confident predictions and ground-truth labels. Specifically, we directly train DNNs", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/148f39659e2b52a154820c65694b1b25353a58beb65760d5b3374293a15f40a8.jpg", + "table_caption": [ + "Table 2: Comparison with state-of-the-art methods on Clothing1M. Baseline results are copied from original papers." + ], + "table_footnote": [], + "table_body": "
MethodWebVisionILSVRC12
top1top5top1top5
MentorNet [18]63.0081.4057.8079.92
Co-teaching [14]63.5885.2061.4884.70
Iterative-CV [7]65.2485.3461.6084.98
DivideMix [24]77.3291.6475.2090.84
RRL [26]77.891.374.490.9
DSOS [1]77.7692.0474.3690.80
SOP [31]76.6-69.1-
UNICON [19]77.6093.4475.2993.72
RankMatch79.9193.6177.3994.26
", + "bbox": [ + 526, + 436, + 867, + 618 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3: Comparison with state-of-the-art methods on (mini) WebVision dataset. Numbers denote top-1 (top-5) accuracy (\\%) on the WebVision and ImageNet ILSVRC12 validation set. Results for baselines are copied from the corresponding papers.", + "bbox": [ + 496, + 628, + 893, + 705 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "for classification on CIFAR-10 under different noise levels and record the following statistics: confident ratio, precision, and recall of confident predictions.", + "bbox": [ + 496, + 732, + 890, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "From the results shown in Figure 4, we discover the following empirical rules: (1) Confident ratio and recall increase in the same trend, while precision continues to decrease, indicating that the process of overfitting to noise label can regard as the process of overconfidence. (2) The precision of confident samples maintains a high level at the early stage, which means that confident predictions selected by the high threshold are reliable after the warm-up stage.", + "bbox": [ + 496, + 779, + 892, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1650", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c91a9a04d13e0ab69939dae5f09f97e3cd7c3ad8932709c34b6ecd81f7050ead.jpg", + "image_caption": [ + "Figure 4: Some key statistics of confident samples on CIFAR-10. The confident samples are selected via the fixed confidence threshold. (a) Precision, ratio of correctly predicted samples in confident samples, maintains a high level (close to $100\\%$ ) at the early stage, but continues to decline afterwards. Under Symmetry-50% noise, there is no confident samples in the early period. Hence, we record the precision after 30 epochs. (b) Recall, ratio of confident samples in correct prediction samples, maintains a low level in early stage, and gradually rises to high level. (c) Confidence ratio, ratio of confident samples in training set, has the same trend with Recall." + ], + "image_footnote": [], + "bbox": [ + 161, + 89, + 379, + 231 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4e1f1e396dbb468b4e7b8a9bbcee66386f12cadd6f7051de0fd87c03f810e769.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 383, + 88, + 591, + 232 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/434620fcf9d79988be07d26af3c457387b557f464e23182bd8c006ce8d9664c4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 598, + 89, + 810, + 232 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/14094a8e410d55d4d9855dc07781864819c12ae2392189ccd081b0c31c06da49.jpg", + "image_caption": [ + "Figure 5: Accuracy $(\\%)$ of the selected clean samples under different symmetric noise rates on CIFAR-100 datasets. Our full method RankMatch is compared with two baselines. One is DivideMix, denoted as GMM and MixMatch. The other is replacing GMM with our proposed Sample-selection via Confident Voting (SCV) method. Compared with GMM, SCV is more efficient to identify the clean samples. And our full model RankMatch has significant improvement in the sample selection stage under high noise rate." + ], + "image_footnote": [], + "bbox": [ + 161, + 352, + 326, + 470 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/498e4f8dfcb62b8592239e5309d1ddfd7b458567ae076371ce6bb8e2707bef08.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 338, + 352, + 486, + 470 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3294cfdda5552561a883f0a1df988ddb93353ac92bc0ede4a9fe742d57573a1b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 352, + 645, + 470 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a1e3871fef9619c2043d47a371d7596bfe923576637b5c74c727ce95ac9fed5e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 661, + 352, + 805, + 470 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(3) However, it is prone to selecting few samples when directly selecting reliable confidence samples by the high threshold because the recall is extremely low under high noise. It forms a dilemma between the quality and quantity of the selected samples.", + "bbox": [ + 75, + 587, + 468, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Sample selection via confident voting (SCV) is one main reason for RankMatch achieving great improvement. To study and verify its effectiveness, we test the accuracy of the selected clean samples under various symmetric noises on CIFAR-100. Since the great success DivideMix has made, we regard the GMM-based sample selection method as our baseline. Figure 5 presents that the SCV-based methods are more accurate than DivideMix in all cases. Furthermore, in the extremely demanding scenario (i.e., Symmetry-80% and Symmetry-90%), SCV based method achieves tremendous improvement. Specifically, DivideMix with SCV achieves over 18% improvement than that with GMM at 80% label noise. In contrast, our full RankMatch achieves over 25% improvement, which implies that the SCV benefits from more robust representation train", + "bbox": [ + 75, + 674, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing. Under the most extreme $90\\%$ label noise, our full RankMatch achieves over $140\\%$ selection accuracy gain, while DivideMix with SCV improves over $75\\%$ . The explanation for this result is that our full model includes consistency regularization and rank contrastive loss. Consistency regularization enhances semantic consistency and rectifies some confident-but-noisy features, which generates more robust prototypes and benefits SCV. Furthermore, rank contrastive loss promotes more discriminative features, improving confident prototype generation. The supplementary material contains other in-depth studies examining the sensitivity of high threshold $\\tau$ and hyper-parameters in SCV.", + "bbox": [ + 496, + 587, + 890, + 768 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effects of RankMatch components. We remove the corresponding components to study the effects of RCL and network ensemble. We remove $\\mathcal{L}_{\\mathrm{RCL}}$ to validate the effect of rank contrastive loss. We replace the SCV module as the sample selection strategy of DivideMix to validate the effectiveness of SCV. We remove the K-means in SCV for detailed study. As the results shown in Table 4, we find that rank contrastive loss is beneficial to RankMatch. The results", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1651", + "bbox": [ + 483, + 944, + 513, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/90bd9610229c4647cd5916059f4cd8c30afa71d3eab129c1e389183e5225b593.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetCIFAR-10CIFAR-100
Noise ratio50%90%50%90%
RankMatchBest95.692.677.950.6
Last95.492.177.649.9
w/o SCVBest95.189.675.345.1
Last94.989.174.944.9
SCV w/o K-meansBest95.491.876.547.9
Last95.291.475.247.5
w/o RCLBest95.290.876.145.6
Last94.988.775.244.5
", + "bbox": [ + 91, + 88, + 455, + 253 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 4: Ablation study results in terms of test accuracy (%) on CIFAR-10 and CIFAR-100 with symmetric label noise.", + "bbox": [ + 76, + 263, + 468, + 294 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "also validate the effectiveness of our proposed SCV. Diversifying the intra-class patterns by K-means is more effective under complex scenario and extreme noise ratio.", + "bbox": [ + 76, + 321, + 468, + 367 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/5e935f793662d03fdc1e2164fe5681cad8be0c45675f118dad6f4f84ec0391dd.jpg", + "image_caption": [ + "Figure 6: Sensitivity to the variance of hyperparameters. Experiments are conducted on CIFAR-10 under $50\\%$ and $90\\%$ symmetric noises." + ], + "image_footnote": [], + "bbox": [ + 81, + 380, + 272, + 525 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/0cbb74d5c15dabc69c6fa3147bacc4baf2605118dee35ca2e80514832d23c5d0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 380, + 455, + 526 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Sensitivity Analysis. SCV introduce the confidence threshold $\\tau$ and number of prototypes $K$ . We range the number of prototypes $K$ from 5 to 30 and vary the threshold $\\tau$ from 0.90 to 0.99. Figure 6 shows that our method is robust against different choices for $\\tau$ and $K$ . More in-depth studies are included in supplementary materials.", + "bbox": [ + 75, + 602, + 468, + 694 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 76, + 708, + 204, + 724 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We presented RankMatch, a novel framework for LNL that strives to combat noisy labels by enhancing confidence and consistency. Confidence-wise, we propose a novel clean sample selection strategy based on confidence representation voting rather than the small-loss criterion. Collecting votes from confident prototypes makes our method robust to noise and can sieve clean samples out with ample quantity. Consistency-wise, we introduce a novel rank contrastive loss based on the rank statistics of principal features instead of the widely-used $L_{2}$ distance. Such a loss could enhance consistency between similar samples even if they", + "bbox": [ + 75, + 734, + 470, + 902 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "were wrongly labeled. Moreover, we leverage consistency regularization to enhance the semantic consistency. We validate our superiority over several challenging benchmarks.", + "bbox": [ + 498, + 90, + 890, + 137 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 150, + 660, + 167 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported in part by the Guangdong Basic and Applied Basic Research Foundation (NO. 2020B1515020048), in part by the National Natural Science Foundation of China (NO. 61976250), in part by the Shenzhen Science and Technology Program (NO. JCYJ20220530141211024).", + "bbox": [ + 498, + 176, + 893, + 267 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 280, + 596, + 296 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Paul Albert, Diego Ortego, Eric Arazo, Noel O'Connor, and Kevin McGuinness. Addressing out-of-distribution label noise in webly-labelled data. 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In ECCV, 2022." + ], + "bbox": [ + 501, + 92, + 890, + 332 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "1654", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/RankMatch_ Fostering Confidence and Consistency in Learning with Noisy Labels/0d715541-80cd-458e-81f4-423a1c46d83e_model.json b/2023/RankMatch_ Fostering Confidence and Consistency in Learning with Noisy Labels/0d715541-80cd-458e-81f4-423a1c46d83e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..705d531930f7761ce7109fbc7bab30f701914f28 --- /dev/null +++ b/2023/RankMatch_ Fostering Confidence and Consistency in Learning with Noisy Labels/0d715541-80cd-458e-81f4-423a1c46d83e_model.json @@ -0,0 +1,2345 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.212, + 0.131, + 0.761, + 0.176 + ], + "angle": 0, + "content": "RankMatch: Fostering Confidence and Consistency in Learning with Noisy Labels" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.203, + 0.878, + 0.221 + ], + "angle": 0, + "content": "Ziyi Zhang\\(^{1,2}\\), Weikai Chen\\(^{3}\\), Chaowei Fang\\(^{4}\\), Zhen Li\\(^{5}\\), Lechao Chen\\(^{6}\\), Liang Lin\\(^{2}\\), Guanbin Li\\(^{2,7*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.222, + 0.855, + 0.256 + ], + "angle": 0, + "content": "\\(^{1}\\)National Key Laboratory of Novel Software Technology, Nanjing University, Nanjing, China \\(^{2}\\)Sun Yat-sen University, Guangzhou, China, \\(^{3}\\)Tencent America" + }, + { + "type": "text", + "bbox": [ + 0.133, + 0.257, + 0.838, + 0.275 + ], + "angle": 0, + "content": "\\(^{4}\\) Xidian University, \\(^{5}\\) The Chinese University of Hong Kong (Shenzhen), \\(^{6}\\) Zhejiang Lab" + }, + { + "type": "text", + "bbox": [ + 0.242, + 0.275, + 0.73, + 0.292 + ], + "angle": 0, + "content": "\\(^{7}\\) Research Institute, Sun Yat-sen University, Shenzhen, China" + }, + { + "type": "text", + "bbox": [ + 0.25, + 0.296, + 0.721, + 0.31 + ], + "angle": 0, + "content": "zhangziyi@lamda.nju.edu.cn,liguanbin@mail.sysu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.345, + 0.314, + 0.361 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.378, + 0.474, + 0.771 + ], + "angle": 0, + "content": "Learning with noisy labels (LNL) is one of the most important and challenging problems in weakly-supervised learning. Recent advances adopt the sample selection strategy to mitigate the interference of noisy labels and use small-loss criteria to select clean samples. However, the one-dimensional loss is an over-simplified metric that fails to accommodate the complex feature landscape of various samples, and, hence, is prone to introduce classification errors during sample selection. In this paper, we propose RankMatch, a novel LNL framework that investigates additional dimensions of confidence and consistency in order to combat noisy labels. Confidence-wise, we propose a novel sample selection strategy based on confidence representation voting instead of the widely-used small-loss criterion. This new strategy is capable of increasing sample selection quantity without sacrificing labeling accuracy. Consistency-wise, instead of the widely adopted feature distance metric for measuring the consistency of inner-class samples, we advocate that the rank of principal features is a much more robust indicator. Based on this metric, we propose rank contrastive loss, which strengthens the consistency of similar samples regardless of their labels and facilitates feature representation learning. Experimental results on noisy versions of CIFAR-10, CIFAR-100, Clothing1M and WebVision have validated the superiority of our approach over existing state-of-the-art methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.802, + 0.21, + 0.818 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.829, + 0.47, + 0.875 + ], + "angle": 0, + "content": "The remarkable success of DNNs stems from the availability of large-scale datasets. However, it is highly laborious to obtain massive data with high-quality annotations." + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.345, + 0.88, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.498, + 0.895, + 0.696 + ], + "angle": 0, + "content": "Figure 1: Motivation of RankMatch. After being trained with noisy labels, the model is validated by the augmented images. Noisy labels leads to high-entropy outputs, which lack confidence. We advocate for the use of confidence criterion for sample selection, as the confident samples are more likely to have clean labels. Moreover, The weakly augmented image is similar to training Image 1 (classified as 'dog'), while the strongly augmented one is similar to training Image 2 (classified as 'deer'). Considering the model tends to produce similar predictions for similar images, the two views of the same image have inconsistent predictions. Consequently, we introduce the rank contrastive loss to enhance the semantic consistency." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.73, + 0.894, + 0.837 + ], + "angle": 0, + "content": "Hence, training DNNs using inexpensive samples from the search engine or machine annotation [27, 33, 11] has become an attractive alternative. However, these methods inevitably introduce erroneous labels, which cause poor performance as DNNs can easily overfit to noises [58]. Hence, learning with noisy labels (LNL) has become an important yet challenging task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Sample selection is a widely adopted strategy in LNL that identifies clean samples from the dataset to alleviate the negative impact of noisy labels. The small-loss criterion is a popular sample selection strategy, which regards" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1644" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.228 + ], + "angle": 0, + "content": "samples with lower loss as clean ones. However, such a one-dimensional loss is too simplified to accommodate the sophisticated distribution of high-dimensional data, such as the image features. As a result, a plethora of easy-but-noisy samples with small loss are often wrongly grouped into the clean set by using the loss-based strategy. This confirmation bias would be gradually amplified in the subsequent loss minimization training and severely impact the final performance [24, 44]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.23, + 0.471, + 0.442 + ], + "angle": 0, + "content": "Another challenge of LNL lies in the difficulty of obtaining robust and consistent representation for samples across categories and subjects [24, 26, 19]. In semi-supervised learning, this issue can be largely addressed by enforcing consistent predictions given different views of the same sample [21]. However, in LNL, due to the existence of wrong labels, different views of the same object could be clustered into different categories, leading to inconsistent estimations (see Figure 1). Though the sample selection mechanism can identify a part of clean samples, the consistent representation learned from this set of clean data only works on simple samples with high confidence. Hence, how to achieve consistent prediction on difficult samples with low confidence remains an open question." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.471, + 0.822 + ], + "angle": 0, + "content": "In this work, we follow the line of sample selection to avoid the adverse impact of noisy labels. However, instead of relying on an over-simplified 1D loss function, we propose to combat the noises by incorporating new perspectives from confidence and consistency. Confidence-wise, to ensure robust selection of clean samples, we leverage the advances of confidence learning (CL) [37] while avoiding its vulnerability to noisy network predictions. In particular, we investigate the performance of clean sample selection using fixed confidence thresholds at different noise levels. The results (Figure 4) show that a fixed high threshold leads to a much more accurate sample selection even at the presence of strong noises. Therefore, we leverage one fixed high confidence threshold for all classes to ensure the purity of confident samples. To address the lack of clean data by using a high threshold, we further propose sample selection via confidence voting (SCV) to ensure an ample collection of clean labels. Specifically, we generate \\( K \\) clusters from confident samples for each class and treat the cluster center as confident prototype. Each sample is considered clean if the label is consistent with the results voted by its \\( k \\) nearest confident prototypes. We empirically find that the proposed confidence voting mechanism can generate reliable and clean samples in sufficient amounts, ensuring both the quality and quantity of clean samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Consistency-wise, in addition to the classic consistency regularization, i.e. enforcing consistent outputs of different views from the same sample, we propose to encourage consistent predictions between similar hard samples of the same category. To achieve this goal, we introduce rank con" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.288 + ], + "angle": 0, + "content": "trastive loss (RCL), a novel metric that fully leverages the rank of principal image features for robust measurement of similar samples. Empirical experiments show that the conventional \\( l_{2} \\) distance cannot exploit the inner structure of feature representation, and, hence, fails to foster consistent clustering in the complex feature space corrupted by noisy samples. Our key observation is that while similar hard samples (with low confidence) of the same class may have a large \\( l_{2} \\) distance in the feature space, the underlying rank of their principal features still remains consistent (see Figure 2). Therefore, our proposed RCL loss is able to promote feature consistency by encouraging correct and discriminative clustering of similar samples with low confidence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.892, + 0.453 + ], + "angle": 0, + "content": "We code our method as RankMatch as the two perspectives of the proposed framework can mutually benefit each other. While more reliable data segmentation based on high confidence can benefit the subsequent representation learning, the consistent representations further improve the confidence of uncertain data samples, and, in turn, strengthen our proposed confidence-based sample-selection mechanism. We validate the superiority of our method over the state-of-the-art approaches on several challenging benchmarks, including CIFAR, Clothing1M, and WebVision. Our contributions can be summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.461, + 0.891, + 0.506 + ], + "angle": 0, + "content": "- A method with new state-of-the-art performance that is specially tailored for LNL problems by fostering both confidence and consistency." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.506, + 0.891, + 0.551 + ], + "angle": 0, + "content": "- A novel sample-selection via confidence voting (SCV) strategy that generates reliable and ample clean samples for the subsequent training." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.552, + 0.891, + 0.655 + ], + "angle": 0, + "content": "- Rank contrastive loss (RCL) based on the rank statistics of principal features that encourages consistency between hard samples of the same category. RCL can further benefit clean sample selection by promoting more discriminative features (see Fig. 1 in the supplementary material) for constructing intra-category clusters." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.461, + 0.891, + 0.655 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.671, + 0.642, + 0.687 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.697, + 0.892, + 0.727 + ], + "angle": 0, + "content": "Most existing methods on LNL can be categorized into two directions: 1) loss correction and 2) sample selection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Loss Correction. For loss correction, mainstream techniques [51, 46, 29, 47, 22] estimate noise transition matrix with a small set of clean samples as prior knowledge. However, estimating the noise transition matrix is challenging, and their assumptions may be too ideal to fit real-world scenarios. To rectify the noisy labels, another line of research proposes self-training architectures where noisy labels are replaced by network predictions [43, 56]. Some methods focus on the design of noisy-tolerant loss functions. For example, [2, 48, 13, 12] leverage bounded loss functions to improve their robustness to noisy labels. Besides, there are" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1645" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.132, + 0.099, + 0.849, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.272, + 0.892, + 0.378 + ], + "angle": 0, + "content": "Figure 2: The training strategy of RankMatch. We use strong and weak augmentation to achieve consistency regularization in LNL. For the clean set, the given labels are used to regularize the network predictions on strongly augmented images via the supervised training loss \\(L_{c}\\). For the noisy set, we first generate pseudo labels from the predictions on weakly augmented images and then use them to regularize the predictions on strongly augmented images via training loss \\(L_{n}\\). Rank contrastive loss pulls similar samples together and pushes others away. The similarity matrix is defined by ranking feature channels instead of Euclidean distance. The final objective function is a joint loss, including a class diversity regularization term in addition." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.404, + 0.471, + 0.511 + ], + "angle": 0, + "content": "some proposed unbiased loss function [35], information-based loss function called \\( L_{DMI} \\) [54], punishment regularization [32], confidence regularization [8], early learning regularization [30], contrastive representation regularization [28] and over-parameterized term [31]. However, it is arduous for loss-correction-based methods to play an advantage in practical scenarios facing high noise ratios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Sample selection. Sample selection-based methods strive to reweight training samples and identify clean data to reduce the interference of noisy labels. Many existing methods propose introducing improved selection criteria to make the selected samples cleaner [23, 59, 3, 36, 24, 1]. Memorization effect [4] illuminates that DNNs learn clean and simple patterns faster than noisy labels, leading to a trend to consider small loss as a criterion for sample selection, which means that samples with smaller loss values are more likely to have clean labels. For instance, [3, 36, 24, 1] leverage clean data distribution as selection criterion by lower-loss component in mixture model fitted by per-sample loss. [55, 19] introduces JS-divergence between network prediction and labels as a selection criterion. [38] leverages the cross-entropy loss between disagreement distribution and labels as selection criterion. However, the loss value is just a scalar, contains limited information, and is prone to errors. For example, it is hard to distinguish between hard-to-learn clean samples and noisy samples after the warm-up stage since both have relatively large loss values. Besides, confirmation bias [44] is a common issue often encountered with the small-loss criterion. Once the noisy samples are wrongly grouped into the clean set by the small-loss criterion, their losses will keep small in the later train" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.404, + 0.892, + 0.616 + ], + "angle": 0, + "content": "ing. It remains challenging to rectify the sample selection errors. Many methods mitigate this issue by training two networks [18, 34, 14, 57, 49, 24, 55]. But it is still a problem to get more accurate labels through the small-loss criterion. More recently, Confident Learning (CL) [37] proposes confident criterion as an alternative for sample selection. It computes a set of thresholds for every class and chooses confident samples whose network predicted highest probabilities are greater than the corresponding thresholds. However, CL directly estimates the noise transition matrix by confident samples, which is vulnerable to the network predictions and threshold setting. And it is prone to fail to perform well in large-scale cases and real-world scenarios with a high noise ratio." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Semi-supervised Learning. The Semi-supervised Learning (SSL) has seen fast progress by leveraging consistency regularization [41, 53, 5, 21, 39, 40, 45], which is used to minimize the difference in network prediction between two views of the same image. FixMatch [21] simply but effectively combines strong and weak augmentation in consistency regularization with confidently pseudo-labeling to achieve great success in semi-supervised learning setting. Most recently, [39] propose an uncertainty-aware pseudolabels selection (UPS) framework to improve pseudo labeling accuracy. RankingMatch [45] introduces a triplet loss, where the similarity between samples is measured by the L2-norm outputs. Furthermore, it is worth noting that the rank statistics of principal features can serve as a metric to measure the pairwise similarity among samples [15]. There are similarities between Learning with Noisy Labels (LNL) problems and semi-supervised learning setting." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1646" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "In semi-supervised learning settings, confident predictions have strong connection with true labels as labeled data regularizing the unlabeled data, which are not easy to overconfident confused by noisy label. And leveraging confident predictions inevitably lacks sample diversity to make pseudo labels more reliable, while difficult samples always have uncertain predictions. Our approach finds a good balance of confidence, sample diversity and consistency." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.228, + 0.169, + 0.243 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.254, + 0.47, + 0.329 + ], + "angle": 0, + "content": "Our method is introduced in three parts: the sample selection mechanism (Figure. 3), the consistency regularization and rank contrastive loss. Figure 2 shows the overview of RankMatch. The algorithm is included in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.471, + 0.499 + ], + "angle": 0, + "content": "Preliminaries. For the \\(C\\)-way image classification task with noisy labels, denoted by \\(\\mathcal{D} = (\\mathcal{X}, \\widetilde{\\mathcal{Y}})\\) the training data, where \\(\\mathcal{X}\\) is training images, and \\(\\widetilde{\\mathcal{Y}}\\) is labels which may be wrongly annotated. We denote the DNNs in training stage as \\(P(F(\\mathbf{x}, \\theta))\\), where \\(\\mathbf{x} \\in \\mathbb{R}^I\\) is the input image, \\(F: \\mathbb{R}^I \\to \\mathbb{R}^L\\) is the feature extractor where \\(I\\) and \\(L\\) stand for the dimension of input space and embedding space respectively, and \\(P: \\mathbb{R}^L \\to \\mathbb{R}^C\\) represents the classifier. \\(\\theta\\) denotes the network parameters of the feature extractor. We use \\(\\mathbf{f}_i\\) and \\(\\mathbf{p}_i\\) as simplified forms of \\(F(\\mathbf{x}_i, \\theta)\\) and \\(P(F(\\mathbf{x}_i, \\theta))\\) respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.509, + 0.418, + 0.526 + ], + "angle": 0, + "content": "3.1. Sample Selection via Confidence Voting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.533, + 0.47, + 0.684 + ], + "angle": 0, + "content": "For the sample selection, we leverage the advantage of confident learning [37] rather than the widely used small-loss criterion. We explore using a fixed confidence threshold to avoid the vulnerability of inaccurate network predictions. Figure 4 illustrates that confident predictions selected by a fixed high threshold are reliable but of a limited number. Hence, we propose a new sample selection strategy based on the confidence criterion that maintains reliability while ensuring sufficient confident samples across categories." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.691, + 0.47, + 0.812 + ], + "angle": 0, + "content": "Confident Samples. In the setting of LNL, it is hard to select confident samples just by a single threshold when facing different levels of noise rates. Some classes are easy-to-learn, and one threshold for all classes is likely to result in class-unbalanced selection. In order to avoid data imbalance among classes, we select the top \\( B \\) basic confident samples \\( \\mathcal{I}_b \\) in each class to ensure each class at least has \\( B \\) samples:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.814, + 0.47, + 0.847 + ], + "angle": 0, + "content": "\\[\n\\mathcal {I} _ {b} ^ {c} = \\underset {| \\hat {\\mathcal {X}} | = B, \\hat {\\mathcal {X}} \\subseteq \\mathcal {X}} {\\arg \\max } \\sum_ {\\mathbf {x} \\in \\hat {\\mathcal {X}}} \\mathbf {p} [ c ], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.855, + 0.471, + 0.903 + ], + "angle": 0, + "content": "where \\(\\mathbf{p}[c]\\) is the \\(c\\)-th element of \\(\\mathbf{p}\\) (\\(= P(F(\\mathbf{x},\\theta))\\)), namely the probability value of the \\(c\\)-th class. And additional samples with prediction probability greater than a threshold as" + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.096, + 0.861, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.269, + 0.894, + 0.359 + ], + "angle": 0, + "content": "Figure 3: Sample-selection via Confidence Voting (SCV) module. We first select the most representative confident samples. Then, the selected confident samples generate prototypes as voting candidates. For each sample, its \\( k \\) nearest prototypes are regarded as voters to identify whether the label is clean." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.39, + 0.706, + 0.404 + ], + "angle": 0, + "content": "the reliable confident samples:" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.42, + 0.892, + 0.436 + ], + "angle": 0, + "content": "\\[\n\\mathcal {I} _ {r} ^ {c} = \\left\\{\\mathbf {x} _ {i} \\mid \\mathbf {p} _ {i} [ c ] > \\tau , \\mathbf {x} _ {i} \\in \\mathcal {X} \\right\\}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.451, + 0.892, + 0.482 + ], + "angle": 0, + "content": "The final selected confident samples is the union of the two sets \\(\\mathcal{I}^c = \\mathcal{I}_b^c\\cup \\mathcal{I}_r^c\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.489, + 0.893, + 0.626 + ], + "angle": 0, + "content": "Confident Prototype Generation. To guarantee the quality of the confident samples, we set high threshold \\(\\tau\\) and small portion \\(B\\), but face the problem of low sample quantity. Although with a small number, the reliable representations of confident samples reflect some common intra-class patterns. Thus, we generate representation prototypes using the selected samples for further selection. Straightforwardly, a representative feature can be generated by averaging features of confident samples for each class:" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.638, + 0.892, + 0.675 + ], + "angle": 0, + "content": "\\[\n\\phi^ {c} = \\frac {1}{| \\mathcal {I} ^ {c} |} \\sum_ {\\mathbf {x} \\in \\mathcal {I} ^ {c}} F (\\mathbf {x}, \\theta). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.893, + 0.87 + ], + "angle": 0, + "content": "Even if the confident samples include some noise during the early training stage, the prototype generation process will predominantly rely on the most clean samples, rendering it robust to noisy labels. However, the mean vector is unable to represent a class with large intra-class variations. We further diversify the intra-class patterns by generating more prototypes of each class. Specifically, we split the confident samples into \\(K\\) clusters for each class by \\(K\\)-means. For the \\(c\\)-th class, we define the average centers of the obtained clusters features as \\(\\Phi^c = \\{\\phi_j^c\\}_{j=1}^K\\). Our sample-selection module is based on the generated confident prototypes \\(\\Phi (= \\bigcup_{c=1}^{C} \\Phi^c)\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Data Segmentation by Confidence Voting. After obtaining \\( C \\times K \\) prototypes, we first find the \\( k \\) nearest prototypes" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1647" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.343, + 0.106 + ], + "angle": 0, + "content": "of \\(\\mathbf{x}_i\\) measured by the cosine similarity:" + }, + { + "type": "equation", + "bbox": [ + 0.169, + 0.12, + 0.469, + 0.154 + ], + "angle": 0, + "content": "\\[\n\\mathcal {V} _ {i} = \\underset {| \\hat {\\Phi} | = k, \\hat {\\Phi} \\subseteq \\Phi} {\\arg \\max } \\sum_ {\\phi \\in \\hat {\\Phi}} \\cos (\\mathbf {f} _ {i}, \\phi). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.167, + 0.469, + 0.228 + ], + "angle": 0, + "content": "The class label to which the most prototypes belong in \\(\\mathcal{V}_i\\) is considered as the voting result \\(\\mathbf{y}_i'\\). Clean samples \\(\\mathcal{D}_{\\mathrm{cln}}\\) are identified by checking whether \\(\\mathbf{y}_i'\\) is consistent with the provided label \\(\\widetilde{\\mathbf{y}}_i\\):" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.24, + 0.469, + 0.259 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} _ {\\mathrm {c l n}} = \\left\\{\\left(\\mathbf {x} _ {i}, \\widetilde {\\mathbf {y}} _ {i}\\right) \\mid \\widetilde {\\mathbf {y}} _ {i} = \\mathbf {y} _ {i} ^ {\\prime}, \\forall \\left(\\mathbf {x} _ {i}, \\widetilde {\\mathbf {y}} _ {i}\\right) \\in \\mathcal {D} \\right\\}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.271, + 0.37, + 0.287 + ], + "angle": 0, + "content": "The remaining noisy set is \\(\\mathcal{D}_{\\mathrm{nsy}} = \\mathcal{D}\\setminus \\mathcal{D}_{\\mathrm{cln}}\\)" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.297, + 0.325, + 0.314 + ], + "angle": 0, + "content": "3.2. Consistency Regularization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.321, + 0.469, + 0.517 + ], + "angle": 0, + "content": "This paper argues that noisy labels lead to inconsistent predictions (Figure 1). To enhance the consistency of the predictions augmented from the same image, we apply two different augmentation methods to generate two views for training images, including \"weak\" augmentation \\((\\mathcal{A}_w)\\) and \"strong\" augmentation \\((\\mathcal{A}_s)\\). Weak augmentation refers to random cropping and flipping, while strong augmentation refers to AutoAugment [9], which uses reinforcement learning to find augmentation strategies automatically and requires labeled data to learn. Note that our sample selection mechanism provides cleaner supervision signals, benefiting AutoAugment to accept a more effective augmentation policy." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.518, + 0.469, + 0.621 + ], + "angle": 0, + "content": "Following [21], we transfer the training image \\(\\mathbf{x}\\) with the two augmentation strategies, resulting in two views: \\(\\mathbf{v}^w = \\mathcal{A}_w(\\mathbf{x})\\), and \\(\\mathbf{v}^s = \\mathcal{A}_s(\\mathbf{x})\\). The corresponding network predictions are denoted as \\(\\mathbf{p}^w\\) and \\(\\mathbf{p}^s\\), respectively. Given that the semantic information of the augmented images is not modified, we assume the two network predictions to be consistent." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.624, + 0.469, + 0.669 + ], + "angle": 0, + "content": "For clean samples, we direct use cross-entropy loss between predictions on strongly augmented images and the original labels:" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.682, + 0.469, + 0.72 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c} = - \\frac {1}{| \\mathcal {D} _ {\\mathrm {c l n}} |} \\sum_ {(\\mathbf {x}, \\widetilde {\\mathbf {y}}) \\in \\mathcal {D} _ {\\mathrm {c l n}}} \\widetilde {\\mathbf {y}} \\circ \\log (\\mathbf {p} ^ {s}), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.732, + 0.308, + 0.747 + ], + "angle": 0, + "content": "where \\(\\circ\\) denotes the inner product." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.748, + 0.469, + 0.793 + ], + "angle": 0, + "content": "For noisy samples with high prediction confidence, we rectify their labels with predictions of weakly augmented images:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.805, + 0.469, + 0.84 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathcal {D}} _ {\\mathrm {n s y}} = \\left\\{\\left(\\mathbf {x} _ {i}, \\hat {\\mathbf {y}} _ {i}\\right) | \\forall \\mathbf {x} _ {i} \\in \\mathcal {X} _ {\\mathrm {n s y}}, \\max _ {c} \\left\\{\\mathbf {p} ^ {w} [ c ] \\right\\} > \\nu , \\hat {\\mathbf {y}} _ {i} = c \\right\\}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.841, + 0.469, + 0.902 + ], + "angle": 0, + "content": "where \\(\\nu\\) is the confidence threshold, we set it the same as that in Eq. 2 to avoid introducing another parameter. Inspired by [21], the cross entropy losses between the predictions of weakly and strongly augmented images are" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "employed as regularizing consistency for the CNN model learning:" + }, + { + "type": "equation", + "bbox": [ + 0.572, + 0.14, + 0.892, + 0.181 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {n} = - \\frac {1}{| \\hat {\\mathcal {D}} _ {\\mathrm {n s y}} |} \\sum_ {(\\mathbf {x}, \\hat {\\mathbf {y}}) \\in \\hat {\\mathcal {D}} _ {\\mathrm {n s y}}} \\hat {\\mathbf {y}} \\circ \\log \\left(\\mathbf {p} ^ {s}\\right). \\tag {8}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.203, + 0.712, + 0.218 + ], + "angle": 0, + "content": "3.3. Rank Contrastive Loss" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.23, + 0.892, + 0.35 + ], + "angle": 0, + "content": "Robust representations can benefit our samples selection strategy. However, some valuable information is excluded by Eq. 7 and Eq. 8 since the hard-to-learn noisy samples have less confident predictions and thus can not be optimized. To obtain complete and robust representations, we propose a rank contrastive loss (RCL) to strengthen the consistency of the \"similar\" samples while pushing \"dissimilar\" ones further." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.355, + 0.892, + 0.567 + ], + "angle": 0, + "content": "The widely used \\( L_{2} \\) distance as the similarity metric is less robust in LNL, as overfitting to noisy labels tends to introduce spurious close euclidean distance. Every convolution kernel filters out certain kinds of attributes in the input image. Similar visual patterns are prone to activate the same representation channel of response maps produced by convolution layers. Hence, the indices of feature elements rank ordered in accordance with their magnitudes, can serve as a metric for assessing the pairwise representations similarity [15]. Although noisy labels affect the feature value, we leverage rank statistics of principal features to estimate the similarity matrix. Specifically, we rank the values in all channels of \\( \\mathbf{f}_i \\) and regard the \\( r \\) channels with the largest activation values as the principal feature dimensions," + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.585, + 0.891, + 0.62 + ], + "angle": 0, + "content": "\\[\n\\mathcal {R} _ {i} = \\underset {| \\hat {\\mathcal {R}} | = r, \\hat {\\mathcal {R}} \\subset \\{1, 2, \\dots , L \\}} {\\arg \\max } \\sum_ {n \\in \\hat {\\mathcal {R}}} \\mathbf {f} _ {i} [ n ], \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.638, + 0.892, + 0.7 + ], + "angle": 0, + "content": "where \\(\\mathbf{f}_i[n]\\) denote the \\(n\\)-th channel of feature \\(\\mathbf{f}_i\\). If two samples \\(\\mathbf{x}_i\\) and \\(\\mathbf{x}_j\\) share the same principal feature dimensions, we assume they are \"similar\". The similarity \\(s_{ij}\\) between \\(\\mathbf{x}_i\\) and \\(\\mathbf{x}_j\\) is evaluated as follows," + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.718, + 0.891, + 0.76 + ], + "angle": 0, + "content": "\\[\ns _ {i j} = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\mathcal {R} _ {i} = \\mathcal {R} _ {j}; \\\\ 0 & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.781, + 0.89, + 0.811 + ], + "angle": 0, + "content": "To achieve clustering in the feature space, we adopt the following binary cross-entropy loss as:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.83, + 0.916, + 0.885 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {R C L}} = - \\frac {1}{N ^ {2}} \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {N} \\left[ s _ {i j} \\log \\left(\\mathbf {p} _ {i} \\circ \\mathbf {q} _ {j}\\right) + \\left(1 - s _ {i j}\\right) \\log \\left(1 - \\mathbf {p} _ {i} \\circ \\mathbf {q} _ {j}\\right) \\right], \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathbf{p}_i = P(F(\\mathbf{v}_i^w,\\theta))\\) and \\(\\mathbf{q}_i = P(F(\\mathbf{v}_i^s,\\theta))\\). The train-" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1648" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.375, + 0.107 + ], + "angle": 0, + "content": "ing loss \\(\\mathcal{L}_{\\mathrm{RCL}}\\) can be divided into two terms:" + }, + { + "type": "text", + "bbox": [ + 0.254, + 0.119, + 0.38, + 0.131 + ], + "angle": 0, + "content": "Consistency regularization" + }, + { + "type": "equation", + "bbox": [ + 0.081, + 0.139, + 0.498, + 0.238 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {R C L}} = - \\frac {1}{N ^ {2}} \\sum_ {i = 1} ^ {N} \\left[ s _ {i i} \\log \\left(\\mathbf {p} _ {i} \\circ \\mathbf {q} _ {i}\\right) + \\left(1 - s _ {i i}\\right) \\log \\left(1 - \\mathbf {p} _ {i} \\circ \\mathbf {q} _ {i}\\right) \\right] \\\\ - \\frac {1}{N ^ {2}} \\sum_ {i = 1} ^ {N} \\sum_ {j \\neq i} [ s _ {i j} \\log (\\mathbf {p} _ {i} \\circ \\mathbf {q} _ {j}) + (1 - s _ {i j}) \\log (1 - \\mathbf {p} _ {i} \\circ \\mathbf {q} _ {j}) ]. \\tag {12} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.239, + 0.433, + 0.254 + ], + "angle": 0, + "content": "Since \\( s_{ii} = 1 \\) always holds, organize the first term as:" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.266, + 0.469, + 0.307 + ], + "angle": 0, + "content": "\\[\n- \\frac {1}{N ^ {2}} \\sum_ {i = 1} ^ {N} \\log \\left(\\mathbf {p} _ {i} \\circ \\mathbf {q} _ {i}\\right) = - \\frac {1}{N ^ {2}} \\sum_ {i = 1} ^ {N} \\log \\left(\\mathbf {p} _ {i} ^ {w} \\circ \\mathbf {p} _ {i} ^ {s}\\right). \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.319, + 0.47, + 0.412 + ], + "angle": 0, + "content": "Minimizing this term is equal to \\(\\max \\{\\mathbf{p}_i^w\\circ \\mathbf{p}_i^s\\}\\), which pulls the outputs of strongly and weakly augmented images closer. Thus, \\(\\mathcal{L}_{\\mathrm{RCL}}\\) in the diagonal of \\(S\\) can be regarded as consistency regularization. Even in the early training stage, \\(S\\) is the identity matrix that removes the second term in Eq. 12, improving the network representation ability." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.421, + 0.285, + 0.435 + ], + "angle": 0, + "content": "3.4. Overall Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.445, + 0.47, + 0.491 + ], + "angle": 0, + "content": "Following [43, 24, 3], we apply the fair class diversity-promoting regularization \\(\\mathcal{L}_{div}\\) to prevent assigning most samples into few classes:" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.502, + 0.47, + 0.543 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d i v} = \\sum_ {c = 1} ^ {C} \\frac {1}{C} \\log \\left(\\frac {1}{C} / \\frac {\\sum_ {i = 1} ^ {N} \\mathbf {p} _ {i} ^ {w} [ c ]}{N}\\right). \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.555, + 0.469, + 0.583 + ], + "angle": 0, + "content": "The overall loss function for network optimization is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.586, + 0.469, + 0.602 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {c} + \\lambda_ {n} \\mathcal {L} _ {n} + \\mathcal {L} _ {\\mathrm {R C L}} + \\mathcal {L} _ {\\text {d i v}}. \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.61, + 0.47, + 0.657 + ], + "angle": 0, + "content": "We following [24, 14, 57, 36] to train two networks to combat the confirmation bias, detailed algorithm is included in supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.671, + 0.21, + 0.687 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.696, + 0.267, + 0.712 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We evaluate the proposed RankMatch on CIFAR-10, CIFAR-100 [20], as well as the real-world datasets Clothing1M [52] and WebVision [27]. Both CIFAR-10 and CIFAR-100 contain 50,000 training images and 10,000 test images of size \\(32 \\times 32\\). Following previous works [43, 25], we conduct experiments requiring noise augmentation, either symmetric or asymmetric [43, 25] label noise injection. We follow the identical implementation of generating symmetric and asymmetric noises on CIFAR datasets with DivideMix [24]. Symmetric noise is generated by randomly replacing the labels for a percentage of the training data with all possible labels. Asymmetric noise is to mimic the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.288 + ], + "angle": 0, + "content": "structure of real-world label noise, where labels are only replaced by similar classes (e.g. deer \\(\\rightarrow\\) horse, dog \\(\\leftrightarrow\\) cat). We adopt 18-layer PreAct Resnet [17] as the backbone. During training, we train DNNs for 300 epochs using SGD optimizer with a momentum of 0.9, with weight decay of 0.0005 for CIFAR-10 and 0.001 for CIFAR-100. The batch size is 64 for CIFAR-10 and 128 for CIFAR-100. We set the initial learning rate as 0.02 and reduce it by a factor of 10 after 150 epochs. The warm-up period is 10 epochs for CIFAR-10 and 30 epochs for CIFAR-100, respectively. For all CIFAR experiments, we set \\(\\tau = 0.95\\), \\(r = 5\\), and choose \\(\\lambda_{n}\\) from \\(\\{0.2, 0.5, 1, 2, 10, 15\\}\\) for a small validation test. More experimental details are in supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.892, + 0.426 + ], + "angle": 0, + "content": "Clothing1M contains 1 million real-world shopping images belonging to 14 classes. We use ResNet-50 [16] with weights pretrained on ImageNet as the classification model. WebVision consists of web-crawled images with the same concepts from ImageNet ILSVRC12 [10]. We follow the previous work [24, 7] and compare baseline methods on the first 50 classes of the Google image subset using the inception-resnet v2 [42]. The training details are delineated in supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.438, + 0.702, + 0.453 + ], + "angle": 0, + "content": "4.2. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.462, + 0.892, + 0.763 + ], + "angle": 0, + "content": "Results on CIFAR. Table 1 illuminates RankMatch outperforms the state-of-the-art models across most noisy levels. RRL [26] combats noisy labels by learning robust representations and slightly outperforms our method on CIFAR-10 with \\(20\\%\\) symmetric label noise. One possible explanation is that the massive clean labels make it easy to rectify the symmetric label noise. Thus, the sample selection strategy is less effective in this scenario but shows great advantages for a high noise ratio and real-world dataset. Benefiting from the advanced confidence sample selection mechanism, RankMatch boosts the averaged test accuracy of the last ten epochs from \\(77.4\\%\\) to \\(92.1\\%\\) on CIFAR-10 and \\(33.1\\%\\) to \\(49.9\\%\\) on CIFAR-100 under the extreme case of \\(90\\%\\) noise. Even without MixMatch [6] technique, RankMatch achieves around 20 points improvement (50.6% vs. \\(31.5\\%\\)) compared to DivideMix [24] on CIFAR-100 with \\(90\\%\\) noisy labels. We surpass CTRR [28], the most recent contrastive learning-based method, under all noise ratios, especially on the more challenging CIFAR-100 dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Results on real-world dataset. Table 2 and Table 3 demonstrate the results on Clothing1M and WebVision, respectively. Our method outperforms all the alternative methods in both noisy real-world datasets. We achieve the improvement of \\(0.18\\%\\) over SFT [50], the most recent sample selection-based method with MixMatch [6]. Besides, the most recent baseline UNICON [19] well combines the advantages of semi-supervised learning (DivideMix-like) and contrastive learning (RRL-like) and achieves great per" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1649" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.189, + 0.089, + 0.783, + 0.358 + ], + "angle": 0, + "content": "
DatasetCIFAR-10CIFAR-100
Method/Noise ratio20%50%80%90%Asym. 40%20%50%80%90%
Cross-EntropyBest86.879.462.942.785.062.046.719.910.1
Last82.757.926.116.872.361.837.38.83.5
PENCILBest92.489.177.558.988.569.457.531.115.3
[56]Last92.088.776.558.288.168.156.420.78.8
Meta-LearningBest92.989.377.458.789.268.559.242.419.5
[25]Last92.088.876.158.388.467.758.040.114.3
DivideMixBest96.194.693.276.093.477.374.660.231.5
[24]Last95.794.492.975.492.176.974.259.631.0
ELR [30]Best95.894.893.378.793.077.673.660.833.4
MOIT [38]Best94.191.175.870.193.275.970.151.424.5
RRL [26]Last96.495.393.377.493.380.376.061.133.1
CTRR [28]Best93.3-86.784.389.070.1-43.7-
RankMatchBest96.595.694.592.694.779.577.967.650.6
Last96.495.494.292.194.479.377.667.249.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.367, + 0.895, + 0.414 + ], + "angle": 0, + "content": "Table 1: Comparison between RankMatch and state-of-the-art methods on CIFAR-10 and CIFAR-100 under symmetric and asymmetric noise. \"Best\" refers to the best test accuracy across all epochs and \"Last\" is the averaged test accuracy over the last 10 epochs." + }, + { + "type": "table", + "bbox": [ + 0.155, + 0.437, + 0.395, + 0.611 + ], + "angle": 0, + "content": "
MethodTest Accuracy
Cross-Entropy69.21
PENCIL [56]73.49
DivideMix [24]74.76
RRL [26]74.97
DSOS [1]73.63
UNICON [19]74.98
SOP [31]73.50
SFT [50]75.08
RankMatch75.22
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.622, + 0.472, + 0.669 + ], + "angle": 0, + "content": "Table 2: Comparison with state-of-the-art methods on Clothing1M. Baseline results are copied from original papers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.697, + 0.47, + 0.804 + ], + "angle": 0, + "content": "formance gain. In particular, RankMatch achieves \\(0.24\\%\\) performance gain over UNICON on the challenging Clothing1M dataset. Moreover, RankMatch obtain over \\(2\\%\\) Top-1 accuracy improvement over state-of-the-art on both mini-WebVison and ILSVRC12 validation sets, and guarantees state-of-the-art Top-5 accuracy on WebVision and ILSVRC12, indicating the effectiveness of our approach." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.816, + 0.231, + 0.833 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.472, + 0.903 + ], + "angle": 0, + "content": "The role of confidence in LNL. To explore the role of the fixed confidence threshold in the LNL setting, we focus on the relationship between confident predictions and ground-truth labels. Specifically, we directly train DNNs" + }, + { + "type": "table", + "bbox": [ + 0.527, + 0.437, + 0.868, + 0.619 + ], + "angle": 0, + "content": "
MethodWebVisionILSVRC12
top1top5top1top5
MentorNet [18]63.0081.4057.8079.92
Co-teaching [14]63.5885.2061.4884.70
Iterative-CV [7]65.2485.3461.6084.98
DivideMix [24]77.3291.6475.2090.84
RRL [26]77.891.374.490.9
DSOS [1]77.7692.0474.3690.80
SOP [31]76.6-69.1-
UNICON [19]77.6093.4475.2993.72
RankMatch79.9193.6177.3994.26
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.629, + 0.895, + 0.707 + ], + "angle": 0, + "content": "Table 3: Comparison with state-of-the-art methods on (mini) WebVision dataset. Numbers denote top-1 (top-5) accuracy (\\%) on the WebVision and ImageNet ILSVRC12 validation set. Results for baselines are copied from the corresponding papers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.892, + 0.779 + ], + "angle": 0, + "content": "for classification on CIFAR-10 under different noise levels and record the following statistics: confident ratio, precision, and recall of confident predictions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.893, + 0.903 + ], + "angle": 0, + "content": "From the results shown in Figure 4, we discover the following empirical rules: (1) Confident ratio and recall increase in the same trend, while precision continues to decrease, indicating that the process of overfitting to noise label can regard as the process of overconfidence. (2) The precision of confident samples maintains a high level at the early stage, which means that confident predictions selected by the high threshold are reliable after the warm-up stage." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1650" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.163, + 0.09, + 0.38, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.384, + 0.089, + 0.592, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.599, + 0.09, + 0.811, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.247, + 0.892, + 0.337 + ], + "angle": 0, + "content": "Figure 4: Some key statistics of confident samples on CIFAR-10. The confident samples are selected via the fixed confidence threshold. (a) Precision, ratio of correctly predicted samples in confident samples, maintains a high level (close to \\(100\\%\\)) at the early stage, but continues to decline afterwards. Under Symmetry-50% noise, there is no confident samples in the early period. Hence, we record the precision after 30 epochs. (b) Recall, ratio of confident samples in correct prediction samples, maintains a low level in early stage, and gradually rises to high level. (c) Confidence ratio, ratio of confident samples in training set, has the same trend with Recall." + }, + { + "type": "image", + "bbox": [ + 0.163, + 0.353, + 0.327, + 0.471 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.339, + 0.353, + 0.487, + 0.471 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.353, + 0.647, + 0.471 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.662, + 0.353, + 0.807, + 0.471 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.485, + 0.892, + 0.561 + ], + "angle": 0, + "content": "Figure 5: Accuracy \\((\\%)\\) of the selected clean samples under different symmetric noise rates on CIFAR-100 datasets. Our full method RankMatch is compared with two baselines. One is DivideMix, denoted as GMM and MixMatch. The other is replacing GMM with our proposed Sample-selection via Confident Voting (SCV) method. Compared with GMM, SCV is more efficient to identify the clean samples. And our full model RankMatch has significant improvement in the sample selection stage under high noise rate." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.588, + 0.47, + 0.665 + ], + "angle": 0, + "content": "(3) However, it is prone to selecting few samples when directly selecting reliable confidence samples by the high threshold because the recall is extremely low under high noise. It forms a dilemma between the quality and quantity of the selected samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Sample selection via confident voting (SCV) is one main reason for RankMatch achieving great improvement. To study and verify its effectiveness, we test the accuracy of the selected clean samples under various symmetric noises on CIFAR-100. Since the great success DivideMix has made, we regard the GMM-based sample selection method as our baseline. Figure 5 presents that the SCV-based methods are more accurate than DivideMix in all cases. Furthermore, in the extremely demanding scenario (i.e., Symmetry-80% and Symmetry-90%), SCV based method achieves tremendous improvement. Specifically, DivideMix with SCV achieves over 18% improvement than that with GMM at 80% label noise. In contrast, our full RankMatch achieves over 25% improvement, which implies that the SCV benefits from more robust representation train" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.588, + 0.892, + 0.77 + ], + "angle": 0, + "content": "ing. Under the most extreme \\(90\\%\\) label noise, our full RankMatch achieves over \\(140\\%\\) selection accuracy gain, while DivideMix with SCV improves over \\(75\\%\\). The explanation for this result is that our full model includes consistency regularization and rank contrastive loss. Consistency regularization enhances semantic consistency and rectifies some confident-but-noisy features, which generates more robust prototypes and benefits SCV. Furthermore, rank contrastive loss promotes more discriminative features, improving confident prototype generation. The supplementary material contains other in-depth studies examining the sensitivity of high threshold \\(\\tau\\) and hyper-parameters in SCV." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effects of RankMatch components. We remove the corresponding components to study the effects of RCL and network ensemble. We remove \\(\\mathcal{L}_{\\mathrm{RCL}}\\) to validate the effect of rank contrastive loss. We replace the SCV module as the sample selection strategy of DivideMix to validate the effectiveness of SCV. We remove the K-means in SCV for detailed study. As the results shown in Table 4, we find that rank contrastive loss is beneficial to RankMatch. The results" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.514, + 0.956 + ], + "angle": 0, + "content": "1651" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.089, + 0.457, + 0.254 + ], + "angle": 0, + "content": "
DatasetCIFAR-10CIFAR-100
Noise ratio50%90%50%90%
RankMatchBest95.692.677.950.6
Last95.492.177.649.9
w/o SCVBest95.189.675.345.1
Last94.989.174.944.9
SCV w/o K-meansBest95.491.876.547.9
Last95.291.475.247.5
w/o RCLBest95.290.876.145.6
Last94.988.775.244.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.265, + 0.47, + 0.295 + ], + "angle": 0, + "content": "Table 4: Ablation study results in terms of test accuracy (%) on CIFAR-10 and CIFAR-100 with symmetric label noise." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.323, + 0.47, + 0.368 + ], + "angle": 0, + "content": "also validate the effectiveness of our proposed SCV. Diversifying the intra-class patterns by K-means is more effective under complex scenario and extreme noise ratio." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.381, + 0.273, + 0.526 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.381, + 0.457, + 0.527 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.539, + 0.47, + 0.586 + ], + "angle": 0, + "content": "Figure 6: Sensitivity to the variance of hyperparameters. Experiments are conducted on CIFAR-10 under \\(50\\%\\) and \\(90\\%\\) symmetric noises." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.603, + 0.47, + 0.695 + ], + "angle": 0, + "content": "Sensitivity Analysis. SCV introduce the confidence threshold \\(\\tau\\) and number of prototypes \\(K\\). We range the number of prototypes \\(K\\) from 5 to 30 and vary the threshold \\(\\tau\\) from 0.90 to 0.99. Figure 6 shows that our method is robust against different choices for \\(\\tau\\) and \\(K\\). More in-depth studies are included in supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.709, + 0.205, + 0.725 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We presented RankMatch, a novel framework for LNL that strives to combat noisy labels by enhancing confidence and consistency. Confidence-wise, we propose a novel clean sample selection strategy based on confidence representation voting rather than the small-loss criterion. Collecting votes from confident prototypes makes our method robust to noise and can sieve clean samples out with ample quantity. Consistency-wise, we introduce a novel rank contrastive loss based on the rank statistics of principal features instead of the widely-used \\(L_{2}\\) distance. Such a loss could enhance consistency between similar samples even if they" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "were wrongly labeled. Moreover, we leverage consistency regularization to enhance the semantic consistency. We validate our superiority over several challenging benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.151, + 0.661, + 0.168 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.177, + 0.894, + 0.268 + ], + "angle": 0, + "content": "This work was supported in part by the Guangdong Basic and Applied Basic Research Foundation (NO. 2020B1515020048), in part by the National Natural Science Foundation of China (NO. 61976250), in part by the Shenzhen Science and Technology Program (NO. JCYJ20220530141211024)." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.281, + 0.597, + 0.297 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.306, + 0.892, + 0.361 + ], + "angle": 0, + "content": "[1] Paul Albert, Diego Ortego, Eric Arazo, Noel O'Connor, and Kevin McGuinness. Addressing out-of-distribution label noise in webly-labelled data. 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In ECCV, 2022." + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1654" + } + ] +] \ No newline at end of file diff --git a/2023/RankMatch_ Fostering Confidence and Consistency in Learning with Noisy Labels/0d715541-80cd-458e-81f4-423a1c46d83e_origin.pdf b/2023/RankMatch_ Fostering Confidence and Consistency in Learning with Noisy Labels/0d715541-80cd-458e-81f4-423a1c46d83e_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8045f4f83b0a14d01f1e47408bf179e7430ba4d0 --- /dev/null +++ b/2023/RankMatch_ Fostering Confidence and Consistency in Learning with Noisy Labels/0d715541-80cd-458e-81f4-423a1c46d83e_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:afd683b9cbff6f7e6d30f15fbd7008286154fe0e364780675838a2a66d079cdc +size 6513997 diff --git a/2023/RankMatch_ Fostering Confidence and Consistency in Learning with Noisy Labels/full.md b/2023/RankMatch_ Fostering Confidence and Consistency in Learning with Noisy Labels/full.md new file mode 100644 index 0000000000000000000000000000000000000000..fd85b2ea3011f8435cb0edc8a1055a7c015dcba9 --- /dev/null +++ b/2023/RankMatch_ Fostering Confidence and Consistency in Learning with Noisy Labels/full.md @@ -0,0 +1,349 @@ +# RankMatch: Fostering Confidence and Consistency in Learning with Noisy Labels + +Ziyi Zhang $^{1,2}$ , Weikai Chen $^{3}$ , Chaowei Fang $^{4}$ , Zhen Li $^{5}$ , Lechao Chen $^{6}$ , Liang Lin $^{2}$ , Guanbin Li $^{2,7*}$ + +$^{1}$ National Key Laboratory of Novel Software Technology, Nanjing University, Nanjing, China $^{2}$ Sun Yat-sen University, Guangzhou, China, $^{3}$ Tencent America + +$^{4}$ Xidian University, $^{5}$ The Chinese University of Hong Kong (Shenzhen), $^{6}$ Zhejiang Lab + +$^{7}$ Research Institute, Sun Yat-sen University, Shenzhen, China + +zhangziyi@lamda.nju.edu.cn,liguanbin@mail.sysu.edu.cn + +# Abstract + +Learning with noisy labels (LNL) is one of the most important and challenging problems in weakly-supervised learning. Recent advances adopt the sample selection strategy to mitigate the interference of noisy labels and use small-loss criteria to select clean samples. However, the one-dimensional loss is an over-simplified metric that fails to accommodate the complex feature landscape of various samples, and, hence, is prone to introduce classification errors during sample selection. In this paper, we propose RankMatch, a novel LNL framework that investigates additional dimensions of confidence and consistency in order to combat noisy labels. Confidence-wise, we propose a novel sample selection strategy based on confidence representation voting instead of the widely-used small-loss criterion. This new strategy is capable of increasing sample selection quantity without sacrificing labeling accuracy. Consistency-wise, instead of the widely adopted feature distance metric for measuring the consistency of inner-class samples, we advocate that the rank of principal features is a much more robust indicator. Based on this metric, we propose rank contrastive loss, which strengthens the consistency of similar samples regardless of their labels and facilitates feature representation learning. Experimental results on noisy versions of CIFAR-10, CIFAR-100, Clothing1M and WebVision have validated the superiority of our approach over existing state-of-the-art methods. + +# 1. Introduction + +The remarkable success of DNNs stems from the availability of large-scale datasets. However, it is highly laborious to obtain massive data with high-quality annotations. + +![](images/b9b9ee18a1798f29c2f62808d16d22753ef7663dba48715495aea1a22e4c9cf7.jpg) +Figure 1: Motivation of RankMatch. After being trained with noisy labels, the model is validated by the augmented images. Noisy labels leads to high-entropy outputs, which lack confidence. We advocate for the use of confidence criterion for sample selection, as the confident samples are more likely to have clean labels. Moreover, The weakly augmented image is similar to training Image 1 (classified as 'dog'), while the strongly augmented one is similar to training Image 2 (classified as 'deer'). Considering the model tends to produce similar predictions for similar images, the two views of the same image have inconsistent predictions. Consequently, we introduce the rank contrastive loss to enhance the semantic consistency. + +Hence, training DNNs using inexpensive samples from the search engine or machine annotation [27, 33, 11] has become an attractive alternative. However, these methods inevitably introduce erroneous labels, which cause poor performance as DNNs can easily overfit to noises [58]. Hence, learning with noisy labels (LNL) has become an important yet challenging task. + +Sample selection is a widely adopted strategy in LNL that identifies clean samples from the dataset to alleviate the negative impact of noisy labels. The small-loss criterion is a popular sample selection strategy, which regards + +samples with lower loss as clean ones. However, such a one-dimensional loss is too simplified to accommodate the sophisticated distribution of high-dimensional data, such as the image features. As a result, a plethora of easy-but-noisy samples with small loss are often wrongly grouped into the clean set by using the loss-based strategy. This confirmation bias would be gradually amplified in the subsequent loss minimization training and severely impact the final performance [24, 44]. + +Another challenge of LNL lies in the difficulty of obtaining robust and consistent representation for samples across categories and subjects [24, 26, 19]. In semi-supervised learning, this issue can be largely addressed by enforcing consistent predictions given different views of the same sample [21]. However, in LNL, due to the existence of wrong labels, different views of the same object could be clustered into different categories, leading to inconsistent estimations (see Figure 1). Though the sample selection mechanism can identify a part of clean samples, the consistent representation learned from this set of clean data only works on simple samples with high confidence. Hence, how to achieve consistent prediction on difficult samples with low confidence remains an open question. + +In this work, we follow the line of sample selection to avoid the adverse impact of noisy labels. However, instead of relying on an over-simplified 1D loss function, we propose to combat the noises by incorporating new perspectives from confidence and consistency. Confidence-wise, to ensure robust selection of clean samples, we leverage the advances of confidence learning (CL) [37] while avoiding its vulnerability to noisy network predictions. In particular, we investigate the performance of clean sample selection using fixed confidence thresholds at different noise levels. The results (Figure 4) show that a fixed high threshold leads to a much more accurate sample selection even at the presence of strong noises. Therefore, we leverage one fixed high confidence threshold for all classes to ensure the purity of confident samples. To address the lack of clean data by using a high threshold, we further propose sample selection via confidence voting (SCV) to ensure an ample collection of clean labels. Specifically, we generate $K$ clusters from confident samples for each class and treat the cluster center as confident prototype. Each sample is considered clean if the label is consistent with the results voted by its $k$ nearest confident prototypes. We empirically find that the proposed confidence voting mechanism can generate reliable and clean samples in sufficient amounts, ensuring both the quality and quantity of clean samples. + +Consistency-wise, in addition to the classic consistency regularization, i.e. enforcing consistent outputs of different views from the same sample, we propose to encourage consistent predictions between similar hard samples of the same category. To achieve this goal, we introduce rank con + +trastive loss (RCL), a novel metric that fully leverages the rank of principal image features for robust measurement of similar samples. Empirical experiments show that the conventional $l_{2}$ distance cannot exploit the inner structure of feature representation, and, hence, fails to foster consistent clustering in the complex feature space corrupted by noisy samples. Our key observation is that while similar hard samples (with low confidence) of the same class may have a large $l_{2}$ distance in the feature space, the underlying rank of their principal features still remains consistent (see Figure 2). Therefore, our proposed RCL loss is able to promote feature consistency by encouraging correct and discriminative clustering of similar samples with low confidence. + +We code our method as RankMatch as the two perspectives of the proposed framework can mutually benefit each other. While more reliable data segmentation based on high confidence can benefit the subsequent representation learning, the consistent representations further improve the confidence of uncertain data samples, and, in turn, strengthen our proposed confidence-based sample-selection mechanism. We validate the superiority of our method over the state-of-the-art approaches on several challenging benchmarks, including CIFAR, Clothing1M, and WebVision. Our contributions can be summarized as follows. + +- A method with new state-of-the-art performance that is specially tailored for LNL problems by fostering both confidence and consistency. +- A novel sample-selection via confidence voting (SCV) strategy that generates reliable and ample clean samples for the subsequent training. +- Rank contrastive loss (RCL) based on the rank statistics of principal features that encourages consistency between hard samples of the same category. RCL can further benefit clean sample selection by promoting more discriminative features (see Fig. 1 in the supplementary material) for constructing intra-category clusters. + +# 2. Related Work + +Most existing methods on LNL can be categorized into two directions: 1) loss correction and 2) sample selection. + +Loss Correction. For loss correction, mainstream techniques [51, 46, 29, 47, 22] estimate noise transition matrix with a small set of clean samples as prior knowledge. However, estimating the noise transition matrix is challenging, and their assumptions may be too ideal to fit real-world scenarios. To rectify the noisy labels, another line of research proposes self-training architectures where noisy labels are replaced by network predictions [43, 56]. Some methods focus on the design of noisy-tolerant loss functions. For example, [2, 48, 13, 12] leverage bounded loss functions to improve their robustness to noisy labels. Besides, there are + +![](images/78471bfa7668c0c88d787e59ef03525109ce850e44aeb845cb25c8173b776e88.jpg) +Figure 2: The training strategy of RankMatch. We use strong and weak augmentation to achieve consistency regularization in LNL. For the clean set, the given labels are used to regularize the network predictions on strongly augmented images via the supervised training loss $L_{c}$ . For the noisy set, we first generate pseudo labels from the predictions on weakly augmented images and then use them to regularize the predictions on strongly augmented images via training loss $L_{n}$ . Rank contrastive loss pulls similar samples together and pushes others away. The similarity matrix is defined by ranking feature channels instead of Euclidean distance. The final objective function is a joint loss, including a class diversity regularization term in addition. + +some proposed unbiased loss function [35], information-based loss function called $L_{DMI}$ [54], punishment regularization [32], confidence regularization [8], early learning regularization [30], contrastive representation regularization [28] and over-parameterized term [31]. However, it is arduous for loss-correction-based methods to play an advantage in practical scenarios facing high noise ratios. + +Sample selection. Sample selection-based methods strive to reweight training samples and identify clean data to reduce the interference of noisy labels. Many existing methods propose introducing improved selection criteria to make the selected samples cleaner [23, 59, 3, 36, 24, 1]. Memorization effect [4] illuminates that DNNs learn clean and simple patterns faster than noisy labels, leading to a trend to consider small loss as a criterion for sample selection, which means that samples with smaller loss values are more likely to have clean labels. For instance, [3, 36, 24, 1] leverage clean data distribution as selection criterion by lower-loss component in mixture model fitted by per-sample loss. [55, 19] introduces JS-divergence between network prediction and labels as a selection criterion. [38] leverages the cross-entropy loss between disagreement distribution and labels as selection criterion. However, the loss value is just a scalar, contains limited information, and is prone to errors. For example, it is hard to distinguish between hard-to-learn clean samples and noisy samples after the warm-up stage since both have relatively large loss values. Besides, confirmation bias [44] is a common issue often encountered with the small-loss criterion. Once the noisy samples are wrongly grouped into the clean set by the small-loss criterion, their losses will keep small in the later train + +ing. It remains challenging to rectify the sample selection errors. Many methods mitigate this issue by training two networks [18, 34, 14, 57, 49, 24, 55]. But it is still a problem to get more accurate labels through the small-loss criterion. More recently, Confident Learning (CL) [37] proposes confident criterion as an alternative for sample selection. It computes a set of thresholds for every class and chooses confident samples whose network predicted highest probabilities are greater than the corresponding thresholds. However, CL directly estimates the noise transition matrix by confident samples, which is vulnerable to the network predictions and threshold setting. And it is prone to fail to perform well in large-scale cases and real-world scenarios with a high noise ratio. + +Semi-supervised Learning. The Semi-supervised Learning (SSL) has seen fast progress by leveraging consistency regularization [41, 53, 5, 21, 39, 40, 45], which is used to minimize the difference in network prediction between two views of the same image. FixMatch [21] simply but effectively combines strong and weak augmentation in consistency regularization with confidently pseudo-labeling to achieve great success in semi-supervised learning setting. Most recently, [39] propose an uncertainty-aware pseudolabels selection (UPS) framework to improve pseudo labeling accuracy. RankingMatch [45] introduces a triplet loss, where the similarity between samples is measured by the L2-norm outputs. Furthermore, it is worth noting that the rank statistics of principal features can serve as a metric to measure the pairwise similarity among samples [15]. There are similarities between Learning with Noisy Labels (LNL) problems and semi-supervised learning setting. + +In semi-supervised learning settings, confident predictions have strong connection with true labels as labeled data regularizing the unlabeled data, which are not easy to overconfident confused by noisy label. And leveraging confident predictions inevitably lacks sample diversity to make pseudo labels more reliable, while difficult samples always have uncertain predictions. Our approach finds a good balance of confidence, sample diversity and consistency. + +# 3. Method + +Our method is introduced in three parts: the sample selection mechanism (Figure. 3), the consistency regularization and rank contrastive loss. Figure 2 shows the overview of RankMatch. The algorithm is included in the supplementary material. + +Preliminaries. For the $C$ -way image classification task with noisy labels, denoted by $\mathcal{D} = (\mathcal{X}, \widetilde{\mathcal{Y}})$ the training data, where $\mathcal{X}$ is training images, and $\widetilde{\mathcal{Y}}$ is labels which may be wrongly annotated. We denote the DNNs in training stage as $P(F(\mathbf{x}, \theta))$ , where $\mathbf{x} \in \mathbb{R}^I$ is the input image, $F: \mathbb{R}^I \to \mathbb{R}^L$ is the feature extractor where $I$ and $L$ stand for the dimension of input space and embedding space respectively, and $P: \mathbb{R}^L \to \mathbb{R}^C$ represents the classifier. $\theta$ denotes the network parameters of the feature extractor. We use $\mathbf{f}_i$ and $\mathbf{p}_i$ as simplified forms of $F(\mathbf{x}_i, \theta)$ and $P(F(\mathbf{x}_i, \theta))$ respectively. + +# 3.1. Sample Selection via Confidence Voting + +For the sample selection, we leverage the advantage of confident learning [37] rather than the widely used small-loss criterion. We explore using a fixed confidence threshold to avoid the vulnerability of inaccurate network predictions. Figure 4 illustrates that confident predictions selected by a fixed high threshold are reliable but of a limited number. Hence, we propose a new sample selection strategy based on the confidence criterion that maintains reliability while ensuring sufficient confident samples across categories. + +Confident Samples. In the setting of LNL, it is hard to select confident samples just by a single threshold when facing different levels of noise rates. Some classes are easy-to-learn, and one threshold for all classes is likely to result in class-unbalanced selection. In order to avoid data imbalance among classes, we select the top $B$ basic confident samples $\mathcal{I}_b$ in each class to ensure each class at least has $B$ samples: + +$$ +\mathcal {I} _ {b} ^ {c} = \underset {| \hat {\mathcal {X}} | = B, \hat {\mathcal {X}} \subseteq \mathcal {X}} {\arg \max } \sum_ {\mathbf {x} \in \hat {\mathcal {X}}} \mathbf {p} [ c ], \tag {1} +$$ + +where $\mathbf{p}[c]$ is the $c$ -th element of $\mathbf{p}$ ( $= P(F(\mathbf{x},\theta))$ ), namely the probability value of the $c$ -th class. And additional samples with prediction probability greater than a threshold as + +![](images/7235a956e775513c21f6c228f280bd344eb80a7ebc64c02bda2cae3b67f428b3.jpg) +Figure 3: Sample-selection via Confidence Voting (SCV) module. We first select the most representative confident samples. Then, the selected confident samples generate prototypes as voting candidates. For each sample, its $k$ nearest prototypes are regarded as voters to identify whether the label is clean. + +the reliable confident samples: + +$$ +\mathcal {I} _ {r} ^ {c} = \left\{\mathbf {x} _ {i} \mid \mathbf {p} _ {i} [ c ] > \tau , \mathbf {x} _ {i} \in \mathcal {X} \right\}, \tag {2} +$$ + +The final selected confident samples is the union of the two sets $\mathcal{I}^c = \mathcal{I}_b^c\cup \mathcal{I}_r^c$ + +Confident Prototype Generation. To guarantee the quality of the confident samples, we set high threshold $\tau$ and small portion $B$ , but face the problem of low sample quantity. Although with a small number, the reliable representations of confident samples reflect some common intra-class patterns. Thus, we generate representation prototypes using the selected samples for further selection. Straightforwardly, a representative feature can be generated by averaging features of confident samples for each class: + +$$ +\phi^ {c} = \frac {1}{| \mathcal {I} ^ {c} |} \sum_ {\mathbf {x} \in \mathcal {I} ^ {c}} F (\mathbf {x}, \theta). \tag {3} +$$ + +Even if the confident samples include some noise during the early training stage, the prototype generation process will predominantly rely on the most clean samples, rendering it robust to noisy labels. However, the mean vector is unable to represent a class with large intra-class variations. We further diversify the intra-class patterns by generating more prototypes of each class. Specifically, we split the confident samples into $K$ clusters for each class by $K$ -means. For the $c$ -th class, we define the average centers of the obtained clusters features as $\Phi^c = \{\phi_j^c\}_{j=1}^K$ . Our sample-selection module is based on the generated confident prototypes $\Phi (= \bigcup_{c=1}^{C} \Phi^c)$ . + +Data Segmentation by Confidence Voting. After obtaining $C \times K$ prototypes, we first find the $k$ nearest prototypes + +of $\mathbf{x}_i$ measured by the cosine similarity: + +$$ +\mathcal {V} _ {i} = \underset {| \hat {\Phi} | = k, \hat {\Phi} \subseteq \Phi} {\arg \max } \sum_ {\phi \in \hat {\Phi}} \cos (\mathbf {f} _ {i}, \phi). \tag {4} +$$ + +The class label to which the most prototypes belong in $\mathcal{V}_i$ is considered as the voting result $\mathbf{y}_i'$ . Clean samples $\mathcal{D}_{\mathrm{cln}}$ are identified by checking whether $\mathbf{y}_i'$ is consistent with the provided label $\widetilde{\mathbf{y}}_i$ : + +$$ +\mathcal {D} _ {\mathrm {c l n}} = \left\{\left(\mathbf {x} _ {i}, \widetilde {\mathbf {y}} _ {i}\right) \mid \widetilde {\mathbf {y}} _ {i} = \mathbf {y} _ {i} ^ {\prime}, \forall \left(\mathbf {x} _ {i}, \widetilde {\mathbf {y}} _ {i}\right) \in \mathcal {D} \right\}, \tag {5} +$$ + +The remaining noisy set is $\mathcal{D}_{\mathrm{nsy}} = \mathcal{D}\setminus \mathcal{D}_{\mathrm{cln}}$ + +# 3.2. Consistency Regularization + +This paper argues that noisy labels lead to inconsistent predictions (Figure 1). To enhance the consistency of the predictions augmented from the same image, we apply two different augmentation methods to generate two views for training images, including "weak" augmentation $(\mathcal{A}_w)$ and "strong" augmentation $(\mathcal{A}_s)$ . Weak augmentation refers to random cropping and flipping, while strong augmentation refers to AutoAugment [9], which uses reinforcement learning to find augmentation strategies automatically and requires labeled data to learn. Note that our sample selection mechanism provides cleaner supervision signals, benefiting AutoAugment to accept a more effective augmentation policy. + +Following [21], we transfer the training image $\mathbf{x}$ with the two augmentation strategies, resulting in two views: $\mathbf{v}^w = \mathcal{A}_w(\mathbf{x})$ , and $\mathbf{v}^s = \mathcal{A}_s(\mathbf{x})$ . The corresponding network predictions are denoted as $\mathbf{p}^w$ and $\mathbf{p}^s$ , respectively. Given that the semantic information of the augmented images is not modified, we assume the two network predictions to be consistent. + +For clean samples, we direct use cross-entropy loss between predictions on strongly augmented images and the original labels: + +$$ +\mathcal {L} _ {c} = - \frac {1}{| \mathcal {D} _ {\mathrm {c l n}} |} \sum_ {(\mathbf {x}, \widetilde {\mathbf {y}}) \in \mathcal {D} _ {\mathrm {c l n}}} \widetilde {\mathbf {y}} \circ \log (\mathbf {p} ^ {s}), \tag {6} +$$ + +where $\circ$ denotes the inner product. + +For noisy samples with high prediction confidence, we rectify their labels with predictions of weakly augmented images: + +$$ +\hat {\mathcal {D}} _ {\mathrm {n s y}} = \left\{\left(\mathbf {x} _ {i}, \hat {\mathbf {y}} _ {i}\right) | \forall \mathbf {x} _ {i} \in \mathcal {X} _ {\mathrm {n s y}}, \max _ {c} \left\{\mathbf {p} ^ {w} [ c ] \right\} > \nu , \hat {\mathbf {y}} _ {i} = c \right\}, \tag {7} +$$ + +where $\nu$ is the confidence threshold, we set it the same as that in Eq. 2 to avoid introducing another parameter. Inspired by [21], the cross entropy losses between the predictions of weakly and strongly augmented images are + +employed as regularizing consistency for the CNN model learning: + +$$ +\mathcal {L} _ {n} = - \frac {1}{| \hat {\mathcal {D}} _ {\mathrm {n s y}} |} \sum_ {(\mathbf {x}, \hat {\mathbf {y}}) \in \hat {\mathcal {D}} _ {\mathrm {n s y}}} \hat {\mathbf {y}} \circ \log \left(\mathbf {p} ^ {s}\right). \tag {8} +$$ + +# 3.3. Rank Contrastive Loss + +Robust representations can benefit our samples selection strategy. However, some valuable information is excluded by Eq. 7 and Eq. 8 since the hard-to-learn noisy samples have less confident predictions and thus can not be optimized. To obtain complete and robust representations, we propose a rank contrastive loss (RCL) to strengthen the consistency of the "similar" samples while pushing "dissimilar" ones further. + +The widely used $L_{2}$ distance as the similarity metric is less robust in LNL, as overfitting to noisy labels tends to introduce spurious close euclidean distance. Every convolution kernel filters out certain kinds of attributes in the input image. Similar visual patterns are prone to activate the same representation channel of response maps produced by convolution layers. Hence, the indices of feature elements rank ordered in accordance with their magnitudes, can serve as a metric for assessing the pairwise representations similarity [15]. Although noisy labels affect the feature value, we leverage rank statistics of principal features to estimate the similarity matrix. Specifically, we rank the values in all channels of $\mathbf{f}_i$ and regard the $r$ channels with the largest activation values as the principal feature dimensions, + +$$ +\mathcal {R} _ {i} = \underset {| \hat {\mathcal {R}} | = r, \hat {\mathcal {R}} \subset \{1, 2, \dots , L \}} {\arg \max } \sum_ {n \in \hat {\mathcal {R}}} \mathbf {f} _ {i} [ n ], \tag {9} +$$ + +where $\mathbf{f}_i[n]$ denote the $n$ -th channel of feature $\mathbf{f}_i$ . If two samples $\mathbf{x}_i$ and $\mathbf{x}_j$ share the same principal feature dimensions, we assume they are "similar". The similarity $s_{ij}$ between $\mathbf{x}_i$ and $\mathbf{x}_j$ is evaluated as follows, + +$$ +s _ {i j} = \left\{ \begin{array}{l l} 1 & \text {i f} \mathcal {R} _ {i} = \mathcal {R} _ {j}; \\ 0 & \text {o t h e r w i s e .} \end{array} \right. \tag {10} +$$ + +To achieve clustering in the feature space, we adopt the following binary cross-entropy loss as: + +$$ +\mathcal {L} _ {\mathrm {R C L}} = - \frac {1}{N ^ {2}} \sum_ {i = 1} ^ {N} \sum_ {j = 1} ^ {N} \left[ s _ {i j} \log \left(\mathbf {p} _ {i} \circ \mathbf {q} _ {j}\right) + \left(1 - s _ {i j}\right) \log \left(1 - \mathbf {p} _ {i} \circ \mathbf {q} _ {j}\right) \right], \tag {11} +$$ + +where $\mathbf{p}_i = P(F(\mathbf{v}_i^w,\theta))$ and $\mathbf{q}_i = P(F(\mathbf{v}_i^s,\theta))$ . The train- + +ing loss $\mathcal{L}_{\mathrm{RCL}}$ can be divided into two terms: + +Consistency regularization + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {R C L}} = - \frac {1}{N ^ {2}} \sum_ {i = 1} ^ {N} \left[ s _ {i i} \log \left(\mathbf {p} _ {i} \circ \mathbf {q} _ {i}\right) + \left(1 - s _ {i i}\right) \log \left(1 - \mathbf {p} _ {i} \circ \mathbf {q} _ {i}\right) \right] \\ - \frac {1}{N ^ {2}} \sum_ {i = 1} ^ {N} \sum_ {j \neq i} [ s _ {i j} \log (\mathbf {p} _ {i} \circ \mathbf {q} _ {j}) + (1 - s _ {i j}) \log (1 - \mathbf {p} _ {i} \circ \mathbf {q} _ {j}) ]. \tag {12} \\ \end{array} +$$ + +Since $s_{ii} = 1$ always holds, organize the first term as: + +$$ +- \frac {1}{N ^ {2}} \sum_ {i = 1} ^ {N} \log \left(\mathbf {p} _ {i} \circ \mathbf {q} _ {i}\right) = - \frac {1}{N ^ {2}} \sum_ {i = 1} ^ {N} \log \left(\mathbf {p} _ {i} ^ {w} \circ \mathbf {p} _ {i} ^ {s}\right). \tag {13} +$$ + +Minimizing this term is equal to $\max \{\mathbf{p}_i^w\circ \mathbf{p}_i^s\}$ , which pulls the outputs of strongly and weakly augmented images closer. Thus, $\mathcal{L}_{\mathrm{RCL}}$ in the diagonal of $S$ can be regarded as consistency regularization. Even in the early training stage, $S$ is the identity matrix that removes the second term in Eq. 12, improving the network representation ability. + +# 3.4. Overall Loss Function + +Following [43, 24, 3], we apply the fair class diversity-promoting regularization $\mathcal{L}_{div}$ to prevent assigning most samples into few classes: + +$$ +\mathcal {L} _ {d i v} = \sum_ {c = 1} ^ {C} \frac {1}{C} \log \left(\frac {1}{C} / \frac {\sum_ {i = 1} ^ {N} \mathbf {p} _ {i} ^ {w} [ c ]}{N}\right). \tag {14} +$$ + +The overall loss function for network optimization is as follows: + +$$ +\mathcal {L} = \mathcal {L} _ {c} + \lambda_ {n} \mathcal {L} _ {n} + \mathcal {L} _ {\mathrm {R C L}} + \mathcal {L} _ {\text {d i v}}. \tag {15} +$$ + +We following [24, 14, 57, 36] to train two networks to combat the confirmation bias, detailed algorithm is included in supplementary material. + +# 4. Experiments + +# 4.1. Experimental Setup + +We evaluate the proposed RankMatch on CIFAR-10, CIFAR-100 [20], as well as the real-world datasets Clothing1M [52] and WebVision [27]. Both CIFAR-10 and CIFAR-100 contain 50,000 training images and 10,000 test images of size $32 \times 32$ . Following previous works [43, 25], we conduct experiments requiring noise augmentation, either symmetric or asymmetric [43, 25] label noise injection. We follow the identical implementation of generating symmetric and asymmetric noises on CIFAR datasets with DivideMix [24]. Symmetric noise is generated by randomly replacing the labels for a percentage of the training data with all possible labels. Asymmetric noise is to mimic the + +structure of real-world label noise, where labels are only replaced by similar classes (e.g. deer $\rightarrow$ horse, dog $\leftrightarrow$ cat). We adopt 18-layer PreAct Resnet [17] as the backbone. During training, we train DNNs for 300 epochs using SGD optimizer with a momentum of 0.9, with weight decay of 0.0005 for CIFAR-10 and 0.001 for CIFAR-100. The batch size is 64 for CIFAR-10 and 128 for CIFAR-100. We set the initial learning rate as 0.02 and reduce it by a factor of 10 after 150 epochs. The warm-up period is 10 epochs for CIFAR-10 and 30 epochs for CIFAR-100, respectively. For all CIFAR experiments, we set $\tau = 0.95$ , $r = 5$ , and choose $\lambda_{n}$ from $\{0.2, 0.5, 1, 2, 10, 15\}$ for a small validation test. More experimental details are in supplementary materials. + +Clothing1M contains 1 million real-world shopping images belonging to 14 classes. We use ResNet-50 [16] with weights pretrained on ImageNet as the classification model. WebVision consists of web-crawled images with the same concepts from ImageNet ILSVRC12 [10]. We follow the previous work [24, 7] and compare baseline methods on the first 50 classes of the Google image subset using the inception-resnet v2 [42]. The training details are delineated in supplementary materials. + +# 4.2. Experimental Results + +Results on CIFAR. Table 1 illuminates RankMatch outperforms the state-of-the-art models across most noisy levels. RRL [26] combats noisy labels by learning robust representations and slightly outperforms our method on CIFAR-10 with $20\%$ symmetric label noise. One possible explanation is that the massive clean labels make it easy to rectify the symmetric label noise. Thus, the sample selection strategy is less effective in this scenario but shows great advantages for a high noise ratio and real-world dataset. Benefiting from the advanced confidence sample selection mechanism, RankMatch boosts the averaged test accuracy of the last ten epochs from $77.4\%$ to $92.1\%$ on CIFAR-10 and $33.1\%$ to $49.9\%$ on CIFAR-100 under the extreme case of $90\%$ noise. Even without MixMatch [6] technique, RankMatch achieves around 20 points improvement (50.6% vs. $31.5\%$ ) compared to DivideMix [24] on CIFAR-100 with $90\%$ noisy labels. We surpass CTRR [28], the most recent contrastive learning-based method, under all noise ratios, especially on the more challenging CIFAR-100 dataset. + +Results on real-world dataset. Table 2 and Table 3 demonstrate the results on Clothing1M and WebVision, respectively. Our method outperforms all the alternative methods in both noisy real-world datasets. We achieve the improvement of $0.18\%$ over SFT [50], the most recent sample selection-based method with MixMatch [6]. Besides, the most recent baseline UNICON [19] well combines the advantages of semi-supervised learning (DivideMix-like) and contrastive learning (RRL-like) and achieves great per + +
DatasetCIFAR-10CIFAR-100
Method/Noise ratio20%50%80%90%Asym. 40%20%50%80%90%
Cross-EntropyBest86.879.462.942.785.062.046.719.910.1
Last82.757.926.116.872.361.837.38.83.5
PENCILBest92.489.177.558.988.569.457.531.115.3
[56]Last92.088.776.558.288.168.156.420.78.8
Meta-LearningBest92.989.377.458.789.268.559.242.419.5
[25]Last92.088.876.158.388.467.758.040.114.3
DivideMixBest96.194.693.276.093.477.374.660.231.5
[24]Last95.794.492.975.492.176.974.259.631.0
ELR [30]Best95.894.893.378.793.077.673.660.833.4
MOIT [38]Best94.191.175.870.193.275.970.151.424.5
RRL [26]Last96.495.393.377.493.380.376.061.133.1
CTRR [28]Best93.3-86.784.389.070.1-43.7-
RankMatchBest96.595.694.592.694.779.577.967.650.6
Last96.495.494.292.194.479.377.667.249.9
+ +Table 1: Comparison between RankMatch and state-of-the-art methods on CIFAR-10 and CIFAR-100 under symmetric and asymmetric noise. "Best" refers to the best test accuracy across all epochs and "Last" is the averaged test accuracy over the last 10 epochs. + +
MethodTest Accuracy
Cross-Entropy69.21
PENCIL [56]73.49
DivideMix [24]74.76
RRL [26]74.97
DSOS [1]73.63
UNICON [19]74.98
SOP [31]73.50
SFT [50]75.08
RankMatch75.22
+ +formance gain. In particular, RankMatch achieves $0.24\%$ performance gain over UNICON on the challenging Clothing1M dataset. Moreover, RankMatch obtain over $2\%$ Top-1 accuracy improvement over state-of-the-art on both mini-WebVison and ILSVRC12 validation sets, and guarantees state-of-the-art Top-5 accuracy on WebVision and ILSVRC12, indicating the effectiveness of our approach. + +# 4.3. Ablation Study + +The role of confidence in LNL. To explore the role of the fixed confidence threshold in the LNL setting, we focus on the relationship between confident predictions and ground-truth labels. Specifically, we directly train DNNs + +Table 2: Comparison with state-of-the-art methods on Clothing1M. Baseline results are copied from original papers. + +
MethodWebVisionILSVRC12
top1top5top1top5
MentorNet [18]63.0081.4057.8079.92
Co-teaching [14]63.5885.2061.4884.70
Iterative-CV [7]65.2485.3461.6084.98
DivideMix [24]77.3291.6475.2090.84
RRL [26]77.891.374.490.9
DSOS [1]77.7692.0474.3690.80
SOP [31]76.6-69.1-
UNICON [19]77.6093.4475.2993.72
RankMatch79.9193.6177.3994.26
+ +Table 3: Comparison with state-of-the-art methods on (mini) WebVision dataset. Numbers denote top-1 (top-5) accuracy (\%) on the WebVision and ImageNet ILSVRC12 validation set. Results for baselines are copied from the corresponding papers. + +for classification on CIFAR-10 under different noise levels and record the following statistics: confident ratio, precision, and recall of confident predictions. + +From the results shown in Figure 4, we discover the following empirical rules: (1) Confident ratio and recall increase in the same trend, while precision continues to decrease, indicating that the process of overfitting to noise label can regard as the process of overconfidence. (2) The precision of confident samples maintains a high level at the early stage, which means that confident predictions selected by the high threshold are reliable after the warm-up stage. + +![](images/c91a9a04d13e0ab69939dae5f09f97e3cd7c3ad8932709c34b6ecd81f7050ead.jpg) +Figure 4: Some key statistics of confident samples on CIFAR-10. The confident samples are selected via the fixed confidence threshold. (a) Precision, ratio of correctly predicted samples in confident samples, maintains a high level (close to $100\%$ ) at the early stage, but continues to decline afterwards. Under Symmetry-50% noise, there is no confident samples in the early period. Hence, we record the precision after 30 epochs. (b) Recall, ratio of confident samples in correct prediction samples, maintains a low level in early stage, and gradually rises to high level. (c) Confidence ratio, ratio of confident samples in training set, has the same trend with Recall. + +![](images/4e1f1e396dbb468b4e7b8a9bbcee66386f12cadd6f7051de0fd87c03f810e769.jpg) + +![](images/434620fcf9d79988be07d26af3c457387b557f464e23182bd8c006ce8d9664c4.jpg) + +![](images/14094a8e410d55d4d9855dc07781864819c12ae2392189ccd081b0c31c06da49.jpg) +Figure 5: Accuracy $(\%)$ of the selected clean samples under different symmetric noise rates on CIFAR-100 datasets. Our full method RankMatch is compared with two baselines. One is DivideMix, denoted as GMM and MixMatch. The other is replacing GMM with our proposed Sample-selection via Confident Voting (SCV) method. Compared with GMM, SCV is more efficient to identify the clean samples. And our full model RankMatch has significant improvement in the sample selection stage under high noise rate. + +![](images/498e4f8dfcb62b8592239e5309d1ddfd7b458567ae076371ce6bb8e2707bef08.jpg) + +![](images/3294cfdda5552561a883f0a1df988ddb93353ac92bc0ede4a9fe742d57573a1b.jpg) + +![](images/a1e3871fef9619c2043d47a371d7596bfe923576637b5c74c727ce95ac9fed5e.jpg) + +(3) However, it is prone to selecting few samples when directly selecting reliable confidence samples by the high threshold because the recall is extremely low under high noise. It forms a dilemma between the quality and quantity of the selected samples. + +Sample selection via confident voting (SCV) is one main reason for RankMatch achieving great improvement. To study and verify its effectiveness, we test the accuracy of the selected clean samples under various symmetric noises on CIFAR-100. Since the great success DivideMix has made, we regard the GMM-based sample selection method as our baseline. Figure 5 presents that the SCV-based methods are more accurate than DivideMix in all cases. Furthermore, in the extremely demanding scenario (i.e., Symmetry-80% and Symmetry-90%), SCV based method achieves tremendous improvement. Specifically, DivideMix with SCV achieves over 18% improvement than that with GMM at 80% label noise. In contrast, our full RankMatch achieves over 25% improvement, which implies that the SCV benefits from more robust representation train + +ing. Under the most extreme $90\%$ label noise, our full RankMatch achieves over $140\%$ selection accuracy gain, while DivideMix with SCV improves over $75\%$ . The explanation for this result is that our full model includes consistency regularization and rank contrastive loss. Consistency regularization enhances semantic consistency and rectifies some confident-but-noisy features, which generates more robust prototypes and benefits SCV. Furthermore, rank contrastive loss promotes more discriminative features, improving confident prototype generation. The supplementary material contains other in-depth studies examining the sensitivity of high threshold $\tau$ and hyper-parameters in SCV. + +Effects of RankMatch components. We remove the corresponding components to study the effects of RCL and network ensemble. We remove $\mathcal{L}_{\mathrm{RCL}}$ to validate the effect of rank contrastive loss. We replace the SCV module as the sample selection strategy of DivideMix to validate the effectiveness of SCV. We remove the K-means in SCV for detailed study. As the results shown in Table 4, we find that rank contrastive loss is beneficial to RankMatch. The results + +
DatasetCIFAR-10CIFAR-100
Noise ratio50%90%50%90%
RankMatchBest95.692.677.950.6
Last95.492.177.649.9
w/o SCVBest95.189.675.345.1
Last94.989.174.944.9
SCV w/o K-meansBest95.491.876.547.9
Last95.291.475.247.5
w/o RCLBest95.290.876.145.6
Last94.988.775.244.5
+ +Table 4: Ablation study results in terms of test accuracy (%) on CIFAR-10 and CIFAR-100 with symmetric label noise. + +also validate the effectiveness of our proposed SCV. Diversifying the intra-class patterns by K-means is more effective under complex scenario and extreme noise ratio. + +![](images/5e935f793662d03fdc1e2164fe5681cad8be0c45675f118dad6f4f84ec0391dd.jpg) +Figure 6: Sensitivity to the variance of hyperparameters. Experiments are conducted on CIFAR-10 under $50\%$ and $90\%$ symmetric noises. + +![](images/0cbb74d5c15dabc69c6fa3147bacc4baf2605118dee35ca2e80514832d23c5d0.jpg) + +Sensitivity Analysis. SCV introduce the confidence threshold $\tau$ and number of prototypes $K$ . We range the number of prototypes $K$ from 5 to 30 and vary the threshold $\tau$ from 0.90 to 0.99. Figure 6 shows that our method is robust against different choices for $\tau$ and $K$ . More in-depth studies are included in supplementary materials. + +# 5. Conclusions + +We presented RankMatch, a novel framework for LNL that strives to combat noisy labels by enhancing confidence and consistency. Confidence-wise, we propose a novel clean sample selection strategy based on confidence representation voting rather than the small-loss criterion. Collecting votes from confident prototypes makes our method robust to noise and can sieve clean samples out with ample quantity. Consistency-wise, we introduce a novel rank contrastive loss based on the rank statistics of principal features instead of the widely-used $L_{2}$ distance. Such a loss could enhance consistency between similar samples even if they + +were wrongly labeled. Moreover, we leverage consistency regularization to enhance the semantic consistency. We validate our superiority over several challenging benchmarks. + +# Acknowledgments + +This work was supported in part by the Guangdong Basic and Applied Basic Research Foundation (NO. 2020B1515020048), in part by the National Natural Science Foundation of China (NO. 61976250), in part by the Shenzhen Science and Technology Program (NO. JCYJ20220530141211024). + +# References + +[1] Paul Albert, Diego Ortego, Eric Arazo, Noel O'Connor, and Kevin McGuinness. Addressing out-of-distribution label noise in webly-labelled data. In Winter Conference on Applications of Computer Vision (WACV), 2022. +[2] Ehsan Amid, Manfred KK Warmuth, Rohan Anil, and Tomer Koren. Robust bi-tempered logistic loss based on bregman divergences. In Advances in Neural Information Processing Systems, pages 14987-14996, 2019. +[3] Eric Arazo, Diego Ortego, Paul Albert, Noel E. O'Connor, and Kevin McGuinness. Unsupervised label noise modeling and loss correction. 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NeurIPS, arXiv:1909.03388, 2019. + +[55] Yazhou Yao, Zeren Sun, Chuanyi Zhang, Fumin Shen, Qi Wu, Jian Zhang, and Zhenmin Tang. Jo-src: A contrastive approach for combating noisy labels. CoRR, abs/2103.13029, 2021. +[56] Kun Yi and Jianxin Wu. Probabilistic end-to-end noise correction for learning with noisy labels. In CVPR, 2019. +[57] Xingrui Yu, Bo Han, Jiangchao Yao, Gang Niu, Ivor W. Tsang, and Masashi Sugiyama. How does disagreement help generalization against label corruption? In ICML, pages 7164-7173, 2019. +[58] Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning requires rethinking generalization. In ICLR, 2017. +[59] Ganlong Zhao, Guanbin Li, Yipeng Qin, Feng Liu, and Yizhou Yu. Centrality and consistency: Two-stage clean samples identification for learning with instance-dependent noisy labels. 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299, + 290, + 610 + ], + "type": "text", + "content": "Learning with noisy labels (LNL) is one of the most important and challenging problems in weakly-supervised learning. Recent advances adopt the sample selection strategy to mitigate the interference of noisy labels and use small-loss criteria to select clean samples. However, the one-dimensional loss is an over-simplified metric that fails to accommodate the complex feature landscape of various samples, and, hence, is prone to introduce classification errors during sample selection. In this paper, we propose RankMatch, a novel LNL framework that investigates additional dimensions of confidence and consistency in order to combat noisy labels. Confidence-wise, we propose a novel sample selection strategy based on confidence representation voting instead of the widely-used small-loss criterion. This new strategy is capable of increasing sample selection quantity without sacrificing labeling accuracy. Consistency-wise, instead of the widely adopted feature distance metric for measuring the consistency of inner-class samples, we advocate that the rank of principal features is a much more robust indicator. Based on this metric, we propose rank contrastive loss, which strengthens the consistency of similar samples regardless of their labels and facilitates feature representation learning. Experimental results on noisy versions of CIFAR-10, CIFAR-100, Clothing1M and WebVision have validated the superiority of our approach over existing state-of-the-art methods." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 635, + 128, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 128, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 128, + 647 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "text", + "content": "The remarkable success of DNNs stems from the availability of large-scale datasets. However, it is highly laborious to obtain massive data with high-quality annotations." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 319, + 273, + 538, + 384 + ], + "blocks": [ + { + "bbox": [ + 319, + 273, + 538, + 384 + ], + "lines": [ + { + "bbox": [ + 319, + 273, + 538, + 384 + ], + "spans": [ + { + "bbox": [ + 319, + 273, + 538, + 384 + ], + "type": "image", + "image_path": "b9b9ee18a1798f29c2f62808d16d22753ef7663dba48715495aea1a22e4c9cf7.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 394, + 547, + 551 + ], + "lines": [ + { + "bbox": [ + 304, + 394, + 547, + 551 + ], + "spans": [ + { + "bbox": [ + 304, + 394, + 547, + 551 + ], + "type": "text", + "content": "Figure 1: Motivation of RankMatch. After being trained with noisy labels, the model is validated by the augmented images. Noisy labels leads to high-entropy outputs, which lack confidence. We advocate for the use of confidence criterion for sample selection, as the confident samples are more likely to have clean labels. Moreover, The weakly augmented image is similar to training Image 1 (classified as 'dog'), while the strongly augmented one is similar to training Image 2 (classified as 'deer'). Considering the model tends to produce similar predictions for similar images, the two views of the same image have inconsistent predictions. Consequently, we introduce the rank contrastive loss to enhance the semantic consistency." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 578, + 547, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 547, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 547, + 662 + ], + "type": "text", + "content": "Hence, training DNNs using inexpensive samples from the search engine or machine annotation [27, 33, 11] has become an attractive alternative. However, these methods inevitably introduce erroneous labels, which cause poor performance as DNNs can easily overfit to noises [58]. Hence, learning with noisy labels (LNL) has become an important yet challenging task." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Sample selection is a widely adopted strategy in LNL that identifies clean samples from the dataset to alleviate the negative impact of noisy labels. The small-loss criterion is a popular sample selection strategy, which regards" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1644" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 180 + ], + "type": "text", + "content": "samples with lower loss as clean ones. However, such a one-dimensional loss is too simplified to accommodate the sophisticated distribution of high-dimensional data, such as the image features. As a result, a plethora of easy-but-noisy samples with small loss are often wrongly grouped into the clean set by using the loss-based strategy. This confirmation bias would be gradually amplified in the subsequent loss minimization training and severely impact the final performance [24, 44]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 182, + 288, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 288, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 288, + 350 + ], + "type": "text", + "content": "Another challenge of LNL lies in the difficulty of obtaining robust and consistent representation for samples across categories and subjects [24, 26, 19]. In semi-supervised learning, this issue can be largely addressed by enforcing consistent predictions given different views of the same sample [21]. However, in LNL, due to the existence of wrong labels, different views of the same object could be clustered into different categories, leading to inconsistent estimations (see Figure 1). Though the sample selection mechanism can identify a part of clean samples, the consistent representation learned from this set of clean data only works on simple samples with high confidence. Hence, how to achieve consistent prediction on difficult samples with low confidence remains an open question." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 352, + 288, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 288, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 288, + 651 + ], + "type": "text", + "content": "In this work, we follow the line of sample selection to avoid the adverse impact of noisy labels. However, instead of relying on an over-simplified 1D loss function, we propose to combat the noises by incorporating new perspectives from confidence and consistency. Confidence-wise, to ensure robust selection of clean samples, we leverage the advances of confidence learning (CL) [37] while avoiding its vulnerability to noisy network predictions. In particular, we investigate the performance of clean sample selection using fixed confidence thresholds at different noise levels. The results (Figure 4) show that a fixed high threshold leads to a much more accurate sample selection even at the presence of strong noises. Therefore, we leverage one fixed high confidence threshold for all classes to ensure the purity of confident samples. To address the lack of clean data by using a high threshold, we further propose sample selection via confidence voting (SCV) to ensure an ample collection of clean labels. Specifically, we generate " + }, + { + "bbox": [ + 46, + 352, + 288, + 651 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 352, + 288, + 651 + ], + "type": "text", + "content": " clusters from confident samples for each class and treat the cluster center as confident prototype. Each sample is considered clean if the label is consistent with the results voted by its " + }, + { + "bbox": [ + 46, + 352, + 288, + 651 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 352, + 288, + 651 + ], + "type": "text", + "content": " nearest confident prototypes. We empirically find that the proposed confidence voting mechanism can generate reliable and clean samples in sufficient amounts, ensuring both the quality and quantity of clean samples." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Consistency-wise, in addition to the classic consistency regularization, i.e. enforcing consistent outputs of different views from the same sample, we propose to encourage consistent predictions between similar hard samples of the same category. To achieve this goal, we introduce rank con" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "trastive loss (RCL), a novel metric that fully leverages the rank of principal image features for robust measurement of similar samples. Empirical experiments show that the conventional " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": " distance cannot exploit the inner structure of feature representation, and, hence, fails to foster consistent clustering in the complex feature space corrupted by noisy samples. Our key observation is that while similar hard samples (with low confidence) of the same class may have a large " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": " distance in the feature space, the underlying rank of their principal features still remains consistent (see Figure 2). Therefore, our proposed RCL loss is able to promote feature consistency by encouraging correct and discriminative clustering of similar samples with low confidence." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 228, + 545, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 358 + ], + "type": "text", + "content": "We code our method as RankMatch as the two perspectives of the proposed framework can mutually benefit each other. While more reliable data segmentation based on high confidence can benefit the subsequent representation learning, the consistent representations further improve the confidence of uncertain data samples, and, in turn, strengthen our proposed confidence-based sample-selection mechanism. We validate the superiority of our method over the state-of-the-art approaches on several challenging benchmarks, including CIFAR, Clothing1M, and WebVision. Our contributions can be summarized as follows." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 365, + 545, + 518 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 317, + 365, + 545, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 365, + 545, + 400 + ], + "spans": [ + { + "bbox": [ + 317, + 365, + 545, + 400 + ], + "type": "text", + "content": "- A method with new state-of-the-art performance that is specially tailored for LNL problems by fostering both confidence and consistency." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 400, + 545, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 400, + 545, + 436 + ], + "spans": [ + { + "bbox": [ + 317, + 400, + 545, + 436 + ], + "type": "text", + "content": "- A novel sample-selection via confidence voting (SCV) strategy that generates reliable and ample clean samples for the subsequent training." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 437, + 545, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 437, + 545, + 518 + ], + "spans": [ + { + "bbox": [ + 317, + 437, + 545, + 518 + ], + "type": "text", + "content": "- Rank contrastive loss (RCL) based on the rank statistics of principal features that encourages consistency between hard samples of the same category. RCL can further benefit clean sample selection by promoting more discriminative features (see Fig. 1 in the supplementary material) for constructing intra-category clusters." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 531, + 392, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 531, + 392, + 544 + ], + "spans": [ + { + "bbox": [ + 306, + 531, + 392, + 544 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 552, + 545, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 552, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 305, + 552, + 545, + 575 + ], + "type": "text", + "content": "Most existing methods on LNL can be categorized into two directions: 1) loss correction and 2) sample selection." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Loss Correction. For loss correction, mainstream techniques [51, 46, 29, 47, 22] estimate noise transition matrix with a small set of clean samples as prior knowledge. However, estimating the noise transition matrix is challenging, and their assumptions may be too ideal to fit real-world scenarios. To rectify the noisy labels, another line of research proposes self-training architectures where noisy labels are replaced by network predictions [43, 56]. Some methods focus on the design of noisy-tolerant loss functions. For example, [2, 48, 13, 12] leverage bounded loss functions to improve their robustness to noisy labels. Besides, there are" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1645" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 80, + 78, + 519, + 201 + ], + "blocks": [ + { + "bbox": [ + 80, + 78, + 519, + 201 + ], + "lines": [ + { + "bbox": [ + 80, + 78, + 519, + 201 + ], + "spans": [ + { + "bbox": [ + 80, + 78, + 519, + 201 + ], + "type": "image", + "image_path": "78471bfa7668c0c88d787e59ef03525109ce850e44aeb845cb25c8173b776e88.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 215, + 545, + 299 + ], + "lines": [ + { + "bbox": [ + 46, + 215, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 545, + 299 + ], + "type": "text", + "content": "Figure 2: The training strategy of RankMatch. We use strong and weak augmentation to achieve consistency regularization in LNL. For the clean set, the given labels are used to regularize the network predictions on strongly augmented images via the supervised training loss " + }, + { + "bbox": [ + 46, + 215, + 545, + 299 + ], + "type": "inline_equation", + "content": "L_{c}" + }, + { + "bbox": [ + 46, + 215, + 545, + 299 + ], + "type": "text", + "content": ". For the noisy set, we first generate pseudo labels from the predictions on weakly augmented images and then use them to regularize the predictions on strongly augmented images via training loss " + }, + { + "bbox": [ + 46, + 215, + 545, + 299 + ], + "type": "inline_equation", + "content": "L_{n}" + }, + { + "bbox": [ + 46, + 215, + 545, + 299 + ], + "type": "text", + "content": ". Rank contrastive loss pulls similar samples together and pushes others away. The similarity matrix is defined by ranking feature channels instead of Euclidean distance. The final objective function is a joint loss, including a class diversity regularization term in addition." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 319, + 288, + 404 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 288, + 404 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 288, + 404 + ], + "type": "text", + "content": "some proposed unbiased loss function [35], information-based loss function called " + }, + { + "bbox": [ + 46, + 319, + 288, + 404 + ], + "type": "inline_equation", + "content": "L_{DMI}" + }, + { + "bbox": [ + 46, + 319, + 288, + 404 + ], + "type": "text", + "content": " [54], punishment regularization [32], confidence regularization [8], early learning regularization [30], contrastive representation regularization [28] and over-parameterized term [31]. However, it is arduous for loss-correction-based methods to play an advantage in practical scenarios facing high noise ratios." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 426, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 713 + ], + "type": "text", + "content": "Sample selection. Sample selection-based methods strive to reweight training samples and identify clean data to reduce the interference of noisy labels. Many existing methods propose introducing improved selection criteria to make the selected samples cleaner [23, 59, 3, 36, 24, 1]. Memorization effect [4] illuminates that DNNs learn clean and simple patterns faster than noisy labels, leading to a trend to consider small loss as a criterion for sample selection, which means that samples with smaller loss values are more likely to have clean labels. For instance, [3, 36, 24, 1] leverage clean data distribution as selection criterion by lower-loss component in mixture model fitted by per-sample loss. [55, 19] introduces JS-divergence between network prediction and labels as a selection criterion. [38] leverages the cross-entropy loss between disagreement distribution and labels as selection criterion. However, the loss value is just a scalar, contains limited information, and is prone to errors. For example, it is hard to distinguish between hard-to-learn clean samples and noisy samples after the warm-up stage since both have relatively large loss values. Besides, confirmation bias [44] is a common issue often encountered with the small-loss criterion. Once the noisy samples are wrongly grouped into the clean set by the small-loss criterion, their losses will keep small in the later train" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 319, + 545, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 545, + 487 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 545, + 487 + ], + "type": "text", + "content": "ing. It remains challenging to rectify the sample selection errors. Many methods mitigate this issue by training two networks [18, 34, 14, 57, 49, 24, 55]. But it is still a problem to get more accurate labels through the small-loss criterion. More recently, Confident Learning (CL) [37] proposes confident criterion as an alternative for sample selection. It computes a set of thresholds for every class and chooses confident samples whose network predicted highest probabilities are greater than the corresponding thresholds. However, CL directly estimates the noise transition matrix by confident samples, which is vulnerable to the network predictions and threshold setting. And it is prone to fail to perform well in large-scale cases and real-world scenarios with a high noise ratio." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": "Semi-supervised Learning. The Semi-supervised Learning (SSL) has seen fast progress by leveraging consistency regularization [41, 53, 5, 21, 39, 40, 45], which is used to minimize the difference in network prediction between two views of the same image. FixMatch [21] simply but effectively combines strong and weak augmentation in consistency regularization with confidently pseudo-labeling to achieve great success in semi-supervised learning setting. Most recently, [39] propose an uncertainty-aware pseudolabels selection (UPS) framework to improve pseudo labeling accuracy. RankingMatch [45] introduces a triplet loss, where the similarity between samples is measured by the L2-norm outputs. Furthermore, it is worth noting that the rank statistics of principal features can serve as a metric to measure the pairwise similarity among samples [15]. There are similarities between Learning with Noisy Labels (LNL) problems and semi-supervised learning setting." + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1646" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "In semi-supervised learning settings, confident predictions have strong connection with true labels as labeled data regularizing the unlabeled data, which are not easy to overconfident confused by noisy label. And leveraging confident predictions inevitably lacks sample diversity to make pseudo labels more reliable, while difficult samples always have uncertain predictions. Our approach finds a good balance of confidence, sample diversity and consistency." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 180, + 103, + 192 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 180, + 103, + 192 + ], + "spans": [ + { + "bbox": [ + 47, + 180, + 103, + 192 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 201, + 287, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 201, + 287, + 260 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 287, + 260 + ], + "type": "text", + "content": "Our method is introduced in three parts: the sample selection mechanism (Figure. 3), the consistency regularization and rank contrastive loss. Figure 2 shows the overview of RankMatch. The algorithm is included in the supplementary material." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "text", + "content": "Preliminaries. For the " + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "text", + "content": "-way image classification task with noisy labels, denoted by " + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = (\\mathcal{X}, \\widetilde{\\mathcal{Y}})" + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "text", + "content": " the training data, where " + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "text", + "content": " is training images, and " + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathcal{Y}}" + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "text", + "content": " is labels which may be wrongly annotated. We denote the DNNs in training stage as " + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "inline_equation", + "content": "P(F(\\mathbf{x}, \\theta))" + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^I" + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "text", + "content": " is the input image, " + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "inline_equation", + "content": "F: \\mathbb{R}^I \\to \\mathbb{R}^L" + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "text", + "content": " is the feature extractor where " + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "text", + "content": " stand for the dimension of input space and embedding space respectively, and " + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "inline_equation", + "content": "P: \\mathbb{R}^L \\to \\mathbb{R}^C" + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "text", + "content": " represents the classifier. " + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "text", + "content": " denotes the network parameters of the feature extractor. We use " + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_i" + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i" + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "text", + "content": " as simplified forms of " + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "inline_equation", + "content": "F(\\mathbf{x}_i, \\theta)" + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "inline_equation", + "content": "P(F(\\mathbf{x}_i, \\theta))" + }, + { + "bbox": [ + 46, + 261, + 288, + 395 + ], + "type": "text", + "content": " respectively." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 403, + 255, + 416 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 403, + 255, + 416 + ], + "spans": [ + { + "bbox": [ + 47, + 403, + 255, + 416 + ], + "type": "text", + "content": "3.1. Sample Selection via Confidence Voting" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 422, + 287, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 541 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 541 + ], + "type": "text", + "content": "For the sample selection, we leverage the advantage of confident learning [37] rather than the widely used small-loss criterion. We explore using a fixed confidence threshold to avoid the vulnerability of inaccurate network predictions. Figure 4 illustrates that confident predictions selected by a fixed high threshold are reliable but of a limited number. Hence, we propose a new sample selection strategy based on the confidence criterion that maintains reliability while ensuring sufficient confident samples across categories." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 547, + 287, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 547, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 547, + 287, + 643 + ], + "type": "text", + "content": "Confident Samples. In the setting of LNL, it is hard to select confident samples just by a single threshold when facing different levels of noise rates. Some classes are easy-to-learn, and one threshold for all classes is likely to result in class-unbalanced selection. In order to avoid data imbalance among classes, we select the top " + }, + { + "bbox": [ + 46, + 547, + 287, + 643 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 547, + 287, + 643 + ], + "type": "text", + "content": " basic confident samples " + }, + { + "bbox": [ + 46, + 547, + 287, + 643 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_b" + }, + { + "bbox": [ + 46, + 547, + 287, + 643 + ], + "type": "text", + "content": " in each class to ensure each class at least has " + }, + { + "bbox": [ + 46, + 547, + 287, + 643 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 547, + 287, + 643 + ], + "type": "text", + "content": " samples:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 110, + 644, + 287, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 644, + 287, + 670 + ], + "spans": [ + { + "bbox": [ + 110, + 644, + 287, + 670 + ], + "type": "interline_equation", + "content": "\\mathcal {I} _ {b} ^ {c} = \\underset {| \\hat {\\mathcal {X}} | = B, \\hat {\\mathcal {X}} \\subseteq \\mathcal {X}} {\\arg \\max } \\sum_ {\\mathbf {x} \\in \\hat {\\mathcal {X}}} \\mathbf {p} [ c ], \\tag {1}", + "image_path": "df2141ae3fb741fe92d40c4fac4afbf90e57eb372b5926cac18c45eff60fb9fc.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{p}[c]" + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": "-th element of " + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "= P(F(\\mathbf{x},\\theta))" + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": "), namely the probability value of the " + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": "-th class. And additional samples with prediction probability greater than a threshold as" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 326, + 76, + 526, + 205 + ], + "blocks": [ + { + "bbox": [ + 326, + 76, + 526, + 205 + ], + "lines": [ + { + "bbox": [ + 326, + 76, + 526, + 205 + ], + "spans": [ + { + "bbox": [ + 326, + 76, + 526, + 205 + ], + "type": "image", + "image_path": "7235a956e775513c21f6c228f280bd344eb80a7ebc64c02bda2cae3b67f428b3.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 213, + 547, + 284 + ], + "lines": [ + { + "bbox": [ + 304, + 213, + 547, + 284 + ], + "spans": [ + { + "bbox": [ + 304, + 213, + 547, + 284 + ], + "type": "text", + "content": "Figure 3: Sample-selection via Confidence Voting (SCV) module. We first select the most representative confident samples. Then, the selected confident samples generate prototypes as voting candidates. For each sample, its " + }, + { + "bbox": [ + 304, + 213, + 547, + 284 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 213, + 547, + 284 + ], + "type": "text", + "content": " nearest prototypes are regarded as voters to identify whether the label is clean." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 308, + 432, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 308, + 432, + 319 + ], + "spans": [ + { + "bbox": [ + 306, + 308, + 432, + 319 + ], + "type": "text", + "content": "the reliable confident samples:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 364, + 332, + 545, + 345 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 332, + 545, + 345 + ], + "spans": [ + { + "bbox": [ + 364, + 332, + 545, + 345 + ], + "type": "interline_equation", + "content": "\\mathcal {I} _ {r} ^ {c} = \\left\\{\\mathbf {x} _ {i} \\mid \\mathbf {p} _ {i} [ c ] > \\tau , \\mathbf {x} _ {i} \\in \\mathcal {X} \\right\\}, \\tag {2}", + "image_path": "4ee40a696d77c2dc36d0d39697461acfed9d0b69cf15682b7d82629fa19a56a2.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 357, + 545, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 357, + 545, + 381 + ], + "spans": [ + { + "bbox": [ + 305, + 357, + 545, + 381 + ], + "type": "text", + "content": "The final selected confident samples is the union of the two sets " + }, + { + "bbox": [ + 305, + 357, + 545, + 381 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^c = \\mathcal{I}_b^c\\cup \\mathcal{I}_r^c" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 387, + 546, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 387, + 546, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 546, + 495 + ], + "type": "text", + "content": "Confident Prototype Generation. To guarantee the quality of the confident samples, we set high threshold " + }, + { + "bbox": [ + 304, + 387, + 546, + 495 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 387, + 546, + 495 + ], + "type": "text", + "content": " and small portion " + }, + { + "bbox": [ + 304, + 387, + 546, + 495 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 387, + 546, + 495 + ], + "type": "text", + "content": ", but face the problem of low sample quantity. Although with a small number, the reliable representations of confident samples reflect some common intra-class patterns. Thus, we generate representation prototypes using the selected samples for further selection. Straightforwardly, a representative feature can be generated by averaging features of confident samples for each class:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 376, + 505, + 545, + 534 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 505, + 545, + 534 + ], + "spans": [ + { + "bbox": [ + 376, + 505, + 545, + 534 + ], + "type": "interline_equation", + "content": "\\phi^ {c} = \\frac {1}{| \\mathcal {I} ^ {c} |} \\sum_ {\\mathbf {x} \\in \\mathcal {I} ^ {c}} F (\\mathbf {x}, \\theta). \\tag {3}", + "image_path": "2733e0224a0f8ae1744f552edb54b9b1dbf2a1037977ff6863f23e6c96cb0d44.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 544, + 546, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 546, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 546, + 689 + ], + "type": "text", + "content": "Even if the confident samples include some noise during the early training stage, the prototype generation process will predominantly rely on the most clean samples, rendering it robust to noisy labels. However, the mean vector is unable to represent a class with large intra-class variations. We further diversify the intra-class patterns by generating more prototypes of each class. Specifically, we split the confident samples into " + }, + { + "bbox": [ + 304, + 544, + 546, + 689 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 544, + 546, + 689 + ], + "type": "text", + "content": " clusters for each class by " + }, + { + "bbox": [ + 304, + 544, + 546, + 689 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 544, + 546, + 689 + ], + "type": "text", + "content": "-means. For the " + }, + { + "bbox": [ + 304, + 544, + 546, + 689 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 544, + 546, + 689 + ], + "type": "text", + "content": "-th class, we define the average centers of the obtained clusters features as " + }, + { + "bbox": [ + 304, + 544, + 546, + 689 + ], + "type": "inline_equation", + "content": "\\Phi^c = \\{\\phi_j^c\\}_{j=1}^K" + }, + { + "bbox": [ + 304, + 544, + 546, + 689 + ], + "type": "text", + "content": ". Our sample-selection module is based on the generated confident prototypes " + }, + { + "bbox": [ + 304, + 544, + 546, + 689 + ], + "type": "inline_equation", + "content": "\\Phi (= \\bigcup_{c=1}^{C} \\Phi^c)" + }, + { + "bbox": [ + 304, + 544, + 546, + 689 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "Data Segmentation by Confidence Voting. After obtaining " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "C \\times K" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " prototypes, we first find the " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " nearest prototypes" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1647" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 209, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 209, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 209, + 83 + ], + "type": "text", + "content": "of " + }, + { + "bbox": [ + 47, + 72, + 209, + 83 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 47, + 72, + 209, + 83 + ], + "type": "text", + "content": " measured by the cosine similarity:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 103, + 95, + 287, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 103, + 95, + 287, + 121 + ], + "spans": [ + { + "bbox": [ + 103, + 95, + 287, + 121 + ], + "type": "interline_equation", + "content": "\\mathcal {V} _ {i} = \\underset {| \\hat {\\Phi} | = k, \\hat {\\Phi} \\subseteq \\Phi} {\\arg \\max } \\sum_ {\\phi \\in \\hat {\\Phi}} \\cos (\\mathbf {f} _ {i}, \\phi). \\tag {4}", + "image_path": "e378655cbfe30fc7bc239a3e397533eab08ca9fa07d8e11c413fa70451a4aaae.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 132, + 287, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 132, + 287, + 180 + ], + "spans": [ + { + "bbox": [ + 47, + 132, + 287, + 180 + ], + "type": "text", + "content": "The class label to which the most prototypes belong in " + }, + { + "bbox": [ + 47, + 132, + 287, + 180 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_i" + }, + { + "bbox": [ + 47, + 132, + 287, + 180 + ], + "type": "text", + "content": " is considered as the voting result " + }, + { + "bbox": [ + 47, + 132, + 287, + 180 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i'" + }, + { + "bbox": [ + 47, + 132, + 287, + 180 + ], + "type": "text", + "content": ". Clean samples " + }, + { + "bbox": [ + 47, + 132, + 287, + 180 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{cln}}" + }, + { + "bbox": [ + 47, + 132, + 287, + 180 + ], + "type": "text", + "content": " are identified by checking whether " + }, + { + "bbox": [ + 47, + 132, + 287, + 180 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i'" + }, + { + "bbox": [ + 47, + 132, + 287, + 180 + ], + "type": "text", + "content": " is consistent with the provided label " + }, + { + "bbox": [ + 47, + 132, + 287, + 180 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{y}}_i" + }, + { + "bbox": [ + 47, + 132, + 287, + 180 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 84, + 190, + 287, + 205 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 190, + 287, + 205 + ], + "spans": [ + { + "bbox": [ + 84, + 190, + 287, + 205 + ], + "type": "interline_equation", + "content": "\\mathcal {D} _ {\\mathrm {c l n}} = \\left\\{\\left(\\mathbf {x} _ {i}, \\widetilde {\\mathbf {y}} _ {i}\\right) \\mid \\widetilde {\\mathbf {y}} _ {i} = \\mathbf {y} _ {i} ^ {\\prime}, \\forall \\left(\\mathbf {x} _ {i}, \\widetilde {\\mathbf {y}} _ {i}\\right) \\in \\mathcal {D} \\right\\}, \\tag {5}", + "image_path": "885bc153aa50fcaff80fe03899690d3f81802a035e5e9986dec60ab975531efc.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 214, + 226, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 214, + 226, + 227 + ], + "spans": [ + { + "bbox": [ + 47, + 214, + 226, + 227 + ], + "type": "text", + "content": "The remaining noisy set is " + }, + { + "bbox": [ + 47, + 214, + 226, + 227 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{nsy}} = \\mathcal{D}\\setminus \\mathcal{D}_{\\mathrm{cln}}" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 235, + 198, + 248 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 235, + 198, + 248 + ], + "spans": [ + { + "bbox": [ + 47, + 235, + 198, + 248 + ], + "type": "text", + "content": "3.2. Consistency Regularization" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 254, + 287, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 254, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 254, + 287, + 409 + ], + "type": "text", + "content": "This paper argues that noisy labels lead to inconsistent predictions (Figure 1). To enhance the consistency of the predictions augmented from the same image, we apply two different augmentation methods to generate two views for training images, including \"weak\" augmentation " + }, + { + "bbox": [ + 46, + 254, + 287, + 409 + ], + "type": "inline_equation", + "content": "(\\mathcal{A}_w)" + }, + { + "bbox": [ + 46, + 254, + 287, + 409 + ], + "type": "text", + "content": " and \"strong\" augmentation " + }, + { + "bbox": [ + 46, + 254, + 287, + 409 + ], + "type": "inline_equation", + "content": "(\\mathcal{A}_s)" + }, + { + "bbox": [ + 46, + 254, + 287, + 409 + ], + "type": "text", + "content": ". Weak augmentation refers to random cropping and flipping, while strong augmentation refers to AutoAugment [9], which uses reinforcement learning to find augmentation strategies automatically and requires labeled data to learn. Note that our sample selection mechanism provides cleaner supervision signals, benefiting AutoAugment to accept a more effective augmentation policy." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 410, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 410, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 410, + 287, + 491 + ], + "type": "text", + "content": "Following [21], we transfer the training image " + }, + { + "bbox": [ + 47, + 410, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 47, + 410, + 287, + 491 + ], + "type": "text", + "content": " with the two augmentation strategies, resulting in two views: " + }, + { + "bbox": [ + 47, + 410, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{v}^w = \\mathcal{A}_w(\\mathbf{x})" + }, + { + "bbox": [ + 47, + 410, + 287, + 491 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 410, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{v}^s = \\mathcal{A}_s(\\mathbf{x})" + }, + { + "bbox": [ + 47, + 410, + 287, + 491 + ], + "type": "text", + "content": ". The corresponding network predictions are denoted as " + }, + { + "bbox": [ + 47, + 410, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{p}^w" + }, + { + "bbox": [ + 47, + 410, + 287, + 491 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 410, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{p}^s" + }, + { + "bbox": [ + 47, + 410, + 287, + 491 + ], + "type": "text", + "content": ", respectively. Given that the semantic information of the augmented images is not modified, we assume the two network predictions to be consistent." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 494, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 494, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 47, + 494, + 287, + 529 + ], + "type": "text", + "content": "For clean samples, we direct use cross-entropy loss between predictions on strongly augmented images and the original labels:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 93, + 540, + 287, + 570 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 540, + 287, + 570 + ], + "spans": [ + { + "bbox": [ + 93, + 540, + 287, + 570 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c} = - \\frac {1}{| \\mathcal {D} _ {\\mathrm {c l n}} |} \\sum_ {(\\mathbf {x}, \\widetilde {\\mathbf {y}}) \\in \\mathcal {D} _ {\\mathrm {c l n}}} \\widetilde {\\mathbf {y}} \\circ \\log (\\mathbf {p} ^ {s}), \\tag {6}", + "image_path": "fc96eb42ac2deca2c7327d19cc4530fb23114bd0b0054e508a9e0889ad11c633.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 579, + 188, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 579, + 188, + 591 + ], + "spans": [ + { + "bbox": [ + 47, + 579, + 188, + 591 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 579, + 188, + 591 + ], + "type": "inline_equation", + "content": "\\circ" + }, + { + "bbox": [ + 47, + 579, + 188, + 591 + ], + "type": "text", + "content": " denotes the inner product." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 592, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 592, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 592, + 287, + 628 + ], + "type": "text", + "content": "For noisy samples with high prediction confidence, we rectify their labels with predictions of weakly augmented images:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 53, + 637, + 287, + 665 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 637, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 53, + 637, + 287, + 665 + ], + "type": "interline_equation", + "content": "\\hat {\\mathcal {D}} _ {\\mathrm {n s y}} = \\left\\{\\left(\\mathbf {x} _ {i}, \\hat {\\mathbf {y}} _ {i}\\right) | \\forall \\mathbf {x} _ {i} \\in \\mathcal {X} _ {\\mathrm {n s y}}, \\max _ {c} \\left\\{\\mathbf {p} ^ {w} [ c ] \\right\\} > \\nu , \\hat {\\mathbf {y}} _ {i} = c \\right\\}, \\tag {7}", + "image_path": "b6e63b816b26bfafd111275832cfd5e3949afc212ef0268e68abaeeddf58d876.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 666, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 666, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 666, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 666, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 47, + 666, + 287, + 714 + ], + "type": "text", + "content": " is the confidence threshold, we set it the same as that in Eq. 2 to avoid introducing another parameter. Inspired by [21], the cross entropy losses between the predictions of weakly and strongly augmented images are" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "employed as regularizing consistency for the CNN model learning:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 350, + 110, + 545, + 143 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 110, + 545, + 143 + ], + "spans": [ + { + "bbox": [ + 350, + 110, + 545, + 143 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {n} = - \\frac {1}{| \\hat {\\mathcal {D}} _ {\\mathrm {n s y}} |} \\sum_ {(\\mathbf {x}, \\hat {\\mathbf {y}}) \\in \\hat {\\mathcal {D}} _ {\\mathrm {n s y}}} \\hat {\\mathbf {y}} \\circ \\log \\left(\\mathbf {p} ^ {s}\\right). \\tag {8}", + "image_path": "6fdab218da7ea0a36072152832d133d6e303c5594f323222b5eac6a146ee4e90.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 160, + 435, + 172 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 160, + 435, + 172 + ], + "spans": [ + { + "bbox": [ + 306, + 160, + 435, + 172 + ], + "type": "text", + "content": "3.3. Rank Contrastive Loss" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 182, + 545, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 182, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 545, + 277 + ], + "type": "text", + "content": "Robust representations can benefit our samples selection strategy. However, some valuable information is excluded by Eq. 7 and Eq. 8 since the hard-to-learn noisy samples have less confident predictions and thus can not be optimized. To obtain complete and robust representations, we propose a rank contrastive loss (RCL) to strengthen the consistency of the \"similar\" samples while pushing \"dissimilar\" ones further." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 281, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 545, + 449 + ], + "type": "text", + "content": "The widely used " + }, + { + "bbox": [ + 304, + 281, + 545, + 449 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 304, + 281, + 545, + 449 + ], + "type": "text", + "content": " distance as the similarity metric is less robust in LNL, as overfitting to noisy labels tends to introduce spurious close euclidean distance. Every convolution kernel filters out certain kinds of attributes in the input image. Similar visual patterns are prone to activate the same representation channel of response maps produced by convolution layers. Hence, the indices of feature elements rank ordered in accordance with their magnitudes, can serve as a metric for assessing the pairwise representations similarity [15]. Although noisy labels affect the feature value, we leverage rank statistics of principal features to estimate the similarity matrix. Specifically, we rank the values in all channels of " + }, + { + "bbox": [ + 304, + 281, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_i" + }, + { + "bbox": [ + 304, + 281, + 545, + 449 + ], + "type": "text", + "content": " and regard the " + }, + { + "bbox": [ + 304, + 281, + 545, + 449 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 281, + 545, + 449 + ], + "type": "text", + "content": " channels with the largest activation values as the principal feature dimensions," + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 353, + 463, + 545, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 463, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 353, + 463, + 545, + 491 + ], + "type": "interline_equation", + "content": "\\mathcal {R} _ {i} = \\underset {| \\hat {\\mathcal {R}} | = r, \\hat {\\mathcal {R}} \\subset \\{1, 2, \\dots , L \\}} {\\arg \\max } \\sum_ {n \\in \\hat {\\mathcal {R}}} \\mathbf {f} _ {i} [ n ], \\tag {9}", + "image_path": "c8d63347c921dd83834218952a385c8cde7f08c2b2443fff76827d86c6dc50d5.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "spans": [ + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_i[n]" + }, + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "type": "text", + "content": " denote the " + }, + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "type": "text", + "content": "-th channel of feature " + }, + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_i" + }, + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "type": "text", + "content": ". If two samples " + }, + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_j" + }, + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "type": "text", + "content": " share the same principal feature dimensions, we assume they are \"similar\". The similarity " + }, + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "type": "inline_equation", + "content": "s_{ij}" + }, + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "type": "text", + "content": " between " + }, + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_j" + }, + { + "bbox": [ + 305, + 505, + 545, + 554 + ], + "type": "text", + "content": " is evaluated as follows," + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 369, + 568, + 545, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 568, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 369, + 568, + 545, + 601 + ], + "type": "interline_equation", + "content": "s _ {i j} = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\mathcal {R} _ {i} = \\mathcal {R} _ {j}; \\\\ 0 & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {10}", + "image_path": "d7ea2824be688471cb26fa1237de14344dbc4e6b34d7044f311ee9b40dc0f50c.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 618, + 544, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 618, + 544, + 642 + ], + "spans": [ + { + "bbox": [ + 306, + 618, + 544, + 642 + ], + "type": "text", + "content": "To achieve clustering in the feature space, we adopt the following binary cross-entropy loss as:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 657, + 560, + 700 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 657, + 560, + 700 + ], + "spans": [ + { + "bbox": [ + 306, + 657, + 560, + 700 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {R C L}} = - \\frac {1}{N ^ {2}} \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {N} \\left[ s _ {i j} \\log \\left(\\mathbf {p} _ {i} \\circ \\mathbf {q} _ {j}\\right) + \\left(1 - s _ {i j}\\right) \\log \\left(1 - \\mathbf {p} _ {i} \\circ \\mathbf {q} _ {j}\\right) \\right], \\tag {11}", + "image_path": "868cd85fb132b8fcac19eeabc762e0dd22e33522a876257f184fd304b510f434.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i = P(F(\\mathbf{v}_i^w,\\theta))" + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_i = P(F(\\mathbf{v}_i^s,\\theta))" + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": ". The train-" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1648" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 229, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 229, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 229, + 84 + ], + "type": "text", + "content": "ing loss " + }, + { + "bbox": [ + 47, + 72, + 229, + 84 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{RCL}}" + }, + { + "bbox": [ + 47, + 72, + 229, + 84 + ], + "type": "text", + "content": " can be divided into two terms:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 155, + 94, + 232, + 103 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 155, + 94, + 232, + 103 + ], + "spans": [ + { + "bbox": [ + 155, + 94, + 232, + 103 + ], + "type": "text", + "content": "Consistency regularization" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 110, + 304, + 188 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 110, + 304, + 188 + ], + "spans": [ + { + "bbox": [ + 49, + 110, + 304, + 188 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {R C L}} = - \\frac {1}{N ^ {2}} \\sum_ {i = 1} ^ {N} \\left[ s _ {i i} \\log \\left(\\mathbf {p} _ {i} \\circ \\mathbf {q} _ {i}\\right) + \\left(1 - s _ {i i}\\right) \\log \\left(1 - \\mathbf {p} _ {i} \\circ \\mathbf {q} _ {i}\\right) \\right] \\\\ - \\frac {1}{N ^ {2}} \\sum_ {i = 1} ^ {N} \\sum_ {j \\neq i} [ s _ {i j} \\log (\\mathbf {p} _ {i} \\circ \\mathbf {q} _ {j}) + (1 - s _ {i j}) \\log (1 - \\mathbf {p} _ {i} \\circ \\mathbf {q} _ {j}) ]. \\tag {12} \\\\ \\end{array}", + "image_path": "ab31c258f1ffc0d3efa5111fbde44582fd988bc8d6916093d3cda37b76a716cf.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 189, + 264, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 189, + 264, + 201 + ], + "spans": [ + { + "bbox": [ + 47, + 189, + 264, + 201 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 47, + 189, + 264, + 201 + ], + "type": "inline_equation", + "content": "s_{ii} = 1" + }, + { + "bbox": [ + 47, + 189, + 264, + 201 + ], + "type": "text", + "content": " always holds, organize the first term as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 210, + 287, + 243 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 210, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 58, + 210, + 287, + 243 + ], + "type": "interline_equation", + "content": "- \\frac {1}{N ^ {2}} \\sum_ {i = 1} ^ {N} \\log \\left(\\mathbf {p} _ {i} \\circ \\mathbf {q} _ {i}\\right) = - \\frac {1}{N ^ {2}} \\sum_ {i = 1} ^ {N} \\log \\left(\\mathbf {p} _ {i} ^ {w} \\circ \\mathbf {p} _ {i} ^ {s}\\right). \\tag {13}", + "image_path": "8d7171c2cf95ac361511b6af920747cdbcbb6ee0d54c2ebb71d1740d9fab3f08.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 252, + 287, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 252, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 47, + 252, + 287, + 326 + ], + "type": "text", + "content": "Minimizing this term is equal to " + }, + { + "bbox": [ + 47, + 252, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\max \\{\\mathbf{p}_i^w\\circ \\mathbf{p}_i^s\\}" + }, + { + "bbox": [ + 47, + 252, + 287, + 326 + ], + "type": "text", + "content": ", which pulls the outputs of strongly and weakly augmented images closer. Thus, " + }, + { + "bbox": [ + 47, + 252, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{RCL}}" + }, + { + "bbox": [ + 47, + 252, + 287, + 326 + ], + "type": "text", + "content": " in the diagonal of " + }, + { + "bbox": [ + 47, + 252, + 287, + 326 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 252, + 287, + 326 + ], + "type": "text", + "content": " can be regarded as consistency regularization. Even in the early training stage, " + }, + { + "bbox": [ + 47, + 252, + 287, + 326 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 252, + 287, + 326 + ], + "type": "text", + "content": " is the identity matrix that removes the second term in Eq. 12, improving the network representation ability." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 333, + 174, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 333, + 174, + 344 + ], + "spans": [ + { + "bbox": [ + 47, + 333, + 174, + 344 + ], + "type": "text", + "content": "3.4. Overall Loss Function" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 352, + 287, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 352, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 47, + 352, + 287, + 388 + ], + "type": "text", + "content": "Following [43, 24, 3], we apply the fair class diversity-promoting regularization " + }, + { + "bbox": [ + 47, + 352, + 287, + 388 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{div}" + }, + { + "bbox": [ + 47, + 352, + 287, + 388 + ], + "type": "text", + "content": " to prevent assigning most samples into few classes:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 86, + 397, + 287, + 430 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 397, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 86, + 397, + 287, + 430 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d i v} = \\sum_ {c = 1} ^ {C} \\frac {1}{C} \\log \\left(\\frac {1}{C} / \\frac {\\sum_ {i = 1} ^ {N} \\mathbf {p} _ {i} ^ {w} [ c ]}{N}\\right). \\tag {14}", + "image_path": "0a256be5d3b9e4c6ffe68280ee46956b26800f528770f6252c46b2563ae206ef.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 439, + 287, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 439, + 287, + 461 + ], + "spans": [ + { + "bbox": [ + 47, + 439, + 287, + 461 + ], + "type": "text", + "content": "The overall loss function for network optimization is as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 99, + 464, + 287, + 476 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 464, + 287, + 476 + ], + "spans": [ + { + "bbox": [ + 99, + 464, + 287, + 476 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {c} + \\lambda_ {n} \\mathcal {L} _ {n} + \\mathcal {L} _ {\\mathrm {R C L}} + \\mathcal {L} _ {\\text {d i v}}. \\tag {15}", + "image_path": "56e5f59c741dc0d061e9724e6bad975e8bfb8371dface89bfa8cb5497a3644f5.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 483, + 287, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 483, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 47, + 483, + 287, + 520 + ], + "type": "text", + "content": "We following [24, 14, 57, 36] to train two networks to combat the confirmation bias, detailed algorithm is included in supplementary material." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 531, + 128, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 531, + 128, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 531, + 128, + 544 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 551, + 163, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 551, + 163, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 551, + 163, + 563 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "content": "We evaluate the proposed RankMatch on CIFAR-10, CIFAR-100 [20], as well as the real-world datasets Clothing1M [52] and WebVision [27]. Both CIFAR-10 and CIFAR-100 contain 50,000 training images and 10,000 test images of size " + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "content": ". Following previous works [43, 25], we conduct experiments requiring noise augmentation, either symmetric or asymmetric [43, 25] label noise injection. We follow the identical implementation of generating symmetric and asymmetric noises on CIFAR datasets with DivideMix [24]. Symmetric noise is generated by randomly replacing the labels for a percentage of the training data with all possible labels. Asymmetric noise is to mimic the" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "structure of real-world label noise, where labels are only replaced by similar classes (e.g. deer " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": " horse, dog " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\leftrightarrow" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": " cat). We adopt 18-layer PreAct Resnet [17] as the backbone. During training, we train DNNs for 300 epochs using SGD optimizer with a momentum of 0.9, with weight decay of 0.0005 for CIFAR-10 and 0.001 for CIFAR-100. The batch size is 64 for CIFAR-10 and 128 for CIFAR-100. We set the initial learning rate as 0.02 and reduce it by a factor of 10 after 150 epochs. The warm-up period is 10 epochs for CIFAR-10 and 30 epochs for CIFAR-100, respectively. For all CIFAR experiments, we set " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\tau = 0.95" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "r = 5" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": ", and choose " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\lambda_{n}" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\{0.2, 0.5, 1, 2, 10, 15\\}" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": " for a small validation test. More experimental details are in supplementary materials." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 228, + 545, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 337 + ], + "type": "text", + "content": "Clothing1M contains 1 million real-world shopping images belonging to 14 classes. We use ResNet-50 [16] with weights pretrained on ImageNet as the classification model. WebVision consists of web-crawled images with the same concepts from ImageNet ILSVRC12 [10]. We follow the previous work [24, 7] and compare baseline methods on the first 50 classes of the Google image subset using the inception-resnet v2 [42]. The training details are delineated in supplementary materials." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 346, + 429, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 346, + 429, + 358 + ], + "spans": [ + { + "bbox": [ + 306, + 346, + 429, + 358 + ], + "type": "text", + "content": "4.2. Experimental Results" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "type": "text", + "content": "Results on CIFAR. Table 1 illuminates RankMatch outperforms the state-of-the-art models across most noisy levels. RRL [26] combats noisy labels by learning robust representations and slightly outperforms our method on CIFAR-10 with " + }, + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "type": "text", + "content": " symmetric label noise. One possible explanation is that the massive clean labels make it easy to rectify the symmetric label noise. Thus, the sample selection strategy is less effective in this scenario but shows great advantages for a high noise ratio and real-world dataset. Benefiting from the advanced confidence sample selection mechanism, RankMatch boosts the averaged test accuracy of the last ten epochs from " + }, + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "type": "inline_equation", + "content": "77.4\\%" + }, + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "type": "inline_equation", + "content": "92.1\\%" + }, + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "type": "text", + "content": " on CIFAR-10 and " + }, + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "type": "inline_equation", + "content": "33.1\\%" + }, + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "type": "inline_equation", + "content": "49.9\\%" + }, + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "type": "text", + "content": " on CIFAR-100 under the extreme case of " + }, + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "type": "text", + "content": " noise. Even without MixMatch [6] technique, RankMatch achieves around 20 points improvement (50.6% vs. " + }, + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "type": "inline_equation", + "content": "31.5\\%" + }, + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "type": "text", + "content": ") compared to DivideMix [24] on CIFAR-100 with " + }, + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 304, + 365, + 545, + 604 + ], + "type": "text", + "content": " noisy labels. We surpass CTRR [28], the most recent contrastive learning-based method, under all noise ratios, especially on the more challenging CIFAR-100 dataset." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Results on real-world dataset. Table 2 and Table 3 demonstrate the results on Clothing1M and WebVision, respectively. Our method outperforms all the alternative methods in both noisy real-world datasets. We achieve the improvement of " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "0.18\\%" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " over SFT [50], the most recent sample selection-based method with MixMatch [6]. Besides, the most recent baseline UNICON [19] well combines the advantages of semi-supervised learning (DivideMix-like) and contrastive learning (RRL-like) and achieves great per" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1649" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 115, + 70, + 479, + 283 + ], + "blocks": [ + { + "bbox": [ + 115, + 70, + 479, + 283 + ], + "lines": [ + { + "bbox": [ + 115, + 70, + 479, + 283 + ], + "spans": [ + { + "bbox": [ + 115, + 70, + 479, + 283 + ], + "type": "table", + "html": "
DatasetCIFAR-10CIFAR-100
Method/Noise ratio20%50%80%90%Asym. 40%20%50%80%90%
Cross-EntropyBest86.879.462.942.785.062.046.719.910.1
Last82.757.926.116.872.361.837.38.83.5
PENCILBest92.489.177.558.988.569.457.531.115.3
[56]Last92.088.776.558.288.168.156.420.78.8
Meta-LearningBest92.989.377.458.789.268.559.242.419.5
[25]Last92.088.876.158.388.467.758.040.114.3
DivideMixBest96.194.693.276.093.477.374.660.231.5
[24]Last95.794.492.975.492.176.974.259.631.0
ELR [30]Best95.894.893.378.793.077.673.660.833.4
MOIT [38]Best94.191.175.870.193.275.970.151.424.5
RRL [26]Last96.495.393.377.493.380.376.061.133.1
CTRR [28]Best93.3-86.784.389.070.1-43.7-
RankMatchBest96.595.694.592.694.779.577.967.650.6
Last96.495.494.292.194.479.377.667.249.9
", + "image_path": "2f197df8d09c5803860e8c13465f02446770bc2573a1ac235e01fca00c4c6e08.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 94, + 346, + 241, + 483 + ], + "blocks": [ + { + "bbox": [ + 46, + 290, + 547, + 327 + ], + "lines": [ + { + "bbox": [ + 46, + 290, + 547, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 547, + 327 + ], + "type": "text", + "content": "Table 1: Comparison between RankMatch and state-of-the-art methods on CIFAR-10 and CIFAR-100 under symmetric and asymmetric noise. \"Best\" refers to the best test accuracy across all epochs and \"Last\" is the averaged test accuracy over the last 10 epochs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 94, + 346, + 241, + 483 + ], + "lines": [ + { + "bbox": [ + 94, + 346, + 241, + 483 + ], + "spans": [ + { + "bbox": [ + 94, + 346, + 241, + 483 + ], + "type": "table", + "html": "
MethodTest Accuracy
Cross-Entropy69.21
PENCIL [56]73.49
DivideMix [24]74.76
RRL [26]74.97
DSOS [1]73.63
UNICON [19]74.98
SOP [31]73.50
SFT [50]75.08
RankMatch75.22
", + "image_path": "e1986ed7b1f0abd51b3a950aeebbc5f644410e4e6e68d732ae09c1d8a6cf085c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 552, + 287, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 287, + 636 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 287, + 636 + ], + "type": "text", + "content": "formance gain. In particular, RankMatch achieves " + }, + { + "bbox": [ + 46, + 552, + 287, + 636 + ], + "type": "inline_equation", + "content": "0.24\\%" + }, + { + "bbox": [ + 46, + 552, + 287, + 636 + ], + "type": "text", + "content": " performance gain over UNICON on the challenging Clothing1M dataset. Moreover, RankMatch obtain over " + }, + { + "bbox": [ + 46, + 552, + 287, + 636 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 46, + 552, + 287, + 636 + ], + "type": "text", + "content": " Top-1 accuracy improvement over state-of-the-art on both mini-WebVison and ILSVRC12 validation sets, and guarantees state-of-the-art Top-5 accuracy on WebVision and ILSVRC12, indicating the effectiveness of our approach." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 646, + 141, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 646, + 141, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 646, + 141, + 659 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "The role of confidence in LNL. To explore the role of the fixed confidence threshold in the LNL setting, we focus on the relationship between confident predictions and ground-truth labels. Specifically, we directly train DNNs" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 322, + 346, + 531, + 490 + ], + "blocks": [ + { + "bbox": [ + 46, + 492, + 288, + 529 + ], + "lines": [ + { + "bbox": [ + 46, + 492, + 288, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 492, + 288, + 529 + ], + "type": "text", + "content": "Table 2: Comparison with state-of-the-art methods on Clothing1M. Baseline results are copied from original papers." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 322, + 346, + 531, + 490 + ], + "lines": [ + { + "bbox": [ + 322, + 346, + 531, + 490 + ], + "spans": [ + { + "bbox": [ + 322, + 346, + 531, + 490 + ], + "type": "table", + "html": "
MethodWebVisionILSVRC12
top1top5top1top5
MentorNet [18]63.0081.4057.8079.92
Co-teaching [14]63.5885.2061.4884.70
Iterative-CV [7]65.2485.3461.6084.98
DivideMix [24]77.3291.6475.2090.84
RRL [26]77.891.374.490.9
DSOS [1]77.7692.0474.3690.80
SOP [31]76.6-69.1-
UNICON [19]77.6093.4475.2993.72
RankMatch79.9193.6177.3994.26
", + "image_path": "148f39659e2b52a154820c65694b1b25353a58beb65760d5b3374293a15f40a8.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 498, + 547, + 559 + ], + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 559 + ], + "type": "text", + "content": "Table 3: Comparison with state-of-the-art methods on (mini) WebVision dataset. Numbers denote top-1 (top-5) accuracy (\\%) on the WebVision and ImageNet ILSVRC12 validation set. Results for baselines are copied from the corresponding papers." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 580, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 545, + 616 + ], + "type": "text", + "content": "for classification on CIFAR-10 under different noise levels and record the following statistics: confident ratio, precision, and recall of confident predictions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 617, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 546, + 715 + ], + "type": "text", + "content": "From the results shown in Figure 4, we discover the following empirical rules: (1) Confident ratio and recall increase in the same trend, while precision continues to decrease, indicating that the process of overfitting to noise label can regard as the process of overconfidence. (2) The precision of confident samples maintains a high level at the early stage, which means that confident predictions selected by the high threshold are reliable after the warm-up stage." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1650" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 99, + 71, + 232, + 183 + ], + "blocks": [ + { + "bbox": [ + 99, + 71, + 232, + 183 + ], + "lines": [ + { + "bbox": [ + 99, + 71, + 232, + 183 + ], + "spans": [ + { + "bbox": [ + 99, + 71, + 232, + 183 + ], + "type": "image", + "image_path": "c91a9a04d13e0ab69939dae5f09f97e3cd7c3ad8932709c34b6ecd81f7050ead.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 195, + 545, + 266 + ], + "lines": [ + { + "bbox": [ + 45, + 195, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 45, + 195, + 545, + 266 + ], + "type": "text", + "content": "Figure 4: Some key statistics of confident samples on CIFAR-10. The confident samples are selected via the fixed confidence threshold. (a) Precision, ratio of correctly predicted samples in confident samples, maintains a high level (close to " + }, + { + "bbox": [ + 45, + 195, + 545, + 266 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 45, + 195, + 545, + 266 + ], + "type": "text", + "content": ") at the early stage, but continues to decline afterwards. Under Symmetry-50% noise, there is no confident samples in the early period. Hence, we record the precision after 30 epochs. (b) Recall, ratio of confident samples in correct prediction samples, maintains a low level in early stage, and gradually rises to high level. (c) Confidence ratio, ratio of confident samples in training set, has the same trend with Recall." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 235, + 70, + 362, + 184 + ], + "blocks": [ + { + "bbox": [ + 235, + 70, + 362, + 184 + ], + "lines": [ + { + "bbox": [ + 235, + 70, + 362, + 184 + ], + "spans": [ + { + "bbox": [ + 235, + 70, + 362, + 184 + ], + "type": "image", + "image_path": "4e1f1e396dbb468b4e7b8a9bbcee66386f12cadd6f7051de0fd87c03f810e769.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 366, + 71, + 496, + 184 + ], + "blocks": [ + { + "bbox": [ + 366, + 71, + 496, + 184 + ], + "lines": [ + { + "bbox": [ + 366, + 71, + 496, + 184 + ], + "spans": [ + { + "bbox": [ + 366, + 71, + 496, + 184 + ], + "type": "image", + "image_path": "434620fcf9d79988be07d26af3c457387b557f464e23182bd8c006ce8d9664c4.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 99, + 279, + 200, + 373 + ], + "blocks": [ + { + "bbox": [ + 99, + 279, + 200, + 373 + ], + "lines": [ + { + "bbox": [ + 99, + 279, + 200, + 373 + ], + "spans": [ + { + "bbox": [ + 99, + 279, + 200, + 373 + ], + "type": "image", + "image_path": "14094a8e410d55d4d9855dc07781864819c12ae2392189ccd081b0c31c06da49.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 384, + 545, + 444 + ], + "lines": [ + { + "bbox": [ + 45, + 384, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 45, + 384, + 545, + 444 + ], + "type": "text", + "content": "Figure 5: Accuracy " + }, + { + "bbox": [ + 45, + 384, + 545, + 444 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 45, + 384, + 545, + 444 + ], + "type": "text", + "content": " of the selected clean samples under different symmetric noise rates on CIFAR-100 datasets. Our full method RankMatch is compared with two baselines. One is DivideMix, denoted as GMM and MixMatch. The other is replacing GMM with our proposed Sample-selection via Confident Voting (SCV) method. Compared with GMM, SCV is more efficient to identify the clean samples. And our full model RankMatch has significant improvement in the sample selection stage under high noise rate." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 207, + 279, + 298, + 373 + ], + "blocks": [ + { + "bbox": [ + 207, + 279, + 298, + 373 + ], + "lines": [ + { + "bbox": [ + 207, + 279, + 298, + 373 + ], + "spans": [ + { + "bbox": [ + 207, + 279, + 298, + 373 + ], + "type": "image", + "image_path": "498e4f8dfcb62b8592239e5309d1ddfd7b458567ae076371ce6bb8e2707bef08.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 279, + 395, + 373 + ], + "blocks": [ + { + "bbox": [ + 307, + 279, + 395, + 373 + ], + "lines": [ + { + "bbox": [ + 307, + 279, + 395, + 373 + ], + "spans": [ + { + "bbox": [ + 307, + 279, + 395, + 373 + ], + "type": "image", + "image_path": "3294cfdda5552561a883f0a1df988ddb93353ac92bc0ede4a9fe742d57573a1b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 405, + 279, + 493, + 373 + ], + "blocks": [ + { + "bbox": [ + 405, + 279, + 493, + 373 + ], + "lines": [ + { + "bbox": [ + 405, + 279, + 493, + 373 + ], + "spans": [ + { + "bbox": [ + 405, + 279, + 493, + 373 + ], + "type": "image", + "image_path": "a1e3871fef9619c2043d47a371d7596bfe923576637b5c74c727ce95ac9fed5e.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 465, + 287, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 465, + 287, + 526 + ], + "spans": [ + { + "bbox": [ + 46, + 465, + 287, + 526 + ], + "type": "text", + "content": "(3) However, it is prone to selecting few samples when directly selecting reliable confidence samples by the high threshold because the recall is extremely low under high noise. It forms a dilemma between the quality and quantity of the selected samples." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "content": "Sample selection via confident voting (SCV) is one main reason for RankMatch achieving great improvement. To study and verify its effectiveness, we test the accuracy of the selected clean samples under various symmetric noises on CIFAR-100. Since the great success DivideMix has made, we regard the GMM-based sample selection method as our baseline. Figure 5 presents that the SCV-based methods are more accurate than DivideMix in all cases. Furthermore, in the extremely demanding scenario (i.e., Symmetry-80% and Symmetry-90%), SCV based method achieves tremendous improvement. Specifically, DivideMix with SCV achieves over 18% improvement than that with GMM at 80% label noise. In contrast, our full RankMatch achieves over 25% improvement, which implies that the SCV benefits from more robust representation train" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 465, + 545, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 465, + 545, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 465, + 545, + 609 + ], + "type": "text", + "content": "ing. Under the most extreme " + }, + { + "bbox": [ + 304, + 465, + 545, + 609 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 304, + 465, + 545, + 609 + ], + "type": "text", + "content": " label noise, our full RankMatch achieves over " + }, + { + "bbox": [ + 304, + 465, + 545, + 609 + ], + "type": "inline_equation", + "content": "140\\%" + }, + { + "bbox": [ + 304, + 465, + 545, + 609 + ], + "type": "text", + "content": " selection accuracy gain, while DivideMix with SCV improves over " + }, + { + "bbox": [ + 304, + 465, + 545, + 609 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 304, + 465, + 545, + 609 + ], + "type": "text", + "content": ". The explanation for this result is that our full model includes consistency regularization and rank contrastive loss. Consistency regularization enhances semantic consistency and rectifies some confident-but-noisy features, which generates more robust prototypes and benefits SCV. Furthermore, rank contrastive loss promotes more discriminative features, improving confident prototype generation. The supplementary material contains other in-depth studies examining the sensitivity of high threshold " + }, + { + "bbox": [ + 304, + 465, + 545, + 609 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 465, + 545, + 609 + ], + "type": "text", + "content": " and hyper-parameters in SCV." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Effects of RankMatch components. We remove the corresponding components to study the effects of RCL and network ensemble. We remove " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{RCL}}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " to validate the effect of rank contrastive loss. We replace the SCV module as the sample selection strategy of DivideMix to validate the effectiveness of SCV. We remove the K-means in SCV for detailed study. As the results shown in Table 4, we find that rank contrastive loss is beneficial to RankMatch. The results" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "text", + "content": "1651" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 279, + 201 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 279, + 201 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 279, + 201 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 279, + 201 + ], + "type": "table", + "html": "
DatasetCIFAR-10CIFAR-100
Noise ratio50%90%50%90%
RankMatchBest95.692.677.950.6
Last95.492.177.649.9
w/o SCVBest95.189.675.345.1
Last94.989.174.944.9
SCV w/o K-meansBest95.491.876.547.9
Last95.291.475.247.5
w/o RCLBest95.290.876.145.6
Last94.988.775.244.5
", + "image_path": "90bd9610229c4647cd5916059f4cd8c30afa71d3eab129c1e389183e5225b593.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 209, + 287, + 233 + ], + "lines": [ + { + "bbox": [ + 47, + 209, + 287, + 233 + ], + "spans": [ + { + "bbox": [ + 47, + 209, + 287, + 233 + ], + "type": "text", + "content": "Table 4: Ablation study results in terms of test accuracy (%) on CIFAR-10 and CIFAR-100 with symmetric label noise." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 255, + 287, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 255, + 287, + 291 + ], + "spans": [ + { + "bbox": [ + 47, + 255, + 287, + 291 + ], + "type": "text", + "content": "also validate the effectiveness of our proposed SCV. Diversifying the intra-class patterns by K-means is more effective under complex scenario and extreme noise ratio." + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 50, + 301, + 167, + 416 + ], + "blocks": [ + { + "bbox": [ + 50, + 301, + 167, + 416 + ], + "lines": [ + { + "bbox": [ + 50, + 301, + 167, + 416 + ], + "spans": [ + { + "bbox": [ + 50, + 301, + 167, + 416 + ], + "type": "image", + "image_path": "5e935f793662d03fdc1e2164fe5681cad8be0c45675f118dad6f4f84ec0391dd.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 426, + 287, + 464 + ], + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 464 + ], + "type": "text", + "content": "Figure 6: Sensitivity to the variance of hyperparameters. Experiments are conducted on CIFAR-10 under " + }, + { + "bbox": [ + 46, + 426, + 287, + 464 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 426, + 287, + 464 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 426, + 287, + 464 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 46, + 426, + 287, + 464 + ], + "type": "text", + "content": " symmetric noises." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 173, + 301, + 279, + 417 + ], + "blocks": [ + { + "bbox": [ + 173, + 301, + 279, + 417 + ], + "lines": [ + { + "bbox": [ + 173, + 301, + 279, + 417 + ], + "spans": [ + { + "bbox": [ + 173, + 301, + 279, + 417 + ], + "type": "image", + "image_path": "0cbb74d5c15dabc69c6fa3147bacc4baf2605118dee35ca2e80514832d23c5d0.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 477, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 477, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 477, + 287, + 550 + ], + "type": "text", + "content": "Sensitivity Analysis. SCV introduce the confidence threshold " + }, + { + "bbox": [ + 46, + 477, + 287, + 550 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 477, + 287, + 550 + ], + "type": "text", + "content": " and number of prototypes " + }, + { + "bbox": [ + 46, + 477, + 287, + 550 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 477, + 287, + 550 + ], + "type": "text", + "content": ". We range the number of prototypes " + }, + { + "bbox": [ + 46, + 477, + 287, + 550 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 477, + 287, + 550 + ], + "type": "text", + "content": " from 5 to 30 and vary the threshold " + }, + { + "bbox": [ + 46, + 477, + 287, + 550 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 477, + 287, + 550 + ], + "type": "text", + "content": " from 0.90 to 0.99. Figure 6 shows that our method is robust against different choices for " + }, + { + "bbox": [ + 46, + 477, + 287, + 550 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 477, + 287, + 550 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 477, + 287, + 550 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 477, + 287, + 550 + ], + "type": "text", + "content": ". More in-depth studies are included in supplementary materials." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 561, + 125, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 561, + 125, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 561, + 125, + 574 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": "We presented RankMatch, a novel framework for LNL that strives to combat noisy labels by enhancing confidence and consistency. Confidence-wise, we propose a novel clean sample selection strategy based on confidence representation voting rather than the small-loss criterion. Collecting votes from confident prototypes makes our method robust to noise and can sieve clean samples out with ample quantity. Consistency-wise, we introduce a novel rank contrastive loss based on the rank statistics of principal features instead of the widely-used " + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": " distance. Such a loss could enhance consistency between similar samples even if they" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "were wrongly labeled. Moreover, we leverage consistency regularization to enhance the semantic consistency. We validate our superiority over several challenging benchmarks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 119, + 404, + 133 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 119, + 404, + 133 + ], + "spans": [ + { + "bbox": [ + 306, + 119, + 404, + 133 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 140, + 547, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 140, + 547, + 212 + ], + "spans": [ + { + "bbox": [ + 305, + 140, + 547, + 212 + ], + "type": "text", + "content": "This work was supported in part by the Guangdong Basic and Applied Basic Research Foundation (NO. 2020B1515020048), in part by the National Natural Science Foundation of China (NO. 61976250), in part by the Shenzhen Science and Technology Program (NO. 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In ECCV, 2022." + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1654" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/RankMixup_ Ranking-Based Mixup Training for Network Calibration/4c024ec3-bba1-4470-bd07-d0e7529be938_content_list.json b/2023/RankMixup_ Ranking-Based Mixup Training for Network Calibration/4c024ec3-bba1-4470-bd07-d0e7529be938_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..0b75685492e3aa33382a4b8cb21d979fa8a1bca4 --- /dev/null +++ b/2023/RankMixup_ Ranking-Based Mixup Training for Network Calibration/4c024ec3-bba1-4470-bd07-d0e7529be938_content_list.json @@ -0,0 +1,1642 @@ +[ + { + "type": "text", + "text": "RankMixup: Ranking-Based Mixup Training for Network Calibration", + "text_level": 1, + "bbox": [ + 129, + 130, + 841, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jongyoun Noh", + "bbox": [ + 163, + 181, + 285, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hyekang Park", + "bbox": [ + 343, + 181, + 459, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Junghyup Lee", + "bbox": [ + 517, + 181, + 633, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Bumsub Ham*", + "bbox": [ + 691, + 181, + 810, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "School of Electrical and Electronic Engineering, Yonsei University https://cvlab.yonsei.ac.kr/projects/RankMixup", + "bbox": [ + 215, + 205, + 750, + 246 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 279, + 313, + 295 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Network calibration aims to accurately estimate the level of confidences, which is particularly important for employing deep neural networks in real-world systems. Recent approaches leverage mixup to calibrate the network's predictions during training. However, they do not consider the problem that mixtures of labels in mixup may not accurately represent the actual distribution of augmented samples. In this paper, we present RankMixup, a novel mixup-based framework alleviating the problem of the mixture of labels for network calibration. To this end, we propose to use an ordinal ranking relationship between raw and mixup-augmented samples as an alternative supervisory signal to the label mixtures for network calibration. We hypothesize that the network should estimate a higher level of confidence for the raw samples than the augmented ones (Fig.1). To implement this idea, we introduce a mixup-based ranking loss (MRL) that encourages lower confidences for augmented samples compared to raw ones, maintaining the ranking relationship. We also propose to leverage the ranking relationship among multiple mixup-augmented samples to further improve the calibration capability. Augmented samples with larger mixing coefficients are expected to have higher confidences and vice versa (Fig.1). That is, the order of confidences should be aligned with that of mixing coefficients. To this end, we introduce a novel loss, M-NDCG, in order to reduce the number of misaligned pairs of the coefficients and confidences. Extensive experimental results on standard benchmarks for network calibration demonstrate the effectiveness of RankMixup.", + "bbox": [ + 75, + 311, + 473, + 750 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 777, + 209, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep neural networks (DNNs) have achieved remarkable advances in numerous computer vision tasks, including image classification, object detection, and semantic segmentation. Despite the impressive performance, DNNs trained using a softmax cross-entropy (CE) loss and one-hot en", + "bbox": [ + 75, + 801, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f74b3e0c14e4a7b98cd5a9a79cbe6530d605d9c43fb2441fc400acac2ff66949.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 522, + 292, + 844, + 366 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3a58cb9035265fe62a3beb81840d8178e4aa279967fb9b8f93f3d213c8b145d6.jpg", + "image_caption": [ + "Figure 1: Motivation of RankMixup. We show raw samples of a cat and dog in red boxes, and mixup-augmented samples in blue boxes with dashed lines. The mixup-augmented samples are generated by linearly interpolating the raw samples with a mixing coefficient $\\lambda$ . We expect that confidences of the raw samples to be higher than that of the augmented sample (top). The augmented samples with larger coefficients $\\lambda$ would have higher confidences than the samples with smaller coefficients (bottom). Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 501, + 369, + 893, + 448 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "coded labels often output overconfident and/or underconfident probabilities, which do not reflect the actual likelihood [10, 32, 41]. This suggests that the networks are not able to estimate the level of confidence, leading to inaccurate and unreliable predictions, which restricts practical applications in real-world systems, particularly for safety-sensitive domains, such as medical diagnosis [18] and autonomous driving [9].", + "bbox": [ + 496, + 612, + 893, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To improve the reliability of DNNs, many methods propose to calibrate the output distribution after or during training. Post-hoc approaches adjust miscalibrated probabilities directly from pretrained networks [7, 10, 12, 21, 27]. Although these approaches are straightforward to apply, calibration performance depends heavily on datasets and networks used for training [25], and they are not robust to distribution shifts between training and test samples [33]. Training-time approaches [4, 8, 14, 25, 28, 29, 30, 41, 51], on the other hand, exploit an additional regularization term along with the CE loss to calibrate the output probabilities", + "bbox": [ + 496, + 734, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1358", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "during training. Early works [29, 30, 41] have explored the effects of regularization techniques, including label smoothing (LS) [40], focal loss (FL) [24], and mixup [49], on network calibration, and shown that the networks trained with these techniques are better calibrated than the ones trained with the CE loss alone. Recently, the works of [8, 25, 29] highlight the limitations of LS and FL in terms of network calibration, and introduce calibration-aware LS and FL. On the contrary, few studies have explored integrating the mixup technique into network calibration. Current mixup-based methods [35, 41, 51] simply interpolate input images and training labels with a mixing coefficient to soften output probabilities, while not considering network calibration itself. Since the interpolated labels may not represent accurately the distribution of the label mixture in augmented images [3, 19, 39, 43], training networks with such uncertain labels degrades the calibration performance.", + "bbox": [ + 75, + 90, + 472, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we present a mixup-based approach to network calibration, dubbed RankMixup, that addresses the problem of directly using the mixture of labels for calibrating network predictions [35, 41, 51]. To this end, we conjecture that networks should give higher confidences for the raw sample, not augmented by the mixup technique, than the augmented one (Fig. 1). To implement this idea, we leverage an ordinal ranking relationship between raw and augmented samples (Fig. 1) and use it as a supervisory signal for network calibration, instead of using the label mixtures. In particular, we introduce a mixup-based ranking loss (MRL) that encourages the confidences of augmented samples to be lower than those of raw samples by a margin, in order to preserve the ranking relationship. To further strengthen the capability of network calibration, we also propose to exploit the ranking relationship for multiple mixup-augmented samples. We expect that higher confidences are favorable for augmented samples with larger mixing coefficients $\\lambda$ , and vice versa (Fig. 1), such that the orders of confidences and mixing coefficients are aligned to each other. To achieve this, we introduce a novel loss, M-NDCG, based on normalized discounted cumulative gain (NDCG) in information retrieval [17], which penalizes the number of misaligned pairs of the coefficients and confidences. Extensive experimental results on standard benchmarks demonstrate the effectiveness of our approach to leveraging the ordinal ranking relationships on network calibration. The main contributions of our work can be summarized as follows:", + "bbox": [ + 75, + 347, + 472, + 785 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a novel mixup-based framework for network calibration, RankMixup, that alleviates the problem of exploiting label mixtures for calibrating network predictions. To the best of our knowledge, we are the first to handle this issue in the context of confidence calibration.", + "- We propose to exploit ordinal ranking relationships between confidence from raw and augmented samples," + ], + "bbox": [ + 73, + 790, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "as well as those among confidences from multiple augmented samples, and use them as supervisory signals, instead of the mixture of labels. To implement this idea, we introduce MRL and M-NDCG that facilitate aligning the confidences and mixing coefficients to preserve the relationships.", + "bbox": [ + 511, + 90, + 890, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We demonstrate that our approach provides better results in terms of expected calibration error (ECE), compared to other mixup-based methods. We also achieve competitive performances on standard benchmarks on network calibration, including CIFAR10/100 [20], TinyImageNet [23], and ImageNet [6] with various network architectures.", + "bbox": [ + 496, + 184, + 893, + 289 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 498, + 301, + 637, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Confidence calibration. The seminal work of [10] provides empirical evidence that DNNs are prone to making overconfident predictions due to miscalibrated output probabilities. In particular, they are typically trained with one-hot encoded labels, which fails to impose any entropy on the supervisory signal. The entropy of output probabilities for the network is thus encouraged to be zero, leading to the overconfident predictions [25]. To address this problem, several approaches have been proposed to augment the entropy of output probabilities, which can be divided into two categories: post-hoc and training-time methods. First, post-hoc approaches adjust the miscalibrated probabilities directly after training using a temperature scaling technique [7, 10, 42] or ranking statistics [27]. The temperature scaling technique, also effective to knowledge distillation [16], raises the entropy of output probabilities using a temperature parameter, optimized on additional validation samples. Although post-hoc approaches have shown the effectiveness on in-distribution datasets, they perform poorly under distribution shifts [33], and inevitably lower the confidence of correct predictions [22, 29]. Second, training-time approaches implicitly or explicitly impose regularization on outputs probabilities during training, usually in combination with post-hoc methods to further improve the calibration accuracy. The implicit methods [4, 4, 8, 25, 30, 35, 41] smooth the output distribution by increasing the entropy of training labels, rather than adjusting output probabilities directly. Several works [29, 30, 41, 51] have demonstrated empirically and theoretically that regularization methods such as LS [40], FL [24], and Mixup [49], which have originally designed to learn discriminative features, can also be effective in network calibration. However, recent works of [8, 25, 35] explore that directly using these methods for network calibration is problematic, and they introduce improved versions to overcome the drawback. For example, MbLS [25] exploits a margin-based LS to address the problem of LS providing non-informative predictions to obtain a better-calibrated network. The works", + "bbox": [ + 496, + 325, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1359", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "of [8, 35] suggest that finding optimal parameters of FL and mixup is crucial for network calibration. The explicit methods [14, 22, 28, 34] adjust confidences of predictions directly by maximizing the entropy of output probabilities [34], using an ordinal ranking relationship [28] or minimizing calibration errors [14, 22]. For example, the ordinal ranking between output probabilities of networks has been proven to be effective to estimate the levels of confidence, providing better calibrated models [28]. It assumes that the predictions with higher confidences are more likely to be accurate than the ones with lower confidences. We explore the effects of mixup [49] in the context of network calibration, similar to other mixup-based methods [35, 41, 51]. They use interpolated labels to train networks for calibrating output probabilities, but the labels do not provide the distribution of the label mixture for the augmented sample accurately [3, 19, 39, 43]. We exploit confidences of augmented samples directly as supervisory signals for network calibration using ordinal ranking relationships between the samples, boosting the calibration performance significantly. The work of [28] is closely related to ours in that it uses an ordinal ranking relationship for raw samples. In contrast to this, our approach exploits more diverse and complex ordinal relationships for confidences. It considers not only the relationship between raw and augmented samples, but also among the augmented samples themselves.", + "bbox": [ + 76, + 90, + 472, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Mixup. Data augmentation has become a standard technique for training DNNs that regularizes the networks to prevent overfitting and improve generalization. Mixup [49] linearly interpolates between pairs of raw data samples. Specifically, it takes a weighted average of two images to obtain a new one. The training label for the augmented sample is also interpolated with the same weight. Many works extend this idea to improve the generalization ability. Manifold-Mixup [45] performs the mixup process in the feature space, while CutMix [47] introduces a regional mixing scheme to preserve fine-grained information of original images. It has recently been explored that using label mixtures in mixup and its variants could provide misleading supervisory signals for training networks, which can be alleviated by saliency-guided mixup schemes [3, 19, 36, 43] or label perturbations [39]. In addition to data augmentation, various applications leverage mixup for, e.g., self-supervised learning [37, 38] and network calibration [35, 41]. We mainly investigate the effect of the vanilla mixup [49] on network calibration. However, as will be shown in our experiments, the variants of mixup, including CutMix [47] and manifold-Mixup [45], can also be readily adapted to our approach.", + "bbox": [ + 76, + 487, + 472, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 76, + 845, + 187, + 863 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We present in this section preliminaries for network calibration and mixup [49] in Sec. 3.1, and provide a detailed", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "description of RankMiup and training losses in Secs. 3.2 and 3.3, respectively.", + "bbox": [ + 498, + 90, + 893, + 122 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 128, + 640, + 143 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Network calibration. Let us suppose a dataset $D = \\{(\\mathbf{x}_i, \\mathbf{y}_i)\\}_{i=1}^N$ of size $N$ , where $\\mathbf{x}_i \\in \\mathcal{X}$ and $\\mathbf{y}_i \\in \\mathcal{Y}$ are an input sample and a ground-truth label with $K$ classes, respectively. DNNs can be considered as a function, parameterized by $\\theta$ , that yields a logit $\\mathbf{z}_i$ of size $K \\times 1$ from the input sample: $\\mathbf{f}_\\theta : \\mathcal{X} \\to \\mathbb{R}^K$ . For multiclass classification, the networks compute class probabilities using the softmax function as follows:", + "bbox": [ + 498, + 152, + 893, + 272 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {i, k} = \\operatorname {s o f t m a x} \\left(\\mathbf {z} _ {i}\\right) = \\frac {\\exp z _ {i , k}}{\\sum_ {j} ^ {K} \\exp z _ {i , j}}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 277, + 890, + 313 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where we denote by $p_{i,k}$ a probability of the $k$ -th class for the $i$ -th input. Based on the probabilities, the networks predict a class for the input sample $\\mathbf{x}_i$ as", + "bbox": [ + 498, + 319, + 892, + 364 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {i} = \\arg \\max _ {k} p _ {i, k}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 630, + 375, + 890, + 396 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The corresponding confidence can then be obtained as follows:", + "bbox": [ + 498, + 402, + 890, + 431 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {p} _ {i} = \\max _ {k} p _ {i, k}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 642, + 434, + 890, + 454 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "During training, the networks are optimized using a cross-entropy (CE) loss as follows:", + "bbox": [ + 498, + 458, + 890, + 488 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {C E} \\left(\\mathbf {x} _ {i}, \\mathbf {y} _ {i}\\right) = - \\sum_ {k = 1} ^ {K} y _ {i, k} \\log p _ {i, k}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 497, + 890, + 539 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $y_{i,k}$ is the $k$ -th element of the one-hot encoded label $\\mathbf{y}_i$ . Recent works [10, 29, 30, 41] have shown that DNNs trained with the CE loss tend to be overconfident, providing higher accuracies than accuracies. To address this problem, confidence calibration methods encourage that the confidence for each sample and the accuracy are the same as follows:", + "bbox": [ + 498, + 546, + 893, + 650 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {p} _ {i} = P \\left(\\hat {y} _ {i} = y _ {i} \\mid \\hat {p} _ {i}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 661, + 890, + 679 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $y_{i}$ is an index of the true class for the ground-truth label $\\mathbf{y}_{i}$ .", + "bbox": [ + 498, + 686, + 890, + 717 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Mixup. Mixup [49] is a data-augmentation technique based on the vicinal risk minimization principle [2]. It introduces the mixup vicinal distribution, which measures the likelihood of finding a pair of an augmented input and a target label, $(\\tilde{\\mathbf{x}}_i,\\tilde{\\mathbf{y}}_i)$ , from the vicinity of the original pair, $(\\mathbf{x}_i,\\mathbf{y}_i)$ . Mixup samples the vicinal distribution to construct a new dataset, $D_{v} = \\{(\\tilde{\\mathbf{x}}_{i},\\tilde{\\mathbf{y}}_{i})\\}_{i = 1}^{N}$ . Here, we denote by $D_{v}$ the vicinal set consisting of pairs of augmented training samples and corresponding target labels. Specifically, it augments training pairs by linearly interpolating the original ones as follows:", + "bbox": [ + 496, + 734, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1360", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\tilde {\\mathbf {x}} = \\lambda \\mathbf {x} _ {i} + (1 - \\lambda) \\mathbf {x} _ {j}, \\\\ \\tilde {\\dots} \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\end{array} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 104, + 467, + 128 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {y}} = \\lambda \\mathbf {y} _ {i} + (1 - \\lambda) \\mathbf {y} _ {j},\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 125, + 349, + 140 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where two pairs of input samples and target labels, $(\\mathbf{x}_i,\\mathbf{y}_i)$ and $(\\mathbf{x}_j,\\mathbf{y}_j)$ , are randomly drawn from the training set $D$ and $\\lambda \\in [0,1] \\sim \\mathrm{Beta}(\\alpha ,\\alpha)$ is a mixing coefficient, sampled from a Beta distribution. Mixup assumes that target labels for the vicinal set should also be interpolated with the same mixing coefficient as input samples during the mixing process. The hyperparameter $\\alpha$ controls the strength of interpolation between the pairs of input samples and target labels. According to [49], the value of $\\alpha$ within the range of [0.1, 0.4] provides better classification performance, while higher values cause significant underfitting. We will also examine the effect of $\\alpha$ in terms of confidence calibration within our framework.", + "bbox": [ + 75, + 148, + 472, + 345 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. RankMixup", + "text_level": 1, + "bbox": [ + 76, + 356, + 207, + 372 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Mixup provides smooth decision boundaries that gradually shift from one class to another, which leads to a regularized estimate of uncertainty (or confidence) [49]. There have been lots of studies to discover underlying principles behind the mixup method [15, 41, 50, 51, 51]. For example, it has proven to give better output probabilities in terms of model calibration, alleviating overconfident predictions [35, 41, 51]. The interpolated labels of augmented samples in the vicinal set do not always model the actual distribution of label mixtures in augmented samples [3, 19, 39, 43], which however has not been considered for designing a network calibration method. To alleviate this problem, we leverage ordinal ranking relationships between confidences from raw and augmented samples, as well as those among confidences from multiple augmented samples. We then propose to use them as supervisory signals for model calibration, rather than using the mixture of labels directly. In the following, we describe our framework with a single mixup-augmented sample, and present a generalized version that can handle multiple augmented samples.", + "bbox": [ + 75, + 380, + 472, + 698 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Single mixup-augmented sample. The sample augmented by mixup $\\bar{\\mathbf{x}}$ in Eq. (6) can be interpreted as a combination of the raw sample $\\mathbf{x}_i$ and structured noise from another one $\\mathbf{x}_j$ , where the degree of noise is determined by the mixing parameter $\\lambda$ . This suggests that DNNs predict the class of the augmented sample with uncertainty imposed by the additional one, making it more difficult to recognize the augmented sample than the raw one. To this end, mixup imposes uncertainty on the label mixtures by adjusting confidence of target labels for the augmented samples by $\\lambda$ (or $1 - \\lambda$ ). Albeit simple, directly using the interpolated labels may provide misleading supervisory signals", + "bbox": [ + 75, + 719, + 472, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to train DNNs. To avoid this, we leverage an ordinal ranking relationship between confidence of raw and augmented samples. Specifically, the ordinal ranking holds for the relationship that confidence levels of easy-to-classify samples should be higher than the ones for hard samples [28]. Accordingly, we conjecture that the confidence levels of raw samples should be greater than those of the augmented samples in the mixing process (Fig.1). Namely, every pair of samples $(\\mathbf{x}_i,\\tilde{\\mathbf{x}}_i)$ should satisfy the following relationship:", + "bbox": [ + 496, + 90, + 893, + 229 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\max _ {k} p _ {i, k} \\geq \\max _ {k} \\tilde {p} _ {i, k}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 241, + 890, + 262 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tilde{p}_{i,k}$ is a predicted probability of the class $k$ for the augmented sample $\\tilde{\\mathbf{x}}_i$ . We devise MRL that encourages the network to learn this relationship without the mixture of labels, which will be described in Sec. 3.3.", + "bbox": [ + 496, + 273, + 893, + 334 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multiple mixup-augmented samples. We extend our framework to exploit multiple mixup-augmented samples. As the mixing ratio $\\lambda$ decreases, augmented samples become more difficult to recognize, which suggests that we can exploit more complex ranking relationships among the multiple augmented samples. Analogous to the single case, we expect that the samples augmented with larger mixing coefficients $\\lambda$ show higher confidence compared to those with smaller coefficients (Fig. 1). For every pair of augmented samples $(\\tilde{\\mathbf{x}}_i,\\tilde{\\mathbf{x}}_j)$ from the vicinal set $D_{v}$ , the confidence of these samples should satisfy the following relationship:", + "bbox": [ + 496, + 356, + 893, + 537 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\lambda_ {i} \\geq \\lambda_ {j} \\Leftrightarrow \\max _ {k} \\tilde {p} _ {i, k} \\geq \\max _ {k} \\tilde {p} _ {j, k}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 551, + 890, + 573 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $(\\lambda_i, \\lambda_j)$ is a pair of mixing ratios for the corresponding pair of augmented samples $(\\tilde{\\mathbf{x}}_i, \\tilde{\\mathbf{x}}_j)$ . Note that we describe the relationship with two samples for simplicity, but our framework can adopt the relationship with any number of augmented samples.", + "bbox": [ + 496, + 585, + 890, + 660 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We then integrate both the relationships in Eqs. (7) and (8) to obtain a general version of RankMixup. With the mixing coefficient of 1.0 for the raw sample, the following relationship should hold for every triplet of samples $(\\mathbf{x}_i,\\tilde{\\mathbf{x}}_i,\\tilde{\\mathbf{x}}_j)^1$ :", + "bbox": [ + 496, + 661, + 893, + 739 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n1. 0 \\geq \\lambda_ {i} \\geq \\lambda_ {j} \\Leftrightarrow \\max _ {k} p _ {i, k} \\geq \\max _ {k} \\tilde {p} _ {i, k} \\geq \\max _ {k} \\tilde {p} _ {j, k}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 751, + 890, + 772 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This allows the network to estimate the levels of confidence better by considering diverse ordinal ranking relationships among the confidences of the raw and multiple mixup-augmented samples. To implement this idea, we align the orders of confidences and mixing ratios during training using M-NDCG (Sec. 3.3).", + "bbox": [ + 496, + 784, + 893, + 875 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "1 Note that Eq. (9) holds only when $\\lambda \\geq 0.5$ .", + "bbox": [ + 517, + 886, + 754, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1361", + "bbox": [ + 483, + 944, + 513, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Training loss", + "text_level": 1, + "bbox": [ + 76, + 90, + 212, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To train our model, we use a CE loss for classification, together with either MRL or M-NDCG for network calibration, balanced by the parameter of $w$ . As supervisory signals, we exploit one-hot encoded labels for classification, and ordinal ranking relationships for input and augmented samples for network calibration.", + "bbox": [ + 75, + 114, + 468, + 205 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "MRL. We introduce MRL facilitating the ordinal relationship in Eq. (7). It encourages confidence of augmented samples to be lower than those of raw samples by a margin, defined as follows:", + "bbox": [ + 75, + 226, + 468, + 286 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {M R L}} = \\max \\left(0, \\max _ {k} \\tilde {p} _ {i, k} - \\max _ {k} p _ {i, k} + m\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 301, + 468, + 324 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the margin $m$ determines acceptable discrepancies between the confidence of raw and augmented samples. The intuition behind using a margin is twofold: (1) It enables maintaining the ranking relationship between confidence, rather than penalizing the exact value of the discrepancies itself. (2) Controlling the confidence discrepancies with a margin allows to consider the uncertainty of inaccurate label mixtures. The vanilla mixup method continues to penalize the confidence of augmented samples, until they reach overconfident values, determined by the label mixtures. In contrast to this, MRL penalizes the confidence, only when the absolute discrepancies between them are below the margin.", + "bbox": [ + 75, + 334, + 468, + 531 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "M-NDCG. MRL is not sufficient to model the relationship in Eq. (9), where the comparison involves more than one augmented sample. M-NDCG addresses this problem that enables multiple confidence values to hold the ordinal ranking relationships. M-NDCG is based on NDCG used for evaluating ranking quality in information retrieval [17, 44]. It measures how many of retrieved results are aligned with the ground-truth ranking order, which can be calculated by normalizing a discounted cumulative gain (DCG) with an ideal DCG (IDCG):", + "bbox": [ + 75, + 551, + 468, + 704 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nN D C G = \\frac {D C G}{I D C G}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 714, + 468, + 746 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "DCG accumulates a relevance score of each retrieval result, weighted by a corresponding rank, and IDCG is computed similarly but with the ground-truth score, as follows:", + "bbox": [ + 75, + 755, + 468, + 801 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} D C G = \\sum_ {q = 1} ^ {Q} \\frac {r _ {q}}{\\log_ {2} (q + 1)}, \\tag {12} \\\\ I D C G = \\sum_ {q = 1} ^ {Q} \\frac {r _ {q} ^ {\\mathrm {g t}}}{\\log_ {2} (q + 1)}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 814, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $r_q$ and $r_q^{\\mathrm{gt}}$ are the relevance and ground-truth scores, respectively, at position $q$ in the result list of size $Q$ .", + "bbox": [ + 498, + 90, + 888, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We consider confidences of predictions and mixing coefficients as the relevance and ground-truth scores, respectively, enabling multiple confidences to satisfy the relationship in Eq. (9). Given $Q$ pairs of confidences and mixing coefficients, we compute $DCG_{\\mathrm{M}}$ and $IDCG_{\\mathrm{M}}$ , as follows:", + "bbox": [ + 498, + 122, + 890, + 196 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} D C G _ {\\mathrm {M}} = \\frac {\\operatorname* {m a x} _ {k} p _ {t , k}}{\\log_ {2} (t + 1)} + \\sum_ {q = 1, q \\neq t} ^ {Q} \\frac {\\operatorname* {m a x} _ {k} \\tilde {p} _ {q , k}}{\\log_ {2} (q + 1)}, \\tag {13} \\\\ I D C G _ {\\mathrm {M}} = 1 + \\sum_ {q = 2} ^ {Q} \\frac {\\lambda_ {q} ^ {\\mathrm {g t}}}{\\log_ {2} (q + 1)}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 220, + 890, + 310 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $t$ is the position of the confidence value for the raw sample, which is set to 1 in order to ensure that its confidence is always ranked first in a descending order, following the ranking relationship in Eq. (9). $Q$ is a hyperparameter that determines the number of augmented samples, i.e., $Q - 1$ augmented samples. $\\lambda_q^{\\mathrm{gt}}$ is the mixing coefficient sorted based on its magnitude, with a value of 1.0 for the raw sample appearing at position of the top rank, i.e., $\\lambda_1^{\\mathrm{gt}} = 1$ . We then define M-NDCG loss as follows:", + "bbox": [ + 498, + 321, + 890, + 470 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {M - N D C G}} = 1 - \\frac {D C G _ {\\mathrm {M}}}{I D C G _ {\\mathrm {M}}}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 469, + 890, + 501 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which is minimized when the ranking orders of the confidences and mixing coefficients are aligned to each other after sorting in a descending order. The network is thus trained to encourage the confidence to hold the ordinal ranking relationship of RankMixup in Eq. (9). M-NDCG also discounts lower-ranked confidence more, preventing the uncertain predictions from being overconfident.", + "bbox": [ + 498, + 505, + 890, + 611 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 625, + 633, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation details", + "text_level": 1, + "bbox": [ + 500, + 650, + 712, + 666 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We mainly perform experiments on CIFAR10/100 [20], Tiny-ImageNet [23] for network calibration. The CIFAR10/100 datasets consist of 50,000 training and 10,000 test images of size $32 \\times 32$ , and provide 10/100 object categories, respectively. Tiny-ImageNet includes 120,000 images of size $64 \\times 64$ for 200 object categories. Each category in Tiny-ImageNet contains 600 images, which are divided into 500, 50 and 50 images for training, validation and test, respectively. Tiny-ImageNet is more challenging, compared to CIFAR10/100, as it contains lots of object classes with a smaller number of samples per category. We further validate the generalization ability of our method on ImageNet [6], which comprises around 1.2M training and 50K validation images across 1K classes. For out-of-distribution (OOD) detection, we train a model", + "bbox": [ + 498, + 674, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1362", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/ab1acc7b0cf63d74137dd8b171a03f6eae4782feee97ef6f558a0f49ac237c40.jpg", + "table_caption": [ + "Table 1: Quantitative comparison with the state of the art in terms of ECE (%) and AECE (%) with 15 bins on the validation splits of CIFAR10/100 [20] and Tiny-ImageNet [23]. Numbers in bold indicate the best performance and underscored ones indicate the second best. Numbers in parentheses represent the results obtained using a TS post-hoc technique [10]." + ], + "table_footnote": [], + "table_body": "
MethodsCIFAR10 [20]CIFAR100 [20]Tiny-ImageNet [23]
ResNet-50 [13]ResNet-101 [13]ResNet-50 [13]ResNet-101 [13]ResNet-50 [13]ResNet-101 [13]
Acc↑ECE↓AEE↓Acc↑ECE↓AEE↓Acc↑ECE↓AECE↓Acc↑ECE↓AECE↓Acc↑ECE↓AECE↓
CE95.383.75(0.97)2.98(1.01)94.463.61(0.92)3.55(0.85)77.8113.59(2.93)13.54(2.86)77.4812.94(2.63)12.94(2.66)64.343.18(3.18)2.87(2.87)66.043.50(3.50)3.52(3.52)
MMCE [22]95.183.88(0.97)3.88(1.12)94.993.88(1.15)3.88(12.9)77.5612.72(2.83)12.71(2.86)77.8213.43(3.06)13.42(2.80)64.802.03(2.03)1.97(1.97)66.443.40(3.40)3.38(3.38)
ECP [34]94.754.01(1.06)3.99(1.53)93.974.41(1.72)4.40(1.70)76.2012.29(2.08)12.28(2.22)76.8113.43(2.92)13.42(3.04)64.881.94(1.94)1.95(1.95)66.202.72(2.72)2.70(2.70)
LS [30]94.873.27(1.58)3.67(3.02)94.183.35(1.51)3.85(3.10)76.456.73(4.23)6.54(4.26)76.917.99(4.38)7.87(4.55)65.463.21(2.51)3.23(2.51)65.523.11(2.51)2.92(2.72)
FL [24]94.823.42(1.07)3.41(0.87)93.593.27(1.12)3.23(1.37)76.412.83(1.66)2.88(1.73)76.123.10(2.58)3.22(2.51)63.082.03(2.03)1.94(1.94)64.022.18(2.18)2.09(2.09)
Mixup [41]94.762.86(1.37)2.81(2.00)95.506.87(1.18)6.79(2.33)78.478.68(2.14)8.68(2.19)78.748.92(3.69)8.91(3.65)65.811.92(1.92)1.96(1.96)66.412.41(1.97)2.43(1.95)
FLSD [29]94.773.86(0.83)3.74(0.96)93.263.92(0.93)3.67(0.94)76.202.86(2.86)2.86(2.86)76.613.29(2.04)3.25(1.78)63.561.93(1.93)1.98(1.98)64.021.85(1.85)1.81(1.81)
CRL [28]95.083.14(0.96)3.11(1.25)95.043.74(1.12)3.73(2.03)77.856.30(3.43)6.26(3.56)77.607.29(3.32)7.14(3.31)64.881.65(2.35)1.52(2.34)65.873.57(1.60)3.56(1.52)
CPC [4]95.045.05(1.89)5.04(2.60)95.364.78(1.52)4.77(2.37)77.2313.29(3.74)13.28(3.82)77.5013.32(2.96)13.28(3.23)65.703.41(3.41)3.42(3.42)66.443.93(3.93)3.74(3.74)
MbLS [25]95.251.16(1.16)3.18(3.18)95.131.38(1.38)3.25(3.25)77.924.01(4.01)4.14(4.14)77.455.49(5.49)6.52(6.52)64.741.64(1.64)1.73(1.73)65.811.62(1.62)1.68(1.68)
RegMixup [35]94.682.76(0.98)2.67(0.92)95.034.75(0.92)4.74(0.94)76.765.50(1.98)5.48(1.98)76.934.20(1.36)4.15(1.92)63.583.04(1.89)3.04(1.81)63.263.35(1.86)3.32(1.68)
RankMixup (MRL)94.591.01(0.84)1.03(0.80)94.182.86(1.08)2.87(1.58)76.653.52(2.40)3.39(2.05)77.264.41(1.68)4.24(1.76)64.541.70(1.70)1.69(1.69)64.802.26(1.78)2.28(1.60)
RankMixup (M-NDCG)94.882.59(0.57)2.58(0.52)94.253.24(0.65)3.21(0.56)77.113.46(1.49)3.45(1.42)76.463.49(1.10)3.49(1.40)64.971.49(1.49)1.44(1.44)64.891.57(1.57)1.94(1.94)
", + "bbox": [ + 78, + 128, + 890, + 287 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "using CIFAR10, and use CIFAR100, Tiny/ImageNet, and SVHN [31] as OOD datasets, following the experimental protocol in [26, 35]. Similarly, CIFAR100 is used to train a model, and evaluate it on CIFAR10, Tiny/ImageNet, and SVHN.", + "bbox": [ + 75, + 303, + 470, + 380 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation protocols. Following the standard protocol [4, 14, 25, 29, 30, 41], we use expected calibration error (ECE) and adaptive ECE (AECE) as evaluation metrics for network calibration. ECE measures the expected absolute difference between confidences and corresponding accuracies:", + "bbox": [ + 75, + 396, + 468, + 484 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} \\left[ \\left| P \\left(\\hat {y} _ {i} = y _ {i} \\mid \\hat {p} _ {i}\\right) - \\hat {p} _ {i} \\right| \\right]. \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 487, + 468, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To compute ECE, we divide a range $(0,1]$ into equidistance bins, and compute an average of the absolute differences, weighted by the size of each bin. We set the number of bins for both ECE and AECE as 15, following the protocol. We also report top-1 classification accuracies to compare discriminative capabilities. We provide results obtained without/with applying a post-hoc technique. In particular, we use the TS method [10], where the temperature is optimized on the validation sets. For OOD detection, we compare the area under the receiver operating characteristics (AUROC), following the standard evaluation protocol [26, 35].", + "bbox": [ + 75, + 511, + 468, + 679 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Methods for comparison. We compare our method with various training-time approaches. In addition to the baseline model using the CE loss, we include implicit methods (LS [30], FL/FLSD [29], Mixup [41], mbLS [25], and RegMixup [35]) and explicit methods (ECP [34], MMCE [22], and CPC [4]). We have reproduced results using official codes with hyperparameter settings provided by the authors, if they are not available. Detailed descriptions for the hyperparameters can be found in the supplement.", + "bbox": [ + 75, + 690, + 468, + 829 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training details. Following [25], we train our network for 200 epochs for CIFAR10/100 [20], with an initial learning rate of 1e-1 and a batch size of 128. We also follow the training setting in [25] for Tiny/ImageNet [23] ex", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1a7d6982f35085efbd11703e6b5d5ebb842d13b905a753732ff443d6078d8095.jpg", + "table_caption": [ + "Table 2: Quantitative comparison with the state of the art in terms of ECE (\\%) and AECE (\\%) with 15 bins on the validation split of ImageNet [6]. Numbers in bold indicate the best performance and underscored ones indicate the second best." + ], + "table_footnote": [], + "table_body": "
MethodsImageNet [6]
ResNet-50 [13]
Acc↑ECE↓AECE↓
CE73.969.109.24
Mixup [41]75.847.077.09
CRL [28]73.838.478.47
MbLS [25]75.394.074.14
RegMixup [35]75.645.345.42
RankMixup (MRL)75.275.705.71
RankMixup (M-NDCG)74.863.933.92
", + "bbox": [ + 552, + 354, + 839, + 462 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "cept for a batch size of 32 due to memory limits. All networks are trained using the SGD optimizer with a momentum of 0.9. The learning rate decreases by a tenth at every fixed intervals. We use ResNet50 [13], and ResNet101 [13] for both CIFAR10/100 [20] and Tiny-ImageNet [23], and ResNet50 for ImageNet [6]. For more comprehensive experiments, we also exploit WideResNet [48] for CIFAR10 and Tiny-ImageNet. We fix the balancing parameter of training loss $w$ to 0.1. We set margin $m$ to 2.0 and 1.0 for CIFAR10/100 and Tiny-ImageNet, respectively, using each validation dataset. Other hyperparameters, such as $\\alpha$ and $Q$ , are chosen similarly. For OOD detection, we train the network using M-NDCG and in-distribution (ID) datasets with the same training settings used for network calibration.", + "bbox": [ + 496, + 487, + 893, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Results", + "text_level": 1, + "bbox": [ + 500, + 710, + 591, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with the state of the art. We compare in Table 1 our method with state-of-the-art calibration approaches. From the tables, we observe four things: (1) Our models outperform other mixup-based methods [35, 41] using label mixtures as supervisions, demonstrating the effectiveness of our approach to leveraging an ordinal ranking relationship for confidences. (2) Our model using M-NDCG achieves the best performance in terms of both ECE and AECE on the challenging TinyImageNet [23] dataset, while providing competitive results on CIFAR10/100. This suggests that the ordinal ranking", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1363", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/26f69d72f87efaa1cca0cc11d4f9249f6d93dec8b3845fd1f58a7c601ad2bc0c.jpg", + "table_caption": [ + "Table 3: Quantitative comparison in terms of ECE (\\%) and AECE (\\%) with 15 bins on the validation splits of CIFAR10 [20] and Tiny-ImageNet [23]. Numbers in bold indicate the best performance and underscored ones are the second best." + ], + "table_footnote": [], + "table_body": "
CIFAR10 [20]Tiny-ImageNet [23]
MethodsWide-ResNet-26-10 [48]
Acc↑ECE↓AECE↓Acc↑ECE↓AECE↓
CE95.802.702.6665.186.086.06
Mixup [41]96.533.143.0866.363.773.75
MbLS [25]95.701.452.7865.302.572.32
RegMixup [35]95.444.183.9963.403.873.93
RankMixup (MRL)95.571.701.3865.343.303.28
RankMixup (M-NDCG)95.731.621.5365.563.833.94
", + "bbox": [ + 109, + 141, + 437, + 237 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/95365df1167a6fc1fc5f2caa7d462d833f48d18d19419f015eb823b9a7ba3a57.jpg", + "table_caption": [ + "Table 4: Quantitative comparison with the state of the art in terms of AUROC $(\\%)$ . Numbers in bold indicate the best performance and underscored ones indicate the second best." + ], + "table_footnote": [], + "table_body": "
IDC10 [20]C100 [20]
OODC100 [20]Tiny [23]SVHN [31]C10 [20]Tiny [23]SVHN [31]
AUROC↑AUROC↑
TS [10]86.7388.0692.1476.3880.1282.41
LS [30]75.2376.2974.2372.9277.5472.33
FL [29]85.6386.8492.6678.3781.2386.37
Mixup [41]82.0784.0979.7278.4681.5576.21
CPC [4]85.2885.1592.7974.6876.6671.72
MbLS [25]86.2087.5589.9873.8879.1973.19
RegMixup [35]87.8287.5483.1576.0080.7275.05
RankMixup (M-NDCG)87.8288.9492.6278.6480.6785.42
", + "bbox": [ + 78, + 291, + 467, + 397 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "relationships among confidences is crucial for network calibration, and M-NDCG effectively encourages our model to provide confidences maintaining the relationships. We can also see that our method generalizes well to the large-scale dataset. (3) Our method outperforms another ranking-based method (CRL)[28] significantly, suggesting that more complex ranking relationship based on augmented samples enables estimating better confidences. (4) Ours with the post-hoc method [10] gives the best results in most settings, which indicates that they are complementary to each other, and exploiting both further boosts the calibration accuracy.", + "bbox": [ + 75, + 415, + 467, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also provide in Tables 2 and 3 quantitative results on ImaergeNet [6] and for the WideResNet backbone [48], respectively. They show similar trends to those in Table 1, validating the effectiveness of our approach across various network architectures and large-scale datasets. Specifically, our models provide competitive results with the state of the art [25], while outperforming mixup-based methods [35, 41] and the ranking-based one [28].", + "bbox": [ + 75, + 580, + 467, + 703 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "OOD detection. We compare in Table 4 the OOD detection accuracy using the ResNet-50 [13] architecture. We use the entropy of the softmax output as an uncertainty measure for binary classification and report AUROC scores for comparison. From the table, we have two findings. Our model trained with M-NDCG outperforms other mixup-based methods and achieves the highest AUROC scores in most settings. This indicates that ordinal ranking relationship of confidences is also crucial for OOD detection, suggesting that models trained with M-NDCG are not only better calibrated but also perform better than other calibration methods under the distributional shifts.", + "bbox": [ + 75, + 719, + 467, + 898 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1eccf02e1eca8cc906bbe36f5523695f052dd60b639f473e8d7e76c6834fba9a.jpg", + "table_caption": [ + "Table 5: Quantitative comparison by varying the margin $m$ . We report the ECE (%) for the models trained with MRL. Numbers in parentheses represent the results obtained using a TS post-hoc technique [10]." + ], + "table_footnote": [], + "table_body": "
CIFAR10 [20]Tiny-ImageNet [23]
ECE↓ECE↓
m = 1.01.54(1.09)1.49(1.49)
m = 2.01.01(0.84)1.70(1.70)
m = 3.02.12(0.93)1.54(1.54)
m = 4.03.12(1.67)2.37(1.77)
m = 5.013.13(0.48)2.42(1.48)
", + "bbox": [ + 583, + 148, + 805, + 229 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d9d908c1dc9cda5c9b3f011492b3ad8720c81b4b41a9e90b379c3aa39c1f1bd8.jpg", + "image_caption": [ + "Figure 2: Quantitative results by varying the margin $m$ . We plot OE (\\%) and UE (\\%) on the validation split of CIFAR10 [20]. Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 540, + 237, + 846, + 358 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Discussion", + "text_level": 1, + "bbox": [ + 500, + 421, + 617, + 435 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we analyze the effects of the hyperparameters in our framework, and show generalization ability by incorporating other mixup techniques into our framework. For the analyses, we mainly adopt the ResNet-50 [13] models trained with M-NDCG, and report ECE and AECE on the validation sets of CIFAR10 [20] and TinyImageNet [23], unless otherwise specified. We use 15 bins to measure the ECE and AECE.", + "bbox": [ + 496, + 444, + 890, + 565 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Margin. We compare in Table 5 the calibration results of the models trained with MRL and various margins. We can see that small margins provide better performances for both datasets. Furthermore, we find that increasing the margin degrades the classification accuracy. A reason is that a large margin could make a significant difference in confidence levels between the raw and augmented samples. That is, with a larger margin, the augmented sample is more likely to have a lower confidence than its actual value.", + "bbox": [ + 496, + 569, + 890, + 703 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To demonstrate this, we compute overconfidence errors (OE) [41] that measure the expected difference between confidence values of overconfident predictions and corresponding accuracies. Given $H$ bins of equal size, OE is defined as follows [41]:", + "bbox": [ + 496, + 705, + 890, + 781 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nO E = \\sum_ {h = 1} ^ {H} \\frac {\\left| B _ {h} \\right|}{N} [ \\operatorname {c o n f} \\left(B _ {h}\\right) \\times \\max \\left(\\operatorname {c o n f} \\left(B _ {h}\\right) - \\operatorname {a c c} \\left(B _ {h}\\right), 0\\right) ], \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 789, + 890, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $N$ is the total number of samples, and $B_{h}$ is the set of samples, whose confidence falls into the $h$ -th bin. We denote by $\\mathrm{acc}(B_h)$ and $\\mathrm{conf}(B_h)$ the accuracy and averaged confidence of the $h$ -th bin, respectively. Similar to OE, we", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1364", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6: Quantitative results of our model with various numbers of the augmented samples. We report the ECE (\\%) for comparison. Numbers in parentheses represent the results obtained using a TS post-hoc technique [10].", + "bbox": [ + 76, + 82, + 468, + 137 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e750be5164c0cb278e9c4b9d6f4610423cffc08ef93c8ddfa93773186fc1d0b9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
CIFAR10 [20]Tiny-ImageNet [23]
ECE↓ECE↓
Q = 23.01(0.82)3.25(1.44)
Q = 32.78(0.50)2.18(1.12)
Q = 42.59(0.57)1.49(1.49)
Q = 52.37(0.64)1.52(1.52)
Q = 62.24(0.59)1.30(1.30)
", + "bbox": [ + 163, + 148, + 375, + 223 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/037e530268de6b85da5a2b9978c74240f2e77d0c316a827c7f278efb7a5b7b32.jpg", + "image_caption": [ + "Figure 3: Probability density function (PDF) of Beta distribution with various $\\alpha$ s." + ], + "image_footnote": [], + "bbox": [ + 117, + 224, + 424, + 405 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "define underconfidence errors (UE) computing the difference using underconfident predictions as follows:", + "bbox": [ + 76, + 450, + 467, + 479 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\nU E = \\sum_ {h = 1} ^ {H} \\frac {\\left| B _ {h} \\right|}{N} [ \\operatorname {c o n f} \\left(B _ {h}\\right) \\times \\max \\left(\\operatorname {a c c} \\left(B _ {h}\\right) - \\operatorname {c o n f} \\left(B _ {h}\\right), 0\\right) ]. \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 492, + 467, + 541 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We plot in Fig. 2 UE and OE for ResNet-50 with MRL on CIFAR10 [20], while varying margins. We can see that UE increases drastically, according to the margins, while OE decreases gradually. This suggests that exploiting a large margin causes underconfidence problems, where the model becomes less confident in its predictions. An underconfident model produces large calibration errors [41, 49], leading to the degraded performance.", + "bbox": [ + 76, + 542, + 467, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Number of augmented samples. We compare in Table 6 the calibration performance in terms of ECE with varying number of augmented samples. We set $\\alpha$ to 2.0 and 1.0 for CIFAR10 and Tiny-ImageNet, respectively. We can observe that ECE improves as more augmented samples are used, suggesting that learning with diverse ranking relationships between a number of augmented samples encourages the model to estimate confidence levels better. This further implies that the mixup coefficient $\\lambda$ is also an important factor, since it enables modeling the diverse ranking relationships. This leads us to analyze the mixup coefficient $\\lambda$ in detail in the following.", + "bbox": [ + 76, + 676, + 467, + 857 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Mixup coefficient. Following [49], we sample the mixup coefficient $\\lambda$ from a Beta distribution, making it possible", + "bbox": [ + 76, + 869, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9e503c86e0d886321b2c716d8c090b96a1ad9df5b2328001d27f87ae5aff3e7d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 542, + 83, + 851, + 202 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0e1b47271a49a8291004667f8e37ef802bbb7b83834049f76980fd077d3103ea.jpg", + "image_caption": [ + "Figure 4: Quantitative results by varying the parameter of the Beta distribution $(\\alpha)$ . We plot ECE $(\\%)$ and AECE $(\\%)$ on the validation split of CIFAR10 [20] (top) and Tiny-ImageNet [23] (bottom). Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 540, + 207, + 849, + 325 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "to generate various augmented samples. Note that the degree of the diversity is determined by how we set the shape parameter for the Beta distribution. For an in-depth analysis, we also show in Fig. 3 the probability density functions (PDFs) of different $Beta(\\alpha, \\alpha)$ distributions, while varying the shape parameter $\\alpha$ . We evaluate the calibration errors of the models trained with M-NDCG along with different shape parameters $\\alpha$ of the Beta distribution, and show the results using 3 augmented images ( $Q = 4$ ) in Fig. 4. From the figures, we observe two things: (1) Our models achieve the best performances with $\\alpha = 2$ and $\\alpha = 1$ on CIFAR10 and Tiny-ImageNet, respectively, where the corresponding PDFs are relatively flat, as shown in Fig. 3. This suggests that diverse mixup coefficients $\\lambda$ drawn from such distributions can enhance the calibration performances, as it allows us to augment the samples in a more diverse way. (2) Our model performs well with large $\\alpha$ , which is in contrast to the vanilla mixup [41, 49], where the value of $\\alpha$ within the range of [0.1, 0.4] yields better classification and calibration performances. When $\\alpha$ is too large, it suffers from an underconfidence problem [41, 49] and is also affected by manifold intrusion [11], leading to significant performance drops in both the classification and calibration. The manifold intrusion happens when the label mixture of an augmented sample differs from the label of the real sample [11]. However, in our framework, we do not explicitly use the label mixtures as supervision, suggesting that our framework is less affected by those problems. Therefore, our framework is more robust to the variation of the parameter $\\alpha$ compared to the vanilla mixup. To further investigate the importance of diverse samples, we also perform experiments with various combinations of $\\alpha$ and $Q$ and provide the results in the supplementary material.", + "bbox": [ + 496, + 407, + 890, + 904 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1365", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8792901cf2e7a2e3e8edb29df7958a17c88b0b79a231d9f701bbb239c52341c8.jpg", + "table_caption": [ + "Table 7: Quantitative comparison of calibration performances using other mixup techniques on the validation splits of CIFAR10 [20] and Tiny-ImageNet [23]." + ], + "table_footnote": [], + "table_body": "
Mixup [49] Manifold [45] CutMix [47]CIFAR10 [20]Tiny-ImageNet [23]
ECE↓AECE↓ECE↓AECE↓
RegMixup [35]✓3.633.574.764.88
✓3.563.542.972.93
RankMixup✓2.922.981.201.22
✓3.263.211.801.66
✓2.592.581.491.44
", + "bbox": [ + 78, + 127, + 465, + 200 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/3785dd90b69774cfacc0350d8aa02ff1d7fe18a8fd76a274f45ecbb4a19e977a.jpg", + "table_caption": [ + "Table 8: Quantitative comparison of classification and calibration performances on the test splits of CIFAR10-LT [1] and CIFAR100-LT [1]. We report the Top-1 accuracy $(\\%)$ and ECE $(\\%)$ with 15 bins." + ], + "table_footnote": [], + "table_body": "
CIFAR10-LT [1]CIFAR100-LT [1]
Methodsρ = 10Acc↑/ECE↓ρ = 100Acc↑/ECE↓ρ = 10Acc↑/ECE↓ρ = 100Acc↑/ECE↓
CE86.39/6.6070.36/20.5355.70/22.8538.32/38.23
Mixup [49]87.10/6.5573.06/19.2058.02/19.6939.54/32.72
Remix [5]88.15/6.8175.36/15.3859.36/20.1741.94/33.56
UniMix [46]89.66/6.0082.75/12.8761.25/19.3845.45/27.12
RankMixup (MRL)88.83/2.1674.16/ 2.0362.84/13.5542.56/ 5.28
RankMixup (M-NDCG)89.80/5.9475.41/14.1063.83/ 9.9943.00/18.74
", + "bbox": [ + 80, + 270, + 460, + 375 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Other mixup techniques. RankMixup employs a vanilla mixup technique that interpolates the input images and the corresponding labels for data augmentation, but other variants can be readily adopted in our framework. We have also tried using Manifold-Mixup [45] and CutMix [47] for the experiments. We show in Table 7 the results of our models using these techniques together with M-NDCG, while setting the shape parameter $\\alpha$ to 1 for the both techniques. For comparison, we report the result of our model with the vanilla mixup, which exploits 3 augmented samples, and additionally show the performances obtained using RegMixup [35] equipped with these variants. For both datasets, our method achieves better calibration errors than RegMixup, indicating that our method has better generalization capability. While our model with vanilla mixup provides the best performance on CIFAR10, employing Manifold-Mixup offers better results on Tiny-ImageNet in terms of calibration errors. Increasing the entropy of supervision is crucial for better-calibrated models [25, 29, 30, 41]. RankMixup exploits the augmented samples as supervision for network calibration, indicating that samples with higher entropies can yield better performances. Manifold-Mixup [45] produces flattened representations that have higher entropies than the mixup-augmented samples, which may explain the reason why our model with Manifold-Mixup performs better on Tiny-ImageNet.", + "bbox": [ + 76, + 391, + 468, + 785 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Long-tailed datasets. We evaluate our method on long-tailed (LT) datasets, where the miscalibration issues of DNNs are more pronounced [46, 52]. Following the experimental settings in [46, 52], we adopt the ResNet32 [13] architecture as our backbone, and exploit CIFAR10/100-LT datasets [1] with two imbalanced factors $(\\rho)$ . We compare in Table 8 our method against the vanilla mixup [49] and two", + "bbox": [ + 75, + 794, + 468, + 901 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "adaptive mixup techniques tailored for LT scenarios [5, 46]. We can see that our models significantly outperform other mixup methods in terms of ECE, while providing competitive accuracies, although they are not specially designed for LT scenarios. This suggests that leveraging the ordinal ranking relationship between confidence is also effective for addressing miscalibration problems in LT scenarios, instead of using label mixtures for other mixup-based augmentations [46, 52]. Note that the number of samples for head and tail classes is highly skewed, suggesting that augmented samples are not diverse in LT scenarios. As this problem is more severe for M-NDCG, it yields worse results, compared to MRL, in the LT datasets.", + "bbox": [ + 496, + 90, + 890, + 287 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 303, + 617, + 318 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We have presented a novel mixup-based framework for network calibration, dubbed RankMixup, alleviating the problem that interpolated labels do not necessarily model the actual distribution of label mixtures. To this end, we have proposed a new supervisory signal based on the ordinal ranking relationship that a higher confidence is more favorable for a raw sample than the one augmented by mixup. We have proposed MRL, which encourages a network to yield confidence that preserve the ranking relationships between the raw and mixup-augmented samples. We have also extended this idea to multiple augmented samples with different mixup coefficients via M-NDCG, enabling a network to predict outputs with higher confidence for augmented samples that are closer to a raw one. We have demonstrated the effectiveness of RankMixup through the extensive experiments and analysis, achieving the best results among mixup-based network calibration approaches.", + "bbox": [ + 496, + 329, + 890, + 585 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgments. This work was supported in part by the NRF and IITP grants funded by the Korea government (MSIT) (No.2023R1A2C2004306, No.2022-0-00124, Development of Artificial Intelligence Technology for Self-Improving Competency-Aware Learning Capabilities, No.2021-0-02068, Artificial Intelligence Innovation Hub), and the Yonsei Signature Research Cluster Program of 2023 (2023-22-0008).", + "bbox": [ + 496, + 604, + 890, + 710 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 726, + 596, + 742 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Kaidi Cao, Colin Wei, Adrien Gaidon, Nikos Arechiga, and Tengyu Ma. Learning imbalanced datasets with label-distribution-aware margin loss. In NIPS, 2019. 9", + "[2] Olivier Chapelle, Jason Weston, Léon Bottou, and Vladimir Vapnik. Vicinal risk minimization. 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In CVPR, 2021. 9" + ], + "bbox": [ + 78, + 90, + 468, + 656 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "1368", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/RankMixup_ Ranking-Based Mixup Training for Network Calibration/4c024ec3-bba1-4470-bd07-d0e7529be938_model.json b/2023/RankMixup_ Ranking-Based Mixup Training for Network Calibration/4c024ec3-bba1-4470-bd07-d0e7529be938_model.json new file mode 100644 index 0000000000000000000000000000000000000000..db0dd2d1d2348c10f402f8f4ce6526f9dc49f53b --- /dev/null +++ b/2023/RankMixup_ Ranking-Based Mixup Training for Network Calibration/4c024ec3-bba1-4470-bd07-d0e7529be938_model.json @@ -0,0 +1,2235 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.13, + 0.131, + 0.842, + 0.154 + ], + "angle": 0, + "content": "RankMixup: Ranking-Based Mixup Training for Network Calibration" + }, + { + "type": "text", + "bbox": [ + 0.165, + 0.182, + 0.286, + 0.2 + ], + "angle": 0, + "content": "Jongyoun Noh" + }, + { + "type": "text", + "bbox": [ + 0.344, + 0.182, + 0.46, + 0.2 + ], + "angle": 0, + "content": "Hyekang Park" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.182, + 0.634, + 0.2 + ], + "angle": 0, + "content": "Junghyup Lee" + }, + { + "type": "text", + "bbox": [ + 0.692, + 0.182, + 0.811, + 0.198 + ], + "angle": 0, + "content": "Bumsub Ham*" + }, + { + "type": "text", + "bbox": [ + 0.217, + 0.206, + 0.751, + 0.247 + ], + "angle": 0, + "content": "School of Electrical and Electronic Engineering, Yonsei University https://cvlab.yonsei.ac.kr/projects/RankMixup" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.28, + 0.314, + 0.296 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.312, + 0.474, + 0.751 + ], + "angle": 0, + "content": "Network calibration aims to accurately estimate the level of confidences, which is particularly important for employing deep neural networks in real-world systems. Recent approaches leverage mixup to calibrate the network's predictions during training. However, they do not consider the problem that mixtures of labels in mixup may not accurately represent the actual distribution of augmented samples. In this paper, we present RankMixup, a novel mixup-based framework alleviating the problem of the mixture of labels for network calibration. To this end, we propose to use an ordinal ranking relationship between raw and mixup-augmented samples as an alternative supervisory signal to the label mixtures for network calibration. We hypothesize that the network should estimate a higher level of confidence for the raw samples than the augmented ones (Fig.1). To implement this idea, we introduce a mixup-based ranking loss (MRL) that encourages lower confidences for augmented samples compared to raw ones, maintaining the ranking relationship. We also propose to leverage the ranking relationship among multiple mixup-augmented samples to further improve the calibration capability. Augmented samples with larger mixing coefficients are expected to have higher confidences and vice versa (Fig.1). That is, the order of confidences should be aligned with that of mixing coefficients. To this end, we introduce a novel loss, M-NDCG, in order to reduce the number of misaligned pairs of the coefficients and confidences. Extensive experimental results on standard benchmarks for network calibration demonstrate the effectiveness of RankMixup." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.778, + 0.21, + 0.793 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.803, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Deep neural networks (DNNs) have achieved remarkable advances in numerous computer vision tasks, including image classification, object detection, and semantic segmentation. Despite the impressive performance, DNNs trained using a softmax cross-entropy (CE) loss and one-hot en" + }, + { + "type": "image", + "bbox": [ + 0.524, + 0.294, + 0.845, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.37, + 0.895, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.459, + 0.895, + 0.584 + ], + "angle": 0, + "content": "Figure 1: Motivation of RankMixup. We show raw samples of a cat and dog in red boxes, and mixup-augmented samples in blue boxes with dashed lines. The mixup-augmented samples are generated by linearly interpolating the raw samples with a mixing coefficient \\(\\lambda\\). We expect that confidences of the raw samples to be higher than that of the augmented sample (top). The augmented samples with larger coefficients \\(\\lambda\\) would have higher confidences than the samples with smaller coefficients (bottom). Best viewed in color." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.895, + 0.734 + ], + "angle": 0, + "content": "coded labels often output overconfident and/or underconfident probabilities, which do not reflect the actual likelihood [10, 32, 41]. This suggests that the networks are not able to estimate the level of confidence, leading to inaccurate and unreliable predictions, which restricts practical applications in real-world systems, particularly for safety-sensitive domains, such as medical diagnosis [18] and autonomous driving [9]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.896, + 0.903 + ], + "angle": 0, + "content": "To improve the reliability of DNNs, many methods propose to calibrate the output distribution after or during training. Post-hoc approaches adjust miscalibrated probabilities directly from pretrained networks [7, 10, 12, 21, 27]. Although these approaches are straightforward to apply, calibration performance depends heavily on datasets and networks used for training [25], and they are not robust to distribution shifts between training and test samples [33]. Training-time approaches [4, 8, 14, 25, 28, 29, 30, 41, 51], on the other hand, exploit an additional regularization term along with the CE loss to calibrate the output probabilities" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1358" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.348 + ], + "angle": 0, + "content": "during training. Early works [29, 30, 41] have explored the effects of regularization techniques, including label smoothing (LS) [40], focal loss (FL) [24], and mixup [49], on network calibration, and shown that the networks trained with these techniques are better calibrated than the ones trained with the CE loss alone. Recently, the works of [8, 25, 29] highlight the limitations of LS and FL in terms of network calibration, and introduce calibration-aware LS and FL. On the contrary, few studies have explored integrating the mixup technique into network calibration. Current mixup-based methods [35, 41, 51] simply interpolate input images and training labels with a mixing coefficient to soften output probabilities, while not considering network calibration itself. Since the interpolated labels may not represent accurately the distribution of the label mixture in augmented images [3, 19, 39, 43], training networks with such uncertain labels degrades the calibration performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.473, + 0.786 + ], + "angle": 0, + "content": "In this work, we present a mixup-based approach to network calibration, dubbed RankMixup, that addresses the problem of directly using the mixture of labels for calibrating network predictions [35, 41, 51]. To this end, we conjecture that networks should give higher confidences for the raw sample, not augmented by the mixup technique, than the augmented one (Fig. 1). To implement this idea, we leverage an ordinal ranking relationship between raw and augmented samples (Fig. 1) and use it as a supervisory signal for network calibration, instead of using the label mixtures. In particular, we introduce a mixup-based ranking loss (MRL) that encourages the confidences of augmented samples to be lower than those of raw samples by a margin, in order to preserve the ranking relationship. To further strengthen the capability of network calibration, we also propose to exploit the ranking relationship for multiple mixup-augmented samples. We expect that higher confidences are favorable for augmented samples with larger mixing coefficients \\(\\lambda\\), and vice versa (Fig. 1), such that the orders of confidences and mixing coefficients are aligned to each other. To achieve this, we introduce a novel loss, M-NDCG, based on normalized discounted cumulative gain (NDCG) in information retrieval [17], which penalizes the number of misaligned pairs of the coefficients and confidences. Extensive experimental results on standard benchmarks demonstrate the effectiveness of our approach to leveraging the ordinal ranking relationships on network calibration. The main contributions of our work can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.791, + 0.47, + 0.866 + ], + "angle": 0, + "content": "- We introduce a novel mixup-based framework for network calibration, RankMixup, that alleviates the problem of exploiting label mixtures for calibrating network predictions. To the best of our knowledge, we are the first to handle this issue in the context of confidence calibration." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "- We propose to exploit ordinal ranking relationships between confidence from raw and augmented samples," + }, + { + "type": "list", + "bbox": [ + 0.075, + 0.791, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.892, + 0.183 + ], + "angle": 0, + "content": "as well as those among confidences from multiple augmented samples, and use them as supervisory signals, instead of the mixture of labels. To implement this idea, we introduce MRL and M-NDCG that facilitate aligning the confidences and mixing coefficients to preserve the relationships." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.185, + 0.895, + 0.29 + ], + "angle": 0, + "content": "- We demonstrate that our approach provides better results in terms of expected calibration error (ECE), compared to other mixup-based methods. We also achieve competitive performances on standard benchmarks on network calibration, including CIFAR10/100 [20], TinyImageNet [23], and ImageNet [6] with various network architectures." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.302, + 0.638, + 0.318 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.327, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Confidence calibration. The seminal work of [10] provides empirical evidence that DNNs are prone to making overconfident predictions due to miscalibrated output probabilities. In particular, they are typically trained with one-hot encoded labels, which fails to impose any entropy on the supervisory signal. The entropy of output probabilities for the network is thus encouraged to be zero, leading to the overconfident predictions [25]. To address this problem, several approaches have been proposed to augment the entropy of output probabilities, which can be divided into two categories: post-hoc and training-time methods. First, post-hoc approaches adjust the miscalibrated probabilities directly after training using a temperature scaling technique [7, 10, 42] or ranking statistics [27]. The temperature scaling technique, also effective to knowledge distillation [16], raises the entropy of output probabilities using a temperature parameter, optimized on additional validation samples. Although post-hoc approaches have shown the effectiveness on in-distribution datasets, they perform poorly under distribution shifts [33], and inevitably lower the confidence of correct predictions [22, 29]. Second, training-time approaches implicitly or explicitly impose regularization on outputs probabilities during training, usually in combination with post-hoc methods to further improve the calibration accuracy. The implicit methods [4, 4, 8, 25, 30, 35, 41] smooth the output distribution by increasing the entropy of training labels, rather than adjusting output probabilities directly. Several works [29, 30, 41, 51] have demonstrated empirically and theoretically that regularization methods such as LS [40], FL [24], and Mixup [49], which have originally designed to learn discriminative features, can also be effective in network calibration. However, recent works of [8, 25, 35] explore that directly using these methods for network calibration is problematic, and they introduce improved versions to overcome the drawback. For example, MbLS [25] exploits a margin-based LS to address the problem of LS providing non-informative predictions to obtain a better-calibrated network. The works" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1359" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.485 + ], + "angle": 0, + "content": "of [8, 35] suggest that finding optimal parameters of FL and mixup is crucial for network calibration. The explicit methods [14, 22, 28, 34] adjust confidences of predictions directly by maximizing the entropy of output probabilities [34], using an ordinal ranking relationship [28] or minimizing calibration errors [14, 22]. For example, the ordinal ranking between output probabilities of networks has been proven to be effective to estimate the levels of confidence, providing better calibrated models [28]. It assumes that the predictions with higher confidences are more likely to be accurate than the ones with lower confidences. We explore the effects of mixup [49] in the context of network calibration, similar to other mixup-based methods [35, 41, 51]. They use interpolated labels to train networks for calibrating output probabilities, but the labels do not provide the distribution of the label mixture for the augmented sample accurately [3, 19, 39, 43]. We exploit confidences of augmented samples directly as supervisory signals for network calibration using ordinal ranking relationships between the samples, boosting the calibration performance significantly. The work of [28] is closely related to ours in that it uses an ordinal ranking relationship for raw samples. In contrast to this, our approach exploits more diverse and complex ordinal relationships for confidences. It considers not only the relationship between raw and augmented samples, but also among the augmented samples themselves." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.488, + 0.473, + 0.835 + ], + "angle": 0, + "content": "Mixup. Data augmentation has become a standard technique for training DNNs that regularizes the networks to prevent overfitting and improve generalization. Mixup [49] linearly interpolates between pairs of raw data samples. Specifically, it takes a weighted average of two images to obtain a new one. The training label for the augmented sample is also interpolated with the same weight. Many works extend this idea to improve the generalization ability. Manifold-Mixup [45] performs the mixup process in the feature space, while CutMix [47] introduces a regional mixing scheme to preserve fine-grained information of original images. It has recently been explored that using label mixtures in mixup and its variants could provide misleading supervisory signals for training networks, which can be alleviated by saliency-guided mixup schemes [3, 19, 36, 43] or label perturbations [39]. In addition to data augmentation, various applications leverage mixup for, e.g., self-supervised learning [37, 38] and network calibration [35, 41]. We mainly investigate the effect of the vanilla mixup [49] on network calibration. However, as will be shown in our experiments, the variants of mixup, including CutMix [47] and manifold-Mixup [45], can also be readily adapted to our approach." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.846, + 0.188, + 0.864 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.871, + 0.472, + 0.903 + ], + "angle": 0, + "content": "We present in this section preliminaries for network calibration and mixup [49] in Sec. 3.1, and provide a detailed" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.894, + 0.123 + ], + "angle": 0, + "content": "description of RankMiup and training losses in Secs. 3.2 and 3.3, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.13, + 0.642, + 0.145 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.153, + 0.894, + 0.273 + ], + "angle": 0, + "content": "Network calibration. Let us suppose a dataset \\(D = \\{(\\mathbf{x}_i, \\mathbf{y}_i)\\}_{i=1}^N\\) of size \\(N\\), where \\(\\mathbf{x}_i \\in \\mathcal{X}\\) and \\(\\mathbf{y}_i \\in \\mathcal{Y}\\) are an input sample and a ground-truth label with \\(K\\) classes, respectively. DNNs can be considered as a function, parameterized by \\(\\theta\\), that yields a logit \\(\\mathbf{z}_i\\) of size \\(K \\times 1\\) from the input sample: \\(\\mathbf{f}_\\theta : \\mathcal{X} \\to \\mathbb{R}^K\\). For multiclass classification, the networks compute class probabilities using the softmax function as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.278, + 0.892, + 0.314 + ], + "angle": 0, + "content": "\\[\np _ {i, k} = \\operatorname {s o f t m a x} \\left(\\mathbf {z} _ {i}\\right) = \\frac {\\exp z _ {i , k}}{\\sum_ {j} ^ {K} \\exp z _ {i , j}}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.32, + 0.893, + 0.366 + ], + "angle": 0, + "content": "where we denote by \\( p_{i,k} \\) a probability of the \\( k \\)-th class for the \\( i \\)-th input. Based on the probabilities, the networks predict a class for the input sample \\( \\mathbf{x}_i \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.632, + 0.376, + 0.892, + 0.397 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {i} = \\arg \\max _ {k} p _ {i, k}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.404, + 0.892, + 0.432 + ], + "angle": 0, + "content": "The corresponding confidence can then be obtained as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.643, + 0.435, + 0.892, + 0.455 + ], + "angle": 0, + "content": "\\[\n\\hat {p} _ {i} = \\max _ {k} p _ {i, k}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.459, + 0.892, + 0.489 + ], + "angle": 0, + "content": "During training, the networks are optimized using a cross-entropy (CE) loss as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.498, + 0.892, + 0.54 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {C E} \\left(\\mathbf {x} _ {i}, \\mathbf {y} _ {i}\\right) = - \\sum_ {k = 1} ^ {K} y _ {i, k} \\log p _ {i, k}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.547, + 0.894, + 0.651 + ], + "angle": 0, + "content": "where \\( y_{i,k} \\) is the \\( k \\)-th element of the one-hot encoded label \\( \\mathbf{y}_i \\). Recent works [10, 29, 30, 41] have shown that DNNs trained with the CE loss tend to be overconfident, providing higher accuracies than accuracies. To address this problem, confidence calibration methods encourage that the confidence for each sample and the accuracy are the same as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.626, + 0.662, + 0.892, + 0.68 + ], + "angle": 0, + "content": "\\[\n\\hat {p} _ {i} = P \\left(\\hat {y} _ {i} = y _ {i} \\mid \\hat {p} _ {i}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.687, + 0.892, + 0.718 + ], + "angle": 0, + "content": "where \\( y_{i} \\) is an index of the true class for the ground-truth label \\( \\mathbf{y}_{i} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Mixup. Mixup [49] is a data-augmentation technique based on the vicinal risk minimization principle [2]. It introduces the mixup vicinal distribution, which measures the likelihood of finding a pair of an augmented input and a target label, \\((\\tilde{\\mathbf{x}}_i,\\tilde{\\mathbf{y}}_i)\\), from the vicinity of the original pair, \\((\\mathbf{x}_i,\\mathbf{y}_i)\\). Mixup samples the vicinal distribution to construct a new dataset, \\(D_{v} = \\{(\\tilde{\\mathbf{x}}_{i},\\tilde{\\mathbf{y}}_{i})\\}_{i = 1}^{N}\\). Here, we denote by \\(D_{v}\\) the vicinal set consisting of pairs of augmented training samples and corresponding target labels. Specifically, it augments training pairs by linearly interpolating the original ones as follows:" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1360" + } + ], + [ + { + "type": "equation", + "bbox": [ + 0.195, + 0.105, + 0.468, + 0.129 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\tilde {\\mathbf {x}} = \\lambda \\mathbf {x} _ {i} + (1 - \\lambda) \\mathbf {x} _ {j}, \\\\ \\tilde {\\dots} \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\end{array} \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.126, + 0.35, + 0.141 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {y}} = \\lambda \\mathbf {y} _ {i} + (1 - \\lambda) \\mathbf {y} _ {j},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.149, + 0.473, + 0.346 + ], + "angle": 0, + "content": "where two pairs of input samples and target labels, \\((\\mathbf{x}_i,\\mathbf{y}_i)\\) and \\((\\mathbf{x}_j,\\mathbf{y}_j)\\), are randomly drawn from the training set \\(D\\) and \\(\\lambda \\in [0,1] \\sim \\mathrm{Beta}(\\alpha ,\\alpha)\\) is a mixing coefficient, sampled from a Beta distribution. Mixup assumes that target labels for the vicinal set should also be interpolated with the same mixing coefficient as input samples during the mixing process. The hyperparameter \\(\\alpha\\) controls the strength of interpolation between the pairs of input samples and target labels. According to [49], the value of \\(\\alpha\\) within the range of [0.1, 0.4] provides better classification performance, while higher values cause significant underfitting. We will also examine the effect of \\(\\alpha\\) in terms of confidence calibration within our framework." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.357, + 0.208, + 0.373 + ], + "angle": 0, + "content": "3.2. RankMixup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.473, + 0.699 + ], + "angle": 0, + "content": "Mixup provides smooth decision boundaries that gradually shift from one class to another, which leads to a regularized estimate of uncertainty (or confidence) [49]. There have been lots of studies to discover underlying principles behind the mixup method [15, 41, 50, 51, 51]. For example, it has proven to give better output probabilities in terms of model calibration, alleviating overconfident predictions [35, 41, 51]. The interpolated labels of augmented samples in the vicinal set do not always model the actual distribution of label mixtures in augmented samples [3, 19, 39, 43], which however has not been considered for designing a network calibration method. To alleviate this problem, we leverage ordinal ranking relationships between confidences from raw and augmented samples, as well as those among confidences from multiple augmented samples. We then propose to use them as supervisory signals for model calibration, rather than using the mixture of labels directly. In the following, we describe our framework with a single mixup-augmented sample, and present a generalized version that can handle multiple augmented samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Single mixup-augmented sample. The sample augmented by mixup \\(\\bar{\\mathbf{x}}\\) in Eq. (6) can be interpreted as a combination of the raw sample \\(\\mathbf{x}_i\\) and structured noise from another one \\(\\mathbf{x}_j\\), where the degree of noise is determined by the mixing parameter \\(\\lambda\\). This suggests that DNNs predict the class of the augmented sample with uncertainty imposed by the additional one, making it more difficult to recognize the augmented sample than the raw one. To this end, mixup imposes uncertainty on the label mixtures by adjusting confidence of target labels for the augmented samples by \\(\\lambda\\) (or \\(1 - \\lambda\\)). Albeit simple, directly using the interpolated labels may provide misleading supervisory signals" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.23 + ], + "angle": 0, + "content": "to train DNNs. To avoid this, we leverage an ordinal ranking relationship between confidence of raw and augmented samples. Specifically, the ordinal ranking holds for the relationship that confidence levels of easy-to-classify samples should be higher than the ones for hard samples [28]. Accordingly, we conjecture that the confidence levels of raw samples should be greater than those of the augmented samples in the mixing process (Fig.1). Namely, every pair of samples \\((\\mathbf{x}_i,\\tilde{\\mathbf{x}}_i)\\) should satisfy the following relationship:" + }, + { + "type": "equation", + "bbox": [ + 0.622, + 0.242, + 0.892, + 0.263 + ], + "angle": 0, + "content": "\\[\n\\max _ {k} p _ {i, k} \\geq \\max _ {k} \\tilde {p} _ {i, k}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.275, + 0.895, + 0.335 + ], + "angle": 0, + "content": "where \\(\\tilde{p}_{i,k}\\) is a predicted probability of the class \\(k\\) for the augmented sample \\(\\tilde{\\mathbf{x}}_i\\). We devise MRL that encourages the network to learn this relationship without the mixture of labels, which will be described in Sec. 3.3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.895, + 0.538 + ], + "angle": 0, + "content": "Multiple mixup-augmented samples. We extend our framework to exploit multiple mixup-augmented samples. As the mixing ratio \\(\\lambda\\) decreases, augmented samples become more difficult to recognize, which suggests that we can exploit more complex ranking relationships among the multiple augmented samples. Analogous to the single case, we expect that the samples augmented with larger mixing coefficients \\(\\lambda\\) show higher confidence compared to those with smaller coefficients (Fig. 1). For every pair of augmented samples \\((\\tilde{\\mathbf{x}}_i,\\tilde{\\mathbf{x}}_j)\\) from the vicinal set \\(D_{v}\\), the confidence of these samples should satisfy the following relationship:" + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.552, + 0.892, + 0.574 + ], + "angle": 0, + "content": "\\[\n\\lambda_ {i} \\geq \\lambda_ {j} \\Leftrightarrow \\max _ {k} \\tilde {p} _ {i, k} \\geq \\max _ {k} \\tilde {p} _ {j, k}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.587, + 0.892, + 0.661 + ], + "angle": 0, + "content": "where \\((\\lambda_i, \\lambda_j)\\) is a pair of mixing ratios for the corresponding pair of augmented samples \\((\\tilde{\\mathbf{x}}_i, \\tilde{\\mathbf{x}}_j)\\). Note that we describe the relationship with two samples for simplicity, but our framework can adopt the relationship with any number of augmented samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.662, + 0.895, + 0.74 + ], + "angle": 0, + "content": "We then integrate both the relationships in Eqs. (7) and (8) to obtain a general version of RankMixup. With the mixing coefficient of 1.0 for the raw sample, the following relationship should hold for every triplet of samples \\((\\mathbf{x}_i,\\tilde{\\mathbf{x}}_i,\\tilde{\\mathbf{x}}_j)^1\\):" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.752, + 0.892, + 0.773 + ], + "angle": 0, + "content": "\\[\n1. 0 \\geq \\lambda_ {i} \\geq \\lambda_ {j} \\Leftrightarrow \\max _ {k} p _ {i, k} \\geq \\max _ {k} \\tilde {p} _ {i, k} \\geq \\max _ {k} \\tilde {p} _ {j, k}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.785, + 0.895, + 0.876 + ], + "angle": 0, + "content": "This allows the network to estimate the levels of confidence better by considering diverse ordinal ranking relationships among the confidences of the raw and multiple mixup-augmented samples. To implement this idea, we align the orders of confidences and mixing ratios during training using M-NDCG (Sec. 3.3)." + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.887, + 0.756, + 0.901 + ], + "angle": 0, + "content": "1 Note that Eq. (9) holds only when \\( \\lambda \\geq 0.5 \\)." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1361" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.214, + 0.108 + ], + "angle": 0, + "content": "3.3. Training loss" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.47, + 0.206 + ], + "angle": 0, + "content": "To train our model, we use a CE loss for classification, together with either MRL or M-NDCG for network calibration, balanced by the parameter of \\( w \\). As supervisory signals, we exploit one-hot encoded labels for classification, and ordinal ranking relationships for input and augmented samples for network calibration." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.227, + 0.47, + 0.287 + ], + "angle": 0, + "content": "MRL. We introduce MRL facilitating the ordinal relationship in Eq. (7). It encourages confidence of augmented samples to be lower than those of raw samples by a margin, defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.111, + 0.302, + 0.469, + 0.325 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {M R L}} = \\max \\left(0, \\max _ {k} \\tilde {p} _ {i, k} - \\max _ {k} p _ {i, k} + m\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.335, + 0.47, + 0.532 + ], + "angle": 0, + "content": "where the margin \\( m \\) determines acceptable discrepancies between the confidence of raw and augmented samples. The intuition behind using a margin is twofold: (1) It enables maintaining the ranking relationship between confidence, rather than penalizing the exact value of the discrepancies itself. (2) Controlling the confidence discrepancies with a margin allows to consider the uncertainty of inaccurate label mixtures. The vanilla mixup method continues to penalize the confidence of augmented samples, until they reach overconfident values, determined by the label mixtures. In contrast to this, MRL penalizes the confidence, only when the absolute discrepancies between them are below the margin." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.47, + 0.705 + ], + "angle": 0, + "content": "M-NDCG. MRL is not sufficient to model the relationship in Eq. (9), where the comparison involves more than one augmented sample. M-NDCG addresses this problem that enables multiple confidence values to hold the ordinal ranking relationships. M-NDCG is based on NDCG used for evaluating ranking quality in information retrieval [17, 44]. It measures how many of retrieved results are aligned with the ground-truth ranking order, which can be calculated by normalizing a discounted cumulative gain (DCG) with an ideal DCG (IDCG):" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.715, + 0.469, + 0.747 + ], + "angle": 0, + "content": "\\[\nN D C G = \\frac {D C G}{I D C G}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.756, + 0.469, + 0.803 + ], + "angle": 0, + "content": "DCG accumulates a relevance score of each retrieval result, weighted by a corresponding rank, and IDCG is computed similarly but with the ground-truth score, as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.815, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} D C G = \\sum_ {q = 1} ^ {Q} \\frac {r _ {q}}{\\log_ {2} (q + 1)}, \\tag {12} \\\\ I D C G = \\sum_ {q = 1} ^ {Q} \\frac {r _ {q} ^ {\\mathrm {g t}}}{\\log_ {2} (q + 1)}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.091, + 0.89, + 0.122 + ], + "angle": 0, + "content": "where \\(r_q\\) and \\(r_q^{\\mathrm{gt}}\\) are the relevance and ground-truth scores, respectively, at position \\(q\\) in the result list of size \\(Q\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.123, + 0.892, + 0.198 + ], + "angle": 0, + "content": "We consider confidences of predictions and mixing coefficients as the relevance and ground-truth scores, respectively, enabling multiple confidences to satisfy the relationship in Eq. (9). Given \\(Q\\) pairs of confidences and mixing coefficients, we compute \\(DCG_{\\mathrm{M}}\\) and \\(IDCG_{\\mathrm{M}}\\), as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.222, + 0.891, + 0.311 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} D C G _ {\\mathrm {M}} = \\frac {\\operatorname* {m a x} _ {k} p _ {t , k}}{\\log_ {2} (t + 1)} + \\sum_ {q = 1, q \\neq t} ^ {Q} \\frac {\\operatorname* {m a x} _ {k} \\tilde {p} _ {q , k}}{\\log_ {2} (q + 1)}, \\tag {13} \\\\ I D C G _ {\\mathrm {M}} = 1 + \\sum_ {q = 2} ^ {Q} \\frac {\\lambda_ {q} ^ {\\mathrm {g t}}}{\\log_ {2} (q + 1)}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.323, + 0.892, + 0.472 + ], + "angle": 0, + "content": "where \\( t \\) is the position of the confidence value for the raw sample, which is set to 1 in order to ensure that its confidence is always ranked first in a descending order, following the ranking relationship in Eq. (9). \\( Q \\) is a hyperparameter that determines the number of augmented samples, i.e., \\( Q - 1 \\) augmented samples. \\( \\lambda_q^{\\mathrm{gt}} \\) is the mixing coefficient sorted based on its magnitude, with a value of 1.0 for the raw sample appearing at position of the top rank, i.e., \\( \\lambda_1^{\\mathrm{gt}} = 1 \\). We then define M-NDCG loss as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.47, + 0.891, + 0.502 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {M - N D C G}} = 1 - \\frac {D C G _ {\\mathrm {M}}}{I D C G _ {\\mathrm {M}}}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.506, + 0.892, + 0.612 + ], + "angle": 0, + "content": "which is minimized when the ranking orders of the confidences and mixing coefficients are aligned to each other after sorting in a descending order. The network is thus trained to encourage the confidence to hold the ordinal ranking relationship of RankMixup in Eq. (9). M-NDCG also discounts lower-ranked confidence more, preventing the uncertain predictions from being overconfident." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.626, + 0.634, + 0.643 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.714, + 0.667 + ], + "angle": 0, + "content": "4.1. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Datasets. We mainly perform experiments on CIFAR10/100 [20], Tiny-ImageNet [23] for network calibration. The CIFAR10/100 datasets consist of 50,000 training and 10,000 test images of size \\(32 \\times 32\\), and provide 10/100 object categories, respectively. Tiny-ImageNet includes 120,000 images of size \\(64 \\times 64\\) for 200 object categories. Each category in Tiny-ImageNet contains 600 images, which are divided into 500, 50 and 50 images for training, validation and test, respectively. Tiny-ImageNet is more challenging, compared to CIFAR10/100, as it contains lots of object classes with a smaller number of samples per category. We further validate the generalization ability of our method on ImageNet [6], which comprises around 1.2M training and 50K validation images across 1K classes. For out-of-distribution (OOD) detection, we train a model" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1362" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.082, + 0.895, + 0.125 + ], + "angle": 0, + "content": "Table 1: Quantitative comparison with the state of the art in terms of ECE (%) and AECE (%) with 15 bins on the validation splits of CIFAR10/100 [20] and Tiny-ImageNet [23]. Numbers in bold indicate the best performance and underscored ones indicate the second best. Numbers in parentheses represent the results obtained using a TS post-hoc technique [10]." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.129, + 0.891, + 0.288 + ], + "angle": 0, + "content": "
MethodsCIFAR10 [20]CIFAR100 [20]Tiny-ImageNet [23]
ResNet-50 [13]ResNet-101 [13]ResNet-50 [13]ResNet-101 [13]ResNet-50 [13]ResNet-101 [13]
Acc↑ECE↓AEE↓Acc↑ECE↓AEE↓Acc↑ECE↓AECE↓Acc↑ECE↓AECE↓Acc↑ECE↓AECE↓
CE95.383.75(0.97)2.98(1.01)94.463.61(0.92)3.55(0.85)77.8113.59(2.93)13.54(2.86)77.4812.94(2.63)12.94(2.66)64.343.18(3.18)2.87(2.87)66.043.50(3.50)3.52(3.52)
MMCE [22]95.183.88(0.97)3.88(1.12)94.993.88(1.15)3.88(12.9)77.5612.72(2.83)12.71(2.86)77.8213.43(3.06)13.42(2.80)64.802.03(2.03)1.97(1.97)66.443.40(3.40)3.38(3.38)
ECP [34]94.754.01(1.06)3.99(1.53)93.974.41(1.72)4.40(1.70)76.2012.29(2.08)12.28(2.22)76.8113.43(2.92)13.42(3.04)64.881.94(1.94)1.95(1.95)66.202.72(2.72)2.70(2.70)
LS [30]94.873.27(1.58)3.67(3.02)94.183.35(1.51)3.85(3.10)76.456.73(4.23)6.54(4.26)76.917.99(4.38)7.87(4.55)65.463.21(2.51)3.23(2.51)65.523.11(2.51)2.92(2.72)
FL [24]94.823.42(1.07)3.41(0.87)93.593.27(1.12)3.23(1.37)76.412.83(1.66)2.88(1.73)76.123.10(2.58)3.22(2.51)63.082.03(2.03)1.94(1.94)64.022.18(2.18)2.09(2.09)
Mixup [41]94.762.86(1.37)2.81(2.00)95.506.87(1.18)6.79(2.33)78.478.68(2.14)8.68(2.19)78.748.92(3.69)8.91(3.65)65.811.92(1.92)1.96(1.96)66.412.41(1.97)2.43(1.95)
FLSD [29]94.773.86(0.83)3.74(0.96)93.263.92(0.93)3.67(0.94)76.202.86(2.86)2.86(2.86)76.613.29(2.04)3.25(1.78)63.561.93(1.93)1.98(1.98)64.021.85(1.85)1.81(1.81)
CRL [28]95.083.14(0.96)3.11(1.25)95.043.74(1.12)3.73(2.03)77.856.30(3.43)6.26(3.56)77.607.29(3.32)7.14(3.31)64.881.65(2.35)1.52(2.34)65.873.57(1.60)3.56(1.52)
CPC [4]95.045.05(1.89)5.04(2.60)95.364.78(1.52)4.77(2.37)77.2313.29(3.74)13.28(3.82)77.5013.32(2.96)13.28(3.23)65.703.41(3.41)3.42(3.42)66.443.93(3.93)3.74(3.74)
MbLS [25]95.251.16(1.16)3.18(3.18)95.131.38(1.38)3.25(3.25)77.924.01(4.01)4.14(4.14)77.455.49(5.49)6.52(6.52)64.741.64(1.64)1.73(1.73)65.811.62(1.62)1.68(1.68)
RegMixup [35]94.682.76(0.98)2.67(0.92)95.034.75(0.92)4.74(0.94)76.765.50(1.98)5.48(1.98)76.934.20(1.36)4.15(1.92)63.583.04(1.89)3.04(1.81)63.263.35(1.86)3.32(1.68)
RankMixup (MRL)94.591.01(0.84)1.03(0.80)94.182.86(1.08)2.87(1.58)76.653.52(2.40)3.39(2.05)77.264.41(1.68)4.24(1.76)64.541.70(1.70)1.69(1.69)64.802.26(1.78)2.28(1.60)
RankMixup (M-NDCG)94.882.59(0.57)2.58(0.52)94.253.24(0.65)3.21(0.56)77.113.46(1.49)3.45(1.42)76.463.49(1.10)3.49(1.40)64.971.49(1.49)1.44(1.44)64.891.57(1.57)1.94(1.94)
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.471, + 0.381 + ], + "angle": 0, + "content": "using CIFAR10, and use CIFAR100, Tiny/ImageNet, and SVHN [31] as OOD datasets, following the experimental protocol in [26, 35]. Similarly, CIFAR100 is used to train a model, and evaluate it on CIFAR10, Tiny/ImageNet, and SVHN." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.397, + 0.47, + 0.485 + ], + "angle": 0, + "content": "Evaluation protocols. Following the standard protocol [4, 14, 25, 29, 30, 41], we use expected calibration error (ECE) and adaptive ECE (AECE) as evaluation metrics for network calibration. ECE measures the expected absolute difference between confidences and corresponding accuracies:" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.488, + 0.469, + 0.505 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} \\left[ \\left| P \\left(\\hat {y} _ {i} = y _ {i} \\mid \\hat {p} _ {i}\\right) - \\hat {p} _ {i} \\right| \\right]. \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.47, + 0.68 + ], + "angle": 0, + "content": "To compute ECE, we divide a range \\((0,1]\\) into equidistance bins, and compute an average of the absolute differences, weighted by the size of each bin. We set the number of bins for both ECE and AECE as 15, following the protocol. We also report top-1 classification accuracies to compare discriminative capabilities. We provide results obtained without/with applying a post-hoc technique. In particular, we use the TS method [10], where the temperature is optimized on the validation sets. For OOD detection, we compare the area under the receiver operating characteristics (AUROC), following the standard evaluation protocol [26, 35]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.691, + 0.47, + 0.83 + ], + "angle": 0, + "content": "Methods for comparison. We compare our method with various training-time approaches. In addition to the baseline model using the CE loss, we include implicit methods (LS [30], FL/FLSD [29], Mixup [41], mbLS [25], and RegMixup [35]) and explicit methods (ECP [34], MMCE [22], and CPC [4]). We have reproduced results using official codes with hyperparameter settings provided by the authors, if they are not available. Detailed descriptions for the hyperparameters can be found in the supplement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Training details. Following [25], we train our network for 200 epochs for CIFAR10/100 [20], with an initial learning rate of 1e-1 and a batch size of 128. We also follow the training setting in [25] for Tiny/ImageNet [23] ex" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.295, + 0.895, + 0.351 + ], + "angle": 0, + "content": "Table 2: Quantitative comparison with the state of the art in terms of ECE (\\%) and AECE (\\%) with 15 bins on the validation split of ImageNet [6]. Numbers in bold indicate the best performance and underscored ones indicate the second best." + }, + { + "type": "table", + "bbox": [ + 0.553, + 0.356, + 0.84, + 0.463 + ], + "angle": 0, + "content": "
MethodsImageNet [6]
ResNet-50 [13]
Acc↑ECE↓AECE↓
CE73.969.109.24
Mixup [41]75.847.077.09
CRL [28]73.838.478.47
MbLS [25]75.394.074.14
RegMixup [35]75.645.345.42
RankMixup (MRL)75.275.705.71
RankMixup (M-NDCG)74.863.933.92
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.488, + 0.895, + 0.701 + ], + "angle": 0, + "content": "cept for a batch size of 32 due to memory limits. All networks are trained using the SGD optimizer with a momentum of 0.9. The learning rate decreases by a tenth at every fixed intervals. We use ResNet50 [13], and ResNet101 [13] for both CIFAR10/100 [20] and Tiny-ImageNet [23], and ResNet50 for ImageNet [6]. For more comprehensive experiments, we also exploit WideResNet [48] for CIFAR10 and Tiny-ImageNet. We fix the balancing parameter of training loss \\( w \\) to 0.1. We set margin \\( m \\) to 2.0 and 1.0 for CIFAR10/100 and Tiny-ImageNet, respectively, using each validation dataset. Other hyperparameters, such as \\( \\alpha \\) and \\( Q \\), are chosen similarly. For OOD detection, we train the network using M-NDCG and in-distribution (ID) datasets with the same training settings used for network calibration." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.711, + 0.593, + 0.725 + ], + "angle": 0, + "content": "4.2. Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Comparison with the state of the art. We compare in Table 1 our method with state-of-the-art calibration approaches. From the tables, we observe four things: (1) Our models outperform other mixup-based methods [35, 41] using label mixtures as supervisions, demonstrating the effectiveness of our approach to leveraging an ordinal ranking relationship for confidences. (2) Our model using M-NDCG achieves the best performance in terms of both ECE and AECE on the challenging TinyImageNet [23] dataset, while providing competitive results on CIFAR10/100. This suggests that the ordinal ranking" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1363" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.082, + 0.47, + 0.138 + ], + "angle": 0, + "content": "Table 3: Quantitative comparison in terms of ECE (\\%) and AECE (\\%) with 15 bins on the validation splits of CIFAR10 [20] and Tiny-ImageNet [23]. Numbers in bold indicate the best performance and underscored ones are the second best." + }, + { + "type": "table", + "bbox": [ + 0.11, + 0.142, + 0.438, + 0.238 + ], + "angle": 0, + "content": "
CIFAR10 [20]Tiny-ImageNet [23]
MethodsWide-ResNet-26-10 [48]
Acc↑ECE↓AECE↓Acc↑ECE↓AECE↓
CE95.802.702.6665.186.086.06
Mixup [41]96.533.143.0866.363.773.75
MbLS [25]95.701.452.7865.302.572.32
RegMixup [35]95.444.183.9963.403.873.93
RankMixup (MRL)95.571.701.3865.343.303.28
RankMixup (M-NDCG)95.731.621.5365.563.833.94
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.246, + 0.468, + 0.286 + ], + "angle": 0, + "content": "Table 4: Quantitative comparison with the state of the art in terms of AUROC \\((\\%)\\). Numbers in bold indicate the best performance and underscored ones indicate the second best." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.292, + 0.468, + 0.398 + ], + "angle": 0, + "content": "
IDC10 [20]C100 [20]
OODC100 [20]Tiny [23]SVHN [31]C10 [20]Tiny [23]SVHN [31]
AUROC↑AUROC↑
TS [10]86.7388.0692.1476.3880.1282.41
LS [30]75.2376.2974.2372.9277.5472.33
FL [29]85.6386.8492.6678.3781.2386.37
Mixup [41]82.0784.0979.7278.4681.5576.21
CPC [4]85.2885.1592.7974.6876.6671.72
MbLS [25]86.2087.5589.9873.8879.1973.19
RegMixup [35]87.8287.5483.1576.0080.7275.05
RankMixup (M-NDCG)87.8288.9492.6278.6480.6785.42
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.416, + 0.468, + 0.581 + ], + "angle": 0, + "content": "relationships among confidences is crucial for network calibration, and M-NDCG effectively encourages our model to provide confidences maintaining the relationships. We can also see that our method generalizes well to the large-scale dataset. (3) Our method outperforms another ranking-based method (CRL)[28] significantly, suggesting that more complex ranking relationship based on augmented samples enables estimating better confidences. (4) Ours with the post-hoc method [10] gives the best results in most settings, which indicates that they are complementary to each other, and exploiting both further boosts the calibration accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.582, + 0.468, + 0.704 + ], + "angle": 0, + "content": "We also provide in Tables 2 and 3 quantitative results on ImaergeNet [6] and for the WideResNet backbone [48], respectively. They show similar trends to those in Table 1, validating the effectiveness of our approach across various network architectures and large-scale datasets. Specifically, our models provide competitive results with the state of the art [25], while outperforming mixup-based methods [35, 41] and the ranking-based one [28]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.468, + 0.9 + ], + "angle": 0, + "content": "OOD detection. We compare in Table 4 the OOD detection accuracy using the ResNet-50 [13] architecture. We use the entropy of the softmax output as an uncertainty measure for binary classification and report AUROC scores for comparison. From the table, we have two findings. Our model trained with M-NDCG outperforms other mixup-based methods and achieves the highest AUROC scores in most settings. This indicates that ordinal ranking relationship of confidences is also crucial for OOD detection, suggesting that models trained with M-NDCG are not only better calibrated but also perform better than other calibration methods under the distributional shifts." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.083, + 0.892, + 0.138 + ], + "angle": 0, + "content": "Table 5: Quantitative comparison by varying the margin \\( m \\) . We report the ECE (%) for the models trained with MRL. Numbers in parentheses represent the results obtained using a TS post-hoc technique [10]." + }, + { + "type": "table", + "bbox": [ + 0.584, + 0.149, + 0.807, + 0.231 + ], + "angle": 0, + "content": "
CIFAR10 [20]Tiny-ImageNet [23]
ECE↓ECE↓
m = 1.01.54(1.09)1.49(1.49)
m = 2.01.01(0.84)1.70(1.70)
m = 3.02.12(0.93)1.54(1.54)
m = 4.03.12(1.67)2.37(1.77)
m = 5.013.13(0.48)2.42(1.48)
" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.238, + 0.847, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.363, + 0.892, + 0.404 + ], + "angle": 0, + "content": "Figure 2: Quantitative results by varying the margin \\( m \\). We plot OE (\\%) and UE (\\%) on the validation split of CIFAR10 [20]. Best viewed in color." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.422, + 0.618, + 0.436 + ], + "angle": 0, + "content": "4.3. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.445, + 0.892, + 0.566 + ], + "angle": 0, + "content": "In this section, we analyze the effects of the hyperparameters in our framework, and show generalization ability by incorporating other mixup techniques into our framework. For the analyses, we mainly adopt the ResNet-50 [13] models trained with M-NDCG, and report ECE and AECE on the validation sets of CIFAR10 [20] and TinyImageNet [23], unless otherwise specified. We use 15 bins to measure the ECE and AECE." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.57, + 0.892, + 0.704 + ], + "angle": 0, + "content": "Margin. We compare in Table 5 the calibration results of the models trained with MRL and various margins. We can see that small margins provide better performances for both datasets. Furthermore, we find that increasing the margin degrades the classification accuracy. A reason is that a large margin could make a significant difference in confidence levels between the raw and augmented samples. That is, with a larger margin, the augmented sample is more likely to have a lower confidence than its actual value." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.706, + 0.892, + 0.782 + ], + "angle": 0, + "content": "To demonstrate this, we compute overconfidence errors (OE) [41] that measure the expected difference between confidence values of overconfident predictions and corresponding accuracies. Given \\( H \\) bins of equal size, OE is defined as follows [41]:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.79, + 0.892, + 0.84 + ], + "angle": 0, + "content": "\\[\nO E = \\sum_ {h = 1} ^ {H} \\frac {\\left| B _ {h} \\right|}{N} [ \\operatorname {c o n f} \\left(B _ {h}\\right) \\times \\max \\left(\\operatorname {c o n f} \\left(B _ {h}\\right) - \\operatorname {a c c} \\left(B _ {h}\\right), 0\\right) ], \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(N\\) is the total number of samples, and \\(B_{h}\\) is the set of samples, whose confidence falls into the \\(h\\)-th bin. We denote by \\(\\mathrm{acc}(B_h)\\) and \\(\\mathrm{conf}(B_h)\\) the accuracy and averaged confidence of the \\(h\\)-th bin, respectively. Similar to OE, we" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1364" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.083, + 0.47, + 0.138 + ], + "angle": 0, + "content": "Table 6: Quantitative results of our model with various numbers of the augmented samples. We report the ECE (\\%) for comparison. Numbers in parentheses represent the results obtained using a TS post-hoc technique [10]." + }, + { + "type": "table", + "bbox": [ + 0.164, + 0.149, + 0.376, + 0.224 + ], + "angle": 0, + "content": "
CIFAR10 [20]Tiny-ImageNet [23]
ECE↓ECE↓
Q = 23.01(0.82)3.25(1.44)
Q = 32.78(0.50)2.18(1.12)
Q = 42.59(0.57)1.49(1.49)
Q = 52.37(0.64)1.52(1.52)
Q = 62.24(0.59)1.30(1.30)
" + }, + { + "type": "image", + "bbox": [ + 0.118, + 0.226, + 0.426, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.41, + 0.468, + 0.436 + ], + "angle": 0, + "content": "Figure 3: Probability density function (PDF) of Beta distribution with various \\(\\alpha\\)s." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.451, + 0.468, + 0.481 + ], + "angle": 0, + "content": "define underconfidence errors (UE) computing the difference using underconfident predictions as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.493, + 0.468, + 0.542 + ], + "angle": 0, + "content": "\\[\nU E = \\sum_ {h = 1} ^ {H} \\frac {\\left| B _ {h} \\right|}{N} [ \\operatorname {c o n f} \\left(B _ {h}\\right) \\times \\max \\left(\\operatorname {a c c} \\left(B _ {h}\\right) - \\operatorname {c o n f} \\left(B _ {h}\\right), 0\\right) ]. \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.543, + 0.468, + 0.664 + ], + "angle": 0, + "content": "We plot in Fig. 2 UE and OE for ResNet-50 with MRL on CIFAR10 [20], while varying margins. We can see that UE increases drastically, according to the margins, while OE decreases gradually. This suggests that exploiting a large margin causes underconfidence problems, where the model becomes less confident in its predictions. An underconfident model produces large calibration errors [41, 49], leading to the degraded performance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.677, + 0.468, + 0.858 + ], + "angle": 0, + "content": "Number of augmented samples. We compare in Table 6 the calibration performance in terms of ECE with varying number of augmented samples. We set \\(\\alpha\\) to 2.0 and 1.0 for CIFAR10 and Tiny-ImageNet, respectively. We can observe that ECE improves as more augmented samples are used, suggesting that learning with diverse ranking relationships between a number of augmented samples encourages the model to estimate confidence levels better. This further implies that the mixup coefficient \\(\\lambda\\) is also an important factor, since it enables modeling the diverse ranking relationships. This leads us to analyze the mixup coefficient \\(\\lambda\\) in detail in the following." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Mixup coefficient. Following [49], we sample the mixup coefficient \\(\\lambda\\) from a Beta distribution, making it possible" + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.084, + 0.852, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.542, + 0.208, + 0.85, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.329, + 0.892, + 0.383 + ], + "angle": 0, + "content": "Figure 4: Quantitative results by varying the parameter of the Beta distribution \\((\\alpha)\\). We plot ECE \\((\\%)\\) and AECE \\((\\%)\\) on the validation split of CIFAR10 [20] (top) and Tiny-ImageNet [23] (bottom). Best viewed in color." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.408, + 0.892, + 0.905 + ], + "angle": 0, + "content": "to generate various augmented samples. Note that the degree of the diversity is determined by how we set the shape parameter for the Beta distribution. For an in-depth analysis, we also show in Fig. 3 the probability density functions (PDFs) of different \\(Beta(\\alpha, \\alpha)\\) distributions, while varying the shape parameter \\(\\alpha\\). We evaluate the calibration errors of the models trained with M-NDCG along with different shape parameters \\(\\alpha\\) of the Beta distribution, and show the results using 3 augmented images (\\(Q = 4\\)) in Fig. 4. From the figures, we observe two things: (1) Our models achieve the best performances with \\(\\alpha = 2\\) and \\(\\alpha = 1\\) on CIFAR10 and Tiny-ImageNet, respectively, where the corresponding PDFs are relatively flat, as shown in Fig. 3. This suggests that diverse mixup coefficients \\(\\lambda\\) drawn from such distributions can enhance the calibration performances, as it allows us to augment the samples in a more diverse way. (2) Our model performs well with large \\(\\alpha\\), which is in contrast to the vanilla mixup [41, 49], where the value of \\(\\alpha\\) within the range of [0.1, 0.4] yields better classification and calibration performances. When \\(\\alpha\\) is too large, it suffers from an underconfidence problem [41, 49] and is also affected by manifold intrusion [11], leading to significant performance drops in both the classification and calibration. The manifold intrusion happens when the label mixture of an augmented sample differs from the label of the real sample [11]. However, in our framework, we do not explicitly use the label mixtures as supervision, suggesting that our framework is less affected by those problems. Therefore, our framework is more robust to the variation of the parameter \\(\\alpha\\) compared to the vanilla mixup. To further investigate the importance of diverse samples, we also perform experiments with various combinations of \\(\\alpha\\) and \\(Q\\) and provide the results in the supplementary material." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.515, + 0.956 + ], + "angle": 0, + "content": "1365" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.083, + 0.47, + 0.125 + ], + "angle": 0, + "content": "Table 7: Quantitative comparison of calibration performances using other mixup techniques on the validation splits of CIFAR10 [20] and Tiny-ImageNet [23]." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.128, + 0.466, + 0.202 + ], + "angle": 0, + "content": "
Mixup [49] Manifold [45] CutMix [47]CIFAR10 [20]Tiny-ImageNet [23]
ECE↓AECE↓ECE↓AECE↓
RegMixup [35]✓3.633.574.764.88
✓3.563.542.972.93
RankMixup✓2.922.981.201.22
✓3.263.211.801.66
✓2.592.581.491.44
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.21, + 0.469, + 0.266 + ], + "angle": 0, + "content": "Table 8: Quantitative comparison of classification and calibration performances on the test splits of CIFAR10-LT [1] and CIFAR100-LT [1]. We report the Top-1 accuracy \\((\\%)\\) and ECE \\((\\%)\\) with 15 bins." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.271, + 0.462, + 0.375 + ], + "angle": 0, + "content": "
CIFAR10-LT [1]CIFAR100-LT [1]
Methodsρ = 10Acc↑/ECE↓ρ = 100Acc↑/ECE↓ρ = 10Acc↑/ECE↓ρ = 100Acc↑/ECE↓
CE86.39/6.6070.36/20.5355.70/22.8538.32/38.23
Mixup [49]87.10/6.5573.06/19.2058.02/19.6939.54/32.72
Remix [5]88.15/6.8175.36/15.3859.36/20.1741.94/33.56
UniMix [46]89.66/6.0082.75/12.8761.25/19.3845.45/27.12
RankMixup (MRL)88.83/2.1674.16/ 2.0362.84/13.5542.56/ 5.28
RankMixup (M-NDCG)89.80/5.9475.41/14.1063.83/ 9.9943.00/18.74
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.392, + 0.47, + 0.786 + ], + "angle": 0, + "content": "Other mixup techniques. RankMixup employs a vanilla mixup technique that interpolates the input images and the corresponding labels for data augmentation, but other variants can be readily adopted in our framework. We have also tried using Manifold-Mixup [45] and CutMix [47] for the experiments. We show in Table 7 the results of our models using these techniques together with M-NDCG, while setting the shape parameter \\(\\alpha\\) to 1 for the both techniques. For comparison, we report the result of our model with the vanilla mixup, which exploits 3 augmented samples, and additionally show the performances obtained using RegMixup [35] equipped with these variants. For both datasets, our method achieves better calibration errors than RegMixup, indicating that our method has better generalization capability. While our model with vanilla mixup provides the best performance on CIFAR10, employing Manifold-Mixup offers better results on Tiny-ImageNet in terms of calibration errors. Increasing the entropy of supervision is crucial for better-calibrated models [25, 29, 30, 41]. RankMixup exploits the augmented samples as supervision for network calibration, indicating that samples with higher entropies can yield better performances. Manifold-Mixup [45] produces flattened representations that have higher entropies than the mixup-augmented samples, which may explain the reason why our model with Manifold-Mixup performs better on Tiny-ImageNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Long-tailed datasets. We evaluate our method on long-tailed (LT) datasets, where the miscalibration issues of DNNs are more pronounced [46, 52]. Following the experimental settings in [46, 52], we adopt the ResNet32 [13] architecture as our backbone, and exploit CIFAR10/100-LT datasets [1] with two imbalanced factors \\((\\rho)\\). We compare in Table 8 our method against the vanilla mixup [49] and two" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.289 + ], + "angle": 0, + "content": "adaptive mixup techniques tailored for LT scenarios [5, 46]. We can see that our models significantly outperform other mixup methods in terms of ECE, while providing competitive accuracies, although they are not specially designed for LT scenarios. This suggests that leveraging the ordinal ranking relationship between confidence is also effective for addressing miscalibration problems in LT scenarios, instead of using label mixtures for other mixup-based augmentations [46, 52]. Note that the number of samples for head and tail classes is highly skewed, suggesting that augmented samples are not diverse in LT scenarios. As this problem is more severe for M-NDCG, it yields worse results, compared to MRL, in the LT datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.304, + 0.619, + 0.319 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.33, + 0.892, + 0.587 + ], + "angle": 0, + "content": "We have presented a novel mixup-based framework for network calibration, dubbed RankMixup, alleviating the problem that interpolated labels do not necessarily model the actual distribution of label mixtures. To this end, we have proposed a new supervisory signal based on the ordinal ranking relationship that a higher confidence is more favorable for a raw sample than the one augmented by mixup. We have proposed MRL, which encourages a network to yield confidence that preserve the ranking relationships between the raw and mixup-augmented samples. We have also extended this idea to multiple augmented samples with different mixup coefficients via M-NDCG, enabling a network to predict outputs with higher confidence for augmented samples that are closer to a raw one. We have demonstrated the effectiveness of RankMixup through the extensive experiments and analysis, achieving the best results among mixup-based network calibration approaches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.606, + 0.892, + 0.711 + ], + "angle": 0, + "content": "Acknowledgments. This work was supported in part by the NRF and IITP grants funded by the Korea government (MSIT) (No.2023R1A2C2004306, No.2022-0-00124, Development of Artificial Intelligence Technology for Self-Improving Competency-Aware Learning Capabilities, No.2021-0-02068, Artificial Intelligence Innovation Hub), and the Yonsei Signature Research Cluster Program of 2023 (2023-22-0008)." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.727, + 0.597, + 0.743 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.752, + 0.892, + 0.793 + ], + "angle": 0, + "content": "[1] Kaidi Cao, Colin Wei, Adrien Gaidon, Nikos Arechiga, and Tengyu Ma. Learning imbalanced datasets with label-distribution-aware margin loss. In NIPS, 2019. 9" + }, + { + "type": "ref_text", + "bbox": [ + 0.509, + 0.794, + 0.892, + 0.819 + ], + "angle": 0, + "content": "[2] Olivier Chapelle, Jason Weston, Léon Bottou, and Vladimir Vapnik. Vicinal risk minimization. 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In CVPR, 2021. 9" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.469, + 0.657 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1368" + } + ] +] \ No newline at end of file diff --git a/2023/RankMixup_ Ranking-Based Mixup Training for Network Calibration/4c024ec3-bba1-4470-bd07-d0e7529be938_origin.pdf b/2023/RankMixup_ Ranking-Based Mixup Training for Network Calibration/4c024ec3-bba1-4470-bd07-d0e7529be938_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0df88b6991b9642c603e7062dab3a17e6651aa78 --- /dev/null +++ b/2023/RankMixup_ Ranking-Based Mixup Training for Network Calibration/4c024ec3-bba1-4470-bd07-d0e7529be938_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:713d4667cac0e69f3e8973a5d22e5459339546eb9dfc0024792acde930472c97 +size 435783 diff --git a/2023/RankMixup_ Ranking-Based Mixup Training for Network Calibration/full.md b/2023/RankMixup_ Ranking-Based Mixup Training for Network Calibration/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d920f405a4ad49693c2f747acd44c1288796e14e --- /dev/null +++ b/2023/RankMixup_ Ranking-Based Mixup Training for Network Calibration/full.md @@ -0,0 +1,343 @@ +# RankMixup: Ranking-Based Mixup Training for Network Calibration + +Jongyoun Noh + +Hyekang Park + +Junghyup Lee + +Bumsub Ham* + +School of Electrical and Electronic Engineering, Yonsei University https://cvlab.yonsei.ac.kr/projects/RankMixup + +# Abstract + +Network calibration aims to accurately estimate the level of confidences, which is particularly important for employing deep neural networks in real-world systems. Recent approaches leverage mixup to calibrate the network's predictions during training. However, they do not consider the problem that mixtures of labels in mixup may not accurately represent the actual distribution of augmented samples. In this paper, we present RankMixup, a novel mixup-based framework alleviating the problem of the mixture of labels for network calibration. To this end, we propose to use an ordinal ranking relationship between raw and mixup-augmented samples as an alternative supervisory signal to the label mixtures for network calibration. We hypothesize that the network should estimate a higher level of confidence for the raw samples than the augmented ones (Fig.1). To implement this idea, we introduce a mixup-based ranking loss (MRL) that encourages lower confidences for augmented samples compared to raw ones, maintaining the ranking relationship. We also propose to leverage the ranking relationship among multiple mixup-augmented samples to further improve the calibration capability. Augmented samples with larger mixing coefficients are expected to have higher confidences and vice versa (Fig.1). That is, the order of confidences should be aligned with that of mixing coefficients. To this end, we introduce a novel loss, M-NDCG, in order to reduce the number of misaligned pairs of the coefficients and confidences. Extensive experimental results on standard benchmarks for network calibration demonstrate the effectiveness of RankMixup. + +# 1. Introduction + +Deep neural networks (DNNs) have achieved remarkable advances in numerous computer vision tasks, including image classification, object detection, and semantic segmentation. Despite the impressive performance, DNNs trained using a softmax cross-entropy (CE) loss and one-hot en + +![](images/f74b3e0c14e4a7b98cd5a9a79cbe6530d605d9c43fb2441fc400acac2ff66949.jpg) + +![](images/3a58cb9035265fe62a3beb81840d8178e4aa279967fb9b8f93f3d213c8b145d6.jpg) +Figure 1: Motivation of RankMixup. We show raw samples of a cat and dog in red boxes, and mixup-augmented samples in blue boxes with dashed lines. The mixup-augmented samples are generated by linearly interpolating the raw samples with a mixing coefficient $\lambda$ . We expect that confidences of the raw samples to be higher than that of the augmented sample (top). The augmented samples with larger coefficients $\lambda$ would have higher confidences than the samples with smaller coefficients (bottom). Best viewed in color. + +coded labels often output overconfident and/or underconfident probabilities, which do not reflect the actual likelihood [10, 32, 41]. This suggests that the networks are not able to estimate the level of confidence, leading to inaccurate and unreliable predictions, which restricts practical applications in real-world systems, particularly for safety-sensitive domains, such as medical diagnosis [18] and autonomous driving [9]. + +To improve the reliability of DNNs, many methods propose to calibrate the output distribution after or during training. Post-hoc approaches adjust miscalibrated probabilities directly from pretrained networks [7, 10, 12, 21, 27]. Although these approaches are straightforward to apply, calibration performance depends heavily on datasets and networks used for training [25], and they are not robust to distribution shifts between training and test samples [33]. Training-time approaches [4, 8, 14, 25, 28, 29, 30, 41, 51], on the other hand, exploit an additional regularization term along with the CE loss to calibrate the output probabilities + +during training. Early works [29, 30, 41] have explored the effects of regularization techniques, including label smoothing (LS) [40], focal loss (FL) [24], and mixup [49], on network calibration, and shown that the networks trained with these techniques are better calibrated than the ones trained with the CE loss alone. Recently, the works of [8, 25, 29] highlight the limitations of LS and FL in terms of network calibration, and introduce calibration-aware LS and FL. On the contrary, few studies have explored integrating the mixup technique into network calibration. Current mixup-based methods [35, 41, 51] simply interpolate input images and training labels with a mixing coefficient to soften output probabilities, while not considering network calibration itself. Since the interpolated labels may not represent accurately the distribution of the label mixture in augmented images [3, 19, 39, 43], training networks with such uncertain labels degrades the calibration performance. + +In this work, we present a mixup-based approach to network calibration, dubbed RankMixup, that addresses the problem of directly using the mixture of labels for calibrating network predictions [35, 41, 51]. To this end, we conjecture that networks should give higher confidences for the raw sample, not augmented by the mixup technique, than the augmented one (Fig. 1). To implement this idea, we leverage an ordinal ranking relationship between raw and augmented samples (Fig. 1) and use it as a supervisory signal for network calibration, instead of using the label mixtures. In particular, we introduce a mixup-based ranking loss (MRL) that encourages the confidences of augmented samples to be lower than those of raw samples by a margin, in order to preserve the ranking relationship. To further strengthen the capability of network calibration, we also propose to exploit the ranking relationship for multiple mixup-augmented samples. We expect that higher confidences are favorable for augmented samples with larger mixing coefficients $\lambda$ , and vice versa (Fig. 1), such that the orders of confidences and mixing coefficients are aligned to each other. To achieve this, we introduce a novel loss, M-NDCG, based on normalized discounted cumulative gain (NDCG) in information retrieval [17], which penalizes the number of misaligned pairs of the coefficients and confidences. Extensive experimental results on standard benchmarks demonstrate the effectiveness of our approach to leveraging the ordinal ranking relationships on network calibration. The main contributions of our work can be summarized as follows: + +- We introduce a novel mixup-based framework for network calibration, RankMixup, that alleviates the problem of exploiting label mixtures for calibrating network predictions. To the best of our knowledge, we are the first to handle this issue in the context of confidence calibration. +- We propose to exploit ordinal ranking relationships between confidence from raw and augmented samples, + +as well as those among confidences from multiple augmented samples, and use them as supervisory signals, instead of the mixture of labels. To implement this idea, we introduce MRL and M-NDCG that facilitate aligning the confidences and mixing coefficients to preserve the relationships. + +- We demonstrate that our approach provides better results in terms of expected calibration error (ECE), compared to other mixup-based methods. We also achieve competitive performances on standard benchmarks on network calibration, including CIFAR10/100 [20], TinyImageNet [23], and ImageNet [6] with various network architectures. + +# 2. Related work + +Confidence calibration. The seminal work of [10] provides empirical evidence that DNNs are prone to making overconfident predictions due to miscalibrated output probabilities. In particular, they are typically trained with one-hot encoded labels, which fails to impose any entropy on the supervisory signal. The entropy of output probabilities for the network is thus encouraged to be zero, leading to the overconfident predictions [25]. To address this problem, several approaches have been proposed to augment the entropy of output probabilities, which can be divided into two categories: post-hoc and training-time methods. First, post-hoc approaches adjust the miscalibrated probabilities directly after training using a temperature scaling technique [7, 10, 42] or ranking statistics [27]. The temperature scaling technique, also effective to knowledge distillation [16], raises the entropy of output probabilities using a temperature parameter, optimized on additional validation samples. Although post-hoc approaches have shown the effectiveness on in-distribution datasets, they perform poorly under distribution shifts [33], and inevitably lower the confidence of correct predictions [22, 29]. Second, training-time approaches implicitly or explicitly impose regularization on outputs probabilities during training, usually in combination with post-hoc methods to further improve the calibration accuracy. The implicit methods [4, 4, 8, 25, 30, 35, 41] smooth the output distribution by increasing the entropy of training labels, rather than adjusting output probabilities directly. Several works [29, 30, 41, 51] have demonstrated empirically and theoretically that regularization methods such as LS [40], FL [24], and Mixup [49], which have originally designed to learn discriminative features, can also be effective in network calibration. However, recent works of [8, 25, 35] explore that directly using these methods for network calibration is problematic, and they introduce improved versions to overcome the drawback. For example, MbLS [25] exploits a margin-based LS to address the problem of LS providing non-informative predictions to obtain a better-calibrated network. The works + +of [8, 35] suggest that finding optimal parameters of FL and mixup is crucial for network calibration. The explicit methods [14, 22, 28, 34] adjust confidences of predictions directly by maximizing the entropy of output probabilities [34], using an ordinal ranking relationship [28] or minimizing calibration errors [14, 22]. For example, the ordinal ranking between output probabilities of networks has been proven to be effective to estimate the levels of confidence, providing better calibrated models [28]. It assumes that the predictions with higher confidences are more likely to be accurate than the ones with lower confidences. We explore the effects of mixup [49] in the context of network calibration, similar to other mixup-based methods [35, 41, 51]. They use interpolated labels to train networks for calibrating output probabilities, but the labels do not provide the distribution of the label mixture for the augmented sample accurately [3, 19, 39, 43]. We exploit confidences of augmented samples directly as supervisory signals for network calibration using ordinal ranking relationships between the samples, boosting the calibration performance significantly. The work of [28] is closely related to ours in that it uses an ordinal ranking relationship for raw samples. In contrast to this, our approach exploits more diverse and complex ordinal relationships for confidences. It considers not only the relationship between raw and augmented samples, but also among the augmented samples themselves. + +Mixup. Data augmentation has become a standard technique for training DNNs that regularizes the networks to prevent overfitting and improve generalization. Mixup [49] linearly interpolates between pairs of raw data samples. Specifically, it takes a weighted average of two images to obtain a new one. The training label for the augmented sample is also interpolated with the same weight. Many works extend this idea to improve the generalization ability. Manifold-Mixup [45] performs the mixup process in the feature space, while CutMix [47] introduces a regional mixing scheme to preserve fine-grained information of original images. It has recently been explored that using label mixtures in mixup and its variants could provide misleading supervisory signals for training networks, which can be alleviated by saliency-guided mixup schemes [3, 19, 36, 43] or label perturbations [39]. In addition to data augmentation, various applications leverage mixup for, e.g., self-supervised learning [37, 38] and network calibration [35, 41]. We mainly investigate the effect of the vanilla mixup [49] on network calibration. However, as will be shown in our experiments, the variants of mixup, including CutMix [47] and manifold-Mixup [45], can also be readily adapted to our approach. + +# 3. Approach + +We present in this section preliminaries for network calibration and mixup [49] in Sec. 3.1, and provide a detailed + +description of RankMiup and training losses in Secs. 3.2 and 3.3, respectively. + +# 3.1. Preliminaries + +Network calibration. Let us suppose a dataset $D = \{(\mathbf{x}_i, \mathbf{y}_i)\}_{i=1}^N$ of size $N$ , where $\mathbf{x}_i \in \mathcal{X}$ and $\mathbf{y}_i \in \mathcal{Y}$ are an input sample and a ground-truth label with $K$ classes, respectively. DNNs can be considered as a function, parameterized by $\theta$ , that yields a logit $\mathbf{z}_i$ of size $K \times 1$ from the input sample: $\mathbf{f}_\theta : \mathcal{X} \to \mathbb{R}^K$ . For multiclass classification, the networks compute class probabilities using the softmax function as follows: + +$$ +p _ {i, k} = \operatorname {s o f t m a x} \left(\mathbf {z} _ {i}\right) = \frac {\exp z _ {i , k}}{\sum_ {j} ^ {K} \exp z _ {i , j}}, \tag {1} +$$ + +where we denote by $p_{i,k}$ a probability of the $k$ -th class for the $i$ -th input. Based on the probabilities, the networks predict a class for the input sample $\mathbf{x}_i$ as + +$$ +\hat {y} _ {i} = \arg \max _ {k} p _ {i, k}. \tag {2} +$$ + +The corresponding confidence can then be obtained as follows: + +$$ +\hat {p} _ {i} = \max _ {k} p _ {i, k}. \tag {3} +$$ + +During training, the networks are optimized using a cross-entropy (CE) loss as follows: + +$$ +\mathcal {L} _ {C E} \left(\mathbf {x} _ {i}, \mathbf {y} _ {i}\right) = - \sum_ {k = 1} ^ {K} y _ {i, k} \log p _ {i, k}, \tag {4} +$$ + +where $y_{i,k}$ is the $k$ -th element of the one-hot encoded label $\mathbf{y}_i$ . Recent works [10, 29, 30, 41] have shown that DNNs trained with the CE loss tend to be overconfident, providing higher accuracies than accuracies. To address this problem, confidence calibration methods encourage that the confidence for each sample and the accuracy are the same as follows: + +$$ +\hat {p} _ {i} = P \left(\hat {y} _ {i} = y _ {i} \mid \hat {p} _ {i}\right), \tag {5} +$$ + +where $y_{i}$ is an index of the true class for the ground-truth label $\mathbf{y}_{i}$ . + +Mixup. Mixup [49] is a data-augmentation technique based on the vicinal risk minimization principle [2]. It introduces the mixup vicinal distribution, which measures the likelihood of finding a pair of an augmented input and a target label, $(\tilde{\mathbf{x}}_i,\tilde{\mathbf{y}}_i)$ , from the vicinity of the original pair, $(\mathbf{x}_i,\mathbf{y}_i)$ . Mixup samples the vicinal distribution to construct a new dataset, $D_{v} = \{(\tilde{\mathbf{x}}_{i},\tilde{\mathbf{y}}_{i})\}_{i = 1}^{N}$ . Here, we denote by $D_{v}$ the vicinal set consisting of pairs of augmented training samples and corresponding target labels. Specifically, it augments training pairs by linearly interpolating the original ones as follows: + +$$ +\begin{array}{l} \tilde {\mathbf {x}} = \lambda \mathbf {x} _ {i} + (1 - \lambda) \mathbf {x} _ {j}, \\ \tilde {\dots} \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \end{array} \tag {6} +$$ + +$$ +\tilde {\mathbf {y}} = \lambda \mathbf {y} _ {i} + (1 - \lambda) \mathbf {y} _ {j}, +$$ + +where two pairs of input samples and target labels, $(\mathbf{x}_i,\mathbf{y}_i)$ and $(\mathbf{x}_j,\mathbf{y}_j)$ , are randomly drawn from the training set $D$ and $\lambda \in [0,1] \sim \mathrm{Beta}(\alpha ,\alpha)$ is a mixing coefficient, sampled from a Beta distribution. Mixup assumes that target labels for the vicinal set should also be interpolated with the same mixing coefficient as input samples during the mixing process. The hyperparameter $\alpha$ controls the strength of interpolation between the pairs of input samples and target labels. According to [49], the value of $\alpha$ within the range of [0.1, 0.4] provides better classification performance, while higher values cause significant underfitting. We will also examine the effect of $\alpha$ in terms of confidence calibration within our framework. + +# 3.2. RankMixup + +Mixup provides smooth decision boundaries that gradually shift from one class to another, which leads to a regularized estimate of uncertainty (or confidence) [49]. There have been lots of studies to discover underlying principles behind the mixup method [15, 41, 50, 51, 51]. For example, it has proven to give better output probabilities in terms of model calibration, alleviating overconfident predictions [35, 41, 51]. The interpolated labels of augmented samples in the vicinal set do not always model the actual distribution of label mixtures in augmented samples [3, 19, 39, 43], which however has not been considered for designing a network calibration method. To alleviate this problem, we leverage ordinal ranking relationships between confidences from raw and augmented samples, as well as those among confidences from multiple augmented samples. We then propose to use them as supervisory signals for model calibration, rather than using the mixture of labels directly. In the following, we describe our framework with a single mixup-augmented sample, and present a generalized version that can handle multiple augmented samples. + +Single mixup-augmented sample. The sample augmented by mixup $\bar{\mathbf{x}}$ in Eq. (6) can be interpreted as a combination of the raw sample $\mathbf{x}_i$ and structured noise from another one $\mathbf{x}_j$ , where the degree of noise is determined by the mixing parameter $\lambda$ . This suggests that DNNs predict the class of the augmented sample with uncertainty imposed by the additional one, making it more difficult to recognize the augmented sample than the raw one. To this end, mixup imposes uncertainty on the label mixtures by adjusting confidence of target labels for the augmented samples by $\lambda$ (or $1 - \lambda$ ). Albeit simple, directly using the interpolated labels may provide misleading supervisory signals + +to train DNNs. To avoid this, we leverage an ordinal ranking relationship between confidence of raw and augmented samples. Specifically, the ordinal ranking holds for the relationship that confidence levels of easy-to-classify samples should be higher than the ones for hard samples [28]. Accordingly, we conjecture that the confidence levels of raw samples should be greater than those of the augmented samples in the mixing process (Fig.1). Namely, every pair of samples $(\mathbf{x}_i,\tilde{\mathbf{x}}_i)$ should satisfy the following relationship: + +$$ +\max _ {k} p _ {i, k} \geq \max _ {k} \tilde {p} _ {i, k}, \tag {7} +$$ + +where $\tilde{p}_{i,k}$ is a predicted probability of the class $k$ for the augmented sample $\tilde{\mathbf{x}}_i$ . We devise MRL that encourages the network to learn this relationship without the mixture of labels, which will be described in Sec. 3.3. + +Multiple mixup-augmented samples. We extend our framework to exploit multiple mixup-augmented samples. As the mixing ratio $\lambda$ decreases, augmented samples become more difficult to recognize, which suggests that we can exploit more complex ranking relationships among the multiple augmented samples. Analogous to the single case, we expect that the samples augmented with larger mixing coefficients $\lambda$ show higher confidence compared to those with smaller coefficients (Fig. 1). For every pair of augmented samples $(\tilde{\mathbf{x}}_i,\tilde{\mathbf{x}}_j)$ from the vicinal set $D_{v}$ , the confidence of these samples should satisfy the following relationship: + +$$ +\lambda_ {i} \geq \lambda_ {j} \Leftrightarrow \max _ {k} \tilde {p} _ {i, k} \geq \max _ {k} \tilde {p} _ {j, k}, \tag {8} +$$ + +where $(\lambda_i, \lambda_j)$ is a pair of mixing ratios for the corresponding pair of augmented samples $(\tilde{\mathbf{x}}_i, \tilde{\mathbf{x}}_j)$ . Note that we describe the relationship with two samples for simplicity, but our framework can adopt the relationship with any number of augmented samples. + +We then integrate both the relationships in Eqs. (7) and (8) to obtain a general version of RankMixup. With the mixing coefficient of 1.0 for the raw sample, the following relationship should hold for every triplet of samples $(\mathbf{x}_i,\tilde{\mathbf{x}}_i,\tilde{\mathbf{x}}_j)^1$ : + +$$ +1. 0 \geq \lambda_ {i} \geq \lambda_ {j} \Leftrightarrow \max _ {k} p _ {i, k} \geq \max _ {k} \tilde {p} _ {i, k} \geq \max _ {k} \tilde {p} _ {j, k}. \tag {9} +$$ + +This allows the network to estimate the levels of confidence better by considering diverse ordinal ranking relationships among the confidences of the raw and multiple mixup-augmented samples. To implement this idea, we align the orders of confidences and mixing ratios during training using M-NDCG (Sec. 3.3). + +# 3.3. Training loss + +To train our model, we use a CE loss for classification, together with either MRL or M-NDCG for network calibration, balanced by the parameter of $w$ . As supervisory signals, we exploit one-hot encoded labels for classification, and ordinal ranking relationships for input and augmented samples for network calibration. + +MRL. We introduce MRL facilitating the ordinal relationship in Eq. (7). It encourages confidence of augmented samples to be lower than those of raw samples by a margin, defined as follows: + +$$ +\mathcal {L} _ {\mathrm {M R L}} = \max \left(0, \max _ {k} \tilde {p} _ {i, k} - \max _ {k} p _ {i, k} + m\right), \tag {10} +$$ + +where the margin $m$ determines acceptable discrepancies between the confidence of raw and augmented samples. The intuition behind using a margin is twofold: (1) It enables maintaining the ranking relationship between confidence, rather than penalizing the exact value of the discrepancies itself. (2) Controlling the confidence discrepancies with a margin allows to consider the uncertainty of inaccurate label mixtures. The vanilla mixup method continues to penalize the confidence of augmented samples, until they reach overconfident values, determined by the label mixtures. In contrast to this, MRL penalizes the confidence, only when the absolute discrepancies between them are below the margin. + +M-NDCG. MRL is not sufficient to model the relationship in Eq. (9), where the comparison involves more than one augmented sample. M-NDCG addresses this problem that enables multiple confidence values to hold the ordinal ranking relationships. M-NDCG is based on NDCG used for evaluating ranking quality in information retrieval [17, 44]. It measures how many of retrieved results are aligned with the ground-truth ranking order, which can be calculated by normalizing a discounted cumulative gain (DCG) with an ideal DCG (IDCG): + +$$ +N D C G = \frac {D C G}{I D C G}. \tag {11} +$$ + +DCG accumulates a relevance score of each retrieval result, weighted by a corresponding rank, and IDCG is computed similarly but with the ground-truth score, as follows: + +$$ +\begin{array}{l} D C G = \sum_ {q = 1} ^ {Q} \frac {r _ {q}}{\log_ {2} (q + 1)}, \tag {12} \\ I D C G = \sum_ {q = 1} ^ {Q} \frac {r _ {q} ^ {\mathrm {g t}}}{\log_ {2} (q + 1)}, \\ \end{array} +$$ + +where $r_q$ and $r_q^{\mathrm{gt}}$ are the relevance and ground-truth scores, respectively, at position $q$ in the result list of size $Q$ . + +We consider confidences of predictions and mixing coefficients as the relevance and ground-truth scores, respectively, enabling multiple confidences to satisfy the relationship in Eq. (9). Given $Q$ pairs of confidences and mixing coefficients, we compute $DCG_{\mathrm{M}}$ and $IDCG_{\mathrm{M}}$ , as follows: + +$$ +\begin{array}{l} D C G _ {\mathrm {M}} = \frac {\operatorname* {m a x} _ {k} p _ {t , k}}{\log_ {2} (t + 1)} + \sum_ {q = 1, q \neq t} ^ {Q} \frac {\operatorname* {m a x} _ {k} \tilde {p} _ {q , k}}{\log_ {2} (q + 1)}, \tag {13} \\ I D C G _ {\mathrm {M}} = 1 + \sum_ {q = 2} ^ {Q} \frac {\lambda_ {q} ^ {\mathrm {g t}}}{\log_ {2} (q + 1)}, \\ \end{array} +$$ + +where $t$ is the position of the confidence value for the raw sample, which is set to 1 in order to ensure that its confidence is always ranked first in a descending order, following the ranking relationship in Eq. (9). $Q$ is a hyperparameter that determines the number of augmented samples, i.e., $Q - 1$ augmented samples. $\lambda_q^{\mathrm{gt}}$ is the mixing coefficient sorted based on its magnitude, with a value of 1.0 for the raw sample appearing at position of the top rank, i.e., $\lambda_1^{\mathrm{gt}} = 1$ . We then define M-NDCG loss as follows: + +$$ +\mathcal {L} _ {\mathrm {M - N D C G}} = 1 - \frac {D C G _ {\mathrm {M}}}{I D C G _ {\mathrm {M}}}, \tag {14} +$$ + +which is minimized when the ranking orders of the confidences and mixing coefficients are aligned to each other after sorting in a descending order. The network is thus trained to encourage the confidence to hold the ordinal ranking relationship of RankMixup in Eq. (9). M-NDCG also discounts lower-ranked confidence more, preventing the uncertain predictions from being overconfident. + +# 4. Experiments + +# 4.1. Implementation details + +Datasets. We mainly perform experiments on CIFAR10/100 [20], Tiny-ImageNet [23] for network calibration. The CIFAR10/100 datasets consist of 50,000 training and 10,000 test images of size $32 \times 32$ , and provide 10/100 object categories, respectively. Tiny-ImageNet includes 120,000 images of size $64 \times 64$ for 200 object categories. Each category in Tiny-ImageNet contains 600 images, which are divided into 500, 50 and 50 images for training, validation and test, respectively. Tiny-ImageNet is more challenging, compared to CIFAR10/100, as it contains lots of object classes with a smaller number of samples per category. We further validate the generalization ability of our method on ImageNet [6], which comprises around 1.2M training and 50K validation images across 1K classes. For out-of-distribution (OOD) detection, we train a model + +Table 1: Quantitative comparison with the state of the art in terms of ECE (%) and AECE (%) with 15 bins on the validation splits of CIFAR10/100 [20] and Tiny-ImageNet [23]. Numbers in bold indicate the best performance and underscored ones indicate the second best. Numbers in parentheses represent the results obtained using a TS post-hoc technique [10]. + +
MethodsCIFAR10 [20]CIFAR100 [20]Tiny-ImageNet [23]
ResNet-50 [13]ResNet-101 [13]ResNet-50 [13]ResNet-101 [13]ResNet-50 [13]ResNet-101 [13]
Acc↑ECE↓AEE↓Acc↑ECE↓AEE↓Acc↑ECE↓AECE↓Acc↑ECE↓AECE↓Acc↑ECE↓AECE↓
CE95.383.75(0.97)2.98(1.01)94.463.61(0.92)3.55(0.85)77.8113.59(2.93)13.54(2.86)77.4812.94(2.63)12.94(2.66)64.343.18(3.18)2.87(2.87)66.043.50(3.50)3.52(3.52)
MMCE [22]95.183.88(0.97)3.88(1.12)94.993.88(1.15)3.88(12.9)77.5612.72(2.83)12.71(2.86)77.8213.43(3.06)13.42(2.80)64.802.03(2.03)1.97(1.97)66.443.40(3.40)3.38(3.38)
ECP [34]94.754.01(1.06)3.99(1.53)93.974.41(1.72)4.40(1.70)76.2012.29(2.08)12.28(2.22)76.8113.43(2.92)13.42(3.04)64.881.94(1.94)1.95(1.95)66.202.72(2.72)2.70(2.70)
LS [30]94.873.27(1.58)3.67(3.02)94.183.35(1.51)3.85(3.10)76.456.73(4.23)6.54(4.26)76.917.99(4.38)7.87(4.55)65.463.21(2.51)3.23(2.51)65.523.11(2.51)2.92(2.72)
FL [24]94.823.42(1.07)3.41(0.87)93.593.27(1.12)3.23(1.37)76.412.83(1.66)2.88(1.73)76.123.10(2.58)3.22(2.51)63.082.03(2.03)1.94(1.94)64.022.18(2.18)2.09(2.09)
Mixup [41]94.762.86(1.37)2.81(2.00)95.506.87(1.18)6.79(2.33)78.478.68(2.14)8.68(2.19)78.748.92(3.69)8.91(3.65)65.811.92(1.92)1.96(1.96)66.412.41(1.97)2.43(1.95)
FLSD [29]94.773.86(0.83)3.74(0.96)93.263.92(0.93)3.67(0.94)76.202.86(2.86)2.86(2.86)76.613.29(2.04)3.25(1.78)63.561.93(1.93)1.98(1.98)64.021.85(1.85)1.81(1.81)
CRL [28]95.083.14(0.96)3.11(1.25)95.043.74(1.12)3.73(2.03)77.856.30(3.43)6.26(3.56)77.607.29(3.32)7.14(3.31)64.881.65(2.35)1.52(2.34)65.873.57(1.60)3.56(1.52)
CPC [4]95.045.05(1.89)5.04(2.60)95.364.78(1.52)4.77(2.37)77.2313.29(3.74)13.28(3.82)77.5013.32(2.96)13.28(3.23)65.703.41(3.41)3.42(3.42)66.443.93(3.93)3.74(3.74)
MbLS [25]95.251.16(1.16)3.18(3.18)95.131.38(1.38)3.25(3.25)77.924.01(4.01)4.14(4.14)77.455.49(5.49)6.52(6.52)64.741.64(1.64)1.73(1.73)65.811.62(1.62)1.68(1.68)
RegMixup [35]94.682.76(0.98)2.67(0.92)95.034.75(0.92)4.74(0.94)76.765.50(1.98)5.48(1.98)76.934.20(1.36)4.15(1.92)63.583.04(1.89)3.04(1.81)63.263.35(1.86)3.32(1.68)
RankMixup (MRL)94.591.01(0.84)1.03(0.80)94.182.86(1.08)2.87(1.58)76.653.52(2.40)3.39(2.05)77.264.41(1.68)4.24(1.76)64.541.70(1.70)1.69(1.69)64.802.26(1.78)2.28(1.60)
RankMixup (M-NDCG)94.882.59(0.57)2.58(0.52)94.253.24(0.65)3.21(0.56)77.113.46(1.49)3.45(1.42)76.463.49(1.10)3.49(1.40)64.971.49(1.49)1.44(1.44)64.891.57(1.57)1.94(1.94)
+ +using CIFAR10, and use CIFAR100, Tiny/ImageNet, and SVHN [31] as OOD datasets, following the experimental protocol in [26, 35]. Similarly, CIFAR100 is used to train a model, and evaluate it on CIFAR10, Tiny/ImageNet, and SVHN. + +Evaluation protocols. Following the standard protocol [4, 14, 25, 29, 30, 41], we use expected calibration error (ECE) and adaptive ECE (AECE) as evaluation metrics for network calibration. ECE measures the expected absolute difference between confidences and corresponding accuracies: + +$$ +\mathbb {E} \left[ \left| P \left(\hat {y} _ {i} = y _ {i} \mid \hat {p} _ {i}\right) - \hat {p} _ {i} \right| \right]. \tag {15} +$$ + +To compute ECE, we divide a range $(0,1]$ into equidistance bins, and compute an average of the absolute differences, weighted by the size of each bin. We set the number of bins for both ECE and AECE as 15, following the protocol. We also report top-1 classification accuracies to compare discriminative capabilities. We provide results obtained without/with applying a post-hoc technique. In particular, we use the TS method [10], where the temperature is optimized on the validation sets. For OOD detection, we compare the area under the receiver operating characteristics (AUROC), following the standard evaluation protocol [26, 35]. + +Methods for comparison. We compare our method with various training-time approaches. In addition to the baseline model using the CE loss, we include implicit methods (LS [30], FL/FLSD [29], Mixup [41], mbLS [25], and RegMixup [35]) and explicit methods (ECP [34], MMCE [22], and CPC [4]). We have reproduced results using official codes with hyperparameter settings provided by the authors, if they are not available. Detailed descriptions for the hyperparameters can be found in the supplement. + +Training details. Following [25], we train our network for 200 epochs for CIFAR10/100 [20], with an initial learning rate of 1e-1 and a batch size of 128. We also follow the training setting in [25] for Tiny/ImageNet [23] ex + +Table 2: Quantitative comparison with the state of the art in terms of ECE (\%) and AECE (\%) with 15 bins on the validation split of ImageNet [6]. Numbers in bold indicate the best performance and underscored ones indicate the second best. + +
MethodsImageNet [6]
ResNet-50 [13]
Acc↑ECE↓AECE↓
CE73.969.109.24
Mixup [41]75.847.077.09
CRL [28]73.838.478.47
MbLS [25]75.394.074.14
RegMixup [35]75.645.345.42
RankMixup (MRL)75.275.705.71
RankMixup (M-NDCG)74.863.933.92
+ +cept for a batch size of 32 due to memory limits. All networks are trained using the SGD optimizer with a momentum of 0.9. The learning rate decreases by a tenth at every fixed intervals. We use ResNet50 [13], and ResNet101 [13] for both CIFAR10/100 [20] and Tiny-ImageNet [23], and ResNet50 for ImageNet [6]. For more comprehensive experiments, we also exploit WideResNet [48] for CIFAR10 and Tiny-ImageNet. We fix the balancing parameter of training loss $w$ to 0.1. We set margin $m$ to 2.0 and 1.0 for CIFAR10/100 and Tiny-ImageNet, respectively, using each validation dataset. Other hyperparameters, such as $\alpha$ and $Q$ , are chosen similarly. For OOD detection, we train the network using M-NDCG and in-distribution (ID) datasets with the same training settings used for network calibration. + +# 4.2. Results + +Comparison with the state of the art. We compare in Table 1 our method with state-of-the-art calibration approaches. From the tables, we observe four things: (1) Our models outperform other mixup-based methods [35, 41] using label mixtures as supervisions, demonstrating the effectiveness of our approach to leveraging an ordinal ranking relationship for confidences. (2) Our model using M-NDCG achieves the best performance in terms of both ECE and AECE on the challenging TinyImageNet [23] dataset, while providing competitive results on CIFAR10/100. This suggests that the ordinal ranking + +Table 3: Quantitative comparison in terms of ECE (\%) and AECE (\%) with 15 bins on the validation splits of CIFAR10 [20] and Tiny-ImageNet [23]. Numbers in bold indicate the best performance and underscored ones are the second best. + +
CIFAR10 [20]Tiny-ImageNet [23]
MethodsWide-ResNet-26-10 [48]
Acc↑ECE↓AECE↓Acc↑ECE↓AECE↓
CE95.802.702.6665.186.086.06
Mixup [41]96.533.143.0866.363.773.75
MbLS [25]95.701.452.7865.302.572.32
RegMixup [35]95.444.183.9963.403.873.93
RankMixup (MRL)95.571.701.3865.343.303.28
RankMixup (M-NDCG)95.731.621.5365.563.833.94
+ +Table 4: Quantitative comparison with the state of the art in terms of AUROC $(\%)$ . Numbers in bold indicate the best performance and underscored ones indicate the second best. + +
IDC10 [20]C100 [20]
OODC100 [20]Tiny [23]SVHN [31]C10 [20]Tiny [23]SVHN [31]
AUROC↑AUROC↑
TS [10]86.7388.0692.1476.3880.1282.41
LS [30]75.2376.2974.2372.9277.5472.33
FL [29]85.6386.8492.6678.3781.2386.37
Mixup [41]82.0784.0979.7278.4681.5576.21
CPC [4]85.2885.1592.7974.6876.6671.72
MbLS [25]86.2087.5589.9873.8879.1973.19
RegMixup [35]87.8287.5483.1576.0080.7275.05
RankMixup (M-NDCG)87.8288.9492.6278.6480.6785.42
+ +relationships among confidences is crucial for network calibration, and M-NDCG effectively encourages our model to provide confidences maintaining the relationships. We can also see that our method generalizes well to the large-scale dataset. (3) Our method outperforms another ranking-based method (CRL)[28] significantly, suggesting that more complex ranking relationship based on augmented samples enables estimating better confidences. (4) Ours with the post-hoc method [10] gives the best results in most settings, which indicates that they are complementary to each other, and exploiting both further boosts the calibration accuracy. + +We also provide in Tables 2 and 3 quantitative results on ImaergeNet [6] and for the WideResNet backbone [48], respectively. They show similar trends to those in Table 1, validating the effectiveness of our approach across various network architectures and large-scale datasets. Specifically, our models provide competitive results with the state of the art [25], while outperforming mixup-based methods [35, 41] and the ranking-based one [28]. + +OOD detection. We compare in Table 4 the OOD detection accuracy using the ResNet-50 [13] architecture. We use the entropy of the softmax output as an uncertainty measure for binary classification and report AUROC scores for comparison. From the table, we have two findings. Our model trained with M-NDCG outperforms other mixup-based methods and achieves the highest AUROC scores in most settings. This indicates that ordinal ranking relationship of confidences is also crucial for OOD detection, suggesting that models trained with M-NDCG are not only better calibrated but also perform better than other calibration methods under the distributional shifts. + +Table 5: Quantitative comparison by varying the margin $m$ . We report the ECE (%) for the models trained with MRL. Numbers in parentheses represent the results obtained using a TS post-hoc technique [10]. + +
CIFAR10 [20]Tiny-ImageNet [23]
ECE↓ECE↓
m = 1.01.54(1.09)1.49(1.49)
m = 2.01.01(0.84)1.70(1.70)
m = 3.02.12(0.93)1.54(1.54)
m = 4.03.12(1.67)2.37(1.77)
m = 5.013.13(0.48)2.42(1.48)
+ +![](images/d9d908c1dc9cda5c9b3f011492b3ad8720c81b4b41a9e90b379c3aa39c1f1bd8.jpg) +Figure 2: Quantitative results by varying the margin $m$ . We plot OE (\%) and UE (\%) on the validation split of CIFAR10 [20]. Best viewed in color. + +# 4.3. Discussion + +In this section, we analyze the effects of the hyperparameters in our framework, and show generalization ability by incorporating other mixup techniques into our framework. For the analyses, we mainly adopt the ResNet-50 [13] models trained with M-NDCG, and report ECE and AECE on the validation sets of CIFAR10 [20] and TinyImageNet [23], unless otherwise specified. We use 15 bins to measure the ECE and AECE. + +Margin. We compare in Table 5 the calibration results of the models trained with MRL and various margins. We can see that small margins provide better performances for both datasets. Furthermore, we find that increasing the margin degrades the classification accuracy. A reason is that a large margin could make a significant difference in confidence levels between the raw and augmented samples. That is, with a larger margin, the augmented sample is more likely to have a lower confidence than its actual value. + +To demonstrate this, we compute overconfidence errors (OE) [41] that measure the expected difference between confidence values of overconfident predictions and corresponding accuracies. Given $H$ bins of equal size, OE is defined as follows [41]: + +$$ +O E = \sum_ {h = 1} ^ {H} \frac {\left| B _ {h} \right|}{N} [ \operatorname {c o n f} \left(B _ {h}\right) \times \max \left(\operatorname {c o n f} \left(B _ {h}\right) - \operatorname {a c c} \left(B _ {h}\right), 0\right) ], \tag {16} +$$ + +where $N$ is the total number of samples, and $B_{h}$ is the set of samples, whose confidence falls into the $h$ -th bin. We denote by $\mathrm{acc}(B_h)$ and $\mathrm{conf}(B_h)$ the accuracy and averaged confidence of the $h$ -th bin, respectively. Similar to OE, we + +Table 6: Quantitative results of our model with various numbers of the augmented samples. We report the ECE (\%) for comparison. Numbers in parentheses represent the results obtained using a TS post-hoc technique [10]. + +
CIFAR10 [20]Tiny-ImageNet [23]
ECE↓ECE↓
Q = 23.01(0.82)3.25(1.44)
Q = 32.78(0.50)2.18(1.12)
Q = 42.59(0.57)1.49(1.49)
Q = 52.37(0.64)1.52(1.52)
Q = 62.24(0.59)1.30(1.30)
+ +![](images/037e530268de6b85da5a2b9978c74240f2e77d0c316a827c7f278efb7a5b7b32.jpg) +Figure 3: Probability density function (PDF) of Beta distribution with various $\alpha$ s. + +define underconfidence errors (UE) computing the difference using underconfident predictions as follows: + +$$ +U E = \sum_ {h = 1} ^ {H} \frac {\left| B _ {h} \right|}{N} [ \operatorname {c o n f} \left(B _ {h}\right) \times \max \left(\operatorname {a c c} \left(B _ {h}\right) - \operatorname {c o n f} \left(B _ {h}\right), 0\right) ]. \tag {17} +$$ + +We plot in Fig. 2 UE and OE for ResNet-50 with MRL on CIFAR10 [20], while varying margins. We can see that UE increases drastically, according to the margins, while OE decreases gradually. This suggests that exploiting a large margin causes underconfidence problems, where the model becomes less confident in its predictions. An underconfident model produces large calibration errors [41, 49], leading to the degraded performance. + +Number of augmented samples. We compare in Table 6 the calibration performance in terms of ECE with varying number of augmented samples. We set $\alpha$ to 2.0 and 1.0 for CIFAR10 and Tiny-ImageNet, respectively. We can observe that ECE improves as more augmented samples are used, suggesting that learning with diverse ranking relationships between a number of augmented samples encourages the model to estimate confidence levels better. This further implies that the mixup coefficient $\lambda$ is also an important factor, since it enables modeling the diverse ranking relationships. This leads us to analyze the mixup coefficient $\lambda$ in detail in the following. + +Mixup coefficient. Following [49], we sample the mixup coefficient $\lambda$ from a Beta distribution, making it possible + +![](images/9e503c86e0d886321b2c716d8c090b96a1ad9df5b2328001d27f87ae5aff3e7d.jpg) + +![](images/0e1b47271a49a8291004667f8e37ef802bbb7b83834049f76980fd077d3103ea.jpg) +Figure 4: Quantitative results by varying the parameter of the Beta distribution $(\alpha)$ . We plot ECE $(\%)$ and AECE $(\%)$ on the validation split of CIFAR10 [20] (top) and Tiny-ImageNet [23] (bottom). Best viewed in color. + +to generate various augmented samples. Note that the degree of the diversity is determined by how we set the shape parameter for the Beta distribution. For an in-depth analysis, we also show in Fig. 3 the probability density functions (PDFs) of different $Beta(\alpha, \alpha)$ distributions, while varying the shape parameter $\alpha$ . We evaluate the calibration errors of the models trained with M-NDCG along with different shape parameters $\alpha$ of the Beta distribution, and show the results using 3 augmented images ( $Q = 4$ ) in Fig. 4. From the figures, we observe two things: (1) Our models achieve the best performances with $\alpha = 2$ and $\alpha = 1$ on CIFAR10 and Tiny-ImageNet, respectively, where the corresponding PDFs are relatively flat, as shown in Fig. 3. This suggests that diverse mixup coefficients $\lambda$ drawn from such distributions can enhance the calibration performances, as it allows us to augment the samples in a more diverse way. (2) Our model performs well with large $\alpha$ , which is in contrast to the vanilla mixup [41, 49], where the value of $\alpha$ within the range of [0.1, 0.4] yields better classification and calibration performances. When $\alpha$ is too large, it suffers from an underconfidence problem [41, 49] and is also affected by manifold intrusion [11], leading to significant performance drops in both the classification and calibration. The manifold intrusion happens when the label mixture of an augmented sample differs from the label of the real sample [11]. However, in our framework, we do not explicitly use the label mixtures as supervision, suggesting that our framework is less affected by those problems. Therefore, our framework is more robust to the variation of the parameter $\alpha$ compared to the vanilla mixup. To further investigate the importance of diverse samples, we also perform experiments with various combinations of $\alpha$ and $Q$ and provide the results in the supplementary material. + +Table 7: Quantitative comparison of calibration performances using other mixup techniques on the validation splits of CIFAR10 [20] and Tiny-ImageNet [23]. + +
Mixup [49] Manifold [45] CutMix [47]CIFAR10 [20]Tiny-ImageNet [23]
ECE↓AECE↓ECE↓AECE↓
RegMixup [35]✓3.633.574.764.88
✓3.563.542.972.93
RankMixup✓2.922.981.201.22
✓3.263.211.801.66
✓2.592.581.491.44
+ +Table 8: Quantitative comparison of classification and calibration performances on the test splits of CIFAR10-LT [1] and CIFAR100-LT [1]. We report the Top-1 accuracy $(\%)$ and ECE $(\%)$ with 15 bins. + +
CIFAR10-LT [1]CIFAR100-LT [1]
Methodsρ = 10Acc↑/ECE↓ρ = 100Acc↑/ECE↓ρ = 10Acc↑/ECE↓ρ = 100Acc↑/ECE↓
CE86.39/6.6070.36/20.5355.70/22.8538.32/38.23
Mixup [49]87.10/6.5573.06/19.2058.02/19.6939.54/32.72
Remix [5]88.15/6.8175.36/15.3859.36/20.1741.94/33.56
UniMix [46]89.66/6.0082.75/12.8761.25/19.3845.45/27.12
RankMixup (MRL)88.83/2.1674.16/ 2.0362.84/13.5542.56/ 5.28
RankMixup (M-NDCG)89.80/5.9475.41/14.1063.83/ 9.9943.00/18.74
+ +Other mixup techniques. RankMixup employs a vanilla mixup technique that interpolates the input images and the corresponding labels for data augmentation, but other variants can be readily adopted in our framework. We have also tried using Manifold-Mixup [45] and CutMix [47] for the experiments. We show in Table 7 the results of our models using these techniques together with M-NDCG, while setting the shape parameter $\alpha$ to 1 for the both techniques. For comparison, we report the result of our model with the vanilla mixup, which exploits 3 augmented samples, and additionally show the performances obtained using RegMixup [35] equipped with these variants. For both datasets, our method achieves better calibration errors than RegMixup, indicating that our method has better generalization capability. While our model with vanilla mixup provides the best performance on CIFAR10, employing Manifold-Mixup offers better results on Tiny-ImageNet in terms of calibration errors. Increasing the entropy of supervision is crucial for better-calibrated models [25, 29, 30, 41]. RankMixup exploits the augmented samples as supervision for network calibration, indicating that samples with higher entropies can yield better performances. Manifold-Mixup [45] produces flattened representations that have higher entropies than the mixup-augmented samples, which may explain the reason why our model with Manifold-Mixup performs better on Tiny-ImageNet. + +Long-tailed datasets. We evaluate our method on long-tailed (LT) datasets, where the miscalibration issues of DNNs are more pronounced [46, 52]. Following the experimental settings in [46, 52], we adopt the ResNet32 [13] architecture as our backbone, and exploit CIFAR10/100-LT datasets [1] with two imbalanced factors $(\rho)$ . We compare in Table 8 our method against the vanilla mixup [49] and two + +adaptive mixup techniques tailored for LT scenarios [5, 46]. We can see that our models significantly outperform other mixup methods in terms of ECE, while providing competitive accuracies, although they are not specially designed for LT scenarios. This suggests that leveraging the ordinal ranking relationship between confidence is also effective for addressing miscalibration problems in LT scenarios, instead of using label mixtures for other mixup-based augmentations [46, 52]. Note that the number of samples for head and tail classes is highly skewed, suggesting that augmented samples are not diverse in LT scenarios. As this problem is more severe for M-NDCG, it yields worse results, compared to MRL, in the LT datasets. + +# 5. Conclusion + +We have presented a novel mixup-based framework for network calibration, dubbed RankMixup, alleviating the problem that interpolated labels do not necessarily model the actual distribution of label mixtures. To this end, we have proposed a new supervisory signal based on the ordinal ranking relationship that a higher confidence is more favorable for a raw sample than the one augmented by mixup. We have proposed MRL, which encourages a network to yield confidence that preserve the ranking relationships between the raw and mixup-augmented samples. We have also extended this idea to multiple augmented samples with different mixup coefficients via M-NDCG, enabling a network to predict outputs with higher confidence for augmented samples that are closer to a raw one. We have demonstrated the effectiveness of RankMixup through the extensive experiments and analysis, achieving the best results among mixup-based network calibration approaches. + +Acknowledgments. This work was supported in part by the NRF and IITP grants funded by the Korea government (MSIT) (No.2023R1A2C2004306, No.2022-0-00124, Development of Artificial Intelligence Technology for Self-Improving Competency-Aware Learning Capabilities, No.2021-0-02068, Artificial Intelligence Innovation Hub), and the Yonsei Signature Research Cluster Program of 2023 (2023-22-0008). + +# References + +[1] Kaidi Cao, Colin Wei, Adrien Gaidon, Nikos Arechiga, and Tengyu Ma. Learning imbalanced datasets with label-distribution-aware margin loss. In NIPS, 2019. 9 +[2] Olivier Chapelle, Jason Weston, Léon Bottou, and Vladimir Vapnik. Vicinal risk minimization. In NeurIPS, 2000. 3 +[3] Jie-Neng Chen, Shuyang Sun, Ju He, Philip HS Torr, Alan Yuille, and Song Bai. TransMix: Attend to mix for vision transformers. In CVPR, 2022. 2, 3, 4 +[4] Jiacheng Cheng and Nuno Vasconcelos. Calibrating deep neural networks by pairwise constraints. 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Recent approaches leverage mixup to calibrate the network's predictions during training. However, they do not consider the problem that mixtures of labels in mixup may not accurately represent the actual distribution of augmented samples. In this paper, we present RankMixup, a novel mixup-based framework alleviating the problem of the mixture of labels for network calibration. To this end, we propose to use an ordinal ranking relationship between raw and mixup-augmented samples as an alternative supervisory signal to the label mixtures for network calibration. We hypothesize that the network should estimate a higher level of confidence for the raw samples than the augmented ones (Fig.1). To implement this idea, we introduce a mixup-based ranking loss (MRL) that encourages lower confidences for augmented samples compared to raw ones, maintaining the ranking relationship. We also propose to leverage the ranking relationship among multiple mixup-augmented samples to further improve the calibration capability. Augmented samples with larger mixing coefficients are expected to have higher confidences and vice versa (Fig.1). That is, the order of confidences should be aligned with that of mixing coefficients. To this end, we introduce a novel loss, M-NDCG, in order to reduce the number of misaligned pairs of the coefficients and confidences. Extensive experimental results on standard benchmarks for network calibration demonstrate the effectiveness of RankMixup." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 616, + 128, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 616, + 128, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 616, + 128, + 628 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 635, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 635, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 635, + 287, + 696 + ], + "type": "text", + "content": "Deep neural networks (DNNs) have achieved remarkable advances in numerous computer vision tasks, including image classification, object detection, and semantic segmentation. Despite the impressive performance, DNNs trained using a softmax cross-entropy (CE) loss and one-hot en" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 320, + 232, + 517, + 290 + ], + "blocks": [ + { + "bbox": [ + 320, + 232, + 517, + 290 + ], + "lines": [ + { + "bbox": [ + 320, + 232, + 517, + 290 + ], + "spans": [ + { + "bbox": [ + 320, + 232, + 517, + 290 + ], + "type": "image", + "image_path": "f74b3e0c14e4a7b98cd5a9a79cbe6530d605d9c43fb2441fc400acac2ff66949.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 307, + 293, + 547, + 355 + ], + "blocks": [ + { + "bbox": [ + 307, + 293, + 547, + 355 + ], + "lines": [ + { + "bbox": [ + 307, + 293, + 547, + 355 + ], + "spans": [ + { + "bbox": [ + 307, + 293, + 547, + 355 + ], + "type": "image", + "image_path": "3a58cb9035265fe62a3beb81840d8178e4aa279967fb9b8f93f3d213c8b145d6.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 363, + 547, + 462 + ], + "lines": [ + { + "bbox": [ + 304, + 363, + 547, + 462 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 547, + 462 + ], + "type": "text", + "content": "Figure 1: Motivation of RankMixup. We show raw samples of a cat and dog in red boxes, and mixup-augmented samples in blue boxes with dashed lines. The mixup-augmented samples are generated by linearly interpolating the raw samples with a mixing coefficient " + }, + { + "bbox": [ + 304, + 363, + 547, + 462 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 363, + 547, + 462 + ], + "type": "text", + "content": ". We expect that confidences of the raw samples to be higher than that of the augmented sample (top). The augmented samples with larger coefficients " + }, + { + "bbox": [ + 304, + 363, + 547, + 462 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 363, + 547, + 462 + ], + "type": "text", + "content": " would have higher confidences than the samples with smaller coefficients (bottom). Best viewed in color." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 485, + 547, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 547, + 581 + ], + "type": "text", + "content": "coded labels often output overconfident and/or underconfident probabilities, which do not reflect the actual likelihood [10, 32, 41]. This suggests that the networks are not able to estimate the level of confidence, leading to inaccurate and unreliable predictions, which restricts practical applications in real-world systems, particularly for safety-sensitive domains, such as medical diagnosis [18] and autonomous driving [9]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": "To improve the reliability of DNNs, many methods propose to calibrate the output distribution after or during training. Post-hoc approaches adjust miscalibrated probabilities directly from pretrained networks [7, 10, 12, 21, 27]. Although these approaches are straightforward to apply, calibration performance depends heavily on datasets and networks used for training [25], and they are not robust to distribution shifts between training and test samples [33]. Training-time approaches [4, 8, 14, 25, 28, 29, 30, 41, 51], on the other hand, exploit an additional regularization term along with the CE loss to calibrate the output probabilities" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "1358" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": "during training. Early works [29, 30, 41] have explored the effects of regularization techniques, including label smoothing (LS) [40], focal loss (FL) [24], and mixup [49], on network calibration, and shown that the networks trained with these techniques are better calibrated than the ones trained with the CE loss alone. Recently, the works of [8, 25, 29] highlight the limitations of LS and FL in terms of network calibration, and introduce calibration-aware LS and FL. On the contrary, few studies have explored integrating the mixup technique into network calibration. Current mixup-based methods [35, 41, 51] simply interpolate input images and training labels with a mixing coefficient to soften output probabilities, while not considering network calibration itself. Since the interpolated labels may not represent accurately the distribution of the label mixture in augmented images [3, 19, 39, 43], training networks with such uncertain labels degrades the calibration performance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 275, + 289, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 289, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 289, + 622 + ], + "type": "text", + "content": "In this work, we present a mixup-based approach to network calibration, dubbed RankMixup, that addresses the problem of directly using the mixture of labels for calibrating network predictions [35, 41, 51]. To this end, we conjecture that networks should give higher confidences for the raw sample, not augmented by the mixup technique, than the augmented one (Fig. 1). To implement this idea, we leverage an ordinal ranking relationship between raw and augmented samples (Fig. 1) and use it as a supervisory signal for network calibration, instead of using the label mixtures. In particular, we introduce a mixup-based ranking loss (MRL) that encourages the confidences of augmented samples to be lower than those of raw samples by a margin, in order to preserve the ranking relationship. To further strengthen the capability of network calibration, we also propose to exploit the ranking relationship for multiple mixup-augmented samples. We expect that higher confidences are favorable for augmented samples with larger mixing coefficients " + }, + { + "bbox": [ + 46, + 275, + 289, + 622 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 275, + 289, + 622 + ], + "type": "text", + "content": ", and vice versa (Fig. 1), such that the orders of confidences and mixing coefficients are aligned to each other. To achieve this, we introduce a novel loss, M-NDCG, based on normalized discounted cumulative gain (NDCG) in information retrieval [17], which penalizes the number of misaligned pairs of the coefficients and confidences. Extensive experimental results on standard benchmarks demonstrate the effectiveness of our approach to leveraging the ordinal ranking relationships on network calibration. The main contributions of our work can be summarized as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 626, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 45, + 626, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 626, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 45, + 626, + 287, + 685 + ], + "type": "text", + "content": "- We introduce a novel mixup-based framework for network calibration, RankMixup, that alleviates the problem of exploiting label mixtures for calibrating network predictions. To the best of our knowledge, we are the first to handle this issue in the context of confidence calibration." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 45, + 689, + 287, + 714 + ], + "type": "text", + "content": "- We propose to exploit ordinal ranking relationships between confidence from raw and augmented samples," + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 545, + 144 + ], + "type": "text", + "content": "as well as those among confidences from multiple augmented samples, and use them as supervisory signals, instead of the mixture of labels. To implement this idea, we introduce MRL and M-NDCG that facilitate aligning the confidences and mixing coefficients to preserve the relationships." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 146, + 547, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 146, + 547, + 229 + ], + "spans": [ + { + "bbox": [ + 304, + 146, + 547, + 229 + ], + "type": "text", + "content": "- We demonstrate that our approach provides better results in terms of expected calibration error (ECE), compared to other mixup-based methods. We also achieve competitive performances on standard benchmarks on network calibration, including CIFAR10/100 [20], TinyImageNet [23], and ImageNet [6] with various network architectures." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 239, + 390, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 239, + 390, + 251 + ], + "spans": [ + { + "bbox": [ + 305, + 239, + 390, + 251 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 258, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 547, + 715 + ], + "type": "text", + "content": "Confidence calibration. The seminal work of [10] provides empirical evidence that DNNs are prone to making overconfident predictions due to miscalibrated output probabilities. In particular, they are typically trained with one-hot encoded labels, which fails to impose any entropy on the supervisory signal. The entropy of output probabilities for the network is thus encouraged to be zero, leading to the overconfident predictions [25]. To address this problem, several approaches have been proposed to augment the entropy of output probabilities, which can be divided into two categories: post-hoc and training-time methods. First, post-hoc approaches adjust the miscalibrated probabilities directly after training using a temperature scaling technique [7, 10, 42] or ranking statistics [27]. The temperature scaling technique, also effective to knowledge distillation [16], raises the entropy of output probabilities using a temperature parameter, optimized on additional validation samples. Although post-hoc approaches have shown the effectiveness on in-distribution datasets, they perform poorly under distribution shifts [33], and inevitably lower the confidence of correct predictions [22, 29]. Second, training-time approaches implicitly or explicitly impose regularization on outputs probabilities during training, usually in combination with post-hoc methods to further improve the calibration accuracy. The implicit methods [4, 4, 8, 25, 30, 35, 41] smooth the output distribution by increasing the entropy of training labels, rather than adjusting output probabilities directly. Several works [29, 30, 41, 51] have demonstrated empirically and theoretically that regularization methods such as LS [40], FL [24], and Mixup [49], which have originally designed to learn discriminative features, can also be effective in network calibration. However, recent works of [8, 25, 35] explore that directly using these methods for network calibration is problematic, and they introduce improved versions to overcome the drawback. For example, MbLS [25] exploits a margin-based LS to address the problem of LS providing non-informative predictions to obtain a better-calibrated network. The works" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1359" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "content": "of [8, 35] suggest that finding optimal parameters of FL and mixup is crucial for network calibration. The explicit methods [14, 22, 28, 34] adjust confidences of predictions directly by maximizing the entropy of output probabilities [34], using an ordinal ranking relationship [28] or minimizing calibration errors [14, 22]. For example, the ordinal ranking between output probabilities of networks has been proven to be effective to estimate the levels of confidence, providing better calibrated models [28]. It assumes that the predictions with higher confidences are more likely to be accurate than the ones with lower confidences. We explore the effects of mixup [49] in the context of network calibration, similar to other mixup-based methods [35, 41, 51]. They use interpolated labels to train networks for calibrating output probabilities, but the labels do not provide the distribution of the label mixture for the augmented sample accurately [3, 19, 39, 43]. We exploit confidences of augmented samples directly as supervisory signals for network calibration using ordinal ranking relationships between the samples, boosting the calibration performance significantly. The work of [28] is closely related to ours in that it uses an ordinal ranking relationship for raw samples. In contrast to this, our approach exploits more diverse and complex ordinal relationships for confidences. It considers not only the relationship between raw and augmented samples, but also among the augmented samples themselves." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 386, + 289, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 386, + 289, + 661 + ], + "spans": [ + { + "bbox": [ + 47, + 386, + 289, + 661 + ], + "type": "text", + "content": "Mixup. Data augmentation has become a standard technique for training DNNs that regularizes the networks to prevent overfitting and improve generalization. Mixup [49] linearly interpolates between pairs of raw data samples. Specifically, it takes a weighted average of two images to obtain a new one. The training label for the augmented sample is also interpolated with the same weight. Many works extend this idea to improve the generalization ability. Manifold-Mixup [45] performs the mixup process in the feature space, while CutMix [47] introduces a regional mixing scheme to preserve fine-grained information of original images. It has recently been explored that using label mixtures in mixup and its variants could provide misleading supervisory signals for training networks, which can be alleviated by saliency-guided mixup schemes [3, 19, 36, 43] or label perturbations [39]. In addition to data augmentation, various applications leverage mixup for, e.g., self-supervised learning [37, 38] and network calibration [35, 41]. We mainly investigate the effect of the vanilla mixup [49] on network calibration. However, as will be shown in our experiments, the variants of mixup, including CutMix [47] and manifold-Mixup [45], can also be readily adapted to our approach." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 670, + 115, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 115, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 115, + 684 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "We present in this section preliminaries for network calibration and mixup [49] in Sec. 3.1, and provide a detailed" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 72, + 547, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 547, + 97 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 547, + 97 + ], + "type": "text", + "content": "description of RankMiup and training losses in Secs. 3.2 and 3.3, respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 102, + 392, + 114 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 102, + 392, + 114 + ], + "spans": [ + { + "bbox": [ + 306, + 102, + 392, + 114 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "spans": [ + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "text", + "content": "Network calibration. Let us suppose a dataset " + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "inline_equation", + "content": "D = \\{(\\mathbf{x}_i, \\mathbf{y}_i)\\}_{i=1}^N" + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "text", + "content": " of size " + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i \\in \\mathcal{X}" + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i \\in \\mathcal{Y}" + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "text", + "content": " are an input sample and a ground-truth label with " + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "text", + "content": " classes, respectively. DNNs can be considered as a function, parameterized by " + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "text", + "content": ", that yields a logit " + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "text", + "content": " of size " + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "inline_equation", + "content": "K \\times 1" + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "text", + "content": " from the input sample: " + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_\\theta : \\mathcal{X} \\to \\mathbb{R}^K" + }, + { + "bbox": [ + 305, + 121, + 547, + 216 + ], + "type": "text", + "content": ". For multiclass classification, the networks compute class probabilities using the softmax function as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 349, + 220, + 545, + 248 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 220, + 545, + 248 + ], + "spans": [ + { + "bbox": [ + 349, + 220, + 545, + 248 + ], + "type": "interline_equation", + "content": "p _ {i, k} = \\operatorname {s o f t m a x} \\left(\\mathbf {z} _ {i}\\right) = \\frac {\\exp z _ {i , k}}{\\sum_ {j} ^ {K} \\exp z _ {i , j}}, \\tag {1}", + "image_path": "4acb8d0e80ba4f6629d47aa215fd723944382b931e2a6bc7e1a82b2dcd921315.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 253, + 546, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 253, + 546, + 289 + ], + "spans": [ + { + "bbox": [ + 305, + 253, + 546, + 289 + ], + "type": "text", + "content": "where we denote by " + }, + { + "bbox": [ + 305, + 253, + 546, + 289 + ], + "type": "inline_equation", + "content": "p_{i,k}" + }, + { + "bbox": [ + 305, + 253, + 546, + 289 + ], + "type": "text", + "content": " a probability of the " + }, + { + "bbox": [ + 305, + 253, + 546, + 289 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 253, + 546, + 289 + ], + "type": "text", + "content": "-th class for the " + }, + { + "bbox": [ + 305, + 253, + 546, + 289 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 253, + 546, + 289 + ], + "type": "text", + "content": "-th input. Based on the probabilities, the networks predict a class for the input sample " + }, + { + "bbox": [ + 305, + 253, + 546, + 289 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 305, + 253, + 546, + 289 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 386, + 297, + 545, + 314 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 386, + 297, + 545, + 314 + ], + "spans": [ + { + "bbox": [ + 386, + 297, + 545, + 314 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {i} = \\arg \\max _ {k} p _ {i, k}. \\tag {2}", + "image_path": "f3c75ac4a976fc412b3882ce314cd16d7a8f639a87062097dbec15d97e9386a6.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 319, + 545, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 319, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 305, + 319, + 545, + 342 + ], + "type": "text", + "content": "The corresponding confidence can then be obtained as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 393, + 344, + 545, + 360 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 393, + 344, + 545, + 360 + ], + "spans": [ + { + "bbox": [ + 393, + 344, + 545, + 360 + ], + "type": "interline_equation", + "content": "\\hat {p} _ {i} = \\max _ {k} p _ {i, k}. \\tag {3}", + "image_path": "144a62b7a468969e2e3eca8a773dfe83e1f6d72c9f6265221c282d983a68ff5c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 363, + 545, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 363, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 305, + 363, + 545, + 387 + ], + "type": "text", + "content": "During training, the networks are optimized using a cross-entropy (CE) loss as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 354, + 394, + 545, + 427 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 394, + 545, + 427 + ], + "spans": [ + { + "bbox": [ + 354, + 394, + 545, + 427 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {C E} \\left(\\mathbf {x} _ {i}, \\mathbf {y} _ {i}\\right) = - \\sum_ {k = 1} ^ {K} y _ {i, k} \\log p _ {i, k}, \\tag {4}", + "image_path": "e5efd265843ab290c75c90c8248894954588cf54df735d1db2d36e7de12ecd87.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 433, + 547, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 433, + 547, + 515 + ], + "spans": [ + { + "bbox": [ + 305, + 433, + 547, + 515 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 433, + 547, + 515 + ], + "type": "inline_equation", + "content": "y_{i,k}" + }, + { + "bbox": [ + 305, + 433, + 547, + 515 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 305, + 433, + 547, + 515 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 433, + 547, + 515 + ], + "type": "text", + "content": "-th element of the one-hot encoded label " + }, + { + "bbox": [ + 305, + 433, + 547, + 515 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i" + }, + { + "bbox": [ + 305, + 433, + 547, + 515 + ], + "type": "text", + "content": ". Recent works [10, 29, 30, 41] have shown that DNNs trained with the CE loss tend to be overconfident, providing higher accuracies than accuracies. To address this problem, confidence calibration methods encourage that the confidence for each sample and the accuracy are the same as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 383, + 524, + 545, + 538 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 524, + 545, + 538 + ], + "spans": [ + { + "bbox": [ + 383, + 524, + 545, + 538 + ], + "type": "interline_equation", + "content": "\\hat {p} _ {i} = P \\left(\\hat {y} _ {i} = y _ {i} \\mid \\hat {p} _ {i}\\right), \\tag {5}", + "image_path": "6ca343a855dd78b47d744d6937b15e1c594f73e7468845cf562f4d603d6ab1be.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 544, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 544, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 305, + 544, + 545, + 568 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 544, + 545, + 568 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 305, + 544, + 545, + 568 + ], + "type": "text", + "content": " is an index of the true class for the ground-truth label " + }, + { + "bbox": [ + 305, + 544, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{i}" + }, + { + "bbox": [ + 305, + 544, + 545, + 568 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": "Mixup. Mixup [49] is a data-augmentation technique based on the vicinal risk minimization principle [2]. It introduces the mixup vicinal distribution, which measures the likelihood of finding a pair of an augmented input and a target label, " + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "inline_equation", + "content": "(\\tilde{\\mathbf{x}}_i,\\tilde{\\mathbf{y}}_i)" + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": ", from the vicinity of the original pair, " + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}_i,\\mathbf{y}_i)" + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": ". Mixup samples the vicinal distribution to construct a new dataset, " + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "inline_equation", + "content": "D_{v} = \\{(\\tilde{\\mathbf{x}}_{i},\\tilde{\\mathbf{y}}_{i})\\}_{i = 1}^{N}" + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": ". Here, we denote by " + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "inline_equation", + "content": "D_{v}" + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": " the vicinal set consisting of pairs of augmented training samples and corresponding target labels. Specifically, it augments training pairs by linearly interpolating the original ones as follows:" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1360" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 119, + 83, + 286, + 102 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 83, + 286, + 102 + ], + "spans": [ + { + "bbox": [ + 119, + 83, + 286, + 102 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\tilde {\\mathbf {x}} = \\lambda \\mathbf {x} _ {i} + (1 - \\lambda) \\mathbf {x} _ {j}, \\\\ \\tilde {\\dots} \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\dots \\end{array} \\tag {6}", + "image_path": "2e388a1e46a7c4fc2b09fd0a9d081992b54343b2e4757b64c90879e684568023.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 120, + 99, + 214, + 111 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 99, + 214, + 111 + ], + "spans": [ + { + "bbox": [ + 120, + 99, + 214, + 111 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {y}} = \\lambda \\mathbf {y} _ {i} + (1 - \\lambda) \\mathbf {y} _ {j},", + "image_path": "3abd61361ed6f4f134628662713f4116e03e8d02ac0ecea0ee22f8c9e7d46091.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 118, + 289, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 118, + 289, + 274 + ], + "spans": [ + { + "bbox": [ + 46, + 118, + 289, + 274 + ], + "type": "text", + "content": "where two pairs of input samples and target labels, " + }, + { + "bbox": [ + 46, + 118, + 289, + 274 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}_i,\\mathbf{y}_i)" + }, + { + "bbox": [ + 46, + 118, + 289, + 274 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 118, + 289, + 274 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}_j,\\mathbf{y}_j)" + }, + { + "bbox": [ + 46, + 118, + 289, + 274 + ], + "type": "text", + "content": ", are randomly drawn from the training set " + }, + { + "bbox": [ + 46, + 118, + 289, + 274 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 118, + 289, + 274 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 118, + 289, + 274 + ], + "type": "inline_equation", + "content": "\\lambda \\in [0,1] \\sim \\mathrm{Beta}(\\alpha ,\\alpha)" + }, + { + "bbox": [ + 46, + 118, + 289, + 274 + ], + "type": "text", + "content": " is a mixing coefficient, sampled from a Beta distribution. Mixup assumes that target labels for the vicinal set should also be interpolated with the same mixing coefficient as input samples during the mixing process. The hyperparameter " + }, + { + "bbox": [ + 46, + 118, + 289, + 274 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 118, + 289, + 274 + ], + "type": "text", + "content": " controls the strength of interpolation between the pairs of input samples and target labels. According to [49], the value of " + }, + { + "bbox": [ + 46, + 118, + 289, + 274 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 118, + 289, + 274 + ], + "type": "text", + "content": " within the range of [0.1, 0.4] provides better classification performance, while higher values cause significant underfitting. We will also examine the effect of " + }, + { + "bbox": [ + 46, + 118, + 289, + 274 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 118, + 289, + 274 + ], + "type": "text", + "content": " in terms of confidence calibration within our framework." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 282, + 127, + 295 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 282, + 127, + 295 + ], + "spans": [ + { + "bbox": [ + 47, + 282, + 127, + 295 + ], + "type": "text", + "content": "3.2. RankMixup" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 301, + 289, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 289, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 289, + 553 + ], + "type": "text", + "content": "Mixup provides smooth decision boundaries that gradually shift from one class to another, which leads to a regularized estimate of uncertainty (or confidence) [49]. There have been lots of studies to discover underlying principles behind the mixup method [15, 41, 50, 51, 51]. For example, it has proven to give better output probabilities in terms of model calibration, alleviating overconfident predictions [35, 41, 51]. The interpolated labels of augmented samples in the vicinal set do not always model the actual distribution of label mixtures in augmented samples [3, 19, 39, 43], which however has not been considered for designing a network calibration method. To alleviate this problem, we leverage ordinal ranking relationships between confidences from raw and augmented samples, as well as those among confidences from multiple augmented samples. We then propose to use them as supervisory signals for model calibration, rather than using the mixture of labels directly. In the following, we describe our framework with a single mixup-augmented sample, and present a generalized version that can handle multiple augmented samples." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": "Single mixup-augmented sample. The sample augmented by mixup " + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{x}}" + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": " in Eq. (6) can be interpreted as a combination of the raw sample " + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": " and structured noise from another one " + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_j" + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": ", where the degree of noise is determined by the mixing parameter " + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": ". This suggests that DNNs predict the class of the augmented sample with uncertainty imposed by the additional one, making it more difficult to recognize the augmented sample than the raw one. To this end, mixup imposes uncertainty on the label mixtures by adjusting confidence of target labels for the augmented samples by " + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "inline_equation", + "content": "1 - \\lambda" + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": "). Albeit simple, directly using the interpolated labels may provide misleading supervisory signals" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 182 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 182 + ], + "type": "text", + "content": "to train DNNs. To avoid this, we leverage an ordinal ranking relationship between confidence of raw and augmented samples. Specifically, the ordinal ranking holds for the relationship that confidence levels of easy-to-classify samples should be higher than the ones for hard samples [28]. Accordingly, we conjecture that the confidence levels of raw samples should be greater than those of the augmented samples in the mixing process (Fig.1). Namely, every pair of samples " + }, + { + "bbox": [ + 304, + 72, + 547, + 182 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}_i,\\tilde{\\mathbf{x}}_i)" + }, + { + "bbox": [ + 304, + 72, + 547, + 182 + ], + "type": "text", + "content": " should satisfy the following relationship:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 380, + 191, + 545, + 208 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 191, + 545, + 208 + ], + "spans": [ + { + "bbox": [ + 380, + 191, + 545, + 208 + ], + "type": "interline_equation", + "content": "\\max _ {k} p _ {i, k} \\geq \\max _ {k} \\tilde {p} _ {i, k}, \\tag {7}", + "image_path": "c1e97a5660389bad99ee3ac3a41c982124332d6f0c0cf7d4ba52f6a1dd77c05a.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 217, + 547, + 265 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 547, + 265 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 547, + 265 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 217, + 547, + 265 + ], + "type": "inline_equation", + "content": "\\tilde{p}_{i,k}" + }, + { + "bbox": [ + 304, + 217, + 547, + 265 + ], + "type": "text", + "content": " is a predicted probability of the class " + }, + { + "bbox": [ + 304, + 217, + 547, + 265 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 217, + 547, + 265 + ], + "type": "text", + "content": " for the augmented sample " + }, + { + "bbox": [ + 304, + 217, + 547, + 265 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{x}}_i" + }, + { + "bbox": [ + 304, + 217, + 547, + 265 + ], + "type": "text", + "content": ". We devise MRL that encourages the network to learn this relationship without the mixture of labels, which will be described in Sec. 3.3." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 282, + 547, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 547, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 547, + 426 + ], + "type": "text", + "content": "Multiple mixup-augmented samples. We extend our framework to exploit multiple mixup-augmented samples. As the mixing ratio " + }, + { + "bbox": [ + 304, + 282, + 547, + 426 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 282, + 547, + 426 + ], + "type": "text", + "content": " decreases, augmented samples become more difficult to recognize, which suggests that we can exploit more complex ranking relationships among the multiple augmented samples. Analogous to the single case, we expect that the samples augmented with larger mixing coefficients " + }, + { + "bbox": [ + 304, + 282, + 547, + 426 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 282, + 547, + 426 + ], + "type": "text", + "content": " show higher confidence compared to those with smaller coefficients (Fig. 1). For every pair of augmented samples " + }, + { + "bbox": [ + 304, + 282, + 547, + 426 + ], + "type": "inline_equation", + "content": "(\\tilde{\\mathbf{x}}_i,\\tilde{\\mathbf{x}}_j)" + }, + { + "bbox": [ + 304, + 282, + 547, + 426 + ], + "type": "text", + "content": " from the vicinal set " + }, + { + "bbox": [ + 304, + 282, + 547, + 426 + ], + "type": "inline_equation", + "content": "D_{v}" + }, + { + "bbox": [ + 304, + 282, + 547, + 426 + ], + "type": "text", + "content": ", the confidence of these samples should satisfy the following relationship:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 356, + 437, + 545, + 454 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 437, + 545, + 454 + ], + "spans": [ + { + "bbox": [ + 356, + 437, + 545, + 454 + ], + "type": "interline_equation", + "content": "\\lambda_ {i} \\geq \\lambda_ {j} \\Leftrightarrow \\max _ {k} \\tilde {p} _ {i, k} \\geq \\max _ {k} \\tilde {p} _ {j, k}, \\tag {8}", + "image_path": "d728483e2656dfdf3324c098793c23655a038b8d0353f30758b313b9814174e9.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 464, + 545, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 464, + 545, + 523 + ], + "spans": [ + { + "bbox": [ + 304, + 464, + 545, + 523 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 464, + 545, + 523 + ], + "type": "inline_equation", + "content": "(\\lambda_i, \\lambda_j)" + }, + { + "bbox": [ + 304, + 464, + 545, + 523 + ], + "type": "text", + "content": " is a pair of mixing ratios for the corresponding pair of augmented samples " + }, + { + "bbox": [ + 304, + 464, + 545, + 523 + ], + "type": "inline_equation", + "content": "(\\tilde{\\mathbf{x}}_i, \\tilde{\\mathbf{x}}_j)" + }, + { + "bbox": [ + 304, + 464, + 545, + 523 + ], + "type": "text", + "content": ". Note that we describe the relationship with two samples for simplicity, but our framework can adopt the relationship with any number of augmented samples." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 524, + 547, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 524, + 547, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 524, + 547, + 586 + ], + "type": "text", + "content": "We then integrate both the relationships in Eqs. (7) and (8) to obtain a general version of RankMixup. With the mixing coefficient of 1.0 for the raw sample, the following relationship should hold for every triplet of samples " + }, + { + "bbox": [ + 304, + 524, + 547, + 586 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}_i,\\tilde{\\mathbf{x}}_i,\\tilde{\\mathbf{x}}_j)^1" + }, + { + "bbox": [ + 304, + 524, + 547, + 586 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 595, + 545, + 612 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 595, + 545, + 612 + ], + "spans": [ + { + "bbox": [ + 313, + 595, + 545, + 612 + ], + "type": "interline_equation", + "content": "1. 0 \\geq \\lambda_ {i} \\geq \\lambda_ {j} \\Leftrightarrow \\max _ {k} p _ {i, k} \\geq \\max _ {k} \\tilde {p} _ {i, k} \\geq \\max _ {k} \\tilde {p} _ {j, k}. \\tag {9}", + "image_path": "00d100a45b472b10211b2e6bebc84f268d15cbd494b23ef2577615d205c7548b.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 621, + 547, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 621, + 547, + 693 + ], + "spans": [ + { + "bbox": [ + 304, + 621, + 547, + 693 + ], + "type": "text", + "content": "This allows the network to estimate the levels of confidence better by considering diverse ordinal ranking relationships among the confidences of the raw and multiple mixup-augmented samples. To implement this idea, we align the orders of confidences and mixing ratios during training using M-NDCG (Sec. 3.3)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 317, + 702, + 462, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 702, + 462, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 702, + 462, + 713 + ], + "type": "text", + "content": "1 Note that Eq. (9) holds only when " + }, + { + "bbox": [ + 317, + 702, + 462, + 713 + ], + "type": "inline_equation", + "content": "\\lambda \\geq 0.5" + }, + { + "bbox": [ + 317, + 702, + 462, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "text", + "content": "1361" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 130, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 130, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 130, + 85 + ], + "type": "text", + "content": "3.3. Training loss" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 163 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 163 + ], + "type": "text", + "content": "To train our model, we use a CE loss for classification, together with either MRL or M-NDCG for network calibration, balanced by the parameter of " + }, + { + "bbox": [ + 46, + 91, + 287, + 163 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 91, + 287, + 163 + ], + "type": "text", + "content": ". As supervisory signals, we exploit one-hot encoded labels for classification, and ordinal ranking relationships for input and augmented samples for network calibration." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 179, + 287, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 179, + 287, + 227 + ], + "spans": [ + { + "bbox": [ + 46, + 179, + 287, + 227 + ], + "type": "text", + "content": "MRL. We introduce MRL facilitating the ordinal relationship in Eq. (7). It encourages confidence of augmented samples to be lower than those of raw samples by a margin, defined as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 239, + 287, + 257 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 239, + 287, + 257 + ], + "spans": [ + { + "bbox": [ + 67, + 239, + 287, + 257 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {M R L}} = \\max \\left(0, \\max _ {k} \\tilde {p} _ {i, k} - \\max _ {k} p _ {i, k} + m\\right), \\tag {10}", + "image_path": "99ea6635c8e6f3897f11c842f7fba1876bf2ffb40e087a87146566b86a680809.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 265, + 287, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 265, + 287, + 421 + ], + "spans": [ + { + "bbox": [ + 46, + 265, + 287, + 421 + ], + "type": "text", + "content": "where the margin " + }, + { + "bbox": [ + 46, + 265, + 287, + 421 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 265, + 287, + 421 + ], + "type": "text", + "content": " determines acceptable discrepancies between the confidence of raw and augmented samples. The intuition behind using a margin is twofold: (1) It enables maintaining the ranking relationship between confidence, rather than penalizing the exact value of the discrepancies itself. (2) Controlling the confidence discrepancies with a margin allows to consider the uncertainty of inaccurate label mixtures. The vanilla mixup method continues to penalize the confidence of augmented samples, until they reach overconfident values, determined by the label mixtures. In contrast to this, MRL penalizes the confidence, only when the absolute discrepancies between them are below the margin." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 437, + 287, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 558 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 558 + ], + "type": "text", + "content": "M-NDCG. MRL is not sufficient to model the relationship in Eq. (9), where the comparison involves more than one augmented sample. M-NDCG addresses this problem that enables multiple confidence values to hold the ordinal ranking relationships. M-NDCG is based on NDCG used for evaluating ranking quality in information retrieval [17, 44]. It measures how many of retrieved results are aligned with the ground-truth ranking order, which can be calculated by normalizing a discounted cumulative gain (DCG) with an ideal DCG (IDCG):" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 125, + 566, + 287, + 591 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 566, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 125, + 566, + 287, + 591 + ], + "type": "interline_equation", + "content": "N D C G = \\frac {D C G}{I D C G}. \\tag {11}", + "image_path": "dbc74fcd4775f45a728d2cfa19ce6b7454780a5f9a34a6b800eee763c311eac4.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 598, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 598, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 598, + 287, + 635 + ], + "type": "text", + "content": "DCG accumulates a relevance score of each retrieval result, weighted by a corresponding rank, and IDCG is computed similarly but with the ground-truth score, as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 111, + 645, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 645, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 111, + 645, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} D C G = \\sum_ {q = 1} ^ {Q} \\frac {r _ {q}}{\\log_ {2} (q + 1)}, \\tag {12} \\\\ I D C G = \\sum_ {q = 1} ^ {Q} \\frac {r _ {q} ^ {\\mathrm {g t}}}{\\log_ {2} (q + 1)}, \\\\ \\end{array}", + "image_path": "99874b6e6c483aca4e8f233e7807cacbd564fb620acc7bfa343544912fc8626a.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "type": "inline_equation", + "content": "r_q" + }, + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "type": "inline_equation", + "content": "r_q^{\\mathrm{gt}}" + }, + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "type": "text", + "content": " are the relevance and ground-truth scores, respectively, at position " + }, + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "type": "text", + "content": " in the result list of size " + }, + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 97, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 97, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 305, + 97, + 545, + 156 + ], + "type": "text", + "content": "We consider confidences of predictions and mixing coefficients as the relevance and ground-truth scores, respectively, enabling multiple confidences to satisfy the relationship in Eq. (9). Given " + }, + { + "bbox": [ + 305, + 97, + 545, + 156 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 305, + 97, + 545, + 156 + ], + "type": "text", + "content": " pairs of confidences and mixing coefficients, we compute " + }, + { + "bbox": [ + 305, + 97, + 545, + 156 + ], + "type": "inline_equation", + "content": "DCG_{\\mathrm{M}}" + }, + { + "bbox": [ + 305, + 97, + 545, + 156 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 97, + 545, + 156 + ], + "type": "inline_equation", + "content": "IDCG_{\\mathrm{M}}" + }, + { + "bbox": [ + 305, + 97, + 545, + 156 + ], + "type": "text", + "content": ", as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 320, + 175, + 545, + 246 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 175, + 545, + 246 + ], + "spans": [ + { + "bbox": [ + 320, + 175, + 545, + 246 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} D C G _ {\\mathrm {M}} = \\frac {\\operatorname* {m a x} _ {k} p _ {t , k}}{\\log_ {2} (t + 1)} + \\sum_ {q = 1, q \\neq t} ^ {Q} \\frac {\\operatorname* {m a x} _ {k} \\tilde {p} _ {q , k}}{\\log_ {2} (q + 1)}, \\tag {13} \\\\ I D C G _ {\\mathrm {M}} = 1 + \\sum_ {q = 2} ^ {Q} \\frac {\\lambda_ {q} ^ {\\mathrm {g t}}}{\\log_ {2} (q + 1)}, \\\\ \\end{array}", + "image_path": "fe5b0dd182f343fbe5cc74afd6bc8c43e1f83b9eaa418c969ed18c2cdb29674b.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 255, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 255, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 305, + 255, + 545, + 373 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 255, + 545, + 373 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 255, + 545, + 373 + ], + "type": "text", + "content": " is the position of the confidence value for the raw sample, which is set to 1 in order to ensure that its confidence is always ranked first in a descending order, following the ranking relationship in Eq. (9). " + }, + { + "bbox": [ + 305, + 255, + 545, + 373 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 305, + 255, + 545, + 373 + ], + "type": "text", + "content": " is a hyperparameter that determines the number of augmented samples, i.e., " + }, + { + "bbox": [ + 305, + 255, + 545, + 373 + ], + "type": "inline_equation", + "content": "Q - 1" + }, + { + "bbox": [ + 305, + 255, + 545, + 373 + ], + "type": "text", + "content": " augmented samples. " + }, + { + "bbox": [ + 305, + 255, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\lambda_q^{\\mathrm{gt}}" + }, + { + "bbox": [ + 305, + 255, + 545, + 373 + ], + "type": "text", + "content": " is the mixing coefficient sorted based on its magnitude, with a value of 1.0 for the raw sample appearing at position of the top rank, i.e., " + }, + { + "bbox": [ + 305, + 255, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\lambda_1^{\\mathrm{gt}} = 1" + }, + { + "bbox": [ + 305, + 255, + 545, + 373 + ], + "type": "text", + "content": ". We then define M-NDCG loss as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 370, + 372, + 545, + 397 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 372, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 370, + 372, + 545, + 397 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {M - N D C G}} = 1 - \\frac {D C G _ {\\mathrm {M}}}{I D C G _ {\\mathrm {M}}}, \\tag {14}", + "image_path": "d9b1175674dcc94cde5984c019ac69b79b4dda6f621d23287ae23f1d2de6d5d7.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 400, + 545, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 400, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 305, + 400, + 545, + 484 + ], + "type": "text", + "content": "which is minimized when the ranking orders of the confidences and mixing coefficients are aligned to each other after sorting in a descending order. The network is thus trained to encourage the confidence to hold the ordinal ranking relationship of RankMixup in Eq. (9). M-NDCG also discounts lower-ranked confidence more, preventing the uncertain predictions from being overconfident." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 495, + 388, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 495, + 388, + 509 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 388, + 509 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 515, + 436, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 436, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 436, + 528 + ], + "type": "text", + "content": "4.1. Implementation details" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 534, + 545, + 713 + ], + "type": "text", + "content": "Datasets. We mainly perform experiments on CIFAR10/100 [20], Tiny-ImageNet [23] for network calibration. The CIFAR10/100 datasets consist of 50,000 training and 10,000 test images of size " + }, + { + "bbox": [ + 305, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 305, + 534, + 545, + 713 + ], + "type": "text", + "content": ", and provide 10/100 object categories, respectively. Tiny-ImageNet includes 120,000 images of size " + }, + { + "bbox": [ + 305, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 305, + 534, + 545, + 713 + ], + "type": "text", + "content": " for 200 object categories. Each category in Tiny-ImageNet contains 600 images, which are divided into 500, 50 and 50 images for training, validation and test, respectively. Tiny-ImageNet is more challenging, compared to CIFAR10/100, as it contains lots of object classes with a smaller number of samples per category. We further validate the generalization ability of our method on ImageNet [6], which comprises around 1.2M training and 50K validation images across 1K classes. For out-of-distribution (OOD) detection, we train a model" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1362" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 102, + 545, + 228 + ], + "blocks": [ + { + "bbox": [ + 46, + 64, + 547, + 99 + ], + "lines": [ + { + "bbox": [ + 46, + 64, + 547, + 99 + ], + "spans": [ + { + "bbox": [ + 46, + 64, + 547, + 99 + ], + "type": "text", + "content": "Table 1: Quantitative comparison with the state of the art in terms of ECE (%) and AECE (%) with 15 bins on the validation splits of CIFAR10/100 [20] and Tiny-ImageNet [23]. Numbers in bold indicate the best performance and underscored ones indicate the second best. Numbers in parentheses represent the results obtained using a TS post-hoc technique [10]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 102, + 545, + 228 + ], + "lines": [ + { + "bbox": [ + 48, + 102, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 48, + 102, + 545, + 228 + ], + "type": "table", + "html": "
MethodsCIFAR10 [20]CIFAR100 [20]Tiny-ImageNet [23]
ResNet-50 [13]ResNet-101 [13]ResNet-50 [13]ResNet-101 [13]ResNet-50 [13]ResNet-101 [13]
Acc↑ECE↓AEE↓Acc↑ECE↓AEE↓Acc↑ECE↓AECE↓Acc↑ECE↓AECE↓Acc↑ECE↓AECE↓
CE95.383.75(0.97)2.98(1.01)94.463.61(0.92)3.55(0.85)77.8113.59(2.93)13.54(2.86)77.4812.94(2.63)12.94(2.66)64.343.18(3.18)2.87(2.87)66.043.50(3.50)3.52(3.52)
MMCE [22]95.183.88(0.97)3.88(1.12)94.993.88(1.15)3.88(12.9)77.5612.72(2.83)12.71(2.86)77.8213.43(3.06)13.42(2.80)64.802.03(2.03)1.97(1.97)66.443.40(3.40)3.38(3.38)
ECP [34]94.754.01(1.06)3.99(1.53)93.974.41(1.72)4.40(1.70)76.2012.29(2.08)12.28(2.22)76.8113.43(2.92)13.42(3.04)64.881.94(1.94)1.95(1.95)66.202.72(2.72)2.70(2.70)
LS [30]94.873.27(1.58)3.67(3.02)94.183.35(1.51)3.85(3.10)76.456.73(4.23)6.54(4.26)76.917.99(4.38)7.87(4.55)65.463.21(2.51)3.23(2.51)65.523.11(2.51)2.92(2.72)
FL [24]94.823.42(1.07)3.41(0.87)93.593.27(1.12)3.23(1.37)76.412.83(1.66)2.88(1.73)76.123.10(2.58)3.22(2.51)63.082.03(2.03)1.94(1.94)64.022.18(2.18)2.09(2.09)
Mixup [41]94.762.86(1.37)2.81(2.00)95.506.87(1.18)6.79(2.33)78.478.68(2.14)8.68(2.19)78.748.92(3.69)8.91(3.65)65.811.92(1.92)1.96(1.96)66.412.41(1.97)2.43(1.95)
FLSD [29]94.773.86(0.83)3.74(0.96)93.263.92(0.93)3.67(0.94)76.202.86(2.86)2.86(2.86)76.613.29(2.04)3.25(1.78)63.561.93(1.93)1.98(1.98)64.021.85(1.85)1.81(1.81)
CRL [28]95.083.14(0.96)3.11(1.25)95.043.74(1.12)3.73(2.03)77.856.30(3.43)6.26(3.56)77.607.29(3.32)7.14(3.31)64.881.65(2.35)1.52(2.34)65.873.57(1.60)3.56(1.52)
CPC [4]95.045.05(1.89)5.04(2.60)95.364.78(1.52)4.77(2.37)77.2313.29(3.74)13.28(3.82)77.5013.32(2.96)13.28(3.23)65.703.41(3.41)3.42(3.42)66.443.93(3.93)3.74(3.74)
MbLS [25]95.251.16(1.16)3.18(3.18)95.131.38(1.38)3.25(3.25)77.924.01(4.01)4.14(4.14)77.455.49(5.49)6.52(6.52)64.741.64(1.64)1.73(1.73)65.811.62(1.62)1.68(1.68)
RegMixup [35]94.682.76(0.98)2.67(0.92)95.034.75(0.92)4.74(0.94)76.765.50(1.98)5.48(1.98)76.934.20(1.36)4.15(1.92)63.583.04(1.89)3.04(1.81)63.263.35(1.86)3.32(1.68)
RankMixup (MRL)94.591.01(0.84)1.03(0.80)94.182.86(1.08)2.87(1.58)76.653.52(2.40)3.39(2.05)77.264.41(1.68)4.24(1.76)64.541.70(1.70)1.69(1.69)64.802.26(1.78)2.28(1.60)
RankMixup (M-NDCG)94.882.59(0.57)2.58(0.52)94.253.24(0.65)3.21(0.56)77.113.46(1.49)3.45(1.42)76.463.49(1.10)3.49(1.40)64.971.49(1.49)1.44(1.44)64.891.57(1.57)1.94(1.94)
", + "image_path": "ab1acc7b0cf63d74137dd8b171a03f6eae4782feee97ef6f558a0f49ac237c40.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 240, + 288, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 240, + 288, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 288, + 301 + ], + "type": "text", + "content": "using CIFAR10, and use CIFAR100, Tiny/ImageNet, and SVHN [31] as OOD datasets, following the experimental protocol in [26, 35]. Similarly, CIFAR100 is used to train a model, and evaluate it on CIFAR10, Tiny/ImageNet, and SVHN." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 314, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 314, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 314, + 287, + 384 + ], + "type": "text", + "content": "Evaluation protocols. Following the standard protocol [4, 14, 25, 29, 30, 41], we use expected calibration error (ECE) and adaptive ECE (AECE) as evaluation metrics for network calibration. ECE measures the expected absolute difference between confidences and corresponding accuracies:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 115, + 386, + 287, + 399 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 386, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 115, + 386, + 287, + 399 + ], + "type": "interline_equation", + "content": "\\mathbb {E} \\left[ \\left| P \\left(\\hat {y} _ {i} = y _ {i} \\mid \\hat {p} _ {i}\\right) - \\hat {p} _ {i} \\right| \\right]. \\tag {15}", + "image_path": "7120a16258c567422788216fe1cf1da1e2a0b717021aa2ad042cb2da2405e31d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 405, + 287, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 287, + 538 + ], + "type": "text", + "content": "To compute ECE, we divide a range " + }, + { + "bbox": [ + 46, + 405, + 287, + 538 + ], + "type": "inline_equation", + "content": "(0,1]" + }, + { + "bbox": [ + 46, + 405, + 287, + 538 + ], + "type": "text", + "content": " into equidistance bins, and compute an average of the absolute differences, weighted by the size of each bin. We set the number of bins for both ECE and AECE as 15, following the protocol. We also report top-1 classification accuracies to compare discriminative capabilities. We provide results obtained without/with applying a post-hoc technique. In particular, we use the TS method [10], where the temperature is optimized on the validation sets. For OOD detection, we compare the area under the receiver operating characteristics (AUROC), following the standard evaluation protocol [26, 35]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 547, + 287, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 547, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 46, + 547, + 287, + 657 + ], + "type": "text", + "content": "Methods for comparison. We compare our method with various training-time approaches. In addition to the baseline model using the CE loss, we include implicit methods (LS [30], FL/FLSD [29], Mixup [41], mbLS [25], and RegMixup [35]) and explicit methods (ECP [34], MMCE [22], and CPC [4]). We have reproduced results using official codes with hyperparameter settings provided by the authors, if they are not available. Detailed descriptions for the hyperparameters can be found in the supplement." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Training details. Following [25], we train our network for 200 epochs for CIFAR10/100 [20], with an initial learning rate of 1e-1 and a batch size of 128. We also follow the training setting in [25] for Tiny/ImageNet [23] ex" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 338, + 281, + 514, + 366 + ], + "blocks": [ + { + "bbox": [ + 304, + 233, + 547, + 277 + ], + "lines": [ + { + "bbox": [ + 304, + 233, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 233, + 547, + 277 + ], + "type": "text", + "content": "Table 2: Quantitative comparison with the state of the art in terms of ECE (\\%) and AECE (\\%) with 15 bins on the validation split of ImageNet [6]. Numbers in bold indicate the best performance and underscored ones indicate the second best." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 338, + 281, + 514, + 366 + ], + "lines": [ + { + "bbox": [ + 338, + 281, + 514, + 366 + ], + "spans": [ + { + "bbox": [ + 338, + 281, + 514, + 366 + ], + "type": "table", + "html": "
MethodsImageNet [6]
ResNet-50 [13]
Acc↑ECE↓AECE↓
CE73.969.109.24
Mixup [41]75.847.077.09
CRL [28]73.838.478.47
MbLS [25]75.394.074.14
RegMixup [35]75.645.345.42
RankMixup (MRL)75.275.705.71
RankMixup (M-NDCG)74.863.933.92
", + "image_path": "1a7d6982f35085efbd11703e6b5d5ebb842d13b905a753732ff443d6078d8095.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 386, + 547, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 386, + 547, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 547, + 555 + ], + "type": "text", + "content": "cept for a batch size of 32 due to memory limits. All networks are trained using the SGD optimizer with a momentum of 0.9. The learning rate decreases by a tenth at every fixed intervals. We use ResNet50 [13], and ResNet101 [13] for both CIFAR10/100 [20] and Tiny-ImageNet [23], and ResNet50 for ImageNet [6]. For more comprehensive experiments, we also exploit WideResNet [48] for CIFAR10 and Tiny-ImageNet. We fix the balancing parameter of training loss " + }, + { + "bbox": [ + 304, + 386, + 547, + 555 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 386, + 547, + 555 + ], + "type": "text", + "content": " to 0.1. We set margin " + }, + { + "bbox": [ + 304, + 386, + 547, + 555 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 386, + 547, + 555 + ], + "type": "text", + "content": " to 2.0 and 1.0 for CIFAR10/100 and Tiny-ImageNet, respectively, using each validation dataset. Other hyperparameters, such as " + }, + { + "bbox": [ + 304, + 386, + 547, + 555 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 386, + 547, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 386, + 547, + 555 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 386, + 547, + 555 + ], + "type": "text", + "content": ", are chosen similarly. For OOD detection, we train the network using M-NDCG and in-distribution (ID) datasets with the same training settings used for network calibration." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 563, + 362, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 362, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 362, + 574 + ], + "type": "text", + "content": "4.2. Results" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "Comparison with the state of the art. We compare in Table 1 our method with state-of-the-art calibration approaches. From the tables, we observe four things: (1) Our models outperform other mixup-based methods [35, 41] using label mixtures as supervisions, demonstrating the effectiveness of our approach to leveraging an ordinal ranking relationship for confidences. (2) Our model using M-NDCG achieves the best performance in terms of both ECE and AECE on the challenging TinyImageNet [23] dataset, while providing competitive results on CIFAR10/100. This suggests that the ordinal ranking" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1363" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 112, + 268, + 188 + ], + "blocks": [ + { + "bbox": [ + 47, + 64, + 287, + 109 + ], + "lines": [ + { + "bbox": [ + 47, + 64, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 47, + 64, + 287, + 109 + ], + "type": "text", + "content": "Table 3: Quantitative comparison in terms of ECE (\\%) and AECE (\\%) with 15 bins on the validation splits of CIFAR10 [20] and Tiny-ImageNet [23]. Numbers in bold indicate the best performance and underscored ones are the second best." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 67, + 112, + 268, + 188 + ], + "lines": [ + { + "bbox": [ + 67, + 112, + 268, + 188 + ], + "spans": [ + { + "bbox": [ + 67, + 112, + 268, + 188 + ], + "type": "table", + "html": "
CIFAR10 [20]Tiny-ImageNet [23]
MethodsWide-ResNet-26-10 [48]
Acc↑ECE↓AECE↓Acc↑ECE↓AECE↓
CE95.802.702.6665.186.086.06
Mixup [41]96.533.143.0866.363.773.75
MbLS [25]95.701.452.7865.302.572.32
RegMixup [35]95.444.183.9963.403.873.93
RankMixup (MRL)95.571.701.3865.343.303.28
RankMixup (M-NDCG)95.731.621.5365.563.833.94
", + "image_path": "26f69d72f87efaa1cca0cc11d4f9249f6d93dec8b3845fd1f58a7c601ad2bc0c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 231, + 286, + 315 + ], + "blocks": [ + { + "bbox": [ + 47, + 194, + 286, + 226 + ], + "lines": [ + { + "bbox": [ + 47, + 194, + 286, + 226 + ], + "spans": [ + { + "bbox": [ + 47, + 194, + 286, + 226 + ], + "type": "text", + "content": "Table 4: Quantitative comparison with the state of the art in terms of AUROC " + }, + { + "bbox": [ + 47, + 194, + 286, + 226 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 47, + 194, + 286, + 226 + ], + "type": "text", + "content": ". Numbers in bold indicate the best performance and underscored ones indicate the second best." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 231, + 286, + 315 + ], + "lines": [ + { + "bbox": [ + 48, + 231, + 286, + 315 + ], + "spans": [ + { + "bbox": [ + 48, + 231, + 286, + 315 + ], + "type": "table", + "html": "
IDC10 [20]C100 [20]
OODC100 [20]Tiny [23]SVHN [31]C10 [20]Tiny [23]SVHN [31]
AUROC↑AUROC↑
TS [10]86.7388.0692.1476.3880.1282.41
LS [30]75.2376.2974.2372.9277.5472.33
FL [29]85.6386.8492.6678.3781.2386.37
Mixup [41]82.0784.0979.7278.4681.5576.21
CPC [4]85.2885.1592.7974.6876.6671.72
MbLS [25]86.2087.5589.9873.8879.1973.19
RegMixup [35]87.8287.5483.1576.0080.7275.05
RankMixup (M-NDCG)87.8288.9492.6278.6480.6785.42
", + "image_path": "95365df1167a6fc1fc5f2caa7d462d833f48d18d19419f015eb823b9a7ba3a57.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 329, + 286, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 329, + 286, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 286, + 460 + ], + "type": "text", + "content": "relationships among confidences is crucial for network calibration, and M-NDCG effectively encourages our model to provide confidences maintaining the relationships. We can also see that our method generalizes well to the large-scale dataset. (3) Our method outperforms another ranking-based method (CRL)[28] significantly, suggesting that more complex ranking relationship based on augmented samples enables estimating better confidences. (4) Ours with the post-hoc method [10] gives the best results in most settings, which indicates that they are complementary to each other, and exploiting both further boosts the calibration accuracy." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 460, + 286, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 286, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 286, + 557 + ], + "type": "text", + "content": "We also provide in Tables 2 and 3 quantitative results on ImaergeNet [6] and for the WideResNet backbone [48], respectively. They show similar trends to those in Table 1, validating the effectiveness of our approach across various network architectures and large-scale datasets. Specifically, our models provide competitive results with the state of the art [25], while outperforming mixup-based methods [35, 41] and the ranking-based one [28]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 286, + 712 + ], + "type": "text", + "content": "OOD detection. We compare in Table 4 the OOD detection accuracy using the ResNet-50 [13] architecture. We use the entropy of the softmax output as an uncertainty measure for binary classification and report AUROC scores for comparison. From the table, we have two findings. Our model trained with M-NDCG outperforms other mixup-based methods and achieves the highest AUROC scores in most settings. This indicates that ordinal ranking relationship of confidences is also crucial for OOD detection, suggesting that models trained with M-NDCG are not only better calibrated but also perform better than other calibration methods under the distributional shifts." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 357, + 118, + 493, + 182 + ], + "blocks": [ + { + "bbox": [ + 305, + 65, + 545, + 109 + ], + "lines": [ + { + "bbox": [ + 305, + 65, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 65, + 545, + 109 + ], + "type": "text", + "content": "Table 5: Quantitative comparison by varying the margin " + }, + { + "bbox": [ + 305, + 65, + 545, + 109 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 65, + 545, + 109 + ], + "type": "text", + "content": " . We report the ECE (%) for the models trained with MRL. Numbers in parentheses represent the results obtained using a TS post-hoc technique [10]." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 357, + 118, + 493, + 182 + ], + "lines": [ + { + "bbox": [ + 357, + 118, + 493, + 182 + ], + "spans": [ + { + "bbox": [ + 357, + 118, + 493, + 182 + ], + "type": "table", + "html": "
CIFAR10 [20]Tiny-ImageNet [23]
ECE↓ECE↓
m = 1.01.54(1.09)1.49(1.49)
m = 2.01.01(0.84)1.70(1.70)
m = 3.02.12(0.93)1.54(1.54)
m = 4.03.12(1.67)2.37(1.77)
m = 5.013.13(0.48)2.42(1.48)
", + "image_path": "1eccf02e1eca8cc906bbe36f5523695f052dd60b639f473e8d7e76c6834fba9a.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 331, + 188, + 518, + 284 + ], + "blocks": [ + { + "bbox": [ + 331, + 188, + 518, + 284 + ], + "lines": [ + { + "bbox": [ + 331, + 188, + 518, + 284 + ], + "spans": [ + { + "bbox": [ + 331, + 188, + 518, + 284 + ], + "type": "image", + "image_path": "d9d908c1dc9cda5c9b3f011492b3ad8720c81b4b41a9e90b379c3aa39c1f1bd8.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 287, + 545, + 319 + ], + "lines": [ + { + "bbox": [ + 305, + 287, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 305, + 287, + 545, + 319 + ], + "type": "text", + "content": "Figure 2: Quantitative results by varying the margin " + }, + { + "bbox": [ + 305, + 287, + 545, + 319 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 287, + 545, + 319 + ], + "type": "text", + "content": ". We plot OE (\\%) and UE (\\%) on the validation split of CIFAR10 [20]. Best viewed in color." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 334, + 378, + 345 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 334, + 378, + 345 + ], + "spans": [ + { + "bbox": [ + 306, + 334, + 378, + 345 + ], + "type": "text", + "content": "4.3. Discussion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "type": "text", + "content": "In this section, we analyze the effects of the hyperparameters in our framework, and show generalization ability by incorporating other mixup techniques into our framework. For the analyses, we mainly adopt the ResNet-50 [13] models trained with M-NDCG, and report ECE and AECE on the validation sets of CIFAR10 [20] and TinyImageNet [23], unless otherwise specified. We use 15 bins to measure the ECE and AECE." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 451, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 451, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 545, + 557 + ], + "type": "text", + "content": "Margin. We compare in Table 5 the calibration results of the models trained with MRL and various margins. We can see that small margins provide better performances for both datasets. Furthermore, we find that increasing the margin degrades the classification accuracy. A reason is that a large margin could make a significant difference in confidence levels between the raw and augmented samples. That is, with a larger margin, the augmented sample is more likely to have a lower confidence than its actual value." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 559, + 545, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 559, + 545, + 619 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 545, + 619 + ], + "type": "text", + "content": "To demonstrate this, we compute overconfidence errors (OE) [41] that measure the expected difference between confidence values of overconfident predictions and corresponding accuracies. Given " + }, + { + "bbox": [ + 304, + 559, + 545, + 619 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 559, + 545, + 619 + ], + "type": "text", + "content": " bins of equal size, OE is defined as follows [41]:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 310, + 625, + 545, + 665 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 625, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 310, + 625, + 545, + 665 + ], + "type": "interline_equation", + "content": "O E = \\sum_ {h = 1} ^ {H} \\frac {\\left| B _ {h} \\right|}{N} [ \\operatorname {c o n f} \\left(B _ {h}\\right) \\times \\max \\left(\\operatorname {c o n f} \\left(B _ {h}\\right) - \\operatorname {a c c} \\left(B _ {h}\\right), 0\\right) ], \\tag {16}", + "image_path": "157f52bffd6f0e9c614f390822c49c4322fe812ced04c9451490738a7a4154e3.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": " is the total number of samples, and " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "B_{h}" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": " is the set of samples, whose confidence falls into the " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "-th bin. We denote by " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{acc}(B_h)" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{conf}(B_h)" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": " the accuracy and averaged confidence of the " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "-th bin, respectively. Similar to OE, we" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1364" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 65, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 65, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 47, + 65, + 287, + 109 + ], + "type": "text", + "content": "Table 6: Quantitative results of our model with various numbers of the augmented samples. We report the ECE (\\%) for comparison. Numbers in parentheses represent the results obtained using a TS post-hoc technique [10]." + } + ] + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 100, + 118, + 230, + 177 + ], + "blocks": [ + { + "bbox": [ + 100, + 118, + 230, + 177 + ], + "lines": [ + { + "bbox": [ + 100, + 118, + 230, + 177 + ], + "spans": [ + { + "bbox": [ + 100, + 118, + 230, + 177 + ], + "type": "table", + "html": "
CIFAR10 [20]Tiny-ImageNet [23]
ECE↓ECE↓
Q = 23.01(0.82)3.25(1.44)
Q = 32.78(0.50)2.18(1.12)
Q = 42.59(0.57)1.49(1.49)
Q = 52.37(0.64)1.52(1.52)
Q = 62.24(0.59)1.30(1.30)
", + "image_path": "e750be5164c0cb278e9c4b9d6f4610423cffc08ef93c8ddfa93773186fc1d0b9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 72, + 178, + 260, + 321 + ], + "blocks": [ + { + "bbox": [ + 72, + 178, + 260, + 321 + ], + "lines": [ + { + "bbox": [ + 72, + 178, + 260, + 321 + ], + "spans": [ + { + "bbox": [ + 72, + 178, + 260, + 321 + ], + "type": "image", + "image_path": "037e530268de6b85da5a2b9978c74240f2e77d0c316a827c7f278efb7a5b7b32.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 324, + 286, + 345 + ], + "lines": [ + { + "bbox": [ + 47, + 324, + 286, + 345 + ], + "spans": [ + { + "bbox": [ + 47, + 324, + 286, + 345 + ], + "type": "text", + "content": "Figure 3: Probability density function (PDF) of Beta distribution with various " + }, + { + "bbox": [ + 47, + 324, + 286, + 345 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 324, + 286, + 345 + ], + "type": "text", + "content": "s." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 357, + 286, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 357, + 286, + 380 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 286, + 380 + ], + "type": "text", + "content": "define underconfidence errors (UE) computing the difference using underconfident predictions as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 52, + 390, + 286, + 429 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 390, + 286, + 429 + ], + "spans": [ + { + "bbox": [ + 52, + 390, + 286, + 429 + ], + "type": "interline_equation", + "content": "U E = \\sum_ {h = 1} ^ {H} \\frac {\\left| B _ {h} \\right|}{N} [ \\operatorname {c o n f} \\left(B _ {h}\\right) \\times \\max \\left(\\operatorname {a c c} \\left(B _ {h}\\right) - \\operatorname {c o n f} \\left(B _ {h}\\right), 0\\right) ]. \\tag {17}", + "image_path": "b79436c35770074f2ee7f221b5888a2ff360dbf77d6e2d6a6536a8ab1910958e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 430, + 286, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 286, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 286, + 525 + ], + "type": "text", + "content": "We plot in Fig. 2 UE and OE for ResNet-50 with MRL on CIFAR10 [20], while varying margins. We can see that UE increases drastically, according to the margins, while OE decreases gradually. This suggests that exploiting a large margin causes underconfidence problems, where the model becomes less confident in its predictions. An underconfident model produces large calibration errors [41, 49], leading to the degraded performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 536, + 286, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 286, + 679 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 286, + 679 + ], + "type": "text", + "content": "Number of augmented samples. We compare in Table 6 the calibration performance in terms of ECE with varying number of augmented samples. We set " + }, + { + "bbox": [ + 47, + 536, + 286, + 679 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 536, + 286, + 679 + ], + "type": "text", + "content": " to 2.0 and 1.0 for CIFAR10 and Tiny-ImageNet, respectively. We can observe that ECE improves as more augmented samples are used, suggesting that learning with diverse ranking relationships between a number of augmented samples encourages the model to estimate confidence levels better. This further implies that the mixup coefficient " + }, + { + "bbox": [ + 47, + 536, + 286, + 679 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 536, + 286, + 679 + ], + "type": "text", + "content": " is also an important factor, since it enables modeling the diverse ranking relationships. This leads us to analyze the mixup coefficient " + }, + { + "bbox": [ + 47, + 536, + 286, + 679 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 536, + 286, + 679 + ], + "type": "text", + "content": " in detail in the following." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": "Mixup coefficient. Following [49], we sample the mixup coefficient " + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": " from a Beta distribution, making it possible" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 332, + 66, + 521, + 160 + ], + "blocks": [ + { + "bbox": [ + 332, + 66, + 521, + 160 + ], + "lines": [ + { + "bbox": [ + 332, + 66, + 521, + 160 + ], + "spans": [ + { + "bbox": [ + 332, + 66, + 521, + 160 + ], + "type": "image", + "image_path": "9e503c86e0d886321b2c716d8c090b96a1ad9df5b2328001d27f87ae5aff3e7d.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 331, + 164, + 520, + 258 + ], + "blocks": [ + { + "bbox": [ + 331, + 164, + 520, + 258 + ], + "lines": [ + { + "bbox": [ + 331, + 164, + 520, + 258 + ], + "spans": [ + { + "bbox": [ + 331, + 164, + 520, + 258 + ], + "type": "image", + "image_path": "0e1b47271a49a8291004667f8e37ef802bbb7b83834049f76980fd077d3103ea.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 260, + 545, + 303 + ], + "lines": [ + { + "bbox": [ + 305, + 260, + 545, + 303 + ], + "spans": [ + { + "bbox": [ + 305, + 260, + 545, + 303 + ], + "type": "text", + "content": "Figure 4: Quantitative results by varying the parameter of the Beta distribution " + }, + { + "bbox": [ + 305, + 260, + 545, + 303 + ], + "type": "inline_equation", + "content": "(\\alpha)" + }, + { + "bbox": [ + 305, + 260, + 545, + 303 + ], + "type": "text", + "content": ". We plot ECE " + }, + { + "bbox": [ + 305, + 260, + 545, + 303 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 260, + 545, + 303 + ], + "type": "text", + "content": " and AECE " + }, + { + "bbox": [ + 305, + 260, + 545, + 303 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 260, + 545, + 303 + ], + "type": "text", + "content": " on the validation split of CIFAR10 [20] (top) and Tiny-ImageNet [23] (bottom). Best viewed in color." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "text", + "content": "to generate various augmented samples. Note that the degree of the diversity is determined by how we set the shape parameter for the Beta distribution. For an in-depth analysis, we also show in Fig. 3 the probability density functions (PDFs) of different " + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "inline_equation", + "content": "Beta(\\alpha, \\alpha)" + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "text", + "content": " distributions, while varying the shape parameter " + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "text", + "content": ". We evaluate the calibration errors of the models trained with M-NDCG along with different shape parameters " + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "text", + "content": " of the Beta distribution, and show the results using 3 augmented images (" + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "inline_equation", + "content": "Q = 4" + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "text", + "content": ") in Fig. 4. From the figures, we observe two things: (1) Our models achieve the best performances with " + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\alpha = 2" + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\alpha = 1" + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "text", + "content": " on CIFAR10 and Tiny-ImageNet, respectively, where the corresponding PDFs are relatively flat, as shown in Fig. 3. This suggests that diverse mixup coefficients " + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "text", + "content": " drawn from such distributions can enhance the calibration performances, as it allows us to augment the samples in a more diverse way. (2) Our model performs well with large " + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "text", + "content": ", which is in contrast to the vanilla mixup [41, 49], where the value of " + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "text", + "content": " within the range of [0.1, 0.4] yields better classification and calibration performances. When " + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "text", + "content": " is too large, it suffers from an underconfidence problem [41, 49] and is also affected by manifold intrusion [11], leading to significant performance drops in both the classification and calibration. The manifold intrusion happens when the label mixture of an augmented sample differs from the label of the real sample [11]. However, in our framework, we do not explicitly use the label mixtures as supervision, suggesting that our framework is less affected by those problems. Therefore, our framework is more robust to the variation of the parameter " + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "text", + "content": " compared to the vanilla mixup. To further investigate the importance of diverse samples, we also perform experiments with various combinations of " + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 323, + 545, + 716 + ], + "type": "text", + "content": " and provide the results in the supplementary material." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1365" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 101, + 285, + 159 + ], + "blocks": [ + { + "bbox": [ + 47, + 65, + 287, + 99 + ], + "lines": [ + { + "bbox": [ + 47, + 65, + 287, + 99 + ], + "spans": [ + { + "bbox": [ + 47, + 65, + 287, + 99 + ], + "type": "text", + "content": "Table 7: Quantitative comparison of calibration performances using other mixup techniques on the validation splits of CIFAR10 [20] and Tiny-ImageNet [23]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 101, + 285, + 159 + ], + "lines": [ + { + "bbox": [ + 48, + 101, + 285, + 159 + ], + "spans": [ + { + "bbox": [ + 48, + 101, + 285, + 159 + ], + "type": "table", + "html": "
Mixup [49] Manifold [45] CutMix [47]CIFAR10 [20]Tiny-ImageNet [23]
ECE↓AECE↓ECE↓AECE↓
RegMixup [35]✓3.633.574.764.88
✓3.563.542.972.93
RankMixup✓2.922.981.201.22
✓3.263.211.801.66
✓2.592.581.491.44
", + "image_path": "8792901cf2e7a2e3e8edb29df7958a17c88b0b79a231d9f701bbb239c52341c8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 49, + 214, + 282, + 297 + ], + "blocks": [ + { + "bbox": [ + 47, + 166, + 287, + 210 + ], + "lines": [ + { + "bbox": [ + 47, + 166, + 287, + 210 + ], + "spans": [ + { + "bbox": [ + 47, + 166, + 287, + 210 + ], + "type": "text", + "content": "Table 8: Quantitative comparison of classification and calibration performances on the test splits of CIFAR10-LT [1] and CIFAR100-LT [1]. We report the Top-1 accuracy " + }, + { + "bbox": [ + 47, + 166, + 287, + 210 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 47, + 166, + 287, + 210 + ], + "type": "text", + "content": " and ECE " + }, + { + "bbox": [ + 47, + 166, + 287, + 210 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 47, + 166, + 287, + 210 + ], + "type": "text", + "content": " with 15 bins." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 214, + 282, + 297 + ], + "lines": [ + { + "bbox": [ + 49, + 214, + 282, + 297 + ], + "spans": [ + { + "bbox": [ + 49, + 214, + 282, + 297 + ], + "type": "table", + "html": "
CIFAR10-LT [1]CIFAR100-LT [1]
Methodsρ = 10Acc↑/ECE↓ρ = 100Acc↑/ECE↓ρ = 10Acc↑/ECE↓ρ = 100Acc↑/ECE↓
CE86.39/6.6070.36/20.5355.70/22.8538.32/38.23
Mixup [49]87.10/6.5573.06/19.2058.02/19.6939.54/32.72
Remix [5]88.15/6.8175.36/15.3859.36/20.1741.94/33.56
UniMix [46]89.66/6.0082.75/12.8761.25/19.3845.45/27.12
RankMixup (MRL)88.83/2.1674.16/ 2.0362.84/13.5542.56/ 5.28
RankMixup (M-NDCG)89.80/5.9475.41/14.1063.83/ 9.9943.00/18.74
", + "image_path": "3785dd90b69774cfacc0350d8aa02ff1d7fe18a8fd76a274f45ecbb4a19e977a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 310, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 310, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 47, + 310, + 287, + 622 + ], + "type": "text", + "content": "Other mixup techniques. RankMixup employs a vanilla mixup technique that interpolates the input images and the corresponding labels for data augmentation, but other variants can be readily adopted in our framework. We have also tried using Manifold-Mixup [45] and CutMix [47] for the experiments. We show in Table 7 the results of our models using these techniques together with M-NDCG, while setting the shape parameter " + }, + { + "bbox": [ + 47, + 310, + 287, + 622 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 310, + 287, + 622 + ], + "type": "text", + "content": " to 1 for the both techniques. For comparison, we report the result of our model with the vanilla mixup, which exploits 3 augmented samples, and additionally show the performances obtained using RegMixup [35] equipped with these variants. For both datasets, our method achieves better calibration errors than RegMixup, indicating that our method has better generalization capability. While our model with vanilla mixup provides the best performance on CIFAR10, employing Manifold-Mixup offers better results on Tiny-ImageNet in terms of calibration errors. Increasing the entropy of supervision is crucial for better-calibrated models [25, 29, 30, 41]. RankMixup exploits the augmented samples as supervision for network calibration, indicating that samples with higher entropies can yield better performances. Manifold-Mixup [45] produces flattened representations that have higher entropies than the mixup-augmented samples, which may explain the reason why our model with Manifold-Mixup performs better on Tiny-ImageNet." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "type": "text", + "content": "Long-tailed datasets. We evaluate our method on long-tailed (LT) datasets, where the miscalibration issues of DNNs are more pronounced [46, 52]. Following the experimental settings in [46, 52], we adopt the ResNet32 [13] architecture as our backbone, and exploit CIFAR10/100-LT datasets [1] with two imbalanced factors " + }, + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "type": "inline_equation", + "content": "(\\rho)" + }, + { + "bbox": [ + 46, + 629, + 287, + 714 + ], + "type": "text", + "content": ". We compare in Table 8 our method against the vanilla mixup [49] and two" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "adaptive mixup techniques tailored for LT scenarios [5, 46]. We can see that our models significantly outperform other mixup methods in terms of ECE, while providing competitive accuracies, although they are not specially designed for LT scenarios. This suggests that leveraging the ordinal ranking relationship between confidence is also effective for addressing miscalibration problems in LT scenarios, instead of using label mixtures for other mixup-based augmentations [46, 52]. Note that the number of samples for head and tail classes is highly skewed, suggesting that augmented samples are not diverse in LT scenarios. As this problem is more severe for M-NDCG, it yields worse results, compared to MRL, in the LT datasets." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 240, + 378, + 252 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 240, + 378, + 252 + ], + "spans": [ + { + "bbox": [ + 306, + 240, + 378, + 252 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 261, + 545, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 261, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 304, + 261, + 545, + 464 + ], + "type": "text", + "content": "We have presented a novel mixup-based framework for network calibration, dubbed RankMixup, alleviating the problem that interpolated labels do not necessarily model the actual distribution of label mixtures. To this end, we have proposed a new supervisory signal based on the ordinal ranking relationship that a higher confidence is more favorable for a raw sample than the one augmented by mixup. We have proposed MRL, which encourages a network to yield confidence that preserve the ranking relationships between the raw and mixup-augmented samples. We have also extended this idea to multiple augmented samples with different mixup coefficients via M-NDCG, enabling a network to predict outputs with higher confidence for augmented samples that are closer to a raw one. We have demonstrated the effectiveness of RankMixup through the extensive experiments and analysis, achieving the best results among mixup-based network calibration approaches." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 563 + ], + "type": "text", + "content": "Acknowledgments. This work was supported in part by the NRF and IITP grants funded by the Korea government (MSIT) (No.2023R1A2C2004306, No.2022-0-00124, Development of Artificial Intelligence Technology for Self-Improving Competency-Aware Learning Capabilities, No.2021-0-02068, Artificial Intelligence Innovation Hub), and the Yonsei Signature Research Cluster Program of 2023 (2023-22-0008)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 575, + 365, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 365, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 365, + 588 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 310, + 595, + 545, + 712 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 310, + 595, + 545, + 628 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 595, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 310, + 595, + 545, + 628 + ], + "type": "text", + "content": "[1] Kaidi Cao, Colin Wei, Adrien Gaidon, Nikos Arechiga, and Tengyu Ma. 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In CVPR, 2021. 9" + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1368" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Rapid Adaptation in Online Continual Learning_ Are We Evaluating It Right_/165500ab-b2c3-4db0-ba04-4570a2ad4282_content_list.json b/2023/Rapid Adaptation in Online Continual Learning_ Are We Evaluating It Right_/165500ab-b2c3-4db0-ba04-4570a2ad4282_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..823bd9290fca839d4ae2a0329c608b71f75c9df3 --- /dev/null +++ b/2023/Rapid Adaptation in Online Continual Learning_ Are We Evaluating It Right_/165500ab-b2c3-4db0-ba04-4570a2ad4282_content_list.json @@ -0,0 +1,1301 @@ +[ + { + "type": "text", + "text": "Rapid Adaptation in Online Continual Learning: Are We Evaluating It Right?", + "text_level": 1, + "bbox": [ + 88, + 128, + 880, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hasan Abed Al Kader Hammoud $^{1*}$ Ameya Prabhu $^{2*}$ Ser-Nam Lim $^{3}$ Philip H.S. Torr $^{2}$ Adel Bibi $^{2\\dagger}$ Bernard Ghanem $^{1\\dagger}$ KAUST $^{1}$ University of Oxford $^{2}$ Meta AI $^{3}$", + "bbox": [ + 125, + 178, + 843, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 253, + 313, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We revisit the common practice of evaluating adaptation of Online Continual Learning (OCL) algorithms through the metric of online accuracy, which measures the accuracy of the model on the immediate next few samples. However, we show that this metric is unreliable, as even vacuous blind classifiers, which do not use input images for prediction, can achieve unrealistically high online accuracy by exploiting spurious label correlations in the data stream. Our study reveals that existing OCL algorithms can also achieve high online accuracy, but perform poorly in retaining useful information, suggesting that they unintentionally learn spurious label correlations. To address this issue, we propose a novel metric for measuring adaptation based on the accuracy on the near-future samples, where spurious correlations are removed. We benchmark existing OCL approaches using our proposed metric on large-scale datasets under various computational budgets and find that better generalization can be achieved by retaining and reusing past seen information. We believe that our proposed metric can aid in the development of truly adaptive OCL methods. We provide code to reproduce our results at https://github.com/drimpossible/EvalOCL.", + "bbox": [ + 75, + 286, + 473, + 612 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 630, + 209, + 646 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The need for learning on continuously changing data streams has led to a proliferation of research in Online Continual Learning (OCL) literature [21, 8]. The primary aim of OCL algorithms is to enable deep models to continuously adapt to new data distributions without compromising the accumulated knowledge. However, we argue that current metrics have deviated significantly from measuring true adaptation capabilities. The majority of recent works on OCL [7, 10] measure the adaptation of OCL algorithms using the metric of online accuracy, defined as the accuracy of a model on the immediate incoming samples. This evaluation practice resulted in the neglect in measuring the capacity of models to retain previous knowledge. As a consequence, several OCL algorithms achieve high online ac", + "bbox": [ + 75, + 656, + 468, + 864 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/81130ff3785a1276538dafa03bb3440bf390e7d545f56878c12f024095b686f6.jpg", + "image_caption": [ + "Figure 1. Effect of Spurious Correlations. Current methods in OCL perform well on rapid adaptation but suffer from abysmal information retention (top). We show that these trends are due to idiosyncrasies in the data stream such as label correlations that favor methods that inadvertently overfit to the latest data. Using our proposed metric that removes these correlations (bottom), different sets of methods achieve good performance, with high information retention being key for achieving high adaptability." + ], + "image_footnote": [], + "bbox": [ + 540, + 257, + 849, + 448 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "curacy [7] but poor performance on other important metrics like information retention which measure catastrophic forgetting of past seen data. Poor information retention performance has been attributed to an inherent stability-plasticity trade-off between learning new concepts and remembering old concepts [6]. However, the ability to preserve information and representations of past data, such as images of a class like the Eiffel Tower, should be crucial for accurately predicting future images of the same class, even if they were taken under novel weather conditions or camera poses. Hence, we find this justification to be unsatisfactory.", + "bbox": [ + 496, + 571, + 892, + 736 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we demonstrate that the conventional metric of measuring online accuracy may lead to misleading conclusions about the adaptation capabilities of OCL algorithms due to the idiosyncrasies of the data stream. To support our claim, we first demonstrate that a simple blind classifier that relies solely on spurious label correlations in the stream achieves unrealistically high online accuracy on large-scale OCL datasets. Furthermore, we show that this behaviour can be exhibited by deep OCL algorithms, where we propose OverAdapt which achieves state-of-the-art performance in online accuracy despite the very poor perfor", + "bbox": [ + 496, + 737, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* authors contributed equally; order decided by a coin flip.", + "bbox": [ + 93, + 875, + 400, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\dagger$ equal supervision", + "bbox": [ + 98, + 887, + 197, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18852", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "mance in information retention. We confirm the findings on two large-scale OCL datasets collected from different sources. This indicates that the problem is not limited to a specific dataset, but may be a general concern.", + "bbox": [ + 75, + 90, + 470, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To overcome this issue, we introduce a new metric called near-future accuracy that measures the adaptation capabilities of OCL algorithms by evaluating the accuracy on samples after a shift of $S$ steps. We choose the minimum shift $S$ which ensures that the samples no longer have spurious label correlations with the current training data. Choosing the minimum value helps minimize any distribution drift between the training and evaluation samples. The case $S = 0$ recovers the online accuracy metric in case of no spurious correlations. We observe a significant drop in performance on this metric compared to their online accuracy with several state-of-the-art OCL algorithms. This suggests that these algorithms inadvertently rely on label correlations in the stream for predictions. On the contrary, we find that algorithms designed primarily to improve information retention perform exceptionally well in our evaluation strategy. This suggests that a better generalization can be achieved by effectively retaining and reusing past information. Figure 1 illustrates that the best algorithms are those that have little discrepancy between information retention and adaptation. These results challenge current beliefs and demonstrate the importance of using a more precise measure of adaptation in evaluating OCL algorithms.", + "bbox": [ + 75, + 154, + 472, + 494 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Overall, our contributions can be summarized as follows:", + "bbox": [ + 76, + 498, + 455, + 512 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We demonstrate that popular metrics like online accuracy can be unreliable in measuring rapid adaptation due to the presence of spurious label correlations in OCL datasets.", + "- We introduce a novel baseline, OverAdapt, which achieves high online accuracy by relying on label correlations, despite forgetting almost all previously seen data.", + "- We propose a novel metric that evaluates the adaptation capabilities of OCL algorithms by measuring accuracy on near-future samples. We select the smallest value of $S$ that removes label correlations and use this metric to evaluate state-of-the-art OCL methods.", + "- Our findings show that existing OCL algorithms perform poorly when evaluated using our proposed evaluation strategy. Algorithms which prevent catastrophic forgetting perform significantly better, suggesting that better adaptation performance can be achieved by retaining and reusing past seen information." + ], + "bbox": [ + 76, + 527, + 468, + 796 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our results challenge the current emphasis on adapting to the latest samples and demonstrate the importance of seeking a more precise measure of adaptation. We note that our contributions are robust, with our findings valid across various OCL approaches, optimization strategies, and large-scale datasets from different sources.", + "bbox": [ + 75, + 811, + 468, + 898 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/c37804e012229a2ce32732cd76b92bbee492ee6ec847f0873245eb4e65a7ec56.jpg", + "table_caption": [ + "Table 1. Properties of OCL Benchmarks. We list benchmarks in the field of OCL along with the works which introduced them. We compare them across six properties: Realistic Data Streams (DO), No Storage Constraints (SC), Rapid Adaptation (RA), Information Retention (IR), Restricts Computational Budgets (CB), Evaluates on long stream sizes (LB), Leverages Pretrained Models (PT). Note that $\\checkmark$ is better than $x$ in all columns." + ], + "table_footnote": [], + "table_body": "
DataOrderBenchmarkDOSCRAIRCBLBPT
Task-Inc.A-GEM[9]XXX✓X✓X
Class-Inc.MIR[1]XXX✓X✓X
DER[4]
BlurryGSS[2]XXX✓X✓X
RM [3]
CLIB[18]
NaturalCLEAR[20]✓X✓✓XX✓
BudgetCL[26]X✓X✓✓X✓
CLOC[7]✓X✓XX✓X
DelayOCL[10]✓X✓X✓✓✓
ACM[25]✓✓✓✓✓✓✓
", + "bbox": [ + 503, + 186, + 890, + 308 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. OCL Evaluation: A Review", + "text_level": 1, + "bbox": [ + 500, + 328, + 756, + 343 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We start with an overview of benchmarks in OCL across different properties of interest. For a more detailed review of the literature, we refer the reader to [30].", + "bbox": [ + 498, + 349, + 890, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1. Realistic Data Streams (DO). The OCL community has been moving towards increasingly realistic benchmarks in terms of data ordering and task setup. Early works [21, 9] assumed access to which subset of classes a test sample is from (task-incremental setup). Subsequent work removed this constraint, requiring models to predict across all seen classes so far (class-incremental setup) [2, 1]. However, these works used incoming samples from disjoint data distributions with artificial task boundaries, resulting in unrealistic ordering. Recent works [3, 18, 26] improved the ordering by mixing samples from different disjoint tasks. Latest works [7, 25, 20] eliminate the need for generating artificial data streams simply by using real-world timestamps to order the data stream. Our work focuses on these real-world data streams on large-scale datasets.", + "bbox": [ + 498, + 406, + 892, + 628 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Towards No Storage Constraints (SC). The majority of prior benchmarks on continual learning constrain the problem by prohibiting access to previously received data [19, 17], with only a small portion of data allowed to be stored in memory [21, 8, 4, 2, 18, 20]. This constraint is often justified by two reasons: (i) storage space is expensive and (ii) access to previous data is prohibited due to privacy constraints. However, recent work [25, 26] shows critical shortcomings of these justifications. They show that (a) storage costs are negligible compared to the computational costs of training a model, and (b) simply restricting access to previous data does not address privacy considerations, as samples can be reconstructed from model weights [13] or detectably change the model output [28]. Interestingly, Goel et al. [11] shows that removing data from the model can be done by catastrophic forgetting, which is antithetical to the objective of OCL approaches. Hence, we do not impose any memory constraints on our evaluation.", + "bbox": [ + 498, + 641, + 892, + 909 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18853", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "3. Towards Better Information Retention (IR). Interestingly, most of the previous benchmarks in OCL focus on preventing catastrophic forgetting of previously learned information, rather than evaluating the ability of models to rapidly learn new concepts [21, 27, 9, 3, 2, 20]. This emphasis on information retention can be attributed to disjoint set-based data ordering, which often involves little to no change in distribution for most of the stream, making it difficult to evaluate rapid adaptation. However, recent works have shifted their focus to rapid adaptation performance in real-world ordered data streams [7, 10]. In our benchmark, our objective is to maintain an additional high degree of retained knowledge from past data as demonstrated in [25, 6].", + "4. Towards Enabling Rapid Adaptation (RA). The goal of online continual learning algorithms is to rapidly adapt to incoming data from changing distributions. Similarly to past work [25, 7, 10], we place a strong emphasis on achieving this goal with better metrics.", + "5. Towards Computational Budgets (CB). Continual learning without memory constraints is primarily a problem of achieving high performance with computational efficiency, as retraining from scratch is an ideal solution to the problem. This setting addresses the real-world problem of reducing the cost of updating a given model with incoming data from a stream [25]. We evaluate OCL approaches under the maximum computational budget for fairness [10], testing across two different budgets.", + "6. Towards Large-Scale OCL (LB). OCL benchmarks have historically focused on learning over samples incoming from a stream over long data streams since the development of GEM [21]. Recent OCL benchmarks [2, 18, 25] have preserved this useful characteristic, while scaling up to larger and more complex data streams. In this work, we use two large-scale OCL benchmarks: Continual Google LandMarks (CGLM) [25] and Continual Localization (CLOC) [7]. CGLM is a landmark classification dataset that consists of a long-tailed distribution with 10,788 classes that simulate images that arrive on a Wikimedia Commons server. CLOC is a dataset focused on geolocation at scale consisting of 713 classes with 39M images simulating images arriving on a Flickr server. As these datasets come from two different sources, the issue of label correlation that we observe is likely to be a repeating pattern across future OCL datasets.", + "7. Leveraging Pretraining for Effective OCL (PT). Traditional methods in online continual learning start with randomly initialized models [21, 1]. However, continual learning approaches can leverage the abundance of large-scale pretrained models to improve computational efficiency [24, 31, 25]. We focus on an evaluation setting that starts with ImageNet1K pretrained models to allow approaches to leverage pretrained information." + ], + "bbox": [ + 75, + 90, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Correcting Evaluations of Rapid Adaptation", + "text_level": 1, + "bbox": [ + 498, + 89, + 890, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We delve into our exploration of the limitations of using online accuracy as a metric to measure adaptation to distribution shifts and present our efforts to alleviate the shortcomings of this metric. We start by identifying the label correlations that affect online accuracy, and then we unveil a technique that enables deep networks to artificially achieve high performance on this metric. This highlights the dependence of the networks on these label correlations. Finally, we introduce a novel evaluation metric, near-future accuracy, and a test to detect and remove label correlations allowing for accurate measurement of the effectiveness of OCL methods in rapidly adapting to new distributions.", + "bbox": [ + 496, + 109, + 893, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Evaluating OCL: A Problem Formulation", + "text_level": 1, + "bbox": [ + 498, + 294, + 857, + 310 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In traditional OCL setups with real-world stream orders [7, 25], the learner is fed a continuous stream of training samples over time steps $t \\in \\{1, 2, \\dots, \\infty\\}$ , consisting of an input datapoint $\\mathbf{x}_t \\in \\mathcal{X}$ and its corresponding label $\\mathbf{y}_t \\in \\mathcal{Y}$ where $(\\mathbf{x}_t, \\mathbf{y}_t) \\sim \\mathcal{D}_{j \\leq t}$ . The distribution $\\mathcal{D}_j$ can change at any stream timestep. The aim is to train a classifier $f_{\\theta_t}: \\mathcal{X} \\to \\mathcal{Y}$ at any given $t$ , which accurately maps a new sample $\\mathbf{x}$ to its label $\\mathbf{y}$ while adapting to the latest information and incorporating it with the historical knowledge acquired from previous data.", + "bbox": [ + 496, + 311, + 890, + 460 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To evaluate the adaptation ability of $f_{\\theta_t}$ , online accuracy measures the performance on the next unseen sample, $(\\mathbf{x}_{t + 1},\\mathbf{y}_{t + 1})$ , i.e., $a_{t} = \\mathbb{1}\\{f_{\\theta_{t}}(\\mathbf{x}_{t + 1}) = \\mathbf{y}_{t + 1}\\}$ . Online accuracy is updated in an online fashion given by $A_{t}^{RA} = \\frac{1}{t}\\left(A_{t - 1}^{RA}\\cdot (t - 1) + a_{t}\\right)$ . For OCL approaches training deep networks, the running average is updated on a batch $\\mathcal{B}$ of the next unseen samples as opposed to a single sample. After the evaluation is carried out, the model $f_{\\theta_i}$ is updated using the same samples.", + "bbox": [ + 496, + 460, + 890, + 593 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The ability of $f_{\\theta_t}$ to retain information is measured by evaluating its accuracy on an unseen test stream that is similar to the training stream. In particular, per time step $t$ , the model trained at the end of step $t$ is evaluated on all test samples from step 0 to step $t$ . We measure Backward Transfer @ $T$ [7] where $T$ is the last time step of the stream. That is to say, the model at the last step of the stream is evaluated on an increasing test test from step 0 to the end of the stream. However, traditional OCL methods targeting natural distribution shifts have neglected this metric [7, 10].", + "bbox": [ + 496, + 593, + 890, + 742 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Isolating and Quantifying Label Correlations", + "text_level": 1, + "bbox": [ + 498, + 750, + 883, + 765 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our objective is to investigate whether using online accuracy to measure adaptation in OCL suffers from drawbacks due to label correlations. To accomplish this, we introduce a very simple algorithm that leverages label correlations and performs well in terms of online accuracy.", + "bbox": [ + 496, + 767, + 890, + 840 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Blind Classifier. We define a blind classifier, similar to prior works [7, 25], as a model that predicts the mode of the last $\\kappa$ samples seen without access to the input images. Formally, at a given new step $t$ , the blind classifier", + "bbox": [ + 496, + 840, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18854", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0b0c220c4da0d9d125da11da0d352f7ee6d9020b90620b0019831cd75bfc0768.jpg", + "image_caption": [ + "Figure 2. Blind Classifier. Performance of a blind classifier on the CGLM (left) and CLOC (right) datasets across varying shift $S$ towards future for selecting evaluation samples alongside the optimal context window size $k$ for the selected shift. (Section 3.2) A blind classifier achieves unrealistically high accuracy on current evaluation of adaptation (dark blue line, $S = 0$ ) on both datasets despite being a trivial baseline. (Section 3.5) The accuracy of the blind classifier on incoming samples with increasing shift $S$ into the future decreases significantly, eventually converging to near-random performance, indicating a lack of label correlations to the current training samples." + ], + "image_footnote": [], + "bbox": [ + 181, + 53, + 480, + 224 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4bbbe4879373d96cc0cddab106031abf725d28ae50093f7b9d8b54d1f701f933.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 53, + 790, + 226 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "predicts the class of $\\mathbf{x}_t$ as the mode of the last revealed labels $\\cup_{j=1,\\dots,k}\\{\\mathbf{y}_{t-j}\\}$ . The optimal context window size $\\mathcal{K}$ is selected by a search over different sizes on the hyperparameter search set.", + "bbox": [ + 75, + 313, + 468, + 372 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Results. We present the performance of the blind classifier on the online accuracy in Figure 2. For this section, we focus solely on measuring online accuracy (indicated by the topmost purple line). Our results indicate that the blind classifier performs remarkably well achieving an average accuracy of $50\\%$ on the CGLM dataset, which consists of 10,788 classes, using only the labels of the last seen training sample $(\\mathcal{K} = 1)$ . Moreover, the blind classifier achieves $17\\%$ on the large-scale CLOC dataset consisting of 718 classes with $\\mathcal{K} = 10$ achieving the best performance. These findings suggest an unusually high degree of label correlation between the past 1-10 samples and the immediate incoming sample in the data stream, especially given that the blind classifier achieves $50\\%$ and $17\\%$ accuracy, while the random baseline achieves $0.01\\%$ and $2\\%$ on CGLM and CLOC datasets, respectively.", + "bbox": [ + 75, + 375, + 470, + 611 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Conclusion. Despite having never processed any input images, the blind classifier achieves a remarkably high online accuracy. This is surprising because it was expected to perform no better than a random classifier. However, it achieves this result by exploiting the label correlations present in OCL datasets. This is a critical drawback in using online accuracy to measure adaptation. In the following sections, we will delve deeper into this issue.", + "bbox": [ + 75, + 613, + 468, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Can Deep Networks Learn Label Correlations?", + "text_level": 1, + "bbox": [ + 76, + 746, + 468, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After demonstrating the effectiveness of the blind classifier in exploiting label correlations in the two large-scale datasets used in OCL settings, a pertinent inquiry arises: Can deep networks inadvertently learn these same label correlations leading to unreasonably high online accuracies? This question warrants investigation to determine to what extent deep OCL algorithms can leverage label correlations and the impact this may have on their performance.", + "bbox": [ + 75, + 765, + 468, + 883 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "An Overfitting-Based Baseline. One approach for DNNs", + "bbox": [ + 76, + 885, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to exploit label correlations is by overfitting to recent data. We investigate algorithmic choices for designing an OCL method that can overfit the most recent labels in a data stream. Specifically, we make two important design choices for our baseline: (i) we update the model only on recent data to achieve overfitting while sacrificing most of the useful information from the past. To this end, we adopt FIFO sampling, a widely-used technique in OCL, to select batches of samples for training. (ii) We fix the feature representations and train only the last linear layer to prevent degradation of feature representations due to overfitting. To improve the quality of the representations, we use a ResNet50 model pretrained on Instagram1B [22]. We refer to this model as OverAdapt. OverAdapt is computationally efficient since training the Linear layer over multiple updates is relatively inexpensive. Moreover, we adopt the fast stream evaluation setting [10], i.e. a setting with a strictly limited computational budget. We set the upper bound for the computation to one gradient update per incoming batch of samples for all methods with no restrictions on storage space.", + "bbox": [ + 496, + 313, + 893, + 611 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Results. We present the results of the proposed OverAdapt compared to state-of-the-art OCL methods trained using an ImageNet1K pretrained ResNet50 model on the CGLM and CLOC datasets in Figure 3. OverAdapt achieves remarkable performance, surpassing the best-performing method ACM on the CGLM dataset by more than $30\\%$ , and outperforming all but the ACM baseline on the CLOC dataset by $10 - 35\\%$ . Notably, OverAdapt achieves an impressive $80\\%$ accuracy on the CGLM dataset.", + "bbox": [ + 496, + 614, + 893, + 748 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Conclusion. After demonstrating that OverAdapt can effectively leverage label correlations from the data stream, we conclude that traditional design choices like the FIFO buffer in past OCL setups [7] improved overfitting to the next sample. It is worrying that future work or existing works could have inadvertently made similar choices leading to perceived improvement in algorithms when instead it is a subtle case of overfitting to the online accuracy metric. We further ensure the validity of our conclusions by investigating whether the effectiveness of this model is due to", + "bbox": [ + 496, + 752, + 895, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18855", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8858ba35790bcb9403096c5e925093ae9a6c89d6d946e797fc07af8feed50782.jpg", + "image_caption": [ + "Figure 3. OverAdapt Classifier. We compare the adaptation performance of our OverAdapt classifier on CGLM (left) and CLOC (right) datasets using online accuracy as a measure. The three top performing OCL methods on CLOC are benchmarked on the CGLM dataset. We see that OverAdapt outperforms recent OCL methods by a large margin of $10 - 40\\%$ in accuracy." + ], + "image_footnote": [], + "bbox": [ + 169, + 59, + 803, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "a good training algorithm or to potential limitations of the evaluation metric. We explore this in the next subsections.", + "bbox": [ + 75, + 287, + 470, + 318 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Exploring Properties of OverAdapt", + "text_level": 1, + "bbox": [ + 76, + 329, + 385, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We investigate the reasons behind the impressive performance of our proposed OverAdapt.", + "bbox": [ + 75, + 348, + 468, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sensitivity Analysis. We start with the sensitivity study of OverAdapt by analyzing the impact of modifying its two key components: (i) FC-Only training with large-data pretrained initialization and (ii) FIFO Sampling. To study the effect of FC-Only training, we replace it with full-model training using an ImageNet1K-pretrained ResNet50 which has been common in prior OCL work [10]. We also analyze the effect of FIFO sample selection by comparing it with uniform sampling, which has been shown to be a simple but effective strategy in limited-compute regimes [26]. We evaluate their performance in terms of online accuracy and information retention at time $T$ after training on the entire stream following prior art [7] as discussed in Section 3.1.", + "bbox": [ + 75, + 378, + 470, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Results. Our results are shown in Figure 4 (left & center).", + "bbox": [ + 76, + 571, + 460, + 587 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "OverAdapt. Strikingly, our analysis reveals that OverAdapt (✓FIFO ✓FC-Only) achieves remarkable performance in rapid adaptation as measured by online accuracy achieving $82\\%$ and $27\\%$ on CGLM and CLOC, respectively. However, this seemingly impressive performance is coupled with an abysmally low information retention when measured by Backward Transfer with OverAdapt performing with $5\\%$ and $1\\%$ accuracy on CGLM and CLOC, respectively. These results demonstrate that OverAdapt is not a superior OCL algorithm but rather a product of a flawed rapid adaptation evaluation.", + "bbox": [ + 75, + 588, + 468, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "FIFO Sampling. Our analysis comparing sampling strategies reveals that models trained using the FIFO sample selection strategy with both FC-Only training ( $\\checkmark$ FIFO $\\checkmark$ FC-Only) and full-model training ( $\\checkmark$ FIFO $\\times$ FC-Only) achieve significantly higher accuracy of $82 / 78\\%$ and $27 / 24\\%$ on CGLM and CLOC, respectively, on online accuracy metric compared to those trained using uniform sampling-based with FC-Only training ( $\\times$ FIFO $\\checkmark$ FC-Only) and full-model training ( $\\times$ FIFO $\\times$ FC-Only). This clearly indicates that FIFO sampling is primarily responsible for the ability to", + "bbox": [ + 75, + 752, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "leverage the latest label correlations. However, models trained with FIFO sampling achieve significantly lower accuracy of $5 / 7\\%$ and $1 / 1\\%$ on CGLM and CLOC, respectively, in terms of information retention as measured by backward transfer in the last timestep, performing close to a random classifier. This highlights their poor representation quality and confirms that models using the FIFO strategy simply overfit to the latest samples.", + "bbox": [ + 496, + 287, + 890, + 406 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "FC-Only Training. Comparing FC-Only training (FIFO $\\sqrt{\\mathsf{FC}}$ -Only) to full-model training (FIFO $\\times$ FFC-Only) under FIFO sampling, we observe that FC-Only training achieves a higher accuracy of $82\\%$ and $27\\%$ on CGLM and CLOC, respectively, in online accuracy. However, for information retention, both models perform poorly due to the impact of FIFO sampling. In contrast full-model training under uniform sampling (XFIFO $\\times$ FFC-Only) achieved a higher accuracy of $34\\%$ and $14\\%$ on CGLM and CLOC, respectively, for online accuracy, compared to full-model training (XFIFO $\\sqrt{\\mathsf{FC}}$ -Only). Additionally, full-model training achieved $42\\%$ and $18\\%$ accuracy on CGLM (comparable to full-model training) and CLOC (higher than full-model training), respectively, in information retention. In general, it is not conclusive whether FC-Only training could substitute full model training, as it performed significantly better in some cases and significantly worse in others.", + "bbox": [ + 496, + 406, + 892, + 656 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Conclusion. Our experiments highlighted critical drawbacks in assessing the rapid adaptation of deep models using online accuracy, due to spurious label correlations in the data stream. Sensitivity analysis revealed that both FIFO sampling and FC-Only training are critical components that helped OverAdapt leverage label correlations where FIFO sampling being the primary contributor. Furthermore, our findings suggest that information retention is a useful indicator for identifying drawbacks of OCL algorithms, such as inadvertent overfitting.", + "bbox": [ + 496, + 657, + 890, + 806 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Removing Correlations to Evaluate Adaptation", + "text_level": 1, + "bbox": [ + 500, + 821, + 890, + 837 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To address the limitations of online accuracy, we propose a new metric, near-future accuracy, which involves evaluating the model on near-future samples rather than immediate next samples. This can mitigate the adverse effects of label", + "bbox": [ + 496, + 840, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18856", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e9093ca2cfb006856a4e21f74e18a81bcaaf1d31606963db24f751de578a4c38.jpg", + "image_caption": [ + "Figure 4. Sensitivity Analysis of OverAdapt Classifier. We illustrate the performance of various components of our OverAdapt classifier on CGLM (top) and CLOC (bottom) datasets measuring: (Section 3.4) information retention (left) and rapid adaptation capability in terms of online accuracy ( $S = 0$ , center) (Section 3.5) rapid adaptation performance in terms of online accuracy ( $S = 0$ , center) with our proposed near-future accuracy ( $S = 256$ in CGLM and, $S = 16384$ in CLOC). Note that information retention (left) is independent of the shift $S$ . The results demonstrate that introducing the shift removes label correlations, leading to dramatic loss in adaptation performance for our OverAdapt method while the uniform baseline stays unaffected." + ], + "image_footnote": [], + "bbox": [ + 207, + 59, + 764, + 268 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/66e6d652baed9b76535ebd0e5c171189fe43d5ffbfcf440a4499d382d6b45b14.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 138, + 369, + 400, + 448 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3dcbbf70790dd92f8680e83547efad6f7c5c9407ff337710c5b698f0fe01abac.jpg", + "image_caption": [ + "Figure 5. Our Evaluation Method. We compare the samples selected for evaluating adaptation performance by our evaluation method. The blue and green arrows indicate the latest batch received from the stream for learning and the samples selected for evaluation respectively. Current evaluation proposes to compute accuracy on the immediate incoming samples $(S = 0)$ , i.e. online accuracy, while we propose to evaluate on the closest future samples $(S = 64)$ , i.e. near-future accuracy, which is free from spurious correlations with the seen batch of images." + ], + "image_footnote": [], + "bbox": [ + 137, + 450, + 400, + 551 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "correlations on the performance by obtaining a more accurate assessment of the adaptation ability of OCL algorithms. Formulation of Proposed Evaluation. As illustrated in Figure 5, we introduce a shift $S$ that represents the number of samples in the future, after which we evaluate the performance of the model. Instead of evaluating on the immediate next sample $(\\mathbf{x}_{t + 1},\\mathbf{y}_{t + 1})$ , we use the next near-future sample after the smallest shift $S$ , namely $(\\mathbf{x}_{t + 1 + S},\\mathbf{y}_{t + 1 + S})$ , so that it has no label correlation with them. We select the smallest shift $S$ instead of an arbitrarily large shift $S$ so that the test sample comes from the same distribution as the latest seen train samples. We calculate the online accuracy as before, where $\\hat{a}_t$ is the running average of the accuracy calculated by first calculating the accuracy $a_{t} =$", + "bbox": [ + 75, + 693, + 472, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$\\mathbb{1}\\{f_{\\theta_t}(\\mathbf{x}_{t + 1 + S}) = \\mathbf{y}_{t + 1 + S}\\}$ and then updating the running average using the formula $A_{t}^{RA} = \\frac{1}{t}\\left(A_{t - 1}^{RA}\\cdot (t - 1) + a_{t}\\right)$ .", + "bbox": [ + 500, + 378, + 890, + 410 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "How To Set the Shift $S$ ? The shift $S$ is the smallest value in the future that has no label correlation with the last seen train samples. We select the smallest $S$ so that the blind classifier performs similarly to a random classifier. As shown in Figure 2 for both CGLM (left) and CLOC (right) datasets, we observe that increasing the shift $S$ decreases the accuracy of the blind classifier down to a similar performance of a random classifier. In particular, at a shift of $S = 256$ for CGLM and $S = 16384$ for CLOC, the label correlations are effectively eliminated. Therefore, we use these shift values for our proposed evaluation strategy. We evaluate OverAdapt and its variants on rapid adaptation with our proposed near-future accuracy and compare it with the previously adopted online accuracy $(S = 0)$ .", + "bbox": [ + 496, + 409, + 892, + 618 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results. Figure 4 presents the results of OverAdapt and its variants on rapid adaptation using two metrics: online accuracy (center) and near-future accuracy (right). When studying FIFO sampling with FC-Only training ( $\\sqrt[3]{\\mathrm{FIFO}} \\sqrt{\\mathrm{FC}}$ -Only) and with full-model training ( $\\sqrt{\\mathrm{FIFO}} \\times \\mathrm{FC}$ -Only), we observe a significant drop in the performance of the methods between the two metrics that overfit using the FIFO sampling by about $70\\%$ in CGLM and $20 - 40\\%$ on CLOC datasets, while the performance of uniform sampling for both FC-Only training ( $\\times \\mathrm{FIFO} \\sqrt{\\mathrm{FC}}$ -Only) and full-model training ( $\\times \\mathrm{FIFO} \\times \\mathrm{FC}$ -Only) remains similar. Interestingly, the trends reverse, with the uniform sampling variants outperforming the FIFO sampling strategy by a large margin. Furthermore, we observe that FC-Only training no longer consistently improves rapid adaptation, proving to be useful in some cases on the new evaluation method.", + "bbox": [ + 496, + 618, + 893, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Conclusion. We propose an evaluation using near-future accuracy which removes label correlations. OverAdapt performs poorly after removing label correlations, compared", + "bbox": [ + 496, + 856, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18857", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "to a uniform baseline, emphasizing the importance of developing OCL algorithms that handle rapid adaptation without overfitting. Additionally, there is no surprising discrepancy between near-future accuracy and information retention across methods, unlike online accuracy. Our strategy allows for better evaluation of OCL algorithms on real-world ordered datasets.", + "bbox": [ + 75, + 90, + 472, + 195 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4. OCL Evaluation by Near-Future Accuracy", + "text_level": 1, + "bbox": [ + 76, + 210, + 460, + 228 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we provide a comprehensive analysis of various OCL approaches under near-future accuracy. We incorporate the latest advancements in setup design into our benchmark and take computational constraints into account for fair comparison. Following the prior art [25, 26], our study assumes no memory constraints, but rather sets constraints on computational budget following [10, 25, 26]. As addressed in prior work, budgeted computation per time step implicitly imposes a limited memory access.", + "bbox": [ + 75, + 229, + 472, + 367 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 375, + 269, + 391 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Datasets and Metrics. We employ two large-scale online continual learning datasets, CGLM with a total of 460K images and CLOC compromising of 39M images in a stream, both of which contain natural distribution shifts [7]. That is to say, the images are temporally ordered. We measure rapid adaptation performance using the average accuracy on near-future samples, as described in Section 3.5, with a shift $S = 256$ for CGLM and $S = 16384$ for CLOC. The choice of both was made such that the blind classifier discussed in Section 3.2 achieves a random accuracy. Additionally, we measure information retention using the Backward Transfer metric following CLOC [7].", + "bbox": [ + 75, + 393, + 472, + 571 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Model and Optimization. In all experiments, we use a ResNet50 with ImageNet1K initialization unless otherwise specified. We adopt the optimization procedure from [10] and train all models using an SGD optimizer, a fixed learning rate of 0.005, and a weight decay of $10^{-4}$ . For both training and evaluation, we batch incoming samples with a batch size $\\mathcal{B}$ of 64 for CGLM [25] and 128 for CLOC [10].", + "bbox": [ + 75, + 573, + 472, + 676 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Compared OCL Approaches. We evaluate five online continual learning methods using our proposed near-future accuracy. For consistency, we use uniform sampling as the sampling strategy, since it was shown in Section 3.4 that it strikes a good balance between adaptation and retention. Again, in uniform sampling, the training batch is constructed by uniformly and sampling $\\mathcal{B}$ samples from all past stored data. The Appendix provides a comprehensive analysis of other sampling techniques.", + "bbox": [ + 75, + 676, + 472, + 810 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ER (Replay Only)[26]. ER (Replay Only) is a simple approach that stores the incoming samples and trains the model on a batch sampled from the set of stored samples. This is the leading method in offline budgeted CL [26].", + "bbox": [ + 76, + 810, + 470, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "FC-Only. FC-Only, referred to as OverAdapt (XFIFO ✓FC-Only) in Section 3.4, is an adapted version of ER (Re", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "play Only) that uses a ResNet50-I1B feature extractor and trains only the last linear layer. This method has been shown to be computationally efficient [26].", + "bbox": [ + 496, + 90, + 893, + 136 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ACE[5]. We replace the CrossEntropy loss in ER (Replay Only) with the ACE Loss proposed in to isolate the effect of ACE loss under the proposed evaluation setting.", + "bbox": [ + 496, + 135, + 893, + 180 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ACM[25]. ACM extracts features from a pretrained ResNet50 model (trained on ImageNet1k) and continually updates a kNN classifier, with $k = 2$ and cosine distance as distance metric, over those features. Additionally, we note that ACM does not train a deep network, thus incurring minimal computational cost. This sets the minimal accuracy requirements for OCL methods. We compare ACM with other popular fixed-feature extractor based methods like NCM [23, 24, 16] and SLDA [14] in the Appendix.", + "bbox": [ + 496, + 180, + 893, + 313 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "CosineFC[15]. This approach replaces the linear layer of ResNet50 in the ER (Replay Only) baseline with a layer that computes the cosine distance between weights and features. We only perform this modification as distillation has been shown to be computationally ineffective [26].", + "bbox": [ + 496, + 313, + 893, + 386 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "By comparing these approaches under our proposed near-future accuracy along with information retention, we aim to provide insights into the strengths and limitations of current OCL methods.", + "bbox": [ + 496, + 387, + 893, + 445 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Results: Varying Stream Speeds", + "text_level": 1, + "bbox": [ + 498, + 453, + 784, + 469 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Following prior work on fair computationally normalized evaluation of online continual learners [10], we evaluate the performance of OCL methods in two different time constraints, namely slow stream and fast stream scenarios.", + "bbox": [ + 496, + 470, + 893, + 530 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Slow Stream. Slow stream is the scenario in which the computational budget for learning is not strictly limited. We enforce all methods to perform the equivalent of 10 and 5 model updates per time step on CGLM and CLOC, respectively. Methods that require a significant overhead will thus perform a fewer number of model updates such that it matches the corresponding computational budget of 10 and 5 updates on the respective datasets. Note that ACM requires negligible training cost, and therefore OCL methods must at least outperform ACM to be considered useful.", + "bbox": [ + 496, + 530, + 893, + 678 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. In Figure 6 (first row), we present the performance of various methods in terms of near-future accuracy for both CGLM and CLOC datasets. CosineFC, originally proposed for offline continual learning, achieves the highest accuracy with $38\\%$ and $16\\%$ accuracy on CGLM and CLOC, respectively. Furthermore, CosineFC also shows impressive information retention performance, achieving an accuracy of $77\\%$ in CGLM. As expected, FC-Only which only finetunes the last linear layer, has the worst retention capabilities due to the restricted access to full-model updates.", + "bbox": [ + 496, + 678, + 893, + 825 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Conclusion. Our evaluation revealed that methods not explicitly designed for adaptation in the OCL setup perform well, indicating that retaining and reusing previously seen information is crucial for achieving better generalization, and that retention and adaptation are closely linked.", + "bbox": [ + 496, + 825, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18858", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a62739252ca9211a1419e9618818edd7a45b9ccff7537437cf4f4438a6addf30.jpg", + "image_caption": [ + "Figure 6. Performance of Methods on Near-Future Accuracy. We evaluate CL methods in slow and fast streams similar to [10]. Near-future accuracy, which eliminates spurious label correlations, shows that retaining and reusing past information is crucial for better generalization and that algorithms not designed for adaptation in OCL can perform well. Hence retention and adaptation are closely linked." + ], + "image_footnote": [], + "bbox": [ + 181, + 51, + 799, + 305 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fast Stream. Fast stream setting refers to the scenario where the computational budget for learning is limited. That is to say, the stream presents samples at a fast rate that provides limited time for learners to train [10]. To evaluate the performance of OCL methods under this setting, we restrict the methods to only use a computation equivalent to one model update per incoming batch for both datasets.", + "bbox": [ + 75, + 381, + 468, + 484 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results. As shown in Figure 6 (second row), our results suggest that the two simplest baselines, namely ACM and FC-Only, achieve the highest accuracy on CGLM with $29\\%$ and $21\\%$ , respectively. On the other hand, ACM achieves the highest information retention of $27\\%$ while simple ER and CosineFC achieve the highest near-future accuracy of around $13\\%$ . These results indicate that the simple baseline methods outperform the more advanced OCL methods in both adaptation and information retention in this setup. This highlights that current OCL methods still have a long way to go to achieve satisfactory performance in the fast stream setting where compute is extremely limited.", + "bbox": [ + 75, + 484, + 470, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conclusion. Under our proposed evaluation approach, in which spurious label correlations are removed, the fast stream setting with its limited computational budget shows that simple baselines can outperform more advanced OCL methods in both adaptation and retention. This finding emphasizes the need to develop OCL methods that can adapt rapidly in severely budgeted settings.", + "bbox": [ + 75, + 662, + 468, + 767 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Further Discussion", + "text_level": 1, + "bbox": [ + 76, + 773, + 261, + 789 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our benchmark of OCL methods on large-scale datasets highlights two key observations. First, the best-performing online adaptation methods often suffer from forgetting due to overfitting to label correlations, challenging the assumption that the performance gap between adaptation and retention is an inherent learning problem [6]. Our proposed near-future accuracy helps reveal label correlations and identifies", + "bbox": [ + 75, + 796, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "whether the underlying algorithm is inadvertently exploiting them. Second, methods with better retention properties tend to generalize better and achieve improved performance on near-future accuracy in relaxed and restricted computational settings [12, 29]. This aligns well with the domain generalization literature [12] and suggests that proper training on previous samples can lead to features that generalize well across domain shifts. Finally, we consistently observe that, under limited computational settings, simpler methods outperform their more computationally involved ones.", + "bbox": [ + 496, + 381, + 893, + 530 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 498, + 542, + 619, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our work proposes a new measure to evaluate adaptation in OCL algorithms and highlights its limitations compared to the standard online accuracy evaluation. We found that many current OCL methods overfit to idiosyncrasies of the stream rather than genuinely adapting to new data, as revealed by poor information retention. Using our proposed metric, near-future accuracy, we observed that algorithms with good retention also had better generalization and adaptation capabilities. Our proposed evaluation can serve as a sanity check for future OCL algorithms to ensure that they are not incorrectly learning spurious label correlations.", + "bbox": [ + 496, + 561, + 893, + 727 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgements", + "text_level": 1, + "bbox": [ + 498, + 739, + 687, + 757 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by the King Abdullah University of Science and Technology - Office of Sponsored Research (OSR) under Award No. OSR-CRG2021-4648, SDAIA-KAUST Center of Excellence in Data Science, Artificial Intelligence, and UKRI grant: Turing AI Fellowship EP/W002981/1. We thank the Royal Academy of Engineering and FiveAI for their support. Ser-Nam Lim from Meta AI has no relationships with the mentioned grants. Ameya Prabhu is funded by Meta AI Grant No. DFR05540.", + "bbox": [ + 496, + 763, + 893, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18859", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rahaf Aljundi, Lucas Caccia, Eugene Belilovsky, Massimo Caccia, Laurent Charlin, and Tinne Tuytelaars. Online continual learning with maximally interfered retrieval. In Conference on Neural Information Processing Systems (NeurIPS), 2019. 2, 3", + "[2] Rahaf Aljundi, Min Lin, Baptiste Goujaud, and Yoshua Bengio. Gradient based sample selection for online continual learning. 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In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022. 3" + ], + "bbox": [ + 78, + 90, + 467, + 299 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "18861", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Rapid Adaptation in Online Continual Learning_ Are We Evaluating It Right_/165500ab-b2c3-4db0-ba04-4570a2ad4282_model.json b/2023/Rapid Adaptation in Online Continual Learning_ Are We Evaluating It Right_/165500ab-b2c3-4db0-ba04-4570a2ad4282_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c17145546d565d337effc2025113299374a9bb59 --- /dev/null +++ b/2023/Rapid Adaptation in Online Continual Learning_ Are We Evaluating It Right_/165500ab-b2c3-4db0-ba04-4570a2ad4282_model.json @@ -0,0 +1,1749 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.089, + 0.13, + 0.882, + 0.154 + ], + "angle": 0, + "content": "Rapid Adaptation in Online Continual Learning: Are We Evaluating It Right?" + }, + { + "type": "text", + "bbox": [ + 0.126, + 0.179, + 0.844, + 0.234 + ], + "angle": 0, + "content": "Hasan Abed Al Kader Hammoud\\(^{1*}\\) Ameya Prabhu\\(^{2*}\\) Ser-Nam Lim\\(^{3}\\) Philip H.S. Torr\\(^{2}\\) Adel Bibi\\(^{2\\dagger}\\) Bernard Ghanem\\(^{1\\dagger}\\) KAUST\\(^{1}\\) University of Oxford\\(^{2}\\) Meta AI\\(^{3}\\)" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.254, + 0.314, + 0.27 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.287, + 0.474, + 0.613 + ], + "angle": 0, + "content": "We revisit the common practice of evaluating adaptation of Online Continual Learning (OCL) algorithms through the metric of online accuracy, which measures the accuracy of the model on the immediate next few samples. However, we show that this metric is unreliable, as even vacuous blind classifiers, which do not use input images for prediction, can achieve unrealistically high online accuracy by exploiting spurious label correlations in the data stream. Our study reveals that existing OCL algorithms can also achieve high online accuracy, but perform poorly in retaining useful information, suggesting that they unintentionally learn spurious label correlations. To address this issue, we propose a novel metric for measuring adaptation based on the accuracy on the near-future samples, where spurious correlations are removed. We benchmark existing OCL approaches using our proposed metric on large-scale datasets under various computational budgets and find that better generalization can be achieved by retaining and reusing past seen information. We believe that our proposed metric can aid in the development of truly adaptive OCL methods. We provide code to reproduce our results at https://github.com/drimpossible/EvalOCL." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.631, + 0.21, + 0.647 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.47, + 0.865 + ], + "angle": 0, + "content": "The need for learning on continuously changing data streams has led to a proliferation of research in Online Continual Learning (OCL) literature [21, 8]. The primary aim of OCL algorithms is to enable deep models to continuously adapt to new data distributions without compromising the accumulated knowledge. However, we argue that current metrics have deviated significantly from measuring true adaptation capabilities. The majority of recent works on OCL [7, 10] measure the adaptation of OCL algorithms using the metric of online accuracy, defined as the accuracy of a model on the immediate incoming samples. This evaluation practice resulted in the neglect in measuring the capacity of models to retain previous knowledge. As a consequence, several OCL algorithms achieve high online ac" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.258, + 0.85, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.452, + 0.895, + 0.562 + ], + "angle": 0, + "content": "Figure 1. Effect of Spurious Correlations. Current methods in OCL perform well on rapid adaptation but suffer from abysmal information retention (top). We show that these trends are due to idiosyncrasies in the data stream such as label correlations that favor methods that inadvertently overfit to the latest data. Using our proposed metric that removes these correlations (bottom), different sets of methods achieve good performance, with high information retention being key for achieving high adaptability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.573, + 0.893, + 0.737 + ], + "angle": 0, + "content": "curacy [7] but poor performance on other important metrics like information retention which measure catastrophic forgetting of past seen data. Poor information retention performance has been attributed to an inherent stability-plasticity trade-off between learning new concepts and remembering old concepts [6]. However, the ability to preserve information and representations of past data, such as images of a class like the Eiffel Tower, should be crucial for accurately predicting future images of the same class, even if they were taken under novel weather conditions or camera poses. Hence, we find this justification to be unsatisfactory." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.738, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In this paper, we demonstrate that the conventional metric of measuring online accuracy may lead to misleading conclusions about the adaptation capabilities of OCL algorithms due to the idiosyncrasies of the data stream. To support our claim, we first demonstrate that a simple blind classifier that relies solely on spurious label correlations in the stream achieves unrealistically high online accuracy on large-scale OCL datasets. Furthermore, we show that this behaviour can be exhibited by deep OCL algorithms, where we propose OverAdapt which achieves state-of-the-art performance in online accuracy despite the very poor perfor" + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.875, + 0.401, + 0.888 + ], + "angle": 0, + "content": "* authors contributed equally; order decided by a coin flip." + }, + { + "type": "page_footnote", + "bbox": [ + 0.099, + 0.888, + 0.198, + 0.9 + ], + "angle": 0, + "content": "\\(\\dagger\\) equal supervision" + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.875, + 0.401, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18852" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.152 + ], + "angle": 0, + "content": "mance in information retention. We confirm the findings on two large-scale OCL datasets collected from different sources. This indicates that the problem is not limited to a specific dataset, but may be a general concern." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.155, + 0.473, + 0.496 + ], + "angle": 0, + "content": "To overcome this issue, we introduce a new metric called near-future accuracy that measures the adaptation capabilities of OCL algorithms by evaluating the accuracy on samples after a shift of \\( S \\) steps. We choose the minimum shift \\( S \\) which ensures that the samples no longer have spurious label correlations with the current training data. Choosing the minimum value helps minimize any distribution drift between the training and evaluation samples. The case \\( S = 0 \\) recovers the online accuracy metric in case of no spurious correlations. We observe a significant drop in performance on this metric compared to their online accuracy with several state-of-the-art OCL algorithms. This suggests that these algorithms inadvertently rely on label correlations in the stream for predictions. On the contrary, we find that algorithms designed primarily to improve information retention perform exceptionally well in our evaluation strategy. This suggests that a better generalization can be achieved by effectively retaining and reusing past information. Figure 1 illustrates that the best algorithms are those that have little discrepancy between information retention and adaptation. These results challenge current beliefs and demonstrate the importance of using a more precise measure of adaptation in evaluating OCL algorithms." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.499, + 0.456, + 0.513 + ], + "angle": 0, + "content": "Overall, our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.528, + 0.469, + 0.573 + ], + "angle": 0, + "content": "- We demonstrate that popular metrics like online accuracy can be unreliable in measuring rapid adaptation due to the presence of spurious label correlations in OCL datasets." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.579, + 0.469, + 0.623 + ], + "angle": 0, + "content": "- We introduce a novel baseline, OverAdapt, which achieves high online accuracy by relying on label correlations, despite forgetting almost all previously seen data." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.629, + 0.469, + 0.702 + ], + "angle": 0, + "content": "- We propose a novel metric that evaluates the adaptation capabilities of OCL algorithms by measuring accuracy on near-future samples. We select the smallest value of \\( S \\) that removes label correlations and use this metric to evaluate state-of-the-art OCL methods." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.709, + 0.469, + 0.797 + ], + "angle": 0, + "content": "- Our findings show that existing OCL algorithms perform poorly when evaluated using our proposed evaluation strategy. Algorithms which prevent catastrophic forgetting perform significantly better, suggesting that better adaptation performance can be achieved by retaining and reusing past seen information." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.528, + 0.469, + 0.797 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.812, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Our results challenge the current emphasis on adapting to the latest samples and demonstrate the importance of seeking a more precise measure of adaptation. We note that our contributions are robust, with our findings valid across various OCL approaches, optimization strategies, and large-scale datasets from different sources." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.087, + 0.892, + 0.183 + ], + "angle": 0, + "content": "Table 1. Properties of OCL Benchmarks. We list benchmarks in the field of OCL along with the works which introduced them. We compare them across six properties: Realistic Data Streams (DO), No Storage Constraints (SC), Rapid Adaptation (RA), Information Retention (IR), Restricts Computational Budgets (CB), Evaluates on long stream sizes (LB), Leverages Pretrained Models (PT). Note that \\( \\checkmark \\) is better than \\( x \\) in all columns." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.187, + 0.892, + 0.309 + ], + "angle": 0, + "content": "
DataOrderBenchmarkDOSCRAIRCBLBPT
Task-Inc.A-GEM[9]XXX✓X✓X
Class-Inc.MIR[1]XXX✓X✓X
DER[4]
BlurryGSS[2]XXX✓X✓X
RM [3]
CLIB[18]
NaturalCLEAR[20]✓X✓✓XX✓
BudgetCL[26]X✓X✓✓X✓
CLOC[7]✓X✓XX✓X
DelayOCL[10]✓X✓X✓✓✓
ACM[25]✓✓✓✓✓✓✓
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.329, + 0.757, + 0.344 + ], + "angle": 0, + "content": "2. OCL Evaluation: A Review" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.35, + 0.892, + 0.394 + ], + "angle": 0, + "content": "We start with an overview of benchmarks in OCL across different properties of interest. For a more detailed review of the literature, we refer the reader to [30]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.407, + 0.893, + 0.63 + ], + "angle": 0, + "content": "1. Realistic Data Streams (DO). The OCL community has been moving towards increasingly realistic benchmarks in terms of data ordering and task setup. Early works [21, 9] assumed access to which subset of classes a test sample is from (task-incremental setup). Subsequent work removed this constraint, requiring models to predict across all seen classes so far (class-incremental setup) [2, 1]. However, these works used incoming samples from disjoint data distributions with artificial task boundaries, resulting in unrealistic ordering. Recent works [3, 18, 26] improved the ordering by mixing samples from different disjoint tasks. Latest works [7, 25, 20] eliminate the need for generating artificial data streams simply by using real-world timestamps to order the data stream. Our work focuses on these real-world data streams on large-scale datasets." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.642, + 0.893, + 0.91 + ], + "angle": 0, + "content": "2. Towards No Storage Constraints (SC). The majority of prior benchmarks on continual learning constrain the problem by prohibiting access to previously received data [19, 17], with only a small portion of data allowed to be stored in memory [21, 8, 4, 2, 18, 20]. This constraint is often justified by two reasons: (i) storage space is expensive and (ii) access to previous data is prohibited due to privacy constraints. However, recent work [25, 26] shows critical shortcomings of these justifications. They show that (a) storage costs are negligible compared to the computational costs of training a model, and (b) simply restricting access to previous data does not address privacy considerations, as samples can be reconstructed from model weights [13] or detectably change the model output [28]. Interestingly, Goel et al. [11] shows that removing data from the model can be done by catastrophic forgetting, which is antithetical to the objective of OCL approaches. Hence, we do not impose any memory constraints on our evaluation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18853" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.287 + ], + "angle": 0, + "content": "3. Towards Better Information Retention (IR). Interestingly, most of the previous benchmarks in OCL focus on preventing catastrophic forgetting of previously learned information, rather than evaluating the ability of models to rapidly learn new concepts [21, 27, 9, 3, 2, 20]. This emphasis on information retention can be attributed to disjoint set-based data ordering, which often involves little to no change in distribution for most of the stream, making it difficult to evaluate rapid adaptation. However, recent works have shifted their focus to rapid adaptation performance in real-world ordered data streams [7, 10]. In our benchmark, our objective is to maintain an additional high degree of retained knowledge from past data as demonstrated in [25, 6]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.294, + 0.473, + 0.371 + ], + "angle": 0, + "content": "4. Towards Enabling Rapid Adaptation (RA). The goal of online continual learning algorithms is to rapidly adapt to incoming data from changing distributions. Similarly to past work [25, 7, 10], we place a strong emphasis on achieving this goal with better metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.378, + 0.473, + 0.513 + ], + "angle": 0, + "content": "5. Towards Computational Budgets (CB). Continual learning without memory constraints is primarily a problem of achieving high performance with computational efficiency, as retraining from scratch is an ideal solution to the problem. This setting addresses the real-world problem of reducing the cost of updating a given model with incoming data from a stream [25]. We evaluate OCL approaches under the maximum computational budget for fairness [10], testing across two different budgets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.521, + 0.473, + 0.773 + ], + "angle": 0, + "content": "6. Towards Large-Scale OCL (LB). OCL benchmarks have historically focused on learning over samples incoming from a stream over long data streams since the development of GEM [21]. Recent OCL benchmarks [2, 18, 25] have preserved this useful characteristic, while scaling up to larger and more complex data streams. In this work, we use two large-scale OCL benchmarks: Continual Google LandMarks (CGLM) [25] and Continual Localization (CLOC) [7]. CGLM is a landmark classification dataset that consists of a long-tailed distribution with 10,788 classes that simulate images that arrive on a Wikimedia Commons server. CLOC is a dataset focused on geolocation at scale consisting of 713 classes with 39M images simulating images arriving on a Flickr server. As these datasets come from two different sources, the issue of label correlation that we observe is likely to be a repeating pattern across future OCL datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.782, + 0.473, + 0.903 + ], + "angle": 0, + "content": "7. Leveraging Pretraining for Effective OCL (PT). Traditional methods in online continual learning start with randomly initialized models [21, 1]. However, continual learning approaches can leverage the abundance of large-scale pretrained models to improve computational efficiency [24, 31, 25]. We focus on an evaluation setting that starts with ImageNet1K pretrained models to allow approaches to leverage pretrained information." + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.903 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.09, + 0.892, + 0.108 + ], + "angle": 0, + "content": "3. Correcting Evaluations of Rapid Adaptation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.11, + 0.895, + 0.289 + ], + "angle": 0, + "content": "We delve into our exploration of the limitations of using online accuracy as a metric to measure adaptation to distribution shifts and present our efforts to alleviate the shortcomings of this metric. We start by identifying the label correlations that affect online accuracy, and then we unveil a technique that enables deep networks to artificially achieve high performance on this metric. This highlights the dependence of the networks on these label correlations. Finally, we introduce a novel evaluation metric, near-future accuracy, and a test to detect and remove label correlations allowing for accurate measurement of the effectiveness of OCL methods in rapidly adapting to new distributions." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.295, + 0.859, + 0.311 + ], + "angle": 0, + "content": "3.1. Evaluating OCL: A Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.313, + 0.892, + 0.461 + ], + "angle": 0, + "content": "In traditional OCL setups with real-world stream orders [7, 25], the learner is fed a continuous stream of training samples over time steps \\( t \\in \\{1, 2, \\dots, \\infty\\} \\), consisting of an input datapoint \\( \\mathbf{x}_t \\in \\mathcal{X} \\) and its corresponding label \\( \\mathbf{y}_t \\in \\mathcal{Y} \\) where \\( (\\mathbf{x}_t, \\mathbf{y}_t) \\sim \\mathcal{D}_{j \\leq t} \\). The distribution \\( \\mathcal{D}_j \\) can change at any stream timestep. The aim is to train a classifier \\( f_{\\theta_t}: \\mathcal{X} \\to \\mathcal{Y} \\) at any given \\( t \\), which accurately maps a new sample \\( \\mathbf{x} \\) to its label \\( \\mathbf{y} \\) while adapting to the latest information and incorporating it with the historical knowledge acquired from previous data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.892, + 0.594 + ], + "angle": 0, + "content": "To evaluate the adaptation ability of \\( f_{\\theta_t} \\), online accuracy measures the performance on the next unseen sample, \\( (\\mathbf{x}_{t + 1},\\mathbf{y}_{t + 1}) \\), i.e., \\( a_{t} = \\mathbb{1}\\{f_{\\theta_{t}}(\\mathbf{x}_{t + 1}) = \\mathbf{y}_{t + 1}\\} \\). Online accuracy is updated in an online fashion given by \\( A_{t}^{RA} = \\frac{1}{t}\\left(A_{t - 1}^{RA}\\cdot (t - 1) + a_{t}\\right) \\). For OCL approaches training deep networks, the running average is updated on a batch \\( \\mathcal{B} \\) of the next unseen samples as opposed to a single sample. After the evaluation is carried out, the model \\( f_{\\theta_i} \\) is updated using the same samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.594, + 0.892, + 0.743 + ], + "angle": 0, + "content": "The ability of \\( f_{\\theta_t} \\) to retain information is measured by evaluating its accuracy on an unseen test stream that is similar to the training stream. In particular, per time step \\( t \\), the model trained at the end of step \\( t \\) is evaluated on all test samples from step 0 to step \\( t \\). We measure Backward Transfer @ \\( T \\) [7] where \\( T \\) is the last time step of the stream. That is to say, the model at the last step of the stream is evaluated on an increasing test test from step 0 to the end of the stream. However, traditional OCL methods targeting natural distribution shifts have neglected this metric [7, 10]." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.75, + 0.884, + 0.766 + ], + "angle": 0, + "content": "3.2. Isolating and Quantifying Label Correlations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.768, + 0.892, + 0.842 + ], + "angle": 0, + "content": "Our objective is to investigate whether using online accuracy to measure adaptation in OCL suffers from drawbacks due to label correlations. To accomplish this, we introduce a very simple algorithm that leverages label correlations and performs well in terms of online accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.842, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Blind Classifier. We define a blind classifier, similar to prior works [7, 25], as a model that predicts the mode of the last \\(\\kappa\\) samples seen without access to the input images. Formally, at a given new step \\(t\\), the blind classifier" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18854" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.182, + 0.054, + 0.482, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.054, + 0.792, + 0.227 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.231, + 0.895, + 0.302 + ], + "angle": 0, + "content": "Figure 2. Blind Classifier. Performance of a blind classifier on the CGLM (left) and CLOC (right) datasets across varying shift \\( S \\) towards future for selecting evaluation samples alongside the optimal context window size \\( k \\) for the selected shift. (Section 3.2) A blind classifier achieves unrealistically high accuracy on current evaluation of adaptation (dark blue line, \\( S = 0 \\)) on both datasets despite being a trivial baseline. (Section 3.5) The accuracy of the blind classifier on incoming samples with increasing shift \\( S \\) into the future decreases significantly, eventually converging to near-random performance, indicating a lack of label correlations to the current training samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.314, + 0.47, + 0.373 + ], + "angle": 0, + "content": "predicts the class of \\(\\mathbf{x}_t\\) as the mode of the last revealed labels \\(\\cup_{j=1,\\dots,k}\\{\\mathbf{y}_{t-j}\\}\\). The optimal context window size \\(\\mathcal{K}\\) is selected by a search over different sizes on the hyperparameter search set." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.375, + 0.471, + 0.612 + ], + "angle": 0, + "content": "Results. We present the performance of the blind classifier on the online accuracy in Figure 2. For this section, we focus solely on measuring online accuracy (indicated by the topmost purple line). Our results indicate that the blind classifier performs remarkably well achieving an average accuracy of \\(50\\%\\) on the CGLM dataset, which consists of 10,788 classes, using only the labels of the last seen training sample \\((\\mathcal{K} = 1)\\). Moreover, the blind classifier achieves \\(17\\%\\) on the large-scale CLOC dataset consisting of 718 classes with \\(\\mathcal{K} = 10\\) achieving the best performance. These findings suggest an unusually high degree of label correlation between the past 1-10 samples and the immediate incoming sample in the data stream, especially given that the blind classifier achieves \\(50\\%\\) and \\(17\\%\\) accuracy, while the random baseline achieves \\(0.01\\%\\) and \\(2\\%\\) on CGLM and CLOC datasets, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.47, + 0.734 + ], + "angle": 0, + "content": "Conclusion. Despite having never processed any input images, the blind classifier achieves a remarkably high online accuracy. This is surprising because it was expected to perform no better than a random classifier. However, it achieves this result by exploiting the label correlations present in OCL datasets. This is a critical drawback in using online accuracy to measure adaptation. In the following sections, we will delve deeper into this issue." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.747, + 0.47, + 0.763 + ], + "angle": 0, + "content": "3.3. Can Deep Networks Learn Label Correlations?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.766, + 0.469, + 0.884 + ], + "angle": 0, + "content": "After demonstrating the effectiveness of the blind classifier in exploiting label correlations in the two large-scale datasets used in OCL settings, a pertinent inquiry arises: Can deep networks inadvertently learn these same label correlations leading to unreasonably high online accuracies? This question warrants investigation to determine to what extent deep OCL algorithms can leverage label correlations and the impact this may have on their performance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.469, + 0.901 + ], + "angle": 0, + "content": "An Overfitting-Based Baseline. One approach for DNNs" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.314, + 0.895, + 0.612 + ], + "angle": 0, + "content": "to exploit label correlations is by overfitting to recent data. We investigate algorithmic choices for designing an OCL method that can overfit the most recent labels in a data stream. Specifically, we make two important design choices for our baseline: (i) we update the model only on recent data to achieve overfitting while sacrificing most of the useful information from the past. To this end, we adopt FIFO sampling, a widely-used technique in OCL, to select batches of samples for training. (ii) We fix the feature representations and train only the last linear layer to prevent degradation of feature representations due to overfitting. To improve the quality of the representations, we use a ResNet50 model pretrained on Instagram1B [22]. We refer to this model as OverAdapt. OverAdapt is computationally efficient since training the Linear layer over multiple updates is relatively inexpensive. Moreover, we adopt the fast stream evaluation setting [10], i.e. a setting with a strictly limited computational budget. We set the upper bound for the computation to one gradient update per incoming batch of samples for all methods with no restrictions on storage space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.615, + 0.895, + 0.749 + ], + "angle": 0, + "content": "Results. We present the results of the proposed OverAdapt compared to state-of-the-art OCL methods trained using an ImageNet1K pretrained ResNet50 model on the CGLM and CLOC datasets in Figure 3. OverAdapt achieves remarkable performance, surpassing the best-performing method ACM on the CGLM dataset by more than \\(30\\%\\), and outperforming all but the ACM baseline on the CLOC dataset by \\(10 - 35\\%\\). Notably, OverAdapt achieves an impressive \\(80\\%\\) accuracy on the CGLM dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.753, + 0.896, + 0.902 + ], + "angle": 0, + "content": "Conclusion. After demonstrating that OverAdapt can effectively leverage label correlations from the data stream, we conclude that traditional design choices like the FIFO buffer in past OCL setups [7] improved overfitting to the next sample. It is worrying that future work or existing works could have inadvertently made similar choices leading to perceived improvement in algorithms when instead it is a subtle case of overfitting to the online accuracy metric. We further ensure the validity of our conclusions by investigating whether the effectiveness of this model is due to" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18855" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.171, + 0.06, + 0.805, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.222, + 0.895, + 0.266 + ], + "angle": 0, + "content": "Figure 3. OverAdapt Classifier. We compare the adaptation performance of our OverAdapt classifier on CGLM (left) and CLOC (right) datasets using online accuracy as a measure. The three top performing OCL methods on CLOC are benchmarked on the CGLM dataset. We see that OverAdapt outperforms recent OCL methods by a large margin of \\(10 - 40\\%\\) in accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.288, + 0.471, + 0.319 + ], + "angle": 0, + "content": "a good training algorithm or to potential limitations of the evaluation metric. We explore this in the next subsections." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.33, + 0.386, + 0.347 + ], + "angle": 0, + "content": "3.4. Exploring Properties of OverAdapt" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.47, + 0.379 + ], + "angle": 0, + "content": "We investigate the reasons behind the impressive performance of our proposed OverAdapt." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.38, + 0.471, + 0.572 + ], + "angle": 0, + "content": "Sensitivity Analysis. We start with the sensitivity study of OverAdapt by analyzing the impact of modifying its two key components: (i) FC-Only training with large-data pretrained initialization and (ii) FIFO Sampling. To study the effect of FC-Only training, we replace it with full-model training using an ImageNet1K-pretrained ResNet50 which has been common in prior OCL work [10]. We also analyze the effect of FIFO sample selection by comparing it with uniform sampling, which has been shown to be a simple but effective strategy in limited-compute regimes [26]. We evaluate their performance in terms of online accuracy and information retention at time \\( T \\) after training on the entire stream following prior art [7] as discussed in Section 3.1." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.573, + 0.462, + 0.588 + ], + "angle": 0, + "content": "Results. Our results are shown in Figure 4 (left & center)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.589, + 0.47, + 0.751 + ], + "angle": 0, + "content": "OverAdapt. Strikingly, our analysis reveals that OverAdapt (✓FIFO ✓FC-Only) achieves remarkable performance in rapid adaptation as measured by online accuracy achieving \\(82\\%\\) and \\(27\\%\\) on CGLM and CLOC, respectively. However, this seemingly impressive performance is coupled with an abysmally low information retention when measured by Backward Transfer with OverAdapt performing with \\(5\\%\\) and \\(1\\%\\) accuracy on CGLM and CLOC, respectively. These results demonstrate that OverAdapt is not a superior OCL algorithm but rather a product of a flawed rapid adaptation evaluation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.753, + 0.471, + 0.903 + ], + "angle": 0, + "content": "FIFO Sampling. Our analysis comparing sampling strategies reveals that models trained using the FIFO sample selection strategy with both FC-Only training (\\(\\checkmark\\)FIFO \\(\\checkmark\\)FC-Only) and full-model training (\\(\\checkmark\\)FIFO \\(\\times\\)FC-Only) achieve significantly higher accuracy of \\(82 / 78\\%\\) and \\(27 / 24\\%\\) on CGLM and CLOC, respectively, on online accuracy metric compared to those trained using uniform sampling-based with FC-Only training (\\(\\times\\)FIFO \\(\\checkmark\\)FC-Only) and full-model training (\\(\\times\\)FIFO \\(\\times\\)FC-Only). This clearly indicates that FIFO sampling is primarily responsible for the ability to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.288, + 0.892, + 0.407 + ], + "angle": 0, + "content": "leverage the latest label correlations. However, models trained with FIFO sampling achieve significantly lower accuracy of \\(5 / 7\\%\\) and \\(1 / 1\\%\\) on CGLM and CLOC, respectively, in terms of information retention as measured by backward transfer in the last timestep, performing close to a random classifier. This highlights their poor representation quality and confirms that models using the FIFO strategy simply overfit to the latest samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.407, + 0.893, + 0.657 + ], + "angle": 0, + "content": "FC-Only Training. Comparing FC-Only training (FIFO \\(\\sqrt{\\mathsf{FC}}\\)-Only) to full-model training (FIFO \\(\\times\\) FFC-Only) under FIFO sampling, we observe that FC-Only training achieves a higher accuracy of \\(82\\%\\) and \\(27\\%\\) on CGLM and CLOC, respectively, in online accuracy. However, for information retention, both models perform poorly due to the impact of FIFO sampling. In contrast full-model training under uniform sampling (XFIFO \\(\\times\\) FFC-Only) achieved a higher accuracy of \\(34\\%\\) and \\(14\\%\\) on CGLM and CLOC, respectively, for online accuracy, compared to full-model training (XFIFO \\(\\sqrt{\\mathsf{FC}}\\)-Only). Additionally, full-model training achieved \\(42\\%\\) and \\(18\\%\\) accuracy on CGLM (comparable to full-model training) and CLOC (higher than full-model training), respectively, in information retention. In general, it is not conclusive whether FC-Only training could substitute full model training, as it performed significantly better in some cases and significantly worse in others." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.807 + ], + "angle": 0, + "content": "Conclusion. Our experiments highlighted critical drawbacks in assessing the rapid adaptation of deep models using online accuracy, due to spurious label correlations in the data stream. Sensitivity analysis revealed that both FIFO sampling and FC-Only training are critical components that helped OverAdapt leverage label correlations where FIFO sampling being the primary contributor. Furthermore, our findings suggest that information retention is a useful indicator for identifying drawbacks of OCL algorithms, such as inadvertent overfitting." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.822, + 0.892, + 0.838 + ], + "angle": 0, + "content": "3.5. Removing Correlations to Evaluate Adaptation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.842, + 0.894, + 0.901 + ], + "angle": 0, + "content": "To address the limitations of online accuracy, we propose a new metric, near-future accuracy, which involves evaluating the model on near-future samples rather than immediate next samples. This can mitigate the adverse effects of label" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18856" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.209, + 0.06, + 0.765, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.273, + 0.895, + 0.355 + ], + "angle": 0, + "content": "Figure 4. Sensitivity Analysis of OverAdapt Classifier. We illustrate the performance of various components of our OverAdapt classifier on CGLM (top) and CLOC (bottom) datasets measuring: (Section 3.4) information retention (left) and rapid adaptation capability in terms of online accuracy (\\(S = 0\\), center) (Section 3.5) rapid adaptation performance in terms of online accuracy (\\(S = 0\\), center) with our proposed near-future accuracy (\\(S = 256\\) in CGLM and, \\(S = 16384\\) in CLOC). Note that information retention (left) is independent of the shift \\(S\\). The results demonstrate that introducing the shift removes label correlations, leading to dramatic loss in adaptation performance for our OverAdapt method while the uniform baseline stays unaffected." + }, + { + "type": "image", + "bbox": [ + 0.139, + 0.37, + 0.401, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.138, + 0.452, + 0.401, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.563, + 0.473, + 0.686 + ], + "angle": 0, + "content": "Figure 5. Our Evaluation Method. We compare the samples selected for evaluating adaptation performance by our evaluation method. The blue and green arrows indicate the latest batch received from the stream for learning and the samples selected for evaluation respectively. Current evaluation proposes to compute accuracy on the immediate incoming samples \\((S = 0)\\), i.e. online accuracy, while we propose to evaluate on the closest future samples \\((S = 64)\\), i.e. near-future accuracy, which is free from spurious correlations with the seen batch of images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.694, + 0.473, + 0.902 + ], + "angle": 0, + "content": "correlations on the performance by obtaining a more accurate assessment of the adaptation ability of OCL algorithms. Formulation of Proposed Evaluation. As illustrated in Figure 5, we introduce a shift \\(S\\) that represents the number of samples in the future, after which we evaluate the performance of the model. Instead of evaluating on the immediate next sample \\((\\mathbf{x}_{t + 1},\\mathbf{y}_{t + 1})\\), we use the next near-future sample after the smallest shift \\(S\\), namely \\((\\mathbf{x}_{t + 1 + S},\\mathbf{y}_{t + 1 + S})\\), so that it has no label correlation with them. We select the smallest shift \\(S\\) instead of an arbitrarily large shift \\(S\\) so that the test sample comes from the same distribution as the latest seen train samples. We calculate the online accuracy as before, where \\(\\hat{a}_t\\) is the running average of the accuracy calculated by first calculating the accuracy \\(a_{t} =\\)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.38, + 0.892, + 0.411 + ], + "angle": 0, + "content": "\\(\\mathbb{1}\\{f_{\\theta_t}(\\mathbf{x}_{t + 1 + S}) = \\mathbf{y}_{t + 1 + S}\\}\\) and then updating the running average using the formula \\(A_{t}^{RA} = \\frac{1}{t}\\left(A_{t - 1}^{RA}\\cdot (t - 1) + a_{t}\\right)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.893, + 0.619 + ], + "angle": 0, + "content": "How To Set the Shift \\( S \\)? The shift \\( S \\) is the smallest value in the future that has no label correlation with the last seen train samples. We select the smallest \\( S \\) so that the blind classifier performs similarly to a random classifier. As shown in Figure 2 for both CGLM (left) and CLOC (right) datasets, we observe that increasing the shift \\( S \\) decreases the accuracy of the blind classifier down to a similar performance of a random classifier. In particular, at a shift of \\( S = 256 \\) for CGLM and \\( S = 16384 \\) for CLOC, the label correlations are effectively eliminated. Therefore, we use these shift values for our proposed evaluation strategy. We evaluate OverAdapt and its variants on rapid adaptation with our proposed near-future accuracy and compare it with the previously adopted online accuracy \\( (S = 0) \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.619, + 0.895, + 0.854 + ], + "angle": 0, + "content": "Results. Figure 4 presents the results of OverAdapt and its variants on rapid adaptation using two metrics: online accuracy (center) and near-future accuracy (right). When studying FIFO sampling with FC-Only training (\\(\\sqrt[3]{\\mathrm{FIFO}} \\sqrt{\\mathrm{FC}}\\)-Only) and with full-model training (\\(\\sqrt{\\mathrm{FIFO}} \\times \\mathrm{FC}\\)-Only), we observe a significant drop in the performance of the methods between the two metrics that overfit using the FIFO sampling by about \\(70\\%\\) in CGLM and \\(20 - 40\\%\\) on CLOC datasets, while the performance of uniform sampling for both FC-Only training (\\(\\times \\mathrm{FIFO} \\sqrt{\\mathrm{FC}}\\)-Only) and full-model training (\\(\\times \\mathrm{FIFO} \\times \\mathrm{FC}\\)-Only) remains similar. Interestingly, the trends reverse, with the uniform sampling variants outperforming the FIFO sampling strategy by a large margin. Furthermore, we observe that FC-Only training no longer consistently improves rapid adaptation, proving to be useful in some cases on the new evaluation method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.857, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Conclusion. We propose an evaluation using near-future accuracy which removes label correlations. OverAdapt performs poorly after removing label correlations, compared" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18857" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.196 + ], + "angle": 0, + "content": "to a uniform baseline, emphasizing the importance of developing OCL algorithms that handle rapid adaptation without overfitting. Additionally, there is no surprising discrepancy between near-future accuracy and information retention across methods, unlike online accuracy. Our strategy allows for better evaluation of OCL algorithms on real-world ordered datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.211, + 0.461, + 0.229 + ], + "angle": 0, + "content": "4. OCL Evaluation by Near-Future Accuracy" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.231, + 0.473, + 0.368 + ], + "angle": 0, + "content": "In this section, we provide a comprehensive analysis of various OCL approaches under near-future accuracy. We incorporate the latest advancements in setup design into our benchmark and take computational constraints into account for fair comparison. Following the prior art [25, 26], our study assumes no memory constraints, but rather sets constraints on computational budget following [10, 25, 26]. As addressed in prior work, budgeted computation per time step implicitly imposes a limited memory access." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.376, + 0.27, + 0.392 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.473, + 0.573 + ], + "angle": 0, + "content": "Datasets and Metrics. We employ two large-scale online continual learning datasets, CGLM with a total of 460K images and CLOC compromising of 39M images in a stream, both of which contain natural distribution shifts [7]. That is to say, the images are temporally ordered. We measure rapid adaptation performance using the average accuracy on near-future samples, as described in Section 3.5, with a shift \\( S = 256 \\) for CGLM and \\( S = 16384 \\) for CLOC. The choice of both was made such that the blind classifier discussed in Section 3.2 achieves a random accuracy. Additionally, we measure information retention using the Backward Transfer metric following CLOC [7]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.574, + 0.473, + 0.677 + ], + "angle": 0, + "content": "Model and Optimization. In all experiments, we use a ResNet50 with ImageNet1K initialization unless otherwise specified. We adopt the optimization procedure from [10] and train all models using an SGD optimizer, a fixed learning rate of 0.005, and a weight decay of \\(10^{-4}\\). For both training and evaluation, we batch incoming samples with a batch size \\(\\mathcal{B}\\) of 64 for CGLM [25] and 128 for CLOC [10]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.678, + 0.473, + 0.811 + ], + "angle": 0, + "content": "Compared OCL Approaches. We evaluate five online continual learning methods using our proposed near-future accuracy. For consistency, we use uniform sampling as the sampling strategy, since it was shown in Section 3.4 that it strikes a good balance between adaptation and retention. Again, in uniform sampling, the training batch is constructed by uniformly and sampling \\(\\mathcal{B}\\) samples from all past stored data. The Appendix provides a comprehensive analysis of other sampling techniques." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.811, + 0.472, + 0.871 + ], + "angle": 0, + "content": "ER (Replay Only)[26]. ER (Replay Only) is a simple approach that stores the incoming samples and trains the model on a batch sampled from the set of stored samples. This is the leading method in offline budgeted CL [26]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.472, + 0.902 + ], + "angle": 0, + "content": "FC-Only. FC-Only, referred to as OverAdapt (XFIFO ✓FC-Only) in Section 3.4, is an adapted version of ER (Re" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.894, + 0.137 + ], + "angle": 0, + "content": "play Only) that uses a ResNet50-I1B feature extractor and trains only the last linear layer. This method has been shown to be computationally efficient [26]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.136, + 0.894, + 0.181 + ], + "angle": 0, + "content": "ACE[5]. We replace the CrossEntropy loss in ER (Replay Only) with the ACE Loss proposed in to isolate the effect of ACE loss under the proposed evaluation setting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.181, + 0.895, + 0.314 + ], + "angle": 0, + "content": "ACM[25]. ACM extracts features from a pretrained ResNet50 model (trained on ImageNet1k) and continually updates a kNN classifier, with \\( k = 2 \\) and cosine distance as distance metric, over those features. Additionally, we note that ACM does not train a deep network, thus incurring minimal computational cost. This sets the minimal accuracy requirements for OCL methods. We compare ACM with other popular fixed-feature extractor based methods like NCM [23, 24, 16] and SLDA [14] in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.314, + 0.894, + 0.387 + ], + "angle": 0, + "content": "CosineFC[15]. This approach replaces the linear layer of ResNet50 in the ER (Replay Only) baseline with a layer that computes the cosine distance between weights and features. We only perform this modification as distillation has been shown to be computationally ineffective [26]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.388, + 0.894, + 0.446 + ], + "angle": 0, + "content": "By comparing these approaches under our proposed near-future accuracy along with information retention, we aim to provide insights into the strengths and limitations of current OCL methods." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.454, + 0.785, + 0.47 + ], + "angle": 0, + "content": "4.2. Results: Varying Stream Speeds" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.472, + 0.894, + 0.531 + ], + "angle": 0, + "content": "Following prior work on fair computationally normalized evaluation of online continual learners [10], we evaluate the performance of OCL methods in two different time constraints, namely slow stream and fast stream scenarios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.895, + 0.679 + ], + "angle": 0, + "content": "Slow Stream. Slow stream is the scenario in which the computational budget for learning is not strictly limited. We enforce all methods to perform the equivalent of 10 and 5 model updates per time step on CGLM and CLOC, respectively. Methods that require a significant overhead will thus perform a fewer number of model updates such that it matches the corresponding computational budget of 10 and 5 updates on the respective datasets. Note that ACM requires negligible training cost, and therefore OCL methods must at least outperform ACM to be considered useful." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.679, + 0.895, + 0.827 + ], + "angle": 0, + "content": "Results. In Figure 6 (first row), we present the performance of various methods in terms of near-future accuracy for both CGLM and CLOC datasets. CosineFC, originally proposed for offline continual learning, achieves the highest accuracy with \\(38\\%\\) and \\(16\\%\\) accuracy on CGLM and CLOC, respectively. Furthermore, CosineFC also shows impressive information retention performance, achieving an accuracy of \\(77\\%\\) in CGLM. As expected, FC-Only which only finetunes the last linear layer, has the worst retention capabilities due to the restricted access to full-model updates." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.827, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Conclusion. Our evaluation revealed that methods not explicitly designed for adaptation in the OCL setup perform well, indicating that retaining and reusing previously seen information is crucial for achieving better generalization, and that retention and adaptation are closely linked." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18858" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.182, + 0.053, + 0.8, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.315, + 0.896, + 0.361 + ], + "angle": 0, + "content": "Figure 6. Performance of Methods on Near-Future Accuracy. We evaluate CL methods in slow and fast streams similar to [10]. Near-future accuracy, which eliminates spurious label correlations, shows that retaining and reusing past information is crucial for better generalization and that algorithms not designed for adaptation in OCL can perform well. Hence retention and adaptation are closely linked." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.382, + 0.47, + 0.485 + ], + "angle": 0, + "content": "Fast Stream. Fast stream setting refers to the scenario where the computational budget for learning is limited. That is to say, the stream presents samples at a fast rate that provides limited time for learners to train [10]. To evaluate the performance of OCL methods under this setting, we restrict the methods to only use a computation equivalent to one model update per incoming batch for both datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.471, + 0.663 + ], + "angle": 0, + "content": "Results. As shown in Figure 6 (second row), our results suggest that the two simplest baselines, namely ACM and FC-Only, achieve the highest accuracy on CGLM with \\(29\\%\\) and \\(21\\%\\), respectively. On the other hand, ACM achieves the highest information retention of \\(27\\%\\) while simple ER and CosineFC achieve the highest near-future accuracy of around \\(13\\%\\). These results indicate that the simple baseline methods outperform the more advanced OCL methods in both adaptation and information retention in this setup. This highlights that current OCL methods still have a long way to go to achieve satisfactory performance in the fast stream setting where compute is extremely limited." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.663, + 0.47, + 0.768 + ], + "angle": 0, + "content": "Conclusion. Under our proposed evaluation approach, in which spurious label correlations are removed, the fast stream setting with its limited computational budget shows that simple baselines can outperform more advanced OCL methods in both adaptation and retention. This finding emphasizes the need to develop OCL methods that can adapt rapidly in severely budgeted settings." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.775, + 0.262, + 0.79 + ], + "angle": 0, + "content": "4.3. Further Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.797, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Our benchmark of OCL methods on large-scale datasets highlights two key observations. First, the best-performing online adaptation methods often suffer from forgetting due to overfitting to label correlations, challenging the assumption that the performance gap between adaptation and retention is an inherent learning problem [6]. Our proposed near-future accuracy helps reveal label correlations and identifies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.382, + 0.895, + 0.531 + ], + "angle": 0, + "content": "whether the underlying algorithm is inadvertently exploiting them. Second, methods with better retention properties tend to generalize better and achieve improved performance on near-future accuracy in relaxed and restricted computational settings [12, 29]. This aligns well with the domain generalization literature [12] and suggests that proper training on previous samples can lead to features that generalize well across domain shifts. Finally, we consistently observe that, under limited computational settings, simpler methods outperform their more computationally involved ones." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.544, + 0.62, + 0.558 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.895, + 0.728 + ], + "angle": 0, + "content": "Our work proposes a new measure to evaluate adaptation in OCL algorithms and highlights its limitations compared to the standard online accuracy evaluation. We found that many current OCL methods overfit to idiosyncrasies of the stream rather than genuinely adapting to new data, as revealed by poor information retention. Using our proposed metric, near-future accuracy, we observed that algorithms with good retention also had better generalization and adaptation capabilities. Our proposed evaluation can serve as a sanity check for future OCL algorithms to ensure that they are not incorrectly learning spurious label correlations." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.74, + 0.688, + 0.758 + ], + "angle": 0, + "content": "6. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.899 + ], + "angle": 0, + "content": "This work was supported by the King Abdullah University of Science and Technology - Office of Sponsored Research (OSR) under Award No. OSR-CRG2021-4648, SDAIA-KAUST Center of Excellence in Data Science, Artificial Intelligence, and UKRI grant: Turing AI Fellowship EP/W002981/1. We thank the Royal Academy of Engineering and FiveAI for their support. Ser-Nam Lim from Meta AI has no relationships with the mentioned grants. Ameya Prabhu is funded by Meta AI Grant No. DFR05540." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "18859" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Rahaf Aljundi, Lucas Caccia, Eugene Belilovsky, Massimo Caccia, Laurent Charlin, and Tinne Tuytelaars. Online continual learning with maximally interfered retrieval. In Conference on Neural Information Processing Systems (NeurIPS), 2019. 2, 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.186, + 0.472, + 0.24 + ], + "angle": 0, + "content": "[2] Rahaf Aljundi, Min Lin, Baptiste Goujaud, and Yoshua Bengio. 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Torr $^{2}$ Adel Bibi $^{2\dagger}$ Bernard Ghanem $^{1\dagger}$ KAUST $^{1}$ University of Oxford $^{2}$ Meta AI $^{3}$ + +# Abstract + +We revisit the common practice of evaluating adaptation of Online Continual Learning (OCL) algorithms through the metric of online accuracy, which measures the accuracy of the model on the immediate next few samples. However, we show that this metric is unreliable, as even vacuous blind classifiers, which do not use input images for prediction, can achieve unrealistically high online accuracy by exploiting spurious label correlations in the data stream. Our study reveals that existing OCL algorithms can also achieve high online accuracy, but perform poorly in retaining useful information, suggesting that they unintentionally learn spurious label correlations. To address this issue, we propose a novel metric for measuring adaptation based on the accuracy on the near-future samples, where spurious correlations are removed. We benchmark existing OCL approaches using our proposed metric on large-scale datasets under various computational budgets and find that better generalization can be achieved by retaining and reusing past seen information. We believe that our proposed metric can aid in the development of truly adaptive OCL methods. We provide code to reproduce our results at https://github.com/drimpossible/EvalOCL. + +# 1. Introduction + +The need for learning on continuously changing data streams has led to a proliferation of research in Online Continual Learning (OCL) literature [21, 8]. The primary aim of OCL algorithms is to enable deep models to continuously adapt to new data distributions without compromising the accumulated knowledge. However, we argue that current metrics have deviated significantly from measuring true adaptation capabilities. The majority of recent works on OCL [7, 10] measure the adaptation of OCL algorithms using the metric of online accuracy, defined as the accuracy of a model on the immediate incoming samples. This evaluation practice resulted in the neglect in measuring the capacity of models to retain previous knowledge. As a consequence, several OCL algorithms achieve high online ac + +![](images/81130ff3785a1276538dafa03bb3440bf390e7d545f56878c12f024095b686f6.jpg) +Figure 1. Effect of Spurious Correlations. Current methods in OCL perform well on rapid adaptation but suffer from abysmal information retention (top). We show that these trends are due to idiosyncrasies in the data stream such as label correlations that favor methods that inadvertently overfit to the latest data. Using our proposed metric that removes these correlations (bottom), different sets of methods achieve good performance, with high information retention being key for achieving high adaptability. + +curacy [7] but poor performance on other important metrics like information retention which measure catastrophic forgetting of past seen data. Poor information retention performance has been attributed to an inherent stability-plasticity trade-off between learning new concepts and remembering old concepts [6]. However, the ability to preserve information and representations of past data, such as images of a class like the Eiffel Tower, should be crucial for accurately predicting future images of the same class, even if they were taken under novel weather conditions or camera poses. Hence, we find this justification to be unsatisfactory. + +In this paper, we demonstrate that the conventional metric of measuring online accuracy may lead to misleading conclusions about the adaptation capabilities of OCL algorithms due to the idiosyncrasies of the data stream. To support our claim, we first demonstrate that a simple blind classifier that relies solely on spurious label correlations in the stream achieves unrealistically high online accuracy on large-scale OCL datasets. Furthermore, we show that this behaviour can be exhibited by deep OCL algorithms, where we propose OverAdapt which achieves state-of-the-art performance in online accuracy despite the very poor perfor + +mance in information retention. We confirm the findings on two large-scale OCL datasets collected from different sources. This indicates that the problem is not limited to a specific dataset, but may be a general concern. + +To overcome this issue, we introduce a new metric called near-future accuracy that measures the adaptation capabilities of OCL algorithms by evaluating the accuracy on samples after a shift of $S$ steps. We choose the minimum shift $S$ which ensures that the samples no longer have spurious label correlations with the current training data. Choosing the minimum value helps minimize any distribution drift between the training and evaluation samples. The case $S = 0$ recovers the online accuracy metric in case of no spurious correlations. We observe a significant drop in performance on this metric compared to their online accuracy with several state-of-the-art OCL algorithms. This suggests that these algorithms inadvertently rely on label correlations in the stream for predictions. On the contrary, we find that algorithms designed primarily to improve information retention perform exceptionally well in our evaluation strategy. This suggests that a better generalization can be achieved by effectively retaining and reusing past information. Figure 1 illustrates that the best algorithms are those that have little discrepancy between information retention and adaptation. These results challenge current beliefs and demonstrate the importance of using a more precise measure of adaptation in evaluating OCL algorithms. + +Overall, our contributions can be summarized as follows: + +- We demonstrate that popular metrics like online accuracy can be unreliable in measuring rapid adaptation due to the presence of spurious label correlations in OCL datasets. +- We introduce a novel baseline, OverAdapt, which achieves high online accuracy by relying on label correlations, despite forgetting almost all previously seen data. +- We propose a novel metric that evaluates the adaptation capabilities of OCL algorithms by measuring accuracy on near-future samples. We select the smallest value of $S$ that removes label correlations and use this metric to evaluate state-of-the-art OCL methods. +- Our findings show that existing OCL algorithms perform poorly when evaluated using our proposed evaluation strategy. Algorithms which prevent catastrophic forgetting perform significantly better, suggesting that better adaptation performance can be achieved by retaining and reusing past seen information. + +Our results challenge the current emphasis on adapting to the latest samples and demonstrate the importance of seeking a more precise measure of adaptation. We note that our contributions are robust, with our findings valid across various OCL approaches, optimization strategies, and large-scale datasets from different sources. + +Table 1. Properties of OCL Benchmarks. We list benchmarks in the field of OCL along with the works which introduced them. We compare them across six properties: Realistic Data Streams (DO), No Storage Constraints (SC), Rapid Adaptation (RA), Information Retention (IR), Restricts Computational Budgets (CB), Evaluates on long stream sizes (LB), Leverages Pretrained Models (PT). Note that $\checkmark$ is better than $x$ in all columns. + +
DataOrderBenchmarkDOSCRAIRCBLBPT
Task-Inc.A-GEM[9]XXX✓X✓X
Class-Inc.MIR[1]XXX✓X✓X
DER[4]
BlurryGSS[2]XXX✓X✓X
RM [3]
CLIB[18]
NaturalCLEAR[20]✓X✓✓XX✓
BudgetCL[26]X✓X✓✓X✓
CLOC[7]✓X✓XX✓X
DelayOCL[10]✓X✓X✓✓✓
ACM[25]✓✓✓✓✓✓✓
+ +# 2. OCL Evaluation: A Review + +We start with an overview of benchmarks in OCL across different properties of interest. For a more detailed review of the literature, we refer the reader to [30]. + +1. Realistic Data Streams (DO). The OCL community has been moving towards increasingly realistic benchmarks in terms of data ordering and task setup. Early works [21, 9] assumed access to which subset of classes a test sample is from (task-incremental setup). Subsequent work removed this constraint, requiring models to predict across all seen classes so far (class-incremental setup) [2, 1]. However, these works used incoming samples from disjoint data distributions with artificial task boundaries, resulting in unrealistic ordering. Recent works [3, 18, 26] improved the ordering by mixing samples from different disjoint tasks. Latest works [7, 25, 20] eliminate the need for generating artificial data streams simply by using real-world timestamps to order the data stream. Our work focuses on these real-world data streams on large-scale datasets. + +2. Towards No Storage Constraints (SC). The majority of prior benchmarks on continual learning constrain the problem by prohibiting access to previously received data [19, 17], with only a small portion of data allowed to be stored in memory [21, 8, 4, 2, 18, 20]. This constraint is often justified by two reasons: (i) storage space is expensive and (ii) access to previous data is prohibited due to privacy constraints. However, recent work [25, 26] shows critical shortcomings of these justifications. They show that (a) storage costs are negligible compared to the computational costs of training a model, and (b) simply restricting access to previous data does not address privacy considerations, as samples can be reconstructed from model weights [13] or detectably change the model output [28]. Interestingly, Goel et al. [11] shows that removing data from the model can be done by catastrophic forgetting, which is antithetical to the objective of OCL approaches. Hence, we do not impose any memory constraints on our evaluation. + +3. Towards Better Information Retention (IR). Interestingly, most of the previous benchmarks in OCL focus on preventing catastrophic forgetting of previously learned information, rather than evaluating the ability of models to rapidly learn new concepts [21, 27, 9, 3, 2, 20]. This emphasis on information retention can be attributed to disjoint set-based data ordering, which often involves little to no change in distribution for most of the stream, making it difficult to evaluate rapid adaptation. However, recent works have shifted their focus to rapid adaptation performance in real-world ordered data streams [7, 10]. In our benchmark, our objective is to maintain an additional high degree of retained knowledge from past data as demonstrated in [25, 6]. +4. Towards Enabling Rapid Adaptation (RA). The goal of online continual learning algorithms is to rapidly adapt to incoming data from changing distributions. Similarly to past work [25, 7, 10], we place a strong emphasis on achieving this goal with better metrics. +5. Towards Computational Budgets (CB). Continual learning without memory constraints is primarily a problem of achieving high performance with computational efficiency, as retraining from scratch is an ideal solution to the problem. This setting addresses the real-world problem of reducing the cost of updating a given model with incoming data from a stream [25]. We evaluate OCL approaches under the maximum computational budget for fairness [10], testing across two different budgets. +6. Towards Large-Scale OCL (LB). OCL benchmarks have historically focused on learning over samples incoming from a stream over long data streams since the development of GEM [21]. Recent OCL benchmarks [2, 18, 25] have preserved this useful characteristic, while scaling up to larger and more complex data streams. In this work, we use two large-scale OCL benchmarks: Continual Google LandMarks (CGLM) [25] and Continual Localization (CLOC) [7]. CGLM is a landmark classification dataset that consists of a long-tailed distribution with 10,788 classes that simulate images that arrive on a Wikimedia Commons server. CLOC is a dataset focused on geolocation at scale consisting of 713 classes with 39M images simulating images arriving on a Flickr server. As these datasets come from two different sources, the issue of label correlation that we observe is likely to be a repeating pattern across future OCL datasets. +7. Leveraging Pretraining for Effective OCL (PT). Traditional methods in online continual learning start with randomly initialized models [21, 1]. However, continual learning approaches can leverage the abundance of large-scale pretrained models to improve computational efficiency [24, 31, 25]. We focus on an evaluation setting that starts with ImageNet1K pretrained models to allow approaches to leverage pretrained information. + +# 3. Correcting Evaluations of Rapid Adaptation + +We delve into our exploration of the limitations of using online accuracy as a metric to measure adaptation to distribution shifts and present our efforts to alleviate the shortcomings of this metric. We start by identifying the label correlations that affect online accuracy, and then we unveil a technique that enables deep networks to artificially achieve high performance on this metric. This highlights the dependence of the networks on these label correlations. Finally, we introduce a novel evaluation metric, near-future accuracy, and a test to detect and remove label correlations allowing for accurate measurement of the effectiveness of OCL methods in rapidly adapting to new distributions. + +# 3.1. Evaluating OCL: A Problem Formulation + +In traditional OCL setups with real-world stream orders [7, 25], the learner is fed a continuous stream of training samples over time steps $t \in \{1, 2, \dots, \infty\}$ , consisting of an input datapoint $\mathbf{x}_t \in \mathcal{X}$ and its corresponding label $\mathbf{y}_t \in \mathcal{Y}$ where $(\mathbf{x}_t, \mathbf{y}_t) \sim \mathcal{D}_{j \leq t}$ . The distribution $\mathcal{D}_j$ can change at any stream timestep. The aim is to train a classifier $f_{\theta_t}: \mathcal{X} \to \mathcal{Y}$ at any given $t$ , which accurately maps a new sample $\mathbf{x}$ to its label $\mathbf{y}$ while adapting to the latest information and incorporating it with the historical knowledge acquired from previous data. + +To evaluate the adaptation ability of $f_{\theta_t}$ , online accuracy measures the performance on the next unseen sample, $(\mathbf{x}_{t + 1},\mathbf{y}_{t + 1})$ , i.e., $a_{t} = \mathbb{1}\{f_{\theta_{t}}(\mathbf{x}_{t + 1}) = \mathbf{y}_{t + 1}\}$ . Online accuracy is updated in an online fashion given by $A_{t}^{RA} = \frac{1}{t}\left(A_{t - 1}^{RA}\cdot (t - 1) + a_{t}\right)$ . For OCL approaches training deep networks, the running average is updated on a batch $\mathcal{B}$ of the next unseen samples as opposed to a single sample. After the evaluation is carried out, the model $f_{\theta_i}$ is updated using the same samples. + +The ability of $f_{\theta_t}$ to retain information is measured by evaluating its accuracy on an unseen test stream that is similar to the training stream. In particular, per time step $t$ , the model trained at the end of step $t$ is evaluated on all test samples from step 0 to step $t$ . We measure Backward Transfer @ $T$ [7] where $T$ is the last time step of the stream. That is to say, the model at the last step of the stream is evaluated on an increasing test test from step 0 to the end of the stream. However, traditional OCL methods targeting natural distribution shifts have neglected this metric [7, 10]. + +# 3.2. Isolating and Quantifying Label Correlations + +Our objective is to investigate whether using online accuracy to measure adaptation in OCL suffers from drawbacks due to label correlations. To accomplish this, we introduce a very simple algorithm that leverages label correlations and performs well in terms of online accuracy. + +Blind Classifier. We define a blind classifier, similar to prior works [7, 25], as a model that predicts the mode of the last $\kappa$ samples seen without access to the input images. Formally, at a given new step $t$ , the blind classifier + +![](images/0b0c220c4da0d9d125da11da0d352f7ee6d9020b90620b0019831cd75bfc0768.jpg) +Figure 2. Blind Classifier. Performance of a blind classifier on the CGLM (left) and CLOC (right) datasets across varying shift $S$ towards future for selecting evaluation samples alongside the optimal context window size $k$ for the selected shift. (Section 3.2) A blind classifier achieves unrealistically high accuracy on current evaluation of adaptation (dark blue line, $S = 0$ ) on both datasets despite being a trivial baseline. (Section 3.5) The accuracy of the blind classifier on incoming samples with increasing shift $S$ into the future decreases significantly, eventually converging to near-random performance, indicating a lack of label correlations to the current training samples. + +![](images/4bbbe4879373d96cc0cddab106031abf725d28ae50093f7b9d8b54d1f701f933.jpg) + +predicts the class of $\mathbf{x}_t$ as the mode of the last revealed labels $\cup_{j=1,\dots,k}\{\mathbf{y}_{t-j}\}$ . The optimal context window size $\mathcal{K}$ is selected by a search over different sizes on the hyperparameter search set. + +Results. We present the performance of the blind classifier on the online accuracy in Figure 2. For this section, we focus solely on measuring online accuracy (indicated by the topmost purple line). Our results indicate that the blind classifier performs remarkably well achieving an average accuracy of $50\%$ on the CGLM dataset, which consists of 10,788 classes, using only the labels of the last seen training sample $(\mathcal{K} = 1)$ . Moreover, the blind classifier achieves $17\%$ on the large-scale CLOC dataset consisting of 718 classes with $\mathcal{K} = 10$ achieving the best performance. These findings suggest an unusually high degree of label correlation between the past 1-10 samples and the immediate incoming sample in the data stream, especially given that the blind classifier achieves $50\%$ and $17\%$ accuracy, while the random baseline achieves $0.01\%$ and $2\%$ on CGLM and CLOC datasets, respectively. + +Conclusion. Despite having never processed any input images, the blind classifier achieves a remarkably high online accuracy. This is surprising because it was expected to perform no better than a random classifier. However, it achieves this result by exploiting the label correlations present in OCL datasets. This is a critical drawback in using online accuracy to measure adaptation. In the following sections, we will delve deeper into this issue. + +# 3.3. Can Deep Networks Learn Label Correlations? + +After demonstrating the effectiveness of the blind classifier in exploiting label correlations in the two large-scale datasets used in OCL settings, a pertinent inquiry arises: Can deep networks inadvertently learn these same label correlations leading to unreasonably high online accuracies? This question warrants investigation to determine to what extent deep OCL algorithms can leverage label correlations and the impact this may have on their performance. + +An Overfitting-Based Baseline. One approach for DNNs + +to exploit label correlations is by overfitting to recent data. We investigate algorithmic choices for designing an OCL method that can overfit the most recent labels in a data stream. Specifically, we make two important design choices for our baseline: (i) we update the model only on recent data to achieve overfitting while sacrificing most of the useful information from the past. To this end, we adopt FIFO sampling, a widely-used technique in OCL, to select batches of samples for training. (ii) We fix the feature representations and train only the last linear layer to prevent degradation of feature representations due to overfitting. To improve the quality of the representations, we use a ResNet50 model pretrained on Instagram1B [22]. We refer to this model as OverAdapt. OverAdapt is computationally efficient since training the Linear layer over multiple updates is relatively inexpensive. Moreover, we adopt the fast stream evaluation setting [10], i.e. a setting with a strictly limited computational budget. We set the upper bound for the computation to one gradient update per incoming batch of samples for all methods with no restrictions on storage space. + +Results. We present the results of the proposed OverAdapt compared to state-of-the-art OCL methods trained using an ImageNet1K pretrained ResNet50 model on the CGLM and CLOC datasets in Figure 3. OverAdapt achieves remarkable performance, surpassing the best-performing method ACM on the CGLM dataset by more than $30\%$ , and outperforming all but the ACM baseline on the CLOC dataset by $10 - 35\%$ . Notably, OverAdapt achieves an impressive $80\%$ accuracy on the CGLM dataset. + +Conclusion. After demonstrating that OverAdapt can effectively leverage label correlations from the data stream, we conclude that traditional design choices like the FIFO buffer in past OCL setups [7] improved overfitting to the next sample. It is worrying that future work or existing works could have inadvertently made similar choices leading to perceived improvement in algorithms when instead it is a subtle case of overfitting to the online accuracy metric. We further ensure the validity of our conclusions by investigating whether the effectiveness of this model is due to + +![](images/8858ba35790bcb9403096c5e925093ae9a6c89d6d946e797fc07af8feed50782.jpg) +Figure 3. OverAdapt Classifier. We compare the adaptation performance of our OverAdapt classifier on CGLM (left) and CLOC (right) datasets using online accuracy as a measure. The three top performing OCL methods on CLOC are benchmarked on the CGLM dataset. We see that OverAdapt outperforms recent OCL methods by a large margin of $10 - 40\%$ in accuracy. + +a good training algorithm or to potential limitations of the evaluation metric. We explore this in the next subsections. + +# 3.4. Exploring Properties of OverAdapt + +We investigate the reasons behind the impressive performance of our proposed OverAdapt. + +Sensitivity Analysis. We start with the sensitivity study of OverAdapt by analyzing the impact of modifying its two key components: (i) FC-Only training with large-data pretrained initialization and (ii) FIFO Sampling. To study the effect of FC-Only training, we replace it with full-model training using an ImageNet1K-pretrained ResNet50 which has been common in prior OCL work [10]. We also analyze the effect of FIFO sample selection by comparing it with uniform sampling, which has been shown to be a simple but effective strategy in limited-compute regimes [26]. We evaluate their performance in terms of online accuracy and information retention at time $T$ after training on the entire stream following prior art [7] as discussed in Section 3.1. + +Results. Our results are shown in Figure 4 (left & center). + +OverAdapt. Strikingly, our analysis reveals that OverAdapt (✓FIFO ✓FC-Only) achieves remarkable performance in rapid adaptation as measured by online accuracy achieving $82\%$ and $27\%$ on CGLM and CLOC, respectively. However, this seemingly impressive performance is coupled with an abysmally low information retention when measured by Backward Transfer with OverAdapt performing with $5\%$ and $1\%$ accuracy on CGLM and CLOC, respectively. These results demonstrate that OverAdapt is not a superior OCL algorithm but rather a product of a flawed rapid adaptation evaluation. + +FIFO Sampling. Our analysis comparing sampling strategies reveals that models trained using the FIFO sample selection strategy with both FC-Only training ( $\checkmark$ FIFO $\checkmark$ FC-Only) and full-model training ( $\checkmark$ FIFO $\times$ FC-Only) achieve significantly higher accuracy of $82 / 78\%$ and $27 / 24\%$ on CGLM and CLOC, respectively, on online accuracy metric compared to those trained using uniform sampling-based with FC-Only training ( $\times$ FIFO $\checkmark$ FC-Only) and full-model training ( $\times$ FIFO $\times$ FC-Only). This clearly indicates that FIFO sampling is primarily responsible for the ability to + +leverage the latest label correlations. However, models trained with FIFO sampling achieve significantly lower accuracy of $5 / 7\%$ and $1 / 1\%$ on CGLM and CLOC, respectively, in terms of information retention as measured by backward transfer in the last timestep, performing close to a random classifier. This highlights their poor representation quality and confirms that models using the FIFO strategy simply overfit to the latest samples. + +FC-Only Training. Comparing FC-Only training (FIFO $\sqrt{\mathsf{FC}}$ -Only) to full-model training (FIFO $\times$ FFC-Only) under FIFO sampling, we observe that FC-Only training achieves a higher accuracy of $82\%$ and $27\%$ on CGLM and CLOC, respectively, in online accuracy. However, for information retention, both models perform poorly due to the impact of FIFO sampling. In contrast full-model training under uniform sampling (XFIFO $\times$ FFC-Only) achieved a higher accuracy of $34\%$ and $14\%$ on CGLM and CLOC, respectively, for online accuracy, compared to full-model training (XFIFO $\sqrt{\mathsf{FC}}$ -Only). Additionally, full-model training achieved $42\%$ and $18\%$ accuracy on CGLM (comparable to full-model training) and CLOC (higher than full-model training), respectively, in information retention. In general, it is not conclusive whether FC-Only training could substitute full model training, as it performed significantly better in some cases and significantly worse in others. + +Conclusion. Our experiments highlighted critical drawbacks in assessing the rapid adaptation of deep models using online accuracy, due to spurious label correlations in the data stream. Sensitivity analysis revealed that both FIFO sampling and FC-Only training are critical components that helped OverAdapt leverage label correlations where FIFO sampling being the primary contributor. Furthermore, our findings suggest that information retention is a useful indicator for identifying drawbacks of OCL algorithms, such as inadvertent overfitting. + +# 3.5. Removing Correlations to Evaluate Adaptation + +To address the limitations of online accuracy, we propose a new metric, near-future accuracy, which involves evaluating the model on near-future samples rather than immediate next samples. This can mitigate the adverse effects of label + +![](images/e9093ca2cfb006856a4e21f74e18a81bcaaf1d31606963db24f751de578a4c38.jpg) +Figure 4. Sensitivity Analysis of OverAdapt Classifier. We illustrate the performance of various components of our OverAdapt classifier on CGLM (top) and CLOC (bottom) datasets measuring: (Section 3.4) information retention (left) and rapid adaptation capability in terms of online accuracy ( $S = 0$ , center) (Section 3.5) rapid adaptation performance in terms of online accuracy ( $S = 0$ , center) with our proposed near-future accuracy ( $S = 256$ in CGLM and, $S = 16384$ in CLOC). Note that information retention (left) is independent of the shift $S$ . The results demonstrate that introducing the shift removes label correlations, leading to dramatic loss in adaptation performance for our OverAdapt method while the uniform baseline stays unaffected. + +![](images/66e6d652baed9b76535ebd0e5c171189fe43d5ffbfcf440a4499d382d6b45b14.jpg) + +![](images/3dcbbf70790dd92f8680e83547efad6f7c5c9407ff337710c5b698f0fe01abac.jpg) +Figure 5. Our Evaluation Method. We compare the samples selected for evaluating adaptation performance by our evaluation method. The blue and green arrows indicate the latest batch received from the stream for learning and the samples selected for evaluation respectively. Current evaluation proposes to compute accuracy on the immediate incoming samples $(S = 0)$ , i.e. online accuracy, while we propose to evaluate on the closest future samples $(S = 64)$ , i.e. near-future accuracy, which is free from spurious correlations with the seen batch of images. + +correlations on the performance by obtaining a more accurate assessment of the adaptation ability of OCL algorithms. Formulation of Proposed Evaluation. As illustrated in Figure 5, we introduce a shift $S$ that represents the number of samples in the future, after which we evaluate the performance of the model. Instead of evaluating on the immediate next sample $(\mathbf{x}_{t + 1},\mathbf{y}_{t + 1})$ , we use the next near-future sample after the smallest shift $S$ , namely $(\mathbf{x}_{t + 1 + S},\mathbf{y}_{t + 1 + S})$ , so that it has no label correlation with them. We select the smallest shift $S$ instead of an arbitrarily large shift $S$ so that the test sample comes from the same distribution as the latest seen train samples. We calculate the online accuracy as before, where $\hat{a}_t$ is the running average of the accuracy calculated by first calculating the accuracy $a_{t} =$ + +$\mathbb{1}\{f_{\theta_t}(\mathbf{x}_{t + 1 + S}) = \mathbf{y}_{t + 1 + S}\}$ and then updating the running average using the formula $A_{t}^{RA} = \frac{1}{t}\left(A_{t - 1}^{RA}\cdot (t - 1) + a_{t}\right)$ . + +How To Set the Shift $S$ ? The shift $S$ is the smallest value in the future that has no label correlation with the last seen train samples. We select the smallest $S$ so that the blind classifier performs similarly to a random classifier. As shown in Figure 2 for both CGLM (left) and CLOC (right) datasets, we observe that increasing the shift $S$ decreases the accuracy of the blind classifier down to a similar performance of a random classifier. In particular, at a shift of $S = 256$ for CGLM and $S = 16384$ for CLOC, the label correlations are effectively eliminated. Therefore, we use these shift values for our proposed evaluation strategy. We evaluate OverAdapt and its variants on rapid adaptation with our proposed near-future accuracy and compare it with the previously adopted online accuracy $(S = 0)$ . + +Results. Figure 4 presents the results of OverAdapt and its variants on rapid adaptation using two metrics: online accuracy (center) and near-future accuracy (right). When studying FIFO sampling with FC-Only training ( $\sqrt[3]{\mathrm{FIFO}} \sqrt{\mathrm{FC}}$ -Only) and with full-model training ( $\sqrt{\mathrm{FIFO}} \times \mathrm{FC}$ -Only), we observe a significant drop in the performance of the methods between the two metrics that overfit using the FIFO sampling by about $70\%$ in CGLM and $20 - 40\%$ on CLOC datasets, while the performance of uniform sampling for both FC-Only training ( $\times \mathrm{FIFO} \sqrt{\mathrm{FC}}$ -Only) and full-model training ( $\times \mathrm{FIFO} \times \mathrm{FC}$ -Only) remains similar. Interestingly, the trends reverse, with the uniform sampling variants outperforming the FIFO sampling strategy by a large margin. Furthermore, we observe that FC-Only training no longer consistently improves rapid adaptation, proving to be useful in some cases on the new evaluation method. + +Conclusion. We propose an evaluation using near-future accuracy which removes label correlations. OverAdapt performs poorly after removing label correlations, compared + +to a uniform baseline, emphasizing the importance of developing OCL algorithms that handle rapid adaptation without overfitting. Additionally, there is no surprising discrepancy between near-future accuracy and information retention across methods, unlike online accuracy. Our strategy allows for better evaluation of OCL algorithms on real-world ordered datasets. + +# 4. OCL Evaluation by Near-Future Accuracy + +In this section, we provide a comprehensive analysis of various OCL approaches under near-future accuracy. We incorporate the latest advancements in setup design into our benchmark and take computational constraints into account for fair comparison. Following the prior art [25, 26], our study assumes no memory constraints, but rather sets constraints on computational budget following [10, 25, 26]. As addressed in prior work, budgeted computation per time step implicitly imposes a limited memory access. + +# 4.1. Experimental Setup + +Datasets and Metrics. We employ two large-scale online continual learning datasets, CGLM with a total of 460K images and CLOC compromising of 39M images in a stream, both of which contain natural distribution shifts [7]. That is to say, the images are temporally ordered. We measure rapid adaptation performance using the average accuracy on near-future samples, as described in Section 3.5, with a shift $S = 256$ for CGLM and $S = 16384$ for CLOC. The choice of both was made such that the blind classifier discussed in Section 3.2 achieves a random accuracy. Additionally, we measure information retention using the Backward Transfer metric following CLOC [7]. + +Model and Optimization. In all experiments, we use a ResNet50 with ImageNet1K initialization unless otherwise specified. We adopt the optimization procedure from [10] and train all models using an SGD optimizer, a fixed learning rate of 0.005, and a weight decay of $10^{-4}$ . For both training and evaluation, we batch incoming samples with a batch size $\mathcal{B}$ of 64 for CGLM [25] and 128 for CLOC [10]. + +Compared OCL Approaches. We evaluate five online continual learning methods using our proposed near-future accuracy. For consistency, we use uniform sampling as the sampling strategy, since it was shown in Section 3.4 that it strikes a good balance between adaptation and retention. Again, in uniform sampling, the training batch is constructed by uniformly and sampling $\mathcal{B}$ samples from all past stored data. The Appendix provides a comprehensive analysis of other sampling techniques. + +ER (Replay Only)[26]. ER (Replay Only) is a simple approach that stores the incoming samples and trains the model on a batch sampled from the set of stored samples. This is the leading method in offline budgeted CL [26]. + +FC-Only. FC-Only, referred to as OverAdapt (XFIFO ✓FC-Only) in Section 3.4, is an adapted version of ER (Re + +play Only) that uses a ResNet50-I1B feature extractor and trains only the last linear layer. This method has been shown to be computationally efficient [26]. + +ACE[5]. We replace the CrossEntropy loss in ER (Replay Only) with the ACE Loss proposed in to isolate the effect of ACE loss under the proposed evaluation setting. + +ACM[25]. ACM extracts features from a pretrained ResNet50 model (trained on ImageNet1k) and continually updates a kNN classifier, with $k = 2$ and cosine distance as distance metric, over those features. Additionally, we note that ACM does not train a deep network, thus incurring minimal computational cost. This sets the minimal accuracy requirements for OCL methods. We compare ACM with other popular fixed-feature extractor based methods like NCM [23, 24, 16] and SLDA [14] in the Appendix. + +CosineFC[15]. This approach replaces the linear layer of ResNet50 in the ER (Replay Only) baseline with a layer that computes the cosine distance between weights and features. We only perform this modification as distillation has been shown to be computationally ineffective [26]. + +By comparing these approaches under our proposed near-future accuracy along with information retention, we aim to provide insights into the strengths and limitations of current OCL methods. + +# 4.2. Results: Varying Stream Speeds + +Following prior work on fair computationally normalized evaluation of online continual learners [10], we evaluate the performance of OCL methods in two different time constraints, namely slow stream and fast stream scenarios. + +Slow Stream. Slow stream is the scenario in which the computational budget for learning is not strictly limited. We enforce all methods to perform the equivalent of 10 and 5 model updates per time step on CGLM and CLOC, respectively. Methods that require a significant overhead will thus perform a fewer number of model updates such that it matches the corresponding computational budget of 10 and 5 updates on the respective datasets. Note that ACM requires negligible training cost, and therefore OCL methods must at least outperform ACM to be considered useful. + +Results. In Figure 6 (first row), we present the performance of various methods in terms of near-future accuracy for both CGLM and CLOC datasets. CosineFC, originally proposed for offline continual learning, achieves the highest accuracy with $38\%$ and $16\%$ accuracy on CGLM and CLOC, respectively. Furthermore, CosineFC also shows impressive information retention performance, achieving an accuracy of $77\%$ in CGLM. As expected, FC-Only which only finetunes the last linear layer, has the worst retention capabilities due to the restricted access to full-model updates. + +Conclusion. Our evaluation revealed that methods not explicitly designed for adaptation in the OCL setup perform well, indicating that retaining and reusing previously seen information is crucial for achieving better generalization, and that retention and adaptation are closely linked. + +![](images/a62739252ca9211a1419e9618818edd7a45b9ccff7537437cf4f4438a6addf30.jpg) +Figure 6. Performance of Methods on Near-Future Accuracy. We evaluate CL methods in slow and fast streams similar to [10]. Near-future accuracy, which eliminates spurious label correlations, shows that retaining and reusing past information is crucial for better generalization and that algorithms not designed for adaptation in OCL can perform well. Hence retention and adaptation are closely linked. + +Fast Stream. Fast stream setting refers to the scenario where the computational budget for learning is limited. That is to say, the stream presents samples at a fast rate that provides limited time for learners to train [10]. To evaluate the performance of OCL methods under this setting, we restrict the methods to only use a computation equivalent to one model update per incoming batch for both datasets. + +Results. As shown in Figure 6 (second row), our results suggest that the two simplest baselines, namely ACM and FC-Only, achieve the highest accuracy on CGLM with $29\%$ and $21\%$ , respectively. On the other hand, ACM achieves the highest information retention of $27\%$ while simple ER and CosineFC achieve the highest near-future accuracy of around $13\%$ . These results indicate that the simple baseline methods outperform the more advanced OCL methods in both adaptation and information retention in this setup. This highlights that current OCL methods still have a long way to go to achieve satisfactory performance in the fast stream setting where compute is extremely limited. + +Conclusion. Under our proposed evaluation approach, in which spurious label correlations are removed, the fast stream setting with its limited computational budget shows that simple baselines can outperform more advanced OCL methods in both adaptation and retention. This finding emphasizes the need to develop OCL methods that can adapt rapidly in severely budgeted settings. + +# 4.3. Further Discussion + +Our benchmark of OCL methods on large-scale datasets highlights two key observations. First, the best-performing online adaptation methods often suffer from forgetting due to overfitting to label correlations, challenging the assumption that the performance gap between adaptation and retention is an inherent learning problem [6]. Our proposed near-future accuracy helps reveal label correlations and identifies + +whether the underlying algorithm is inadvertently exploiting them. Second, methods with better retention properties tend to generalize better and achieve improved performance on near-future accuracy in relaxed and restricted computational settings [12, 29]. This aligns well with the domain generalization literature [12] and suggests that proper training on previous samples can lead to features that generalize well across domain shifts. Finally, we consistently observe that, under limited computational settings, simpler methods outperform their more computationally involved ones. + +# 5. Conclusion + +Our work proposes a new measure to evaluate adaptation in OCL algorithms and highlights its limitations compared to the standard online accuracy evaluation. We found that many current OCL methods overfit to idiosyncrasies of the stream rather than genuinely adapting to new data, as revealed by poor information retention. Using our proposed metric, near-future accuracy, we observed that algorithms with good retention also had better generalization and adaptation capabilities. Our proposed evaluation can serve as a sanity check for future OCL algorithms to ensure that they are not incorrectly learning spurious label correlations. + +# 6. Acknowledgements + +This work was supported by the King Abdullah University of Science and Technology - Office of Sponsored Research (OSR) under Award No. OSR-CRG2021-4648, SDAIA-KAUST Center of Excellence in Data Science, Artificial Intelligence, and UKRI grant: Turing AI Fellowship EP/W002981/1. We thank the Royal Academy of Engineering and FiveAI for their support. Ser-Nam Lim from Meta AI has no relationships with the mentioned grants. Ameya Prabhu is funded by Meta AI Grant No. DFR05540. + +# References + +[1] Rahaf Aljundi, Lucas Caccia, Eugene Belilovsky, Massimo Caccia, Laurent Charlin, and Tinne Tuytelaars. Online continual learning with maximally interfered retrieval. In Conference on Neural Information Processing Systems (NeurIPS), 2019. 2, 3 +[2] Rahaf Aljundi, Min Lin, Baptiste Goujaud, and Yoshua Bengio. Gradient based sample selection for online continual learning. In Conference on Neural Information Processing Systems (NeurIPS), 2019. 2, 3 +[3] Jihwan Bang, Heesu Kim, YoungJoon Yoo, Jung-Woo Ha, and Jonghyun Choi. Rainbow memory: Continual learning with a memory of diverse samples. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2021. 2, 3 +[4] Pietro Buzzega, Matteo Boschini, Angelo Porrello, Davide Abati, and Simone Calderara. Dark experience for general continual learning: a strong, simple baseline. 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However, we show that this metric is unreliable, as even vacuous blind classifiers, which do not use input images for prediction, can achieve unrealistically high online accuracy by exploiting spurious label correlations in the data stream. Our study reveals that existing OCL algorithms can also achieve high online accuracy, but perform poorly in retaining useful information, suggesting that they unintentionally learn spurious label correlations. To address this issue, we propose a novel metric for measuring adaptation based on the accuracy on the near-future samples, where spurious correlations are removed. We benchmark existing OCL approaches using our proposed metric on large-scale datasets under various computational budgets and find that better generalization can be achieved by retaining and reusing past seen information. We believe that our proposed metric can aid in the development of truly adaptive OCL methods. We provide code to reproduce our results at https://github.com/drimpossible/EvalOCL." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 499, + 128, + 512 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 499, + 128, + 512 + ], + "spans": [ + { + "bbox": [ + 47, + 499, + 128, + 512 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 520, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 287, + 685 + ], + "type": "text", + "content": "The need for learning on continuously changing data streams has led to a proliferation of research in Online Continual Learning (OCL) literature [21, 8]. The primary aim of OCL algorithms is to enable deep models to continuously adapt to new data distributions without compromising the accumulated knowledge. However, we argue that current metrics have deviated significantly from measuring true adaptation capabilities. The majority of recent works on OCL [7, 10] measure the adaptation of OCL algorithms using the metric of online accuracy, defined as the accuracy of a model on the immediate incoming samples. This evaluation practice resulted in the neglect in measuring the capacity of models to retain previous knowledge. As a consequence, several OCL algorithms achieve high online ac" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 331, + 204, + 520, + 355 + ], + "blocks": [ + { + "bbox": [ + 331, + 204, + 520, + 355 + ], + "lines": [ + { + "bbox": [ + 331, + 204, + 520, + 355 + ], + "spans": [ + { + "bbox": [ + 331, + 204, + 520, + 355 + ], + "type": "image", + "image_path": "81130ff3785a1276538dafa03bb3440bf390e7d545f56878c12f024095b686f6.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 357, + 547, + 445 + ], + "lines": [ + { + "bbox": [ + 305, + 357, + 547, + 445 + ], + "spans": [ + { + "bbox": [ + 305, + 357, + 547, + 445 + ], + "type": "text", + "content": "Figure 1. Effect of Spurious Correlations. Current methods in OCL perform well on rapid adaptation but suffer from abysmal information retention (top). We show that these trends are due to idiosyncrasies in the data stream such as label correlations that favor methods that inadvertently overfit to the latest data. Using our proposed metric that removes these correlations (bottom), different sets of methods achieve good performance, with high information retention being key for achieving high adaptability." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 453, + 546, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 546, + 583 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 546, + 583 + ], + "type": "text", + "content": "curacy [7] but poor performance on other important metrics like information retention which measure catastrophic forgetting of past seen data. Poor information retention performance has been attributed to an inherent stability-plasticity trade-off between learning new concepts and remembering old concepts [6]. However, the ability to preserve information and representations of past data, such as images of a class like the Eiffel Tower, should be crucial for accurately predicting future images of the same class, even if they were taken under novel weather conditions or camera poses. Hence, we find this justification to be unsatisfactory." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 584, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 584, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 584, + 547, + 715 + ], + "type": "text", + "content": "In this paper, we demonstrate that the conventional metric of measuring online accuracy may lead to misleading conclusions about the adaptation capabilities of OCL algorithms due to the idiosyncrasies of the data stream. To support our claim, we first demonstrate that a simple blind classifier that relies solely on spurious label correlations in the stream achieves unrealistically high online accuracy on large-scale OCL datasets. Furthermore, we show that this behaviour can be exhibited by deep OCL algorithms, where we propose OverAdapt which achieves state-of-the-art performance in online accuracy despite the very poor perfor" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 693, + 245, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 693, + 245, + 703 + ], + "spans": [ + { + "bbox": [ + 57, + 693, + 245, + 703 + ], + "type": "text", + "content": "* authors contributed equally; order decided by a coin flip." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 60, + 703, + 121, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 703, + 121, + 712 + ], + "spans": [ + { + "bbox": [ + 60, + 703, + 121, + 712 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 60, + 703, + 121, + 712 + ], + "type": "text", + "content": " equal supervision" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18852" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": "mance in information retention. We confirm the findings on two large-scale OCL datasets collected from different sources. This indicates that the problem is not limited to a specific dataset, but may be a general concern." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 122, + 289, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 122, + 289, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 122, + 289, + 392 + ], + "type": "text", + "content": "To overcome this issue, we introduce a new metric called near-future accuracy that measures the adaptation capabilities of OCL algorithms by evaluating the accuracy on samples after a shift of " + }, + { + "bbox": [ + 46, + 122, + 289, + 392 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 122, + 289, + 392 + ], + "type": "text", + "content": " steps. We choose the minimum shift " + }, + { + "bbox": [ + 46, + 122, + 289, + 392 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 122, + 289, + 392 + ], + "type": "text", + "content": " which ensures that the samples no longer have spurious label correlations with the current training data. Choosing the minimum value helps minimize any distribution drift between the training and evaluation samples. The case " + }, + { + "bbox": [ + 46, + 122, + 289, + 392 + ], + "type": "inline_equation", + "content": "S = 0" + }, + { + "bbox": [ + 46, + 122, + 289, + 392 + ], + "type": "text", + "content": " recovers the online accuracy metric in case of no spurious correlations. We observe a significant drop in performance on this metric compared to their online accuracy with several state-of-the-art OCL algorithms. This suggests that these algorithms inadvertently rely on label correlations in the stream for predictions. On the contrary, we find that algorithms designed primarily to improve information retention perform exceptionally well in our evaluation strategy. This suggests that a better generalization can be achieved by effectively retaining and reusing past information. Figure 1 illustrates that the best algorithms are those that have little discrepancy between information retention and adaptation. These results challenge current beliefs and demonstrate the importance of using a more precise measure of adaptation in evaluating OCL algorithms." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 395, + 279, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 395, + 279, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 395, + 279, + 406 + ], + "type": "text", + "content": "Overall, our contributions can be summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 418, + 287, + 631 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 47, + 418, + 287, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 418, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 418, + 287, + 453 + ], + "type": "text", + "content": "- We demonstrate that popular metrics like online accuracy can be unreliable in measuring rapid adaptation due to the presence of spurious label correlations in OCL datasets." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 458, + 287, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 458, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 47, + 458, + 287, + 493 + ], + "type": "text", + "content": "- We introduce a novel baseline, OverAdapt, which achieves high online accuracy by relying on label correlations, despite forgetting almost all previously seen data." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 498, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 287, + 555 + ], + "type": "text", + "content": "- We propose a novel metric that evaluates the adaptation capabilities of OCL algorithms by measuring accuracy on near-future samples. We select the smallest value of " + }, + { + "bbox": [ + 47, + 498, + 287, + 555 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 498, + 287, + 555 + ], + "type": "text", + "content": " that removes label correlations and use this metric to evaluate state-of-the-art OCL methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 561, + 287, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 561, + 287, + 631 + ], + "spans": [ + { + "bbox": [ + 47, + 561, + 287, + 631 + ], + "type": "text", + "content": "- Our findings show that existing OCL algorithms perform poorly when evaluated using our proposed evaluation strategy. Algorithms which prevent catastrophic forgetting perform significantly better, suggesting that better adaptation performance can be achieved by retaining and reusing past seen information." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 643, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 643, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 643, + 287, + 712 + ], + "type": "text", + "content": "Our results challenge the current emphasis on adapting to the latest samples and demonstrate the importance of seeking a more precise measure of adaptation. We note that our contributions are robust, with our findings valid across various OCL approaches, optimization strategies, and large-scale datasets from different sources." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 308, + 148, + 545, + 244 + ], + "blocks": [ + { + "bbox": [ + 305, + 68, + 545, + 144 + ], + "lines": [ + { + "bbox": [ + 305, + 68, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 305, + 68, + 545, + 144 + ], + "type": "text", + "content": "Table 1. Properties of OCL Benchmarks. We list benchmarks in the field of OCL along with the works which introduced them. We compare them across six properties: Realistic Data Streams (DO), No Storage Constraints (SC), Rapid Adaptation (RA), Information Retention (IR), Restricts Computational Budgets (CB), Evaluates on long stream sizes (LB), Leverages Pretrained Models (PT). Note that " + }, + { + "bbox": [ + 305, + 68, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\checkmark" + }, + { + "bbox": [ + 305, + 68, + 545, + 144 + ], + "type": "text", + "content": " is better than " + }, + { + "bbox": [ + 305, + 68, + 545, + 144 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 68, + 545, + 144 + ], + "type": "text", + "content": " in all columns." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 148, + 545, + 244 + ], + "lines": [ + { + "bbox": [ + 308, + 148, + 545, + 244 + ], + "spans": [ + { + "bbox": [ + 308, + 148, + 545, + 244 + ], + "type": "table", + "html": "
DataOrderBenchmarkDOSCRAIRCBLBPT
Task-Inc.A-GEM[9]XXX✓X✓X
Class-Inc.MIR[1]XXX✓X✓X
DER[4]
BlurryGSS[2]XXX✓X✓X
RM [3]
CLIB[18]
NaturalCLEAR[20]✓X✓✓XX✓
BudgetCL[26]X✓X✓✓X✓
CLOC[7]✓X✓XX✓X
DelayOCL[10]✓X✓X✓✓✓
ACM[25]✓✓✓✓✓✓✓
", + "image_path": "c37804e012229a2ce32732cd76b92bbee492ee6ec847f0873245eb4e65a7ec56.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 260, + 463, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 260, + 463, + 272 + ], + "spans": [ + { + "bbox": [ + 306, + 260, + 463, + 272 + ], + "type": "text", + "content": "2. OCL Evaluation: A Review" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 277, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 277, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 305, + 277, + 545, + 312 + ], + "type": "text", + "content": "We start with an overview of benchmarks in OCL across different properties of interest. For a more detailed review of the literature, we refer the reader to [30]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 322, + 546, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 322, + 546, + 498 + ], + "spans": [ + { + "bbox": [ + 305, + 322, + 546, + 498 + ], + "type": "text", + "content": "1. Realistic Data Streams (DO). The OCL community has been moving towards increasingly realistic benchmarks in terms of data ordering and task setup. Early works [21, 9] assumed access to which subset of classes a test sample is from (task-incremental setup). Subsequent work removed this constraint, requiring models to predict across all seen classes so far (class-incremental setup) [2, 1]. However, these works used incoming samples from disjoint data distributions with artificial task boundaries, resulting in unrealistic ordering. Recent works [3, 18, 26] improved the ordering by mixing samples from different disjoint tasks. Latest works [7, 25, 20] eliminate the need for generating artificial data streams simply by using real-world timestamps to order the data stream. Our work focuses on these real-world data streams on large-scale datasets." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 508, + 546, + 720 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 508, + 546, + 720 + ], + "spans": [ + { + "bbox": [ + 305, + 508, + 546, + 720 + ], + "type": "text", + "content": "2. Towards No Storage Constraints (SC). The majority of prior benchmarks on continual learning constrain the problem by prohibiting access to previously received data [19, 17], with only a small portion of data allowed to be stored in memory [21, 8, 4, 2, 18, 20]. This constraint is often justified by two reasons: (i) storage space is expensive and (ii) access to previous data is prohibited due to privacy constraints. However, recent work [25, 26] shows critical shortcomings of these justifications. They show that (a) storage costs are negligible compared to the computational costs of training a model, and (b) simply restricting access to previous data does not address privacy considerations, as samples can be reconstructed from model weights [13] or detectably change the model output [28]. Interestingly, Goel et al. [11] shows that removing data from the model can be done by catastrophic forgetting, which is antithetical to the objective of OCL approaches. Hence, we do not impose any memory constraints on our evaluation." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18853" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 715 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 227 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 227 + ], + "type": "text", + "content": "3. Towards Better Information Retention (IR). Interestingly, most of the previous benchmarks in OCL focus on preventing catastrophic forgetting of previously learned information, rather than evaluating the ability of models to rapidly learn new concepts [21, 27, 9, 3, 2, 20]. This emphasis on information retention can be attributed to disjoint set-based data ordering, which often involves little to no change in distribution for most of the stream, making it difficult to evaluate rapid adaptation. However, recent works have shifted their focus to rapid adaptation performance in real-world ordered data streams [7, 10]. In our benchmark, our objective is to maintain an additional high degree of retained knowledge from past data as demonstrated in [25, 6]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 232, + 289, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 232, + 289, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 232, + 289, + 293 + ], + "type": "text", + "content": "4. Towards Enabling Rapid Adaptation (RA). The goal of online continual learning algorithms is to rapidly adapt to incoming data from changing distributions. Similarly to past work [25, 7, 10], we place a strong emphasis on achieving this goal with better metrics." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 299, + 289, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 299, + 289, + 406 + ], + "spans": [ + { + "bbox": [ + 46, + 299, + 289, + 406 + ], + "type": "text", + "content": "5. Towards Computational Budgets (CB). Continual learning without memory constraints is primarily a problem of achieving high performance with computational efficiency, as retraining from scratch is an ideal solution to the problem. This setting addresses the real-world problem of reducing the cost of updating a given model with incoming data from a stream [25]. We evaluate OCL approaches under the maximum computational budget for fairness [10], testing across two different budgets." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 412, + 289, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 412, + 289, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 289, + 612 + ], + "type": "text", + "content": "6. Towards Large-Scale OCL (LB). OCL benchmarks have historically focused on learning over samples incoming from a stream over long data streams since the development of GEM [21]. Recent OCL benchmarks [2, 18, 25] have preserved this useful characteristic, while scaling up to larger and more complex data streams. In this work, we use two large-scale OCL benchmarks: Continual Google LandMarks (CGLM) [25] and Continual Localization (CLOC) [7]. CGLM is a landmark classification dataset that consists of a long-tailed distribution with 10,788 classes that simulate images that arrive on a Wikimedia Commons server. CLOC is a dataset focused on geolocation at scale consisting of 713 classes with 39M images simulating images arriving on a Flickr server. As these datasets come from two different sources, the issue of label correlation that we observe is likely to be a repeating pattern across future OCL datasets." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 619, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 619, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 619, + 289, + 715 + ], + "type": "text", + "content": "7. Leveraging Pretraining for Effective OCL (PT). Traditional methods in online continual learning start with randomly initialized models [21, 1]. However, continual learning approaches can leverage the abundance of large-scale pretrained models to improve computational efficiency [24, 31, 25]. We focus on an evaluation setting that starts with ImageNet1K pretrained models to allow approaches to leverage pretrained information." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 71, + 545, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 71, + 545, + 85 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 545, + 85 + ], + "type": "text", + "content": "3. Correcting Evaluations of Rapid Adaptation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 87, + 547, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 87, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 87, + 547, + 228 + ], + "type": "text", + "content": "We delve into our exploration of the limitations of using online accuracy as a metric to measure adaptation to distribution shifts and present our efforts to alleviate the shortcomings of this metric. We start by identifying the label correlations that affect online accuracy, and then we unveil a technique that enables deep networks to artificially achieve high performance on this metric. This highlights the dependence of the networks on these label correlations. Finally, we introduce a novel evaluation metric, near-future accuracy, and a test to detect and remove label correlations allowing for accurate measurement of the effectiveness of OCL methods in rapidly adapting to new distributions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 233, + 525, + 246 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 233, + 525, + 246 + ], + "spans": [ + { + "bbox": [ + 305, + 233, + 525, + 246 + ], + "type": "text", + "content": "3.1. Evaluating OCL: A Problem Formulation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "content": "In traditional OCL setups with real-world stream orders [7, 25], the learner is fed a continuous stream of training samples over time steps " + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "inline_equation", + "content": "t \\in \\{1, 2, \\dots, \\infty\\}" + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "content": ", consisting of an input datapoint " + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t \\in \\mathcal{X}" + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "content": " and its corresponding label " + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_t \\in \\mathcal{Y}" + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}_t, \\mathbf{y}_t) \\sim \\mathcal{D}_{j \\leq t}" + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "content": ". The distribution " + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_j" + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "content": " can change at any stream timestep. The aim is to train a classifier " + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "inline_equation", + "content": "f_{\\theta_t}: \\mathcal{X} \\to \\mathcal{Y}" + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "content": " at any given " + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "content": ", which accurately maps a new sample " + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "content": " to its label " + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "content": " while adapting to the latest information and incorporating it with the historical knowledge acquired from previous data." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 365, + 545, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 470 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 470 + ], + "type": "text", + "content": "To evaluate the adaptation ability of " + }, + { + "bbox": [ + 304, + 365, + 545, + 470 + ], + "type": "inline_equation", + "content": "f_{\\theta_t}" + }, + { + "bbox": [ + 304, + 365, + 545, + 470 + ], + "type": "text", + "content": ", online accuracy measures the performance on the next unseen sample, " + }, + { + "bbox": [ + 304, + 365, + 545, + 470 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}_{t + 1},\\mathbf{y}_{t + 1})" + }, + { + "bbox": [ + 304, + 365, + 545, + 470 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 304, + 365, + 545, + 470 + ], + "type": "inline_equation", + "content": "a_{t} = \\mathbb{1}\\{f_{\\theta_{t}}(\\mathbf{x}_{t + 1}) = \\mathbf{y}_{t + 1}\\}" + }, + { + "bbox": [ + 304, + 365, + 545, + 470 + ], + "type": "text", + "content": ". Online accuracy is updated in an online fashion given by " + }, + { + "bbox": [ + 304, + 365, + 545, + 470 + ], + "type": "inline_equation", + "content": "A_{t}^{RA} = \\frac{1}{t}\\left(A_{t - 1}^{RA}\\cdot (t - 1) + a_{t}\\right)" + }, + { + "bbox": [ + 304, + 365, + 545, + 470 + ], + "type": "text", + "content": ". For OCL approaches training deep networks, the running average is updated on a batch " + }, + { + "bbox": [ + 304, + 365, + 545, + 470 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 304, + 365, + 545, + 470 + ], + "type": "text", + "content": " of the next unseen samples as opposed to a single sample. After the evaluation is carried out, the model " + }, + { + "bbox": [ + 304, + 365, + 545, + 470 + ], + "type": "inline_equation", + "content": "f_{\\theta_i}" + }, + { + "bbox": [ + 304, + 365, + 545, + 470 + ], + "type": "text", + "content": " is updated using the same samples." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 470, + 545, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 470, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 304, + 470, + 545, + 588 + ], + "type": "text", + "content": "The ability of " + }, + { + "bbox": [ + 304, + 470, + 545, + 588 + ], + "type": "inline_equation", + "content": "f_{\\theta_t}" + }, + { + "bbox": [ + 304, + 470, + 545, + 588 + ], + "type": "text", + "content": " to retain information is measured by evaluating its accuracy on an unseen test stream that is similar to the training stream. In particular, per time step " + }, + { + "bbox": [ + 304, + 470, + 545, + 588 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 470, + 545, + 588 + ], + "type": "text", + "content": ", the model trained at the end of step " + }, + { + "bbox": [ + 304, + 470, + 545, + 588 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 470, + 545, + 588 + ], + "type": "text", + "content": " is evaluated on all test samples from step 0 to step " + }, + { + "bbox": [ + 304, + 470, + 545, + 588 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 470, + 545, + 588 + ], + "type": "text", + "content": ". We measure Backward Transfer @ " + }, + { + "bbox": [ + 304, + 470, + 545, + 588 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 470, + 545, + 588 + ], + "type": "text", + "content": " [7] where " + }, + { + "bbox": [ + 304, + 470, + 545, + 588 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 470, + 545, + 588 + ], + "type": "text", + "content": " is the last time step of the stream. That is to say, the model at the last step of the stream is evaluated on an increasing test test from step 0 to the end of the stream. However, traditional OCL methods targeting natural distribution shifts have neglected this metric [7, 10]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 594, + 541, + 606 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 594, + 541, + 606 + ], + "spans": [ + { + "bbox": [ + 305, + 594, + 541, + 606 + ], + "type": "text", + "content": "3.2. Isolating and Quantifying Label Correlations" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 608, + 545, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 608, + 545, + 666 + ], + "spans": [ + { + "bbox": [ + 304, + 608, + 545, + 666 + ], + "type": "text", + "content": "Our objective is to investigate whether using online accuracy to measure adaptation in OCL suffers from drawbacks due to label correlations. To accomplish this, we introduce a very simple algorithm that leverages label correlations and performs well in terms of online accuracy." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 666, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 547, + 714 + ], + "type": "text", + "content": "Blind Classifier. We define a blind classifier, similar to prior works [7, 25], as a model that predicts the mode of the last " + }, + { + "bbox": [ + 304, + 666, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 304, + 666, + 547, + 714 + ], + "type": "text", + "content": " samples seen without access to the input images. Formally, at a given new step " + }, + { + "bbox": [ + 304, + 666, + 547, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 666, + 547, + 714 + ], + "type": "text", + "content": ", the blind classifier" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18854" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 111, + 42, + 294, + 178 + ], + "blocks": [ + { + "bbox": [ + 111, + 42, + 294, + 178 + ], + "lines": [ + { + "bbox": [ + 111, + 42, + 294, + 178 + ], + "spans": [ + { + "bbox": [ + 111, + 42, + 294, + 178 + ], + "type": "image", + "image_path": "0b0c220c4da0d9d125da11da0d352f7ee6d9020b90620b0019831cd75bfc0768.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 182, + 547, + 239 + ], + "lines": [ + { + "bbox": [ + 46, + 182, + 547, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 547, + 239 + ], + "type": "text", + "content": "Figure 2. Blind Classifier. Performance of a blind classifier on the CGLM (left) and CLOC (right) datasets across varying shift " + }, + { + "bbox": [ + 46, + 182, + 547, + 239 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 182, + 547, + 239 + ], + "type": "text", + "content": " towards future for selecting evaluation samples alongside the optimal context window size " + }, + { + "bbox": [ + 46, + 182, + 547, + 239 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 182, + 547, + 239 + ], + "type": "text", + "content": " for the selected shift. (Section 3.2) A blind classifier achieves unrealistically high accuracy on current evaluation of adaptation (dark blue line, " + }, + { + "bbox": [ + 46, + 182, + 547, + 239 + ], + "type": "inline_equation", + "content": "S = 0" + }, + { + "bbox": [ + 46, + 182, + 547, + 239 + ], + "type": "text", + "content": ") on both datasets despite being a trivial baseline. (Section 3.5) The accuracy of the blind classifier on incoming samples with increasing shift " + }, + { + "bbox": [ + 46, + 182, + 547, + 239 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 182, + 547, + 239 + ], + "type": "text", + "content": " into the future decreases significantly, eventually converging to near-random performance, indicating a lack of label correlations to the current training samples." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 299, + 42, + 484, + 179 + ], + "blocks": [ + { + "bbox": [ + 299, + 42, + 484, + 179 + ], + "lines": [ + { + "bbox": [ + 299, + 42, + 484, + 179 + ], + "spans": [ + { + "bbox": [ + 299, + 42, + 484, + 179 + ], + "type": "image", + "image_path": "4bbbe4879373d96cc0cddab106031abf725d28ae50093f7b9d8b54d1f701f933.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 248, + 287, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 248, + 287, + 295 + ], + "spans": [ + { + "bbox": [ + 46, + 248, + 287, + 295 + ], + "type": "text", + "content": "predicts the class of " + }, + { + "bbox": [ + 46, + 248, + 287, + 295 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 46, + 248, + 287, + 295 + ], + "type": "text", + "content": " as the mode of the last revealed labels " + }, + { + "bbox": [ + 46, + 248, + 287, + 295 + ], + "type": "inline_equation", + "content": "\\cup_{j=1,\\dots,k}\\{\\mathbf{y}_{t-j}\\}" + }, + { + "bbox": [ + 46, + 248, + 287, + 295 + ], + "type": "text", + "content": ". The optimal context window size " + }, + { + "bbox": [ + 46, + 248, + 287, + 295 + ], + "type": "inline_equation", + "content": "\\mathcal{K}" + }, + { + "bbox": [ + 46, + 248, + 287, + 295 + ], + "type": "text", + "content": " is selected by a search over different sizes on the hyperparameter search set." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "type": "text", + "content": "Results. We present the performance of the blind classifier on the online accuracy in Figure 2. For this section, we focus solely on measuring online accuracy (indicated by the topmost purple line). Our results indicate that the blind classifier performs remarkably well achieving an average accuracy of " + }, + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "type": "text", + "content": " on the CGLM dataset, which consists of 10,788 classes, using only the labels of the last seen training sample " + }, + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "type": "inline_equation", + "content": "(\\mathcal{K} = 1)" + }, + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "type": "text", + "content": ". Moreover, the blind classifier achieves " + }, + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "type": "inline_equation", + "content": "17\\%" + }, + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "type": "text", + "content": " on the large-scale CLOC dataset consisting of 718 classes with " + }, + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "type": "inline_equation", + "content": "\\mathcal{K} = 10" + }, + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "type": "text", + "content": " achieving the best performance. These findings suggest an unusually high degree of label correlation between the past 1-10 samples and the immediate incoming sample in the data stream, especially given that the blind classifier achieves " + }, + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "type": "inline_equation", + "content": "17\\%" + }, + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "type": "text", + "content": " accuracy, while the random baseline achieves " + }, + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "type": "inline_equation", + "content": "0.01\\%" + }, + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 46, + 297, + 288, + 484 + ], + "type": "text", + "content": " on CGLM and CLOC datasets, respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 486, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 581 + ], + "type": "text", + "content": "Conclusion. Despite having never processed any input images, the blind classifier achieves a remarkably high online accuracy. This is surprising because it was expected to perform no better than a random classifier. However, it achieves this result by exploiting the label correlations present in OCL datasets. This is a critical drawback in using online accuracy to measure adaptation. In the following sections, we will delve deeper into this issue." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 591, + 287, + 604 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 591, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 47, + 591, + 287, + 604 + ], + "type": "text", + "content": "3.3. Can Deep Networks Learn Label Correlations?" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 606, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 606, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 606, + 287, + 700 + ], + "type": "text", + "content": "After demonstrating the effectiveness of the blind classifier in exploiting label correlations in the two large-scale datasets used in OCL settings, a pertinent inquiry arises: Can deep networks inadvertently learn these same label correlations leading to unreasonably high online accuracies? This question warrants investigation to determine to what extent deep OCL algorithms can leverage label correlations and the impact this may have on their performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "content": "An Overfitting-Based Baseline. One approach for DNNs" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 248, + 547, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 248, + 547, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 248, + 547, + 484 + ], + "type": "text", + "content": "to exploit label correlations is by overfitting to recent data. We investigate algorithmic choices for designing an OCL method that can overfit the most recent labels in a data stream. Specifically, we make two important design choices for our baseline: (i) we update the model only on recent data to achieve overfitting while sacrificing most of the useful information from the past. To this end, we adopt FIFO sampling, a widely-used technique in OCL, to select batches of samples for training. (ii) We fix the feature representations and train only the last linear layer to prevent degradation of feature representations due to overfitting. To improve the quality of the representations, we use a ResNet50 model pretrained on Instagram1B [22]. We refer to this model as OverAdapt. OverAdapt is computationally efficient since training the Linear layer over multiple updates is relatively inexpensive. Moreover, we adopt the fast stream evaluation setting [10], i.e. a setting with a strictly limited computational budget. We set the upper bound for the computation to one gradient update per incoming batch of samples for all methods with no restrictions on storage space." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 487, + 547, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 487, + 547, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 547, + 593 + ], + "type": "text", + "content": "Results. We present the results of the proposed OverAdapt compared to state-of-the-art OCL methods trained using an ImageNet1K pretrained ResNet50 model on the CGLM and CLOC datasets in Figure 3. OverAdapt achieves remarkable performance, surpassing the best-performing method ACM on the CGLM dataset by more than " + }, + { + "bbox": [ + 304, + 487, + 547, + 593 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 304, + 487, + 547, + 593 + ], + "type": "text", + "content": ", and outperforming all but the ACM baseline on the CLOC dataset by " + }, + { + "bbox": [ + 304, + 487, + 547, + 593 + ], + "type": "inline_equation", + "content": "10 - 35\\%" + }, + { + "bbox": [ + 304, + 487, + 547, + 593 + ], + "type": "text", + "content": ". Notably, OverAdapt achieves an impressive " + }, + { + "bbox": [ + 304, + 487, + 547, + 593 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 304, + 487, + 547, + 593 + ], + "type": "text", + "content": " accuracy on the CGLM dataset." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 596, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 596, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 596, + 548, + 714 + ], + "type": "text", + "content": "Conclusion. After demonstrating that OverAdapt can effectively leverage label correlations from the data stream, we conclude that traditional design choices like the FIFO buffer in past OCL setups [7] improved overfitting to the next sample. It is worrying that future work or existing works could have inadvertently made similar choices leading to perceived improvement in algorithms when instead it is a subtle case of overfitting to the online accuracy metric. We further ensure the validity of our conclusions by investigating whether the effectiveness of this model is due to" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18855" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 104, + 47, + 492, + 167 + ], + "blocks": [ + { + "bbox": [ + 104, + 47, + 492, + 167 + ], + "lines": [ + { + "bbox": [ + 104, + 47, + 492, + 167 + ], + "spans": [ + { + "bbox": [ + 104, + 47, + 492, + 167 + ], + "type": "image", + "image_path": "8858ba35790bcb9403096c5e925093ae9a6c89d6d946e797fc07af8feed50782.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 175, + 547, + 210 + ], + "lines": [ + { + "bbox": [ + 46, + 175, + 547, + 210 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 547, + 210 + ], + "type": "text", + "content": "Figure 3. OverAdapt Classifier. We compare the adaptation performance of our OverAdapt classifier on CGLM (left) and CLOC (right) datasets using online accuracy as a measure. The three top performing OCL methods on CLOC are benchmarked on the CGLM dataset. We see that OverAdapt outperforms recent OCL methods by a large margin of " + }, + { + "bbox": [ + 46, + 175, + 547, + 210 + ], + "type": "inline_equation", + "content": "10 - 40\\%" + }, + { + "bbox": [ + 46, + 175, + 547, + 210 + ], + "type": "text", + "content": " in accuracy." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 288, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 288, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 288, + 252 + ], + "type": "text", + "content": "a good training algorithm or to potential limitations of the evaluation metric. We explore this in the next subsections." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 261, + 236, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 261, + 236, + 274 + ], + "spans": [ + { + "bbox": [ + 47, + 261, + 236, + 274 + ], + "type": "text", + "content": "3.4. Exploring Properties of OverAdapt" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 276, + 287, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 287, + 300 + ], + "type": "text", + "content": "We investigate the reasons behind the impressive performance of our proposed OverAdapt." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 300, + 288, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 288, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 288, + 453 + ], + "type": "text", + "content": "Sensitivity Analysis. We start with the sensitivity study of OverAdapt by analyzing the impact of modifying its two key components: (i) FC-Only training with large-data pretrained initialization and (ii) FIFO Sampling. To study the effect of FC-Only training, we replace it with full-model training using an ImageNet1K-pretrained ResNet50 which has been common in prior OCL work [10]. We also analyze the effect of FIFO sample selection by comparing it with uniform sampling, which has been shown to be a simple but effective strategy in limited-compute regimes [26]. We evaluate their performance in terms of online accuracy and information retention at time " + }, + { + "bbox": [ + 46, + 300, + 288, + 453 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 300, + 288, + 453 + ], + "type": "text", + "content": " after training on the entire stream following prior art [7] as discussed in Section 3.1." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 453, + 282, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 282, + 465 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 282, + 465 + ], + "type": "text", + "content": "Results. Our results are shown in Figure 4 (left & center)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 466, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 466, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 466, + 287, + 594 + ], + "type": "text", + "content": "OverAdapt. Strikingly, our analysis reveals that OverAdapt (✓FIFO ✓FC-Only) achieves remarkable performance in rapid adaptation as measured by online accuracy achieving " + }, + { + "bbox": [ + 46, + 466, + 287, + 594 + ], + "type": "inline_equation", + "content": "82\\%" + }, + { + "bbox": [ + 46, + 466, + 287, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 466, + 287, + 594 + ], + "type": "inline_equation", + "content": "27\\%" + }, + { + "bbox": [ + 46, + 466, + 287, + 594 + ], + "type": "text", + "content": " on CGLM and CLOC, respectively. However, this seemingly impressive performance is coupled with an abysmally low information retention when measured by Backward Transfer with OverAdapt performing with " + }, + { + "bbox": [ + 46, + 466, + 287, + 594 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 466, + 287, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 466, + 287, + 594 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 466, + 287, + 594 + ], + "type": "text", + "content": " accuracy on CGLM and CLOC, respectively. These results demonstrate that OverAdapt is not a superior OCL algorithm but rather a product of a flawed rapid adaptation evaluation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "text", + "content": "FIFO Sampling. Our analysis comparing sampling strategies reveals that models trained using the FIFO sample selection strategy with both FC-Only training (" + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\checkmark" + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "text", + "content": "FIFO " + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\checkmark" + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "text", + "content": "FC-Only) and full-model training (" + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\checkmark" + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "text", + "content": "FIFO " + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "text", + "content": "FC-Only) achieve significantly higher accuracy of " + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "inline_equation", + "content": "82 / 78\\%" + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "inline_equation", + "content": "27 / 24\\%" + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "text", + "content": " on CGLM and CLOC, respectively, on online accuracy metric compared to those trained using uniform sampling-based with FC-Only training (" + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "text", + "content": "FIFO " + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\checkmark" + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "text", + "content": "FC-Only) and full-model training (" + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "text", + "content": "FIFO " + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 46, + 596, + 288, + 715 + ], + "type": "text", + "content": "FC-Only). This clearly indicates that FIFO sampling is primarily responsible for the ability to" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 228, + 545, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 322 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 322 + ], + "type": "text", + "content": "leverage the latest label correlations. However, models trained with FIFO sampling achieve significantly lower accuracy of " + }, + { + "bbox": [ + 304, + 228, + 545, + 322 + ], + "type": "inline_equation", + "content": "5 / 7\\%" + }, + { + "bbox": [ + 304, + 228, + 545, + 322 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 228, + 545, + 322 + ], + "type": "inline_equation", + "content": "1 / 1\\%" + }, + { + "bbox": [ + 304, + 228, + 545, + 322 + ], + "type": "text", + "content": " on CGLM and CLOC, respectively, in terms of information retention as measured by backward transfer in the last timestep, performing close to a random classifier. This highlights their poor representation quality and confirms that models using the FIFO strategy simply overfit to the latest samples." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "text", + "content": "FC-Only Training. Comparing FC-Only training (FIFO " + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "inline_equation", + "content": "\\sqrt{\\mathsf{FC}}" + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "text", + "content": "-Only) to full-model training (FIFO " + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "text", + "content": " FFC-Only) under FIFO sampling, we observe that FC-Only training achieves a higher accuracy of " + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "inline_equation", + "content": "82\\%" + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "inline_equation", + "content": "27\\%" + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "text", + "content": " on CGLM and CLOC, respectively, in online accuracy. However, for information retention, both models perform poorly due to the impact of FIFO sampling. In contrast full-model training under uniform sampling (XFIFO " + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "text", + "content": " FFC-Only) achieved a higher accuracy of " + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "inline_equation", + "content": "34\\%" + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "inline_equation", + "content": "14\\%" + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "text", + "content": " on CGLM and CLOC, respectively, for online accuracy, compared to full-model training (XFIFO " + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "inline_equation", + "content": "\\sqrt{\\mathsf{FC}}" + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "text", + "content": "-Only). Additionally, full-model training achieved " + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "inline_equation", + "content": "42\\%" + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "inline_equation", + "content": "18\\%" + }, + { + "bbox": [ + 304, + 322, + 546, + 520 + ], + "type": "text", + "content": " accuracy on CGLM (comparable to full-model training) and CLOC (higher than full-model training), respectively, in information retention. In general, it is not conclusive whether FC-Only training could substitute full model training, as it performed significantly better in some cases and significantly worse in others." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 521, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 639 + ], + "type": "text", + "content": "Conclusion. Our experiments highlighted critical drawbacks in assessing the rapid adaptation of deep models using online accuracy, due to spurious label correlations in the data stream. Sensitivity analysis revealed that both FIFO sampling and FC-Only training are critical components that helped OverAdapt leverage label correlations where FIFO sampling being the primary contributor. Furthermore, our findings suggest that information retention is a useful indicator for identifying drawbacks of OCL algorithms, such as inadvertent overfitting." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 651, + 545, + 663 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 651, + 545, + 663 + ], + "spans": [ + { + "bbox": [ + 306, + 651, + 545, + 663 + ], + "type": "text", + "content": "3.5. Removing Correlations to Evaluate Adaptation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "type": "text", + "content": "To address the limitations of online accuracy, we propose a new metric, near-future accuracy, which involves evaluating the model on near-future samples rather than immediate next samples. This can mitigate the adverse effects of label" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18856" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 127, + 47, + 468, + 213 + ], + "blocks": [ + { + "bbox": [ + 127, + 47, + 468, + 213 + ], + "lines": [ + { + "bbox": [ + 127, + 47, + 468, + 213 + ], + "spans": [ + { + "bbox": [ + 127, + 47, + 468, + 213 + ], + "type": "image", + "image_path": "e9093ca2cfb006856a4e21f74e18a81bcaaf1d31606963db24f751de578a4c38.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 216, + 547, + 281 + ], + "lines": [ + { + "bbox": [ + 45, + 216, + 547, + 281 + ], + "spans": [ + { + "bbox": [ + 45, + 216, + 547, + 281 + ], + "type": "text", + "content": "Figure 4. Sensitivity Analysis of OverAdapt Classifier. We illustrate the performance of various components of our OverAdapt classifier on CGLM (top) and CLOC (bottom) datasets measuring: (Section 3.4) information retention (left) and rapid adaptation capability in terms of online accuracy (" + }, + { + "bbox": [ + 45, + 216, + 547, + 281 + ], + "type": "inline_equation", + "content": "S = 0" + }, + { + "bbox": [ + 45, + 216, + 547, + 281 + ], + "type": "text", + "content": ", center) (Section 3.5) rapid adaptation performance in terms of online accuracy (" + }, + { + "bbox": [ + 45, + 216, + 547, + 281 + ], + "type": "inline_equation", + "content": "S = 0" + }, + { + "bbox": [ + 45, + 216, + 547, + 281 + ], + "type": "text", + "content": ", center) with our proposed near-future accuracy (" + }, + { + "bbox": [ + 45, + 216, + 547, + 281 + ], + "type": "inline_equation", + "content": "S = 256" + }, + { + "bbox": [ + 45, + 216, + 547, + 281 + ], + "type": "text", + "content": " in CGLM and, " + }, + { + "bbox": [ + 45, + 216, + 547, + 281 + ], + "type": "inline_equation", + "content": "S = 16384" + }, + { + "bbox": [ + 45, + 216, + 547, + 281 + ], + "type": "text", + "content": " in CLOC). Note that information retention (left) is independent of the shift " + }, + { + "bbox": [ + 45, + 216, + 547, + 281 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 45, + 216, + 547, + 281 + ], + "type": "text", + "content": ". The results demonstrate that introducing the shift removes label correlations, leading to dramatic loss in adaptation performance for our OverAdapt method while the uniform baseline stays unaffected." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 85, + 293, + 245, + 355 + ], + "blocks": [ + { + "bbox": [ + 85, + 293, + 245, + 355 + ], + "lines": [ + { + "bbox": [ + 85, + 293, + 245, + 355 + ], + "spans": [ + { + "bbox": [ + 85, + 293, + 245, + 355 + ], + "type": "image", + "image_path": "66e6d652baed9b76535ebd0e5c171189fe43d5ffbfcf440a4499d382d6b45b14.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 84, + 357, + 245, + 437 + ], + "blocks": [ + { + "bbox": [ + 84, + 357, + 245, + 437 + ], + "lines": [ + { + "bbox": [ + 84, + 357, + 245, + 437 + ], + "spans": [ + { + "bbox": [ + 84, + 357, + 245, + 437 + ], + "type": "image", + "image_path": "3dcbbf70790dd92f8680e83547efad6f7c5c9407ff337710c5b698f0fe01abac.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 445, + 289, + 543 + ], + "lines": [ + { + "bbox": [ + 46, + 445, + 289, + 543 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 289, + 543 + ], + "type": "text", + "content": "Figure 5. Our Evaluation Method. We compare the samples selected for evaluating adaptation performance by our evaluation method. The blue and green arrows indicate the latest batch received from the stream for learning and the samples selected for evaluation respectively. Current evaluation proposes to compute accuracy on the immediate incoming samples " + }, + { + "bbox": [ + 46, + 445, + 289, + 543 + ], + "type": "inline_equation", + "content": "(S = 0)" + }, + { + "bbox": [ + 46, + 445, + 289, + 543 + ], + "type": "text", + "content": ", i.e. online accuracy, while we propose to evaluate on the closest future samples " + }, + { + "bbox": [ + 46, + 445, + 289, + 543 + ], + "type": "inline_equation", + "content": "(S = 64)" + }, + { + "bbox": [ + 46, + 445, + 289, + 543 + ], + "type": "text", + "content": ", i.e. near-future accuracy, which is free from spurious correlations with the seen batch of images." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 549, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 549, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 549, + 289, + 714 + ], + "type": "text", + "content": "correlations on the performance by obtaining a more accurate assessment of the adaptation ability of OCL algorithms. Formulation of Proposed Evaluation. As illustrated in Figure 5, we introduce a shift " + }, + { + "bbox": [ + 46, + 549, + 289, + 714 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 549, + 289, + 714 + ], + "type": "text", + "content": " that represents the number of samples in the future, after which we evaluate the performance of the model. Instead of evaluating on the immediate next sample " + }, + { + "bbox": [ + 46, + 549, + 289, + 714 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}_{t + 1},\\mathbf{y}_{t + 1})" + }, + { + "bbox": [ + 46, + 549, + 289, + 714 + ], + "type": "text", + "content": ", we use the next near-future sample after the smallest shift " + }, + { + "bbox": [ + 46, + 549, + 289, + 714 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 549, + 289, + 714 + ], + "type": "text", + "content": ", namely " + }, + { + "bbox": [ + 46, + 549, + 289, + 714 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}_{t + 1 + S},\\mathbf{y}_{t + 1 + S})" + }, + { + "bbox": [ + 46, + 549, + 289, + 714 + ], + "type": "text", + "content": ", so that it has no label correlation with them. We select the smallest shift " + }, + { + "bbox": [ + 46, + 549, + 289, + 714 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 549, + 289, + 714 + ], + "type": "text", + "content": " instead of an arbitrarily large shift " + }, + { + "bbox": [ + 46, + 549, + 289, + 714 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 549, + 289, + 714 + ], + "type": "text", + "content": " so that the test sample comes from the same distribution as the latest seen train samples. We calculate the online accuracy as before, where " + }, + { + "bbox": [ + 46, + 549, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\hat{a}_t" + }, + { + "bbox": [ + 46, + 549, + 289, + 714 + ], + "type": "text", + "content": " is the running average of the accuracy calculated by first calculating the accuracy " + }, + { + "bbox": [ + 46, + 549, + 289, + 714 + ], + "type": "inline_equation", + "content": "a_{t} =" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 300, + 545, + 325 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 300, + 545, + 325 + ], + "spans": [ + { + "bbox": [ + 306, + 300, + 545, + 325 + ], + "type": "inline_equation", + "content": "\\mathbb{1}\\{f_{\\theta_t}(\\mathbf{x}_{t + 1 + S}) = \\mathbf{y}_{t + 1 + S}\\}" + }, + { + "bbox": [ + 306, + 300, + 545, + 325 + ], + "type": "text", + "content": " and then updating the running average using the formula " + }, + { + "bbox": [ + 306, + 300, + 545, + 325 + ], + "type": "inline_equation", + "content": "A_{t}^{RA} = \\frac{1}{t}\\left(A_{t - 1}^{RA}\\cdot (t - 1) + a_{t}\\right)" + }, + { + "bbox": [ + 306, + 300, + 545, + 325 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 324, + 546, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 546, + 490 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 546, + 490 + ], + "type": "text", + "content": "How To Set the Shift " + }, + { + "bbox": [ + 304, + 324, + 546, + 490 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 324, + 546, + 490 + ], + "type": "text", + "content": "? The shift " + }, + { + "bbox": [ + 304, + 324, + 546, + 490 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 324, + 546, + 490 + ], + "type": "text", + "content": " is the smallest value in the future that has no label correlation with the last seen train samples. We select the smallest " + }, + { + "bbox": [ + 304, + 324, + 546, + 490 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 324, + 546, + 490 + ], + "type": "text", + "content": " so that the blind classifier performs similarly to a random classifier. As shown in Figure 2 for both CGLM (left) and CLOC (right) datasets, we observe that increasing the shift " + }, + { + "bbox": [ + 304, + 324, + 546, + 490 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 324, + 546, + 490 + ], + "type": "text", + "content": " decreases the accuracy of the blind classifier down to a similar performance of a random classifier. In particular, at a shift of " + }, + { + "bbox": [ + 304, + 324, + 546, + 490 + ], + "type": "inline_equation", + "content": "S = 256" + }, + { + "bbox": [ + 304, + 324, + 546, + 490 + ], + "type": "text", + "content": " for CGLM and " + }, + { + "bbox": [ + 304, + 324, + 546, + 490 + ], + "type": "inline_equation", + "content": "S = 16384" + }, + { + "bbox": [ + 304, + 324, + 546, + 490 + ], + "type": "text", + "content": " for CLOC, the label correlations are effectively eliminated. Therefore, we use these shift values for our proposed evaluation strategy. We evaluate OverAdapt and its variants on rapid adaptation with our proposed near-future accuracy and compare it with the previously adopted online accuracy " + }, + { + "bbox": [ + 304, + 324, + 546, + 490 + ], + "type": "inline_equation", + "content": "(S = 0)" + }, + { + "bbox": [ + 304, + 324, + 546, + 490 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 490, + 547, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 490, + 547, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 490, + 547, + 676 + ], + "type": "text", + "content": "Results. Figure 4 presents the results of OverAdapt and its variants on rapid adaptation using two metrics: online accuracy (center) and near-future accuracy (right). When studying FIFO sampling with FC-Only training (" + }, + { + "bbox": [ + 304, + 490, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\sqrt[3]{\\mathrm{FIFO}} \\sqrt{\\mathrm{FC}}" + }, + { + "bbox": [ + 304, + 490, + 547, + 676 + ], + "type": "text", + "content": "-Only) and with full-model training (" + }, + { + "bbox": [ + 304, + 490, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\sqrt{\\mathrm{FIFO}} \\times \\mathrm{FC}" + }, + { + "bbox": [ + 304, + 490, + 547, + 676 + ], + "type": "text", + "content": "-Only), we observe a significant drop in the performance of the methods between the two metrics that overfit using the FIFO sampling by about " + }, + { + "bbox": [ + 304, + 490, + 547, + 676 + ], + "type": "inline_equation", + "content": "70\\%" + }, + { + "bbox": [ + 304, + 490, + 547, + 676 + ], + "type": "text", + "content": " in CGLM and " + }, + { + "bbox": [ + 304, + 490, + 547, + 676 + ], + "type": "inline_equation", + "content": "20 - 40\\%" + }, + { + "bbox": [ + 304, + 490, + 547, + 676 + ], + "type": "text", + "content": " on CLOC datasets, while the performance of uniform sampling for both FC-Only training (" + }, + { + "bbox": [ + 304, + 490, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\times \\mathrm{FIFO} \\sqrt{\\mathrm{FC}}" + }, + { + "bbox": [ + 304, + 490, + 547, + 676 + ], + "type": "text", + "content": "-Only) and full-model training (" + }, + { + "bbox": [ + 304, + 490, + 547, + 676 + ], + "type": "inline_equation", + "content": "\\times \\mathrm{FIFO} \\times \\mathrm{FC}" + }, + { + "bbox": [ + 304, + 490, + 547, + 676 + ], + "type": "text", + "content": "-Only) remains similar. Interestingly, the trends reverse, with the uniform sampling variants outperforming the FIFO sampling strategy by a large margin. Furthermore, we observe that FC-Only training no longer consistently improves rapid adaptation, proving to be useful in some cases on the new evaluation method." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 678, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 678, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 678, + 547, + 713 + ], + "type": "text", + "content": "Conclusion. We propose an evaluation using near-future accuracy which removes label correlations. OverAdapt performs poorly after removing label correlations, compared" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18857" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 155 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 155 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 155 + ], + "type": "text", + "content": "to a uniform baseline, emphasizing the importance of developing OCL algorithms that handle rapid adaptation without overfitting. Additionally, there is no surprising discrepancy between near-future accuracy and information retention across methods, unlike online accuracy. Our strategy allows for better evaluation of OCL algorithms on real-world ordered datasets." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 167, + 282, + 181 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 167, + 282, + 181 + ], + "spans": [ + { + "bbox": [ + 47, + 167, + 282, + 181 + ], + "type": "text", + "content": "4. OCL Evaluation by Near-Future Accuracy" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 182, + 289, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 289, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 289, + 291 + ], + "type": "text", + "content": "In this section, we provide a comprehensive analysis of various OCL approaches under near-future accuracy. We incorporate the latest advancements in setup design into our benchmark and take computational constraints into account for fair comparison. Following the prior art [25, 26], our study assumes no memory constraints, but rather sets constraints on computational budget following [10, 25, 26]. As addressed in prior work, budgeted computation per time step implicitly imposes a limited memory access." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 297, + 165, + 310 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 297, + 165, + 310 + ], + "spans": [ + { + "bbox": [ + 47, + 297, + 165, + 310 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 312, + 289, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 289, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 289, + 453 + ], + "type": "text", + "content": "Datasets and Metrics. We employ two large-scale online continual learning datasets, CGLM with a total of 460K images and CLOC compromising of 39M images in a stream, both of which contain natural distribution shifts [7]. That is to say, the images are temporally ordered. We measure rapid adaptation performance using the average accuracy on near-future samples, as described in Section 3.5, with a shift " + }, + { + "bbox": [ + 46, + 312, + 289, + 453 + ], + "type": "inline_equation", + "content": "S = 256" + }, + { + "bbox": [ + 46, + 312, + 289, + 453 + ], + "type": "text", + "content": " for CGLM and " + }, + { + "bbox": [ + 46, + 312, + 289, + 453 + ], + "type": "inline_equation", + "content": "S = 16384" + }, + { + "bbox": [ + 46, + 312, + 289, + 453 + ], + "type": "text", + "content": " for CLOC. The choice of both was made such that the blind classifier discussed in Section 3.2 achieves a random accuracy. Additionally, we measure information retention using the Backward Transfer metric following CLOC [7]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 454, + 289, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 454, + 289, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 454, + 289, + 536 + ], + "type": "text", + "content": "Model and Optimization. In all experiments, we use a ResNet50 with ImageNet1K initialization unless otherwise specified. We adopt the optimization procedure from [10] and train all models using an SGD optimizer, a fixed learning rate of 0.005, and a weight decay of " + }, + { + "bbox": [ + 46, + 454, + 289, + 536 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 46, + 454, + 289, + 536 + ], + "type": "text", + "content": ". For both training and evaluation, we batch incoming samples with a batch size " + }, + { + "bbox": [ + 46, + 454, + 289, + 536 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 454, + 289, + 536 + ], + "type": "text", + "content": " of 64 for CGLM [25] and 128 for CLOC [10]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 536, + 289, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 289, + 642 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 289, + 642 + ], + "type": "text", + "content": "Compared OCL Approaches. We evaluate five online continual learning methods using our proposed near-future accuracy. For consistency, we use uniform sampling as the sampling strategy, since it was shown in Section 3.4 that it strikes a good balance between adaptation and retention. Again, in uniform sampling, the training batch is constructed by uniformly and sampling " + }, + { + "bbox": [ + 46, + 536, + 289, + 642 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 536, + 289, + 642 + ], + "type": "text", + "content": " samples from all past stored data. The Appendix provides a comprehensive analysis of other sampling techniques." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 642, + 288, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 288, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 288, + 689 + ], + "type": "text", + "content": "ER (Replay Only)[26]. ER (Replay Only) is a simple approach that stores the incoming samples and trains the model on a batch sampled from the set of stored samples. This is the leading method in offline budgeted CL [26]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "FC-Only. FC-Only, referred to as OverAdapt (XFIFO ✓FC-Only) in Section 3.4, is an adapted version of ER (Re" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 547, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 108 + ], + "type": "text", + "content": "play Only) that uses a ResNet50-I1B feature extractor and trains only the last linear layer. This method has been shown to be computationally efficient [26]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 107, + 547, + 143 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 107, + 547, + 143 + ], + "spans": [ + { + "bbox": [ + 304, + 107, + 547, + 143 + ], + "type": "text", + "content": "ACE[5]. We replace the CrossEntropy loss in ER (Replay Only) with the ACE Loss proposed in to isolate the effect of ACE loss under the proposed evaluation setting." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 143, + 547, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 143, + 547, + 248 + ], + "spans": [ + { + "bbox": [ + 304, + 143, + 547, + 248 + ], + "type": "text", + "content": "ACM[25]. ACM extracts features from a pretrained ResNet50 model (trained on ImageNet1k) and continually updates a kNN classifier, with " + }, + { + "bbox": [ + 304, + 143, + 547, + 248 + ], + "type": "inline_equation", + "content": "k = 2" + }, + { + "bbox": [ + 304, + 143, + 547, + 248 + ], + "type": "text", + "content": " and cosine distance as distance metric, over those features. Additionally, we note that ACM does not train a deep network, thus incurring minimal computational cost. This sets the minimal accuracy requirements for OCL methods. We compare ACM with other popular fixed-feature extractor based methods like NCM [23, 24, 16] and SLDA [14] in the Appendix." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 248, + 547, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 248, + 547, + 306 + ], + "spans": [ + { + "bbox": [ + 304, + 248, + 547, + 306 + ], + "type": "text", + "content": "CosineFC[15]. This approach replaces the linear layer of ResNet50 in the ER (Replay Only) baseline with a layer that computes the cosine distance between weights and features. We only perform this modification as distillation has been shown to be computationally ineffective [26]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 307, + 547, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 307, + 547, + 353 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 547, + 353 + ], + "type": "text", + "content": "By comparing these approaches under our proposed near-future accuracy along with information retention, we aim to provide insights into the strengths and limitations of current OCL methods." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 359, + 480, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 359, + 480, + 372 + ], + "spans": [ + { + "bbox": [ + 305, + 359, + 480, + 372 + ], + "type": "text", + "content": "4.2. Results: Varying Stream Speeds" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 373, + 547, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 547, + 420 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 547, + 420 + ], + "type": "text", + "content": "Following prior work on fair computationally normalized evaluation of online continual learners [10], we evaluate the performance of OCL methods in two different time constraints, namely slow stream and fast stream scenarios." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 420, + 547, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 547, + 537 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 547, + 537 + ], + "type": "text", + "content": "Slow Stream. Slow stream is the scenario in which the computational budget for learning is not strictly limited. We enforce all methods to perform the equivalent of 10 and 5 model updates per time step on CGLM and CLOC, respectively. Methods that require a significant overhead will thus perform a fewer number of model updates such that it matches the corresponding computational budget of 10 and 5 updates on the respective datasets. Note that ACM requires negligible training cost, and therefore OCL methods must at least outperform ACM to be considered useful." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 537, + 547, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 537, + 547, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 537, + 547, + 654 + ], + "type": "text", + "content": "Results. In Figure 6 (first row), we present the performance of various methods in terms of near-future accuracy for both CGLM and CLOC datasets. CosineFC, originally proposed for offline continual learning, achieves the highest accuracy with " + }, + { + "bbox": [ + 304, + 537, + 547, + 654 + ], + "type": "inline_equation", + "content": "38\\%" + }, + { + "bbox": [ + 304, + 537, + 547, + 654 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 537, + 547, + 654 + ], + "type": "inline_equation", + "content": "16\\%" + }, + { + "bbox": [ + 304, + 537, + 547, + 654 + ], + "type": "text", + "content": " accuracy on CGLM and CLOC, respectively. Furthermore, CosineFC also shows impressive information retention performance, achieving an accuracy of " + }, + { + "bbox": [ + 304, + 537, + 547, + 654 + ], + "type": "inline_equation", + "content": "77\\%" + }, + { + "bbox": [ + 304, + 537, + 547, + 654 + ], + "type": "text", + "content": " in CGLM. As expected, FC-Only which only finetunes the last linear layer, has the worst retention capabilities due to the restricted access to full-model updates." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": "Conclusion. Our evaluation revealed that methods not explicitly designed for adaptation in the OCL setup perform well, indicating that retaining and reusing previously seen information is crucial for achieving better generalization, and that retention and adaptation are closely linked." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18858" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 111, + 41, + 489, + 242 + ], + "blocks": [ + { + "bbox": [ + 111, + 41, + 489, + 242 + ], + "lines": [ + { + "bbox": [ + 111, + 41, + 489, + 242 + ], + "spans": [ + { + "bbox": [ + 111, + 41, + 489, + 242 + ], + "type": "image", + "image_path": "a62739252ca9211a1419e9618818edd7a45b9ccff7537437cf4f4438a6addf30.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 249, + 548, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 249, + 548, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 249, + 548, + 285 + ], + "type": "text", + "content": "Figure 6. Performance of Methods on Near-Future Accuracy. We evaluate CL methods in slow and fast streams similar to [10]. Near-future accuracy, which eliminates spurious label correlations, shows that retaining and reusing past information is crucial for better generalization and that algorithms not designed for adaptation in OCL can perform well. Hence retention and adaptation are closely linked." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 302, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 302, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 302, + 287, + 384 + ], + "type": "text", + "content": "Fast Stream. Fast stream setting refers to the scenario where the computational budget for learning is limited. That is to say, the stream presents samples at a fast rate that provides limited time for learners to train [10]. To evaluate the performance of OCL methods under this setting, we restrict the methods to only use a computation equivalent to one model update per incoming batch for both datasets." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 384, + 288, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 288, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 288, + 525 + ], + "type": "text", + "content": "Results. As shown in Figure 6 (second row), our results suggest that the two simplest baselines, namely ACM and FC-Only, achieve the highest accuracy on CGLM with " + }, + { + "bbox": [ + 46, + 384, + 288, + 525 + ], + "type": "inline_equation", + "content": "29\\%" + }, + { + "bbox": [ + 46, + 384, + 288, + 525 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 384, + 288, + 525 + ], + "type": "inline_equation", + "content": "21\\%" + }, + { + "bbox": [ + 46, + 384, + 288, + 525 + ], + "type": "text", + "content": ", respectively. On the other hand, ACM achieves the highest information retention of " + }, + { + "bbox": [ + 46, + 384, + 288, + 525 + ], + "type": "inline_equation", + "content": "27\\%" + }, + { + "bbox": [ + 46, + 384, + 288, + 525 + ], + "type": "text", + "content": " while simple ER and CosineFC achieve the highest near-future accuracy of around " + }, + { + "bbox": [ + 46, + 384, + 288, + 525 + ], + "type": "inline_equation", + "content": "13\\%" + }, + { + "bbox": [ + 46, + 384, + 288, + 525 + ], + "type": "text", + "content": ". These results indicate that the simple baseline methods outperform the more advanced OCL methods in both adaptation and information retention in this setup. This highlights that current OCL methods still have a long way to go to achieve satisfactory performance in the fast stream setting where compute is extremely limited." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 525, + 287, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 287, + 608 + ], + "type": "text", + "content": "Conclusion. Under our proposed evaluation approach, in which spurious label correlations are removed, the fast stream setting with its limited computational budget shows that simple baselines can outperform more advanced OCL methods in both adaptation and retention. This finding emphasizes the need to develop OCL methods that can adapt rapidly in severely budgeted settings." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 613, + 160, + 625 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 160, + 625 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 160, + 625 + ], + "type": "text", + "content": "4.3. Further Discussion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 631, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 631, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 631, + 288, + 715 + ], + "type": "text", + "content": "Our benchmark of OCL methods on large-scale datasets highlights two key observations. First, the best-performing online adaptation methods often suffer from forgetting due to overfitting to label correlations, challenging the assumption that the performance gap between adaptation and retention is an inherent learning problem [6]. Our proposed near-future accuracy helps reveal label correlations and identifies" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 302, + 547, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 302, + 547, + 420 + ], + "spans": [ + { + "bbox": [ + 304, + 302, + 547, + 420 + ], + "type": "text", + "content": "whether the underlying algorithm is inadvertently exploiting them. Second, methods with better retention properties tend to generalize better and achieve improved performance on near-future accuracy in relaxed and restricted computational settings [12, 29]. This aligns well with the domain generalization literature [12] and suggests that proper training on previous samples can lead to features that generalize well across domain shifts. Finally, we consistently observe that, under limited computational settings, simpler methods outperform their more computationally involved ones." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 430, + 379, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 430, + 379, + 441 + ], + "spans": [ + { + "bbox": [ + 305, + 430, + 379, + 441 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 445, + 547, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 547, + 576 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 547, + 576 + ], + "type": "text", + "content": "Our work proposes a new measure to evaluate adaptation in OCL algorithms and highlights its limitations compared to the standard online accuracy evaluation. We found that many current OCL methods overfit to idiosyncrasies of the stream rather than genuinely adapting to new data, as revealed by poor information retention. Using our proposed metric, near-future accuracy, we observed that algorithms with good retention also had better generalization and adaptation capabilities. Our proposed evaluation can serve as a sanity check for future OCL algorithms to ensure that they are not incorrectly learning spurious label correlations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 586, + 421, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 586, + 421, + 600 + ], + "spans": [ + { + "bbox": [ + 305, + 586, + 421, + 600 + ], + "type": "text", + "content": "6. Acknowledgements" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 712 + ], + "type": "text", + "content": "This work was supported by the King Abdullah University of Science and Technology - Office of Sponsored Research (OSR) under Award No. OSR-CRG2021-4648, SDAIA-KAUST Center of Excellence in Data Science, Artificial Intelligence, and UKRI grant: Turing AI Fellowship EP/W002981/1. We thank the Royal Academy of Engineering and FiveAI for their support. Ser-Nam Lim from Meta AI has no relationships with the mentioned grants. Ameya Prabhu is funded by Meta AI Grant No. DFR05540." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "18859" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Rahaf Aljundi, Lucas Caccia, Eugene Belilovsky, Massimo Caccia, Laurent Charlin, and Tinne Tuytelaars. 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In contrast to training-time robustness mechanisms that attempt to anticipate and counter the shift, we create a closed-loop system and make use of test-time feedback signal to adapt a network on the fly. We show that this loop can be effectively implemented using a learning-based function, which realizes an amortized optimizer for the network. This leads to an adaptation method, named Rapid Network Adaptation (RNA), that is notably more flexible and orders of magnitude faster than the baselines. Through a broad set of experiments using various adaptation signals and target tasks, we study the generality, efficiency, and flexibility of this method. We perform the evaluations using various datasets (Taskonomy, Replica, ScanNet, Hypersim, COCO, ImageNet), tasks (depth, optical flow, semantic segmentation, classification), and distribution shifts (Cross-datasets, 2D and 3D Common Corruptions) with promising results.", + "bbox": [ + 75, + 340, + 473, + 613 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 646, + 209, + 662 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Neural networks are found to be unreliable against distribution shifts [23, 35, 43, 42, 29]. Examples of such shifts include blur due to camera motion, object occlusions, changes in weather conditions and lighting, etc. The training-time strategies to deal with this issue attempt to anticipate the shifts that may occur and counter them at the training stage – for instance, by augmenting the training data or updating the architecture with corresponding robustness inductive biases. As the possible shifts are numerous and unpredictable, this approach has inherent limitations. This is the main motivation behind test-time adaptation methods, which instead aim to adapt to such shifts as they occur and recover from failure. In other words, these methods choose adaptation over anticipation (see Fig. 1). In this work, we propose a test-time adaptation framework that aims to perform an ef", + "bbox": [ + 75, + 674, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/23a0149ecf8d4c09bbae0937e2218779aeba8a354c644fe1acc4ba08d4696173.jpg", + "image_caption": [ + "Figure 1: Adaptive vs non-adaptive neural network pipelines. Top: In order to be robust, non-adaptive methods include training-time interventions that anticipate and counter the distribution shifts that will occur at test-time (e.g., via data augmentation). The learned model, $f_{\\theta}$ , is frozen at test-time, thus upon encountering an out-of-distribution input, its predictions may collapse. Bottom: Adaptive methods create a closed-loop and use an adaptation signal at test-time. The adaptation signal is a quantity that can be computed at test-time from the environment. $h_{\\phi}$ acts as a \"controller\" by taking in an error feedback, computed from the adaptation signal and model predictions, to adapt $f_{\\theta}$ accordingly. It can be implemented as a (i) standard optimizer (e.g., using SGD) or (ii) neural network. The former is equivalent to test-time optimization (TTO), while the latter aims to amortize the optimization process, by training a controller network to adapt $f_{\\theta}$ - thus, it can be more efficient and flexible. In this work, we study the latter approach and show its efficiency and flexibility." + ], + "image_footnote": [], + "bbox": [ + 532, + 306, + 864, + 571 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ficient adaptation of a given main network using a feedback signal.", + "bbox": [ + 496, + 777, + 890, + 808 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "One can consider performing \"test-time optimization\" (TTO) for this purpose, similar to previous works [91, 108, 27] e.g. simply using SGD to finetune the network to reduce a proxy loss [91]. While this can successfully adapt a network, it is unnecessarily inefficient as it does not make use of the learnable regularities in the adaptation pro", + "bbox": [ + 496, + 810, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4674", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "cess, and consequently, unconducive for real-world applications. It also results in a rigid framework as the update mechanism is fixed to be the same as the training process of neural networks (SGD). We show this process can be effectively amortized using a learning-based feed-forward controller network, which yields orders of magnitude faster results (See Fig. 1, Sec. 4.3). In addition, it provides flexibility advantages as the controller is implemented using a neural network and can be engineered to include arbitrary inductive biases and desired features that could counter the suboptimalities of the adaptation signal.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 271, + 218, + 286 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work focuses on how to adapt a neural network efficiently at test-time on a range of tasks and adaptation signals. We give an overview of relevant topics. See the supplementary Sec. 7 for more related works.", + "bbox": [ + 76, + 296, + 468, + 356 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Robustness methods anticipate the distribution shift that can occur and incorporate inductive biases into the model to help it generalize. Popular methods include data augmentation [61, 107, 57, 37, 103, 101, 34, 43], self-/pre-training [36, 95, 25, 72, 96, 75, 32], architectural changes [19, 8, 82, 62, 55] or ensembling [48, 67, 99, 73, 40, 68]. We focus on adaptation mechanisms and identifying practical adaptation signals that can be used at test-time.", + "bbox": [ + 75, + 357, + 468, + 477 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Amortized optimization methods make use of learning to improve (e.g., speed-up) the solution of optimization problems, particularly for settings that require repeatedly solving similar instances of the same underlying problem [49, 11, 4, 106, 26, 94, 60, 14, 3]. Fully amortized optimization methods model the shared structure between past instances of solved problems to regress the solution to a new problem [31, 21, 52]. As adapting to distribution shifts can be cast as solving an optimization problem at test-time, our method can be seen as an amortized solution.", + "bbox": [ + 75, + 478, + 468, + 628 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Test-time adaptation methods for geometric tasks. Many existing frameworks, especially in geometric tasks such as aligning a 3D object model with an image of it, in effect instantiate a task-specific case of closed-loop optimization for each image [60, 106, 63]. Common sources of their adaptation quantity include sensor data [92, 98, 15, 89, 102, 18], structure from motion (SFM) [93, 47], motion [12], and photometric and multi-view consistency constraints (MVC) [58, 45]. Many of the latter methods often focus on depth prediction and they introduce losses that are task-specific, e.g., [93] optimize a photometric consistency loss. We differ by aiming to investigate a more general framework for test-time adaptation that can be applied to several tasks. For MVC, while we adopt the same losses as [58], we show under collapsed predictions, optimizing only MVC constraints is not sufficient for recovering predictions; depth predictions need to be adapted and this can be done efficiently using our framework (see Sec. 4.3).", + "bbox": [ + 75, + 628, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Test-time adaptation methods for semantic tasks. Most of these works involve optimizing a self-supervised objective at test-time [85, 91, 54, 27, 28, 108, 9, 51, 100]. They differ in the choice of self-supervised objectives, e.g., prediction entropy [91], mutual information [51], and parameters optimized [9]. However, as we will discuss in Sec. 3.2, and as shown by [9, 27, 65], existing methods can fail silently, i.e. successful optimization of the adaptation signal loss does not necessarily result in better performance on the target task. We aim to have a more efficient and flexible method and also show that using proper adaptation signals results in improved performance.", + "bbox": [ + 496, + 90, + 890, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-modal frameworks are models that can use the information from multiple sources, e.g., RGB image, text, audio, etc., [13, 5, 86, 50, 2, 16, 72, 1, 6, 30]. Schematically, our method has similarities to multi-modal learning (as many amortized optimization methods do) since it simultaneously uses an input RGB image and an adaptation signal. The main distinction is that our method implements a particular process toward adapting a network to a shift using an adaptation signal from the environment – as opposed to a generic multi-modal learning.", + "bbox": [ + 496, + 272, + 890, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 436, + 589, + 450 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In Fig. 1, we schematically compared methods that incorporate robustness mechanisms at training-time (thus anticipating the distribution shift) with those that adapt to shifts at test-time. Our focus is on the latter. In this section, we first discuss the benefits and downsides of common adaptation methods (Sec. 3.1). We then propose an adaptation method that is fast and can be applied to several tasks (Sec. 3.1.1). To adapt, one also needs to be able to compute an adaptation signal, or proxy, at the test-time. In the second part of the section (Sec. 3.2), we study a number of practical adaptation signals for a number of tasks.", + "bbox": [ + 496, + 460, + 890, + 627 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. How to adapt at test-time?", + "text_level": 1, + "bbox": [ + 500, + 636, + 738, + 651 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "An adaptive system is one that can respond to changes in its environment. More concretely, it is a system that can acquire information to characterize such changes, e.g., via an adaptation signal that provides an error feedback, and make modifications that would result in a reduction of this error (see Fig. 1). The methods for performing the adaptation of the network range from gradient-based updates, e.g. using SGD to fine-tune the parameters [85, 91, 27], to the more efficient semi-amortized [110, 88] and amortized approaches [90, 66, 77] (see Fig. 6 of [77] for an overview). As amortization methods train a controller network to substitute the explicit optimization process, they only require a forward pass at test-time. Thus, they are computationally efficient. Gradient-based approaches, e.g., TTO, can be powerful adaptation methods when the test-time signal is robust and well-suited for the task (see Fig. 4). How-", + "bbox": [ + 496, + 659, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4675", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ever, they are inefficient and have the risk of failing silently and the need for carefully tuned optimization hyperparameters [9]. In this work, we focus on an amortization-based approach.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Notation. We use $\\mathcal{X}$ to denote the input image domain, and $\\mathcal{Y}$ to denote the target domain for a given task. We use $f_{\\theta}:\\mathcal{X}\\to \\mathcal{Y}$ to denote the model to be adapted, where $\\theta$ denotes the model parameters. We denote the model before and after adaptation as $f_{\\theta}$ and $f_{\\hat{\\theta}}$ respectively. $\\mathcal{L}$ and $\\mathcal{D}$ are the original training loss and training dataset of $f_{\\theta}$ , e.g., for classification, $\\mathcal{L}$ will be the cross-entropy loss and $\\mathcal{D}$ the ImageNet training data. As shown in Fig. 1, $h_\\phi$ is a controller for $f_{\\theta}$ . It can be an optimization algorithm, e.g., SGD, or a neural network. $\\phi$ denotes the optimization hyperparameters or the network's parameters. The former case corresponds to TTO, and the latter is the proposed RNA, which will be explained in the next subsection. Finally, the function $g:\\mathcal{X}^M\\rightarrow \\mathcal{Z}$ returns the adaptation signal by mapping a set of images $\\mathcal{B} = \\{I_1,\\dots,I_M\\} \\in \\mathcal{X}^M$ to a vector $g(\\mathcal{B}) = z\\in \\mathcal{Z}$ . This function $g$ is given, e.g., for depth, $g$ returns the sparse depth measurements from SFM.", + "bbox": [ + 75, + 152, + 470, + 409 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1.1 Rapid Network Adaptation (RNA)", + "text_level": 1, + "bbox": [ + 76, + 420, + 372, + 435 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For adaptation, we use a neural network for $h_{\\phi}$ . The adaptation signal and model predictions are passed as inputs to $h_{\\phi}$ and it is trained to regress the parameters $\\hat{\\theta}(\\phi) = h_{\\phi}(f_{\\theta}(\\mathcal{B}), z)$ . This corresponds to an objective-based amortization of the TTO process [3]. Using both the adaptation signal $z$ and model prediction $f_{\\theta}(\\mathcal{B})$ informs the controller network about the potential errors of the model. The training objective for $h_{\\phi}$ is $\\min_{\\phi} \\mathbb{E}_{\\mathcal{D}}[\\mathcal{L}(f_{\\hat{\\theta}(\\phi)}(\\mathcal{B}), y)]$ , where $(\\mathcal{B}, y) \\sim \\mathcal{D}$ is a training batch sampled from $\\mathcal{D}$ . Note that the original weights of $f$ are frozen and $h_{\\phi}$ is a small network, having only 5-20% of the number of parameters of $f$ , depending on the task. We call this method as rapid network adaptation (RNA) and experiment with different variants of it in Sec. 4.", + "bbox": [ + 75, + 444, + 468, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "There exist various options for implementing the amortization process, e.g., $h_{\\phi}$ can be trained to update the input image or the weights of $f_{\\theta}$ . We choose to modulate the features of $f_{\\theta}$ as it has been shown to work well in different domains [24] and gave the best results. To do this, we insert $k$ Feature-wise Linear Modulation (FiLM) layers [71] into $f_{\\theta}$ (see Fig. 2). Each FiLM layer performs: $\\mathrm{FiLM}(\\mathbf{x}_i; \\gamma_i, \\beta_i) = \\gamma_i \\odot \\mathbf{x}_i + \\beta_i$ , where $\\mathbf{x}_i$ is the activation of layer $i$ . $h_{\\phi}$ is a network that takes as input the adaptation signal $z$ and model predictions and outputs the coefficients $\\{\\gamma_i, \\beta_i\\}$ of all $k$ FiLM layers. $h_{\\phi}$ is trained on the same dataset $\\mathcal{D}$ as $f_{\\theta}$ , therefore, unlike TTO, it is never exposed to distribution shifts during training. Moreover, it is able to generalize to unseen shifts (see Sec. 4.3). See the supplementary for the full details, other RNA implementations we investigated, and a comparison of RNA against other ap", + "bbox": [ + 75, + 659, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7e679470370fff7ba52ed61f9cdc251b6ff92a26714717cca94f412b5cdcad27.jpg", + "image_caption": [ + "Figure 2: Architecture of RNA. $x$ is the input image, $f_{\\theta}$ is the model to be adapted and $f_{\\theta}(x)$ the corresponding prediction. To perform adaptation, we freeze the parameters of $f_{\\theta}$ and insert several FiLM layers into $f_{\\theta}$ . We then train $h_{\\phi}$ to take in $z$ , the adaptation signal, and $f_{\\theta}(x)$ to predict the parameters of these FiLM layers. This results in an adapted model $f_{\\hat{\\theta}}$ and improved predictions, $f_{\\hat{\\theta}}(x)$ ." + ], + "image_footnote": [], + "bbox": [ + 531, + 88, + 864, + 191 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "proaches that aim to handle distribution shifts.", + "bbox": [ + 498, + 279, + 805, + 292 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Which test-time adaptation signals to use?", + "text_level": 1, + "bbox": [ + 500, + 303, + 859, + 319 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While developing adaptation signals is not the main focus of this study and is independent of the RNA method, we need to choose some for experimentation. Existing test-time adaptation signals, or proxies, in the literature include prediction entropy [91], spatial autoencoding [27], and self-supervised tasks like rotation prediction [85], contrastive [54] or clustering [9] objectives. The more aligned the adaptation signal is to the target task, the better the performance on the target task [85, 54]. More importantly, a poor signal can cause the adaptation to fail silently [9, 27]. Figure 3 shows how the original loss on the target task changes as different proxy losses from the literature, i.e. entropy [91], consistency between different middle domains [99, 104] are minimized. In all cases, the proxy loss decreases, however, the improvement in the target loss varies. Thus, successful optimization of existing proxy losses does not necessarily lead to better performance on the target task. In this paper, we adopt a few practical and real-world signals for our study. Furthermore, RNA turns out to be less susceptible to a poor adaptation signal vs TTO (see supplementary Tab. 1). This is because RNA is a neural network trained to use these signals to improve the target task, as opposed to being fixed at being SGD, like in TTO.", + "bbox": [ + 496, + 325, + 892, + 674 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1 Employed test-time adaptation signals", + "text_level": 1, + "bbox": [ + 500, + 681, + 820, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We develop test-time adaptation signals for several geometric and semantic tasks as shown in Fig. 4. Our focus is not on providing an extensive list of adaptation signals, but rather on using practical ones for experimenting with RNA as well as demonstrating the benefits of using signals that are rooted in the known structure of the world and the task in hand. For example, geometric computer vision tasks naturally follow the multi-view geometry constraints, thus making that a proper candidate for approximating the test-time error, and consequently, an informative adaptation signal.", + "bbox": [ + 496, + 703, + 890, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Geometric Tasks. The field of multi-view geometry and its theorems, rooted in the 3D structure of the world, provide a rich source of adaptation signals. We demonstrate", + "bbox": [ + 498, + 854, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4676", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/414d86d40713ed35662fab933544db2bb7afe8b11c447173724456c57b2dced1.jpg", + "image_caption": [ + "Figure 3: Adaptation using different signals. Not all improvements in proxy loss translates into improving the target task's performance. We show the results of adapting a pre-trained depth estimation model to a defocus blur corruption by optimizing different adaptation signals: prediction entropy [91], a self-supervised task (sobel edge prediction error [99]), and sparse depth obtained from SFM. The plots show how the $\\ell_1$ target error with respect to ground-truth depth (green, left axis) changes as the proxy losses (blue, right axis) are optimized (shaded regions represent the $95\\%$ confidence intervals across multiple runs of stochastic gradient descent (SGD) with different learning rates). Only adaptation with the sparse depth (SFM) proxy leads to a reduction of the target error. This signifies the importance of employing proper signals in an adaptation framework. Furthermore, we show that RNA is less susceptible to poorer adaptation signal, which results in comparable or improved performance while being significantly faster (see supplementary Table 1)." + ], + "image_footnote": [], + "bbox": [ + 81, + 87, + 467, + 156 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "our results on the following target tasks: monocular depth estimation, optical-flow estimation, and 3D reconstruction. For all, we first run a standard structure-from-motion (SFM) pipeline [81] to get sparse 3D keypoints. For depth estimation, we employ the z-coordinates of the sparse 3D keypoints i.e., noisy sparse depth, from each image as the adaptation signal. For optical flow, we perform keypoint matching across images (which returns sparse optical flow). Lastly, for 3D reconstruction, in addition to the previous two signals, we employ consistency between depth and optical flow predictions as another signal.", + "bbox": [ + 75, + 356, + 467, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Semantic Tasks. For semantic segmentation, we first experiment with using a low number of click annotations for each class, similar to the works on active annotation tools [17, 83, 69]. This gives us sparse segmentation annotations. Likewise, for classification, we use the hierarchical structure of semantic classes, and use coarse labels generated from the WordNet tree [64], similar to [38]. Although these signals (click annotations and coarse labels) are significantly weaker versions of the actual ground truth, thus being cheaper to obtain, it may not be realistic to assume access to them at test-time for certain applications, e.g., real-time ones. Thus, we also show how these can be obtained via $k$ -NN retrieval from the training dataset and patch matching using spatial features obtained from a pretrained self-supervised vision backbone [10] (see Fig. 4).", + "bbox": [ + 75, + 523, + 467, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 768, + 207, + 784 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We demonstrate that our approach consistently outperforms the baselines for adaptation to different distribution shifts (2D and 3D Common Corruptions [35, 43, 44], cross-datasets), over different tasks (monocular depth, image classification, semantic segmentation, optical flow) and datasets (Taskonomy [105], Replica [84], ImageNet [22], COCO [53], ScanNet [20], Hypersim [78]). The source", + "bbox": [ + 75, + 795, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/98d2302b857e9ed23cc310928363630d787968eb8b80abdf3a51089b7e3ade38.jpg", + "image_caption": [ + "Figure 4: Examples of employed test-time adaptation signals. We use a range of adaptation signals in our experiments. These are practical to obtain and yield better performance compared to other proxies. In the left plot, for depth and optical flow estimation, we use sparse depth and optical flow via SFM. In the middle, for classification, for each test image, we perform $k$ -NN retrieval to get $k$ training images. Each of these retrieved image has a one hot label associated with it, thus, combining them gives us a coarse label that we use as our adaptation signal. Finally, for semantic segmentation, after performing $k$ -NN as we did for classification, we get a pseudo-labelled segmentation mask for each of these images. The features for each patch in the test image and the retrieved images are matched. The top matches are used as sparse supervision. See Sec. 4.1 for more details." + ], + "image_footnote": [], + "bbox": [ + 504, + 87, + 888, + 178 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "code can be found on our project page.", + "bbox": [ + 500, + 342, + 756, + 356 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 364, + 687, + 380 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We describe our experimental setup, i.e. different adaptation signals, adaptation mechanisms, datasets and baselines, for different tasks. See Tab. 1 for a summary.", + "bbox": [ + 498, + 388, + 890, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Baselines. We evaluate the following baselines:", + "bbox": [ + 519, + 433, + 834, + 448 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Pre-Adaptation Baseline: The network $f_{\\theta}$ that maps from RGB to the target task, e.g., depth estimation, with no test-time adaptation. We denote this as Baseline for brevity.", + "bbox": [ + 503, + 448, + 890, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Densification: A network that maps from the given adaptation signal for the target task to the target task, e.g., sparse depth from SFM to dense depth. This is a control baseline and shows what can be learned from the test-time supervision alone, without employing input image information or a designed adaptation architecture. See Sec. 4.3 for a variant which includes the image as an additional input.", + "bbox": [ + 501, + 496, + 890, + 602 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "TTO (episodic): We adapt the Baseline model to each episode by optimizing the proxy loss (see Tab. 1 for the adaptation signal used for each task.) at test-time. Its weights are reset to the Baseline model's after optimizing each batch, similar to [91, 108].", + "bbox": [ + 503, + 604, + 890, + 679 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "TTO (online): We continually adapt to a distribution shift defined by a corruption and severity. Test data is assumed to arrive in a stream, and each data point has the same distribution shift, e.g., noise with a fixed standard deviation [91, 85]. The difference with TTO (episodic) is that the model weights are not reset after each iteration. We denote this as TTO for brevity.", + "bbox": [ + 503, + 683, + 890, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "TTO with Entropy supervision (TENT [91]): We adapt the Baseline model trained with log-likelihood loss by optimizing the entropy of the predictions. This is to reveal the effectiveness of entropy as a signal as proposed in [91].", + "bbox": [ + 503, + 792, + 888, + 852 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "TTO with Sobel Edges supervision (TTO-Edges): We adapt the Baseline model trained with an additional decoder that predicts a self-supervised task, similar to [85]. We choose", + "bbox": [ + 503, + 854, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4677", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/702b0f88563add2e394cda85194f9812b194ed50a448e2a749d6a433f36cefd9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TaskAdaptation signalAdapted modelTraining dataOOD evaluation dataBaselines
DepthSFM, masked GTUNet [80], DPT [74]TaskonomyFor SFM: Replica, Replica-CC, ScanNet, For masked GT: Taskonomy-CC,-3DCC, HypersimPre-adaptation, densification, TENT, TTO-edges, TTO
Optical flowKeypoint matchingRAFT [87]FlyingChairs, FlyingThings [87]Replica-CCPre-adaptation
3D reconstructionSFM, keypoint matching,consistencyDepth, optical flow modelsDepth, optical flow dataReplica-CCPre-adaptation, TTO
Semantic segmentationClick annotations, patch matchingFCN [56]COCO (20 classes from Pascal VOC)For click annotations: COCO-CC, For patch matching: ImageNet-CPre-adaptation, densification, TENT, TTO
ClassificationCoarse labels (WordNet, DINO k-NN)ResNet50 [33], ConvNext [55]ImageNetImageNet-C, ImageNet-3DCC, ImageNet-V2Pre-adaptation, DINO k-NN, densification, TENT, TTO
", + "bbox": [ + 84, + 88, + 885, + 189 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1: Overview of the experiments for different target tasks, adaptation methods, and adaptation signals. For each task, we list the adaptation signal (Sec. 3.2) that we use for adaptation. We also list the models that we adapt, and the out-of-distribution (OOD) data used for evaluations and the relevant baselines. When there are different options for adaptation signal, e.g., in the case of depth, the signal is denoted in italics followed by the corresponding OOD dataset. The weights for the semantic segmentation, classification and optical flow models were taken from PyTorch [70].", + "bbox": [ + 75, + 200, + 893, + 251 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a3387b40c39fd6ab0bd7db7ba83502a0b6dee9e02d02fc449b7340cc9d89701e.jpg", + "image_caption": [ + "Figure 5: RNA can achieve similar performance as TTO in a much shorter time. We compare how the $\\ell_1$ errors of the adaptation mechanisms decrease over wall-clock time (s). The errors are averaged over all episodes (and all corruptions for Replica-CC). RNA only requires a forward pass at test-time, while TTO requires multiple forward and backward passes. On ScanNet and Replica-CC, RNA takes 0.01s, while TTO takes 3s to achieve similar performance. Furthermore, RNA is not trained with test-time shifts unlike TTO, thus, it learned to use the additional supervision to adapt to unseen shifts." + ], + "image_footnote": [], + "bbox": [ + 78, + 257, + 272, + 321 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f0ecfc202b74f3c5d625567c624991de8520097a82224ce68553f85c52a1f8f5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 272, + 257, + 468, + 321 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to predict Sobel edges as it has been shown to be robust to certain shifts [99]. We optimize the error of the edges predicted by the model and edges extracted from the RGB image to reveal the value of edge error as a supervision.", + "bbox": [ + 78, + 449, + 468, + 511 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "RNA configurations. At test-time, we first get the predictions of the Baseline model and compute the adaptation signal. The predictions and adaptation signal are then passed to $h_{\\phi}$ which adapts $f_{\\theta}$ to $f_{\\hat{\\theta}}$ . The test images are then passed to $f_{\\hat{\\theta}}$ to get the final predictions. We evaluate following variants of RNA.", + "bbox": [ + 75, + 522, + 468, + 613 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "RNA (frozen $f$ ): Baseline model weights, $f_{\\theta}$ , are frozen when training $h_{\\phi}$ . We call this variant RNA for brevity.", + "bbox": [ + 80, + 619, + 468, + 652 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "RNA (jointly trained $f$ ): In contrast to the frozen $f$ variant, here we train $h_{\\phi}$ jointly with the Baseline network. This variant requires longer training.", + "bbox": [ + 80, + 652, + 468, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Adaptation signal. As described in Sec. 3.2, we compute a broad range of test-time signals from the following processes. Each case describes a process applied on query image(s) in order to extract a test-time quantity.", + "bbox": [ + 75, + 710, + 468, + 773 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Structure-from-motion (SFM): Given a batch of query images, we use COLMAP [81] to run SFM, which returns sparse depth. The percentage of valid pixels, i.e. depth measurements, is about $0.16\\%$ on Replica-CC and $0.18\\%$ on Replica. For ScanNet we use the pre-computed sparse depth from [79], which has about $0.04\\%$ valid pixels. As running SFM on corrupted images results in noisy sparse depth, we train $h_{\\phi}$ to be invariant to noise [102, 79].", + "bbox": [ + 78, + 779, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Masked ground truth (GT): We apply a random mask to the GT depth of the test image. We fixed the valid pixels to $0.05\\%$ of all pixels, i.e. similar sparsity as SFM (see the supplementary for other values). This a control proxy as it enables a better evaluation of the adaptation methods without conflating with the shortcomings of adaptation signals. It is also a scalable way of simulating sparse depth from real-world sensors, e.g., LiDAR, as also done in [92, 59, 41].", + "bbox": [ + 501, + 258, + 892, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Click annotations: We generate click annotations over random pixels for each class in a given image using GT - simulating an active annotation pipeline. The number of pixels ranges from 3 to 25, i.e. roughly $0.01\\%$ of the total pixels, similar to [7, 69, 83, 109, 17].", + "bbox": [ + 501, + 397, + 892, + 472 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Patch matching: To not use GT click annotations, for each test image, we first retrieve its $k$ -NN images from the original clean training dataset using DINO features [10]. We then get segmentation masks on these $k$ images. If the training dataset has labels for segmentation we use them directly, otherwise we obtain them from a pretrained network. For each of the $k$ training images and test image, we extract non-overlapping patches. The features for each patch that lie inside the segmentation masks of the $k$ training images are matched to the features of every patch in the test image. These matches are then filtered and used as sparse segmentation annotations. See Fig. 4 for illustration.", + "bbox": [ + 501, + 474, + 893, + 656 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Coarse labels (WordNet): We generate 45 coarse labels from the 1000-way ImageNet labels, i.e. making the labels $22 \\times$ coarser, using the WordNet tree [64], similar to [39]. See supplementary for more details on the construction and results for other coarse label sets.", + "bbox": [ + 501, + 659, + 893, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Coarse labels (DINO $k$ -NN): For each test image, we retrieve the $k$ -NN images from the training dataset using DINO features [10]. Each of these $k$ training images is associated with an ImageNet class, thus, combining $k$ one-hot labels gives us a coarse label.", + "bbox": [ + 501, + 737, + 893, + 813 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Keypoint matching: We perform keypoint matching across images to get sparse optical flow.", + "bbox": [ + 503, + 816, + 892, + 847 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4678", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d7d5106eb9e34079491ea4e5bc50440aebc555d81ec897feae52c98224fa9153.jpg", + "image_caption": [ + "Figure 6: Qualitative results of RNA vs the baselines for semantic segmentation on random query images on COCO-CC (left) and depth on images from ScanNet, Taskonomy-3DCC and Replica-CC (right). For semantic segmentation, we use 15 pixel annotations per class. For Taskonomy-3DCC, we use sparse depth with $0.05\\%$ valid pixels (30 pixels per image). See Fig. 7 for results on different adaptation signal levels. For ScanNet and Replica-CC, the adaptation signal is sparse depth measurements from SFM [81] with similar sparsity ratios to Taskonomy-3DCC. The predictions with proposed adaptation signals are shown in the last two rows. They are noticeably more accurate compared to the baselines. Comparing TTO and RNA, RNA's predictions are more accurate for segmentation, and sharper than TTO for depth (see the ellipses) while being significantly faster. See 4.2 and supplementary for more results." + ], + "image_footnote": [], + "bbox": [ + 138, + 88, + 830, + 375 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Adaptation with RNA vs TTO", + "text_level": 1, + "bbox": [ + 76, + 483, + 344, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here we summarize our observations from adapting with RNA vs TTO. As described, TTO represents the approach of closed-loop adaptation using the adaptation signal but without benefiting from amortization and learning (the adaptation process is fixed to be standard SGD). These observations hold across different tasks. See Sec. 4.3 for results.", + "bbox": [ + 75, + 507, + 470, + 611 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "RNA is efficient. As RNA only requires a forward pass at test-time, it is orders of magnitude faster than TTO and is able to attain comparable performance to TTO. In Fig. 5, we compare the runtime of adaption with RNA and TTO for depth prediction. On average, for a given episode, RNA obtains similar performance as TTO in 0.01s, compared to TTO's 3-5s. Similarly, for dense 3D reconstruction, RNA is able to adapt in 0.008s compared to TTO's 66s (see Fig. 9). This suggests a successful amortization of the adaptation optimization by RNA.", + "bbox": [ + 75, + 613, + 468, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Furthermore, RNA's training is also efficient as it only requires training a small model, i.e. $5 - 20\\%$ of the Baseline model's parameters, depending on the task. Thus, RNA has a fixed overhead, and small added cost at test-time.", + "bbox": [ + 75, + 763, + 468, + 824 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "RNA's predictions are sharper than TTO for dense prediction tasks. From the last two rows of Fig. 6, it can be seen that RNA retains fine-grained details. This is a noteworthy point and can be attributed to the fact that RNA benefits from a neural network, thus its inductive biases can", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "be beneficial (and further engineered) for such advantages. This is a general feature that RNA, and more broadly using a learning-based function to amortize adaptation optimization, brings – in contrast to limiting the adaptation process to be SGD, as represented by TTO.", + "bbox": [ + 496, + 483, + 890, + 559 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "RNA generalizes to unseen shifts. RNA performs better than TTO for low severities (see supplementary for more details). However, as it was not exposed to any corruptions, the performance gap against TTO narrows at high severities as expected, which is exposed to corruptions at test-time.", + "bbox": [ + 496, + 560, + 890, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We hypothesize that the generalization property of RNA is due to the following reasons. 1. Even though $f_{\\theta}$ was trained to convergence, it does not achieve exactly 0 error. Thus, when $h_{\\phi}$ is trained with a frozen $f_{\\theta}$ with the training data, it can still learn to correct the errors of $f_{\\theta}$ , thus, adapting $f_{\\theta}$ . 2. Adaptation signals, by definition, are expected to be relatively robust to distribution shifts. Even though the RGB image has been corrupted or from a new domain, the adaptation signal is more aligned with the target task. Thus, the input to $h_{\\phi}$ does not undergo a significant shift and is able to adapt $f_{\\theta}$ .", + "bbox": [ + 496, + 637, + 890, + 803 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Experiments using Various Target Tasks", + "text_level": 1, + "bbox": [ + 498, + 815, + 844, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we provide a more comprehensive set of evaluations covering various target tasks and adaptation signals. In all cases, RNA is a fixed general framework without being engineered for each task and shows supportive results.", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4679", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b8da78e7fff73c44e55e16f83c7a235230bad61ea2a430e11f7a8dbcf784087d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Adaptation SignalSFMSparse GTRelative Runtime
DatasetReplicaScanNetTaskonomyHypersim
ShiftCDSCCCDSNoneCC3DCCCDS
Pre-adaptation Baseline1.756.083.302.685.744.7533.641.00
Densification2.504.192.351.721.721.7217.251.00
TENT [91]2.036.094.035.515.514.4835.4515.85
TTO-Edges [85]1.736.143.282.705.694.7433.6920.98
RNA (frozen f)1.724.261.771.121.681.4916.171.56
RNA (jointly trained f)1.663.411.741.111.501.3717.131.56
TTO (Episodic)1.723.311.851.622.992.3117.7714.85
TTO (Online)1.823.161.761.131.481.3414.1714.85
", + "bbox": [ + 78, + 89, + 470, + 209 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2: Quantitative adaptation results on depth estimation. $\\ell_1$ errors on the depth prediction task. (Lower is better. Multiplied by 100 for readability. The best models within 0.0003 error are shown in bold.) We generate distribution shifts by applying Common Corruptions (CC), 3D Common Corruptions (3DCC) and from performing cross-dataset evaluations (CDS). The results from CC and 3DCC are averaged over all distortions and severity levels on Taskonomy and 3 severity levels on Replica data. The adaptation signal from Taskonomy is masked GT (fixed at $0.05\\%$ valid pixels) while that from Replica and ScanNet is sparse depth from SFM. RNA and TTO notably outperform the baselines. RNA successfully matches the performance of TTO while being around 10 times faster.", + "bbox": [ + 76, + 219, + 468, + 351 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "See supplementary for the losses for different corruption types, sparsity levels, and the results of applying RNA to other adaptation signals.", + "bbox": [ + 76, + 352, + 468, + 377 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e7e769338393d03bb39644f20fd6c0faa1d25f8eb07477a726622d292d273109.jpg", + "image_caption": [ + "Figure 7: Qualitative adaptation results on semantic segmentation on random query images on COCO-CC. RNA notably improves the prediction quality using error feedback from as few as 3 random pixels." + ], + "image_footnote": [], + "bbox": [ + 86, + 388, + 460, + 505 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/320af74ca6b0453873f53973af492360f55e3e049d93d41b27a0093712d3d65b.jpg", + "image_caption": [ + "Figure 8: Quantitative adaptation results on semantic segmentation. Each point shows the mean IOU over 15 corruptions and 5 severities. RNA significantly improves over baselines. Black dashed line shows the mean IOU of the baseline model for clean validation images, and is provided as an upper bound on performance. Numbers in the legend denote averages over all supervision pixel counts. See supplementary for a breakdown." + ], + "image_footnote": [], + "bbox": [ + 89, + 551, + 457, + 693 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Depth. We demonstrate the results quantitatively in Tab. 2 and Fig. 5 and qualitatively in Fig. 6. In Tab. 2, we compare RNA against all baselines, and over several distribution shifts and different adaptation signals. Our RNA variants outperform the baselines overall. TTO (online) has a better performance than TTO (episodic) as it assumes a smoothly changing distribution shift, and it continuously updates the model weights. RNA (jointly trained $f$ ) has a", + "bbox": [ + 75, + 780, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "better performance among RNA variants. This is reasonable as the target model is not frozen, thus, is less restrictive.", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As another baseline, we trained a single model that takes as input a concatenation of the RGB image and sparse supervision, i.e. multi-modal input. However, its average performance on Taskonomy-CC was $42.5\\%$ worse than RNA's (see sup. mat. Sec. 3.2). Among the baselines that do not adapt, densification is the strongest under distribution shift due to corruptions. This is expected as it does not take the RGB image as input, thus, it is not affected by the underlying distribution shift. However, as seen from the qualitative results in Figs. 6, 7, unlike RNA, densification is unable to predict fine-grained details (which quantitative metrics often do not well capture). We also show that the gap between RNA and densification widens with sparser supervision (see sup. mat. Fig. 1), which confirms that RNA is making use of the error feedback signal, to adapt $f$ .", + "bbox": [ + 496, + 122, + 892, + 349 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/eeb125b83fedddb1ae3b62ea13e5a467fef066c1736069bc593cbbdb9a18ea8b.jpg", + "image_caption": [ + "Figure 9: Adaptation results for 3D reconstruction. Using appropriate adaptation signals from multi-view geometry can recover accurate 3D reconstructions. We report the average $\\ell_1$ error between ground truth 3D coordinates and the estimated ones. The titles above each column refers to the depth model used to get the reconstruction. TTO+MVC corresponds to the predictions after multi-view consistency optimization. It can be seen that RNA and TTO improve the reconstructions over the baselines with RNA being significantly faster. See supplementary Fig. 4 for more results and the corresponding error maps." + ], + "image_footnote": [], + "bbox": [ + 519, + 359, + 872, + 694 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Dense 3D Reconstruction. Here, we combine multiple adaptation signals from multi-view geometry. First, we adapt the weights of the depth and optical flow models independently. The results from this adaptation can be found in the previous paragraph (for depth) and supplementen", + "bbox": [ + 496, + 825, + 890, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4680", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5e0cf43e8e6861500e3e10516eea6f401d6ab2a12be782ee4a41703768494e91.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Adaptation SignalDatasetCleanIN-CIN-3DCCIN-V2Rel. Runtime
-Pre-adaptation Baseline23.8561.6654.9737.151.00
EntropyTENT24.6746.1947.1337.075.51
Coarse labels (wordnet)Densification95.5095.5095.5095.50-
TTO (Online)24.7240.6242.9036.775.72
RNA (frozen f)16.7241.2140.3725.531.39
Coarse labels (DINO)DINO (k-NN)25.5652.6448.2437.39-
TTO (Online)24.5951.5949.1836.965.72
RNA (frozen f)24.3654.8652.2936.881.39
", + "bbox": [ + 86, + 88, + 455, + 175 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tary (for optical flow). Next, the two models are adapted to make their predictions consistent with each other. This is achieved using the same process as [58], i.e. multi-view-consistency (MVC). See supplementary for details.", + "bbox": [ + 75, + 250, + 468, + 310 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 9 shows the point cloud visualizations on Replica where the input was corrupted with Gaussian Noise. This results in collapsed depth predictions, thus, reconstructions are unusable (Baseline column) and performing MVC is not helpful (Baseline+MVC). Adapting the depth predictions using TTO and MVC improves the reconstruction notably while RNA achieves a similar performance significantly faster.", + "bbox": [ + 75, + 311, + 468, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Semantic Segmentation. We experiment with click annotations and DINO patch matching as adaptation signals. Click annotations: In Fig. 8, we show how the IoU changes with the adaptation signal level on COCO-CC. As the Baseline and TENT do not make use of this signal, their IoU is a straight line. RNA clearly outperforms the baselines for all levels of adaptation signal. Figure 7 shows the qualitative results with increasing supervision, and Fig. 6 (left) a comparison against all baselines, demonstrating higher quality predictions with RNA.", + "bbox": [ + 75, + 431, + 468, + 582 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "DINO patch matching: We perform patch matching on DINO features (described in Sec. 4.1) to get the adaptation signal. As the patch matching process can be computationally expensive, we demonstrate our results on all cat classes in ImageNet and over one noise, blur and digital corruption for 3 levels of severity. We used the predictions of a pretrained FCN on the clean images as pseudolabels to compute IoU. The mean IoU averaged over these corruptions and severities is 48.98 for the baseline model, 53.45 for TTO. RNA obtains a better IOU of 58.04, thus it can make use of the sparse annotations from DINO patch matching.", + "bbox": [ + 75, + 583, + 468, + 748 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Image Classification. We experiment with coarse labels from WordNet and DINO $k$ -NN as adaptation signals.", + "bbox": [ + 75, + 750, + 468, + 779 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Coarse labels (WordNet): Table 3 shows the results from using 45-coarse labels on ImageNet- $\\{\\mathrm{C},3\\mathrm{DCC},\\mathrm{V}2\\}$ . This corresponds to $22\\mathrm{x}$ coarser supervision compared to the 1000 classes that we are evaluating on. TENT seems to have notable improvements in performance under corruptions for classification, unlike for semantic segmentation and depth. We show that using coarse supervision results in even better performance, about a further 5 pp reduction", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "in error. Furthermore, on uncorrupted data, i.e. clean, and ImageNet-V2 [76], RNA gives roughly 10 pp improvement in performance compared to TTO. Thus, coarse supervision provides a useful signal for adaptation while requiring much less effort than full annotation [97]. See supplementary for results on other coarse sets.", + "bbox": [ + 496, + 90, + 890, + 180 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Coarse labels (DINO $k$ -NN): We also show results from using coarse sets generated from DINO $k$ -NN retrieval. This is shown in the last 3 rows of Tab. 3. Both RNA and TTO use this coarse information to outperform the non-adaptive baselines. However, they do not always outperform TENT, which could be due to the noise in retrieval.", + "bbox": [ + 496, + 181, + 890, + 271 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablations and additional results", + "text_level": 1, + "bbox": [ + 500, + 281, + 781, + 295 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ca75b643d88d4494cbc0e33df3685dfa1c078f89092ceee3df0de679c7dff09a.jpg", + "table_caption": [ + "Table 3: Quantitative adaptation results on on ImageNet (IN) classification task. We evaluate on the clean validation set, ImageNet-C,3DCC,V2}. We report average error $(\\%)$ for 1000-way classification task over all corruptions and severities. For the coarse labels with WordNet supervision, we use 45-coarse labels. For DINO $k$ NN, we set $k = 20$" + ], + "table_footnote": [], + "table_body": "
Task (Arch.)Depth (DPT [74])Classification (ConvNext [55])
ShiftCleanCCRel. RuntimeCleanIN-CRel. Runtime
Pre-adaptation Baseline2.233.761.0018.1342.951.00
TTO (Online)1.822.6113.8517.8341.4411.04
RNA (frozen f)1.131.561.0114.3238.041.07
", + "bbox": [ + 503, + 306, + 888, + 368 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Aaptations of main network $f_{\\theta}$ with different backbones. Previous results in the paper were from adapting $f_{\\theta}$ with a UNet architecture. Here, we study the performance of RNA on other architectures of $f_{\\theta}$ , namely, the dense prediction transformer (DPT) [74] for depth and ConvNext [55] for image classification. Table 4 shows the results of incorporating RNA to these architectures. In both cases, RNA is able to improve on the error and runtime of TTO. Thus, RNA can be applied to a range of architectures.", + "bbox": [ + 496, + 444, + 890, + 580 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/475a5981322b7227c2c41561ba3cdf58594e580fcccd23467285e840b5f33da9.jpg", + "table_caption": [ + "Table 4: RNA works across different architectures of the main network $f_{\\theta}$ such as DPT [74] and ConvNext [55]. Quantitative adaptation results on depth estimation and image classification on Taskonomy and ImageNet datasets, respectively. (Lower is better. $\\ell_1$ errors for depth estimation are multiplied by 100 for readability.)" + ], + "table_footnote": [], + "table_body": "
Method\\ShiftNoneTaskonomy-CCTaskonomy-3DCCHypersimBlendedMVG
Pre-adaptation0.0270.0570.0480.3363.450
RNA (HyperNetwork-x)0.0190.0410.0330.2572.587
RNA (FiLM-x)0.0190.0390.0330.2792.636
RNA (FiLM-f)0.0130.0240.0200.1982.310
", + "bbox": [ + 503, + 592, + 888, + 642 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5: Implementations of different architectures for the controller network $h_{\\phi}$ . $\\ell_1$ errors on the depth estimation task under distribution shifts are reported. The adaptation signal here is masked GT, fixed at 0.05% of valid pixels.", + "bbox": [ + 496, + 652, + 890, + 702 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Implementations of different architectures for the controller network $h_{\\phi}$ . We experiment with different architectures for $h_{\\phi}$ e.g., HyperNetworks [31], other FiLM variants, or adapting the input instead of the model parameters. Instead of adding FiLM layers to adapt $f_{\\theta}$ (denoted as FiLM- $f$ ), as described in Sec. 3.1, we also experimented with adding FiLM layers to a UNet model that is trained to update the input image $x$ (denoted as FiLM- $x$ ). For FiLM- $x$ , only $x$ is updated and there is no adaptation on $f_{\\theta}$ . Lastly, as Hypernetworks [31] have been shown to be expressive and suitable for adaptation, we trained a HyperNetwork, in this case an MLP, to predict the weights of a 3-layer convolutional network that updates $x$ (denoted as HyperNetwork-", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4681", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "$x$ ). The results of adaptation with these variants of RNA are shown in Table 5. The FiLM- $f$ variant performed best, thus, we adopted it as our main architecture. See supplementary Sec. 2.2 for more details and a discussion on the trade-offs of the choices of implementing this closed-loop \"control\" system, namely those that make stronger model-based assumptions.", + "bbox": [ + 75, + 90, + 468, + 196 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Controlling for number of parameters. We ran a control experiment where all methods have the same architecture, thus, same number of parameters. The results are in the supplementary Table 2. RNA still returns the best performance. Thus, its improvement over the baselines is not due to a different architecture or number of parameters but due to its test-time adaptation mechanism.", + "bbox": [ + 75, + 196, + 470, + 303 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Approaches for handling distribution shifts", + "text_level": 1, + "bbox": [ + 76, + 318, + 464, + 335 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this section, we provide a unified discussion about the approaches that aim to handle distribution shifts. Figure 10 gives an overview of how these approaches can be characterized. Open-loop systems predict $y$ by only using their inputs without receiving feedback. Training-time robustness methods, image modifications, and multi-modal methods fall into this category. These methods assume the learned model is frozen at the test-time. Thus, they aim to incorporate inductive biases at training time that could be useful against distribution shifts at the test-time. The closed-loop systems, on the other hand, are adaptive as they make use of a live error feedback signal that can be computed at test-time from the model predictions and an adaptation signal.", + "bbox": [ + 75, + 344, + 468, + 541 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In the interest of space, we move the detailed discussion about each of these variants to Sec. 1.2 of the supplementary. In particular, elaboration of the distinction between a model-based vs model-free approach, denoising/image-modification methods, multi-modal methods, and our observations over comparing the conclusions of [46] el al. and our experiments are provided there.", + "bbox": [ + 75, + 541, + 468, + 647 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Conclusion and Limitations", + "text_level": 1, + "bbox": [ + 76, + 662, + 333, + 678 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We presented RNA, a method for efficient adaptation of neural networks at test-time using a closed-loop formulation. It involves training a side network to use a test-time adaptation signal to adapt a main network. This network acts akin to a \"controller\" and adapts the main network based on the adaptation signal. We showed that this general and flexible framework can generalize to unseen shifts, and as it only requires a forward pass at test-time, it is orders of magnitude faster than TTO. We evaluated this approach using a diverse set of adaptation signals and target tasks. We briefly discuss the limitations and potential future works:", + "bbox": [ + 75, + 688, + 468, + 853 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Different instantiation of RNA and amortization. While we experimented with several RNA variants (see supplementary for details), further investigation toward a stronger", + "bbox": [ + 76, + 854, + 470, + 900 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/a81f6ddc1ff511cba8c550d9522a0d86cdf1e26e5c7318429b26a4acbfa7890a.jpg", + "image_caption": [ + "Figure 10: An overview of methods that aim to handle distribution shifts. Left: Open-loop systems predict $y$ by only using their inputs without receiving feedback. The first and popular example of open-loop systems is training-time robustness methods (data augmentation, architectural changes, etc.). The next example is the methods that modify the input $x$ , e.g. denoising or style changes, to recover the original image before corruption, independent of $y$ . Furthermore, there are multi-modal methods that use an additional input $z$ . As the learned model is frozen at test-time, these methods need to anticipate the distribution shift by incorporating inductive biases at training time (See also Fig. 1.). Right: In contrast, closed-loop systems make use of its current output, $y$ , and an adaptation signal, $z$ , to form an error feedback signal that can be used to update its predictions. Thus, they adapt to the shifts as they occur. We can then group closed-loop systems into model-based and model-free methods. The former performs adaptation by estimating the parameters $e$ of specific modeled distribution shift families, while the latter performs adaptation in a data-driven way without explicitly modeling certain distribution shifts. Adaptation can be performed via running an optimization, i.e. TTO via SGD, or via amortization, i.e., training a side controller network to predict TTO updates that minimize the error feedback. Our proposed method, RNA, belongs to the model-free adaptation approach that makes use of amortization for efficiency." + ], + "image_footnote": [], + "bbox": [ + 527, + 85, + 864, + 258 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "instantiation of RNA which can generalize to more shifts and handle more drastic changes, e.g. via building in a more explicit \"model\" of the shifts and environment (see the discussion about [46]), is important. In general, as the role of the controller network is to amortize the training optimization of the main network, the amortized optimization literature [3] is one apt resource to consult for this purpose.", + "bbox": [ + 496, + 534, + 890, + 640 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Hybrid mechanism for activating TTO in RNA. TTO constantly adapts a model to a distribution shift, hence, in theory, it can adapt to any shift despite being comparatively inefficient. To have the best of both worlds, investigating mechanisms for selectively activating TTO within RNA when needed can be useful.", + "bbox": [ + 496, + 641, + 890, + 729 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Finding adaptation signals for a given task. While the focus of this study was not on developing new adaption signals, we demonstrated useful ones for several core vision tasks, but there are many more. Finding these signals requires either knowledge of the target task so a meaningful signal can be accordingly engineered or core theoretical works on understanding how a proxy and target objectives can be \"aligned\" for training.", + "bbox": [ + 496, + 732, + 890, + 852 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgement: The authors thank Onur Beker. This work was partially supported by the ETH4D and EPFL EssentialTech Centre Humanitarian Action Challenge Grant.", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "4682", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Hassan Akbari, Liangzhe Yuan, Rui Qian, Wei-Hong Chuang, Shih-Fu Chang, Yin Cui, and Boqing Gong. Vatt: Transformers for multimodal self-supervised learning from raw video, audio and text. Advances in Neural Information Processing Systems, 34:24206-24221, 2021. 2", + "[2] Jean-Baptiste Alayrac, Adria Recasens, Rosalia Schneider, Relja Arandjelovic, Jason Ramapuram, Jeffrey De Fauw, Lucas Smaira, Sander Dieleman, and Andrew Zisserman. Self-supervised multimodal versatile networks. 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PMLR, 2019. 2" + ], + "bbox": [ + 78, + 90, + 468, + 501 + ], + "page_idx": 13 + }, + { + "type": "page_number", + "text": "4687", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 13 + } +] \ No newline at end of file diff --git a/2023/Rapid Network Adaptation_ Learning to Adapt Neural Networks Using Test-Time Feedback/32896e91-9d8e-4427-a165-f57c45c9afec_model.json b/2023/Rapid Network Adaptation_ Learning to Adapt Neural Networks Using Test-Time Feedback/32896e91-9d8e-4427-a165-f57c45c9afec_model.json new file mode 100644 index 0000000000000000000000000000000000000000..a70d14e95f005345d12bef63f1405330b7e0954b --- /dev/null +++ b/2023/Rapid Network Adaptation_ Learning to Adapt Neural Networks Using Test-Time Feedback/32896e91-9d8e-4427-a165-f57c45c9afec_model.json @@ -0,0 +1,3022 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.166, + 0.131, + 0.804, + 0.177 + ], + "angle": 0, + "content": "Rapid Network Adaptation: Learning to Adapt Neural Networks Using Test-Time Feedback" + }, + { + "type": "text", + "bbox": [ + 0.191, + 0.204, + 0.284, + 0.221 + ], + "angle": 0, + "content": "Teresa Yeo" + }, + { + "type": "text", + "bbox": [ + 0.324, + 0.204, + 0.477, + 0.222 + ], + "angle": 0, + "content": "Oguzhan Fatih Kar" + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.204, + 0.636, + 0.222 + ], + "angle": 0, + "content": "Zahra Sodagar" + }, + { + "type": "text", + "bbox": [ + 0.676, + 0.204, + 0.774, + 0.221 + ], + "angle": 0, + "content": "Amir Zamir" + }, + { + "type": "text", + "bbox": [ + 0.268, + 0.226, + 0.712, + 0.243 + ], + "angle": 0, + "content": "Swiss Federal Institute of Technology Lausanne (EPFL)" + }, + { + "type": "text", + "bbox": [ + 0.301, + 0.259, + 0.668, + 0.273 + ], + "angle": 0, + "content": "https://rapid-network-adaptation.epfl.ch/" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.308, + 0.314, + 0.324 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.474, + 0.614 + ], + "angle": 0, + "content": "We propose a method for adapting neural networks to distribution shifts at test-time. In contrast to training-time robustness mechanisms that attempt to anticipate and counter the shift, we create a closed-loop system and make use of test-time feedback signal to adapt a network on the fly. We show that this loop can be effectively implemented using a learning-based function, which realizes an amortized optimizer for the network. This leads to an adaptation method, named Rapid Network Adaptation (RNA), that is notably more flexible and orders of magnitude faster than the baselines. Through a broad set of experiments using various adaptation signals and target tasks, we study the generality, efficiency, and flexibility of this method. We perform the evaluations using various datasets (Taskonomy, Replica, ScanNet, Hypersim, COCO, ImageNet), tasks (depth, optical flow, semantic segmentation, classification), and distribution shifts (Cross-datasets, 2D and 3D Common Corruptions) with promising results." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.647, + 0.21, + 0.663 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Neural networks are found to be unreliable against distribution shifts [23, 35, 43, 42, 29]. Examples of such shifts include blur due to camera motion, object occlusions, changes in weather conditions and lighting, etc. The training-time strategies to deal with this issue attempt to anticipate the shifts that may occur and counter them at the training stage – for instance, by augmenting the training data or updating the architecture with corresponding robustness inductive biases. As the possible shifts are numerous and unpredictable, this approach has inherent limitations. This is the main motivation behind test-time adaptation methods, which instead aim to adapt to such shifts as they occur and recover from failure. In other words, these methods choose adaptation over anticipation (see Fig. 1). In this work, we propose a test-time adaptation framework that aims to perform an ef" + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.308, + 0.865, + 0.572 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.587, + 0.895, + 0.771 + ], + "angle": 0, + "content": "Figure 1: Adaptive vs non-adaptive neural network pipelines. Top: In order to be robust, non-adaptive methods include training-time interventions that anticipate and counter the distribution shifts that will occur at test-time (e.g., via data augmentation). The learned model, \\( f_{\\theta} \\), is frozen at test-time, thus upon encountering an out-of-distribution input, its predictions may collapse. Bottom: Adaptive methods create a closed-loop and use an adaptation signal at test-time. The adaptation signal is a quantity that can be computed at test-time from the environment. \\( h_{\\phi} \\) acts as a \"controller\" by taking in an error feedback, computed from the adaptation signal and model predictions, to adapt \\( f_{\\theta} \\) accordingly. It can be implemented as a (i) standard optimizer (e.g., using SGD) or (ii) neural network. The former is equivalent to test-time optimization (TTO), while the latter aims to amortize the optimization process, by training a controller network to adapt \\( f_{\\theta} \\) - thus, it can be more efficient and flexible. In this work, we study the latter approach and show its efficiency and flexibility." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.779, + 0.892, + 0.809 + ], + "angle": 0, + "content": "ficient adaptation of a given main network using a feedback signal." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.903 + ], + "angle": 0, + "content": "One can consider performing \"test-time optimization\" (TTO) for this purpose, similar to previous works [91, 108, 27] e.g. simply using SGD to finetune the network to reduce a proxy loss [91]. While this can successfully adapt a network, it is unnecessarily inefficient as it does not make use of the learnable regularities in the adaptation pro" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4674" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "cess, and consequently, unconducive for real-world applications. It also results in a rigid framework as the update mechanism is fixed to be the same as the training process of neural networks (SGD). We show this process can be effectively amortized using a learning-based feed-forward controller network, which yields orders of magnitude faster results (See Fig. 1, Sec. 4.3). In addition, it provides flexibility advantages as the controller is implemented using a neural network and can be engineered to include arbitrary inductive biases and desired features that could counter the suboptimalities of the adaptation signal." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.272, + 0.22, + 0.287 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.297, + 0.47, + 0.357 + ], + "angle": 0, + "content": "Our work focuses on how to adapt a neural network efficiently at test-time on a range of tasks and adaptation signals. We give an overview of relevant topics. See the supplementary Sec. 7 for more related works." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.358, + 0.47, + 0.478 + ], + "angle": 0, + "content": "Robustness methods anticipate the distribution shift that can occur and incorporate inductive biases into the model to help it generalize. Popular methods include data augmentation [61, 107, 57, 37, 103, 101, 34, 43], self-/pre-training [36, 95, 25, 72, 96, 75, 32], architectural changes [19, 8, 82, 62, 55] or ensembling [48, 67, 99, 73, 40, 68]. We focus on adaptation mechanisms and identifying practical adaptation signals that can be used at test-time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.479, + 0.47, + 0.629 + ], + "angle": 0, + "content": "Amortized optimization methods make use of learning to improve (e.g., speed-up) the solution of optimization problems, particularly for settings that require repeatedly solving similar instances of the same underlying problem [49, 11, 4, 106, 26, 94, 60, 14, 3]. Fully amortized optimization methods model the shared structure between past instances of solved problems to regress the solution to a new problem [31, 21, 52]. As adapting to distribution shifts can be cast as solving an optimization problem at test-time, our method can be seen as an amortized solution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Test-time adaptation methods for geometric tasks. Many existing frameworks, especially in geometric tasks such as aligning a 3D object model with an image of it, in effect instantiate a task-specific case of closed-loop optimization for each image [60, 106, 63]. Common sources of their adaptation quantity include sensor data [92, 98, 15, 89, 102, 18], structure from motion (SFM) [93, 47], motion [12], and photometric and multi-view consistency constraints (MVC) [58, 45]. Many of the latter methods often focus on depth prediction and they introduce losses that are task-specific, e.g., [93] optimize a photometric consistency loss. We differ by aiming to investigate a more general framework for test-time adaptation that can be applied to several tasks. For MVC, while we adopt the same losses as [58], we show under collapsed predictions, optimizing only MVC constraints is not sufficient for recovering predictions; depth predictions need to be adapted and this can be done efficiently using our framework (see Sec. 4.3)." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.092, + 0.892, + 0.272 + ], + "angle": 0, + "content": "Test-time adaptation methods for semantic tasks. Most of these works involve optimizing a self-supervised objective at test-time [85, 91, 54, 27, 28, 108, 9, 51, 100]. They differ in the choice of self-supervised objectives, e.g., prediction entropy [91], mutual information [51], and parameters optimized [9]. However, as we will discuss in Sec. 3.2, and as shown by [9, 27, 65], existing methods can fail silently, i.e. successful optimization of the adaptation signal loss does not necessarily result in better performance on the target task. We aim to have a more efficient and flexible method and also show that using proper adaptation signals results in improved performance." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.273, + 0.892, + 0.424 + ], + "angle": 0, + "content": "Multi-modal frameworks are models that can use the information from multiple sources, e.g., RGB image, text, audio, etc., [13, 5, 86, 50, 2, 16, 72, 1, 6, 30]. Schematically, our method has similarities to multi-modal learning (as many amortized optimization methods do) since it simultaneously uses an input RGB image and an adaptation signal. The main distinction is that our method implements a particular process toward adapting a network to a shift using an adaptation signal from the environment – as opposed to a generic multi-modal learning." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.437, + 0.591, + 0.451 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.462, + 0.892, + 0.628 + ], + "angle": 0, + "content": "In Fig. 1, we schematically compared methods that incorporate robustness mechanisms at training-time (thus anticipating the distribution shift) with those that adapt to shifts at test-time. Our focus is on the latter. In this section, we first discuss the benefits and downsides of common adaptation methods (Sec. 3.1). We then propose an adaptation method that is fast and can be applied to several tasks (Sec. 3.1.1). To adapt, one also needs to be able to compute an adaptation signal, or proxy, at the test-time. In the second part of the section (Sec. 3.2), we study a number of practical adaptation signals for a number of tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.637, + 0.74, + 0.652 + ], + "angle": 0, + "content": "3.1. How to adapt at test-time?" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "An adaptive system is one that can respond to changes in its environment. More concretely, it is a system that can acquire information to characterize such changes, e.g., via an adaptation signal that provides an error feedback, and make modifications that would result in a reduction of this error (see Fig. 1). The methods for performing the adaptation of the network range from gradient-based updates, e.g. using SGD to fine-tune the parameters [85, 91, 27], to the more efficient semi-amortized [110, 88] and amortized approaches [90, 66, 77] (see Fig. 6 of [77] for an overview). As amortization methods train a controller network to substitute the explicit optimization process, they only require a forward pass at test-time. Thus, they are computationally efficient. Gradient-based approaches, e.g., TTO, can be powerful adaptation methods when the test-time signal is robust and well-suited for the task (see Fig. 4). How-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4675" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "ever, they are inefficient and have the risk of failing silently and the need for carefully tuned optimization hyperparameters [9]. In this work, we focus on an amortization-based approach." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.153, + 0.471, + 0.41 + ], + "angle": 0, + "content": "Notation. We use \\(\\mathcal{X}\\) to denote the input image domain, and \\(\\mathcal{Y}\\) to denote the target domain for a given task. We use \\(f_{\\theta}:\\mathcal{X}\\to \\mathcal{Y}\\) to denote the model to be adapted, where \\(\\theta\\) denotes the model parameters. We denote the model before and after adaptation as \\(f_{\\theta}\\) and \\(f_{\\hat{\\theta}}\\) respectively. \\(\\mathcal{L}\\) and \\(\\mathcal{D}\\) are the original training loss and training dataset of \\(f_{\\theta}\\), e.g., for classification, \\(\\mathcal{L}\\) will be the cross-entropy loss and \\(\\mathcal{D}\\) the ImageNet training data. As shown in Fig. 1, \\(h_\\phi\\) is a controller for \\(f_{\\theta}\\). It can be an optimization algorithm, e.g., SGD, or a neural network. \\(\\phi\\) denotes the optimization hyperparameters or the network's parameters. The former case corresponds to TTO, and the latter is the proposed RNA, which will be explained in the next subsection. Finally, the function \\(g:\\mathcal{X}^M\\rightarrow \\mathcal{Z}\\) returns the adaptation signal by mapping a set of images \\(\\mathcal{B} = \\{I_1,\\dots,I_M\\} \\in \\mathcal{X}^M\\) to a vector \\(g(\\mathcal{B}) = z\\in \\mathcal{Z}\\). This function \\(g\\) is given, e.g., for depth, \\(g\\) returns the sparse depth measurements from SFM." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.421, + 0.373, + 0.436 + ], + "angle": 0, + "content": "3.1.1 Rapid Network Adaptation (RNA)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.47, + 0.657 + ], + "angle": 0, + "content": "For adaptation, we use a neural network for \\( h_{\\phi} \\). The adaptation signal and model predictions are passed as inputs to \\( h_{\\phi} \\) and it is trained to regress the parameters \\( \\hat{\\theta}(\\phi) = h_{\\phi}(f_{\\theta}(\\mathcal{B}), z) \\). This corresponds to an objective-based amortization of the TTO process [3]. Using both the adaptation signal \\( z \\) and model prediction \\( f_{\\theta}(\\mathcal{B}) \\) informs the controller network about the potential errors of the model. The training objective for \\( h_{\\phi} \\) is \\( \\min_{\\phi} \\mathbb{E}_{\\mathcal{D}}[\\mathcal{L}(f_{\\hat{\\theta}(\\phi)}(\\mathcal{B}), y)] \\), where \\( (\\mathcal{B}, y) \\sim \\mathcal{D} \\) is a training batch sampled from \\( \\mathcal{D} \\). Note that the original weights of \\( f \\) are frozen and \\( h_{\\phi} \\) is a small network, having only 5-20% of the number of parameters of \\( f \\), depending on the task. We call this method as rapid network adaptation (RNA) and experiment with different variants of it in Sec. 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.471, + 0.902 + ], + "angle": 0, + "content": "There exist various options for implementing the amortization process, e.g., \\( h_{\\phi} \\) can be trained to update the input image or the weights of \\( f_{\\theta} \\). We choose to modulate the features of \\( f_{\\theta} \\) as it has been shown to work well in different domains [24] and gave the best results. To do this, we insert \\( k \\) Feature-wise Linear Modulation (FiLM) layers [71] into \\( f_{\\theta} \\) (see Fig. 2). Each FiLM layer performs: \\( \\mathrm{FiLM}(\\mathbf{x}_i; \\gamma_i, \\beta_i) = \\gamma_i \\odot \\mathbf{x}_i + \\beta_i \\), where \\( \\mathbf{x}_i \\) is the activation of layer \\( i \\). \\( h_{\\phi} \\) is a network that takes as input the adaptation signal \\( z \\) and model predictions and outputs the coefficients \\( \\{\\gamma_i, \\beta_i\\} \\) of all \\( k \\) FiLM layers. \\( h_{\\phi} \\) is trained on the same dataset \\( \\mathcal{D} \\) as \\( f_{\\theta} \\), therefore, unlike TTO, it is never exposed to distribution shifts during training. Moreover, it is able to generalize to unseen shifts (see Sec. 4.3). See the supplementary for the full details, other RNA implementations we investigated, and a comparison of RNA against other ap" + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.089, + 0.865, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.199, + 0.894, + 0.274 + ], + "angle": 0, + "content": "Figure 2: Architecture of RNA. \\( x \\) is the input image, \\( f_{\\theta} \\) is the model to be adapted and \\( f_{\\theta}(x) \\) the corresponding prediction. To perform adaptation, we freeze the parameters of \\( f_{\\theta} \\) and insert several FiLM layers into \\( f_{\\theta} \\). We then train \\( h_{\\phi} \\) to take in \\( z \\), the adaptation signal, and \\( f_{\\theta}(x) \\) to predict the parameters of these FiLM layers. This results in an adapted model \\( f_{\\hat{\\theta}} \\) and improved predictions, \\( f_{\\hat{\\theta}}(x) \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.28, + 0.807, + 0.294 + ], + "angle": 0, + "content": "proaches that aim to handle distribution shifts." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.304, + 0.86, + 0.32 + ], + "angle": 0, + "content": "3.2. Which test-time adaptation signals to use?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.327, + 0.893, + 0.675 + ], + "angle": 0, + "content": "While developing adaptation signals is not the main focus of this study and is independent of the RNA method, we need to choose some for experimentation. Existing test-time adaptation signals, or proxies, in the literature include prediction entropy [91], spatial autoencoding [27], and self-supervised tasks like rotation prediction [85], contrastive [54] or clustering [9] objectives. The more aligned the adaptation signal is to the target task, the better the performance on the target task [85, 54]. More importantly, a poor signal can cause the adaptation to fail silently [9, 27]. Figure 3 shows how the original loss on the target task changes as different proxy losses from the literature, i.e. entropy [91], consistency between different middle domains [99, 104] are minimized. In all cases, the proxy loss decreases, however, the improvement in the target loss varies. Thus, successful optimization of existing proxy losses does not necessarily lead to better performance on the target task. In this paper, we adopt a few practical and real-world signals for our study. Furthermore, RNA turns out to be less susceptible to a poor adaptation signal vs TTO (see supplementary Tab. 1). This is because RNA is a neural network trained to use these signals to improve the target task, as opposed to being fixed at being SGD, like in TTO." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.682, + 0.821, + 0.697 + ], + "angle": 0, + "content": "3.2.1 Employed test-time adaptation signals" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.856 + ], + "angle": 0, + "content": "We develop test-time adaptation signals for several geometric and semantic tasks as shown in Fig. 4. Our focus is not on providing an extensive list of adaptation signals, but rather on using practical ones for experimenting with RNA as well as demonstrating the benefits of using signals that are rooted in the known structure of the world and the task in hand. For example, geometric computer vision tasks naturally follow the multi-view geometry constraints, thus making that a proper candidate for approximating the test-time error, and consequently, an informative adaptation signal." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Geometric Tasks. The field of multi-view geometry and its theorems, rooted in the 3D structure of the world, provide a rich source of adaptation signals. We demonstrate" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4676" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.088, + 0.468, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.168, + 0.468, + 0.348 + ], + "angle": 0, + "content": "Figure 3: Adaptation using different signals. Not all improvements in proxy loss translates into improving the target task's performance. We show the results of adapting a pre-trained depth estimation model to a defocus blur corruption by optimizing different adaptation signals: prediction entropy [91], a self-supervised task (sobel edge prediction error [99]), and sparse depth obtained from SFM. The plots show how the \\(\\ell_1\\) target error with respect to ground-truth depth (green, left axis) changes as the proxy losses (blue, right axis) are optimized (shaded regions represent the \\(95\\%\\) confidence intervals across multiple runs of stochastic gradient descent (SGD) with different learning rates). Only adaptation with the sparse depth (SFM) proxy leads to a reduction of the target error. This signifies the importance of employing proper signals in an adaptation framework. Furthermore, we show that RNA is less susceptible to poorer adaptation signal, which results in comparable or improved performance while being significantly faster (see supplementary Table 1)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.357, + 0.468, + 0.522 + ], + "angle": 0, + "content": "our results on the following target tasks: monocular depth estimation, optical-flow estimation, and 3D reconstruction. For all, we first run a standard structure-from-motion (SFM) pipeline [81] to get sparse 3D keypoints. For depth estimation, we employ the z-coordinates of the sparse 3D keypoints i.e., noisy sparse depth, from each image as the adaptation signal. For optical flow, we perform keypoint matching across images (which returns sparse optical flow). Lastly, for 3D reconstruction, in addition to the previous two signals, we employ consistency between depth and optical flow predictions as another signal." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.468, + 0.75 + ], + "angle": 0, + "content": "Semantic Tasks. For semantic segmentation, we first experiment with using a low number of click annotations for each class, similar to the works on active annotation tools [17, 83, 69]. This gives us sparse segmentation annotations. Likewise, for classification, we use the hierarchical structure of semantic classes, and use coarse labels generated from the WordNet tree [64], similar to [38]. Although these signals (click annotations and coarse labels) are significantly weaker versions of the actual ground truth, thus being cheaper to obtain, it may not be realistic to assume access to them at test-time for certain applications, e.g., real-time ones. Thus, we also show how these can be obtained via \\( k \\)-NN retrieval from the training dataset and patch matching using spatial features obtained from a pretrained self-supervised vision backbone [10] (see Fig. 4)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.769, + 0.208, + 0.785 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We demonstrate that our approach consistently outperforms the baselines for adaptation to different distribution shifts (2D and 3D Common Corruptions [35, 43, 44], cross-datasets), over different tasks (monocular depth, image classification, semantic segmentation, optical flow) and datasets (Taskonomy [105], Replica [84], ImageNet [22], COCO [53], ScanNet [20], Hypersim [78]). The source" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.088, + 0.89, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.191, + 0.892, + 0.335 + ], + "angle": 0, + "content": "Figure 4: Examples of employed test-time adaptation signals. We use a range of adaptation signals in our experiments. These are practical to obtain and yield better performance compared to other proxies. In the left plot, for depth and optical flow estimation, we use sparse depth and optical flow via SFM. In the middle, for classification, for each test image, we perform \\( k \\)-NN retrieval to get \\( k \\) training images. Each of these retrieved image has a one hot label associated with it, thus, combining them gives us a coarse label that we use as our adaptation signal. Finally, for semantic segmentation, after performing \\( k \\)-NN as we did for classification, we get a pseudo-labelled segmentation mask for each of these images. The features for each patch in the test image and the retrieved images are matched. The top matches are used as sparse supervision. See Sec. 4.1 for more details." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.343, + 0.757, + 0.357 + ], + "angle": 0, + "content": "code can be found on our project page." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.366, + 0.689, + 0.381 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.389, + 0.891, + 0.433 + ], + "angle": 0, + "content": "We describe our experimental setup, i.e. different adaptation signals, adaptation mechanisms, datasets and baselines, for different tasks. See Tab. 1 for a summary." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.434, + 0.836, + 0.449 + ], + "angle": 0, + "content": "Baselines. We evaluate the following baselines:" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.449, + 0.891, + 0.495 + ], + "angle": 0, + "content": "Pre-Adaptation Baseline: The network \\( f_{\\theta} \\) that maps from RGB to the target task, e.g., depth estimation, with no test-time adaptation. We denote this as Baseline for brevity." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.497, + 0.891, + 0.603 + ], + "angle": 0, + "content": "Densification: A network that maps from the given adaptation signal for the target task to the target task, e.g., sparse depth from SFM to dense depth. This is a control baseline and shows what can be learned from the test-time supervision alone, without employing input image information or a designed adaptation architecture. See Sec. 4.3 for a variant which includes the image as an additional input." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.606, + 0.891, + 0.68 + ], + "angle": 0, + "content": "TTO (episodic): We adapt the Baseline model to each episode by optimizing the proxy loss (see Tab. 1 for the adaptation signal used for each task.) at test-time. Its weights are reset to the Baseline model's after optimizing each batch, similar to [91, 108]." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.684, + 0.891, + 0.789 + ], + "angle": 0, + "content": "TTO (online): We continually adapt to a distribution shift defined by a corruption and severity. Test data is assumed to arrive in a stream, and each data point has the same distribution shift, e.g., noise with a fixed standard deviation [91, 85]. The difference with TTO (episodic) is that the model weights are not reset after each iteration. We denote this as TTO for brevity." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.793, + 0.89, + 0.853 + ], + "angle": 0, + "content": "TTO with Entropy supervision (TENT [91]): We adapt the Baseline model trained with log-likelihood loss by optimizing the entropy of the predictions. This is to reveal the effectiveness of entropy as a signal as proposed in [91]." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.856, + 0.891, + 0.901 + ], + "angle": 0, + "content": "TTO with Sobel Edges supervision (TTO-Edges): We adapt the Baseline model trained with an additional decoder that predicts a self-supervised task, similar to [85]. We choose" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.956 + ], + "angle": 0, + "content": "4677" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.086, + 0.089, + 0.887, + 0.19 + ], + "angle": 0, + "content": "
TaskAdaptation signalAdapted modelTraining dataOOD evaluation dataBaselines
DepthSFM, masked GTUNet [80], DPT [74]TaskonomyFor SFM: Replica, Replica-CC, ScanNet, For masked GT: Taskonomy-CC,-3DCC, HypersimPre-adaptation, densification, TENT, TTO-edges, TTO
Optical flowKeypoint matchingRAFT [87]FlyingChairs, FlyingThings [87]Replica-CCPre-adaptation
3D reconstructionSFM, keypoint matching,consistencyDepth, optical flow modelsDepth, optical flow dataReplica-CCPre-adaptation, TTO
Semantic segmentationClick annotations, patch matchingFCN [56]COCO (20 classes from Pascal VOC)For click annotations: COCO-CC, For patch matching: ImageNet-CPre-adaptation, densification, TENT, TTO
ClassificationCoarse labels (WordNet, DINO k-NN)ResNet50 [33], ConvNext [55]ImageNetImageNet-C, ImageNet-3DCC, ImageNet-V2Pre-adaptation, DINO k-NN, densification, TENT, TTO
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.201, + 0.895, + 0.252 + ], + "angle": 0, + "content": "Table 1: Overview of the experiments for different target tasks, adaptation methods, and adaptation signals. For each task, we list the adaptation signal (Sec. 3.2) that we use for adaptation. We also list the models that we adapt, and the out-of-distribution (OOD) data used for evaluations and the relevant baselines. When there are different options for adaptation signal, e.g., in the case of depth, the signal is denoted in italics followed by the corresponding OOD dataset. The weights for the semantic segmentation, classification and optical flow models were taken from PyTorch [70]." + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.258, + 0.273, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.258, + 0.47, + 0.323 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.324, + 0.473, + 0.435 + ], + "angle": 0, + "content": "Figure 5: RNA can achieve similar performance as TTO in a much shorter time. We compare how the \\(\\ell_1\\) errors of the adaptation mechanisms decrease over wall-clock time (s). The errors are averaged over all episodes (and all corruptions for Replica-CC). RNA only requires a forward pass at test-time, while TTO requires multiple forward and backward passes. On ScanNet and Replica-CC, RNA takes 0.01s, while TTO takes 3s to achieve similar performance. Furthermore, RNA is not trained with test-time shifts unlike TTO, thus, it learned to use the additional supervision to adapt to unseen shifts." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.45, + 0.47, + 0.512 + ], + "angle": 0, + "content": "to predict Sobel edges as it has been shown to be robust to certain shifts [99]. We optimize the error of the edges predicted by the model and edges extracted from the RGB image to reveal the value of edge error as a supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.47, + 0.614 + ], + "angle": 0, + "content": "RNA configurations. At test-time, we first get the predictions of the Baseline model and compute the adaptation signal. The predictions and adaptation signal are then passed to \\( h_{\\phi} \\) which adapts \\( f_{\\theta} \\) to \\( f_{\\hat{\\theta}} \\). The test images are then passed to \\( f_{\\hat{\\theta}} \\) to get the final predictions. We evaluate following variants of RNA." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.621, + 0.47, + 0.653 + ], + "angle": 0, + "content": "RNA (frozen \\( f \\)): Baseline model weights, \\( f_{\\theta} \\), are frozen when training \\( h_{\\phi} \\). We call this variant RNA for brevity." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.654, + 0.47, + 0.701 + ], + "angle": 0, + "content": "RNA (jointly trained \\( f \\)): In contrast to the frozen \\( f \\) variant, here we train \\( h_{\\phi} \\) jointly with the Baseline network. This variant requires longer training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.712, + 0.47, + 0.775 + ], + "angle": 0, + "content": "Adaptation signal. As described in Sec. 3.2, we compute a broad range of test-time signals from the following processes. Each case describes a process applied on query image(s) in order to extract a test-time quantity." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.78, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Structure-from-motion (SFM): Given a batch of query images, we use COLMAP [81] to run SFM, which returns sparse depth. The percentage of valid pixels, i.e. depth measurements, is about \\(0.16\\%\\) on Replica-CC and \\(0.18\\%\\) on Replica. For ScanNet we use the pre-computed sparse depth from [79], which has about \\(0.04\\%\\) valid pixels. As running SFM on corrupted images results in noisy sparse depth, we train \\(h_{\\phi}\\) to be invariant to noise [102, 79]." + }, + { + "type": "text", + "bbox": [ + 0.502, + 0.259, + 0.893, + 0.395 + ], + "angle": 0, + "content": "Masked ground truth (GT): We apply a random mask to the GT depth of the test image. We fixed the valid pixels to \\(0.05\\%\\) of all pixels, i.e. similar sparsity as SFM (see the supplementary for other values). This a control proxy as it enables a better evaluation of the adaptation methods without conflating with the shortcomings of adaptation signals. It is also a scalable way of simulating sparse depth from real-world sensors, e.g., LiDAR, as also done in [92, 59, 41]." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.398, + 0.893, + 0.473 + ], + "angle": 0, + "content": "Click annotations: We generate click annotations over random pixels for each class in a given image using GT - simulating an active annotation pipeline. The number of pixels ranges from 3 to 25, i.e. roughly \\(0.01\\%\\) of the total pixels, similar to [7, 69, 83, 109, 17]." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.476, + 0.895, + 0.657 + ], + "angle": 0, + "content": "Patch matching: To not use GT click annotations, for each test image, we first retrieve its \\( k \\)-NN images from the original clean training dataset using DINO features [10]. We then get segmentation masks on these \\( k \\) images. If the training dataset has labels for segmentation we use them directly, otherwise we obtain them from a pretrained network. For each of the \\( k \\) training images and test image, we extract non-overlapping patches. The features for each patch that lie inside the segmentation masks of the \\( k \\) training images are matched to the features of every patch in the test image. These matches are then filtered and used as sparse segmentation annotations. See Fig. 4 for illustration." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.66, + 0.894, + 0.735 + ], + "angle": 0, + "content": "Coarse labels (WordNet): We generate 45 coarse labels from the 1000-way ImageNet labels, i.e. making the labels \\(22 \\times\\) coarser, using the WordNet tree [64], similar to [39]. See supplementary for more details on the construction and results for other coarse label sets." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.738, + 0.894, + 0.814 + ], + "angle": 0, + "content": "Coarse labels (DINO \\( k \\)-NN): For each test image, we retrieve the \\( k \\)-NN images from the training dataset using DINO features [10]. Each of these \\( k \\) training images is associated with an ImageNet class, thus, combining \\( k \\) one-hot labels gives us a coarse label." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.817, + 0.893, + 0.848 + ], + "angle": 0, + "content": "Keypoint matching: We perform keypoint matching across images to get sparse optical flow." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4678" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.139, + 0.089, + 0.831, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.38, + 0.895, + 0.466 + ], + "angle": 0, + "content": "Figure 6: Qualitative results of RNA vs the baselines for semantic segmentation on random query images on COCO-CC (left) and depth on images from ScanNet, Taskonomy-3DCC and Replica-CC (right). For semantic segmentation, we use 15 pixel annotations per class. For Taskonomy-3DCC, we use sparse depth with \\(0.05\\%\\) valid pixels (30 pixels per image). See Fig. 7 for results on different adaptation signal levels. For ScanNet and Replica-CC, the adaptation signal is sparse depth measurements from SFM [81] with similar sparsity ratios to Taskonomy-3DCC. The predictions with proposed adaptation signals are shown in the last two rows. They are noticeably more accurate compared to the baselines. Comparing TTO and RNA, RNA's predictions are more accurate for segmentation, and sharper than TTO for depth (see the ellipses) while being significantly faster. See 4.2 and supplementary for more results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.484, + 0.345, + 0.5 + ], + "angle": 0, + "content": "4.2. Adaptation with RNA vs TTO" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.471, + 0.612 + ], + "angle": 0, + "content": "Here we summarize our observations from adapting with RNA vs TTO. As described, TTO represents the approach of closed-loop adaptation using the adaptation signal but without benefiting from amortization and learning (the adaptation process is fixed to be standard SGD). These observations hold across different tasks. See Sec. 4.3 for results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.47, + 0.765 + ], + "angle": 0, + "content": "RNA is efficient. As RNA only requires a forward pass at test-time, it is orders of magnitude faster than TTO and is able to attain comparable performance to TTO. In Fig. 5, we compare the runtime of adaption with RNA and TTO for depth prediction. On average, for a given episode, RNA obtains similar performance as TTO in 0.01s, compared to TTO's 3-5s. Similarly, for dense 3D reconstruction, RNA is able to adapt in 0.008s compared to TTO's 66s (see Fig. 9). This suggests a successful amortization of the adaptation optimization by RNA." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.825 + ], + "angle": 0, + "content": "Furthermore, RNA's training is also efficient as it only requires training a small model, i.e. \\(5 - 20\\%\\) of the Baseline model's parameters, depending on the task. Thus, RNA has a fixed overhead, and small added cost at test-time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "RNA's predictions are sharper than TTO for dense prediction tasks. From the last two rows of Fig. 6, it can be seen that RNA retains fine-grained details. This is a noteworthy point and can be attributed to the fact that RNA benefits from a neural network, thus its inductive biases can" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.484, + 0.892, + 0.56 + ], + "angle": 0, + "content": "be beneficial (and further engineered) for such advantages. This is a general feature that RNA, and more broadly using a learning-based function to amortize adaptation optimization, brings – in contrast to limiting the adaptation process to be SGD, as represented by TTO." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.637 + ], + "angle": 0, + "content": "RNA generalizes to unseen shifts. RNA performs better than TTO for low severities (see supplementary for more details). However, as it was not exposed to any corruptions, the performance gap against TTO narrows at high severities as expected, which is exposed to corruptions at test-time." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.638, + 0.892, + 0.804 + ], + "angle": 0, + "content": "We hypothesize that the generalization property of RNA is due to the following reasons. 1. Even though \\( f_{\\theta} \\) was trained to convergence, it does not achieve exactly 0 error. Thus, when \\( h_{\\phi} \\) is trained with a frozen \\( f_{\\theta} \\) with the training data, it can still learn to correct the errors of \\( f_{\\theta} \\), thus, adapting \\( f_{\\theta} \\). 2. Adaptation signals, by definition, are expected to be relatively robust to distribution shifts. Even though the RGB image has been corrupted or from a new domain, the adaptation signal is more aligned with the target task. Thus, the input to \\( h_{\\phi} \\) does not undergo a significant shift and is able to adapt \\( f_{\\theta} \\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.816, + 0.846, + 0.833 + ], + "angle": 0, + "content": "4.3. Experiments using Various Target Tasks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.903 + ], + "angle": 0, + "content": "In this section, we provide a more comprehensive set of evaluations covering various target tasks and adaptation signals. In all cases, RNA is a fixed general framework without being engineered for each task and shows supportive results." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4679" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.09, + 0.472, + 0.21 + ], + "angle": 0, + "content": "
Adaptation SignalSFMSparse GTRelative Runtime
DatasetReplicaScanNetTaskonomyHypersim
ShiftCDSCCCDSNoneCC3DCCCDS
Pre-adaptation Baseline1.756.083.302.685.744.7533.641.00
Densification2.504.192.351.721.721.7217.251.00
TENT [91]2.036.094.035.515.514.4835.4515.85
TTO-Edges [85]1.736.143.282.705.694.7433.6920.98
RNA (frozen f)1.724.261.771.121.681.4916.171.56
RNA (jointly trained f)1.663.411.741.111.501.3717.131.56
TTO (Episodic)1.723.311.851.622.992.3117.7714.85
TTO (Online)1.823.161.761.131.481.3414.1714.85
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.22, + 0.47, + 0.352 + ], + "angle": 0, + "content": "Table 2: Quantitative adaptation results on depth estimation. \\(\\ell_1\\) errors on the depth prediction task. (Lower is better. Multiplied by 100 for readability. The best models within 0.0003 error are shown in bold.) We generate distribution shifts by applying Common Corruptions (CC), 3D Common Corruptions (3DCC) and from performing cross-dataset evaluations (CDS). The results from CC and 3DCC are averaged over all distortions and severity levels on Taskonomy and 3 severity levels on Replica data. The adaptation signal from Taskonomy is masked GT (fixed at \\(0.05\\%\\) valid pixels) while that from Replica and ScanNet is sparse depth from SFM. RNA and TTO notably outperform the baselines. RNA successfully matches the performance of TTO while being around 10 times faster." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.353, + 0.469, + 0.378 + ], + "angle": 0, + "content": "See supplementary for the losses for different corruption types, sparsity levels, and the results of applying RNA to other adaptation signals." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.389, + 0.462, + 0.506 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.507, + 0.47, + 0.545 + ], + "angle": 0, + "content": "Figure 7: Qualitative adaptation results on semantic segmentation on random query images on COCO-CC. RNA notably improves the prediction quality using error feedback from as few as 3 random pixels." + }, + { + "type": "image", + "bbox": [ + 0.09, + 0.553, + 0.459, + 0.694 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.697, + 0.47, + 0.771 + ], + "angle": 0, + "content": "Figure 8: Quantitative adaptation results on semantic segmentation. Each point shows the mean IOU over 15 corruptions and 5 severities. RNA significantly improves over baselines. Black dashed line shows the mean IOU of the baseline model for clean validation images, and is provided as an upper bound on performance. Numbers in the legend denote averages over all supervision pixel counts. See supplementary for a breakdown." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Depth. We demonstrate the results quantitatively in Tab. 2 and Fig. 5 and qualitatively in Fig. 6. In Tab. 2, we compare RNA against all baselines, and over several distribution shifts and different adaptation signals. Our RNA variants outperform the baselines overall. TTO (online) has a better performance than TTO (episodic) as it assumes a smoothly changing distribution shift, and it continuously updates the model weights. RNA (jointly trained \\( f \\)) has a" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "better performance among RNA variants. This is reasonable as the target model is not frozen, thus, is less restrictive." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.123, + 0.893, + 0.35 + ], + "angle": 0, + "content": "As another baseline, we trained a single model that takes as input a concatenation of the RGB image and sparse supervision, i.e. multi-modal input. However, its average performance on Taskonomy-CC was \\(42.5\\%\\) worse than RNA's (see sup. mat. Sec. 3.2). Among the baselines that do not adapt, densification is the strongest under distribution shift due to corruptions. This is expected as it does not take the RGB image as input, thus, it is not affected by the underlying distribution shift. However, as seen from the qualitative results in Figs. 6, 7, unlike RNA, densification is unable to predict fine-grained details (which quantitative metrics often do not well capture). We also show that the gap between RNA and densification widens with sparser supervision (see sup. mat. Fig. 1), which confirms that RNA is making use of the error feedback signal, to adapt \\(f\\)." + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.361, + 0.874, + 0.695 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.707, + 0.892, + 0.816 + ], + "angle": 0, + "content": "Figure 9: Adaptation results for 3D reconstruction. Using appropriate adaptation signals from multi-view geometry can recover accurate 3D reconstructions. We report the average \\(\\ell_1\\) error between ground truth 3D coordinates and the estimated ones. The titles above each column refers to the depth model used to get the reconstruction. TTO+MVC corresponds to the predictions after multi-view consistency optimization. It can be seen that RNA and TTO improve the reconstructions over the baselines with RNA being significantly faster. See supplementary Fig. 4 for more results and the corresponding error maps." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Dense 3D Reconstruction. Here, we combine multiple adaptation signals from multi-view geometry. First, we adapt the weights of the depth and optical flow models independently. The results from this adaptation can be found in the previous paragraph (for depth) and supplementen" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4680" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.088, + 0.089, + 0.457, + 0.176 + ], + "angle": 0, + "content": "
Adaptation SignalDatasetCleanIN-CIN-3DCCIN-V2Rel. Runtime
-Pre-adaptation Baseline23.8561.6654.9737.151.00
EntropyTENT24.6746.1947.1337.075.51
Coarse labels (wordnet)Densification95.5095.5095.5095.50-
TTO (Online)24.7240.6242.9036.775.72
RNA (frozen f)16.7241.2140.3725.531.39
Coarse labels (DINO)DINO (k-NN)25.5652.6448.2437.39-
TTO (Online)24.5951.5949.1836.965.72
RNA (frozen f)24.3654.8652.2936.881.39
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.181, + 0.47, + 0.242 + ], + "angle": 0, + "content": "Table 3: Quantitative adaptation results on on ImageNet (IN) classification task. We evaluate on the clean validation set, ImageNet-C,3DCC,V2}. We report average error \\((\\%)\\) for 1000-way classification task over all corruptions and severities. For the coarse labels with WordNet supervision, we use 45-coarse labels. For DINO \\(k\\) NN, we set \\(k = 20\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.25, + 0.469, + 0.311 + ], + "angle": 0, + "content": "tary (for optical flow). Next, the two models are adapted to make their predictions consistent with each other. This is achieved using the same process as [58], i.e. multi-view-consistency (MVC). See supplementary for details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.312, + 0.469, + 0.432 + ], + "angle": 0, + "content": "Figure 9 shows the point cloud visualizations on Replica where the input was corrupted with Gaussian Noise. This results in collapsed depth predictions, thus, reconstructions are unusable (Baseline column) and performing MVC is not helpful (Baseline+MVC). Adapting the depth predictions using TTO and MVC improves the reconstruction notably while RNA achieves a similar performance significantly faster." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.469, + 0.583 + ], + "angle": 0, + "content": "Semantic Segmentation. We experiment with click annotations and DINO patch matching as adaptation signals. Click annotations: In Fig. 8, we show how the IoU changes with the adaptation signal level on COCO-CC. As the Baseline and TENT do not make use of this signal, their IoU is a straight line. RNA clearly outperforms the baselines for all levels of adaptation signal. Figure 7 shows the qualitative results with increasing supervision, and Fig. 6 (left) a comparison against all baselines, demonstrating higher quality predictions with RNA." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.469, + 0.749 + ], + "angle": 0, + "content": "DINO patch matching: We perform patch matching on DINO features (described in Sec. 4.1) to get the adaptation signal. As the patch matching process can be computationally expensive, we demonstrate our results on all cat classes in ImageNet and over one noise, blur and digital corruption for 3 levels of severity. We used the predictions of a pretrained FCN on the clean images as pseudolabels to compute IoU. The mean IoU averaged over these corruptions and severities is 48.98 for the baseline model, 53.45 for TTO. RNA obtains a better IOU of 58.04, thus it can make use of the sparse annotations from DINO patch matching." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.469, + 0.78 + ], + "angle": 0, + "content": "Image Classification. We experiment with coarse labels from WordNet and DINO \\(k\\)-NN as adaptation signals." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Coarse labels (WordNet): Table 3 shows the results from using 45-coarse labels on ImageNet-\\(\\{\\mathrm{C},3\\mathrm{DCC},\\mathrm{V}2\\}\\). This corresponds to \\(22\\mathrm{x}\\) coarser supervision compared to the 1000 classes that we are evaluating on. TENT seems to have notable improvements in performance under corruptions for classification, unlike for semantic segmentation and depth. We show that using coarse supervision results in even better performance, about a further 5 pp reduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.181 + ], + "angle": 0, + "content": "in error. Furthermore, on uncorrupted data, i.e. clean, and ImageNet-V2 [76], RNA gives roughly 10 pp improvement in performance compared to TTO. Thus, coarse supervision provides a useful signal for adaptation while requiring much less effort than full annotation [97]. See supplementary for results on other coarse sets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.182, + 0.892, + 0.272 + ], + "angle": 0, + "content": "Coarse labels (DINO \\(k\\)-NN): We also show results from using coarse sets generated from DINO \\(k\\)-NN retrieval. This is shown in the last 3 rows of Tab. 3. Both RNA and TTO use this coarse information to outperform the non-adaptive baselines. However, they do not always outperform TENT, which could be due to the noise in retrieval." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.282, + 0.782, + 0.296 + ], + "angle": 0, + "content": "4.4. Ablations and additional results" + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.307, + 0.89, + 0.369 + ], + "angle": 0, + "content": "
Task (Arch.)Depth (DPT [74])Classification (ConvNext [55])
ShiftCleanCCRel. RuntimeCleanIN-CRel. Runtime
Pre-adaptation Baseline2.233.761.0018.1342.951.00
TTO (Online)1.822.6113.8517.8341.4411.04
RNA (frozen f)1.131.561.0114.3238.041.07
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.38, + 0.892, + 0.44 + ], + "angle": 0, + "content": "Table 4: RNA works across different architectures of the main network \\( f_{\\theta} \\) such as DPT [74] and ConvNext [55]. Quantitative adaptation results on depth estimation and image classification on Taskonomy and ImageNet datasets, respectively. (Lower is better. \\( \\ell_1 \\) errors for depth estimation are multiplied by 100 for readability.)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.445, + 0.892, + 0.581 + ], + "angle": 0, + "content": "Aaptations of main network \\( f_{\\theta} \\) with different backbones. Previous results in the paper were from adapting \\( f_{\\theta} \\) with a UNet architecture. Here, we study the performance of RNA on other architectures of \\( f_{\\theta} \\), namely, the dense prediction transformer (DPT) [74] for depth and ConvNext [55] for image classification. Table 4 shows the results of incorporating RNA to these architectures. In both cases, RNA is able to improve on the error and runtime of TTO. Thus, RNA can be applied to a range of architectures." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.593, + 0.89, + 0.643 + ], + "angle": 0, + "content": "
Method\\ShiftNoneTaskonomy-CCTaskonomy-3DCCHypersimBlendedMVG
Pre-adaptation0.0270.0570.0480.3363.450
RNA (HyperNetwork-x)0.0190.0410.0330.2572.587
RNA (FiLM-x)0.0190.0390.0330.2792.636
RNA (FiLM-f)0.0130.0240.0200.1982.310
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.654, + 0.892, + 0.703 + ], + "angle": 0, + "content": "Table 5: Implementations of different architectures for the controller network \\( h_{\\phi} \\). \\( \\ell_1 \\) errors on the depth estimation task under distribution shifts are reported. The adaptation signal here is masked GT, fixed at 0.05% of valid pixels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Implementations of different architectures for the controller network \\( h_{\\phi} \\). We experiment with different architectures for \\( h_{\\phi} \\) e.g., HyperNetworks [31], other FiLM variants, or adapting the input instead of the model parameters. Instead of adding FiLM layers to adapt \\( f_{\\theta} \\) (denoted as FiLM- \\( f \\)), as described in Sec. 3.1, we also experimented with adding FiLM layers to a UNet model that is trained to update the input image \\( x \\) (denoted as FiLM- \\( x \\)). For FiLM- \\( x \\), only \\( x \\) is updated and there is no adaptation on \\( f_{\\theta} \\). Lastly, as Hypernetworks [31] have been shown to be expressive and suitable for adaptation, we trained a HyperNetwork, in this case an MLP, to predict the weights of a 3-layer convolutional network that updates \\( x \\) (denoted as HyperNetwork-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.956 + ], + "angle": 0, + "content": "4681" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.198 + ], + "angle": 0, + "content": "\\(x\\)). The results of adaptation with these variants of RNA are shown in Table 5. The FiLM-\\(f\\) variant performed best, thus, we adopted it as our main architecture. See supplementary Sec. 2.2 for more details and a discussion on the trade-offs of the choices of implementing this closed-loop \"control\" system, namely those that make stronger model-based assumptions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.198, + 0.471, + 0.304 + ], + "angle": 0, + "content": "Controlling for number of parameters. We ran a control experiment where all methods have the same architecture, thus, same number of parameters. The results are in the supplementary Table 2. RNA still returns the best performance. Thus, its improvement over the baselines is not due to a different architecture or number of parameters but due to its test-time adaptation mechanism." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.319, + 0.465, + 0.337 + ], + "angle": 0, + "content": "5. Approaches for handling distribution shifts" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.345, + 0.47, + 0.542 + ], + "angle": 0, + "content": "In this section, we provide a unified discussion about the approaches that aim to handle distribution shifts. Figure 10 gives an overview of how these approaches can be characterized. Open-loop systems predict \\( y \\) by only using their inputs without receiving feedback. Training-time robustness methods, image modifications, and multi-modal methods fall into this category. These methods assume the learned model is frozen at the test-time. Thus, they aim to incorporate inductive biases at training time that could be useful against distribution shifts at the test-time. The closed-loop systems, on the other hand, are adaptive as they make use of a live error feedback signal that can be computed at test-time from the model predictions and an adaptation signal." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.542, + 0.47, + 0.648 + ], + "angle": 0, + "content": "In the interest of space, we move the detailed discussion about each of these variants to Sec. 1.2 of the supplementary. In particular, elaboration of the distinction between a model-based vs model-free approach, denoising/image-modification methods, multi-modal methods, and our observations over comparing the conclusions of [46] el al. and our experiments are provided there." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.663, + 0.334, + 0.679 + ], + "angle": 0, + "content": "6. Conclusion and Limitations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.854 + ], + "angle": 0, + "content": "We presented RNA, a method for efficient adaptation of neural networks at test-time using a closed-loop formulation. It involves training a side network to use a test-time adaptation signal to adapt a main network. This network acts akin to a \"controller\" and adapts the main network based on the adaptation signal. We showed that this general and flexible framework can generalize to unseen shifts, and as it only requires a forward pass at test-time, it is orders of magnitude faster than TTO. We evaluated this approach using a diverse set of adaptation signals and target tasks. We briefly discuss the limitations and potential future works:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Different instantiation of RNA and amortization. While we experimented with several RNA variants (see supplementary for details), further investigation toward a stronger" + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.087, + 0.866, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.265, + 0.892, + 0.53 + ], + "angle": 0, + "content": "Figure 10: An overview of methods that aim to handle distribution shifts. Left: Open-loop systems predict \\( y \\) by only using their inputs without receiving feedback. The first and popular example of open-loop systems is training-time robustness methods (data augmentation, architectural changes, etc.). The next example is the methods that modify the input \\( x \\), e.g. denoising or style changes, to recover the original image before corruption, independent of \\( y \\). Furthermore, there are multi-modal methods that use an additional input \\( z \\). As the learned model is frozen at test-time, these methods need to anticipate the distribution shift by incorporating inductive biases at training time (See also Fig. 1.). Right: In contrast, closed-loop systems make use of its current output, \\( y \\), and an adaptation signal, \\( z \\), to form an error feedback signal that can be used to update its predictions. Thus, they adapt to the shifts as they occur. We can then group closed-loop systems into model-based and model-free methods. The former performs adaptation by estimating the parameters \\( e \\) of specific modeled distribution shift families, while the latter performs adaptation in a data-driven way without explicitly modeling certain distribution shifts. Adaptation can be performed via running an optimization, i.e. TTO via SGD, or via amortization, i.e., training a side controller network to predict TTO updates that minimize the error feedback. Our proposed method, RNA, belongs to the model-free adaptation approach that makes use of amortization for efficiency." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.641 + ], + "angle": 0, + "content": "instantiation of RNA which can generalize to more shifts and handle more drastic changes, e.g. via building in a more explicit \"model\" of the shifts and environment (see the discussion about [46]), is important. In general, as the role of the controller network is to amortize the training optimization of the main network, the amortized optimization literature [3] is one apt resource to consult for this purpose." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.892, + 0.731 + ], + "angle": 0, + "content": "Hybrid mechanism for activating TTO in RNA. TTO constantly adapts a model to a distribution shift, hence, in theory, it can adapt to any shift despite being comparatively inefficient. To have the best of both worlds, investigating mechanisms for selectively activating TTO within RNA when needed can be useful." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.892, + 0.853 + ], + "angle": 0, + "content": "Finding adaptation signals for a given task. While the focus of this study was not on developing new adaption signals, we demonstrated useful ones for several core vision tasks, but there are many more. Finding these signals requires either knowledge of the target task so a meaningful signal can be accordingly engineered or core theoretical works on understanding how a proxy and target objectives can be \"aligned\" for training." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement: The authors thank Onur Beker. This work was partially supported by the ETH4D and EPFL EssentialTech Centre Humanitarian Action Challenge Grant." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4682" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.096, + 0.116, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Hassan Akbari, Liangzhe Yuan, Rui Qian, Wei-Hong Chuang, Shih-Fu Chang, Yin Cui, and Boqing Gong. Vatt: Transformers for multimodal self-supervised learning from raw video, audio and text. 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PMLR, 2019. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4687" + } + ] +] \ No newline at end of file diff --git a/2023/Rapid Network Adaptation_ Learning to Adapt Neural Networks Using Test-Time Feedback/32896e91-9d8e-4427-a165-f57c45c9afec_origin.pdf b/2023/Rapid Network Adaptation_ Learning to Adapt Neural Networks Using Test-Time Feedback/32896e91-9d8e-4427-a165-f57c45c9afec_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..683793491edfd394fee235d99b76a6681d0039e7 --- /dev/null +++ b/2023/Rapid Network Adaptation_ Learning to Adapt Neural Networks Using Test-Time Feedback/32896e91-9d8e-4427-a165-f57c45c9afec_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ad39c1b0bef809ad92652f0a7842df696e73b14a015f54b243178b4d10516295 +size 9188153 diff --git a/2023/Rapid Network Adaptation_ Learning to Adapt Neural Networks Using Test-Time Feedback/full.md b/2023/Rapid Network Adaptation_ Learning to Adapt Neural Networks Using Test-Time Feedback/full.md new file mode 100644 index 0000000000000000000000000000000000000000..3c3f3ed2eb3d7642c29f57e4cc1bda193e2a796c --- /dev/null +++ b/2023/Rapid Network Adaptation_ Learning to Adapt Neural Networks Using Test-Time Feedback/full.md @@ -0,0 +1,377 @@ +# Rapid Network Adaptation: Learning to Adapt Neural Networks Using Test-Time Feedback + +Teresa Yeo + +Oguzhan Fatih Kar + +Zahra Sodagar + +Amir Zamir + +Swiss Federal Institute of Technology Lausanne (EPFL) + +https://rapid-network-adaptation.epfl.ch/ + +# Abstract + +We propose a method for adapting neural networks to distribution shifts at test-time. In contrast to training-time robustness mechanisms that attempt to anticipate and counter the shift, we create a closed-loop system and make use of test-time feedback signal to adapt a network on the fly. We show that this loop can be effectively implemented using a learning-based function, which realizes an amortized optimizer for the network. This leads to an adaptation method, named Rapid Network Adaptation (RNA), that is notably more flexible and orders of magnitude faster than the baselines. Through a broad set of experiments using various adaptation signals and target tasks, we study the generality, efficiency, and flexibility of this method. We perform the evaluations using various datasets (Taskonomy, Replica, ScanNet, Hypersim, COCO, ImageNet), tasks (depth, optical flow, semantic segmentation, classification), and distribution shifts (Cross-datasets, 2D and 3D Common Corruptions) with promising results. + +# 1. Introduction + +Neural networks are found to be unreliable against distribution shifts [23, 35, 43, 42, 29]. Examples of such shifts include blur due to camera motion, object occlusions, changes in weather conditions and lighting, etc. The training-time strategies to deal with this issue attempt to anticipate the shifts that may occur and counter them at the training stage – for instance, by augmenting the training data or updating the architecture with corresponding robustness inductive biases. As the possible shifts are numerous and unpredictable, this approach has inherent limitations. This is the main motivation behind test-time adaptation methods, which instead aim to adapt to such shifts as they occur and recover from failure. In other words, these methods choose adaptation over anticipation (see Fig. 1). In this work, we propose a test-time adaptation framework that aims to perform an ef + +![](images/23a0149ecf8d4c09bbae0937e2218779aeba8a354c644fe1acc4ba08d4696173.jpg) +Figure 1: Adaptive vs non-adaptive neural network pipelines. Top: In order to be robust, non-adaptive methods include training-time interventions that anticipate and counter the distribution shifts that will occur at test-time (e.g., via data augmentation). The learned model, $f_{\theta}$ , is frozen at test-time, thus upon encountering an out-of-distribution input, its predictions may collapse. Bottom: Adaptive methods create a closed-loop and use an adaptation signal at test-time. The adaptation signal is a quantity that can be computed at test-time from the environment. $h_{\phi}$ acts as a "controller" by taking in an error feedback, computed from the adaptation signal and model predictions, to adapt $f_{\theta}$ accordingly. It can be implemented as a (i) standard optimizer (e.g., using SGD) or (ii) neural network. The former is equivalent to test-time optimization (TTO), while the latter aims to amortize the optimization process, by training a controller network to adapt $f_{\theta}$ - thus, it can be more efficient and flexible. In this work, we study the latter approach and show its efficiency and flexibility. + +ficient adaptation of a given main network using a feedback signal. + +One can consider performing "test-time optimization" (TTO) for this purpose, similar to previous works [91, 108, 27] e.g. simply using SGD to finetune the network to reduce a proxy loss [91]. While this can successfully adapt a network, it is unnecessarily inefficient as it does not make use of the learnable regularities in the adaptation pro + +cess, and consequently, unconducive for real-world applications. It also results in a rigid framework as the update mechanism is fixed to be the same as the training process of neural networks (SGD). We show this process can be effectively amortized using a learning-based feed-forward controller network, which yields orders of magnitude faster results (See Fig. 1, Sec. 4.3). In addition, it provides flexibility advantages as the controller is implemented using a neural network and can be engineered to include arbitrary inductive biases and desired features that could counter the suboptimalities of the adaptation signal. + +# 2. Related Work + +Our work focuses on how to adapt a neural network efficiently at test-time on a range of tasks and adaptation signals. We give an overview of relevant topics. See the supplementary Sec. 7 for more related works. + +Robustness methods anticipate the distribution shift that can occur and incorporate inductive biases into the model to help it generalize. Popular methods include data augmentation [61, 107, 57, 37, 103, 101, 34, 43], self-/pre-training [36, 95, 25, 72, 96, 75, 32], architectural changes [19, 8, 82, 62, 55] or ensembling [48, 67, 99, 73, 40, 68]. We focus on adaptation mechanisms and identifying practical adaptation signals that can be used at test-time. + +Amortized optimization methods make use of learning to improve (e.g., speed-up) the solution of optimization problems, particularly for settings that require repeatedly solving similar instances of the same underlying problem [49, 11, 4, 106, 26, 94, 60, 14, 3]. Fully amortized optimization methods model the shared structure between past instances of solved problems to regress the solution to a new problem [31, 21, 52]. As adapting to distribution shifts can be cast as solving an optimization problem at test-time, our method can be seen as an amortized solution. + +Test-time adaptation methods for geometric tasks. Many existing frameworks, especially in geometric tasks such as aligning a 3D object model with an image of it, in effect instantiate a task-specific case of closed-loop optimization for each image [60, 106, 63]. Common sources of their adaptation quantity include sensor data [92, 98, 15, 89, 102, 18], structure from motion (SFM) [93, 47], motion [12], and photometric and multi-view consistency constraints (MVC) [58, 45]. Many of the latter methods often focus on depth prediction and they introduce losses that are task-specific, e.g., [93] optimize a photometric consistency loss. We differ by aiming to investigate a more general framework for test-time adaptation that can be applied to several tasks. For MVC, while we adopt the same losses as [58], we show under collapsed predictions, optimizing only MVC constraints is not sufficient for recovering predictions; depth predictions need to be adapted and this can be done efficiently using our framework (see Sec. 4.3). + +Test-time adaptation methods for semantic tasks. Most of these works involve optimizing a self-supervised objective at test-time [85, 91, 54, 27, 28, 108, 9, 51, 100]. They differ in the choice of self-supervised objectives, e.g., prediction entropy [91], mutual information [51], and parameters optimized [9]. However, as we will discuss in Sec. 3.2, and as shown by [9, 27, 65], existing methods can fail silently, i.e. successful optimization of the adaptation signal loss does not necessarily result in better performance on the target task. We aim to have a more efficient and flexible method and also show that using proper adaptation signals results in improved performance. + +Multi-modal frameworks are models that can use the information from multiple sources, e.g., RGB image, text, audio, etc., [13, 5, 86, 50, 2, 16, 72, 1, 6, 30]. Schematically, our method has similarities to multi-modal learning (as many amortized optimization methods do) since it simultaneously uses an input RGB image and an adaptation signal. The main distinction is that our method implements a particular process toward adapting a network to a shift using an adaptation signal from the environment – as opposed to a generic multi-modal learning. + +# 3. Method + +In Fig. 1, we schematically compared methods that incorporate robustness mechanisms at training-time (thus anticipating the distribution shift) with those that adapt to shifts at test-time. Our focus is on the latter. In this section, we first discuss the benefits and downsides of common adaptation methods (Sec. 3.1). We then propose an adaptation method that is fast and can be applied to several tasks (Sec. 3.1.1). To adapt, one also needs to be able to compute an adaptation signal, or proxy, at the test-time. In the second part of the section (Sec. 3.2), we study a number of practical adaptation signals for a number of tasks. + +# 3.1. How to adapt at test-time? + +An adaptive system is one that can respond to changes in its environment. More concretely, it is a system that can acquire information to characterize such changes, e.g., via an adaptation signal that provides an error feedback, and make modifications that would result in a reduction of this error (see Fig. 1). The methods for performing the adaptation of the network range from gradient-based updates, e.g. using SGD to fine-tune the parameters [85, 91, 27], to the more efficient semi-amortized [110, 88] and amortized approaches [90, 66, 77] (see Fig. 6 of [77] for an overview). As amortization methods train a controller network to substitute the explicit optimization process, they only require a forward pass at test-time. Thus, they are computationally efficient. Gradient-based approaches, e.g., TTO, can be powerful adaptation methods when the test-time signal is robust and well-suited for the task (see Fig. 4). How- + +ever, they are inefficient and have the risk of failing silently and the need for carefully tuned optimization hyperparameters [9]. In this work, we focus on an amortization-based approach. + +Notation. We use $\mathcal{X}$ to denote the input image domain, and $\mathcal{Y}$ to denote the target domain for a given task. We use $f_{\theta}:\mathcal{X}\to \mathcal{Y}$ to denote the model to be adapted, where $\theta$ denotes the model parameters. We denote the model before and after adaptation as $f_{\theta}$ and $f_{\hat{\theta}}$ respectively. $\mathcal{L}$ and $\mathcal{D}$ are the original training loss and training dataset of $f_{\theta}$ , e.g., for classification, $\mathcal{L}$ will be the cross-entropy loss and $\mathcal{D}$ the ImageNet training data. As shown in Fig. 1, $h_\phi$ is a controller for $f_{\theta}$ . It can be an optimization algorithm, e.g., SGD, or a neural network. $\phi$ denotes the optimization hyperparameters or the network's parameters. The former case corresponds to TTO, and the latter is the proposed RNA, which will be explained in the next subsection. Finally, the function $g:\mathcal{X}^M\rightarrow \mathcal{Z}$ returns the adaptation signal by mapping a set of images $\mathcal{B} = \{I_1,\dots,I_M\} \in \mathcal{X}^M$ to a vector $g(\mathcal{B}) = z\in \mathcal{Z}$ . This function $g$ is given, e.g., for depth, $g$ returns the sparse depth measurements from SFM. + +# 3.1.1 Rapid Network Adaptation (RNA) + +For adaptation, we use a neural network for $h_{\phi}$ . The adaptation signal and model predictions are passed as inputs to $h_{\phi}$ and it is trained to regress the parameters $\hat{\theta}(\phi) = h_{\phi}(f_{\theta}(\mathcal{B}), z)$ . This corresponds to an objective-based amortization of the TTO process [3]. Using both the adaptation signal $z$ and model prediction $f_{\theta}(\mathcal{B})$ informs the controller network about the potential errors of the model. The training objective for $h_{\phi}$ is $\min_{\phi} \mathbb{E}_{\mathcal{D}}[\mathcal{L}(f_{\hat{\theta}(\phi)}(\mathcal{B}), y)]$ , where $(\mathcal{B}, y) \sim \mathcal{D}$ is a training batch sampled from $\mathcal{D}$ . Note that the original weights of $f$ are frozen and $h_{\phi}$ is a small network, having only 5-20% of the number of parameters of $f$ , depending on the task. We call this method as rapid network adaptation (RNA) and experiment with different variants of it in Sec. 4. + +There exist various options for implementing the amortization process, e.g., $h_{\phi}$ can be trained to update the input image or the weights of $f_{\theta}$ . We choose to modulate the features of $f_{\theta}$ as it has been shown to work well in different domains [24] and gave the best results. To do this, we insert $k$ Feature-wise Linear Modulation (FiLM) layers [71] into $f_{\theta}$ (see Fig. 2). Each FiLM layer performs: $\mathrm{FiLM}(\mathbf{x}_i; \gamma_i, \beta_i) = \gamma_i \odot \mathbf{x}_i + \beta_i$ , where $\mathbf{x}_i$ is the activation of layer $i$ . $h_{\phi}$ is a network that takes as input the adaptation signal $z$ and model predictions and outputs the coefficients $\{\gamma_i, \beta_i\}$ of all $k$ FiLM layers. $h_{\phi}$ is trained on the same dataset $\mathcal{D}$ as $f_{\theta}$ , therefore, unlike TTO, it is never exposed to distribution shifts during training. Moreover, it is able to generalize to unseen shifts (see Sec. 4.3). See the supplementary for the full details, other RNA implementations we investigated, and a comparison of RNA against other ap + +![](images/7e679470370fff7ba52ed61f9cdc251b6ff92a26714717cca94f412b5cdcad27.jpg) +Figure 2: Architecture of RNA. $x$ is the input image, $f_{\theta}$ is the model to be adapted and $f_{\theta}(x)$ the corresponding prediction. To perform adaptation, we freeze the parameters of $f_{\theta}$ and insert several FiLM layers into $f_{\theta}$ . We then train $h_{\phi}$ to take in $z$ , the adaptation signal, and $f_{\theta}(x)$ to predict the parameters of these FiLM layers. This results in an adapted model $f_{\hat{\theta}}$ and improved predictions, $f_{\hat{\theta}}(x)$ . + +proaches that aim to handle distribution shifts. + +# 3.2. Which test-time adaptation signals to use? + +While developing adaptation signals is not the main focus of this study and is independent of the RNA method, we need to choose some for experimentation. Existing test-time adaptation signals, or proxies, in the literature include prediction entropy [91], spatial autoencoding [27], and self-supervised tasks like rotation prediction [85], contrastive [54] or clustering [9] objectives. The more aligned the adaptation signal is to the target task, the better the performance on the target task [85, 54]. More importantly, a poor signal can cause the adaptation to fail silently [9, 27]. Figure 3 shows how the original loss on the target task changes as different proxy losses from the literature, i.e. entropy [91], consistency between different middle domains [99, 104] are minimized. In all cases, the proxy loss decreases, however, the improvement in the target loss varies. Thus, successful optimization of existing proxy losses does not necessarily lead to better performance on the target task. In this paper, we adopt a few practical and real-world signals for our study. Furthermore, RNA turns out to be less susceptible to a poor adaptation signal vs TTO (see supplementary Tab. 1). This is because RNA is a neural network trained to use these signals to improve the target task, as opposed to being fixed at being SGD, like in TTO. + +# 3.2.1 Employed test-time adaptation signals + +We develop test-time adaptation signals for several geometric and semantic tasks as shown in Fig. 4. Our focus is not on providing an extensive list of adaptation signals, but rather on using practical ones for experimenting with RNA as well as demonstrating the benefits of using signals that are rooted in the known structure of the world and the task in hand. For example, geometric computer vision tasks naturally follow the multi-view geometry constraints, thus making that a proper candidate for approximating the test-time error, and consequently, an informative adaptation signal. + +Geometric Tasks. The field of multi-view geometry and its theorems, rooted in the 3D structure of the world, provide a rich source of adaptation signals. We demonstrate + +![](images/414d86d40713ed35662fab933544db2bb7afe8b11c447173724456c57b2dced1.jpg) +Figure 3: Adaptation using different signals. Not all improvements in proxy loss translates into improving the target task's performance. We show the results of adapting a pre-trained depth estimation model to a defocus blur corruption by optimizing different adaptation signals: prediction entropy [91], a self-supervised task (sobel edge prediction error [99]), and sparse depth obtained from SFM. The plots show how the $\ell_1$ target error with respect to ground-truth depth (green, left axis) changes as the proxy losses (blue, right axis) are optimized (shaded regions represent the $95\%$ confidence intervals across multiple runs of stochastic gradient descent (SGD) with different learning rates). Only adaptation with the sparse depth (SFM) proxy leads to a reduction of the target error. This signifies the importance of employing proper signals in an adaptation framework. Furthermore, we show that RNA is less susceptible to poorer adaptation signal, which results in comparable or improved performance while being significantly faster (see supplementary Table 1). + +our results on the following target tasks: monocular depth estimation, optical-flow estimation, and 3D reconstruction. For all, we first run a standard structure-from-motion (SFM) pipeline [81] to get sparse 3D keypoints. For depth estimation, we employ the z-coordinates of the sparse 3D keypoints i.e., noisy sparse depth, from each image as the adaptation signal. For optical flow, we perform keypoint matching across images (which returns sparse optical flow). Lastly, for 3D reconstruction, in addition to the previous two signals, we employ consistency between depth and optical flow predictions as another signal. + +Semantic Tasks. For semantic segmentation, we first experiment with using a low number of click annotations for each class, similar to the works on active annotation tools [17, 83, 69]. This gives us sparse segmentation annotations. Likewise, for classification, we use the hierarchical structure of semantic classes, and use coarse labels generated from the WordNet tree [64], similar to [38]. Although these signals (click annotations and coarse labels) are significantly weaker versions of the actual ground truth, thus being cheaper to obtain, it may not be realistic to assume access to them at test-time for certain applications, e.g., real-time ones. Thus, we also show how these can be obtained via $k$ -NN retrieval from the training dataset and patch matching using spatial features obtained from a pretrained self-supervised vision backbone [10] (see Fig. 4). + +# 4. Experiments + +We demonstrate that our approach consistently outperforms the baselines for adaptation to different distribution shifts (2D and 3D Common Corruptions [35, 43, 44], cross-datasets), over different tasks (monocular depth, image classification, semantic segmentation, optical flow) and datasets (Taskonomy [105], Replica [84], ImageNet [22], COCO [53], ScanNet [20], Hypersim [78]). The source + +![](images/98d2302b857e9ed23cc310928363630d787968eb8b80abdf3a51089b7e3ade38.jpg) +Figure 4: Examples of employed test-time adaptation signals. We use a range of adaptation signals in our experiments. These are practical to obtain and yield better performance compared to other proxies. In the left plot, for depth and optical flow estimation, we use sparse depth and optical flow via SFM. In the middle, for classification, for each test image, we perform $k$ -NN retrieval to get $k$ training images. Each of these retrieved image has a one hot label associated with it, thus, combining them gives us a coarse label that we use as our adaptation signal. Finally, for semantic segmentation, after performing $k$ -NN as we did for classification, we get a pseudo-labelled segmentation mask for each of these images. The features for each patch in the test image and the retrieved images are matched. The top matches are used as sparse supervision. See Sec. 4.1 for more details. + +code can be found on our project page. + +# 4.1. Experimental Setup + +We describe our experimental setup, i.e. different adaptation signals, adaptation mechanisms, datasets and baselines, for different tasks. See Tab. 1 for a summary. + +Baselines. We evaluate the following baselines: + +Pre-Adaptation Baseline: The network $f_{\theta}$ that maps from RGB to the target task, e.g., depth estimation, with no test-time adaptation. We denote this as Baseline for brevity. + +Densification: A network that maps from the given adaptation signal for the target task to the target task, e.g., sparse depth from SFM to dense depth. This is a control baseline and shows what can be learned from the test-time supervision alone, without employing input image information or a designed adaptation architecture. See Sec. 4.3 for a variant which includes the image as an additional input. + +TTO (episodic): We adapt the Baseline model to each episode by optimizing the proxy loss (see Tab. 1 for the adaptation signal used for each task.) at test-time. Its weights are reset to the Baseline model's after optimizing each batch, similar to [91, 108]. + +TTO (online): We continually adapt to a distribution shift defined by a corruption and severity. Test data is assumed to arrive in a stream, and each data point has the same distribution shift, e.g., noise with a fixed standard deviation [91, 85]. The difference with TTO (episodic) is that the model weights are not reset after each iteration. We denote this as TTO for brevity. + +TTO with Entropy supervision (TENT [91]): We adapt the Baseline model trained with log-likelihood loss by optimizing the entropy of the predictions. This is to reveal the effectiveness of entropy as a signal as proposed in [91]. + +TTO with Sobel Edges supervision (TTO-Edges): We adapt the Baseline model trained with an additional decoder that predicts a self-supervised task, similar to [85]. We choose + +
TaskAdaptation signalAdapted modelTraining dataOOD evaluation dataBaselines
DepthSFM, masked GTUNet [80], DPT [74]TaskonomyFor SFM: Replica, Replica-CC, ScanNet, For masked GT: Taskonomy-CC,-3DCC, HypersimPre-adaptation, densification, TENT, TTO-edges, TTO
Optical flowKeypoint matchingRAFT [87]FlyingChairs, FlyingThings [87]Replica-CCPre-adaptation
3D reconstructionSFM, keypoint matching,consistencyDepth, optical flow modelsDepth, optical flow dataReplica-CCPre-adaptation, TTO
Semantic segmentationClick annotations, patch matchingFCN [56]COCO (20 classes from Pascal VOC)For click annotations: COCO-CC, For patch matching: ImageNet-CPre-adaptation, densification, TENT, TTO
ClassificationCoarse labels (WordNet, DINO k-NN)ResNet50 [33], ConvNext [55]ImageNetImageNet-C, ImageNet-3DCC, ImageNet-V2Pre-adaptation, DINO k-NN, densification, TENT, TTO
+ +Table 1: Overview of the experiments for different target tasks, adaptation methods, and adaptation signals. For each task, we list the adaptation signal (Sec. 3.2) that we use for adaptation. We also list the models that we adapt, and the out-of-distribution (OOD) data used for evaluations and the relevant baselines. When there are different options for adaptation signal, e.g., in the case of depth, the signal is denoted in italics followed by the corresponding OOD dataset. The weights for the semantic segmentation, classification and optical flow models were taken from PyTorch [70]. + +![](images/a3387b40c39fd6ab0bd7db7ba83502a0b6dee9e02d02fc449b7340cc9d89701e.jpg) +Figure 5: RNA can achieve similar performance as TTO in a much shorter time. We compare how the $\ell_1$ errors of the adaptation mechanisms decrease over wall-clock time (s). The errors are averaged over all episodes (and all corruptions for Replica-CC). RNA only requires a forward pass at test-time, while TTO requires multiple forward and backward passes. On ScanNet and Replica-CC, RNA takes 0.01s, while TTO takes 3s to achieve similar performance. Furthermore, RNA is not trained with test-time shifts unlike TTO, thus, it learned to use the additional supervision to adapt to unseen shifts. + +![](images/f0ecfc202b74f3c5d625567c624991de8520097a82224ce68553f85c52a1f8f5.jpg) + +to predict Sobel edges as it has been shown to be robust to certain shifts [99]. We optimize the error of the edges predicted by the model and edges extracted from the RGB image to reveal the value of edge error as a supervision. + +RNA configurations. At test-time, we first get the predictions of the Baseline model and compute the adaptation signal. The predictions and adaptation signal are then passed to $h_{\phi}$ which adapts $f_{\theta}$ to $f_{\hat{\theta}}$ . The test images are then passed to $f_{\hat{\theta}}$ to get the final predictions. We evaluate following variants of RNA. + +RNA (frozen $f$ ): Baseline model weights, $f_{\theta}$ , are frozen when training $h_{\phi}$ . We call this variant RNA for brevity. + +RNA (jointly trained $f$ ): In contrast to the frozen $f$ variant, here we train $h_{\phi}$ jointly with the Baseline network. This variant requires longer training. + +Adaptation signal. As described in Sec. 3.2, we compute a broad range of test-time signals from the following processes. Each case describes a process applied on query image(s) in order to extract a test-time quantity. + +Structure-from-motion (SFM): Given a batch of query images, we use COLMAP [81] to run SFM, which returns sparse depth. The percentage of valid pixels, i.e. depth measurements, is about $0.16\%$ on Replica-CC and $0.18\%$ on Replica. For ScanNet we use the pre-computed sparse depth from [79], which has about $0.04\%$ valid pixels. As running SFM on corrupted images results in noisy sparse depth, we train $h_{\phi}$ to be invariant to noise [102, 79]. + +Masked ground truth (GT): We apply a random mask to the GT depth of the test image. We fixed the valid pixels to $0.05\%$ of all pixels, i.e. similar sparsity as SFM (see the supplementary for other values). This a control proxy as it enables a better evaluation of the adaptation methods without conflating with the shortcomings of adaptation signals. It is also a scalable way of simulating sparse depth from real-world sensors, e.g., LiDAR, as also done in [92, 59, 41]. + +Click annotations: We generate click annotations over random pixels for each class in a given image using GT - simulating an active annotation pipeline. The number of pixels ranges from 3 to 25, i.e. roughly $0.01\%$ of the total pixels, similar to [7, 69, 83, 109, 17]. + +Patch matching: To not use GT click annotations, for each test image, we first retrieve its $k$ -NN images from the original clean training dataset using DINO features [10]. We then get segmentation masks on these $k$ images. If the training dataset has labels for segmentation we use them directly, otherwise we obtain them from a pretrained network. For each of the $k$ training images and test image, we extract non-overlapping patches. The features for each patch that lie inside the segmentation masks of the $k$ training images are matched to the features of every patch in the test image. These matches are then filtered and used as sparse segmentation annotations. See Fig. 4 for illustration. + +Coarse labels (WordNet): We generate 45 coarse labels from the 1000-way ImageNet labels, i.e. making the labels $22 \times$ coarser, using the WordNet tree [64], similar to [39]. See supplementary for more details on the construction and results for other coarse label sets. + +Coarse labels (DINO $k$ -NN): For each test image, we retrieve the $k$ -NN images from the training dataset using DINO features [10]. Each of these $k$ training images is associated with an ImageNet class, thus, combining $k$ one-hot labels gives us a coarse label. + +Keypoint matching: We perform keypoint matching across images to get sparse optical flow. + +![](images/d7d5106eb9e34079491ea4e5bc50440aebc555d81ec897feae52c98224fa9153.jpg) +Figure 6: Qualitative results of RNA vs the baselines for semantic segmentation on random query images on COCO-CC (left) and depth on images from ScanNet, Taskonomy-3DCC and Replica-CC (right). For semantic segmentation, we use 15 pixel annotations per class. For Taskonomy-3DCC, we use sparse depth with $0.05\%$ valid pixels (30 pixels per image). See Fig. 7 for results on different adaptation signal levels. For ScanNet and Replica-CC, the adaptation signal is sparse depth measurements from SFM [81] with similar sparsity ratios to Taskonomy-3DCC. The predictions with proposed adaptation signals are shown in the last two rows. They are noticeably more accurate compared to the baselines. Comparing TTO and RNA, RNA's predictions are more accurate for segmentation, and sharper than TTO for depth (see the ellipses) while being significantly faster. See 4.2 and supplementary for more results. + +# 4.2. Adaptation with RNA vs TTO + +Here we summarize our observations from adapting with RNA vs TTO. As described, TTO represents the approach of closed-loop adaptation using the adaptation signal but without benefiting from amortization and learning (the adaptation process is fixed to be standard SGD). These observations hold across different tasks. See Sec. 4.3 for results. + +RNA is efficient. As RNA only requires a forward pass at test-time, it is orders of magnitude faster than TTO and is able to attain comparable performance to TTO. In Fig. 5, we compare the runtime of adaption with RNA and TTO for depth prediction. On average, for a given episode, RNA obtains similar performance as TTO in 0.01s, compared to TTO's 3-5s. Similarly, for dense 3D reconstruction, RNA is able to adapt in 0.008s compared to TTO's 66s (see Fig. 9). This suggests a successful amortization of the adaptation optimization by RNA. + +Furthermore, RNA's training is also efficient as it only requires training a small model, i.e. $5 - 20\%$ of the Baseline model's parameters, depending on the task. Thus, RNA has a fixed overhead, and small added cost at test-time. + +RNA's predictions are sharper than TTO for dense prediction tasks. From the last two rows of Fig. 6, it can be seen that RNA retains fine-grained details. This is a noteworthy point and can be attributed to the fact that RNA benefits from a neural network, thus its inductive biases can + +be beneficial (and further engineered) for such advantages. This is a general feature that RNA, and more broadly using a learning-based function to amortize adaptation optimization, brings – in contrast to limiting the adaptation process to be SGD, as represented by TTO. + +RNA generalizes to unseen shifts. RNA performs better than TTO for low severities (see supplementary for more details). However, as it was not exposed to any corruptions, the performance gap against TTO narrows at high severities as expected, which is exposed to corruptions at test-time. + +We hypothesize that the generalization property of RNA is due to the following reasons. 1. Even though $f_{\theta}$ was trained to convergence, it does not achieve exactly 0 error. Thus, when $h_{\phi}$ is trained with a frozen $f_{\theta}$ with the training data, it can still learn to correct the errors of $f_{\theta}$ , thus, adapting $f_{\theta}$ . 2. Adaptation signals, by definition, are expected to be relatively robust to distribution shifts. Even though the RGB image has been corrupted or from a new domain, the adaptation signal is more aligned with the target task. Thus, the input to $h_{\phi}$ does not undergo a significant shift and is able to adapt $f_{\theta}$ . + +# 4.3. Experiments using Various Target Tasks + +In this section, we provide a more comprehensive set of evaluations covering various target tasks and adaptation signals. In all cases, RNA is a fixed general framework without being engineered for each task and shows supportive results. + +
Adaptation SignalSFMSparse GTRelative Runtime
DatasetReplicaScanNetTaskonomyHypersim
ShiftCDSCCCDSNoneCC3DCCCDS
Pre-adaptation Baseline1.756.083.302.685.744.7533.641.00
Densification2.504.192.351.721.721.7217.251.00
TENT [91]2.036.094.035.515.514.4835.4515.85
TTO-Edges [85]1.736.143.282.705.694.7433.6920.98
RNA (frozen f)1.724.261.771.121.681.4916.171.56
RNA (jointly trained f)1.663.411.741.111.501.3717.131.56
TTO (Episodic)1.723.311.851.622.992.3117.7714.85
TTO (Online)1.823.161.761.131.481.3414.1714.85
+ +Table 2: Quantitative adaptation results on depth estimation. $\ell_1$ errors on the depth prediction task. (Lower is better. Multiplied by 100 for readability. The best models within 0.0003 error are shown in bold.) We generate distribution shifts by applying Common Corruptions (CC), 3D Common Corruptions (3DCC) and from performing cross-dataset evaluations (CDS). The results from CC and 3DCC are averaged over all distortions and severity levels on Taskonomy and 3 severity levels on Replica data. The adaptation signal from Taskonomy is masked GT (fixed at $0.05\%$ valid pixels) while that from Replica and ScanNet is sparse depth from SFM. RNA and TTO notably outperform the baselines. RNA successfully matches the performance of TTO while being around 10 times faster. + +See supplementary for the losses for different corruption types, sparsity levels, and the results of applying RNA to other adaptation signals. + +![](images/e7e769338393d03bb39644f20fd6c0faa1d25f8eb07477a726622d292d273109.jpg) +Figure 7: Qualitative adaptation results on semantic segmentation on random query images on COCO-CC. RNA notably improves the prediction quality using error feedback from as few as 3 random pixels. + +![](images/320af74ca6b0453873f53973af492360f55e3e049d93d41b27a0093712d3d65b.jpg) +Figure 8: Quantitative adaptation results on semantic segmentation. Each point shows the mean IOU over 15 corruptions and 5 severities. RNA significantly improves over baselines. Black dashed line shows the mean IOU of the baseline model for clean validation images, and is provided as an upper bound on performance. Numbers in the legend denote averages over all supervision pixel counts. See supplementary for a breakdown. + +Depth. We demonstrate the results quantitatively in Tab. 2 and Fig. 5 and qualitatively in Fig. 6. In Tab. 2, we compare RNA against all baselines, and over several distribution shifts and different adaptation signals. Our RNA variants outperform the baselines overall. TTO (online) has a better performance than TTO (episodic) as it assumes a smoothly changing distribution shift, and it continuously updates the model weights. RNA (jointly trained $f$ ) has a + +better performance among RNA variants. This is reasonable as the target model is not frozen, thus, is less restrictive. + +As another baseline, we trained a single model that takes as input a concatenation of the RGB image and sparse supervision, i.e. multi-modal input. However, its average performance on Taskonomy-CC was $42.5\%$ worse than RNA's (see sup. mat. Sec. 3.2). Among the baselines that do not adapt, densification is the strongest under distribution shift due to corruptions. This is expected as it does not take the RGB image as input, thus, it is not affected by the underlying distribution shift. However, as seen from the qualitative results in Figs. 6, 7, unlike RNA, densification is unable to predict fine-grained details (which quantitative metrics often do not well capture). We also show that the gap between RNA and densification widens with sparser supervision (see sup. mat. Fig. 1), which confirms that RNA is making use of the error feedback signal, to adapt $f$ . + +![](images/eeb125b83fedddb1ae3b62ea13e5a467fef066c1736069bc593cbbdb9a18ea8b.jpg) +Figure 9: Adaptation results for 3D reconstruction. Using appropriate adaptation signals from multi-view geometry can recover accurate 3D reconstructions. We report the average $\ell_1$ error between ground truth 3D coordinates and the estimated ones. The titles above each column refers to the depth model used to get the reconstruction. TTO+MVC corresponds to the predictions after multi-view consistency optimization. It can be seen that RNA and TTO improve the reconstructions over the baselines with RNA being significantly faster. See supplementary Fig. 4 for more results and the corresponding error maps. + +Dense 3D Reconstruction. Here, we combine multiple adaptation signals from multi-view geometry. First, we adapt the weights of the depth and optical flow models independently. The results from this adaptation can be found in the previous paragraph (for depth) and supplementen + +
Adaptation SignalDatasetCleanIN-CIN-3DCCIN-V2Rel. Runtime
-Pre-adaptation Baseline23.8561.6654.9737.151.00
EntropyTENT24.6746.1947.1337.075.51
Coarse labels (wordnet)Densification95.5095.5095.5095.50-
TTO (Online)24.7240.6242.9036.775.72
RNA (frozen f)16.7241.2140.3725.531.39
Coarse labels (DINO)DINO (k-NN)25.5652.6448.2437.39-
TTO (Online)24.5951.5949.1836.965.72
RNA (frozen f)24.3654.8652.2936.881.39
+ +tary (for optical flow). Next, the two models are adapted to make their predictions consistent with each other. This is achieved using the same process as [58], i.e. multi-view-consistency (MVC). See supplementary for details. + +Figure 9 shows the point cloud visualizations on Replica where the input was corrupted with Gaussian Noise. This results in collapsed depth predictions, thus, reconstructions are unusable (Baseline column) and performing MVC is not helpful (Baseline+MVC). Adapting the depth predictions using TTO and MVC improves the reconstruction notably while RNA achieves a similar performance significantly faster. + +Semantic Segmentation. We experiment with click annotations and DINO patch matching as adaptation signals. Click annotations: In Fig. 8, we show how the IoU changes with the adaptation signal level on COCO-CC. As the Baseline and TENT do not make use of this signal, their IoU is a straight line. RNA clearly outperforms the baselines for all levels of adaptation signal. Figure 7 shows the qualitative results with increasing supervision, and Fig. 6 (left) a comparison against all baselines, demonstrating higher quality predictions with RNA. + +DINO patch matching: We perform patch matching on DINO features (described in Sec. 4.1) to get the adaptation signal. As the patch matching process can be computationally expensive, we demonstrate our results on all cat classes in ImageNet and over one noise, blur and digital corruption for 3 levels of severity. We used the predictions of a pretrained FCN on the clean images as pseudolabels to compute IoU. The mean IoU averaged over these corruptions and severities is 48.98 for the baseline model, 53.45 for TTO. RNA obtains a better IOU of 58.04, thus it can make use of the sparse annotations from DINO patch matching. + +Image Classification. We experiment with coarse labels from WordNet and DINO $k$ -NN as adaptation signals. + +Coarse labels (WordNet): Table 3 shows the results from using 45-coarse labels on ImageNet- $\{\mathrm{C},3\mathrm{DCC},\mathrm{V}2\}$ . This corresponds to $22\mathrm{x}$ coarser supervision compared to the 1000 classes that we are evaluating on. TENT seems to have notable improvements in performance under corruptions for classification, unlike for semantic segmentation and depth. We show that using coarse supervision results in even better performance, about a further 5 pp reduction + +in error. Furthermore, on uncorrupted data, i.e. clean, and ImageNet-V2 [76], RNA gives roughly 10 pp improvement in performance compared to TTO. Thus, coarse supervision provides a useful signal for adaptation while requiring much less effort than full annotation [97]. See supplementary for results on other coarse sets. + +Coarse labels (DINO $k$ -NN): We also show results from using coarse sets generated from DINO $k$ -NN retrieval. This is shown in the last 3 rows of Tab. 3. Both RNA and TTO use this coarse information to outperform the non-adaptive baselines. However, they do not always outperform TENT, which could be due to the noise in retrieval. + +# 4.4. Ablations and additional results + +Table 3: Quantitative adaptation results on on ImageNet (IN) classification task. We evaluate on the clean validation set, ImageNet-C,3DCC,V2}. We report average error $(\%)$ for 1000-way classification task over all corruptions and severities. For the coarse labels with WordNet supervision, we use 45-coarse labels. For DINO $k$ NN, we set $k = 20$ + +
Task (Arch.)Depth (DPT [74])Classification (ConvNext [55])
ShiftCleanCCRel. RuntimeCleanIN-CRel. Runtime
Pre-adaptation Baseline2.233.761.0018.1342.951.00
TTO (Online)1.822.6113.8517.8341.4411.04
RNA (frozen f)1.131.561.0114.3238.041.07
+ +Aaptations of main network $f_{\theta}$ with different backbones. Previous results in the paper were from adapting $f_{\theta}$ with a UNet architecture. Here, we study the performance of RNA on other architectures of $f_{\theta}$ , namely, the dense prediction transformer (DPT) [74] for depth and ConvNext [55] for image classification. Table 4 shows the results of incorporating RNA to these architectures. In both cases, RNA is able to improve on the error and runtime of TTO. Thus, RNA can be applied to a range of architectures. + +Table 4: RNA works across different architectures of the main network $f_{\theta}$ such as DPT [74] and ConvNext [55]. Quantitative adaptation results on depth estimation and image classification on Taskonomy and ImageNet datasets, respectively. (Lower is better. $\ell_1$ errors for depth estimation are multiplied by 100 for readability.) + +
Method\ShiftNoneTaskonomy-CCTaskonomy-3DCCHypersimBlendedMVG
Pre-adaptation0.0270.0570.0480.3363.450
RNA (HyperNetwork-x)0.0190.0410.0330.2572.587
RNA (FiLM-x)0.0190.0390.0330.2792.636
RNA (FiLM-f)0.0130.0240.0200.1982.310
+ +Table 5: Implementations of different architectures for the controller network $h_{\phi}$ . $\ell_1$ errors on the depth estimation task under distribution shifts are reported. The adaptation signal here is masked GT, fixed at 0.05% of valid pixels. + +Implementations of different architectures for the controller network $h_{\phi}$ . We experiment with different architectures for $h_{\phi}$ e.g., HyperNetworks [31], other FiLM variants, or adapting the input instead of the model parameters. Instead of adding FiLM layers to adapt $f_{\theta}$ (denoted as FiLM- $f$ ), as described in Sec. 3.1, we also experimented with adding FiLM layers to a UNet model that is trained to update the input image $x$ (denoted as FiLM- $x$ ). For FiLM- $x$ , only $x$ is updated and there is no adaptation on $f_{\theta}$ . Lastly, as Hypernetworks [31] have been shown to be expressive and suitable for adaptation, we trained a HyperNetwork, in this case an MLP, to predict the weights of a 3-layer convolutional network that updates $x$ (denoted as HyperNetwork- + +$x$ ). The results of adaptation with these variants of RNA are shown in Table 5. The FiLM- $f$ variant performed best, thus, we adopted it as our main architecture. See supplementary Sec. 2.2 for more details and a discussion on the trade-offs of the choices of implementing this closed-loop "control" system, namely those that make stronger model-based assumptions. + +Controlling for number of parameters. We ran a control experiment where all methods have the same architecture, thus, same number of parameters. The results are in the supplementary Table 2. RNA still returns the best performance. Thus, its improvement over the baselines is not due to a different architecture or number of parameters but due to its test-time adaptation mechanism. + +# 5. Approaches for handling distribution shifts + +In this section, we provide a unified discussion about the approaches that aim to handle distribution shifts. Figure 10 gives an overview of how these approaches can be characterized. Open-loop systems predict $y$ by only using their inputs without receiving feedback. Training-time robustness methods, image modifications, and multi-modal methods fall into this category. These methods assume the learned model is frozen at the test-time. Thus, they aim to incorporate inductive biases at training time that could be useful against distribution shifts at the test-time. The closed-loop systems, on the other hand, are adaptive as they make use of a live error feedback signal that can be computed at test-time from the model predictions and an adaptation signal. + +In the interest of space, we move the detailed discussion about each of these variants to Sec. 1.2 of the supplementary. In particular, elaboration of the distinction between a model-based vs model-free approach, denoising/image-modification methods, multi-modal methods, and our observations over comparing the conclusions of [46] el al. and our experiments are provided there. + +# 6. Conclusion and Limitations + +We presented RNA, a method for efficient adaptation of neural networks at test-time using a closed-loop formulation. It involves training a side network to use a test-time adaptation signal to adapt a main network. This network acts akin to a "controller" and adapts the main network based on the adaptation signal. We showed that this general and flexible framework can generalize to unseen shifts, and as it only requires a forward pass at test-time, it is orders of magnitude faster than TTO. We evaluated this approach using a diverse set of adaptation signals and target tasks. We briefly discuss the limitations and potential future works: + +Different instantiation of RNA and amortization. While we experimented with several RNA variants (see supplementary for details), further investigation toward a stronger + +![](images/a81f6ddc1ff511cba8c550d9522a0d86cdf1e26e5c7318429b26a4acbfa7890a.jpg) +Figure 10: An overview of methods that aim to handle distribution shifts. Left: Open-loop systems predict $y$ by only using their inputs without receiving feedback. The first and popular example of open-loop systems is training-time robustness methods (data augmentation, architectural changes, etc.). The next example is the methods that modify the input $x$ , e.g. denoising or style changes, to recover the original image before corruption, independent of $y$ . Furthermore, there are multi-modal methods that use an additional input $z$ . As the learned model is frozen at test-time, these methods need to anticipate the distribution shift by incorporating inductive biases at training time (See also Fig. 1.). Right: In contrast, closed-loop systems make use of its current output, $y$ , and an adaptation signal, $z$ , to form an error feedback signal that can be used to update its predictions. Thus, they adapt to the shifts as they occur. We can then group closed-loop systems into model-based and model-free methods. The former performs adaptation by estimating the parameters $e$ of specific modeled distribution shift families, while the latter performs adaptation in a data-driven way without explicitly modeling certain distribution shifts. Adaptation can be performed via running an optimization, i.e. TTO via SGD, or via amortization, i.e., training a side controller network to predict TTO updates that minimize the error feedback. Our proposed method, RNA, belongs to the model-free adaptation approach that makes use of amortization for efficiency. + +instantiation of RNA which can generalize to more shifts and handle more drastic changes, e.g. via building in a more explicit "model" of the shifts and environment (see the discussion about [46]), is important. In general, as the role of the controller network is to amortize the training optimization of the main network, the amortized optimization literature [3] is one apt resource to consult for this purpose. + +Hybrid mechanism for activating TTO in RNA. TTO constantly adapts a model to a distribution shift, hence, in theory, it can adapt to any shift despite being comparatively inefficient. To have the best of both worlds, investigating mechanisms for selectively activating TTO within RNA when needed can be useful. + +Finding adaptation signals for a given task. While the focus of this study was not on developing new adaption signals, we demonstrated useful ones for several core vision tasks, but there are many more. Finding these signals requires either knowledge of the target task so a meaningful signal can be accordingly engineered or core theoretical works on understanding how a proxy and target objectives can be "aligned" for training. + +Acknowledgement: The authors thank Onur Beker. This work was partially supported by the ETH4D and EPFL EssentialTech Centre Humanitarian Action Challenge Grant. + +# References + +[1] Hassan Akbari, Liangzhe Yuan, Rui Qian, Wei-Hong Chuang, Shih-Fu Chang, Yin Cui, and Boqing Gong. Vatt: Transformers for multimodal self-supervised learning from raw video, audio and text. 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PMLR, 2019. 2 \ No newline at end of file diff --git a/2023/Rapid Network Adaptation_ Learning to Adapt Neural Networks Using Test-Time Feedback/images.zip b/2023/Rapid Network Adaptation_ Learning to Adapt Neural Networks Using Test-Time Feedback/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..f5b065c2e23bf32c093deec6e641b5db0284e37d --- /dev/null +++ b/2023/Rapid Network Adaptation_ Learning to Adapt Neural Networks Using Test-Time Feedback/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3d4ef6035a56000358dc0c33fab4e731a98ef4a47e8336cc1907109f3879fe33 +size 522965 diff --git a/2023/Rapid Network Adaptation_ Learning to Adapt Neural Networks Using Test-Time Feedback/layout.json b/2023/Rapid Network Adaptation_ Learning to Adapt Neural Networks Using Test-Time Feedback/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..6e2e0f831590ebdd89879b53df64155c12af16c0 --- /dev/null +++ b/2023/Rapid Network Adaptation_ Learning to Adapt Neural Networks Using Test-Time Feedback/layout.json @@ -0,0 +1,12002 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 101, + 103, + 492, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 103, + 492, + 140 + ], + "spans": [ + { + "bbox": [ + 101, + 103, + 492, + 140 + ], + "type": "text", + "content": "Rapid Network Adaptation: Learning to Adapt Neural Networks Using Test-Time Feedback" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 116, + 161, + 173, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 161, + 173, + 175 + ], + "spans": [ + { + "bbox": [ + 116, + 161, + 173, + 175 + ], + "type": "text", + "content": "Teresa Yeo" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 198, + 161, + 291, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 198, + 161, + 291, + 175 + ], + "spans": [ + { + "bbox": [ + 198, + 161, + 291, + 175 + ], + "type": "text", + "content": "Oguzhan Fatih Kar" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 315, + 161, + 389, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 161, + 389, + 175 + ], + "spans": [ + { + "bbox": [ + 315, + 161, + 389, + 175 + ], + "type": "text", + "content": "Zahra Sodagar" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 413, + 161, + 473, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 413, + 161, + 473, + 175 + ], + "spans": [ + { + "bbox": [ + 413, + 161, + 473, + 175 + ], + "type": "text", + "content": "Amir Zamir" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 164, + 178, + 435, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 164, + 178, + 435, + 192 + ], + "spans": [ + { + "bbox": [ + 164, + 178, + 435, + 192 + ], + "type": "text", + "content": "Swiss Federal Institute of Technology Lausanne (EPFL)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 184, + 205, + 408, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 184, + 205, + 408, + 216 + ], + "spans": [ + { + "bbox": [ + 184, + 205, + 408, + 216 + ], + "type": "text", + "content": "https://rapid-network-adaptation.epfl.ch/" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 243, + 192, + 256 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 243, + 192, + 256 + ], + "spans": [ + { + "bbox": [ + 143, + 243, + 192, + 256 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 270, + 290, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 290, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 290, + 486 + ], + "type": "text", + "content": "We propose a method for adapting neural networks to distribution shifts at test-time. In contrast to training-time robustness mechanisms that attempt to anticipate and counter the shift, we create a closed-loop system and make use of test-time feedback signal to adapt a network on the fly. We show that this loop can be effectively implemented using a learning-based function, which realizes an amortized optimizer for the network. This leads to an adaptation method, named Rapid Network Adaptation (RNA), that is notably more flexible and orders of magnitude faster than the baselines. Through a broad set of experiments using various adaptation signals and target tasks, we study the generality, efficiency, and flexibility of this method. We perform the evaluations using various datasets (Taskonomy, Replica, ScanNet, Hypersim, COCO, ImageNet), tasks (depth, optical flow, semantic segmentation, classification), and distribution shifts (Cross-datasets, 2D and 3D Common Corruptions) with promising results." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 512, + 128, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 512, + 128, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 512, + 128, + 525 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 534, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 287, + 715 + ], + "type": "text", + "content": "Neural networks are found to be unreliable against distribution shifts [23, 35, 43, 42, 29]. Examples of such shifts include blur due to camera motion, object occlusions, changes in weather conditions and lighting, etc. The training-time strategies to deal with this issue attempt to anticipate the shifts that may occur and counter them at the training stage – for instance, by augmenting the training data or updating the architecture with corresponding robustness inductive biases. As the possible shifts are numerous and unpredictable, this approach has inherent limitations. This is the main motivation behind test-time adaptation methods, which instead aim to adapt to such shifts as they occur and recover from failure. In other words, these methods choose adaptation over anticipation (see Fig. 1). In this work, we propose a test-time adaptation framework that aims to perform an ef" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 326, + 243, + 529, + 453 + ], + "blocks": [ + { + "bbox": [ + 326, + 243, + 529, + 453 + ], + "lines": [ + { + "bbox": [ + 326, + 243, + 529, + 453 + ], + "spans": [ + { + "bbox": [ + 326, + 243, + 529, + 453 + ], + "type": "image", + "image_path": "23a0149ecf8d4c09bbae0937e2218779aeba8a354c644fe1acc4ba08d4696173.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 464, + 547, + 610 + ], + "lines": [ + { + "bbox": [ + 304, + 464, + 547, + 610 + ], + "spans": [ + { + "bbox": [ + 304, + 464, + 547, + 610 + ], + "type": "text", + "content": "Figure 1: Adaptive vs non-adaptive neural network pipelines. Top: In order to be robust, non-adaptive methods include training-time interventions that anticipate and counter the distribution shifts that will occur at test-time (e.g., via data augmentation). The learned model, " + }, + { + "bbox": [ + 304, + 464, + 547, + 610 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 464, + 547, + 610 + ], + "type": "text", + "content": ", is frozen at test-time, thus upon encountering an out-of-distribution input, its predictions may collapse. Bottom: Adaptive methods create a closed-loop and use an adaptation signal at test-time. The adaptation signal is a quantity that can be computed at test-time from the environment. " + }, + { + "bbox": [ + 304, + 464, + 547, + 610 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 304, + 464, + 547, + 610 + ], + "type": "text", + "content": " acts as a \"controller\" by taking in an error feedback, computed from the adaptation signal and model predictions, to adapt " + }, + { + "bbox": [ + 304, + 464, + 547, + 610 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 464, + 547, + 610 + ], + "type": "text", + "content": " accordingly. It can be implemented as a (i) standard optimizer (e.g., using SGD) or (ii) neural network. The former is equivalent to test-time optimization (TTO), while the latter aims to amortize the optimization process, by training a controller network to adapt " + }, + { + "bbox": [ + 304, + 464, + 547, + 610 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 464, + 547, + 610 + ], + "type": "text", + "content": " - thus, it can be more efficient and flexible. In this work, we study the latter approach and show its efficiency and flexibility." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 616, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 616, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 616, + 545, + 640 + ], + "type": "text", + "content": "ficient adaptation of a given main network using a feedback signal." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": "One can consider performing \"test-time optimization\" (TTO) for this purpose, similar to previous works [91, 108, 27] e.g. simply using SGD to finetune the network to reduce a proxy loss [91]. While this can successfully adapt a network, it is unnecessarily inefficient as it does not make use of the learnable regularities in the adaptation pro" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4674" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "cess, and consequently, unconducive for real-world applications. It also results in a rigid framework as the update mechanism is fixed to be the same as the training process of neural networks (SGD). We show this process can be effectively amortized using a learning-based feed-forward controller network, which yields orders of magnitude faster results (See Fig. 1, Sec. 4.3). In addition, it provides flexibility advantages as the controller is implemented using a neural network and can be engineered to include arbitrary inductive biases and desired features that could counter the suboptimalities of the adaptation signal." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 215, + 134, + 227 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 215, + 134, + 227 + ], + "spans": [ + { + "bbox": [ + 47, + 215, + 134, + 227 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 235, + 287, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 235, + 287, + 282 + ], + "spans": [ + { + "bbox": [ + 47, + 235, + 287, + 282 + ], + "type": "text", + "content": "Our work focuses on how to adapt a neural network efficiently at test-time on a range of tasks and adaptation signals. We give an overview of relevant topics. See the supplementary Sec. 7 for more related works." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 283, + 287, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 283, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 283, + 287, + 378 + ], + "type": "text", + "content": "Robustness methods anticipate the distribution shift that can occur and incorporate inductive biases into the model to help it generalize. Popular methods include data augmentation [61, 107, 57, 37, 103, 101, 34, 43], self-/pre-training [36, 95, 25, 72, 96, 75, 32], architectural changes [19, 8, 82, 62, 55] or ensembling [48, 67, 99, 73, 40, 68]. We focus on adaptation mechanisms and identifying practical adaptation signals that can be used at test-time." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 379, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 379, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 379, + 287, + 498 + ], + "type": "text", + "content": "Amortized optimization methods make use of learning to improve (e.g., speed-up) the solution of optimization problems, particularly for settings that require repeatedly solving similar instances of the same underlying problem [49, 11, 4, 106, 26, 94, 60, 14, 3]. Fully amortized optimization methods model the shared structure between past instances of solved problems to regress the solution to a new problem [31, 21, 52]. As adapting to distribution shifts can be cast as solving an optimization problem at test-time, our method can be seen as an amortized solution." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "type": "text", + "content": "Test-time adaptation methods for geometric tasks. Many existing frameworks, especially in geometric tasks such as aligning a 3D object model with an image of it, in effect instantiate a task-specific case of closed-loop optimization for each image [60, 106, 63]. Common sources of their adaptation quantity include sensor data [92, 98, 15, 89, 102, 18], structure from motion (SFM) [93, 47], motion [12], and photometric and multi-view consistency constraints (MVC) [58, 45]. Many of the latter methods often focus on depth prediction and they introduce losses that are task-specific, e.g., [93] optimize a photometric consistency loss. We differ by aiming to investigate a more general framework for test-time adaptation that can be applied to several tasks. For MVC, while we adopt the same losses as [58], we show under collapsed predictions, optimizing only MVC constraints is not sufficient for recovering predictions; depth predictions need to be adapted and this can be done efficiently using our framework (see Sec. 4.3)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "content": "Test-time adaptation methods for semantic tasks. Most of these works involve optimizing a self-supervised objective at test-time [85, 91, 54, 27, 28, 108, 9, 51, 100]. They differ in the choice of self-supervised objectives, e.g., prediction entropy [91], mutual information [51], and parameters optimized [9]. However, as we will discuss in Sec. 3.2, and as shown by [9, 27, 65], existing methods can fail silently, i.e. successful optimization of the adaptation signal loss does not necessarily result in better performance on the target task. We aim to have a more efficient and flexible method and also show that using proper adaptation signals results in improved performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 216, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 216, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 216, + 545, + 335 + ], + "type": "text", + "content": "Multi-modal frameworks are models that can use the information from multiple sources, e.g., RGB image, text, audio, etc., [13, 5, 86, 50, 2, 16, 72, 1, 6, 30]. Schematically, our method has similarities to multi-modal learning (as many amortized optimization methods do) since it simultaneously uses an input RGB image and an adaptation signal. The main distinction is that our method implements a particular process toward adapting a network to a shift using an adaptation signal from the environment – as opposed to a generic multi-modal learning." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 346, + 361, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 346, + 361, + 357 + ], + "spans": [ + { + "bbox": [ + 306, + 346, + 361, + 357 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 365, + 545, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 497 + ], + "type": "text", + "content": "In Fig. 1, we schematically compared methods that incorporate robustness mechanisms at training-time (thus anticipating the distribution shift) with those that adapt to shifts at test-time. Our focus is on the latter. In this section, we first discuss the benefits and downsides of common adaptation methods (Sec. 3.1). We then propose an adaptation method that is fast and can be applied to several tasks (Sec. 3.1.1). To adapt, one also needs to be able to compute an adaptation signal, or proxy, at the test-time. In the second part of the section (Sec. 3.2), we study a number of practical adaptation signals for a number of tasks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 504, + 452, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 504, + 452, + 516 + ], + "spans": [ + { + "bbox": [ + 306, + 504, + 452, + 516 + ], + "type": "text", + "content": "3.1. How to adapt at test-time?" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": "An adaptive system is one that can respond to changes in its environment. More concretely, it is a system that can acquire information to characterize such changes, e.g., via an adaptation signal that provides an error feedback, and make modifications that would result in a reduction of this error (see Fig. 1). The methods for performing the adaptation of the network range from gradient-based updates, e.g. using SGD to fine-tune the parameters [85, 91, 27], to the more efficient semi-amortized [110, 88] and amortized approaches [90, 66, 77] (see Fig. 6 of [77] for an overview). As amortization methods train a controller network to substitute the explicit optimization process, they only require a forward pass at test-time. Thus, they are computationally efficient. Gradient-based approaches, e.g., TTO, can be powerful adaptation methods when the test-time signal is robust and well-suited for the task (see Fig. 4). How-" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4675" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "ever, they are inefficient and have the risk of failing silently and the need for carefully tuned optimization hyperparameters [9]. In this work, we focus on an amortization-based approach." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": "Notation. We use " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": " to denote the input image domain, and " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": " to denote the target domain for a given task. We use " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "f_{\\theta}:\\mathcal{X}\\to \\mathcal{Y}" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": " to denote the model to be adapted, where " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": " denotes the model parameters. We denote the model before and after adaptation as " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "f_{\\hat{\\theta}}" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": " respectively. " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": " are the original training loss and training dataset of " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": ", e.g., for classification, " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": " will be the cross-entropy loss and " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": " the ImageNet training data. As shown in Fig. 1, " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "h_\\phi" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": " is a controller for " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": ". It can be an optimization algorithm, e.g., SGD, or a neural network. " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": " denotes the optimization hyperparameters or the network's parameters. The former case corresponds to TTO, and the latter is the proposed RNA, which will be explained in the next subsection. Finally, the function " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "g:\\mathcal{X}^M\\rightarrow \\mathcal{Z}" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": " returns the adaptation signal by mapping a set of images " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{B} = \\{I_1,\\dots,I_M\\} \\in \\mathcal{X}^M" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": " to a vector " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "g(\\mathcal{B}) = z\\in \\mathcal{Z}" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": ". This function " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": " is given, e.g., for depth, " + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 121, + 288, + 324 + ], + "type": "text", + "content": " returns the sparse depth measurements from SFM." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 333, + 228, + 345 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 333, + 228, + 345 + ], + "spans": [ + { + "bbox": [ + 47, + 333, + 228, + 345 + ], + "type": "text", + "content": "3.1.1 Rapid Network Adaptation (RNA)" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "text", + "content": "For adaptation, we use a neural network for " + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "text", + "content": ". The adaptation signal and model predictions are passed as inputs to " + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "text", + "content": " and it is trained to regress the parameters " + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}(\\phi) = h_{\\phi}(f_{\\theta}(\\mathcal{B}), z)" + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "text", + "content": ". This corresponds to an objective-based amortization of the TTO process [3]. Using both the adaptation signal " + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "text", + "content": " and model prediction " + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "inline_equation", + "content": "f_{\\theta}(\\mathcal{B})" + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "text", + "content": " informs the controller network about the potential errors of the model. The training objective for " + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "inline_equation", + "content": "\\min_{\\phi} \\mathbb{E}_{\\mathcal{D}}[\\mathcal{L}(f_{\\hat{\\theta}(\\phi)}(\\mathcal{B}), y)]" + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "inline_equation", + "content": "(\\mathcal{B}, y) \\sim \\mathcal{D}" + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "text", + "content": " is a training batch sampled from " + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "text", + "content": ". Note that the original weights of " + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "text", + "content": " are frozen and " + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "text", + "content": " is a small network, having only 5-20% of the number of parameters of " + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 352, + 287, + 520 + ], + "type": "text", + "content": ", depending on the task. We call this method as rapid network adaptation (RNA) and experiment with different variants of it in Sec. 4." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": "There exist various options for implementing the amortization process, e.g., " + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": " can be trained to update the input image or the weights of " + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": ". We choose to modulate the features of " + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": " as it has been shown to work well in different domains [24] and gave the best results. To do this, we insert " + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": " Feature-wise Linear Modulation (FiLM) layers [71] into " + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": " (see Fig. 2). Each FiLM layer performs: " + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{FiLM}(\\mathbf{x}_i; \\gamma_i, \\beta_i) = \\gamma_i \\odot \\mathbf{x}_i + \\beta_i" + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": " is the activation of layer " + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": " is a network that takes as input the adaptation signal " + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": " and model predictions and outputs the coefficients " + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\{\\gamma_i, \\beta_i\\}" + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": " of all " + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": " FiLM layers. " + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": " is trained on the same dataset " + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 522, + 288, + 714 + ], + "type": "text", + "content": ", therefore, unlike TTO, it is never exposed to distribution shifts during training. Moreover, it is able to generalize to unseen shifts (see Sec. 4.3). See the supplementary for the full details, other RNA implementations we investigated, and a comparison of RNA against other ap" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 325, + 70, + 529, + 152 + ], + "blocks": [ + { + "bbox": [ + 325, + 70, + 529, + 152 + ], + "lines": [ + { + "bbox": [ + 325, + 70, + 529, + 152 + ], + "spans": [ + { + "bbox": [ + 325, + 70, + 529, + 152 + ], + "type": "image", + "image_path": "7e679470370fff7ba52ed61f9cdc251b6ff92a26714717cca94f412b5cdcad27.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "lines": [ + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "spans": [ + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "text", + "content": "Figure 2: Architecture of RNA. " + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "text", + "content": " is the input image, " + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "text", + "content": " is the model to be adapted and " + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "inline_equation", + "content": "f_{\\theta}(x)" + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "text", + "content": " the corresponding prediction. To perform adaptation, we freeze the parameters of " + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "text", + "content": " and insert several FiLM layers into " + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "text", + "content": ". We then train " + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "text", + "content": " to take in " + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "text", + "content": ", the adaptation signal, and " + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "inline_equation", + "content": "f_{\\theta}(x)" + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "text", + "content": " to predict the parameters of these FiLM layers. This results in an adapted model " + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "inline_equation", + "content": "f_{\\hat{\\theta}}" + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "text", + "content": " and improved predictions, " + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "inline_equation", + "content": "f_{\\hat{\\theta}}(x)" + }, + { + "bbox": [ + 305, + 157, + 547, + 217 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 221, + 493, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 221, + 493, + 232 + ], + "spans": [ + { + "bbox": [ + 305, + 221, + 493, + 232 + ], + "type": "text", + "content": "proaches that aim to handle distribution shifts." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 240, + 526, + 253 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 240, + 526, + 253 + ], + "spans": [ + { + "bbox": [ + 306, + 240, + 526, + 253 + ], + "type": "text", + "content": "3.2. Which test-time adaptation signals to use?" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 258, + 546, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 546, + 534 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 546, + 534 + ], + "type": "text", + "content": "While developing adaptation signals is not the main focus of this study and is independent of the RNA method, we need to choose some for experimentation. Existing test-time adaptation signals, or proxies, in the literature include prediction entropy [91], spatial autoencoding [27], and self-supervised tasks like rotation prediction [85], contrastive [54] or clustering [9] objectives. The more aligned the adaptation signal is to the target task, the better the performance on the target task [85, 54]. More importantly, a poor signal can cause the adaptation to fail silently [9, 27]. Figure 3 shows how the original loss on the target task changes as different proxy losses from the literature, i.e. entropy [91], consistency between different middle domains [99, 104] are minimized. In all cases, the proxy loss decreases, however, the improvement in the target loss varies. Thus, successful optimization of existing proxy losses does not necessarily lead to better performance on the target task. In this paper, we adopt a few practical and real-world signals for our study. Furthermore, RNA turns out to be less susceptible to a poor adaptation signal vs TTO (see supplementary Tab. 1). This is because RNA is a neural network trained to use these signals to improve the target task, as opposed to being fixed at being SGD, like in TTO." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 540, + 502, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 502, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 502, + 552 + ], + "type": "text", + "content": "3.2.1 Employed test-time adaptation signals" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 557, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 677 + ], + "type": "text", + "content": "We develop test-time adaptation signals for several geometric and semantic tasks as shown in Fig. 4. Our focus is not on providing an extensive list of adaptation signals, but rather on using practical ones for experimenting with RNA as well as demonstrating the benefits of using signals that are rooted in the known structure of the world and the task in hand. For example, geometric computer vision tasks naturally follow the multi-view geometry constraints, thus making that a proper candidate for approximating the test-time error, and consequently, an informative adaptation signal." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "type": "text", + "content": "Geometric Tasks. The field of multi-view geometry and its theorems, rooted in the 3D structure of the world, provide a rich source of adaptation signals. We demonstrate" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4676" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 69, + 286, + 124 + ], + "blocks": [ + { + "bbox": [ + 50, + 69, + 286, + 124 + ], + "lines": [ + { + "bbox": [ + 50, + 69, + 286, + 124 + ], + "spans": [ + { + "bbox": [ + 50, + 69, + 286, + 124 + ], + "type": "image", + "image_path": "414d86d40713ed35662fab933544db2bb7afe8b11c447173724456c57b2dced1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 133, + 286, + 275 + ], + "lines": [ + { + "bbox": [ + 47, + 133, + 286, + 275 + ], + "spans": [ + { + "bbox": [ + 47, + 133, + 286, + 275 + ], + "type": "text", + "content": "Figure 3: Adaptation using different signals. Not all improvements in proxy loss translates into improving the target task's performance. We show the results of adapting a pre-trained depth estimation model to a defocus blur corruption by optimizing different adaptation signals: prediction entropy [91], a self-supervised task (sobel edge prediction error [99]), and sparse depth obtained from SFM. The plots show how the " + }, + { + "bbox": [ + 47, + 133, + 286, + 275 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 47, + 133, + 286, + 275 + ], + "type": "text", + "content": " target error with respect to ground-truth depth (green, left axis) changes as the proxy losses (blue, right axis) are optimized (shaded regions represent the " + }, + { + "bbox": [ + 47, + 133, + 286, + 275 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 47, + 133, + 286, + 275 + ], + "type": "text", + "content": " confidence intervals across multiple runs of stochastic gradient descent (SGD) with different learning rates). Only adaptation with the sparse depth (SFM) proxy leads to a reduction of the target error. This signifies the importance of employing proper signals in an adaptation framework. Furthermore, we show that RNA is less susceptible to poorer adaptation signal, which results in comparable or improved performance while being significantly faster (see supplementary Table 1)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 282, + 286, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 282, + 286, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 286, + 413 + ], + "type": "text", + "content": "our results on the following target tasks: monocular depth estimation, optical-flow estimation, and 3D reconstruction. For all, we first run a standard structure-from-motion (SFM) pipeline [81] to get sparse 3D keypoints. For depth estimation, we employ the z-coordinates of the sparse 3D keypoints i.e., noisy sparse depth, from each image as the adaptation signal. For optical flow, we perform keypoint matching across images (which returns sparse optical flow). Lastly, for 3D reconstruction, in addition to the previous two signals, we employ consistency between depth and optical flow predictions as another signal." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 415, + 286, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 286, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 286, + 594 + ], + "type": "text", + "content": "Semantic Tasks. For semantic segmentation, we first experiment with using a low number of click annotations for each class, similar to the works on active annotation tools [17, 83, 69]. This gives us sparse segmentation annotations. Likewise, for classification, we use the hierarchical structure of semantic classes, and use coarse labels generated from the WordNet tree [64], similar to [38]. Although these signals (click annotations and coarse labels) are significantly weaker versions of the actual ground truth, thus being cheaper to obtain, it may not be realistic to assume access to them at test-time for certain applications, e.g., real-time ones. Thus, we also show how these can be obtained via " + }, + { + "bbox": [ + 46, + 415, + 286, + 594 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 415, + 286, + 594 + ], + "type": "text", + "content": "-NN retrieval from the training dataset and patch matching using spatial features obtained from a pretrained self-supervised vision backbone [10] (see Fig. 4)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 609, + 127, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 127, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 127, + 621 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": "We demonstrate that our approach consistently outperforms the baselines for adaptation to different distribution shifts (2D and 3D Common Corruptions [35, 43, 44], cross-datasets), over different tasks (monocular depth, image classification, semantic segmentation, optical flow) and datasets (Taskonomy [105], Replica [84], ImageNet [22], COCO [53], ScanNet [20], Hypersim [78]). The source" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 309, + 69, + 544, + 141 + ], + "blocks": [ + { + "bbox": [ + 309, + 69, + 544, + 141 + ], + "lines": [ + { + "bbox": [ + 309, + 69, + 544, + 141 + ], + "spans": [ + { + "bbox": [ + 309, + 69, + 544, + 141 + ], + "type": "image", + "image_path": "98d2302b857e9ed23cc310928363630d787968eb8b80abdf3a51089b7e3ade38.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 151, + 545, + 265 + ], + "lines": [ + { + "bbox": [ + 305, + 151, + 545, + 265 + ], + "spans": [ + { + "bbox": [ + 305, + 151, + 545, + 265 + ], + "type": "text", + "content": "Figure 4: Examples of employed test-time adaptation signals. We use a range of adaptation signals in our experiments. These are practical to obtain and yield better performance compared to other proxies. In the left plot, for depth and optical flow estimation, we use sparse depth and optical flow via SFM. In the middle, for classification, for each test image, we perform " + }, + { + "bbox": [ + 305, + 151, + 545, + 265 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 151, + 545, + 265 + ], + "type": "text", + "content": "-NN retrieval to get " + }, + { + "bbox": [ + 305, + 151, + 545, + 265 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 151, + 545, + 265 + ], + "type": "text", + "content": " training images. Each of these retrieved image has a one hot label associated with it, thus, combining them gives us a coarse label that we use as our adaptation signal. Finally, for semantic segmentation, after performing " + }, + { + "bbox": [ + 305, + 151, + 545, + 265 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 151, + 545, + 265 + ], + "type": "text", + "content": "-NN as we did for classification, we get a pseudo-labelled segmentation mask for each of these images. The features for each patch in the test image and the retrieved images are matched. The top matches are used as sparse supervision. See Sec. 4.1 for more details." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 271, + 463, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 271, + 463, + 282 + ], + "spans": [ + { + "bbox": [ + 306, + 271, + 463, + 282 + ], + "type": "text", + "content": "code can be found on our project page." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 289, + 421, + 301 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 289, + 421, + 301 + ], + "spans": [ + { + "bbox": [ + 306, + 289, + 421, + 301 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 308, + 545, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 308, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 305, + 308, + 545, + 342 + ], + "type": "text", + "content": "We describe our experimental setup, i.e. different adaptation signals, adaptation mechanisms, datasets and baselines, for different tasks. See Tab. 1 for a summary." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 318, + 343, + 511, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 343, + 511, + 355 + ], + "spans": [ + { + "bbox": [ + 318, + 343, + 511, + 355 + ], + "type": "text", + "content": "Baselines. We evaluate the following baselines:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 308, + 355, + 545, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 355, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 308, + 355, + 545, + 392 + ], + "type": "text", + "content": "Pre-Adaptation Baseline: The network " + }, + { + "bbox": [ + 308, + 355, + 545, + 392 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 308, + 355, + 545, + 392 + ], + "type": "text", + "content": " that maps from RGB to the target task, e.g., depth estimation, with no test-time adaptation. We denote this as Baseline for brevity." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 307, + 393, + 545, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 393, + 545, + 477 + ], + "spans": [ + { + "bbox": [ + 307, + 393, + 545, + 477 + ], + "type": "text", + "content": "Densification: A network that maps from the given adaptation signal for the target task to the target task, e.g., sparse depth from SFM to dense depth. This is a control baseline and shows what can be learned from the test-time supervision alone, without employing input image information or a designed adaptation architecture. See Sec. 4.3 for a variant which includes the image as an additional input." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 308, + 479, + 545, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 479, + 545, + 538 + ], + "spans": [ + { + "bbox": [ + 308, + 479, + 545, + 538 + ], + "type": "text", + "content": "TTO (episodic): We adapt the Baseline model to each episode by optimizing the proxy loss (see Tab. 1 for the adaptation signal used for each task.) at test-time. Its weights are reset to the Baseline model's after optimizing each batch, similar to [91, 108]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 308, + 541, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 541, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 308, + 541, + 545, + 624 + ], + "type": "text", + "content": "TTO (online): We continually adapt to a distribution shift defined by a corruption and severity. Test data is assumed to arrive in a stream, and each data point has the same distribution shift, e.g., noise with a fixed standard deviation [91, 85]. The difference with TTO (episodic) is that the model weights are not reset after each iteration. We denote this as TTO for brevity." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 308, + 628, + 544, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 628, + 544, + 675 + ], + "spans": [ + { + "bbox": [ + 308, + 628, + 544, + 675 + ], + "type": "text", + "content": "TTO with Entropy supervision (TENT [91]): We adapt the Baseline model trained with log-likelihood loss by optimizing the entropy of the predictions. This is to reveal the effectiveness of entropy as a signal as proposed in [91]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 308, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 308, + 677, + 545, + 713 + ], + "type": "text", + "content": "TTO with Sobel Edges supervision (TTO-Edges): We adapt the Baseline model trained with an additional decoder that predicts a self-supervised task, similar to [85]. We choose" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4677" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 70, + 542, + 150 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 542, + 150 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 542, + 150 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 542, + 150 + ], + "type": "table", + "html": "
TaskAdaptation signalAdapted modelTraining dataOOD evaluation dataBaselines
DepthSFM, masked GTUNet [80], DPT [74]TaskonomyFor SFM: Replica, Replica-CC, ScanNet, For masked GT: Taskonomy-CC,-3DCC, HypersimPre-adaptation, densification, TENT, TTO-edges, TTO
Optical flowKeypoint matchingRAFT [87]FlyingChairs, FlyingThings [87]Replica-CCPre-adaptation
3D reconstructionSFM, keypoint matching,consistencyDepth, optical flow modelsDepth, optical flow dataReplica-CCPre-adaptation, TTO
Semantic segmentationClick annotations, patch matchingFCN [56]COCO (20 classes from Pascal VOC)For click annotations: COCO-CC, For patch matching: ImageNet-CPre-adaptation, densification, TENT, TTO
ClassificationCoarse labels (WordNet, DINO k-NN)ResNet50 [33], ConvNext [55]ImageNetImageNet-C, ImageNet-3DCC, ImageNet-V2Pre-adaptation, DINO k-NN, densification, TENT, TTO
", + "image_path": "702b0f88563add2e394cda85194f9812b194ed50a448e2a749d6a433f36cefd9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 159, + 547, + 199 + ], + "lines": [ + { + "bbox": [ + 46, + 159, + 547, + 199 + ], + "spans": [ + { + "bbox": [ + 46, + 159, + 547, + 199 + ], + "type": "text", + "content": "Table 1: Overview of the experiments for different target tasks, adaptation methods, and adaptation signals. For each task, we list the adaptation signal (Sec. 3.2) that we use for adaptation. We also list the models that we adapt, and the out-of-distribution (OOD) data used for evaluations and the relevant baselines. When there are different options for adaptation signal, e.g., in the case of depth, the signal is denoted in italics followed by the corresponding OOD dataset. The weights for the semantic segmentation, classification and optical flow models were taken from PyTorch [70]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 48, + 204, + 167, + 255 + ], + "blocks": [ + { + "bbox": [ + 48, + 204, + 167, + 255 + ], + "lines": [ + { + "bbox": [ + 48, + 204, + 167, + 255 + ], + "spans": [ + { + "bbox": [ + 48, + 204, + 167, + 255 + ], + "type": "image", + "image_path": "a3387b40c39fd6ab0bd7db7ba83502a0b6dee9e02d02fc449b7340cc9d89701e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 256, + 289, + 344 + ], + "lines": [ + { + "bbox": [ + 46, + 256, + 289, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 289, + 344 + ], + "type": "text", + "content": "Figure 5: RNA can achieve similar performance as TTO in a much shorter time. We compare how the " + }, + { + "bbox": [ + 46, + 256, + 289, + 344 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 46, + 256, + 289, + 344 + ], + "type": "text", + "content": " errors of the adaptation mechanisms decrease over wall-clock time (s). The errors are averaged over all episodes (and all corruptions for Replica-CC). RNA only requires a forward pass at test-time, while TTO requires multiple forward and backward passes. On ScanNet and Replica-CC, RNA takes 0.01s, while TTO takes 3s to achieve similar performance. Furthermore, RNA is not trained with test-time shifts unlike TTO, thus, it learned to use the additional supervision to adapt to unseen shifts." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 167, + 204, + 287, + 255 + ], + "blocks": [ + { + "bbox": [ + 167, + 204, + 287, + 255 + ], + "lines": [ + { + "bbox": [ + 167, + 204, + 287, + 255 + ], + "spans": [ + { + "bbox": [ + 167, + 204, + 287, + 255 + ], + "type": "image", + "image_path": "f0ecfc202b74f3c5d625567c624991de8520097a82224ce68553f85c52a1f8f5.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 356, + 287, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 356, + 287, + 405 + ], + "spans": [ + { + "bbox": [ + 48, + 356, + 287, + 405 + ], + "type": "text", + "content": "to predict Sobel edges as it has been shown to be robust to certain shifts [99]. We optimize the error of the edges predicted by the model and edges extracted from the RGB image to reveal the value of edge error as a supervision." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 414, + 287, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 287, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 287, + 486 + ], + "type": "text", + "content": "RNA configurations. At test-time, we first get the predictions of the Baseline model and compute the adaptation signal. The predictions and adaptation signal are then passed to " + }, + { + "bbox": [ + 46, + 414, + 287, + 486 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 46, + 414, + 287, + 486 + ], + "type": "text", + "content": " which adapts " + }, + { + "bbox": [ + 46, + 414, + 287, + 486 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 414, + 287, + 486 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 414, + 287, + 486 + ], + "type": "inline_equation", + "content": "f_{\\hat{\\theta}}" + }, + { + "bbox": [ + 46, + 414, + 287, + 486 + ], + "type": "text", + "content": ". The test images are then passed to " + }, + { + "bbox": [ + 46, + 414, + 287, + 486 + ], + "type": "inline_equation", + "content": "f_{\\hat{\\theta}}" + }, + { + "bbox": [ + 46, + 414, + 287, + 486 + ], + "type": "text", + "content": " to get the final predictions. We evaluate following variants of RNA." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 49, + 491, + 287, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 491, + 287, + 517 + ], + "spans": [ + { + "bbox": [ + 49, + 491, + 287, + 517 + ], + "type": "text", + "content": "RNA (frozen " + }, + { + "bbox": [ + 49, + 491, + 287, + 517 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 49, + 491, + 287, + 517 + ], + "type": "text", + "content": "): Baseline model weights, " + }, + { + "bbox": [ + 49, + 491, + 287, + 517 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 49, + 491, + 287, + 517 + ], + "type": "text", + "content": ", are frozen when training " + }, + { + "bbox": [ + 49, + 491, + 287, + 517 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 49, + 491, + 287, + 517 + ], + "type": "text", + "content": ". We call this variant RNA for brevity." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 49, + 517, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 517, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 49, + 517, + 287, + 555 + ], + "type": "text", + "content": "RNA (jointly trained " + }, + { + "bbox": [ + 49, + 517, + 287, + 555 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 49, + 517, + 287, + 555 + ], + "type": "text", + "content": "): In contrast to the frozen " + }, + { + "bbox": [ + 49, + 517, + 287, + 555 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 49, + 517, + 287, + 555 + ], + "type": "text", + "content": " variant, here we train " + }, + { + "bbox": [ + 49, + 517, + 287, + 555 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 49, + 517, + 287, + 555 + ], + "type": "text", + "content": " jointly with the Baseline network. This variant requires longer training." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 563, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 563, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 287, + 613 + ], + "type": "text", + "content": "Adaptation signal. As described in Sec. 3.2, we compute a broad range of test-time signals from the following processes. Each case describes a process applied on query image(s) in order to extract a test-time quantity." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 48, + 617, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 617, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 48, + 617, + 288, + 715 + ], + "type": "text", + "content": "Structure-from-motion (SFM): Given a batch of query images, we use COLMAP [81] to run SFM, which returns sparse depth. The percentage of valid pixels, i.e. depth measurements, is about " + }, + { + "bbox": [ + 48, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "0.16\\%" + }, + { + "bbox": [ + 48, + 617, + 288, + 715 + ], + "type": "text", + "content": " on Replica-CC and " + }, + { + "bbox": [ + 48, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "0.18\\%" + }, + { + "bbox": [ + 48, + 617, + 288, + 715 + ], + "type": "text", + "content": " on Replica. For ScanNet we use the pre-computed sparse depth from [79], which has about " + }, + { + "bbox": [ + 48, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "0.04\\%" + }, + { + "bbox": [ + 48, + 617, + 288, + 715 + ], + "type": "text", + "content": " valid pixels. As running SFM on corrupted images results in noisy sparse depth, we train " + }, + { + "bbox": [ + 48, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 48, + 617, + 288, + 715 + ], + "type": "text", + "content": " to be invariant to noise [102, 79]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 307, + 205, + 546, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 205, + 546, + 312 + ], + "spans": [ + { + "bbox": [ + 307, + 205, + 546, + 312 + ], + "type": "text", + "content": "Masked ground truth (GT): We apply a random mask to the GT depth of the test image. We fixed the valid pixels to " + }, + { + "bbox": [ + 307, + 205, + 546, + 312 + ], + "type": "inline_equation", + "content": "0.05\\%" + }, + { + "bbox": [ + 307, + 205, + 546, + 312 + ], + "type": "text", + "content": " of all pixels, i.e. similar sparsity as SFM (see the supplementary for other values). This a control proxy as it enables a better evaluation of the adaptation methods without conflating with the shortcomings of adaptation signals. It is also a scalable way of simulating sparse depth from real-world sensors, e.g., LiDAR, as also done in [92, 59, 41]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 307, + 315, + 546, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 315, + 546, + 374 + ], + "spans": [ + { + "bbox": [ + 307, + 315, + 546, + 374 + ], + "type": "text", + "content": "Click annotations: We generate click annotations over random pixels for each class in a given image using GT - simulating an active annotation pipeline. The number of pixels ranges from 3 to 25, i.e. roughly " + }, + { + "bbox": [ + 307, + 315, + 546, + 374 + ], + "type": "inline_equation", + "content": "0.01\\%" + }, + { + "bbox": [ + 307, + 315, + 546, + 374 + ], + "type": "text", + "content": " of the total pixels, similar to [7, 69, 83, 109, 17]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 307, + 376, + 547, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 376, + 547, + 520 + ], + "spans": [ + { + "bbox": [ + 307, + 376, + 547, + 520 + ], + "type": "text", + "content": "Patch matching: To not use GT click annotations, for each test image, we first retrieve its " + }, + { + "bbox": [ + 307, + 376, + 547, + 520 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 307, + 376, + 547, + 520 + ], + "type": "text", + "content": "-NN images from the original clean training dataset using DINO features [10]. We then get segmentation masks on these " + }, + { + "bbox": [ + 307, + 376, + 547, + 520 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 307, + 376, + 547, + 520 + ], + "type": "text", + "content": " images. If the training dataset has labels for segmentation we use them directly, otherwise we obtain them from a pretrained network. For each of the " + }, + { + "bbox": [ + 307, + 376, + 547, + 520 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 307, + 376, + 547, + 520 + ], + "type": "text", + "content": " training images and test image, we extract non-overlapping patches. The features for each patch that lie inside the segmentation masks of the " + }, + { + "bbox": [ + 307, + 376, + 547, + 520 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 307, + 376, + 547, + 520 + ], + "type": "text", + "content": " training images are matched to the features of every patch in the test image. These matches are then filtered and used as sparse segmentation annotations. See Fig. 4 for illustration." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 307, + 522, + 547, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 522, + 547, + 582 + ], + "spans": [ + { + "bbox": [ + 307, + 522, + 547, + 582 + ], + "type": "text", + "content": "Coarse labels (WordNet): We generate 45 coarse labels from the 1000-way ImageNet labels, i.e. making the labels " + }, + { + "bbox": [ + 307, + 522, + 547, + 582 + ], + "type": "inline_equation", + "content": "22 \\times" + }, + { + "bbox": [ + 307, + 522, + 547, + 582 + ], + "type": "text", + "content": " coarser, using the WordNet tree [64], similar to [39]. See supplementary for more details on the construction and results for other coarse label sets." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 307, + 584, + 547, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 584, + 547, + 644 + ], + "spans": [ + { + "bbox": [ + 307, + 584, + 547, + 644 + ], + "type": "text", + "content": "Coarse labels (DINO " + }, + { + "bbox": [ + 307, + 584, + 547, + 644 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 307, + 584, + 547, + 644 + ], + "type": "text", + "content": "-NN): For each test image, we retrieve the " + }, + { + "bbox": [ + 307, + 584, + 547, + 644 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 307, + 584, + 547, + 644 + ], + "type": "text", + "content": "-NN images from the training dataset using DINO features [10]. Each of these " + }, + { + "bbox": [ + 307, + 584, + 547, + 644 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 307, + 584, + 547, + 644 + ], + "type": "text", + "content": " training images is associated with an ImageNet class, thus, combining " + }, + { + "bbox": [ + 307, + 584, + 547, + 644 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 307, + 584, + 547, + 644 + ], + "type": "text", + "content": " one-hot labels gives us a coarse label." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 308, + 647, + 546, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 647, + 546, + 671 + ], + "spans": [ + { + "bbox": [ + 308, + 647, + 546, + 671 + ], + "type": "text", + "content": "Keypoint matching: We perform keypoint matching across images to get sparse optical flow." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4678" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 85, + 70, + 508, + 297 + ], + "blocks": [ + { + "bbox": [ + 85, + 70, + 508, + 297 + ], + "lines": [ + { + "bbox": [ + 85, + 70, + 508, + 297 + ], + "spans": [ + { + "bbox": [ + 85, + 70, + 508, + 297 + ], + "type": "image", + "image_path": "d7d5106eb9e34079491ea4e5bc50440aebc555d81ec897feae52c98224fa9153.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 300, + 547, + 369 + ], + "lines": [ + { + "bbox": [ + 46, + 300, + 547, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 547, + 369 + ], + "type": "text", + "content": "Figure 6: Qualitative results of RNA vs the baselines for semantic segmentation on random query images on COCO-CC (left) and depth on images from ScanNet, Taskonomy-3DCC and Replica-CC (right). For semantic segmentation, we use 15 pixel annotations per class. For Taskonomy-3DCC, we use sparse depth with " + }, + { + "bbox": [ + 46, + 300, + 547, + 369 + ], + "type": "inline_equation", + "content": "0.05\\%" + }, + { + "bbox": [ + 46, + 300, + 547, + 369 + ], + "type": "text", + "content": " valid pixels (30 pixels per image). See Fig. 7 for results on different adaptation signal levels. For ScanNet and Replica-CC, the adaptation signal is sparse depth measurements from SFM [81] with similar sparsity ratios to Taskonomy-3DCC. The predictions with proposed adaptation signals are shown in the last two rows. They are noticeably more accurate compared to the baselines. Comparing TTO and RNA, RNA's predictions are more accurate for segmentation, and sharper than TTO for depth (see the ellipses) while being significantly faster. See 4.2 and supplementary for more results." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 383, + 211, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 383, + 211, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 383, + 211, + 396 + ], + "type": "text", + "content": "4.2. Adaptation with RNA vs TTO" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 402, + 288, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 288, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 288, + 484 + ], + "type": "text", + "content": "Here we summarize our observations from adapting with RNA vs TTO. As described, TTO represents the approach of closed-loop adaptation using the adaptation signal but without benefiting from amortization and learning (the adaptation process is fixed to be standard SGD). These observations hold across different tasks. See Sec. 4.3 for results." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 486, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 605 + ], + "type": "text", + "content": "RNA is efficient. As RNA only requires a forward pass at test-time, it is orders of magnitude faster than TTO and is able to attain comparable performance to TTO. In Fig. 5, we compare the runtime of adaption with RNA and TTO for depth prediction. On average, for a given episode, RNA obtains similar performance as TTO in 0.01s, compared to TTO's 3-5s. Similarly, for dense 3D reconstruction, RNA is able to adapt in 0.008s compared to TTO's 66s (see Fig. 9). This suggests a successful amortization of the adaptation optimization by RNA." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "text", + "content": "Furthermore, RNA's training is also efficient as it only requires training a small model, i.e. " + }, + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "inline_equation", + "content": "5 - 20\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "text", + "content": " of the Baseline model's parameters, depending on the task. Thus, RNA has a fixed overhead, and small added cost at test-time." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "RNA's predictions are sharper than TTO for dense prediction tasks. From the last two rows of Fig. 6, it can be seen that RNA retains fine-grained details. This is a noteworthy point and can be attributed to the fact that RNA benefits from a neural network, thus its inductive biases can" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 383, + 545, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 383, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 383, + 545, + 443 + ], + "type": "text", + "content": "be beneficial (and further engineered) for such advantages. This is a general feature that RNA, and more broadly using a learning-based function to amortize adaptation optimization, brings – in contrast to limiting the adaptation process to be SGD, as represented by TTO." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 444, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 545, + 504 + ], + "type": "text", + "content": "RNA generalizes to unseen shifts. RNA performs better than TTO for low severities (see supplementary for more details). However, as it was not exposed to any corruptions, the performance gap against TTO narrows at high severities as expected, which is exposed to corruptions at test-time." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 505, + 545, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 505, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 505, + 545, + 636 + ], + "type": "text", + "content": "We hypothesize that the generalization property of RNA is due to the following reasons. 1. Even though " + }, + { + "bbox": [ + 304, + 505, + 545, + 636 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 505, + 545, + 636 + ], + "type": "text", + "content": " was trained to convergence, it does not achieve exactly 0 error. Thus, when " + }, + { + "bbox": [ + 304, + 505, + 545, + 636 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 304, + 505, + 545, + 636 + ], + "type": "text", + "content": " is trained with a frozen " + }, + { + "bbox": [ + 304, + 505, + 545, + 636 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 505, + 545, + 636 + ], + "type": "text", + "content": " with the training data, it can still learn to correct the errors of " + }, + { + "bbox": [ + 304, + 505, + 545, + 636 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 505, + 545, + 636 + ], + "type": "text", + "content": ", thus, adapting " + }, + { + "bbox": [ + 304, + 505, + 545, + 636 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 505, + 545, + 636 + ], + "type": "text", + "content": ". 2. Adaptation signals, by definition, are expected to be relatively robust to distribution shifts. Even though the RGB image has been corrupted or from a new domain, the adaptation signal is more aligned with the target task. Thus, the input to " + }, + { + "bbox": [ + 304, + 505, + 545, + 636 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 304, + 505, + 545, + 636 + ], + "type": "text", + "content": " does not undergo a significant shift and is able to adapt " + }, + { + "bbox": [ + 304, + 505, + 545, + 636 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 505, + 545, + 636 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 646, + 517, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 646, + 517, + 659 + ], + "spans": [ + { + "bbox": [ + 305, + 646, + 517, + 659 + ], + "type": "text", + "content": "4.3. Experiments using Various Target Tasks" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "In this section, we provide a more comprehensive set of evaluations covering various target tasks and adaptation signals. In all cases, RNA is a fixed general framework without being engineered for each task and shows supportive results." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4679" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 71, + 288, + 166 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 288, + 166 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 288, + 166 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 288, + 166 + ], + "type": "table", + "html": "
Adaptation SignalSFMSparse GTRelative Runtime
DatasetReplicaScanNetTaskonomyHypersim
ShiftCDSCCCDSNoneCC3DCCCDS
Pre-adaptation Baseline1.756.083.302.685.744.7533.641.00
Densification2.504.192.351.721.721.7217.251.00
TENT [91]2.036.094.035.515.514.4835.4515.85
TTO-Edges [85]1.736.143.282.705.694.7433.6920.98
RNA (frozen f)1.724.261.771.121.681.4916.171.56
RNA (jointly trained f)1.663.411.741.111.501.3717.131.56
TTO (Episodic)1.723.311.851.622.992.3117.7714.85
TTO (Online)1.823.161.761.131.481.3414.1714.85
", + "image_path": "b8da78e7fff73c44e55e16f83c7a235230bad61ea2a430e11f7a8dbcf784087d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 174, + 287, + 278 + ], + "lines": [ + { + "bbox": [ + 47, + 174, + 287, + 278 + ], + "spans": [ + { + "bbox": [ + 47, + 174, + 287, + 278 + ], + "type": "text", + "content": "Table 2: Quantitative adaptation results on depth estimation. " + }, + { + "bbox": [ + 47, + 174, + 287, + 278 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 47, + 174, + 287, + 278 + ], + "type": "text", + "content": " errors on the depth prediction task. (Lower is better. Multiplied by 100 for readability. The best models within 0.0003 error are shown in bold.) We generate distribution shifts by applying Common Corruptions (CC), 3D Common Corruptions (3DCC) and from performing cross-dataset evaluations (CDS). The results from CC and 3DCC are averaged over all distortions and severity levels on Taskonomy and 3 severity levels on Replica data. The adaptation signal from Taskonomy is masked GT (fixed at " + }, + { + "bbox": [ + 47, + 174, + 287, + 278 + ], + "type": "inline_equation", + "content": "0.05\\%" + }, + { + "bbox": [ + 47, + 174, + 287, + 278 + ], + "type": "text", + "content": " valid pixels) while that from Replica and ScanNet is sparse depth from SFM. RNA and TTO notably outperform the baselines. RNA successfully matches the performance of TTO while being around 10 times faster." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 279, + 287, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 279, + 287, + 299 + ], + "spans": [ + { + "bbox": [ + 47, + 279, + 287, + 299 + ], + "type": "text", + "content": "See supplementary for the losses for different corruption types, sparsity levels, and the results of applying RNA to other adaptation signals." + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 53, + 308, + 282, + 400 + ], + "blocks": [ + { + "bbox": [ + 53, + 308, + 282, + 400 + ], + "lines": [ + { + "bbox": [ + 53, + 308, + 282, + 400 + ], + "spans": [ + { + "bbox": [ + 53, + 308, + 282, + 400 + ], + "type": "image", + "image_path": "e7e769338393d03bb39644f20fd6c0faa1d25f8eb07477a726622d292d273109.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 401, + 287, + 431 + ], + "lines": [ + { + "bbox": [ + 47, + 401, + 287, + 431 + ], + "spans": [ + { + "bbox": [ + 47, + 401, + 287, + 431 + ], + "type": "text", + "content": "Figure 7: Qualitative adaptation results on semantic segmentation on random query images on COCO-CC. RNA notably improves the prediction quality using error feedback from as few as 3 random pixels." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 55, + 437, + 280, + 549 + ], + "blocks": [ + { + "bbox": [ + 55, + 437, + 280, + 549 + ], + "lines": [ + { + "bbox": [ + 55, + 437, + 280, + 549 + ], + "spans": [ + { + "bbox": [ + 55, + 437, + 280, + 549 + ], + "type": "image", + "image_path": "320af74ca6b0453873f53973af492360f55e3e049d93d41b27a0093712d3d65b.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 552, + 287, + 610 + ], + "lines": [ + { + "bbox": [ + 46, + 552, + 287, + 610 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 287, + 610 + ], + "type": "text", + "content": "Figure 8: Quantitative adaptation results on semantic segmentation. Each point shows the mean IOU over 15 corruptions and 5 severities. RNA significantly improves over baselines. Black dashed line shows the mean IOU of the baseline model for clean validation images, and is provided as an upper bound on performance. Numbers in the legend denote averages over all supervision pixel counts. See supplementary for a breakdown." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": "Depth. We demonstrate the results quantitatively in Tab. 2 and Fig. 5 and qualitatively in Fig. 6. In Tab. 2, we compare RNA against all baselines, and over several distribution shifts and different adaptation signals. Our RNA variants outperform the baselines overall. TTO (online) has a better performance than TTO (episodic) as it assumes a smoothly changing distribution shift, and it continuously updates the model weights. RNA (jointly trained " + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": ") has a" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "better performance among RNA variants. This is reasonable as the target model is not frozen, thus, is less restrictive." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 97, + 546, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 97, + 546, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 97, + 546, + 277 + ], + "type": "text", + "content": "As another baseline, we trained a single model that takes as input a concatenation of the RGB image and sparse supervision, i.e. multi-modal input. However, its average performance on Taskonomy-CC was " + }, + { + "bbox": [ + 304, + 97, + 546, + 277 + ], + "type": "inline_equation", + "content": "42.5\\%" + }, + { + "bbox": [ + 304, + 97, + 546, + 277 + ], + "type": "text", + "content": " worse than RNA's (see sup. mat. Sec. 3.2). Among the baselines that do not adapt, densification is the strongest under distribution shift due to corruptions. This is expected as it does not take the RGB image as input, thus, it is not affected by the underlying distribution shift. However, as seen from the qualitative results in Figs. 6, 7, unlike RNA, densification is unable to predict fine-grained details (which quantitative metrics often do not well capture). We also show that the gap between RNA and densification widens with sparser supervision (see sup. mat. Fig. 1), which confirms that RNA is making use of the error feedback signal, to adapt " + }, + { + "bbox": [ + 304, + 97, + 546, + 277 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 97, + 546, + 277 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 318, + 285, + 534, + 550 + ], + "blocks": [ + { + "bbox": [ + 318, + 285, + 534, + 550 + ], + "lines": [ + { + "bbox": [ + 318, + 285, + 534, + 550 + ], + "spans": [ + { + "bbox": [ + 318, + 285, + 534, + 550 + ], + "type": "image", + "image_path": "eeb125b83fedddb1ae3b62ea13e5a467fef066c1736069bc593cbbdb9a18ea8b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 559, + 545, + 646 + ], + "lines": [ + { + "bbox": [ + 304, + 559, + 545, + 646 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 545, + 646 + ], + "type": "text", + "content": "Figure 9: Adaptation results for 3D reconstruction. Using appropriate adaptation signals from multi-view geometry can recover accurate 3D reconstructions. We report the average " + }, + { + "bbox": [ + 304, + 559, + 545, + 646 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 304, + 559, + 545, + 646 + ], + "type": "text", + "content": " error between ground truth 3D coordinates and the estimated ones. The titles above each column refers to the depth model used to get the reconstruction. TTO+MVC corresponds to the predictions after multi-view consistency optimization. It can be seen that RNA and TTO improve the reconstructions over the baselines with RNA being significantly faster. See supplementary Fig. 4 for more results and the corresponding error maps." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 654, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 715 + ], + "type": "text", + "content": "Dense 3D Reconstruction. Here, we combine multiple adaptation signals from multi-view geometry. First, we adapt the weights of the depth and optical flow models independently. The results from this adaptation can be found in the previous paragraph (for depth) and supplementen" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4680" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 70, + 279, + 139 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 279, + 139 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 279, + 139 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 279, + 139 + ], + "type": "table", + "html": "
Adaptation SignalDatasetCleanIN-CIN-3DCCIN-V2Rel. Runtime
-Pre-adaptation Baseline23.8561.6654.9737.151.00
EntropyTENT24.6746.1947.1337.075.51
Coarse labels (wordnet)Densification95.5095.5095.5095.50-
TTO (Online)24.7240.6242.9036.775.72
RNA (frozen f)16.7241.2140.3725.531.39
Coarse labels (DINO)DINO (k-NN)25.5652.6448.2437.39-
TTO (Online)24.5951.5949.1836.965.72
RNA (frozen f)24.3654.8652.2936.881.39
", + "image_path": "5e0cf43e8e6861500e3e10516eea6f401d6ab2a12be782ee4a41703768494e91.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 198, + 287, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 198, + 287, + 246 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 287, + 246 + ], + "type": "text", + "content": "tary (for optical flow). Next, the two models are adapted to make their predictions consistent with each other. This is achieved using the same process as [58], i.e. multi-view-consistency (MVC). See supplementary for details." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 247, + 287, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 287, + 342 + ], + "type": "text", + "content": "Figure 9 shows the point cloud visualizations on Replica where the input was corrupted with Gaussian Noise. This results in collapsed depth predictions, thus, reconstructions are unusable (Baseline column) and performing MVC is not helpful (Baseline+MVC). Adapting the depth predictions using TTO and MVC improves the reconstruction notably while RNA achieves a similar performance significantly faster." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 342, + 287, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 461 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 461 + ], + "type": "text", + "content": "Semantic Segmentation. We experiment with click annotations and DINO patch matching as adaptation signals. Click annotations: In Fig. 8, we show how the IoU changes with the adaptation signal level on COCO-CC. As the Baseline and TENT do not make use of this signal, their IoU is a straight line. RNA clearly outperforms the baselines for all levels of adaptation signal. Figure 7 shows the qualitative results with increasing supervision, and Fig. 6 (left) a comparison against all baselines, demonstrating higher quality predictions with RNA." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 462, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 287, + 593 + ], + "type": "text", + "content": "DINO patch matching: We perform patch matching on DINO features (described in Sec. 4.1) to get the adaptation signal. As the patch matching process can be computationally expensive, we demonstrate our results on all cat classes in ImageNet and over one noise, blur and digital corruption for 3 levels of severity. We used the predictions of a pretrained FCN on the clean images as pseudolabels to compute IoU. The mean IoU averaged over these corruptions and severities is 48.98 for the baseline model, 53.45 for TTO. RNA obtains a better IOU of 58.04, thus it can make use of the sparse annotations from DINO patch matching." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 617 + ], + "type": "text", + "content": "Image Classification. We experiment with coarse labels from WordNet and DINO " + }, + { + "bbox": [ + 46, + 594, + 287, + 617 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 594, + 287, + 617 + ], + "type": "text", + "content": "-NN as adaptation signals." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "Coarse labels (WordNet): Table 3 shows the results from using 45-coarse labels on ImageNet-" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\{\\mathrm{C},3\\mathrm{DCC},\\mathrm{V}2\\}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": ". This corresponds to " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "22\\mathrm{x}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " coarser supervision compared to the 1000 classes that we are evaluating on. TENT seems to have notable improvements in performance under corruptions for classification, unlike for semantic segmentation and depth. We show that using coarse supervision results in even better performance, about a further 5 pp reduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 143 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 143 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 143 + ], + "type": "text", + "content": "in error. Furthermore, on uncorrupted data, i.e. clean, and ImageNet-V2 [76], RNA gives roughly 10 pp improvement in performance compared to TTO. Thus, coarse supervision provides a useful signal for adaptation while requiring much less effort than full annotation [97]. See supplementary for results on other coarse sets." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 144, + 545, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 545, + 215 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 545, + 215 + ], + "type": "text", + "content": "Coarse labels (DINO " + }, + { + "bbox": [ + 304, + 144, + 545, + 215 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 144, + 545, + 215 + ], + "type": "text", + "content": "-NN): We also show results from using coarse sets generated from DINO " + }, + { + "bbox": [ + 304, + 144, + 545, + 215 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 144, + 545, + 215 + ], + "type": "text", + "content": "-NN retrieval. This is shown in the last 3 rows of Tab. 3. Both RNA and TTO use this coarse information to outperform the non-adaptive baselines. However, they do not always outperform TENT, which could be due to the noise in retrieval." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 223, + 478, + 234 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 223, + 478, + 234 + ], + "spans": [ + { + "bbox": [ + 306, + 223, + 478, + 234 + ], + "type": "text", + "content": "4.4. Ablations and additional results" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 308, + 243, + 544, + 292 + ], + "blocks": [ + { + "bbox": [ + 47, + 143, + 287, + 191 + ], + "lines": [ + { + "bbox": [ + 47, + 143, + 287, + 191 + ], + "spans": [ + { + "bbox": [ + 47, + 143, + 287, + 191 + ], + "type": "text", + "content": "Table 3: Quantitative adaptation results on on ImageNet (IN) classification task. We evaluate on the clean validation set, ImageNet-C,3DCC,V2}. We report average error " + }, + { + "bbox": [ + 47, + 143, + 287, + 191 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 47, + 143, + 287, + 191 + ], + "type": "text", + "content": " for 1000-way classification task over all corruptions and severities. For the coarse labels with WordNet supervision, we use 45-coarse labels. For DINO " + }, + { + "bbox": [ + 47, + 143, + 287, + 191 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 143, + 287, + 191 + ], + "type": "text", + "content": " NN, we set " + }, + { + "bbox": [ + 47, + 143, + 287, + 191 + ], + "type": "inline_equation", + "content": "k = 20" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 243, + 544, + 292 + ], + "lines": [ + { + "bbox": [ + 308, + 243, + 544, + 292 + ], + "spans": [ + { + "bbox": [ + 308, + 243, + 544, + 292 + ], + "type": "table", + "html": "
Task (Arch.)Depth (DPT [74])Classification (ConvNext [55])
ShiftCleanCCRel. RuntimeCleanIN-CRel. Runtime
Pre-adaptation Baseline2.233.761.0018.1342.951.00
TTO (Online)1.822.6113.8517.8341.4411.04
RNA (frozen f)1.131.561.0114.3238.041.07
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Method\\ShiftNoneTaskonomy-CCTaskonomy-3DCCHypersimBlendedMVG
Pre-adaptation0.0270.0570.0480.3363.450
RNA (HyperNetwork-x)0.0190.0410.0330.2572.587
RNA (FiLM-x)0.0190.0390.0330.2792.636
RNA (FiLM-f)0.0130.0240.0200.1982.310
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The adaptation signal here is masked GT, fixed at 0.05% of valid pixels." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "Implementations of different architectures for the controller network " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": ". We experiment with different architectures for " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " e.g., HyperNetworks [31], other FiLM variants, or adapting the input instead of the model parameters. Instead of adding FiLM layers to adapt " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " (denoted as FiLM- " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "), as described in Sec. 3.1, we also experimented with adding FiLM layers to a UNet model that is trained to update the input image " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " (denoted as FiLM- " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "). For FiLM- " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": ", only " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " is updated and there is no adaptation on " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": ". Lastly, as Hypernetworks [31] have been shown to be expressive and suitable for adaptation, we trained a HyperNetwork, in this case an MLP, to predict the weights of a 3-layer convolutional network that updates " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " (denoted as HyperNetwork-" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "4681" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": "). The results of adaptation with these variants of RNA are shown in Table 5. The FiLM-" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": " variant performed best, thus, we adopted it as our main architecture. See supplementary Sec. 2.2 for more details and a discussion on the trade-offs of the choices of implementing this closed-loop \"control\" system, namely those that make stronger model-based assumptions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 156, + 288, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 156, + 288, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 288, + 240 + ], + "type": "text", + "content": "Controlling for number of parameters. We ran a control experiment where all methods have the same architecture, thus, same number of parameters. The results are in the supplementary Table 2. RNA still returns the best performance. Thus, its improvement over the baselines is not due to a different architecture or number of parameters but due to its test-time adaptation mechanism." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 252, + 284, + 266 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 252, + 284, + 266 + ], + "spans": [ + { + "bbox": [ + 47, + 252, + 284, + 266 + ], + "type": "text", + "content": "5. Approaches for handling distribution shifts" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 273, + 287, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 273, + 287, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 287, + 429 + ], + "type": "text", + "content": "In this section, we provide a unified discussion about the approaches that aim to handle distribution shifts. Figure 10 gives an overview of how these approaches can be characterized. Open-loop systems predict " + }, + { + "bbox": [ + 46, + 273, + 287, + 429 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 273, + 287, + 429 + ], + "type": "text", + "content": " by only using their inputs without receiving feedback. Training-time robustness methods, image modifications, and multi-modal methods fall into this category. These methods assume the learned model is frozen at the test-time. Thus, they aim to incorporate inductive biases at training time that could be useful against distribution shifts at the test-time. The closed-loop systems, on the other hand, are adaptive as they make use of a live error feedback signal that can be computed at test-time from the model predictions and an adaptation signal." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 429, + 287, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 429, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 46, + 429, + 287, + 513 + ], + "type": "text", + "content": "In the interest of space, we move the detailed discussion about each of these variants to Sec. 1.2 of the supplementary. In particular, elaboration of the distinction between a model-based vs model-free approach, denoising/image-modification methods, multi-modal methods, and our observations over comparing the conclusions of [46] el al. and our experiments are provided there." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 525, + 204, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 204, + 537 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 204, + 537 + ], + "type": "text", + "content": "6. Conclusion and Limitations" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 545, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 676 + ], + "type": "text", + "content": "We presented RNA, a method for efficient adaptation of neural networks at test-time using a closed-loop formulation. It involves training a side network to use a test-time adaptation signal to adapt a main network. This network acts akin to a \"controller\" and adapts the main network based on the adaptation signal. We showed that this general and flexible framework can generalize to unseen shifts, and as it only requires a forward pass at test-time, it is orders of magnitude faster than TTO. We evaluated this approach using a diverse set of adaptation signals and target tasks. We briefly discuss the limitations and potential future works:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "type": "text", + "content": "Different instantiation of RNA and amortization. While we experimented with several RNA variants (see supplementary for details), further investigation toward a stronger" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 323, + 68, + 529, + 205 + ], + "blocks": [ + { + "bbox": [ + 323, + 68, + 529, + 205 + ], + "lines": [ + { + "bbox": [ + 323, + 68, + 529, + 205 + ], + "spans": [ + { + "bbox": [ + 323, + 68, + 529, + 205 + ], + "type": "image", + "image_path": "a81f6ddc1ff511cba8c550d9522a0d86cdf1e26e5c7318429b26a4acbfa7890a.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 209, + 545, + 419 + ], + "lines": [ + { + "bbox": [ + 305, + 209, + 545, + 419 + ], + "spans": [ + { + "bbox": [ + 305, + 209, + 545, + 419 + ], + "type": "text", + "content": "Figure 10: An overview of methods that aim to handle distribution shifts. Left: Open-loop systems predict " + }, + { + "bbox": [ + 305, + 209, + 545, + 419 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 209, + 545, + 419 + ], + "type": "text", + "content": " by only using their inputs without receiving feedback. The first and popular example of open-loop systems is training-time robustness methods (data augmentation, architectural changes, etc.). The next example is the methods that modify the input " + }, + { + "bbox": [ + 305, + 209, + 545, + 419 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 209, + 545, + 419 + ], + "type": "text", + "content": ", e.g. denoising or style changes, to recover the original image before corruption, independent of " + }, + { + "bbox": [ + 305, + 209, + 545, + 419 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 209, + 545, + 419 + ], + "type": "text", + "content": ". Furthermore, there are multi-modal methods that use an additional input " + }, + { + "bbox": [ + 305, + 209, + 545, + 419 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 209, + 545, + 419 + ], + "type": "text", + "content": ". As the learned model is frozen at test-time, these methods need to anticipate the distribution shift by incorporating inductive biases at training time (See also Fig. 1.). Right: In contrast, closed-loop systems make use of its current output, " + }, + { + "bbox": [ + 305, + 209, + 545, + 419 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 209, + 545, + 419 + ], + "type": "text", + "content": ", and an adaptation signal, " + }, + { + "bbox": [ + 305, + 209, + 545, + 419 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 209, + 545, + 419 + ], + "type": "text", + "content": ", to form an error feedback signal that can be used to update its predictions. Thus, they adapt to the shifts as they occur. We can then group closed-loop systems into model-based and model-free methods. The former performs adaptation by estimating the parameters " + }, + { + "bbox": [ + 305, + 209, + 545, + 419 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 305, + 209, + 545, + 419 + ], + "type": "text", + "content": " of specific modeled distribution shift families, while the latter performs adaptation in a data-driven way without explicitly modeling certain distribution shifts. Adaptation can be performed via running an optimization, i.e. TTO via SGD, or via amortization, i.e., training a side controller network to predict TTO updates that minimize the error feedback. Our proposed method, RNA, belongs to the model-free adaptation approach that makes use of amortization for efficiency." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 545, + 507 + ], + "type": "text", + "content": "instantiation of RNA which can generalize to more shifts and handle more drastic changes, e.g. via building in a more explicit \"model\" of the shifts and environment (see the discussion about [46]), is important. In general, as the role of the controller network is to amortize the training optimization of the main network, the amortized optimization literature [3] is one apt resource to consult for this purpose." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 508, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 545, + 578 + ], + "type": "text", + "content": "Hybrid mechanism for activating TTO in RNA. TTO constantly adapts a model to a distribution shift, hence, in theory, it can adapt to any shift despite being comparatively inefficient. To have the best of both worlds, investigating mechanisms for selectively activating TTO within RNA when needed can be useful." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 580, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 545, + 675 + ], + "type": "text", + "content": "Finding adaptation signals for a given task. While the focus of this study was not on developing new adaption signals, we demonstrated useful ones for several core vision tasks, but there are many more. Finding these signals requires either knowledge of the target task so a meaningful signal can be accordingly engineered or core theoretical works on understanding how a proxy and target objectives can be \"aligned\" for training." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement: The authors thank Onur Beker. This work was partially supported by the ETH4D and EPFL EssentialTech Centre Humanitarian Action Challenge Grant." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4682" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 53, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 58, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 58, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Hassan Akbari, Liangzhe Yuan, Rui Qian, Wei-Hong Chuang, Shih-Fu Chang, Yin Cui, and Boqing Gong. 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